shot peening processes to obtain nanocrystalline surfaces in metal alloys: frattura ed integrità strutturale, 8 (2009) 2 il 9 ed il 10 marzo 2009 si è svolto a forni di sopra, provincia di udine, il workshop igf dal titolo “progettazione a fatica di giunzioni saldate (… e non)”. grazie all’impegno degli organizzatori locali, bruno atzori e luca susmel, è stato ottenuto un successo notevole sia per il numero di partecipanti che per il numero e la qualità delle memorie presentate. il soggiorno è stato reso piacevolissimo dalle particolari condizioni metereologiche, con neve abbondantissima ed uno splendido sole. il lavori sono stati raccolti in un volume di atti (disponibile nella sezione archivio giornate del sito igf) e, come ormai tradizione per l’igf, tutte le presentazioni sono state videoregistrate e sono disponibili in streaming nel sito web (nella sezione webtv).. a questo proposito è sicuramente doveroso ringraziare tutti i relatori che hanno aderito con entusiasmo e disponibilità all’iniziativa, rendendo possibile una continua fruizione dell’evento. e’ ormai prossimo il convegno nazionale igf xx (torino 24-26 giugno 2009). prestigiosa sede dell’evento sarà lo splendido castello del valentino. per la registrazione potete utilizzare la sezione dedicata nel sito igf, dove sono anche riportate le modalità di invio dei lavori. questi potranno essere inviati in formato word, qualunque versione, senza alcuna particolare formattazione e senza limiti nel numero di pagine o nella dimensione del file. la segreteria igf si occuperà dell’impaginazione. le date da ricordare sono: 30.03.2009: invio abstract 15.04.2009: accettazione abstract 18.05.2009: invio memorie 05.06.2009: invio agli autori di una bozza di stampa l’igf non termina con l’appuntamento di torino le proprie attività del 2009. infatti, stiamo organizzando: una sessione tematica durante il prossimo convegno aias (associazione italiana analisi sollecitazioni; torino dal 9 all’11 settembre 2009) dal titolo “integrità strutturale”. il coordinatore di questa sessione sarà franco furgiuele, cui potete far riferimento per aderire (furgiuele@unical.it); una sessione tematica durante il prossimo convegno aipnd (associazione italiana prove non distruttive; roma dal 15 al 17 ottobre 2009). il coordinatore di questa sessione sarà stefano beretta, cui potete far riferimento per aderire all’iniziativa (stefano.beretta@polimi.it) infine, l’igf patrocina il prossimo ninth international seminar on experimental techniques and design in composite materials (dal 30 settembre al 2 ottobre 2009, a vicenza). la data limite per l’invio degli abstract è prevista per fine maggio 2009. non mancate, a presto francesco iacoviello segretario igf il 9 ed il 10 marzo 2009 si è svolto a forni di sopra, provincia di udine, il workshop igf dal titolo “progettazione a fatica di giunzioni saldate (… e non)”. grazie all’impegno degli organizzatori locali, bruno atzori e luca susmel, è stato ottenuto ... e’ ormai prossimo il convegno nazionale igf xx (torino 24-26 giugno 2009). prestigiosa sede dell’evento sarà lo splendido castello del valentino. per la registrazione potete utilizzare la sezione dedicata nel sito igf, dove sono anche riportate le mod... una sessione tematica durante il prossimo convegno aias (associazione italiana analisi sollecitazioni; torino dal 9 all’11 settembre 2009) dal titolo “integrità strutturale”. il coordinatore di questa sessione sarà franco furgiuele, cui potete far... una sessione tematica durante il prossimo convegno aipnd (associazione italiana prove non distruttive; roma dal 15 al 17 ottobre 2009). il coordinatore di questa sessione sarà stefano beretta, cui potete far riferimento per aderire all’iniziativa (s... infine, l’igf patrocina il prossimo ninth international seminar on experimental techniques and design in composite materials (dal 30 settembre al 2 ottobre 2009, a vicenza). la data limite per l’invio degli abstract è prevista per fine maggio 2009. microsoft word numero 16 articolo 3 r. laczkó et alii, frattura ed integrità strutturale, 16 (2011) 28-33; doi: 10.3221/igf-esis.16.03 28 damages to stent stabilized left ventricular pacemaker electrodes during simulated lead extraction romola laczkó, tibor balázs, eszter bognár bme, dept. of materials science and engineering. h-1111 budapest, bertalan l. u. 7. hungary jános ginsztler research group for metals technology of has and bme, 1111 budapest, goldmann ter 3. hungary abstract. during biventricular pacemaker implantation stents can be applied for coronary sinus lead stabilization to prevent lead dislocations. a lot of issues have been raised in connection with the use of the stent. in some cases the implanted left ventricular lead must be explanted. it is crucial to avoid any injury to the heart when the electrode is removed. another very important question concerns the type of injuries the electrode may cause during the removal process. an extraction model has been prepared using a special curve and a polymer tube. after the pacemaker leads were extracted, various microscopic examinations were executed. the findings may to make such intervention methods more successful, helping to better stabilize the electrode and to keep injuries during interventions to a minimum. keywords. coronary stent; left ventriculal pacemaker electrode; simulated lead extraction. introduction pacemaker (pm) is an electronic device implanted in the body to regulate the heart beat. it consists of a battery and electronic circuits enclosed in a hermetically sealed can. the pm delivers electrical stimuli over leads with electrodes in contact with the heart [1]. fig. 1 shows an x-ray picture of an implanted pacemaker system in a human chest. cardiac resynchronization refers to stimulation techniques that change the degree of atrial and ventricular electromechanical asynchrony in patients with major intra-atrial or interatrial and ventricular conduction disorders. more recently for the treatment of heart failure, the left ventricle may be paced by inserting a lead into a tributary of the coronary sinus, a venous structure on the epicardial surface of the left ventricle [1]. despite major advances of lead and pacemaker techniques, the implantation of a biventricular pacemaker is still a challenging and complex procedure. introducing the left ventricular pacing lead into the sinus coronaries may cause difficulties. the dislocation rate of coronary sinus (cs) leads used for biventricular stimulation is high. stent implantation to stabilize the left ventricular lead is a useful and safe procedure in the treatment of cs lead instability. the electrode is positioned into the desired position, and a metal coronary stent is introduced via a guide wire through the coronary sinus. after pacing measurements the stent is deployed at 5 to 30 mm proximal to the tip of the electrode [2]. fig. 2 presents the parts of a steroid eluting pacemaker head. there is a risk of incidents, especially infections when the implanted left ventriculum lead is to be explanted. therefore, it is crucial to avoid any injury to the heart when the electrodes are removed. during the process of removal the vein wall may be injured. to avoid this, it is to be decided first if the electrode can be explanted as the stent may damage the a http://dx.medra.org/10.3221/igf-esis.16.03&auth=true http://www.gruppofrattura.it r. laczkó et alii, frattura ed integrità strutturale, 16 (2011) 28-33; doi: 10.3221/igf-esis.16.03 29 electrode in a way it may break and the tip may be left in the vessel or the coating may be damaged. it is also important to consider the type and size of the stent in order ensure the most appropriate fixation. the aim of our article is to examine the damages the electrode explantation may cause to the electrodes and stents and to find the most convenient stent for electrode fixation. figure 1: x-ray picture of an implanted pacemaker and electrodes [5]. figure 2: the head of a pacemaker electrode methods special curve was shaped to model the bend of the outer surface of the left ventricle. the curve was formed in a sheet made from foamed polystyrene show in fig. 3. the sheet was 50 mm long, 30 mm wide and 30 mm thick. the left ventricular diastolic diameter (lvdd) is typically about 70 mm and the representative wall thickness of the left ventriculum of patients receiving cardiac resynchronization therapy is 10 to 20 mm [3]. accordingly, the radius of the test curve was 90 mm. a silicon tube was inserted into the curve and the electrodes were stabilized with coronary stents in the tube. figure 3: curve to model the bend of the left ventriculum where the lead is implanted. the first step of the procedure was to fill the tube with physiological saline. since the electrode is surrounded by blood in the ventricle, similar wet conditions had to be ensured in order to minimize the friction between the stent and the electrode. it was achieved by filling the tube with physiologic solution. secondly, the electrode was led up to the end of the tube and coronary stents attached to a balloon were used to fix the electrode. the stents were expanded with an indeflator. the indeflator is a pump complete with a pressure meter and is filled with ringer’s solution. since maximum pressure is normally used to expand stents in practice, the same pressure (26 bar) was chosen in our experiments. our aim was to achieve the maximum available diameter of stents with this method. after the electrode was fixed with the expanded stent, the guide wire and balloon catheter were removed. finally the electrode was slowly and carefully extracted. the procedure was monitored with stereomicroscope. the indeflator was filled with a turquoise liquid for better visibility because polymer tube modelling the vein is not completely transparent. this method makes it possible to follow the process of the expansion more precisely: in the picture the silhouette is sharp. a http://dx.medra.org/10.3221/igf-esis.16.03&auth=true http://www.gruppofrattura.it r. laczkó et alii, frattura ed integrità strutturale, 16 (2011) 28-33; doi: 10.3221/igf-esis.16.03 30 the electrodes and stents examined ive coronary stents and corox otw 75-up steroid eluting electrodes were examined. the inner diameter of the polymer tube was 5 mm and the maximum diameter of the electrodes was 1.95 mm. using this method, the experiments were made only with the minimum 3 mm – diameter stents. they were examined with a stereo microscope (nikon smz2t), a scanning electron microscope (philips xl 30) and a metallograph inspection microscope (olympus pmg-3 with olympus digital camera). 4.5/13 mm stent during the process shown in fig.4, the stent did not slip out or split. this way the vein can be protected against perforation. in picture a), the stent is placed next to the electrode. in picture b), the stent is expanded with the balloon filled with turquoise liquid. in picture c), the balloon is removed and the electrode is fixed by the stent. in picture d), the electrode is extracted and the stent is deformed slightly. a) b) c) d) figure 4: stereomicroscopic pictures of the procedure: stent is crimpled and electrode is in the tube (a), balloon expanded stent (b), fixed electrode (c), stent after the extraction of the electrode (d). 4.5/24 mm stent the head of the electrode caught the stent which can cause injuries to the inner surface of the vessels. fig. 2 demonstrates the damages to the stent after electrode extraction. figure 5: liberté stent creased (left) and fractured (right) parts. f http://dx.medra.org/10.3221/igf-esis.16.03&auth=true http://www.gruppofrattura.it r. laczkó et alii, frattura ed integrità strutturale, 16 (2011) 28-33; doi: 10.3221/igf-esis.16.03 31 4.5/30 mm stent in the picture below (fig.6) it is seen clearly how the flanges stick up on the strut of the stent. the struts were deformed sorely. figure 6: the head of the electrode during extraction (left) and the deformed stent after the procedure (right). 3.5/10 mm stent this is a drug eluting stent in a reservoir-base stent design. the stent became completely deformed and turned across in the tube which would involve grave consequences for human vessels during explantation. the reservoirs and slim parts of the struts may concentrate strain which may weaken the mechanical characteristics. fig. 7 shows electron microscopic photographs of the damaged stent. figure 7: deformed shape and damages to a reservoir stent. 3.5/10 mm stent the stent slipped out and was sheared as the electrode was removed. in the case of in vivo implantation, endothelisation occurs over time so a stent slipping out may cause internal injury. figs. 8 and 9 demonstrate the stent became deformed during electrode extraction. figure 8: the beginning of electrode extraction figure 9: “s”-shaped stent after extraction http://dx.medra.org/10.3221/igf-esis.16.03&auth=true http://www.gruppofrattura.it r. laczkó et alii, frattura ed integrità strutturale, 16 (2011) 28-33; doi: 10.3221/igf-esis.16.03 32 damages to the electrodes he insulation of the electrode was damaged only once and not seriously. the scratch is not deep or long enough to prevent electric functioning (fig. 10). however, the steroid ring was broken several times (fig. 11). in the course of the experiments, the electrodes were in the tube only for a few minutes; implanted in vessels, they work for years and the steroid comes loose. this raises a question if an aged ring could lead to complications during explantation. to ensure greater security, another type of electrodes is recommended for use for stent implantation. figure 10: damages to the electrode tip fixed with stent 2. figure 11: damaged steroid rings on electrodes fixed with stent 3 (left) and stent 4 (right). conclusions o damages were identified on the coating of the electrodes during microscopic examinations. the steroid ring peeled off from the tip of the electrode. it can cause complications only when the peeling is so substantial that the ring slips off and remains in the vessel during explantation. as regards design, stents with reservoirs may cause more problems during explantation. as regards length, shorter stents 4. 3.5/10 mm and 5. 3.5/10 mm are less suitable for fixation than longer ones. stent implantation to stabilize the left ventricular lead with suitable stents is a useful and safe procedure in the treatment of cs lead instability. t n http://dx.medra.org/10.3221/igf-esis.16.03&auth=true http://www.gruppofrattura.it r. laczkó et alii, frattura ed integrità strutturale, 16 (2011) 28-33; doi: 10.3221/igf-esis.16.03 33 references [1] ss. barold, rx. stroobandt, af. sinnaeve, cardiac pacemakers step by step, blackwell publishing, isbn: 1-40511647-1, (2004). [2] sz. szilagyi, b. merkely, e.zima, a. roka, g. szücs, v. kutyifa, a. apor, l.gellér in: congress of the hungarian society of cardiology, balatonfüred, hungary, (2008). [3] a. achilli, f. turreni, m. gasparini, m. lunati, m. sassara, m. santini, m. landolina, l. padeletti, a. puglisi, m. bocchiardo, s. orazi, g. b. perego, s. valsecchi, a. denaro, efficacy of cardiac resynchronization therapy in very old patients: the insync/insync icd italian registry, (2007). [4] p. szabadits, zs. puskás, j. dobránszky, acta of bioengineering and biomechanics, 11 (3) (2009) 11. [5] crt – cardiac resynchronization therapy implantation procedure biotronik presentations. http://dx.medra.org/10.3221/igf-esis.16.03&auth=true http://www.gruppofrattura.it microsoft word numero_27_art_5 m.-p. luong et alii, frattura ed integrità strutturale, 27 (2014) 38-42; doi: 10.3221/igf-esis.27.05 38 focussed on: infrared thermographic analysis of materials characterization of mechanical damage in granite minh-phong luong, mehrdad emami lms (solids mechanics laboratory), civil engineering, department of mechanics ecole polytechnique – cnrs umr7649, 91128 palaiseau cedex, france luong@lms.polytechnique.fr, luong_mp@yahoo.com abstract. this paper aims to illustrate the use of infrared thermography as a non-destructive and non-contact technique to observe the phenomenological manifestation of damage in granite under unconfined compression. it allows records and observations in real time of heat patterns produced by the dissipation of energy generated by plasticity. the experimental results show that this technique, which couples mechanical and thermal energy, can be used for illustrating the onset of damage mechanism by stress concentration in weakness zones. keywords. differential thermography; intrinsic dissipation; mechanical damage in granite; threshold of acceptable damage. introduction urrent technological developments tend towards increased exploitation of material strengths and towards tackling extreme loads and environmental actions. the tendency to extend the service life of materials and structures by increasing maintenance, rather than replacement, increases the need for monitoring structures and supports the need to perform global or local test loading. diverse damage analysis methodologies for engineering materials have been developed in recent years which isolate the factors affecting crack initiation and growth, and enable the prediction of their cumulative effects on the fatigue performance of structural components [1]. in cases where continuum mechanics can be applied, the concept of an effective stress ef = /(1-) has been introduced with a continuous variable  related to the scalar density of defects or faults. this has been the starting point of damage theories developed for fatigue, creep, and creep-fatigue interaction in engineering materials. brittle geomaterials are mainly characterized by their salient fracturing nature. a different approach has been proposed using the plasticity formalism with the concept of a fracturing stress (considered hereafter as a threshold of acceptable damage tad) or a fracturing strain to describe the inelastic behavior of progressively fracturing solids [2]. failure in brittle geomaterial may be viewed as a micro-structural process through the activation and growth of one pre-existing flaw or site of weakness, or through the coalescence of a system of interacting small flaws and growing micro-cracks [3]. the formation of micro-cracks are often associated with points of stress concentration that are located on flaws present in the material, or on existing cracks and notches. several scientific studies have been carried out in recent years on the infrared radiation in the process of rock deformation leading to fracturing and failure [4-6]. within the framework of a consistent theoretical approach, this paper emphasizes the application and use of infrared thermography to detect and evaluate quantitatively the extent of damage in brittle geomaterials owing to the non-linear coupled thermomechanical effects. c http://dx.medra.org/10.3221/igf-esis.27.05&auth=true http://www.gruppofrattura.it m.-p. luong et alii, frattura ed integrità strutturale, 27 (2014) 38-42; doi: 10.3221/igf-esis.27.05 39 background of thermomechanical coupling in solids he development of the thermo-elasticplasticity governing equations [7] leads to the following coupled thermomechanical equation:  cv ,t = r + div (k grad) ( : d : ee,t)  + s : ei,t (1) where  (kg-1.m-3) denotes the mass density, cv (j.kg-1.k-1) the specific heat at constant deformation, ,t (k.sec-1) the time derivative of the absolute temperature, r the heat sources, div the divergence operator, k (w.m-1.k-1) the thermal conductivity, grad the gradient operator,  (k-1) the coefficient of the thermal expansion matrix, : the scalar product operator, d the fourth-order elastic stiffness tensor, ee,t the time derivative of the elastic strain tensor, s the second piolakirchhoff stress tensor and finally ei the inelastic strain tensor. the volumetric heat capacity c =  cv of the material is the energy required to raise the temperature of a unit volume by 1°c (or 1 kelvin). this coupled thermomechanical equation suggests the potential applications of the infrared scanning technique in diverse engineering domains [8-10]: detection of fluid leakage, non-destructive testing using thermal conduction phenomena, elastic stress measurements, and localization of dissipative phenomena. thus the detected temperature change, resulting from four quite distinctive phenomena (heat sources, thermal conduction, thermo-elasticity and intrinsic dissipation), must be correctly discriminated by particular test conditions and/or specific data reduction. this analysis is the principal difficulty when interpreting the thermal images obtained from experiments under the usual conditions. infrared thermography nfrared thermography allows imaging and measuring temperature from radiation in the infrared spectral band. in this paper the infrared imaging system utilizes an infrared focal plane camera operating in mwir wavelength band (midwave infrared window from 3 to 5 m) and in snap shot mode of image capture. the infrared detector converts the emitted radiation into electrical signals that are recorded and displayed on a color or black & white computer monitor. since infrared radiation is emitted by all objects according to the black body radiation law, the amount of radiation emitted by an object increases with temperature, thermography allows the detections of variations in temperature. the quantity of energy emitted as infrared radiation is a function of the temperature and the emissivity of the specimen according to the stefan-boltzman equation. the higher the temperature, the more important is the emitted energy. differences of radiated energy reflect temperature differences. (1a) testing equipment 1 test machine 2 rock specimen 3 infrared thermal imager 4 thermal image (1b) granite specimen figure 1: experimental setup of infrared thermography on a granite specimen. infrared thermovision of rock failure n the laboratory, a fully digital servo-hydraulic test machine, mts 100 kn, was used for uniaxial loading test. the test machine is controlled by a sophisticated closed-loop electronic control system. the sample is scanned in a nondestructive, non-contact manner by means of an infrared thermographic system. the thermal image is shown on the t i i http://dx.medra.org/10.3221/igf-esis.27.05&auth=true http://www.gruppofrattura.it m.-p. luong et alii, frattura ed integrità strutturale, 27 (2014) 38-42; doi: 10.3221/igf-esis.27.05 40 monitor screen (fig. 1). temperature differences in heat patterns as fine as 0.1oc are discernible instantly and represented by several pseudo color grades. brittle geomaterials often present a very low thermomechanical conversion under monotonic loading. in addition the thermal image of the specimen is often affected by several other factors such as the induced heat of the loading machine system, the undesired effects of the specimen ends, etc. this difficulty can be overcome when using thermal image subtraction or differential thermography. this procedure of thermal image processing readily evidences the manifestation of damage caused by the loading application between the two thermograms. the resulting image is a subtracted image showing the temperature change between two compared images, obtained under nearly identical test conditions, as shown in fig. 2. this thermal image processing provides quantitative values of dissipation. the damaged areas are precisely located and highlighted by heat patterns in pseudo colors. (2a) thermogram recorded at reference load level. (2b) thermogram recorded at a given load level. (2c) = thermogram (2b) – thermogram (2a). figure 2: the differential infrared thermography enhances the localization of intrinsic dissipation (temperature changes are given in °c). experimental results he proposed technique has been applied in our laboratory on two brittle rock specimens: massif central diorite (france) and viseu granite (portugal). (3a) quasi homogeneous diorite d. grain size 400-800 µm, plagioclase feldspar (> 60%) and few percents of hornblende and biotite. (3b) heterogeneous granite g. grain size 100µm-10mm, quartz (≈ 20%), plagioclase feldspar (≈ 20%), orthoclase (≈ 20%), microcline (≈ 10%), biotite and muscovite (≈ 25%), few percents of apatite and altered minerals. figure 3: sem (scanning electron microscopy) images of the 2 specimens the parameter investigated in this work is the heat generation due to the dissipative behavior of the material under cyclic loading. the thermal images are recorded when the compressive cyclic loading is applied on the test specimen (fig. 4). the contribution of the plasticity term is revealed by the rapid evolution of dissipation, evidencing the occurrence of damage caused by stress concentration in the central part of the specimen. t http://dx.medra.org/10.3221/igf-esis.27.05&auth=true http://www.gruppofrattura.it m.-p. luong et alii, frattura ed integrità strutturale, 27 (2014) 38-42; doi: 10.3221/igf-esis.27.05 41 (4a) quasi homogeneous diorite d. (4b) heterogeneous granite g. figure 4: different stages of heat dissipation describing the process of the damage extent in the granite specimen (characterized by its compressive strength rc). graphical determination of the threshold of acceptable damage tad of tested materials subject to unconfined loading up to failure. when the compressive loading (maximal cyclic loading at 50hz and 0.10rc of amplitude) is applied on the specimen up to failure, the results suggest a threshold of acceptable damage tad, separating low and high regimes of dissipation or damage. this threshold tad is readily determined graphically on figs. (4a) and (4b) for diorite d and granite g owing to the change of slope of the experimental curve. its value is consistent with characteristic data obtained from other testing techniques based on strain gages, acoustic emission ae or wave propagation phenomena (fig. 5) despite of their quite different nature. (5a) strain based technique (5b) ae based technique (5c) non-linearity based technique figure 5: experimental results obtained when using other testing techniques on granite specimen. concluding remarks his work has demonstrated that (1) the evolution of heat change facilitates the detection of damage extent in geomaterials (even for very brittle rocks) subjected to loading up to failure, and (2) the dissipative behavior of geomaterials under solicitations is a highly sensitive and accurate manifestation of damage. thanks to the thermomechanical coupling, the proposed differential infrared thermography offers a non-destructive, noncontact and real-time testing technique to observe quantitatively the dissipative mechanism of damage in geomaterials. it thus readily provides a measure of the material damage and allows the definition of a threshold of acceptable damage tad under load beyond which the material is susceptible to failure. t http://dx.medra.org/10.3221/igf-esis.27.05&auth=true http://www.gruppofrattura.it m.-p. luong et alii, frattura ed integrità strutturale, 27 (2014) 38-42; doi: 10.3221/igf-esis.27.05 42 the main interest of this energy approach is to unify microscopic and macroscopic test data. the parameter intrinsic dissipation under consideration is a scalar quantity, easy to evaluate accurately. subsequently it may suggest multiaxial design criteria, highly relevant for full-scale testing on engineering rock structures. in conjunction with others testing techniques based on quite different physical nature, the proposed differential infrared thermography promotes the possibility of investigating more thoroughly the mechanical behavior of brittle geomaterials up to failure from different physical points of view. references [1] bui, h.d., fracture mechanics. inverse problems and solutions. springer, (2006). [2] dougill, j.w., path dependence and a general theory for progressively fracturing solid, proc. roy. soc. lond., a, 319 (1983) 341-451. [3] luong, m.p., infrared thermographic observations of rock failure, in comprehensive rock engineering, principles, practices & projects, ed by j.a. hudson, pergamon press, 4 (26) (1983) 715-730. [4] liu, s., wu, l., wu, y., infrared radiation of rock at failure, int. j. rock mech. & min. sci., 43 (6) (2006) 972-979. [5] wu, l., liu, s., wu, y., precursos for rock fracturing and failure, i & 2, int. j. rock mech. & min. sci., 43(3) (2006) 473-493. [6] wu, l., liu, s., wu, y., wu, h., changes in infrared radiation with rock deformation, int. j. rock mech. & min. sci., 39(6) (2002) 825-831. [7] kratochvil, j., dillon, o.w. jr., thermodynamics of elastic-plastic materials as a theory with internal state variables, j. appl. phys., 40 (1969) 3207-3218. [8] luong, m.p., infrared thermographic scanning of fatigue in metals, nuclear engineering and design, 158 (1995) 363376. [9] luong, m.p., introducing infrared thermography in soil dynamics, infrared physics and technology, 49(3) (2007) 306-311. [10] luong, m.p., non-destructive testing of sports engineering: the use of infrared thermography, materials in sports equipment, ed.: alexandar subic, woodhead publishing in materials, isbn 978-1-84569-131-8, 2 (2007) 35-59. http://dx.medra.org/10.3221/igf-esis.27.05&auth=true http://www.gruppofrattura.it microsoft word numero_30_art_37 p. corigliano et alii, frattura ed integrità strutturale, 30 (2014) 304-310; doi: 10.3221/igf-esis.30.37 304 focussed on: fracture and structural integrity related issues fe analysis of cruciform welded joints considering different mechanical properties for base material, heat affected zone and weld metal pasqualino corigliano, vincenzo crupi, eugenio guglielmino department of electronic engineering, chemistry and industrial engineering, university of messina, contrada di dio 98166 sant'agata, messina, italy pcorigliano@unime.it, crupi.vincenzo@unime.it, eguglie@unime.it wolfgang fricke hamburg university of technology. institut für konstruktion und festigkeit von schiffen w.fricke@tu-harburg.de abstract. the aim of this scientific work was to investigate the behaviour of cruciform welded joints under static loading using a full-field technique: digital image correlation. the material curves, relative to different zones (base material, heat affected zone, weld), were obtained by hardness measurements, which were done by means of a fully automated hardness scanner with high resolution. this innovative technique, based on the uci method, allowed to identify the different zones and to assess their different mechanical properties, which were considered in the finite element model. finally the finite element model was validated experimentally, comparing the results with the measurements obtained using the digital image correlation technique. keywords. cruciform welded joints; ship structures; hardness measurements; digital image correlation; fe analysis. introduction elds sometimes represent a weak point, due to the presence of possible crack-like defects along with high stress concentration effects and tensile residual stresses caused by the thermal welding process itself. the strength of welded structures reduces in presence of fatigue loading. the literature on fatigue analysis of welded joints was reviewed in [1, 2]. the fatigue strength of welded joints in high cycle fatigue (hcf) [4] and low cycle fatigue (lcf) [5] regimes was already investigated by the authors. the assessment of the fatigue strength becomes more complex in presence of a multiaxial stress state [6, 7] and complex structures [8]. the welding process induces variations depending also on microstructural factors. the local mechanical properties are expected to change from the melted to the heat affected zone and generally they will be different from the base material ones [3]. local approaches are applied in these cases and are mainly based on local displacement and strain measurements by strain gauges. the aim of this scientific work was to investigate the behaviour of cruciform welded joints under static loading, considering the different material properties of base material (bm), heat affected zone (haz) and weld metal (wm). the material curves, relative to the different zones were obtained by hardness measurements, which were done by means of a w p. corigliano et alii, frattura ed integrità strutturale, 30 (2014) 304-310; doi: 10.3221/igf-esis.30.37 305 fully automated hardness scanner with high resolution, and were considered in the fe analysis. the fe model was validated by means of the results obtained using a full-field technique: digital image correlation (dic). materials and methods he investigated cruciform joint, shown in fig. 1, is made of s235jr mild steel, which is commonly applied in shipbuilding. its nominal dimensions are reported in fig. 2, misalignment is around 1 mm. full-penetration welding was performed using the mag process. tensile tests were carried out on specimens made of the same steel and quasi-static tests in displacement control on welded joints. figure 1: cruciform welded joint. figure 2: specimen geometry. results and discussion hardness measurements he specimen was polished and it was possible to see the three different zones of the material (bm, haz, wz) depicted in fig. 3. hardness measurements were performed at the helmholtz-zentrum in geesthacht-germany, using the ultrasonic contact impedance (uci) method. the uci method is based on the natural resonance frequency of a bar, which pushes the vickers diamond to penetrate into the sample. the measured frequency change depends on the size of the contact surface between the diamond and the sample for a fixed test load, which is related to the hardness of the sample. the aim of the present investigation was to investigate how hardness values influence the global behavior of the weld. the measurements (fig. 4) showed few zones with different hardness values. different groups of hardness measurements were identified and they are shown in fig. 5. the relationship between the ultimate strength u (in mpa) and hb hardness can be described by a second-order polynomial equation proposed in [9] and given by: 20.0012 3.3u hb hb     (1) this equation is a better approximation, especially for high hardness values, than the commonly used linear relations. the yield strength y was also found as a function of the brinell hardness (hb) according to the following equation [9]: 20.0039 1.62u hb hb     (2) t t p. corigliano et alii, frattura ed integrità strutturale, 30 (2014) 304-310; doi: 10.3221/igf-esis.30.37 306 four groups of hardness were used to define different σ-ε curves. in particular hv=140-160 was found to be coherent with respect to the experimental σ-ε curves previously performed on specimens, made of the same steel, and it was used for the assessment of the base material properties; values of hv=190, 230 and 270 were used for the heat affected zones and welded zones. hv values were first converted in hb hardness, then static tensile properties were calculated and reported in tab. 1. finally the true σ-ε curves were evaluated. the elastic strains (fory) were simply calculated as /e; while the elastic-plastic strains (for y) were taken from the ramberg-osgood equation and the parameters were calibrated using the experimental σ-ε curve of the base material, keeping the horizontal lüder’s plateau. fig. 6 shows the material curves, obtained by hardness measurements and by tensile test carried out on a specimen made of the same steel. the hardest fillet weld could be the last one which was made during the welding process because the heat input may affect the hardness of the previously welded ones. figure 3: different material zones. figure 4: hardness measurements. figure 5: hardness values. hv y [mpa] u [mpa] e [mpa] 140 300 460 205000 190 421 636 230 542 780 270 656 908 table 1: hardness measurements and related mechanical properties. figure 6: true stress-strain curve depending on hardness measurements. p. corigliano et alii, frattura ed integrità strutturale, 30 (2014) 304-310; doi: 10.3221/igf-esis.30.37 307 experimental tests and dic analysis displacement controlled tests at r=-1 (ux=±1.2 mm) were performed, where x is the vertical direction. the images of the specimen during the tests were acquired and processed by means of the aramis system using the dic technique. the experimental set-up is shown in fig. 7. fig. 8 shows the values of force and displacement, measured in two cycles. it can be noted that the imposed displacement is symmetric, while the measured force has different absolute values at maximum fmax and mininum fmin loads, due to the structural weakness under compressive load caused by axial misalignment and due to the presence of residual stresses caused by the welding process. furthermore, the value of fmin is not in correspondence of the minimum displacement value, in fact as shown by fig 9, the specimen deforms in a way that bending (buckling) arises causing a diminution of the load. this behavior is also confirmed by the dic analysis, shown in fig. 10 and 11, which illustrate the strain in the x–direction εx (vertical longitudinal direction) at fmax and fmin, respectively. fig. 10 shows a difference in terms of εx from the left side (about 1%) to the right side (about 0.5%), which means that not only tensile stresses are occurring, but there is also a bending component. this effect is increased under compressive loads in fig. 11, which exhibits negative and positive strains respectively of +1.2 and -1.2%. the dic results, shown in fig. 10 and 11, illustrate that large strains occur close to the notch and they become even larger along the base material. figure 7: experimental setup. figure 8: imposed displacement and measured force. figure 9: deformed specimen at fmin. figure 10: εx at fmax (ux = 1.2 mm). figure 11: εx at fmin (ux=-1.2 mm). finite element analysis and comparison to dic results ansys software was used for a nonlinear fe analysis of the cruciform welded joint. the mesh elements of the 3d fe model are of type solid186. fig. 12 shows the local geometry used in the fe model for the welds and the notches, with a notch radius of 1 mm. the minimum size of the element is 0.018 mm in the radial direction, 0.018 mm in the p. corigliano et alii, frattura ed integrità strutturale, 30 (2014) 304-310; doi: 10.3221/igf-esis.30.37 308 circumferential direction, and 1.2 mm along the thickness direction. different material zones (bm, haz, wm) were considered in the fe model with their different σ-ε curves according to fig. 6, no misalignment was considered in the fe model. figure 12: different material zones defined in the fe model. a preliminary fe analysis at high nominal stress (0<n<530 mpa) was performed in order to capture and highlight the influence of the different hardnesses. the geometry and the boundary conditions were the same as in the experimental test, the load is applied to the superior vertical plate, while the inferior vertical plate is clamped. the nominal stress (n) was determined from the introduced force. fig. 13 to 15 show the results in terms of strains and stresses in the x direction. in the elastic phase, the values of εx are higher getting closer to the notch, while, as n exceeds the y value, the strain in the notch depicted in fig. 15 is higher than that the one in fig. 13, but it is smaller near the notch than in the base material (excluding the sharp notch). this effect is due to the differences induced by the hardness values to the material characteristics. figure 13: x for n =180 mpa (n <y). figure 14: x for n =180 mpa (n <y). figure 15: x for n =530 mpa (n >y). figure 16: x for n =530 mpa (n >y). moreover, a fe analysis was performed using the same boundary and loading conditions of the experimental tests (the load was introduced by prescribing a displacement of ±1.2 mm to the superior vertical plate). fig. 17 and 18 show a comparison between the deformed shapes of the real specimen and the fe model at fmin. fig. 19 and 20 confirm the result of the experimental analysis: there are both the components of axial and bending stresses, especially at fmin. furthermore, the strains are larger along the base material than in the weld metal. p. corigliano et alii, frattura ed integrità strutturale, 30 (2014) 304-310; doi: 10.3221/igf-esis.30.37 309 figure 19: εx at fmax (ux = 1.2 mm). figure 17: deformed shape of specimen at fmin. figure 18: fe deformed shape at fmin. figure 20: εx at fmin (ux=-1.2 mm). although the behavior is well represented, the values, in terms of εx at fmax and fmin, differ from the experimental data, due to residual stresses. for this reason a further analysis of the strain range δεx, evaluated between fmax and fmin, i.e. after relaxation during initial loading, was done and the results were compared with dic data, as shown in fig. 21. the comparison, in this case, shows a general good agreement, but the fe analysis exhibits larger strains in the notch proximity. figure 21: dic vs fe values of δεx. conclusions procedure was developed to analyze the response of the investigated cruciform welded joint under static loading. it is based on the following steps: the hardness measurements, using an innovative method for the identification of the different zones (bm, haz, and wm) and the assessment of their constitutive curves, the realization of a nonlinear finite element analysis considering the different material properties and, finally, the validation of fe model by means of the experimental data, obtained by dic technique. the applied procedure allows providing useful information to the development of models for the prediction of fracture behaviour of the welded joints also under fatigue loading. a p. corigliano et alii, frattura ed integrità strutturale, 30 (2014) 304-310; doi: 10.3221/igf-esis.30.37 310 aknowledgments he authors are grateful to the institute of materials research, materials mechanics, solid-state joining processes at the helmholtz-zentrum geesthacht in germany for the technical support and the efficient cooperation during the hardness measurements. references [1] fricke, w., recent developments and future challenges in fatigue strength assessment of welded joints, accepted for publication in the special issue, fatigue design and analysis in transportation engineering, p i mech. eng. c – j. mec, (2015). [2] radaj, d., sonsino, c.m., fricke, w., fatigue assessment of welded joints by local approaches. cambridge: woodhead publ series in welding and other joining technologies, 59 (2006). [3] asm metals handbook, welding, brazing and soldering, asm international, 6 (1993). [4] crupi, v., guglielmino, e., risitano, a., taylor, d., different methods for fatigue assessment of t welded joints used in ship structures, j. ship res, 51 (2) (2007) 150-159. [5] crupi, v, chiofalo, g., guglielmino, e., using infrared thermography in low-cycle fatigue studies of welded joints. weld j, 89(9) (2010) 195 – 200. [6] susmel, l., multiaxial notch fatigue: from nominal to local stress-strain quantities. woodhead & crc, cambridge, uk, (2009). [7] susmel, l., nominal stresses and modified wöhler curve method to perform the fatigue assessment of uniaxially loaded inclined welds, accepted for the publication on the special issue, fatigue design and analysis in transportation engineering, p i mech. eng. c – j. mec, (2015). [8] atzori, b., lazzarin, p., meneghetti, g., ricotta, m., fatigue design of complex welded structures, int j fatigue, 31 (2009) 59–69. [9] lopez, z., fatemi, a., a method of predicting cyclic stress-strain curve from tensile properties for steels, mat sci eng a-struct, 556 (2012) 540–550. t microsoft word numero 17 articolo 2.docx b. atzori et alii, frattura ed integrità strutturale, 17 (2011) 15-22; doi: 10.3221/igf-esis.17.02 15 analysis of the fatigue strength under two load levels of a stainless steel based on energy dissipation b. atzori, g. meneghetti, m. ricotta university of padova, department of mechanical engineering, 35131 padova, italy giovanni.meneghetti@unipd.it published in proceedings of 14th international conference on experimental mechanics icem14, poitiers, france, 4-9 july, 2010 the european physical journal epj web of conferences volume 6-2010 isbn: 978-2-7598-0565-5 riassunto. in questo lavoro è stato analizzato il comportamento a fatica di un acciaio inossidabile aisi 304l. nella prima parte del lavoro sono presentati i risultati ottenuti da prove ad ampiezza di sollecitazione costante sintetizzati sia in ampiezza di tensione sia in termini di densità di energia dissipata dal materiale per ciclo, q. successivamente alcuni provini sono stati sollecitati ad un livello di carico superiore al limite di fatica per circa il 70% della presunta vita e poi ad un livello di tensione inferiore al limite di fatica ad ampiezza costante precedentemente determinato ed è stata confrontata l’energia dissipata nella seconda parte della prova con quella trovata in una prova ad ampiezza costante, allo stesso livello di tensione. il confronto ha mostrato come per il materiale analizzato il parametro q sia sensibile al danneggiamento precedentemente subito. abstract. in this paper the fatigue behaviour of a stainless steel aisi 304l is analysed. in the first part of the work the results obtained under constant amplitude fatigue are presented and synthesised in terms of both stress amplitude and energy released to the surroundings as heat by a unit volume of material per cycle, q. then some specimens have been fatigued in variable amplitude, two different load level tests: the first level was set higher while the second was lower than the constant amplitude fatigue limit. the q values, evaluated during the second part of the fatigue test, have been compared with those calculated under constant amplitude fatigue at the same load level. the comparison allowed us to notice that the q parameter is sensitive to the fatigue damage accumulated by the material during the first part of the fatigue test. keywords. aisi 304l; dissipated energy; fatigue; stainless steel; two load levels; miner rule. introduction he evaluation of fatigue limit of materials based on the experimental measurements of thermal increments is an experimental procedure well documented in the literature [1-3]. recently one of the authors suggested to adopt the energy released to the surroundings as heat by a unit volume of material per cycle, q, as a fatigue damage indicator [4]. in view of this, a particular strategy was conceived in order to derive the q parameter from measurements of the material surface temperature. parameter q was able to correlate the fatigue strength of smooth and notched specimens made of stainless steel, fatigued under constant amplitude stress. to the authors’ knowledge, the material behaviour in terms of q in the case of variable amplitude fatigue load was never investigated. in this paper two load level fatigue tests t http://www.gruppofrattura.it http://dx.medra.org/10.3221/igf-esis.17.02&auth=true b. atzori et alii, frattura ed integrità strutturale, 17 (2011) 15-22; doi: 10.3221/igf-esis.17.02 16 were carried out in order to investigate the sensitivity of q parameter as damage indicator in the case of variable amplitude fatigue. theoretical model to estimate the q parameter he experimental technique used to evaluate the q parameter is based on a theoretical model presented elsewhere [4], so that only the main features will be presented here. let us consider a control volume dv of material under fatigue loading conditions, as shown in fig. 1. the first law of thermodynamics applied to the control volume can be written in terms of power as:   dvcd cv ir p t w dv h h h dv c e t                 (1) where w is the expended mechanical power in a unit volume; hcd, hcv, hir represent the thermal power dissipated in a unit volume due to conduction, convection and radiation, respectively; the last term in the second member is the rate of variation of the internal energy, which is related to the material density , the specific heat c, the time variation of the temperature t and to the time variation of energy absorbed by the material pe  . the term pe represents the rate of accumulation of plastic hysteresis energy, i.e. fatigue damage. dv w q u figure 1: first law of thermodynamics applied to a control volume of material undergoing a fatigue test. usually the surface temperature of material rapidly increases during the first part of fatigue test and then reaches a stationary value which depends on the applied stress level [3, 4]. in steady state conditions eq. (1) becomes   cd cv ir pw h h h e     (2) by considering a sudden stop of fatigue test, the terms w and pe  become zero and then from eq. (1):  cd cv ir t c h h h t          (3) is possible to evaluate the thermal power h dissipated in steady state conditions (eq.(2)) by measuring the time derivative of temperature (see eq.(3)). finally, the energy released to the surroundings as heat by a unit volume of material per cycle, q, can be calculated as: h q f  (4) where f is the test frequency. material, specimen geometry and test procedure he experimental tests were carried out on specimens prepared from 6-mm-thick aisi 304l stainless steel sheets. the specimen geometries used for static and fatigue tests are shown in fig. 2a and fig. 2b, respectively. tests were carried out at room temperature on a schenck hydropuls psa 100 servo-hydraulic test machine, t t http://www.gruppofrattura.it http://dx.medra.org/10.3221/igf-esis.17.02&auth=true b. atzori et alii, frattura ed integrità strutturale, 17 (2011) 15-22; doi: 10.3221/igf-esis.17.02 17 equipped with a 100 kn load cell. the static behaviour was investigated by means of tensile tests under displacement control with a crosshead speed equal to 2 mm/min. during the static test the axial strain was measured by means of a mts extensometer having a gauge length of 25 mm. the fatigue tests were carried out under load control, with a sinusoidal wave, nominal load ratio r (r = min/max) equal to -1 and a test frequency variable in the range of 2-36 hz depending on the applied stress level. to investigate the material fatigue behaviour, constant amplitude fatigue tests were carried out up to the specimen failure. concerning the two load level fatigue tests, some specimens were fatigued at a stress level higher than the fatigue limit for a significant fraction of fatigue life. then the stress level was decreased lower than the fatigue limit and kept constant up to 10 millions of cycles or specimen failure. temperature increments were monitored by means of an agema thv 900 lw/st infrared camera able to detect infrared radiation in the range of wave lengths between 8 and 12 m with a resolution of 0.1 °c. the thermal images were post processed by using the dedicated software agema research 2.1. r30 48 50 5 0 12 20 5 (a) 1 1 3 3 0 30 3 0 r30 10 7 (b) figure 2: specimen geometry for static (a) and fatigue (b) tests. experimental results n order to characterise the material static behaviour, five tests were carried out. the mean value of elastic modulus e, engineering tensile strength r, proof strength p0,2 and true fracture strain a% are summarised in tab. 1. by means of an electrolytic etching (stainless steel anode and cathode, voltage 1.2 v, current 0.2 a) on a 60% nitric acid solution the microstructure was analysed. a typical example is shown in fig. 3: the white matrix represents the austenitic phase while the dark zones inside the grains are ferrite, which represents the 1% of the volume. e [mpa] p0,2 [mpa] r [mpa] a% 194750 315 699 59% table 1: material properties of aisi 304l stainless steel (a) (b) figure 3: example of microstructure observed in the cross section: mid-thickness (a) and below surface (b). i 60 m 60 m http://www.gruppofrattura.it http://dx.medra.org/10.3221/igf-esis.17.02&auth=true b. atzori et alii, frattura ed integrità strutturale, 17 (2011) 15-22; doi: 10.3221/igf-esis.17.02 18 the grain size was assessed according to astm e112 standard [5]. two specimens were analysed and three measurements were done on each of them: in particular, two measurements were performed in the cross-section (one in the mid thickness and one below specimen’s surface) and one on the surface of the sheet. the mean values are listed in tab. 2. one can note that the grains are bigger in the external surface, as it can be expected in the case of rolling sheets. finally, measurements of vickers micro-hardness (applied load 0.2 kg) were carried out. tab. 3 shows the results obtained in the middle of the thickness and at 0.2 mm below the surface. specimen 1 [m] specimen 2 [m] below surface 37 27 mid-thickness 30 27 surface 41 35 table 2: experimentally measured grain size. specimen 1 specimen 2 below surface 175 163 151 155 157 151 mid-thickness 169 162 162 170 163 167 table 3: measured values of vickers micro-hardness (applied load 0.2 kg). synthesis of experimental data in terms of stress amplitude the material fatigue limit was evaluated according to a shortened stair-case procedure according to dixon’s rule [6], which involved 7 specimens. tests were stopped after 10 million cycles. as a results, the fatigue limit in terms of stress amplitude a,-1 resulted equal to 217 mpa. the wöhler curve, shown in fig. 4, was evaluated via statistical analysis of the available fatigue data, by assuming lognormal distribution of the number of cycles to failure. in the same figure the fatigue limit a,-1, the 10-90% scatter band, the value of the inverse slope k of wöhler curve, the scatter index t (t = a,-1,10%/a,-1,90%), the scatter index tn, (tn,= tk) and the number of cycles na, which corresponds to the knee point of the curve, are listed. figure 4: wöhler curve and 10%-90% scatter band of the aisi 304 l stainless steel. synthesis of experimental data in terms q parameter as already discussed, the evaluation of q parameter is based on the measurement of the cooling rate just after a sudden interruption of the fatigue test, according to eqs. (3) and (4). the material density, experimentally measured by using archimedes method and a sartorius 1801 balance, with a resolution of 10-7 kg, was 7940 kg/m3. by using a calorimeter, the specific heat c was determined equal to 507 j·kg-1·k-1. r=-1 t=1.20 k=12.9 tn,=10.5 a = 217 mpa na=165800 300 200 104 105 106 107 108 n. cycles  a [m p a] 10% 90% broken run-out broken stair case procedure 140 http://www.gruppofrattura.it http://dx.medra.org/10.3221/igf-esis.17.02&auth=true b. atzori et alii, frattura ed integrità strutturale, 17 (2011) 15-22; doi: 10.3221/igf-esis.17.02 19 the cooling rate after a sudden interruption of the fatigue test was measured by using the infrared camera and by considering the maximum value of the temperature inside on area encompassing the reduced section of the specimen. the maximum sampling frequency of the thermal images allowed by the available measuring system was 7 hz. fig. 5a shows an example of an infrared image: the rectangle identifies the area where the maximum surface temperature was detected. a typical example of the recorded temperature trend is plotted in fig. 5b: t0 indicates the time when the fatigue test was stopped while in the y-axis the temperature variation with respect to that stabilized before the test stop is shown. after evaluating the cooling gradient, q was derived according to eqs. (3) and (4). (a) (b) figure 5: example of control area surrounding the specimen where the maximum temperature was analysed (a) and typical maximum temperature signal measured after a sudden interruption of fatigue test (b) (a=210 mpa, run out). in order to evaluate the evolution of q parameter, each fatigue test was interrupted several times. fig. 6 shows the q values plotted versus the number of cycles normalised with respect to the number of cycles to failure or, in the case of run-out specimens, with respect to 10 millions. it can be noted that the value of q reached a constant value after about 50% of the total fatigue life. moreover, the plotted curves show as soon as the stress amplitude is increased above the fatigue limit (a > 220 mpa) then the stabilised values of q increase of a factor 7 (from  100 kj/(m3·cycle) to  700 kj/(m3·cycle)). the fatigue data were analysed in terms of the stabilised energy parameter found during each fatigue test, by assuming a log-normal distribution of the number of cycles to failure, according to the following equation: coskq n t  (5) where n represents the number of cycles to failure and k is the inverse slope of the new fatigue curve. figure 6: evolution of the specific energy loss versus the normalised fatigue life. 0 200 400 600 800 1000 1200 1400 0 0.2 0.4 0.6 0.8 1 260 mpa 240 mpa 230 mpa 220 mpa 210 mpa 190 mpa q [ k j/ (m 3 c y cl e) ] n/nf http://www.gruppofrattura.it http://dx.medra.org/10.3221/igf-esis.17.02&auth=true b. atzori et alii, frattura ed integrità strutturale, 17 (2011) 15-22; doi: 10.3221/igf-esis.17.02 20 fig. 7 shows the fatigue data analysed according to eq. (5), with the 10-90% scatter band, the reference q value evaluated at 10 millions of cycles, the value of exponent k, the scatter index tq (tq =q,10%/q,90%) and the scatter index tn,q (tn,q= tqk). the experimental data can be synthesised in a unique scatter band characterised by a constant slope k from 104 to 107 cycles. it is interesting to note that the scatter index tn,q results by far lower than tn, shown in fig. 4. figure 7: fatigue data synthesised in terms of specific energy loss q for the aisi 304 l stainless steel. two load level fatigue tests ith the aim to evaluate the sensitivity of the q parameter to prior fatigue damage, some specimens were fatigued in variable amplitude, two different load level tests: the first level was chosen higher (a=230 mpa) than the material fatigue limit (a,=217 mpa) and it was applied for a significant fraction of fatigue life (ranging from 80 to 86%) as evaluated according to the q-n curve, previously obtained by means of constant amplitude fatigue tests (see fig. 7). the second load level (a=190 mpa) was lower than the fatigue limit. it should be noted that the two-load level fatigue tests presented in this paper are different from those presented in [4], where both levels were higher than the constant amplitude fatigue limit. the q values, evaluated during the second step of the fatigue test, have been compared with those measured during some tests carried out under constant amplitude fatigue at the same load level on undamaged specimens. figure 8: results of two load level fatigue tests in terms of stress. scatter band is that reported in fig. 4. figure 9: results of two load level fatigue tests in terms of q. the scatter band is that reported in fig. 7. the results of the two load level fatigue tests are shown in fig. 8 in terms of stress amplitude. it can be noted that only two of four specimens failed during the second level fatigue test. the same results were re-analysed on the basis of the energy parameter q and plotted in fig. 9: in the case of specimens that failed, the q values measured during the second 10 100 1000 10000 1.e+04 1.e+05 1.e+06 1.e+07 1.e+08 q [ k j/ (m 3 c y cl e) ] n. cycles r=-1 k=2.25 qa,50%=87 kj/(m 3 cycle) tq=1.92 tn,q=4.34 10% 90% 50% broken run-out broken stair case procedure 300 200 104 105 106 107 108 n. cycles  a [m p a] 10% 90% 140 open symbols: first block of cycles filled symbols: second block of cycles first load level: a=230 mpa second load level: a=190 mpa specimen 1 specimen 2 specimen 3 specimen 4 10 100 1000 10000 specimen 1 specimen 2 specimen 3 specimen 4 n. cycles q value measured at constant amplitude stress  a = 190 mpa on undamaged specimens open symbols: first block of cycles filled symbols: second block of cycles first load level:  a =230 mpa second load level:  a =190 mpa q [ k j/ (m 3 c yc le ) 104 105 106 107 108 w http://www.gruppofrattura.it http://dx.medra.org/10.3221/igf-esis.17.02&auth=true b. atzori et alii, frattura ed integrità strutturale, 17 (2011) 15-22; doi: 10.3221/igf-esis.17.02 21 block of cycles were definitely higher than those observed during constant amplitude fatigue tests at the same stress level on the undamaged material. on the contrary, specimens 3 and 4 exceeded 10 millions of cycles once loaded at the second stress level. in fact for these specimens the q values measured during the second block of cycles were very close to those detected during constant amplitude fatigue tests at 190 mpa on undamaged material. then, as far as the experimental data analysed in the present paper are concerned, it can be concluded that the parameter q is sensitive to the fatigue damage accumulated prior to the second block of fatigue cycles. finally, by considering only the two specimens that failed, the damage d was evaluated on the basis of the q-n curve shown by fig. 7, according to the miner’s rule (eq. 6): 2 1 2 1 1 2 i i i n n n d n n n    (6) where ni is the number of cycles carried out at a,i stress amplitude and ni represents the corresponding number of cycles to failure. figure 10 compares the experimental results obtained for specimen 1 and 2 with miner’s hypothesis (d=1): the horizontal and the vertical axis represent the fraction of fatigue life spent during the first block (n1/n1) and during the second block (n2/n2) of load, respectively. the comparison allowed us to notice that the miner’s hypothesis, based on the q-n curve, is in good agreement with the experimental results. figure 10: comparison between the experimental data and miner’s rule applied in terms of q. conclusions n this paper the fatigue behaviour of a stainless steel aisi 304 l was analysed in terms of energy released to the surroundings as heat by a unit volume of material per cycle, q. after evaluating the material constant amplitude fatigue limit under completely reversed axial stress, the fatigue data were analysed in terms of both stress amplitude and energy parameter q, according to [4]. then some specimens were fatigued in variable amplitude, two load levels to investigate the sensitivity of the q parameter to prior fatigue damage. the main results can be summarised as follows:  the wöhler curve of material generated from constant amplitude fatigue tests presents a knee point at 165800 cycles;  the average curve which synthesises the fatigue data in terms of the energy parameter q presents a constant slope from 104 to 107 cycles;  the data dispersion in terms of fatigue lives is reduced by a factor greater than two if the experimental data are processed by using the energy parameter q rather than the applied stress amplitude;  the observed energy parameter q increases by a factor of about seven if specimens are tested just 13 mpa above the fatigue limit with respect to the values measured at or below the fatigue limit itself;  it can be concluded that the parameter q is a fatigue indicator sensitive to the damage accumulated during the prior load history;  miner’s hypothesis applied on the basis of the q-n curve is in good agreement with the experimental data available. as a final remark, additional work is needed to further support the experimental findings presented in this paper. 0 0.2 0.4 0.6 0.8 1 0 0.2 0.4 0.6 0.8 1 specimen 1 specimen 2 miner's rule 1 1 n n 2 2 n n 1 n n n n d 2 2 1 1  i http://www.gruppofrattura.it http://dx.medra.org/10.3221/igf-esis.17.02&auth=true b. atzori et alii, frattura ed integrità strutturale, 17 (2011) 15-22; doi: 10.3221/igf-esis.17.02 22 references [1] d. dengel, h. harig, fatigue fract. engng. mater. struct., 3 (1980) 113. [2] m.p. luong, mech. mater., 28 (1988) 155. [3] g. la rosa, a. risitano, int. j. fatigue, 22 (2000) 65. [4] g. meneghetti, int. j. fatigue, 29 (2007) 81. [5] astm e112 96(2004)e2 standard test methods for determining average grain size. [6] w. dixon, f. massey, introduction to statistical analysis, mcgraw-hill, new york (1966). http://www.gruppofrattura.it http://dx.medra.org/10.3221/igf-esis.17.02&auth=true microsoft word numero_37_art_40 u. muhin et alii, frattura ed integrità strutturale, 37 (2016) 305-311; doi: 10.3221/igf-esis.37.40 305 focused on fracture mechanics in central and east europe simulation of accelerated strip cooling on the hot rolling mill run-out roller table u. muhin, s. belskij, e.makarov lipetsk state technical university, lipetsk, russia nemistade@mail.ru t. koynov university of chemical technology and metallurgy, sofia, bulgaria toni309@koinov.com abstract. a mathematical model of the thermal state of the metal in the run-out roller table continuous wide hot strip mill. the mathematical model takes into account heat generation due to the polymorphic γ → α transformation of supercooled austenite phase state and the influence of the chemical composition of the steel on the physical properties of the metal. the model allows calculation of modes of accelerated cooling strips on run-out roller table continuous wide hot strip mill. winding temperature calculation error does not exceed 20°c for 98.5 % of strips of low-carbon and low-alloy steels keywords. hot rolled; wide-strip; accelerated cooling; run-out roller table; polymorphic transformation; mathematical modeling. introduction n a highly competitive market, each steel group strives to improve product quality. the most important factor affecting the quality of products, ensuring accuracy is a necessary process parameter throughout the production cycle. when thermomechanical processing of metals in the hot rolling mill main controllable parameters are the temperature of the end of the rolling and winding, the thickness, width, profile and flatness of the strip. at the present time to provide the necessary parameters in a narrow permitted range is not possible without automation of the production process. in this regard, the development of mathematical models, based on which is more precise control of process parameters is an urgent task. matematical model of the thermal state of the metal in the collecting roller table urrently, broadband hot rolling mills for rapid cooling strips on collecting roller table used as a rule, the collector jet (laminar) cooling. when you turn on the system of forced cooling of the heat exchange with the band by exhausting heat out of the jets of water coming from the upper and lower reservoirs, the layer of water flowing i c u. muhin et alii, frattura ed integrità strutturale, 37 (2016) 305-311; doi: 10.3221/igf-esis.37.40 306 from the upper surface of the strip, and the environment. temperature monitoring of the end of the rolling and coiling by radiation pyrometers. the mathematical model of the thermal state of the metal in the collecting roller table is based on the definition of the space-time temperature field strip. the calculated field is found by solving one-dimensional unsteady heat conduction equation (1) the numerical method the method of finite differences:          2 2 ( ) ( ) ( ) v t t t c t t q x (1) where: ρ density of the metal, kg/m3; c specific heat of the metal j/(kg×k); λ thermal conductivity of the metal, w/(m×k); t temperature of the metal, k; τ – time, s; x coordinate of the strip thickness, m; qv power density heat sources, w/m3. heat loss from strip cooling water, radiation, and interaction with the ambient air are described by the boundary conditions of the second and third kind, and for the difference scheme are given in the following form:        ср t q t t x where: tsr ambient temperature; q heat flux, w/m2; α heat transfer coefficient, w/(m2×k). the solution of the heat is carried by the sweep method. as a finite-difference scheme is used implicit scheme. the calculation of heat flow and heat transfer coefficient is performed on the dependence presented in [1-3] for the conditions of collecting roller table of continuous strip hot rolling mill (cshrm). on cooling the strip to the collecting roller table mill hot rolling the metal undergoes a polymorphic transformation of γ → α, which is accompanied by significant heat release. the vast majority of mathematical models of the thermal state of the band on the collecting roller table, for example, [2-6], does not include a calculation of the polymorphic transformation as transportation for the band collecting roller table, which can lead to substantial error in the prediction of coiling temperature variation of process parameters in a wide range. to calculate the polymorphic transformation in the collecting roller table to know ar3 transformation temperature of the beginning and end of the conversion of ar1. these parameters depend on the chemical composition of steel, the cooling rate, the dislocation density in the crystal lattice, the grain size and strain rate prior to the metal. in constructing a mathematical model of calculation of the critical points ar3 and ar1 made only according to the chemical composition of the steel, cooling rate and, indirectly, on the grain size, by choosing for the calculation of thermokinetic decomposition diagrams of supercooled austenite with austenite temperature, similar to the conditions cshrm. the density and thermal conductivity of the metal is given according to the reference data. specific heat of the metal is calculated by the formula:     1c xc x c where: x the share of the formed α-phase; cα the heat capacity of α-phase; cγ the heat capacity of γ-phase. the quantity of x is calculated as follows according to [7]:    1 exp nx by (2)    3 3 1 jar t y ar ar u. muhin et alii, frattura ed integrità strutturale, 37 (2016) 305-311; doi: 10.3221/igf-esis.37.40 307   30.009 14.521b ar ,  30.018 9.293n ar , where: tj metal temperature at the collecting roller table in the j-th time, °c; ar3 and ar1 the critical point, °c. ar1 and ar3 temperature, depending on the chemical composition of steel and the cooling rate can be described by the equation [8]:   ni iar kw mw a ,°с,  1, 3i ; (3)    кп j масс масс j тр t t w , where: w the rate of cooling, °c/s; ai isothermal value based on the chemical composition; k, m, n coefficients; tmaxkp-averaged temperature at the end of rolling, °c; tmaxj-averaged temperature of the strip in the j-th time; tmpj transportation time of the calculated cross sections in the j-th moment of time from the end of rolling pyrometer, s. according to estimates in the demo-version of the thermo-calc heat when γ → α transformation of pure iron was 136.93 mj/m3, then the expression for the power density due to heating of the strip of polymorphic transformation can be written as:          1 1 136, 93 j j v j j x x q , 3 мвт м , where: τ – time, s. adaptation of a mathematical model he mathematical model of the thermal state of the metal in the collecting roller table adapted to the conditions of continuous wide hot-rolling mill 2000 "nlmk", russia. the existing mill in the accelerated cooling unit consists of 80 upper and lower sections, equipped with reservoirs of jet cooling. the scheme of collecting roller table with the installation of cooling is shown in fig. 1. the total length of the outlet roller mill in 2000 is 206.6 m figure 1: cooling scheme on outlet roller of mill 2000. t u. muhin et alii, frattura ed integrità strutturale, 37 (2016) 305-311; doi: 10.3221/igf-esis.37.40 308 adaptation of a mathematical model was to minimize the error between the calculated and actual measured temperature coiling. during the first stage adaptation of the method of nelder-mida determined the unknown coefficients of the mathematical model (the emissivity of the surface of the strip, the coefficient of proportionality flow characteristics of reservoir cooling, etc.). in adapting the model used two samples of hot-rolled strips of low carbon and low alloy steels: an adaptation and control. adaptive sampling is designed to find the optimal values of the coefficients of the model, and control adapted to assess the adequacy of the mathematical model. the total number of bands in the adaptation and control samples was 5441 and 5442, respectively. in the second phase of adaptation was performed at a rate of iteration n (2) to minimize errors in the calculation, since the coefficient n is obtained only through a thermokinetic diagram of decomposition of supercooled austenite of low carbon steels. as a result, we obtain the following regression equation:                                   2 3 4 5 3 3 3 3 3 3 1984.74 0.0144 -5204.1 2918.4 2854.6 3596.9 1035.6кп кп кп кп кп t t t t t n ar ar ar ar ar ar where: tkp temperature of the end of rolling, controlled by the radiation pyrometer, °c. the comparison of the calculated and actual values of temperature coiling after adaptation of the mathematical model is presented in fig. 2. the number of bands with an error of calculation of more than 20 ° c for adaptation and control samples was 1.43% and 1.16% respectively. the result of calculation of the mathematical model for the length of the collecting roller table for a design section is shown in fig. 3. the result is presented for a strip of steel st3sp standard size 4x1500 mm, the filling speed of 7.2 m/s. a 500 550 600 650 700 750 800 500 550 600 650 700 750 800 b 500 550 600 650 700 750 800 500 550 600 650 700 750 800 experimental temperature, °c figure 2: comparison of calculated and measured values of the winding temperature: a) adaptive sampling; b) the control one. to compare the calculated and actual distributions of temperature along the length of coiling were selected band of low-carbon steels (fig. 4). the mathematical model allows to calculate the number of cooling sections, which should be included to ensure the desired temperature, depending on the coiling temperature and rolling speed mode and cooling strategies. fig. 5 shows a comparison of estimated and actual number of cooling sections of mill 2000 when rolling strip 3.5 x1300 mm of steel st1ps with increased acceleration and application between standing cooling in the finishing group (rolling speed 10-13.4 m/s, acceleration 0.056 m2/s, the flow of water in the cooling system 960 m3/h, coil weight 26 tons) u. muhin et alii, frattura ed integrità strutturale, 37 (2016) 305-311; doi: 10.3221/igf-esis.37.40 309 figure 3: cooling of the calculated cross stripes on the different rollertable figure 4: the temperature regime of rolling strip 08ps, 2,7 x1290 mm: 1) the actual value, and 2) the calculated value u. muhin et alii, frattura ed integrità strutturale, 37 (2016) 305-311; doi: 10.3221/igf-esis.37.40 310 figure 5: comparison of estimated and actual modes of cooling on the mill 2000 different rollertable . strip 3,5 x1300 mm, steel st1ps; 1 actual temperature, 2 calculated temperature, 3 setting management system accelerated cooling the strip to include the cooling sections, 4 calculated number of cooling sections. conclusion mathematical model of the thermal state of the metal in the collecting rollertable continuous wide hot strip mill, which takes into account heat generation due to the polymorphic transformation of supercooled austenite is developed. the calculate error of cooling temperature does not exceed 20°c for 98.5 % of the strips in a wide range of rolled product of low-carbon and low alloy steels and process parameters of hot rolling. the developed model can be used in the control system in the construction of algorithms for automatic control by setting the accelerated cooling of the metal in the collecting roller table continuous wide hot strip mill or casting rolling plant. a u. muhin et alii, frattura ed integrità strutturale, 37 (2016) 305-311; doi: 10.3221/igf-esis.37.40 311 references [1] labeish, v.g, liquid-cooled high-temperature metal l. because of the lgu, (1983) [2] nenakhov, v.a., increase the efficiency of production of hot-rolled bands due to the optimization of the production program of rolling: diss. candidate. technical. science, lipetsk, lgtu, (2007). [3] koinov, t.a., gurov, a.s., shatalov, r.l., software tools 50870000614. economic-mathematical model of continuous hot strip rolling. programs and algorithms, inf. bull., 11 (1987), moscow, (in russian). [4] masur, i.p., development theory and the improvement of production technology for sheet metal castingrolling complexes: diss. doctor. technical. science, lipetsk, lgtu, (2003). [5] koinov, t., kihara, j., process optimization for hot strip mill. trans. of the isi of japan, 26 (1986) 895 – 902. [6] senichev, g.s., medvedev, g.a., denisov, s.a., medvedev, a.g., method of calculating the cooling of steel strips on the collecting roller table, steel, 2 (2007) 77-78. [7] boyadjiev, i.i., thomson, p.f., lam, y.c., computation of the diffusional transformation of continuously cooled austenite for predicting the coefficient of thermal expansion in the numerical analysis of thermal stress, isij international, 36(11) (1996) 1413-1419. [8] mukhin, j.a., bobkov, e.b., relationship of hot rolling parameters and kinetics of decomposition of supercooled austenite, math, university. iron and steel, 5 (1996) 27-29. << /ascii85encodepages false /allowtransparency false /autopositionepsfiles true /autorotatepages /none /binding /left /calgrayprofile (dot gain 20%) /calrgbprofile (srgb iec61966-2.1) /calcmykprofile (u.s. web coated \050swop\051 v2) /srgbprofile (srgb iec61966-2.1) /cannotembedfontpolicy /error /compatibilitylevel 1.4 /compressobjects /tags /compresspages true /convertimagestoindexed true /passthroughjpegimages true /createjobticket false /defaultrenderingintent /default /detectblends true /detectcurves 0.0000 /colorconversionstrategy /cmyk /dothumbnails false /embedallfonts true /embedopentype false /parseiccprofilesincomments true /embedjoboptions true /dscreportinglevel 0 /emitdscwarnings false /endpage -1 /imagememory 1048576 /lockdistillerparams false /maxsubsetpct 100 /optimize true /opm 1 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/hrv (za stvaranje adobe pdf dokumenata najpogodnijih za visokokvalitetni ispis prije tiskanja koristite ove postavke. stvoreni pdf dokumenti mogu se otvoriti acrobat i adobe reader 5.0 i kasnijim verzijama.) /hun 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/pdfxoutputintentprofileselector /documentcmyk /preserveediting true /untaggedcmykhandling /leaveuntagged /untaggedrgbhandling /usedocumentprofile /usedocumentbleed false >> ] >> setdistillerparams << /hwresolution [2400 2400] /pagesize [612.000 792.000] >> setpagedevice microsoft word numero 9 art 14 finale r. tovo et alii, frattura ed integrità strutturale, 9 (2009) 135 144; doi: 10.3221/igf-esis.09.14 135 il gradiente implicito nella verifica a fatica di giunzioni saldate sollecitate a fatica r. tovo, p. livieri università di ferrara, dipartimento di ingegneria, via saragat 1, 44100 ferrara, roberto.tovo@unife.it riassunto. l’incremento delle potenzialità di strumenti per la progettazione assistita (come modellatori solidi e strumenti per fea in grado di gestire modelli molto complessi) permette di ipotizzare lo sviluppo di strumenti numerici specifici per la previsione della resistenza a fatica delle giunzioni saldate. tali strumenti potrebbero essere in grado di valutare l’influenza di geometria e carichi senza la necessità di elaborazioni successive, e spesso, del progettista (come nelle tensioni di hot spot). il presente lavoro propone una metodologia di calcolo adatta alla previsione della vita a fatica di giunzioni saldate complesse. un indice di resistenza è ottenuto innanzitutto risolvendo il problema tensionale completamente in modo numerico (agli elementi finiti) . la previsione della resistenza a fatica, è calcolata facendo uso di un modello analitico basato sul gradiente implicito che assume come tensione efficace la tensione equivalente non locale derivante dalla tensione principale. dapprima verrà tarato il metodo su prove sperimentali eseguite su giunzioni saldate a croce, successivamente il metodo verrà utilizzato per la verifica a fatica di giunzioni saldate più complesse a sviluppo tridimensionale. abstract. in this paper, a non-local equivalent stress is calculated by solving a second order differential equation of implicit type. the solution is obtained by assuming a linear elastic constitutive behaviour and the maximum principal stress as equivalent stress. fatigue behaviour of steel welded joints is taken into account and a general fatigue scatter band is proposed. the non local stress is computed, namely the effective stress, by means of a completely numerical solution of local elastic stress field. in complex 3d welded details the critical point turns out from the analysis and it is not assumed a priori. parole chiave. fatica, giunti saldati, tensioni non-locali. introduzione l disegno e la modellazione tridimensionale assistiti negli ultimi anni sono diventati, in molte aziende del settore meccanico, uno standard di progettazione che offre il vantaggio di cogliere l'aspetto e il funzionamento nelle tre dimensioni nonché la possibilità di usare la formulazione matematica dei volumi considerati per ulteriori elaborazioni. nel caso delle saldature, ed in particolare dei cordoni d’angolo, nella rappresentazione tridimensionale diviene naturale la schematizzazione con figure prismatiche o di rivoluzione aventi spigoli vivi. tale assunzione è di fatto vicina alla realtà in quanto i cordoni di saldatura ottenuti ad arco, sono caratterizzati da raggi di raccordo il cui valore medio è nell’ordine di grandezza di qualche decimo di millimetro [1-3]. se da una parte, l’adozione di uno spigolo vivo può semplificare la modellazione del componente, dall’altra, dal punto di vista dell’analisi strutturale , si introduce nel campo tensionale una singolarità (ossia un punto con soluzione tendente all’infinito) che impedisce l’uso di modelli di verifica basati sulla imposizione di un limite tensionale. l’idea di confrontare un limite ritenuto ammissibile per il materiale con il valore di picco del campo di tensione, non può essere adottato in quanto qualunque valore assunto per la tensione ammissibile viene inevitabilmente superato purché ci si avvicini sufficientemente allo spigolo. in queste situazioni la letteratura scientifica a volte consiglia di utilizzare le tensioni nominali o le tensioni di hot spot [4]. purtroppo le prime (nominali) spesso non sono definite o calcolabili in modelli solidi geometricamente complessi. le tensioni di hot spot hanno altri problemi: il primo è che necessitano di un post-processing manuale e spesso non chiaro i http://www.gruppofrattura.it/ http://dx.medra.org/10.3221/igf-esis.09.14&auth=true mailto: roberto.tovo@unife.it r. tovo et alii, frattura ed integrità strutturale, 9 (2009) 135 144; doi: 10.3221/igf-esis.09.14 136 nella procedura da seguire; inoltre le previsioni sono a volte imprecise (approssimative), non valutano l’effetto scala o non sono in grado di predire il comportamento meccanico di punti di rottura diversi dal piede del cordone (come i cedimenti alla radice del cordone). per una trattazione teorica degli aspetti matematici e geometrici, in presenza di un raggio di raccordo nullo dei cordoni di saldatura, è possibile affidarsi ad approcci locali basati sul calcolo dei notch stress intensity factors (nsif) valutati in prossimità dei punti in cui innesca la cricca per fatica [6-11]. nel caso in cui solo modo i sia singolare o di modo i predominante su modo ii, l’nsif può essere usato direttamente per il calcolo della vita a fatica utilizzando specifiche bande di dispersione [7, 8, 11], mentre in condizioni di modo misto di sollecitazione, o nell’ottica di utilizzare un’unica banda di dispersione valida per qualunque angolo di apertura del cordone di saldatura, si rende necessario l’impiego di un parametro di validità più generale come, ad esempio, l’energia media all’interno di un settore circolare posto in prossimità del punto critico [9-11]. per gli aspetti più applicativi sarebbe opportuno disporre di un approccio metodologico che sia congruente con l’inquadramento agli nsif per l’analisi del comportamento a fatica, ma al contempo adatto all’impiego per un computo interamente numerico del problema della resistenza a fatica indipendentemente dalla complessità del giunto senza assumere a priori il punto di innesco della cricca. ossia l’obiettivo è quello di proporre una metodologia, adatta al calcolo della resistenza a fatica delle giunzioni saldate e capace, indipendentemente della complessità del giunto, di riportare la verifica a fatica al calcolo di un valore “efficace” della tensione calcolabile con strumenti automatici integrati con solutori agli elementi finiti. la presente memoria presenta una possibile soluzione del problema metodologico attraverso l’approccio denominato “gradiente implicito” [12-14]. per validare il metodo proposto, saranno considerati dati sperimentali presi dalla letteratura di giunzioni saldate analizzabili con schemi bidimensionali, altresì a dettagli strutturali complessi schematizzati con modelli tridimensionali. modello non locale ssegnato un corpo generico di volume v, in accordo con le referenze [15] e [16] è possibile definire una tensione equivalente non locale  nel punto generico p del volume v come media integrale di una tensione equivalente locale eq pesata con una opportuna funzione  che tiene in considerazione la distanza s del generico punto q dal punto p dei punti del volume v (s= pq ):   v eq r vindv)q()pq( )p(v 1 )p( (1) nell’equazione (1), il simbolo )p(vr denota il volume di riferimento calcolato come  v r dv)pq()p(v . senza entrare nel dettaglio dei modelli non locali, il problema del calcolo della tensione equivalente non locale  può essere trasferito alla risoluzione di una equazione differenziale del secondo ordine [17]. dopo aver assunto la  come tensione efficace ai fini della resistenza a fatica (eff), l’integrale (1) equivale a risolvere la seguente equazione differenziale: vinc eqeff 22 eff  (2) dove c è una dimensione intrinseca legata al materiale in esame, 2 è l’operatore di laplace e eq è la tensione equivalente locale ritenuta responsabile del danno a fatica (per una trattazione più approfondita del problema si rimanda alle referenze [12-14]). calcolo della tensione efficace ’obiettivo del presente lavoro è quello di risolvere l’equazione differenziale (2) in presenza di singolarità tensionali indotte dai cordoni di saldatura pensati come intagli ideali a spigolo vivo. a tale scopo, è stata messa a punto una procedura di tipo numerico capace di risolvere il problema (2) della non-località della tensione in modo completamente automatico. a l http://www.gruppofrattura.it/ http://dx.medra.org/10.3221/igf-esis.09.14&auth=true r. tovo et alii, frattura ed integrità strutturale, 9 (2009) 135 144; doi: 10.3221/igf-esis.09.14 137 nel caso di sollecitazione a fatica con carichi in fase, le direzioni principali rimangono invariate nel tempo ed il calcolo a fatica può risolversi facendo riferimento ai soli valori minimi e massimi della tensione efficace. in particolare, per le saldature che non hanno subito un trattamento di distensione termica, è sufficiente far riferimento al solo range della tensione efficace (eff). perciò, per le saldature, nella (2) andranno inserite le variazioni  che subiscono le tensioni nel ciclo di fatica. figura 1: geometria di riferimento. soluzione numerica 2d alcune tipologie di giunti saldati come i giunti a croce e i giunti a t, possono essere studiati come giunzioni a sviluppo bidimensionale ipotizzando nulli i gradienti di tensione nella terza dimensione. noto il parametro c del materiale in esame e le condizione al bordo, è possibile risolvere l’equazione ellittica (2) nell’intero volume v in funzione della tensione equivalente eq scelta. espressioni asintotiche della tensione eq equivalente possono essere valutate se si conoscono a priori i valori dei notch stress intensity factors (nsif) nel punto in cui innesca la cricca per fatica [13]. sfruttando un sistema di riferimento polare, la soluzione numerica può essere ottenuta su un settore circolare di raggio rd di dimensioni maggiori al parametro c del materiale (c<<rd). la fig. 1 mostra il dominio di integrazione e le condizioni al bordo applicate. come condizioni al bordo, in [13] sono state prese in esame solo le condizioni di neumann che esprimono l’ortogonalità del gradiente della soluzione cercata con la normale uscente al bordo del dominio di integrazione (dal punto di vista fisico ciò equivale ad imporre un flusso nullo della soluzione in direzione ortogonale al bordo). ciò nonostante, se non sono noti gli nsif della saldatura si può comunque ricorrere ad una soluzione completamente numerica del problema differenziale. la fig. 2, riporta un esempio di calcolo della tensione eff (adimensionalizzata rispetto alla tensione nominale nel piatto più spesso) ottenuta a partire da una analisi lineare elastica del problema tensionale che vede nei sei punti indicati in figura una singolarità del campo di tensione in accordo con la soluzione di williams [18]. in fig. 2, come tensione equivalente eq locale è stata assunta la tensione principale massima. appare evidente che la singolarità del campo di tensione di partenza viene smussata, ottenendo un campo di tensione equivalente non locale di tipo continuo su tutto il giunto. la sola analisi della tensione efficace riportata come grafico tridimensionale al di sopra del dominio di integrazione, fornisce contemporaneamente la posizione di probabile innesco del difetto per fatica ed il valore del picco della tensione efficace. va comunque sottolineato che a sostegno di quanto calcolato numericamente, accurate soluzioni analitiche di casi monodimensionali e bi-dimensionali sono riportate nelle referenze [12, 13]. soluzione numerica 3d nel caso di strutture saldate complesse per le quali non sia possibile ridursi ad uno schema di calcolo bidimensionale o nel caso in cui gli nsif non siano noti, la procedura presentata al punto soluzione numerica 2d non può essere applicata. per superare il problema, è stata messa a punto una procedura di calcolo integrata, che partendo da un modello cad 3d della saldatura è capace di risolvere il problema del calcolo della tensione efficace eff sull’intero componente. il problema della realizzazione di una mesh sufficientemente accurata sia per il calcolo tensionale che per la risoluzione del sistema differenziale (2), può essere gestito in modo completamente automatico con mesh di tipo adattativo. in questo modo non è richiesta a priori la conoscenza del punto di innesco della cricca da parte dell’operatore ma è necessario fornire solamente la geometria, i vincoli ed i carichi esterni agenti. le fig. 3 e 4 mostrano esempi di modelli cad e delle relative mesh 3d, ad elementi tetraedrici, adatte per la risoluzione dell’eq. (2). nelle figure vine anche illustrato il campo tensionale non locale eff. la lettura del picco di eff, accompagnato da una mappatura a scale di colori, consentirà al http://www.gruppofrattura.it/ http://dx.medra.org/10.3221/igf-esis.09.14&auth=true r. tovo et alii, frattura ed integrità strutturale, 9 (2009) 135 144; doi: 10.3221/igf-esis.09.14 138 progettista di localizzare la zona critica della connessione saldata permettendo inoltre di calcolare il coefficiente di sicurezza o la vita a fatica del particolare saldato sulla base delle curva di progetto riportate nei successivi capitoli. gli esempi riportati nel seguito mostreranno l’efficienza del metodo e la sua capacità di prevedere la resistenza a fatica di strutture complesse tridimensionali. figura 2: tipica soluzione in termini di tensione efficace di una giunzione piana a cordone portante. la tensione non locale è adimensionalizzata rispetto alla tensione nominale nel piatto di maggiore spessore. (a) (b) (c) figura 3: esempio di mesh e soluzione ottenuto in automatico partendo dal modello cad di un giunto complesso: a) modello cad di un giunto a cordone portante sollecitato a trazione sul piatto principale. b) mesh ad elementi tetraedrici utilizzata per analizzare il giunto; c) mappatura a scale di colori della tensione efficace (massima tensione principale come tensione equivalente non locale; c=0.2 mm). http://www.gruppofrattura.it/ http://dx.medra.org/10.3221/igf-esis.09.14&auth=true r. tovo et alii, frattura ed integrità strutturale, 9 (2009) 135 144; doi: 10.3221/igf-esis.09.14 139 (a) (b) figura 4: esempio di mesh e soluzione ottenuta in automatico partendo dalla geometria del giunto. a) modello cad di un giunto a cordone portante sollecitato a flesso-torsione. b) mesh ad elementi tetraedrici utilizzata per analizzare il giunto; c) mappatura a scale di colori della tensione efficace (massima tensione principale come tensione equivalente non locale; c=0.2 mm); d) andamento della tensione principale massima 1 e della tensione efficace eff lungo una generatrice esterna del cilindro. i valori sono normalizzati rispetto al valore massimo della tensione efficace eff, max e sono rappresentati in funzione della distanza z dal piede del cordone normalizzata rispetto al diametro esterno del tubo d. valutazione del parametro c per le saldature potizzato che il parametro c dipenda solamente dal materiale, è possibile calcolarne il suo valore numerico confrontando la resistenza a fatica, in termini di variazione della tensione efficace eff, di saldature con rotture alla radice (2=0°) con saldature aventi rotture al piede (2=135°). in accordo con la referenza [12], il valore di c per le saldature ad arco in acciaio è di circa 0.2 mm (c2=0.04 mm2). d’altra parte, analisi numeriche [12] e soluzioni analitiche [13] hanno evidenziato che c è legato attraverso una costante di proporzionalità z alla distanza critica di el-haddad et al. [21], definita dal limite di fatica del provino liscio o e dal valore di soglia dello stress intensity factor kth: 2 0 th 0 k1 a           (5) perciò, in un caso generale noto a0 risulta immediato il calcolo di c in relazione alla tensione equivalente assunta. la relazione fra a0 e c può essere così riassunta [12]: 0azc  (6) la tab. 1 propone il valore di z per le diverse tensioni equivalenti. (c) (d) i http://www.gruppofrattura.it/ http://dx.medra.org/10.3221/igf-esis.09.14&auth=true r. tovo et alii, frattura ed integrità strutturale, 9 (2009) 135 144; doi: 10.3221/igf-esis.09.14 140 tabella 1: valori del parametro z per differenti tensioni equivalenti [12]. banda di dispersione per le saldature e curva di progetto l metodo del gradiente implicito consente di rendere continuo un campo di tensione singolare anche nell’ipotesi di materiale lineare elastico. con tale formulazione è possibile, utilizzare il picco di tensione direttamente per il calcolo del coefficiente di sicurezza senza incorrere in errori formali. utilizzando dati sperimentali di letteratura è possibile tracciare una banda di dispersione per le saldature nel campo della vita a termine fra 104 e 5106 cicli. con riferimento alle serie sperimentali precedentemente analizzati nelle referenze[7, 8, 11], in fig. 4 è stata tracciata la banda di dispersione in termini di variazione della tensione equivalente non locale massima max,eff calcolata in prossimità del punto di innesco della cricca. gli spessori del piatto principale e degli irrigidimenti variavano da 3 a 100 mm. il valore della pendenza della curva di wöhler risulta pari a 3 ed il valore di riferimento a 2106 cicli al 97.7% di probabilità di sopravvivenza è di 151 mpa. in fig. 4 è possibile osservare che la curva di progetto proposta dall’eurocodice 3 [5] per i particolari tagliati all’ossitaglio automatico presenta una classe di resistenza (140 mpa a 2106) di poco inferiore al valore ottenuto per una probabilità di sopravvivenza del 97.7% (151 mpa). perciò, in analogia con l’eurocodice 3 potremo dire che le giunzioni saldate, indipendentemente dalla loro forma, sollecitate principalmente a modo i, ricadono tutti all’interno di una stessa classe, quantificabile in circa 150 mpa con pendenza fra 104 e 5106 cicli pari a 3. caso s [mm] h [mm] t1 [mm] t2 [mm] 1 6 14 14 14 2 6 14 9 14 3 6 6 9 14 4 6 6 9 25 tabella 2: valori dei parametri geometrici di fig. 2. esempi applicativi l problema differenziale (2), tranne nel caso di una cricca su una piastra di dimensione infinita [13], non è di semplice soluzione e comunque impone la conoscenza degli nsif. perciò ai fini progettuali risulta sicuramente molto efficiente una soluzione completamente numerica del problema differenziale. a tale scopo, è stata messa a punto una procedura di calcolo che richiede all’operatore come dati di ingresso la geometria del giunto e la costante c del materiale tensione equivalente locale tipo di sollecitazione z oazc  massima principale stato piano di tensione 0.545 von mises stato piano di tensione 0.456 tresca stato piano di tensione 0.545 massima principale stato piano di deformazione 0.545 von mises stato piano di deformazione 0.224 tresca stato piano di deformazione 0.267 i i http://www.gruppofrattura.it/ http://dx.medra.org/10.3221/igf-esis.09.14&auth=true r. tovo et alii, frattura ed integrità strutturale, 9 (2009) 135 144; doi: 10.3221/igf-esis.09.14 141 ignorando completamente il problema della singolarità in prossimità degli intagli acuti ed affidando il problema della convergenza a soluzioni di tipo adattivo. giunzioni a t sollecitate a flessione in fig. 5, sono riportati i valori sperimentali di rotture avvenute al piede del cordone di saldatura per una giunzione avente un angolo diverso da quello esaminato in fig. 4. i risultati numerici contrassegnati dal simbolo sono relativi ad un giunto a t sollecitato a flessione con angolo di apertura del cordone di 118° . tali punti vanno a cadere all’interno della banda di dispersione precedentemente calcolata. figura 5: banda di dispersione per giunzioni saldate ad arco in acciaio in termini di tensione efficace massima ottenuta con il metodo del gradiente implicito (r rapporto di ciclo) previsione della zona di innesco della cricca per giunzioni a croce a cordone portante sollecitare a trazione un altro interessante esempio è quello relativo allo studio del punto di innesco della cricca per fatica in un giunto a croce a cordone portante sollecitato a trazione in cui gli spessori dei piatti principali siano diversi [22]. la fig. 6 mostra la geometria del giunto in esame mentre le dimensioni geometriche delle 4 serie analizzate nella referenza [22] sono riportate in tab. 2. i punti critici di probabile innesco della cricca per fatica sono i punti evidenziati con un “cerchio” in fig. 2.. nonostante le differenze geometriche fra le quattro serie di tab. 2, dal punto di vista sperimentale si sono sempre osservate rotture alla radice del cordone di saldatura dalla parte piatto più spesso. i risultati della relativa elaborazione numerica del campo di tensione sono riportati in fig. 2 adimensionalizzati rispetto alla tensione nominale applicata al piatto di spessore maggiore. il picco della tensione equivalente non locale risulta massimo in prossimità della radice del cordone di saldatura sul piatto di spessore maggiore esattamente nel punto in cui l’evidenza sperimentale indica il punto di rottura. previsione della vita a fatica in giunti complessi tridimensionali in generale nei componenti saldati, le cricche nucleano in corrispondenza dei piedi o delle radici dei cordoni cosicché il problema del valore dei carichi da applicare al componente è soprattutto legato all’individuazione del punto di innesco della cricca per fatica. per mostrare la versatilità del gradiente implicito allo studio della resistenza a fatica di strutture saldate complesse, saranno analizzati quattro differenti tipologie di giunti la cui geometria non può essere ridotta al 2d: a) giunti con irrigidimento longitudinale (spessore piatto principale 2 o 6 mm); b) giunti con irrigidimento circolare (spessore piatto principale 8 mm); c) giunti a cordone portante sollecitati a flessione ( spessore piatti 12 mm); d) giunti saldati composti da profilati tubolari a sezione rettangolare (spessore profili 7.9 mm). la fig. 7, a titolo di esempio, mostra il valore della tensione effettiva ottenuta a partire dalla tensione massima principale. le zone in cui si ha la massima sollecitazione effettiva eff, coincidono, di fatto, con quelle in cui si ha la frattura per fatica. http://www.gruppofrattura.it/ http://dx.medra.org/10.3221/igf-esis.09.14&auth=true r. tovo et alii, frattura ed integrità strutturale, 9 (2009) 135 144; doi: 10.3221/igf-esis.09.14 142 l’accordo fra risultati sperimentali e previsione della vita a fatica è soddisfacente per i giunti delle serie (a) e (b) come evidenziato in fig. 8. per le serie (c) e (d) la previsione della vita a fatica appare conservativa (vedere fig. 9) e ciò potrebbe essere giustificato fondamentalmente per due motivi: 1) nella serie (c) e (d) è presente un carico di torsione nei cordoni di saldatura che comporta la presenza di un modo iii singolare assente nelle giunzioni a croce sollecitate a trazione o a flessione; 2) il metodo del gradiente implicito così come è stato proposto in questa sede, è adatto per il calcolo della vita di innesco e di prima propagazione del difetto per fatica. nel caso di strutture complesse, tale approccio potrebbe risultare in vantaggio di sicurezza nel momento in cui si trascurata completamente la fase di propagazione del difetto. tuttavia, per quanto riguarda il primo dei due aspetti, gli autori stanno cercando di introdurre nel modello di calcolo del gradiente implicito un approccio di tipo multiassiale alla fatica capace di prendere in considerazione il completo stato di tensione locale. figura 6: previsione della resistenza a fatica calcolata per via completamente numerica di una saldatura a t avente angolo di apertura di 118° sollecitata a flessione (t=10 mm, s= 7.8 mm, r=0.1). figure 7: modelli e risultati ottenuti in termini di tensione effettiva per piastre irrigidite sollecitate a trazione (massima tensione principale come tensione equivalente non locale, c=0.2 mm). http://www.gruppofrattura.it/ http://dx.medra.org/10.3221/igf-esis.09.14&auth=true r. tovo et alii, frattura ed integrità strutturale, 9 (2009) 135 144; doi: 10.3221/igf-esis.09.14 143 figura 8: previsione della vita a fatica di giunti irrigiditi utilizzando il metodo del gradiente implicito (t spessore piatto principale). figura 9: previsione della vita a fatica di giunti con irrigidimento non simmetrico e di giunti ottenuti con profili tubolari (t spessore piatto principale). conclusioni na procedura di verifica a fatica basata sul metodo del gradiente implicito consente di affrontare il problema della singolarità del campo di tensione senza ricorrere a modifiche geometriche del componente in esame o all’impiego di schematizzazioni non lineari del materiale. disaccoppiando il problema della resistenza dall’effetto gradiente per durate a fatica superiori a 104 cicli, il materiale può essere schematizzato come lineare elastico. per giunzioni saldate sollecitate prevalentemente a modo i, il valore del massimo della tensione equivalente non locale, ottenuto dall’analisi numerica, può essere usato come dato di ingresso nella curva di riferimento del comportamento a fatica delle saldature. in questo caso, il metodo del gradiente implicito riporta il calcolo della vita a fatica delle saldature complesse al metodo delle tensioni ammissibili indipendentemente dalla forma del componente in esame. per giunzioni sollecitate a modo mosto è necessario l’impiego di una procedura più articolata la quale punto per punto del cordone di saldatura costruisce la curva di woehler in funzione delle reali condizioni di sollecitazione del corpo. il problema delle singolarità tensionali nella progettazione a fatica, in questo articolo, è stato risolto proponendo una filosofia di progettazione basata sui metodi a gradiente implicito capaci di rendere continui i campi di tensione singolari indotti dalla presenza di intagli a spigolo vivo. tali metodi hanno il vantaggio di poter considerare il materiale come lineare u    4 cicli a rottura n 10 5 10 6 10 7 10 298 151 eff, max [mpa] 100 500 1000 3000 c = 0.2 mm t = 2 mm [23] t = 8 mm [24] r = 0 r = 0.1 t = 6 mm [23]    4 cicli a rottura n 10 5 10 6 10 7 10 298 151 eff,max [mpa] 100 500 1000 3000 c = 0.2 mm t=7.9 mm [26] r=-1 t=12 mm [25] r= 0 (as-welded) http://www.gruppofrattura.it/ http://dx.medra.org/10.3221/igf-esis.09.14&auth=true r. tovo et alii, frattura ed integrità strutturale, 9 (2009) 135 144; doi: 10.3221/igf-esis.09.14 144 elastico trasformando il problema del gradiente tensionale nella risoluzione di una equazione differenziale definita sull’intero corpo in esame. la soluzione trovata, definita come tensione equivalente non locale assume il ruolo di tensione efficace per la valutazione della vita a fatica. operando in questo modo è possibile studiare il comportamento a fatica delle giunzioni saldate utilizzando un’unica banda di dispersione, definita in questa sede sulla base di numerose prove sperimentali tratte dalla letteratura. il metodo proposto offre il vantaggio di prestarsi per una soluzione completamente numerica del calcolo della vita a fatica delle giunzioni saldate complesse. bibliografia [1] t. lassen, welding journal 69, research supplement, (1990) 75s. [2] i. huther, l. primot, h.p. lieurade, j.j. janosch, d. colchen, s. debicz, welding in the world, 35 (2) (1995) 118. [3] k.a. macdonald, p.j. haagensen, engineering failure analysis, 6 (1999) 113. [4] d. radaj, c.m. sonsino, w. fricke, fatigue assessment of welded joints by local approaches, abington publishing, abington (2006). [5] eurocode 3: design of steel structures; general rules. 1993-1-1 (1993). [6] y. verreman, b.nie, fatigue and fracture of engineering materials and structures, 19 (1996) 669. [7] p. lazzarin, r. tovo, fatigue and fracture of engineering materials and structures, 21 (1998) 1089. [8] p. lazzarin, p.livieri, int. j. of fatigue, 23 (2001) 225. [9] p. lazzarin, t.lassen, p. livieri, fatigue and fracture of engineering materials and structures, 26 (2003) 49. [10] p. lazzarin, r. zambardi, int. j. of fracture, 112 (2001) 275. [11] p. livieri, p. lazzarin, int. j. of fracture, 133 (2005) 247. [12] r. tovo, p. livieri, e. benvenuti, int. j. of fracture, 141 (2006) 497. [13] r. tovo, p. livieri, engineering fracture mechanics, 74 (2007) 515. [14] r. tovo, p. livieri, engineering fracture mechanics engineering fracture mechanics, 75 (7) (2008) 1804. [15] e. kroener, int. j. sol. struct., 3 (1967) 731. [16] c.a. eringen, d.g.b. edelen, int. j. engng. science, (1972) 233. [17] r.h.j. peerlings, r. de borst, w.a.m. brekelmans, j.h.p. de vree, int. j. num. meth. engn., 39 (1996) 3391. [18] m.l. williams, j.l of applied mechanics, 19 (1952) 526. [19] p. lazzarin, r. tovo, int. j. of fracture”, 78 (1996) 3. [20] b. gross, a. mendelson, int. j. of fracture mechanics, 8 (1972) 267. [21] m. h. el haddad, t.h.topper, k. n.smith, asme, j.of engineering material and technology, 101 (1979) 42. [22] s. kainuma, i.t. kim, int. j. of fatigue, 27 (2005) 810. [23] t.r.gurney, fatigue of thin walled joints under complex loading. abington publishing, abington (1997). [24] l. susmel, r. tovo, int. j. of fatigue, 28 (2006) 564. [25] w. fricke, o. doerk, int. j. of fatigue, 28 (2006) 141. [26] h kyuba, p. dong, int. j. of fatigue, 27 (2005) 85. http://www.gruppofrattura.it/ http://dx.medra.org/10.3221/igf-esis.09.14&auth=true microsoft word numero_38_art_23 c. gourdin et alii, frattura ed integrità strutturale, 38 (2016) 170-176; doi: 10.3221/igf-esis.38.23 170 focussed on multiaxial fatigue and fracture equi-biaxial loading effect on austenitic stainless steel fatigue life c. gourdin cea, den, dm2s, semt, lisn, f-91191 gif-sur-yvette, france, cedric.gourdin@cea.fr s. bradaï, s. courtin areva np sas, tour areva, f-92084 paris la défense, france. j.c. le roux edf, r&d, site des renardières, f-77818 moret sur loing cedex, france. c. gardin institut pprime, cnrs-ensma upr 3346 bp40109, f-86961 futuroscope chasseneuil cedex, france. abstract. fatigue lifetime assessment is essential in the design of structures. under-estimated predictions may result in unnecessary in service inspections. conversely, over-estimated predictions may have serious consequences on the integrity of structures. in some nuclear power plant components, the fatigue loading may be equibiaxial because of thermal fatigue. so the potential impact of multiaxial loading on the fatigue life of components is a major concern. meanwhile, few experimental data are available on austenitic stainless steels. it is essential to improve the fatigue assessment methodologies to take into account the potential equi-biaxial fatigue damage. hence this requires obtaining experimental data on the considered material with a strain tensor in equibiaxial tension. two calibration tests (with strain gauges and image correlation) were used to obtain the relationship between the imposed deflection and the radial strain on the fabime2 specimen. a numerical study has confirmed this relationship. biaxial fatigue tests are carried out on two austenitic stainless steels for different values of the maximum deflection, and with a load ratio equal to -1. the interpretation of the experimental results requires the use of an appropriate definition of strain equivalent. in nuclear industry, two kinds of definition are used: von mises and tresca strain equivalent. these results have permitted to estimate the impact of the equibiaxiality on the fatigue life of components. keywords. design fatigue curve; equibiaxiality; experimental device; austenitic steel. citation: gourdin, c., bradaï, s. courtin, s., le roux, j.c., gardin, c., equi-biaxial loading effect on austenitic stainless steel fatigue life, frattura ed integrità strutturale, 38 (2016) 170-176. received: 12.05.2016 accepted: 14.06.2016 published: 01.10.2016 copyright: © 2016 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. c. gourdin et alii, frattura ed integrità strutturale, 38 (2016) 170-176; doi: 10.3221/igf-esis.38.23 171 introduction and aim he problem of multiaxial fatigue is a major concern and has been extensively studied in the literature. more or less innovative experimental means have been developed. however, some references which deal with the multiaxial aspect in steels show, blatantly, the aggravating effect on multiaxiality and in particular of biaxiality on the fatigue curves. the service lives are significantly reduced [1-6]. unfortunately, there is no experimental data available concerning fatigue strength for the austenitic stainless steels subjected to multiaxial loadings, which are used for power plants components. in order to obtain fatigue strength data under multiaxial loading, biaxial test means were developed at lisn. the particularity of this equipment is to consider only isothermal equibiaxial mechanical loadings, which are both in phase and proportional. it will be possible to conclude from the tests conducted on the specimen “fabime2” whether the austenitic stainless steel material is sensitive or not to the biaxial state loading in the high cycle fatigue regime. on the other hand, tests undertaken by poncelet et al. [6] on 304l austenitic stainless steel cruciform specimens have concluded that equibiaxial stress state is not detrimental compared with uniaxial fatigue. another conclusion made by these authors is the penalizing effect of the mean stress. the experimental device he objective of this new experimental fatigue test is to dissociate the effect of the mean stress and equibiaxial state loading. indeed, we try to obtain a negative load ratio in order to get the same results as the uniaxial data and eliminate the residual strain. in this study, equibiaxial state loading generated from fatigue will be considered. it will be used to optimize the geometry of a disk specimen refined in its center. it is used as a circumferentially embedded diaphragm with an applied pressure on both sides in order to obtain an equivalent strain in each loading direction in the plane (fig. 1). figure 1: principle of the new experimental fatigue test. the experimental device called “fabime 2” is divided into four parts [7]: fatigue cell (fig. 2) which contains the spherical bending specimen pressure generating system until 100 bars electrical enclosure homemade software developed under labview that provides control and acquisition data during the tests two half-shells allow the positioning of the spherical bending specimen. seal and embedment are realized by bolting these two parts. maximum experimental conditions are 100 bars for the pressure and 90°c for the temperature. an alternative differential pressure between the two sides of the spherical specimen is applied during the fatigue test. t t c. gourdin et alii, frattura ed integrità strutturale, 38 (2016) 170-176; doi: 10.3221/igf-esis.38.23 172 figure 2: view of the spherical bending device and technical view of the fatigue cell. to ensure well-defined experimental conditions, various measuring means are located symmetrically at the two half-shells • pressure sensor with a measuring range between 0 to 100 bars • type k thermocouple to measure the temperature of the fluid inside the fatigue cell • displacement sensor (lvdt) to measure the deflection at the center of the spherical bending specimen. this sensor has a 5mm range. realizations of surface observations after the fatigue test show that the contact between lvdt and specimen is negligible (no fretting). no crack initiation is also observed directly under the lvdt. • two visualization windows on each half-shell, oriented at 45° with a diameter of 20 mm. the constitutive material is borosilicate glass with a permissible operating pressure of 100 bars. the fatigue cell is built under european security directives (machines 2006/42/ce, pression 97/23/ce). the experimental protocol he experimental protocol is the following: • implementation of the spherical bending specimen, with a slight overpressure to ensure a first purge, • several blocks of 50 cycles with an increasing displacement loading. the aim of these steps is to ensure proper implementation of the components under the effect of pressure, and to ensure the best purge is possible. • beginning of the fatigue test at the chosen deflection with “slow” cycles every 500 cycles allowing taking photographs through the windows. the objectives of these particular cycles is to taking into account the good value of the residual strain at no pressure due to the elasto-plastic behavior of the specimen. the “center” of the elasto-plastic loop behavior of the specimen can be estimate and the range of deflection is adjusting within this information. the spherical bending fatigue test is stopped when cracks have propagated outside the central zone. calibration tests with the new experimental fatigue device are conducted with imposed displacement or deflection. in order to properly connect the strain level in the central area with the measured deflection, we need to define an experimental curve which represents the measured deflection versus the corresponding strains in this zone. a calibration phase is necessary to obtained the appropriate curve [∆r; deflection ] directly from experimental results, and with these methods, the obtained curve is taking into account the real mechanical behavior of the specimen. two experimental calibration methods have been carried out in the lisn laboratory with the fabime2 device. specimens used are in stainless austenitic steel type 316l [8]. t c. gourdin et alii, frattura ed integrità strutturale, 38 (2016) 170-176; doi: 10.3221/igf-esis.38.23 173 calibration with strain gauges the first calibration test was performed with a specimen instrumented with 9 strain gauges: • delta rosette composed by 3 radial strain gauges located at the center of the specimen and inside a 5mm circle. • 3 radial strain gauges between 20 mm to 300 mm of the center of the specimen • 3 tangential strain gauges between 20 mm to 300 mm of the center of the specimen calibration with stereo correlation the second calibration test is based on the technique of stereoscopy image correlation. in collaboration with “videométric technology” company and cea laboratory “emsi”, a speckle pattern was realized in the central area of the “fabime2” specimen. the specimen is placed in the fatigue cell using the same additional component as used in the first calibration method (strain gauges). indeed, this additional part permits that the speckle pattern is completely visible for the picture acquisition. reference picture with no pressure and picture for different levels of pressure were acquired. the pressure is thus applied unilaterally. the post processing of the experimental data obtained in the calibration test gave results with an error of 0.01 % in strain and a displacement measurement error equal to 0.2 m. 0 0,05 0,1 0,15 0,2 0,25 0,3 0,35 0 0,2 0,4 0,6 0,8 1 1,2 1,4 1,6 m e a su re d  s tr a in  ( ra d ia l  in  % ) deflection (mm) experimental data (strain gauges and dic) poly. (experimental data (strain gauges and dic)) figure 3: deflection-strain calibration curve obtained on the fatigue device “fabime2”. on the fig. 3, experimental data obtained with the two calibration methods show the evolution of the radial train versus the deflection. thus, we can conclude that the two experimental methods are in good agreement. the crack initiation detection method during the equibiaxial fatigue tests, two methods are used to determine the number of cycles corresponding crack initiation. the first one consists in following the change in the specimen compliance. the second corresponds to a visual detection through visualization windows on each half-shell. some examples of images obtained from the camera on both sides are given below in fig. 4. four phases can be distinguished. the typical size of the detectable crack is about 5 mm in surface. • no crack initiation • first detection of crack initiation after 11500 cycles on side 2 • first detection of crack initiation after 16500 cycles on side 1, while crack is propagating on the other side (fig. 4-a) • crack propagation on both sides during the fatigue test until the stop of the test (22000cycles) (fig. 4-b). it must be noted that on side 2, one single crack is propagating. on side 2, this same crack also exists, but other cracks also propagated in directions mainly perpendicular. the experimental results biaxial fatigue tests are carried out on two austenitic stainless steels: “316l thy”, and “304l cli”. the first material has been provided by thyssen krupp materials france as a 15mm thickness rolled sheet. the second material supplied by edf is characterized by a thickness of 30 mm rolled sheet. c. gourdin et alii, frattura ed integrità strutturale, 38 (2016) 170-176; doi: 10.3221/igf-esis.38.23 174 the first fatigue test campaign is performed on austenitic stainless steel type 316l. five levels of deflection are studied: 1.6 / 1.4 / 1.2 / 1.1 and 0.9 mm. a) propagation of crack at 16500 cycles b) propagation of crack at 22000 cycles figure 4: image from the camera 2 (side 2) (a) and from the camera 1 (side 1) (b). in the frame of cea-edf-areva working group, a second fatigue test campaign is performed on austenitic stainless steel 304-cli provided by edf. this material completely agrees with the rcc-mrx [9] and rcc-m [10] specification. three levels of deflection are carried out 1.4 / 1.3 and 1.2 mm. interpretation of the experimental results ll tests performed in this study are carried out with imposed displacement (strain) with alternating load (without mean stress or strain), means with a stress ratio r=-1. to compare the experimental data obtained from uniaxial and equibiaxial tests, it is necessary to define a total equivalent strain. two definitions of equivalent strain are proposed: the first is based on the definition of von mises (used in the rcc-mrx) and the second on the definition of tresca (used in the rcc-m, rse-m). 0,000 0,100 0,200 0,300 0,400 0,500 0,600 0,700 0,800 0,900 1,000 1000 10000 100000 1000000 10000000 100000000 e q u iv a le n t  s tr a in  ( % ) cycles number 316l von mises 316l tresca uniaxiale 316l 304cli von mises 304cli tresca uniaxiale 304cli /2 figure 5: austenitic stainless steel fatigue curve for 304l-cli and 316l under uniaxial and equibiaxial loadings a c. gourdin et alii, frattura ed integrità strutturale, 38 (2016) 170-176; doi: 10.3221/igf-esis.38.23 175 the proposal approach to determine the level of the equivalent strain for each fabime2 test is as follows: • determination of the value of the radial strain corresponding to the imposed deflection from the strain-deflection calibration curve obtained in the previous part of this paper. with a similar mechanical behavior, the calibration curve can be used for the two materials (fig. 3). • determination of the von mises or tresca equivalent strain from the relation between the radial strain and the equivalent strain (von mises or tresca). this relation has been determined by elasto-plastic calculation of the fatigue test. theses elastic-plastic behavior computations are used to determine the “real” value of the poisson’s ratio by taking into account the elastic and plastic part. this method has been applied to the equi-biaxial fatigue tests presented earlier. the corresponding fatigue life curves are compared to that under uniaxial loading in fig. 5. it appears that there is also no impact of equi-biaxial fatigue for the two types of materials, considering both von mises and tresca equivalent strains. conclusions his paper is focusing on the study of the impact on the equibiaxiality on the fatigue curves. a new experimental fabime2 device has been developed at lisn. two calibration tests (with strain gauges and image correlation) were used to obtain the relationship between the imposed deflection and the radial strain on the fabime2 specimen. biaxial fatigue tests are carried out on two austenitic stainless steels: 316l thy and 304l cli for different values of the maximum value of deflection, and with a load ratio equal to -1. the interpretation of the experimental results requires the use of an appropriate definition of equivalent strain. in nuclear industry, two kinds of definition are used: von mises and tresca equivalent strains. the results obtained during the experimental campaigns carried out in the context of our study and for two austenitic stainless steels submitted to equibiaxial loadings show that crack initiation have a low impact on the fatigue life, which remains in the field covered by the design curve defined and used in the codification. this fabime2 device allowed the study of the impact of fatigue life on equibiaxial loadings and crack propagation in austenitic stainless steel. so, the device has the capability to study other different aggravating factors like surface roughness, mean stress or strain, residual stress, pre-hardening. a new device based on fabime2 is under development for the study of the impact of the environmental effect. this device will study the impact of the equibiaxial loadings with a primary water environment pwr (300°c with a permanent pressure of 140 bars). references [1] fissolo, a., et al., crack initiation under thermal fatigue: an overview of cea experience, part 1 : thermal fatigue appears to be more damaging than uniaxial isothermal fatigue, int. journal of fatigue, 31(3) (2009) 587-600. [2] fissolo, a., et al., crack initiation under thermal fatigue: an overview of cea experience, part 2 : application of various criteria to biaxial thermal fatigue tests and a first proposal to improve the estimation of the thermal fatigue, int. journal of fatigue, 31(7) (2009) 1196-1210. [3] lefebvre, d.f., hydrostatic pressure effect on life prediction in biaxial low-cycle fatigue”, biaxial and multiaxial fatigue, egf 3, (1989). [4] itoh, t., sakane, m., et al., a design procedure for assessing low cycle fatigue life under proportional and nonproportional loading, int. journal of fatigue, 28 (2006). [5] parsons, m. w., pascoe, k. j., development of a biaxial fatigue testing rig, journal of strain analysis, 10(1) (1975) 1-3. [6] poncelet, m., et al., biaxial high cycle fatigue of a type 304l stainless steel: cyclic strains and crack initiation detection by digital image correlation, european journal of mechanics a/solids, (2010). [7] gourdin, c., fissolo, a., balestreri, f., crack initiation under an equibiaxial fatigue, development of a particular equibiaxial fatigue device, transactions of smirt 21, new delhi, india, (2011). [8] bradai, s., et al., crack initiation under equibiaxial fatigue, development of a particular equibiaxial fatigue device. pvp2013-97200, paris, france (2013). t c. gourdin et alii, frattura ed integrità strutturale, 38 (2016) 170-176; doi: 10.3221/igf-esis.38.23 176 [9] rcc-mrx, règles de conception et de construction des matériels mécaniques des installations nucléaires applicables aux structures à haute température et à l'enceinte à vide iter, afcen code, association française pour les règles de conception et de construction des chaudières électronucléaires. www.afcen.com, (2012). 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can be opened with acrobat and adobe reader 5.0 and later.) >> /namespace [ (adobe) (common) (1.0) ] /othernamespaces [ << /asreaderspreads false /cropimagestoframes true /errorcontrol /warnandcontinue /flattenerignorespreadoverrides false /includeguidesgrids false /includenonprinting false /includeslug false /namespace [ (adobe) (indesign) (4.0) ] /omitplacedbitmaps false /omitplacedeps false /omitplacedpdf false /simulateoverprint /legacy >> << /addbleedmarks false /addcolorbars false /addcropmarks false /addpageinfo false /addregmarks false /convertcolors /converttocmyk /destinationprofilename () /destinationprofileselector /documentcmyk /downsample16bitimages true /flattenerpreset << /presetselector /mediumresolution >> /formelements false /generatestructure false /includebookmarks false /includehyperlinks false /includeinteractive false /includelayers false /includeprofiles false /multimediahandling /useobjectsettings /namespace [ (adobe) (creativesuite) (2.0) ] /pdfxoutputintentprofileselector /documentcmyk /preserveediting true /untaggedcmykhandling /leaveuntagged /untaggedrgbhandling /usedocumentprofile /usedocumentbleed false >> ] >> setdistillerparams << /hwresolution [2400 2400] /pagesize [612.000 792.000] >> setpagedevice microsoft word numero_41_art_44.docx g. g. cunto et alii, frattura ed integrità strutturale, 41 (2017) 332-338; doi: 10.3221/igf-esis.41.44 332 application of leak-before-break concept in 316ln austenitic steel pipes welded using 316l gabriel giannini de cunto navy technological center in são paulo, brasil gabriel.giannini@gmail.com arnaldo homobono paes de andrade nuclear and energy research institute arnaldo.homobono@gmail.com waldemar alfredo monteiro nuclear and energy research institute wamontei@ipen.br abstract. the paper presents a study of the application of leak-beforebreak (lbb) concept in a relatively small-diameter high energy reactor coolant line, where it is proposed type aisi 316ln to be used as base material welded with type aisi 316l coated electrode considering a pipe with diameter of 273 mm. the pipe material was characterized in terms of tensile test with ramberg-osgood analyses and fracture toughness tests with j-resistance curve determination, considering base material, weld joint and heat affected zones. for the mechanical properties found in tensile tests and using the picep software, were determined the leak rate curves versus crack sizes, to determine the size of a detectable leakage crack, and the critical crack sizes, considering failure by plastic collapse. for the critical crack sizes found in weld, which presented the lowest toughness, j-integral analysis was performed considering failure by tearing instability. results show a well-defined mechanical behavior where base material has a high toughness, weld has a low toughness, and haz showed intermediate properties. for the load limit analysis, the lowest critical crack size was found for base material presenting circumferential cracks. for jintegral analysis, it was demonstrated that failure by tearing instability will not occur. keywords. leak-before-break; 316ln; weld 316l. citation: cunto, g. g., andrade, a. h. p., monteiro, w. a., application of leak-beforebreak concept in 316ln austenitic steel pipes welded using 316l, frattura ed integrità strutturale, 41 (2017) 332-338. received: 11.03.2017 accepted: 27.04.2017 published: 01.07.2017 copyright: © 2017 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. g. g. cunto et alii, frattura ed integrità strutturale, 41 (2017) 332-338; doi: 10.3221/igf-esis.41.44 333 introduction he labgene is a 48 mw thermal pwr prototype reactor under development in brazil, that aims to develop and test the capability to design small and medium power reactors for electricity production and for nuclear propulsion. leak-before-break (lbb) is a method used in design of nuclear power reactor coolant loop piping to eliminate consideration of the dynamic effects of pipe rupture. the exclusion of dynamic effects associated with pipe rupture from the design basis is allowed when analyses demonstrate that the probability of pipe rupture is extremely low for the applied loading resulting from normal conditions and a postulated safe shutdown earthquake (sse). a deterministic lbb evaluation performed using guidance from nureg-1061 volume 3 [1] and srp 3.6.3 [2] is usually used to demonstrate this low probability of pipe rupture. this examination is based on fracture mechanics analysis that is used to demonstrate that a crack leak, present in a pipe, can be detected by the plant leak detection systems, with a factor of 10 between the predicted leakage and the plant leakage detection capability. if the leakage crack size is smaller than the critical crack size by a factor of two, then lbb requirements are satisfied and the dynamic effects of pipe rupture need not be considered in the plant design basis [1]. for the critical flaw sizes determination, it can be used either limit load with net section collapse criterion or j-integral and tearing modulus (j/t) analysis for tearing instability criterion. for the leak rate determination, a well know and extensively validated computer program called picep [3] is usually used for determination of leakage. this program contains a methodology for computing crack opening area based on elastic plastic fracture mechanics analysis and its flow rate equations are based on a modification of henry’s homogeneous non-equilibrium critical flow model. nonetheless, the small size of the reactor coolant piping, considered in labgene project, can makes it difficult to meet the same lbb standards that were developed for large commercial reactors, when nureg-1061 volume 3 [1] and nureg-0800 standard review plan 3.6.3 [2] were initially developed. furthermore, the small pipe diameter makes the usual ferritic coolant pipe with inside austenitic cladding, impossible to be performed, then a fully austenitic pipe shall be used. austenitic stainless steels pipes made by material type aisi 316 and its variants have been chosen for applications in nuclear power plants owing of their good high temperature mechanical properties and creep and corrosion resistance. a low carbon choice alloyed with nitrogen of this steel, designated as aisi 316ln, is a possible chose for the labgene reactor coolant piping. moreover, due to the need of connecting the pipes spools by use of weld, a shielded metal arc welds (smaw) using aisi 316l coated electrode was select as the most appropriate commercial weld join material. this proposal welded pipe is tested and analyzed as three-component composed of weld metal, base material and heat affected zone (haz). inadequate mechanical properties in any of these three zones is a threat to the lbb analysis. methodology ollowing is provided a summary of the methodology used for the lbb evaluation in the labgene’s reactor coolant loop piping. determination of loads and stress the loads to be used in lbb evaluations is considered as normal operating loads for leakage determination and normal plus seismic sse loads for critical crack determination. the normal operating loads consist of pressure, dead weight, and thermal expansion loads. for calculation of critical flaw size, it was considered the maximum of sse loads added to the normal operating loads. the piping dimension is considered with an outside diameter of 273 mm and a thickness of 28.57 mm, the operating conditions for the lbb feasibility evaluation are considered as the usual one for a pwr plant, with operation temperature of 288 ˚c and internal pressure of 25.17 mpa in the reactor coolant line. determination of material properties material properties to be used in the lbb evaluation shall be evaluated by stress-strain curve determination using rambergosgood (ro) analysis, and material toughness is obtaining by resistance curve test method with the determination of material j-r curve. t f g. g. cunto et alii, frattura ed integrità strutturale, 41 (2017) 332-338; doi: 10.3221/igf-esis.41.44 334 the hot tensile tests were performed at temperature of 288 °c in according to the standard astm e8/e8m-13a and astm e21-09. the evaluation of the hot tensile tests includes the yield strength (σ0) tensile strength (σr), flow stress (σf) and uniform elongation determination. the analysis includes also the determination of the stress-strain curve by means of the ramberg-osgood eq. 1, as following:               0 0 0 n (1) where: σ = stress value; ε = strain value; σ0 = reference stress; ε0 = reference strain (σo/e); α = parameter from curve fitting of data; and n = strain-hardening exponent. the ro parameters were obtained using the engineering stress-strain curve, fitting the data in the range between 0.1 % strain and the strain corresponding to 80 % of the ultimate strength. the fracture toughness tests were performed in accordance to the astm e1820-13 standard at temperature of 288 °c. the evaluation of the toughness tests includes the determination of the material resistance j-r curve, the initiation of stable crack growth jic and the material power law formula for the j-r data, obtained using a linear regression analysis, as following:    mmatj c a (2) where: jmat = jdeformation in units of kj.m-2; δa = crack extension in mm; c = material constant; and m = exponent. the hot tensile and toughness tests were performed considering the three-component weld metal, base material and haz piping zones. tested specimens quantity and orientation are showed in tab. 1. once only circumferential weld is used, it was considered that in the weld and haz zones only circumferential cracks could exists, so the transverse specimens orientation for the hot tensile test and c-l for the toughness test were considered only for the base material. test type specimen orientation pipe zone base material aisi 316ln haz weld aisi 316l hot tensile test longitudinal 3 3 3 transverse 3 -- hot toughness test l-c 3 3 3 c-l 3 -- table 1: quantity of specimens for hot tensile and toughness tests determination of the critical through-wall cracks size and the leakage cracks size the sizes of critical through-wall cracks and the leakage crack were determined using net section collapse (limit load) analysis. for the critical cracks found in these analyses, it was verified if fail would occur by tearing collapse using elastic-plastic jintegral analysis. the computer program picep [3] was used for the limit load analysis for determination both the size of critical cracks and the size of leakage cracks. for a given set of input conditions, including operation conditions, applied loads, crack g. g. cunto et alii, frattura ed integrità strutturale, 41 (2017) 332-338; doi: 10.3221/igf-esis.41.44 335 morphology and material properties (obtained by hot tensile test), picep return as output the size of a critical crack and a curve of leakage flow rate versus crack size. for the tearing collapse verification, the elastic-plastic j-integral analysis is, in general, applied with the aid of finite element methods. for usual engineering cases, such as piping with a through-wall crack, solutions listed in manuals that are derived from numerical solutions are available. one of the most well-known and valid reference is the ductile fracture handbook developed by zahoor [4], that provides solutions for applied j and t, where each solution corresponds to a system of geometry, crack orientation, applied loading, and material properties. the applied j-integral equation, proposed by zahoor, for a circumferential through-wall crack present in a piping, considering bending moment loads, is the following:  elastic plasticj j j (3)                    122 0 0 13 2 0 1 n b jelastic jplastic f m m j r h mr t e (4) where: m = is the applied bending moment; 0 and bf m = are parameters that depend on pipe dimensions, load conditions, crack size and orientation and material properties; h1 = is based on finite element analyses, and can be found in reference [4]; r, t e θ = are the pipe mean radius, wall thickness and crack half-angle, respectively; and e, α, σ0, ε0 and n = are constants in the ro stress-strain relation as showed in eq. 1. determination of lbb viability it shall be determinate the size of through-wall cracks that will result in a detectable leakage with a margin of 10 applied between the predicted leakage and the detectable leak, to cover various uncertainties associated with leakage prediction and leakage detection. historically, a leakage detection capability of 1 gallon per minute (gpm) that presents 3.78 liters per minute in a pwr plant has been used for leakage detection capability [5]. consequently, a 10 gpm leakage crack is considered in the lbb analysis. lbb viability for an analyzing pipe system is demonstrated if a margin of at least two exists between the leakage crack size and the critical through-wall crack size. results mechanical tests results ot tensile test results show a well-defined behavior among the three zones, where the base material has a high toughness behavior with relative low yield strength and high uniform elongation, the weld show a low toughness behavior with relative high yield strength and low uniform elongation, and the haz showed intermediate mechanical properties between the base material and the weld. fig. 1 present typical stress x strain curves for the three different zones of the welded pipe. ramberg-osgood analyses according eq. 1 were performed for all specimen data, tested according to tab. 1 for hot tensile test. the results of yield strength (σ0) tensile strength (σr), flow stress (σf), elongation, ramberg-osgood parameter (α) and strain-hardening exponent (n) are presented in tab. 2. fig. 2 present typical j-r curves obtained for the three different zones in the welded pipe. the results of all base material and haz are not valid according to astm e1820-13 because jq is much larger than the jlimit value. all jq results for the weld zone have met the criteria of validity of the standard and can be considered valid jic values. for the power law analyses, according eq. 2, only one weld specimen, ct2 of tab. 3, fulfilled all the requirements to be validate. even though the results for the base material and haz did not present valid jic values, the tests demonstrated the high toughness of these zones of the welded pipe. thus, for the elastic-plastic j-integral analysis, only the weld zone will be considered, once that the analysis of the weld will bring the most conservative results. the results of jic and power law material constant (c) and exponent (m) obtained from the weld j-r curves and eq. 2 are presented in tab. 3. h g. g. cunto et alii, frattura ed integrità strutturale, 41 (2017) 332-338; doi: 10.3221/igf-esis.41.44 336 figure 1: typical stress x strain curves for different zones in the welded pipe. pipe zone specimen orientation σ0 [mpa] σr [mpa] σf [mpa] elong. [%] ramberg-osgood α n base material aisi 316ln bm1 longitudinal 166 483 325 30.7 8.0 3.4 bm2 longitudinal 167 481 324 30.1 7.7 3.4 bm3 longitudinal 149 458 303 31.8 8.7 3.2 bm4 transverse 167 459 313 30.1 8.2 3.5 bm5 transverse 177 473 325 31.8 7.3 3.7 bm6 transverse 175 476 326 32.2 7.4 3.7 weld aisi 316l wm1 longitudinal 360 463 412 9.0 1.3 9.9 wm2 longitudinal 358 454 406 11.7 1.2 9.2 wm3 longitudinal 354 455 405 16.7 1.3 11.4 haz hz1 longitudinal 249 495 372 17.2 2.7 5.4 hz2 longitudinal 249 486 368 14.7 2.4 5.5 hz3 longitudinal 265 481 373 13.8 2.0 6.2 table 2: results of hot tensile tests. figure 2: typical j-r curves for different zones in the welded pipe. g. g. cunto et alii, frattura ed integrità strutturale, 41 (2017) 332-338; doi: 10.3221/igf-esis.41.44 337 specimen orientation jlimit [kj.m-2] jmax [kj.m-2] jic [kj.m-2] c m ct1 l-c 537 857 199 -- ct2 l-c 540 701 168 355 0.621 ct3 l-c 535 653 193 -- table 3: results of j-integral tests for the weld aisi 316l fracture mechanics analyses applying the mechanical properties found in the tensile test and a specific load, that considers normal operation condition, in the leak calculation software picep, the leak rate curves versus crack size were determined. fig. 3 present the typical leak flow rate versus crack length found for the three different zones in the welded pipe. figure 3: typical leak flow rate x crack length for different zones in welded pipe. considering that a typical detectable leakage capability of 1 gpm is considered for pwr plants and the margin of 10 shall be applied, it was possible to determinate the size of through-wall cracks that will result in detectable leakage of 10 gpm for each tested hot tensile specimen. figure 4: average sizes for critical crack and 10 gpm leakage crack for different zones in welded pipe. using also the picep software, but considering normal plus seismic sse loads conditions, size of critical through-wall cracks were found for all three zones of the welded pipe. fig. 4 shows both the size of through-wall cracks that will result in leakage of 10 gpm and the size of critical cracks for all the three different zones and orientation in the welded pipe. g. g. cunto et alii, frattura ed integrità strutturale, 41 (2017) 332-338; doi: 10.3221/igf-esis.41.44 338 fig. 4 shows that all the material zones and crack orientation fulfill the requirements for lbb application, since all critical cracks size considered are more than twice the size of the crack that would causes a 10gpm leak. for the critical crack size found in the weld, which is the region that presented the lowest toughness, elastic-plastic j-integral analysis was performed, to verify the possibility of tearing instability failure. in this analysis, two important consideration shall be taken, specifically, initiation or first extension of an existing crack denoted as jic, and stability or instability of a growing crack. if the material toughness jic is bigger than the applied value of j, the not occurrence of crack initiation or significant growth is guaranteed. when the jic is less than the applied j, the crack growth must be evaluated by a ductile instability analysis, e.g. tearing modulus analysis, to determine if the crack grows in a stable manner, or if the crack will grow unstably resulting in a structural collapse [6]. the applied j calculated using eq. 4, considering the normal plus seismic sse loads conditions, the size of critical throughwall crack found for the weld zone, and the material properties for the weld zone found in the hot tensile tests, was: japlied = 164 kj.m-2 this value is less than the lower jic value of 168 kj.m-2 found in the toughness test performed in weld zone. this way, it was demonstrated that the failure by tearing instability will not occur under the considered conditions. conclusions he lowest critical crack size was found for the base material presenting circumferential orientation crack. after a certain crack size, the leak rate in base material is much higher than for the haz and for the weld zones. for the critical crack size found in the weld, integral-j analysis was performed, considering failure by tearing instability. it has been demonstrated that the failure by tearing instability will not occur under the considered conditions of this project. all critical cracks size found for the three different zones and two different orientation, are more than twice the size of the crack that would causes a 10 gpm leak. thereby, it can be concluded that the investigated 316ln austenitic steel pipes welded using 316l can be applied in the labgene reactor coolant loop considering lbb criterion. acknowledgments his work has been performed as a part of the labgene program supported by navy technological center in são paulo. references [1] nureg-1061, report of the u. s. nuclear regulatory commission piping review committee, piping review committee, nrc, volume 1-5, (1984). [2] nureg-0800, srp standart review plan, nuclear regulatory guide, united states nuclear regulatory commission, (1987). [3] norris, d. m., chexal, b., picep: pipe crack evaluation program (revision 1) epri np-3596-sr, (1987). [4] zahoor, a., ductile fracture handbook, np-6301-d research project, electronic power research institute, (1989). [5] regulatory guide 1.45, reactor coolant pressure boundary leakage detection system, usnrc-united states nuclear regulatory commission, (2007). [6] anderson, t.l, fracture mechanics: fundamentals and applications. 3rd edition, crc press, taylor & francis group, (2005). t t << /ascii85encodepages false /allowtransparency false /autopositionepsfiles true /autorotatepages /none /binding /left /calgrayprofile (dot gain 20%) /calrgbprofile (srgb iec61966-2.1) /calcmykprofile (u.s. web coated \050swop\051 v2) /srgbprofile (srgb iec61966-2.1) /cannotembedfontpolicy /error /compatibilitylevel 1.4 /compressobjects /tags /compresspages true /convertimagestoindexed true /passthroughjpegimages true /createjobticket false /defaultrenderingintent /default /detectblends true /detectcurves 0.0000 /colorconversionstrategy /cmyk /dothumbnails false /embedallfonts true /embedopentype false /parseiccprofilesincomments true /embedjoboptions true /dscreportinglevel 0 /emitdscwarnings false /endpage -1 /imagememory 1048576 /lockdistillerparams false /maxsubsetpct 100 /optimize true /opm 1 /parsedsccomments true /parsedsccommentsfordocinfo true 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/hrv (za stvaranje adobe pdf dokumenata najpogodnijih za visokokvalitetni ispis prije tiskanja koristite ove postavke. stvoreni pdf dokumenti mogu se otvoriti acrobat i adobe reader 5.0 i kasnijim verzijama.) /hun 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/pdfxoutputintentprofileselector /documentcmyk /preserveediting true /untaggedcmykhandling /leaveuntagged /untaggedrgbhandling /usedocumentprofile /usedocumentbleed false >> ] >> setdistillerparams << /hwresolution [2400 2400] /pagesize [612.000 792.000] >> setpagedevice microsoft word numero_42_art_14.docx v. růžička et alii, frattura ed integrità strutturale, 42 (2017) 128-135; doi: 10.3221/igf-esis.42.14 128 focused on mechanical fatigue of metals over-deterministic method: the influence of rounding numbers on the accuracy of the values of williams’ expansion terms vladimír růžička brno university of technology, faculty of civil engineering, institute of structural mechanics, veveří 331/95, 602 00 brno, czech republic ruzicka@musicer.net lucie malíková, stanislav seitl academy of sciences of the czech republic, institute of physics of materials, v. v. i., žižkova 22, 616 62 brno, czech republic malikova.l@fce.vutbr.cz, http://orcid.org/0000-0001-5868-5717 seitl@ipm.cz, http://orcid.org/0000-0002-4953-4324 abstract. a study on the accuracy of the values of williams’ expansion terms influenced by rounding numbers is presented. the results are presented taking into account a three-point bend single edge notched beam. crack tip stress tensor components are expressed using the linear elastic fracture mechanics (lefm) theory in this work, more precisely via its multi-parameter formulation, i.e. by williams’ power series (wps). determination of the coefficients of the terms of this series is performed using the least squaresbased regression technique known as the over-deterministic method (odm), for which displacements data obtained numerically in software ansys are taken as inputs. the values of williams’ expansion terms based on the displacement data obtained are calculated by using various levels of rounding numbers and the results are compared and discussed. keywords. over-deterministic method; rounding numbers; williams’ expansion; fracture mechanics; stress field. citation: ruzicka,v., malikova, l., seitl, s., over-deterministic method: the influence of rounding numbers on the accuracy of the values of williams’ expansion terms, frattura ed integrità strutturale, 42 (2017)128-135. received: 10.06.2017 accepted: 16.06.2017 published: 01.10.2017 copyright: © 2017 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. introduction ometimes it is necessary to describe the crack-tip stress field by means of more than only one singular term (the wellknown stress intensity factor, see e.g. [1-4] or two-parameter fracture mechanics, see e.g. [5-10]) of williams’ expansion (we). it has been shown that so-called multi-parameter fracture mechanics can be helpful when the fracture process occurs in the more extensive surroundings of the crack tip, see for material like concrete [11-19]. then, a particular number of the we terms needs to be taken into account for a more complex fracture analysis. in this paper, the focus is devoted to investigations into the accuracy of the higher-order terms of the we when various types of rounding s v. růžička et alii, frattura ed integrità strutturale, 42 (2017) 128-135; doi: 10.3221/igf-esis.42.14 129 numbers are considered. there exist various kinds of software that enable to calculate higher-order terms of the we, see [20-22]. for each of them a specific accuracy of the numbers used is defined, which can play a key role when the we terms are calculated. the analysis presented deals with various numbers of the decimal places that are considered in the calculations of the we terms and brings practical recommendations how the analysis should be performed in order to obtain accurate results. theoretical background fracture mechanics: williams’ expansion s it has been mentioned, the paper is based on the idea that the near crack-tip stress field tensor components are approximated via williams’ expansion [23] that was originally derived for a homogeneous elastic isotropic cracked body subjected to arbitrary remote loading and is expressed via the infinite power series for loading mode i as follows:  nfarn ij n n n ij , 21 1 2       , where i,j {x,y}. (1) the meaning of the symbols used in eq. 1 can be described in the following way: (r, θ) are polar coordinates centred at the crack tip; are known functions corresponding to the stress distribution; the symbols an correspond to the unknown coefficients of williams’ expansion terms (this is to emphasize that their values depend on the specimen geometry, relative crack length  and loading conditions). over-deterministic method when the effect of rounding numbers is investigated, the over-deterministic method is assumed to be used for determination of various numbers of the we terms [24]. this method is based on the least-squares technique and was used as one of the methods that do not require any special crack elements or implementation of other difficult fracture mechanics concepts. the method uses the displacement field estimated around the crack tip via the finite element method and together with the polar coordinates of the nodes, where the displacements are investigated, a system of linear equations is solved according to the definition:   ,,, 0 2/ enfaru ui n n n i     , where i {x,y}. (2) when the k number of nodes is investigated, then 2k of displacements (u and v) can be used and 2k of equations can be formed in the following way [24]:                                                                                                      n kk v rnkk v rkk v r v rn v r v r v rn v r v r kk u rnkk u rkk u r u rn u r u r u rn u r u r k k a a a rfrfrf rfrfrf rfrfrf rfrfrf rfrfrf rfrfrf v v v u u u            1 0 10 22221220 11111110 10 22221220 11111110 2 1 2 1 ,,, ,,, ,,, ,,, ,,, ,,,       (3) the solution of the system of the equation can be written as:           ucccx t1t  (4) a v. růžička et alii, frattura ed integrità strutturale, 42 (2017) 128-135; doi: 10.3221/igf-esis.42.14 130 it is always necessary to prescribe the number of the terms of the we terms, n, that shall be calculated. this is also one of the parameters that is varied in the analysis presented. data structure used in common software nowadays, most personal computers used for calculation of mathematical tasks are constructed by 32 or 64 bit data architecture, see [25, 26], i.e. 4 or 8 bytes are used for one number. for representation of numbers, mathematical software can use a structure with or without a floating point. counting with numbers without a floating point is not usable for very low and very high numbers, especially with some decimal numbers. for counting with decimal numbers, it is necessary to use a data structure with a floating point; it gives maximally 15 decimal numbers plus an exponent in 64 bit data architecture or only 6 decimal numbers in 32 bit data architecture. for this reason, all the common software (e.g. maple [20], matlab [21], mathematica [22],) uses the data structure with a floating point or a special data structure to extend the count of decimal numbers. one of the methods how to increase the count of decimal numbers is to convert the original number to a string of characters and then to carry out calculating with strings in specially programmed procedures. numerical example of 3pb or the analysis a very simple model of a three-point-bending specimen was used, see fig. 1. the detailed geometry can be found in [27, 28] (c = 0.2 mm, d = 1 mm, p = 1 n). because of the symmetry, only one half of the specimen could be modelled in order to obtain a set of displacement data at the distance of 0.1 mm from the crack tip. figure 1: schema of the three-point-bending specimen used for the analysis presented. the data of the displacement vector obtained from the ansys finite element software [29] can be found in tab. 1. the values introduced in the referred table were used as inputs for eq. 3 and 4 respectively. results and discussion he main goal was to validate the odm concept in order to obtain a reliable procedure for further analysis of the stress field near the crack tip in civil engineering materials. therefore, a basic cracked specimen configuration (3pb) has been investigated and higher-order terms coefficients estimated. data comparison can be found in tab. 2. note that only the first five terms are mostly available in literature [27, 28, 30]. it can be seen in tab. 2 that the coefficients calculated by means of the odm correspond very well with the data published in literature. f t v. růžička et alii, frattura ed integrità strutturale, 42 (2017) 128-135; doi: 10.3221/igf-esis.42.14 131 nr. node nr. radius [mm] theta [deg] u [mm] v [mm] 1 2 0.1 0 -27.077 0.0000 2 13 0.1 9 -27.066 0.0639 3 14 0.1 18 -27.034 0.1325 4 15 0.1 27 -26.984 0.2100 5 16 0.1 36 -26.919 0.3000 6 17 0.1 45 -26.843 0.4072 7 18 0.1 54 -26.765 0.5292 8 19 0.1 63 -26.688 0.6691 9 20 0.1 72 -26.618 0.8250 10 21 0.1 81 -26.564 0.9945 11 12 0.1 90 -26.529 1.1737 12 97 0.1 99 -26.517 1.3584 13 98 0.1 108 -26.534 1.5431 14 99 0.1 117 -26.581 1.7226 15 100 0.1 126 -26.659 1.8915 16 101 0.1 135 -26.768 2.0460 17 102 0.1 144 -26.906 2.1766 18 103 0.1 153 -27.069 2.2843 19 104 0.1 162 -27.253 2.3634 20 105 0.1 171 -27.449 2.4105 21 87 0.1 180 -27.651 2.4236 table 1: the displacements and polar coordinates of the selected nodes around the crack tip obtained from the ansys finite element software. 3pb [27] [28] data calculated a1 1.8530 1.8538 1.8538 a2 -0.3533 -0.3527 -0.3527 a3 -0.7149 -0.7202 -0.7202 a4 -0.0896 -0.1019 -0.1019 a5 -1.3717 -1.3565 -1.3565 table 2: higher-order terms coefficients determined by means of the odm in comparison to data published in literature for 3pb, see [27, 28]. on the basis of php software [31] the special software tool was programmed considering various levels of rounding numbers in order to analyze how many decimal numbers are needed to obtain precise values of we terms. the software was based on the idea of representation of numbers by means of strings. the values of the we terms were calculated step by step assuming two changing parameters: the level of rounding numbers and the number of calculated we terms. v. růžička et alii, frattura ed integrità strutturale, 42 (2017) 128-135; doi: 10.3221/igf-esis.42.14 132 figure 2: dependence of a1 corresponding to the stress intensity factor on the number of the we terms considered for various numbers of the decimal places taken into account during the analysis. figure 3: dependence of the 5th we term on the number of the we terms considered for various numbers of the decimal places taken into account during the analysis. several phenomena can be observed from the investigation. for example the first coefficient a1 (corresponding to the stress intensity factor k) differs significantly when 5, 6 or 10 decimal numbers are taken into account and these values are nearly independent of the number of the we terms calculated (the minimum counted values were 5, the maximum 20), see fig. 2. v. růžička et alii, frattura ed integrità strutturale, 42 (2017) 128-135; doi: 10.3221/igf-esis.42.14 133 similar dependences can also be observed for other values of the we terms of higher-orders. it holds that the level of rounding numbers is more important when the analysis for a higher index of the we terms coefficients is performed. for example, a5 (the 5th coefficient of we) does not seem to be precise enough until 15 decimal numbers are considered within the counting numbers (see fig. 3); and a10 (the 10th coefficient) needs rounding by 20 decimal numbers, see fig. 4. figure 4: dependence of the 10th we term on the number of the we terms considered for various numbers of the decimal places taken into account during the analysis. a similar trend is also expected for the coefficients of the we terms of higher orders: the higher index of the we term, the higher number of decimal places needed. simultaneously it holds that more we terms need to be considered during the analysis when the coefficient of the we term of some higher-order is required. conclusions pecial computing software tool based on the concept of representation of numbers by means of strings was developed which enables to calculate with numbers with up to 100 or 200 decimal places. the software was used in order to perform an extended analysis dealing with the influence of rounding numbers on the accuracy of the we terms coefficients determined via the over-deterministic method. the results show that it is enough to use numbers with up to 20 decimal characters to obtain good results for 10 initial coefficients of williams’ expansion. a final conclusion/recommendation based on the research presented can be stated: the higher number of the coefficients of we terms is requested, the higher number of decimal places used within rounding numbers is needed. acknowledgement he authors acknowledge the support of czech sciences foundation project no.17-01589s. s t v. růžička et alii, frattura ed integrità strutturale, 42 (2017) 128-135; doi: 10.3221/igf-esis.42.14 134 references [1] anderson, t. l., fracture mechanics fundamentals and applications, crc press (1991). [2] pook l. p., linear elastic fracture mechanics for engineers. theory and applications. wit press, southampton (2000). [3] pook, l. p. crack paths, wit press, southampton (2002). [4] astm e399 12e3 standard test method for linear-elastic plane-strain fracture toughness kic of metallic materials, doi: 10.1520/e0399. [5] leevers, p.s., radon, j.c., inherent stress biaxiality in various fracture specimen geometries, international journal of fracture, 19(4) (1982) 311–325. doi: 10.1007/bf00012486. [6] karihaloo b.l., abdalla h.m., xiao q.z., size effect in concrete beams, engng. fract. mech., 70 (2003) 979–993. [7] seitl, s., veselý, v., řoutil, l. two-parameter fracture mechanical analysis of a near-crack-tip stress field in wedge splitting test specimens, computers and structures 89(21-22) (2011) 1852–1858. doi: 10.1016/j.compstruc.2011.05.020. [8] chao z.j., zhang x., constraint effect in brittle fracture, in: piacik et al (eds) proceedings of the 27th national symposium on fatigue and fracture, philadelphia, (1997) 41–60. [9] du, z.z., hancock, j.w., the effect of non-singular stresses on crack tip constraint, j. mech. phys. solids, 39 (1991) 555–567. [10] dyskin, a.v., crack growth criteria incorporating non-singular stresses: size effect in apparent fracture toughness, int. j. fract., 83 (1997) 191–206. [11] ayatollahi, m.r., akbardoost, j., size effects on fracture toughness of quasi-brittle materials – a new approach, engng. fract. mech., 92 (2012) 89–100. [12] berto, f., lazzarin, p., on higher order terms in the crack tip stress field, int. j. fract., 161 (2010) 221–226. [13] vesely, v., sobek, j., sestakova, l., frantik, p., seitl s. multi-parameter crack tip stress state description for estimation of fracture process zone extent in silicate composite wst specimens, frattura ed integrita strutturale, 7(25) (2013) 69– 78. [14] veselý, v., frantík, p., an application for the fracture characterisation of quasi-brittle materials taking into account fracture process zone influence, advances in engineering software, 72 (2014) 66–76. [15] veselý, v., frantík, p., sobek, j., malíková, l., seitl, s. multi-parameter crack tip stress state description for evaluation of nonlinear zone width in silicate composite specimens in component splitting/bending test geometry, fatigue and fracture of engineering materials and structures, 38(2) (2015) 200–214 [16] veselý, v., sobek, j., frantík, p., seitl, s., multi-parameter approximation of the stress field in a cracked body in the more distant surroundings of the crack tip, international journal of fatigue, 89 (2015) 20–35 [17] stepanova, l., roslyakov, p., complete williams asymptotic expansion near the crack tips of collinear cracks of equal lengths in an infinite, procedia structural integrity, 2 (2016) 1789–1796, doi: 10.1016/j.prostr.2016.06.225 [18] stepanova, l., roslyakov, p., gerasimova, t., complete williams asymptotic expansion near the crack tips of collinear cracks of equal lengths in an infinite plan", solid state phenomena, 258 (2017) 209–212. doi: 10.4028/www.scientific.net/ssp.258.209 [19] stepanova, l., roslyakov, p., multi-parameter description of the crack-tip stress field: analytic determination of coefficients of crack-tips stress expansions in the vicinity of the crack tips of two finite in an infinite plane medium, international journal of solids and structutes, 100-101 (2016) 11–28. [20] http://www.maplesoft.com/ [21] https://www.mathworks.com/products/matlab.html [22] https://www.wolfram.com/mathematica/ [23] williams, m.l., on the stress distribution at the base of a stationary crack, j. appl. mech., 24 (1957) 109–114 [24] ayatollahi m, nejati m. an over‐deterministic method for calculation of coefficients of crack tip asymptotic field from finite element analysis. fatigue fract eng mater struct, 34 (2011) 159–76. [25] cody, j.w., et al. ieee standards 754 and 854 for floating-point arithmetic: for a readable, account ieee magazine micro, (1984) 84–100. [26] kahan, w. ieee standard 754 for binary floating-point arithmetic, lecture notes on the status of ieee, 754 (1997) 1–30. v. růžička et alii, frattura ed integrità strutturale, 42 (2017) 128-135; doi: 10.3221/igf-esis.42.14 135 [27] karihaloo, b.l., xiao, q.z., higher order terms of the crack tip asymptotic field for a notched three-point bend beam, int. j. fract., 112 (2001) 111–128. [28] šestáková, l., tuning of an over-deterministic method for calculation of higher-order terms coefficients of the williams expansion for basic cracked specimen configurations, applied mechanics 2011 (on cd) [29] ansys program documentation, user’s manual version 10.0. swanson analysis system, inc., houston (2005). [30] karihaloo, b.l. xiao, q.z., accurate determination of the coefficients of elastic crack tip asymptotic field by a hybrid crack element with p-adaptivity, engineering fracture mechanics, 68 (2001) 1609–1630 [31] http://php.net/software.php << /ascii85encodepages false /allowtransparency false /autopositionepsfiles true /autorotatepages /none /binding /left /calgrayprofile (dot gain 20%) /calrgbprofile (srgb iec61966-2.1) /calcmykprofile (u.s. web coated \050swop\051 v2) /srgbprofile (srgb iec61966-2.1) /cannotembedfontpolicy /error /compatibilitylevel 1.4 /compressobjects /tags /compresspages true /convertimagestoindexed true /passthroughjpegimages true /createjobticket false /defaultrenderingintent /default /detectblends true /detectcurves 0.0000 /colorconversionstrategy /cmyk /dothumbnails false /embedallfonts true /embedopentype false /parseiccprofilesincomments true /embedjoboptions true /dscreportinglevel 0 /emitdscwarnings false /endpage -1 /imagememory 1048576 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/hrv (za stvaranje adobe pdf dokumenata najpogodnijih za visokokvalitetni ispis prije tiskanja koristite ove postavke. stvoreni pdf dokumenti mogu se otvoriti acrobat i adobe reader 5.0 i kasnijim verzijama.) /hun 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can be opened with acrobat and adobe reader 5.0 and later.) >> /namespace [ (adobe) (common) (1.0) ] /othernamespaces [ << /asreaderspreads false /cropimagestoframes true /errorcontrol /warnandcontinue /flattenerignorespreadoverrides false /includeguidesgrids false /includenonprinting false /includeslug false /namespace [ (adobe) (indesign) (4.0) ] /omitplacedbitmaps false /omitplacedeps false /omitplacedpdf false /simulateoverprint /legacy >> << /addbleedmarks false /addcolorbars false /addcropmarks false /addpageinfo false /addregmarks false /convertcolors /converttocmyk /destinationprofilename () /destinationprofileselector /documentcmyk /downsample16bitimages true /flattenerpreset << /presetselector /mediumresolution >> /formelements false /generatestructure false /includebookmarks false /includehyperlinks false /includeinteractive false /includelayers false /includeprofiles false /multimediahandling /useobjectsettings /namespace [ (adobe) (creativesuite) (2.0) ] /pdfxoutputintentprofileselector /documentcmyk /preserveediting true /untaggedcmykhandling /leaveuntagged /untaggedrgbhandling /usedocumentprofile /usedocumentbleed false >> ] >> setdistillerparams << /hwresolution [2400 2400] /pagesize [612.000 792.000] >> setpagedevice microsoft word numero_38_art_7 t. lassen et alii, frattura ed integrità strutturale, 38 (2016) 54-60; doi: 10.3221/igf-esis.38.07 54 focussed on multiaxial fatigue and fracture fatigue methodology for life predictions for the wheel-rail contact area in large offshore turret bearings t. lassen university of agder, grimstad and apl, norway, national oilwell varco, arendal, norway tom.lassen@uia.no z. mikulski university of agder, grimstad, norway zbigniew.mikulski@uia.no abstract. the present report presents a fatigue life prediction method for large roller bearings applied in the turret turn table for large loading buoy units. the contact points between wheel and rail in these bearings are subjected to a multi-axial fluctuating stress situation and both surface wear and fatigue cracking may occur. a methodology based on the dang van fatigue criterion is adopted. the criterion is based on an equivalent stress defined as a combination of the fluctuation of the shear stress from its mean value at a critical plane and the associated hydrostatic stress at the given time. the present work is supporting the theoretical model by extensive laboratory testing. both full scale testing of wheel on rail and small scale testing for characterizing the steel material are carried out. an experimental program was carried out with the high strength stainless steel s165m. the dang van stress concept is applied in combination with the random fatigue limit method (rflm) for life data analyses. this approach gives the opportunity to include both finite lives and the run-outs in a rational manner without any presumption of the existence of a fatigue limit in advance of the data. this gives a non-linear s-n curve for a log-log scale in the very high cycle regime close to the fatigue limit. it is demonstrated how the scatter in fatigue limit decreases when the dang van stress concept is applied and that the fatigue limit is occurring beyond 107 cycles. keywords. dang van criterion; random fatigue limit method; rolling contact fatigue. citation: lassen, t, mikulski, z., fatigue methodology for life predictions for the wheel-rail contact area in large offshore turret bearings, frattura ed integrità strutturale, 38 (2016) 54-60. received: 27.04.2016 accepted: 10.06.2016 published: 01.10.2016 copyright: © 2016 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. t. lassen et alii, frattura ed integrità strutturale, 38 (2016) 54-60; doi: 10.3221/igf-esis.38.07 55 introduction ffshore loading buoy units are often constructed with a large central turret in order to allow the floating unit to weathervane. the geostationary moored turret has a turn table with a bearing arrangement in the top. the turn table can be based on a sliding bearing concept, but for larger turrets a roller bearing design is usually preferred. the wheels are rolling on a circular rail mounted on the top of the floaters deck structure, see fig. 1. the durability of these bearings during a typical target service life of 25 years is a matter of concern. during inspection of rails in service, surface cracks have been detected on former installations. these cracks may eventually obstruct the rotation that allows the floating unit to weathervane. the cracks are thus considered as a hazard due to the risk of encountering unforeseen loading condition if the buoy should be locked in one direction. furthermore, the bearings are so huge that replacement in-situ will be very cumbersome and expensive. this makes the fatigue safe life limit (sll) a major design criterion. further details are given in [1]. figure 1: wheel rail connection, ref. [1]. the objectives of the present work are: • study the fatigue resistance of the martensitic-austenitic stainless steel s165m particularly when subjected to multiaxial stress situation typical for rolling contact fatigue (rcf). • apply the random fatigue limit method (rflm) as a supplement to conventional stare case methods that in the authors’ opinion are outdated. • demonstrate the ability of the dang van multi-axial stress concept to reduce scatter in the fatigue limit. this is demonstrated by small scale testing with specimens subjected to pulsating and alternating tension. • the dang van based fatigue limit can be used to ensure safe life condition during the service for the offshore installation in question. this is verified by full scale fatigue testing. the practical design based on the obtained model is verified by full scale testing and the reader is referred to [2] on this subject. the dang van stress concept for multiaxial fatigue he sub-surface stress situation in the contact point between wheel and rail is multi-axial and may lead to fatigue cracking under repetitive loading. it is a common hypothesis that it is the shear stress amplitude that is the key variable to the fatigue crack initiation, but also other stress contributions may play a role. the multi-axial fatigue criterion according to the dang van approach reads, [3, 5]:    a dv h e t t a tmax       (1) where τa is the acting shear stress amplitude (deviation from mean shear stress) at any time, whereas σh is the simultaneous acting hydrostatic stress. τe is the shear stress amplitude strength (fatigue endurance limit) when no other stress o t t. lassen et alii, frattura ed integrità strutturale, 38 (2016) 54-60; doi: 10.3221/igf-esis.38.07 56 components are present. the hydrostatic stress is a simplified bulk measure for any complex stress situation. the material constants τe and adv are determined from two test series. the curve associated with eq. (1) is shown in fig. 2. the parameter τe is the ordinate value of the curve whereas adv is the slope of the curve. the two test series will give data at the two points that are denoted pulsating (p) and alternating (a) stress in fig. 2. the line is typically defined based on the assumption that the fatigue limit is defined at n=107 cycles. it is not clarified in the original work how scatter is treated, [3, 5]. it is one of the goals of the present work to bring some light on these issues. figure 2: the dang van design line for the fatigue limit at n=107 cycles. the rail will be the most critical component with respect to fatigue and a martensitic stainless steel 165m is selected. this is to have a steel that has high resistance both with respect to fatigue and corrosion as the bearing is located in the splash zone. the steel has a typical yield stress of 700 mpa. for s165m there is not much data available on the fatigue strength in the literature. the acting shear stress amplitude τa in a typical wheel-rail design will typically be 140 mpa at zero hydrostatic stress for the extreme load case. hence, based on preliminary assumptions taken from the literature studies the stress situation shall not lead to fatigue cracking. this will be corroborated by the testing described in the next section. the fatigue test series wo special small scale test series were carried out to characterize the multiaxial fatigue resistance. the first test series is under pulsating tension, whereas the second one is under alternating tension. both test series are planned with classical dog-boned specimens with diameter 10 mm. the surface finish was r=0.8 that reflects the surface of the rail in service, the small scale test results were used as theoretical support for the large scale rolling test. a number of 10 specimens were manufactured for each test series, i.e. 20 tests in total. the test series were carried out as follows: test series 1: pulsating tension, r=0.05 at 100 hz the actual stress situation is shown in fig. 3 where the x-axis is the specimen pulling direction. as can be seen the plane oriented 45 degrees will be subject to the maximum shear stress τ and a normal stress component σ. it is this stress combination that will be the driving force for the crack initiation. figure 3: stress situation in the material for a rod subjected to tension in x-direction. t t. lassen et alii, frattura ed integrità strutturale, 38 (2016) 54-60; doi: 10.3221/igf-esis.38.07 57 test series 2: alternating compression and tensile testing at r=-1 for this series the actual stress situation will again be as shown in fig. 3, but as this stress history is partly compressive the maximum hydrostatic stress decreases compared with test series 1. the following equations for the stress situation apply for the two test series: h a ,    3 4         4  test series 1 (2) h a ,    2 3 4          test series 2 (3) due to the lower hydrostatic stress in test series 1 this series will sustain higher shear amplitude as predicted by eq. (1) and illustrated in fig. 2. all the tests were run to failure or stopped at n=2·107 cycles. failure is defined by total fracture of the specimen. the fatigue limit is defined at n=107 cycles as is in accordance with rule and regulations. typically applied normal stress for test series 1 was close to a range of 450 mpa, whereas the stress range for series 2 was close to 500 mpa. the applied loading was tuned in after the first tests have been completed. the rflm model was applied to determine the fatigue limit, see description next section. hence, the two test series gives us two points on the dang van design curve as shown in fig. 2. consequently, the slope of the curve denoted adv is determined. the random fatigue limit methodology for data analysis he conventional statistical analyses of data points are based on linear regression of fatigue life data only, [5] or by the staircase method for the fatigue limit only, [6]. in the present case with large scatter in both fatigue life and the fatigue limit these methods are regarded as less appropriate. due to the uncertainty and large scatter in fatigue life in the region close to 107 cycles, an s-n curve based on a random fatigue-limit model (rflm) is adopted in the present work, [4]. the basic feature of the model is that both fatigue life and the fatigue-limit are treated as random variables simultaneously. the fatigue limit should not be treated separately as it is done for the bi-linear curves. the s-n curve obtained from the rflm will not have an abrupt change from an inclined straight line to a horizontal line, but a gradually change in slope as stress ranges get very low. it then remains to be seen if the slope goes asymptotically towards a horizontal line as the number of cycles increases. if this is not the case the existence of a fatigue-limit should be rejected. we shall not elaborate the method in the present article but outline the most important characteristics. the method applies a maximum likelihood method that gives a rational treatment of run outs. the basic equations are:    n s0 0ln ln        (4) where ln denotes the natural logarithm and γ = δs0 is the fatigue-limit. the parameters β0 and β1 are fatigue curve coefficients. for given sample data wi and xi from various test specimens i = 1,…n, the model parameters can be determined by the maximum likelihood (ml) function:       n i i w i i w i i i l f w x f w x 1 1 ; 1 ;           q q q (5) where δi = 1 if wi is a failure and δi = 0 if wi is a censored observation (run out). the vector q contains the model parameters:  s0 1,   , ,  ,      q (6) where σ is the standard deviation for the natural logarithm to fatigue life, whereas µγ and sγ are the mean value and standard deviation respectively for the fatigue limit lnγ. once these parameters have been determined from optimization t t. lassen et alii, frattura ed integrità strutturale, 38 (2016) 54-60; doi: 10.3221/igf-esis.38.07 58 of eq. (5), the corresponding confidence intervals can be obtained by a profile likelihood method using the profile ratio of the variables together with chi-square statistics. when the parameters are determined we can calculate the fatigue life for a chosen probability p of failure using eq. (4). hence, the median curve and percentile curves for design purpose are obtained. for further details the reader is referred to pascal and meeker, [4]. it should be mentioned that the optimization of eq. (5) may be difficult due to local optimum points. test results and discussion he obtained life data were analyzed in 3 steps based on the methodology described in the section above. the rflm approach was first used to determine the mean fatigue limit for the direct applied stress range δσx for test series 1 and 2 separately. the results are shown in the lower and upper part of fig. 4. the fatigue limit was determined for both test series. as can be seen the mean value for the fatigue limit for the series 1 is 457 mpa where it reaches 535 mpa for test series 2 when taken 107 cycles. this increase from test series 1 to series 2 is explained by the fact that series 2 has a smaller maximum normal stress on the 45 degrees plane than series 1 has, see fig. 4. hence, the shear stress amplitude in series 1 will be more damaging than the shear amplitude of the same magnitude in series 2 due to the fact that the simultaneously occurring normal stress σ has decreased for series 2. this phenomenon is taken into account by the hydrostatic stress term in eq. (1). a similar analysis carried out by the staircase method gave typically 5% higher mean fatigue limits, [2]. the large scatter for series 2 is peculiar. as can be seen the data points for the rupture have a positive correlation for cycles versus stress range. more data points are needed to get the expected behavior. figure 4: illustration of mean curve change in fatigue limit from test series 1 to test series 2. subsequently, in the second step, the associated dang van equivalent stress limit was determined for the two series based on eqs. (1). this also gives the necessary information to determine the dang van constants. the results are shown in fig. 2 given in tab. 1 based on the mean stresses and the dang van constant is determined to 0.28. this slope is obtained by entering the results from eq. (2) and (3) respectively into eq. (1). the obtained value is somewhat lower than obtained for ferritic steels. in the last third step all the data was gathered on one plot applying the dang van equivalent stress as the explaining variable to fatigue life. this equivalent stress is defined:  eq a dv h t t amax      (7) the advantage of this analysis is that the number of data points is doubled and the confidence intervals for the parameters become smaller. the data points and the associated curves are shown in fig. 5. as can be seen the results for the dang t t. lassen et alii, frattura ed integrità strutturale, 38 (2016) 54-60; doi: 10.3221/igf-esis.38.07 59 van equivalent stress fatigue limit is 140 mpa at a 2.5% percentile defined at n=107 cycles. as can be seen the curve has not become asymptotically horizontal at n=107 cycles, this will occur when approaching 108 cycles. in addition to the mean design curve based on the fatigue limit as was shown in fig. 2, an entire s-n curve is now obtained as shown in fig. 5. the purpose of the curve is to be able to calculate the damage accumulation according to the miner summation for variable amplitude loading. the curve is directly applicable in the test region, i.e. at dang van stress ranges below 200 mpa. the shape of the curve will result in exclusion of many stress cycles in a typical in-service load spectrum as they will become non-damaging according to the curve. very many of these cycles will typically be below a range of 160 mpa. tab. 1 gives the scatter band for the fatigue limit when defined between 107 and 2∙107 cycles. the standard deviation sγ is also given. as can be seen the magnitude is 0.11 and 0.22 for series 1 and 2 respectively when each series is treated separately. applying the dang van equivalent amplitude stress for all data gathered gives a relative scatter band close to 0.16 which is in between the values obtained when each series is handled separately. it demonstrates how the influence of r ratio implicitly is taken care of by the dang van stress multiaxial stress concept. data points explaining stress maximum scatter band standard deviation sγ all r=0 and r=-1 δσx 180 r=0 only δσx 110 0.11 r=-1 only δσx 80 0.22 all r=0 and r=-1 σeq (eq. (7)) 35 0.16 table 1: table scatter in stress data between n=107 and 2∙107 cycles dependent on explaining stress. figure 5: rflm analysis of both test series based on applied dang van equivalent stress. as a close to this section it shall briefly be mentioned that the practical application of the established s-n curve directly obtained by first require that the maximum acting equivalent stress in the rail during service shall be less than the curve in figure 5. the acting stress can be found by empirical equations or by advanced finite element models for the contact between wheel and rail. we will not pursue this procedure in the present article; the reader is referenced to [1, 2]. conclusions he dang van defined equivalent stress is suggested for fatigue life predictions under the multi-axial stress situations imposed at the wheel rail contact point. originally the method was applied for verifying the fatigue limit usually chosen at 107 cycles. in the present work a random fatigue limit model is applied for a more consistent statistical data analysis. the result is a non-linear s-n curve for a log-log scale in the high cycle regime close to the fatigue t t. lassen et alii, frattura ed integrità strutturale, 38 (2016) 54-60; doi: 10.3221/igf-esis.38.07 60 limit. the fatigue limit is defined as the horizontal asymptote is appearing at a given number of cycles. it is demonstrated how difference in the fatigue limit for different r ratios reduces when applying the dang van stress concept. the fatigue resistance of the martensitic-austenitic stainless steel s165m is quite good, but somewhat poorer than for comparable non-stainless steels with the same yield stress. there is also a considerable scatter in the fatigue life limit for the present steel. the applicability of the results is verified by full scale testing and a practical multiaxial fatigue design tool has been established and applied in practice. this will be presented in a future work. acknowledgment he authors would like to express their gratitude to advanced production and loading (apl) for giving permission to publish the present article. references [1] lassen, t., hansen, s., askestad, s., fatigue design of roller bearing for large fpso turrets, in: 31th international conference on ocean offshore and arctic engineering, rio de janeiro, brazil (2012). [2] van lieshout, p.s. et al., validation of the dang van multiaxial fatigue criterion when applied to turret bearings of fpso offloading buoys, submitted to journal of ship and offshore structures. [3] dang van, k, maitournam, m.h., rolling contact in railways: modelling, simulation and damage prediction, journal of fatigue and fracture of engineering materials and structures, 26 (2001) 939–948. [4] pascual, f.g., meeker, w. q., estimating fatigue curves with random fatigue–limit model, technometrics, 41 (1999) 277–302 [5] dang van, k et al., criterion for high cycle fatigue failure under multiaxial loading, in: carpinteri a., de freitas m., spagnoli a. (eds.), biaxial and multiaxial fatigue, egf 3, mechanical engineering publication, london, (1989) 459– 478. [6] best practice guidance on statistical analysis of fatigue data, doc: iiw-xiii-wg1–114–03. 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can be opened with acrobat and adobe reader 5.0 and later.) >> /namespace [ (adobe) (common) (1.0) ] /othernamespaces [ << /asreaderspreads false /cropimagestoframes true /errorcontrol /warnandcontinue /flattenerignorespreadoverrides false /includeguidesgrids false /includenonprinting false /includeslug false /namespace [ (adobe) (indesign) (4.0) ] /omitplacedbitmaps false /omitplacedeps false /omitplacedpdf false /simulateoverprint /legacy >> << /addbleedmarks false /addcolorbars false /addcropmarks false /addpageinfo false /addregmarks false /convertcolors /converttocmyk /destinationprofilename () /destinationprofileselector /documentcmyk /downsample16bitimages true /flattenerpreset << /presetselector /mediumresolution >> /formelements false /generatestructure false /includebookmarks false /includehyperlinks false /includeinteractive false /includelayers false /includeprofiles false /multimediahandling /useobjectsettings /namespace [ (adobe) (creativesuite) (2.0) ] /pdfxoutputintentprofileselector /documentcmyk /preserveediting true /untaggedcmykhandling /leaveuntagged /untaggedrgbhandling /usedocumentprofile /usedocumentbleed false >> ] >> setdistillerparams << /hwresolution [2400 2400] /pagesize [612.000 792.000] >> setpagedevice shot peening processes to obtain nanocrystalline surfaces in metal alloys: d.-h. zhang et alii, frattura ed integrità strutturale, 55 (2021) 316-326; doi: 10.3221/igf-esis.55.24 316 numerical analysis and thermal fatigue life prediction of solder layer in a sic-igbt power module dian-hao zhang, xiao-guang huang*, bin-liang cheng, neng zhang college of pipeline and civil engineering, china university of petroleum (east china), qingdao, 266580, china. huangxg@upc.edu.cn abstract. limited by the mechanical properties of materials, silicon (si) carbide insulated gate bipolar transistor (igbt) can no longer meet the requirements of high power and high frequency electronic devices. silicon carbide (sic) igbt, represented by sic mosfet, combines the excellent performance of sic materials and igbt devices, and becomes an ideal device for high-frequency and high-temperature electronic devices. even so, the thermal fatigue failure of sic igbt, which directly determines its application and promotion, is a problem worthy of attention. in this study, the thermal fatigue behavior of sic-igbt under cyclic temperature cycles was investigated by finite element method. the finite element thermomechanical model was established, and stress-strain distribution and creep characteristics of the snagcu solder layer were obtained. the thermal fatigue life of the solder was predicted by the creep, shear strain and energy model respectively, and the failure position and factor of failure were discussed. keywords. sic-igbt; thermal cycle; thermal fatigue life; creep; solder layer. citation: zhang, d.h., huang, x. g., wang, z. q., thermal fatigue analysis of the solder layer of sic-igbt power module, frattura ed integrità strutturale, 55 (2021) 278-288. received: 23.10.2020 accepted: 22.12.2020 published: 01.01.2021 copyright: © 2021 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. introduction he application in aerospace, automobile, oil drilling and other fields accelerates the improvement of electronic device of high power, high packaging density and high frequency. under such working conditions, the reliability of solder layer in these electronic devices has become increasingly important. at present, the traditional silicon (si) and gallium arsenide (gaas) solders have been unable to meet the requirements of working environment characterized by high temperature, high-power and high-frequency, due to the limitations of the materials themselves. and their performances could not get a considerable progress from the manufacturing process or structural optimization [1-3]. silicon carbide (sic) material has better material properties has shown a broader prospect in electronic packaging, which is attributed to its high strength si-c bonding [4]. silicon carbide insulated gate bipolar transistors (sic-igbts) are characterized by higher breakdown voltage, fast operating frequency, high power speed and high current density [5], therefore, they have better heat resistance than conventional si-igbts and a wide potential application. at the same time, the highest operating junction temperature of the sic-igbt can be as high as 175 °c, which allows the device itself be more adaptable to higher power density [6]. sic-igbt has become an ideal device in high-voltage and high-current applications, for instance, switching power supplies, ac motors, radar transmitters, inverters, and other power electronic devices [7]. t https://youtu.be/i_olqnp8pqg d.-h. zhang et alii, frattura ed integrità strutturale, 55 (2021) 316-326; doi: 10.3221/igf-esis.55.24 317 it is proved that the most common failure mode in sic-igbt power modules, which was encapsulated by more than two sic-igbt semiconductor chips in the same substrate according to a certain circuit [8], is main caused by the interfacial cracking from the junction between solder and chip when undergoing alternating thermal loads or called thermal fatigue failure [9-10]. therefore, it is significant to research the reliability of solder layer under the thermal cycles. knecht and fox [11] identified creep strain as the main cause of solder failure and proposed a model based on the creep strain range. syed [12] investigated the development of a life prediction model for snagcu solders and predicted the fatigue life of solders under different intrinsic models using creep strain and creep energy dissipation density. choi et al. [13] investigated the effect of different temperature changing frequencies on the life of igbt power modules and established the relevant life factors, as well as the failure analysis of the tested igbt modules. zhu et al. [14] proposed a new creep-fatigue life model for solder joints at high strain rates, in which the creep damage and fatigue damage was calculated by monkman-grant equation and coffin-manson model, respectively. it was verified that the predictions were in good agreement with experimental results according to the creep tests, and creep-fatigue tests performed. elakkiya et al. [15] studied the effect of solder joint thickness on the service life of igbt power semiconductors subjected to severe thermal stress. the results showed that creep strain occurred at the corner point of the solder layer and that the thinner the solder joint, the creep strain accumulated with temperature cycles. samavatian et al. [16] found that the creep was the main failure mode of solder joints in the power semiconductors. the reliability of sic-igbt power module is always threatened with the high operating temperature and high electric field strength in the switching process. it is of significance to carry out the structural analysis of the sic-igbt power module, and the results could provide certain advice for the optimization of sic-igbt package structure. therefore, the thermomechanical finite element (fe) model under cyclic temperatures was established based on the creep constitutive model in this paper, and the cyclic stress and accumulated creep strain of sn-ag-cu solder in the sic-igbt power module was estimated. as a result, the thermal fatigue of the sic-igbt power module was predicted from the perspective of creep strain and strain energy, and the main failure mode was discussed. numerical modelling sic-igbt mode igure 1 shows a schematic diagram of the sic-igbt cross-section, the layered structure are cu base plate, base plate solder (sn3ag0.5cu tim2), cu, ceramic (alo) layer, cu, chip solder (sn3ag0.5cu tim1) and sic-igbt chip and silica gel from bottom to top. in order to reduce the semiconductor losses in this process, a thick layer and low resistivity direct bonded copper-ceramic substrate is used which connects the chip to the substrate via a solder layer. solder layer, which mainly achieve the link between the substrate and the chip by the reflow process, plays an important role in electrical connection between the chip and substrate and providing mechanical support for heat dissipation channels in the igbt package module. also, the solder layer should have a good thermal conductivity. at the same time, ultrasonic lead bonding technology is used to interconnect the chips and the external components. efficient heat dissipation is achieved by the proper arrangement of the igbt chip and the freewheeling diode. figure 1: igbt power module package structure diagram during the operating state, frequent switching or external environment causes the internal temperature variation inside the sic-igbt power modules. due to the mismatch of the coefficients of thermal expansion between silicon carbide, copper, ceramics, etc., and the geometrical constraint between each other in the package, the temperature change leads to the warp cu base plate base plate solder ceramic layers cu cu chip solder sic-igbt silica gel tim1 tim2 f d.-h. zhang et alii, frattura ed integrità strutturale, 55 (2021) 316-326; doi: 10.3221/igf-esis.55.24 318 and warpback of the package body. as a visco-elastic intermediate layer, the solder layer always undergoes a great cyclic shear stress and creep strain, resulting in the thermal fatigue cracking of the solder layer. therefore, the thermal fatigue behavior which caused by environment temperature has become a key issue in the reliability of sic-igbt power modules. creep constitutive model of sn3ag0.5cu. according to the viscoelastic theory, the typical strain rate-stress relationship of sn3ag0.5cu solder is linear at low stress, and power law creep at middle and high stresses. on the basis of the previous literature [17, 18], a hyperbolic sine power constitutive model is adopted, in which the relationship of strain rate with stress is linear at low stress and is hyperbolic sine power at the middle and high stresses, as shown in eq. (1). at each temperature t, there exists a critical stress σv (t), which is used to separate the linear and power law creep stages. according to the creep results of two solder materials sn3ag0.5cu and pb5sn, the strain rates under various stress levels and temperature-dependent σv are determined as follows: ( ) n v 0 v q a bσ σ > σ rt ε = q a σ σ σ rt                   sinh exp when exp when （1） in which ( ) ( ) = + 2 0 1 2-v r rc c t t c t t （2） where v  is the linear creep limit, which is the cut-off point between linear and power creep, t is the absolute temperature, q is the activation energy, r is the universal gas constant,  is the equivalent stress, tr is 273 k. for sn3ag0.5cu solder, q/r=12993, n=5.85, b=0.145mpa-1, c0=17.357 mpa, c1=0.1219 mpa.k-1, c2=2.457×10-4 mpa.k-2, a=2.039×10-4 s-1, and a0=2.039×10-4 mpa-1.s-1 [9]. material elastic modulus gpa poisson’s ratio coefficient of thermal expansion 10-6 /k coefficient of heat transfer w/(m.k) specific heat j/(kg.k) density kg/m3 cu 110 0.34 16.4 398 385 8590 alo 300 0.22 6.4 25 880 3800 sic chip 400 0.14 4.2 150 700 3210 sn3ag0.5cu 42.8 0.35 21.5 57 217 7390 table 1: the mechanical property of the sic-igbt power module. fe model of sic-igbt the finite element method is used to study the cyclic stress-strain behavior of a single-chip structure intercepted in the sicigbt power module during thermal cycles. since the operating temperature of sic is higher than that of si material, the temperature cycle shown in fig. 2 was adopted in the thermomechanical simulation of sic-igbt power module. in order to reduce the amount of calculation, 1/4 three-dimensional model, shown in fig. 3, was established due to the structural symmetry of a single chip. a fixed constraint is applied at the bottom center point, and a symmetric boundary condition is applied to the symmetric plane. the sample is initially placed in a temperature field of 25℃, and then the cycle temperature is applied to the surface of the power module. the size of the power module is as follows. the size of silicon carbide chip is 10 10 0.18mm, tim1 is 10 10  0.1mm, the size of copper layer between the chip and dbc substrate is 15 15 0.3mm, the size of middle alumina is 17 17 0.38mm, the size of copper layer under middle alumina is 15 15 0.15mm, tim2 is 15 15 0.2mm, and the size of the bottom copper substrate is 30 30 3mm, and the related material constants d.-h. zhang et alii, frattura ed integrità strutturale, 55 (2021) 316-326; doi: 10.3221/igf-esis.55.24 319 are shown in tabs. 1-2. the symmetric constraints were applied in the x and y directions, and the z direction nodal displacement was restricted at the bottom surface of the model. the cyclic temperature was loaded at the exterior surface of the power module. temperature ℃ elastic modulus/ gpa poisson’s ratio coefficient of thermal expansion 10-6 /k coefficient of heat transfer w/(m.k) specific heat j/(kg.k) density kg/m3 yield strength -75 54.311 0.35 9.8 57 217 7390 57.568 -25 48.392 15.9 41.253 25 42.892 21.5 29.00 75 37.811 22 20.82 125 33.148 22.7 16.98 175 28.903 23.6 16.64 table 2: thermomechanical property of sn3ag0.5cu. figure 2: cyclic temperatures in thermal fatigue figure 3: the 1/4 fe model thot=175℃ tcold=-55℃ 10℃/min chip solder(tim1) silica gel sic igbt cu cu base plate solder(tim2) cu d.-h. zhang et alii, frattura ed integrità strutturale, 55 (2021) 316-326; doi: 10.3221/igf-esis.55.24 320 the sic-igbt model was divided into a series of three dimensional 8-node reduced integration (c3d8r) elements. to select a suitable mesh density, we firstly conducted the reconstructed the convergence analysis of finite element model. fig. 4 (a) –(c) illustrate the stress distribution in the solder layers with the coarse, medium and fine mesh, respectively. a comparison of the stresses shows that the results corresponding to the fine mesh presented in fig. 4 are the most satisfactory. therefore, this mesh density is selected in the following calculations, and the minimum mesh size at the interface of solder layer is refined to 0.01 × 0.01 × 0.002 mm. to verify the reliability of the finite element simulation, the igbt in xu’s work [19], which has the same dimension, material properties and loading condition as our model and but different chip material (sic replaced by si) is established and the typical creep strain accumulation at the elements which has the maximum creep strain are demonstrated in fig. 5 for comparison. it can be seen that the strain accumulations of tim1 and tim2 in our analysis has good agreement with xu’s result, indicating the analysis credibility of our finite element model. figure 4: convergence of stresses in the solder layers: (a) stress contours of coarse mesh, (b) stress contours of medium density mesh, (c) stress contours of fine mesh. figure 5: accumulated creep strain fe analysis results fig. 6 illustrates the overall temperature and mises stress distribution of sic-igbt the maximum stress moment after ten thermal cycles. the maximum stress is located on the chip itself. however, due to creep properties and structural reasons, the failure of solder layer is what we focus on. fig. 7 shows the mises stress distribution in the tim2 layer, the stresses at the corners are significantly higher than that in other positions. it may be caused by the interfacial effect in the solder layer near the interface. although the maximum mises stress in the solder does not exceed its yield strength which was showed in tab. 2, the creep viscoelasticity that the material exhibits, will lead to the strain accumulation of elements in the solder layer. once the accumulative creep strain exceed the critical strain, the element fails and the micro crack nucleates from the corner at the solder-chip or solder-substrate interface. the facts also proved that the thermal fatigue failure generally initiates from the corner of solder layer connected with the chip or substrate [9, 10]. (a) (c)(b) d.-h. zhang et alii, frattura ed integrità strutturale, 55 (2021) 316-326; doi: 10.3221/igf-esis.55.24 321 figure 6: stress distribution of 1/4 sic-igbt power module. figure 7: the stress distribution of tim2 solder layer fig. 8 shows the temperature and mises stress time history in the corner elements e1 and e2 at tim1 and tim2 layers, which are shown in fig. 6, in first 10 temperature cycles. due to the good thermal conduction capacity, the temperatures at elements e1 and e2 are almost same to the environmental temperature. there is a clear time lag between the stress history and environmental temperature history, which may attribute to the fact that it cost a little time for the creep strain of the solder accumulating to its maximum. the stress straights up at the heating process. subsequently, the stress decreases nonlinearly due to stress relaxation and form a transient platform during the high temperature holding process. in the cooling stage, the stress decreases rapidly and reaches its minimum. it can be seen that the stress histories at the e1 and e2 are almost the same, although the maximum stress at e2 is relatively larger. tim2 layer has a larger size and the stronger constraint on the deformation induced by thermal cycles, in other words, the effect of thermal deformation mismatch at tim2 layer is more prominent. figure 8: mises stress time history of the elements e1 and e2. selected corner elements e1and e2 at thetim1 and tim2 tim2 tim1 tim2 tim1 d.-h. zhang et alii, frattura ed integrità strutturale, 55 (2021) 316-326; doi: 10.3221/igf-esis.55.24 322 figure 9: shear stress distribution in the solder layer. figure 10: shear strain distribution in the solder layer. (a) (b) figure 11: shear stress-strain of element e2 at tim2 solder layer: (a) stress, (b) strain. figs. 9-10 show the distribution of the maximum shear stress and shear strain of tim1 and tim2 layers, respectively. whether in tim1 and tim2, the shear stress at the up surface is higher than that in the down surface, which may induce down down up up base plate solder（tim2） chip solder（tim1） updown updown chip solder（tim1） base plate solder（tim2） d.-h. zhang et alii, frattura ed integrità strutturale, 55 (2021) 316-326; doi: 10.3221/igf-esis.55.24 323 slight shear warpages in the solder layers. although the maximum shear stress in tim1 and tim2 layers are about the same, the maximum shear strain in tim2 is far higher than that in tim1. the fact indicates that the sic-igbt may fail from tim2 if the shear strain is the main failure mechanism. fig. 11 shows the time history of shear strain and shear stress of element e2 at tim2 solder layer. whether shear stress and shear strain exhibit good periodicities, which is consistent with the temperature cycle. the maximum shear stress in heating and cooling process both maintain unchanged. however, it is obvious that the shear strain gradually accumulates with the temperature cycles, which is related to the creep characteristics of the solder itself. fatigue life prediction number of thermomechanical fatigue life prediction models have been developed for the sn3ag0.5cu solder joint [20], 17]. according to the creep mechanism, the coffin-manson based engelmaier model [21], the accumulated creep strain based model and accumulated creep strain energy density based model, proposed by syed [12, 24], were adopted to evaluate the thermal fatigue life, respectively. engelmaier model considers the effect of frequency and temperature amplitude on fatigue life, and its formula follows:       1/α f f 1 δ n = 2 2ε （3） where nf is the fatigue life of the weld layer, δϒ is the range of shear strain within one cycle, εf is the fatigue ductility coefficient of the solder, α is the fatigue ductility index of the solder related to the frequency and amplitude of cycling temperature, which is expressed as follows:       0 1 sj 2 dwell 360 α=λ +λ t +λ ln 1+ t （4） where tsj is the average cyclical temperature of the solder layer, tdwell is the holding time of high and low temperature, λ0, λ1 and λ2 are the material constants. for sn3ag0.5cu solder, λ0=-0.367, λ1=-9.69×10-4, λ2=2.21×10-2 [23]. accordingly, the accumulated creep strain based life model could be described by the following equation:  / -1 f accn = (c δ ) （5） where δεacc is the accumulated creep strain per cycle, c/ is the inverse of creep ductility, c/=0.0405 for sn3ag0.5cu material . if the accumulated creep strain energy density is adopted as the key parameter which controls the thermal fatigue failure, the life prediction model could be simplified as / -1 f accn = (w δ )w （6） where δwacc is the accumulated creep strain energy density per cycle, w/ is the creep energy density for failure, w/=0.0014 [22]. fig. 12 shows the shear stress-strain hysteresis curve of element e2 at tim2 solder layer. as the temperature cycles increases, the hysteresis curve gradually tends to coincide, i.e., the dissipated energy in every cycle reaches a steady state. the average shear strain range δϒ of tim2 is 0.0378. fig. 13 shows the creep strain and creep energy density curve of tim2 solder layer. the creep strain and strain energy density increase gradually with temperature cycling. the calculated creep strain increment δεacc and strain energy increment δwacc per cycle are 0.047 and 2.572 j, respectively. the predicted thermal fatigue life of tim2 by different models are listed in tab. 3, respectively, and the relative errors among three models are also listed for comparison. it can be seen that the predicted results from the engelmaier model and creep strain energy density model are almost the same, and the thermal fatigue life from creep strain model is relatively shorter. but on the whole, the prediction results of these three models are acceptable. a d.-h. zhang et alii, frattura ed integrità strutturale, 55 (2021) 316-326; doi: 10.3221/igf-esis.55.24 324 figure 12: cyclic stress/strain curves of solder layer tim2 figure 13: accumulated creep strain and creep dissipation energy density distribution in solder join per cycle theoretical model predicted results relative error (%) engelmaier model 325 18.6 creep strain model 274 17.0 creep strain energy density model 330 table 3: the predicted fatigue life of the tim2 layer in sic-igbt power module. conclusion n this paper, the finite element thermomechanical model of sic-igbt power module was established, and the cyclical stress-strain distribution and creep behavior of the sn3ag0.5cu solder layers was obtained under -55 oc~175 oc cyclic ambient temperature loading. consequently, according to the obtained range of shear strain, accumulated creep strain and creep strain energy density at the corner point of the solder layer, the corresponding thermal fatigue lives were determined by engelmaier model, creep strain model and creep strain energy density model, respectively. the comparisons of the predicted lives indicate that the thermal fatigue lives predicted are in an acceptable agreement. the proposed constitutive model of sn3ag0.5cu solder and the fe-based thermal fatigue evaluation for the sic-igbt power module is feasible. acknowledgment he research work was supported by the national natural science foundation of china (no. 11972376), the national natural science foundation of shandong province (no. zr201910250083) and the fundamental research funds for the central universities of china (no.20cx02308a). wacc acc  i t d.-h. zhang et alii, frattura ed integrità strutturale, 55 (2021) 316-326; doi: 10.3221/igf-esis.55.24 325 references [1] han, l., liang, l., kang, y., qiu, y. (2021). a review of sic igbt: models, fabrications, characteristics, and applications. ieee transactions on power electronics, 36(2), pp. 2080-93. doi: 10.1109/tpel.2020.3005940. [2] he, p.z., zheng, l.b., fang, h.c., wang, c.l., hua, j. (2013). investigation of the temperature character of igbt failure mode based the 3-d thermal-electro coupling fem. advanced materials research, 655-657, pp.1576-1580. doi: 10.4028/www.scientific.net/amr.655-657.1576. [3] ren, n., hu, h., lyu, x.f., wu, j.p., xu, h.y., li, r.g., zuo, z., wang, k., sheng, k. (2019). investigation on single pulse avalanche failure of sic mosfet and si igbt. solid-state electronics, 152, pp. 33-40. doi: 10.1016/j.sse.2018.11.010. [4] wright, n.g., horsfall, a.b., vassilevski, k. (2008). prospects for sic electronics and sensors. materials today, 11(12), pp.16-21. doi:10.1016/s1369-7021(07)70348-6. [5] nawaz, m., chimento, f. (2013). on the assessment of temperature dependence of 10–20 k v 4h–sic igbts using tcad. mater sci forum,740–742, pp.1085–8. doi: 10.4028/www.scientific.net/msf.740-742.1085. [6] madhusoodhanan, s., mainali, k., tripathi, a., kadavelugu, a., patel, d., bhattacharya s. (2016). power loss analysis of medium voltage three-phase converters using 15 kv/40 a sic n-igbt. ieee journal of emerging and selected topics in power electronics, 4(3), pp.901-917. doi:10.1109/jestpe.2016.2587666. [7] choi, u., blaabjerg, f., lee, k. (2015). study and handing methods of power igbt module failures in power electronic converter systems. ieee transaction on power electronics, 30 (5), pp.2517-2533. doi:10.1109/tpel.2014.2373390. [8] rashid, m. h. (2003). power electronics: circuits, devices, and applications. pearson education india. [9] huang, x.g. (2019). simulation on the interfacial singular stress-strain induced cracking of microelectronic chip under power on-off cycles. journal of microelectronics, electronic components and materials, 49 (2), pp.69-77. doi: 10.33180/infmidem2019.203. [10] huang, x.g., wang, zq. (2020). thermal fatigue evaluation model of a microelectronic chip in terms of interfacial singularity. journal of electronic package, 142(011013), pp, 1-9. doi: 10.1115/1.4045255. [11] knecht, s., fox, l.r. (1990). constitutive relation and creep–fatigue life model for eutectic tin-lead solder. ieee transactions on components hybrids and manufacturing technology, 13, pp.424–33. doi: 10.1109/33.56179. [12] syed, a.r. (2004). accumulated creep strain and energy density based thermal fatigue life prediction models for snagcu solder joints. in the 54th electronic components and technology conference, pp. 737–746. [13] choi, u-m., blaabjerg, f., jorgensen, s. (2017). study on effect of junction temperature swing duration on lifetime of transfer molded power igbt modules. ieee transactions on power electronics, 32(8), pp. 6434-6443. doi: 10.1109/tpel.2016.2618917. [14] zhu, y., li, x., wang c., gao, r. (2015). a new creep–fatigue life model of lead-free solder joint. microelectronics reliability, 55(7), pp.1097-100. doi: 10.1016/j.microrel.2015.03.019. [15] elakkiya, r., kavithaa, g., samavatian, v., alhaifi, k., kokabi, a., moayedi, h. (2020). reliability enhancement of a power semiconductor with optimized solder layer thickness. ieee transactions on power electronics, 35(6), pp.63976404. doi: 10.1109/tpel.2019.2951815. [16] samavatian, v., iman-eini, h., avenas, y., samavatian, m. (2020). effects of creep failure mechanisms on thermomechanical reliability of solder joints in power semiconductors. ieee transactions on power electronics, 35(9), pp. 8956-8964. doi: 10.1109/tpel.2020.2973312. [17] kim, j.w., kim, d.g., jung, s.b. (2006). evaluation of displacement rate effect in shear test of sn-3ag-0.5cu solder bump for flip chip application. microelectronics reliability, 46, pp.535-542. doi: 10.1016/j.microrel.2005.06.008. [18] zhang, y.m., zhu, h.l., fujiwara, m., xu, j.q., dao, m. (2013). low-temperature creep of snpb and snagcu solder alloys and reliability prediction in electronic packaging modules. scripta materialia, 68, pp. 607–610. doi: 10.1016/j.scriptamat.2012.12.017. [19] xu, l. (2016). research on reliability of igbt power module packaging. wuhan: doctoral dissertation of huazhong university of science and technology. (in chinese) [20] wiese, s., meusel, e. (2003). characterization of lead-free solders in flip chip joints. journal of electronic packaging, 125 (4), pp. 531-538. doi:10.1115/1.1604155. [21] chauhan, p., pecht, m., osterman, m., leer, s.w.r. (2009). critical review of the engelmaier model for solder joint creep fatigue reliability. ieee transactions on components & packaging technologies, 32(3), pp.693-700. d.-h. zhang et alii, frattura ed integrità strutturale, 55 (2021) 316-326; doi: 10.3221/igf-esis.55.24 326 doi: 10.1109/tcapt.2009.2030983. [22] syed, a.r. (1997). aces of finite element and life prediction models for solders and solder interconnections. in the symposium on the tms conference, pp. 347–355. [23] chai, f., osterman, m., pecht, m. (2014). strain-range-based solder life predictions under temperature cycling with varying amplitude and mean. ieee transactions on device and materials reliability, 14(1), pp.351-357. doi: 10.1109/tdmr.2013.2273121. microsoft word numero_38_art_36 n.o. larrosa et alii, frattura ed integrità strutturale, 38 (2016) 266-272; doi: 10.3221/igf-esis.38.36 266 focussed on multiaxial fatigue and fracture ductile fracture modelling and j-q fracture mechanics: a constraint based fracture assessment approach n.o. larrosa, r.a. ainsworth the university of manchester, manchester m13 9pl, uk nicolas.larrosa@manchester.ac.uk abstract. the reduced state of stress triaxiality observed in shallow cracked components allows an increased capacity to resist crack propagation compared to that observed in deeply cracked specimens. this may be regarded as a higher fracture toughness value which allows a reduction in the inherent conservatism when assessing components in low constraint conditions. this study uses a two-parameter fracture mechanics approach (jq) to quantify the level of constraint in a component (e.g. a pipe with a surface crack) and in fracture test specimens, i.e. single edge tension [se(t]) and compact tension [c(t)] specimens, of varying constraint level. the level of constraint of the component is matched to a specific test specimen and therefore the ability of the structure to resist fracture is given by the fracture toughness of the test specimen with a similar j-q response. fracture toughness values for different specimens have been obtained from tearing resistance curves (j-r curves) constructed by means of a virtual testing framework. the proposed engineering approach shows that the combination of a local approach and two-parameter fracture mechanics can be used as a platform to perform more accurate fracture assessments of defects in structures with reduced constraint conditions. keywords. crack tip constraint; ductile fracture modelling; j-q fracture mechanics. citation: larrosa, n.o., ainsworth, r.a., ductile fracture modelling and j-q fracture mechanics: a constraint based fracture assessment approach., frattura ed integrità strutturale, 38 (2016) 266-272. received: 21.04.2016 accepted: 01.06.2016 published: 01.10.2016 copyright: © 2016 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. introduction n structural integrity assessments, the fracture toughness value used to determine the onset of fracture, kmat, is commonly derived from deeply cracked specimens with almost square ligaments, using recommended testing standards and validity criteria (e.g. astm e1820 [1] and esis-p2 [2]). these are designed to ensure high constraint conditions near the crack tip that correspond to lower-bound toughness values independent of specimen size and geometry. there exist cases in which low constraint conditions can be demonstrated. for example, in the oil and gas (o&g) industry, during installation, pipeline girth welds are predominantly loaded in tension even if the pipe is globally subjected to bending. the flaw sizes of interest are usually controlled by the weld pass height and are therefore relatively small, i n.o. larrosa et alii, frattura ed integrità strutturale, 38 (2016) 266-272; doi: 10.3221/igf-esis.38.36 267 typically 2-6 mm in height [3]. both these aspects result in reduced crack tip constraint in the component compared to the deeply notched standard specimens. furthermore, there is experimental evidence showing that panels loaded in tension exhibit higher resistance to fracture since these conditions lead to lower constraint around the crack [4]. as a result, in these cases, the material capacity to withstand load is underestimated and it would be useful to perform assessments with a fracture resistance value obtained from a test specimen with a crack tip constraint condition similar to that in the actual component [5]. materials can exhibit a change in toughness with specimen geometry for both cleavage and ductile fracture modes. here, attention is focussed on ductile crack propagation behaviour (microvoid coalescence). a ductile fracture simulation approach has been implemented in previous work [6,7] to evaluate the fracture resistance curves (j-r) for different test specimens. although these procedures are useful tools to evaluate fracture resistance for structural components, the development and calibration of the finite element assessment (fea) model requires extensive expertise and the application of the procedures becomes prohibitive for routine assessments. an alternative framework is then of interest for more rapid assessments. the j–q two-parameter fracture mechanics [8,9] approach has been extensively used to characterize elastic–plastic crack front fields. the parameter q characterizes the degree of crack tip constraint, by quantifying the level of deviation of stress/strain fields from reference fields. in this work, we conduct investigations on the j-q two parameter characterisation approach to compare the constraint conditions of a pipe under different loading modes with those observed in c(t) and se(t) specimens. the aim of this is to support the use of a low constraint fracture toughness value by showing that at the same applied driving force (j), the level of constraint (q) at the pipe is similar to that in the se(t) specimen. theoretical background two parameter j-q theory n small-scale yielding, there is always a zone of single parameter (k, j, ctod) dominance. the crack-tip conditions are fully defined by the single parameter, whose value depends on load, crack size and geometry. the situation changes as plasticity develops when the loss of constraint becomes apparent (e.g., fully plastic response or shallow cracks), and single parameter dominance does not hold. under these circumstances, the stresses near the crack tip are not given by the single parameter but also depend on the configuration (loading type, geometry and material properties). in low constraint geometries the near tip stress distribution can be significantly lower than the high constraint j-dominant state. the j-q approach to elastic-plastic fracture mechanics was introduced to remove some of the conservatism inherent in the single parameter approach based on the j integral. the following equation provides an approximate description of the near tip stress field, over physically significant distances [8,9]: ref ijij ij q 0   (1) where ij is the kronecker delta, 0 is the yield stress and ref ij is a reference field, often taken as the hrr field, the near crack tip fields for power-law plastic materials derived in [10,11]. thus, the q-factor quantifies the difference between the actual local stress at a certain reference location near the crack tip and the theoretical hrr-stress field and is given by: ref ij ij q 0 -    (2) the actual stress field in a component and the hrr field in the forward sector of the crack-tip region differ by an approximately uniform hydrostatic stress independently of distance from the crack tip, for given values of j [8,9]. therefore, eq (1) means that with the addition of the second parameter, a range of stress states can be obtained at a fixed deformation level (as characterised by j), differing by a hydrostatic stress (as characterised by q). in practice, the stress field is more complex than eq. (1) but this simplification has been found to apply for the region at the crack tip where [8,9], corresponding to the near crack tip zone where the fracture process zone (fpz) for both cleavage and ductile i n.o. larrosa et alii, frattura ed integrità strutturale, 38 (2016) 266-272; doi: 10.3221/igf-esis.38.36 268 fracture is active but outside the area where crack blunting becomes significant. negative q values indicate lower constraint conditions compared to the reference field and positive q values higher constraint conditions. a local approach to ductile fracture an alternative framework for constraint analyses and effective fracture toughness assessment is the application of failure models, often referred to as local approaches. local approaches couple the loading history (stress-strain) near the crack-tip region with micro-structural features of the fracture mechanisms involved [12]. since the fracture event is described locally, the mechanical factors affecting fracture are included in the predictions of the model. the parameters depend only on the material and not on the geometry, and this leads to improved transferability from specimens to structures than oneand two-parameter fracture mechanics methods [13]. a fracture model accounting for the ductile damage processes has been used to quantify the increased resistance of blunt defects relative to sharp ones and to demonstrate that a loss of constraint leads to an increase in the fracture properties of these materials. a phenomenological model [14] based on a stress modified fracture strain concept was used in [6,7] to construct j-r curves of notched compact tension c(t) and single edge tension se(t). it has been demonstrated that true fracture strain for ductile materials is strongly dependent on the level of stress triaxiality [15-17]. the model used in this study therefore uses an exponential relationship between the true fracture strain, f , and stress triaxiality: m e f exp -=             (3) where and  are material constants obtained by fitting test data for smooth and notched bars and the triaxiality is: m e e 1 2 3 3         (4) where σi (i=1-3) are principal stresses and σe is the von mises stress. using a fe analysis technique, this model is implemented in a step-by step procedure in which at each loading step, the incremental damage, ∆ω, produced by incremental strain is assessed and added to the total damage, ω, produced in previous steps. the quantification of the incremental damage definition is performed in each finite element of the model as follows: p e i i i i i f , 1 ; =             (5) where pi is the equivalent plastic strain increment and f is determined by the local triaxiality in the element using eq. (3). when the total damage becomes equal to unity (ω=1), local failure is assumed to occur at the element and the initiation and propagation of a crack is simulated by reducing all the stress components to a sufficiently small value to make the contribution of the element to the resistance of the component negligible. it should be noted that this local approach with the simulation procedure briefly summarised above has been verified by comparison with experimental data on fracture toughness test specimens and pressurised pipes which serves as validation for this purpose. all material constants in eq. (3) with the crack tip element size for the material and tensile properties used in this study were determined by the procedure and also verified with experimental data. more details on the numerical implementation of the model can be found in [6,7,18]. finite element analysis shallow cracked se(t) specimen and a deeply cracked c(t) specimen were modelled by means of 3-d finite elements. the relevant dimensions of these specimens and the pipe component assessed in this work are shown in fig. 1. the material properties used in the numerical models are for an api x65 steel used in [6,19]. a n.o. larrosa et alii, frattura ed integrità strutturale, 38 (2016) 266-272; doi: 10.3221/igf-esis.38.36 269 fig. 2 shows the fe models. due to symmetric conditions of loading and geometry a quarter of c(t) and se(t) specimens were modelled, to improve computational efficiency. one half of the pipe was modelled in order to be able to apply pure bending. in [6], it was shown that element size in the defect section affects the results for the damage accumulation process; therefore, this value must be determined by comparison with experimental results. for api x65, the element size is 0.15mm [6]. the material constants to apply the fracture criterion of eq. (3) for api x65, based on the defined element size are =3.29, = -1.54 and γ=0.01. the damage model is implemented within c3d8 hexahedron solid elements using the abaqus uhard and usdfld user-defined subroutines [20] coded in fortran 90. the total numbers of elements/nodes in the fe models are from 23,366/26,016, 82,520/88,929 and 117,595/130,416 for the se(t) specimen, c(t) specimen and the pipe, respectively. (a) (b) (c) figure 1: schematic illustration of fracture toughness specimens showing the dimensions: (a) c(t) specimen; (b) se(t) specimen; (c) pipe with surface circumferential crack. (a) (b) (c) figure 2. finite element models: (a) c(t) specimen; (b) se(t) specimen; (c) pipe with surface circumferential crack. n.o. larrosa et alii, frattura ed integrità strutturale, 38 (2016) 266-272; doi: 10.3221/igf-esis.38.36 270 results he numerical j-r curves obtained by the implementation of the damage model are shown in fig. 3. a standard deeply cracked c(t) specimen and a shallow cracked se(t) specimen are modelled. the use of the esis p2 procedure [2] for the estimation of the effective initiation fracture toughness is illustrated. next, the j-q approach is applied to the pipe component for internal pressure and pure bending in order to show the effect of the loading mode on constraint level. in general, the value of q depends on load magnitude (and therefore on j) as well as loading mode, being proportional to load in small-scale yielding but weakly dependent on j at large loads. the values of q have therefore been evaluated at applied j values, see fig. 4, for the pipe at loads which cover the range of j at initiation in c(t) and se(t) specimens. it can be seen that at these values, the stress fields in the pipe when plotted against normalised distance are weakly dependent on j. hence, q is also weakly dependent on j in this practical range. it can then be assumed that the pipe would have the same effective initiation toughness as a specimen with the same j-q value. for fracture assessments where it is not possible to match the q value of the pipe with that of a test specimen, the specimen with the closest higher value of q will be a conservative choice. the q-stress is generally evaluated at the distance r = 2j/σ0 from the crack tip and using the opening stress obtained by detailed finite element analysis, eq. (2). the reference field in eq. (1) is obtained from a boundary layer analysis at the same applied j with t=0, as this enables the approach to be applied to materials which do not follow the power-law form which enables the hrr field to be used as the reference field in eq. (1). 0.0 0.2 0.4 0.6 0.8 1.0 0 200 400 600 800 1000 1200 e s is -p 2 ( j 0 .2 ) domain integral c(t), a o /w=0.5 se(t), a o /w=0.2 jin te g ra l (k j/ m 2 ) a(mm) api x65 jse(t) 0.2 jc(t) 0.2 figure 3. j-r curves of shallow cracked se(t) and deeply cracked c(t) specimens. fig. 4 shows the normalised values of the crack tip opening stress field for the test specimens, the pipe component under two loading types and the modified boundary layer model. it is readily observed from the figure that, from all the components assessed here, the severest stress field is that of the c(t) specimen. the vertical distance from any of the curves to the mbl curve gives the value of q. as the stress field in the se(t) specimen is greater than that in the pipe for both loading conditions (more negative value of q), can be used as a conservative critical value for crack initiation for the pipe under either loading condition for the crack size assessed. conclusions rack size, loading mode and material properties can have a strong effect on constraint conditions, affecting the material resistance to fracture. in this work, finite element ductile fracture simulation has been used to construct j-r curves for 2 test specimens with different constraint conditions. the ductile fracture model only considers a small area ahead of the crack tip t c n.o. larrosa et alii, frattura ed integrità strutturale, 38 (2016) 266-272; doi: 10.3221/igf-esis.38.36 271 (geometry independent) and couples the loading history (stress-strain) with phenomenological features of the microstructural fracture mechanism (material + loading history dependent). in addition, a two parameter fracture mechanics approach has been applied to match the constraint conditions present in a defective structural component to those present in the test specimens. by doing this, the j-q approach allows an improved assessment of the fracture resistance of the component, by using the fracture resistance of the test specimen with similar constraint conditions to reduce over-conservatism in fracture assessments c(t), j 0.2 =477.62 kj/m2 se(t), j 0.2 =653.28 kj/m2 mbl, t=0 j=653.28 kj/m2, internal pressure (p) j=477.62 kj/m2, internal pressure (p) j=653.28 kj/m2, pure bending (m) j=477.62 kj/m2, pure bending (m) 1 2 3 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5 6.0 q pipe (m) q pipe (p) q se(t) api x65 r 0 /j / 0 q c(t) figure 4. normalized crack-opening stress distribution for the different components. acknowledgements he authors would like to acknowledge the funding and technical support from bp through the bp international centre for advanced materials (bp-icam) which made this research possible. references [1] astm e1820-06a, american society for testing and materials. standard test method for measurement of fracture toughness (2001). [2] esis p2-92: procedure for determining the fracture behaviour of materials (1992). [3] dnv-rp-f108, det norske veritas: fracture control for pipeline installation methods introducing cyclic plastic strain (2006). [4] anderson, t.l., fracture mechanics: fundamentals and applications. crc press, taylor & francis, boca raton, florida, usa, (1995). [5] cravero, s., ruggieri, c., correlation of fracture behaviour in high pressure pipelines with axial flaws using constraint designed test specimens part i: plane-strain analyses, engineering fracture mechanics, 72 (2005) 1344–1360. [6] oh, c.-s., kim, n.-h., kim, y.-j., baek, j.-h., kim, y.-p., kim, w.-s., a finite element ductile failure simulation method using stress-modified fracture strain model, engineering fracture mechanics, 78 (2011) 124–137. [7] han, j.-j., kim, y.-j., ainsworth, r.a., constraint effects in ductile fracture on j-resistance curve for full-scale cracked pipes and fracture toughness testing specimens. american society of mechanical engineers, pressure vessels and piping division, 5 (2014). [8] o’dowd, n.p., shih, c.f., family of crack-tip fields characterized by a triaxiality parameter-i: structure of fields, journal of the mechanics and physics of solids, 39 (1991) 989–1015. t n.o. larrosa et alii, frattura ed integrità strutturale, 38 (2016) 266-272; doi: 10.3221/igf-esis.38.36 272 [9] o’dowd, n.p., shih, c.f., family of crack-tip fields characterized by a triaxiality parameter-ii: fracture applications, journal of the mechanics and physics of solids, 40 (1992) 939–963. [10] hutchinson, j.w., singular behaviour at the end of a tensile crack tip in a hardening material, journal of the mechanics and physics of solids, 16 (1968) 13–31. [11] rice, j.r., rosengren, g.f., plane strain deformation near a crack tip in a power-law hardening material. journal of the mechanics and physics of solids, 16 (1968) 1–12. [12] pineau, a., development of the local approach to fracture over the past 25 years: theory and applications, international journal of fracture, 138 (2006) 39–166. [13] ruggieri, c., dodds jr, r.h., a transferability model for brittle fracture including constraint and ductile tearing effects: a probabilistic approach, international journal of fracture, 79 (1996) 309–340. [14] bao, y, dependence of ductile crack formation in tensile tests on stress triaxiality, stress and strain ratios, engineering fracture mechanics, 72 (2005) 505– 522. [15] mcclintock, f.a., a criterion for ductile fracture by the growth of holes. journal of applied mechanics, 35 (1968) 363–371. [16] rice, j.r., tracey, d. m., on the ductile enlargement of voids in triaxial stress fields. journal of the mechanics and physics of solids, 17(3) (1969) 201–217. [17] hancock, j.w., mackenzie, a.c., on the mechanisms of ductile failure in high-strength steels subjected to multi-axial stress-states, journal of the mechanics and physics of solids, 24 (1976) 147–160. [18] kim, y.-j., kim, j.-s., cho, s.-m.,kim, y.-j., 3-d constraint effects on j testing and crack tip constraint in m(t), se(b), se(t) and c(t) specimens: numerical study, engineering fracture mechanics, 71 (2004) 1203–1218. [19] han, j-j., larrosa, n.o., kim, y-j., ainsworth, r.a., blunt defect assessment in the framework of the failure assessment diagram. international journal of pressure vessels and piping, (2016) submitted. 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/hrv (za stvaranje adobe pdf dokumenata najpogodnijih za visokokvalitetni ispis prije tiskanja koristite ove postavke. stvoreni pdf dokumenti mogu se otvoriti acrobat i adobe reader 5.0 i kasnijim verzijama.) /hun 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can be opened with acrobat and adobe reader 5.0 and later.) >> /namespace [ (adobe) (common) (1.0) ] /othernamespaces [ << /asreaderspreads false /cropimagestoframes true /errorcontrol /warnandcontinue /flattenerignorespreadoverrides false /includeguidesgrids false /includenonprinting false /includeslug false /namespace [ (adobe) (indesign) (4.0) ] /omitplacedbitmaps false /omitplacedeps false /omitplacedpdf false /simulateoverprint /legacy >> << /addbleedmarks false /addcolorbars false /addcropmarks false /addpageinfo false /addregmarks false /convertcolors /converttocmyk /destinationprofilename () /destinationprofileselector /documentcmyk /downsample16bitimages true /flattenerpreset << /presetselector /mediumresolution >> /formelements false /generatestructure false /includebookmarks false /includehyperlinks false /includeinteractive false /includelayers false /includeprofiles false /multimediahandling /useobjectsettings /namespace [ (adobe) (creativesuite) (2.0) ] /pdfxoutputintentprofileselector /documentcmyk /preserveediting true /untaggedcmykhandling /leaveuntagged /untaggedrgbhandling /usedocumentprofile /usedocumentbleed false >> ] >> setdistillerparams << /hwresolution [2400 2400] /pagesize [612.000 792.000] >> setpagedevice shot peening processes to obtain nanocrystalline surfaces in metal alloys: p. jinlong et alii, frattura ed integrità strutturale, 54 (2020) 169-181; doi: 10.3221/igf-esis.54.12 169 numerical analysis of circular and square concrete filled aluminum tubes under axial compression pan jinlong, li guanhua, cai jingming* southeast university, china cejlpan@seu.edu.cn, guanhuali1997@gmail.com, https://orcid.org/0000-0003-2235-1402 jingming.cai@kuleuven.be, https://orcid.org/0000-0003-2453-582x abstract. in this paper, the finite element (fe) method was used to investigate the axial compressive behaviors of circular and square concrete filled aluminum tubes (cfat). firstly, the simulation results were compared with the experimental results and the accuracy of the proposed fe model was verified. on this basis, the fe model was further applied to compare the mechanical properties of both circular and square cfats under axial compression. it was found that the circular cfats have a better effect on restraining the core concrete than square cfats. the parametric analysis was also conducted based on the proposed fe model. it was noticed that the mechanical differences of the two kinds of cfats gradually decreased with the increase of the aluminum ratio, aluminum strength and concrete strength. keywords. cfat; numerical simulation; finite element analysis; parameter analysis. citation: jinlong, p., guanhua, l., jingming, c., numerical analysis of circular and square concrete filled aluminum tubes under axial compression, frattura ed integrità strutturale, 54 (2020) 169-181. received: 28.05.2020 accepted: 24.08.2020 published: 01.10.2020 copyright: © 2020 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. introduction oncrete filled steel tube (cfst) has favorable ductility, high strength and energy dissipation performance because of the constraint effect of steel tube on the core concrete [1]. the aluminum alloy has good corrosion resistance and prominent exterior, which makes the aluminum tube column have been gradually used in the construction of humid and corrosive environment [2,3]. similar to cfst, concrete filled aluminum tube (cfat) is expected to have an excellent restraining effect on core concrete. among the many sections of cfat, circular section and square section are the most typical. circular section cfat has better confinement to the core concrete, while square section cfat is prone to local buckling. but in some cases, for example, when there are requirements for architectural design, frame joint and section bending stiffness, square cfat has more advantages. as a composite structure of aluminum and concrete, cfat’s axial compression performance is worthy of in-depth investigation. in aspect of numerical simulations studies, zhou and young [4] studied circular section cfat short columns loaded axially. in experimental aspect, zhou and young [5,6] studied circular, square and rectangular section cfat short columns under axial loads. these studies revealed that aluminum tubes filled with concrete can remarkably improve axial c mailto:cejlpan@seu.edu.cn https://orcid.org/0000-0003-2453-582x https://youtu.be/cqhj_haiyo8 p. jinlong et alii, frattura ed integrità strutturale, 54 (2020) 169-181; doi: 10.3221/igf-esis.54.12 170 compressive strength of the section and bring better corrosion resistance, while the presence of core concrete can significantly alleviate and delay local buckling of aluminum tubes. some experiments and numerical simulations on cfats’ bearing capacity have been carried out. gardner and ashraf [7] first put forward the non-linear material model of aluminum alloy materials. on this basis, wang et al. [8] studied the bearing capacity and stiffness of circular aluminum tube concrete column under axial compression through experiments and numerical simulations. it was concluded that circular cfat specimen had good bearing capacity and ductility as conventional cfst specimen. compared with experimental data, general design rule cannot give a good prediction, so zhou and young [4,6] put forward a design criterion of square and circular cfat’s bearing capacity under axial compression, as shown in eq. (1) 0.85p a y c c c yp a f a f a f= + + (1) where pp is the proposed strength of cfat; aa denotes the full cross section area of aluminum tube; yf is 0.2% proof stress of aluminum; ca is the area of core concrete; cf is the cylinder strength of concrete;  is a geometric parameter. nevertheless, due to the limitation of the scale and conditionality of the cfat axial compression test, there is no uniform compression standard. there exist mechanical differences between square and circular cfats, but current researches on the comparison of axial compression performance of circular and square cfats are very limited. in this paper, mechanical properties of circular and square cfat under axial compression were studied by numerical simulation. compared with the above researches, this research has following improvements: (1) in order to make the comparison of compression test on two kinds of cfats more meaningful, this experiment ensured that the material type and material consumption of two cfats were consistent except for the difference of cross-section geometry. under this condition, the compression of two cfats was comparable. (2) in this study, by comparing the interaction between aluminum tube and core concrete of two cfats, essential differences of stress mechanism between circular and square cfat under axial load were revealed. (3) in the comparison of two kinds of cfats in whole load-displacement process, it was clearly shown that the behavior of circular and square cfats under axial load was different. (4) three parameters (core concrete strength, aluminum strength and aluminum ratio) were set. on the basis of parameter study, the trend of variation of parameters was analyzed. the practicability of abaqus software was proved, and then the mechanical properties of two kinds of cfats under axial compression were compared by abaqus software. the research in this paper provided a reference for engineering application of cfat and pointed out ideas for optimization design. reliability of finite element modeling constitutive model of aluminum material lastic-plastic model was applied to describe constitutive behavior of aluminum. it is assumed that aluminum have isotropic constitutive behavior. based on the compression concern and extensive usage of aluminum [9,10], it can be specifically described as ramberg-osgood formula and its extension, as shown in eq. (2) and eq. (3) for 0.2   : 0 0.2 = 0.002 n e     +     (2) for 0.2   : ' 0.2 ,1.00.2 1.0 0.2 0.2 0.2 0.2 0.2 1.0 0.2 = (0.008 )( ) n e e  −   −   −   + − +   −  (3) where  and  represent the strain and stress of aluminum tube, 0.2 and 1.0 are 0.2% and 1.0% proof stress, 0.2 is the strain at 0.2 . 0e and 0.2e are aluminum materials’ young modulus and tangent stiffness at 0.2 respectively. ' 0.2,1.0n is a strain hardening coefficient, representing nonlinearity extent of the stress-strain response, which is taken as 4.5 for t4, t5 and t6 temper materials [7]. according to en 1999-1-1 [3], it is suggested that the usage of 70000 2 n mm for young's e p. jinlong et alii, frattura ed integrità strutturale, 54 (2020) 169-181; doi: 10.3221/igf-esis.54.12 171 modulus of aluminum and 0.3 for poisson’s ratio is acceptable. representative material stress-strain graph for aluminum is shown in fig. 1 (a) in order to see the constitutive relationship more intuitively. constitutive model of concrete because of the similarity of the mechanical properties between cfat core concrete and cfst core concrete [5], the stressstrain model for cfst’s core concrete proved by han et al. [11,12] can be used for concrete of cfat. therefore, the core concrete model in cfst was used as core concrete model of cfat reasonably, as shown in eq. (4) 2 0 2 , 1 , 1 ( 1) n n n m n n n n   −   =    − + (4) where ' cm f=  , 0/n =   ; ' cf represents concrete cylinder compressive strength;  and  denotes the strain and stress of concrete respectively; 0 is the strain where maximum equivalent of concrete stress is obtained. 2 = is for circular section, 1.6 1.5 / n= + is for square and rectangular section. 0 is a model calculation parameter and it is given in eq. (5) and eq. (6) for circular cfat: 7 5 [ 0.25 ( 0.5) ] ' 0.5 0 (2.36 10 ) ( ) 0.5 0.12cf − + −  =     (5) for square cfat: ' 0.1 0 ( ) 1.2 1 cf = +  (6) where  is a confinement factor. according to aci 318-11 [13], ' cf and 0.2 are recommended for elastic modulus and poisson’s ratio of concrete, respectively. in addition, representative material stress-strain graphs for concrete are shown in fig. 1 (b). figure 1: material stress-strain graphs for cfat: (a) representative material stress-strain curve of aluminum; (b) representative material stress-strain curves of concrete element type, boundary condition and loading mode abaqus [14] was selected as the calculation software. eight-node 3d solid element (c3d8) was used to simulate concrete part, and four-node conventional plate shell element (s4r) was used to simulate aluminum tube. two rigid elastic blocks with large rigidity were used to simulate the plates at both ends, which had negligible deformation. "hard contact" was chosen for the contact relation between end-plates and concrete part, while "tie" was chosen for the contact relation between end-plates and aluminum tube. in this way, both displacements and rotation angles of contact elements were guaranteed to be the same. as it’s known to us, there is no contact pressure between aluminum tube and concrete unless one surface contacts the other. in order to simulate this characteristic, "hard contact" was also used in the normal direction p. jinlong et alii, frattura ed integrità strutturale, 54 (2020) 169-181; doi: 10.3221/igf-esis.54.12 172 of contact surfaces between aluminum tube and core concrete, which allowed contact surfaces to separate from each other after contact. schneider [15] took 0.25 for friction coefficient of the contact surfaces. because of the slight effect of bonding between aluminum tube and core concrete and inadequate testing on these mechanical properties, 0.25 was taken as friction coefficient for cfats in consideration of smoother contact surface between aluminum tube and concrete. verification of the finite element model zhou et al. [5,6] studied axial compression performance of circular and square cfats. through their experiments of several specimens, the influence of aluminum tube shape, wall thickness and concrete strength on cfat’s ultimate strength was been studied. material properties of aluminum tube specimens in zhou and young’s tests were determined by tensile coupon tests according to american society for testing and materials standard [16], which requests tensile tests in a displacementcontrolled mts (machinal tractor station) testing machine using friction grips. material properties of concrete in their tests were determined by standard cylinder tests. the concrete cylinder dimensions and test procedure conformed to the american specification [17]. because the mean value of their measured concrete strength had a relatively small coefficient of variation (cov), the number of specimens per tested column type is one in zhou and young’s tests [5,6]. label of specimen d(mm) t(mm) 0.2 (mpa) u (mpa) 0e (gpa) ' cf (mpa) ce (gpa) c1 150.1 2.53 267.9 282.9 64.9 44.8 31.7 c2 50.0 3.13 238.4 259.1 66.1 44.8 39.6 s1 88.0×88.0 1.76 246 263 67.3 108.6 49.3 s2 100×44.1 1.57 263 284 68.1 74.4 40.8 table 1: specimen parameters (d: diameter or length, t: thickness of the aluminum tube, 0.2 : 0.2% proof stress of aluminum, u : tensile strength of aluminum, 0e : initial young’s modulus of aluminum, ' cf : compressive strength of concrete, ce : young’s modulus of concrete). in this study, experimental values of the specimens (c1, c2, s1 and s2; “c” stands for circular cfat, “s” stands for square cfat) were compared with simulated results, therefore, finite element model could be verified. detailed parameters of four groups of test pieces are given in tab. 1. the comparison between calculated load-displacement (l-d) curves and experimental results is shown in fig. 2 and fig. 3. it was found that the maximum error between simulation data and experimental values can be controlled within 8.5%, and simulation values were relatively smooth. on the whole, the simulation values attain a good agreement with the outcome of experiments. figure 2: the experimental and simulation l-d curves of circular cfat. p. jinlong et alii, frattura ed integrità strutturale, 54 (2020) 169-181; doi: 10.3221/igf-esis.54.12 173 figure 3: the experimental and simulation l-d curves of square cfat. comparative study n the comparative study, two kinds of cfats were designed, as shown in fig. 4. it was shown that these two cfat columns were rigorously the same except for geometric difference by simple calculating. according to gb50010-2010 [18], c30 was set for concrete and nominal value of concrete cube compressive strength can be read from grade of concrete, for example, the following notation “c30” and “c40” indicate the cube strength (mpa) with 95% guarantee rate measured after curing to 28 days under standard curing conditions (temperature around 20 ℃, relative humidity above 95%), where “c30” indicates 30 mpa, and “c40” indicates 40 mpa. the elastic modulus could be calculated by ' cf ., which was described above. what’s more, a common kind of aluminum alloy 6063/t6 was used for the tube. the material composition of circular and square cfat was the same, and both circular and square cfat were 800 mm high. typical failure model after calculation and post-processing by abaqus software, the failure modes of circular cfat and square cfat under axial compression are shown in fig. 5. it is clearly found that circular cfat changed into drum-like shape, that is, the middle of circular cfat is thicker than both ends of column, and local buckling was not be discovered; while square cfat not only have local buckling at the two ends near the plates, but also expand in the middle part apparently. the middle section of circular cfat and square cfat damaged by axial compression are shown in fig. 6. it is obvious that the core concrete area of circular cfat is in close contact with aluminum tube. however, the core concrete of square cfat only keeps contact with aluminum tube at four corners and the separation of core concrete and aluminum tube occurs in other position. figure 4: design dimension of cross section for circular and square cfat. i p. jinlong et alii, frattura ed integrità strutturale, 54 (2020) 169-181; doi: 10.3221/igf-esis.54.12 174 figure 5: failure model of circular and square cfst under axial compression figure 6: middle section of circlar and square cfat damaged by compression interaction characteristics between aluminum tube and core concrete as shown in fig. 7, three different points were selected for the core concrete of circular cfat, which named a, b and c. similarly, three different points were for square cfat, namely a', b' and c'. it is worth noting that these six points are located in or near the middle of each cfat. since it was interesting in the stress state at the local buckling of square aluminum tube, d’ point was added to the local buckling. in addition, circular cfat had no local buckling in aluminum tube, so there was no such d point corresponding to it. figure 7: point location of each cfat’s core concrete p. jinlong et alii, frattura ed integrità strutturale, 54 (2020) 169-181; doi: 10.3221/igf-esis.54.12 175 the contact stresses at these six points are shown in fig. 8. the performances of contact stresses in point a, b and c were almost the same. it was found that the smooth curves of a, b and c was zero at the initial stage until the axial deformation was about 5mm. this is because the poisson's ratio of aluminum tube was larger than that of concrete at the beginning, which led to the lateral expansion of aluminum tube larger than that of core concrete, so there was no contact stress between them. with the increase of the axial deformation, concrete in the core area had cracks and obvious transverse plastic deformation. this made the poisson's ratio of core concrete increased and exceeded that of aluminum, so that the interaction between aluminum tube and core concrete increased gradually. however, the performance of square cfat was totally different from that of circular cfat. point a' and c' were in expansion area of aluminum tube, and contact stress of point a' and c' did not exist until the axial deformation reached 8mm, and then aluminum tube lost contact with concrete due to the expansion of aluminum tube. point b' had contact stress at the beginning and the contact stress increased rapidly with axial deformation rose. this phenomenon could be explained by the fact that point b' located in the corner region. then a declining segment appeared, which was because that core concrete had entered the stage of elastic-plastic deformation. point d' was located in the area of depression of concrete, and the contact pressure gradually increased after local buckling of aluminum tube. figure 8: contact stress of circular (a, b, c) and square (a’, b’, c’,d’) columns analysis of load-deformation histories load-deformation curves of circular cfat core concrete, square cfat core concrete, aluminum tube of circular cfat and aluminum tube of square cfat are shown in fig. 9. loading process could be divided into four stages distinctly by analyzing the above graphs: stage 1 (points o-a): linear elastic region. two curves of circular cfat and square cfat almost coincided. at this stage, both cfats remained linear elasticity. for circular cfat, the pressure of core concrete at point a was about 70% of its peak value strength, while that of square cfat was about 90%, which showed that square cfat relied more on concrete at the early stage of loading. stage 2 (points a-b or ab'): the characteristic of this stage was described as rising load-displacement curves of two cfats and continuous declined in the slope of the curves. in this stage, microcracks of core concrete developed constantly, which made the poisson's ratio of concrete exceed that of aluminum tube. at point b or b ', the ultimate strength of two types of aluminum tubes was attained. because circular section provided more constraint to the core concrete, two cfat curves deviated incrementally. at the end of this stage, the axial pressure of circular cfat was 1.3 times that of square cfat. stage 3 (points b-c or b'c'): axial pressure of both circular and square cfats decreased gradually and axial deformation increased rapidly. due to circular section’s strong constraint on the core concrete, the reduction of curve of circular cfat was less than that of square cfat, and the process of circular cfat in this stage was significantly longer than that of square cfat. at point c or c ', the curves of both cfats reached a low valley. at the end of this stage, the axial pressure of circular cfat was 1.5 times that of square cfat. it is indicated that the average slope of the curve at this stage can indirectly represent the ductility of cfat, which is similarly described by ductility index (di) in zhao and han’s study [8]. the smaller the slope is, the worse the ductility is. p. jinlong et alii, frattura ed integrità strutturale, 54 (2020) 169-181; doi: 10.3221/igf-esis.54.12 176 stage 4 (points c-d or c'-d'): because the thickness of the aluminum tube was large enough, these two curves grew steady and slowly, which indicated that circular and square cfats had good ductility. finally, the axial pressure of circular cfat was 1.6 times that of square cfat. figure 9: axial pressure-deformation curves of circular and square cfat it was found that the ultimate bearing capacity of circular cfat was higher than that of square cfat in the analysis of these four stages and circular cfat had a better performance than square cfat in restraining the core concrete. one main reason is that the contact stress distribution of circular cfat is more uniform, which makes its core concrete under triaxial compression and the constraint effect of aluminum tube gets better. however, the core concrete of square cfat is under complex stress state. therefore, the above differences result in different performances of circular cfat and square cfat. parameter analysis omparative parameters adopted in this paper were: core concrete strength, 0.2% proof stress of aluminum tube and aluminum ratio. in order to better compare the difference between circular cfat and square cfat, a parameter named pressure ratio (  ) was defined.  can be calculated by the following formula: c sf f = , where cf is the axial pressure of circular and sf is the axial pressure of square cfat. pressure ratio  of standard line represents that the axial pressure of the two cfats is the same. it is obvious that the closer the curve is to the standard line, the more similar the mechanical properties of two kinds of cfats are. core concrete strength different mechanical performance of circular and square cfats under axial compression caused by the change of core concrete strength is shown in fig. 10 and fig. 11. with the increase of concrete strength, ultimate compressive strength of both cfats increased, but the slope of the third segment of this curve became smaller, which meant the ductility decreased. in fig. 12, with the increase of core concrete strength,  -d curve was gradually close to the standard line, which meant that the performance of the two cfats tended to be the same. this phenomenon was explained by the fact that the brittleness of concrete increased when compressive strength rose. hence the ductility of circular cfat decreased and became a component with certain brittleness like square cfat. c p. jinlong et alii, frattura ed integrità strutturale, 54 (2020) 169-181; doi: 10.3221/igf-esis.54.12 177 figure 10: influence of concrete strength on load-deformation curve of circular cfat figure 11: influence of concrete strength on load-deformation curve of square cfat figure 12: influence of concrete strength on  -d curve p. jinlong et alii, frattura ed integrità strutturale, 54 (2020) 169-181; doi: 10.3221/igf-esis.54.12 178 0.2% proof stress of aluminum aluminum is a kind of non-linear material without a sharply defined yield point [7], so the universally accepted method of adopting the stress at 0.2% plastic strain (0.2% proof stress 0.2 ) was used here. several common kinds of aluminum materials were used for this simulation experiment: 5083/t6, 6063/t6, 6082/t6 and 7020/t6. according to gb/t 3880.22012 [19], material specifications (0.2% proof stress and ultimate strength) of these kinds of aluminum are shown in tab. 2. under ideal condition, elastic modulus of the above aluminum is 70 gpa and poisson's ratio is 0.34. it is noteworthy that the 0.2% proof stress increases in this order：5083/t6, 6063/t6, 6082/t6 and 7020/t6. the transformations of mechanical properties under axial compression of two cfats due to the change of 0.2% proof stress of aluminum are shown in fig. 13 and fig. 14. with the increase of the 0.2% proof stress of the aluminum, the ultimate compressive strength of these two cfats increased, while descent segment of the third stage of the curve decreased or even disappeared. the λ d curve was closer to the standard line with the increase of 0.2 . this phenomenon shows that with the increase of 0.2 , the performance of two cfats gets closer, and the ductility is also improved. figure 13: influence of 0.2 on load-deformation curve of circular cfat figure 14: influence of 0.2 on load-deformation curve of square cfat figure 15: influence of 0.2 on  -d curve p. jinlong et alii, frattura ed integrità strutturale, 54 (2020) 169-181; doi: 10.3221/igf-esis.54.12 179 type 5083/t6 6063/t6 6082/t6 7020/t6 t(mm) 6.0~12.5 12.5~40.0 0.5~5.0 5.0~20.0 0.14~6.0 6.0~22.5 1.5~40.0 0.2 (mpa) 125 125 190 150 260 255 280 u (mpa) 275 275 240 230 310 300 350 table 2: material specifications of aluminum used in numerical analysis (sign convention is the same as tab. 1). aluminum ratio a significant parameter named aluminum ratio (  ) was defined by a ca a = , where aa was the cross-section area of aluminum tube, ca was the cross-section area of concrete. as shown in fig. 16 and fig. 17, with the increase of  , the ultimate bearing capacity of circular and square cfat increased, and the slope of the third stage of the curves gradually increased too, which indicated an increase in ductility. λ-d curves kept approaching the standard line with the increase of  , showing that the increase of  made the performance of two cfats closer, as shown in fig. 18. in addition, it is worth noting that according to the four-stage theory mentioned above, the performance of circular cfat with low  is close to that of square cfat; while the performance of square cfat with high  is close to that of circular cfat. the inspiration for us is that increasing aluminum ratio can improve the ultimate bearing capacity of cfat and reduce its brittleness in design of cfat component. figure 16: influence of  on load-deformation curve of circular cfat conclusions ased on the above results, the following conclusions are drawn: (1) finite element models of circular and square cfats were established. considering interaction between core concrete and aluminum tube as well as material nonlinearity, simulation values were basically consistent with experimental results. (2) study on interaction characteristics between aluminum tube and core concrete was conducted. it is found that the contact pressures between core concrete and aluminum tube of circular and square section cfats with the same materials have different behavior. the local contact pressure of square cfat is higher than that of circular cfat, and the core concrete is under complex stress state. the contact pressure distribution of circular cfat tube is more uniform. b p. jinlong et alii, frattura ed integrità strutturale, 54 (2020) 169-181; doi: 10.3221/igf-esis.54.12 180 figure 17: influence of  on load-deformation curve of square cfat figure 18: influence of  on  -d curve (3) axial compression-deformation curves of different part of circular and square cfats were analyzed. four stages exist in axial compression-deformation curves of circular and square cfats. it is apparent that the aluminum tubes of circular and square cfats have similar characteristic of mechanical stage, but core concrete of two kinds of cfats performance differently. (4) influence of three parameters (core concrete strength, 0.2% proof stress of aluminum tube and aluminum ratio) on performance difference of circular and square section cfats was investigated. it is indicated that the ultimate strength and ductility of these two kinds of cfats increase as the increasing of either 0.2% proof stress of aluminum tube or aluminum ratio. with the increase of concrete strength, ultimate strength of circular and square cfats increase, while the ductility decreases at the same time. p. jinlong et alii, frattura ed integrità strutturale, 54 (2020) 169-181; doi: 10.3221/igf-esis.54.12 181 (5) in the aspect of improving the ductility of cfat, it is more effective to increase the aluminum ratio than to increase the 0.2% proof stress of aluminum or reduce the strength of concrete. increasing aluminum ratio not only changes the ultimate bearing capacity of square and circular cfats, but also changes the third stage of load-displacement curves, even makes the slope of the third stage change from negative to positive, which means ductility has been greatly improved. however, the other two parameters have less influence on the third stage. (6) aluminum ratio has more influence on the difference between circular and square cfat. the variation range of λ-d curve peak of concrete strength is 1.72~1.90 under the same aluminum ratio, and the variation range of λ-d curve peak of aluminum strength under the same aluminum ratio is 1.78~1.92. however, under the same concrete strength and aluminum strength, a wider range of 1.70~2.09 can be obtained by changing aluminum ratio. references [1] han, l.h., li, w., bjorhovde, r. (2014). developments and advanced applications of concrete-filled steel tubular (cfst) structures: members, j. constr. steel res., 100, pp. 211–228, doi: 10.1016/j.jcsr.2014.04.016. [2] su, m.n., young, b., gardner, l. (2016). the continuous strength method for the design of aluminium alloy structural elements, eng. struct., 122, pp. 338–348, doi: 10.1016/j.engstruct.2016.04.040. [3] european committee for standardization (ec9). (2007). en 1999-1-1:2007, design of aluminum structures-general structure rules, brussels, cen. [4] zhou, f., young, b. (2012). numerical analysis and design of concrete-filled aluminum circular hollow section columns, thin-walled struct., 50(1), pp. 45–55, doi: 10.1016/j.tws.2011.10.002. [5] zhou, f., young, b. (2009). concrete-filled aluminum circular hollow section column tests, thin-walled struct., 47(11), pp. 1272–1280, doi: 10.1016/j.tws.2009.03.014. [6] zhou, f., young, b. (2008). tests of concrete-filled aluminum stub columns, thin-walled struct., 46(6), pp. 573–583, doi: 10.1016/j.tws.2008.01.003. [7] gardner, l., ashraf, m. (2006). structural design for non-linear metallic materials, eng. struct., 28(6), pp. 926–934, doi: 10.1016/j.engstruct.2005.11.001. [8] wang, f.c., zhao, h.y., han, l.h. (2019). analytical behavior of concrete-filled aluminum tubular stub columns under axial compression, thin-walled struct., 140(august 2018), pp. 21–30, doi: 10.1016/j.tws.2019.03.019. [9] su, m.n., young, b., gardner, l. (2014). testing and design of aluminum alloy cross sections in compression, j. struct. eng., 140(9), doi: 10.1061/(asce)st.1943-541x.0000972. [10] wang, f.c., han, l.h. (2019). analytical behavior of carbon steel-concrete-stainless steel double-skin tube (dst) used in submarine pipeline structure, mar. struct., 63, pp. 99–116, doi: 10.1016/j.marstruc.2018.09.001. [11] han, l.h., yao, g.h., tao, z. (2007). performance of concrete-filled thin-walled steel tubes under pure torsion, thinwalled struct., 45(1), pp. 24–36, doi: 10.1016/j.tws.2007.01.008. [12] l. han. (2016). concrete filled steel tubular structures-theory and practice ,third (in chinese), beijing, china science publishing & media ltd. [13] american concrete institute. (2011). building code requirements for structural concrete (aci 318-11) and commentary, farmington hills, mi. doi: 10.1016/0262-5075(85)900326. [14] abaqus. (2014). abaqus standard user’s manual, version 6.14, dassault systemes corp., providence, ri (usa). [15] schneider, s.p. (1999). axially loaded concrete-filled steel tubes closure, j. struct. eng., 125(10), pp. 1206, doi: 10.1061/(asce)0733-9445(1999)125:10(1206.x). [16] american society for testing and materials. (1997). standard test methods for tension testing of metallic materials (e 8m-97), west conshohocken, usa [17] american concrete institute. (1995). building code requirements for structure concrete and commentary (aci 318-95), detroit, usa [18] china moc. (2010). code for design of concrete structures, beijing, china construction industry publishing house. [19] china's general administration of quality supervision (aqsiq). (2012). wrought aluminium and aluminium alloy plates, sheet and strips for general engineering-part 2: mechanical properties, bejing, national standardization administration of china microsoft word numero 10 art 1 a. carpinteri et alii, frattura ed integrità strutturale, 10 (2009) 3-11; doi: 10.3221/igf-esis.10.01 3 complexity: a new paradigm for fracture mechanics a. carpinteri, s. puzzi politecnico di torino, department of structural and geotechnical engineering, corso duca degli abruzzi 24, 10129 torino, italy, alberto.carpinteri@polito.it; simone.puzzi@polito.it riassunto. le cosiddette scienze della complessità sono un argomento di interesse in forte crescita all'interno della comunità scientifica. in realtà, i ricercatori non sono ancora giunti ad un’unica definizione di complessità, per il fatto che essa si manifesta attraverso svariate forme [1]. questo campo d’indagine, infatti, non è rappresentato da una singola disciplina, ma piuttosto da un insieme eterogeneo costituito da differenti tecniche matematiche e da diversi ambiti della scienza. sotto l’allocuzione di scienze della complessità comprendiamo una grande varietà di approcci: la dinamica non lineare, la teoria del caos deterministico, la termodinamica del non-equilibrio, la geometria frattale, l’asintoticità intermedia, l’autosomiglianza completa ed incompleta, la teoria del gruppo di rinormalizzazione, la teoria delle catastrofi, la criticalità auto-organizzata, le reti neurali, gli automi cellulari, la logica sfumata (fuzzy logic), etc. scopo del presente lavoro è quello di approfondire il ruolo della complessità nel campo della scienza dei materiali e della meccanica della frattura [2-3]. gli esempi presentati riguarderanno il fenomeno instabile dello snap-back nel comportamento di strutture composite (carpinteri [4-6]), l’insorgere di pattern frattali e dell’autosomiglianza nella deformazione e nel danneggiamento dei materiali eterogenei, oltre agli effetti di scala sulle proprietà meccaniche nominali dei materiali disordinati (carpinteri [7,8]). ulteriori esempi si occuperanno dell’interpretazione dei fenomeni critici e degli effetti di scala temporale sulla vita ultima delle strutture per mezzo della emissione acustica (carpinteri et al.[9]). infine, verranno presentati risultati sulla transizione verso il caos nel comportamento dinamico di travi fessurate (carpinteri and pugno [10,11]). abstract. the so-called complexity sciences are a topic of fast growing interest inside the scientific community. actually, researchers did not come to a definition of complexity, since it manifests itself in so many different ways [1]. this field itself is not a single discipline, but rather a heterogeneous amalgam of different techniques of mathematics and science. in fact, under the label of complexity sciences we comprehend a large variety of approaches: nonlinear dynamics, deterministic chaos theory, nonequilibrium thermodynamics, fractal geometry, intermediate asymptotics, complete and incomplete similarity, renormalization group theory, catastrophe theory, self-organized criticality, neural networks, cellular automata, fuzzy logic, etc. aim of this paper is at providing insight into the role of complexity in the field of materials science and fracture mechanics [2-3]. the presented examples will be concerned with the snap-back instabilities in the structural behaviour of composite structures (carpinteri [4-6]), the occurrence of fractal patterns and selfsimilarity in material damage and deformation of heterogeneous materials, and the apparent scaling on the nominal mechanical properties of disordered materials (carpinteri [7,8]). further examples will deal with criticality in the acoustic emissions of damaged structures and with scaling in the time-to-failure (carpinteri et al. [9]). eventually, results on the transition towards chaos in the dynamics of cracked beams will be reported (carpinteri and pugno [10,11]). keywords. catastrophe theory, fractal geometry, scaling of material properties, self-organized criticality, deterministic chaos. http://dx.medra.org/10.3221/igf-esis.10.01&auth=true http://www.gruppofrattura.it mailto: alberto.carpinteri@polito.it simone.puzzi@polito.it a. carpinteri et alii, frattura ed integrità strutturale, 10 (2009) 3-11; doi: 10.3221/igf-esis.10.01 4 introduction omplexity, as a discipline, generally refers to the study of large-scale systems with many interacting components, in which the overall system behaviour is qualitatively different from (and not encoded in) the behaviour of its components. complex systems lie somehow in between perfect order and complete randomness –the two extreme conditions that occur only very seldom in nature– and exhibit one or more common characteristics, such as: sensitivity to initial conditions, pattern formation, spontaneous self-organization, emergence of cooperation, hierarchical or multiscale structure, collective properties beyond those directly contained in the parts, scale effects. complexity has two distinct and almost opposite meanings: the first goes back to kolmogorov's reformulation of probability and his algorithmic theory of randomness via a measure of complexity, now referred to as kolmogorov complexity [1]; the second to the shannon's studies of communication channels via his notion of information. in both cases, complexity is a synonym of disorder and lack of a structure: the more random a process is, the more complex it results to be. the second meaning of complexity refers instead to how intricate, hierarchical, structured and sophisticated a process is. associated with these two almost opposite meanings, are two natural trends of composite systems, and two corresponding questions: how does order and structure emerge from large, complicated systems? and, conversely, how do randomness and chaos arise from systems with only simple constituents, whose behaviour does not directly encode randomness? the former case is typical of all those phenomena which could be described through the concepts of scale invariance, phase transition, and with the use of power laws. the latter case is that of instability and bifurcations and of dynamical systems showing chaotic attractors and transition to chaos. in this paper, several fracture mechanics applications will be shown, in which both trends are present. the nonlinear cohesive crack model: snap-back instability as a cusp catastrophe he first example dates back to the 1980's, when the senior author [4-6] approached the snap-back instability of cracked bodies with a cohesive crack model, which can be interpreted in the general framework of catastrophe theory (thom [12]). this first section is thus devoted to a brief review of the ductile-to-brittle transition in the mechanical behaviour of cracked solids, described by means of the cohesive crack model. the cohesive crack model was initially proposed by barenblatt [13] and dugdale [14]. subsequently, dugdale's model was reconsidered by several other authors (for a review see [15]); hillerborg et al. [16] proposed the fictitious crack model in order to study crack propagation in concrete. the cohesive crack model is based on the following assumptions ([4,15]): 1. the cohesive fracture zone (plastic or process zone) begins to develop when the maximum principal stress achieves the ultimate tensile strength u. 2. the material in the process zone is partially damaged but still able to transfer stress. such a stress is dependent on the crack opening displacement w. the energy gf necessary to produce a unit crack surface is given by the area under the w diagram. the real crack tip is defined as the point where the distance between the crack surfaces is equal to the critical value of crack opening displacement wc and the normal stress vanishes. on the other hand, the fictitious crack tip is defined as the point where the normal stress attains the maximum value and the crack opening vanishes (fig. 1). with some modifications, the cohesive crack model has been applied to model a wide range of materials and fracture mechanisms, most prominently concrete. regarding this material, there is a very large literature; for a review, the reader is referred to the review papers by carpinteri and co-workers [15,17]. now, let us quantify the ductile-to-brittle transition by showing synthetically the numerical results for concrete elements in mode i conditions (three point bending test tpbt), based on the cohesive model, obtained using the finite element code fr.ana. (fracture analysis carpinteri [5,18,19]). extensive series of analyses were carried out from 1984 to 1989 by a. carpinteri and co-workers. the experimental results can be found in the rilem report [20]. the cases described in the reference papers regard three slenderness ratios, and four initial crack depths, and a concrete-like material. fig. 2a refers to the case of an initially uncracked beam, whilst fig. 2b reports results for the case of an initially cracked beam with relative crack depth equal to 0.5. for each ratio, the response was analyzed for different values of the brittleness number, se [4]. as can be seen from the diagrams, by increasing se the behaviour of the element changes from brittle to ductile. generally speaking, the specimen behaviour is brittle (snap-back) for low se numbers, i.e., for low fracture toughness, gf, high tensile strengths, u, and/or large sizes, h. in particular, in the case of uncracked beam, for se 10.45x10-5, the p–δ curve presents positive slope in the c t http://dx.medra.org/10.3221/igf-esis.10.01&auth=true http://www.gruppofrattura.it a. carpinteri et alii, frattura ed integrità strutturale, 10 (2009) 3-11; doi: 10.3221/igf-esis.10.01 5 softening branch and a catastrophical event occurs if the loading process is deflection-controlled. such indenting branch is not virtual only if the loading process is controlled by a monotonically increasing function of time (biolzi et al. [21]). figure 1: constitutive laws of the cohesive crack model: (a) undamaged material; (b) process zone. in the case of the cracked beam, on the contrary, the initial crack makes the specimen behaviour more ductile; for the set of se numbers considered in fig. 2b, the snap-back does not occur. by varying the initial crack depth, it is possible to describe the gradual transition from simple fold catastrophe (softening) to bifurcation or cusp catastrophe (snap-back instability), generating an entire equilibrium surface, or the catastrophe manifold. figure 2: dimensionless load vs. deflection diagrams by varying the brittleness number se, initially uncracked (a) and cracked (b) specimen the fractal interpretation of the size-scale effect he second topic is concerned with the size-scale effects on the mechanical properties of heterogeneous disordered materials that can be interpreted synthetically through the use of fractal sets. fractal sets are characterized by noninteger dimensions (mandelbrot [22]). for instance, the dimension α of a fractal set in the plane can vary between 0 and 2. accordingly, increasing the measure resolution, its length tends to zero if its dimension is smaller than 1 or tends to infinity if it is larger. in these cases, the length is a nominal, useless quantity, since it diverges or vanishes as the measure resolution increases. a finite measure can be achieved only using noninteger units, such as meters raised to αl. fractals sets can be profitably used to describe the size-scale effects on the parameters of the cohesive crack model. as shown in the previous section, this model captures the ductile-brittle transition occurring by increasing the size of the structure. on the other hand, uniaxial tensile tests on dog-bone shaped specimens [23,24] have shown that the three material parameters defining the cohesive law are size dependent: increasing the specimen size, the tensile strength u, tends to decrease, whilst the fracture energy gf and the critical displacement wc increase. in order to overcome the original cohesive crack model drawbacks, a scale-independent (fractal) cohesive crack model has been proposed recently by the first author [25]. this model is based on the assumption of a fractal-like damage localization, suggested by experimental evidence [26,27]. t u u f u c 1 2 wg http://dx.medra.org/10.3221/igf-esis.10.01&auth=true http://www.gruppofrattura.it a. carpinteri et alii, frattura ed integrità strutturale, 10 (2009) 3-11; doi: 10.3221/igf-esis.10.01 6 let us consider fractal geometries for both the resistant cross section at maximum load (fig. 3a) and the dissipation domain (fig. 3c) [25]. hence we can compute the maximum load f, the critical displacement wc and the total dissipated energy w as: * * u 0 u resa af    (1a) ε1-*ε ε dc c cw b b  (1b) * f 0 f disa a *w  g g (1c) these quantities are size-dependent. the true scale-independent quantities are the right hand side ones, i.e. the fractal strength u*, the fractal critical strain εc* and the fractal fracture energy gf*. they show non-integer physical dimensions: [f][l]–(2–dσ) for u*, [l](dε) for wc and [fl][l] –(2+dg) for gf*. because of the measure of the resistant cross section ares and the dissipation domain adis, from eqs. (1) the scaling laws for strength, critical displacement and fracture energy can be obtained: σ* u u db   (2a) ε1-*ε dc cw b (2b) f f d*b   gg g (2c) figure 3: a concrete specimen subjected to tension. fractal localization of the resistant cross section (a); fractal localization of the strain (b) and the energy dissipation inside the damaged band (c). the three size effect laws (2) of the cohesive law parameters are not completely independent of each other. in fact, there is a relation among the scaling exponents that must be always satisfied. in order to get this relation, the simplest path is to consider the damage domain in fig. 3c as the cartesian product of those in figs. 3a and 3b. as a result, we obtain: σ ε 1d d d  g (3) according to these definitions, we call the *ε* diagram the fractal or scale-independent cohesive law. contrarily to the classical cohesive law, which is experimentally sensitive to the structural size, this curve is an exclusive property of the material since it is able to capture the fractal nature of the damage process. the area below the softening fractal stressstrain diagram represents the fractal fracture energy gf*. in order to validate the model, it has been applied to the data obtained in 1994 by carpinteri and ferro [23,24] for tensile tests on dog-bone shaped concrete specimens of various sizes under controlled boundary conditions (fig. 4a). they http://dx.medra.org/10.3221/igf-esis.10.01&auth=true http://www.gruppofrattura.it a. carpinteri et alii, frattura ed integrità strutturale, 10 (2009) 3-11; doi: 10.3221/igf-esis.10.01 7 interpreted the size effects on the tensile strength and the fracture energy by fractal geometry. fitting the experimental results, they found the values dσ= 0.14 and dg= 0.38. some of the –ε (stress vs. strain) and –w diagrams are reported respectively in fig. 4b and 4c, where w is the displacement localized in the damaged band. eq. (3) yields dε= 0.48, so that the fractal cohesive laws can be plotted in fig. 4d. as expected, all the curves related to the single sizes tend to merge in a unique, scale-independent cohesive law. the overlapping of the cohesive laws for the different sizes proves the soundness of the fractal approach to the interpretation of concrete size effects. figure 4: tensile test on dog-bone shaped specimens (a) by carpinteri and ferro [28]; stress-strain diagrams (b), cohesive law diagrams (c), fractal cohesive law diagrams (d). the fractal interpretation of multiscale cracking phenomena he third topic deals with the criticality of the complex multiscale cracking phenomena in heterogeneous and disordered materials, evaluated by means of the acoustic emission (ae) technique. acoustic emission (ae) is represented by the class of phenomena whereby transient elastic waves are generated by the rapid release of energy from localized sources within a material. all materials produce ae during both the generation and propagation of cracks. the elastic waves move through the external solid surface, where they are detected by sensors. in this way, information about the existence and location of possible damage sources is obtained. this is similar to seismicity, where seismic waves reach the station placed on the earth surface (richter [28]). with regard to the basis of ae research in concrete, the early scientific papers were published in the 1960s. particularly interesting are the contributions by rusch [29], l'hermite [30] and robinson [31]. they discussed the relation between fracture process and volumetric change in the concrete under uniaxial compression. the most important applications of ae to structural concrete elements started in the late 1970s [32]. regarding the determination of the defects position and orientation in the material, research has been growing at a fast rate in the last decade (shah & zongjing [33] and ohtsu [34]). in the last few years the ae technique has been applied to identify defects and damage in reinforced concrete structures and masonry buildings (carpinteri & lacidogna [35,36]). by means of this technique, a particular methodology has been put forward for crack propagation monitoring and crack stability assessment in structural elements under service conditions. this technique permits to estimate the amount of energy released during fracture propagation and to obtain information on the criticality of the ongoing process [9,37]. without entering the details, recent developments in fragmentaron theories (carpinteri & pugno [38,39]) have shown that the energy dissipation e during microcrack propagation occurs in a fractal domain comprised between a surface and the t http://dx.medra.org/10.3221/igf-esis.10.01&auth=true http://www.gruppofrattura.it a. carpinteri et alii, frattura ed integrità strutturale, 10 (2009) 3-11; doi: 10.3221/igf-esis.10.01 8 specimen volume v. the fractal criterion predicts a volume-effect on the maximum number of acoustic emission events nmax, that, in a bilogarithmic diagram, would appear as: maxlog log log v 3 ae d n    (4) with a slope equal to d/3, where γae is the critical value of fractal acoustic emission density and d is the fractal exponent, comprised between 2 and 3 [37]. experiments carried out by carpinteri et al. [36] on concrete specimens tested in compression confirm the soundness of the proposed approach. for all the tested specimens, the critical number of acoustic emissions nmax was evaluated in correspondence to the peak-stress u. the compression tests show an increase in ae cumulative event number by increasing the specimen volume. more in detail, subjecting the average experimental data to a statistical analysis, the parameters d and γae in eq. (4) were quantified. from the best-fitting, reported graphically in fig. 5, the estimated value of the slope was computed as d/3 = 0.766, so that, as predicted by the fragmentation theories, 2d3. this result is a confirmation of the fact that the energy dissipation, measured by the number of acoustic emissions n, occurs over a fractal domain. interestingly, the criticality of the cracking phenomena does appear not only in space, but also in time. a scaling relation of the type of eq. (4) can be written for the time t, allowing one to define the damage parameter , which can be expressed [9,37] as a function of different parameters, i.e., stress σ, strain ε or time t: σ ε tβ β β max max max max σ ε η σ ε n t n t                      (5) where the exponents β can be obtained from the ae data of a reference specimen. the fractal multiscale criterion of eq. (5) is a fundamental result, since it allows to predict the damage evolution also in large concrete structural elements. monitoring the damage evolution by ae, it is therefore possible to evaluate the damage level as well as the time to the final collapse [9]. figure 5: volume effect on the maximum number of acoustic emissions. route towards chaos in the dynamics of cracked beams he fourth and last topic is concerned with the dynamical behaviour of cracked beams (carpinteri and pugno [40,10,11]. dealing with the presence of a crack in the structure, previous studies have demonstrated that a transverse crack can change its state (from open to closed and vice versa) when the structure, subjected to an external load, vibrates. as a consequence, a nonlinear dynamic behavior is introduced. this phenomenon has been detected during experimental testing performed by gudmundson [41], in which the influence of a transverse breathing crack upon the natural frequencies of a cantilever beam was investigated. t http://dx.medra.org/10.3221/igf-esis.10.01&auth=true http://www.gruppofrattura.it a. carpinteri et alii, frattura ed integrità strutturale, 10 (2009) 3-11; doi: 10.3221/igf-esis.10.01 9 several models have been proposed in the past for dealing with cracked vibrating beams [42-44], but, in all these models, the main assumption has been that the crack can be either fully open or fully closed during the vibration. carpinteri and pugno [10] recently developed a coupled theoretical and numerical approach to evaluate the nonlinear complex oscillatory behaviour in damaged structures under excitation. in their approach, they have focused their attention on a cantilever beam with several breathing transverse cracks and subjected to harmonic excitation perpendicular to its axis. the method, that is an extension of the super-harmonic analysis carried out by pugno et al. [45] to subharmonic and zero frequency components, has allowed to capture the complex behavior of the nonlinear system, e.g., the occurrence of period doubling, as experimentally observed by brandon and sudraud [46] in cracked beams. a pioneer work on period doubling was written in 1978, when mitchell feigenbaum [47] developed a theory to treat the route from ordered to chaotic states. even if oscillators showing the period doubling can be of different nature, as in mechanical, electrical, or chemical systems, they all share the characteristic of recursiveness. he provided a relationship in which the details of the recursiveness become irrelevant, through a kind of universal parameter, measuring the ratio of the distances between successive period doublings, the so called feigenbaum's delta. his understanding of the phenomenon was later experimentally confirmed [48], so that today we refer to the so-called feigenbaum's period doubling cascade. however, even if the period doubling has a long history, only recently it has been experimentally observed in the dynamics of cracked structures [46]. to highlight the influence of the crack on the beam dynamics, let us consider two different numernical examples: a wikely nonlinear structure and a strongly nonlinear one. only in the latter case the so called period doubling phenomenon clearly appears. details about the beam geometry and materials can be found in [10]. for each of the two considered structures (figs. 6a and 6b) the trajectory in the phase space is represented in figs. 7a and 7b. in a hypothetical linear structure, the structural response is linear by definition with obviously only one harmonic component at the same frequency of the excitation. in the weakly nonlinear structure of fig. 6a, the response converges and it appears only weakly nonlinear. the trajectory in the phase diagram is close to an ellipse. the diagram is nonsymmetric as the spatial positions of the cracks (placed in the upper part of the beam). the trajectory is an unique closed curve since here the period of the response is equal to the period of the excitation. figure 6: damaged structures: weakly nonlinear (a) and strongly nonlinear (b). figure 7: dimensionless phase diagram of the response (free end displacement): weakly (a) and strongly (b) non linear structure. in the strongly nonlinear structure of fig. 6b the nonlinearity increases. the harmonic components in the structural response are the zero one, the superharmonics as well as the subharmonic ones. it should be emphasized that a strong nonlinearity causes the period doubling of the response, i.e., the ω/2 component. the free-end vibrates practically with a period doubled with respect to the excitation. a nonnegligible component at ω/4 is observed too, representing a route to chaos through a period doubling cascade. the corresponding phase diagram clearly evidences this: the trajectory is composed by multiple cycles since here the period of the response is not equal to the period of the excitation. the http://dx.medra.org/10.3221/igf-esis.10.01&auth=true http://www.gruppofrattura.it a. carpinteri et alii, frattura ed integrità strutturale, 10 (2009) 3-11; doi: 10.3221/igf-esis.10.01 10 distortions in the trajectory are consequences of the presence of the superor subharmonics. also in this case, the diagram is nonsymmetric as the spatial positions of the cracks. this method is able to catch the transition toward deterministic chaos, like the occurrence of a period doubling, as shown in the numerical examples and experimentally observed in the context of cracked beam by brandon and sudraud [46]. conclusions he so-called "complexity sciences" represent a subject of fast-growing interest in the scientific community. they have entered also our more circumscribed communities of material science and material strength, as the proposed examples may confirm. the presented topics were concerned with the structural behaviour of composite structures with snap-back instabilities (an example of cusp catastrophe), the occurrence of fractal patterns and geometrically self-similar morphologies in deformation, damage and fracture of heterogeneous materials, the apparent scaling in the nominal mechanical properties of disordered materials, the acoustic emission criticality in progressive structural collapse, the route towards chaos in the dynamics of cracked structures. as shown in these examples, the most interesting behaviors and phenomena can be synthetically interpreted only through the use of new and refined conceptual tools in the framework of "complexity sciences". acknowledgements he authors would like to gratefully acknowledge the contributions made to this work by all members of the research group led by the senior author at the department of structural éngineering and geotechnics of the politécnico di torino. in particular, the warmest thanks go to giuseppe ferro, nicola pugno, pietro cornetti and giuseppe lacidogna. support by the european community is gratefully acknowledged by the authors. thanks are also due to the italian ministry of university and research (miur). references [1] m.s. garrido, r.vuela mendes, complexity in physics and technology, world scientific, singapore, (1992). [2] a. carpinteri, s. puzzi, strength, fracture and complexity, 4 (2006) 189. [3] a. carpinteri, s. puzzi, strength, fracture and complexity, 4 (2006) 201. [4] a. carpinteri, in application of fracture mechanics to cementitious composites, edited by s.p. shah, martinus nijhoff publishers, dordrecht, (1985) 287. [5] a. carpinteri, j. mech. phys. solids, 37 (1989) 567. [6] a. carpinteri, int. j. frac., 44 (1990) 57. [7] a. carpinteri, mech. mater., 18 (1994) 89. [8] a. carpinteri, int. j. solids struct., 31 (1994) 291. [9] a. carpinteri, g. lacidogna, n. pugno, engng. frac. mech., 74 (2007) 273. [10] a. carpinteri, n. pugno, j. appl. mech., 72 (2005) 511. [11] a. carpinteri, n. pugno, j. appl. mech., 72 (2005) 519. [12] r. thom, structural stability and morphogenesis: an outline of a general theory of models. benjamin (1975). [13] g. i. barenblatt, j. appl. math. mech., 23 (1959) 622. [14] d. s. dugdale, j. mech. phys. solids, 8 (1960) 100. [15] a. carpinteri, p. cornetti, f. barpi, s. valente, engng. frac. mech., 70 (2003) 1809. [16] a. hillerborg, m. modeer, p.e. petersson, , cement concr. res., 6 (1976) 773. [17] a. carpinteri, p. cornetti, s. puzzi, appl. mech. rev., 59 (2006) 283. [18] a. carpinteri, int. j. solids struct., 25 (1989) 407. [19] a. carpinteri, engng. frac. mech., 32 (1989) 265. [20] determination of the fracture energy of mortar and concrete by means of three-point bending tests on notched beams. technical report 18, materials and structures, r.i.l.e.m. (1985). [21] l. biolzi, s. cangiano, g.p. tognon, a. carpinteri, mater. struct., 22 (1989) 429. [22] b.b. mandelbrot, the fractal geometry of nature. new york: freeman (1982). t t http://dx.medra.org/10.3221/igf-esis.10.01&auth=true http://www.gruppofrattura.it a. carpinteri et alii, frattura ed integrità strutturale, 10 (2009) 3-11; doi: 10.3221/igf-esis.10.01 11 [23] a. carpinteri, g. ferro, mater. struct., 28 (1994) 563. [24] a. carpinteri, g. ferro, mater. struct., 31 (1998) 303. [25] a. carpinteri, b. chiaia, p. cornetti, eng. frac. mech., 69 (2002) 207. [26] a. carpinteri, b. chiaia, k.m. nemati, mech. mater., 26 (1997) 93. [27] a. carpinteri, b. chiaia, s. invernizzi, theor. appl. frac. mech., 31 (1999) 163. [28] c.f. richter, , elementary seismology, w.h. freeman & company, san francisco and london (1958). [29] h. rusch, , zement-kalk-gips (wiesbaden), 12 (1959) 1. [30] r.g. l'hermite, in proc. 4th int. symp. on chemistry of cement, v-3. nbs monograph 43, nbs, washington dc, (1960) 659. [31] g. s. robinson, in proc. int. conf. on the structure of concrete and its behavior under load, cement and concrete association, (1965) 131. [32] w. m. mccabe, r. m. koerner, a. e. jr. load, , aci journal, 13 (1976) 367. [33] p. shah, l. zongjin, , aci mater. j., 91 (1994) 372. [34] m. ohtsu, , magazine concr. res., 48 (1996) 321. [35] a. carpinteri, g. lacidogna, in proc. of stremah vii (bologna, 2001), wit press, southampton, (2001) 327. [36] a. carpinteri, g. lacidogna, italian patent n. to 2002 a000924, deposited on 23 october 2002. [37] a. carpinteri, g. lacidogna, n. pugno, in fracture mechanics of concrete and concrete structures (proceedings of the 5th international framcos conference, vail, colorado, usa, (2004), edited by v.c. li et al., 1 (2004) 31. [38] a. carpinteri, n. pugno, magazine concr. res., 54 (2002) 473. [39] a. carpinteri, n.pugno, int. j. numer. anal. methods geomech., 26 (2002) 499. [40] a. carpinteri, n. pugno, proceedings of the 9th international congress on sound and vibration, orlando, usa, cdrom, (2002) paper n. 114. [41] p. gudmundson, j. mech. phys. solids, 31 (1983) 329. [42] m.i. friswell, j. e. t. penny, in proc. x int. modal analysis conf., (1992) 516. [43] w. ostachowicz, m. krawczuk, comput. struct., 36 (1990) 245. [44] r. ruotolo, c. surace, p. crespo, d. storer, comput. struct., 61 (1996) 1057. [45] n. pugno, c. surace, r. ruotolo, j. sound vib., 235 (2000) 749. [46] j. a. branden, c. sudraud, , j. sound vib., 211 (1998) 555. [47] m. j. feigenbaum, j. stat. phys., 19 (1978) 25. [48] p.s. linsay, phys. rev. lett., 47 (1981) 1349. http://dx.medra.org/10.3221/igf-esis.10.01&auth=true http://www.gruppofrattura.it microsoft word numero_38_art_43 i. n. shardakov et alii, frattura ed integrità strutturale, 38 (2016) 331-338; doi: 10.3221/igf-esis.38.43 331 delamination of carbon-fiber strengthening layer from concrete beam during deformation (infrared thermography) i. n. shardakov, a. p. shestakov institute of continuous media mechanics of the ural branch of russian academy of science (icmm ub ras), korolev str., 1, perm, 614013, russia. shardakov@icmm.ru, shap@icmm.ru a.a. bykov perm national research polytechnic university, komsomolsky ave., 29, perm, 614990, russia violentharpy@ya.ru abstract. technology of strengthening reinforced concrete structures with composite materials has found wide application. the effectiveness of strengthening of concrete structures with externally bonded reinforcement is supported by a great deal of experimental evidence. however, the problem of serviceability of such structures has not been adequately explored. the present work describes the results of experimental studies on the loadcarrying capacity of concrete beams strengthened with carbon fiber reinforced plastic (cfrp). special emphasis is placed on studying the debonding of the strengthening layer from the concrete surface and analyzing its influence on the load-carrying capacity of beams. infrared thermography is used to detect the first signs of debonding and to assess the debond growth rate. keywords. carbon fiber reinforced plastic; reinforced concrete beams; strengthening; intermediate crack debonding; infrared thermography; quality control; non-destructive testing methods. citation: shardakov, i. n., bykov, a.a., shestakov, a. p., delamination of carbonfiber strengthening layer from concrete beam during deformation (infrared thermography), frattura ed integrità strutturale, 38 (2016) 331-338. received: 02.06.2016 accepted: 30.08.2016 published: 01.10.2016 copyright: © 2016 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. introduction t present, the technology of strengthening reinforced concrete structures with composite materials is extensively used in the constructional industry. there are many studies supporting the efficiency of strengthening of concrete structures with externally bonded reinforcement, but the evaluation of serviceability of such structures is still the problem to be solved. there are several possible options of failure of composite reinforced concrete beams [1]: rupture of fiber-reinforced plastic, crushing of compressive concrete, shear failure, concrete cover separation, plate and interfacial debonding, and intermediate crack induced interfacial debonding. in designing structures reinforced with composite materials, the liming state of such structures is considered to be the state of structure deformation, at which the debonding of the composite material from the concrete surface occurs. according to russian (sp 164.1325800.2014, [2]) and american (aci 440.2ra i. n. shardakov et alii, frattura ed integrità strutturale, 38 (2016) 331-338; doi: 10.3221/igf-esis.38.43 332 08, [3]) regulations, this approach is applied to bending elements reinforced by a strengthening sheet with anchorage and without it. in works [4-6], a series of tests have been performed to study the deformation behavior of a beam initially subjected to loading up to crack generation and then strengthened with cfrp. besides, the dependence of the strength and stiffness of such beams on preliminary loading was shown. however in the structural practice the reinforcement of beams is usually performed directly during loading and followed by grouting cracks before gluing cfrp sheet. the question of how such a restoring procedure affects the strength properties of beams has not received enough attention yet. the influence of the degree of debonding on the carrying capacity of beams deserves further studies as well. this work studies the debonding of cfrp sheet from the surface of reinforced concrete beams subjected to bending loading. during the experiment carried out in the laboratory at perm national research polytechnic university, we have investigated the strain behavior of beams strengthened until loading and beams strengthened during loading after the appearance of first cracks and their grouting. infrared thermography techniques [7, 8] were applied to identify the first signs of debonding. heat transfer processes develop differently in a multi-layer systems with and without air gaps. the analysis of surface temperature of the beam at its heating and cooling yielded information about the existence and distribution of debonding on the beam surface. program and methods of testing n our experiments we used concrete beams made of concrete b20 (group b1) and concrete b35 (group b2). totally 22 sample-beams were prepared and tested. the schematic representation of a sample strengthened with steel reinforcement rods and a composite layer is shown in fig. 1. the choice of such reinforcement was mainly caused by the condition of equal strength for beam elements in bending. each group of beams (b1 and b2) was divided into 3 series with 3–5 samples in each of them: series a – reference samples (ordinary concrete beams with steel reinforcement); series b – preliminary strengthened beams, i.e beams strengthened by the cfrp before load application; series c – beams strengthened at a certain stage of loading after the appearance of first visible cracks and their grouting. during the strengthening procedure cfrp sheet sikawrap-230 40 mm width and 0.13 mm thickness was glued to the beam bottom surface using epoxy resin sikadur-330. carbon fiber sheet was also fixed with transverse wrapping anchorage by cfrp straps in two support sections of the beam. for the beams of cerise c strengthening procedure additionally included widening and grouting of cracks with a repair compound and crack injection with a low-viscosity epoxy resin before gluing of cfrp. strain gauges were installed on steel reinforcement rods, the carbon-fiber sheet and the surface of all beams to control deformations along the beam axes. figure 1: schematic representation of the concrete beam with steel reinforcement and the carbon fiber strengthening layer: 1 – carbon fiber sheet, 2 – carbon fiber strip, 3 – carbon fiber wrapping anchorage, 4, 5 – steel reinforcement with a diameter of 6 mm and 12 mm, respectively. the tests were performed on a specially designed four-point bending test set-up (fig. 2a). the loading of the beams was performed by a successive increasing quasistatic load with а step of 2 kn representing 4–6% of the fracture load. at each i i. n. shardakov et alii, frattura ed integrità strutturale, 38 (2016) 331-338; doi: 10.3221/igf-esis.38.43 333 step a 5–10-minute pause was made to record temperature on the stretched surface of the beam. simultaneously, crack patterns and widths were obtained. to excite heat transfer processes, the beam was subjected to external heat pulse (magnitude of 926 w and duration of 10 sec) and then cooled. temperature recorded along the whole surface of the cfrp layer using infrared imager flir t620 ([9-11]). shots were taken “through the mirror”, which ensured the safety of people and equipment at loads close to the destruction of the beam (fig. 2b). (a) (b) figure 2: load testing machine (a) and infrared shooting arrangement (b). the details of experimental techniques were determined based on the analysis of the results of numerical solution of nonstationary heat conduction problem in a system of "carbon sheet epoxy concrete delamination concrete". difference in surface temperature of the multi-layered system with and without debondings at corresponding instants of time at heating and cooling is called here a temperature response to the presence of delamination. numerical simulations enabled us to assess the conditions at which the temperature response will be the most. it appears that on heating of the beam by the heat source of 926 w for 10 seconds, the temperature response should be measured at the stage of its cooling, namely 8 seconds after its start (i.e. 18 seconds after the beginning of observation) [12]. thermography images of the composite surface were obtained at each loading step. the initial thermograms for each j-th step (fig.3a) is a two-dimensional array of differential temperature values ( , )jt x y determined at 19th and 0th seconds at points with coordinates  ,x y . the index 0,j n specifies the number of loading step; loading is absent at 0j  . the obtained initial thermograms were processed using an algorithm specifically designed using matlab programs. in the first step of the algorithm, we calculate the normalized thermograms        * * * *0, , , / ,j j jtn x y t x y t x y t x y where  ,jt x y is the initial temperature difference at the j-th loading step at the point  ,x y ,  * *0 ,t x y and  * *,jt x y are the initial temperature differences at the 0-th and j-th loading steps at the point * *,x y where no debonding is known to be present. normalized thermograms for successive loading steps are given in fig.3b. next the temperature contrast  ,jc x y (figure 3c) is determined: i. n. shardakov et alii, frattura ed integrità strutturale, 38 (2016) 331-338; doi: 10.3221/igf-esis.38.43 334        0 0, , , / , 100%j jc x y tn x y t x y t x y     in order to make a decision on the existence of bebonding at the point with the coordinates  ,x y , we calculate a threshold value for the temperature contrast *c . for making it estimate, we determine, at each loading step, the average value jc and the standard deviation j in those areas of the thermograms, where debonding is known to be absent. the threshold value is calculated by the formula * 3j jс с   . the areas of the crfp layer surface, where the temperature contrast exceeds the threshold value, are identified as the areas with debonding and the remaining ones as the areas free of defect. in the binary defect map shown in fig.3d, the defect-free areas are shown in white color and the areas of debonding in black color. (a) (b) (c) (d) figure 3: thermal infrared images obtained using the developed algorithm: (а) initial thermogram; (b) normalized thermogram; (c) temperature contrast map; (d) binary card of defects. results and discussions he summary data of the static test results for the beams of the series a and b are shown in tab. 1, the series c – in tab. 2, where mcrc is the bending moment corresponding to the onset of cracking, acrc, is the maximum crack opening width, fult is the elastic deflection, mult is the maximum bending moment, fult is the maximum deflection, εf,ult is the strain of the carbon-fiber sheet at rupture. before tests the class of concrete was specified for each beam sample. for the marking of samples were used the following notation: b1 or b2 – groups of concrete, "a", "b", "c" – series, i – sample number. during the tests we observed two forms of delamination. for the beams, whose surface had been cleaned with a wire brush before sticking cfrp, the delamination occurred according to the adhesive scenario. for the beams, refined with an abrasive tool to a depth of 2-3 mm, the delamination occurred according to the cohesive scenario. for the nonstrengthened beams (series a) the destruction state was determined by the rupture of metal reinforcement rods and crushing of the concrete in the compressed zone, for the strengthened ones (series b and c) – by the rupture of cfrp layer, in a number of cases accompanied by the rupture of metal reinforcement. fig. 4 shows the dependence of the maximum beam deflection on the bending moment obtained for three series of beams. the comparison of the graphs obtained in the series a and b clearly demonstrates an increase in the bearing capacity of the beams strengthened before loading. the maximum bending moment, which such beams can stand, has happened to be by 37–39% higher than the reference samples. the graphs reflect the appearance of the first cracks in the concrete: it corresponds to a sharp change in the slope angle of the curves. t i. n. shardakov et alii, frattura ed integrità strutturale, 38 (2016) 331-338; doi: 10.3221/igf-esis.38.43 335 specimen concrete class mcrc, knm rebound deflection, mm mult, knm fult, mm acrc,max , mm εf,ult, με debonding type specimen failure behavior bla-1 b25 3.81 0.183 6.13 9.50 2.7 rr* bla-2 b25 3.91 7.45 19.84 2.0 rr+ccc bla-3 b25 4.27 6.92 21.43 2.0 rr*+ccc mean value 4.00 0.183 6.83 2.2 b1b-1 b25 4.28 10.05 14.29 1.1 12170 mixture frpr* blb-2 b25 5.07 10.42 11.16 0.5 11170 mixture frpr* blb-3 b20 4.33 0.206 10.25 8.30 1.0 13370 cohesion frpr blb-4 b30 5.40 0.257 10.10 8.08 0.9 12180 cohesion. frpr blb-5 b20 4.32 0.218 11.07 9.78 1.1 15040 cohesion. frpr mean (adhesive) 4.68 10.24 12.72 0.9 11670 mean (cohesive) 0.227 10.47 8.72 13530 b2a-1 b35 4.74 6.98 10.60 1.5 rr* b2a-2 b35 5.15 6.98 15.75 7.0 rr+ccc b2a-3 b40 4.98 0.221 7.39 19.73 3.0 rr*+ccc mean value 4.96 0.221 7.12 2.2 b2b-1 b35 6.14 10.03 10.37 0.8 12180 mixture. frpr* b2b-2 b40 5.79 10.19 12.52 1.6 10860 adhesion frpr* b2b-3 b40 5.49 0.260 10.56 8.92 1.1 13790 cohesion. frpr b2b-4 b40 5.09 0.213 11.46 9.31 1.0 14280 cohesion. frpr b2b-5 b40 5.43 0.252 10.27 8.06 1.3 12190 cohesion. frpr mean (adhesive) 5.59 10.11 11.44 1.1 11520 mean (cohesive) 0.242 10.76 8.76 13420 notes: rr reinforcement rupture, ccc crushing of compressive concrete, rr* reinforcement rupture sectional weakened spot welding, frpr midspan frp rupture, frpr* frp rupture sectional strap anchorage, mix. mixed debonding, coh. cohesive debonding, adh. adhesive debonding table 1: the results of static test of beams of series a and b. specimen concrete class loading before the appearance of the first cracks bending moment during reinforcement, knm loading after the appearance of the first cracks and their grouting debonding type specimen failure behavior mcrc, knm rebound deflection, mm maximum bending moment, knm acrc,max , mm mcrc, knm mult, mm fult, mm acrc,max , mm εf,ult, με blc-1 b20 3.32 0.142 5.15 1.0 4.30 6.79 10.39 10.80 1.4 11680 cohes. frpr blc-2 b20 3.60 0.164 5.23 1.5 4.81 7.19 8.75 9.19 1.5 10190 cohes. frpr blc-3 b30 3.86 0.186 5.20 1.0 4.59 6.59 10.19 11.07 1.3 12760 cohes. frpr mean value 3.60 5.19 1.2 4.57 6.86 10.29 1.4 11540 b2c-1 b40 4.30 0.179 5.49 1.0 4.56 6.88 1137 10.29 1.1 14180 cohes. frpr b2c-2 b40 4.92 0.214 5.64 0.9 4.79 7.02 9.03 9.75 1 8655 cohes. rr*+ frpr b2c-3 b40 5.19 0.202 5.52 1.0 4.58 7.69 10.62 10.72 1.3 12430 cohes. frpr mean value 4.80 5.55 1.0 4.64 7.19 11.00 1.1 13305 table 2: the results of static tests of beams of series c. the evolution of deformation in the beams reinforced under the load is of particular interest. at the initial stage of loading such a beam behaves in the same way as a nonstrengthened one (fig. 4, solid thick lines). the i. n. shardakov et alii, frattura ed integrità strutturale, 38 (2016) 331-338; doi: 10.3221/igf-esis.38.43 336 appearance of the first cracks in the concrete causes a sharp increase in deformation. the subsequent grouting of cracks in the beam under the load leads to the restoration of its rigidity. at this stage, the deformation curve has the "step", on which the slope of the curve is almost restored to its initial value. with a further increase in the bending moment beam displays the same behavior pattern, as the preliminarily strengthened one. the beams strengthened under the load showed an increase in their carrying capacity by 38–49% compared to the nonstrengthened samples, and the appearance of the second generation cracks started when the bending moment increased by 45–71%. in the graphs the loading intervals are marked (circled zones), corresponding to the beginning of cohesive delamination of cfrp. in the beams strengthened under loading delamination begins when the bending moment is on average 75% of the maximum value. thus, our tests show that the loss of the bearing capacity of the beam cannot be correlated with the beginning of delamination of cfrp layer. as shown in the graphs of fig. 4, from the beginning of delamination the beam continues to perceive the load and reduction of rigidity does not take place. this means that from the appearance of the first cracks to the total loss of the bearing capacity the beam has some strength reserve which is about 25% of the ultimate load. (a) (b) figure 4: bending moment–deflection relationships for series a, b and c: group b1 (a), group b2 (b). the algorithm of thermogram transformation allows one to estimate the relative area of delamination, accumulated in the beams at each loading step. the data presented in tab. 3 show that the relative area of delamination in the beams reinforced under loading is on average 2.1–2.3 times greater than in the preliminary strengthened ones. the comparison of the experimental strain values, corresponding to the onset of cohesive delamination of cfrp, with the data theoretically obtained from 5 different methods used in practice, demonstrates a low reliability of these calculation methods (fig. 5). for instance, the values calculated by the regulatory method used in russia exceeds the experimentally registered by 15–75% for different classes of concrete. conclusion . it is shown that for the bearing capacity of cfrp beams destroyed due to the rupture of cfrp does not depend on the point when the strengthening is performed. the beams strengthened before loading and under the load after the appearance of first cracks and their grouting demonstrate the bearing capacity that is higher by 37–39% and 3849%, respectively, than the ordinary cr beams. grouting of cracks in the beams under loading allows one to increase the limiting value of the bending moment by 45–71% compared to the unstrengthened beams. 2. it is established that the process of cfrp delamination in the beams strengthened under loading begins at strain which is 4-65% lower and the relative area of delamination is 2.1-2.3 times higher compared to the beams strengthened before loading. 1 series b series c series a series c series b series a i. n. shardakov et alii, frattura ed integrità strutturale, 38 (2016) 331-338; doi: 10.3221/igf-esis.38.43 337 3. the onset of delamination of cfrp sheet corresponds to the bending moment, which is 75% of the limit value. thus, the presence of delamination does not determine the limiting state of cfrp beams with anchorage of cfrp tape on the bearings. therefore, it is possible to use the breaking strain of the composite as a limiting value of deformations in the limit state design. the existence of cohesive delamination does not reduce the stiffness of the reinforced structure. specimen binary card of defects the relative area of the delamination, % cfrp strain, με particular value average value b1b-3 7.8 9.71 10300 b1b-4 12.99 10660 b1b-5 8.34 10140 b1c-1 19.77 22.93 10280 b1c-2 22.59 8020 b1c-3 26.43 10240 b2b-3 11.78 14.90 10810 b2b-4 20.18 10200 b2b-5 12.73 10070 b2c-1 17.86 32.41 8970 b2c-2 33.08 7220 b2c-3 46.29 10450 table 3: the results of static tests of beams of series c. figure 5: the comparison of experimental and theoretical values of deformations corresponding to the onset of cohesive delamination. acknowledgment this research was supported by the russian science foundation, project no. 14-2900172. references [1] teng, j.g., failure modes of frp-strengthened restructures, 26th conference on our world in concrete & structures: 27-28 august, singapore (2001) 627-634. [2] sp 164.1325800.2014. strengthening of reinforced concrete structures with composite materials. design rules (2014) (in russian). [3] aci 440.2r-08. guide for the design and construction of externally bonded frp systems for strengthening concrete structures. aci (2008). [4] zhang, a., jin, w., li, g., behavior of preloaded rc beams strengthened with cfrp laminates, journal of zhejiang university science a, 7 (2006) 436-444. i. n. shardakov et alii, frattura ed integrità strutturale, 38 (2016) 331-338; doi: 10.3221/igf-esis.38.43 338 [5] parikh, k., modhera, c.d., application of gfrp on preloaded retrofitted beam for enhancement in flexural strength, international journal of civil and structural engineering, 2 (2012) 1070-1080. [6] al-salloum, y.a., flexural behavior of rc beams strengthened with frp composite sheets subjected to different load cases, king saud university, saudi arabia. http://faculty.ksu.edu.sa/ysalloum/documents/my%20papers/flexure%20uk%202006.pdf. [7] vavilov, v.p., thermal/infrared nondestructive testing, ndt handbooks series, moscow 5(2009). [8] concu, g., de nicolo, b., piga, c., trulli, n., infrared thermography as a tool for quality control of frp and frcm application, proceedings of the 6th international conference on frp composites in civil engineering. – rome, (2012). [9] valluzzi, m.r., grinzato, e., pellegrino, c., modena, c., ir thermography for interface analysis of frp laminates externally bonded to rc beams, materials and structures, 42 (2009) 25-34. [10] shirazi, а., karbhar, v.m., quantifying defects and progression of damage in frp rehabilitation of concrete through ir thermography, asia-pacific conference on frp in structures (apfis 2007). international institute for frp in construction, (2007). [11] taillade, f., quiertant, m., benzarti, k., dumoulin, j., aubagnac, ch., nondestructive evaluation of frp strengthening systems bonded on rc structures using pulsed stimulated infrared thermography, ifsttar, f-75015 paris, (2012) 193-208. [12] bykov, a., matveenko, v., serovaev, g., shardakov, i., shestakov, a., determination of thermography modes for recording delamination between composite material and reinforced concrete structures, solid state phenomena, ttp, (2016) 97-104. << /ascii85encodepages false /allowtransparency false /autopositionepsfiles true /autorotatepages /none /binding /left /calgrayprofile (dot gain 20%) /calrgbprofile (srgb iec61966-2.1) /calcmykprofile (u.s. web coated \050swop\051 v2) /srgbprofile (srgb iec61966-2.1) /cannotembedfontpolicy /error /compatibilitylevel 1.4 /compressobjects /tags /compresspages true /convertimagestoindexed true /passthroughjpegimages true /createjobticket false /defaultrenderingintent /default /detectblends true /detectcurves 0.0000 /colorconversionstrategy /cmyk /dothumbnails false /embedallfonts true /embedopentype false /parseiccprofilesincomments true /embedjoboptions true /dscreportinglevel 0 /emitdscwarnings false /endpage -1 /imagememory 1048576 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can be opened with acrobat and adobe reader 5.0 and later.) >> /namespace [ (adobe) (common) (1.0) ] /othernamespaces [ << /asreaderspreads false /cropimagestoframes true /errorcontrol /warnandcontinue /flattenerignorespreadoverrides false /includeguidesgrids false /includenonprinting false /includeslug false /namespace [ (adobe) (indesign) (4.0) ] /omitplacedbitmaps false /omitplacedeps false /omitplacedpdf false /simulateoverprint /legacy >> << /addbleedmarks false /addcolorbars false /addcropmarks false /addpageinfo false /addregmarks false /convertcolors /converttocmyk /destinationprofilename () /destinationprofileselector /documentcmyk /downsample16bitimages true /flattenerpreset << /presetselector /mediumresolution >> /formelements false /generatestructure false /includebookmarks false /includehyperlinks false /includeinteractive false /includelayers false /includeprofiles false /multimediahandling /useobjectsettings /namespace [ (adobe) (creativesuite) (2.0) ] /pdfxoutputintentprofileselector /documentcmyk /preserveediting true /untaggedcmykhandling /leaveuntagged /untaggedrgbhandling /usedocumentprofile /usedocumentbleed false >> ] >> setdistillerparams << /hwresolution [2400 2400] /pagesize [612.000 792.000] >> setpagedevice microsoft word numero_29_art_3 a. caporale et alii, frattura ed integrità strutturale, 29 (2014) 19-27; doi: 10.3221/igf-esis.29.03 19 focussed on: computational mechanics and mechanics of materials in italy a micromechanical four-phase model to predict the compressive failure surface of cement concrete a. caporale, r. luciano department of civil and mechanical engineering, university of cassino and southern lazio a.caporale@unicas.it, luciano@unicas.it abstract. in this work, a micromechanical model is used in order to predict the failure surface of cement concrete subject to multi-axial compression. in the adopted model, the concrete material is schematised as a composite with the following constituents: coarse aggregate (gravel), fine aggregate (sand) and cement paste. the cement paste contains some voids which grow during the loading process. in fact, the non-linear behavior of the concrete is attributed to the creation of cracks in the cement paste; the effect of the cracks is taken into account by introducing equivalent voids (inclusions with zero stiffness) in the cement paste. the three types of inclusions (namely gravel, sand and voids) have different scales, so that the overall behavior of the concrete is obtained by the composition of three different homogenizations; in the sense that the concrete is regarded as the homogenized material of the two-phase composite constituted of the gravel and the mortar; in turn, the mortar is the homogenized material of the two-phase composite constituted of the sand inclusions and a (porous) cement paste matrix; finally, the (porous) cement paste is the homogenized material of the two-phase composite constituted of voids and the pure paste. the pure paste represents the cement paste before the loading process, so that it does not contain voids or other defects due to the loading process. the abovementioned three homogenizations are realized with the predictive scheme of mori-tanaka in conjunction with the eshelby method. the adopted model can be considered an attempt to find micromechanical tools able to capture peculiar aspects of the cement concrete in load cases of uni-axial and multi-axial compression. attributing the non-linear behavior of concrete to the creation of equivalent voids in the cement paste provides correspondence with many phenomenological aspects of concrete behavior. trying to improve this correspondence, the influence of the parameters of the evolution law of the equivalent voids in the cement paste is investigated, showing how the parameters affect the uni-axial stress-strain curve and the failure surfaces in bi-axial and tri-axial compression. keywords. cement concrete; micromechanics; compressive strength. introduction icromechanical methods [1-3] have been widely used to homogenize fiber reinforced composites such as frp, frequently employed to strengthen existing structures made of concrete [4-8]. micromechanics has also been adopted for the analysis of different types of heterogeneous materials such as masonry arrangements [9,10] and cement concrete [11-16]. in [17], a four-phase micromechanical model has been proposed in order to simulate the nonlinear instantaneous pre-peak response of cement concrete subjected to monotonically increasing loads of uni-axial m a. caporale et alii, frattura ed integrità strutturale, 29 (2014) 19-27; doi: 10.3221/igf-esis.29.03 20 compression. in this work, the micromechanical model presented in [17] is used in order to predict the failure surface of cement concrete subject to multi-axial compression. it is underlined that stress-strain curves in uni-axial compression are provided in [17], whereas failure curves in the plane of the principal stresses in concrete are considered in this work. the failure curves provided by the proposed micromechanical method can also be obtained with experimental tests which involve high economical costs as equipment able to impose bi-axial and tri-axial states of compression is required. the aim of the work is to determine theoretically the mechanical parameters that affect more the behavior of cement concrete in order to reduce the number of expensive experimental tests on concrete specimens. micromechanical model n the proposed model, the concrete material is viewed as a composite with the following constituents: coarse aggregate (gravel), fine aggregate (sand) and cement paste. the cement paste contains some voids which grow during the loading process. in fact, the non-linear behavior of the concrete is attributed to the creation of cracks in the cement paste; the effect of the cracks is taken into account by introducing equivalent voids (inclusions with zero stiffness) in the cement paste. the three types of inclusions (namely gravel, sand and voids) have different scales, so that the overall behavior of the concrete is obtained by the composition of three different homogenizations; in the sense that the concrete is regarded as the homogenized material of the two-phase composite constituted of the gravel and the mortar; in turn, the mortar is the homogenized material of the two-phase composite constituted of the sand inclusions and a (porous) cement paste matrix; finally, the (porous) cement paste is the homogenized material of the two-phase composite constituted of voids and the pure paste; the pure paste represents the cement paste before the loading process, so that it does not contain voids or other defects due to the loading process. the pure paste can contain defects but these are due to the production process of the cement paste and not to the loading process. the above-mentioned three homogenizations are realized with the predictive scheme of mori-tanaka in conjunction with the eshelby method, frequently used in the homogenization of composites [11,13]. the micromechanical method described in [17] provides the stress in the concrete material subject to a prescribed strain and, vice versa, the strain in concrete material subject to a prescribed stress. the volume fraction of the voids in the cement paste is denoted by vf . the overall elasticity of the porous cement paste, mortar and concrete are denoted by  pc ,  mc and  cc , respectively. considering that the paste is composed of pure paste and voids, the overall elasticity  pc of the paste is a function of the volume fraction vf of the voids. as a consequence, the overall elasticity of mortar and concrete are also functions of vf . the overall elasticity of paste, mortar and concrete are evaluated with the moritanaka method in conjunction with the result of the eshelby’s problem of an ellipsoidal inclusion in a homogeneous, linearly elastic and infinitely extended medium (see also [17]). the overall compliances of the cement paste, mortar and concrete are denoted by  pd ,  md and  cd , respectively; these compliances are obtained by inverting the corresponding overall elasticity and are also functions of vf :                            1 1 1 p p v v m m v v c c v v f f f f f f       d c d c d c (1) in this work, a macro-stress σ is prescribed to the concrete and the average stress and strain in the constituents of concrete and corresponding to σ are evaluated with the following iterative procedure, which makes use of a secant approach. the value of the void volume fraction vf at the generic ith iteration is denoted by ,v if . the average stress and strain in the constituents of concrete at the generic ith iteration are evaluated by assuming that it is known , 1v if , i.e. the void volume fraction at the previous iteration  1i . specifically, the following overall elasticity and compliance corresponding to , 1v if are evaluated in the ith iteration of the procedure:                             , 1 , 1 , 1 , 1 , 1 , 1, , , , , p pm c m cv i v i v i v i v i v if f f f f fc c c d d d (2) i a. caporale et alii, frattura ed integrità strutturale, 29 (2014) 19-27; doi: 10.3221/igf-esis.29.03 21 it is noted that the iterative procedure begins with the first iteration (  1i ), where the void volume fraction  , 1 ,0v i vf f is required: ,0vf may represent a measure of the defects in the paste before the loading process. if this information is already contained in the constant elasticity  ppc of the pure paste then ,0vf can be assumed equal to zero. the concrete twophase composite has mortar as matrix and gravel as inclusions; at the ith iteration, the average stress  mσ in the mortar of the concrete two-phase composite subject to σ is given by        , 1m m v ifσ b σ (3) where    , 1m v ifb is the average stress concentration tensor of the mortar in the concrete and depends on    , 1c v ifd and    , 1m v ifd , as well as on the constant compliance  gd of the gravel. then, the average stress  mσ evaluated in (3) becomes the far-field stress applied on the mortar two-phase composite, which has paste as matrix and sand as inclusions; at the ith iteration, the average stress  pσ in the paste of the mortar two-phase composite subject to  mσ is         , 1p p mv ifσ b σ (4) where    , 1p v ifb is the average stress concentration tensor of the paste in the mortar and depends on    , 1m v ifd and    , 1p v ifd , as well as on the constant compliance  sd of the sand. finally, the average stress  pσ evaluated in (4) becomes the far-field stress applied on the paste two-phase composite, which has pure paste as matrix and voids as inclusions. the average stress  ppσ in the pure paste of the paste two-phase composite subject to  pσ is evaluated by using the stress average theorem:        , 11pp p v ifσ σ (5) once  ppσ has been evaluated at the ith iteration by means of (5), it is possible to determine the corresponding average strain  ppε in the pure paste:      pp pp ppε d σ (6) where  ppd is the constant compliance of the pure paste. the value of the void volume fraction at the current ith iteration is given by        , ,0 , , pp pp v i v v m m v eq eqf f f f (7) where                                11 22 33 2 , , 3 3 pp pp pp pp pp pp pp pp pp pp m ij ij m ij eq ij ije e e (8) and   ppij are the components of the second-order strain tensor  ppε in (6), equal to the symmetric part of the displacement gradient. relation (7) is the evolution law of the voids in the paste and depends on the following five parameters: ,0vf , ,v mf , ,v eqf ,  ,  . if the error , , 1v i v if f is less than or equal to a given tolerance then further iterations are not necessary and the average stress and strain evaluated in the current ith iteration are correct; otherwise, the void volume fraction ,v if in the current ith iteration provided by (7) becomes the value of vf to consider at the a. caporale et alii, frattura ed integrità strutturale, 29 (2014) 19-27; doi: 10.3221/igf-esis.29.03 22 beginning of the successive iteration  1i . in the iteration  1i , the relations (2)-(7) are evaluated again by substituting ,v if for , 1v if into (2)-(5). the average stress σ prescribed to the concrete composite represents the input load and must be less than or equal to the strength of the concrete which is unknown. if the prescribed stress σ is greater than concrete strength then ,v if at an iteration i usually results greater than one, causing the stopping of the iterative procedure as a void volume fraction vf greater than one is physically unacceptable. moreover, the void volume fraction ,v if at the generic ith iteration should not be excessively large as the used homogenization methods provide acceptable estimates if the volume fraction of the inclusions is not so large. damage and failure of brittle and ductile materials are very sensitive to the von mises equivalent stress and strain, which are often encountered in damage and failure criteria of materials, as well as in the proposed evolution law (7) in the form of  ppeq defined in (8). the parameter ,v eqf is used to weight the influence of the von mises equivalent strain  pp eq on the void evolution. on the other hand, the parameter ,v mf has been introduced in the evolution law (7) in order to take into account also a void growth in presence of hydrostatic compression characterized by      11 22 33 0 pp pp pp     and   0ppeq  : in this case, no void evolution could occur if ,v mf was equal to zero. in the proposed model, the damage is smeared over the whole volume of concrete while in the post-peak behavior the damage localizes in limited zones [18]. for this reason the proposed model, valid in the pre-peak range, results not suitable to capture the post-peak behavior. in this work, the pre-peak behavior provides essential information, such as the initial young’s modulus of concrete and the compressive strength in multi-axial stress state. in the load case of prescribed uni-axial compression, the uni-axial stress can be plotted against the uni-axial strain so as to obtain the compressive stress-strain curve of concrete. the stress-strain curves provided in [17] in the load case of uniaxial compression exhibit a maximum compressive stress denoted by  p , which represents the compressive strength  c of concrete. in [17], the proposed micromechanical model has been used in order to capture peculiar aspects of the stressstrain curve in the load case of uni-axial compression:  in most concrete materials, a higher compressive strength is associated with a higher initial tangent young’s modulus 0e ;  the formation and evolution of voids in the cement paste cause a reduction of the tangent line to the stress-strain curve;  a higher w c ratio of water to cement involves a concrete with a lower compressive strength  c and a lower tangent line 0e at the origin of the stress-strain curve;  the concrete materials having the same initial stiffness 0e also have the same  p p ratio of peak stress to peak strain, as predicted by phenomenological curves [19];  p is the strain corresponding to  p in the concrete stressstrain curve. in this work, the micromechanical model presented in [17] and briefly described in this paragraph is used in order to predict the failure surface of cement concrete subject to multi-axial compression. firstly, further analyses with uni-axial compression are presented in the next paragraph. influence of the model parameters on the uni-axial compressive stress-strain curve he iterative procedure previously described is used to estimate the stress-strain curve  11 11 of concrete subject to uni-axial compression: in this stress state, concrete is subject to the average stress  cσ and all the components of  cσ are equal to zero except     11 11 0 c . in fig. 1, the normal stress    11 11 c is plotted against the normal strain    11 11 c of concrete subject to uni-axial compression, where  cε is the average strain in concrete. in the examples of this work, the constituents pure paste, sand and gravel are considered homogeneous, isotropic and linear elastic; they have the geometrical and mechanical properties reported in tab. 1. the parameters of the evolution law (7) adopted for the curves of fig. 1 assume the following values. in the solid black curves of fig. 1, ,v eqf varies between 30 and 50,  is equal to 0.7,  , ,0vf and ,v mf are assumed equal to zero. in the solid red curves of fig. 1, ,v eqf varies t a. caporale et alii, frattura ed integrità strutturale, 29 (2014) 19-27; doi: 10.3221/igf-esis.29.03 23 between 30 and 50,  is equal to 0.8,  , ,0vf and ,v mf are assumed equal to zero. in the green curves of fig. 1, ,0vf is assumed equal to zero, ,v mf varies between 10 and 20, ,v eqf is equal to 30,  and  are assumed equal to 0.8. the tangent line to a curve of fig. 1 at the origin of the 11 and 11 -axes is the overall initial stiffness 0e . each curve of fig. 1 has a maximum denoted by  p and attained when  11 p . the tangent line to the curves of fig. 1 at the endpoint   , p p is about horizontal. in case of uni-axial compression, the peak  p of the stress-strain curve represents the compressive strength  c of concrete. the curves of fig. 1 have the same initial stiffness 0e : in fact, 0e depends on the properties reported in tab. 1 and the initial porosity ,0vf , which are constants that do not vary among the curves of fig. 1. the curves with a given value of  have the same ratio  p p : e.g. in the black curves characterized by   0.7 , the ratio  p p is about 0 2e ; in the red and green curves characterized by   0.8 , the ratio  p p is always constant and is greater than 0 2e . the exponent   0.7 was chosen in order to have   0 2p pe , as predicted by the following phenomenological curve proposed by desayi and krishnan [19]            0 11 11 11 2 111 p e (9) the generic curve of fig. 1 is obtained by connecting the point   11 11, ; the end-point of this curve is   , p p , whose coordinates are used to have the dimensionless curve     11 11, p p . in fig. 2,  11 p is plotted against  11 p for the eight curves of fig. 1. the eight dimensionless curves of fig. 2 are the same; this behavior is also exhibited by the experimental stress-strain curves and the curve (9). constituent young’s modulus poisson’s ratio volume fractions in cement concrete gravel 45 gpa 0.23 0.4 sand 65 gpa 0.21 0.326 cement paste 0.274 pure paste 15 gpa 0.22 table 1: geometrical and mechanical properties of the four-phase composite. 0,000 0,020 0,040 0,060 0,080 0,100 0,120 0,000 0,001 0,002 0,003 0,004 0,005 0,006   ( g p a)   f v,eq , f v,m   = 0.8, f v,eq = 30, f v,m = 10, 20   = 0.7, f v,m = 0, f v,eq = 30, 40, 50   = 0.8, f v,m = 0, f v,eq = 30, 40, 50 figure 1: stress-strain curves of concrete in uni-axial compression. a. caporale et alii, frattura ed integrità strutturale, 29 (2014) 19-27; doi: 10.3221/igf-esis.29.03 24 0,0 0,2 0,4 0,6 0,8 1,0 0,0 0,2 0,4 0,6 0,8 1,0    p   p   = 0.8, f v,eq = 30, f v,m = 10, 20   = 0.7, f v,m = 0, f v,eq = 30, 40, 50   = 0.8, f v,m = 0, f v,eq = 30, 40, 50 figure 2: dimensionless stress-strain curves of concrete in uni-axial compression. compressive failure surfaces he proposed model can also be used to determine the behavior of cement concrete in load cases of multi-axial compression. this is done in this work, where the failure surface of concrete subject to bi-axial or tri-axial compression is determined by using the previously described iterative procedure. the objective is to represent the compressive failure surface of cement concrete in the space of the eigenvalues of the average stress  cσ in concrete. the eigenvalues are the principal stresses in concrete and are contained in the vector     t1 2 3 e e e eσ . the generic direction in the space of the eigenvalues of  cσ is represented by the unit vector      t 1 2 3 ˆ ˆ ˆ n . the proposed method determines the average strain  cε in cement concrete subject to a prescribed stress     t1 2 3ˆ ˆ e eσ , where  is a positive parameter which increases during the loading process; 1ˆ , 2ˆ and  3e are constants with  1ˆ 0 and  2ˆ 0 . the principal directions of  cσ coincide with the coordinate axes, i.e.                  tt 1 2 3 11 22 33 ˆ ˆ c c ce eσ . in order to determine a point of the failure surface, the loading parameter  increases from zero up to the admissible maximum value  max . the above-mentioned iterative procedure is executed for each value of  . after the admissible values of  have been determined for given directions 1ˆ and 2ˆ and given stress  3e , the stress     cii ii for  1, 2i can be plotted against the corresponding strain    cii ii so as to obtain a  ii ii stress-strain curve in the ith direction. from a physical point of view, it is interesting to consider the  ii ii stress-strain curve when  ˆ ˆj i with i j , i.e.  ii jj ; this curve exhibits a maximum stress denoted by   , c ii p and the tangent line to the curve at the maximum is about horizontal. the searched point of the failure surface of cement concrete in multi-axial compression is therefore given by       tt , max 1 max 2 3 11, 22 , 3 ˆ ˆ c ce e p e p p e            σ σ (10) next, the points ,e pσ are estimated with the previously described iterative procedure and assuming     t 1 2 ˆ ˆ 0n with  1ˆ 0 and  2ˆ 0 , i.e. a bi-axial compression is imposed to cement concrete. in this case, the points ,e pσ represent a failure curve in the negative quadrant of the plane with  1e and  2e -axes. in fig. 3, the failure curves are illustrated for the cement concrete characterized by the geometric and mechanical properties reported in tab. 1. the parameters of the evolution law (7) adopted for the curves of fig. 3 have the same values assumed in fig. 1: e.g., in the solid black curves of fig. 3,   ,0 , 0v v mf f , , 30, 40, 50v eqf ,   0.7 . the failure curves exhibit an elliptical shape and the curves t a. caporale et alii, frattura ed integrità strutturale, 29 (2014) 19-27; doi: 10.3221/igf-esis.29.03 25 characterized by , 0v mf have values of  max greater than the uni-axial compressive strength  c . the failure curves reflect the uni-axial behavior observed in fig. 1: for a given direction     t 1 2 ˆ ˆ 0n ,  max decreases with increasing ,v eqf and ,v mf . -0,12 -0,10 -0,08 -0,06 -0,04 -0,02 0,00 -0,12 -0,10 -0,08 -0,06 -0,04 -0,02 0,00  e 2 ( g p a)  e  (gpa)   = 0.8, f v,eq = 30, f v,m = 10, 20   = 0.7, f v,m = 0, f v,eq = 30, 40, 50   = 0.8, f v,m = 0, f v,eq = 30, 40, 50 f v,eq , f v,m figure 3: failure curves in bi-axial compression. -1,50 -1,00 -0,50 0,00 -1,50 -1,00 -0,50 0,00  e   c  e  c   = 0.8, f v,eq = 30, f v,m = 10, 20   = 0.7, f v,m = 0, f v,eq = 30, 40, 50   = 0.8, f v,m = 0, f v,eq = 30, 40, 50 f v,m figure 4: dimensionless failure curves in bi-axial compression. the generic curve of fig. 3 is obtained by connecting the points        1 2 max 1 2ˆ ˆ, , 0 , , 0e e ; this curve intersects the coordinate axes at the points   , 0,0c and  0, , 0c , where  c is the uni-axial compressive strength of concrete and is used to determine the dimensionless curve     1 2 maxˆ ˆ, , 0 c . in fig. 4, the eight curves of figure 3 are plotted in the dimensionless form: these curves depend on the parameter ,v mf . in fact, the curves characterized by , 0v mf are the same whatever the parameter  is, whereas the remaining curves vary with ,v mf : the area bounded by the dimensionless failure curve decreases with increasing ,v mf . fig. 4 shows that the adopted values of ,v mf should be small as large values of ,v mf provide a bi-axial compressive strength max 2 2 less than the uni-axial compressive strength when the average stress  2 2 , 2 2 , 0 is prescribed on concrete, in contrast with the experimental failure curve of concrete. a. caporale et alii, frattura ed integrità strutturale, 29 (2014) 19-27; doi: 10.3221/igf-esis.29.03 26 in fig. 5, six failure curves are plotted: the black curves refer to , 0v mf  whereas the turquoise curves refer to , 10v mf  . moreover, the solid curves are the failure curves in bi-axial compression; the dotted curves are the intersection of the failure surfaces with the plane 3σ 0.01e gpa, where 3σe is the third of the three coordinate axes of the stress space where the failure surface is plotted; the dashed curves are the intersection of the failure surfaces with the plane  3σ 0.01e gpa (for the dotted and dashed curves, the load direction is different from     t 1 2 ˆ ˆ 0n ). as it is expected, the admissible domain bounded by the failure curve increases in presence of a negative 3σe (compression) and decreases in presence of a positive 3σe (traction). -0,12 -0,10 -0,08 -0,06 -0,04 -0,02 0,00 -0,12 -0,10 -0,08 -0,06 -0,04 -0,02 0,00  e 2 (g p a)  e  (gpa)   = 0.7, f v,m = 0, f v,eq = 40,  e 3 = 0  e 3   = 0.7, f v,m = 0, f v,eq = 40,  e 3 = 0.01 gpa   = 0.7, f v,m = 0, f v,eq = 40,  e 3 = 0.01 gpa   = 0.8, f v,m = 10, f v,eq = 30,  e 3 = 0   = 0.8, f v,m = 10, f v,eq = 30,  e 3 = 0.01 gpa   = 0.8, f v,m = 10, f v,eq = 30,  e 3 = -0.01 gpa figure 5: failure curves in bi-axial and tri-axial compression. conclusions n this work, a micromechanical model is used for estimating the failure curves of cement concrete in bi-axial and triaxial compression. the concrete failure is due to the creation and evolution of voids in the cement paste. the void evolution decreases the tangent stiffness to the concrete stress-strain curve and the concrete compressive strength is attained when this tangent line becomes horizontal. this condition is used to determine the failure curves of concrete in bi-axial and tri-axial compression. mori-tanaka and eshelby homogenization methods are used to determine the overall behavior of concrete. the micromechanical analyses show which values of the void evolution parameters represent better the concrete behavior. as a future development, micromechanical methods different from the mori-tanaka one will be used and different evolution laws of the voids will be considered in the attempt to capture better the multi-axial concrete behavior. acknowledgments his research was carried out in the framework of the dpc/reluis 2014 – aq dpc/reluis 2014-2016 project (theme: reinforced concrete structures) funded by the italian department of civil protection. references [1] bruno, d., greco, f., lonetti, p., blasi, p.n., sgambitterra, g., an investigation on microscopic and macroscopic stability phenomena of composite solids with periodic microstructure, international journal of solids and structures, 47 (2010) 2806-24. i t a. caporale et alii, frattura ed integrità strutturale, 29 (2014) 19-27; doi: 10.3221/igf-esis.29.03 27 [2] caporale, a., luciano, r., micromechanical analysis of periodic composites by prescribing the average stress, annals of solid and structural mechanics, 1 (2010) 117-137. [3] greco, f., leonetti, l., lonetti, p., a two-scale failure analysis of composite materials in presence of fiber/matrix crack initiation and propagation, composite structures, 95 (2013) 582-97. [4] lau, k.-t., zhou, l.-m., mechanical performance of composite-strengthened concrete structures, composites part b: engineering, 32 (2001) 21-31. [5] aprile, a., benedetti, a., coupled flexural-shear design of r/c beams strengthened with frp, composites part b: engineering, 35 (2004) 1-25. [6] agbossou, a., michel, l., lagache, m., hamelin, p., strengthening slabs using externally-bonded strip composites: analysis of concrete covers on the strengthening, composites part b: engineering, 39 (2008) 1125-35. [7] d’ambrisi, a., feo, l., focacci, f., bond-slip relations for pbo-frcm materials externally bonded to concrete, composites part b: engineering, 43 (2012) 2938-49. [8] d’ambrisi, a., feo, l., focacci, f., experimental analysis on bond between pbo-frcm strengthening materials and concrete, composites part b: engineering, 44 (2013) 524-32. [9] milani, g., esquivel, y.w., lourenço, p.b., riveiro, b., oliveira, d.v., characterization of the response of quasiperiodic masonry: geometrical investigation, homogenization and application to the guimarães castle, portugal, engineering structures, 56 (2013) 621-41. [10] caporale, a., parisi, f., asprone, d., luciano, r., prota, a., micromechanical analysis of adobe masonry as twocomponent composite: influence of bond and loading schemes, composite structures, 112 (2014) 254-63. [11] yang, c.c., huang, r., a two-phase model for predicting the compressive strength of concrete, cement and concrete research, 26 (1996) 1567-77. [12] yang, c.c., approximate elastic moduli of lightweight aggregate, cement and concrete research, 27 (1997) 1021-30. [13] yang, c.-c., huang, r., approximate strength of lightweight aggregate using micromechanics method, advanced cement based materials, 7 (1998) 133-8. [14] li, g., zhao, y., pang, s.-s., four-phase sphere modeling of effective bulk modulus of concrete, cement and concrete research, 29 (1999) 839-45. [15] hashin, z., monteiro, p.j.m., an inverse method to determine the elastic properties of the interphase between the aggregate and the cement paste, cement and concrete research, 32 (2002) 1291-300. [16] hernández, m.g., anaya, j.j., ullate, l.g., ibañez, a., formulation of a new micromechanic model of three phases for ultrasonic characterization of cement-based materials, cement and concrete research, 36 (2006) 609-16. [17] caporale, a., feo, l., luciano, r., damage mechanics of cement concrete modeled as a four-phase composite, composites part b: engineering, in press. http://dx.doi.org/10.1016/j.compositesb.2014.02.006 [18] watanabe, k., niwa, j., yokota, h., iwanami, m., experimental study on stress-strain curve of concrete considering localized failure in compression, journal of advanced concrete technology, 2 (2004) 395-407. [19] desayi, p., krishnan, s., equation for the stress–strain curve of concrete, aci j 61 (1964) 345–50. microsoft word numero_39_art_13 s. seitl et alii, frattura ed integrità strutturale, 39 (2017) 118-128; doi: 10.3221/igf-esis.39.13 118 focussed on modelling in mechanics modified compact tension specimen for experiments on cement based materials: comparison of calibration curves from 2d and 3d numerical solutions s. seitl, v. viszlay brno university of technology, faculty of civil engineering, veveří 331/95, brno 602 00, czech republic seitl.s@fce.vutbr.cz, http://orcid.org/0000-0002-4953-4324, viszlay.v@fce.vutbr.cz abstract. the evaluation of fracture mechanics parameters of materials has become very important part of considering the condition of older constructions as well as properties of newly developed materials. this contribution focuses on a numerical simulation and a calculation of fracture mechanical properties of modified compact tension test configuration. it is possible to prepare the specimens used for this test very easily from a drilled core or from specimens used for cylindrical compression test. the focus of contribution is to compare selected outputs from numerical solution of 2d (plane strain conditions) with 3d models. particularly, the determination of the influence of 2d and 3d model on the calibration curves for selected fracture mechanics parameters is of interest. finite element software ansys was used for the numerical analysis. keywords. stress intensity factor; cod; cmod; biaxiality factor; modified compact tension test; fracture mechanics of concrete. citation: seitl, s., viszlay, v., modified compact tension specimen for experiments on cement based materials: comparison of calibration curves from 2d and 3d numerical solutions, frattura ed integrità strutturale, 39 (2017) 118-128. received: 17.07.2016 accepted: 22.09.2016 published: 01.01.2017 copyright: © 2017 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. introduction ompact tension (ct) tests have been widely and successfully applied for measuring the fracture properties of several materials, such as metals (astm standard e-399 [3]), or even composite materials with limited orthotropy [1]. note that for test of fracture properties is not prepared norm only recommendation rilem for three point bending test [17], rilem for bending test for concrete with fibers [16, 18] and as a standard test the wedge splitting test is used (cube or cylindrical [12, 14, 19, 20]). the compact tension fracture toughness test (ct test [11, 22]) is essentially performed by applying equal and opposite forces through two holes previously made in the specimen, to propagate an initial crack. however, its applicability in concrete is characterized by some disadvantages, such as drilling the holes necessary to apply c http://www.gruppofrattura.it/pdf/rivista/numero39/audio/13.mp3 s. seitl et alii, frattura ed integrità strutturale, 39 (2017) 118-128; doi: 10.3221/igf-esis.39.13 119 the pulling forces and the hazard of a local fracture originated at these holes. the modified compact tension test (mct [4, 5, 9, 10, 21, 23) is a quite new test configuration on notched specimens to obtain fracture mechanics parameters of materials in laboratory conditions, note that test is derived from classic ct test. a detailed research program/campaign has to be done before the configuration starts to be used as a standard. the several authors used cohesive crack model and prepared mct model in software atena [10] or in software abaqus [5]. pilot experimental measurement and comparison of selected configurations with three point bending specimen is introduced in contributions [4, 9]. the main advantage of mct test is a round shape of the specimen that makes it appropriate for testing cement based composites. due to its shape, it is easy to prepare specimen both ways: by cutting them of the drilled core in case of constructions which are already being used [6-8, 15,] as well as in forms from the fresh concrete mixture [24]. the geometry of the specimen is shown in fig. 1. figure 1: modified compact tension test: a) schema of the test and b) a photo from the test. the aim of the paper is to provide calibration curves according to four different fracture mechanics parameters and to compare selected case with the values obtained from 3d model with the results from 2d model, which have already been published in [21]. the first considered parameter is stress intensity factor ki [mpa·m1/2], see e.g. [1, 3, 11]. the value of stress intensity factor for each normalized crack length a/w is obtained by linear extrapolation from values in particular nodes behind the crack tip up to 3 mm distance. values in a number of first nodes had to be neglected due to big mistake caused by stress singularity near to the crack tip. values of t-stress [mpa] defined e.g. were obtained by different method. both parameters were normalized as dimensionless biaxiality factors b1 [-] and b2 [-] by (1) using the eqs. (2) and (3), see [11, 13]: ,0 wt p k  (1) , 0 1 k k b i (2) ,2 ik at b   (3) where p is loading force in [n], t is thickness of the specimen in [mm], w stands for the position of loading force in [mm] and a is the crack length in [mm]. a) b) 1 .3 5 w x y z s. seitl et alii, frattura ed integrità strutturale, 39 (2017) 118-128; doi: 10.3221/igf-esis.39.13 120 the next two considered parameters were opening displacements. the first, crack opening displacement cod [mm] is an opening displacement under the load force (at loadline), 5 mm from the crack path. the second one, crack mouth opening displacement cmod [mm] is measured at crack edge. in both cases, the outputs were dimensionless compliance functions fcod(a/w) [-] and fcmod(a/w) [-] obtained from measured values of displacement by using normalization eq. (4) in the eq. (5). , 22 )1(/   e wak f inorm   (4)   ,/ norm y f u waf  (5) where uy is selected point displacement in [mm], ν is poisson’s ratio [-] and e is young’s modulus [mpa]. the positions of selected points are related to the experimental set-up position: cmod-clip gage at the end of specimen and cod – by displacement of machine load set up or both (cmod, cod) points by system aramis or other digidal image correlation system. the considered values of material characteristics are sumarized in tab. 1. elastic properties e [mpa]  [-] steel 210 000 0.3 concrete 5 5 000 0.2 concrete 20 20 000 0.2 concrete 25, see [21] 25 000 0.2 concrete 60 60 000 0.2 concrete 100 100 000 0.2 table 1: characteristics of used materials as the input parameters for numerical calculation. numerical solution n this paper, the 2d and 3d models for numerical solution will be compared in a range of two-parameter fracture mechanics (see [11, 20]). the finite element software ansys was used for numerical analysis [2]. element type plane183 was used for 2d simulation which is able to degenerate from 8-node to 6-node and therefore is able to fit better stress singularity due to translocate to middle node to ¼ distance from crack tip. for 2d model, the plane-strain conditions were applied due to experiment specimen thickness 50 mm. the 2d solution is described and discussed in [21]. for 3d model, the element solid186 was used. this type of element is suitable for irregular meshes, tetrahedral and pyramid options could be used. the specimen thickness for 3d model was 50 mm (full specimen). a diameter of specimen used for simulations was selected as d=150 mm as an appropriate size of a drill which is commonly used to obtain this type of specimen from a construction element. a considered length of the steel bars was 110 mm on each side of the specimen and used load force was p=1500 n. the load force was applied as a pressure on the area at the end of the bar so the stress was applied uniformly. the end part of the steel bar (last 30 mm) was considered to be gripped into hydraulic testing machine. therefore for this part, a displacement in x and z directions was set to zero. the diameter of the steel bars was 8 mm. an interface among the steel bar and a concrete matrix was modeled without any transitional layer (perfect adhesion). the perpendicular distance between steel bars and the middle of the specimen was 45 mm. a relative crack length α (stands for a/w ratio) varied from 0.1 to 0.9 in steps of 0.1. the density of the mesh was refinded in the vicinity of the crack tip, where average element size was 0.2 mm. then the element size fluently increases to the value of 5 mm on the outer sides of the specimen. the advantage of symmetric specimen was exploited and so only 1/4 of 3d model was built. the symmetric boundary conditions were applied along the vertical cross-section.the meshed model for α=0.4 is shown in fig. 2. i s. seitl et alii, frattura ed integrità strutturale, 39 (2017) 118-128; doi: 10.3221/igf-esis.39.13 121 numerical results and discussion he finite element simulations were performed for various values of material properties listed in tab. 1 (effect of change elasticity modulus ratio – constant value of young’s modulus for steel and the value of young modulus for concrete is changed), and effect of 2d and 3d model solutions for various crack lengths, subjected to uniform load. the results of stress intensity factors k and t-stress are normalized by eq. (2) and (3). in figs. 3 and 8, the examples of deformed finite element models of 2d and 3d solutions are shown. the calibration curves are introduced in eqs. (6-24) for each selected case. figure 2: example of finite element 3d model used for numerical study =0.4. effect of elasticity modulus ratio the numerically obtain results from 2d model solution covering the effect of elastic modulus ratio are shown in figs. 4-7 (stress intensity factor, t-stress, cod and cmod). the results of stress intensity factors and t-stress are normalized by eqs. (2) and (3). the functions of the calibration curve for mct specimens with steel bars with diameter 150 mm have to be calculated for each value of young’s modulus, especially, for long cracks from 0.6 to 1, see example for selected values. figure 3: example of 2d finite element model after deformation. t s. seitl et alii, frattura ed integrità strutturale, 39 (2017) 118-128; doi: 10.3221/igf-esis.39.13 122 the b1 curves are practically the same values for all five various materials. it only changes for values of relative crack length longer than α =0.5 (see fig. 4). the functions of calibration curves for selected young’s modulus of concrete e= 5, 20 and 100 gpa can be introduced as follows: b1 (e=5)= 5.5881 34.181α + 239.39α2 594.79α3 + 688.58α4 251.61α5 (6) b1 (e=20)= -2.3617 + 117.22α 736.11α2 + 2191.5α3 2926.8α4 + 1503.9α5 (7) b1 (e=100)= -16.91 + 389.22α 2465.6α2 + 7030.8α3 9049.3α4 + 4371.4α5 (8) figure 4: values of dimensionless b1 factor (stress intensity factor) versus a/w, the effect of elasticity modulus ratio (steel e=210 gpa). figure 5: values of dimensionless b2 factor (t-stress) versus a/w, the effect of elasticity modulus ratio (steel e=210 gpa). fig. 5 shows that the b2 parameter changes practically negligibly, only for very low values of young’s modulus e=5 gpa, there is relatively small deviation from another curves. 0 20 40 60 80 100 120 0 0,1 0,2 0,3 0,4 0,5 0,6 0,7 0,8 0,9 1 b 1 [‐ ] a/w[‐] e=5 gpa e=20 gpa e=60 gpa e=100 gpa ‐0,4 ‐0,2 0,0 0,2 0,4 0,6 0,8 1,0 1,2 1,4 1,6 1,8 0 0,1 0,2 0,3 0,4 0,5 0,6 0,7 0,8 0,9 1 b 2  [ ‐] a/w[‐] e=5 gpa e=20 gpa e=60 gpa e=100 gpa s. seitl et alii, frattura ed integrità strutturale, 39 (2017) 118-128; doi: 10.3221/igf-esis.39.13 123 b2 (e=5)= -0.5625 + 5.0149α 7.4585α2 + 5.1659α3 0.636α4 (9) b2 (e=20)= -0.4339 + 3.7445α 2.3166α2 2.6828α3 + 3.5752α4 (10) b2 (e=100)= -0.2136 + 1.0257α + 7.8949α2 17.492α3 + 10.933α4 (11) figure 6: values of cod (opening at load line) versus a/w, the effect of elasticity modulus ratio (steel e=210 gpa). figure 7: values of cmod (crack mouth open displacement) versus a/w, the effect of elasticity modulus ratio (steel e=210 gpa). compliance functions (according eqs. (4) and (5)) for opening displacement under the loading force (cod) and for opening displacement at the crack mouth (cmod) follow for young’s modulus of concrete e=5, 20 and 100 gpa, respectively: for cod 0,0 5,0 10,0 15,0 20,0 25,0 30,0 0 0,1 0,2 0,3 0,4 0,5 0,6 0,7 0,8 0,9 1 f c o d [‐ ] a/w[‐] e=5 gpa e=20 gpa e=60 gpa e=100 gpa 0,0 5,0 10,0 15,0 20,0 25,0 30,0 35,0 0 0,1 0,2 0,3 0,4 0,5 0,6 0,7 0,8 0,9 1 f c m o d [‐ ] a/w[‐] e=5 gpa e=20 gpa e=60 gpa e=100 gpa s. seitl et alii, frattura ed integrità strutturale, 39 (2017) 118-128; doi: 10.3221/igf-esis.39.13 124 fcod (e=5)= 6.0419 4.4767α + 77.12α2 153.38α3 + 106.59α4 (11) fcod (e=20)= 6.7211 12.764α + 111.24α2 208.43α3 + 138.35α4 (12) fcod (e=100)= 7.491 + 21.077α + 139.81α2 248.63α3 + 158.95α4 (13) and for cmod fcmod (e=5)= 10.54 10.549α + 100.94α2 194.05α3 + 132.77α4 (14) fcmod (e=20)= 12.478 27.907α + 162.68α2 285.45α3 + 182.31α4 (15) fcmod (e=100)= 15.905 55.717α + 245.61α2 390.95α3 + 231.39α4 (16) effect of 2d and 3d model solutions the results of 2d and 3d model solutions (steel e=210 gpa, concrete e=25 gpa) are shown in figs. 9-12 (stress intensity factor, t-stress, cod and cmod). the model of 3d model solution was prepared as ¼ of all body, the steel part was as ½ of the round bar. the example of the model after deformation is shown in fig. 8. figure 8: example of 3d finite element model after deformation. figure 9: values of dimensionless b1 factor (stress intensity factor) versus a/w, effect of elasticity modulus ratio (steel e=210 gpa). s. seitl et alii, frattura ed integrità strutturale, 39 (2017) 118-128; doi: 10.3221/igf-esis.39.13 125 the b1 curves are practically the same for both cases. it only changes for values of relative crack length longer than α =0.7 (see in fig. 9). the functions of calibration curve for both (2d and 3d) solutions (with young’s modulus of concrete e= 25 gpa) can be introduced as follows: b1 (2d)= -4.4888 + 157.35α 992.61α2 + 2913.2α3 3845.6α4 + 1937.8α5 (17) b1 (3d)= -19.17 + 437.74α 2795.2α2 + 7977.5α3 10259α4 + 4936.2α5 (18) figure 10: values of dimensionless b2 factor (t-stress) versus a/w, the effect of elasticity modulus ratio (steel e=210 gpa). fig. 10 shows that the b2 parameter changes practically negligibly. only for very long cracks 0.7 and longer, some differences can be seen between curves. b2 (2d)= -0.352 + 2.6238α + 2.2014α2 9.8235α3 + 7.4131α4 (19) b2 (3d)= -0.2905 + 2.2439α + 2.305α2 8.4968α3 + 6.315α4 (20) figure 11: values of cod (opening at load line) versus a/w, the effect of elasticity modulus ratio (steel e=210 gpa). the curves obtained by 3d model solution do not differ very much and they follow the shape of ones obtained by 2d model solution. the main differences come for relative long crack =0.8 for the values of stress intensity factor results, see s. seitl et alii, frattura ed integrità strutturale, 39 (2017) 118-128; doi: 10.3221/igf-esis.39.13 126 fig. 9. the obtained values are a little higher over a whole range of relative crack length and that’s caused by z stress component. compliance functions for opening displacement under the loading force (cod) and for opening displacement at the crack mouth (cmod) (according eqs. (4) and (5)) follow from 2d and 3d model solutions, respectively: for cod fcod (2d)= 6.8209 13.922α + 115.54α2 214.86α3 + 141.81α4 (21) fcod (3d)= 7.7038 18.056α + 131.72α2 239.55α3 + 155.85α4 (22) and for cmod fcmod (2d)= 12.849 31.071α + 172.7α2 298.93α3 + 188.98α4 (23) fcmod (3d)= 15.138 43.207α + 210.8α2 350.23α3 + 215.04α4 (24) figure 12: values of cmod (crack mouth open displacement) versus a/w, the effect of elasticity modulus ratio (steel e=210 gpa). conclusions he finite element analysis of two effects on modified compact tension test for specimens like concrete is introduced by means of a constraint-based two parameter fracture mechanic approach. five various materials configurations (steel and concrete) and 2d and 3d solutions were investigated. the following principal conclusions could be derived:  the influence of elasticity modulus ratio (constant value of young’s modulus defined for steel and different values for concrete) on the calibration curve is not negligible and for each case a different polynomial function has to be used.  the curves obtained by 3d model solution don’t differ very much and they follow the shape of ones obtained with 2d model solution very well, the largest differences are related to long crack in stress intensity factor results. the obtained values are a little higher over a whole range of relative crack length and that’s caused by z stress component.  the results from 2d model solution can be used instead of ones from 3d model solution and they are in a range of acceptance. moreover, they can be calculated much faster for another specimen sizes or bars positions. t s. seitl et alii, frattura ed integrità strutturale, 39 (2017) 118-128; doi: 10.3221/igf-esis.39.13 127 acknowledgement his paper has been worked out under the “national sustainability programme i” project “admas up – advanced materials, structures and technologies” (no. lo1408) supported by the ministry of education, youth and sports of the czech republic. references [1] anderson, t., l. fracture mechanics fundamentals and applications, crc press (1991) [2] ansys reference, www.ansys.com [3] astm e399 12e3 standard test method for linear-elastic plane-strain fracture toughness kic of metallic materials, doi: 10.1520/e0399. [4] cifuentes, h., lozano, m., holušová, t., medina, f., seitl, s., and canteli, a. applicability of a modified compact tension specimen for measuring the fracture energy of concrete, anales de mecánica de la fractura, 32 (2015) 208– 213. [5] fernández-canteli, a., castañón, l., nieto, b., lozano, m., holušová, t., seitl, s. determining fracture energy parameters of concrete from the modified compact tension test, frattura ed integrità strutturale, 30 (2014) 383–393. doi: 10.3221/igf-esis.30.46. [6] gaedicke, c., marines, a., miankodila, f., assessing the abrasion resistance of cores in virgin and recycled aggregate pervious concrete, construction and building materials, 68 (2014) 701-708. doi: 10.1016/j.conbuildmat.2014.07.001 [7] gaedicke, c., torres, a., huynh k.c.t., marines, a., a method to correlate splitting tensile strength and compressive strength and compressive strength of pevious concrete and cores, construction and building materials 125(2016) 271– 278. doi: 0.1016/j.conbuildmat.2016.08.031. [8] hidayat, a., purwanto, p., puspowardojo, j., aziz, f.a., the influence of graded concrete strength on concrete element, procedia engineering, 125(2015) 1023–1029. doi: 10.1016/j.proeng.2015.11.157 [9] holušová, t., lozano, m., canteli, a., komárková, t., kocáb, d., seitl, s. influence of the gripping fixture on modified compact tension test results: evaluation of the experiments on cylindrical concrete specimens, transactions of the všb – ostrava technical university of ostrava civil engineering series, 15(2) (2015) 10. doi: 10.1515/tvsb-2015-0010. [10] holušová, t., seitl, s., canteli, a. numerical simulation of modified compact tension test depicting of experimental measurement by aramis, key engineering materials 627 (2015) 277–280. doi: 10.4028/www.scientific.net/kem.627.277 [11] knésl, z., bednář, k. two parameter fracture mechanics: calculation of parameters and their values, institute of physics of materials academy of science of the czech republic, (1998). [12] korte, s., boel, v., de corte, w., de schutter, g., static and fatigue mechanics properties of self-compacting concrete using three-point bending tests and wedge-splitting tests, construction and building materials, 57(2014) 1–8. doi: 10.1016/j.conbuildmat.2014.01.090. [13] leevers, p.s., radon, j.c., inherent stress biaxiality in various fracture specimen geometries, international jouirnal of fracture, 19(4) (1982) 311–325. doi: 10.1007/bf00012486. [14] merta, i., tschegg, e.k., fracture energy of natural fibre reinforced concrete, construction and building materials, 40 (2013) 991–997. doi:10.1016/j.conbuildmat.2012.11.060. [15] mynarcik, p., core sampling for fiber concrete constructions-context between quantity of core samples and evaluation of fiber concrete characteristics, procedia engineering 114 (2015) 493–499. doi:10.1016/j.proeng.2015.08.097. [16] ponikiewski, t., katzer, j., properties of fresh scc mix reinforced by different types of steel and polymer fibre, construction and building materials, 62 (2014) 96–101. doi: 10.1016/j.conbuildmat.2014.03.037. [17] rilem publications sarl, determination of the fracture energy of mortar and concrete by means of three-point bend tests on notched beams, (1985) 285–290. [18] rilem tc 162-tdf: test and design methods for steel fibre reinforced concrete, bending test, materials and structure, 35 (2002) 579–582. [19] řoutil, l., veselý, v., seitl, s. fracture analysis of cubeand cylindershaped wst specimens made of cementitious composites with various characteristic length, 188-489 (2012) 533–536. doi: 10.4028/www.scientific.net/kem.488-489.533. t s. seitl et alii, frattura ed integrità strutturale, 39 (2017) 118-128; doi: 10.3221/igf-esis.39.13 128 [20] seitl, s., veselý, v., řoutil, l., two-parameter fracture mechanical analysis of a near-crack-tip stress field in wedge splitting test specimens, computers and structures, 21-22 (2011) 1852–1858. doi: 10.1016/j.compstruc.2011.05.020. [21] seitl, s., viszlay, v., cifuentes, h., canteli, a. effects of specimen size and crack depth ratio on calibration curves for modified compact tension specimens, transactions of the všb – technical university of ostrava civil engineering series, 15(2), (2015) 23. doi: 10.1515/tvsb-2015-0023. [22] tada, h., paris p.c., irwin, r.g. the stress analysis of cracks handbook (3rd edition). new york: asm international, (2000). [23] veselý, v., sobek, j., numerical study of failure of cementitious composite specimens in modified compact tension fracture test, transactions of the všb – technical university of ostrava, civil engineering series, 13(2) (2013) 180– 187, doi: 10.2478/tvsb-2013-0025, [24] wu, y., xu, s., li, q., ruiz, g., yu, r.c., estimation of real fracture parameters of a dam concrete with large size aggregates through wedge splitting tests of drilled cylindrical specimens, engineering fracture mechanics, (2016). doi: 10.1016/j.engfracmech.2016.06.012. << /ascii85encodepages false /allowtransparency false /autopositionepsfiles true /autorotatepages /none /binding /left /calgrayprofile (dot gain 20%) /calrgbprofile (srgb iec61966-2.1) /calcmykprofile (u.s. web coated \050swop\051 v2) /srgbprofile (srgb iec61966-2.1) /cannotembedfontpolicy /error /compatibilitylevel 1.4 /compressobjects /tags /compresspages true /convertimagestoindexed true /passthroughjpegimages true /createjobticket false 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/hrv (za stvaranje adobe pdf dokumenata najpogodnijih za visokokvalitetni ispis prije tiskanja koristite ove postavke. stvoreni pdf dokumenti mogu se otvoriti acrobat i adobe reader 5.0 i kasnijim verzijama.) /hun 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can be opened with acrobat and adobe reader 5.0 and later.) >> /namespace [ (adobe) (common) (1.0) ] /othernamespaces [ << /asreaderspreads false /cropimagestoframes true /errorcontrol /warnandcontinue /flattenerignorespreadoverrides false /includeguidesgrids false /includenonprinting false /includeslug false /namespace [ (adobe) (indesign) (4.0) ] /omitplacedbitmaps false /omitplacedeps false /omitplacedpdf false /simulateoverprint /legacy >> << /addbleedmarks false /addcolorbars false /addcropmarks false /addpageinfo false /addregmarks false /convertcolors /converttocmyk /destinationprofilename () /destinationprofileselector /documentcmyk /downsample16bitimages true /flattenerpreset << /presetselector /mediumresolution >> /formelements false /generatestructure false /includebookmarks false /includehyperlinks false /includeinteractive false /includelayers false /includeprofiles false /multimediahandling /useobjectsettings /namespace [ (adobe) (creativesuite) (2.0) ] /pdfxoutputintentprofileselector /documentcmyk /preserveediting true /untaggedcmykhandling /leaveuntagged /untaggedrgbhandling /usedocumentprofile /usedocumentbleed false >> ] >> setdistillerparams << /hwresolution [2400 2400] /pagesize [612.000 792.000] >> setpagedevice microsoft word numero_39_art_24 o. daghfas et alii, frattura ed integrità strutturale, 39 (2017) 263-273; doi: 10.3221/igf-esis.39.24 263 experimental and numerical study on mechanical properties of aluminum alloy under uniaxial tensile test o. daghfas, a. znaidi, a. ben mohamed, r. nasri university of tunis manar, national school of engineers of tunis, lr-mai-enit bp37, 1002 tunisie daghfasolfa@yahoo.fr, amna.znaidi@laposte.net, ahmed82enit@yahoo.fr, rachid.nasri@enit.rnu.tn abstract. the main objective is to model the behavior of 7075 aluminum alloy and built an experimental database to identify the model parameters. the first part of the paper presents an experimental database on 7075 aluminum alloy. thus, uniaxial tensile tests are carried in three loading directions relative to the rolling direction, knowing that the fatigue of aircraft structures is traditionally managed based on the assumption of uniaxial loads. from experimental database, the mechanical properties are extracted, particularly the various fractures owing to pronounced anisotropy relating to material. in second part, plastic anisotropy is then modeled using the identification strategy which depends on yield criteria, hardening law and evolution law. in third part, a comparison with experimental data shows that behavior model can successfully describe the anisotropy of the lankford coefficient. keywords. aluminum alloy; experimental tensile test; identification; lankford coefficient; mechanical properties. citation: daghfas, o., znaidi, a., ben mohamed, a., nasri, r., experimental and numerical study on mechanical properties of aluminum alloy under uniaxial tensile test, frattura ed integrità strutturale, 39 (2017) 263-273. received: 04.11.2016 accepted: 09.12.2016 published: 01.01.2017 copyright: © 2017 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. introduction he study of the behavior of metallic materials during the forming process is an important subject. the nature of the used materials and solicitations require a formulation taking into account elastoplastic behavior, finite deformation and the anisotropy of the material, in particular for thin sheet metal forming [1]. despite the importance of the work in this field, aluminum alloys continue to be the center of interests of several researches in materials science. their use in the automotive and aviation industry depends largely on their mechanical and thermal characteristics. the addition of zinc in aluminum does not alter the mechanical properties. therefore metallurgists have turned to ternary aluminum-zinc-magnesium alloys (with or without copper) of the 7000 series that have been widely used as structural materials due to their attractive comprehensive properties, such as low density, high strength, ductility, toughness and resistance to fatigue [2, 3]. the 7075 aluminum alloy (a typical al–zn–mg–cu alloy) is one of the most important engineering alloys. it is mainly used in the automotive industry, in transport and aeronautics due to its excellent strength/weight ratio [4]. these alloys have very good mechanical properties; it is the high-strength aluminum alloys with a low resistance to corrosion. the t http://www.gruppofrattura.it/pdf/rivista/numero39/audio/24.mp3 o. daghfas et alii, frattura ed integrità strutturale, 39 (2017) 263-273; doi: 10.3221/igf-esis.39.24 264 mechanical strength of these alloys is increased by structural hardening phenomenon [5]. this type of alloy is mainly used in the automotive industry, in transport and aeronautics especially in the design of the fuselage of the airbus [6]. metal sheets, that have undergone extensive plastic deformation by rolling or extrusion, exhibit a significant anisotropy of mechanical properties. thus, they have a particular texture, characterized by a preferred orientation of the grains constituting the material [7]. this texture gives the sheet a special plastic behavior. for modeling the plastic behavior, two aspects of the anisotropy are taken into account: the initial anisotropy due to the initial texture of the metal sheets and the anisotropy induced by cold working [8], mainly due to the development of dislocation structures in the material [9; 10]. recently, researches on aluminum alloy are focused on mechanical properties, texture and anisotropic behavior that give rise from processing of aluminum alloy sheet [6-7, 10-11]. there has been little research on formability and anisotropic behavior of commercialized 7075 aluminum alloy. however, the influences of loading orientations on aluminum alloy plate are still an open question. the purpose of the present study is to describe and characterize the mechanical properties, anisotropic behavior of highstrength aluminum alloy loaded at 0°, 45°and 90° to the rolling direction of the 3 mm thick plate, and provide direction for obtaining the optimized parameters for 7075 aluminum alloy in metal forming. as the initial anisotropy is taken into account through a yield criterion [9], the yld91 anisotropic yield function proposed by barlat et al. [12] is chosen to model the elastoplastic behavior of the 7075-t7 aluminum alloy. the plastic parameters were determined using an experimental database from uniaxial tensile tests. numerical simulations of the experimental tensile tests were performed using the anisotropic elastoplastic model. predicted stress-strain curves were in very good agreement with the experimental curves for three loading directions. the results of simple tensile test were used subsequently to show the evolution of plastic anisotropy called lankford coefficient and load surface for several tests. experimental procedure material he 7075 aluminum alloy with structural hardening is used. this alloy is a thin rolled sheet with a thickness of 3.5 mm. the material used in this investigation is a commercially produced 7075 aluminum alloy with the following chemical compositions: alzn (6.1%)-mg (2.1%)-cu (1.2%) and balance al (all in mass pct) [13]. the heat treatment process for this material is t7351. t7 temper is achieved by solution-treatment at 465°c (  5°c), quenching in water (<40°c), maturation at room temperature during 4 days and tempering (135°c  5°c 12h) and then 2% pre-stretching to release residual stress [13]. dimensions and form of the test specimens the uniaxial test is ensured by a specific geometry defined by the standard nf a 03-151 [14]. schematic tensile specimen used for this study is shown in fig. 1. the current dimensions of useful part are l0=50mm and b0=12.5mm. the specimens are cut in three directions relative to the rolling direction (rd) in the plane of the sheet (see fig. 2 (a)). in the following, the rolling direction is referred to as rd, the transverse direction as td and the direction (45° from the rd) as dd. the angle between the loading direction and the rolling direction will be noted subsequently . three samples were prepared for each loading direction to verify repeatability. each specimen was machined in different directions of the plate to enlighten the anisotropy of the material. figure 1: tensile specimen used in the present study, the useful area (l0=50mm, b0 = 12.5mm). t r20 rd y x t  o. daghfas et alii, frattura ed integrità strutturale, 39 (2017) 263-273; doi: 10.3221/igf-esis.39.24 265 (a) (b) (c) (d) figure 2: (a) loading direction of cutting (b) electronic extensometer (c) tensile test machine and (d) acquisition chain. experimental set the test is carried out on a hydraulic press (shimadzu) that has a maximum load capacity of 30 kn (fig. 2 (c)), class 0.5 bs en iso-1 [15]. a chain acquisition (see fig. 2 (d)) allows recording the strain as a function of stress. the loading speed is 4mpa.s-1. two electronic extensometers are used to measure the strain rate according to the width and the thickness along the tensile test (fig. 2(b)). experimental results experimental database contains three tensile curves and their experimental lankford coefficients (r0°, r45° and r90° presented in tab. 1). experimental tensile curves of 7075-t7 in three directions 0°(rd), 45° (dd) and 90°(td) from the rolling direction are presented in fig. 3. uniaxial tensile tests taken for three orientations to the rolling direction reveal the nature of anisotropy in this material where strengths and ductility vary with orientation in the plane of the sheet. fig. 3 shows similar yield strength and plastic deformation characteristics in the rolled rd and dd directions until 11.5% in strain. the td direction has a similar yield strength but different hardening characteristics and lower elongation (8%). this result exhibit a marked tensile anisotropy. fig. 3 indicate that the 7075 in temper t7 is defined by maximum percentage elongation along the rolling direction and minimum value along the transverse direction. o. daghfas et alii, frattura ed integrità strutturale, 39 (2017) 263-273; doi: 10.3221/igf-esis.39.24 266 figure 3: experimental tensile curves obtained at rd, dd and td from the rd. the 7075-t7 aluminum alloy has high mechanical properties both in terms of strength and ductility compared to pure aluminum a5 [16]. maximum yield re and tensile rm strengths are observed especially in the transverse direction but a significant decrease in percentage elongation a%. this is explained by the structural hardening. the commercialized aluminum alloy in t7 temper is much stronger than pure aluminum (around 40 mpa against 430 mpa for the yield strength), but it has a failure elongation (maximum plastic deformation of 0.13 against 0.27 for pure aluminum). according to the experimental results we are seeing the influence of the anisotropy on the specimen fracture especially after transverse loading (90°). we present in tab.1 the experimental lankford coefficients relating to three loading directions. ψ r(ψ) 00° 0.069 45° 0.138 90° 0.099 table1: experimental lankford coefficient for different loading directions. the anisotropy coefficient illustrates the deformation mode of the metal sheet. a small lankford coefficients indicated by 7075-t7 led to a significant reduction in thickness. the tensile test is the simplest and most widely used because it allows obtaining a lot of information (elastic modulus, yield strength, maximum load, elongation at break ...) and maintaining a homogeneous strain in the useful part. anisotropic elasto-plastic model his work is limited to plastic orthotropic behavior. the materials are treated as incompressible with negligible elastic deformations. models are formulated for standard generalized materials with an isotropic hardening described by an internal hardening variable, a law of evolution and an equivalent deformation. the material is initially orthotropic and remains orthotropic; isotropic hardening is assumed to be captured by a single scalar internal hardening variable denoted by p . t o. daghfas et alii, frattura ed integrità strutturale, 39 (2017) 263-273; doi: 10.3221/igf-esis.39.24 267 the behavior model is defined by: yield function in particular, we will assume that the elastic range evolves homothetically, the yield criterion is then written as follows:      p pc sf , 0     q q (1) c : equivalent stress is given by the barlat criterion 91[12]:     m c 1m mm 1 2 2 3 1 3= q q + q q + q q q (2) where kq 1,2,3 are the eigenvalues of a modified stress deviator tensor q defined as follows: d:q α  (3) d is the deviator of the cauchy stress tensor (incompressible plasticity). the fourth order tensor α carries the anisotropy by 6 coefficients c1, c2, c3, c4, c5, c6.  ps  : isotropic hardening function; where p is the equivalent plastic strain. hardening law using as a hardening function respectively a hollomon and voce laws [17]: hollomon law    np ps k   (4) k and n: the hollomon parameters to be identified voce law     p ps s 1 exp     σ ε (5) this law introduces a hardening saturation s ,  and  describe the non-linear part of the curve during the onset of plasticity where 0< <1 and  <0) evolution law the direction of the plastic strain rate p is perpendicular to the yield surface and is given by: p d f     ε σ  (6) with  plastic multiplier that can be determined from the consistency condition f 0 lankford coefficient in the characterization of thin sheets, the plastic anisotropy with different directions is frequently measured by the lankford coefficient r that is given by the following expression: o. daghfas et alii, frattura ed integrità strutturale, 39 (2017) 263-273; doi: 10.3221/igf-esis.39.24 268 yy zzr      (7) where yy and zz are the plastic strain rates in-plane and through the thickness, respectively. the subscript specifies the angle between the axis of the specimen and the rolling direction (fig 2 a). in the case of orthotropy r varies depending on the off axis angle  .this scalar quantity is used extensively as an indicator of the formability. identification procedures n this section we focus on the phenomenology of plastic behavior; especially modeling plasticity and hardening based on experimental data represented as families of hardening curves, and lankford coefficient data. in order to simplify our identification process, the following assumptions are adopted: identification through “small perturbations” process, the tests used are treated as homogeneous tests, we neglect the elastic deformation; the behavior is considered rigid plastic incompressible, the plasticity surface evolves homothetically (isotropic hardening) and all tests are performed in the plane of the sheet resulting in a plane stress condition. the identification of this constitutive law requires the identification of the hardening function, the anisotropy coefficients c1, c2, c3, c4, c5, c6 of the barlat criterion (eq. 2), the shape factor m and the lankford coefficients r ( ) . the barlat criterion or yield 91 is proposed by barlat et al [12] as a non quadratic criterion for anisotropic materials. respecting to plane stress condition, the anisotropy coefficients are reduced to 4 (c1, c2, c3, c4). first identification step by smoothing the experimental tensile curves the hollomon and the voce parameters are determined for three loading directions. tab. 2, tab. 3 and tab. 4 illustrate respectively the identified parameters of hollomon and voce laws. knowing that the coefficient n is the same for all tests [18-19], by convention we choose n for traction in direction ψ = 00° as reference. for n=0.0718, we present different values of k (see tab. 3). the different values of voce parameters are illustrated in tab. 4. ψ k n 00° 606.8441 0.0718 45° 622.0848 0.0766 90° 671.2648 0.0853 table 2: identification of the constants of hollomon law for different loading directions. ψ k 00° 606.8441 45° 613.0297 90° 640.4611 table 3: identification of the constant hardening law for fixed n. ψ s   00° 508.0623 0.2111 -36.8421 45° 511.1316 0.2161 -39.3294 90° 531.9995 0.2613 -49.5677 table 4: identified parameters of voce law. i o. daghfas et alii, frattura ed integrità strutturale, 39 (2017) 263-273; doi: 10.3221/igf-esis.39.24 269 the identified curves by hollomon and voce laws compared to the experimental hardening curves obtained in the two directions relative to the rolling direction (00° and 45°) are presented in fig. 4a and fig.4 b respectively. then a comparison is made in order to show the most suitable law for the identification of hardening curves. a significant difference in result between the two laws is visible by zooming the curves. it is seen that in the homogeneous part of the plastic deformation the voce law describes the specimen fracture better than the hollomon law for two loading directions from the rolling direction. by convention, the voce hardening law is selected subsequently to identify anisotropy behavior relating to this alloy. (a) ψ = 00° (b) ψ = 45° figure 4: identification of the hardening curve: (a) ψ = 00° (b) ψ = 45°. second identification step using the simplex algorithm and using the non-quadratic barlat criterion (2) and respecting the assumptions, the second step of identification strategy is equivalent to choosing the coefficients of anisotropy (c1, c2, c3, c4) and the shape coefficient m (tab. 5) while minimizing the squared difference between the theoretical and experimental results. c1 c2 c3 c4 m 0.3612 0.3431 0.113 1.0539 6.2486 table 5: identification of anisotropic coefficients and a shape coefficient m. o. daghfas et alii, frattura ed integrità strutturale, 39 (2017) 263-273; doi: 10.3221/igf-esis.39.24 270 using the identified anisotropic coefficients, the evolution of lankford coefficient and the anisotropy based on off-axis angles are presented in fig. 5(a) and fig. 5(b) respectively. fig. 5 (a) displays the evolutions of lankford coefficient based on off-axis angle ψ . a good agreement has found between experimental and predicted lankford coefficients with respect to the rolling direction. thus, the behavior model describes very satisfactory the plastic behavior of this alloy because its yield function and its hardening law are suitable for aluminum alloys. the evolution of anisotropy of 7075-t7 is more pronounced especially in 45°direction from the rolling direction (see fig. 5(b)), therefore the 7075-t7 is more suitable for forming process for the manufacture of the aerospace parts. it is shown that this material has the best performance for plastic forming for the 45° direction from the rolling direction. (a) (b) figure 5: (a) evolution of lankford coefficient (b) evolution of the yield stress anisotropy based an off axis  . third identification step: validation in order to validate the behavior model, the experimental tensile curve in transverse direction and the identified anisotropic parameters of behavior model are used. fig. 6 shows a good agreement between the theoretical results of behavior model and the experimental data for transverse direction. evolution of the yield surface in deviatory plane  x x2 3, and the yield stress anisotropy after having identified and validate the behavior model, we will study the evolution of load surfaces for several tests and the stress anisotropy of material. o. daghfas et alii, frattura ed integrità strutturale, 39 (2017) 263-273; doi: 10.3221/igf-esis.39.24 271 using the identified anisotropic coefficients (tab. 2), the behavior model allows to represent the load surfaces on each test (simple tensile st for 3  , simple shear ss for 2  , wide tensile wt for 6  ) in the deviatory plan [16, 19], where d d x x 2 3 sin cos 2 sin sin 2           (8) fig. 7 shows the comparison between the yield surfaces calculated by behavior model on different tests. figure 6: validation of hardening tensile curve at 90   . figure 7: evolution of the load surface in the deviatory plan  x x2 3, . it appears also that this material is resistant to simple shear much more than simple tensile and wide tensile. furthermore, for simple tensile and simple shear tests the 7075-t7 alloy is plasticized quickly along the 45° direction from the rolling direction. it is deduced that the best shaping in the design of the fuselage is realized using the 7075 alloy in the 45° direction. in contrast, in wide tensile, it is achieved at the same time at three loading directions. conclusion ince the commercial 7075 aluminum alloys are essentially aeronautics alloys, off axis tensile tests are carried on 7075aluminum alloy through three loading directions from the rolling direction. these experimental results have allowed to investigate the mechanical properties and to identify the plastic behavior model using a proposed s o. daghfas et alii, frattura ed integrità strutturale, 39 (2017) 263-273; doi: 10.3221/igf-esis.39.24 272 identification strategy. in this study, barlat yield criterion with isotropic hardening is used. by comparing both experimentally measured and calculated data based on this criterion, it is demonstrated that this criterion leads to a good description of the phenomena. however, the barlat criterion with isotropic hardening may be sufficient to correctly identify the behavior of the aluminum alloy in uniaxial test. the influence of the off-axis angle on anisotropy is studied. the results of simple tensile test were used subsequently to show the evolution of load surface for several tests. it is deduced that the best shaping in the design of the fuselage and the radom is realized using the 7075 alloy in the 45° direction. this direction allows us to have a good formatting with minimal fracture comparing with directions 0° and 90°. in mechanical construction the shaping of materials requires good mechanical characteristic. it is seen that this type of alloy has the important mechanical strengths but low percentage elongation. in order to remedy tis disadvantage a succession of thermo-mechanical treatments will be applied to this commercial aluminum alloy. this latter point presents the topic of the next work. acknowledgements would emphasize the help that i have had from the doctor gahbiche amen of the mechanical engineering laboratory (lgm) of the national school of engineers el monastir, where i carried out my present experimental studies in the course of this work. references [1] kim, j.m., yang, d. y., yoon, j. w, barlat, f., the effect of plastic anisotropy on compressive instability in sheet metal forming, international journal of plasticity, 16 (2000) 649-676. [2] yespica, w. j. p., comparative study of the electrochemical behavior of 2024 -t351 and 7075-t7351 aluminum alloys neutral sodium sulfate middle, phd thesis in science at the toulouse university, (2012). [3] xiaobo, y., fatigue crack growth of alumina alloy 7075-t651 under non proportional mixed mode i and mode ii loads, frattura ed integrità strutturale, 38 (2016) 148-154. doi: 10.3221/igf-esis.38.20. [4] williams, j.c., starke, e.a., progress in structural materials for aerospace systems, acta materialia, 51 (2003) 5775– 5799. [5] dursun, t., soutis, c., recent developments in advanced aircraft aluminium alloys, materials and design, 56 (2015) 862–871. [6] ben mohamed, a., znaidi, a., baganna, m., nasri, r.., the study of the hardening precipitates and the kinetic precipitation. its influence on the mechanical behavior of 2024 and 7075 aluminum alloys used in aeronautics, springer, 2 (2014) 219–228. [7] lee, n.s., chen, j.h, kao, p.w., chang, l.w., tseng, t.y., su j.r., anisotropic tensile ductility of cold-rolled and annealed aluminum alloy sheet and the beneficial effect of post-anneal rolling, scripta materialia, 60 (2009) 340–343. [8] ben mohamed, a., znaidi, a., daghfas, o., nasri, r., evolution of mechanical behavior of aluminum alloy al 7075 during the time of maturation, international journal of technology, 6 (2016) 1076-1084. [9] dogui, a., anisotropic plasticity in large deformation, ph.d thesis of sciences, university claude bernard-lyon i, (1989). [10] boumaiza, a., influence of structural anisotropy of the plastic behavior during deformation by stamping, ph.d thesis of sciences at the university mentouri, constantine, (2008). [11] tajally, m., emadoddin, e., mechanical and anisotropic behaviors of 7075 aluminum alloy sheets, materials and design, (2010). doi:10.1016/j.matdes.2010.09.001. [12] barlat, f., lege, d.j., brem, j.c., a six-component yield function for anisotropic materials, international. journal of plasticity, 7 (1991) 693–712. [13] barralis, j., maeder, g., specificmetallurgydevelopment, structures, properties normalization afnor, nathan, (1995). [14] develay, r., properties of aluminum and aluminum alloys, technical engineer, m440 (1990). [15] french norm nf a 03-151, tensile test, french association for standardization afnor, (1971). i o. daghfas et alii, frattura ed integrità strutturale, 39 (2017) 263-273; doi: 10.3221/igf-esis.39.24 273 [16] znaidi, a., daghfas, o., gahbiche, a., nasri, r., identification strategy of anisotropic behavior laws: application to thin sheets of a5, journal of theoretical and applied mechanics, 54 (2016) 1147-1156. [17] voce, e., the relationship between stress and strain for homogeneous deformations, journal of the institute of metals, 74 (1948) 537-562. [18] daghfas, o., znaidi, a., nasri, r., numerical simulation of a biaxial tensile test applied to an aluminum alloy 2024, the international conference on advances in mechanical engineering and mechanics, hammamet, tunisia, (2015). [19] znaidi, a., daghfas, o., nasri, r., theorical study on mechanical properties of az31b magnesium alloy sheets under multiaxial loading, frattura ed integrità strutturale, 38 (2016) 135-140. doi: 10.3221/igf-esis.38.18. << /ascii85encodepages false /allowtransparency false /autopositionepsfiles true /autorotatepages /none /binding /left /calgrayprofile (dot gain 20%) /calrgbprofile (srgb iec61966-2.1) /calcmykprofile (u.s. web coated \050swop\051 v2) /srgbprofile (srgb iec61966-2.1) /cannotembedfontpolicy /error /compatibilitylevel 1.4 /compressobjects /tags /compresspages true /convertimagestoindexed true /passthroughjpegimages true /createjobticket false /defaultrenderingintent /default /detectblends true /detectcurves 0.0000 /colorconversionstrategy /cmyk /dothumbnails false /embedallfonts true /embedopentype false /parseiccprofilesincomments true /embedjoboptions true /dscreportinglevel 0 /emitdscwarnings false /endpage -1 /imagememory 1048576 /lockdistillerparams false 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can be opened with acrobat and adobe reader 5.0 and later.) >> /namespace [ (adobe) (common) (1.0) ] /othernamespaces [ << /asreaderspreads false /cropimagestoframes true /errorcontrol /warnandcontinue /flattenerignorespreadoverrides false /includeguidesgrids false /includenonprinting false /includeslug false /namespace [ (adobe) (indesign) (4.0) ] /omitplacedbitmaps false /omitplacedeps false /omitplacedpdf false /simulateoverprint /legacy >> << /addbleedmarks false /addcolorbars false /addcropmarks false /addpageinfo false /addregmarks false /convertcolors /converttocmyk /destinationprofilename () /destinationprofileselector /documentcmyk /downsample16bitimages true /flattenerpreset << /presetselector /mediumresolution >> /formelements false /generatestructure false /includebookmarks false /includehyperlinks false /includeinteractive false /includelayers false /includeprofiles false /multimediahandling /useobjectsettings /namespace [ (adobe) (creativesuite) (2.0) ] /pdfxoutputintentprofileselector /documentcmyk /preserveediting true /untaggedcmykhandling /leaveuntagged /untaggedrgbhandling /usedocumentprofile /usedocumentbleed false >> ] >> setdistillerparams << /hwresolution [2400 2400] /pagesize [612.000 792.000] >> setpagedevice microsoft word numero_54_art_15_2805 m. belaïd et alii, frattura ed integrità strutturale, 54 (2020) 202-210; doi: 10.3221/igf-esis.54.15 202 probabilistic elastic-plastic fracture mechanics analysis of propagation of cracks in pipes under internal pressure mechab belaïd, medjahdi malika, salem mokadem, serier boualem university of djillali liabes, sidi bel abbes, algeria bmechab@yahoo.fr, mmedjahdi@yahoo.fr, moka_salem@yahoo.fr, boualems@yahoo.fr abstract. this study presents a three dimensional finite element method analysis of semi-elliptical surface cracks in pipes under internal pressure load. in the elastic–plastic case, estimates of the j-integral are presented for various ratios including crack depth to pipe thickness (a/t) and strain hardening index in the (r-o) ramberg-osgood (n). finally, failure probability is accessed by a statistical analysis for uncertainties in loads and material properties, and structural reliability and crack size. the monte carlo method is used to predict the distribution function of the mechanical response. according to the obtained results, we note that the stress variation and the crack size are important factors influencing on the distribution function of (j/je). keywords. failure; pipe; fracture mechanics; monte carlo method. citation: mechab, b., medjahdi, m., salem, m., serier, b., probabilistic elastic-plastic fracture mechanics analysis of propagation of cracks in pipes under internal pressure, frattura ed integrità strutturale, 54 (2020) 202-210. received: 27.04.2020 accepted: 11.08.2020 published: 01.10.2020 copyright: © 2020 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. introduction xternal cracks can occur in many structural components of cylindrical form. they are the cause of premature damage in structures such as piping, bolts, pins and reinforcements of aircraft. the fracture prediction and the reliability of such piping systems in various practical applications are primordial given their impact on the economic plan and security [1]. several authors [2-5] have been studied pipe fracture problems by means of numerical simulation in order to assess the mechanical integrity, taking into account different crack shapes. raju and newman [6] have obtained linear elastic fracture mechanics based stress intensity factors for a wide range of internal and external semi-elliptical surface cracks in a cylinder. the j-integral fracture parameter proposed by [7] has been extensively used in assessing fracture integrity of cracked engineering structures, which undergo large plastic deformation. for elastic–plastic problems, it is interpreted by [8] and [9] as the strength of the asymptotic crack-tip fields and represents the crux of the basis for ‘j-controlled’ crack growth behaviour. for stability assessment in piping components, it is important to calculate the point of initiation of the crack and to monitor the subsequent crack propagation behaviour [10]. integrity assurance of secondary system components becomes an important issue relating to impacts on large and early release frequency as well as core damage frequency due to piping failures in nuclear power plant [11]. e https://youtu.be/tbxrmlm0r58 m. belaïd et alii, frattura ed integrità strutturale, 54 (2020) 202-210; doi: 10.3221/igf-esis.54.15 203 probabilistic assessments of cracked components are considered in [12]. several computer programs and benchmark results are available [13-15]. moreover, probabilistic methods are included in the latest versions of the structural integrity assessment procedures [16-17]. probabilistic fracture mechanics is a means of quantifying the failure probability resulting from uncertainties in the values of the parameters used to perform a failure assessment of cracked structures through probabilistic analysis techniques [18]. this paper presents a three dimensional finite element method analysis of semi-elliptical surface cracks in pipes under internal pressure load. the effect of the ratios (a/t) and (n) is presented for evaluating the j-integral. finally, the monte carlo method is used to predict the distribution function of the mechanical response and the possibility of failure. geometrical models he geometry of the semi elliptical surface cracks of pipe subjected to internal pressure is represented in fig. 1. it can be described by the non-dimensional ratios of crack depth to its length (a/c), crack depth to the pipe’s wall thickness (a/t) and mean pipe’s radius to its thickness (rm/t). in this study, (β/π) is from 0.1, a/t from 0.3 to 0.7 and (rm/t) from 20. figure 1: geometrical model. material model he material in the fe analyses is assumed to follow the ramberg-osgood (r-o) relation: 0 n y y                (1) where eε0=σy where e is the young’s modulus, taken as e=200gpa; σy denotes the 0.2% proof (yield) stress; and α and n are the r-o parameters. in the present fe analysis, α and σy are fixed to α=1 and σy=400mpa. the values of the strain hardening index, n, however, are systematically varied; n=1(elastic), 3, 5 and 10. finite element mesh he fig. 2 presents, a typical fe mesh of the cracked pipe. twenty-node isoparametric quadratic brick elements with reduced integration (c3d20r in abaqus) were used to construct a quarter model of the pipe. values of the jintegral were extracted using a domain integral method implemented within abaqus [19]. in this study, the entire mesh of the model was constructed from two blocks consisting of the pipe’s block and the crack’s block. a series of tests were undertaken to estimate mesh sensitivity on the results of the j-integral. an initial mesh of 10568 elements in total was employed and refined several times (17811, 25736, 34058) until reaching 41353 elements. results of the j-integrals from t t t m. belaïd et alii, frattura ed integrità strutturale, 54 (2020) 202-210; doi: 10.3221/igf-esis.54.15 204 this mesh were practically similar to those of the previous mesh. this was judged adequate to use for all future computations. it is to be noted that for each refined mesh the crack’s tip block was refined several times to achieve stable results. the crack tip was modeled with focused elements composed of five contours. solutions were checked against those employing eight contours, and the results were almost identical. figure 2: meshing model of the cylinder. results and discussion ipes are considered as one of the important members in the primary heat transport system of power plants. for stability assessment in piping components, it is important to calculate the point of initiation of the crack and to monitor the subsequent crack propagation behaviour [20,21]. evaluation of the j-integral for cracked welded structures is usually performed by numerical analysis and quick engineering estimation techniques. using fem, one can simulate various weld and crack geometries and mis-matching variables. this work presents a three-dimensional finite element method analysis of a thick cracked pipe in mode i under internal pressure. the elastic fe results (the case of n=1) (ainsworth. ra, [22]) provide the elastic component of the j-integral, je, from which the stress intensity factor ki can be found as: 2 ' i e k j e  (2)   where e’=e/(1-υ2) for plane strain the elastic-plastic fe analysis provides the values of the j-integral as a function of load, for a given geometry and a type of loading. for the r-o materials (see eqn. (1)), the fully plastic part of the j-integral, jp, for pipes with semi elliptical surface cracks can be expressed as: fe fep ej j j  (3) for the plastic limit internal pressure pl, the following expression is used in the present work miller [23]:  12 / 2sin sin / 2 1 y l m t a t a t p r               (4) p m. belaïd et alii, frattura ed integrità strutturale, 54 (2020) 202-210; doi: 10.3221/igf-esis.54.15 205 1.767 0.156 0.101 0.627 a a t t                                (5) the ge/epri-type j estimation equations, given in this section, can be used to estimate j, for pipes with semi elliptical surface cracks subject to internal pressure. in the ge/epri method, as demonstred by ainsworth[22]. the elastic part of j in eqn.(2) cab be expressed as :   222 1 1 ' yi e l k q j w h n e e q               (6) where h1(n=1) denotes the value of h1(n) for elastic (n=1) materials. inserting eqn. (2) in to eqn. (6) gives value of h1(n=1) as a function of the crack geometry. normalizing eqn. (3) with respect to eqn. (2) gives:     1 1 1 1 n p e l h nj q j h n q          (7) where ql= pl (8) variation of h1(n)/h1(n=1), determined from the fe results, with the strain hardening index n are shown in fig. 3, for the internal pressure. the results show that the values of h1(n)/h1(n=1) are quite sensitive to n .in particular sensitivity of h1(n)/h1(n=1) to n for the case of internal pressure should be noted. for internal pressure, they range from 1to 50 for n ranging from 1 to 10. figure 3: variation of the h1(n)/h1(n = 1) values with n, for internal pressure. the total j-integral can be estimated by adding the elastic component with plasticity correction (r6) [11]: j=je +jp (9) 2 1 2 ref ref ref e ref y ref ej j e                (10) where ref y or q q          (11) m. belaïd et alii, frattura ed integrità strutturale, 54 (2020) 202-210; doi: 10.3221/igf-esis.54.15 206 or orq p (12) the figs. 4 and 5 respectively present the variation of (j/je) according to the pressure ratio (p/por) for a different ratio (a/t) for n=5 and n=10. compared with the analytical solution of eqn. (10) found in the literature, it can be noticed that the effect of the ratio a/t becomes sensible when the ratio (p/por) exceeds 1.0. this shows a very good correlation between the two methods when the ratio a/t = 0.2 and a/t = 0.5, for a/t = 0.7 the difference is significant especially at high (p/por) but for n=10 the difference is significant (see fig. 5). figure 4: comparison of the fe j results with those estimated from the proposed ersm for the internal pressure for n=5 figure 5: comparison of the fe j results with those estimated from the proposed ersm for the internal pressure for n=10. probabilistic elastic-plastic fracture mechanic analysis random parameters and fracture response he j-integral is an appropriate fracture parameter that describes the crack-tip stress and strain fields adequately when there are no constraint effects [24]. probabilistic models have also been developed to estimate various response statistics and reliability [25]. using fem, one can calculate j for any crack geometry and load conditions. however, it is also useful to have simplified estimation methods for routine engineering calculations. accordingly, the probabilistic epfm analyses based on both methods have been reported [26,27] t m. belaïd et alii, frattura ed integrità strutturale, 54 (2020) 202-210; doi: 10.3221/igf-esis.54.15 207 the uncertainties are related to load estimation, geometrical fluctuations and scatter of material properties; these parameters are modeled by random variables, described by distribution type and parameters (i.e., mean and coefficient of variation cov). for design purpose, the system uncertainties should be controlled in order to avoid unsafe situations. eight random variables are considered to model the thick pipes uncertainties related material properties (young modulus (e), crack length (a/t), mean pipe’s radius to its thickness (rm/t) and applied stress (σ). tab. 1 indicates the mean values and coefficients of variation for the six selected random variables. hence, any relevant fracture response, such as the (j/je) (x), should be evaluated by the probability. ( / ) ( / )( ) ( ) pr ( / )( ) ƒ ( ) o def def j je o o xj je x j f j j je x j x dx                                                                        (13) ( / ) ( / )( ) /j je j je o of df j dj (14) or the probability density function (pdf), where ( / )( )j je of j . is the cumulative distribution function of (j/je) and ƒx(x) is the known joint probability density function of x. variable mean coefficient of variation (cov) young modulus (e) 200 gpa 1% crack length (a/t) 0.3, 0.5, 0.7 2% mean pipe’s radius to its thickness (rm/t) 20 3% applied stress (σ) 400 mpa 2% table 1: random variables and corresponding parameters. the density function is evaluated by using monte carlo method. the basic idea is to draw random samples for the input parameters, then to compute the mechanical response for each sample. when a large number of monte carlo samples are achieved, it becomes possible to make statistical analysis of the response sets in order to provide the probability density functions of the (j/je), the failure probability can be obtained by computing the ratio between the number of failed samples and the total number of drawn samples. the sensitivity measures can be also obtained by computing the dispersion of the mechanical response in terms of the scatter of the input parameters. in order to analyze the ductile cracked structures with bonded composite patch by the fortran program, which are developed by the authors: the first program provides the mechanical response by calculating the (j/je) distribution and the second program computes the probabilistic response by using monte carlo simulations. to achieve a high accuracy of the results, we have carried out 105 simulations. figure 6: histogram and probability density function of j/je. probabilistic results fig.6 plots the histograms of the (j/je) obtained by monte carlo simulations. the probability density function (pdf) is obtained by fitting the histogram with theoretical models. two distribution laws are investigated: gaussian (normal law) m. belaïd et alii, frattura ed integrità strutturale, 54 (2020) 202-210; doi: 10.3221/igf-esis.54.15 208 and polynomial (9th order); from fig. 6, it can be clearly observed that the three distributions give more or less good approximation of the (j/je). the polynomial distribution gives a lower mean value than for gaussian distribution. by comparing these three distributions, we can conclude that the gaussian law offers an acceptable approximation of the (j/je) probability density function, with good estimation of the average (see fig. 6). the safety margin (j/je) (xi) is the probabilistic design rule, which defines the plate safety by the condition (j/je) (xi) > 0 and the plate failure by (j/je) (xi) ≤ 0. the figs. 7 and 8 present the cumulative and the probability density of (j/je) for different values of the stress and length of crack. we noted that when the stress and length of crack is large the value of the probability density of (j/je) is small. it can be seen that the margin increases significantly with the uncertainties related to the load applied and length of crack, leading to larger failure probability, finally, the failure probabilities depend on the load applied and length of crack. figure 7: probability density and the cumulative of (j/je) for different values of stress figure 8: probability density and the cumulative of (j/je) for different values of length of crack. conclusion ipelines are important components in a piping system. this study presents a three dimensional finite element method analysis of semi-elliptical surface cracks in pipes under internal pressure load. a probabilistic model was developed for predicting elastic-plastic fracture mechanic response and reliability. the monte carlo method is used to predict the distribution function of the mechanical response. according to the obtained results, we note that the stress variation p m. belaïd et alii, frattura ed integrità strutturale, 54 (2020) 202-210; doi: 10.3221/igf-esis.54.15 209 and the crack length variations are important factors influencing the distribution function of (j/je). the uncertainty in these parameters has a significant effect on increasing the probability of failure of pipe and reducing the durability of structure. references [1] kim, y.j. shim, d.j. (2005), relevance of plastic limit loads to reference stress approach for surface cracked cylinder problems, int. j. pres. ves. pip. 82, pp. 687–699. doi:10.1016/j.ijpvp.2005.03.007. [2] kim, y.jae. kim, j.s. park, y.j. kim, y.j. (2004), elastic-plastic fracture mechanics method for finite internal axial surface cracks in cylinders, eng. fract. mech. 71, pp. 925–944. doi:10.1016/s0013-7944(03)00159-0. [3] mechab, b., serier, b., bachir bouiadjra, b., kaddouri, k., feaugas, x. (2011), linear and non-linear analyses for semielliptical surface cracks in pipes under bending, int. j. pres. ves. pip. 88, pp. 57–63. doi: 10.1016/j. ijpvp. 2010.11.001. [4] chapuliot, s. (2000), k formula for pipes with a semi-elliptical longitudinal or circumferential, internal or external surface crack, in: cea report cea-r-5900. cea/saclay, france. [5] available at: https://inis.iaea.org/collection /nclcollectionstore/_public/31/058/31058406.pdf [6] marie, s., chapuliot, s., kayser, y., lacire, m.h, drubay, b., barthelet, b., et al. (2007), french rse-m and rcc-mr code appendices for flaw analysis: presentation of the fracture parameters calculation – part v: elements of validation. int. j. pres. ves. pip. 84, pp. 687–696. doi:10.1016/j.ijpvp.2007.05.007. [7] raju, i.s., newman, jr. (1982), stress-intensity factors for internal and external surface cracks in cylindrical vessels, j press vessel technol, asme trans 104(4), pp. 293–299. doi:10.1115/1.3264220. [8] bach, m. x., wang.(2013), constraint-based fracture mechanics analysis of cylinders with internal circumferential cracks, struct. eng. mech. 47(1), pp. 131–147. doi:10.12989/sem.2013.47.1.131. [9] staat, m., vu, d.k. 2013), limit analysis of flaws in pressurized pipes and cylindrical vessels, part ii: circumferential defects. eng. fract. mech. 97, pp. 314–333. doi:10.1016/j.engfracmech.2012.05.017. [10] chattopadhyay, j., dutta,b.k., vaze, k.k.(2014), development of new correlations for improved integrity assessment of pipes and pipe bends, nucl .eng. des, 269, pp. 108–115. doi:10.1016/j.nucengdes.2013.08.015. [11] lee, s.m., chang, y.s., choi , j.b., kim ,y.j. (2006). failure probability assessment of wall thinned nuclear pipes using probabilistic fracture mechanics, nucl. eng. des, 236, pp. 350-358. doi:10.1016 /j.nucengdes.2005. 09.008. [12] r6 (2001). assessment of the integrity of structures containing defects, revision 4. british energy generation ltd, gloucester. [13] qian, g., niffenegger, m., karanki d.r., li, s. (2013). probabilistic leak beforebreak analysis with correlated input parameters, nucl. eng. des. 254, pp. 266–271. doi: 10.1016/s0308-0161(96)00034-8. [14] tee, k.f., khan, l.r., chen, h.p. (2013). probabilistic failure analysis of underground flexible pipes, struct. eng. mech. 47(2), pp. 167–183. doi: 10.12989/sem.2013.47.2.167. [15] rahman, s. (1995). a stochastic model for elastic-plastic fracture analysis of circumferential through-wall-cracked pipes subject to bending, eng. fract. mech. 52, pp. 265–288. doi:10.1016/0013-7944(95)00018-q. [16] rahman, s. (2000). probabilistic elastic-plastic fracture analysis of circumferentially cracked pipes with finite-length surface flaws, nucl. eng. des. 195, pp. 239–260. doi:10.1016/s0029-5493(99)00214-9. [17] cizelj, l., mavko, b., riesch, oppermann, h. (1994). application of first and second order reliability n methods in the safety assessment of cracked steam generator tubing, nucl. eng des, 147, pp. 359-368. doi: 10.1016/0029-5493(94)90218-6. [18] sandvik, a., østby, e., thaulow, c. (2006). probabilistic fracture assessment of surface cracked pipes using strain-based approach, eng. fract. mech. 73, pp. 1491–1509. doi: 10.1016/j.engfracmech.2006.01.026. [19] rahman, s. (1997). probabilistic fracture analysis of pipes with circumferential flaws, int. j. pres. ves. pip. 70, pp. 223– 236. doi: 10.1016/s0308-0161(96)00034-8. [20] abaqus (1998), abaqus standard/user’s manual, version 5.8-1. hibbit karlsson & sorensen, inc., pawtucket, ri, usa. [21] kim, y.j., kim, j.s., lee, y.z., kim, y.j. (2002). non-linear fracture mechanics analyses of part circumferential surface cracked pipes, int. j. fract., 116, pp. 347–375. doi: 10.1023/a:1020779611803. [22] peng, j., zhou, c.y., xue, j.l., dai, q., he, x.h. (2011). safety assessment of pipes with multiple local wall thinning defects under pressure and bending moment, nucl. eng. des, 241, pp. 2758–2765. doi: 10.1016/j.nucengdes.2011.06.030. m. belaïd et alii, frattura ed integrità strutturale, 54 (2020) 202-210; doi: 10.3221/igf-esis.54.15 210 [23] ainsworth, r.a. (1984). the assessment of defects in structures of strain hardening materials, eng. fract. mech. 19, pp. 633–642. doi: 10.1016/0013-7944(84)90096-1. [24] miller, a.g. (1988). review of limit loads of structures containing defects, int. j. pres. ves. pip. 32, pp. 191–327. doi: 10.1016/0308-0161(88)90073-7. [25] mechab, b., chioukh, n., mechab, boubaker., serier, b. (2018). probabilistic fracture mechanics for analysis of longitudinal cracks in pipes under internal pressure, journal of failure analysis and prevention, 18(6), pp. 1643-651. doi: 10.1007/s11668-018-0564-8. [26] salem.b., mechab, b., berrahou, m., bachir bouiadjra, b., serier, b. (2019). failure analyses of propagation of cracks in repaired pipe under internal pressure, journal of failure analysis and prevention. 19(1), pp 212–218. doi:10.1007/s11668-019-00592-3. [27] rahman, s., brust, f.w. (1997), approximate methods for predicting j-integral of a circumferentially surface-cracked pipe subject to bending, int. j. fract. 85, pp. 11–130. doi:10.1023/a:1007322018722. [28] rahman, s., ghadiali, n., paul, d., wilkowski, g. (1995), probabilistic pipe fracture evaluations for leak-ratedetection applications, nureg:cr-6004. u.s. nuclear regulatory commission, washington, dc. doi:10.2172/50938. << /ascii85encodepages false /allowtransparency false /autopositionepsfiles true /autorotatepages /none /binding /left /calgrayprofile (dot gain 20%) /calrgbprofile (srgb iec61966-2.1) /calcmykprofile (u.s. web coated \050swop\051 v2) /srgbprofile (srgb iec61966-2.1) /cannotembedfontpolicy /error /compatibilitylevel 1.4 /compressobjects /tags /compresspages true /convertimagestoindexed true /passthroughjpegimages true /createjobticket false /defaultrenderingintent /default /detectblends true /detectcurves 0.0000 /colorconversionstrategy /cmyk /dothumbnails false /embedallfonts true /embedopentype false /parseiccprofilesincomments true /embedjoboptions true /dscreportinglevel 0 /emitdscwarnings false /endpage -1 /imagememory 1048576 /lockdistillerparams false /maxsubsetpct 100 /optimize true /opm 1 /parsedsccomments 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/hrv (za stvaranje adobe pdf dokumenata najpogodnijih za visokokvalitetni ispis prije tiskanja koristite ove postavke. stvoreni pdf dokumenti mogu se otvoriti acrobat i adobe reader 5.0 i kasnijim verzijama.) /hun 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/pdfxoutputintentprofileselector /documentcmyk /preserveediting true /untaggedcmykhandling /leaveuntagged /untaggedrgbhandling /usedocumentprofile /usedocumentbleed false >> ] >> setdistillerparams << /hwresolution [2400 2400] /pagesize [612.000 792.000] >> setpagedevice microsoft word numero 9 art 4 finale b. atzori et alii, frattura ed integrità strutturale, 9 (2009) 33 – 45; doi: 10.3221/igf-esis.09.04 33 resistenza a fatica di strutture in leghe di alluminio: normative a confronto e verifica sperimentale b. atzori, g. meneghetti, b. rossi università di padova, dipartimento di ingegneria meccanica, bruno.atzori@unipd.it riassunto. le problematiche relative all’utilizzo delle normative nell’ambito della progettazione a fatica di strutture in leghe di alluminio sono state di recente affrontate in numerosi lavori che hanno messo in luce sia le difficoltà legate al passaggio da normative oramai obsolete ad altre di nuova concezione, ma di caratteristiche e struttura completamente diverse, che la sostanziale carenza anche all’interno delle più recenti normative europee, quale l’eurocodice 9, di molti risultati e metodi sviluppati in anni di ricerca scientifica e ormai indiscutibilmente consolidati. il presente lavoro si propone di approfondire entrambe le tematiche tramite il confronto tra risultati sperimentali tratti da letteratura e le corrispondenti curve di resistenza proposte rispettivamente dalla normativa italiana uni 8634, di recente ritirata, e dall’eurocodice 9. in questo modo verranno messe in luce le differenze tra i valori di resistenza proposti dalle due norme e verrà illustrata sia la corrispondenza a volte poco soddisfacente con i risultati sperimentali che le conseguenze dovute alla mancata applicazione di assodati risultati teorici. abstract. the employment of standard codes in fatigue design of aluminium alloy structures has been the subject of many recent papers where both the comparison among different design standards and the lack of application, even in the latest european codes, of reliable theoretical results were discussed. the aim of this work is to deepen the comparison between the italian code uni 8634, recently withdrawn, and the european standard eurocode 9, published in 2007, through the comparison of experimental data taken from literature with the corresponding design curves proposed by both of codes. in this way, the differences between the fatigue resistance data will be pointed out together with the effects of neglecting well known and reliable theoretical results. parole chiave. lega leggera; fatica; giunti saldati; normative; dati sperimentali introduzione ell’ambito della progettazione di strutture in leghe di alluminio, una delle prime normative in assoluto a presentare dati relativi alla resistenza a fatica di particolari strutturali di diverso tipo è stata la normativa italiana uni 8634 [1]. tale norma, emanata nel 1985 e rimasta in vigore fino a dicembre del 2008, si basava sulla vasta attività di ricerca e rianalisi di dati sperimentali effettuata tra il 1975 ed il 1980 dal prof. atzori prima presso il laboratorium für betriebsfestigkeit di darmstadt e poi presso l’università di bari [2-4]. tali ricerche avevano condotto, su analogia di quanto già ottenuto dal prof. haibach per le giunzioni in acciaio, alla definizione di una banda di dispersione unificata (fig. 1) capace di interpretare i risultati di prove di fatica su giunti di geometrie e dimensioni assolute diverse, purché la cricca si inneschi al piede del cordone di saldatura. tale risultato [3] era stato assunto come principio base della normativa italiana, tenendo conto che la diversa tipologia di giunto causa una semplice traslazione verticale della banda di dispersione se le tensioni considerate sono quelle nominali calcolate sulla lamiera principale. la uni 8634, che per facilitare i progettisti riproduceva la normativa per le strutture in acciaio allora in vigore [5] non venne mai aggiornata per mantenere la corrispondenza con la successiva versione della uni 10011 sugli acciai [6] in n http://www.gruppofrattura.it/ http://dx.medra.org/10.3221/igf-esis.09.04&auth=true mailto: bruno.atzori@unipd.it b. atzori et alii, frattura ed integrità strutturale, 9 (2009) 33 45; doi: 10.3221/igf-esis.09.04 34 quanto alla fine degli anni ’80 venne istituita una commissione cen per la stesura di una normativa europea su tematiche analoghe. i lavori portarono nel 2002 all’emissione di una prenorma [7] ed infine nel 2007 all’emissione della norma definitiva [8], che dopo il ritiro della uni 8634 si configura a livello italiano, oltre che europeo, come normativa di riferimento per la progettazione a fatica di strutture in lega leggera. al fine di mantenere una certa omogeneità nella presentazione dei risultati, l’eurocodice 9 riproduce la struttura adottata dall’eurocodice 3 per gli acciai [9] e risulta pertanto avere un formato notevolmente diverso rispetto alla normativa italiana. figura 1: banda di dispersione relativa alle giunzioni saldate in lega leggera [2]. le difficoltà presenti nel passaggio da una normativa all’altra sono state messe in luce in recenti lavori [10, 11] sia per quanto riguarda la corrispondenza tra i dettagli strutturali che dal punto di vista dei valori di resistenza. inoltre, durante il lungo periodo di stesura dell’eurocodice 9, le analisi teoriche nell’ambito delle giunzioni saldate hanno avuto notevolissimo impulso, soprattutto dopo la scelta di considerare il piede del cordone di saldatura, nel caso di cordoni d’angolo, come un intaglio acuto con raggio di raccordo nullo e di assumere per il cordone uno spessore ed un’inclinazione di 45° costanti [12, 13] che ha portato a legare le problematiche delle giunzioni saldate a quelle degli intagli acuti in generale. numerose analisi sono state sviluppate su queste basi [14-20] negli anni successivi portando, tra i molteplici risultati, a definire, per giunti con cordoni d’angolo e rottura a piede cordone, un’unica banda di dispersione unificata (fig. 2, [20]), con valori di pendenza e dispersione molto prossimi a quelli determinati in passato (fig. 1) ma che esprimendo in punti sperimentali in funzione non delle tensioni nominali, bensì delle tensioni locali immediatamente prossime alla zona di innesco cricca tramite l’utilizzo del parametro locale k1n, ovvero fattore di intensificazione delle tensioni di intaglio di modo i, elimina la traslazione verticale dovuta alle differenti concentrazioni di tensione strutturale. un’espressione conveniente del fattore di intensificazione delle tensioni di intaglio di modo i per i giunti saldati [14] risulta essere: k1n = k1σnt0.326 (1) dove k1 è un coefficiente adimensionale, analogo al coefficiente teorico di concentrazione delle tensioni kt, che dipende dalla geometria delle parti collegate e del cordone di saldatura stesso, σn è il range di tensione nominale applicata, t lo spessore del piatto principale caricato, 0.326 esponente valido nell’ipotesi di cordone di saldatura schematizzato come intaglio con angolo di apertura 135° (caso tipico di cordone d’angolo). si noti come l’eq. 1 permetta una valutazione ed una formalizzazione accurata dell’effetto scala, prima difficilmente descrivibile in termini rigorosi. in questo modo l’ approccio allo studio della resistenza a fatica di giunzioni saldate basato sulle tensioni nominali è stato soppiantato dallo studio dell’effettivo campo di tensione locale che è stato interpretato anche come sovrapposizione dell’intaglio acuto al piede del cordone di saldatura e dell’intaglio strutturale dovuto alla geometria complessiva della giunzione [21]. se i risultati teorici qui brevemente riassunti non erano presenti, per ovvie questioni temporali, nella uni 8634, risultano molto poco recepiti anche dall’eurocodice 9, che come evidenziato da recenti lavori [22, 23] sottostima notevolmente http://www.gruppofrattura.it/ http://dx.medra.org/10.3221/igf-esis.09.04&auth=true b. atzori et alii, frattura ed integrità strutturale, 9 (2009) 33 – 45; doi: 10.3221/igf-esis.09.04 35 l’effetto scala considerandolo solo in un numero molto limitato di casi e soprattutto ignora completamente l’utilizzo di approcci di tipo locale, prevedendo al più l’uso di metodi di tipo “hot spot” che analizzano però il solo campo di tensione strutturale dovuto alla geometria complessiva della giunzione escludendo invece gli effetti di intaglio acuto al piede del cordone di saldatura. nella memoria verrà ripresa nei tratti salienti la descrizione di entrambe le normative (uni 8634 e eurocodice 9) mentre verrà dato ampio spazio al confronto delle curve di progettazione con i risultati sperimentali, evidenziando in particolare le incongruenze e le conseguenze delle lacune rispetto alle analisi teoriche. figura 2: resistenza a fatica di giunti a croce in acciaio e lega leggera in funzione del fattore di intensificazione delle tensioni di intaglio di modo i k1n [20]. normative di progettazione ome anticipato al paragrafo precedente, la normativa italiana uni 8634, sintetizza i dati di resistenza a fatica relativi a prove effettuate su provini di geometria diversa sulla base del concetto di banda di dispersione unificata, sviluppato negli anni precedenti. viene così presentata un’unica curva di resistenza a fatica (fig. 3) che riporta in scale relative, ovvero riferite alle coordinate del ginocchio della curva stessa, l’ampiezza di sollecitazione fd,a = (σmax σmin)/2 al variare del numero di cicli n. in questa forma generale la curva è valida per tutti i materiali, i tipi di giunto e le condizioni di sollecitazione e va particolarizzata in base al tipo di lega, alla geometria del collegamento e al rapporto di sollecitazione dello specifico caso considerato tramite gli opportuni valori numerici. in base alla tipologia di giunto considerata (la normativa identifica 7 gruppi corrispondenti ad altrettante geometrie) si ottiene così una famiglia di curve aventi tutte la medesima pendenza (k’ = 4.3) ma che traslano nel piano σ-n per tener conto dei diversi effetti di concentrazione delle tensioni dovuti alle diverse geometrie strutturali. in particolare la normativa fornisce (tab. 1) per ciascuno dei gruppi considerati, la posizione del ginocchio ng, il corrispondente valore della resistenza di progetto fd,-1(n = ng), ovvero σmax,-1(n = ng), relativo ad un rapporto di sollecitazione μ = σmin/σmax = -1 e ad una probabilità di sopravvivenza del 97.7% (media meno due deviazioni standard) nonché il valore della resistenza statica ft noti tali dati è immediato risalire , tramite un tradizionale diagramma di smith, al valore della resistenza di progetto fd,μ (n = ng) relativa al particolare rapporto di sollecitazione considerato e quindi al valore dell’ampiezza fd,a (n = ng). mentre, come già osservato, la pendenza della curva rimane la medesima per tutte la tipologie di dettagli strutturali, viceversa la posizione del ginocchio della curva varia. inoltre non si considera definibile un limite di fatica. per ovvie ragioni di data di emanazione, la uni 8634 non tiene conto dell’effetto delle dimensioni assolute dei giunti, né prevede la possibilità di utilizzo di approcci di tipo alternativo a quello in tensioni nominali nel caso di geometrie complesse. viceversa, essendo la normativa basata principalmente su prove eseguite su giunti saldati semplici, essa ritiene la resistenza c http://www.gruppofrattura.it/ http://dx.medra.org/10.3221/igf-esis.09.04&auth=true b. atzori et alii, frattura ed integrità strutturale, 9 (2009) 33 45; doi: 10.3221/igf-esis.09.04 36 a fatica dipendente dal rapporto di sollecitazione e dal tipo di lega impiegata, aspetti che in seguito sono stati invece ritenuti ininfluenti sul comportamento a fatica [24]. figura 3: curva di resistenza a fatica per giunti saldati in lega d’alluminio secondo uni 8634 [1]. gruppo ng fd,-1(n=ng) [mpa] ft [mpa] a 2·106 83* 278* b 2·106 43 278* c 2·106 38 278* d 2·106 31 278* e 2·106 27 278* f 3.2·106 20 278* g 107 10 278* tabella 1: posizione del ginocchio della curva di woehler e valori di resistenza per i diversi gruppi di giunti considerati nell’uni 8634 (*= valore medio, per i valori precisi riferiti ai vari tipi di lega si rimanda al prospetto 53 della normativa). molto diverso dalla uni 8634 già per quanto riguarda l’impostazione di base, l’ eurocodice 9 fa riferimento a dati di resistenza a fatica relativi a risultati ottenuti su strutture reali, e non su provini come nel caso della norma italiana, sintetizzandoli in curve standard, la cui forma generale è illustrata in fig. 4. tale curva descrive, su scala doppio logaritmica e con riferimento ad una probabilità di sopravvivenza del 97.7%, l’andamento della resistenza a fatica in termini di range di tensione (σ = σ max – σ min), in funzione del numero di cicli n. nel diagramma, si possono distinguere tre punti particolari: il punto c (nc = 2·106cicli/σc), utilizzato come valore di riferimento per definire la categoria dei dettagli strutturali, il punto d (nd = 5·106cicli/σd), limite di fatica per storie di carico ad ampiezza costante, e il punto l (nl = 108cicli/σl), cut-off limit, ovvero valore tale da ritenere che sollecitazioni di ampiezza inferiore ad esso non influenzino la vita a fatica del componente. la curva presenta pendenza inversa m1 nel tratto n<nd, pendenza m2 = m1 +2 nel tratto nd<n<nl; tuttavia il valore di m1 non è standardizzato bensì varia a seconda della tipologia di giunto considerata, in disaccordo sia con la uni che con le analisi teoriche [2, 14, 18, 23]; viceversa i valori di nc, nd, nl restano costanti per tutte le categorie di dettagli strutturali. nell’eurocodice la resistenza a fatica viene ritenuta indipendente dal rapporto di ciclo r = σmin / σmax e dal tipo di lega di alluminio (tranne nel caso di dettagli strutturali per materiale base in lega 7020). la curva di woehler illustrata in fig. 4 va particolareggiata con gli opportuni valori numerici a seconda della tipologia di giunto considerata. a questo scopo nell’eurocodice viene definita una serie di valori standardizzati di σc (ricavati da storie di carico con rapporto di ciclo r ≥ 0.5) riportati in tab. 2. in tabella 3 vengono illustrate invece le diverse tipologie di giunti considerate dall’eurocodice 9 e la corrispondenza con i gruppi proposti dalla normativa italiana. si noti come la varietà di dettagli strutturali classificati sia notevolmente maggiore http://www.gruppofrattura.it/ http://dx.medra.org/10.3221/igf-esis.09.04&auth=true b. atzori et alii, frattura ed integrità strutturale, 9 (2009) 33 – 45; doi: 10.3221/igf-esis.09.04 37 nel caso dell’eurocodice. inoltre mentre nella uni 8634 ad un determinato gruppo di giunti corrisponde un solo valore di resistenza di progetto, all’interno di ciascuna tipologia di dettaglio riportata in tab. 3 sono presenti più sotto categorie identificate da valori di resistenza σc diversi. figura 4: curva di resistenza a fatica per giunti saldati in lega d’alluminio secondo l’eurocodice 9 [8]. 12, 14, 16, 18, 20 ,23, 25, 28, 32, 36 ,40, 45 ,50 ,56, 63 ,71, 80, 90, 100, 112 ,125, 140 tabella 2: valori standardizzati di σc [mpa] secondo l’eurocodice 9. tipologia di dettagli strutturali eurocodice 9 uni 8634 materiale base tav. j.1 a parti aggiunte tramite cordoni trasversali tav. j.3 d, e, g saldature longitudinali tav. j.5 c giunti saldati di testa tav. j.7 b, d, f saldature d’angolo tav. j.9 f collegamenti con bulloni tav. j.15 giunti incollati tav. e.1 travi saldate tav. j.11 parti aggiunte su travi saldate tav. j.13 tabella 3: tipologie di dettagli strutturali considerate nell’ eurocodice 9 e nella uni 8634. in generale nell’eurocodice viene indicata la possibilità di rivalutare o penalizzare di una o due categorie (passando cioè al σc standardizzato immediatamente superiore o inferiore rispetto a quello caratteristico del dettaglio considerato e mantenendo invece m1 costante) alcune tipologie di dettagli strutturali. questo modo di procedere viene applicato ad esempio per tener conto dell’effetto scala, limitatamente al caso di cordoni d’angolo non portanti, o nel caso di giunti saldati testa a testa con geometrie complesse. per quanto riguarda l’effetto della tensione media, l’eurocodice ne tiene conto espressamente nel solo caso di materiale base, per il quale, nel caso di storie di carico con rapporto di ciclo r<0.5, è possibile sostituire al valore di riferimento per la resistenza a fatica σc, il valore σc(r) così definito: σc(r) = f(r)·σc ; (2) dove f(r) è un fattore di incremento della resistenza a fatica che vale, limitatamente al caso di materiale base, f(r)=1.20.4r. viceversa, nel caso di giunti saldati, non è previsto considerare l’effetto del rapporto di ciclo, a meno che non sia possibile determinare le tensioni residue sul componente. http://www.gruppofrattura.it/ http://dx.medra.org/10.3221/igf-esis.09.04&auth=true b. atzori et alii, frattura ed integrità strutturale, 9 (2009) 33 45; doi: 10.3221/igf-esis.09.04 38 nel caso di geometrie complesse ove l’approccio in tensioni nominali risulti difficilmente applicabile, l’ eurocodice 9 prevede l’utilizzo di un approccio di tipo hot spot da applicare nei casi di innesco cricca a piede cordone. si tenga presente tuttavia che, come già messo in luce al paragrafo precedente, tale approccio analizza solo il campo di tensione strutturale dovuto alla geometria complessiva della giunzione, escludendo invece gli effetti dell’intaglio acuto al piede del cordone di saldatura, che risultano al contrario fondamentali per la previsione di resistenza a fatica. viceversa non è previsto l’utilizzo di approcci di tipo locale. confronto con dati sperimentali e curve di resistenza a fatica proposte dalle normative sono state confrontate con i dati sperimentali ricavati da letteratura e relativi a 15 serie di giunti di geometria diversa. ciascuna serie di dati è stata sottoposta ad analisi statistica e sono state ricavate le curve di resistenza a fatica per una probabilità di sopravvivenza del 97.7% con confidenza 95%. i risultati sono riportati in fig. 5-12. in tab. 4 si riporta invece l’intera gamma dei dati sperimentali analizzati indicando per ciascuna serie il valore di σ n = 2·106, p.s. = 97.7% e la pendenza k della curva ricavati dall’analisi statistica. per ciascuna serie si riportano inoltre le corrispondenti classi di resistenza fornite dalle normative e i relativi valori di σ n = 2·106, p.s. = 97.7% e k. nel caso di giunti a t e a croce le indicazioni riportate tra parentesi fanno riferimento alle dimensioni, in mm, del piatto principale caricato e della lamiera trasversale, rispettivamente. per quanto riguarda i valori di resistenza, ad esclusione del caso del materiale base, dove, come indicato al paragrafo materiale base si è tenuto conto dell’effetto del rapporto di sollecitazione, per la uni 8634 si è fatto riferimento ai valori relativi ad r = 0 (la maggior parte dei risultati sperimentali utilizzati per la norma italiana si riferivano infatti a 0<r<0.1) mentre per l’eurocodice i valori di resistenza sono ricavati da dati con r>0.5. le serie sperimentali sono invece tutte relative a prove con r~0.1. materiale base per un corretto confronto con i dati sperimentali (r = 0.1), i valori di resistenza forniti dall’eurocodice sono stati incrementati di un fattore f(r) = 1.15 (eq. 2). nel caso di provini forati (serie al 1 e al 3) il valore risultante è stato quindi abbattuto di un fattore 2.4 per tener conto dell’effetto di concentrazione delle tensioni (valore suggerito dall’eurocodice stesso per la tipologia di intaglio considerata, ovvero foro circolare centrato di diametro 20 mm su provino di larghezza 60 mm). per quanto riguarda la uni 8634 sono stati calcolati i valori di resistenza per r = 0.1, tenendo conto delle diverse tipologie di lega analizzate. nel caso di provini forati tale valore è stato abbattuto dello stesso coefficiente 2.4 suggerito dall’eurocodice. le due normative forniscono valori di resistenza molto simili che risultano in netto vantaggio di sicurezza nel caso della lega 6060 (fig. 5), viceversa a sfavore di sicurezza per la lega 7012 (fig. 6, 7). figura 5: confronto tra curve di resistenza a fatica per materiale base in lega 6060 (provini forati). l http://www.gruppofrattura.it/ http://dx.medra.org/10.3221/igf-esis.09.04&auth=true b. atzori et alii, frattura ed integrità strutturale, 9 (2009) 33 – 45; doi: 10.3221/igf-esis.09.04 39 serie tipologia di giunto fonte dato riferimento categoria dettaglio σ [mpa] n=2·106, p.s.=97.7% k al 1 materiale base lega p-al-mg-si (6060) provini forati sperimentale bellemo [25] 62.4 5.9 uni 8634 gruppo a 47 7.1 eurocodice 9 dett. 1.6 47.9 7 al 2 materiale base lega zergal 4 (7012) provini lisci sperimentale bellemo [25] 45.1 3.7 uni 8634 gruppo a 110.7 7.1 eurocodice 9 dett. 1.6 115 7 al 3 materiale base lega zergal 4 (7012) provini forati sperimentale bellemo [25] 19.5 2.8 uni 8634 gruppo a 46.1 7.1 eurocodice 9 dett. 1.6 47.9 7 al 4 giunto testa a testa sperimentale van straalen et al. [26] 46.5 4.7 uni 8634 gruppo d 41.5 4.3 eurocodice 9 dett. 7.3.1 40 4.3 al 5 al 6 lamiera con irrigidimento trasversale (giunto a t) sperimentale meneghetti [27] (12/10) 47.4 4.2 ribeiro [28] (12/12) 35 3.8 uni 8634 gruppo d 41.5 4.3 eurocodice 9 dett. 3.1 32 3.4 al 7 al 8 al 9 al 10 al 11 lamiera con irrigidimenti trasversali simmetrici (giunto a croce, cordone non portante) sperimentale maddox [29] (3/3) 45.2 3.7 maddox [29] (6/6) 37.3 4.3 maddox [29] (12/12) 34.7 3.8 maddox [29] (24/6) 43.1 3.8 maddox [29] (12/6) 39.3 3.7 uni 8634 gruppo e 36 4.3 eurocodice 9 dett. 3.1 32 3.4 al 12 al 13 giunto a croce, cordone portante (cordone d’angolo o parziale penetrazione) sperimentale ribeiro [28] 20.3 4.6 jacoby [30] 28 4.4 uni 8634 gruppo f 29.5 4.3 eurocodice 9 dett. 9.1 28 3.4 al 14 attacchi longitudinali sperimentale van straalen et al. [31] 25.6 3.3 uni 8634 gruppo g 19.5 4.3 eurocodice 9 dett. 3.8 23 3.4 al 15 attacchi longitudinali su travi sperimentale voutaz et al. [32] 23.5 3.6 uni 8634 gruppo g 19.5 4.3 eurocodice 9 dett. 13.2 18 3.4 tabella4: serie sperimentali analizzate: corrispondenza con le normative e confronto dei valori di resistenza. giunti testa a testa i dati sperimentali fanno riferimento a giunti testa a testa saldati su un solo lato con ripresa. lo spessore delle lamiere saldate è pari a 12 mm. le prove a fatica sono state realizzate in trazione, le rotture sono avvenute a piede del cordone di saldatura. come si evince da fig. 8 le normative forniscono valori di resistenza molto simili e in accordo, con lieve margine di sicurezza, con i dati sperimentali. lamiera con irrigidimento trasversale (giunto a t) i dati sperimentali fanno riferimento a serie avente uguale spessore del piatto principale (12 mm) e spessori differenti della lamiera trasversale. le prove a fatica sono state realizzate in trazione e le rotture si sono verificate a piede del cordone di saldatura. http://www.gruppofrattura.it/ http://dx.medra.org/10.3221/igf-esis.09.04&auth=true b. atzori et alii, frattura ed integrità strutturale, 9 (2009) 33 45; doi: 10.3221/igf-esis.09.04 40 per questa tipologia di giunto la normativa italiana fornisce dei valori di resistenza superiori a quelli dell’ eurocodice, come prevedibile tenendo conto che la uni 8634 si basa su dati ricavati da provini. mentre l’eurocodice risulta a vantaggio di sicurezza, la uni 8634 non lo è se si fa riferimento alla serie al 5. i diversi valori di resistenza delle due serie non risultano imputabili a diversi campi di tensione locale (tali serie analizzate in termini di tensioni locali [17] hanno evidenziato uno stesso effetto di concentrazione delle tensioni dovuto alla geometria complessiva delle parti collegate e del cordone di saldatura, ovvero uno stesso valore del parametro k1 in eq. 1) ma viceversa sembrano dovuti alla dispersione statistica dei risultati. difatti i valori di σ n = 2·106, p.s. = 50% risultano rispettivamente di 57 mpa per la serie al 5 e 62 mpa per la serie al 6, tuttavia, mentre per la serie al 5 il parametro di dispersione tσ = σ2.3%/σ97.7% risulta pari a 1.4, per la serie al 6 tale parametro risulta 3.1 figura 6: confronto tra curva di resistenza a fatica per materiale base in lega 7012 (provini lisci). figura 7: confronto tra curva di resistenza a fatica per materiale base in lega 7012 (provini forati). lamiera con irrigidimenti trasversali simmetrici (giunto a croce, cordone non portante) i dati sperimentali fanno riferimento a serie aventi diverse dimensioni delle parti saldate. le prove a fatica sono state realizzate in trazione e tutte le rotture sono avvenute a piede del cordone di saldatura. dal grafico di fig. 10 che riporta le curve di resistenza a fatica per giunti di uguale geometria (stessi rapporti l/t) ma dimensioni assolute diverse appare chiaramente come il non tener conto dell’ effetto scala da parte sia dell’uni 8634 che dell’eurocodice 9 (che lo prevede solo per lunghezze della lamiera trasversale maggiori di 20 mm e con un esponente pari in media a circa 0.17 anziché 0.326 [22]), sebbene in parziale vantaggio di sicurezza, non permetta di apprezzare la variazione di resistenza associata a dimensioni assolute diverse. in fig. 11 e 12 si illustrano invece le variazioni di resistenza associate a variazioni geometriche, ovvero variazioni dello spessore del piatto principale a parità di dimensioni della lamiera trasversale o viceversa. tali variazioni, che vengono trascurate dalle normative, verrebbero invece messe in luce da un’analisi dei diversi campi di tensione locale [17] dovuti alle diversi geometrie di giunto pur all’interno di una medesima classe. infatti per i giunti in fig. 11 all’aumentare dello spessore del piatto principale il valore di k1 diminuisce. 10 100 1000 104 105 106 107 n  σ [ m p a] dati sperimentali_al 2 (lega 7012, provini lisci) uni 8634_ gruppo a eurocodice 9_dett. 1.6 10 100 1000 104 105 106 107 n dati sperimentali_al 3 (lega 7012, provini forati) uni 8634_ gruppo a eurocodice 9_dett. 1.6  σ [ m p a] http://www.gruppofrattura.it/ http://dx.medra.org/10.3221/igf-esis.09.04&auth=true b. atzori et alii, frattura ed integrità strutturale, 9 (2009) 33 – 45; doi: 10.3221/igf-esis.09.04 41 analogamente, nel caso dei giunti in fig. 12 l’aumento di spessore della lamiera trasversale comporta una maggiore gravosità del giunto indicata da un aumento del parametro k1 e quindi, a parità di spessore del piatto principale, in base all’eq. 1, una diminuzione della resistenza a fatica. si noti, con riferimento a quanto dimostrato da meneghetti e tovo [33] come l’utilizzo di un approccio di tipo hot spot per questa tipologia di giunti possa condurre a conclusioni errate. figura 8: confronto tra curva di resistenza a fatica per giunti testa a testa. figura 9: confronto tra curva di resistenza a fatica per lamiera con irrigidimento trasversale (giunto a t). figura 10: confronto tra curva di resistenza a fatica per lamiere con irrigidimenti trasversali simmetrici (giunti a croce,cordone non portante). http://www.gruppofrattura.it/ http://dx.medra.org/10.3221/igf-esis.09.04&auth=true b. atzori et alii, frattura ed integrità strutturale, 9 (2009) 33 45; doi: 10.3221/igf-esis.09.04 42 figura 11: confronto tra curva di resistenza a fatica per lamiere con irrigidimenti trasversali simmetrici (giunti a croce,cordone non portante). figura 12: confronto tra curva di resistenza a fatica per lamiere con irrigidimenti trasversali simmetrici (giunti a croce,cordone non portante). giunto a croce, cordone portante i dati sperimentali fanno riferimento a due serie che differiscono unicamente per lo spessore del cordone di saldatura. le prove a fatica sono state realizzate in trazione e le rotture sono avvenute a piede del cordone di saldatura. la diversa criticità delle due serie, riscontrabile tramite un’ analisi in tensioni locali [17] che evidenzia valori inferiori di k1 all’aumentare delle dimensioni del cordone di saldatura, non viene considerata dalle normative di progettazione che forniscono per altro delle curve a svantaggio di sicurezza. e’ opportuno specificare tuttavia, che per i rapporti dimensioni del cordone e del piatto principale caricato presenti nelle due serie, l’eurocodice prevede l’innesco di cricca alla radice del cordone di saldatura anziché al piede, con conseguente riduzione della classe di resistenza del giunto. attacchi longitudinali i dati sperimentali fanno riferimento a due serie, la prima (al 14) relativa ad attacchi longitudinali di lunghezza 120 mm saldati su piatto principale di lamiera di spessore 12 mm e testati in trazione, la seconda (al 15) relativa ad attacchi longitudinali di lunghezza 200 mm saldati su una trave ad i (larghezza 101 mm, altezza 216 mm) avente spessore dell’ala 11 mm e testati in flessione. in entrambe le serie di prove le rotture si sono manifestate a piede del cordone di saldatura in direzione trasversale. entrambe le normative presentano delle curve di resistenza a vantaggio di sicurezza rispetto ai risultati sperimentali, con l’eurocodice che fornisce dei valori di resistenza leggermente superiori rispetto alla uni. la leggera diminuzione di http://www.gruppofrattura.it/ http://dx.medra.org/10.3221/igf-esis.09.04&auth=true b. atzori et alii, frattura ed integrità strutturale, 9 (2009) 33 – 45; doi: 10.3221/igf-esis.09.04 43 resistenza della serie al 15 rispetto alla serie al 14 pare rendere ragione all’individuazione, nell’eurocodice 9, di classi di resistenza differenti per attacchi longitudinali su lamiera o su travi. figura 13: confronto tra curva di resistenza a fatica per giunti a croce, cordone portante. figura 14: confronto tra curva di resistenza a fatica per attacchi longitudinali. figura 15: confronto tra curva di resistenza a fatica per attacchi longitudinali su travi. http://www.gruppofrattura.it/ http://dx.medra.org/10.3221/igf-esis.09.04&auth=true b. atzori et alii, frattura ed integrità strutturale, 9 (2009) 33 45; doi: 10.3221/igf-esis.09.04 44 conclusioni e curve di resistenza a fatica proposte dalla normativa italiana uni 8634 e dall’eurocodice 9 sono state confrontate con i valori di resistenza ricavati da dati sperimentali tratti da letteratura e riferiti a 15 serie di geometria diversa. benché nella maggior parte dei casi in esame i valori forniti dalle normative o rispecchiano fedelmente i risultati sperimentali (giunti testa a testa), o si pongono a vantaggio di sicurezza (materiale base in lega 6060, giunti a croce non portante, attacchi longitudinali); in alcuni casi le curve di progettazione risultano pericolosamente a sfavore di sicurezza (materiale base in lega 7012, giunti a croce portante). in altri casi le due normative, seppure entrambe a vantaggio di sicurezza, forniscono valori di resistenza significativamente differenti tra loro (attacchi longitudinali) con conseguenti difficoltà nel passaggio da una normativa ad un’altra. il confronto con i dati sperimentali ha inoltre permesso di confermare un’ingiustificata sottovalutazione dell’effetto scala, e di mostrare come l’utilizzo dell’approccio in tensioni nominali non permetta di stimare variazioni di resistenza legate alla geometria complessiva sia del giunto che del cordone di saldatura e valutabili invece solo tramite un’analisi dei campi di tensione locali. bibliografia [1] uni 8634 strutture in leghe di alluminio. istruzioni per il calcolo e l’esecuzione (1985). [2] e.haibach, b. atzori, lbf rep. no. fb-116 (1974). [3] e. haibach, b. atzori, aluminium. (1975) [4] b. atzori, v. dattoma, proc. iiw annual assembly, iiw doc. xiii-1088/3, porto, portugal (1981). [5] cnr uni 10011 costruzioni in acciaio. istruzioni per il calcolo, l’esecuzione, la manutenzione (1980). [6] cnr uni 10011 costruzioni in acciaio. istruzioni per il calcolo, l’esecuzione, la manutenzione (1986). [7] uni env 1999-2 eurocodice 9. progettazione delle strutture di alluminio. parte 2: strutture sottoposte a fatica (2002). [8] uni en 1999-1-3 eurocodice 9. progettazione delle strutture di alluminio. parte 1-3: strutture sottoposte a fatica (2007). [9] uni en 1993-19 eurocodice 3. progettazione delle strutture di acciaio. parte 1-9: fatica (2005). [10] b. atzori, b. rossi, k. heuler, atti del xxvi convegno nazionale aias, napoli (2007). [11] b. atzori, b. rossi, rivista italiana della saldatura 1 (2008) 93. [12] b. atzori, e. haibach, atti del xvii convegno nazionale aias, cagliari (1979). [13] b. atzori, g. blasi, c. pappalettere, exp. mech., 25(2) (1985)129. [14] p. lazzarin, r. tovo, fatigue fract. engng mater. struct., 21 (1998) 1089. [15] b. atzori, p. lazzarin, r. tovo, fatigue fract. engng mater. struct. 22 (5) (1999)369. [16] b. atzori, p. lazzarin, r. tovo, j. strain anal. eng. 34 (1999) 437. [17] p. lazzarin, p. livieri, int. j. fatigue, 23 (2001) 225. [18] b. atzori, g. meneghetti, int. j. fatigue, 23 (8) (2001) 713. [19] b. atzori, g. meneghetti, l. susmel, int. j. fatigue, 24 (2002) 591. [20] p. livieri, p. lazzarin, int. j. fracture, 133 (2005) 247. [21] b. atzori, g. meneghetti, proceedings of the international conference of new trends in fatigue and fracture, metz (2002) . [22] b. atzori, g. meneghetti, m. ricotta, atti del xxxvi convegno nazionale aias, napoli (2007). [23] b. atzori, p. lazzarin, g. meneghetti, m. ricotta, int. j. fatigue, 31 (2009) 59. [24] b. atzori, rivista italiana della saldatura, lii (1) (2000). [25] s. bellemo i materiali metallici nelle strutture soggette a fatica: confronto tra le leghe leggere e gli acciai. tesi di laurea, dipartimento di ingegneria meccanica, università di padova (1988). [26] ij. j. van straalen, f. soetens, o. d. dijkstra, tno building and construction research-report 94-con-r1563 (1994). [27] g. meneghetti metodologie di analisi e progettazione di giunti saldati. tesi di dottorato, università di padova (1998). [28] as. ribeiro, jp. gonçalves, f. oliveira, pt. castro, aa. fernandes, proceedings of the sixth international conference on aluminium weldments, cleveland, ohio, (1995) 65. [29] j. maddox, proceedings of the sixth international conference on aluminium weldments, cleveland ohio, (1995) 77. l http://www.gruppofrattura.it/ http://dx.medra.org/10.3221/igf-esis.09.04&auth=true b. atzori et alii, frattura ed integrità strutturale, 9 (2009) 33 – 45; doi: 10.3221/igf-esis.09.04 45 [30] g. jacoby über das verhalten von schweissverbindungen aus aluminiumlegierungen bei schwingbeanspruchung. dissertation, technische hochschule, hannover (1961). [31] ij. j. van straalen, f. soetens, o. d. dijkstra, tno building and construction research-report 94-con-r1566 (1994). [32] b. voutaz, i.f. smith, m.a. hirt, proceedings of the third international conference on steel and aluminium structures, istanbul, turkey (1995). [33] g. meneghetti, r. tovo, proceedings inalco int. conference, cambridge, uk (1998). http://www.gruppofrattura.it/ http://dx.medra.org/10.3221/igf-esis.09.04&auth=true microsoft word numero_41_art_14.docx m. a. meggiolaro et alii, frattura ed integrità strutturale, 41 (2017) 98-105; doi: 10.3221/igf-esis.41.14 98 focused on multiaxial fatigue on the applicability of miner’s rule for multiaxial fatigue life calculations under non-proportional load histories marco antonio meggiolaro, jaime tupiassú pinho de castro, samuel elias ferreira pontifical catholic university of rio de janeiro, puc-rio, r. marquês de são vicente 225, rio de janeiro, 22451-900, brazil meggi@puc-rio.br, jtcastro@puc-rio.br, ferreirase@hotmail.com hao wu school of aerospace engineering and applied mechanics tongji university, siping road 1239, 200092, shanghai, p.r.china wuhao@tongji.edu.cn abstract. fatigue design routines and computer codes must use some damage accumulation rule to deal with variable amplitude loadings (val), usually palmgren-miner (or miner’s) linear rule for lack of a clearly better option. nevertheless, fatigue lives are intrinsically sensitive to the order of val events, which may e.g. induce residual stresses and thus change the critical point stress state, much affecting its subsequent residual life. on the other hand, in general, non-linear damage accumulation rules are not robust, resulting in better predictions than miner’s rule only for some specific load orders, requiring a case-by-case analysis. therefore, miner’s linear damage rule still is the usual choice in practical fatigue calculations and assessments, giving reasonable predictions at least when properly combined with approaches that sequentially consider plasticity-induced effects, following the critical point stress/strain history in a cycle-by-cycle basis. in this work, miner’s rule is evaluated for non-proportional tension-torsion loadings on annealed tubular 316l stainless steel specimens. normal-shear strain histories following either cross, diamond, circular or square paths are applied, and their fatigue lives are measured. then, more complex val paths consisting of combinations of these individual path shapes are applied in other specimens, whose associated fatigue lives are predicted based on miner’s rule. keywords. miner’s rule; multiaxial fatigue; non-proportional loading; variable amplitude loading. citation: meggiolaro, m.a., castro, j.t.p., wu, h., ferreira s.e., on the applicability of miner’s rule for multiaxial fatigue life calculations under non-proportional load histories, frattura ed integrità strutturale, 41 (2017) 98-105. received: 28.02.2017 accepted: 15.04.2017 published: 01.07.2017 copyright: © 2017 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. m. a. meggiolaro et alii, frattura ed integrità strutturale, 41 (2017) 98-105; doi: 10.3221/igf-esis.41.14 99 introduction lthough practical fatigue analyses usually involve variable amplitude loads (val), material data (if available) normally is measured in constant amplitude load (cal) tests. so, fatigue design routines must use some damage accumulation rule to deal with val. the classic linear damage accumulation rule, known as the palmgren-miner rule (or as miner’s rule) [1-2], predicts fatigue failures when the sum of the damage induced by each load event (di) equals the critical damage dc the piece can sustain. dc is usually arbitrarily defined as dc  1  (ni/ni) = 1, where ni is the number of cycles of the i-th load event, and ni is the number of cycles the piece would last if only that event loaded it. this heuristic hypothesis implicitly assumes that the various load events are independent. partial loss of available life is a simple way to quantify fatigue damage, but it is not the only one. as terminal fatigue failures occur at a critical crack size ac, accumulated damage can be defined e.g. by the ratio d  a/ac in crack growth problems, where a is the current crack size. too many other semi-empirical rules are available to model fatigue damage accumulation under val. some try to consider sequence effects not predictable by palmgren-miner (if it is used non-sequentially like a statistics), while others try to use less heuristic damage concepts. fatemi and yang [3] list 56 such rules, subdividing them into 6 groups: (i) linear damage evolution rules; (ii) bilinear damage evolution rules; (iii) rules that use modified fatigue life curves (sn or n) to consider some sequence effects; (iv) fracture mechanics-based rules; (v) continuum damage mechanics-based rules; and (vi) rules based on energy methods. although damage accumulation modeling still is a fascinating research subject, none of such other (too many) rules got consensus to forever retire the old palmgren-miner rule, which has been used by structural engineers since 1924. indeed, despite countless criticisms, it keeps on being by far the most used damage accumulation tool for fatigue design applications, bravely resisting to its poor performance with ordered loads, not to mention its lack of academic sophistication. continuum damage mechanics, in particular, is a modern technique that has many interesting features, among them be based on much more sound mechanical fundamentals that most of the concurrent heuristic rules. it associates different damage mechanisms to the apparent young modulus’ variation they cause in standard specimens, or to other similarly distributed parameters [4-5]. therefore, it is no surprise it has been more useful to describe damage accumulation when it is caused by distributed damage mechanisms. however, its localized damage models, needed to describe most fatigue failures, still are at best controversial. the value dc  1 usually chosen to quantify the critical damage is certainly arbitrary, since it is based on heuristic arguments, not on suitable mechanical foundations. hence, it is no surprise to find ni/ni  1 in practical applications. miner himself quoted 0.7 < ni/ni < 2.2 as typical values obtained in fatigue tests performed under random loads or load blocks [2]. juvinall [6] affirms that usually ni/ni >> 1 in two step loads when all small load events are applied before the large ones, whereas ni/ni<< 1 when all large load events act before the small ones, and that such ordered load blocks may have a huge dispersion, namely 0.18 < ni/ni < 23. however, as such well-ordered loading is rare in practice, for engineering purposes the linear damage accumulation rule produces reasonable and frequently conservative predictions in many fatigue design problems under real service loads, the main cause for its perennial popularity. however, such a popularity does not mean that sn models applied with miner’s rule can safely solve all practical fatigue crack initiation assessment problems, even if applied to a rainflow-counted representative sample of the load history. in fact, fatigue lives are intrinsically sensitive to the order of val events, which may e.g. induce residual stresses and change the critical point stress state, much affecting its subsequent residual life. all statistics ignore sequence effects, but the palmgren-miner rule does not need to be used as so. indeed, fatigue damage can be sequentially accumulated considering at least residual stress variations associated with cyclic yielding at every load event [7], using linear or fancier damage accumulation models. to do so, ordered damage calculations by n techniques may recognize such plasticity-induced effects, following the critical point stress/strain history in a cycle-by-cycle basis, and they can even be included in simpler sn calculation routines to quantify the effect of residual stress changes caused by high-load events that induce local yielding. this strategy can be numerically efficient when such macroscopic plasticity events are rare. however, the order of the individual load events is also important even in the absence of macroscopic plasticity, probably due to its effect on localized microplasticity around the crack initiation point. this is an important issue when measuring gassner curves obtained by applying sequences of load blocks composed by a series of cal steps containing many cycles each. indeed, even under the high cycle fatigue regime, it cannot be expected that the damage caused by a single ordered load block, with all its steps applied in a low  high  low sequence, is identical to the damage caused by the same steps, a m. a. meggiolaro et alii, frattura ed integrità strutturale, 41 (2017) 98-105; doi: 10.3221/igf-esis.41.14 100 but applied in a high  low  high order. in fact, such ordered loadings tend to generate very different fatigue lives, see fig. 1 [8]. this figure also shows that the highest scatter in miner’s rule predictions happens at high mean stress values, indicating that load order effects are more important under higher stress levels. figure 1: step order and mean-stress effects on the lives of notched al 7075-t6 test specimens with stress concentration factor 4, subjected to load blocks formed by the same load steps (these steps have the same mean stress m, but practical spectra can produce steps with different m) [8]. therefore, it could be argued that one of the main reasons for the variability of the critical damage dc is the load order effect associated with higher stress levels or overloads, which can induce residual stresses ahead of the initiating microcrack, affecting its subsequent fatigue life. as discussed before, if such load order effects are sequentially accounted for by n techniques or even by da/dn short crack concepts, then miner’s rule should give predictions with improved reliability. for instance, elber’s plasticity-induced crack closure idea [9-10] can be adapted to model the m influence on uniaxial n tests, assuming the fatigue damage process only continues after the microcrack is completely open. indeed, topper’s group found they remain partially closed during part of their loading cycle. hence, they assumed m or max effects on the so-called crack initiation phase would be caused by such crack opening loads, and proposed a new model to quantify these effects on n curves [11-12]. in this way, fatigue damage would occur only on eff, the effective portion of the hysteresis loop above the stress level op that completely opens the microcrack at min  op, see fig. 2. eff =  op (1) to precisely measure op is no trivial task, but in many cases it can be assumed that op is approximately elastic, so  op = eff  (op min)/e (2) this effective strain range, which would be the cause for fatigue damage in the fatigue crack initiation stage, is illustrated in fig. 2 as well. duquesnay et al. [12] proposed an empirical equation to estimate the opening stress op in n specimens, as a function of the applied maximum and minimum stresses, the cyclic yield strength syc, and two material-dependent parameters  and  (which, for their 1045 steel, were   0.845 and   0.125):              op ycs 2 max max min1 (3) m. a. meggiolaro et alii, frattura ed integrità strutturale, 41 (2017) 98-105; doi: 10.3221/igf-esis.41.14 101 figure 2: the effective strain range of the hysteresis loop, eff    op, is the loop portion where the microcrack is completely open, thus can suffer fatigue damage. the opening stress op, which depends on m and affects eff, would be the physical cause for mean stress effects on fatigue crack initiation. topper’s tests showed that the ratio op/max can be negative, meaning microcracks can be entirely open even under a compressive load op < 0, in particular under high stresses and negative stress ratios r min/max. therefore, it is interesting to rewrite eq. (3) as a function of r as:            op ycs r 2 max max1 (4) if fatigue damage is caused by eff    (op  min)/e, to calculate it using n curves available in the literature, which associate  (not eff) to the fatigue crack initiation life n, they should be properly adapted. to do so, topper and coworkers proposed (and validated for some materials) an equation eff n that intrinsically includes the mean load effects:       ceff cl n2 ( 2 ) (5) this eff  n curve is illustrated in fig. 3, where c and c' are material properties, usually different from the equivalent coffin-manson’s parameters, and l is the strain fatigue limit, defined as the largest effective strain amplitude eff/2 that does not cause fatigue damage in n specimens. figure 3: universal eff  n curve, which describes fatigue lives under any mean load. m. a. meggiolaro et alii, frattura ed integrità strutturale, 41 (2017) 98-105; doi: 10.3221/igf-esis.41.14 102 the strain fatigue can be estimated from the traditional stress limit sl under r 1, assuming eff/2 is purely elastic under infinite life and sl max << syc, hence:                   op l op lop ll s ss e emax 2 1 2 (6) values of c , c', and l in eq. (5) can be fitted from standard n tests under r 1, using eq. (1)-(5) to calculate op and op and convert n into eff  n data. moreover, sparse periodic compressive underloads can be applied to conventional n tests to guarantee that the initiated microcrack remains fully open, making op = 0 and so   eff [11]. after calibrated, these equations can be used to predict initiation lives under other stress ratios r, assuming mean load effects are caused solely by microcrack closure. the expression for the microcrack opening load op was obtained from fatigue tests under constant strain range . to use it for real service loads, duquesnay et al. assume the smallest op value calculated during the entire variable amplitude load history remains invariable [12]. according to them, this hypothesis would be conservative, but it would produce fatigue damage predictions close to those measured experimentally. in this way, when sup  syc is the largest and inf is the smallest stress of the loading history, the smallest microcrack opening load would be given byop* where:               op ycs 2 * sup sup inf1 (7) this idea can be used to evaluate the effects of tensile ep overloads on fatigue crack initiation, as well as the effects of compressive underloads that reduce op* , facilitating the opening of microcracks and increasing the effective strain range of subsequent load events, making them more harmful. overloads and underloads are causes of very important load order effects on macrocrack fatigue propagation. according to this idea, the effective strain range eff, calculated considering the smallest microcrack opening stress op* (or the value corresponding to e.g. the 0.5% smallest) induced by the loading history, would be the parameter that quantifies mean load effects under real service loads. this method was qualified using standard n specimens, but it might, at least in principle, be generalized for notched structural components [12]. damage accumulation in multiaxial fatigue here are several cycle-based models to quantify fatigue damage under multiaxial loading using some damage accumulation rule. most of them can be separated into two classes, namely the invariant-based approach and the critical-plane approach, discussed as follows. the invariant-based approach assumes fatigue damage is due to a mises equivalent range, which mixes stress or strain components that act in all directions at the critical point. this approach assumes damage is due to a suitable combination of all stress components, so it is recommended for describing distributed-damage materials, or to model damage mechanisms such as multiple cracking in concrete, cavitation in ductile fracture, or fiber rupture in isotropic fiberreinforced composites. in multiaxial fatigue applications based on this approach, the general moment of inertia method [13] or some convex-enclosure method [14] must be applied after the use of a multiaxial rainflow count, to quantify load events and to obtain the associated stress or strain ranges, and then the corresponding damage using some invariant-based model such as sines’ or crossland’s. then, the damage can be accumulated e.g. applying miner’s rule to combine the contributions of all multiaxial rainflow-counted load events. the critical-plane approach, on the other hand, considers that fatigue damage is a truly local and directional problem, hence that only the most damaged plane of the critical point (or sometimes the plane experiencing maximum shear, depending on the fatigue damage model adopted) should be used to calculate fatigue lives. therefore, it assumes that the critical plane of the critical point do not interact with the other planes, or else that there is no interaction among damage values eventually accumulated on planes that do not contain the fatigue crack. this approach should be preferred for describing fatigue damage in directional-damage materials, those which tend to fail by fatigue due to the formation and growth of a single dominant crack. this is the case of most metallic alloys, so the critical plane approach is very useful for practical applications. moreover, this approach predicts both fatigue life and the orientation of the microcrack initiation plane. t m. a. meggiolaro et alii, frattura ed integrità strutturale, 41 (2017) 98-105; doi: 10.3221/igf-esis.41.14 103 therefore, in the critical-plane approach, the stress or strain history must be projected onto several candidate planes at the critical point to identify the critical one. to predict the initiation of tensile microcracks along planes perpendicular to the free surface, a uniaxial rainflow count is applied to the projected normal stress or strain history to calculate accumulated mode i damage e.g. using the multiaxial smith-watson-topper (swt) equation, or any other suitable model to describe tensile-sensitive materials [7]. miner’s rule could be then applied to accumulate the tensile damage of all events counted by the uniaxial rainflow. for shear microcracks on planes perpendicular to the free surface, miner’s rule is applied instead to the accumulation of multiaxial fatigue damage using, e.g., fatemi-socie’s model [7], a suitable model to describe shear-sensitive materials. it could be argued that both tensile and shear damage from a given plane should be added up using miner’s linear rule, however this would require e.g. that both swt and fatemi-socie’s models had been calibrated considering this combination of tensile and shear damage. instead, in practice these models are calibrated only considering respectively the tensile or shear damage parameters, neglecting their interaction. therefore, such an interaction should be disregarded in the subsequent predictions, to be coherent with the adopted model and its calibration routine. miner’s rule should thus be applied to either tensile or to shear damage on a given material plane, without adding them up. to predict the initiation of shear microcracks along planes inclined 45o with respect to the free surface, the projected shear history must be rainflow-counted for each candidate plane. this counting must be done using a two-dimensional (2d) rainflow routine, e.g. a 2d version of the modified wang-brown rainflow [7] method, to combine non-proportional (np) histories of in-plane and out-of-plane shear stresses a and b (or strains a and b). after this 2d rainflow, the 2d moi or a convex enclosure method should be used in each rainflow-counted half-cycle to combine both shear stresses (or strains) into a path-equivalent shear range used in damage calculation with, e.g., fatemi-socie’s shear-based damage model. miner’s rule can then used to obtain the accumulated damage on each candidate plane. in summary, to properly describe fatigue damage under val conditions, all cycle-based multiaxial fatigue approaches require, in the end, some damage accumulation rule. almost invariably, this is performed using miner’s linear rule because, in general, non-linear damage accumulation rules are not robust [3], resulting in better predictions than miner’s only for some load paths, but much worse for others. however, most evaluations of miner’s rule are based either on uniaxial or on proportional multiaxial loading histories. its applicability to non-proportional multiaxial load histories has not been much explored in the literature. however, np outof-phase histories have a very significant effect on fatigue damage when compared to proportional in-phase load histories. under strain control, np load histories are in general more damaging than proportional history paths with same longest chord l for two reasons: (i) the path-equivalent stress or strain range of the np history is always larger than the proportional range l, as verified from the moi [13] and convex enclosure methods [14], since longer load paths tend to induce more damage; and (ii) np hardening, if present in the considered material (as in all austenitic stainless steels), tends to increase peak tensile normal stresses perpendicular to the critical plane. on the other hand, under stress control, np hardening could actually decrease the resulting strains, decreasing fatigue damage and thus competing with the path-equivalent effect. hence, the fatigue analyst should be careful not to forget to consider in the calculations such different behaviors under strain or stress control, to avoid blaming miner’s rule for the scatter in the multiaxial damage predictions. as shown following, miner’s rule can be a very reasonable tool if the physics of the problem is properly understood and, in particular, if load-order plasticity effects are properly accounted for, either directly or indirectly. experimental verification of miner’s rule under np multiaxial loadings n this section, miner’s rule is evaluated for selected np tension-torsion load histories with similar amplitudes. as discussed before, overloads or large differences in subsequent load amplitudes can induce significant load order effects, even in fatigue crack initiation problems. however, since the following analysis does not consider such effects, loading histories with similar amplitudes have been selected. the main objective of the following experiments is not to evaluate overload-induced effects, but to verify whether miner’s rule can give reasonable fatigue damage predictions not only for uniaxial and proportional, but also for np multiaxial loadings. the experimental evaluation uses complex 2d tension-torsion stress histories, applied on annealed tubular 316l stainless steel specimens in a tension-torsion servo-hydraulic testing machine, see fig. 4. the experiments consist of straincontrolled tension-torsion cycles applied to six tubular specimens, each one of them following one of the six periodic x×xy/3 histories from fig. 5. all tubular specimens had 30 mm outside diameter and 2mm cylindrical wall, to avoid significant strain gradients. the strains have been measured by a commercial tension-torsion clip-gage. i m. a. meggiolaro et alii, frattura ed integrità strutturale, 41 (2017) 98-105; doi: 10.3221/igf-esis.41.14 104 the individual amplitudes of each x and xy/3 strain component are 0.6% for all six experiments. the first four experiments involve basic load path shapes: cross, diamond, circle and square, see fig. 5. the last two involve combinations of the previous four: the square/cross path load blocks consisting of one square cycle followed by one cross cycle, while each load block of the square/circle/diamond path involved one square, one circle and one diamond cycle, in that order. all the tests were carried out until a small crack was detected on the surface by visual inspection. in all specimens, the initiated crack was later confirmed to have surface widths between 1 and 2 mm. this variability contributes to the uncertainties in the experimental data, even though it can be inferred that the number of growth cycles between 1 and 2mm should be relatively small, since the visual inspection was carried out on a frequent basis. tab. 1 shows the observed fatigue lives in number of blocks, where each block consists of a full load period. figure 4: tension-torsion testing machine and extensometer mounted on a tubular specimen. figure 5: applied periodic x×xy/3 strain paths on six tension-torsion tubular specimens, all of them with normal and effective shear amplitudes 0.6%. tension-torsion path observed life (blocks) miner’s prediction (blocks) cross 1535 diamond 976 circle 837 square 772 square/cross 342 514 square/circle/diamond 288 285 table 1: observed initiation lives, in number of blocks, for each applied tension-torsion path, and miner’s predictions. m. a. meggiolaro et alii, frattura ed integrità strutturale, 41 (2017) 98-105; doi: 10.3221/igf-esis.41.14 105 tab. 1 also shows miner’s rule predictions for the square/cross and square/circle/diamond paths, calculated from the observed lives of the four specimens subjected to the cross, diamond, circle and square paths. for the square/cross path, miner’s prediction for the number of blocks b is such that 1/b = 1/772  1/1535, giving b = 514 blocks, an error of approximately 50%. besides the usual scatter in fatigue (due to undetected microscopic defects) and of miner’s rule predictions, this error might also be attributed to the difficulty to detect a small crack on the surface, which was used as the initiation criterion to measure the number of blocks. moreover, the critical plane of the square, cross and square/cross path specimens, where the microcrack initiates, could be significantly different, requiring the application of the critical plane approach to account for this and only then apply miner’s rule. for the square/circle/diamond path, miner’s prediction is such that 1/b = 1/772  1/837  1/976, giving b = 285 blocks, an unusually small prediction error of only 1%. this result is reassuring towards the continued use of miner’s rule, at least for such np loading paths with similar stress levels and amplitudes. but since miner’s rule is not a physical law, it can still result in significant prediction errors for some particularly ordered histories, or in variable amplitude histories with large variations in stress or strain amplitude. conclusions oad order effects can be very important in crack initiation, and must be considered to properly account for residual stress effects and micro/macro plastic memory in general, especially under low-cycle conditions. nevertheless, miner’s rule can be applied for both high and low-cycle fatigue, as long as any significant plasticity effect is considered, in the original order it was applied. it was found that miner’s rule provides reasonable predictions for selected non-proportional tension-torsion histories, at least when the variable amplitude loading cycles have equivalent amplitudes that do not differ too much from each other. finally, be aware that, in general, non-linear damage accumulation rules are not robust; therefore, miner’s linear damage rule still is the best choice in multiaxial fatigue calculations, giving accurate predictions when combined e.g. with the critical-plane approach. references [1] palmgren, a., die lebensdauer von kugellagern (life time of bearings). verfahrenstechinik, 68 (1924) 339-341. [2] miner, m.a., cumulative damage in fatigue, j. app. mech., 12 (1945) a159-a164. [3] fatemi, a., yang, l., cumulative fatigue damage and life prediction theories: a survey of the state of the art for homogeneous materials. int. j. fatigue, 20 (1998) 9-34. [4] lemaitre, j., a course on damage mechanics, springer, (1996). [5] lemaitre, j., chaboche, j. l., mécanique des matériaux solides, 2ème ed. dunod, (2004). [6] juvinall, r.c., stress, strain and strength, mcgraw-hill, (1967). [7] castro, j.t.p., meggiolaro, m.a., fatigue design techniques v. 2: low-cycle and multiaxial fatigue. createspace (2016). [8] schijve, j., fatigue of structures and materials, kluwer, (2001). [9] elber, w., fatigue crack closure under cyclic tension, eng fract mech, 2 (1970) 37-45. [10] elber, w., the significance of fatigue crack closure. astm stp 486 (1971) 230-242. [11] duquesnay, d.l., topper, t.h., yu, m.t., pompetzki, m.a., the effective stress range as a mean stress parameter, int. j. fatigue, 14 (1992) 45-50. [12] duquesnay, d.l., pompetzki, m.a., topper, t.h., fatigue life predictions for variable amplitude strain histories. sae paper 930400, (1993). [13] meggiolaro, m.a., castro, j.t.p., wu, h., zhong, z., generalization of the moment of inertia method to predict equivalent amplitudes of non-proportional multiaxial stress or strain histories. 14th pan-american congress of applied mechanics, chile (2014). [14] meggiolaro, m.a., castro, j.t.p., an improved multiaxial rainflow algorithm for non-proportional stress or strain histories part i: enclosing surface methods, int. j. fatigue, 42 (2012) 217-226. l << /ascii85encodepages false /allowtransparency false /autopositionepsfiles true /autorotatepages /none /binding /left /calgrayprofile (dot gain 20%) /calrgbprofile (srgb iec61966-2.1) /calcmykprofile (u.s. web coated \050swop\051 v2) /srgbprofile (srgb iec61966-2.1) /cannotembedfontpolicy /error /compatibilitylevel 1.4 /compressobjects /tags /compresspages true /convertimagestoindexed true /passthroughjpegimages true /createjobticket false /defaultrenderingintent /default /detectblends true /detectcurves 0.0000 /colorconversionstrategy /cmyk /dothumbnails false /embedallfonts true /embedopentype false /parseiccprofilesincomments true /embedjoboptions true /dscreportinglevel 0 /emitdscwarnings false /endpage -1 /imagememory 1048576 /lockdistillerparams false /maxsubsetpct 100 /optimize 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/hrv (za stvaranje adobe pdf dokumenata najpogodnijih za visokokvalitetni ispis prije tiskanja koristite ove postavke. stvoreni pdf dokumenti mogu se otvoriti acrobat i adobe reader 5.0 i kasnijim verzijama.) /hun 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can be opened with acrobat and adobe reader 5.0 and later.) >> /namespace [ (adobe) (common) (1.0) ] /othernamespaces [ << /asreaderspreads false /cropimagestoframes true /errorcontrol /warnandcontinue /flattenerignorespreadoverrides false /includeguidesgrids false /includenonprinting false /includeslug false /namespace [ (adobe) (indesign) (4.0) ] /omitplacedbitmaps false /omitplacedeps false /omitplacedpdf false /simulateoverprint /legacy >> << /addbleedmarks false /addcolorbars false /addcropmarks false /addpageinfo false /addregmarks false /convertcolors /converttocmyk /destinationprofilename () /destinationprofileselector /documentcmyk /downsample16bitimages true /flattenerpreset << /presetselector /mediumresolution >> /formelements false /generatestructure false /includebookmarks false /includehyperlinks false /includeinteractive false /includelayers false /includeprofiles false /multimediahandling /useobjectsettings /namespace [ (adobe) (creativesuite) (2.0) ] /pdfxoutputintentprofileselector /documentcmyk /preserveediting true /untaggedcmykhandling /leaveuntagged /untaggedrgbhandling /usedocumentprofile /usedocumentbleed false >> ] >> setdistillerparams << /hwresolution [2400 2400] /pagesize [612.000 792.000] >> setpagedevice microsoft word numero_42_art_23.docx m. peron et alii, frattura ed integrità strutturale, 42 (2017) 214-222; doi: 10.3221/igf-esis.42.23 214 local strain energy density for the fracture assessment of polyurethane specimens weakened by notches of different shape m. peron, s.m.j. razavi ,f. berto, j. torgersen department of mechanical and industrial engineering, norwegian university of science and technology (ntnu), richard birkelands vei 2b, 7491, trondheim, norway. mirco.peron@ntnu.no, javad.razavi@ntnu.no, filippo.berto@ntnu.no, jan.torgersen@ntnu.no l. marsavina department of mechanics and strength of materials, univeritatea politehnica timisoara, timisoara, romania msvina@mec.upt.ro abstract. recent studies on local stress fields in proximity of crack and notch tips have shown that strain energy density (sed), averaged in a circular control volume surrounding the point of stress singularities, represents a reliable engineering approach for assessing the brittle fracture of several brittle materials. it is worthy of notice that the application of sed criterion and the reliability of its results are strictly related to the proper determination of fracture parameters, i.e. the critical value of deformation energy wc and the radius rc of the control volume. this work presents an experimental methodology for their determination by means of notched specimens for different polyurethane densities, ranging from 100 to 651 kg/m3. then, once obtained these critical parameters, the failure load in different types of notches and cracked specimens under mode i have been predicted. moreover, for cracked specimens under mixed mode and mode ii, the authors propose a personal approach that confirms pur foams can be treated as brittle materials keywords. strain energy density; pur foams; tensile fracture; critical radius; fracture parameters. citation: peron, m., razavi, s.m.j., berto, f. torgersen, j., marsavina, l., local strain energy density for the fracture assessment of polyurethane specimens weakened by notches of different shape, frattura ed integrità strutturale, 42 (2017) 214-222. received: 28.06.2017 accepted: 31.07.2017 published: 01.10.2017 copyright: © 2017 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. introduction n the last years, polyurethane (pur) has widely gained interest in industrial applications because of its high versatility. in fact, as other polymers like polyethylene (pe), pur materials can be manufactured in a wide range of densities, obviously determining different applications. in fact at low densities (30 200 kg/m3), being rigid foams having a close cell cellular structure, they are employed as high-resilience seating, rigid foam insulation panels, microcellular foam seals and gaskets, high durable elastomeric wheels and tires and as automotive suspension bushings [1]. whereas, at higher i m. peron et alii, frattura ed integrità strutturale, 42 (2017) 214-222; doi: 10.3221/igf-esis.42.23 215 densities (> 200 kg/m3) they show a porous solid structure, and they are used for fixtures and gauges, master and copy models, draw die moulds, hard parts for electronic instruments [1]. their mechanical properties have been extensively investigated in the past, showing a relationship, based on the geometry of cellular structure and the relative density, with solid materials used for manufacturing [2,3], and revealing a crushable behaviour in compression, characterized by the capability to absorb considerable amount of energy due to plateau and densification regions. finally marsavina [4] reports that they behave as brittle materials under tensile loading, being characterized by a linear elastic behaviour up to fracture. it is worth to notice that usually in the industrial applications components are designed with notches or they are affected by manufacturing induced defects, which are widely reported to reduce both tensile and fatigue strength [5-7]. several criteria have been proposed in literature for facture assessment of cracked and notched components [8-16], but among all a strain energy based (sed) approach has revealed to be the most robust in the assessment of brittle fracture resistance of several materials [17-20]. the criterion states that brittle fracture failures occur when the strain energy density averaged in a circular control volume of radius rc, which surrounds a crack or notch tip, reaches a critical value wc dependent on the material. the robustness of this criterion has been proved by several works on different notches geometries and on different loading conditions [21-27]. the main purpose of this work is to evaluate the effectiveness of sed criterion on pur foams, aiming to experimentally evaluate the main parameters of this method, i.e. rc and wc. materials olyurethane materials of four different densities (100, 145, 300 and 708 kg/m3) manufactured by necumer gmbh – germany, under commercial designation necuron 100, 160, 301 and 651, were experimentally investigated. at low densities 100 and 145 kg/m3 the materials have a rigid closed cellular structure, while the pur materials of higher densities show a porous solid structure (300 and 708 kg/m3). a quanta™ feg 250 sem was used to investigate the microstructures of the materials at different magnifications. the cell diameter and wall thickness were determined by statistical analysis, together with the density of pur materials obtained experimentally according with astm d1622-08. the elastic properties young modulus and poisson ratio were determined by impulse excitation technique (astm e-1876-01). tensile strength was determined on dog bone specimens according with a gage length of 50 mm and a cross section in the calibrated zone with 10 mm width and 4 mm thickness, according to en iso 527, and described in the research published by marsavina et al. [28]. pur density 100 145 300 708 young’s modulus [mpa] 30.18±1.75 66.89±1.07 281.39±2.92 1250±15.00 poisson’s ratio [-] 0.285 0.285 0.302 0.302 tensile strength [mpa] 1.16±0.024 1.87±0.036 3.86±0.092 17.40±0.32 mode i fracture toughness [mpa m0.5] 0.087±0.003 0.131±0.003 0.372±0.014 1.253±0.027 mode ii fracture toughness [mpa m0.5] 0.050±0.002 0.079±0.004 0.374±0.013 1.376±0.047 table 1: elastic, mechanical and fracture properties of pur materials, by varying the density. the mode i and ii fracture toughness were determined on asymmetric semi-circular bend (ascb) specimens. a detailed description of these tests is presented in [29,30]. the experimentally values of elastic, mechanical and fracture toughness properties are presented in tab. 1. experimental investigation tensile test ifferent notched specimens were tested under tensile load. notched specimens with geometries presented in fig. 1.a,b,c having lateral v, rounded u and circular holes of different diameters d were tested in tensile. the u notched specimens, with blunt curvature radius (r = 4.25 mm), were tested for each density, respectively holed p d m. peron et alii, frattura ed integrità strutturale, 42 (2017) 214-222; doi: 10.3221/igf-esis.42.23 216 plates with different diameters were tested only for the highest density (708 kg/m3), geometries and maximum load presented in tab. 2. tests were performed at room temperature, on a zwick/roell z005 testing machine with 5 kn maximum load, using a loading rate of 2 mm/min. four tests were performed for each notch geometry. the specimens’ dimensions and the average maximum load are listed in tab. 2. the obtained load-displacement curves show a linear behavior without plasticity, the failure occurs suddenly and the behavior is brittle. table 2: geometrical parameters and average maximum load of notched components. table 3: the average maximum load from testing of specimens with hole on tensile. bending of asymmetric semi-circular bend (ascb) ascb specimens with vertical crack were considered, fig. 1.d. the crack tip was introduced using a razor blade. different types of applied mixed mode are easily obtained only by changing one of the supports position (s2) and keeping constant the other support (s1). the load is applied on the symmetry axis of the specimen using three point bending grips. stress intensity factors (sifs) solution for ascb specimen [31]: 1 2( / , / , / ) , 2 max i i p k ay a r s r s r i i ii rt   (1) were obtained by finite element analysis (lazzarin and filippi, [32] and are plotted for a crack length a = 20 mm, specimen radius r = 40 mm, distance to fixed support s1 = 30 mm, thickness t = 10 mm, resulting a/r = 0.5, s1/r = 0.75. it could be observed that changing the distance s2 from 30 mm to 3 mm, the loading conditions change from pure mode i to dominant mode ii conditions. moreover, using a polynomial interpolation the exact position of left support, leading to pure mode ii loading condition, was determined at distance s2 = 2.66 mm. the recorded load–displacement curves were linear (no significant non-linearity identified) and the fracture occurred suddenly, indicating that the specimens failed in a brittle manner, fig. 1.e. tab. 4 presents the average fracture load values fmax obtained at each loading configuration for the four considered materials. for all the tested specimens the thickness was equal to 10 mm. the mixed mode ratio was quantified using the mode mixity through the dimensionless parameter me, proposed by ayatollahi and torabi [33]. me (s2 [mm]) density [kg/m3] 1(30) 0.83 (12) 0.651 (8) 0.472 (6) 0.206 (4) 0.004 (2.66) 100 43.8 88.5 91.47 102.55 97.3 92.4 145 67.8 133.5 152.5 158 151.25 148.67 300 190 397.5 535.5 645 601.75 712.3 708 704.3 1340 1680 1910 2133 2130 average fracture load value [n] table 4: average fracture loads values for ascb specimens. notch shapes geometrical parameters [mm] pur density [kg/m3] 100 145 300 708 l w b d r average maximum load fmax [n] v 100 25 15 0.25 146.39 185.92 353.74 1811.43 u 100 25 15 2 189.45 262.4 397.71 2109.96 100 30 14 4.25 236.5 329 443.6 2173.4 o 100 25 10 187.89 267.31 521.5 1960.31 notch shape: o length l = 100 mm width w = 25 mm hole diameter [mm] 10 8 7 6 5 3.5 average maximum load [n] 1960.31 2197.27 2290.76 2491.03 2544.66 2944.64 m. peron et alii, frattura ed integrità strutturale, 42 (2017) 214-222; doi: 10.3221/igf-esis.42.23 217 figure 1: notched specimens on tensile, (a) lateral rounded v notch, (b) lateral u notches, (c) circular hole and (d) ascb specimen; (e) typical load-displacement curves on tensile and bending specimens. theoretical background erto and lazzarin [27], and later radaj and vormwald [34], presented comprehensive overview of the volumebased strain energy density criterion. below, only a reminder of the main concepts of the sed regarding brittle fracture of notched components is reviewed. sed criterion assumes that failure occurs when the mean value w of deformation energy in a local finite volume around the notch tip (control volume) reaches a critical value wc; the failure occurs when cw w , independent of the notch opening angle and loading type. if the material exhibits an ideally brittle behaviour until fracture, the parameter wc is calculated from the ultimate tensile strength σu: 2 / 2c uw e (2) under the situations when plain specimens exhibit a non-linear behaviour, whereas the notched specimens behave linear, seweryn [35] recommended that the stress σu should be replaced by “the maximum normal stress existing at the edge at the moment preceding the cracking” determined on tensile specimens with blunt curvature radius, where semi-circular notches are recommended. in plane problems, the control volume becomes a circle or a circular sector with a radius rc in the case of cracks or pointed v-notches in mode i or mixed, i + ii, mode loading (fig. 2a and b). under plane strain conditions, a useful expression for rc has been provided considering the crack case [36, 37]:    2 1 5 8 4 ic c t v v k r            (3) if the critical value of the nsif is determined by means of specimens with α ≠ 0, the critical radius can be estimated by means of the expression:    1 1 2 2 2 1 1 1 4 c c c i k r ew           (4) when 2α = 0, k1c equals the fracture toughness kic. for rounded v-notches, a crescent-shaped control volume bounded by two radii differently centered was introduced: a circular notch edge with radius q as the inner boundary and a circle arc with radius r0 + rc as the outer boundary, (fig. 2c). the length r0 represents the distance between the origin of the polar coordinates (used to express the stress field) and the notch tip. the parameters r0 depends from q then it’s function only from the geometry (the opening angle 2α); r0 is defined as 0 / ( 1)r qr q  where (2 2 ) /q     . b m. peron et alii, frattura ed integrità strutturale, 42 (2017) 214-222; doi: 10.3221/igf-esis.42.23 218 figure 2: control volume for sharp v notch (a), crack case (b) and rounded v notch under mode i loading. the radius of the control volume and the critical strain energy density depend only from the mechanical properties of the material as the young’s modulus, the fracture toughness, the poisson’s ratio and the ultimate tensile strength σu or σt. numerical investigations determination sed parameters he quasi ideally brittle behavior, for these foams, is exhibited for notched components, fig. 1e, so the ultimate tensile strength σu should be substituted with σt, the maximum normal tension presents at the notch tip in the moment that proceed the crack, tension calculated in a notched specimen under tensile load, specimen with a bland curvature radius. this σt can be evaluated using u notched specimen with a curvature radius greater than 4 mm, a bland notch: is recommended to use a semi-circular notches, in this paper it has been choose to use a plate with symmetric u notch. a linear-elastic finite element analysis was carried out in ansys 14.5 software for all specimen geometries. based on symmetry of loading and boundary conditions quarter of geometry was considered. the average maximum load was applied to the models for each notch geometry as uniaxial loads. the plane184 plane 8-node biquadratic elements with a suitably high mesh density in the area of the notch tip were employed, the analysis are under plane strain conditions. according with the procedure described above, it’s possible to define the tension at the notch tip. in tab. 4 is exhibit the tension σt and the parameters of sed method, calculated through eq. 2 and 3. density [kg/m3] σt [mpa] rc [mm] wc [mj/m3] 100 3.19 0.20 0.169 145 4.39 0.24 0.143 300 6.06 1.0 0.065 708 26.7 0.62 0.285 table 5: values of tension at the notch tip and respective sed parameters. application sed method on specimens with different type of notch, mode i through the sed parameters determined previously, is possible to apply the sed method on the notched specimens tested in the previous paragraphs. in the same way followed to determine the σt tension, the sed method were applied through linear elastic finite element analysis, using plane elements (plane 184) and creating the control volume around the notch tip. the results are reported in fig. 3.a. all the specimens are in mode i loads configuration. for the majority of the results, the scatter band is contained between + 10 % and – 22 %, a reasonable dispersion in engineering field. application sed method on specimens with different type of notch, mode i ascb specimens were tested under pure mode i, pure mode ii and mixed mode i+ii. the first approach is to use the sed parameters defined for mode i (tab. 5) in the case of the mode ii and mixed mode: for the higher densities, in mixed mode and in mode ii the error is greater than 35 %, while for the lowest densities the error is contained between ± 10 %, graph 1b. it has been noticed that the strain energy density increase from mode i to mode ii. if it’s possible to t m. peron et alii, frattura ed integrità strutturale, 42 (2017) 214-222; doi: 10.3221/igf-esis.42.23 219 define the sed parameters, then the hypothesis that the material has a brittle behavior is valid and in the crack case (the control volume is a sector centered at the notch tip, fig. 2.b) the strain energy density can be express through eq. (3). 1 2 2 2 1 2 2 (1 ) 2(1 ) i ii c c e k e k w e r e r     (5) the authors proposed the following approach: the control volume remains the same in all load configurations and it’s equal to the control volume defined under pure mode i: in this way it’s possible to recalculate the value of the critical strain energy density in mixed mode i+ii and in pure mode ii. under this hypothesis, the scatter band is contained between ± 10 %, as it seen fig. 3.c. in fig. 3 the error is calculated using the wc defined through the σt tension; the wc can be redefined through the mean value of the strain energy density of each specimens. the new values of wc are listed in table 5: the errors using these values of critical energy density are presented in fig. 4; except necuron 301, the scatter band is contained between ± 15 %. density [kg/m3] rc [mm] wc [mj/m3] 100 0.20 0.140 145 0.24 0.111 300 1.0 0.039 708 0.62 0.21 table 6: new values of critical energy density that fit better the results. figure 3: ratio between the predictions of maximum loads and experimental loads: a) notched specimens, b) ascb specimens under mixed mode, c) personal approach for ascb specimens under mixed mode, d) all notched specimens under mode i. m. peron et alii, frattura ed integrità strutturale, 42 (2017) 214-222; doi: 10.3221/igf-esis.42.23 220 density [kg/m3] σt [mpa] σ0,tcd [mpa] 100 3.19 2.17 145 4.39 3.19 300 6.06 5.6 708 26.7 23.14 table 7: comparison between stress of tcd method and sed method. figure 4: ratio between the predictions of maximum loads and experimental loads using the new values of critical energy density. conclusions xcept some value, the relative errors is contained between +10 % and –22 %, a reasonable prediction in engineering field, figs. 3 and 4. from these results it’s possible to notice that the sed method works for these foams and the parameters (rc and wc) can be determined through experimental tests on tensile notched specimens. in a research by negru et al. (2015) it’s defined the inherent stress for the theory of critical distance (tcd), an approach based on the same theory of sed method, they belong to the linear elastic mechanic fracture theory (lefm). the inherent stress in tcd method is equivalent to the failure stress and this tension is defined in a different way: the stress σt defined in this paper is compared with the inherent stress of tcd method, tab. 6. two different approach give values of the tensions very similar, with the same order of magnitude, this confirms that it’s possible to apply the sed method on these foams and the tensions σt that valid the sed for each type of notch have the same order of magnitude and it’s similar. the personal approach works but the hypothesis that the control volume remains the same it’s only a personal view of the problem; this assumption it has been made only to prove that the pur foams can be treated as a brittle materials and the sed approach can be applied, in fact the strain energy density defined through eq. 3 differs less than ± 8% from the numerical strain energy density defined through the numerical investigations. it’s possible to define a new values of critical energy density for each density that permit to decrease the errors, in fact more than 95 % of the results are contained between ± 15 %, so the new values of wc fit better the results. the paper represents an entry level approach for the determination of the sed parameters for these foams, it’s necessary further studies and tests. e m. peron et alii, frattura ed integrità strutturale, 42 (2017) 214-222; doi: 10.3221/igf-esis.42.23 221 acknowledgments he experimental results presented here were performed under the grant of the romanian national authority for scientific research, cncs-uefiscdi, project pn-ii-id-pce-2011-3-0456, contract number 172/2011. mr. alberto piccotin was supported by erasmus program to carry on a research stage at university politehnica timisoara. references [1] http://www.necumer.com/index.php/en/produkte-2/board-materials.html, (2014). [2] gibson, l.j., ashby, m.f., cellular solids, structure and properties, second ed., cambridge university press, (1997). [3] ashby, m.f., cellular solids – scaling of proprieties, in: m. scheffler, p. colombo (eds.), cellular ceramics, structure, manufacturing, properties and applications, wiley-vch verlag gmbh & co., (2005) 3–17. [4] marsavina, l., fracture mechanics of cellular solids, in: h. altenbach, a. ochsner (eds.), cellular and porous materials in structures and processes, springer, wien, (2010) 1–46. [5] lazzarin, p., comportamento a fatica dei giunti saldati in funzione della densità di energia di deformazione locale: influenza dei campi di tensione singolari e non singolari, frattura ed integrità strutturale, 9 (2009) 13-26. [6] maragoni, l., carraro, p. a., peron, m. and quaresimin, m., fatigue behaviour of glass/epoxy laminates in the presence of voids, int. j. fatigue, 95 (2017) 18–28. [7] brotzu, a., felli, f. and pilone, d., effects of the manufacturing process on fracture behaviour of cast tial intermetallic alloys, frattura ed integrità strutturale, 27 (2013) 66-73. [8] ayatollahi, m.r., razavi, s.m.j., rashidi moghaddam, m., berto, f., mode i fracture analysis of polymethylmetacrylate using modified energy—based models. phys. mesomec., 18 (2015) 53-62. [9] ayatollahi, m.r., rashidi moghaddam, m., razavi, s.m.j., berto, f., geometry effects on fracture trajectory of pmma samples under pure mode-i loading. eng. fract. mech., 163 (2016) 449–461. [10] ayatollahi, m.r., razavi, s.m.j., sommitsch, c., moser, c., fatigue life extension by crack repair using double stophole technique, mater. sci. forum, 879 (2017) 3-8. [11] razavi, s.m.j., ayatollahi, m.r., sommitsch, c., moser, c., retardation of fatigue crack growth in high strength steel s690 using a modified stop-hole technique, eng. fract. mech., 169 (2017) 226–237. [12] rashidi moghaddam, m., ayatollahi, m.r., razavi, s.m.j., berto, f., mode ii brittle fracture assessment using an energy based criterion, phys. mesomec. (in press). [13] sih, g.c., some basic problems in fracture mechanics and new concepts, eng. fract. mech., 5 (1973) 365-377. [14] sih, g.c., strain-energy-density factor applied to mixed mode crack problems, int. j. fracture, 10 (1974) 305-321. [15] kipp, m.e., sih, g.c., the strain energy density failure criterion applied to notched elastic solids, int. j. solids struct., 11 (1975) 153-173. [16] sih, g.c., ho, j.w., sharp notch fracture strength characterized by critical energy density, theor. appl. fract. mec., 16 (1991) 179-214. [17] lazzarin, p. and zambardi, r., a finite-volume-energy based approach to predict the static and fatigue behavior of components with sharp v-shaped notches, int. j. fract., 112 (2001) 275–298. [18] berto, f., lazzarin, p. and ayatollahi, m. r., brittle fracture of sharp and blunt v-notches in isostatic graphite under torsion loading, carbon n. y., 50 (2012) 1942–1952. [19] berto, f. and barati, e., fracture assessment of u-notches under three point bending by means of local energy density, mater. des., 32 (2011) 822–830. [20] radaj, d., berto, f., and lazzarin, p., local fatigue strength parameters for welded joints based on strain energy density with inclusion of small-size notches, eng. fract. mech., 76 (2009) 1109–1130. [21] lazzarin, p., berto, f., some expressions for the strain energy in a finite volume surrounding the root of blunt vnotches, int. j. fract., 135 (2005) 161-185. [22] gómez, f.j., elices, m., berto, f., lazzarin, p., local strain energy to assess the static failure of u-notches in plates under mixed mode loading, int. j. fract., 145 (2007) 29-45. [23] berto, f., lazzarin, p., gómez, f.j., elices, m., fracture assessment of u-notches under mixed mode loading: two procedures based on the ‘equivalent local mode i’ concept, int. j. fract., 148 (2007) 415-433. t m. peron et alii, frattura ed integrità strutturale, 42 (2017) 214-222; doi: 10.3221/igf-esis.42.23 222 [24] lazzarin, p., livieri, p., berto, f. and zappalorto, m., local strain energy density and fatigue strength of welded joints under uniaxial and multiaxial loading, eng. fract. mech., 75 (2008) 1875–1889. [25] lazzarin, p., berto, f., gómez, f.j., zappalorto, m., some advantages derived from the use of the strain energy density over a control volume in fatigue strength assessments of welded joints, int. j. fract., 30 (2008) 1345-1357. [26] lazzarin, p., berto, f., elices, m. and gómez, j., brittle failures from uand v-notches in mode i and mixed, i + ii, mode: a synthesis based on the strain energy density averaged on finite-size volumes, fatigue fract. eng. m., 32 (2009) 671–684. [27] berto, f., lazzarin, p., a review of the volume-based strain energy density approach applied to v-notches and welded structures, theor. appl. fract. mec., 52 (2009) 183-194. [28] marsavina, l., constantinescu, d.m., linul, e., apostol, d.a., voiconi, t., sadowski, t., refinements on fracture toughness of pur foams, eng. fract. mech., 129 (2014) 54–66. [29] marsavina, l., constantinescu, d.m., linul, e., apostol, d.a., voiconi, t., sadowski, t., evaluation of mixed mode fracture for pur foams, procedia materials science, 3 (2014) 1342–1352. [30] negru, r., marsavina, l., filipescu, h., pasca, n., investigation of mixed mode i/ii brittle fracture using ascb specimen, int. j. fracture, 18 (2013) 155–161. [31] ayatollahi, m.r., torabi, a.r., 2009, a criterion for brittle fracture in u-notched components under mixed-mode loading, eng. fract. mech., 76 (2009) 1883-1896. [32] lazzarin, p. and filippi, s., a generalized stress intensity factor to be applied to rounded v-shaped notches. international j. solids struct., 43 (2006) 2461-2478. [33] ayatollahi, m.r., torabi, a.r., a criterion for brittle fracture in u-notched components under mixed-mode loading. eng. fract. mech., 76 (2009) 1883-1896. [34] radaj, d., vormwald, m., advanced methods of fatigue assessment, springer-verlag, berlin, (2013). [35] seweryn, a., brittle fracture criterion for structures with sharp notches, eng. fract. mech., 47 (1994) 673-681. [36] yosibash, z., bussiba, a., gilad, i., failure criteria for brittle elastic materials, int. j. fracture, 125 (2004) 307–333. [37] gallo, p., berto, f., glinka, g generalized approach to estimation of strains and stresses at blunt v-notches under non-localized creep, fatigue fract. eng. mater. struct., 39 (2016) 292-306. << /ascii85encodepages false /allowtransparency false /autopositionepsfiles true /autorotatepages /none /binding /left /calgrayprofile (dot gain 20%) /calrgbprofile (srgb iec61966-2.1) /calcmykprofile (u.s. web coated \050swop\051 v2) /srgbprofile (srgb iec61966-2.1) /cannotembedfontpolicy /error /compatibilitylevel 1.4 /compressobjects /tags /compresspages true /convertimagestoindexed true /passthroughjpegimages true /createjobticket false /defaultrenderingintent /default /detectblends true /detectcurves 0.0000 /colorconversionstrategy /cmyk /dothumbnails false /embedallfonts true /embedopentype false /parseiccprofilesincomments true /embedjoboptions true /dscreportinglevel 0 /emitdscwarnings false /endpage -1 /imagememory 1048576 /lockdistillerparams false /maxsubsetpct 100 /optimize true 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can be opened with acrobat and adobe reader 5.0 and later.) >> /namespace [ (adobe) (common) (1.0) ] /othernamespaces [ << /asreaderspreads false /cropimagestoframes true /errorcontrol /warnandcontinue /flattenerignorespreadoverrides false /includeguidesgrids false /includenonprinting false /includeslug false /namespace [ (adobe) (indesign) (4.0) ] /omitplacedbitmaps false /omitplacedeps false /omitplacedpdf false /simulateoverprint /legacy >> << /addbleedmarks false /addcolorbars false /addcropmarks false /addpageinfo false /addregmarks false /convertcolors /converttocmyk /destinationprofilename () /destinationprofileselector /documentcmyk /downsample16bitimages true /flattenerpreset << /presetselector /mediumresolution >> /formelements false /generatestructure false /includebookmarks false /includehyperlinks false /includeinteractive false /includelayers false /includeprofiles false /multimediahandling /useobjectsettings /namespace [ (adobe) (creativesuite) (2.0) ] /pdfxoutputintentprofileselector /documentcmyk /preserveediting true /untaggedcmykhandling /leaveuntagged /untaggedrgbhandling /usedocumentprofile /usedocumentbleed false >> ] >> setdistillerparams << /hwresolution [2400 2400] /pagesize [612.000 792.000] >> setpagedevice microsoft word numero_29_art_8 a fortini et alii, frattura ed integrità strutturale, 29 (2014) 74-84; doi: 10.3221/igf-esis.29.08 74 focussed on: computational mechanics and mechanics of materials in italy twsme of a niti strip in free bending conditions: experimental and theoretical approach a. fortini, m. merlin, r. rizzoni department of engineering (endif), university of ferrara, (italy) annalisa.fortini@unife.it, mattia.merlin@unife.it, raffaella.rizzoni@unife.it s. marfia department of civil and mechanical engineering (dicem), university of cassino and lazio meridionale, (italy) marfia@unicas.it abstract. this paper deals with the two-way shape memory effect (twsme) induced on a strip of a nearequiatomic niti alloy by means of the shape memory cycling training method. this procedure is based on the deformation in martensite state to reach the desired cold shape followed by cycling the temperature from above af to below mf. to this end, the sample was thermally treated to memorise a bent shape, thermomechanical trained as described and thermally cycled in unloaded conditions in order to study the stability of the induced twsme. heating to af was reached by a hot air stream flow whereas cooling to mf was achieved through natural convection. the evolution of the curvature with the increasing number of cycles was evaluated. the thermomechanical behaviour of the strip undergoing uniform bending was simulated using a one-dimensional phenomenological model based on stress and the temperature as external control variables. both martensite and austenite volume fractions were chosen as internal parameters and kinetic laws were used in order to describe their evolution during phase transformations. the experimental findings are compared with the model simulation and a numerical prediction based on the approach proposed in [25]. keywords. niti-based alloys; two-way shape memory effect; thermomechanical training; bending. introduction hape memory alloys (smas) are an interesting class of metallic materials with the ability of recovering seemingly permanent deformation when they are deformed in the martensitic low temperature phase and subsequently heated to the austenitic high temperature phase. shape memory effect (sme) and superelasticity (se) are associated with diffusionless solid-state transformations between two crystallographic phases: the cubic crystal structure, stable at high temperature, and the monoclinic crystal structure, stable at low temperature. the forward transformation from austenite to martensite occurs during cooling, begins at the martensitic start temperature ms and ends at the martensitic finish temperature mf. the reverse transformation from martensite to austenite occurs upon heating, begins at the austenitic start temperature as and finishes at the austenitic finish temperature af. over the last decades a wide variety of smas have been investigated and several compositions have been studied, by adding different alloying elements (such as zinc, copper, gold and iron) to existing alloys. among the different shape memory alloys compositions, the niti alloy system is the most extensively studied and used in the greatest number of commercial applications mainly because of its excellent mechanical properties, high corrosion resistance and s a. fortini et alii, frattura ed integrità strutturale, 29 (2014) 74-84; doi: 10.3221/igf-esis.29.08 75 biocompatibility. in particular, the near-equiatomic niti alloys are the most important practical shape memory alloys, extensively used for an increasing number of applications in different fields of engineering. the niti alloy system, in addition to the one-way shape memory effect (owsme) may also show the two-way shape memory effect (twsme). through the sme the material could recover the macroscopic shape of the austenitic parent phase upon heating above af, while through the twsme, it also exhibits a return to the reoriented martensitic shape upon cooling below mf, in the absence of applied stress. this spontaneous repeatable shape change on heating and cooling is an acquired behaviour, rather than an inherent property of the material, obtained by specific thermomechanical loading cycles, named training treatments, to which the sma has been subjected [1, 2]. this procedure develops a residual internal stress state which guides the growth of certain martensitic variants, towards the preferred orientations, regarding the deformation adopted during training, when sma is stress-free cooled [3]. from a crystallographic point of view, it is widely accepted that preferential martensite formation is due to the generation of permanent defects in the parent phase resulting from training procedure [2, 4]. as a result the material will change its shape as it changes its phase. different training methods for obtaining a twsme are described in literature and the influence of the type and training parameters, the stability of the twsme during thermal cycling as well as the efficiency of the methods have been widely investigated [1, 2, 5-10]. generally, training procedures have the purpose to induce the low temperature shape in the sample introducing permanent defects such as dislocations, stabilised stress induced martensite and precipitates [4, 5, 11, 12]. common methods of training include: shape memory cycling, pseudoelastic cycling, combined shape memory cycling/pseudoelastic cycling and constrained cycling of deformed martensite [1, 5, 13, 14]. all of these thermomechanical treatments deal with the repetition of a procedure that considers the transformation from austenite to a preferentially oriented martensite or from deformed martensite to austenite [13]. due to their attractive behaviour, niti shape memory alloys have been successfully applied in a broad set of innovative applications in aerospace, biomedical, mechanical and civil engineering fields. in particular, smas are excellent materials to be used as actuating elements in smart structures given that they could generate large force and displacement during the phase transformation. many active deformable structures, in which niti strips or wires are embedded in a polymeric matrix, are based on the owsme and, as a consequence, an external force is required to bring back the structure to its original shape. to this end, the application of the twsme on the sma elements plays an important role since it make possible to achieve more compact and simple configuration systems with improved performances upon demand, thanks to the integration of multiple functions in a single component. a twsme behaviour in bending gives the macroscopic reversible shape change of the functional structure upon heating and cooling, without demanding the recovery to the elasticity of the polymeric structure. the sme behaviour in bending has been experimentally and theoretically investigated by many authors. the works [15, 16] have focused on the bending properties of polymer-sma composite microdevices, for example, microvalves. in these actuators, the right combination of the polymer and sma thin film leads to a two-way stable behaviour during heating and cooling. more recently, roh and bae [17] have numerically and experimentally investigated the thermo-mechanical behaviour of niti strips associated with stress and temperature-induced transformations. the activation of the sma strips causes a bending deformation on the actuator, which has remarkable vertical tip deflections. larger deflections can be obtained by increasing the initial strain of the sma. irzhak et al. [18] observed giant reversible bending deformation at a sub-micrometre scale by using a nichel-sma composite strip. furthermore, some authors focused on the effects of the pre-strain, recovery temperature and bending deformation on the shape memory effects [9, 19-24]. to predict the onedimensional thermomechanical behaviour of sma, several macroscopic constitutive models are currently available in literature, an overview can be found in [3, 23, 25-28]. it is widely known that the response of sma is dependent on stress and temperature fields and it is closely connected with the crystallographic phase of the material and the thermodynamics underlying the transformation processes. while some studies are focused on the two-way shape memory effect exhibited by bent wires [9, 13, 19], the present study is aimed at investigating the stability of the twsme behaviour induced on near-equiatomic niti strips by means of the so-called shape memory cycling method, which here is applied to bending deformations. in particular, the possibility to take advantage of the twsme is here considered in order to optimise the behaviour of strips embedded in active deformable structures. to this end, a strip is firstly subjected to a specific thermomechanical treatment, in order to memorise a bent shape with a uniform curvature, and then trained to realise the spontaneous recovery to the martensitic shape upon cooling. in particular, the training process basically consists of the repetition of the following steps: i) cooling the sma to below mf to form martensite, ii) deforming to the desired cold shape, below the shape memory limit, iii) heating in stress-free condition to above af to recover the original high temperature shape [13, 14]. it should be highlighted that the amount of spontaneous shape change on cooling is significantly less than those being induced in the ii) deformation step and it is typically between 0.2 and 0.25% of the training strain value [4, 14]. after the training a fortini et alii, frattura ed integrità strutturale, 29 (2014) 74-84; doi: 10.3221/igf-esis.29.08 76 procedure, the stability of the induced twsme with the increasing number of cycles is assessed considering the curvatures assumed at each cycle on heating/cooling. moreover, the behaviour of the sma undergoing bending is simulated by means of a phenomenological model, based on the use of stress and temperature as control variables, but proposing an original approximated relation for the evolution of the curvature with the temperature, according to the model developed in [20]. this relation, useful to practitioners, is coupled with a phenomenological description of the phenomena occurring during the training process, which are supposed to be based on the martensite accumulation during cycling. shape recovery simulations for the niti strip undergoing uniform bending are considered and the ability of the model to reproduce experimental data is evaluated. the resulting evolution of the curvature with the number of cycles obtained with this model is also compared with the experimental data. furthermore, all these results are compared with a numerical simulation based on the model proposed in [25]. material characterisation commercial niti shape memory alloy of nominal composition ni-50.8 at%ti was used in the present study. a strip of 0.8 x 7 x 107 mm in dimension was cut by means of electro-erosion starting from a plane foil of the assupplied material. in order to fix the strip during both the training process and the twsme cycles, a "l" shape was chosen, as depicted in fig. 1. figure 1: strip shape. the sample was annealed at 700 °c for 20 min followed by controlled cooling to room temperature, at a cooling rate of 1 °c/min, in order to delete any residual stresses of previous deformation history. to evaluate the characteristic martensitic and austenitic starting and finishing temperatures as well as the latent heats per unit mass, a differential scanning calorimetry (dsc) test was carried out, after annealing, at a heating/cooling rate of 10 °c/min. the transformation temperatures (ttrs), summarised in tab. 1, were extrapolated from dsc data through the tangential line method. as [°c] af [°c] δha [mpa/°c] ms [°c] mf [°c] δhm [mpa/°c] 82 104 24.7 69 46 25.3 table 1: transformation temperatures and latent heats per unit mass obtained by dsc. mechanical properties of the material were obtained through uniaxial tensile tests performed at 25 °c and 150 °c respectively under displacement controlled loading conditions. an instron 4467 testing machine with a 30 kn load cell was used and the loading rate of 1 mm/min was set in order to minimise the self-heating effect due to the transformation latent heat. according to ttrs data, the elastic modulus of the martensite, em, the transformation stresses at the onset/end of the martensitic plateau, σs and σf, and the maximum recoverable strain εl were estimated at 25 °c while the elastic modulus of the austenite, ea, was estimated at 150 °c. these material properties are listed in tab. 2. σs [mpa] σf [mpa] εl em [mpa] ea [mpa] ca [mpa/°c] cm [mpa/°c] 149 210 0.06 28423 63475 7.25 8.22 table 2: material properties obtained by tensile tests. the stress-influence coefficients ca and cm were obtained using the clausius-clapeyron equation: a a. fortini et alii, frattura ed integrità strutturale, 29 (2014) 74-84; doi: 10.3221/igf-esis.29.08 77 ρ δh ε   aa cr l c t (1) ρ δh ε    m m cr l c t (2) where the niti density ρ is assumed 6.45 g/cm3 and the critical temperature tcr is calculated as (as+af)/2. to memorise the bent shape, the strip was subjected to a double heat treatment: it was previously strained at room temperature and wounded on a cylindrical jig to reach a circle shape. this fixture was placed into a tube furnace, heated at 450 °c for 25 min and quenched by water-cooling. these specific temperature and time were chosen according to the results of a previous experimental study [15], which demonstrated that this combination allows reaching a 92% of shape recovery. subsequently, the strip was strained at room temperature applying opposite bending couples acting at the ends and locked into an arc clamp. the strip was thus thermally treated as previous to memorise this bent shape, with an initial curvature radius r0 equal to 42.32 mm. training procedure the heat-treated niti strip was subjected to the thermomechanical cycling by means of the shape memory cycling method [13]. a specifically designed training sequence was applied to the sample repeating the following steps for 30 cycles: pre-straining at a t< mf (room temperature) to reach the desired cold shape, ii) heating the specimen above af (140 °c) through a hot air stream flow, iii) cooling below mf (room temperature) by natural convection. therefore, the strip was strained to a flat shape, applying a uniform bending load at room temperature, and fixed into a supporting structure, with one end held in a clamp. in order to ensure reaching the phase transformation temperature on heating, a k-type thermocouple was placed in the inner radius of the strip and kept in good thermal contact with it by conductive aluminum tape. heating the strip to high temperature above af was achieved by hot air stream flow whereas cooling to room temperature, below mf, was realised through natural convection. to study the curvature evolution, sample images were acquired by a digital camera at the end of the heating process, fig. 2a, as well as after cooling to room temperature, fig. 2b. interpolating the axis of the strip with a three-point arc, by means of a cad software, the hot radius, rh, and the cold radius, rc, were collected. (a) (b) figure 2: (a) hot shape; (b) cold shape. it is well known that there is a limit to the amount of reversible strain that can be achieved in twsme [14]. in particular, the two-way recoverable strain is significantly less than the one-way recoverable strain and it is typically in the neighborhood of 2%. in the present study the bending deformation strain was calculated according to eq. (3): 0 ε 2r  tr t t (3) a fortini et alii, frattura ed integrità strutturale, 29 (2014) 74-84; doi: 10.3221/igf-esis.29.08 78 where t is the thickness of the strip and r0 is the radius of the memorised shape. therefore, the target two-way recoverable strain between the desired hot shape of the arc and the desired cold shape of the straight line, in this case was equal to 0.9%, less than the threshold of 2%. the amount of twsme was assessed by thermally cycling the trained strip without any applied external stress. to evaluate the stability of the two-way memory behaviour, 30 cycles were performed. results and discussion experimental results he evolution of hot and cold shapes over the range of the training cycles is reported in fig. 3a. the desired hot shape corresponds to the curvature = 1/r0= 23.63 * 10-3 mm-1 of the memorised arc, while the desired cold shape corresponds to the straight line and it is therefore equal to 0. during the training process, the evolution of hot curvature suggests that, apart from the initial cycles where a gradual loss in the memorised shape occurs, the data level off to a value close to 15 * 10-3 mm-1. as regard the cold curvature, the curve trend decreases as the numbers of training cycles increases. as can be seen, the difference between hot curvature and cold curvature progressively increases and reaches the maximum value of 7.26 * 10-3 mm-1 after 30 cycles. it is known that the training process is aimed at producing dislocation arrangements that create an isotropic stress field in the austenite phase, responsible for the further spontaneous shape change upon cooling. however, the dislocation structure is often accompanied by a permanent strain that would degrade the memory of the hot shape [13]. according to the results reported in fig. 3a it is clear that the deformation in full martensitic state and the consequent progress of dislocation arrangements are linked to the loss of memory for the hot shape with increasing the number of training cycles. as regards the cold curvature and its progressively decrease to the desired cold shape it is likely that in the initial cycles the dislocation arrangements are readily introduced and, due to the greatly increase, the level of memory in the cold shape runs up [13]. as a result, at each cycle the amount of single-variant martensite increases, improving the memory of the cold shape. the amount of two-way behaviour through training cycles is calculated as the difference and depicted in fig. 3b. is the curvature at the austenite state (hot) and is the curvature at the martensite (cold) state. the gradual increase with training cycles is consistent with the progressive stabilisation of the behaviour achieved by the training procedure. it should be highlighted that, as depicted in fig. 3a, the increase of the two-way behaviour reported in fig. 3b is completely due to the improved cold curvature behaviour, which gets closer to the desired cold shape, rather than the hot curvature evolution, which is almost steady as the number of cycles increases. the spontaneous shape change, simply upon heating and cooling, was assessed through additional 30 cycles (twsme cycles). the curvature values assumed by the strip at each cycle are reported in fig. 4 from which it is evident that, while the hot curvature has a slightly increase to the desired hot shape, the cold curvature shows a quite constant evolution rather than a decrease to the desired cold shape. the difference between the hot and cold curvature is almost constant with increasing the number of cycles, but this doesn't mean the establishment of the two-way behaviour. it can be pointed out that during the twsme cycles, where no external stress is applied, the amount of single-variant martensite will decrease and, as a result, the cold behaviour moves away from the desired cold shape. (a) (b) figure 3: (a) comparison of hot and cold curvature curves versus training cycles; (b) two-way behaviour versus training cycles. -5 0 5 10 15 20 25 30 0 5 10 15 20 25 30 χ [m m -1 ]* 10 -3 training cycles χ hot χ cold desired hot shape desired cold shape t a. fortini et alii, frattura ed integrità strutturale, 29 (2014) 74-84; doi: 10.3221/igf-esis.29.08 79 figure 4: two-way recoverable shape change versus twsme cycles. constitutive modelling he thermomechanical behaviour of the sma strip in bending is simulated by using the results obtained in [20], which are briefly reviewed in this section. in [20] a one-dimensional phenomenological model is adopted, based on external control variables, the stress σ and the temperature t, and on internal variables, which are the singlevariant martensite, multi-variant martensite and austenite volume fractions. the phase production processes that are considered during bending and free shape recovery under heating are the following: during bending at low temperature, multi-variant martensite transforms into single-variant martensite; during shape recovery upon heating, both multi-variant and single-variant martensite volume fractions transform to austenite. each phase production is detailed by kinetic equations describing the evolution of the phase fractions during transformation in terms of the current values of the stress and the temperature. the kinetic equations are assumed to be linear for simplicity and the reader is referred to [20] for further details. the stress σ is related to the strain via the following constitutive eq. (4):     0       l s l s e if e otherwise         (4) here >0 is the maximum strain achievable by the transformation of multi-variant into single-variant (detwinning), is the elastic modulus, assumed to take the same value, 28423 mpa, for all the three phases and ξs is the single-variant martensite volume fraction. the behavior is assumed symmetric in traction and compression. the first bending at low temperature (t<mf) of the niti strip is modeled as the uniform bending of a beam entirely made of multi-variant martensite. the beam is taken to be l =107 mm long, and it has the same rectangular cross-section of the niti strip, with thickness h = 0.8 mm and width b = 7 mm. two opposite couples are applied to the ends of the beam, to bend it from the initial memorised curvature  = 23.63 * 10-3 mm-1 to the final curvature reached after elastic springback r= 0.00 m-1, corresponding to a flat shape. using the euler-bernoulli theory as done in [20], it can be shown that during bending single-variant forms initially at the outer and inner fibers of the cross-section and the transformation spreads inside the beam as the value of the applied couples is further increased. the residual stress and single-variant martensite distributions, calculated using the material data listed in tab. 2, are piecewise linear and they are shown in fig. 5. in the following, will denote the distance from the neutral axis to the level at which the residual single-variant fraction sr vanishes. for the free shape recovery under heating, a semi-analytical solution is proposed in [20] and here applied for the data of the alloy studied in this paper. the solution, valid under the assumption of a uniform temperature distribution throughout the cross-section, is based on the existence of transformation fronts, nucleating from the points where the residual stress vanishes and evolving with the temperature. indeed, the kinetic relations for the transformation of multi and single-variant martensite into austenite considered in [20] impose that points at zero stress transform first. there are two points at which the residual stress vanishes: one is the origin, and the other is calculated at the distance z0(as) = 0.27 mm from the origin. the single-variant martensite is absent at the origin (cfr. fig. 5), thus from the origin only a front nucleates, that one for -5 0 5 10 15 20 25 30 0 5 10 15 20 25 30 χ [m m -1 ]* 10 -3 twsme cycles χ hot χ cold desired hot shape desired cold shape t a fortini et alii, frattura ed integrità strutturale, 29 (2014) 74-84; doi: 10.3221/igf-esis.29.08 80 the transformation of the residual multi-variant martensite into austenite. this front is denoted zm in fig. 6. from the point z0(as) two transformation fronts nucleate, denoted z+ and z0 in fig. 6, which shows the evolution of the fronts with the temperature calculated using the material data listed in tab. 2. in the region between z+ and z0, both multiand singlevariant martensite transform into austenite. at the temperature t1 = 90.4 °c, the fronts zm and z+ coalesce, thus for t>t1 multi-variant martensite transforms into austenite between the origin and the front z0, and single-variant martensite transforms into austenite between z+(=) and z0. at t =af, the transformation of both martensite variants into austenite finishes and the beam recovers its original (memorised) curvature . as the fronts evolve, the curvature of the beam also evolves along the continuous curve plotted in fig. 7. correspondingly, the single-variant martensite fraction and stress distributions also change inside the cross-section and fig. 8 shows the calculated evolutions. the details for calculating the curves shown in fig. 6, 7 and 8 are given in [20]. figure 5: calculated stress ( ) and single-variant martensite (sr) residual distributions after the first bending. for symmetry reasons, only the distributions in the upper half of the cross-section are shown. figure 6: calculated evolution of the phase transformation fronts with the temperature; z indicates the coordinate along the thickness of the cross-section. at the temperature as, single-variant martensite is present only below (cfr. fig. 5) and multi-variant martensite is present throughout the cross-section. for temperatures between as and t1, multi-variant martensite transforms into austenite in the region between the origin and the front zm (dot-dashed line), and both multi-variant and single-variant martensite transform into austenite in the region between the fronts z+ (dashed line) and z0 (continuous line). at the temperature t1, the fronts zm and z+ coalesce, thus for t>t1 multi-variant martensite transforms into austenite between the origin and the front z0 and single-variant martensite transforms into austenite between z+(= ) and z0. a. fortini et alii, frattura ed integrità strutturale, 29 (2014) 74-84; doi: 10.3221/igf-esis.29.08 81 figure 7: calculated curvature evolution (continuous line) and its cubic approximation based on eq. (6) (dashed line) for the first free recovery upon heating. (a) (b) figure 8: calculated evolution of the stress distribution (a) and of the single-variant martensite fraction distribution (b) in the upperhalf of the cross-section for the first free recovery upon heating. the front zalsodescribed in the solution proposed in [20] and corresponding to the transformation of the martensite in the compressed part of the cross-section, does not exists here because, given the material parameters listed in tab. 2, it would violates the activation conditions of the kinetic laws. indeed one has1:   0 0 ( ) ( / 2) ( / 2) ( )( / 2 )         a f s r l sr l sr r c a a e h h h          (5) which implies that the phase transformation occurs only in traction. if condition (5) applies, then the evolution of the front z0 displayed in fig. 6 suggests an asymptotic behavior of the function ⟶ near af. indeed, the expression for z0 (eq. (40) in [20]) is:     0 0 ( / 2) ( ) ( ) / 2 ( ) ( / 2)       sr l l sr h f t z t t h f t h         (6) 1 condition (5) is equivalent to the condition e-(z0) <0 (see [20]). a fortini et alii, frattura ed integrità strutturale, 29 (2014) 74-84; doi: 10.3221/igf-esis.29.08 82 where f(t)=(af-t)/(af-as), and sr(-h/2)=0.2 is the value taken by the single-variant martensite distribution at the point z=-h/2 at the end of the uniform bending at low temperature (sr(-h/2)=0.2 for the parameters listed in tab. 2, see fig. 5). thus, assuming that z0 -h/2) as ⟶af and using (6), one obtains the following asymptotic behavior of near af:   0 ( )2 ( / 2) ( )      f l sr f s a t t h h a a    (7) one could tentatively approximate the curvature evolution with a cubic curve having minimum at t=as (and the minimum value is ) passing through the point (af, ) and having tangent line at t=af given by (7). for the material parameters of the alloy studied in this paper, the result turns out to be in acceptable agreement with the exact curvature evolution in almost all the range of temperatures (as, af), as shown in fig. 7. so far only the first free recovery upon heating has been considered, and the results have been obtained under the assumption that the beam recovers completely its original curvature  at t=af. however, the experimental data described in the previous sections indicates that this does not occur, and that the curvature recovered at the end of heating decreases with the number of cycles. this could be attributed to the presence of residual martensite in the parent phase at macroscopic free stress state, due to accumulation of plastic dislocations. experimental evidence of residual strain due to accumulated martensite has been reported in [23, 29]. to phenomenologically describe the accumulation of martensite, one could assume that sr(-h/2) depends upon the number of cycles as follows: 0(1 / ) 0( / 2; ) (1 )      n n sr h n e   (8) where = 0.2 is the value calculated for the first cycle, and are two material parameters. substituting (8) into (7) gives an equation for the curvature evolution near af with the number of cycles. fig. 9 shows the plot of the curvature at t= 101 °c as a function of obtained with the following values of the material parameters: =4.75 and =0.32these values have been chosen so as to fit the experimental data at high temperature (points labeled with the circles in fig. 9) as close as possible. fig. 9 shows also the numerical results obtained using the model proposed in [25], which is adopted to reproduce the experimental data during the training and in particular, the evolution of the curvature at high temperature during the cycles. figure 9: evolution of the recovered curvature with the number of cycles. triangles: recovered curvatures measured at high temperature. squares: recovered curvatures measured at low temperature after cooling. continuous line: theoretical evolution based upon the phenomenological assumption (8). dotted line: simulated evolution based on the model proposed in [25]. a. fortini et alii, frattura ed integrità strutturale, 29 (2014) 74-84; doi: 10.3221/igf-esis.29.08 83 conclusions he bending behaviour of a niti strip, trained in order to induce the twsme, was experimentally and theoretically investigated. the evolution of the curvature with the increasing number of training cycles revealed that the memory of the cold shape progressively increases. this effect can be attributed to dislocations rearrangements produced during the training process and the resulting accumulation of residual martensite, which has been previously reported in traction tests [23, 29]. even though the martensite accumulation improves the memory of the cold shape, the presence of permanent strains, which is related to the dislocation structure, is thought to be responsible for the degradation of the memory of the hot shape. a one-dimensional phenomenological model was applied to describe the evolution of single-variant martensite and the residual stress in the cross-section of the strip upon uniform bending: single-variant forms initially at the outer and inner fibers of the cross-section and the transformation spreads inside the beam as the value of the applied couples is further increased [20]. an original approximated relation for the evolution of the curvature with the temperature was also proposed and coupled with a phenomenological description of the martensite accumulation, which was assumed to occur during the training process. the resulting evolution of the hot curvature with the number of cycles was compared with the experimental data for the training cycles and with a numerical simulation based on the model proposed by auricchio et al. [25]. the compared simulations of the curvature evolution were found to be in good agreement with the experimental data. future developments will concern the simulation of the whole experimental tests adopting the numerical model proposed in [25]. acknowledgments he financial supports of prin 2010-11, project ”advanced mechanical modeling of new materials and technologies for the solution of 2020 european challenges” cup n. f11j12000210001 are gratefully acknowledged. the authors wish also to thank fratelli rosati s.r.l. of leinì (torino – italy) for the financial support in this research. references [1] liu, y., liu, y., van humbeeck, j., two-way shape memory effect developed by martensite deformation in niti, acta mater., 47 (1999) 199-209. [2] liu, y., mccormick, p.g., factor influencing the development of two-way shape memory in niti, acta metall. mater., 38 (1990) 1321-1326. [3] lagoudas d.c., shape memory alloys: modeling and engineering applications, springer-verlag, (2008). [4] perkins, j., sponholz, r.o., stress-induced martensite transformation cycling and two-way shape memory training in cu-zn-al alloys, metall. trans. a, 15a (1984) 313-321. [5] scherngell, h., kneissl, a.c., influence of the microstructure on the stability of the intrinsic two-way shape memory effect, mater. sci. eng. a, 273-275 (1999) 400-403. [6] wang, z.g., zu, x.t., feng, x.d., lin, l.b., zhu, s., you, l.p., wang, l.m., design of tini alloy two-way shape memory coil extension spring, mater. sci. eng. a, 345 (2003) 249-254. [7] wang, z.g, zu, x.t., dai, j.y., fu, p., feng, x.d., effect of thermomechanical training temperature on the two-way shape memory effect of niti and tinicu shape memory alloys springs, mater. lett., 57 (2003) 1501-1507. [8] lahoz, r., puértolas, j.a., training and two-way shape memory in niti alloys: influence on thermal parameters, j. alloys compd., 381 (2004) 130-136. [9] lahoz, r., gracia-villa, l., puértolas, j.a., training of the two-way shape memory effect by bending in niti alloys, j. eng. mater. technol., 124 (2002) 397-401. [10] merlin, m., soffritti, c., fortini, a., studio del trattamento termico di lamine in lega a memoria di forma niti per la realizzazione di strutture funzionali, la metallurgia italiana, 11-12 (2011) 17-21. [11] wasilewski, r.j., on the “reversible shape memory effect” in martensitic transformation, scr. metall., 9 (1975) 417421. [12] guilemany, j.m., fernández, j., effect of training time on two way shape memory effect obtained by stabilised stress induced martensite, scr. metall. mater., 30 (1994) 59-61. t t a fortini et alii, frattura ed integrità strutturale, 29 (2014) 74-84; doi: 10.3221/igf-esis.29.08 84 [13] luo, h.y., abel, e.w., a comparison of methods for the training of niti two-way shape memory alloy, smart mater. struct., 16 (2007) 2543-2549. [14] perkins, j., hodgson, d., the two way shape memory effect, in: duerig, t.w. et al (eds.), engineering aspect of shape memory alloys, butterworth-heinmann, (1990) 195-206. [15] kohl, m., dittmann, d., quandt, e., winzek, b., miyazaki, s., allen, d. shape memory microvalves based on thin films or rolled sheets. mater. sci. eng. a 273-275, (1999) 784-788. [16] winzek, b., sterzl, t., quandt, e. bistable thin film composites with tihfni shape memory alloys. in: proceedings of the international conference transducers ’01/eurosensors xv, vol. 1, pp. 706–709. münchen, germany (2001). [17] roh, j., bae, j. thermomechanical behavior of ni-ti shape memory alloy ribbons and their numerical modeling. mech. mater. 42, (2010) 757-773. [18] irzhak, a., kalashnikov, v., koledov, v., kuchin, d., lebedev, g., lega, p., pikhtin, n., tarasov, i., shavrov, v., shelyakov, a. giant reversible deformations in a shape-memory composite material. tech. phys. lett. 36, (2010) 329332. [19] meng, x., cai, w., zheng, y., rao, y., zhao, l. two-way shape memory effect induced by martensite deformation and stabilization of martensite in ti36ni49hf15 high temperature shape memory alloy. mater. lett. 57, (2003) 4206– 4211. [20] rizzoni, r., merlin, m., casari d., shape recovery behaviour of shape memory thin strips in cylindrical bending: experiments and modelling, continuum mech. therm., 25 (2013) 207-227. [21] kirindi, t., sari, u., dikici, m. the effects of pre-strain, recovery temperature, and bending deformation on shape memory effect in an fe–mn–si–cr–ni alloy. j. alloy. compd. 475, (2009) 145-150. [22] balak, z., abbasi, s. m., effect of primary microstructures during training producers on twsme in niti alloys. int. j. eng., 25, (2012), 337-341. [23] saint-sulpice, l., arbab chirani s., calloch s., a 3d super-elastic model for shape memory alloys taking into account progressive strain under cyclic loadings. mech. mat., 41 (2009) 12-26. [24] mehrabi, k., bruncko, m., kneissl, a. c., microstructure, mechanical and functional properties of niti-based shape memory ribbons. j. alloys compd., 526 (2012) 45-52. [25] auricchio, f., marfia, s., sacco, e., modelling of sma materials: training and two-way memory effects, comput. struct., 81(2003) 2301-2317. [26] khandelwal, a., buravalla, v., models for shape memory alloy behavior: an overview of modeling approaches, int. j. struct. changes solids mech. appl., 1 (2009) 1-30. [27] paiva, a., savi, m.a., an overview of constitutive models for shape memory alloys, math. prob. eng., (2006) 1-30. [28] marfia, s., rizzoni, r., one-dimensional constitutive sma model with two martensite variants: analytical and numerical solutions, eur. j. mech. a. solids, 40 (2013), 166-185. [29] kang g., kan q., qian l., liu y., ratchetting deformation of super-elastic and shape-memory niti alloys, mech. mat., 41 (2009) 139-153. microsoft word numero 15 articolo 3 c di kl ch kla de fra ab cer dir add itse hig th mi nu th str int cra len th est tre ke in m rack pro irect bo laus vogel hemnitz unive aus.vogel@s20 etlef billep aunhofer resea bstract. w rtain interme rect bonding dition to the elf. it can va gher toughne he fracture to cro-chevron merical anal he maximum ess intensity tensity coeffi ack. the str ngth itself. he paper is timation of d eatments and eywords. c ntroductio icro e comp millimm opagati onded si , dirk wu ersity of techno 005.tu-chemni p, maik wi arch institutio wafer bondin ediate layers g technology e wafer mat ary for differ ess of the bo oughness is n-specimen, lysis with exp m force is m y coefficient ficient is the ress intensity focused on dimensionle d annealing t compliance m on electro mech plex by using metre range ( ion in m ilicon-si ensch, ale ology, 09107 itz.de, dirk.wu iemer on for electron ng describe . current inv y. it is carrie terials, the t rent pre-trea onded interf a suitable va the fractur perimental m measured dur t can be det compliance y coefficien the micross stress inte temperatures method; fe hanical system g different m (smaller than k. vogel et micro-ch ilicon w exey shapo chemnitz uensch@zfm.tu nic nano syste s all techno vestigations ed out witho toughness o atments. fur face. alue to descr re toughnes measuremen ring a micro termined by method. th t can be dir -chevron-tes ensity coeffi s on the mea e-analysis; fr ms (mems) a aterials in on 100 µm) wh alii, frattura ed hevron-t wafers orin, jan m tu-chemnitz.de ems enas, ologies for j are focused out intermed f the bonde rthermore, a ribe the dam ss can be d nt of the max o-chevron-te y a fe-simu he complian rectly derive st for direct icient as a fu asured maxi racture tough are applied in ne system. me hich determin d integrità struttu test sam mehner technologie-c joining two d on so-calle diate layers ed interface an increase o mage behavio determined ximum force est using a m ulation only. ce of the wh ed from the t bonded sil unction of ge imum force hness; micro n a wide indus ems have at nes its functio turale, 15 (2011) mples of campus 3, 091 or more s d low tempe and at temp also depend of the annea our of the bo either num e. mode i load one possib hole specime e simulated licon-silicon eometry, the are analysed o-chevron-te strial range. t t least one ty on [1]. they ) 21-28; 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wafer bonding to provide da on the bonde re substrates es [2, 3]. mate ) ut on polish of an dopin chem ng silico mater ng subst ing silico polym (ceram epoxy ceram ing subst table 1: overv advantage wit required. thi aling them to duction can b ment. the sur commonly us 10 pa to 20 p red to conven sma treatmen ess includes t g covalent bo nds between t ngth especiall ater molecule fers. thereby he bulk mater ncreasing the ; doi: 10.3221/ig g. to ensure ata for furth ed interface an directly or rial hed wafers of ny orientation ng with natur mical, or therm on, borosilicat rials such as c trate and au on / glass, pla mers, special m mics, metals, y resins, uv mic adhesives trate + glass f view of bondin thin the pack is technology o temperatur be done using rface can be sed mode is th pa with a con ntionally bias nt on the su the pre-bond nds. for hyd the water mo ly depends on s. a subseque y, the water m rial. the wafe temperature gf-esis.15.03 their functio her fe-simula nd the bondi using certain f silicon (wafe and basic ral, thin mal oxide ) te glass cu, au, ti astics / materials pcb, tapes), adhesives, , photo resist frit substrate ng technologie kaging proces y uses the for res up to 110 g surface activ activated by he reactive io ntinuous gas f s voltage the i urface, it is n ding at room drophilic dire olecules loca n the number ent heat treat molecules dif ers move clos the opposin onality and re ations, signifi ing process it n intermediat tempe fers low tem 110 … high te 800 … 210 … 300 … au-si au-sn cu-sn al-si 5 ts room t e 430 °c es. s because no rmation of co 00 °c. for m vating proced a variety of n-etching (ri flow in the re ions are only necessary to e m temperatur ect bonding, t ted on the o r of hydrogen tment (anneal ffuse out eith ser towards ea ng silanol gro eliability as w ficant materia tself. wafer b te layers. tab erature mperature bo … 400 °c, emperature b … 1100 °c … 450 °c … 400 °c 363 °c, n 280 °c, n 350 °c, 577 °c temperature c additional in ovalent bonds many applica dures prior to f low pressure ie). the rie eactor chamb y accelerated b explain the p re and an an the bonding opposing waf n bonds and ling) is carried her along the ach other and oups react wi well as the qu al parameters onding descr b. 1 provides onding onding … 300 °c ntermediate la s for joining ations these h bonding suc e plasma mo e-system oper ber. an opera by approxima procedure of nnealing at h process at ro fer surfaces a therefore on d out, to incr e interface to d form hydro ith each othe uality s are ribes s an ayers two high ch as odes. rates ation ately f the high oom after n the rease the ogen er to http://dx.medra.org/10.3221/igf-esis.15.03&auth=true http://www.gruppofrattura.it th mic exp th th as uns th app par wh ym on ana t he fracture tou cro-chevronperimental de heory he analy width w of 10 m he height of th well as the structured ch he bonded chi proximately t rameters widt ick  hile the maxi min is determin ne possibility alysis. with t ughness is on specimen, the etermination c ysed samples w and thicknes m, fig. 1. he specimen d structure hei hip varies for d figu ip is loaded p to a mode i th and thickn max min f y t w   imum force f ned by fe-sim to estimate th an extension ne of the suita e fracture tou can be execut consist of tw ss t are equal depends on t ight, fig. 2. different mat ure 1: geometr figure 2: mic perpendicular i crack open ness by fmax can be mulation. he stress inten n of the cra k. vogel et able values to ughness of th ted by combin wo single chi [9, 10]. the the height of while the h terial combina ry of a micro-ch cro-chevron-sp to the x-y-pl ning. so the measured du nsity coefficie ack length, t alii, frattura ed o describe the his specimen c ning experim ips bonded to analysis is fo the unstructu height of the ations. hevron-specim pecimen prepa lane in front fracture toug uring a tensil ent is the com the complian d integrità struttu damage beha can be determ ment with num ogether. beca ocused on spe ured wafer hw1 e structured men compared ared from a pro of the sharp ghness kic c le test, the m mpliance meth nce of the s turale, 15 (2011) aviour of the mined numeri merical analysi ause they hav ecimens with 1 and the heig chip is kept to an one cent ocessed wafer. notch. the li can be calcul minimum of t hod. it comb specimen inc ) 21-28; 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decreasing a ecimen fails. t rimental setup on the heat tion has been 0.01 0.02 ap ement curves fo e leads to an emperature o ly 40 °c. alii, frattura ed d. therefore rack length a again. when the measured for the measu treatment of n carried out. 2 0.03 pplied displace for different he n increase of of 150 °c, the d integrità struttu a micro-chev a reaches its c the crack len d force becom rement of the f the specime their anneal 0.04 0.05 ement [mm] eat treatments the measured e measured m turale, 15 (2011) vron-tester is ritical value, t ngth exceeds mes almost ze maximum forc ens. all spec ling temperat 0.06 0 40°c 100°c 150°c (annealing tem d maximum f maximum for ) 21-28; doi: 10 used to mea the measured the value a1 ero again. ce. cimens have tures vary bet 0.07 mperatures). force. for sp rce is about 3 0.3221/igf-esis. asure the reac d force conve 1 the stable c no further tween 40 °c pecimens with 35 % higher t 15.03 25 ction erges rack preand h no than http://dx.medra.org/10.3221/igf-esis.15.03&auth=true http://www.gruppofrattura.it k. v 26 in in dur ref pla five sam for wit for re wa neg th coe bas the par a h me sur ap spe act sam tem t vogel et alii, fra addition to th the introduct ration of the ference specim asma (n2-plas e minutes. th mples vary be r specimens w thout any pla r oxygen plasm esults he varia therefor by keep fers (si-si geo gligible variati he variation of efficients. so sed on the ge e fracture tou rameters of th heat treatmen easured maxim rfaces of the w pplying the sa ecimens is hig tivated specim mples with an mperatures. t attura ed integrit he heat treatm tion, the surf plasma treat mens have n sma) have bee he annealing etween 1.38 n m ea su re d fo rc e [n ] with plasma a asma activatio ma. ation of geom re to different ping the struc ometry 2) ins ion of y() c f the wafer h the values of eometry, the m ughness can he manufactu nt at higher t mum force a wafers, either ame annealing gher than the mens varies fo n annealing tà strutturale, 15 ment, the infl face activatio tment can als no plasma ac en taken into temperature n and 4.26 n, 0.00 0 0 1 2 3 4 5 figure 6: f activation, th on. the maxim metries and bo t fracture tou cture height h tead of a sam can be observ height leads to f y() decreas minima of the be determin uring process. temperatures and the fractu r in oxygen or g temperature e one of sam or different a temperature 5 (2011) 21-28; luence of the on can be car so vary. thre ctivation. mo account. the of 100 °c w , fig. 6. 0.02 0.04 applie force displacem e measured m mum forces ond paramete ughness. hs constant, a mple consistin ved, fig. 7. o a significant se with increa e stress inten ned. using th . smaller frac leads to hig ure toughnes r nitrogen pla e, the maxim mples with any annealing tem of 40 °c is ; doi: 10.3221/ig pre-treatmen rried out usin ee different p reover, plasm e duration for was the same 4 0.06 ed displaceme ment curves fo maximum for for samples a ers leads to di and changing ng of an unstr t deviation be asing wafer he sity coefficien he same geo cture toughne gher maximum ss of the spec asma, before b mum force an y other pre-t mperatures. fu much highe gf-esis.15.03 nt has to be c ng different pre-treatments ma activation r the plasma t for all three s 0.08 0 ent [mm] or different pre rces are appro activated in n ifferent functi g the position ructured and etween the fu eight. nt and the ma ometries the esses can be o m forces and cimens can b bonding, fig. d therefore t treatment. th urthermore, t er than the o characterised plasmas and s are compar ns in oxygen treatment for stacks, too. t 0.10 0.12 reference oxygen plasm nitrogen plasm -treatments. oximately thr nitrogen plasm ions for the s n of the struc a structured c unctions and aximum force fracture toug observed for l d also to high be significantl . 8. the fracture to he deviation b the fracture t one of non-a as well. as al different pro red in the pre (o2-plasma) r the activated the maximum 2 ma ma ee times high ma are a little stress intensit cture by usin chip (si-si ge minima of th e recorded du ghness only lower anneali her fracture t ly increased oughness of between oxyg toughness of activated spec lready mentio ocess gases. esent paper. and in nitro d stacks was b m forces of th her than the o e bit smaller t ty coefficient ng two structu ometry 1), on he stress inten uring experim depends on ing temperatu toughnesses. by activating oxygen activ gen and nitro plasma activ cimens at hig oned the the ogen both hese once than and ured nly a nsity ment, the ures. the g the vated ogen vated gher http://dx.medra.org/10.3221/igf-esis.15.03&auth=true http://www.gruppofrattura.it co act of b t onclusion he comp the influ treatmen tivated wafers bonding stren t st re ss in te ns ity co ef fic ie nt y ( ) figure 7: e ns pliance meth uence of the s nt and the b s during the m ngth. 0.0 50 60 70 80 90 100 st re ss in te ns ity c oe ffi ci en t y ( ) estimation of 0 0 1 2 3 4 5 6 m ax im um fo rc e [n ] figure 8: m od is a suitab specimen geo bonding temp manufacturin k. vogel et 0.1 0 r dimensionless 50 40 ann maximum forc ble approach ometry is con perature itself ng process lea alii, frattura ed .2 0.3 relative crack min s stress intensit 100 nealing tempe non-activate oxygen acti nitrogen act ces for differen to estimate nsidered durin f directly affe ads to signific d integrità struttu 0.4 length  si-si geom si-si geom ty coefficient a 0 1 erature [°c] ed vated tivated nt pre and heat the fracture t ng the calcula ect the measu cantly reduced turale, 15 (2011) 0.5 metry 1 metry 2 as a function of 150 anne treatments. toughness of ation of stress ured maximu d annealing t ) 21-28; doi: 10 0.6 f geometry. ealing [°c] f direct bond s intensity coe um force. th temperatures 0.3221/igf-esis. ed wafers. w efficient, the he use of pla without any 15.03 27 while preasma loss http://dx.medra.org/10.3221/igf-esis.15.03&auth=true http://www.gruppofrattura.it k. v 28 cu the dep re [1] [2] [3] [4] [5] [6] [7] [8] [9] [10 vogel et alii, fra urrently, the s e results of t pending on th eferences g. gerlach, m. wiemer b. michel, r m. wiemer, d. wuensch q. tong, u m. wiemer 682e (2001 a. ploessl, g t. suni, di (2006). j. bagdahn, 0] d. munz, r attura ed integrit stress intensit the complian he applied loa s , w. doetzel: r, j. froemel, r. aschenbre , j. froemel, m h, b. mueller, u. goesele, se , t. otto, t. ). g. kraeuter, irect wafer b a. ploessl, m r.t. bubsey, j tà strutturale, 15 ty coefficient nce method. ad will be carr introduction t. gessner, enner, (2004) m. haubold, , m. wiemer, emiconductor gessner, k. materials sci bonding for m. wiemer, m j.e. srawley, i 5 (2011) 21-28; is calculated in addition t ried out in fu n to microsys t. otto, in: t 307. c. jia, d. wu , t. gessner, r wafer bondi hiller, k. ka ence and eng mems and m. petzold, el int. j. of frac ; doi: 10.3221/ig d using anoth to the nume uture. tem technolo the world o uensch, t. ge h. mischke, ing, john wile apser, h. seid gineering, r2 microelectro lectrochemica cture, 16(4) (1 gf-esis.15.03 her numeric a eric calculatio ogy. john wil of electronic essner, ecs t in: mni pro ey & sons, lt del, j. bagdah 5 (1999) 1. onics, phd th al society, (20 1980) 359. approach, the ons the meas ley & sons, l packaging an transactions, ceedings, da td., new yor hn, m. petzol hesis, helsink 001) 218. e energy relea surement of ltd., (2008). nd system in , 16(8) (2008) rmstadt, (201 rk, (1999). d, materials r ki university ase rate, to ve the crack len tegration, ed 81. 10) 66. research soc y of technol erify ngth d. by ciety, logy, http://dx.medra.org/10.3221/igf-esis.15.03&auth=true http://www.gruppofrattura.it << /ascii85encodepages false /allowtransparency false /autopositionepsfiles true /autorotatepages /none /binding /left /calgrayprofile (dot gain 20%) /calrgbprofile (srgb 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can be opened with acrobat and adobe reader 5.0 and later.) >> /namespace [ (adobe) (common) (1.0) ] /othernamespaces [ << /asreaderspreads false /cropimagestoframes true /errorcontrol /warnandcontinue /flattenerignorespreadoverrides false /includeguidesgrids false /includenonprinting false /includeslug false /namespace [ (adobe) (indesign) (4.0) ] /omitplacedbitmaps false /omitplacedeps false /omitplacedpdf false /simulateoverprint /legacy >> << /addbleedmarks false /addcolorbars false /addcropmarks false /addpageinfo false /addregmarks false /convertcolors /converttocmyk /destinationprofilename () /destinationprofileselector /documentcmyk /downsample16bitimages true /flattenerpreset << /presetselector /mediumresolution >> /formelements false /generatestructure false /includebookmarks false /includehyperlinks false /includeinteractive false /includelayers false /includeprofiles false /multimediahandling /useobjectsettings /namespace [ (adobe) (creativesuite) (2.0) ] /pdfxoutputintentprofileselector /documentcmyk /preserveediting true /untaggedcmykhandling /leaveuntagged /untaggedrgbhandling /usedocumentprofile /usedocumentbleed false >> ] >> setdistillerparams << /hwresolution [2400 2400] /pagesize [612.000 792.000] >> setpagedevice microsoft word numero_42_art_9.docx p. j. huffman et alii, frattura ed integrità strutturale, 42 (2017) 74-84; doi: 10.3221/igf-esis.42.09 74 focused on mechanical fatigue of metals fatigue crack propagation prediction of a pressure vessel mild steel based on a strain energy density model p. j. huffman john deere, one john deere place, moline, il 61265, usa huffman.peter.j@gmail.com j. ferreira, j.a.f.o. correia, a.m.p. de jesus inegi, faculty of engineering, university of porto, rua dr. roberto frias, 4200-465 porto, portugal em12236@fe.up.pt, jacorreia@inegi.up.pt, ajesus@fe.up.pt http://orcid.org/0000-0002-4148-9426, http://orcid.org/0000-0002-1059-715x g. lesiuk faculty of mechanical engineering, department of mechanics, material science and engineering, wrocław university of science and technology, smoluchowskiego 25, 50-370 wrocław, poland grzegorz.lesiuk@pwr.edu.pl, https://orcid.org/0000-0003-3553-6107 f. berto department of industrial and mechanical design, norwegian university of science and technology, norway berto@gest.unipd.it, filippo.berto@ntnu.no, http://orcid.org/0000-0002-4207-0109, http://orcid.org/0000-0002-0591-0754 a. fernández-canteli department of construction and manufacturing engineering, univ. of oviedo, 33203 gijón, spain afc@uniovi.es, http://orcid.org/0000-0001-8071-9223 g. glinka department of mechanical engineering, university of waterloo, 200 univ. avenue west, waterloo, on, 2l 3g1, canada gggreg@uwaterloo.ca, http://orcid.org/0000-0001-8452-8803 abstract. fatigue crack growth (fcg) rates have traditionally been formulated from fracture mechanics, whereas fatigue crack initiation has been empirically described using stress-life or strain-life methods. more recently, there has been efforts towards the use of the local stress-strain and similitude concepts to formulate fatigue crack growth rates. a new model has been developed which derives stress-life, strain-life and fatigue crack growth rates from strain energy density concepts. this new model has the advantage to predict an intrinsic stress ratio effect of the form σar=(σamp)γ·(σmax )(1-γ), which is citation: huffman, p.j., ferreira, j., correia, j.a.f.o., de jesus, a.m.j., lesiuk, g., berto, f., glinka, g., fernández-canteli, a., fatigue crack propagation prediction of a pressure vessel mild steel based on a strain energy density model, frattura ed integrità strutturale, 42 (2017) 74-84. received: 16.06.2017 p. j. huffman et alii, frattura ed integrità strutturale, 42 (2017) 74-84; doi: 10.3221/igf-esis.42.09 75 dependent on the cyclic stress-strain behaviour of the material. this new fatigue crack propagation model was proposed by huffman based on walkerlike strain-life relation. this model is applied to fcg data available for the p355nl1 pressure vessel steel. a comparison of the experimental results and the huffman crack propagation model is made. keywords. fatigue crack growth; strain energy; unigrow model; pressure vessel steel. accepted: 21.06.2017 published: 01.10.2017 copyright: © 2017 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. introduction atigue crack initiation, usually modelled by strain-life or stress-life, has traditionally been considered to be a separate physical phenomenon from fatigue crack propagation. however, some more recent models of fatigue crack growth have been based on the assumption that each crack growth increment is physically similar to the initiation process. that is, the individual crack growth increments are successive initiations of the crack locally at the crack tip [1-4]. such models consider fatigue crack initiation and propagation to be physically similar, and they can be used in a unified approach to calculate total fatigue life as the sum of initiation and propagation [5-7]. some authors, as glinka [2], peeker and niemi [3], noroozi et al. [4,6,7], hurley and evans [5] developed approaches to represent fatigue crack propagation using local fatigue models based on strain parameters. glinka was one of the precursors to describe the fatigue crack propagation modelling using a strain-based fatigue relation [2]. similarly, the model proposed by peeker and niemi [3] allowed the near threshold fatigue crack propagation data and the stable crack growth to be described. for the near threshold fatigue crack propagation, the authors derived analytical relations which are functions of the strain-life relation constants. hurley and evans [5] proposed the use of an elastoplastic finite element analysis to compute the process zone and using the walker-like strain correlated directly with the fatigue life from experimental data thru a power relation to correlate with the fatigue crack increment. other authors, such as, correia et al. [8-14] and hafezi et al. [15] used the strain and swt fatigue local relations [16], based on unigrow model [4,6,7] to predict the fatigue crack propagation using the numerical analysis to obtain residual stresses distribution. correia et al. [9,17,18] proposed a procedure to derive probabilistic s–n–r fields for notched structural details or mechanical components, which is based on the unigrow model and numerical analysis aiming at computing the elastoplastic stresses and strains at process zone ahead the crack tip. alternatively, analytical methods such as the ones proposed by neuber [19] and moftakhar et al. [20] may be applied to perform the elastoplastic analysis taking into account the elastic stress/strain fields computed around the crack tip, using available linear elastic fracture mechanics solutions [4,20,21]. recently, huffman [1] suggested new developments related with the fatigue crack propagation modelling using strain energy density-based model. fatigue evaluation of notched details based on unified local probabilistic approaches was also proposed by huffman [22] considering the walker-like strain-life relation in conjunction with the probabilistic model proposed by castillo and fernández-canteli [23]. in present research, the huffman crack propagation model is applied to the p355nl1 pressure vessel steel and a comparison with experimental results is made. overview of local stress/strain approaches atigue crack growth modelling like the paris law relation, uses linear-elastic fracture mechanics (lefm) to describe cracking driving forces. local approaches, however, explicitly consider stresses and strains near the crack tip, and associate those with the stress intensity factors. using the assumption that the stresses or strains near the crack tip are related to fatigue crack growth in the same way that global stresses and strains are related to stress-life and strain-life, an association can be made between damage parameters, such as the swt damage parameter [16] or the damage parameter introduced by huffman [1] and the fatigue crack growth. f f p. j. huffman et alii, frattura ed integrità strutturale, 42 (2017) 74-84; doi: 10.3221/igf-esis.42.09 76 the latter approach assumes that stress-life, strain-life, and fatigue crack growth are all different expressions of the same phenomenon which is directly associated with the cyclic stress-strain behaviour. according to that work, the stress life, strain life, and fatigue crack growth rate can all be expressed in terms of material parameters. the damage parameter in this case is * 2 2 pe d c d c f uu n d u u n            (1) where ue is the elastic strain energy density and up* is the complimentary plastic strain energy density, both from integrating the cyclic ramberg-osgood stress-strain curve [24], c is the critical dislocation density, du is the dislocation strain energy, and d is the damage corresponding to those strain energy inputs. the dislocation strain energy is calculated as   2 2 1 d e u b          (2) where  is the poisson’s ratio and b  is the burger’s vector. the damage stress based is then defined as    1 ' 2 ' max2 2 2 ' 1 1 1 ' ' 2 n n a d c f n d u n k n                (3) the morrow constants can be calculated as follows.   ' 1/ ' 1 3 ' 1 2 ' '' 2 2 2 1 ' ' 1 ' n n n n n f d c n e e u k n                   (4) where e is the elastic modulus, k’ is the cyclic strength coefficient, n’ is the cyclic strain hardening exponent and 'f is the fatigue strength coefficient. in this model, k’ and n’ come from fitting the cyclic stress and strain amplitude to the ramberg-osgood equation. ' 1 3 ' n b n    (5) where b is the fatigue strength exponent.   1 3 1 3 ' ' 2 2 2 ' ' 1 ' n f d c k n e u e n            (6) where 'f is the fatigue ductility coefficient 1 1 3 ' c n    (7) where c is the fatigue ductility exponent. the product of eq. (3) by a , results a method for calculating the fatigue crack growth rates: p. j. huffman et alii, frattura ed integrità strutturale, 42 (2017) 74-84; doi: 10.3221/igf-esis.42.09 77    1 ' 2 ' max2 2 ' 1 1 ' ' 0 n n a d c f a n a da u n k n dn                  (8) where the stresses are the local stresses at the crack tip. this can be related to the stress intensity factor to yield a formula similar to what is used by noroozi et al. [4,6,7] or alternatively to use the procedure to obtain the fatigue crack growth driving force,  , considering a finite element analysis to compute residual stress intensity factor, kr, proposed by correia et al. [8-14] and hafezi et al. [15],  da c dn   (9) where c is the fatigue crack growth rate coefficient,  is the fatigue crack growth rate exponent, and  , the fatigue crack growth driving force.  1max ppk k    (10) where 2 ' 1 3 ' n p n   (11) the fatigue crack growth rate exponent can be shown to be 2 6 ' 2 1 ' n n b c        (12) for predominantly plastic stresses at the crack tip, the fatigue crack growth rate coefficient under the same conditions is given by,     1 3 '1 2 4 ' 2 ' 1 ' 1 ' ' 1 2 2 ' 1 1 ' 1 ' 2 2 n n n n n n d c a n c k e u n x                              (13) application of the strain energy density approach to fcg data experimental fatigue crack growth data he p355nl1 steel is a pressure vessel steel and was selected to apply the strain energy density approach to fatigue crack growth data. the mechanical properties of this steel was collected from the references [9,12,25,26]. in this sub-section the monotonic strength data, the cyclic elastoplastic fatigue data and the fatigue crack growth data obtained for the p355nl1 steel [9,12,25,26] are presented. the elastic and monotonic tensile properties for this steel under investigation, such as the young modulus, e, poisson ratio, ν, the ultimate tensile strength, fu, upper yield stress, fy, monotonic strain hardening coefficient, k, and monotonic strain hardening exponent, n, are shown in tab. 1. also, in tab. 1, the ramberg-osgood parameters are presented including the cyclic strain hardening coefficient, k’, and the cyclic strain exponent, n’. the strain-life behaviour of the p355nl1 steel was evaluated through fatigue tests of smooth specimens, carried out under strain-controlled conditions, according to the astm e606 standard [27]. two series of specimens are tested under distinct strain ratios, rε=0 and -1, 19 and 24 specimens, respectively. the cyclic ramberg-osgood [24] and morrow [2830] strain-life parameters of the p355nl1 steel are summarized in tab. 2, for the conjunction of both strain ratios. the morrow strain-life parameters, such as, the fatigue ductility coefficient, εf', the fatigue ductility exponent, c, the fatigue strength coefficient, σf', and the fatigue strength exponent, b, were collected in references [9,12,25,26]. t p. j. huffman et alii, frattura ed integrità strutturale, 42 (2017) 74-84; doi: 10.3221/igf-esis.42.09 78 material e (gpa) ν fy (mpa) fu (mpa) k (mpa) n k’ (mpa) n’ p355nl1 205.0 0.275 361.99 361.99 611.49 0.063 948.35 0.1533 table 1: elastic, monotonic tensile and ramberg-osgood properties for the p355nl1 steel. material ' f (mpa) b ' f c p355nl1 1005.50 -0.1033 0.3678 -0.5475 table 2: morrow constants for the p355nl1 steel for strain r-ratios, rε=-1 + rε=0. the experimental results of the fatigue crack growth rates of the investigated material are also evaluated for several stress r-ratios, using ct specimens, following the recommendations of the astm e647 standard [31]. the ct specimens of p355nl1 steel are defined with a width, w=40mm and a thickness, b=4.5mm [9,12,25,26]. the tests were performed in air, at room temperature, under a sinusoidal waveform at a maximum frequency of 20 hz. in fig. 1, the crack growth data derived for the p355nl1 steel, for three tested stress ratios, rσ=0.0, rσ=0.5 and rσ=0.7, are shown. the crack propagation rates are only slightly influenced by the stress ratio. higher stress ratios provide higher crack growth rates [9,12,25,26]. a) b) figure 1: fatigue crack growth data of the p355nl1 steel: a) experimental data; b) paris correlations for each stress r-ratio. k [n.mm‐3/2] d a /d n  [ m m /c yc le ] mb02(r=0.0) mb04(r=0.0) mb03(r=0.5) mb05(r=0.5) mb06(r=0.7) 1.0e‐6 1.0e‐3 1.0e‐2 250 1000 1.0e‐4 1.0e‐5 1500500 k [n.mm‐3/2] d a /d n  [ m m /c yc le ] r=0 r=0.5 r=0.7 1.0e‐6 1.0e‐3 1.0e‐2 1.0e‐4 1.0e‐5 250 1000 1500500 da/dn=7.195e‐15×k3.499 r 2 =0.9960 da/dn=6.281e‐15×k3.555 r 2 =0.9840 da/dn=2.037e‐13×k3.003 r 2 =0.9850 p. j. huffman et alii, frattura ed integrità strutturale, 42 (2017) 74-84; doi: 10.3221/igf-esis.42.09 79 brief description of the numerical analysis in this sub-section, a brief description of the numerical analysis of the ct specimens performed by correia et al. [9,10,13] is presented. this author developed two dimensional numerical models of the ct specimens using non-linear elastoplastic finite element analysis. fig. 2 illustrates the finite element mesh of the ct specimen along with the respective boundary conditions. one half of the geometry is modelled, taking advantage of the existing symmetry. 2d plane stress elements are used since the specimens’ thickness is relatively small (b=4.5mm). quadratic triangular elements (6-noded elements) are selected and applied with a full integration formulation. the pin loading applied to the ct specimens is simulated with a rigid-to-flexible frictionless contact, the pin being modelled as a rigid circle controlled by a pilot node. all numerical simulations are carried out using the ansys® 12.0 code [32]. the 6-noded plane element adopted in the fe (finites elements) analyses is the plane181 element available in the ansys® 12.0 code library. the contact and target elements used in the pin-loading simulation are, respectively, the conta172 and targe169 elements available in ansys® 12.0 code [32]. a parametric model is built using the apdl language. the surface of the holes is modelled as flexible, using conta172 elements. the augmented lagrange contact algorithm is used. the associative von mises (j2) yield criterion with multilinear kinematic hardening is used to model the plastic behaviour. the multilinear kinematic hardening uses the besseling model, also called the sublayer or overlay model, so that the bauschinger effect is included. the plasticity model was fitted to the stabilized or half-life pseudo stabilized cyclic curve of the materials. the plasticity model is fitted to the cyclic curve of the material using the cyclic ramberg-osgood properties of the tab. 1. the finite element model is applied to perform elastic and elastoplastic stress analyses. one important assumption of the huffman fatigue crack propagation model consists in applying the compressive residual stresses that are computed ahead of the crack tip, in the crack faces, in a symmetric way with respect to the normal to crack face that passes thru the crack tip. the residual stresses distribution was estimated using the numerical simulation proposed by correia et al. [9]. the resulting residual stress intensity factor, kr, was computed using the weight function method [33], for each of the stress ratios covered by the testing program. fig. 3 presents the residual stress intensity factor range [12] as a function of the applied stress intensity factor range, obtained with the numerical analysis, which is consistent with the analytical analysis followed in the unigrow model published in the literature. a very high linear correlation between the residual stress intensity factor and the applied stress range is verified, for each stress r-ratio. this linear relation agrees with the proposition by noroozi et al. [4], based on analytical analysis. the numerical solution, for the residual stresses, is adopted in the crack propagation prediction using huffman fatigue crack propagation model [1]. figure 2. finite element mesh of the ct specimen [9]. application and results this sub-section presents the application of the strain energy density approach to fatigue crack propagation data of the p355nl1 pressure vessel steel. from the application of this model, the morrow and fatigue crack growth constants, as well as, the strain-life and stress-life curves are evaluated. the fatigue crack propagation model based on the strain energy density approach requires the calibration of model parameters, such as, the critical dislocation density, ρc, crack increment, δa, and distance from the crack tip, x. p. j. huffman et alii, frattura ed integrità strutturale, 42 (2017) 74-84; doi: 10.3221/igf-esis.42.09 80 figure 3. residual stress intensity factor as a function of the kapplied for the ct geometry. the morrow constants resulting from eqs. (4)-(7) can be seen in tab. 3. these constants, estimated using the strain energy density approach, are similar to those obtained by fitting the coffin-manson and morrow relation. in this way, it is demonstrated that the huffman fatigue crack propagation model leads to good results. the fatigue crack growth rate constants are shown in tab. 4, as well as the critical dislocation density for the material. these fcg rate constants were estimated using the strain energy density approach related to the stress intensity factor used by noroozi et al. [4] and considering the residual stresses distribution obtained numerically (proposed by correia et al. [9]). material ' f (mpa) b ' f c p355nl1 959 -0.105 1.08 -0.685 table 3: morrow constants for the p355nl1 calculated as per eqs. (4)-(7). material c (m/m3) δa (m) x (m) p355nl1 7.0x10-15 4.5e-3 3.0e-5 table 4: fatigue crack growth rate constants from eq. (8). the stress-life and strain-life curves, and fatigue crack growth rates calculated from the strain energy based damage model are presented, respectively, in the figs. 4, 5 and 6. a good agreement between the experimental strain-life test results and stressand strain-life curves estimated using the strain energy density approach is verified. a good agreement can be considered between the experimental fcg results and the results obtained on the basis of the huffman fatigue crack propagation model for the stress r-ratio equal to 0 and the set of experimental fcg results for all stress r-ratios. this model shows to be very conservative for the stress r-ratios equal to 0.5 and 0.7, describing a possible mean stress effect that is not verified for this material. the critical dislocation density and basic fatigue crack growth rates constants (tab. 4) for the p355nl1 steel are similar when compared with others materials of identical mechanical properties. k r = 0.3383. k applied  ‐ 50.184 r 2  = 0.9992 k r = 0.1488. k applied  ‐ 27.44 r 2  = 0.9944 k r = 0.1207. k applied  ‐ 23.161 r 2  = 0.9996 0 50 100 150 200 250 300 350 400 200 400 600 800 1000 1200 kapplied [n.mm ‐1.5 ] k re si d u a l [ n .m m ‐1 .5 ] r=0.0 r=0.5 r=0.7 p. j. huffman et alii, frattura ed integrità strutturale, 42 (2017) 74-84; doi: 10.3221/igf-esis.42.09 81 figure 4. stress-life curve of the p355nl1 steel, per reference [1]. figure 5. strain-life curve of the p355nl1 steel, per reference [1]. a) 0 100 200 300 400 500 600 1.0e+02 1.0e+03 1.0e+04 1.0e+05 1.0e+06 1.0e+07 s tr e ss  a m p li tu d e ,  δ σ /2 [‐ ] reversals to failure, 2nf experimental data: r=‐1 + r=0 huffman model 1.0e‐05 1.0e‐04 1.0e‐03 1.0e‐02 1.0e‐01 1.0e+00 1.0e+02 1.0e+03 1.0e+04 1.0e+05 1.0e+06 1.0e+07 s tr a in  a m p li tu d e ,  δ ε /2 [‐ ] reversals to failure, 2nf experimental data: r=‐1 + r=0 huffman model d a /d n  ( m m /c yc le ) k (n.mm‐3/2) huffman model for r=0 mb‐02: experimental data mb‐04: experimental data 1.0e‐6 1.0e‐3 1.0e‐2 200 1600500 1.0e‐4 1.0e‐5 1000 r=0 p. j. huffman et alii, frattura ed integrità strutturale, 42 (2017) 74-84; doi: 10.3221/igf-esis.42.09 82 b) c) d) figure 6. fatigue crack growth rate of p355nl1 steel obtained using the huffman model, as per reference [1]: a) r=0; b) r=0.5; c) r=0.75; d) r=0 + r=0.5 + r=0.75. d a /d n  ( m m /c yc le ) k (n.mm‐3/2) peter huffman for r=0.5 mb_03: experimental data mb_05: experimental data 1.0e‐6 1.0e‐3 1.0e‐2 200 1600500 1.0e‐4 1.0e‐5 1000 r=0.5 d a /d n  ( m m /c yc le ) k (n.mm‐3/2) huffman model for r=0.75 mb_06: experimental data 1.0e‐6 1.0e‐3 1.0e‐2 200 1600500 1.0e‐4 1.0e‐5 1000 r=0.75 d a /d n  ( m m /c yc le ) k (n.mm‐3/2) mb‐02: experimental data ‐ r=0.0 mb‐04: experimental data ‐ r=0.0 mb‐03: experimental data ‐ r=0.5 mb‐05: experimental data ‐ r=0.5 mb‐06: experimental data ‐ r=0.75 huffman model: r=0.0 huffman model: r=0.5 huffman model: r=0.75 1.0e‐6 1.0e‐3 1.0e‐2 200 1600500 1.0e‐4 1.0e‐5 1000 r=0 + r=0.5 + r=0.75 p. j. huffman et alii, frattura ed integrità strutturale, 42 (2017) 74-84; doi: 10.3221/igf-esis.42.09 83 conclusions he huffman fatigue crack initiation and propagation model based on a strain energy based damage model can be used to predict the stress-life and strain-life curves, as well as the fatigue crack propagation rates in paris’ law regime, along with the corresponding stress ratio effect. a good agreement between the experimental strain-life results and huffman analytical stressand strain-life curves is verified. the model is able to obtain fatigue local relations for other fatigue damage parameters, such as swt fatigue damage parameter. the application of the huffman model to the fatigue crack propagation data of the p355nl1 steel proved to be promising. some aspects related with the mean stresses and stress r-ratios effects have to be improved in order to correctly describe the fatigue crack growth behaviour of the material under consideration. a comparison with other models of fatigue crack propagation based on fatigue local approaches should be made, such as unigrow model using neuber analytical approaches or numerical modelling to obtain the residual stresses distribution. a unified two-stage fatigue approach using the huffman fatigue crack initiation and propagation model applied to the structural details can be suggested. acknowledgements he authors acknowledge the portuguese science foundation (fct) for the financial support through the postdoctoral grant sfrh/bpd/107825/2015. the authors gratefully acknowledge the funding of scitech: science and technology for competitive and sustainable industries, r&d project cofinanced by programa operacional regional do norte (norte2020), through fundo europeu de desenvolvimento regional (feder). references [1] huffman, p.j., a strain energy based damage model for fatigue crack initiation and growth, international journal of fatigue, 88 (2016) 197–204. [2] glinka, g., a notch stress-strain analysis approach to fatigue crack growth, engineering fracture mechanics, 21 (1985) 245-261. [3] peeker, e., niemi, e., fatigue crack propagation model based on a local strain approach, journal of constructional steel research, 49 (1999) 139–155. [4] noroozi, a.h., glinka, g., lambert, s., a two parameter driving force for fatigue crack growth analysis, international journal of fatigue, 27 (2005) 1277-1296. [5] hurley, p.j., evans, w.j., a methodology for predicting fatigue crack propagation rates in titanium based on damage accumulation, scripta materialia, 56 (2007) 681–684. [6] noroozi, a.h., glinka, g., lambert, s., a study of the stress ratio effects on fatigue crack growth using the unified two-parameter fatigue crack growth driving force, international journal of fatigue, 29 (2007) 1616-1633. [7] noroozi, a.h., glinka, g., lambert, s., prediction of fatigue crack growth under constant amplitude loading and a single overload based on elasto-plastic crack tip stresses and strains, engineering fracture mechanics, 75 (2008) 188206. [8] correia, j.a.f.o., de jesus, a.m.p., fernández-canteli, a., a procedure to derive probabilistic fatigue crack propagation data, international journal of structural integrity, 3(2) (2012) 158–183. [9] correia, j.a.f.o., de jesus, a.m.p., fernández-canteli, a., local unified model for fatigue crack initiation and propagation: application to a notched geometry, engineering structures, 52 (2013) 394–407. [10] correia, j.a.f.o., an integral probabilistic approach for fatigue lifetime prediction of mechanical and structural components, ph.d. thesis, university of porto, (2014) 382. [11] correia, j.a.f.o., de jesus, a.m.p., fernández-canteli, a., calçada, r.a.b., modelling probabilistic fatigue crack propagation rates for a mild structural steel, frattura ed integrita strutturale, 31 (2015) 80-96. [12] de jesus, a.m.p., correia, j.a.f.o., critical assessment of a local strain-based fatigue crack growth model using experimental data available for the p355nl1 steel, journal of pressure vessel technology, 135(1) (2013) 011404-1– 0114041-9. t t p. j. huffman et alii, frattura ed integrità strutturale, 42 (2017) 74-84; doi: 10.3221/igf-esis.42.09 84 [13] correia, j.a.f.o., de jesus, a.m.p., moreira, p.m.g.p., calçada, r.a.b., fernández-canteli, a., fatigue crack propagation rates prediction using probabilistic strain-based approaches, chapter 11, pp. 245-273, in: fracture mechanics – properties, patterns and behaviours, lucas alves (ed.), (2016). [14] hafezi, m.h., abdullah, n.n., correia, j.a.f.o., de jesus, a.m.p., an assessment of a strain-life approach for fatigue crack growth, international journal of structural integrity, 3(2) (2012) 344–376. [15] correia, j.a.f.o., de jesus, a.m.p., ribeiro, a.s., strain-based approach for fatigue crack propagation simulation of the 6061-t651 aluminum alloy, international journal of materials and structural integrity, (2017, in press). [16] smith, k.n., watson, p., topper, t.h., a stress-strain function for the fatigue of metals, journal of materials, 5(4) (1970) 767-778. [17] sampayo, l.m.c.m.v., monteiro, p.m.f., correia, j.a.f.o., xavier, j.m.c., de jesus, a.m.p., fernandez-canteli, a., calçada, r.a.b., probabilistic s-n field assessment for a notched plate made of puddle iron from the eiffel bridge with an elliptical hole, procedia engineering, 114 (2015) 691 – 698. [18] raposo, p., correia, j.a.f.o., de jesus, a.m.p., calçada, r.a.b., lesiuk, g., hebdon, m., fernández-canteli, a., probabilistic fatigue s-n curves derivation for notched components, frattura ed integrità strutturale, (2017, in press). [19] neuber, h., theory of stress concentration for shear-strained prismatic bodies with arbitrary nonlinear stress–strain law. trans. asme journal of applied mechanics, 28 (1961) 544–551. [20] moftakhar a, buczynski a, glinka g. calculation of elasto-plastic strains and stresses in notches under multiaxial loading. international journal of fracture, 70 (1995) 357-373. [21] reinhard w, moftakhar a, glinka g. an efficient method for calculating multiaxial elasto-plastic notch tip strains and stresses under proportional loading. fatigue and fracture mechanics, vol. 27, astm stp 1296, r.s. piascik, j.c. newman, n.e. dowling, eds., american society for testing and materials, (1997) 613-629. [22] huffman, p., correia, j.a.f.o., mikheevskiy, s., de jesus, a.m.p., cicero, s., fernández-canteli, a., berto, f., glinka, g., fatigue evaluation of notched details based on unified local probabilistic approaches, international symposium on notch fracture (isnf2017), santander, spain, (2017). [23] castillo, e., fernández-canteli, a., a unified statistical methodology for modeling fatigue damage, springer, 2009. [24] ramberg, w., osgood, w.r., description of the stress-strain curves by the three parameters, naca tn-902, national advisory committee for aeronautics, (1943). [25] de jesus, a.m.p., ribeiro, a.s., fernandes, a.a., influence of the submerged arc welding in the mechanical behaviour of the p355nl1 steel—part ii: analysis of the low/high cycle fatigue behaviours, j. mater. sci., 42 (2007) 5973–5981. [26] correia, j.a.f.o., de jesus, a.m.p., moreira, p.m.g.p., tavares, p.j., crack closure effects on fatigue crack propagation rates: application of a proposed theoretical model, advances in materials science and engineering, (2016) 3026745. [27] astm – american society for testing and materials. astm e606-92: standard practice for strain controlled fatigue testing. in: annual book of astm standards, part 10; (1998) 557–571. [28] coffin, l.f., a study of the effects of the cyclic thermal stresses on a ductile metal, trans asme, 76 (1954) 931–950. [29] manson, s.s., behaviour of materials under conditions of thermal stress, naca tn-1170, national advisory committee for aeronautics, report 1170, (1954) 591–630. [30] morrow, j.d., cyclic plastic strain energy and fatigue of metals, int frict damp cyclic plast astm stp., 378 (1965) 45–87. [31] astm—american society for testing and materials. astm e647: standard test method for measurement of fatigue crack growth rates. in: annual book of astm standards, vol. 03.01. west conshohocken, pa: astm—american society for testing and materials; (2000) 591–630. [32] sas, ansys, swanson analysis systems, inc., houston, version 12.0, (2011). [33] glinka, g., development of weight functions and computer integration procedures for calculating stress intensity factors around cracks subjected to complex stress fields. progress report no.1: stress and fatigue-fracture design, petersburg ontario, canada, (1996). << /ascii85encodepages false /allowtransparency false /autopositionepsfiles true /autorotatepages /none /binding /left /calgrayprofile (dot gain 20%) /calrgbprofile (srgb iec61966-2.1) /calcmykprofile (u.s. web coated \050swop\051 v2) /srgbprofile (srgb iec61966-2.1) /cannotembedfontpolicy /error /compatibilitylevel 1.4 /compressobjects /tags /compresspages true /convertimagestoindexed true /passthroughjpegimages true /createjobticket false /defaultrenderingintent /default /detectblends true /detectcurves 0.0000 /colorconversionstrategy /cmyk /dothumbnails false /embedallfonts true /embedopentype false /parseiccprofilesincomments true /embedjoboptions true /dscreportinglevel 0 /emitdscwarnings false /endpage -1 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can be opened with acrobat and adobe reader 5.0 and later.) >> /namespace [ (adobe) (common) (1.0) ] /othernamespaces [ << /asreaderspreads false /cropimagestoframes true /errorcontrol /warnandcontinue /flattenerignorespreadoverrides false /includeguidesgrids false /includenonprinting false /includeslug false /namespace [ (adobe) (indesign) (4.0) ] /omitplacedbitmaps false /omitplacedeps false /omitplacedpdf false /simulateoverprint /legacy >> << /addbleedmarks false /addcolorbars false /addcropmarks false /addpageinfo false /addregmarks false /convertcolors /converttocmyk /destinationprofilename () /destinationprofileselector /documentcmyk /downsample16bitimages true /flattenerpreset << /presetselector /mediumresolution >> /formelements false /generatestructure false /includebookmarks false /includehyperlinks false /includeinteractive false /includelayers false /includeprofiles false /multimediahandling /useobjectsettings /namespace [ (adobe) (creativesuite) (2.0) ] /pdfxoutputintentprofileselector /documentcmyk /preserveediting true /untaggedcmykhandling /leaveuntagged /untaggedrgbhandling /usedocumentprofile /usedocumentbleed false >> ] >> setdistillerparams << /hwresolution [2400 2400] /pagesize [612.000 792.000] >> setpagedevice microsoft word numero_40_art_8 i. doulamis et alii, frattura ed integrità strutturale, 40 (2017) 85-94; doi: 10.3221/igf-esis.40.08 85 focussed on recent advances in “experimental mechanics of materials” in greece exercise as a mean to reverse the detrimental effect of high-fat diet on bone’s fracture characteristics ilias doulamis, despina n. perrea laboratory for experimental surgery and surgical research “n.s. christeas”, national and kapodistrian universtiy of athens, medical school, agiou thoma str. 15b, 11527, athens, greece. panagiotis e. chatzistergos school of health sciences and education, staffordshire university, stoke-on-trent, uk. panagiotis.chatzistergos@staffs.ac.uk athanasios s. mitousoudis, stavros k. kourkoulis unit of biomechanics, department of mechanics, school of applied mathematical and physical sciences, national technical university of athens, zografou campus, 15773, athens, greece. abstract. the aim of this study is to investigate whether exercise can reverse some of the adverse effects of high-fat-diet-induced obesity on lipid metabolism and bone biomechanical properties. a total of 26 adult male c57bl/6j mice were randomly assigned into three groups: (a) control group (n=6), (b) high-fat diet group (n=10), (c) high-fat diet and exercise group (n=10). body mass and relevant biochemical parameters were measured for the duration of the experimental protocol (37 weeks). mechanical strength of both femurs of each animal was assessed in-vitro based on three point bending tests. it was revealed that exposure to high-fat diet led to significant increase of body mass and cholesterol levels and also to substantial changes in bone morphology and strength. ultimate stress for the animals exposed to high-fat diet and those exposed to high-fat-diet and exercise was 25% and 24% lower compared to control, respectively. exercise increased bone thickness by 15% compared to animals that were not exposed to exercise. it was concluded that high-fat-diet appears to have a detrimental effect on bone biomechanics and strength. exercise reversed the reduction in bone thickness that appears to be induced by high-fat diet. however no statistically significant increase in bone strength was observed. keywords. bone biomechanics; mice; femur; high-fat-diet; three-point bending; bending strength. citation: doulamis, i., chatzistergos, p.e., mitousoudis, a.s., kourkoulis, s.k., perrea, d.n., exercise as a mean to reverse the detrimental effect of high-fat diet on bone’s fracture characteristics, frattura ed integrità strutturale, 40 (2017) 85-94. received: 17.02.2017 accepted: 10.03.2017 published: 01.04.2017 copyright: © 2017 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. i. doulamis et alii, frattura ed integrità strutturale, 40 (2017) 85-94; doi: 10.3221/igf-esis.40.08 86 introduction besity's adverse effects on health include increased risk for diabetes (type-2), heart disease and certain types of cancer [1] leading to poor quality of life and ultimately to reduced life expectancy [2]. the continuous rise in its prevalence worldwide has highlighted obesity as one of the major epidemics of our time [3]. with regards to the risk for bone fracture, obesity has been traditionally believed to have a protective role [4,5]. moreover a significant number of studies reported a positive relation between body mass index (bmi) and bone density [6]. however, the aforementioned classic view on the effect of obesity has been put into question from findings that link obesity to the loss of bone mass and osteopenia [7, 8] and studies highlighting lean body mass as a stronger determinant of bone density in men than bmi [9, 10]. currently adipose tissue (i.e. body fat) is considered to be hormonally active with a pivotal role with regards to energy homeostasis and metabolism and not just an organ for storing excess energy [11]. more specifically, adipose tissue has been found to produce and secrete numerous substances including the hormone adiponectin. adiponectin is exclusively secreted by adipose tissue and appears to be linked to increased insulin sensitivity and to have anti-atherogenic and antiinflammatory properties [12]. the levels of plasma adiponectin are strongly associated with bmi and appear to be higher in obese subjects compared to lean subjects [13, 14]. animal models have been widely used for the investigation of the effect of obesity, nutrition and exercise. according to these models obesity is induced by subjecting the animals (mainly rats or mice) to a high-fat diet (hfd) [15]. according to literature one of possible ways to prevent bone mass loss is exercise [16, 17]. besides of its overall positive effect on health, exercise is considered to positively influence bone microstructure [18] and improved strength [19, 20]. in this context the aim of this study is to assess the effect of hfd induced obesity on bone biomechanics and biochemical measurements and investigate whether exercise can reverse its potentially negative effects. materials and methods selection and description of animals total of 26 male c57bl/6 mice, aged 10-11 weeks, were used. the mice were housed in groups of three in the animal housing facility of the laboratory of experimental surgery and surgical research “n.s. christeas”, national and kapodistrian university of athens, in a controlled environment. all conditions followed national and european legislation and standards, including cages (tecniplast s.p.a., italy) and the environment with 55% relative humidity, central ventilation (15 air changes/h), temperature of 20°c ± 2°c and artificial 12-h light-dark cycle. access to food and water was ad libitum. the experimental protocol was approved by the ethics committee of the local veterinary directorate. following acclimatization, the rodents were randomized and allocated into three groups: control group (group a, n=6), which received a standard chow diet for 37 weeks; high fat diet (hfd) group (group b, n=10), which received a high fat diet (standard chow diet enriched with 45% fat) for 37 weeks; high fat diet and exercise (hfde) group (group c, n=10), which received the same diet as group b for 37 weeks and ran on a treadmill three times a week for the last nine weeks of the experimental protocol. treadmill exercise the duration of the exercise of group c was nine weeks in total. a specially designed treadmill was used (columbus instruments, usa, model: exer-3/6). an escalation of the vigorousness of exercise was followed. more specifically, the first two weeks were characterized as the adjustment period. meanwhile, the mice began to run at speed of 5 m/min and gradually (additional 5 m/min per time) reached the speed of 30 m/min at the end of the second week. this was their final running speed until the end of the study. each exercise session lasted precisely 30 minutes. biochemical measurements blood samples were collected at baseline, at 12 weeks, at 28 weeks and at the end of the study (37 weeks) prior to euthanasia following a 12-h fast of the animals. animals were anesthetized with ether and a quantity of approximately 500 μl of blood was collected from the ocular canthus of each mouse. blood was collected in vacutainer tubes (bd diagnostics, nj, usa). serum was separated by centrifugation at 3000 rpm for 10 minutes and was stored at -20°c until analysis. o a i. doulamis et alii, frattura ed integrità strutturale, 40 (2017) 85-94; doi: 10.3221/igf-esis.40.08 87 total serum cholesterol (t-chol), high-density lipoprotein cholesterol (hdl-c) serum triglycerides (tg) and serum glucose concentrations were determined enzymatically with commercially available kits (biosis biotechnological applications, athens, greece). due to the nonconfirmed validity of the friedewald formula for the calculation of low-density lipoprotein (ldl) in rodents this parameter was not included in our study. moreover, serum adiponectin levels (adipo) were estimated with enzyme-linked immunosorbent assay (mouse adiponectin elisa kit, intra-assay cv 5.3%, inter-assay cv 9.9% abcam, cambridge cb4 0fl uk). mechanical testing after euthanasia, both left and right femur of each animal were resected and stored in gauze immersed into n/s 0.9%. the mechanical behaviour and the strength of the specimens was assessed from three point bending tests. all biomechanical tests were performed within four hours from the time the samples were harvested. mechanical testing was performed with the use of an electromechanical uniaxial load frame (instron) which was equipped with a high accuracy tension-only load cell (50 n, instron). because of the use of a tension-only load cell, a custom device had to be used to transform tensional loading to three point bending (fig. 1). this device comprises two main parts: part a which was fixed to the load frame's base and b which was attached to its movable crosshead. part a included the centrally placed cylindrical pin while part b included the two support pins (fig. 1). the diameter of all three pins was 2 mm and the distance between the two support pins was 14 mm. to improve the reliability of the testing procedure the distance between the stationary central pin and the movable support pins was directly measured using a lased micrometer (keyence ls-3000) (fig. 1). all samples were loaded with a displacement rate of 5 mm/min until failure. the sampling frequency for the distance between the central and the support pins as well as for the force was 3 hz. figure 1: the custom device that was used to perform three point bending tests with a tension only load cell. the device comprises two parts: (a) which was fixed to the load frame's base and (b) which was attached to its movable crosshead. before testing, the maximum and minimum external thickness of each sample was measured at the central part of their diaphysis using a digital calliper. assuming that the cross-section of the diaphysis is elliptical means that the aforementioned maximum and minimum external thickness correspond to the major axis (a) and minor axis (b) of the ellipse respectively (fig. 2). after the end of the test the actual thickness of the bone cross-section was also measured on the surface of fracture. the measurement of wall thickness was repeated four times for each sample: two at opposite sides of the sample’s major axis (t1,t2 in fig. 2) and two at opposite sides of the sample's minor axis (t3,t4 in fig. 2). in the end, these four measurements were used to calculate the average thickness of the sample (t) on the surface of failure. the recorded data in terms of force were used to find the maximum force that was sustained by each sample, namely the fracture force. the force data combined with the measurements of the distance between the central and support pins were used to draw the force/deflection curve of each test and calculate the stiffness of each sample and also their energy to i. doulamis et alii, frattura ed integrità strutturale, 40 (2017) 85-94; doi: 10.3221/igf-esis.40.08 88 failure. sample stiffness was calculated as the slope of the linear part of the force/deflection curve while energy as the area below the curve. ultimate stress was also calculated based on the assumption of elliptical cross-section with constant thickness (t) [21]. figure 2: a schematic representation of the three point bending test. the measurement sites for thickness (t1-4) and lengths of the major (right) and minor axis (left) of the samples are also presented. statistical analysis the results for the three groups were compared to each other and the statistical significance of the differences that were observed was evaluated following one way analysis of variance (anova). the level of statistical significance was considered to be equal to 0.05. the effect of exercise on the biochemical profile and body mass of group c was also investigated. for this purpose one way repeated measures anova (statistical significance level = 0.05) with bonferroni confidence interval adjustment was used to assess the statistical significance of differences between the measurements that were taken before the start and after the end of the exercise protocol (i.e. week 28 vs 37). in order to assess the relationship between biomechanical and biochemical parameters and the effect of hfd, the correlation between the average biomechanical measures for each animal (i.e. average for left and right femur) and the biochemical measurements was investigated for groups b and c using pearson correlation analysis. the correlation between biomechanical measures and body mass was also assessed. all data were tested for linearity, normality and homoscedasticity. the statistical analyses were performed using ibm® spss®v.21. results biochemical measurements t the beginning of the protocol differences between the three groups were non-significant (fig. 3), with the exception of tg levels, which were somehow higher in group a (an issue that should be considered further). during week 12, the first changes that can be attributed to hfd are observed in the case of hdl-c, with groups b and c having significantly higher hdl-c levels compared to control (group a). differences in biochemical parameters become clearer during week 28 when significant differences in terms of body mass are also observed. more specifically, groups b and c appear to have significantly higher body mass and higher levels of hdl-c and t-chol compared to control. group c has significantly higher body mass than group b too (average (±stdev) body mass for groups a, b and c is equal to 29.3kg (±2.4kg) 35.0kg (±4.2kg) and 39.2kg (±2.3kg), respectively). at the end of the experimental protocol (i.e. week 37) the difference in terms of body mass between control and groups b and c appears to crystallise (average (±stdev) body mass for groups a, b and c is equal to 27.5kg (±1.4kg) 32.0kg (±3.0kg) and 31.8kg (±3.5kg) respectively). moreover, groups b and c also have significantly higher levels of t-chol compared to control. at the end of the protocol, group c also appears to have significantly higher levels of tg compared to the other two groups (fig. 3). at this point it should be highlighted that group c was exposed to exercise only during the last nine weeks of the experimental protocol (i.e. weeks 28-37). therefore any difference between groups b and c that is observed during the 28th week of the experimental protocol (or earlier than that) cannot be attributed to exercise (fig. 3). one way repeated measures anova for group c before and after the introduction of exercise showed statistically significant: a i. doulamis et alii, frattura ed integrità strutturale, 40 (2017) 85-94; doi: 10.3221/igf-esis.40.08 89  decrease in body mass (wilks’ lambda=0.276, f(1,9)= 23.649, p=0.001)  decrease in the levels of t-chol (wilks’ lambda=0.357, f(1,9)= 16.97, p=0.003)  decrease in the levels of hdl-c (wilks’ lambda=0.135, f(1,9)= 57.193, p<0.0005)  increase in the level of tg (wilks’ lambda=0.068, f(1,9)= 124.149, p<0.0005)  decrease in the levels of adipo (wilks’ lambda=0.244, f(1,9)= 27.816, p=0.001) figure 3: the change in biochemical measures and body mass for the duration of the study. more specifically, biochemical results for the levels of serum glucose, total serum cholesterol (t-chol), high-density lipoprotein cholesterol (hdl-c), serum triglycerides (tg) and serum adiponectin levels (adipo) are presented. statistically significant differences (i.e. p<0.05) between groups a and b, a and c and between groups b and c are noted using *, ** or *** respectively. the time period when group c was exposed to exercise (i.e. weeks 28-37) is also highlighted. i. doulamis et alii, frattura ed integrità strutturale, 40 (2017) 85-94; doi: 10.3221/igf-esis.40.08 90 mechanical testing some of the samples were damaged before testing during harvesting. in the end, the number of sample pairs (i.e. left and right femurs) that were tested was 3, 6, and 10 for groups a, b and c respectively. the average values and standard deviations for all biomechanical parameters measured in the context of this study are presented in tab. 1. table 1: the average values for the biomechanical parameters measured. the respective standard deviations are shown in brackets. one way anova revealed statistically significant differences between the three groups in terms of minor axis length (b), major axis length (a) and thickness of the cross-section (t) and also in terms of ultimate stress (fig. 4). no statistically significant difference was found in terms of force, stiffness or energy to failure. figure 4: comparative results in terms of bone morphology and mechanical strength. the lengths of the minor axis (b), of the major axis (a), of cortical shell thickness and of ultimate stress are presented. more specifically the average minor axis (b) of group a was smaller than group's b and c by 12% (p=0.040) and 7% (p<0.001) respectively. the respective difference between groups b and c was 4% (p=0.041) with the minor axis of group group: a b c max force (n) 16.4 14.2 15.6 (2.6) (2.6) (2.2) stiffness (n/mm) 77 90 89 (25) (34) (28) energy (n*mm) 3.16 2.64 3.36 (0.85) (0.92) (1.20) b (mm) 1.42 1.59 1.53 (0.06) (0.07) (0.11) a (mm) 2.05 2.19 2.16 (0.04) (0.10) (0.11) t (mm) 0.24 0.22 0.25 (0.03) (0.03) (0.04) stress (mpa) 58 43 44 (12) (7) (11) * * * * * * * * i. doulamis et alii, frattura ed integrità strutturale, 40 (2017) 85-94; doi: 10.3221/igf-esis.40.08 91 c being the smallest of the two groups. the major axis of group a was also smaller that group b and c by 7% (p=0.026) and 5% (p=0.004) respectively. the thickness of group c was bigger than group b by 15% (p=0.010). finally the ultimate stress of group a was higher than b and c by 25% (p=0.021) and 24% (p=0.001) respectively (fig. 4). pearson correlation analysis revealed a strong positive correlation between serum glucose and fracture force (r=0.560, n=18, p=0.016) and between glucose and energy (r=0.660, n=18, p=0.008) (fig. 5a,b). body mass was strongly and positively correlated to fracture force (r=0.606, n=18, p=0.008) and negatively correlated to minor axis length (b) (r=0.644, n=18, p=0.004) (fig. 5c,d). t-chol was negatively correlated to minor axis length (r=-0.644, n=18, p=0.011) (fig. 5e). the aforementioned correlations indicate that fracture force tends to be higher in animals with higher glucose levels and in animals with higher body mass. moreover, fracture energy tends also to be higher in animals with higher glucose levels while the minor axis (b) appears to be smaller in animals with higher levels of t-chol and in animals with higher body mass. figure 5: correlations between biomechanical parameters, body mass and biochemical measurements. y = 0.0675x + 7.1551 r² = 0.3137 0 5 10 15 20 50 100 150 200 f ra ct u re fo rc e ( n ) glucos e (mg/dl) y = 0.0299x 0.419 r² = 0.4359 0 2 4 6 50 100 150 200 e n e rg y (n m m ) glucos e (mg/dl) y = 0.4267x + 1.0464 r² = 0.367 0 5 10 15 20 5 15 25 35 45 f ra ct u re fo rc e ( n ) body mas s (g) y = -0.0188x + 2.1768 r² = 0.415 0 0.5 1 1.5 2 1 11 21 31 41 b ( m m ) body mas s (g) (a) (b) (c) (d) y = -0.0026x + 1.8432 r² = 0.3376 0 0.5 1 1.5 2 1 51 101 151 201 b ( m m ) t-chol(mg/dl) (e) i. doulamis et alii, frattura ed integrità strutturale, 40 (2017) 85-94; doi: 10.3221/igf-esis.40.08 92 discussion and conclusions his study aimed to assess the effect of obesity and exercise on bone biomechanics and biochemical measurements and investigate the potentially beneficial role of exercise. for this purpose, a well-established mouse model of hfd–induced obesity was used [7, 15]. more specifically, mice were randomly assigned in three groups, namely control (group a), hfd with no exercise (group b) and hfd with exercise (group c). body mass and relevant biochemical parameters were measured for the duration of the study (i.e. 37 weeks). during the first 28 weeks of the experimental protocol groups b and c were exposed to exactly the same conditions. indeed, exercise was not introduced to the protocol until the end of the 28th week. this means that analysing the results for the first 28 weeks enables only the assessment of the effect of hfd on body mass and the biochemical profile of the animals. any difference between groups b and c up to week 28 could be attributed to variations that are inherent in invivo testing. as expected hfd had a significant effect on body mass [15]. more specifically, the animals that received hfd gradually increased their body mass relatively to control with statistically significant differences appearing during the 28th week of the study. with regards to the biochemical measurements, hfd appears to consistently lead to higher levels of cholesterol (t-chol and hdl-c). one way repeated measures anova for group c indicates that the introduction of exercise is followed by some changes, including a drop in body mass, increase in tg levels etc. however, in most cases these changes are not substantial enough to make group c significantly different compared to group b (fig. 3). the fact that the introduction of exercise didn’t appear to lead to substantial changes in body mass and the biochemical profile of group c could be attributed to the specific exercise protocol employed in this study and its relatively limited duration (i.e. 9 weeks). indeed, there is evidence in literature that exercise of different intensity, frequency and duration can lead to different results in animal hdlinduced obesity models [20]. the levels of adiponectin were also not affected by hfd or exercise. adiponectin has been reported in literature to have a positive effect on bone properties by activating osteoblastogenesis and suppressing osteoclastogenesis, thus leading to increased bone mass [22]. however, the fact that the results of the present study didn’t reveal any statistically significant difference between groups with regards to adiponectin levels means that no relevant conclusion can be drawn. so far, the effect of exercise and diet on bone strength has been either inferred based on non-invasive measurements and/or computer modelling [23] or directly measured through in-vitro testing [19, 20, 24, 25]. the most commonly used testing techniques are three point bending and torsion which are typically used to measure the maximum sustained force [25] or moment [20], respectively as a measure of strength. these studies have indicated that obesity and exercise can affect both the structure and also the mechanical characteristics of bones [19, 23, 24]. assessing ultimate stress along with the maximum sustained force enables separating the effect of changes in geometry from changes in the actual material properties of bone tissue [19, 24]. in order to enable the calculation of ultimate stress from the measured fracture force, the cross-section of the specimens was considered to be elliptical with constant thickness [21]. this simplification was deemed to be necessary considering the small size of the samples. indeed, the longest cross-sectional distance was smaller than 3 mm. the results from biomechanical testing indicated that the morphology and mechanical strength of femurs was significantly affected by diet and exercise. in terms of morphology, hfd appears to increase the external dimensions of femur regardless of the exposure to exercise. however, the group that received hfd but was not exposed to exercise (group b) also appeared to have significantly lower bone thickness compared to the other two groups. these findings indicate that exercise tends to limit the hfd-induced loss of bone mass by increasing the thickness of the femurs’ cortical shell. interestingly though, this positive effect of exercise was not translated into increased ultimate stress. hence, both groups that received hfd had significantly lower ultimate stress relatively to control. no statistically significant difference was found in terms of fracture force or total energy. the aforementioned findings are in agreement with observations linking obesity to the loss of bone mass and osteopenia [7, 8]. high-fat diets in particular have been found to reduce the ability for calcium absorption with possible adverse effects on bone mineralization in growing animals [8]. an investigation of correlations between biomechanical parameters, body mass and biochemical measurements that was focused only on the mice that received hfd (i.e. groups b and c) revealed strong positive associations between fracture force and serum glucose and body mass. more specifically, the femurs of mice that, at the end of the protocol, had higher body mass or glucose levels were found to be stronger compared to mice with lower body mass or glucose levels. t i. doulamis et alii, frattura ed integrità strutturale, 40 (2017) 85-94; doi: 10.3221/igf-esis.40.08 93 one of the key limitations of the present study is the relatively small number of femurs that were included in the biomechanical testing. due to the small size of the samples a significant number was damaged during harvesting making it impossible to use them for testing. in conclusion, the results of this study suggest that exercise can partially reverse the detrimental effects of hfd on bone biomechanics by increasing the thickness of the femurs’ cortical shell and thus limiting the hfd-induced loss of bone mass. however, the aforementioned positive effect of exercise was not translated to increased bone strength. further in vitro/in vivo studies in experimental models and clinical trials are required to unveil the effect of hfd and exercise on bone metabolism and strength. references [1] haslam, d.w., james, w.p.t., obesity, lancet, london, england, 366 (2005) 1197–209. [2] berrington de gonzalez, a., hartge, p., cerhan, j.r., flint, a.j., hannan, l., macinnis, r.j., et al., body-mass index and mortality among 1.46 million white adults, n engl j med, 363 (2010) 2211–2219. [3] berghöfer, a., pischon, t., reinhold, t., apovian, c.m., sharma, a.m., willich, s.n., obesity prevalence from a european perspective: a systematic review, bmc public health, 8 (2008) 200. [4] van coeverden, s.c., de ridder, c.m,, roos, j.c., van’t hof, m.a., netelenbos, j.c., delemarre-van de waal, h.a., pubertal maturation characteristics and the rate of bone mass development longitudinally toward menarche, j bone miner res, 16 (2001) 774–781. [5] schwartz, a.v., diabetes mellitus: does it affect bone?, calcif tissue int., 73 (2003) 515–519. [6] felson, d.t., zhang, y., hannan, m.t., anderson, j.j., effects of weight and body mass index on bone mineral density in men and women: the framingham study, j bone miner res, 8 (1993) 567–573. [7] patsch, j.m., kiefer, f.w., varga, p., pail, p., rauner, m., stupphann, d., et al., increased bone resorption and impaired bone microarchitecture in short-term and extended high-fat diet-induced obesity, metabolism, 60 (2011) 243–249. [8] wohl, g.r., loehrke, l., watkins, b.a., zernicke, r.f., effects of high-fat diet on mature bone mineral content, structure, and mechanical properties, calcif tissue int, 63 (1998) 74–79. [9] reid, i.r., plank, l.d., evans, m.c., fat mass is an important determinant of whole body bone density in premenopausal women but not in men, j clin endocrinol metab, 75 (1992) 779–782. [10] barondess, d.a., nelson, d.a., schlaen, s.e., whole body bone, fat, and lean mass in black and white men, j bone miner res, 12 (1997) 967–971. [11] trayhurn, p., beattie, j.h., physiological role of adipose tissue: white adipose tissue as an endocrine and secretory organ, proc nutr soc, 60 (2001) 329–339. [12] díez, j.j., iglesias, p., the role of the novel adipocyte-derived hormone adiponectin in human disease, eur j endocrinol, 148 (2003) 293–300. [13] lihn, a.s., pedersen, s.b., richelsen, b., adiponectin: action, regulation and association to insulin sensitivity, obes rev, 6 (2005) 13–21. [14] gavrila, a., chan, j.l., yiannakouris, n., kontogianni, m., miller, l.c., orlova, c., et al. serum adiponectin levels are inversely associated with overall and central fat distribution but are not directly regulated by acute fasting or leptin administration in humans: cross-sectional and interventional studies, j clin endocrinol metab, 88 (2003) 4823–4831. [15] buettner, r., schölmerich, j., bollheimer, l.c., high-fat diets: modeling the metabolic disorders of human obesity in rodents, obesity (silver spring) 15 (2007) 798–808. [16] nikander, r., sievänen, h., heinonen, a., daly, r.m., uusi-rasi, k., kannus, p., targeted exercise against osteoporosis: a systematic review and meta-analysis for optimising bone strength throughout life, bmc med, 8 (2010) 8:47. [17] shimano, r.c., macedo, a.p., falcai, m.j., ervolino, e., shimano, a.c., issa, j.p.m., biomechanical and microstructural benefits of physical exercise associated with risedronate in bones of ovariectomized rats, microsc res tech, 77 (2014) 431–438. [18] gerbaix, m., metz, l., mac-way, f., lavet, c., guillet, c., walrand, s., et al., a well-balanced diet combined or not with exercise induces fat mass loss without any decrease of bone mass despite bone micro-architecture alterations in obese rat, bone, 53 (2013) 382–390. [19] miyagawa, k., kozai, y., ito, y., furuhama, t., naruse, k., nonaka, k., et al., a novel underuse model shows that inactivity but not ovariectomy determines the deteriorated material properties and geometry of cortical bone in the tibia of adult rats, j bone miner metab, 29 (2011) 422–436. i. doulamis et alii, frattura ed integrità strutturale, 40 (2017) 85-94; doi: 10.3221/igf-esis.40.08 94 [20] macedo, a.p., shimano, r.c., ferrari, d.t., issa, j.p.m., jordão, a.a., shimano, a.c., influence of treadmill training on bone structure under osteometabolic alteration in rats subjected to high-fat diet, scand j med sci sports, 27 (2017) 167–176. [21] mandi, j.l., markel, d.m., bending tests of bones. in: an, y., draughn, r., editors, mechanical testing of bone and thew bone-implant interface, boca raton: crc press, (2000) 207–217. [22] oshima, k., nampei, a., matsuda, m., iwaki, m., fukuhara, a., hashimoto, j., et al., adiponectin increases bone mass by suppressing osteoclast and activating osteoblast, biochem biophys res commun, 331 (2005) 520–526. [23] woo, d.g., lee, b.y., lim, d., kim, h.s., relationship between nutrition factors and osteopenia: effects of experimental diets on immature bone quality, j biomech, 42 (2009) 1102–1107. [24] fried, a., manske, s.l., eller, l.k., lorincz, c., reimer, r.a., zernicke, r.f., skim milk powder enhances trabecular bone architecture compared with casein or whey in diet-induced obese rats, nutrition, 28 (2012) 331–335. [25] lambert, j., lamothe, j.m., zernicke, r.f., auer, r.n., reimer, r.a., dietary restriction does not adversely affect bone geometry and mechanics in rapidly growing male wistar rats, pediatr res, 57 (2005) 227–231. << /ascii85encodepages false /allowtransparency false /autopositionepsfiles true /autorotatepages /none /binding /left /calgrayprofile (dot gain 20%) /calrgbprofile (srgb iec61966-2.1) /calcmykprofile (u.s. web coated \050swop\051 v2) /srgbprofile (srgb iec61966-2.1) /cannotembedfontpolicy /error /compatibilitylevel 1.4 /compressobjects /tags /compresspages true /convertimagestoindexed true /passthroughjpegimages true /createjobticket false /defaultrenderingintent /default /detectblends true /detectcurves 0.0000 /colorconversionstrategy /cmyk /dothumbnails false /embedallfonts true /embedopentype false /parseiccprofilesincomments true /embedjoboptions true /dscreportinglevel 0 /emitdscwarnings false /endpage -1 /imagememory 1048576 /lockdistillerparams false /maxsubsetpct 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/hrv (za stvaranje adobe pdf dokumenata najpogodnijih za visokokvalitetni ispis prije tiskanja koristite ove postavke. stvoreni pdf dokumenti mogu se otvoriti acrobat i adobe reader 5.0 i kasnijim verzijama.) /hun 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can be opened with acrobat and adobe reader 5.0 and later.) >> /namespace [ (adobe) (common) (1.0) ] /othernamespaces [ << /asreaderspreads false /cropimagestoframes true /errorcontrol /warnandcontinue /flattenerignorespreadoverrides false /includeguidesgrids false /includenonprinting false /includeslug false /namespace [ (adobe) (indesign) (4.0) ] /omitplacedbitmaps false /omitplacedeps false /omitplacedpdf false /simulateoverprint /legacy >> << /addbleedmarks false /addcolorbars false /addcropmarks false /addpageinfo false /addregmarks false /convertcolors /converttocmyk /destinationprofilename () /destinationprofileselector /documentcmyk /downsample16bitimages true /flattenerpreset << /presetselector /mediumresolution >> /formelements false /generatestructure false /includebookmarks false /includehyperlinks false /includeinteractive false /includelayers false /includeprofiles false /multimediahandling /useobjectsettings /namespace [ (adobe) (creativesuite) (2.0) ] /pdfxoutputintentprofileselector /documentcmyk /preserveediting true /untaggedcmykhandling /leaveuntagged /untaggedrgbhandling /usedocumentprofile /usedocumentbleed false >> ] >> setdistillerparams << /hwresolution [2400 2400] /pagesize [612.000 792.000] >> setpagedevice microsoft word numero_53_art_01_2631 l. hadid et alii, frattura ed integrità strutturale, 53 (2020) 1-12; doi: 10.3221/igf-esis.53.01 1 finite element analysis of the interface defect in ceramic-metal assemblies: alumina-silver lamia hadid lmpm, mechanical engineering department, university of sidi bel abbes, sidi bel abbes 22000, algeria l.hadid@outlook.fr , http://orcid.org/0000-0002-9628-193x farida bouafia lmpm, mechanical engineering department, university of sidi bel abbes, sidi bel abbes 22000, algeria mechancal engineering department, university centre of ain temouhent 46000, algeria fbouafia2011@yahoo.fr , http://orcid.org/0000-0002-1695-1500 boualem serier lmpm, mechanical engineering department, university of sidi bel abbes, sidi bel abbes 22000, algeria boualems@yahoo.fr, http://orcid.org/0000-0002-1460-9322 sardar sikandar hayat* department of physics, international islamic university, islamabad 44000, pakistan sikandariub@yahoo.com, https://orcid.org/0000-0001-6018-7354 abstract. in the present work, the finite element analysis was employed to study the distribution of mechanical stress generated in metal-ceramic bimaterial. a micromechanical model is proposed to explain a phenomenon of defect observed in the metal-ceramic interface. the distribution of this stress in the ceramic around this defect was the subject of a numerical analysis using the finite element method. the analysis has been extended to the effect of defect-defect interaction, defect size and form. keywords. finite element method; mechanical stress; defects; interface; metal; ceramic. citation: hadid, l., bouafia, f., serier, b., sikandar hayat, s., finite element analysis of the interface defect in ceramic-metal assemblies: alumina-silver, frattura ed integrità strutturale, 53 (2020) 1-12. received: 06.09.2019 accepted: 27.04.2020 published: 01.07.2020 copyright: © 2020 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. introduction etal-ceramic bi-materials offer superior properties over conventional alloys and have been widely studied because of their many potential applications. ceramics such as zirconia, silicon carbides, silicon nitrides and alumina find a great number of applications in the field of mechanics and thermo-mechanics. the alumina remains practically the technical most current ceramics. in addition to the mechanical applications, it also gains first place m https://youtu.be/i54vm8zkc-a l. hadid et alii, frattura ed integrità strutturale, 53 (2020) 1-12; doi: 10.3221/igf-esis.53.01 2 in the electronics industry and electro-technical due to its interesting electrical properties such as great resistivity, significant dielectric constant and weak dielectric loss factor. very often to benefit the maximum of these advantages, it is necessary to bind ceramics and more particularly alumina with metals and their alloys. under the simultaneous action of the temperature and the elaboration constraint of the bimaterial, the metal deforms plastically and becomes encrusted in the roughness defects of the ceramic. this incrustation leads to a good mechanical attachment between these two protagonists and ensures very good adhesion between metal and ceramic. the joining of ceramics with metals is inherently difficult because of their distinctly different properties. during recent past years, considerable studies have been devoted to the technology development of ceramic/metal joining. it has been led to significant successes [1]. dissimilar materials need to be joined together in many technical areas. one example of the ceramic to metal joint combines the wear resistance, high temperature strength and thermal or electrical resistance of the ceramic with the ductility of the metal. due to the difference of the elastic properties and the thermal expansion coefficients of the ceramic and metal, high stresses occur at the intersection of edges which leads the interface of the joint under mechanical or thermal loading [2-3]. the joining of ceramics with metals is a critically important technology for the effective use of advanced materials [4]. metal-ceramic interfaces have wide applications, and the interface fractures play an important role in determining mechanical behaviours of related structures [5]. the study of the interface separation behaviours of interfaces with the atomic vacancy and dislocations indicates that the interface strength decreases for the interfaces with defects, and the defects decrease the catastrophic tendency [5]. joining dissimilar materials implies property mismatches and structure discontinuities [6]. interfaces must typically sustain mechanical and thermo-elastic stresses without failure. consequently, they exert an important influence on the performance of the material [7-8]. due to differences in thermal and mechanical properties, the stresses and strains can develop near a ceramic-metal interface stress concentration. this can result in the plastic deformation of metal during both fabrication and under subsequent thermal or mechanical loading (cracking within the ceramic). tremendous efforts have been made to understand these phenomena [7–12]. nevertheless, the effects of material properties and specimen geometry on stress and strain distributions, and fracture mechanisms are reasonably well understood. the realization of silver-alumina junction is made in solid state. the mechanical resistance of this assembly depends primarily on the conditions of its elaboration, particularity on the atmosphere of elaboration. the fracture resistance is generally determined according to the nature of the elaboration the atmosphere of this kind of junctions [12–14]. silver is a noble metal and reacting with the alumina does not give an intermediate compound. the assembly of this metal in alumina form no-reactive junction. the objective of this study is to numerically analyse silver-alumina junction by the finite element method. the effect of the interface defect between the metal and ceramic on the stress level has been studied in this work. finite element model he finite element model is already explained in our previous work [15-17]; however, salient features of the model which is used in this work are discussed here. a three-dimensional finite element analysis is developed for this investigation. a 2–d schematic view of the metal / ceramic bi-materials with an interface defect is shown in fig. 1(a). one half of the model is selected as the analysis model (because of the symmetry) in order to reduce the calculation time (see fig. 1(b)). the geometrical characteristics of the structure are the length l (l=350 µm), the width w and the thickness (e1 and e2) such as l/e1 = 7, e2/e1 = 6, l/w = 2. the plate is subjected to a uniformly distributed tensile load with p = 70 mpa. the diameter of the interface defect is 50 µm which characterize an average size of interface defect site. these defects are simulated with half-spherical cavities located at alumina interface with well-defined size ((see fig. 1(e)). numerical modelling has been taken using the abaqus [18] finite element program. the precision of numerical computation is strongly related to the quality of the mesh in the structure. additionally, due to the stress concentrations expected at the metal/ceramic interface, the mesh is refined at this zone and a 4-node linear tetrahedron (c3d4) finite element is used for the model (see fig. 1(c)). the finite element model with 75801 elements is shown in fig. 1(c). it has a fine grid at the metal/ceramic interface. the refinement of the mesh also shows its influence on the accuracy of numerical results, and number of elements higher than 75801 leads to similar and much more precise values (fig. 2). the surface between the metal and the ceramic is defined as the surface to surface contact (perfect surface). here, the ceramic has been selected as a slave and the metal as a master surface. t l. hadid et alii, frattura ed integrità strutturale, 53 (2020) 1-12; doi: 10.3221/igf-esis.53.01 3 silver bonded to alumina is selected in this study. pure silver is defined as an elastic plastic material (fig. 3) with a value of the modulus of elasticity e = 81.90 gpa and poisson's ratio ν = 0.31. the behaviour of alumina is considered as an isotropic elastic material. alumina is assumed to be elastic with modulus of elasticity value e= 390 gpa and poisson’s ratio ν = 0.25. figure 1: (a) a 2–d schematic view of metal/ceramic with the site of interface defect, (b) geometry of model, (c) finite element mesh, (d) boundary condition and loading condition and (e) site of interface defect-defect interaction. figure 2: effect of mesh size convergence on ceramic/defect interface for p = 70 mpa. path1 uz=0 p p (d) d (e) (a) (b) (c) metal ceramic defect y x e1 e2 l interface defect l. hadid et alii, frattura ed integrità strutturale, 53 (2020) 1-12; doi: 10.3221/igf-esis.53.01 4 figure 3: the true stress-strain curve of pure silver [19]. results and discussion he simultaneous action of the pressure and temperature (thermo-compression) during the elaboration of connecting ceramics-metal involves a plastic flow of the metal. the plastic flow speed of deformation is overall high as these two physical parameters are significant. this plastic flow leads to a friction interface between ceramics and metal. thus involve a significant wrenching of the surface grains of alumina contact. in this context, here the results are discussed to numerically analyse the stress distribution near the interface defect using tridimensional the finite element method. figure 4: von-mises equivalent and normal stress distribution for p = 70 mpa. stresses distribution the distribution of normal and von mises equivalent stresses for the silver and alumina near the interface defect during the preparation of their junction is represented in fig. 4. the normal stress induced along the x-direction is highly concentrated on the metal at the interface near the edge of the connection, while the volume of silver is in the opposite direction of this site (see fig. 4(b)). the stress generated along the z-direction is on the same level and its distribution is comparable to that induced following the first axis (x-axis) of the assembly (see fig. 4(d)). the normal stress along the yt l. hadid et alii, frattura ed integrità strutturale, 53 (2020) 1-12; doi: 10.3221/igf-esis.53.01 5 axis, which is the axis of application of mechanical loading, is at a much higher level than the other two normal stresses, which are highly concentrated for the alumina and silver in the neighborhood near the defect (see fig. 4(c)). the von mises equivalent stress is highly concentrated near the site. its distribution reflects the normal stresses (see fig. 4(a)). the illustrations of results in fig. 4 clearly show that the defect is at a special place of stress concentration by notch effect. effect of loading fig. 5 shows the variation of normal stresses for the ceramic and metal near the defect as a function the normalized distance (x-values correspond to each point’s distance along the path as a fraction of the total length of the path (see fig.1d)) and according to the applied mechanical load. these stresses are heavily concentrated around the interfacial defects. interfacial defects effects are increased with increasing applied stress. this type of loading compresses the cavity along xand z-direction. the compression ratio becomes higher when the intensity of loading increases. these stresses vanish for the defect. stresses along the y-direction of mechanical stress set the cavity in tension. the intensity of these stresses holds more importance than those for the other two axes of the structure. the variation of von mises stresses around the defect as a function of the applied stress is shown in fig. 5(a). the analysis of this figure clearly shows that the presence of this defect on the surface of the ceramic-related metal plays a leading role of stress concentration, whose intensity increases with the increase in mechanical loading of the junction. figure 5: variation of equivalent and normal stresses according to mechanical loading. effect of defect size the size of interfacial defect does not merely determine the distribution and the level of the stresses of this defect, nevertheless, also measures the surface of effective adhesion. its analysis carries great importance for the performance and the mechanical resistance of the junction. fig. 6 illustrates the variation of induced normal stresses nearby to the defect applying a mechanical stress as a function of its diameter. this figure shows that large defects induce more significant 0,0 0,2 0,4 0,6 0,8 1,0 0 20 40 60 80 100 (a) s eq ui ( m p a) normalize distance p = 50 mpa p = 70 mpa p = 100 mpa 0.0 0.2 0.4 0.6 0.8 1.0 0 20 40 60 80 100 (c) s y y ( m p a) normalize distance p = 50 mpa p = 70 mpa p = 100 mpa 0.0 0.2 0.4 0.6 0.8 1.0 -100 -80 -60 -40 -20 0 20 40 interface ceramic/defect i n te rf a ce m e ta l/d e fe ct (b) s x x ( m p a) normalize distance p = 50 mpa p = 70 mpa p = 100 mpa 0.0 0.2 0.4 0.6 0.8 1.0 -80 -60 -40 -20 0 20 40 (d) s z z ( m p a) normalize distance p = 50 mpa p = 70 mpa p = 100 mpa normalized distance normalized distance normalized distance normalized distance l. hadid et alii, frattura ed integrità strutturale, 53 (2020) 1-12; doi: 10.3221/igf-esis.53.01 6 stresses. these results show that the stress concentration increases proportionally with the increase of the defect size to reach the maximum value for the biggest size. such a behaviour can present a risk of decoherence of the junction. the site of the interface defect (seat of stress concentration) is a privileged place of initiation and propagation of cracks. . figure 6: variation of mechanical stresses according to a defect size in metal/defect interface for p = 70 mpa the variation of stress concentration factor as a function of the interface defect size is represented in fig. 7. this figure well illustrates that this factor varies almost linearly with the variation in size. this clearly shows that the presence of large defects on the surface of the ceramic can lead to the initiation and the propagation of cracks and consequently to the damage of alumina-silver assembly by cohesive or adhesive rupture depending the mechanical strength of the interface. thus, they are able to lead to a cohesive or adhesive rupture, according with the resistance. figure 7: variation of stress concentration factor according to a defect size for p = 70 mpa. stresses distribution around the defect the level of stresses around the site of interface defect exploits a dominating role in the start-up and the performance of the ceramics-metal junction. its analysis carries great importance for the mechanical resistance and the durability of this junction. figs. 8(b), 8(c) and 8(d) represent the distribution of induced normal stresses according to three axes of the structure along the perimeter (path 2) of the interfacial defect (see fig. 8(a)). the analysis of this figure shows that according to the x-direction, at the ends, i.e. in the vicinity of the interface with metal, (when θ < 20°) the defect is subject to the normal stresses of tension, and far from this zone to compressive stresses. along the direction of applied load, which is y60 80 100 120 140 160 180 200 -150 -100 -50 0 50 100 150 m ec ha ni ca l s tr es s (m p a) defect size (m) s equi s xx s yy defect size 60 80 100 120 140 160 180 200 2.5 3.0 3.5 4.0 4.5 5.0 s tr es s c on ce nt ra ti on f ac to r (k t) defect size (m) size l. hadid et alii, frattura ed integrità strutturale, 53 (2020) 1-12; doi: 10.3221/igf-esis.53.01 7 direction, the normal stresses of tension are higher at the defect/metal interface (when θ = 0° and θ = 180°) and very low in the zone far from the plane of the alumina-silver junction (when θ = 90°) (see fig. 8(c)). a contrary behaviour is observed along the z-direction; indeed, the compression stresses are intensively concentrated in ceramics,(when θ = 90°), while their level decreases considerably in the mid of this interface (when θ = 0° and θ = 180°) (see fig. 8(d)). the tangential stresses are most significant specific to the xoy planes of the assembly. the highest stresses are localized at θ = 45° and 135° (see fig. 8(e)). figure 8: variation of equivalent, normal and shear stresses according to peripheral angle and mechanical loading. effect of defect geometry the effect of the defect form, which is defined by the x/y ratio, is analysed, and the effect of the defect volume on the distribution of equivalent and normal stresses near to the interface with metal is characterized. this analysis is made for an invariable size x along path 1 (see fig. 1). the obtained results are represented in figs. 9 and 10. path2 0o 180o metal ceramic 0 30 60 90 120 150 180 -15 -10 -5 0 5 10 15 (e) s x y ( m p a) peripheral angle  p = 50 m pa p = 70 m pa p = 100 mpa 0 30 60 90 120 150 180 -50 -40 -30 -20 -10 0 10 20 (b) s x x ( m p a) peripheral angle  p = 50 mpa p = 70 mpa p = 100 mpa 0 30 60 90 120 150 180 0 40 80 120 160 (a) s eq ui ( m p a) peripheral angle  p = 50 mpa p = 70 mpa p = 100 mpa 0 30 60 90 120 150 180 0 30 60 90 120 150 180 (c) s y y ( m p a) peripheral angle  p = 50 mpa p = 70 mpa p = 100 mpa 0 30 60 90 120 150 180 -50 -40 -30 -20 -10 0 10 (d) s z z ( m p a) peripheral angle  p = 50 mpa p = 70 mpa p = 100 mpa l. hadid et alii, frattura ed integrità strutturale, 53 (2020) 1-12; doi: 10.3221/igf-esis.53.01 8 figure 9: variation of equivalent and normal stresses depending on defect geometry in metal. the influence of the parameter y on the level of the normal stresses is generated in the silver along xand zdirection of the junction. along these directions and far from the interface, the metal is in tension, whereas in its close vicinity it is in compression. the intensity of these stresses increases with the volume of interface defect (see figs. 9(a) and 9(c)). along the y-axis, which is the direction of mechanical load application, the normal stresses decrease approaching the interface with ceramics. an increase in the x/y ratio involves a light amplification of these stresses. their amplitude is annulled in the plane of the junction (see fig. 9(b)). the von mises equivalent stress in the metal gradually decreases towards the interface with alumina, then grows slightly near to this defect. this stress is overall more significant as the x/y ratio increases (see fig. 9(d)). the distribution and level of the von mises and normal stresses induced in alumina as a function of the x/y ratio are represented in fig. 10. the induced normal stresses along xand z-direction seems not to dependent on the shape of the interface defect. indeed, the intensity of these stresses practically does not vary with the variation in the x/y ratio (see figs. 10(b) and 10(d)). an increase in the x/y ratio involves an increase in the von mises and y-direction normal stresses generated in the vicinity of interface defect (see figs. 10(a) and 10(c)). the effect of the defect shape on the distribution of equivalent stress and its intensity is analysed in terms of stress concentration factor (see fig. 11). this figure shows that the decrease in the parameter involves a high stress concentration factor. the interface defect having such a form is the seat of stress concentration. effect of defect-defect interaction the previously obtained results show that the alumina defect is a privileged place of stress concentration whose level and distribution does not merely depend on its size, but also on its form. however, several grains are snatched by interfacial friction between these two components during the realization of metal-ceramics junction. these sites are represented by interfacial defects of spherical symmetry. this is why, an analysis of the effect of defect-defect interaction at the interfacial 0.0 0.2 0.4 0.6 0.8 1.0 0 10 20 30 40 50 60 70 80 (c) s y y ( m p a) normalize distance x/y =2 x/y =4 x/y =6 0.0 0.2 0.4 0.6 0.8 1.0 -30 -20 -10 0 10 20 30 (b) s x x ( m p a) normalize distance x/y =2 x/y =4 x/y =6 0,0 0,2 0,4 0,6 0,8 1,0 10 20 30 40 50 60 (a) interface metal/defect metal s eq ui ( m p a) normalize distance x/y =2 x/y =4 x/y =6 0,0 0,2 0,4 0,6 0,8 1,0 -30 -20 -10 0 10 20 30 (d) s z z ( m p a) normalize distance x/y =2 x/y =4 x/y =6 normalized distance normalized distance normalized distance normalized distance l. hadid et alii, frattura ed integrità strutturale, 53 (2020) 1-12; doi: 10.3221/igf-esis.53.01 9 level and the distribution of stresses is carried out. the so obtained results are illustrated in fig. 12. this last one shows the variation of von mises and normal stresses according to the distance separating the sites from two defects. figure 10: variation of equivalent and normal stresses according to defect geometry in ceramic. figure 11: variation of stress concentration factor according to defect geometry. 2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5 6.0 1.0 1.5 2.0 2.5 s tr es s c on ce nt ra ti on f ac to r (k t) ratio x/y 0,0 0,2 0,4 0,6 0,8 1,0 40 50 60 70 80 90 (a) ceramic i n te rf a c e c e ra m ic /d e fe c t s eq ui ( m p a) normalize distance x/y =2 x/y =4 x/y =6 0.0 0.2 0.4 0.6 0.8 1.0 -70 -60 -50 -40 -30 -20 -10 0 10 (b) s x x ( m p a) normalize distance x/y =2 x/y =4 x/y =6 0.0 0.2 0.4 0.6 0.8 1.0 -10 0 10 20 30 40 50 60 70 (c) s y y ( m p a) normalize distance x/y =2 x/y =4 x/y =6 0.0 0.2 0.4 0.6 0.8 1.0 -70 -60 -50 -40 -30 -20 -10 0 10 (d) s z z ( m p a) normalize distance x/y =2 x/y =4 x/y =6 normalized distance normalized distance normalized distance normalized distance l. hadid et alii, frattura ed integrità strutturale, 53 (2020) 1-12; doi: 10.3221/igf-esis.53.01 10 figure 12: variation of internal equivalent and normal stresses according to the defect-defect interaction for p = 70 mpa. the stress intensity induced along the xand z-direction of the assembly grows with the reduction in the defectdefect interdistance. indeed, bringing together these two defects leads to the intensification of these stresses. these last tend towards their maximum level when the sites of the interface defect are very close to the other one (see figs. 12(b) and 12(c)). a tendency of an interfacial defect towards the other involves an amplification of the normal stresses which are generated along the y-direction which is requested by the external mechanical loads. two defects are close neighbors which generate much more intense normal stresses, whose level is approximately twice more significant than that of the load applied (see fig. 12(c)). the tangential stresses are most significantly related to the plane (x, o, y) of the structure. the level of these stresses grows with the reduction in the defect-defect inter-distance. maximum sites of the interface defect are close to each other and the shear stresses induced in this plane are strong (see fig. 12(e)). fig. 12(a) shows the effect of -0.10 -0.05 0.00 0.05 0.10 20 30 40 50 60 (d) s z z ( m p a) distance (mm) d1=25 m d2=40 m d3=100 m d4=160 m -0.10 -0.05 0.00 0.05 0.10 -40 -30 -20 -10 0 10 20 30 (e) s x y ( m p a) distanc (mm) d1=25 m d2=40 m d3=100 m d4=160 m d -0,10 -0,05 0,00 0,05 0,10 60 80 100 120 140 (a) s eq ui ( m p a) distance (mm) d1=25 m d2=40 m d3=100 m d4=160 m -0.10 -0.05 0.00 0.05 0.10 20 30 40 50 60 70 (b) s x x ( m p a) distance (mm) d1=25 m d2=40 m d3=100 m d4=160 m -0.10 -0.05 0.00 0.05 0.10 60 80 100 120 140 160 (c) s y y ( m p a) distance (mm) d1=25 m d2=40 m d3=100 m d4=160 m d (x, y, z)= (0, 0, 0) l. hadid et alii, frattura ed integrità strutturale, 53 (2020) 1-12; doi: 10.3221/igf-esis.53.01 11 this inter-distance on the amplitude of von mises stress. this figure shows that bringing together these sites leads to the strong intensification of equivalent stress. the results obtained in this analysis clearly show that the distance separating the sites from the defect with the metal determines the level and distribution of the stresses induced with their interface. indeed, the more these sites are close to each others, the more their stress field is reacting between them. thus, the amplification of these constraints is involved with the effect of the interaction. this effect is dominated when the vicinity sites are very close to each other. the distance of one of these sites compared to the others minimizes the effect of the interaction. this finally is annulled when the sites of the interface defect are very far from each other, then their stress fields are isolated from each other. conclusions n the present work, 3-dimensional finite element method was used to investigate the effects of the defect in metal– ceramic bimaterial. the results obtained in this study allow us to draw the following conclusions: the sites of interface defect during the elaboration by interfacial friction with the silver are the privileged places of stress concentration by notch effect. the level and the distribution of the normal, tangential and the von mises equivalent stresses are not dependent merely on the intensity of the mechanical loading, nevertheless, also on the size of the sites of interface defect (characteristic of the site volume). these stresses are overall higher as the volume of this site grows. the stress concentration factor grows with the increase in the volume. thus, the coarse interface defects do concentrate more stresses relative to the small ones. the form which is defined by the x/y ratio of this defect plays a role to determine the level of the von mises and normal stresses. a small ratio involves an increase in the induced normal stresses of the silver, relating to the xand z-direction of the assembly, while a reduction of the normal stress relating to the y-axis. the von mises stress is overall weak as the x/y ratio is small. in alumina, the normal stresses generated along xand z-axes of the structure seem not dependent on the form of the site of interface defect. in this component, the stress induced according to the direction is not very sensitive to the form of this site. the von mises stress grows with the increase in x/y ratio. the stress concentration factor decreases with the increase of this ratio. the intensity and the distribution of the normal, tangential and equivalent stress depend on the defect-defect interdistance. bringing together these sites one towards the other, lead to an intensification of these constraints. these stresses are overall higher as the defects are very close to each other. references [1] boutabout, b., chama, m., bouiadjra, b.a.b., serier, b., lousdad, a. (2009). effect of thermomechanical loads on the propagation of crack near the interface brittle/ductile, comput. mater. sci., 46(4), pp. 906–911. doi: 10.1016/j.commatsci.2009.04.039. [2] yang, y.y., munz, d. (1997). stress singularities in a dissimilar materials joint with edge tractions under mechanical and thermal loadings, int. j. solids struct., 34(10), pp. 1199–1216. doi: 10.1016/s0020-7683(96)00097-2. [3] nikbakt, s., kamarian, s., shakeri, m. (2018). a review on optimization of composite structures part i: laminated composites, compos. struct., 195, pp. 158–185. doi: 10.1016/j.compstruct.2018.03.063. [4] williamson, r.l., rabin, b.h., byerly, g.e. (1995). fem study of the effects of interlayers and creep in reducing residual stresses and strains in ceramic-metal joints, compos. eng, 5(7), pp. 851–863. doi: 10.1016/0961-9526(95)00035-l. [5] you, x.m., liang, l.h., wei, y.g. (2018). the atomistic simulation study of ag/mgo interface tension fracture, comput. mater. sci., 142, pp. 277–284. doi: 10.1016/j.commatsci.2017.10.029. [6] nascimento, r.m. do., martinelli, a.e., buschinelli, a.j.a. (2003). review article: recent advances in metal-ceramic brazing, cerâmica, 49(312), pp. 178–198. doi: 10.1590/s0366-69132003000400002. [7] li, v. (2004). fracture mechanics of concrete structures: proceedings of the fifth international conference on fracture mechanics of concrete and concrete structures, vail colorado, {usa}, april 12 16. [8] drake, j.t., williamson, r.l., rabin, b.h. (1993). finite element analysis of thermal residual stresses at graded ceramic/metal interfaces, part ii: optimization for residual stress reduction, j. appl. phys., 74(2), pp. 1321-1326. doi:10.1063/1.354911. i l. hadid et alii, frattura ed integrità strutturale, 53 (2020) 1-12; doi: 10.3221/igf-esis.53.01 12 [9] gill, s.c., clyne, t.w. (1990). stress distributions and material response in thermal spraying of metallic and ceramic deposits, metall. trans. b, 21(2), pp. 377–385. doi: 10.1007/bf02664205. [10] suganuma, k., miyamoto, y., koizumi, m. (1988). joining of ceramics and metals, annu. rev. mater. sci., 18(1), pp. 47–73. doi: 10.1146/annurev.ms.18.080188.000403. [11] evans, a. g., dalgleish, b. j. (1993). the fracture resistance of metal-ceramic interfaces, materials science and engineering: a, 162(1-2), 1–13. doi: 10.1016/0921-5093(90)90025-x. [12] elssner, g., petzow, g. (1990). metal/ceramic joining, isij int., 30(12), pp. 1011–1032. doi: 10.2355/isijinternational.30.1011. [13] serier, b. (1991). etude et caractérisation des liaisons céramique-mètal élaborées par solid state bonding, application au couple ag/al2o3. available at: http://www.theses.fr/1991ecdl0019. [14] sérier, b., berroug, a., juvé, d., tréheux, d., moya, e.g. (1993). silver-alumina solid state bonding: study of diffusion and toughness close to the interface, j. eur. ceram. soc., 12(5), pp. 385–390. doi: 10.1016/0955-2219(93)90008-f. [15] fekirini, h., serier, b., bouafia, f., bouiadjra, b.a.b., hayat, s.s., bouafia, s.a. (2012). effect of precipitate– precipitate interaction on residual stress in welded structure, comput. mater. sci., 65, pp. 207–215. doi: 10.1016/j.commatsci.2012.06.005. [16] souad, s., serier, b., bouafia, f., bouidjra, b.a.b., hayat, s.s. (2013). analysis of the stresses intensity factor in alumina–pyrex composites, comput. mater. sci., 72, pp. 68–80. doi: 10.1016/j.commatsci.2013.01.030. [17] bouafia, f., serier, b., serier, n., hayat, s.s. (2014). effect of density and pointed corner degree of pore on local stress in welded structures: defect in marine structures, isrn mech. eng., 2014, pp. 1–7. doi: 10.1155/2014/834659. [18] dassaut systèmes simulia corp-abaqus/cae 6.11 user’s manual. available at: https://www.3ds.com/productsservices/simulia. [19] huo, y., lee, c.c. (2016). the growth and stress vs. strain characterization of the silver solid solution phase with indium, j. alloys compd., 661, pp. 372–379. doi: 10.1016/j.jallcom.2015.11.212. << /ascii85encodepages false /allowtransparency false /autopositionepsfiles true /autorotatepages /none /binding /left /calgrayprofile (dot gain 20%) /calrgbprofile (srgb iec61966-2.1) /calcmykprofile (u.s. web coated \050swop\051 v2) /srgbprofile (srgb iec61966-2.1) /cannotembedfontpolicy /error /compatibilitylevel 1.4 /compressobjects /tags /compresspages true /convertimagestoindexed true /passthroughjpegimages true /createjobticket false /defaultrenderingintent /default /detectblends true /detectcurves 0.0000 /colorconversionstrategy /cmyk /dothumbnails false /embedallfonts true /embedopentype false /parseiccprofilesincomments true /embedjoboptions true /dscreportinglevel 0 /emitdscwarnings false /endpage -1 /imagememory 1048576 /lockdistillerparams false /maxsubsetpct 100 /optimize true /opm 1 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can be opened with acrobat and adobe reader 5.0 and later.) >> /namespace [ (adobe) (common) (1.0) ] /othernamespaces [ << /asreaderspreads false /cropimagestoframes true /errorcontrol /warnandcontinue /flattenerignorespreadoverrides false /includeguidesgrids false /includenonprinting false /includeslug false /namespace [ (adobe) (indesign) (4.0) ] /omitplacedbitmaps false /omitplacedeps false /omitplacedpdf false /simulateoverprint /legacy >> << /addbleedmarks false /addcolorbars false /addcropmarks false /addpageinfo false /addregmarks false /convertcolors /converttocmyk /destinationprofilename () /destinationprofileselector /documentcmyk /downsample16bitimages true /flattenerpreset << /presetselector /mediumresolution >> /formelements false /generatestructure false /includebookmarks false /includehyperlinks false /includeinteractive false /includelayers false /includeprofiles false /multimediahandling /useobjectsettings /namespace [ (adobe) (creativesuite) (2.0) ] /pdfxoutputintentprofileselector /documentcmyk /preserveediting true /untaggedcmykhandling /leaveuntagged /untaggedrgbhandling /usedocumentprofile /usedocumentbleed false >> ] >> setdistillerparams << /hwresolution [2400 2400] /pagesize [612.000 792.000] >> setpagedevice microsoft word numero_42_art_30.docx j.-m. nianga et alii, frattura ed integrità strutturale, 42 (2017) 280-292; doi: 10.3221/igf-esis.42.30 280 theoretical model of homogenized piezoelectric materials with small non-collinear periodic cracks jean-marie nianga, driss marhabi pôle de recherche « structures & matériaux », hautes etudes d’ingénieur – (hei), 13 rue de toul, 59046 lille cedex, france jean-marie.nianga@yncrea.fr abstract. an analytical model for the homogenization of a piezoelectric material with small periodic fissures is proposed on the basis of the method of asymptotic expansions for the elastic displacement, the electric scalar potential and the test functions. starting from the variational formulation of the three-dimensional problem of linear piezoelectricity, we have at first obtained that concerning a cracked piezoelectric structure, before the implementation of homogenized equations for a piezoelectric structure with a periodic distribution of cracks. it then follows, the characterization of the homogenized law between the mechanical strain and the electric potential, on one hand, and the mechanical stress and the electric displacement, on the other hand. contrary to the previous investigations, the focus of this paper is the development of a mathematical model taking the non-parallelism of cracks into account. keywords. piezoelectric material; asymptotic expansions; homogenization; variational formulation; periodic cracks. citation: nianga, j.-m., marhabi, d., theoretical model of homogenized piezoelectric materials with small noncollinear periodic cracks, frattura ed integrità strutturale, 42 (2017) 280-292. received: 01.02.2017 accepted: 04.07.2017 published: 01.10.2017 copyright: © 2017 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. introduction he piezoelectric materials are used in an increasing way in technological applications [1-3]. among the numerous problems which can arise, there is that concerning the global estimation of the homogenized characteristics of non-homogeneous materials, in particular those presenting a periodic distribution of singularities. significant efforts had been made to the study of periodical cracks in linear piezoelectricity, through an extension to piezoelectric materials of the modeling of periodic cracks in elastic materials [4, 5]. gao and al.[6] studied, in terms of the parton assumption and stroh formalism, the problem of a half-infinite crack in piezoelectric media with periodic crack; reducing it to hilbert one and getting therefore the closed-form solutions in the media and inside the cracks. wang and al. [7] provided a theoretical treatment of the dynamic interaction between cracks in a piezoelectric medium under anti-plane mechanical and in-plane electrical incident wave. they used fourier transform to study the dynamic electromechanical behavior of a single crack, and solved the obtained singular integral equations by chebyshev polynomials. the single crack solution was then implemented into a pseudo-incident wave method to account for the interaction between cracks. t j.-m. nianga et alii, frattura ed integrità strutturale, 42 (2017) 280-292; doi: 10.3221/igf-esis.42.30 281 somme years more-late, han and al. [8] obtained the development of a mathematical model to predict the length scale for the spacing of transverse cracks forming in a piezoelectric material subjected to a coupled electro-mechanical external loading condition. in particular, they analyzed the interactions of a row of cracks periodically located in a piezoelectric material layer. although, one of the remaining problems that need to be treated is that of a periodic array of non-collinear cracks. so, the present paper provides a theoretical model of homogenized piezoelectric materials with small non-collinear periodic cracks through an extension of previous works [9] and [10]. it is organized as follows: section 2 describes the variational formulation for the three-dimensional problem of linear piezoelectricity. section 3 develops a variational formulation for the problem of a fissured piezoelectric structure. in section 4, are presented the homogenized problem of a piezoelectric material with small periodic cracks. section 5 is then devoted to the formulation of the homogenized local problem in the homogenization period. the analysis of the relationship between the strain and the electric potential on one hand, and the stress and the electric field secondly, is presented in section 6, just above the conclusion. variational formulation for the three-dimensional problem of linear piezoelectricity et  be an open connected domain of 3 with smooth boundary  made of two parts 1 and  2  in the mechanical sense, and of 3  and 4  in the electrical one. these parts of  represent portions of regular surfaces with smooth common boundary, respectively. moreover,  may be divided into two parts by a smooth surface .s figure 1: representation of the open  . in the framework of linear piezoelectricity, the elastic and electric effects are coupled by the constitutive equations: k ij ijkl kij k j u a e e x      (1) k i ij j ikl l u d e e x      (2) where { }iu u is the elastic displacement, { }ij  is the symmetric stress tensor, { }ie e is the electric field vector, and { }id d is the electric displacement vector, with (i, j, k, l) = (1, 2, 3). we now assume that the elastic coefficients at zero elastic field ijkla , the piezoelectric coefficients kije and the dielectric constants ij at vanishing strain satisfy the following symmetry and positivity properties: ; ;ijkl jikl klij kij kji ij jia a a e e      (3) 0, , 0 :ij ij ji ijkl kl ij ij jie e e a e e e e     (4) l j.-m. nianga et alii, frattura ed integrità strutturale, 42 (2017) 280-292; doi: 10.3221/igf-esis.42.30 282 1 1, 0 :i ij j i i i           (5) where 1 and 0 are constants; a superimposed bar denoting the complex conjugate. but, under the quasi-electrostatic approximation [9], there exists an electric scalar potential  such that: i i e x     (6) moreover, if 0 0 0, ,j jt u w and 0 are prescribed values per unit area, the mechanical boundary conditions can be written as: 0 1j ij in t on    (7) 0 2j ju u on   (8) and the electric ones are in the following forms: 0 3i in d w on    (9) 40 on    (10) the piezoelectric plate is supposed to be clamped by 2 ;  and n represents the unit outer normal to . if the body force and extrinsic bulk charge are assumed to be negligible, and d are divergence-free, i.e. 0 ij j in x     (11) 0i i d in x     (12) on the other hand, we have:   0i ij ij sn on     (13)   0i i su u on    (14)   0 son     (15)   0i i i sn d d on    (16) the variational problem (vp) corresponding to eqs. (7) to (12) is obtained by introducing the following spaces:  1 02 2; ( ),i i iv u u h u u     (17) j.-m. nianga et alii, frattura ed integrità strutturale, 42 (2017) 280-292; doi: 10.3221/igf-esis.42.30 283  14 4; ( ), 0v h        (18) problem (vp): find 2 4( , )u inv v  such that: 0 2 1 0 4 4 ( , ) ( , ) ( , ) ( , ) a u v b v t v ds v v c d u w ds v                          (19) where ( , ) ( ) ( )ijkl kl ija u v a e u e v dv   (20) ( , ) iijk k j v b v e dv x x        (21) ( , ) ij j i c dv x x            (22) ( , ) kikl l i u d u e dv x x          (23) proposition1. problem (vp) is equivalent to eqs. (7) to (12). proof. (19)1 is obtained by multiplying (11) par a test function vi and by integrating by parts; taking into account the boundary conditions (7) and (8). by analogy, we obtain (19)2, by multiplying (12) par a test function  and by integrating by parts; taking into account the boundary conditions (9) and (10). the coefficients ijkla are assumed to be continuous on s . for the existence and uniqueness of the solution of problem (vp), see [9]. variational formulation for the problem of a fissured piezoelectric structure e now consider a piezoelectric structure containing a closed crack c, i.e. c c (24) where c is the closure of c, and where c is assumed to be smooth. let us introduce the open subset ,c verifying: c c    (25) the local equations of linear piezoelectricity for a fissured piezoelectric structure can then be written as follows [10]: 0 ij c j in x     (26) 0i c i d in x     (27) w j.-m. nianga et alii, frattura ed integrità strutturale, 42 (2017) 280-292; doi: 10.3221/igf-esis.42.30 284 0iu on  (28)   0i iu n on c (29) 0 on   (30)   0 on c  (31) , , , 11 2 ( ) ( ) ( )ijkl k l j kij k j ijkl k l j kij k j nnkl k l knn k ia u n e e n a u n e e n a u e e n on c      (32) , 0nnkl k l knn ka u e e on c  (33) 1 2 0i i i id n d n on c   (34) where n and n represent the unit normal to c, outer to its side 1, see (fig. 2), and the unit outer normal to the open domain ,c c    respectively. figure 2: representation of the fissured piezoelectric structure c . these relations express a compression on c according to (33), as well as the normality of the force which acts; with an opposition between the action and the reaction, according to (32). consequently, the variational formulation (fvp) for the problem of such a fissured piezoelectric structure can be stated as follows: problem (fvp): find * *( , ) uu inv v   such that: * * ( , ) ( , ) 0 ( , ) ( , ) 0 ua u v u b v u v v c d u v                       (35) where  1( ); ( ); 0u i i c iv u u u h u      (36)   * ( ); ; 0u ui i i iv u u u v u n    (37)  1; ( ); 0cv h        (38) j.-m. nianga et alii, frattura ed integrità strutturale, 42 (2017) 280-292; doi: 10.3221/igf-esis.42.30 285   * ; ; 0v v      (39) and where a, b, c, and d are bilinear forms on * * * * *, , ,u u uv v v v and v v    respectively. proposition2. problem (fvp) is equivalent to eqs. (26) to (34). the proof is analogous to that of proposition 1, by taking into account eqs. (29) and (31). homogenized equations-formal expansion e now consider a linear piezoelectric plate with a   periodic distribution of fissures, so that, the period y of 3 ,r admits a smooth fissure c verifying: c y   (40) figure 3: representation of the period y with a smooth fissure c. the fissured material denoted by c is then defined as follows:  1 2 3( , , );c cxx x x x y y y c         (41) and we assume that, there is no fissure intersecting the boundary  of the open . introducing the following spaces:  1( ); ( ); 0u i i c iv u u u h u       (42)   * ( ); ; 0u ui i i iv u u u v u n     (43)  1; ( ); 0cv h        (44)   * ; ; 0v v      (45) the corresponding variational formulation ( fvp ) of such a piezoelectric problem in ,c is then defined as follows: w j.-m. nianga et alii, frattura ed integrità strutturale, 42 (2017) 280-292; doi: 10.3221/igf-esis.42.30 286 problem ( fvp ): find * *( , ) uu inv v     such that: * * ( , ) ( , ) 0 ( , ) ( , ) 0 ua u v u b v u v v c d u v                             (46) in order to study the asymptotic behavior of the solution when  tends to zero, we use the classical following expansions, both for the unknown and the test functions: 0 1 2 2( ) ( ) ( , ) ( , ) ...u x u x u x y u x y      (47) 0 1 2 2( ) ( ) ( , ) ( , ) ...x x x y x y        (48) 0 1 2 2( ) ( ) ( , ) ( , ) ...v x v x v x y v x y      (49) 0 1 2 2( ) ( ) ( , ) ( , ) ...x x x y x y        (50) introducing the following spaces:  1( ); ( );uyc i i cv v v v h y y periodic    (51)  ( ); ; 0u uyc i ycv v v v v v     (52)   * ( ); ; 0u uyc i yc i iv v v v v v n on c    (53)  * *( ); ; 0u uyc i ycv v v v v v     (53)  1; ( );yc cv h y y periodic     (54)  ; ; 0yc ycv v       (55)   * ; ; 0yc ycv v      (56)  * *; ; 0yc ycv v       (57) comparing (47)-(50) with (46), we get the following relations: 0 0 1 1 0 00 0 1 1 11 0 0 1 10 0 ( ) ( ) ( ) ( ) ( ) ( ) j j j j j jk k k ijkl ijkl ijkl l i l i l i j jk i i i i ijkl ijk ijk l i k j k j v u v u v uu u u a dx a dx a dx x x x y y x v uu v u v u a dy e dx e y y x x x y                                                             0 0 1 11 1 0 1 1 3 0 ( ) ( ) 0; , ( ( ))i i i iijk ijk k j k j dx v u v u e dx e dy v v h y x y y                                                   (58) j.-m. nianga et alii, frattura ed integrità strutturale, 42 (2017) 280-292; doi: 10.3221/igf-esis.42.30 287 0 0 1 1 0 00 0 1 0 01 1 0 0 1 11 ( ) ( ) ( ) ( ) ( ) ( ) ij ij ij j i j i j i k k ij ikl ikl j i l i i i dx dx dx x x x y y x u u dy e dx e dx y y x x xl y e                                                                                            1 10 0 1 1 0 1 1 0 ( ) ( ) 0; , ( )k kkl ikl l i l i u u dx e dy h y x y y                                                 (59) with  represents the operator average defined on any y-periodic function f(y) by: 1 ( )f f y dyyy   (60) in the particular case where 1 1 1 1 ,v u and    we get: 0 00 1 0 00 1 0 1 1 3 0 ( ) ( ) 0; , ( ( )) j jk k i i ijkl ijk l l i k k j v uu u v u a dx e dx x y x x y x v v h                                         (61) 0 10 0 0 00 1 0 1 1 0 ( ) ( ) 0; , ( ) k k ij ikl j j i l l i u u dx e dx x y x x y x h                                               (62) consequently, the corresponding homogenized equations in which there are no more fissures then follow: 0 0 1 0 1 0 0 ij j k k ij ijkl ijk l l k k x u u a e x y x y                                      (63) and 0 0 10 1 0 0 i i k k i ij ikl j l l d x u u d e xj y x y                                 (64) j.-m. nianga et alii, frattura ed integrità strutturale, 42 (2017) 280-292; doi: 10.3221/igf-esis.42.30 288 homogenized local problem in the period y et us choose the fields 1 1v and  as: 1 1 1 * ( , ) ( , ) ( ) ( , ) ( ); 0 1; u u u u u u yc v x y u x y w y u x y d w v                  (65) 1 1 1 * ( , ) ( , ) ( ) ( , ) ( ); 0 1; yc x y x y w y x y d w v                           (66) where ( )d  represents the set of the infinitely derivable functions with compact support in  . when we take (64) and (65) into account, then the comparison of (58) and (59) with (60) and (61) respectively, gives the following equations, 10 1 10 1( ) ( ) 0 ( ); 0 1 u u j j u uk k i i ijkl ijk l l i k k j u u w uu u w u a dy e dy x y y x y y d                                                          (67) 0 11 10 1 ( ) ( ) 0 ( ); 0 1 k k ij ikl j j i l l i u uw w dy e dy x y y x y y d                                                               (68) therefore, we locally obtain, respectively: 10 1 10 1 * ( ) ( ) 0; u u j j u uk k i i ijkl ijk yc l l i k k j w uu u w u a e w v x y y x y y                                           (69) 0 11 10 1 *( ) ( ) 0;k kij ikl yc j j i l l i u uw w e w v x y y x y y                                             (70) and the local homogenized problem (lhp) in y, then follows: problem (lhp): find 1 1 * *( , ) u uyc ycu inv v   such that we obtain, for given 0 0( ) ( )u x and x : 10 1 10 1 * ( ) ( ) 0 u u j jk k i i ijkl ijky y l l i k k j u u yc w uu u w u a dy e dy x y y x y y w v                                               (71) and l j.-m. nianga et alii, frattura ed integrità strutturale, 42 (2017) 280-292; doi: 10.3221/igf-esis.42.30 289 0 11 10 1 * ( ) ( ) 0k kij ikly y j j i l l i yc u uw w dy e dy x y y x y y w v                                                   (72) all these results can then be summarized through the following proposition: proposition3. under the expansions (47) and (48) for the solution ( ( , ), ( , ))u x y x y  of problem (46), the first term 0 0( ( ), ( ))u x x satisfies eqs. (62)-(63) and appropriate boundary conditions. furthermore, for given 0 0( ( ), ( )),u x x the field 1 1( ( , ), ( , ))u x y x y is the solution of the nonlinear problem (lhp; eqs. 70-71), and ( 0ij , 0 id ) is therefore, defined as functions of 0 0( ( )) ( ( )).x xgrad u x and grad x so, eqs. (70)-(71) represent a nonlinear piezoelectric law. analysis of the (strain, electric potential)-(stress, electric displacement) law remark1. problem (lhp) can be written as in the following simplified form: find 1 1 * *( , ) u uyc ycu inv v   such that we obtain, for given 0 0( ) ( )u x and x :     0 1 1 0 1 1 * ( ) ( ) ( ) ( ) ( ) ( ) 0 (.) (.) (.) (.) ; (.) ; (.) u ijkl klx kly jiyy u ijk kx ky ijyy k k klx kly kx l l l u u yc a h u h u h w u dy e h h h w u dy h h h x y x w v                             (73) and    0 1 1 0 1 1 * ( ) ( ) ( ) ( ) ( ) ( ) 0 (.) (.) ij jx jy iy ikl klx kly iyy y iy k yc h h h w dy e h u h u h w dy h y w v                          (74) remark2. denoting 0 1 1 1 0 0( ); ( ); ; ; ;kl klx kl kly ij ij i ih h u h h u u u d d         (75) problem (lhp) can then be formulated as follows: find * *( , ) u uyc ycu inv v   such that we obtain, for given 6 3 kl kh and h r r :     * ( ) ( ) ( ) ( ) 0u uijkl kl kl ji ijk k k ijy y u u yc a h h u h w u dy e h h h w u dy w v                (76) j.-m. nianga et alii, frattura ed integrità strutturale, 42 (2017) 280-292; doi: 10.3221/igf-esis.42.30 290 and     * ( ) ( ) ( ) ( ) 0ij j j i ikl kh kl iy y yc h h h w dy e h h u h w dy w v                     (77) therefore, 0ij ij  and 0 i id d can be written as follows:         ( ) ( ) ( ) ( ) ij ijkl kl kl ijk k k i ij j j ikl kl kl a h h u e h h d h h e h h u              (78) so, the homogenized (strain, electric potential)-(stress, electric displacement) law is characterized by the function defined by: ( , ) ( , )kl kl ij ih h d   (79) nevertheless, for the study of (79), let us introduce the following functions, defined from 6 3r r towards r , by:       1 ( , ) ( ) ( ) 2 1 ( ) ( ) 2 sm s ijkl ij ij lm lmy ijk i i jk jky w h h a h h u h h u dy y e h h h h u dy y          (80)       * 1( , ) ( ) ( ) 2 1 ( ) ( ) 2 sm s ij i i j jy ikl ik ik l ly w h h h h h h dy y e h h u h h dy y             (81) moreover, the proposition that follows presents the main result of this analysis: proposition 4. the functions defined above, through (80) and (81), are of class c1, positive; and d   satisfying the following relations: * 1 2 1 2 ij ij i i w h w d h              (82) proof. as u and  are continuous functions of     1,2,3, 1,2,3ij i ii jh h and h h   , defined from 6 3( . )respr r towards ( . ),uyc ycv resp v  *w and w are then of class 0 .c let us now introduce: * * ( ) ( ) ij ij ij i i i h h u h and h h u h         (83) j.-m. nianga et alii, frattura ed integrità strutturale, 42 (2017) 280-292; doi: 10.3221/igf-esis.42.30 291 so, by virtue of (3)-(5), we can formulate the variation of w and w* as follows: * * * * * * * * * * * * * 1 1 1 2 2 1 1 2 2 1 1 1 2 2 1 2 ijkl ij kl ijkl ij kl ijk i jky y y ijk i jk ijk i jky y ijkl ij kl ijkl ij kl ijk i ijy y y kl kl w a h h dy a h h dy e h h dy y y y e h h dy e h h dy y y a h h dy a h h dy e h h dy y y y h                                (84) * * * * * * * * * * * * * 1 1 1 2 2 1 1 2 2 1 1 1 2 2 2 ij i j ij i j ikl ik ly y y ikl ik l ikl ik ly y ij i j ikl ik l j jy y w h h dy h h dy e h h dy y y y e h h dy e h h dy y y h h dy e h h dy d h y y                                 (85) taking (76) and (77) into account, we get: 1 2 1 2 ij kl i i w h w d h              (86) conclusion rom the variational formulation of the three-dimensional problem of linear piezoelectricity, we deduced that corresponding to a cracked piezoelectric structure. considering afterward the case of a structure presenting a periodic distribution of cracks, we managed to build, on the homogenization period, the homogenized formulation of the corresponding problem, as a result of an asymptotic development of the solution. a nonlinear law between the mechanical strain and the electric potential on one hand, and the mechanical stress and the electric displacement on the other hand, has been then established. references [1] dieulesaint, e., royer, d., ondes élastiques dans les solides. application au traitement du signal, paris, (1974). [2] alshits, i., darinskii, a.n., lothe, j., on the existence of surface waves in half-anisotropic elastic media with piezoelectric and piezomagnetic properties, wave. motion., 16 (1992) 265 – 283. [3] li, j.y., dunn, m.l., micromechanics of magnetoelectroelastic composite materials: average fields and effective behavior, j. intell. mater. syst. struct., 7 (1998) 404 – 416. [4] zhag, t.y., tong, p., fracture mechanics for a mode iii crack in a piezoelectric material, int. j. solids. struct, 33 (1996) 343 – 359. [5] suo, z., kuo, c.m., barnett, d.m., willis, j.r., fracture mechanics for piezoelectric ceramics, j. mech. phys. solids, 40 (1992) 739 – 765. [6] gao, c.f., wang, m.z., periodical cracks in piezoelectric media, mech. rech. commun, 26 (1999) 427 – 432. f j.-m. nianga et alii, frattura ed integrità strutturale, 42 (2017) 280-292; doi: 10.3221/igf-esis.42.30 292 [7] wang, x.d., meguid, s.a., modelling and analysis of the dynamic behavior of piezoelectric materials containing interacting cracks, mech. materials, 32 (2000) 723 – 737. [8] han, j.c., wang, b.l., electromechanical model of periodic cracks in piezoelectric materials, mech. materials, 37 (2005) 1180 – 1197. [9] turbé, n., maugin, g.a., on the linear piezoelectricity of composite materials, math. methods. applied. sciences, 14 (1991) 403 – 412. 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/hrv (za stvaranje adobe pdf dokumenata najpogodnijih za visokokvalitetni ispis prije tiskanja koristite ove postavke. stvoreni pdf dokumenti mogu se otvoriti acrobat i adobe reader 5.0 i kasnijim verzijama.) /hun 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can be opened with acrobat and adobe reader 5.0 and later.) >> /namespace [ (adobe) (common) (1.0) ] /othernamespaces [ << /asreaderspreads false /cropimagestoframes true /errorcontrol /warnandcontinue /flattenerignorespreadoverrides false /includeguidesgrids false /includenonprinting false /includeslug false /namespace [ (adobe) (indesign) (4.0) ] /omitplacedbitmaps false /omitplacedeps false /omitplacedpdf false /simulateoverprint /legacy >> << /addbleedmarks false /addcolorbars false /addcropmarks false /addpageinfo false /addregmarks false /convertcolors /converttocmyk /destinationprofilename () /destinationprofileselector /documentcmyk /downsample16bitimages true /flattenerpreset << /presetselector /mediumresolution >> /formelements false /generatestructure false /includebookmarks false /includehyperlinks false /includeinteractive false /includelayers false /includeprofiles false /multimediahandling /useobjectsettings /namespace [ (adobe) (creativesuite) (2.0) ] /pdfxoutputintentprofileselector /documentcmyk /preserveediting true /untaggedcmykhandling /leaveuntagged /untaggedrgbhandling /usedocumentprofile /usedocumentbleed false >> ] >> setdistillerparams << /hwresolution [2400 2400] /pagesize [612.000 792.000] >> setpagedevice microsoft word numero_54_art_07_2860 o. shallan et al., frattura ed integrità strutturale, 54 (2020) 104-115; doi: 10.3221/igf-esis.54.07 104 effect of stiffener characteristics on the seismic behavior and fracture tendency of steel shear walls osman shallan, hassan m. maaly, mohammed m. elgiar zagazig university, egypt osmanshalan@yahoo.com, https://orcid.org/0000-0002-6471-5561 dr_h_maaly@yahoo.com, https://orcid.org/0000-0002-2000-8136 mohamedelgyar07@gmail.com, https://orcid.org/0000-0001-8463-7276 alaa a. el-sisi university of missouri, usa; on research leave of zagazig university, egypt aep64@mail.missouri.edu, https://orcid.org/0000-0001-8190-6100 abstract. the steel plate shear walls (spsw) are currently being considered as a lateral load resisting system. a numerical method was proposed to have a comprehensive comparison of seismic behaviors of the plane wall (pw) and stiffened plane wall (spw) with different stiffener characteristics, having the same weight, by using finite element modeling (fem). the model was validated by using previously published experimental works. the material and geometric nonlinearity were taken into consideration. in this paper, the effect of using stiffeners with different cross-section shapes and directions will be studied, and key issues, such as load-carrying capacity, stiffness, and energydissipation capacity were discussed in depth. it was found that the proposed spw with horizontal l, t, and u stiffeners could effectively improve loadcarrying capacity by about 4, 20, and 23%, respectively. diagonally and horizontally spw with u stiffeners have higher energy-dissipation capacity than pw by about 57, 50%, respectively. this method provides a combination of high-performance stiffeners form and material use for improving the seismic behavior of spw. keywords. backbone curve; energy-dissipation capacity; hysteretic behavior; steel plate shear wall; seismic behavior. citation: shallan, o., maaly, h. m., elgiar, m. m., el-sisi, a. a., effect of stiffener characteristics on the seismic behavior and fracture tendency of steel shear walls, frattura ed integrità strutturale, 54 (2020) 104-115. received: 01.07.2020 accepted: 27.07.2020 published: 01.10.2020 copyright: © 2020 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. https://youtu.be/gskw5evov8m o. shallan et al., frattura ed integrità strutturale, 54 (2020) 104-115; doi: 10.3221/igf-esis.54.07 105 introduction he spsw is used in many countries as a lateral load resisting system, due to its advantages over the concrete walls such as high ductility, good seismic behavior, easy retrofit, lightweights, and less footing depth. spsw consists of the boundary frame and infill plate, as shown in fig.1.a. using spsws in high rise buildings was studied [1]. to improve the seismic behavior of spsws, previous research works were focused on two aspects. firstly, the design principle of “strong frame, weak wall”, in which thin plane wall (pw) had used. secondly, the stiffened plane wall (spw), which can be used to avoid large out-of-plane deformations [4, 8, 10, 11]. in this field of researches, all the previous studies focused on a few stiffener details. no comprehensive comparison of seismic performance of spws with different stiffener characteristics, having the same weight, had been implemented. several works were conducted on the pw system to evaluate its seismic performance, load-carrying capacity, stiffness, ductility, and energy dissipation capacity [2,3, 6–18,]. the general results show that thin pw has early elastic buckling of the infill steel plate. however, pw still has high post-buckling lateral strength. this might be attributed to tension fields, which act like plastic hinges and dissipate more energy [7]. spsw with a single span and three-stories was experimentally studied [12]. the parametric study included the effect of infill panel, thickness of infill, and span-to-height ratio under cyclic load was investigated. it was found that the thickness of the infill panel has a great influence on seismic behavior. the cyclic test was conducted on thin unstiffened spsw with four-stories [8]. the results showed good seismic performance, as story drift reached 4% before reached to failure and high energydissipation capacity. a lot of studies had worked to delay the buckling behavior of pws using spws, which can be stiffened by vertical slits [8, 15,16], cross, or diagonal stiffeners [4, 11, 13, 14]. it was found that the ductility ratio and energydissipation capacity can be improved by preventing the failure, which can be attributed to the out-of-plane large deformation. an experimental study on the seismic behavior of spsw with slits was conducted [10]. the test was conducted on 42 walls where the walls were subjected to cyclic and monotonic loads. it was found that using vertical slits improves the seismic behavior of walls. it was also found that walls can reach 3% drift without failure in cases of width to thickness ratio less than 20. an experimental study was conducted on diagonally stiffened spsw [2]. it was found that using diagonally spws improves seismic behavior and improves the ductility ratio of about 14% greater than pw. although a lot of research works focused on the seismic behavior of spws there is a need to perform a comparative study to investigate the different behavior of spws with different stiffener characteristics, which have the same weight. this paper studied the effect of stiffener cross-section shape l, t, or u and stiffener direction under cyclic loading test fig. 1.c. this paper studied the cyclic nonlinear behavior of pw and spws. finite element models were developed by using abaqus software [19]. previous experimental work was used to validate the finite element model [20]. different seismic behavior, load-carrying capacity, stiffness, degradation characteristics, energy dissipationcapacity, fracture tendency and out-of-plane deformations were analyzed and compared for different models. the study aimed to achieve the combination of high-performance stiffeners form and high-performance material. problem description even models of thin pw and spw were modeled using abaqus software. the parametric study includes the effect of panel type, stiffeners cross-section shape, and direction. panel type can be plane (pw), or stiffened plane wall (spw). the spw can be stiffened by l (spw-hl), t (spw-ht), or u shape stiffeners (spw-hu). the stiffener's direction can be horizontal (spw-hu), vertical (spw-vu), cross (spw-cu), or diagonal stiffeners (spw-du). fig.1.c shows the sections of l, t, and u stiffeners. the two legs of l stiffeners had a height of 120mm. the flange and height of t stiffeners were 120 mm. the height of u stiffeners was 120 mm, while the flanges were 60 mm. the thickness of l, t, and u stiffeners was 5 mm. the boundary elements were designed according to aisc design guide [21,22]. the beam section was hm500×300×11×15 similar to w21×68 and the column section was hw400×400×13×21 similar to w14×132. wall panels had a height of 3000 mm, a span of 3000 mm, and a thickness of 5 mm. the models of spw-hl, spw-ht, spw-hu, spw-vu, and spw-cu have the same weight. the parametric case study is shown in tab. 1. fig. 2 shows the details for different models. t s o. shallan et al., frattura ed integrità strutturale, 54 (2020) 104-115; doi: 10.3221/igf-esis.54.07 106 a) pw b) cyclic drifts l section t section u section c) stiffener cross-section shape. figure 1: geometric properties of spsw. model id stiffener direction stiffener cross -section pw none none spw-hl horizontal l spw-ht horizontal t spw-hu horizontal u spw-du diagonal u spw-vu vertical u spw-cu cross u table 1: parametric case study. finite element modeling o study the nonlinear behavior of pw, and spws, accurate finite element analysis (fea) should be conducted. the boundary frame, stiffeners, and infill panel were modeled using the 4(four)-node shell element (s4r) with reduced integration [19], to avoid shear locking phenomena. mechanical properties of materials, the boundary condition of models, and the time history of loading and initial defect are presented in detail as follows. mechanical properties of steel materials the boundary frame steel, steel plate, and the stiffeners materials have a yielding strength of 345 mpa, and 235 mpa, respectively. the materials elastic modulus e = 206 gpa, poisson’s ratio ν = 0.3 and hardening modulus eh = 1/100e. the behavior of the materials becomes nonlinear, after reaches to maximum yield stress [23–25]. moreover, due to changes in the deformed shape during the loading process, the geometric nonlinearity should be taken into consideration. the isotropic hardening behavior was considered [19]. time (sec.) d ri ft , % 0 8 16 24 32 40 48 56 64 72 -4 -2.4 -0.8 0.8 2.4 4 drift t o. shallan et al., frattura ed integrità strutturale, 54 (2020) 104-115; doi: 10.3221/igf-esis.54.07 107 a) spw-hl b) spw-ht c) spw-hu d) spw-du e) spw-vu f) spw-cu figure 2: geometric properties of spsw modal analysis and initial defect the out-of-plane initial imperfection, which may occur due to the manufacturing process, storage, and installation process should be taken into consideration in cyclic analysis, thus it might affect the plate strength. initial imperfection was set as 1/1000 of the plate height. the eigenvalue buckling analysis was used to evaluate the imperfection distribution over the panel by multiplying the major buckling modes by the scale factor. boundary conditions and history loading the nonlinear cyclic analysis was conducted on groups of thin pw and spws. the lateral displacement was applied to the exterior column flange. the lateral displacement increased gradually to produce drift ratios of 0.25%, 0.5%, 1%, 1.5%, 2%, 2.5%, 3% and 4%. the amplitudes were repeated twice, as shown in fig. 1.b. the column base regions had a fixed boundary condition, in which all these nodes restrained in all the six degrees of freedom. the out-of-plane displacement for the nodes of the beam centerline and all nodes of the column-beam connections were constrained, to prevent the out-of-plane buckling of the whole system. o. shallan et al., frattura ed integrità strutturale, 54 (2020) 104-115; doi: 10.3221/igf-esis.54.07 108 experimental work details and numerical model validation o verify the accuracy of numerical simulation, quasi-static tests were conducted on park’s experiment test [20]. five unstiffened steel plate shear wall specimens with a single bay and three stories were tested in reference [20]. the experimental test of wc4t was selected for validation in this paper. the span, height, and thickness of the plates were 1500, 1000 mm, and 5 mm, respectively. the internal beams section was h200×200×16×16 mm, the top beam was h400×200×16×16 and columns were h250×250×9×12. the material of infill panels and boundary elements was sm490 with yield stress fy = 330 mpa. the cyclic constitutive model was used to simulate the cyclic hardening, local buckling, and degradation characteristics due to cyclic loading. the chaboche constitutive model [26,27] is adopted therefore, the combined hardening behavior was considered [19]. the cyclic hardening parameters of the material are shown in tab. 2; where c1, c2, c3, and c4 are the kinematic hardening modulus, γ1, γ2, γ3, and γ4 are the rates at which hardening modulus decreases with the plastic strain, q∞ is the maximum change in the size of the yield surface and b is the rate at which initial yield stress change with the plastic strain. the initial out of plane defect was selected 1/1000 height of steel plate. “imperfection” command was used to modify the coordinates of plat’s nodes by multiply the major buckling modes by a scale factor. the bottom of the model had a fixed boundary condition. the cyclic horizontal displacements were applied in the middle of the upper beam using a reference point. q ͚ , n/mm2 b c1, n/mm2 γ1 c2, n/mm2 γ2 c3, n/mm2 γ3 c4, n/mm2 γ4 21 1.2 7993 175 6773 116 2854 34 1450 29 table 2: material hardening parameters. the load-horizontal displacement curve for the experimental test and present finite element modeling was compared in fig. 3, which shows a good agreement with the experimental results. tab. 3 shows the cyclic results of the experimental test and present fea for the wc4t specimen. where v max is the load-carrying capacity and ki is the initial stiffness of the specimen. from fig. 3 and tab. 3, it can be concluded that the present fea shows a difference in the initial stiffness by about 1.4% and a difference in load-carrying capacity by about 2.8% in the positive direction. it can be seen that the current numerical simulation can be used to predict the nonlinear behavior of spsws with acceptable accuracy. figure 3: compare between results of experimental and numerical for wc4t specimen result positive direction negative direction exp. fea error, % exp. fea error, % v max, kn 1520 1563.1 2.8 -1526 -1555.9 2.0 ki, kn/mm 59.2 60.0 1.4 65.6 61.2 -6.7 table 3: cyclic results of experimental test and present fea for wc4t specimen. top displacement, mm v , k n -125 -75 -25 25 75 125 -1600 -1200 -800 -400 0 400 800 1200 1600 fem result exp. result t o. shallan et al., frattura ed integrità strutturale, 54 (2020) 104-115; doi: 10.3221/igf-esis.54.07 109 effect of panel type and stiffener shape o show the effect of panel type and stiffeners cross-section shape, the results of the models pw, spw-hl, spwht, and spw-hu will be compared and discussed. the models spw-hl, spw-ht, and spw-hu have the same weight for comparison reasons. the hysteretic behavior was recorded. hysteretic behavior of pw, and spw-hl, spw-ht, and spw-hu are shown in fig. 4, in which the drift ratio is presented on the x-axis (%) and load-carrying capacity is presented on the y-axis (kn). the hysteretic curves show that panel type (pw and spw) and the cross-section shape of stiffeners, which has the same weight, has an obvious effect on the load-carrying capacity. fig. 4.a shows that both spw-hu and pw have the same lateral strength mechanism, which depends on tensionfield action, which produces a post-buckling load-carrying capacity. it also indicates that spw-hu has a much plumped hysteretic curve than pw, higher load-carrying capacity, and stiffness. fig. 4.b shows a comparison between the hysteretic curves of spws with different cross-section shapes of stiffeners. fig. 4.b shows that the stiffeners cross-section shape has a significant effect on seismic behavior when the other properties remain the same. spw-hu has higher initial stiffness and load-carrying capacity in comparison with the spw-hl and spw-ht. the backbones curves can be obtained from the hysteretic curves in both pull and push directions, as shown in fig. 5. the initial stiffness (ki), the second cyclic stiffness at drift ratio 0.5% (k2), load-carrying capacity, yield points, and maximum points can be concluded from the backbone curves, as shown in tab. 4. the yield point is a point, at which local buckling and plastic deformations appear in the system. symbol δy is the yield displacement (mm), vy is the yield force (kn), δm is the displacement at maximum load-carrying capacity (mm) and vm is the maximum load-carrying capacity (kn). from fig. 5 and tab. 4, in the push direction, it can be seen that the stiffened walls spw-hl, spw-ht, and spw-hu had a k2 value higher than pw by about 5.5, 8, and 9%, respectively. at 4% drift in the push direction, spw-hl, spw-ht, and spw-hu had a higher load-carrying capacity than pw by about 4, 20, 23%, respectively. the cases of spw-hu and spw-hl had the maximum and minimum increasing percentages values. therefore, the u stiffeners were studied deeply in the other parametric study. model direction ki, kn/mm k2, kn/mm δy, mm vy, kn vm, kn pw push 300.8 152.1 16.3 2479.5 3267.1 pull + 299.9 158.0 16.3 2855.2 3203.3 spw-hl push 299.3 160.6 7.8 2426.2 3403.4 pull + 299.9 157.9 7 2066 3464.6 spw-ht push 301.0 164.1 16.3 2667 3914.0 pull + 300.1 168.1 16.3 2864.4 3878.8 spw-hu push 303.1 166.1 8.1 2472.1 4016.8 pull + 302 162.6 8.1 2463.2 3989.5 table 4: cyclic analyses of pw and spw with different stiffener’s cross section shape. effect of stiffener direction o show the effect of stiffener's direction on the seismic behavior, the results of the models spw-hu, spw-vu, spw-cu, and spw-du will be compared and discussed deeply. the models spw-hu, spw-vu, spw-cu had the same weight, while spw-du had higher weight than other models. the hysteretic curves of spw-hu, spwvu, spw-cu, and spw-du were presented and compared to pw in this section, as shown in fig. 6.a and b. fig. 6.a compares between the hysteretic curve of stiffened walls spw-vu, spw-cu, and spw-du to horizontally stiffened wall spw-hu. from fig. 6.a, it can be observed that spw-du had higher initial stiffness and load-carrying capacity than other stiffened walls in the first stages. however, in the last stages, spw-hu had a higher load-carrying capacity than spw-du. this might be attributed to diagonal stiffeners, which increase the diagonal stiffness, where tension fields form. fig. 6.b shows that using horizontally and diagonally stiffeners increase initial stiffness and load-carrying capacity especially t t o. shallan et al., frattura ed integrità strutturale, 54 (2020) 104-115; doi: 10.3221/igf-esis.54.07 110 diagonally stiffeners in the first stages. backbone curves for spws with different directions were extracted in pull and push directions from all hysteretic curves, as shown in fig. 7. initial stiffness, load-carrying capacity, and feature points were extracted from backbone curves for all models, as shown in tab. 5. a) b) figure 4: hysteretic curves of systems. (a) pw and spw-hu, (b) spw-hl, spw-ht, and spw-hu figure 5: backbone curves of pw, spw-hl, spw-ht, and spw-hu. a) b) figure 6: hysteretic curves of systems. (a) spw-hu, spw-vu, spw-cu, and spw-du, (b) spw-hu, spw-du, and pw. drift, % v , k n -5 -4 -3 -2 -1 0 1 2 3 4 5 -5000 -3000 -1000 1000 3000 5000 spw-hu pw drift, % v , kn -5 -4 -3 -2 -1 0 1 2 3 4 5 -5000 -3000 -1000 1000 3000 5000 spw-hl spw-ht spw-hu drift, % v , kn -4 -3 -2 -1 0 1 2 3 4 -5000 -4000 -3000 -2000 -1000 0 1000 2000 3000 4000 5000 pw spw-hu spw-ht spw-hl drift, % v , kn -5 -4 -3 -2 -1 0 1 2 3 4 5 -5000 -3000 -1000 1000 3000 5000 spw-hu spw-vu spw-cu spw-du drift, % v , kn -5 -4 -3 -2 -1 0 1 2 3 4 5 -5000 -3000 -1000 1000 3000 5000 spw-hu spw-du pw o. shallan et al., frattura ed integrità strutturale, 54 (2020) 104-115; doi: 10.3221/igf-esis.54.07 111 model direction ki, kn/mm k2, kn/mm δy, mm vy, kn vm, kn pw push 300.8 152.1 16.3 2479.5 3267.1 pull + 299.9 158.0 16.3 2855.2 3203.3 spw-hu push 303.1 166.18 8.1 2472.1 4016.8 pull + 302 162.6 8.1 2463.2 3989.5 spw-vu push 246.6 162.0 5 1726.4 3730.7 pull + 277.0 162.3 8.2 2432.1 3687.6 spw-cu push 303.4 165.6 8.2 2474.3 3809.0 pull + 302.3 172.9 16.3 2713 3803.6 spw-du push 357.9 199.2 8.1 2899.1 4043.3 pull + 356.1 197.1 8.1 2879.8 3823.4 table 5: cyclic analyses of spw with different stiffener’s directions. from fig. 7 and tab. 5, in the push direction, it can be concluded that stiffened wall with different stiffeners directions spw-hu, spw-vu, spw-cu, and spw-du had a k2 value higher than pw by about 9.2, 6.5, 9, and 31%, respectively. at the 4% drift in the push direction, it can be observed that the load-carrying capacity for stiffened walls increased by percentage values of 23, 14, 17, and 23%, respectively. the cases of spw-hu and spw-vu had the maximum and minimum increasing percentage values. this might be attributed to the accordion effect, which means that the stiffeners increase the system stiffness in its direction. therefore, the horizontal stiffeners had better seismic behavior than vertical stiffeners. figure 7: backbone curves of pw, spw-hu, spw-vu, spw-cu, and spw-du properties degradation and energy dissipation capacity ateral strength degradation reflects the system plastic deformations, columns local failure, and the damage occurs during the loading process. the strength degradation coefficient (η) can be defined as (the ratio between the second and first load-carrying capacity at the same drift ratio). fig. 8.a shows the lateral strength degradation ratio (η) for different systems, it can be seen that η are varying between 0.85 and 1 except the second cycle of pw at the drift ratio 0.5%, where η is about 0.8. this might be attributed to the initial yielding of the system. the cyclic stiffness (ki) describes the stiffness degradation for the different models during the loading process. ki can be calculated by the method described in ref [28] as errore. l'origine riferimento non è stata trovata.. drift, % v , k n -4 -3 -2 -1 0 1 2 3 4 -5000 -4000 -3000 -2000 -1000 0 1000 2000 3000 4000 5000 spw-hu spw-vu spw-cu spw-du pw l o. shallan et al., frattura ed integrità strutturale, 54 (2020) 104-115; doi: 10.3221/igf-esis.54.07 112 1 1/ n ni i j ji ii pk     (1) where, ijp is peak lateral shear capacity in each cycle and i j is peak displacement for each cycle drift. fig. 8.b shows the stiffness degradation for pw and spws. it can be seen that stiffness degradation decreases stably during the cyclic loading process. the cases of spw-hu and pw had maximum and minimum stiffness values. energy dissipation capacity reflects the seismic performance of the lateral resisting system. the energy dissipation capacity for each cycle is equal to the enclosed area of each hysteretic curve. the much plump the hysteretic curve is the more dissipated capacity. fig. 9.a shows the energy dissipation capacity for pw, spw-hl, spw-ht, and spw-hu for cyclic number n=16. from fig. 9.a, it can be concluded that the stiffener cross-section shape had a significant effect on the system energy dissipation capacity. the stiffeners increase the energy dissipation capacity in the stiffened walls spw-hl, spw-ht, and spw-hu by percent values of 28, 46, and 50%, respectively. the cases of the spw-hu and spw-hl had the maximum and minimum increasing values. it was found that u stiffeners had the best seismic behavior. therefore, u stiffeners will be studied deeply in the following parametric study. fig. 9.b shows the accumulated energy dissipation capacity for pw and spw-hu, spw-vu, spw-cu, and spw-du for cyclic number n=16. from fig. 9.b, it can be observed that the stiffener's direction has a significant effect on the wall energy-dissipation capacity. the stiffeners caused energydissipation capacity increasing in the stiffened walls spw-hu, spw-vu, spw-cu, and spw-du by percentage values of 50, 39, 44, and 57%, respectively. the cases of spw-du and spw-vu had the maximum and minimum increasing percentage values. this might be attributed to the diagonal stiffeners, which increased the rigidity in the diagonal direction, where the diagonal tension field action occurred. a) b) figure 8: degradation characteristics. a) strength degradation. b) stiffness degradation. a) effect of stiffener shape. b) effect of stiffener direction. figure 9: accumulated energy dissipation capacity for n=16. drift, %  -4 -3 -2 -1 0 1 2 3 4 0.5 0.6 0.7 0.8 0.9 1 1.1 pw spw-hu spw-ht spw-hl drift, % k i, kn /m m -4 -3 -2 -1 0 1 2 3 4 0 40 80 120 160 200 240 280 320 360 400 pw spw-hu spw-ht spw-hl n, #  e , kn .m 0 2 4 6 8 10 12 14 16 0 600 1200 1800 2400 3000 3600 4200 4800 5400 6000 pw spw-hu spw-ht spw-hl n, #  e , kn .m 0 2 4 6 8 10 12 14 16 0 600 1200 1800 2400 3000 3600 4200 4800 5400 6000 spw-hu spw-vu spw-cu spw-du pw o. shallan et al., frattura ed integrità strutturale, 54 (2020) 104-115; doi: 10.3221/igf-esis.54.07 113 a) pw b) spw-hl c) spw-ht d) spw-hu e) spw-vu f) spw-cu g) spw-du figure 10: comparison of peeq distribution at drift 4% comparison of fracture tendency and failure modes he equivalent plastic strain (peeq) describes the fracture tendency as a cumulative variable [19]. the maximum peeq values are the actual fracture zones. therefore, in practical engineering, these results can be used to avoid fractures in advance. fig. 10 shows the peeq distributions of pw and spws. tab. 6 shows the maximum peeq and out-of-plane deformations (mm). it can be seen that the stiffener details can change peeq, failure modes, and deformation distributions. the peeq values of stiffened walls spw-hl, spw-ht, spw-hu, spw-vu, spw-cu, and spw-du are higher than pw by about 64, 31, 21, 203, 87, and 1116%, respectively. this might be attributed to the stress concentration, local buckling of stiffeners. the plastic strain accumulation of spw-du increased at the corners due to the effect of both diagonal tension fields and diagonal stiffeners, so higher columns stiffness are needed to avoid the columns fracture. tab. 6 also shows the maximum out-of-plane deformations, in which the deformation of spw-hu is the smallest, showing that the deformations are effectively restrained by the horizontal u stiffeners. one main wave was formed in the case of pw with clear two-way tension fields. for spw-hl, spw-ht, spw-hu, spw-vu, and spw-cu tension fields were formed in stiffener compartments. in the case of spw-du, the maximum deformation occurred at the stiffeners intersection due to limited stiffeners stiffness and a main wave failure mode can be observed. t o. shallan et al., frattura ed integrità strutturale, 54 (2020) 104-115; doi: 10.3221/igf-esis.54.07 114 model id peeq final position pw 1.9 264 spw-hl 3.12 179 spw-ht 2.49 176 spw-hu 2.29 117 spw-vu 5.76 157 spw-cu 3.56 161 spw-du 23.1 307 table 6: comparison of the equivalent plastic strains and the out-of-plane deformations (mm) at drift 4%. conclusions n this paper, nonlinear cyclic analyses were conducted using numerical simulation and finite element models for pw and spw, to investigate the influence of panel type, stiffeners cross-section shape, and stiffeners direction on loadcarrying capacity, stiffness, and energy dissipation capacity. the main topic focused on this paper is the seismic behavior of stiffened steel walls with different stiffeners characteristics, which have the same weight. this paper provides an economic evaluation for the practical engineer. based on the current study numerical simulation and parametric study, some conclusions are shown as follows: ‐ finite element models were created and validated with published experimental and numerical works. the models were able to predict the load-carrying capacity and the system stiffness of the previous results with a percentage error of 3%, 1.5%, respectively. ‐ the stiffener’s cross-section shape has a greater impact on the load-carrying capacity than the wall stiffness. horizontally stiffened wall with u stiffeners has higher load-carrying capacity than l, and t stiffeners by about 18%, and 3%, respectively. ‐ spw with horizontal u stiffeners has higher stiffness, load-carrying capacity, and energy-dissipation capacity than pw by about 9, 23, and 50%, respectively. while, spw–du has a higher energy-dissipation capacity than pw by about 57%. ‐ the appropriate stiffener details can effectively improve the fracture properties and failure modes. the out-of-plane deformations of spw-hl, spw-ht, spw-hu, spw-vu, and spw-cu were effectively lessened. using horizontal u stiffeners reduced deformations by about 56%. diagonal stiffeners increase the effects of tension fields on the columns, so higher column stiffness is needed to avoid columns fracture. ‐ in the high seismic zones, economic performance should be taken into account to choose appropriate stiffener characteristics. the proposed horizontal and diagonal u stiffeners effectively improve seismic behavior, fracture behavior, and energy-dissipation capacity. this paper achieves the combination of high-performance stiffeners form an ‐ d performance material for improving the seismic behavior of stiffened steel walls. references [1] youssef, n., wilkerson, r., fischer, k., tunick, d. (2010). seismic performance of a 55-storey steel plate shear wall, struct. des. tall spec. build., 19(1–2), pp. 139–165, doi: 10.1002/tal.545. [2] alavi, e., nateghi, f. (2013). experimental study on diagonally stiffened steel plate shear walls with central perforation, j. constr. steel res., 89(1), pp. 9–20, doi: 10.1016/j.jcsr.2013.06.005. [3] alinia, m.m., dastfan, m. (2007). cyclic behaviour, deformability and rigidity of stiffened steel shear panels, j. constr. steel res., 63(4), pp. 554–563, doi: 10.1016/j.jcsr.2006.06.005. [4] guo, h.c., li, y.l., liang, g., liu, y.h. (2017). experimental study of cross stiffened steel plate shear wall with semirigid connected frame, j. constr. steel res., 135(1), pp. 69–82, doi: 10.1016/j.jcsr.2017.04.009. [5] cao, c.h., hao, j.p., zhong, w.h., li, f., wang, y.c. (2008).cyclic test of diagonal stiffened steel plate shear walls. the 10th international symposium on structural engineering for young experts, changsha, 19-21 october. i o. shallan et al., frattura ed integrità strutturale, 54 (2020) 104-115; doi: 10.3221/igf-esis.54.07 115 [6] vian, d., bruneau, m., purba, r. (2009). special perforated steel plate shear walls with reduced beam section anchor beams. ii: analysis and design recommendations, j. struct. eng., 135(3), pp. 221–228, doi: 10.1061/(asce)07339445(2009)135:3(221). [7] thorburn, l.j., montgomery, c.j., kulak, g.l. (2012). analysis of steel plate shear walls, department of civil engineering, university of alberta. [8] driver, r.g., kulak, g.l., kennedy, d.j.l., elwi, a.e. (1998). cyclic test of four-story steel plate shear wall, j. struct. eng., 124(2), pp. 112–120, doi: 10.1061/(asce)0733-9445(1998)124:2(112). [9] nie, j., fan, j., liu, x., huang, y. (2013). comparative study on steel plate shear walls used in a high-rise building, j. struct. eng. (united states), 139(1), pp. 85–97, doi: 10.1061/(asce)st.1943-541x.0000613. [10] hitaka, t., matsui, c. (2003). experimental study on steel shear wall with slits, j. struct. eng., 129(5), pp. 586–595, doi: 10.1061/(asce)0733-9445(2003)129:5(586). [11] chen, s.j., jhang, c. (2011). experimental study of low-yield-point steel plate shear wall under in-plane load, j. constr. steel res., 67(6), pp. 977–985, doi: 10.1016/j.jcsr.2011.01.011. [12] caccese, v., elgaaly, m., chen, r. (1993). experimental study of thin steel-plate shear walls under cyclic load, j. struct. eng. (united states), 119(2), pp. 573–587, doi: 10.1061/(asce)0733-9445(1993)119:2(573). [13] li, f., li, h., li, z.m., li, z.j., chen, x.f., ding, l. (2009). cyclic test of diagonally stiffened steel plate shear wall, j. xi’an univ. archit. technol., 41(1), pp. 57–62. [14] choi, i.r., park, h.g. (2009). steel plate shear walls with various infill plate designs, j. struct. eng., 135(3), pp. 785–796, doi: 10.1061/(asce)0733-9445(2009)135:7(785). [15] nakashimal, m., akazawa, t., tsuji, b. (1995). strain-hardening behavior of shear panels made of low-yield steel. ii: model, j. struct. eng., 121(12), pp. 1750–1757, doi: 10.1061/(asce)0733-9445(1995)121:12(1750). [16] shi, y., wang, m., wang, y. (2011). experimental and constitutive model study of structural steel under cyclic loading, j. constr. steel res., 67(8), pp. 1185–1197, doi: 10.1016/j.jcsr.2011.02.011. [17] nakashima, m., iwai, s., iwata, m., takeuchi, t., konomi, s., akazawa, t., saburi, k. (1994). energy dissipation behaviour of shear panels made of low yield steel, earthq. eng. struct. dyn., 23(12), pp. 1299–1313, doi: 10.1002/eqe.4290231203. [18] chen, s.j., jhang, c. (2006). cyclic behavior of low yield point steel shear walls, thin-walled struct., 44(7), pp. 730–738, doi: 10.1016/j.tws.2006.08.002. [19] abaqus., simulia, d.s., fallis, a., techniques, d. (2013). abaqus analysis user’s guide (6.14)., abaqus 6.12, , doi: 10.1017/cbo9781107415324.004. [20] park, h.g., kwack, j.h., jeon, s.w., kim, w.k., choi, i.r. (2007). framed steel plate wall behavior under cyclic lateral loading, j. struct. eng., 133(3), pp. 378–388, doi: 10.1061/(asce)0733-9445(2007)133:3(378). [21] sabelli, r., bruneau, m. (2006). steel plate shear walls (steel design guide 20), chicago, american institute of steel construction, inc. [22] aisc. (2010). seismic provisions for structural steel buildings, chicago, american institute of steel construction, inc. [23] el emam, h.m., el-sisi, a.e.m., salim, h.a., sallam, h.e.m. (2015).cyclic deformation at the tip of inclined cracks in steel plates. pressure vessels and piping conference (asme 2015 ), 6a-2015, boston. [24] sallam, h.e.m., matar, e.b., el-sisi, a.e., el-hussieny, o.m. (2009).crack tip plasticity of short fatigue crack emanating from riveted/bolted steel connections. the 13th international conference on structural and geotechnical engineering (icsge), cairo. [25] el-emam, h., elsisi, a., salim, h., sallam, h. (2018). fatigue crack tip plasticity for inclined cracks, int. j. steel struct., 18(2), doi: 10.1007/s13296-018-0016-z. [26] chaboche, j.l. (1986). time-independent constitutive theories for cyclic plasticity, int. j. plast., 2(2), pp. 149–188, doi: 10.1016/0749-6419(86)90010-0. [27] chaboche, j.l. (1989). constitutive equations for cyclic plasticity and cyclic viscoplasticity, int. j. plast., 5(3), pp. 247– 302, doi: 10.1016/0749-6419(89)90015-6. [28] nie, j., qin, k., cai, c.s. 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/hrv (za stvaranje adobe pdf dokumenata najpogodnijih za visokokvalitetni ispis prije tiskanja koristite ove postavke. stvoreni pdf dokumenti mogu se otvoriti acrobat i adobe reader 5.0 i kasnijim verzijama.) /hun 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can be opened with acrobat and adobe reader 5.0 and later.) >> /namespace [ (adobe) (common) (1.0) ] /othernamespaces [ << /asreaderspreads false /cropimagestoframes true /errorcontrol /warnandcontinue /flattenerignorespreadoverrides false /includeguidesgrids false /includenonprinting false /includeslug false /namespace [ (adobe) (indesign) (4.0) ] /omitplacedbitmaps false /omitplacedeps false /omitplacedpdf false /simulateoverprint /legacy >> << /addbleedmarks false /addcolorbars false /addcropmarks false /addpageinfo false /addregmarks false /convertcolors /converttocmyk /destinationprofilename () /destinationprofileselector /documentcmyk /downsample16bitimages true /flattenerpreset << /presetselector /mediumresolution >> /formelements false /generatestructure false /includebookmarks false /includehyperlinks false /includeinteractive false /includelayers false /includeprofiles false /multimediahandling /useobjectsettings /namespace [ (adobe) (creativesuite) (2.0) ] /pdfxoutputintentprofileselector /documentcmyk /preserveediting true /untaggedcmykhandling /leaveuntagged /untaggedrgbhandling /usedocumentprofile /usedocumentbleed false >> ] >> setdistillerparams << /hwresolution [2400 2400] /pagesize [612.000 792.000] >> setpagedevice microsoft word numero_29_art_18 d. de domenico et alii, frattura ed integrità strutturale, 29 (2014) 209-221; doi: 10.3221/igf-esis.29.18 209 focussed on: computational mechanics and mechanics of materials in italy limit analysis on frp-strengthened rc members d. de domenico, a.a. pisano, p. fuschi university mediterranea of reggio calabria, department pau dario.dedomenico@unirc.it, aurora.pisano@unirc.it, paolo.fuschi@unirc.it dedicated to professor castrenze polizzotto on the occasion of his 90th birthday abstract. reinforced concrete (rc) members strengthened with externally bonded fiber-reinforced-polymer (frp) plates are numerically investigated by a plasticity-based limit analysis approach. the key-concept of the present approach is to adopt proper constitutive models for concrete, steel reinforcement bars (re-bars) and frp strengthening plates according to a multi-yield-criteria formulation. this allows the prediction of concrete crushing, steel bars yielding and frp rupture that may occur at the ultimate limit state. to simulate such limitstate of the analysed elements, two iterative methods performing linear elastic analyses with adaptive elastic parameters and finite elements (fes) description are employed. the peak loads and collapse mechanisms predicted for frp-plated rc beams are validated by comparison with the corresponding experimental findings. keywords. finite element modelling; multi-yield-criteria limit analysis; reinforced concrete elements; frpstrengthening systems. introduction any existing steel-reinforced concrete structures, including decks and beams in highway bridges as well as beams, slabs and columns in buildings, are being assessed as having insufficient load carrying capacity due to their deterioration, ageing, poor initial design and/or construction, lack of maintenance, corrosion of steel reinforcement or underestimated design loads. in other cases they no longer comply with the current standards and requirements because of changed load conditions or modification of structural system for some reason. it is both economically and environmentally preferable to upgrade these structures rather than replace/rebuild them, even more if rapid, simple and effective strengthening techniques are employed. in this context, flexural and/or shear repair and rehabilitation of rc structures with externally bonded fiber reinforced polymer sheets, strips and fabrics is generally viewed as a valid and viable solution. moreover, these techniques can be carried out while the structure is still in use as well as they can be targeted at where the structural deficiency is more marked [1, 2]. on the other hand, to estimate the actual efficacy of the strengthening system, without performing expensive laboratory tests, as well as to design the proper repair interventions to reach a given gain in load carrying capacity, analytical tools and predictive numerical models are highly needed. experimental investigations confirm that, after the application of such frp techniques [3], a significant increase in flexural/shear capacity of the rc elements (up to about 125%) is achieved. experiments also show the enhancement of the confinement effect exerted on concrete by the frp laminates, resulting in shifting the failure mode of the strengthened elements from brittle concrete crushing to more ductile steel yielding and/or frp rupture [4]. in fact, the frp strengthening system mitigates crack development and, as a result, increases the overall ductility of the rc element. the above considerations make indeed a limit analysis plasticity-based numerical approach, among many others presented in m d. de domenico et alii, frattura ed integrità strutturale, 29 (2014) 209-221; doi: 10.3221/igf-esis.29.18 210 the relevant literature (see e.g. [5–8]), both applicable and effective, especially when primary interest is in determining the limit (peak) load of frp-strengthened rc elements. it is worth noting that all the phenomena arising just after a state of incipient collapse, such as delamination [9], debonding [10], damage in a wider sense, are not treatable and this consistently with the spirit of a limit analysis approach. accurate treatment of such post-elastic phenomena is prosecutable only with more accurate step-by-step fe nonlinear analyses. aware of such limitation, the methodology here proposed should then be viewed only as a preliminary design tool to gain a quick insight into the bearing capacity evaluation of the analyzed elements by determination of the peak load value, the prediction (but not the description) of failure mode as well as the detection of critical zones within the addressed frp-strengthened rc elements. the numerical methodology here referred, already used by the authors to predict the limit-state solution of rc elements (see e.g. [11, 12]) and of pinned-joint orthotropic composite laminates (see e.g. [14, 15]), is quite versatile and is based on iterative linear fe analyses carried out on the structure endowed with spatially varying moduli and, if necessary, given initial stresses. such quantities, viewed as pertaining to a fictitious material substituting the real one, are iteratively adjusted in such a way as to build, with reference to the assumed yield criteria, a collapse mechanism and an admissible stress field for the real structure so as to apply the kinematic and the static approaches of limit analysis, respectively. if a nonstandard nature of the constitutive behaviour has to be postulated, the peak load value of the analysed elements can, in fact, be numerically detected by predicting an upper and a lower bound to it. in the present study a very general multi-yield-criteria formulation of the above-mentioned limit analysis methodology is presented to appropriately describe the behaviour at collapse of structural elements of engineering interest strengthened by frp techniques. precisely, to simulate the behaviour at a state of incipient collapse of the three main constituent materials, concrete is described by a menétrey–willam-type yield criterion endowed with cap in compression, steel reinforcement bars are handled by the von mises yield criterion, frp strengthening laminates are governed by a tsai–wutype criterion and the quoted methodology is applied in concomitance to the three yield criteria. to demonstrate the actual capabilities of the proposed approach, large-scale prototypes of a few frp-strengthened rc beams, experimentally tested up to collapse [4, 16], are numerically investigated. theoretical background and fundamentals constitutive models of concrete, steel and frp oncrete is assumed as an isotropic, nonstandard material obeying a plasticity model derived from the menétrey– willam (m–w) failure criterion [17]. the latter provides a three parameter failure surface having the following expression: 2 ' ' ' ( , , ) 1.5 ( , ) 1 0 6 3c c c f m r e f f f                        (1) where ' 2 ' 22 2 2 ' '2 2 2 2 4(1 ) cos (2 1) ( , ) ; 3 12(1 ) cos (2 1) 4(1 ) cos 5 4                c t c t f fe e e r e m ef fe e e e e (2) eq. (1) is expressed in terms of the three stress invariants , ,   known as the haigh–westergaard (h–w) coordinates (i.e. hydrostatic and deviatoric stress invariants and lode angle); m is the friction parameter of the material depending, as shown in eq. (2), on the compressive strength 'cf , the tensile strength ' tf as well as the eccentricity parameter e . the eccentricity e , whose value governs the convexity and smoothness of the elliptic function ( , )r e , describes the out-ofroundness of the m–w deviatoric trace and it strongly influences the biaxial compressive strength of concrete. the failure surface (1) is open along the direction of triaxial compression; therefore, to limit the concrete strength in high hydrostatic regime, a cap in compression closing the surface (1) is adopted. the cap is formulated in the h–w coordinates as follows: ( , ) ( , ) ( ) for /( ) mw b acap a a b b a b                              2 2 2 2 0 3 (3) where ( , )mw a  is the explicit form of the parabolic meridian of the m–w surface easily obtainable from eq. (1). the values a and b entering eq. (3), namely the hydrostatic stress values corresponding to the intersection of the cap surface with the m–w surface and the hydrostatic axis, respectively, locate the cap position and can be calibrated c d. de domenico et alii, frattura ed integrità strutturale, 29 (2014) 209-221; doi: 10.3221/igf-esis.29.18 211 according to experimental results [18]. due to the dilatancy of concrete, a non-associated flow rule is postulated for the adopted m–w-type yield surface. steel is modelled as an isotropic, perfectly plastic material obeying the well-established von mises yield criterion. for a multi-axial loading scenario the von mises yield condition is expressed as: ( ) ( )i j i j yf f     0 (4) where ( )i j  is the von mises effective stress and yf is the yield strength. since in the fe-model the steel reinforcement are modelled by 1d truss elements, a uniaxial stress condition is considered in the following and eq. (4) applies in the simpler shape r yf  , r being the stress in the re-bar longitudinal direction. finally, the frp strengthening plates are modelled as orthotropic laminates in plane stress conditions obeying a tsai–wutype yield criterion [19]. for a unidirectional lamina in plane stress case the tsai–wu polynomial criterion has the following form: f f f f f f           2 2 211 1 22 2 66 6 12 1 2 1 1 2 22 1 (5) where 1 and 2 denote the principal directions of orthotropy (the fibres are directed along the material axis 1) and 6 12  in the contracted notation. the coefficients if and i jf ( , 1, 2, 6)i j  entering eq. (5) are functions of the strength parameters of the unidirectional lamina: : ; : ; : ; : ; : ; : t c t c t c t c f f f f f f f f x x y y x x y y s           1 2 11 22 66 12 11 222 1 1 1 1 1 1 1 1 2 (6) with: tx , cx the lamina longitudinal tensile and compressive strengths, respectively; ty , cy the lamina transverse tensile and compressive strengths, respectively; s the shear strength of the lamina. in the expressions (6) the compressive strengths cx and cy have to be considered intrinsically negative. also frp composite plates are considered as nonstandard material and, therefore, a non-associated flow rule is postulated for their constitutive behaviour. numerical limit analysis methodology two distinct limit analysis methods are applied simultaneously. the former, based on the kinematic approach of limit analysis, is able “to build” the collapse mechanism of the analysed structure and to compute an upper bound to the peak load multiplier. the latter, based on the static approach of limit analysis, is instead oriented “to build” a statically and plastically admissible stress field (corresponding to a given load) so giving a lower bound to the peak load multiplier. the reason for computing two bounds arises from the postulated non associativity of concrete and frp composite material that injects such characteristic on the behaviour of the whole rc-structural element. the two methods, conceived in [20] and [21] with reference to von mises materials, are known as linear matching method (lmm) and elastic compensation method (ecm), respectively. both have been rephrased and widely employed by the authors [14], [15]. their use to bracket the real peak load value of a structure made of a nonstandard material has been also experienced with success [11]–[13]. all the analytical details of lmm and ecm are in the above quoted papers and are here omitted for brevity. the novelty or key-feature of the present study is actually the implementation of lmm and ecm with reference to three different constitutive criteria at the same time. indeed, the three criteria are those given in the previous section for the three main constituents of the frp-strengthened rc members here addressed, i.e.: menétrey–willam-type for concrete; tsai–wu-type for frp sheets; von mises for steel bars. for completeness, the two methods are briefly expounded looking only at their geometrical interpretation sketched in fig. 1 and 2. on taking into account that both methods are performed iteratively, the sketches refer to a current iteration, say (k-1)th. looking at the geometrical interpretation of the lmm sketched in fig. 1, at the current iteration, say at the (k-1)th feanalysis, a fictitious structure (i.e. the structure under study with its real geometry, boundary and loading conditions but made of fictitious material) is analysed under loads ( 1)k ip p  , with ( 1)kp  load multiplier and ip assigned reference loads. the fictitious linear solution computed at each gauss point (gp) of the fe mesh, can be represented, at the generic gp, by a point ( 1)kl  lying on the complementary dissipation rate equipotential surface referred to the fictitious viscous material, say ( 1) ( 1) ( 1) ( 1)( , , )k k k kj i jw d w      , whose geometrical dimensions and centre position depend on the fictitious values ( 1)kid  and ( 1)kj  fixed at the current gp ( i ranging over the elastic constants entering the considered material; j d. de domenico et alii, frattura ed integrità strutturale, 29 (2014) 209-221; doi: 10.3221/igf-esis.29.18 212 ranging over the needed stress components). the point ( 1)kl  with its coordinates, say ( 1)kj  in the chosen principal stress space, shown in the sketch of fig. 1, represents the fictitious solution in terms of stresses while the outward normal at ( 1)kl  , say the normal of components ( 1)kj  , represents the fictitious solutions in terms of linear viscous strain rates. the fictitious moduli and initial stresses are then modified so that ( 1)kl  is brought onto the yield surface of the real constitutive material the analysed structure is made with. the latter surface is here presented by the ellipsoidal shaded surface of fig. 1. namely ( 1)kl  is brought to identify with point ( 1)km  , having the same outward normal as ( 1)kl  but lying on the real material yield surface. the described modification of ( 1)kid  and ( 1)kj  implies that the “modified” ( 1) ( 1) ( 1) ( 1)( , , )k k k kj i jw d w      matches the yield surface at point ( 1)km  , this step is the so called “matching procedure”, see again fig. 1. the fictitious solution in terms of strain rates, namely ( 1) ( 1)k c kj j     where the apex c stands for “at collapse”, as well as the stress coordinates of ( 1)km  , say the stresses at yield ( 1)y kj  , give all the information pertaining to a state of incipient collapse built at the current gp. in particular, the fictitious strain rates ( 1) ( 1)k c kj j     , with the associated displacement rates ( 1) ( 1)k c kj ju u    , define a collapse mechanism. the related stresses ( 1)y kj  are the pertinent stresses at yield.   ( , , ) 0  j i j yield s e f urfac d ( ) ( ) ( ) ( ) ( 1), ,      k k k k k j i jw d w  ( 1) ( 1)k kc    ( 1)k m  ( 1) ( 1) ( 1) ( 1) ( 1), ,         k k k k k j i jw d w  ( 1)k l  ( 1)k   3 2 1 3 2 o 1 ( 1)ky  figure 1: geometrical sketch, in the principal stress space, of the matching procedure, from iteration (k-1) to (k) at the current gp within the current element if the expounded rationale is repeated at all gps of the mesh, a collapse mechanism, ( 1) ( 1)( , )c k c kj iu    , with the related stresses at yield, ( 1)y kj  , can be defined for the whole structure and an upper bound value to the collapse load multiplier, say ( 1)kubp  , can be evaluated at current (k-1)th fe elastic analysis. however, the above stress at yield, computed through the matching, do not meet the equilibrium conditions with the acting loads ( 1)k ip p  and the procedure, as said, is carried on iteratively until the difference between two subsequent ubp values is less than a fixed tolerance. also the ecm can easily be explained by means of a geometrical sketch as the one given in fig. 2 with reference to a generic yield surface ( , , ) 0j i jf d   . the ecm starts with a first sequence, say 1s  , of fe analyses, carried on the d. de domenico et alii, frattura ed integrità strutturale, 29 (2014) 209-221; doi: 10.3221/igf-esis.29.18 213 structure endowed with the proper (real) material elastic parameters and suffering applied initial loads ( ) ( )1d di i sp p p p , and by the initial real values of the elastic parameters. at the current iteration, say at the (k-1)th fe analysis, the elastic stress solution is computed at the gps of the mesh. such values, averaged within the current element #e , allow to define a solution “at element level”, which, as shown in the sketch of fig. 2, locates in the principal stress space a stress point, say ( 1)ke e   . ( 1)kye  denotes the corresponding stress point at yield (i.e. lying on the yield surface) measured on the direction / | | e e e eo o      . in the figure are reported other stress points, representing the average stress elastic solution within elements #1, #2, , # , , #e n  . if the elastic solution at the # the  element is such that ( 1) ( 1)| | | |yk k e e eo o         then the element’s young modulus is reduced according to the formula: ( ) ( ) ( ) ( ) | | | | y k k k k e e e e e o e e o                 2 1 1 1   (7) where the square of the updating ratio, within the square brackets, is used to increase the convergence rate.   ( , , ) 0  j i j yield s e f urfac d 3 o ( 1) 2 ke   ( 1) 2 ky  p ( 1) 1 ke   ( 1) 1 ky   2 1 ( 1) ( 1) k k r e e    ( 1) ( 1) k k r y y e    ( 1)ky n  ( 1)k n e   figure 2: geometrical sketch, in the principal stress space, of the ecm at current iteration (k-1) of the current sequence s. stress points representing the elastic solution at elements #1, #2, , # , , #e n  ; with ( 1)kr  “maximum stress” among all the elements after the above moduli variation, the maximum stress value has to be detected in the whole fe mesh, namely the value corresponding to the stress point farthest away from the yield surface, say ( 1)kr  in the sketch of fig. 2. if ( 1)| | kro    is greater than ( 1)| |y kro    (as drawn in fig. 2) a new fe analysis is performed within the current sequence trying to re-distribute the stresses within the structure; and this by keeping fixed the applied loads but with the updated ( )kee values given by eq. (7). the iterations are carried on, inside the given sequence, until all the stress points just reach or are below their corresponding yield values, which means that an admissible stress field has been built for the given loads. increased values of loads are then considered in subsequent sequences of analyses, each one with an increased value of ( )d sp , till further load increase does not allow the stress point ( 1)kr  to be brought below yield by the re-distribution procedure. a lbp load multiplier can then be evaluated at last admissible stress field attained for a maximum acting load ( )d i sp p , say at s s , and at last fe analysis, say at k k , as ( ( ) ( ) ) | | | | d lb y k r k r sp o p o    (8) d. de domenico et alii, frattura ed integrità strutturale, 29 (2014) 209-221; doi: 10.3221/igf-esis.29.18 214 numerical simulations of experimental tests analysed full-scale tests he numerical study has comprised 6 rc beams, flexuralor shear-strengthened with different layers and configurations of externally bonded carbon frp (cfrp) or glass frp (gfrp) sheets. full-scale four-point bending experimental tests [4, 16] are numerically simulated to predict peak load and failure mechanism. precisely: two experimental campaigns have been taken into considerations in this paper. the first campaign includes 3 rc beams tested by shahawy et al. [4] (namely beams labelled s5-pre1, s6-pre3, s6-pre5) strengthened with 1 to 3 layers of cfrp laminates which were bonded to the soffit of the beam. such tests were carried out up to failure to investigate mainly the effects of a variable number of cfrp laminates on the first crack load, cracking behaviour, deflections, serviceability loads, ultimate strength as well as failure modes. the second campaign was carried out at the oregon department of transportation by kachlakev et al. [16] in the late 1990s within an experimental project aimed to investigate the structural behaviour of the horsetail creek bridge. precisely, 3 full-scale rc beams were constructed and tested to experimentally replicate the structural behaviour of the actual strengthened bridge beams. different configurations and strengthening schemes were adopted: a) one beam was flexural-strengthened by cfrp sheets, applied to the bottom of the element and having fibres oriented along the length of the beam (specimen f-sb); b) one beam was shear-strengthened by gfrp sheets, applied on the side of the element and having fibres oriented perpendicular to the length of the beam (specimen s-sb); c) one beam (specimen fs-sb) was both shearand flexural-strengthened with combined systems a) plus b). a quite ductile behaviour was observed in almost all the 6 examined specimens and the increased flexural/shear capacity was fully activated. in particular, in [4] all the strengthened beams failed by concrete crushing with a significant rise in the flexural capacity and ductility as the number of laminates increases; the restraining effect conveyed by the cfrp laminates was experienced even at first crack, the strengthened beams exhibiting closely spaced cracks as compared with several widely spaced cracks of the corresponding control (un-strengthened) beam. similarly, in [16] the application of frp sheets increased the load-carrying capacity and improved ductility of the beams, with greater deflections at failure; moreover, the addition of shear gfrp sheets compensated for the lack of stirrups and altered the failure mode from diagonal tension (shear) failure to ductile (flexure) failure. the beams, in fact, failed by flexure at the mid-span, with yielding of steel re-bars followed, after extended deflections, by crushing of concrete at the top of the beam in compression zone. however, it is worth noting that specimen fs-sb actually did not fail in the experimental test, the loading being terminated because of limitations in the testing machine capacity. materials properties of concrete, steel re-bars and frp laminates of the analysed beams are reported in tab. 1–3. for all the examined specimens the poisson’s ratio for concrete and steel has been assumed as 0.2  and 0.3  , respectively. where not explicitly given as experimental data, the value of the concrete tensile strength reported in tab. 2 has been assumed as 1/ 2' '0.33 ( )t cf f according to [22], while that of the young modulus .'( / )c ce f 0322 10 . likewise, with regard to the frp strengthening sheets, typical values of the frp lamina moduli and strengths, according to [23], have been assumed in tab. 3 where not directly available in the experimental campaigns. reinforcement bar d (mm) a (mm2) fy (mpa) es (gpa) φ3 3 7.0 468.84 200.0 φ9 9 50.3 468.84 200.0 φ13 13 132.7 468.84 200.0 #5 15.9 199 410 200.0 #6 19.1 284 410 200.0 #7 22.2 387 410 200.0 table 1: material properties and geometrical data of reinforcement bars of the analysed specimens t d. de domenico et alii, frattura ed integrità strutturale, 29 (2014) 209-221; doi: 10.3221/igf-esis.29.18 215 specimen label 'cf (mpa) 'tf (mpa) ce (gpa) s5-pre1 29.65 1.80 30.48 s6-pre3 41.37 2.12 33.68 s6-pre5 41.37 2.12 33.68 f-sb 13.75 2.31 17.55 s-sb 14.73 2.39 18.16 fs-sb 13.02 2.25 17.08 table 2: material properties of concrete of the analysed specimens frp system # frp lamina properties frp lamina strengths f t (mm) e1 (gpa) e2 (gpa) e6 (gpa) 12 (-) tx (mpa) cx (mpa) ty (mpa) cy (mpa) s (mpa) 1: cfrp unidirectional 0.17 141.3 14.5 5.86 0.21 2758 -2758 52 -206 93 2: cfrp unidirectional 1.00 62.0 4.8 3.27 0.22 958.4 -599 57 -228 99.97 3: gfrp unidirectional 1.30 21.0 7.0 1.52 0.26 599.8 -333.2 39 -128 30.34 table 3: material properties of strengthening frp systems of the analysed specimens mechanical model, cross-section details and fe modelling the mechanical model of the analysed beams is shown in fig. 3: geometry loading and boundary conditions of the beams are reported in fig. 3a; cross-section details with frp strengthening schemes for each rc beam are instead sketched in fig. 3b. the beams were tested in four-point bending, i.e. they were simply supported and loaded by two equal line loads symmetrically placed about mid-span and denoted as p p , with p being the load multiplier and p the reference load whose magnitude has been assumed so as to be equivalent to a total load of 100kn. the symmetry of the problem allows modelling only half specimen: zero displacements in z direction are set on the shaded symmetry plane shown in fig. 3a. note that the flexural and shear frp sheets of the beams tested in [16] were wrapped continuously around the bottom of the beam, that is a u-shaped strengthening system has been adopted as shown in fig. 3b. tab. 4 specifies, for each specimen, geometrical data, mechanical details, steel re-bars arrangement and frp configuration. the elastic fe analyses, representing the iterations within the two limit analysis methods, have been performed by the fecode adina [24]. 3d-solid 8-nodes elements, with 2x2x2 gps per element, are adopted for modelling concrete; steel rebars and stirrups are modelled by 1d truss elements, having 2 nodes and 1 gp per element; 2d-solid 4-nodes membrane elements, under plane stress hypothesis and with 2x2 gps per element, are used for the thin frp strengthening sheets. each node is endowed with the three translational degrees of freedom, while a perfect bond between concrete and steel re-bars as well as between concrete and frp sheets is postulated in the fe-model. concrete, steel re-bars and stirrups are assumed isotropic; an orthotropic material formulation has been adopted for frp sheets in the material reference system (1,2,3) where (1,2) define the orthotropy plane of the lamina with fibres oriented along the direction 1. concerning the m– w-type yield function, for the eccentricity e , whose value can be related to the material brittleness ' '/t cf f , the expression proposed by balan et al. [25] has been used. the cap surface, eq. (3), is instead defined by the values '. ca f  0 7923 and '.b cf 18964 as suggested by li and crouch [18]. to give an idea of the fe modelling, the meshes of two of the analysed specimens are reported in fig. 4. it is worth noting that the fully 3d fe model used (i.e. 3d fes in conjunction with 3d constitutive concrete laws), is more accurate and truthful than 2d numerical approaches often employed in this context. in addition, the frp strengthening plates have been modelled by 2d orthotropic laminae so taking into account the transverse stiffness contribution across the plates, though not comparable to that along the direction of the fibres. the thickness of such 2d-solid elements has been set in accordance with the number of the layers of the frp strengthening sheets. the number of fes, summarised in tab. 5, has been chosen after a preliminary mesh sensitivity study to assure an accurate fe elastic solution. finally, a fortran main program has been utilised to control the “adjusting” of the elastic parameters at each gp of each element to accomplish the matching, when performing the lmm, and to realise the stress redistribution, within the ecm. d. de domenico et alii, frattura ed integrità strutturale, 29 (2014) 209-221; doi: 10.3221/igf-esis.29.18 216 numerical predictions against experimental findings the values of the numerically predicted upper (pub) and lower bound (plb) to the peak load multiplier are reported in tab. 6 and compared to the experimentally detected ones (pexp) for all the examined specimens. by inspection of the numerical results, the proposed limit analysis methodology appears to be an accurate predictive tool for determining the loadcarrying capacity of frp-plated rc elements. the upper bound values, predicted by the lmm, are always above the experimental ones, with relative errors of approximately 5%. likewise, the lower bound values, predicted by the ecm, are below the corresponding experimental values with relative errors of less than 10%. the use of the lmm and of the ecm, both applied simultaneously to the three yield criteria of the main constituents of the analysed structural elements (the latter being the key feature of the numerical methodology here proposed), allows “bracketing” the real collapse load value by two bounds that are sufficiently close to each other so giving a very precise result in terms of peak load multiplier. the average (among all the considered specimens) relative errors concerning the pub and plb predictions are of 6.08% and 7.55%, respectively. a) z x y 0zu  /2b 0l h l p p p p 1l b) yd yd ft top re-bars bottom re-bars u-shaped frp (flexural-strengthening) b h f-sb yd yd b h ft s5 pre1, s6 pre3, s6 pre5 stirrups top re-bars bottom re-bars frp sheet (flexural-strengthening) ft yd yd ft top re-bars bottom re-bars u-shaped frp (shear-strengthening) b h ft s-sb figure 3: mechanical model of the analysed specimens: a) geometry, loading and boundary conditions; b) cross-section details with frp strengthening schemes d. de domenico et alii, frattura ed integrità strutturale, 29 (2014) 209-221; doi: 10.3221/igf-esis.29.18 217 specimen label geometrical details steel re-bars arrangement frp arrangement b (mm) h (mm) l (mm) l0 (mm) l1 (mm) dy (mm) top re-bars bottom re-bars stirrups frp system # n layers s5-pre1 203 305 2743 2439 305 54 2 φ3 2 φ13 φ9@203 1a 1 s6-pre3 203 305 2743 2439 305 54 2 φ3 2 φ13 φ9@203 1a 2 s6-pre5 203 305 2743 2439 305 54 2 φ3 2 φ13 φ9@203 1a 3 f-sb 305 768 6096 5486 1828 63.5 2#6, 1#5 3#7, 2#6 – 2a 1–3 s-sb 305 768 6096 5486 1828 63.5 2#6, 1#5 3#7, 2#6 – 3b 2, 4 fs-sb 305 768 6096 5486 1828 63.5 2#6, 1#5 3#7, 2#6 – 2a+3b 1–3+ 2, 4 a the fibres are oriented along the length of the beam; b the fibres are perpendicular to the length of the beam. table 4: geometrical and mechanical details of the analysed specimens 1 layer frp system  2 layers frp system  3 layers frp system  fibre orientation f-sb z x y z x x y a) b) figure 4: fe-model of two analysed specimens: a) specimen f-sb; b) specimen s-sb d. de domenico et alii, frattura ed integrità strutturale, 29 (2014) 209-221; doi: 10.3221/igf-esis.29.18 218 specimen label number of fes in the specimen models 3d-solid elements 2d-solid elements truss elements total elements number of nodes s5-pre1 672 100 168 940 1397 s6-pre3 672 100 168 940 1397 s6-pre5 672 100 168 940 1397 f-sb 816 150 132 1098 1402 s-sb 816 280 132 1228 1402 fs-sb 816 430 132 1378 1402 table 5: number of fes for the analysed specimens. specimen label peak load multipliers pexp pub plb pub/pexp plb/pexp s5-pre1 0.666 0.720 0.570 1.081 0.856 s6-pre3 0.979 1.093 0.913 1.116 0.933 s6-pre5 1.162 1.206 1.076 1.038 0.926 f-sb 6.900 7.255 6.730 1.051 0.975 s-sb 6.900 7.164 6.497 1.038 0.942 fs-sb 9.300a 9.685 8.512 1.041 0.915 a beam fs-sb actually did not fail in the test and the reported value has been predicted by a nonlinear fe analysis [16]. table 6: peak load multipliers for the analysed specimens fig. 5 shows, for two of the analysed specimens, namely beam s6-pre5 and f-sb, the plots of the upper and lower bounds to the peak load multiplier versus the iteration number. analogous results are obtained for all the other specimens but are omitted for sake of brevity. as shown, only a few iterations are sufficient to obtain a converged solution in terms of both pub and plb value. a) b) figure 5: values of the upper (pub) and lower (plb) bounds to the peak load multiplier versus iteration number against to the collapse experimental threshold (pexp): a) specimen s6-pre6; b) specimen f-sb. d. de domenico et alii, frattura ed integrità strutturale, 29 (2014) 209-221; doi: 10.3221/igf-esis.29.18 219 the numerical methodology also gives some hints on the state of specimens at incipient collapse by pointing out the plastic zones (collapse mechanism) built by the lmm at the last converged solution. fig. 6a and 7a show the strain rate components at collapse, cxx , of concrete fes in the deformed configuration for beam fsb and s6-pre3, respectively. the plastic zones arise at the mid-span of the element, while the remaining portions of the beam rotate rigidly around a sort of plastic hinge as observed in the experimental flexural collapse mechanism. the predicted plastic zones appear sufficiently confined and reasonably close to the damaged zones experimentally detected, see [4] and [16]. the beams fail due to concrete crushing near the loading point in the compression zone as observed in the experimental test. the collapse mechanism is also described by the strain rates at collapse of frp fes in the fibre direction, i.e. 1c , reported in figs. 6b and 7b in the un-deformed configurations for the two analysed beams. the most critical frp zones are highlighted and, obviously, these zones are those where the frp sheets, to a greater extent, bear the load and act compositely with concrete in the global collapse mechanism. finally, it is worth noting that for both the predicted collapse mechanisms the stresses numerically obtained in the steel fes at the mid-span (where a plastic hinge develops) are just yielded as observed in the experimental outcomes. other types of frp-strengthened rc-elements have been analysed within the same research programme, obtaining encouraging confirmations on the predictive performance of the proposed approach, see e.g. [26]. a) b) figure 6: collapse mechanism of the specimen f-sb: a) contour plot of the strain rate components cxx of concrete fes reported in the deformed configuration of the beam; b) contour plot of the strain rates 1c of frp fes in the fibre direction a) b) figure 7: collapse mechanism of the specimen s6-pre3: a) contour plot of the strain rate components cxx of concrete fes reported in the deformed configuration of the beam; b) contour plot of the strain rates 1c of frp fes in the fibre direction concluding remarks numerical limit analysis methodology has been presented to analyse rc members strengthened with externally bonded frp plates. a multi-yield-criteria formulation has been proposed to appropriately describe the behaviour, at a state of incipient collapse, of the three main constituent materials: concrete, steel-bars and frp laminates. the latter formulation is essential to deal with concrete crushing, steel bars yielding and frp rupture that may occur at ultimate limit states. the lack of associativity postulated for concrete and frp composite laminates has resulted in adopting a nonstandard limit analysis approach which underlies the use of two numerical methods for limit analysis, the lmm and the ecm, to search for an upper and a lower bound to the actual peak load multiplier. operationally, as compared to previous results presented in [12] or to alternative numerical approaches e.g. [16, 27, 28], the multi-yield-criteria formulation here proposed does not entail any significant computational cost: simple fe analyses (performable with any commercial fe-code) have to be solved. the more accurate and consistent 3d modelling that accounts for three materials through three distinct yield criteria seems to give good results. the reliability and effectiveness of the proposed methodology have been proved by analysing full-scale laboratory tests on rc beams strengthened with externally bonded frp sheets. the obtained numerical results, in terms of peak load a d. de domenico et alii, frattura ed integrità strutturale, 29 (2014) 209-221; doi: 10.3221/igf-esis.29.18 220 multiplier and collapse mechanism, are very satisfactory and correlate well with the corresponding experimental findings [4, 16]. the methodology appears able to deal with practical engineering problems such as the estimate of the loadcarrying capacity of rc beams strengthened by frp sheets, issue of great significance in civil engineering. the numerical methodology may be also viewed as an useful predictive tool for estimating the actual efficacy of strengthening systems for existing structures. references [1] american concrete institute aci 440, guide for the design and construction of externally bonded frp systems for strengthening concrete structures, aci 440.2r-08 (2008). [2] fib bulletin 14, externally bonded frp reinforcement for rc structures, task group 9.3, international federation of structural concrete, (2001). [3] dong, j., wang, q., guan, z., structural behaviour of rc beams with external flexural and flexural–shear strengthening by frp sheets, composites part b, 44 (2013) 604–612. [4] shahawy, m.a., arockiasamy, m., beitelmant, t., sowrirajan, r., reinforced concrete rectangular beams strengthened with cfrp laminates, composites part b, 27b (1996) 225–233. [5] maier, g., pan, l., perego, u., geometric effects on shakedown and ratchetting of axisymmetric cylindrical shells subjected to variable thermal loading, engineering structures, 15(6) (1993) 453–466. [6] ardito, r., cocchetti, g., maier, g., generalised limit analysis in poroplasticity by mathematical programming, archive of applied mechanics, 80 (2010) 57–72. [7] caporale, a., feo, l., luciano, r., limit analysis of frp strengthened masonry arches via nonlinear and linear programming, composites part b: engineering, 43(2) (2012) 439–446. [8] grande e., milani g., sacco e., modelling and analysis of frp-strengthened masonry panels, engineering structures, 30(7) (2008) 1842–1860. [9] benvenuti, e., vitarelli, o., tralli, a., delamination of frp-reinforced concrete by means of an extended finite element formulation, composites part b: engineering, 43(8) (2012) 3258–3269. [10] marfia, s., sacco, e., toti, j., a coupled interface-body nonlocal damage model for the analysis of frp strengthening detachment from cohesive material, fracture and structural integrity, 18 (2011) 23–33. [11] pisano, a.a., fuschi, p., de domenico, d., a kinematic approach for peak load evaluation of concrete elements, computers and structures, 119 (2013), 125–139. [12] pisano, a.a., fuschi, p., de domenico, d., peak loads and failure modes of steel-reinforced concrete beams: predictions by limit analysis, engineering structures, 56 (2013) 477–488. [13] pisano, a.a., fuschi, p., de domenico, d., limit state evaluation of steel-reinforced concrete elements by von-mises and menétrey–willam-type yield criteria, international journal of applied mechanics, (accepted for publication). [14] pisano, a.a., fuschi, p., de domenico, d., a layered limit analysis of pinned-joints composite laminates: numerical versus experimental findings, composites part b, 43 (2012) 940–952. [15] pisano, a.a., fuschi, p., de domenico, d., failure modes prediction of multi-pin joints frp laminates by limit analysis, composites part b, 46 (2013), 197–206. [16] kachlakev, d., miller, t., yim, s., chansawat, k., potisuk, t., finite element modeling of reinforced concrete structures strengthened with frp laminates, final report spr 316 (2001), oregon department of transportation research group, usa, may 2001. [17] menétrey, p., willam, k.j., a triaxial failure criterion for concrete and its generalization, aci structural journal, 92 (1995) 311–318. [18] li, t., crouch, r., a c2 plasticity model for structural concrete, computers and structures, 88 (2010) 1322–1332. [19] tsai, s.w., wu, e.m., a general theory of strength for anisotropic materials, j. of comp. mater., 5 (1971) 58–80. [20] ponter, a.r.s., carter, k.f., limit state solutions, based upon linear elastic solutions with spatially varying elastic modulus, comput. methods appl. mech. eng., 140 (1997) 237–258. [21] mackenzie, d., boyle, j.t., a method of estimating limit loads by iterative elastic analysis parts i, ii, iii, international journal of pressure vessels and piping, 53 (1993), 77–142. [22] bresler, b., scordelis, a.c., shear stength of reinforced concrete beams, j. of am. concr. inst., 60(1) (1963) 51–72. [23] daniel, i.m., ishai, o., engineering mechanics of composite materials, oxford university press, usa, 1994. [24] adina r & d, inc. theory and modeling guide volume i: adina, report ard 11-8, watertown (ma,usa), (2011). d. de domenico et alii, frattura ed integrità strutturale, 29 (2014) 209-221; doi: 10.3221/igf-esis.29.18 221 [25] balan, t.a., spacone, e., kwon, m., a 3d hypoplastic model for cyclic analysis of concrete structures, engineering structures, 23 (2001) 333–342. [26] de domenico, d., pisano, a.a., fuschi, p., a fe-based limit analysis approach for concrete elements reinforced with frp bars, composite structures, 107 (2014) 594–603. [27] hu, h.t., lin, f.m., jan, y.y., nonlinear finite element analysis of reinforced concrete beams strengthened by fiberreinforced plastics, composite structures, 63 (2004) 271–281. [28] limam, o., foret, g., ehrlacher, a., rc beams strengthened with composite material: a limit analysis approach and experimental study, composite structures, 59 (2003) 467–472. microsoft word numero 16 articolo 4 f. carta et alii, frattura ed integrità strutturale, 16 (2011) 34-42; doi: 10.3221/igf-esis.16.04 34 damage tolerance analysis of aircraft reinforced panels f. carta, a. pirondi industrial engineering department, university of parma, v.le g.p. usberti 181/a, 43124 parma – italy abstract. this work is aimed at reproducing numerically a campaign of experimental tests performed for the development of reinforced panels, typically found in aircraft fuselage. the bonded reinforcements can significantly reduce the rate of fatigue crack growth and increase the residual strength of the skin. the reinforcements are of two types: stringers and doublers. the former provides stiffening to the panel while the latter controls the crack growth between the stringers. the purpose of the study is to validate a numerical method of analysis that can predict the damage tolerance of these reinforced panels. therefore, using a fracture mechanics approach, several models (different by the geometry and the types of reinforcement constraints) were simulated with the finite element solver abaqus. the bonding between skin and stiffener was taken either rigid or flexible due to the presence of adhesive. the possible rupture of the reinforcements was also considered. the stress intensity factor trend obtained numerically as a function of crack growth was used to determine the fatigue crack growth rate, obtaining a good approximation of the experimental crack propagation rate in the skin. therefore, different solutions for improving the damage tolerance of aircraft reinforced panels can be virtually tested in this way before performing experiments. keywords. aircraft stiffened panels; fatigue crack growth; damage tolerance analysis. introduction n aircraft fuselage, aluminum stiffeners are connected to panel in longitudinal and circumferential directions. a particularly significant application is the direct bonding between stringers and the surface of the fuselage skin. the main features of the reinforced bonded panels concern better damage tolerance and higher stability at different types of loads [1, 2]. the experiments on aluminum panels with bonded stiffeners show that a limit of the aluminum reinforcement is the premature rupture of the reinforcement caused by the load transfer from the skin to the stiffeners when the crack runs underneath it. to improve the tolerance to the fracture, the doublers or reinforcement cords should preferably be made of material resistant to fatigue, with high stiffness and static strength [3, 4]. panels made of a thin metal skins stiffened with bonded reinforcements insensitive to fatigue, can ensure slow crack propagation if not its arrest, and the capability to withstand a large damage, combined with a low structural weight. the effects of this bonded reinforcements or doublers are very difficult to predict numerically or analytically, because of the complex mechanisms of failure: separation at the interface between skin and reinforcement around the area of nucleation and propagation of the crack; load redistribution between the damaged and undamaged reinforcement; fatigue damage of the reinforcement which may cause his premature rupture; crack bridging by the doublers thanks if they have a sufficiently high fatigue strength. i http://dx.medra.org/10.3221/igf-esis.16.04&auth=true http://www.gruppofrattura.it f. carta et alii, frattura ed integrità strutturale, 16 (2011) 34-42; doi: 10.3221/igf-esis.16.04 35 in addition, secondary effects, such as residual stresses generated by the bonding process and bending caused by the eccentricity of the load with respect to the neutral axis of the reinforced panel cross-section, increase the complexity of the phenomenon. reliable predictions of crack growth and residual strength in bonded structures can be based mainly on empirical considerations. the experimental results which support the numerical analysis reported in this work refer to an experimental investigation carried out by airbus in a period from 2002 to 2007. through an extensive campaign of tests, several methods of reinforcement were analyzed, using bonded reinforcements in the fuselage panels. to achieve a quantitative study, in the analysis different types of connection between the reinforcements and the skin were considered. in the literature, numerical studies on fcp (fatigue crack propagation) in reinforced structures are available. however, if the damage tolerance assessments appear to be practicable in integral reinforced structures [5], the same assessment is not straightforward in differential structures with bonded joints between skin and chords [6, 7] due to the complex mechanisms mentioned previously. stiffened differential structures he stiffened differential structures can actually be reproduced with proper models that allow replicating the stiffener effect using the “crack arrest” philosophy design. in this approach after an initial propagation, the crack arrests due to a stiffener when a given length is reached (see fig. 1). figure 1: comparison between the several design solutions according the “crack arrest” method.   in the differential structures the crack propagates typically only in the skin, then the completely intact stiffeners can control the defect evolution during the propagation, due to the load transfer from the skin to the stiffeners which, in turn, means that the stress intensity factor decreases. this fact underlines the effectiveness design of crack arrest. several experiments have shown a significant beneficial effect due to the presence of reinforcements in differential structures [1, 2]. in many engineering fields such as aeronautics, automotive, marine or civil engineering, plates and shell made with laminate composite structures are largely used in load-bearing structural members. important examples of these applications can be observed in aerospace engineering, where thin laminates are reinforced by a certain number of profiles (the so called stringers).     figure 2: cross sections of several kinds of stringers. such structural parts can readily be found in fuselages, tail planes, or wind covers of aircrafts and typically consist of a thin plate or moderately curved thin shell that is stiffened by a certain number of shaped stringers (see fig. 2). especially stringers which have a closed-profile cross-section may provide a high torsional stiffness to the plate such that the composite plate itself can be assumed to be elastically restrained to some degrees [8]. t http://dx.medra.org/10.3221/igf-esis.16.04&auth=true http://www.gruppofrattura.it f. carta et alii, frattura ed integrità strutturale, 16 (2011) 34-42; doi: 10.3221/igf-esis.16.04 36 another kind of reinforcement, called doubler, is usually positioned in the separation zone between stringers, oriented parallel to them (see fig. 3). figure 3: representations of the possible placements of the doublers: in the middle of the bay (between the stringers) or under the stringers. because of their shape, the doublers have not a stiffening function, but they slow down the crack grow rate in the zone between the stringers (the so-called bays). the doublers are typically bonded to the skin and experimental studies are showed they are more efficient with a thick section rather than a thin section [2]. experiments total of 35 stiffened panels, representative of a typical fuselage skin of a long-range family aircraft, were manufactured and tested in the laboratories of eads-iw ottobrunn. the fatigue crack propagation (fcp) rate was investigated for twenty-four of them. the remaining eleven panels were tested for the residual strength. the panel shown in fig. 4 has been tested and it is characterized by a skin (1224 mm wide and 1455 mm long) with seven equally spaced bonded stringers. in addition to the stringers, bonded doublers are positioned below and between the stringers in order to provide additional reinforcement. all the doublers are placed orthogonal to the direction of crack propagation alike the stringers. figure 4: representation of a “seven stringers” panel with doublers bonded between and under the stringers (a) and with an additional glass fiber reinforcement (b). the tests were performed by means of a servo-hydraulic instron 8805 machine with a 1mn load cell. the clamping was specifically designed for the 7-stringers panels (see fig. 5). an anti-bending device was installed to prevent the out of plane deflection of the panel during the test (see fig. 5). the skin, like the doublers, were made of 2024-t3 aluminum alloys with 1,4 mm thickness the former and 0,8 mm the latter. the stringers were “j”-shape extruded profiles made of high strength 7349-t76511 aluminum alloy. an antibending device was installed to prevent the out-of-plane deflection of the panel during the test (see fig 5). in the experiments, the fatigue crack propagation was investigated starting from a through-the-thickness, 50 mm-long, machined notch. the crack was placed across the middle stringer; this stringer and the underlying doubler (when present) were also cut. the loading parameters were the same for all the tested configurations (constant amplitude loading, 280 kn maximum force and 0.1 load ratio). the tests ended when the crack was “four bays” long or in case of panel failure. a http://dx.medra.org/10.3221/igf-esis.16.04&auth=true http://www.gruppofrattura.it f. carta et alii, frattura ed integrità strutturale, 16 (2011) 34-42; doi: 10.3221/igf-esis.16.04 37 figure 5: representation of the clamping system (on the left) and of the anti-bending device (on the right). the observed crack lengths within the two bays were practically symmetrical: this has permitted to draw the crack propagation curves [a = f(n)] considering the average crack length between the left and right crack tip displacement (see fig. 6). figure 6: experimental fcp curve illustration of left and right crack length and their average values (two bays-cracked panel). numerical modeling he panels tested at eads-iw are simulated using finite element analysis with the commercial software abaqus. a quarter of the panel was modeled so as to limit the computational complexity. two important approximations in the fe analysis are: the propagation occurs in the perpendicular direction to that of load application (mode i); the front of the crack is assumed to be straight and modeled with two elements in the thickness (see fig. 7). figure 7: straight crack front in the thickness direction. t http://dx.medra.org/10.3221/igf-esis.16.04&auth=true http://www.gruppofrattura.it f. carta et alii, frattura ed integrità strutturale, 16 (2011) 34-42; doi: 10.3221/igf-esis.16.04 38 material properties the following elastic constants were used in the fe analysis. skin and doublers: e = 73100 mpa young’s modulus ν = 0,33 poisson’s ratio. stringers: e = 71700 mpa young’s modulus ν = 0,33 poisson’s ratio. loads and constraints n fig. 8, the loads and the constraints are shown, while the bonding between the components of the panel was reproduced in abaqus with the tie constraint. in the simulation analysis the maximum load of the experimental tests was considered (fmax= 280 kn). figure 8: loads and constraints on the quarter of the panel modeling and mesh n the study, two typologies of element (shell and solid) and different refinements of the mesh at the crack tip were considered (see fig. 9), namely: a 3d model with shell elements; a 3d model with solid elements (linear or quadratic geometric order) a 3d model with discretization by means of shell-to-solid coupling. (a) (b) (c) (d) figure 9: different modeling typologies: second-order shell elements with collapsed quarter-point node elements at the crack tip (a), first-order solid elements collapsed at the crack tip (b), second-order solid elements with collapsed quarter-point node elements at the crack tip (c), same as (a) (c) with shell-to solid coupling between solid and shell parts (d). i i http://dx.medra.org/10.3221/igf-esis.16.04&auth=true http://www.gruppofrattura.it f. carta et alii, frattura ed integrità strutturale, 16 (2011) 34-42; doi: 10.3221/igf-esis.16.04 39 geometrically linear analyses were performed to find, for each crack length analyzed, the value of k corresponding to the maximum load of the test. the stress intensity factor range k was then calculated according to the load ratio used in the experiments. the mode i, ii and iii stress intensity factors are calculated using the contour integral method and they showed a limited variability with the distance of the contour from the crack tip. the kii and kiii parameters assume always values close to zero, therefore the crack propagation is mode i-dominated. for each size of the defect an average value of the k factor was calculated across the thickness (see fig. 10). figure 10: k value in 4 different positions of the crack tip across a doubler and a stiffener. after a study of convergence based on analysis between various discretization solutions, a modeling with linear solid elements was chosen (see tab.1), in this way through a mobile partition (see fig. 11) with good density of elements near to the fracture tip (see fig. 7), a good compromise between the convergence of the numerical results in terms of stress intensity factor and acceptable computation times was achieved. element characteristics k1 [mpam] process time2 k deviation3 [%] shell linear 1771.3 5.2 3.46 shell parabolic (qpnt) 1780.5 33.1 3.99 solid linear 1780.7 7.4 4.01 solid parabolic (qpnt) 1712 100 0 1 values obtained by the solver taking into account the follow conditions of analysis: same configuration of loads and constraints; same crack length (a = 42,71 mm); same element dimensions in the plane of extension of the skin in the panel; 2 normalized values in respect to computation time with modeling elements solid parabolic (qpnt) 3 the deviations were assessed against the best geometric discretization (with solid parabolic elements qpnt) table 1: comparison between the discretization solutions considered in the fe study (qpnt is quarter-point node technique). figure 11: the mobile partition around the crack tip. http://dx.medra.org/10.3221/igf-esis.16.04&auth=true http://www.gruppofrattura.it f. carta et alii, frattura ed integrità strutturale, 16 (2011) 34-42; doi: 10.3221/igf-esis.16.04 40 once chosen the modeling of the skin, stringer/doubler and crack tip, different models of skin-reinforcement coupling were considered. the main differences consist in the modeling of the presence of the adhesive or not and of the rupture of a reinforcement after the crack has passed it (see tab.2 and fig. 13). the presence of an anti-bending device was also reproduced (model id 4-nb – see fig. 12). figure 12: representation of the anti-bending device developed in the fe modeling of panel 4-nb (no bending). model id characteristics skin doublers stringers adhesive stiffeners 1 al-alloy 2024-t3 al-alloy 2024-t3 al-alloy 7075t73511 unbroken 2 al-alloy 2024-t3 al-alloy 2024-t3 al-alloy 7075t73511 fm73m0.3 unbroken 3 al-alloy 2024-t3 al-alloy 2024-t3 al-alloy 7075t73511 fm73m0.3 adhesive transversal separation 4 al-alloy 2024-t3 al-alloy 2024-t3 al-alloy 7075t73511 fm73m0.3 adhesive transversal separation + 1rst doublers rupture 4-nb* al-alloy 2024-t3 al-alloy 2024-t3 al-alloy 7075t73511 fm73m0.3 adhesive transversal separation + 1rst doublers rupture * model with the same characteristics of the model 4, but with the implementation of a no-bending device with a contact analysis between the skin and a transversal toolbar table 2: fe models developed in this work. figure 13: representation of the different skin-stiffener couplings simulated. to assess the number of cycles to attain a given crack length, the following procedure was considered: in the range of interest, the fcp data of the skin material, were approximated with a straight line in a bi-logarithmic da/dn-δk plane (paris regime); the experimental data were taken from afgrow database [9]. http://dx.medra.org/10.3221/igf-esis.16.04&auth=true http://www.gruppofrattura.it f. carta et alii, frattura ed integrità strutturale, 16 (2011) 34-42; doi: 10.3221/igf-esis.16.04 41 in the fe model, the k factor calculation was done in steps, then a model for each specific crack length was made (see fig. 10). since the crack growth rate varies significantly near the reinforcements, most of the steps were concentrated in those areas; the number of cycles was obtained by a numerical integration with a trapezoidal rule: , 1 , 1 1 1 1 1 2 i i i im m i i n a c k c k            where i and i+1 are the limits of a single increment. other details considered after preliminary studies are the effective load ratio at the crack tip, which changes during the crack propagation, and the effect of considering a geometric nonlinearity in the analysis of reinforced panels. results and discussion n the following figures, the analysis results are shown for each of the different models. with two elements in the skin thickness, the stress contour map at the crack tip is represented on fig. 14. figure 14: node positions in seven contours chosen for the crack modeling. the number 1 is the surface where the stiffeners are bonded. at first, the influence of the presence of the adhesive between skin and stiffeners was assessed (model 02 vs. model 01). where adhesive was introduced, the final crack length is reached in a lower number of cycles (see fig. 15). in model 03, the separation of the adhesive under the first doubler was modeled and an increase of crack growth rate in the first bay is observed. in the panels 4 and 4-nb, the increase of k factors after the crack runs beyond the first stiffener is caused by the (simulated) rupture of the first doubler (see fig. 16). figure 15: comparison between experimental and numerical fcp curves (models 01, 02 and 03). i http://dx.medra.org/10.3221/igf-esis.16.04&auth=true http://www.gruppofrattura.it f. carta et alii, frattura ed integrità strutturale, 16 (2011) 34-42; doi: 10.3221/igf-esis.16.04 42 the model 01 showed the most faithful reproduction of the crack propagation. the absence of the adhesive in the simulation brings in a higher rigidity near the reinforcements that apparently reproduces the stresses in the skin better than the other models. the inclusion of the anti-bending device in the model 04-nb until the second reinforcement leads at a more faithful reproduction of the initial stage of crack propagation. figure 16: comparison between experimental and numerical fcp curves (models 4 and 4-nb). conclusions n this study, the influence of several parameters that affect the crack propagation rate was evaluated and the focus was aimed at obtaining results comparable with experiments. the effect of type of skin-stiffener coupling has been simulated, with particular interest on the assessment of the presence of the adhesive and the possible debonding. the possibility of first doubler breakage was also considered. finally, by introducing an anti-bending device, a good correspondence in the first phase of propagation was obtained, differently from the other models simulated. acknowledgements he authors gratefully acknowledge dr. ing. marco pacchione, airbus, for supplying the experimental data. references [1] m. pacchione, e. hombergsmeier, in: proceedings of the 1st international conference of engineering against fracture, university of patras, patras, greece (2008). [2] meneghin, m. pacchione, p. vermeer, in: 25° icaf symposium – rotterdam, (2009). [3] m. b. heinimann, r. j. bucci, m. kulak, m. garratt, in: proceedings of the 23rd icaf symposium, ed. dalle donne c, (2005) 197. [4] m. heinimann, m. kulak, r. bucci, m. james, g. wilson, j. brockenbrough, h. zonker, h. sklyut, in: proceedings of icaf 24th, ed lazzeri l, naples, (2007) 206. [5] m. giglio, a.manes, engng fract mech., 75 (2008) 866. [6] r.c. alderliesten, international journal of fatigue, 31(6) (2009)1024. [7] x zhang, m boscolo, d figueroa-gordon, g allegri, p. e. irving, eng fracture mechanics, 76 (2009) 114. [8] c. mittelstedt, composite structures (2008). [9] afgrow website: http://www.afgrow.net/. i t http://dx.medra.org/10.3221/igf-esis.16.04&auth=true http://www.gruppofrattura.it microsoft word numero_30_art_8 l. náhlík et alii, frattura ed integrità strutturale, 30 (2014) 55-61; doi: 10.3221/igf-esis.30.08 55 focussed on: fracture and structural integrity related issues critical applied stresses for a crack initiation from a sharp v-notch l. náhlík, p. hutař institute of physics of materials, academy of sciences of the czech republic, žižkova 22, 616 62 brno, czech republic nahlik@ipm.cz, hutar@ipm.cz k. štegnerová institute of physics of materials, academy of sciences of the czech republic faculty of mechanical engineering, brno university of technology, brno, czech republic stegnerova@ipm.cz abstract. the aim of the paper is to estimate a value of the critical applied stress for a crack initiation from a sharp v-notch tip. the classical approach of the linear elastic fracture mechanics (lelm) was generalized, because the stress singularity exponent differs from 0.5 in the studied case. the value of the stress singularity exponent depends on the v-notch opening angle. the finite element method was used for a determination of stress distribution in the vicinity of the sharp v-notch tip and for the estimation of the generalized stress intensity factor depending on the v-notch opening angle. critical value of the generalized stress intensity factor was obtained using stability criteria based on the opening stress component averaged over a critical distance d from the v-notch tip and generalized strain energy density factor. calculated values of the critical applied stresses were compared with experimental data from the literature and applicability of the lefm concept is discussed. keywords. crack initiation; v-notch; critical stress; strain energy density factor; generalized linear elastic fracture mechanics; fracture criteria. introduction any of material discontinuities can be treated as notches which causes high stress and strain concentration near the notch root. due to nature of notch, which represents stress concentrator, the crack can initiate in the notch root and consequently its existence can lead to the failure of the whole structure. due to this reason, the notch behavior and crack initiation from the notch are still in the interest of researchers and engineers. the problem of stress singularities at angular corners was firstly solved by williams [1, 2] and others [3, 4]. kotousov followed up williams’ works and studied the corner singularities for a sector plate within the first-order plate theory by using stress resultant and displacement functions [5-7] and adapting the eigenfunction expansion approach of williams [1]. however, the specificity of the singular stress field in the vicinity of v-notch is studied from experimental side as well, see e.g. [8, 9]. in the last five years occur works pointing out on the complexity of the stress field around the notch tip and influence of out-of-plane singularity caused in the so-called vertex point [10-14]. the knowledge of the m l. náhlík et alii, frattura ed integrità strutturale, 30 (2014) 55-61; doi: 10.3221/igf-esis.30.08 56 stress distribution near the v-notch tip is basic precondition for estimation of v-notch behaviour under specific loading conditions. the v-notch behaviour under static or quasi static loading was analyzed by many researchers (see, among the others [15-22]). the crack initiation from the sharp v-notch under conditions of fatigue loading is still in the focus of researchers, see e.g. [23-26]. presented paper is focused on the estimation of critical value of applied stress for a crack propagation from sharp (radius in the notch tip is considered as zero) v-notch in the case of tensile loading. different materials are considered in the presented study and applicability of the lefm concept is discussed. theoretical background nder the assumptions of linear elastic fracture mechanics the stress field near the crack tip in a homogenous material can be described by stress intensity factor [1, 2]. this stress distribution is characterized by stress intensity factor k [mpam] and the stress singularity exponent p = 0.5. in the case of a v-notch a classical approach based on the stress intensity factor cannot be used. the value of the stress singularity exponent p differs from 0.5 in this case and depends on v-notch opening angle. the stress distribution around the notch tip can be expressed as follows, e.g. [1]:  , , 2 i ij ijp h f p r        (1) where p ih mpa m   is generalized stress intensity factor, r, θ are polar coordinates with the origin at the v-notch tip, p is the stress singularity exponent and  , ,ijf p  are known functions. the stress singularity exponent can be obtained analytically by solution of characteristic equation and hi from numerical solution of the problem (e.g. finite element method can be used with an advantage). two different stability criteria are used in the paper for an estimation of beginning of crack propagation from the sharp vnotch. the first one is based on generalized sih´s concept of strain energy density factor (sedf). generalized sedf concept leads to the following expression for the critical value of the generalized stress intensity factor hic, see e.g. [27, 28]:     1 2 1 1 4 0 0 p n ic ic n k h k d k u v       (2) where kic is fracture toughness of the material, kn is function of the poisson´s ratio ν, u1, v1 are functions of the stress singularity exponent p (see [27,28] for details), d is parameter corresponding to the mechanism of the body failure. this parameter is usually called critical distance. the stability criterion has the form: i ich h (3) the crack starts to propagate from the v-notch tip if the value of generalized strass intensity factor reaches its critical value hic. the critical value is determined from (2) and value hi can be obtained from numerical solution of the stress distribution in front of the tip of the stress concentrator. the second criterion, used in the presented study, is based on an average value of concentrator opening stress ahead of the notch tip. this criterion assumes that the crack behaviour is controlled by the value of the opening stress ahead of the notch tip. if the average stress calculated over the distance d ahead of the notch tip reaches its critical value a failure occurs. the critical value is related to the average stress ahead of the crack calculated over the distance d during the remote tensile load on the level of kic, see [22] for details. the critical value of the generalized stress intensity factor can be expressed as [22]: u l. náhlík et alii, frattura ed integrità strutturale, 30 (2014) 55-61; doi: 10.3221/igf-esis.30.08 57    1 22 2 1 p ic ic d h k p q     (4) where q is a known function and other quantities are defined above. an advantage of used criteria is that for their application it is necessary only knowledge of fracture toughness of the material and its elastic constants. no other experimental measurements are necessary. from the practical point of view the value of critical tensile applied stress can be defined as follows: , ic appl crit appl c h h   (5) where appl is a remote applied stress on the body with v-notch (value hi corresponds to this load) ,appl crit is critical value of remote applied tensile stress when the crack starts to propagate from v-notch tip. numerical calculations n the following the behaviour of double edge notch specimen loaded by tension is studied, see fig. 1. stability criteria (3) and (4) were applied after numerical calculations. values of the critical applied stress appl ,critσ necessary for the estimation of v-notch behaviour were determined. the geometry of the specimen, loading and material characteristics were considered according to reference [29]. dimensions of the specimens were:  length 192 l mm  width 2 109   w mm  notch depth 27 a mm  thickness 4 t mm  v-notch opening angle 0   70    (varies with step of 10°). the specimens were made of polymethyl methacrylate (pmma). the material was considered as linear-elastic and isotropic with following material properties:  young´s modulus 2.3 gpae   poisson´s ratio 0.36   fracture toughness 1.9 mpa mick   tensile strength of the material 70 mpac  . finite element system ansys was used for the modelling. the eighth of the specimen was modelled due to the symmetry in geometry and loading conditions. considerable mesh refinement around the v-notch tip was used to obtain accurate stress distribution around of the v-notch tip. figure 1: double edge notch specimen under tensile loading. i l. náhlík et alii, frattura ed integrità strutturale, 30 (2014) 55-61; doi: 10.3221/igf-esis.30.08 58 stability criteria (3) and (4) were applied after numerical calculations. values of the critical applied stress ,appl crit necessary for the estimation of v-notch behaviour were determined. the value of critical distance d was chosen according to reference [29]: 2 1 1.122 ic c k d          (6) note, that the expression (6) was derived for brittle materials on the base of strain energy release rate. results obtained are summarized in fig. 2. good agreement between calculated and experimental data is evident for range of  from 10° to 60°. only for the highest considered angle 70   the generalized sedf criterion exhibits difference of 10% and ms criterion exhibits difference about 15% between calculated and experimental data. figure 2: estimated values of the critical applied stress ,appl crit for different v-notch opening angle  and both stability criteria: based on generalized strain energy density factor (gsedf) and on the mean stress ahead of the v-notch (ms). material pmma. in the following the same specimen made of duraluminum was considered. the geometry, loading and boundary conditions were the same as in the case of pmma specimen except of thickness, which was t = 5 mm in this case. material properties used in analytical and numerical calculations were:  young´s modulus 72 gpae   poisson´s ratio 0.33   fracture toughness 54.3 mpa mick   tensile strength of the duraluminum 454 mpac   yield strength 260 mpa.y  comparison of estimated critical applied stresses and experimental values is shown in the fig. 3. it should be noticed that the results obtained (shown in fig. 3) are influenced by good plastic properties of duraluminum. therefore, elastic-plastic numerical calculations (bilinear material curve was considered) were performed to obtain reliable estimation of the plastic zone size ahead of the v-notch tip. the results show an important plastic zone size around the v-notch tip, see fig. 4 (the plastic zone size is marked by grey colour). for the estimation of the plastic zone size the von mises stress was used and value of the yield stress was considered as 260 mpa. the plastic zone size increases with vnotch opening angle α. it is evident that conditions of small scale yielding are not fulfilled in this study. in spite of big plastic zone size a relatively good agreement between numerically predicted values of critical applied stress and the one experimentally obtained was reached. especially in the case of gsedf criterion the difference between calculated and measured date was smaller than 15%. these results surprisingly show good applicability of the gsedf criterion even if the yielding conditions are quite far from the small scale. l. náhlík et alii, frattura ed integrità strutturale, 30 (2014) 55-61; doi: 10.3221/igf-esis.30.08 59 figure 3: estimated values of the critical applied stress ,appl crit for different v-notch opening angle  and both stability criteria: based on generalized strain energy density factor (gsedf) and on the mean stress ahead of the v-notch (ms). material duraluminum. a) mn mx x y z b) mn mx x y z c) mn mx x y z figure 4: distribution of von mises stress ahead of v-notch tip in duraluminum sample. the plastic zone is marked by grey colour. numerical calculations were performed for v-notch opening angle: a) α=10°, b) α=40° and c) α=70°. the remote applied tensile load corresponded to the critical one. conclusions he work is devoted to the estimation of critical applied stresses for a crack initiation from a sharp v-notch tip. the estimations are done under assumptions of linear elastic fracture mechanics. due to stress singularity exponent different from 0.5 in the case of v-notch, generalized form of lefm was used. two different stability criteria based on different physical bases were applied. the first one is based on generalized sih´s strain energy density factor and the second one is based on the average value of opening stress ahead of the tip of the stress concentrator calculated over the critical distance d. chosen specimens were loaded by tensile loading. comparison of calculated critical applied stresses and experimentally measured data took from the literature was performed. very good agreement was found for both applied stability criteria in the case of specimen made of pmma. following analysis was performed for specimen made of duraliminum. very important plastic zone size ahead of the stress concentrator tip was determined by elastic-plastic numerical calculations. both considered stability criteria were applied in spite of important plasticity. good agreement between calculated and experimentally obtained data was surprisingly found in the studied case of duraluminum specimens. the paper shows applicability of two stability criteria in the case of tensile loaded bodies with v-notches. while both are derived under assumptions of lefm, they can be applied with care too in the cases, where the plastic zone size exceeds small scale. t l. náhlík et alii, frattura ed integrità strutturale, 30 (2014) 55-61; doi: 10.3221/igf-esis.30.08 60 acknowledgement his work was supported through the grant no. cz.1.07/2.3.00/30.0063 (k. štegnerová), no. fsi-s-14-2311 (specific academic research grant provided to faculty of mechanical engineering, brno university of technology) and no. cz.1.07/2.3.00/20.0214 of the ministry of education, youth and sports of the czech republic. references [1] williams, m.l., stress singularities resulting from various boundary conditions in angular corners of plate in extension, journal of applied mechanics, 19 (1952) 526–534. [2] williams, m.l., on the stress distribution at the base of a stationary crack, journal of applied mechanics, 24 (1957) 109–114. [3] england, a. h., on stress singularities in linear elasticity. int. j. eng. science 9 (1971) 571-585. [4] atkinson, c., bastero, j. m. , martinez-esnaola, j. m., stress analysis in sharp angular notches using auxiliary fields. eng. frac. mech, 31 (1988) 637-646. [5] kotousov, a., wang, c.h., three-dimensional stress constraint in an elastic plate with a notch, international journal of solids and structures, 39(16) (2002) 4311–4326. [6] kotousov, a., an application of the kane and mindlin theory to crack problems in plates of arbitrary thickness, meccanica, 39(6) (2004) 495–509. [7] kotousov, a., lew, y. t., stress singularities resulting from various boundary conditions in angular corners of plates of arbitrary thickness in extension, international journal of solids and structures, 43(17) (2006) 5100-5109. [8] ayatollahi, m.r., nejati, m., experimental evaluation of stress field around the sharp notches using photoelasticity, materials and design, 32 (2011) 561–569. [9] ayatollahi, m.r., dehghany, m., mirsayar, m.m., a comprehensive photoelastic study for mode i sharp v-notches, european journal of mechanics a/solids, 37 (2013) 216-230. [10] kotousov, a., lazzarin, p., berto, f., pook, l.p., three-dimensional stress states at crack tip induced by shear and anti-plane loading, engineering fracture mechanics, 108 (2013) 65-74. [11] berto, f., lazzarin, p., kotousov, a., pook, l.p., induced out-of-plane mode at the tip of blunt lateral notches and holes under in-plane shear loading, fatigue fract engng mater struct, 35(6) (2012) 538–555. [12] kotousov, a., berto, f., lazzarin, p., pegorin, f., three dimensional finite element mixed fracture mode under antiplane loading of a crack, theor appl fract mech, 62 (2012) 26–33 . [13] berto, f., lazzarin, p., kotousov, a., on higher order terms and out-of-plane singular mode, mech mater, 43 (2011) 332–341. [14] berto, f., lazzarin, p., kotousov, a., on the presence of the out-of-plane singular mode induced by plane loading with kii = ki = 0, int j fract, 167 (2011) 119–126. [15] carpinteri, a., stress singularity and generalised fracture toughness at the vertex of re-entrant corners. engineering fracture mechanics, 26 (1987) 143–155. [16] chen, d.h., stress intensity factors for v-notched strip under tension or in-plane bending. international journal of fracture, 70 (1995) 81–97. [17] dunn, m.l., suwito, w., cunningham, s.j., fracture initiation at sharp notches: correlation using critical stress intensities. international journal of solids and structures, 34 (1997) 3873–3883. [18] gómez, f.j., elices, m., a fracture criterion for sharp v-notched samples. international journal of fracture, 123 (2003) 163–175. [19] lazzarin, p., zambardi, r., a finite-volume-energy based approach to predict the static and fatigue behaviour of components with sharp v-shaped notches, international journal of fracture, 112 (2001) 275–298. [20] seweryn, a., brittle fracture criterion for structures with sharp notches, engineering fracture mechanics, 47 (1994) 673–681. [21] strandberg, m., fracture at v-notches with contained plasticity, engineering fracture mechanics, 69 (2002) 403–415. [22] knésl, z., a criterion of v-notch stability. international journal of fracture, 48 (1991) 79-83. [23] klusák, z. knésl, j., evaluation of the threshold values for the propagation of a fatigue crack starting at a v-notch, computer assisted mechanics and engineering sciences, 9(4) (2002) 459-468. t l. náhlík et alii, frattura ed integrità strutturale, 30 (2014) 55-61; doi: 10.3221/igf-esis.30.08 61 [24] susmel, s., the theory of critical distances: a review of its applications in fatigue, engineering fracture mechanics, 75 (2008) 1706–1724. [25] susmel, s., taylor, d., the theory of critical distances to estimate lifetime of notched components subjected to variable amplitude uniaxial fatigue loading, international journal of fatigue, 33 (2011) 900–911. [26] susmel, s., taylor, d., the theory of critical distances to estimate finite lifetime of notched components subjected to constant and variable amplitude torsional loading, engineering fracture mechanics, 98 (2013) 64–79. [27] sih, g.c., ho, j.w., sharp notch fracture strength characterized by critical energy, theoretical and applied fracture mechanics, 16(3) (1991) 179-214. [28] knésl, z., the application of the strain energy density concept to the determination of a crack propagation direction initiated at a sharp notch tip, acta technica čsav, 38 (1993) 221-234. [29] seweryn, a., brittle fracture criterion for structures with sharp notches, engineering fracture mechanics, 47 (1994) 673–681. microsoft word numero_38_art_42 c. xianmin et alii, frattura ed integrità strutturale, 38 (2016) 319-330; doi: 10.3221/igf-esis.38.42 319 a statistically self-consistent fatigue damage accumulation model including load sequence effects under spectrum loading chen xianmin, sun qin, dui hongna school of aeronautics, northwestern polytechnical university, xi’an, 710072 pr china fan junling aircraft strength research institute, xi’an, 710065, pr china abstract. a probabilistic methodology is proposed to evaluate fatigue damage accumulation and fatigue lives of specimens under variable amplitude loading. with probabilistic modifications in the present model, the calculative consistency is achieved between fatigue damage and fatigue life. the load sequence effects on fatigue damage accumulation are properly accounted for variable amplitude loading. the developed damage model overcomes the inherent deficiencies in the linear damage accumulation rule, but still preserves its simplicity for engineering application. based on the monte carlo sampling method, numerical verification of this model is conducted under two kinds of spectrum loading. the predicted probabilistic distributions of fatigue lives are validated by fatigue tests on al-alloy straight lugs. keywords. fatigue damage; fatigue life; probabilistic statistical model; load sequence effect; statistical self-consistency. citation: xianmin, c., qin, s., hongna, d., junling, f., a statistically self-consistent fatigue damage accumulation model including load sequence effects under spectrum loading, frattura ed integrità strutturale, 38 (2016) 319-330. received: 03.05.2016 accepted: 30.08.2016 published: 01.10.2016 copyright: © 2016 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. introduction atigue damage is one of the most common failure modes encountered in engineering structures. therefore fatigue failure prediction is widely carried out during various processes, such as engineering structural design, safety assessment and optimization. in the past decades, many damage models have been presented to quantitatively analyze fatigue damage and failure of materials and components. however, the mechanisms and process of fatigue failure under variable amplitude loading conditions are random in nature owing to a variety of indeterminable factors in materials as well as external environments. the linear cumulative damage rule, firstly proposed by palmgren in 1924 and subsequently by miner in 1945 [1], is widely used for fatigue analyses of structures under variable amplitude loading. it can be expressed as: d=∑(ni/ni). after that, many developments have been made to get more accurate predictions, including the nonlinear damage rules, such as damage curve based method [2], ductility exhaustion model [3], continuum damage mechanics approach [4] and energybased damage method [5]. the fatigue damage accumulation within these models and approaches are mostly based on deterministic concepts, whereas in practice, damage accumulation is usually of stochastic nature. f c. xianmin et alii, frattura ed integrità strutturale, 38 (2016) 319-330; doi: 10.3221/igf-esis.38.42 320 several probabilistic approaches have been established for damage accumulation evaluation. many issues related to statistical characteristics of fatigue have been involved, such as the combined randomness of loading process and fatigue resistance of materials [6], probabilistic density function of failure cycles [7], complexity of loading conditions [8], random critical damage [9], frequency domain approach [10] and time domain approach [11]. however, few of them focused both on the load sequence effect and the probabilistic nature of fatigue damage. based on morrow’s nonlinear plastic work interaction damage rule, w.-f.wu and t.-h. huang [8] proposed an approach to predict the fatigue damage and fatigue life under random loading considering the loading history and the statistical feature. in this paper, a new model is proposed to predict fatigue damage and fatigue lives of specimens under spectrum loading. the effect of high load retardation on damage accumulation is taken into account by introducing an exponential function exp(-fj) in the model. the independent variable fj is related to the stress ratio of high and low stress levels. the statistically self-consistency between the probabilistic distributions of fatigue damage and failure cycles is also achieved by introducing a consistent index b (greater than one) and a random disturbance δ. in the damage model, the fatigue damage and fatigue life are predicted using the probabilistic sampling method supported by test data. as for the critical damage dc, i.e. the damage value at failure, there are mainly two points of view: (1) dc is deterministic, equal to or smaller than unit; (2) dc is a random variable, with mean value equal to unit. in the present paper, the second view point is adopted. the fatigue life n is assumed to follow the two-parameter weibull distribution, w(α,β) [12]. the shape parameter α is set as 4 [13] for aluminum alloy according to a lot of fatigue test data. in order to verify the reliability and feasibility of this model, the predicted fatigue life is compared with that of the fatigue test results. a statistically self-consistent model for fatigue damage and fatigue life prediction or constant amplitude loading, palmgren-miner’s linear damage accumulation rule, which is widely used in engineering, is expressed as 1 1 1 n f c ii d n   (1) where ni is the fatigue life under the ith stress level, which actually obeys some distribution; nf is the cycle number to failure; and the critical damage value dc is assumed to be one. obviously, when n is taken as a constant, eq. (1) can be simplified to the form of nf/n=1, which is the most common form of miner’s damage criterion. however, in actual situations, n has probability characteristics, thus nf is also correspondingly statistical rather than deterministic. with a given distribution of n, the equation can be called statistically consistent if nf obtained from eq. (1) with the monte carlo sampling method is approximate to n with respect to probability distribution. in practice, fatigue life n is exactly reflected in the number of load cycles to failure, so it is necessary that the damage criterion be statistically consistent. however, it can be verified that eq. (1) is statistically inconsistent as follows. through numerical simulation with the monte carlo sampling method [14], it can be found that the cycle number nf obtained from eq. (1) is not identical to the original fatigue life n considering probability distribution. assuming n～w(α, β), with α=2.1, β=1129, the mean value μ=1000, and the standard deviation σ=500, sufficient random sampling(2,000 times) of eq. (1) is performed. as a result, 2000 different nfs can be obtained and then statistics of nf are calculated as: μ=670, σ=41. it should be noted that both the mean value and standard deviation are smaller than those of the original n, especially for standard derivation. thus it can be concluded that eq. (1) is statistically inconsistent. in order to enlarge the mean value and the standard deviation of nf, a consistent index b (greater than one) and a random disturbance δ with mean value equal to zero are introduced to the left and right sides of eq. (1) respectively, which makes the linear fatigue damage prediction model statistically consistent, given by    1 1 1 , bn f i ii n e n n e n             (2) where, ni is a random fatigue life from certain distribution, which corresponds to the ith load cycle, and e(n) is the mean value of the life distribution. f c. xianmin et alii, frattura ed integrità strutturale, 38 (2016) 319-330; doi: 10.3221/igf-esis.38.42 321 the self-consistent index b is related to statistical parameters α and β of fatigue life distribution. it can be solved by comparing the mean values of nf with n through numerical simulation. the right-hand side term (1+δ) indicates that the critical damage is a random variable. assuming n～w(α, β), (1+δ) obeys w(α, β/μ) distribution, with its mean value equal to unit and standard derivation equal to σ/μ, respectively. here, σ is the standard derivation of fatigue life n. assuming n～w(α, β), α=2.1, β=1129 and accordingly μ=1000, σ=500, through large number of monte carlo sampling tests, it is found that if the consistent index b is taken as 1.065, the mean values of nf and n can be comparable. repeating monte carlo sampling of eq. (2) for 2000 times, the statistics of nf are calculated as: α=2.1, β=1139, μ=1009, σ=513. comparing with the original fatigue life, it can be noted that nf is close to n with respect to the mean value and standard deviation, as well as the maximum likelihood estimations of parameters α and β. furthermore, in the goodness of fit test with the original weibull distribution, nf has passed k-s test and w2 test quite well. therefore, the new cumulative damage criterion expressed in eq. (2) can be considered statistically consistent. through some appropriate transformation of eq. (2), a statistically consistent fatigue damage model that can quantitatively calculate the statistical properties of damage under spectrum loading conditions can be achieved. for simplicity, the case of constant amplitude loading is first presented. it should be mentioned that in practice, for the case of constant amplitude loading, the concept of loading block generally does not exist. here, it is used for the generalization to the case of variable amplitude loading. assuming there are n load cycles in one loading block, the equation to calculate the damage db caused by one loading block can be established by moving the random disturbance δ to the left-hand side of eq. (2), written as    1 1 bn i b ii n e n d n e n          (3) then, the fatigue life can be predicted by 1 f b n n d   (4) only if the predicted fatigue life nf obtained by eq. (4) is approximate to the original n, can the fatigue damage model be called statistically consistent. a coefficient relative to the cycle number n must be added in front of δ to make db satisfy the boundary conditions: (1) damage value is zero when the cycle number is zero; (2) the mean value of damage is approximate to 1 when the cycle number equals to the mean value of fatigue life. in addition, the coefficient should increase with the number of cycles. through the large number of monte carlo sampling tests, it is found that when the coefficient in front of δ is defined as n/ni, nf can be close to n for the probabilistic properties. thus, the damage caused by one loading block db can be given by    1 1 bn i b i ii n e nn d n n e n          (5) eq. (5) can be extended to the case of spectrum loading naturally, written as    1 1 1 1 1 b jn jm j jj b ji jj i j m f j b j n e nn d n n e n n n d                      (6) where db is the damage introduced by one loading block with m stress levels; m is the number of stress levels in a spectrum loading; nj is the cycle number under the jth stress level; aj is the self-consistent exponent dependent on the fatigue life distribution under jth load level , which makes the mean value of nf (eq.(2 )) approximate to the original n; nj c. xianmin et alii, frattura ed integrità strutturale, 38 (2016) 319-330; doi: 10.3221/igf-esis.38.42 322 is a random number obeying the distribution of fatigue life under jth stress level; e(nj) is the mean value of fatigue life under the jth load level and nf is the random fatigue life under spectrum loading. for the case of constant amplitude loading, the self-consistency of fatigue damage and fatigue life prediction model can be verified by comparing the failure cycles nf obtained from model with the original fatigue life n. however, this rule does not work when it comes to the case of spectrum loading, because the distributions of original fatigue lives are not unique. in order to verify the fatigue damage and fatigue life under spectrum loading predicted by eq. (6), two engineering assumptions are firstly made on the basis that there are no load sequence effect: 1) the fatigue life distribution under spectrum loading, nf, should be closer to nj with larger damage ratio nj/e(nj), and the mean value of nf should be in the range of [e(nj)min, e(nj)max]; 2) the mean value of nf should be very close to the one calculated by palmgren-miner’s linear damage accumulation rule. numerical sampling test and parameter estimation are carried out according to eq. (6) under two-level spectrum loading. the parameters of fatigue life distribution for each load level are shown in tab. 1. four projects with different combinations of load cycles and stress levels are employed in this test and the corresponding simulation results are listed in tab. 2. the probabilistic density function(pdf) of different fatigue life distributions are compared with each other, as shown in fig. 1. j αj βj e(nj) σ exponent aj 1 2.7 1125 1000 400 1.038 2 3.7 11079 10000 3000 1.014 table 1: parameters of fatigue life distribution for each load level. project n1 n2 n1/e1 n2/e2 n f n /n f n 1 200 100 0.2 0.01 1386 1429 0.97 2 400 100 0.4 0.01 1211 1220 0.99 3 100 3000 0.1 0.3 7344 7750 0.95 4 100 5000 0.1 0.5 8278 8500 0.97 table 2: simulation results of 4 projects of two-level spectrum loading. figure 1: comparisons of fatigue life distributions of different projects with the original constant amplitude loading. from fig. 1, the pdfs of project 1(nf1) and project 2(nf2), which have larger damage ratios of n1/e1, are closer to the 1st level(n1) rather than to the 2nd level(n2). furthermore, the pdf of project 2 is closer to the 1st level than project 1. the pdfs of project 3(nf3) and project 4(nf4), which have larger damage ratios of n2/e2, are closer to the 2nd level(n2) rather than the 1st level. furthermore, the pdf of project 4 is closer to the 2nd level than project 3. the mean values of nf are in the range of [e(n1), e(n2)]. this simulation results verifies the first assumption. in tab. 2, the mean value of fatigue life c. xianmin et alii, frattura ed integrità strutturale, 38 (2016) 319-330; doi: 10.3221/igf-esis.38.42 323 calculated by this model is almost the same as the one given by palmgren-miner’s linear damage accumulation rule, which is consistent with the second assumption. thus, eq. (6) is verified to be a reasonable model for fatigue damage prediction based on numerical calculation. however, it should be further validated by experimental tests before practical application. statistical distribution of fatigue life under constant amplitude loading n order to calculate the fatigue damage and fatigue life by eq. (6) for structures subjected to variable amplitude loading, statistical distributions of fatigue lives under constant amplitude loading are needed as a baseline data. axial fatigue test on straight lugs specimens was conducted by using instron-1342 fatigue test machine at a frequency of 20hz at room temperature with the stress ratio r of 0.06.the geometry of the specimen is shown in fig.2 and the test results are listed in tab. 3 [15]. figure 2: geometry of straight lugs specimen for fatigue testing, dimensions in mm. stress level sa (mpa) r(stress ratio) fatigue life(cycles) 1 38.46 0.06 365105,171327,230701,119173,408225,346068 2 42.73 0.06 264258,114391,184623,94016,128481,274699 3 47.00 0.06 142472,153949,58218,61666,77398,125822 table 3: fatigue test results of straight lugs subjected to constant amplitude loading. for median fatigue life ranging from 104 to 106 cycles, the relations of s-np and s-β could be written as lgβ=b1lgs+a1 (7) lgnp=b2lgs+a2 (8) where a1, b1, a2 and b2 are constant coefficients; s is the stress level of the constant amplitude loading; β is the characteristic life of test sample and np is the fatigue life of the test sample with reliability of p. the values of a1, b1, a2 and b2 can be determined by least square method with given s, β and np. due to the time and cost, only six fatigue life data is acquired for each stress level. to get more reliable information from these limited numbers of tests, three statistical methods are employed to analyze the data in tab. 3, i.e. bayesian jerry prior method (bjpm), bayesian conjugate prior method (bcpm) and the bootstrap method (btpm). the estimation of characteristic life( ̂ ), the estimation of characteristic life with confidence level of c (βc) and the fatigue life with 95% reliability and 95% confidence level (n95/95) are all obtained. it is also verified whether the original fatigue test data fall into the 95% confidence intervals of the probabilistic distributions based on the above three statistical methods (tab. 4). from a statistical point of view, the more test data fall into the 95% confidence interval, the more reasonable the probabilistic distribution is. fatigue life distributions under constant amplitude loading based on the three statistical methods are shown in fig. 3, where the original test data is marked on the curve. the fatigue life with 95% confidence interval is denoted by the vertical lines. i c. xianmin et alii, frattura ed integrità strutturale, 38 (2016) 319-330; doi: 10.3221/igf-esis.38.42 324 stress level statistical methods ̂ βc n95/95 number of data out of the 95% confidence interval 1 bjpm 321095 279087 132816 1 bcpm 318112 295985 140858 1 btpm 329156 297991 141813 1 2 bjpm 212586 184774 87933 0 bcpm 207824 186917 88953 0 btpm 217875 197179 93837 0 3 bjpm 121001 105170 50050 0 bcpm 119321 109461 52092 0 btpm 124085 112271 53429 0 table 4: estimated parameters of straight lugs fatigue tests under constant amplitude loading based on bjpm, bcpm and btpm. figure 3: fatigue life distributions under constant amplitude loading based on bjpm, bcpm and btpm. all the statistical results obtained through the three statistical methods are similar and the probabilistic distributions are very close to each other. meanwhile, almost all the test data fall into the 95% confidence interval of the probabilistic distribution, indicating that the probabilistic distributions based on the three statistical methods are reasonable and reliable enough. moreover, the bjpm is more conservative and simple to use, without super parameters, sample size enlarging or resampling. thus, the test results in the following are processed by bjpm. the fitted values of a1, b1, a2, b2 in eq. (7) and eq. (8) are listed in tab. 5, where r is the correlation coefficient of the linear fitting. a1 b1 a2 b2 r 13.2024 -4.8468 12.8190 -4.8468 0.9930 table 5: coefficients of s-n curves. for an arbitrarily stress level sj with constant stress ratio of 0.06, the corresponding statistical parameters, i.e. β and n95/95, can be calculated by eq. (7) and eq. (8). then, the probabilistic distribution of fatigue life nj corresponding to sj can be obtained by numerical sampling based on the weibull distribution, which provides necessary parameters for the fatigue damage and fatigue life prediction under variable amplitude loading. c. xianmin et alii, frattura ed integrità strutturale, 38 (2016) 319-330; doi: 10.3221/igf-esis.38.42 325 the consistent index b is closely related to statistical parameters α and β of fatigue life distribution and can be solved by monte carlo sampling test according to eq. (2). when α is assumed as 4, the quantitative relation between index b and scale parameter β can be obtained through large number of sample tests, the results are shown in tab. 6. note that the general trend is that b decreases with β and b stay constant in some interval of β instead of changing continuously with β. β (8×103,104] (104,5×104] (5×104,105] (105,106] b 1.011 1.010 1.009 1.008 β (106,6×106] (6×106,5×107] (5×10 7,5×108] (5×108,1010] b 1.007 1.006 1.005 1.004 table 6: quantitative relation between the consistent index b and scale parameter β(α=4). experimental verification of the statistical fatigue damage model under spectrum loading fatigue tests under spectrum loading he specimens are the same as those used in the fatigue tests under constant amplitude loading [15]. the load spectra and fatigue life results are listed in tab. 7. spectrum load order 1 2 3 4 5 cycles to failure 5-level sa(mpa) 17.09 27.77 42.73 36.32 21.36 500826，686156，2445490，1201897，2 253944 cycles 1000 500 200 600 900 3-level sa(mpa) 27.77 42.73 36.32 \ \ 371112，522772，670298，507405，426 219，364397 cycles 500 302 600 \ \ table 7: fatigue test results of straight lugs under spectrum loading. using the data in tab. 7, the statistical parameters of fatigue life under spectrum loading can be obtained by bjpm, including ̂ ,e，σ, n95/95 and the interval of 95% fatigue life (β1, β2), (e1,e2) and (σ1,σ2) . here σ is the standard deviation of the test results, demonstrating the scatter characteristics of fatigue lives. experimental verification of the fatigue damage model statistical parameters for each stress level of the multilevel spectrum are obtained via the s-n curves described in section 3, including characteristic life β, the average life e, n95/95 and the self-consistent index a, listed in tab. 8. sa(mpa) 17.09 27.77 42.73 36.32 21.36 st at is ti ca l p ar am et er s β 158271738 1605853 198884 437239 6180778 e 143457895 1455549 180269 396314 5602272 n95/95 65467281 664242 82266 180859 2556608 self-consistent index a 1.006 1.007 1.008 1.008 1.008 table 8: statistical parameters of fatigue life distributions under constant amplitude loading. two thousand values of nf can be acquired using eq. (6) from 2000 groups of random sampling based on the fatigue life t c. xianmin et alii, frattura ed integrità strutturale, 38 (2016) 319-330; doi: 10.3221/igf-esis.38.42 326 distributions under constant amplitude loading, as shown in tab. 8. the steps of random sampling are as follows: 1) for the jth stress level, do nj times of sampling according to the probabilistic distribution of fatigue life nji using parameters in tab. 8. the damage caused by the jth level of stress(dbj) is obtained through eq. (6). 2) the whole fatigue damage db in one loading block can be obtained by summing up dbj from the 1st level to the mth level. 3) fatigue life(nf ) under spectrum loading is calculated using the second formula of eq. (6). 4) repeating steps 1), 2)and 3) for 2000 times. based on 2000 values of nf, the statistical parameters of fatigue lives, including ̂ (shape parameter), ̂ , e, σ and n95/95, are estimated by the method of maximum likelihood. the ratios of parameters between model and test data are indicated by re, rσ and rn95 respectively. the results are listed in tab. 9. n1 is the number of test data outside the 95% confidence interval of the model’s probability distribution, which reflects the rationality of the model. whether e and σ from test data, respectively, fall into the interval (e1,e2) and (σ1,σ2) from the model also indicates the validity of the prediction, as listed in the last 2 columns of tab. 9. load level ̂ ̂ (×106) e (×105) re  (×105) r n95/95 (×105) rn95 n1 fall into (e1, e2) fall into (1,  2) 5 5.833 1.035 9.585 0.555 1.906 0.394 6.180 0.772 2 no no 3 5.283 0.404 3.717 0.801 0.810 0.622 2.284 1.061 2 no no table 9: comparisons of parameters based on the statistical fatigue damage model with those from fatigue tests. the predicted pdfs of fatigue life under spectrum loading are compared with the test results, as shown in fig. 4. the comparisons indicate that significant discrepancy exists in the mean values, standard deviation and lateral deviations, especially for the 5-level spectrum loading. in addition, as shown in fig.4, the schematic pdfs of predicted fatigue life nf and the test results are quite different. load sequence effect is believed to be the main reason for the difference between prediction and tests [16]. therefore, improvements have to be brought to this model since interactions among variable stress levels should be considered. a) fatigue life distributions under 5-level spectrum loading. b) fatigue life distributions under 3-level spectrum loading. figure 4: fatigue life distributions under spectrum loading. a modified fatigue damage accumulation model under spectrum loading considering load sequence effect he difference between the model and the tests under spectrum loading is mainly attributed to the load sequence effects, i.e. the acceleration effect and the retardation effect, as demonstrated by many researches in various fatigue tests [17, 18]. this direct effect of loading sequence plays an important role in the process of damage t c. xianmin et alii, frattura ed integrità strutturale, 38 (2016) 319-330; doi: 10.3221/igf-esis.38.42 327 accumulation if the difference between load levels is large enough. usually the retarding effect is more remarkable than the acceleration effect and easier to be defined quantitatively. therefore, the retardation effect of high stress level is taken into account only in this work. the retardation effect is due to the high stress level in the loading spectrum. the fatigue damage accumulation rate of specimens under a low stress level slows down since a high stress level may leads to micro-plasticity of material and compressive residual stress. the retardation effect is apparently related to the disparity between high and low load levels. in a variable amplitude stress condition, according to morrow’s plastic work interaction damage rule [19], the fatigue damage caused by the stress amplitude sk can be written as: max d k k k k n s d n s        (9) where smax is the maximum stress amplitude in the stress history; nk is the cycle number of stress peak at level sk; nk is the number of stress peak to cause failure if the constant amplitude sk is considered; and d is morrow’s plastic work interaction exponent which can be considered as the stress sequence effect on the fatigue damage. using the similar principle as morrow’s plastic work interaction damage rule, an exponential function exp(-fj) is introduced to modify the fatigue damage caused by the low stress level, seen in eq. (10). as the independent variable , fj, in this exponential function is larger than one and related to the stress ratio of high and low load level, i.e. 1 max j j s s  , where sj is the stress peak of the jth stress level and 1max js  is the maximum stress peak among the stress levels from s1 to sj-1. in addition, a constant coefficient v is defined to accommodate the model to the test data, which can be fitted by comparing the calculated fatigue life through large number of monte carlo sampling with the test data. in order to reduce the damage accumulation rate of the lower stress levels, negative one is set as a multiplier to the independent variable fj. the modified fatigue damage model with load retardation effect under multilevel spectral loading is given as:       1 1 1 1 max 11 max 1 11max max 1 exp 1 0, 1 , max ~ , a jn jm j jj b j ji j jj i m f j b j j j jj j jj j j n e nn d f n n n n n d j or s s f and s s ss v s s s                                        (10) where v is a constant depending on the material itself and the assumption of fatigue life distribution. the load retardation effect index has no effect on the fatigue damage produced by the first stress level or the stress level higher than the previous maximum stresses , since exp(-fj)=1 in eq. (10). however, the fatigue damage is affected by the load retardation effect index when the current stress level is lower than the previous maximum stresses , since exp(-fj)<1. simulation work (detailed steps presented in section 4.2) has been done by using this modified model to determine the value of v. it is found that the fatigue life distribution of the model matches that of the test well when v=1. the statistical parameters estimated by the modified model are given in tab. 10. load level ̂ ̂ (×106) e (×106) re  (×105) r n95/95 (×105) rn95 n1 fall into (e1, e2) fall into (1,  2) 5 3.643 1.689 1.523 0.882 4.647 0.960 7.397 0.924 0 yes yes 3 3.888 0.589 0.533 1.148 1.533 1.177 2.716 1.262 0 yes yes table 10: comparisons of parameters based on the modified statistical fatigue damage model with those of the fatigue tests. c. xianmin et alii, frattura ed integrità strutturale, 38 (2016) 319-330; doi: 10.3221/igf-esis.38.42 328 the predicted pdfs of fatigue life by the modified model considering load sequence effect are compared with the test results under spectrum loading, as shown in fig. 5. the original test data is also marked in the curve and the fatigue life with 95% intervals are denoted by the vertical lines. it can be found that the test data all fall into the 95% interval of life distributions based on the modified fatigue damage accumulation model under the spectrum loading. the average life and the standard deviation based on the modified model both fall into the 95% interval estimation of test data, and the ratio of model to test is close to 1. the shape parameter obtained by the modified model is closer to 4 indicating that the modified model is more coincident with the fatigue test than the original model. in addition, as shown in fig.5, the schematic pdfs of predicted fatigue life nf and the test results are quite close. therefore, it can be concluded that the modified model can precisely predict the fatigue damage and fatigue life under spectrum loading, and at the same time, properly reflect the stochastic nature and load sequence effects on fatigue behavior. a) fatigue life distributions under 5-level spectrum loading. b) fatigue life distributions under 3-level spectrum loading. figure 5: fatigue life distributions under spectrum loading. moreover, the mean fatigue lives e and n95/95 are also calculated by palmgren-miner’s linear damage summation rule and are compared with those based on test data, as listed in tab. 11. load level e (×106) re n95/95 (×105) rn95,95 e fall into the (e1, e2) interval 5 1.0209 0.5914 4.6588 0.5820 no 3 0.39686 0.8551 1.8111 0.8415 yes table 11: comparisons of parameters based on palmgren-miner’s linear damage summation rule with those of fatigue tests. the results illustrate that the fatigue lives calculated by palmgren-miner’s linear damage summation rule are too conservative, especially for the 5-level spectrum loading. the modified model is more accurate and reasonable than the palmgren-miner’s rule in engineering applications, and can be easily expanded to the application of other metal materials. the fatigue damage calculation steps are summarized as follows. 1) conduct the fatigue test under constant amplitude loading with 3 stress levels. at each stress level, the number of test specimens is not less than 6. according to the test data, the p-s-n curve is fitted. 2) the fatigue life distribution is assumed to obey the weibull distribution, and the parameters are obtained based on the p-s-n curve. 3) get the consistent index b corresponding to different stress levels through the large number of monte carlo sampling using eq. (2). 4) calculate the fatigue damage under spectrum loading using eq. (10). as for the application of the statistical fatigue damage accumulation model, two aspects should be noted. firstly, the shape parameter of al-alloy is different in the data processing. for the experiments, it is assumed to be 4 for both constant and variable amplitude loading conditions; however, for the model simulation, it is estimated by the maximum likelihood method based on the large number of monte carlo sampling (not equal to 4, as shown in tab. 9 and tab. 10. secondly, the stress ratio r may be different for each load level in variable spectrum loading. the method based on p-s-n curve and constant life diagram could be applied [20]. the stress level at arbitrary r can be converted to the stress level at c. xianmin et alii, frattura ed integrità strutturale, 38 (2016) 319-330; doi: 10.3221/igf-esis.38.42 329 the r0 under which p-s-n curve is available using the constant life diagram [21]. conclusions atigue damage and fatigue life prediction for structures under variable amplitude loading are discussed in this paper. several conclusions are made and listed as follows. the statistical damage accumulation model is based on palmgren-miner’s linear rule. however, the critical damage is considered as a variable depending on fatigue life distribution rather than a constant. its mean value equals to unit. therefore, the model is made self-consistent by introducing a consistent index b determined by numerical simulation and a random disturbance δ. the load sequence effects are properly accounted in this model to accurately predict the fatigue life under variable amplitude loading. an exponential function exp(-fj) is used to slow down the fatigue damage accumulation rate of materials under the low stress levels. this function is dependent on the stress ratio, i.e. 1max / j js s  and the multiplier v. this fatigue damage accumulation model provides a quantitative approach to statistically calculate the fatigue damage and fatigue life by considering the load sequence effects. the predictions by the present model coincide quite well with experimental results, indicating that it can well demonstrate the probabilistic nature of fatigue behavior. acknowledgement he support from the national natural science foundation of china (project no. 51601175) is greatly acknowledged. references [1] miner, m.a., cumulative damage in fatigue, j. appl. mech., 67 (1945) a159-164. [2] marco, s.m., starkey, w. l., a concept of fatigue damage, transaction of the asme, 76 (1954) 627-632. [3] guangxu, c., plumtree, a., a fatigue damage accumulation model based on continuum damage mechanics and ductility exhaustion, int. j. fatigue, 20(7) (1998) 495-501. [4] oller, s., salomón, o., oñate, e., a continuum mechanics model for mechanical fatigue analysis, comput. mater. sci., 32 (2005)175-195. doi: 10.1016/j.commatsci.2004.08.001. [5] scott-emuakpor, o., an energy-based uniaxial fatigue life prediction method for commonly used turbine engine materials, asme, j. eng. gas turbines power, 130 (2005) 062504. [6] shen, h., lin, j., mu, e., probabilistic model on stochastic fatigue damage, int. j. fatigue, 22(7) (2000) 569–572. [7] nagode, m., fajdiga, m., on a new method for prediction of the scatter of loading spectra, int. j. fatigue, 20(4) (1998) 271–277. [8] wu, w.-f., huang, t.-h., prediction of fatigue damage and fatigue life under random loading, int. j. pres. ves. pip., 53(2) (1993) 273–298. [9] wang, p., coit, d. w., reliability and degradation modeling with random or uncertain failure threshold, reliability and maintainability symposium, (2007) 392–397. [10] tovo, r., a damage-based evaluation of probability density distribution for rain-flow ranges from random processes, int. j. fatigue, 22 (2000) 425–429. [11] castillo, e., fernández-canteli, a., ruiz-ripoll, m. l., a general model for fatigue damage due to any stress history, int. j. fatigue, 30(1) (2008) 150–164. doi: doi:10.1016/j.ijfatigue.2007.02.011. [12] rathod, v., probabilistic modeling of fatigue damage accumulation for reliability prediction, int. j. qual. stat. reliab., (2011) 718901. [13] xiasheng, s., et al, guidelines for the analysis and design of durability aircraft structures, xi’an pr china, (2007). [14] luc, d., non-uniform random variate generation, springer-verlag, new york, (1986). [15] yanbin, l., study on the aircraft structure fatigue acceleration spectrum and the wide spread damage probabilistic model, chinese aeronautical research institute, (2011). f t c. xianmin et alii, frattura ed integrità strutturale, 38 (2016) 319-330; doi: 10.3221/igf-esis.38.42 330 [16] rasool, i., zhang, x., cui, d., fatigue life prediction of 3-d problems by damage mechanics with spectrum loading, in: icas 2002, (2002). [17] jobn, h., effects of loading sequence for notched specimens under high-low two-step fatigue loading, nasa tn d6558, (1971). [18] hélder, f. s., pereira, g., et al, influence of loading sequence and stress ratio on fatigue damage accumulation of a structural component, ciência e tecnologia dos materiais, 20 (2008) 60-67. [19] morrow, j. d., the effect of selected subcycle sequences in fatigue loading histories, in random fatigue life predictions, asme publication pvp, 72 (1986) 43-60. [20] nijssen, r.p.l., van delft, d.r.v., van wingerde, a.m., alternative fatigue lifetime prediction formulations for variable-amplitude loading, j sol energy eng, 124(4396) (2002) 396-403. [21] ling, j., pan, j., a maximum likelihood method for estimating p-s-n curves, int. j. fatigue, 19(5) (1997) 415-419. nomenclature b = self-consistent exponent dependent on the fatigue life distribution bj = the self-consistent exponent dependent on the fatigue life distribution under jth load level δ = a random variable with mean value equal to zero d = morrow’s plastic work interaction exponent d = damage value db = damage caused by one loading block dbj = damage caused by the jth level of stress dc = critical damage value e = mathematical expectation m = number of stress levels in a spectrum loading n = cycle number in one loading block ni = cycle number under the ith stress level nj = cycle number under the jth stress level nf = cycle number to failure n = fatigue life n95/95 = fatigue life with 95% reliability and 95% confidence level ni = fatigue life under the ith stress level nj = a random number obeying the distribution of fatigue life under jth stress level nk = the number of stress peak to cause failure under the constant stress amplitude of sk nf = the predicted fatigue life under block loading np = the fatigue life of the test sample with reliability of p re = the ratios of mathematical expectation between model and test data rσ = the ratios of standard deviation between model and test data rn95 = the ratios of n95/95 between model and test data s = the stress level of the constant amplitude loading sj = stress peak of the jth stress level sk = stress peak of the kth stress level smax = the maximum stress in the stress history 1 max js = the maximum stress among the stress levels from s1 to sj-1 v = a constant depending on the material itself and the assumption of fatigue life distribution α = shape parameter α of weibull distribution ̂ = the estimation of shape parameter β = scale parameter of weibull distribution βc = the estimation of characteristic life with confidence level of c ̂ = the estimation of characteristic life μ = mean value of 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can be opened with acrobat and adobe reader 5.0 and later.) >> /namespace [ (adobe) (common) (1.0) ] /othernamespaces [ << /asreaderspreads false /cropimagestoframes true /errorcontrol /warnandcontinue /flattenerignorespreadoverrides false /includeguidesgrids false /includenonprinting false /includeslug false /namespace [ (adobe) (indesign) (4.0) ] /omitplacedbitmaps false /omitplacedeps false /omitplacedpdf false /simulateoverprint /legacy >> << /addbleedmarks false /addcolorbars false /addcropmarks false /addpageinfo false /addregmarks false /convertcolors /converttocmyk /destinationprofilename () /destinationprofileselector /documentcmyk /downsample16bitimages true /flattenerpreset << /presetselector /mediumresolution >> /formelements false /generatestructure false /includebookmarks false /includehyperlinks false /includeinteractive false /includelayers false /includeprofiles false /multimediahandling /useobjectsettings /namespace [ (adobe) (creativesuite) (2.0) ] /pdfxoutputintentprofileselector /documentcmyk /preserveediting true /untaggedcmykhandling /leaveuntagged /untaggedrgbhandling /usedocumentprofile /usedocumentbleed false >> ] >> setdistillerparams << /hwresolution [2400 2400] /pagesize [612.000 792.000] >> setpagedevice microsoft word numero_27_art_6 g. kuidong et alii, frattura ed integrità strutturale, 27 (2014) 43-52; doi: 10.3221/igf-esis.27.06 43 a theoretical model for predicting the peak cutting force of conical picks gao kuidong, du changlong, jiang hongxiang, liu songyong school of mechanical and electrical engineering, china university of mining & technology, xuzhou 221116, china luck_honey@163.com abstract. in order to predict the pcf (peak cutting force) of conical pick in rock cutting process, a theoretical model is established based on elastic fracture mechanics theory. the vertical fracture model of rock cutting fragment is also established based on the maximum tensile criterion. the relation between vertical fracture angle and associated parameters (cutting parameter  and ratio b of rock compressive strength to tensile strength) is obtained by numerical analysis method and polynomial regression method, and the correctness of rock vertical fracture model is verified through experiments. linear regression coefficient between the pcf of prediction and experiments is 0.81, and significance level less than 0.05 shows that the model for predicting the pcf is correct and reliable. a comparative analysis between the pcf obtained from this model and evans model reveals that the result of this prediction model is more reliable and accurate. the results of this work could provide some guidance for studying the rock cutting theory of conical pick and designing the cutting mechanism. keywords. conical pick; peak cutting force; fracture angle. introduction n tunneling and mining, interaction between cutting mechanism (shearer drum and cutting head) and rock realizes rock fragmentation. cutting ability, crushing effect and production efficiency of cutting mechanism, determine the working performance of tunneling and mining equipment. however, the pcf prediction of conical pick plays an important role in the design of cutting mechanism. a considerable amount of research has been conducted on the pcf prediction base on theoretical, experimental and numerical method. the first pcf prediction model of conical pick was established by evans based on the maximal tension stress theory [1], and roxborough & liu [2] and goktan [3] appropriately modified the evans mathematical model. according to experiment data from various rock cutting by conical pick, regression expressions between cutting force and rock compressive strength, tensile strength, dynamic and static modulus of elasticity, brittle index were established by bilgin [4-5]. tiryaki [6] adopted multiple linear and non-linear regression, regression tree model and neural networks method to predict the pcf of conical pick. numerical method [7-9] is also applied to predict the pcf of conical pick. viewing the references mentioned above, we find that: compared with experimental date, the result calculated by current theoretical model exists a notable divergence; for the limitation of experimental date, application of empirical models is limited to a specific scope; experimental method and numerical simulation method can obtain proper cutting force, but some disadvantages exist such as high cost and low efficiency. for these reasons, the vertical fracture mechanics model of rock cutting fragment is established based on the maximum tensile criterion and rock cutting theory in this paper firstly; then, the theoretical model for predicting the pcf of conical pick is i http://dx.medra.org/10.3221/igf-esis.27.06&auth=true http://www.gruppofrattura.it g. kuidong et alii, frattura ed integrità strutturale, 27 (2014) 43-52; doi: 10.3221/igf-esis.27.06 44 established based on elastic fracture mechanics theory; finally, the reliability and accuracy of pcf model is verified with experimental date. theoretical model he problem of the indentation of the plane surface of elastic solid with a rigid body was first considered by boussinesq [10], then sneddon [11] adopted hankel transforms and elementary solution to solve the boussinesq problem, and the total penetration depth and force of the rigid body were presented. therefore, the applied force of conical pick on rock could be approximately expressed as:   2 2 2 tan 1 e h p v     (1) where: p is the penetration force of conical pick; e is elastic modulus of rock;  is semi-angel of conical pick;  is poisson ratio of rock; h is the penetration depth of conical pick. integrating eq.1 with respect to the penetration depth, the work we can be obtained and it is expressed as:     2 3 2 2 0 0 tan tan 1 3 1 h h e e e w p dh h dh h v v           (2) therefore, when the main rock fragment formed, the total work wt can be expressed as:   max 3 2 2 tan 3 1 t e w h v     (3) where hmax is the maximum penetration depth at the time of main rock fragment formed. the fracture surface of main rock fragment is simplified without influence of pcf prediction, and it is shown in fig.1. as fig.1 shown, the new fracture surface area a of main rock fragment can be expressed as: 2 2tan tan tan sin sin cos d def a          (4) where: e and f are the geometry shape parameters of main rock fragment; d is cutting depth of conical pick; θ is horizontal fracture angles; ψ is vertical fracture angle. figure 1: schematic diagram of fracture surface of rock fragment. t http://dx.medra.org/10.3221/igf-esis.27.06&auth=true http://www.gruppofrattura.it g. kuidong et alii, frattura ed integrità strutturale, 27 (2014) 43-52; doi: 10.3221/igf-esis.27.06 45 according to the relevant references, the work done by conical pick mainly translate into rock fracture energy, damage energy, plastic strain energy and so on [12-13]. the fracture energy ef can be express as: f te kw (5) where k is an ideal coefficient which only has relation with pick’s shape and cutting angle, and it can be obtained through rock cutting test. in verification of the model paragraph, acquisition process of k value will be presented. on the basis of griffith fracture mechanics theory [14], the fracture energy ef for generating new fracture surface when the main rock fragment formed can be expressed as: 2 2 2 s i f s 2 tan 2 tan 2 cos cos g d k d e g a e        (6) where gs represents surface free energy per unit area of rock material; ki stands for fracture toughness of rock material in the type of model i cracking, it can be approximately calculated by σt /6.88 [15]; σt is rock tensile strength. combining eqs. 3-6, the maximum penetration depth of conical pick before main rock fragment formed can be expressed by:   1 2 2 2 3 max 2 3 1 tan tan cos ik d h k e              (7) submitted eq.7 to eq.1, then the peak cutting force of conical pick pc can be expressed as: 1 2 42 i3 3 3 2 3 tantan 2( ) ( ) cos(1 )c k p d ke      (8) calculation of rock fracture surface area he similarity of geometry shape of brittle material (glass, ceramic, rock, coal and so on) fragment under indenters or cutting tools has been verified through experiments, and there are linear relationship between width, length of fragments and cutting depth [16-18]. according to eq.8, it is visible that the area calculation of new facture surface generated by conical pick is the basis for predicting the peak cutting force of conical pick, which means to establish the calculative method for horizontal and vertical fracture angle of rock fragment. calculation of horizontal fracture angle orizontal fracture angle of rock fragment is directly related to the optimal intercept of conical picks. the optimal intercept of conical picks in rock cutting process is 3.46 times the cutting depth according to evans calculate method [1]. optimal intercepts of 22 different rock types have been obtained through rock cutting experiments by bilgin [5], and their values are very close to 3.23 times the cutting depth. in view of 7% difference between evans calculated result and bilgin experimental result, evans calculate method is considered reliable and correct. so, in this paper, horizontal fracture angle of rock fragment in the mathematical model for predicting the peak cutting force will adopts evans calculate model, which means that horizontal fracture angle is equal to 60 degree. calculation of vertical fracture angle he influence of cutting angle on the rock fragment is ignored in evans theory, but the geometric shape of rock cutting fragment has play an important role in perfect prediction of peak cutting force. base on evans theory, some assumptions are put forward in present paper: rock broken is caused by tensile failure, and it accords with the maximum tension theory; the generated total force by tensile stress in fracture surface is through the center of arc ac; the crushing zone caused by conical pick head is shown in fig.2, and ag is an arc with the center o. t h t http://dx.medra.org/10.3221/igf-esis.27.06&auth=true http://www.gruppofrattura.it g. kuidong et alii, frattura ed integrità strutturale, 27 (2014) 43-52; doi: 10.3221/igf-esis.27.06 46 figure 2: vertical mechanical model of rock fragment. based on these assumptions, vertical mechanical model of rock fragment by conical pick is shown in fig.2. according to the geometrical relationship in fig.2, the force r is the resultant force of extrusion forces which acted on crush zone, and it has the relation with rock compressive strength and crush area. meanwhile, the force r also increased with the height of crush zone (a), and it will reach a maximum when the torques caused by force t and force r on point c get balance. the force r can be expressed as: 90 c c ( 90 ) cos sin( 2 ) sin aa r d              (9) where: γ is the cutting angle of conical pick; a is the height of crushing zone; σc represents rock comprehensive strength;  is the cutting parameter of pick, and it equals to (γ+)/2. rock will fracture along the arc ac when the force of conical pick applied on rock is big enough. however, the extreme state of rock fragment is determined by rock tensile strength, and the force t is the resultant force of tensile forces which acted on crack path. it can be expressed as: t t tcos 2 sin sin t d r d r              (10) where: r is the radius of the fracture arc ac;  stands for the complementary angle of vertical fracture angle. the force r and force t will reach a moment balance when the rock fragment forms. therefore, an equation between them can be obtained according to geometrical conditions, and it can expressed as: sin cos( ) 0 sin 2 sin d d r a t            (11) submitting eq.9 and eq.10 to eq.11, we have: 2 c t 2 cos( ) sin 0 sin sin 2 sin a dd a               (12) changing eq.12 to the form of quadratic equation: 2 t 2 c cos( ) 1 ( ) ( ) 0 sin sin 2 sin wa a d d         (13) solving eq.13, the parameter a/d can be obtained and expressed as: http://dx.medra.org/10.3221/igf-esis.27.06&auth=true http://www.gruppofrattura.it g. kuidong et alii, frattura ed integrità strutturale, 27 (2014) 43-52; doi: 10.3221/igf-esis.27.06 47 2 t 2 c cos ( ) cos( ) 2 2 sin4 sin ( ) sin a d             (14) in this paper, the derivation process of theoretical model takes evans work as reference. so, the energy of cutting system will be minimum at the moment of rock broken presumed by evans as an equilibrium situation. for this reason, this paper can use the ‘minimum energy theory’ as theoretical basis. according to the minimum energy theory: d( / ) / d 0a d   (15) now, the relationship between  and  can be obtained and expressed as: 2 2 2 t t 2 2 c c 2 sin( ) cos( ) sin( ) 2 sin cos ( ) cos ( ) cos( ) 4 sin ( ) cos ( ) 2 2 2 sin4 sin 4 sin 0 sin sin                                     (16) b represents the ratio of rock compressive strength to tensile strength. from eq.16, we can conclude that it is difficult to get the analytical solution of eq.16. consequently, the effects of cutting parameter  and ratio b on vertical fracture angle ψ are investigated, and the change law of ψ along with  and b is shown in fig.3. fig.3 shows that ψ increases with  and b. in order to get intuitive relationship among ψ,  and b, the data points of numerical solution in fig.3 are regressed based on space surface regression method. the regression formula of vertical fracture angle ψ can be expressed as eq.17, and the correlation coefficient of formula is 0.994. 248.87 0.526 0.224 0.994b r     (17) figure 3: variation law of vertical fracture angle of rock fragment. verification of the model orizontal fracture angle of rock fragment is directly related to the optimal intercept of conical picks. the optimal intercept of conical picks in rock cutting process is 3.46 times the cutting depth according to evans calculate method [1]. optimal intercepts of 22 different rock types have been obtained through rock cutting experiments by bilgin [5], and their values are very close to 3.23 times the cutting depth. in view of 7% difference between evans calculated result and bilgin experimental result, evans calculate method is considered reliable and correct. so, in this paper, horizontal fracture angle of rock fragment in the mathematical model for predicting the peak cutting force will adopts evans calculate model, which means that horizontal fracture angle is equal to 60 degree. verification of vertical fracture angle in order to verify the correctness of vertical mechanical model of rock fragment in this paper, rock cutting experiments are carried in laboratory as shown in fig.4. the semi-angel of conical pick is 40 degree, cutting angle of conical pick is selected in range of 45~55 degree according to actual working condition, and the mechanical properties of marble is h http://dx.medra.org/10.3221/igf-esis.27.06&auth=true http://www.gruppofrattura.it g. kuidong et alii, frattura ed integrità strutturale, 27 (2014) 43-52; doi: 10.3221/igf-esis.27.06 48 shown in tab.1. the shape and interrelated geometric parameters are shown in fig.5. fig.6 shows the theoretical and experimental vertical fracture angle under different cutting angle, the difference less than 5 percent between them indicates that the established vertical mechanical model of rock fragment is valid. properties value modulus of elasticity e(gpa) 19 density ρ(kg/m3) 2650 fracture toughness ki (mpa.m1/2) 1.1 compression strength σc(mpa) 103.2 tensile strength σt(mpa) 7.1 table 1: mechanical properties of marble. figure 4: laboratory furniture of rock cutting linearly: 1-rock specimen; 2-guideways; 3-clamping device of conical pick; 4-conical pick; 5advancing hydro-cylinder. figure 5: geometric feature parameters of rock fragment. figure 6: vertical fracture angle of experiments and theoretical model. verification of peak cutting force the k is a geometric factor of the pick independent of material properties which has been mentioned in front contents. in reference [18], the researchers also took an intensive study and detailed explanation of the k. according to eq.5, the k can be obtained by experiments. fig.7 is the variation curve of cutting force in rock cutting process, which corresponds to fig.5. so, the k can be expressed as: 2 2 2 2 f i i t c max 2 tan 4 tan coscos ( )d e k d k d k w e p he p h h        (18) http://dx.medra.org/10.3221/igf-esis.27.06&auth=true http://www.gruppofrattura.it g. kuidong et alii, frattura ed integrità strutturale, 27 (2014) 43-52; doi: 10.3221/igf-esis.27.06 49 submitted the rock mechanical properties and the geometric parameters of rock fragment to eq.18, then the k can be obtained as 0.0102. according to the value of k, we can conclude that the fracture energy for generating new fracture surface accounts for only a small part of total work, and the most part of total work is used for rock plastic deformation, rock damage, crushing zone formed and so on. now, we get the value of k, and if we also get the other parameter values, we can obtain the peak cutting force pc by eq.8. figure 7: variation curve of cutting force. the peak cutting forces of experiments, this model and evans model with different rock types and cutting parameters are shown in tab.2 [5-7]. the relationships between experimental peak cutting force with theoretical peak cutting force from this model and evans model are investigated by linear regression method, and their linear regression results are shown in tab.3. the significance of regression result less than 0.05 indicates that the regression relationships are correct and reliable. fig.8 and fig.9 shows the fitted relationships between experimental peak cutting force and two theoretical models (evans model and this model) respectively. the correlation between experimental and theoretical peak cutting force of this model is better than evans’s, and the slopes of the fitted line equations are 2.11 and 5.13. it indicates that the prediction of peak cutting force by this model has more correctness and reliabilities than evans theory. type σc σt e ki d=9mm d=5mm pcexp(n) pc(n) pc e(n) pcexp(n) pc(n) pc e(n) chromite1 32 3.7 3.5 0.538 14830 8230 3660 7160 3759 920 chromite2 47 4.5 2.3 0.654 26490 12642 3690 10210 5773 920 chromite3 46 3.7 2.9 0.538 16240 9309 2550 8710 4251 3190 harsburgite 58 5.5 2.1 0.799 26910 17057 4470 14970 7789 1120 serpantinite 38 5.7 2.3 0.828 20150 16338 7320 7850 7462 1830 trona 30 2.2 3.4 0.320 12260 4503 1380 3880 2056 350 anhydrite 82 5.5 11.0 0.799 16300 10558 3160 12520 4822 790 sandstone1 114 6.6 17.0 0.959 25920 12138 3270 19690 5544 820 sandstone2 174 11.6 28.0 1.686 48100 20946 6620 23250 9566 1660 sandstone3 87 8.3 33.3 1.206 15920 11739 6780 9090 5361 1700 tuff1 10 0.9 1.1 0.131 4020 1911 690 2050 873 170 tuff2 11 1.2 1.4 0.174 11840 2509 1120 7080 1145 280 tuff3 27 2.6 2.4 0.378 7200 5993 2140 3770 2735 540 tuff4 14 1.5 1.6 0.218 7300 3239 1380 2830 1479 340 tuff5 19 2.3 1.3 0.334 7350 6037 2380 3440 2757 600 tuff6 6 0.2 0.4 0.029 2180 523 57 1330 238 14 pc exp: the pcf of experiments; pc e: the pcf of evans model; pc: the pcf of this model table 2: rock mechanical property and the pcf. http://dx.medra.org/10.3221/igf-esis.27.06&auth=true http://www.gruppofrattura.it g. kuidong et alii, frattura ed integrità strutturale, 27 (2014) 43-52; doi: 10.3221/igf-esis.27.06 50 item df ss ms f-value prob>f p ce x p p c model 1 2.5e9 2.5e9 133.7 1.4e-12 error 30 5.6e8 1.9e7 total 31 3.1e9 1.6 p ce x p p ce model 1 1.6e9 1.6e9 31.7 3.7e-6 error 30 1.5e9 5.0e7 total 31 3.1e9 df: degrees of freedom; ss: sum of squares; ms: mean square table 3: the regression analysis results of the pcf obtained from different method. figure 8: the relationship between the predicted and experimental pcf. figure 9: the relationship between the pcf of evans model and experiments. conclusions n this paper, a theoretical model for predicting the peak cutting force has been set up and verified, we get following conclusions: (1) the theoretical model of rock vertical fracture has been established by maximum tensile criterion and verified i http://dx.medra.org/10.3221/igf-esis.27.06&auth=true http://www.gruppofrattura.it g. kuidong et alii, frattura ed integrità strutturale, 27 (2014) 43-52; doi: 10.3221/igf-esis.27.06 51 through experiments. the regression formula of vertical fracture angle also has been obtained by numerical analysis and polynomial regression. all of these work can provide a basis for the research on rock cutting theory. (2) a theoretical model for predicting peak cutting force of conical pick in rock cutting process has been established by elastic fracture mechanics theory. the regression analysis between the results of experimental and predicted by this model shows that correlation coefficient is equal to 0.81 and significance is less than 0.05. (3) the relationships between experimental peak cutting force and calculated values by the present model and evans model are investigated by linear regression analysis, and it shows that the prediction of peak cutting force of this model has more correctness and reliabilities than evans model. the model established by this paper can provide a better guidance for design and study of conical pick and cutting mechanism. acknowledgements he paper was financially supported by the national 863 plan of china(2012aa062104), national natural science foundation of china(51005232), jiangsu ordinary university graduate students scientific research innovation project(cxzz11-0289), the jiangsu provincial natural science foundation of china (no. bk20131116), the fundamental research funds for the central universities (project no.2012qna22) and the priority academic program development of jiangsu higher education institutions. references [1] evans, i., a theory of the picks cutting force for point-attack, international journal of mining engineering, 2(1) (1984) 63-71. [2] roxborough, f.f, liu, z.c., theoretical considerations on pick shape in rock and coal cutting. proceedings of sixth underground operator’s conference, australia, (1995) 189-193. [3] goktan, r. m., a suggested improvement on evans’s cutting theory for conical bits, proceedings of fourth symposium on mine mechanization automation, 1 (1997) 57-61. [4] copur, h., bilgin, n., et al., a set of indices based on indentation tests for assessment of rock cutting performance and rock properties, the journal of the south african institute of mining and metallurgy, 11 (2003) 589-599. [5] bilgin, n., demircin, m. a., et al., dominant rock properties affecting the performance of conical picks and the comparison of some experimental and theoretical results, international journal of mining engineering, 43(1) (2006) 139-156. [6] tiryaki, b., boland, j.n., li, x.s., empirical models to predict mean cutting forces on point attack pick cutters, international journal of rock mechanics & mining sciences, 47(5) (2010) 858-864. [7] su o., akcin n.a., numerical simulation of rock cutting using the discrete element method, international journal of rock mechanics & mining sciences, 48(3) (2011) 434-442. [8] rojek, j., onate, e., et al., discrete element simulation of rock cutting, international journal of rock mechanics & mining sciences, 48 (2011) 996 -1010. [9] john, p., loui, u.m., rao k., numerical studies on chip formation in drag-pick cutting of rocks, geotechnical and geological engineering, 30(1) (2011) 145-161. [10] sneddon, i.n., boussinesq’s problem for a rigid cone, mathematical proceedings of the cambridge philosophy society, 44(4) (1948) 492-507. [11] chiaia, b., fracture mechanics induced in a brittle material by hard cutting indenter, international journal of solids and structures, 38 (2001) 7747-7768. [12] li, l.y., ju, y., zhao, z.w., et al., energy analysis of rock structure under static and dynamic loading conditions, journal of china coal society, 34(6) (2009) 737-741.(in chinese) [13] xie, h.p., ju, y., li, l.y., criteria for strength and structural failure of rocks based on energy dissipation and energy release principles, chinese journal of rock mechanics and engineering, 24(17) (2005) 3003-3010. (in chinese) [14] lawn, b., fracture of brittle solids, cambridge: cambridge university press (1993). [15] zhang, z.x., an empirical relation between mode i fracture toughness and the tensile strength of rock, international journal of rock mechanics & mining sciences, 39 (2002) 401-406. [16] almond, e., mccormick, n., constant-geometry edge-flaking of brittle materials, nature, 321(3) (1986) 53-55. t http://dx.medra.org/10.3221/igf-esis.27.06&auth=true http://www.gruppofrattura.it g. kuidong et alii, frattura ed integrità strutturale, 27 (2014) 43-52; doi: 10.3221/igf-esis.27.06 52 [17] chai, h., lawn, b., a universal relation for edge chipping from sharp contacts in brittle materials: a simple means of toughness evaluation, acta materialia, 55(7) (2007) 2555-2561. [18] bao, r.h., zhang, l.c., et al., estimating the peak indentation force of the edge chipping of rocks using single pointattack pick, rock mechanics and rock engineering, 44 (2011) 339-347. http://dx.medra.org/10.3221/igf-esis.27.06&auth=true http://www.gruppofrattura.it microsoft word numero_26_art_6 a. tridello et alii, frattura ed integrità strutturale, 26 (2013) 49-56; doi: 10.3221/igf-esis.26.06 49 comparison between dog-bone and gaussian specimens for size effect evaluation in gigacycle fatigue a. tridello, d.s. paolino, g. chiandussi, m. rossetto department of mechanical and aerospace engineering, politecnico di torino, 10129 turin, italy, andrea.tridello@polito.it, davide.paolino@polito.it, giorgio.chiandussi@polito.it, massimo.rossetto@polito.it abstract. gigacycle fatigue properties of materials are strongly affected by the specimen risk volume (volume of material subjected to a stress amplitude larger than the 90% of the maximum stress). gigacycle fatigue tests, performed with ultrasonic fatigue testing machines, are commonly carried out by using hourglass shaped specimens with a small risk volume. the adoption of traditional dog-bone specimens allows for increasing the risk volume, even if the increment is quite limited. in order to obtain larger risk volumes, a new specimen shape is proposed (gaussian specimen). the dog-bone and the gaussian specimens are compared through finite element analyses and the numerical results are validated experimentally by means of strain gages measurements. the range of applicability of the two different specimens in terms of available risk volume and stress concentration effects due to the cross section variation is determined. keywords. very-high-cycle fatigue; ultrasonic testing machine; risk volume; wave propagation equations; stress concentration factor. introduction n recent years, the interest in gigacycle fatigue behaviour of metallic materials (up to 1010 cycles) is significantly increased. design requirements in specific industrial fields (aerospace, mechanical and energy industry) for structural components characterized by even larger fatigue lives (gigacycle fatigue) lead to a more detailed investigation on material properties in the gigacycle regime. experimental results, obtained by using testing machines working in resonance conditions and capable of reaching a loading frequency equal to 20 khz (ultrasound), have shown that specimens may fail also at levels of stress amplitude below the conventional fatigue limit [1-3]. when specimens are subjected to stress amplitudes below the conventional fatigue limit, failures are generally due to cracks which nucleate internally from inclusions or defects; whereas when specimens are subjected to stress amplitudes above the conventional fatigue limit, failures are generally due to cracks which nucleate from the surface of the specimen. recently, models able to take into account these two different modes of failure have been proposed in the literature [4-6]. in case of internal crack nucleation, fatigue strength decreases when the specimen size increases. as reported in [7-9], the decrement in fatigue strength is physically justifiable by considering the probability of finding inclusions causing failure when the risk volume (volume of material subjected to a stress amplitude above the 90% of the maximal stress [7]) increases. since experimental tests are carried out almost entirely by means of ultrasonic fatigue testing machines, the specimen size and the consequent specimen risk volume are imposed by resonance condition and are generally significantly limited. experimental tests exploring the gigacycle fatigue properties of materials have been generally carried out by using i http://www.gruppofrattura.it http://dx.medra.org/10.3221/igf-esis.26.06&auth=true a. tridello et alii, frattura ed integrità strutturale, 26 (2013) 49-56; doi: 10.3221/igf-esis.26.06 50 hourglass shaped specimens with a small diameter (3-6 mm) and a small risk volume. in order to increase the risk volume, dog-bone shaped specimens have been adopted in [7-9]. however, the risk volume of tested specimens (maximum 1000 mm3) is significantly limited due to the non uniform stress distribution along the specimen length with constant cross section. the paper proposes a new specimen shape (gaussian specimen) for gigacycle fatigue tests: wave propagation equations are analytically solved in order to obtain a specimen shape characterized by a uniform stress distribution on an extended specimen length and, as a consequence, by a larger risk volume. dog-bone and gaussian specimens with different risk volumes are compared through finite element analyses and the range of applicability of the two different specimens in terms of available risk volume is determined. the stress concentration effect due to cross section variation in the specimens is also taken into account in the analyses. finally, the stress distribution of a dog-bone and a gaussian specimen with a theoretical risk volume of 5000 mm3 is experimentally validated through strain gage measurements. specimen design pecimens adopted for ultrasonic fatigue tests are designed on the basis of equations for wave propagation in an elastic material with the specimen modelled as a one dimension linear elastic body. stresses are considered uniformly distributed on the cross section and transverse displacements are considered as negligible if compared to longitudinal displacements. in this respect, the displacement amplitude along the specimen,  u z , can be obtained by solving the webster’s equation for a plane wave:          '' ' 2 /      0 ds z dz u z u z k u z s z      (1) where    ' /u z du z dz ,    '' 2 2/u z d u z dz , and  2 / dek f     , being f the resonance frequency, and  and de the specimen material density and dynamic elastic modulus respectively. by inverting and integrating eq. 1, the specimen cross-section variation for an imposed displacement  u z is expressed by the following equation:         2 '' ' 0 k u z u z dz u zs z s e       (2) where 0s is a constant of integration depending on the boundary conditions. in order to obtain a uniform stress distribution along the specimen, the displacement distribution must be linear:    3u z a kz b   (3) where  3u z denotes the displacement amplitude in part 3 of the gaussian specimen (fig. 1) and a and b are constant coefficients. boundary conditions for ultrasonic specimens require  3 3 0u l  , where 3l is half of the total length of part 3 of the specimen (fig. 1). the constant of integration 0s is obtained considering that   220 / 4 s d for 0z  (fig. 1) and eq. 2 becomes:     22 33 22 2 2 / 4 k z lkl s z d e e               (4) figure 1: gaussian specimen. s http://www.gruppofrattura.it http://dx.medra.org/10.3221/igf-esis.26.06&auth=true a. tridello et alii, frattura ed integrità strutturale, 26 (2013) 49-56; doi: 10.3221/igf-esis.26.06 51 therefore, according to eq. 4, the specimen cross-section that leads to a uniform stress distribution entails the typical gaussian shape. the total volume of the gaussian specimen part (i.e., the theoretical risk volume theov ) can be computed by integrating the cross-section of specimen part 3 with respect to z from 0 to 3l and multiplying it by two:   2 33 3/22 2 32 0 2 erf 2 2 kll theo kld v s z dz e k                       (5) where   erf  denotes the error function (i.e.,   2 0 2 erf x tx e dt    ). eq. 5 allows to compute the length 3l for the desired risk volume, specimen material (i.e., for a chosen value of k ) and for the diameter 2d . part 3 of the specimen is thus completely designed, since 2d , 3l and k uniquely define the gaussian specimen part. in order to determine specimen lengths 1l and 2l , equations for wave propagation along a straight and catenoidal specimen profile [1], respectively part 1 and part 2 of the specimen (fig. 1), are solved. the boundary conditions require to have maximum displacement amplitude equal to inu at the interface between the horn and the specimen (i.e., at  1 2z l l   ), continuity of displacement and strain amplitude at the interface between part 1 and part 2 (i.e., at 2z l  ) and at the interface between part 2 and part 3 (i.e., at 0z  ) of the specimen. a further boundary condition concerning the required stress amplitude in the risk volume is taken into account. let define the stress amplification factor of the specimen, m , as the ratio between the constant stress amplitude in the gaussian specimen part,  , and the maximum stress amplitude in part 1 of the specimen [1], 1 (i.e.,  1/ / d inm e ku     ). according to the assumption of linear elasticity and introducing the boundary conditions, the stress amplification factor can be expressed as:               2 2 2 2 2 3 1 cos tan sin/   tan /1 tan l l lk m n l k klkl              (6) where 1 2/n d d , being 1d the diameter of the cylindrical part (part 1 in fig. 1),     2 2 2 2acosh /kl n l   and:             3 2 2 1 2 3 2 / tan 1 acosh atan 1 tan / / k kl l n kl n l k kl kl                   (7) according to eq. 6 and eq. 7 and for a given value of 3kl , both m and 1kl depend on the diameter ratio n and on the adimensionalized variable 2kl . therefore for a chosen resonance frequency, specimen material, diameter ratio n and inu value, the lengths 2l and 1l giving a stress amplitude equal to  in the gaussian specimen part are obtained and specimen geometry is thus completely defined. finite element analysis: actual risk volume and stress concentration evaluation og-bone and gaussian specimens with different theoretical risk volumes are tested through finite element analyses (fea) by using the commercial finite element program ansys. half of the specimen geometrical model is considered in each analysis due to its symmetry and eight-node quadrilateral elements (plane 82) with the axisymmetric option are used for the finite element models. the numerical models count for a number of elements ranging from 21200 to 53700 elements. a suitable fillet radius between specimen parts 2 and 3 is considered for the gaussian specimen model. d http://www.gruppofrattura.it http://dx.medra.org/10.3221/igf-esis.26.06&auth=true a. tridello et alii, frattura ed integrità strutturale, 26 (2013) 49-56; doi: 10.3221/igf-esis.26.06 52 dog-bone and gaussian specimens are designed considering steel ( 206 gpade  , 0.29  and 37800 kg / m  ), a resonance frequency of 20 khz (ultrasonic testing machine working frequency), a diameter 1d equal to 20 mm and a length 2l equal to 10.2 mm (almost equal to the value adopted in [7-9]). the theoretical risk volume is varied by steps of 31000 mm : the range considered is within 32000 mm and the maximum theoretical risk volume allowing for an amplification factor m larger than 1.05 . the analysis is repeated considering three different diameter ratios n : 1.6 , 2 and 2.5 . fig. 2 reports the typical mesh adopted for the dog-bone and the gaussian specimen models; the enlargements show the dimensions of the elements at the transition between part 2 and part 3 of the specimen. (a) (b) figure 2: typical mesh for the specimen models: (a) dog-bone specimen; (b) gaussian specimen. the actual risk volume and the stress concentration factor are considered in each analysis. according to [10], the actual risk volume ( realv ) is the volume of material subjected to a stress amplitude larger than the 96% of the maximum stress reached in specimen part 3. in order to evaluate the stress concentration effects, the stress concentration factor tk is conservatively considered in place of the fatigue strength reduction factor fk . for tk computation, the nominal stress amplitude is considered equal to the maximum stress reached in specimen part 3 along the longitudinal axes. fig. 3 shows the actual risk volume variation of both types of specimen with respect to the length 3l . according to fig. 3, the maximum actual risk volume attainable using dog-bone specimens is smaller than 33000 mm . an increment of the length with constant cross section gives no effect in the 3 considered case, since the actual risk volume does not change. gaussian specimens permit to reach larger actual risk volume, up to 38450 mm with a diameter ratio of 1.6 . the actual risk volume increases with the length 3l . as expected, for both types of specimen, a small diameter ratio ( 1.6n  ) permits to obtain the largest actual risk volume. 5 10 15 20 25 30 35 40 45 1000 2000 3000 4000 5000 6000 7000 8000 9000 l 3 [mm] v re a l [ m m 3 ] n=1.6 n=2 n=2.5 dog bone gaussian figure 3: realv of dog-bone and gaussian specimens with respect to the length 3l . http://www.gruppofrattura.it http://dx.medra.org/10.3221/igf-esis.26.06&auth=true a. tridello et alii, frattura ed integrità strutturale, 26 (2013) 49-56; doi: 10.3221/igf-esis.26.06 53 fig. 4 reports the percent ratio between the actual risk volume and the theoretical risk volume with respect to the length 3l . according to fig. 4 and considering dog-bone specimens, the efficiency is high (above 90% ) for values of length 3l smaller than 15 mm , while it decreases (up to 25% ) when the length 3l increases. differently, when considering the gaussian specimen, the efficiency is almost constant (above 90% ). 5 10 15 20 25 30 35 40 45 20 30 40 50 60 70 80 90 100 l 3 [mm] v re a l/ v th e o n=1.6 n=2 n=2.5 dog bone gaussian figure 4: percent ratio /real theorv v in dog-bone and gaussian specimens with respect to the length 3l . finally, the stress concentration factor is taken into consideration. fig. 5 shows the variation of tk with respect to the length 3l . according to fig. 5, the gaussian specimens show larger tk values. considering dog-bone specimens, there is no stress concentration for 3l larger than 25 mm . indeed the stress amplitude significantly decreases in specimen part 3 as the length 3l increases. as a consequence, the maximum stress reached at the transition between parts 2 and 3 of the specimen is smaller or equal to the stress reached at the specimen mid-section. 5 10 15 20 25 30 35 40 45 1 1.05 1.1 1.15 l 3 [mm] k t n=1.6 n=2 n=2.5 dog bone gaussian figure 5: stress concentration factor of dog-bone and gaussian specimens with respect to the length 3l . the tk values of the gaussian specimens are smaller than 1.15 . taking into account the largest diameter ratio ( 2.5n  ), the tk value reduces up to 1.12 . at the transition between part 2 and part 3 of the specimen, two http://www.gruppofrattura.it http://dx.medra.org/10.3221/igf-esis.26.06&auth=true a. tridello et alii, frattura ed integrità strutturale, 26 (2013) 49-56; doi: 10.3221/igf-esis.26.06 54 concomitant stress concentrations are present: the first one is due to the shoulder fillet in specimen part 2 and the second one is due to the sharp geometrical transition between part 2 and part 3 of the specimen. the resulting tk value is due to the interaction between the two stress concentrations. it is well-known that the stress concentration due to the shoulder fillet increases with n ; finite element analyses carried out on the sharp geometrical transition at the interface showed that the stress concentration increases with the difference between 3d and 2d , being 2 3 21 3 2 1 kl d d d e n                 . to sum up, if n increases, then the stress concentration due to the shoulder fillet increases, while the stress concentration factor due to the sharp transition decreases. as shown in fig. 5, in case of 2.5n  , the decrement in the stress concentration due to the sharp transition outperforms the increment in the stress concentration due to the shoulder fillet. a larger reduction of the stress concentration factor can be obtained by increasing the length 2l . in this respect, a proper choice of the length 2l and of the diameter ratio allows to design specimens with large actual risk volume and limited tk value. for instance, a diameter ratio equal to 1.33 and a length 2l equal to 17.2 mm allows for an actual risk volume larger than 35000 mm and a tk equal to 1.06 . finally, the adoption of dog-bone specimens is appropriate for small risk volumes (smaller than 33000 mm ). gaussian specimens must be adopted for large risk volumes. the length 2l and the diameter ratio must be properly chosen in order to reduce the stress concentration effects. experimental validation he stress distribution in the two specimen types is experimentally validated through strain gage measurements. a dog-bone and a gaussian specimen with a theoretical risk volume of 35000 mm , diameter ratio 2n  ( 1 20 mmd  ) and 2l equal to 10.2 mm are produced in aisi 1040 carbon steel. three t-rosettes strain gages (hbm 1-xy31-1.5/350), each with two strain gages connected at half bridge, are used for the evaluation of strain values at the specimen surface. for both specimens, the rosettes are bonded along the specimen central part: the first rosette is bonded at the specimen mid-section, the second rosette at the 70% of 3l and the third rosette at the 85% of 3l . fig. 6 shows the specimens after the application of the rosettes. 46 19.3 68 85% 70% 92 91 45.5 26.3 70% 85% 68.8 (a) (b) figure 6: specimens after application of strain gage rosettes: (a) dog-bone shaped specimen; (b) gaussian specimen. a strain gage amplifier (el-sga-2/b by elsys ag) is used for the completion of the wheatstone bridge of each rosette and for the amplification of the signal. the measurement is acquired at a sample rate of 600 khz by a national instruments data acquisition card (pcie-6363). an ultrasonic testing machine for fully reversed tension compression tests developed by the authors [11] is used for the test: specimens are subjected to load cycles for 3 seconds. fig. 7 and 8 show the stress measured at each point normalized by the value detected at the specimen mid-section, center . the acquired signals are fitted with a sine function (for each case, the correlation coefficient is larger than 99.99% and the mean value is equal to zero). as shown in fig. 7 and 8, the stress amplitude distribution is not uniform for the dog-bone shaped specimen while it is almost uniform for the gaussian specimen. tab. 1 reports a comparison between the stress variation obtained with the finite element analysis (fea) and the experimental test. according to tab. 1, the fea results are included in the experimental confidence intervals. therefore, t http://www.gruppofrattura.it http://dx.medra.org/10.3221/igf-esis.26.06&auth=true a. tridello et alii, frattura ed integrità strutturale, 26 (2013) 49-56; doi: 10.3221/igf-esis.26.06 55 it can be concluded that no significant statistical difference exists between fea and experimental results. it is worth to note that, for the gaussian specimen, the values larger than the 100% indicate a maximum stress amplitude not reached at the specimen mid-section. (a) (b) figure 7: stress variation measured by strain gage rosettes bonded to the dog-bone shaped specimen: (a) rosette at 70% of 3l ; (b) rosette at 85% of 3l . (a) (b) figure 8: stress variation measured by strain gage rosettes bonded to the gaussian specimen: (a) rosette at 70% of 3l ; (b) rosette at 85% of 3l . analysis type 3/ 70z l % 3/ 85z l % dog-bone gaussian dog-bone gaussian finite element 85.8 % 100. 0% 80.2 % 100.2 % experimental (95 % confidence interval)  85.4;86.5  %  99.6;100.8  %  80.1;81.4  %  100.0;101.1  % note: confidence intervals are obtained from 180 tests; for each experimental test, stress amplitude is evaluated with a minimum of 1000 data points. table 1: comparison between numerical and experimental results: values of the centerσ / σ percent ratio. conclusions he proposed gaussian shape allows to obtain specimens characterized by a very large risk volume. dog-bone and gaussian specimens are compared through a finite element analysis. the finite element models are experimentally validated by means of strain gages measurements. t http://www.gruppofrattura.it http://dx.medra.org/10.3221/igf-esis.26.06&auth=true a. tridello et alii, frattura ed integrità strutturale, 26 (2013) 49-56; doi: 10.3221/igf-esis.26.06 56 the results show that dog-bone specimens are appropriate only for small risk volumes, while the gaussian shape allows to design specimens with larger risk volumes (up to 38500 mm ). the stress concentration effect due to the cross section variation along the specimen is also taken into account. stress concentration factor is limited for dog-bone specimen. gaussian specimen shows larger stress concentration factors; an appropriate choice of the length 2l and of the diameter ratio n allows to design gaussian specimens with large risk volume and tk values equal or even smaller than that of the traditional dog-bone specimens. acknowledgments he authors gratefully acknowledge financial support from the piedmont region industrial research project ngp – bando misura ii.3. references [1] bathias, c., paris, p.c., gigacycle fatigue in mechanical practice, crc dekker, new york (2005). [2] bathias, c., there is no infinite fatigue life in metallic materials, fatigue fract. eng. mater. struct., 22 (1999) 559-565. [3] pyttel, b., schwerdt, d., berger, c., very high cycle fatigueis there a fatigue limit?, int. j. fatigue, 33 (2011) 49-58. [4] shiozawa, k., lu, l. ishihara, s. s-n curve characteristics and subsurface crack initiation behaviour in ultra-long life of fatigue of a high carbon-chromium bearing steel, fatigue fract. eng. mater. struct., 24 (2001) 781–790. [5] sakai, t., lian, b., takeda, m., shiozawa, k., oguma, n., ochi, y., nakajima, m., nakamura, t., statistical duplex sn characteristics of high carbon chromium bearing steel in rotating bending in very high cycle regime, int. j. fatigue, 32 (2010) 497-504. [6] paolino, d.s., chiandussi g., rossetto, m., a unified statistical model for s-n fatigue curves: probabilistic definition, fatigue fract. eng. mater. struct., 36 (2013) 187-201. [7] furuya, y., specimen size effects on gigacycle fatigue properties of high-strength steel under ultrasonic fatigue testing, scripta materialia, 58 (2008) 1014-1017. [8] furuya, y., size effects in gigacycle fatigue of high-strength steel under ultrasonic fatigue testing, procedia engineering, 2 (2010) 485–490. [9] furuya, y., notable size effects on very high cycle fatigue properties of high strength steel, material science and engineering, a 528 (2011) 5234–5240. [10] tridello, a., paolino, d.s., chiandussi g., rossetto, m., provini di fatica per la valutazione dell’effetto scala in campo gigaciclico, in: proceedings of the 42th aias italian national conference, salerno, (2013). [11] paolino, d.s., rossetto, m., chiandussi, g. tridello, a., sviluppo di una macchina a ultrasuoni per prove di fatica gigaciclica, in: proceedings of the 41th aias italian national conference, vicenza, (2012). t http://www.gruppofrattura.it http://dx.medra.org/10.3221/igf-esis.26.06&auth=true microsoft word numero 9 art 15 finale s. beretta et alii, frattura ed integrità strutturale, 9 (2009) 145152; doi: 10.3221/igf-esis.09.15 145 analisi basata sugli sforzi locali della resistenza a fatica di giunzioni incollate di materiali compositi s. beretta, a. bernasconi politecnico di milano, dipartimento di meccanica, via la masa 34 – 20156 milano, stefano.beretta@polimi.it a. pirondi, f. moroni università degli studi di parma, dipartimento di ingegneria industriale, viale g.p. usberti, 181/a 43100 parma riassunto. il lavoro prende spunto dai risultati di un’analisi sperimentale del comportamento a fatica di giunzioni incollate di materiali compositi laminati di elevato spessore formati da strati di unidirezionale e di tessuto di fibra di carbonio. i giunti sono stati realizzati in modo tale da saggiare l’influenza della lunghezza di sovrapposizione (da 25,4 mm a 110,8 mm), della forma del giunto (con e senza rastremazione), e della composizione degli aderendi (sostituzione di uno degli aderendi in composito con uno in acciaio). mediante analisi 2d elastiche con il metodo degli elementi finiti sono state ricavate le distribuzioni degli sforzi all’interno dello strato di adesivo, al fine di individuare un parametro utile alla descrizione del comportamento a fatica in termini di sforzi locali numero di cicli a rottura. il ruolo della fase di propagazione viene discusso alla luce di osservazioni dell’avanzamento della frattura, condotta su alcuni dei giunti testati. abstract. results of fatigue tests on adhesive lap joints of thick (10 mm) composite laminates are presented and discussed. specimens of different overlap length (from 25 to 110 mm), different shape (with and without taper) and different materials (composite on composite, composite on steel) were fatigue tested. in order to investigate on the relationship between peak elastic stresses in the adhesive layer and fatigue life, a 2d structural analysis of the joints by the finite element method was performed. this analysis suggested that peak elastic stresses in the adhesive layer could be adopted as a design criterion, at least as an engineering tool for industrial applications. the role of crack propagation is also discussed, on the basis of some observations during fatigue tests. parole chiave. fatica; giunti incollati; sforzi locali; materiali compositi introduzione a resistenza a fatica delle giunzioni incollate di materiali compositi riveste particolare importanza per molte applicazioni in cui si renda necessario adottare la soluzione dell’incollaggio per abbinare l’efficienza meccanica dei materiali compositi con le proprietà di altri materiali, per esempio per inserti resistenti all’usura, oppure quanto dettato da esigenze costruttive o economiche (può risultare utile collegare parti in composito tra loro per ridurre i costi più stampi di forme meno complesse invece di un unico stampo più complesso – o per garantire la modularità per componenti appartenenti a piattaforme di prodotto differenti). inoltre il fenomeno della fatica di queste giunzioni presenta aspetti peculiari legati alle caratteristiche degli aderendi in materiale composito [1]. in questo lavoro sono state analizzate alcune giunzioni incollate di materiali compositi e di materiale composito su acciaio, al fine di verificare se fosse possibile adottare un criterio di resistenza a fatica basato sui valori degli sforzi assunti localmente nello strato di adesivo, come suggerito in [2]. una soluzione di questo tipo si è infatti dimostrata valida per interpretare la resistenza statica [3]. sebbene in questo modo il risultato sia semplicemente una condizione limite per le l http://www.gruppofrattura.it http://dx.medra.org/10.3221/igf-esis.09.15&auth=true mailto: stefano.beretta@polimi.it s. beretta et alii, frattura ed integrità strutturale, 9 (2009) 145152; doi: 10.3221/igf-esis.09.15 146 forze trasmesse dai giunti, rinunciando a priori ad una descrizione dettagliata del fenomeno fisico (nucleazione e propagazione [4], variazioni di percorso delle fratture durante la propagazione, effetto della singolarità degli sforzi in corrispondenza delle discontinuità geometriche, come mostrato ad esempio in [5]), tale soluzione presenta l’indubbio vantaggio di prestarsi facilmente al trasferimento ad applicazioni industriali. attività sperimentale a forma e le dimensioni dei provini utilizzati per le prove di fatica sono riportati in fig. 1. in fig. 1 sono anche riportate le sigle utilizzate nel seguito per indicare i lotti di provini. si tratta di quattro lotti di giunti a sovrapposizione semplice. per tre di questi lotti gli aderendi sono entrambi di materiale composito, mentre per il restante lotto uno dei due aderendi è realizzato in acciaio strutturale ad alta resistenza s690. il materiale composito è un laminato di 9.9 mm di spessore, composto da alternanze di lamine unidirezionali e di tessuto di fibre di carbonio a basso modulo immerse in matrice polimerica, la cui legge di laminazione è riporta in tab. 1. l’adesivo utilizzato è un epossidico bi-componente ad alta resistenza (3m 9323). lo spessore di 0.2 mm dello strato di adesivo è stato assicurato mediante inserimento di fili di rame di diametro calibrato disposti longitudinalmente rispetto all’asse dei provini, con eccezione dei provini ls 25,4 mm. ls 24.5 mm ls 50.8 mm tc 110.8 mm sc 24.5 mm figura 1: forma e dimensioni dei provini (non in scala). l   60 larghezza di tutti i provini 25.4 mm lamiera fes690 spessore 6 mm 150 150 25.4 205 205 25.4 60 60 60 205 205 50.8 60 60 205 205 50.8 30 60 60 http://www.gruppofrattura.it http://dx.medra.org/10.3221/igf-esis.09.15&auth=true s. beretta et alii, frattura ed integrità strutturale, 9 (2009) 145152; doi: 10.3221/igf-esis.09.15 147 t 45°/ ud5 / t 0° / t 45° 2 / t 0° 2 / t 45° 2 / t 0° / ud5 / t 45° tabella 1: legge di laminazione del laminato (t, tessuto da 0.66 mm di spessore; ud, unidirezionale di 0.33 mm di spessore). per poter eseguire le prove senza introdurre componenti di flessione durante l'afferraggio dei giunti nella macchina di prova, sono stati aggiunti mediante incollaggio talloni di alluminio di spessore uguale a quello del laminato. per i provini della serie rastremata, è stato richiesto di terminare la rastremazione con un dente iniziale di altezza 1 mm. la geometria del dente è riportata in fig. 2. le prove sono state eseguite presso i laboratori del dipartimento di meccanica del politecnico di milano, utilizzando una macchina di prova servo-idraulica schenck hydropuls da 250 kn di portata. le prove sono state condotte in un ambiente a temperatura variabile tra 23°c e 26 °c, con il solo controllo della temperatura mediante impianto di condizionamento. le prove di fatica sono state condotte in controllo di carico ad una frequenza di 2 hz. le prove sono state interrotte alla completa separazione della giunzione. il rapporto di carico r = fmin/fmax è stato imposto uguale a 0. figura 2: dettaglio del dente al termine della rastremazione. la caratterizzazione dell’adesivo è stata invece eseguita presso i laboratori del dipartimento di ingegneria industriale dell’università degli studi di parma. le proprietà dell’adesivo sono state determinate mediante prove di trazione su un provino ottenuto colando l’adesivo in uno stampo avente forma di un provino standard astm 628 tipo iv e attendendone la solidificazione in forno secondo il ciclo di cura previsto dal produttore. il provino è stato strumentato con un clip-gage e due strain-gages rispettivamente a 0° e 90° rispetto alla direzione del carico, in modo da poter valutare il modulo elastico e ed il coefficiente di poisson . i valori così ottenuti sono e = 2300 mpa,  = 0,33. risultati iportando in un unico grafico i valori di forza massima applicata (normalizzate rispetto alla forza media necessaria per portare a rottura i giunti ls 25,4 mm in 100.000 cicli) e il corrispondente numero di cicli a rottura, i punti sperimentali relativi ai quattro lotti di giunti si dispongono come in fig. 3, dove sono riportate anche le quattro curve interpolanti i risultati sperimentali secondo una legge lineare in scala doppio logaritmica. e’ evidente che a seconda del tipo e della forma del giunto, nonché della lunghezza di sovrapposizione, si ottengono quattro curve distinte. figura 3: curve forze-numero di cicli a rottura dei quattro lotti di giunti. r http://www.gruppofrattura.it http://dx.medra.org/10.3221/igf-esis.09.15&auth=true s. beretta et alii, frattura ed integrità strutturale, 9 (2009) 145152; doi: 10.3221/igf-esis.09.15 148 analisi delle fratture separazione finale dei due aderendi avvenuta, l’ispezione delle superfici di frattura rivela nella maggior parte dei campioni ls 25,4 mm una zona di probabile cedimento contenuta all’interno dello strato di adesivo, che interessa tutta l’area di sovrapposizione, come mostrato in fig. 4. ciò invece non è avvenuto nei giunti sc 25,4 mm, in cui il cedimento è presumibilmente avvenuto sempre all’interfaccia adesivo-acciaio o adesivo-composito, come si può dedurre dall’aspetto delle superfici di frattura, tutte simili a quella riportata in fig. 5. nel caso dei giunti con maggior lunghezza di sovrapposizione (da 50,8 mm a 110 mm) si è osservato una maggioranza di cedimenti riconducibili ad una fase di nucleazione in corrispondenza di uno o di entrambi gli estremi della sovrapposizione, seguita da apparente propagazione nello strato di adesivo e ulteriore propagazione interlaminare tra primo strato di tessuto e unidirezionale che ha interessato buona parte della sovrapposizione, come si può osservare in fig. 6 per i giunti ls 50,8 mm e in fig. 7 per i giunti tc 110,8 mm. figura 4: superficie di frattura di un giunto ls 25,4 mm. figura 5: superficie di frattura di un giunto sc 25,4 mm. figura 6: superficie di frattura di giunti ls 50,8 mm . figura 7: superficie di frattura di un tc 110,8 mm. a http://www.gruppofrattura.it http://dx.medra.org/10.3221/igf-esis.09.15&auth=true s. beretta et alii, frattura ed integrità strutturale, 9 (2009) 145152; doi: 10.3221/igf-esis.09.15 149 interpretazione dei risultati sulla base degli sforzi locali giunti sono stati analizzati con il metodo degli elementi finiti, con lo scopo di determinare la distribuzione degli sforzi all’interno dello strato di adesivo. per fare ciò, sono stati adottati modelli 2d in stato di deformazione piana, utilizzando per la modellazione dello strato di adesivo elementi quadratici a 8 nodi di altezza pari a 0,05 mm, così da distribuire quattro elementi nello spessore dello strato di adesivo. gli aderendi sono stati modellati rispettando la legge di laminazione, assegnando cioè le costanti elastiche delle rispettive lamine alle partizioni del modello operate per rappresentare fedelmente la sovrapposizione dei diversi strati. sono state condotte analisi elastiche lineari, adottando per lo strato di adesivo una legge elastica lineare, con i valori di modulo elastico e coefficiente di poisson ricavati dalle prove di caratterizzazione sull’adesivo colato in massa. le costanti elastiche delle lamine sono state assegnate sulla base dei risultati di prove di caratterizzazione meccanica eseguite presso i laboratori del dipartimento di meccanica del politecnico di milano, utilizzando una macchina di prova elettromeccanica mts rf 150. i valori degli sforzi tangenziali paralleli al piano dell’adesivo, degli sforzi perpendicolari allo stesso piano, dello sforzo tangenziale massimo, misurato attraverso la definizione di sforzo equivalente secondo tresca e dello sforzo principale massimo, sono stati letti sul piano medio dell'adesivo in corrispondenza del nodo maggiormente sollecitato. figura 8: diagramma numero di cicli a rottura sforzo massimo di taglio parallelo allo strato di adesivo (a) e numero di cicli a rottura – sforzo massimo di tresca (b), calcolati con modelli 2d agli elementi finiti. figura 9: diagrammi numero di cicli a rottura sforzo massimo normale perpendicolare allo strato di adesivo (a) e numero di cicli a rotturasforzo principale massimo (b), calcolati con modelli 2d agli elementi finiti. i http://www.gruppofrattura.it http://dx.medra.org/10.3221/igf-esis.09.15&auth=true s. beretta et alii, frattura ed integrità strutturale, 9 (2009) 145152; doi: 10.3221/igf-esis.09.15 150 i punti sperimentali sono stati quindi riportati nei grafici delle fig. 8 e 9, dove i numeri di cicli a rottura sono stati riportati in funzione rispettivamente dello sforzo massimo di taglio, dello sforzo massimo normale, dello sforzo massimo di tresca e dello sforzo principale massimo. tutte le grandezze sono state normalizzate dividendo per il valore relativo ai provini di tipo ls 25.4 mm, per una durata media di 100.000 cicli. come si può osservare in fig. 8a, la correlazione tra numero di cicli e sforzo massimo di taglio è migliore di quella esistente tra cicli e sforzo massimo normale (fig. 9a), sebbene in quest'ultimo caso la maggior parte della dispersione sia da attribuire al giunto acciaio-composito, in cui si è osservato come la fattura sia propagata essenzialmente all’interfaccia tra acciaio e adesivo (fig. 5). il ruolo degli sforzi normali, già proposto come parametro di verifica in [7], sembra tuttavia essere meglio interpretato se si valuta la loro combinazione con gli sforzi tangenziali, attraverso la misura di tresca. in questo caso, come è possibile osservare nel grafico di fig. 9b, si ottiene un’ulteriore riduzione della dispersione rispetto all’adozione della sola componente di taglio. ciò sembrerebbe suggerire l’adozione di questo parametro come criterio di verifica valido per tutti i tipi di giunzione (invece, analogamente a quanto osservato per lo sforzo normale, anche lo sforzo principale massimo – fig. 9b – presenta una correlazione più bassa con il numero di cicli). tuttavia è necessario sottolineare come questo modello, sebbene consenta un’ottima correlazione con i dati sperimentali, non tenga in nessun conto l’effettivo meccanismo di evoluzione del danno di fatica, che è caratterizzato da un ruolo predominante delle fase di propagazione, come mostrato di seguito. analisi delle fasi di nucleazione e di propagazione er meglio comprendere il ruolo della fase di nucleazione e le modalità di propagazione, alcuni provini (in più rispetto a quelli di cui sono riportati i risultati in fig. 3) sono stati monitorati durante la prova di fatica mediante osservazione al microscopio ottico dello strato di adesivo affiorante sul fianco del provino. le osservazioni sono state fatte ad intervalli regolari, sospendendo la prova e ponendo il giunto in tensione ad un carico uguale al carico massimo nel ciclo per il tempo strettamente necessario per l’acquisizione dell’immagine. in fig. 10 sono riportate le osservazioni dell’evoluzione del danneggiamento di un giunto ls 25,4 mm. la prova è durata complessivamente 17200 cicli e si è interrotta per la completa separazione dei lembi del giunto. come si può osservare dalla figura, la frattura è nucleata già a soli 500 cicli, rappresentata da una delaminazione all’interno del primo strato di tessuto sottostante l’adesivo, osservabile in corrispondenza dell’inizio della sovrapposizione degli aderendi. questa frattura è poi propagata nella lamina e tra 12500 e 16000 cicli la frattura ha deviato al’interno dello strato di adesivo fino a quando è intervenuto il cedimento, avvenuto in corrispondenza di un avanzamento della frattura di circa 7 mm. figura 10: osservazioni dell’evoluzione del danneggiamento di un giunto da ls 25,4 mm (durata della prova: 17200 cicli). p http://www.gruppofrattura.it http://dx.medra.org/10.3221/igf-esis.09.15&auth=true s. beretta et alii, frattura ed integrità strutturale, 9 (2009) 145152; doi: 10.3221/igf-esis.09.15 151 figura 11: osservazioni dell’evoluzione del danneggiamento di un giunto da tc 110.8 mm (durata della prova: 18700 cicli). figura 12: osservazioni dell’evoluzione del danneggiamento di un giunto da tc 110.8 mm (durata della prova: 140500 cicli). nel caso invece di un giunto tc 110.8 mm, come è possibile osservare in fig. 11, la fase di nucleazione è iniziata a circa 3000 cicli (su una durata complessiva della prova di 18700 cicli), con lo sviluppo di una frattura all’interno dello strato di adesivo, visibile in corrispondenza del termine della sovrapposizione rastremata. fino a 9000 cicli la propagazione è avvenuta all’interno dello strato di adesivo, per poi interessare la lamina sottostante, con un successivo percorso di avanzamento della frattura caratterizzato da numerosi cambi di direzione, presumibilmente attribuibili alla struttura non omogenea della lamina di tessuto. il cedimento finale è avvenuto dopo un avanzamento della frattura di più di 50 mm dall’estremo della sovrapposizione. nel caso infine di una prova condotta ancora su un giunto da 110 mm di sovrapposizione rastremato, ma ad un livello di forza massima inferiore, tale da determinare una durata di 140500 cicli, si è osservata una nucleazione per de laminazione in corrispondenza dell’inizio della sovrapposizione, nell’aderendo superiore (fig. 12). a 75000 cicli il percorso della frattura ha deviato nell’interfaccia tra l’aderendo inferiore e l’adesivo, accompagnato da una contemporanea delaminazione nell’aderendo inferiore, come si può vedere dall’immagine ripresa a 100000 cicli. la propagazione ha successivamente http://www.gruppofrattura.it http://dx.medra.org/10.3221/igf-esis.09.15&auth=true s. beretta et alii, frattura ed integrità strutturale, 9 (2009) 145152; doi: 10.3221/igf-esis.09.15 152 interessato la lamina di unidirezionale sottostante il primo strato di tessuto, raggiungendo un’estensione di più di 80 mm (di cui 40 mm percorsi negli ultimi 20000 cicli). tipo di giunto ntot ni ni / ntot ls 25.4 mm 17200 500 0.03 tc 110.8 mm 18700 3000 0.16 tc 110.8 mm 140500 25000 0.18 tabella 2: valori della frazione di vita ni/ntot spesa nella fase di nucleazione. mentre nel caso di giunti ad elevata lunghezza di sovrapposizione la fase di propagazione risulta sempre evidente anche ad occhio nudo in virtù degli elevati valori di apertura dei lembi della frattura, a sua volta effetto delle elevate lunghezze di propagazione, per individuare questo fenomeno nei giunti da 25,4 mm di sovrapposizione è stata necessaria l’osservazione al microscopio. sebbene non siano state monitorate tutte le prove, sulla base di queste osservazioni è ragionevole concludere che l’effettivo meccanismo di evoluzione del danno di fatica sia caratterizzato da un ruolo predominante delle fase di propagazione, come riassunto in tabella 2, in cui viene riportato per ciascun provino la frazione ni/ntot , dove rispetto al numero di cicli totale ntot, ni corrisponde al momento in cui è stata rilevata la nucleazione della frattura. i valori riportati confermano il ruolo predominante della fase di propagazione e risultano mediamente più bassi rispetto ai valori riportati in [8], ricavati da una base molto più ampia di osservazioni, ma che si riferiscano a laminati più sottili (spessore 1,6 mm contro i 9,9 mm dei giunti oggetto di questo lavoro). conclusioni ’analisi numerica mediante modelli agli elementi finiti di giunzioni incollate di aderendi realizzati in materiale composito di elevato spessore ha permesso di definire lo sforzo equivalente di tresca quale parametro utile alla previsione del comportamento a fatica in termini di numero di cicli totale. il valore dello sforzo equivalente è stato ricavato da modelli 2d e fa riferimento alla sollecitazione massima registrata in corrispondenza del piano medio dell’adesivo. l’adozione di questo parametro ha permesso di ottenere una buona correlazione con il numero di cicli a rottura, indipendentemente dalla forma del giunto, dalla lunghezza di sovrapposizione e del tipo di aderendi (limitatamente all’alternativa tra acciaio e un particolare laminato, mentre non sono state prese in considerazione leggi di laminazione differenti da quella testata). questi risultati sembrano suggerire che uno sforzo equivalente locale possa essere proposto come strumento di uso ingegneristico per la verifica di giunzioni incollate di materiali compositi. tuttavia, alla luce di alcune osservazioni del comportamento locale delle giunzioni durante le prove di fatica, è stato evidenziato un ruolo predominante della fase di propagazione, che avviene sia nello strato di adesivo sia per cedimento intere intra-laminare. l’attività di ricerca futura si orienterà pertanto nella direzione di caratterizzare il comportamento a frattura del sistema composito/adesivo e di sviluppare modelli adeguati alla previsione della fase di propagazione in giunti incollati di materiale composito di elevato spessore. bibliografia [1] w.c. de goeij, m.j.l. van tooren, a. beukers, materials and design, 20 (1999) 213. [2] a.d. crocombe, g.richardson, int. j. of adhesion and adhesives, 19 (1999) 19. [3] l. goglio, m. rossetto, e. dragoni, int. j. of adhesion & adhesives, 28 (2008) 427. [4] m. dessureault, j. k. spelt, int. j. of adhesion and adhesives, 17 (1997) 183. [5] m. quaresimin, m. ricotta, int. j. of fatigue, 28 (2006) 1166. [6] h. hadavinia, a. j. kinloch, m.s.g. little, a.c. taylor, int. j. of adhesion and adhesives, 23 (2003) 449. [7] m. imanaka, h. nakayama, k. morikawa, m. nakamura, composite structures, 31 (1995) 235. [8] m. quaresimin, m. ricotta, composites science and technology, 66 (2006) 176. l http://www.gruppofrattura.it http://dx.medra.org/10.3221/igf-esis.09.15&auth=true microsoft word numero_37_art_41 u. muhin et alii, frattura ed integrità strutturale, 37 (2016) 312-317; doi: 10.3221/igf-esis.37.41 312 focused on fracture mechanics in central and east europe application of betweenstand cooling in the production hot – rolled strips u. muhin, s. belskij, e.makarov lipetsk state technical university, lipetsk, russia nemistade@mail.ru t. koynov university of chemical technology and metallurgy, sofia, bulgaria toni309@koinov.com abstract. medium grain size has been uneven over the length of hot-rolled strips of austenite of low-carbon steel during rolling on continuous mill. assess the possibilities of metal microstructure of hot-rolled strip stabilization system between-stand refrigeration line. rolling low carbon strips developed modes with increasing temperature end rolling along the length of the strips and rolling modes using between-stand cooling with variable flow cooling water. using this technology mode allows you to get a uniform cooling microstructure of metal strips and cut to length machine time rolling on 14 – 18%. treatment with an increased acceleration stabilizes the metal microstructure on rolling strips on top of the thread speed and reduces the machine time rolling on 3-9%. keywords. hot rolling mills; between-stand cooling; microstructure; increased cooling acceleration; mathematical modeling. introduction he most important indicators of the effectiveness of continuous strip hot rolling mills include performance and mechanical properties of the rolled strip. the use of cooling systems rolled strips, which include cooling between stands of finishing group and accelerated cooling in run-out roller table, to control capacity of the mill, and mechanical properties of hot rolled strips. on the process of softening metal affect the extent and rate of deformation, temperature, chemical composition of the steel, grain size, time [1]. to ensure a uniform microstructure of the metal leaving the finishing group, the entire length of the strip should maintained the above parameters constant. when hot strip mill generally accepted strategy for maintaining the temperature of the end of the strip rolling along at a constant level. this consistency provides accelerated finishing train, but there is heterogeneity of the microstructure of the metal from the front to the rear end of the band [2]. one way to stabilize the temperature and the speed limit, and therefore the microstructure and mechanical properties of the metal, is the application of installation coil box, which requires significant capital investment and reduces the productivity of the mill. t u. muhin et alii, frattura ed integrità strutturale, 37 (2016) 312-317; doi: 10.3221/igf-esis.37.41 313 another way to stabilize the microstructure is the temperature increase by the end of the rolling length of the strip, which compensates for the temperature drop at the entrance to a peal finishing train. temperature increase can be achieved by the end of rolling two ways that do not require additional capital expenditures: 1) using a rolling with between stands cooling mode for variable-speed distribution of cooling water; 2) rolling with an increased acceleration of finishing group. between stands cooling mode with variable flow rates is to reduce the supply of water along the rolled strip. this mode eliminates the rolling acceleration, thereby virtually eliminating the negative effects arising from its use. mode with high acceleration to stabilize the microstructure of the metal and reduce the computing time in the production of rolled strips, which increases the rolling speed cannot be applied because of the technical features of the mill. application of the cooling capacity is limited only by the installation of accelerated cooling strip on the run-out roller conveyor and power parameters of the rolling process in the strips production. technique to study the thermal and structural states of the metal tudy of the thermal and structural states of the metal was carried out using mathematical modeling for the conditions of continuous broadband hot rolling mill 2000 “nlmk”, russia. the mill includes 5 methodical furnaces, roughing group of stands, intermediate roller table with installing thermal screening lag, 7 stands finishing group, run-out roller table with installation of fast cooling strip and coiler area. the finishing group is equipped with a system of cooling the strip which can significantly increase its throughput. the maximum flow rate of cooling water in the cooling system is 1200 m3/h. calculation of the temperature strip mill line was carried out using the developed mathematical model of the thermal state of the metal from the issuance of a peal of roughing stands to strip winding into a roll. a mathematical model based on the solution of one-dimensional transient heat conduction eq. (1) finite difference method.          2 2 ( ) ( ) ( ) v t t t c t t q x (1) where: ρ is the density of the metal, kg/m3; c specific heat capacity of the metal j/(kg.k); λ thermal conductivity of the metal, w/(m.k); t temperature of the metal, k; τ – time, s; x coordinate of the strip thickness, m; qv power density heat sources, w/m3. mathematical model takes into account the effect of the screening device of roll, cooling strip in finishing group, heat generation due to plastic deformation of the metal, and polymorphic γ → α transformation of super-cooled austenite on the thermal state of the metal [3,4]. the model also accounts for the effect of the phase state and chemical composition of the steel on the physical properties of the metal. a mathematical model of the thermal state of the metal was adapted to the conditions of the mill 2000. share lanes with an error calculating the metal temperature over 20°c was less than 2 %. the calculation of the microstructure of the metal in the rolling mill finishing train carried by mathematical models recrystallized austenite low carbon steel grades set out in [4-8]. the calculation of the microstructure in finishing train was limited to the determination of the recrystallized volume fraction and the average grain size of austenite along the strip. hot strip rolling with using the between stands cooling influence of the cooling for formation of cooling metal microstructure nvestigation of the effect of cooling in finishing group on the structural state of the metal made in modeling for the strip 3x1250 mm of steel grade 08u of the mill in 2000 for four modes is shown in tab. 3. the chemical composition of the steel is shown in tab. 1. the deformation mode in finishing group is shown in tab. 2. s i u. muhin et alii, frattura ed integrità strutturale, 37 (2016) 312-317; doi: 10.3221/igf-esis.37.41 314 temperature-speed (t-s) mode and the water flow through the between stands cooling section for test modes are presented in tab. 3. al cu mn n p s si 0.045 0.037 0.186 0.003 0.008 0.10 0.015 table 1: chemical composition of steel 08u (%). in tabs. 2 and 3: hp, hsp, h6 -h12 – metal thickness after: roughing group; descaler; stands of finishing group, acc.; tp and tf – metal temperature before and after finishing group, acc.; vs and a thred speed and acceleration in finishing group, acc.; q1 – q6 – finishing stands gaps acc. hp hsp h6 h7 h8 h9 h10 h11 h12 thichness,mm 34.7 34.0 20.3 12.5 8.4 5.89 4.45 3.45 3.00 relative reduction, % 9 0.3 8.5 32.8 29.9 24.4 25.5 13.1 table 2: the deformation mode in finishing group rolling for strip 3x1250 mm, steel 08u. № of regime rolling parameters water slow, m3/h tр, tf vs, a τm, q1, q2, q3, q4, q5, q6, °c °c m/s m/s2 s m3/h m3/h m3/h m3/h m3/h m3/h 1 1000 840 8.97 0.026 87.4 0 0 0 0 0 0 2 1000 840 11.95 0.026 68.8 200 200 200 200 200 200 3 1000 840 10.25 0.026 78.4 200 200 200 0 0 0 4 1000 840 10.25 0.026 78.4 0 0 0 40 200 200 table 3: technological parameters of studied rolling regimes with between stand cooling. length of hot-rolled strip is 884 m. the research results are presented in fig. 1. according to the study, the primary recrystallization process time to get fully only in the first three gaps [9] on all four modes (fig. 1.a). recent the between standing cooling does not have time for fully recrystallizing of austenite grain and growth is difficult (fig. 1.b). the share of the recrystallized volume and average grain size of austenite. fig. 1 shows the entry point for the front end of the strip in the deformation and at the end of the pyrometer for the temperature of the end of rolling. application cooling (regime 3) reduces the average grain size of austenite at the exit of the stands and thus improve the mechanical properties of the metal. in regime 2 on the average grain size in the central layers of the band decreases from 18.1 to 16.9 mcm for the front end (fig.1c) and from 15.9 mcm to 15.3 for the rear end (fig.1.d) than with number 1. reducing the size of the austenite grain from the front to the rear end of the strip associated with the use of acceleration in the finishing train (breaks are reduced in the process of rolling) and a constant temperature by the end of the rolling length of the bar in the presence of a temperature “wedge” at the entrance to the finishing group. application cooling mode at number 3 lowers the temperature of the metal in the last gap, which leads to a decrease in the average grain size at the exit of the mill. as opposed to the regime number 3, in the last three cooling intervals (mode number 4) gives the average grain size of austenite grain size is close to rolling without cooling (mode number 1) at the same speed mode. u. muhin et alii, frattura ed integrità strutturale, 37 (2016) 312-317; doi: 10.3221/igf-esis.37.41 315 thus, the cooling section should be included, since the last finishing stand. by increasing the thickness of the final sections of the rolled strip inclusion cooling should be transferred to the latter gap to the first, to minimize the heterogeneity of the austenite grain on the strip thickness and suppress the recrystallization process during long pauses. figure 1: comparison of the structural state of rolled strips using between standing cooling. development of hot strip rolling regimes according to studies by rolling strips 3x1250 mm of steel 08u constant finishing temperature tf = 840°c, the temperature after roughing stands tr = 1000°c, thred speed vth = 9 m/s and acceleration a = 0.026 m/s2 decrease in the average grain size of austenite along a strip in finishing train was 2.3 microns. change the size of the austenite grain along the strip leads to uneven metal microstructure after winding into a roll. according to the hall-petch equation decrease in grain size increases the yield strength and ultimate strength along the length of finished hot-rolled strips. in order to stabilize the microstructure of the metal strip along the rolling schedule is calculated using betweenstand cooling with variable flow of cooling water. stabilization of the microstructure of the metal can reach the end of rolling temperature increase of 7°c during rolling acceleration without finishing group and with a rolling speed ve = 11.2 m/s. the drop in temperature at the inlet to peal finishing in the rolling process is compensated by the change of the total water flow in the cooling system betweenstand band from 840 m3/h to 0. water flow in the system qmko changes synchronously to each gap. comparison of existing and design modes hot rolling is shown in fig. 2. rolling without acceleration in the finishing train almost completely stabilize the cooling conditions of the band on the run-mill roller table. temperature increase by the end of the rolling length of the bar and the stabilization conditions of accelerated cooling can solve the problem of a uniform microstructure of metal for a significant proportion of the bands mix mill 2000. application between stand cooling of size bands and temperature regimes rolling limited to a maximum filling rate band, which for the mill 2000 is 12.5 m/s. this level is the maximum speed of a gas due to the necessity of accident-free transportation of the front end of the strip to a discharge roller conveyor mill due to the aerodynamic effect. stabilization of microstructure metal along bands which use rolling betweenstand cooling impossible can be achieved with high values of acceleration of finishing group. the task of rolling mode destination, depending on the thickness of the strip and the required temperature level to the end of the rolling mill 2000 mix resolved on the basis of the developed mathematical model of the thermal state of the metal. u. muhin et alii, frattura ed integrità strutturale, 37 (2016) 312-317; doi: 10.3221/igf-esis.37.41 316 figure 2: calculated parameters of hot rolling and accelerated cooling. strip 3x1250 mm of steel 08u (tr = 1000°c, vth = 9 m/s, a = 0,026 m/s, tf = constant (840°c), cooling temperature (tc) + 640°c, qmko = 0; tr = 1000°c, vth = 11,2 m/s, a = 0, tf = constant, qmko = constant, tc = 640°c; in fig. 2a, water slow in fig. 2b, m3/h; fig. 2c – average grain size after finishing group, mcm, in fig. 2c and number of cooling units in fig. 2d). rolling without acceleration in the finishing train almost completely stabilize the cooling conditions of the band on the run-mill roller table. temperature increase by the end of the rolling length of the bar and the stabilization conditions of accelerated cooling can solve the problem of a uniform microstructure of metal for a significant proportion of the bands mix mill 2000. application betweenstand cooling of size bands and temperature regimes rolling limited to a maximum filling rate band, which for the mill 2000 is 12.5 m/s. this level is the maximum speed of a gas due to the necessity of accident-free transportation of the front end of the strip to a discharge roller conveyor mill due to the aerodynamic effect stabilization of metal structure along the strips which use rolling of between stand cooling impossible can be achieved with high values of acceleration of finishing group. the task of rolling mode destination, depending on the thickness of the strip and the required temperature level to the end of the rolling mill 2000 mix resolved on the basis of the developed mathematical model of the thermal state of the metal. calculation results are presented in fig. 3. figure 3: assignment mode rolling strips in finishing group: a) tr = 1000°c; b) tr = 1030°c. (a unreachable area, b rolling with hither acceleration, c rolling with qmko = var). u. muhin et alii, frattura ed integrità strutturale, 37 (2016) 312-317; doi: 10.3221/igf-esis.37.41 317 in the rolling low carbon the strips thickness regime using cooling with variable flow water temperature increment of the end for rolling thin strips was 7-8°c and for thick strips thicker than 4.2 mm 16-18°c. machine time rolling of strip thickness over 2,7 mm decreased by 14-18 % compared to the rolling on the regime without cooling. in the rolling strips of low carbon steel on the regime with an increased acceleration without screening peal at the intermediate roller table stabilizing metal microstructure at the exit of finishing train can reach the end of rolling temperature increment equal 13-17°c, with rolling of strip thickness less 2,5 mm using a screening of roll increment is 610°c. rolling schedule with high acceleration can reduce the rolling machine time by 3-9 %, depending on the thickness of the strip. conclusions regime of hot-rolled strips of low-carbon steel with increasing temperature for the conditions of the end of rolling continuous wide 2000 hot rolling mill “nlmk” is developed that improve the performance of the mill and stabilize the microstructure of the metal along the hot-rolled strip, in contrast to the existing regimes. stabilization of the microstructure is achieved by increasing the temperature tf at 6-10°c when rolling of strip thickness less 2.5 mm, and at 13-18°c wen rolling of strip thickness over 2.5 mm. the rolling of strip using between stands cooling with variable water flow leads to reduction of the rolling machine time by 14-18 %, according to the regime with an increased acceleration by 3 9 %. references [1] humphreys, f.j., hatherly, m., recrystallization and related annealing phenomena, oxford, elsevier ltd, (2004). [2] kotsar, s.l., abelyansky, d., mukhin, u., plate rolling technology, moscow, metallurgy, (1997), (in russian). [3] koinov, t., gurov, a., shatalov, r., software tools 50870000614. economic-mathematical model of continuous hot striprolling, programs and algorithms, inf. bull., 11 (1987), moscow, (in russian). [4] koinow, т., yordanova, р., mathematical modelling of production and operation exploit of steel products”, 5th congress of metallurgists of makedonia, ohrid, (2008). [5] siciliano, f. jr., minami, k., maccagno,t.m., jonas, j.j., mathematical modeling of the mean flow stress, fractional softening and grain size during the hot strip rolling of c-mn steels, isij international, 36(12) (1996) 1500-1506. [6] beynon, j.h.,. sellars, c.m., modelling microstructure and its effects during multipass hot rolling, isij international, 32(3) (1992) 359-367. [7] senuma, t., yada, h., matsumura, y., futamura, t., structure of austenite of carbon steels in high speed hot working processes, tetsu-to-hagané, 70(15) (1984) 2112-2119. [8] maccagno, t.m., jonas, j.j., hodgson, p.d., spreadsheet modelling of grain size evolution during rod rolling, isij international, 36(6) (1996) 720-728. [9] koinov, t., angelova, d., shatalov, r., theoretical and experimental studies of the formation of metal structure in continuous finishing train, collection of proceedings of the international conference “theory and practice of producing sheet metal”, lipetsk, part i (2005) 195 200. 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can be opened with acrobat and adobe reader 5.0 and later.) >> /namespace [ (adobe) (common) (1.0) ] /othernamespaces [ << /asreaderspreads false /cropimagestoframes true /errorcontrol /warnandcontinue /flattenerignorespreadoverrides false /includeguidesgrids false /includenonprinting false /includeslug false /namespace [ (adobe) (indesign) (4.0) ] /omitplacedbitmaps false /omitplacedeps false /omitplacedpdf false /simulateoverprint /legacy >> << /addbleedmarks false /addcolorbars false /addcropmarks false /addpageinfo false /addregmarks false /convertcolors /converttocmyk /destinationprofilename () /destinationprofileselector /documentcmyk /downsample16bitimages true /flattenerpreset << /presetselector /mediumresolution >> /formelements false /generatestructure false /includebookmarks false /includehyperlinks false /includeinteractive false /includelayers false /includeprofiles false /multimediahandling /useobjectsettings /namespace [ (adobe) (creativesuite) (2.0) ] /pdfxoutputintentprofileselector /documentcmyk /preserveediting true /untaggedcmykhandling /leaveuntagged /untaggedrgbhandling /usedocumentprofile /usedocumentbleed false >> ] >> setdistillerparams << /hwresolution [2400 2400] /pagesize [612.000 792.000] >> setpagedevice microsoft word numero_38_art_24 a. niesłony, frattura ed integrità strutturale, 38 (2016) 177-183; doi: 10.3221/igf-esis.38.24 177 focussed on multiaxial fatigue and fracture a critical analysis of the mises stress criterion used in frequency domain fatigue life prediction adam niesłony opole university of technology, poland a.nieslony@po.opole.pl, http://orcid.org/0000-0002-1218-8341 abstract. multiaxial fatigue failure criteria are formulated in time and frequency domain. the number of frequency domain criteria is rather small and the most popular one is the equivalent von mises stress criterion. this criterion was elaborated by preumont and piefort on the basis of well-known von mises stress concept, first proposed by huber in 1907, and well accepted by the scientific community and engineers. it is important to know, that the criterion was developed to determine the yield stress and material effort under static load. therefore the direct use of equivalent von mises stress criterion for fatigue life prediction can lead to some incorrectness of theoretical and practical nature. in the present study four aspects were discussed: influence of the value of fatigue strength of tension and torsion, lack of parallelism of the sn curves, abnormal behaviour of the criterion under biaxial tensioncompression and influence of phase shift between particular stress state components. information contained in this article will help to prevent improper use of this criterion and contributes to its better understanding. keywords. mises stress; frequency domain; multiaxial fatigue. citation: niesłony, a., a critical analysis of the mises stress criterion used in frequency domain fatigue life prediction, frattura ed integrità strutturale, 38 (2016) 177-183. received: 05.05.2016 accepted: 10.06.2016 published: 01.10.2016 copyright: © 2016 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. introduction ultiaxial fatigue life criteria are used during fatigue life prediction to compute equivalent uniaxial strain or stress state. this procedure is essential for the calculation of final fatigue life based on uniaxial fatigue characteristics. there are many propositions of multiaxial fatigue failure criteria in the literature based on stress invariants, critical plane concept, integral criteria and other [1–3]. most of them are defined in time domain and implemented for working on stress or strain time histories or on sets of amplitudes. there are only few propositions dedicated for frequency based fatigue life assessment were the frequency domain definition of the criterion is expected [4, 5]. one of them is the criterion of equivalent von mises stress (ems), which is nowadays more and more popular and well accepted by engineers [6]. in this paper advantages and possible risks of usage of this criterion are taken under discussion. particular four aspects were presented in details which are causing significant effect on computed fatigue life:  differences between fraction of fatigue strength of pure tension and torsion and the value of square root of 3,  lack of parallelism of the s-n curves for pure tension and torsion, m a. niesłony, frattura ed integrità strutturale, 38 (2016) 177-183; doi: 10.3221/igf-esis.38.24 178  abnormal behaviour of the criterion under biaxial tension-compression loading condition in comparison to the experimental results presented in the literature,  influence of phase shift between particular stress state components on the value of equivalent stress. the aim of this paper is the clear presentation of the theoretical limitation and the area of practical application of the ems criterion. examples based on technical experiments are recalled which confirms the correctness of discussed limitations. provided information are highly important for engineers which are using equivalent von mises stress in frequency domain as well as for researchers who are working on new multiaxial fatigue failure criteria where von mises stress is using as a part of the definition. equivalent von mises stress criterion in frequency domain he main reason for creating of this document are increasingly frequent, uncritical application of the equivalent von mises stress (ems) criterion in engineering calculations in the field of fatigue assessment. since m.t. huber in 1904 [7] and r. von mises in 1913 [8] publish the theoretical background of the possibility of measurement of material effort by specific work of strain ems criterion has become the most widely used in industry and science, among others in determining equivalent uniaxial stress, yield strength limit or other parameters used for example in constitutive equations [9]. without going into details about derivation, which are well presented in many publications, the final equation for equivalent stress ems criterion can be written as follow:        ems xx yy yy zz zz xx xy yz zx 2 2 2 2 2 21 6 2                      (1) or        ems xx xx xx xx xx yy zz zz xx xy yz zx 2 2 2 2 2 2 23 3 3                     (2) using proper components of the stress tensor: xx xy xz yx yy yz zx zy zz                     σ (3) in 1994 preumont and piefort [10] represent a breakthrough adapt of the von mises criterion for determining the material fatigue directly in frequency domain. they propose to calculate of the power spectral density of equivalent von mises stress directly in frequency domain as follow  ems mg f f( ) trace ( ) q g (4) however in the referenced paper [10] plane stress state was analysed presented method is well applicable also in spatial stress state with following power spectral density matrix:           xx xx xx yz yz xx yz yz g f g f f g f g f , , , ,            g      (5) defined according to vector of stress tensor components xx yy zz xy yz zx[ ]     s (6) and with von mises coefficient matrix [11] t a. niesłony, frattura ed integrità strutturale, 38 (2016) 177-183; doi: 10.3221/igf-esis.38.24 179 m 1 0.5 0.5 0 0 0 0.5 1 0.5 0 0 0 0.5 0.5 1 0 0 0 0 0 0 3 0 0 0 0 0 0 3 0 0 0 0 0 0 3                       q (7) after solving eq. (4) using (5) and (7) following expression for psd of ems can be written       ems xx xx yy yy zz zz xy xy yz yz zx zx xx yy yy zz zz xx g f g f g f g f g f g f g f g f g f g f , , , , , , , , , ( ) ( ) ( ) ( ) 3 ( ) 3 ( ) 3 ( ) re ( ) re ( ) re ( )           (8) psd of equivalent von mises stress in the form of eq. (8) can be useful while programing this criterion in low level programing languages where matrix operation (4) cannot be easily realised. limitations on the use of ems criterion in the fatigue calculation fraction of fatigue strengths of tension and torsion let us set the loading of an abstract structure and the reference axes in such a way as to obtain only one a non-zero shear stress component tor xy. [ 0 0 0 0 0 ]s (9) in practice this can be a stress state observed at surface of round specimen under pure torsion. in such a case psd matrix will possess only one nonzero component – the component gxy,xy( f ). according to the eq. (8) equivalent psd function of stress reduce to the following form ems xy xyg f g f,( ) 3 ( ) (10) generally speaking psd function of stress describes how power of a stress history is distributed over frequency. ‘the power’ should be understood as the variance of the stress history, what can be expressed as follow g f df 0 ( )    (11) where  is the variance of the stress history. also, it is possible to calculate the expected signal amplitude for a specified small frequency range of a width of f fr f a fr g f df2 2 ( )       (12) analysing the eq. (10) it can be seen that according to the von mises stress criterion for computing psd of equivalent uniaxial stress is to multiply psd for pure torsion times 3. transforming this action to the stress amplitude following the relationship presented in eq. (12) we get the equation: a. niesłony, frattura ed integrità strutturale, 38 (2016) 177-183; doi: 10.3221/igf-esis.38.24 180 af af af af 3 3 1.7321         (13) what is also valid for basic von mises criterion in time domain, eqs. (1) and (2). according to numerous reported experimental results such an equality is fulfilled only for few materials. usually the ratio (13) varies between 1 and 2 for fatigue strength and fatigue limit as well. it is important to know how much influence have a deviation from the specified square root of three value (13) on calculated fatigue life. in order to present the scale of the problem fatigue life was calculated for round specimen under random, narrow-banded and gaussian, pure torsion loading. in such a kind of loading the probability density function (pdf) of amplitudes describe rayleigh distribution [12]. on the fig. 1a) pdf for shear stress amplitudes and equivalent tension amplitudes according ems criterion were presented. it was also assumed that the miner rule is applicable and constant amplitude sn curves for pure torsion and tension are known and described as follow m m a f a f n n s t n n 1 1 ,                      (14) where: sf and tf – fatigue limits for tension and torsion; n and n – number of cycles for knee points; m and m – slopes of the sn curves. on the fig. 1b) two sn curve are presented which satisfy the sf / tf = 1.7321 condition, eq. (13). computed fatigue life t1 according pdf of shear stress amplitudes and sn curve for torsion are equal to t2 computed from pdf of equivalent tension amplitudes and sn curve for tension. for materials that do not meet the condition (13) computed fatigue life t1 and t2 differ significantly. such a case is presented on fig. 1c) for sf / tf = 1.5 what results in t1 / t2 = 3.16. lack of parallelism of the sn curves lack of parallelism is a special situation of the problem discussed in previous section. in this case the equality (13) cannot be fulfilled in whole range of cycles to failure. depends on the m and m slopes of sn curves different deviation from t1 / t2 = 1 can be obtained. this effect was illustrated in figs. 1d) 1e) 1f) where computed results obtained with the same procedure as described in previous section were presented. abnormal behaviour of the ems criterion under biaxial tension-compression biaxial tension-compression is a plane stress state where for specific reference axes only the shear component is constant and equal zero bi xx yy. [ 0 0 0 0 ] s (15) pure biaxial tension-compression is rarely found in practice but it is used for verification of multiaxial fatigue failure criteria. such kind of stress state is released on so called cruciform specimens through loading of two sets of arms in perpendicular direction [13]. this two loading components can be of any type, for example in-phase, out-of-phase or random with given correlation coefficient. in biaxial tension-compression the psd of equivalent stress can be computed as follow (16) real part of cross spectral density re[gxx,yy(f)] is equal 0 for fully uncorrelated loading components xx(t) and yy(t). there are some interesting results published in the literature which are showing basic biaxial fatigue behaviours of tested materials. cláudio et al. [13] presenting results from which it appears that the ems criterion does not fit the real behaviour of material. this can be observed on the fig. 2 where ems criterion for correlated data gives lower stress amplitudes and for out-ofphase loading higher stress amplitudes than expected. ems xx xx yy yy xx yyg f g f g f g f, , ,( ) ( ) ( ) re[ ( )]   a. niesłony, frattura ed integrità strutturale, 38 (2016) 177-183; doi: 10.3221/igf-esis.38.24 181 a) b) c) d) e) f) figure 1: pdf of amplitudes used for computation of fatigue life t1 and t2 (a) and five sets of sn curves for torsion and uniaxial tension (b), (c), (d), (e), and (f). influence of phase shift between particular stress state components it is well known under fatigue community that the phase shift between particular components of the multiaxial loading are influencing the fatigue life. a special interest among scientists and researchers has a combination of tension-compression or bending and torsion, as it is commonly encountered in a responsible machine elements such as shafts. many test results have been published in this area. all of them show a significant effect of the phase shift fatigue. analysed criterion does not have such properties. under a combination of tension and torsion (17) 0 100 200 300 400 500 600 700 800 0 1 2 3 4 5 6 7 x 10 −3 σ a , τ a , mpa p σ a (σ a ), p τ a (τ a ), m p a − 1 p σa (σ a ) pτa (τa) 10 2 10 4 10 6 10 8 10 2 10 3 n, cycles σ a , τ a , m p a t1 t2 = 1.0 tension: s f = √ 3 · 200; m = 8; n0 = 2 · 106 torsion: t f = 200; m = 8; n0 = 2 · 106 10 2 10 4 10 6 10 8 10 2 10 3 n, cycles σ a , τ a , m p a t1 t2 = 3.16 tension: sf = 300; m = 8; n0 = 2 · 106 torsion: t f = 200; m = 8; n0 = 2 · 106 10 2 10 4 10 6 10 8 10 2 10 3 n, cycles σ a , τ a , m p a t1 t2 = 0.133 tension: s f = √ 3 · 200; m = 8; n0 = 2 · 106 torsion: t f = 200; m = 12; n0 = 2 · 106 10 2 10 4 10 6 10 8 10 2 10 3 n, cycles σ a , τ a , m p a t1 t2 = 0.421 tension: sf = 300; m = 8; n0 = 2 · 106 torsion: t f = 200; m = 12; n0 = 2 · 106 10 2 10 4 10 6 10 8 10 2 10 3 n, cycles σ a , τ a , m p a t1 t2 = 0.0422 tension: sf = 400; m = 8; n0 = 2 · 106 torsion: t f = 200; m = 12; n0 = 2 · 106 tt xx xy. [ 0 0 0 0 ] s a. niesłony, frattura ed integrità strutturale, 38 (2016) 177-183; doi: 10.3221/igf-esis.38.24 182 the eq. (8) for psd of ems simplify to following expression (18) as we can see cross power spectrum is not present. this function is the only one which includes information about correlation (phase shift for one harmonic component) what can be treat as a proof of the omission of phase shift effect. figure 2: sn curves uniaxial and biaxial data presented by cláudio et al. [13]. remarks and final conclusions 1. it is not recommended to use the ems criterion in a case where the shear stresses dominate, and the ratio of fatigue limits is different from the square root of three. 2. abnormal behaviour of ems criterion it can be observed in comparison to experimental results under biaxial tensioncompression. for example uniaxial and in-phase biaxial loading give the same equivalent amplitude according this criterion but the test results showing shortening of the fatigue life, see fig. 2. 3. the impact of non-parallelism of fatigue characteristics on calculated life is significant and depends on loading level. 4. correlation between normal and shear stress components are neglected. therefore, this criterion can be used for materials that do not show sensitivity to the phase shift between these components. references [1] karolczuk, a., macha, e., a review of critical plane orientations in multiaxial fatigue failure criteria of metallic materials, int j fract., 134 (2005) 267–304. doi:10.1007/s10704-005-1088-2. [2] wang, y., susmel, l., the modified manson–coffin curve method to estimate fatigue lifetime under complex constant and variable amplitude multiaxial fatigue loading, int. j. fatigue., 83 (2016) 135–149. doi:10.1016/j.ijfatigue.2015.10.005. [3] ince, a., glinka, g., a generalized fatigue damage parameter for multiaxial fatigue life prediction under proportional and non-proportional loadings, int. j. fatigue. 62 (2014) 34–41. doi:10.1016/j.ijfatigue.2013.10.007. [4] pitoiset, x., preumont, a., spectral methods for multiaxial random fatigue analysis of metallic structures, int. j. fatigue. 22 (2000) 541–550. doi:10.1016/s0142-1123(00)00038-4. [5] niesłony, a., comparison of some selected multiaxial fatigue failure criteria dedicated for spectral method, j. theor. appl. mech., 48 (2010) 233–254. [6] de la fuente, e., an efficient procedure to obtain exact solutions in random vibration analysis of linear structures, engineering structures, 30 (2008) 2981–2990. doi:10.1016/j.engstruct.2008.04.015. [7] huber, m.t., specific work of strain as a measure of material effort, archives of mechanics, 56 (2004) 173–190. [8] v mises, r., mechanik der festen körper im plastischdeformablen zustand, nachrichten von der gesellschaft der wissenschaften zu göttingen, mathematisch-physikalische klasse, 1913 (1913) 582–592. ems xx xx xy xyg f g f g f, ,( ) ( ) 3 ( )  10 4 10 5 10 6 10 7 10 8 10 2 n, cycles σ x x , a , σ e m s , a , m p a uniaxial: data uniaxial: fit biaxial δ = 0◦: data biaxial δ = 0◦: fit biaxial δ = 90◦: data biaxial δ = 90◦: fit biaxial δ = 180◦: data biaxial δ = 180◦: fit a. niesłony, frattura ed integrità strutturale, 38 (2016) 177-183; doi: 10.3221/igf-esis.38.24 183 [9] hashiguchi, k., cyclic plasticity models: critical reviews and assessments, in: elastoplasticity theory, springer berlin heidelberg, (2014) 187–202. http://link.springer.com/chapter/10.1007/978-3-642-35849-4_8 (accessed january 30, 2016). [10] preumont, a., piefort, v., predicting random high-cycle fatigue life with finite elements, j. vib. acoust., 116 (1994) 245–248. doi:10.1115/1.2930420. [11] de la fuente, e., von mises stresses in random vibration of linear structures, computers & structures, 87 (2009) 1253– 1262. doi:10.1016/j.compstruc.2009.06.008. [12] benasciutti, d., tovo, r., comparison of spectral methods for fatigue analysis of broad-band gaussian random processes, probabilistic engineering mechanics, 21 (2006) 287–299. doi:16/j.probengmech.2005.10.003. [13] cláudio, r.a., reis, l. , freitas, m., biaxial high-cycle fatigue life assessment of ductile aluminum cruciform specimens, theor. appl. fract. mech., 73 (2014) 82–90. doi:10.1016/j.tafmec.2014.08.007. << /ascii85encodepages false /allowtransparency false /autopositionepsfiles true /autorotatepages /none /binding /left /calgrayprofile (dot gain 20%) /calrgbprofile (srgb iec61966-2.1) /calcmykprofile (u.s. web coated \050swop\051 v2) /srgbprofile (srgb iec61966-2.1) /cannotembedfontpolicy /error /compatibilitylevel 1.4 /compressobjects /tags /compresspages true /convertimagestoindexed true /passthroughjpegimages true /createjobticket false /defaultrenderingintent /default /detectblends true /detectcurves 0.0000 /colorconversionstrategy /cmyk /dothumbnails false /embedallfonts true /embedopentype false /parseiccprofilesincomments true /embedjoboptions true /dscreportinglevel 0 /emitdscwarnings false /endpage -1 /imagememory 1048576 /lockdistillerparams false /maxsubsetpct 100 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/hrv (za stvaranje adobe pdf dokumenata najpogodnijih za visokokvalitetni ispis prije tiskanja koristite ove postavke. stvoreni pdf dokumenti mogu se otvoriti acrobat i adobe reader 5.0 i kasnijim verzijama.) /hun 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can be opened with acrobat and adobe reader 5.0 and later.) >> /namespace [ (adobe) (common) (1.0) ] /othernamespaces [ << /asreaderspreads false /cropimagestoframes true /errorcontrol /warnandcontinue /flattenerignorespreadoverrides false /includeguidesgrids false /includenonprinting false /includeslug false /namespace [ (adobe) (indesign) (4.0) ] /omitplacedbitmaps false /omitplacedeps false /omitplacedpdf false /simulateoverprint /legacy >> << /addbleedmarks false /addcolorbars false /addcropmarks false /addpageinfo false /addregmarks false /convertcolors /converttocmyk /destinationprofilename () /destinationprofileselector /documentcmyk /downsample16bitimages true /flattenerpreset << /presetselector /mediumresolution >> /formelements false /generatestructure false /includebookmarks false /includehyperlinks false /includeinteractive false /includelayers false /includeprofiles false /multimediahandling /useobjectsettings /namespace [ (adobe) (creativesuite) (2.0) ] /pdfxoutputintentprofileselector /documentcmyk /preserveediting true /untaggedcmykhandling /leaveuntagged /untaggedrgbhandling /usedocumentprofile /usedocumentbleed false >> ] >> setdistillerparams << /hwresolution [2400 2400] /pagesize [612.000 792.000] >> setpagedevice microsoft word numero_29_art_4 g. carta et alii, frattura ed integrità strutturale, 29 (2014) 28-36; doi: 10.3221/igf-esis.29.04 28 focussed on: computational mechanics and mechanics of materials in italy elastic wave propagation and stop-band generation in strongly damaged solids g. carta, m. brun department of mechanical, chemical and materials engineering, university of cagliari, italy giorgio_carta@unica.it, mbrun@unica.it a.b. movchan department of mathematical sciences, university of liverpool, uk abm@liverpool.ac.uk abstract. in this work, we study the propagation of elastic waves in elongated solids with an array of equallyspaced deep transverse cracks, focusing in particular on the determination of stop-bands. we consider solids with different types of boundary conditions and different lengths, and we show that the eigenfrequencies associated with non-localized modes lie within the pass-bands of the corresponding infinite periodic system, provided that the solids are long enough. in the stop-bands, instead, eigenfrequencies relative to localized modes may be found. furthermore, we use an asymptotic reduced model, whereby the cracked solid is approximated by a beam with elastic connections. this model allows to derive the dynamic properties of damaged solids through analytical methods. by comparing the theoretical dispersion curves yielded by the asymptotic reduced model with the numerical outcomes obtained from finite element computations, we observe that the asymptotic reduced model provides a better fit to the numerical data as the slenderness ratio increases. finally, we illustrate how the limits of the stop-bands vary with the depth of the cracks. keywords. elastic waves; dispersion; stop-bands; elastic solids; cracks; asymptotics. introduction iscontinuities in elastic solids give rise to stop-bands, which are intervals of frequencies for which waves travelling through the solid are attenuated in amplitude, also if damping is absent. examples of discontinuities are cracks, imperfections and defects. in addition, discontinuities may be represented by non-smooth reductions of cross-sections due to design purposes. for instance, long bridges consisting of several spans that are simply-supported on piers usually present narrower cross-sections in correspondence of the piers, where the spans are connected only by the upper deck. the generation of stop-bands is generally accompanied by localization phenomena, such as trapped modes occurring near discontinuities. localization has been observed in different elastic systems, like beams [1], plates [2] and micro-structured media [3-5]. localization around defects in bi-material delaminating systems is investigated in [6,7], where a lowerdimensional asymptotic model is introduced to study the dispersion properties of the medium. an improved formulation d g. carta et alii, frattura ed integrità strutturale, 29 (2014) 28-36; doi: 10.3221/igf-esis.29.04 29 with higher-order terms in the asymptotic approximation of the system is proposed in [8] for the analysis of floquetbloch waves. an elongated elastic solid with a deep transverse crack is examined in [9,10] for the cases of static longitudinal and transverse loads, respectively. in [9,10] a reduced model is formulated, in which the cracked region is approximated asymptotically by an elastic connection, which accounts for the decay of the boundary layer arising near the crack. this model is extended in [11] to dynamic problems. the presence of a crack influences the vibration response of a beam, since it locally modifies the flexibility of the structural element [12]. in [13] the effects of both a double-sided and a single-sided crack on the natural frequencies of a cantilever beam are investigated. in [14] the changes in the lowest eigenfrequency of a simply-supported beam produced by a breathing edge crack are discussed in comparison with experimental results. in this paper, we analyze the dynamic response of an elongated elastic solid with a distributed damage, represented by equally-spaced transverse cracks. first, we determine numerically the eigenfrequencies and eigenmodes of cracked solids with different boundary conditions and different lengths, and we compare the results with the dispersion curves computed for solids with infinite length. successively, we assess the validity of the reduced asymptotic model examined in [11] for different values of the slenderness ratio of the solid, and we evaluate the positions of the stop-bands in relation with the depth of the cracked sections. finally, we summarize the results and we discuss briefly the practical applications that can be related to this work. dynamic properties of elongated damaged solids with different boundary conditions e examine the dynamic behavior of an elongated elastic solid with equally-spaced cracks. an example of such a solid with a rectangular cross-section and simply-supported conditions is drawn in fig. 1a, where l is the distance between cracks, while l, h and b are the length, the height and the thickness of the solid, respectively. since the distance between cracks is constant, the solid can be modeled as a sequence of repetitive cells, one of which is shown in fig. 1b, where s denotes the height of the cracked section. figure 1: (a) simply-supported elongated solid with cracks located at regular intervals of length l ; (b) repetitive cell of the solid. we consider time-harmonic waves propagating along the axis of the solid that consist of oscillations occurring in the direction of the solid height. this assumption allows to study the solid as a two-dimensional strip subjected to transverse oscillations. by using a finite element model developed in the software comsol multiphysics, we obtain the eigenfrequencies and eigenmodes of damaged solids with different lengths. in figs. 2a-2e we report the results relative to five different boundary conditions: a hinge and a roller, both ends fixed, a fixed end and a roller, a slider and a roller, a slider and a fixed end. the parameter n in the horizontal axes stands for the number of repetitive cells, while the quantity ϕ in the vertical axes is a non-dimensional frequency given by ϕ = (ρaω2l4/ej)1/4. w b h l l h (a) (b) l s l l l l /2 l /2 g. carta et alii, frattura ed integrità strutturale, 29 (2014) 28-36; doi: 10.3221/igf-esis.29.04 30 figure 2: (a)-(e) eigenfrequencies of cracked solids with different lengths and different boundary conditions, sketched at the top-right corner of each figure; (f) dispersion curves (black dots) and pass-bands (grey lines) for the solid with infinite length. (a) (b) (c) (d) (e) (f) n k l n n n n ϕ ϕ ϕ ϕ ϕ ϕ g. carta et alii, frattura ed integrità strutturale, 29 (2014) 28-36; doi: 10.3221/igf-esis.29.04 31 in this paper, e is the young's modulus, ν is the poisson's ratio, ρ is the mass density, ω is the angular frequency, while a and j are the area and the second moment of inertia of the cross-section of the solid. the results in figs. 2a-2e are determined by assigning the following properties to the solid: e = 31 gpa, ν = 0.2, ρ = 2500 kg/m3, l = 3 m, h = 0.3 m, s = 0.1 m, b = 0.5 m. the black dots indicate the eigenfrequencies associated with propagating modes, while the grey dots represent the eigenfrequencies corresponding to localized modes. examples of propagating and localized modes for the different cases are shown in fig. 3. we point out that the solid with a slider and a roller does not exhibit localized modes (see fig. 2d). figure 3: examples of propagating eigenmodes ((a), (c), (e), (g), (h), (i)) and localized eigenmodes ((b), (d), (f), (j)) of solids with n = 5 repetitive cells and with different boundary conditions, shown in the insets. the dispersion curves for an infinite cracked solid are shown in fig. 2f, where k is the wavenumber. the dispersion curves are obtained from a finite element model in comsol multiphysics by imposing floquet-bloch conditions at the vertical sides of the repetitive cell in fig. 1b. the frequency ranges for which waves propagate without attenuation are denoted by "pass-bands" and are illustrated in grey color on the right of figs. 2a-2f. on the other hand, the frequency ranges for which waves decay exponentially are called "stop-bands". from the outcomes in fig. 2 we infer that the majority of the eigenfrequencies associated with propagating modes fall inside the pass-bands, while most of the eigenfrequencies relative to localized modes lie within the stop-bands. ϕ = 7.043 ϕ = 8.381 ϕ = 7.230 ϕ = 8.368 ϕ = 7.047 ϕ = 8.442 ϕ = 4.329 ϕ = 7.144 ϕ = 6.837 ϕ = 8.434 (a) (b) (c) (d) (e) (f) (g) (h) (i) (j) g. carta et alii, frattura ed integrità strutturale, 29 (2014) 28-36; doi: 10.3221/igf-esis.29.04 32 nonetheless, there are some exceptions: especially for short solids, namely for low values of n, some eigenfrequencies corresponding to propagating modes are found outside the pass-bands, though close to their limits; however, these modes tend to become localized as the length of the solid or, equivalently, n is increased. therefore, the effect of periodicity is more evident in long solids, as could be predicted. the results discussed above are in agreement with those presented in [15] for mono-coupled systems, in [11] for a strip made of steel with free ends, and in [16] for a real bridge. assessment of an asymptotic reduced model for the dynamic study of elongated solids he analytical determination of the dynamic properties of cracked solids modeled as two-dimensional or threedimensional continuous media is not a straightforward task. therefore, simpler analytical models have been proposed in the literature. in particular, we investigate the "asymptotic reduced model", firstly formulated in [10] for static problems and later extended in [11] to dynamic problems. this model is defined as "reduced" because it approximates the elongated strip in fig. 1 as a beam, in which the cracked sections are treated as elastic connections consisting of rotational and translational springs. the stiffnesses of these springs are evaluated via asymptotic techniques [10,11,17], which explains the use of the adjective "asymptotic" appended to the definition of the model in exam. in this work, we assess the validity of the asymptotic reduced model for different values of the "slenderness ratio" l/h. we consider both cracked and undamaged solids, and we compute the dispersion curves of the corresponding beam models. in order to obtain the dispersion curves for a beam with elastic connections, we consider an infinite periodic beam made of repetitive cells, as that drawn in fig. 4. here, kb and ks are the rotational (or bending) and translational (or shear) stiffnesses of the springs that simulate the cracked sections of the solid. they are expressed by [10,11]    2π 4 5 2 1 b e b s k      (1) and    2 π 4 1 log / s e b k h s   (2) respectively. all the quantities appearing in the formulae above have been defined in the previous section. we derive the dispersion curves by using the method based on the transfer matrix [18-21]. the transfer matrix links the generalized displacements and forces at the two ends of the repetitive cell of a periodic structure. for the case at hand, the transfer matrix is given by [11]       2 3 2 2 cos( ) cosh( ) sin( ) sinh( ) cos( ) cosh( ) sin( ) sinh( ) 1 2 2 2 2 sin( ) sinh( ) cos( ) cosh( ) sin( ) sinh( ) cos( ) cosh( )1 2 2 2 2 cos( ) cosh( ) sin( ) sinh( ) cos( ) cosh( ) 2 2 s b ej ej k ej k ej ej ej                                               t      3 2 sin( ) sinh( ) 2 2 sin( ) sinh( ) cos( ) cosh( ) sin( ) sinh( ) cos( ) cosh( ) 2 2 2 2 ej ej                                            (3) where β = ϕ/l. floquet-bloch conditions lead to the following equation:   idet e 0klt i (4) where i is the identity matrix. eq. (4) represents the dispersion relation for the beam with elastic connections. it can also be applied to an undamaged beam by taking kb → ∞ and ks → ∞. t g. carta et alii, frattura ed integrità strutturale, 29 (2014) 28-36; doi: 10.3221/igf-esis.29.04 33 figure 4: repetitive cell of an infinite periodic beam with elastic connections. we plot the analytical results in fig. 5 in solid lines. figs. 5a, 5c and 5e contain the dispersion curves for cracked beams, while figs. 5b, 5d and 5f show the dispersion curves for undamaged beams. three different values of slenderness ratio are considered: l/h = 5 (figs. 5a and 5b), l/h = 10 (figs. 5c and 5d) and l/h = 20 (figs. 5e and 5f). the dots represent instead the numerical outcomes relative to strips having the same properties as the beams, which are derived from finite element computations. in particular, the numerical results in fig. 5c are identical to those reported in fig. 2f. the diagrams in fig. 5 show that the range of validity of the asymptotic reduced model increases with the slenderness of the solid. more specifically, for l/h = 5 only the first dispersion curve for the solid (either cracked or undamaged) is predicted well by the beam model; for l/h = 10, the first two theoretical dispersion curves determined with the asymptotic reduced model fit well the numerical data computed for the solid; for l/h = 20, the effectiveness of the beam model extends to the first four dispersion curves. as shown in [11], the limits of the stop-bands coincide with the eigenfrequencies of the simple beams sketched at the bottom-right corners of figs. 6a-6d. therefore, simple analytical expressions can be used to determine the limits of the pass (propagation) and stop (non propagation) bands. the positions of the stop-bands along the frequency axis depend on the stiffnesses of the elastic junctions kb and ks . for the case of beams with rectangular cross-sections, kb and ks can be expressed in normalized form as functions of the slenderness ratio l/h, the "integrity ratio" s/h and the poisson's ratio ν, as follows:               2 3π 5 2 1 b b k l l s ej h h (5)            33 2 3π 1 1 log / s s k l l ej h h s (6) in the formulae above, b and s are the normalized bending and shear stiffnesses, respectively. in figs. 6a-6d, we illustrate the relations between the first normalized eigenfrequencies ϕ1 of the four simple beams shown in the figures and the integrity ratio s/h, for given values of the slenderness ratio and poisson's ratio. the diagrams in figs. 6a-6d are obtained, respectively, from the following approximate formulae [11], after substituting the expressions of b and s given by eqs. (5) and (6):      41 2 6 2 b b (7)            2 4 1 840 35 105 6720 336 11 2 6 336 s s s s (8)            2 4 1 21 7 7 53 30 5 2 3 10 5 b b b b (9)            2 4 1 840 7 35 20160 48 2 3 10 720 s s s s (10) g. carta et alii, frattura ed integrità strutturale, 29 (2014) 28-36; doi: 10.3221/igf-esis.29.04 34 figure 5: theoretical (solid lines) and numerical (dots) dispersion curves for cracked and undamaged solids with l = 1.5 m ((a), (b)), l = 3 m ((c), (d)) and l = 6 m ((e), (f)). the other quantities have the following values: h = 0.3 m, s = 0.1 m, b = 0.5 m, e = 31 gpa, ν = 0.2, ρ = 2500 kg/m3. cracked l/h = 5 cracked l/h = 10 cracked l/h = 20 undamaged l/h = 5 undamaged l/h = 10 undamaged l/h = 20 (a) (b) (c) (d) (e) (f) ϕ kl kl kl kl kl kl ϕ ϕ ϕ ϕ ϕ g. carta et alii, frattura ed integrità strutturale, 29 (2014) 28-36; doi: 10.3221/igf-esis.29.04 35 the diagrams in figs. 6a and 6b represent the limits of the first stop-band, while the curves in figs. 6c and 6d describe the limits of the second stop-band. we note that the lower limits of the first stop-band (fig. 6a) and of the second stop-band (fig. 6c) change significantly with s/h; on the other hand, the upper limits of the first stop-band (fig. 6b) and of the second stop-band (fig. 6d) are almost constant. therefore, the main effect of the cracks is to open stop-bands in correspondence of the values that the dispersion curves for undamaged beams assume at kl = 0 and kl = π (see fig. 5d), keep the upper limits of the stop-bands almost constant and shift downwards the lower limits by an amount proportional to the depth of the crack. figure 6: first eigenfrequencies versus integrity ratio s/h of simple beams with different boundary conditions, defining the limits of the stop-bands predicted by the beam model (l/h = 10, ν = 0.2). conclusions n this paper, we have examined the dynamic properties of elongated elastic solids with a distributed damage, studied as two-dimensional strips with equally-spaced cracks. by performing finite element simulations, we have found that the eigenfrequencies of long finite strips corresponding to propagating modes fall inside the pass-bands of infinite strips with the same properties, for any boundary conditions imposed at the ends. on the other hand, the eigefrequencies associated with localized modes are found in the stop-bands. the above considerations apply also to shorter strips, though in this case some exceptions are observed. successively, we have tested the effectiveness of an asymptotic reduced model, which approximates the cracked solid as a beam with elastic connections. this model allows to evaluate analytically the dynamic properties of the cracked solid. we have demonstrated that the validity of the model is enhanced as the slenderness of the beam is increased. in addition, we have provided the explicit expressions of the limits of the first two stop-bands as functions of the ratio between the heights of the cracked and undamaged sections of the beam. i ϕ ϕ ϕ ϕ s/h s/h s/h s/h l/2 l/2 l/2 l/2 2 kb 2 kb 2 ks 2 ks (a) (b) (c) (d) g. carta et alii, frattura ed integrità strutturale, 29 (2014) 28-36; doi: 10.3221/igf-esis.29.04 36 the results of this work can be used in the context of structural health monitoring for the detection of cracks, defects and imperfections in structural elements. moreover, they can be exploited to design filtering systems with appropriate discontinuities that can stop the transmission of waves of specified frequencies. it remains a big challenge to study analytically the dynamic properties of solids with randomly-distributed cracks or defects. references [1] movchan, a.b., slepyan, l.i., band gap green's functions and localized oscillations, proc. r. soc. a, 463 (2007) 27092727. [2] poulton, c.g., movchan, a.b., movchan, n.v., mcphedran, r.c., analytic theory of defects in periodically structured elastic plates, proc. r. soc. a, 468 (2012) 1196-1216. [3] mishuris, g.s., movchan, a.b., slepyan, l.i., localization and dynamic defects in lattice structures, in: v.v. silberschmidt (ed.), computational and experimental mechanics of advanced materials (cism courses and lectures), vol. 514, springer, wien, (2009) 51-82. [4] bigoni, d., guenneau, s., movchan, a.b., brun, m., elastic metamaterials with inertial locally resonant structures: application to lensing and localization, phys. rev. b, 87 (2013) 174303. [5] carta, g., jones, i.s., brun, m., movchan, n.v., movchan, a.b., crack propagation induced by thermal shocks in structured media, int. j. solids struct., 50 (2013) 2725-2736. [6] mishuris, g.s., movchan, a.b., bercial, j.p., asymptotic analysis of bloch-floquet waves in a thin bi-material strip with a periodic array of finite-length cracks, waves random complex media, 17 (2007) 511-533. [7] vellender, a., mishuris, g.s., movchan, a.b., weight function in a bimaterial strip containing an interfacial crack and an imperfect interface. application to bloch-floquet analysis in a thin inhomogeneous structure with cracks, multiscale model. simul., 9 (2011) 1327-1349. [8] vellender, a., mishuris, g.s., eigenfrequency correction of bloch-floquet waves in a thin periodic bi-material strip with cracks lying on perfect and imperfect interfaces, wave motion, 49 (2012) 258-270. [9] zalipaev, v.v., movchan, a.b., jones, i.s., two-parameter asymptotic approximations in the analysis of a thin solid fixed on a small part of its boundary, q. j. mech. appl. math., 60 (2007) 457-471. [10] gei, m., jones, i.s., movchan, a.b., junction conditions for cracked elastic thin solids under bending and shear, q. j. mech. appl. math., 62 (2009) 481-493. [11] carta, g., brun, m., movchan, a.b., dynamic response and localization in strongly damaged waveguides, proc. r. soc. a, 470 (2014) 20140136. [12] dimarogonas, a.d., vibration of cracked structures: a state of the art review, eng. fract. mech., 55 (1996) 831-857. [13] ostachowicz, w.m., krawczuk, m., analysis of the effect of cracks on the natural frequencies of a cantilever beam, j. sound vib., 150 (1991) 191–201. [14] chondros, t.g., dimarogonas, a.d., yao, j., vibration of a beam with a breathing crack, j. sound vib., 239 (2001) 57-67. [15] mead, d.j., wave propagation and natural modes in periodic systems: i. mono-coupled systems, j. sound vib., 40 (1975) 1–18. [16] brun, m., giaccu, g.f., movchan, a.b., movchan, n.v., asymptotics of eigenfrequencies in the dynamic response of elongated multi-structures, proc. r. soc. a, 468 (2012) 378-394. [17] ciarlet, p.g., mathematical elasticity volume ii: theory of plates, first ed., north-holland, amsterdam, (1997). [18] pestel, e.c., leckie, f.a., matrix methods in elastomechanics, first ed., mcgraw-hill, new york, (1963). [19] faulkner, m.g., hong, d.p., free vibrations of mono-coupled periodic system, j. sound vib., 99 (1985) 29–42. [20] lekner, j., light in periodically stratified media, j. opt. soc. am. a, 11 (1994) 2892–2899. [21] romeo, f., luongo, a., invariants representation of propagation properties for bi-coupled periodic structures, j. sound vib., 257 (2002) 869–886. microsoft word numero 9 art 5 finale an. carpinteri et alii, frattura ed integrità strutturale, 9 (2009) 46 54; doi: 10.3221/igf-esis.09.05 46 fatigue life estimation in welded joints under multiaxial loadings andrea carpinteri, andrea spagnoli, sabrina vantadori university of parma, department of civil and environmental engineering and architecture, via g.p. usberti 181/a, 43100 parma, italy; andrea.carpinteri@unipr.it riassunto. le giunzioni saldate sono frequentemente zone di innesco di fessure che possono poi provocare la crisi per fatica dell’intera struttura. stati tensionali e deformativi biassiali o triassiali sono presenti in prossimità delle giunzioni saldate a causa della concentrazione indotta dalla geometria della giunzione stessa, dal processo di saldatura e/o dalla presenza di carichi multiassiali. la determinazione della vita a fatica di giunzioni saldate in presenza di carichi multiassiali ciclici proporzionali può essere eseguita adottando criteri locali basati su ipotesi convenzionali (criterio di mises o criterio di tresca). in presenza di carichi ciclici multiassiali non proporzionali, invece, è stato osservato sperimentalmente che, valutando la vita a fatica attraverso ipotesi convenzionali, si giunge a previsioni che non sono a favore di sicurezza. un criterio è stato proposto dagli autori per determinare la vita a fatica di componenti strutturali soggetti a stati tensionali multiassiali. il criterio è stato inizialmente sviluppato per i componenti lisci e intagliati e poi esteso, con opportune modifiche, ai componenti saldati. la determinazione della vita a fatica viene eseguita considerando una funzione quadratica in cui compaiono l'ampiezza della componente tangenziale di tensione (agente sul piano critico) e l’ampiezza e il valore medio della componente normale di tensione (agente sul piano critico). scopo di questo lavoro è il confronto tra la previsione della vita a fatica ottenuta mediante il presente criterio in termini di tensioni nominali e la vita a fatica sperimentale per dati relativi a prove biassiali di fatica reperibili in letteratura. abstract. welded joints are frequently locations for cracks initiation and propagation that may cause fatigue failure of engineering structures. biaxial or triaxial stress-strain states are present in the vicinity of welded joints, due to local geometrical constraints, welding processes and/or multiaxial external loadings. fatigue life evaluation of welded joints under multiaxial proportional (in-phase) cyclic loading can be performed by using conventional hypotheses (e.g. see the von mises criterion or the tresca criterion) on the basis of local approaches. on the contrary, the fatigue life predictions of welded joints under non-proportional (out-ofphase) cyclic loading are generally unsafe if these conventional hypotheses are used. a criterion initially proposed by the authors for smooth and notched structural components has been extended to the fatigue assessment of welded joints. in more detail, fatigue life of welded joints under multiaxial stress states can be evaluated by considering a nonlinear combination of the shear stress amplitude (acting on the critical plane) and the amplitude and the mean value of the normal stress (acting on the critical plane). in the present paper, fatigue lifetimes predicted through the proposed criterion are compared with experimental fatigue life data available in the literature, related to fatigue biaxial tests. keywords. welded joints; nominal stresses; lifetime prediction; critical plane approach introduction etallic structural components are very often jointed together by welds, and such joints are frequently critical locations for fatigue failures. that has yielded a wealth of research studies aiming at predicting the fatigue strength of welded joints. m http://www.gruppofrattura.it/ http://dx.medra.org/10.3221/igf-esis.09.05&auth=true mailto: andrea.carpinteri@unipr.it an. carpinteri et alii, frattura ed integrità strutturale, 9 (2009) 46 – 54; doi: 10.3221/igf-esis.09.05 47 several methods are available in the literature to perform fatigue strength and service life assessment of welded joints under uniaxial fatigue loading [1]. the most common uniaxial approach, encapsulated by most of the standard codes in force for metallic structures [2], proceeds by comparing the nominal stress amplitudes applied to the joint with the nominal stress values obtained from s-n curves. local approaches based on local parameters have recently attracted increasing attention in the research community: for example, structural stress and strain approaches [3,4], notch stress and strain approaches [5,6], fracture mechanics approaches [7,8], critical distance approaches [9,10]. the fatigue assessment of welded joints employing local parameters becomes more complex when multiaxial fatigue stress-strain states are present in the vicinity of welded joints. when a weld structure is subjected to in-phase multiaxial fatigue loading, the stress-strain state can be reduced to an equivalent stress/strain based on conventional hypotheses used for static strength evaluation (e.g. see the von mises criterion or the tresca criterion). however, some experimental results [11] on welded steel joints show a decrease of fatigue life in presence of out-of-phase multiaxial loadings as compared to fatigue life under in-phase multiaxial loadings. the critical plane-based multiaxial fatigue criterion proposed by carpinteri and spagnoli (the c-s criterion) for smooth and notched specimens [12-17] has recently been extended to welded structural components by employing the nominal stresses [18]. in the present paper, a comparison between lifetime predictions and experimental data available in the literature [11, 19-21] is carried out, for both in-phase and out-of-phase biaxial cyclic loadings with constant amplitude. the c-s criterion multiaxial fatigue criterion based on the so-called critical plane approach has been proposed by carpinteri and spagnoli to estimate the high-cycle fatigue strength (either endurance limit or fatigue lifetime) of both smooth and notched structural components [12-17]. the main steps of the c-s criterion are as follows: (i) averaged directions of the principal stress axes are determined on the basis of their instantaneous directions; (ii) the orientation of the initial (hereafter termed critical) crack plane and that of the final fracture plane are linked to the averaged directions of the principal stress axes (two material parameters are required at this step: fatigue limit 1,af under fully reversed normal stress, and fatigue limit 1,af under fully reversed shear stress); (iii) the mean value and the amplitude (in a loading cycle) of the normal stress and shear stress, respectively, acting on the critical plane are computed; (iv) the fatigue strength estimation is performed via a quadratic combination of normal and shear stress components acting on the above critical plane (in the case of finite-life fatigue evaluation, two further material parameters are required at this step: the slope m of the s-n curve in the high-cycle regime under fully reversed normal stress, and the slope *m of the s-n curve in the high-cycle regime under fully reversed shear stress). in the following sub-sections, the c-s criterion is briefly reviewed, and an extension to the fatigue assessment of welded structural components under inand out-of-phase loadings is discussed [18]. averaged directions of the principal stress axes at a given material point p , the direction cosines of the instantaneous principal stress directions 1, 2 and 3 (being      ttt 321  ) with respect to a fixed pxyz frame can be worked out from the time-varying stress tensor  tσ . then the orthogonal coordinate system p123 with origin at point p and axes coincident with the principal stress directions (fig.1) can be defined through the ‘principal euler angles’,  , , , which represent three counter-clockwise sequential rotations around the z -axis, y -axis and 3 -axis, respectively (  20  ;  0 ;  20  ). the procedure to obtain the principal euler angles from the direction cosines of the principal stress directions consists of two stages, described in ref.[12]. the averaged directions of the principal stress axes 2̂,1̂ and 3̂ are obtained from the averaged values  ˆ ,ˆ ,ˆ of the principal euler angles. such values are computed by independently averaging the instantaneous values      ttt  , , as follows [12,13]:    dttwt w t  0 1ˆ     dttwt w t  0 1ˆ     dttwt w t  0 1 ˆ  (1) a http://www.gruppofrattura.it/ http://dx.medra.org/10.3221/igf-esis.09.05&auth=true an. carpinteri et alii, frattura ed integrità strutturale, 9 (2009) 46 54; doi: 10.3221/igf-esis.09.05 48 with t = period of the loading cycle and  tw = weight function given by:  max,11 )()(   thtw (2) where  h is the heaviside function (   1xh for 0x ,   0xh for 0x ), and max,1 is the maximum value (in the loading cycle) of the maximum principal stress 1 . the proposed weight function is such that no averaging procedure is actually required (this makes the implementation of the criterion rather simple), since the averaged principal stress axes coincide with the instantaneous principal directions corresponding to the time instant at which the maximum principal stress 1 achieves its maximum value in the loading cycle. figure 1: principal stress directions 1, 2 , 3 described through the euler angles  , , . critical plane and final fatigue fracture plane fatigue crack propagation can be distinguished into two stages [22]: a first stage in which a crack nucleates along a shear slip plane (stage 1, fatigue crack initiation plane or critical plane) and a second stage in which crack propagates in a plane normal to the direction of the maximum principal stress (stage 2, final fatigue fracture plane). according to the present criterion, the normal to the estimated final fatigue fracture plane (stage 2), which is the one observed post mortem at the macro level, is assumed to be coincident with the averaged direction 1̂ of the maximum principal stress 1 [14]. on the other hand, the critical plane (stage 1) is the verification material plane, where fatigue strength assessment is to be performed. the orientation of the critical plane has been proposed to be correlated with the averaged directions of the principal stress axes [15] and the empirical expression of the off angle  between the normal w to the critical plane (where w belongs to the averaged principal plane 3̂1̂ ) and the averaged direction 1̂ of the maximum principal stress 1 is given by:                    2 1, 1, 1 8 3 af af    (3) equation (3) is valid for hard metals, which are characterised by values of the ratio 1,1,   afaf ranging from 31 to 1. the off angle  is assumed to be equal to 0 for 11,1,  afaf  , whereas  is taken to be equal to 4/ for 311,1,  afaf  . mean value and amplitude of normal stress and shear stress the critical plane  passing through a given point p in a solid and the attached orthogonal coordinate system puvw are considered (fig.2), where the u-axis belongs to the plane formed by the w-axis (normal to the critical plane) and the zhttp://www.gruppofrattura.it/ http://dx.medra.org/10.3221/igf-esis.09.05&auth=true an. carpinteri et alii, frattura ed integrità strutturale, 9 (2009) 46 – 54; doi: 10.3221/igf-esis.09.05 49 axis. the direction cosines of u -, v and w -axis can be computed with respect to the pxyz frame, as a function of the two angles  and  . figura 2: pxyz and puvw coordinate systems, with the w -axis normal to the critical plane  . the stress vector ws acting at point p , the normal stress vector n and the shear stress vector c acting on the critical plane are given by: wσsw    wswn w nsc w  (4) for multiaxial constant amplitude cyclic loading, the direction of the normal stress vector  tn is fixed with respect to time and consequently, the mean value mn and the amplitude an of the vector modulus  tn can readily be calculated. on the other hand, the definitions of the mean value mc and amplitude ac are not unique owing to the generally timevarying direction of the shear stress vector )(tc . the procedure proposed by papadopoulos [23] to determine mc and ac is adopted [14]. fatigue strength estimation the multiaxial fatigue limit condition presented in ref.[15] corresponds to a nonlinear combination of the maximum normal stress ( am nnn max ) and the shear stress amplitude ( ac ) acting on the critical plane: 1 2 1, 2 1, max                    af a af cn (5) as is well-known, the effect of a tensile mean normal stress superimposed upon an alternating normal stress strongly reduces the fatigue resistance of metals, while a mean shear stress superimposed upon an alternating shear stress does not affect the fatigue life [24]. therefore, the following multiaxial fatigue limit condition is here adopted [18]: 1 2 1, 2 1, ,                    af a af eqa cn (6) where:          u m afaeqa n nn 1,, (7) http://www.gruppofrattura.it/ http://dx.medra.org/10.3221/igf-esis.09.05&auth=true an. carpinteri et alii, frattura ed integrità strutturale, 9 (2009) 46 54; doi: 10.3221/igf-esis.09.05 50 with u = ultimate tensile strength. equation (7) is based on the well-known linear interaction between normal stress amplitude and normal stress mean value (diagram of goodman). in order to transform the actual periodic multiaxial stress state into an equivalent uniaxial normal stress state (with amplitude eqa, ), equation (6) can be rewritten as follows: 1, 2 2 1, 1,2 ,,                afa af af eqaeqa cn (8) for fatigue strength assessment at finite life, the fatigue limits 1,af and 1,af appearing in eqs (6) and (8) should be replaced by the corresponding fatigue strengths. hence, using a basquin-like relationship for both fully reversed normal stress (   mfafaf nn 01,1,   , with  1,af fatigue strength for fully reversed normal stress at finite life fn , and 0n = reference number of loading cycles, e.g. 2  106) and fully reversed shear stress (   *01,1, mfafaf nn  , with  1,af fatigue strength for fully reversed shear stress at finite life fn ), equation (8) becomes:   m f afa m f m f af af eqa n n c n n n n n                                   0 1, 2 *2 0 2 0 2 1, 1,2 , (9) where the equivalent normal stress amplitude, eqan , , at finite life fn is given by:                u m m f afaeqa n n n nn 0 1,, (10) now substituting eq.(10) into eq.(9), the number fn of loading cycles to failure can be determined by solving the nonlinear equation obtained. experimental applications and discussion n the present section, the above fatigue criterion is applied to some experimental results, obtained from finite-life fatigue tests, related to welded joints subjected to bending (or tension), torsion, in-phase or out-of-phase combined bending (or tension) and torsion [11, 19-21]. some mechanical characteristics of the materials examined are reported in ref. [18]. the values of the following material parameters: 1,af , 1,af , m and *m , required by the proposed criterion to evaluate fatigue life, are those determined in ref.[25] by susmel and tovo, who analysed the experimental data reported in refs [11, 19-21]. note that such parameters have been deduced by susmel and tovo [25] analysing the above experimental data found in the literature, except for the data set reported in ref.[19], since the s-n curve related to bending cannot be determined due to the limited number of experimental results. therefore, the values given by eurocode 3 [2] are herein adopted for the above parameters. the geometries of the specimens examined are circular tube-to-plate joints, box beams with longitudinal attachments and square tube-to-plate joints. the most critical point (point p) for fatigue crack initiation is assumed to be at the weld toe, since cracks in welded structural components often initiate along the weld toes, where high stress concentrations and local geometric irregularities exist. i http://www.gruppofrattura.it/ http://dx.medra.org/10.3221/igf-esis.09.05&auth=true an. carpinteri et alii, frattura ed integrità strutturale, 9 (2009) 46 – 54; doi: 10.3221/igf-esis.09.05 51 the c-s criterion is hereafter applied in terms of nominal stresses. the nominal loading paths analysed are reported in fig.3, where normal stress x and shear stress xy at point p are the stress perpendicular and that tangent to the weld bead, respectively. figure 3: summary of nominal loading paths. in order to determine the mean directions of the principal stress axes at point p , the instantaneous values of the principal euler angles are averaged by employing the weight function  tw proposed in eq.(2). then, the angle  between 1̂ and w is determined by using eq.(3). as is mentioned above, such an equation was originally proposed in ref.[15] for hard metals which are characterised by values of the ratio 1,1,   afaf ranging from 31 to 1. for data set reported in ref.[21] the ratio 1,1,   afaf is greater than 1. this is to be expected because the fatigue limits 1,af and 1,af are derived by testing welded specimens [11, 19-21] and, therefore, the values of such parameters are influenced by the presence of fillet welds. as is stated in section 2.2, the off angle  is assumed to be equal to 0 when 11,1,   afaf . fig. 4 shows a comparison between experimental fatigue life ( expn ) and calculated fatigue life ( caln ) for each experimental data set considered above, where the solid line indicates expcal nn  , the dashed lines correspond to expcal nn / equal to 1/2 and 2 (scatter band with coefficient 2) and the dashed-dotted lines correspond to expcal nn / equal to 1/3 and 3 (scatter band with coefficient 3). note that the run-out tests are excluded from the present analysis. tab. 1 reports the number of specimens tested and the percentage of the results of fatigue life estimation included into the scatter band with coefficient 2 and into the scatter band with coefficient 3, for each data set analyzed. the quality of the predictions made by applying the extended c-s criterion can be evaluated through an error index, i (), defined as follows:              expcal cal calexp expcal exp calexp nn n nn nn n nn i for% for% (12) http://www.gruppofrattura.it/ http://dx.medra.org/10.3221/igf-esis.09.05&auth=true an. carpinteri et alii, frattura ed integrità strutturale, 9 (2009) 46 54; doi: 10.3221/igf-esis.09.05 52 for each data set presented above, the relative frequency of the error index is shown in fig.5. the values of i , ranging from %100 to %100 , have been separated in 20 classes of 10% range. such a relative frequency represents the number of experimental tests whose error index falls in the interval considered, normalised with respect to the total number of tests. note that a positive value of i represents a conservative prediction. figure 4: experimental fatigue life expn vs predicted fatigue life caln for each experimental data set analysed [11, 19–21]. figure 5: error index distribution for each experimental data set analysed [11,19–21]. http://www.gruppofrattura.it/ http://dx.medra.org/10.3221/igf-esis.09.05&auth=true an. carpinteri et alii, frattura ed integrità strutturale, 9 (2009) 46 – 54; doi: 10.3221/igf-esis.09.05 53 reference no. specimens scatter band 2 % scatter band 3 % archer [19] 18 94 100 siljander et al. [20] 30 77 97 bäckström et al. [21] 21 24 29 sonsino et al. [11] 43 65 81 table 1: percentage of the results included into the scatter bands with coefficients 2 and 3, for each experimental data set analysed [11, 19–21]. conclusions n the present paper, the criterion proposed by carpinteri and spagnoli for both smooth and notched structural components is extended to the fatigue assessment of welded joints under in-phase or out-of-phase loadings. the averaged principal stress axes, determined through the weight function method, are used to predict the orientation of the critical plane where to perform the fatigue failure assessment. then a fatigue failure criterion based on a nonlinear combination of an equivalent normal stress amplitude and the shear stress amplitude acting on the critical plane is employed to carry out such an assessment. the criterion proposed is applied to relevant experimental results, available in the literature, related to welded joints subjected to bending (or tension), torsion, in-phase or out-of-phase combined bending (or tension) and torsion. it can be remarked that, in most of the cases here examined, the fatigue life predictions of the present criterion fall within a scatter band of coefficient 3. acknowledgements he authors gratefully acknowledge the research support for this work provided by the italian ministry for university and technological and scientific research (miur). references [1] d. radaj, (1990). design and analysis of fatigue-resistant welded structures. abington publishing, cambridge, uk. [2] european committee for standardization. eurocode 3. design of steel structures. part 1-1: general rules and rules for buildings. env 1993-1 (1992). [3] e. haibach, b. atzori, applied to welded joints in almg5. society of environmental engineers fatigue group, midyear conference (1975). [4] t.r. gurney, fatigue of welded structures. cambridge university press, cambridge, uk (1979). [5] p. lazzarin, r. tovo, fatigue fract. engng. mater. struct., 21, (1998) 1089. [6] p. lazzarin, c.m.sonsino, r.zambardi, fatigue fract. engng. mater. struct., 27 (2004) 127. [7] d. radaj, z. zheng, w. möhrmann, engng fract. mechs., 37 (1990) 933. [8] d. taylor, engng failure analysis, 3 (1996) 129. [9] c.m. sonsino, d. radaj, u. brandt, h.p. lehrke, int. j. fatigue, 21 (1999) 985. [10] d. taylor, n. barrett, g. lucano, int. j. fatigue, 24 (2002) 509. [11] c.m. sonsino, m. kueppers, fatigue fract. engng. mater. struct., 24 (2001) 309. [12] a. carpinteri, r. brighenti, e. macha, a. spagnoli, int. j. fatigue, 21 (1999) 83. [13] a. carpinteri, r. brighenti, e. macha, a. spagnoli, int. j. fatigue, 21 (1999)89. [14] a. carpinteri, r. brighenti, a. spagnoli, fatigue fract. engng. mater. struct. 23 (2000) 355. [15] a. carpinteri, a. spagnoli, int. j. fatigue, 23 (2001) 135. [16] a. carpinteri, a. spagnoli, s. vantadori, fatigue fract. engng. mater. struct., 26 (2003) 515. [17] a. carpinteri, a. spagnoli, s. vantadori, d. viappiani, engng fract. mechs., 75 (2008) 1864. [18] a.carpinteri, a. spagnoli, s. vantadori, int. j. fatigue, 31 (2009) 188. i t http://www.gruppofrattura.it/ http://dx.medra.org/10.3221/igf-esis.09.05&auth=true an. carpinteri et alii, frattura ed integrità strutturale, 9 (2009) 46 54; doi: 10.3221/igf-esis.09.05 54 [19] r. archer, proceedings of the fatigue of welded constructions, brighton, uk(1987) 63. [20] a. siljander, p. kurath, f.v. lawrence, in: advances in fatigue lifetime predictive techniques, astm stp 1122, philadelphia, pa. (1992) 319 [21] m. bäckström, g. marquis, fatigue fract. engng. mater. struct. 24 (2001) 279. [22] m.w. brown, k.j. miller, fatigue fract. engng. mater. struct., 1 (1979) 231. [23] i.v. papadopoulos, fatigue fract. engng. mater. struct., 21 (1998) 269. [24] h.j. gough, h.v. pollard, w.j. clenshaw, aeronautical res. council reports, r and m 2522, hmso, london (1951) [25] l. susmel, r. tovo, fatigue fract. engng. mater. struct., 27 (2004) 1005. http://www.gruppofrattura.it/ http://dx.medra.org/10.3221/igf-esis.09.05&auth=true microsoft word numero_38_art_9 m.a. meggiolaro et alii, frattura ed integrità strutturale, 38 (2016) 67-75; doi: 10.3221/igf-esis.38.09 67 focussed on multiaxial fatigue and fracture incorporation of mean/maximum stress effects in the multiaxial racetrack filter marco antonio meggiolaro, jaime tupiassú pinho de castro pontifical catholic university of rio de janeiro, puc-rio, r. marquês de são vicente 225, rio de janeiro, 22451-900, brazil meggi@puc-rio.br, jtcastro@puc-rio.br hao wu school of aerospace engineering and applied mechanics tongji university, siping road 1239, 200092, shanghai, p.r.china wuhao@tongji.edu.cn abstract. this work extends the multiaxial racetrack filter (mrf) to incorporate mean or maximum stress effects, adopting a filter amplitude that depends on the current stress level along the stress or strain path. in this way, a small stress or strain amplitude event can be filtered out if associated with a non-damaging low mean or peak stress level, while another event with the very same amplitude can be preserved if happening under a more damaging high mean or peak stress level. the variable value of the filter amplitude must be calculated in real time, thus it cannot depend on the peak or mean stresses along a load event, because it would require cycle identification and as so information about future events. instead, mean/maximum stress effects are modeled in the filter as a function of the current (instantaneous) hydrostatic or normal stress along the multiaxial load path, respectively for invariantbased and critical-plane models. the mrf efficiency is evaluated from tension-torsion experiments in 316l stainless steel tubular specimens under non-proportional (np) load paths, showing it can robustly filter out nondamaging events even under multiaxial np variable amplitude loading histories. keywords. multiaxial racetrack filter; mean/peak stress effects; nondamaging events; multiaxial loads. citation: meggiolaro, m.a., de castro, j.t.p., wu, h., incorporation of mean/maximum stress effects in the multiaxial racetrack filter, frattura ed integrità strutturale, 38 (2016) 67-75. received: 12.05.2016 accepted: 10.06.2016 published: 01.10.2016 copyright: © 2016 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. introduction nlike frequency filters that clean but distort originally noisy signals, the uniaxial racetrack filter [1, 2] is an efficient and well-proven amplitude filter. it can eliminate non-damaging events from uniaxial load histories without changing the original loading order and its overall shape, much improving the efficiency of practical fatigue u m.a. meggiolaro et alii, frattura ed integrità strutturale, 38 (2016) 67-75; doi: 10.3221/igf-esis.38.09 68 damage calculations from unavoidably noisy strain signals measured under actual field conditions. the racetrack generalization to properly filter multiaxial non-proportional (np) variable amplitude loading (val) histories is even more useful for practical applications. in fact, it can allow a dramatic reduction in the intrinsically high computational cost of fatigue damage calculations from multiaxial strain measurements, which besides noisy, usually are oversampled, too long, and/or contain too many non-damaging low-amplitude events that do not affect the damage values, but can much delay their calculation. however, multiaxial racetrack filter (mrf) procedures are not as simple as the uniaxial ones. indeed, not even the removal from multiaxial val histories of apparently redundant data points that are not reversals of any of their stress or strain components is appropriate because: (i) the path between two load reversals is needed to evaluate the path-equivalent stress or strain associated with each rainflow count, e.g. using a convex-enclosure method [3, 4]; and (ii) reversal points from a multiaxial rainflow algorithm might not occur at a reversal of one of the stress or strain components. to solve issues like those, a truly mrf that can remove non-damaging events from multiaxial load paths represented in a sub-space from the 6d stress or strain space has been recently proposed in [5], extending its peg inside a slot 1d analogy illustrated in fig. 1 to the 6d stress or strain spaces. its specifiable filter amplitude defines the radius of a hyper-sphere (or a sphere in 3d or a circle in 2d load histories, respectively), which translates along the load path while filtering out any small load oscillations happening within its interior region. the basic mrf procedures are briefly outlined in fig. 2. further details on the basic mrf procedures can be found in [5, 6]. figure 1: analogy between the uniaxial racetrack filter and a peg p oscillating inside a slotted plate with center o and slot range 2r. the peg oscillates following the original history, resulting in translations of o represented by the dashed line. the use of a 5d deviatoric stress or strain space allows the mrf to be applied to invariant-based damage models, which assume fatigue damage is controlled by invariants like the von mises ranges and hydrostatic stresses, such as in crossland’s pioneer model [7]. for a given stress history, this 5d space is represented by the deviatoric vector t y zx y z xy xz yzs ( ) 2 ( ) 3 2 3 3 3              (1) since the norm of s  is equal to the von mises stress, all distances and filter amplitudes in this 5d sub-space have a physical meaning, they are the von mises range or the relative von mises stresses mises for a straight path between two stress states. alternatively, for a given strain history, the 5d space is defined by the deviatoric vector m.a. meggiolaro et alii, frattura ed integrità strutturale, 38 (2016) 67-75; doi: 10.3221/igf-esis.38.09 69 t x y z y z xy xz yze ( ) 2 ( ) 3 2 3 2 3 2 3 2               (2) a sixth dimension could also be considered in the above 5d spaces, which would store the hydrostatic stress h or strain h of the current state, allowing the filtering of not only deviatoric components, but also of their hydrostatic components. for 2d tension-torsion histories with stress paths defined by the normal and shear components x and xy, it is found that y zxzyz0, while yz ·x and xzyz0, where  is an effective poisson ratio. in this case, t x xys 0 3 0 0       and t x xye (1 ) 0 3 2 0 0         (3) therefore the stress or strain paths of such tension-torsion histories can be represented in the 2d deviatoric diagrams x xy 3  or x xy(1 ) 3 2     , which are sub-spaces from the 5d deviatoric spaces from eq. (3). figure 2: multiaxial racetrack algorithm, with the filtered history resulting from the p  output values, where n  is the hyper-sphere translation direction and io  its center during each loading event i. fig. 3 shows an idealized tension-torsion history represented in the x xy 3  normal-effective shear stress diagram, with the original path points represented as  markers. for a filter amplitude r = 80mpa (the radius of the circle shown in the figure centered at the end of the history, assuming it represents well the fatigue damage threshold), the mrf results in a much reduced number of points, represented with square and triangular markers. note in this figure that many points from such oversampled example are filtered out. note as well that small and supposedly non-damaging normal stress or effective shear stress oscillations are also filtered out, as seen in the upper part of the figure. the original 1,315 data points of this idealized history are dramatically reduced to only 56, significantly reducing the computational cost of subsequent multiaxial rainflow or fatigue damage calculations, without affecting their results if the filter amplitude is well chosen. this simple example should be enough to justify the claim that the mrf is a much useful tool for practical fatigue damage calculations. in fact, its major drawback, the proper specification of the value of the filter amplitude, is not a major issue m.a. meggiolaro et alii, frattura ed integrità strutturale, 38 (2016) 67-75; doi: 10.3221/igf-esis.38.09 70 when using the mrf. it is in fact similar to the problem of finding a properly refined mesh for finite element calculations, which in practice can be found by sequentially refining it until the calculations converge. the mrf can also be used for projected histories on a candidate plane, to reduce computational costs in multiaxial fatigue damage calculations based on critical-plane approaches [2-4, 8]. for shear-based models, the 2d spaces a bt or a bt could be adopted in the mrf, where the subscripts a and b represent the in-plane and out-of-plane shear directions of a candidate plane. for tensile-based damage models, the traditional uniaxial racetrack filter could be applied to the 1d spaces or , where  and  are the normal stress and strain perpendicular to the candidate plane. alternatively, for multiaxial models that mix both shear and tensile damage, the 3d stress or strain spaces a b t or a b t could be used instead in the mrf. however, the original mrf uses fixed filter amplitudes, not a good choice for load histories that contain significant mean load variations due to the asymmetric fatigue damage behavior, which is much more sensitive to tensile mean loads. the purpose of this work is to properly solve this issue. figure 3: original points from an idealized x×xy3 stress path ( markers), and outputs from the mrf (square and triangular markers) for a filter amplitude r = 80mpa. mrf with mean/maximum stress effects s mentioned above, the original implementation of the mrf [5-6] uses a fixed filter amplitude r. however, since tensile load histories tend to be more damaging due to mean/maximum stress effects in multiaxial fatigue, they would benefit from a choice of lower values of r, to avoid filtering out damaging events. on the other hand, compressive histories could allow the choice of higher filter amplitudes, filtering out more points without compromising the damage calculations. such an improved mrf, optimized to consider mean/maximum stress effects on fatigue damage, can be implemented adopting a filter amplitude r that depends on the current stress level. in this way, a small stress or strain amplitude event a m.a. meggiolaro et alii, frattura ed integrità strutturale, 38 (2016) 67-75; doi: 10.3221/igf-esis.38.09 71 could be filtered out if associated with a non-damaging low peak-stress level, while another event with the same amplitude could be preserved if happening under a damaging high peak-stress level. however, this is easier said than done. the filter amplitude must be calculated in real time (or else it would lose efficiency), so it cannot be a function of the peak or mean stresses along a load event, which would require cycle identification and information about future events. instead, mean/maximum-stress effects are modeled in the filter in a simplified way, as a function of the current (instantaneous) hydrostatic h or normal  stress along the load path, respectively for invariant-based and critical-plane models, as briefly outlined in [6]. crossland’s invariant-based model [7], e.g., adopts an infinite-life criterion mises c h cmax2 (3 )        (4) where mises is a path-equivalent von mises shear stress range, hmax is the peak hydrostatic component, and c and c are material constants. if this damage model is adopted, then the stress history could be represented in the previously defined 5d deviatoric space s  , assuming a h-dependent variable filter amplitude mises mises c c hr 2 3 2 ( 3) (3 3 )           (5) on the other hand, findley’s critical-plane model [9] assumes that f fmax2       (6) where  and max are the shear stress range and peak normal stress on the critical plane, and f and f are material constants. using this damage model, the shear stress history on the considered candidate plane could be represented in the 2d shear stress space a bt, while adopting a -dependent variable filter amplitude f fr max2       (7) fatemi-socie’s critical-plane model [10] assumes that b cc fs c yc n n s g max1 ( 2 ) ( 2 ) 2               (8) where  and max are the shear strain range and peak normal stress on the critical plane, n is the associated fatigue life in cycles, g and syc are the material’s shear modulus and cyclic yield strength, and fs, c, c, b and c are material constants. for this damage model, the shear strain history on the considered candidate plane could be represented in the 2d shear strain space a bt, while adopting a -dependent variable filter amplitude b cc c fsll yc r n n g s ( 2 ) ( 2 ) 1 2                      (9) where nl is the number of cycles associated with the stress-life fatigue limit, or any other user-defined fatigue life level. a high-cycle variation of the above variable filter amplitude can also be defined, based on a shear stress instead of shear strain amplitude, giving  l u ur s1     (10) where l is the shear fatigue limit under zero mean stresses, u is a material constant and su is its ultimate strength. in all above cases for crossland’s, findley’s and fatemi-socie’s models or its variations, the filter amplitude r becomes instantaneously smaller for higher h or  stress levels, to avoid filtering out damaging events. analogously, similar expressions for such a variable r could be easily derived for other multiaxial fatigue damage models. m.a. meggiolaro et alii, frattura ed integrità strutturale, 38 (2016) 67-75; doi: 10.3221/igf-esis.38.09 72 these ideas have been implemented in a suitable computer code and used to analyze the results obtained from two challenging tests that involved non-proportional tension-torsion load histories applied on tubular specimens, as well as another idealized bi-axial load history that illustrates well the effects of high mean loads, as discussed next. experimental results he improved version of the mrf, proposed in this work to properly consider the difference between the wellknown effects caused by tensile and compressive mean loads on fatigue damage, is evaluated using experimental and idealized tension-torsion 2d stress histories. the experiments are performed on annealed tubular 316l stainless steel specimens in a multiaxial servo-hydraulic testing machine. the cyclic properties of this 316l steel are obtained from simple uniaxial tests, using standard procedures. its ramberg-osgood uniaxial cyclic hardening coefficient and exponent are 874mpa and 0.123, with young’s modulus 193gpa and poisson ratio 0.3. this material has been chosen for those tests because it presents a significant non-proportional (np) hardening effect as well, which cannot be neglected in multiaxial fatigue damage calculations, as discussed below. the two experiments reported below consist of strain-controlled tension-torsion cycles applied to identical tubular specimens, one for the cross and one for the x-shaped paths from fig. 2, represented in the normal-effective shear strain space x×xy/3. figure 2: applied x×xy/3 strain paths on two tension-torsion tubular specimens, with successively imposed amplitudes a = 0.2%, 0.4%, 0.6% and 0.8% in each case. figure 3: experimentally measured data points ( markers) from the x×xy3 stress paths induced by the cross and x-shaped inputs from fig. 2, and associated outputs from the mrf (solid lines) for a chosen filter amplitude r = 7mpa. t m.a. meggiolaro et alii, frattura ed integrità strutturale, 38 (2016) 67-75; doi: 10.3221/igf-esis.38.09 73 for each specimen, several load periods are applied for a given normal strain amplitude a  0.2%, 0.4%, 0.6% and 0.8%. the resulting normal-effective shear stress paths x×xy3 are very complex, involving high np hardening effects and transients, see fig. 3. fig. 3 shows the experimentally measured data points ( markers) from each of the two specimens, as well as the mrf output (solid lines) for a filter amplitude r = 7mpa. for the cross-shaped path, 95% of the measured points were filtered out, while for the x-shaped case 87% were eliminated, significantly reducing the computational costs of subsequent fatigue life calculations. notice that, despite being highly filtered, the mrf outputs can almost exactly describe the original history, capturing not only all reversal points but also the path shape, which is a most important feature for equivalentrange multiaxial fatigue damage calculations. fig. 4 shows a random single period of each of the fig. 3 paths, where the square markers represent the mrf output, filtering out most of the original stress points. figure 4: experimentally measured data points ( markers) for a single period of the cross and x-shaped histories, and associated outputs from the mrf (square markers) for a filter amplitude r = 7mpa. to better evaluate the mean/maximum stress effects in the proposed modification of the mrf, the idealized tensiontorsion stress history from fig. 1 is now filtered according to a filter amplitude based e.g. on fatemi-socie’s model, shown in eqs. (9) and (10) respectively for strain or stress histories. fig. 5 plots the idealized tension-torsion stress history in a normal-effective shear stress diagram, with the original path points represented as  markers. assuming fig. 5 represents the a 3   history of the normal stress and in-plane shear stress components on a candidate plane, the variable filter amplitude from eq. (10) could be used, but multiplied by 3 (due to the scaling from a to a 3 ) to give  l u ur s3 1     (11) for a hypothetical component with l mpa3 80  , su = 515mpa, and u = 0.66, the above variable filter amplitude becomes  r 80 1 0.66 515   . fig. 5 shows the mrf output adopting such a variable r, where the remaining (unfiltered) points are marked as squares or triangles. notice how most of the normal oscillations were filtered out under a 300mpa compressive mean normal stress, while very few of them were filtered under +300mpa. and the small shear cycle near the 120mpa compressive normal stress was filtered out, while the same shear cycle at +180mpa was not, a desirable behavior for an amplitude filter that considers mean/maximum stress effects. m.a. meggiolaro et alii, frattura ed integrità strutturale, 38 (2016) 67-75; doi: 10.3221/igf-esis.38.09 74 figure 5: original points from an idealized a 3   stress path ( markers), and outputs from the mrf (square and triangular markers), considering mean stress effects. conclusions he multiaxial racetrack filter (mrf) is an efficient amplitude filter applicable to multiaxial histories and fatigue damage models based on invariants or on the critical-plane approach. the mrf is able to filter out low-amplitude events, significantly decreasing the computational cost of subsequent multiaxial fatigue-damage calculations. in this work, mean/maximum stress effects were incorporated into the mrf. the proposed variable filter amplitudes allowed the algorithm to efficiently filter out events based on their damage parameter. in this way, lower filter amplitudes are automatically used for tensile histories, and higher filter amplitudes for compressive ones, optimizing the filter efficiency without neglecting significant damaging events. references [1] fuchs, h.o., nelson, d.v., burke, m.a., toomay, t.l., shortcuts in cumulative damage analysis, sae automobile engineering meeting paper 730565 (1973). [2] castro, j.t.p., meggiolaro, m.a., fatigue design techniques (in 3 volumes), createspace, scotts valley, ca, usa (2016). [3] meggiolaro, m.a., castro, j.t.p., an improved multiaxial rainflow algorithm for non-proportional stress or strain histories part i: enclosing surface methods, int. j. fatigue, 42 (2012) 217-226. doi:10.1016/j.ijfatigue.2011.10.014 [4] meggiolaro, m.a., castro, j.t.p., wu, h., invariant-based and critical-plane rainflow approaches for fatigue life prediction under multiaxial variable amplitude loading, procedia engineering, 101 (2015) 69-76. doi: 10.1016/ j.proeng.2015.02.010 [5] meggiolaro, m.a., castro, j.t.p., wu, h., shortcuts in multiple dimensions: the multiaxial racetrack filter, frattura ed integrità strutturale, 33 (2015) 368-375. doi: 10.3221/igf-esis.33.40 [6] wu, h., meggiolaro, m.a., castro, j.t.p., validation of the multiaxial racetrack amplitude filter, int. j. fatigue, 87 (2016) 167-179. doi: 10.1016/j.ijfatigue.2016.01.016 t m.a. meggiolaro et alii, frattura ed integrità strutturale, 38 (2016) 67-75; doi: 10.3221/igf-esis.38.09 75 [7] crossland, b., effect of large hydrostatic pressures on the torsional fatigue strength of an alloy steel. int. conf. on fatigue of metals, london: imeche (1956) 138-149. [8] bannantine, j.a., socie, d.f., a variable amplitude multiaxial fatigue life prediction method, in fatigue under biaxial and multiaxial loading, esis, 10 (1991) 35-51. [9] findley, w.n., a theory for the effect of mean stress on fatigue of metals under combined torsion and axial load or bending, j. eng. industry, 81 (1959) 301-306. [10] fatemi, a., socie, d.f., a critical plane approach to multiaxial damage including out-of-phase loading, fatigue fract. eng. mater. struct., 11 (1988) 149-166. << /ascii85encodepages false /allowtransparency false /autopositionepsfiles true /autorotatepages /none /binding /left /calgrayprofile (dot gain 20%) /calrgbprofile (srgb iec61966-2.1) /calcmykprofile (u.s. web coated \050swop\051 v2) /srgbprofile (srgb iec61966-2.1) /cannotembedfontpolicy /error /compatibilitylevel 1.4 /compressobjects /tags /compresspages true /convertimagestoindexed true /passthroughjpegimages true /createjobticket false /defaultrenderingintent /default /detectblends true /detectcurves 0.0000 /colorconversionstrategy /cmyk /dothumbnails false /embedallfonts true /embedopentype false /parseiccprofilesincomments true /embedjoboptions true /dscreportinglevel 0 /emitdscwarnings false /endpage -1 /imagememory 1048576 /lockdistillerparams false /maxsubsetpct 100 /optimize true /opm 1 /parsedsccomments true 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/pdfxoutputintentprofileselector /documentcmyk /preserveediting true /untaggedcmykhandling /leaveuntagged /untaggedrgbhandling /usedocumentprofile /usedocumentbleed false >> ] >> setdistillerparams << /hwresolution [2400 2400] /pagesize [612.000 792.000] >> setpagedevice microsoft word numero 8 art 1 e. sacco et alii, frattura ed integrità strutturale, 8 (2009) 3-20; doi: 10.3221/igf-esis.08.01 3 elementi di interfaccia per l’analisi di strutture murarie elio sacco, jessica toti università di cassino, di.m.s.a.t., via g. di biasio 43, 03043 cassino (fr), sacco@unicas.it riassunto. il presente articolo riguarda la modellazione del comportamento meccanico di elementi in muratura intesi come sistemi eterogenei composti da malta, blocchi ed interfacce di connessione. la strategia computazionale che viene adottata consiste nel modellare separatamente i blocchi, i letti di malta ed le interfacce responsabili di fenomeni di decoesione malta-blocco; a tale scopo, si propone uno speciale modello di interfaccia che combina il danneggiamento con l’attrito. si sviluppa una procedura numerica, basata sull’algoritmo backward di eulero, per risolvere il problema evolutivo; per il passo temporale si utilizza invece la tecnica predictor-corrector a controllo di spostamenti. si effettuano alcune applicazioni numeriche con lo scopo di verificare la capacità del modello e dell’algoritmo proposto nel riprodurre la risposta non lineare della muratura dovuta a fenomeni di degrado localizzati. infine, si conduce lo studio della modellazione di un arco murario, confrontando i risultati numerici con quelli sperimentali; si dimostra la abilità del modello proposto nel simulare il comportamento globale della struttura ad arco in termini di carico ultimo e di meccanismo di collasso. abstract. the present paper deals with the modelling of the mechanical behaviour of masonry elements regarded as heterogeneous systems, made of mortar, bricks and interfaces. thus, the adopted computational strategy consists in modelling the brick units, the mortar joints and the interfaces responsible for the mortarbrick decohesion mechanisms; to this end, a special interface model combining damage and friction is proposed. a numerical procedure, based on the backward euler time-integration scheme, is introduced; the time step is solved adopting a displacement driven predictor-corrector scheme. some numerical applications are performed in order to assess the performances of the proposed model and algorithm in reproducing the nonlinear response of masonry material due to damage localization. finally, a masonry arch model is studied, comparing the numerical results with experimental ones; it is show the ability of the proposed model to simulate the global behaviour of the arch structure in term of ultimate load and collapse mechanism. parole chiave. interfacce, danno, attrito, muratura, elementi finiti. introduzione n molti problemi dell’ingegneria, gli effetti non lineari dei materiali si localizzano in zone di piccolo spessore, dove si sviluppano elevati gradienti di deformazione. lo spessore di questi strati è così piccolo che spesso viene sostituito nella modellazione da interfacce, che sono particolari superfici di materiale lungo le quali si possono manifestare discontinuità di spostamento. i modelli di interfaccia sono caratterizzati da relazioni costitutive che legano le tensioni agenti su tali superfici alla discontinuità di spostamento. molte sono le formulazioni sui comportamenti di interfaccia presenti in letteratura; in particolare, alcune sono state sviluppate per simulare il graduale processo dell’apertura di una fessura, per la quale l’incipiente separazione viene impedita da sforzi coesivi, originati dall’interazione e dall’attrito tra i grani o da altri fenomeni di bridging. l’idea di adottare un modello coesivo di interfaccia è nata intorno agli anni ’60. i primi ad introdurre tale concetto furono dugdale [1] e barenblatt [2], che proposero differenti distribuzioni delle tensioni coesive. successivamente sono state i http://dx.medra.org/10.3221/igf-esis.08.01&auth=true http://www.gruppofrattura.it mailto:sacco@unicas.it e. sacco et alii, frattura ed integrità strutturale, 8 (2009) 3-20; doi: 10.3221/igf-esis.08.01 4 proposte altre modellazioni e, per la varietà di problemi di natura numerica e meccanica e per la lunga serie di possibili applicazioni esistenti, sono stati studiati e sviluppati, anche negli ultimi anni, numerosi modelli di zona coesiva. relativamente alla modellazione di interfacce in meccanica della muratura, tra gli altri, lofti and shing [3] hanno proposto un modello costitutivo di interfaccia capace di simulare l’iniziazione e la propagazione della frattura dovuta all’effetto della presenza delle tensioni normali e tangenziali agenti nella malta e considerando l’effetto della dilatanza. giambanco e di gati [4] hanno formulato un modello coesivo basato su una superficie limite del tipo bilineare alla coulomb con cut-off a trazione e legge evolutiva non associata. gambarotta e lagomarsino [5] hanno sviluppato un modello coesivo di interfaccia che considera l’effetto del danneggiamento e dell’attrito nei giunti di malta soggetti a carichi ciclici. lourenço e rots [6] e, successivamente, oliveira e lourenço [7] hanno implementato un modello costitutivo di interfaccia basato sulla teoria della plasticità, capace di simulare il comportamento ciclico della zona coesiva, riproducendo la risposta non lineare in fase di scarico. giambanco e mroz [8] hanno presentato un modello di interfase che permette di tenere in conto l’interazione fra le tensioni e le deformazioni di contatto con quelle interne al giunto che risulta separato dai blocchi attraverso due interfacce. alfano e sacco [9] hanno proposto un modello di interfaccia che combina il danneggiamento con l’attrito sulla base di una modellazione micromeccanica. tale modello è stato utilizzato per simulare alcune sperimentazioni; in particolare, è stato riprodotto il comportamento di un pannello murario tramite elementi elastici ed interfacce, che colgono il comportamento sia dei giunti di malta che delle possibili fratture nei blocchi. nel presente lavoro si introduce il modello di interfaccia sviluppato da alfano e sacco [9], al quale si apportano alcune modifiche. il modello è capace di simulare il comportamento della connessione malta-blocco. infatti, la sperimentazione mostra che il fenomeno di distacco della malta dal blocco è il maggiore responsabile della risposta non lineare della connessione tra i blocchi [10]. il legame costitutivo di interfaccia è determinato sviluppando una semplice ma sistematica analisi micromeccanica del fenomeno della decoesione e dell’attrito. tale approccio micromeccanico è stato introdotto, nell’ambito della modellazione di un mezzo continuo e coesivo, da ragueneau et al. [11]. quindi, l’approccio micromeccanico è stato rivisto da marfia et al. [12] per sviluppare un modello di interfaccia capace di accoppiare il danneggiamento con l’attrito. successivamente, è stato ripreso da uva e salerno [13] per la modellazione della malta nell’ambito di una procedura di omogeneizzazione di muratura regolare. nei paragrafi successivi, si definisce il modello di interfaccia, riportando le equazioni di stato e le leggi evolutive del danno e dell’attrito modellato tramite la teoria della plasticità. il modello proposto presenta un accoppiamento tra il danneggiamento e l’attrito derivato tramite un semplice ma razionale approccio micromeccanico. il problema evolutivo non lineare è integrato nel tempo utilizzando un algoritmo backward di eulero, mentre il passo finito è risolto tramite la tecnica predictor-corrector. sono quindi illustrate alcune applicazioni numeriche che mostrano la capacità del modello di riprodurre il comportamento dei giunti malta-blocco. quindi, si mostrano alcune applicazioni su semplici elementi strutturali per verificare la robustezza dell’algoritmo numerico implementato. infine, viene studiato il comportamento di un arco soggetto a peso proprio ed ad una forza nella prossimità della chiave, confrontando i risultati ottenuti da una sperimentazione sviluppata recentemente [14] con quelli forniti dalla modellazione proposta. modello coesivo di interfaccia n questo paragrafo viene esposto il modello coesivo di interfaccia che accoppia il danno e l’attrito. tale modello, sviluppato sulla base di quello proposto inizialmente da alfano e sacco [9], si basa su un’analisi micromeccanica. infatti, il legame costitutivo nel generico punto dell’interfaccia, che modella il comportamento della connessione malta-blocco, si ricava considerando l’elemento rappresentativo di area (rae: representative area element). in fig. 1 è illustrato schematicamente il modello micromeccanico: nel punto a dell’interfaccia malta-blocco, l’elemento rappresentativo rae della connessione a livello micromeccanico non presenta microfratture e, considerando una schematizzazione semplificata, l’area totale rappresentativa di interazione risulta completamente integra; nel punto b, il rae presenta dei parziali distacchi, ovvero delle microfratture, per cui l’area totale rappresentativa di interazione può essere ripartita in una parte danneggiata ed una integra; infine, nel punto c del giunto di malta, il rae presenta una frattura completa, per cui l’area totale rappresentativa risulta completamente danneggiata. i http://dx.medra.org/10.3221/igf-esis.08.01&auth=true http://www.gruppofrattura.it e. sacco et alii, frattura ed integrità strutturale, 8 (2009) 3-20; doi: 10.3221/igf-esis.08.01 5 figura 1: modello micromeccanico dell’interfaccia malta-blocco. in definitiva, si assume che l’area rappresentativa elementare del rae può essere divisa in una parte integra, non danneggiata, ua , e una parte completamente danneggiata, da , come illustrato in fig.1. il rapporto tra l’area danneggiata e l’area elementare considerata rappresenta il danno e viene denotato con d :  d a d a (1) per cui le due aliquote di area ua e da posso essere scritte nel seguente modo:  d ua a a (2) con    (1 ) ,u da d a a ad cinematica indicando con s il vettore spostamento relativo in corrispondenza del generico punto dell’interfaccia malta-blocco, si considera il rae soggetto ad uno spostamento medio pari ad s . si tratta allora di determinare la distribuzione degli spostamenti relativi che si verificano nel rae, che rappresenta un punto della zona di interazione malta-blocco. tale distribuzione di spostamenti relativi dovrebbe essere valutata risolvendo un opportuno modello micromeccanico. allo scopo di semplificare la trattazione, si può assumere che lo spostamento relativo possa essere considerato costante in ognuna delle due parti di area che compongono il rae. in particolare, si indica con us lo spostamento relativo nella parte di area non danneggiata ua e con ds quello in corrispondenza della zona danneggiata da . il vettore spostamento relativo sulla parte danneggiata del rae risulta diviso in una aliquota elastica des ed una inelastica dis :   d de dis s s (3) mentre il vettore spostamento relativo, che interessa la zona non danneggiata, è totalmente elastico:  u ues s (4) gli spostamenti relativi us e ds , nello spirito dell’analisi micromeccanica, si possono determinare in funzione dello spostamento relativo medio s in rae ricorrendo all’uso di opportuni tensori di localizzazione da e ua , così che d ds a s and u us a s . un approccio ulteriormente semplificato del problema micromeccanico, che conduce zona di processo frattura a b parte integra au=a ad=0 microscala (rae) representative area element parte integra parte danneggiata au ad parte danneggiata au=0 ad=a b c a c interfaccia integra t n t n t n t n malta blocco malta blocco malta blocco malta blocco http://dx.medra.org/10.3221/igf-esis.08.01&auth=true http://www.gruppofrattura.it e. sacco et alii, frattura ed integrità strutturale, 8 (2009) 3-20; doi: 10.3221/igf-esis.08.01 6 comunque ad una formulazione molto soddisfacente relativamente al problema micromeccanico in esame, fu proposto da voigt [15], assumendo  d ua a i . quindi, per l’ipotesi appena introdotta, vale l’uguaglianza:   u ds s s (5) il vettore spostamento relativo ha componenti   t n ts ss , avendo indicato rispettivamente con gli indici n e t le componenti nella direzione normale e tangente all’interfaccia, in accordo con il sistema di riferimento locale illustrato in fig. 1. legame costitutivo le tensioni di interfaccia sono differenti sulla parte del rae danneggiata e su quella non danneggiata. le tensioni relative all’area danneggiata si denotano con uτ e sono legate agli spostamenti us attraverso un matrice diagonale k in cui sono contenuti i valori di rigidezza nella direzione normale e tangenziale dell’interfaccia. considerando l’eq. (5), si può scrivere la seguente relazione:         0 0 nu t k k τ k s k (6) sulla parte di area danneggiata le tensioni sono indicate con dτ e sono legate agli spostamenti elastici di tale zona tramite la seguente espressione :          ( ) d de diτ ks k s s k s c p (7) dove il vettore degli spostamenti anelastici è decomposto in un vettore che tiene conto del contatto unilatero e in un vettore che tiene conto dell’effetto di attrito; con si denota la funzione di heaviside, pari a se , se il valore di tensione dell’interfaccia sull’area elementare rappresentativa viene indicato con τ e si ottiene come somma pesata dei due valori dτ e uτ come segue:                    1 1 ( ) ( ) u dd d d d d τ τ τ k s k s c p k s c p (8) le componenti di tensione normali e tangenziali dei vettori τ , dτ e uτ vengono indicate, rispettivamente, con:                                 , , u d n n nu d u d t t t τ τ τ (9) leggi evolutive lo spostamento relativo inelastico , che fisicamente rappresenta lo slittamento che avviene sulla zona danneggiata del rae, è governato dalla classica legge di attrito di coulomb:  dis c p   ( ) tn n th s s sc   0 ttpp  h    1h x  0x    0h x  0x p http://dx.medra.org/10.3221/igf-esis.08.01&auth=true http://www.gruppofrattura.it e. sacco et alii, frattura ed integrità strutturale, 8 (2009) 3-20; doi: 10.3221/igf-esis.08.01 7           d d d d d n t n tτ (10) dove  rappresenta il coefficiente di attrito e il simbolo   denota la parte negativa della tensione inelastica. per l’evoluzione di p si considera la legge non associata:                         00 d t dd tt d d p (11) insieme alle condizioni di khun-tucker: (12) relativamente all’evoluzione del parametro di danno d si considera un modello che tiene conto dell’accoppiamento della frattura del modo i e del modo ii. vengono infatti definite due quantità n e t che dipendono dalle tensioni di picco  0n e  0 t , dagli spostamenti relativi di prima fessurazione 0 ns e 0ts e dalle energie specifiche di frattura cng e ctg :      0 0 0 0, 2 2 n n t t n t cn ct s s g g (13) si definisce un parametro  che lega i due modi di apertura di frattura:        2 2 2 1 1 n n t ts s (14) con  parte positiva dell’argomento e  che dipende dalle componenti di spostamento relativo:     2 2 n ts s (15) il parametro di danno è valutato quindi attraverso la seguente relazione:   max min 1, history d d (16) dove:           1 1 d (17) essendo                2 2 0 0 1n t n t s s s s (18) procedura numerica i espone la procedura numerica adottata per la valutazione della risposta meccanica del modello di interfaccia caratterizzato dalle relazioni costitutive precedentemente introdotte. le equazioni evolutive sono integrate nel tempo adottando una procedura del tipo backward di eulero con controllo degli spostamenti relativi. s         0, 0, 0d dτ τ http://dx.medra.org/10.3221/igf-esis.08.01&auth=true http://www.gruppofrattura.it e. sacco et alii, frattura ed integrità strutturale, 8 (2009) 3-20; doi: 10.3221/igf-esis.08.01 8 il processo di analisi viene infatti diviso in un numero finito di passi; all’istante nt si assume nota la soluzione, le quantità valutate al tempo nt sono contraddistinte dal pedice , mentre le quantità al tempo attuale 1nt non presentano alcun indice. lo schema di integrazione adottato è il seguente: si assume noto lo spostamento relativo di interfaccia s ; si determina il valore del parametro di danno d tramite le formule (14)-(18); si valuta la tensione di prova della zona danneggiata attraverso l’espressione:    ( )del nτ k s c p (19) si determina il valore della funzione limite   delτ utilizzando la formula (10). se    0delτ ,  np p e d delτ τ ; se    0delτ lo spostamento inelastico deve essere aggiornato tramite le seguenti relazioni:                      0 1d d d t eln n el t el td t el k p p (20) si determina la tensione all’interfaccia tramite l’eq. (8). la procedura di integrazione descritta è implementata in un elemento finito interfaccia a quattro nodi, con due gradi di libertà per nodo, e spessore nullo. in definitiva, nel generico passo temporale finito, si tratta di risolvere il sistema algebrico non lineare scritto in forma residuale:               ˆ; ˆˆ ˆ ˆ; r λ u u f 0 r λ u u f 0 (21) dove i vettori u e û rappresentano gli spostamenti nodali liberi incogniti e vincolati, rispettivamente, mentre f e f̂ sono le forze esterne assegnate e le reazioni vincolari incognite. il problema algebrico non lineare è risolto sviluppando una procedura iterativa di tipo newton-raphson; alla k-esima iterazione, la soluzione si determina tramite le relazioni:                   11 , 1 , 1 ˆ ˆ ˆ k t k k k k t k k uu uu u k r f r k u (22) dove             , , ˆ ˆ t k t k k k uu uu r r k k u u (23) la successione converge quando i residui  kr e ˆ kr tendono a zero. si definisce errore alla k-esima iterazione, la quantità scalare:  1 k ke r r (24) la soluzione viene considerata soddisfacente quando accade che l’errore è più piccolo di una prefissata tolleranza, ke tol . il calcolo delle matrici tangenti   ,t k uu k e  , ˆ t k uu k richiedono la determinazione della derivata consistente con l’algoritmo di integrazione nel tempo del legame τ s . si tratta allora di determinare la derivata  /τ s . tenuto conto dell’eq. (8) si ha: n http://dx.medra.org/10.3221/igf-esis.08.01&auth=true http://www.gruppofrattura.it e. sacco et alii, frattura ed integrità strutturale, 8 (2009) 3-20; doi: 10.3221/igf-esis.08.01 9                               ( ( )t d d d τ c p k k s c p k i c p s s s s s (25) la derivata del temine  /d s è nulla quando non c’è evoluzione del danno, cioè quando  nd d ovvero  1d ; tenuto conto della formula (17), si ha:                                se 1 1 se 1 n n n d d d d d d d d d d d d d 0 s s s (26) dove, tenendo conto delle eq. (14)-(18), si ha:                                       22 4 1 1 1 2 1 1 n t d d qs as s s (27) essendo                            2 2 0 2 2 0 1 0 0 10 0 t n n n t t s s s s s s q a s (28) sostituendo le espressioni delle derivate parziali si ottiene:                          24 2 34 3 1 2 1 1 n t d a q s ps s (29) la derivata del temine è diversa da zero solo quando la componente del vettore di spostamento relativo è positivo, in esplicito si ha:       se 0 / se 0 n n s s 0 c s i (30) per quanto riguarda il termine  /p s , si può verificare il caso in cui nel passo finito non avviene evoluzione dello spostamento relativo inelastico,   0 , oppure c’è evoluzione dello slittamento dovuto all’attrito,   0 . nel primo caso la derivata è nulla, mentre nel secondo è diversa da zero solo se la componente di spostamento relativo ns assume valore non positivo. in definitiva si ha:                    0 0 0 e 01 1/ altrimenti d d t el n n d t t el s k k τ p s 0 (31)  /c s ns http://dx.medra.org/10.3221/igf-esis.08.01&auth=true http://www.gruppofrattura.it e. sacco et alii, frattura ed integrità strutturale, 8 (2009) 3-20; doi: 10.3221/igf-esis.08.01 10 applicazioni numeriche l modello di interfaccia e la procedura numerica proposta nei paragrafi precedenti sono stati utilizzati per sviluppare alcune applicazioni numeriche. si tratta di tre tipologie di applicazione. nella prima parte si riportano i risultati di alcuni dei calcoli effettuati, che hanno avuto lo scopo di verificare le capacità del modello a riprodurre il comportamento delle interfacce coesive. nella seconda parte si sviluppano alcune analisi di semplici elementi strutturali per verificare la correttezza e le capacità di convergenza della procedura numerica implementata. nella terza parte viene invece presentata l’applicazione riguardante la modellazione agli elementi finiti di un arco in muratura, la cui risposta in termini di curve forza-spostamento, ottenuta numericamente, viene confrontata con dei risultati sperimentali derivati da una campagna di indagine effettuata precedentemente presso il laboratorio di analisi e progettazione strutturale dell’università di cassino, discussi in dettaglio in [14]. comportamento dell’interfaccia si riportano in tale paragrafo alcuni esempi di risposta meccanica del modello di interfaccia al fine di evidenziarne alcuni aspetti peculiari. i parametri di interfaccia considerati nell’analisi sono riportati in tab.1. 0 n [n/mm2] cng [n/mm] nk [n/mm3] 0 t [n/mm2] ctg [n/mm] tk [n/mm3]  3 0.3 150 3 0.3 150 0.5 tabella 1: parametri di interfaccia del modo i e del modo ii. una caratteristica importante del legame di interfaccia introdotto è il comportamento attritivo che viene mostrato attraverso la determinazione delle diverse curve  t ts , ottenute incrementando il valore della componente di spostamento relativo tangenziale ts ed assegnando e mantenendo costante durante la storia di carico quella normale ns . come si può notare dalla fig. 2, la risposta meccanica è caratterizzata dal raggiungimento di una maggiore resistenza tangenziale di picco per i processi di carico contraddistinti da un valore di spostamento normale negativo più elevato in valore assoluto. inoltre, per le curve caratterizzate da  0ns , si ha un comportamento lineare fino al raggiungimento di  0n , quindi si ottiene un andamento crescente non lineare fino al raggiungimento di una resistenza di picco max . infine, ad un aumento ulteriore dello spostamento ts corrisponde un decremento di tensione tangenziale, fino al raggiungimento del valore   t n , in corrispondenza del quale il parametro di danno risulta pari ad 1 e la resistenza tangenziale, che rimane costante con ns , è solo dovuta all’effetto dell’attrito. figura 2: curve  -t ts per differenti valori di ns . 0.00 1.00 2.00 3.00 4.00 5.00 6.00 7.00 8.00 9.00 0.00 0.05 0.10 0.15 0.20 0.25 s t [mm]  t [n/mm 2 ] s1=-0.1 s1=-0.05 s1=-0.02 s1=0 s1=0.01 s1=0.05 s= -0.1 s n =0.1 s n =0.05 s n =0.02 sn = 0 sn = 0.01 sn = 0.05 sn =-0.1 sn =-0.05 sn =-0.02 sn = 0 sn = 0.01 sn = 0.05 st [mm] t [n/mm2] 0.00 1.00 2.00 3.00 4.00 5.00 6.00 7.00 8.00 9.00 0.00 0.05 0.10 0.15 0.20 0.25 s t [mm]  t [n/mm 2 ] s1=-0.1 s1=-0.05 s1=-0.02 s1=0 s1=0.01 s1=0.05 s= -0.1 s n =0.1 s n =0.05 s n =0.02 sn = 0 sn = 0.01 sn = 0.05 sn =-0.1 sn =-0.05 sn =-0.02 sn = 0 sn = 0.01 sn = 0.05 st [mm] t [n/mm2] i http://dx.medra.org/10.3221/igf-esis.08.01&auth=true http://www.gruppofrattura.it e. sacco et alii, frattura ed integrità strutturale, 8 (2009) 3-20; doi: 10.3221/igf-esis.08.01 11 nel caso in cui, al contrario, è assegnato e mantenuto costante durante tutta la storia di carico uno spostamento normale positivo (  0ns ), la resistenza di piccomax non raggiunge mai  0 n ; inoltre, nel caso in cui si ha  0n ns s , anche nel tratto iniziale si può avere un forte comportamento non lineare, perché già all’inizio dell’analisi si ha danneggiamento per effetto della decoesione. un altro caso di analisi molto interessante è la risposta meccanica di interfaccia a seguito di una storia di carico ciclica, in cui la componente di spostamento ts assume ai vari tempi i valori riportati in tab.2, mentre la componente lungo la direzione normale viene invece mantenuta costante. tempo [s] ns [mm] ts [mm] 0 -0.07 0 1 -0.07 0.08 2 -0.07 -0.10 3 -0.07 0.30 tabella 2: storia di carico. figura 3: curva -t ts ottenuta da una storia di carico ciclica. l’andamento della tensione tangenziale in funzione dello spostamento relativo ts è riportato in fig. 3 ed è caratterizzata dal comportamento descritti come segue. dall’origine al punto (a): durante questa fase di carico il comportamento dell’interfaccia è inizialmente lineare; si manifesta in seguito un danno parziale che porta ad un comportamento non lineare e allo sviluppo dell’effetto di attrito sulla parte del rae danneggiato. dal punto (a) al punto (b): fase di scarico durante la quale non si ha evoluzione del danno. la risposta è lineare e la pendenza della curva coincide con quella del tratto iniziale della prima fase di carico. dal punto (b) al punto (c): la curva cambia di pendenza perché si sviluppano spostamenti inelastici negativi senza evoluzione del danno. dal punto (c) al punto (d): in tale tratto avviene un aumento del parametro di danno. dal punto (d) al punto (e): durante questa fase di ricarico si osserva una pendenza del ramo coincidente con quella del tratto iniziale della prima fase di carico. dal punto (e) al punto (f): la curva cambia di pendenza perché si sviluppano spostamenti inelastici senza evoluzione del danno. st [mm]st [mm] -8.00 -6.00 -4.00 -2.00 0.00 2.00 4.00 6.00 8.00 -0.10 -0.05 0.00 0.05 0.10 0.15 0.20 0.25 0.30 st [mm] tt[n/mm2]t [n/mm2] f) b) e) g) c)d) a) st [mm]st [mm] -8.00 -6.00 -4.00 -2.00 0.00 2.00 4.00 6.00 8.00 -0.10 -0.05 0.00 0.05 0.10 0.15 0.20 0.25 0.30 st [mm] tt[n/mm2]t [n/mm2] st [mm]st [mm] -8.00 -6.00 -4.00 -2.00 0.00 2.00 4.00 6.00 8.00 -0.10 -0.05 0.00 0.05 0.10 0.15 0.20 0.25 0.30 st [mm] tt[n/mm2]t [n/mm2] f) b) e) g) c)d) a) http://dx.medra.org/10.3221/igf-esis.08.01&auth=true http://www.gruppofrattura.it e. sacco et alii, frattura ed integrità strutturale, 8 (2009) 3-20; doi: 10.3221/igf-esis.08.01 12 dal punto (f) al punto (g): si ha una evoluzione del parametro di danno fino a raggiungimento di decoesione completa in cui  1d e la resistenza residua è dovuta solo all’effetto di attrito. analisi di un elemento strutturale si considera un semplice pannello rettangolare di dimensioni b h , vincolato tramite interfaccia al suolo rigido, come schematicamente illustrato in fig. 4. il pannello è caratterizzato dalle seguenti proprietà geometriche e meccaniche:  1000 mmb ,  1000 mmh , spessore  1 mms , modulo elastico  10000 mpae , rapporto di poisson   0.25 . si adotta per il pannello una mesh regolare di 5x5 elementi isoparametrici a 4 nodi e si utilizzano di conseguenza 5 elementi interfaccia a 4 nodi per simulare l’effetto del contatto parete-suolo. la storia di carico consiste nell’applicare sul lato cd del pannello un carico verticale costante uniformemente distribuito  1 n/mmq ed imporre sempre sul lato cd uno spostamento orizzontale crescente  , il cui valore ultimo all’istante finale dell’analisi sia pari a 1 mm. figura 4: pannello rettangolare vincolato tramite interfaccia ad un corpo rigido. si effettuano tre differenti analisi in cui si calibrano opportunamente i valori delle proprietà meccaniche dell’interfaccia al fine di verificare, per il prefissato valore di spostamento ultimo applicato nella sommità della parete, separatamente e insieme il comportamento unilatero e attritivo dell’interfaccia. ciascuna classe di parametri assegnati all’interfaccia costituisce un differente materiale e i rispettivi valori sono riportati in tab. 3. in realtà, si può osservare dai dati riportati nella tabella che i tre materiali sono caratterizzati da diverse proprietà meccaniche unicamente nella direzione tangenziale. materiale 0 n [n/mm2] cng [n/mm] nk [n/ mm3] 0 t [n/ mm2] ctg [n/mm] tk [n/mm3]  1 2 0.3 760 3 0.3 760 0.3 2 2 0.3 760 1 0.03 760 0.3 3 2 0.3 760 0.03 0.003 760 0.3 tabella 3: parametri del modo i e del modo ii per i tre materiali di interfaccia. la risposta meccanica del pannello viene fornita in termini di forza orizzontale totale in funzione di alcune componenti di spostamento nodali. la forza orizzontale totale t è stata valutata sommando le reazioni nodali espletate dai vincoli applicati nella sommità della parete. nei grafici che seguono vengono mostrate le differenti risposte del pannello per i tre materiali di interfaccia considerati ed, in particolare, si riporta: nella fig. 5, l’andamento di t in funzione della componente orizzontalec del punto c; nella fig. 6, l’andamento di t in funzione della componente verticalec del punto c; nella fig. 7, l’andamento di t in funzione della componente di spostamento orizzontaleb del punto b. http://dx.medra.org/10.3221/igf-esis.08.01&auth=true http://www.gruppofrattura.it e. sacco et alii, frattura ed integrità strutturale, 8 (2009) 3-20; doi: 10.3221/igf-esis.08.01 13 figura 5: forza orizzontale totale t in funzione della componente di spostamento c. figura 6: forza orizzontale totale t in funzione della componente di spostamento c. figura 7: forza orizzontale totale t in funzione della componente di spostamento b. 0 0.2 0.4 0.6 0.8 1 1.2 1.4 0.00 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90 1.00 c mm t[n] materiale 1 materiale 2 materiale 3 0.5 resistenza limite teorica 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 c[mm] t[n] materiale 1 materiale 2 materiale 3 0 0.2 0.4 0.6 0.8 1 1.2 1.4 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 b[mm] t[n] materiale 1 materiale 2 materiale 3 http://dx.medra.org/10.3221/igf-esis.08.01&auth=true http://www.gruppofrattura.it e. sacco et alii, frattura ed integrità strutturale, 8 (2009) 3-20; doi: 10.3221/igf-esis.08.01 14 nella fig. 8, invece, vengono mostrate per ciascun materiale di interfaccia utilizzato le configurazioni di equilibrio della parete in corrispondenza di tre valori di spostamento orizzontale del nodo c. in particolare viene riportata: nella fig. 8a il cinematismo sviluppato dal pannello con interfaccia di materiale 1, nella fig. 8b, il cinematismo sviluppato dal pannello con interfaccia di materiale 3 e, nella fig. 8c, il cinematismo sviluppato dal pannello con interfaccia di materiale 2. la scelta del materiale 1 permette di verificare prevalentemente il comportamento unilatero dell’interfaccia; infatti, dalla fig. 8a si osserva che la parete tende a sviluppare un cinematismo di ribaltamento intorno al punto b. le componenti di spostamento orizzontale e verticale del punto c risultano dello stesso ordine di grandezza (vedi fig. 5 e fig. 6) mentre la componente di spostamento orizzontale del punto b è quasi assente (vedi fig. 7). inoltre, nel grafico di fig. 5 viene riportato anche il valore del carico limite ottenuto analiticamente tramite una semplice equazione di equilibrio alla rotazione del pannello intorno al polo b. si può osservare che il valore di resistenza ultima ottenuto numericamente tende al valore di 0.5n che è in pieno accordo con la previsione teorica dedotta dall’equilibrio. nell’applicazione effettuata con il materiale 3, si verifica sostanzialmente il comportamento attritivo dell’interfaccia. infatti, riducendo di due ordini di grandezza i valori delle proprietà meccaniche in direzione tangenziale rispetto ai quelli normali, si favorisce un cinematismo di un puro scorrimento della parete rispetto al suolo rigido (vedi fig. 8b). le componenti orizzontali dei punti b e c crescono indefinitamente con una resistenza allo slittamento costante e pari a 0.3n dovuta unicamente all’effetto dell’attrito parete-suolo (vedi fig. 5 e fig. 7), mentre l’andamento della componente verticale del punto c risulta trascurabile (vedi fig. 6). infine, è stata eseguita un’ultima analisi in cui si sono utilizzati i valori delle proprietà meccaniche relativi all’interfaccia di materiale 2. in tal caso, considerando parametri caratteristici del modo ii intermedi tra quelli del materiale 1 e del materiale 3, si è riusciti a cogliere insieme il comportamento unilatero e attritivo dell’interfaccia. il pannello, infatti, nella fase iniziale dell’analisi tende a ruotare in senso orario intorno al polo b e da un certo istante in poi inizia a ritornare nella configurazione non ruotata continuando contemporaneamente a scorrere rispetto al suolo rigido (vedi fig. 8c). si può osservare dal grafico di fig. 6 che avviene un sollevamento della parete e quindi la sua rotazione fin quando la componente verticale del punto c assume valore di 0.5 mm. la parete invece torna nella configurazione non ruotata in corrispondenza di uno spostamento orizzontale del nodo b e c di circa 0.7 mm, superato tale valore si attiva il meccanismo di puro scorrimento con una resistenza allo slittamento dovuta unicamente all’effetto dell’attrito parete-suolo (vedi fig. 5 e fig. 7). i risultati numerici delle applicazioni svolte hanno quindi messo in evidenza che la risposta dell’elemento finito interfaccia è perfettamente coerente al comportamento del modello di interfaccia sviluppato. inoltre, le elaborazioni numeriche sviluppate hanno mostrato l’affidabilità dello strumento di calcolo realizzato, il quale è stato successivamente utilizzato come mezzo di analisi per un’applicazione ingegneristica significativa. figura 8: a) ribaltamento (comportamento unilatero); b) scorrimento (comportamento attritivo); c) ribaltamento-scorrimento (comportamento unilatero e attritivo). http://dx.medra.org/10.3221/igf-esis.08.01&auth=true http://www.gruppofrattura.it e. sacco et alii, frattura ed integrità strutturale, 8 (2009) 3-20; doi: 10.3221/igf-esis.08.01 15 analisi di un arco in muratura e’ stata sviluppata un’analisi numerica di un arco in muratura per il quale si è effettuata una sperimentazione presso il laboratorio di analisi e progettazione strutturale, dell’università di cassino da parte di cancelliere et al. [14], dove vengono riportati tutti i dati ed i risultati relativi all’attività sperimentale. si tratta di un arco che geometricamente assume l’aspetto di un settore di corona circolare, come illustrato in fig. 9. i dati geometrici dell’arco sono i seguenti: raggio esterno  560 mmestr , raggio interno int 440 mmr , spessore  250 mms , anomalia di imposta   8or . l’arco è realizzato con 23 blocchi e 22 malte di allettamento. le caratteristiche meccaniche dei materiali costituenti l’arco sono state dedotte da opportune prove sperimentali, riportate in dettaglio in 0; il modulo elastico, il rapporto di poisson e la resistenza a compressione del mattone e della malta valgono rispettivamente:  216000 n/mmbe   0.2b   238.5 n/mmyb  21500 n/mmme   0.2m   24.5 n/mmym il peso per unità di volume del blocco e della malta è pari a   317 kn/mmb   320 kn/mmm . figura 9: modello geometrico dell’arco. l’arco è soggetto inizialmente al peso proprio e quindi ad una forza concentrata crescente diretta verso il basso, applicata mediante l’azione espletata dal martinetto sull’estradosso dell’arco in corrispondenza del centro del 14° mattone, come illustrato in fig. 10. l’arco è vincolato alle imposte in modo da impedire scorrimenti orizzontali; in tal modo si è favorito un cinematismo di collasso caratterizzato dalla formazione delle quattro classiche cerniere, due di intradosso e due di estradosso (vedi fig. 10). in particolare, dalla sperimentazione si è ottenuto che la prima cerniera si forma sull’estradosso tra la malta 13 ed il mattone 14, la seconda cerniera si forma sull’intradosso tra la malta 7 ed il mattone 7, quindi si forma la cerniera sull’estradosso tra il mattone 1 e la malta 1, ed infine all’intradosso tra il mattone 19 e la malta 19, come illustrato in dettaglio nelle fotografie riportate in fig. 11. x y o rint rest c r x y o rint rest c r http://dx.medra.org/10.3221/igf-esis.08.01&auth=true http://www.gruppofrattura.it e. sacco et alii, frattura ed integrità strutturale, 8 (2009) 3-20; doi: 10.3221/igf-esis.08.01 16 figura 10: arco sperimentale: numerazione dei mattoni e cinematismo di collasso. figura 11: immagini delle posizione delle cerniere dell’arco. per la modellazione dell’arco in muratura si è adottato un approccio micromeccanico, in cui i mattoni e la malta sono modellati con elementi continui mentre le interfacce blocchi-malta o mattone-base di appoggio dell’arco con superfici di discontinuità. in particolare per la malta e il mattone si sono utilizzati elementi bidimensionali elastici e il numero delle superfici di discontinuità che si sono considerate nella modellazione sono 24 e vengono simulate da elementi interfaccia a quatto nodi. figura 12: discretizzazione (nh=3, nb=5 e nm=2) e vincoli. 1° 2° 3° 4° 1° 2° 3° 4° elemento del mattone b h elemento di interfaccia m elemento della malta t=0 elemento del mattone b h elemento di interfaccia m elemento della malta t=0 http://dx.medra.org/10.3221/igf-esis.08.01&auth=true http://www.gruppofrattura.it e. sacco et alii, frattura ed integrità strutturale, 8 (2009) 3-20; doi: 10.3221/igf-esis.08.01 17 nei calcoli effettuati sono state considerate diverse discretizzazioni dell’arco; i parametri utilizzati per individuare le differenti discretizzazioni sono nh, nb e nm che rappresentano rispettivamente il numero di divisioni con cui viene discretizzata l’altezza h del mattone, la base b del mattone e lo strato di malta. in fig. 12 è riportato un esempio della mesh nel caso in cui nh=3, nb=5 e nm=2. in realtà, i difetti e le irregolarità dei letti di malta, che si hanno durante le procedure di messa in opera dell’arco, hanno ridotto la sezione di contatto tra un blocco e l’altro (vedi fig. 11). questo importante aspetto è stato tenuto in conto nelle simulazione numeriche considerando per il parametro b, a seguito di un indagine statistica, non l’effettiva dimensione della base del mattone ma la sua reale lunghezza ridotta di 14 mm. nelle simulazioni numeriche si è scelto di riprodurre l’azione del carico applicato sull’arco tramite martinetto, applicando una forza incrementale lungo le direzione y del sistema di riferimento in corrispondenza del nodo centrale superiore della base del mattone 14°. allo scopo di seguire completamente la risposta meccanica dell’arco, l’analisi numerica è stata svolta utilizzando una tecnica arc-length con controllo locale dello spostamento verticale del nodo in cui è applicato il carico. le proprietà meccaniche degli elementi interfaccia sono state tarate andando a considerare uno strato di malta unitario. 0 n [n/mm2] cng [n/mm] nk [n/ mm3] 0 t [n/ mm2] ctg [n/mm] tk [n/ mm3]  0.3 0.3 1500 3 0.3 1500 0.5 tabella 4: parametri di interfaccia del modo i e del modo ii. nelle prime tre modellazioni realizzate si sono scelti per i parametri nh e nm i medesimi valori e pari rispettivamente a 2 e 1, mentre si è variato il parametro nb assumendo in ordine di esecuzione dei modelli valore 5, 10 e 20. i risultati delle analisi numeriche sono mostrati nel grafico di fig. 13, in cui si riporta l’andamento della forza verticale applicata in funzione dello spostamento incrementale negativo applicato. inoltre, sulla base del cinematismo di collasso caratterizzato dalla formazione delle quattro cerniere, il carico ultimo è stato anche valutato tramite il teorema cinematico dell’analisi limite, il quale ha fornito un valore di resistenza ultima pari a 650 n. figura 13: risultati del primo gruppo di analisi. dal confronto delle analisi numeriche del primo gruppo di modellazioni insieme ai risultati sperimentali e all’analisi limite (vedi fig.13) emerge che: aumentando la discretizzazione lungo la base del mattone, il risultato numerico si avvicina a quello sperimentale; le tre modellazioni convergono ad uno stesso risultato, poiché quest’ultimo non dipende fortemente dalla mesh adottata; le analisi numeriche risultano stabili; il carico di collasso dedotto dall’analisi limite rappresenta il limite superiore della resistenza ultima dell’arco. nella fig. 14 si possono osservare, per le differenti discretizzazioni strutturali dell’arco delle prime tre modellazioni eseguite, nella sua parte sinistra, le configurazioni indeformate del solido murario mentre in quella di destra, le corrispondenti configurazioni deformate ottenute nell’istante finale dell’analisi in corrispondenza di uno spostamento -900 -650 -400 -150 100 350 -0.10-0.08-0.06-0.04-0.020.00 f [n] v [mm] risultati sperimentali nh=2; nb=5; nm=1 nh=2; nb=10; nm=1 nh=2; nb=20; nm=1 analisi limite risultati numerici: -900 -650 -400 -150 100 350 -0.10-0.08-0.06-0.04-0.020.00 f [n] v [mm] risultati sperimentali nh=2; nb=5; nm=1 nh=2; nb=10; nm=1 nh=2; nb=20; nm=1 analisi limite risultati numerici: risultati sperimentali nh=2; nb=5; nm=1 nh=2; nb=10; nm=1 nh=2; nb=20; nm=1 analisi limite risultati numerici: http://dx.medra.org/10.3221/igf-esis.08.01&auth=true http://www.gruppofrattura.it e. sacco et alii, frattura ed integrità strutturale, 8 (2009) 3-20; doi: 10.3221/igf-esis.08.01 18 verticale del punto di applicazione della forza pari a 0.1 mm. dalle deformate delle tre modellazioni, si può evidenziare che le discontinuità locali di spostamento si sono ottenute esattamente in quelle zone in cui sperimentalmente si sono manifestate le fessure. figura 14: a) configurazione indeformata; b) configurazione deformata. figura 15: risultati del secondo gruppo di analisi. -900 -650 -400 -150 100 350 -0.10-0.08-0.06-0.04-0.020.00 risultati sperimentali nh=2; nb=10; nm=1; 3 punti di gauss nh=2; nb=20; nm=1; 3 punti di gauss analisi limite risultati numerici: f [n] v [mm] -900 -650 -400 -150 100 350 -0.10-0.08-0.06-0.04-0.020.00 risultati sperimentali nh=2; nb=10; nm=1; 3 punti di gauss nh=2; nb=20; nm=1; 3 punti di gauss analisi limite risultati numerici: risultati sperimentali nh=2; nb=10; nm=1; 3 punti di gauss nh=2; nb=20; nm=1; 3 punti di gauss analisi limite risultati numerici: f [n] v [mm] http://dx.medra.org/10.3221/igf-esis.08.01&auth=true http://www.gruppofrattura.it e. sacco et alii, frattura ed integrità strutturale, 8 (2009) 3-20; doi: 10.3221/igf-esis.08.01 19 sono state in seguito effettuate un secondo gruppo di analisi in cui si è incrementato da 2 a 3 il numero di punti di gauss per gli elementi interfaccia. dai risultati riportati in fig. 15 emerge che: aumentando il numero dei punti di gauss, le analisi convergono ad uno stesso valore del carico ultimo indipendentemente dalla mesh; le analisi numeriche risultano stabili. conclusioni a modellazione strutturale attraverso l’utilizzo dei modelli di interfaccia risulta uno strumento efficace nello studio del comportamento delle strutture eterogenee, come quelle in muratura. infatti in queste ultime la principale causa della risposta non lineare è dovuta generalmente a fenomeni di degrado che tendono a localizzarsi in corrispondenza delle superfici di contatto mattone-malta. nel presente lavoro il fenomeno di distacco giunto di malta-blocco viene simulato attraverso una versione modificata del modello costitutivo di interfaccia proposto inizialmente da alfano e sacco. le applicazioni numeriche, eseguite su semplici elementi strutturali, hanno mostrato la capacità del modello a riprodurre il comportamento non lineare dell’interfaccia giunto di malta mattone e la robustezza dell’algoritmo implementato nel portare a termine le analisi. successivamente, l’applicazione riguardante l’arco murario ha dimostrato come i modelli e i metodi di calcolo proposti riescano a riprodurre il graduale sviluppo dei meccanismi di degrado che si localizzano in alcune zone del solido murario prima ancora che esso giunga a collasso. i risultati numerici, messi a confronto con quelli sperimentali, hanno confermato una buona corrispondenza in termini quantitativi. infatti l’andamento della curva forza – spostamento, ottenuta nel corso della sperimentazione è prossima a quella ricavata dalla simulazione. inoltre, grazie al particolare modello di interfaccia implementato, si è riusciti a cogliere molto bene il cinematismo di collasso sviluppato dall’arco nel corso della prova, poiché le discontinuità locali di spostamento si sono ottenute esattamente in quelle zone in cui sperimentalmente si sono manifestate le fessure. i risultati conseguiti nel presente lavoro hanno provato che il modello di interfaccia introdotto insieme alla procedura numerica implementata hanno consentito un’analisi affidabile della risposta non lineare del solido murario, per cui in futuro il loro utilizzo potrebbe essere esteso ad ulteriori applicazioni in cui sia fondamentale non trascurare quei fenomeni di degrado che si sviluppano in certe zone critiche della muratura. ringraziamenti i ringrazia il consorzio universitario reluis (dipartimento della protezione civile) per il finanziamento che ha reso possibile questa attività di ricerca. bibliografia [1] d.s. dugdale, journal of mechanics and physics of solids, 8 (1960) 100-104. [2] g.i. barenblatt, advances in applied mechanics, 7 (1962) 55-129. [3] h.r. lotfi, p.b. shing, journal of structural engineering, 120(1) (1994) 63-80. [4] g. giambanco, l. di gati, mechanics renear& communications, 24(5) (1997) 503-512. [5] l. gambarotta, s. lagomarsino, earthquake engineering and structural dynamics, 26 (1997). [6] p.b. lourenço, j. rots, journal of engineering mechanics, asce, 123(7) (1997) 660-668. [7] d.v. oliveira, p.b. lourenço, computers and structures, 82 (2004) 1451–1461. [8] g. giambanco, z. mroz, meccanica 36 (2001) 111–130. [9] g. alfano, e. sacco, international journal for numerical methods in engineering; 68 (2006) 542–582. [10] f. fouchal, f. lebon, i. titeux, construction and building materials, doi:10.1016/j.conbuildmat.2008.10.011. [11] f. ragueneau, ch. la borderie, j. mazars, mechanics of cohesive-frictional materials, 5 (2000) 607-625. l s http://dx.medra.org/10.3221/igf-esis.08.01&auth=true http://www.gruppofrattura.it e. sacco et alii, frattura ed integrità strutturale, 8 (2009) 3-20; doi: 10.3221/igf-esis.08.01 20 [12] s. marfia, g. alfano, e. sacco, proceedings of the 4th european congress on computational methods in applied science and engineering, eccomas 2004, jyvaskyla, finlandia, july 24-28, 2004. [13] g. uva, g. salerno, international journal of solids and structures, 43 (2006) 3739–3769. [14] i. cancelliere, m. imbimbo, e. sacco, numerical and experimental study of masonry arches. submitted for the publication, (2008). [15] t. mura, micromechanics of defects in solids. second, revised edition. martinus. (1987). http://dx.medra.org/10.3221/igf-esis.08.01&auth=true http://www.gruppofrattura.it microsoft word numero_38_art_37 f. majid et alii, frattura ed integrità strutturale, 38 (2016) 273-280; doi: 10.3221/igf-esis.38.37 273 focussed on multiaxial fatigue and fracture pressure vessels design methods using the codes, fracture mechanics and multiaxial fatigue fatima majid, jilali nattaj, mohamed elghorba university of hassan ii, national superior school of electricity and mechanics casablanca (ensem) lccmms majidfatima9@gmail.com, http://orcid.org/0000-0001-8909-8232 abstract. this paper gives a highlight about pressure vessel (pv) methods of design to initiate new engineers and new researchers to understand the basics and to have a summary about the knowhow of pv design. this understanding will contribute to enhance their knowledge in the selection of the appropriate method. there are several types of tanks distinguished by the operating pressure, temperature and the safety system to predict. the selection of one or the other of these tanks depends on environmental regulations, the geographic location and the used materials. the design theory of pvs is very detailed in various codes and standards api, such as asme, codap ... as well as the standards of material selection such as en 10025 or en 10028. while designing a pv, we must design the fatigue of its material through the different methods and theories, we can find in the literature, and specific codes. in this work, a focus on the fatigue lifetime calculation through fracture mechanics theory and the different methods found in the asme viii div 2, the api 579-1 and en 13445-3, annex b, will be detailed by giving a comparison between these methods. in many articles in the literature the uniaxial fatigue has been very detailed. meanwhile, the multiaxial effect has not been considered as it must be. in this paper we will lead a discussion about the biaxial fatigue due to cyclic pressure in thick-walled pv. besides, an overview of multiaxial fatigue in pvs is detailed. keywords. pressure vessel design; asme viii; multiaxial fatigue; fracture mechanics; cumulative damage. citation: majid, f., nattaj, j., elghorba, m., multi-purpose fatigue sensor. part 2. pressure vessels design methods using the codes, fracture mechanics and multiaxial fatigue, frattura ed integrità strutturale, 38 (2016) 273-280. received: 15.05.2016 accepted: 20.06.2016 published: 01.10.2016 copyright: © 2016 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. introduction he pressure vessels (pv) are among the most used storage means in many industries, particularly in the ammonia, gas, petrochemical industries. they may be cylindrical, spherical depending on the nature of the stored product, its environment and its use. the pvs are more complex in design and safety component management. they are t f. majid et alii, frattura ed integrità strutturale, 38 (2016) 273-280; doi: 10.3221/igf-esis.38.37 274 interacting with the stored product and the external environment such as climate conditions and earthquakes. the higher number of pvs accidents [1] oblige us to be careful when using such equipments and to go beyond the codes and the standards for further detailed engineering design, develop new concepts in the performance framework and create a more dynamic vision and methodology as part of predictive and autonomous maintenance. the designers do usually a routine design of the pvs, but they don’t take into consideration the fatigue and the cumulative damage calculations for lifetime prediction. a lot of researchers are usually dealing with the uniaxial fatigue. but many other researchers tried to deal with the multiaxial fatigue to show the complexity of the phenomenon. a pv is always subjected to multiaxial loadings and multiaxial stresses. meanwhile, the prediction of industrial equipments’ reliability and availability still a difficult task for final clients and engineers. thus five approaches dealing with multiaxial fatigue exist in the literature. the first approach is the stress or strain invariant approach leaded by many authors [28]. the second one is the critical plan approach leaded by brown and miller [9-28]. the third one is the integral approach leaded by [29-32]. the fourth one is the energetic approach leaded by [33, 34]. the fifth and the last one are the empiric formulas leaded by [35-38] for high cycle fatigue et mowbray [39], manson and halford kalluri and bonacuse for low cycle fatigue. the metal’s damage due to fatigue has a well-known cycle, going through micro crack initiation, then its propagation until the rupture at the end. the fatigue rupture causes 50% to 90% of all the mechanical failures. according to many researches as fatemi, 2010 and nasa, 1994 for metal, micro cracks of about 10 to 100 micrometers uses 60 to 80% of the fatigue resistance, in other words the metal life time. that’s why it is very interesting to study the small cracks in progress ie the first stage (stage i) of crack. one of the major pv’s failures is the fatigue’s cracking. for that reason, we have to predict and analyze the cracks behavior, and specifically the crack propagation, in order to ensure the correct maintenance of pv. many studies have been developed to face this kind of failures. pressure vessels design he tanks are classified into three groups according to the operating pressure the atmospheric storage tanks for operating pressure of less than 18 kpa which are managed by the api 650 standard, the low-pressure storage tanks 18 kpa <p <100 kpa which are managed by the api 620 standard and pvs whose operating pressure p> 100 kpa which are managed by asme sec viii [40]. in this part of work, we developed a standard methodology for pvs design. we start by defining the design assumptions through the pv’s geometry, the site conditions, the service conditions, the test conditions and the design conditions. then, the material choice is done through the clients recommendations and the international standards codap, asme ii, en13345 or en 10222-4 or standards for materials choice en-10025, en 10028, iso 9327-4: 1999, jis g 3202: 1988 and astm. in the next step, we define the codes for pv calculation, figure (a), such as asme, codap or api. next, we define earthquake, safety elements, metallic construction codes such as cm66, and the regulations for the stored product. after that, we start the pv element calculation through the shell’s thickness calculation, figure (a), head’s thickness calculation, figure (b), nozzles calculation, figure (c), saddles calculation, seismic through ubc 1997 ground supported code and wind through the building code asce 7-05 verifications, calculation of lifting lugs, figure (d), and finally the calculation of fire circuit tanks through nfpa or other recognized standard [50]. pressure vessels multiaxial fatigue design v is subjected to repeated loading that could cause failure by the development of progressive fracture, asme section viii division 2, api 579-1 and en 13445-3 annex b has detailed procedures for determining if a vessel in cyclic service requires a detailed fatigue analysis or not, and how to conduct the analysis. the asme code is taking into consideration non conservative approaches, which are dealing combined load sources, rather than the other codes. the exemption of fatigue calculation is given by 3 screening procedure. the first one is based on successful experience and the second one, method a, uses a simple six step procedure for material with tensile strength of 550 mpa maximum. the third one, method b, is the most important one and it is developed in the table below according to the section viii division 2 paragraph 5.5.2.4. we start by determining the history of the loading given by the specs (step1) and then we determine screening criteria factors, c1 and c2 (step2). then, we proceed directly to fatigue analysis if any step inequation is false, else if we pass to the next step. the fatigue life is predicted from the s-n curve, results of fatigue tests on smooth bar, based on fatigue strength reduction factors (kf). t p f. majid et alii, frattura ed integrità strutturale, 38 (2016) 273-280; doi: 10.3221/igf-esis.38.37 275 figure 1: illustration of pressure vessels elements. step step detail formulas e xe m p ti o n m et h o d b step3full range pressure cycles fpn n c s1( )  (1) step4maximum range of pressure a p pn s np c s1 ( ) ( )  (2) step5-maximum temperature difference between two adjacent points a tn tn ym s np c c e1 1 ( ) ( )    (3) step6-maximum temperature difference fluctuation between two adjacent points a tn r ym s np t c c e1 1 ( ) ( )    (4) step7-maximum temperature difference fluctuation for differents components materials a tm r y y s n t c e e2 1 1 2 2 ( ) ( ) ( . . )     (5) step8equivalent stress range mlr a ss s n( )  (6) f at ig ue a ss es sm en t elastic stress analysis equivalent stress e k p k lt k v k lt k k s s k s s , , , , ,( ) ) 2       (7) elastic-plastic stress analysisequivalent strain ya k eff ke s , , 2   (8) peq k y s e ,       (9) table 1: pressure vessels fatigue design. f. majid et alii, frattura ed integrità strutturale, 38 (2016) 273-280; doi: 10.3221/igf-esis.38.37 276 multiaxial fracture of thick wall cylinder he wall of the pressure cylinders generally undergoes triaxial loading axial, circumferential and radial. in fact, many theories have been developed to predict the fracture of pressure cylinder by determining the limit charges. there are some theories which are dealing only with the internal pressure. other theories are focusing on the applied axial stress. and the last category is dealing with both of them. in the table below, we present a review of almost all the theories dealing with the limit internal pressure and the combined internal pressure and applied axial stress. for the first category, they are predicting the rupture pressure. meanwhile, the second category they are fixing either the internal pressure or the applied axial stress and predicting the other one. theories author,year equation in te rn al p re ss ur e hill, 1950 [41]. y i d p d 02 ln 3         (10) nadai, 1950 [42]. uts i d p d 02 ln 3         (11) faupel, 1956 [43]. y y uts i d p d 02 2 ln 3                (12) asser brabin, 2009 [44]. y y uts i d p d 02 (1 1 ln 3                        (13) dnv,2010 [45]. y m t p d 2 2 3  (14) kleverfj, 2006 [46]. stewart g, 1994 [47].   utsn n m t p d1 1 2 1 2 23               (15) c o m b in ed in te rn al p re ss ur e an d ax ia l a p p lie d st re ss klever fj, 2006 [46]. stewart g, 1994[47].   n n n i eff uts uts m p t d 1 1 1 31 4 3 24                     (16)   i m n n utsn n uts p d tp 2 1 1 1 1 2 4 3 41 33                   (17) table 2: overview of multiaxial fracture in the limit conditions. cumulative damage evaluation by a theory combination he prediction of intervention’s time by the maintenance services is generally very difficult unless we figure out when the damage could occur. in fact, determining the damage, in the asme code, is generally evaluated through linear methods like miner, although the results obtained by this method are very approximate. however, the non-linear quantifications of the damage seem difficult due to the big number of parameter. t t f. majid et alii, frattura ed integrità strutturale, 38 (2016) 273-280; doi: 10.3221/igf-esis.38.37 277 in this perspective, simplifying the testing procedures is required by opting for static tests instead of dynamic tests which are so expensive and difficult. the unified theory developed by bui quoc in 1971, has the advantage of ensuring an assessment of the damage through dynamic and static tests. in this paper we evaluated the damage through a combined theory using the unified theory [48,49] and burst pressure eq. (16) and (17). ur u s a u p p d p p 1 1    (18) where pur is the burst pressure for notched cylinder, pu is the burst pressure for a unotched cylinder and pa is the pressure before rupture. the approach presented in this part of the paper is based on artificial damage creation by creating a notch with a variable depth and then we evaluate the damage for each depth. the cylinder we are working on has a thickness of 5.8 mm, an external diameter of 63 mm and a length of 400 mm. the operating pressure for the case study is 0.6 mpa. the mechanical properties of the studied material are given in the tab. 3 obtained from mechanical characterization we did through tensile tests. (a) (b) figure 2: notched cylinder (a) fea of notched cylinder (b). material yield stress σy (mpa) ultimate stress σu(mpa) p265gh 320 470 a36 372 621 table 3: mechanical properties of materials. in this part of the paper, we proved that a combination between the unified theory and the burst pressure formulas is possible. then we showed that we can predict the fracture by theoretical calculations. we proved also that the unified theory can be used with burst pressure formulas based on combined applied axial stress and internal pressure. the burst pressure is decreasing while the notch depth increases. meanwhile, the cumulative based on the burst pressure formulas is almost the same as the one obtained by experimental tests and the use of the unified theory. conclusion ressure vessel design pass through many steps as shown in this article. the minimum requirement according the asme code has been resumed in the first part of the article. then, a review and a discussion of pressure vessels fatigue design have been detailed. in the third part of the article, we discussed the multiaxial fracture by giving an overview of almost the methods and formulas of burst or rupture pressure. the limit pressure is determined through the p f. majid et alii, frattura ed integrità strutturale, 38 (2016) 273-280; doi: 10.3221/igf-esis.38.37 278 internal pressure, applied stress or the combination of both of them. in the last part, we want to make these formulas in proof by a combination of the unified theory and the burst pressure formulas for static damage evaluation. the obtained result was compared with the damage of a36 steel subjected to uniaxial fatigue tests and tensile tests. we noticed that the results are almost the same. the validation of this combination was done for p265gh and a36 steel. a) b) figure 3: failure pressure (a) and damage and reliability (b) of p265gh and a36 function of the ratio notch depth-thickness. references [1] barpi. echelle de gravité des accidents industriels. bureau d'analyse des risques et pollutions industrielles, ministère chargé de l'environnement, direction de la prévention des pollutions et des risques, service de l'environnement industriel. édition binôme, (1993). [2] sines, g., ohgi, g., fatigue criteria under combined stresses or strains, j. of eng materials and technology, 103(2) (1981) 82-90. [3] hashin, z., fatigue failure criteria for combined cyclic stress, int. j. fracture, 17(2) (1981) 101-109. [4] chaudonneret, m., a simple and efficient multiaxial fatigue damage model for engineering applications of macrocrack initiation, j. engng. mater and technology., 115(4) (1993) 373-379. [5] ballard, p., van, k. d., deperrois, a., papadopoulos, y. v. high cycle fatigue and a finite element analysis, fatigue & fracture eng materials & structures, 18(3) (1995), 397-411. [6] crossland, b., bones, j. a., behavior of thick-walled steel cylinders subjected to internal pressure, in: proceedings of the institution of mechanical engineers. 172(1) (1958) 777-804. [7] deperrois, a., ph.d. thesis, ecole polytechnique, paris, (1994). [8] munday, e. g., mitchell, l. d., the maximum-distortion-energy ellipse as a biaxial fatigue criterion in view of gradient effects, experimental mechanics, 29(1) (1989) 12-15. f. majid et alii, frattura ed integrità strutturale, 38 (2016) 273-280; doi: 10.3221/igf-esis.38.37 279 [9] brown, m. w., miller, k. j., a theory for fatigue failure under multiaxial stress-strain conditions. proceedings of the institution of mechanical engineers, 187(1) (1973) 745-75. [10] findley, w.n., coleman, j.j., handley, b.c. in: proc. conf. on the fatigue of metals, the institution of mechanical engineers, new york. (1956)150 [11] socie, d.f., wail, l.a., dittmer, d.f. in multiaxial fatigue, astm stp 853, american society for testing and materials, pa, (1985) 463. [12] jordan, e.h., brown, m.w., miller, k., in multiaxial fatigue, astm stp 853, american society for testing and materials, pa, (1985) 569. [13] jacquelin, b., hourlier, f. pineau, a., in multiaxial fatigue, astm stp 853, american society for testing and materials, pa, (1985) 285. [14] wu, h. c., yang, c. c., on the influence of strain-path in multiaxial fatigue failure. journal of engineering materials and technology, 109(2) (1987) 107-113. [15] fatemi, a., socie, d., a critical plane approach to multiaxial fatigue damage including out of phase loading. fatigue & fracture of engineering materials & structures, 11(3) (1988) 149-165. [16] nitta, a., ogata, t., kuwabara, k., fracture mechanisms and life assessment under high strain biaxial cyclic loading of type 304 stainless steel, fatigue & fracture of engineering materials & structures, 12(2) (1989)77-92. [17] cailletaud, g., doquet, v., pineau, a., cyclic multiaxial behavior of an austenitic stainless steel: microstructural observations and micromechanical modeling, in fatigue under biaxial and multiaxial loading, (1991)131-149. [18] macha, e., simulation investigations of the position of fatigue fracture plane in materials with biaxial loads. materialwissenschaft und werkstofftechnik, 20(4) (1989) 132-136. [19] lefebvre, d., mebrouk, h., makinde. a., strain parameters for fatigue life prediction under out-of-phase biaxial fatigue.third international conference on biaxial/multiaxial fatigue, (1989) 433. [20] wang, c. h., brown, m. w., life prediction techniques for variable amplitude multiaxial fatigue—part 1: theories. journal of engineering materials and technology, 118(3) (1996) 367-370 [21] lin, h., nayeb-hashemi, h., in advances in multiaxial fatigue, astm stp 1191, american society for testing and materials, pa, (1993) 151. [22] shatil, g., smith, d. j., ellison, e. g., high strain biaxial fatigue of a structural steel. fatigue & fracture of engineering materials & structures, 17(2) (1994) 159-170. [23] chu, c-c., fatigue damage calculation using the critical plane approach, journal of engineering materials and technology, 117(1) (1995) 41-49. [24] mcdiarmid, d. l., the effects of mean stress and stress concentration on fatigue under combined bending and twisting. fatigue & fracture of engineering materials & structures, 8(1) (1985) 1-12. [25] flavenot, j. f., skalli, n. a., biaxial and multiaxial fatigue ecf 3: a critical depth criterion for the evaluation of longlife fatigue strength under multiaxial loading and a stress gradient. (1989). [26] będkowski, w., lachowicz, c., macha, e., the variance method of predicting the fatigue fracture plane under multiaxial random loadings. proceedings of 3rd international conference on biaxial/multiaxial fatigue, stuttgart. 1 (1989) 425. [27] van k., griveau, b., on new multiaxial fatigue limit criterion: theory and application, biaxial and multiaxial fatigue, egf 3, eds mw brown and kj miller, (1989) 479-496. [28] papadopoulos, i. v., panoskalliss, v. p., gradient-dependent multiaxial high-cycle fatigue criterion. icbmff4. (2013). [29] papadopoulos, i. v., a new criterion of fatigue strength for out-of-phase bending and torsion of hard metals. international journal of fatigue, 16(6) (1994) 377-384. [30] sonsino, m., grubisic, v., in multiaxial fatigue, astm stp 853, american society for testing and materials, pa, (1985) 586-605 [31] zenner, h., heidenreich, r., richter, i., dauerschwingfestigkeit bei nichtsynchroner mehrachsiger beanspruchung, materialwissenschaft und werkstofftechnik, 16(3) (1985) 101-112. [32] hug j, lui, j., schram, a., zenner, h., the influence of multiple axes on crack formation and spreading on swing loading. in25 th meeting of the fracture group of dvm. crack formation and crack propagation under multiaxial mechanical and thermal loads, (1993) 59-74. [33] ellyin, f., golos, k., multi. axial fatigue damage criterion, j. of eng. met. and tech. trans. asme, 10(1) (1988) 63. [34] liu, k.c., in advances in multiaxial fatigue, astm stp 1191, american society for testing and materials, pa, (1993) 67 [35] garud, y.s., proc. symp. on methods for predicting material life in fatigue, asme, new york, (1979) 247 f. majid et alii, frattura ed integrità strutturale, 38 (2016) 273-280; doi: 10.3221/igf-esis.38.37 280 [36] leis, b.n., trans. asme. 99 (1977) 524 [37] froustey, c., lasserre, s., multiaxial fatigue endurance of 30ncd16 steel, int. j. of fatigue, 11(3) (1989)169-175. [38] lasserre, s., froustey, c., multiaxial fatigue of steel testing out of phase and in blocks: validity and applicability of some criteria. int. j. of fatigue, 14(2) (1992) 113-120. [39] mowbray, d. f., a hydrostatic stress-sensitive relationship for fatigue under biaxial stress conditions. journal of testing and evaluation, 8(1) (1980) 3-8. [40] asme std sec viii. american society of mechanical engineers, (2013). [41] hill, r., the mathematical theory of plasticity, oxford university press, oxford, (1950). [42] nadai, a., plasticity of metals, (1950). [43] faupel, j. h., furbeck, a. r., influence of residual stress on behavior of thick-wall closed-end cylinders. trans. asme, 75 (1953) 345-354. [44] brabin, a. t., christopher, t., nageswara, b., investigation on failure behavior of unflawed steel cylindrical pressure vessels using fea, multidiscipline modeling in materials and structures, 5 (2009) 29-42. [45] veritas, det norske. offshore standard dnv-os-f101, submarine pipeline systems, (2010). [46] klever, f. j., formulas for rupture, necking, and wrinkling of octg under combined loads. spe annual technical conference and exhibition. society of petroleum engineers. (2006). [47] stewart, g., klever, f. j., ritchie, d., an analytical model to predict the burst capacity of pipelines. no. conf940230--. american society of mechanical engineers, new york, ny (united states), (1994). [48] elghorba, m., , thesis ecole polytechnique de monreal, (1986). [49] dubuc, j., et al .unified theory of cumulative damage in metal fatigue (cumulative damage in metal fatigue, suggesting unified theory applicable to stress or strain controlled conditions).wrc bulletin, (1971) 1-20. 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can be opened with acrobat and adobe reader 5.0 and later.) >> /namespace [ (adobe) (common) (1.0) ] /othernamespaces [ << /asreaderspreads false /cropimagestoframes true /errorcontrol /warnandcontinue /flattenerignorespreadoverrides false /includeguidesgrids false /includenonprinting false /includeslug false /namespace [ (adobe) (indesign) (4.0) ] /omitplacedbitmaps false /omitplacedeps false /omitplacedpdf false /simulateoverprint /legacy >> << /addbleedmarks false /addcolorbars false /addcropmarks false /addpageinfo false /addregmarks false /convertcolors /converttocmyk /destinationprofilename () /destinationprofileselector /documentcmyk /downsample16bitimages true /flattenerpreset << /presetselector /mediumresolution >> /formelements false /generatestructure false /includebookmarks false /includehyperlinks false /includeinteractive false /includelayers false /includeprofiles false /multimediahandling /useobjectsettings /namespace [ (adobe) (creativesuite) (2.0) ] /pdfxoutputintentprofileselector /documentcmyk /preserveediting true /untaggedcmykhandling /leaveuntagged /untaggedrgbhandling /usedocumentprofile /usedocumentbleed false >> ] >> setdistillerparams << /hwresolution [2400 2400] /pagesize [612.000 792.000] >> setpagedevice microsoft word numero_42_art_10.docx m. kowalski, frattura ed integrità strutturale, 42 (2017) 85-92; doi: 10.3221/igf-esis.42.10 85 focused on mechanical fatigue of metals identification of fatigue and mechanical characteristics of explosively welded steel titanium composite m. kowalski opole university of technology m.kowalski@po.opole.pl abstract. paper presents results of fatigue tests performed on s355j2 steel titanium grade 1 composite produced in explosive welding technology. specimens were subjected to cyclic tension-compression loading with zero mean value and controlled force. also mechanical properties were investigated. keywords. welding; explosive; fatigue; bimetal; steel; titanium. citation: kowalski, m., identification of fatigue and mechanical characteristics of explosively welded steel titanium composite, frattura ed integrità strutturale, 42 (2017) 8592. received: 31.05.2017 accepted: 09.06.2017 published: 01.10.2017 copyright: © 2017 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. introduction echnology of the explosive welding is based on principles of joining dissimilar materials with the energy from explosive detonation. phenomena of the explosive material joining was observed for the first time during the first world war, but from the commercial point of view technology became appreciated in the 1950's [7]. explosive welding is defined as a solid state process. bond between materials results from the impact effects during detonation. stable joint between materials is attained if energy of the detonation cause hydrodynamic behavior of the material [7,8,16]. characteristic feature of the interface lines is their wavy shape (fig. 1). bond and strength parameters are influenced by basic welding parameters: detonation velocity, standoff distance and welding angle [1,2]. research on welding parameters and overall properties of multilayer material influenced on range of their industrial application. especially in industry branches demanding universal properties of the construction materials for example: high strength and chemical resistance. at the present time explosively welded composites are used in industrial areas such as: chemical and nuclear engineering in example: tube sheets, heat exchangers. in the literature explosively welded multilayer materials are mainly investigated in terms of operational and design aspects like welding parameters and their impact on microstructure changes[2–4,6,9]. influence of the heat treatment on overall properties of the material is also examined [5]. however, although the fatigue phenomenon which is very important from a design calculation and operational point of view [13, 14] is rarely investigated. t m. kowalski, frattura ed integrità strutturale, 42 (2017) 85-92; doi: 10.3221/igf-esis.42.10 86 figure 1: wavy interface line in steel – titanium bimetal. fatigue properties of clad materials are subject of the lower number of studies than other topics combined with explosive technology. some scientific and technical information concerning fatigue resistance and behavior can be found in fallowing papers [10,11,15]. fatigue curves for bimetallic materials are presented in [11,12]. in the case of building fatigue curves for multilayer materials difficulty can be related to stress inhomogeneity caused by different young’s modulus of joint metals. problem can be extended to the uniformity of mechanical properties in the particular layers of joined materials. studies performed on steel titanium bimetallic plates exhibited inhomogeneity of basic mechanical properties [17]. taking into account some assumption which will be described later bimetallic material can be split on fallowing sections: sections of base and clad materials and the interface section zone characterized by substitute mechanical properties (fig. 2). figure 2: interface zone location stresses calculated on the basis of mechanical properties of each section can be used in finite element method or in characterization of fatigue properties. the main aim of this paper is presentation of experimental fatigue test results carried out on specimens made of steel-titanium bimetal subjected to cyclic tension-compression loading. the experimental research results in presentation of mechanical properties and demonstration of strain based fatigue characteristics. material properties pecimens used in study were cut from the bimetal plate carried out in the explosive welding process of the s355j steel and the titanium grade 1. material was heat-treated after the welding process. heating took place for 90 minutes at 600°c and then the material and a furnace were cooled to 300°c (at cooling velocity 100°c/h). the final cooling stage was carried out in the calm air. mechanical properties and of joined materials are presented in tab. 1. material mechanical properties re, mpa rm, mpa e, mpa g, mpa , a5, % s355j2 382-395 598-605 220000 84000 0.3 24-34 grade 1 189-215 (r02) 308-324 100000 38000 0.39 43-56 table 1: mechanical properties of steel s355j2 and titanium grade 1. s m. kowalski, frattura ed integrità strutturale, 42 (2017) 85-92; doi: 10.3221/igf-esis.42.10 87 example microstructure is shown on fig. 2. microstructure observations revealed local melting zones in the interface line. in the steel layer, decarburization occurred near interface line. on the other hand, in the titanium layer, recrystallization induced by the heat treatment appeared. figure 2: interface zone location mechanical properties of the interface layer in steel-titanium bimetal were obtained on the basis of fallowing assumptions: near the interface zone mechanical properties of joined materials undergo a strong change, and calculation of stress in each material layer located near interface line is impossible, properties of the interface zone can be described taking into account behavior of the thick substitute layer. for the identification of interface layer mechanical properties specimens were carry out using water jet technology. application of water abrasive technology has prevented introduction of the residual stress and microstructure changes caused by cutting process. shape and dimension of the specimen are presented on fig. 3. figure 3: shape and dimensions of the interface zone specimens results were presented in form of the table including test details (tab. 2). interface layer was characterized by averaged properties eint=157 gpa, υint=0,27. stresses existing in material layers can calculated taking into account fallowing assumptions: homogeneous strain distribution throughout the specimen cross section ( resulting from the displacement of the specimen grips), no defects, elastic deformation range, flat interface line, uniaxial stress state. analytical expressions for stress in steel, titanium and substitute interface zones: m. kowalski, frattura ed integrità strutturale, 42 (2017) 85-92; doi: 10.3221/igf-esis.42.10 88 specimen dimensions, mm fm, kn fu, kn fp02, kn υsub, esub, gpa w h b1 12.2 3.3 20.0 16.2 12.8 0.27 151 b2 12 2.95 17.6 14.5 15.5 0.27 158 b3 11.98 2.96 18.0 14.5 12.2 0.27 157 b4 12.3 3.0 18.2 14.7 13.5 0.27 161 b5 12.5 2.95 17.7 15.1 11.1 0.27 155 b6 12.1 2.85 18.1 14.9 14.2 0.28 160 b7 12.1 2.92 17.7 14.6 13.0 0.27 155 b8 11.88 3.05 18.3 16.0 14.7 0.28 156 averaged 0.27 157 where: w, h –specimen section dimensions , esub – substitute young modulus, υsub – substitute poisson ratio, fm – maximum force, fu –breaking force, fp02 – foce at 0.2% strain. table 2: mechanical properties of the interface zone. figure 4: dimensions of specimen cross section. 2 2 ti ti int ti st e f t t e t w e w h h e w h                  (1) 2 2 int int int ti st e f t t e t w e w h h e w h                  (2) 2 2 st st int ti st e f t t e t w e w h h e w h                  (3) where: eti , eint, est – young modulus of titanium, interface and steel layers respectively, f – force, w, h, h, t – characteristic dimensions of the composite. among the specimens not used during the study phenomenon of residual stresses relaxation in titanium layer was observed. relaxation progressed gradually in about 2 weeks after cut (fig. 5). m. kowalski, frattura ed integrità strutturale, 42 (2017) 85-92; doi: 10.3221/igf-esis.42.10 89 figure 5: deformation of samples caused by residual stress relaxation. fatigue tests atigue tests were performed using hydraulic testing machine equipped with a force and a displacement sensors. strain was registered by extensometer mounted on the specimen (steel side). a force control was used in all of fatigue tests. loadings applied to specimens were generated up to the formula f(t)=fasin(2πft). tests were performed at various frequencies f from 2 to 12hz. a moment of total material interruption was considered as the specimen destruction. because of limited research range of a fatigue testing machine, each specimen were milled to 9 mm total thickness (fig. 6). figure 6: shape and dimensions of the fatigue specimens. result and parameters of tests were presented in tab. 3. during the fatigue tests loading and strain were registered. the dependence between those two parameters is very important and contain an information about changes which proceed in the material. in fatigue tests with controlled force only the strain amplitude can undergo a change, an amplitude of loading force remain constant. in case of increasing strain amplitude tested material is classified as cyclic softening. non uniform properties of welded materials cause that description of material behavior in case of bimetal is more complicated. lack of an information about cyclic elastic-plastic properties of joined materials and in particular of the created interface zone makes determining a curve of dependence between stresses and strains difficult. it is, however, possible to obtain the dependence between the registered force f and strain ε. strains occurring in particular layers are homogeneous because displacement generated by holder of a testing machine is forced and identical as displacement of specimen grips. in case of the elastic strain the ε-f dependence is a straight line, appearance of a hysteresis loop indicates the plastic strain. registered ε-f loops (fig. 7) identify stability of the bimetal (softening or hardening). hysteresis loops were created for selected load cycles. parameter n used in figure signify the damage amount, which is quotient of the actual number of cycles to the total number of cycles. characteristic feature of tested bimetals is quick transition from the elastic range (no hysteresis loops) to the plastic strain range. in next cycles of the fatigue loading a ratcheting phenomenon appears (fig. 8). ratcheting is defined as phenomenon of accumulation of plastic strains in the direction of stretching). f m. kowalski, frattura ed integrità strutturale, 42 (2017) 85-92; doi: 10.3221/igf-esis.42.10 90 specimen w, h, fa, kn stress, mpa nexp, cycles mm mm σti σint σst p01 10 9 24 155.3 233.0 326.2 6650 p02 10 9 21.5 139.2 208.7 292.2 98310 p03 9.7 9 19.9 132.8 199.2 278.9 895970 p04 9.62 9.02 23 154.5 231.8 324.6 34390 p05 9.54 8.74 24.5 169.1 253.6 355.0 26570 p06 9.46 8.96 22 150.9 226.4 316.9 104820 p07 9.76 9.02 23.1 153.0 229.5 321.3 22980 p08 9.84 9 21.1 138.8 208.2 291.5 134850 p09 9.7 9.08 23.1 153.3 230.0 322.0 28860 p10 9.7 9 19.6 130.8 196.2 274.6 263540 p11 9.82 9 21 138.4 207.6 290.7 117640 p13 10.08 9.08 25 159.7 239.6 335.4 132600 p14 9.9 9 25 163.4 245.2 343.2 195050 p15 9.85 8.93 28 184.8 277.2 388.1 31100 p16 9.85 8.93 30 198.0 297.0 415.9 9100 p17 9.85 8.85 33 219.0 328.5 459.8 2710 where: w, h –specimen section dimensions , σti – stress in titanium layer, σint – stress in interface zone, σst – stress in steel layer fa – force amplitude. table 3: results of the fatigue tests. figure 7: hysteresis loops recorded during fatigue tests. m. kowalski, frattura ed integrità strutturale, 42 (2017) 85-92; doi: 10.3221/igf-esis.42.10 91 figure 8: amplitude and mean value of strain during fatigue test, where: εz – strain amplitude. results of performed experiments are presented as experimental points on the background of s355j2 steel fatigue characteristic (fig. 9). according to the astm standard e2207-08 [18] recommends to build fatigue characteristics for strain amplitudes registered in the middle of the fatigue test, i.e. for n=0. 5. figure 9: experimental points (steel – titanium specimens) and fatigue characteristic of s355j2 steel. conclusions s a result of the performed fatigue tests, the following conclusions were drawn. substitute mechanical properties obtained during identification of mechanical properties are close to the average of the elasticity coefficients for materials before welding (approximately 157gpa). in the case of the poisson ratio, substitute value (0.27) is close to the value of factor for the steel before welding process. obtained substitute mechanical properties of the interface zone can be supplement to material data for numerical analysis. fatigue tests have shown the cyclic instability of steel-titanium composite. in case of bimetal, cyclical instability (softening) combined with cyclical flow of material has been observed (for some specimens from the first load cycles). these phenomena were characterized by increasing amplitude values of deformation εa and mean values of deformation εm. residual stress relaxation phenomena was also observed. a m. kowalski, frattura ed integrità strutturale, 42 (2017) 85-92; doi: 10.3221/igf-esis.42.10 92 references [1] acarer, m., demir, b., an investigation of mechanical and metallurgical properties of explosive welded aluminum– dual phase steel, materials letters, 62 (2008) 4158–4160. [2] acarer, m., gülenç, b., findik, f., investigation of explosive welding parameters and their effects on microhardness and shear strength, materials & design, 24 (2003) 659–664. [3] akbari-mousavi, s.a.a., barrett, l.m., al-hassani, s.t.s., explosive welding of metal plates, journal of materials processing technology, 202 (2008) 224–239. [4] akbari mousavi, s.a.a., farhadi sartangi, p., experimental investigation of explosive welding of cp-titanium/aisi 304 stainless steel, materials & design,. 30 (2009) 459–468. [5] akbari mousavi, s.a.a., sartangi, p.f., effect of post-weld heat treatment on the interface microstructure of explosively welded titanium–stainless steel composite, materials science and engineering: a, 494 (2008) 329–336. [6] čižek, l., ostroushko, d., szulc, z., molak, r., pramowski, m., properties of sandwich me-tals joined by explosive cladding method, archives of materials science and engineering, (2010) 21–29. [7] crossland, b., explosive welding of metals and its application, clarendon press, (1982). [8] ferjutz, k., davis, j.r., asm handbook: volume 6: welding, brazing, and soldering, 10th ed., asm international, (1993). [9] findik, f., recent developments in explosive welding, materials & design, 32 (2011) 1081–1093. [10] karolczuk, a., kluger, k., kowalski, m., żok, f., robak, g., residual stresses in steel-titanium composite manufactured by explosive welding, materials science forum, 726 (2012) 125–132. [11] karolczuk, a., kowalski, m., structural and fatigue properties of titanium-steel bimetallic composite obtained by explosive welding technology, key engineering materials, 592-593 (2013) 594–597. [12] karolczuk, a., kowalski, m., bański, r., żok, f., fatigue phenomena in explosively welded steel–titanium clad components subjected to push–pull loading, international journal of fatigue, 48 (2013) 101–108. [13] marciniak, z., rozumek, d., models of initiation fatigue crack paths proposed by macha, fracture and structural integrity, 9(34) (2015) 1-10. doi 10.3221/igf-esis.34.01. [14] niesłony, a., böhm, m., determination of fatigue life on the basis of experimental fatigue diagrams under constant amplitude load with mean stress, materials science forum, 726 (2012) 33–38. [15] prażmowski, m., paul, h., rozumek, d., marcisz, e., influence of the microstructure near the interface on the fatigue life of explosively welded (carbon steel)/zr clads, key engineering materials, 592-593 (2013) 704–707. [16] rinehart, j.s.p. j., explosive working of metals, pergamon press, (1963). [17] sołtysiak, r., boroński, d., karolczuk, a., kowalski, m., experimental study of non-uniform distribution of basic mechanical parameters in steel-titanium bimetal, solid state phenomena, 224 (2014) 192–197. [18] astm e2207 02 practice for strain-controlled axial-torsional fatigue testing with thin-walled tubular specimens, astm international, (2013). << /ascii85encodepages false /allowtransparency false /autopositionepsfiles true /autorotatepages /none /binding /left /calgrayprofile (dot gain 20%) /calrgbprofile (srgb iec61966-2.1) /calcmykprofile (u.s. web coated \050swop\051 v2) /srgbprofile (srgb iec61966-2.1) /cannotembedfontpolicy /error /compatibilitylevel 1.4 /compressobjects /tags /compresspages true /convertimagestoindexed true /passthroughjpegimages true /createjobticket false /defaultrenderingintent /default /detectblends true /detectcurves 0.0000 /colorconversionstrategy /cmyk /dothumbnails false /embedallfonts true /embedopentype false /parseiccprofilesincomments true /embedjoboptions true /dscreportinglevel 0 /emitdscwarnings false /endpage -1 /imagememory 1048576 /lockdistillerparams false /maxsubsetpct 100 /optimize true /opm 1 /parsedsccomments true 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<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> /enu (use these settings to create adobe pdf documents best suited for high-quality prepress printing. created pdf documents can be opened with acrobat and adobe reader 5.0 and later.) >> /namespace [ (adobe) (common) (1.0) ] /othernamespaces [ << /asreaderspreads false /cropimagestoframes true /errorcontrol /warnandcontinue /flattenerignorespreadoverrides false /includeguidesgrids false /includenonprinting false /includeslug false /namespace [ (adobe) (indesign) (4.0) ] /omitplacedbitmaps false /omitplacedeps false /omitplacedpdf false /simulateoverprint /legacy >> << /addbleedmarks false /addcolorbars false /addcropmarks false /addpageinfo false /addregmarks false /convertcolors /converttocmyk /destinationprofilename () /destinationprofileselector /documentcmyk /downsample16bitimages true /flattenerpreset << /presetselector /mediumresolution >> /formelements false /generatestructure false /includebookmarks false /includehyperlinks false /includeinteractive false /includelayers false /includeprofiles false /multimediahandling /useobjectsettings /namespace [ (adobe) (creativesuite) (2.0) ] /pdfxoutputintentprofileselector /documentcmyk /preserveediting true /untaggedcmykhandling /leaveuntagged /untaggedrgbhandling /usedocumentprofile /usedocumentbleed false >> ] >> setdistillerparams << /hwresolution [2400 2400] /pagesize [612.000 792.000] >> setpagedevice microsoft word numero 11 art 1 d. taylor, frattura ed integrità strutturale, 11 (2009) 3-9; doi: 10.3221/igf-esis.11.01 3 on the application of the theory of critical distances for prediction of fracture in fibre composites david taylor engineering school, trinity college dublin, ireland; dtaylor@tcd.ie abstract. this paper is concerned with the fracture of composite materials containing stress concentration features such as notches and holes. in particular, it addresses the question of the use of the theory of critical distances (tcd) – a method which is widely used for predicting notch effects in fatigue and fracture. the tcd makes use of a length constant, l, known as the critical distance, which is normally assumed to be a material property. however, many workers in the field of composite materials have suggested that the critical distance is not a constant, but rather is a function of notch size. i examined the evidence for this assertion, and concluded that it arises for four different reasons, two of which (process zone size and constraint) are real material effects whilst the other two (choice of test specimen and estimation of the stress field) arise due to errors in making the assessments. from a practical point of view, the assumption of a constant value for l leads to only small errors, so it is recommended for engineering design purposes. keywords. fibre composites; fracture; notch; hole; critical distance introduction hen engineering components fail, they almost always do so from stress concentration features: geometrical discontinuities such as holes, notches and corners. fibre composite materials are no exception, and much work has been done over the years to understand and predict the effects of these features on the load-bearing capacity of these materials. this paper is concerned with one particular method of prediction, which goes by various names but which i will call the theory of critical distances (tcd). here i will consider the application of this theory to the broad range of long-fibre laminate-type composite materials, and from the outset i should point out that i do not consider myself an expert on this class of materials. in that respect the paper is being written from the outside looking in, and i apologise in advance for any errors or misunderstandings that may arise as a result. my investigations into the tcd began in the field of metal fatigue, where the approach has been used for over half a century [1, 2]. examination of the published literature revealed that the same methodology was also being applied to predict monotonic fracture in composites, since first being proposed by whiney and nuismer in 1974 [3]. further reading showed that work in the two areas (metal fatigue and composite fracture) has proceeded on parallel lines for the last thirty years, both in fundamental research and in industrial applications, with workers in one field being apparently unaware of the activities of those in the other. as a result, the approach has developed some particular characteristics: for example in the field of metal fatigue it is generally assumed that the critical distance, l, which is the fundamental parameter in the theory, is a material constant, unaffected by the geometry of the notch. in composites research, however, it has become common to assume that l is not a material constant, but rather that it varies with the size of the notch. this question is of fundamental importance because the theory is much easier to use if we can assume a constant value for l. if a constant value of l cannot be accepted then more fundamental studies are needed to develop a general approach which would allow l to be calculated for any problem. some workers, including ourselves, have indeed proposed such w http://www.gruppofrattura.it http://dx.medra.org/10.3221/igf-esis.11.01&auth=true d. taylor, frattura ed integrità strutturale, 11 (2009) 3-9; doi: 10.3221/igf-esis.11.01 4 approaches [4, 5] and they have been found to be necessary in certain other materials, such as concrete, where the critical distance can be so large as to be similar to the size of the test specimen. in this paper, i consider the evidence for and against the use of a constant l value in continuous-fibre composite laminate materials, both from a fundamental scientific perspective and from the viewpoint of the practical engineering application of the tcd. the tcd: a brief introduction or those not familiar with critical distance methods, here follows a brief introduction. a recent paper provides further information [6] and those interested in a more comprehensive review are directed to a recent book on the subject [7]. in the great majority of cases, the tcd is implemented using a linear elastic stress analysis. the point of maximum stress is located (e.g. at the root of a notch) and a line is drawn from this point which is known as the focus path. stress is plotted as a function of distance, r, along this line. there are two different variants of the approach, which i refer to as the point method and the line method. in the point method, the stress is considered at a single point, located at a distance of r=l/2. in the line method, the stress to be considered is the average stress along the line from r=0 to 2l. failure is predicted to occur if this stress is greater than some critical value, o. fig. 1 illustrates these approaches schematically. there are other variants of the tcd; for example some workers use l in a modified form of linear elastic fracture mechanics lefm) in which l is considered to be the length of an imaginary crack at the notch root, or alternatively the crack is considered to advance in finite growth steps of magnitude 2l. these methods do not concern us here, except in so far as they can be combined with the stress-based methods to give approaches in which l is no longer a constant. the point and line methods have the great advantage of simplicity: they can be very easily used in conjunction with finite element analysis and applied to any type of stress concentration feature, including those on engineering components. extensive research has shown that they can give very accurate predictions in a wide variety of materials, for those mechanisms of failure which involve cracking, such as brittle fracture and fatigue [7]. an important relationship exists between the two constants in the tcd and the material’s fracture toughness, kc. this relationship can be derived by assuming that the tcd is applicable to cracks as well as notches: 2 1        o c k l  (1) figure 1: schematic illustration of the point method and line method application of the tcd to composite materials he use of this approach in the field of composites stems from the seminal paper by whitney and nuismer in 1974 [3] which was followed a short time later by a slightly more detailed treatment in a book by whitney et al [8]. the original paper has been extremely influential in this field: at the time of writing there have been over 300 citations to this paper, in publications ranging from fundamental studies to engineering applications. the paper is very comprehensive, describing both the pm and the lm, which whitney and nuismer referred to as the point stress criterion and the average stress criterion. the validity of the method was tested against experimental data: figs 2 and 3 are examples reproduced from the original paper. the theoretical link to kc (as in eq. 2 above) was also derived. importantly, f t http://www.gruppofrattura.it http://dx.medra.org/10.3221/igf-esis.11.01&auth=true d. taylor, frattura ed integrità strutturale, 11 (2009) 3-9; doi: 10.3221/igf-esis.11.01 5 this paper established that the critical stress o was equal to the ultimate tensile strength of the material as measured in tests on plain (i.e. unnotched) specimens. in other classes of materials this is not always the case but it appears to be true universally for composite laminates, and to my knowledge no one has proposed otherwise. a significant limitation of the paper was that only two types of notches were considered: circular holes located centrally in flat plates, and sharp edge notches in which the notch root radius was very small. figure 2: data and predictions (using the point method) from whitney & nuismer [3], showing the effect of hole radius on fracture strength (nominal stress, normalised by the plain-specimen strength) in a quasi-isotropic glass/epoxy laminate. the three prediction lines were drawn using slightly different values of the critical distance, do which is equivalent to l/2. figure 3: data from whitney and nuismer [3] showing the effect of notch length (c) on fracture toughness, for sharp notches in a graph-epoxy laminate material. prediction lines using the point method, drawn at different values of the critical distance do (equivalent to l/2). within a decade of the publication of this original paper, a lot of experimental data had been generated to demonstrate the truth of whitney and nuismer’s proposal. awerbuch and madhukar [9] presented an enormous study covering over 2800 test results, and wetherhold and mahmoud [10] also considered a large set of data, both reports showing that the tcd could be applied successfully to a wide range of materials, mostly polymer-matrix long-fibre materials but also including some metal-matrix composites and some materials with discontinuous fibres. interestingly, despite the wide range of strengths and toughnesses in these materials, it was found that l fell within a narrow range of values, being almost always between 1 and 5mm, sometimes as high as 15mm. more recent literature has extended the subject in various ways, which i have reviewed elsewhere [7]. however, the overwhelming impression is that most workers have followed closely the lead taken by whitney and nuismer. as a result, http://www.gruppofrattura.it http://dx.medra.org/10.3221/igf-esis.11.01&auth=true d. taylor, frattura ed integrità strutturale, 11 (2009) 3-9; doi: 10.3221/igf-esis.11.01 6 most papers are confined to studies of tensile test specimens containing either circular holes or very sharp edge notches. the limited range of test specimens studied is, in my view, the source of some misconceptions about the use of the tcd. this contrasts with work in the parallel field of metal fatigue, where different types of notches have been investigated, especially with regard to the effects of notch root radius, along with different types of loading. does l vary with notch size? he large amount of data collected by awerbuch and madhukar allowed various correlations to be studied. one trend which emerged was that in some cases the value of l which best predicted the results tended to vary, increasing with the size of the hole or notch. these effects seemed quite significant, for example these workers show a case in which changing the length of a sharp notch from about 1mm to 20mm caused the best-fit value of l to approximately double in size. further work was done by other researcher, to investigate this phenomenon, especially for the case of circular holes. as a result, two equations were developed which are now in common use. the first is that of karlak [11], which relates l to the hole diameter (a) using a constant c1, as follows: l = c1a1/2 (2) the second equation is that proposed by pipes et al [12] who developed a more general relationship including another constant m: l = c2am (3) this second equation covers a wide range of possible conditions: two interesting cases are m=0, for which l becomes a material constant and m=1 which leads to a situation in which the size of the hole has no effect on the fracture strength, since l scales in direct proportion to a. in the example mentioned above, from awerbuch and madhukar, the value of m was 0.235. in fact, even the original data in whitney and nuismer shows something of this effect: for example in fig.2 prediction lines were drawn using different values of the critical distance and one can see that the data tend to move from the smallest to the largest value with increasing hole size. investigating the data and the methods of analysis in some detail, i have come to the conclusion that there are four separate reasons for this effect, as follows. stress analysis errors in calculating the stresses in the vicinity of the notch, for use in the point method or line method, whitney and nuismer used the following approximate method. they started from the equation for a notch in an infinite body: for example for a circular hole they used the well-known airy equation for the stress (r) as a function of distance r :                        42 2 3 2 1 1)( ra a ra a r  (4) they then modified this equation to take account of the finite width of the plate, w, multiplying it by the following factor y: )1(3 )1(2 3 w a w a y    (5) the same approach has been followed by many subsequent researchers in this field. unfortunately, this approach is not precise, and leads to significant errors. fig. 4 compares the stress/distance curve predicted by these equations to an accurate result obtained using finite element analysis, for the case of a hole with a/w = 0.375. the two curves begin to deviate significantly around r/a = 1. unfortunately, many test specimens use a/w values equal to or greater than this, and in many cases the relevant values of r are quite large, given that l typically takes a value of several millimetres in these materials. one can appreciate that this error will lead to a situation in which l appears to increase with notch size, because if notch size increases (at constant w) then the estimated stress at the point l/2 will deviate more and more from the actual stress, t http://www.gruppofrattura.it http://dx.medra.org/10.3221/igf-esis.11.01&auth=true d. taylor, frattura ed integrità strutturale, 11 (2009) 3-9; doi: 10.3221/igf-esis.11.01 7 leading to an erroneously low prediction of the fracture strength of the specimen, an error which can apparently be corrected by letting l increase. figure 4: stress as a function of distance from notch root, calculated using the approximate formula (eq. 5), compared to an accurate result obtained from fea. choice of test specimen fig. 5a shows stress/distance curves calculated for the specimens tested by whitney and nuismer (as reproduced here in fig. 2), for loading conditions corresponding to fracture of the specimen in each case. if the point method is exactly correct then all of these curves should pass through a single point, at which r = l/2 and the stress is equal to the uts (represented here by a horizontal dashed line). based on this data one would conclude that there is a tendency for l to increase with increasing hole radius, by about a factor of 2. however, the situation changes drastically if we add data from specimens containing sharp notches (see fig. 5b). the sharp-notch data shows no such trend, and the fracture strength of all the specimens can be predicted using a constant value of l, with a prediction error of no more than 10%. figure 5a: stress-distance curves at failure for specimens containing holes as shown in fig.2. the symbols r1-r6 indicate increasing hole radius. figure 5b: the same data as in fig.5a, plus lines representing the stresses in sharply-notched specimens of the same material. the symbols n1-n4 represent increasing notch depth. many workers have based their conclusions solely on data from circular holes. this is a mistake because the stress gradients in these specimens are quite shallow, so it is difficult to obtain an accurate value of l in any case, since the estimate relies on finding the point at which the stress/distance curve crosses the horizontal line representing the uts. http://www.gruppofrattura.it http://dx.medra.org/10.3221/igf-esis.11.01&auth=true d. taylor, frattura ed integrità strutturale, 11 (2009) 3-9; doi: 10.3221/igf-esis.11.01 8 sharper notches are better in this respect because they give steeper gradients, and the best strategy is to use at least two different notch types, as shown here. process zone size the above two effects arise essentially due to errors or inaccuracies, however there are also some reasons why the value of l would tend to increase in reality. the first of these relates to the size of the process zone. to illustrate this i have chosen some data from kennedy et al [13], who tested centre-notched plates of an orthotropic graphite/epoxy composite, using very sharp, crack-like notches. i have chosen this data because it shows the largest change in l which i have been able to find. according to these workers, l changed by a factor of 3, from 8.4mm to 24.4mm, when the length of the notch was increased from 6.35mm to 305mm. the value of a/w was kept constant at 0.25, which is convenient because it means we can rule this out as a complicating factor. the value of l gives an approximate estimate of the size of the process zone, or damage zone that occurs ahead of the notch prior to failure. from this we can conclude that the larger specimens were failing under lefm conditions because the size of the damage zone at failure was much smaller than the remaining ligament (w-a). however this is not the case for the smaller specimens, for which l was a significant proportion of (w-a), and for the very smallest specimen it is likely that the process zone had spread completely across the specimen width before failure. we have encountered similar situations before, most obviously in the case of building materials such as concrete, which have equally large l values of the order of 5-10mm. if the specimen size is particularly small then this can lead to the absurd situation in which the critical point (or part of the critical line) lies outside the specimen. in such cases if the tcd can be used at all it must be with a smaller value of l. approaches developed by myself and colleagues [5] and also by leguillon [4], allow l to vary in such cases by using two failure criteria – one stress based and one stress-intensity based, which are assumed to apply simultaneously. the details of the approach are beyond the scope of the present paper: suffice it to say that the result is an l value which is constant when the remaining ligament (w-a) is much larger than l, but changes in size in such a way that it remains always smaller than (w-a). these modified approaches can be applied to problems of the type shown above, and should be able to give improved predictions. however, it may not be worth the trouble. regarding the data from kennedy et al, which as i said showed the largest variation in l of any which i could find for composite materials, if we use a constant l value it is possible to predict all the data with errors no greater than 13% on stress. this seems strange at first but the anomaly is resolved by noting that the stress distance curves are quite shallow, even for relatively sharp notches, so a large change in distance r gives only a relatively small change in stress. consequently it is permissible to make a relatively large error in the value of l because this will lead to only a small error in the predicted strength. constraint effects when reading articles on composite materials i was struck by the fact that little attention seems to be given to possible changes in constraint that arise when changing specimen thickness. in metallic materials the measured fracture toughness can change considerably if thickness is reduced in such a way as to reduce the out-of-plane constraint, changing from plane strain to plane stress conditions. some workers have reported this effect in composite materials, but in most papers it is not mentioned, and awerbuch and madhukar actually reported a case of the opposite effect, whereby the measured toughness increased with increasing specimen thickness [9]. given that most composite-laminate specimens tested are quite thin, one would expect that they are experiencing either plane stress or conditions which are intermediate between plane stress and plain strain. the change in kc is due largely to changes in the degree of triaxiality in the plastic zone, and though the polymer and metal matrices of these composites will yield, it is possible that these effects are modified by the existence of microdamage in these zones. considering the relationship between fracture toughness and l (eq. 1 above) one would expect l to increase on moving from plane strain to plane stress, and we showed previously that this is indeed the case for brittle fracture in metals [14]. a feature of small cracks in all materials is that they have lower fracture toughness values than large cracks. this effect occurs if the crack length is similar to, or less than, l. such cracks will require less stress intensity to cause failure, so for a given specimen thickness they will experience more constraint, and hence can be expected to show a smaller value of l. conclusions 1) some apparent changes in the critical distance l with notch size reported in the literature arise due to inaccuracies caused by the choice of test specimen and the use of imprecise methods of stress analysis. http://www.gruppofrattura.it http://dx.medra.org/10.3221/igf-esis.11.01&auth=true d. taylor, frattura ed integrità strutturale, 11 (2009) 3-9; doi: 10.3221/igf-esis.11.01 9 2) we can, however, expect that l will change with notch size and other aspects of specimen geometry, if this causes changes in constraint or if the process zone size is a significant proportion of the remaining ligament. 3) despite these changes, the assumption of a constant value of l leads to only small errors in the prediction of fracture stress in long-fibre composite laminate materials, so this approach is recommended for engineering applications. references [1] h. neuber, theory of notch stresses: principles for exact calculation of strength with reference to structural form and material, 2 ed., springer verlag, berlin, (1958) 292. [2] r. e.peterson, in: metal fatigue, edited by g. sines and j. l. waisman mcgraw hill, new york, (1959) 293. [3] j.m. whitney, nuismer, r. j., "stress fracture criteria for laminated composites containing stress concentrations," journal of composite materials, vol. 8, 1974, pp. 253-265. [4] d. leguillon, european journal of mechanics a/solids, 21 (2002) 61. [5] p. cornetti, n. pugno, a. carpinteri, d. taylor, engineering fracture mechanics, 73(14) (2006) 2021. [6] d. taylor, engineering fracture mechanics, 75 (2008) 1696. [7] d. taylor, the theory of critical distances: a new perspective in fracture mechanics, elsevier, oxford, uk, (2007). [8] j.m. whitney, i.m. daniel, r.b. pipes, experimental mechanics of fiber reinforced composite materials, society for experimental stress analysis, connecticut (1982). [9] j. awerbuch, m.s. madhukar, journal of reinforced plastics and composites, 4 (1985) 3. [10] r.c. wetherhold, m.a. mahmoud, materials science and engineering, 79 (1986) pp. 55. [11] r.f. karlak, in: proceedings of failure modes in composites iv, the metallurgical society of aime, chicago (1977) 105. [12] r.b. pipes, r.c. wetherhold, j.w. gillespie, journal of composite materials, 12 (1979) 148. [13] t.c. kennedy, m.h. cho, m.e. kassner, composites part a, 33 (2002) 583. [14] d. taylor, structural integrity and durability, 1 (2006) 145. http://www.gruppofrattura.it http://dx.medra.org/10.3221/igf-esis.11.01&auth=true << /ascii85encodepages false /allowtransparency false /autopositionepsfiles true /autorotatepages /none /binding /left /calgrayprofile (dot gain 20%) /calrgbprofile (srgb iec61966-2.1) /calcmykprofile (u.s. web coated \050swop\051 v2) /srgbprofile (srgb iec61966-2.1) /cannotembedfontpolicy /error /compatibilitylevel 1.4 /compressobjects /tags /compresspages true /convertimagestoindexed true /passthroughjpegimages true /createjobticket false /defaultrenderingintent /default /detectblends true /detectcurves 0.0000 /colorconversionstrategy /cmyk /dothumbnails false /embedallfonts true /embedopentype false /parseiccprofilesincomments true /embedjoboptions true /dscreportinglevel 0 /emitdscwarnings false /endpage -1 /imagememory 1048576 /lockdistillerparams false /maxsubsetpct 100 /optimize true /opm 1 /parsedsccomments true 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/hrv (za stvaranje adobe pdf dokumenata najpogodnijih za visokokvalitetni ispis prije tiskanja koristite ove postavke. stvoreni pdf dokumenti mogu se otvoriti acrobat i adobe reader 5.0 i kasnijim verzijama.) /hun 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can be opened with acrobat and adobe reader 5.0 and later.) >> /namespace [ (adobe) (common) (1.0) ] /othernamespaces [ << /asreaderspreads false /cropimagestoframes true /errorcontrol /warnandcontinue /flattenerignorespreadoverrides false /includeguidesgrids false /includenonprinting false /includeslug false /namespace [ (adobe) (indesign) (4.0) ] /omitplacedbitmaps false /omitplacedeps false /omitplacedpdf false /simulateoverprint /legacy >> << /addbleedmarks false /addcolorbars false /addcropmarks false /addpageinfo false /addregmarks false /convertcolors /converttocmyk /destinationprofilename () /destinationprofileselector /documentcmyk /downsample16bitimages true /flattenerpreset << /presetselector /mediumresolution >> /formelements false /generatestructure false /includebookmarks false /includehyperlinks false /includeinteractive false /includelayers false /includeprofiles false /multimediahandling /useobjectsettings /namespace [ (adobe) (creativesuite) (2.0) ] /pdfxoutputintentprofileselector /documentcmyk /preserveediting true /untaggedcmykhandling /leaveuntagged /untaggedrgbhandling /usedocumentprofile /usedocumentbleed false >> ] >> setdistillerparams << /hwresolution [2400 2400] /pagesize [612.000 792.000] >> setpagedevice microsoft word numero 24 articolo 13 yu. g. matvienko, frattura ed integrità strutturale, 24 (2013) 119-126; doi: 10.3221/igf-esis.24.13 119 special issue: russian fracture mechanics school the failure criterion based on hydrogen distribution ahead of the fatigue crack tip yu. g. matvienko mechanical engineering research institute of the russian academy of sciences, 4 m. kharitonievsky per., 101990 moscow, russia matvienko7@yahoo.com abstract. the hydrogen effect on the fracture toughness and fatigue crack growth behaviour in the martensitic high strength steel is investigated. the secondary ion mass spectrometry method has been employed to analyse the distribution of hydrogen concentration in the zone of the crack tip and at its edges. changes in hydrogen concentration are observed in the vicinity of the propagating crack tip and at a remote site. the hydrogen peak hc is reduced and moves away from the fatigue crack tip with the increase of the maximum stress intensity factor maxk . the concept of damage evolution is used to explain fatigue crack propagation in connection with the hydrogen redistribution ahead of the crack tip. the physical failure criterion based on the hydrogen peak in the vicinity of the fatigue crack tip and the maximum stress intensity factor has been proposed. the criterion reflects changes in the hydrogen peak which resulted from the hydrogen redistribution due to the increase of the maximum stress intensity factor as the crack length increases under fatigue loading. keywords. hydrogen distribution ahead of the crack tip; fatigue crack growth; sims; local failure criterion; high strength steel. introduction ecently many works have been performed on the hydrogen embrittlement of high strength steels (e.g., [1-4]). the deleterious effects of hydrogen on the mechanical properties of high strength martensitic steels are known to have caused premature failures. for example, it was found that the threshold stress intensity factor in steels decreases drastically in response to increased dissolved hydrogen concentration (e.g., [2, 5, 6]). although it has been reported that hydrogen degrades mechanical properties of metallic materials, there have been few studies on the effect of hydrogen on fatigue behaviour ([7-9]). it has been known that the fracture initiates in region of highly localized stress in which hydrogen is concentrated as a result of an augmented diffusion of hydrogen. to explain this phenomenon in the case of monotonic loading, a diffusion model was proposed by liu [10] and developed by kim et al. [3] introducing a fracture criterion as the critical hydrogen concentration at a critical distance ahead of the crack tip. however, until recently only a few papers [11-13] have reported on the experimental distribution of hydrogen ahead of a crack tip. under monotonic mixed (i/ii) mode loading there are two hydrogen accumulation peaks ahead of the crack tip [13], which correspond to the maximum hydrostatic stress and the maximum equivalent plastic strain, respectively. the experimental results also revealed that hydrogen distribution in the vicinity of the fatigue crack tip is related to the stress-strain fields surrounding the crack tip [12, 14]. it should be also r http://dx.medra.org/10.3221/igf-esis.24.13&auth=true http://www.gruppofrattura.it yu. g. matvienko, frattura ed integrità strutturale, 24 (2013) 119-126; doi: 10.3221/igf-esis.24.13 120 noted that the most essential results on the numerical analysis of the effect of cyclic loading on hydrogen diffusion and concentration around a crack tip was published by a.t. yokobori et al. [15]. in this research, experimental analysis of the distribution of hydrogen concentration ahead of the crack tip in the martensitic high strength steel under hydrogen induced cracking and fatigue i mode loading conditions has been carried out. the generalized concept of damage evolution has been employed to explain fatigue crack propagation in connection with the hydrogen redistribution ahead of the crack tip. the physical criterion of local failure based on the hydrogen peak in the fracture process zone and the maximum stress intensity factor has been suggested. experimental procedures he martensitic high strength steel is investigated to analyse the effect of hydrogen charge on the fracture toughness, the fatigue crack growth rate and the distribution of hydrogen concentration ahead of the crack tip. the fraction of retained austenite in the steel did not exceed 10%. chemical composition of the studied steels is given in tab. 1. mechanical properties of the steel at room temperature are the following: the young’s modulus e=210 gpa, yield strength y =850 mpa and ultimate strength u =1150 mpa. c cr ni si mn p s 0.06 16 7 <0.8 <0.8 <0.03 <0.02 table 1: chemical composition of high strength steel (weight %). the hydrogen-charged and pre-fatigued specimens were employed. hydrogen was artificially charged into specimens by a cathodic charging method before the tests. the solution used for the cathodic charging was a 10 mass% h2so4 aqueous solution with an addition of seo2. the current density was i=1 a/dm2 and charging time was 5 hours. prior to immersing the specimen in the solution, its surface (with the exception of the crack surface) was coated with a chemically stable lacquer. the testes were carried out on hus-1025 machine at room temperature in laboratory air. the fracture toughness ck was measured using compact-tension specimens (60x60 mm) with 5 mm thickness according to the standard method reported in the astm standard e399. the fatigue crack growth tests were conducted in order to clarify the hydrogen effect on fatigue crack growth behaviour and the distribution of hydrogen concentration ahead of the fatigue crack tip. rectangular specimens 50 mm high and 5 mm thick with an edge crack loaded in cantilever bending were employed. the loading frequency was 20 hz with a constant amplitude sinusoidal waveform for the applied load. the stress ratio was maintained at r=-0.3. the length of a growing fatigue crack was recorded by an optical microscope. at the given load or fatigue crack length the specimen was unloaded and 10x10 mm templates, which included the zone of the crack tip, were cut out from it. template sizes were caused by sizes of the analytical chamber of the mass spectrometer. the secondary ion mass spectrometry method was then used to analyse the distribution of hydrogen in the zone of the crack tip and at its edges [12]. the small size of the analysed area (5 m ) was ensured using a molybdenum diaphragm placed on the specimen. prior to this, molybdenum was degassed in vacuum. the sensitivity of analysis for hydrogen was 10-2 cm3/100 g. the reproducibility of the results of determining the intensities of the spectral lines was high. the mass spectrometric results were calibrated using reference specimens employed in installations for vacuum heating manufactured by leco company with linear grain sizes in the metal larger than 30 m . this eliminated the apparatus error in recording local hydrogen concentrations associated with segregations of hydrogen at the grain boundary in the reference specimen since the size of the ion beam in analysis was smaller than the size of the grain within which the distribution of hydrogen was usually uniform. it should be noted that secondary ion mass spectrometry was successfully employed for an analyses of the hydrogen distribution around the fatigue crack on type 304 stainless steel [16]. according to the reported data [17], the fatigue crack growth is accompanied by microplastic deformation and formation of hydrogen collectors and traps. this greatly reduces the diffusion mobility of hydrogen in the zone of the crack tip. the curve of hydrogen distribution through thickness for the specimen during removal of layers of the material was constructed (fig. 1). it can be seen that the position of the maximum hydrogen concentration remains unchanged in specimens with different crack lengths. after finding the depth with the maximum concentration of hydrogen, the distribution of hydrogen ahead of the fatigue crack tip was measured at this depth. t http://dx.medra.org/10.3221/igf-esis.24.13&auth=true http://www.gruppofrattura.it yu. g. matvienko, frattura ed integrità strutturale, 24 (2013) 119-126; doi: 10.3221/igf-esis.24.13 121 figure 1: hydrogen distribution hc through the thickness for the hydrogen-charged specimen at the distance of 30 m from the crack tip ( max 20k  mmpa ). hydrogen charging conditions he problem of the effect of hydrogen charging conditions on the character of the hydrogen distribution in the specimen with a crack has been analysed. for this reason, the fatigue pre-cracked ct specimens were hydrogen charged in the same solution as the main set of the specimens at different values of the current density over a period of 2 hours under constant static load corresponding to two applied (constant) stress intensity factor values 10k (tab. 2). 10k ( mmpa ) current density (a/dm2) 0 /cch 30 6 10 2.9 3.0 50 6 10 3.8 3.8 table 2: the effect of hydrogen charging conditions on the hydrogen distribution ahead of the crack tip on crack extension line. the distribution of hydrogen ahead of the crack tip was measured by the same procedure as for the specimens after the fatigue test [12]. the values of the ratio of the maximum local concentration hc of hydrogen ahead of the crack tip to the volume concentration 0c of hydrogen in the specimen were estimated. the results clearly show that the variation of the cathodic current density in these ranges does not influence on the 0/hc c ratio which is determined only by the value of the applied stress intensity factor 10k . the effect of hydrogen on fatigue crack behaviour negligible crack tip plastic zone is created due to the hydrogen embrittlement, mechanical properties of the highstrength steel and a low applied stress. it means that a linear elastic fracture mechanics methodology can be used to quantify the fracture toughness and fatigue crack growth behaviour. it follows that the maximum stress intensity factor must have an influence on fatigue damage evolution and the hydrogen distribution in the vicinity of the crack tip and, as a result, the physical growth of the fatigue crack. t a http://dx.medra.org/10.3221/igf-esis.24.13&auth=true http://www.gruppofrattura.it yu. g. matvienko, frattura ed integrità strutturale, 24 (2013) 119-126; doi: 10.3221/igf-esis.24.13 122 material ( )ck mpa m   / n m cycle c mpa m          m * ( / )v micron cycle 1 uncharged 85 2.53·10-12 2.74 3.84 hydrogencharged 75 4.62·10-12 2.95 3.36 table 3: the fracture toughness and the fatigue crack growth rate parameters 1/ the value of *v corresponds to the stress intensity factor range k varied from 20 mpa•m1/2 to 50 mpa•m1/2. to analyse the effect of hydrogen on the fracture toughness and fatigue crack propagation, the procedure, described in experimental procedures section for hydrogen charged specimens and tests, has been employed. experimental results revealed that the fracture toughness ck and fatigue crack growth behaviour in the high-strength steel are in general dependent on the hydrogen content (tab. 3). the fatigue crack growth rate parameters c and m refers to the paris relationship. the fatigue crack growth rate dndl / versus the stress intensity factor range k curve in the uncharged specimen is lower than that in the hydrogen-charged specimens (fig. 2). the fatigue crack in the hydrogen-charged specimens propagates at the same value of dndl / as in the uncharged specimen at lower (by 30-40%) values of k in the near-threshold region. however, there is no significant difference in the fatigue fracture toughness fck of the uncharged and hydrogen-charged specimens. figure 2: fatigue crack growth behaviour: 1 uncharged specimens, 2 hydrogen-charged specimens experimental analysis of the distribution of hydrogen ahead of the crack tip under hydrogen induced cracking and fatigue i mode loading conditions has been carried out on a secondary ion mass spectroscope. the results on the distribution of hydrogen had been obtained and summarized for various periods of fatigue crack growth (or the maximum stress intensity factor) [12]. the concentration curves of hydrogen distribution in the sections normal to the crack surface and ahead of the crack tip on the crack extension line are plotted in fig. 3 and 4, where hc is the local hydrogen concentration. it can be seen that there is a hydrogen accumulation peak ahead of the crack tip, which is located on some distance ahead of the crack tip (fig. 4). changes in the hydrogen concentration were observed in the vicinity of the propagating crack tip and at a remote site. the hydrogen peak hc is reduced and moves away from the crack tip as the maximum stress intensity factor maxk increases. the hydrogen concentration gradient also decreases. at the same time, the hydrogen concentration far away from the crack tip is increased by increasing the value of maxk . so, the values and sites of hydrogen accumulation under fatigue loading are dependent on the magnitude of the maximum stress intensity factor. http://dx.medra.org/10.3221/igf-esis.24.13&auth=true http://www.gruppofrattura.it yu. g. matvienko, frattura ed integrità strutturale, 24 (2013) 119-126; doi: 10.3221/igf-esis.24.13 123 figure 3: hydrogen distribution hc in the section normal to the crack surface at a distance of 3 mm behind the crack tip. figure 4: hydrogen distribution hc ahead of the crack tip on the crack extension line: line 1 corresponds to max 20k  mpa m , line 2 corresponds to max 68k  mpa m . the trend of the redistribution of hydrogen ahead of the propagating fatigue crack tip can be reflected on the basis of the generalized concept of damage evolution [12, 14]. the concept of damage evolution he evolution approach [18] has been extended to deformation and fracture processes of a mechanical loaded system, i.e. “solid damage”. it is assumed [14] that the accumulation of damage (the system state) is determined by the scalar 0 1   which is the single state variable q   . the controlling parameters  for deformation and failure processes of solids could be stress and strain, the stress intensity factor, temperature and other parameters, which are essential in the consideration of the damage accumulation process. it is postulated that deformation and fracture processes are governed by some general functional law of damage accumulation [14]. for a simple case the damage evolution law can be formulated as n d a d          (1) where 0, n 0a   are material (the “solid damage” system) constants for the fracture process under study.. the evolution law (1) can be made more precise when the physical and mechanical aspects of a failure process are more clearly understood by examining the fracture mechanisms of the solid and the type of loading under study. the value of  decreases with an increase of time  during the process of the accumulation of damage in a solid. the value 1  corresponds to the non-damaged state of a solid when 0  , and the value c   corresponds to the critical state when c  , where c is the critical time. so, failure occurs in a solid if the damage reaches the critical value c   at c  . the following relationship can be written as follows by integrating eq. (1) from 1  to c   t http://dx.medra.org/10.3221/igf-esis.24.13&auth=true http://www.gruppofrattura.it yu. g. matvienko, frattura ed integrità strutturale, 24 (2013) 119-126; doi: 10.3221/igf-esis.24.13 124  1 0 1 1 c n n c a n d        (2) eq. (2) is transformed into the following equation for the determination of the critical time c   11 1 n c c na n       (3) if the controlling parameter  is constant. taking into account eqs. (1) and (3), the cumulative damage law is expressed in the integral form 0 1 c c d     (4) the influence of the controlling parameter  on the critical time may now be analysed for damage evolution in solids. first it is assumed that the critical value c is constant for the deformation and failure process under study, and the critical state of a damaged solid can be reached for various combinations of the controlling parameter and time  . it has been suggested therefore that the critical value c [eq. (2)] is also reached when the controlling parameter  is equal to the critical value c at some fixed time (or a unit of time) * c    , that is  1 *1 1n nc ca n       (5) the evolution equation at c =const is derived from eqs. (2) and (5), namely * 0 c n n cd      (6) this equation may be rewritten at const  as * n c c            (7) the damage evolution equation allows one to estimate the critical time for a solid to reach its critical state under the given controlling parameter for the deformation and fracture processes being studied. it should be noted that exponent n in basic equations has different physical meaning for different physical phenomena and corresponding equations. what is why, this exponent has different table of symbols for below-mentioned equations. the failure criterion ccording to the above-mentioned concept, using the maximum stress intensity factor maxk as the controlling parameter  and replacing critical time c with the critical hydrogen accumulation peak (maximum local hydrogen concentration) maxhc ahead of the crack tip, the damage evolution equation can be written as max max b hc k const (8) it is assumed that the shape of the loading cycle is not changed. eq. (8) gives the physical criterion for local fatigue failure in the fracture process zone, i.e. in the vicinity of the fatigue crack tip, and reflects changes in the hydrogen peak which resulted from the hydrogen redistribution due to the increase of the maximum stress intensity factor as the crack length increases under fatigue loading. this conclusion is in agreement with the observed experimental results (fig. 4) for different values of the maximum stress intensity factor. fatigue crack growth behaviour can be described by the following equation [12] a http://dx.medra.org/10.3221/igf-esis.24.13&auth=true http://www.gruppofrattura.it yu. g. matvienko, frattura ed integrità strutturale, 24 (2013) 119-126; doi: 10.3221/igf-esis.24.13 125  * 'max max1 k k k fc kdl v c r k dn k          (9) where  * ' 1 k kfcv c r k  , 'c and k are constants of the material and loading conditions. the process of local failure in the vicinity of the crack tip has interrupted nature and the crack propagates by means of discrete extension (crack jump) by the value ia . after the jump, further crack propagation requires a certain time (cycle n of loading) to accumulate fatigue damage and redistribute hydrogen in the vicinity of the crack tip until the condition (8) is reached. thus, the parameter * /iv a n   is connected with the discrete nature of fatigue crack propagation. the value *v slightly decreases for the hydrogen-charged specimens (tab. 3). this variation is associated with a reduction of the crack increment ia in the hydrogen-charged specimen rather than with an increase of n . it should be also mentioned that in the presence of a microcracks, the steel with internal hydrogen can be regarded as a system subjected to the effect of an external hydrogen environment. in this case, the localisation of deformation caused by hydrogen can be considered as one of the hydrogen embrittlement mechanisms [17]. it is obvious that more intensive localisation of deformation caused by interaction of hydrogen with moving dislocations and by activation of their sources will be also observed if the steel contains steep hydrogen concentration gradients. conclusions he effect of hydrogen, which was artificially charged into specimens by a cathodic charging method, on the fracture toughness and fatigue crack growth behaviour in the martensitic high strength steel has been investigated. the distribution of hydrogen concentration in the zone of the fatigue crack tip and at its edges has been analysed by the secondary ion mass spectrometry method. the following conclusions can be drawn from the present study. the variation of the cathodic current density does not influence on the ratio of the maximum local concentration hc of hydrogen ahead of the crack tip to the volume concentration 0c of hydrogen which is determined by the value of the applied stress intensity factor 10k . the generalized concept of damage evolution has been employed to describe fatigue crack propagation in connection with the hydrogen redistribution ahead of the crack tip. the failure criterion based on the hydrogen peak in the vicinity of the fatigue crack tip and the maximum stress intensity factor has been proposed. the local concentration of hydrogen in the vicinity of the crack tip is a function of the stress intensity factor, i.e. higher values of maxk lead to the lower hydrogen peak. the criterion explains experimentally observed changes in the hydrogen peak which resulted from the hydrogen redistribution due to the increase of the maximum stress intensity factor as the crack length increases under fatigue loading. references [1] s.a. ahmad, d.a. ryder, t.a. davis, engineering fracture mechanics, 7 (1975) 357. [2] r.l.s. thomas, j.r. scully, r.p. gangloff, metallurgical and materials transactions, 34(a) (2003) 327. [3] y. kim, y. j. chao, marty j. pechersky, michael j. morgan, int. j. of fracture, 134 (2005) 339. [4] j. capelle, j. gilgert, i. dmytrakh, g. pluvinage, engineering fracture mechanics, 78 (2011) 364. [5] c.j. mcmahon, engineering fracture mechanics, 68 (2001) 773. [6] a.t. yokobori, int. j. of fracture, 128 (2004) 121. [7] y. oda, h. noguchi, int. j. of fracture, 132 (2005) 99. [8] y. murakami, int. j. of fracture, 138 (2006) 167. [9] i. dmytrakh, o. smiyan, a. syrotyuk, in: proceedings of the 18th european conference on fracture. fracture of materials and structures from micro to macro scale. dresden, germany. (2010) 13. [10] h.w. liu, transaction of asme: j of basic engineering, 92 (1070) 633. [11] s. wu, l. chen, m. liu, acta metall. sinica., 26 (1990) a86. [12] yu.g. matvienko, v. e. vygovskii, e. n. lubnin, v. b. spiridonov, materials sciences, 26 (3) (1990) 251. t http://dx.medra.org/10.3221/igf-esis.24.13&auth=true http://www.gruppofrattura.it yu. g. matvienko, frattura ed integrità strutturale, 24 (2013) 119-126; doi: 10.3221/igf-esis.24.13 126 [13] h. gao, w. cao, c. fang, e. r. de los rios, fatigue and fracture of engineering materials and structures, 17 (1994) 1213. [14] yu.g. matvienko, in: integrity of pipelines transporting hydrocarbons, nato science for peace and security series c: environmental security / eds.: g. bolzon, t. boukharouba, g. gabetta, m. elboujdaini and m. mellas, springer netherlands: (2011) 227. [15] a. t. uesugi, m. sendoh, and m. shibata, strength, fracture and complexity, 1 (4) (2003) 187. [16] n. saintier, t. awane, j.m. olive, s. matsuoka, y. murakami. international journal of hydrogen energy, 36 (2011) 8630. [17] m.r. louthan, scripta metall., 17 (1983) 451. [18] h. haken advanced synergetic: instability hierarchies of self-organizing systems and devices. berlin, heidelberg, new york, tokyo: springer-verlag, (1983). http://dx.medra.org/10.3221/igf-esis.24.13&auth=true http://www.gruppofrattura.it 404 not found not found the requested url was not found on this server. microsoft word numero_40_art_11 n. g. pnevmatikos et alii, frattura ed integrità strutturale, 40 (2017) 129-136; doi: 10.3221/igf-esis.40.11 129 focussed on recent advances in “experimental mechanics of materials” in greece earthquake design for controlled structures nikos g. pnevmatikos technological educational institution of athens, greece pnevma@teiath.gr george a. papagiannopoulos university of patras, greece gpapagia@upatras.gr george d. hatzigeorgiou hellenic open university, greece hatzigeorgiou@eap.gr abstract. an alternative design philosophy, for structures equipped with control devices, capable to resist an expected earthquake while remaining in the elastic range, is described. the idea is that a portion of the earthquake loading is undertaken by the control system and the remaining by the structure which is designed to resist elastically. the earthquake forces assuming elastic behavior (elastic forces) and elastoplastic behavior (design forces) are first calculated according to the codes. the required control forces are calculated as the difference from elastic to design forces. the maximum value of capacity of control devices is then compared to the required control force. if the capacity of the control devices is larger than the required control force then the control devices are accepted and installed in the structure and the structure is designed according to the design forces. if the capacity is smaller than the required control force then a scale factor, α, reducing the elastic forces to new design forces is calculated. the structure is redesigned and devices are installed. the proposed procedure ensures that the structure behaves elastically (without damage) for the expected earthquake at no additional cost, excluding that of buying and installing the control devices. keywords. response spectrum analysis; structural control; earthquake engineering. citation: pnevmatikos ν., papagiannopoulos g., hatzigeorgiou g., earthquake design for controlled structures, frattura ed integrità strutturale, 40 (2017) 129-136. received: 05.12.2016 accepted: 13.03.2017 published: 01.04.2017 copyright: © 2017 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. introduction ver the past few decades various control algorithms and control devices have been developed, modified and investigated by various groups of researchers. the works of yao, 1975, housner et al., 1994, kobori et al., 1998, and soong 1998 are representative [1-4]. there have been some attempts to connect the control forces with the o n. g. pnevmatikos et alii, frattura ed integrità strutturale, 40 (2017) 129-136; doi: 10.3221/igf-esis.40.11 130 design codes. yang et al. 2003 [5] suggested the maximum control force to be a percentage of the building weight, while cai et al., 1997, [6] give this force as a portion of the seismic force. lee et al., 2004, [7] determined the upper limit of control force based on the response spectrum of the external earthquake. during the past years the design philosophy of new structure was to design stiff structures with high strength to resist the earthquake in the elastic range. after that the design philosophy moves one step further. using the ductility of the material, structures were designed to resist lower level of earthquake forces within the elastic range but to have adequate ductility in order to face the attack of stronger earthquakes and prevent them from collapse. this drives to lighter structures compared to the previous structures and more economical. however, the capacity design and the reinforcement details increased the cost. taking in account the cost of repair of the retrofitting of structure, after a strong earthquake, the design of ductile structures should be under consideration. the design philosophy proposed here is to use control devices installed in the structure and provide a reservoir of strength, stiffness or damping, necessary for preventing the structure from damage when an expected earthquake will occur. thus, the control system will drive the structure to behave in the elastic range when it is attacked by the expected earthquake and no damages will occur. as far as the cost is concerned, it is possible to achieve substantial savings by avoiding retrofit of structure during the lifetime of structure and utilize these savings for installing a control system. a systematic procedure to achieve the above objective is proposed in this work. design procedure for structures equipped with a control system he evolution of the design philosophy of structures passes through different stages. fist the engineers design stiff and massive structures in order to behave elastically during the expected earthquake. as years passed and damages were observed after earthquakes the design philosophy was moved from the resistance of structure to energy dissipation capacity of the structural elements and design of structures with an overall ductile behavior. this drives engineers to perform capacity design for structures. this philosophy is nowadays included in all current design regulations. however, observing the damages to the structures that were designed with the latter philosophy and making calculations, the repair cost of the capacity design emerged and came into consideration. the answer to the previous consideration is the new and proposed design philosophy where the structure is oriented to capacity design equipped with control devices that will absorb a portion of seismic energy induced to the structure and as a result to keep the structure in the elastic range. the three design philosophies are depicted in fig. 1. the proposed design procedure for the spectrum is calculated in such a way that one portion of earthquake forces is taken by the structure and the remaining ones are taken by the control devices. figure 1: the three design philosophies of design of structures. t n. g. pnevmatikos et alii, frattura ed integrità strutturale, 40 (2017) 129-136; doi: 10.3221/igf-esis.40.11 131 finalized design accepted control system installation calculation of elastic and design forces no yes redesign of structure estimate α>(1/q) reduced elastic spectrum by α elastic spectrum new design spectrum a design initially, accepted time history control analysis of structure, with saturation and time delay response satisfies the elastic criteria? no yes design of structure, according to eurocodes elastic spectrum design spectrum 1/q is the difference of elastic to design forces lower than the device capacity? redesign of structure with higher α initially, the controlled structure is designed based on a design spectrum provided by the pertinent code (eurocodes) with a specific level of ductility. the required control forces that will take a portion of earthquake forces are calculated as the difference from forces obtained from the elastic spectrum to those obtained from the design spectrum. the maximum value of capacity of the control devices is compared with the required control force. if the capacity of the control devices is larger than the required control force then the control devices are accepted and installed into the structure. if the capacity is smaller than the required control force then a control device with larger capacity should be chosen or more devices per floor should be installed in case the maximum available control device capacity is smaller than the required control force, or, there is a limitation to the number of control devices, then using an iterative procedure, a scale factor, α, higher than the value 1/q that reduces the elastic response spectrum is calculated. the structure is redesigned based on the new reduced spectrum by scale factor, a, and then the devices are installed into the structure. the flow chart of the procedure is shown in fig. 2 with a solid line. figure 2: the flow chart of the proposed design procedure. estimation of scale factor, a. from the elastic seismic forces and the maximum capacity of the control device a scale factor α is obtained and applied on the elastic spectrum. knowing the mass and initial stiffness of the structure the eigenmodes φi, eigenperiods ti or eigenfrequencies fi and the corresponding damping ratios ξi of the uncontrolled system are obtained. the participation factor ψi, and elastic seismic forces fq,el,i for the ith eigenmode are given as: t i i t i i ψ = , i=1,...,n φ me φ mφ (1) , , , ( , ), 1,...,q el i i i e i i is t i n  f mφ (2) where e is the direction matrix for the earthquake and se,i(ti, ξi) is the elastic spectral acceleration. the maximum elastic seismic forces fq,e for each degree of freedom are obtained combining the square root of sum squares method (srss) the elastic seismic forces from each eigenmode, thus: n. g. pnevmatikos et alii, frattura ed integrità strutturale, 40 (2017) 129-136; doi: 10.3221/igf-esis.40.11 132 n 2 q,e q,e,i i = f f (3) if fd,max is the maximum control device capacity (maximum possible control force), then the maximum control force that can be applied on the system is: d,max f d,maxff e (4) where ef is the location matrix for the control devices on the structure. assuming that one part, up to fd,max, of elastic seismic forces are carried by control devices, the remaining seismic forces which go directly and force the structural elements are: q,e q d,max q d,max q, new q d,max sign( ) if = 0 if      f f f f f f f f (5) fq new is a vector with n forces, where n is the degree of freedom of the system. these forces correspond to a reduced spectral acceleration. from eq. (2) this new spectral acceleration sd,i,new(ti, ξi), corresponding to new seismic forces, can be obtained:  -1 ti q,new d,i,new i i i s ( t ,ξ ) , i=1,...,n ψ  mφ f (6) the reduction factor α can be obtained by dividing the new spectral acceleration sd,i,new(ti, ξi) by the corresponding initial one: d,i,new i i i e,i i i s ( t ,ξ ) α , i=1,...,n s ( t ,ξ )  (7) the elastic spectrum is scaled using the maximum value of αi and the structure is redesigned based on the reduced spectrum. the value of a is: iα max(α ) (8) in order to ensure a linear behavior of the structure, dynamic control analysis is performed for a range of earthquakes (high and low frequency characteristics), with saturation control and time delay. if the response satisfies the elastic criteria, then the value of α is accepted, otherwise it is slightly increased and the above procedure is repeated. the flow chart of this procedure is shown in fig. 2 with a dashed line. the equation of motion of a controlled structural system with n degrees of freedom subjected to an earthquake excitation ag in the state space approach is: g g f a  x ax b b f (9) the matrixes x, a, bg, bf are given by new g f1 1 1 f2 1 2 12 2 2 1 , , , nx nxnx n nx                               0 i 0u 0 x a b b u em k m c m e (10) n. g. pnevmatikos et alii, frattura ed integrità strutturale, 40 (2017) 129-136; doi: 10.3221/igf-esis.40.11 133 where m and c denote the mass and damping matrices of the structure, respectively, knew is the new stiffness matrix of the redesigned structure, and f is the control force matrix. the control force f is determined by linear state feedback as follows:  1 2 1 2             u f g u g u g g gx u   (11) g is the gain matrix, which will be calculated by pole assignment method and according to the desired poles of the controlled system. if the response obtained for the controlled system satisfies the design criteria, then the reduction by q or by a scale factor, α, is accepted. in this work a representative design criterion was used, that the story drift does not exceed h/300 (where h is the story height). this value does not cause member yielding. in a similar way, additional design criteria concerning the rotation and strength of structural members can be used. the above procedure was tested for a number of numerical simulations, and some representative examples are presented next. results and discussion he proposed approach is demonstrated by means of numerical example where an eight-story building, described in the work of yang et al, 1995 [7], is analyzed. initially the elastic and design spectra are calculated based on eurocode 8 (ec8) seismic code. based on those spectra and on dynamic characteristics of building the seismic forces fq,i for each eigenmode and their combination are calculated for both elastic and design spectrum. the seismic forces which are obtained from elastic and design spectrum and their differences are shown in fig. 3(a). assuming that the control devices are installed on each floor and the maximum capacity is 1000kn, following the proposed procedure the scale factor α is calculated to be equal to 0.49 or the equivalent reduction from the elastic spectrum 1-α which is equal to 51%. the elastic and design spectra and the reduced spectrum by 51% from the elastic spectrum, for which the structure will be redesigned, are illustrated in fig. 3(b). in order to ensure that the structure remains in the elastic range after redesigning, dynamic time control analysis history, with saturation control and time delay, for a wide range of earthquakes should be performed. the numerical simulations were performed in simulink toolbox of matlab software. the numerical simulation of the control scheme is described in fig. 3(c). the response (displacement and acceleration) of the system subjected to athens earthquake 1999 were calculated. from the numerical results it was seen that full compensation of the displacements was achieved. according to the work of yang et al. (2003) when one control force corresponds for each degree of freedom then complete compensation of the response can be achieved and the response state vector can be reduced to zero. another reason that the relative displacements are near to zero is that the elastic response spectrum of the athens earthquake are lower than the elastic spectrum that was used initially for the design procedure. the acceleration is equal to the external signal and the building behaves like executing a rigid body motion. the control forces are identical, with maximum value at 917 kn and rms value at 134 kn, because the mass of each story is the same. the storey drift between the floors was not exceeded the limit value h/300=10 mm. time history of displacement and the acceleration from 8th floor for the controlled and uncontrolled structure is shown in fig. 4. summary and conclusions procedure to design a structure equipped with control devices is described. the structure is designed based on a reduced spectrum. a scale factor α which multiplies the elastic spectrum and produces a reduced spectrum is proposed. the design philosophy is that one part of seismic forces are taken by control devices and to the rest of earthquake forces taken up from the structure. the numerical results indicate that reduction of the spectrum can be achieved using control devices. the cost of repairing the post-earthquake damages of an uncontrolled structure which was design based on ductility demand can be considered as a motivation to install a control system which will keep the structure in the elastic range. the control system is acceptable if the results obtained from the dynamic control analysis t a n. g. pnevmatikos et alii, frattura ed integrità strutturale, 40 (2017) 129-136; doi: 10.3221/igf-esis.40.11 134 0 500 1000 1500 2000 2500 3000 3500 4000 0 1 2 3 4 5 6 7 8 earthquake force (kn) s to ri e s 500 (kn) 1000 (kn) 1500 (kn) 1850 (kn) 2000 (kn) 2200 (kn) 2700 (kn) 2800 (kn) earthquake force (kn) st o ri es 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 0 1 2 3 4 5 6 7 8 period (sec) a c c e le ra ti o n ( m /s e c 2 ) period (sec) a cc el er at io n (m /s ec 2 ) keep the structure within the elastic limit. design criteria such as inter-story drift which shouldn’t exceed a specific value that causes yielding of the structural members could be used in order to ensure elastic behavior. (a) (b) (c) figure 3: the difference between elastic and design forces for each story, (a), the elastic and design spectrum, (solid lines), and the reduced elastic spectrum (dash line) for the structure with control devices, (b). model and control scheme in simuling toolbox (c). earthquake model response g saturation time delay n. g. pnevmatikos et alii, frattura ed integrità strutturale, 40 (2017) 129-136; doi: 10.3221/igf-esis.40.11 135 0 5 10 15 20 25 30 35 40 -0.2 -0.15 -0.1 -0.05 0 0.05 0.1 0.15 time (sec) d is p la c e m e n t 8 th ( m ) (a) (b) figure 4: displacement and the acceleration from 8th floor for the controlled and uncontrolled structure. the proposed procedure was applied to 8-story building and the numerical results show the effectiveness of the procedure. the control system helps the structure not only to reduce the maximum response (displacements and accelerations) and keep it in the elastic range, but also to perform at much lower level than the maximum response values. this is proved by comparison of the root mean square (rms) values with the maximum values of response. the proposed design procedure seems to be an effective tool for designing controlled structures although further numerical research and experimental verification are needed. additionally, the methodology should be applied to a space and irregular structures with significant participation of higher modes and with torsional effects. 0 5 10 15 20 25 30 35 40 -15 -10 -5 0 5 10 15 time (sec) a c c e le ra ti o n 8 th ( m /s e c 2 ) n. g. pnevmatikos et alii, frattura ed integrità strutturale, 40 (2017) 129-136; doi: 10.3221/igf-esis.40.11 136 references [1] yao, j.t.p., concepts of structural control, journal of structural engineering asce, 98(7) (1972) 1567-1574. [2] housner, g. w., bergman, l. a., caughey, t. k., chassiakos, a. g., claus, r. o., masri, s. f., skelton, r. e., soong, t. t., spencer, jr., b. f., and yao, j. t. p., structural control: past, present and future, journal of engineering mechanics, 123(9) (1997) 897–971. [3] kobori, t., inoue, y., seto, k., iemura, h., nishitani, a., procedings 2nd world conf. on structural control, kyoto, japan, ii (1998) 171-188. [4] soong, t.t., active structural control: theory and practice, longman scientific &technical/wiley london/new york, 1990. [5] yang, j.n., wu, j.c., agrawal a.k., hsu s.y., sliding mode control of seismically excited linear structures, journal of engineering mechanics, asce, 121 (2003) 1386-1390. [6] cai, g.p., huang, j.z., sun, f., wang, c., modified sliding mode bang-bang control for seismically excited linear structure, earthquake engineering and structural dynamic, 29 (1997) 1647-1657. [7] lee, s.h., min, k.w., lee, y.c., chung, l., improved design of sliding mode control for civil structures with saturation problem, earthquake engineering and structural dynamics, 33 (2004) 1147-1164. [8] yang, j.n., wu, j.c., agrawal, a.k., hsu, s.y., sliding mode control for non linear and hysteretic structures, journal of engineering mechanics asce, 121 (1995) 1330-1339. << /ascii85encodepages false /allowtransparency false /autopositionepsfiles true /autorotatepages /none /binding /left /calgrayprofile (dot gain 20%) /calrgbprofile (srgb iec61966-2.1) /calcmykprofile (u.s. web coated \050swop\051 v2) /srgbprofile (srgb iec61966-2.1) /cannotembedfontpolicy /error /compatibilitylevel 1.4 /compressobjects /tags /compresspages true /convertimagestoindexed true /passthroughjpegimages true /createjobticket false /defaultrenderingintent /default /detectblends true /detectcurves 0.0000 /colorconversionstrategy /cmyk /dothumbnails false /embedallfonts true /embedopentype false /parseiccprofilesincomments true /embedjoboptions true /dscreportinglevel 0 /emitdscwarnings false /endpage -1 /imagememory 1048576 /lockdistillerparams false /maxsubsetpct 100 /optimize true /opm 1 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/hrv (za stvaranje adobe pdf dokumenata najpogodnijih za visokokvalitetni ispis prije tiskanja koristite ove postavke. stvoreni pdf dokumenti mogu se otvoriti acrobat i adobe reader 5.0 i kasnijim verzijama.) /hun 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can be opened with acrobat and adobe reader 5.0 and later.) >> /namespace [ (adobe) (common) (1.0) ] /othernamespaces [ << /asreaderspreads false /cropimagestoframes true /errorcontrol /warnandcontinue /flattenerignorespreadoverrides false /includeguidesgrids false /includenonprinting false /includeslug false /namespace [ (adobe) (indesign) (4.0) ] /omitplacedbitmaps false /omitplacedeps false /omitplacedpdf false /simulateoverprint /legacy >> << /addbleedmarks false /addcolorbars false /addcropmarks false /addpageinfo false /addregmarks false /convertcolors /converttocmyk /destinationprofilename () /destinationprofileselector /documentcmyk /downsample16bitimages true /flattenerpreset << /presetselector /mediumresolution >> /formelements false /generatestructure false /includebookmarks false /includehyperlinks false /includeinteractive false /includelayers false /includeprofiles false /multimediahandling /useobjectsettings /namespace [ (adobe) (creativesuite) (2.0) ] /pdfxoutputintentprofileselector /documentcmyk /preserveediting true /untaggedcmykhandling /leaveuntagged /untaggedrgbhandling /usedocumentprofile /usedocumentbleed false >> ] >> setdistillerparams << /hwresolution [2400 2400] /pagesize [612.000 792.000] >> setpagedevice microsoft word numero_30_art_38 yu.g. matvienko, frattura ed integrità strutturale, 30 (2014) 311-316; doi: 10.3221/igf-esis.30.38 311 focussed on: fracture and structural integrity related issues the effect of thickness on out-of-plane constraint in terms of the t-stress yu.g. matvienko mechanical engineering research institute of the russian academy of sciences, moscow, russia ygmatvienko@gmail.com abstract. the plastic zone is theoretically and numerically analyzed for various combinations of the nonsingular terms xxt to zzt ratios in connection with specimen thickness under mode i loading. the plastic zone size distribution is based on the mises yield criterion for mode i conditions and mapped in the specimen thickness direction. it is shown that the plastic zone size is affected by the zzt -stress, i.e. there is strong effect of out-of-plane constraint (thickness) on crack tip plastic zones. in addition, to study the effect of thickness and loading mode mixity (mode i and ii) of the specimen on the singular (ki, kii) and the non-singular ( xxt , zzt ) terms along the 3d crack front, three-dimensional stress fields are analyzed by means of finite element analysis. the strong effect of thickness and mixed mode loading conditions on the zzt -stress is observed. at the same time, there is not the effect of thickness on the nonsingular xxt -stress at the same loading conditions. keywords. non-singular t-stresses; thickness; mixed mode; in-plane and out-of-plane constraint; plastic zone; introduction he results of analytical and numerical calculations show that stress fields in the vicinity of the crack tip, in many cases, are strongly dependent on constraint. the source of a change of out-of-plane constraint is thickness. in contrast to out-of-plane constraint, the different sources of a change in in-plane constraint at the crack tip are associated with crack size, geometry of specimens and type of loading. to describe in-plane and out-of-plane constraint effects in fracture analysis, the following parameters can be used, namely, zt -parameter [1], local triaxiality parameter [2] and nonsingular components of the t-stresses ( xxt and zzt ) [3]. not emphasize attention on merits and demerits of the above-mentioned parameters of constraint at the crack tip, this paper is concentrated on the nonsingular components of the t-stresses in the vicinity of the crack tip. it is well-known that the sign and value of the xxt -stresses considerably effect on the shape and size of the plastic zone at the crack tip. at the same time, there is no information about influence of thickness on the zzt component as well as the size of the plastic zone in literature. moreover, an analysis of joint influence of the nonsingular t-stress ( zzt and xxt ) terms on the fracture mechanics parameters is not carried out yet. t yu.g. matvienko, frattura ed integrità strutturale, 30 (2014) 311-316; doi: 10.3221/igf-esis.30.38 312 theoretical and numerical analysis of three-dimensional stress fields in the vicinity of through-thickness crack tip under mode i and mixed mode (i + ii) loading is carried out to estimate the effect of thickness on the nonsingular xxt and zzt stresses. the effect of out-of-plane constraint on the crack tip plastic zone basic equations he components of the stress field, which take into consideration three-dimensionality of the stress state near mode i crack front in isotropic elastic body, can be represented in the manner of asymptotic formulas given in ref. [3] 1 3 3 cos 1 sin sin sin 2 cos cos 2 2 2 2 2 22 1 3 3 cos 1 sin sin sin cos cos 2 2 2 2 2 22 1 3 3 sin cos cos cos 1 sin sin 2 2 2 2 2 22 xx i ii xx yy i ii xy i ii k k t r k k r k k r                                                                         2 cos sin 2 22 0, 0 zz i ii zz yz zx zz zz xx k k t r t e t                        (1) here, xx, yy, zz, xy, yz, zx, – components of the stress tensor which define stress state at the arbitrary point near the crack tip; r and  – polar coordinates (fig. 1); ik and iik are stress intensity factors,  is poisson's ratio. the model of the crack tip plastic zone the von mises yield criterion can be employed to estimate the influence of the nonsingular xxt and zzt -stresses in the vicinity of the crack tip on the shape and size of the plastic zone under mode i loading [4, 5]. in this case, the yield criterion can be written in the form        2 2 2 2 2 2 26 2xx yy yy zz zz xx xy yz zx y                  , (2) where y is the yield strength. figure 1: stress components in the vicinity of the crack tip. substitution of asymptotic formulas (1) into the criterion (2) allows determining size pr of the crack tip plastic zone t yu.g. matvienko, frattura ed integrità strutturale, 30 (2014) 311-316; doi: 10.3221/igf-esis.30.38 313 22 2 2 1 yp i i ii p r k d ak r                   (3) here, some parameters are denoted as follows                     zz zz xxxxi t t ttd 2 cos16 2 cos8 2 5 cos3 2 cos 2       (4)      12cos 4 3 cos121 2   i a (5) plastic zone sizes can be estimated by the following equations   u wuvv r p 2 42 1   ,   u wuvv r p 2 42 2   (6) as a result, the plastic crack zone is determined as follows     2 1 2,p pr positive r r     (7) it should be noted that the value of 1pr is positive in the wide range of coefficients u, v, w. at the same time, the value of 2pr has a negative sign. the effect of constraint on the crack tip plastic zone the calculation results of the angular size distribution of the plastic zone around the crack tip in ct specimen with various relations between specimen thickness b and specimen width w are presented in fig. 2. figure 2: the angular distribution of crack tip plastic zone sizes for the middle plane in the ct specimen. the stress intensity factor ki is assumed to be constant independently on specimen thickness and equal to 66 mpam1/2. corresponding values of the t-stress components are presented in tab. 1. sizes of the plastic zone around the crack tip with provision for the spatial stress state (3d analysis) are surrounded by sizes of the zones corresponding to two limit yu.g. matvienko, frattura ed integrità strutturale, 30 (2014) 311-316; doi: 10.3221/igf-esis.30.38 314 conditions, namely, plane stress and plane strain. moreover, when specimen thickness increases, the shape and size of the plastic zones tend to zones which are typical for plane strain conditions. thus, the results clearly show that triaxiality of the stress state around the crack tip should be taken into account by means of both non-singular xxt -stress and zzt -stress according to eq. (6). the validity of analytical equations for calculation of the plastic zone around the crack tip is demonstrated by means of finite element analysis [4, 5]. the deviation between analytical and numerical results does not exceed 20% in the angular range (0, 30…45) and (90…100,135…145). it should be noted that the deviations between the results of the numerical analysis and the analytical calculation in the angular range (0°–145°) can be explained by the fact that the tstress components around the plastic zone can be not constant and depend on angle as reported in ref. [4]. loading parameters b/w=0.25 b/w =0.40 b/w =0.50 p, kn 6.0 9.6 12.0 ki, mpam1/2 66.0 66.0 66.0 txx, mpa 186.59 182.36 176.28 tzz, mpa -159.47 -106.81 -84.97 table 1: loading conditions of the ct specimen. the effect of thickness on the non-singular t-stresses under mixed mode loading loading conditions inite element analysis of 3d stress fields in the vicinity of the crack front is performed for the center cracked circular disc (cccd-specimen) with the thorough-thickness crack of arbitrary space orientation. the specimen is loaded by 2 compressive forces acting in the vertical direction. this configuration of the specimen is very suitable to create different conditions of mixed mode (i + ii) loading [6]. the orientation of the crack plane with respect to the disk is determined by the angle α. changing the angle can provide almost any relationship between the magnitudes of stress intensity factors, namely, ik and iik . loading mode mixity is characterized by the following parameter 2 ( )ie ii k m arctg k  (8) calculation of fracture mechanics parameters the evaluation of the stress intensity factor is based on the well-known approach that includes the calculating this parameter in a number of points (at varied r) using relations from formulas (1) and extrapolation of the obtained values of the stress intensity factors to the point r=0  02 | | | 2 i xx xx xx r k              (9)  | | 8 ii xx xx r k          . (10) the computational procedure considers the nodes of the finite element mesh as the calculation points, but the nodes are located at some small distance from the crack front. to obtain the distribution of the stress intensity factor along the crack front, this procedure is used for a number of planes (x0y) orthogonal to the crack front [79]. their location is characterized by local coordinate s along the front and starts from the center of the crack front. the calculation of the xxt and zzt -stress is performed using the stresses in the points on the crack surface 1 2 xx xx xxt          (11) f yu.g. matvienko, frattura ed integrità strutturale, 30 (2014) 311-316; doi: 10.3221/igf-esis.30.38 315 1 2 zz zz zzt              (12) the determination of xxt and zzt is similar to the procedure for the stress intensity factor including extrapolation to the point r=0. the effect of thickness and loading mode mixity to study the effect of thickness and loading mode mixity of the specimen on zzt -stress, the compressive load is adjusted so that the xxt -stress is remained approximately constant at variation of the specimen thickness (b= 10; 20; 040 and 80 mm) at constant crack length (for the corresponding values of mixity parameter me). to reflect mixed mode loading conditions, an effective stress intensity factor keff is introduced into consideration as follows 2 2eff i iik k k  (13) the results of calculation of the effective stress intensity factor and the zzt -stress in the middle plane of the crack front (s=0) for different mixed mode loading conditions and thickness of the specimen are summarized in fig. 3. the increase of the specimen thickness is 8 times greatly reduces the zzt -stress (up to 75% at me=0,25), whereas the value of xxt is virtually unchanged [8]. thus, magnitudes of the zzt -stress have significant correlation with thickness of the specimen and allows taking into account the level of the out-of-constraint which should be included into assessment of the fracture toughness of full-scale structures. figure 3: the effect of thickness and loading mode mixity on the effective stress intensity factor and out-of-plane constraint in the middle plane of the crack front. conclusions he theoretical analysis of the joint influence of the nonsingular components of the t-stresses ( xxt and zzt ) on the plastic zone around the crack tip of mode i is carried out with attraction of asymptotic formulas, which take into account triaxiality of the stress state at the crack tip, and the von mises yield criterion. the size of the plastic zone around the crack tip at the middle plane of the ct specimen decreases with the increase of specimen thickness. it is confirmed that the plastic zone is affected by the zzt -stress, i.e. there is strong effect of out-of-plane constraint on crack tip plastic zones. t yu.g. matvienko, frattura ed integrità strutturale, 30 (2014) 311-316; doi: 10.3221/igf-esis.30.38 316 the three-dimensional stress field ahead of the through-thickness crack under mixed mode (i+ii) loading conditions is also analyzed. the in-plane and out-of-plane constraint effect are discussed from viewpoint of the non-singular terms, namely, xxt -stress and zzt -stress, respectively. the significant effect of thickness and loading mode mixity of specimen on the zzt -stress in the middle plane of the crack front has been observed at the same non-singular xxt -stress. acknowledgements he author acknowledges the support of the russian science foundation (project n 14-19-00383). references [1] guo, w., three-dimensional analyses of plastic constraint for through-thickness cracked bodies, engineering fracture mechanics, 62 (1999) 383-407. [2] henry, b.s., luxmoore, a.r., the stress triaxiality constraint and the q-value as ductile fracture parameter, engineering fracture mechanics, 57 (1997) 375-390. [3] nakamura, t., parks, d. m., determination of elastic t-stress along three-dimensional crack fronts using an interaction integral, int. j. of solids and structures, 29 (1992) 1597-1611. [4] matvienko, yu.g., pochinkov, r.a., effect of nonsingular t-stress components on the plastic deformation zones near the tip of a mode i crack, russian metallurgy (metally), 4 (2013) 262–271. [5] matvienko, yu.g., the effect of the non-singular t-stress components on crack tip plastic zone under mode i loading, procedia materials science 3 (2014) 141 – 146. [6] aliha, m.r.m., ayatollahi, m.r., smith, d.j., pavier, m.j., geometry and size effects on fracture trajectory in a limestone rock under mixed mode loading, engineering fracture mechanics, 7 (2010) 2200–2212. [7] matvienko, yu. g., chernyatin, a. s., razumovsky, i. a., shi, h.-j., wang, z.-x., the effect of thickness on components of the non-singular t-stress under mixed mode loading, in: 13th international conference on fracture (icf13), beijing, china, (2013). [8] matvienko, yu. g., chernyatin, a. s., rasumovskii, i. a., numerical analysis of the components of the threedimensional non-singular stress field at a mixed-type crack tip, journal of machinery manufacture and reliability, 43 (2014) 242-249. [9] matvienko, yu.g., two-parameter fracture mechanics in contemporary strength problems, journal of machinery manufacture and reliability, 42 (2013) 374-381. t microsoft word numero_41_art_15.docx j.v. sahadi et alii, frattura ed integrità strutturale, 41 (2017) 106-113; doi: 10.3221/igf-esis.41.15 106 focused on multiaxial fatigue prediction of fatigue crack initiation under biaxial loading j.v. sahadi, d. nowell, r.j.h. paynter university of university of oxford, department of engineering science, parks road, oxford, ox1 3pj, uk. joao.sahadicavalheiro@eng.ox.ac.uk, david.nowell@eng.ox.ac.uk, robert.paynter@eng.ox.ac.uk abstract. this investigation revisits biaxial fatigue experiments carried out with the nickel-based superalloy termed waspaloy. recently, yield criteria extended to multiaxial fatigue and stress based approaches were analysed and their performance to correlate the biaxial test data was evaluated. it was concluded that despite their reliable results, the parameters did not properly represent the physical behaviour of the material. in this context, an extension of this study was executed considering the strain based critical plane approaches proposed by fatemi-socie (fs) and smithwatson-topper (swt). the first parameter presented overly conservative predictions with large scatter of results. in contrast, more accurate predictions were obtained with the swt parameter. keywords. biaxial fatigue; fatigue life; waspaloy; critical plane approach. citation: sahadi, j.v., nowell, d., paynter, r.j.h., prediction of fatigue crack initiation under biaxial loading, frattura ed integrità strutturale, 41 (2017) 106-113. received: 28.02.2017 accepted: 15.04.2017 published: 01.07.2017 copyright: © 2017 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. introduction dvances in material testing equipment and techniques during the past 40 years enabled the development of more realistic multiaxial fatigue tests by applying loads representative of service life, at different temperature settings (room, low or elevated temperatures), test frequencies and load phase shift. among the most used techniques, cruciform specimens and thin-walled tubular specimens have been broadly used for fatigue testing under biaxial stress states [1]. yet tension-torsion specimens pose limitations when it comes to probing the entire principal stress plane, 1 vs  2 , and only 2 of its 4 quadrants can be investigated. nevertheless, with different techniques, such as internally pressurized tubular specimens, it is possible to access more of the principal stress plane. the combination of cruciform specimens and axial-torsional specimens, internally pressurized, allow the investigation of almost the entire principal stress plane. however, for cruciform specimens the assessment of biaxial compression region is commonly challenging due to testing machine limitations. in the literature, examples of fatigue life investigation using tubular specimens are available in [2–4]. cruciform specimens and biaxial test rigs allow the investigation of a broad range of biaxiality. however, specimens are expensive and testing is complex. work on biaxial testing with cruciform specimens can be found in [5–7]. recent work at oxford on biaxial fatigue testing and total life prediction using multiaxial fatigue criteria has been presented at the eleventh international conference on multiaxial fatigue and fracture and published on the special issue of the conference [8]. the present paper presents further developments on the investigation of multiaxial fatigue criteria and their predictions for the biaxial test results presented at [8] a j.v. sahadi et alii, frattura ed integrità strutturale, 41 (2017) 106-113; doi: 10.3221/igf-esis.41.15 107 material and experimental work ur earlier work on multiaxial fatigue has presented biaxial tests employed for characterizing the fatigue behaviour of waspaloy [8], a nickel-based superalloy widely used in aero-engines. although the tests previously presented were performed at room temperature, this material presents elevated creep resistance, high fatigue strength, low thermal expansion coefficient and high thermal conductivity; essential characteristics to sustain the extreme mechanical and thermal loads which aero-engine disks are subject to. in terms of its mechanical properties, this material has an elastic poisson's ratio of νe= 0.284 and young's modulus of 213gpa. load controlled tests were carried out at a load ratio of r  0.05 and 0.5hz frequency using a biaxial servo-hydraulic rig, developed and built at the university of oxford. fig. 1(a) presents the rig, which consists of two independent frames carrying hydraulic actuators such that the perpendicular load vectors meet at the centre of the specimen. the vertical load path has a fixed clamp at the top and an actuator at the bottom capable of providing up to 350kn. the horizontal load path has two actuators, providing up to 100kn each. the two frames are connected to each other through a set of springs, which allows vertical movement of the horizontal actuators according to the deformations of the specimen. fig. 1 (b) illustrates the cruciform specimen with reduced thickness gauge section at the centre. the centre portion (excluding the gauge section) was shot peened to increase the fatigue strength of the external edges between the arms and hence to inhibit failure away from the gauge section. strain gauge rosettes were mounted on both front and back face of the gauge section and at the narrow point of the arms. the outputs from these were recorded, together with the applied loads, to determine a calibration of the specimen. figure 1: (a) biaxial test rig. (b) cruciform specimen, applied loads and definition of θ, positive clockwise. load combinations the original load conditions were set to have the same maximum principal stress in each case, varying the other in-plane principal stress. as the gauge section is only 2mm thick and 15mm across, the assumption is made that the local behaviour is equivalent to plane stress conditions, i.e. that the stress in the through thickness direction is zero. the following combinations were investigated:  equal biaxial tension (eb): equal load applied to each arm ( 1 2 );  pure shear (ps): stresses on the two axes are equal and opposite (  1 2 );  single actuator (uniaxial load – ul): load applied on one axis only;  uniaxial stress (us): both axes are used to create an uniaxial equivalent stress state at the gauge section  2 0 );  minimum von mises (mv): the combination of loads that gives the minimum von mises equivalent stress (octahedral shear stress) at the gauge section. experimental results tab. 1 summarizes the results obtained after testing 11 specimens. as presented in more detail at [8], the initial tests compared different biaxialities at the same σ1,peak but different σ2,peak   for each test. following tests for pure shear and uniaxial o j.v. sahadi et alii, frattura ed integrità strutturale, 41 (2017) 106-113; doi: 10.3221/igf-esis.41.15 108 stress cases were run at lower peak stresses. it was observed that in most cases yielding occurred during the first cycle, but no “reversed yielding'' took place when load was removed. hence subsequent load cycles at the same load level did not cause additional plastic deformation despite the material being loaded close to the elastic limit on each cycle. such observation is very important as it set the ground for the multiaxial criteria candidates for fatigue life prediction. exp. no. load case peak load [kn] norm. peak strain norm. peak stress biaxiality ratio cycles horizontal vertical εx εy σx σy σvm load strain stress cx01 single actuator 117 0 1.31 −0.71 1.21 −0.36 1.43 0 −0.54 −0.30 87,765 cx02 equi-biaxial 170 170 0.88 0.88 1.23 1.23 1.23 1 1 1 65,426 cx03 equi-biaxial 170 170 0.88 0.88 1.23 1.23 1.23 1 1 1 57,884 cx04 single actuator 117 0 1.31 −0.71 1.21 −0.36 1.43 0 −0.54 −0.30 97,560 cx05 pure shear 90 −90 1.56 −1.56 1.21 −1.21 2.1 −1.00 −1.00 −1.00 25,789 cx06 pure shear, low ε 51 −51 0.88 −0.88 0.69 −0.69 1.19 −1.00 −1.00 −1.00 510,000 (runout) cx07 uniaxial eq. 128.5 38.5 1.21 −0.34 1.21 0 1.21 0.3 −0.28 0 154,396 cx08 min von mises 147.8 102.8 1.04 0.26 1.21 0.61 1.05 0.7 0.25 0.5 107,004 cx09 uniaxial eq., low ε 93.6 28.1 0.88 −0.25 0.88 0 0.88 −1.00 −0.28 0 658,164 cx10 pure shear, low σ 65.5 −65.5 1.13 −1.13 0.88 −0.88 1.53 −1.00 −1.00 −1.00 236,935 cx11 pure shear 90 −90 1.56 −1.56 1.21 −1.21 2.1 −1.00 −1.00 −1.00 21,684 table 1: experimental tests parameters and results. analysis stress-based criteria n introductory analysis of the test data was achieved by considering extensions of yield theories to multiaxial fatigue and stress based criteria. the formulations of von mises, elastic strain energy equivalent stress, crossland [9], findley [10]and matake [11] were investigated. among them, the energy parameter and crossland’s invariant based approach gave the best predictions. the elastic strain energy density is the sum of the products of strain and stress (divided by 2). in the case of plane stress and no shear, a uniaxial stress with equivalent strain energy to a biaxial stress state is formulated as:         u 2 2 2 2e 1 2 1 22 (1) where  represents the poisson's ratio. fig. 2 (a) presents the correlation between this parameter normalized and the test data in cycles to failure. the stress-life curve was obtained using basquin’s relation (power relationship) and using the equivalent stress presented in eq. (1). the criterion presented good results with a coefficient of correlation, r2, of 0.868. among all the test cases, the pure shear low stress case was the furthest to the trend line. in sequence, some of the most widely used stress based criteria were investigated. the stress invariant based criterion proposed by crossland [9] considers the amplitude of the second invariant of the deviatoric stress tensor, j2a (which corresponds to the amplitude of von mises equivalent stress) and the maximum value of the first invariant of cauchy’s a j.v. sahadi et alii, frattura ed integrità strutturale, 41 (2017) 106-113; doi: 10.3221/igf-esis.41.15 109 stress tensor, i.e. the maximum hydrostatic stress, σh,max. this last term accounts for the mean stress effect. the criterion is given as:   aj 2 h,max , (2) where  and  are material constants determined under fully reversed tension (1 ) and torsion (1 ) tests with smooth specimens respectively:             1 1 3 3 ;   1 , (3) fig. 2 (b) presents the fatigue life predictions obtained with this formulation, considering various fatigue thresholds, i.e. a test case below a line is predicted to have a longer fatigue life than the threshold of the line. on the other hand, a point above it represents a test case with shorter life. the light grey shade area corresponds to the calibrated region (tensiontorsion), and is delimited by the uniaxial tension dashed lines. the darker grey shade area is delimited by the equi-biaxial line. the dashed black lines connect test cases with the same  1,peak, in order to illustrate the biaxiality effect when  2, peak is changed. it was concluded that in general the model presents good correlation with experimental data both within and outside the calibration region (tension-torsion region). non-conservative predictions were obtained for negative values of σ2,peak (pure shear and uniaxial load cases -cx01, cx04, cx05 and cx10). in contrast, as σ2,peak increases towards higher positive values, the criterion becomes proportionally more conservative (min von mises and equi-biaxial – cx08, cx02 and cx03). (a) (b) figure 2: (a) fatigue life predictions with elastic strain energy density. (b) according to crossland’s criterion. strain-based criteria despite the satisfactory results obtained with the stress-based criteria, it was concluded in the previous investigation that the concept of additive parameters does not properly represent the physical behaviour of materials. in this context, a further investigation was performed considering strain based critical plane approaches. this class of strain-based methods is based on the search for critical planes (one or more) where a particular damage parameter reaches its maximum magnitude. this methodology has gained great attention over the past 40 years as it mathematically describes the physical phenomenon and is capable of predicting damage and also the crack orientation (for ductile materials cracks typically nucleate along slip planes, where the maximum shear stress occurs [12,13]). in this sense, among the most widely used criteria the fatemi-socie [14] and smith-watson-topper [15] parameters were evaluated. based on the work of brown and miller [13], fatemi and socie [14] arrived at the conclusion that tensile normal stress in the maximum shear stress plane accelerates crack growth by separating the crack surfaces and consequently reducing frictional forces. the following damage model may be interpreted as the cyclic shear strain modified by the normal stress to include the crack closure effects described. 104 105 106 0.5 1 1.5 2 2.5 rsquared = 0.8677 j.v. sahadi et alii, frattura ed integrità strutturale, 41 (2017) 106-113; doi: 10.3221/igf-esis.41.15 110                    fn fn n g ' b c,max 'max f f' yield 1 2 2 2 (4) where δγmax/2 is the maximum shear strain amplitude and σn,max is the maximum normal stress on the plane where δγmax/2 occurs. the material parameter  represents the influence of the normal stress, σn,max. in addition, σ’yield represents the cyclic yield strength of the material and is included to make the maximum normal stress component dimensionless and proportional to the shear strain. τ'f and bγ are the shear fatigue strength coefficient and exponent respectively. γ'f and cγ are the shear fatigue ductility coefficient and exponent respectively. the material parameter  is given as:                                         f f f f f n n g n n n e ' b c' 'f f yield ' b' b c' f e f p f 2 2 1 2 1 2 1 2 (5) fig. 3(a) illustrates the evolution of the fatemi-socie (fs) parameter presented in eq. (4) and (5), the shear strain amplitude (δγ/2) and the normal stress (σn) as a function of the angle θ, varying from 0 to 180º. considering the angle orientation presented in fig. 1 (b), for all the tests analysed in here the critical planes predicted by this parameter are orientated at 45º and 135º from the y-axis. (a) (b) figure 3: (a) evolution of fatemi-socie parameter (fs), δγ/2 and σn as a function of angle θ for proportional loading. (b) evolution of smith-watson-topper parameter (swt), δε1/2 and σn as a function of angle θ for proportional loading. smith-watson-topper the second damage parameter considered was proposed by smith et al. [59], swt, and was proposed for predicting fatigue life under uniaxial tension-compression conditions. the parameter was originally defined as,          fa f fn n e ' 2 2b b+c' ' n, max f f2 2 , (6) where σ’f and b are the axial fatigue strength coefficient and exponent respectively. similarly ε’f and c represents the axial fatigue ductility coefficient and exponent. this parameter was modified for proportional and non-proportional multiaxial loading conditions of materials that fail predominantly by crack growth on planes of maximum tensile strain or stress, according to crack mode i. in these materials, cracks nucleate in shear, but early life is controlled by crack growth on planes perpendicular to the maximum principal stress and strain. socie [16] proposed a modification to the swt parameter in order to take into account only stresses and strains occurring in the critical plane. this became the most well-known form of the parameter and is mathematically represented by 0 50 100 150 0 5 10-3 0 200 400 600 800 1000 0 5 10-3 0 50 100 150 -5 0 5 0 200 400 600 800 1000 0 2 4 10-3 j.v. sahadi et alii, frattura ed integrità strutturale, 41 (2017) 106-113; doi: 10.3221/igf-esis.41.15 111            f f fn n e ' 2 2b b+c' '1 n, max f f2 2 2 , (7) where, δε1/2 represents the maximum normal stress, and accordingly σn,max is calculated on the plane where δε1/2 occurs. fig. 3 (b) illustrates the evolution of this parameter with respect to θ, along with δεn/2 and σn. the critical planes predicted with this formulation are orientated at 0 and 180º from the y-axis, as oriented in fig. 1 (b). fig. 5 presents the fully reversed normal strain-life curve used to calibrate the models. since no shear strain-life curves were available at the time of this analysis, the additional material parameters needed for the fatemi-socie criterion were estimated based on the relationships presented in tab. 2. moreover, the results and material parameters presented in the work of lopez-crespo et al [17] were used as a benchmark for verifying the implementation of both parameters. parameter axial shear fatigue strength coefficient  f '   f f ' '    / 3 fatigue strength exponent b γb b fatigue ductility coefficient  f '   f ' ' fγ 3 fatigue ductility exponent c γc c modulus e     e g  2 1 table 2: correlation between material fatigue parameters. figure 4: strain-life curve used for model calibration. fatigue life prediction after calibrating both models, their performances were assessed using the biaxial test data presented in tab. (1) (for this analysis, the runout (cx06) was not considered). fatigue lives were calculated using eqs. (4), (5) and (7) at the material plane where each of the parameters (fs and swt) reached their maximum. the results were plotted against the experimental fatigue lives in fig. 5 and summarized in tab. (3). the solid black line in the plot represents perfect correlation between predicted and experimental life. in contrast, predictions lying above this line represent non-conservative predictions, and data points below the line represents conservative predictions. further, the dashed lines represent the bounds of twice and half of the fatigue life. it is observed that the fatemi-socie parameter presented conservative predictions, with all its results in the safe area of the plot. as σ2,peak magnitude decreases towards the uniaxial loading and uniaxial stress conditions(cx1, cx4 and cx07), the prediction error increased proportionally. the farthest point to the solid black line corresponds to cx07 under uniaxial stress state condition. nevertheless, the parameter presented good correlation with the equi-biaxial loading cases (cx02 and 102 103 104 105 10-2 10-1 100 101 102 j.v. sahadi et alii, frattura ed integrità strutturale, 41 (2017) 106-113; doi: 10.3221/igf-esis.41.15 112 cx03), with predictions within the bound of half of fatigue life. the inferior performance of the parameter could be attributed to the estimation of shear strain-life coefficients and exponents based on the available normal strain-life curve. dissimilarly, predictions with the swt parameter are in better correlation with the experimental data, with less scatter. most of the fatigue life predictions lie within the two bound lines. the data points closely aligned with the solid black line represent the pure shear (cx05, cx10, cx11), the uniaxial equivalent (cx09) and the minimum von mises (cx08) cases. the conditions slightly out of the area delimited by the two dashed black line correspond to single actuator and equi-biaxial loading conditions, which presented the largest error. analogously, the superior performance of this second parameter could be related to its calibration, independent of the shear strain-life curve parameters. figure 5: fatigue life predicted with fatemi-socie and smith-watson-topper parameters. exp. № load case fatemi-socie smith-watson-topper critical planes   predicted life critical planes predicted life cx01 single actuator 45º and 135º 7,170 0º and 180º 44,910 cx02 equi-biaxial 45º and 135º 32,680 0º and 180º 213,570 cx03 equi-biaxial 45º and 135º 32,680 0º and 180º 213,570 cx04 single actuator 45º and 135º 7,170 0º and 180º 44,910 cx05 pure shear 45º and 135º 5,010 0º and 180º 22,790 cx07 uniaxial eq. 45º and 135º 9,200 0º and 180º 62,880 cx08 min von mises 45º and 135º 16,430 0º and 180º 117,380 cx09 uniaxial eq., low ε 45º and 135º 117,910 0º and 180º 842,890 cx10 pure shear, low σ 45º and 135º 56,460 0º and 180º 302,600 cx11 pure shear 45º and 135º 5,010 0º and 180º 22,790 table 3: fatigue life predictions with fatemi-socie and smith-watson topper parameters. p re di ct ed f at ig ue l if e [c yc le s] j.v. sahadi et alii, frattura ed integrità strutturale, 41 (2017) 106-113; doi: 10.3221/igf-esis.41.15 113 conclusions urther investigation of the biaxial fatigue behaviour of waspaloy concluded that even more advanced formulations, as the strain based critical plane approaches assessed here, give poor correlations for the equi-biaxial loading cases. the lack of torsional fatigue data, and the estimation of some of these parameter for the implementation of the fatemi-socie formulation, resulted in poor correlation with most test cases. furthermore, the fs parameter presented an overly conservative behaviour with great scatter of results. in contrast, the swt parameter presented better correlation with the biaxial fatigue data. predictions obtained with it lied mostly within or near the bounds of twice and half of the fatigue life. finally, regarding the evaluation of critical planes, the fs parameter predicted failure nucleating on planes at 45º and 135º of the vertical axis, and the swt predicted failures on planes at 0º and 180º. acknowledgments he authors are grateful for the support of rolls-royce plc and the brazilian national council of technological and scientific development (cnpq), grant number 207297/2015-0. a portion of this work was part of a collaborative r&t project siloet supported by the technology strategy board. references [1] bonnand, v., et al. investigation of multiaxial fatigue in the context of turboengine disc applications. international journal of fatigue, 33(8) (2011) 1006-1016. [2] kalluri, s., bonacuse, p. j., in-phase and out-of-phase axial-torsional fatigue behavior of haynes 188 superalloy at 760 c. advances in multiaxial fatigue. astm international, (1993). [3] found, m. s., upul, s. f., miller, k. j., requirements of a new multiaxial fatigue testing facility. multiaxial fatigue. astm international, (1985). [4] andrews, j. m. h., ellison, e. g., a testing rig for cycling at high biaxial strains. journal of strain analysis, 8(3) (1973) 168-175. [5] makinde, a., thibodeau, l., neale, k. w., development of an apparatus for biaxial testing using cruciform specimens. experimental mechanics, 32(2) (1992) 138-144. [6] boehler, j. p., demmerle, s., koss, s., a new direct biaxial testing machine for anisotropic materials. experimental mechanics, 34(1) (1994) 1-9. [7] hannon, a., tiernan, p., a review of planar biaxial tensile test systems for sheet metal. journal of materials processing technology, 198(1) (2008) 1-13. [8] sahadi, j. v., et al., comparison of multiaxial fatigue parameters using biaxial tests of waspaloy. international journal of fatigue (2017). [9] crossland, b., effect of large hydrostatic pressures on the torsional fatigue strength of an alloy steel. proc. int. conf. on fatigue of metals. vol. 138. institution of mechanical engineers london, (1956). [10] findley, w. n., a theory for the effect of mean stress on fatigue of metals under combined torsion and axial load or bending. no. 6. engineering materials research laboratory, division of engineering, brown university, (1958). [11] matake, t., an explanation on fatigue limit under combined stress. bulletin of jsme 20.141 (1977) 257-263. [12] socie, d. f., marquis, g. b., multiaxial fatigue. warrendale, pa: society of automotive engineers, (2000). [13] brown, m. w., miller, k. j., a theory for fatigue failure under multiaxial stress-strain conditions. proceedings of the institution of mechanical engineers, 187(1) (1973) 745-755. [14] kurath, p., multiaxial fatigue life predictions under the influence of mean-stresses. urbana, 51 (1988) 61801. [15] smith, k. n., topper, t. h., watson, p., a stress-strain function for the fatigue of metals(stress-strain function for metal fatigue including mean stress effect), journal of materials, 5 (1970) 767-778. [16] socie, d. f., multiaxial fatigue damage models. transactions of the asme. journal of engineering materials and technology, 109(4) (1987) 293-298. [17] lopez-crespo, p., et al. study of crack orientation and fatigue life prediction in biaxial fatigue with critical plane models. engineering fracture mechanics, 136 (2015) 115-130. f t << /ascii85encodepages false /allowtransparency false /autopositionepsfiles true /autorotatepages /none /binding /left /calgrayprofile (dot gain 20%) /calrgbprofile (srgb iec61966-2.1) /calcmykprofile (u.s. web coated \050swop\051 v2) /srgbprofile (srgb iec61966-2.1) /cannotembedfontpolicy /error /compatibilitylevel 1.4 /compressobjects /tags /compresspages true /convertimagestoindexed true /passthroughjpegimages true /createjobticket false /defaultrenderingintent /default /detectblends true /detectcurves 0.0000 /colorconversionstrategy /cmyk /dothumbnails false /embedallfonts true /embedopentype false /parseiccprofilesincomments true /embedjoboptions true /dscreportinglevel 0 /emitdscwarnings false /endpage -1 /imagememory 1048576 /lockdistillerparams false /maxsubsetpct 100 /optimize true /opm 1 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/hrv (za stvaranje adobe pdf dokumenata najpogodnijih za visokokvalitetni ispis prije tiskanja koristite ove postavke. stvoreni pdf dokumenti mogu se otvoriti acrobat i adobe reader 5.0 i kasnijim verzijama.) /hun 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/pdfxoutputintentprofileselector /documentcmyk /preserveediting true /untaggedcmykhandling /leaveuntagged /untaggedrgbhandling /usedocumentprofile /usedocumentbleed false >> ] >> setdistillerparams << /hwresolution [2400 2400] /pagesize [612.000 792.000] >> setpagedevice microsoft word numero_40_art_5 v. shlyannikov et alii, frattura ed integrità strutturale, 41 (2017) 31-39; doi: 10.3221/igf-esis.41.05 31 focused on multiaxial fatigue effect of different environmental conditions on surface crack growth in aluminum alloys v. shlyannikov, r. yarullin, i. ishtyryakov kazan scientific center of the russian academy of sciences, russia shlyannikov@mail.ru, yarullin_r@mail.ru, ivan_200999@mail.ru abstract. fatigue surface crack growth is studied through experiments and computations for aluminum alloys d16t and b95at (analogue of 2024 and 7075 aluminum). subjects for studies are cylindrical hollow specimens with external semi-elliptical surface crack. the variation of fatigue crack growth rate and surface crack paths behavior was studied under cyclic loading for different environmental conditions. uniaxial tension tests were carried out at low (-60°c), room (+23°c) and high (+250°c) temperature. for the same specimen configuration and the different crack front position as a function of cyclic loading and temperatures conditions the distributions of governing parameter of the elastic-plastic stress fields in the form of in-factor along various crack fronts was determined from numerical calculations. this governing parameter was used as the foundation of the elastic-plastic stress intensity factor (sif). both elastic and plastic sif approach was applied to the fatigue crack growth rate interpretation. it is found that there is a steady relationship between the crack growth rate and the plastic sif in the form of general curve within a relatively narrow scatter band for all tested specimens at different temperatures. keywords. surface crack; aluminum alloys; crack growth; environmental conditions; fatigue fracture diagram; plastic sif. citation: shlyannikov, v., yarullin, r., ishtyryakov., i., effect of different environmental conditions on surface crack growth in aluminum alloys, 41 (2017) 31-39. received: 28.02.2017 accepted: 15.04.2017 published: 01.07.2017 copyright: © 2017 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. introduction he circular cylindrical metallic components of aircraft structure, power engineering elements, pressure vessel and piping are subjected to temperature variations from -60°c (213k) to more than 250°c (523k). in most cases, part-through flaws appear on the free surface of the cylinder and defects are approximately considered as semielliptical cracks. the fatigue growth analysis of surface cracks under different environmental conditions is very important for many engineering applications in order to quantify the structural safety according to the so-called damage tolerant design. furthermore, other environmental effects should be taken into account to assess the structural component safety: for example, the humidity and salt air content play an important role especially under fatigue loading. t v. shlyannikov et alii, frattura ed integrità strutturale, 41 (2017) 31-39; doi: 10.3221/igf-esis.41.05 32 in this paper, only the temperature effects are considered and the fatigue crack propagation is examined. firstly, main mechanical properties of considered alloys are determined on different temperature conditions. secondly, experimental results of fatigue crack growth for a crack starting from a semi-elliptical edge notch in cylindrical hollow specimens under low/high and room temperature are given. the relations of crack mouth opening displacement (cmod) and crack length on the free surface of specimens are obtained. using the aforementioned relations, the crack front shape and crack growth rate in the depth direction can be predicted. third, constrain parameters behaviour and governing parameter of elasticplastic stress field distribution along the crack front was obtained using fem analysis. crack growth interpretation is performed using the traditional elastic and new plastic sif [1-3]. it is found that there is a steady relationship between the crack growth rate and the plastic sif in the form of general curve within a relatively narrow scatter band for all tested specimens at different temperatures. specimens and material properties he crack growth rate tests were carried out for cylindrical hollow specimens with semi-elliptical surface cracks. the hollow cylindrical specimen geometry configuration is shown in fig. 1a. the diameter is equal to 28 mm in the test section and the length is equal to 130 mm. using electro spark method surface edge cracks were cut with initial flaw depths equal to 3.0mm. the geometric parameters of the specimen test section and of the growing crack are shown in figs. 1b. in this figure, b is the current crack depth, with the crack front approximated by an elliptical curve with major axis 2c and minor axis 2a. the crack length b is obtained by measuring the distance between the advancing crack break through point and the notch break through point. the depth of the initial curvilinear edge notch is denoted by a and the initial notch length by h. both the optical microscope measurements and the crack mouth opening displacement (cmod) method are used to monitor and calculate both crack depth and crack length during the tests. the cmod is measured on the free hollow specimen cylindrical surface, in the central plane of symmetry as shown in fig. 1c. a) b) c) figure 1: details of the hollow specimen geometry and initial notch. the test materials are most popular in aircraft industry aluminum alloys d16t and b95at (analogue of 2024 and 7075 aluminum). all tests were carried out at room (23°c or 296k), low (-60°c or 213k) and high (250°c or 523k) temperature with sinusoidal loading form with load control. low/high temperature tests were performed by using following equipment: bi-00-101 utm test system with fatigue rated axial dynamic load cell (capacity +/50kn) and bi-06303 series axial extensometer; climatic chamber cm envirosystems with temperature range: -60°c to 250°c (fig.2). for the cyclic tension fatigue tests, the specimens are tested with an applied maximum nominal stress equal to 65 mpa and with a frequency value 10 hz. the main mechanical properties of considered alloys were determined in accordance with astm e8 for each temperature level [4]. obtained main mechanical properties are listed in tab. 1, where e is the young’s modulus, σs is the nominal ultimate tensile strength, σ0 is the monotonic tensile yield strength, σu is the true ultimate tensile strength, δ is the elongation, ψ is the reduction of area, n is the strain hardening exponent and α is the strain hardening coefficient. t v. shlyannikov et alii, frattura ed integrità strutturale, 41 (2017) 31-39; doi: 10.3221/igf-esis.41.05 33 figure 2: low/high temperature test equipment. material temperature, °c σ0, mpa σs, mpa σu, mpa α n e, gpa δ, % ψ, % d16t -60 406 545 633 2.56 5.32 79.232 15 17 +23 438 594 665 1.54 5.86 76.557 11 11 +250 294 339 371 1.44 8.39 75.246 4 27 b95at -60 506 621 694 1.64 7.71 75.935 11 13 +23 520 586 775 1.44 10.37 75.274 14 36 +250 415 422 436 1.22 12.00 72.737 6 37 table 1: main mechanical properties of aluminum alloys under different temperature. features of the tests in climatic chamber the fatigue surface crack growth rate study for different environmental conditions has several limitations. firstly, measurements of crack length b on free surface of specimens by microscope for the test in climatic chamber sometimes are impossible. secondly, determination of crack size by compliance is not correct, because for surface flaws the crack growth rate value changes along the crack front from the free surface toward the mid-plane. therefore, two different stress ratio r values (0.1 and 0.5) are applied several times to the specimens in order to fix current crack front position: during each test, beach marks are produced on each specimen by increasing the applied stress ratio from 0.1 to 0.5 at a constant value of the maximum cyclic nominal stress, when the surface crack length is approximately increased to b≈0.1 mm. in this manner the marker loading does not induce load history effects or overload retardation [5, 6]. the typical surface marks on the fracture cross section of specimens are shown in fig. 3 for different temperature conditions. figure 3: fracture surface of the hollow specimens at different temperatures: (a) -60°c, (b) +23°c, (c) +250°c. v. shlyannikov et alii, frattura ed integrità strutturale, 41 (2017) 31-39; doi: 10.3221/igf-esis.41.05 34 from the crack front shape obtained in this way, the relations between the relative crack depth a/d and the surface crack chord length b/d can be measured using a comparison microscope (fig. 4). in addition, based on periodically measured increments of surface crack chord length b, the curve of surface crack propagation versus cycle numbers db/dn can be obtained. afterwards, utilizing the relation of crack depth versus surface crack chord length, it is possible to obtain the crack growth rates da/dn in the depth direction. 0.2 0.4 0.6 0.8 1 1.2 1.4 0 0.2 0.4 0.6 0.8 a/d a /c d16t, т=‐60°c d16t, т=+23°c d16t, т=+250°c в95ат, т=‐60°c в95ат, т=+23°c в95ат, т=+250°c a 0.2 0.4 0.6 0.8 1 1.2 1.4 0 0.1 0.2 0.3 0.4 0.5 0.6 b/d a /c d16t, т=‐60°c d16t, т=+23°c d16t, т=+250°c b 0.2 0.4 0.6 0.8 1 1.2 0 0.1 0.2 0.3 0.4 b/d a /c в95ат, т=‐60°c в95ат, т=+23°c в95ат, т=+250°c c figure 4: aspect ratio versus crack depth (a) and crack length (b, c) for both alloys and different temperature conditions. the evolution of the crack growth rate of the elliptical-fronted edge cracks during the tests is determined using cmod and the microscope. fig. 5 shows relations between cmod and crack length b on free surface for both alloys and three temperatures. it is found strong correlation between these two parameters which can be very useful for automation of experimental studies of fatigue and fracture under multiaxial stress state. it should be noted, that the measurements of crack length b by microscope on free surface of specimens for the test in climatic chamber are impossible. for these specimens crack length b was obtained on the base of experimental relations represented on fig. 5. 0.02 0.07 0.12 0.17 0.22 0 5 10 15 20 b, mm c m o d , m m d16t, t=+250°c d16t, t=+23°c d16t, t=-60°c 0.02 0.12 0.22 0.32 0 5 10 15 20 b, mm c m o d , m m b95at, t=+250°c b95at, t=+23°c b95at, t=-60°c figure 5: relationship between cmod and crack length on free surface of hollow specimen under different temperature conditions. numerical study he main purpose of the present study is the interpretation of the surface crack growth rate data in terms of elastic and plastic fracture mechanics parameters. in our previous work we calculated different constraint parameters distribution along the crack front. that is the elastic constraint parameters in the form of the non-singular t-stress and tz -factor as well as the elastic-plastic constraint parameters in the form of local stress triaxiality h and in-factor for the specified combinations of tested material and temperature conditions [4]. fem analysis was performed for semi-elliptical cracks in the cylindrical hollow specimens to determine the stress strain fields along the crack front. typical finite element meshes for the cylindrical hollow specimens are illustrated in fig. 6. the stress-strain state and constraint parameters at the crack tip for each type of the tested specimens were calculated by using the corresponding static material properties listed in tab. 1, ranges of the testing loads and temperatures. these distributions correspond to the crack front positions at the accumulated number of loading cycles: initial front, intermediate front and final failure front (fig. 7). one of the purposes of the work is to obtain an accurate description for the distribution along the crack front of the governing parameter of the elastic-plastic solution in the form of an in-integral t v. shlyannikov et alii, frattura ed integrità strutturale, 41 (2017) 31-39; doi: 10.3221/igf-esis.41.05 35 and to determine the accuracy of this type of calculation, which will be used later for the general 3d problem to provide for the plastic sif. figure 6: typical fem-mesh for cylindrical hollow specimens with semi-elliptical surface crack. figure 7: fem crack front geometry: initial (a), intermediate (b, c), final (d). the distributions of in-integral along the crack front were used to determine the plastic sif kp. for cylindrical hollow specimens the plastic sif kp in pure mode i can be expressed directly in terms of the corresponding elastic sif k1 using rice’s j-integral as follows:      2 2 1 10 ' ' n n p k j i k e e     (1)        1/ 11/ 1 22 2 1 1 1 1 00 ( / ) ( / ) ; ( / ) , ,( / ) , ,( / ) nn p fem fem n n k a w y a w k k y a w i n a w i n a w                              (2) where 1 1 /k k w is normalized by a characteristic size of cracked body elastic stress intensity factor and e'e  for plane stress and  2' 1e e   for plane strain. in the above equations,  and n are the hardening parameters, a w  is the dimensionless crack length, w is characteristic size of specimen (for our case that is specimen diameter),  is the nominal stress, and 0 is the yield stress. the procedure for calculating of the governing parameter of the elastic–plastic stress–strain fields in the form of in-integral for the different specimen geometries by means of the elastic–plastic feanalysis of the near crack-tip stress-strain fields suggested by [1-3]. in this case, the numerical integral of the crack tip field in changes not only with the strain hardening exponent n but also with the relative crack length b/d and the relative crack depth a/d: v. shlyannikov et alii, frattura ed integrità strutturale, 41 (2017) 31-39; doi: 10.3221/igf-esis.41.05 36     1 cos sin 1 , , , 1 cos 1 fem femfemn fem fem fem femr e rr r r fem n fem fem fem fem rr r r du dun u u b a n d d i n d d d u u n                                                                        (3) where ij dimensionless stress components, iu dimensionless displacement components, ,r  polar coordinates. the distributions of the elastic and plastic sif along the initial crack front for both alloys and three temperatures are plotted in fig. 8. the constraint parameters are plotted against the normalized coordinate rr. in this plot rr = 0.0 is the specimen free surface, rr = 1.0 is the mid-plane of the hollow specimen thickness. it can be observed, that all constraint parameters essentially changed along the crack front from the free surface toward to mid-plane. 2 4 6 8 0 0.2 0.4 0.6 0.8 1 rr e la st ic  s if  [ m p a * m ^ 0 .5 ] ‐60°c +23°c +250°c d16t, b95at 0.3 0.4 0.5 0.6 0.7 0.8 0 0.2 0.4 0.6 0.8 1 rr p la st ic  s if d16t +250°c +23°c ‐60°c 0.3 0.4 0.5 0.6 0.7 0.8 0 0.2 0.4 0.6 0.8 1 rr p la st ic  s if ‐60°c +23°c +250°c b95at figure 8: elastic and plastic sif distributions for initial crack front. fig. 8 gives a clear illustration of the necessity to take into account the plastic properties of the material in the interpretation of the characteristics of the material resistance to crack propagation. the distributions of elastic sif are the same for both tested materials, because elastic properties of tested materials approximately the same (tab. 1). contrary to that, the plastic sif shows very useful effect of the sensitivity to the plastic properties of the tested materials. it can be seen from fig. 8 that the plastic sif gradually increases by increasing the test temperature conditions. the data presented very obvious advantages of using the plastic sif to characterize the material's resistance to cyclic crack growth. numerical data for the elastic and plastic sif behaviors accounting for the material properties and temperature conditions will be used to interpret the characteristics of the material resistance to crack propagation. experimental results and discussion he first part of experimental results includes the data of direct measurements of the objective parameters such as the crack length b and the cmod on the free surface of specimens for all considered alloys and temperature conditions. fig. 9 represents the surface crack growth rate db/dn versus cmod on the hollow cylindrical specimens. it is found that the crack growth rate along the external surface direction as a function of cmod described by a various curves with a small scatter band of the experimental results for both tested aluminum alloys. also, looking at fig.4b, 4c and considering changes in the general durability of the specimens in low/high temperature test, significant differences in the crack growth rate in the depth direction a and on the free surface b of hollow specimens under the above temperature conditions are expected. the second part of the experimental data relates to the interpretation of the surface crack growth rate for aluminum alloys at different temperature conditions with the involvement of the numerical results for elastic and plastic sif's distributions presented in the previous section of this paper. based on the interpretation of experimental fatigue fracture diagrams in terms of traditional elastic sif it is found that there are three separate diagrams for each temperature on the free surface of the hollow cylindrical specimen (fig. 10a). in t v. shlyannikov et alii, frattura ed integrità strutturale, 41 (2017) 31-39; doi: 10.3221/igf-esis.41.05 37 contrast, by interpretation of the same experimental crack growth rate diagrams in terms of plastic sif for free surface of the hollow cylindrical specimens of d16t at -60с +250с temperatures a different picture is observed. it is shown that the individual test results at a fixed temperature form a common experimental curve partially overlapping crack growth rate ranges. 1.0e-07 1.0e-06 1.0e-05 1.0e-04 1.0e-03 1.0e-02 0.01 0.1 1 cmod, mm d b /d n [ m m /c y c le ] d16t, t=+250°c b95at, t=+250°c d16t, t=+23°c b95at, t=+23°c d16t, t=-60°c b95at, t=-60°c figure 9: crack growth rate on the free surface of hollow specimen versus cmod for different temperature conditions. a) b) figure 10: crack growth rate as a function of (a) elastic and (b) plastic sifs for free surface of the specimen. the same trend observed for the deepest point of the crack front (fig. 11a, b). moreover, compared with an elastic interpretation of the processes of fatigue failure, the interpretation of cyclic fracture diagrams in terms of the plastic sif's has more uniform character with a small scatter band. the data presented very obvious advantages of using the plastic sif's to characterize the material's resistance to cyclic crack growth. this conclusion is confirmed by the relative position of crack growth curves in figs.10 and 11 for the tested aluminum alloy d16t in the terms of the elastic and the dimensionless plastic sif kp. fig. 12 shows the influence of material properties. on this figure the comparison of crack growth data on the free surface in terms of elastic and plastic sif for both tested materials are presented. experimental data interpretations in terms of plastic sif, which take into account the influence of plastic material properties, give us two different curves for considered alloys. from fig. 12b, the difference in the crack growth rate on the d16t and b95at remains permanently during low temperature and gradually disappears during room temperature test condition. as presented in fig. 12, the experimental data clearly illustrates the effect of temperature on the surface crack growth rate in aluminum alloys tested at the same loading conditions. v. shlyannikov et alii, frattura ed integrità strutturale, 41 (2017) 31-39; doi: 10.3221/igf-esis.41.05 38 a) b) figure 11: crack growth rate as a function of (a) elastic and (b) plastic sifs for deepest point of the crack front. a) b) figure 12: crack growth rate as a function of (a) elastic and (b) plastic sifs for both alloys and different temperature conditions. conclusions atigue surface crack growth is studied through experiments and computations for aluminum alloys d16t and b95at (analogue of 2024 and 7075 aluminum). for both alloys the increasing of test temperature leads to degradation of mechanical properties. by experimental studies for considered temperature conditions the relations between the crack sizes on the free surface of specimen, cmod, crack growth rate and aspect ratio were obtained. for the same specimen configuration and the different crack front position the elastic and elastic-plastic constraint parameters were analyzed as a function of material properties and temperatures conditions. it is stated that the plastic sif, which is sensitive to the constraint effects and elastic-plastic material properties, is attractive as the self-dependent unified parameter for characterization of the material fracture resistance properties. references [1] shlyannikov, v.n., tumanov, a.v., characterization of crack tip stress fields in test specimens using mode mixity parameters, int. j. fract., 185 (2014) 49-76. [2] shlyannikov, v.n., zakharov, a.p., multiaxial crack growth rate under variable t-stress, eng. fract. mech., 123 (2014) 86–99. f v. shlyannikov et alii, frattura ed integrità strutturale, 41 (2017) 31-39; doi: 10.3221/igf-esis.41.05 39 [3] shlyannikov, v.n., tumanov, a.v., zakharov, a.p., the mixed mode crack growth rate in cruciform specimens subject to biaxial loading, theoret. appl. fract. mech., 73 (2014) 68-81. [4] yarullin r., ishtyryakov i., fatigue surface crack growth in aluminum alloys under different temperatures, procedia engineering, vol. 160, 2016, 199–206. [5] slyannikov, v., yarullin, r., ishtyryakov, i., surface crack growth in cylindrical hollow specimen subject to tension and torsion, frattura ed integrita structurale, 33 (2015) 335-344. [6] shlyannikov, v., tumanov, a., zakharov, a., gerasimenko, a., surface flaws behavior under tension, bending and biaxial cyclic loading, int. j. fatigue., 92 (2) (2016) 557-576. << /ascii85encodepages false /allowtransparency false /autopositionepsfiles true /autorotatepages /none /binding /left /calgrayprofile (dot gain 20%) /calrgbprofile (srgb iec61966-2.1) /calcmykprofile (u.s. web coated \050swop\051 v2) /srgbprofile (srgb iec61966-2.1) /cannotembedfontpolicy /error /compatibilitylevel 1.4 /compressobjects /tags /compresspages true /convertimagestoindexed true /passthroughjpegimages true /createjobticket false /defaultrenderingintent /default /detectblends true /detectcurves 0.0000 /colorconversionstrategy /cmyk /dothumbnails false /embedallfonts true /embedopentype false /parseiccprofilesincomments true /embedjoboptions true /dscreportinglevel 0 /emitdscwarnings false /endpage -1 /imagememory 1048576 /lockdistillerparams false /maxsubsetpct 100 /optimize true /opm 1 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can be opened with acrobat and adobe reader 5.0 and later.) >> /namespace [ (adobe) (common) (1.0) ] /othernamespaces [ << /asreaderspreads false /cropimagestoframes true /errorcontrol /warnandcontinue /flattenerignorespreadoverrides false /includeguidesgrids false /includenonprinting false /includeslug false /namespace [ (adobe) (indesign) (4.0) ] /omitplacedbitmaps false /omitplacedeps false /omitplacedpdf false /simulateoverprint /legacy >> << /addbleedmarks false /addcolorbars false /addcropmarks false /addpageinfo false /addregmarks false /convertcolors /converttocmyk /destinationprofilename () /destinationprofileselector /documentcmyk /downsample16bitimages true /flattenerpreset << /presetselector /mediumresolution >> /formelements false /generatestructure false /includebookmarks false /includehyperlinks false /includeinteractive false /includelayers false /includeprofiles false /multimediahandling /useobjectsettings /namespace [ (adobe) (creativesuite) (2.0) ] /pdfxoutputintentprofileselector /documentcmyk /preserveediting true /untaggedcmykhandling /leaveuntagged /untaggedrgbhandling /usedocumentprofile /usedocumentbleed false >> ] >> setdistillerparams << /hwresolution [2400 2400] /pagesize [612.000 792.000] >> setpagedevice microsoft word numero_42_art_24.docx m. peron et alii, frattura ed integrità strutturale, 42 (2017) 223-230; doi: 10.3221/igf-esis.42.24 223 fracture assessment of magnetostrictive materials m. peron, s.m.j. razavi, f. berto, j. torgersen department of mechanical and industrial engineering, norwegian university of science and technology (ntnu), richard birkelands vei 2b, 7491, trondheim, norway. mirco.peron@ntnu.no, javad.razavi@ntnu.no, filippo.berto@ntnu.no, jan.torgersen@ntnu.no m. colussi department of engineering and management, university of padova, stradella s. nicola 3, 36100, vicenza (italy) abstract. giant magnetostrictive materials are gaining interest in the field of smart material, especially the commercially known terfenol-d, that is an alloy made out of iron, terbium and dysprosium (tb0.3dy0.7fe1.9). since these smart materials are subjected to both mechanical loads and magnetic field during their industrial applications, an extensive characterization on the influence of a magnetic field and of defects on their fracture behavior is needed. very few works can be found in literature about this topic and, thus, the purpose of this work is to partially fill this lack by means of three-point bending tests on single-edge pre-cracked terfenol-d specimens. failure loads have been measured at different loading rates and under magnetic fields of various intensities. since giant magnetostrictive materials are very brittle, the strain energy density (sed) approach has been exploited by means of couplefield finite element analyses. sed has revealed itself as a robust parameters in the assessment of the magnetic field and loading rate effects on fracture resistance, allowing also to propose a relationship between the radius of the control volume and the loading-rate. keywords. strain energy density; fracture toughness; loading rates; magnetic field; giant magnetostrictive materials; terfenol-d. citation: peron, m., razavi, s.m.j., berto, f., torgersen, j., colussi, m., fracture assessment of magnetostrictive materials, frattura ed integrità strutturale, 42 (2017) 223-230. received: 15.07.2017 accepted: 17.08.2017 published: 01.10.2017 copyright: © 2017 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. introduction utomotive industry, avionics and robotics are constantly looking for innovations, especially in the field of sensors, actuators and energy harvesting devices where smart material, such as magnetostrictive materials, are widely exploited [1]. this kind of material can convert magnetic energy into kinetic energy, i.e. it exhibits deformation once an external magnetic field is applied, or the reverse, i.e. an applied force determines a magnetization change. such industrial applications require remarkable elongation and high energy density capacity at room temperature, features widely a m. peron et alii, frattura ed integrità strutturale, 42 (2017) 223-230; doi: 10.3221/igf-esis.42.24 224 present in the tb0.3dy0.7fe1.9 alloy, commercially known as terfenol-d. thus, among all the giant magnetostrictive materials, the (tb0.3dy0.7fe1.9) alloy has broadly gained interest in the last years. however, despite of the great attention that this alloy has gained in the industrial applications and though it is susceptible to in-service fracture due to its brittleness [2], very few works are available concerning the assessment of the influence of manufacturing induced defect and cracks on magnetostricitve material performances, notwithstanding the widely reported harmful effects of notches [3–5]. moreover, the fracture behavior of these materials are highly affected by the presence of magnetic fields, since the fracture resistance uder mode i is inversely related to the intensity of the field narita et al. [6]. regarding the determination of the fracture behavior of different materials, it is widely reported that brittle and high-cycle fatigue failures of components weakened by different notches geometries occur when the strain energy density (sed) averaged in a control volume surrounding a crack or notch tip reaches a critical value [7-15]. colussi et al. [16] showed that this criterion could be extended also to giant magnetostrictive materials, under mode i loading condition, employing a control volume having radius 0.07 mm. in this work, three point bending tests on terfenol-d have been carried out, assessing the failure load at different loading rates both in presence and absence of an applied magnetic field. then, coupled-field finite element analysis have been performed in order to evaluate the effect of the loading rate and of the magnetic field, allowing the development of a relationship between the critical radius rc of the control volume and the loading rate. analysis basic equations of the material he basic equations for magnetostrictive materials are outlined as follows. considering a cartesian coordinate system, o-x1 x2 x3, the equilibrium equations are given by: σji,j = 0; εijk hk,j = 0; (1) bi,i = 0 where σji, hi and bi are respectively the components of the stress tensor, the intensity vector of the magnetic field and the magnetic induction vector, whereas εijk is the levi-civita symbol. a comma followed by an index denotes partial differentiation with respect to the spatial coordinate x and the einstein’s summation convention for repeated tensor indices is applied. the constitutive laws are given as: h ij ijkl kl kij k t i ikl kl ik k s d h b d h         (2) where ij are the components of the strain tensor and h ijkls , ikld , t ik are respectively the magnetic field elastic compliance, the magnetoelastic constants and the magnetic permittivity. valid symmetry conditions are: h h h h ijkl jikl ijlk klij kij kji t t ij ji s s s s d d        (3) the relation between the strain tensor and the displacement vector ui is:  , , 1 2 ij j i i ju u   (4) the magnetic field intensity, named φ the potential, is written as: ,i ih  (5) t m. peron et alii, frattura ed integrità strutturale, 42 (2017) 223-230; doi: 10.3221/igf-esis.42.24 225 for terfenol-d, the constitutive relations can be written as: 11 11 3111 12 13 22 22 3112 11 13 33 33 3313 13 33 23 23 1544 31 31 1544 12 1266 0 00 0 0 0 00 0 0 0 00 0 0 2 0 00 0 0 0 0 2 0 0 0 0 0 2 0 0 0 0 0 h h h h h h h h h h h h ds s s ds s s ds s s ds ds s                                                                  1 2 3    0 0 0 0 0 h h h                         (6) 11 22 1 15 11 1 33 2 15 11 2 23 3 31 31 33 33 3 31 12 0 0 0 0 0 0 0 0 0 0      0 0 0 0    0 0 0 0 0 t t t b d h b d h b d d d h                                                            (7) where:   23 32 31 13  12 21 23 32  31 13 12 21 11 1111 2222 12 1122 13 1133 2233 33 3333 44 2323 3131 66 1212 11 12  ,   ,   ,    ,       ,    ,    ,     4 4  ,   4 2                      h h h h h h h h h h h h h h h h h s s s s s s s s s s s s s s s s s                                 15 131 223 31 311 332 33 333    2 2  ,    ,  d d d d d d d d         averaged strain energy density (sed) approach according to lazzarin and zambardi [10], the brittle failure of a component occurs when the total strain energy, w , averaged in a specific control volume located at a notch or crack tip, reaches the critical value wc. in agreement with beltrami [17], named σt the ultimate tensile strength under elastic stress field conditions and e the young's modulus of the material, the critical value of the total strain energy can be determined by the following: 2 2 t cw e   (8) the control volume takes different shapes based on the kind of notch. if the notch is represented by a crack, its opening angle is equal to zero and the control volume is a circumference of radius rc, centered on the crack tip. being this the case, the radius rc can be evaluated once known the fracture toughness, kic, the tensile stress and the poisson's ratio, ν, of the material, by means of the following expression proposed by yosibash et al. [18]: 2 (1 )(5 8 ) 4 ic c t k r             (9) the sed averaged in the control volume can be computed directly by means of a finite element analysis. finite element model in order to compute the averaged strain energy density, w , analyses were performed by means of ansys r14.5 finite element code, both in plane strain and plane stress conditions depending on the specimens' width. for the purpose, solid models were used to determine which was the most appropriate condition. as shown by tiersten [19], the basic equations for magnetostrictive materials are mathematically equivalent to those of the piezoelectric materials, so four nodes plane13 and eight node solid5 coupled-field solid elements from ansys' m. peron et alii, frattura ed integrità strutturale, 42 (2017) 223-230; doi: 10.3221/igf-esis.42.24 226 library were used, respectively for plane and solid models, and the magnetic field has been introduced by a voltage difference. the coordinate axes x = x1 and z = x3 are chosen such that the y = x2 axis coincides with the thickness direction and such that the easy axis of magnetization is the z-direction. because of symmetry, only the half of the model was used in the fea. before carrying out simulations, a mesh sensitivity study was undertaken to determine the adequate finite element (fe) number to be used. sed value have been first determined from a very refined mesh and then from some coarser meshes. the refined mesh had the same fe number adopted in a previous work by the authors, in which finite element models with 6400 elements were used to evaluate the energy release rate by means of j-integral on the same geometry. among different coarse mesh patterns, it has been found suitable for compute sed without accuracy lost a mesh with 274 elements, of which at 10 elements placed inside the control volume. the results are summarized in tab. 1, where the sed value from the proposed coarse mesh is compared with that from the very refined one. the mesh insensitivity is a consequence of the finite element method, in which the elastic strain energy is computed from the nodal displacements, without involving stresses and strains, as shown by lazzarin et al. [10]. the relationship between magnetostriction and magnetic field intensity is essentially non-linear. nonlinearity arises from the movement of the magnetic domain walls, as shown by wan et al. [20]. to take into account this non-linear behavior, the constants d15, d31 and d33 for terfenol-d, in presence of bz = b0, are given by: 15 15 31 31 31 33 33 33 m m z m z d d d d m h d d m h      (10) where 15 md , 31 md and 33 md are the piezomagnetic constants, whereas m31 and m33 are the second order magnetoelastic constants. jia et al. [21] proved that if the specimen's dimension in the direction in which the magnetic field is applied is at least two times greater than the other two dimensions, then the longitudinal magnetostriction is prevailing and it can be assumed that only d33 is a function of the magnetic field hz and that m31 is equal to zero. number fe (control volume) control volume control volume number fe model) w [mj.m3] w [%] 128 6400 0.01461 10 274 0.01457 -0.3 table 1: mean values of sed for different mesh refinement. material elastic compliance [10-12 m2.n-1] piezo-magnetic constants [10-9 ma-1] magnetic permeability [10-6 hm-1] densit y [kg.m-3] 11 hs 33 hs 44 hs 12 hs 13 hs 31 md 33 md 15 md 11 t 33 t ρ terfenol-d 17.9 17.9 26.3 -5.88 -5.88 -5.3 11 28 6.29 6.29 9250 table 2: terfenol-d material properties. m. peron et alii, frattura ed integrità strutturale, 42 (2017) 223-230; doi: 10.3221/igf-esis.42.24 227 experimental procedure mong giant magnetostrictive materials, the commercially named terfenol-d alloy, supplied by etrema products, inc. (usa) was used in all tests and analyses. the material properties are listed in tab. 2. test were performed with the aim to measure the fracture load, pc, of single edge precracked specimens, subjected to three point bending, in presence and in absence of the magnetic field and at various loading-rates. specimens were 5 mm thick, 3 mm wide and 15 mm long. before testing, all specimens were weakened on one side by a 0.5 mm deep crack, which was introduced using a tungsten cutter. tested specimen is showed in fig. 1. figure 1: specimen’s geometry and edge micrograph of the introduced crack. the load p has been impressed at the midpoint of the specimens, which were simply supported with span of 13 mm, by means of a 250 n load cell (resolution: 0.01 n). the load was applied for different loading-rates: 0.05, 0.5 and 3.0 ns-1. a uniform magnetic field, with magnetic induction b0, has been applied in the longitudinal direction through an electromagnet. as devices in which terfenol-d is employed commonly work in magnetic induction range which varies from 0.02 t to 0.05 t, the representative value of 0.03 t has been adopted in all tests. it is due to point out that, as alloying elements in terfenol-d are terbio and disprosio, which are very expensive rare earths, the number of tested specimens was limited: from two to three at each condition. by means of experimental procedure it has also been possible to assess the second order magnetoelastic constant, m33. let consider a cartesian coordinate system, o-x y z, which origin is located at the top center of an uncracked specimen. varying the intensity of the magnetic field applied in the z-direction (longitudinal direction), the trend of magnetostriction has been measured through a strain gauge located at x = y = z = 0 mm. by comparison between the measured strain εzz and the numerically obtained one, it has been found that the proper value for the second order magnetoelastic constant is 4.82×10-12 m2a-2. this value has been used in the analyses to compute the sed. results and discussion racture load, pc, in presence and absence of the magnetic field have been experimentally measured at each loadingrate. data, in terms of fracture load, are summarized in tab. 3. bold numbers represent the average value at each condition, whereas numbers in brackets represent the relative standard deviations. average fracture loads are presented in fig. 2. the error bars indicate the maximum and minimum values of pc the average fracture load at 0.05 ns-1, 0.50 ns-1 and 3.0 ns-1 are decreased respectively about 7%, 9% and 14% in the presence of the magnetic field. it has also been found that terfenol-d shows a decrease in fracture load as the loading-rate decreases. similar behavior has been observed for other materials such as tial alloys, by cao et al. ([22]) and piezoelectric ceramics, by shindo et al. ([23-24]) and narita et al. ([25]). to take into account the effect of the loading-rate on terfenol-d fracture load, here it is assumed that the critical radius rc, which depends on the material and on the notch opening angle, varies also with the speed at which the load is applied. by plotting the averaged sed related to the mean values of critical loads in tab. 3, in presence and in absence of the magnetic field, as a function of control volume radius, it is possible to determine different intersections for each loadingrate. the intersections have been found at 0.05, 0.056 and 0.1 mm respectively for the loading-rates 0.05, 0.5 and 3.0 ns-1. a f m. peron et alii, frattura ed integrità strutturale, 42 (2017) 223-230; doi: 10.3221/igf-esis.42.24 228 this means that, at the critical load, the material is characterized by a value of strain energy density, averaged in a control volume having size variable with the loading-rate, which is independent of the ratio between the applied load and magnetic field. a good fit of rc versus loading-rate to a linear model has been found, then, adopting a simple linear regression model, the following relationship is proposed: 0.0195 0.05c dp r dt   (11) pc [n] dp/dt b = 0 t b = 0.03 t 0.05 ns-1 58.3 59.2 65.8 61.9 74.7 64.6 66.3 (5.81) 61.9 (1.91) 0.5 ns-1 66.6 60.7 68.5 61.6 67.5 (0.78) 61.1 (0.37) 3.0 ns-1 71.0 74.2 79.2 59.3 60.0 75.1 (3.35) 64.5 (5.95) table 3: measured fracture loads as a function of the loading-rate and the magnetic field figure 2: mean fracture loads as a function of the loading-rate and the magnetic field the approximated critical radius of 0.07 mm, obtained from (9) and suggested by colussi et al. [16] without taking into account the loading-rate, falls amid of the range of variation here proposed. fig. 3 shows a summary of the experimental data in terms of the square root of the ratio between the averaged strain energy density, w , and the critical value of strain energy, wc. this parameter has been chosen because of its proportionality to the fracture load. the averaged strain energy density, w , has been computed in control volumes having radius given by (11), whereas a critical strain energy equal to 0.02 mj.m-3 is assumed. this critical value is obtained from eq. (8), assuming young's modulus equal to 30 gpa, poisson's ratio equal to 0.25 and tensile strength equal to 34 mpa, which are the medium characteristics provided by the material supplier. here, young's modulus is assumed independent from the applied magnetic field. this assumption is reasonable in the range of variation of the applied magnetic field. in fig. 3 experimental data from narita et al. [25] have also been summarized. data referred to fracture loads measured under three point bending, with and without magnetic a 0.03 t magnetic field, at the following loadingrate: 0.2 ns-1 and 3.0 ns-1. specimens were 3 mm thick, 5 mm wide and 15 mm long. crack depth was 0.5 mm. due to the different geometry (ratio between width and thickness equal to 5/3 instead of 3/5) plane strain condition instead of plane stress condition resulted more appropriate for their modeling. it has been found that about all experimental data fit in a narrow scatter band, which limits are drown here with an engineering judgment from 0.80 to 1.20 (4 data over 35 0 10 20 30 40 50 60 70 80 90 100 0.05 0.5 3 p c  [n ] dp/dt [n/s] 0 t 0.03 t m. peron et alii, frattura ed integrità strutturale, 42 (2017) 223-230; doi: 10.3221/igf-esis.42.24 229 being outside of this range). the few data which exceed the band fall however in the safety region of the plot. the averaged sed criterion appears suitable for fracture strength assessment of cracked specimens made out of terfenol-d alloy, under mode i condition, in presence or absence of the magnetic field and with variable loading-rate. in the authors' opinion the result is satisfactory and the sed criterion permits the reliable assessment of terfenol-d brittle failure by means of coarse mesh based finite element models. the proposed relationship between the size of the control volume and the loading-rate also permit to take into account the loading-rate by means of static analyses. some future developments will involve also high temperature applications [26]. figure 3: mean fracture loads as a function of the loading-rate and the magnetic field b. conclusions combined experimental and numerical study was conducted to understand the defect sensitivity of giant magnetostrictive materials. under mode i loading condition, it has been found that terfenol-d shows a decrease in fracture load in presence of a magnetic field. this behavior in justified by the increase of the strain energy with increasing magnetic fields. terfenol-d also shows a decrease in fracture loads as the loading-rate decreases. results indicate that sed criterion in able to capture this behavior if a linear relationship between the size of the control volume and the loading-rate is assumed. a good match between experimental results and numerical predictions has been found and a substantial mesh insensitivity of sed approach has been proved. references [1] zhao, x., lord, d.g., application of the villari effect to electric power harvesting, j. appl. phys., 99 (2006) 08m703 [2] peterson, d.t., verhoeven, j.d., mcmasters, o.d., spitzig, w.a., strength of terfenol-d. j. appl. phys., 65 (1989) 3712. [3] lazzarin, p., comportamento a fatica dei giunti saldati in funzione della densità di energia di deformazione locale: influenza dei campi di tensione singolari e non singolari, frattura ed integrità strutturale, 9 (2009) 13-26. [4] maragoni, l., carraro, p. a., peron, m. and quaresimin, m., fatigue behaviour of glass/epoxy laminates in the presence of voids, int. j. fatigue, 95 (2017) 18–28. [5] brotzu, a., felli, f. and pilone, d., effects of the manufacturing process on fracture behaviour of cast tial intermetallic alloys, fract. struct. integr. 27 (2013), 66-73. [6] narita, f., morikawa, y., shindo, y., sato, m., dynamic fatigue behavior of cracked piezoelectric ceramics in threepoint bending under ac electric fields, j. eur. cera. soc., 32 (2012) 3759–3766. [7] ayatollahi, m.r., razavi, s.m.j., rashidi moghaddam, m., berto, f., mode i fracture analysis of polymethylmetacrylate using modified energy—based models. phys. mesomec., 18 (2015) 53-62. a m. peron et alii, frattura ed integrità strutturale, 42 (2017) 223-230; doi: 10.3221/igf-esis.42.24 230 [8] ayatollahi, m.r., rashidi moghaddam, m., razavi, s.m.j., berto, f., geometry effects on fracture trajectory of pmma samples under pure mode-i loading. eng. fract. mech., 163 (2016) 449–461. [9] rashidi moghaddam, m., ayatollahi, m.r., razavi, s.m.j., berto, f., mode ii brittle fracture assessment using an energy based criterion, phys. mesomec. (in press). [10] lazzarin, p. and zambardi, r., a finite-volume-energy based approach to predict the static and fatigue behavior of components with sharp v-shaped notches, int. j. fract., 112 (2001) 275–298. [11] berto, f., lazzarin, p. and ayatollahi, m. r., brittle fracture of sharp and blunt v-notches in isostatic graphite under torsion loading, carbon n. y., 50 (2012) 1942–1952. [12] radaj, d., berto, f., and lazzarin, p., local fatigue strength parameters for welded joints based on strain energy density with inclusion of small-size notches, eng. fract. mech., 76 (2009) 1109–1130. [13] berto, f., croccolo, d. and cuppini, r., fatigue strength of a fork-pin equivalent coupling in terms of the local strain energy density, mater. des., 29 (2008) 1780–1792. [14] berto, f. and barati, e., fracture assessment of u-notches under three point bending by means of local energy density, mater. des., 32 (2011) 822–830. [15] berto, f. and ayatollahi, m. r., fracture assessment of brazilian disc specimens weakened by blunt v-notches under mixed mode loading by means of local energy, mater. des., 32 (2011) 2858–2869. [16] colussi, m., berto, f., mori, k., narita, f., effect of the loading rate on the brittle fracture of terfenol-d specimens in magnetic field: strain energy density approach, strength mater, (in press). [17] beltrami, e., sulle condizioni di resistenza dei corpi elastici, rendiconti del regio istituto lombardo xviii, (1885) 704-714. [18] yosibash z., bussiba a. r., g.i., failure criteria for brittle elastic materials. int. j. fracture, 125 (2004) 307–333. [19] tiersten, h.f., 1969. linear piezoelectric plate vibrations: elements of the linear theory of piezoelectricity and the vibrations of piezoelectric plates. springer, new york, (1969). [20] wan, y., fang, d., hwang, k.c., non-linear constitutive relations for magnetostrictive materials, int. j. nonlinear mech., 38 (2003) 1053–1065. [21] jia, z., liu, w., zhang, y., wang, f., g.d., a nonlinear magnetomechanical coupling model of giant magnetostrictive thin films at low magnetic fields, sens. actuators a, 128 (2006) 158-164. [22] cao, r., lei, m.x., chen, j.h., zhang, j., effects of loading rate on damage and fracture behavior of tial alloys. mater. sci. eng., 465 (2007) 183–193. [23] shindo, y., mori, k., narita, f., electromagneto-mechanical fields of giant magnetostrictive / piezoelectric laminates. acta mech., 212 (2010) 253-261. [24] shindo, y., narita, f., mori, k., nakamura, t., nonlinear bending response of giant magnetostrictive laminated actuators in magnetic fields, j. mech. mater. struct., 4 (2009) 941–949. [25] narita, f., morikawa, y., shindo, y., sato, m., dynamic fatigue behavior of cracked piezoelectric ceramics in threepoint bending under ac electric fields, j. eur. ceram. soc., 32 (2012) 3759–3766. [26] gallo, p., berto, f., glinka, g generalized approach to estimation of strains and stresses at blunt v-notches under non-localized creep, fatigue fract. eng. mater. struct, 39 (2016) 292-306. << /ascii85encodepages false /allowtransparency false /autopositionepsfiles true /autorotatepages /none /binding /left /calgrayprofile (dot gain 20%) /calrgbprofile (srgb iec61966-2.1) /calcmykprofile (u.s. web coated \050swop\051 v2) /srgbprofile (srgb iec61966-2.1) /cannotembedfontpolicy /error /compatibilitylevel 1.4 /compressobjects /tags /compresspages true /convertimagestoindexed true /passthroughjpegimages true /createjobticket false /defaultrenderingintent /default /detectblends true /detectcurves 0.0000 /colorconversionstrategy /cmyk /dothumbnails false /embedallfonts true /embedopentype false /parseiccprofilesincomments true /embedjoboptions true /dscreportinglevel 0 /emitdscwarnings false /endpage -1 /imagememory 1048576 /lockdistillerparams false /maxsubsetpct 100 /optimize true 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/hrv (za stvaranje adobe pdf dokumenata najpogodnijih za visokokvalitetni ispis prije tiskanja koristite ove postavke. stvoreni pdf dokumenti mogu se otvoriti acrobat i adobe reader 5.0 i kasnijim verzijama.) /hun 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can be opened with acrobat and adobe reader 5.0 and later.) >> /namespace [ (adobe) (common) (1.0) ] /othernamespaces [ << /asreaderspreads false /cropimagestoframes true /errorcontrol /warnandcontinue /flattenerignorespreadoverrides false /includeguidesgrids false /includenonprinting false /includeslug false /namespace [ (adobe) (indesign) (4.0) ] /omitplacedbitmaps false /omitplacedeps false /omitplacedpdf false /simulateoverprint /legacy >> << /addbleedmarks false /addcolorbars false /addcropmarks false /addpageinfo false /addregmarks false /convertcolors /converttocmyk /destinationprofilename () /destinationprofileselector /documentcmyk /downsample16bitimages true /flattenerpreset << /presetselector /mediumresolution >> /formelements false /generatestructure false /includebookmarks false /includehyperlinks false /includeinteractive false /includelayers false /includeprofiles false /multimediahandling /useobjectsettings /namespace [ (adobe) (creativesuite) (2.0) ] /pdfxoutputintentprofileselector /documentcmyk /preserveediting true /untaggedcmykhandling /leaveuntagged /untaggedrgbhandling /usedocumentprofile /usedocumentbleed false >> ] >> setdistillerparams << /hwresolution [2400 2400] /pagesize [612.000 792.000] >> setpagedevice microsoft word numero_29_art_9 v. sepe et alii, frattura ed integrità strutturale, 29 (2014) 85-96; doi: 10.3221/igf-esis.29.09 85 focussed on: computational mechanics and mechanics of materials in italy response of porous sma: a micromechanical study v. sepe, s. marfia university of cassino and southern lazio v.sepe@unicas.it, marfia@unicas.it f. auricchio university of pavia auricchio@unipv.it abstract. lately porous shape memory alloys (sma) have attracted great interest as low weight materials characterized by high energy dissipation capability. in the present contribution a micromechanical study of porous sma is proposed, introducing the simplifying hypothesis of periodic distribution of voids. the mechanical response of the heterogeneous porous medium is derived by performing nonlinear finite element micromechanical analyses considering a typical repetitive unit cell made of a circular hole in a dense sma matrix and prescribing suitable periodicity and continuity conditions. the constitutive behavior and the dissipation energy capability of the porous nitinol are examined for several porosity levels. numerical applications are performed in order to test the ability of the proposed procedure to well capture the overall behavior and the key features of the special heterogeneous material. keywords. shape memory alloys; porous material; micromechanics; dissipation. introduction hape memory alloys (sma) are characterized by a very special behavior due to their capability to undergo reversible changes of the crystallographic structure, depending on the temperature and on the stress state. these changes can be interpreted as reversible martensitic transformations between a crystallographic more-ordered parent phase, the austenite, and a crystallographic less-ordered product phase, the martensite. thanks to their unique properties over the last decades sma have been used for a large number of applications in several engineering fields, from aerospace to medical device industries. recently, driven by biomedical applications, a great interest has arisen concerning a particular class of sma: the porous sma. currently, several methods are adopted for manufacturing porous sma from elemental powders. many porous niti sma with different structures of pores have been successfully produced by sintering at elevated pressure via a hot isostatic press or metal injection molding [1], spark plasma sintering [2], combustion synthesis with a self-propagating wave [3]. the possibility of producing sma in porous form has opened new fields of applications owing to their low-weight with high energy dissipation properties. porous shape memory alloys combine benefits from dense sma and porous structure. in fact, even beyond the shape memory characteristics, porous sma with a relatively low density can enlarge the applicability of dense sma. in addition to the large recoverable strains observed by sma, the porous counterpart offers s v. sepe et alii, frattura ed integrità strutturale, 29 (2014) 85-95; doi: 10.3221/igf-esis.29.09 86 the possibility of undergoing greater overall strains as well as higher specific energy absorption under dynamic loading conditions due to the possibility of wave scattering. in the biomedical field, thanks to their high biocompatibility [4] and their capacity to exhibit high strength, niti foams have been tested as bone implant materials [5], effectively exhibiting a considerable amount of bone ingrowth. in particular, these materials display unique characteristics such as: relatively low stiffness, useful to minimize stress shielding phenomenon, shape recovery effect, that facilitates implant insertion and ensures good mechanical stability within the host tissue, elevated osteoconductivity and better osseointegration and osteoconductivity than bulk niti alloys. in the last years, applications of porous sma in the field of civil and mechanical engineering have also been considered. the potential applications of porous sma exploit their ability to carry significant loads and their high energy absorption capability. in fact, the porous sma shows a higher specific damping capacity under dynamic loading conditions with respect to the dense sma, because the pores facilitate an additional absorption of the impact energy. in order to correctly reproduce the behavior of the porous sma, the development of accurate models describing their properties is needed. several papers have been published concerning the modeling of porous sma (e.g. [6-8]). the porous sma material can be treated as a composite with sma as the matrix and pores as the inclusions. in order to derive the mechanical response of porous sma, micromechanical averaging techniques have been developed in the available literature, as for instance [9, 10]. indeed, different micromechanical and homogenization techniques, usually applied to study composites can be used to model porous sma, such as the eshelby dilute inclusion technique or the mori-tanaka scheme [11, 12] or the selfconsistent method. an interesting approach that has been adopted to study the behavior of porous materials is based on the assumption of having a periodic distribution of pores. in this case, the problem can be solved by using a computational homogenization technique based, for instance, on nonlinear finite element analyses of a single unit cell with suitable boundary conditions. the behavior of porous sma under cyclic loading conditions has been studied in [13], where the constitutive law has been enhanced to account for the development of permanent inelastic strains due to stress concentrations in the porous microstructure. aim of the present contribution is to propose a micromechanical study of porous sma. in particular, the response of porous sma is derived by performing the nonlinear finite element micromechanical analysis for the typical repetitive unit cell, considering periodicity conditions. the constitutive model, proposed in [15] and [16] and able to reproduce the main properties of dense shape memory alloys response, is adopted in order to simulate the behavior of the porous sma. the constitutive response and the dissipation energy capability of the porous nitinol are investigated for several values of porosity. numerical applications are developed in order to assess the ability of the presented procedure to well capture the overall behavior of the special heterogeneous material, correctly reproducing the pseudoelastic effect., a key feature of the shape memory alloys. porous sma modeling he porous sma is a composite material in which voids can be considered as inclusion in a dense sma matrix. the study of the mechanical response of porous sma can be conducted performing micromechanical analyses which accounts for the presence of a random distribution of voids characterized by different shape and dimensions. in this study, developed in the framework of small strains, the simplifying hypothesis of regular, i.e. periodic, distribution of voids is introduced: in other words, it is assumed that all the voids have the same dimension and shape. in such a way, the study can be limited to the analysis of a unit cell (uc) which is representative of the heterogeneous material and that completely accounts for the geometry and material properties of the constituents of the composite. such a simplified approach allows to derive the influence of the void volume fraction on the mechanical response. sma constitutive model concerning the modeling of dense sma material, the model initially proposed by souza et al. [14] and modified first by auricchio and petrini [15] and, then, by evangelista et al. [16] is adopted to reproduce the shape memory alloys behavior. in the following discussion, the voigt notation is adopted, so that second order tensors are represented as vectors and fourth order tensors as matrices. in particular, the strains and the stresses are reported as vectors with 6 components, while symmetric 6×6 matrix defines the elastic constitutive matrix. the use of this notation is preferred as it enables a straightforward implementation in a numerical code. t v. sepe et alii, frattura ed integrità strutturale, 29 (2014) 85-96; doi: 10.3221/igf-esis.29.09 87 the model is thermodynamically consistent and it assumes the total strain ε and the absolute temperature t as control variables and the transformation strain vector d as internal variable. the transformation strain d describes the strain associated to the phase transformation and, in particular, to the conversion from austenite or multivariant martensite to single-variant martensite. the norm of d , denoted as  , is constrained to satisfy the inequalities 0 l   , where l is a material parameter indicating the maximum transformation strain reached at the end of the conversion from austenite or multivariant martensite to single-variant martensite, during a uniaxial test. according to the thermodynamic formulation, the existence of a thermodynamic potential is postulated and a free specific energy function is introduced through a convex potential as:        , , , , ,e p idt t t t      ε d ε d d (1) where: e represents the elastic strain energy due to the thermo-elastic material deformations, depending on the total strain ε , on the inelastic strain d and on the absolute temperature t ; p is the inelastic energy which accounts for all the inelastic phenomena and that is related to the internal variable d and to the absolute temperature t ; id is defined as the free energy due to the change in temperature with respect to the reference state for an incompressible ideal solid [14, 15, 16]. in particular, the thermo-elastic potential e is defined as:      1, , 2 t e t   ε d ε d c ε d (2) where c is the elasticity constitutive matrix and the superscript t denotes the transposition operation. the inelastic potential in the dense sma is set as proposed in [16] and it is function of the temperature and the transformation strain d :    21, 2 l p ft t m h        d  (3) where:   is a material parameter linked to the dependence of the transformation stress threshold on the temperature;  fm represents the finishing temperature of the austenite-martensite phase transformation evaluated at a stress free state;  the symbol  indicates the positive part of the argument;  t v  d m d with 1 2 v         i 0 m 0 i (4) i and 0 being the 3 3 identity and zero matrices, respectively;  h is a material parameter associated to the slope of the linear relation ruling the value of the transformation stress threshold with the temperature in the uniaxial case;    l  is the indicator function introduced in order to satisfy the fulfillment of the constraint on the transformation strain norm: 0 if ( ) ifl l l             (5) which ensures that the norm of the transformation strain has to be bounded between zero, for the case of a material without oriented martensite, and the maximum value l , for the case in which the material is fully transformed in singlevariant oriented martensite. the state laws can be derived as: v. sepe et alii, frattura ed integrità strutturale, 29 (2014) 85-95; doi: 10.3221/igf-esis.29.09 88    σ ε (6)     x d (7) which define the thermoelastic laws for the stress and the thermodynamic force, respectively. the latter quantity x represents the thermodynamic variable associated with the transformation strain and it is indicated as the transformation stress. the eq. (6) and (7) state that σ and x are the quantities thermodynamically conjugated to the deformation-like variables ε and d , respectively. therefore, the state laws assume the expressions:   σ c ε d (8) [ ]ft m h            x σ d (9) where  is an element of the subdifferential of the indicator function   l  which results as:   0 if if if l l l l                    (10) eq. (9) can be rewritten in the following form:  x σ α (11) with α playing a role similar to the back stress in the classical plasticity theory with kinematic hardening; it is defined as: [ ]ft m h           α d (12) resulting a linear function of the temperature when ft m . the yield function is assumed to depend on the deviatoric part of the thermodynamic force and it is introduced as:    22d df j r x x (13) where:  r represents the radius of the elastic domain in the deviatoric space, given by the relation: 2 3 tr  (14) with t the uniaxial critical stress evaluated at ft m ;  dx is the deviatoric part of the associated variable x and it is computed as: d devx i x (15) where: 2 3 1 3 1 3 with 1 3 2 3 1 3 1 3 1 3 2 3 dev                   dev 0 i dev 0 i (16)  2j is the second invariant of dx determined through the following formula:  2 1 with 22 td s d sj           i 0 x m x m 0 i (17) v. sepe et alii, frattura ed integrità strutturale, 29 (2014) 85-96; doi: 10.3221/igf-esis.29.09 89 the equation describing the associative normality rule for the internal variable d is:  df     x d x  (18) with  the plastic multiplier. from the analysis of the flow rule form it can be noted that the transformation strain d is a deviator vector and, thus, the condition of incompressibility during the inelastic flow is recovered. the model is completed introducing the classical kuhn-tucker conditions: 0 0 0f f     (19) that reduce the problem to a constrained optimization problem. the normality properties are sufficient to guarantee the satisfaction the second principle of thermodynamics in the form of the clausius-duhem inequality [17]. thus, the proposed model results to be consistent with the thermodynamic formulation. periodic microstructure the periodic microstructure of the analyzed material allows to consider a repetitive unit cell (uc) subjected to suitable boundary conditions in order to determine the overall behavior of the whole heterogeneous material. in the following, the uc, composed of the sma matrix and the pore, is denoted as  and the discussion is limited to the framework of 2d plane strain problems. the components of the 2d macroscopic fields of the average strain vector  11 22 12 t   ε and of the average stress vector  11 22 12 t   σ can be defined in  , respectively, as: 1 1 2 2 2 1 2 1 0 0 1 1 0 , 0 n x n da x da v v n n x x                      ε u σ t (20) where  n x represents the normal to the boundary of the unit cell  ,  u x is displacement vector and  t x is the traction vector defined as 11 1 2 22 2 1 12 0 . 0 n n n n                  t in the presence of pores the average strain and stress fields take the following form: 1 2 2 1 0 1 1 1 0 , h n dv n da dv v v v n n               ε ε u σ σ (21) where h is the union of the surfaces of voids present in the uc made of porous material. in eq. (21)2 the term: 1 2 2 1 0 1 0 h x x da v x x           t has not been reported, since pores are considered regions with null tractions and at the interfaces h the continuity of the tractions has to be ensured. for periodic media, introducing a cartesian reference system 1 2(o, , )x x in the uc, the displacement field  1 2 t u uu in the typical point  1 2 t x xx of the unit cell is given by the relations: 1 11 1 12 2 1 2 12 1 22 2 2 1 , 2 1 , 2 u x x u u x x u             (22) v. sepe et alii, frattura ed integrità strutturale, 29 (2014) 85-95; doi: 10.3221/igf-esis.29.09 90 where 11 , 22 and 12 are the components of ε , the effective strain acting on the uc; 1u and 2u are the components of  u x , the vector representing the periodic part of the displacement. from formula (22), the total strain in the typical point x of the unit cell is given by:     ε x ε ε x (23) where  ε x represents the periodic part of the strain, characterized by null average in  and associated to the periodic displacement  u x . as suggested in [18, 9], for rectangular 2d unit cells with the total dimensions along the two coordinate axes 1x , 2x denoted by 12a and 22a , the classical periodicity conditions:             1 2 1 2 2 2 2 1 2 1 2 1 1 1 , , , , , , i i i i u a x u a x x a a u x a u x a x a a               (24) have to be prescribed to the displacement field, being 1, 2i  . numerical results n the following numerical applications 2d micromechanical analyses are developed in order to study the overall mechanical response of periodic porous shape memory alloys and to investigate the influence of the volume fraction of voids on their mechanical behavior. a square periodic uc made of a circular hole embedded in a dense nitinol matrix is analyzed. the constituent material properties adopted for the dense sma matrix are set as in [16] and are defined in tab. 1, where the symbols e and  indicate the young modulus and the poisson ratio, respectively. niti mechanical properties 1 53000 mpa 0.36 1000 mpa 2.1mpak 0.06 223 k 61.23 mpa l f t e h m             table 1: material properties for the porous niti sma. fig. 1 shows the uc geometry where a unit thickness is considered. different volume fractions of voids are analyzed keeping constant the side l of the uc and varying the radius r of the pore. in particular six ucs are examined with different values of porosity set as: 5%, 10%, 20%, 35%, 45% and 55%. the mechanical response of the heterogeneous media, when the pseudoelastic effect is activated, is investigated. in fact, an increasing value of the average strain 11 is prescribed in the ucs until the value 11 0.02  is reached at a constant temperature 270 kt  , greater than fa , temperature at which the more-ordered austenitic phase is stable. then, the prescribed strain is removed allowing the recovery of the transformation strain in the porous sma, exploiting the niti pseudoelasticity. the described loading history is prescribed on the six unit cells characterized by the different volume fractions of voids and on a uc made of homogeneous material (0% porosity) with the same mechanical properties defined in tab. 1. fig. 2 shows the behavior of the unit cells in terms of the average normal stress 11 versus the average strain 11 for all the different analyses characterized by the different volume of voids (denoted in the legend with the acronym vv). then, the same loading history is assigned on the considered unit cells, but prescribing a higher value of the average normal strain 11 at the end of the loading phase, up to 4%. the mechanical responses of the porous sma cells with i v. sepe et alii, frattura ed integrità strutturale, 29 (2014) 85-96; doi: 10.3221/igf-esis.29.09 91 different porosities are illustrated in figure 3, where the average normal stress versus the average normal strain along the 1x -direction is plotted. figure 1: porous niti sma periodic unit cell. figure 2: mechanical responses of the porous ucs along 1x -direction for the first loading history. from fig. 2 and fig. 3 it can be pointed out that the constitutive model adopted to reproduce the porous sma response is able to correctly capture the pseudoelastic effect for both the loading histories characterized by different values of the maximum average strain prescribed at the end of the loading phase. it can be observed that for the homogeneous sma specimen with no pores (fig. 2 and fig. 3) the stress-strain slope occurring during transformation is rather high due to the fact that the analyses are performed under plane strain conditions. moreover it can be remarked that for both the loading histories the value of the maximum average normal stress along the 1x -direction ( max 11 ), reached at the end of the loading step, decreases for increasing values of porosity. 0 0.002 0.004 0.006 0.008 0.01 0.012 0.014 0.016 0.018 0.02 -200 0 200 400 600 800 1000 1200 1400 vv=0% vv=5% vv=10% vv=20% vv=35% vv=45% vv=55%  11 mpa 11 v. sepe et alii, frattura ed integrità strutturale, 29 (2014) 85-95; doi: 10.3221/igf-esis.29.09 92 the results obtained by the adopted micromechanical approach underline that both the stress-strain slope during transformation and the yield strength significantly reduce with the increase in porosity. these outcomes are well supported and justified by a large amount of experimental data, such as the ones provided in [11, 20-24] for porous shape memory alloys. fig. 4 shows the trend of the maximum value of the average normal stress along 1x -direction achieved for the different volume fractions of voids. in particular, a comparison between the results obtained for the first loading history ( 11 2%  ) and denoted with the triangle marker, and the results provided by the second loading history ( 11 4%  ) and indicated with the round symbol, is given. it can be noted that being equal the volume fraction of voids, the value of the maximum average tensile stress is obviously higher for the analyses in which the average strain reaches the value of 11 0.04  . figure 3: mechanical responses of the porous ucs along 1x -direction for the second loading history. however the difference between the values of max11 for the two loading histories tends to decrease with the increasing of porosity, so that for a high level of voids fraction the increase of the average strain leads to a low increase of the maximum tensile average stress. the energy dissipation capability of the porous niti, due to the stress hysteresis based on the pseudoelastic properties, has also been investigated for the considered unit cells and for both the loading histories. in fig. 5 the ratio between the dissipated energy and the volume of the solid fraction is plotted in function of the porosity for the two loading paths. the comparison between the results obtained by the two loading cases shows that the higher is the level of the prescribed average strain on the ucs, the higher is the energy dissipated by the porous sma in relation to its own weight. it can be put in evidence that for the first loading history the energy dissipated per solid volume during the pseudoelastic loading cycle increases with the increasing of the porosity level until the volume fraction of voids is equal to 20%. as the value of the volume of voids continues to increase, the dissipated energy tends to keep almost constant, with a value that is higher than the one obtained for the case of homogeneous shape memory alloys. furthermore, for the second loading history characterized by a maximum value of average strain up to 4%, it can be underlined that the energy dissipation capability increases in function of the volume fraction of voids, providing the maximum value for the case of porosity equal to 55%. thus the performed analyses show that the energy dissipation capability of porous materials is obviously influenced by the entity of the prescribed loading strain. moreover it can be remarked that high levels of volume fraction of voids can lead 0 0.005 0.01 0.015 0.02 0.025 0.03 0.035 0.04 -500 0 500 1000 1500 2000 2500 3000 vv=0% vv=5% vv=10% vv=20% vv=35% vv=45% vv=55%  11 mpa 11 v. sepe et alii, frattura ed integrità strutturale, 29 (2014) 85-96; doi: 10.3221/igf-esis.29.09 93 to a heterogeneous material able to dissipate more than shape memory alloys characterized by low porosity or dense material. figure 4: maximum average normal stress for the considered porosities provided by the two loading histories. figure 5: dissipated energy per solid volume for the considered porosities provided by the two loading histories. conclusions he mechanical behavior of porous sma has been investigated in the present work. the simplifying hypothesis of considering a periodic distribution of voids all characterized by the same shape and dimensions has been assumed so that a typical repetitive unit cell, representative of the heterogeneous material and able to account for the properties of the composite medium, has been analyzed. the model proposed by [15] and [16] for dense sma has been adopted to reproduce the constitutive behavior of porous shape memory alloys. 0 0.1 0.2 0.3 0.4 0.5 0.6 0 500 1000 1500 2000 2500 3000 voids fraction loading history 1 loading history 2  max11 mpa 0 0.1 0.2 0.3 0.4 0.5 0.6 1 2 3 4 5 6 7 voids fraction d is si pa te d e ne rg y / s ol id v ol um e [ m j/ m 3 ] loading history 1 loading history 2 t v. sepe et alii, frattura ed integrità strutturale, 29 (2014) 85-95; doi: 10.3221/igf-esis.29.09 94 plane strain 2d micromechanical analyses have been developed to derive the influence of the volume fraction of voids on the mechanical response of the porous niti. in particular, the behavior of the heterogeneous material when the pseudoelastic effect is activated, has been investigated considering different periodic unit cells characterized by several values of porosity. the performed analyses have shown the ability of the adopted constitutive model to reproduce the pseudoelastic effect for porous sma. moreover the influence of the volume of voids on the maximum tensile stresses reached by the porous material and on the energy dissipation capability has been examined for two different values of prescribed average strain. the obtained results have demonstrated that the value of the maximum average normal stresses reached during the loading phase decreases for increasing values of porosity and that for a high level of the volume fraction of voids the increase of the prescribed average strain leads to a low increase of the maximum value of the tensile average stress. furthermore, analyzing the dissipation capability of the porous medium during the pseudoelastic loading cycle, the developed analyses have put in evidence that the higher is the porosity level the higher is the capability of the porous sma to dissipate energy in relation to its own weight. thus the attractive feature of low-weight with high energy dissipation of the porous shape memory alloys is well captured by the proposed simplified micromechanical approach. future developments will be focused on other particular porous sma issues, such as the presence of pores with different shapes and of interconnected pores or the possible presence of porous internal pressure, relevant for the case of smart biomedical applications. moreover an extension of the analyses to the finite strain regime will be considered in future works in order to account also for the variation of the pore shape during the loading histories. acknowledgement the financial supports of prin 2010-11, project ”advanced mechanical modeling of new materials and technologies for the solution of 2020 european challenges” cup n. f11j12000210001 are gratefully acknowledged. the authors wish to thank prof. elio sacco for his useful comments and suggestions. references [1] krone, l., schüller, e., bram, m., hamed, o., buchkremer, h.p., stöver, d., mechanical behaviour of niti parts prepared by powder metallurgical methods. mater. sci. eng. a, 378 (2004) 185–190. [2] shearwood, c., fu, y.q., yu, l., khor, k.a., spark plasma sintering of tini nano-powder. scr. mater., 52 (2005) 455–460. [3] whitney, m., corbin, s.f., gorbet, r.b., investigation of the mechanisms of reactive sintering and combustion synthesis of niti using differential scanning calorimetry and microstructural analysis. acta mater., 56 (2008) 559–570. [4] shabalovskaya, s.a., on the nature of the biocompatibility and on medical applications of niti shape memory and superelastic alloys, bio-medical materials and engineering, 6 (4) (1996) 267-289. [5] bansiddhi, a., sargeant, t. d., stupp, s. i., dunand, d. c., porous niti for bone implants: a review, acta biomaterialia, 4 (2008) 773–782. [6] entchev,p.b. and lagoudas,d.c., modeling of transformation-induced plasticity and its effect on the behavior of porous shape memory alloys. part ii: porous sma respons. mechanics of materials, 36(9) (2004) 893-913. [7] nemat-nasser,s., su,y., guo,w.g. and isaacs,j., experimental characterization and micromechanical modeling of superelastic response of a porous niti shape-memory alloy. journal of the mechanics and physics of solids, 53(10) (2005) 2320-2346. [8] liu, b., dui, g., zhu, y., on phase transformation behavior of porous shape memory alloys, journal of the mechanical behavior of biomedical materials, 5 (2012) 9-15. [9] qidwai, m.a., entchev, p.b, lagoudas, d.c., de giorgi, v.g., modeling of the thermomechanical behavior of porous shape memory alloys. int. j. of solids struct., 38 (48-49) (2001) 8653–8671. [10] entchev, p.b., lagoudas, d.c., modeling porous shape memory alloys using micromechanical averaging techniques, mechanics of materials, 34 (1) (2002) 1–24. [11] zhao,y. and taya,m., analytical modeling for stress-strain curve of a porous niti. journal of applied mechanics, 74(2) (2007) 291-297. [12] zhu, y., dui, g., a model considering hydrostatic stress of porous niti shape memory alloys, acta mechanica solida sinica, 24 (4) (2011). v. sepe et alii, frattura ed integrità strutturale, 29 (2014) 85-96; doi: 10.3221/igf-esis.29.09 95 [13] panico, m., brinson, l.c., computational modeling of porous shape memory alloys, int. j. solids struct., 45 (2008) 5613–5626. [14] souza a.c., mamiya e.n., zouain n., three-dimensional model for solids undergoing stress-induced phase transformations, european journal of mechanics a/solids, 17 (1998) 789-806. [15] auricchio, f., petrini, l., a three-dimensional model describing stress-temperature induced solid phase transformations: solution algorithm and boundary value problems, int. j. for numer. meth. eng., 61 (2004) 807–836. [16] evangelista, v., marfia, s., and sacco, e., phenomenological 3d and 1d consistent models for shape memory alloy materials, comput. mech., 44 (2009) 405-421. [17] lemaitre, j., chaboche, j., mecanique des materiaux solides, dunod, paris, (1988). [18] suquet, p., elements of homogenization for inelastic solid mechanics. in: homogenization techniques for composite media (edited by e. sanchez-palencia and a zaoui). lecture notes in physics vol. 272. springer, berlin, (1987) 194275. [19] luciano, r., sacco, e., variational methods for the homogenization of periodic heterogeneous media. european journal of mechanics a/solids, 17-4 (1998) 599-617. [20] greiner, c., oppenheimer, s.m., dunand, d.c, high strength, low stiffness, porous niti with superelastic properties. acta biomaterialia 1 (2005) 705–716. [21] imwinkelried, t., mechanical properties of open-pore titanium foam. journal of biomedical materials research part a, 81(4) (2007) 964-970. [22] xiong, j.y., li, y.c., wang, x.j.,. hodgson, p.d, wen, c.e., titanium–nickel shape memory alloy foams for bone tissue engineering. journal of the mechanical behavior of biomedical materials i (2008) 269-273. [23] wang, x., y. li, et al., porous tinbzr alloy scaffolds for biomedical applications. acta biomaterialia, 5(9) (2009) 3616-3624. [24] wen, c.e., xiong, j.y., li, y.c. and hodgson, p.d., porous shape memory alloy scaffolds for biomedical applications: a review. phys. scr. t139 (2010). microsoft word numero_41_art_32.docx v.m. machado et alii, frattura ed integrità strutturale, 41 (2017) 236-244; doi: 10.3221/igf-esis.41.32 236 focused on crack tip fields on short cracks that depart from elastoplastic notch tips verônica miquelin machado, jaime tupiassú pinho de castro, marco antonio meggiolaro pontifical catholic university of rio de janeiro, puc-rio, r. marquês de são vicente 225, rio de janeiro, 22451-900, brazil vetiksm@gmail.com, jtcastro@puc-rio.br, meggi@puc-rio.br abstract. the behavior of short cracks that depart from elastoplastic notch tips is modeled to estimate the stresses required to initiate and to propagate cracks in notched structural components, and to evaluate the size of tolerable crack-like defects under general loading conditions. this analysis can model both fatigue and environmentally assisted cracking problems; can evaluate notch sensitivity in both cases; and can as well be used to establish design or acceptance criteria for tolerable non-propagating crack-like defects in such cases. the growth of short cracks is assumed driven by the applied stresses and by the stress gradient ahead the notch tip, and supported by the material resistances to crack initiation and to long crack propagation by fatigue or eac. in the elastoplastic case, the stress gradient ahead of the notch tip is quantified by a j-field to consider the short crack behavior. the tolerable short crack predictions made by this model are evaluated by suitable fatigue and eac tests of notched specimens specially designed to start nonpropagating cracks from the notch tips, both under elastic and elastoplastic conditions. keywords. short cracks; notch sensitivity; fatigue cracking; environmentally assisted cracking; elastoplastic behavior; j-integral. citation: machado, v.m., castro, j.t.p., meggiolaro, m.a., on short cracks that depart from elastoplastic notch tips, frattura ed integrità strutturale, 41 (2017) 236-244. received: 28.02.2017 accepted: 03.05.2017 published: 01.07.2017 copyright: © 2017 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. introduction t is well-known that abrupt geometric transitions (like holes, slots, grooves, keyways, shoulders, corners, threads, weld fillets, reinforcements, etc.), generically called notches, can significantly perturb the local stress field around their borders. in particular, notches induce a localized stress concentration factor (scf) kt  max/n, where max is the maximum stress at the notch tip and n is the nominal stress that would act there if the notch did not disturb the stress field in its vicinity. scf can be calculated by linear elastic (le) procedures when such conditions apply around the notch borders, but not if the material yields at the notch tip [1]. it is also well-known that notch-induced effects under fatigue load conditions can be smaller than it would be predicted from ktn, in particular if kt is high. if this was not so, small sharp scratches would be able to ruin any structural component subjected to fatigue loads. therefore, notch effects in fatigue are often quantified in practical applications by kf  1  q(kt  1), where 0  q  1 is the notch sensitivity factor. i v.m. machado et alii, frattura ed integrità strutturale, 41 (2017) 236-244; doi: 10.3221/igf-esis.41.32 237 for design purposes, q-values are traditionally estimated by fitting semi-empirical models to data from fatigue tests of notched components. however, q has long been associated to non-propagating short cracks that start at the notch tips but stop after growing for a small distance [2-4]. consequently, q-values can also be analytically modeled by studying the behavior of those short fatigue cracks. in particular, the model proposed in [5-7] estimates q-values for fatigue loading conditions using sound mechanical principles and well-defined mechanical properties, without the need for any additional data-fitting parameter. moreover, it allows the notch sensitivity concept to be extended to environmentally-assisted cracking (eac) problems as well, and its predictions have been validated under liquid metal embrittlement conditions by testing notched al samples in a ga environment [8], as well as under hydrogen embrittlement conditions by testing similar steel samples in aqueous h2s environments [9]. this versatile notch sensitivity model is extended in this work to deal with elastoplastic (ep) problems using j-integral techniques properly adapted to consider the short crack behavior near the notch tips. influence of short cracks in the fatigue limit of notched structural components atigue cracks are very sensitive to local load conditions, so they usually initiate at notch tips due to the stress concentration effects induced by the notch. a similar behavior occurs under eac conditions as well. however, it is less well-known that short cracks initiated at notch tips can stop to grow if the stress gradient ahead of the tip is steep enough. in fact, albeit such non-propagating cracks induce damage, they can be tolerated whenever the loading conditions cannot induce the higher local stresses needed to restart their growing process. moreover, this apparently odd behavior can be easily explained by the competition between the opposing effects of the decreasing stress  ahead of the crack tip (due to the stress gradient that acts there) and of the increasing crack size a on its stress intensity factor (sif) ki  (a), which can be seen as the crack driving force under le conditions. to make the crack size dependent sif compatible with a fatigue limit when a  0, el-haddad, topper, and smith (ets) redefined the sif range acting in a griffith plate by [10-11]      0k a a( ) (1) where a0  (1/)(k0/s0)2 is the short crack characteristic size, kth0 is the long fatigue crack growth threshold and sl0 is the fatigue limit at r  min/max  0, both well-defined material properties that can be measured by standard procedures. this simple but clever trick reproduces the correct limits (a  0)  s0 for very short cracks and k(a  a0)  kth0 for long cracks, as well as the data trend in a kitagawa-takahashi a diagram by predicting that cracks do not grow whenever   kth0/(a  a0) [4]. since cracks that depart from notches are driven by the local stress field around their tips, if the geometry factors g(a/w) used in their sifs ki  (a) g(a/w) include kt effects, as usual, it is convenient to split it into two parts, g(a/w) (a). in this way (a) quantifies stress gradient effects near the notch and tends towards kt at its tip, (a  0)  kt; whereas  accounts for other effects that affect the sif, like the free surface, for instance. moreover, since the sif is a crack driving force, it should be material-independent. so, the a0 effect on the short-crack behavior should be used to modify the fatigue crack growth (fcg) threshold kth(r), which is a material property, instead of the loading parameter k, making it a function of the crack size and of the fatigue limits, a trick that is quite convenient for operational purposes. in this way, the fcg threshold for pulsating loads kth(a, r  0) kth0(a) is given by:                   ( ) ( ) ( ) ( ) ( ) ( ) 0 0 0 0 th 1 2 th th 0 th 00 k a a g a w a k ka 1 a a k a aa a g a w (2) however, since fcg depends both on k and kmax, eq. (2) should be modified to consider the kmax (or the r-ratio) effect on the short crack behavior. moreover, it can also be seen as just one of the models that obey the long-crack and the microcrack limits, so it can include a data fitting parameter  [5]. so, if kthr  kth(a >> ar, r) is the fcg threshold for long cracks and slr  sl(r) is the fatigue limit of the material, both measured (or estimated) at the desired r-ratio, then: f v.m. machado et alii, frattura ed integrità strutturale, 41 (2017) 236-244; doi: 10.3221/igf-esis.41.32 238        r r 12 th th rk a k 1 a a /( ) ( ) , where  r r 2 r th la (1 ) k s        (3) equation (3) reproduces the ets model when  2, and the bi-linear limits in kitagawa-takahashi diagrams as well, see [4] for details. but much more important, it can be used to answer questions that are quite important in practical applications. this model can be used for practical applications. for example, it can check if it is possible to replace a central circular hole with diameter d  20mm by an elliptical one with axes 2b  20mm (perpendicular to n) and 2c  2mm, in a large notched steel plate with tensile strength su  600mpa, sl  200mpa, and kth0  9mpam, which works under a constant fatigue loadn  100mpa and r 1. neglecting buckling to start with, using classic sn design procedures [12-14], the circular hole would have a safety factor f  sl/kfn200/150  1.33 against fatigue crack initiation, since due to its large radius it has kf  kt 3. however, since the much sharper elliptical hole tip radius c2/b  0.1mm  kt 2b/c21  kf  1  q(kt  1)  7.33 (as, according to the traditional peterson’s estimate, q  (1 )1  [1  0.185(700/600)/0.1]1  0.32 [15]), it should fail by classic sn procedures. indeed, it would work under a stress amplitude a  kfn  367mpa > sl. nevertheless, since this kf value is larger than the kf < 4 typically obtained from notched coupons fatigue data [4], it is worthwhile to reevaluate this prediction. this can be done assuming e.g. kth0(a) kth0/[1  (a0/a)]0.5 (by ets), the steel fatigue limit sl  su/2 (as usual, noticing that sl is an amplitude whereas sl is a range), sl0  su/1.5 (by goodman), and a0  (1/)(kth0/sl0)2  (1/)(1.5kth0/1.12su)2  0.13mm. using these estimates, then the sif ranges ki(a) estimated for the two holes by the procedures developed in [5] are compared to the short-crack threshold kth0(a) in fig. 1. notice that crossings between the ki loading and the kth(a) resistance curves in this figure define crack arrest, so the largest tolerable crack sizes. hence, considering the effect of the stress gradient ahead of the notch tip on the growth behavior of short cracks, this model predicts that both the circular and the elliptical holes could support the nominal load range n without failing by fatigue. figure 1: according to the short crack model, cracks should not initiate at the circular hole (which tolerates cracks atol < 1.52mm), while the crack that initiates at the elliptical hole tip should stop when reaching a size ast  0.33mm. it is interesting to emphasize the practical usefulness of modeling the short crack behavior in notched components. the classic sn and n methodologies are very much used to analyze and to design supposedly crack-free structural components in engineering applications, even though it is impossible to guarantee that they are really free of cracks smaller than the guaranteed detection threshold of the non-destructive inspection method used to identify them. in fact, although large cracks may be detected and dealt with in practice, microcracks and short cracks are practically undetectable by traditional non-destructive inspection methods. nevertheless, most components are still designed against fatigue crack initiation using procedures that do not recognize such unavoidable small flaws. so, their service life expectancy may become unreliable when such tiny defects are introduced by any means during manufacturing or service. therefore, structural components that must last for long fatigue lives should be designed not only to avoid crack initiation, but also to be tolerant to undetectable short cracks. indeed, continuous work under fatigue loads cannot be guaranteed if any of the flaws that they might have (because they could not be or have not been detected) can somehow v.m. machado et alii, frattura ed integrità strutturale, 41 (2017) 236-244; doi: 10.3221/igf-esis.41.32 239 propagate during their service lives. however, despite self-evident, this prudent requirement is still not included in most sn and n fatigue design routines used in practice. in fact, most long-life designs just intend to maintain the service stresses at the structural component’s critical point below its fatigue limit,  < slr/f, where f is a suitable safety factor for fatigue applications. so, although such calculations can be quite complex (e.g. when analyzing fatigue crack initiation caused by random multiaxial non-proportional loads), their so-called safe-life philosophy is not intrinsically safe. however, despite neglecting the effect of any cracks or crack-like defects, most long-life fatigue designs do work quite well in practice. this means that they are in fact somehow tolerant to undetectable or to functionally-admissible short cracks. nevertheless, the question “how much tolerant” cannot be answered by sn and n procedures alone. this potentially important problem can be dealt with by adding short crack concepts to their infinite life design criteria, which may be given (in its simplest version) by           r 12th f rk a g a w 1 a a( ) ( ) , r rth l    2ra 1 k s( ) ( ) (4) since the fatigue limit slr at a given fixed {, r} condition already reflects the effect of microstructural defects inherent to the material, eq. (4) complements it by describing the tolerance to small cracks that may go unnoticed in actual service conditions. a practical example can illustrate well how these ideas can be useful in engineering applications. due to a rare manufacturing problem, a batch of a small but important structural component was delivered with tiny scratch-like elongated surface cracks only detectable by under a microscope, causing some serious unexpected failures when mounted in the machine it usually worked forever. the question is how to estimate the effect of such small crack-like defects in the fatigue strength of those components, knowing that each piece has a 2 by 3.4mm rectangular cross-section and is made of a steel with ultimate strength su = 990mpa and (uncracked) fatigue limit sl = 246mpa. the piece fatigue limit is about su/4, whereas steels typically have sl  su/2  495mpa. this difference may be due to a surface finish factor ksf  0.5, a value between those proposed by juvinall for su  1gpa steels with cold-drawn or machined surfaces, 0.45  ksf  0.7 [13]. although surface finish should not affect the growth of fatigue cracks, the measured value could be due to other factors as well, like e.g. tensile residual stresses near the piece surface. hence, the only safe option is to use sl  246mpa to evaluate the short crack effects, estimating the fatigue limit at r > 1 (or at m > 0) e.g. by goodman as sl(r)  slr  slsu(1  r)/[su(1  r)  sl(1  r)]. the fcg threshold is also needed to model short crack effects. if data is not available, as in this case, it must be estimated e.g. by kth(r  0.17)  kth0 = 6mpam and kthr(r > 0.17)  7(1  0.85r) [4]. this risky practice increases the prediction uncertainty, but it was the only option available. however, this estimate is conservative regarding typical data, which tend to indicate 6 < kth0 < 12mpam. moreover, it assumes kthr(r < 0)  kth0, usually a safe estimate as well (unless the load history contains severe compressive underloads that may accelerate the crack, not the case here). using the sif of an edge-cracked strip of width w loaded in mode i [4], fig. 2 shows the tolerable stress ranges under pulsating axial loads estimated within a fatigue safety factor f by:                              0th f 0 123 0 k a aa 2w a a a0 752 2 02 0 37 1 1wa2w 2w 2w a sec tan . . . sin (5) this simple (but quite reasonable) model indicates that the studied structural component tolerates well small edge cracks up to a  30m, since they almost do not affect its original fatigue limits. however, since this conclusion is based on estimated properties, fig. 3 evaluates the influence of the threshold kth0 and of the data-fitting exponent  on the values estimated for the tolerable stress ranges, enhancing how important it is to measure them to obtain less-scattered predictions. nevertheless, in spite of this scatter, such estimates can be very useful for designers and quality control engineers. they can be used e.g. as a quantitative tool if a production or an operational accident damages the surface of otherwise well-behaved components, to help deciding whether they can be kept in service or must be recalled. these estimates provide interesting results, but they have some intrinsic limitations. they assume the short crack grows unidimensionally, thus can be characterized by its size a only, when surface flaws much smaller than the piece dimensions probably look like small surface or corner cracks, and should be treated as so. 2d cracks grow by fatigue in two directions, usually changing their shape at every load cycle, although maintaining their original plane under mode i loads, see [4]. in v.m. machado et alii, frattura ed integrità strutturale, 41 (2017) 236-244; doi: 10.3221/igf-esis.41.32 240 fact, cracks (short or long) should not be modeled as 1d unless their fronts uniformly cut the whole piece thickness and can be described by just 1 coordinate. moreover, these estimates are only valid for mechanically short cracks, those with both a and a0 larger than the grain size of the material gr. the fcg behavior of microcracks with sizes a and a0 < gr is sensitive to microstructural features, but since grains (let alone dislocations) cannot be mapped in practical applications yet, their use for structural engineering purposes may be questionable. figure 2: larger stress ranges  tolerable by the studied component under many r–ratios as a function of the size a of an edge crack, for w = 3.4mm, h = 1.12, kth0  6mpam, a0  59mm,  6, and f  1.6. figure 3: influence of the typical ranges of fcg threshold 6 < kth0 < 12mpam and of bazant’s data-fitting exponent 1.5 <  < 8 on the largest stress ranges 0 tolerated by the studied piece. the behavior of short cracks under ep conditions nder contained elastoplastic conditions around crack tips, which invalidate the use of sifs to quantify the local crack driving forces, the non-propagating crack problem can be modeled using the j-integral approach [16-17], as originally proposed in [11]. however, since like in the le case short fatigue cracks present higher fcg rates than long cracks in the ep case as well, it is operationally convenient to modify their jth(a) propagation threshold to consider the effects of the short crack characteristic size a0 when accounting for their peculiar behavior near ep notch tips. in the le case, the size-dependent threshold jth(a) must of course be given by kth(a)2/e', where e'  e or e'  e/(1  2) for plane stress or plane strain limit conditions. in this way, jth(a) can then be easily compared with the crack driving force quantified by j when modeling the ep short crack behavior. if the stresses controlled by j grow proportionally to the load u v.m. machado et alii, frattura ed integrità strutturale, 41 (2017) 236-244; doi: 10.3221/igf-esis.41.32 241 p applied on the cracked piece, then for a ramberg-osgood material with strain-hardening coefficient h and exponent h, it can be shown [4] that the crack driving force j is given in a clearer engineering notation by:                1 h h 1 h2 el pl i pc yj j j k e p p s w a h a w h ( ) ( , )h (4) where ki(p) is the sif applied on the cracked piece (as if it remained le), ppc is the plastic collapse load, sy is the yielding strength, w is the cracked piece width, w  a is its residual ligament, and h is a non-dimensional function that depends on the cracked piece geometry and on the strain-hardening exponent h. although not as easy to find as ki values, h-values may be found in tables for some simple geometries. however, this is not a major barrier in practice, since they can nowadays be calculated in most finite element (fe) codes for more complex components. to model the short crack behavior, like its le analog kth(a), the size-dependent crack propagation threshold jth(a) must include the a0 effect:  th th 0j a j 1 a a( ) ( ) (5) hence, like in the le case, ep cracks grow whenever their driving force j is higher than their size-dependent threshold jth(a), a material property that can be properly measured, and stop otherwise. cracks that depart from a notch tip can be much affected by its stress gradient when their size is small or similar to the notch tip radius , so they can start and then stop after growing for a while, becoming thus non-propagating. figure 4 e.g. shows this behavior for a crack that departs from a notch with   1mm and stops at a size a  1.8mm, when its j become smaller than its threshold jth(a), becoming non-propagating. if p remains fixed, notice that this cracked component would then tolerate cracks with size 1.8 < a < 9mm. figure 4: ep crack that starts at a notch tip and then stops after growing for 1.8mm. experimental eac results urves ki(a)a and ji(a)a are calculated for notched dc(t) specimens by finite element analyses made using a suitable 2d abaqus/cae fe model, considering ep conditions near the notch tip as needed. these curves, which quantify the crack driving force, can be compared with the keacth(a)a and jeacth(a)a curves, which quantify the material resistance to eac conditions, including short crack effects. such visual comparisons are very helpful in practice, since they can map the whole cracking problem. this technique is then used to make predictions about the short crack behavior that can be experimentally verified. to do so, notched dc(t)s of aisi 4140 steel (whose crack initiation and long crack growth eac thresholds in a solution of h2s, seac  332mpa and keacth  34.2mpam, have been previously measured by astm f1624 and iso 7539 standards, and by nace procedures [18-19]) are tested under eac conditions as follows. first, two dc(t)s with a useful width w  60mm and a notch of length b  15mm and tip radius  2mm are eac tested in the h2s solution under two load levels, p  6750n and p  8250n, which induce le conditions around the notch tip. c v.m. machado et alii, frattura ed integrità strutturale, 41 (2017) 236-244; doi: 10.3221/igf-esis.41.32 242 according to the short crack models presented above, the first should generate a non-propagating crack, see fig. 5, whereas the second should start and propagate a crack, see fig. 6, as indeed they did, see fig. 7. in the sequence, two other similar dc(t) specimens, one with notch tip radius  0.2mm and loaded by p  3.1kn and the other with  0.3mm and loaded by p  6kn, were eac tested in the same aggressive environment, but now under ep conditions around the notch tip. considering their size-dependent threshold jth(a) and their crack driving forces j, both specimens should withstand the loads without breaking, as indeed they did, see fig. 8-10. figure 5: curves ki(a)a and keacth(a)a generated by the analysis of the linear elastic dc(t) under eac and p  6750n. figure 6: curves ki(a)a and keacth(a)a generated by the analysis of the linear elastic dc(t) under eac and p  8250n. figure 7: le specimens after working 30 days under eac conditions in an aqueous hydrogen sulfide environment. v.m. machado et alii, frattura ed integrità strutturale, 41 (2017) 236-244; doi: 10.3221/igf-esis.41.32 243 figure 8: curves ji(a)a and jeacth(a)a generated by the analysis of the dc(t) loaded by p  3.1kn under ep conditions. figure 9: curves ji(a)a and jeacth(a)a generated by the analysis of the dc(t) loaded by p  6kn under ep conditions. figure 10: ep specimens after 30 days under eac in aqueous hydrogen sulfide environment. conclusions he model proposed here can evaluate the propagating or non-propagating behavior of short cracks that depart from notch tips under linear elastic and elastoplastic load regimes, and can estimate the size of tolerable short cracks or crack-like defects in practical applications. experimental evidence presented here supports this claim under stress corrosion cracking conditions, but a similar mechanics is also valid for modeling the behavior of short fatigue cracks. t v.m. machado et alii, frattura ed integrità strutturale, 41 (2017) 236-244; doi: 10.3221/igf-esis.41.32 244 references [1] meggiolaro, m.a., castro, j.t.p., góes, r.c.o., elastoplastic nominal stress effects in the estimation of the notch-tip behavior in tension, theor appl fract mech 84 (2016) 86-92. [2] frost, n.e., marsh, k.j., pook, l.p., metal fatigue, dover (1999). [3] taylor, d., the theory of critical distances, elsevier (2007). [4] castro, j.t.p., meggiolaro, m.a., fatigue design techniques, in 3 volumes. createspace (2016). [5] meggiolaro, m.a., miranda, a.c.o., castro, j.t.p., short crack threshold estimates to predict notch sensitivity factors in fatigue, int j fatigue, 29 (2007) 2022–2031. [6] castro, j.t.p., meggiolaro, m.a., miranda, a.c.o., wu, h., imad, a., nouredine, b., prediction of fatigue crack initiation lives at elongated notch roots using short crack concepts, int j fatigue, 42 (2012) 172-182. [7] castro, j.t.p, meggiolaro, m.a., is notch sensitivity a stress analysis problem?, frattura ed integrità strutturale, 25 (2013) 79-86. [8] castro, j.t.p., landim, r.v., leite, j.c.c., meggiolaro, m.a., prediction of notch sensitivity effects in fatigue and eac, fatigue fract eng mater struct, 38 (2015) 161-179. [9] castro, j.t.p., landim, r.v., meggiolaro, m.a., defect tolerance under environmentally-assisted cracking conditions. corrosion reviews, 33 (2015) 417-432. [10] el haddad, m.h., topper, t.h., smith, k.n., prediction of non-propagating cracks, eng fract mech, 11 (1979) 573584. [11] el haddad, m.h. et. al., j-integral applications for short fatigue cracks at notches, int j fract, 16 (1980) 15-30. [12] shigley, j.e., mischke, c.r., budynas, r.g., mechanical engineering design, 7th ed., mcgraw-hill, (2004). [13] juvinall, r.c., marshek, k.m., fundamentals of machine component design, 4th ed., wiley, (2005). [14] norton, r.l., machine design, an integrated approach, 3rd ed., prentice-hall, (2005). [15] peterson, r.e., stress concentration factors, wiley, (1974). [16] shih, c.f., hutchinson, j.w., fully plastic solutions and large scale yielding estimates for plane stress crack problems, j eng mater technology, 98 (1976) 289-295. [17] goldman, n.l., hutchinson, j.w., fully plastic crack problems: the center-cracks strip under plane strain, int j solids struct, 11 (1975) 575-591. [18] astm e-1820-13: standard test method for measurement of fracture toughness, astm, (2014). 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/hrv (za stvaranje adobe pdf dokumenata najpogodnijih za visokokvalitetni ispis prije tiskanja koristite ove postavke. stvoreni pdf dokumenti mogu se otvoriti acrobat i adobe reader 5.0 i kasnijim verzijama.) /hun 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can be opened with acrobat and adobe reader 5.0 and later.) >> /namespace [ (adobe) (common) (1.0) ] /othernamespaces [ << /asreaderspreads false /cropimagestoframes true /errorcontrol /warnandcontinue /flattenerignorespreadoverrides false /includeguidesgrids false /includenonprinting false /includeslug false /namespace [ (adobe) (indesign) (4.0) ] /omitplacedbitmaps false /omitplacedeps false /omitplacedpdf false /simulateoverprint /legacy >> << /addbleedmarks false /addcolorbars false /addcropmarks false /addpageinfo false /addregmarks false /convertcolors /converttocmyk /destinationprofilename () /destinationprofileselector /documentcmyk /downsample16bitimages true /flattenerpreset << /presetselector /mediumresolution >> /formelements false /generatestructure false /includebookmarks false /includehyperlinks false /includeinteractive false /includelayers false /includeprofiles false /multimediahandling /useobjectsettings /namespace [ (adobe) (creativesuite) (2.0) ] /pdfxoutputintentprofileselector /documentcmyk /preserveediting true /untaggedcmykhandling /leaveuntagged /untaggedrgbhandling /usedocumentprofile /usedocumentbleed false >> ] >> setdistillerparams << /hwresolution [2400 2400] /pagesize [612.000 792.000] >> setpagedevice microsoft word numero_39_art_14 j. sobek et alii, frattura ed integrità strutturale, 39 (2017) 129-142; doi: 10.3221/igf-esis.39.14 129 focussed on modelling in mechanics analysis of accuracy of williams series approximation of stress field in cracked body – influence of area of interest around crack-tip on multi-parameter regression performance j. sobek, p. frantík, v. veselý brno university of technology, faculty of civil engineering, institute of structural mechanics, brno, czech republic sobek.j@fce.vutbr.cz, http://orcid.org/0000-0003-4215-1029 kitnarf@centrum.cz vesely.v1@ fce.vutbr.cz, http://orcid.org/0000-0002-7723-971x abstract. a study on the accuracy of an approximation of the stress field in a cracked body is presented. crack-tip stress tensor is expressed using the linear elastic fracture mechanics (lefm) theory in this work, more precisely via its multi-parameter formulation, i.e. by williams power series (wps). determination of coefficients of terms of this series is performed using a least squares-based regression technique known as over-deterministic method (odm) for which results from finite element (fe) method computation are usually taken as inputs. main attention is paid to a detailed analysis of a suitable selection of fe nodes whose results serve as the inputs to the employed method. two different ways of fe nodal selection are compared – nodes selected from the crack tip vicinity lying at a ring of a certain radius versus nodes selected more or less uniformly from a specified part of the test specimen body. comparison of these approaches is made with the help of procedures developed by the authors which enable both the determination of the coefficients of terms of the analytical wps approximation of the stress field based on the fe results and the backward reconstruction of the field (again using wps) from those determined terms’ coefficients/functions. the wedge-splitting test (wst) specimen with a crack is taken as example for the study. keywords. multi-parameter fracture mechanics; williams power series; crack-tip fields; over-deterministic method; higher order terms. citation: sobek, j., frantík, p., veselý, v., analysis of accuracy of williams series approximation of stress field in cracked body – influence of area of interest around cracktip on multi-parameter regression performance, frattura ed integrità strutturale, 39 (2017) 129-142. received: 20.07.2016 accepted: 19.09.2016 published: 01.01.2017 copyright: © 2017 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. introduction etermination of the higher order terms of williams power series [1] approximating the fields of stress and displacements in a cracked body is of substantial interest of the presented work. particular motivation of it is represented by the need for capturing the crack-tip fields in a farther distance from the crack tip. d http://www.gruppofrattura.it/pdf/rivista/numero39/audio/14.mp3 j. sobek et alii, frattura ed integrità strutturale, 39 (2017) 129-142; doi: 10.3221/igf-esis.39.14 130 tensile failure of the quasi-brittle materials is accompanied with a crack propagation together with a nonlinear zone [2] (fracture process zone – fpz) development, where the decrease of material integrity takes place. the size of the fpz is not negligible in comparison with the rest of the body. processes of failure therefore occur in a wider area around the crack tip. the description of failure mechanism must be in agreement with the stress and displacement field around the crack tip in an extended area. recent works of many authors show the relevance of the topic of the crack tip fields accurate description [3–6], moreover, extending it into 3d and taking into account the effects of various loading modes [7–12]. special focus on brittle and quasi-brittle fracture is summarized in [13]. works [3,14,15] reported the fact, that for the description of the stress/displacement field in a cracked body in a more distant surroundings from the crack tip the necessity of usage of the several terms of williams expansion (we), not only the first or the first two terms, is crucial. procedures enabling the multi-parameter description of the near crack-tip fields (using e.g. hybrid crack elements [16] formulation, over-deterministic method [17] based on standard fe computation, or other techniques based e.g. on extrapolation of displacements of selected nodes of fe mesh) usually process results from fe nodes selected from the close vicinity of the crack tip. this is adequate for determination of the classical/two-parameter lefm characteristics (sif, t-stress). however, several questions arise if the area of accurate enough description of the stress and displacement field extends to a greater distance from the crack tip, where k + t dominance vanishes? how many terms of the series should be taken into account? how to select the fe nodes considered for the regression technique? and how to optimize the mutual relationship between the area from where the nodes are considered for the regression (and how are they located/distributed in that area) and the extent where the approximation of the fields is of relevant accuracy? answering these questions presents the actual motivation of this work. this paper investigates the above-described issue via a parametric study evaluating the influence of the nodal selection on the quality of the obtained approximation of the field. the work presented here further builds on previous studies. a classical (common) way of nodal selection, where the nodes are selected from a ring in the vicinity of the crack tip was used in recent papers. influences of several parameters on the description of stress/displacement fields in cracked bodies by williams series were investigated. reconstruction of the stress field with the help of a software tool developed by the author’s team was shown in [14,15] where the accuracy of the approximation by we was verified by a visual comparison (which was regarded as sufficient for its intended purpose) with the fe solution (which was regarded as the exact solution). however, the nodal selection that was used for obtaining the we terms was performed from the ring around the crack tip (with the distance given by recommendation from [17,18]). published study [19] on wps approximation with nodal selection from more than one ring around the crack tip resulted into next studies. another type of nodal selection was considered in subsequent works by the authors [20,21,22]; the nodes were selected from specific parts of the test specimen body with specific distribution functions of their distance and angular position from the crack tip. this way was employed with expectations that the fields will be better (more accurately/efficiently) approximated. an automatic utility to determine the values of coefficients of the higher order terms of wps using the over-deterministic method was developed [20] to enable multi-parameter description of stress field, where the coefficients of wps terms are calculated from several layers and angular sections. and the distance distribution of the nodal selection is governed by various functions. comparison between those used variants was given by visual technique again [21]. hence, a new detailed way for evaluation of the accuracy of the reconstruction was used in [22]. method based on the plot of the relative deviation (percent difference) of the stress field between the correct solution (the fe solution) and the solution given by the approximation using wps with a certain variant of nodal selection was introduced. main motivation of this study is to find the easiest way for the multi-parameter stress field description to obtain the sufficiently accurate solution valid for the as far as possible area from the crack tip. methods multi-parameter linear elastic fracture mechanics (mp-lefm) he stress and displacement fields in a planar homogeneous isotropic cracked body can be formulated as an infinite power expansion – williams series [1] by eq. (1) and (2), respectively – for more details see [14,21,22,23].           1 2 , 1 , , , , 2 n ij n ij n n a r f n i j x y (1) t j. sobek et alii, frattura ed integrità strutturale, 39 (2017) 129-142; doi: 10.3221/igf-esis.39.14 131          2 ,u 1 , , , , , n i n i n u a r f n e i x y (2) in this study, the attention is paid to the mode i crack problem. mp-lefm takes into account several initial terms of we, i.e. n ranges from 1 to n (not ∞); coefficients of these terms are often expressed as dimensionless shape functions gn (functions of the relative crack length  = a/w ). over-deterministic method for determination of coefficients of the williams series terms the so-called over-deterministic method (odm, [17]) is used. based on the linear least-squares formulation, it solves a system of 2k equations, where k represents the number of selected nodes (in the original paper, they were selected from a nodal ring around the crack tip), for n chosen terms of the power series. detailed analyses of this method can be found in works [18,19,24]. displacements of selected nodes, together with their coordinates, serve as the input to that method. this issue was studied in detail in previous works which presented, among others, an implementation of this technique into an automatic numerical tool called odemapp [20] – the odm analysis based on an arbitrary nodal selection and test specimen geometry variant is enabled. refrapro approach the refrapro (reconstruction of fracture process [25]) is a java application which allows an advanced determination of fracture characteristics of materials failing in a quasi-brittle manner (silicate-based materials). estimation of the fpz (its shape and size) is implemented by a technique developed by the authors combining mp-lefm, classical non-linear models and plasticity approach. reconstruction of the fracture process is made by this application generally based on the measured loading curves and basic mechanical properties of the material. for the purpose of this study, a part of this program is used which provides the reconstruction of stress field from the available shape functions (corresponding to values of coefficients of terms of the we) for the given test geometry. this part is accompanied with a special tool (a class called percentdifference) which allows the display of the deviance (percent difference) between the approximated stress field and the exact solution (for which the fe solution is regarded) to test the accuracy of the solution with nodal selection from an area of interest around the crack tip. the deviation itself is expressed via pixmap grid as the relative difference [22]. numerical study or the analysis of the accuracy of the wps approximation, the wedge-splitting test specimen (wst) is used. specimen loaded by eccentric tension through two steel platens with pins among which the steel wedge is impressed was developed by linsbauer and tscheg in [26]. schema of the analysed test configuration is displayed in fig. 1 left accompanied with drawings of its geometry in fig. 1 right. computations of the stress and displacement fields were realized in the ansys finite element software [27]. crack elements (plane82) were utilized for the fe solution. an automatic interconnection procedure has been developed between the computational tool and the odemapp technique for the shape functions determination. a wst variant with two supports and specimens width w = 100 mm (fig. 1 right) was considered. the employed fe mesh is shown in fig. 2a with the crack-tip details, where two basic nodal selections (serving as the reference nodal selections) are depicted. the first is taken from the ring at the distance of 5 mm from the crack tip (fig. 2b) and the second selection is taken from the ring at the distance of 0.5 mm from the crack tip (see fig. 2c). these variants are labelled as ring 5 mm and ring 0.5 mm further in the text. fig. 3a shows the fe mesh intended for models with a more general nodal selection. variant from fig. 3b labelled as con 180° (0°) represents a nodal selection governed by a constant distribution function (in the distance selection) taken from the whole area of test specimen (except of steel platens); qua 90° (45°) – a nodal selection with a quadratic distance distribution function from area of 90° angular section with the origin rotated by 45° angle (from the crack propagation direction) displayed in fig. 3c; exp 90° (80°) – a nodal selection (from fig. 3d with an exponential distribution function from the 90° section with initial rotation angle of 80°. detailed description of the method for the conducted nodal selection, including several other variants, is carried out in [20,21,22]. the number of selected nodes is kept the same for each selection type, k = 49. f j. sobek et alii, frattura ed integrità strutturale, 39 (2017) 129-142; doi: 10.3221/igf-esis.39.14 132 figure 1: wedge splitting test with the schema of loading imposition (left); geometry of the analysed wedge splitting test specimen (right)[15]. shape functions, representing the non-dimensional expressions of the coefficients of the higher order terms of the we as functions of the relative crack length , corresponding to the mentioned nodal selection variants were determined by the odemapp procedure and then they were used as inputs for refrapro application (which allows displaying the relative deviation from the “exact” solution of the stress field distribution). subsequently, a post-processing regarding the stress fields reconstructions based on one, two and even higher order terms of the wps was conducted. figure 2a: numerical model of the wedge splitting test, finite element mesh. figure 2b: detail of the fe mesh for the ring 5 mm variant with nodal selection (red dots at the distance 5 mm from the crack tip). figure 2c: detail of the fe mesh for ring 0.5 variant with nodal selection (red dots at the distance 0.5 mm from the crack tip). j. sobek et alii, frattura ed integrità strutturale, 39 (2017) 129-142; doi: 10.3221/igf-esis.39.14 133 figure 3a: numerical model of the wst specimen, used finite element mesh [22]. figure 3b: distribution of fe nodes for con 180° (0°) variant of nodal selection [22]. figure 3c: distribution of fe nodes for qua 90° (45°) variant of nodal selection [22]. figure 3d: distribution of fe nodes for exp 90° (80°) variant of nodal selection [22]. results and discussion he reconstruction of the fields of the principal tensile stress 1 and the crack opening stress yy was performed and compared to the exact solution. figs. 4 and 5 display the relative differences between the approximation of the field corresponding to chosen variant of nodal selection and the fem solution. only few examples of the reconstruction (based on the number of used williams series’ terms equal to 1, 2, 4, 7 and 11 – positioned horizontally) are given for illustration. cases with the relative crack length  = 0.5 are shown here as an example. it can be seen that low number of terms of the williams series used provides very inaccurate approximation of the stress field (mainly for a wider area around the crack tip). usage of only first two terms leads to a sufficient accuracy only in the very vicinity of the crack tip (where the classical and two-parameter lefm holds). a sufficiently accurate solution can be provided by a usage of at least four terms of williams expansion if an area of about 2 cm from the crack tip is requested. comparison between the used variants of nodal selection shows one important fact – in general [21,22], variant con 180° (0°) (uniform selection from the whole body of the test specimen with the constant distribution function of distance selection) comes out as the best variant of nodal selection (in fig. 4 and 5 it is emphasized by a green coloured frame). as it can be seen, the greater is the share of the red colour in the percent difference diagram the larger is the relative error from the fe solution. that is why this variant appears in next analyses as the reference one for comparison with variants of nodal selection from just one ring; moreover, from a closer distance from the crack tip. in some cases the variant qua 90° (45°) looks also promising and is comparable with the con variant. nevertheless, this is true only for the chosen  = 0.5. work [22] provides detailed views also at different  values. next figures compare results of two basic variants of nodal selection from the vicinity of the crack tip with the con 180° (0°) variant of the nodal selection, i.e. from the whole body of the test specimen. fig. 6 shows contour plots of the relative deviation of principal stress 1 for variants of nodal selection con 180° (0°), ring 5 mm and ring 0.5 mm for the wst specimen with relative crack length  = 0.5. as far as four terms of williams expansion for approximation is used the same trend in the relative deviation can be observed. with increasing n the results of ring 0.5 mm variant appear to be very inaccurate which can be seen on the extension of the red colour area (denoting a large proportion of 40% difference from the fe solution). t j. sobek et alii, frattura ed integrità strutturale, 39 (2017) 129-142; doi: 10.3221/igf-esis.39.14 134 1 gn  = 0.5 1 2 4 7 11 co n 18 0° ( 0° ) qu a 90 ° (4 5° ) ex p 90 ° (8 0° ) figure 4: relative error of principal tensile stress 1 field approximation for chosen variants of nodal selection. cr ac k ti p j. sobek et alii, frattura ed integrità strutturale, 39 (2017) 129-142; doi: 10.3221/igf-esis.39.14 135 yy gn  = 0.5 1 2 4 7 11 co n 18 0° ( 0° ) qu a 90 ° (4 5° ) ex p 90 ° (8 0° ) figure 5: relative error of crack opening stress yy field approximation for chosen variants of nodal selection. j. sobek et alii, frattura ed integrità strutturale, 39 (2017) 129-142; doi: 10.3221/igf-esis.39.14 136 1 gn  = 0.50 1 2 4 7 11 co n 18 0° ( 0° ) ri ng , 5 m m ri ng , 0 .5 m m figure 6: relative error of principal tensile stress 1 field approximation for chosen variants of nodal selection. j. sobek et alii, frattura ed integrità strutturale, 39 (2017) 129-142; doi: 10.3221/igf-esis.39.14 137 yy gn  = 0.50 1 2 4 7 11 co n 18 0° ( 0° ) ri ng , 5 m m ri ng , 0 .5 m m figure 7: relative error of crack opening stress yy field approximation for chosen variants of nodal selection. j. sobek et alii, frattura ed integrità strutturale, 39 (2017) 129-142; doi: 10.3221/igf-esis.39.14 138 results of variant con 180° (0°) and ring 5 mm seem to be very close which can be investigated in detail also on the comparison of the relative error of crack opening stress field yy progress for all considered variants in fig. 7 with  = 0.5. again, the variant ring 0.5 mm shows very inaccurate progress of the stress field reconstruction and should be avoided without usage of more than four terms of the williams expansion. this fact is described in detail in fig. 8, which illustrates the relative errors just for ring 0.5 mm variant and its progress with the usage of 4, 5, 6 and 7 terms of expansion for reconstruction of principal and crack opening stress field with  = 0.5. from the fourth term the error grows rapidly. ring 0.5 mm gn  = 0.5 4 5 6 7 1 yy  figure 8: progress of relative error of the 1 and yy reconstruction with increasing number of williams series terms used. results depicted in figs. 9 and 10 show the percent differences of 1 and yy, respectively, stress field reconstruction. fig. 9 represents result with  = 0.25 for selected terms of williams series (g4, g7 and g11). these images confirm conclusion that variant ring 0.5 mm is very inaccurate for reconstruction of stress field far from the vicinity of the crack tip. comparison between ring 0.5 mm and con 180° (0°) variant of nodal selection provides a conclusion that a usage of constant variant is better in case of  = 0.25 (fig. 9) and also  = 0.75 (fig. 10). with one exception in fig. 10 – progress of the g4 for  = 0.75 in yy reconstruction. so, in some cases, it is slightly better to use ring 5 mm variant instead of constant distribution function from the whole body of the test specimen. j. sobek et alii, frattura ed integrità strutturale, 39 (2017) 129-142; doi: 10.3221/igf-esis.39.14 139 general quantification of the accuracy of the performed variants of the multi-parameter approximation is not easy to obtain, because the large amount of the nodal selection variants, as were used in the study, lead to combinations, where recommendations cannot be simply stated. an attempt of at least some aspects of such quantification is introduced in this work through the relative error contour plots. the progress of the relative error in the contour maps shows a distance from the crack tip, where the approximation of the stress field is of sufficient accuracy – the blue field may be considered as such a region, because the relative error of approximation here is up to 5 %. particular example of such quantification can be explained with the help of results from fig. 7: with usage (for all variants of nodal selection the trend is the same) of only the first term (g1) and then also with the first two terms (g2) the blue region (of the accurate enough approximation) is within a radius of about 5 mm. for the variant con 180° (0°) and with usage of 11 terms of the we the radius increases to about 23 mm. on the other hand, the variant ring 0.5 mm with the number of we terms up to 11 shows a decreasing trend where the utilizable area is of a radius of only about 1 mm. 1 yy  con 180° (0°) ring 5 mm ring 0.5 mm con 180° (0°) ring 5 mm ring 0.5 mm g 4 ,  = 0 .2 5 g 7 ,  = 0 .2 5 g 1 1,  = 0 .2 5 figure 9: progress of relative error of the 1 and yy reconstruction for selected terms of williams series used. j. sobek et alii, frattura ed integrità strutturale, 39 (2017) 129-142; doi: 10.3221/igf-esis.39.14 140 conclusions detailed analysis of the accuracy of the williams series approximation of the stress tensor components (principal stress and crack opening stress) in the cracked wst specimen was shown. the area of interest around the crack tip was investigated from two stand points within this analysis:  the area from where the nodes are taken into account for the regression technique should be somehow easily defined (easiest way is the ring of nodes around the crack tip), moreover it is convenient to use the ring of small radius to be able to create reasonably good fe mesh also for very short and very long cracks. in total, five variants of nodal selection were introduced (which followed on at previous published studies) and recommendations are as follows: 1 yy  con 180° (0°) ring 5 mm ring 0.5 mm con 180° (0°) ring 5 mm ring 0.5 mm g 4 ,  = 0 .7 5 g 7 ,  = 0 .7 5 g 1 1,  = 0 .7 5 figure 10: progress of relative error of the 1 and yy reconstruction for selected terms of williams series used. a j. sobek et alii, frattura ed integrità strutturale, 39 (2017) 129-142; doi: 10.3221/igf-esis.39.14 141  variant con 180° (0°), which represents the nodal selection governed by a uniform distribution from the whole body of the test specimen, seems to be the best choice (and was used as the reference for the next analysis step).  nodal selection of variant ring 5 mm is still comparable with the uniform nodal distribution variant. this is true up to the highest number of the used williams series terms that was tested in this study, i.e. n = 11.  using of variant ring 0.5 mm provides a sufficiently accurate results only up to the number of williams expansion terms n = 4. this is not valid for the (very) close vicinity of the crack tip, where the results are still accurate enough. future work will provide analysis of variant ring 5 mm (or other convenient value of the ring radius) with a particular focus on how many terms n of the williams series are optimal for the crack-tip field reconstruction at a given distance from the crack tip. physical significance of the higher order terms of the williams series should be better explained and will be analysed via a real experiment (with utilization of digital image correlation technique, similarly to the case of [28]), which is under preparation by authors of this paper. however, for the purpose of the analysis shown in this paper this knowledge is not relevant – the coefficients of terms of the regression are not used here as fracture parameters as it is within the classical or the two-parameter fracture mechanics (k or/and t). here, they are used only as coefficients of a regression function for the stress field approximation. the aim of this approach is to use the approximation of the field in further fracturemechanical application (i.e. the plastic zone or the fracture process zone size and shape estimation, etc.). acknowledgment his paper has been worked out under the project no. lo1408 “admas up – advanced materials, structures and technologies”, supported by ministry of education, youth and sports under the “national sustainability programme i”. references [1] williams, m.l., on the stress distribution at the base of a stationary crack, journal of applied mechanics (asme), 24 (1957) 109–114. [2] anderson, t.l., fracture mechanics. fundamentals and applications, boca raton: crc press, (2005). [3] berto, f., lazzarin, p., on higher order terms in the crack tip stress field, international journal of fracture, 161 (2010) 221–226. [4] pook, l.p., the linear elastic analysis of cracked bodies and crack paths, theoretical and applied fracture mechanics, 79 (2015) 34–50. [5] ayatollahi, m.r., rashidi moghaddam, m., razavi, s.m.j., berto, f., geometry effects on fracture trajectory of pmma samples under pure mode-i loading, engineering fracture mechanics, (2016), in press. [6] pook, l.p., the linear elastic analysis of cracked bodies, crack paths and some practical crack path examples, engineering fracture mechanics, (2016), in press. [7] berto, f., lazzarin, p., kotousov, a., on higher order terms and out-of-plane singular mode, mechanics of materials, 43 (2011) 332–341. [8] berto, f., lazzarin, p., multiparametric full-field representations of the in-plane stress fields ahead of cracked components under mixed mode loading, international journal of fatigue, 46 (2013) 16–26. [9] pook, l.p., berto, f., campagnolo, a., lazzarin, p., coupled fracture mode of a cracked disc under anti-plane loading, engineering fracture mechanics, 128 (2014) 22–36. [10] ayatollahi, m.r., rashidi moghaddam, m., berto, f., a generalized strain energy density criterion for mixed mode fracture analysis in brittle and quasi-brittle materials, theoretical and applied fracture mechanics, 79 (2015) 70–76. [11] pook, l.p., campagnolo, a., berto, f., lazzarin, p., coupled fracture mode of a cracked plate under anti-plane loading, engineering fracture mechanics, 134 (2015) 391–403. [12] saboori, b., ayatollahi, m.r., torabi, a.r., berto, f., mixed mode i/iii brittle fracture in round-tip v-notches, theoretical and applied fracture mechanics, 83 (2016) 135–151. [13] berto, f., lazzarin, p., recent developments in brittle and quasi-brittle failure assessment of engineering materials by means of local approaches, material science and engineering r, 75 (2014) 1–48. t j. sobek et alii, frattura ed integrità strutturale, 39 (2017) 129-142; doi: 10.3221/igf-esis.39.14 142 [14] veselý, v., sobek, j., malíková, l., frantík, p., seitl, s., multi-parameter crack tip stress state description for estimation of fracture process zone extent in silicate composite wst specimens, frattura ed integrità strutturale, 25 (2013) 69–78. [15] veselý, v., frantík, p., sobek, j., malíková, l., seitl, s., multi-parameter crack tip stress state description for evaluation of nonlinear zone width in silicate composite specimens in component splitting/bending test geometry, fatigue & fracture of engineering materials & structures, 38-2 (2014) 200–214. doi: 10.1111/ffe.12170. [16] karihaloo, b.l., abdalla, h., xiao, q.z., coefficients of the crack tip asymptotic field for wedge splitting specimens, engineering fracture mechanics, 70 (2003) 2407–2420. [17] ayatollahi, m.r., nejati, m., an over-deterministic method for calculation of coefficients of crack tip asymptotic field from finite element analysis, fatigue & fracture of engineering materials & structures, 34 (2010) 159–176. [18] sobek, j., veselý, v., šestáková, l., accuracy of approximation of stress and displacement fields in cracked body for estimation of failure zone extent, transactions of the všb–technical university of ostrava, civil engineering series, xii-2 (2012) 1–10. doi: 10.2478/v10160-012-0031-5. [19] malíková, l., multi-parameter fracture criteria for the estimation of crack propagation direction applied to a mixedmode geometry, engineering fracture mechanics, 143 (2015) 32–46. [20] sobek, j., pail, t., veselý, v., evaluation of crack tip stress field using combination of advanced implementation of over-deterministic method and fe analysis, key engineering materials, 627 (2015) 273–276. doi: 10.4028/www.scientific.net/kem.627.273. [21] veselý, v., sobek, j., tesař, d., frantík, p., pail, t., seitl, s., multi-parameter approximation of stress field in a cracked specimen using purpose-built java applications, frattura ed integrità strutturale, 33 (2015) 120–133. [22] veselý, v., sobek, j., frantík, p., seitl, s., multi-parameter approximation of the stress field in a cracked body in the more distant surroundings of the crack tip, international journal of fatigue, 89 (2016) 20–35. doi: 10.1016/j.ijfatigue.2016.02.016 [23] malíková, l., veselý, v., seitl, s., estimation of the crack propagation direction in a mixed-mode geometry via multi parameter fracture criteria, frattura ed integrità strutturale, 33 (2015) 25–32. [24] malíková, l., veselý, v., significance of higher-order terms of the williams expansion for plastic zone extent estimation demonstrated on a mixed-mode geometry, procedia materials science, 3 (2014) 1383–1388. [25] veselý, v., frantík, p., an application for the fracture characterisation of quasi-brittle materials taking into account fracture process zone influence, advances in engineering software, 72 (2014) 66–76. doi: 10.1016/j.advengsoft.2013.06.004. [26] linsbauer, h.n., tscheg, e.k., fracture energy determination of concrete with cube-shaped specimens, zement und beton, 31 (1986) 38–40. [27] ansys documentation, version 11.0, swanson analysis system, inc., houston, pennsylvania, (2007). [28] vargas, r., neggers, j., canto, r.b., rodrigues, j.a., hild, f., analysis of wedge splitting test on refractory castable via integrated dic, journal of the european ceramics society, 36 (2016) 4309–4317. << /ascii85encodepages false /allowtransparency false /autopositionepsfiles true /autorotatepages /none /binding /left /calgrayprofile (dot gain 20%) /calrgbprofile (srgb iec61966-2.1) /calcmykprofile (u.s. web coated \050swop\051 v2) /srgbprofile (srgb iec61966-2.1) /cannotembedfontpolicy /error /compatibilitylevel 1.4 /compressobjects /tags /compresspages true /convertimagestoindexed true /passthroughjpegimages true /createjobticket false /defaultrenderingintent /default /detectblends true /detectcurves 0.0000 /colorconversionstrategy /cmyk /dothumbnails false /embedallfonts true /embedopentype false /parseiccprofilesincomments true /embedjoboptions true /dscreportinglevel 0 /emitdscwarnings false /endpage -1 /imagememory 1048576 /lockdistillerparams false /maxsubsetpct 100 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can be opened with acrobat and adobe reader 5.0 and later.) >> /namespace [ (adobe) (common) (1.0) ] /othernamespaces [ << /asreaderspreads false /cropimagestoframes true /errorcontrol /warnandcontinue /flattenerignorespreadoverrides false /includeguidesgrids false /includenonprinting false /includeslug false /namespace [ (adobe) (indesign) (4.0) ] /omitplacedbitmaps false /omitplacedeps false /omitplacedpdf false /simulateoverprint /legacy >> << /addbleedmarks false /addcolorbars false /addcropmarks false /addpageinfo false /addregmarks false /convertcolors /converttocmyk /destinationprofilename () /destinationprofileselector /documentcmyk /downsample16bitimages true /flattenerpreset << /presetselector /mediumresolution >> /formelements false /generatestructure false /includebookmarks false /includehyperlinks false /includeinteractive false /includelayers false /includeprofiles false /multimediahandling /useobjectsettings /namespace [ (adobe) (creativesuite) (2.0) ] /pdfxoutputintentprofileselector /documentcmyk /preserveediting true /untaggedcmykhandling /leaveuntagged /untaggedrgbhandling /usedocumentprofile /usedocumentbleed false >> ] >> setdistillerparams << /hwresolution [2400 2400] /pagesize [612.000 792.000] >> setpagedevice microsoft word numero_42_art_15.docx correia et alii, frattura ed integrità strutturale, 42 (2017) 136-146; doi: 10.3221/igf-esis.42.15 136 focused on mechanical fatigue of metals statistical analysis of fatigue crack propagation data of materials from ancient portuguese metallic bridges j.a.f.o. correia, a.m.p. de jesus, r. calçada faculty of engineering, university of porto, rua dr. roberto frias, 4200-465 porto, portugal. jacorreia@inegi.up.pt, http://orcid.org/0000-0002-4148-9426 ajesus@fe.up.pt, http://orcid.org/0000-0002-1059-715x ruiabc@fe.up.pt, http://orcid.org/0000-0002-2375-7685 b. pedrosa, c. rebelo, luis simões da silva isise, department of civil engineering, university of coimbra, rua luís reis santos, pólo ii, 3030-788 coimbra, portugal. brunoalex_pedrosa@hotmail.com, crebelo@dec.uc.pt g. lesiuk faculty of mechanical engineering, department of mechanics, material science and engineering, wrocław university of science and technology, smoluchowskiego 25, 50-370 wrocław, poland grzegorz.lesiuk@pwr.edu.pl, https://orcid.org/0000-0003-3553-6107 abstract. in portugal there is a number of old metallic riveted railway and highway bridges that were erected by the end of the 19th century and beginning of the 20th century, and are still in operation, requiring inspections and remediation measures to overcome fatigue damage. residual fatigue life predictions should be based on actual fatigue data from bridge materials which is scarce due to the material specificities. fatigue crack propagation data of materials from representative portuguese riveted bridges, namely the pinhão and luiz i road bridges, the viana road/railway bridge, the fão road bridge and the trezói railway bridge were considered in this study. the fatigue crack growth rates were correlated using the paris’s law. also, a statistical analysis of the pure mode i fatigue crack growth (fcg) data available for the materials from the ancient riveted metallic bridges is presented. based on this analysis, design fcg curves are proposed and compared with bs7910 standard proposal, for the paris region, which is one important fatigue regime concerning the application of the fracture mechanics approaches, to predict the remnant fatigue life of structural details. keywords. fracture mechanics; fatigue crack growth; statistical analysis; old steels; ancient bridges; bs7910. citation: correia, j.a.f.o., de jesus, a.m.p., calçada, r., pedrosa, b., rebelo, c., simões da silva, l., lesiuk, g., statistical analysis of fatigue crack propagation data of materials from ancient portuguese metallic bridges, frattura ed integrità strutturale, 42 (2017) 136-146. received: 08.06.2017 accepted: 17.06.2017 published: 01.10.2017 copyright: © 2017 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. correia et alii, frattura ed integrità strutturale, 42 (2017) 136-146; doi: 10.3221/igf-esis.42.15 137 introduction n portugal, the major concern of governmental agencies is related with the maintenance and safety of centenaries riveted steel bridges. these old riveted road and railway bridges were fabricated and placed into service during the 19th century and beginning of 20th century. the traffic conditions both in terms of vehicle gross weight and frequency, are today completely different from those considered in the design phase. additionally, the original design procedures of these bridges did not account for fatigue, since fatigue understanding only achieved the maturity after the design of those structures. in the 19th century the designer engineers were not aware of some important damage phenomena including fatigue. fatigue was only intensively studied in the 20th century. in order to maintain the high safety levels of old riveted steel bridges, road and railway authorities have to invest heavily in inspection, maintenance and retrofitting, with those activities supported by fatigue assessment studies, including remnant life calculations [1]. the crack propagation data is essential to perform fatigue life predictions according to the linear elastic fracture mechanics (lefm), which is an important alternative to the usual code-based s-n curve procedures, mainly in what concerns residual life estimations. in this perspective, the knowledge about design fatigue crack growth curves for materials from ancient portuguese steel bridges is extremely appropriate [1]. the present paper reports research work carried out to determine the design fcg curves of materials from ancient portuguese riveted bridges, namely the pinhão, fão and luiz i road bridges, built in 1906, 1891 and 1886, respectively, the eiffel road/railway bridge (inaugurated in 1878) and the trezói railway bridge (inaugurated in 1956). the design fcg curves were obtained using the procedure proposed by gallegos mayorga et al. [2] and a comparison with design crack propagation curves proposed by bs7910 standard [3] is made. the authors have investigated the mechanical behaviour of those bridge materials, such as, metallographic, chemical composition, monotonic and fatigue behaviours of the materials of the old riveted steel bridges have been characterized [4-7]. others authors have performed similar work for other centenary bridges [8,9]. correia et al. [6,10,11] and bogdanov et al. [12] have proposed probabilistic curves for the fatigue crack growth propagation curves for several materials. correia et al. [6,10,11] proposed the probabilistic fields for fatigue crack growth using the probabilistic fatigue local approaches using old materials from riveted steel bridges and current steels. meanwhile, bogdanov et al. [12] proposed a probabilistic analysis of the fatigue crack growth rates based on the monte-carlo method applied to the unigrow model. fatigue life evaluation based on fracture mechanics ypically, the fatigue life predictions of structural details based on fracture mechanics are used for residual fatigue life assessments containing initially known defects acting as cracks and are typically used as evaluation criteria for planning in-service inspections [13]. de jesus et al. [13] evaluated the residual fatigue life of an ancient riveted steel road bridge using fracture mechanics approach based on experimental fatigue crack propagation data obtained for the old material from the pinhão bridge. thus, fatigue crack propagation data are fundamental to be used in fatigue life prediction approaches using fracture mechanics. in this sense, design fatigue crack growth curves are extremely important to establish and maintain the safety levels of the structural details and consequently of the structures. in fig. 1, a schematic bi-logarithm representation of the three fatigue crack growth regimes, between /da dn (crack growth rate) and k (stress intensity factor range), is showed. this behaviour shows two vertical asymptotes: one on the left, at thk k   , indicates that k values below this threshold level are too low to cause macro crack growth; and the right asymptote occurs for a ∆k cycle with max ck k , which leads to complete failure of the specimen. these three regimes can be denominated as: i – the threshold region; ii – the paris region; iii the unstable tearing crack growth region [14]. paris and erdogan [15] established a power function (eq. (1)) to describe the relation between /da dn and k :   mda c k dn    (1) where c and m are material parameters. this law is used to describe the so-called paris region and the experimental data follows a linear relation when using bi-logarithmic scales are used, as shown in fig. 1. i t correia et alii, frattura ed integrità strutturale, 42 (2017) 136-146; doi: 10.3221/igf-esis.42.15 138 figure 1: three crack growth regimes for ( /da dn ) versus k [11]. the integration of the fatigue crack propagation laws should be made between the initial crack size, ia , and the final crack size, fa , as indicated by eq. (2): 1 f i a f m a n da c k   (2) the final crack size, , is established by unstable crack propagation, dictated by material toughness, or plastic failure at the net section. the initial crack size, , is assumed around 0.25 to 1 mm for metals underestimating fatigue life of the component [16-18]. furthermore, a crack depth of 0.5 mm can be assumed in fracture mechanics analysis if it is not indicated by the available standards [3]. the stress intensity factor, , can be evaluated using the weight functions [19] and finite element analysis or using finite element analysis [20] to calculate the stresses and displacements on the crack front followed by the implementation of the virtual crack closure technique (vcct) [21]. alternatively, this parameter can be obtained by analytical relations that were established by several authors depending of the geometry. the definition of a design fatigue crack propagation curve for current steels and old materials is of great importance for obtaining safe residual fatigue lives of structural details from old metallic bridges. statistical evaluation of experimental fatigue crack propagation data statistical procedure n this paper, the statistical procedure to determine the design curves for the experimental fatigue crack propagation data used was proposed by gallegos mayorga et al. [2]. this procedure follows the same recommendations that were proposed by astm e739-91 standard [22]. this statistical procedure is based on the linear paris law that is described by eq. (3), where da dn is the fatigue crack growth (fcg) rates, k is the applied stress intensity factor range, c and m are material constants, * log da da dn dn            ,  * logc c , *m m and  * logk k   .   * ** *da c m k dn          (3) i correia et alii, frattura ed integrità strutturale, 42 (2017) 136-146; doi: 10.3221/igf-esis.42.15 139 this procedure considers that the fatigue crack growth (fcg) data pertain to a random sample where all * i da dn       are independent and there are no run-outs or suspended tests for the entire range of  *k . furthermore, the linear model for the paris relation can be rewritten as eq. (4) shows, where * i da dn       is the estimative (estimator) for the values of fcg rates.    * ** * i i da c m k dn          (4) the characterization parameters of the statistical analysis, such as the variance and the standard deviation must be defined. regarding the variance of the log-normal distribution, it is constant and maximum likelihood estimators of *c and *m are, respectively, defined by eqs. (5) and (6).     * * * ** * * 1 1 k k i i i i da k dadn c m m k k k dn                     (5)           * * * * 1 * 2 * * 1 k ii i k ii da da k k dn dn m k k                         (6) where * da dn       is the average values of * i da dn       ,  *k is the average value of  * i k and k is the total number of readings during the test by specimen. the average values * da dn       and  *k are determined as shown in eq. (7).     * * * * ;   k k i i i i da k da dn k k dn k                (7) where  * i k represents the computed during the test of the stress intensity factor ranges and * i da dn       represents the readings during the test of the fcg rates. concerning the standard deviation of the normal distribution for  log k , it is defined through the eq. (8). * * 1 2 k i i i da da dn dn s k                  (8) aiming the definition of a design fcg curve, rectilinear confident bands were defined as eq. (9) shows, where  is an integer. correia et alii, frattura ed integrità strutturale, 42 (2017) 136-146; doi: 10.3221/igf-esis.42.15 140       * * ** * * *da c m k s c s m k dn                   (9) in this analysis, it is assumed that = 2 which means that the confident band will cover approximately 95%. design fcg curve is defined through the upper boundary of this confident band. the material parameters and are defined by eqs. (10) and (11).  * 2 10 c s c   (10) *m m (11) this statistical procedure can be completed for several slopes in the fcg law using the notes proposed by bogdanov et al. [12]. in these notes, the fcg law may have three or four slopes identified [12,23,24], hence three or four pairs of  * *,i ic m coefficients that are needed to fit the experimental fatigue crack propagation data. each pair { * *,i ic m } corresponds to a segment with linear behaviour between  log /da dn and  log k values. slopes  *i im m are obtained using eq. (6). the materials constants of fatigue crack growth { * *,i ic m } and standard deviations can be obtained using eqs. (5), (6) and (8). several authors have discussed the evaluation of the fatigue crack propagation rates using statistical assumptions [6,7,10, 12,23,24], demonstrating the importance that the subject raises in the scientific community and engineers. experimental data the experimental fatigue crack growth data from the old riveted metallic bridges are collected for the statistical analysis proposed by gallegos mayorca et al. [2] aiming at obtaining the design curves for these materials. the experimental fatigue crack propagation data was derived accordingly astm e647 standard procedures [25]. this standard establishes the geometry of compact tension specimens – ct specimens and middle tension specimens – mt specimens. ct specimens were used for materials from eiffel ( w = 40 mm; b = 4.35 mm), fão ( w = 50 mm; b = 8 mm), pinhão ( w = 40 mm; b = 4.35 mm) and trezói ( w = 50 mm; b = 8 mm) bridges. specimens from luiz i bridge were manufactured as mt specimens ( w = 40 mm; b = 10 mm). all tests were carried out under a sinusoidal waveform with a frequency of 20 hz except for luiz i bridge specimens that were tested at a frequency of 10 hz. two travelling microscopes with accuracy of 0.001 mm were used to measure the crack growth on both faces of the specimens by direct visual inspection. regarding the number of tested specimens, five were manufactured from the eiffel bridge (four according to the transverse direction and one according to the longitudinal direction), twelve from the fão bridge, thirteen from the pinhão bridge (six from a diagonal and seven from a bracing), eight from the trezói bridge and four specimens from the luiz i bridge [1]. the following stress ratios were investigated for each material: ‐ eiffel bridge: r = 0.1 and r = 0.5; ‐ luiz i bridge: r = 0.1; ‐ fão bridge: r = 0.1; ‐ pinhão bridge: r = 0.0, r = 0.1 and r = 0.5; ‐ trezói bridge: r = 0.0, r = 0.25 and r = 0.5. experimental results from all tested specimens are presented in fig. 2. in each case, fatigue crack growth data is correlated using the previously referred power law developed by paris and erdogan [15] (see eq. (1)). application and discussion the statistical analysis described in the research work proposed by gallegos mayorca et al. [2] was used to estimate the probabilistic field of the fcg data for all old materials from the ancient riveted metallic bridges. the c and m parameters for the materials from the eiffel and fão bridges were estimated by gallegos mayorca et al. [2]. the fcg constants of the material from eiffel bridge using the statistical procedure are the following: * 17.614c   correia et alii, frattura ed integrità strutturale, 42 (2017) 136-146; doi: 10.3221/igf-esis.42.15 141 ( 171.199 10c   ), *m =4.69 (m=4.69) and 0.3463s  . for the material from the fão bridge, the fcg constants are: * 15.126c   ( 151.237 10c   ), *m =4.03 ( 4.03m  ) and 0.2378s  . all fcg constants were obtained with /da dn in mm/cycle and k in n.mm-1.5. a) b) c) d) e) figure 2. crack propagation data correlated with the paris law: (a) eiffel; (b) luiz i; (c) fão; (d) pinhão; (e) trezói. figs. 3 to 8 show the experimental fcg data, mean curve and the mean curve 2s (5% and 95% of probability of failure). all experimental results and probabilistic fields for the fatigue crack propagation data were compared with the design fcg curve of the stage b (mean curve 2s , with 2.88m  and 136.77 10c   where /da dn is in /mm cycle and k in 1.5.n mm  ) proposed by the bs7910 standard [3]. it should be noted that the design fcg curve proposed in correia et alii, frattura ed integrità strutturale, 42 (2017) 136-146; doi: 10.3221/igf-esis.42.15 142 the bs7910 standard [3] is indicated for current structural steels. this standard use the mean curve 2s to describe the design curve for the fatigue crack growth rates. in tab. 1 the c and m parameters are presented for all materials from portuguese metallic bridges and also the standard deviation, s , which is used to define the mean fcg curve 2s . this design curve is important to be used in rehabilitation studies of historical bridges (to analyse the fatigue residual life of structural details). the design fcg curve proposed by bs7910 standard when compared with each material from the eiffel, luiz i and fão bridges revealed not be representative of these materials. however, when compared to the experimental fcg data of the pinhão and trezói bridges, the design fcg curve proposed by bs7910 standard, seems to be more representative of these old materials. it should be noted that the materials of the pinhão and trezói bridges are more recent when compared to the other materials. in the fig. 8, the statistical analysis using the mean fcg curve 2s applied to the experimental data for all materials from ancient riveted bridges proved to be reasonably satisfactory, however the use of the mean fcg curve 3s to cover all experimental data is suggested. the slopes of the fcg curves of the materials from the eiffel, luiz i and fão bridges revealed to be similar, indicating the tendency exhibited for old materials. however, the slopes of the fcg curves for the materials from pinhão and trezói bridges exhibited a consistent behaviour with the slope of the design fcg curve proposed by bs 7910 standard [3]. the statistical analysis applied to fcg data proved to be efficient. material *c s c *m m eiffel 17.614 0.3463 171.199 10 4.69 luiz i 19.543 0.2548 209.243 10 5.50 fão 15.126 0.2378 152.237 10 4.03 pinhão 14.539 0.1082 154.757 10 3.62 trezói 14.278 0.1317 159.660 10 3.54 all materials 13.998 0.2967 143.940 10 3.47 table 1: constants of the mean fcg curve for all materials from the portuguese old metallic bridges, with /da dn in /mm cycle and k in 1.5.n mm  . figure 3: statistical analysis of the fcg data for the material from the eiffel bridge. 1.0e‐8 1.0e‐7 100 500 1000 1500 1.0e‐6 1.0e‐5 1.0e‐4 1.0e‐3 1.0e‐2 1.0e‐1 [n.mm‐1.5] [m m /c y cl e ] mean curve ‐ exp. data mean fcg curve + 2s mean fcg curve ‐ 2s mean curve + 2s: stage b; bs7910 mean curve: stage b; bs7910 2t1 (r=0.1) 2t2 (r=0.1) 2t3 (r=0.5) 2t4 (r=0.5) 2l1 (r=0.1) correia et alii, frattura ed integrità strutturale, 42 (2017) 136-146; doi: 10.3221/igf-esis.42.15 143 figure 4: statistical analysis of the fcg data for the material from the luiz i bridge. figure 5: statistical analysis of the fcg data for the material from the fão bridge. figure 6: statistical analysis of the fcg data for the material from the pinhão bridge. s1 (r=0.0) s2 (r=0.0) s3 (r=0.0) s4 (r=0.0) mean curve +2s: satge b; bs7910 mean curve: stage b; bs 7910 mean curve ‐ exp. data mean fcg curve + 2s mean fcg curve ‐ 2s 100 500 1000 1.0e‐6 1.0e‐5 1.0e‐4 1.0e‐3 1.0e‐2 [n.mm‐1.5] [m m /c y cl e ] 1.0e‐8 1.0e‐7 100 500 1000 1500 1.0e‐6 1.0e‐5 1.0e‐4 1.0e‐3 1.0e‐2 1.0e‐1 [n.mm‐1.5] [m m /c yc le ] p‐00 (r=0.0) p‐25 (r=0.25) p‐05 (r=0.5) p‐75 r=0.75) mean curve ‐ exp. data mean fcg curve + 2s mean fcg curve ‐ 2s mean curve + 2s: stage b; bs7910 mean curve: stage b; bs7910 b1 (r=0.0) b2 (r=0.0) b3 (r=0.0) b4 (r=0.0) d1 (r=0.0) d2 (r=0.0) b1 (r=0.1) d1 (r=0.1) d2 (r=0.1) b1 (r=0.5) b2 (r=0.5) d1 (r=0.5) d2 (r=0.5) mean curve ‐ exp. data mean fcg curve ‐ 2s mean fcg curve + 2s mean curve +2s: stage b; bs7910 mean curve: stage b; bs7910 300 500 1000 1500 1.0e‐6 1.0e‐5 1.0e‐4 1.0e‐3 1.0e‐2 [n.mm‐1.5] [m m /c y cl e ] correia et alii, frattura ed integrità strutturale, 42 (2017) 136-146; doi: 10.3221/igf-esis.42.15 144 figure 7: statistical analysis of the fcg data for the material from the trezói bridge. figure 8: statistical analysis of the fcg data for all materials from ancient riveted bridges. conclusions he statistical procedure used to analyse the experimental fcg data of the materials from the portuguese ancient metallic bridges proved to be efficient. the design fcg curves proposed by bs7910 standard are not representative of all materials from old metallic bridges. the slopes of the design curves for the fatigue crack growth data of the materials from eiffel, luiz i and fão bridges revealed to be similar. however, the slopes of the design curves for the fcg data of the materials from pinhão and trezói bridges exhibited a consistent behaviour and similar when compared with the slope of the design fcg curve proposed by bs 7910 standard. it should be noted that the latter materials are more recent and have mechanical properties similar to current constructional steels. further statistical analysis of the experimental fcg data from old materials is therefore necessary to better represent their behaviour. a comparison between this statistical analysis for fcg curve using several pairs { *ic , * im } and the probabilistic approaches for evaluating the fcg rates using local approaches should also be performed. acknowledgements he authors of this paper thank the scitech-science and technology for competitive and sustainable industries, r&d project norte-01-0145-feder-000022 co-financed by programme operational regional do norte ("norte2020") through fundo europe de desenvolvimento regional (feder) and the portuguese science r=0.0 r=0.25 r=0.5 mean curve ‐ exp. data mean fcg curve + 2s mean fcg curve ‐ 2s mean curve +2s: stage b; bs7910 mean curve: stage b; bs7910 100 500 1000 1500 1.0e‐6 1.0e‐5 1.0e‐4 1.0e‐3 1.0e‐2 [n.mm‐1.5] [m m /c y cl e ] 2000 luiz i pinhão eiffel trezói fão mean curve ‐ exp. data mean fcg curve + 2s mean fcg curve ‐ 2s mean curve +2s: satge b; bs7910 mean curve: satge b; bs790 100 2000 1.0e‐7 1.0e‐6 1.0e‐5 1.0e‐3 1.0e‐2 [n.mm‐1.5] [m m /c y cl e ] 1.0e‐4 1000500 1500 t t correia et alii, frattura ed integrità strutturale, 42 (2017) 136-146; doi: 10.3221/igf-esis.42.15 145 foundation (fct) through the post-doctoral grant sfrh/bpd/107825/2015 the for their collaboration, financial and technical support during these research works. the authors gratefully also acknowledge to the institute for sustainability and innovation in structural engineering (isise) by financial support through of the european project which is named of prolife prolonging life time of old steel and steel-concrete bridges (rfsr-ct-2015-00025) by research fund for coal and steel (rfcs). references [1] correia, j.a.f.o., jesus, a.m.p., figueiredo, m.a.v., ribeiro, a.s., fernandes, a.a., variability analysis of fatigue crack growth rates of materials from ancient portuguese steel bridges. proceedings of the 4th international conference on bridge maintenance, safety and management, (2008) 290-291. [2] gallegos mayorga, l., sire, s., correia, j.a.f.o., de jesus, a.m.p., rebelo, c., fernández-canteli, a., ragueneau, m., plu, b., statistical evaluation of fatigue strength of double shear riveted connections and crack growth rates of materials from old bridges, engineering fracture mechanics, (in press). [3] bs7910:2005, guidance on methods for assessing the acceptability of flaws in metallic structures, bsi, (2005). [4] de jesus, a.m.p., da silva, a.l.l., correia, j.a.f.o., fatigue of riveted and bolted joints made of puddle iron— a numerical approach, journal of constructional steel research, 102 (2014) 164–177. [5] de jesus, a.m.p., silva, a.l.l., figueiredo, m.v., correia, j.a.f.o., ribeiro, a.s., fernandes, a.a., strain-life and crack propagation fatigue data from several portuguese old metallic riveted bridges, engineering failure analysis, 17 (2010) 1495–1499. [6] correia, j.a.f.o., de jesus, a.m.p., fernández-canteli, a., a procedure to derive probabilistic fatigue crack propagation data, international journal of structural integrity, 3(2) (2012) 158-183. [7] sampayo, l.m.c.m.v., monteiro, p.m.f., correia, j.a.f.o., xavier, j.m.c., de jesus, a.m.p., fernandez-canteli, a., calçada, r.a.b., probabilistic s-n field assessment for a notched plate made of puddle iron from the eiffel bridge with an elliptical hole, procedia engineering, 114 (2015) 691-698. [8] lesiuk, g., szata, m., bocian, m., the mechanical properties and the microstructural degradation effect in an old low carbon steels after 100-years operating time, archives of civil and mechanical engineering, 15 (4) (2015) 786-797. [9] kucharski, p., lesiuk, g., szata, m., skibicki, d., description of fatigue crack growth in steel structural components using energy approach-influence of the microstructure on the fcgr, aip conference proceedings, 1780 (1) (2016) 050003. [10] correia, j.a.f.o., de jesus, a.m.p., fernández-canteli, a., local unified probabilistic model for fatigue crack initiation and propagation: application to a notched geometry. engineering structures, 52 (2013) 394-407. [11] correia, j.a.f.o., de jesus, a.m.p., fernández-canteli, a., calçada, r.a.b., modelling probabilistic fatigue crack propagation rates for a mild structural steel, frattura ed integrita strutturale, 31 (2015) 80-96. [12] bogdanov, s., mikheevskiy, s., glinka, g., probabilistic analysis of the fatigue crack growth based on the application of the monte-carlo method to unigrow model, materials performance and characterization, 3(3) (2014) 214–231. [13] de jesus, a.m.p., figueiredo, m.a.v., ribeiro, a.s., de castro, p.m.s.t., fernandes, a.a., residual lifetime assessment of an ancient riveted steel road bridge, strain: an international journal for experimental mechanics, 47(1) (2011) 402–415. [14] schijve, j., fatigue of structures and materials, kluwer academic publishers, new york, (2004). [15] paris, p., erdogan, f., a critical analysis of crack propagation laws, trans. asme, series d, 85 (1963) 523-535. [16] joint service specification guide aircraft structures, jssg-2006. united states of america: department of defense; (1998). [17] gallagher, j.p., berens, a.p., engle jr, r.m., usaf damage tolerant design handbook: guidelines for the analysis and design of damage tolerant aircraft structures, final report. (1984). [18] merati, a., eastaugh, g., determination of fatigue related discontinuity state of 7000 series of aerospace aluminum alloys. eng failure anal, 14(4) (2007) 673–685. [19] hafezi, m.h., abdullah, n.n., correia, j.a.f.o., de jesus, a.m.p., an assessment of a strain-life approach for fatigue crack growth, int. j. struct. integrity, 3(4) (2012) 344–376. [20] correia, j.a.f.o., blasón, s., de jesus, a.m.p., canteli, a.f., moreira, p.m.g.p., tavares, p.j., fatigue life prediction based on an equivalent initial flaw size approach and a new normalized fatigue crack growth model, engineering failure analysis, 69 (2016) 15-28. correia et alii, frattura ed integrità strutturale, 42 (2017) 136-146; doi: 10.3221/igf-esis.42.15 146 [21] krueger, r., virtual crack closure technique: history, approach, and applications, appl mech rev, 57(2) (2004) 109– 43. [22] astm e739-91: standard practice for statistical analysis of linear or linearized stress-life (s-n) and strain life (εn) fatigue data. annual book of astm standards, american society for testing and materials, (1991) 597-603. [23] correia, j.a.f.o., blasón, s., arcari, a., calvente, m., apetre, n., moreira, p.m.g.p., de jesus, a.m.p., canteli, a.f., modified ccs fatigue crack growth model for the aa2019-t851 based on plasticity-induced crack-closure. theoretical and applied fracture mechanics, 85(1) (2016) 26-36. [24] castillo, e., fernández-canteli, a., siegele, d., obtaining s-n curves from crack growth curves: an alternative to self-similarity. international journal of fracture, 187 (1) (2014) 159-172. [25] astm – american society for testing and materials, astm e647: standard test method for measurement of fatigue crack growth rates, in: annual book of astm standards, astm – american society for testing and materials, west conshohocken, pa, 03.01 (1999) 591-630. << /ascii85encodepages false /allowtransparency false /autopositionepsfiles true /autorotatepages /none /binding /left /calgrayprofile (dot gain 20%) /calrgbprofile (srgb iec61966-2.1) /calcmykprofile (u.s. web coated \050swop\051 v2) /srgbprofile (srgb iec61966-2.1) /cannotembedfontpolicy /error /compatibilitylevel 1.4 /compressobjects /tags /compresspages true /convertimagestoindexed true /passthroughjpegimages true /createjobticket false /defaultrenderingintent /default /detectblends true /detectcurves 0.0000 /colorconversionstrategy /cmyk /dothumbnails false /embedallfonts true /embedopentype false /parseiccprofilesincomments true /embedjoboptions true /dscreportinglevel 0 /emitdscwarnings false /endpage -1 /imagememory 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can be opened with acrobat and adobe reader 5.0 and later.) >> /namespace [ (adobe) (common) (1.0) ] /othernamespaces [ << /asreaderspreads false /cropimagestoframes true /errorcontrol /warnandcontinue /flattenerignorespreadoverrides false /includeguidesgrids false /includenonprinting false /includeslug false /namespace [ (adobe) (indesign) (4.0) ] /omitplacedbitmaps false /omitplacedeps false /omitplacedpdf false /simulateoverprint /legacy >> << /addbleedmarks false /addcolorbars false /addcropmarks false /addpageinfo false /addregmarks false /convertcolors /converttocmyk /destinationprofilename () /destinationprofileselector /documentcmyk /downsample16bitimages true /flattenerpreset << /presetselector /mediumresolution >> /formelements false /generatestructure false /includebookmarks false /includehyperlinks false /includeinteractive false /includelayers false /includeprofiles false /multimediahandling /useobjectsettings /namespace [ (adobe) (creativesuite) (2.0) ] /pdfxoutputintentprofileselector /documentcmyk /preserveediting true /untaggedcmykhandling /leaveuntagged /untaggedrgbhandling /usedocumentprofile /usedocumentbleed false >> ] >> setdistillerparams << /hwresolution [2400 2400] /pagesize [612.000 792.000] >> setpagedevice microsoft word numero_41_art_63.docx m.f. funari et alii, frattura ed integrità strutturale, 41 (2017) 524-535; doi: 10.3221/igf-esis.41.63 524 dynamic debonding in layered structures: a coupled ale-cohesive approach marco francesco funari, fabrizio greco, paolo lonetti department of civil engineering, university of calabria, via p. bucci, cubo39b, 87030, rende, cosenza, italy marcofrancesco.funari@unical.it, https://orcid.org/0000-0001-9928-3036 fabrizio.greco@unical.it, https://orcid.org/0000-0001-9423-4964 paolo.lonetti@unical.it, https://orcid.org/0000-0003-0678-6860 abstract. a computational formulation able to simulate crack initiation and growth in layered structural systems is proposed. in order to identify the position of the onset interfacial defects and their dynamic debonding mechanisms, a moving mesh strategy, based on arbitrary lagrangian-eulerian (ale) approach, is combined with a cohesive interface methodology, in which weak based moving connections are implemented by using a finite element formulation. the numerical formulation has been implemented by means of separate steps, concerned, at first, to identify the correct position of the crack onset and, subsequently, the growth by changing the computational geometry of the interfaces. in order to verify the accuracy and to validate the proposed methodology, comparisons with experimental and numerical results are developed. in particular, results, in terms of location and speed of the debonding front, obtained by the proposed model, are compared with the ones arising from the literature. moreover, a parametric study in terms of geometrical characteristics of the layered structure are developed. the investigation reveals the impact of the stiffening of the reinforced strip and of adhesive thickness on the dynamic debonding mechanisms. keywords. debonding; ale; dynamic delamination; fem; crack onset. citation: funari, m. f., greco, f., lonetti, p., dynamic debonding in layered structures: a coupled ale-cohesive approach, frattura ed integrità strutturale, 41 (2017) 524-535. received: 30.04.2017 accepted: 31.05.2017 published: 01.07.2017 copyright: © 2017 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. introduction uring the last decades, layered structures in the form of laminates or thin films have employed extensively in many engineering fields, ranging from nano to macro scale applications. typically, such materials are formed by strong layers and weak interfaces, in which internal material discontinuities may evolve, producing relevant loss of stiffness [1]. moreover, the crack evolution is strongly affected by the time rate of the external loading, which typically produces high amplifications of the fracture parameters. as a matter of fact, the measured crack tip speeds, during crack propagation, are relatively high, ranging also close to the rayleigh wave speed of the material [2,3]. therefore, in order to predict the interfacial crack growth, models developed also in a dynamic framework are much required. d m.f. funari et alii, frattura ed integrità strutturale, 41 (2017) 524-535; doi: 10.3221/igf-esis.41.63 525 in order to simulate debonding phenomena in layered structures, several approaches have been proposed in the literature. however, among the most important ones, fracture mechanics (fm) and cohesive zone model (czm) are widely utilized in practice [4]. in fm, the total energy release rate and its individual mode components need to be evaluated to predict delamination growth. for general configurations, the energy release rates can be computed by using a very accurate mesh of solid finite elements and the virtual crack closure method (vccm) [5]. such models calculate the energy release rate as the work performed by the internal traction forces at the crack faces during a virtual crack advance of the tip. moreover, in dynamic fracture mechanics, the vccm is applied by using the modified form, in which the err, during the time evolution, is evaluated by the product between the reaction forces and the relative displacements at the crack tip and at the nodes closer to the crack tip front, respectively, [6,7]. the prediction of the energy release rate is strictly dependent from the mesh discretization of the crack tip. alternatively, cohesive models propose an easy way to simulate debonding phenomena including also crack onset. distributed or discrete interface elements are introduced between continuum elements based on traction separation damage laws. however, such modeling is strictly dependent from the mesh discretization since the direction of crack propagation is restricted by the element size and orientation adopted by the user [8]. moreover, the presence of an initial finite stiffness may produce in brittle solids an excess of compliance and, in those cases in which a high stiffness is introduced, spurious traction oscillations [9]. such problems may be partially circumvented by introducing a very fine discretization at the crack tip front, to obtain a high resolution of the characteristic fracture length of the interface [10]. however, the resulting model is affected by computational complexities, because of the large number of variables and nonlinearities involved along the interfaces. in order to avoid such problems, combined formulations based on fracture and moving mesh methodologies are proposed [11,12]. in particular, the former is able to evaluate the variables, which govern the conditions concerning the crack initiation and growth, whereas the latter is utilized to simulate the evolution of the crack growth by means of ale formulation [13,14]. it is worth noting that the use of moving mesh method, combined with regularization and smoothing techniques, appears to be quite efficient to reproduce the evolution of moving discontinuities. however, existing models based on ale and fm are based on a full coupling of the governing equations, arising in both structural and ale domain. in this framework, material and mesh points in the structural domain produce convective contributions and thus nonstandard terms in both inertial and internal forces. in the proposed formulation, the use of a weak discontinuity approach avoids the modification of the governing equations arising from the structural model and thus a lower complexity in the governing equations and the numerical computation is expected. despite exiting numerical methodologies based on pure czm, the present approach reduces the nonlinearities involved in the governing equations to a small region containing the process zone, leading to a quite stable and efficient procedure to identify the actual solution in terms of both crack initiation and evolution. in order to verify the consistency of the proposed model, comparisons with existing formulations for several cases involving single and multiple delaminations are developed. the outline of the paper is as follows. at first, the formulation of the governing equations for the ale and interface approach is presented and, subsequently, the numerical implementation of the finite element model is reported. finally, comparisons and parametric results to investigate static and dynamic behavior of the debonding phenomena are proposed. theoretical formulation of the model he proposed model is presented in the framework layered structures, in which thin layers are connected through adhesive elements. in particular, a shear deformable beam model with a proper number of mathematical elements along the thickness direction is utilized to reproduce a high order zig-zag kinematic (fig.1). however, each layer is connected to the adjoining ones by means of imperfect interfaces, in which debonding phenomena may affect the adhesion between layers introducing material discontinuities and traction forces along normal or sliding directions. in order to simulate debonding phenomena, a fundamental task to be achieved is to identify the position, in which the onset of interfacial mechanisms is produced and subsequently to simulate the evolution of the cracked length. the theoretical formulation is articulated into two steps, which are presented separately. at first, when the crack onset condition is not satisfied, the moving mesh elements are inactive and only the structural problem is considered. subsequently, when the debonding process is triggered, the ale elements are activated introducing moving traction forces which follows the process zone length. governing equations the governing equations of the fe model are derived by means the principle of virtual works. in particular, for the general dynamic problem presented in fig. 1 it is required that the total virtual work is stationary: t m.f. funari et alii, frattura ed integrità strutturale, 41 (2017) 524-535; doi: 10.3221/igf-esis.41.63 526 0t u w     (1) where t is the virtual work of the inertial forces, u is the work of the internal forces and the tractions across the interfaces and w is the work of the external forces. according to the first-order transverse shear deformable laminate theory and multilayered approach, the variational form of the governing equations can be expressed by means of the following expressions:       1 2 0 1 0 1 1 10 0 1 10 0 1 2 l l i l l ln l l l l l ll l l lnn i i l l l l l l l i l ln n l l l l l l l l t u u dx, u n t m dx t dx , w f u h dx p u dx u u                                                     (2) where the subscripts l=1,..,n and i=1,..,n-1 indicate the numbering of the layers (n) and the interfaces (n-1),  , ,   with   11 2 ' ' ' ,xu , u ,        represent the generalized strains,  n ,t ,m are the generalized stresses defined as a function of the classical extensional  a , bending  d , bending–extensional coupling  d and the shear stiffness  h variables,  i t nt t t is the cohesive interfaces traction vector ,   i t n   is the cohesive interface displacement jump vector,  and 0 are the mass and polar mass per unit length of the layer and lf  and lp  ,with  1 2 0lf f f  and  1 2lp p p m  , are the per unit volume and area forces acting on the l-th layer, respectively. figure 1: layered structure: geometry, interfaces and tsl m.f. funari et alii, frattura ed integrità strutturale, 41 (2017) 524-535; doi: 10.3221/igf-esis.41.63 527 the cohesive interfaces the cohesive interfaces are introduced between the sublayers in which the crack initiation could be potentially activated. the crack onset definition is described by means of a mixed crack growth, which is a function of the fracture variables, coinciding with the ratio between err mode components and corresponding critical values, as follows: ( ) ( ) ( ) 1 1 1 2 2 1 r r i i i iii i f ic iic g x g x g x g g æ ö æ ö÷ ÷ç ç÷ ÷ç ç÷ ÷= + -ç ç÷ ÷ç ç÷ ÷÷ ÷ç çè ø è ø (3) where i represents the generic i-th interface in which debonding phenomena may occur, r is the constant utilized to describe fracture in different material and( ),ic iicg g are the total area under the traction separation law, whereas ( ),i iig g are the individual energy release rates calculated as ( ) 0 c n i n n ng t d d = d dò and ( ) 0 c t ii t t tg t d d = d dò . for each mode components, the traction separation law (tsl) is assumed to be described by the critical cohesive stresses, ( ),c ct nt t , the critical and initial opening or transverse relative displacements, namely ( )0 , cn nd d and ( )0 , ct td d . it is worth nothing that the proposed model is quite general to include other existing cohesive formulation on a different tsl or stress based initiation criteria, just by modifying the analytical expression defined in eq. 3. figure 2: representation of the coordinate systems employed: before crack initiation (a), after crack initiation, material and moving coordinates systems are coincident (b), ale formulation: referential and moving configuration introduced to described debonding phenomena (c). (a) (b) (c) m.f. funari et alii, frattura ed integrità strutturale, 41 (2017) 524-535; doi: 10.3221/igf-esis.41.63 528 the interfaces moving mesh strategy until the crack onset condition is not satisfied the ale equations are inactive and the position of the computational mesh points is expressed in the fixed material frame fm identified by the x1-x 2 coordinates (fig. 2a), which coincides, at this stage, with the moving (m) frame m (x1-x2) . it worth noting that the difference between fm and m is mainly in the mesh element number involved in the numeric model. in particular, in fm a coarse mesh is required to identify the of the crack onset position, whose accuracy is verified introducing more finite elements by using a remeshing procedure in the m configuration (fig. 2b). this procedure leads to the evaluation of the crack initiation position 1 ix which sets to zero eq. 3. the mathematical description of the moving mesh modeling is defined by a mapping operator φ , which relies a particle in a fixed referential frame r and the one in current moving coordinate system (fig. 2c). the mesh motion in terms of displacement field, at the i-th interface, is described as the difference between material 1 ix and the referential coordinates ( )x : ( ) ( ) ( ) ( )1 1 , i i i i i ix x t t t t onx x xd = =f w (4) where i ib hw = ´ represents the region in which the debonding mechanisms are produced. in order to reduce mesh distortions, produced by the mesh movements, rezoning or smoothing equations are introduced to simulate the grid motion consistently to laplace based equation which is, in the case of one dimensional domain for both static (s) and dynamic (d) cases, defined on the basis of the following relationships [15]:  2 ii , i ,t x         (s),  3 2 i i , ,t x t           (d) (5) eqs.(5) should be completed by means of boundary equations to reproduce the crack tip motion on the basis of the assumed crack growth criterion, namely ifg . in particular, for a fixed position in which the crack initiation occurs, different boundary conditions should be introduced to enforce internal or external debonding mechanisms. in particular, once the position of the crack onset is determined, i.e.at 1 1 ix x , a geometrical debonding with length equal to 2 is introduced in the numerical model, producing two potential finite crack tips in which debonding phenomena can be triggered (fig. 2b). in order to described the evolution of debonding phenomena the following boundary conditions should be introduced, which are completed by the kuhn-tucker optimality conditions:     1 1 0 0 0 0 0 0 i ii i i i i i tt f t f t f i ii i i i i i tt f t f t f x , g with x g x g , at x x x , g with x g x g , at x x                                       (6) where itx indicates the displacement of the crack tip front of the k-th debonded interface, i fg is the fracture function defined in eq,(3) and   /  represents the value of the   variable evaluated at left (-) or right (+) crack tip position. however, additional relationships are required for the ale formulation to reproduce the crack tip motion and boundary conditions. in particular, the displacements of the computational nodes are assumed to be zero at the boundaries of the structure, whereas small portions, close to the crack tip for the left and right debonding mechanisms, namely i  and i  , are assumed to be moved rigidly, enforcing the computational nodes at the extremities to have the same displacements. this choice ensures that the nls involved in the debonding mechanisms are constrained to a small portion containing the process zone, reducing the total complexities of the model. consequently, the following boundary conditions should be considered in the analysis (fig. 2b): m.f. funari et alii, frattura ed integrità strutturale, 41 (2017) 524-535; doi: 10.3221/igf-esis.41.63 529           1 1 1 11 1 1 11 1 0 0i i i ii i i i ii i i x , at x ,l , x x x x x x x x                    (7) it is worth noting that  i i,   can be considered as variable quantities for each crack path, that should be determined during the crack evolution. in particular, from the physical point of view, they represent the portion in which the traction separation laws are distributed. since those regions are assumed to be moved rigidly, by means of the ale strategy, the nonlinearities involved by the traction forces may be reduced to a small region close to the crack tip, avoiding as a result spurious and oscillatory effects typically documented in pure czms. from the numerical point of view, displacements of the debonding regions are determined on the basis of the values of the fracture function at their extremities by enforcing that during the crack growth a null value of the fracture function on the debonding region is achieved. therefore, by using a linear approximation function along the debonding region, the current crack tip displacement can be expressed by means of the following relationship:       1 1 1 0 0 0 ii fi ii i i t tf fi ii i i f f g x x g , x g g x g x                   (8) numerical implementation overning equations introduced in previous section are formulated by means of a numerical formulation based on the finite element (fe) approach. in particular, the derivation of the fe starts from the principle of virtual works in terms of displacements, integrating the equations on the volume of the elements. a lagrange cubic approximation is adopted to describe both displacement and rotation fields, whereas linear interpolation functions are utilized for the axial displacements. moreover, for the variables concerning moving mesh equations, quadratic interpolation functions are assumed to describe the mesh position of the computational nodes. the proposed approach takes the form of a set of nonlinear differential equations, whose solution is obtained by using a customized version of the finite element package comsol multiphysics combined with matlab script files [16]. the model can be solved in both static and dynamic framework, taking into account the time dependent effects produced by the inertial characteristics of the structure and the boundary motion involved by debonding phenomena. in both cases, since the governing equations are essentially nonlinear, an incremental-iterative procedure is needed to evaluate the solution [17]. in the case of static analysis, the resulting equations are solved by using a nonlinear methodology based on newton-raphson or arc-length integration procedures. in the framework of a dynamic analysis, the algebraic equations are solved by using an implicit time integration scheme based on a variable step-size backward differentiation formula (bdf). a synoptic representation of the numerical procedure as well as the computational algorithm implemented in the fe environmental program are reported in fig. 3. results n this section, results are developed with the purpose to verify the consistency and the reliability of the proposed model. at first, a layered structured formed by four mathematical layers and three intact interfaces are investigated in the static framework. the main aim of the present analysis is to validate the proposed procedure to predict the onset conditions and crack growth for a case involving multiple debonding mechanisms. subsequently, in order to validate the procedure to describe the crack front speed, dynamic debonding mechanisms concerning a frp strengthened steel beam specimen have been investigated by means comparisons with numerical results arising from the literature. g i m.f. funari et alii, frattura ed integrità strutturale, 41 (2017) 524-535; doi: 10.3221/igf-esis.41.63 530 figure 3: schematic representation of the algorithm for layered structure, crack initiation and evolution. layered structure – multiple debonding mechanisms the loading scheme, reported in fig. 4, is based on clamped end conditions and concentrated untisymmetric opening forces. the mechanical properties assumed for the laminate are reported in tab. 1, whereas those concerning the cohesive interface are reported in tab. 2. the numerical model is discretized along the thickness by using one mathematical layer for each sublaminate, whereas, for the interfaces, three ale elements are introduced between the sublayers, in which the crack initiation could be potentially activated. the analysis is developed under a displacement control mode, to ensure a stable crack propagation. in order to verify the stability and accuracy of the solution, several mesh discretizations, ranging from a coarse uniform distribution to a refined one, are considered. in particular, for the proposed model, the following numerical cases are analyzed:  uniform discretization with a characteristic element mesh equal δd/l=2/200 (m1) with 1841 dofs;  uniform discretization with a characteristic element mesh equal δd/l=1/200 (m2) with 3633 dofs; in addition, in order to verify the consistency of the proposed approach, a model based on pure cohesive approach, namely pc1, is developed, in which a uniform discretization of the mesh with a length equal δd/l=0.2/200 involving in 12012 dofs is adopted. figure 4: laminate configuration and loading scheme. 1e [gpa] 12g [gpa] cl [mm] cb [mm] h [mm] h [mm] e [mm]  [kg/mc] 130 3 200 20 2 12 20 1500 table 1: geometrical and mechanical properties of the laminate. m.f. funari et alii, frattura ed integrità strutturale, 41 (2017) 524-535; doi: 10.3221/igf-esis.41.63 531 icg [n/mm] c nt [mpa] 0 nδ [mm] nδ c [mm] iicg [n/mm] ctt [mpa] 0δt [mm] δ c t [mm] 0.26 30 0.00173 0.0173 1.02 60 0.00334 0.0334 table 2: interface properties of the laminate. in fig. 5a, results in terms of resistance curve are reported. the loading curve, obtained by the proposed model, is in agreement with the results obtained by using refined czm approach. moreover, in the case of a very low mesh element number (m1), the prediction in terms of resistance curve is not affected by a divergent behavior, but it is always very close to enriched one, namely pc1. in fig. 5b, the evolution between crack tip and applied displacements for two different mesh discretizations are considered. the results show that the proposed model is quite stable, since the predictions in terms of crack tip displacements coincide with that of the pc1 solution. however, it should be noted that in the case of a pure cohesive approach, the crack tip position is taken as the point where the fracture function of the cohesive interface tends to zero, whereas, in the proposed model, an explicit movement of ale region is identified, since it corresponds to a variable which enters in the computation. figure 5: comparisons in terms of loading curve with pure cohesive approach (a); comparisons in terms of cracks tip position with pure cohesive approach (b). figure 6: steel beam configuration and loading scheme. frp strengthened steel beam specimen the analyses are developed with reference to loading schemes based on the 4-point bending, in which the dynamic effects are considered from both onset and evolution mechanisms. the loading, the boundary conditions and the geometry are illustrated in in fig. 6, whereas the mechanical properties assumed for the steel, the adhesive, the frp strip and those m.f. funari et alii, frattura ed integrità strutturale, 41 (2017) 524-535; doi: 10.3221/igf-esis.41.63 532 concerning the potential cohesive zone model are reported in tabs. 3-6, respectively. in the present study, comparisons with results arising from the literature [18, 19] are developed. the main model refers to a steel beam, strengthened with frp strip elements. the model is based on two cohesive interface elements, which are introduced between adhesive-steel and adhesive-frp strip elements. as a consequence, debonding phenomena may affect the layered structures at two different interface levels. the interface law utilized to reproduce the debonding process is consistent with the model proposed by [20]. 1e s [gpa] 12g s [gpa] ls [mm] 1l s [mm] 2l s [mm] cs [mm] as [mm] bs [mm] hs [mm] s [kg/mc] 190 79.3 280 30 20 35 105 50 20 7500 table 3: geometrical and mechanical properties of the steel beam. 1e adh [gpa] 12g adh [gpa] ladh [mm] b adh [mm] hadh [mm] adh [kg/mc] 5 0.350 160 50 3 2000 table 4: geometrical and mechanical properties of the adhesive layer. 1e frp [gpa] 12g frp [gpa] lfrp [mm] b frp [mm] h frp [mm] frp [kg/mc] 165 60 160 50 1.2 2000 table 5: geometrical and mechanical properties of the frp strip. adhesive-steel interface (as) adhesive-frp interface (af) as [n/mm] asn [mm] as [n/mm] asn [mm] 0.350 0.01 0.350 0.01 table 6: interfaces parameters of the adhesive-steel interface (as) and adhesive-frp interface (af). in order to obtain a stable crack propagation, the structure is loaded under a displacement control mode. in particular, to avoid the dynamic effects due to the external load, a very small loading rate equal to 1 mm/s is assumed. however, time steps are modified during the computation from 1e-3 to 1e-7 sec, before and after the activation of the debonding phenomena, to capture accurately the effects produced by crack growth. in fig. 7, results in terms of resistance curve and crack speed time histories for different thickness of the frp strips are reported. at first, the structure presents a linear, stable and quasi-static behavior. subsequently, when the crack growth criterion is satisfied in the adhesive-steel interface, the ale interface is activated to reproduce the debonding phenomena. during the activation of debonding mechanisms, the resistance curve presents an oscillatory and variable behavior which varies very fast. in the same figure, a detail of the resistance curve at the point in which the crack onset is activated is also reported. this trend is quite in agreement with similar experimental results available from the literature [21], which show the importance of the dynamic effects during the crack growth. it is worth nothing that the resistance curves are quite dependent from the thickness properties of frp strip. in particular, an increase of the frp strip thickness reveals a similar impact on the critical displacement and load at the onset of the dynamic process (fig. 7). increasing the thickness of the frp strip, the edge debonding strength of the beam is reduced (fig. 7a). this effect is attributed to the increased amount of energy that is accumulated in the stiffened frp layer and the corresponding increment of the edge stresses. once the dynamic process is activated, the influence of the frp strip thickness produces an increase of the crack speeds, which leads to more severe failure mechanisms. contrarily to the properties of the frp layer, which are well documented in the literature, the influence of the adhesive on the debonding phenomena is not completely investigated. to this end, in fig. 8, results in terms of resistance curves and crack speed time histories for different values of the thicknesses of the adhesive layer are presented. in particular, an increment of the adhesive thickness reveals a different impact with respect the previous analyses in terms of frp strip characteristics, i.e. fig. 7. as a matter of fact, the results show how by using thin adhesive layers, an increase of the dynamic debonding strength is observed (fig. 8a) leading the structure to be affected to a more severe dynamic state (fig. 8b), since the observed crack tip speeds tend to be increased. from the results reported in fig. 7 and 8, a good agreement with the data available from the literature is also observed [18]. m.f. funari et alii, frattura ed integrità strutturale, 41 (2017) 524-535; doi: 10.3221/igf-esis.41.63 533 in fig. 9 the interfacial tractions across the two cohesive interfaces, i.e. adhesive-steel (as) and adhesive-frp (af), for different time steps of the delamination process, are reported. at first, in fig.9(a), the distribution of the interfacial traction forces is presented for the status a of the zoom reported in fig. 7a and 8a, which basically corresponds to the peak load of the quasi-static branch. it represents the stage just before the initiation of the debonding process, in which all layers are still bonded together. however, at the point a, the non-linear response of the cohesive adhesive-steel interface shows how the interfacial normal and tangential tractions tend to zero. this reflects the initiation of the dynamic debonding failure. in figs. 9b-d, the representation of the evolution of the dynamic debonding, in terms of interfacial traction, has been reported for different lengths of the debondend region. in particular, the results are referred to the points b, c, d of the zoom reported in figs. 7a-8a, in which the debonding lengths of adhesive-steel region are equal to 25, 50 and 75mm, respectively. figure 7: comparisons in terms of loading curve for different thickness of the frp strip (a); comparisons in terms of time histories of the debonding front speed for different thickness of the frp strip (b). figure 8: comparisons in terms of loading curve for different thicknesses of the adhesive layer (a); comparisons in terms of time histories of the debonding front speed for different thickness of the adhesive layer (b). it is worth noting that the af does not debond but it is able to provide interfacial tractions between the mathematical layers (fig. 9). finally, the consistency of the proposed model has been investigated also in terms of computational efforts. in m.f. funari et alii, frattura ed integrità strutturale, 41 (2017) 524-535; doi: 10.3221/igf-esis.41.63 534 particular, in order to satisfy the solution accuracy, the numerical model arising from [18] is based on a discretization with 560 and 320 elements for the steel and frp strip layer, respectively. moreover, the discretization of the 2d adhesive layer presents a uniform length equal to 0.5. as a consequence, the total number of dofs is approximately 7100. contrarily, by using the proposed approach, in which also the adhesive layer is simulated by means the shear deformable beam elements, the number of variables is strongly reduced. in particular, the proposed model has been discretized by means a uniform mesh length equal to 1 mm for the laminate and 1 mm for the interface involving 3018 dofs. therefore, a computational saving approximately equal to 60% is achieved. figure 9: comparisons in terms of interfacial tractions across the two cohesive interfaces for different positions of debonding front: x =0mmast (a); x =25mm as t (b); x =50mm as t (c); x =75mm as t (d). conclusions he proposed model is developed with the purpose to study the delamination processes in layered structures. the work flow is based on two different stages solved simultaneously, which are devoted to identify onset crack position along the interfaces and the corresponding evolution. compared with existing formulations available from literature, this model presents lower computational efforts and complexities in the governing equations. as a matter of fact, the use of debonding length concept coupled with a moving mesh approach based on ale formulation strongly reduces the computational complexities, since the mesh discretization is concentrated on a small portion coinciding to the process zone or the characteristic fracture length of the laminate. finally, the numerical approach is quite general since it does not depend from tsl or the structural formulation and can be easily implemented in conventional fe software. in order to validate the proposed model comparisons with numerical results obtained by pure cohesive approach are reported. finally, some parametric studies have been developed in terms of geometric characteristics of the layered structures for frp strengthened steel beams, which reveal a good agreement with existing results available from the literature. t m.f. funari et alii, frattura ed integrità strutturale, 41 (2017) 524-535; doi: 10.3221/igf-esis.41.63 535 references [1] barbero, e.,. introduction to composite materials design. crc press, (2010). [2] bruno, d., greco, f., lonetti, p., a 3d delamination modelling technique based on plate and interface theories for laminated structures. european journal of mechanics a-solids, 24 (2005), 127-149. doi: 10.1016/j.euromechsol.2004.11.005. [3] greco, f., lonetti, p., mixed mode dynamic delamination in fiber reinforced composites. composites part bengineering, 40 (2009) 379-392. doi: 10.1016/j.compositesb.2009.03.003. [4] rabinovitch, o., cohesive interface modeling of debonding failure in frp strengthened beams. journal of engineering mechanics-asce 134(2008) 578-588. doi: 10.1061/(asce)0733-9399(2008)134%3a7(578). [5] camacho, g.t., ortiz, m., computational modelling of impact damage in brittle materials. international journal of solids and structures, 33(1966) 2899-2938. doi: 10.1016/0020-7683(95)00255-3. [6] bruno, d., greco, f., lonetti, p., computation of energy release rate and mode separation in delaminated composite plates by using plate and interface variables. mechanics of advanced materials and structures, 12 (2005) 285-304. doi: 10.1080/15376490590953563. [7] bruno, d., greco, f., lonetti, p., dynamic mode i and mode ii crack propagation in fiber reinforced composites. mechanics of advanced materials and structures, 16 (2009) 442-455. doi: 10.1080/15376490902781183. [8] fortunato, g., funari, m.f., lonetti, p., survey and seismic vulnerability assessment of the baptistery of san giovanni in tumba (italy). journal of cultural heritage, accepted for the pubblication. doi: 10.1016/j.culher.2017.01.010. [9] greco, f., leonetti, l., lonetti, p., nevone blasi, p., crack propagation analysis in composite materials by using moving mesh and multiscale techniques. computers and structures, 153 (20159) 201-216. doi: 10.1016/j.compstruc.2015.03.002. [10] de borst, r., remmers, j.j.c, needleman, a., mesh-independent discrete numerical representations of cohesive-zone models. engineering fracture mechanics, 73(2006) 160-177. doi: 10.1016/j.engfracmech.2005.05.007. [11] funari, m.f., greco, f., lonetti, p., a moving interface finite element formulation for layered structures. composites part b-engineering, 96 (2016) 325-337. doi: 10.1016/j.compositesb.2016.04.047. [12] funari, m.f., greco, f., lonetti, p., a cohesive finite element model based ale formulation for z-pins reinforced multilayered composite beams. procedia structural integrity, 2 (2016) 452-459. doi: 10.1016/j.prostr.2016.06.059. [13] bruno, d., greco, f., lonetti, p., a fracture-ale formulation to predict dynamic debonding in frp strengthened concrete beams. composites part b-engineering, 46 (2013) 46-60. doi: 10.1016/j.compositesb.2012.10.015. [14] greco, f., leonetti, l., lonetti, p., a novel approach based on ale and delamination fracture mechanics for multilayered composite beams. composites part b-engineering, 78 (2015) 447-458. doi: 10.1016/j.compositesb.2015.04.004. [15] lonetti, p., dynamic propagation phenomena of multiple delaminations in composite structures. computational materials science, 48 (2010) 563-575. doi: 10.1016/j.commatsci.2010.02.024. [16] comsol multiphysics reference guide. (2014). [17] funari, m.f., lonetti, p., initiation and evolution of debonding phenomena in layered structures. theoretical and applied fracture mechanics, (2017). accepted for the pubblication. doi: 10.1016/j.tafmec.2017.05.030. [18] mulian, g., rabinovitch, o., debonding dynamics in frp plated beams: high order cohesive fe formulation and parametric sensitivity, international journal of fracture, 195 (2015) 53-78. doi: 10.1007/s10704-015-0048-8. [19] mulian, g., rabinovitch, o., experimental and analytical study of the dynamic debonding in frp plated beams, international journal of solids and structures, 92-93 (2016) 121-134. doi: 10.1016/j.ijsolstr.2016.03.020. [20] volokh, k. yu., needleman, a., buckling of sandwich beams with compliant interfaces. computers and structures 80 (2002) 1329–1335. doi: 10.1016/s0045-7949(02)00076-7. [21] lundsgaard-larsen, c., massabo, r., cox, b.n., on acquiring data for large-scale crack bridging at high strain rates. journal of composite materials, 46 (2012) 949-971. doi: 10.1177/0021998311413622. << /ascii85encodepages false /allowtransparency false /autopositionepsfiles true /autorotatepages /none /binding /left /calgrayprofile (dot gain 20%) /calrgbprofile (srgb iec61966-2.1) /calcmykprofile (u.s. web coated \050swop\051 v2) /srgbprofile (srgb iec61966-2.1) /cannotembedfontpolicy /error /compatibilitylevel 1.4 /compressobjects /tags /compresspages true /convertimagestoindexed true /passthroughjpegimages true /createjobticket false /defaultrenderingintent /default /detectblends true /detectcurves 0.0000 /colorconversionstrategy /cmyk /dothumbnails false /embedallfonts true /embedopentype false /parseiccprofilesincomments true /embedjoboptions true /dscreportinglevel 0 /emitdscwarnings false /endpage -1 /imagememory 1048576 /lockdistillerparams false /maxsubsetpct 100 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can be opened with acrobat and adobe reader 5.0 and later.) >> /namespace [ (adobe) (common) (1.0) ] /othernamespaces [ << /asreaderspreads false /cropimagestoframes true /errorcontrol /warnandcontinue /flattenerignorespreadoverrides false /includeguidesgrids false /includenonprinting false /includeslug false /namespace [ (adobe) (indesign) (4.0) ] /omitplacedbitmaps false /omitplacedeps false /omitplacedpdf false /simulateoverprint /legacy >> << /addbleedmarks false /addcolorbars false /addcropmarks false /addpageinfo false /addregmarks false /convertcolors /converttocmyk /destinationprofilename () /destinationprofileselector /documentcmyk /downsample16bitimages true /flattenerpreset << /presetselector /mediumresolution >> /formelements false /generatestructure false /includebookmarks false /includehyperlinks false /includeinteractive false /includelayers false /includeprofiles false /multimediahandling /useobjectsettings /namespace [ (adobe) (creativesuite) (2.0) ] /pdfxoutputintentprofileselector /documentcmyk /preserveediting true /untaggedcmykhandling /leaveuntagged /untaggedrgbhandling /usedocumentprofile /usedocumentbleed false >> ] >> setdistillerparams << /hwresolution [2400 2400] /pagesize [612.000 792.000] >> setpagedevice shot peening processes to obtain nanocrystalline surfaces in metal alloys: z. li et alii, frattura ed integrità strutturale, 53 (2020) 446-456; doi: 10.3221/igf-esis.53.35 446 a coupled elastoplastic damage model for brittle rocks zheng li, yundong shou* school of civil engineering, wuhan university, china lizheng872@163.com, https://orcid.org/0000-0003-0321-0567 shouyundong@whu.edu.cn, https://orcid.org/0000-0001-7424-4006 deping guo xuzhen railway co.,ltd. zhaotong 657900, yunnan, china guodeping99@qq.com filippo berto norwegian university of science and technology, norway filippo.berto@ntnu.no abstract. brittle rock contains an important plastic deformation, which causes microcracks when coupled with stress-induced damage. a new coupled elastoplastic damage model is established in order to discuss the damage behaviors found in brittle rock, based on theoretical analysis and experiments. micromechanic considerations determine the effective elastic properties of anisotropic damaged geomaterials. an energy-based damage criterion is used to deduce the damage initiation and the damage evolution law of the brittle rocks. moreover, the non-linear unified strength criterion is modified. it takes anisotropic damage and the effects of intermediate principal stress into account, in order to determine both the yield and plastic potential functions. the non-associated plastic flow rule is utilized. the consistency condition of plastic and damage is applied in the coupled process. the damage evolution rule and the coupled plastic damage of brittle rock are conceived within the framework of irreversible thermodynamics. by comparing the simulations and the experimental data from limestone that was subjected to various loading paths, a strong connection between the numerical simulations and experimental data is therefore obtained. the numerical results show that the new model is able to describe the main features of the mechanical properties observed in brittle rock. keywords. coupled elastoplastic damage model; non-associated plastic flow rule; anisotropic damage behaviors; brittle rock. citation: li, z., shou, y.d., guo, d.p., berto, f., a coupled elastoplastic damage model for brittle rocks, frattura ed integrità strutturale, 53 (2020) 446-456. received: 23.4.2020 accepted: 05.06.2020 published: 01.07.2020 copyright: © 2020 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. https://youtu.be/qcldo-efmz4 z. li et alii, frattura ed integrità strutturale, 53 (2020) 446-456; doi: 10.3221/igf-esis.53.35 447 introduction hina is one of the few countries in the world that use coal as an important power source. more than 70% of its total power generation is thermal power [1]. its output has exceeded one third of the world's total output. the coal industry has played an important role in promoting national economic development, rapid economic growth and social progress. however, with the vigorous development of the coal industry, coal mine accidents have become a major obstacle to its development. coal mine accidents are mainly included in the fields of gas burst, roof fall, rock burst and so on. roof fall, as shown in fig 1, is the most ordinary accident in coal mine. the number of roof fall accidents is accounting for 43% in coal mining accidents. coal is a complex fractured geological medium containing numerous randomly distributed micro holes and cracks. its mechanical properties are important essential parameters for the mining design, roadway support and some other underground coal engineering [2-4]. therefore, the constitutive relation and damage model of coal-rock is still a major issue to be solved urgently. figure 1: a roof fall accident happened in coal mine. for the mechanical properties of coal-rock, the plastic/elastoplastic and damage model were the focus issues in the previous researches. chen et al.[5] established a new permeability model considering plastic and failure behavior for coal, and discovered that the mechanical state (or deformation stage) of coal had a significant effect on permeability. wu et al. [6] developed a plastic strain-based damage model that consists of the heterogeneity function, the damage stress-strain function, the cohesion function and the dilation angle function based on analysing the characteristics of coal dilation and strain hardening/softening during deformation. zhou et al. [7] proposed a nonlinear constitutive equation of rocks by taking the nonlinear deformation properties of rocks into consideration. moreover, both the nonlinear damage evolution equation and constitutive equation of rocks were deduced by applying the thermodynamics conservation laws [7]. rock belongs to a typical heterogeneous material with very low tensile strength. the effects of temperature gradient on the damage of rocks were investigated by zhou et al. [8] and zuo et al. [9]. li et al. [10] proposed a theoretical evaluation model of rock brittleness based on the statistical damage theory and the energy evolution law of rock failure process. in this model, the damage evolution of coal in loading process was considered. the micromechanical damage mechanics approach leads to an improved understanding of the underlying physical processes [7,11-12]. in the micromechanical approach, researchers study the growth, nucleation, and coalescence of microcracks and their influence on the mechanical properties, which is reflected in the constitutive relation in certain ways [11-19]. among these, the most widely used models are the dilute-concentration method (dcm), the self-consistent method [20-22], the differential method (dm) [23-24], the generalized self-consistent method (gscm) [25], and finally, the effective selfconsistent method [26]. however, the micromechanical damage mechanics model is often difficult to implement in engineering applications, because of its proclivity to cause 3d problems. therefore, the phenomenological approach is adapted in the new model. this article proposes a coupled elastoplastic damage model in order to discuss the plastic deformation and induced damage found in brittle geomaterials. furthermore, the new coupled model describes the anisotropic damage behaviors of geomaterials in triaxial and uniaxial compressive tests. c z. li et alii, frattura ed integrità strutturale, 53 (2020) 446-456; doi: 10.3221/igf-esis.53.35 448 general idea for the coupled elastoplastic damage model ased on our theoretical analysis and experimental investigations, a coupled elastoplastic damage model is established to describe the mechanical behaviors of semi-brittle geomaterials. as mentioned earlier, an anisotropic damage model can be used to describe the degradation process that is induced by the microcracks found in semi-brittle geomaterials. generally, small strain assumption is adopted, and the total strain tensor can be decomposed into an elastic part, e ε and a plastic part, p ε [7,12, 27-28] e p =ε ε + ε (1) in an isothermal process without viscous dissipation, helmholtz free energy is dependent on three state variables: ( , , ) e p  = d (2) where ε denotes the elastic strain tensor, p represents the scalar-valued internal variables of plasticity, and d refers to the tensor-valued internal variables of damage. assuming that a thermodynamic potential exists in the damaged elastoplastic geomaterials, plastic deformation and plastic hardening both occur within the damage process. helmholtz free energy can be resolved into elastic and plastic components: ( , , ) ( , ) ( , ) e p p p     = = +d d dε ε (3) where 0 ( , ) (1 ( ) p p p ptr    = −d d) , ( ) ( ) ( ) 0 0 0 0 2 ( ) m m m p p p p p p p p p pb         = − + − + − , 0 p is the initial plastic yielding threshold, m p is the ultimate value of hardening function, b is a model’s parameter controlling plastic hardening rate, and  is the model’s parameter coupling of damage evolution and plastic flow. to insure that the second law of thermodynamics is justified, the clausius–duhem's inequality principle indicates that the reduced dissipation inequality contains: : 0  − σ (4) the evaluation of the inequality involves the time derivative of the helmholtz free energy: ( , , ) : : e e p p p p p             = + + +    d d d d d ε ε ε (5) substitution in the reduced dissipation inequality results in: : : :: 0 e e e p p p p              − + − − −        p e e ε d d d dε ε   (6) where the additive decomposition is utilized in consideration of the elastic and plastic strain contributions. the thermodynamic conjugate forces for plasticity and damage are, respectively: p p p r    = −  (7)  = −  y d (8) b z. li et alii, frattura ed integrità strutturale, 53 (2020) 446-456; doi: 10.3221/igf-esis.53.35 449 non-linear poroelastic behavior consider a geomaterial sample with the size v weakened by microcracks. it is assumed that the damage tensor is just the second-order fabric tensor. then, the damage tensor can be defined as [29] 3 1 1 n r v    = = d n n (9) where r and  n are the radius and normal vector of the αcrack. if the crack density is small, interaction among cracks can be neglected. the helmholtz free energy function can be expressed as follows [30-31]: ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) 2 2 0 0 1 0 0 2 3 4 , 2 1 1 2 e e e e e e e e e e e e e tr tr b tr tr b tr b tr tr b tr tr       = +  +  + −  +   +  +  ε d ε ε ε d ε ε ε d ε ε d d ε ε (10) where 0e is young’s modulus, 0v is poisson’s ratio, ( ) ( ) ( ) ( ) ( ) 2 2 2 20 1 1 0 2 0 3 0 0 4 0 02 2 0 0 1 1 2 1 1 2 e b a a a a         = − + + + + + −  + − , ( ) 2 2 0 2 2 01 a e b  = − + , ù ( ) ( ) ( ) 2 0 3 2 0 3 02 0 0 2 1 1 1 2 e b a a    = − + +   + − , ( ) 2 4 0 4 2 01 a e b  = − + , 1 2 3 4 7 2 , , , 70 7 7 35 c c c c a h a h a h a h + = − = = = − , ( ) ( ) 2 0 0 0 16 1 3 2 h e   − = − , 0c v= − (when cracks are open), 2c = − (when cracks are closed). the standard derivation of the thermodynamic potential satisfies the state equation: ( ) ( ) , : e e e e  = =  ε d σ e d ε ε (11) where ( ) ( )( ) ( ) ( ) ( ) ( ) ( ) ( )( ) 0 0 0 0 0 0 1 1 22 3 4 1 1 2 2 1 2 ijkl ij kl ik jl il jk ij kl ik jl il jk ik jl il jk ij kl ij kl ik jl il jk e e e b tr b d d d d b d d b tr                       = + + + − + + + + + + + + + + d d eqn. (9) and eqn. (11) describe the initial anisotropic elastic damage behaviors of geomaterials. damage characterization damage kinetics may be determined by the pseudo-potential of dissipation. the damage initiation and the damage evolution law are controlled by the damage’s energy release. the damage initiation and the damage evolution law are concluded in the case of non-viscous dissipation using a damage criterion, which is a scalar-valued function of damage energy release. the energy-based damage criterion is contemplated in the following form [32-33]: z. li et alii, frattura ed integrità strutturale, 53 (2020) 446-456; doi: 10.3221/igf-esis.53.35 450 ( ) ( )0( , ) 0 d d df y y k tr= − +   r = yy d d d (12) where ( ) 1 2 d tr=   y y y , 0y represents the damage energy release threshold at a given value of damage, and k is the parameter controlling the damage evolution rate. a normal dissipation scheme is utilized to obtain the damage evolution rate. the damage evolution rate is expressed as follows: ( , ) d d f   =  y d d y (13) in which the damage multiplier d  is a positive scalar originated from the loading–unloading conditions. the kuhn–tucker relations can be written as: ( , ) 0, 0, ( , ) 0 d d d d f f =  =y d y d (14) specifically, in the case of elastic damage loading without plastic flow ( 0 p  = ), the damage consistency condition is expressed by: ( ) : : 0 d d d f f f   = =   ,y d y + d y d , and eqn. (13) gives the rate of the damage multiplier: ( ( ) : ) :1 : ( ) ( ) e d e r r   = = −   e ε εy ε ε d d d (15) where ( )   e d e (d) = d , ( ) ( ) r r   =  d d d . therefore, the rate form of constitutive equation turns into: ed =σ e ( ) : εd (16) where ed e ( )d is the tangent elastic damage tensor: 1 ( ( ) ) ( ( ) ) ( ) ed e e r  = −   e ( ) e( ) e : ε e : εd d d d d (17) eqn. (17) can easily describe the anisotropic damage behaviors of geomaterials in triaxial and uniaxial compressive tests. plastic characterization the plastic strain rate is determined by the plastic yield function, the plastic hardening law, and the plastic flow rule in the case of non-viscous dissipation. an anisotropic plasticity framework is used due to the initial anisotropy of geomaterials. for most geomaterials, the non-linear unified strength criterion can be applied in order to produce the transition from plastic volumetric compressibility to dilatancy. the nonlinear unified strength theory has the following characteristics: (1) it is able to reflect the fundamental characteristics of rock, i.e., different tensile and compressive strengths, hydrostatic pressure effects, the effects of intermediate principal stress, zonal change, and material dependence. (2) it has a clear physics and mechanics background, a unified mathematical model, and simple and explicit criteria, which includes all independent stress components and simple material parameters. (3) it is also suitable for different types of rocks under various stress states, and it is consistent with other research regarding triaxial tests. the coupled elastoplastic damage models of geomaterials are z. li et alii, frattura ed integrità strutturale, 53 (2020) 446-456; doi: 10.3221/igf-esis.53.35 451 different than those of metals. generally, the plastic yield criterion and plastic potential can be conveyed by a scalar valued function that determines the thermodynamic force, stress tensor and damage variable, conjugated with an internal hardening variable. yield function can be written as follows: ( ), , 0p pf  σ d (18) plastic potential function can be expressed as: ( , ) 0pq  σ (19) the following modification of the three-dimensional nonlinear strength criterion proposed by zhou et al. [34] is introduced to determine the damage of rock 2 1 3 2 3( ) ( ) p c cf n m      = + + (20) where n and m are the strength parameters, c denotes uniaxial compressive strength of rocks, 1 2 3, ,   are the major, intermediate and minor principal stresses, respectively. when the damage variable is considered, the nonlinear strength criterion eqn. (20) is rewritten in another form ( ) ( )2 1 2( , , ) 2 3 cos 3 1 3 cos 3 2 sin 0 3 p p c c tr f j i m n j m m n             = − − + + − + − =        d d (21) where the stress angle is equal to 3 1 2 1 2 2 ( ) arctan 3( )         − + =   +  , 30 30 o o −   , 1i is the first invariant of stress, 2j is the second invariant of deviatoric stress tensor, c is an uniaxial compressive strength of an intact rock material, m and n are strength parameters of rocks. the equivalent deviatoric plastic strain p is defined in terms of the odquist parameter, which is traditionally used in 2j plasticity to express plastic dissipation, in terms of von mises stress and it includes the equivalent plastic strain rate: 2 : 3 p = p p e e (22) where p e denotes the rate of deviatoric plastic strain. to ascertain the direction of the plastic strain rate, the following modification of the non-linear loading function is considered as a plastic potential function: ( )22 2 1 3 ( , ) 4 cos cos 2 sin 3 3 c p cq j m n j i            = + + − −    (23) here, the dilatation parameter  is used to control inelastic volume expansion: 3 0( ) p m m e       − = − − (24) where the parameter 3 denotes the exponential rule of the dilatation parameter  . a non-associated plastic flow rule is utilized. the non-associated plastic flow rule and loading–unloading condition are described in the following: z. li et alii, frattura ed integrità strutturale, 53 (2020) 446-456; doi: 10.3221/igf-esis.53.35 452 ( , )p p q    =  p ε   (25) ( ) ( ), , 0, 0, , , 0p p p pf f   =  =σ d σ d (26) the change rate of the mean plastic strain p m and deviatoric plastic strain p e is defined by: 22 p m p p p j     =   =   s e (27) from eqn. (3), the plastic hardening function ( , )p p  d is concluded by a standard derivative of the thermodynamic potential [35]: ( )0 0 ( ) ( , (1 2 m m p p p p p p p p tr b               = = − − + −   p, d, d) d) (28) the scalar valued function ( ,pa  )d indicates the plastic hardening modulus, which is expressed as follows: ( , : ( : p p p p p f q f q a e         = −        ) p d d) : σ σ σε (29) if 0d = , the plastic multiplier is resolved from the plastic consistency condition: : : ( : : p p p p f f q a    =     e(d) ε σ , d) + e(d) σ σ (30) the rate form of constitutive equations can be expressed as follows: : ep =σ e ε (31) where ep e is the fourth order tangent elastoplastic tensor given by: : : ( , ) ( : : p ep p p q f a f q a              = −     e(d) e(d) σ σ e d e(d) , d) + e(d) σ σ (32) coupled elastoplastic damage behavior under general loading conditions, plastic flow and damage evolution occur in a coupled process. both the plastic strain and damage evolution rates should be determined concurrently, by applying the plastic and damage consistency conditions in a coupled system [36]. z. li et alii, frattura ed integrità strutturale, 53 (2020) 446-456; doi: 10.3221/igf-esis.53.35 453 ( , , ) : : 0 p p p p p p p f f f f       = + + =    σ d σ d σ d (33) ( , ) : : 0 d d d f f f   = =   y d y + d y d (34) by drawing the constitutive equations, the plastic hardening law, and damage criterion (33)~(34), into one system, the plastic and damage multiplier can be determined [37-39]: 3 4 1 6 2 6 3 5 1 5 2 4 2 6 3 5 p d r r r r r r r r r r r r r r r r   − =  −  − =  − (35) where 1 : p f r  =  σ σ , 2 26 p ij ij p s sf r j  =  , 3 : p d f r y   =      y d , 2 4 : : e e d r y     = −   y d , 2 5 2 : 6 ij ij d p s s r y j    = −   y d , 2 6 : : d d d f r y y      = −          y y d d d . numerical simulations or limestone, the below parameters are obtained in triaxial compression tests: 0 88.198e gpa= , 0 0.255v = , 0.004r m = , 1.5k = , 1 133 = , 2 1800 = , 11.5m = , 7.5n = , 0.13 = , 0 0.00012 = , 0.00014m = , 0.25b = − , 3 1.33 = , 5 0 4.9795 10y =  pa. the dilute scheme, which is used for an elastic solid that has been weakened by an isotropic distribution of non-interacting closed microcracks[40-42], yields the following theoretical initial values of damage variable: 11 0.02d = , 22 0.02d = . figure 2: simulation of stress-strain curve under triaxial compressive test with confining pressure 10mpa 0 20 40 60 80 100 120 140 160 -2000 -1500 -1000 -500 0 500 1000 1500 2000 2500 3000 3500 present model experimental data ε1x10 -6 ε2x10 -6 (σ1-σ2)/mpa f z. li et alii, frattura ed integrità strutturale, 53 (2020) 446-456; doi: 10.3221/igf-esis.53.35 454 figure 3: simulation of stress-strain curve under uniaxial compressive test fig. 2 and fig. 3 show comparisons between the experimental data for confining pressure at 10mpa and 0 mpa. a strong connection between the numerical simulations and experimental data was obtained. since the triaxial tests have only determined the parameters of model, this comparison just verifies the consistency of the parameters. conclusions ur research proposes a new coupled elastoplastic damage model that addresses the coupled elastoplastic damage, found in the thermodynamics of semi-brittle geomaterials that have been subjected to compressive stresses. our experiments applied the coupled elastoplastic damage model to a representative semi-brittle rock, namely limestone. the model can be used to describe anisotropic damage behaviors, elastoplastic deformation, pressure sensitivity, plastic compressibility and dilatancy, the degradation of elastic properties, and coupling between the plastic flow and damage of semi-brittle geomaterials, in triaxial and uniaxial compressive tests. the new model contains a small number of parameters, which can be obtained from standard triaxial compression tests. this study reveals a strong link between the numerical simulations and our experimental data, derived from our research with semi-brittle limestone that has been subjected to various loading paths. acknowledgments he work is supported by the national natural science foundation of china (nos. 41807251, 51809198 and 51839009), and the fundamental research funds for the central universities (grant no. 2042019kf0037). references [1] liu, x.s., tan, y.l., ning, j.g., lu, y.w., gu, q.h. (2018). mechanical properties and damage constitutive model of coal in coal-rock combined body, int. j. rock. mech. min. 110, pp.140-150. doi: 10.1016/j.ijrmms.2018.07.020. [2] xie, h.p., zhao, x.p., liu, j.f., zhang, r., xue, d. (2012). influence of different mining layouts on the mechanical properties of coal, int. j. min. sci. tech. 22(6), pp.749-755. doi: 10.1016/j.ijmst.2012.12.010. [3] poulsen, b.a., shen, b., williams, d.j., huddlestone-holmes, c., erarslanb, n., qin, j. (2014). strength reduction on saturation of coal and coal measures rocks with implications for coal pillar strength, int. j. rock. mech. min. 71, pp.4152. doi: 10.1016/j.ijrmms.2014.06.012. 0 10 20 30 40 50 60 70 80 -300 -200 -100 0 100 200 300 400 500 600 700 800 900 1000 experimental data present model σ1/m pa ε1/x10 -6 ε2/x10 -6 o t z. li et alii, frattura ed integrità strutturale, 53 (2020) 446-456; doi: 10.3221/igf-esis.53.35 455 [4] bertuzzi, r., douglas, k., mostyn, g. (2016). an approach to model the strength of coal pillars, int. j. rock. mech. min. 89, pp.165-175. doi: 10.1016/j.ijrmms.2016.09.003. [5] chen, d., pan z.j., shi j.q., si, g., ye, z., zhang, j. (2016). a novel approach for modelling coal permeability during transition from elastic to post-failure state using a modified logistic growth function, int. j. coal geol. 163, pp. 132139. doi: 10.1016/j.coal.2016.07.007. [6] wu, c., dou, l.m., ju, y., cao, w., yuan, s., si, g. (2018). a plastic strain-based damage model for heterogeneous coal using cohesion and dilation angle, int. j. rock. mech. min.110, pp. 151-160. doi: 10.1016/j.ijrmms.2018.08.001. [7] zhou, x.p., zhang, y.x., ha, q.l., zhu, k.s. (2008). micromechanical modelling of the complete stress-strain relationship for crack weakened rock subjected to compressive loading, rock mech. rock eng. 41(5), pp. 747–769. doi: 10.1016/0020-7683(76)90044-5. [8] zhou, x.p., li, g.q., ma, h.c. (2020). real-time experiment investigations on the coupled thermomechanical and cracking behaviors in granite containing three pre-existing fissures, eng. fract. mech. 224, 106797. doi:10.1016/j.engfracmech.2019.106797. [9] zuo, j.p., xie, h.p., zhou, h.w. (2007). thermal-mechanical coupled effect on fracture mechanism and plastic characteristics of sandstone, sci. china ser. e. 50, pp. 833-843. doi: 10.1007/s11431-007-0081-6. [10] li, y.w., long, m., zuo, l.h., li, w., zhao, w. (2019). brittleness evaluation of coal based on statistical damage and energy evolution theory, j. petrol sci. eng. 172, pp. 753-763. doi: 10.1016/j.petrol.2018.08.069. [11] zhou, x.p. (2004). analysis of the localization of deformation and the complete stress–strain relation for mesoscopic heterogeneous brittle rock under dynamic uniaxial tensile loading, int. j. solids struct. 41 (5–6) , pp. 1725–1738. doi: 10.1016/j.ijsolstr.2003.07.007. [12] zhou, x.p., ha, q.l., zhang, y.x., zhu, k.s. (2004). analysis of deformation localization and the complete stress– strain relation for brittle rock subjected to dynamic compressive loads, int. j. rock. mech. min. 41 (2) , pp. 311–319. doi:10.1016/s1365-1609(03)00094-7. [13] shao, j. f., lu, y.f., lydzba, d. (2004). damage modeling of saturated rocks in drained and undrained conditions, j. eng. mech.-asce 130(6), pp. 733–740. doi: 10.1061/(asce)0733-9399(2004)130:6(733). [14] ortiz,m. (1985). a constitutive theory for the inelastic behavior of concrete, mech. mater. 4, pp. 67–93. doi: 10.1016/0167-6636(85)90007-9. [15] chow, c.l., june, w. (1987). an anisotropic theory of elasticity for continuum damage mechanics, int. j. fracture, 33, pp. 3–16. doi: 10.1007/bf00034895. [16] zhou, x.p., yang, h.q. (2007). micromechanical modeling of dynamic compressive responses of mesoscopic heterogenous brittle rock, theor. appl. fract. mec. 48(1), pp. 1–20. doi: 10.1016/j.tafmec.2007.04.008. [17] zhou, x.p. (2005). triaxial compressive behavior of rock with mesoscopic heterogenous behavior: strain energy density factor approach, theor. appl. fract. mec. 45(1), pp. 46–63, doi: 10.1016/j.tafmec.2005.11.002. [18] zhou, x.p. (2005). localization of deformation and stress-strain relation for mesoscopic heterogeneous brittle rock materials under unloading, theor. appl. fract. mec. 44(1), pp. 27–43. doi: 10.1016/j.tafmec.2005.05.003. [19] shao, j.f., jia, y., kondo, d., chiarelli, a.s. (2006). a coupled elastoplastic damage model for semi-brittle materials and extension to unsaturated conditions, mech. mater. pp. 38(3), 218–232. doi: 10.1016/j.mechmat.2005.07.002. [20] zhang, j.x., wong, t.f., davis, d.m. (1990). micromechanics of pressured-induced grain crushing in porous rocks, j. geophys res.-sol. ea. 95, pp. 341–351. doi: 10.1029/jb095ib01p00341. [21] budiansky, b., o’connell, r.j. (1976). elastic moduli of a cracked solid, int. j. solids struct.12, pp. 81–97. doi: 10.1016/0020-7683(76)90044-5. [22] yang, x.b., xia, y.j., wang, x.j. (2012). investigation into the nonlinear damage model of coal containing gas, safety sci. 50, pp. 927-930. doi: 10.1016/j.ssci.2011.08.001. [23] horii, h., nemat-nasser, s. (1983). overall moduli of solids with microcracks: load-induced anisotropy, j. mech. phys. solids. 31, pp. 155–171. doi: 10.1016/0022-5096(83)90048-0. [24] zhou, x.p., wang, j.h. (2005). study on the coalescence mechanism of splitting failure of crack-weakened rock subjected to compressive loads, mech. res. commun. 32(2), pp. 161–171. doi: 10.1016/j.mechrescom.2004.06.003. [25] hashin, z. (1988). the differential scheme and its application to cracked materials, j. mech. phys. solids, 36, 719–734. doi: 10.1016/0022-5096(88)90005-1. [26] aboudi, j., benveniste, y. (1987). the effective moduli of cracked bodies in plane deformations, eng. fract. mech. 26(2), pp. 171–184. doi: 10.1016/0013-7944(87)90195-0. [27] zhou, x.p., zhang, y.x., ha, q.l., zhu, k.s., (2004). bounds on the complete stress-strain relation for a crackweakened rock mass under compressive loads, int. j. solids struct. 41(22/23), pp. 6173–6196. doi: 10.1016/j.ijsolstr.2004.04.023. z. li et alii, frattura ed integrità strutturale, 53 (2020) 446-456; doi: 10.3221/igf-esis.53.35 456 [28] zhou, x.p. (2006). upper and lower bounds for constitutive relation of crack-weakened rock masses under dynamic compressive loads, theor. appl. fract. mec. 46(1), pp. 75–86. doi: 10.1016/j.tafmec.2006.05.004. [29] swoboda, g., yang, q. (1999). an energy-based damage model of geomaterials ii: deduction of damage evolution laws, int. j. solids struct. 36, pp. 1735–1755. doi: 10.1016/s0020-7683(98)00164-4. [30] ostwald, r.，bartel, t., menzel, a. (2015). an energy-barrier-based computational micro-sphere model for phasetransformations interacting with plasticity, comput. method appl. m. 293, pp. 232–265. doi: 10.1016/j.cma.2015.04.008. [31] abou-chakra, guéry, cormery, f., shao, j. f., kondo, d. (2008). a micromechanical model of elastoplastic and damage behavior of a cohesive geomaterial, int. j. solids struct. 45(5), pp. 1406–1429. doi: 10.1016/j.ijsolstr.2007.09.025. [32] salar, m. r., saeb, s., willam, k. j., patchet, j., carrasco, r.c. (2004).a coupled elastoplastic damage model for geomaterials, comput. method appl. m. 193(27–29), pp. 2625–2643. doi: 10.1016/j.cma.2003.11.013. [33] welemane, h., cormery, f. (2003). an alternative 3d model for damage induced anisotropy and unilateral effect in microcracked materials, j. phys. iv france. 105, pp. 329–338. doi: 10.1051/jp4:20030204. [34] zhou, x.p., shou, y.d., qian, q.h., yu, m.h. (2014). three-dimensional nonlinear strength criterion for rock-like materials based on the micromechanical method, int. j. rock. mech. min. 72, pp. 54-60. doi: 10.1016/j.ijrmms.2014.08.013. [35] zheng, q.s., du, d.x. (2001). an explicit and universally applicable estimate for the effective properties of multiphase composites which account for inclusion distribution, j. mech. phys. solids. 49, pp. 2765–2788. doi: 10.1016/s0022-5096(01)00078-3. [36] zhou, x.p., li, x.h. (2009). constitutive relationship of brittle rock subjected to dynamic uniaxial tensile loads with microcrack interaction effects, theor. appl. fract. mec. 52(3), pp. 140–145. doi: 10.1016/j.tafmec.2009.09.002. [37] hashin, z. (1988). the differential scheme and its application to cracked materials, j. mech. phys. solids. 36, pp. 719– 734. doi: 10.1016/0022-5096(88)90005-1. [38] aboudi, j., benveniste, y. (1987). the effective moduli of cracked bodies in plane deformations, eng. fract. mech. 26(2), pp. 171–184. doi: 10.1016/0013-7944(87)90195-0. [39] zhang, j.x., wong, t.f., davis, d.m. (1990). micromechanics of pressured-induced grain crushing in porous rocks, j. geophys res.-sol. ea. 95, pp. 341–351. doi: 10.1029/jb095ib01p00341. [40] zhou, x.p., zhang, j.z., wong, l.n.y., (2018). experimental study on the growth, coalescence and wrapping behaviors of 3d cross-embedded flaws under uniaxial compression, rock mech. rock eng. 51(5), pp. 1379-1400. doi: 10.1007/s00603-018-1406-4. [41] zhou, x.p., zhang, j.z., qian, q.h., niu, y., (2019). experimental investigation of progressive cracking processes in granite under uniaxial loading using digital imaging and ae techniques, j. struct. geol. 126, pp. 129-145. doi: 10.1016/j.jsg.2019.06.003. [42] zhou, x.p., lian, y.j., wong, l.n.y., berto, f. (2018). understanding the fracture behavior of brittle and ductile multiflawed rocks by uniaxial loading by digital image correlation，eng. fract. mech. 199, pp. 438-460. doi: 10.1016/j.engfracmech.2018.06.007. microsoft word numero_53_art_30_2840 a. kostina et alii, frattura ed integrità strutturale, 53 (2020) 394-405; doi: 10.3221/igf-esis.53.30 394 applicability of vyalov’s equations to ice wall strength estimation a. kostina, m. zhelnin, o. plekhov, i. panteleev institute of continuous media mechanics of the ural branch of russian academy of science, russia kostina@icmm.ru, http://orcid.org/0000-0002-5721-3301 zhelnin.m@icmm.ru, http://orcid.org/0000-0003-4498-450x poa@icmm.ru, http://orcid.org/0000-0002-0378-8249 pia@icmm.ru, http://orcid.org/0000-0002-7430-3667 l. levin, m. semin mining institute of the ural branch of russian academy of science, russia aerolog_lev@mail.ru, http://orcid.org/0000-0003-0767-9207 seminma@outlook.com, http://orcid.org/0000-0001-5200-7931 abstract. a simple analytical relations are commonly used in engineering practice to calculate ice wall thickness. one of them is vyalov’s relation that takes into account the features of a real technological process of tubing lining and the inelastic deformation associated with frozen soil creep. an estimation of applicability and margin of safety of this equation is an issue of engineering mechanics. in this paper, we propose a mathematical model for description of ice wall deformation under natural external loading and present the results of the computational experiments in which an optimal thickness for the ice wall is determined. based on this simulation, we modify the existing analytical relation, which makes it possible to calculate the thickness of an ice wall of unlimited height. keywords: ice wall; frozen soil; mine shaft; vyalov’s equation. citation: kostina, a., zhelnin, m., plekhov, o., panteleev, i., levin, l., semin, m., applicability of vyalov’s equations to ice wall strength estimation, frattura ed integrità strutturale, 53 (2020) 394-405. received: 20.05.2020 accepted: 01.06.2020 published: 01.07.2020 copyright: © 2020 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. introduction he ice wall is an important engineering structure the integrity of which determines the safety of sinking operations in vertical mine shafts under construction. the effectiveness of the ice wall as a temporary protective lining depends on the adequate evaluation of its thickness. optimal assessment of the wall thickness comes from the need to reduce the cost of mining operations at the design stage. this will help to exclude the failure of an ice wall and the breakthrough of groundwater into the mine. furthermore, the savings in artificial freezing costs may be significant. engineering calculations for ice walls are currently performed for two limit states strain condition and strength condition. in strain calculations, it is necessary to determine the minimum thickness of the ice wall at which its deformation in the design phase does not exceed the value acceptable for shaft construction and promotes no dangerous movements of freezing columns. the objective of the limit strength design is to calculate the optimal minimum thickness of the ice wall which t https://youtu.be/lmykqbpy_ik a. kostina et alii, frattura ed integrità strutturale, 53 (2020) 394-405; doi: 10.3221/igf-esis.53.30 395 prevents its failure under external loads, i.e. no cracks occur in the wall. at this thickness value, the ice wall is in the ultimate stress-strain state, i.e., in the state where the stresses at a given instant of time do not exceed the frozen soil strength at the same instant. the most common methods for calculating of ice wall thickness are those proposed by domke [1] and lame-gadolin [1]. the lame-godolin formula was obtained in a linear elastic approximation and did not prove effectiveness at soil depths of more than 50 m. the domke equation takes into account the plastic deformations of frozen soil, the onset of which is determined according to the criterion for the difference between the largest and smallest principal normal stresses. because the strength of saturated soils increases with an increase in the mechanical pressure up to a certain value, the application of the mohr-coulomb and druker-prager criteria makes it possible to calculate plastic strain with higher accuracy and to take into account the fact that the frozen soil strength increases with decreasing temperature [2]. the triggering of high hydrostatic pressure leads to melting and failure of the ice contained in the pores. this has given impetus to different modifications of these criteria [3]. the thermo-hydro-dynamical models of soil freezing which take into account plastic strains are presented in [4-7]. in [4-6], the so-called barcelona basic model [8] is used to describe the plastic deformations of saturated frozen soils. according to this model, the stress-strain state of soils is determined by analyzing two state variables – effective stress and a parameter that describes the moisture migration effect. for the non-frozen soil, the barcelona basic model is simplified and reduced to the modified cam-clay model. the thermo-hydro-dynamical models based on this approach can be employed to consider the influence of moisture migration and mechanical pressure on the plastic deformation of frozen soils. in [6], the barcelona basic model is generalized to the case of large deformations. another way [7] has been proposed to derive the constitutive relations for describing the elastoplastic behavior of frozen soils in the framework of a thermodynamic approach. it has been suggested in [9] that the yield surface defined in terms of a double clay hardening model can be used to assess plastic strains. elastic and plastic strains characterize the instantaneous response of the material to the applied loads. however, due to the pronounced rheological behavior of saturated soils under long-term loads, their deformation increases and strength reduces. this feature of soils is of prime importance for shaft sinking where the loads from the surrounding rocks and ground water are taken over by the lateral surface of a mine during the entire time required for lining construction. in order to calculate the optimal thickness of an ice wall () and to take into account the rheological behavior of frozen soils, s.s.vyalov suggested the following relations [10, 11]:     1 111 1 ' 1 ,                     mm m p m p h e a k a t t a (1)                          1 2 1 1 2 , m m p m p e a a t t a (2)   3   s p ph e t (3)                              2 0 1 2 0 45 /2 1 0 45 / 2 1 1 1 2 45 / 2 tg p p tg e a c t tg (4) where  is the optimal ice wall thickness, a is the cylinder inner radius, k’ is the coefficient dependent on soil compaction conditions, m, a(tp, ) are the parameters characterizing the rheological behavior of the soil, tp is the loading period, p is the load applied to the ice wall, h is the height of unfixed part of mine shaft, is the maximum radial movement of the frozen a. kostina et alii, frattura ed integrità strutturale, 53 (2020) 394-405; doi: 10.3221/igf-esis.53.30 396 soil, s(tp) is the ultimate strength of frozen soil to uniaxial compression, c(tp) is the cohesion, and  is the angle of internal friction. eqns. (1)-(2) estimate for the cylinder wall thickness according to the criterion for the maximum radial movement of its internal wall, and eqns. (3)-(4) the ultimate stress criterion. we notice that eqns. (1) and (3) are obtained on the assumption that the ice wall is a cylinder of finite height, and eqns. (2) and (4) – on the assumption that the ice wall is a cylinder of unlimited height. it is also worth noting that formula (3) is obtained based on relationship (1) assuming that the frozen soil exhibits ideal plastic behavior described by the von mises model. in [12], the applicability of formula (1) for calculating the frozen wall thickness was evaluated. the aim of our work is to analyze the correctness of analytical relationships (3) and (4) for calculating the frozen wall thickness according to the ultimate stress criterion. for this purpose, the ice wall thickness calculated by these formulas was compared with the numerical simulation results obtained by the formulation whose geometry is close to the real shaft sinking conditions. using the obtained data, we propose a modification of formula (4) because it shows better agreement with the numerical simulation results. in addition, we perform a comparative analysis of the values of ice wall thickness calculated by formulas (1)-(4) and by their modifications, which provides guidelines for using each of these formulas. mathematical formulation n order to evaluate the correctness of relations (3) and (4), we have computed the problem of deformation of ice wall exposed to the external radial load p applied to the lateral surface of the cylinder and the vertical load p’ acting on the upper end of the cylinder. the calculation scheme of shaft sinking is given in fig.1. an ice wall is modeled as a twopiece cylinder. one part is a hollow cylinder of a height equal to that of the ice wall section without lining, and another part is a solid section. the soil inside the ice wall is assumed to be a thawed soil that experiences only elastic deformations. the load applied to the lateral surface of the cylinder is calculated by the formula for mining and hydrostatic pressure, which takes into account the influence of cohesive forces and the results of hydrogeological observations. figure 1: computational domain the mathematical model is based on the following hypotheses and assumptions: 1) the computational domain has radial symmetry, and therefore calculations are made in axisymmetric formulation. 2) the rocks under consideration are isotropic at macrolevel. 3) deformations as well as strain increments at each step are small. 4) the time and temperature effects on the strength and elastic characteristics of rocks are taken into account parametrically. 5) the surrounding thawed and burden formations generate constant rock pressure. 6) a linear relation exists between the stress and elastic strain tensors. 7) the minimum value for the ice wall thickness is determined on the assumption that no plastic deformations are present on its internal wall. 8) the mohr-coulomb criterion is used as a yield criterion that is commonly applied to describe soil failure (especially, that of cohesionless soil). by this criterion, the rock failure begins when the maximum tangential stress n reaches the critical value which is dependent on the normal stress n in the same area. the mathematical statement of the problem includes equilibrium eqn. (5), hooke’s law (6), geometric relation for small strain tensor (7), yield condition (8), and associated plastic flow rule (9): i a. kostina et alii, frattura ed integrità strutturale, 53 (2020) 394-405; doi: 10.3221/igf-esis.53.30 397   σ 0 (5)  : σ c ε εp (6)  1 2      ε u u t (7) 0     nnf tg c (8)     ε σ  p f (9) where ={r, ,z, rz} is the stress tensor, ={r, ,z, rz} is the strain tensor, с is the tensor of elastic constants which reduces in the isotropic case to two elastic constants (e′ – young’s modulus,  – poisson’s ratio), u={ur, uz} is the displacement vector, p={pr, p,pz, prz} is the plastic strain tensor, f is the mohr-coulomb yield criterion, n is the maximum tangential stress in the area with a normal n, n is the normal stress operating in the same area,  is the indefinite multiplier determined using prager’s compatibility conditions, and the dots over the symbols denote time derivatives. the prager compatibility conditions are written as 0, 0  f , (or 0f (10) 0, 0   f , (and 0f ) (11) the system of eqns. (5)-(11) is supplemented with boundary conditions that correspond to the calculation scheme from fig.1. 1 0 zu (12) 2   n σ p (13) 3 '  n σ p (14) where the vectors p={p,0} and p′={p′,0} correspond to the calculated loads obtained by the formulas:  r hp p p (15) 0 0 2 90 90' 2 2 2                      r mp g h tg c tg (16)   h w gwp g h (17) ' '  mp g h (18) in formulas (15) (18), the following notation is used: m=2000 kg/m3 – average density of the material, h′ – bed rock density, w=1000 kg/m3 – water density, g=10 m/s2 – gravitational constant, hgw=1.5 m – groundwater depth. the load ph is considered only for saturated rocks. a. kostina et alii, frattura ed integrità strutturale, 53 (2020) 394-405; doi: 10.3221/igf-esis.53.30 398 materials and method he allowable ice wall thickness was determined for three typical materials: sand, chalk and clay. we considered the bed rock depth values of 100m, 200m, 300m, and 500m. tabs. 1 and 2 give the mechanical parameters of the soil in thawed and frozen states which were provided by the institute of nature management of the nas of belarus. the parameters of the frozen soil were obtained at t=-80c and for load duration of 12 h. these data were used for calculating the load acting on the ice wall according to formulas (15) – (18). the obtained data are given in tabs. 3-5. soil e′, gpa  с, kpa , 0 sand 0.32 0.3 9.6 30 chalk 0.3 0.35 1 31.5 clay 0.364 0.18 105 25 table 1: mechanical parameters for the soil in thawed state. soil e′, gpa  с, mpa , 0 s, mpa sand 5.3 0.18 6.33 37 4.4 chalk 2.5 0.15 6.20 24 7 clay 1.7 0.17 3.78 10 2.2 table 2: mechanical parameters for the soil at t=-80c. load 100 m 200 m 300 m 500 m p, mpa 1.557 3.222 4.889 8.222 p′, mpa 2 4 6 10 table 3: loads acting on the frozen sand ice wall load 100 m 200 m 300 m 500 m p,mpa 0.626 1.253 1.881 3.135 p′,mpa 2 4 6 10 table 4: loads acting on the frozen chalk ice wall. load 100 m 200 m 300 m 500 m p, mpa 0.678 1.490 2.301 3.925 p′, mpa 2 4 6 10 table 5: loads acting on the frozen clay ice wall. the finite-element method was used for the solution of boundary value problem. the examined area was divided into rectangular elements. we controlled the convergence of the numerical solution based on a series of calculations on grids with elements of different sizes for the clay layer at a depth of 200m. the sizes of elements in the ice wall area with no mine working support (lining) varied from 1.28 to 0.02m. the relative error erri is defined by the formula t a. kostina et alii, frattura ed integrità strutturale, 53 (2020) 394-405; doi: 10.3221/igf-esis.53.30 399 min min 100%       i i m m m err (19) where i[0.02; 1.28] indicates the size of the element used to determine the von mises stress value m on the internal wall of the ice cylinder, and minm is the von mises stress value on the internal wall of the ice cylinder obtained in the solution of the problem with minimum element size. fig. 2 shows the effect of size of the finite element of the grid on relative error. the results demonstrate that the optimal size of the element is 0.04m. it is interesting that if the element size is maximum (1.28m), then the relative error does not exceed 8.3%, which is well within the permissible limits of an engineering error. figure 2: relative error vs finite element size. results and discussion comparison of numerical simulation results and analytical estimates he developed mathematical model is used for assessing the optimal ice wall thickness according to the criterion for ultimate stress-strain state. the calculation results are summarized in tab. 6. when the optimal ice wall thickness is calculated by eqn. (2), the ultimate uniaxial compression strength values are taken from tab. 2. the values for the cohesion and internal friction angle used in eqn. (4) are also given in tab. 2. the calculation results are summarized in tabs. 7 and 8. the obtained results demonstrate that, for all materials under study, the design thicknesses obtained by eqn. (3) exceed those found using eqn. (4). this can be attributed to the fact that the internal friction is ignored, which increases the strength. in general, the scatter in the estimates obtained by eqns. (3) and (4) is great (12 times for sand); especially, when the ice wall experiences high loads. h′, m sand chalk clay 100 1.05 0.35 0.75 200 1.75 0.50 1.2 300 2.35 0.75 1.4 500 2.5 1.05 2.6 table 6: ice wall thickness obtained via numerical simulation. h′, m sand chalk clay 100 3.065 0.774 2.667 200 6.342 1.550 5.864 300 9.623 2.327 9.058 500 16.183 3.879 15.451 table 7: ice wall thickness calculated by formula (3). t a. kostina et alii, frattura ed integrità strutturale, 53 (2020) 394-405; doi: 10.3221/igf-esis.53.30 400 h′, m sand chalk clay 100 0.304 0.171 0.404 200 0.595 0.340 0.910 300 0.860 0.508 1.441 500 1.330 0.838 2.582 table 8: ice wall thickness calculated by formula (4). a comparison of the ice wall thickness values found during the numerical solution of problem (5)-(18) with the results obtained by eqns. (3) and (4) is illustrated in fig.3. for all materials under study, eqn. (3) shows the most distinction from the numerical simulation results (fig. 3a). the greatest ice wall thickness reserve is seen for clay and sand, especially, for the layers at a depth of 500 m. this is because the ice wall is subjected to maximum loads at this depth. in this case, the deviations from the numerical results obtained for clay and sand are the greatest, 12.8 m and 13.7m, respectively. (a) (b) figure 3: difference between the designed ice wall thickness obtained via numerical simulations and the analytical estimations for the ice wall thickness found by eqns. (3) (a) and (4) (b). it was found that the results of numerical simulations of the ice wall thickness for chalk and sand are higher than the estimations obtained by eqn. (4) (fig.3 b). the most distinction from the numerical simulation results is 1.49m for sand at a depth of 300 m and 0.242 for chalk at a depth of 300 m. a comparison of the same results but obtained for clay shows that the numerical calculations give the higher ice wall thickness values for the material at depths of 100-200 m. at depths of 300-500 m, the simulation results are comparable with those obtained by formula (4); the relative error does not exceed 2.8%. modification of eqn. (4) analysis of the obtained results has revealed that eqn. (4) has the best correlation with the numerical simulation results. this equation was modified here in order to get a more accurate description of the relation between the designed ice wall thickness and the applied load. the modification made it possible to minimize the difference between the calculation results obtained by this formula and the numerical simulation data. thus, we have                                   2 0 1 2 0 45 /2 1 0 45 / 2 1 1 1 2 45 / 2 tgp tg e k a d c tg (20) where k and d are the piecewise constants 1 1 2 2 2 3   , ,       k p p p k k p p p a. kostina et alii, frattura ed integrità strutturale, 53 (2020) 394-405; doi: 10.3221/igf-esis.53.30 401 1 1 2 2 2 3   , ,       d p p p d d p p p the intervals for the coefficients for each material were set reasoning from the best agreement with the numerical simulation data. approximations of the parameters k and d for each material are given in tab. 9 and 10. the calculated results for the designed ice wall thickness for chalk, clay and sand obtained by new eqn. (20) are presented in fig.4. soil k1 k2 p1, mpa p2, mpa p3, mpa sand 2.337 0.319 1.557 4.889 8.222 chalk 1.186 0.909 0.626 1.881 3.135 clay 0.624 1.052 0.678 2.301 3.925 table 9: approximation of the coefficient k. soil d1 d2 p1, mpa p2, mpa p3, mpa sand -6.674 5.648 1.557 4.889 8.222 chalk -0.847 0.760 0.626 1.881 3.135 clay 2.516 -0.387 0.678 2.301 3.925 table 10: approximation of the coefficient d. (a) (b) (c) figure 4: approximation of eqn. (4) (solid lines) by the piecewise-linear functions (dashed lines) for sand (a), chalk (b) and clay (c). a. kostina et alii, frattura ed integrità strutturale, 53 (2020) 394-405; doi: 10.3221/igf-esis.53.30 402 in addition to approximation (20), it is suggested that formula (4) can be modified as                                   2 0 1 2 0 45 /2 1 0 45 / 2 1 1 1 2 45 / 2 tgp tg e a z c tg (21) the values of parameter z for sand, chalk and clay are given in tab. 11. the calculated results are obtained for the designed thickness by eqn. (21) and the numerical simulation results are shown for each material in fig.5. the approximations are nonlinear, which is caused by the nonlinear dependence of stress on the radial coordinate and, as a consequence, on the desired ice wall thickness. the nonlinear character is determined by the material parameters of the soil, e.g., for chalk and sand, the curve is convex upwards and for clay – downwards. chalk and sand exhibit similar cohesion values (6.2 and 6.33 mpa), and clay has significantly lower cohesion value (3.78 mpa). it is interesting that almost the same nonlinear behavior is observed for eqn. (4). sand chalk clay z 1.140 0.198 0.153 table 11: values of the parameter z, entering eqn. (21). (a) (b) (c) figure 5: results of approximation of eqn. (4) (curve 2) by function (21) (curve 1) for sand (a), chalk (b), clay (c). markers – numerical solution. a. kostina et alii, frattura ed integrità strutturale, 53 (2020) 394-405; doi: 10.3221/igf-esis.53.30 403 a comparison of the results of approximation by eqn. (4) shows that in case of piecewise-linear dependence (20) they are in rather good qualitative and quantitative agreement. a deficiency of this approach is the necessity of calculating four material parameters, as well as the intervals for determining piecewise-linear correction coefficients. therefore, it is advisable to use formula (21) in order make rapid estimation for the designed ice wall thickness. in this case, it is necessary to determine only one material parameter, whereas formula (20) can be used when there is a need for more accurate calculation. comparative analysis of vyalov’s formulas for ultimate displacements and stresses fig. 6 presents the calculation results for ice wall thickness obtained for sand, chalk and clay by eqns. (1)-(2) recommended for ultimate displacement calculations and by eqns. (3)-(4) for strength calculations. apart from these formulas, this figure also shows the calculation results obtained by eqn. (20) and by the equation which is a modification of relation (1) [12]:                         1 111 1 ( ) 1 2 , mm m p m p ha e g p a t t a (22) where the material function g(p) is dependent on the value of the load acting on the ice wall and determined by applying the numerical simulation results. the function for the materials under study was taken from [12]. (a) (b) (c) figure 6: dependence of the designed ice wall thickness on the load for sand (a), chalk (b), clay (c): curve 1 – eqn. (1), curve 2 – eqn. (2), curve 3 – eqn. (3), curve 4 – eqn. (1), curve 5 – eqn. (20), curve 6 – eqn. (22). for sand (fig.6a), the maximum discrepancy between eqns. (4) and (20) is 1.49m, which corresponds to the load of 889 мpа. analogous thicknesses are determined using eqns. (3) and (22) for the load less than 4.889 мpа. besides, for the load not exceeding 3.222 мpа, the thickness calculated by eqn. (2) is close to the value obtained by eqns. (3) and (22). eqn. (2) a. kostina et alii, frattura ed integrità strutturale, 53 (2020) 394-405; doi: 10.3221/igf-esis.53.30 404 cannot be used in this case to calculate the ice wall thickness at a depth of 500 m because the base of power function becomes negative. for chalk fig.6(b), there are two similar data blocks. the first group includes eqns. (4) and (20), and another – eqns. (2), (3) and (22). eqn. (1) yields the maximum ice wall thickness reserve at all loads examined here. the maximum difference between eqns. (4) and (20) is equal to 0.242 m and is achieved at the load of 1.881 мpа. the ice wall thicknesses which enter the second group have similar values up to the load of 1.881 мpа. at loads more than 2.25 мpa, eqn. (2) gives values that exceed those calculated by eqns. (3) and (22). analogous results are obtained for clay (fig. 6c). two groups of equations provide almost similar values for ice wall thickness: (4), (20) and (2), (22). the maximum difference between eqns. (4) and (20) corresponds to the load of 0.678 мpа and is equal to 0.35m. eqns. (2) and (22) yield close thickness values at the load less than 2.301 mpa , and eqn. (2) cannot be used to calculate the ice wall thickness at the load exceeding this value. the maximum margin of safety is obtained using eqn. (3). on the basis of the obtained results, some conclusions were drawn regarding the applicability of the analyzed relations to ice wall thickness calculations. to perform strength calculations, it is desirable that eqn. (20) would be used for all soils under study because eqn. (3) yields excess thickness, and eqn. (4) is obtained on the assumption of the ultimate state of the ice wall, and therefore it should be used with some prescribed margin of safety. in ultimate displacement calculations for chalk, it is advisable to use eqn. (22) because eqn. (1) yields the excess thickness for all loads under consideration. at loads less than 2.25 mpa (this value corresponds to a depth of 300 m), eqn. (2) can be applied. in ultimate displacements calculations for clay up to the load of 2.301 мpа (this value corresponds to a depth of 300m), relations (2) and (22) can be used. in ice wall thickness calculations for frozen sand at the load no less than 4.889 мpа (this value corresponds to a depth of 300 m), it is desirable that relation (22) is used. at loads less than 3.222 mpa (this value corresponds to a depth of 200 m), eqn. (2) can also be applied. at high loads that exceed 4.899 for sand and 2.301 mpa for clay (these values correspond to a depth of 300 m), the ice wall thicknesses calculated by eqns. (1)-(4), (20) and (22) exhibit great scatter, which generates a need for further investigations aimed at modifying the existing constitutive equations. this necessity stems from the fact that at great loads the hydrostatic pressure can have a significant effect on the stress-strain state of rocks. conclusion e have performed a theoretical study to evaluate the applicability of analytical vyalov’s formulas to the calculation of the ultimate stress state of an ice-rock cylinder of unlimited and finite heights. the numerical results showed that the design values of the ice wall thickness obtained by the formula for a cylinder of limited height have a margin of safety for all considered rocks (sand, chalk, and clay). this is associated with the fact that the internal friction is ignored, which increases the strength. the application of the coulomb–mohr criterion made it possible to model the deformation of the ice-rock cylinder. a comparison of the thicknesses obtained numerically with the results found by eqn. (3) showed that the greatest thickness reserve was observed for clay and sand. using the results of numerical simulation of the stress-strain state of the ice wall, we suggested two modifications of eqn. (4). the first variant involves the use of the piecewise-linear relation and enables describing the simulation results both qualitatively and quantitatively. the second is a simple variant and it can be used for making rapid estimation for the designed ice-wall thickness. a comprehensive comparative analysis of six formulas (four vyalov’s formulas and two modifications) has revealed that in strength calculations it is advisable to use eqn. (20) for all soils examined here because eqn. (3) causes the excess margin of thickness to occur, and eqn. (4) must be used with some prescribed margin of safety. in ultimate displacement calculations for chalk, eqn. (22) or (2) should be used at the load not exceeding 2.25 mpa, which corresponds to the soil depth of 300 m. in creep calculations for clay at the load of 2.301 mpa, which corresponds to the soil depth of 300 m, relations (2) and (22) can be used. in order to calculate the ice-wall made of frozen sand at the load less than 4.889 mpa (up to the soil depth of 300 m), it is advisable to use relation (22) and relation (2) at the load less than 3.222 mpa (up to the soil depth of 200 m). at high loads that exceed 4.899 mpa for sand and 2.301 mpa for clay there is a need for further investigations so that the existing constitutive equations describing the stress-strain state of rocks can be modified. w a. kostina et alii, frattura ed integrità strutturale, 53 (2020) 394-405; doi: 10.3221/igf-esis.53.30 405 acknowledgments his research was supported by 17-11-01204 project (russian science foundation). references [1] levin, l. yu, semin, m.a. and plekhov, o.a. (2018). comparative analysis of existing methods for calculation frozen wall thickness for mine shafts under construction, bulletin of pnrpu. construction and architecture, 9(4), pp. 93-103. doi: 10.15593/2223-9826/2018.4.09. [2] lai, y., xu, x., dong, y. and li, s. (2013). present situation and prospect of mechanical research on frozen soils in china, cold reg. sci. technol., 87, pp. 6-18. doi: 10.1016/j.coldregions.2012.12.001 [3] liu, x., liu, e., zhang, d., zhang, g. and song, b. (2019). study on strength criterion for frozen soil. cold reg. sci. technol.,161, pp. 1-20. doi: 10.1016/j.coldregions.2019.02.009. [4] nishimura, s., gens, a., olivella, s. and jardine, r. j. (2009). thm-coupled finite element analysis of frozen soil: formulation and application, geotechnique, 59(3), p. 159. doi: 10.1680/geot.2009.59.3.159. [5] ghoreishian, a. s. a., grimstad, g., kadivar, m. and nordal, s. (2016). constitutive model for rate-independent behavior of saturated frozen soils. can. geotech. j., 53(10), pp. 1646-1657. doi: 10.1139/cgj-2015-0467. [6] na, s. h. and sun, w. c. (2017). computational thermo-hydro-mechanics for multiphase freezing and thawing porous media in the finite deformation range. comput. methods. appl. mech. eng.,318, pp. 667-700. doi: 10.1016/j.cma.2017.01.028. [7] liu, e., lai, y., wong, h. and feng, j. (2018). an elastoplastic model for saturated freezing soils based on thermoporomechanics. int. j. plasticity,107, pp. 246-285. doi: 10.1016/j.ijplas.2018.04.007. [8] alonso, e. e., gens, a. and josa, a. (1990). a constitutive model for partially saturated soils, géotechnique, 40(3), pp. 405-430. doi: 10.1680/geot.1990.40.3.405. [9] liu, e. l. and xing h. l. (2009). a double hardening thermo-mechanical constitutive model for overconsolidated clays. acta geotech., 4(1), pp. 1-6. doi: 10.1007/s11440-008-0053-4. [10] vyalov, s.s., zaretsky, y.k., gorodetsky, s.e. (1979). stability of mine workings in frozen soils, engineering geology, 13 (1-4), pp. 339-351. doi: 10.1016/0013-7952(79)90041-3. [11] vyalov, s.s. (1986). rheological fundamentals of soil mechanics. elsevier, amsterdam, the netherlands [12] zhelnin, m., kostina, a., plekhov, o., panteleev, i. and levin, l. 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can be opened with acrobat and adobe reader 5.0 and later.) >> /namespace [ (adobe) (common) (1.0) ] /othernamespaces [ << /asreaderspreads false /cropimagestoframes true /errorcontrol /warnandcontinue /flattenerignorespreadoverrides false /includeguidesgrids false /includenonprinting false /includeslug false /namespace [ (adobe) (indesign) (4.0) ] /omitplacedbitmaps false /omitplacedeps false /omitplacedpdf false /simulateoverprint /legacy >> << /addbleedmarks false /addcolorbars false /addcropmarks false /addpageinfo false /addregmarks false /convertcolors /converttocmyk /destinationprofilename () /destinationprofileselector /documentcmyk /downsample16bitimages true /flattenerpreset << /presetselector /mediumresolution >> /formelements false /generatestructure false /includebookmarks false /includehyperlinks false /includeinteractive false /includelayers false /includeprofiles false /multimediahandling /useobjectsettings /namespace [ (adobe) (creativesuite) (2.0) ] /pdfxoutputintentprofileselector /documentcmyk /preserveediting true /untaggedcmykhandling /leaveuntagged /untaggedrgbhandling /usedocumentprofile /usedocumentbleed false >> ] >> setdistillerparams << /hwresolution [2400 2400] /pagesize [612.000 792.000] >> setpagedevice microsoft word numero 17 articolo 1 m. paggi et alii, frattura ed integrità strutturale, 17 (2011) 5-14; doi: 10.3221/igf-esis.17.01 5 numerical modelling of intergranular fracture in polycrystalline materials and grain size effects m. paggi department of structural and geotechnical engineering, politecnico di torino, torino (italy) marco.paggi@polito.it p. wriggers institut für kontinuumsmechanik, leibniz universität hannover, hannover (germany) wriggers@ikm.uni-hannover.de abstract. in this paper, the phenomenon of intergranular fracture in polycrystalline materials is investigated using a nonlinear fracture mechanics approach. the nonlocal cohesive zone model (czm) for finite thickness interfaces recently proposed by the present authors is used to describe the phenomenon of grain boundary separation. from the modelling point of view, considering the dependency of the grain boundary thickness on the grain size observed in polycrystals, a distribution of interface thicknesses is obtained. since the shape and the parameters of the nonlocal czm depend on the interface thickness, a distribution of interface fracture energies is obtained as a consequence of the randomness of the material microstructure. using these data, fracture mechanics simulations are performed and the homogenized stress-strain curves of 2d representative volume elements (rves) are computed. failure is the result of a diffuse microcrack pattern leading to a main macroscopic crack after coalescence, in good agreement with the experimental observation. finally, testing microstructures characterized by different average grain sizes, the computed peak stresses are found to be dependent on the grain size, in agreement with the trend expected according to the hall-petch law. sommario. in questo articolo, il fenomeno della frattura intergranulare nei material policristallini è studiato mediante un approccio di meccanica della frattura non lineare. il modello non locale di frattura coesiva per interfacce con spessore finito recentemente proposto dai presenti autori è impiegato per descrivere il fenomeno di separazione ai bordi di grano. da un punto di vista modellistico, considerando la dipendenza dello spessore dei bordi di grano dalla dimensione del grano stesso, si è ottenuta una distribuzione delle proprietà meccaniche delle interfacce. essendo la forma ed i parametri del modello non locale della frattura coesiva dipendenti dallo spessore dell'interfaccia, si ottiene una distribuzione di energie di frattura come conseguenza della variabilità statistica della microstruttura del materiale. usando tali dati si conducono simulazioni di meccanica della frattura su elementi di volumi rappresentativi (rve) in 2d e si determinano le rispettive curve di tensionedeformazione. la frattura è il risultato di un insieme di microfessure diffuse che danno luogo alla propagazione di una fessura macroscopica principale, in ottimo accordo con quanto osservato sperimentalmente. infine, testando microstrutture dotate di diversi diametri medi dei grani, si osserva come le tensioni di picco siano dipendenti dal diametro del grano, secondo un trend in accordo con la legge di hall e petch. keywords. nonlocal cohesive zone model; nonlinear and stochastic fracture mechanics; finite thickness interfaces; finite elements; polycrystalline materials. http://dx.medra.org/10.3221/igf-esis.17.01&auth=true http://www.gruppofrattura.it m. paggi et alii, frattura ed integrità strutturale, 17 (2011) 5-14; doi: 10.3221/igf-esis.17.01 6 introduction olycrystalline materials present heterogeneous microstructures where polyhedral grains are separated by interfaces. a typical scanning electron microscope (sem) image of these microstructures is shown in fig. 1(a). the different colours of the crystals indicate their different crystallographic orientations. the mechanical behaviour is strongly affected by the grain boundaries which govern the strength, the toughness and the ductility of the material. these properties are of paramount importance in forming processes and for the design of super-hard materials. as a general trend, the smaller the grain, the higher the material strength and the hardness. interfaces are also important in conduction processes. in this case, however, they should be viewed as defects and the material conductivity of single crystalline materials is usually much higher than that of their polycrystalline counterparts. fracture in polycrystalline materials can be schematically classified according to two different types: intergranular and transgranular. the former mode of fracture corresponds to the decohesion of the grains along the interfaces. correspondingly, the material response is quite brittle. the latter is characterized by a propagation of cracks into the grains, with the occurrence of high plastic deformations leading to a much more ductile response. in spite of the fact that failure is often the result of a combination of these two modes of fracture, it is instructive to investigate each mode separately and understand the underlying mechanisms. in the present study, attention is paid to intergranular fracture, which is typically observed in brittle polycrystals. during a tensile test, microcracks develop at the grain boundaries (see fig. 1(b) taken from [1]). at a certain deformation level, the microcracks coalescence and lead to the final failure with the propagation of a single main crack. correspondingly, the stress-strain curve reaches a maximum and a sudden loss of load carrying capacity takes place. in order to investigate the effect of interfaces on the mechanical response of polycrystalline materials, a nonlinear fracture mechanics model is herein proposed. intergranular fracture is depicted as a phenomenon of progressive separation at the grain boundaries governed by a nonlinear traction-separation law, or cohesive zone model (czm). in this context, the finite thickness properties of interfaces are suitably taken into account by using the nonlocal czm recently proposed in [2, 3] and briefly summarized in the next section. virtual tensile tests of representative volume elements (rves) of material microstructures are carried out in order to simulate the phenomena of crack nucleation, coalescence and strain localization. finally, grain size effects are investigated by changing the average grain size of the polycrystalline material and computing the peak stress of the simulated stress-strain curves. as it will be shown, numerical results are in agreement with the trend expected by the hall-petch law. this result confirms that fracture mechanics of interfaces is one of the most important factors governing the strength of polycrystalline materials. (a) sem image of the microstructure (b) microcracks observed during a tensile test figure 1: sem images of brittle polycrystalline materials showing microcracks (courtesy of dr. ing. m. schaper [1]). a nonlocal cohesive zone model for interface fracture olycrystals are an important example of a material with finite thickness interfaces. in particular, examining the materials science literature [4], a power-law dependency of the interface thickness on the grain diameter has been noticed. figure 2 shows the relation proposed in [4], where the grain diameter is computed as the mean diameter p p http://dx.medra.org/10.3221/igf-esis.17.01&auth=true http://www.gruppofrattura.it m. paggi et alii, frattura ed integrità strutturale, 17 (2011) 5-14; doi: 10.3221/igf-esis.17.01 7 of two grains sharing the same interface. a criterion of equivalence of cross-sectional areas is used to compute the diameter d of a polyhedral grain. although the interface thickness l2 is approximately one order of magnitude smaller than the grain diameter, as shown in fig. 2(b), its simplification as a zero-thickness region, also called boundary layer, is not always possible. numerical simulations considering an elasto-plastic behaviour of the interfaces suggest that the ductility of the material is strongly affected by these finite thickness regions [4]. figure 2: dependency of the interface thickness on the grain diameter according to the relation proposed in [4]. in order to simplify the real material microstructure by considering a finite element discretization with zero-thickness interfaces, a suitable interface constitutive law has to be used (see [5-16] for a wide range of problems modelled using czms). here, we consider the nonlocal czm recently proposed in [2] for finite thickness interfaces. the tractionseparation relations that describe the nonlinear response of the interface are the following: 1 t e e gd d      (1a) 1 n e e gd d      (1b) where  and  are the tangential and normal cohesive tractions. the parameters tg and ng denote, respectively, the tangential and normal anelastic displacements evaluated at the boundaries of the finite thickness interface. finally, e and e are the threshold values of the cohesive tractions for the onset of damage that correspond to the global tangential and normal displacements e and e of the interface region. the damage variable d (0 1)d  is computed as follows: / 22 2 c c w u d w u                   (2) where cw and cu are material parameters analogous to the critical opening and sliding displacements ncl and tcl used in standard czms [9] and  is a free parameter. the displacements u and w are given by: 2 2 t e l u g g     (3a) 2 2 n e l w g e     (3b) where 2l is the thickness of the interface, 2e and 2g are the initially undamaged normal and tangential elastic moduli of the interface material. changing the parameter  , different shapes of the czm can be obtained, as shown in fig. 3 for a d l2 d = grain diameter l2 = interface thickness http://dx.medra.org/10.3221/igf-esis.17.01&auth=true http://www.gruppofrattura.it m. paggi et alii, frattura ed integrità strutturale, 17 (2011) 5-14; doi: 10.3221/igf-esis.17.01 8 mode i problem. similar considerations apply for mode mixity. for more details about the calibration of the model parameters using molecular dynamics simulations, the readers are referred to [2]. figure 3: shape of the mode i nonlocal czm as a function of  . this nonlocal czm has been implemented in the fe code feap [17] using zero-thickness interface elements, see [3] for more details about the computational aspects. the anelastic relative displacements ng and tg are the main input of the element subroutine and are obtained as the difference between the normal and tangential displacements of the nodes of the finite elements of the continuum opposite to the shared interface. the residual vector and the tangent stiffness matrix of the interface element are computed by linearizing the corresponding weak form using a newton-raphson algorithm. due to the implicit form of the czm in eq. (1), since the damage variable d on the r.h.s. of eq. (1) is a function of the unknown cohesive tractions through eqs. (2) and (3), a nested newton-raphson iterative scheme is used in to compute the cohesive tractions. a quadratic convergence is achieved, as shown in fig. 4 for a mode i problem. figure 4: quadratic convergence of the newton-raphson method used for the computation of the cohesive tractions, for three different values of /n cg w and for / 0t cg u  . applications to polycrystalline materials he proposed nonlocal czm for finite thickness interfaces is applied to the polycrystalline material microstructure of copper analyzed in [1] and depicted in fig. 5. from this input geometry, the grain size distribution, shown in fig. 6(a), can be computed. the average grain diameter is 1 μm and its r.m.s. deviation is 0.26 μm. the interface thickness distribution is also computed and shown in fig. 6(b). t http://dx.medra.org/10.3221/igf-esis.17.01&auth=true http://www.gruppofrattura.it m. paggi et alii, frattura ed integrità strutturale, 17 (2011) 5-14; doi: 10.3221/igf-esis.17.01 9 figure 5: material microstructure of polycrystalline copper numerically analyzed in this work. (a) (b) figure 6: (a) grain size distribution and (b) interface thickness distribution of the microstructure shown in fig. 5. according to the thickness-dependent nonlocal czm summarized in the previous section, the distribution of the mode i interface fracture energy, represented by the area below the mode i traction-separation curve, is obtained and shown in fig. 7. it is interesting to note that the distribution of mode i interface fracture energies for the present case (dots in fig. 7) is better approximated by a gaussian than by a weibull distribution (see the probability plots in fig. 7(a) and 7(b), where the gaussian and weibull distributions computed from the sample population are depicted with dashed-dotted lines). this is in general agreement with ductility of the material microstructure herein examined. incidentally, we note that the weibull modulus for these data is equal to 7.7, which is in agreement with the typical range of variation between 5 and 10 found in polycrystals [16]. this can be considered as an indirect experimental confirmation of the fact that the interface thickness distribution is responsible for the interface fracture energy distribution. (a) gaussian probability plot (b) weibull probability plot figure 7: mode i interface fracture energy distribution and comparison with the gaussian and the weibull distributions. 1 μmdm http://dx.medra.org/10.3221/igf-esis.17.01&auth=true http://www.gruppofrattura.it m. paggi et alii, frattura ed integrità strutturale, 17 (2011) 5-14; doi: 10.3221/igf-esis.17.01 10 the parameters of the average mode i traction-separation curve, corresponding to an average value of l2=0.15 μm, were selected in order to obtain an average mode i fracture energy of 0.18 n/mm and a peak stress of 500 n/mm2, as suggested in [6] for polycrystalline interfaces (see the corresponding curve in fig. 8 with solid line). more specifically, 0.53c c   μm, 500e c   n/mm2, 3 2 110 10e   n/mm2 were set for the grains, and the parameter α was selected as 0.0035. alternatively, the parameters of the nonlocal czm can be tuned to fit md simulations, as illustrated in [2]. interestingly, the shape of the nonlocal czm can be matched with a good approximation with the standard czm proposed by tvergaard [9]. it is superimposed to fig. 8 with dashed line and has the same mode i fracture energy as our model. figure 8: shape of the nonlocal czm (average curve) used for the fracture simulations and that of the tvergaard [9] model with the same average fracture energy. to quantify the effect of using the nonlocal czm with random properties instead of the tvergaard czm with the same properties for all the interfaces, we consider an elastic modulus of the grains equal to 31 110 10e   n/mm2 and a poisson ratio equal to ν=0.3 for all the grains. the material microstructure shown in fig. 5 is first simplified by augmenting the size of the grains, according to the procedure outlined in [2]. after this preliminary operation, each grain is meshed with constant strain triangular elements according to a delauney triangulation. then, zero-thickness interface elements governed by the thickness-dependent nonlocal czm are placed along the grain boundaries. the size of the finite elements used for discretizing the continuum has been chosen in order to be one order of magnitude smaller than the process zone size, estimated according to the method suggested in [16]. the dirichlet boundary conditions imposed on the model are selected to reproduce a tensile test, i.e., the nodes pertaining to the left vertical boundary are restrained to the horizontal displacements, whereas horizontal displacement are imposed on the nodes of the vertical boundary on the right. a newton-raphson solution scheme is adopted to solve the nonlinear boundary value problem at each step. the tolerance for the internal newton-raphson loop used to compute the residual and the tangent stiffness matrix of the interface elements is chosen as 1×10−12. in fig. 9, the evolution of the crack pattern using the tvergaard czm with the same parameters for all the interfaces (pictures at the top) is compared with that obtained using the nonlocal czm and random fracture properties (pictures at the bottom), for three different deformation levels, =0.100, 0.115 and 0.124. the last deformation level corresponds to the final failure of the samples. dashed lines correspond to fictitious cracks, i.e., microcracks where cohesive tractions are still acting. solid lines correspond to the interfaces with d=1, i.e., real stress-free microcracks. the evolution of cohesive microcracks is widely distributed in both cases. at a certain point, when the microcracks coalescence into a single rough macrocrack, a phenomenon of strain localization takes place. the cohesive microcracks far from the main crack experience a stress relief, whereas the deformation accumulates on the main crack. this is well evidenced by the fact that microcracks (dashed segments) almost disappear at the deformation level of 0.124. the final crack pattern in case of uniform interface fracture properties appears to be characterized by a single main crack. on the contrary, using the nonlocal czm with thickness dependent fracture properties, we obtain a separation of some grains and a more diffuse crack pattern, which is often found in experiments. the homogenized stress-strain responses of the composite cell are compared in fig. 10. the homogenized stress is computed by summing the horizontal reactions of the constrained nodes on the vertical boundary on the right, and dividing it for its length. the use of the tvergaard model (local czm with uniform interface fracture properties) leads to a higher peak stress than using the proposed nonlocal czm. this is mainly due to the prevalence of subvertical microcracks http://dx.medra.org/10.3221/igf-esis.17.01&auth=true http://www.gruppofrattura.it m. paggi et alii, frattura ed integrità strutturale, 17 (2011) 5-14; doi: 10.3221/igf-esis.17.01 11 subjected to pure mode i. in both cases, the final failure of the sample is characterized by a sudden stress drop in the stress-strain diagram, probably due to a snap-back instability, typical of cohesive solids. figure 9: crack patterns (cohesive microcracks with dashed line and stress-free cracks with solid line) for different strain levels. figure 10: homogenized stress-strain curve. the nonlocal czm response (with stochastic distribution of interface properties) is compared with the prediction of the local czm by tvergaard with the same fracture energy for all the interfaces. the proposed nonlocal czm is also able to capture the grain-size effects on the tensile strength. in polycrystalline materials, the tensile strength significantly depends on the grain size. an empirical correlation was proposed by hall [18] and petch [19], suggesting that the tensile strength is in general proportional to the inverse of the square root of the grain size at the microscale. to assess the capability of the proposed nonlocal czm to capture this effect, we consider different material microstructures, replicas of that in fig. 5, obtained by rescaling the diameters of the grains. since the interface thicknesses depend on the grain size according to the power-law relation displayed in fig. 2(b), the rescaled geometries are not selfsimilar. as a consequence, the distribution of the interface fracture parameters will also depend on the grain size. the mode i fracture energy distributions corresponding to microstructures with average grain sizes of 0.1μm, 1μm and 10μm are shown in fig. 11. the shapes of the czm for the three cases are similar to that shown in fig. 8. in particular, the maximum cohesive stress of the curves changes, whereas the critical separation remains the same. the average fracture =0.100 =0.124 =0.115 local czm nonlocal czm cohesive microcracks — stress-free cracks http://dx.medra.org/10.3221/igf-esis.17.01&auth=true http://www.gruppofrattura.it m. paggi et alii, frattura ed integrità strutturale, 17 (2011) 5-14; doi: 10.3221/igf-esis.17.01 12 energy for the three cases is equal to 0.8974 n/mm, 0.1794 n/mm and 0.0361 n/mm, for dm=0.1μm, 1μm and 10μm, respectively. the r.m.s values are equal to 0.122 n/mm, 0.024 n/mm and 0.005 n/mm, respectively. figure 11: distribution of interface fracture energies for three different average grain sizes. the peak stress of the stress-strain curves, obtained from tensile test simulations on the different cases, considering also dm=0.5μm, 2μm and 5μm in addition to 0.1μm, 1μm and 10μm, are shown in fig. 12 vs. the grain diameter. the fe simulations lead to a peak stress which is a decreasing function of the grain size, in general agreement with the hall-petch relation that is superimposed to the same data in fig. 12 by the dashed line. therefore, the nonlocal czm is fully able to reproduce the scaling of the tensile strength through the variation of fracture mechanics parameters connected to the variation of the interface thicknesses with the grain size. these numerical results imply that thicker interfaces are weaker than the thinner ones. figure 12: numerically predicted vs. experimentally obtained peak stress vs. average grain size. conclusions n this paper, intergranular fracture in polycrystalline materials has been numerically investigated using finite elements. the main novelty with respect to previous contributions based on czms is represented by the use of a more sophisticated czm whose properties (shape, fracture energy, peak stress) depend on the finite thickness of the interface. this is particularly suitable for polycrystalline materials in the micro-scale range, where the grain boundary thickness is not negligible and has an important role. the proposed nonlocal czm is based on continuum damage i dm=10 m dm=1 m dm=0.1 m hall-petch law dm [m] fe results http://dx.medra.org/10.3221/igf-esis.17.01&auth=true http://www.gruppofrattura.it m. paggi et alii, frattura ed integrità strutturale, 17 (2011) 5-14; doi: 10.3221/igf-esis.17.01 13 mechanics through the introduction of a damage variable that reduces the elastic modulus of the interface material. this approach allows us to perform an upscaling of the complex nonlinear mechanisms occurring in the interface region. the parameters entering the damage formulation can be tuned according to simple axial and shear tests to be performed on rves of the interface microstructure. this strategy has the great advantage of avoiding computationally expensive multiscale simulations based on the fe2 method which requires, for each gauss point, a micromechanical computation of the response of a lower scale rve with a complete description of its constitutive nonlinearities [20-22]. possible applications to fiber-reinforced interfaces and polymeric interfaces are therefore envisaged, with a tuning of the damage evolution law depending on the actual forms of nonlinearities present in those materials. finally, regarding the grain size effects on the tensile strength of polycrystals, it has to be remarked that an inversion of the trend suggested by hall and petch has been observed at the nanoscale. although a different description of the material has probably to be invoked, using molecular dynamics simulations instead of continuum mechanics, our proposed model may provide an insight into this debated problem. the results obtained in the present study show that the thinner the interface, the higher its fracture energy. as a result, the tensile strength of the material increases by refining the material microstructure. this suggests that an inversion of the hall-petch law may occur in case of thicker interfaces at the nanoscale. experimental results seem to confirm this predicted trend. in fact, data in [23] show that the grain boundary thickness tends to vanish at the nanoscale. however, the percentage of atoms at the grain vertices, the so called triple junctions, drastically increases. as a result, the volumetric content of the all interface atoms (the sum of the atoms belonging to triple junctions and those belonging to grain boundaries), is much higher than that suggested by the scaling law holding at the microscale and shown in fig. 2. acknowledgements he support of ait, miur and daad to the vigoni 2011-2012 project "3d modelling of fracture in polycrystalline materials" is gratefully acknowledged. mp would also like to thank the alexander von humboldt foundation for supporting his research fellowship at the institut für kontinuumsmechanik, leibniz universität hannover (hannover, germany) from february 1, 2010, to january 31, 2011. references [1] p. kustra, a. milenin, m. schaper, a. gridin, computer methods in materials science, 9 (2009) 207. [2] m. paggi, p. wriggers, computational materials science, 50 (2011) 1625. [3] m. paggi, p. wriggers, computational materials science, 50 (2011) 1634. [4] d.j. benson, h.-h. fu, m.a. meyers, materials science and engineering a, 319–321 (2001) 854. [5] yan-qing wu, hui-ji shi, ke-shi zhang, hsien-yang yeh, international journal of solids and structures, 43 (2006) 4546. [6] t. luther, c. könke, engineering fracture mechanics, 76 (2009) 2332. [7] p.d. zavattieri, p.v. raghuram, h.d. espinosa, journal of the mechanics and physics of solids, 49 (2001) 27. [8] g. beer, international journal for numerical methods in engineering, 21 (1985) 585. [9] v. tvergaard, material science and engineering a, 107 (1990) 23. [10] n. point, e. sacco, international journal of fracture, 79 (1996) 225. [11] m. ortiz, a. pandolfi, international journal for numerical methods in engineering, 44 (1999) 1267. [12] j. segurado, j. llorca, international journal of solids and structures, 41 (2005) 2977. [13] s. li, m.d. thouless, a.m. waas, j.a. schroeder, p.d. zavattieri, composites science and technology, 65 (2005) 281. [14] c. leppin, p. wriggers, computers & structures, 61 (1996) 1169. [15] j.c.j. schellekens, r. de borst, international journal for numerical methods in engineering, 36 (1993) 43. [16] h.d. espinosa, p.d. zavattieri, mechanics of materials, 35 (2003) 365. [17] o.c. zienkiewicz, r.l. taylor, the finite element method, 5th ed., butterworth-heinemann, oxford and boston, (2000). [18] e.o. hall, proceedings of the physical society of london b, 64 (1951) 747. [19] n.j. petch, journal of the iron steel institute of london, 173 (1953) 25. [20] c.b. hirschberger, s. ricker, p. steinmann, n. sukumar, engineering fracture mechanics, 76 (2009) 793. t http://dx.medra.org/10.3221/igf-esis.17.01&auth=true http://www.gruppofrattura.it m. paggi et alii, frattura ed integrità strutturale, 17 (2011) 5-14; doi: 10.3221/igf-esis.17.01 14 [21] k. matous, m.g. kulkarni, p.h. geubelle, journal of the mechanics and physics of solids, 56 (2008) 1511. [22] m.g. kulkarni, k. matous, p.h. geubelle, international journal for numerical methods in engineering, 84 (2010) 916. [23] y. zhou, u. erb, k.t. aust, g. palumbo, scripta materialia, 48 (2003) 825. http://dx.medra.org/10.3221/igf-esis.17.01&auth=true http://www.gruppofrattura.it microsoft word numero_38_art_44 i. n. shardakov et alii, frattura ed integrità strutturale, 38 (2016) 339-350; doi: 10.3221/igf-esis.38.44 339 process of cracking in reinforced concrete beams (simulation and experiment) i. n. shardakov, a. p. shestakov, i.o. glot institute of continuous media mechanics of the ural branch of russian academy of science (icmm ub ras), korolev str., 1, perm, 614013, russia. shardakov@icmm.ru, shap@icmm.ru, glot@icmm.ru a.a. bykov perm national research polytechnic university, komsomolsky ave., 29, perm, 614990, russia violentharpy@ya.ru abstract. the paper presents the results of experimental and theoretical investigations of the mechanisms of crack formation in reinforced concrete beams subjected to quasi-static bending. the boundary-value problem has been formulated in the framework of brittle fracture mechanics and solved using the finite-element method. numerical simulation of the vibrations of an uncracked beam and a beam with cracks of different size serves to determine the pattern of changes in the spectrum of eigenfrequencies observed during crack evolution. a series of sequential quasi-static 4-point bend tests leading to the formation of cracks in a reinforced concrete beam were performed. at each loading step, the beam was subjected to an impulse load to induce vibrations. two stages of cracking were detected. during the first stage the nonconservative process of deformation begins to develope, but has not visible signs. the second stage is an active cracking, which is marked by a sharp change in eingenfrequencies. the boundary of a transition from one stage to another is well registered. the vibration behavior was examined for the ordinary concrete beams and the beams strengthened with a carbon-fiber polymer. the obtained results show that the vibrodiagnostic approach is an effective tool for monitoring crack formation and assessing the quality of measures aimed at strengthening concrete structures. keywords. reinforced concrete; crack nucleation; vibrodiagnostics; experiment; mathematical modeling. citation: shardakov, i. n., bykov, a.a., shestakov, a. p., glot, i.o., process of cracking in reinforced concrete beams (simulation and experiment), frattura ed integrità strutturale, 38 (2016) 339-350. received: 02.06.2016 accepted: 30.08.2016 published: 01.10.2016 copyright: © 2016 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. introduction einforced concrete structures have found wide application in the construction industry. like other construction materials, reinforced concrete has limited strength characteristics. when these limiting values are exceeded, the structure may fail. fracture of concrete usually occurs as the process of nucleation and growth of cracks. initially r i. n. shardakov et alii, frattura ed integrità strutturale, 38 (2016) 339-350; doi: 10.3221/igf-esis.38.44 340 the crack formation does not lead to complete loss of the carrying capacity of the structure, but it can be considered as a fracture precursor. knowledge of the crack nucleation process is important to ensure early prediction of emergency situations and prompt use of techniques to restore damaged reinforced concrete structures. nowadays, there are many ways to monitor cracks in concrete structures. common visual observation methods are helpful in the evaluation of big visible damages, while the hidden or inaccessible defects cannot be identified. the local methods of inspection are actively used as well. they involve recording various physical quantities, such as ultrasonic waves [1], eddy currents [2], temperature fields [3], acoustic emission [4], x-ray, magnetic particles [5], and so on. a survey of nondestructive testing methods applied to reinforced concrete structures can be found in [6]. these methods also have some limitations: one should know a priori the region with defects or use many transducers; the region where a defect may appear should be accessible for examination. the location of a defect may remain unexamined because only a small part of the structure can be examined with these methods. most local methods are rather expensive, and it takes much time to investigate the structure using these techniques. the methods for crack detection and pattern recognition based on image processing are described in [7]. another direction in flaw detection technology includes global methods aimed at discovering damage via the assessment of the mechanical behavior of the entire structure. the main advantage of such methods is that they do not require a great number of transducers to be located in close proximity to defects. most commonly used and promising global methods of nondestructive testing are vibration approaches [8]. they are based on the fact that the variations of physical properties (mass, rigidity, damping) of an object cause the changes in modal parameters, which qualitatively and quantitatively characterize natural vibrations. a survey of vibration approaches is provided in [9-11], and their applications to reinforced concrete structures are described in [12]. vibration nondestructive testing methods employ various modal parameters. the analysis of eigenfrequencies allowing early damage detection is given in [13]. damage localization problems have been solved by using a criterion based on the comparison of two mode shapes in damaged and undamaged states [14]. information about the curvature of eigenmode shapes serves as an indicator of defects in beam structures [15]. data on eigenmode shape deformation energy have been used for damage localization in [16]. a method for estimating the state of bridges, which is based on the information regarding a compliance matrix, is described in [17]. in connection with the vibration methods of study of quasi-brittle materials destruction the works [18-20] should be noted were the methods of wavelet analysis are successfully used to identify the fracture process. in the present paper, we propose a new variant of the vibration method to detect the crack location and crack opening degree by analyzing the changes in the eigenfrequencies spectrum associated with the occurrence of cracks. the method allows us to perform monitoring the strain state of structures, where the region of most probable fracture is known, but free access to it is absent. mathematical model of deformation processes in reinforced structure he stress-strain state of reinforced concrete beams under quasi-static four-point bending is studied. the beam is reinforced by two plane steel frameworks joined together by vertical elements. the structural scheme and characteristic sizes of the beam are shown in fig. 1 (a). at a certain stage of the loading, cracking starts in the beam. works [21, 22] focus on the mathematical modeling of this process and comparing the simulation results and experimental data. the proposed approach is based on the analysis of vibrations of a reinforced concrete beam that occur in response to impact loads applied to a certain part of the beam. comparison of the vibration response of a solid beam and a beam having different-size cracks makes it possible:  to evaluate the sensitivity of spectral properties of a reinforced concrete beam to crack nucleation and growth;  to find pulse load, causing vibrations with eigenfrequencies most sensitive to cracking and to define load parameters;  to identify patterns of change in eigenfrequencies associated with the emergence and growth of cracks. a calculation scheme for the problem of vibrations of a reinforced beam having a crack is given in fig. 1 (b). a crack that occurs in concrete is represented as a volume v2 occupied by the material exhibiting practically zero mechanical properties. this approach is valid for cracks called opening mode cracks. it is precisely these cracks that appear in the beam tested under four-point bending conditions used in our experiment. as regards other types of cracks, having no gap between the edges of the crack, it is necessary to consider the interaction between the opposite surfaces of the crack, taking into account the dissipation of mechanical energy. our approach can be adapted for these types of cracks. t i. n. shardakov et alii, frattura ed integrità strutturale, 38 (2016) 339-350; doi: 10.3221/igf-esis.38.44 341 figure 1: four-point bending of reinforced concrete beam (a) and the calculation scheme of the beam with a crack (b). according to fig. 1, the developed mathematical model describes all structural elements of the beam: concrete (1), steel reinforcement (2), and supporting elements (3). the problem is formulated by using the virtual displacement principle [23]. b o a b o af f fa a a a a a            . (1) boundary and initial conditions are specified as u u u l u u l1 2 3 1 2 3 20, ; 0,      x x i it t u u t i x v v1 20 00, 0, 1, 3;        (2) n pp t x s( ),   n n boundary conditions imposed on free surfaces, contact lines between the beam and supporting elements and boundary between the steel reinforcement and concrete follow from the variational eq. (1). the variation of the work of internal and external forces for the structural elements of the beam can be written as: k k k ij ij bv k k k k ki f i i i b bv s p a dv u a u dv p u ds t 2 2                  (3) expressions (1)-(3) contain the following notation: a – variation of the work of internal forces; fa – variation of the work of inertia and external forces; the superscripts b o a, , denote concrete, supporting elements and a reinforcement rods, respectively, the upper index k is used as “b” “a” and “o” for different structural elements, i, j – integer indices taking values 1, 2, 3 in accordance with the axes of cartesian coordinate system ( x x x1 2 3, , ); k iu – displacement vector components; kij , k ij – strain and stress tensor components; k – material density; kip – components of the external force vector describing the impulse force applied along the normal n to the localized surface areas sp of the beam. i. n. shardakov et alii, frattura ed integrità strutturale, 38 (2016) 339-350; doi: 10.3221/igf-esis.38.44 342 the strain tensor components kij are determined by the relations: bb uu jk i ij x xj i 1 2           (4) according to the hooke’s law, the stress tensor components kij are written as: k k ke ek k k ij ij kk ijb b b1 (1 )(1 2 )              (5) tab. 1 summarizes the physical properties of materials of the structural elements of the beam. structural element elastic modulus e, mpa density ρ, kg/m3 poisson’s ratio,  concrete 0.35·105 2400 0.12 steel reinforcement and supporting elements 2·105 7800 0.3 carbon fiber sheet 2.52·105 2000 0.28 table 1: physical properties of materials of the structural elements of the beam. numerical implementation of the model is performed using the fem package ansys. fig. 2 presents finite-element meshes used to model a concrete beam with supporting elements and steel reinforcement. to describe the deformation process, we used solid186 (3-d 20-node solid element having 3 degrees of freedom per node and exhibiting quadratic displacement behavior) for concrete, solid189 (3-node beam element with quadratic approximation of displacements) for reinforcement, and shell281 (8-nodes shell element with 6 degrees of freedom per node and quadratic approximation of displacements and rotation angles) for supporting plates. figure 2: finite-element mesh: concrete and supporting elements (a) and steel reinforcement (b). the finite-element analogue of the variation equation written in matrix form is the system of ordinary linear differential equations:        m u k u f t( )  (6) i. n. shardakov et alii, frattura ed integrità strutturale, 38 (2016) 339-350; doi: 10.3221/igf-esis.38.44 343 where  m is the mass matrix,  k is the rigidity matrix  u and  u are the nodal displacement and the nodal acceleration vectors, and  f t( ) is the external force vector. variation of natural frequencies due to crack initiation he matrix equation for eigenmodes and eigenfrequencies of reinforced concrete beam obtained from (6) has the form      k m2 0   (7) where   is the vector specifying an eigenmode, and 2  is the eigenvalue equal to the squared circular eigenfrequency. the solution of system (7) determines the set of eigenmodes i and eigenfrequencies i (i = 1, 2,. . . ., n), where n is the order of symmetric positive definite rigidity and mass matrices. the crack initiation affects the rigidity of the originally intact beam and, as a consequence, changes eigenfrequencies and eigenmodes. for a quantitative description of these changes, we introduce small perturbations of the stiffness matrix, eigenfrequencies and eigenmode in the form      o o o oi i i i i ik k k m m[ ] [ ] [ ], [ ] [ ], ,               (8) all variables with superscript ‘o’ correspond to the beam without the crack, and the variables with superscript ‘*’ determine the value of perturbation due to the crack appearance. if we substitute (8) into (7) and linearize the obtained expression with respect to the perturbation, then, after simple transformations, we get the formula         t to o o i i i i t to o o i i k k [ ] [ ]          (9) this relation allows assessment of variations in the i-th unperturbed mode  o i  and the frequency oi at small perturbation of the rigidity matrix k *   . the quantity i * is called here the sensitivity parameter of the i-th eigenfrequency to crack formation. a comparative analysis of the values of i * shows the eigenfrequencies of the available frequency spectrum, which demonstrate the strongest response to the prescribed perturbation of the rigidity matrix. information on these most sensitive eigenfrequencies and on the distribution of corresponding vibration forms over the surface of the beam allows us to determine the location, direction, and duration of the external action required to effectively initiate this oscillation and to find a point on the beam, at which the registration of vibration parameters will be most effective. the spectral analysis of measured vibration parameter (displacement, velocity, acceleration) ensures the possibility of assessing crack nucleation in the originally projected point or its lack. analysis of the spectral properties of the reinforced concrete beam having the crack of 10 mm depth and 1 mm width in its central section, showed that there are four natural frequencies in the range of 0 – 5 khz exhibiting the greatest response to the occurrence of such a crack [21]. they are eigenfrequencies no 14 (2072 khz) and 23 (3897 khz), corresponding to the bending modes, and eigenfrequencies no 16 (2298 khz) and 23 (3845 khz), corresponding to the torsion modes. fig. 3 shows the local areas to which the load is applied in order to excite bending and torsion vibrations, and the positions of sensors (accelerometers) capable to register these oscillations. the solution of the initial boundary value problem modeling the vibrations in reinforced concrete beam caused by the impact impulse applied at the selected point can provide information on displacements and accelerations of arbitrary part of the structure. t i. n. shardakov et alii, frattura ed integrità strutturale, 38 (2016) 339-350; doi: 10.3221/igf-esis.38.44 344 fig. 4 shows the fourier vibroacceleration image at the sensor location point in two forms: as a diagram illustrating the frequency spectrum of vibroaccelerations (a) and as a grey scale image where different shades of grey show the intensity of the signal of prescribed frequency (b). these results were found for the beam having a crack with a depth of 10 mm and width of 1 mm. figure 3: scheme of local application of pulse load and the location of the accelerometer. figure 4: fourier image of vibroacceleration: as a graph (а) and as a tone distribution (b). by solving a series of analogous problems, in which the crack depth varies from 0 to 180 mm (the crack propagating through the entire cross-section of the beam), we have obtained a set of grey-scale images, which allowed us to get a pattern of changes in eigenfrequences with crack extension. the results are shown in fig. 5. the dark lines in these graphs correspond to the natural frequencies. lines 1–4 with the greatest intensity correspond to frequencies that give the most intense signal in the fourier image (lines 1 and 3 correspond to eigenfrequences no 14 and 23, lines 2 and 4 – to eigenfrequences no 16 and 24). the figure shows that as the crack depth increases, the eigenfrequencies reduce. figure 5: changes in eigenfrequencies caused by crack propagation: bending vibration mode (a) and torsion vibration modes (b). i. n. shardakov et alii, frattura ed integrità strutturale, 38 (2016) 339-350; doi: 10.3221/igf-esis.38.44 345 experiment n our experiments, we used a set-up specially designed for sequential quasistatic four-point loading of a reinforced beam to initiate crack nucleation in concrete. during the experiment the beams were subjected to additional impulse loading at each loading stage. mathematical modeling of the vibration process allowed us to calculate the parameters necessary to provide eigenmodes exhibiting the strongest response to nucleation and evolution of cracks. piezoelectric transducers were employed to register the vibrations. simultaneously, visible cracks on the side surface of the beam were registered. tone images based on the fourier analysis of vibrorecords were obtained from vibroacceleration measurements for each quasistatic loading step. a set of these images corresponding to increasing bending moments was used to get twodimensional tone images in coordinates: frequency and number of the loading stage (or an appropriate bending moment). fig. 6(a) presents the diagrams illustrating the changes in eigenfrequencies pertaining to the bending eigenmodes, and fig. 6(b) shows patterns of visible cracks observed at appropriate loading stages. in the diagrams, the lines corresponding to eigenfrequencies are clearly visible so that one can trace the changes in eigenfrequencies as the load increases. it is seen that before the appearance of the first crack, eigenfrequencies remain almost unchanged. the first crack with the opening width of 0.05 mm occurs at the bending moment of 4.4 knm. at that instant, the active nucleation of many cracks began in concrete. in the tone image, this stage is witnessed by a sharp reduction in eigenfrequencies. for three identified eigenfrequencies, 2069, 3904, 4798 hz, the measured eigenfrequency changes in the interval from the start of loading until the propagation of cracks through the entire cross section of the beam are, respectively, 7.2, 13.7, and 18.7% (tab. 2). by solving a series of problems of vibrations of a reinforced beam with a crack propagating through its central crosssection with increasing bending moment, we obtained theoretically the changes in eigenfrequences. tab. 2 shows the calculated changes in the eigenfrequencies of a beam having a crack extending through the entire cross-section (corresponding bending moment 5.0 knm). as can be seen from the table, the experimentally determined changes in eigenfrequencies associated with cracking in concrete agree well with the results of numerical simulation. figure 6: changing in eigenfrequencies, corresponding bending vibration modes (a) and observed pattern of cracks (b). a detailed study of the eigenfrequency diagram shows that at the initial stage of deformation, when no visible changes are present in concrete, the changes in eigenfrequencies have already started, yet constituting no more than 0.5% of their original value (fig. 6(c)). accordingly, we can identify two characteristic stages in the process of loading. at the first stage, the nonconservative deformation process begins. the signs of this process cannot be observed visually, but if we have a recording apparatus with sufficient sensitivity, they can be well recorded. the second stage is characterized by active i i. n. shardakov et alii, frattura ed integrità strutturale, 38 (2016) 339-350; doi: 10.3221/igf-esis.38.44 346 cracking reflecting by a sharp decrease in eingenfrequencies. it is of importance that the moment of transition from one stage to another is very well registered, because it suggests that the phase of active cracking starts. , khz experiment: , hz (/, %) simulation: , hz (/, %) 2.069 148 (7.2) 109 (5.3) 3.904 534 (13.7) 489 (12.5) 4.798 898 (18.7) 1022 (21.4) table 2: changing in eigenfrequencies at the instant of significant opening of the first crack (step 43, m=5.0 knm). the strengthening of reinforced concrete structures with carbon fiber reinforced polymers (cfrp) is currently extensively used. the developed method of vibration diagnostics turns out to be a promising tool to analyze the deformation behavior of a concrete beam reinforced with carbon fiber plastic and to evaluate the effectiveness of this way of strengthening concrete structures. we tested the beams strengthened with carbon fiber sheet sikawrap-230 of 40 mm width and 0.13 mm thickness (see also the paper by i n. shardakov, a.a. bykov, a p. shestakov in the present issue). a series of physical experiments were carried out to explore the spectrum of eigenfrequencies of the beam strengthened prior loading. during stepwise increasing quasistatic loading in combination with additional impulse loading, the grey-scale fourier images were obtained (fig. 7(a)). it is seen that a sharp change in eigenfrequencies corresponding to the formation of first visible cracks is associated with the bending moment m = 5.2 knm; the limiting state accompanied by the rapture of the cfrp sheet is achieved at m* = 10.4 knm. both values are essentially higher than the relevant values obtained for the unstrengthened beam. tab. 3 presents data showing changes in three selected eigenfrequencies registered at successive loading stages (fig. 7). the bending moment m* refers to the instant when the rapture of the strengthening layer takes place. the loading stages prior to the onset of first cracks are accompanied by slight changes in eigenfrequencies (~0,6%). the nucleation of cracks causes an abrupt change in eigenfrequencies, which reaches at the instant of the rapture of cfrp about 60% of their initial values. figure 7: changing in eigenfrequencies for the beam preliminary strengthened with the cfrp sheet (a) and observed pattern of cracks (b). i. n. shardakov et alii, frattura ed integrità strutturale, 38 (2016) 339-350; doi: 10.3221/igf-esis.38.44 347 n , khz before 1-st crack m<0.56m* 1-st crack m=0.56 m* cracks m=0.8 m* numerous cracks m=m* rapture of cfrp sheet 1 0.751 0.6 2.7 45.8 55.8 60.5 2 1.413 0.7 8.0 41.5 54.0 60.5 3 2.173 0.6 3.3 35.0 x x table 3: relative change in eigenfrequencies / (%) in the preliminary reinforced beam. the diagram of changes in eigenfrequencies reflects the processes taking place in the beam during its repair and restoring at some intermediate loading stage (fig. 8). the restoration procedure carried out directly under the load and consisted of the injection of cracks with the low-viscous epoxy material and gluing carbon fiber sheet to the stretched beam surface. in the loading range from 0 to 4.5 knm, the eigenfrequencies remained practically the same, and their values reduced sharply at the onset of formation of first visible crack (м=5.7knm). in the diagram, one can observe the "restoring" of eigenfrequencies after the procedure of crack treatment: they are recovered almost to their original values, which are kept over the load range from 5.7 to 7.2 knm. a further increase in the bending moment leads to the nucleation of new generation cracks (fig. 8(b), light lines) and therefore to new reducing in eigenfrequencies. a total loss of the bearing capacity of the beam occurs at the instant of rapture of the cfrp sheet at the bending moment of 10.4 knm. thus, the diagram of eigenfrequencies enables one to visualize the sharp changes in eigenfrequencies at the instant of nucleation of both primary and secondary cracks in concrete, and to identify the stage characterized by a full loss of the bearing capacity of the beam. figure 8: changes in eigenfrequencies for the beam strengthened with the cfrp sheet under the load (a) and the observed pattern of cracks (b). n , khz before 1-st crack m<0.56m* 1-st crack (i generation) m=0.44m* 1-mm crack m=0.53m* after treatment *0.53m m 1-st crack (ii generation) m=0.67m* cracks m=0.8m* numerous cracks m=m* rapture of cfrp sheet 1 0.746 0.4 6.0 38.6 1.9 3.7 36.9 50.5 58.1 2 1.367 0.6 3.5 35.8 1.2 6.9 26.8 41.0 48.7 3 2.109 0.4 6.9 24.3 2.0 3.5 26.7 x x table 4: relative change in eigenfrequencies / (%) of the beam reinforced under the loading. i. n. shardakov et alii, frattura ed integrità strutturale, 38 (2016) 339-350; doi: 10.3221/igf-esis.38.44 348 based on the diagram given fig. 9, the values of loading at which first cracks occur in concrete are compared with the limiting values. as a limiting condition, we assume a state when multiple cracks spread over the entire cross-section of the beam, and the bearing capacity of the beam is completely ensured by the steel reinforcement (in the experiment it is the bending moment equal to 6.5 knm). the experiment proves that, from the appearance of the first cracks until the loss of the bearing capacity (4.4 knm to 6.5 knm), the beam continues to be functional despite of nucleation of new cracks and propagation of existing ones. in this case, the beam has the strength reserve constituting ~32% of the limiting load. the beam reinforced with the cfrp sheet also retains its workability after the onset of first cracks. the bending moment of the preliminary strengthened beam corresponding to the full rapture of the sheet exceeds the load at which the occurrence of first cracks has been registered by ~45%, and the bending moment of the beam strengthened during the loading by ~56%. the analysis of the diagram confirms the validity of procedures aimed at strengthening a beam under the loading. the effectiveness of such reinforcement techniques is competitive with that of the procedures for preliminary strengthening of beams with a composite material. summing up, our experiment clearly demonstrates that crack formation in concrete is not a critical factor affecting the loss of bearing capacity by a reinforced concrete beam. figure 9: critical values of the bending moment. conclusion ased on the results of experimental and theoretical studies, we conclude that vibration diagnostics of reinforced concrete structures is an effective tool for early detection, assessment, and monitoring of cracking. the real-time vibration analysis gives a great deal of information about the level of cracking and the residual life of the concrete structure. the developed method of vibration diagnostics enables one to assess the degree of efficiency of measures for the restoration and strengthening of the structure. the obtained data provide a general algorithm for creating and performing procedures for vibration diagnostics of cracking in reinforced concrete structures. the algorithm consists of the following steps: 1) based on mathematical modeling, the deformation state of the structure is assessed by using information on actual loading conditions. the most probable locations of cracks are predicted. 2) a series of numerical experiments are carried out to simulate vibrations in the structure. eigenmodes and eigenfrequences are analyzed for the entire structure and the structure having cracks in the predicted areas. 3) using numerical simulation results, the parameters of vibrodiagnostic testing are specified, namely:  technical characteristics of vibration sensors that provide registration of vibrations in a predetermined frequency range with a required precision;  vibration sensors location points;  position and duration of external impact, ensuring excitation of vibrations with required natural frequencies. 4) rational scheme for strengthening a reinforced concrete structure based on numerical simulation data is developed. 5) block diagram for the system of vibration diagnostics of cracking in reinforced concrete structures is elaborated. b i. n. shardakov et alii, frattura ed integrità strutturale, 38 (2016) 339-350; doi: 10.3221/igf-esis.38.44 349 acknowledgment his research was supported by the russian science foundation, project no. 14-2900172. references [1] raghavan, a., cesnik, c.e.s., shock and vibration digest, 39 (2007) 91-116. [2] grimberg, r., premel, d., savin, a., bihan, y. le, placko, y. d., eddy current holography evaluation of delamination in carbon-epoxy composites, insight, 34 (2001) 260-264. [3] maldague, x.p.v., nondestructive evaluation of materials by infrared thermography, springer, london, (2011). [4] ermolov, i.n., aleshin, n.p., potapov, a.i., acoustic testing methods. moscow, vysshaya shkola, (1991) (in russian). [5] chikhunov, d., methods and devices for nondestructive testing of physical properties of concretes, stroit.inzhener 3(2005) 55–59 (in russian). [6] verma, k., bhadauria, s.s., akhtar, s., review of non destructive testing methods for condition monitoring of concrete structures, journal of construction engineering (2013). http://dx.doi.org/10.1155/2013/834572. [7] rahmani, t., kiani, b., bakhshi, m., shekarchizadeh, m., application of different fibers to reduce plastic shrinkage cracking of concrete, 7th rilem international conference on cracking in pavements, (2012) 635-642. [8] cao, m., ren, q., qiao, p., nondestructive assessment of reinforced concrete structures based on fractal damage characteristic factors, journal of engineering mechanics, 132 (2006) 924-931. [9] adams, d., farrar, c., classifying linear and nonlinear structural damage using frequency domain arx models,. structural health monitoring, 1 (2002) 185–201. [10] doebling, s., farrar, c., prime, m., shevitz, d., damage identification and health monitoring of structural and mechanical systems from changes in their vibration characteristics: a literature review, los alamos national laboratory, los alamos, new mexico, (1996). [11] fan, w., qiao, p., vibration-based damage identification methods: a review and comparative study, structural health monitoring, 10 (2011) 83-111. doi: 10.1177/1475921710365419. [12] wang, l., chan, t.h.t., review of vibration-based damage detection and condition assessment of bridge structures using structural health monitoring, proc. 2-nd infrastructure theme postgraduate conference. queensland university of technology, (2009). [13] cawley, p., adams, r.d., the location of defects in structures from measurements of natural frequencies, journal of strain analysis, 14 (1997) 49-57. [14] west, w.m., illustration of the use of modal assurance criterion to detect structural changes in an orbiter test specimen, proc. 4th international modal analysis conference, union college, (1986). [15] pandey, a.k, biswas, m., samman, m.m., damage detection from changes in curvature mode shapes, journal of sound and vibration, 145 (1991) 321–332. doi:10.1016/0022-460x(91)90595-b [16] stubbs, n., kim, j.t., damage detection in offshore jacket structures from limited modal information, international journal of offshore and polar engineering 5(1995) 58-66. [17] aktan, a.e., lee, k.l., chuntavan, c., aksel, t., modal testing for structural identification and condition assessment of constructed facilities, proc. 12th international modal analysis conference, (1994) 462–468. [18] spagnoli, a., carpinteri, a., ferretti, d., vantadori, s., an experimental investigation on the quasi-brittle fracture of marble rocks, fatigue and fracture of engineering materials and structures, 39 (2016) 956-958. doi:10.111file 12429. [19] montanari, l., spagnoli, a., basu, b., broderick, b., on the effect of spatial sampling in damage detection of cracked beams by continuous wavelet transform, journal of sound and vibration, 345 (2015) 233-249. doi: 10.1016/j.jsv.2015.01.048. [20] montanari, l., basu, b., spagnoli, a., broderick, b.m., a padding method to reduce edge effects for enhanced damage identification using wavelet analysis, mechanical systems and signal processing, 52-53 (2015) 264-277. doi: 10.1016/j.ymssp.2014.06.014. t i. n. shardakov et alii, frattura ed integrità strutturale, 38 (2016) 339-350; doi: 10.3221/igf-esis.38.44 350 [21] bykov, a.a., matveenko, v.p., serovaev, g.s., shardakov, i.n., shestakov, a.p., mathematical modeling of vibration processes in reinforced concrete structures for setting up crack initiation monitoring, mechanics of solids, 50 (2015) 160–170. [22] bykov, a.a., matveenko, v.p., serovaev, g.s., shardakov, i.n., shestakov, a.p., analysis of the influence of dynamic phenomena on the fracture of a reinforced concrete beam under quasistatic loading (computations and experiment), mechanics of solids, 50 (2015) 118–129. 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/hrv (za stvaranje adobe pdf dokumenata najpogodnijih za visokokvalitetni ispis prije tiskanja koristite ove postavke. stvoreni pdf dokumenti mogu se otvoriti acrobat i adobe reader 5.0 i kasnijim verzijama.) /hun 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/pdfxoutputintentprofileselector /documentcmyk /preserveediting true /untaggedcmykhandling /leaveuntagged /untaggedrgbhandling /usedocumentprofile /usedocumentbleed false >> ] >> setdistillerparams << /hwresolution [2400 2400] /pagesize [612.000 792.000] >> setpagedevice microsoft word numero_51_art_21_2634 a. namdar, frattura ed integrità strutturale, 51 (2020) 267-274; doi: 10.3221/igf-esis.51.21 267 the multilayered soil-structure seismic interaction and structure vibration mechanism abdoullah namdar faculty of architecture and civil engineering, huaiyin institute of technology, huai’an, china department for management of science and technology development, ton duc thang university, ho chi minh city, vietnam faculty of environment and labour safety, ton duc thang university, ho chi minh city, vietnam abdoullah.namdar@tdtu.edu.vn abstract. the morphology of subsoil influences the soil-structure interaction and it makes complex to predict seismic structural stability. the structural elements seismic response associate to soil-structure interaction requires expansive investigation considering soil morphology. the main objective of the present study is to identify the influence of near-fault ground motion mechanism reached by the structure element for evaluating strain energy modification due to the morphology of subsoil and developing load and displacement on the structural element with built-up synthetic subsoil for soil-structure seismic interaction design. the results of the numerical simulation revealed that (i) the displacement mechanism and the applied seismic load of the structural element, (ii) the strain energy modification and (iii) the structural vibration patterns of continuous beam in a timber frame have been changed in association to the soil foundation characteristics. the innovation of this study is the soil-structure interaction, the soil layers interaction, the near-fault ground motion and the mechanical properties of the soil at different location of the soil foundation, that are fundamental parameters to control continuous timber beam seismic design. keywords. multilayered soil; structure; strain energy; displacement; vibration patterns. citation: namdar, a., the multilayered soilstructure seismic interaction and structure vibration mechanism, frattura ed integrità strutturale, 51 (2020) 267-274. received: 14.09.2019 accepted: 28.11.2019 published: 01.01.2020 copyright: © 2020 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. introduction he structure seismic response is extremely related to near-fault ground motion characteristics and, on the other hand, due to subsoil morphology at different locations of the earth, the seismic travel paths characteristics are changed during seismic wave travel from the source to the base of the structure. also, seismic wave changes in the construction site from a location to nearby location considerably, this alters the seismic wave and creates complex prediction for seismic stability of a structure. in the most urban construction site, the buildings behave with different seismic response t http://www.gruppofrattura.it/va/51/2634.mp4 a. namdar, frattura ed integrità strutturale, 51 (2020) 267-274; doi: 10.3221/igf-esis.51.21 268 and result in various seismic resistance of different structures while the applied near-fault ground motion was the same from the source and the urban construction site mostly content different soil layers. in the seismic design of the structure, the underground simulation modeling is extremely important to predict seismic response of the structure and subsoil. for structure, seismic design in the urban construction site, not only soil or structure improvement, is applied in the most consultation and research works, and effect of soil in structural element seismic response has not been studied and reported in the literature. in several small projects at the urban construction site is not economic to consider soil, structure, and nearfault ground motion characteristics; however, due to this limitation always many individual small buildings do not have sufficient seismic stability. the mechanical properties of soils have been investigated in order to analyze liquefaction which is one of a disaster occurring after a strong earthquake, and it has been realized that the site geological structure governs seismic wave which produces the liquefaction in the soil [1]. the tsunami producing dynamic wave in subsoil has been simulated and in order to maintain subsoil dynamic stability the sea forests were proposed to enhance subsoil trough the modification of wave geometry by reducing seawater depth, strengthening soil mechanical properties and preventing tsunami debris transfer debride tsunami to the city after the shear strength of the subsoil reached near zero and liquefaction occurred with maximum magnitude [2], the liquefaction in the coastal line causes the lateral and vertical pressures to the building and subsoil, on the other hand, tsunami may produce debride and, in this case debride accelerates tsunami destructive power, in order to prevent accelerate debride development, dynamic stability of the subsoil is significantly required using advances geotechnical engineering techniques. the numerical analysis has been used to assess the bearing capacity of different soils under normal and frozen conditions [3-5]. the mechanical properties, the strength and the bearing capacity of soils are very important in soil tension and compressive response during the soil is subjected to the loading in a different direction and it leads to developing displacement and deformation of the soil [6-7]. in other words, strain energy and damage have been investigated to solve several engineering problems and strain energy needs to be investigated further [8-16]. there are several types of research on flexural load applied on structure and materials [17-21]. however, the seismic travel paths characteristics in the urban construction site for identifying seismic wave applied to each individual building has not been investigated and it required expansive investigation. based on soil seismic response and structures seismic response mechanism, it is required to investigate the bridge between soil response and structure response. the seismic responses of multilayered soil effect on the structural elements seismic response have not been investigated considering strain, displacement and seismic load response for evaluating structural vibration patterns when the near-fault ground motions applied on the model and seismic wave are changed with travel from multilayered soils. in the present study, the numerical analysis has been done to evaluate strain energy modification due to the morphology of subsoil and developing load and displacement of a continuous beam in the timber frame with built-up synthetic subsoil for understanding soil-structure seismic interaction design. however, it is aimed to analyze the energies interaction and the nonlinear displacement of the structural elements. it hopes the outcomes of this research work support in enhancement of the seismic stability of small individual buildings. modeling methodology, materials and seismic loading he soil-structure interaction is a complex problem in geotechnical earthquake engineering and it requires to investigating seismic stability enhancement of structure and soil developing appropriate modeling, to recognize suitable near-fault ground motion and to apply powerful software in order to minimize research cost, to predict in detail the soil-structure interaction model behavior and to produce best seismic design guideline. for understanding the relationship between soil, structural elements and seismic loading excitation, the structure-multilayered soil seismic response is simulated and the near-fault ground motion is applied to the configuration using acceleration history of near-fault ground motion reported in the literature by means of abaqus software for performing the numerical simulation. the numerical simulation was performed considering the applied near-fault ground motion and the response of near-fault ground motion in form of strain energy, displacement and seismic load response within the selected structural elements; comparative analysis has been done with two simulated archetypes. the near-fault ground motion response characteristics studied in association with the multilayered soil were configured at two different subsoil models and the structural frame is constant at all configuration. when the two multilayered soils were designed, the structure was modeled with fixed base boundary condition. the multilayered soils interact was simulated using the deformable mesh. using deformable mesh in the numerical simulation, as the model is subjected to seismic excitation is a supportive technique to develop cyclic graphs for displacement, strain and seismic load response. in studying the simulated configuration, the seismic load response, strain, and displacement are required to realize seismic stiffness and strength of the structural elements and soil at all stages of t a. namdar, frattura ed integrità strutturale, 51 (2020) 267-274; doi: 10.3221/igf-esis.51.21 269 applied seismic loading on the model. however, in comparative soil and structure for the seismic response, the small displacement theory is applicable and the small displacement theory is one of advanced concepts to explain strain energy function in dynamic excitation of soil-structure interaction. in the present study, the nonlinear graphs of the straindisplacement were developed based on the small displacement theory and based on the numerical analysis results the comparation has been made only for structural elements seismic response. the near-fault ground motion mechanism was simulated with seismic load excitation transfer from an element and node to neighboring element and node respectively, the nodes and elements interaction patterns were adopted in the numerical simulation to execute software. after executing the software, the most critical structural elements affected by near-fault ground motion were selected for more detail analysis by depicting the cyclic graphs. the seismic excitation, rest and seismic dissipation of the structural elements have been explained using cyclic graphs. the acceleration history of near-fault ground motion applied in the numerical simulation is shown in figure 1. the acceleration history was applied to soil basis after seismic wave travelled from the soil layers and seismic wave influenced by soil layer interaction, the seismic wave reached the fixed base of the structure and the seismic excitation transferred within all over the structural elements. based on the near-fault ground motion excitation and finite element method (fem), this study discovers the effect of the multilayered soil arrangement on the structural elements seismic stability, understanding seismic soil-structure interaction in reference to the small displacement theory. this numerical simulation is essential in the seismic design of the low-cost individual building. the mechanical properties of the soils and timber have been indicated in table 1. the previous researches mostly concentrated on the concrete structure-soil interaction and steel structure-soil interaction, while in the present study the timber structure-soil interaction has been investigated and footing, foundation, columns, and beams have been simulated using the timber materials. the timber frame structure as an independent structural system interacts with multilayered soil, and the seismic stability of the timber frame is examined. in order to enhance quality of the soil-timber structure interaction, in the numerical simulation small size of 50 mm the mesh for timber structure has been selected, and the horizontal and vertical soil-timber footing interaction has been characterized based on the node to node and element to element interaction between the soil and the timber footing. from the point of view of design half of the footing, height was embedded in the soil. in performing the numerical simulation by means of abaqus software the combination of the forcing frequency and near-fault ground motion has been adopted and applied to all archetypes simultaneously. the soils and beams were characterized and depicted in figure 2. the beam was characterized by 12.9 meters length and 0.3 x 0.3 meters cross-section. the column size was the 2.7-meters length, and 0.3 x 0.3 meters of the cross-section in both models. the timber frame was installed on a foundation of 0.3x0.3x0.3 meters and, beneath the foundation, a footing was designed with dimensions of 0.9x0.9x0.4 meters. the footing was designed with 0.4 meters height and 0.2 meters of footing height was embedded in the soil foundation. the difference between models 1 and 2 was the soil foundation. model 1 was built up with the soil-a, and model 2 was built up with the soil-a and soil-b. model 1 had dimension of 15.3x2.7x1.0 meters and was fully made of soil-a. model 2 was built up with the two equal partitions and each part had size of 7.65x2.7x1.0 meters, and part one of model 2 was built up of soil-a, and part two of the model 2 was built up of soil-b. the threedimensional models with mesh on all parts of archetype are shown in figure 3, two different sizes of the mesh were employed to study the soil-structure under seismic response with half-height embedded foundation in the soil. 0 1 2 3 4 5 6 -2.0 -1.5 -1.0 -0.5 0.0 0.5 1.0 1.5 2.0 time [sec] a cc el er at io n [ m /s 2 ] figure 1: acceleration history of near-fault ground motion is applied in the numerical simulation [22]. a. namdar, frattura ed integrità strutturale, 51 (2020) 267-274; doi: 10.3221/igf-esis.51.21 270 figure 2: the soil configuration and timber frame archetype used in the numerical simulation. figure 3: the mesh is developed for the numerical simulation type of material modulus elasticity, e (mpa) poisson’s ratio, ν unit weight, γ (kn/m3) cohesion, c (kpa) friction angle, ϕ (degree) dilatancy angle, ψ (degree) timber 6750 0.30 7.00 soil-a 131 0.34 21.4 0.08 46 20 soil-b 78 0.31 18.3 20 10 4 table 1: soils and timber mechanical properties. a. namdar, frattura ed integrità strutturale, 51 (2020) 267-274; doi: 10.3221/igf-esis.51.21 271 interpretation of the numerical simulation results n this study, the main objective is to examine the effects of soil-structure interaction on strain energy development which leads to inelastic and elastic displacements forming of a continuous timber beam installed on a timber frame that contained three spans, four equal columns, footing and foundation. in the numerical analysis, the applied seismic loading was not the same as the soil and structural response, the configuration of the model played a key function in seismic response. the multilayered soils interact was responsible for the displacement, the deformation, and the strain energy transfer mechanism; however, this process-controlled failure and vibration patterns of the frame. the structure was extremely vibrated with the modification of seismic loading excitation. the softened and hardening soil layers interaction developed the shear modulus with characterized nonlinearly and the transmitted near-fault ground motion exhibited differently at each archetype; however, the geometrical and mechanical characteristics of the soil and structure controlled the structural elements seismic response. figure 4 shows the load versus the cyclic displacement of the continuous beam in models 1 and 2. in model 1 the soil foundation built up from the type a soil, while in the second model the soil foundation configuration contained types a and b soils. the continuous beam exhibited higher differential displacement in the archetype 2. the differential displacement was represented by two models for each model; they appeared with a different mechanism. in the first model the symmetric differential displacement occurred and in the second model the differential displacement of the continuous beam took place with nonsymmetrical morphology, so the soil foundation changes significantly influenced the continuous beam differential displacement morphology. according to the table 1, the mechanical properties reported for soil types a and b were not the same, and the type-a soil exhibited higher strength and stiffness compared to the type-b soil, on the other words the stiffness and strength changes of the soil were used in the built-up soil foundation, and it caused the modification of the soil displacement morphology, and also this modification of displacement was transferred to the continuous beam and all structural elements. based on the soil-structure seismic response for analysis displacement morphology of the continuous beam, the numerical analysis showed that the near-fault ground motion interacted with the different soil foundations and resulted in inelastic displacement ratios. the differential displacement mechanism of soil was associated with soil-structure interaction, and differential displacement mechanism of soil influenced the continuous beam seismic resistance. the interesting point is that the ground motion led to differential displacement and the subsoil morphology accelerated the differential displacement if the subsoil contained more types of the soil. the unallowable differential displacement across the continuous beam maybe caused the breaking up of the structural elements and minor and major damage on the wall surface in a timber structured building. increasing the differential displacement generally led to the appearance of shear crack on the building timber structured wall, while the linear differential displacement did not cause the shearing crack on the timber structured building. the shearing crack was associated with seismic excitation when the seismic wave was strengthened in relation to subsoil characteristics. after the initial displacement due to the seismic excitation model, the nonlinear cyclic displacements at each model related to changing hysteretic damping and led to occurrence of the peak displacement. increasing hysteretic damping in the continuous beam with attention to the capacity of differential displacement structural elements, the plastic displacement at each point of the structural element was predictable. -10 -5 0 5 10 -400 -200 0 200 400 displacement (mm) l o ad ( kn ) model-1 -10 -5 0 5 10 -400 -200 0 200 400 displacement (mm) l o ad ( k n ) model-2 figure 4: load vs displacement on timber beam models. i a. namdar, frattura ed integrità strutturale, 51 (2020) 267-274; doi: 10.3221/igf-esis.51.21 272 figure 5 shows the strain versus the cyclic displacement of the continuous beam in models 1 and 2. the strain energy distribution had two different magnitudes in both models. the strain energy releasing in model 2 was higher than model 1, the soil layers interaction increased the quantity of strain energy releasing, and this process led to increasing differential displacement of the continuous beam. the mechanical properties of the two soil layers were responsible for damping magnitude, and the damping magnitude would cause the displacement mechanism. the geometry of the soil foundation along with the two soil layers interaction supported increasing total strain energy differently at each model, and the vibration transferring from the soil foundation to structural elements behaved differently. the strain-displacement graphs were applicable in predicting shearing deformations of a continuous beam in a timber frame structure. the variation of the strain energy at failure controlled shear deformation and modified the strength and stiffness of the timber beam; afterward, the displacement of the beam at each model exhibited differently. the strain energy confinement of the timber and the soil collaborated in displacement development; the configuration soil layers were associated with the strain energy transfer and the soil-structure effect by the strain energy confinement in the soil foundation. the soil-structure interaction, the soil layers interaction, the near-fault ground motion and the mechanical properties of the soil at different locations of the soil foundation are fundamental parameters to recognize structural element strain-displacement behavior. in order to provide guidance to seismic design for soil-structure interaction, the strain has been correlated to all sections of ground accelerations for realizing displacement of the continuous timber beam. along with soil-structure interaction, the soil layers interaction played a significant role in seismic continuous timber beam design. soil-structure damping ratio depended on the average induced strain energy and it was associated with the decrease factors for the soil seismic strength and the occurrence of the soil foundation differential displacement. -10 -5 0 5 10 -0.0012 -0.0009 -0.0006 -0.0003 0.0000 0.0003 0.0006 0.0009 0.0012 s tr ai n model-1 displacement (mm) -10 -5 0 5 10 -0.0012 -0.0009 -0.0006 -0.0003 0.0000 0.0003 0.0006 0.0009 0.0012 s tr ai n displacement (mm) model-2 figure 5: strain vs displacement on timber beam models. figure 6 shows the load versus the strain of the continuous beam in the models 1 and 2. the state-of-the-art numerical analysis was performed using the finite element method to depict load-strain cyclic graphs, and there is a meaningful relationship between seismic load response and strain in the comparative seismic resistance of all simulated models. in order to evaluate health monitoring timber structure frame through assessment soil-structure interaction, it required to clearly realize the load response, strain and displacement developed by internal and external forces interaction of each simulated model. the study has shown that the soil-structure interaction was effective in increasing induced strains and load in the continuous beam. soil layers interaction with modification of seismic wave relationship induced strains energy mechanism and resulted in the highest strains due to increased forces interaction in the timber frame. in the present study, the results of the finite element model deeply provided load, displacement and strain at different locations of the continuous beam when the near-fault ground motion interacted with the different soil foundation and the seismic excitation transferred to all parts of the soil foundation and the timber frame. the results of this numerical simulation were very difficult to achieve under laboratory conditions with this accuracy of the structural element seismic simulation. due to the triggering high level of nonlinear strain energy in the model 2, the soil faced the high level of seismic vibration compared to the model 1, eventually higher strain energy dissipation occurred in the model 2; however, the high level of triggering and dissipation of strain energy caused the soil vibration and this vibration mechanism of the soil was transferred to the frame. the vibration stiffness of soil against differential displacement and nonlinear deformation restrained frame seismic excitation mechanism. a. namdar, frattura ed integrità strutturale, 51 (2020) 267-274; doi: 10.3221/igf-esis.51.21 273 -0.0012 -0.0009 -0.0006 -0.0003 0.0000 0.0003 0.0006 0.0009 0.0012 -400 -200 0 200 400 strain l o ad ( k n ) model-1 -0.0012 -0.0009 -0.0006 -0.0003 0.0000 0.0003 0.0006 0.0009 0.0012 -400 -200 0 200 400 model-2 strain l oa d ( k n ) figure 6: load vs strain displacement on timber beam models. conclusion n the most of urban construction site, the buildings show different seismic response and result in various seismic resistance of different structures while the applied near-fault ground motion used from the station for earthquake data collection is the same, and also the urban construction sites always contain different soil layers. in the seismic design of the structure, the underground simulation is extremely important. in the present study, the following goals have been achieved for enhancement timber frame seismic design.  for the urban construction site, to use an accurate near-fault ground motion is required for the seismic design for each individual building, in order to provide sufficient seismic stability of the structure. the results showed that the near-fault ground motion characteristics changed with the site morphology and effected seismic stability of the structure significantly.  in the first model of the numerical simulation, the symmetric differential displacement occurred and in the second model the differential displacement of the continuous beam took place with nonsymmetrical morphology. the changes of soil foundation characteristics significantly influenced the continuous beam differential displacement morphology.  the stiffness and strength modification of the soils were used in the built-up soil foundation and it caused variation of the soil foundation displacement morphology, and also this modification of soil foundation displacement was transferred to the structural elements and each part of the continuous beam faced different morphology of the differential displacement.  the soil-structure seismic based on the near-fault ground motion interacted with the different soil foundation. the soil foundation with different layers resulted in inelastic displacement ratios modification and subsoil effect on continuous beam strength reduction in association with the soil-structure systems. the enhancement of the soil layers interaction significantly improved timber frame stability.  the soil-structure interaction, the soil-layers interaction, the near-fault ground motion and the mechanical properties of the soil at different locations of the soil foundation were fundamental parameters to recognize structural element strain-displacement in seismic timber design. soil-structure damping ratio depended on the average induced strain energy and was associated with the decrease factors for the soil seismic strength and the occurrence of the differential displacement of the soil foundation.  the numerical analysis results provided load, displacement and strain at different locations of the continuous beam when the beam was subjected to seismic excitation, which was very difficult to achieve under laboratory conditions with this accuracy of the structural element seismic simulation. the numerical analysis is a cost-effective technique with high accuracy to solve scientific problems. i a. namdar, frattura ed integrità strutturale, 51 (2020) 267-274; doi: 10.3221/igf-esis.51.21 274 references [1] namdar, a., pelko, a. k. and nusrath, a. (2010). liquefaction mathematical analysis for improvement structures stability, fract struct int, 4(14), pp. 75-80. doi: 10.3221/igf-esis.14.08. [2] namdar, a. and nusrath, a. (2010). tsunami numerical modeling and mitigation, fract struct int, 4 (12), pp. 57-62. doi: 10.3221/igf-esis.12.06. [3] namdar, a. and feng, x. (2014). evaluation of safe bearing capacity of soil foundation by using numerical analysis method, fract struct int, 8 (30), pp. 138-144. doi: 10.3221/igf-esis.30.18. [4] namdar, a. and pelko, m. k. (2009). numerical analysis of soil bearing capacity by changing soil characteristics, fract struct int, 3 (10), pp. 38-42. doi: 10.3221/igf-esis.10.05. [5] zhelnin, m., kostina, a., plekhov, o., panteleev, i. and levin, l. (2019). numerical analysis of application limits of vyalov’s formula for an ice-soil thickness, fract struct int, 13(49), pp. 156-166. doi: 10.3221/igf-esis.49.17. [6] li, y., zhang, k., liu, b. and pan, z. (2015). on the decay of strength in guilin red clay with cracks, fract struct int, 9(34). doi: 10.3221/igf-esis.34.66. [7] namdar, a. and pelko, m. k. (2009). bearing capacity of mixed soil model, fract struct int, 3 (7), pp. 73-79. doi: 10.3221/igf-esis.07.06. [8] lazzarin, p., livieri, p., berto, f. and zappalorto, m. (2008). local strain energy density and fatigue strength of welded joints under uniaxial and multiaxial loading. eng fract mech, 75 (7), pp. 1875-1889. doi: 10.1016/j.engfracmech.2006.10.019. [9] nicola bonora, domenico gentile, pietro paolo milella, golam newaz, francesco iacoviello. (2000). ductile damage evolution under different strain rate conditions. appl. mech. div. asme, 246, pp 145-154. [10] panin, s., vinogradov, a., moiseenko, d., maksimov p., berto, f., byakov, a., eremin, a., narkevich. n., (2016). numerical and experimental study of strain localization in notched specimens of a ductile steel on mesoand macroscales, adv eng mater, 18(12), pp. 2095-2106. doi: 10.1002/adem.201600206. [11] boniardi, m., tagliabue, c. and venturini, n. (2006). residual stress origin: plastic deformation and machining, metall ital, 98(11), pp. 53-60. [12] namdar, a., dong, y. and liu, y. (2019). the effect of nonlinearity of acceleration histories to timber beam seismic response, mater des proces communic, 1 (2), pp. 1-4. doi:10.1002/mdp2.53. [13] ayatollahi, mr., rashidi moghaddam, m. and berto, f. (2015). a generalized strain energy density criterion for mixed mode fracture analysis in brittle and quasibrittle materials, theor appl fract mec, (79), pp. 70–76. doi: 10.1016/j.tafmec.2015.09.004. [14] košíková, b., sláviková, e. and sasinková, v. (2006). the use of various yeast strains for removal of pine wood extractive constituents, wood res. 51(4). pp. 47-54. [15] iacoviello, f., di cocco, v. and cavallini, m. (2015). fatigue crack tip damaging micromechanisms in a ferriticpearlitic ductile cast iron, fract struct int, 9(33), pp. pages 111-119. doi: 10.3221/igf-esis.33.15. [16] berto, f. and foti, p. (2019). evaluation of the strain energy density value without the construction of the control volume in the preprocessing phase of the finite element analysis, proc struct integ, (18), pp. 183-188. doi: 10.1016/j.prostr.2019.08.152. [17] berto, f. and razavi, j. (2019). fatigueless structures inspired by nature: a case study, mater des proces communic, 1 (3), pp. 1-3. doi: org/10.1002/mdp2.27. [18] iacoviello, f., di cocco, v., cavallini, m., marcu, t. and molinari, a. (2005). influence of sintered stainless steel microstructure on fatigue crack paths, fatigue fract eng m, 28(1–2), pp. 187‐193. doi: 10.1111/j.1460-2695.2005.00836.x. [19] adelaide parisi, m. and piazza, m. (2015). seismic strengthening and seismic improvement of timber structures, constr build mater, 97 (30), pp. 55-66. doi: 10.1016/j.conbuildmat.2015.05.093. [20] namdar, a., darvishi, e., feng, x., zakaria, i. and yahaya, f.m. (2016). effect of flexural crack on plain concrete beam failure mechanism a numerical simulation. fract struct int, 10 (36), pp. 168-181. doi: 10.3221/igf-esis.36.17. [21] bellini, c., di cocco, v., iacoviello, f. and sorrentino, l. (2019). experimental analysis of aluminium/carbon epoxy hybrid laminates under flexural load, fract struct int, 13(49), pp. 739-747. doi: 10.3221/igf-esis.49.66. 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can be opened with acrobat and adobe reader 5.0 and later.) >> /namespace [ (adobe) (common) (1.0) ] /othernamespaces [ << /asreaderspreads false /cropimagestoframes true /errorcontrol /warnandcontinue /flattenerignorespreadoverrides false /includeguidesgrids false /includenonprinting false /includeslug false /namespace [ (adobe) (indesign) (4.0) ] /omitplacedbitmaps false /omitplacedeps false /omitplacedpdf false /simulateoverprint /legacy >> << /addbleedmarks false /addcolorbars false /addcropmarks false /addpageinfo false /addregmarks false /convertcolors /converttocmyk /destinationprofilename () /destinationprofileselector /documentcmyk /downsample16bitimages true /flattenerpreset << /presetselector /mediumresolution >> /formelements false /generatestructure false /includebookmarks false /includehyperlinks false /includeinteractive false /includelayers false /includeprofiles false /multimediahandling /useobjectsettings /namespace [ (adobe) (creativesuite) (2.0) ] /pdfxoutputintentprofileselector /documentcmyk /preserveediting true /untaggedcmykhandling /leaveuntagged /untaggedrgbhandling /usedocumentprofile /usedocumentbleed false >> ] >> setdistillerparams << /hwresolution [2400 2400] /pagesize [612.000 792.000] >> setpagedevice microsoft word numero_27_art_9 x. ran et alii, frattura ed integrità strutturale, 27 (2014) 74-82; doi: 10.3221/igf-esis.27.09 74 research on borehole stability of shale based on seepage-stress-damage coupling model xiaofeng ran key laboratory of exploration technologies for oil and gas resources of ministry of education, yangtze university, wuhan, hubei 430100, china. sniperpilot@163.com yuezhi wang key laboratory of exploration technologies for oil and gas resources of ministry of education, yangtze university, wuhan, hubei 430100, china. cjdxwyz@126.com shanpo jia school of urban construction, yangtze university, jingzhou, hubei 434023, china. jiashanporsm@163.com abstract. in oil drilling, one of the most complicated problems is borehole stability of shale. based on the theory of continuum damage mechanics, a modified mohr-coulomb failure criterion according to plastic damage evolution and the seepage-stress coupling is established. meanwhile, the damage evolution equation which is based on equivalent plastic strain and the permeability evolution equation of shale are proposed in this paper. the physical model of borehole rock for a well in china western oilfield is set up to analyze the distribution of damage, permeability, stress, plastic strain and displacement. in the calculation process, the influence of rock damage to elastic modulus, cohesion and permeability is involved by writing a subroutine for abaqus. the results show that the rock damage evolution has a significant effect to the plastic strain and stress in plastic zone. different drilling fluid density will produce different damage in its value, range and type. this study improves the theory of mechanical mechanism of borehole collapse and fracture, and provides a reference for the further research of seepage-stress-chemical-damage coupling of wall rock. keywords. shale; seepage-stress coupling; damage; permeability; finite element method; borehole stability. introduction n oil drilling, the study of borehole stability is a complicated task which involved with many factors. different researchers studied in different aspects [1] includes non-uniform ground stress, drilling fluid [2], bottom hole temperature [3] and fluid-structure coupling [4], etc. however, most researchers consider that mechanics is the primary cause of borehole instability. other factors can change the rock mechanics properties or stress state in different i http://dx.medra.org/10.3221/igf-esis.27.09&auth=true http://www.gruppofrattura.it x. ran et alii, frattura ed integrità strutturale, 27 (2014) 74-82; doi: 10.3221/igf-esis.27.09 75 degrees. at present, there are several models applied to analyze borehole stabilization, such as liner elastic model, elasticplastic model [5] and fluid-solid coupling model of porous media [4]. however, most of studies pay little attention to rock damage. practically,the stress redistribution after excavation will cause the produce of damage (fig.1). in the process of rock damage, permeability will change greatly with the fracture producing, extending and connecting [6]. meanwhile, rock strength and elastic modulus will decrease obviously. all of this can effects the result of force analysis, so it is necessary to involve the damage in seepage-stress coupling calculation of wall rock. figure 1: damage zone of wall rock in the uniform ground stress. under the change of external load or environment, the macro-mechanical properties deterioration of materials or structure caused by the initiation and propagation of microstructure defects (such as micro-cracks, micro-porosity, etc.) or other irreversible changes is called damage. in the study of seepage in fractured rock mass of damage mechanics, yi [7] established a seepage-damage coupling model, and a damage evolution equation in the compression shear or tensile shear state. zheng [8] proposed a seepage-damage coupling theory and a permeability tensor expression which considered the effect of damage of fractured rock. jiang tao [9] deduced a damage constitutive model and a seepage-damage constitutive model of brittle rock based on mesomechanics. yang [10] and zhao [11] studied the seepage-damage-fracture coupling theory and its application. based on poroelastic theory, selvadurai [12] studied the damage and permeability variation of geological materials which relate to stress. for the rock, the meaning of plasticity mainly refers to the sliding between inner fissuring. but the damage refers to the producing and extending of inner fissuring. the damage means a decrease of net loaded area in geometry. using the plastic-damage coupling constitutive model, the mechanical behaviour could be represented exactly. based on the theory of continuum damage mechanics, the damage evolution model according to equivalent plastic strain is established in this paper. additionally, the permeability evolution equation is established in relation to the evolution of plastic damage. aiming at a practical drilling process in an oilfield in western china, the physical model of borehole rock is built. using this model to simulate the disturbance damage and the permeability evolution in drilling, the distribution of stress of wall rock and the relationship between borehole instability and drilling fluid density is obtained. this study will improve the theory of mechanical mechanism of borehole collapse and fracture. seepage-stress-damage coupling model onlinear behaviour of rock caused mainly by micro cracks. if the micro cracks become a macro-fracture by accumulating, extending and connecting, then the degradation of material property which includes the strength, rigidity and ductility will arise. for describing it, the damage variable is needed according to irreversible thermodynamics. the damage variable can be chosen from the characteristics of micro-structure (the quantity, length, area and volume of micro cracks) or the experiment date (the elastic modulus, strain, yield stress, density and wave velocity). to apply the model in practical engineering, the damage variable and its evolution law is need to define. in this paper, the damage variable is supposed as follows: 1) rock damage occurs and increases with plastic deformation simultaneously. 2) the rate of damage rise is gradually diminishing with the development of plastic deformation. n http://dx.medra.org/10.3221/igf-esis.27.09&auth=true http://www.gruppofrattura.it x. ran et alii, frattura ed integrità strutturale, 27 (2014) 74-82; doi: 10.3221/igf-esis.27.09 76 elastic-plastic damage model he effective shear strength parameters *c and * is influenced by rock damage [13]. so the *c and * is a function of damage state. when the effect of damage and pore pressure is involved, the mohr-coulomb failure criterion can be indicated as eq. (1). * *tan 1 1 n n wpc            (1) where:  is damage variable; n and n are stresses on the failure surface; wp is the pore pressure. in this paper, the internal frictional angle is deemed to be changeless. but the cohesion will decrease gradually with the accumulation of damage. their relationship can be represented by a power-law function:  m m r pc c c c     (2) where: mc is the cohesion of shale with no damage; rc is the cohesion of shale with complete damage;  is the material parameter, 0 1  . the elastic modulus of the damaged shale is:   01e e   (3) where 0e is elastic modulus of shale with no damage. according to (3), 0e  when 1  . this does not match the actual reality. in fact, the rock also has a certain elastic modulus after damage. so, eq. (3) needs to modify as:  0 0 re e e e    (4) where re is elastic modulus of shale with complete damage. damage evolution equation f the stress exceeded rock strength at the condition of fluid-solid coupling, plastic deformation will be produced in wall rock. the equivalent plastic strain is:      2 2 21 2 2 3 3 12 3 p p p p p p p            (5) where 1p , 2p and 3p are the three principal plastic strains. in this paper, the damage variable is the first order index decay function of equivalent plastic strain which is as follows [14]: / 0 0 pn aa e b     (6) 0 1/ 1 1a a e   ; 0 1/ 1 1a b e    where pn is normalized equivalent plastic strain; a is material parameter which can be measured by experiments. t i http://dx.medra.org/10.3221/igf-esis.27.09&auth=true http://www.gruppofrattura.it x. ran et alii, frattura ed integrità strutturale, 27 (2014) 74-82; doi: 10.3221/igf-esis.27.09 77 permeability evolution equation n the stage of elastic deformation, rock permeability is decreasing when the compression stress increases. when plastic deformation takes place, rock permeability will increase slowly first and then sharply with the new crack extending and connecting. the permeability evolution equation of shale under different stress states can be indicated as follows [15]:      / 3 3 1/30 0 0 0 0 11 1 1 , 0 10 , 0 v v d m ae b n k n nk k                                   (7) where 3m  , which means shale permeability will rise about 3 orders of magnitude when rock fractured; 0k is permeability of shale with no damage. v is elastic strain. the porosity evolution equation is [16]: 0 3/2 0 1 1 , 0 0.61 , 0 vd n n n             (8) where 0n is porosity of shale with no damage. numerical simulation modelling or the shale drilling at the depth of 3500 m in china western oilfield, the physical model is established by using porous media fluid-solid coupling unit (cpe4p) in software abaqus (fig.1). by considering the disturbance damage and rock permeability changes during drilling, the stress distribution and influence of drilling fluid density is studied. the physical model parameters (ⅰ) are indicated in tab. 1. the parameter wr is the borehole radius;  is the average density of rock; h is the maximum horizontal ground stress; h is the minimum horizontal ground stress; v is the vertical ground stress; pp is the pore pressure; ip is the drilling fluid pressure; m is the drilling fluid density;  is the effective stress coefficient. in boundary conditions setting process, the wall is permeable boundary and its displacement is unconstrained. the computational process is divided into three steps: (1) balance the initial stress field; (2) kill the borehole unit and load drilling fluid pressure; (3) calculate seepage-stress-damage coupling in 20 days. figure 2: finite element model. i f http://dx.medra.org/10.3221/igf-esis.27.09&auth=true http://www.gruppofrattura.it x. ran et alii, frattura ed integrità strutturale, 27 (2014) 74-82; doi: 10.3221/igf-esis.27.09 78 parameterⅰ value parameterⅰ value parameterⅱ value parameterⅱ value h /m 3500  0.95 e / gpa 2 mc / mpa 12 wr / mm 158  /(g/cm3) 2.13  0.2  0.2 h / mpa 75 m /(g/cm3) 1.60 e 0.25 h / mpa 54 ip / mpa 55  /° 25 v / mpa 70 pp / mpa 45 0k / (m/s) 3×10-12 table 1: model parameters. setting mechanic parameters the mechanic parameters (ⅱ) of undamaged shale are shown in tab. 1. the parameter e is the elastic modulus;  is the poisson ratio; e is the void ratio;  is the harden parameter; mc is the cohesion;  is the frictional angle; 0k is the permeability. the mechanic parameters and hydraulic parameters of damaged rock is need to write in abaqus through software fortran, which include c , e , dk and dn . choose the equivalent plastic strain as damage variable and define the damage  is field variable according to eq. (6). define the c , e , dk and dn are state variables according to eq. (2), (4), (7) and (8). it is too small to ignore the influence of damage on poisson ratio. results hen the drilling fluid m = 1.6 g/cm3, the damage distribution and permeability change of wall rock is calculated. additionally, the distribution of pore pressure, stress and displacement is obtained. damage and permeability. the distribution of damage is shown in fig.3. in the non-uniform ground stress, most of wall rock is in elastic zone or protolith zone. the rock damage only occurred on the side of the minimum ground stress near the wall when m = 1.6 g/cm3. the maximum value of damage is 0.59 on the wall. the depth of damage rock is about 0.4 wr and the value of damage is decreasing with the increase of distance far from the wall. figure 3: the distribution of damage. figure 4: the distribution of permeability. the permeability variation of rock is indicated in fig.4. compared with fig.3, we can see that the distribution of permeability is corresponds with damage. the maximum permeability reach up to 1.76×10-9 m/s in damaged area. the permeability has no change in undamaged area. w http://dx.medra.org/10.3221/igf-esis.27.09&auth=true http://www.gruppofrattura.it x. ran et alii, frattura ed integrità strutturale, 27 (2014) 74-82; doi: 10.3221/igf-esis.27.09 79 equivalent plastic strain. the fig.5 shows the influence of damage to equivalent plastic strain. the curves are plastic strain when existed damage or no, and existed damage but not consider the change of elastic modulus or permeability or cohesion. from the diagram we can see that the range of plastic area is always 0.4 wr which not changed in different conditions. but the maximum value of plastic strain will be affected by different conditions, especially the change of elastic modulus. for example, the maximum plastic strain will change from 0.04 to 0.15 if exists damage but not consider the change of elastic modulus. figure 5: the influence of rock damage on plastic strain. stress state: 20 days after drilling a borehole, the hoop stress (  ) and radial stress ( r ) in the direction of the minimum ground stress is indicated in fig. 6(a). radial stress on the wall is reduced rapidly owing to excavation. 0.4 wr far from the wall, there is the maximum hoop stress and the maximum difference between hoop stress and radial stress. so combined with fig.3 we can find that there is shear damage in the range of 0.4 wr from the wall. now, the wall rock is also stable through damaged. if the pressure of drilling fluid or pore pressure changed, however, the shear damage will changed correspondingly. once the value of shear damage reached to its limit ( maxd ), the rock collapsed. therefore, it is necessity to analyze the damage evolution and the distribution of stress in damaged area. (a) (b) figure 6. the distribution of hoop-radial stresses: (a) mc =12 mpa; (b) mc =50 mpa. if the rock strength is very large (assume mc =50 mpa), rock damage is not occur (fig. 6(b)). there are only elastic zone and protolith zone in the wall rock. the maximum difference between hoop stress and radial stress is occurred on the wall. this means rock shear damage is appeared firstly on the wall, and then extended along the direction of the minimum ground stress. the rock collapse will be moved in a similar way. displacement. fig. 7 shows the rock displacement along the direction of the maximum and the minimum ground stress. the points in the direction of the maximum ground stress all moved toward the centre of borehole. the maximum displacement is 3.06 mm at the point on the wall, and it reduces gradually away from the borehole. the points in the direction of the minimum ground stress all moved deviate from the centre of borehole. the maximum displacement is 1.24 mm at the point 0.4 wr far from the wall. http://dx.medra.org/10.3221/igf-esis.27.09&auth=true http://www.gruppofrattura.it x. ran et alii, frattura ed integrità strutturale, 27 (2014) 74-82; doi: 10.3221/igf-esis.27.09 80 figure 7: the distribution of displacements. pore pressure. the distribution of pore pressure of well wall rock at different time after drilling is shown in fig. 8. due to the non-uniform ground stress, the maximum pore pressure is occurred at the direction of minimum horizontal ground stress, and the minimum pore pressure is occurred in the direction of maximum horizontal ground stress. with the passage of time, the pore pressure is dissipated gradually. after ten days, it tends to uniform in any direction. it is equal to the well fluid pressure at the well wall and to the initial pore pressure in the distance. it presents linear distribution between of them. (a) (b) (c) (d) figure 8: the pore pressure at different time (unit: pa). (a) 100s; (b) 1h; (c) 10h; (d) 10d. different drilling fluid density ig. 9 shows the distribution of damage when m =1.98 g/cm3. both the direction of maximum and minimum ground stress exist damage near the wall. the range and value of damage in the direction of maximum ground stress are larger than the direction of minimum ground stress. the hoop stress (  ) and radial stress ( r ) in the direction of the maximum ground stress is indicated in fig. 10. it is found that both hoop stress and radial stress are tensile stress. so there is a tensile damage in this direction. it can be deduced that the rock fracture when tensile damage reached to its limit ( maxtd ). f http://dx.medra.org/10.3221/igf-esis.27.09&auth=true http://www.gruppofrattura.it x. ran et alii, frattura ed integrità strutturale, 27 (2014) 74-82; doi: 10.3221/igf-esis.27.09 81 figure 9: damage when m =1.98g/cm3. figure 10: the hoop-radial stress. when drilling fluid density changed from 1.4 g/cm3 to 2.1 g/cm3, the value and range of damage in the direction of maximum and minimum ground stress are analyzed in figs. 11 and 12. with the increase of drilling fluid density, the maximum value (at node 2) and range of damage are decreased gradually in the direction of minimum ground stress. when drilling fluid density reached to 1.75 g/cm3, the tensile damage occurred at node 1, and then increased gradually with its range in the direction of maximum ground stress. figure 11: the value of damage at different drilling fluid density. figure 12: the range of damage at different drilling fluid density. therefore, if the drilling fluid density too low to produce the shear damage exceed its limit ( maxd d  ), the wall rock in the direction of minimum ground stress will be collapsed; if the drilling fluid density too high to produce the tensile damage exceed its limit ( maxt td d ), the wall rock in the direction of maximum ground stress will be fractured. the parameters maxd and maxtd can be obtained by experiment. if the rock is brittle, there is max max 0td d   . this means the damage zone in figs. 3 and 9 would become a crushing zone. conclusions ccording to a fluid-solid coupling theory, the concept of seepage coupled with plastic damage evolution is brought into mohr-coulomb failure criterion. the iterative calculation model of seepage-stress coupling which involving dynamic evolution of damage and permeability has been established. for analyzing the practical drilling process, the physical model of borehole rock is built by using software abaqus. in the process of calculation, the change of elastic modulus, cohesion and permeability caused by rock damage is considered. the results include damage, permeability, stress, plastic strain, pore pressure and displacements. the result shows that rock damage has a certain effect on plastic strain and stress distribution in plastic zone. the real and reliable result need to calculate using the coupled model which considered wall rock damage. a http://dx.medra.org/10.3221/igf-esis.27.09&auth=true http://www.gruppofrattura.it x. ran et alii, frattura ed integrità strutturale, 27 (2014) 74-82; doi: 10.3221/igf-esis.27.09 82 the drilling fluid density too high or too low will cause the tensile damage in the direction of maximum ground stress or the shear damage in the direction of minimum ground stress. if the damage exceeded its limit, the wall rock fractured or collapsed and a new shape borehole would be generated. this study will improve the mechanical mechanism of borehole collapse and fracture, and provide a reference for the further research of seepage-stress-chemical-damage coupling of wall rock. acknowledgements he study was supported by the natural science foundation of china (51174036, 41102182) and the natural science foundation of hubei province (2011cdb008). references [1] yu, b.h., wang, z.z., guo, b., borehole unstability theory of shale and its research progress, drilling and production technology, 30(3) (2007) 16-20. [2] chen, m., yu, g., chenvert, m.e., et al., chemical and thermal effects on wellbore stability of shale formation, spe 71366 (2001). [3] jia, s.p., zou, c.s., wang, y.z., numerical analysis of construction process of petroleum drilling based on thermalhydro-mechanical coupling, rock and soil mechanics, 33(2) (2012) 321-328. [4] han, g., maurice, b., dusseault, description of fluid flow around a wellbore with stress-dependent porosity and permeability, journal of petroleum science & engineering, 40 (2003) 1-16. [5] anthony, j.l., crook, yu, j.g., development of an orthotropic 3d elastoplastic material model for shale, spe/isrm 78238 (2002). [6] jiang, z.q., ji, l.j., the laboratory study on behavior of permeability of rock along the complete stress-strain path, chinese journal of geotechnical engineering, 23(2) (2001) 153-156. [7] yi, s.m., zhu, z.d., introduction to damage mechanics of fractured rock mass, beijing: science press (2005). [8] zheng, s.h., research on coupling theory between seepage and damage of fractured rock mass and its application to engineering. phd thesis, wuhan. institute of rock and soil mechanics, the chinese academy of sciences (2004). [9] jiang, t., study on constitutive model of coupled damage-permeability process of brittle rock based on micromechanics, phd thesis, nanjing: hohai university (2006). [10] yang, t.h., infiltrate character, theory, model and application in rock failure process, beijing: science press (2004). [11] zhao, y.l., coupling theory of seepage-damage-fracture in fractured rock masses and its application, phd thesis, central south university (2009). [12] selvadurai, a.p.s., shirazi, a., mandel-cryer effects in fluid inclusions in damage-susceptible poroelastic geologic media, computers and geotechnics, 31 (2004) 285-300. [13] zhang, w.h., jin, w.l., li, h.b., stability analysis of rock slope based on random damage mechanics, journal of hydraulic engineering, 36(4) (2005) 413-419. [14] jia, s.p., chen, w.z., yu, h.d., et al., research on seepage-stress coupling damage model of boom clay during tunnelling, rock and soil mechanics, 30(1) (2009) 19-26. [15] wei, l.d., yang, c.h., xu, w.y., study of statistical seepage model and statistical damage constitutive model of rock, rock and soil mechanics, 25(10) (2004) 1527-1536. [16] xue, x.h., non-linear damage mechanics theory of coupled fluid-solid with numerical analysis of geo-materials, phd thesis, zhejiang university (2008). t http://dx.medra.org/10.3221/igf-esis.27.09&auth=true http://www.gruppofrattura.it microsoft word numero_54_art_09_2863 i. el-sagheer et alii, frattura ed integrità strutturale, 54 (2020) 128-135; doi: 10.3221/igf-esis.54.09 128 finite element analysis of the behavior of bonded composite patches repair in aircraft structures i. el-sagheer, m. taimour, m. mobtasem, amr a. abd-elhady department of mechanical design, faculty of engineering, university of helwan, egypt islam.ismaail@gmail.com, maitaimour@gmail.com, mariamzaki1818@gmail.com, aaa_elhady@yahoo.com, https://orcid.org/0000-0002-1298-281x hossam el-din m. sallam materials engineering department, university of zagazig, zagazig, egypt hem_sallam @yahoo.com, https://orcid.org/0000-0001-9217-9957 abstract. this paper aims to analyze the multi-effects of the glass fiber reinforced polymer (gfrp) composite patch to repair the inclined cracked 2420-t3 aluminum plate. three-dimensional finite element method (fem) was used to study the effect of gfrp composite patch with different stacking composite laminate sequence, [0°]4, [90o]4, [45o]4, [0o/45o]2s, and [0°/90°]2s, on the crack driving force, j-integral, of inclined cracked 2420-t3 aluminum plate. furthermore, the effects of patch geometry, number of layers, single or double side patch, and crack inclination angle are described. the present results show that the patch has a high effect in case of a crack in pure mode i. the effectiveness of the composite patch increases with increasing the crack length. moreover, the efficiency of the composite patch has a high effect by changing the fiber orientation, the number of layers, and the single or double side patch. keywords. mode of mixity; j-integral; aluminum alloy; 3-d fem; composite repair patch. citation: el-sagheer, i., taimour, m., mobtasrm, m., abd-elhady, a., sallam, h., finite element analysis of the behavior of bonded composite patches repair in aircraft structures, frattura ed integrità strutturale, 54 (2020) 128-135. received: 04.07.2020 accepted: 10.08.2020 published: 01.10.2020 copyright: © 2020 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. introduction n aircraft applications, service life is very important. it is affected by structural and aerodynamic loads as landing, take off, fatigue, ground handling, and bird strikes. the repair or reinforcement method is essential to improve service life without increasing the budget. composite patches are used over the cracked area that prevents or delays crack propagation due to the reduction in the stress intensity factor [1–9]. fiber-reinforced polymers are used to repair the cracked structure because they have many advantages like high strength to weight ratio, fatigue resistance, corrosion i https://youtu.be/jjwbauc6xrw i. el-sagheer et alii, frattura ed integrità strutturale, 54 (2020) 128-135; doi: 10.3221/igf-esis.54.09 129 resistance, and good mechanical properties [4,5]. bouiadjra et al. [6] compared the performances of using composite and metallic patches for repairing cracked aircraft structures. they found that the composite patch is more efficient than a metallic patch for reducing the stress intensity factor of cracked aircraft structures. many researchers used a composite patch to repair the cracked structure and they studied different parameters to improve the efficiency of the composite patch. ramji and srilakshmi [4] studied single and double-sided patch on center-cracked aluminum panel. furthermore, madani et al. [5] used the single and double composite patch to repair the crack exerted from circular notch by using the finite element method. brighenti et al. [7, 8] used the biology-based method to obtain the optimal shape of patch repairs for cracked plates. huang and feng [9] used the finite element method to study the effect of carbon fiber reinforced polymer (cfrp) repaired for edge crack under different failure modes. sadek et al. [10] compared between carbon-epoxy and boron-epoxy patches with four different shapes: circular, rectangular, trapezoid, and elliptical. moreover, ouinas et al. [11] compared boron-epoxy and graphite-epoxy patches and also studied the effects of the adhesive properties and patch size on crack propagation. deghoul et al. [12] studied the effect of temperature and patch shapes on the bonded composite repair performance of the aluminum plate. gu et al. [13] studied the effect of number, material, and thickness of composite-patch repair to transfer load from cracked structures and to reduce the crack mouth opening displacement (cmod) of cracked structures. furthermore, budhe et al. [14] studied the effect the environmental influence (moisture, temperature, humidity etc.) on the mechanical performance of composite repair bonded joint. thus, kaddouri et al. [15] used the numerical finite element method to study the effect of geometrical and mechanical of boron/epoxy composite patch to reduce the driving force stress intensity factor of the central cracked plate. they found that the stress intensity factor at the repaired crack with the composite patch is highly influenced by changing the geometrical and mechanical of boron/epoxy composite patch. ounias et al. [16] used a bonded boron/epoxy composite patch to repair a cracked aluminum plate with imperfection in the bond between the patch and the plate. they showed that the stress intensity factor is affected by these debonds. furthermore, the effect of welded [17] or bonded [18–22] stiffeners on the crack tip deformation was studied previously by the authors. the present work is an attempt to investigate numerically the effect of patch geometry, the number of patch layers, single or double patch, stacking composite laminate sequence of repair patch, and crack inclination angle that can improve the composite repairing patch of a cracked plate. the gfrp is used to repair a plate with an inclined crack with different crack lengths. furthermore, the inclination angle is changed to cover the effect of the composite repairing patch on the mode i or mixed mode fracture of the cracked plate. moreover, the stacking composite laminate sequence and geometry of the patch are changed. figure 1: specimen details-cracked plate, adhesive and patch t  2420-t3 aluminum plate  gfrp composite patch adhesive layer     a w  h     l   applied load  e i. el-sagheer et alii, frattura ed integrità strutturale, 54 (2020) 128-135; doi: 10.3221/igf-esis.54.09 130 geometrical model ig. 1 shows the main plate, adhesive, and patch geometry analyzed in this work. the main plate contains an inclined crack with different crack length, a, and inclined angle, ,. gfrp composite patch consists of many layers with different stacking composite laminate sequence (where: 90o fiber angle means the fiber is perpendicular to the load direction as shown in fig. 1) to study the effect of the number of layers, n, and stacking composite laminate sequence on the efficiency of the patch. furthermore, the height of the patch, h, has several values to show if it has any effect on the efficiency of the patch. the patch width, e, is selected to be less than the maximum crack length to study the effect of the repair if the crack length exceeds the width of the patch. it is worth noting that the efficiency of the patch may be depending on the patch width, patch position on the cracked plate, and the thickness of the adhesive material. all these parameters will be taken into consideration by the authors in future work. the gfrp composite patch is bonded to the main plate by using the adhesive layer with the same cross-section of the patch and has a thickness of 0.1 mm. all geometric data for the main plate, adhesive layer, and composite patch can be shown in tab. 1. finite element modeling he three-dimensional finite element method (3d-fem) is utilized to show the effect of gfrp patch on repairing the cracked aluminum plate under static load. abaqus/standard code [23] is used to simulate the present model to study the effectiveness of a composite patch on the driving force of a cracked aluminum plate. the validation and accuracy of the present models were checked previously by the authors [18, 19, 22]. symbol value description l 100 the height of the main plate, (mm) w 50 the width of the main plate, (mm) t 2 the thickness of the main plate, (mm) a/w 0.02, 0.05, 0.1, 0.2, 0.3, 0.4, 0.5 and 0.6 inclined crack length ratio (mm/mm)  0o, 15o, 30o, 45o and 60o inclined crack angle e 20 gfrp composite patch width, (mm) h 30, 40, 50 and 60 gfrp composite patch height. (mm) tp 0.2 the thickness of each layer of the patch (mm) ta 0.1 the thickness of the adhesive (mm) [0], [0/90], [90], [45], [0/45] stacking composite laminate sequence n 0, 2, 4, 6 number of patch layers table 1: gfrp composite repaired inclined cracked 2420-t3 aluminum plate geometry. a 2024-t3 aluminum alloy has been selected for material of the main plate and it was simulated as isotropic material with mechanical properties tabulated in tab. 2. the glass fiber reinforced epoxy polymer, gfrp is used as a material of the patch and it was modeled as a composite layup in the property module in abaqus/standard [23]. the gfrp composite material’s unidirectional stiffness properties were listed in tab. 2. furthermore, the adhesive layer simulated as isotropic material with mechanical property described in tab. 2. the mechanical properties of the 2024-t3 aluminum alloy, glass epoxy composite repair wrap material and film adhesive epoxy fm 73 are taken from ref. [12]. uniform axial tensile stress of 120 mpa was acting on the plate as shown in fig. 1. the composite patches are bonded on the surface of the plate covering crack. the layers of the composite patch are assumed as a complete bond on each other. furthermore, film adhesive epoxy was used to bond the composite patch on the aluminum plate by using the tie contact option in the abaqus/standard. the contour integral method is used to compute the value of j-integral [17, 18]. in the present model, c3d8r: an eightnode linear brick was used to mesh each element of the main plate, adhesive, and the composite patch. the refining process of mesh was carried out to assure that results are not dependent upon the size of the element. a complete mesh of a composite repaired aluminum plate model is shown in fig. 2. f t i. el-sagheer et alii, frattura ed integrità strutturale, 54 (2020) 128-135; doi: 10.3221/igf-esis.54.09 131 symbol value property glass epoxy composite repair wrap material’s properties e11 27.82 young's modulus in fiber direction (gpa) e22 5.83 young's modulus in the transverse direction (gpa) (in y direction) e33 5.83 young's modulus in the transverse direction (gpa) (in z direction) g12 2.56 in-plane shear modulus (gpa) (x-y plane) g13 2.56 in-plane shear modulus (gpa) (x-z plane) g23 2.24 in-plane shear modulus (gpa) (y-z plane) 12 0.31 poisson's ratio (x-y plane) 13 0.31 poisson's ratio (x-z plane) 23 0.41 poisson's ratio (y-z plane) aluminum 2024-t3 material’s properties e 71.02 young’s modulus (gpa)  0.3 poisson’s ratio film adhesive fm 73 material’s properties e 1.83 young’s modulus (gpa)  0.33 poisson’s ratio table 2: material properties of 2024-t3 aluminum alloy, adhesive layer and glass/epoxy composite patch [12] figure 2: typical mesh of the present model. results and discussion he main objective of the present work is to study the efficiencies of the repaired bonded gfrp composite patch on the reduction of the crack tip driving forces, j-integral value. therefore, in the present figures, the values of jintegral are presented in normalized form, i.e. the values of the repaired joints divided by the unrepaired ones. fig. 3 shows the effect of stacking composite laminate sequence of the repaired patch on the values of normalized j-integral of the inclined crack with a constant number of layers, n = 4, and at h = 50 mm with different crack length. the value of normalized j-integral decreases by increasing the value of crack length ratio, a/w, as shown in fig. 3. that means the efficiency of the composite patch increases by increasing the values of crack length. this may be attributed that when the t i. el-sagheer et alii, frattura ed integrità strutturale, 54 (2020) 128-135; doi: 10.3221/igf-esis.54.09 132 crack length increases, the composite patch can more close the crack. moreover, the best effect of stacking composite laminate sequence of the repaired patch is at uniaxial direction [0]4 whatever the value of the inclined crack angle. on the other hand, the composite patch which has stacking composite laminate sequence [90o] is the lowest efficiency as shown in fig. 3. when a/w reaches 0.4, crack length (a) is equal to the width of the patch (e), i.e. a vertical dash line is drawn at a/w = 0.4. after that the curves show the effect of the patch on the cracked plate when the crack length is higher than patch width. the effect of the patch is still very high till the end of the curves. this means that the patch has a higher efficiency to reduce the value of crack tip driving force, j-integral, even if the crack length exceeds the width of the patch. from fig. 3, it can be concluded that the gfrp composite patch is a good method to repair the cracked plate regardless its crack length. figure 3: the effect of stacking composite laminate sequence of repair patch on the values of normalized j-integral of edge repaired cracked plate with: (a)  = 0o, (b)  = 15o, (c)  = 30o and (d)  = 45o fig. 4 a and b depict the effect of the inclined crack angle, , on the value of normalized j-integral of edge repaired cracked plate for different stacking composite laminate sequence of repair patch [0]4 and [0/45]2s respectively, with a constant value of h and n. from fig. 4 it can be concluded that the composite patch has the highest efficiency when  = 0º, while it has the worst efficiency when  = 45º. fig. 5. shows the effect of patch height, h, on the values of normalized j-integral of edge repaired cracked plate with stacking composite laminate sequence [0]4. from fig. 5 it can be seen that the height of the patch does not considerably affect the efficiency of the repair. fig. 6 illustrates the effect of numbers of patch layers n, on the values of normalized j-integral of edge repaired cracked plate versus a/w at h = 50,  = 0o and stacking composite laminate sequence [0]. as expected, it can be shown that the effect of composite patch increases with increasing the numbers of layers. as described in fig. 6 the numbers of layers improve the efficiency of the composite patch so that if another patch put at the other side of the composite patch can improve the effect of composite patch. fig. 7 shows a comparison between the effect of single and double patch on the 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 0 0.1 0.2 0.3 0.4 0.5 0.6 n o rm a ll iz e d  j ‐i n te g ra l a/w [0]4 [45]4 [90]4 [0/45]2s [0/90]2s (a)       h = 50 & n = 4 &  = 0 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 0 0.1 0.2 0.3 0.4 0.5 0.6 n o rm a ll iz e d  j ‐i n te g ra l a/w [0]4 [45]4 [90]4 [0/45]2s [0/90]2s (b)         h = 50 & n = 4 &  = 15 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 0 0.1 0.2 0.3 0.4 0.5 0.6 n o rm a ll iz e d  j ‐i n te g ra l a/w [0]4 [45]4 [90]4 [0/45]2s [0/90]2s (c)    h = 50 & n = 4 &  = 30 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 0 0.1 0.2 0.3 0.4 0.5 0.6 n o rm a ll iz e d  j ‐i n te g ra l a/w [0]4 [45]4 [90]4 [0/45]2s [0/90]2s (d) h = 50 & n = 4 &  = 45 i. el-sagheer et alii, frattura ed integrità strutturale, 54 (2020) 128-135; doi: 10.3221/igf-esis.54.09 133 values of normalized j-integral of edge repaired cracked plate versus a/w. the use of a double composite patch has a higher effect than using a single composite patch as shown in fig. 7. figure 4: the effect of inclined crack angle, , on the values of normalized j-integral of edge repaired cracked plate with: (a) [0]4 and (b) [0/45]2s. figure 5: the effect of patch height length, h, on the values of normalized j-integral of edge repaired cracked plate with: (a)  = 0o and (b)  = 60o. figure 6: the effect of patch number of layers, n, on the values of normalized j-integral of edge repaired cracked plate. 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 0 0.1 0.2 0.3 0.4 0.5 0.6 n o rm a ll iz e d  j ‐i n te g ra l a/w 0  15  30 45 (a)        h = 50 & n = 4 & [0]4   0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 0 0.1 0.2 0.3 0.4 0.5 0.6 n o rm a ll iz e d  j ‐i n te g ra l a/w 0 15 30 45  (b)   h = 50 & n = 4 & [0/45]4  0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0 0.1 0.2 0.3 0.4 0.5 0.6 n o rm a ll iz e d  j ‐i n te g ra l a/w 30 40 50 60 (a)             =  0 &  [0]4 h, mm 0 0.2 0.4 0.6 0.8 1 1.2 0 0.1 0.2 0.3 0.4 0.5 0.6 n o rm a ll iz e d  j ‐i n te g ra l a/w 30 40 50 60 (b)        =  60 &  [0]4 h, mm 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 0 0.1 0.2 0.3 0.4 0.5 0.6 n o rm a ll iz e d  j ‐i n te g ra l a/w 2 4 6 n h = 50 & [0]4 &  = 0 i. el-sagheer et alii, frattura ed integrità strutturale, 54 (2020) 128-135; doi: 10.3221/igf-esis.54.09 134 figure 7: shows a comparison between the effect of single and double patch on the values of normalized j-integral of edge repaired cracked plate. conclusion rom the present numerical work, it can be concluded that:  the efficiency of the composite patch is depend on the fiber orientation with respect to the load direction, where the higher efficiency of composite repaired patch happens when it has a higher stiffness in the direction parallel to the load direction (mode-i), whatever the value of the inclined crack angle.  the patch has the highest efficiency in case of a crack in pure mode i for the present study.  the gfrp composite patch is a good candidate method to repair the cracked plate even if the crack length exceeds the width of the patch.  the efficiency of the composite patch improves when the number of layers increases.  the use of a composite patch on the other side of the cracked plate increases the efficiency of the composite patch to restrain the crack propagation.  the height of the composite patch does not considerably affect the efficiency of the repair of the cracked plate. references [1] makwana, a., shaikh, a.a., bakare, a.k., saikrishna, c. (2018). 3d numerical investigation of aluminum 2024-t3 plate repaired with asymmetric and symmetric composite patch, mater. today proc., 5(11), pp. 23638–23647. [2] hosseini-toudeshky, h., mohammadi, b. (2009). thermal residual stresses effects on fatigue crack growth of repaired panels bounded with various composite materials, compos. struct., 89(2), pp. 216–223. [3] hosseini-toudeshky, h., mohammadi, b. (2009). mixed-mode numerical and experimental fatigue crack growth analyses of thick aluminium panels repaired with composite patches, compos. struct., 91(1), pp. 1–8. [4] ramji, m., srilakshmi, r. (2012). design of composite patch reinforcement applied to mixed-mode cracked panel using finite element analysis, j. reinf. plast. compos., 31(9), pp. 585–595. [5] madani, k., touzain, s., feaugas, x., benguediab, m., ratwani, m. (2009). stress distribution in a 2024-t3 aluminum plate with a circular notch, repaired by a graphite/epoxy composite patch, int. j. adhes. adhes., 29(3), pp. 225–233. [6] bouiadjra, b.b., benyahia, f., albedah, a., bouiadjra, b.a.b., khan, s.m.a. (2015). comparison between composite and metallic patches for repairing aircraft structures of aluminum alloy 7075 t6, int. j. fatigue, 80, pp. 128–135. [7] brighenti, r., carpinteri, a., vantadori, s. (2006). a genetic algorithm applied to optimisation of patch repairs for cracked plates, comput. methods appl. mech. eng., 196(1–3), pp. 466–475. [8] brighenti, r. (2007). patch repair design optimisation for fracture and fatigue improvements of cracked plates, int. j. solids struct., 44(3–4), pp. 1115–1131. [9] huang, c., chen, t., feng, s. (2019). finite element analysis of fatigue crack growth in cfrp-repaired four-point bend 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0 0.1 0.2 0.3 0.4 0.5 0.6 n o rm a ll iz e d  j ‐i n te g ra l a/w single patch double patch h = 50 & n = 4 & [0]4 &  = 0 f i. el-sagheer et alii, frattura ed integrità strutturale, 54 (2020) 128-135; doi: 10.3221/igf-esis.54.09 135 specimens, eng. struct., 183, pp. 398–407. [10] sadek, k., aour, b., bachir bouiadjra, b.a., fari bouanani, m., khelil, f. (2018).analysis of crack propagation by bonded composite for different patch shapes repairs in marine structures: a numerical analysis. international journal of engineering research in africa, vol. 35, trans tech publ, pp. 175–184. [11] ouinas, d., bouiadjra, b.b., serier, b., saidbekkouche, m. (2007). comparison of the effectiveness of boron/epoxy and graphite/epoxy patches for repaired cracks emanating from a semicircular notch edge, compos. struct., 80(4), pp. 514–522. [12] deghoul, n., errouane, h., sereir, z., chateauneuf, a., amziane, s. (2019). effect of temperature on the probability and cost analysis of mixed-mode fatigue crack propagation in patched aluminium plate, int. j. adhes. adhes., 94, pp. 53–63. [13] gu, l., kasavajhala, a.r.m., zhao, s. (2011). finite element analysis of cracks in aging aircraft structures with bonded composite-patch repairs, compos. part b eng., 42(3), pp. 505–510. [14] budhe, s., banea, m.d., de barros, s. (2018). bonded repair of composite structures in aerospace application: a review on environmental issues, appl. adhes. sci., 6(1), pp. 3. [15] kaddouri, k., ouinas, d., bouiadjra, b.b. (2008). fe analysis of the behaviour of octagonal bonded composite repair in aircraft structures, comput. mater. sci., 43(4), pp. 1109–1111. [16] ouinas, d., bouiadjra, b.b., himouri, s., benderdouche, n. (2012). progressive edge cracked aluminium plate repaired with adhesively bonded composite patch under full width disbond, compos. part b eng., 43(2), pp. 805–811. [17] abd-elhady, a.a. (2013). effect of location and dimensions of welded cover plate on stress intensity factors of cracked plates, ain shams eng. j., 4(4), pp. 863–867. [18] abd-elhady, a.a., sallam, h.e.-d.m., mubaraki, m.a. (2017). failure analysis of composite repaired pipelines with an inclined crack under static internal pressure, procedia struct. integr., 5, pp. 123–130. [19] abd-elhady, a.a., sallam, h.e.-d.m., alarifi, i.m., malik, r.a., el-bagory, t.m.a.a. (2020). investigation of fatigue crack propagation in steel pipeline repaired by glass fiber reinforced polymer, compos. struct., 242, pp. 112189. [20] el-emam, h.m., salim, h.a., sallam, h.e.m. (2017). composite patch configuration and prestress effect on sifs for inclined cracks in steel plates, j. struct. eng., 143(5), pp. 4016229. [21] el-emam, h.m., salim, h.a., sallam, h.e.-d.m. (2016). composite patch configuration and prestraining effect on crack tip deformation and plastic zone for inclined cracks, j. compos. constr., 20(4), pp. 4016002. [22] abd-elhady, a.a., sallam, h.e.-d.m. (2017). discussion of “fatigue behavior of cracked steel plates strengthened with different cfrp systems and configurations” by hai-tao wang, gang wu, and jian-biao jiang, j. compos. constr., 21(3), pp. 7016004. [23] systèmes, d. 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/hrv (za stvaranje adobe pdf dokumenata najpogodnijih za visokokvalitetni ispis prije tiskanja koristite ove postavke. stvoreni pdf dokumenti mogu se otvoriti acrobat i adobe reader 5.0 i kasnijim verzijama.) /hun 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can be opened with acrobat and adobe reader 5.0 and later.) >> /namespace [ (adobe) (common) (1.0) ] /othernamespaces [ << /asreaderspreads false /cropimagestoframes true /errorcontrol /warnandcontinue /flattenerignorespreadoverrides false /includeguidesgrids false /includenonprinting false /includeslug false /namespace [ (adobe) (indesign) (4.0) ] /omitplacedbitmaps false /omitplacedeps false /omitplacedpdf false /simulateoverprint /legacy >> << /addbleedmarks false /addcolorbars false /addcropmarks false /addpageinfo false /addregmarks false /convertcolors /converttocmyk /destinationprofilename () /destinationprofileselector /documentcmyk /downsample16bitimages true /flattenerpreset << /presetselector /mediumresolution >> /formelements false /generatestructure false /includebookmarks false /includehyperlinks false /includeinteractive false /includelayers false /includeprofiles false /multimediahandling /useobjectsettings /namespace [ (adobe) (creativesuite) (2.0) ] /pdfxoutputintentprofileselector /documentcmyk /preserveediting true /untaggedcmykhandling /leaveuntagged /untaggedrgbhandling /usedocumentprofile /usedocumentbleed false >> ] >> setdistillerparams << /hwresolution [2400 2400] /pagesize [612.000 792.000] >> setpagedevice microsoft word numero_37_art_42 u. muhin et alii, frattura ed integrità strutturale, 37 (2016) 318-324; doi: 10.3221/igf-esis.37.42 318 focused on fracture mechanics in central and east europe study of the influence between the strength of antibending of working rolls on the widening during hot rolling of thin sheet metal u. muhin, s. belskij lipetsk state technical university, lipetsk, russia, nemistade@mail.ru t. koynov university of chemical technology and metallurgy, sofia toni309@koinov.com abstract. based on the variation principle of jourdan was developed a mathematical model of the process of widening freely in hot rolling of thin sheet metal. the principle applies to rigid-plastic materials and for the cinematically admissible area of speeds. the developed model allows to study the distribution of the widening on the length of the deformation zone depending on the parameters of the rolling process and sheet metal. results are obtained, characterizing the size of the widening and effectiveness of the process control on tension at the entrance and exit from the stand. the widening is dependent on the strength of anti bending. keywords. widening; anti bending; hot rolling; thin sheet; model a theoretical analysis of the process of broadening or theoretical analysis of sheet rolling, in particular, the process of broadening of the metal in the deformation zone, successfully using the energy method, based on the beginning of the possible changes of the deformed state (beginning of lagrange). it is a kind of variation principle jourdain, according to which the variation of the flow velocity of the metal to be in the focus of the plastic deformation. jourdain's variation equation for the plastic deformation zone is written as follows:       s n i is is n v dsvdsvd 1 0)(   , (1) where:    0 dv the speed potential; t and h the intensity of shear stress and shear rate; n  , v  the total stress on the surface s with unit outward normal n  and the appropriate movement speed; f u. muhin et alii, frattura ed integrità strutturale, 37 (2016) 318-324; doi: 10.3221/igf-esis.37.42 319 iv the velocity jump at ithe cut surface is ;  a symbol of variation; s the yield stress in shear. for rigid-plastic medium (1) is rewritten as follows:       s n i is is n s dsvdsvd 1 0)(   (2) the first integral (2) is the power of internal resistance, the second power of the external forces on the borders of the center the forces of friction between the rolls and the strip, front and rear tension, the third power cut. when using the ritz variation equation for the case of rolling jourdain with tension in the expanded form is written as follows [1]:   054321   nnnnn aj , (3) where: n1 the power of internal resistance; n2 power sliding friction forces; n3 forces cut power; n4 power forward tension; n5 power adjustable tension; aj variable parameters. under the sign of differentiation is the expression for the total power rolling. to describe the process of broadening the focus of the plastic deformation in the calculated use the circuit shown in fig. 1. hotbed of plastic deformation is divided into two areas the zone and the zone timing lag. form edge (dashed line) approximated by two straight segments for the zone and the zone timing lag. in accordance with the scheme of the following symbols: yx vvvv ,,, 10 entrance and exit strip speed and projection velocity metal side edge on the axis x and y, respectively; 1010 ,,,,, bbbhhh íí the thickness and half-width of the entrance and the neutral section and the output, respectively; íx, the length of the deformation zone and the zone of advance. the equations that describe the shape of the side edges of the strip in the hearth of plastic deformation can be written as follows: a) for the area lead íxx 0 ; and b)  xxí for the zone gap   í tîï x x bxb )(1)( 0   ,   x tt bxb í t í t îò     11 1)( 0  where: .,,,, 001 00  í íít t t x tbbbbbb b b b b       from kinematic considerations we obtain the following conditions for the edge: a) for the area lead íxx 0 , b) for the zone gap  xxí í t êð x y x bb v v   , í t êð x y x b v v     . for every material point of the current coordinate (x, y) determined in accordance with [2-3] following law changes the flow velocity of the metal: a) for the area lead íxx 0 ; b) for the zone gap  xxí u. muhin et alii, frattura ed integrità strutturale, 37 (2016) 318-324; doi: 10.3221/igf-esis.37.42 320 p îïí t x y xb y x bb v v        )( , p îòí t x y xb y x b v v          )( , (4) where p the variable parameter. speed vx is determined by the law of the constancy of the second volumes: cos111000 ííâxxx bhvbhvbhvbhv  , (5) where: vathe peripheral speed of the work roll;  neutral corner; r radius of the work roll; 2 1cos        r xí . figure 1: design scheme. using well-known relations of the theory of plasticity, and acting in the same way as in [2-3], we find an expression for the intensity of the strain rate, the capacity of the internal resistance and friction, shear and tension. compared with the model [2-3] in the developed model will be power cut in the neutral section and the power of the front and back tension. obtain a system of three equations:                        0 )( 0 )( 0 54321 54321 54321 nnnnn b nnnnn b nnnnn p t , (6) system (6) is a mathematical model of the process of broadening the rolled strip, which can be used to study the distribution of the broadening in the deformation as a function of various parameters of rolling and strip, including the tension. u. muhin et alii, frattura ed integrità strutturale, 37 (2016) 318-324; doi: 10.3221/igf-esis.37.42 321 experimental study of the process of broadening o test the developed model, an experiment was conducted in a laboratory mill (diameter work rolls 120 mm). we rolled lead samples without tension, after the front end of the sample from the roll gap dwell, the rolls were bred, and the sample removed for measurement. conditions and results of the experiment are shown in tabs. 1 3. n of exp. 0h , mm 02b , mm 1h , mm 12b , mm h , mm b2 ,mm äåôîðì ,mm 1 10.1 30.1 8.15 31.4 1.95 1.3 15.0 2 10.0 15.4 7.8 16.8 2.2 1.4 16.0 table 1: experimental conditions distance from the inlet section, mm 0 3.0 6.0 9.0 12.0 15.0 )(2 xb , mm 30.1 30.45 30.8 31.1 31.3 31.4 table 2: measuring the width of the sample in the deformation zone (experiment 1). distance from the inlet section, mm 0 4.0 7.0 10.0 13.0 16.0 )(2 xb , mm 15.4 15.8 16.2 16.6 16.7 16.8 table 3: measurer width of the sample in the deformation zone (experiment 2). the results of theoretical calculations of the experiments are presented in tab. 4 and figs. 2 and 3. n of exp. äåôîðìl , mm íx , mm tb2 , mm b2 , mm exp.theory relative error,% 1 15.3 5.2 1.1 1.37 -0.07 -5.4 2 16.25 4.4 1.16 1.28 0.12 8.6 table 4: the results of theoretical calculations. figure 2: comparison of the experimental and calculated data (a) experiment 1; b) experiment 2). in fig. 2 a and b shows: a thin line – experiments data, and colon the result of a theoretical calculation. to study the effect of tension on the broadening of the two cases were calculated by application alternating front and back tension. in both cases, the specific tension was assumed to be 20% of the yield strength in tension. at this point, you must cast the remark i.ya.tarnovskogo [1] on a constant value by varying the tension of the full value of broadening, only t u. muhin et alii, frattura ed integrità strutturale, 37 (2016) 318-324; doi: 10.3221/igf-esis.37.42 322 then can the correct application of the jordan’s principle. the results of calculation are shown in figs. 3a and 3b. figure 3: effect of the anterior and posterior tension on broadening (the conditions of experiment 1, b) the conditions of experiment 2). thick line corresponds to the distribution of outbreak strain broadening without tension, dashed by applying only the front tension, fine just by applying back tension. theoretical calculation of the behavior of the side edges of the deformation zone by applying tension corresponds to practical results. for example, the independence of the broadening of the front tension v.n.vydrina noted in [4] and v.p.kalinina [5]. the uneven distribution of stresses on the specific bandwidth and broadening e now turn to the eq. (3) it consists of different signs power front tension, and power adjustable tension. according to this equation, the value of broadening for the combination of thickness and tension when these power offset each other, must be equal to the broadening of the rolling without tension. however, numerous experimental studies have shown that the value of broadening the rolling with front and rear tension less than the rolling without tension. the question arises of how these facts are consistent with the energy balance equation. it can be assumed that the application is the cause of tension in the eq. (3) additional capacity of the forces acting on the inlet and outlet sections of the deformation zone. to test this hypothesis using the software package nisa/display firm emrc (usa) finite element stress fields were built in the plate, one side of which is fixed on the movement, and the other is uniformly loaded with tensile stress. entrenchment simulates the output section of the deformation zone. the stress field for the case of uniformly distributed applications tension within the bandwidth of the deformation zone is shown in fig. 4. it can be seen that the distribution of the tensile stress at the exit of the deformation zone has a pronounced unevenness, which generally can be described as a function. )(yx   . this non-uniformity due to the appearance of power, called the power consumed bandwidth on the accumulation of potential energy [6,7], which is bringing a band of the deformation zone. its value is calculated as follows:  b x sïîò dy e hvn 0 2 11 2   . (7) this power should appear in eq. (3), together with the power of the front tension. in addition, tension band to which a tension, characterized by compressive stresses in the direction perpendicular to the rolling direction, which also influence the decrease of the broadening of the band at rolling with tension. similar reasoning applies to the back tension. changing the amount of force bending of the work rolls promotes redistribution of specific tension in width rolled strip. this changes the balance of power, and, therefore, changes the value of broadening (fig. 5). w u. muhin et alii, frattura ed integrità strutturale, 37 (2016) 318-324; doi: 10.3221/igf-esis.37.42 323 figure 4: distribution of tensile stress. figure 5: impact of the work roll bending efforts on the distribution of specific tensions at the entrance and exit of deformation zone u. muhin et alii, frattura ed integrità strutturale, 37 (2016) 318-324; doi: 10.3221/igf-esis.37.42 324 when reducing the effort antibend f1 or increasing efforts further work roll bending f2 tensile stress in the marginal areas of the rolled strip reduced thus broadening of the band increases. conversely, an increase in effort antibend f1 or reduction efforts f2 additional bending tensile stress in the marginal areas increased thus broadening of the band decreases. conclusions athematical model of broadening rolled bands is developed and confirmed experimentally. the model allows to investigate the distribution of broadening along the source of plastic deformation, depending on the parameters of the strip rolling. it is shown that the tension decreases with the broadening of hot rolled sheet. it is shown that the hot-rolled sheet with a tension force of bending of the work rolls is effective. references [1] tarnovskij, y., rimm, e.r., broadening and power consumption while rolling in smooth rolls with tension, trans. ferrous metallurgy, 7 (1964) 96-103, (in russian). [2] belskij, s.m., tretjakov, b.a., barishev, v.v., kudinov, s.v., the study of the formation of slab width in the roughing mill broadband, trans. ferrous metallurgy, 1 (1998) 24-29, (in russian). [3] skorohodov, v.n., chernov, p.p., muhin, u.a., belskij, s.m., a mathematical model of the process of broadening the free rolling bands, steel, 3 (2001) 38-40, (in russian). [4] vidrin, v.n., batin, u.t., effect of tension (backwater) to transverse strain, vn vidrin, ed., proceedings of the theory and rolling technology, chelyabinsk, release 54(1968) 220-224, (in russian). [5] celikov, a.i., tomlenov, a.d., zuzin, v.i. at al., the theory of rolling, handbook, moscow, metallurgy, 1982, (in russian). [6] grigorian, g.g., kocar, s.l., jeleznov, u.d., accounting schemes in the analysis of deformation in the process of forming sheet rollingtrans. of high schools. ferrous metallurgy, 7 (1976) 88-92 (in russian). [7] shatalov, r.l., koinov, t.a., litvinova, n.n., automation of technological rolling processes and heat treatment of metals and alloys. publisher. metallurgy, moscow, (2010), in russian m << /ascii85encodepages false /allowtransparency false /autopositionepsfiles true /autorotatepages /none /binding /left /calgrayprofile (dot gain 20%) /calrgbprofile (srgb iec61966-2.1) /calcmykprofile (u.s. web coated \050swop\051 v2) /srgbprofile (srgb iec61966-2.1) /cannotembedfontpolicy /error /compatibilitylevel 1.4 /compressobjects /tags /compresspages true /convertimagestoindexed true /passthroughjpegimages true /createjobticket false /defaultrenderingintent /default /detectblends true /detectcurves 0.0000 /colorconversionstrategy /cmyk /dothumbnails false /embedallfonts true /embedopentype false /parseiccprofilesincomments true /embedjoboptions true /dscreportinglevel 0 /emitdscwarnings false /endpage -1 /imagememory 1048576 /lockdistillerparams false /maxsubsetpct 100 /optimize true /opm 1 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/hrv (za stvaranje adobe pdf dokumenata najpogodnijih za visokokvalitetni ispis prije tiskanja koristite ove postavke. stvoreni pdf dokumenti mogu se otvoriti acrobat i adobe reader 5.0 i kasnijim verzijama.) /hun 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can be opened with acrobat and adobe reader 5.0 and later.) >> /namespace [ (adobe) (common) (1.0) ] /othernamespaces [ << /asreaderspreads false /cropimagestoframes true /errorcontrol /warnandcontinue /flattenerignorespreadoverrides false /includeguidesgrids false /includenonprinting false /includeslug false /namespace [ (adobe) (indesign) (4.0) ] /omitplacedbitmaps false /omitplacedeps false /omitplacedpdf false /simulateoverprint /legacy >> << /addbleedmarks false /addcolorbars false /addcropmarks false /addpageinfo false /addregmarks false /convertcolors /converttocmyk /destinationprofilename () /destinationprofileselector /documentcmyk /downsample16bitimages true /flattenerpreset << /presetselector /mediumresolution >> /formelements false /generatestructure false /includebookmarks false /includehyperlinks false /includeinteractive false /includelayers false /includeprofiles false /multimediahandling /useobjectsettings /namespace [ (adobe) (creativesuite) (2.0) ] /pdfxoutputintentprofileselector /documentcmyk /preserveediting true /untaggedcmykhandling /leaveuntagged /untaggedrgbhandling /usedocumentprofile /usedocumentbleed false >> ] >> setdistillerparams << /hwresolution [2400 2400] /pagesize [612.000 792.000] >> setpagedevice microsoft word numero_38_art_45 a. eberlein et alii, frattura ed integrità strutturale, 38 (2016) 351-358; doi: 10.3221/igf-esis.38.45 351 the effect of varying loading directions and loading levels on crack growth at 2dand 3d-mixed-mode-loadings a. eberlein, h.a. richard institue of applied mechanics, university of paderborn, pohlweg 47-49, 33098 paderborn, germany eberlein@fam.upb.de abstract. while product’s operation the loading situation commonly changes. the local loading situation on an existing crack then can shift to a combined loading, composed of mode i, mode ii and mode iii, and consequently influence the product’s durability significantly. this influence on further fatigue crack growth and structures’ failure can be positive or negative. present article describes and discusses the effect of varying loading directions from mode ito 2d-mixed-mode-loading as well as from mode ito mixedmode i + iii-loading. moreover, experiments on varying loading levels are performed by interspersing mixed-mode block loads in cyclic mode i base load, cyclic mode ii base load as well as in cyclic mode iii base load. keywords. 3d-mixed-mode; loading directions; loading levels; ctsrspecimen; 3d-fatigue crack growth. citation: eberlein, a., richard h. a., the effect of varying loading directions and loading levels on crack growth at 2dand 3d-mixed-mode-loadings, frattura ed integrità strutturale, 38 (2016) 351-358. received: 01.06.2016 accepted: 30.06.2016 published: 01.10.2016 copyright: © 2016 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. introduction arts in many technical applications often are subjected to variable cyclic loading. while service life these products due to transportation, assemblage, site of operating as well as in use experience time-dependent loadings, so-called service loadings, which result from single over-/underloads, variable loading levels as well as changing loading directions. thereby the crack growth can both accelerate and retard. anyway, the fatigue crack growth is not only controlled by the current loading parameters δk and r-ratio, but also by the loading history. due to the fact that different loading changes interact with each other during a service loading, the characterisation of the whole interaction effects on fatigue crack growth under variable loading amplitude are generally investigated separately by means of four different categories. sander [1] classify these in single over-/underloads, over-/underload sequences, block loading and service loading. the experimental investigations in this contribution study the fatigue crack growth under variable loading amplitude by interspersing block loading into a constant baseline-level loading. block loadings represent several succeeding overloads. generally, block loadings are distinguished between high-low, low-high or the appropriate combination low-high-low sequences [2]. within the block loadings the r-ratio can be different. therefore block loadings can be classified in three types of low-high-low sequences, whereby always one characteristic parameter during the transition from one to the next block load is constant. the characteristic parameters are kbl,min = const., r = const. and δkbl = const. in this paper the block loading tests were performed with a constant r-ratio, as fig. 1 shows. p a. eberlein et alii, frattura ed integrità strutturale, 38 (2016) 351-358; doi: 10.3221/igf-esis.38.45 352 figure 1: crack retardation and acceleration while low-high-low block load sequence; (a) parameters of a low-high-low block load sequence with constant r-ratio; (b) schematic a-n-curve after a low-high-low block load sequence according to richard and sander [2]. hereby the definition of characteristic variables can be extracted from fig. 1 a). a crucial influence on component’s durability has the level of the block loading. as within this experiments also mixed-mode-block loadings are interspersed, the level of the block loading is defined by the block loading ratio rv,block as follows: k r k v,block v,block bl,max  (1) kv,block is the maximum comparative stress intensity factor during the block loading and kbl,max is the maximum stress intensity factor of the baseline-level loading. the maximum comparative stress intensity factor can be determined by: k k k k k i,block 2 2 2 v,block i,block ii,block iii,block 1 5.336 4 2 2        (2) such a block loading test with a number of block cycles nblock causes after a short acceleration phase a higher crack growth rate during the block loading. after that a retardation phase of the crack growth follows, which continues till the crack, if able to propagate, reaches its crack growth rate (da/dn)bl of the baseline-level loading before the block loading (shown in fig. 1 b)). apart from changing loading levels also changing in essential loading as well as changing loading directions can appear while product’s operation. consequently, a variation of the global loading can effect a locally changing of the crack fracture mode e. g. from pure mode i-loading to an in-plane mixed-modeor a 3d-mixed-modeloading situation. ctsr-specimen and loading device he experimental tests were performed using the ctsr-specimen (compact-tension-shear-rotation-specimen) with the corresponding loading device developed by schirmeisen [3] and can be also found in eberlein [4]. fig. 2 illustrates the specimen’s geometry (fig. 2 a)) and the adjustment of the fracture modes (mode i, mode ii and mode iii) by the loading angles α and β on the loading device. the corresponding loading device basically consists of two sickles and two inboard so-called turrets, where the specimen is fixed. by varying the loading angle α in the range of 0° till 90° by 15°-steps the mode i-ratio to mode ii respectively mode iii is regulated. a mounting position of the loading device of α = 0° corresponds with a pure mode i-loading at the crack front of the ctsr-specimen, as in fig. 2 b) illustrated. mounting the loading device with the specimen in a position t a. eberlein et alii, frattura ed integrità strutturale, 38 (2016) 351-358; doi: 10.3221/igf-esis.38.45 353 of α = 90° and varying the loading angle β by rotating the turrets in the range of 0° till 90° by 15°-steps the loading situation at the crack front of the specimen can be adjusted from pure mode ii-loading to pure mode iii-loading, as fig. 2 b) shows. are both loading angles in a range between 15° and 75° this concept enables investigating the crack growth under 3d-mixed-mode-loading conditions. figure 2: ctsr-specimen and corresponding loading device. (a) specimen’s geometry and dimensions: length l, width w, initial crack length a0, thickness t and ligament in sectional view; (b) adjustment of loading angles α and β on loading device. experiments ithin this contribution different series of crack growth experiments were performed. therefor the ctsrspecimens were made from aluminium alloy 7075-t651. the different test series are described below in detail. series of experiments in the first test series various in-plane mixed-mode-ratios with δki ≠ 0 and δkii ≠ 0 respectively spatial mixed-moderatios with δki ≠ 0 and δkiii ≠ 0 by shifting the loading device are adjusted after a mode i-crack growth of δa = 3.5 mm under constant cyclic stress intensity factor δki = const. after changing the loading direction the tests again start under constant cyclic loading force conditions δf = const., from which a cyclic comparative stress intensity factor δkv results, which is equivalent to the cyclic stress intensity factor δki just before changing the loading direction. thereby similar loading conditions before and after the mixed-mode-adjustment are given at the crack front. the second test series investigate possible impacts of changing loading levels on crack growth by interspersed mixedmode-block loads in mode i-, mode iias well as in mode iii-base loads. in mode iand in mode ii-base load the cyclic stress intensity factor is δki,bl = δkii,bl = 90 mpa mm . whereas the level of mode iii-base load is δkiii,bl = 160 mpa mm . the r-ratio of the base load is 0.1. after a crack growth of δa = 2.0 mm in the base loading the mixed-mode-block loads are interspersed for nblock = 10,000 cycles with a block loading ratio of rv,block = 2.0 (cf. eq. 1). thereafter the loading direction is changed again to the base loading by shifting the loading device. varying loading directions with constant cyclic comparative stress intensity factor δkv starting from a pure mode i-loading fig. 3 shows the impacts on fatigue crack growth after changing loading directions from mode i-loading to mode i and mode ii loading combinations. the region, where δkv is nearly constant w a. eberlein et alii, frattura ed integrità strutturale, 38 (2016) 351-358; doi: 10.3221/igf-esis.38.45 354 85 mpa mm is encircled. with increasing mode ii-part a growing crack growth retardation is noticeable. the crack kinks directly after changing loading direction in a new orientation and propagates significantly slower at kii/ki-ratios ≥ 0.99. the greatest effect in retardation resp. the greatest advantage in durability causes changing loading direction from pure mode i-loading to pure shear loading (mode ii). figure 3: a-n-curves before and after change of mode i-mode ii-loading direction. similar investigations on the impact of mode i-mode ii-changing loading directions on an initial mode i-loading already were performed by sander and richard [5] and richard et al. [6]. the findings herein agree with their results. however possible effects of changing loading directions on 3d-mixed-mode were not investigated therein. therefore fig. 4 illustrates the influence of mode i-mode iii-changing loading directions on an initial mode i-loading. due to the mode iii-loading part hereby a significantly higher cyclic comparative stress intensity factor of δkv = 140 mpa mm was chosen, so that the crack still is able to propagate under pure mode iii-loading. this high loading level explains the steep slope of the mode i-crack growth. here the end crack length of a = 7 mm is reached after approximately n = 70,000 cycles by kiii/ki-ratios < 0.57. figure 4: a-n-curves before and after change of mode i-mode iii-loading direction. similar to the in-plane mixed-mode-changing loading directions the mode i-mode iii-changing loading directions also show an increasing crack growth retardation with growing mode iii-part. at the moment of changed loading direction the crack realigns by twisting out of its initial position. the crack growth process at mixed-mode-loadings in presence of a. eberlein et alii, frattura ed integrità strutturale, 38 (2016) 351-358; doi: 10.3221/igf-esis.38.45 355 mode iii-loading component is completely different to other combined loading conditions without mode iii-part. along the crack front several fatigue cracks initiate facetedly, so that each facet forms a new crack front. fig. 5 presents typical fractured surfaces resulting from performed experiments depending on the mode iii-part of the kiii/(ki + kiii)-ratio. figure 5: facet formation depending on mode iii-part. conspicuous within this experiments is that no facet formation occurs below a kiii/(ki + kiii)-ratio of 0.26. many small and wispy facets start to create from a kiii/(ki + kiii)-ratio of 0.37 (that means kiii/ki = 0.57) and coarsen their shape with increasing mode iii-part obviously. the number of facets concurrently declines up to a few big facets as the fractured surface resulting from pure mode iii-loading in fig. 5 depicts. concerning the crack deflection angles the changing loading directions show no unexpected impacts. fig. 6 a) shows the measured crack kinking angle φ0 compared to the hypothesis by richard [7]. hereby just the changing loading direction from pure mode ito pure mode ii-loading exhibits a ca. 10° lower crack kinking angle as the hypothesis predicts. the comparison of the crack twisting angle ψ0 with the hypothesis by richard [7] in fig. 6 b) shows overall good accordance. figure 6: crack deflection angles φ0 and ψ0 depending on the ratio of stress intensity factor. (a) crack kinking angle φ0 depending on kii/(ki + kii); (b) crack twisting angle ψ0 depending on kiii/(ki + kiii). influence of varying loading levels on mode i-, mode iiand mode iii-crack growth different crack growth retardations due to mode i-, mode i-mode iiiand mode iii-block loads on mode i-base load are shown in fig. 7. the kiii/ki-ratios denoted in fig. 7 are valid for the point of interspersing the block loads. in fig. 7 it can be seen that the greatest crack growth retardation occurs by a pure mode i-block load. in this case the crack even arrests. because even after 107 cycles a crack growth was not measured anymore. to maintain the overview the x-axis is cut here at n = 1.5 ·106 cycles. due to the mode i-block load a bigger plastic zone at the crack front generates wherein residual compressive stresses form, which close the crack flanks. moreover, the effect of retardation decreases with increasing mode iii-part in order that a pure mode iii-block load shows no influence on a crack growth in mode i-base load. this is affiliated to the displacement of the crack flanks. under pure mode iii-loading the biggest displacement of the crack flanks happens in z-direction and not as under mode i-loading in y-direction (perpendicular to the crack propagation). accordingly, it can be assumed that a mode iii-block load leads to twisting the plastic zone in z-direction so that a mode iii-block load does not influence a crack in mode i-base load. sander and richard [8] already showed for in-plane mixed-mode-block loads that the plastic zone turns due to a shear loading (mode ii). moreover, the retardation effect on a mode i-loaded crack thereby decreases or is not existing anymore. the impacts a. eberlein et alii, frattura ed integrità strutturale, 38 (2016) 351-358; doi: 10.3221/igf-esis.38.45 356 of interspersed mode i-mode ii-block loads on mode ii-base load are shown in fig. 8. here a pure mode ii-block load causes the greatest retardation effect on the crack growth in mode ii-base load. figure 7: crack growth retardation due to interspersed mode i-mode iii-block loads in mode i-base load. figure 8: crack growth retardation due to interspersed mode i-mode ii-block loads in mode ii-base load. indeed, the displacement according to amount of the crack flanks increases in y-direction with increasing mode icomponent of the mode i-mode-ii-block load and enlarges the plastic zone at the crack front, but the residual compressive stresses does not retard the crack growth in mode ii-base load. the reason for that is the displacement of the crack flanks in mode ii-base load, which takes place parallel to the crack growth direction. in comparison to the crack growth in mode iand mode ii-base load the crack growth in mode iii-base load due to interspersed mode i-, mode iiias well as mode i-mode iii-block load combinations shows varyingly strong retardations (see fig. 9). indeed, it can be observed that the retardation effect decreases with increasing ki/kiii-ratio, nevertheless the influence of the mode i-component in the mode i-mode iii-block loads on a mode iii-loaded crack is still existing. a part of typical fractured surfaces developed within the experiments are presented in fig. 10. the fractured surfaces show for interspersed mode i-mode ii-block loads in mode ii-base load expected characteristics. due to a pure mode i-block load a significant step on the fractured surface arises (fig. 10 a)). concerning the crack growth direction a crack kinking angle φ0 of ca. 63° was measured before as well as after interspersing the block load. the fractured surfaces resulting from interspersed mode i-mode iii-block loads in mode iii-base load, shown in fig. 10 b), reveal several facets and are relatively jagged. in conclusion, it can be registered that the greatest retardation effects respectively the greatest advantages a. eberlein et alii, frattura ed integrità strutturale, 38 (2016) 351-358; doi: 10.3221/igf-esis.38.45 357 in durability are obtained, if the crack loading mode of the block loading coincides with the crack loading mode of the base loading. figure 9: crack growth retardation due to interspersed mode i-mode iii-block loads in mode iii-base load figure 10: typical fractured surfaces by varying loading levels. (a) mode i-mode ii-block loads in mode ii-base load; (b) mode i-mode iii-block loads in mode iii-base load. references [1] sander, m., einfluss variabler belastung auf das ermüdungsrisswachstum in bauteilen und strukturen. fortschritt-berichte vdi: reihe 18, mechanik, bruchmechanik, band 287, vdi-verlag, düsseldorf, (2003). [2] richard, h. a., sander, m., ermüdungsrisse. 3. auflage, vieweg+teubner, wiesbaden, (2012). [3] schirmeisen, n.-h., risswachstum unter 3d-mixed-mode-beanspruchung. fortschritt-berichte vdi: reihe 18, mechanik, bruchmechanik, band 335, vdi-verlag, düsseldorf, (2012). [4] eberlein, a., einfluss von mixed-mode-beanspruchung auf das ermüdungsrisswachstum in bauteilen und strukturen. fortschritt-berichte vdi: reihe 18, mechanik, bruchmechanik, band 344, vdi-verlag, düsseldorf, (2016). a. eberlein et alii, frattura ed integrità strutturale, 38 (2016) 351-358; doi: 10.3221/igf-esis.38.45 358 [5] sander, m., richard, h. a., effects of block loading and mixed mode loading on the fatigue crack growth, in: proceedings of the 8th international fatigue congress (fatigue 2002), blom a. f. (ed.), stockholm, sweden, (2002) 2895-2902. [6] richard, h. a., linnig, w., henn, k., fatigue crack propagation under combined loading. forensic engineering 3 (1991) 99-109. [7] richard, h. a., fulland, m., sander, m., theoretical crack path prediction. fat. & frac. of eng. mat. & struc., 28 (2005) 3-12. [8] sander, m., richard, h. a., finite element analysis of fatigue crack growth with interspersed mode i and mixed mode overloads. international journal of fatigue, 28 (2005) 905-913. << /ascii85encodepages false /allowtransparency false /autopositionepsfiles true /autorotatepages /none /binding /left /calgrayprofile (dot gain 20%) /calrgbprofile (srgb iec61966-2.1) /calcmykprofile (u.s. web coated \050swop\051 v2) /srgbprofile (srgb iec61966-2.1) /cannotembedfontpolicy /error /compatibilitylevel 1.4 /compressobjects /tags /compresspages true /convertimagestoindexed true /passthroughjpegimages true /createjobticket false /defaultrenderingintent /default /detectblends true /detectcurves 0.0000 /colorconversionstrategy /cmyk /dothumbnails false /embedallfonts true /embedopentype false /parseiccprofilesincomments true /embedjoboptions true /dscreportinglevel 0 /emitdscwarnings false /endpage -1 /imagememory 1048576 /lockdistillerparams false /maxsubsetpct 100 /optimize true /opm 1 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/hrv (za stvaranje adobe pdf dokumenata najpogodnijih za visokokvalitetni ispis prije tiskanja koristite ove postavke. stvoreni pdf dokumenti mogu se otvoriti acrobat i adobe reader 5.0 i kasnijim verzijama.) /hun 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/pdfxoutputintentprofileselector /documentcmyk /preserveediting true /untaggedcmykhandling /leaveuntagged /untaggedrgbhandling /usedocumentprofile /usedocumentbleed false >> ] >> setdistillerparams << /hwresolution [2400 2400] /pagesize [612.000 792.000] >> setpagedevice microsoft word numero_26_art_13 t. ingrassia et alii, frattura ed integrità strutturale, 26 (2013) 132-142; doi: 10.3221/igf-esis.26.13 132 behaviour of a speargun with a novel muzzle comportamento di un fucile subacqueo con testata innovativa t. ingrassia, m. mucera, v. nigrelli dipartimento di ingegneria chimica, gestionale, informatica, meccanica università degli studi di palermo viale delle scienze, 90128 palermo (italy) tommaso.ingrassia@unipa.it abstract. the paper presents the results of a numerical and experimental investigation performed on a barrel of a speargun equipped with two kinds of muzzle. in particular, a standard muzzle for speargun (having an elastic propulsion) has been compared with an innovative one called ‘roller’. this new muzzle is equipped with two rollers and special bands. the rubber bands, fixed at the lower side of the barrel, run through the rollers and are engaged in suitable seats of the shaft. these bands are, therefore, longer than the traditional ones and, consequently, with equal force applied by the diver, the roller speargun has a longer range. thanks to the particular geometry of the new muzzle, one of the front constraints of the elastic bands is moved to the lower part of the barrel or the handle. as a consequence, the scheme of the loads applied on the speargun remarkably changes passing from a standard muzzle to a roller one. all that has a great influence on the level of deformation of the barrel and, consequently, on the accuracy of the shot. because of the low velocity of the spear (if compared with the firearms), in fact, the accuracy of the shoot if strongly influenced by the barrel bending due to the forces applied by means of the elastic bands. in this paper it is experimentally evaluated the bending of the barrel equipped both with the innovative muzzle and with the traditional one in order to compare their performances. the experimental analysis of the barrel was performed by electrical strain gauges suitably located at the section with the highest values of the strains. in order to find the barrel section with the highest strain values where to locate the strain gauges, a preliminary numerical fem analysis has been performed. the loads and constraints scheme has been evaluated both for the standard and the new muzzle. in particular, the forces due to the elastic bands, their application points and directions have been experimentally obtained. to speed up the process of numerical simulation, without invalidating the results reliability, simplified fem models have been used. in particular, a very accurate model of the barrel has been shaped, whereas the models of the muzzles and the handle have been simplified. the forces due to the elastic bands, experimentally obtained, have been applied on the fem models. the maps of the maximum and minimum principal strains have allowed to find the area with the highest strain values, placed in rear part of the barrel (near the handle). the strain values experimentally measured on the speargun have been very similar to the ones calculated by means of the numerical simulations. that demonstrates the developed fem models are very reliable and can ben used to predict the performances of the speragun under different loads conditions. the speargun with the new roller muzzle shows very lower strain values if compared with the ones measured in the standard one. nevertheless, considering the two spearguns have different elastic bands setup, it has been thought the comparison of their performances should be made hypothesizing the same maximum force applied during the speargun charge. this condition, moreover, could be really obtained by changing the kind of the http://www.gruppofrattura.it http://dx.medra.org/10.3221/igf-esis.26.13&auth=true t. ingrassia et alii, frattura ed integrità strutturale, 26 (2013) 132-142; doi: 10.3221/igf-esis.26.13 133 elastic bands in the speargun with the roller muzzle. for this reason, during the results analysis phase, the strain values measured on the roller speargun have been ‘normalized’ by increasing them of a value equal to the ratio of the maximum forces due to the rubber bands. the data post processing has allowed to evaluate the forces and the bending moments on the barrels with the standard muzzle and the roller one. results show the barrel with the innovative muzzle has, also considering equal forces applied by the diver, a lower bending than the barrel with a traditional muzzle. to evaluate the maximum deflection of both the spearguns, a new numerical simulation has been set up. in particular, in this fem analysis, the roller speargung has been loaded with a maximum force comparable with the standard one. the obtained results show that the standard speargun has a higher value of the maximum deflection respect to the roller one. since higher deflection values of the barrel make worse the accuracy of the shot, these results demonstrate the novel speargun can be more precise than the traditional one. sommario. in questo lavoro vengono presentati i risultati relativi ad un’indagine numerico-sperimentale condotta sul fusto di un fucile subacqueo dotato di una nuova testata. questa testata, chiamata roller, è munita di due rotelle e di elastici particolari. quest’ultimi vengono fissati nella parte inferiore del fusto, si avvolgono attorno alle rotelle e infine si impegnano in un’apposita cava ricavata sull’asta del fucile. gli elastici utilizzati con questo tipo di testata sono molto più lunghi di quelli tradizionali e ciò permette, a parità di forza applicata dall’utente, una maggiore gittata. a causa della bassa velocità di avanzamento dell’asta, se confrontata con le armi da fuoco terrestri, la precisione del tiro è fortemente influenzata dall’inflessione del fusto dovuta alle forze applicate dagli elastici. in questo lavoro è stata sperimentalmente valutata la sollecitazione sul fusto di un fucile attrezzato prima con testata standard e, successivamente, con testata roller al fine di confrontarne il comportamento sotto carico e, di conseguenza, la prestazione. l’analisi sperimentale è stata condotta usando estensimetri elettrici posizionati opportunamente nella sezione con valori di deformazione più elevati, individuata preventivamente per mezzo di analisi fem. i risultati mostrano che il fusto con la testata innovativa ha, anche a parità di forza applicata dall’utente durante la fase di carica del fucile, una minore deformazione rispetto al fusto con testata tradizionale. questo rende il nuovo fucile più preciso di quello tradizionale. keywords. speargun; strain gauges; fem; roller muzzle. introduzione om'è noto, in balistica la precisione di tiro è influenzata dal rinculo [1-2] che determina l’arretramento e l’impennamento del fusto o della canna da sparo. nei fucili subacquei si è costretti a lanciare aste di grande massa per vincere con la loro inerzia le forti resistenze idrodinamiche. d'altra parte la massa del fucile non si può aumentare troppo per non ridurre il suo brandeggio e la sua maneggiabilità nell'acqua. nella balistica subacquea il rapporto tra la massa dell'asta e quella del fucile che rincula è circa 1/5 (400 grammi di massa dell'asta rapportata a 2 chili circa di massa del fucile), mentre nelle armi da sparo il rapporto può essere inferiore a 1/100 [1]. per tale motivo i fucili subacquei sono molto svantaggiati rispetto alle armi da sparo terrestri e richiedono uno studio molto più approfondito sotto il profilo della stabilità nel tiro. gli attrezzi da lancio devono nascere molto più equilibrati, il momento di rinculo deve risultare il più piccolo possibile, altrimenti l'impennamento del fusto può rendere molto imprecisa la traiettoria dell’asta dato che quest’ultima, essendo meno veloce dei proiettili delle armi da sparo, segue per un tempo più lungo la guida sul fusto e ne subisce le deviazioni rispetto all'allineamento di mira. la precisione del tiro è però influenzata anche dall’inflessione del fusto che può essere determinata, nel caso di fucili a propulsione elastica, dalla forza esercitata dagli elastici. tale inflessione, all’atto dello sgancio dell’asta, tende rapidamente ad annullarsi con conseguente disturbo della traiettoria di quest’ultima. c http://dx.medra.org/10.3221/igf-esis.26.13&auth=true http://www.gruppofrattura.it t. ingrassia et alii, frattura ed integrità strutturale, 26 (2013) 132-142; doi: 10.3221/igf-esis.26.13 134 in questo lavoro è stato eseguito uno studio numerico-sperimentale, tramite modelli fem ed estensimetri elettrici, finalizzato alla valutazione delle sollecitazioni agenti sul fusto di due fucili a propulsione elastica (arbalete): il primo attrezzato con testata classica, il secondo con testata roller. in particolare, dopo aver rilevato i carichi agenti sul fucile, sono state eseguite delle analisi fem per individuare le zone con i più elevati valori di deformazioni nelle quali, durante la successiva fase di rilevazione sperimentale, sono stati installati gli estensimetri. i risultati ottenuti sono stati opportunamente elaborati al fine di ottenere valori confrontabili a parità di forza massima applicata durante la fase di carica del fucile. materiali e metodi ’arbalete in studio (fig. 1) è un fucile da pesca subacquea a propulsione elastica. esso è composto da quattro principali elementi: fusto, impugnatura (o calcio), testata ed elastici. figura 1: arbalete geronimo pro 105 della cressi sub. figure 1: cressi sub geronimo pro 105 speargun. il fusto è l’elemento d’unione tra l’impugnatura, contenente il congegno di sparo, e la testata. è realizzato in lega di alluminio ed ha una lunghezza in centimetri (che dà il nome al tipo di fucile) pari a 105. la struttura tubolare del fusto ha una sezione variabile in forma e dimensione. l’impugnatura è una delle parti più importanti del fucile in quanto influenza la qualità del tiro. essa è stampata a caldo con tecnopolimeri e rappresenta il vincolo dell’asta. la testata costituisce il vincolo d’estremità degli elastici. le testate analizzate in questo studio sono due: standard di tipo chiuso (fig. 2) e roller (fig. 3). figura 2: testata standard chiusa. figure 2: standard muzzle. la testata roller utilizzata è caratterizzata da una coppia di rotelle con diametro 30 mm che ruotano su cuscinetti di vetro [3]. grazie alla particolare geometria, essa permette lo spostamento di uno dei vincoli di estremità degli elastici dalla testata alla parte inferiore del fusto o dell’impugnatura. l http://dx.medra.org/10.3221/igf-esis.26.13&auth=true http://www.gruppofrattura.it t. ingrassia et alii, frattura ed integrità strutturale, 26 (2013) 132-142; doi: 10.3221/igf-esis.26.13 135 figura 3: testata roller. figure 3: roller muzzle. come naturale conseguenza, lo schema dei carichi applicati sul fucile cambia considerevolmente passando da una testata standard ad una roller. tutto ciò ha una notevole influenza sullo stato di deformazione della struttura del fusto e, conseguentemente, sulla qualità e precisione del tiro. gli elastici utilizzati sono realizzati in poliisoprene a basso rilassamento degli sforzi [4], le cui principali caratteristiche meccaniche sono presentate nella tab. 1. tensione di rottura a trazione 28 mpa allungamento a rottura 550-600% modulo di young (100%) 1.5 mpa tabella 1: caratteristiche del poliisoprene utilizzato per gli elastici del fucile. table 1: mechanical properties of the polyisoprene used in the elastic bands. gli elastici si impegnano in un apposito intaglio praticato sull’asta mediante un archetto metallico detto ogiva. dipendentemente dal tipo di allestimento scelto è possibile utilizzare uno o più elastici. nel caso in studio vengono utilizzati più elastici per entrambi gli allestimenti. in quello con testata standard sono stati utilizzati: una coppia di elastici avvitati all'estremità ed un circolare che passa attraverso un foro presente sulla testata stessa (fig. 4). il fucile ‘roller’, invece, è stato attrezzato con una coppia di elastici circolari (fig. 5) fissati inferiormente sull’elsa (anello di protezione) del grilletto. esc figura 4: arbalete con testata chiusa. figure 4: speargun with standard muzzle. figura 5: arbalete con testata roller. figure 5: speargun with roller muzzle. http://dx.medra.org/10.3221/igf-esis.26.13&auth=true http://www.gruppofrattura.it t. ingrassia et alii, frattura ed integrità strutturale, 26 (2013) 132-142; doi: 10.3221/igf-esis.26.13 136 determinazione dei carichi agenti le forze esercitate dagli elastici sono state rilevate sperimentalmente tramite un dinamometro meccanico analogico della tiedemann collegato all’ogiva degli elastici, simulando la reale procedura di carica del fucile. i punti di applicazione e le direzioni dei carichi sono stati determinati per mezzo di rilievo della geometria. gli schemi di carico analizzati sono mostrati nelle fig. 6 e 7. figura 6: schema di carico del fucile con testata standard. figure 6: standard muzzle speargun loads scheme. figura 7: schema di carico del fucile con testata roller. figure 7: roller muzzle speargun loads scheme. i valori, le direzioni e i bracci d’azione delle forze sono riportati per il fucile con testata standard e con testata roller rispettivamente nelle tab. 2 e 3. elastici forza (n) angolo α angolo β e1 (mm) e2 (mm) coppia 1150 0,4° 4 circolare 1100 1,3° 3 tabella 2: fucile normale – valore delle forze esercitate dagli elastici, degli angoli e dei bracci con cui esse agiscono sulla struttura schematizzata in fig. 6. table 2: standard speargun – values of the forces of the elastic bands, angles and arms. elastici forza (n) angolo α angolo β e1 (mm) e2 (mm) roller 1 650 1,09° 22 roller 2 650 1,31° 25 tabella 3: fucile roller – valore delle forze esercitate dagli elastici, degli angoli e dei bracci con cui esse agiscono sulla struttura schematizzata in fig. 7. table 3: roller speargun – values of the forces of the elastic bands, angles and arms. studio numerico e sperimentale l confronto del comportamento del fusto del fucile con testata normale e con testata roller è stato effettuato rilevando i massimi valori di deformazione del fusto mediante estensimetri elettrici a resistenza. i http://dx.medra.org/10.3221/igf-esis.26.13&auth=true http://www.gruppofrattura.it t. ingrassia et alii, frattura ed integrità strutturale, 26 (2013) 132-142; doi: 10.3221/igf-esis.26.13 137 procedura numerica per individuare la sezione con i valori più elevati (di trazione e compressione) di deformazione sulla quale installare gli estensimetri, si è preliminarmente eseguita una simulazione numerica impiegando un codice di calcolo agli elementi finiti (ansys workbench), largamente utilizzato in svariati settori come il biomeccanico [5], quello della sicurezza passiva [6-8], la caratterizzazione e ottimizzazione dei materiali compositi. nel presente lavoro, al fine di semplificare il processo di simulazione numerica, senza però inficiare l’attendibilità dei risultati, sono stati utilizzati modelli fem semplificati. in particolare, è stato utilizzato un modello del fusto perfettamente aderente al reale, mentre sono stati realizzati modelli semplificati delle due testate e dell’impugnatura. inoltre, non sono stati modellati gli elastici le cui azioni, tuttavia, sono state simulate attraverso l’applicazione delle forze secondo gli schemi di carico mostrati nelle fig. 6-7. le ulteriori condizioni al contorno hanno previsto, sia nel caso di testata standard che di testata roller, un vincolo di tipo incastro in corrispondenza dell’impugnatura (fig. 8). per la discretizzazione sono stati utilizzati elementi “brick” ad otto nodi ed elementi di contatto di tipo “shell” in corrispondenza delle interfacce fusto-testata e fusto-impugnatura. figura 8: modello fem del fucile roller: carichi e vincoli. figure 8: fem model of the roller speargun: loads and constraints. la mappatura delle deformazioni principali massima e minima permette di affermare che la zona con livelli di deformazione più elevati si trova, in entrambi i casi (testata standard e roller), a circa 1020 mm dall’estremità del fusto. in particolare, il valore assoluto massimo calcolato è relativo alla deformazione principale minima. le mappe delle deformazioni principali minime sono riportate nelle fig. 9-10. figura 9: mappa delle deformazioni principali minime nel fucile con testata standard. figure 9: map of the minimum principal strains on the speargun with standard muzzle. le mappe delle deformazioni lungo l’asse del fusto, nella zona con i livelli di deformazione più elevati, sono riportate in fig. 11. i valori sono sostanzialmente coincidenti con le deformazioni principali massima e minima. ciò permette di affermare che le deformazioni principali sono praticamente longitudinali. http://dx.medra.org/10.3221/igf-esis.26.13&auth=true http://www.gruppofrattura.it t. ingrassia et alii, frattura ed integrità strutturale, 26 (2013) 132-142; doi: 10.3221/igf-esis.26.13 138 figura 10: mappa delle deformazioni principali minime nel fucile con testata roller. figure 10: map of the minimum principal strains on the speargun with roller muzzle figura 11: mappa delle deformazioni lungo l’asse del fusto nella zona maggiormente deformata per fucile standard (a sx) e roller (a dx). figure 11: maps of the longitudinal strains in the highest strained area on the standard speargun (on the left) and the roller one (on the right). procedura sperimentale il rilievo sperimentale della deformazione nella sezione con i maggiori livelli di deformazione, distante 1020 mm dall’estremità del fusto (fig.12), è stato effettuato mediante n. 4 estensimetri elettrici a resistenza (er). figura 12: schema del posizionamento longitudinale (a sinistra) e trasversale (a destra) degli er. figure 12: scheme of the longitudinal (on the left) and transversal (on the right) positioning of the strain gauges. sulla base dei risultati numerici, gli estensimetri sono stati posizionati come mostrato nello schema di fig. 12, angolarmente distanti di 90° uno dall’altro e con gli assi longitudinali paralleli all’asse dell’asta. gli estensimetri utilizzati sono autocompensati per alluminio con grid resistance 120+/-0.6% ω, gadge factor (+2.120 +/0.5) e sono stati collegati ad una centralina ‘vischay p3’ utilizzando lo schema a quarto di ponte [9] (fig. 13). http://dx.medra.org/10.3221/igf-esis.26.13&auth=true http://www.gruppofrattura.it t. ingrassia et alii, frattura ed integrità strutturale, 26 (2013) 132-142; doi: 10.3221/igf-esis.26.13 139 figura 13: er installati sul fucile. figure 13: strain gauges on the speargun. per rilevare eventuali effetti di rilassamento degli sforzi negli elastici, le deformazioni sono state registrate per una durata di 300 secondi circa. gli andamenti delle deformazioni nel tempo rilevati dai quattro estensimetri per il fucile munito di testata standard e roller sono riportati rispettivamente nelle fig. 14 e 15. figura 14: grafico deformazioni-tempo nella prova per fucile standard. figure 14: strain vs time plots in standard speargun. figura 15: grafico deformazioni-tempo nella prova per fucile “roller”. figure 15: strain vs time plots in roller speargun. gli elastici non manifestano alcun effetto di rilassamento degli sforzi. http://dx.medra.org/10.3221/igf-esis.26.13&auth=true http://www.gruppofrattura.it t. ingrassia et alii, frattura ed integrità strutturale, 26 (2013) 132-142; doi: 10.3221/igf-esis.26.13 140 risultati valori di deformazione calcolati numericamente (nei punti corrispondenti ai centri degli estensimetri) e quelli rilevati sperimentalmente sono riportati, per fucile con testata standard e roller, nella tab. 4. tipo di testata valutazione est.1 (µm/m) est. 2 (µm/m) est. 3 (µm/m) est. 4 (µm/m) standard numerica -634 -185 -185 277 sperimentale -673 -175 -207 318 roller numerica -259 -101 -101 41 sperimentale -250 -105 -102 40 tabella 4: deformazioni sul fucile con testata standard e sul roller. table 4: strain values measured on the standard and roller spearguns. l’analisi dei dati presentati in tab. 4 permette di affermare che esiste un ottimo grado di correlazione fra i risultati sperimentali e quelli numerici. sul fucile con testata roller i livelli di deformazione sono molto minori rispetto a quelli rilevati per il fucile con testata standard. tuttavia, considerato che i fucili in studio sono equipaggiati con elastici differenti, si è ritenuto che un confronto efficace del comportamento dovesse effettuarsi presupponendo l’uguaglianza della forza massima esercitata (pari a 1150 n) durante la fase di carica dei fucili, potendo questa essere rappresentativa del livello di difficoltà di carica del fucile da parte dell’utente. tale condizione, fra l’altro, è realmente ottenibile cambiando tipologia di elastico nel fucile roller. per tale motivo le deformazioni rilevate sul roller sono state “normalizzate”, incrementandole del rapporto fra i valori delle forze massime esercitate dagli elastici (riportati nelle tab. 2 e 3). i valori di deformazione normalizzate sono presentati in tab. 5. est.1 (µm/m) est. 2 (µm/m) est. 3 (µm/m) est. 4 (µm/m) -442 -185 -180 70 tabella 5 – fucile roller – deformazioni normalizzate per il confronto. table 5: roller speargun – normalized strain values. l’analisi delle deformazioni misurate in corrispondenza dei quattro estensimetri permette di asserire che, in entrambi i casi (fucile standard e roller), il fusto è soggetto sostanzialmente ad una sollecitazione di compressione e di flessione con asse praticamente coincidente con l’asse x di fig. 12 (le deformazioni misurate dagli estensimetri 2 e 3, posizionati in modo diametralmente opposto lungo x, sono infatti paragonabili). al fine di confrontare il comportamento dei due fucili, si è calcolato il momento flettente mf agente. dalla risoluzione del sistema di eq. (1): 1 2 3 4 n fx n fy n fy n fx                        (1) dove: ε1, ε2, ε3 e ε4, sono le deformazioni misurate dai quattro estensimetri, si possono calcolare: εn, deformazione di compressione dovuta al carico normale p; εfx e εfy, deformazioni dovute rispettivamente alle sollecitazioni di flessione lungo gli assi x e y. note εn, εfx e εfy, è possibile valutare i corrispondenti valori delle tensioni σn, σfx e σfy, mediante la ben nota relazione costitutiva dei materiali con comportamento lineare elastico, assumendo un valore del modulo di young pari a 70.000 mpa (considerato che il fusto del fucile in studio è in alluminio). dai valori di tensione, si sono calcolati, nota la sezione i http://dx.medra.org/10.3221/igf-esis.26.13&auth=true http://www.gruppofrattura.it 141 t. ingrassia et alii, frattura ed integrità strutturale, 26 (2013) 132-142; doi: 10.3221/igf-esis.26.13 resistente (circolare cava con raggio esterno 15 mm e raggio interno 13mm), il carico normale alla sezione stessa, p, e il momento flettente mf. tali valori sono riassunti in tab. 6. standard roller p (n) 2265 2266 mf (n·mm) 40020 20750 tabella 6: carico normale (p) e momento flettente (mf) agente sui fucili. table 6: normal force (p) and bending moment (mf) on the spearguns. dai dati calcolati si evince che, a parità di carico massimo applicato dall’utente, il fucile dotato di testata standard è soggetto ad un momento flettente (mfstandard = 40020n mm) superiore rispetto a quello con testata roller pari a mfroller = 20750 n mm. il maggior valore di momento flettente, inoltre, determina una maggiore inflessione del fusto. tale affermazione è confermata dai risultati ottenuti da un’ulteriore analisi fem nella quale sul fucile roller sono stati incrementati i valori dei carichi agenti per renderli paragonabili a quelli agenti nel fucile standard. figura 16: mappa degli spostamenti lungo z nel fucile con testata standard. figure 16: standard speargun map of the displacements along the z axis. figura 17: mappa degli spostamenti lungo z nel fucile con testata roller. figure 17: roller speargun map of the displacements along the z axis. le mappe degli spostamenti presentate nelle fig. 16-17 dimostrano che, anche a parità di forza applicata dall’utente durante la fase di carica del fucile, la freccia massima nel caso di fucile standard ustandard ≈ 6.4 mm è superiore a quella calcolata per il roller uroller ≈ 2.8 mm. conclusioni n questo lavoro è stata eseguita un’indagine numerico-sperimentale al fine di confrontare il comportamento di due fucili subacquei, uno munito di testata standard, l’altro di testata roller. in particolare, dopo avere rilevato sperimentalmente i carichi agenti e individuato, per mezzo di analisi agli elementi finiti, la zona con i valori di i http://dx.medra.org/10.3221/igf-esis.26.13&auth=true http://www.gruppofrattura.it t. ingrassia et alii, frattura ed integrità strutturale, 26 (2013) 132-142; doi: 10.3221/igf-esis.26.13 142 deformazione più elevati, sono stati installati degli estensimetri elettrici per la rilevazione delle deformazioni nelle reali condizioni di carico. i dati rilevati sono stati opportunamente processati al fine di eseguire un confronto coerente fra le due differenti configurazioni, ragionando a parità di forza massima esercitata all’atto di carica del fucile. la procedura sviluppata, partendo dai valori di deformazioni rilevati, ha permesso di calcolare il momento flettente agente su entrambi i fucili, il quale è risultato di molto superiore nel caso di fucile standard (mfstandard = 40020 n·mm > mfroller = 20750 n·mm). inoltre, tramite simulazione fem, si è verificato che, a parità di forza massima applicata, l’inflessione del fucile standard è sensibilmente superiore a quella del roller. tale informazione è di particolare interesse se si tiene conto della balistica di un fucile subacqueo. in questo genere di armi, infatti, la bassa velocità di avanzamento dell’asta (rispetto alle armi da fuoco) costringe la stessa a seguire per un tempo più lungo la guida sul fusto, subendone le eventuali deviazioni rispetto all'allineamento di mira. elevati valori di inflessione del fusto, quindi, influenzano negativamente la precisione del tiro. conseguentemente, il fucile con testata roller è da preferire all’analogo con testata standard, per quanto riguarda l’influenza dell’inflessione sulla precisione del tiro. bibliografia [1] yao, y., simulation test system of gun recoil and numerical calculations, binggong xuebao/acta armamentarii, 22 (2) (2001) 152-155. [2] zong, s.-z., qian, l.-f., xu, y.-d., dynamic coupling analysis and optimization of gun recoil mechanism. binggong xuebao/acta armamentarii, 28 (3) (2007) 272-275. [3] chunfu, g., xueqing, b., shiju, e., wear experiments of glass ceramics and bearing steel, journal of rare earths, 25 (2) (2007) 327-329. [4] sreeja, t. d., kutty, s. k., cure characteristics and mechanical properties of natural rubber/reclaimed rubber blends, polymer plastics technology and engineering, 39 (3) (2000) 501-512. [5] ingrassia, t., nalbone, l., nigrelli, v., tumino, d., ricotta, v., finite element analysis of two total knee joint prostheses, international journal on interactive design and manufacturing, 7 (2) (2013) 91-101. [6] ingrassia, t., mancuso, a., virtual prototyping of a new intramedullary nail for tibial fractures, international journal on interactive design and manufacturing, 7 (3) (2013) 159-169. [7] ingrassia, t., nigrelli, v., design optimization and analysis of a new rear underrun protective device for truck, in: 8th international symposium on tools and methods of competitive engineering, tmce 2010, 2 (2010) 713-725. [8] ingrassia, t., nigrelli, v., buttitta, r., a comparison of simplex and simulated annealing for optimization of a new rear underrun protective device, engineering with computers, 29 (3) (2013) 345-358. [9] ajovalasit, a., the measurement of large strains using electrical resistance strain gages, experimental techniques, 36 (3) (2012) 77-82. http://dx.medra.org/10.3221/igf-esis.26.13&auth=true http://www.gruppofrattura.it microsoft word numero_29_art_20 r massabò, frattura ed integrità strutturale, 29(2014) 230-240; doi: 10.3221/igf-esis.29.20 230 focussed on: computational mechanics and mechanics of materials in italy influence of boundary conditions on the response of multilayered plates with cohesive interfaces and delaminations using a homogenized approach r. massabò university of genova, genova, italy roberta.massabo@unige.it abstract. stress and displacement fields in multilayered composites with interfacial imperfections, such as imperfect bonding of the layers or delaminations, or where the plies are separated by thin interlayers allowing relative motion, have large variations in the thickness, with characteristic zigzag patterns and jumps at the layer interfaces. these effects are well captured by a model recently formulated by the author for multilayered plates with imperfect interfaces and affine interfacial traction laws (massabò & campi, meccanica, 2014, in press; compos struct, 2014, 116, 311-324). the model defines a homogenized displacement field, which satisfies interfacial continuity, and uses a variational technique to derive equilibrium equations depending on only six generalized displacement functions, for any arbitrary numbers of layers and interfaces. the model accurately predicts stresses and displacements in simply supported, highly anisotropic, thick plates with continuous, sliding interfaces. in this paper the model is applied to wide plates with clamped edges and some inconsistencies, which have been noted in the literature for models based on similar approaches and have limited their utilization, are explained. a generalized transverse shear force is introduced as the gross stress resultant which is directly related to the bending moment in the equilibrium equations of multilayered structures with imperfect interfaces and substitutes for the shear force of single-layer theory. an application to a delaminated wide plate highlights the potential and limitations of the proposed model for the solution of fracture mechanics problems. keywords. composites; cohesive interfaces; delamination; plate theories. introduction tress and displacement fields in multilayered composites with interfacial imperfections, such as imperfect bonding of the layers or delaminations, or where the plies are separated by thin interlayers allowing relative motion, have large variations in the thickness, with characteristic zigzag patterns and jumps at the interfaces. these effects cannot be captured using classical firstor higher-order single-layer theories and require models based on a discrete-layer approach, where the number of unknowns is typically large and depends on the number of layers/interfaces and on the layer kinematic fields. this limits the range of problems which can be solved analytically and makes computational solutions necessary for most cases, in particular when the status of the interfaces evolves during loading due to delamination fracture [1-7]. zigzag theories [8-10] were originally proposed for multilayered systems with perfectly bonded interfaces in order to overcome the limitations of discrete-layer approaches and satisfy continuity of transverse and normal stresses at the s r massabò, frattura ed integrità strutturale, 29 (2014) 230-240; doi: 10.3221/igf-esis.29.20 231 interfaces. the theories, through the imposition of interfacial continuity conditions, define a homogenized displacement field which depends on a limited number of unknowns and is able to reproduce through-thickness zigzag patterns due to the material inhomogeneities. later, the zigzag theories were extended to describe plates and shells with imperfectly bonded, purely elastic interfaces in [11-14]. the extended theories however manifest a number of inconsistencies: (i) they are unable to reproduce the expected transitions in the internal gross stress resultants on varying the stiffness of the imperfect interfaces (first noted in [11,15,16]); (ii) they give rise to unrealistic effects in the transverse displacements, which are larger than those of fully debonded plates in partially bonded plates (this effect was defined shear-locking in [15]); (iii) they show some inconsistencies in plates with clamped edges (noted in [17]). recently the author formulated in [18,19] a theory which, starting from those in [11-14], extends the formulation to plates and beams with interfaces characterized by affine interfacial traction laws (to describe piecewise linear cohesive functions) and accounts for the energy contribution of the imperfect interfaces in the derivation of the equilibrium equations. this contribution was erroneously omitted in the original theories and in all theories derived later from the original models (see [18] for a list). corrected formulations of the models [11-14] are presented in the appendices in [18]. the accuracy of the theory proposed in [18,19] has been verified against exact 2d elasticity solutions in highly anisotropic, simply supported, multilayered plates, with continuous sliding interfaces and deforming in cylindrical bending. the model accurately describes stress and displacement fields in plates with different numbers of interfaces, equally and unequally spaced in the thickness, over the whole range of interfacial stiffnesses, from fully bonded to fully debonded. a limitation of the theory has been observed when dealing with very thick, highly anisotropic plates with compliant interfaces, where the shear deformations are underestimated in the derivation of the transverse displacements as a consequence of the assumed continuity between interfacial tractions and shear stresses. it is expected that this problem could be solved using a shear correction factor which depends on the interfacial properties (work in progress). in this paper, the issues noted in [17] in beams with clamped ends, where the zigzag theory proposed in [9,10] for fully bonded systems shows some apparent inconsistencies in the transverse shear force, are discussed; and the equilibrium equations derived in [19] for plates in cylindrical bending are restated to clarify the problem. the new formulation introduces a generalized transverse shear force, which is the gross stress resultant directly related to the bending moment in the equilibrium equations of multilayered plates with imperfect interfaces and substitutes for the shear force of singlelayer theory. finally, a delaminated cantilevered wide plate with a clamped edge is studied as a preliminary investigation of the applicability of the model to fracture mechanics problems. model onsider a rectangular multilayered plate of thickness h and in-plane dimensions 1l and 2 l l , with 1 2l l . a system of cartesian coordinates, 1 2 3 x x x , is introduced with the axis 3x normal to the reference surface of the plate, which is arbitrarily chosen, and measured from it (fig. 1). the plate consists of n layers exhibiting different mechanical properties and joined by 1n interfaces, which are described as mathematical surfaces where the material properties and the displacements may change discontinuously while the interfacial tractions are continuous. the layer k, where the index 1 ,..,k n is numbered from bottom to top, is defined by the coordinates 1 3 kx and 3 kx of its lower and upper interfaces, s( )k and s( )k , and has thickness ( )k h , fig. 1 (the k superscript in brackets identifies affiliation with layer k). each layer is linearly elastic, homogeneous and orthotropic with material axes parallel to the geometrical axes. the displacement vector of an arbitrary point of the plate at the coordinate  1 2 3x , , t x x x is  1 2 3 v , , t v v v w . the plate is subjected to distributed loads acting on the upper and lower surfaces, s and s , and on the lateral bounding surface, b , is in plane strain conditions parallel to the plane 2 3x x and deforms in cylindrical bending. in addition, the plate is assumed to be incompressible in the thickness direction and the interfaces to be rigid against mode i (opening) relative displacements. this latter assumption, which is often used in the literature, is rigorously correct only in problems where the conditions along the interfaces are purely mode ii. the assumption, however, is acceptable in the presence of continuous interfaces, when the interfacial normal tractions are small compared to the tangential tractions and interfacial opening is prevented, e.g. by a through-thickness reinforcement or other means. to describe cohesive delaminations under general mixed mode conditions, the general treatment, which has been proposed in [18], for plates, and in [19], for wide plates in cylindrical bending, and accounts for interfacial opening, must be applied. based on the c r massabò, frattura ed integrità strutturale, 29(2014) 230-240; doi: 10.3221/igf-esis.29.20 232 assumptions above, the displacement components then simplify in 1 0v , 2 2 2 3 ( , )v v x x and 3 2 ( )v w x . following the classical assumption of lower-order plate theories, in the constitutive relationships for the generic layer k the normal stresses, 3 3 ( )k for k =1..n-1, are assumed to be negligibly small compared to the other components. this yields: 22 22 22  ( ) ( ) ( )k k kc and 23 55 232  ( ) ( ) ( )k k kc (1a)  2222 22  ( )( ) ( )kk ka and 23 55 232   ( ) ( ) ( )k k ka (1b) with  22 22 23 32 33  ( )( ) / kk c c c c c and  22 22 21 12 11 ( )( ) / kk a a a a a  , where the ( )k ijc and ( )k ija are the coefficients of the 6×6 stiffness and compliance matrices (engineering notation). transverse normal tractions will then be derived a posteriori from local equilibrium. the interfaces are described by interfacial traction laws which relate the interfacial shear tractions, acting along the surface of the layer k at the interface with unit positive normal vector, s( )k , 23 2 23 2 3 3     ( )ˆ ˆ ( ) ( , )k k k ks x x x x (2) to the interface relative sliding displacement:        12 2 2 2 2 3 3 2 2 3 3    ˆ ˆ ( ) , ,k kk k k kv v x v x x x v x x x (3) the interfacial traction law is generally nonlinear to represent different physical mechanisms, which may include the elastic response of thin interfacial layers, cohesive/bridging mechanisms developed by trans-laminar reinforcements or other means, material rupture, elastic contact along the delamination surfaces [3-7,20,21]. the law can be approximated as a piecewise linear function so that the arbitrary branch i is described by an affine function of the relative displacement: 23 2ˆ ˆ ˆ i k i k i k k i k s s sk v t    (4a)  2  ˆˆk i k i k i ks s sv b t (4b) where i ksk and i k sb are the interface tangential stiffness and compliance and i k st is a constant interfacial traction which is assumed to act when 2 0ˆ kv  , and is typically positive/negative for positive/negative 2̂ kv , i.e. 2 2    ˆ ˆ( ) h( ) i k k k i k s st h v v t with h the heaviside step function. a purely elastic interface is described by a single branch with 0kst , perfectly bonded interfaces are defined by 0kst and  k sb 0, which yields 2 ˆ kv 0, and fully debonded interfaces by 0kst and ksk 0, which yields  ˆ k s 0. for 0 k st , the affine law of eq. (4) could describe the bridging mechanisms developed by a through-thickness reinforcement, e.g. stitching, applied to a laminated composite [21]. if the relationship (4) is used to represent branches of cohesive traction laws, different linear functions may be needed to represent processes inducing loading and unloading of the delaminations and the associated sliding and reverse-sliding mechanisms. in this paper, equilibrium equations will be derived for plates with interfaces described by the arbitrary branch i of eq. (4) and, for the sake of simplicity, the superscript i will be removed. two length-scales displacement field the displacement field is assumed to be given by the superposition of a global field and local perturbation terms (or enrichments). the nonzero components of the displacement vector at an arbitrary point  1 2 3x , , t x x x are: 1 1 2 2 3 02 2 3 2 3 3 2 1 1             ˆ( , ) ( ) n n k k k k k k k v x x v x x x h v h (5a) 3 2 2 0( ) ( ) v x w x w  (5b) where 3 3 ( ) k kh h x x  3 30 , ;kx x 3 31 , kx x and the terms on the right hand side of eq. (5a) denote different contributions in the displacement representation: 02 02 2 ( )v v x , 0 0 2 ( )w w x and 2 2 2( )x  define standard first order shear deformation theory terms, which are continuous with continuous derivatives in the thickness direction, 1 3c , and, r massabò, frattura ed integrità strutturale, 29 (2014) 230-240; doi: 10.3221/igf-esis.29.20 233 when the reference surface coincides with the mid-surface of the bottom layer, define the generalized displacement components of its points. the third term in eq. (5a), with summations on the n-1 of interfaces, supply the zig-zag contributions, 2 k , [9,10], which are continuous in 3x but with jumps in the first derivatives at the interfaces, 0 3c , and are necessary to satisfy continuity of the shear tractions at the interfaces in plates with arbitrary stacking sequences; the fourth term, with summations on the n-1 interfaces, define a discontinuous field and supply the contribution of the relative displacements (jumps) at the cohesive interfaces. eq. (5) define a first order model, since the displacements are piecewise linear functions of 3x . higher order models have been proposed in the theories in [11,13], which however have no advantages over i order models in the presence of imperfect interfaces, as it was proven in [18]. the linear infinitesimal nonzero strain components at the coordinate 3x within layer k are derived using eq. (5):     1 1 22 02 2 2 2 3 2 2 3 3 2 2 1 1             , , , ,ˆ k k k j j j j j v x x x v (6a)   1 23 0 2 2 2 1 2        , k k j j w (6b) where the comma followed by a subscript denotes a derivative with respect to the corresponding coordinate. figure 1: (a) composite plate showing discretization into layers, imperfect/cohesive interfaces and delaminations. (b) infinitesimal element of layer k showing stress resultants and couples and interfacial tractions. homogenized displacement field the n-1 unknown zigzag functions 2 2 ( ) k x for k = 1..n-1 in eq. (5a) are determined as functions of the global displacement variables and displacement jumps by imposing continuity of the shear tractions, eq. (2), across the layer interfaces, which yields: 1 23 3 23 3  ( ) ( )( ) ( ), k k k kx x for k =1..n-1. (7) through eq. (7), (6) and (1) the kth zig-zag function is defined in terms of the global displacement variables:    12 0 2 2 22    ;, kk w (8) where:   22 55 55    ; ( )i j i jc a and 1    ( ) ( )k k kij ij ija a a . (9) once the functions 2 2 ( ) k x , for k =1...n-1, have been defined, the relative displacement at each cohesive interface, 2 ˆkv , is defined through the constitutive law of the interface, eq. (4b), using eq. (1a), (2), (6b) and (8). the expression for the displacement jump at the s( )k interface at the coordinate 3 kx in terms of the global displacement variables is: x3 k-1 x3 k p (x2, t) kth layer cohesive interfaces delaminations x1 x3 x2 h l2 l1 r massabò, frattura ed integrità strutturale, 29(2014) 230-240; doi: 10.3221/igf-esis.29.20 234  2 0 2 2 22   ,ˆ k k k ks sv w b t (10) with    1122 55 22 1 1            ; k jkk k s j c b (11) eq. (8) and (10) can then be inserted into eq. (5) to obtain the homogenized displacement field. the displacement components within layer k are:      1 2 02 2 3 0 2 2 22 1         , k k k i i s s s i v v x w r b t (12a)   0 k w w (12b) where:      1 1 22 22 3 22 3 3 22 1               ;( ) k ik k i i s s i r r x x x (13) eq. (12) highlight that the displacement field is fully defined by the 3 displacement variables, 02 0 2, , v w , which describe the global part of the field, and are underlined in the equations, and by parameters which depend on the elastic constants of the material, the layup and the geometry (no line) and parameters depending on the properties of the interfaces through the assumed interfacial traction laws (curved line on top). for perfectly bonded layers, when ksb 0 for k = 1..n-1, all terms with the curved line on top vanish and the equations are those of first order zig-zag theory [9,10]. the strain components in the layer k in terms of the homogenized displacement variables are:          1 1 23 0 2 2 22 3 0 2 2 22 1 2 1 1 ;, , , k k ik s i w r w                  (14a)   22 02 2 2 2 3 2 2 0 22 22, , , ,( ) k k sv x w r      (14b) the interfacial tractions at the ( )k s interface at the coordinate 3 kx , in terms of the homogenized displacements are:  23 0 2 2 22,ˆ ˆk k k ks sk w      (15) equilibrium equations equilibrium equations and boundary conditions are derived in weak form through the principle of virtual works:     1 22 22 23 23 2 3 3 3 3 1 2 0                            v s s s b( ) ˆ ˆ k n k k k s s b s s i i k dv t v ds f v ds f v ds f v db (16) where v is the volume of the plate and i = 2,3; the virtual displacements are assumed to be independent and arbitrary and to satisfy compatibility conditions. the first term on the left hand side defines the strain energy in the volume of the body; the second term, with the flat line on top, the energy contributions due to the interfacial tractions on the n-1 interfaces. the last terms define the work done by the external forces, with 3 sf  (top), 3 sf  (bottom) and bif (lateral) the components of the forces acting along the bounding surfaces of the plate, s , s and b . tangential forces acting on s and s have been assumed to be zero (refer to [18,19] for more general loading conditions). the term related to the interfacial tractions was not present in the models where this approach was first proposed for plates with linear-elastic interfaces [11-14]. the terms were also missing in all subsequent models which extended the theories to different problems (see list in [18]). it has been recently proved in [18] that, in the absence of these terms, the solutions are accurate only in the limiting cases of fully bonded and fully debonded interfaces. virtual strains and displacements in eq. (16) are defined as functions of the global displacement variables using eq. (10), (12) and (14). then, by applying green’s theorem wherever possible and after lengthy calculations, eq. (16) yields the equilibrium equations and boundary conditions. dynamic equilibrium equations and boundary conditions for multilayered r massabò, frattura ed integrità strutturale, 29 (2014) 230-240; doi: 10.3221/igf-esis.29.20 235 plates with arbitrary stacking sequences, mixed mode interfaces and under arbitrary loadings have been derived in [18]; a particularization of the equations to plates deforming in cylindrical bending have been presented in [19]. the equilibrium equations for wide plates with sliding only interfaces and quasi-static loading with 2 0   ,s sf are presented here in a form that highlights similarities and differences with respect to single-layer theory: 02 :v 22 2 0,n (17a) 2 : 22 2 2 0 , b gm q (17b) 0 :w 2 2 3 3 0    , s s gq f f (17c) where 22n and 2 2 bm are normal force and bending moment in the 2x direction and 2 gq is a generalized transverse shear force which is statically equivalent, at any arbitrary sections of the plate with outward normal n = 20 1 0 , , t n , to the vertical equilibrant of the external forces acting on the portion of the plate to the right of the sections (fig. 1a):  normal force:  3 1 3 22 22 3 1      k k n x k x k n dx (18a)  bending moment:  3 1 3 22 22 3 3 1      k k n x kb x k m x dx (18b)  generalized shear force:  1 2 2 2 22 2 22 2 2    , , ˆ b z z s gq q q m m (18c) where  transverse shear force:  3 1 3 2 23 3 1 k k n x kb x k q dx     (18d)  gross resultants and couples associated to the multilayered structure:     3 1 3 1 1 2 23 22 3 1 1         ; , k k n kx k iz x k i q dx      3 1 3 1 1 22 22 22 3 3 3 1 1          ; k k n kx k iz i x k i m x x dx (18e)  gross resultants and couples associated to the cohesive interfaces:    3 1 3 1 22 22 22 3 1 1 k k n kx ks i x k i m dx        ,    11 2 22 1        ˆ ˆ n l l l s s l t (18f) the terms in the eq. (18e) vanish in unidirectionally reinforced systems and those in eq. (18f) vanish in fully bonded systems. the generalized shear force then coincides with the resultant of the transverse shear stresses, 2 2 b gq q , when the layers have the same elastic constants, namely when  122 0 ; j  so that 22 0 zm  and 2 0 zq  , and the interfaces are perfect, namely when 0kst  , k sb  0 and 2ˆ kv  0 so that 2 2 0 sm  and 1 2 0̂  ; in this case the equilibrium equations coincide with those of single layer theory. in all other cases, the generalized shear force depends on the multilayered structure, through 2 zq and 2 2 zm , and on the status of the cohesive interfaces, through 2 2 sm and 1 2̂ , and the classical relation between bending moment and shear force of single-layer theory is modified as in eq. (17b). the mechanical/geometrical boundary conditions on c , at 2 0 ,x l , with n =  20 1 0 , , t n the outward normal, are: r massabò, frattura ed integrità strutturale, 29(2014) 230-240; doi: 10.3221/igf-esis.29.20 236 02 :v 22 2 2  bn n n or 02 02 v v (19a) 2 : 22 2 2  b bbm n m or 2 2   (19b) 0 :w 2 2 3  b gq n n or 0 0 w w (19c) 0 2 , :w   22 2 22 2 2 2    z s zb sbm n m n m m or 0 2 0 2 , ,w w (19d) where   3 1 3 3 1 2 3, for , k k n x kb b i i x k n f dx i     (20a)   3 1 3 2 2 3 3 1     , k k n x kbb b x k m f x dx (20b)   3 1 3 1 2 2 22 3 1 1        , k k n kx ksb b i x k i m f d x (20c)      3 1 3 1 1 2 2 22 3 3 3 1 1 ; , k k n kx k izb b i x k i m f x x dx         (20d) terms with the tilde define prescribed values of generalized displacements and gross forces and couples applied to b . equilibrium and boundary conditions can be expressed in terms of the homogenized displacement variables using the constitutive and compatibility eq. (1), (12), (14) and (15). the equations are presented in [19]. eq. (14a) and (9) show that the transverse shear stress, 23 , obtained from the shear strains, 23 , through the constitutive eq. (1), is constant in the thickness and related to the transverse shear force, eq. (18d), through 23 2  / bq h . this stress does not describe the effective status of the material, but for the limit case of a system with perfectly bonded interfaces and layers with the same elastic constants, where 1 2 22 2 22 2 2 0, , ˆ z z sq m m     and 2 2 b gq q . in the presence of imperfect interfaces, 23 follows the dependence of the interfacial tractions on the stiffness of the interfaces, due to the imposed continuity, eq. (7)-(10), and progressively goes to zero when the stiffness of the interfaces decreases; in fully bonded systems with a multilayered structure, where 2 2 2 22 2   , b z z gq q q m , 23 2  / bq h again does not describe the actual stress distribution but for the special case of layers with the same elastic constants where 2 22 2 0 , z zq m . based on the observations above, a generalized transverse shear stress can be introduced, which is the relevant internal stress for strength predictions, 23 2g gq h  . the generalized transverse shear stress, 23 g , averages the actual shear stress distribution which can be obtained a posteriori from the bending stresses by satisfying local equilibrium, 22 2 23 3 0   ( ) ( ) , , k k post , so that 3 1 3 23 23 3 1 1      ( )/ k k n x k post g x k h dx . similarly, the transverse shear strain, which is related to the transverse shear stress through the constitutive eq. (1), 23 23 552 / c  , only partly describes the shear deformations of the plate whose correct measure within this model is given by a generalized shear strain 23 23 552 /g g c  . in order to account for the correct shear deformations in the solution of the differential equations, a shear correction factor, 2k , can be introduced such that 223 23 552 / ( )k c  . 2k is equal to 5/6 in fully bonded unidirectionally reinforced plates, to account for the approximated constant distribution of 23 in the thickness, and it becomes a problem dependent parameter in multilayered plates, e.g. [22]; in [9] it was shown that, for simply supported plates with common layups and geometrical/loading conditions, the homogenized zigzag theory with 2k = 1 leads to accurate predictions of the displacement field. in plates with imperfect interfaces, 2k must depend on the stiffness of the interfaces. work in in progress on the derivation of 2k and results are presented here for 2k =5/6 (see also [18-19]). r massabò, frattura ed integrità strutturale, 29 (2014) 230-240; doi: 10.3221/igf-esis.29.20 237 applications highly anisotropic, simply supported, multilayered wide plates with imperfect interfaces he homogenized model for multilayered plates with imperfect interfaces has been verified against exact 2d elasticity solutions in [18,19]. simply supported, highly anisotropic multilayered plates, loaded quasi-statically, with one or more weak layers have been examined on varying the properties of both layers and interfaces. the whole transition between fully bonded and fully debonded plates has been considered. the diagrams in fig. 2 show exemplary results taken from [19] and refer to a highly anisotropic, thick plate, with two imperfect interfaces having different stiffnesses. (a) (b) (d) (e) figure 2. simply supported wide plate with l/h = 4 subjected to a sinusoidal transverse load,  0 2 sinq q x l . stacking sequence: three layers, (0/90/0), elastic constants: 25/t le e , 50/lt lg e , 125/tt lg e and 0 25.lt tt   [1]. (a) longitudinal displacements and (b) transverse shear stresses at the end support, (c) bending stresses and (d) transverse normal stresses at mid-span. stresses are shown through the thickness (transverse shear/normal stresses derived a posteriori from equilibrium). lower interface, 1 4s tb e h  (very compliant), with 21/ ( )t t tte e   , upper interface, 2 4 11 10s sb b   (almost fully bonded). (modified after [19]). wide plates with clamped edges the zigzag theory for fully bonded plates [9,10] was applied in [17] to a multilayered cantilever beam subjected to a concentrated force f at the free end. the authors noted that the shear force was not constant along the beam length, as they would have expected given the linear distribution of the bending moment. in addition, the shear force increased from zero (at the clamped edge) to an asymptotic value higher than f. these apparent inconsistencies are explained by eq. (17b), (18c) and (19c), which show that the internal gross stress resultant related to the bending moment, through eq. (17b), is the generalized transverse shear force, eq. (18c), which is statically equivalent to the vertical equilibrant of the external forces acting on the portion of the plate to the right of each arbitrary cross section, 2 gq f . the diagrams in fig. 3 refer to a cantilevered wide plate of length l/h = 10 made with two unidirectionally reinforced layers with elastic constants, 25/t le e , 50/lt lg e , and 0 25.lt tt   , connected by a linearly elastic weak layer with 1 1 123 2ˆ ˆ ˆs sk v   . diagram (a) depicts the transverse shear force, 2 bq eq. (18d), along the plate length for different values of the elastic interfacial stiffness and highlights the apparent inconsistency noted in [17] for a fully bonded multilayered plate. note that 2 bq is forced to be zero at the boundary by the geometric boundary conditions at 2 0x  , 0 2 0 2 0  ,w w eq. (19c,d), which yield 23 23 2 0 bq    . diagram (b) highlights that the generalized transverse shear force in eq. (18c), 2 gq , correctly coincides with the external applied force f at all coordinates and 1 2 22 2 2, ˆb sq f m    (in the example 2 22 2 0, z zq m  since the layers are equals; in [17] 2 2 2 22 2, b z z gq q q m   and 1 22 2 2 0, ˆ sm   since the plate is multilayered and fully bonded). diagram (c) compares the values of the interfacial tractions along the plate length, obtained a posteriori from local equilibrium, with those obtained with a classical discrete layer approach [6-8] and shows the existence of a boundary region near the clamped edge where the interfacial tractions predicted through the homogenized approach are not correctly described (bending stresses, not shown, are accurately t r massabò, frattura ed integrità strutturale, 29(2014) 230-240; doi: 10.3221/igf-esis.29.20 238 predicted in all cases). this is a consequence of the geometric boundary conditions imposed at the clamped boundary. the size of this boundary region depends on the interfacial stiffness and is negligible for very stiff and very compliant interfaces. in a multilayered plate the size of the boundary region is nonzero even when the layers are fully bonded, since 2 22 2 0,, z zq m  , eq. (18c). the diagrams (d) and (e) show bending and transverse shear stresses at the mid-span for different values of the interfacial stiffness. predictions are accurate in all cases. (a) (b) (c) (d) (e) figure 3. wide plate clamped at 2 0x and subjected to a concentrated force f at 2x l . two layers, unidirectionally reinforced with 25/t le e , 50/lt lg e , 125/tt lg e and 0 25.lt tt   , 1/ ( )l l l t tle e    ; interface at the midplane. (a) transverse shear force along plate length. (b) generalized transverse shear force, shear force and equilibrating resultants. (c) interfacial tractions along plate length; homogenized model (thick lines), discrete-layer model (thin lines). (d-e) bending (d) and shear (e) stresses through thickness at 2 2/x l . (shear stresses calculated a posteriori from local equilibrium). plates with delaminations as a preliminary investigation of the applicability of the theory to fracture problems, the interface in the cantilevered plate studied before has been assumed to be fully bonded, for 20 2/x l  , and fully debonded, for 22/l x l  . homogenized equilibrium equations have been derived for the two regions in terms of the homogenized displacement variables, 02 0 2, , v w  , and continuity conditions applied at the delamination tip, at 2x l . the model accurately predicts gross stress resultants/couples and stress components. bending and transverse shear stresses are depicted by the solid curves (thick lines for 2 2/x l and thin lines for 2 2/x l ) in figs. 3d,e. incompatible displacements are predicted in the layers to the immediate right and left of the cross section at 2 2/x l , for 3 0x  ; this is due to the imposition of the continuity conditions on the homogenized displacement variables only (see eq. (12a) and (19)). the incompatibility produces unreliable predictions of the stresses in a very small region localized at the crack tip, of size 50/l . accurate predictions of energy release rate and stress intensity factors are obtained using expressions derived for orthotropic layers in [23], which depend on stress resultants and couples at the crack tip. 0 1. and fully bondeds lk h e  0 01.s lk h e  0 001.s lk h e  fully debonded r massabò, frattura ed integrità strutturale, 29 (2014) 230-240; doi: 10.3221/igf-esis.29.20 239 conclusions quilibrium equations were derived in [18,19] for multilayered composite plates with cohesive interfaces and delaminations which depend on only six unknown displacement functions (three for wide plates) for any arbitrary numbers of layers and interfaces. the equations have been particularized here to plates deforming in cylindrical bending and restated in a form similar to that of single-layer theory. this introduces a generalized transverse shear force which is directly related to the bending moment, as the shear force is in single-layer theory, and depends on the multilayered structure of the material and the status of the interfaces. the new equations explain the apparent inconsistencies which have been observed in the shear force when using zigzag theories to model plates with clamped edges. applications to cantilevered wide plates with imperfect interfaces and delaminations confirm the accuracy of the proposed model in predicting stress and displacement fields in thick, highly anisotropic, multilayered plates. they also highlight the existence of boundary regions, near the clamped edges and at the delamination tips, where gross stress resultants and couples are accurately predicted, while stresses and displacements in the layers are not, as a consequence of the imposition of boundary/continuity conditions on the global displacement variables only. the size of the boundary region at the delamination tip in a unidirectionally reinforced laminate is very small, 50/l with l the characteristic inplane dimension. the presence of the boundary regions must be accounted for in the solution of the problems and fracture mechanics predictions must rely on expressions depending on gross stress resultants and couples, which should be calculated at the boundary of the region surrounding the crack tip. it is expected that improvements in the prediction of stresses and displacements in the boundary regions may be obtained through the introduction of a shear factor which depends on the status of the interfaces. acknowledgements upport by u.s. office of naval research, onr, grant no. n00014-14-1-0229 (administered by dr. rajapakse). references [1] pagano, n. j., exact solutions for composite laminates in cylindrical bending, j compos mater, 3 (1969) 398-411. [2] carrera, e. theories and finite elements for multilayered, anisotropic, composite plates and shell. arch comput method e, 9 (2) (1997) 87–140 [3] williams, t. o., and addessio, f. l., a general theory for laminated plates with delaminations, int j solids struct, 34 (1997) 2003-2024. [4] allix o, ladeveze p, corigliano, damage analysis of interlaminar fracture specimens, compos struct 31 (1995) 66-74. [5] andrews, m.g., massabò, r., cavicchi, a., b.n. cox, dynamic interaction effects of multiple delaminations in plates subject to cylindrical bending, int j solids struct, 46 (2009) 1815-1833. [6] andrews, m.g., massabò, r., and cox, b.n., elastic interaction of multiple delaminations in plates subject to cylindrical bending, int j solids struct, 43(5) (2006) 855-886. [7] massabò, r., and cavicchi, a., interaction effects of multiple damage mechanisms in composite sandwich beams subjected to time dependent loading, int j solids struct, 49 (2012) 720-738. [8] carrera, e., historical review of zig-zag theories for multilayered plates and shells, appl mech rev, 56, 3, 2003. [9] di sciuva, m., bending, vibration and buckling of simply supported thick multilayered orthotropic plates: an evaluation of a new displacement model, j sound vib, 105 (3) (1986) 425-442. [10] di sciuva, m., an improved shear-deformation theory for moderately thick multilayered anisotropic shells and plates, j appl mech, 54 (1987) 589-596. [11] cheng, z. q., jemah, a. k., and williams, f. w., theory for multilayered anisotropic plates with weakened interfaces, j appl mech, 63 (1996) 1019-1026. [12] schmidt, r., and librescu, l., “geometrically nonlinear theory of laminated anisotropic composite plates featuring interlayer slips,” nova journal of mathematics, game theory, and algebra, 5 (1996) 131-147. [13] di sciuva, m., geom. nonlinear theory of multilayered plates with interlayer slips, aiaa j., 35 (1997) 1753-1759. e s r massabò, frattura ed integrità strutturale, 29(2014) 230-240; doi: 10.3221/igf-esis.29.20 240 [14] librescu, l., and schmidt, r., a general theory of laminated composite shells featuring interlaminar bonding imperfections, int j solids struct, (2001) 3355-3375. [15] di sciuva m, gherlone m. a global/local third-order hermitian displacement field with damaged interfaces and transverse extensibility fem formulation. compos struct 59 (2003) 433–44. [16] chen, w. q., cai, j. b., and ye, g. r., exact solutions of cross-ply laminates with bonding imperfections, aiaa j, 41 (11) (2003) 2244-2250. [17] tessler, a., di sciuva, m., gherlone, m., a refined beam theory for composite and sandwich beams, journal of composite materials 43 (9) (2009) 1051-1081. [18] massabò, r., campi, f., assessment and correction of theories for multilayered plates with imperfect interfaces, meccanica, 2014, in press. [19] massabò r. and campi f., an efficient approach for multilayered beams and wide plates with imperfect interfaces and delaminations, compos struct 116 (2014) 311-324. [20] sridhar, n., massabò, r., cox, b.n., and beyerlein, i., delamination dynamics in through-thickness reinforced laminates with application to dcb specimen, int j fracture, 118 (2002) 119-144 [21] massabò, r., mumm, d., and cox, b.n., characterizing mode ii delamination cracks in stitched composites, int j fracture, 92(1) (1998) 1-38. [22] bert, cw, simplified analysis of static shear factors for beams of nonhomogeneous cross section, j composite materials, 3, 525, 1973. [23] andrews, m.g. and massabò, r., the effects of shear and near tip deformations on energy release rate and mode mixity of edge-cracked orthotropic layers, eng fract mech, 74 (2007) 2700-2720. shot peening processes to obtain nanocrystalline surfaces in metal alloys: a. namdar, frattura ed integrità strutturale, 8 (2009) 21-29; doi: 10.3221/igf-esis.08.02 21 evaluation of seismic mitigation of embankment model abdollah namdar mysore university, mysore 570006, india, sina_a_n@yahoo.com abstract. conducting experiment on embankment model by shaking table could be an accurate method to evaluate the behavior of embankment or any structures under seismic loading. in this research work, in order to assess the function of seismic force and accurate placement of dense zone in the embankment model, the results of three experiments have been considered. to evaluate the reaction of the embankment model, it was measured the stress in the system and photographs were taken. the results of three experiments indicated that suitable arrangement of dense zone is the main factor at the play in embankment stability, and in predicting the possibility of embankment behavior. keywords. liquefaction, stress, dense zone, pore water pressure introduction eismic liquefaction refers to a sudden loss in stiffness and strength of soil as a result of cyclic loading effects of an earthquake. this loss arises from the soil tendency to contract under cyclic loading. if such contraction is prevented or curtailed by the presence of entrapped water in the pores, it leads to a rise in pore water pressure and a resulting decrease in effective stress. if the effective stress drops to zero (100 per cent pore water pressure rise), the strength and stiffness also drop to zero and the soil behaves as a heavy liquid [1]. at the time of the earthquake, the embankment rested on saturated loose sandy subsoil faces high level of liquefaction risk and may bridge to failure of the embankment. seismic force creates liquefaction due to nonlinear stress up on the model. constructing dense zone in the subsoil is a method to reduce the effect of stress in the embankment model [2]. a research work on dynamic properties and liquefaction potential of soils has been presented [3]. jack w. baker and michael h. faber [4]conducted a research by using random-field theory and geostatistics tools to model soil properties and earthquake shaking intensity. he wanted to present a potential extent of liquefaction by accounting spatial dependence of soil properties and potential future earthquake shaking. dash et al. investigated the use of reinforcement in increasing stability of soil foundation [5]. schimizu and inui [6] carried out load tests on a single six-sided cell of geo-textile wall buried in the subsurface of the soft ground and also mandal and manjunath [7] used geo-grid and bamboo sticks as vertical reinforcement elements and studied their effect on the soil bearing capacity. rajagopal et al. [8] have studied the strength of confined sand and the influence of geo-cell confinement on the strength and stiffness behavior of granular soils. seismic motion could be responsible for instability of embankment model. it is possible to control seismic motion by provision of a dense zone in the subsoil as a feasible method. embankment with good enough foundation stability could be more resistant against seismic force and could increases the safety factor in the system. methodology and experiments he evaluation of embankment model behavior, when it is under seismic force by manual-shaking table, provided insight in understanding seismic mitigation of embankment. the dense zone, consisted of composite material confined in geo-textile in loose saturated sandy subsoil, was studied to assess disability of liquefaction. the manual-shaking table was used to vibrate in one direction figs. 1-3. it consisted of two wooden panels with a steel plate in between which produced harmonic vibration at frequency of 1 hz to 3 hz when an approximately around 75kg force s t http://dx.medra.org/10.3221/igf-esis.08.02&auth=true http://www.gruppofrattura.it mailto: sina_a_n@yahoo.com a. namdar, frattura ed integrità strutturale, 8 (2009) 21-29; doi: 10.3221/igf-esis.08.02 22 was applied on model. one type of transducer (acceleration sensors (a1-a3)) was used to measure the acceleration and its results integrated to draw shear stress graph. test procedure of experimental are following as the filter plates were fixed and sealed on top of baffle walls inside the acrylic box. the aluminum channels were fixed with gum tape inside the acrylic box. signal conditioner of acceleration sensor was switched. the prepared sand was laid. acceleration sensors were placed at required locations. the colored sand was laid at every 10 cm height horizontally and at 10 cm vertically in aluminum channels. the water was allowed through baffle walls at very slow rate for saturating the ground. the shaking was carried out uniformly. the results recorded in the computer and created in the form of the graphs. dense wall 1.5 1 20 30 208020 20 20 toe of embankmentembankment subsoil 20 gl ( cm ) figure 1: model of loose sandy embankment and loose sandy saturated subsoil consists of dense wall made up from composite material (60 % sand and 40 % gravel) confined in geo textile installed outside toe of embankment dense wall 1.5 1 404040 2020 20 30 toe of embankmentloose embankment loose subsoil gl ( cm ) 20 figure 2: model of loose sandy embankment and loose sandy saturated subsoil consists of dense wall made up from composite material (60 % sand and 40 % gravel) confined in geo textile installed inside toe of embankment 1.5 1 20 30 306030 20 20 toe of embankment20 dense wall gl ( cm ) loose embankment loose subsoil figure 3: model loose sandy embankment and loose sandy saturated subsoil made up from composite material (60 % sand and 40 % gravel) confined in geo textile centrally installed on the toe of embankment. http://dx.medra.org/10.3221/igf-esis.08.02&auth=true http://www.gruppofrattura.it a. namdar, frattura ed integrità strutturale, 8 (2009) 21-29; doi: 10.3221/igf-esis.08.02 23 figure 4: transducer position three different types of models have been developed. the first model is loose sandy embankment and loose sandy saturated subsoil. it consists of dense wall made up from composite material (60 % sand and 40 % gravel) confined in geo textile installed outside toe of embankment . the second model is loose sandy embankment and loose sandy saturated subsoil consists of dense wall made up from composite material (60 % sand and 40 % gravel) confined in geo textile installed inside toe of embankment . the third model is loose sandy embankment and loose sandy saturated subsoil made up from composite material (60 % sand and 40 % gravel) confined in geo textile centrally installed on the toe of embankment. (figs. 1-3). fig. 4 shows the cross section of ground and water level with positions of acceleration transducers in the model. the horizontal shear strain γ is obtained from the differential displacement between two adjacent accelerometers, as illustrated in fig. 5. it is given by γ = hd ∆∆ / where d∆ = differential horizontal displacement between two adjacent points h∆ = distance between the two acceleration points maxτ figure 5: key sketch for the computation of shear stress and shear strain in the embankment (a = acceleration, d = corresponding displacement). displacement can be obtained by double integration of the acceleration records. in a sand deposit, let’s consider a column of soil of height ‘h’ and unit area of cross section subjected to maximum ground acceleration amax. assuming a soil column to behave as a rigid body, the maximum shear stress maxτ at a depth ‘h’ is given by: { }τ γ=∑max max/s h g a where g = acceleration due to gravity γ s= unit weight of soil http://dx.medra.org/10.3221/igf-esis.08.02&auth=true http://www.gruppofrattura.it a. namdar, frattura ed integrità strutturale, 8 (2009) 21-29; doi: 10.3221/igf-esis.08.02 24 results and discussion nstalling a dense zone in the subsoil is the easiest method to make an embankment enough stable, when it is subjected to a dynamic force. the aim of this investigation has been to find the right location of the subsoil for a dense zone installation. the results of experiments has been recorded in the form of tables, graphs and photos. the stress characteristic is responsible for controlling liquefaction at the time that the system is under shaking. from the results of all experiments, it could be mention that the main reason of increasing embankment instability is the weakness of dense zone in controlling lateral force due to bad dense zone placement. in the test c (fig 6c), due to suitable placement of dense zone, it could be observed low liquefaction level and higher stability. suitable placement of dense wall is like constructing strong sufficient column in the right place of structure. photographs a, b and c (fig6a-c) provide sufficient evidence at the time of embankment breakdown at any second. referring to figs (7a1c2) and tab.1, it could observed that the maximum level of stress appeared below the embankment and the minimum level of stress occurred far from the embankment. this phenomenon is due to subsoil pressure caused by the weight of the embankment. the model c (with maximum level of stress applied on the model), due to suitable installation of dense zone, resulted significantly controlling lateral force, deformation and creep deformation in the subsoil and increased time stability of dense zone and embankment. easy collapsing of embankment during earthquake is due to any reason could accelerate excess pore water pressure and placing system in the great danger. the immediate collapse of embankment, pressurizing more subsoil, due to dynamic falling weight of embankment on subsoil, could increases seismic force. the ability of seismic forces upon model is the results of a model characteristic. arranging dense zone with proper material reduces speed of collapsing of embankment as as well as creep deformation and settlement of whole model. here it could be observed vertical dynamic force created in the model. embankment satiability is dependent of subsoil strength and deformation during vibrating model by seismic force. intensity of displacement, deformation, stress, pore water pressure and liquefaction as well as restricting seismic force in the embankment models are results of selecting accurate place of dense wall. liquefied soil exerts higher pressure on retaining walls, which can cause theirs tilt or slide. this movement can cause settlement of the retained soil and destruction of structures on the ground surface. increased water pressure can also trigger landslides and cause the collapse of dams [9]. the lateral shear forces developed under the embankment should be compared with the shear strength of the subsoil [10]. the improvement of soil strength with geotextile material depends on the soil grading. the effect is significant for soil with more fine percent [11]. the liquefaction potential of a soil mass during an earthquake is dependent on both seismic and soil parameters [12]. test name at the below of embankment (kpa) at the away from the embankment (kpa) a b c table 1: maximum stresses at each test conclusions the construction of any embankment needs to consider soil foundation behavior with accurate interpretation of the results. the results of three experiments have been carried out. they indicated the possibility of understanding behavior of embankment when it is under dynamic loading. placement of dense wall in suitable location of subsoil is like constructing strong sufficient column in the right place of structure. suitable placement of dense zone can more control pore water pressure and lateral force in the system and reducing of settlement and creep deformation of the subsoil and embankment as well as increases time stability of embankment during the earthquake. easy collapsing of embankment during earthquake could accelerate excess pore water pressure. collapsing of embankment has effect on neighboring area of the subsoil of embankment in term of increasing deformation, stress and excess pore water pressure. all ability of seismic force activity in the system is result of model characteristics. i http://dx.medra.org/10.3221/igf-esis.08.02&auth=true http://www.gruppofrattura.it a. namdar, frattura ed integrità strutturale, 8 (2009) 21-29; doi: 10.3221/igf-esis.08.02 25 test a starting condition after one second after two seconds after three seconds after four seconds after five seconds figure 6a: deformation shape of embankment subsoil (up to five seconds, test a). http://dx.medra.org/10.3221/igf-esis.08.02&auth=true http://www.gruppofrattura.it a. namdar, frattura ed integrità strutturale, 8 (2009) 21-29; doi: 10.3221/igf-esis.08.02 26 test b starting condition after one second after two seconds after three seconds after four seconds after five seconds figure 6b: deformation shape of embankment subsoil (up to five seconds, test b). http://dx.medra.org/10.3221/igf-esis.08.02&auth=true http://www.gruppofrattura.it a. namdar, frattura ed integrità strutturale, 8 (2009) 21-29; doi: 10.3221/igf-esis.08.02 27 test c starting condition after one second after two seconds after three seconds after four seconds after five seconds figure 6c: deformation shape of embankment subsoil (up to five seconds, test c). http://dx.medra.org/10.3221/igf-esis.08.02&auth=true http://www.gruppofrattura.it a. namdar, frattura ed integrità strutturale, 8 (2009) 21-29; doi: 10.3221/igf-esis.08.02 28 figure 7a1: stress strain history in the subsoil away from the embankment (test a). figure 7a2: stress strain history in the subsoil below the embankment (test a). figure 7b1: stress strain history in the subsoil away from the embankment (test b) figure 7b2: stress strain history in the subsoil below the embankment (test b). figure 7c1: stress strain history in the subsoil away from the embankment (test c) figure 7c2: stress strain history in the subsoil below the embankment (test c). references [1] m. seid-karbasi, p.m. byrne, hydropower & dams, 2 (2004). [2] zhaohui yang, ahmed elgamal, j. of engineering mechanics, (2002) 720-729. [3] t. g. sitharam, l. govinda raju, a. sridharan, current science, 87(10) (2004) 1370-1378. http://dx.medra.org/10.3221/igf-esis.08.02&auth=true http://www.gruppofrattura.it a. namdar, frattura ed integrità strutturale, 8 (2009) 21-29; doi: 10.3221/igf-esis.08.02 29 [4] jack w. baker, michael h. faber, j. of geotechnical and geoenvironmental engineering, asce, (2008) 14-23. [5] s. dash, k. rajagopal, n. krishnaswamy, geotextile and geomembrane, 19 (2001) 529-538. [6] m. schimizu, t. inui, proc. of 4th international conference on geotextiles, geomembranes and related products, 1 (1990) 254. [7] j.m. mandal, v.r. manjunath, construction and building material, 9 (1) (1995) 35-38. [8] k.rajagopal, n. krishnaswamy, g. latha, geotextile and geomembrane, 17, (1999) 171-184. [9] t.l. youd, i.m. idriss, journal of geotechnical and geoenvironmental engineering, asce, 127(4) (2001) 297-313. [10] headquarters departments of the army air force manual and the air force washington, engineering use of geotextiles dc (1995). [11] s. a. naeini, m. mirzakhanlari, the effect of geotextile and grading on the bearing ratio of granular soils, ejge, 13 ( j) 2008 [12] derin n. ural, hasan saka, liquefaction assessment by artificial neural networks, ejge, 3 (1998) http://dx.medra.org/10.3221/igf-esis.08.02&auth=true http://www.gruppofrattura.it mysore university, mysore 570006, india, sina_a_n@yahoo.com table 1: maximum stresses at each test / / / / / / figure 7a2: stress strain history in the subsoil figure 7a1: stress strain history in the subsoil below the embankment (test a). away from the embankment (test a). / / figure 7b2: stress strain history in the subsoil figure 7b1: stress strain history in the subsoil below the embankment (test b). away from the embankment (test b) / / figure 7c2: stress strain history in the subsoil figure 7c1: stress strain history in the subsoil below the embankment (test c). away from the embankment (test c) references microsoft word numero_38_art_25 d. carrella-payan et alii, frattura ed integrità strutturale, 38 (2016) 184-190; doi: 10.3221/igf-esis.38.25 184 focussed on multiaxial fatigue and fracture implementation of fatigue model for unidirectional laminate based on finite element analysis: theory and practice d. carrella-payan, b. magneville, m. hack, c. lequesne siemens plm software delphine.carrella@siemens.com, benoit.magneville@siemens.com, michael.hack@siemens.com, cedric.lequesne@siemens.com t. naito, y. urushiyama honda r&d co ltd, tochigi, japan tadashi_naito@n.t.rd.honda.co.jp, yuta_urushiyama@n.t.rd.honda.co.jp w. yamazaki, t. yokozeki university of tokyo, japan (jp) yamazaki_w@aastr.t.u-tokyo.ac.jp, yokozeki@aastr.t.u-tokyo.ac.jp w. van paepegem ghent univeristy, belgium wim.vanpaepegem@ugent.be abstract. the aim of this study is to deal with the simulation of intralaminar fatigue damage in unidirectional composite under multi-axial and variable amplitude loadings. the variable amplitude and multi-axial loading is accounted for by using the damage hysteresis operator based on brokate method [6]. the proposed damage model for fatigue is based on stiffness degradation laws from van paepegem combined with the ‘damage’ cycle jump approach extended to deal with unidirectional carbon fibres. the parameter identification method is here presented and parameter sensitivities are discussed. the initial static damage of the material is accounted for by using the ladevèze damage model and the permanent shear strain accumulation based on van paepegem’s formulation. this approach is implemented into commercial software (siemens plm). the validation case is run on a bending test coupon (with arbitrary stacking sequence and load level) in order to minimise the risk of inter-laminar damages. this intra-laminar fatigue damage model combined efficient methods with a low number of tests to identify the parameters of the stiffness degradation law, this overall procedure for fatigue life prediction is demonstrated to be cost efficient at industrial level. this work concludes on the next challenges to be addressed (validation tests, multiple-loadings validation, failure criteria, inter-laminar damages…). keywords. composite; fatigue; variable amplitude; stiffness degradation. citation: carrella-payan, d., magneville, b., hack, m., lequesne, c., naito, t., urushiyama, y., yamazaki, w., yokozeki, t., van paepegem, w., implementation of fatigue model for unidirectional laminate based on finite element analysis: theory and practice, frattura ed integrità strutturale, 38 (2016) 184-190. received: 10.05.2016 accepted: 25.06.2016 published: 01.10.2016 copyright: © 2016 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. d. carrella-payan et alii, frattura ed integrità strutturale, 38 (2016) 184-190; doi: 10.3221/igf-esis.38.25 185 introduction he increase of lightweight material in transportation industries is today facing more than ever questions on fatigue life prediction of composite structures. the critical step towards accurate prediction is to reproduce the loading conditions undergone by the composite component. in automotive application, the challenge is related to the variability of those conditions: multi-axial and variable amplitude on long duration fatigue loading. this is why siemens plm software has developed an innovative composite fatigue cae methodology (patent pending) keeping track of the material degradation under such conditions. sevenois [1] reviewed and compared the state of the art for fatigue model techniques of woven and ud composite. the study concluded that out of the four modelling methodologies (fatigue life, residual strength, residual stiffness and mechanistic model) the residual stiffness models are suitable for mechanical performance using experimental data and can also be combined with residual strength approach. the presented methodology is based on residual stiffness fatigue law combined with an efficient damage operator approach to calculate the residual stiffness. this approach will be able to perform fatigue simulations for variable amplitude loads and will allow ply-stacking optimization without additional testing or material characterizations. intra-laminar fatigue solution with damage jump he intralaminar fatigue model strategy is herein presented in the following order: definition of the stiffness degradation law, then calculation optimization algorithm (n-jump and damage jump combined to the damage operator) and finally, description of parameter identification procedure used in siemens plm commercial software. fatigue and stiffness degradation – theory fatigue damage laws the damage evolution law is based on the work of van paepegem for woven glass fibers [2]. three intra-laminar damage variables d11, d22 and d12 are defined at ply level and linked to the stress tensor by the following behavior law, eq.(1)  phch     (1) where c is the stiffness tensor, εp is a permanent strain tensor and h is defined as d d d 11 22 12 1 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 h 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 1                     (2) in [2] the damage variables dij were split into a positive and a negative part ( ijd  and ijd  ), where the positive part increases when the stress is positive, and the negative one when it is negative. at the end the two parts were added, including a crack closure coefficient for combination of tension of compression. in this work, only positive stress ratios are used, which means that there is no switch between tension and compression over a cycle and simplifies the problem. either the stress is always positive and the damage dij is equal to ijd  ; or it is always negative and it is equal to ijd  , eq.(3) . besides, the formulations of van paepegem [2] must be adapted to unidirectional plies. first of all, to account for the high in-plane orthotropy of unidirectional plies, independent ci parameters are defined for the three components of the damage. therefore, fifteen parameters are used (ci,jk) instead of five. for the same reason, the coupling between d11 and d12 which t t d. carrella-payan et alii, frattura ed integrità strutturale, 38 (2016) 184-190; doi: 10.3221/igf-esis.38.25 186 was implemented for woven is removed for ud: in woven fabrics, matrix de-cohesion clearly affects the stiffness in longitudinal and transverse directions, whereas in unidirectional plies, the effect of matrix degradation on longitudinal behavior can be neglected. however, the coupling between d22 and d12 remains mandatory and has been maintained. finally, the deletion of this coupling imposes the addition of a propagation term in the formulation of d12, so that a pure shear load in a ply remains able to lead to its collapse. with these assumptions applied to the formulations taken from [2], the evolution laws for the damage variables become:    f d d d c exp c c d exp c c dn cd d d c exp c c d exp c dn d d c d dn 211 11 1,11 11 2,11 3,11  11 11 5,11 11 4 ,11 11 3 5,11211 11 1,11 11 2,11 3,11  11 11 11 4 ,11 11 222 1,22 12 ( )   ( )   3 ( ) 1                                                        f d exp c c d exp c c d 222 22 2,22 3,22  22 22 5,22 22 4 ,22 2 2212   1                            f f cd d d c d exp c c d exp c dn d d d d c d exp c c d exp c dn d 3 5,222 222 22 1,22 22 2,22 3,22  22 22 22 4 ,2212 2 2212 2 212 12 1,12 12 12 2,12 3,12  12 12 5,12 2 12 12 ( ) 1   31 ( ) 1   2 1                                                              c d d d c d exp c c d exp c c dn d 12 4 ,12 2 212 12 1,12 12 12 2,12 3,12  12 12 5,12 12 4 ,12 2 12 12 ( ) 1   2 1                             (3) where ci,jk are the 15 fatigue material coefficients that must be identified, the fatigue failure indices σij are the ratio between the effective stress and the ultimate strength of the material in the ij component, and ij ij ij cycle ij ij cycle ij ij ij ij ij ij ij max max where ; 0,   0     ,   0                                   (4) ij ij ij ij where 0,   0     ,   0        accumulated permanent strain in addition to these damage evolution laws, the model takes into account the permanent strain which appears in the ply due to a cyclic shear loading. some matrix debris formed by the shear stress is accumulated in the opening matrix cracks during tension stress [2], which leads to a non-reversible deformation of the ply. the c9 parameter drives the fatigue permanent strain accumulation following the formulation: . p t t d dd dd c max c max dn dn dn 12 12 12 9 12 9 12            . (5) d. carrella-payan et alii, frattura ed integrità strutturale, 38 (2016) 184-190; doi: 10.3221/igf-esis.38.25 187 initial degradation of the ply it is also important to consider the effect of the first static loading of the ply on its fatigue damage and strain behavior, as it is not included in the fatigue degradation. therefore, the static damage and permanent strain are evaluated with a static damage model [2] by running a first non-linear analysis up to the peak load of the cyclic fatigue analysis. the resulting initial damage and permanent strain are imposed as initial state of the fatigue analysis and the first cycle can be computed with a correct stress distribution. the fatigue damage tensor df is then added to the initial damage tensor ds d = ds + df (6) the same operation is done with the permanent strain. calculation optimization: from n-jump to damage jump block loading: n-jump the purpose of the n-jump algorithm is to avoid running a full fe analysis at each load cycle and to deliberately choose a few relevant load cycles only. the cycles with no significant damage growth are “jumped”. from a first fe analysis, at each gauss point of the fe model, the theoretical number of cycles to jump njump1 is estimated by extrapolating the damage, eq. (1) and applying to eq. (7) n njump n if d d d d d if d if d 20 1 10     0     0.5    0 0.2 0.1    0.2              (7) a global cycle jump njump is defined such that p% of gauss points verify njump1 < njump for the three components. the value of p has been set to 5% in this study. the damage is finally extrapolated after njump, using again the progressive damage formulations eq.(3). to validate this algorithm and the value of p, three similar fatigue analyses (three points bending) have been run on the first 100 loading cycles with a 45 degrees layup; one without njump, one with p=1% and one with p=5%. fig. 1 compares the stiffness degradation observed in the three analyses and validates the accuracy of the njump algorithm. figure 1: effect of the n-jump algorithm on stiffness degradation. variable amplitude: damage accumulation jump and damage hysteresis operator n automotive industry, the synthesis of realistic fatigue loading involves complex load schedules for different roads with variable loading (fig. 2). the aforementioned jump algorithm is given for block loading. also, the n-jump is calculating the damage status by extrapolation (eq. 7). here, the damage accumulation jump aims to accurately calculate locally the progressive damage and stiffness degradation. i d. carrella-payan et alii, frattura ed integrità strutturale, 38 (2016) 184-190; doi: 10.3221/igf-esis.38.25 188 figure 2: variable amplitude example in automotive application. for variable amplitude, traditional fatigue approaches for metallic material use sn curves, linear miner-palmgren damage accumulation and cycle (rainflow) based damage evaluations [3-5]. sn curves are test based on curve fitting techniques which does not take into account the loading history of the material. in 1945, miner developed a linear damage accumulation method, based on the work of palmgren and added the contribution of various stress amplitude loading to the damage. however, as for sn curves, the loading history of the material is not accounted for. in rainflow counting methods the damage level depends on full closing hysteresis loops of load cycles (fig. 3). figure 3: illustration of rainflow method based on stresses/strains with nested cycles. in the case of composite materials, the fatigue behavior is changing over time due to changes in the matrix damage state. when applying variable amplitude loading, the largest load cycles – that contribute to the larger amount of damage – commonly take a very long time to complete, due to the many nested cycles (fig. 3). in this case the approach to only consider cycles when they are completed can no longer be justified. the damage hysteresis operator approach based on brokate works [6] is able to calculate damage at defined time increment instead of ‘closed load increment’. this operator allows to up-date the damage status depending on the predamage and any other external factors (i.e. temperature, humidity…). these operators are therefore suited to follow the progressive damage curves and also to include damage history of the material. this approach gives good prediction when applied to temperature dependent fatigue analysis with non-linear damage accumulation [7-8-9] and for full car structures with full load histories [10]. parameter identification procedure tests protocol n this study, two different tests protocols are proposed. the first one is a traditional approach with tensile tests on five layups and five load levels per layup capturing a representative span of fatigue life (based on test method [11]). this results in twenty five configurations. the second one is an application of a more innovative approach with one-i d. carrella-payan et alii, frattura ed integrità strutturale, 38 (2016) 184-190; doi: 10.3221/igf-esis.38.25 189 sided bending tests on the same five layups, but with only one load level for each layup, so only five configurations. the idea is to assess if the load distribution on this kind of specimen can provide enough information to feed the damage model, as a three-points-bending test results in progressive load levels along the same specimen, both in tension and compression. peak data such as load, displacement, strains from extensometers and gauges, temperature are measured from these tests at several representative cycles. the stiffness degradation of each specimen can be estimated from these evolutions. additionally, running-in and unloading raw data are extracted to analyse the initial stiffness drop of the specimens and their final permanent strain. parameters identification protocol the parameters identification consists in an fe-based optimization of the fifteen fatigue parameters to fit simulated stiffness degradation with experimental results. a step-by-step methodology identifying the parameters one by one from specific experimental data has been setup. as illustrated by two examples in fig. 4, each ci parameter has a specific contribution on the numerical stiffness degradation, and therefore can be adjusted to perfectly fit with experimental results. figure 4: effect of c2,12 (left) and c4,12 (right) on numerical stiffness degradation therefore, two volume finite elements models reproducing the two testing procedures have been created, and the nonlinear fatigue solver with n-jump algorithm is used to efficiently correlate the stiffness degradation of each testing configuration by adjusting the fifteen ci,jk parameters (note that the n-jump is herein used as tests are carried out under constant amplitude loading). an illustration of the resulting correlation between experimental and simulated stiffness evolutions is given in fig. 5. figure 5: correlation between experimental and simulated stiffness evolutions ([0]20 layup in 3pts bending). finally, the parameter c9 is estimated by crosschecking the raw data of the unloading of some of the specimens. d. carrella-payan et alii, frattura ed integrità strutturale, 38 (2016) 184-190; doi: 10.3221/igf-esis.38.25 190 validation/application he first validation has been conducted on a coupon at constant amplitude loading. the same three points bending analysis as above is run on 80 000 cycles at an imposed load level. a more complex quasi-isotropic layup [0/60/60]4s is now studied. the resulting stiffness degradation is compared to experimental data (fig. 6). the good predictability illustrates the main interest of a ply-level damage law: identification is performed on specific layups, and the resulting material data remains available for any layup without additional identification. figure 6: predictability of stiffness reduction of a 3pts-bending quasi-isotropic coupon. further validation cases have been investigated (i.e. flat and v-shaped components) but the overall stiffness degradation contribution from the fatigue loading in these cases were due to the interlaminar delamination. additional validation cases are under investigations to account for higher stiffness degradations. this brings to the next challenges to extend this methodology to a complete intralaminar and interlaminar fatigue damage solution for variable amplitude and multi-axial loadings. references [1] sevenois, r.d.b., van paepegem, w., fatigue damage modeling techniques for textile composites: review and comparison with unidirectional composite modeling techniques, appl. mech. reviews, 67 (2015). [2] van paepegem w., development and finite element implementation of a damage model for fatigue of fibrereinforced polymers, phd thesis, ghent university, belgium, (2002). [3] miner, m.a, cumulative damage in fatigue, journal of applied mechanics, 67 (1945) a159-a164. [4] matsuishi, m., endo, t., fatigue of metals subjected to varying stress, presented at japanese society of mechanical engineers, fukuoka, japan, (1968). [5] dowling, n. e., fatigue failure predictions for complicated stress-strain histories, journal of materials, jmlsa, 7(1) (1972) 71-87. [6] brokate, m., dressler, k., krejci, p., rainflow counting and energy dissipation in elasto-plasticity, eur. j. mech. a/solids, 15 (1996) 705-737. [7] nagode, m., hack, m., the damage operator approach, creep fatigue and visco-plastic modeling in thermomechanical fatigue, sae international journal of materials & manufacturing, 4(1) (2011) 632-637. doi:10.4271/201101-0485. [8] nagode, m., hack, m., fajida, m., low cycle thermo-mechanical fatigue: damage operator approach, fatigue fract engng mater struct, 33(3) (2010) 149-160. [9] šeruga, d., hack, m., nagode, m., thermomechanical fatigue life predictions of exhaust system components, mtz worldwide, 77(3) (2016) 44-49. [10] brune, m., et al., fem based durability analysis of the knuckle of the 5 series bmw, fatigue design’98, helsinki (1998). 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can be opened with acrobat and adobe reader 5.0 and later.) >> /namespace [ (adobe) (common) (1.0) ] /othernamespaces [ << /asreaderspreads false /cropimagestoframes true /errorcontrol /warnandcontinue /flattenerignorespreadoverrides false /includeguidesgrids false /includenonprinting false /includeslug false /namespace [ (adobe) (indesign) (4.0) ] /omitplacedbitmaps false /omitplacedeps false /omitplacedpdf false /simulateoverprint /legacy >> << /addbleedmarks false /addcolorbars false /addcropmarks false /addpageinfo false /addregmarks false /convertcolors /converttocmyk /destinationprofilename () /destinationprofileselector /documentcmyk /downsample16bitimages true /flattenerpreset << /presetselector /mediumresolution >> /formelements false /generatestructure false /includebookmarks false /includehyperlinks false /includeinteractive false /includelayers false /includeprofiles false /multimediahandling /useobjectsettings /namespace [ (adobe) (creativesuite) (2.0) ] /pdfxoutputintentprofileselector /documentcmyk /preserveediting true /untaggedcmykhandling /leaveuntagged /untaggedrgbhandling /usedocumentprofile /usedocumentbleed false >> ] >> setdistillerparams << /hwresolution [2400 2400] /pagesize [612.000 792.000] >> setpagedevice microsoft word numero_55_art_15_2943 p. santos et alii, frattura ed integrità strutturale, 55 (2021) 198-212; doi: 10.3221/igf-esis.55.15 198 mechanical characterization of different epoxy resins enhanced with carbon nanofibers p. santos, a. maceiras, s. valvez, p.n.b. reis university of beira interior, centre for mechanical and aerospace science and technologies (c-mast-ubi), depart. of electromechanical engineering, 6201-100 covilhã, portugal paulo.sergio.santos@ubi.pt, https://orcid.org/0000-0001-9026-5966 alberto.maceiras@ubi.pt, https://orcid.org/0000-0002-1948-6560 sara.valvez@ubi.pt, https://orcid.org/0000-0001-8285-1332 preis@ubi.pt, https://orcid.org/0000-0001-5203-3670 abstract. epoxy with carbon nanofibers (cnfs) are effective nano enhanced materials that can be prepared by easy and low-cost method. the present paper compares the improvements, in terms of flexural and viscoelastic properties, of two epoxy resins reinforced with different weight percentages (wt.%) of cnfs. these epoxy resins have different viscosities, and weight contents between 0% and 1% of cnfs were used to achieve the maximum mechanical properties. subsequently, for the best configurations obtained, the sensitivity to the strain rate and the viscoelastic behaviour (stress relaxation and creep) were analysed based on international standards. it was possible to conclude that, for both resins, carbon cnfs promote significant improvements in all the studied mechanical properties, even for different contents by weight. keywords. composites; epoxy resins; carbon nanofibers; mechanical properties. citation: santos, p., maceiras, a., valvez, s., reis, p.n.b., mechanical characterization of different epoxy resins enhanced with carbon nanofibers, frattura ed integrità strutturale, 55 (2021) 198-212. received: 27.10.2020 accepted: 08.12.2020 published: 01.01.2021 copyright: © 2021 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. introduction poxy resins are a class of thermosetting polymers frequently used as matrices in polymeric composites due to their interesting characteristics, such as dimensional stability, chemical resistance, good stiffness, high specific strength and good adhesion to various types of reinforcements [1, 2]. epoxy resin is a thermostable polymer consisted of two principal parts: resin and hardener. diglycidyl ethers of bisphenol-f and/or bisphenol-a are the main elements of the most normal epoxy resins. hardeners are curing agents that react with a resin and become part of the solid final epoxy through cross-linking chemical reaction when these two chemicals are mixed together [3]. these curing compounds can have different types of molecules such as amines, amideamines, anhydrides, carboxylic acids, polyamides or imidazoles. these molecules have in common that they are able to initiate the polymerization process when their reactive hydrogen or hydroxyl group that react with the oxirane (epoxy) rings. e https://youtu.be/07vu7sqnxru p. santos et alii, frattura ed integrità strutturale, 55 (2021) 198-212; doi: 10.3221/igf-esis.55.15 199 amines are one of the most frequent and important curing agents. the range of alternatives is huge since they are present in different chemical configurations. amines can have two free hydrogens (primary amine), one free hydrogen (secondary) or no hydrogens (tertiary), and they may have a cyclic benzene structure (aromatic) or straight chains (aliphatic). in general, for low-temperature curing systems like adhesive or coatings, aliphatic primary and secondary are the most used, whereas, for fibre-reinforced composites, aromatic amines are chosen. primary amines react speedily at room temperature with epoxies, through epoxy ring-opening, and the thermosetting results in highly cross-linked networks with short curing life and high curing rates. aromatic curing agents react more slowly but impart higher general stability than their aliphatic amine counterparts. in his case, the resulting system needs longer curing time and higher temperature to reach optimum properties, but their chemical resistance, electrical, mechanical and heat resistance is better. therefore, different types of amines that can be used present advantages and disadvantages, commercial hardeners contain a mixture of different types to broader its applicability [4]. apart from the resin and the hardener, commercial epoxies present diluents as other important components. diluents are low-viscosity and low-molecular-weight molecules applied to reduce the viscosity and enhance the resinhardener solubility. normally, these compounds do not leach or outgas during thermal-vacuum exposure because amid curing reactions are being combined and linked chemically with the resin [5]. despite having many desirable properties, neat epoxies typically have low mechanical toughness. in the last few decades, a wide range of nano filers has been added to commercial epoxy resin to increase the mechanical properties, such as clays [6], alumina [7], graphene nanoplatelets (gnps) [8], carbon nanotubes (cnts) and carbon nanofibers (cnfs) [9, 10]. enhancement in mechanical properties of cnfs based epoxy composites have been well illustrated in the literature by the achievement of good dispersion of additives within the matrix and maximized interfacial adhesion is required to ensure uniform stress distribution, [11–13]. cnfs are carbon-based materials that present good compatibility with many polymer matrixes, and they can be disseminated following anisotropic and isotropic distributions. their chemical structure, good qualities, and versatility are responsible for the outstanding thermal and electrical conductivity, a mechanical performance that can be introduced in a huge variety of matrices of different origins such as metals, ceramics and polymers. if literature presents benefits when the resin is filled by cnfs, it also evidences that the same are sensitive to the strain rate. there exist some previous works in nano-enhanced resins with cnfs about the strain rate effect on mechanical properties. zhou et al. [14], for example, observed that in uniaxial tensile tests, neat and cnfs modified epoxy are strain rate dependent materials and the elastic modulus and tensile strength of the materials both increased with higher strain rates between 0.00033 and 0.033 s-1. proveda et al. [15] observed for a cnfs/epoxy resin, under compression for 5×10-3 2800 s-1 strain rates, that the strength and modulus increased by a maximum of 180.7 and 241.7%, respectively. nevertheless, for longterm applications, composites based on polymers have the limitation of suffering stress relaxation and creep. according to the open literature, for example, in polymers there are mainly two mechanisms involved in stress relaxation: a) molecular rearrangements that demand little primary breakage or bond arrangement (physical stress); and b) crosslink formation, scission, or chain scission (chemical stress). on the other hand, creep is the combined result of the viscous flow and elastic deformation and happens because of the molecular rearrangements in the backbone and depends on the stress degree. therefore, the main goal of this work is to compare sensitive to the strain rate, stress relaxation and creep behaviour of two commercial epoxy resins and understand the influence of cnfs as nano-reinforcements. for this purpose, several percentages by weight of cnfs were mixed in two different resins by the technique of mechanical agitation and simultaneously the application of ultrasound. both resins are widely used in the automotive and aeronautical sector. the bending mode was selected for this study because is the type of analysis with greater sensitivity and one of the most employed in the field. materials and experimental procedure wo types of epoxy resin were used to produce nanocomposites enhanced by cnfs. for this purpose, an epoxy resin sr 8100 and a hardener sd 8822, both supplied by sicomin, and an epoxy resin ah 150 and a hardener ip 430, both supplied by ebalta, were selected due to their different viscosities, as reported in tab. 1. epoxy-based materials are very interesting from an engineering point of view because of their properties and characteristics are directly controlled by their molecular structures. epoxy resins thanks to their two main components implementation are available in a range of molecular structures, suitable for reaction with a large variety of different curing agents, for a multitude of end uses. therefore, in order to control and understand the mechanical behaviour of these materials is a key factor to know their composition (chemical structures), and relative quantities of their components. in this work, both epoxy materials were purchased from a private company and part of the data is protected by intellectual property. unfortunately, not all the components and quantities are disclosed in their technical datasheet to the general public. for the sicomin sr 8100/sd 8824 the information was more detailed than for the ebalta ah 150/ip 430, as the resin relative composition and t p. santos et alii, frattura ed integrità strutturale, 55 (2021) 198-212; doi: 10.3221/igf-esis.55.15 200 the hardener chemical components were not indicated for the latter one. in this sense, tab. 2 summarizes all the known relevant information about the chemical compositions of the two resin formulas obtained from the datasheet, and fig. 1 shows their chemical structures. property sicomin sr 8100/sd 8824 ebalta ah 150/ip430 colour light yellow liquid opaque viscosity (@ 25 ºc) [mpa×s] 285 ± 60 250 ± 50 density at 20 ºc [g/cm3] 1.13 ± 0.02 modulus of elasticity [n/mm2] 2970 3400 ± 300 maximum resistance [n/mm2] 108 125 ± 1.2 elongation at max. load [%] 4.9 elongation at break [%] 11.8 5.9 ± 0.1 charpy impact strength [kj/m2] 52 60 ± 6 glass transition / dcc [ºc] 63 water absorption 48 h/70 °c [%] 1.2 table 1: main mechanical and physical properties of the epoxy resins. type of component identification number sicomin sr 8100/sd 8824 ebalta ah 150/ip430 resin cas: 1675-54-3 ec: 216-823-5 bisphenol a epoxy resin (dgeba) composition: 10 <= x % < 25 composition: % not specified mw≤700 cas.: 9003-36-5 ec: 500-006-8 bisphenol f epoxy resin (dgebf) composition: 50 <= x % < 100 composition: % not specified mw≤700 diluent cas: 16096-31-4 ec: 240-260-4 1,6-bis(2,3-epoxypropoxy)hexane composition: 10 <= x % < 25 composition: % not specified hardener: amines cas: 15520-10-2 ec: 239-556-6 2-methylpentane-1,5-diamine composition: 25 <= x % < 50 composition: molecules and % not specified cas: 1477-55-0 ec: 216-032-5 m-phenylenebis(methylamine) composition: 25 <= x % < 50 cas: 39423-51-3 ec: 500-105-6 trimethylolpropane tris[poly(propylene glycol), amine terminated] ether composition: 2.5 <= x % < 10 table 2: chemical composition of the epoxy resins, diluent and hardeners used in this study based on the data known from their technical datasheets. regarding the carbon nanofibers (cnfs), their technical specifications are summarized in tab. 3 and fig. 2 shows the sem images of the cnfs used in this study. in terms of dimensions, as shown, the average diameter is about 130 nm, the length ranges from 20 to 200 µm and the average specific surface area around 54 m2/g. in terms of manufacture process, and after weighing, cnfs were added to the epoxy resin and several contents by weight were studied: 0.25, 0.5, 0.75 and 1 %. the dispersion into the resin was conducted using, simultaneously, a high-speed shear mixer at a shear rate of 1000 rpm and sonication (using an ultrasonic bath with a frequency of 40 khz) for 3 hours at room temperature. this procedure took another 10 minutes, with a rotation speed of just 150 rpm, to mix the hardener into the system. the low rotation speed aimed to minimize the formation of air bubbles and to promote only a homogeneous mixture of the hardener into the system. the rotation speed and time of mixture were optimized in previous studies. the p. santos et alii, frattura ed integrità strutturale, 55 (2021) 198-212; doi: 10.3221/igf-esis.55.15 201 mixture was again degassed in a vacuum oven to remove remaining air bubbles and then poured into a cardboard mould with dimensions of 100×130×3 mm3. finally, all nanocomposites produced with sicomin resin were cured at room temperature for 24 hours and subjected to a post-cure at 40ºc for 24 hours, while those that were produced with ebalta resin were cured at room temperature for 48 hours and subjected to a post-cure at 80ºc for 5 hours. figure 1: chemical structures of (a) bisphenol a epoxy resin (dgeba), (b) bisphenol f epoxy resin (dgebf), (c) 1,6-bis(2,3epoxypropoxy)hexane, (d) 2-methylpentane-1,5-diamine, (e) m-phenylenebis(methylamine) and (f) trimethylolpropane tris[poly(propylene glycol), amine terminated] ether. property value assay > 98% carbon basis form platelets (conical) powder diameter × length 100 nm × 20 200 µm average diameter 130 nm impurities < 14,000 ppm iron content pore size 0.12 cm3/g average pore volume 89.3 å average pore diameter surface area average specific surface area 54 m2/g mp 3652-3697 c density 1.9 g/ml at 25 ºc bulk density 0.5 3.5 lb/cu.ft table 3: technical specifications of the cnfs used in this study. for the tests to be performed, the samples were obtained from the original plates to specimens with the dimensions and geometry shown in fig. 3. following the recommendations of the european standard en iso 178:2003, three-point p. santos et alii, frattura ed integrità strutturale, 55 (2021) 198-212; doi: 10.3221/igf-esis.55.15 202 bending (3pb) static tests were carried out at room temperature and using a span length of 50 mm. an autograph ags-x universal testing machine, from shimadzu, with a 10 kn load cell and a displacement rate of 2 mm/min was used to test six different samples for each configuration. figure 2: sem images of the cnfs used in this study. a) b) figure 3: a) geometry of the specimens; b) three-point bending apparatus. all dimensions in mm. the bending strength was obtained from the nominal stress at the central span section by:   2 3 2 pl bh (1) where p is the load, l the span length, b the width and h the thickness of the sample. the stiffness modulus was determined from the linear elastic bending beams theory relationship:    3 48 pl e ul (2) where i, δp and δu are, respectively, the moment of inertia of the cross-section, the load range and flexural displacement range in the middle span for an interval in the linear region of the load versus displacement plot. finally, the flexural strain was calculated according to the european standard en iso 178:2003 by the following equation:   2 6 f sh l (3) 50 80 3 10 1 m p. santos et alii, frattura ed integrità strutturale, 55 (2021) 198-212; doi: 10.3221/igf-esis.55.15 203 where s is the deflexion, l the span length and h the thickness of the specimen. displacement rates of 200, 20, 2, 0.2 and 0.02 mm/min were employed, which corresponds to strain rates () of 9.7 × 100, 9.7 × 10−1, 9.7 × 10−2, 9.7 × 10−3, 1.3 × 10−4 s−1 according to eqn. (4):     2 6f td v h dt l (4) in this equation  is the peripheral fibre strain, t is the time, vt is the cross‐head speed, l the span length and h the thickness of the specimen. for each condition, six specimens were tested. finally, the same machine was used to carried out stress relaxation and creep tests, at room temperature and with similar samples to those shown in fig. 3. for the first tests a fixed displacement was applied, and the stress recorded during the loading time, while for creep tests a fixed stress was applied and the displacement registered during the loading period. for both resins, a bending stress of 50 mpa was considered in order to ensure that all tests were carried out on the elastic region of the bending stress-strain curve. results and discussion tatic bending tests were performed according to the experimental procedure described in the previous section and with a strain rate   of 9.7×10−2 s−1 (corresponding to a displacement rate of 2 mm/min), in order to find the best amount of nano reinforcement to maximize the bending properties. in this context, fig. 4 presents typical flexural stress-strain curves obtained for different conditions, but they are representative of all curves obtained in this analysis. figure 4: representative flexural stress-strain curves obtained for 9.7×10−2 s−1. comparison between neat and the best nano enhanced resin. in all curves, a linear increase in the bending stress with the strain (linear elastic region) is observed, followed by a nonlinear performance where the maximum bending stress is reached. after the peak load, the bending stress drop significantly, evidencing the imminent collapse of the nanocomposites. fig. 5 summarizes the main bending properties, obtained from these curves, in terms of average values (symbols) and respective maximum and minimum values (dispersion bands). for both resins, it is noticed that the increase in cnfs promotes higher values of bending strength, but after a certain content of nanoparticles these values decrease due to the aggregates/agglomerates that have occurred due to intermolecular interactions (van der waals forces and chemical bonds). while the maximum bending stress occurs with 0.75 wt.% of cnfs for the sicomin resin, this property reached its maximum for 0.5% of cnfs when the ebalta resin is considered. in comparison with the control samples (neat resin), an increase around 11.7% was observed for both resins. in fact, according to the open literature, agglomerations/aggregations are expected for higher filler contents, which, in addition to being treated as defects, are responsible for significant concentrations of stresses in nanocomposites [16–18]. they also reduce the interfacial area between the polymeric matrix and nanoparticles, which reduces the mechanical 0 20 40 60 80 100 120 140 0 2 4 6 8 f le xu ra l s tr es s [m p a] strain [%] neat resin sicomin 0.75 wt.% cnfs neat resin ebalta 0.50 wt.% cnfs s p. santos et alii, frattura ed integrità strutturale, 55 (2021) 198-212; doi: 10.3221/igf-esis.55.15 204 involvement of polymeric chains in the nanoparticles [19]. on the other hand, only a few polymer molecules can penetrate between the nanoparticles, which promotes an exceptional increase in viscosity, even for relatively low filler contents [20]. however, due to the higher viscosity of the sicomin resin (compared to ebalta), it was expected to obtain the highest flexural strength with lower content of cnfs. regardless of fiedler et al. [21] report that the low viscosity of a resin allows a better organization of the nanoparticles, they also consider that the manufacturing process as well as the properties of the particles and matrix are determinants in the interfacial strength of the composite and dispersibility of the fillers during the production. a) b) c) figure 5: nano enhanced resin sicomin sr 8100 and ebalta ah 150 with different percentages of cnfs: (a) bending stress; (b) bending stiffness; (c) bending strain. although cnfs are considered ideal materials for reinforcing polymers due to their excellent mechanical properties, a good interaction between reinforcement cnfs and polymer matrix is necessary to obtain composites with optimal properties. for that reason, the knowledge of the chemical composition of resins and hardeners is essential to understand the physicochemical interactions between the matrix and the fillers, in order to overcome possible incompatibilities and to optimize the composite mechanical behaviour [22]. however, from the chemical point of view, both resins are based on the same components, bisphenol a (dgeba) and bisphenol f epoxy resin (dgbf), respectively. the most relevant and employed epoxy resin is the dgeba, which results from the chemical reaction of bisphenol a with epichlorohydrin. manufactured dgeba resin usually presents a distribution of molecular weight and a certain preference to have a crystalline solid material when is stored at room temperature. but, dgebf is usually less viscous and once cured has greater toughness and flexibility. nonetheless, although the use of both resins is indicated in their technical datasheets, there exists a lack of information about the exact proportion of both components and their molecular weight in the final commercial products (sicomin sr 8100 and ebalta ah 150). these differences in the epoxy resin compositions (dgebf/deba), molecular 2 4 6 8 -0,25 0 0,25 0,5 0,75 1 1,25 b en di n g st ra in [ % ] wt.% cnfs sicomin sr 8100 ebalta ah 150 90 100 110 120 130 -0,25 0 0,25 0,5 0,75 1 1,25 b en di n g st re ss [m p a] wt.% cnfs sicomin sr 8100 ebalta ah 150 0 1 2 3 4 -0,25 0 0,25 0,5 0,75 1 1,25 b en di n g st if fn es s [g p a] wt.% cnfs sicomin sr 8100 ebalta ah 150 p. santos et alii, frattura ed integrità strutturale, 55 (2021) 198-212; doi: 10.3221/igf-esis.55.15 205 weights and the quantity of diluent [1,6-bis(2,3-epoxypropoxy)hexane] probably explain the different viscosity referenced for sicomin sr 8100 (285 ± 60 mpa×s) and ebalta ah 150 (250 ± 50 mpa×s) resins at 25ºc in their datasheets. with respect to hardeners, the situation is more difficult because there was no information about the composition in the ebalta technical datasheet. as it was explained before, hardeners based on amines as curing agents become part of the chemical structure of the solid epoxy through cross-linking after reacting with a resin. therefore, the influence in the general properties of the materials is at least as much important as the resins. for instance, to obtain the best properties it is necessary an optimum curing reaction, which implies that the amount of curing reagent employed must be stoichiometric. the number of epoxy groups and reactive hydrogens of the hardener must be equal, which is the amine molecular weight divided by the number of hydrogens (amine-equivalent weight, aew) [23]. the curing process and the chemical phenomena of cross-linking are responsible for many of the properties of the solidstate in epoxy derived materials. the cross-link density is the spacing between successive cross-link sites, and normally, when the cross-link density increases, the glass transition temperature, thermal stability, and chemical resistance increase, but the fracture toughness and the strain to failure decreases [24]. therefore, during the curing reaction was observed a difference of colour with a naked eye between the two resin materials, light yellow liquid (sicomin sr 8100/sd 8824) and opaque (ebalta ah 150/ip 430). this difference of colour can be explained because of the different hardeners formulations since both resin products are based on the same two polymers (dgeba and dgbf). the introduction of new molecular chains of different lengths, with pendant groups, aliphatic or aromatic elements, vary many physicochemical and solid-state properties of the composites. for example, heterocyclic and aromatic curing reagents are responsible for higher temperature stabilities than their aliphatic amine alternatives [25]. an increment in the flexible amine content decreases the tensile and flexible strength related to a reduced crosslinking density [26]. in summary, the higher modulus of elasticity and maximum resistance of the ebalta ah 150/ip 430 over the sicomin sr 8100/sd 8824, referenced in these neat cured resins, could be explained from the different chemical relative composition (dgeba/dgbf) of both resins, and for their different hardeners employed. in the case of epoxy resins reinforced with cnfs the introduction of cnfs was aimed to enhance the mechanical properties of the two epoxy materials. properties of composites are ruled not only by the carbon fibre, the resin matrix, but also are influenced by the interface formed between the two constituents. favourable interfacial adhesion can efficiently transfer stress from matrix to fillers, which plays a key role in the mechanical properties as well as the reliability [27]. although carbon nanofibers are increasingly used in various industries, these materials present some drawbacks. the smooth pristine surface of carbon fibre is non-polar and affects the interfacial adhesion between carbon fibres and resin matrix, which has a negative effect on the overall performance. the composite interfacial shear strength reflects the load transfer efficiency between the nanofibers and the resin, and has a relevant function in the mechanical properties. the general idea is to reach an efficient load transfer between both constituents to strengthen the nanofiber-matrix interface to overcome the lack of good interfacial bonding limited by the non-polar and smooth surface of cnfs. the fillers-resin adhesion may require strengthened by treating the fillers with a coupling agent or functionalization that bridges their molecules together. then, the creation of covalent bonds or van der waals forces of attraction would enhance the adhesion between the two materials (fillers/matrix) [28, 29]. advances in interfacial improvement have been made, but the mechanisms of interfacial adhesion are difficult to be fully understood. the most common explanations for enhancement mechanisms by fillers are: a) stiffer matrix/fibres interfaces with a higher shear modulus are formed, which promotes the stress transfer; b) the presence of fibres in the interface assists in holding back excessive stress spreading in the flaw and provides a crack deflection mechanism; c) chemical interaction among cnfs, sizing and resin matrix can be improved when the nanoparticles are modified with a surface modifier. in this context, a uniform dispersion and good wetting of the nanofibers within the matrix are necessary to ensure maximum utilization of the nanofibers’ characteristics, because a good cnfs dispersion can be critical to obtaining a homogeneous dispersion. high shear mixing, ultrasonication, the employment of surfactants, or the dilution method are some of the alternatives [30, 31]. according to the results, 0.75 wt.% of cnfs is the content that promotes the maximum bending stress for the sicomin resin, while for ebalta resin is 0.5% of cnfs. since the mixture and dispersion procedure was exactly the same, in both commercial pre-cured resins, the difference in the filler percentage values can be attributed to variation in the matrix-fibre interfaces that modify the stress transfer and spreading in the flaws and crack deflection. normally, the variation in the interfaces can be explained by different factors, such as a) diverse aggregation formation, b) different chemical composition of the polymer matrixes and hardeners, and c) the effect of fillers on the kinetics of epoxy cure. as was explained previously, in this work both commercial matrixes have very similar compositions, the same two epoxy materials and diluent. the exact composition is not known because are protected by copyrights, but to the best of our knowledge are analogous due to the information disclosed in datasheets. probably, the variation in their relative compositions is responsible for the different viscosity previous curing. in theory, in less viscous fluids (ebalta) a uniform p. santos et alii, frattura ed integrità strutturale, 55 (2021) 198-212; doi: 10.3221/igf-esis.55.15 206 dispersion of the nanofibers within the matrix would be easier to perform, limiting the tendency to form cnfs agglomerates, which are responsible for an excessive stress concentration and origin of flaws. nonetheless, from our results, the difference in viscosities does not seem a relevant parameter, because the maximum percentage in ebalta (0.5%) is lower than in sicomin (0.75%). therefore, the difference in filler acceptance from the matrix should be attributed to greater physicochemical compatibility of the sicomin and not the viscosity. what is different is the hardener chemical formula composed of different types of amine molecules. the difference in composition affects clearly many parameters in pristine epoxies and it is more relevant when the parameter of fillers appears. surface polarity is one of the most important physicochemical attributes of both materials that affect the interface quality of the filler/matrix. however, due to their important polarity and attractive forces formed between the resin and the other material, epoxies adhere satisfactorily to multiple surfaces. normally, strong polar attractions or direct bonds that can be formed between reactive sites in the resin and polar sites on the surface of the filler. most inorganic materials (metals, minerals, glasses, ceramics) have some polarity so they have high surface energy, whereas organic polymer surfaces are generally less polar (more covalent) and lower surface energy [32, 33]. in a very wide range of epoxy resins, polarity varies depending the molecules and curing conditions involved. the nonepoxy part of the chemical structures presents multiple possibilities, because it may have aromatic, cycloaliphatic and/or aliphatic molecules that vary its polarity and general properties. in the same way for the amines, i.e. cross-linking and chain extension reagents. the amino group shows some polar character because the n‒h bonds are more electronegative than the c‒h bonds [34]. on the other hand, pristine cnfs are basically non-polar materials, i.e. a molecule where the electrons between the two atoms are equally shared or where the polar bonds of the global structure are symmetrically disposed. therefore, despite the great properties of these nanofibers, cnfs/epoxy composites can have unsatisfactory mechanical properties because cnfs have poor interfacial adhesion due to their non-polar surface. in short, the different hardeners (several amine molecules) could affect the overall polarity of the epoxy cured materials which as a relevant effect in the fillers/resin compatibility. in the optimum based nanocomposites (0.5%), the matrix/fibres interface interaction is worse than in sicomin (0.75%), which has an impact on the cnfs percentage that can accept before having a detrimental effect on the mechanical characteristics, such as bending stress. other possible explanation, apart from polarity mismatch, is the effects of cnfs fillers on the curing processes, since it is accepted that the physicochemical and thermo-mechanical characteristics of the cured epoxy resin depend on the curing reaction conditions (temperature and time), degree of cure (curing extent) and network of crosslinking. since the overall characteristics arises in great part from the curing reactions, their curing kinetics should be studied by differential scanning calorimetry (dsc). for example, tao et al. [35] reported that carbon nanotubes (cnts) are able of modifying the curing process, initiating the curing reactions at inferior temperatures with respect to a neat epoxy resin. the presence of cnts modified the curing kinetics, reduced the crosslinking density and the glass transition temperature [36]. silanized cnfs exhibited lower peak temperature as well as higher heat of cure, and maximization in the cure reaction rates at the very initial stage of the reaction compared to those without the pristine cnfs. the curing and post-cure procedures for sicomin and ebalta resins in terms of temperature and time were obtained from their datasheets and were optimized from the manufacturers for neat epoxy formulas, i.e. without fillers, in this case, cnfs. that means the curing mechanism should be corroborated and maybe optimized for each filler content [37]. in this context, because the resin was the only different variable in this study, it is possible to conclude that ebalta enables the formation of stronger covalent bonds and/or polar interactions between the resin and the cnfs. on the other hand, higher specific surface area already encourages the formation of agglomerates due to the intermolecular interactions. in terms of bending stiffness, and for sicomin neat resin, the maximum valor is about 2.68 gpa, while for similar resin filled by 0.75 wt. % cnfs this value is about 2.99 gpa (11.76% higher). for ebalta neat resin, these values are around 2.84 gpa and resin filled by 0.5 wt. % cnfs this value is about 3.16 gpa, respectively (11.3% higher). the strain rate effects on the flexural properties are shown in fig. 6. typical bending stress versus flexural strain curves, for all strain rates, are plotted in fig. 6a) and 6b), respectively, for sicomin sr 8100 with 0.75 wt.% cnfs and ebalta ah 150 with 0.5 wt.% cnfs. both curves exhibit two different regimens, a quasi‐linear zone, which is followed by a nonlinear region where the maximum bending stress occurs. however, it is noticed that for higher strain rates the linear region is longer for both systems and considerably affect bending properties. for example, independently of the resin, higher values of strain rate promote higher bending stress and stiffness, but the highest values are always obtained when cnfs are added to the resin. a linear model, as suggested by the literature [38–40], can be fitted to the data according with the following equations:     a b e (5)    e a b e (6) p. santos et alii, frattura ed integrità strutturale, 55 (2021) 198-212; doi: 10.3221/igf-esis.55.15 207 a) b) c) d) e) f) figure 6: effect of the strain-rate: (a) for resin sicomin sr 8100 with 0.75 wt.% cnfs; (b) for resin ebalta ah 150 with 0.5 wt.% cnfs;(c) bending stress sicomin; (d) bending stress ebalta; (e) bending stiffness sicomin; (f) bending stiffness ebalta; (g) bending strain sicomin; (h) bending strain ebalta. where σ is the maximum bending stress, e is the bending modulus, ε is the strain at maximum bending stress, 𝑒 is the logarithm of strain rate and a and b constants presented in tab. 4. from this table, it is possible to conclude that those linear relationships between the logarithm of strain rate () and the mechanical properties present good accuracy, and they can be used as models to predict the strain rate effect on the bending properties. 0 40 80 120 160 0 2 4 6 8 f le xu ra l s tr es s [m p a] strain [%]  1.4 10 𝑠  1.4 10 𝑠 0 40 80 120 160 0 2 4 6 8 f le xu ra l s tr es s [m p a] strain [%]  1.4 10 𝑠  1.4 10 𝑠 60 80 100 120 140 160 -4,5 -3,5 -2,5 -1,5 -0,5 0,5 b en di n g st re ss [m p a] log strain rate [s-1] neat resin 0.75 wt.% cnfs 60 80 100 120 140 160 -4,5 -3,5 -2,5 -1,5 -0,5 0,5 b en d in g s tr es s [m p a] log strain rate [s-1] neat resin 0.50 wt.% cnfs 2,0 2,5 3,0 3,5 4,0 -4,5 -3,5 -2,5 -1,5 -0,5 0,5 b en di n g st if fn es s [g p a] log strain rate [s-1] neat resin 0.75 wt.% cnfs 2,0 2,5 3,0 3,5 4,0 -4,5 -3,5 -2,5 -1,5 -0,5 0,5 b en di n g st if fn es s [g p a] log strain rate [s-1] neat resin 0.50 wt.% cnfs p. santos et alii, frattura ed integrità strutturale, 55 (2021) 198-212; doi: 10.3221/igf-esis.55.15 208 material properties parameters correlation coefficient a b r neat sicomin resin bending stress () 133.12 11.04 0.997 bending modulus (e) 3.20 0.124 0.977 sicomin with 0.75 wt.% cnfs bending stress () 141.34 11.12 0.992 bending modulus (e) 3.31 0.082 0.947 neat ebalta resin bending stress () 131.13 10.40 0.991 bending modulus (e) 3.17 0.144 0.963 ebalta with 0.50 wt.% cnfs bending stress () 141.02 11.06 0.994 bending modulus (e) 3.46 0.159 0.982 table 4: parameters of the equations that fits the effect of the strain‐rate on the nanocomposites. apart from high stiffness and strength, the matrix should present viscoelastic and/or viscoplastic behaviour to eliminate brittle fracture of the composite. good dispersion and adequate introduction of cnfs with the interfacial area and high aspect ratio into an epoxy matrix controls the long-term deformability and strength of the composite, and decrease the rate of creep strain [41]. the addition of a certain quantity of cnfs or cnt could enhance the efficiency of interfacial stress transfer thanks to an improvement in the interlaminar shear strength. however, in case of poor quality of adhesion, the damage process of the bulk resin can be accelerated, especially under shear loading, because of the increase in the number of dissipation sites, i.e. cnfs/epoxy interfaces. with respect to viscoelastic behaviour, fig. 7 shows the stress relaxation curves for both neat resins (ebalta and sicomin) and their respective cnfs nanocomposites. in these graphs, the average bending stress versus time are plotted, where  is the bending stress at any specific instant of the test and  is the initial bending stress. for all samples tested, it was noticed that, independently of the resin type and cnfs percentage, the stress decreases with time, but the neat sicomin resin has an inferior tendency to stress relaxation than ebalta resin. for instance, after 180 min and for neat sicomin resin, this drop is about 10%, while for the same resin with 0.75 wt.% cnfs is about 7.9%. for ebalta neat resin this decrease is around 14.8%, and for ebalta resin with 0.5 wt.% cnfs is about 13.2%. a) b) figure 7: relaxation curves for: (a) neat sicomin sr 8100 and nano enhanced resin with 0.75 wt.% cnfs, bending stress of 50 mpa; (b) neat ebalta ah 150 and nano enhanced resin with 0.5 wt.% de cnfs, bending stress of 50 mpa. for the neat resins, in the literature essentially two mechanisms are referenced that can induce stress relaxation: a) chemical stress relaxation due to chain scission and crosslinking formation or scission, and b) physical stress relaxation due to molecular rearrangements that involve little primary bonding formation or breakage [42]. however, the cnfs presence demonstrated an effective enhancement of the mechanical properties with increasing filler content, up to 0.75% for sicomin and 0.5% for ebalta [43]. nonetheless, the degree of improvement showed in the results is lower than expected because the increase in mechanical performance is restricted by a concentration limit, and the great properties of cnfs are not fully 40 42 44 46 48 50 52 0 50 100 150 200 b en di n g st re ss [m p a] time [min] neat resin epoxy + 0.75 wt.% cnfs sicomin sr 8100 40 42 44 46 48 50 52 0 50 100 150 200 b en di n g st re ss [m p a] time [min] neat resin epoxy + 0.5 wt.% cnfs ebalta ah 150 p. santos et alii, frattura ed integrità strutturale, 55 (2021) 198-212; doi: 10.3221/igf-esis.55.15 209 achieved. in epoxy composites, a good load transfer efficiency combined with the dispersion state plays a relevant role in the enhancement of performance. a suboptimal dispersion state and the cnfs random orientation during the fabrication may result in an ineffective reinforcement or even negative effect. in general, the load transfer reflects the interfacial interactions: weak fillers/polymer van der waals interactions and polymer matrix, ionic or covalent bonding when chemical treatments are applied, and the mechanical interlocking caused by unsmooth fibre surfaces. since in this work cnfs were not chemically treated the interfacial adhesion is originated from the non-bonded interactions, which produces inefficient load transfer. due to the fact that both cured epoxy matrixes are not the same and present important differences, their different results showed in their relaxation curves can be attributed to their different interfacial adhesion and the different physical interactions turned out from the non-identical polarity of both resins. regarding the creep behaviour, fig. 8 shows typical curves obtained from the experimental tests, where the displacement is the result measured at any moment of the test (d) divided by its first value (d0). in all curves is observed an instantaneous displacement, which depends on the stress level, and is followed by primary and secondary creep stages that are typical in creep curves. for these settings, the third stage occurs only for extended periods of time or higher stress values. in detail, fig. 8b) shows that ebalta resin with 0.5 wt. % cnfs presents greater creep displacements than neat ebalta resin. for example, the creep strain increases about 18.2% after 180 min for ebalta resin with 0.5wt. % cnfs and 13.2% for neat ebalta resin. similarly, for neat sicomin resin and sicomin resin with 0.75 wt. % cnfs, this value increases 8.6% and 9.4%, respectively. a) b) figure 8: creep curves for: a) neat sicomin sr 8100 and nano-enhanced resin with 0.75 wt.% cnfs, at bending stress of 50 mpa, b) neat ebalta ah 150 and nano-enhanced resin with 0.5 wt.% cnfs, at bending stress of 50 mpa. in this case, for neat resins, the creep is a consequence of the combining effect of viscous flow and elastic deformation [41]. according to bouafif et al. [44], molecular motions in the backbone polymer arrangement is responsible for the creep phenomenon, and it is conditioned by the stress level. jian et al. [45] suggested that there is a quantitative connection between molecular mobility and macroscopic deformation. a relatively low quantity of cnfs has a hindrance effect on polymer chain mobility of the epoxy matrix, as well as the chain disentanglement and slippage. it was mentioned that the presence of cnfs can hinder the motion of the epoxy polymer chains leading to an improved creep performance but depending on the filler concentration a contradictory response to the above said have also been detailed. cnfs-epoxy nanocomposites tend to exhibit time-dependent deformations on account of the inherent viscoelastic behaviour of polymers, over a wide range of temperatures which can be depicted by creep for a constant load. the presence of fillers can lead to a relevant improvement in the creep resistance. however, in the case of local aggregation of cnts or cnfs, the creep resistance does not increase continuously with growing the filler weight fraction in particular at elevated percentages [46]. the creep response in an epoxy nanocomposite is affected by an irregular dispersion of cnfs in the matrix and a weakened filler/polymer interfacial region derived from the bad compatibility between both materials. hassanzadehaghdam et al. [46] explained that an increment in the interface thickness appeared to improve the nanocomposite creep resistance because the interface had lower compliance. the reinforcing capability in nanocomposites is weaker with higher weight fraction and creep loads as the agglomeration occurs and the filler/epoxy adhesion deteriorates [45]. however, an increment in filler weight fraction with good dispersion may result in a perceptible reduction of creep displacements. thus, 1,00 1,05 1,10 1,15 1,20 0 50 100 150 200 d is pl ac em en t [] time [min] neat resin epoxy + 0.5 wt.% cnfs ebalta ah 150 1,00 1,05 1,10 1,15 1,20 0 50 100 150 200 d is p le ce m en te [] time [min] neat resin epoxy + 0.75wt.% cnfs sicomin sr 8100 p. santos et alii, frattura ed integrità strutturale, 55 (2021) 198-212; doi: 10.3221/igf-esis.55.15 210 a greater comprehension of the creep deformation and the reinforcing mechanism of creep resistance in nanocomposites at the molecular level is still imperative because the creep response is a matter of concern for long‐term durability of these materials [47]. one the one hand, from the comparison of the creep curves for neat sicomin sr 8100 and nano-enhanced resin with 0.75 wt.% de cnfs it can be observed that the effect of the filler presence is almost irrelevant, neither positive nor detrimental. there was a slight increment of creep displacement, especially after 50-75 minutes, which shows a slightly negative effect of the cnfs in the long-term durability. one the other hand, for the neat ebalta ah 150 and the nano-enhanced resin with 0.5 wt.% de cnfs, it can be clearly observed the negative effect of the fillers in the overall creep behaviour. the ebalta based nanocomposite creep displacement increases noticeably respect to the pristine resin meaning that the creep resistance decreases in an important way. the harmful effects of a weakened filler/polymer interfacial region and/or the bad state of dispersion of cnfs into the polymer matrix are detected in the ebalta sample. the reason may come from the different physical interactions yield from the distinctive polarities of both resins since their chemical compositions are not identical. conclusions ifferent percentages of cnfs were used to improve the mechanical properties of two commercial epoxy resin, particularly their static and viscoelastic properties. it was possible to observe that, independently of the epoxy resin, higher values of cnfs added to the resin promoted higher flexural stress and modulus. the best weight content was 0.75% for sicomin sr 8100 and 0.5% for ebalta ah 150. regarding the strain‐rate sensitivity, independently of the resin and nanocomposite, it was possible to observe that both materials are strain‐rate sensitivity. the bending stress and modulus increase for higher values of strain rate. finally, from the stress relaxation tests, it is clear that stress is reduced over time, but when the cnfs are added to the resins, they are less prone to stress relaxation. in the case of creep response, the displacement increases with time for all systems, but, in this case, nanocomposites are more prone to creep. acknowledgements his work was supported by the project centro-01-0145-feder-000017 emades energy, materials and sustainable development, co-financed by the portugal 2020 program (pt 2020), within the regional operational program of the center (centro 2020) and the european union through the european regional development fund (erdf). references [1] kancherla, k.b., subbappa, d.b., hiremath, s.r., raju, b., roy mahapatra, d. (2019). enhancing mechanical properties of glass fabric composite with surfactant treated zirconia nanoparticles, compos. part a appl. sci. manuf., 118(september 2018), pp. 131–41, doi: 10.1016/j.compositesa.2018.12.023. [2] balasubramaniam, b., sathiyan, g., palani, g.s., iyer, n.r., gupta, r.k. (2019).fiber reinforced polymer nanocomposites for structural engineering applications. materials science and technology, wiley, pp. 1–20. [3] licari, j.j., swanson, d.w. (2011).chapter 3 chemistry, formulation, and properties of adhesives. adhesives technology for electronic applications, elsevier, pp. 75–141. [4] fiore, v., valenza, a. (2013).epoxy resins as a matrix material in advanced fiber-reinforced polymer (frp) composites. advanced fibre-reinforced polymer (frp) composites for structural applications, elsevier, pp. 88–121. [5] takeichi, t., furukawa, n. (2012).epoxy resins and phenol-formaldehyde resins. polymer science: a comprehensive reference, vol. 5, elsevier, pp. 723–51. [6] reis, p.n.b., ferreira, j.a.m., santos, p., richardson, m.o.w., santos, j.b. (2012). impact response of kevlar composites with filled epoxy matrix, compos. struct., 94(12), pp. 3520–8, doi: 10.1016/j.compstruct.2012.05.025. [7] kaybal, h.b., ulus, h., demir, o., şahin, ö.s., avcı, a. (2018). effects of alumina nanoparticles on dynamic impact responses of carbon fiber reinforced epoxy matrix nanocomposites, eng. sci. technol. an int. j., 21(3), pp. 399–407, doi: 10.1016/j.jestch.2018.03.011. [8] shen, m.-y., chang, t.-y., hsieh, t.-h., li, y.-l., chiang, c.-l., yang, h., yip, m.-c. (2013). mechanical properties d t p. santos et alii, frattura ed integrità strutturale, 55 (2021) 198-212; doi: 10.3221/igf-esis.55.15 211 and tensile fatigue of graphene nanoplatelets reinforced polymer nanocomposites, j. nanomater., 2013, pp. 1–9, doi: 10.1155/2013/565401. [9] gao, x., lan, j., jia, x., cai, q., yang, x. (2016). improving interfacial adhesion with epoxy matrix using hybridized carbon nanofibers containing calcium phosphate nanoparticles for bone repairing, mater. sci. eng. c, 61, pp. 174–9, doi: 10.1016/j.msec.2015.12.033. [10] liu, x., yue, d., yang, c., li, n., gao, s., liu, y., mo, g., wu, z., yin, j., su, b., li, l. (2019). fluorinated carbon nanofiber/polyimide composites: electrical, mechanical, and hydrophobic properties, surf. coatings technol., 361(august 2018), pp. 206–11, doi: 10.1016/j.surfcoat.2019.01.033. [11] liu, w., wang, y., wang, p., li, y., jiang, q., hu, x., wei, y., qiu, y., shahabadi, s.i.s., lu, x. (2017). a biomimetic approach to improve the dispersibility, interfacial interactions and toughening effects of carbon nanofibers in epoxy composites, compos. part b eng., 113, pp. 197–205, doi: 10.1016/j.compositesb.2017.01.040. [12] gantayat, s., rout, d., swain, s.k. (2017). structural and mechanical properties of functionalized carbon nanofiber/epoxy nanocomposites, mater. today proc., 4(8), pp. 9060–4, doi: 10.1016/j.matpr.2017.07.259. [13] buchanan, j.p., reed-gore, e.r., jefcoat, j.a., moser, r.d., klaus, k.l., peel, h.r., buchanan, r.k., barnes, e., alberts, e.m., shukla, m.k. (2019). increasing mechanical resilience and enhanced electrical conductivity through the incorporation of cnf reinforcing additives in pa6 nanocomposites, struct. chem., 30(1), pp. 341–9, doi: 10.1007/s11224-018-1236-8. [14] zhou, y., akanda, s.r., jeelani, s., lacy, t.e. (2007). nonlinear constitutive equation for vapor-grown carbon nanofiber-reinforced sc-15 epoxy at different strain rate, mater. sci. eng. a, 465(1–2), pp. 238–46, doi: 10.1016/j.msea.2007.04.042. [15] poveda, r.l., gupta, n. (2016). change in failure mode of carbon nanofibers in nanocomposites as a function of loading rate, j. mater. sci., 51(10), pp. 4917–27, doi: 10.1007/s10853-016-9796-8. [16] zare, y. (2016). the roles of nanoparticles accumulation and interphase properties in properties of polymer particulate nanocomposites by a multi-step methodology, compos. part a appl. sci. manuf., 91, pp. 127–32, doi: 10.1016/j.compositesa.2016.10.003. [17] oberdisse, j. (2006). aggregation of colloidal nanoparticles in polymer matrices, soft matter, 2(1), pp. 29–36, doi: 10.1039/b511959f. [18] padmanabhan, v., frischknecht, a.l., mackay, m.e. (2012). effect of chain stiffness on nanoparticle segregation in polymer/nanoparticle blends near a substrate, macromol. theory simulations, 21(2), pp. 98–105, doi: 10.1002/mats.201100048. [19] ma, x., zare, y., rhee, k.y. (2017). a two-step methodology to study the influence of aggregation/agglomeration of nanoparticles on young’s modulus of polymer nanocomposites, nanoscale res. lett., 12, pp. 0–6, doi: 10.1186/s11671-017-2386-0. [20] shaffer, m.s.p., fan, x., windle, a.h. (1998). dispersion and packing of carbon nanotubes, carbon n. y., 36(11), pp. 1603–12, doi: 10.1016/s0008-6223(98)00130-4. [21] fiedler, b., gojny, f.h., wichmann, m.h.g., nolte, m.c.m., schulte, k. (2006). fundamental aspects of nanoreinforced composites, compos. sci. technol., 66(16), pp. 3115–25, doi: 10.1016/j.compscitech.2005.01.014. [22] liu, s., chevali, v.s., xu, z., hui, d., wang, h. (2018). a review of extending performance of epoxy resins using carbon nanomaterials, compos. part b eng., 136, pp. 197–214, doi: 10.1016/j.compositesb.2017.08.020. [23] ignatenko, v.y., ilyin, s.o., kostyuk, a. v., bondarenko, g.n., antonov, s. v. (2020). acceleration of epoxy resin curing by using a combination of aliphatic and aromatic amines, polym. bull., 77(3), pp. 1519–40, doi: 10.1007/s00289-019-02815-x. [24] garcia, f.g., soares, b.g., pita, v.j.r.r., sánchez, r., rieumont, j. (2007). mechanical properties of epoxy networks based on dgeba and aliphatic amines, j. appl. polym. sci., 106(3), pp. 2047–55, doi: 10.1002/app.24895. [25] baig, z., akram, n., zia, k.m., saeed, m., khosa, m.k., ali, l., saleem, s. (2020). influence of amine‐terminated additives on thermal and mechanical properties of diglycidyl ether of bisphenol a (dgeba) cured epoxy, j. appl. polym. sci., 137(8), pp. 48404, doi: 10.1002/app.48404. [26] cai, h., li, p., sui, g., yu, y., li, g., yang, x., ryu, s. (2008). curing kinetics study of epoxy resin/flexible amine toughness systems by dynamic and isothermal dsc, thermochim. acta, 473(1–2), pp. 101–5, doi: 10.1016/j.tca.2008.04.012. [27] nie, y., hübert, t. (2011). effect of carbon nanofiber (cnf) silanization on the properties of cnf/epoxy nanocomposites, polym. int., 60(11), pp. 1574–80, doi: 10.1002/pi.3124. [28] bal, s. (2010). experimental study of mechanical and electrical properties of carbon nanofiber/epoxy composites, mater. des., 31(5), pp. 2406–13, doi: 10.1016/j.matdes.2009.11.058. p. santos et alii, frattura ed integrità strutturale, 55 (2021) 198-212; doi: 10.3221/igf-esis.55.15 212 [29] wu, q., zhao, r., ma, q., zhu, j. (2018). effects of degree of chemical interaction between carbon fibers and surface sizing on interfacial properties of epoxy composites, compos. sci. technol., 163(december 2017), pp. 34–40, doi: 10.1016/j.compscitech.2018.05.013. [30] prolongo, s.g., burón, m., gude, m.r., chaos-morán, r., campo, m., ureña, a. (2008). effects of dispersion techniques of carbon nanofibers on the thermo-physical properties of epoxy nanocomposites, compos. sci. technol., 68(13), pp. 2722–30, doi: 10.1016/j.compscitech.2008.05.015. [31] zhu, j., wei, s., ryu, j., budhathoki, m., liang, g., guo, z. (2010). in situ stabilized carbon nanofiber (cnf) reinforced epoxy nanocomposites, j. mater. chem., 20(23), pp. 4937–48, doi: 10.1039/c0jm00063a. [32] wang, j., gong, j., gong, z., yan, x., wang, b., wu, q., li, s. (2010). effect of curing agent polarity on water absorption and free volume in epoxy resin studied by pals, nucl. instruments methods phys. res. sect. b beam interact. with mater. atoms, 268(14), pp. 2355–61, doi: 10.1016/j.nimb.2010.04.010. [33] sandler, s.r., berg, f.r. (1965). effect of polarity of bisphenol a epoxy resins on adhesion at cryogenic and elevated temperatures, j. appl. polym. sci., 9(11), pp. 3707–19, doi: 10.1002/app.1965.070091118. [34] wilson, a.d., stewart, f.f. (2014). structure-function study of tertiary amines as switchable polarity solvents, rsc adv., 4(22), pp. 11039–49, doi: 10.1039/c3ra47724j. [35] tao, k., yang, s., grunlan, j.c., kim, y.s., dang, b., deng, y., thomas, r.l., wilson, b.l., wei, x. (2006). effects of carbon nanotube fillers on the curing processes of epoxy resin-based composites, j. appl. polym. sci., 102(6), pp. 5248–54, doi: 10.1002/app.24773. [36] seyhan, a.t., sun, z., deitzel, j., tanoglu, m., heider, d. (2009). cure kinetics of vapor grown carbon nanofiber (vgcnf) modified epoxy resin suspensions and fracture toughness of their resulting nanocomposites, mater. chem. phys., 118(1), pp. 234–42, doi: 10.1016/j.matchemphys.2009.07.045. [37] dutta, a., ryan, m.e. (1979). effect of fillers on kinetics of epoxy cure, j. appl. polym. sci., 24(3), pp. 635–49, doi: 10.1002/app.1979.070240302. [38] ingram, j., zhou, y., jeelani, s., lacy, t., horstemeyer, m.f. (2008). effect of strain rate on tensile behavior of polypropylene and carbon nanofiber filled polypropylene, mater. sci. eng. a, 489(1–2), pp. 99–106, doi: 10.1016/j.msea.2008.01.010. [39] delhaye, v., clausen, a.h., moussy, f., othman, r., hopperstad, o.s. (2011). influence of stress state and strain rate on the behaviour of a rubber-particle reinforced polypropylene, int. j. impact eng., 38(4), pp. 208–18, doi: 10.1016/j.ijimpeng.2010.11.004. [40] reis, p.n.b., gorbatikh, l., ivens, j., lomov, s.v. (2019). strain-rate sensitivity and stress relaxation of hybrid selfreinforced polypropylene composites under bending loads, compos. struct., 209(august 2018), pp. 802–10, doi: 10.1016/j.compstruct.2018.11.030. [41] glaskova-kuzmina, t., aniskevich, a., zarrelli, m., martone, a., giordano, m. (2014). effect of filler on the creep characteristics of epoxy and epoxy-based cfrps containing multi-walled carbon nanotubes, compos. sci. technol., 100, pp. 198–203, doi: 10.1016/j.compscitech.2014.06.011. [42] reis, p.n.b., silva, m.p., santos, p., parente, j.m., valvez, s., bezazi, a. (2020). mechanical performance of an optimized cork agglomerate core-glass fibre sandwich panel, compos. struct., 245, pp. 112375, doi: 10.1016/j.compstruct.2020.112375. [43] jian, w., lau, d. (2020). understanding the effect of functionalization in cnt-epoxy nanocomposite from molecular level, compos. sci. technol., 191(november 2019), pp. 108076, doi: 10.1016/j.compscitech.2020.108076. [44] bouafif, h., koubaa, a., perré, p., cloutier, a. (2013). creep behaviour of hdpe/wood particle composites, int. j. microstruct. mater. prop., 8(3), pp. 225, doi: 10.1504/ijmmp.2013.055385. [45] jian, w., lau, d. (2019). creep performance of cnt-based nanocomposites: a parametric study, carbon n. y., 153, pp. 745–56, doi: 10.1016/j.carbon.2019.07.069. [46] hassanzadeh-aghdam, m.k., mahmoodi, m.j., ansari, r. (2019). creep performance of cnt polymer nanocomposites -an emphasis on viscoelastic interphase and cnt agglomeration, compos. part b eng., 168(august 2018), pp. 274–81, doi: 10.1016/j.compositesb.2018.12.093. [47] nomula, s.s.r., rathore, d.k., ray, b.c., prusty, r.k. (2019). creep performance of cnt reinforced glass fiber/epoxy composites: roles of temperature and stress, j. appl. polym. sci., 136(25), pp. 47674, doi: 10.1002/app.47674. microsoft word numero 9 art 6 finale d. castagnetti et alii, frattura ed integrità strutturale, 9 (2009) 55 – 63; doi: 10.3221/igf-esis.09.06 55 modellazione efficiente agli elementi finiti per l’analisi a collasso di strutture incollate complesse d. castagnetti, a. spaggiari, e. dragoni università di modena e reggio emilia, dipartimento di scienze e metodi dell’ingegneria, via amendola, 2 –42100 reggio andrea.spaggiari@unimore.it riassunto. il lavoro verifica l’applicabilità di un modello semplificato agli elementi finiti per l’analisi a collasso post elastico di strutture incollate complesse in parete sottile. al fine di superare le limitazioni dei modelli di letteratura come l’uso di elementi speciali, il lavoro sfrutta un modello ridotto già presentato dagli autori in campo elastico. tale modello è basato sulla rappresentazione degli aderendi mediante elementi semistrutturali (piastre o gusci) e dell’adesivo per mezzo di speciali elementi coesivi. la continuità strutturale tra aderendi e adesivo è ottenuta mediante vincoli interni (tied mesh) che accomunano i gradi di libertà dei nodi mutuamente affacciati di aderendi ed adesivo. la struttura analizzata è un simulacro di incollaggio industriale e produce nella strato adesivo una sollecitazione complessa, analizzabile solo con modelli numerici. si considera una struttura tubolare in parete sottile a sezione quadrata, fatta di due spezzoni posti testa a testa e incollati con fazzoletti di lamiera sui quattro lati. la struttura è sottoposta a flessione a tre punti fino al cedimento e la zona incollata posta disassata rispetto al punto di applicazione del carico riceve una sollecitazione indiretta. i risultati dell’analisi fem, confrontati direttamente con le curve sperimentali forza-spostamento, evidenziano una buona accuratezza del metodo, in termini di rigidezza, forza massima e comportamento post elastico della struttura, accompagnati da ridotte dimensioni del modello e tempi di calcolo molto contenuti. grazie a questi vantaggi, la procedura si presta ad effettuare l’analisi di strutture incollate complesse, altrimenti ingestibili se affrontate con una modellazione agli elementi finiti tradizionale. abstract. the paper deals with the application of an efficient finite element (fe) model for the failure analysis of bonded structures. aim of the work is to assess the accuracy and applicability of the computational model in the prediction of the post-elastic response of large and complex bonded structures. in order to overcome the limitations encountered in the technical literature, such as the use of special elements, the present work assesses the applicability of a reduced computational method, previously presented by the authors. the method is based on standard modeling tools, which are available in most of commercial fe packages. the method describes the adherends by semi-structural elements (plates or shells), and the adhesive by means of a single layer of cohesive elements. this work applies the proposed reduced method to a complex, industrial-like, structure. a square thin-walled beam is considered, made of two different portions joined head to head by overlapping thin plates on each side. the beam is loaded by a three point bending fixture up to failure which originates an indirect, complex stress field on the bonded region. the benchmark for the computational analyses are the force-displacement curves obtained by experimental tests on two different geometries. the comparison with the experimental data shows a good accuracy of the proposed method in terms of structure stiffness, maximum load and post-elastic behaviour up to the collapse of the structure. the numerical precision and the computational speed make the proposed method very useful for the efficient analysis of complex bonded structure, both for research and industrial purposes. parole chiave. metodi numerici efficienti, analisi a collasso, costruzioni incollate http://www.gruppofrattura.it/ http://dx.medra.org/10.3221/igf-esis.09.06&auth=true mailto: andrea.spaggiari@unimore.it d. castagnetti et alii, frattura ed integrità strutturale, 9 (2009) 55 63; doi: 10.3221/igf-esis.09.06 56 introduzione l lavoro riguarda l’applicazione di un modello efficiente agli elementi finiti (ef), precedentemente verificato dagli autori in campo elastico, per l’analisi a collasso di strutture incollate. l’obiettivo del lavoro è di valutare l’accuratezza e l’applicabilità del modello computazionale nella previsione della risposta post-elastica di strutture incollate complesse di dimensioni anche elevate utilizzando strumenti computazionali standard. la motivazione della ricerca risiede nel fatto che l’applicazione industriale delle giunzioni strutturali incollate è legata allo sviluppo di metodi di calcolo semplici, veloci e accurati per la previsione della loro resistenza meccanica. in letteratura si ritrovano numerosi metodi agli elementi finiti per l’analisi delle giunzioni incollate [1-10]. molti di questi metodi sono basati su elementi speciali per descrivere lo strato adesivo o la zona di sovrapposizione. i principali svantaggi di questi metodi risiedono nel fatto che gli elementi speciali da essi impiegati sono difficili da implementare nei software agli elementi finiti commerciali impiegati nell’ambito industriale e il loro uso è confinato ad applicazioni di ricerca. in lavori recenti, invece, i metodi più comunemente impiegati adottano approcci basati sulla meccanica della frattura [11-14]. in questo caso, i criteri di cedimento impiegati, richiedono dati che difficilmente sono forniti dal produttore dell’adesivo e devono quindi essere ottenuti sperimentalmente. per superare queste limitazioni, il presente lavoro approfondisce l’analisi di un metodo computazionale semplificato, già presentato dagli autori in [15], per l’analisi di giunzioni strutturali in parete sottile. il metodo è basato su strumenti di modellazione standard e su elementi finiti comuni, implementati nella maggior parte dei software di calcolo commerciali. il metodo descrive gli aderendi mediante elementi semi-strutturali (piastre o gusci), l’adesivo mediante un singolo strato di elementi solidi e ricorre a vincoli cinematici interni per riprodurre la continuità strutturale. in [15] si è dimostrata l’efficienza e l’accuratezza del modello ridotto nel calcolare la distribuzione delle tensioni elastiche lungo il piano medio dello strato adesivo per parecchie geometrie 2d e 3d. successivamente, gli autori hanno esteso il metodo in campo postelastico [17, 22] adottando il semplice criterio di cedimento alle tensioni regolarizzate proposto in [16, 20] ed ottenendo risultati incoraggianti. questo lavoro estende l’applicazione del metodo ridotto ad una trave tubolare, composta da due tratti diseguali incollati testa a testa mediante sovrapposizione di lamierini. la trave è caricata a flessione su tre punti fino a completo collasso ed origina uno stato tensionale complesso sulla zona di incollaggio. si è implementato un criterio di cedimento secondo l’approccio della zona coesiva come proposto in [21] in modo da unire accuratezza del modello e velocità di calcolo. l’elemento di confronto per le analisi computazionali è rappresentato dalle curve forza-spostamento ottenute da prove sperimentali su giunzioni tubolari incollate con la stessa geometria di quelle studiate numericamente. l’originalità del lavoro consiste nella semplicità degli strumenti computazionali proposti, basati su opzioni standard di modellazione disponibili in ogni pacchetto di calcolo agli elementi finiti commerciale. ne deriva un metodo generale e di facile impiego, caratterizzato da una forte riduzione del costo computazionale (occupazione di memoria e tempo di calcolo), conseguente alla minimizzazione dei gradi di libertà del modello. semplicità, generalità ed efficienza fanno del metodo proposto un valido strumento industriale per simulare il comportamento meccanico di strutture incollate grandi e complesse. materiali e metodi l lavoro è diviso in due fasi: analisi computazionali e prove sperimentali, queste ultime ancora in fase esplorativa e condotte solo su due tipi di geometria. e’ stata considerata una struttura trabeiforme (fig. 1), costituita da due spezzoni di tubo quadro uniti da piastrine di collegamento incollate per sovrapposizione semplice su ciascun lato. la struttura viene caricata a flessione su tre punti. essendo la zona di unione lontana dalla mezzeria, nell’adesivo delle giunzioni si sviluppa uno stato di sollecitazione indiretto e complesso. la struttura, di semplice realizzazione, è più un simulacro di una struttura reale incollata che una semplice provino di laboratorio e costituisce un buon banco di prova per il metodo proposto. le prove sia computazionali che sperimentali sono stato condotte fino al collasso della struttura. prove sperimentali le prove sperimentali svolte sono state di carattere esplorativo per valutare quali e quanti fattori considerare in una futura serie di prove sistematiche. la fig. 1 rappresenta schematicamente la geometria considerata per la giunzione. in fig. 1-a si i i http://www.gruppofrattura.it/ http://dx.medra.org/10.3221/igf-esis.09.06&auth=true d. castagnetti et alii, frattura ed integrità strutturale, 9 (2009) 55 – 63; doi: 10.3221/igf-esis.09.06 57 riportano le dimensioni della struttura incollata mentre in fig. 1-b si riporta la geometria della struttura tubolare semplice, senza giunzione. quest’ultima ha la funzione di riferimento per valutare l’influenza globale della giunzione sulla resistenza della struttura. sono state considerate due differenti dimensioni degli aderendi per ognuna delle due configurazioni. in tabella 1 sono riportate le dimensioni e i materiali scelti. gli aderendi sono tubi quadri in acciaio da costruzione fe510 e l’adesivo impiegato è un epossidico bi-componente ad alta resistenza (henkel 9466 [18]). la tabella 1 raccoglie le proprietà elastiche degli aderendi e dell’adesivo mentre il loro comportamento post-elastico è descritto dalle curve di fig. 2a e 2b. la larghezza delle piastre di collegamento è di 25 mm e lo spessore dello strato adesivo è stato ottenuto portando a contatto le parti e lo si è ipotizzato pari a 0.05mm, dovuto solo alla rugosità degli aderendi. gli aderendi sono stati preparati, prima di incollarli, attraverso una levigazione meccanica con carta abrasiva (grana 200) e successivamente puliti con il solvente sgrassatore henkel loctite 7063 [19], per garantire una migliore adesione substratoadesivo. le prove sperimentali sono state svolte ad una velocità costante della traversa di 60 mm/s fino al collasso completo del giunto. la macchina di prova usata è una mts mini bionix 858, servo idraulica, con capacita assiale di 25kn. (a) (b) figura 1: schema della struttura tubolare incollata (a) e del tubo quadro integro (b) geometria l (mm) 25 40 b (mm) 50 100 spessore adesivo (mm) 0.05 materiali aderendi adesivo acciaio henkel loctite 9466 modulo di young (mpa) 206.000 1718 coefficiente di poisson 0.3 0.3 tensione elastica massima (mpa) 500 60 tabella 1: variabili geometriche e proprietà meccaniche materiali. http://www.gruppofrattura.it/ http://dx.medra.org/10.3221/igf-esis.09.06&auth=true d. castagnetti et alii, frattura ed integrità strutturale, 9 (2009) 55 63; doi: 10.3221/igf-esis.09.06 58 (a) (b) figura 2: legame coesivo adesivo (a) e legame costitutivo acciaio elastoplastico (b) analisi computazionale lo scopo dell’analisi computazionale è di ottenere la curva forza spostamento fino al collasso completo, permettendo un confronto diretto con i risultati sperimentali. il modello computazionale è stato sviluppato in forma tridimensionale sia per la struttura tubolare incollata sia la struttura integra. gli aderendi sono stati descritti mediante elementi semi-strutturali di tipo piastra (shell) collocati sulle superfici medie delle pareti del tubo. lo strato adesivo è descritto mediante un singolo strato di elementi coesivi solidi. la modellazione degli aderendi mediante elementi strutturali determina una discontinuità virtuale tra aderendi ed adesivo. per ripristinare il collegamento, si impiegano vincoli cinematici interni che rendono uguali i gradi di libertà corrispondenti delle parti vincolate. sia gli aderendi sia l’adesivo sono stati modellati per mezzo di elementi lineari ad integrazione ridotta, aventi forma quadrata. la dimensione della mesh sull’aderendo è pari alla distanza dei piani medi degli aderendi, mentre l’adesivo è discretizzato con elementi aventi lato pari a un quarto della distanza dei piani medi degli aderendi. questa scelta, derivante da osservazioni effettuate in lavori precedenti degli autori, ha fornito un buon compromesso tra precisione dei risultati e tempi di calcolo ragionevoli [22]. i modelli computazionali sono stati sviluppati per tutte le configurazioni esaminate sperimentalmente e sono stati implementati mediante il solutore esplicito del software agli elementi finiti abaqus 6.8 [23]. gli aderendi sono stati modellati con un semplice legame elasto-plastico incrudente bilineare (fig. 2a), mentre l’adesivo è stato descritto mediante il modello di zona coesiva di fig. 2b. i valori di snervamento degli aderendi sono stati ottenuti sulla base dei dati forniti dal produttore dei tubi mentre i parametri che governano l’andamento della zona coesiva (tensione massima = 60 mpa, energia di frattura = 0.69 n/m) sono stati ricavati da lavori di letteratura [24] riguardanti il medesimo adesivo. il criterio scelto prevede che al raggiungimento del limite elastico, in modo i, ii, iii l’adesivo perda progressivamente le sue proprietà meccaniche con legge esponenziale. al modello agli elementi finiti è stato applicata centralmente una velocità di spostamento di 150 mm/s, di poco superiore a quella sperimentale, e l’opzione di scalatura della massa, tecniche che consentono di ridurre i tempi di analisi, senza pregiudicarne i risultati. dalle analisi si è ricavato il carico di reazione della struttura fino al suo cedimento. tutti i modelli sono stati risolti mediante un processore intel core duo mobile t7200. risultati a fig. 3 raccoglie i risultati sperimentali, in termini di diagramma forza-spostamento, per le configurazioni considerate. la fig 3a si riferisce al tubo di lato 25mm mentre la fig 3b è relativa al giunto di lato 40 mm. in ogni diagramma è rappresentata sia la curva prodotta dalla trave incollata (linea nera sottile) che la curva generata dall’analogo tubolare integro (linea grigia spessa). l http://www.gruppofrattura.it/ http://dx.medra.org/10.3221/igf-esis.09.06&auth=true d. castagnetti et alii, frattura ed integrità strutturale, 9 (2009) 55 – 63; doi: 10.3221/igf-esis.09.06 59 per ogni prova sperimentale si è effettuata la relativa simulazione agli elementi finiti. in fig. 4 si riporta il confronto tra la simulazione numerica (linea nera spessa) e la prova sperimentale (curva grigia sottile) per quanto riguarda il tubo integro, mentre in fig. 5 si riporta il confronto sul tubo incollato. in tab. 2 sono riportati i tempi di calcolo per le prove numeriche effettuate con una macchina di fascia media, processore intel t7200 1.99ghz, ram 2gb. in fig. 6 si mostra invece il confronto tra le immagini sperimentali delle prove di flessione e le relative simulazioni agli elementi finiti. in fig 6a si riporta la prova sperimentale sul tubo di lato 25mm, fig 6b si riporta la prova sperimentale sul tubo di lato 40mm, in fig. 6c la simulazione del tubo di lato 25mm e in fig. 6d la simulazione del tubo di lato 40mm. (a) (b) figura 3: curve sperimentali forza – corsa del tubo lato 25mm (a) e lato 40mm (b). (a) (b) figura 4: confronto numerico-sperimentale tubo integro lato 25mm (a) e lato 40mm (b). lato tubo (mm) tipo tubo 25 40 integro 96.5 340.3 incollato 5085 5438 tabella 2: tempi di analisi (s) – processore intel t7200 1.99ghz, ram 2gb. http://www.gruppofrattura.it/ http://dx.medra.org/10.3221/igf-esis.09.06&auth=true d. castagnetti et alii, frattura ed integrità strutturale, 9 (2009) 55 63; doi: 10.3221/igf-esis.09.06 60 (a) (b) figura 5: confronto numerico-sperimentale tubo incollato lato 25mm (a) e lato 40mm (b). (a) (b) (c) (d) figura 6: prova sperimentale su tubo incollato lato 25mm (a) e lato 40mm (b). simulazione numerica (mappa degli spostamenti) del tubo incollato lato 25mm (c) e lato 40mm (d). discussione prove sperimentali n primo luogo si nota dalle curve sperimentali riportate in fig. 3 che il carico sostenuto dal tubo quadro integro è inferiore a quello dello stesso tubo tagliato e incollato. questo comportamento si riscontra per entrambe le geometrie considerate. ciò è spiegabile in parte poiché lo spessore di parete nella zona incollata sostanzialmente raddoppia aumentando quindi il modulo di resistenza della sezione, ma è anche indice che l’adesivo trasferisce il i http://www.gruppofrattura.it/ http://dx.medra.org/10.3221/igf-esis.09.06&auth=true d. castagnetti et alii, frattura ed integrità strutturale, 9 (2009) 55 – 63; doi: 10.3221/igf-esis.09.06 61 completamente ed efficientemente il carico. da questo punto di vista è importante notare che in ambedue le prove lo snervamento dell’acciaio avviene prima del cedimento dell’adesivo (fig. 3). nel caso del tubo di lato 25mm (fig. 5a), l’adesivo non presenta cedimenti catastrofici e la prova è stata terminata quindi per il raggiungimento della corsa massima disponibile. l’oscillazione nel tratto iniziale è forse imputabile a una microfrattura nella zona incollata, in quanto durante l’esecuzione della prova si sono rilevati rumori che sembravano indicare una nascente cricca nell’adesivo. questo cedimento probabilmente è occorso in una zona incollata non critica, forse a causa di inclusioni di aria, e la prova è quindi continuata senza cedimenti della struttura fino alla completa plasticizzazione del tubo. dal diagramma di fig. 3b si osserva inoltre che la curva sperimentale del tubo incollato di lato 40mm pur avendo un carico massimo maggiore del tubo integro ha un cedimento prematuro con rottura catastrofica della struttura. non avendo effettuato ripetizioni della prova questo non è un dato statisticamente rilevante ma è possibile motivare la differenza a fronte di alcune considerazioni sulla differente geometria delle strutture. in fig. 6-a si nota come nella prova di flessione nel tubo di lato 25mm la cerniera plastica, originata sugli aderendi dal carico flessionale, è sufficientemente lontana dalla zona incollata e non influisce quindi sulla zona di incollaggio. nel caso della prova di fig. 6-b, invece, l’inizio del tratto incollato è molto più vicino alla cerniera plastica. vi è quindi una influenza diretta della deformazione prodotta nell’aderendo dalla cerniera plastica sulla zona di incollaggio. questo può determinare una possibile causa del cedimento prematuro della struttura. un’altra differenza rispetto alla struttura incollata di lato 25mm è che la piastra incollata sul tubo di lato 40mm è più stretta rispetto al lato del tubo, infatti il rapporto tra la piastra e il tubo da 40mm è 0.625 mentre è 1 per il tubo di lato 25mm. questo significa che il tubo di lato 25mm è più rinforzato rispetto all’altro e questo giustifica la sua maggiore capacità di sostenere carico. confronto numerico sperimentale in fig. 4 si evidenzia un buon accordo tra le curve sperimentali e la simulazione agli elementi finiti del tubo integro per tutte le configurazioni esaminate. la differenza maggiore si ha nel tratto elastico ed è spiegabile in quanto l’inizio della prova sperimentale è affetto da un assestamento della struttura alla prima applicazione del carico e ciò comporta una discrepanza tra le curve. inoltre la mesh sugli aderendi è abbastanza rada il che irrigidisce ulteriormente la struttura. la pendenza del tratto elastico, però, è comparabile e l’errore sulla rigidezza molto contenuto. per quanto riguarda la resistenza della struttura l’errore sulla forza massima è inferiore a ±7% e anche il tratto post elastico viene ben colto dalla simulazione. la fig. 5 mostra un discreto accordo tra le curve sperimentali (linee grigie sottili) e la simulazione agli elementi finiti del tubo incollato (linee nere spesse). in primo luogo si rileva che le oscillazioni presenti nelle curve numeriche sono dovute alla modalità di simulazione esplicita che è stata adottata e pertanto non vanno considerate. e’ stato anche effettuata una scalatura della massa della struttura che aumenta questo effetto, ma consente di abbreviare in maniera consistente il tempo di analisi. in fig 5a si mostra il confronto per il tubo di lato 25mm. non si è verificato il collasso del tubo e quindi non si hanno informazioni precise né sulla energia assorbita dallo strato adesivo né sull’istante di collasso, ma si registra solamente che la giunzione è sufficientemente resistente per portare a snervamento completo il tubo. la simulazione evidenzia una rigidezza comparabile a quella della prova di flessione e una forza massima di 10.98 kn, di poco superiore al dato sperimentale di 9.8 kn, con un errore del 10%. il tratto post elastico della simulazione decresce in maniera meno accentuata rispetto alla prova reale ma ciò è probabilmente imputabile al modello di materiale bilineare incrudente usato per gli aderendi. in fig 5b, invece, si osserva che, per il tubo incollato di lato 40mm la risposta della simulazione è più rigida nel primo tratto elastico a causa sia della cedevolezza della attrezzatura sperimentale, ma anche della mesh rada sull’aderendo che irrigidisce ulteriormente la struttura. in fig. 6c si riporta la mappa degli spostamenti della simulazione sul tubo di lato 25mm, in ottimo accordo con la prova sperimentale di fig. 6a, mentre in fig. 6d si mostra la mappa degli spostamenti del tubo di lato 40mm all’istante in cui avviene il cedimento completo dell’adesivo. e’ interessante notare il buon accordo tra le deformate sperimentali e quelle simulate, anche se la fig. 6d presenta una differenza sostanziale con la prova sperimentale di fig. 6b dovuta alla mancanza della forza di gravità. infatti nella prova sperimentale i due spezzoni di tubo, dopo il cedimento dell’adesivo si adagiano http://www.gruppofrattura.it/ http://dx.medra.org/10.3221/igf-esis.09.06&auth=true d. castagnetti et alii, frattura ed integrità strutturale, 9 (2009) 55 63; doi: 10.3221/igf-esis.09.06 62 l’uno sull’altro, mentre nella simulazione la rottura dello strato adesivo crea un effetto di ritorno elastico per cui i due spezzoni tendono ad allontanarsi. la forza massima sviluppata dalla simulazione nel caso del tubo di lato 40mm è 14.2 kn contro i 13.2 kn della prova sperimentale con un errore del 7.5%. la previsione computazionale del tratto post-elastico mostra una discesa prematura del carico sopportato dalla struttura mentre prevede in ottimo accordo con la curva sperimentale con esattezza il livello di inflessione che porta a completo collasso la struttura. il tempo necessario all’analisi, di una costruzione incollata di questo genere mostrato in tab. 2, si attesta sui 5000 secondi. ciò rende il metodo proposto valido anche per l’analisi costruzioni di dimensioni maggiori, che si possono facilmente incontrare in un contesto industriale, senza compromettere la precisione dei risultati che si mantiene buona, essendo l’errore sempre inferiore al 10%. conclusioni l lavoro mostra l’applicabilità di un modello semplificato agli elementi finiti per l’analisi a collasso di strutture incollate complesse. il modello è applicato ad una struttura tubolare incollata ed è confrontato direttamente con le prime prove sperimentali esplorative realizzate. il modello è basato sulla rappresentazione degli aderendi mediante elementi shell e dell’adesivo per mezzo di speciali elementi coesivi. i nodi corrispondenti di aderendi ed adesivo sono collegati da vincoli interni tipo tied-mesh per ripristinare virtualmente la continuità fisica della giunzione. il confronto con i risultati sperimentali evidenzia una buona accuratezza del metodo sia in termini di forza massima prevista sia di comportamento post-elastico. in particolare si hanno stime sulla forza massima sopportata dal giunto con errori inferiori al 10%, una buona previsione dell’istante di collasso (ove esso si verifica) e una discreta previsione della rigidezza. la buona precisione numerica ed il ridotto peso computazionale (bassa occupazione di memoria e bassi tempi di calcolo) rendono il metodo proposto particolarmente adatto per l’analisi efficiente di costruzioni incollate complesse di interesse industriale. bibliografia [1] b. n. rao, y. v. k. s. rao, s. yadagiri, fibre science and technology, 17 (1982) 77. [2] j. n. reddy, s.roy, int. j. non-linear mechanics, 23 (1988) 97. [3] u. edlund, a.klarbring, computer methods in applied mechanics and engineering, 96 (1992) 329. [4] r. h. andruet, d. a. dillard, s. m. holzer, int. j. of adhesion and adhesives, 21 (2001) 17. [5] j. p. m. goncalves, m. f. s. f. moura, p.m.s.t.castro, int. j. of adhesion and adhesives, 22 (2002) 357. [6] l. tong, x. sun, computational mechanics, 30 (2003) 143. [7] a. d. crocombe, d. a. bigwood, g. richardson, 10 (3) (1990) 167. [8] d. a. bigwood, a. d.crocombe, int. j. of adhesion and adhesives, 10 (1) (1990). [9] j. a. harris, r. d. adams, int. j. adhesion and adhesives, 4 (2) (1984) 65. [10] t. carlberger, u. stigh, engng. fracture mech, 74(14) (2007) 2247. [11] j. p. m. goncalves, m. f. s. f.de moura et al, fatigue fract. engng master struct, 26(5) (2003) 479. [12] h. hadavinia, l. kawashita, a. j. kinloch, d. r. moore, j. g. williams, engng. fracture mechanics, 73(16) (2006) 2324. [13] p. schmidt, u. edlund , int. j. for num. meth. in engng, 1 (2005) 1. [14] n. valoroso, l. champaney, engng fracture mechanics, 73 (18) (2006) 2274. [15] d. castagnetti, e. dragoni, int. j. adhes. and adhes., 29 (2009) 125. [16] l. goglio et al., int. j. adhes. and adhes, 28 (2008) 427. [17] d. castagnetti, a. spaggiari, e. dragoni, proceedings of the 36th aias, ischia (na) (2007). [18] loctite – hysol 9466, technical data sheet, (febbraio 2006). [19] loctite –7063, technical data sheet, (febbraio 2006). [20] d. a. bigwood, a. d.crocombe, int. j. adhes. and adhes, 9 (1989) 229. [21] a. pirondi, f. moroni, abaqus regional users’ meeting, milano (2008). i http://www.gruppofrattura.it/ http://dx.medra.org/10.3221/igf-esis.09.06&auth=true d. castagnetti et alii, frattura ed integrità strutturale, 9 (2009) 55 – 63; doi: 10.3221/igf-esis.09.06 63 [22] d. castagnetti, , a. spaggiari, , e. dragoni, “efficient post-elastic analysis of bonded joints by standard finite element techniques” , (2008, in press). [23] abaqus 6.7, “users’ manual”, hks inc. (2006). [24] a. pirondi, d. fersini, e. perotti, f. moroni”, atti del 19° congresso igf, milano (2007). http://www.gruppofrattura.it/ http://dx.medra.org/10.3221/igf-esis.09.06&auth=true microsoft word numero_38_art_26 r. pezer et alii, frattura ed integrità strutturale, 38 (2016) 191-197; doi: 10.3221/igf-esis.38.26 191 focussed on multiaxial fatigue and fracture atomistic modeling of different loading paths in single crystal copper and aluminum r. pezer university of zagreb faculty of metallurgy, sisak, croatia rpezer@simet.hr i. trapić university of zagreb faculty of mechanical engineering and naval architecture, zagreb, croatia ivan.trapic@fsb.hr abstract. utilizing molecular dynamics (md) integration model we have investigated some of the relevant physical processes caused by different loading paths at the atomic level in cu and al monocrystal specimen. interactions among the atoms in the bulk are modeled with the standard realistic embedded atom method (eam) potentials. md simulation gives us the detailed information about non-equilibrium dynamics including crystal structure defects, vacancies and dislocations. in particular, we have obtained result that indicate increase in the total energy of the crystal during loading (especially cyclic) that provides us direct quantitative evidence of the metal weakening. for the basic response, we have deformed copper and aluminum single crystal according to the simple loading path and a series of multiaxial loading-paths including cyclic repetition. we compute equivalent stress-strain diagrams as well as dislocation total length vs time graphs to describe signatures of the anisotropic response of the crystal. keywords. molecular dynamics; fatigue, multiaxial; copper; aluminum; lammps. citation: pezer., r., trapić, i., atomistic modeling of different loading paths in single crystal copper and aluminum, frattura ed integrità strutturale, 38 (2016) 191-197. received: 15.05.2016 accepted: 20.06.2016 published: 01.10.2016 copyright: © 2016 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. introduction ne of the landmark observation found in a macroscopic piece of polycrystalline engineering metal materials is existence of well-defined mechanic properties like yield stress or ultimate tensile strength. tension test is most common experimental approach to examine structural materials. however, as great physicist and originator of our modern understanding of plasticity e. orowan beautifully stated [1]: "the tensile test [is] very easily and quickly performed but it is not possible to do much with its results, because one does not know what they really mean. they are the outcome of a number of very complicated physical processes.". even today our ability to quantitatively predict plasticity and fatigue properties like dislocation nucleation and multiaxial stress state properties are rather limited. the o r. pezer et alii, frattura ed integrità strutturale, 38 (2016) 191-197; doi: 10.3221/igf-esis.38.26 192 problem is not only due to the immense complexity of the dislocation dynamics coming from atomic degrees of freedom but also because it is governed by phenomena at multiple length and time scales. in last two decades we witness substantial improvement of computing power and accompanied development of the sophisticated physical models [2,3] providing us with possibility to complement information from simple tensile test with numerical simulation. this fact calls for computational experiments that give us direct control over the whole range of scales involved so that we can avoid difficulties like short length ultraviolet divergences in standard crack dynamics laws. crystals are among the most prominent examples of the decisive role of the sub micrometer scales governing the dislocation dynamics. another prominent example is crack propagation accompanied with crystals surface production energy ("fracture energy") that is orientation dependent so that crystal response can be highly anisotropic even in a peace of material that is completely isotropic on the macroscale. at the atomic level in metal systems, interactions that capture complexity that accounts for fatigue and fracture must include terms beyond pairwise interactions. such realistic potentials exist [4, 5] and are constantly improved to provide us with detailed information about non-equilibrium dynamics including crystal structure defects like vacancies and dislocations. the task to develop successful dislocation theory to model plastic phenomena in metal materials proved to be very difficult one. indeed, a great deal of theoretical work has been expended in the past 5 decades in attempts to explain the phenomena of metal plasticity by means of dislocation theory yet no comprehensive theory has been achieved. there has been substantial progress in modeling nucleation and growth of fatigue cracks under multiaxial stresses like fatemi-socie [6] parameter applied to steel specimens. however, at the fundamental atomic scale it turns out that the full resolved stresses play also very important role [7, 8]. here we utilize md simulations to help elucidate how the principal and resolved stress components on the primary slip plane(s) impact dislocation nucleation in fcc cu and al perfect crystals at room temperature. in contrast to prior studies of those systems here we perform both multiaxial and fatigue tests where we quantitatively examine sensitive dislocations effects that govern materials response under the plastic deformation. we are focused mostly on the yielding deformation zone where dislocation nucleation starts at the very high rate. in this sense, cu and al (apart from applicative interest in itself) are interesting fcc candidates. those metals share crystal structure but behave very differently: soft cu contains almost no discernible straight part while al experience very graduate transition from straight to the curved zone of the stress-strain diagram. in short the goal of this work is to examine correlation of the loading axis orientation, stress components resolved onto the {1 1 1} primary slip plane and dislocation density dynamics. here we have found that dynamic properties in fcc single crystals critically depend on the magnitude and loading axis orientation. for the basic response, we have deformed cu and al single crystal according to simple loading path including cyclic fatigue harmonic tensile deformation. in order to further study complex patterns of fracture effects in crystal sample we prepare whole range of different loading-paths. this way we are able to specifically probe anisotropic response in the sample subject to different loading directions and look for the signatures of the multiaxial stress states at the atomic scale. in order to show distinct features of stress-strain relationship for several loading paths first we have simulated evolution by deforming entire model system at the usual ps time scale isothermally at 300 k. the strain rate is several orders higher than we usually see in lab or industry setting but is due to the intrinsic limit of the md time propagation of the atomistic system dynamics. however, since we are following trajectories at individual atoms level the time scales separation is part of the complex process of information transport to meso and macroscale. what is the real information at the atomic level that survives and govern tensile test in the experiment is one of the important questions in solving mechanical properties puzzle. simulation models and methods embedded atom method he semi-empirical embedded-atom method (eam) potentials are energy functions and govern the interaction among the neighboring atoms. it is commonly used approach for metals because it captures main features of the metallic bonding. the potential proposed by m. s. daw and m. i. baskes [9, 10], was based on the quantum mechanical density functional theory. they combined theoretical considerations with a fitting of parameters to the main properties of the bulk crystal. their approach leads to the following expression for the total potential energy of a crystal:    ij i h i i j i e v r ftot , 1 2      (1) t r. pezer et alii, frattura ed integrità strutturale, 38 (2016) 191-197; doi: 10.3221/igf-esis.38.26 193 first term is central repulsive short range pairwise interaction while the second one is a multi-body term (attractive interaction) that models “embedding” a positively charged pseudo-atom core into the “sea” of free electrons created by the surrounding atoms. it is described by the semi-empirical energy function fi with argument describing host electron distribution at atom i. due to the weak bonding directionality cu is an ideal fcc material for accurate characterization by the non-directional generic feature of the eam. essentially all of the physics is contained in eq. (1) and the calculated properties are complex manifestation of the huge number of atoms mutually interacting with one another. during the time evolution atoms are simultaneously exposed to environment forces that give raise to deformation response and defects nucleation that is subject of this work. interatomic potential for aluminum is also very well established and thoroughly checked against many basic equilibrium properties like the elastic constants, the vacancy formation and migration energies, the stacking fault energies and the surface energies. for both, cu and al potentials, it is expected to be applicable to different local environments encountered in present simulations of dislocation and plastic properties within the md simulation framework. simulation modeling as already mentioned in the introduction section, the time step size is difficult to decide because of the intrinsic simulation limits of the method. trial and error process is usual choice but whatever the strategy we take most important is to make sure the total energy conservation is not violated to cause system instabilities. it is desirable to propagate the system as far as possible but characteristic time scale relevant for atoms makes 100 ps as appropriate option. property\metal copper aluminum box size (in lattice constants) 25 25 box size before relaxation (nm) 9.025 10.125 box size after relaxation (nm) 9.080 10.160 temperature (k) 300 300 number of atoms 62500 62500 equilibration time (ps) 20 20 simulation time (ps) 75 75 strain amplitude εa, period tp (ps) 0.18, 25 0.18, 25 table 1: parameters used for md simulations. after the perfect crystal is prepared (initial lattice constants 0.361 and 0.405 nm for cu and al, respectively) in the desired crystallographic orientation, the system of atoms is equilibrated for 20 ps. usual md thermostating procedure has been employed in the isobaric-isothermal (npt) ensemble at a zero pressure and temperature of 300 k. periodic boundary conditions were used along all three axis. summary of all parameters is given in tab. 1. equilibration and simulation time are chosen in order to cause appreciable dislocation nucleation and fatigue phenomena. at the beginning of the simulation, atoms just vibrate around their perfect crystal positions. as the load increase after initial elastic response dislocation nucleation starts and we see characteristic signature of the process qualitatively similar to usual tensile test. md simulation generate huge and abundant information about atomic system and here we use several sophisticated algorithms to extract relevant physical information. however, it is important to keep in mind that physical observables we see in this numerical simulation do not represent measured macroscopic quantities in lab conditions. although correlated quantities, they are distinct. we stress that nevertheless we use even millions of atoms our crystal system is still far from anything to be considered macroscopic. this correlation proves to be difficult tasks to accomplish in theory development and is still part of the ongoing research. r. pezer et alii, frattura ed integrità strutturale, 38 (2016) 191-197; doi: 10.3221/igf-esis.38.26 194 eq 0 0.05 0.1 0.15 0.2 0 2 4 6 8 10 = 0° = 30° = 45° eq 0 0.05 0.1 0.15 0.2 0 1 2 3 4 5 = 0° = 30° = 45° eq 0 0.05 0.1 0.15 0.2 0 1 2 3 4 5 6 7 = 0° = 30° = 45° eq 0 0.05 0.1 0.15 0.2 ( g p a) 0 0.5 1 1.5 2 2.5 3 3.5 = 0° = 30° = 45° results and discussion ig. 1 and 2 shows the equivalent stress-strain diagrams and resolved shear stress onto the {1 1 1} primary slip plane for cu and al monocrystal at room temperature, respectively. equivalent tensile stress is defined in terms of principal values as usual:      2 22eq 1 2 2 3 3 1 1 2             (2) (a) (b) figure 1: different loading paths defined by deformation speeds along system axis. loading speeds are expressed as δε/δt and total magnitude is 0.01 ps-1. (a) equivalent stress-strain diagram (see eq. 2). (b) a resolved shear stress upon the {1 1 1} slip plane in the slip direction. the graphs clearly show strong dependency of the stress-strain correlation to multiaxial character of the loading to crystal system orientation. we note not only quantitative differences but also completely different curvature and smearing out of the peak stress value. effects are much less pronounced in al than in cu system. nevertheless both metals show strong orientation dependency, which alarms for careful analysis when we develop phenomenological or qualitative models of polycrystalline materials. (a) (b) figure 2: same as fig. 1 but this time for al. f r. pezer et alii, frattura ed integrità strutturale, 38 (2016) 191-197; doi: 10.3221/igf-esis.38.26 195 t (ps) 0 12.5 25 37.5 50 62.5 75 0 2 4 6 8 10 = 0° = 30° = 45° t (ps) 0 12.5 25 37.5 50 62.5 75 0 1 2 3 4 5 6 7 = 0° = 30° = 45° it is unlikely that we will develop a single model applicable for all materials and states of stress for the multiaxial fatigue even for the metallic systems. therefore, an important ingredient for successful theory is to take into account whole range of important properties heavily influenced by atomic distribution symmetries in space coordinates. they are associated with the crystallography of the grains and the structure of grain boundaries [8]. fig. 3 shows stress-time evolution during cyclic loading in three directions with respect to x axis in the xy perfect crystal plane where cyclic loading was harmonic and in phase given by following general formula for the strains along x and y axis (angle φ is given in legend of the figures):                     a p cos π 1 sin 2π 2 2 x t t t (3a)                     a p sin π 1 sin 2π 2 2 y t t t (3b) the simulation parameters are given in tab. 1. cycling strain amplitude has been selected so that deformation reaches deep enough into the plastic zone in order to get substantial dislocation density as seen on fig. 4 where it is clear that dislocation nucleation dynamics for cu and al crystal is quite different depending on the deformation direction. (a) (b) figure 3: stress during cyclic loading providing fatigue test for different loading paths defined by deformation angle of stress direction and x-axis in xy plane of the perfect crystal (see eq. 3a, b). (a) copper. (b) aluminum we clearly see completely different response of the cu and al crystal to cyclic in phase (uni)multiaxial loading. while al single crystal shows no significant difference with regard to multiaxial stress state. in a way, al crystal is able to recover after loading no matter what deformation direction we apply. there is also significant difference regarding stress response phase among different deformation orientations. cu system tends to go out of the phase for φ=45º angle of simulation box deformation. one of the obvious physical properties to be reason for this discrepancy between two fcc metals is the stacking-fault energy (sfe). as is well known low sfe is usually accompanied by the lower mobility of a dislocation in a crystal. for al it falls within 160-200 mj/m2 range, and for the cu it is considerably smaller 70-80 mj/m2. critical resolved shear stress in cu and al is affected by the normal stress components acting to the slip plane as shown in [11] suggesting that factors beyond standard given by schmid are necessary for dislocation nucleation description. r. pezer et alii, frattura ed integrità strutturale, 38 (2016) 191-197; doi: 10.3221/igf-esis.38.26 196 motivated by this observation we have performed full atomistic simulation and dislocation identification using advanced dxa algorithm [3]. in fig. 4 we show dislocation density (total length of dislocation line is divided by the system volume) during simulation. we note similar differences between cu and al behavior as we saw in fig. 3 for equivalent stress dynamics. the dislocation morphology is rather consistent for both metals since they are mostly of shockley partial dislocation type. this result is consistent with stacking faults presence mentioned in context of fig. 3 regarding different cyclic loading response in cu and al single crystal. (a) (b) figure 4: the dislocation density during cyclic loading for different loading paths defined by deformation angle of stress direction and x-axis in xy plane of the perfect crystal (see eq. 3a, b). (a) copper. (b) aluminum. conclusions n this paper atomistic simulations of multiaxial strain, including cyclic fatigue harmonic loading, in face centre cubic (fcc) single crystal have been performed for two common metals: cu and al. in addition, we have examined dislocation nucleation as identified during time evolution. the stress response behaviors on main slip plane {1 1 1} have been investigated using resolved shear stress. it has been found that the response to the fatigue significantly differs for cu and al system. time evolution of the dislocation density shows completely different pattern for two metals. connection with significantly different sfe for two metals is discussed. we conjecture that development of a single universal model applicable for all metallic materials and states of stress and the multiaxial fatigue is practically ruled out by complexity of the physical properties at the atomic level. acknowledgments his work has been supported by croatian science foundation under the project multiscale numerical modeling of material deformation responses from macroto nanolevel (2516). references [1] orowan, e., discussion of the significance of tensile and other mechanical test properties of metals, proc. instn. mech. engrs. 151 (1944) 131-146 (p. 133 discussion of paper by h. o’neill). [2] plimpton, s., fast parallel algorithms for short-range molecular-dynamics, j. comput. phys., 117 (1995) 1-19. doi: 10.1006/jcph.1995.1039. [3] stukowski, a., a triangulation-based method to identify dislocations in atomic models, j. mech. phys. solids, 70 (2014) 314-319. doi: 10.1016/j.jmps.2014.06.009. [4] mishin, y., farkas, d., mehl, m.j., papaconstantopoulos, d.a., voter, a.f., kress, j.d., interatomic potentials for monoatomic metals from experimental data and ab initio calculations, phys. rev. b, 59 (1999) 3393. doi: 10.1103/physrevb.59.3393. i t r. pezer et alii, frattura ed integrità strutturale, 38 (2016) 191-197; doi: 10.3221/igf-esis.38.26 197 [5] mishin, y., mehl, m.j., papaconstantopoulos, d.a., voter, a.f., kress, j.d., structural stability and lattice defects in copper: ab initio, tight-binding, and embedded-atom calculations, phys. rev. b, 63 (2001) 224106. doi: 10.1103/physrevb.63.224106 [6] fatemi, a., socie, d., a, critical plane approach to multiaxial fatigue damage including out-of-phase loading, fatigue fracture eng. mater. struct., 11 (1988) 149–165. [7] tschopp, m.a., mcdowell, d.l., influence of single crystal orientation on homogeneous dislocation nucleation under uniaxial loading, j. mech. phys. solids, 56 (2008) 1806-1830. doi: 10.1016/j.jmps.2007.11.012. [8] wan, l., ju, l., shear responses of [(1)over-bar 1 0]-tilt {115}/{111} asymmetric tilt grain boundaries in fcc metals by atomistic simulations, modelling simul. mater. sci. eng., 21 (2013) 055013. doi: 10.1088/0965-0393/21/5/055013. [9] daw, m.s., baskes, m.i., embedded-atom method – derivaton and application to impurities, surfaces, and other defects in metals, phy. rev. b, 29(12) (1984) 6443-6453, doi: 10.1103/physrevb.29.6443. [10] daw, m.s., foiles, s.m., baskes, m.i., the embedded-atom method – a review of theory and applications, mater. sci. rep., 9 (1993) 251, doi: 10.1016/0920-2307(93)90001-u. [11] ogata, s., ju, l., yip, s., ideal pure shear strength of aluminum and copper, science, 298 (2002) 807–811. doi: 10.1126/science.1076652. << /ascii85encodepages false /allowtransparency false /autopositionepsfiles true /autorotatepages /none /binding /left /calgrayprofile (dot gain 20%) /calrgbprofile (srgb iec61966-2.1) /calcmykprofile (u.s. web coated \050swop\051 v2) /srgbprofile (srgb iec61966-2.1) /cannotembedfontpolicy /error /compatibilitylevel 1.4 /compressobjects /tags /compresspages true /convertimagestoindexed true /passthroughjpegimages true /createjobticket false /defaultrenderingintent /default /detectblends true /detectcurves 0.0000 /colorconversionstrategy /cmyk /dothumbnails false /embedallfonts true /embedopentype false /parseiccprofilesincomments true /embedjoboptions true /dscreportinglevel 0 /emitdscwarnings false /endpage -1 /imagememory 1048576 /lockdistillerparams false /maxsubsetpct 100 /optimize true /opm 1 /parsedsccomments true 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/hrv (za stvaranje adobe pdf dokumenata najpogodnijih za visokokvalitetni ispis prije tiskanja koristite ove postavke. stvoreni pdf dokumenti mogu se otvoriti acrobat i adobe reader 5.0 i kasnijim verzijama.) /hun 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can be opened with acrobat and adobe reader 5.0 and later.) >> /namespace [ (adobe) (common) (1.0) ] /othernamespaces [ << /asreaderspreads false /cropimagestoframes true /errorcontrol /warnandcontinue /flattenerignorespreadoverrides false /includeguidesgrids false /includenonprinting false /includeslug false /namespace [ (adobe) (indesign) (4.0) ] /omitplacedbitmaps false /omitplacedeps false /omitplacedpdf false /simulateoverprint /legacy >> << /addbleedmarks false /addcolorbars false /addcropmarks false /addpageinfo false /addregmarks false /convertcolors /converttocmyk /destinationprofilename () /destinationprofileselector /documentcmyk /downsample16bitimages true /flattenerpreset << /presetselector /mediumresolution >> /formelements false /generatestructure false /includebookmarks false /includehyperlinks false /includeinteractive false /includelayers false /includeprofiles false /multimediahandling /useobjectsettings /namespace [ (adobe) (creativesuite) (2.0) ] /pdfxoutputintentprofileselector /documentcmyk /preserveediting true /untaggedcmykhandling /leaveuntagged /untaggedrgbhandling /usedocumentprofile /usedocumentbleed false >> ] >> setdistillerparams << /hwresolution [2400 2400] /pagesize [612.000 792.000] >> setpagedevice microsoft word numero_30_art_10 f. burgio et alii, frattura ed integrità strutturale, 30 (2014) 68-74; doi: 10.3221/igf-esis.30.10 68 focussed on: fracture and structural integrity related issues cf/c composites: correlation between cvi process parameters and pyrolytic carbon microstructure f. burgio, p. fabbri, g. magnani, m. scafè enea faenza technical unit for material technologies (uttmatf) via ravegnana, 186 – 48018 faenza italy federica.burgio@enea.it, paride.fabbri@enea.it, giuseppe.magnani@enea.it, matteo.scafe@enea.it l. pilloni enea, chemical and technology unit (uttmat-chi) luciano.pilloni@enea.it a. brentari certimac s.c.a.r.l. alida.brentari@enea.it a. brillante, t. salzillo university of bologna aldo.brillante@unibo.it, tommaso.salzillo@unibo.it abstract. chemical vapour infiltration (cvi) technique has been long used to produce carbon/carbon composites. the pyrolytic carbon (py-c) matrix infiltrated by cvi could have different microstructures, i.e. rough laminar (rl), smooth laminar (sl) or isotropic (iso). these matrix microstructures, characterized by different properties, influence the mechanical behaviour of the obtained composites. tailoring the process parameters, it is possible to direct the infiltration towards a specific py-c type. however, the factors, influencing the production of a specific matrix microstructure, are numerous and interconnected, e.g. temperature, pressure, flow rates etc. due to the complexity of the physical and chemical phenomena involved in cvi process, up to now it has not been possible to obtain a general correlation between cvi process parameters and py–c microstructure. this study is aimed at investigating the relationship between infiltration temperature and the microstructure of obtained py-c, for a pilot sized cvi/cvd reactor. fixing the other process parameters and varying only the temperature, from 1100°c to 1300°c, the py-c infiltration was performed on fibrous preforms. polarized light microscopy, with quantitative measurements of average extinction angle (ae), and raman spectroscopy were used to characterize the obtained py-c microstructures. keywords. cf/c composites; cvi; py-c microstructure; temperature. f. burgio et alii, frattura ed integrità strutturale, 30 (2014) 68-74; doi: 10.3221/igf-esis.30.10 69 introduction he applications of pyrolytic carbon (py-c) are numerous and range over many fields, such as aerospace, nuclear and medical. pyrolytic carbon is mainly produced as matrix phase of carbon/carbon (cf/c) composites. thanks to their excellent mechanical properties at elevated temperatures, combined with light weight and good frictional performances, cf/cs are employed for the fabrication of components, as leading edges, brake discs, exit cones etc., for aerospace field. py-c are also produced as coating material for nuclear industry, i.e. coatings of nuclear fuel particles, and in medical applications for heart valves and bone prostheses [1, 2, 3, 4]. is widely recognized that chemical vapour infiltration (cvi) process is the ideal for obtaining high performance cf/c composites. cvi technique allows, under mild temperature conditions, the production of pyrolytic carbon matrix with controlled composition and microstructure, without organic by-products, that required post-production treatments for their removing, and, as consequence, composites with a high degree of densification [5]. cvi process leads to py-c with different microstructures and textures. in particular, the texture anisotropy of the py-c matrix is a key parameter affecting the final mechanical properties of the derived cf/cs. several studies have been dedicated to the py-c classification, based on optical measurements of its anisotropy . the py-c was classified as isotropic (iso), dark laminar (dl), smooth laminar (sl), rough laminar (rl) and regenerative laminar (rel) or in more general way as isotropic, low, medium and high textured [6, 7, 8]. despite the py-c anisotropy has been studied since the 60th, there is no clear evidence of a defined correlation between cvi process parameters and obtained py-c structure. this probably arises from the fact that the parameters, affecting the py-c chemical vapour infiltration, are numerous and interconnected (gaseous precursors, temperature, pressure, gas flow rates, residence time, methane/hydrogen concentration ratio, etc.) and as a consequence the literature experimental conditions are very variable [9]. the objective of this study is to point out the correlation of cvi process parameters with py-c microstructures. as a consequence of the results gained in the previous work [10], that evidenced, at the used operating conditions, no influence of hydrogen concentration and residence time on the py-c microstructure, here it was decided to study in particular the temperature affect. the selected process temperatures were 1100, 1200 and 1300 °c respectively, while the other process parameters, such as pressure, methane/hydrogen ratio, gas flow rates etc, were maintained constant. the py-c chemical vapour infiltration was performed on carbon fibre preforms, by means of a pilot-sized cvi/cvd reactor. the anisotropy of the obtained py-c was evaluated coupling the extinction angle measurements, by polarized light microscopy (plm), with raman analyses. the temperature effect on the py-c infiltration behaviour was also investigated. experimental sample preparation he py-c infiltrations were performed at 3 different temperatures, 1100 °c, 1200 °c and 1300 °c, in a pilot – sized cvi/cvd plant, using methane as carbon source precursor, hydrogen as carrier gas and argon as purge gas. the other process conditions were those fixed in the previous work [10]. tab. 1 summarizes the cvi operating conditions used for each infiltration test: test temperature pressure qch4 qh2 α flow rate τ infiltration length [°c] [mbar] [sccm] [sccm] [m/s] [s] [h] cvi1 1100 18 800 2400 0.3 0.21 3.3 100 cvi2 1200 0.23 3.1 50 cvi3 1300 0.24 2.9 50 table 1: operating condition of the cvi experiments where qi, α and τ are gas volumetric flow rate, methane/hydrogen ratio and residence time respectively. the pilot-sized cvi/cvd plant consists of a 700 mm long cylindrical graphite reaction chamber with a 300 mm diameter, heated with graphite resistance elements. gases are delivered into the reaction chamber, from a graphite multi-hole t t f. burgio et alii, frattura ed integrità strutturale, 30 (2014) 68-74; doi: 10.3221/igf-esis.30.10 70 distributor, in a top down direction and the continuous flow is obtained by means of two volumetric vacuum pumps. the furnace, with the gas delivery system, is shown in fig. 1. figure 1: cvi/cvd plant. sample characterization polarized light microscopy was employed to characterize the anisotropy of py-c deposited around the carbon fibres, by the measurement of the extinction angle (ae). the used apparatus consisted of a zeiss microscope equipped with an halogen light source, x16 and x40 objectives, and with two rotating polarizer/analyzer. extinction angle is the measure, expressed in deg, obtained rotating the analyzer from the maltese cross condition to the maximum extinction of the first quadrant [11]. fig. 2 shows the typical plm micrographs, where are evident the maltese crosses of the py-c matrix around the carbon fibres. in particular these micrographs are related to the cf/c composites obtained at 1300 °c. figure 2: plm micrographs of py-c deposited around the carbon fibres at 1300 °c. the extinction angle is related to the py-c anisotropy and has been long used to classify the large number of py-c [11, 12]. tab. 2 summarizes the typical values of ae and the density of the different py–c optical textures [11, 13, 14]. optical texture domain of extinction angle ae density rough laminar (rl) ≥ 18° 2.0 – 2.2 smooth laminar (sl) 12° 18° 1.8 – 1.9 dark laminar (dl) 4° 12° 1.6 – 1.8 isotropic (iso) < 4° < 1.6 table 2: classification of py-c optical texture. 40 µm 40 µm f. burgio et alii, frattura ed integrità strutturale, 30 (2014) 68-74; doi: 10.3221/igf-esis.30.10 71 the degree of crystallinity and the micro-structural features of the py-c, obtained at the different temperatures, were also investigated by raman analyses. raman spectra were collected using a renishaw single grating spectrometer, equipped with a suitable notch filter and ccd detector. the raman scattering was excited using an ar+ laser tuned at 514.5 nm with 25 mw of power. the spectrometer was interfaced to an optical microscope (olympus bx40) with x50 or x100 objectives, which produced a spatial resolution from about 0.75 to 1 μm, with a theoretical field depth ranging from about 7 to 25 μm. the incoming laser output power was reduced with a neutral filter, whose optical density was selected in each experiment to prevent sample damage, the actual power focused on the sample being anyway always less than 1 mw. the bulk density of the produced cf/cs was derived from their volume measurements, with an helium pycnometer (accupyc 1330 pycnometer – micromeritics). furthermore, in order to study the infiltration behaviour, the steady-state deposition rates (rdeposition) of py-c were determined by sem (sem leo 438 vp equipped with eds – link isis 300) measurements of the py-c thickness, deposited on the inner and outer fibres of the cf/c composites. the infiltration behaviour was also analyzed by optical microscopy observations (reichert – jung mef3) of the cf/cs. all the optical analyses were performed on cf/c polished cross sections. results he measured extinction angle values were in the range of 4 to 8 degrees, for all the temperature conditions: this could be an indication of a dark laminar texture [11, 13, 14]. despite the easiness and rapidity of the ae measurement method, it can be employed only as a qualitative indication of the py-c texture. this is mainly due to the fact that the measurements are affected by human eye sensitivity, not able to individuate the minimum intensity conditions with high accuracy [12]. more detailed information, regarding the influence of temperature on py-c microstructures, was derived from raman analyses. the recorded spectra were those typical of py-c, with two first-order bands, the disorder induced d and the graphite induced g at 1360 and 1580 cm-1 respectively, and two second-order bands at 2700 and 2900 cm-1. fig. 3 summarizes the obtained spectra. the comparison of the obtained raman spectra with literature ones, did not evidence a clear correspondence with sl, rl or rel py-c spectra [15]. this could support the hypothesis of a dl texture. dark laminar is a py-c transition structure between isotropic and smooth laminar ones: it has low density and weak anisotropy [16]. as a consequence, it is not being considered of technological interest, the related raman spectra are not available in literature. figure 3: raman spectra of py-c deposited at 1100, 1200 and 1300 °c. however, the raman analyses evidenced differences in the order and crystallinity of the py–c obtained at increasing temperatures. in particular, it was evidenced that the py-c structures exhibited an increasing degree of structural ordering and graphitization with the temperature increasing. it could be deduced from many parameters. firstly from the intensity ratio of d and g bands (id/ig), that is inversely proportional to the degree of graphitization [2, 17]. fig. 4 shows that the higher the temperature, the lower the id/ig ratio. secondly, it was deduced from the decreasing of the full width at half maximum (fwhm) intensity of the d bands with the temperature, as shown in fig. 5. the full width at half maximum t f. burgio et alii, frattura ed integrità strutturale, 30 (2014) 68-74; doi: 10.3221/igf-esis.30.10 72 (fwhm) of the d band has been correlated to the in-plane structural ordering, in particular the larger the fwhmd, the higher the structural disorder [15, 18]. furthermore, with the temperature increasing the second-order band became more evident (fig. 3). the second-order band has been related to the three dimensional order. so, it could be deduced that at 1300°c a more ordered structured py-c was obtained. figure 4: intensity ratio of d and g bands of py-c deposited at 1100, 1200 and 1300 °c. figure 5: full width at half maximum (fwhm) of the d band of py-c deposited at 1100, 1200 and 1300 °c. after the py-c matrix infiltration, there was a bulk density decrease from the starting value of the fibre preforms, 1.8 g/cm3, to the final average value of the composites, 1.6 g/cm3, at all the infiltration temperatures. the values are reported in fig. 6 as a function of the cvi temperature and the sample distance from the gas inlet in the reaction chamber. the cf/c density decrease could be reasonably ascribed to the low density of the py-c infiltrated. this hypothesis was also confirmed by sem observations of the py–c microstructures. in fig. 7, sem micrograph highlights the high degree of porosity of the py –c. the low density and the high porosity of the py-c supported the initial hypothesis of a dark laminar texture obtained at all the operating temperatures here investigated. figure 6: cf/c bulk density. figure 7: sem micrographs of py-c. the py–c steady – state deposition rates are summarized in tab. 3, in correlation with the temperature and the residence time of the infiltration processes. it was evident that only at 1200 °c the inner and the outer deposition rate values were comparable, while at 1100 °c and 1300 °c the two values were widely different and in both cases the inner deposition rate resulted lower than the outer one. the differences between the py–c inner and outer values of deposition rate, for the 3 temperatures, resulted in a different infiltration behaviour of the cf/cs as is shown in fig. 8. the optical images of the cf/c cross sections, for each process temperature, evidences the effect of deposition rate on the preform infiltration mode. at 1100 and 1300 °c, the py-c was mainly deposited on the outer fibres, instead at 1200 °c its intermediate value of deposition rate allowed a more uniform py-c infiltration between inner and outer fibres. the resulting different infiltration behaviour was probably due to the different residence time of the process gases, as already evidenced in the previous work [10]. at low residence times, and therefore at high flow rates, methane has no sufficient time to diffuse inside the inner porosities: this is the condition occurred at 1300 °c. on the other side, at higher 500 nm f. burgio et alii, frattura ed integrità strutturale, 30 (2014) 68-74; doi: 10.3221/igf-esis.30.10 73 residence times and lower flow rates, 1100 °c situation, the hydrogen, flowed in the internal porosities, has sufficient time to inhibit the methane decomposition lowering the deposition rate. at 1200°c, with intermediate values of both residence time and flow rate, a compromise condition between diffusion and inhibition was established. temperature residence time flow rate deposition rate [μm/h] [°c] [s] [m/s] from py-c thickness of the inner fibres from py-c thickness of the outer fibres 1100 3.3 0.21 0.06 0.12 1200 3.1 0.23 0.11 0.13 1300 2.9 0.24 0.02 0.7 table 3: steady – state py-c deposition rates. (a) (b) (c) figure 8: optical micrographs the cf/c cross sections at (a) 1100 °c, (b) 1200 °c and (c) 1300 °c. conclusions he effects of cvi temperature on py-c microstructure and infiltration behaviour have been investigated. it was found that the temperature variation in the range of 1100 to 1300 °c, at the operating condition here considered, did not affect the py-c texture: a dark laminar py-c was indeed obtained at all the analyzed conditions of temperature. the dark laminar texture was identified by extinction angle measurements. raman analyses evidenced the temperature influence on microstructural order and on degree of graphitization of the obtained pyrolytic carbon: at the higher temperature (1300 °c) a more ordered and graphitized py-c microstructure was obtained. moreover, the process temperature affected the infiltration behaviour: at 1200 °c the py-c infiltration resulted more homogeneous than at the other two temperatures, in terms of internal and external porosities densification. in order to obtain a dense cf/c with high mechanical properties two main features are required: an optimum value of residence time, that allows a gradual reduction of the porosities, and a py-c matrix microstructure with high density. the results, obtained in this work, allowed to fix the residence time obtained at 1200 °c, 3.1 s, as an optimal value from the point of view of the infiltration behaviour. the change of the alfa values could lead to the obtaining of py-c structure with higher density. references [1] lopez-honorato, e., meadows p.j., xiao p., fluidized bed chemical vapor deposition of pyrolytic carbon – i. effect of deposition conditions on microstructure, carbon, 47 (2009) 396-410. [2] zou, l., huang, b., huang, y., huang, q., wang, c., an investigation of heterogeneity of the degree of graphitization in carbon–carbon composites, materials chemistry and physics, 82 (2003) 654–662. [3] ozcan, s., filip, p., microstructure and wear mechanisms in c/c composites, wear, 259 (2005) 642–650. [4] chen, t., gong, w., liub, g., zhang, f., influence of graphite foils on i-cvi densification rate and microstructure of obtained pyrolytic carbon of carbon–carbon composites, composites: part a, 36 (2005) 1494–1498. t 40 µm 40 µm 40 µm f. burgio et alii, frattura ed integrità strutturale, 30 (2014) 68-74; doi: 10.3221/igf-esis.30.10 74 [5] naslain r., design, preparation and properties of non-oxide cmcs for application in engines and nuclear reactors: an overview, composites science and technology, 64 (2004) 155-170. [6] reznik, b., huttinger, k.j., on the terminology for pyrolytic carbon, carbon, 40 (2002) 617 –636. [7] bortchagovsky, e.g., reznik, b., gerthsen, d., pfrang, a., schimmel, th., optical properties of pyrolytic carbon deposits deduced from measurements of the extinction angle by polarized light microscopy, carbon, 41 (2003) 2427 – 2451. [8] bourrat, x., langlais, f., chollon, g., vignoles, g., low temperature pyrocarbons: a review, j. braz. chem. soc., 17, (2006) 1090-1095. [9] oberlin, a., review pyrocarbons, carbon, 40 (2002) 7–24. [10] burgio, f., pilloni, l., labanti, m., scafè, m., brentari, a., falconieri, m., sangiorgi, s., validation of py-c chemical vapour deposition and infiltration process codes, in: proceeding of 15th european conference on composite materials and oral presentation, venice, italy (2012). [11] bourrat, x., trouvat, b., limousin, g., vignoles, g., pyrocarbon anisotropy as measured by electron diffraction and polarized light, j. mater. res., 15 (2000). [12] vallerot, j.m., bourrat, x., pyrocarbon optical properties in reflected light, carbon, 44 (2006) 1565–1571. [13] dupel, p., bourbat, x., pailler, r., structure of pyrocarbon infiltrated by pulse-cvi, carbon, 33 (1995) 1193-1204. [14] morgan, p., carbon fibers and their composites, taylor & francis group, (2005). [15] vallerot, j.m., bourrat, x., mouchon, a., chollon, g., quantitative structural and textural assessment of laminar pyrocarbons through raman spectroscopy, electron diffraction and few other techniques, carbon 44 (2006) 1833– 1844. [16] bourrat, x., structure of pyrocarbons, in delhaès p. (eds.), fibers and composites, taylor & francis, 8 (2003). [17] zhang, d., li, k., li, h., guo l., lu, j., the influence of deposition temperature on the microstructure of isotropic pyrocarbon obtained by hot-wall chemical vapor deposition, j mater sci, 46 (2011) 3632–3638. [18] bourrat, x., pyrocarbon performances and characterization, in: proceed. carbon’09, world conf on carbon, biarritz (2009) t11-id 792. microsoft word numero_41_art_6 carpinteri a. et alii, frattura ed integrità strutturale, 41 (2017) 40-44; doi: 10.3221/igf-esis.41.06 40 focused on multiaxial fatigue effect of spectral cross-correlation on multiaxial fatigue damage: simulations using the critical plane approach andrea carpinteri, andrea spagnoli, sabrina vantadori university of parma, italy andrea.carpinteri@unipr.it, http://orcid.org/0000-0002-8489-6005 andrea.spagnoli@unipr.it, http://orcid.org/0000-0002-0592-7003 sabrina.vantadori@unipr.it, http://orcid.org/0000-0002-1904-9301 abstract. the present paper aims to discuss a frequency-domain multiaxial fatigue criterion based on the critical plane approach, suitable for fatigue life estimations in the presence of proportional and non-proportional random loading. the criterion consists of the following three steps: definition of the critical plane, power spectral density (psd) evaluation of an equivalent normal stress, and estimation of fatigue damage. such a frequency-domain criterion has recently been validated by using experimental data available in the literature, related to combined proportional and non-proportional bending and torsion random loading. the comparison with such experimental data has been quite satisfactory. in order to further validate the above criterion, numerical simulations are herein performed by employing a wide group of combined bending and torsion signals. each of such signals is described by an ergodic, stationary and gaussian stochastic process, with zero mean value. the spectrum of each signal is assumed to be represented by a psd function with rectangular shape. different values of correlation degree, variance and spectral content are examined. keywords. critical plane-based criterion; frequency-domain criterion; power spectral density. citation: carpinteri, a., spagnoli, a., vantadori, s., effect of spectral crosscorrelation on multiaxial fatigue damage: simulations using the critical plane approach, frattura ed integrità strutturale, 41 (2017) 4044. received: 28.02.2017 accepted: 15.04.2017 published: 01.07.2017 copyright: © 2017 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. introduction ngineering structures suffer from failure associated with fatigue, both at the stage of manufacturing and under service conditions [1]. examples in the civil engineering field are jack-up platforms, bridges, towers and masts, for which their structural integrity is of paramount importance both to avoid huge material losses and ecological disaster and to ensure the life and health of people. fatigue damage in structures is caused by progressive crack growth under time-varying loading [2]. a method of analysis, named time-domain analysis, is that to consider a loading time history on the structure to find the output response caused e carpinteri a. et alii, frattura ed integrità strutturale, 41 (2017) 40-44; doi: 10.3221/igf-esis.41.06 41 by such an input. however, most structures experience a variety of loadings. therefore, since many load cases are necessary for fatigue analysis, the computational time can become extremely high or even unacceptable [2]. a much more efficient method of analysis, named frequency-domain or spectral analysis, is that to consider the power spectral density (psd) function of the loading on the structure, which represents the frequency content of the loading time history. generally, such methods employ an equivalent uniaxial loading to represent the actual multiaxial stress state, opening the possibility to use timeand frequency-domain methods originally proposed for fatigue analysis under uniaxial variable or random amplitude loading. the spectral method employed in this paper was proposed by the authors to determine fatigue damage in structures under multiaxial stationary random gaussian loading [3]. in the recent past, the method was validated by employing experimental data available in the literature [3-7]. numerical simulations are here developed, by considering random biaxial loading characterized by different values of the correlation coefficient, zero order moments ratio and central frequencies ratio. frequency-domain critical plane (f-d/cp) criterion he input data for the fatigue damage calculation is the psd matrix of the stress tensor (step 1 in fig.1). the determination of the expected critical plane orientation constitutes an important part of the algorithm (step from 2 to 4 in fig.1). the psd function of an equivalent stress is defined as a linear combination of the psd functions of suitable stress components acting on the critical plane. finally, the expected fatigue damage per unit time is obtained (step 5 in fig.1). details of each step of the f-d/cp criterion are reported in refs [3-7]. determination of the psd matrix s() determination of the critical plane orientation 11 3 12 4 5 xyz determination of the psd matrix s()x'y'z' determination of the psd matrix s()x''y''z'' calculation of expected fatigue damage rate e[d] figure 1: algorithm for damage determination using the f-d/cp criterion. random biaxial loading: numerical simulations let us consider the following stress tensor        xyz 1 2 3 4 5 6 x y z y xz x 0 0 0 0t t tz xy xyt s , s , s , s , s , s , , , , , , , , , ,         s with respect to the fixed frame xyz . by assuming that the random features can be described by a two-dimensional ergodic stationary gaussian stochastic process with zero mean value, the psd matrix with respect to xyz is here displayed:   11 16 xyz 61 66 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 s s s s                      s (1) t carpinteri a. et alii, frattura ed integrità strutturale, 41 (2017) 40-44; doi: 10.3221/igf-esis.41.06 42 where  is the pulsation. the symbols 11s and 66s represent the auto-spectral density function of the stress components 1s and 6s (i.e. x and xy ), respectively, whereas 16s and 61s represent the cross-spectral density functions of the above stress components. it is here assumed that the imaginary part of 16s is equal to zero and, consequently, even the imaginary part of 61s is equal to zero: that is, 16 61s s [8]. in such a case, the psd matrix is symmetric. now a rectangular spectrum is assumed for both 11s and 66s . let us introduce the correlation coefficient given by: 0,16 16 0,11 0,66 r      (2) where 0,16 , 0,11 , and 0,66 represent the zero order moment of 16s , 11s and 66s , respectively (more precisely, 0,16 is the co-variance of 16s , whereas 0,11 , and 0,66 are the variances of 11s and 66s , respectively). note that, for proportional stress components, 16r tends to the unity, while 16r tends to zero for highly uncorrelated loading. the central frequency, ,11c , and the height, 11h , related to 11s are assumed to be equal to 10hz and 11mpa2/hz, respectively. different values of the ratio between the central frequencies, , ,66 ,11/c r c c   are examined: ,c r  0.1, 1.0, 1.1, 5.0, and 10.0. the maximum to minimum frequency ratio is equal to 1.1/0.9. the variance of the stress component x turns out to be equal to 22 mpa2. different values of the ratio between the zero order moments, 0, 0,66 0,11/r   are examined: 0,r  0, 1, 100, and  . three different types of spectral cross-correlation for 11s and 66s are examined, that is: (i) totally separated spectra (fig.2(a)). in such a case: ,c r  0.1, 5.0 and 10.0, and 16r is equal to zero; (ii) completely overlapped spectra (fig.2(b)). in such a case: ,c r  1.0, and different values of 16r are assumed, i.e. 16r  0.00, 0.25, 0.50, 0.75, and 1.00; (iii) partially overlapped spectra (fig.2(c)). in such a case: ,c r  1.1, and different values of 16r are assumed, i.e. 16r  0.00, 0.25, 0.50, 0.75, and 1.00. by exploiting both eq.(1) and the schwartz inequality [8], which states that 16s is non-negative only where 11s and 66s are overlapped and zero elsewhere, the height 16h of the rectangular cross-spectrum is computed for each considered biaxial loading state. c,11 h11 h66 o n e -s id e d p s d f u n c t io n , 2 s o r 2 s 1 1 6 6 pulsation,  (a) c,66 h11 h66 (b) c,11 pulsation,  c,66 h11 h66 (c) c,11 pulsation,  c,66 figure 2: one-sided psd functions: (a) totally separated spectra (i), (b) completely overlapped spectra (ii), and (c) partially overlapped spectra (iii). the reference fatigue parameters used in the analysis are: , 1af   79.37(10)-4 mpa, 0n  2(10)6 cycles, c  1.0 and 3.0k  for fully reversed tension or bending, whereas , 1af   , 1 / 3af  for fully reversed torsion [8]. carpinteri a. et alii, frattura ed integrità strutturale, 41 (2017) 40-44; doi: 10.3221/igf-esis.41.06 43 figures 3-5 present overall damage comparisons, by plotting the ratio of expected fatigue damage per unit time, [ ]e d , to the reference damage per unit time, [ ]refe d . such a reference value [ ]refe d depends on the spectra type: for type (i), it represents the damage produced by two sinusoidal signals characterized by pulsations equal to ,11c and ,66c , respectively, and variance equal to 0,11 and 0,66 , respectively; for types (ii) and (iii), it represents the damage produced by three sinusoidal signals characterized by pulsations equal to ,11c , ,66c , and ,16c , respectively, and variance equal to 0,11 , 0,66 and 0,16 , respectively. 0 1 100 zero order moments ratio, 0,r 0.0 0.5 1.0 1.5 2.0 d a m a g e r a t io , e [d ] / e re f [ d ] 8 0.1 5.0 10.0 c,r figure 3: comparison between [ ]e d and [ ]refe d : totally separated spectra. 0 1 100 zero order moments ratio, 0,r 0.0 0.5 1.0 1.5 2.0 d a m a g e r a t io , e [d ] / e re f [ d ] 8 0.00 0.25 0.50 r16 0.75 1.00 figure 4: comparison between [ ]e d and [ ]refe d : completely overlapped spectra. carpinteri a. et alii, frattura ed integrità strutturale, 41 (2017) 40-44; doi: 10.3221/igf-esis.41.06 44 0 1 100 zero order moments ratio, 0,r 0.0 0.5 1.0 1.5 2.0 d a m a g e r a t io , e [d ] / e re f [ d ] 8 0.00 0.25 0.50 r16 0.75 1.00 figure 5: comparison between [ ]e d and [ ]refe d : partially overlapped spectra. it can be observed that, in general, fatigue damage rate is slightly lower than that of the reference sinusoidal loading. only in the case of bending and torsion loads of the same variance, a fatigue damage rate up to about 60% higher than that of the reference loading case is recorded for completely uncorrelated signals ( 16 0r  ). conclusions n the present paper a frequency-domain multiaxial fatigue criterion based on the critical plane approach, suitable for fatigue life estimations in the presence of proportional and non-proportional random loading, has been discussed. in order to validate the above criterion, numerical simulations have herein been performed by employing a wide group of combined bending and torsion signals. the narrow-band spectrum of each signal has been assumed to be represented by a psd function with rectangular shape. different values of correlation degree, variance and spectral content have been examined. among the cases being simulated, the most damaging one is identified in the loading combination of bending and torsion having same variance but being completely uncorrelated (correlation coefficient equal to zero). references [1] niesłony, a., macha, spectral method in multiaxial random fatigue, springer-verlag, berlin heidelberg, (2007). [2] carpinteri, a., handbook of fatigue crack propagation in metallic structures, elsevier, amsterdam, 1-2 (1994). [3] carpinteri, a., spagnoli, a., vantadori, s., reformulation in the frequency domain of a critical plane-based multiaxial fatigue criterion. int. j. fatigue, 67 (2014) 55–61. [4] carpinteri, a., spagnoli, a., ronchei, c., scorza, d., vantadori, s. critical plane criterion for fatigue life calculation: time and frequency domain formulations. procedia eng., 101 (2015), 518–523. [5] carpinteri, a., spagnoli, a., ronchei, c., vantadori, s., time and frequency domain models for multiaxial fatigue life estimation under random loading. frat. ed integrita strutt., 9 (2015), 376–381. [6] carpinteri, a., fortese, g., ronchei, c., scorza, d., spagnoli, a., vantadori, s., fatigue life evaluation of metallic structures under multiaxial random loading. int. j. fatigue, 90 (2016), 191–199. [7] carpinteri, a., fortese, g., ronchei, c., scorza, d., vantadori, s. spectral fatigue life estimation for non-proportional multiaxial random loading. theor. appl. fract. mech., 83 (2016) 67-72. [8] cristofori, a., benasciutti, d., tovo, r. a stress invariant based spectral method to estimate fatigue life under multiaxial random loading. int. j. fatigue, 33 (2011), 887–899. i << /ascii85encodepages false /allowtransparency false /autopositionepsfiles true /autorotatepages /none /binding /left /calgrayprofile (dot gain 20%) /calrgbprofile (srgb iec61966-2.1) /calcmykprofile (u.s. web coated \050swop\051 v2) /srgbprofile (srgb iec61966-2.1) /cannotembedfontpolicy /error /compatibilitylevel 1.4 /compressobjects /tags /compresspages true /convertimagestoindexed true /passthroughjpegimages true /createjobticket false /defaultrenderingintent /default /detectblends true /detectcurves 0.0000 /colorconversionstrategy /cmyk /dothumbnails false /embedallfonts true /embedopentype false /parseiccprofilesincomments true /embedjoboptions true /dscreportinglevel 0 /emitdscwarnings false /endpage -1 /imagememory 1048576 /lockdistillerparams false /maxsubsetpct 100 /optimize true /opm 1 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can be opened with acrobat and adobe reader 5.0 and later.) >> /namespace [ (adobe) (common) (1.0) ] /othernamespaces [ << /asreaderspreads false /cropimagestoframes true /errorcontrol /warnandcontinue /flattenerignorespreadoverrides false /includeguidesgrids false /includenonprinting false /includeslug false /namespace [ (adobe) (indesign) (4.0) ] /omitplacedbitmaps false /omitplacedeps false /omitplacedpdf false /simulateoverprint /legacy >> << /addbleedmarks false /addcolorbars false /addcropmarks false /addpageinfo false /addregmarks false /convertcolors /converttocmyk /destinationprofilename () /destinationprofileselector /documentcmyk /downsample16bitimages true /flattenerpreset << /presetselector /mediumresolution >> /formelements false /generatestructure false /includebookmarks false /includehyperlinks false /includeinteractive false /includelayers false /includeprofiles false /multimediahandling /useobjectsettings /namespace [ (adobe) (creativesuite) (2.0) ] /pdfxoutputintentprofileselector /documentcmyk /preserveediting true /untaggedcmykhandling /leaveuntagged /untaggedrgbhandling /usedocumentprofile /usedocumentbleed false >> ] >> setdistillerparams << /hwresolution [2400 2400] /pagesize [612.000 792.000] >> setpagedevice microsoft word numero 24 articolo 9 a. v. babushkin et alii, frattura ed integrità strutturale, 24 (2013) 89-95; doi: 10.3221/igf-esis.24.09 89 special issue: russian fracture mechanics school research of the effectiveness of mechanical testing methods with analysis of features of destructions and temperature effects a.v. babushkin, d.s. lobanov, a.v. kozlova, i.d. morev perm national research polytechnic university, 614990, komsomolsky av., 29, perm, russia bav651@yandex.ru abstract. in this paper is carried out the comparative analysis of effectiveness of test methods of determination of stiffness and strength properties of highly filled unidirectional fiberglass (direct "e" roving 0.7 orthophthalic polyester resin 0.3) via tensile testing along the reinforcement and three-point bending testing at several bases. the necessity of deviation from standard procedures is substantiated. deformation and failure features of the material under quasi-static loading, as well as at low and high temperatures, are shown. keywords. composite materials; highly filled fiberglass; test methods; deformation and failure; high and low temperature. introduction or designing and providing reliable operation of high loaded shell structures from layered-fiber cross-reinforced composites are relevant issues of an adequate definition of effective elastic and strength properties of the material. these issues are usually resolved with help of mathematical modeling or tests. in this case, the structuralphenomenological modeling should be also based on the test determination of properties and features of the mechanical behavior of structural components of the composite. for modeling of a cross-reinforced fiberglass are most relevant properties of texture layer that is a unidirectional fiber composite. determination of unidirectional fiber composite properties is usually based on astm d 3039. in the test research of composite materials in the product is convenient to use method of beam-specimens bending on different bases, as this method allows determine the longitudinal strength and elastic modulus, shear modulus and shear (interlayer) strength [1]. according to this method, the properties are determined by three-point bending testing on different bases of beam-specimens, which are cut in the appropriate direction of finished product. this approach allows take into account technological features of the material production into product. however, this method gives obviously lower results, as work conditions of relatively short reinforcing fibers in cut specimen and continuous fibers in the product are significantly different. anyway, in both cases, the result is based on test data. in practice, the lower results at test are interpreted as a certain margin of safety in product designing. naturally, questions of estimation of this stock value and the adequacy of various test methods for providing structural mathematical modeling on the one hand, and product design in the framework of phenomenological approaches on the other, arise. in this paper is held a comparative analysis of different methods of test determination of unidirectional fiberglass stiffness and strength properties, deformation and fracture characteristics of these materials under quasi-static loading and also at low and high temperatures. f http://dx.medra.org/10.3221/igf-esis.24.09&auth=true http://www.gruppofrattura.it a. v. babushkin et alii, frattura ed integrità strutturale, 24 (2013) 89-95; doi: 10.3221/igf-esis.24.09 90 materials and conditions of test uniaxial tensile testing of unidirectional fiberglass ests of unidirectional fiberglass (direct "e" roving 0.7 orthophthalic polyester resin 0.3) were carried out in the direction of reinforcement. this material has main feature, which is high (70%) content of the reinforcing component. increase of fibers volume fraction increases material strength in the direction of the reinforcement and a sharp decrease in strength in the transverse direction. the desire to test at high and low temperatures imposes certain restrictions on the size of the specimen. these circumstances lead to restrictions on the usage of standard approaches and methods (astm d 3039 / d 3039m-08) for the material testing. the grip in a form of sleeve has been designed and produced specifically for uniaxial tensile testing along the reinforcement. one of the device features is the lack of cross-compression in the gripping part of the specimen [2]. unidirectional fiberglass specimen is made in a form of rod with a constant cross section. a specimen is holding in gripping area by adhesion, while it is being deformed and failed. strength of this design is determined by the properties of the adhesive and the depth of the immersion. in this case, specimen length with the steel gripping sleeve is limited by working area of a temperature chamber. on the specimen gage length were applied labels for using non-contact extensometer instron ave, as shown in fig. 1. figure 1: the appearance of highly filled fiberglass specimen for uniaxial tensile test with applied labels for using non-contact extensometer instron ave [2] tensile tests of unidirectional fiberglass along the reinforcement were held on a universal electromechanical system instron 5882 with video extensometer instron ave. climate chamber instron 3119-407 was used at low and high temperatures tests. on fig. 2 are shown testing system instron 5882 (1), video extensometer (2) and a climatic chamber (3), and a specimen of the proposed construction in grips at tensile test at room temperature (22°c). the necessity of a non-contact extensometer is explained by fracture behavior of specimens, which are made from this material. figure 2: the appearance of the unidirectional fiberglass specimen in grips at tensile tests: instron 5882 test set (1), video extensometer (2), climate chamber (3). twelve specimens were tested at room temperature. at low temperature were tested only 8 unidirectional fiberglass specimens: 4 specimens at 30°c, 4 specimens at 0°c. at high temperatures, were tested three specimens at each temperature of 40°c and 50°c. it should be noted, that the usage of sleeves and epoxy binder as an adhesive at high t 3 1 2 http://dx.medra.org/10.3221/igf-esis.24.09&auth=true http://www.gruppofrattura.it a. v. babushkin et alii, frattura ed integrità strutturale, 24 (2013) 89-95; doi: 10.3221/igf-esis.24.09 91 temperatures sometimes leads to the failure, which happens in form of creep of rod out sleeves without fiber failure of the specimen. for providing the compactness of the general assembly and for determination of fiberglass stiffness and strength properties was made an attempt of using upgraded grip-sleeves, shown in fig. 3. [2] the essence of this device is to have a tapered hole, through which was expected to create a uniform compliance (glue) cross-compression of rod specimen at tension test. however, this test circuit didn’t always provide a positive result. so, ultimate tensile strength of fiberglass (direct "e" roving 0.7 orthophthalic polyester resin 0.3) at 50ºc in this test wasn’t determined. figure 3: scheme of device for unidirectional rod specimen testing at high temperatures [3] types of diagrams of unidirectional fiberglass (direct "e" roving 0.7 orthophthalic polyester resin 0.3) deformation in tensile test at various temperatures came out similar. on fig. 4 is shown typical diagram of unidirectional fiberglass deformation in tensile test with usage of videoextensometer instron ave. figure 4: the appearance of typical diagram of unidirectional fiberglass direct "e" roving 0.7 orthophthalic polyester resin 0.3 deformation in tensile test. thus, as a result of specimen testing of highly filled unidirectional fiberglass on uniaxial tensile along the direction of reinforcing at room, low and high temperatures, have been identified elastic and strength characteristics of the material. three-point bending testing of unidirectional fiberglass main characteristics of unidirectional composite were also determined at bending tests. tests were carried out by threepoint bending method of beam specimens with various lengths between brackets. for calculation of mechanical characteristics were used mathematical tools for anisotropic materials [1]. testing scheme is shown on the fig. 5. in whole http://dx.medra.org/10.3221/igf-esis.24.09&auth=true http://www.gruppofrattura.it a. v. babushkin et alii, frattura ed integrità strutturale, 24 (2013) 89-95; doi: 10.3221/igf-esis.24.09 92 testing technique is similar to astm d2344. at this case, fiberglass (direct "e" roving 0.7 orthophthalic polyester resin 0.3) specimens were cut along reinforcement in a form of beams with cross section 5х5 mm. three specimens were tested on each of four bases: l1 = 30 mm, l2 = 50 mm, l3 = 70 mm, l4 = 100 mm. specimen lengths respectively were defined like li = li + li/5. by the results of tests were made force-displacement diagrams. mechanical characteristics calculations from test results of three specimens on one base were averaged. figure 5: bending test of unidirectional fiberglass (direct "e" roving 0.7 orthophthalic polyester resin 0.3). the processing of the experimental data rom uniaxial tension test could be determined the ultimate tensile strength σb, elastic modulus e and poisson’s ratio . in this case, tensile strength and young’s modulus were determined [2]. necessary stress and strain for these characteristics calculations were on gage length. ultimate tensile strength was determined by formula max b p f   where maxp – maximum force at specimen deformation, f – initial cross section area of gage length. longitudinal deformations were measured by non-contact videoextensometer instron ave and were calculated by formula e      where  – increment of stress on linear region of deformation curve,  – corresponding increment of specimen linear deformation. for calculation of elastic and strength characteristics at bending of fiberglass specimens was used improved theory [1]. in addition to the normal stress in the bent beam there are tangential stresses, influence of which on the strength and stiffness of isotropic composites is negligible. at bending tests of anisotropic beams, depended on the nature of the failure of specimen, can be determined flexural strength or strength at interlaminar shear. in practice, both normal and shear stresses are working in the specimen, so the determination of the properties of anisotropic composite materials at bending should take into account their mutual influence. the adjusted formula for determination of maximum of normal stress b at bending has the following form 2 4 1 15 525 b f             and for determination of maximum of shear stress 2 4 1 60 12600 b f             , where max 2 3 2 i f p l bh     and max 3 4 f p bh    , so 2 f i eh l g     – parameter of anisotropy, fe – fictitious elastic modulus; g – interlayer shear modulus; b – specimen width, il –length between brackets at three-point bending. f http://dx.medra.org/10.3221/igf-esis.24.09&auth=true http://www.gruppofrattura.it a. v. babushkin et alii, frattura ed integrità strutturale, 24 (2013) 89-95; doi: 10.3221/igf-esis.24.09 93 for defying elastic modulus at three point bending of laminate composite material should be used refined dependencies, which consider influence of shear deformations and binding maximum flexure max of the beam in the middle of brackets with applied force p, true elastic modulus at bending tfe and interlayer shear modulus g : 23 max 1 48 fi k f i ep l h e i l g               (1) where k – coefficient, which depends on cross section form of the beam (for rectangular 1.2k  ); 3 12 bh i  – moment of inertia of beam cross section. true elastic modulus at bending tfe is bonded with fictitious modulus 3 max48 i f p l e i      in the following ratio 2 1 1 1.2 t f f i h e e g l         (2) the higher ratio of thickness of the specimen to its length i h l and the higher degree of anisotropy of composite material, characterized by t fe g , the more different true elastic modulus from fictitious. with one test it is impossible to calculate elastic modulus by formula (1) as it has two unknowns fe and g . so for their determination are tested several specimens with different ratios i h l       and then was diagram made, where on the horizontal axis was put off value 2 i h l       and on the vertical axis – 1 fe . in this coordinates, relation (2) has to be represented as a straight line, which crosses the vertical axis at the point 1 t fe and slope of this line to the horizontal axis equal 1.2 g . then value of tfe and g are determined by method of least square. discussion of results ension test results of highly filled fiberglass specimens (direct "e" roving 0.7 orthophthalic polyester resin 0.3) are in the tab. 1. temperature, °c tensile strength at break b mpa young's modulus in tension e, gpa -30 922.1 34.2 0 980.2 36.8 +22 987.1 47.8 +40 690.5 38.8 +50 37.4 table 1: unidirectional fiberglass (direct "e" roving 0.7 orthophthalic polyester resin 0.3) properties at tension test [3]. t http://dx.medra.org/10.3221/igf-esis.24.09&auth=true http://www.gruppofrattura.it a. v. babushkin et alii, frattura ed integrità strutturale, 24 (2013) 89-95; doi: 10.3221/igf-esis.24.09 94 according to the table, highest values of the characteristics are at test at room temperature. when temperature is lower or higher, then room temperature, characteristic value decreases. strength at 50°с couldn’t be determined. in the tab. 2 there are three-point bending test results of highly filled fiberglass specimens (direct "e" roving 0.7 orthophthalic polyester resin 0.3). it should be noted, that this method allows getting more characteristics: to young’s modulus е and to longitudinal strength σb are added interlayer shear modulus g and shear strength τb. there were no problems with testing at various temperatures. however, this method is more sensitive to the quality of the test. in [1] there are range of parameters, which influence on results: slide from brackets, optimal ratio h/li, and edge effects. there are no clear tendencies of temperature effects. value of normal strength is lower on 20-25%, then values which were got at tensile tests. influence of shear components on comparable (е, σb) characteristics is clearly noticeable. temperature, °c properties e, gpa g, mpa σb, mpa τb, mpa 30 40.4 762 682 24 + 22 30.7 924 674 32 + 50 35.7 1142 489 38 table 2: unidirectional fiberglass (direct "e" roving 0.7 orthophthalic polyester resin 0.3) properties at bending tests features of failure ll tested unidirectional fiberglass specimens at uniaxial tensile, regardless of the temperature, failed like it is shown on fig. 6. this type of failure is typical for fiber exfoliation and complete matrix destruction. obviously, is the presence of shear deformation, which was not taken into account at stress calculation. this kind of failure may be associated with the grip construction without crimping. figure 6: failed unidirectional fiberglass (direct "e" roving 0.7 orthophthalic polyester resin 0.3) specimens after uniaxial tensile tests. the same influence of specimen and grip construction was also noted in the paper [4] when was used nol-method for getting characteristics of unidirectional fiberglass, fig. 7, a. however, preliminary cyclic loading leaded to qualitative change in the type of failure (fig. 7, b), whereas specimen and grip construction wasn’t changed. (a) (b) figure 7: rbn 1680-up 2217 fiberglass failure at static deformation by rigid half-discs (a) and after cyclic loading (b). a http://dx.medra.org/10.3221/igf-esis.24.09&auth=true http://www.gruppofrattura.it a. v. babushkin et alii, frattura ed integrità strutturale, 24 (2013) 89-95; doi: 10.3221/igf-esis.24.09 95 on fig. 8 are shown types of failure of beam specimens at three point bending tests on large (a) and small (b) bases. clearly seen failure character: on long base – from normal stresses at tearing and crushing of fibers; on short base – mainly on in-plain shear, perpendicular to the plain of loading. figure 8: failed unidirectional fiberglass (direct "e" roving 0.7 orthophthalic polyester resin 0.3) at three point bending tests on large (a) and small (b) bases. conclusion hus, the identified properties of unidirectional fiberglass in two ways: in the direction of the tensile reinforcement and in three-point bending at different bases. tests were carried out at normal, high and low temperatures. values of comparable properties are close, but obvious tendency of temperature effect at tensile tests doesn’t confirm at bending tests. strength of normal separation, measured at bending testing, is lower on 20-25% than strength, measured at tensile testing. both test methods are forced to differ from standard methods. at tensile tests were used grips without lateral compression of specimen material or with uniform pliable compression, which is caused by wedge effect. bending tests can determine more characteristics, are not critical to changes of temperature and use improved theory of bending. type of failure of unidirectional fiberglass at tensile tests along reinforcement is similar to the usage of nol-method in the absence of damage accumulation. this type of failure suggests a significant influence of shear deformations. at three point bending tests specimen failed traditionally: on long bases – mainly from normal stresses, on short – from tangent. acknowledgments esearch were carried out on equipment of the center of experimental mechanics of perm national research polytechnic university with financial support from grant rfbr № 12-08-31336. references [1] y. m. tarnopolsky, t. y. kintsis, methods of static tests of reinforced plastics, chemistry, moscow (1981). [2] a.v. babushkin, v.e. wildemann, d.s. lobanov, factory laboratory. materials’ diagnostics, 76(7) (2010) 57. [3] d.s. lobanov, a.v. babushkin, in: proc. of eccm15: european conference on composite materials, venice, italy, (2012), paper id: 1224. – isbn 978-88-88785-33-2. [4] a.v. babushkin, a.v. kozlova, composites: mechanics, compositions, applications. an international journal, 2(3) (2011) 223. t r a) b) http://dx.medra.org/10.3221/igf-esis.24.09&auth=true http://www.gruppofrattura.it microsoft word numero_41_art_17 k. slámečka et alii, frattura ed integrità strutturale, 41 (2017) 123-128; doi: 10.3221/igf-esis.41.17 123 focused on multiaxial fatigue simple criterion for predicting fatigue life under combined bending and torsion loading k. slámečka, j. pokluda brno university of technology, central european institute of technology, purkyňova 123, 612 00 brno, czech republic karel.slamecka@ceitec.vutbr.cz, http://orcid.org/0000-0001-8847-075x jaroslav.pokluda@ceitec.vutbr.cz, http://orcid.org/0000-0002-8449-1200 abstract. multiaxial fatigue is a challenging problem and, consequently, a number of methods has been developed to aid in design of components and assemblies. following the complexity of the problem, these approaches are often elaborate and it is difficult to use them for simple loading cases. in this paper, an empirical approach for constant amplitude, proportional axial and torsion loading is introduced to serve as a basic engineering tool for estimating fatigue life of rotational structural parts. the criterion relies on a quadratic equivalent-stress formula and requires one constant parameter to be determined from experiments. the comparison with similar classical stressbased approaches using data on diverse materials (several steels, aluminium alloy, and nickel base superalloy) reveals very good agreement with experimental data. keywords. multiaxial fatigue; life prediction; equivalent stress. citation: slámečka, k., pokluda, j., simple criterion for predicting fatigue life under combined bending and torsion loading, frattura ed integrità strutturale, 41 (2017) 123-128. received: 28.02.2017 accepted: 15.04.2017 published: 01.07.2017 copyright: © 2017 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. introduction atigue failure under multiaxial cyclic loading is undoubtedly one of the most common concerns among engineers. the multiaxial fatigue process itself is rather complex and a tremendous effort has been invested in developing methods capable of capturing some of its most relevant aspects, such as the importance of shear stresses for the fatigue crack initiation stage, the short crack problem, crack closure, or non-proportional hardening observed in some materials [1, 2]. consequently, these methods are often quite elaborate and their employment may require a skilled person using a specialized software. on the other hand, the first-approximation estimation of multiaxial fatigue failure is frequently based on the von mises stress, the tresca criterion, or some other static hypothesis, e.g. [3, 4], which apparently are among a few simple formulas qualified for a widespread usage. as these simple methods are known to be generally not acceptable, the purpose of this work was to introduce a similarly simple empirical approach which is intended to serve as a basic engineering tool for initial estimation of fatigue life under combine proportional axial and torsion loading, being of a special interest for rotational structural parts operating under such conditions. the method relies on fitting the f k. slámečka et alii, frattura ed integrità strutturale, 41 (2017) 123-128; doi: 10.3221/igf-esis.41.17 124 experimental data for the two loading channels and formulating the equivalent loading based on a single constant parameter. the new s-n curve and the benchmark criteria n the following, the combined cyclic loading is considered to be proportional, i.e., it consists of well-defined loading cycles and no additional non-proportionality effects, need to be taken into account. furthermore, we assume that the relationship between loading and fatigue life, nf, over the studied life range is reasonably linear in log-log coordinates. this relationship is expressed in terms of stresses using the formalism in astm e 739 standard [5]. for symmetric loading, the new equivalent s-n curve (the middle-curve criterion) is constructed as  2 2f σ,τ σ,τ eq,a σ,τ σ,τ a 0 a1log log log 2 n a m a m k       , (1) where a and m are the intercept and the (negative) slope and eq,a is the amplitude of the equivalent stress expressed as a quadratic combination of bending and torsion amplitudes, a and a. the constant k0 which describes the relation between bending and torsion loading is obtained as 2 a0 0 2 a0 k    , (2) where a0 and a0 are bending and torsion fatigue strengths corresponding to fatigue life nf = nf0 being in the middle between the axial and torsion midpoints (log nf0 = ½ (log f 0 an + log f 0 tn )), see fig. 1, where superscripts a and t reference, respectively, to the axial and torsion s-n curves and f 0 an and f 0 tn correspond to the middles of the curves. the middle curve intersects the axial s-n curve at a0, nf0 and bisects the angle between the axial and torsion s-n curves. its intercept and slope can be obtained from the intercepts and the slopes of bending (a, m) and torsion (a, m) curves: σ τ σ,τ arctan arctan tan 2 m m m       , (3)  σ,τ f 0 σ,τ 0a σ σ σ,τ 0alog log loga n m a m m      . (4) figure 1: definition of nf0, σa0, and τa0 using data of s355j2g3 alloy steel reported by karolczuk et al. [4,5]. i k. slámečka et alii, frattura ed integrità strutturale, 41 (2017) 123-128; doi: 10.3221/igf-esis.41.17 125 this method (eqs. 1-4) was compared to the von mises (eq. 5) and tresca (eq. 6) criteria and to the gough-pollard criterion for ductile metals (eq. 7), which are similar quadratic formulas:  2 2f σ σ eq,a σ σ a a1log log log 3 2 n a m a m       , (5) 2 2 f τ τ eq ,a τ τ a a 1 1 log log log 2 4 n a m a m           , (6) 2 2 a a c c 1                  . (7) in eq. (7), c and c are the axial and torsion fatigue strengths that, conceptually, correspond to the same fatigue life. therefore, this criterion reflects the non-parallelism of the s-n curves (variation of the c/c ratio), as the middle curve criterion does, but is more difficult to apply, e.g. [7]. the middle-curve criterion is more general than the von mises and tresca criteria. indeed, when c/c = √3 (or c/c = 2) holds in the whole range of fatigue life, the middle-curve criterion becomes equivalent to the von mises (or tresca) criterion. furthermore, the middle-curve becomes equal to the goughpollard criterion for materials with parallel s-n curves but gives better results for materials with non-parallel s-n curves (see hereafter). experimental data he studied methods were evaluated using plane-bending/torsion data on 2017a-t4 aluminium alloy, s355j2wp and s355j2g3 alloy steels, 30crnimo8 medium alloy steels, and inconel 713lc nickel-base superalloy, see refs. [6-9] and references therein for more detailed information on these fatigue experiments. tab. 1 summarizes the ultimate strength σu and the yield strength σy of all materials and the parameters of bending and torsion s-n curves. the angle  is the angle between the two curves and its positive value means that the axial curve is steeper. except for 2017at4 aluminum alloy, the s-n curves are clearly not parallel. material σu (mpa) σy (mpa) σy/σu σa τm τa  (°) 2017a-t4 [8] 545 395 0.72 -7.0 21.8 -7.1 20.3 0.1 s355j2wp [6] 556 414 0.74 -12.5 37.6 -5.8 18.6 -5.3 s355j2g3 [6,7] 611 394 0.64 -7.2 23.9 -11.7 32.8 3.0 inc713lc [9] 982 801 0.82 -4.5 17.4 -7.5 23.9 4.8 30crnimo8 [6] 1014 812 0.80 -8.1 27.6 -24.7 69.7 4.7 table 1: basic material properties and the parameters related to the bending and torsion s-n curves. results and discussion ab. 2 summarizes parameters related to the middle-curve criterion. note that the constant k0 lies in the range from 2.22 to 4.29. since k0 = 3 for the von mises criterion, this criterion can be expected to provide a plausible prediction for all materials except for s355j2wp steel, which should comply with the predictions obtained from the tresca criterion. fig. 2 compares the experimental and calculated fatigue lives, nf,exp and nf,calc, in the log-log space. a full diagonal line signifies a perfect agreement between predicted and observed values. the dashed and dash-dot lines constitute factors of two and three bandwidths. fig. 3 plots the distribution of deviations from the perfect-agreement line for all materials t t k. slámečka et alii, frattura ed integrità strutturale, 41 (2017) 123-128; doi: 10.3221/igf-esis.41.17 126 using the box charts. additional information is shown in tab. 3 that summarizes the mean values obtained for each material. material n0 0,a (mpa) 0,a (mpa) k0 σ,τm σ,τa 2017a-t4 6.4×105 189 111 2.89 -7.1 21.9 s355j2wp 5.7×105 343 166 4.29 -7.9 25.9 s355j2g3 6.9×105 328 204 2.57 -8.9 28.2 inc713lc 5.7×104 606 364 2.78 -5.7 20.5 30crnimo8 1.1×105 623 418 2.22 -12.2 39.1 table 2: parameters related to the middle-curve criterion. figure 2: comparison of experimental and predicted fatigue lives. k. slámečka et alii, frattura ed integrità strutturale, 41 (2017) 123-128; doi: 10.3221/igf-esis.41.17 127 the results reveal that the middle-curve criterion provides, in general, the best estimates of fatigue life. the goughpollard criterion also yields very reasonable predictions but it is computationally more complicated since it requires an iterative solution. as expected, the von mises criterion provides good results for materials with the k0-value close to 3 but much worse estimates for s355j2wp steel with k0 = 4.29, for which the tresca criterion is more suitable. the latter criterion is, however, generally inaccurate and nonconservative. figure 3: box chart of prediction differences: mc – middle curve, vm – von mises, tr – tresca, gp – gough-pollard. material mc vm tr gp 2017a-t4 1.4 1.5 -1.2 1.4 s355j2wp 1.2 -3.8 1.1 1.1 s355j2g3 1.5 1.6 -1.9 1.5 inc713lc -1.3 1.0 -2.5 -1.4 30crnimo8 1.5 3.0 -78 1.7 table 3: average band factors. conclusions and prospects his paper introduces a simple, computationally non-intensive empirical method, termed as the middle-curve criterion, to be used as a fast and efficient tool for the initial estimate of life of structural component subjected to combined bending and torsion proportional loading. the criterion requires one constant material parameter, k0, to be determined from experiments based on a suitably defined reference number of cycles to failure nf0. the new referential s-n curve is obtained as the curve that intersects the axial s-n curve at nf0 and bisects the angle between the axial and torsion curves, thus reflecting the fact that the axial and torsion curves are generally divergent. the von mises and tresca criteria are special cases of the middle-curve criterion which is equal to the gough-pollard criterion for materials with parallel s-n curves. a comparison of all these criteria was made by using experimental data on five diverse metallic materials and the analysis clearly demonstrated advantages of the new criterion over the studied classical criteria. therefore, the middle-curve criterion is very useful for a preliminary estimation of life of rotational structural parts under mixed axial and torsion loading. despite the formulas presented in this paper do not account for the mean stress effect, it can be easily included by using experimental data obtained from non-zero mean stress tests. transformation of the data based on the goodman diagram or other similar methods [10] is also possible. furthermore, our unpublished data show that the precision of prediction can be increased by using referential s-n curve obtained by fitting of joined axial data and torsion data expressed in terms of equivalent stress  1/22 2a 0 ak  . the non-proportionality of loading can also be taken into account by a suitable definition of a dependence of k0 on the phase shift. t k. slámečka et alii, frattura ed integrità strutturale, 41 (2017) 123-128; doi: 10.3221/igf-esis.41.17 128 acknowledgement he authors acknowledge the financial support of this work by the czech science foundation (ga cr) in the frame of the project no. 17-18566s and by the ministry of education, youth and sports of the czech republic under the project ceitec 2020 (lq1601). references [1] you, b.r., lee, s.b., a critical review on multiaxial fatigue assessments of metals, int. j. fat., 18 (1996) 235–244. [2] socie, d.f., marquis, g.b., multiaxial fatigue, sae international, warrendale, pa, (2000). [3] slámečka, k., šesták, p., vojtek, t., kianicová, m., horníková, j., šandera, p., pokluda, j., a fractographic study of bending/torsion fatigue failure in metallic materials with protective surface layers, adv. mater. sci. eng., 2016 (2016) 8952657. doi: 10.1155/2016/8952657. [4] nikitin, a., palin-luc, t., shanyavskiy, a., bathias, c., comparison of crack paths in a forged and extruded aeronautical titanium alloy loaded in torsion in the gigacycle fatigue regime, eng. frac. mech., 167 (2016) 259-272. doi: 10.1016/j.engfracmech.2016.05.013 [5] astm e739-91(1998) standard practice for statistical analysis of linearized stress-life (s-n) and strain-life (ε-n) fatigue data. astm international, west conshohocken, pa, (1998). [6] karolczuk, a., kluger, k., analysis of the coefficient of normal stress effect in chosen multiaxial fatigue criteria, theor. appl. frac. mec., 73 (2014) 39–47. doi:10.1016/j.tafmec.2014.07.015. 234. [7] karolczuk, a., kluger, k., łagoda, t., a correction in the algorithm of fatigue life calculation based on the critical plane approach, int. j. fat. 83 (2016) 174–183. doi:10.1016/j.ijfatigue.2015.10.011. 236. [8] kluger, k., łagoda, t., new energy model for fatigue life determination under multiaxial loading with different mean values, int. j. fat., 66 (2014) 229–245. doi:10.1016/j.ijfatigue.2014.04.008. [9] slámečka, k., pokluda, j., kianicová, m., horníková, j., obrtlík, k.. fatigue life of cast inconel 713lc with/without protective diffusion coating under bending, torsion and their combination, eng. frac. mech., 110 (2013) 459–467. doi: 10.1016/j.engfracmech.2013.01.001. [10] dowling n.e. mean stress effects in stress-life and strain-life fatigue. sae paper no. 2004-01-2227. in: fatigue 2004: second sae brasil international conference on fatigue, são paulo, june 2004. t << /ascii85encodepages false /allowtransparency false /autopositionepsfiles true /autorotatepages /none /binding /left /calgrayprofile (dot gain 20%) /calrgbprofile (srgb iec61966-2.1) /calcmykprofile (u.s. web coated \050swop\051 v2) /srgbprofile (srgb iec61966-2.1) /cannotembedfontpolicy /error /compatibilitylevel 1.4 /compressobjects /tags /compresspages true /convertimagestoindexed true /passthroughjpegimages true /createjobticket false /defaultrenderingintent /default /detectblends true /detectcurves 0.0000 /colorconversionstrategy /cmyk /dothumbnails false /embedallfonts true /embedopentype false /parseiccprofilesincomments true /embedjoboptions true /dscreportinglevel 0 /emitdscwarnings false /endpage -1 /imagememory 1048576 /lockdistillerparams false /maxsubsetpct 100 /optimize 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can be opened with acrobat and adobe reader 5.0 and later.) >> /namespace [ (adobe) (common) (1.0) ] /othernamespaces [ << /asreaderspreads false /cropimagestoframes true /errorcontrol /warnandcontinue /flattenerignorespreadoverrides false /includeguidesgrids false /includenonprinting false /includeslug false /namespace [ (adobe) (indesign) (4.0) ] /omitplacedbitmaps false /omitplacedeps false /omitplacedpdf false /simulateoverprint /legacy >> << /addbleedmarks false /addcolorbars false /addcropmarks false /addpageinfo false /addregmarks false /convertcolors /converttocmyk /destinationprofilename () /destinationprofileselector /documentcmyk /downsample16bitimages true /flattenerpreset << /presetselector /mediumresolution >> /formelements false /generatestructure false /includebookmarks false /includehyperlinks false /includeinteractive false /includelayers false /includeprofiles false /multimediahandling /useobjectsettings /namespace [ (adobe) (creativesuite) (2.0) ] /pdfxoutputintentprofileselector /documentcmyk /preserveediting true /untaggedcmykhandling /leaveuntagged /untaggedrgbhandling /usedocumentprofile /usedocumentbleed false >> ] >> setdistillerparams << /hwresolution [2400 2400] /pagesize [612.000 792.000] >> setpagedevice microsoft word numero_41_art_48.docx e. nurullaev et alii, frattura ed integrità strutturale, 41 (2017) 369-377; doi: 10.3221/igf-esis.41.48 369 dependence of mechanical characteristics from composition and structure and optimization of mechanical fracture energy of polymer composite material based on high-molecular rubbers e. nurullaev, a. s. ermilov, n. yu. lyubimova perm national research polytechnic university, russia ergnur@mail.ru, ermilov@tpmp.perm.ru, ninalu76@mail.ru abstract. by means of numerical experiment the authors investigate dependence of conventional rupturing stress and mechanical fracture energy at uniaxial tension from fractional composition of dispersed filler, plasticizer volume fraction in polymer binder, effective density of transverse bonds, applied to development of covering for different purposes and with advanced service life in temperature range from 223 to 323 k. they compare mechanical characteristics of polymer composite materials (pcms) based on highand low-molecular rubbers. it was shown that rupturing stress of high-molecular rubber-based pcm is of a higher magnitude than the stress of low-molecular rubber-based one at almost invariable rupturing deformation. numerical simulation by variation of composition parameters and molecular structure enables evaluation of its maximum fracture energy which is 1000 times higher than mechanical fracture energy of similar composites based on low-molecular rubbers. keywords. high-molecular rubbers; deformation; composites; mechanical stress; envelopes of fracture points; optimization; plasticizer; polymer composite; linking; glass transition temperature. citation: nurullaev, e., ermilov, a. s., lyubimova, n. yu., dependence of mechanical characteristics from composition and structure and optimization of mechanical fracture energy of polymer composite material based on high-molecular rubbers, frattura ed integrità strutturale, 41 (2017) 369-377. received: 28.11.2016 accepted: 06.05.2017 published: 01.07.2017 copyright: © 2017 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. introduction ractional composition of dispersed filler is very essential both for formation of rheological properties of suspensions based on viscous-liquid polymer binders and mechanical characteristics of 3d-linked filled polymer composite materials (pcms). at that basic formulation parameter is effective extent of volume filling –  / m , where  is volume fraction of filler solids, m maximum volume filling depending on particle shape, fractional composition and physicochemical interaction on filler – binder interface. f e. nurullaev et alii, frattura ed integrità strutturale, 41 (2017) 369-377; doi: 10.3221/igf-esis.41.48 370 structural and mechanical dependence of conventional stress ( ) from relative elongation degree ( ) in case of no lamination between filler particles and polymer binder, for example in road asphalt covering, was proved in previous work [1]. nowadays it is important to develop polymer composite material [2] as a covering for roofs of residential and industrial buildings, sports grounds, and road asphalt with advanced service life in comparison with commonly used pcm. to accelerate development of mentioned polymer composites, it is necessary first of all to investigate relation between molecular structure of polymer binder, effective extent of volume filling, mechanical characteristics and mechanical fracture energy of pcm [3]. previously we have shown that effective mole concentration of transverse chemical and intermolecular bonds is key structural parameter of 3d-linked elastomers filled with solids and based on low-molecular rubbers with terminal functional groups [4]. unfortunately mechanical characteristics of 3d-linked rubbers are usually evaluated without construction of envelopes of sample rupture points according to t. l. smith at uniaxial tension and different temperatures and deformation rates [3, 5]. the latter enable to predict service life of advanced pcm in different coverings. this work is intended to investigate numerically the dependence of conventional rupturing stress and mechanical fracture energy at uniaxial tension from fractional composition of dispersed filler, plasticizer volume fraction in polymer binder, effective density of transverse bonds, applied to development of covering for different purposes and with advanced service life in temperature range from 223 to 323 k. object of numerical experiment bject of numerical experiment is 3d-linked polymer composite material based on mixture of high-molecular rubbers: isoprene of grade ir and butadiene of grade br. [6, 7]. linking agent – sulfur; vulcanization accelerator – tetralkyltiuramdisulfide (“tiuram-d”); catalyst of cross-linking reaction – zinc oxide [6]. plasticizing oil is used as a plasticizer [7]. dispersed filler – silica (silicon dioxide, silica sand) with different fractional compositions. theoretical part omputer prediction (calculation) for diagram of uniaxial tension of filled elastomer sample is based on description of its structural and mechanical behavior [1]. at that dependence of conventional (related to initial cross-section of the sample) stress (σ) from relative elongation (α), which is related to deformation (ε) by the expression: α = 1+ε/100%, comprises following basic structural parameters and deformation conditions:   mcch , where  is polymer density, mc – average internodal molecular weight of the polymer binder; φr =1φsw – polymer volume fraction in the composite binder, sw – plasticizer volume fraction in the binder; r – universal gas constant; t∞ – equilibrium temperature, at which concentration of “physical” (intermolecular) bonds (νph) is negligible; tg – glass transition temperature of the polymer binder; t – sample test temperature (of numerical experiment);    1 a – velocity shift coefficient,    1 a = 1 at standard relative extension rate    1, c accepted for science and industry; φ – filler volume fraction; φm – maximum filler volume fraction, depending on fractional composition, particle shape and physicochemical interaction on the filler – binder interface. basic equation is as follows:                                                        1 23 1 13 2 2 2 1 1 1 29 exp 0.225 10 11 1.25 1 exp 0.5 21 ch r g n m i i i m i rt t t a t dt o c e. nurullaev et alii, frattura ed integrità strutturale, 41 (2017) 369-377; doi: 10.3221/igf-esis.41.48 371 where accumulation kinetics of internal composite damage as lamination between the polymer binder and filler particles is described in gaussian function; n – quantity of volume fractions φi of delaminated dispersed filler fractions (types);      /0.5t ii si – function parameter, α0.5i – sample elongation corresponding to the half volume of delaminated particles with i –type filler fraction (type),  si – mean-square dispersion for i –type filler fraction (type). value α0.5i determines delimitation initiation,  si characterizes composite integrity violation rate. as long as there is no the interfacial delamination in the elastomeric composite, limiting (rupturing) mechanical characteristics σb, αb can be evaluated by considering of deformation rate and size of average polymer binder interlayer between filler solids:                          03 3 3 3 1 ; 0 f m mf bb m m where indexes «f» and «o» stand for filled and free state elastomeric, respectively. in terms of rupturing deformation the following relation results:      0 3 1f mbb value  0 b is derived out of the curve   0 f effb which was obtained earlier by summarizing of multiple experimental data [1]. effective concentration of transverse bonds is equal to the total concentrations of chemical (determinant for 3dlinking of initial linear polymers) and physical (intermolecular, depending on polymer structure and experiment temperature) bonds:                      1/3 1/3 3 2 ( 1 ) 1 29 exp 0 ,225 10 ( )t t geff ch r ph ch r for example, if νeff =1mol/m3 and t= 293k rupturing deformation of 3d-linked elastomeric binder  0 b is almost 1000%. stated curve is part of the computer program as a calibrating one [8]. if sample integrity has been damaged up to the rupture, limiting mechanical characteristics are maximum point values for hump-shaped tension diagrams (σmax, εmax) or values of constrained maximum point assuring serviceability of partly disrupted composite, despite of possible sample tension. to evaluate dependence of material service time from internal damage level of filled polymer composite material by tension, we use envelopes of sample fracture points if no laminations (σb, εb) or maximum points mentioned above (σmax, εmax). these envelopes were introduced by smith as following dependences “logσb,max – logεb, max ” [9, 10]. problem of fractional composition optimization for dispersed components of polymer material (for given average particle sizes) considering fulfillment of optimization conditions for other performance characteristics could be defined in the following nonlinear programming statement:        ( , , ) max; min; min; q d e m r r              ... ; 1 2 3 1 m j opt jvj j j j jm j v          min max 0 1, 1, 2 , 3 , ..., if ;v m i jv jv jv j j n       / , / opt x jopt j optj x jj j in where     , , q d are vectors of volume fractions, porosities and particle sizes of dispersed components in the polymer material, respectively,     optj is optimal volume fraction of the filler in the composition, φjv – volume fraction of v-th fraction with j-type filler in the composition, mj – fraction number of j-type dispersed component,   min max ,   jv jv are upper and lower limits for solids volume fractions in the composition, respectively,   optx j is optimum mass concentration of solid e. nurullaev et alii, frattura ed integrità strutturale, 41 (2017) 369-377; doi: 10.3221/igf-esis.41.48 372 dispersed ingredients in the polymer composition for corresponding characteristics set, for example mechanical, γj are densities of dispersed components, in is variety of indexes for filler types being part of polymer material formulation. because of the difficulty, given problem which includes limitation of equation types is converted into the nonlinear programming problem with limitation of in equation types. at that quantity of optimizable independent variables is n = (mj) m, where m is quantity of polymer material solids types. normalizing ratio:        1 1 m j opt jv j j i j in nv is automatically fulfilled in case of problem solution. then we determine the vector of optimum volume fractions for filler fraction in the composition:        ( ; ); 1, 2 , 3 , ..., , opt opt i v m jv j n j where optjv is optimum volume fraction of v-th fraction for j-type filler. transformation to optimum mass concentrations of the corresponding solids       ( ; ; 1, 2, 3, ..., ) opt opt x x i v m j jv j n j is carried out by formula:     ( ) / ( / ) , opt opt opt x p jv jv j j j where       1 m j opt opt p x xjv j j i j in nv is the sum of mass concentrations (ratios) of polymer material solids. mechanical fracture energy (w) of pcm depending on rupturing elongation degree (αb) is calculated by formula [11]:   2 3 3 21 3 3 2 2 3 123 11 1.25 29 exp 0/225 10 21 2 2 bm b b bw rt t t agch r m b b                                                    (1) mathematical problem statement for maximum fracture energy search when limitations of other characteristics are fulfilled can be described as following nonlinear programming problem:                                            , , max 5 50.1 10 2 10 0.3 1 0.7 0.5 1 w ch r m ch i ii n r sw i m i                   (2) where:    , , ch r m – vectors of cross-linking mole concentration, polymer volume fraction in the binder and effective extent of volume filling, respectively; φsw– plasticizer volume fraction, coherent with polymer volume fraction (φm) as ratio   ( ) 1r sw ; in – variety of indexes for composition; n –quantity of composition calculation types. e. nurullaev et alii, frattura ed integrità strutturale, 41 (2017) 369-377; doi: 10.3221/igf-esis.41.48 373 numerical experimentation ab. 1 presents optimized parameter values of silica fraction mixtures in the pcm which are calculated using computer program being developed by the authors [8]. numerical experiments are carried out for: νch = 3 mol/m3, which is chosen according to predesigned as most effective one. plasticizer volume fractions in the polymer binder are chosen in form of three values 0.05; 0.1; 0.3 to provide development of the pcm with low viscosity. the last one is required for good component mixing. tab. 2 presents data required for numerical experimentation. table 1: optimum parameter values of silica fraction mixtures. fraction quantity 2; 3; 4 experiment temperature, к 223; 273; 323 glass transition temperature of the polymer 1 (isoprene of ir grade) к 200 glass transition temperature of the polymer 2 (butadiene of br grade), к 178 molecular weight of the polymer 1 (isoprene of ir grade) 372802 molecular weight of the polymer 2 (butadiene of br grade) 198775 density of the polymer 1 (isoprene of ir grade) kg/m3 900 density of the polymer 2 butadiene of br grade) kg/m3 890 volume fraction of the polymer 1 (isoprene of ir grade) in the binder 0.7; 0.65; 0.5 volume fraction of the polymer 2 (butadiene of br grade) in the binder 0.25; 0.25; 0.2 volume fraction of the filler 0.75 chemical bond density, mol/m3 3 design glass transition temperature of the rubber, к 192.3 molecular weight of the plasticizer (plasticizing oil of mpa grade) 1010 glass transition temperature of the plasticizer, к 169 density of the plasticizer, kg/сm3 890 volume fraction of the plasticizer 0.05; 0.1; 0.3 table 2: data required for numerical experimentation. tab. 3 presents numerical experimentation results about dependence of rupturing stress from rupturing deformation of the pcm depending on plasticizer volume fractions in the binder from 0.05 to 0.3 vol. fraction, on filler fraction t fraction number particle diameter, ϻ void volume ratio optimum values of fraction volume ratio maximum volume filling two fractions 1 15 0.386 0.2 0.84 2 600 0.244 0.8 three fractions 1 1 0.465 0.05 0.94 2 15 0.386 0.149 3 600 0.244 0.801 four fractions 1 1 0.465 0.028 0.96 2 15 0.386 0.082 3 240 0.367 0.226 4 600 0.244 0.664 e. nurullaev et alii, frattura ed integrità strutturale, 41 (2017) 369-377; doi: 10.3221/igf-esis.41.48 374 composition. analysis of numerical experimentation results has shown, that increase of plasticizer volume fraction from 0.05 to 0.3 (experiment temperature is 223 k; four – fraction silica) causes decrease of rupturing stress (from 12 to 9 mpa) at slight deformation increase (from 26 to 27%,). experiment temperature increase does not change this tendency (tab. 3). increase of silica fraction quantity in the pcm from two to four causes decrease of conventional rupturing stress from 28 to 11 mpa at rupturing deformation increase from 12 to 26% (numerical experiment temperature is 223 k, 0.1 vol. fraction plasticizer). if т = 273 к, 0.1 vol. fraction plasticizer, conventional rupturing stress decreases from 12 to 4 mpa at deformation increase from 17 to 36%; if т = 323 к – from 3 мpа (22%) to 1 мpа (45%). basic requirements to different coverings, especially to road asphalt, are the followings: rupturing stress – ap. 8 mpa and deformation – at least 12 – 15% at the temperature 223k. table 3: numerical experimentation results about dependence of rupturing stress from rupturing deformation of the pcm. according to the tab. 3, pcm based on 3d-linked high-molecular rubbers, filled with four silica fraction mixture at plasticizer volume fraction 0,05 in the binder, fully complies with given requirements. fig. 1 presents envelopes of rupture points for the pcm according to t. l. smith for different filler fraction values at 0.05 plasticizer volume fraction in the binder and cross-binding concentration νch = 3 mol/m3 at different temperatures of numerical experiment. it is obvious, that pcm filled with optimum mixture of four silica fractions meets the requirements to different coverings, especially to road asphalt. figure 1: envelopes of rupture points for polymer composite material according to t. l. smith for different filler fraction values at 0.05 plasticizer volume fraction in the binder and νch = 3 mol/m3 at different temperatures of numerical experiment. experiment temperature: 1 – 223 к ; 2. – 273 к; 3. – 323 к; a two-fraction silica; b four-fraction silica; c three-fraction silica. plasticizer volume fraction φsw = 0.05 vol. fraction dispersed filler two-fraction silica three-fraction silica four-fraction silica experiment temperature. к experiment temperature. к experiment temperature. к 223 273 323 223 273 323 223 273 323 σb. мpа 29 12 3 5.5 2.1 0.6 12 4 1 εb. % 12 16 22 42 58 75 26 36 45 plasticizer volume fraction φsw = 0.1 vol. fraction σb. мpа 28 12 3 7 2.6 0.75 11 4 1 εb. % 12 17 22 37 52 64 26 36 45 plasticizer volume fraction φsw = 0.3 vol. fraction σb. мpа 25 9 2 6 2 0.6 9 3.2 1 εb. % 13 18 22 38 54 65 27 39 47 e. nurullaev et alii, frattura ed integrità strutturale, 41 (2017) 369-377; doi: 10.3221/igf-esis.41.48 375 previously the authors have proposed polymer composite material for road covering based on low-molecular rubbers of butadiene + dieneepoxyetherurethane [12]. for comparison of mechanical behavior of low-molecular and high-molecular rubber-based pcms, fig. 2 presents envelopes of rupture points for polymer composite materials according to t. l. smith. figure 2: envelopes of rupture points for polymer composite materials according to t. l. smith: 1 – based on low-molecular rubbers br-ktr + pdi3b; 2 – based on high-molecular rubbers ir + br it is obvious that rupturing stress of pcm based on high-molecular rubber mixture is of a higher magnitude than of the low-molecular rubber-based one (12 against 1.2 mpa), at almost the same rupturing deformation. table 4: numerical experimentation results by determination of maximum mechanical fracture energies for pcm. determination of maximum fracture energy of filled plasticized polymer composite material echanical fracture energy is optimized for νch = 3 mol/m3. plasticizer volume fractions in the binder are chosen in form of three values: 0.05; 0.1; 0.3. tab. 4 presents numerical experimentation results by determination of maximum mechanical fracture energy for pcm. analysis of simulated results has shown, describes dependence between mechanical fracture energies and pcm fraction composition. it is obvious, that increase of fraction quantity causes decrease of fracture energy from 1800 to 1650 kj at plasticizer volume fraction φsw = 0,05 vol. fraction dispersed filler two-fraction silica three-fraction silica four-fraction silica experiment temperature, к experiment temperature, к experiment temperature, к 223 273 323 223 273 323 223 273 323 w, kj 1800 1100 400 1500 850 300 1700 920 350 εb, % 12 16 25 35 50 70 30 46 55 plasticizer volume fraction φsw = 0,1 vol. fraction w, kj 1750 1050 350 1400 800 300 1550 900 320 εb, % 12 17 22 40 55 70 26 36 50 plasticizer volume fraction φsw = 0,3 vol. fraction w, kj 1650 900 300 1350 700 250 1500 750 300 εb, % 13 18 22 38 54 65 27 37 45 m e. nurullaev et alii, frattura ed integrità strutturale, 41 (2017) 369-377; doi: 10.3221/igf-esis.41.48 376 the temperature 223 k, and rupturing deformation increases from 12% to 35%; at 273 k – from 1100 to 900 kj; rupturing deformation – from 16% to 46%; at 323 k – from 400 to 350 kj, rupturing deformation – from 25% to 55%. fig. 3 presents for the first time by the authors constructed envelopes mechanical destruction energy values for the four fractions of silicon dioxide at a volume fraction of the plasticizer φsw = 0.05 and temperatures of numerical experiment 223 k, 273 k, 323 k. envelopes of rupture points of polymer composite material according to t. l. smith qualitatively characterize material service time. in contrast to that, envelopes of mechanical fracture energies quantitatively evaluate service life of pcm. envelopes of mechanical fracture energies for pcm based on low-molecular and high-molecular rubber mixtures are constructed for comparison (fig. 4). it was shown, that mechanical fracture energy of pcm based on high-molecular rubber mixture is 1000 times higher than of the low-molecular rubber-based one. figure 3: envelopes of mechanical fracture energies. φsw = 0.05; vol. fraction; experiment temperature: 1 – 223 к; 2 – 273 к; 3 – 273 к. a two-fraction silica; b four-fraction silica; c three-fraction silica figure 4: envelopes of mechanical fracture energies for pcm: 1 – based on low-molecular rubbers br-ktr + pdi3b; 2 – based on high-molecular rubbers ir + br. conclusions 1. optimized parameter values of silica fraction mixtures in polymer composite materials are calculated using computer program being developed by the authors. e. nurullaev et alii, frattura ed integrità strutturale, 41 (2017) 369-377; doi: 10.3221/igf-esis.41.48 377 2. increase of silica fraction quantity in the composite from two to four causes decrease of conventional rupturing stress at rupturing deformation increase at every temperature of numerical experiment. 3. for the first time the authors constructed envelopes of sample rupture points according to t. smith at uniaxial tension and different temperatures, plasticizer volume fractions in the polymer binder and different filler fraction mixture values, which enable basically predict service live of advanced polymer composite materials in different coverings. 4. to compare mechanical behavior of composites based on low-molecular and high-molecular rubbers, envelopes of rupture points are constructed according to t. l. smith. it is shown that rupturing stress of covering material based on high-molecular rubbers is far above than of the low-molecular ones. 5. it is shown, that composite filled with optimum mixture of four silica fractions at plasticizer volume fraction 0.05 in the binder fully complies with given requirements to different coverings, especially to road asphalt. 6. maximum mechanical fracture energy for filled composite material is determined. it is shown, that mechanical fracture energy maximizes when the polymer binder is filled with four-fraction silica. 7. for the first time the authors constructed envelopes of mechanical fracture energies depending on plasticizer volume fraction, fraction composition of polymer composite material and experiment temperature. it is stated, that mechanical characteristics, first of all mechanical fracture energy, maximizes at plasticizer volume fraction 0.05 – 0.3 volume fractions in the binder from operating temperature. 8. it is stated, that mechanical fracture energy of polymer composite material based on high-molecular rubbers is 1000 times higher than of the low-molecular rubber-based one references [1] ermilov, a. s., nurullaev, e. m., mechanical properties of elastomers filled with solid particles, mechanics of composite materials, 48 (3) (2012) 243-252. [2] garifullin, a., iblyaminov, f. f., constructional rubber and methods for determining their mechanical properties, kazan, (2000). [3] smith, t. l., ultimate tensile properties of elastomers, j. appl. phys., 35 (1964) 27-34. [4] ermilov, a. s., nurullaev, e. m., numerical simulation and derivation of an equation for calculation of the mechanical fracture energy of elastomer filled with multifractional silica // russian journal of applied chemistry, 87 (4) (2014) 500-508. [5] smith, t. l., limited characteristic of cross-linked polumers, j. appl. phys., 35 (1964) 27-32. [6] dick, j. s., rubber technology. compounding and testing for performance. hanser gardner publications, inc., cincinati, (2010). [7] mark, dzh., ehrman, b., airich, f., science and technology of rubber, academic press is an imprint of elsevier. (2005). [8] certificate no. 2012613349 rf a software for determination and optimization of packing density of solid disperse fillers of polymer composite materials, ermilov, a. s., nurullaev, e. m, duregin, k. a., priority of 09.04.2012. [9] smith, t. l., symposium on stress-strain-time-temperature relationships in materials, amer. soc. test. mat. spec. publ., 325 (1962) 60-89. [10] smith, t. l., relation between the structure of elastomers and their tensile strength, in: mechanical properties of new materials [russian translation], mir, moscow, (1966) 174-190. [11] nurullaev, e. m., ermilov, a. s., dependence of mechanical fracture energy of the polymeric composite material from the mixture of filler fractions, fracture end structural integrity, 31 (2015) 120-126. [12] patent no. 2473581, rf a waterproof frost-resistant asphalt covering for highways, ermilov, a. s., nurullaev, e. m., alikin, v. n., priority of 31.05.2011. << /ascii85encodepages false /allowtransparency false /autopositionepsfiles true /autorotatepages /none /binding /left /calgrayprofile (dot gain 20%) /calrgbprofile (srgb iec61966-2.1) /calcmykprofile (u.s. web coated \050swop\051 v2) /srgbprofile (srgb iec61966-2.1) /cannotembedfontpolicy /error /compatibilitylevel 1.4 /compressobjects /tags /compresspages true /convertimagestoindexed true /passthroughjpegimages true /createjobticket false /defaultrenderingintent /default /detectblends true /detectcurves 0.0000 /colorconversionstrategy /cmyk /dothumbnails false /embedallfonts true /embedopentype false /parseiccprofilesincomments true /embedjoboptions true /dscreportinglevel 0 /emitdscwarnings false /endpage -1 /imagememory 1048576 /lockdistillerparams false /maxsubsetpct 100 /optimize true /opm 1 /parsedsccomments true 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/hrv (za stvaranje adobe pdf dokumenata najpogodnijih za visokokvalitetni ispis prije tiskanja koristite ove postavke. stvoreni pdf dokumenti mogu se otvoriti acrobat i adobe reader 5.0 i kasnijim verzijama.) /hun 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can be opened with acrobat and adobe reader 5.0 and later.) >> /namespace [ (adobe) (common) (1.0) ] /othernamespaces [ << /asreaderspreads false /cropimagestoframes true /errorcontrol /warnandcontinue /flattenerignorespreadoverrides false /includeguidesgrids false /includenonprinting false /includeslug false /namespace [ (adobe) (indesign) (4.0) ] /omitplacedbitmaps false /omitplacedeps false /omitplacedpdf false /simulateoverprint /legacy >> << /addbleedmarks false /addcolorbars false /addcropmarks false /addpageinfo false /addregmarks false /convertcolors /converttocmyk /destinationprofilename () /destinationprofileselector /documentcmyk /downsample16bitimages true /flattenerpreset << /presetselector /mediumresolution >> /formelements false /generatestructure false /includebookmarks false /includehyperlinks false /includeinteractive false /includelayers false /includeprofiles false /multimediahandling /useobjectsettings /namespace [ (adobe) (creativesuite) (2.0) ] /pdfxoutputintentprofileselector /documentcmyk /preserveediting true /untaggedcmykhandling /leaveuntagged /untaggedrgbhandling /usedocumentprofile /usedocumentbleed false >> ] >> setdistillerparams << /hwresolution [2400 2400] /pagesize [612.000 792.000] >> setpagedevice shot peening processes to obtain nanocrystalline surfaces in metal alloys: s. jing et alii, frattura ed integrità strutturale, 43 (2018) 33-42; doi: 10.3221/igf-esis.43.02 33 experimental study on uniaxial tensile and compressive behavior of high toughness cementitious composite shiyong jiang training department, logistical engineering university. chongqing, 401311, p.r. china jiangshiy@163.com shuai tao, wei fei, xueyang li civil engineering department, logistical engineering university. chongqing, 401311, p.r. china taos0313@163.com, 1063408903@qq.com, tmlt92@163.com abstract. though the principle of orthogonal experimental design, the uniaxial compression experiment and uniaxial tensile experiment were carried out on nine groups of high toughness cementitious composites with different mixing ratios to study the influence of four factors, namely fly ash content, water-binder ratio, sand-binder ratio and plasticizer content on the compressive strength and ultimate tensile strain of high toughness cementitious composites. the experiment results show that pva fibers content greatly influenced the flexural behavior and the influence of the four factors on the compressive strength and ultimate tensile strain of high toughness cementitious composite is basically the same, the primary and secondary order is: water-binder ratio, fly ash content, plasticizer content and sand-binder ratio. keywords. high toughness cementitious composite; orthogonal experiment design; mixing ratio; compressive strength; ultimate tensile strain. citation: s. jing, s. tao, w. fei, x.y. li, experimental study on uniaxial tensile and compressive behavior of high toughness cementitious composite, frattura ed integrità strutturale, 43 (2017) 33-42. received: 07.08.2017 accepted: 05.09.2017 published: 01.01.2018 copyright: © 2018 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. introduction igh toughness cementitious composite is a new type of composite material which is formed by the incorporation of monofilament staple fibers into the cement matrix and homogeneously dispersed. it is also called engineered cementitious composite (ecc), which was initially developed by victor c. li [1, 2]. this material can generate multiple fine cracks in the tension process. ultimate tensile strain may reach several hundred times that of ordinary concrete, while the stress may increase when the strain increases, so it has a quasi-strain hardening property and excellent toughness [3, 4]. ecc can be used in road surface, bridge and dam maintenance as well as aseismic hardening or serves as a new important material for new structures [5]. however, at present there is no recognized ecc mix design. besides, there are no established norms or standards proposed regarding the regularities between mixing ratios and the mechanical h s. jing et alii, frattura ed integrità strutturale, 43 (2018) 33-42; doi: 10.3221/igf-esis.43.02 34 properties of ecc. in concrete structures, the compression performance must be guaranteed for columns, walls and other load-bearing members. due to the deficiency of coarse aggregate, the increase in strength of ecc will be limited to a certain extent. therefore, in order to promote the ecc in concrete structures, it is necessary to design an appropriate mix ratio to ensure that it has reliable strength, but also good toughness. the classic mixing ratio of ecc showed that the raw materials made up of cement, fly ash, fine quartz sand, water and monofilament staple fibers. on the one hand, an excessive water-binder ratio could severely reduce the strength of the material because it lacks coarse aggregate; on the other hand, if the water-binder ratio is too small, the fluidity of the mixture may deteriorate, which could hinder the dispersion of fibers. in this experiment, the superplasticizer was used to reduce the amount of water, while ensuring a good fluidity of the mixture. in this paper, four main factors, namely fly ash content, sand-binder ratio, water-binder ratio and plasticizer content were considered, using the compressive strength and ultimate tensile strain of ecc as indexes. the influence of the regularities of various factors on the strength and toughness of high toughness cementitious composites was studied through the orthogonal experiment. experimental design experimental materials he cementitious materials consist of p.o 42.5 ordinary portland cement and first-grade fly ash. fine quartz sand with a size of 0.1mm-0.2mm was used as fine aggregate. ordinary tap water with polycarboxylic superplasticizer was used to mix the dry material. previous studies showed that polyvinyl alcohol (pva) and polyethylene (pe) fiber were the primary types of fiber to manufacture ecc. c. redon adopted different amounts of special oil coated with the surface of pva fiber, and found those which could dissipate a large amount of energy in the process of gradually pulling out from the cement matrix [6]. in this paper, kuraraytm pva fiber (φ15μm×12mm) was used to manufacture high toughness cementitious composites. orthogonal design the mix proportion of concrete is commonly tested with either one variable or multiple variables at a time. each of the two methods has its unique advantages and disadvantages. the one-variable-at-a-time method is not representative enough and limited to a small range, while the multiple-variable-at-a-time method requires repeated tests on the interacting factors. for instance, in the case of three factors and three levels, 27 tests need to be carried out, making the experiment extremely complicated. the merits of the above two methods are combined into the orthogonal test method. based on mathematical statistics principles, the test solution relies on a set of orthogonal forms to sieve out the most representative samples for comprehensive tests, aiming to obtain the effect of factors on indices and identify the best combinations of influencing factors [7]. in the orthogonal test, the test factors refer to those influencing the object, and the levels denote the conditions of the test factors. in this research, the test factors include fly ash content, sand-binder ratio, water-binder ratio and plasticizer content, each of which has three levels of conditions. the purpose of the orthogonal test is to examine the impact of the test factors on the compressive strength and the ultimate tensile strain of materials. level of factor fly ash content sand-binder ratio water-binder ratio plasticizer content (a) (b) (c) (d) 1 0.9 0.30 0.20 0.40% 2 1.2 0.33 0.23 0.70% 3 1.5 0.36 0.26 1.00% table 1: factors and levels of orthogonal test. mixing ratio this study took fiber with a volume content of 2.0% as an invariant, considered the four factors fly ash content, sandbinder ratio, water-binder ratio and plasticizer content. each factor includes three levels,as shown in table 1. three-level variables of fly ash content adopted the mass ratio of fly ash to cement (mfa/c), being equal to 0.9, 1.2 and 1.5 which were respectively expressed by a1, a2 and a3. three-level variables of the sand-cement ratio adopted the mass ratio of sand to cementing materials (ms/b) for the 0.30, 0.33 and 0.36 and were respectively expressed by b1, b2 and b3. three-level t s. jing et alii, frattura ed integrità strutturale, 43 (2018) 33-42; doi: 10.3221/igf-esis.43.02 35 variables of the water-cement ratio adopted the mass ratio of water to cementing materials (mw/b), being equal to 0.20, 0.23 and 0.26, respectively expressed by c1, c2 and c3. after the preliminary exploratory experiment, the mass ratios of superplasticizer to cementing material were set to 0.4%, 0.7% and 1.0%, which were expressed by d1, d2 and d3 respectively. experimental procedure uniaxial compression experiment he compressive strength of concrete is one of the basic mechanical properties; however, for ecc compression performance experiments, there are currently no uniform standards and norms. victor c. li [8] carried out the axial compression experiment with an ecc cylinder with a specimen of the size φ75mm×150mm and compared the test results to ordinary concrete. the team of shilang xu [9] conducted the uniaxial compression experiment with an ecc cube that has a side length of 40 mm and a 40mm×40mm×160mm prism specimen, and measured the uniaxial compressive stress-strain curves. chunhong hu et al. [10] used a 40mm×40mm×160mm prism of ecc specimens to study the strength under uniaxial compression and found the rule that the peak strain and ultimate compressive strain were both significantly larger than that of ordinary concrete. mingke deng et al. [11]used ecc cubes with side lengths of 100mm and 70.7mm to carry out the uniaxial compression experiment, then found the secondary compressive strength of the ecc was close to the first compressive strength, which shows that the resistance to damage of ecc is obviously better than that of ordinary concrete. in this paper, the uniaxial compression experiment on an ecc cube with the size of 100mm×100mm×100mm was carried out. the fibers were mixed last when producing ecc; that is, the cement, fly ash and sand were first put into the blender and mixed for 1 to 2min, then the water and superplasticizer were added and mixed for 4 to 5min, fibers were slowly added and finally mixed 8 to 10min until the it were dispersed evenly. the specimens should undergo vibrating compaction after ecc is poured into the mold, then released after standing 36 hours and put into the standard curing box for curing. the orthogonal experiment includes nine groups' mixing ratios. the uniaxial compression experiment was carried out on each specimen in accordance with relevant provisions of gb/t 50081-2002 ordinary concrete mechanical performance test method standards [12]. experimental phenomena and results during the experiment, it was found that the compression failure process of high toughness cementitious composite was obviously different from ordinary concrete. during the loading process, the vertical micro cracks first appeared in the central part of the specimen. as the load continued to increase, the cracks developed obliquely toward the end of the specimen and new fine cracks were formed near the original crack zone. when the load was applied close to the ultimate load, the crack developed rapidly and the width of the crack began to increase; simultaneously, the lateral deformation of the specimen increased gradually and the sound of fiber breaking and pulling out of the specimen could be heard. finally, part of the cracks across the entire section and the bearing capacity began to decline, which indicated specimen failure. all the specimens in the experiment did not show the phenomenon of bursting apart and peeling similar to ordinary concrete, but after unloading, the specimens were found to have undergone obvious compression deformation, but to maintain good integrity. the experimental data of each group mixing ratio were obtained and reported in table 2. orthogonal analysis taking factor (a fly ash content) as an example, below is a simple illustration of how the range of a factor is determined. if we denote the total compressive strength of factor a at each of the three levels as k1, k2 and k3, respectively, and the average compressive strength at each of the three levels as k — 1, k — 2 and k — 3, respectively, then we have: k1＝55.3+47.4+39.9=142.6, (z1, z2, z3 test group) (1) k2＝47.3+38.5+61.4=147.2, (z3, z4, z5 test group) (2) k3＝37.9+55.4+43.3=136.6, (z6, z7, z8 test group) (3) k — 1=k1/3=142.6/3=47.5 (4) t s. jing et alii, frattura ed integrità strutturale, 43 (2018) 33-42; doi: 10.3221/igf-esis.43.02 36 k — 2 =k2/3=147.2/3=49.0 (5) k — 3 =k3/3=136.6/3=45.5 (6) the size of the range r is introduced to measure the impact of factors on the test indices. the importance of a factor is positively correlated with the size of its range. if a factor has a big range, any variation in the level of the factor will significantly affect the test indices, and the inverse is true. the size of the range r is calculated as follows: r＝(k — i) max-(k — j ) min＝49.0-45.5＝3.5 (7) the range of other factors is calculated in the same way. the results are listed in table 2. test group a fly ash content b sand-binder ratio c waterbinder ratio d plasticizer content compressive strength (mpa) z1 1(0.9) 1(0.30) 1(0.20) 1(0.40%) 55.3 z2 1(0.9) 2(0.33) 2(0.23) 2(0.70%) 47.4 z3 1(0.9) 3(0.36) 3(0.26) 3(1.00%) 39.9 z4 2(1.2) 1(0.30) 2(0.23) 3(1.00%) 47.3 z5 2(1.2) 2(0.33) 3(0.26) 1(0.40%) 38.5 z6 2(1.2) 3(0.36) 1(0.20) 2(0.70%) 61.4 z7 3(1.5) 1(0.30) 3(0.26) 2(0.70%) 37.9 z8 3(1.5) 2(0.33) 1(0.20) 3(1.00%) 55.4 z9 3(1.5) 3(0.36) 2(0.23) 1(0.40%) 43.3 k1 142.6 140.5 172.1 137.1 k2 147.2 141.3 138.0 146.7 k3 136.6 144.6 116.3 142.6 k — 1 47.5 46.8 57.3 45.7 k — 2 49.0 47.1 46.0 48.9 k — 3 45.5 48.2 38.7 47.5 r 3.5 1.4 18.6 3.2 table 2: orthogonal experiment result of compressive property. as can be seen in table 2, for the four factors considered in the experiment, the range in decreasing order is: water-binder ratio, fly ash content, plasticizer content and sand-binder ratio. the range of the water-binder ratio is 18.6, which is far greater than the range of the other three factors. this result indicates that the water-binder ratio has the greatest influence on the compressive strength of ecc, followed by fly ash content, plasticizer content and sand-binder ratio. in order to further analyze the impact of each factor on the compressive strength, a relationship curve diagram was drawn, taking the change of each factor as an abscissa and the average compressive strength k — i as an ordinate. according to the results of the range analysis and figure 2: 1) the water-binder ratio is the key factor in the compressive strength of high toughness cementitious composites, and the strength increases with the decrease of the water-binder ratio. if the water-binder ratio is too large, the internal porosity of the material will increase, which can directly lead to lower compressive strength. 2) in the experiment, the mass ratio of fly ash to cement is in the range of 0.9 1.5. the compressive strength increases first and decreases later with increasing fly ash content. fly ash is made up of a large number of subtle spherical vitreous compositions with fine particle size, which can play a role in improving the mobility of the mixture. meanwhile, there is the pozzolanic effect of fly ash, namely the chemical reaction of fly ash and cement hydrate. the products of the chemical reaction are often filled in the pores of the cement hydrate, reducing the interior porosity of the mixture and improving the compactness of the material. however, the active effect of fly ash should lag behind the hydration reaction s. jing et alii, frattura ed integrità strutturale, 43 (2018) 33-42; doi: 10.3221/igf-esis.43.02 37 of cement, which may cause a negative influence on the density and strength of the materials in the early stage of hydration [13]. 3) the addition of superplasticizer can disperse and lubricate the cement, which reduces the water consumption and makes the uniformity of the mixture better. however, if the plasticizer content is too large, it may extend the setting time of the high toughness cementitious composite and reduce its initial strength. in this experiment, the compressive strength first increases and then decreases with the mass ratio of superplasticizer to cementing material changing from 0.4% to 1.0%, indicating there is an optimum dosage of superplasticizer. 4) experimental data indicate that the compressive strength increases by 0.6% and 3.0% with the sand-binder ratio changing from 0.30 to 0.33 and 0.36. according to the result of the range analysis, the impact of sand-binder on the compressive strength of the material is minimal. figure 1: failure mode of test specimens. figure 2: influence of changes in factors on compressive strength. uniaxial tensile experiment iterature [14] found through a large number of experiments that cracks could be extended to steady-state cracking mode during the tensile experiment of the high toughness cementitious composite. the tensile stress instantly dropped when the first crack appeared and then immediately returned, then new cracks were created as the load increased without increasing the crack width. jun zhang et al. [15] carried out the tensile experiment with ecc prism specimens using six different mixing ratios. the tensile stress-strain curve was measured and the ultimate tensile strain was found to be 1.7%. shilang xu [16] used thin plate specimens of ecc to carry out the tensile experiment. the result showed that ecc had a significant quasi-strain hardening property and the crack width could be effectively controlled within 100 μm. figure 3: the thin plate specimen for uniaxial compression experiment. figure 4: experimental set-up for niaxial tensile test. l s. jing et alii, frattura ed integrità strutturale, 43 (2018) 33-42; doi: 10.3221/igf-esis.43.02 38 in this paper, the uniaxial tensile experiment on an ecc thin plate specimen of the size 300mm×50mm×15mm was carried out. steel sheets with a thickness of 1 mm were affixed to both ends of the specimen to prevent partial damage to the holding parts of the specimen, as shown in figure 3. the experiment was carried out on a 1000kn microcomputer-controlled servo-hydraulic testing machine and the load was applied in the displacement control mode at a speed of 0.0025 mm/s. meanwhile, the strain data were collected on both sides of the specimen with extensometers. the test apparatus is shown in figure 4. experimental phenomena and results the results showed that the failure process of all specimens could be divided into three stages: elastic stage, multiple crack development stage and failure stage. during the loading process, the first crack was found to have appeared in the weak section, and then there were many fine cracks that appeared immediately around it. all specimens exhibited quasi-strain hardening behaviour, and the ultimate tensile strain of ecc was much larger than that of ordinary concrete. the experimental results of the nine groups of different mixing ratios are shown in figure 5. figure 5: tensile stress strain curve of 9 experimental groups. orthogonal analysis it’s similar to the range calculation method of factor a in terms of compressive strength so it’s not repeated hereby. calculation results are shown in table 3. as can be seen in table 3, the range decreasing order is: water-binder ratio, fly ash content, plasticizer content and sand-binder ratio, and the range of water-binder ratio is 1.051, which is far greater than the range of the other three factors. this indicates that the water-binder ratio has the greatest influence on the ultimate tensile strain of ecc, followed by fly ash content, plasticizer content and sand-binder ratio. the relationship curve diagram shows the change of each factor as an abscissa and the average ultimate tensile strain as an ordinate. based on the results: 1) the water-binder ratio is the key factor that affects the ultimate tensile strain of high toughness cementitious composite, and the greater the water-binder ratio is, the higher the ultimate tensile strain is, meaning the better the toughness is. 2) the ultimate tensile strain increases with the increase of fly ash content. the chemical reaction of fly ash with cement hydrate can improve the properties of the interface between fibers and matrix; moreover, there are a large number of fly ash spherical particles attached at the surface of the fibers, reducing the adhesion between fiber and matrix and having a positive impact on the realization of the strain-hardening. 3) the experimental results show that the sand-binder ratio and plasticizer content have little effect on the ultimate tensile strain. s. jing et alii, frattura ed integrità strutturale, 43 (2018) 33-42; doi: 10.3221/igf-esis.43.02 39 test group a fly ash content b sand-binder ratio c water-binder ratio d plasticizer content ultimate tensile strain （ %） z1 1(0.9) 1(0.30) 1(0.20) 1(0.40%) 0.458 z2 1(0.9) 2(0.33) 2(0.23) 2(0.70%) 0.825 z3 1(0.9) 3(0.36) 3(0.26) 3(1.00%) 1.482 z4 2(1.2) 1(0.30) 2(0.23) 3(1.00%) 0.96 z5 2(1.2) 2(0.33) 3(0.26) 1(0.40%) 1.51 z6 2(1.2) 3(0.36) 1(0.20) 2(0.70%) 0.424 z7 3(1.5) 1(0.30) 3(0.26) 2(0.70%) 1.575 z8 3(1.5) 2(0.33) 1(0.20) 3(1.00%) 0.532 z9 3(1.5) 3(0.36) 2(0.23) 1(0.40%) 1.045 k1 2.765 2.993 1.414 3.013 k2 2.894 2.867 2.830 2.824 k3 3.152 2.951 4.567 2.974 k — 1 0.922 0.998 0.471 1.004 k — 2 0.965 0.956 0.943 0.941 k — 3 1.051 0.984 1.522 0.991 r 0.129 0.042 1.051 0.063 table 3: orthogonal experiment result of tensile property. figure 6: influence of changes in factors on ultimate tensile strain. discussion about the toughening mechanism of pva fibers n general, the numerous initial microdefects in the concrete matrix were demonstrated as tiny cracks in the loading process. according to the test, it is concluded that fibers should take up 2% of the volume of the specimen and should be randomly distributed throughout the specimen. capable of bridging the initial microdefects, plenty of fibers can obviously reduce the occurrence and expansion of tiny cracks. as much of the matrix is held together by fibers, it is less likely for microdefects to develop in the initial phase. thanks to the fibers, the specimen is fortified on the inside, making the matrix more resistant to deformation [17]. i s. jing et alii, frattura ed integrità strutturale, 43 (2018) 33-42; doi: 10.3221/igf-esis.43.02 40 figure 7 displays the form of the specimen at the peak load and after the failure. no burst fracture is observed in the test. at the peak load, the multiple tiny vertical cracks on the specimen gradually developed into major connected cracks; the crack development is accompanied by the sound of fibers being strained or broken. whereas the fibers hold the matrix together and the material has the strain-hardening property, the stress state of the ecc in uniaxial loading is similar to that of the confined concrete under conventional triaxial loading. in this test, the specimen exhibited the squeezing flow failure similar to that of confined concrete [18]. when macroscopic cracks begin forming (fig.8, a), fibers between the crack sections are interlaced and evenly distributed. fibers at the crack parts bear the majority of the tensile force, which prevents further development of cracks. the cracks at this stage are mainly the outcome of the bridging role of fibers. in other words, on the crack surface, the concrete matrix delivers the stress to fibers which rely the surface to convey the stress to the concrete matrix around that doesn’t have cracks. when the cracking strength of the matrix around reaches the limit, new cracks will appear, which is reflected in increasing cracks on specimens. strain hardening is realized through formation of multiple cracks. the process will last until the surface fibers are collectively pulled out or broken. specimens show remarkable extensibility [19]. fig. 8(b) displays the failure mode of specimens in the direct tensile test. it can be noted that a number of cracks show up on the specimen surface, which indicates that desirable adhesive performance exists between pva fibers and the matrix. it prevents further expansion of tiny cracks. with such strain hardening behavior, the strength and toughness of materials are significantly enhanced [20]. figure 7: failure mode comparison of ecc cube specimens in different phases of loading. (a) (b) figure 8: (a) micro-crack bridging and ductility enhancement effect of pva fibers; (b) typical multiple cracks on ecc thin plate specimen under tensile load. s. jing et alii, frattura ed integrità strutturale, 43 (2018) 33-42; doi: 10.3221/igf-esis.43.02 41 conclusion n this paper, the orthogonal experiment was carried out to study the compressive property and tensile property of high toughness cementitious composite, and the preliminary conclusions are as follows: 1) the failure pattern of high toughness cementitious composite is significantly different from ordinary concrete. there is no phenomenon of sudden collapse when it is damaged by compression, and all the specimens can maintain a good integrity without the phenomenon of peeling. there are a large number of fine cracks that appeared in almost the entire area of the specimen during the process of tension, showing the characteristic of significant quasi-strain hardening. finally, it is proved that the ultimate tensile strain of high toughness cementitious composites is much larger than that of ordinary concrete. 2) no matter whether for compressive strength or ultimate tensile strain, the primary and secondary order of the influence of the four factors is: water-binder ratio, fly ash content, plasticizer content and sand-binder ratio. in terms of compressive strength, the smaller the water-binder ratio, the higher the strength; and the compressive strength increases first and then decreases with the addition of fly ash or plasticizer content. however, the effect of sand-binder ratio on the compressive strength is relatively small. for the toughness of the material, the ultimate tensile strain improves with the increase of the water-binder ratio or fly ash content; the influence of sand-binder ratio and plasticizer content is not obvious. 3) considering both compressive strength and toughness, the water-binder ratio is the key factor, because the influence of it on both is far greater than that of other factors. yet it should be noted that the influence of water-binder ratio on compressive strength and toughness is diametrically opposed. taking into account the main feature of ecc, namely its superior toughness, the water-binder ratio should be increased as much as possible while ensuring the compressive strength will not be too low. acknowledgments he authors are grateful to the finical support from the key projects of college outstanding achievements transformation (kjzh14220). references [1] zhang, j., li., v. c., effect of inclination angle on fiber rupture load in fiber reinforced cementitious composites, composites science & technology, 62 (2002) 775–781. [2] li, v. c., large volume, high-performance applications of fibers in civil engineering, journal of applied polymer science, 83 (2010) 660-686. [3] li, v. c., leung, c. k. y., theory of steady state and multiple cracking of random discontinuous fiber reinforced brittle matrix composites, asce journal of engineering mechanics, 118 (1992) 2246―2264. [4] wang, s., li, v. c., engineered cementitious composites with high-volume fly ash, aci materials journal, 104 (2007) 233-241. [5] mirandola, a., lorenzini, e., energy, environment and climate: from the past to the future, international journal of heat and technology, 34 (2016) 159-164. [6] redon, c., li, v. c., wu, c., et al. measuring and modifying interface properties of pva fibers in ecc matrix, journal of materials in civil engineering, 13 (2001) 399-406. [7] chi, y., xu, l., zhang, y., experimental study on hybrid fiber–reinforced concrete subjected to uniaxial compression, journal of materials in civil engineering, 26 (2014) 211-218. [8] li, v. c., mishra, d. k., wu, h. c., matrix design for pseudo strain-hardening fiber reinforced cementitious composites, material and structures, 28 (1995) 586-l595. [9] xu, s. l., cai, x. r., zhang, y. h., uniaxial compressive stress-strain full curves and measurement of ultrahigh toughness fiber reinforced cement matrix composites, china civil engineering journal, 42 (2009) 79-85. [10] hu, c. h., gao, y. e., ding, w. c., experimental on compression properties of ultrahigh toughness cementitious composite properties, journal of building structures, 34 (2013) 128-132. i t s. jing et alii, frattura ed integrità strutturale, 43 (2018) 33-42; doi: 10.3221/igf-esis.43.02 42 [11] deng, m. k., qin, m., liang, x. w., experimental research on high ductile fiber reinforced concrete compressive properties, industrial construction, 45 (2015) 120-126. [12] gb/t 50081-2002 ordinary mechanical properties of concrete test method standards, beijing: china building industry press, (2003). [13] zhang, h.y., thermodynamic property of concrete and temperature field analysis of the base plate of intake tower during construction period, international journal of heat and technology, 33 (12015) 145-154. [14] li, v. c., wang, s., wu, c., tensile strain-hardening behavior of polyvinyl alcohol engineered cementitious composite (pva-ecc), aci materials journal, 98 (2001) 483-492. [15] gong, c. x., zhang, j., tensile performance of high ductile fiber reinforced cementitious composite, journal of hydraulic engineering, 39 (2008) 361-366. [16] xu, s. l., li, h. d., uniaxial tensile experiments of ultra high toughness cementitious composite, china civil engineering journal, 42 (2009) 32-41. [17] spagnoli, a., a micromechanical lattice model to describe the fracture behaviour of engineered cementitious composites, computational materials science, 46 (2009) 7-14. [18] kabele, p., multiscale framework for modeling of fracture in high performance fiber reinforced cementitious composites, engineering fracture mechanics, 74 (2007) 194-209. [19] li, v. c., wang, s., microstructure variability and macroscopic composite properties of high performance fiber reinforced cementitious composites, probabilistic engineering mechanics, 21 (2006) 201-206. [20] yang, e. h., yang, y. z., li, v. c., use of high volumes of fly ash to improve ecc mechanical properties and material greenness, aci materials journal, 104 (2007) 620-628. microsoft word numero_39_art_16 da rifare m. muñiz calvente et alii, frattura ed integrità strutturale, 39 (2017) 160-165; doi: 10.3221/igf-esis.39.16 160 a probabilistic approach for multiaxial fatigue criteria m. muñiz calvente, s. blasón, a. fernández canteli department of construction and manufacturing engineering, univ. of oviedo, 33203 gijón, spain munizcmiguel@uniovi.es, http://orcid.org/0000-0003-1769-2309 http://orcid.org/0000-0001-8071-9223 a. de jesús, j. correia faculty of mechanical engineering, feup, university of porto, portugal http://orcid.org/0000-0002-1059-715x http://orcid.org/0000-0002-4148-9426 abstract. models proposed to study the multiaxial fatigue damage phenomenon generally lack probabilistic interpretation due to their deterministic form. this implies failure compulsory happening at the plane exhibiting the maximum damage value, whereas the remaining planes are disregarded. nevertheless, the random orientation of the predominant defect evidences the possibility of failure being initiated as a function of the predominant defect presence without requiring, necessarily, maximum values of the damage parameter, which emphasizes the need of introducing probabilistic concepts into the failure prediction analysis. in this paper, a probabilistic model is presented that enables the failure probability to be found for any selected plane orientation by considering the damage gradient as a parameter for both proportional and non-proportional loading. the applicability of the model is elucidated by means of an example. assuming the cdf for the local failure of the material to be known, the probability of failure is calculated for a cross shaped specimen in which shift between the principal stresses xx and yy ranges from 0º to 180º. keywords. fatigue weibull model; multiaxial fatigue; generalized local model. citation: muñiz calvente, m., blasón, s., de jesús, a., correia, j., fernández canteli, a., a probabilistic approach for multiaxial fatigue criteria, frattura ed integrità strutturale, 39 (2017) 160-165. received: 11.06.2016 accepted: 10.10.2016 published: 01.01.2017 copyright: © 2017 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. introduction sually, models proposed to study the multiaxial fatigue damage phenomenon are applied in their deterministic form. this implies failure always happening compulsory at the plane exhibiting the maximum damage, whereas the remaining planes are disregarded. nevertheless, the random orientation of the predominant defect evidences u http://www.gruppofrattura.it/pdf/rivista/numero39/audio/16.mp3 m. muñiz calvente et alii, frattura ed integrità strutturale, 39 (2017) 160-165; doi: 10.3221/igf-esis.39.16 161 the possibility of failure being initiated as a function of the predominant defect presence without requiring maximum values of the damage parameter, which emphasizes the need of introducing probabilistic concepts in the failure prediction analysis. the generalization of the probabilistic fatigue model of castillo-canteli [1] proposed by muniz-calvente et al. [2] allows the primary weibull cdf of failure to be derived for any failure parameter, regardless of its distribution. in this way, any multiaxial damage value can be related to a number of cycles for a certain probability of failure. once this relation is established, the probability of failure for any of the orientation planes can be calculated as a function of the local multiaxial damage value and, by extension, the global probability of failure for the component can be determined from the survival probabilities for all the planes assuming the weakest link principle. from a purely deterministic viewpoint, two specimens exhibiting the same maximum damage value would yield the same lifetime, what contradicts the inherent scatter of the experimental data, which must be necessarily taken into account. moreover, a deterministic approach is insensitive to the variation of the damage parameter in planes adjacent to the critical one thus ignoring the angular interval at which failure is likely to happen. on the contrary, the probabilistic model proposed in this paper enables the failure probability to be found for any plane orientation, distinct from the one related to the maximum damage, by considering the local damage value in each plane. the main objective of this study is to determine the probability of failure resulting for each plane orientation by considering a suitable damage parameter as the generalized parameter (gp) causing failure. in order to take into account the variation of the gp for the different planes, the extension of the glm to fatigue problems [2] is considered. the glm stablishes that the probability of failure for a plane exhibiting a certain value of the generalized parameter (gp) can be obtained by using the primary failure cumulative distribution function (pfcdf):                      cnbgp p )log()log( exp1 (1) where n is the number of cycles and  ,  ,  , b , c are, respectively, the weibull parameters estimated from the iterative process shown in fig.1a and explained in the following section. the applicability of the model is elucidated by means of an example. assuming the cdf for the local failure of the material to be known, the probability of failure is calculated for a cross shaped specimen in which shift between the principal stresses xx and yy ranges from 0º to 180º. probabilistic multiaxial fatigue model ig. 1a illustrates the iterative process applied for deriving the pfcdf that relates damage parameter exhibit at each plane studied to a certain probability of failure. in the following, each step is explained in detail: step 1: performing an experimental program: to perform an experimental program using different biaxial loading ranges and to obtain the fatigue life for each experiment step 2: calculation of multiaxial fatigue parameter: the different biaxial loading ranges selected in the previous step are using to obtain the values of gp for each plane of the specimen. some examples of the results of this step are found in fig. 3. step 3: equivalent angle interval for each experiment: the equivalent angle interval, ieqa , , is defined as the angle interval that subject to the maximum gp value occurring at test failure would have the same probability of failure than the real distribution of the gp at failure. it is given by:              cnbgp spa ref refiieq )log()log( )1log( int,, (2) where ipint, is the global probability of failure [3]: f m. muñiz calvente et alii, frattura ed integrità strutturale, 39 (2017) 160-165; doi: 10.3221/igf-esis.39.16 162                       nj jij ref j ni sfaili cnbgp a a pp ij ...1...1 ,int, )log()log( exp1)1(1    (3) where ja is the angle interval assigned to each value of ijgp , which is the damage value for the plane j of the specimen i. to start the iteration process, an initial estimation of ieqa , , close to 40º, must be assumed because it depends on the values of b, c and the three weibull parameters, which are still unknown. figure 1: a) iterative process applied to fit the pfcdf; b) material plane selected for the projection of the normal and shear stresses [10]; c) difference between mcc and mce multiaxial fatigue criteria [10]. step 4: estimation of b and c: the estimation of b and c must be obtained by minimizing the least square equation proposed in [1] with respect to b, c and 1 , 2 , … t for different sizes: 2 1 log log          i i i i cgp bnq  (4) where  is the median value for each of the different equivalent angle intervals obtained in the previous step, n is the sample size and igp and in are the maximum value of the critical parameter and the number of cycles to failure of the i-th specimen, respectively. step 5: estimation of weibull parameters: the probability of failure for each of the specimens is obtained using a plotting point position rule [4]: 4.0 3.0    n i p (5) a) b) c) m. muñiz calvente et alii, frattura ed integrità strutturale, 39 (2017) 160-165; doi: 10.3221/igf-esis.39.16 163 finally, the results are obtained by fitting eq.(1) to a straight line using a probabilistic paper or a matlab subroutine [5]. step 6: convergence of the model: when the variation of the sum of all the parameters becomes less than a certain threshold,  , the fitting process is considered to be fulfilled.    111 iiiiii (6) otherwise, the iterative process continues returning to step 3. example of application any multiaxial fatigue limits criteria, such as sines [6] or crossland [7] criteria, are based on the calculation of a equivalence shear stress amplitude, aj2 , which becomes quite complex to be obtained for general multiaxial loading [8]. some examples of models to handle the multiaxial fatigue damage phenomenon are the maximum circumscribe circle (mcc) and the maximum circumscribe ellipse (mce) models, which propose the calculation of the equivalent shear stress amplitude as proposed by papadopoulos [9] and freitas et al. [10]. both multiaxial fatigue criteria are based on the calculation of the curve described by the shear stress in the critical plane during a cycle. with the aim of calculating the path described by the shear stress, it is necessary to define a material plane (see fig. 1b), δ, passing through the selected point and assuming a biaxial loading state, i.e.:                       000 0)sin(0 00)sin( 000 00 00 , , yyayy axx yy xx wt wt      in order to evaluate the stress vector t acting on the plane δ passing through the point considered, a local coordinate system is defined by three unit vectors:      0)cos()sin( )sin()sin()cos()cos()cos( )cos()sin()sin()cos()sin(       l r n where n is the vector perpendicular to the plane and r and l are vectors in the plane, which define an orthogonal basis with the previous one.  and  are the angles between these vectors and the xyz axes. thus, the stress vector t acting on the plane can be obtained by the cauchy's theorem:  0)sin()sin()cos()sin(·  yyxxnt  then, the stress vector could be decomposed in two stresses: a normal stress, nn , that changes in magnitude but not in direction during a cycle of loading; and a shear stress,  , that changes in magnitude and direction along each loading cycle, and can be decomposed in two directions rr and ll :      yyxxll yyxxrr yyxxnn tl tr tn       )sin()cos()sin('· )(sin)(cos)sin()cos('· )(sin)(cos)(sin'· 22 222 m m. muñiz calvente et alii, frattura ed integrità strutturale, 39 (2017) 160-165; doi: 10.3221/igf-esis.39.16 164 the variation of the shear stress, , during a cycle defines a closed curve ,  , that is different for each plane passing through the selected point. as a consequence the equivalent shear stress amplitude aj2 , which is a function of the mcc or mce that could envelop  (see fig. 1c), is a function of  and  . in other words, ),(2 aj . figure 2: distribution of ),(2 aj calculated by the mcc and mce criteria for 1,,  ayyaxx  and  60300yy ; mcm and mce criteria differ in that the first one is based on the calculation of the minimum radius ( ar ) of the circumference circumscribing the shear stress path, aa rj 2 ; whilst the second one is based on the combination of the two radios ( ar br ) of the minimum ellipse that circumscribes the shear stress path baa rrj 2 . fig. 1c shows the difference between the two multiaxial fatigue criteria. fig. 2 displays some examples of the aj2 distribution over all planes (all combinations of  and  ), for different angular offsets  60300yy , assuming unit values of axx, and ayy, . as can be seen, there is a difference that depends on the angular offset applied ( yy ). imagine that an experimental program proves that the minimum value of aj2 producing failure at a certain number of cycles n happens to be 0.7 (see fig. 2), that is, any plane subject to a 7.02 aj could fail. this methodology allows us to evaluate the local probability of failure for any plane subjected to a value of aj2 during n cycles by applying eq.1. after that, it is possible to obtain the global probability of failure as the combination of the local probabilities using eq.3, which allows the risk of failure over all planes to be taken into account. m. muñiz calvente et alii, frattura ed integrità strutturale, 39 (2017) 160-165; doi: 10.3221/igf-esis.39.16 165 conclusions he main conclusions of this work are the following: failure for a certain multiaxial fatigue loading must not happen, necessarily, at the plane subject to the maximum value of the multiaxial fatigue criteria (mce or mcc in this case), but it may occur at other planes subjected to lower values of the critical parameter due to its interaction with the existence of local defects. the probabilistic model proposed in this paper enables the failure probability for any plane orientation to be found. the applicability of this methodology is not limited to the use of these two criteria (mce or mcc), but the iterative process can be extended to any other failure criterion regardless of the complexity of its calculation. in this work, an analytical solution for the local calculation of the critical parameter is assumed, but as in the glm, this is not mandatory, so that the calculation of the critical parameter distribution in other complex cases can be found using the finite element method. acknowledgements he authors gratefully acknowledge the severo ochoa pre-doctoral grants program of the regional government of asturias (spain) and the spanish ministry of science and innovation (micinn) under project bia2010-19920 for funding support. references [1] castillo, e., fernández-canteli, a., a unified statistical methodology for modeling fatigue damage, springer, (2009). [2] muniz-calvente, m., de jesus, a.m.p., correia, j.a.f.o., fernández-canteli, a., a generalized probabilistic approach for fatigue crack initiation taking into account scale effects and non-uniform damage fields, fatigue & fracture of engineering materials & structures, (submitted). [3] muñiz-calvente, m., ramos, a., shlyannikov, v., lamela, m.j., fernández-canteli, a., hazard maps and global probability as a way to transfer standard fracture results to reliable design of real components, engineering failure analysis, 69 (2016) 135-146. [4] bernard, a., bos-levenbach, e. c., the plotting of observations on probability-paper. stichting mathematisch centrum. statistische afdeling, (1955). [5] fitting a univariate distribution using cumulative probabilities matlab & simulink example mathworks. [6] sines, g., behaviour of metals under complex static and alternating stresses, in: metal fatigue, g. sines and j. l. waisman, eds., mcgraw-hill, new york, (1959) 145–169. [7] crossland, b., effect of large hydrostatic pressures on the torsional fatigue strength of an alloy steel, in: proc. int. conf. on fatigue of metals, institution of mechanical engineers, london, (1956) 138–149. [8] papadopoulos, i. v., a review of multiaxial fatigue limit criteria, advanced course on high-cycle metal fatigue, (1997). [9] papadopoulos, i. v., davoli, p., gorla, c., filippin, m., bernasconi, a., a comparative study of multiaxial high-cycle fatigue criteria for metals, international journal of fatigue, 19(3) (1997) 219–235. [10] li, b., santos, j. l. t., de freitas, m., a unified numerical approach for multiaxial fatigue limit evaluation. mechanics of structures and machines, 28 (1) (2000). t t << /ascii85encodepages false /allowtransparency false /autopositionepsfiles true /autorotatepages /none /binding /left /calgrayprofile (dot gain 20%) /calrgbprofile (srgb iec61966-2.1) /calcmykprofile (u.s. web coated \050swop\051 v2) /srgbprofile (srgb iec61966-2.1) /cannotembedfontpolicy /error /compatibilitylevel 1.4 /compressobjects /tags /compresspages true /convertimagestoindexed true /passthroughjpegimages true /createjobticket false /defaultrenderingintent /default /detectblends true /detectcurves 0.0000 /colorconversionstrategy /cmyk /dothumbnails false /embedallfonts true /embedopentype false /parseiccprofilesincomments true /embedjoboptions true /dscreportinglevel 0 /emitdscwarnings false /endpage -1 /imagememory 1048576 /lockdistillerparams false /maxsubsetpct 100 /optimize true /opm 1 /parsedsccomments 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/hrv (za stvaranje adobe pdf dokumenata najpogodnijih za visokokvalitetni ispis prije tiskanja koristite ove postavke. stvoreni pdf dokumenti mogu se otvoriti acrobat i adobe reader 5.0 i kasnijim verzijama.) /hun 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can be opened with acrobat and adobe reader 5.0 and later.) >> /namespace [ (adobe) (common) (1.0) ] /othernamespaces [ << /asreaderspreads false /cropimagestoframes true /errorcontrol /warnandcontinue /flattenerignorespreadoverrides false /includeguidesgrids false /includenonprinting false /includeslug false /namespace [ (adobe) (indesign) (4.0) ] /omitplacedbitmaps false /omitplacedeps false /omitplacedpdf false /simulateoverprint /legacy >> << /addbleedmarks false /addcolorbars false /addcropmarks false /addpageinfo false /addregmarks false /convertcolors /converttocmyk /destinationprofilename () /destinationprofileselector /documentcmyk /downsample16bitimages true /flattenerpreset << /presetselector /mediumresolution >> /formelements false /generatestructure false /includebookmarks false /includehyperlinks false /includeinteractive false /includelayers false /includeprofiles false /multimediahandling /useobjectsettings /namespace [ (adobe) (creativesuite) (2.0) ] /pdfxoutputintentprofileselector /documentcmyk /preserveediting true /untaggedcmykhandling /leaveuntagged /untaggedrgbhandling /usedocumentprofile /usedocumentbleed false >> ] >> setdistillerparams << /hwresolution [2400 2400] /pagesize [612.000 792.000] >> setpagedevice microsoft word numero_29_art_5 m.l. de bellis et alii, frattura ed integrità strutturale, 29 (2014) 37-48; doi: 10.3221/igf-esis.29.05 37 focussed on: computational mechanics and mechanics of materials in italy a micromechanical approach for the micropolar modeling of heterogeneous periodic media m.l. de bellis, d. addessi dipartimento di ingegneria strutturale e geotecnica, università di roma “sapienza”, via eudossiana, 18, 00184 roma, italy marialaura.debellis@uniroma1.it, daniela.addessi@uniroma1.it abstract. computational homogenization is adopted to assess the homogenized two-dimensional response of periodic composite materials where the typical microstructural dimension is not negligible with respect to the structural sizes. a micropolar homogenization is, therefore, considered coupling a cosserat medium at the macro-level with a cauchy medium at the micro-level, where a repetitive unit cell (uc) is selected. a third order polynomial map is used to apply deformation modes on the repetitive uc consistent with the macro-level strain components. hence, the perturbation displacement field arising in the heterogeneous medium is characterized. thus, a newly defined micromechanical approach, based on the decomposition of the perturbation fields in terms of functions which depend on the macroscopic strain components, is adopted. then, to estimate the effective micropolar constitutive response, the well known identification procedure based on the hill-mandel macro-homogeneity condition is exploited. numerical examples for a specific composite with cubic symmetry are shown. the influence of the selection of the uc is analyzed and some critical issues are outlined. keywords. composites; homogenization; micropolar continua; periodicity. introduction he use of composite materials in various fields of engineering, both for standard and innovative applications, has been widely researched. a thorough understanding of the mechanical behavior of existing materials is a fundamental step towards the design of new composites, characterized by increasingly high performances. various approaches, marked out by different formulations and modeling the materials at different scales, have been proposed to deal with the constitutive response of composite materials. this study focuses on homogenization techniques, a very effective tool to obtain accurate results with low computational efforts. the actual heterogeneous medium is analyzed at two different scales: the macro-scale, where an equivalent homogenized medium is considered, characterized by overall effective mechanical properties, and the micro-scale, where detailed information about the texture, geometry and constitutive laws of the constituents are available. different continuum models can be adopted, at the two levels. the classical cauchy continuum provides an appropriate description of the actual heterogeneous response in the case of small microscopic length compared to the macro-scale structural length [1, 2, 3, 4]. on the contrary, when strong strain and stress gradients at the macro-level occur, or when the microscopic length of the constituents is comparable to the wavelength of variation of the strain and stress mean fields at the macro-level, some intrinsic limits emerge. this is due to the fact that the cauchy theory does not account for length t m.l. de bellis et alii, frattura ed integrità strutturale, 29 (2014) 37-48; doi: 10.3221/igf-esis.29.05 38 scales. by adopting generalized continua this limit is overcome. many authors have focused on coupling different continuum models at the two scales. in most cases, at the microscopic level, the classical cauchy continuum is adopted, especially because nonlinear constitutive relationships are well-established in this framework. among various generalized continua (second-gradient, couple stress, micropolar or multifield), a micropolar cosserat continuum at the macro-level and a cauchy continuum at the micro-level are used here to study the homogenized response of periodic composite materials. the computational homogenization technique adopted effectively predicts the macroscopic behavior of composite materials [5, 6]. since composite materials, characterized by regular textures are analyzed, a unit cell (uc) is selected at the micro-level. consistently with the strain-driven approach, the two levels are linked through a kinematic map based on a third order polynomial expansion, previously derived by the authors in [7], from an original idea developed in [1]. the displacement field at the micro-level is represented as the superposition of the kinematic map and an unknown perturbation field, due to the heterogeneous nature of the material. for classical first order computational homogenization the perturbation fields are periodic [8], but this is not true when higher order polynomial terms are considered, as underlined in [9,10]. in this study, the problem of determining the displacement perturbation fields, with particular reference to its influence on the structural response evaluation, is investigated. to this end, the three following techniques are adopted. the first is based on the solution of the boundary value problem (bvp) by applying periodic boundary conditions on the uc. the second is the 3 steps homogenization, presented by the authors in [11], and based on the decomposition of the perturbation fields in terms of functions which depend on the macroscopic strain components. finally the bvp is solved by applying special boundary conditions on the uc, as derived in [7]. furthermore, the identification of the homogenized linear elastic 2d cosserat constitutive parameters is performed, by using the hill-mandel technique, based on the generalized macro-homogeneity condition presented in [11]. as known, this technique has inherent limitations, leading to physically inconsistent results [9, 12, 13]. for example, higher order constitutive components are identified, also when a homogeneous elastic material at the micro-level is considered. despite the drawbacks, this technique has been widely used, at least when asymptotic techniques [14] cannot be applied, as in the case of coupling micropolar and classical continua. the influence of the selection of the uc is analyzed and some key issues are outlined. by considering two different ucs, selected for representing the composite texture, it emerges that the constitutive response of the homogenized medium depends on the choice of the cell. indeed, while the elastic cauchy coefficients are irrespective of the uc selected, this does not occur for the bending and skew-symmetric shear cosserat coefficients, at least with regard to computational homogenization. this fact is also confirmed by the results obtained from the structural applications. two numerical tests are presented to highlight the main aspects of the presented micropolar computational homogenization technique and to emphasize the differences obtained using the three procedures to describe the perturbation fields. micropolar homogenization he computational homogenization technique used here adopts a 2d micropolar continuum at the macro-level and a classical 2d cauchy continuum at the micro-level. at typical macro-level material point, the displacement vector 1 2={ , , } tu u u is defined, where 1u and 2u are the translational degrees of freedom and  is the rotational degree. the micropolar strain vector is characterized by six components as follows: 1 2 12 1 2 = e e k k                     e (1) where 1e , 2e and 12 are the axial and symmetric shear strains, 1k and 2k are the curvature components, while  is the skew-symmetric shear component. the compatibility equations can be written in compact form as: t m.l. de bellis et alii, frattura ed integrità strutturale, 29 (2014) 37-48; doi: 10.3221/igf-esis.29.05 39 =e lu (2) where the compatibility operator is defined as 1 2 2 1 2 1 1 2 0 0 0 0 0 = . 2 0 0 0 0                                          x x x x x x x x l (3) according to the strain driven approach, the macroscopic strain components, evaluated at ,x are used as input variables for the microscopic level. the kinematic map, expressed in function of the vector ,e is imposed on the uc, properly defining a bvp. at the micro-level a repetitive rectangular uc is selected, whose size is 1 22 2a a and its centre is located at the macroscopic point ,x characterized by the displacement field 1 2={ , } tu uu , defined at each point  1 2= , t x xx of the uc domain  . the displacement field, resulting in the uc after solving the bvp, can be represented as the superposition of the assigned field  u x, x and a perturbation field    :u x,x       =  u x, x u x, x u x, x (5) the strain vector at the microscopic level is derived by applying the kinematic operator defined for the 2d cauchy problem and, in expanded form, it results as:   1 ,1 2 ,2 12 ,2 ,1 0 = , with and = 0                        ε lu ε l x (6) with ,i indicating the partial derivative with respect to .ix according to eq. (5), the strain can be written as:      , = , , ε x x ε x x ε x x (7) the third order polynomial map, proposed in [5 ,6] and modified in [7], is used. different material symmetries can be considered ranging between the isotropic and the orthotropic case. in the considered orthotropic case, the kinematic map can be written in compact form as:      , =u x x a x e x (8) with           2 2 2 3 1 2 1 1 2 2 2 1 12 1 3 1 1 2 1 2 2 2 2 3 2 1 1 1 12 2 2 1 2 3 2 1 2 2 1 1 1 0 3 2 2 1 1 0 3 2 2 x x x x x x s b x x c x x x x x x x s b x x c x                         a x (9) m.l. de bellis et alii, frattura ed integrità strutturale, 29 (2014) 37-48; doi: 10.3221/igf-esis.29.05 40 where 1 2 1= /e e , 1e and 2e are the values of young’s modulus of the equivalent homogenized orthotropic material, 12 the poisson ratio and:  21 1 12 1 2 2 2 2 2 1 12 2 1 2 = 1 , = 2 , = , = 2 , b c b b c b             (10) 2 2 12= /e g , 12g being the homogenized shear modulus, while 2 1= /a a the ratio between the dimensions of the uc and       2 2 2 2 4 1 1 1 12 2 10 1 = . 2 1 s a               (11) the dependence of the kinematic map on the effective elastic coefficients is a consequence of the enforcement of the balance equations in the uc, ensuring that the kinematic map is the solution of the bvp in the uc made of the homogenized material. the quantities 1 , 2 and 3 account for the effects of the perturbation parts of the displacement field in determining the average macroscopic strains and are presented in detail in [11]. in this work linear elastic isotropic behavior is assumed for the constituents at the micro-level. a straightforward extension to the case of non-linear material behavior can be, however, easily made. heterogeneous material: perturbation field in the uc domain he characterization of the perturbation field   u x,x , arising in the uc when a heterogeneous medium is taken into account, is discussed. depending on the choice of the boundary conditions imposed at the micro-level, very different results can be obtained in terms of displacement fields solution of the bvp. it is well established that, in the case of first order homogenization,   u x, x is a periodic field. in this instance, the periodic boundary conditions (pbcs) are suitable to correctly reproduce the unknown perturbation field. the extension to the case in which higher order polynomial terms are considered in the kinematic map is not trivial and it is not possible to a-priori assume the periodicity of   u x,x , as remarked in [7, 9, 11]. in this section, three approaches are introduced to characterize the perturbation field. in the first approach, the classical periodicity conditions are considered. the second technique assumes the decomposition of the perturbation field in different contributions, related to the first, second and third order gradients of the kinematic map as proposed in [11]. the last approach is based on the enforcement of proper boundary conditions (bcs) on the uc, as described in [7], resulting from the analysis of the actual perturbation field distribution in the rve undergoing remote fully displacement bcs. finally, the comparison between the numerical results obtained using the adopted procedures for a paradigmatic example of a two-phase composite material, characterized by cubic symmetry, is presented. procedure a: periodic bcs (pbcs) in the uc the first procedure to characterize the field   u x, x involves the solution of the bvp in the uc under standard pbcs. corresponding points on opposite sides of the uc are constrained to undergo the same perturbation displacement. the following conditions are imposed on the sides of the uc:             1 2 1 2 2 2 2 1 2 1 2 1 1 1 , , , , , , , , a x a x x a a x a x a x a a           u u u u     (12) where the dependence on x has been omitted for the sake of brevity. in the presence of nonvanishing components 1k , 2k and  , this assumption leads to unrealistic distributions of the perturbation field. t m.l. de bellis et alii, frattura ed integrità strutturale, 29 (2014) 37-48; doi: 10.3221/igf-esis.29.05 41 procedure b: 3 step homogenization this procedure has been proposed by the authors in [11] as an extension to the 2d micropolar computational homogenization of the homogenization of second gradient continua via the asymptotic approach [12, 15]. here, the basic idea is recalled and the main steps are addressed. it is assumed that the total perturbation displacement vector   u x,x can be expressed as the sum of three fields evaluated in sequence. initially, only the first order terms of the kinematic map, multiplying the components 1e , 2e and 12 in (8), are activated; subsequently, the effects of the quadratic terms related to 1k and 2k are considered and, finally, the third order term associated with  is taken into account. therefore, the vector results as:         1 2 3 , , , , .  u x x r x x r x x r x x   (13) when only the linear terms of the kinematic map are considered, the case of the first order homogenization is recovered. here, it is assumed that   1 r x,x is evaluated as the product of unknown functions times the independent components of the first gradient of the kinematic map, as:       11 1=r x, x λ x γ x, x (14) where            1 1 1 1 11 2 12 1 2 3= , = t          γ x, x λ x x x x (15)  1i x , = 1, 2, 3,i being evaluated by applying the components 1e , 2e and 12 on the uc undergoing pbcs. in this case   1 r x, x results as periodic functions. when the presence of the curvatures 1k and 2k is also considered, with = 0 , the perturbation field can be expressed as:         1 21, = , ,u x x λ x γ x x r x x (16) where now   2 r x,x is the only unknown field. following the same procedure as for the first term   1 r x, x , it is assumed that   2 r x, x is expressed as the product of unknown functions and   2 γ x,x , i.e. the nonvanishing components of the first gradient of   1 γ x, x . then, the unknown field   2 r x, x is represented in the form:       22 2, = ,r x x λ x γ x x (17) with              2 2 2 2 2 21,1 1,2 2,1 2,2 1 2 3 4= , = t             γ x, x λ x x x x x (18)  2i x , = 1,.., 4,i being periodic functions evaluated in the uc when 1 0k  and 2 0k  . finally, when the component  is also taken into account, it results that:             1 2 31 2, = , , , . u x x λ x γ x x λ x γ x x r x x (19) the field   3 r x,x is written as the product of unknown functions times the relevant and nonvanishing components of the first gradient of   2 γ x, x , and it results:       33 3=r x, x λ x γ x, x (20) with m.l. de bellis et alii, frattura ed integrità strutturale, 29 (2014) 37-48; doi: 10.3221/igf-esis.29.05 42            3 3 3 3 31,12 2,12 12,12 1 2 3, = , =          t γ x x λ x x x x (21)  3i x , = 1, .., 3i , being periodic functions evaluated in the uc when 0  . procedure c: analysis of the perturbation field in the rve the characterization of the perturbation field u is performed in [7] by evaluating its actual distribution. to this end, a rve obtained as assemblage of a large number of ucs for a selected two-phase periodic composite material is considered and remote fully displacement bcs are prescribed. in particular, the micropolar deformation modes are imposed on the boundary, according to the kinematic map in eq. (8), and the rve response is evaluated by finite element method. hence, the distribution of the perturbation field arising in the central uc of the rve is taken as the benchmark. thus, the suitable bcs to impose on the single uc are derived, in order to reproduce, with a satisfactory level of accuracy, the actual distribution of the perturbation field. some selected two-phase composite materials, characterized by material symmetries, ranging from cubic to orthotropic, are analyzed. in all the cases considered, similar distributions of the perturbation displacement fields on the uc boundary emerge. differently from the case of the first order homogenization procedure, where periodic bcs are suitably adopted, in the analyzed cases more complex bcs have to be considered, which are different for the two components of u . in fig. 1 the derived bcs are summarized. in the first row, the applied cosserat macroscopic deformation components are reported; in the second row the bcs for the component 1u along the horizontal and vertical edges of the uc are schematically reported, while in the third row those for the displacement component 2u are shown. the symbol “p” indicates periodic bcs , see eq. 12; “s” refers to skew-periodic bcs, that is:             1 2 1 2 2 2 2 1 2 1 2 1 1 1 , , , , , , , , a x a x x a a x a x a x a a             u u u u     (22) finally, “0” indicates zero perturbation displacement bcs. figure 1: boundary conditions to impose on the uc to evaluate the perturbation fields, derived in [7]. comparison between procedures a, b and c the approaches presented were compared by carrying out some numerical tests. this subsection is devoted to a qualitative discussion of the results obtained that are reported in detail in [11]. reference is made to a specific two-phase composite material, characterized by cubic symmetry, whose texture is made from a soft matrix with stiff square inclusions, both isotropic and regularly spaced. the volume fraction ,f defined as the ratio between the area of the inclusions and the total area of the uc, is set equal to 36%. as reference solution the distribution of the perturbation field arising in the central uc of a sufficiently large rve, undergoing remote fully displacement boundary conditions, is considered. the three procedures lead to the same correct results, if the classical macroscopic strain components 1 ,e 2e and 12 are activated. for the components 1k , 2k and , different considerations apply. for both components 1k and  procedure b provides the best estimate of the perturbation fields. in the case of 1k only the vertical component of the perturbation field, evaluated along the horizontal edges of the uc, slightly differs from the referential solution, while in the case of  a very good approximation is guaranteed anywhere on the edges. m.l. de bellis et alii, frattura ed integrità strutturale, 29 (2014) 37-48; doi: 10.3221/igf-esis.29.05 43 to be noted is that the solution corresponding to the curvature 2k can be obtained by rotating that evaluated for 1k . adopting procedure a, the field u differs qualitatively from the actual solution and it can be concluded that this procedure leads to grossly erroneous results. finally, the results obtained by applying procedure c are close to those evaluated with procedure b, although the vertical perturbation components along the horizontal lines in presence of 1k and  are worse approximated. identification procedure: hill-mandel macro-homogeneity condition he identification procedure adopted in this study is based on the generalized hill-mandel macro-homogeneity condition. the virtual work evaluated at the macroscopic cosserat point is set equal to the average virtual work of the heterogeneous cauchy medium in the uc. thus, the following expression holds: =t t  σ e σ ε (22) where σ is the micropolar stress vector evaluated at the macroscopic point, while σ is the cauchy stress vector at the typical point of the uc. after solving the bvp on the uc and determining the microscopic stress and strain fields, σ and ε , the homogenized cosserat elastic constitutive matrix c can be derived by using eq. (22). considering a two-phase composite material with a regular arrangement of the inclusions, characterized by orthotropic texture, the homogenized cosserat elastic constitutive matrix, expressed in a reference frame aligned with the principal axes of the material, results as: 11 12 12 22 33 44 55 66 0 0 0 0 0 0 0 0 0 0 0 0 0 = 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0                    c c c c c c c c c (23) regarding the two-phase composite medium examined in subsection comparison between procedures a, b and c, the macroscopic micropolar elasticity matrix c has been evaluated, referring to two different ucs obtained by translation in the same heterogeneous medium, see fig. 2. a) b) figure 2: a) uc1 texture; b) uc2 texture. the results, presented in [11], are critically discussed to highlight the dependence of the identification equivalent coefficients on the centering of the uc. indeed, differently from the cauchy coefficients, which are proved to be irrespective of the choice of uc, for the bending and skew-symmetric shear micropolar coefficients this is not straightforward, at least in the framework of computational homogenization. in the following the focus is on the determination of 44c , 55c and 66c , governing the bending and skew-symmetric shear behavior of the micropolar equivalent medium. t m.l. de bellis et alii, frattura ed integrità strutturale, 29 (2014) 37-48; doi: 10.3221/igf-esis.29.05 44 aiming at estimating the coefficient 44c , the macroscopic strain component 1 1k  is applied to the uc, with all the other components set equal to zero. note that, due to the cubic symmetry of the composite material, the case 2 1k  leads to results which are the rotated results of the case 1 1k  , so that 55 44 .c c for the two selected ucs, procedures a, b and c are applied. it emerges that procedures b and c lead to homogenized constitutive parameters that differ by about 8% for the same uc, while procedure a provides results that differ by an order of magnitude. moreover, the obtained results depend on the choice of the uc. indeed, the values of 44c computed for the two ucs differ by 14%, for procedure b and about 27% for procedure c. these results can be explained by taking into account the explicit expression of the internal work at the right-hand side of eq. (22). it emerges, in fact, that the relative position of the two (stiffer and softer) constituents, with respect to the uc center, strongly influences the value of the identified parameter. this problem is well known [2, 8, 11] and is related to the definition of the higher-order or couple stresses as the volume average of the product of microscopic stresses and microscopic coordinates over the uc. similar considerations apply when the component 1  is considered, while all the other macro-level strain components are set equal to zero. again, different results are obtained for the two ucs and for the adopted methods. further numerical tests are performed to investigate on the influence of the size of the rve [9]. various square rves are considered, taking into account assemblages of 3 3 , 5 5 , 7 7 , 9 9 ,… 15 15 ucs, subjected to the bcs shown in fig. 1, which correspond to the procedure c. the average internal work is evaluated over the entire rve domains. it emerges that, by introducing proper scaling factor depending on the size l of the square rve, in both cases of 44c and 66c , as the rve size increases, the different ucs converge to the same quantity, from above and from below, respectively. numerical example rectangular wall under vertical loading rectangular wall made from a periodic composite material is studied. in fig. 3 the geometry is reported together with loading and boundary conditions. first, the capability of the homogenized cosserat model to account for size effects is analyzed. the following dimensionless parameters b/h 1.3 , b/h 0.3 , 2/ 10i me e  , h/p 30000ie  , 0.3i  and 0.3m  are set. three cases are analyzed, considering the wall made from the periodic repetition of ucs: 16 12 , 8 6 and 4 3 ucs. for each case, it is assumed that the heterogeneous material is obtained by adopting the uc1 in fig. 2-a or uc2 in fig. 2-b. figure 3: schematic of the rectangular wall: geometry, loading and boundary conditions. in fig. 3 the arrangement considered for the case of 16 12 ucs, by adopting both uc1 (left side) and uc2 (right side), is shown. the numerical simulations are performed considering the response of the two heterogeneous materials characterized by the arrangements shown in fig. 3, compared with the response of the homogenized micropolar media. the structural a m.l. de bellis et alii, frattura ed integrità strutturale, 29 (2014) 37-48; doi: 10.3221/igf-esis.29.05 45 stiffness is evaluated by dividing the total base vertical reaction by the maximum vertical displacement measured at the midspan of the top edge. in tab. 1 the values of the stiffness, obtained considering uc1 for the three assemblages ( 16 12 , 8 6 and 4 3 ), are shown. in the first column the results obtained with the micromechanical model and representing the reference solution are reported. in the second column the stiffness values, computed by adopting a standard first order computational homogenization (cauchy), are shown, normalized with respect to the reference solution. finally, in the last three columns, cos a, cos b and cos c refer to the responses obtained using the micropolar homogenized model whose homogenized elastic coefficients 44c , 55c and 66c are derived by means of procedure a, procedure b and procedure c, respectively. these are also normalized with respect to the reference solution. the comparison of the values collected in tab. 1 highlights that cos b provides the best estimation of the structural stiffness, while cos a gives a response overestimating by out 23% the actual stiffness for 16 12 ucs and by about 29% for 4 3 ucs. in tab. 2 the same results reported in tab. 1 are shown, when uc2 is taken into account. also in this case, the results obtained via procedure b are in very good agreement with the micromechanical model. considering the results in both tab. 1 and 2, it emerges that the micropolar effects become more evident as the number of ucs decreases, since the ratio between the microstructural size, directly related to the dimension of the inclusions, and a typical structural dimension, increases. as expected, the cauchy model gives the same results in all the considered cases and is suitable to correctly estimate the structural response as the above ratio increases. heter cauchy cos a cos b cos c 16 12 ucs 147.82 0.990 1.228 1.007 1.016 8 6 ucs 152.01 0.965 1.254 0.999 1.003 4 3 ucs 159.00 0.921 1.288 0.998 1.002 table 1: structural stiffness in the case of different assemblages of uc1: heter = micromechanical model; cauchy= homogenized first order model; cos a = homogenized cosserat with procedure a; cos b = homogenized cosserat with procedure b; cos c = homogenized cosserat with procedure c. heter cauchy cos a cos b cos c 16 12 ucs 142.22 1.029 0.876 0.992 0.987 8 6 ucs 141.76 1.032 0.913 1.007 1.024 4 3 ucs 141.93 1.031 1.085 1.009 0.998 table 2: structural stiffness in the case of different assemblages of uc2: heter = micromechanical model; cauchy= homogenized first order model; cos a = homogenized cosserat with procedure a; cos b = homogenized cosserat with procedure b; cos c = homogenized cosserat with procedure c. moreover, it is noteworthy that the position of the inclusions in the heterogeneous medium significantly influences the response. indeed, especially for the 4 3 ucs significantly different results are obtained by adopting the two arrangements. finally, to investigate the influence of the aspect ratio on the global elastic response, three different geometries are considered, corresponding to b/h 1.3 , b/h 1.6 and b/h 2 . the first geometry is the same presented above corresponding to 16 12 ucs. in tab. 3 and 4 the results of the structural stiffness (adopting the same normalization as m.l. de bellis et alii, frattura ed integrità strutturale, 29 (2014) 37-48; doi: 10.3221/igf-esis.29.05 46 before), as the aspect ratio changes, are reported for uc1 and uc2, respectively. it can be remarked that procedure b confirms to be the most suitable to reproduce the actual behavior of the heterogeneous medium. moreover, the slenderer the wall ( b/h 1.3 ) the closer the values obtained with the first order technique are to the response of the micromechanichal models. the micropolar effects are, thus, more pronounced for the squat wall ( b/h 2 ). also in this case, procedure b gives results which best match those obtained with the micromechanical model. simple shear test of a composite strip as a second example, a displacement driven shear test on a 2d structure, made from the same composite medium considered in the previous example, is presented. a strip with b/h 0.1 is considered assuming plane strain condition. in fig. 4 the schematic of the geometry and boundary conditions is shown for two possible strips, corresponding to assemblages of uc1 and uc2 in fig. 2-a and e 2-b, respectively. the strips are fixed at both bottom and top edges and a horizontal displacement d=h/100 is prescribed at the top. heter cauchy cos a cos b cos c b/h 1.3 147.82 0.990 1.228 1.007 1.016 b/h 1.6 153.81 0.986 1.349 1.013 1.036 b/h 2 162.43 0.931 1.560 1.012 1.024 table 3: structural stiffness for different ratios of b/h in the case of uc1: heter = micromechanical model; cauchy= homogenized first order model; cos a = homogenized cosserat with procedure a; cos b = homogenized cosserat with procedure b; cos c = homogenized cosserat with procedure c. heter cauchy cos a cos b cos c b/h 1.3 142.22 1.029 0.876 0.992 0.987 b/h 1.6 143.74 1.033 0.808 0.993 0.982 b/h 2 143.85 1.051 0.708 0.995 0.982 table 4 structural stiffness for different ratios of b/h in the case of uc2: heter = micromechanical model; cauchy= homogenized first order model; cos a = homogenized cosserat with procedure a; cos b = homogenized cosserat with procedure b; cos c = homogenized cosserat with procedure c. in fig. 5-a the displacement horizontal component, evaluated along the vertical symmetry axis of each strip along the vertical axis of the strip is shown. the responses of the micromechanical models are represented in solid line (heter1) and in dash-dot line (heter2) for the strips reported in fig. 4-a and 4-b, respectively. the homogenized constitutive coefficients adopted in the micropolar models are evaluated using procedure b. the squares represent the response of the homogenized micropolar model adopting the uc1 in fig. 2-a (cosb_uc1) and the circles represent the response with uc2 in fig. 2-b (cosb_uc2). finally, the dotted line refers to the response obtained by the standard first order computational homogenization (cauchy), able to reproduce a linear variation of the horizontal displacement component along the height of the strip. no relevant differences between the results obtained with the two micromechanical models arise and both the homogenized micropolar models can satisfactorily follow the expected displacement distribution. in fig. 5-b the rotation evaluated along the vertical symmetry axis of each strip versus the vertical axis is reported. owing to the symmetry of this displacement component with respect to a horizontal axis located at the mid height, only one half of the strip height is depicted. due to the different natures of the compared models, the rigid rotation  , i.e. the skewsymmetric part of the displacement gradient, is reported for micromechanical and cauchy models, while the cosserat rotation  is shown for the micropolar homogenized model. line styles and symbols have the same meaning as in fig. 5 m.l. de bellis et alii, frattura ed integrità strutturale, 29 (2014) 37-48; doi: 10.3221/igf-esis.29.05 47 a. the micromechanical models show locally variable trends, which, however, fluctuate around the same mean values. it emerges that, while the cauchy model captures only a constant value of the mean rotation along the strip, the micropolar homogenized model provides a very good evaluation of the considered field with both uc1 and uc2. a) b) figure 4: a) strip1 arrangement; b) strip2 arrangement. a) b) figure 5: a) horizontal displacement versus vertical abscissa; b) rotation versus vertical abscissa. conclusions he micropolar computational homogenization are considered. the perturbation fields in the presence of higher order polynomial boundary conditions is analyzed adopting three different procedures, which lead to different results. the first method is based on the imposition of periodic boundary conditions, classically adopted in the standard first order homogenization, also in the presence of higher order terms of the polynomial map and provides qualitatively incorrect results. the second procedure (3 step homogenization) adopted, although the most complex, produces the best results. finally, the methodology characterizing the perturbation fields on the basis of the direct observation of the large heterogeneous medium behavior gives results slightly differing from the 3 step homogenization, but is much simpler. thus, this appears as the best compromise between accuracy and efficiency in correctly reproducing the actual trends of perturbation fields, when a single uc is analyzed. moreover, the identification of the homogenized linear elastic constitutive parameters adopting the classical hill-mandel procedure is addressed. considering different ucs, referred to the same composite material, it emerged that the constitutive response of the homogenized medium depends on the choice of the cell, adopting all the three procedures exploited for reproducing the perturbation fields. indeed, while the elastic cauchy coefficients are irrespective of the uc selected, for the bending and skew-symmetric shear micropolar coefficients this does not occur, at least not in the framework of computational homogenization. t m.l. de bellis et alii, frattura ed integrità strutturale, 29 (2014) 37-48; doi: 10.3221/igf-esis.29.05 48 two structural examples are presented. the aim is to discuss the key aspects of the adopted micropolar formulation and to stress the differences obtained using the three presented procedures in terms of the global response. it would appear relevant to carry out further developments, focusing on the formulation of the kinematic map linking the macroand micro-levels, as well as on the improvement of the identification procedure. the purpose is to better clarify some ongoing issues and to solve inherent limitations of the procedure, as for example the contradictory result consisting in nonvanishing micropolar effects in the presence of homogeneous materials. references [1] forest, s., sab, k., cosserat overall modeling of heterogeneous materials. mech res commun 25 (1998) 449-454. [2] kouznetsova, v. g., computational homogenization for the multi-scale analysis of multi-phase materials. ph.d. thesis, technische universiteit eindhoven, (2002). [3] bacigalupo, a., gambarotta, l., second-order computational homogenization of heterogeneous materials with periodic microstructure. zamm-z angew math me, 90 (11) (2011)796-811. [4] addessi, d., sacco, e., a multi-scale enriched model for the analysis of masonry panel. int. j. solids struct. 49 (2012) 865–880. [5] de bellis, m. l., addessi, d., a cosserat based multi-scale model for masonry structures. int. j. multiscale comput. eng. 9 (2011) 543–563. [6] addessi, d., sacco, e., paolone, a., cosserat model for periodic masonry deduced by nonlinear homogenization. eur. j. mech. a solid 29 (2010) 724–737. [7] addessi, d., de bellis, m. l., sacco, e., micromechanical analysis of heterogeneous materials subjected to overall cosserat strains. mech res commun 54, (2013) 27-34. [8] miehe, c., schröder, j., becker, m., computational homogenization analysis in finite elasticity: material and structural instabilities on the microand macro-scales of periodic composites and their interaction, computer methods in applied mechanics and engineering 191 (2002), pp. 4971-5005. [9] forest, s., trinh, d., generalized continua and non-homogeneous boundary conditions in homogenisation methods. zamm-z angew math me 91 (2) (2011) 90-109. [10] bouyge, f., jasiuk, i., boccara, s., ostoja-starzewski, m., a micromechanically based couple-stress model of an elastic orthotropic two-phase composite. eur j mech a-solid, 21 (2002) 465-481. [11] addessi, d., de bellis, m. l., sacco, e., cosserat modeling of heterogeneous periodic media adopting a micromechanical approach. int. j. solids struct., (2014) under review. [12] yuan, x., tomita, y., andou, t., 2008. a micromechanical approach of nonlocal modelling for media with periodic microstructures. mech res commun, 35 (1-2) (2008) 126 -133. [13] tran, t. h., monchiet, v., bonnet, g., a micromechanics-based approach for the derivation of constitutive elastic coefficients of strain-gradient media, int j solids struct, 49 (2012) 783-792. [14] bacigalupo, a., gambarotta, l., computational two-scale homogenization of periodic masonry: characteristic lengths and dispersive waves, comput method appl m., 213-216 (2012) 16-28. [15] bacigalupo, a., gambarotta, l., second-order computational homogenization of heterogeneous materials with periodic microstructure. zamm-z angew math me, 90 (11) (2011) 796-811. microsoft word numero_53_art_32_2820 y. saadallah, frattura ed integrità strutturale, 53(2020) 417-425; doi: 10.3221/igf-esis.53.32 417 modeling of mechanical behavior of cork in compression younès saadallah university of mohamed seddik ben yahia, jijel, algeria sayounes@live.fr, http://orcid.org/0000-0003-1265-3677 abstract. the present work consists of a contribution in modeling the mechanical behavior of cork in compression. for this purpose, compression tests are performed in the non-radial direction on high density reproduction cork samples. cork shows stress-strain curves, typical of cellular materials, characterized by an elastic slope followed by an important plateau corresponding to buckling of cells; and finally hardening due to the densification of the material. two behavior models are proposed to represent this behavior. a trilinear model in which each slope represents one of the three domains and whose parameters are identified directly from the stressstrain curves. a more nonlinear model corresponding to a third-order polynomial whose parameters are identified by means of a polynomial regression. test-model comparisons reveal little relevance of the results given by the trilinear model whereas a very good consistency is observed for the results given by the nonlinear model. keywords. cork; compression; behavior model; parameters identification; stress-strain. citation: saadallah, y., modeling of mechanical behavior of cork in compression, frattura ed integrità strutturale, 53 (2020) 417-425 received: 13.05.2020 accepted: 02.06.2020 published: 01.07.2020 copyright: © 2020 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. introduction hoosing the right materials to use to perform specific functions is always a very important step. different criteria are then taken into account, including cost and properties; but also, their impact on the environment. environmental protection has become a major issue in recent times, it is extremely vital to look for ecological materials. among these are natural materials including wood and cork. cork is a natural product obtained from the outer bark of an oak species, the cork oak. the cork layers that are produced in its bark form a continuous envelope with appreciable thickness around the trunk and branches. the cork can be removed from the stem without endangering the vitality of the tree, which then rebuilds a new layer of cork. this is the basis of sustainable cork production during the long life of cork oak [1]. lightness, high compressibility, dimensional recovery, thermal and sound insulation, very low permeability to liquids and gases and chemical stability are properties that make cork a widely used material in various applications [2-6]. the cost of this material is also an attractive factor. these so particular properties, still little explained, strongly encourage further research. the elastic properties of cork have been studied by several researchers. gibson et al [5] focused on the identification of elastic parameters in the three radial, axial and tangential directions. the elastic modulus, the shear modulus and the c https://youtu.be/9k9lqqxpjks y. saadallah, frattura ed integrità strutturale, 53(2020) 417-425; doi: 10.3221/igf-esis.53.32 418 poisson's ratio have been determined. the results obtained show that cork is almost isotropic in non-radial directions. however, it has a larger young's modulus and a zero poisson's ratio when it is stressed in the radial direction. oliveira et al. [7], studied the variability of the compressive properties of cork. the results show that the radial direction has the greatest compressive strength while the resistance in the axial and tangential directions is almost similar. anjos et al. [8] investigated the effect of density on the properties of cork in compression. this results in an increase of the young's modulus with the increase of the density especially beyond the elastic region. garcía et al. [9] have sought a compression model linking physical properties (porosity, density and test direction) to mechanical properties using a classical linear regression technique. the compressive strain stress curves reveal an elastic domain at (5-7) % followed by a large plateau for strains caused by the progressive buckling of the cell walls until a strain of (50-70) %, and a steep stress increase for higher strains corresponding to cell collapse [5, 7, 8, 10]. cork has the distinction of having an insignificant poisson's ratio [2]. this is explained by its nature and highly porous and cellular structure. indeed, cork has the ability to undulate its cell walls when it is compressed and thus it can have a large longitudinal compression deformation without lateral expansion [10]. complete densification corresponds to 85% strain without fracture [7]. indeed, the fracture occurs in the case of a tensile stress. after the removal of the load, the cork recovers. the rate of recovery decreases over time [11]. for a strain level of 50%, half of the dimensions recover after the first day and end at 90% in the fifteenth day [8]. for a strain level of 30%, the recovery is total after 20 days of removal of the load [11] while it is not total for a level exceeding 80%. the behavior of the tensile cork in the tangential and axial direction has been studied respectively in the references [12, 13]. it follows that the tensile strength in the tangential direction is lower than that in the axial direction. in comparison with its compression behavior, cork has a lower tensile elastic domain. this area is around 2% in both tangential and axial directions. the fracture takes place respectively in the tangential and axial directions at 5% and 7.1%. on the other hand, in the radial direction, it corresponds to an 18% strain value [14]. it follows that the resistance of the cork is much greater in the radial direction as well in compression as in traction. many studies have focused on the analysis of cork behavior through its parameters such as the young's modulus, the elastic limit and the stresses corresponding to certain critical strain values [5, 7-9, 11-13]. however, few of them have focused on the proposal of models to predict the overall behavior of cork. the present work is a contribution in the modeling of the mechanical behavior of cork in compression. to do this, compression tests are conducted in the non-radial direction. on the basis of qualitative analysis of stress-strain curves, two models of behavior are proposed: a trilinear model and nonlinear model. the parameters that manage these models are identified. model test comparisons are presented and discussed. experimental protocol material of study he material of study is a cultivated breeding cork from the forests of the jijel area in algeria. the cork plank (reproduction cork) obtained are wetted in boiled water at atmospheric pressure for 1 h and left to air-dry to get rid of any impurities. it is a procedure widely applied in the cork industry. specimens are cut into cubes of 20 mm on the side, with their faces perpendicular to each of the three main directions. (fig. 1). this geometry is chosen for the sake of conformity with previous works, including, for example, references [7, 9]. the density was measured from the volume and weight in g.cm-3. experimental procedure the compression tests in the non-radial direction were done at a constant crosshead speed of 2 mm.min-1. the test machine is a zwick 1476 with a capacity of 100 kn (fig. 2) driven by software suitable for computer control of the test. the test conditions are summarized in a temperature of 26 °c and a relative humidity of 30%. behavior modeling as illustrated in fig. 3, the stress-strain curves obtained from a compression test on a sample show a three-domain behavior: first, an elastic domain; then a domain of buckling cells with low slope; finally, a densification area with a high slope. in the light of these findings, two approaches are proposed, in this work, to predict the behavior of cork in compression: linear and nonlinear. the linear approach considers that the behavior is linear throughout its evolution where the three domains are modeled by lines of different slopes. average slopes are represented by the following formulas: t y. saadallah, frattura ed integrità strutturale, 53(2020) 417-425; doi: 10.3221/igf-esis.53.32 419 /  e ee   ;    /  f e f ef       ;    /d f d fd       (1) figure 1: scanning electron micrographs of the three sections of cork [5]. figure 2: test set-up and cork specimen. where e, f, d are respectively the slopes of the three different domains. e ,   f ,   d and e . ,, d represent respectively the stresses and strains at the boundaries of each of the three domains. so, we write the behavior model as follows:                                                    e e e f e f f d e e f f e e f f d d d ef f . (2) radial section axial section tangential section y. saadallah, frattura ed integrità strutturale, 53(2020) 417-425; doi: 10.3221/igf-esis.53.32 420 σ and ε being respectively the stress and the strain, the parameters are determined by a direct linear regression from the stress-strain curves. in addition, the nonlinear approach states that the behavior is non-linear in all domains. a polynomial of three degrees with four parameters is proposed. 3 2      a b c k (3) where a, b, c and k are positive parameters;  and  are respectively the stress and the strain. since the polynomial is nonlinear of third order, recourse to numerical computation is necessary for the determination of its parameters. a polomial regression was favored to identify the behavior. figure 3: typical stress-strain curve of cork in compression. results and discussion he discussion of the results consists of a comparative study of the results obtained by the two models proposed. the identified parameters are presented and discussed. test-model confrontations are put in place to judge the relevance of the results. stress-strain curves aspect fig. 4 illustrates the mechanical behavior of a sample of cork in compression in the non-radial direction. there are three domains that will be called elastic domain, buckling domain and densification domain. the elastic domain spreads at a strain of 7% while the buckling domain of the cells is limited to about 55% strain for all densities. density is one of the parameters that influences cork resistance behavior [8, 15]. it is noted that this influence is apparent especially in buckling and densification levels. it should be emphasized that density is not the only factor to govern the behavior of cork. other factors, such as porosity, quality [12], also have a significant effect on the strength of the material. linear model since the behavior is trilinear, it is governed by three parameters representing the slopes of the lines and two other parameters corresponding to the limit stresses of the elastic and buckling domains as illustrated in fig. 3. the results of the parameters obtained are summarized in tab. 1. in sum, the parameters of the least dense sample are small compared to the parameters of the other two samples. it is also noted that the slopes of the buckling domains f and densification d are largest for the densest sample. it should be mentioned that the stress d . is not a significant parameter because it only corresponds to the end of the test. however, it can provide us with information on the stress corresponding to the final strain of the test which is 66.9%. the injection of these parameters into the trilinear behavior model formulated in eqn. (2) makes it possible to compare the model test results as illustrated in fig. 5. good consistency in the elastic domain is observed. indeed, the elastic domain is linear for most materials. linearity is maintained at the beginning of the buckling step or the pace changes to nonlinear moving towards the densification zone. a relatively large gap appeared in the intersection of the buckling and densification t y. saadallah, frattura ed integrità strutturale, 53(2020) 417-425; doi: 10.3221/igf-esis.53.32 421 domains. the slope of the densification domain exhibits the strongest nonlinearity by comparing it with the other two domains. figure 4: stress-strain curves in compression in the non-radial direction of cork at different densities. density (g/cm3) 0.2340 0.2477 0.2534 15.5 f (mpa) 2.85 3.33 3.45 d (mpa) 13.2 16.5 20 e . (mpa) 1.3 1.4 1.1  f . (mpa) 2.55 2.9 2.7 d at 66.9 % (mpa) 4.36 5.16 5.37 table 1: trilinear model parameters as a function of density. fig. 6 shows the difference in absolute value between the experimental recordings and the model results for the three samples of different densities. there is a minimum difference in the elastic range and the buckling step with a maximum value of 0.14 mpa. however, the intersection of the straight lines of buckling and densification knows a significant gap that reaches 0.29 mpa. it retains its importance in the field of densification where it reaches its maximum value of 0.29 mpa as well. as a function of density, the highest difference is found in the densest sample. (a) y. saadallah, frattura ed integrità strutturale, 53(2020) 417-425; doi: 10.3221/igf-esis.53.32 422 (b) (c) figure 5: linearization of cork behavior in compression at different densities in g.cm-3: a) 0.2340 ; b) 0.2477 ; c) 0.2534). figure 6: test-model gap. nonlinear model the nonlinear model is a third-order polynomial driven by four parameters. these parameters are identified by means of a polynomial regression and are presented in tab. 2. it is noted that the parameter a is independent of the density while the y. saadallah, frattura ed integrità strutturale, 53(2020) 417-425; doi: 10.3221/igf-esis.53.32 423 other three depend on it weakly. this low dependence probably results from the small difference in the densities of the samples. it would therefore be interesting to plan other studies with samples of remarkably different densities. density (g/cm3) 0.2340 0.2477 0.2534 a (mpa) 5.10-5 5.10-5 5.10-5 b (mpa) 0.0044 0.0049 0.0045 c (mpa) 0.1583 0.1722 0.1456 k (mpa) 0.0234 0.0445 0.0641 table 2: nonlinear model parameters by density. fig. 7 establishes a test-model comparison between stress-strain curves of cork in compression in a non-radial direction. there is a very good consistency of the results with the nonlinear model in the three domains, but even better in the densification domain. in contrast to the case of the tri-linear model, there is a minimum difference in the densest sample. by deriving the polynomial of the loading with respect to the strain in the case of the nonlinear model, we obtain the loading derivative. fig. 8 shows us that this derivative decreases up to 30% of deformation where it reaches its minimum value. this minimum can be considered as another parameter of the cork from which the material hardens and thus the loading derivative increases until the end of the test. (a) (b) y. saadallah, frattura ed integrità strutturale, 53(2020) 417-425; doi: 10.3221/igf-esis.53.32 424 (c) figure 7: nonlinear behavior of cork in compression at different densities in g.cm-3: a) 0.2340 ; b) 0.2477 ; c) 0.2534). figure 8: evolution of the loading derivative. . conclusion he present work aimed to establish two models for the representation of the behavior of cork in compression. compression tests were conducted on cubic samples of cork in the non-radial direction. the shape of the curves with three domains made it possible to propose first a trilinear model of which each domain is represented by a slope. then, another non-linear model with four parameters was put in place. the parameters of the trilinear model are determined by direct linear regression from the stress-strain curves while those of the nonlinear model required a third order polynomial regression. the comparison of test-model results reveals that the nonlinear model is more refined and has fewer parameters than the trilinear model. it was concluded that the trilinear model, being relatively crude, is suggested to fulfill educational functions. however, the nonlinear model, because of its relevance, can serve as a tool of choice to exploit in the field of behavior modeling of materials. references [1] pereira, h. (2011). cork: biology, production and uses, elsevier. t y. saadallah, frattura ed integrità strutturale, 53(2020) 417-425; doi: 10.3221/igf-esis.53.32 425 [2] silva, s., sabino, m., fernandes, e., correlo, v., boesel, l. and reis, r. (2005). cork: properties, capabilities and applications, international materials reviews, 50, pp. 345-365, doi:10.1179/174328005x41168. [3] mano, j. (2007). creep-recovery behaviour of cork, materials letters, 61, pp. 2473-2477, doi: 10.1016/j.matlet.2006.03.157. [4] knapic, s., oliveira, v., machado, j. s. and pereira, h. (2016). cork as a building material: a review, european journal of wood and wood products, 74, pp. 775-791, doi: 10.1007/s00107-016-1076-4. [5] gibson, l., easterling, k. and ashby, m. f. (1981). the structure and mechanics of cork, proceedings of the royal society of london. a. mathematical and physical sciences, 377, pp. 99-117, doi: 10.1098/rspa.1981.0117. [6] gil, l. (2015). cork, in materials for construction and civil engineering, ed: springer, pp. 585-627. [7] oliveira, v., rosa, m. e. and pereira, h. (2014). variability of the compression properties of cork, wood science and technology, 48, pp. 937-948, doi: 10.1007/s00226-014-0651-2. [8] anjos, o., rodrigues, c., morais, j. and pereira, h. (2014). effect of density on the compression behaviour of cork, materials & design, 53, pp. 1089-1096, doi: 10.1016/j.matdes.2013.07.038. [9] garcía, á., anjos, o., iglesias, c., pereira, h., martínez, j. and taboada, j. (2015). prediction of mechanical strength of cork under compression using machine learning techniques, materials & design, 82, pp. 304-311, doi: 10.1016/j.matdes.2015.03.038. [10] pereira, h. (2015). the rationale behind cork properties: a review of structure and chemistry, 10, p. 1-23, doi: 10.15376/biores.10.3.pereira. [11] rosa, m. e. and fortes, m. a. (1988). rate effects on the compression and recovery of dimensions of cork, journal of materials science, 23, pp. 879-885, doi: 10.1007/bf01153983. [12] anjos, o., pereira, h. and rosa, m. e. (2010). tensile properties of cork in the tangential direction: variation with quality, porosity, density and radial position in the cork plank, materials & design, 31, pp. 2085-2090, doi: 10.1016/j.matdes.2009.10.048. [13] anjos, o., pereira, h. and rosa, m. e. (2011). tensile properties of cork in axial stress and influence of porosity, density, quality and radial position in the plank, european journal of wood and wood products, 69, pp. 85-91, doi: /10.1007/s00107-009-0407-0. [14] rosa, m. e. and fortes, m. a. (1991), deformation and fracture of cork in tension, journal of materials science, 26, pp. 341-348, doi: 10.1007/bf00576525. [15] anjos, o., pereira, h. and rosa, m. e. 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/hrv (za stvaranje adobe pdf dokumenata najpogodnijih za visokokvalitetni ispis prije tiskanja koristite ove postavke. stvoreni pdf dokumenti mogu se otvoriti acrobat i adobe reader 5.0 i kasnijim verzijama.) /hun 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/pdfxoutputintentprofileselector /documentcmyk /preserveediting true /untaggedcmykhandling /leaveuntagged /untaggedrgbhandling /usedocumentprofile /usedocumentbleed false >> ] >> setdistillerparams << /hwresolution [2400 2400] /pagesize [612.000 792.000] >> setpagedevice microsoft word numero 10 art 2 d. taylor et alii, frattura ed integrità strutturale, 10 (2009) 12-20; doi: 10.3221/igf-esis.10.02 12 the theory of critical distances applied to problems in fracture and fatigue of bone david taylor, saeid kasiri, emma brazel engineering school, trinity college, dublin 2, ireland dtaylor@tcd.ie abstract. the theory of critical distances (tcd) has been applied to predict notch-based fracture and fatigue in a wide range of materials and components. the present paper describes a series of projects in which we applied this approach to human bone. using experimental data from the literature, combined with finite element analysis, we showed that the tcd was able to predict the effect of notches and holes on the strength of bone failing in brittle fracture due to monotonic loading, in different loading regimes. bone also displays short crack effects, leading to r-curve data for both fracture toughness and fatigue crack propagation thresholds; we showed that the tcd could predict this data. this analysis raised a number of questions for discussion, such as the significance of the l value itself in this and other materials. finally, we applied the tcd to a practical problem in orthopaedic surgery: the management of bone defects, showing that predictions could be made which would enable surgeons to decide on whether a bone graft material would be needed to repair a defect, and to specify what mechanical properties this material should have. keywords. bone; fracture; fatigue; critical distance. introduction he critical distance approach is now well established as a method for the prediction of fatigue and fracture, and is being used extensively both in research and in engineering design. a recent book [1] describes the approach in detail. it is applicable for predicting failure in bodies containing notches or other stress concentrations, in situations where the mechanism of failure is one involving cracking. it has been employed by many workers for the solution of problems which can be described as essentially linear-elastic, i.e. problems in which any non-linear material behaviour (due to plasticity or damage) is localised in a small process zone: in this respect it has been used to predict brittle fracture and fatigue in all types of materials: metals, polymers, ceramics and composites. the history of this type of use goes back more than fifty years: more recent work has shown that the approach can also be applied to problems involving more extensive plasticity, such as low and medium-cycle fatigue and the static fracture of tough metallic materials. the present paper is concerned with the application of these methods, hereafter referred to as the theory of critical distances (tcd), to the prediction of a number of fracture problems in a particular material which is of interest to us all: human bone. what follows is essentially a summary of work conducted in our research group over the last four years, published previously in a number of journal articles. we hypothesised that the tcd could be applied to human bone, because bone is a quasi-brittle, fibrous composite material whose mechanical behaviour has many similarities with that of two well-known classes of engineering materials, namely fibre reinforced polymers and concrete. the tcd has previously been applied successfully to both of these types of materials [2, 3]. the mechanism of failure in bone always involves cracking, and the failure process is accompanied by both plasticity (of a limited but significant extent) and damage (in the form of microcracks, delaminations etc). we attempted to use the tcd to predict experimental data, taken from the literature, on the monotonic fracture of bone samples containing cracks, notches and holes, and on the fatigue behaviour t http://dx.medra.org/10.3221/igf-esis.10.02&auth=true http://www.gruppofrattura.it mailto: dtaylor@tcd.ie d.taylor et alii, frattura ed integrità strutturale, 10 (2009) 12-20; doi: 10.3221/igf-esis.10.02 13 of short cracks. following the success of this work, we then applied the approach to some problems of clinical significance. one example of this type of work is described: the surgical management of bone defects. the theory of critical distances: a brief introduction hat follows is a very brief introduction to the tcd: further details are available in [1] and in many other recent publications. the tcd recognises the fact that, in order to predict failure arising from a stress concentration feature such as a notch, it is not sufficient to know the stress and strain at the notch surface, at the maximum stress point, often known as the “hot spot”. rather, it is essential to have information about the stress field in the vicinity of the notch, because fracture processes that involve crack initiation and propagation are strongly influenced by aspects of the stress field in this region, such as the gradient of stress or, to put it another way, the absolute volume of material which is experiencing high stress. this recognises the fact that cracking-type failures require, in general, a solution of the type which is now generally referred to as a “non-local approach”, characterised by a physical mechanism of failure involving a process zone in the vicinity of the crack tip in which failure, deformation and damage processes occur. a variety of methods, more or less complex, have been devised to make predictions using stress and strain information in this critical region. in our most strict definition of the tcd, it consists of a group of methods which have the following two features in common. firstly, the use of a linear, elastic material model for the stress analysis. secondly, the use of a material parameter which has the units of length, known as the critical distance, l. the value of l cannot be known a priori; it can only be found by processing data from samples containing stress concentrations, tested to failure in the particular failure mode of interest. it is taken to represent a critical dimension in the material over which relevant failure processes occur. for example, in many cases it is found to be related to critical microstructural parameters such as grain size, which are known to control the material’s strength and toughness: this relationship will be discussed further below. having stated this strict definition, it is important to point out that exceptions do occur, in which the tcd is used in cases where these conditions are violated. for example it may be appropriate to use a non-linear material model, and we have indeed done so ourselves as will be discussed below. also, some realisations of the theory make use of a value of l which is not a material constant [4, 5], though these will not be considered in the present paper. we can define two different types of tcd methods. in the first type, predictions are made using information about the stress field, specifically the stress as a function of distance from the hot spot, on a line (known as the focus path) along which crack growth is expected to occur. the simplest example of this approach is the so-called point method, which uses only the stress at a given point, located a distance l/2 from the hot spot. failure is predicted to occur if the stress at this point exceeds a critical value. a variant of this approach is the line method, in which the stress parameter is the average stress along the line, over a distance from zero to 2l from the hot spot. area and volume averages have also been used, though these more complex methods do not seem to confer any more accuracy than the simple point and line methods. the second type of tcd method involves a modification of fracture mechanics, whereby the critical distance appears as the length of an imaginary crack located at the notch, or, alternatively, as the magnitude of finite crack growth increments [6]. once such a modification is accepted, normal linear-elastic fracture mechanics approaches can be used. in what follows we will use approaches of the first type, i.e. stress-based methods, making use of finite element analysis (fea) to obtain the appropriate stress fields. initial validation: notch fracture data e obtained from the published literature three extensive sets of data on the effect of notches on brittle fracture in bone. all three involved tests in which monotonically-increasing loads were applied until failure occurred. one publication [7] was concerned with the effect of notch length for sharp notches machined in bone samples, whilst the other two [8, 9] reported the results of tests conducted on whole bones, loaded in bending and torsion respectively, containing circular holes of various sizes. we found that the tcd was able to predict all this data. fig.1 shows an example: the effect of hole size on failure load for bones loaded in torsion. further details can be found in a recent publication [10]. at this point it may be worth pointing out that the tcd can be used with any type of applied loading, including multiaxial load cases, though an appropriate multiaxial failure criterion should be used. in the present study our criterion was simply the maximum principal stress: we have reported the use of other multiaxial criteria to predict fatigue and fracture in various materials, in an extensive series of previous publications (e.g. [11-13] ). w w http://dx.medra.org/10.3221/igf-esis.10.02&auth=true http://www.gruppofrattura.it d. taylor et alii, frattura ed integrità strutturale, 10 (2009) 12-20; doi: 10.3221/igf-esis.10.02 14 note in particular from fig. 1 that the tcd was able to predict the fact that small holes (hole diameter = 0.1 x bone diameter) have no effect on strength, a very useful finding for clinicians and one that was not predicted by other approaches. in the tcd approach this finding arises because if a notch is very small, the critical distance (being constant) becomes effectively much larger than the hole, so the stress at the critical point is similar to the nominal applied stress: effectively the hole has become “invisible” as far as this approach is concerned. a particularly encouraging aspect of this validation exercise was the fact that the appropriate value of the critical distance was found to be almost constant across the three sets of data. it is well known that other mechanical properties of bone, such as stiffness and strength, vary considerably, so we had expected that l would also vary, but this seems not to be the case: a value of 0.32-0.38mm was able to give good predictions throughout. figure 1: the effect of hole diameter (normalized by bone diameter) on fracture torque (normalized by fracture torque for bones containing no hole), for whole bones tested in torsion, containing single transcortical holes of various diameters. predictions using the tcd and two other theories. the same situation arises in fibre composite materials, which are also known to have only a small range of l values [14]. in those materials, strength and toughness are roughly proportional to each other over quite a wide range of values, so that an increase in strength (for example by increasing the proportion of fibres) confers a similar proportional increase in toughness. an equation can be derived which links three material constants used in the tcd: l, kc and the critical stress for failure o, as follows: 2 1        o c k l  (1) since l is related to the ratio of strength to toughness, it stays constant if these two properties change in a proportionate manner. the critical stress parameter defining failure in bone, o, was found to be slightly larger than the material’s tensile strength, u as measured from tests conducted on plain, unnotched samples. we found that accurate predictions could be made using a critical stress of tu where t had a constant of value 1.33. this finding is in line with our investigations of other materials, in which the value of t has been found to take values close to 1.0 for brittle ceramics and composites [15], in the range 1.4-3 for polymers [1] and values typically greater than 3 for metals [16]. a precise interpretation of the meaning of the t parameter is still unclear. in considering the significance of this value it is worth noting the link between the three parameters of toughness, strength and l, as shown in equation 1 above. if two of these constants are known, the third can be calculated, which implies that only two of these three constants are of fundamental significance. in my personal opinion, the two fundamental parameters are l and kc. the value of o differs from that of u, in my view, because of two assumptions which we make in this analysis. firstly, we assume that the material is linear and elastic, which of course it is not. it is significant that values of t become larger in materials and fracture processes involving more plasticity. secondly, we assume that the mechanism of failure in a plain specimen is the same as that in a notched specimen. this is clearly not the case in some materials: plain specimens may fail differently due to, for example, plastic instability (necking) in ductile materials or the presence of pre-existing defects in brittle materials. it is interesting to note that, when we http://dx.medra.org/10.3221/igf-esis.10.02&auth=true http://www.gruppofrattura.it d.taylor et alii, frattura ed integrità strutturale, 10 (2009) 12-20; doi: 10.3221/igf-esis.10.02 15 conducted a different analysis of bone, to predict indentation fracture, for which a non-linear material model was needed, we found that t=1 [13]. short crack behaviour in fatigue and brittle fracture t is well known than short cracks often display behaviour which does not conform to linear elastic fracture mechanics. for example, the values of toughness (kc) and fatigue threshold (kth) for short cracks are often smaller than the material-constant values measured from long cracks. data in which the measured kc (or kth) is plotted as a function of crack length are known as resistance curves, or r-curves. figs 2 and 3 show r-curve data for bone, for brittle fracture and fatigue respectively, along with predictions using the tcd. in this case the analysis can be made very easily using the line method, because predictions for the case of a small crack (length a) in an infinite body can be expressed using the following simple equation: la a k k c ca   (2) figure 2: two sets of data showing the variation of measured fracture toughness as a function of crack length for bone along with tcd predictions. for more details see [17]. 0 1 2 3 4 5 6 0 1 2 3 4 5 6 7 crack length (mm) f ra c tu re t o u g h n e s s k c ( m p a .m ^ 0 .5 ) tcd prediction lakes 0 0.5 1 1.5 2 2.5 3 0 0.02 0.04 0.06 0.08 crack length (mm) f ra c tu re t o u g h n e s s k c (m p a .m ^ 1 /2 ) tcd prediction mullins i http://dx.medra.org/10.3221/igf-esis.10.02&auth=true http://www.gruppofrattura.it d. taylor et alii, frattura ed integrità strutturale, 10 (2009) 12-20; doi: 10.3221/igf-esis.10.02 16 figure 3: threshold stress intensity range for fatigue crack growth in bone, defined at a crack growth rate of 3-6 x 10-8m/cycle; for details see [17]. as can be seen from the figures, the predictions are very satisfactory for both types of failure, even including data for very small crack lengths obtained using nanoindentation experiments [18]. it should be remarked that currently there is considerable controversy in the literature about the validity of measuring toughness using indentation, a technique which has been used for brittle material for many years but which is now being seriously questioned. the interested reader may wish to refer to recent letters in the journal of biomechanics arising from the publication by mullins et al [18]. currently, indentation is one of the few options available for estimating the toughness of materials at very small length scales, a subject which is of increasing interest given the advent of micro and nano scale materials and devices. the data in figs 2 and 3 here all refer to crack growth in the transverse direction: bone is highly anisotropic so further work is needed to explore fracture properties in different directions. in making these predictions we used the same value for l as previously obtained from the predictions of notch fracture behaviour. this implies that l takes the same value in fatigue as in brittle fracture in this material, at least for cracking in the transverse direction. we have previously found significant differences between l values for fatigue and brittle fracture in metallic materials, but similar values for a polymer, pmma. in the present case the fatigue data available are relatively sparse, so further validation is needed before this conclusion can be stated with confidence. it is perhaps worth considering at this stage why bone has this particular value of l. as noted above, l values for many materials are often related to the size of microstructural features which control fracture behaviour. bone has a hierarchical structure, displaying features at a range of size scales, especially nanometres (the thickness of reinforcing crystals of hydroxyapatite), microns (the thickness of lamellae consisting of crystals and collagen fibres in a composite structure) and hundreds of microns (the size and spacing of structural units known as osteons). a number of mechanisms operating at the hundred-micron scale have been identified, notably uncracked ligaments bridging the crack faces [19] and the role of the osteon boundary in crack arrest (o'brien et al., 2005), in a manner similar to the grain boundary in metals. figs 4 and 5 show examples of these mechanisms. ritchie and co-workers have investigated these mechanisms in some detail and have laid particular emphasis on the role of uncracked ligaments. they showed a definite relationship between the rising rcurve for a given crack and the increasing number of uncracked ligaments observed as the crack extended [20]. in our studies on high-cycle fatigue in bone we have placed emphasis on the role of the osteon boundary, showing that the great majority of fatigue cracks become non-propagating when they reach the first boundary and developing relationships between crack length, growth rate and the proximity of this boundary [21, 22]. all of these various observations imply that l takes a value equal to a few hundred microns because this corresponds to the size scale on which important toughening mechanisms operate in this material. in fact, this turns out to be the case for many different materials. fig.6 shows the value of l for various different classes of materials, plotted against the relevant structural parameter d. in some cases there are very clear and demonstrable relationships between l and d: for example we showed that l takes values very close to d in steels failing by brittle cleavage fracture at low temperatures [23]. in other cases the relationship is less clear but for most materials it seems that l falls between d and 10d in magnitude. there are, however, some important exceptions: for example amorphous polymers such as pmma have no microstructure as such, and yet have l values of the order of 0.1mm. this coincides with the typical size of crazes in the material. 0 0.2 0.4 0.6 0.8 1 1.2 0 0.5 1 1.5 2 2.5 3 crack length (mm) s tr e s s in te n s it y r a n g e ( m p a .m ^ 1 /2 ) tcd prediction kruzic http://dx.medra.org/10.3221/igf-esis.10.02&auth=true http://www.gruppofrattura.it d.taylor et alii, frattura ed integrità strutturale, 10 (2009) 12-20; doi: 10.3221/igf-esis.10.02 17 it is perhaps not surprising that there should be a relationship between l and d, since in most materials the microstructure plays a strong role in determining properties related to crack growth, such as toughness and fatigue behaviour. thus, knowing a value of l for a particular material may shed light on the physical mechanism of failure and may give hints about how changing microstructural parameters could affect performance. (a) (b) figure 4: two sem images showing cracks in bone which display bridges consisting of uncracked ligaments across the crack faces. photo (a) from tests conducted in our laboratories by stewart mahoney; photo (b) from [19]. figure 5: image taken using optical fluorescence microscopy of a transverse section of bone, showing a crack (c), of length approximately 100m, whose left-hand tip has stopped growing on reaching the boundary of an osteon (o). from [21]. figure 6: values of l and d in various classes of materials. c ri ti ca l d is ta n ce , l microstructure size, d 1nm 1m 1mm 1m 1nm m 1mm 1m l= d l= 10 d metals, brittle fracture metals, fatigue amorphous polymers ceramics nanomaterials? fibre composites concretes bone http://dx.medra.org/10.3221/igf-esis.10.02&auth=true http://www.gruppofrattura.it d. taylor et alii, frattura ed integrità strutturale, 10 (2009) 12-20; doi: 10.3221/igf-esis.10.02 18 practical applications: the management of bone defects great advantage of the tcd is that it can be applied very easily to practical problems; in this respect the stressbased methods are particularly attractive because they can be used in any situation where a stress analysis can be conducted using fea or similar numerical techniques. stress concentrations frequently arise in bone as a result of disease or clinical intervention. surgeons use the terminology “bone defect” to refer to any hole which occurs in a bone, i.e. any part of the bone cortex or internal cancellous structure which is missing. defects occur for various reasons, for example they may also arise following a complex fracture: when the broken parts of a bone are reassembled there may be some pieces missing. also, holes may be deliberately drilled to take samples for biopsy or for the fixation of fracture plates which may be later removed. one method for the replacement of the anterior cruciate ligament in the knee involves taking a piece of bone from the patella of the other knee, often leaving a square hole with sharp corners. in a previous study we showed that the impact energy of this patella was significantly reduced by the presence of the hole, and that the situation could be considerably improved by cutting a hole with round corners [24]. this is a good example of how a concept which is very obvious to the mechanical engineer can have immediate benefits in the field of medicine. if the hole is considered to confer significant risk of failure, the surgeon may fill it using a bone graft material. various types of materials are used, including the patient’s own bone (taken from some other site and ground into a powder) and various artificial materials. over a period of time, the patient’s own natural healing processes will cause the hole to be filled with new, living bone, so the bone graft material is intended only as a temporary substitute, required to last for a few months at the most. artificial bone graft materials are designed to provide a scaffold for the rapid ingrowth of bone, and recently there has been much interest in the use of tissue engineering techniques for the development of these materials. scaffolds have been made from a wide variety of materials, including porous metals, ceramics and hydrogels. there is great interest in the use of resorbable materials which can gradually dissolve, aiding the development of new bone, but current versions of these materials are relatively weak, increasing the risk of fracture in the critical period just after surgery. a major problem is the lack of a predictive model to aid surgeons in deciding what to do about a given defect, whether to use a bone graft material and, if so, what the properties of that material should be. such a predictive model, presented in the form of a computer simulation of the defective bone, could greatly aid in the planning of surgical operations. as an initial step towards developing such a tool, we carried out some simple simulations of the behaviour of bone defects. fig 7 shows the geometry used for the finite element model: the bone is envisaged as a simple tube, containing a defect: we modelled square and circular holes of various sizes. a complete description of the methodology and results can be found in a recent publication [25]. in brief, we used a damage mechanics approach to predict the increase of fatigue damage due to cyclic loading in normal daily activities. the tcd was incorporated by performing all the damage calculations at the critical point, i.e. a distance l/2 from the hole, rather than at the hot spot. the capacity of bone to repair itself was included in the model as a constant, negative damage rate, following earlier work [26]. the use of different bone graft materials was modelled by filling the hole with a material of given young’s modulus, eo. bone ingrowth was included in the simulation by allowing the young’s modulus of the graft material to gradually increase over time, from eo to a value typical for normal cortical bone (17gpa). fig. 7 shows an example of the results of the simulation. if repair and ingrowth are not modelled, damage increases rapidly. incorporating ingrowth causes damage to level out to a plateau value, and the additional incorporation of repair allows the damage to return to normal levels after peaking. the value of the peak is of course the critical one: provided this is less than unity we predict that no failure will occur.as fig.8 shows, there is a very strong effect arising from the value of eo, the stiffness of the bone graft material. this occurs because the stress concentrating effect of the hole is greatly reduced, even when the material in the hole has much less stiffness than the surrounding bone. this analysis enabled us to make a specification for a safe value of eo,as a function of hole size as shown in fig.8. obviously the result also depends on the shape of the hole, and on the assumed daily loading, i.e. the activity level of the person. these predictions show that small holes (in this case less than 5mm diameter) do not need to be filled in with graft material: this finding is in agreement with the current practice of surgeons who regard such small holes as innocuous. larger holes do require filling, but here we predict that the material needed can have an eo value which is considerably smaller than that of normal bone: this finding is original and potentially of great value to researchers and manufacturers who are developing new types of bone graft materials. this work is very preliminary in nature, but has the potential to be developed to a greater level of sophistication, for example incorporating the changing behaviour of resorbable materials and the effect of different postoperative activity levels, such as walking with the support of a crutch or cane or carrying out more strenuous exercise. a http://dx.medra.org/10.3221/igf-esis.10.02&auth=true http://www.gruppofrattura.it d.taylor et alii, frattura ed integrità strutturale, 10 (2009) 12-20; doi: 10.3221/igf-esis.10.02 19 figure 7: the geometry used to study defects of various shapes and sizes in a typical long bone – the focus path is the line on which tcd calculations are carried out. typical predictions showing the effect on damage evolution of including ingrowth of bone into the defect, and bone repair processes. (a) (b) figure 8: (a) variation of peak damage amount with young’s modulus of the bone graft material; (b) specification for the safe value of eo (i.e. the value above which failure will not occur) as a function of hole size. concluding remarks his work has shown that the tcd can be used to study fracture and fatigue problems in bone. classic problems which the tcd has been able to solve in other materials, such as notch-initiated fracture and fatigue and the short crack problem, have been successfully addressed in this material. even though bone shows large variations in its mechanical properties, it seems that l remains approximately constant, of the order of 0.3-0.4mm, which is very convenient when making predictions. this value reflects the role of osteons and other microstructural features in impeding crack growth and thus controlling toughness and fatigue. current work has been limited to cases where crack growth occurs across the bone, i.e. in the transverse direction: longitudinal crack growth requires separate study. we have also limited ourselves to cortical bone: the failure of spongy, cancellous bone is also of great interest and merits further attention. the tcd can be employed as part of a practical software tool to aid orthopaedic surgeons in the planning of operations and of post-operative treatments. acknowledgements e are grateful to the higher education authority of ireland for provision of funding for part of the work described above, which was conducted in collaboration with the institute of technology, sligo, ireland. t w http://dx.medra.org/10.3221/igf-esis.10.02&auth=true http://www.gruppofrattura.it d. taylor et alii, frattura ed integrità strutturale, 10 (2009) 12-20; doi: 10.3221/igf-esis.10.02 20 reference list [1] d. taylor, the theory of critical distances: a new perspective in fracture mechanics. elsevier, oxford, uk (2007). [2] j. m. whitney, r.j. nuismer, journal of composite materials, 8 (1974) 253. [3] p. cornetti, n. pugno, d. taylor, proceedings of the 11th international conference on fracture esis, turin, italy (2005) 73. [4] p. cornetti, n. pugno, a. carpinteri, d. taylor, engineering fracture mechanics, 73 (2006) 2021. [5] d. leguillon, european journal of mechanics a/solids, 21 (2002) 61. [6] d. taylor, p. cornetti, n. pugno, engineering fracture mechanics, 72 (2005) 1021. [7] w. bonfield, p.k. datta, journal of biomechanics, 9 (1976) 131. [8] r.j. mcbroom, e.j. cheal, w.c. hayes, journal of orthopaedic research, 6 (1988) 369. [9] j.a. hipp, b.c. edgerton, k.n. an, w.c. hayes, journal of biomechanics, 23 (1990) 1261. [10] s. kasiri, d. taylor, journal of biomechanics 41 (2008) 603-609. [11] l. susmel, fatigue and fracture of engineering materials and structures, 27 (2004) 391. [12] f. pessot, l. susmel, d. taylor, in crack paths conference parma, italy (2006). [13] s. kasiri, g. reilly, d. taylor, wit transactions on biomedicine and health, 12 (2007) 113. [14] j. awerbuch, m. s. madhukar, journal of reinforced plastics and composites, 4 (1985) 3. [15] d. taylor, engineering fracture mechanics, 71 (2004) 2407. [16] d. taylor, structural integrity and durability, 1 (2006) 145. [17] d. taylor, s. kasiri, in proc asme summer bioengineering conference asme, usa (2008). [18] l. p. mullins, m. s. bruzzi, p. e. mchugh, journal of biomechanics, 40 (2007) 3285. [19] nalla,r.k., kinney,j.h., and ritchie,r.o. (2003) mechanistic fracture criteria for the failure of human cortical bone. nature materials 2, 164-168. [20] r. k. nalla, j. s. lken, j. h. kinney, r. o. ritchie, journal of biomechanics, 38 (2005) 1517. [21] f. j. o'brien, d. taylor, t.c. lee, journal of orthopaedic research, 23 (2005) 475. [22] d. taylor, f. o'brien, t. c. lee, meccanica, 37 (2002) 397. [23] d. taylor, microstructural parameters in the theory of critical distances (2008). [24] k. moholkar, d. taylor, m. o'reagan, g. fenelon, journal of bone and joint surgery, 84a (2002) 1782. [25] e. brazel, d. taylor, predicting the structural integrity of bone defects repaired using bone graft materials; computer methods in biomechanics and biomedical engineering, in press. [26] p. j. prendergast, d. taylor, journal of biomechanics, 27 (1994) 1067. http://dx.medra.org/10.3221/igf-esis.10.02&auth=true http://www.gruppofrattura.it microsoft word numero_37_art_43 c. patil et alii, frattura ed integrità strutturale, 37 (2016) 325-332; doi: 10.3221/igf-esis.37.43 325 experimental investigation of hardness of fsw and tig joints of aluminium alloys of aa7075 and aa6061 chetan patil mechanical department, pse, saki-palsana, gujarat (india) hemant patil mechanical department, d. n. patel c.o.e., shahada, maharashtra, (india) hspatil28@gmail.com hiralal patil mechanical department, gdec, abrama, gujarat (india) abstract. this paper reports hardness testing conducted on welded butt joints by fsw and tig welding process on similar and dissimilar aluminium alloys. fsw joints were produced for similar alloys of aa7075t651 and dissimilar alloys of aa7075t651aa6061t6. the friction stir welds of aa7075 & aa6061 aluminium alloy were produced at different tool rotational speeds of 650,700, 800, 900, 1000 and transverse speed of 30, 35, 40 mm/min. tig welding was conducted along the rolling direction of similar and dissimilar aluminium plates. the brinell hardness testing techniques were employed to conduct the tests; these tests were conducted on the welds to ascertain the joint integrity before characterization to have an idea of the quality of the welds keywords. fsw; rotation speed; transverse speed; hardness. introduction riction stir welding (fsw), a solid state joining process was developed and patented by the welding institute (twi) in 1991 [1]. fsw is considered to be the potentially useful solid state welding technique in which welding is done below the melting point of the work piece material [2-3]. because of low heat input and absence of complete melting, fsw offers several benefits over the conventional fusion welding process. metallurgical benefits includes good dimensional stability, repeatability, no loss of alloying elements, excellent mechanical properties in the joint area due to re crystallized micro structure in the stir zone. environmentally the process is a green one because it eliminates grinding wastages, no harmful emissions, required minimum surface cleaning [4]. fsw has various application in the fields of marine like hulls, superstructures, storage vessels for the shipbuilding, in aerospace like airframes, fuselages, wings, fuel tanks; in railway like high speed trains, railway wagon; in automotive like chassis, truck bodies [5]. a cylindrical shouldered tool with different pin probe is rotated and slowly plunged into the joint line between plate materials, until the shoulder of the tool forcibly contacts the upper surface of the material and the pin is a short distance from the back plate. the pieces are rigidly clamped onto a backing plate in a manner that prevents the abutting joint faces from being forced apart. the fixturing prevents the plates from spreading apart or lifting during welding. frictional heat is generated between the tool f c. patil et alii, frattura ed integrità strutturale, 37 (2016) 325-332; doi: 10.3221/igf-esis.37.43 326 shoulder and the work piece. this heat causes the latter to reach a visco-plastic state that allows traversing of the tool along the weld line. the plasticized material is transferred from the leading edge of the tool to the trailing edge of the tool probe and is forged by the intimate contact of the tool shoulder and the pin profile. it leaves a solid phase bond between the two pieces [6]. the fig. 1describes the basic principle of the fsw process. caroline et al [7] has welded aa2014-t6 and aa7075-t6 aluminium alloys for various welding parameters. torque, temperature, macrograph and micro hardness were measured and concluded that torque, temperature and hardness profile depend on the amount material mixture in the stir zone. s. rajakumar et.al [8] studied the influence of process parameters on friction stir welding of al 7075 alloy and concluded that higher tool rotation speed resulted in higher heat generation which caused slower cooling rate and leads to formation of coarse grains which in turn produced lower hardness. moreira et al [9] produced fsw of aa6082t6 with aa6061-t6. the welds exhibited intermediate properties and the tensile tests failures occurred near the weld edge line where a minimum value of hardness was observed. khodir et al [10] studied the microstructure and mechanical properties of dissimilar joints of 2024-t3 to 7075-t6 al alloy and observed that the rise in welding speed caused formation of kissing bond and pores especially when the 2024 al alloy plate was located on the retreating side. minimum hardness was observed in the haz of both sides and their values increased with welding speed. shen et al [11] used aa 7075 plates of 2 mm thickness, for various rotational speeds and the dwell time. they investigated the microstructure and the mechanical properties of the refilled friction stir spot welding of aa7075. the keyhole of the weld was refilled successfully, the microstructure of the weld exhibits variations in the grain additionally, they observed, and defects associated to the material flow, such as hook, voids, bonding ligament and incomplete refill. vladvoj et al [12] presents the results of microstructure analysis, hardness measurements and tensile tests of fs-welded sheets of two aluminium alloys aa5083 and aa7075.ericsson and sandstrom [13] investigated the influence of welding speed on fatigue behavior of fsw, mig and tig process. moreira et al. [14] investigated the fatigue behavior of joints of fsw and metal inert gas (mig) welding. squillace et al. [15] investigated the microstructure and pitting corrosion resistance in tig and fsw joints for 2024-t3 alloy. munoz et al. [16] investigated the microstructure and mechanical properties of fsw and tig for almg-sc alloy. taban et al [17] studied the microstructure and mechanical properties in mig, tig and fsw joints for 5083h321 aluminum alloy. this paper presents the effect variable rotational speed and transverse speed on hardness properties of similar fsw joints of aa7075-t651 and dissimilar fsw joints of aa7075-t651-aa6061-t6 and also comparison between fsw and tig welding were studied. figure 1: working principle of friction stir welding. materials and experimental methods materials luminium alloys aa7075-t651 and aa6061-t6 sheet was cut on shear machine and brought to required size of 150 mm x 70 mm x 6.35 mm for fsw & tig welding. the fsw tool employed was square trapezoidal pin of h13 tool steel material with dimensions of 4mm bottom face and 6mm top face, 20mm flat shoulder diameter and 6mm pin height. the chemical composition of base material is as shown in tab. i. a c. patil et alii, frattura ed integrità strutturale, 37 (2016) 325-332; doi: 10.3221/igf-esis.37.43 327 chemical composition % aa7075t651 elements si fe cu mn mg cr ni zn ti zr required 0.4 0.5 1.2-2 0.3 2.1-2.9 0.18-0.28 5.1-6.1 0.2 contents 0.05 0.18 1.4 0.04 2.5 0.19 5.9 0.08 aa6061t6 elements required 0.4-0.8 0.7 0.15-0.40. 0.15 0.8-1.2 0.04-0.35 0.25 0.15 contents 0.62 0.45 0.2 0.13 1.05 0.09 0.03 0.07 table i: chemical composition of base aluminium alloys welding procedures fsw method. the fsw joints were produced for similar alloys aa7075 and dissimilar alloys aa7075-aa 6061.the fsw welding parameter used in this experiment were tool rotation speed of 650,700, 800 rpm, 900 rpm and 1000 rpm; transverse speed of 30 mm/min, 35 mm/min and 40 mm/min. the tool tilt was maintained 00 during the experiment and plunge depth was of 6mm throughout the weld path. tool tip plunge feed was 10 mm/min throughout the weld path. the plates to be welded by fsw process were fixed by a clamping fixture on a joyti cnc vertical machining center px20 series as shown in fig. 2. the initial joint configuration was obtained by securing the plates in position using mechanical clamps. the direction of welding was normal to the rolling direction. single pass welding procedure was used to fabricate the fsw joint. figure 2: friction stirs welding on vmc machine with fsw joint. welding procedures tig method. tig welding was conducted on tig weld machine along the rolling direction of plates. the tig joints were also produced for similar alloys aa7075 and dissimilar alloys aa7075-aa6061.the the welding parameter used in tig welding were; welding filler wire for tig welding was al-si alloy with diameter of 4 mm, the flow rate of argon shield was 15 l/min, the welding voltage and current were 80 v and 280 a, respectively, and the speed of welding was 15 mm/s. hardness testing method using hardened steel ball indenter of 10mm diameter was fixed on the bhn machine demonstrated in the experimental set up as shown in fig. 3. c. patil et alii, frattura ed integrità strutturale, 37 (2016) 325-332; doi: 10.3221/igf-esis.37.43 328 figure 3: brinell hardness testing machine. the fsw specimen was mounted on to the machine and the machine was loaded with load of 250 kgf for time of 20seconds and then removed. the resulting depth of impression was measured by the help of a microscope as shown in fig. 4. figure 4: microscope with depth of impression. a chart was then used to convert depth of impression to brinell hardness number. all friction stir welded samples for different weld parameter were tested for brinell hardness and the impression converted into bhn is shown in tab. ii for various fsw weld parameter. in tab. ii, sample number a to g presents fsw joints of similar alloys aa7075t651 and sample number a1, a4 presents fsw joints of dissimilar alloys aa7075t651aa6061t6. b1, b2 represents similar and dissimilar joints of tig welding respectively. c. patil et alii, frattura ed integrità strutturale, 37 (2016) 325-332; doi: 10.3221/igf-esis.37.43 329 fsw sample no. rotation speed (rpm) transverse speed (mm/min) impression (d) (mm) bhn a 900 30 1.62 121 b 900 35 1.90 87.4 c 900 40 1.80 97.4 d 800 30 1.71 108 e 800 35 1.62 121 f 800 40 1.70 109 g 1000 30 2.10 71.4 h 1000 35 1.70 109 a1 700 40 2.80 40.0 a4 650 35 2.20 65.0 b1 2.50 50.1 b2 2.11 70.7 table ii: brinell hardness test result. results and discussion n heat treatable alloys, the precipitates only impart strength to the alloy. dissolution of these strengthening precipitates weakens the mechanical properties of weld joints. in all the fsw joints, the temperature experienced during welding can induce an over ageing of the precipitate particle, resulting in decrease of mechanical characteristics. actually, by inspecting hardness of fsw joints as shown in fig. 5-6, the hardness values in all welded samples are reduced compared with base metal, this means that the generated heat during fsw causes softening of the welded area due to dissolution of precipitates (fig. 7a). figure 5: effect of transverse speed on hardness for similar fsw & tig joints. i c. patil et alii, frattura ed integrità strutturale, 37 (2016) 325-332; doi: 10.3221/igf-esis.37.43 330 figure 6: effect of transverse speed on hardness for dissimilar fsw & tig joints. figure 7: microstructure of fsw and tig showing precipitates and voids figure 8: hardness values in the microstructural weld zones. fsw temperatures coming to the nz and tmaz will cause at least partial dissolution of the hardening phases. normally, therefore, some softening within the nz should be expected in heat treatable alloys that were welded in t-tempers. some c. patil et alii, frattura ed integrità strutturale, 37 (2016) 325-332; doi: 10.3221/igf-esis.37.43 331 grain coarsening and softening could also take place in the haz. the reducing in the weld hardness can be attributed to the dissolution of precipitates and subsequently the weld cooling rates do not favor nucleation and growth of all precipitates. the variation in hardness values in the microstructural weld zones are shown in fig. 7. due to the high temperature required for fusion welding, the heat affected zone region was large as well as and the subsequent melting and solidification that occur, voids are common defects found in fusion welds. the presence of voids (fig.-7b) in the tig welds contributes to the reduced hardness (fig. 5-6) observed during testing in respect of friction stirs welds. conclusion he minimum hardness was recorded in the weld metal for tig welding of about 50.1bhn for similar joint and 70.7 bhn for dissimilar joints. while for fsw joint the minimum hardness was recorded about 70.1 bhn and maximum hardness about 121bhn as compared with 170bhn for the base alloy. a hardness value has mixed result with respect to rotations speed and transverse speed for similar fsw joints. but in case of dissimilar fsw joints hardness value decreases with increase rotations speed and transverse speed. hardness was strongly affected by precipitate distribution.the voids presence in the tig welds contributes to the reduced hardness. it is observed that of fsw joints has more hardness than tig joints. references [1] thomas, w.m., et al., friction stir butt welding, international patent application pct/gb92, patent application gb9125978.8, 6, (1991). [2] muthukrishnan, m., marimuthu, k., some studies on mechanical properties of friction stir butt welded al-6082t6 plates, ieee, (2010). [3] yan-hua zhao, t., san-bao lin, lin wu, fu-xingqu, the influence of pin geometry on bonding and mechanical properties in friction stir weld 2014 al alloy, materials letters, 59 (2005) 2948 – 2952. [4] mishra, r. s., mahoney, m. w., friction stir welding and processing materials park, oh, asm international, (2007). [5] jonhson, r., kallee, s., friction stir welding, materials world, 7(12) (1999) 751-753. [6] patil, h.s., soman, s.n., experimental study on the effect of welding speed and tool pin profiles on aa6082-o aluminium friction stir welded butt joints, international journal of engineering, science and technology, 2(5) (2010) 268-275. [7] caroline, j., bruno, d., anne, d., aude, s., torque, temperature and hardening precipitation evolution in dissimilar friction stir welds between 6061-t6 and 2014-t6 aluminum alloys. journal of materials processing technology, 213 (2013) 826– 837. [8] rajakumar, s., muralidharan, c., balasubramanian, v., influence of friction stir welding process and tool parameters on strength properties of aa7075-t6 aluminium alloy joints, materials and design, 32 (2011) 535–549. [9] moreira, p.m.g.p., santos, t., tavares, s.m.o., richter-trummer, v., vilaca, p., de castro, p.m.s.t., mechanical and metallurgical characterization of friction stir welding joints of aa6061-t6 with aa6082-t6, materials and design, 30 (2009) 180–187. [10] khodir, s. a., shibayanagi, t., friction stir welding of dissimilar aa2024 and aa7075 aluminum alloys, material science and engineering b, 148 (2008) 82–87. [11] zhikangshen, xinqi, y., zhang, z., cui, l., li, t., microstructure and failure mechanisms of refill friction stir spot welded 7075-t6 aluminum alloy joints, materials and design, 44 (2013) 476–486. [12] vladvoj, m., jorge f. p., microstructure and properties of friction stir welded aluminium alloys, metal, (2005) 1-8. [13] ericsson, m., sandstrom, r., influence of welding speed on the fatigue of friction stir welds and comparison with mig and tig, j. fatigue, 25 (2003) 13791387. [14] moreira, p.m.g.p., defigueiredo, m.a.v., de castro, p.m.s.t., fatigue behaviour of fsw and mig weldments for aluminum alloys. j. theoretical appl. fracture mech., 48 (2007) 169-177. [15] squillace, a., de fenzo, g., giorleo, f., bellucci, a comparison between fsw and tig welding techniques: modifications of microstructure and pitting corrosion resistance in aa 2024-t3 butt joints, journal of materials processing technology, 152 (2004) 97-105. t c. patil et alii, frattura ed integrità strutturale, 37 (2016) 325-332; doi: 10.3221/igf-esis.37.43 332 [16] munoz, a.c., ruckert, g., hunean, b., sauvage, x., maryav, s., comparison of tig welded and friction welded al4.5 mg0.26 sc alloy. j. materials proc. technol., 197 (2008) 337-343. [17] taban, e., kaluc, e., microstructural and mechanical properties of double-sided mig, tig and friction stir welded 5083-h321 aluminum alloy j. kovove mater met. mater., 44 (2006) 25-33. << /ascii85encodepages false /allowtransparency false /autopositionepsfiles true /autorotatepages /none /binding /left /calgrayprofile (dot gain 20%) /calrgbprofile (srgb iec61966-2.1) /calcmykprofile (u.s. web coated \050swop\051 v2) /srgbprofile (srgb iec61966-2.1) /cannotembedfontpolicy /error /compatibilitylevel 1.4 /compressobjects /tags /compresspages true /convertimagestoindexed true /passthroughjpegimages true /createjobticket false /defaultrenderingintent /default /detectblends true /detectcurves 0.0000 /colorconversionstrategy /cmyk /dothumbnails false /embedallfonts true /embedopentype false /parseiccprofilesincomments true /embedjoboptions true /dscreportinglevel 0 /emitdscwarnings false /endpage -1 /imagememory 1048576 /lockdistillerparams false /maxsubsetpct 100 /optimize true /opm 1 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/hrv (za stvaranje adobe pdf dokumenata najpogodnijih za visokokvalitetni ispis prije tiskanja koristite ove postavke. stvoreni pdf dokumenti mogu se otvoriti acrobat i adobe reader 5.0 i kasnijim verzijama.) /hun 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can be opened with acrobat and adobe reader 5.0 and later.) >> /namespace [ (adobe) (common) (1.0) ] /othernamespaces [ << /asreaderspreads false /cropimagestoframes true /errorcontrol /warnandcontinue /flattenerignorespreadoverrides false /includeguidesgrids false /includenonprinting false /includeslug false /namespace [ (adobe) (indesign) (4.0) ] /omitplacedbitmaps false /omitplacedeps false /omitplacedpdf false /simulateoverprint /legacy >> << /addbleedmarks false /addcolorbars false /addcropmarks false /addpageinfo false /addregmarks false /convertcolors /converttocmyk /destinationprofilename () /destinationprofileselector /documentcmyk /downsample16bitimages true /flattenerpreset << /presetselector /mediumresolution >> /formelements false /generatestructure false /includebookmarks false /includehyperlinks false /includeinteractive false /includelayers false /includeprofiles false /multimediahandling /useobjectsettings /namespace [ (adobe) (creativesuite) (2.0) ] /pdfxoutputintentprofileselector /documentcmyk /preserveediting true /untaggedcmykhandling /leaveuntagged /untaggedrgbhandling /usedocumentprofile /usedocumentbleed false >> ] >> setdistillerparams << /hwresolution [2400 2400] /pagesize [612.000 792.000] >> setpagedevice microsoft word numero_38_art_48 g. s. serovaev et alii, frattura ed integrità strutturale, 38 (2016) 392-398; doi: 10.3221/igf-esis.38.48 392 numerical study of the response of dynamic parameters to defects in composite structures grigorii s. serovaev, valery p. matveenko perm national research polytechnic university, department of applied mathematics and mechanics, 29 komsomolsky prospekt, perm, 614990, russia serovaev@icmm.ru, mvp@icmm.ru abstract. the purpose of this work is to study three different models of delamination in composite plate (the free mode model, the constrained model and the contact model) and applicability of this models to the vibrational method of damage detection based on frequency shifts. the results of numerical simulation have shown that the free mode model leads to abrupt changes in natural frequencies due to non-physical condition of mutual penetration of adjacent volumes in the defect zone. the constrained and the contact models yield qualitative agreement in shifts of natural frequencies with a change of the defect size. all models have shown the necessity of analyzing shifts of high frequencies to detect small size delamination. keywords. natural frequencies; vibrational methods of damage detection; delamination. citation: serovaev, g.s., matveenko, v. p., numerical study of the response of dynamic parameters to defects in composite structures, frattura ed integrità strutturale, 38 (2016) 392-398. received: 28.08.2016 accepted: 15.09.2016 published: 01.10.2016 copyright: © 2016 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. introduction he estimation of the mechanical state of a structure during its operation based on detection of internal damages has gained a great importance for such rapidly developing fields of production as mechanical engineering, aerospace industry, etc., whose recent trends are toward an increased use of new types of materials. the most widely spread type of defects in composite constructions is delamination, which leads to a separation of the object in the defect zone into several parts, which begin to respond to loads independently of each other [1] while the stiffness of each part is significantly lower than the stiffness of the whole object. the appearance of delamination may be the cause of the deprivation of bearing capacity of the structure, its breakage and decommissioning which indicates the relevance of the problem of damage detection at an early stage of development. the application of visual methods of damage detection is difficult due to internal location of delamination. it is well known that the appearance of defects in a particular place of the structure influences the local stiffness in this zone, which leads to a shift of natural frequencies. this specific feature of structure response is behind the global vibrational methods of damage detection. these methods use different dynamic parameters (eigenfrequencies, mode shapes, curvatures of mode shapes, etc.) to evaluate the state of the investigated structure [2-5]. t g. s. serovaev et alii, frattura ed integrità strutturale, 38 (2016) 392-398; doi: 10.3221/igf-esis.38.48 393 the methods of numerical simulation allow us to investigate the processes occurring in structures during application of different damage detection methods and receive the answers to many questions without performing expensive experiments. moreover, it is due to numerical methods that we can track the evolution of different parameters with a change of the defect size. studies of objects with delamination type defects have received considerable attention in scientific literature. analytical description of the free mode model of delamination in a beam, which allows the mutual penetration of volumes in the zone of delamination, is given in [6]. this disadvantage is eliminated in the constrained model where areas in the delamination zone have equal vertical displacements [7]. only few low frequencies are considered in these studies. the presence of multiple delaminations is discussed in [8]. experimental investigations of vibrations of delaminated structures are performed in [9, 10]. excitation of vibrations and measurement of the signal must be implemented using actuators and special measurement devices (sensors). the capabilities of using piezoelements for registration of high frequency vibrations are described in [11]. the authors of this research capture vibrations of the plate up to 40 khz with the help of a piezoelectric sensor which proves the possibility of using such devices for measuring high frequency vibrations. the method of electromechanical impedance (emi), which is one of the vibrational methods of damage detection applied to delaminated composite beam, is given in [12]. the need to place the actuator close to the defect and hence the requirement of arrangement of a dense grid of piezoelectric devices or prior knowledge of the location of defect is the main disadvantage of such a kind of damage detection method. on the other hand natural frequencies give integral characteristic of the object of research. in [13-15] vibrations of delaminated structures with different geometries such as beam, cylindrical and conical shells are studied. a numerical study of the dynamic parameter response to defects of different sizes is carried out in the framework of three models of delamination in a composite structure, the advantages and drawbacks of each model are estimated in the process of simulation. first, we consider a free mode model of delamination, in which the adjacent volumes in the zone of the defect are not coupled with each other and therefore they are assumed to be mutually penetrable. in the second, the so-called constrained model, the coincident nodes in the zone of delamination are coupled by one component of the displacement, while other components of the displacement remain independent. the last one is the model that takes into account the contact forces. the free mode and constrained models allow us to perform a modal analysis for computing the eigenfrequencies of the structure. with contact forces taken into account the problem becomes nonlinear. the algorithm for calculating the spectrum of eigenfrequencies in the nonlinear problem includes the following steps: setting of impact load, transient analysis, measurements of signal at a certain point of the structure with a subsequent conversion of the received response of the structure from the amplitude-time to amplitude-frequency domain with the help of the fourier transform numerical modeling numerical study was performed on a square plate of size l = 0.15х0.15 m, made of a layered composite material. the thickness of one layer is h1c = 0.0003 m. there are a total of n = 15 layers across the thickness of the plate therefore the total thickness is h1c*n = 0.0045 m (fig. 1). the square shape delamination of size ld m is located between 6 and 7th layers. the center of delamination coincides with the center of the plate. the composite material is modeled as a homogeneous body with the following orthotropic effective mechanical properties (reinforcing direction is not taken into account). ex = 24 gpa, ey = 18 gpa, ez = 6 gpa, gxy = 4 gpa, gyz = 3 gpa, gxz = 3 gpa, vxy = 0.15, vyz = 0.18, vxz = 0.42, ρ = 1800 kg/m3. the presence of composite layers is taken into account only by geometrical dimensions. finite elements with quadratic approximation providing more accurate results in terms of out of plane strains were used in the simulation. the principle of virtual work is used for the mathematical formulation of the problem i i i i i ij ij v s v u f u dv p u ds dv t 2 2 (             (1) where iu components of the displacement vector, ji ij j i uu x x 1 ( ) 2       components of strain tensor, ij ijkl klc   components of stress tensor, ijklc stiffness tensor,  material density, if components of body forces vector, ip components of surface tractions vector. a g. s. serovaev et alii, frattura ed integrità strutturale, 38 (2016) 392-398; doi: 10.3221/igf-esis.38.48 394 figure 1: geometrical representation of the plate. the boundary condition corresponds to the cantilever fixing of the plate on the border x = l the free mode model allows the mutual penetration of volumes (fig. 2), hence surfaces s1 and s2 are free from stresses and boundary conditions for this models have the following form: zz zx zys s s s s s, , ,1 2 1 2 1 2 0     for the constrained model, the coincident nodes associated with the surfaces s1 and s2 have equal displacements in the z axis direction while other components of the displacement remain independent therefore the boundary conditions can be written as follows zx zys s s s z zs s u u , ,1 2 1 2 1 2 0    a numerical solution of the dynamic problem of vibration of a plate was found by the finite element method using the commercial package ansys. the finite-element formulation in matrix form can be written as follows        m u k u f t( )  (2) where  m mass matrix of the system,  k stiffness matrix of the system,  f t( ) time dependent load function,  u the vector of nodal displacements,  u the vector of nodal accelerations. in the absence of external influences, the problem is reduced to the typical problem of finding eigenvalues and eigenvectors i t i iu x t e x( , ) ( )    (3) where  natural frequency, i eigenvector or mode shape. the finite element formulation of the problem has the following form        k m u2 0 0   (4) where  u0 the vector of nodal values of natural vibration modes. g. s. serovaev et alii, frattura ed integrità strutturale, 38 (2016) 392-398; doi: 10.3221/igf-esis.38.48 395 figure 2: models of delamination. results he frequency range from 0-20 khz was analyzed. the size of delamination was changed from 0 to 0,05 m with a step of 0.002 m. the change of eigenfrequencies, depending on the size of delamination in the range of 0-20 khz, is shown in fig. 3 and 4 (the upper plots show the results for the free mode model of delamination, the lower – for constrained model). the vertical axis represents the defect size, the horizontal axis corresponds to the frequency of oscillations in hertz. the reaction of the natural frequencies to increase in the size of the defect for the free mode model is not observed up to 4 khz. at higher frequencies a sudden drop in the natural frequencies for the defect of the large size is observed. figure 3: shifts of natural frequencies in the range of 0-10 khz. in the range of frequencies from 10-20 khz a similar abrupt pattern of natural frequency shifts is observed (fig. 4). restriction applied to the component of displacement in the delamination zone and thereby precluding mutual penetration of the adjacent volumes in this area significantly affects the results. this model is characterized by a more gradual and smaller change in magnitude of natural frequencies with increasing the size of the defect. for both models a clear tendency towards greater sensitivity of high frequency vibrations to the defects of a smaller size is observed, which is explained by the fact that the reaction of frequencies to the appearance of a defect depends not only on its size but also on its location. if a defect is located in the area of small or zero strains of mode shape, the frequency will remain unchanged. the mode shapes of high frequencies have a large number of zones with non-zero strains (bends), providing greater sensitivity of these frequencies to the defect. that's what makes these frequencies more appropriate for detection of small sized defects. t g. s. serovaev et alii, frattura ed integrità strutturale, 38 (2016) 392-398; doi: 10.3221/igf-esis.38.48 396 figure 4: shifts of natural frequencies in the range of 10-20 khz. the third variant of the model of delamination is the most accurate and complete, as it uses contact elements to model the interaction of adjacent surfaces in the delamination zone. thus, several options for the contact status are possible (fig. 5): 1) open contact where the nodes, between which the contact is defined, are divided; 2) closed contact, in this case, the nodes are in contact with each other and their relative behavior is determined by the contact stiffness, by default, equal to the modulus of elasticity of the material multiplied by the size of the element adjacent to the contact surface. in this problem the node to node type of contact (element conta178) is used because mode superposition transient analysis, which supports only this type of nonlinearity, was performed. a significant advantage of this type of calculation is its performance, compared to the full method of transient analysis. figure 5: state of the contact. in contrast to the free mode model and constrained model where natural frequencies could be calculated by the modal analysis, the spectrum of frequencies in transient analyses is calculated using the fourier transform of a signal recorded at a certain point of the plate. since accelerometers are usually used as sensors to measure the acceleration in the experiment, in the numerical model the accelerations are also calculated at the point. increasing the size of the centrally located delamination, the graphs similar to ones in fig. 3 and 4 are received which reflect the change of the natural frequencies of the spectrum when you change the size of the defect. this type of analysis requires a more profound approach, as a reflection of the resonant frequencies on the spectrum significantly depends on the type of the input signal, the points of impact and measurement. if these points are located on the nodal line of mode shape, this frequency will not be excited and will not affect the resulting spectrum. the algorithm of calculation of the nonlinear dynamic problem with contact interaction taken into account consists of the following steps (fig. 6). impact load is applied to a certain area on the surface of the plate (step i) g. s. serovaev et alii, frattura ed integrità strutturale, 38 (2016) 392-398; doi: 10.3221/igf-esis.38.48 397 m of t sin f t sin f t( ) ( 2 ) ( 2 )  where om f f n2  – modulation frequency, of – central frequency. on the time interval t = 0.4 s. mode superposition transient analysis is performed. the result of this analysis is the component of acceleration az registered at the node at the specified time period (step ii). the received signal includes a set of steady-state oscillations of different frequencies, which is obtained by decomposition of the signal using the fourier transform (step iii). figure 6: algorithm of transient analysis resonance peaks on the resulting graph correspond to the eigenfrequencies. internal dissipation was not considered in the current study, therefore, the analysis of the amplitudes of the resonance peaks was not performed. by implementing this algorithm, and increasing the size of the defect at each step, it is possible to monitor changes in natural frequencies. figure 7: shifts of natural frequencies in the contact model of delamination. the general nature of the frequency response to an increase of the damage size is similar to the models described above. we can see the lack of influence of damage on low frequencies and high frequency sensitivity to the defect of a small size. g. s. serovaev et alii, frattura ed integrità strutturale, 38 (2016) 392-398; doi: 10.3221/igf-esis.38.48 398 the sharpness of the frequency spectrum picture will significantly depend on relative location of impact and the measurement and type of impact load. conclusions he comparison of the three considered models of delamination with respect to their applicability to the solution of the problem of analysis of changes of natural frequencies of a composite plate shows that in spite of the indisputable simplicity of the free mode model, the results show an excessive drop in eigenfrequencies. the constrained and the contact models yield qualitative agreement in shifts of natural frequencies with a change of the defect size. the calculation of the constrained model is much easier and faster. however, the algorithm of calculation of the model with the contact repeats the steps performed during the experiment and more fully reflects special features typical for real structures. the results suggest that for detection of defects at an early stage of their development it is necessary to record the change in the spectrum in the high frequency range (in this case greater than 4 khz). a numerical model of the studied structure allows to analyse frequency response to the occurrence of the defect and to determine the most sensitive of them to a specific type of defect. acknowledgments he study was performed in perm national research polytechnic university with the support of the russian science foundation (project №15-19-00243) references [1] zhang, z., shankar, k., ray, t., morozov, e.v., tahtali, m., vibration-based inverse algorithms for detection of delamination in composites, composite structures, 102 (2013) 226-236. [2] stepinski, t., uhl, t., staszewski, w., advanced structural damage detection: from theory to engineering applications, john wiley & sons, (2013). [3] adams, d.e., health monitoring of structural materials and components, john wiley & sons, (2007). [4] morassi, a., vestroni, f., dynamic methods for damage detection in structures. springer wien new york, (2008). [5] zou, y., tong, l., steven, g.p., vibration-based model-dependent damage (delamination) identification and health monitoring for composite structures – a review. journal of sound and vibration, 230(2) (2000) 357-378. [6] wang, j.t.s., liu, y.y., gibby, j.b., vibrations of split beams. journal of sound and vibration, 84 (1982) 491-502. [7] mujumdar, p.m., suryanarayan, s., flexural vibrations of beams with delaminations, journal of sound and vibration, 125(3) (1988) 441-461. [8] lee, j., free vibration analysis of delaminated composite beams. computers and structures, 74 (2000) 121-129. [9] shen, m.h., j.e. grady. free vibrations of delaminated beams. aiaa journal. 30(5) (1992) 1361-1370. [10] valdes diaz, s.h., soutis, c., delamination detection in composite laminates from variations of their modal characteristics. journal of sound and vibration, 228(1) (1999) 1-9. [11] chuang, k.-c., liou, h.-c., ma, c.-c., investigation of polyvinylidene fluoride(pvdf) films in identifying highfrequency vibration modes of flexible plates. ieee transactions on ultrasonic, ferroelectrics, and frequency control, 61(6) (2014) 1047-1058. [12] yan, w., wang, j., chen, w.q., delamination assessment of a laminated composite beam using distributed piezoelectric sensor/actuator, smart. mater. struct., 20 (2011) 1-14. [13] rout., m., baishya, n., effects of delamination on the vibration characteristics of composite beams, noize and vibration worldwide, 24-29 (2010). [14] muc, a., stawiarski, a., identification of damages in composite multilayered cylindrical panels with delaminations. composite structures. 94 (2012) 1871-1879. 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can be opened with acrobat and adobe reader 5.0 and later.) >> /namespace [ (adobe) (common) (1.0) ] /othernamespaces [ << /asreaderspreads false /cropimagestoframes true /errorcontrol /warnandcontinue /flattenerignorespreadoverrides false /includeguidesgrids false /includenonprinting false /includeslug false /namespace [ (adobe) (indesign) (4.0) ] /omitplacedbitmaps false /omitplacedeps false /omitplacedpdf false /simulateoverprint /legacy >> << /addbleedmarks false /addcolorbars false /addcropmarks false /addpageinfo false /addregmarks false /convertcolors /converttocmyk /destinationprofilename () /destinationprofileselector /documentcmyk /downsample16bitimages true /flattenerpreset << /presetselector /mediumresolution >> /formelements false /generatestructure false /includebookmarks false /includehyperlinks false /includeinteractive false /includelayers false /includeprofiles false /multimediahandling /useobjectsettings /namespace [ (adobe) (creativesuite) (2.0) ] /pdfxoutputintentprofileselector /documentcmyk /preserveediting true /untaggedcmykhandling /leaveuntagged /untaggedrgbhandling /usedocumentprofile /usedocumentbleed false >> ] >> setdistillerparams << /hwresolution [2400 2400] /pagesize [612.000 792.000] >> setpagedevice microsoft word numero_41_art_33.doc t. vojtek et alii, frattura ed integrità strutturale, 41 (2017) 245-251; doi: 10.3221/igf-esis.41.33 245 focused on crack tip fields on the connection between mode ii and mode iii effective thresholds in metals tomáš vojtek, stanislav žák, jaroslav pokluda central european institute of technology (ceitec), brno university of technology, purkyňova 123, 612 00 brno, czech republic tomas.vojtek@ceitec.vutbr.cz, stanislav.zak@ceitec.vutbr.cz, pokluda@fme.vutbr.cz abstract. closure-free long cracks under the remote mode iii loading grow in a more complicated way than those under the remote mode ii. for bcc metals, a coplanar in-plane spreading of tongues driven by the local mode ii loading components at crack-front asperities prevails while twisting of crack-front segments to mode i, often leading to factory-roof morphology, is typical for other materials. in bcc metals, therefore, the formulation of a quantitative relationship connecting effective thresholds in modes ii and iii demands to calculate the local mode ii components of stress intensity factors at typical asperities of a crack front loaded in the remote mode iii. therefore, a numerical model of a serrated crack front was created and the results were compared with experimentally determined ratio of mode ii and iii effective thresholds for the armco iron. although the calculated crack-front roughness needs an experimental verification, the preliminary results indicate that the model can provide a quantitative explanation of the experimentally observed ratio of mode ii and mode iii effective thresholds in bcc metals. keywords. modes ii and iii; effective threshold; micromechanism; finite element method; armco iron. citation: vojtek, t., žák, s., pokluda, j., on the connection between mode ii and mode iii effective thresholds in metals, frattura ed integrità strutturale, 40 (2017) 245-251. received: 28.02.2017 accepted: 03.05.2017 published: 01.07.2017 copyright: © 2017 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. introduction espite the applied (remote) shear-mode ii, iii or ii+iii loading, the fronts of long cracks in metallic materials are, particularly in the small-scale yielding case, always loaded in a local mixed mode i+ii+iii due to their 3d microscopic tortuosity and frictionally induced mode i (e.g. [1], [2]). the contact of asperities in the crack wake (friction stress) induces a rather high crack tip shielding level which, as a rule, makes the extrinsic component of the resistance to the crack growth higher than the intrinsic one [3]. after a certain crack extension, such cracks start to deflect from the plane of the maximum shear stress to reduce the extrinsic resistance (the friction stress) by increasing the mode i loading component [4 – 9]. consequently, the shear-mode cracks usually rather quickly become opening-mode cracks and the investigation of shear-mode crack-growth mechanisms and the related intrinsic resistance is very difficult. however, one can still experimentally uncover the crack growth mechanisms and the intrinsic resistance (effective thresholds) for d t. vojtek et alii, frattura ed integrità strutturale, 41 (2017) 245-251; doi: 10.3221/igf-esis.41.33 246 loading modes ii and iii by minimizing the extrinsic resistance by the preparation of fatigue precracks using cyclic compressive loading and subsequent annealing [10]. such experiments revealed two basic types of closure-free propagation of mode ii and mode iii cracks in metallic materials [3]. first, the shear-mode propagation coplanar with precrack was observed for mode ii loading in the case of bcc metals (e.g. ferritic steel or niobium) [11, 12]. in these materials, the dense set of slip planes in the bcc crystal lattice enabled creation and movement of dislocations in the slip planes lying sufficiently close to the plane of the maximum shear stress and thus possessing a high schmid factor. the crack growth then proceeded along this plane in a nearly coplanar manner. the propagation of mode iii cracks in the bcc metals was also found to be coplanar but the micromechanism revealed to be a spreading of in-plane tongues inclined by only very small angles to the macroscopic mode iii crack front, thus driven by local mode ii loading components [13]. these tongues mostly initiated on asperities (protrusions) of the microscopically tortuous crack fronts. the second (noncoplanar) type of crack growth was observed in materials with a low spatial density of slip systems (fcc) or with microstructural barriers for dislocation movement such as the pearlitic steel. in these materials, the fronts of the mode ii cracks immediately deflected from the shear plane to experience a pure mode i loading whereas the mode iii crack fronts locally twisted to create mode i segments which could lead to a formation of the factory-roof morphology. the growth mechanism in hcp materials represented a transition between the above mentioned two principal types [14, 15]. thus, for the same specimen geometry and the same kind of shear-mode loading, different materials exhibit different crack paths. however, just a combination of local mode i and local mode ii growth mechanisms is relevant for description of behaviour of most metallic materials [3, 12, 13] under all kinds of shear-modes (ii, iii and ii+iii). the classical criteria for mixed-mode crack propagation [16 – 18] do not take these differences into account and do not reflect the physical nature of the process. such criteria cannot be reliably applied to mode ii and mode iii crack growth since there is no local mode iii growth mechanism adequately efficient with respect to that of the mode ii [19, 20]. the cracks grow under local mode i or ii mechanisms instead [15, 21]. to apply the approach of local growth mechanism it is necessary to determine the local sifs for the spatially oriented crack fronts. such analysis was already done for remote mode ii cracks [15]. the results led to a formulation of predictive relationship for the effective mode ii threshold, which was verified by experimentally measured values. in the case of mode iii cracks, however, the analysis is much more difficult due to the complicated mechanisms of local mode ii crack advances or factory roof formation. therefore, no quantitative expression for prediction of the effective mode iii threshold was found hitherto. the present paper addresses the problem of the prediction of effective mode iii threshold for the armco iron as a case study of materials with coplanar shear-mode crack propagation. for such materials, the 2d (in-plane) modelling of the tortuous crack geometry is sufficiently relevant and, therefore, the finite element analysis of the local mode ii component for a crack with serrated (zig-zag) front loaded in the remote mode iii was performed. the results are useful for expression of the ratio k2/kiii of local mode ii sif to the global mode iii sif for a straight crack front, which can be compared with the experimentally measured ratio of effective thresholds δkiieff,th and δkiiieff,th. material and experiments xperimental data were evaluated for the armco iron which is a nearly pure ferrite, as a representative of pure bcc metals. the mode iii fatigue crack propagation experiment was performed using specimens cyclically loaded in torsion. the cylindrical specimens had a circumferential notch with the outer diameter d = 25 mm and the inner diameter d = 12 mm. a detailed description of the experimental arrangement can be found in [10]. the precracks were generated at the notch root by cyclic compressive loading [22 – 24] which resulted in an open precrack and avoided closure effects such as friction and contact of the fracture surfaces. after precracking the specimens were annealed in vacuum in order to eliminate the plastic zone in the vicinity of the crack tip and to avoid creation of an oxide layer. in this way, the effective (closure-free) mode iii crack propagation threshold was measured. after applying n = 105 loading cycles with the cyclic stress ratio r = 0.1 at room temperature the experiments were stopped and the specimens were fractured by cyclic push-pull loading in mode i. the fracture surfaces were observed in the scanning electron microscope (sem), where the crack length was measured. numerical model o evaluate local stress intensity factors along the tortuous precrack front a finite element model [25] created with ansys finite element modeller was adapted. because of the applied loading and the geometry of the specimen a full 3d model had to be used for the torsion specimen and one symmetry plane was used for the shear specimen. e t t. vojtek et alii, frattura ed integrità strutturale, 41 (2017) 245-251; doi: 10.3221/igf-esis.41.33 247 also, a submodelling procedure was employed to minimize the computational time. the first stage model (global model) described deformation of whole specimen with smooth precrack front (no tortuosity) under respective loads. the second stage model (submodel) contained the tortuous precrack front. its geometry was parameterized and defined by the main dimensions of the tortuosity (tooth height and length). a zig-zag shape of the precrack front was created by alternating key-points between maximal (rmax) and minimal (rmin) precrack front radii and by connecting these points to create the serrated crack front (see fig. 1). a scripted code ensured that the number of modelled teeth was an integer (to avoid discontinuities at the crack front). figure 1: scheme of the precrack emanating from the notch and possessing a serrated front. geometrical model was discretized by a very fine mesh of finite elements. ansys quadratic elements (solid186) were used and the rotational symmetry was employed to create a mostly uniform mesh. the model was adjusted to have 10 elements in the radial direction from the notch tip to the precrack front and 4 elements along each half-tooth at the precrack front. figure 2: submodel (finite element mesh). this arrangement resulted in 9 nodes along each half-tooth. to evaluate the sifs the ansys code used a domain integration around each evaluated point at the precrack front to compute the so-called interaction integral. then the local sifs were calculated from this integral [26] with respect to local coordinate systems. this calculation was performed for all nodes along the precrack front which provided 17 values of local sifs (including one value for the conjoint node) along each precrack tooth. results and discussion ocal sifs k1, k2 and k3 were evaluated for the remote mode iii loaded crack with two crack geometries [27]. the first one was a smooth circular crack front and the second one was the serrated front (roughness asperities) characterized by the angle α. the inclination of the crack front segments with respect to the remote shear stress resulted in a non-zero local mode ii component. significance of this component was assessed by the ratio of the local mode ii sif k2 and the remote mode iii sif kiii determined for crack without ledges (asperities). this ratio was denoted rcal and plotted in fig. 4 for one half of l t. vojtek et alii, frattura ed integrità strutturale, 41 (2017) 245-251; doi: 10.3221/igf-esis.41.33 248 the asperity (see fig. 3). the points at which the values were calculated are denoted by integers from 1 to 9 and they define the horizontal axis of fig. 4. only the values for points 2 to 8 are shown, since the extreme points 1 and 9 represent a discontinuity of the crack front and the corresponding sifs are not well defined. ratios rcal = k2/kiii were calculated as functions of different angles α in all nodes along the half tooth and plotted in fig. 4. in this figure each data line corresponds to one angle α. figure 3: the detail of roughness asperities characterized by the angle α. 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1 1 2 3 4 5 6 7 8 9 ra ti o   r ca l =  k 2 /k ii i evaluated points α = 41.65° α = 38.32° α = 34.65° α = 30.61° α = 26.20° α = 21.42° α = 17.19° α = 11.80° α = 6.20° α = 3.35° figure 4: results of rcal for different asperity angles α in the range from 3.35° to 41.65° in points showed in fig. 3. although the ratio rcal is changing along the asperity, a useful dependence of the ratio rcal on the asperity angle α can be still constructed from the computed curves in fig. 4. indeed, two special values of rcal can be selected: the average value rcal,av (calculated from points 2 to 8) and the maximum value rcal,max (at the point 3) that is probably relevant for the first extension of local tongues at the threshold. both rcal,av and rcal,max as functions of α are plotted in fig. 5. the sif range δkiii measured at the mode iii threshold under the presumption of a smooth circumferential crack front is equal to δkiiieff,th. simultaneously, the local mode ii component of the sif range δk2 at the asperities (initiation sites of mode ii tongues) should be equal to the measured δkiieff,th. this means that the following formula must hold at the mode iii threshold:        iieff,th2 2 cal exp iii iii iiieff,th kk k r r k k k (1) the agreement between theory and experiment could be tested by eq. (1) since, for the armco iron [10], the experimental ratio rexp was obtained as      1/2 iieff,th exp 1/2 iiieff,th 1.5 mpa m 0.58 2.6 mpa m k r k (2) the value rexp = 0.58 was plotted in fig. 5 as the horizontal dashed line and its intersection with the relevant curve rcal,max vs. α indicates that the characteristic angle α of the asperities at the precrack fronts in the armco iron specimens should α points in fig. 4 shear stress maximal k2 1 2 8 9 3 precrack t. vojtek et alii, frattura ed integrità strutturale, 41 (2017) 245-251; doi: 10.3221/igf-esis.41.33 249 be of 23°. this value must be, of course, verified by the measured linear roughness of these precrack fronts. nevertheless, it seems to be plausible and sufficiently small to allow the local mode ii mechanism operate at real micro-tortuous crack fronts without sharp protrusions. 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1 0 5 10 15 20 25 30 35 40 45 ra ti o    r c a l =  k 2 /k ii i asperity angle  α [°] maximum average experimental δkiieff,th/δkiiieff,th figure 5: dependences of rcal,max and rcal,av on the asperity angle α calculated for the respective points of the maximal value (stress concentration at point 3 in fig. 3) and of the averaged value of the ratio rcal along the half tooth (points 2 to 8). the horizontal dashed line represents the experimental ratio of effective thresholds δkiieff,th / δkiiieff,th. the model of local mode i/ii crack growth was already able to explain the existence of crystallographic facets oriented nearly parallel with the shear stress direction. it was also used to propose the formula for prediction of the intrinsic mode ii threshold [15], which was found in a good agreement with experiments for many metallic materials. this study represents an important further step on the way to achieve an appropriate quantitative description of the effective mode iii thresholds too. the results obtained by relatively complicated numerical calculations made to determine the local mode ii sifs of the serrated crack front seem to be very promising in terms of finding such a relationship. conclusion his study represents an important step on the way to quantitatively describe the effective mode iii thresholds in metallic materials with the bcc crystal lattice. in these materials, the micromechanism of propagation of mode iii cracks was found to be a coplanar (in-plane) spreading of tongues driven by the local mode ii loading component at asperities of microtortuous crack fronts. since the in-plane 2d modelling of the tortuous crack geometry is sufficiently relevant here, the finite element analysis of the local mode ii component for a precrack with serrated front loaded in the remote mode iii was performed. comparison of the calculated results with experimentally determined ratio of mode ii and iii effective thresholds revealed that, for the armco iron as a case study, the characteristic angle α of the asperities (saw teeth) at the precrack front should be of 23°. although this value must be verified by the measured linear roughness of the precrack fronts in the armco specimens, it seems to be plausible and sufficiently small to allow the local mode ii mechanism operate at real micro-tortuous crack fronts without any sharp protrusions. thus, the result achieved is promising in terms of finding a physically justified formula for mode iii effective thresholds in metallic materials with bcc lattice. acknowledgements he authors acknowledge the financial support of this work by the czech science foundation (ga cr) in the frame of the projects no. 17-15716y and no. 17-18566s, and by the ministry of education, youth and sports of the czech republic under the project ceitec 2020 (lq1601). t t t. vojtek et alii, frattura ed integrità strutturale, 41 (2017) 245-251; doi: 10.3221/igf-esis.41.33 250 references [1] pokluda, j., šandera, p., micromechanisms of fracture and fatigue. in a multiscale context, london, uk: springer; (2010). [2] gross, t.s., mendelsohn, d., mode i stress intensity factors induced by fracture surface roughness under pure mode iii loading: application to the effect of loading modes on stress corrosion crack growth, metal. transactions, 20a (1989) 1989–1999. doi: 10.1007/bf02650285. [3] pokluda, j., pippan, r., vojtek, t., hohenwarter, a., near-threshold behaviour of shear-mode fatigue cracks in metallic materials, fatigue fract. eng. mater. struct., 37 (2014) 232–254. doi: 10.1111/ffe.12131. [4] pinna, c., doquet, v., the preferred fatigue crack propagation mode in a m250 maraging steel loaded in shear, fatigue fract. eng. mater. struct., 22 (1999) 173–183. doi: 10.1046/j.1460-2695.1999.00161.x. [5] doquet, v., pommier, s., fatigue crack growth under non-proportional mixed-mode loading in ferritic-pearlitic steel, fatigue fract. eng. mater. struct., 27 (2004) 1051–1060. doi: 10.1111/j.1460-2695.2004.00817.x. [6] doquet, v., bertolino, g., local approach to fatigue cracks bifurcation, int. j. fract., 30 (2008) 942–950. doi: j.ijfatigue.2007.06.001. [7] doquet, v., abadi, m., bui, q.h., pons, a., influence of the loading path on fatigue crack growth under mixed-mode loading, int. j. fract., 159 (2009) 219–232. doi: 10.1007/s10704-009-9396-6. [8] murakami, y., metal fatigue: effects of small defects and nonmetallic inclusions, amsterdam – tokyo, elsevier, (2002). [9] gates, n., fatemi, a., friction and roughness induced closure effects on shear-mode crack growth and branching mechanisms, int. j. fatigue, 92 (2016) 442–458. doi: 10.1016/j.ijfatigue.2016.01.023. [10] vojtek, t., pippan, r., hohenwarter, a., holáň, l., pokluda, j., near-threshold propagation of mode ii and mode iii fatigue cracks in ferrite and austenite, acta mater., 61 (2013) 4625-4635. doi: 10.1016/j.actamat.2013.04.033. [11] vojtek, t., pokluda, j., hohenwarter, a., pippan, r., three-dimensional morphology of fracture surfaces generated by modes ii and iii fatigue loading in ferrite and austenite, eng. fract. mech., 108 (2013), 285–293. doi: 10.1016/j.engfracmech.2013.02.022. [12] vojtek, t., pokluda, j., hohenwarter, a., pippan, r., progress in understanding of intrinsic resistance to shear-mode fatigue crack growth in metallic materials, int. j. fatigue, 89 (2016) 36–42. doi: 10.1016/j.ijfatigue.2016.01.009. [13] vojtek, t., hohenwarter, a., pippan, r., pokluda, j, experimental evidence of a common local mode ii growth mechanism of fatigue cracks loaded in modes ii, iii and ii + iii in niobium and titanium, int. j. fatigue, 92 (2016) 470–477. doi: 10.1016/j.ijfatigue.2016.02.042. [14] vojtek, t., pippan, r., hohenwarter, a., pokluda, j., prediction of effective mode ii fatigue crack growth threshold for metallic materials, eng. fract. mech., 174 (2017), 117–126. doi: 10.1016/j.engfracmech.2016.11.024. [15] vojtek, t., pokluda, j., experimental investigation of modes ii and iii fatigue crack growth in unalloyed titanium, key engineering materials, 592-593 (2014) 797–800. doi: 10.4028/www.scientific.net/kem.592-593.797. [16] sih, g.c., some basic problems in fracture mechanics and new concepts, eng. fract. mech., 5 (1973) 365–377. [17] magill, m.a., an analysis of sustained mixed mode fatigue crack growth, eng. fract. mech., 56 (1997) 9–24. doi: 10.1016/s0013-7944(96)00106-3. [18] richard, h.a., schramm, b., schirmeisen, n.-h., cracks on mixed mode loading – theories, experiments, simulations, int. j. fatigue, 62 (2014) 93–103. doi:10.1016/j.ijfatigue.2013.06.019. [19] pokluda, j., pippan, r., can a pure mode iii fatigue loading contribute to crack propagation in metallic materials?, fatigue fract. eng. mater. struct., 28 (2005) 179–185. doi: 10.1111/j.1460-2695.2004.00843.x. [20] doquet, v., bui, q.h., bertolino, g., merhy, e., alves, l., 3d shear-mode fatigue crack growth in maraging steel and ti-6al-4v, int. j. fract, 165 (2010) 61–76. doi: 10.1007/s10704-010-9504-7. [21] martins, r.f., ferreira, l., reis, l., chambel, p., fatigue crack growth under cyclic torsional loading, theor. appl. fract. mech., 85a (2016) 56–66. doi: 10.1016/j.tafmec.2016.08.016. [22] suresh, s., crack initiation in cyclic compression and its applications, eng. fract. mech., 21 (1985) 453–463. doi: 10.1016/s0013-7944(85)80038-2. [23] pippan, r., the growth of short cracks under cyclic compression, fatigue fract. eng. mater. struct., 9 (1987) 319– 328. doi: 10.1111/j.1460-2695.1987.tb00459.x. [24] newman, j.c., yamada, y., compression precracking methods to generate near-threshold fatigue-crack-growth-rate data, int. j. fatigue, 32 (2010) 879–885. doi: 10.1016/j.ijfatigue.2009.02.030. t. vojtek et alii, frattura ed integrità strutturale, 41 (2017) 245-251; doi: 10.3221/igf-esis.41.33 251 [25] žák, s., horníková, j., šandera, p., pokluda, j., verification of linear dependence of plastic zone size on j-integral for mixed-mode loading, appl. mech. mater.,. 751 (2015) 15–20. doi: 10.4028/www.scientific.net/amm.751.15. [26] ansys r16.2 help (manual), ansys inc., (2015). 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can be opened with acrobat and adobe reader 5.0 and later.) >> /namespace [ (adobe) (common) (1.0) ] /othernamespaces [ << /asreaderspreads false /cropimagestoframes true /errorcontrol /warnandcontinue /flattenerignorespreadoverrides false /includeguidesgrids false /includenonprinting false /includeslug false /namespace [ (adobe) (indesign) (4.0) ] /omitplacedbitmaps false /omitplacedeps false /omitplacedpdf false /simulateoverprint /legacy >> << /addbleedmarks false /addcolorbars false /addcropmarks false /addpageinfo false /addregmarks false /convertcolors /converttocmyk /destinationprofilename () /destinationprofileselector /documentcmyk /downsample16bitimages true /flattenerpreset << /presetselector /mediumresolution >> /formelements false /generatestructure false /includebookmarks false /includehyperlinks false /includeinteractive false /includelayers false /includeprofiles false /multimediahandling /useobjectsettings /namespace [ (adobe) (creativesuite) (2.0) ] /pdfxoutputintentprofileselector /documentcmyk /preserveediting true /untaggedcmykhandling /leaveuntagged /untaggedrgbhandling /usedocumentprofile /usedocumentbleed false >> ] >> setdistillerparams << /hwresolution [2400 2400] /pagesize [612.000 792.000] >> setpagedevice microsoft word numero 24 articolo 11 andrey e. buzyurkin et alii, frattura ed integrità strutturale, 24 (2013) 102-111; doi: 10.3221/igf-esis.24.11 102 special issue: russian fracture mechanics school study of the conditions of fracture at explosive compaction of powders andrey e. buzyurkin, evgeny i. kraus khristianovich institute of theoretical and applied mechanics of siberian branch of ras, 4/1 instituskaya str., novosibirsk, 630090, russia buzjura@itam.nsc.ru, kraus@itam.nsc.ru yaroslav l. lukyanov lavrentyev institute of hydrodynamics of siberian branch of ras, 15 lavrentyev pr., novosibirsk, 630090, russia lukyanov@hydro.nsc.ru abstract. joint theoretical and experimental investigations have allowed to realize an approach with use of mathematical and physical modeling of processes of a shock wave loading of powder materials. in order to gain a better insight into the effect of loading conditions and, in particular, to study the effect of detonation velocity, explosive thickness, and explosion pressure on the properties of the final sample, we numerically solved the problem about powder compaction in the axisymmetric case. the performed analysis shows that an increase in the decay time of the pressure applied to the sample due to an increase of the explosive thickness or the external loading causes no shrinkage of the destructed region at a fixed propagation velocity of the detonation wave. simultaneously, a decrease in the propagation velocity of the detonation wave results in an appreciable shrinkage of this region. keywords. shock waves; fracture; powder. introduction ethods of explosive loading of powder materials in conservation ampoules are applied in order to obtain new materials including composite ones with the unique physical and mechanical properties. in addition, these methods can be used to study phase transitions occurring in materials at high pressures and temperatures taking place behind shock waves, as well as for the synthesis of metastable phases. in recent decades, significant development has been achieved in such a scientific and technical branch of materials science as powder metallurgy. this term is currently understood a whole complex of problems connected with the design of materials and products from metal and nonmetal powders. interest in these problems is quite understandable since the opportunity to create new classes of materials with unique and controllable properties which can not be obtained by ordinary metallurgy methods has arisen. a special place in the powder metallurgy is occupied by explosive compaction of powder materials. it is easy to explain the strong interest in the explosive compaction. it consists in the fact that virtually all the methods of composite materials' production from powder mixtures lead to a change in initial material properties due to high temperatures and relatively long duration of the process. m http://dx.medra.org/10.3221/igf-esis.24.11&auth=true http://www.gruppofrattura.it andrey e. buzyurkin et alii, frattura ed integrità strutturale, 24 (2013) 102-111; doi: 10.3221/igf-esis.24.11 103 since the powders being in the form of granules, fibers, needles and ribbons, possessing the necessary properties in the initial state, can not be used directly to produce semi-finished products or components, the methods of compaction of these materials perform two tasks at once. on the one hand the compaction changes the shape and size of the powders, and on the other hand it produces the material itself. from this point of view, the short exposure to high temperatures and pressures during explosive compaction allows, in general, to keep the original structure and properties of the components. at the same time, varying of the intensity and time exposure to high pressure and temperature in shock compression allows to modify, if necessary, the structure and properties of the compacts a controlled manner. the loading of the powder materials in the conservation ampoules can be carried out by means of both plane and oblique shock waves. each of the methods has its pros and cons. the explosive loading by oblique shock wave is characterized by high values of shear strain, in comparison with the plane impact, which leads to stronger bonds between the compacted particles. in addition, this scheme allows to obtain the compacts not only in the form of plates, but pipes, rods, cones, etc as well. one can also get the compacts of large sizes. the loading by plane shock waves allow to vary the pressure and temperature behind the shock front in a wider range and to reach much higher values of these parameters. at the same time, the method is more material-consuming and has limitations on the size of the loaded samples. investigation into the interaction between oblique shock waves in porous materials and powders is a topical problem in optimization of loading conditions for obtaining, from a given sample, a compacted material with spatially uniform physical and mechanical properties. in compacting a powder in the cylindrical scheme, an irregular interaction between shock waves occurs. the compacted powder displays substantial non-uniformity in particle displacements, resulting in inhomogeneity of powder characteristics and, in some cases, even in material failure. in compacting porous material and powders, the strong bonding between particles is achieved through the combined pressure-shear loading. during the compacting, a substantial energy is released at the interfaces between powder particles, resulting in surface cleaning and material melting in narrow interfacial regions. as a result, pore collapsing, giving rise to strong bonding between particles, occurs. below, this phenomenon is termed compaction. v.f. nesterenko proposed the following criterion for the formation of a strong compact: > 2 vp h (1) where, according to [1], 3v sh y . following [1], we can write criterion (1), deduced from experimental data, as > 6 sp y (2) in turn, r. prummer [2] uses the following condition for obtaining a uniform, in its physical properties, cylindrical compact with no mach reflection induced singularities at its center:  vp h , where p is the detonation pressure. comparing condition (1) with the condition  vp h , nesterenko [1] arrives at a conclusion that it is impossible in principle, without a central rod, to obtain a spatially uniform compact in the cylindrical loading scheme since the shock pressure required for obtaining a dense compact (2) will always lead to mach reflection at the center of the sample. another important problem is preservation of the finish compact after loading. with the arrival of unloading waves, there arises a tensile stress that results in partial or complete destruction of the sample. we assume that the sample undergoes mechanical failure if the maximum tensile stress max reaches a certain critical value * . in line with the adopted hypothesis, the following condition for the sample failure should be assumed: *>max  (3) where max is the highest stress among the principal stresses for the strained state under study and * is the critical stress. in the present work, the critical stress * is estimated as * 1= (2 / 3) (1/ )sy ln m where 1m is the residual porosity. taking the finish-compact density to equal 99%, we obtain 1 = 0.01m and * 3  sy . for the principal stresses, we have: 2 21 1 = ( ) 4 2 2 xx yy xx yy xy           2 2 2 1 = ( ) 4 2 2 xx yy xx yy xy           http://dx.medra.org/10.3221/igf-esis.24.11&auth=true http://www.gruppofrattura.it andrey e. buzyurkin et alii, frattura ed integrità strutturale, 24 (2013) 102-111; doi: 10.3221/igf-esis.24.11 104 3 =   experimental study of the compact structure xperiments on the explosive compaction have been conducted by a cylindrical scheme without a central rod. the powder has consisted of particles of nearly spherical shape and with size of 145-310 µm (fig. 1). bulk density of the powder has been in all experiments for copper equal to -5.0 ± 0.05 g/cm3, for aluminum -1.4 g/cm3. the experimental arrangement is shown in fig. 2. figure1: initial cooper powder. figure 2: scheme of explosive compaction: 1 – detonator, 2 – explosive charge, 3 – steel plugs, 4 – container (steel tube 12 mm in diameter), 5 – copper powder, 6 – momentum trap. explosive compaction occurs under the action of the detonation products of the contact explosive charges. for varying of the detonation velocity the charges were made from ammonite, rdx and mixture of ammonite with rdx in different proportions. the detonation velocity (d) was measured by electrical contact technique, and ranged from 3.19 to 5.26 km/s. container wall was thin compared to the thickness of explosive layer and diameter of the powder sample. structure of compacts cross-sections were studied using an optical microscope neophot. in fig. 3 the structures of the cross sections near the axis of the samples is shown for three different values of detonation velocity (3.19, 3.95 and 5.26 km/s) and at the same thickness of explosive charge – 5 mm. (a) (b) (c) figure 3: the structures of the cross sections of the samples for three different values of d and at the same thickness of explosive charge – 5 mm: a) d=3.19 km/s; b) d=3.95 km/s; c) d=5.26 km/s. it can be noted that with the increase of the detonation velocity, and hence the shock pressure, a compacts structures change. at minimum value of d compact is homogeneous. then, in the center due to the irregular reflection of the converging shock wave a zone of melt appear. and at d=5.26 km/s in the compact the radial cracks arise. a further increase in d can lead to the destruction of the container. to investigate the effect of the thickness of the explosive charge on the crack formation, an experiment was conducted in which the thickness of the charge was increased to 10 mm, and the detonation velocity was 5.17 km/s. the structure of this compact is shown in fig. 4. e http://dx.medra.org/10.3221/igf-esis.24.11&auth=true http://www.gruppofrattura.it andrey e. buzyurkin et alii, frattura ed integrità strutturale, 24 (2013) 102-111; doi: 10.3221/igf-esis.24.11 105 figure 4: the structures of the cross section of the sample loaded at d=5.12 km/s and thickness of the explosive charge 10 mm. comparing structures from fig. 3а and fig. 4, it is visible, that in spite of approximately identical detonation regimes, in a compact in fig. 4 cracks are absent. numerical simulation of the explosive loading n order to gain a better insight into the effect of loading conditions and, in particular, to study the effect of detonation velocity, explosive thickness, and explosion pressure on the properties of the final sample, we numerically solved the problem about powder compaction in the axisymmetric case using conditions of above mentioned experiments. the problem statement according to experimental scheme is clear from fig. 5. d p powder explosive y x figure 5: the problem statement. we solved the full system of equations governing the deformation of a porous elastic-plastic material [3]. the action of the explosion products on the sample was modeled with a pressure applied to the upper border of the sample. the pressure was calculated by the approximation formula for the pressure upon unrestricted dispersion of detonation products [4]: 1 1 3( 1) ( ) = exp( ( / ) / ), = 4( 1) e e h e p t p t x d t t d        here e is the explosive thickness and e is the adiabatic exponent of the detonation products. since the problem is symmetric, a half of the experimental assembly is considered. the symmetry axis is the axis of the container with the powder. on the symmetry axis rigid wall boundary conditions are set. the right boundary is considered to be free of stress, and at the left boundary condition of a rigid wall is put. computation of the contact boundaries is performed by using a symmetric algorithm [5]. the calculations are carried out by the m.l. wilkins scheme [6]. the shock wave propagates from left to right. geometric dimensions and values of the physical parameters correspond to the experimental data mentioned above. in this paper a few-parametric equation of state is applied [7], which has allowed to simulate shock-wave processes with a minimal number of physical parameters as the initial data. i http://dx.medra.org/10.3221/igf-esis.24.11&auth=true http://www.gruppofrattura.it andrey e. buzyurkin et alii, frattura ed integrità strutturale, 24 (2013) 102-111; doi: 10.3221/igf-esis.24.11 106 2/3 2 , , 0 0 2 32 , , 0 0 1 2 1 3 x v l v e l v l v ex v e e c t c t v c t c tde v p dv v v v                        or, in terms of free energy 2/3 2 , , 0 0 ( ) 1 ( , ) ( ) ln 2 x v l v e v v f v t e v c t c t t v              where xp and xe pressure and specific internal energy of the zero isotherm, t temperature, , ,v v l v ec c c  heat capacity at constant volume, ( )v the debye temperature. the equation of state presented here is based on the dependence of the gruneisen coefficient γ on the volume [8] 0( ) 2 / 3 2 / (1 / )v av v    ,01 2 / ( 2 ) 2 /s t sa p k     where 0 /s s vk v c  , sk adiabatic bulk modulus,  -oefficient of thermal expansion, ,0tp heat pressure under the normal conditions. to find the elastic curves a generalized model describing the gruneisen coefficient  v is used:       2 2 /3 2 2 /3 /2 3 2 / t x t x d p v dvt v v d p v dv               at 0t  the equation corresponds to the landau and slater theory [8, 9], at 1t  it corresponds to the dugdale and macdonald hypothesis [10], and at 2t  to the theory of free volume [11]. in the physics of shock waves a method of calculating the pressure at the hugoniot adiabat of the porous material by pressure on the “reference” hugoniot adiabat of monolithic material [12] is known:        0 , 00 1 0.5 1 1 0.5 1 h h p p v v v p v v v        here v is the specific volume of the hugoniot adiabats, 0v and 00v are specific volumes of monolithic and porous materials , respectively, at the normal initial conditions. calculation results and discussion ig. 6, a and b shows the pressure isolines for the cases of planar and cylindrical symmetries with identical loading conditions. it is seen from fig. 6 that, in the planar statement of the problem, a regular reflection of the incident shock wave takes place. in the case of the cylindrical loading scheme, the incident shock waves bends as it approaches the cylinder axis, and, under the same loading conditions, an irregular reflection occurs. fig. 7a shows the pressure profile near the symmetry axis for the cases of planar and cylindrical statements (solid and dashed curves, respectively). an appreciable pressure rise near the symmetry axis is observed in the case of cylindrical configuration compared to the planar problem due to the divergence of the shock wave to the axis. fig. 7b shows the profile of the longitudinal velocity xu across the sample under loading behind the shock front. the solid and dashed lines show the data for the planar and axisymmetric problem statements, respectively. it is clearly seen that the velocity in the cylindrical case is much greater than in the planar variant. as stated above, an important problem is preservation of finish compact, i.e., preventing its mechanical failure and obtaining a sample with uniform properties. using criterion (3), we can find the interface between the solid and distructed materials. the regions of the compacted and porous materials for various explosive thicknesses for the external pressures f http://dx.medra.org/10.3221/igf-esis.24.11&auth=true http://www.gruppofrattura.it andrey e. buzyurkin et alii, frattura ed integrità strutturale, 24 (2013) 102-111; doi: 10.3221/igf-esis.24.11 107 = 0.05p mbar and = 0.075p mbar are shown in fig. 8, a and b, respectively. in these calculations, the detonation velocity was = 5d km/s. the solid, dashed, and dot-and-dash lines outline the destruction regions for the explosive thicknesses = 2e cm, = 3e cm, and = 5e cm, respectively. region 1 is the compacted region, and region 2, the destruction region. an analysis of these graphs shows that an increase in the explosive thickness and, hence, an increase of the loading decay time does not cause any substantial shrinkage of the destruction region. x, cm y , cm 12 13 14 0..5 1 x, cm y ,c m 10 11 12 13 14 15 0 0..5 1 1..5 а) b) 155 10 a) b) p, mbar x, cm ux, cm/msec 0.35 0.25 0.15 0.05 0.05 0.0 0.2 0.8 0.6 0.4 0.140.06 0.08 0.120.10.040.02 y, cm figure 6: pressure isolines: a) planar geometry; b) cylindrical configuration. figure 7: pressure profile (a) and longitudinal-velocity profile ( )xu y (b) for the planar and cylindrical geometries (solid and dashed lines, respectively). x, cm y , cm 9 1 2 x, cm y ,c m 9 1 2 2 1 2 1 а) b) 1 3 5 7 1 3 5 7 figure 8: compacted and destruction regions for various explosive thicknesses under external pressures = 0.05p mbar (a) and = 0.075p mbar (b). the detonation velocity is = 5d km/s. the solid, dashed, and dot-and-dash lines refer to the explosive thicknesses = 2e cm, = 3e cm, and = 5e cm, respectively. the compacted and destruction regions are indicated by 1 and 2. it should be emphasized that this conclusion is valid for criterion (3). in derivation of (3), it was implicitly assumed that the interfacial melted zones are narrow, and the material in these zone rapidly solidifies as the particles in the bulk of the material undergo cooling. if this condition does not hold, then there can be a situation in which, by the moment of arrival of the unloading wave, the material in the interfacial zones still remains melted, which will prevent compaction. in this case, the dimensions of the destruction region will be dependent on the loading decay time and on the explosive thickness. the explosive thickness should be large enough to prevent shock wave damping in the powder and to enable complete pore collapsing in the sample. fig. 9, a and b shows the density isolines for the explosive thickness = 0.5e cm and the external pressure = 0.05p mbar. parts a and b of fig. 9 depict the data for the axisymmetric and planar problem statements. damping of the incident shock wave is evident from the figure. this results in incomplete powder compaction; the latter is clear from fig. 10, which shows the distribution of porosity 1m across the sample. the solid and dashed lines in this figure correspond to the planar case and to the cylindrical configuration, respectively. an analysis of http://dx.medra.org/10.3221/igf-esis.24.11&auth=true http://www.gruppofrattura.it andrey e. buzyurkin et alii, frattura ed integrità strutturale, 24 (2013) 102-111; doi: 10.3221/igf-esis.24.11 108 these graphs shows that, in the axisymmetric case, due to the wave divergence to the axis, the pores undergo collapsing in a larger volume than in the planar variant. x, cm y , cm 0. 5 1 1. 5 x, cm y ,c m 2 0. 5 1 1. 5 а) b) 864 2 864 y , c m 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 0.20.1 porosity figure 9: density isolines for = 0.5e cm: а) cylindrical configuration; b) planar statement. figure 10: porosity 1m for = 0.5e cm: solid line is planar statement; dashed line is cylindrical configuration. a twofold increase in the explosive thickness makes the decay of the incidence shock wave less intensive. the density isolines for the explosive thickness = 1e cm and the external pressure = 0.05p mbar are shown in fig. 11, a and b. parts a and b of this figure shows the calculation data for the axisymmetric and planar statements, respectively. it is clearly seen that in the case of cylindrical symmetry the shock wave bends near the axis, giving rise to an irregular reflection; in the planar configuration, a regular interaction occurs. fig. 12, which depicts the distribution of porosity 1m across the sample compacted in the cylindrical geometry (the dashed line in fig. 12), is indicative of complete collapsing of pores over the entire thickness of the sample. in the planar case (see the dashed line in fig. 12), the complete collapsing of pores is observed approximately over half the thickness of the sample, and the porosity near the symmetry axis is close to the initial one, 01m . x, cm y , cm 0.5 1 1.5 x, cm y, c m 2 0.5 1 1.5 а) b) 864 2 864 y , c m 0.2 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 0.10 porosity figure 11: density isolines for = 1e cm: a) cylindrical configuration; b) planar configuration. figure 12: porosity 1m for = 1e cm: solid line planar statement; dashed line cylindrical configuration. the density isolines for the explosive thickness = 2e cm are shown in fig. 13, a and b. the external pressure was taken to be = 0.05p mbar. parts a and b of this figure show the calculation data for the axisymmetric and planar statements. in the cylindrical case (see fig. 13, a), an irregular reflection is clearly observed, whereas in the planar case (see fig. 13, b) the http://dx.medra.org/10.3221/igf-esis.24.11&auth=true http://www.gruppofrattura.it andrey e. buzyurkin et alii, frattura ed integrità strutturale, 24 (2013) 102-111; doi: 10.3221/igf-esis.24.11 109 incident shock wave interacts with the rigid wall in the regular manner. in both cases, all pores in the sample collapse completely. further calculations were carried out for the explosive thicknesses = 2e cm, = 3e cm and = 5e cm. fig. 14, a and b illustrates the effect of applied pressure on the thickness of the destruction region. in the calculations, the external pressures were = 0.05p mbar and = 0.075p mbar, respectively, and the detonation velocity in both cases was = 7d km/s. the solid and dashed lines show the data for the explosive thicknesses = 3e cm and = 5e cm. regions 1 and 2 are the compacted and destruction regions. as is seen from the figure, an increase in the external load causes no shrinkage of the destruction zone. thus, it can be concluded that an increase in the decay time of the pressure applied to the sample resulting from an increase in the explosive thickness or in the value of the external load does not make the destruction zone shrink at a fixed propagation velocity of the detonation wave. x, cm y , cm 0.5 1 1.5 x, cm y , c m 2 0.5 1 1.5 а) b) 864 2 864 x, cm y , cm 1 2 x, cm y , cm 1 2 2 1 b) 2 1 а) 1 9753 1 9753 figure 13: density isolines for = 2e cm: a) cylindrical configuration; b) planar statement. figure 14: compacted and destructed regions for two values of external pressure, = 0.05p mbar (a) and = 0.075p mbar (b). the detonation velocity is = 7d km/s. the solid and dashed lines show the calculation data for the explosive thicknesses = 3e cm and = 5e cm. as shown by above mentioned experiments an increase of the velocity of the detonation wave results in a considerable shrinkage of the destruction region. fig. 15 show the compacted (1) and destructed (2) regions in the sample for the detonation velocities = 3d , 5, 7 km/s at a fixed explosive thickness = 5e cm and at a fixed external pressure = 0.05p mbar. the solid, dashed, and dot-and-dash lines show the calculation data for the detonation velocities = 3d km/s, = 5d km/s, and = 7d km/s. x, cm y , c m 1 2 2 1 1 9753 figure 15: compacted (1) and destructed (2) regions for three values of the detonation velocity. the solid, dashed, and dot-and-dash lines refer to = 3d km/s, = 5d km/s, and = 7d km/s. the isolines of pressure for the indicated loading parameters are shown in fig. 16, a-c. it is seen from the graphs that, as the shock-wave propagation velocity increases, the angle of incidence decreases and the reflected shock causes material destruction (see fig. 16, b and c). as the velocity of the detonation wave increases, the angle of incidence of the incident shock wave increases and, as it is seen from fig. 16, a, at the velocity = 3d km/s the incident shock wave is close to the normal shock and the amplitude of the reflection wave is almost zero. since in the case of cylindrical symmetry no regular reflection occurs, the final sample turns out to be inhomogeneous. fig. 17 shows the distribution of the longitudinal velocity xu (fig. 17, a) and temperature t (fig. 16, b) across the sample http://dx.medra.org/10.3221/igf-esis.24.11&auth=true http://www.gruppofrattura.it andrey e. buzyurkin et alii, frattura ed integrità strutturale, 24 (2013) 102-111; doi: 10.3221/igf-esis.24.11 110 in the compacted region for the detonation velocity = 5d km/s. an appreciable non-uniformity in the distribution of parameters is evident from the graphs. near the axis, both the velocity and temperature are greater than in the region some distance away from it. x, cm y, cm 8 0 0.5 x, cm y, cm 0.5 x, cm y, cm 2 0.5 а) b) c) 64 82 64 82 64 figure 16: pressure isolines: a) detonation velocity = 7d km/s; b) detonation velocity = 5d km/s; c) detonation velocity = 3d km/s. ux, cm/msec y, cm t, k 0.2 0.10.05 0.8 0.6 0.4 0.15 0.2 y, cm 0.2 0.8 0.6 0.4 30050 150 200 250 figure 17: predicted distributions of the longitudinal velocity xu (a) and temperature t (b) across the compacted region of the sample for the detonation velocity = 5d km/s. parts a and b of fig. 18 show the distributions of the longitudinal velocity xu and temperature t across the compacted region of the sample predicted for the detonation velocity = 3d km/s. here, under identical loading parameters, the final sample is quire homogeneous. as a result, it becomes possible to obtain spatially uniform compacted samples. the necessary condition for this is sufficiently low detonation velocity, equal, for the aluminum powder, to 0.3 cm/ m sec. here, on the one hand, compaction condition (1) should be fulfilled and, on the other, the uniformity of loading parameters across the sample should be ensured. thus, the compaction of powders with low detonation velocities results in a considerable shrinkage of destruction zones in finish samples and in spatial uniformity of material parameters in their compacted parts. the performed analysis shows that an increase in the decay time of the pressure applied to the sample due to an increase of the explosive thickness or the external loading causes no shrinkage of the destructed region at a fixed propagation velocity of the detonation wave. simultaneously, a decrease in the propagation velocity of the detonation wave results in an appreciable shrinkage of this region. http://dx.medra.org/10.3221/igf-esis.24.11&auth=true http://www.gruppofrattura.it andrey e. buzyurkin et alii, frattura ed integrità strutturale, 24 (2013) 102-111; doi: 10.3221/igf-esis.24.11 111 ux, cm/msec t, k 0.2 0.8 0.6 0.4 0.2 0.8 0.6 0.4 300100 200-0.25 0.250 0.5 y, cm y, cm figure 18: distributions of the longitudinal velocity xu (a) and temperature t (b) across the compacted region of the sample for the detonation velocity = 3d km/s. conclusions oint theoretical and experimental studies have allowed to implement an approach that uses mathematical and physical simulation of shock-wave loading of powdered materials. a numerical simulation of shock wave propagation and deformation of the experimental assembly has been performed. the temperature distributions over the sample thickness in the compacted zone for several values of detonation velocity show that at higher speeds there is considerable heterogeneity in the temperature distribution over the sample thickness. near the axis of the sample the temperature has a higher value than in distance from it. an increase in the pressure decay time due to increasing either the explosive thickness or the external loading intensity causes no shrinkage of the destruction zone at a fixed propagation velocity of the detonation wave. compaction of powders with low detonation velocities results in a considerable shrinkage of destruction zones in finish samples and in a uniform distribution of material parameters in the compacted region. references [1] v.f. nesterenko, high-rate deformation of heterogeneous materials, nauka, novosibirsk (1992) (in russian). [2] r. prümmer, powder compaction. explosive welding, forming and compaction, london; new york: appl. sci. publ., (1983). [3] s.p. kiselev, v.m. fomin, j. of applied mechanics and technical physics. 34(6) (1993) 861. [4] v.v. pai, g.e. kuz'min, i.v. yakovlev, combustion, explosion, and shock waves, 31(3) (1995) 124. [5] a.i. gulidov, i.i. shabalin, numerical realization of the boundary conditions in dynamic contact problems, preprint itam sb ras, novosibirsk (1987) (in russian). [6] m. l. wilkins, computer simulation of dynamic phenomena, springer, berlin, heidelberg (1999). [7] e. i. kraus, vestnik ngu. fizika, 2(2) (2007) 65 (in russian). [8] c. slater, introduction in the chemical physics.– new-york-london: mcgraw book company, inc., (1935) 239. [9] l. d. landau, k.p. stanyukovich, dokl. akad. nauk sssr, 46 (1945) 399 (in russian). [10] j. s. dugdale, d. mcdonald, phys. rev., 89 (1953) 832. [11] v.ya. vaschenko, v.n. zubarev, sov. phys. solid state, 5 (1963) 653. [12] r. g. mcqueen, s. p. marsh, j. w. taylor, j. n. fritz, high-velocity impact phenomena, ed. by r. kinslow, new york: academic press (1970) 293. j http://dx.medra.org/10.3221/igf-esis.24.11&auth=true http://www.gruppofrattura.it microsoft word numero_26_art_7 a. de iorio et alii, frattura ed integrità strutturale, 26 (2013) 57-68; doi: 10.3221/igf-esis.26.07 57 about the certification of railway rails a. de iorio, m. grasso, f. penta, g.p. pucillo università di napoli federico ii, dipartimento di ingegneria industriale, p.le v. tecchio 80 – 80125 napoli, italy antdeior@unina.it abstract. when the compliance with the european code of some rail steel has to be verified, the need of carrying out the experimental activities in accordance with several testing standards forces the operator both to solve the problems related to the choice of a suitable testing practice and often to interpret subjectively standards guidelines. this does not facilitate the comparability and/or the quality of the results produced by several laboratories. with reference to a series of fatigue, fracture toughness and fatigue crack growth tests carried out by the authors on specimens extracted from rails, the main lacks in the current standards, related to both the choice of the control parameters and the testing procedures, are pointed out. regarding the crack growth testing, several procedures to compute the crack growth rates to be compared with the limits prescribed by the code are proposed. these procedures have been applied to a data set produced during the aforementioned testing activity, in order to highlight, by comparison of the results obtained by them, the significant differences in the crack growth rate estimates and the magnitude of the errors that can be done due to the lacks in the standard practices currently adopted. keywords. railway rail steel; crack growth testing; fatigue crack propagation; raw data analysis; fatigue damage; railway certification. introduction uring the last decade the methods and central ideas of damage tolerance design raised an increasing interest from railway researchers, in particular concerning the service life and crack inspection of rails [1-4], since there are still many unresolved technical problems and intensely debated scientific issues. in example, the demand of verifying that a rail steel meets also the fatigue crack growth requirements established by current regulations [5] making it able to be put to use, imposes that the operators pay the maximum attention in carrying out both the experimentation and the analysis of results, due to the high technical and commercial importance that the outcomes of these activities have. since the testing procedures are defined by the standards and the standards have always to be fulfilled, it is very common considering, also among the insiders, this problem trivial or even out of place. however, the scatter in the experimental data and the possible anomalies in the results, which often are unpredictable and/or uncontrollable and are caused by the testing equipment, the control of testing parameters and the analysis of experimental data, do not allow identifying unambiguously the testing outcome. more specifically, with regard to the fatigue crack growth tests, it is not possible to compute directly the particular crack growth rate value to be compared with the reference value prescribed by the code, to establish if the rail steel can be qualified for the use. also in the case of the other rail qualification tests, current standards do not seem to be enough robust to guarantee the comparability and reproducibility of the experimental results, since they are significantly dependent also on the free interpretation of rules or procedures not univocally or clearly defined. in this paper, the main phases of a complete series of certification tests on a d http://www.gruppofrattura.it http://dx.medra.org/10.3221/igf-esis.26.07&auth=true a. de iorio et alii, frattura ed integrità strutturale, 26 (2013) 57-68; doi: 10.3221/igf-esis.26.07 58 rail steel are reported, in order to point out the aforementioned problems and for describing the solutions adopted as well as the detailed procedures that can be used to fill the gap left by the current standards. experimental activity he testing activity has been carried out at the mechanics of materials and structures laboratory department of industrial engineering of federico ii university. test articles were obtained from n.7 line production batches of rail 60e1 steel grade r260 manufactured by manoir industries outreau (france). the exact composition of the steel used in the current investigation cannot be given, however it is within the composition range reported in the uni en 13674-1:2011. among all tests prescribed by the standard to qualify the rail steel, only fatigue tests, fracture toughness tests and fatigue crack growth tests have been carried out in the department lab. for each batch, the specimens were extracted from n.2 rail sections (fig. 1) and marked in accordance with recommendations of ref. [5]. figure 1: rail sections from which specimens have been extracted. type of test number of tests uni en 13674-1:2011 fatigue 3 par. 8.4 fatigue crack growth rate 3 par. 8.3 fracture toughness 5 par. 8.2 table 1: number of samples for each type of test and corresponding paragraph in the standard. the geometry of some specimens employed for the tests are shown in fig. 2. figure 2: specimens prototypes used for the testing activity. fatigue tests or each material batch, according with the requirements of the uni standard [5], n.3 cylindrical specimens (fig. 2, f), have been tested after having preliminarily inspected their surface with a 30x microscope (instead of the 20x prescribed by the standard) to verify that any circumferential scratch within the specimen gauge length was absent. t f f ft fcg http://www.gruppofrattura.it http://dx.medra.org/10.3221/igf-esis.26.07&auth=true a. de iorio et alii, frattura ed integrità strutturale, 26 (2013) 57-68; doi: 10.3221/igf-esis.26.07 59 tests have been carried out under strain control with strain ratio r = -1 on a digitally controlled universal testing machine that was programmed to stop cycling after 5 x 106 cycles, as prescribed by the standard. before starting the fatigue testing activities, two problems arose: the first one was related to the test control parameter, the second to the definition of the value to be assigned to it. regarding the controlled parameter, the uni en 13674 requires that fatigue tests have to be carried out under strain control, applying a "total strain amplitude" equal to 1350 μm/m, while for all other needed information related to the experimental set-up and testing procedure the iso 1099 [6] is invoked even if this standard concerns fatigue testing under stress control. the iso standard to be adopted for testing under strain control is instead the iso 12106 [7]. concerning the value to be assigned to the controlled parameter, namely the stress amplitude, σa or sa, the iso 1099, after having defined it as "one-half the algebraic difference between the maximum stress and the minimum stress in a stress cycle", in the same figure referred by the definition, identifies it as the stress range, called "stress amplitude δσa". thus, the correct interpretation of the standards should lead to the choose of the strain amplitude as controlled parameter for fatigue tests and to a value of the total strain range equal to twice the reference amplitude value of 1350 μm/m defined in the uni en. the aforementioned ambiguity misled well-known qualified laboratories that carried out tests using strain amplitude equal to half of the prescribed value. a further basic problem related to the adoption of the correct strain amplitude value was the failure of the screw end of the specimens in the last thread engaged with the sleeve of the test fixture caused by the high stress concentration at the root of the coarse thread, that had geometry in accordance with the standards uni en 13674 and was obtained by turning (fig. 3). figure 3: fractured head of a fatigue specimen. since the specimens were already manufactured, this problem has been overcome making more gradual the way the load was transferred from the fixture to the specimen. however, it could be more easily avoided simply choosing a fine tread for the heads of the specimens, during the scheduling phase of the tests. by means of the aforementioned solutions and standard interpretations previously described, all fatigue tests have been carried out without further problems, anomalies or premature specimen failures. fracture toughness tests or each production batch, n.5 fracture toughness tests at low temperature (t = -20 °c) were carried out in accordance with the uni en [5]. sen(b) specimens having a chevron notch and thickness equal to 25 mm (fig. 2, ft) were used. experimental set-up and testing conditions complied with the prescriptions of the uni en 13674, annex b whereby the astm e 399 [8] is referenced for all other information not specified in the uni standard. since the uni [5] gives limited guidelines and the astm [8] has a quite wide range of applicability and does not consider specifically tests at low temperature, it was necessary to overcome many drawbacks to define the testing procedure to be adopted. for this reason, it is not possible to find in it clear and unambiguous data about both the stepped load shedding procedure to be adopted during the precracking phase, the notch geometry, the notch machining method, the way the prescribed temperature (t = -20 °c) has to be reached before test and, finally, the parameter to be controlled, since the tests may be carried out either under position control, according to the uni [5], or under loading control, as reported in the astm [8]. due to all these uncertainties, a significant randomness has to be expected in toughness tests results that can lead to erroneous conclusions or even compromises the certification of the rail steel. f http://www.gruppofrattura.it http://dx.medra.org/10.3221/igf-esis.26.07&auth=true a. de iorio et alii, frattura ed integrità strutturale, 26 (2013) 57-68; doi: 10.3221/igf-esis.26.07 60 the adopted solutions for these tests, whose results are reported in tab. 2 in term of mean value and standard deviation of each production batch, are: i. experimental set-up and stress ratio value (r = 0.1) of the fatigue loading, are those prescribed by the uni en 13674, but regarding the precracking procedure and the other recommendations that are not considered in this standard, it was necessary to refer to the astm e399. this latter, being totally general, does not provide any specific indication regarding the maximum value of the fatigue load to be applied during the crack nucleation phase. it defines only the way the load maximum value has to be reduced by step (without exceeding 10 % of the load maximum value reached in the previous step) and the minimum crack length increment of each step j of load shedding, which has to be computed as:   2 0 ,2 1max j p k j a r          (1) moreover, the standard [5] prescribes that the ratio a/w at the end of the pre-cracking phase has to be in the range 0.45 ÷ 0.55 as well as in the last 1.25 mm of crack growth the kmax value has to be in the range 18 ÷ 22 mpam. on the basis of these data, it was possible to define the load spectrum adopted for the whole precracking phase in terms of maximum applied loads (fig. 4). figure 4: load spectrum for the precracking phase. batch kq (mean) (mpam) standard dev. (mpam) a 37.41 5.31 b 39.42 6.64 c 35.20 4.58 d 33.08 2.55 e 31.35 0.59 a1 37.26 7.49 b1 38.35 2.32 table 2: mean and standard deviation of the kq values. ii. the chevron notch, whose depth on the specimen lateral faces was equal to 10 mm and whose width h was equal to 5 mm, was obtained by electro-discharge machining. the astm e399 also allows other machining methods to create the notch, even though they can be responsible of strong differences in the behaviour of the specimens during the crack nucleation phase, since a uniform quality of machining cannot be obtained along the whole chevron notch root. iii. to take the specimen to the temperature of -20 °c, which is the value prescribed from the standard [5], initially the temperature inside the environmental chamber was reduced to t = -50 °c, monitoring the specimen temperature during this phase. when a value equal to -15 °c was reached, a warming ramp was applied until the temperature inside the chamber was -25 °c and the specimen temperature was stabilized on the test value of -20 °c. http://www.gruppofrattura.it http://dx.medra.org/10.3221/igf-esis.26.07&auth=true a. de iorio et alii, frattura ed integrità strutturale, 26 (2013) 57-68; doi: 10.3221/igf-esis.26.07 61 iv. final quasi-static tests, to cause specimens fractures, were carried out under position control, with a loading rate equal to 0.0083 mm/s and acquiring at a frequency of 50 hz the output signals of both the load cell and the cod gauge needed to determine the kq value. fatigue crack growth tests atigue crack growth tests were carried out on n. 3 specimens obtained from each material batch, according to the uni en 13674. sen(b) specimens having a chevron notch obtained by electro-discharge machine and thickness equal to 20 mm were used. after the dimensional checks, all specimens were instrumented with crack gauges applied on both lateral specimen faces to monitor and acquire the growth of the crack. however, when the crack grew in the chevron notch, cod gauge has been used to monitor its depth. acquiring also the cod increments δv’s as function of the number of cycles proved to be useful even for determining the crack depth threshold value corresponding to the condition of emerging crack on one of the two specimen faces, being the only number of applied load cycles completely insufficient to detect this particular condition, due to its high dependency on the local geometry and microstructure of the material near the chevron notch root. experimental set-up was in accordance with the qualification standard [5], but the precracking procedure was defined as for the fracture toughness tests obtaining the load spectrum represented the diagrams of fig. 5 both in term of the load maximum value and the corresponding sif ranges. figure 5: precracking load spectrum of the fcg tests. since the stepped load shedding procedure is quite complex, researchers often prefer to carry out the test with a single loading level for the whole test, applying during the pre-cracking phase a stress ratio r = 0.1, so as to reduce its duration, instead of r = 0.5, that is the value prescribed by the certification standard [5] for the fatigue crack propagation tests. however, this approach even if it is not in contrast with the prescriptions of the standards [bs [9] and uni [5]], it is not in accordance with the guidelines reported in the astm e647 [10]. moreover, passing from the precracking to the propagation phase, the crack growth rate could be less than that would occur if a stress ratio equal to 0.5 was used from the beginning of the test, since with r = 0.1 the loading range would be higher and, consequently, the plastic region ahead the crack tip would be more extended. concerning these aspects, the astm e647 recommends to adopt the same values of the r ratio for the whole test duration or, when r changes are needed, to increment the load maximum value in order to avoid retardation effects due to an extended plastic region at the crack tip. regarding the analysis of results, it has been observed that standards do not give any guidelines about the procedure to be used to evaluate the required crack growth rates, corresponding to the two particular sif range values: 10 mpam e 13.5 mpam, that have to be compared with the minimum values equal to 17 m/gc and 55 m/gc, respectively, prescribed by the certification standard [5]. on the other hand, whichever would be the chosen maximum load value, it is never possible to carry out the tests in such a way that the analysis of the results gives the required exact δk values. furthermore, when a single maximum load value is adopted for the whole test, the applied δk range could not include one of the two reference values. for this reason, it is necessary to evaluate the crack growth rate values by an ad hoc interpolation and extrapolation method of the raw data, which has to be fully defined due to the lack in the reference standards. obviously, as fully discussed in the following f http://www.gruppofrattura.it http://dx.medra.org/10.3221/igf-esis.26.07&auth=true a. de iorio et alii, frattura ed integrità strutturale, 26 (2013) 57-68; doi: 10.3221/igf-esis.26.07 62 section, the crack growth rate values are affected also by the method adopted to evaluate them, thus it would be desirable that this lack in the standard would be soon fill in the near future. a synthetic list of the possible procedures that could be adopted to evaluate the crack growth rates is reported in the following. a. raw data in term of crack length versus number of cycles, collected during tests carried out under the k-increasing condition, are analysed by means of the 7-points incremental polynomial method [10]. the discrete points δk da/dn obtained by this method are locally interpolated using either a second or a third order polynomial function. the crack growth rate values to be compared with the reference limits reported in the standard are evaluated by the fitting polynomial function. b. raw data produced under the k-increasing condition are interpolated using the three-parameters model [11]. by sampling the model, it is possible to obtain a significant number of pairs of values (a,n) in the suitable ranges including the reference δk values. these pairs can be analysed as for the previous point. c. the same raw data are interpolated using the three-parameters model, so by means of the derivative of the fitting function it is possible to compute the crack growth rate values corresponding to a significant number of crack length values, a. then, the computed crack growth rates together with the corresponding δk values are fitted using either a second or a third order polynomial function in order to obtain the rate values to be compared with the limits of the standard. d. raw data produced under the k-increasing condition are interpolated using the three-parameters model and the derivative of the fitting function is evaluated. by means of its analytical expression it is possible to evaluate the crack growth rate values for the crack lengths corresponding to the prescribed δk values. since the testing conditions and the specimen geometry are known, by means of the expression of δk it is possible to evaluate the geometry function g(α) of the sen(b) sif expression, and to obtain the corresponding α values by one of the following methods:  solving the equation obtained by substituting the computed g(α) value in the following expression      23 2 6 ( ) 1.99 1 2.15 3.93 2.7 1 2 1 g                  (2)  computing the α value using the following equation: 3 2 2 0.0004464 ( ) 0.9019 ( ) 6.597 ( ) 11.7 ( ) 1.017 ( ) 14.01 g g g g g             (3) eq. (3) is the best fitting function of the pairs α g(α), computed using the geometry function (2) in the range 0.2<α<0.85. it has been determined by the least squares method and has coefficient of determination r2 equal to 1. in both cases, by the α values it is possible to compute the corresponding crack lengths and, finally, the crack growth rates by the equation.   1 ln c a f cda dn n e                        (4) e. in order to give with a more comprehensive overview on the procedures employed for rail steel certification, a further practice to evaluate the crack growth rate, widely adopted by some qualified laboratories, is reported. all δk and da/dn values, computed using the experimental data, are employed to estimate the c and m constants of the paris model. then, the paris equation is used to evaluate the crack growth rates to be compared with the limits prescribed by the standard. procedures comparison n order to highlight analogies and differences among the proposed procedures, some crack growth data obtained by the authors and reported in fig. 6 and corresponding to one of the two faces of the specimen kdp_1 are analysed. i http://www.gruppofrattura.it http://dx.medra.org/10.3221/igf-esis.26.07&auth=true a. de iorio et alii, frattura ed integrità strutturale, 26 (2013) 57-68; doi: 10.3221/igf-esis.26.07 63 procedure i adopting the procedure described in the appendix x1.2 of the astm e647, the crack growth rates and the corresponding δk values were computed (fig. 7). figure 6: raw fatigue crack growth data. figure 7: fatigue crack propagation curve. the crack growth rates are computed by means of local fitting of the raw data using either a second order or a third order polynomial function (fig. 8 and 9). for each fitting n. 6 δk values in the neighbourhood of the references values have been chosen. a less number of points could result in a poor fitting. δk (mpam) da/dn (m/gc) second order polynomial function 10 13.49 13.5 31.88 third order polynomial function 10 13.55 13.5 31.75 table 3: crack growth rate computed using the procedure i. figure 8: second order polynomial fit of the crack growth rates. http://www.gruppofrattura.it http://dx.medra.org/10.3221/igf-esis.26.07&auth=true a. de iorio et alii, frattura ed integrità strutturale, 26 (2013) 57-68; doi: 10.3221/igf-esis.26.07 64 figure 9: third order polynomial fit of the crack growth rates. procedure ii in fig. 10 fitting of the experimental data using the three-parameters model [11] is shown. the corresponding model parameters are reported in tab. 4 together with the goodness-of-fit parameter r2. figure 10: raw crack growth data and three-parameters fitting function. α β γ r2 0.8283 0.3861 1e-04 0.9992 table 4: model parameters values (kdp_1 specimen). by sampling the fitting function in the δk ranges 9.5÷10.5 mpam e 13÷14 mpam, pairs of values δk – da/dn to be analysed by the procedure reported at the previous point are obtained. the corresponding crack growth rates are reported in tab. 5 and diagrammed in fig. 11 together with the crack propagation curves. from these diagrams it can be inferred that by the second and third order polynomial functions very similar goodness-of-fit are obtained. δk (mpam) da/dn (m/gc) second order polynomial function 10 14.30 13.5 31.65 third order polynomial function 10 14.30 13.5 31.65 table 5: crack growth rates computed using the procedure ii. http://www.gruppofrattura.it http://dx.medra.org/10.3221/igf-esis.26.07&auth=true a. de iorio et alii, frattura ed integrità strutturale, 26 (2013) 57-68; doi: 10.3221/igf-esis.26.07 65 figure 11: crack propagation curves and local interpolation ranges. procedure iii fatigue crack propagation curves, represented in fig. 12, have been obtained computing the crack growth rates by the analytical expression of the derivative of the three-parameters model. in the same figure, the δk ranges where interpolation by the second and third order polynomial functions is carried out are shown and the computed crack growth rates are diagrammed. these latter are reported in tab. 6 as well. figure 12: crack propagation curves, local interpolation ranges and crack growth rate values. δk (mpa*m0.5) da/dn (m/gc) second order polynomial function 10 14.28 13.5 31.51 third order polynomial function 10 14.28 13.5 31.51 table 6: crack growth rates computed using the procedure iii. procedure iv fitting the experimental data, since g(α) has the following expression:      23 2 6 ( ) 1.99 1 2.15 3.93 2.7 1 2 1 g a w                    (5) http://www.gruppofrattura.it http://dx.medra.org/10.3221/igf-esis.26.07&auth=true a. de iorio et alii, frattura ed integrità strutturale, 26 (2013) 57-68; doi: 10.3221/igf-esis.26.07 66 being 1.5 ( ) 10 k b w g f       (6) it is possible to compute the α values corresponding to the reference δk values, being known the applied δf during the test and the specimen geometry, with which can be evaluated the crack growth rates reported in tab. 7, using the eq. (3) obtained from the model. when to evaluate the crack lengths the following equation is used: 3 2 2 0.0004464 ( ) 0.9019 ( ) 6.597 ( ) 11.7 ( ) 1.017 ( ) 14.01 g g g g g             (7) the crack growth rates reported in tab. 8 are obtained. δk (mpam) da/dn (m/gc) 10 13.79 13.5 32.81 table 7: crack growth rates computed using the procedure iv. δk (mpam) da/dn (m/gc) 10 13.82 13.5 32.84 table 8: crack growth rates computed using the procedure iv. procedure v in fig. 13, the data points obtained analysing the raw data using the astm method together with the paris model are reported. figure 13: crack propagation curves and paris law. in tab. 9 the numerical crack growth rate values computed using the paris model are given. http://www.gruppofrattura.it http://dx.medra.org/10.3221/igf-esis.26.07&auth=true a. de iorio et alii, frattura ed integrità strutturale, 26 (2013) 57-68; doi: 10.3221/igf-esis.26.07 67 δk (mpam) da/dn (m/gc) paris 10 13.48 13.5 34.70 table 9: crack growth rates computed using the procedure v. all the crack growth rates computed using the discussed procedures are shown in fig. 14 together with the fatigue crack propagation curves obtained analysing the experimental data by the procedure suggested by the astm [10]. figure 14: comparison among crack growth rates corresponding to the different k. δk (mpam) μ (mpam) σ (mpam) 10 13.92 0.37 13.5 32.26 1.05 table 10: estimated crack growth rates: means and standard deviations. means and standard deviations of the crack growth rate estimates computed with the different procedures are given in tab. 10 for several values of k. the greatest deviation from the mean value occurs at the maximum δk (13.5 mpam). however, this result is essentially due to the excessive deviation of the value computed using the paris model (see fig. 14 right) from the crack propagation curve. for δk = 10 mpam the maximum deviations occur for the procedure identified as i and ii, probably due to the adoption of the three-parameters model to fit the experimental data points. conclusions uring the experimental activities carried out for the certification of rail steel, significant lacks in the current standard that regulates the principal tests arose. in the present paper the main results of the testing activities and the adopted procedures are reported. also, the adopted choices in order to either implement the guidelines given by the reference standards or to fill the aforementioned gaps left by these latter are described. in particular, due to the lacks in all current standards, some alternative procedures to compute the crack growth rates to be compared with the reference values prescribed by the standard have been proposed and verified. the final considerations about the obtained results represent a contribution to provide a mean for better understand and apply the current standards to produce reliable results in the complex task of certifying a rail steel. d http://www.gruppofrattura.it http://dx.medra.org/10.3221/igf-esis.26.07&auth=true a. de iorio et alii, frattura ed integrità strutturale, 26 (2013) 57-68; doi: 10.3221/igf-esis.26.07 68 acknowledgements he supply of materials by manoir industries outreau (france) is greatly appreciated. references [1] jeong, d.y., correlations between rail defect growth data and engineering analyses, part i: laboratory tests, uic/wec joint research project on rail defect management. u.s. department of transportation (2003). [2] ravaee, r., hassani, a., fracture mechanics determinations of allowable crack size in railroad rails, j fail. anal. and preven., 7 (2007) 305–310. [3] seo, j. w., kwon, s. j., lee, d. h., kwon, s. t., choi, h. y., fatigue crack growth and fracture behavior of rail steels, int. j. of railway, 5(3) (2013) 129-134. [4] de iorio, a., grasso, m., kotsikos, g., penta, f., pucillo, g. p., development of predictive models for fatigue crack growth in rails, key engineering materials, 488-489 (2012) 13-16. [5] uni en 13674-1:2011, railway applications track rail part 1: vignole railway rails 46 kg/m and above. [6] iso 1099:2006, metallic materials fatigue testing axial force-controlled method. [7] iso 12106:2003 metallic materials fatigue testing axial-strain-controlled method. [8] astm e399-09e2, standard test method for linear-elastic plane-strain fracture toughness kic of metallic materials. [9] bs-iso 12108:2002, metallic material fatigue testing fatigue crack growth method. [10] astm e 647: standard test method for measurement of fatigue crack growth rates, usa, (2011). [11] de iorio, a., grasso, m., penta, f., pucillo, g.p., a three-parameter model for fatigue crack growth data analysis, frattura ed integrità strutturale, 21 (2012) 21-29. t http://www.gruppofrattura.it http://dx.medra.org/10.3221/igf-esis.26.07&auth=true microsoft word numero 11 art 2 m. beghini et alii, frattura ed integrità strutturale, 11 (2009) 10-20; doi: 10.3221/igf-esis.11.02 10 modello di tenuta della flangia bullonata, senza guarnizione, mediante l’analogia della meccanica della frattura di una fessura parzialmente aperta m. beghini, l. bertini, c. santus università di pisa, dipartimento di ingegneria meccanica, nucleare e della produzione. largo lucio lazzarino 1, 56126 pisa. ciro.santus@ing.unipi.it c. cagnarini, p. romanello general electric, oil & gas, nuovo pignone – 50127 firenze. riassunto. i compressori centrifughi di elevate dimensioni non permettono l’utilizzo di guarnizioni deformabili, per cui le due metà della flangia di connessione sono forzate mediante bullonatura e la tenuta è affidata al contatto completo delle due superfici. la previsione della pressione di perdita è un aspetto di progetto di notevole interesse per questa tecnologia. l’azione della pressione interna sollecita la separazione delle superfici della flangia, che invece è contrastata dall’azione di serraggio dei bulloni. il presente lavoro propone un modello per prevedere la condizione di perdita, basato sulla meccanica della frattura. dato che le due superfici della flangia sono semplicemente a contatto, esse costituiscono una vera e propria fessura parzialmente aperta. come ben noto il fattore di intensificazione di una fessura parzialmente aperta è nullo. imponendo che le due superfici siano parzialmente separate ad una distanza fino al bordo del foro del bullone (che offre un canale di fuoriuscita per il fluido in pressione), e imponendo la condizione di fattore di intensificazione nullo, è possibile determinare la pressione di perdita, analiticamente, mediante la tecnica delle “weight functions” (o “funzioni peso”). il presente lavoro riporta una positiva validazione del modello proposto mediante sia simulazione numerica sia risultati sperimentali in piena scala e in scala ridotta. il modello analitico proposto offre uno strumento di progetto di immediata implementazione per comparare diverse geometrie di flangia bullonata. abstract. the use of a gasket made in soft material is not recommended for large size centrifugal compressor case flanges. the two case halves are assembled with bolted flanges and the leakage is prevented by the “metal– to–metal” contact of the flange surfaces. the prediction of the leakage condition is an important engineering challenge for this technology. a new model to predict the leakage condition, based on fracture mechanics, is here presented. the partially open flange surfaces interface can be regarded as a partially open crack. the stress intensity factor of a partially open crack is zero, since the flange surfaces can not transfer tensile traction, being just in contact (not “glue” or “welded”). the extension of the open zone, i.e. the crack length, can be obtained imposing the zero stress intensity factor condition. the leakage is expected as the flange surface open front reaches the bolt hole, that produces a way out path for the internal pressurized fluid. by means of the weight functions analytical technique, the leakage pressure can be calculated. the proposed model was then successfully validated by means of both numerical simulations and full scale and small scale experimental tests. the proposed analytical model can be used to compare different flange geometries and then it is a useful design tool. parole chiave. tenuta. flangia bullonata. meccanica della frattura. fessura parzialmente aperta. http://dx.medra.org/10.3221/igf-esis.11.02&auth=true http://www.gruppofrattura.it m. beghini et alii, frattura ed integrità strutturale, 11 (2009) 10-20; doi: 10.3221/igf-esis.11.02 11 introduzione compressori centrifughi di elevate dimensioni non prevedono l’utilizzo di guarnizioni di tenuta in materiale deformabile, che invece vengono comunemente usati per flangie di minore dimensioni. la tenuta fra le due metà della cassa del compressore è garantita dal contatto diretto (definito come “metal-to-metal”) fra le due superfici della flangia, fig.1. tali superfici sono premute da una distribuzione di bulloni opportunamente preserrati. nonostante non esista una guarnizione viene comunque applicato un opportuno sigillante immediatamente prima di portare a contatto le superfici, al fine di migliorare la prestazione di tenuta della flangia, principalmente per riempire gli inevitabili solchi di rugosità nonostante la prescritta elevata finitura superficiale. l’utilizzo del sigillante è di fatto la norma, nonostante la flangia venga definita come “metal-to-metal”. in letteratura sono reperibili studi recenti sulle condizioni di perdita di flange senza guarnizione, tuttavia non esiste un modello di tenuta che descriva il fenomeno in funzione dei parametri macroscopici geometrici. i principali risultati riportati in letteratura sono:  la planarità della superficie ha un ruolo significativo, la tolleranza di planarità deve essere molto stretta al fine di evitare perdite locali di contatto che producono un canale di perdita preferenziale [1];  in modo analogo, anche se ad un livello di scala differente, la rugosità deve essere minima per sfavorire perdite dovute ad un contatto non completo fra le superfici della flangia [2];  l’orientamento dei solchi di rugosità deve essere non allineato con l’eventuale verso del flusso di perdita, quindi possibilmente ortogonale ad esso [3];  l’irregolarità della superficie e la rugosità vengono in buona parte compensate con l’introduzione del sigillante (tipicamente siliconico) [4,5]. figura 1: tipiche dimensioni di un compressore centrifugo e relativa flangia bullonata di tenuta. molti studi presentano analisi agli elementi finiti (ef), utilizzando elementi di contatto (che comportano analisi di tipo non lineare) per determinare la distribuzione delle pressioni di contatto fra le due superfici della flangia [6-18], spesso offrendo soltanto analisi di carattere comparativo fra diverse configurazioni. alcuni studi dimostrano l’effettiva importanza del sigillante [11]. la condizione di perdita è solitamente associata alla perdita di pressione di contatto fra le flange accoppiate [6-10] oppure al verificarsi di una tensione di trazione sufficiente a provocare il distacco fra il sigillante ed una delle due superfici della flangia [6]. l’effettivo valore del preserraggio imposto al bullone è ampiamente accettato come una delle principali cause di non affidabilità della flangia bullonata in termini di tenuta. infine, alcuni studi propongono analisi su come ottimizzare la sequenza di serraggio per garantire un preserraggio dei bulloni il più possibile uniforme [14-21]. il presente lavoro ha come obbiettivo quello di proporre un modello semplice ed efficace, in grado di determinare la condizione di perdita della flangia senza guarnizione, descrivendo la (parziale) separazione delle superfici della flangia con concetti di meccanica della frattura, ossia modellando l’interfaccia di separazione come una vera e propria fessura. questo approccio permette di ottenere un modello analitico più veloce rispetto ad un calcolo agli elementi finiti, che quindi si presta ad un’analisi preliminare e di prima ottimizzazione dei parametri macroscopici della geometria della connessione. i http://dx.medra.org/10.3221/igf-esis.11.02&auth=true http://www.gruppofrattura.it m. beghini et alii, frattura ed integrità strutturale, 11 (2009) 10-20; doi: 10.3221/igf-esis.11.02 12 la geometria della connessione è rappresentata in fig.2(a). i parametri geometrici principali sono: vd diametro interno della cassa, vt spessore della parete della cassa, z posizione dell’asse del bullone (o del prigioniero) rispetto alla superficie interna della cassa, hd diametro del foro del bullone, bp passo della fila di bulloni in direzione assiale, h altezza di ciascuna delle superfici della flangia, w larghezza della flangia, ed infine h / 2l z d  è la “distanza di perdita” ossia l’estensione della separazione fra le due superfici della flangia che porta in comunicazione il volume interno, contenente fluido in pressione, con il foro del bullone che quindi è aperto verso l’esterno (in quanto il collegamento filettato non garantisce nessun tipo di tenuta). in altre parole, se la lunghezza di separazione 0l fra le due superfici della flangia è inferiore a l non si ha perdita, mentre si ha immediatamente perdita quando la lunghezza di separazione 0l raggiunge la lunghezza l , fig.2(b). (a) (b) figura 2: (a) dimensioni principali della geometria della flangia. (b) condizione di perdita. la condizione di perdita assunta nel presente modello prevede che le superfici della flangia siano inizialmente perfettamente piane, e che la loro deformazione sia dovuta soltanto alla deformazione elastica, mentre invece le superfici posso presentare degli errori di forma (ad esempio dovuti al rilassamento di tensioni residue) e/o difetti locali come la rugosità oppure solchi o graffi nonostante l’applicazione del sigillante. un analisi ef di contatto ha permesso di verificare la pressione interna prevista dal modello che porta il fronte di separazione in corrispondenza del foro del bullone. tuttavia, un’analisi numerica non può permettere di verificare la qualità dell’assunzione di perfetta planarità delle superfici che invece richiede una validazione sperimentale. tale validazione è stata ottenuta (ed è presentata nel lavoro) mediante prove sia in piena scala sia in scala ridotta. modello analitico a porzione di distacco fra le superfici della flangia può essere interpretata come una vera e propria fessura. le due piastre della flangia sono semplicemente appoggiate, tuttavia la zona in cui il contatto rimane chiuso è equivalente, in termini di stato di tensione, ad un'unica porzione di materiale senza soluzione di continuità, in quanto non si hanno slittamenti significativi. essendo le due piastre a contatto non è possibile avere uno stato di tensione positiva (trazione) fra le due superfici. anche la presenza del sigillante non garantisce uno stato di trazione significativo, ma soltanto l’opportunità di riempire i solchi della rugosità. come ben noto dalla meccanica della frattura, lo stato di tensione in corrispondenza dell’apice della fessura è definito dal fattore di amplificazione delle tensioni k . il fattore di amplificazione (primo modo di apertura) non può mai essere negativo dal momento che questa condizione implica il contatto fra i lembi della fessura. d’altro canto la vd vt h bd z w bp bolt pitch along the axial direction l hd transverse section plane vertical symmetry plane ol l o o no leak.: , leakage: l l l l   l http://dx.medra.org/10.3221/igf-esis.11.02&auth=true http://www.gruppofrattura.it m. beghini et alii, frattura ed integrità strutturale, 11 (2009) 10-20; doi: 10.3221/igf-esis.11.02 13 condizione di semplice contatto fra le superfici della piastra non permette un fattore di amplificazione positivo, dato che in tal caso le tensioni all’apice della fessura dovrebbero essere positive, addirittura singolari, per cui molto elevate in un introno dell’apice stesso. quindi, il fattore di amplificazione è necessariamente nullo in corrispondenza del fronte di separazione. la condizione di perdita pertanto può essere espressa in termini di meccanica della frattura: fronte di separazione esteso fino al foro del bullone 0l l e fattore di intensificazione nullo 0k  , fig.3(a). (a) (b) figura 3: (a) condizione di perdita espressa in termini di meccanica della frattura. (b) integrazione della weight function, caso di una fessura parzialmente aperta. la tecnica delle “weight functions” (wf) permette di esprime il fattore di intensificazione delle tensioni di una fessura come integrale esteso su tutta la lunghezza della fessura (in uno schema piano, altrimenti su tutta la superficie della fessura, in uno schema tridimensionale) della tensione nominale moltiplicata per una funzione “kernel” che è appunto la wf [2226]. la condizione di perdita può quindi essere scritta nel seguente modo, eq.(1): n0 ( ) ( , ) d 0 l k x h x l x  (1) in cui la n ( )x è la distribuzione di tensione “nominale”, mentre la ( , )h x l è la wf. come ben noto, la tensione nominale è quella distribuzione di tensione che si avrebbe in corrispondenza della linea della fessura (in uno schema piano) se la fessura non ci fosse, ossia se il materiale fosse continuo. è importante sottolineare che la wf ( , )h x l è soltanto funzione della geometria e non della tensione nominale. tuttavia, la wf ( , )h x l e la tensione nominale n ( )x non possono essere espresse in forma chiusa per questa particolare geometria, quindi sono necessarie delle semplificazioni per ottenere una buona approssimazione della tensione nominale e della wf. nel presente problema della flangia bullonata la distribuzione di tensione nominale è la sovrapposizione della distribuzione di tensione dovuta al serraggio del bullone (che ovviamente produce tensioni di compressione, ovvero negative) e la distribuzione di tensione dovuta alla pressione interna alla cassa, che tende a distaccare le due piastre della flangia (tensioni di trazione, positive). la wf non è uniforme ma è comunque sempre positiva, per cui le tensioni nominali di trazione tendono a produrre k positivo, mentre le tensioni di compressione dovute al preserraggio del bullone producono un contributo negativo, e quindi benefico ai fini della tenuta. di seguito si riportano le approssimazioni introdotte:  schema di calcolo piano, per cui la ripetizione dei fori viene schematizzata come un’unica cava continua di area equivalente, in modo da garantire, la stessa area di contatto, fig.4(a), questa assunzione è incentivata anche dal fatto che il passo dei bulloni bp è più piccolo possibile, in modo da favorire l’azione di serraggio stessa;  in virtù di questa assunzione, si fa riferimento ad uno schema piano trascurando la ripetizione ciclica dei fori, per cui la wf di integrazione è relativa ad uno schema di fessura nel piano;  per semplicità si trascurano gli effetti di bordo e si utilizza la wf di una fessura (di lunghezza finita) in un semipiano, di cui sono noti gli integrali per le più semplici distribuzioni di tensione nominale; 0k  lo leakage: l l x closed crack length a oa n ( )x open crack length 0 0 o o n 00 n 00 ( ) 0 ( ) ( ) ( , ) d ( ) ( , ) d 0 a a k a k a x h x a x x h x a x        http://dx.medra.org/10.3221/igf-esis.11.02&auth=true http://www.gruppofrattura.it m. beghini et alii, frattura ed integrità strutturale, 11 (2009) 10-20; doi: 10.3221/igf-esis.11.02 14  si assume la distribuzione lineare per la tensione nominale dovuta alla pressione interna, e si determina tale distribuzione imponendo l’equivalenza (risultante e momento risultante) con la forza di trazione, per unità di profondità, attraverso la parete della cassa, fig.4(b);  si assume la distribuzione della tensione nominale di compressione, dovuta al preserraggio dei bulloni, a tronco di piramide, rifacendosi al comune schema usuale nei testi di costruzione di macchine [27], avendo precedentemente assunto uno schema piano, la distribuzione a tronco di cono non è possibile, la relativa vicinanza dei bulloni ( bp più piccolo possibile) ha suggerito la assunzione a tronco di piramide;  essendo la flangia relativamente stretta rispetto alla larghezza della distribuzione delle tensioni di compressione dovute al preserraggio dei bulloni, una porzione di tale distribuzione cade fuori dalla larghezza della flangia, al fine di garantire l’equivalenza è necessario sovrapporre una distribuzione equilibrante, assunta anch’essa lineare, equivalente alla distribuzione che cade fuori dalla larghezza della flangia, fig.4(c). (a) (b) (c) figura 4: (a) approssimazione geometrica della fila di bulloni come un’unica cava continua di area equivalente. (b) assunzione di distribuzione lineare delle tensioni nominali di trazione dovute alla pressione interna. (c) assunzione di distribuzione delle tensioni nominali di compressione dovute al preserraggio dei bulloni, re-distribuzione delle tensioni fuori dalla larghezza della flangia. le distribuzioni nominali (pressione interna e preserraggio dei bulloni) possono essere ottenute imponendo rispettivamente pressione interna alla cassa unitaria, e tensione di preserraggio del bullone anch’essa unitaria e successivamente moltiplicando per l’effettiva pressione interna e l’effettiva tensione di preserraggio. la distribuzione di tensione nominale può quindi essere espressa mediante la seguente combinazione lineare: n n, 1 b n,b1( ) ( ) ( )px p x p x    (2) da notare che la tensione nominale prodotta dalla pressione interna è positiva (trazione), mentre la tensione nominale prodotta dal preserraggio e negativa (pressione). avendo assunto distribuzioni lineari delle componenti della tensione nominale, l’integrazione della wf si riduce alla combinazione lineare dell’integrazione di una distribuzione uniforme e di una variabile linearmente, fig.5. sostituendo l’eq.2 nell’eq.1, e avendo i risultati delle integrazioni, riportati nella fig.5, è possibile ottenere il valore di pressione di perdita: n,b1 n,b1l b n, 1 n, 1 (0) 1.55 ( ) (0) 1.55 ( )p p p p l p l       (3) nell’eq.3, i termini n,b1 n,b1(0), ( )p p l e n, 1 n, 1(0), ( )p p l  sono i valori di tensione nominale per 0x  e x l , rispettivamente, ossia alla posizione interna della cassa e alla distanza di perdita. tuttavia, quando una porzione delle superfici della flangia perde contatto, inevitabilmente penetra del fluido in pressione, che tende ad incentivare la separazione fra le due superfici. al fine di considerare tale effetto, seguendo l’approccio proposto, è sufficiente aggiungere un termine di trazione alla distribuzione di tensione nominale, pari al valore della bp l hd h'd x l n, 1 (0)p b v / 2 ( 1mpa) pp d p  v / 2s n, 1 ( )p x n, 1 ( )p l x 1f 2f 1 2 press.distr. equivalent to: ,f f l bolt pressure distribution, larger than the flange surface  n,b1 (0)p b b b b( 1mpa)f a   x n,b1 ( )p l  bolt pressure actual distribution http://dx.medra.org/10.3221/igf-esis.11.02&auth=true http://www.gruppofrattura.it m. beghini et alii, frattura ed integrità strutturale, 11 (2009) 10-20; doi: 10.3221/igf-esis.11.02 15 pressione interna stessa. dato il significato dei termini n, 1 n, 1(0), ( )p p l  e grazie alla linearità delle integrazioni della wf, è quindi necessario aggiungere ad entrambi un termine unitario. l’eq.4 costituisce il modello analitico definitivo per determinare la pressione di perdita: n,b1 n,b1l b n, 1 n, 1 (0) 1.55 ( ) ( (0) 1) 1.55 ( ( ) 1)p p p p l p l         (4) come descritto in precedenza le tensioni nominali unitarie possono essere dedotte sulla base di considerazioni di equilibrio, anche se approssimate. pertanto non è necessaria alcuna simulazione numerica per ottenere i termini che compaiono nell’eq.3. tuttavia, il modello ef successivamente riportato è stato sviluppato al fine di verificare i risultati del modello analitico. (a) (b) figura 5: (a) integrazione della wf con distribuzione di tensione nominale uniforme. (b) integrazione della wf con distribuzione di tensione nominale variabile linearmente. modello elementi finiti a porzione di flangia modellata agli elementi finiti è rappresentata in fig.6(a). l’analisi si limita alla porzione rettilinea delle flange ed inoltre si sfruttano le due simmetrie dovute alla ripetizione geometrica dei bulloni, fig.6(b). (a) (b) (c) figura 6: (a) porzione di flangia modellata. (b) modello ef, utilizzo delle simmetrie. (c) distacco degli elementi di contatto e condizione di perdita in fig.6(c) si mostra l’evoluzione del fronte di apertura all’aumentare della pressione interna alla cassa, fino alla condizione di perdita, ossia quando il fronte di distacco raggiunge il punto più interno del perimetro del foro del bullone. il valore a n 0  0 01.1215k a  a n 1 x a   1 10.6820k a  x fe model region b bolt pitch p flange interface symm. symm. increasing the internal pressure p open contact front leakage ol l http://dx.medra.org/10.3221/igf-esis.11.02&auth=true http://www.gruppofrattura.it m. beghini et alii, frattura ed integrità strutturale, 11 (2009) 10-20; doi: 10.3221/igf-esis.11.02 16 della pressione di perdita prevista dal modello ef, l,fep , si determina semplicemente osservando la posizione del fronte di apertura, per piccoli incrementi della pressione interna. è importante sottolineare che, nonostante la non linearità di contatto, la pressione di perdita prevista dal modello ef, è legata linearmente al preserraggio del bullone, dato che si impone una specifica posizione del fronte di apertura. questo risultato è in accordo con l’evidente linearità, prevista dal modello analitico, fra pressione di perdita lp e il preserraggio del bullone. in fig.7 si mostra l’ottima correlazione fra la pressione di perdita prevista dal modello analitico rispetto alla pressione di perdita prevista dal modello ef, per 12 diverse configurazioni di casse. è quindi evidente che le approssimazioni introdotte non hanno prodotto errori significativi. tuttavia, come già accennato nell’introduzione, il modello ef rappresenta una validazione per il modello analitico in termini di previsione della posizione del fronte di apertura, mentre la modalità di perdita assunta, ossia il fluido che fuoriesce dalla cassa soltanto se il fronte di separazione fra le superfici delle flange raggiunge il bordo del foro del bullone, necessita di una conferma sperimentale. figura 7: correlazione fra la pressione di perdita prevista con modello ef e pressione di perdita prevista con modello analitico basato sulla meccanica della frattura. validazione sperimentale prove in piena scala a fig.8 riporta le prove di pressurizzazione in piena scala per le stesse 12 configurazioni precedentemente investigate con il modello ef. ciascuna tipologia di cassa è stata testata prima di essere messa in esercizio, mediante prove di pressurizzazione. questo tipo di prova prevede di introdurre del liquido (anche se si tratta di compressori per gas) raggiungendo un certo valore di pressione, maggiorato rispetto al valore di esercizio, e di verificare l’eventualità della perdita. figura 8: prove in piena scala di pressurizzazione. corretta previsione, mediante il modello analitico, del singolo caso di perdita. 0 0.2 0.4 0.6 0.8 1 0 0.2 0.4 0.6 0.8 1 l,fe l,fe,max/p p l l,fe,max/p p 2 0.99r  0 0.2 0.4 0.6 0.8 1 0 0.2 0.4 0.6 0.8 1 leakage test no leakage tests l/p p l l,fe,max/p p l http://dx.medra.org/10.3221/igf-esis.11.02&auth=true http://www.gruppofrattura.it m. beghini et alii, frattura ed integrità strutturale, 11 (2009) 10-20; doi: 10.3221/igf-esis.11.02 17 soltanto per un caso è stato possibile portare la pressione interna ad un valore più elevato di quello previsto dalla prova di pressurizzazione, fino a raggiungere la perdita, fig.8. per tale prova, è stato opportunamente estensimetrato un bullone della flangia per conoscere con elevata confidenza l’effettivo preserraggio, mentre negli altri casi il precarico del bullone è stato soltanto stimato sulla base del valore imposto mediante il tensionatore idraulico. da notare che nell’unico caso di perdita la previsione del modello è stata accurata, in quanto il rapporto l/p p è risultato molto prossimo all’unità. nelle altre configurazioni non è stata raggiunta la pressione di perdita, per necessità di servizio e quindi il margine di previsione del modello è rimasto incerto. prove in scala ridotta si è ritenuto opportuno eseguire ulteriori prove, in scala ridotta, per la validazione del modello analitico, in modo da monitorare con accuratezza il preserraggio dei bulloni e poter raggiungere la condizione di perdita senza particolari restrizioni. la fig.9(a) mostra una vite estensimetrata, il relativo schema per l’acquisizione del segnale, in modo da misurare solo la trazione ed eliminare l’effetto di flessione e temperatura, mentre la fig.9(b) mostra l’attrezzatura di prova in scala. (a) (b) figura 9: (a) vite estensimetrata, l’utilizzo di due estensimetri permette di eliminare eventuale flessione ed effetto di temperatura, oltre ad ottenere sensibilità del segnale doppia. (b) attrezzatura sperimentale per riprodurre in scala ridotta una cassa flangiata con bullonatura di tenuta. i bulloni estensimetrati sono stati applicati nella zona centrale della flangia bullonata, ed è stato eseguito un serraggio controllato. gli altri bulloni sono stati serrati con un precarico molto maggiore anche se non controllato. in questo modo la perdita è stata condizionata a manifestarsi in corrispondenza dei bulloni estensimetrati. per ciascuna prova sono stati applicati incrementi di pressione fino al verificarsi della perdita, messa in evidenza dal liquido colorato introdotto, fig.10. figura 10: prove in scala ridotta con liquido in pressione (acqua colorata). evidenza di perdita superata la pressione di perdita, si manifesta il gocciolamento continuo con una certa frequenza. ovviamente la frequenza di gocciolamento è funzione crescente della pressione interna del fluido. la portata di perdita è stata valutata misurando la massa di una singola goccia, misurando l’intervallo di tempo fra il manifestarsi di una goccia e la successiva e quindi dividendo massa per tempo. riportando su un grafico la portata di perdita in funzione della pressione interna, è intuitivo definire come la pressione (sperimentale) di perdita il valore di intercetta di un andamento lineare approssimante delle singole misurazioni di portata di perdita, fig.11. 1r 2r 1r 2r 3r 4r (dummy) (dummy) refv outv p manometro trasduttore digitale di pressione 350 mm http://dx.medra.org/10.3221/igf-esis.11.02&auth=true http://www.gruppofrattura.it m. beghini et alii, frattura ed integrità strutturale, 11 (2009) 10-20; doi: 10.3221/igf-esis.11.02 18 figura 11: definizione sperimentale della pressione di perdita. i risultati delle prove in scala ridotta sono riportati in tab.1. l’errore percentuale di previsione della pressione di perdita non supera il 7%. prova preserraggio bulloni pressione di perdita sperimentale pressione di perdita prevista dal modello errore percentuale [ kn ] [ bar ] [ bar ] 1 30.7 63 59 6 % 2 20.2 41 41 < 1% 3 20.1 43 41 6 % 4 20.4 41 41 < 1% 5 30.5 57 61 7% tabella 1: risultati delle prove in scala ridotta. analisi di sensibilità ai parametri geometrici a disponibilità di un modello analitico semplice (e validato) in grado di valutare la pressione di perdita, rappresenta uno strumento di progetto molto utile, soprattutto in una prima fase di definizione dei parametri macroscopici della flangia. è stata quindi eseguita un’analisi di sensibilità al variare di un parametro tenendo costante gli altri ed ottenendo i seguenti risultati:  la pressione di perdita lp è lineare con il preserraggio dei bulloni, risultato ovvio considerando l’eq.3, per cui è buona norma scegliere bulloni di classe elevata in modo da poter sfruttare al meglio il preserraggio, al fine di aumentare b ;  la pressione di perdita diminuisce all’aumentare del passo dei bulloni bp , fig.12(a), in quanto l’azione media di preserraggio si riduce, oltretutto si tende a produrre una disuniformità della pressione di contatto in direzione assiale (non prevista dal modello), rischiando di avere una locale riduzione di pressione di contatto fra le superfici della flangia, in definitiva è buona norma ridurre il passo assiale dei bulloni al minimo tenendo conto degli ingombri;  la pressione di perdita aumenta all’aumentare della larghezza della flangia w , fig.12(b), in modo non molto sensibile, fino ad un livello di saturazione, oltre al quale la pressione di perdita rimane costante nonostante un ulteriore aumento della larghezza della flangia;  la pressione di perdita è pressoché insensibile all’altezza della flangia h , fig.12(c), qualora sia sufficientemente più grande della dimensione del bullone;  la pressione di perdita diminuisce all’aumentare della posizione dell’asse del bullone z , ovvero la distanza dalla superficie interna, fig.12(d), in quanto l’azione di preserraggio risulta più remota rispetto alla zona della flangia interessata dalla perdita. la possibilità di avere maggiore pressione di perdita all’aumentare del preserraggio del bullone, apparentemente, potrebbe indurre a pensare che sia utile introdurre un diametro maggiore del bullone, in modo quindi da avere maggiore preserraggio. tuttavia è bene tenere presente gli ingombri, mostrati in fig.2(a). aumentare il diametro del bullone provoca un aumento del passo e un aumento della distanza dalla superficie interna, e quindi un effetto negativo sulla pressione di perdita. d’altro canto un bullone di diametro piccolo produrrebbe una ridotta (in modulo) pressione di serraggio. bolt presetting1 bolt presetting 2 leakeage rate internal pressure experimental leak. pressure l http://dx.medra.org/10.3221/igf-esis.11.02&auth=true http://www.gruppofrattura.it m. beghini et alii, frattura ed integrità strutturale, 11 (2009) 10-20; doi: 10.3221/igf-esis.11.02 19 evidentemente, esiste un compromesso della dimensione di diametro del bullone, che massimizza la pressione di perdita. la disponibilità di un modello analitico, permette di trovare tale compromesso con un’analisi parametrica comparativa. conclusioni l presente lavoro propone un modello di tenuta dedotto sulla base della meccanica della frattura. la condizione di perdita è la parziale separazione delle superfici della flangia fino al raggiungimento del foro del bullone. la separazione può essere vista come una fessura parzialmente aperta, pertanto il fattore di intensificazione della fessura costituita dalle flange in contatto è necessariamente nullo. l’utilizzo delle “weight functions” ha permesso di descrivere tale condizione in funzione delle tensioni nominali, ossia delle tensioni che si avrebbero se la flangia fosse un unico componente. al fine di ottenere un modello analitico facilmente risolvibile sono state introdotte delle semplificazioni, che tuttavia a posteriori si sono dimostrate lecite, in quanto le validazioni del modello (numerica e sperimentali) hanno dato esito positivo. il modello analitico di tenuta proposto, non è in grado di valutare l’effetto di aspetti di dettaglio quali: lo stato della superficie (tolleranza di planarità, rugosità, presenza del sigillante), oppure la sequenza di serraggio dei bulloni che può generare disuniformità di preserraggio, oppure la presenza di un gas in pressione piuttosto che un liquido. tuttavia, il presente modello permette di eseguire un’analisi comparativa di sensibilità ai principali parametri geometrici della flangia quali: passo assiale e distanza dalla superficie interna dell’asse dei bulloni, altezza e larghezza della flangia, offrendo quindi un utile strumento di progetto e di ottimizzazione. (a) (b) (c) (d) figura 12. sensibilità della pressione di contatto ai principali parametri geometrici: (a) passo assiale dei bulloni, (b) larghezza della superficie di contatto della flangia, (c) altezza della flangia, (d) posizione dell’asse del bullone. 1 1.5 2 2.5 3 3.5 0 0.2 0.4 0.6 0.8 1 1.2 1.4 analytical prediction fe prediction case a case b case c b v/p t l l,fe,max/p p 2 3 4 5 6 0 0.2 0.4 0.6 0.8 1 1.2 1.4 analytical prediction fe prediction case a case b case c v/w t l l,fe,max/p p 2.5 3 3.5 4 0 0.2 0.4 0.6 0.8 1 1.2 analytical prediction fe prediction case a case b case c v/h t l l,fe,max/p p 1.4 1.6 1.8 2 2.2 2.4 0 0.2 0.4 0.6 0.8 1 analytical prediction fe prediction case a case b case c v/z t l l,fe,max/p p i http://dx.medra.org/10.3221/igf-esis.11.02&auth=true http://www.gruppofrattura.it m. beghini et alii, frattura ed integrità strutturale, 11 (2009) 10-20; doi: 10.3221/igf-esis.11.02 20 bibliografia [1] d.k. nash, m. abid, in: proceedings of the institution of mechanical engineers, part e: journal of process mechanical engineering, 218 (4) (2004) 205. [2] t. nakamura, k. funabashi, lubrication science, 4 (1) (1991) 13. [3] j. arghavani, m. derenne, l. marchand, the international journal of advanced manufacturing technology, 21 (10– 11) (2003) 713. [4] g. murtagian, v. fanelli, j. villasante, d. johnson, h. ernst, journal of tribology, 126 (3) (2004) 591–596. [5] f. kirkemo, in: proceedings of 2002 asme pressure vessels and piping conference (pvp2002). vancouver, bc, canada, (2002) 1087. [6] h. kawamura, t. sawa, m. yoneno, journal of adhesion science and technology, 17 (8) (2003) 1109. [7] m. abid, d. nash, international journal of pressure vessels and piping, 80 (12) (2003) 831. [8] m. abid, international journal of mechanics and materials in design, 2 (1–2) (2005) 35. [9] m. abid, international journal of pressure vessels and piping, 83 (6) (2006) 433. [10] m. abid, international journal of mechanics and materials in design, 2 (1–2) (2005) 129. [11] e. roos, h. kockelmann, r. hahn, international journal of pressure vessels and piping, 79 (1) (2002) 45. [12] h. estrada, i. parsons, international journal of pressure vessels and piping, 76 (8) (1999) 543. [13] t. sawa, n. ogata, journal of pressure vessel technology, 124 (4) (2002) 385. [14] m. abid, d. nash, international journal of solids and structures, 43 (14–15) (2006) 4616. [15] t. fukuoka, t. takaki, journal of mechanical design, 125 (4) (2003) 823. [16] j. mackerle, international journal of pressure vessels and piping, 82 (7) (2005) 571. [17] j. mackerle, international journal of pressure vessels and piping, 80 (4) (2003) 253. [18] j. mackerle, finite elements in analysis and design, 20 (3) (1995) 205. [19] h. tsuji, m. nakano, in: proceedings of 2002 asme pressure vessels and piping conference (pvp2002). vancouver, bc, canada, (2002) 1094. [20] t. fukuoka, journal of pressure vessel technology, 127 (4) (2005) 402. [21] t. fukuoka, t. takaki, journal of pressure vessel technology, 125 (4) (2003) 371. [22] m. beghini, l. bertini, engineering fracture mechanics, 54 (5) (1996) 667. [23] m. beghini, l. bertini, v. fontanari, fatigue & fracture of engineering materials & structures, 28 (1–2) (2005) 31. [24] m. beghini, l. bertini, v. fontanari, international journal of fracture, 112 (1) (2001) 57. [25] x.-r. wu, a. carlsson, weight functions and stress intensity factor solutions. pergamon press, oxford (1991). [26] t. fett, d. munz, stress intensity factors and weight functions. computational mechanics, billerica, ma (1997). [27] j. shigley, c. mischke, r. budynas. mechanical engineering design, 7 ed. mcgraw-hill science/engineering/math, (2003). http://dx.medra.org/10.3221/igf-esis.11.02&auth=true http://www.gruppofrattura.it microsoft word numero_42_art_12.docx p. raposo et alii, frattura ed integrità strutturale, 42 (2017) 105-118; doi: 10.3221/igf-esis.42.12 105 focused on mechanical fatigue of metals probabilistic fatigue s-n curves derivation for notched components p. raposo, j.a.f.o. correia, a.m.p. de jesus, r.a.b. calçada inegi and construct, faculty of engineering, university of porto, rua dr. roberto frias, 4200-465 porto, portugal praposo@inegi.up.pt, http://orcid.org/0000-0002-9415-8209 jacorreia@inegi.up.pt, http://orcid.org/0000-0002-4148-9426 ajesus@fe.up.pt, http://orcid.org/0000-0002-1059-715x ruiabc@fe.up.pt, http://orcid.org/0000-0002-2375-7685 g. lesiuk faculty of mechanical engineering, department of mechanics, material science and engineering, wrocław university of science and technology, smoluchowskiego 25, 50-370 wrocław, poland grzegorz.lesiuk@pwr.edu.pl, https://orcid.org/0000-0003-3553-6107 m. hebdon virginia polytechnic institute and state university, department of civil engineering, blacksburg, united states mhebdon@vt.edu a. fernández-canteli department of construction and manufacturing engineering, univ. of oviedo, 33203 gijón, spain afc@uniovi.es, http://orcid.org/0000-0001-8071-9223 abstract. europe has a number of ancient riveted metallic bridges, constructed during the second half of the 19th century up to the middle of the 20th century, which are still in operation. in this paper, a unified approach is presented to generate probabilistic s-n curves to be applied to structural components, accounting for uncertainties in material properties. the approach is particularly demonstrated for a plate with a circular hole, made of puddle iron from the portuguese eiffel bridge. this paper presents an extension of the local strain-based fatigue crack propagation model proposed by noroozi et al. the latter model is applied to derive the probabilistic fatigue crack propagation field (p-s-np field). the probabilistic fatigue crack initiation field (p-s-ni field) is determined using a notch elastoplastic approach, to calculate the fatigue failure of the first elementary material block ahead of the notch root. keywords. fatigue; probabilistic approach; puddle iron; notched plate; local approaches. citation: raposo, p., correia, j.a.f.o., de jesus, a.m.p., calçada, r.a.b., lesiuk, g., hebdon, m., fernández-canteli, a., probabilistic fatigue s-n curves derivation for notched components, frattura ed integrità strutturale, 42 (2017) 105-118. received: 30.04.2017 accepted: 31.05.2017 published: 01.10.2017 copyright: © 2017 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. p. raposo et alii, frattura ed integrità strutturale, 42 (2017) 105-118; doi: 10.3221/igf-esis.42.12 106 introduction he majority of fatigue models proposed in the literature are deterministic. their application for design purposes requires additional safety margins defined with supplementary statistical arguments in order to allow the establishment of an appropriate safe design. in this paper, a probabilistic approach is applied to generate probabilistic s-n curves for notched details such as a notched plate (plate with circular hole) made of puddle iron from the eiffel bridge, based on local strain fatigue approaches [1]. the plate with a circular hole is of interest since it shows similitudes with the riveted plates. their study allows a better understanding of the fatigue behaviour of riveted joints. the model applied in this paper is an extension of the fatigue crack propagation model proposed by noroozi et al. [2-4] which is based on a local strain approach to fatigue. the latter model, named as unigrow model, is a fatigue crack propagation model based on residual stress considerations [2,3]. the selected model is applied in this paper to derive a probabilistic fatigue crack propagation field (p-s-np field) for a detail tested under stress control and a null stress r-ratio. the fatigue crack propagation is considered a damaging process consisting on continuous crack initializations over adjacent material representative elements of a size, ρ*. based on pure fatigue crack growth data, the material representative element size, ρ*, was previously estimated as can be consulted in references [5-9]. probabilistic fatigue crack initiation fields (p-s-ni fields) are determined using an elastoplastic approach together with the material p-swt-n fields. predicted global p-s-n fields (combination of fatigue crack initiation and propagation phases) are compared with experimental s-n fatigue data for the notched plate, with a circular hole, made of puddle iron from the eiffel bridge [10]. general procedure to generate p–s–n–r fields for notched details description of the procedure he procedure proposed by correia et al. [1] to derive probabilistic s–n–r fields for notched structural details or mechanical components is based on the assumption that crack path is discretized into elementary material blocks of length ρ*, placed along the assumed crack path (see fig. 1). the process is then pictured according to the following steps: 1. estimation of the p–swt–n or p–εa–n material fields, as described in next section, using experimental fatigue data from smooth specimens. these probabilistic fields will be the basis of the proposed model to evaluate the probabilistic s–n fields of the notched details. the selection of the damage parameter (swt: smith-watson-topper or εa: strain amplitude) will depend on material/detail sensitivity to the mean stress or stress ratio. 2. estimation of the elementary material block size, ρ*, using fatigue crack propagation data from fatigue crack propagation tests as for example using ct specimens, following the procedure by noroozi et al. [2,3]. the elementary material block size is estimated using an iterative optimization procedure in order to result a good fit of the experimental fatigue crack propagation data, for several stress ratios, within the estimated s-n field. 3. elastoplastic analysis of the uncracked detail in order to evaluate the average local stresses and strains at the first element block size ahead of the notch root. this step was performed in this research, using the finite element method (see fig. 2). 4. application of the p–swt–n or p–εa–n fields to derive the p–s–ni–r field representative of the macroscopic crack initiation, in the structural detail/mechanical component, which corresponds to the failure of the first elementary material block in the notch root. 5. application of a modified version of the unigrow model to evaluate the fatigue crack propagation in the structural detail, using the elementary material block size computed previously on step 2. the residual stress field required in the unigrow model is computed in this paper using elastoplastic finite element analysis. 6. computation of the p–s–np–r field corresponding to the fatigue crack propagation in the notched detail/mechanical component (see fig. 3). 7. combination of probabilistic fields from steps 4 and 6 to evaluate the global p–s–nf–r field for the detail under analysis. the procedures adopted to compute the probabilistic s–ni–r and s–np–r fields, for structural details are summarized in figs. 2 and 3, respectively [1,5]. t t p. raposo et alii, frattura ed integrità strutturale, 42 (2017) 105-118; doi: 10.3221/igf-esis.42.12 107 figure 1: representative material blocks along the postulated crack propagation path of a notched detail. figure 2: procedure for the estimation of the probabilistic fatigue crack initiation field for notched geometries. additional considerations on the application of the unigrow model the unigrow model was proposed by noroozi et al. [2] to compute the elastoplastic stresses and strains at the elementary material blocks ahead of the crack tip, and was further developed in the current study, particularly in what concerns the determination of the number of cycles to failure of the elementary material blocks, in the fatigue crack propagation regime, according to the following procedure: i) the stress intensity factors are determined for the detail under investigation using linear elastic finite element analysis and the j-integral method. ii) the original procedure for the computation of the residual stress distribution consisted in the following actions: a) elastic stress fields ahead of the crack tip are estimated using analytical solutions for a crack with a tip radius, ρ*, and using the stress intensity factors solutions from analytical formulae. b) the actual elastoplastic stresses and strains, ahead of the crack tip, are computed using neuber’s or glinka’s approach [11,12]. c) the residual stress distribution ahead of the crack tip is computed using the maximum actual elastoplastic stresses resulting at the end of the first load reversal and the subsequent cyclic elastoplastic stress range, σr =σmax σ. elastoplastic stress analysis  (uncracked geometry)    fem  or  analytical  (neuber, glinka, seeger‐heuler)  δσapplied , r  ε‐n exp. data  p‐ε‐n or p‐swt‐n  weibull fields  p‐s‐ni‐r fields  failure of the first  elementary  material block  p. raposo et alii, frattura ed integrità strutturale, 42 (2017) 105-118; doi: 10.3221/igf-esis.42.12 108 figure 3. procedure for the estimation of the probabilistic fatigue crack propagation fields for the notched geometries. in this study, sub-steps a), b) and c) were replaced by an elastoplastic finite element analysis in order to allow the direct computation of the residual stress fields to be performed. iii) the residual stress distribution computed ahead of the crack tip is assumed to be applied on the crack faces, behind the crack tip, in a symmetric way with respect to the crack tip. the residual stress intensity factor, kr, is then computed using the weight function method according to the following general expression [13]:     0 . , a r rk x m x a dx  (1) to this purpose, the weight function m(x,a) was computed for the cracked detail under consideration using the following expression [10]:   1 , . yuh m x a k a    (2) elastoplastic stress analysis  (cracked geometry)  fem  linear‐elastic stress analysis  (cracked geometry)  fem  residual stress, σr weight function    a u k h a,xm y i      stress intensity factor  (j‐integral method)  kapplied and kmax,applied  residual stress intensity factor      dxa,xmxk a 0 rr      rappliedtot rappliedmax,totmax, kkk kkk    actual elastoplastic stresses and strains  (σmax and ε/2)  neuber’s approach  δσapplied , r  crack propagation data  and  unigrow model  elementary material block size  a = ai = *  kmax,applied < kc  yes  a = a + *  no  ε‐n exp. data  p‐ε‐n or p‐swt‐n  weibull fields p‐s‐np‐r fields  end  p. raposo et alii, frattura ed integrità strutturale, 42 (2017) 105-118; doi: 10.3221/igf-esis.42.12 109 where h=e (young's modulus) for generalized plane stress, and h=e/(1-v2) for plane strain, v being the poisson's ratio; ki is the stress intensity factor and uy is the corresponding crack opening displacement. in this research the weight functions were computed using a linear elastic finite element model for the cracked geometries. iv) the applied stress intensity factor (maximum and range values) is corrected using the residual stress intensity value, resulting in the total effective values, kmax,tot and ktot [2,3]. for positive applied stress ratios, kmax,tot and ktot may be computed as follows: , ,max tot max applied r tot applied r k k k k k k       (3) where kr takes a negative value corresponding to the compressive stress field. this residual stress correction makes the crack propagation model sensitive to the stress ratio effects. in fact, the compressive stresses decrease with increasing stress ratio. consequently, the total stress intensity factors tend to the corresponding applied stress intensity factor. for lower stress ratios, the total stress intensity factors will be lower than the applied ones. this step, corresponding to the original proposal of noroozi et al. [2] was followed in this study. v) using the total values of the stress intensity factors, the above steps ii.a) and ii.b) are applied to determine the updated values of the actual maximum stress and actual strain range for the material representative elements. then, smith-watsontopper (swt)-n [14] or morrow’s relations [15] are applied to compute the number of cycles required for the material representative element to fail. for materials with the stress propagation rates more sensitivity to the stress ratio, smithwatson-topper (swt)-n [14] should be used; otherwise, morrow’s relation [15] may be adequate. morrow’s equation considered here corresponds to the superposition of basquin [16] and coffin-manson relations [17,18] without any mean stress correction. the unigrow crack propagation model will be applied to compute the number of cycles required to propagate an initial crack at the notch root of a detail until the critical dimension, responsible for the collapse of the component, is achieved. in this research, it is postulated that the crack initiation corresponds to the development of a crack with a size equal to the elementary material block dimension, ρ*. in addition to the number of cycles required to propagate the crack, the number of cycles required to initiate a crack of a size equal to the elementary material block, ρ*, will be also computed using a local approach. for this purpose, an elastoplastic stress/strain analysis will be carried out for the uncracked geometry to derive the average stress/strains at the first elementary material block ahead of the notch root (see fig. 2). probabilistic εa-n and swt-n fields oth crack initiation and crack propagation simulations are based on a fatigue damage relation, which is required to compute the number of cycles to fail the elementary material block. in this paper, probabilistic fatigue models are proposed rather than the deterministic swt-n or εa-n models defined by references [14] or [15], respectively. castillo and fernández-canteli [19] proposed a probabilistic εa-n field, based on the weibull distribution, which allows the correlation of the experimental strain-life data. besides the original p-εa-n field proposed by castillo and fernándezcanteli [19], a generalization of the probabilistic field is proposed in this paper, using an alternative damage parameter. in particular, the swt (=σmax.εa) damage parameter, proposed by smith-watson-topper [14] to account for mean stress effects on fatigue life, was used to generate an alternative probabilistic field, sensitive to mean stress effects. any combination of maximum stress and strain amplitude that leads to the same swt parameter should predicts the same fatigue life. the swt-n and εa-n fields exhibit similar characteristics. therefore, the p-εa-n field proposed by castillo and fernández-canteli may be extended to represent the p-swt-n field as follows:   0 0 0 0 . * ; * 1 . f f f n swt log log n swt p f n swt exp n swt log log n swt                                              (4) b p. raposo et alii, frattura ed integrità strutturale, 42 (2017) 105-118; doi: 10.3221/igf-esis.42.12 110 where swt0 is the fatigue limit defined in terms of the swt parameter. the new probabilistic field is illustrated in the fig. 4. figure 4: percentile curves representing the relationship between the dimensionless lifetime, nf*, and the damage parameter, swt*. the threshold parameters log (n0)=b and log(0)=c of the p--n model or log(n0)=b and log(swt0)=c of the p-swt-n model may be estimated using a constrained least squares method. in turn, the weibull parameters, β, λ and δ, are estimated by the maximum likelihood method. more details about the parameters identification procedure can be found in reference [19]. experimental fatigue data of the puddle iron and notched detail from the eiffel bridge he puddle iron from the portuguese eiffel bridge is considered in this study. the eiffel bridge was designed by gustave eiffel and was inaugurated in 1878 (see fig. 5). the fatigue behaviour of the material from the eiffel bridge was determined based on fatigue tests of smooth specimens and fatigue crack propagation tests. the fatigue tests of smooth specimens were carried out according to the astm e606 standard [20], under strain controlled conditions and are summarized in tabs. 1 and 2. figure 5: riveted metallic eiffel bridge in viana do castelo (portugal). the fatigue crack propagation tests were performed using ct specimens, in accordance with the procedures of the astm e647 standard [21], under load controlled conditions. ct specimens from the eiffel bridge were defined with a width, w=40 mm, and a thickness, b=4.5 mm. the fatigue crack propagation tests were performed for stress r-ratios, r=0.1 log nf*  swt0  n0  p=0   p=0.05   p=0.5   p=0.95 l o g  s w t *    t p. raposo et alii, frattura ed integrità strutturale, 42 (2017) 105-118; doi: 10.3221/igf-esis.42.12 111 and r=0.5. the experimental fatigue data is plotted in fig. 6, along with the regression lines, for each stress r-ratio, which were defined according to the paris’s law [22]. the fatigue crack propagation data of the material from the eiffel bridge shows important scatter due to the significant amount of heterogeneities that characterizes the puddle irons [23]. details about the properties evaluation can be found in reference [24]. e (gpa)  uf (mpa) yf (mpa) k’ (mpa) n’ 193.11 0.30 342.0 292.0 645.95 0.0946 table 1: monotonic and cyclic elastoplastic properties of the material from the eiffel bridge. ' f (mpa) b ' f c 602.5 -0.0778 0.1595 -0.7972 table 2: morrow constants of the material from the eiffel bridge. the observation of the fig. 6b) reveals that the material fatigue crack propagation rates are sensitive to the stress ratio. due to this result, the fatigue crack propagation rates for this material will be modelled using the unigrow model based on the swt damage parameter. using the experimental fatigue data from the smooth specimens, the p-εa-n and p-swt-n fields of the material from the eiffel bridge were evaluated and presented in figs. 7 and 8, respectively. the constants of the weibull field are also included in the figures, in particular the threshold constants (b and c) and the weibull parameters (β, λ and δ). the weibull field shows a hyperbolic behaviour with the horizontal asymptote representing the fatigue limit of the material. a plate with a circular hole, made of puddle iron from the eiffel bridge, as illustrated in fig. 9, was considered in this investigation. this geometry was fatigue tested under remote stress controlled conditions, for stress r-ratio equal to 0. the s-n results presented in this sub-section were obtained using fatigue tests of specimens subjected to load controlled conditions, for stress r-ratio equal to 0, and performed on a servo-hydraulic machine rated to 100kn at test frequencies, f, ranging between 5 and 10hz. a total of 15 specimens were tested. the respective fatigue data can be found in fig. 10 [10]. the stress range plotted in fig. 10 corresponds to the net stress range computed at the central section of the plate. the p-swt-n field will be used to model the fatigue crack initiation and propagation fields for the notched structural detail. a) b) figure 6: fatigue crack propagation data of the material from the eiffel bridge for distinct stress ratios: a) experimental data; b) trend lines for each stress r-ratio. 2t1 (r=0.1) 2t2 (r=0.1) 2t3 (r=0.5) 2t4 (r=0.5) 2l1 (r=0.1) 300 k [n.mm-1.5] 1.0e-5 1.0e-3 d a/ d n [ m m /c yc le ] 1.0e-4 500 1000 1.0e-6 1.0e-2 1200 r=0.1 r=0.5 r=0.1 + r=0.5 300  1000  k [n.mm‐1.5]  1.0e‐5  1.0e‐3  d a /d n  [ m m /c yc le ]  1.0e‐4  500  1200  1.0e‐6  da/dn=3.0907e‐20k5.5347  r 2 =0.9604  da/dn=1.5624e‐19k5.0585  r 2 =0.8644  1.0e‐2  da/dn=2.4329e‐18k4.6899  r 2 =0.71971  p. raposo et alii, frattura ed integrità strutturale, 42 (2017) 105-118; doi: 10.3221/igf-esis.42.12 112 figure 7: p-εa-n field for the material from the eiffel bridge. figure 8: p-swt-n field for the material from the eiffel bridge. figure 9: plate made of puddle iron from the eiffel bridge with a circular hole (dimensions in mm). 1.0e‐04 1.0e‐03 1.0e‐02 1.0e‐01 1.0e+01 1.0e+02 1.0e+03 1.0e+04 1.0e+05 1.0e+06 1.0e+07 cycles to failure, n f   /2 [] p=1% p=5%  p=50% p=95% p=99% experimental data b = ‐13.9697 c = ‐10.0419 β = 7.6103 λ = 68.4171 δ = 18.2667 0.1 1 10 1.0e+01 1.0e+02 1.0e+03 1.0e+04 1.0e+05 1.0e+06 1.0e+07 cylces to failure, n f  s w t  [ m p a ] p=1% p=5%  p=50% p=95% p=99% experimental data b = ‐63.8216 c = ‐17.2436 β = 13.6002 λ = 1051.0599  = 164.0604 p. raposo et alii, frattura ed integrità strutturale, 42 (2017) 105-118; doi: 10.3221/igf-esis.42.12 113 figure 10: s-n data of the plate with a circular hole made of puddle iron from the eiffel bridge. prediction of the probabilistic s-n field for a notched detail n this section the probabilistic s-n field of the notched detail is computed. the total number of cycles to failure is assumed to follow the following split relation: f i pn n n  (5) the crack initiation corresponds to the initiation of a crack of a size equal to the elementary material block size, *. the number of crack propagation cycles corresponds to the number of cycles required to propagate the initial crack with the size of the elementary material block until failure, i.e. unstable crack propagation. the crack initiation is modelled using the p-swt-n field, due to the sensitivity of the material to the stress ratio, which is visible on the fatigue crack propagation rates. the crack propagation will be performed using the so-called unigrow model, using probabilistic fatigue damage fields. the value of the elementary material block size, ρ*=12×10-4m, was estimated in the reference [9], using fatigue crack propagation data from ct specimens. finite element analysis of the notched detail a 2d finite element model of the notched detail was proposed, using ansys® code [25]. fig. 11 illustrates a typical finite element mesh of the detail, with and without a crack. this mesh exhibits a crack on the left side of the notch. in the practice, cracks started at both sides of the notch root and propagated symmetrically in the plate. taking into account the existing symmetry planes, only ¼ of the geometry is modelled. plane stress quadratic triangular elements were used in the analysis due to the limited specimen thickness. the plane 181 elements were used in the analysis of the notch plate from the eiffel bridge. a highly refined mesh at the crack tip region was used in order to model the crack tip notch radius, ρ* (see magnification in fig. 11). the von mises yield criterion with multilinear kinematic hardening, was used in simulations aiming an estimation of the residual stresses. the plasticity model was fitted to the stabilized cyclic curve of the material, see fig. 12. prediction of the probabilistic s-ni-r field the p-swt-n model is used to predict the fatigue crack initiation (failure of the first elementary material block) at the notch root of the detail – according to the procedure illustrated in fig. 2. an elastoplastic finite element analysis was used to compute the stress/strain history at the notch root. in order to facilitate the strain amplitude computation, loading followed by unloading steps were simulated using a plasticity model identified with the stabilised cyclic stress-strain curve of the material. fig. 13 shows the p-s-ni field corresponding to the fatigue crack initiation for the detail, for r=0.0. the cycles to failure, n f exp. data ‐ r=0.0 1.0e4 1.0e5 1.0e6 100  σ    [m p a ] 1.0e3 200 300 400 1.0e7 i p. raposo et alii, frattura ed integrità strutturale, 42 (2017) 105-118; doi: 10.3221/igf-esis.42.12 114 analysis of the figure reveals that fatigue crack initiation is dominant, since it gives already a good description of the s-n fatigue data of the detail. a) b) c) figure 11: finite element mesh of the plate with a circular hole: a) ¼ of the finite element mesh of the structural retail; b) without crack; c) with a side crack and tip notch radius of 1200μm. figure 12: cyclic curve of the material from eiffel bridge. figure 13: p-s-ni field for the structural detail made of material from the eiffel bridge. prediction of the probabilistic s-np-r field the procedure adopted to compute the probabilistic s-np field for the notched plate is illustrated in the fig. 3. a value of the elementary material block size, ρ*=12×10-4m, was previously estimated using an independent identification based on pure fatigue crack propagation data (see reference [9] for details). finite element models of the detail were used to perform elastoplastic stress analyses aiming the computation of the residual stresses. in addition, linear elastic finite element models were used to compute the weight functions required for the residual stress intensity factor computation as well as the stress intensity factor solutions for the notched geometry. the stress intensity factors were determined based on a linear-elastic finite element analysis using the j-integral method. fig. 14 presents the stress intensity factor evolution with the crack length for a unit remote stress, which was used to determine the kapplied. fig. 15 presents the elastoplastic stress distribution along the y direction, ahead of the crack tip, and obtained at the end of the first load reversal using an elastoplastic finite element analysis. fig. 16 presents the residual stress distribution along the y direction ahead of the crack tip, resulting from the elastoplastic finite element analysis. these residual stresses were computed after loading-unloading steps. high compressive stresses are observed at the vicinity of the crack tip. the residual stress intensity factor, kr, was 0 100 200 300 400 500 600 0.00e+00 1.00e‐02 2.00e‐02 3.00e‐02 4.00e‐02 5.00e‐02  [‐]    [ m p a ] ramberg‐osgood fem ‐ multilinear cycles to failure, n i exp. data p=0.01 p=0.05 p=0.50 p=0.95 p=0.99 1.0e4 1.0e5 1.0e6 100  σ    [m p a ] 1.0e3 200 300 400 r=0.0 1.0e7 p. raposo et alii, frattura ed integrità strutturale, 42 (2017) 105-118; doi: 10.3221/igf-esis.42.12 115 determined using the weight functions technique as proposed by eq. (1) and eq. (2) and using results from linear elastic finite element analysis. those weight functions allow the residual stress intensity factor, kr, to be computed. fig. 17 shows the evolution of kr with the applied stress intensity factor range. the resulting data shows a good linear correlation. the p-s-np field of the structural detail was calculated for r=0 using the p-swt-n field of the material from the eiffel bridge together with the unigrow model proposed by noroozi et al. [2], and assuming ρ*=12×10-4m (see reference [9]). the use of the p-swt-n field of the material from the eiffel bridge to model the fatigue crack propagation is justified by the fact that the material showed a crack propagation rate sensitivity to stress ratio effects as argued in reference [9]. fig. 18 illustrates the p-s-np field obtained for the structural detail under consideration. the comparison of the experimental fatigue data with the crack propagation field shows that the crack propagation, despite not negligible, is not the dominant damage process, at least for low stress ranges/ high fatigue lives. figure 14: stress intensity factors as a function of the crack length, for a unit load (elastic analysis). figure 15: elastoplastic stress distributions along y (load) direction for the notched plate, for crack size equal to 2.25 mm. figure 16: residual stress distributions for the notched plate for crack size equal to 2.25mm. figure 17: residual stress intensity factor as a function of the applied stress intensity factor range for the notched plate. prediction of the probabilistic s-nf-r field the combined crack initiation and crack propagation s-n fields were computed for the notched plate, using eq. (5). fig. 19 presents the combined (superimposed) results. the analysis of the resulting s-n field highlights the accuracy of the proposed methodology. the experimental fatigue data falls inside the 5%-95% failure probability band. the unified approach proposed by correia et al. [1] seems to give fairly promising predictions for notched components [10], in this case a plate with a circular hole. 0 10 20 30 40 0 5 10 15 a [mm] k /   [ m m 0 .5 ] j‐integral applied remote stress 1n/mm 2 0 200 400 600 0 1 2 3 4 5 6 distance from the crack tip [mm] e la st o p la st ic  s tr e ss ,   y  [ m p a ] 175 200 225 275 a=2.25mm applied nominal stress [mpa], r=0.0 ‐400 ‐200 0 200 0 1 2 3 4 distance from the crack tip [mm] r e si d u a l  st re ss ,   r  [m p a ] 175 200 225 275a=2.25mm nominal stress range [mpa], r=0.0 p. raposo et alii, frattura ed integrità strutturale, 42 (2017) 105-118; doi: 10.3221/igf-esis.42.12 116 figure 18: p-s-np field obtained for the notched plate made of material from the eiffel bridge. figure 19: p-s-nf field obtained for the notched plate made of material from eiffel bridge. conclusions unified approach to derive probabilistic s-n fields proposed by correia et al. [1] for structural details taking into account both crack initiation and crack propagation was applied in this paper. this approach combines finite element analyses with the unigrow model and probabilistic fatigue damage fields of the base material. one key parameter in this approach is the definition of the elementary material block size, which was identified using an independent procedure based on pure fatigue crack propagation data. the predicted p-s-ni field for fatigue crack initiation on the structural detail, based on the p-swt-n model and elastoplastic finite element analysis provided a good agreement with the experimental results, for r=0. the adaptation of the unigrow model allowed to reproduce satisfactorily crack propagation prediction using residual compressive stress estimation, based on elastoplastic finite element analysis of the notched detail, and the p-swt-n damage model. in this study, and for the plate with the circular hole the crack initiation was the dominating fatigue damaging process, while the fatigue crack propagation exerts a small influence on global predictions of the p-s-n field, mainly in the high-cycle fatigue regime. the procedure proposed to derive the probabilistic s-n curves for structural details shows satisfactory results and proved to be quite efficient since it cycles to failure, n p exp. data p=0.01 p=0.05 p=0.50 p=0.95 p=0.99 1.0e4 1.0e5 1.0e6 100  σ    [m p a ] 1.0e3 200 300 400 r=0.0 1.0e7 cycles to failure, n f exp. data p=0.01 p=0.05 p=0.50 p=0.95 p=0.99 1.0e4 1.0e5 1.0e6 100  σ    [m p a ] 1.0e3 200 300 400 r=0.0 1.0e7 a p. raposo et alii, frattura ed integrità strutturale, 42 (2017) 105-118; doi: 10.3221/igf-esis.42.12 117 can be used to reduce the need for extensive testing of structural components. only small-scale testing data is required, fundamentally fatigue data from smooth specimens will be enough. in addition, the representative material block size needs to be calibrated for the material and for that purpose the use of pure fatigue crack propagation data will be the most adequate choice. acknowledgements he authors acknowledge the portuguese science foundation (fct) for the financial support through the postdoctoral grant sfrh/bpd/107825/2015. the authors gratefully acknowledge the funding of scitech: science and technology for competitive and sustainable industries, r&d project cofinanced by programa operacional regional do norte (norte2020), through fundo europeu de desenvolvimento regional (feder). references [1] correia, j. a. f. o., de jesus, a. m. p., fernández-canteli, a. local unified probabilistic model for fatigue crack initiation and propagation: application to a notched geometry, engineering structures., 52 (2013) 394-497. [2] noroozi, a. h., glinka, g., lambert, s., a two parameter driving force for fatigue crack growth analysis, international journal of fatigue, 27 (2005) 1277-1296. [3] noroozi, a. h., glinka, g., lambert, s., a study of the stress ratio effects on fatigue crack growth using the unified two-parameter fatigue crack growth driving force, international journal of fatigue, 29 (2007) 1616-1633. [4] mikheevskiy, s., glinka, g., elastic–plastic fatigue crack growth analysis under variable amplitude loading spectra, international journal of fatigue., 31 (2009) 1828–1836. [5] correia, j. a. f. o., de jesus, a. m. p., fernández-canteli, a., a procedure to derive probabilistic fatigue crack propagation data, international journal of structural integrity, 3 (2012) 158. [6] hafezi, m. h., abdullah, n. n., correia, j. a. f. o., de jesus, a.m.p., an assessment of a strain-life approach for fatigue crack growth, international journal structural integrity, 3 (2012) 344-376. [7] de jesus, a. m. p., correia, j. a. f. o., critical assessment of a local strain-based fatigue crack growth model using experimental data available for the p355nl1 steel, journal of pressure vessel technology, 135(1) (2013) 011404:1-9. [8] correia, j. a. f. o., de jesus, a. m. p., ribeiro, a. s., strain-based approach for fatigue crack propagation simulation of the 6061-t651 aluminum alloy, international journal of materials and structural integrity (in press). [9] correia, j. a. f. o., de jesus, a. m. p., fernández-canteli, a., calçada, r. a. b., modelling probabilistic fatigue crack propagation rates for a mild structural steel, frattura ed integrita strutturale, 31 (2015) 80-96. [10] correia, j. a. f. o., de jesus, a. m. p., fernández-canteli, a., calçada, r. a. b., probabilistic fatigue behaviour of structural details of puddle iron from the eiffel bridge, proceedings of the 3.º congresso de segurança e conservação de pontes (ascp’13), (2013). [11] neuber, h., theory of stress concentration for shear-strained prismatic bodies with arbitrary nonlinear stress–strain law, journal of applied mechanics. transactions asme, 28 (1961) 544–551. [12] molski, k., glinka, g., a method of elastic-plastic stress and strain calculation at a notch root, materials science and engineering, 50 (1981) 93-100. [13] ma, c.-c., huang, j.-i., tsai, c.-h., weight functions and stress intensity factors for axial cracks in hollow cylinders, journal pressure vessel technology, (1994) 116-423. [14] smith, k. n., watson, p., topper, t. h., a stress-strain function for the fatigue of metals, journal of materials, 5(4) (1970) 767-78. [15] morrow, j. d., cyclic plastic strain energy and fatigue of metals, int. friction, damping and cyclic plasticity. astm stp 378, (1965) p. 45-87. [16] basquin, o. h., the exponential law of endurance tests. proc. annual meeting american society for testing materials, 10 (1910) 625-630. [17] coffin, l.f., a study of the effects of the cyclic thermal stresses on a ductile metal. trans asme 76 (1954) 931–950. [18] manson ss. behaviour of materials under conditions of thermal stress, naca tn-2933. national advisory committee for aeronautics, (1954). [19] castillo, e., fernández-canteli, a., a unified statistical methodology for modeling fatigue damage. springer (2009). t p. raposo et alii, frattura ed integrità strutturale, 42 (2017) 105-118; doi: 10.3221/igf-esis.42.12 118 [20] astm e606: standard practice for strain-controlled fatigue testing, annual book of astm standards. astm, west conshohocken, pa, usa, 03.01 (1998) [21] astm e647: standard test method for measurement of fatigue crack growth rates, annual book of astm standards. astm, west conshohocken, pa, usa, 03.01 (2000) [22] paris, p. c., gomez, m., anderson, w. e., a rational analytic theory of fatigue, trend engineering, 13 (1961) 9-14. [23] lesiuk, g., szata, m., bocian, m., the mechanical properties and the microstructural degradation effect in an old low carbon steels after 100-years operating time, archives of civil and mechanical engineering, 15(4) (2015) 786-797. [24] de jesus, a. m. p., silva, a. l. l., figueiredo, m. v., correia, j. a. f. o., ribeiro, a. s., fernandes, a. a., strain-life and crack propagation fatigue data from several portuguese old metallic riveted bridges, engineering failure analysis, 17 (2010) 1495–1499. 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can be opened with acrobat and adobe reader 5.0 and later.) >> /namespace [ (adobe) (common) (1.0) ] /othernamespaces [ << /asreaderspreads false /cropimagestoframes true /errorcontrol /warnandcontinue /flattenerignorespreadoverrides false /includeguidesgrids false /includenonprinting false /includeslug false /namespace [ (adobe) (indesign) (4.0) ] /omitplacedbitmaps false /omitplacedeps false /omitplacedpdf false /simulateoverprint /legacy >> << /addbleedmarks false /addcolorbars false /addcropmarks false /addpageinfo false /addregmarks false /convertcolors /converttocmyk /destinationprofilename () /destinationprofileselector /documentcmyk /downsample16bitimages true /flattenerpreset << /presetselector /mediumresolution >> /formelements false /generatestructure false /includebookmarks false /includehyperlinks false /includeinteractive false /includelayers false /includeprofiles false /multimediahandling /useobjectsettings /namespace [ (adobe) (creativesuite) (2.0) ] /pdfxoutputintentprofileselector /documentcmyk /preserveediting true /untaggedcmykhandling /leaveuntagged /untaggedrgbhandling /usedocumentprofile /usedocumentbleed false >> ] >> setdistillerparams << /hwresolution [2400 2400] /pagesize [612.000 792.000] >> setpagedevice microsoft word numero_51_art_17_2635 p. farazmand et alii, frattura ed integrità strutturale, 51 (2021) 215-224; doi: 10.3221/igf-esis.51.17 215 relationship between microscopic analysis and quantitative and qualitative indicators of moisture susceptibility evaluation of warmmix asphalt mixtures containing modifiers pooyan farazmand, parham hayati department of civil engineering, science and research branch, islamic azad university, iran pooyanfarazmand1@gmail.com, p.hayati@srbiau.ac.ir hamid shaker iran university of science and technology, iran h_shaker@civileng.iust.ac.ir, https://orcid.org/0000-0002-8524-1676 sajad rezaei department of civil engineering, pooyesh institute of higher education, iran rezaei@pooyesh.ac.ir, https://orcid.org/0000-0001-7394-8001 abstract. given the defects of bitumen in asphalt mixtures particularly exposed to moisture, this study mainly aims to investigate the relationship between qualitative and quantitative results of moisture susceptibility tests on asphalt mixtures modified by zycotherm, nanoclay, nanosilica and sbs. the marshall stability, modulus of resilience and indirect tensile strength tests are carried out. boiling water and sem qualitative tests are also used. eventually, the qualitative tests results are digitalized through image processing by matlab and compared with the moisture susceptibility results of indirect tensile strength test. for modulus of resilience testing, the results show that this modifier has the maximum impact on marshall stability, improving it by about 23%. for moisture susceptibility testing, the nanosilica-modified mixture has the maximum effect among anti-stripping additives, with an improvement by about 20%. an investigation into the results of sem images and boiling water test via matlab indicates the high accuracy of sem images and their results show the most compatibility with the results of quantitative data. keywords. modifier; moisture susceptibility; image processing; scanning electron microscopy (sem) of bitumen. citation: farazmand, p., hayati, p., shaker, h., rezaei, s., n., relationship between microscopic analysis and quantitative and qualitative indicators of moisture susceptibility evaluation of warm-mix asphalt mixtures containing modifiers, frattura ed integrità strutturale, 51 (2020) 215-224. received: 14.09.2019 accepted: 24.11.2019 published: 01.01.2020 copyright: © 2020 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. http://www.gruppofrattura.it/va/51/2635.mp4 p. farazmand et alii, frattura ed integrità strutturale, 51 (2021) 215-224; doi: 10.3221/igf-esis.51.17 216 introduction he design and construction of asphalt pavements are essentially aimed to ensure the best performance under a variety of conditions, e.g. weather changes. asphalt mixtures should possess proper durability and stability in order to achieve the best performance in asphalt pavements [1]. the efficiency of asphalt pavements mostly depends on the adhesion and bond between bitumen and aggregate. stripping is a major failure of asphalt pavements due to the penetration of water between aggregate and bituminous binder, which occurs as a result of loss of adhesion between bituminous binder and aggregate [2]. since moisture-induced damage in asphalt mixtures was first detected as a problem, considerable efforts have been made to specify its basic mechanisms and to develop a variety of tests for prediction and prevention of moisture damages [3]. the constituent characteristics play a key role in the properties of structural pavements. although the bitumen content is far less than the aggregate in weight, it plays a significant role in the performance of asphalt pavements and the durability and stability of asphalt mixtures and any variation of performance of bitumen causes dramatic changes in the performance of asphalt mixtures [4]. the use of appropriate aggregate in asphalt mixtures usually can prevent stripping, but the bitumen modification is also of great importance. the application of modified bitumen can reduce stripping. in addition to impacts on the bond between aggregate and bitumen, anti-stripping materials can change the hardness and rutting resistance and increase or decrease the propagation of cracks[5]. on the other hand, the image processing of asphalt mixture specimens was first conducted for a project entitled “thermography image processing in an asphalt core” in 1993 at the university of southern california. this study was carried out in cooperation with civil, electrical engineering, radiology, metallurgy, chemical engineering and asphalt experts. the study aimed to investigate the asphalt core after construction and to find deformations and failures before and after loading. this technique became popular in pavement engineering after this study [6]. later, a variety of image processing methods were employed for 3d modeling of these specimens [7] [8]. in 2013, ki hoon conducted an analysis of structure of asphalt mixtures using digital image processing techniques [9], which was developed according to the research by zelelew et al [10]. different components of asphalt mixture and volumetric information were assessed in this study. the applied methods were based on the detection of threshold between the air, mastic (bitumen and filler) and aggregate according to the experimental data. this study aims to evaluate the relationship between quantitative and qualitative results of moisture susceptibility tests on asphalt mixtures containing zycotherm, nanoclay, sbs and nanosilica modifiers. it is investigated using indirect tensile strength, marshall stability, modulus of resilience, boiling water and sem tests. materials n this study, bitumen performance grade pg 58-22 is used, produced by the pasargad oil company in tehran according to the standard (tab. 1). calcareous aggregate extracted from the telo mine in tehran is also used, graded as shown in fig. 1. the grading is according to the iranian highway asphalt paving code no. 234 (grading no. 4). bitumen 60-70standard limits testing method properties upper limit lower limit 1.03 1.06 1.01 astm d-70 specific weight at 25 °c 64 70 60 astm d-5 penetration grade at 25 °c 54 56 49 astm d-36 softening point (°c) 102 100 astm d-113 ductility at 25 °c 305 250 astm d-92 fire point table 1: specifications of bitumen in this study, nano-zycotherm, nanoclay, nanosilica, sbs modifiers are used at their optimum contents. the modifiers are mixed with bitumen using a high shear mixer at 4200 rpm for 45 min at mixing temperature of 175 °c. eventually, the specimens are named in tab. 3. optimum bitumen content is determined 5.1 for the control specimen using the marshall method, according to which all specimens are made and evaluated. t i p. farazmand et alii, frattura ed integrità strutturale, 51 (2021) 215-224; doi: 10.3221/igf-esis.51.17 217 test results allowable limits of the code no. 234 test standarddescription top coat binder 22.3 30 40 aashto t96 maximum abrasion by los angeles abrasion test (%) 16 25 30 bs 812 maximum flakiness index (%) 93 90 80 astm d5821minimum percent of particles with two fractured faces for sieve no. 4 (%) 2.2 2.5 2.5 aashto t85 maximum percent of water absorption (coarsegrained aggregate) 2.4 2.5 2.8 aashto t84 maximum percent of water absorption (fine-grained aggregate) 2.59-astm c127true specific gravity of coarse-grained aggregate 2.32 astm c128 true specific gravity of fine-grained aggregate table 2: specifications of aggregate figure 1: particle size distribution for stone mastic asphalt mixture. applied content abbrev. name modifier mix design no 0 ac control 1 0.1% of bitumen in weight [11] za zycotherm modified by zycotherm 2 4% of bitumen in weight [12] ncnanoclaymodified by nanoclay3 4.5% of bitumen in weight [13] sb sbs modified by sbs 4 4% of bitumen in weight [14] ns nanosilica modified by nanosilica 5 table 3: name of specimens and percent of each material for optimum bitumen content. experimental test initial tests n this study, the marshall stability test is done according to the astm d-1559, the modulus of resilience test is done according to the astm d-4123, the moisture susceptibility of mixture is measured based on indirect tensile strength test according to the aashto t283 and the boiling water test is done according to the astm d-3625 [15] [16] [17]. i p. farazmand et alii, frattura ed integrità strutturale, 51 (2021) 215-224; doi: 10.3221/igf-esis.51.17 218 sem scanning electron microscopy (sem) is a qualitative investigation which can be used to analyze various properties of a mixture by processing of captured images. to capture images, the specimens are taken from the first quartile (250 g) of mixture and put in boiling water for 10 min. then, about 1.18 g of the specimen is taken and placed in the machine and the images are prepared. image processing technique and comparison of results using matlab as a practical software has been seen in previous recent research [18]. in this research, matlab programing as a neural network has been employed and the properties of asphalt were estimated with using this software. in the present study, the matlab software is utilized to quantify the qualitative results of image processing. in this process, the pixels of each image are converted to 0 and 1. accordingly, a value is determined as histogram threshold on the grayscale by converting the image to a negative (black and white) image and assigning a set of values to each greyscale shade. in this study, the threshold is considered 128 with black shade corresponded to 0 and white shade corresponded to 255 and the pixels of black and white shades are specified. hence images taken from boiling water and sem test specimens are imported into matlab and the outputs, i.e. white and black percent, as quantitative results are compared to the results of marshall stability, modulus of resilience and moisture susceptibility of mixture based on indirect tensile strength test. the kruskal-wallis test is thus applied for the comparison. this is a non-parametric statistical test. non-parametric tests have particular conditions corresponding to the parametric f-test; they are applied like the real f-test when the number of population groups is independent and more than 2 to k groups are available. the measurement scale for kruskal-wallis test should be at least ordinal. result marshall stability he results of marshall stability test on modified and non-modified specimens are illustrated in fig. 2. as the chart shows, all additives have a positive effect on marshall stability and this positive effect varies for different specimens. the additives increase the hardness in sbs, nanoclay and nanosilica modified specimens, causing an increased marshall stability. the increase for zycotherm modified specimens is less than the other. figure 2: results of marshall stability for modified and non-modified specimens modulus of resilience the results of this test are demonstrated in fig. 3. the modulus of resilience is tested for the assessment of hardening in the mixture and gives the designer an important parameter for determining the thickness. in this study, all additives except zycotherm increase the modulus of resilience. however, the nanoclay, sbs and nanosilica modified mixtures experience higher increases. to justify the trend, it can be deduced that the hardness somewhat increases for mixtures containing nanoclay and sbs. on the other hand, the decrease for the specimen containing zycotherm can be justified in regard to the additive properties; so that sbs and nanoclay increase the hardening in the bitumen and, consequently, the asphalt and zycotherm reacts vice versa. t p. farazmand et alii, frattura ed integrità strutturale, 51 (2021) 215-224; doi: 10.3221/igf-esis.51.17 219 figure 3: results of modulus of resilience for modified and non-modified specimens indirect tensile strength fig. 4 shows the results of indirect tensile strength test for both dry and wet conditions. as demonstrated in the chart, the addition of modifiers results in significant changes in the specimens and alters both wet and dry strengths and the variations are almost the same under wet and dry conditions for each specimen. for the zycotherm-modified specimen, its wet strength is almost equal to that of the control specimen, but its dry strength declines and approaches its wet strength. for example, the wet and dry strengths of nanoclay, nanosilica and sbs modified specimens increase in comparison with the control specimen, along which the difference between wet and dry strengths decreases. figure 4: results of indirect tensile strength for modified and non-modified specimens. moisture susceptibility based on indirect tensile strength (its) the moisture susceptibility is described in terms of the parameter tsr which is calculated through dividing the wet strength by dry strength in indirect tensile strength test and expressed in percent. in the figure above, this parameter is presented for the control and modified specimens in form of a chart. as shown in the chart, all additives improve the stripping and enhance the tsr. this increase is higher for the specimens containing zycotherm and nanosilica than the other. to justify the trend, it can be argued that as the wet and dry strengths approach together, the moisture susceptibility improves. depending on properties of the material, however, this approach is either accompanied by a decrease in dry tensile strength or an increase in wet tensile strength. for the zycotherm-modified specimen, for example, the improvement of moisture susceptibility leads to a decrease in dry indirect tensile strength, while other specimens undergo a rise in both strengths with the wet strength increased more than the dry strength. p. farazmand et alii, frattura ed integrità strutturale, 51 (2021) 215-224; doi: 10.3221/igf-esis.51.17 220 figure 5: quantitative results of moisture susceptibility for modified and non-modified specimens. boiling water the qualitative experiments include both boiling water and sem tests, so that the results of boiling water test are assessed initially. nanoclay-modified specimen (nc)zycotherm-modified specimen (za)control specimen (ac) nanosilica-modified specimen (ns)sbs-modified specimen (sb) figure 6: results of boiling water for modified and non-modified specimens the results of boiling water test are represented in fig. 6. as explained previously, the results of boiling water test indicate the qualitative result of moisture susceptibility. as shown in the figures, the control specimen experiences the highest stripping, while the specimen containing nanosilica undergoes the lowest stripping. sem the results of sem are represented in fig. 7. two types of sem images can be presented: the first image is related to the qualitative analysis of stripping, in which the white points indicate higher bitumen content and the black points show the lower bitumen content; the second image represents the distribution of nanomaterials within the mixture, which is presented for modifiers containing nanomaterials. p. farazmand et alii, frattura ed integrità strutturale, 51 (2021) 215-224; doi: 10.3221/igf-esis.51.17 221 sbs-modified specimen (sb)control specimen (ac) zycotherm-modified specimen (za) nanoclay-modified specimen (nc) nanosilica-modified specimen (ns) figure 7: results of sem test for modified and non-modified specimens (samples containing nanoparticles have also been taken for further zooming). comparison of quantitative and qualitative results he images shown in figs. 6 and 7 are imported to the matlab software and the outputs are given in tabs. 4 and 5. c=(a/b)*100 non-stripped percent (b)stripped percent (a) specimen 24 80.7419.26 ac 7 93.45 6.55 za 6 94.66 5.34 nc 1 99.39 0.61 sb 1 98.84 1.16 ns table 4: matlab output for boiling water specimens t p. farazmand et alii, frattura ed integrità strutturale, 51 (2021) 215-224; doi: 10.3221/igf-esis.51.17 222 c=(a/b)*100 non-stripped percent (b)stripped percent (a) specimen 30 77.03 22.97 ac 3 96.88 3.12 za 1 99.2 0.8 nc 16 86.2213.78 sb 1 98.91 1.09 ns table 5: matlab output for sem specimens the comparison of results of parameter c with those of (100-tsr) can indicate the relationship between quantitative and qualitative results of moisture susceptibility. figure 8: investigation into results of parameter c for boiling water and sem tests and results of (100-tsr) according to fig. 8, the more stripping occurs in the specimen, the higher result of parameter c is obtained for the specimen; and the less stripping happens in the specimen, the lower result of parameter c is obtained and its value approaches 1 or 0. another important point is related to the sbs-modified specimens. the evaluation of parameter c suggests that the results of boiling water test for the sbs-modified specimen are less accurate compared to the results of sem test for the same specimen and for other samples, however, the situation was reversed, i.e. the boiling water test returned closer results, implying that there is no general principle in this respect. considering the higher accuracy of the sem analysis and the captured images in this analysis, it could be stipulated that the only advantage offered by the sem analysis, as compared to the boiling water test, was the acquisition of more accurate images, which could somehow reduce the resultant error npar tests /k-w=data by group (1 3) /missing analysis. npar tests [dataset0] kruskal-wallis test ranks group n mean rank data 1 7 9.79 2 7 8.79 3 7 14.43 total 21 test statistics a,b data chi-square 3.374 df 2 asymp. sig. 0.185 a. kruskal-wallis test; b. grouping variable: group table 6: results of statistical test considering the obtained value of sig (0.185, as tabulated in tab. 6), the kruskal-wallis instability test method (the value of sig was not smaller than 0.05) indicated that the difference between results of the boiling water test and sem analysis was no significant. p. farazmand et alii, frattura ed integrità strutturale, 51 (2021) 215-224; doi: 10.3221/igf-esis.51.17 223 conclusion his study is associated with an investigation into the relationship between quantitative and qualitative results of moisture susceptibility tests on asphalt mixtures modified by zycotherm, nanoclay, nanosilica and sbs the following results are obtained:  the results of marshall stability test indicate that all additives lead to better results compared to the control specimen. hence it can be concluded that all additives used in this study improve the compressive strength.  the results of modulus of resilience test suggest that nanosilica and zycotherm reduce the modulus of resilience, while other additives such as nano silica and sbs improve the modulus of resilience in comparison with the control specimen.  according to the results of indirect tensile strength test, the indirect tensile strength is improved almost in all wet specimens. for dry specimens, all additives except zycotherm improve the dry indirect tensile strength with the best result obtained for the sbs samples.  the results of moisture susceptibility test based on indirect tensile strength (its) show that stripping is improved in all specimens. moreover, it is possible to observe the improvement process of stripping through the assessment of wet/dry indirect tensile strength ratio (tsr). for example, zycotherm creates the trend by reducing the wet indirect tensile strength, while stripping is improved in other specimens by increasing both wet and dry tensile strengths with the wet condition improved more than the dry condition.  given the results of qualitative tests, it can be concluded that these tests supplement and confirm quantitative tests. moreover, it is possible to analyze the images by assessing the results of these tests, e.g. sem test, along with those of quantitative tests and present a single process for the images.  the results of investigation into the relationship between boiling water and sem tests and moisture susceptibility quantitative tests demonstrate that, in fact, qualitative tests have a relatively high accuracy. references [1] xiao, f., et al. (2010). influence of antistripping additives on moisture susceptibility of warm mix asphalt mixtures. journal of materials in civil engineering 22.10, pp. 1047-1055. [2] behiry, a. e., abu el-maaty. laboratory evaluation of resistance to moisture damage in asphalt mixtures. ain shams engineering journal 4.3 (2013): 351-363. [3] behbahani, h., et al. evaluation of performance and moisture sensitivity of glasphalt mixtures modified with nanotechnology zycosoil as an anti-stripping additive. construction and building materials 78 (2015): 60-68 [4] jahanian, h. r., shafabakhsh, gh. and divandari, h. (2017). performance evaluation of hot mix asphalt (hma) containing bitumen modified with gilsonite. construction and building materials 131, pp.156-164. [5] yilmaz, m., and yalcin, e. (2016). the effects of using different bitumen modifiers and hydrated lime together on the properties of hot mix asphalts. road materials and pavement design 17.2, pp. 499-511. [6] wang, h., hao, p. (2010). numerical simulation of indirect tensile test based on the microstructure of asphalt mixture. journal of materials in civil engineering, 23.1, pp. 21-29. [7] moon, k. h., falchetto, a., jeong, j. h. (2013). microstructural analysis of asphalt mixtures using digital image processing techniques. canadian journal of civil engineering, 41.1, pp. 74-86. [8] zelelew, h. m., papagiannakis, a. t. and masad, e. (2008). application of digital image processing techniques for asphalt concrete mixture images. in: the 12th international conference of international association for computer methods and advances in geomechanics (iacmag). pp. 119-124. [9] nejad, f. m., et al. (2015). an image processing approach to asphalt concrete feature extraction. journal of industrial and intelligent information, 3.1. [10] al-qadi, i. l., et al. (2010). in-place hot-mix asphalt density estimation using ground-penetrating radar. transportation research record, 2152.1, pp. 19-27. [11] ayazi, m. j., moniri, a. and barghabany, p. (2017). moisture susceptibility of warm mixed-reclaimed asphalt pavement containing sasobit and zycotherm additives. petroleum science and technology 35.9, pp. 890-895. [12] galooyak, s., sadeghpour, b., dabir, a., nazarbeygi, e., moeini, a. and berahman, b. (2011). the effect of nanoclay on rheological properties and storage stability of sbs-modified bitumen. petroleum science and technology 29(8) pp. t p. farazmand et alii, frattura ed integrità strutturale, 51 (2021) 215-224; doi: 10.3221/igf-esis.51.17 224 850-859. [13] rezaei, s., ziari, h. and nowbakht, s. (2016). low temperature functional analysis of bitumen modified with composite of nano-sio2 and styrene butadiene styrene polymer. petroleum science and technology 34(5), pp. 415-421. [14] rezaei, s., khordehbinan, m., fakhrefatemi, s. m. r., ghanbari, s., and ghanbari, m. (2017). the effect of nano-sio2 and the styrene butadiene styrene polymer on the high-temperature performance of hot mix asphalt. petroleum science and technology, 35(6), pp. 553-560. [15] american association of state highways and transportation officials. resistance of compacted bituminous mixture to moisture induced damage aashto d4123. [16] american association of state highways and transportation officials. resistance of compacted bituminous mixture to moisture induced damage aashto t283. [17] american association of state highways and transportation officials. resistance of compacted bituminous mixture to moisture induced damage aashto d3625. [18] ameri, m., nemati, m., shaker, h. and jafari, f. (2019) experimental and numerical investigation of the properties of the hot mix asphalt concrete with basalt and glass fiber, frattura ed integrità strutturale, 13(50), pp. 149-162. doi: 10.3221/igf-esis.50.14. << /ascii85encodepages false /allowtransparency false /autopositionepsfiles true /autorotatepages /none /binding /left /calgrayprofile (dot gain 20%) /calrgbprofile (srgb iec61966-2.1) /calcmykprofile (u.s. web coated \050swop\051 v2) /srgbprofile (srgb iec61966-2.1) /cannotembedfontpolicy /error /compatibilitylevel 1.4 /compressobjects /tags /compresspages true /convertimagestoindexed true /passthroughjpegimages true /createjobticket false /defaultrenderingintent /default /detectblends true /detectcurves 0.0000 /colorconversionstrategy /cmyk /dothumbnails false /embedallfonts true /embedopentype false /parseiccprofilesincomments true /embedjoboptions true /dscreportinglevel 0 /emitdscwarnings false /endpage -1 /imagememory 1048576 /lockdistillerparams false /maxsubsetpct 100 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can be opened with acrobat and adobe reader 5.0 and later.) >> /namespace [ (adobe) (common) (1.0) ] /othernamespaces [ << /asreaderspreads false /cropimagestoframes true /errorcontrol /warnandcontinue /flattenerignorespreadoverrides false /includeguidesgrids false /includenonprinting false /includeslug false /namespace [ (adobe) (indesign) (4.0) ] /omitplacedbitmaps false /omitplacedeps false /omitplacedpdf false /simulateoverprint /legacy >> << /addbleedmarks false /addcolorbars false /addcropmarks false /addpageinfo false /addregmarks false /convertcolors /converttocmyk /destinationprofilename () /destinationprofileselector /documentcmyk /downsample16bitimages true /flattenerpreset << /presetselector /mediumresolution >> /formelements false /generatestructure false /includebookmarks false /includehyperlinks false /includeinteractive false /includelayers false /includeprofiles false /multimediahandling /useobjectsettings /namespace [ (adobe) (creativesuite) (2.0) ] /pdfxoutputintentprofileselector /documentcmyk /preserveediting true /untaggedcmykhandling /leaveuntagged /untaggedrgbhandling /usedocumentprofile /usedocumentbleed false >> ] >> setdistillerparams << /hwresolution [2400 2400] /pagesize [612.000 792.000] >> setpagedevice microsoft word numero_42_art_25.docx a. de santis et alii, frattura ed integrità strutturale, 42 (2017) 231-238; doi: 10.3221/igf-esis.42.25 231 classification of ductile cast iron specimens: a machine learning approach alberto de santis, daniela iacoviello department of computer, control and management engineering antonio ruberti, sapienza university of rome, via ariosto 25, 00185, rome, italy desantis@dis.uniroma1.it, orcid.org/0000-0001-5175-4951 iacoviello@dis.uniroma1.it, orcid.org/0000-0003-3506-1455 vittorio di cocco, francesco iacoviello department of civil and mechanical engineering, università di cassino e del lazio meridionale, via g. di blasio 43, 03043 cassino (fr), italy v.dicocco@unicas.it iacoviello@unicas.it, orcid.org/0000-0002-9382-6092 abstract. in this paper an automatic procedure based on a machine learning approach is proposed to classify ductile cast iron specimens according to the american society for testing and materials guidelines. the mechanical properties of a specimen are strongly influenced by the peculiar morphology of their graphite elements and useful characteristics, the features, are extracted from the specimens’ images; these characteristics examine the shape, the distribution and the size of the graphite particle in the specimen, the nodularity and the nodule count. the principal components analysis are used to provide a more efficient representation of these data. support vector machines are trained to obtain a classification of the data by yielding sequential binary classification steps. numerical analysis is performed on a significant number of images providing robust results, also in presence of dust, scratches and measurement noise. keywords. ductile cast irons; graphite nodules; machine learning approach. citation: de santis, a., iacoviello, d., di cocco, v. iacoviello, f., classification of ductile cast iron specimens: a machine learning approach, frattura ed integrità strutturale, 42 (2017) 231-238. received: 25.06.2017 accepted: 15.08.2017 published: 01.10.2017 copyright: © 2017 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. introduction iscovered in the years 1943-48, ductile cast irons (dcis) offer a really interesting combination of cast irons peculiarities (first of all, castability) and of carbon steels mechanical properties (e.g., toughness), [1]. small additions of elements like mg or ce allow to modify the graphite elements shapes, from lamellae (extremely d a. de santis et alii, frattura ed integrità strutturale, 42 (2017) 231-238; doi: 10.3221/igf-esis.42.25 232 dangerous) to spheroids (with a decrease of the stress intensification near the graphite elements): these grades are widely used to produce pressure pipes and fittings, in the automotive industry (e.g., crankshafts), in road and construction application. graphite elements morphology peculiarities (e.g. shape, dimension, distribution) are crucial to define the dci mechanical properties. image analysis has been using extensively in the last two decades in order to automatically characterize specimens in material science, [2-4]. the aim is to provide quantitative characterization of the materials in order to determine mechanical properties and establish relationship with damaging mechanisms, [5-6]. nevertheless up to now the official guide of the international standard [7] is applied almost manually for visual inspection. only few attempts have been made to automatize the classification of microstructural image data [8]. in this paper the aim is to provide an automatic procedure to classify specimens according to the american society for testing and materials (astm) standard with respect to the graphite elements shape, the “type” parameter. as will be recalled in section ii, the shape is the first characteristic to be evaluated in order to determine whether a graphite has a desirable shape or not. in case the shape is not nodular, different levels are possible and it could be determined if the graphite has vermicular aspect or if it contains exploded nodules and so on. given the images classified by two experts, useful features are extracted and re-arranged by principal components analysis (pca) [9] in order to enhance the informative and useful content of the data. the classification is performed by support vector machine (svm) suitably trained, [10]; it is a versatile tool useful to classify signals of different nature [11-12]. the classes identified with respect to the type in the astm 2016 are seven; nevertheless binary classifiers are trained in order to simplify the classification step and guarantee the modularity of the procedure. the paper is organized as follows: in section ii, after the description of the data, the image analysis and features extraction is described. then the training and classification procedure by the svm is outlined. in section iii numerical results are proposed and discussed, whereas in section iv conclusions and future work are presented. materials and methods n this section the procedure for the image acquisition and classification is outlined. different dcis have been considered, focusing the attention only on the graphite elements morphological peculiarities and not on the metal matrix microstructure. specimens have been obtained by means of a metallographic preparation according to the following procedure: specimen sectioning operation by abrasive cutting; specimen mounting; specimen grinding (decreasing grit sizes for abrasive papers up to p1200) and polishing (6 micron diamond followed by 1 micron diamond on low napped polishing cloths); observation of the metallographically prepared specimen by means of a light optical microscope (lom); graphite elements characterization is usually performed by means of a visual inspection and a qualitatively evaluation according to the standards [7, 13]. the standardized procedure is based on the visual comparison between the observed images and the charts that are available in the standards. to classify automatically images of ductile cast iron specimens the idea is to extract features useful to describe the specimens and, once the classes of interest are defined, train a classifier able to assign each image to the specific class. this implies the identification of a sort of signature of the images, so that once a new unknown image is proposed, it could be classified by evaluating its signature. on the basis of the international standard astm [7] the information to be retrieved from the images are: the shape, in particular a measure of its nodularity in shape; the classes with respect to the shape are indicated by: type i-ii-iii-iv-v-vi-vii; the distribution of the graphite in the specimen: it is particularly important in rating the flake graphite and the distribution is described by the letters a-b-c-d-e; the size of the graphite particles, and the classes are indicated by 1-2-3-4-5-6-7-8 depending on the actual dimension ; the nodularity, measured as the percentage of the nodular particles present in the microstructure; the nodule count evaluated as the number of nodules per mm2 at a magnification of 100x. in fig. 1 examples of specimens belonging to the type i, iv-and vii (whose differences between them are more evident) are proposed. i a. de santis et alii, frattura ed integrità strutturale, 42 (2017) 231-238; doi: 10.3221/igf-esis.42.25 233 it is worth noting that, starting from the classification with respect to the shape (the type), all the characterizations (distribution, size, nodularity, nodule count) could be further particularized with respect to the other properties, suggesting a sequential procedure for the classification. therefore, first it will be determined the type-class to which the specimen belongs and then the other characterizations will be established. (a) (b) (c) figure 1: examples graphite morphologies: a) type i; b) type vi; c) type vii; [7]. an efficient procedure to classify the specimens with respect to the type is to use binary classifiers in a sequential way: step 1: with a binary classifier c1 first establish if a specimen could be assigned to type i class or not if it belongs to type i class one can refine the classification with respect to the other characteristics. if the specimen does not belong to type i one proceeds to step 2; step 2: with a binary classifier c2 establish if the specimen (that is not of typei) may be classified of type ii or of type iii-iv-v-vi-vii. if it belongs to type ii, then again one refines the classification with respect to the other characteristics, otherwise one goes to step 3 using another binary classifier c3 and so on. as it can be noted the core of the global procedure is the binary classification step. from now on we will refer to the first step in which one wants to classify a specimen as belonging to the class 1 (type i specimen) or the class 2 (type ii-iii-iv-v-vi-vii specimens), thus determining the classifier c1. therefore it will be possible to distinguish the specimens with normal and well-formed nodules with respect to all the other situations. in fig. 2 a scheme of the overall classification procedure, simplified when considering only three types, is presented. the classifiers distinguishes the specimens on the basis of suitable features that are evaluated from a simplified representation of the image obtained by using a segmentation procedure; then the features are efficiently modified by the principal components analysis that provides the most efficient data representation. finally a classifier is obtained by using the support vector machine. the block diagram of the binary classification step is outlined in fig.3. it consists of two steps; a first one is off-line, aiming at determining the classifier after a proper data processing (image segmentation, features computation and extraction) and training. the second step is on-line, and represents the application of the classifier over images of specimens not used for training. a. de santis et alii, frattura ed integrità strutturale, 42 (2017) 231-238; doi: 10.3221/igf-esis.42.25 234 figure 3: block diagram of the classification procedure image analysis and features extraction given an image, it could be noted that, though it is of good quality, it requires a segmentation process in order to evaluate the properties of each nodule and their spatial distribution. the segmentation with respect to the gray level allows to represent the data with a reduced number of gray levels, thus allowing to retrieve useful information on the nodules, such as the area, or the eccentricity, or their spatial distribution, for example. different segmentation methods could be applied, [14,15] and in this case, with the nodules well defined over the background, the results obtained with different methods are quite equivalent. moreover, since the images are of good quality, a binarization is sufficient to enhance the nodules with respect to the background and to determine the properties of interest. the features to be extracted from the images should be chosen in order to determine the best characterization of the data. the indications in the international standard astm 2016 suggest that useful information to be retrieved to determine the classifier c1 concern the roundness of the nodules and their area. therefore the following features are identified: features if , 1, 2, 3i  that are the number of nodules with area (in pixels) in the intervals  1 25, 125i  ,  2 126 500i  ,  3 501, 900i  , respectively. nodules with area less than 25 pixels are discarded since could be associated to dust or measurement noise; nodules with are greater than 900 pixels are in general not present; feature 4f defined as the number of elements with area greater than the minimum one (25 pixels) normalized with respect to the area of the background: it is a measure of the presence of the nodules; features jf , 5, 6, 7j  that are the solidities of the nodules in the three intervals ii , 1, 2, 3i  respectively; the solidity is defined as the area of the nodule over the convex area, that is the area of the smallest convex polygon that can contain the nodule; features kf , 8, 9,10k  that are the eccentricities of the nodules in the three intervals ii , 1, 2, 3i  respectively, and are a measure of the roundness of the nodules. therefore, given a set of images of specimens js , 1, 2,...,j n , a vector of 10fn  features is calculated  1 2 3 4 5 6 7 8 9 10f f f f f f f f f f f for each image; these information are collected in a dataset matrix d of dimension fn n , where on the k -th row the fn features of the specimen ks are collected. the fn features have been chosen in order to determine the best characteristics useful to distinguish specimens of class 1 with respect to specimens of class 2; nevertheless if one uses directly these features to train a classifier, maybe they don’t a. de santis et alii, frattura ed integrità strutturale, 42 (2017) 231-238; doi: 10.3221/igf-esis.42.25 235 represent at best the data, or maybe some of them yields the same information. to this aim the principal component analysis, that will be herein briefly recalled, yields the best data representation, [16]. the pca is a linear data transformation aiming at reducing the redundancy of the data covariance matrix and maximizing the information retrieved; in the new reference coordinate the new variables are independent one another. one can consider the features selections, when a subset of the original features is considered, or the features extraction, when a new set of features is built suitably weighting the information of interest. of course, when the dimensionality of the data is reduced it is mandatory to quantify the loss of information. in this paper the pca are used aiming at the features extraction. more precisely, the covariance matrix dc of size f fn n of the data matrix d is evaluated and its eigenvalues  1,..., n f  are sorted according to decreasing order. the corresponding unit eigenvectors iv , 1, 2, ..., fi n are the directions of maximum variance of the data; the transformation yielding the new data representation in the principal components z is: z d v  (1) where 1 n fv v v      is the matrix constituted by the ordered eigenvectors. therefore, for example, the first principal component is:    1 11 1 1 1 1p n fz z z d v d v   being 1d the first row of matrix d . generally the number of principal components pn is chosen in order to retrieve the p-percentage of the information content, that is: 1 1 100 % n p i i n f i i p         (2) it means that from now on, instead of trying to classify the data collected in the matrix d of dimension fn n , the data to be considered are the first pn principal components. training and classification the pca allows to reduce the dimensionality of the data preserving adequately the information; therefore now each image x is described by a new set of feature. the aim is to determine a classifier able to assign each set of feature (and therefore each image) to class 1 or to class 2. to train a classifier able to separate the available data into two classes, the set of n images is split into two groups, the training set, trn , and the test set testn . to the data corresponding to images belonging to the class 1 it is assigned label 1, whereas label 0 is assigned to the data belonging to the class 2. the training set trn is divided into two groups, 1trn and 2trn ; the first one is used to train the classifier; the second one 2trn is used to determine the classification accuracy. the support vector machine determines the optimal hyperplane that splits the data into two groups, [17]; it is a tradeoff between the requirement of minimizing the error on misclassified points and maximizing the euclidean distance between the closest points, see fig.4. the optimal hyperplane is obtained as the solution of the quadratic programming problem: , , 1 1 min 2 n t i w b i w w h      a. de santis et alii, frattura ed integrità strutturale, 42 (2017) 231-238; doi: 10.3221/igf-esis.42.25 236 with the constraint:   1 , 0ti i i iy w x b      , where w is the vector of the points perpendicular to the separating hyperplane and h>0 is a penalty parameter on the error term. figure 4: representation of the classification problem. to make the elements ix of the two classes linearly separable, the data are mapped into a richer space, and the separating hyperplane is determined in that space. a possible choice for the mapping function  is the radial basis function and, denoting with 2 the 2l -norm, for the kernel function it is assumed: 2 2 2 ( , ) ( ) ( ) exp 2 i jt i j i j x x k x x x x             the two parameters to be evaluated, h and  , may be determined during the training phase, by using the 10-fold cross validation, [18]. the classification is performed by the svm algorithm libsvm 3.18, [1920]. once the optimal parameters  ,h   have been determined, the classifier is trained; the classification accuracy, evaluated on the 2trn , is defined as the percentage of correctly classified data with the optimal choice  ,h   and it is a property of the classifier. with this calculation the off-line phase of the classification procedure is over. the obtained classifier is tested over the test set testn , not used for the training, simulating the situation of unlabeled data. the percentage of misclassified images is the error of the classifier. the same procedure is applied to train the classifier c2 able to assign a specimen (not belonging to type i class) to type ii class or to type iii-iv-v-v-vii class and so on, according to the scheme of fig. 2. numerical results and discussion n this section the results of the classification procedure are described. as could be noted in the international standard [7], the specimens of type i, ii and iii, though they could present a similarity between each other, they differ significantly from the other types. therefore out attention will be focused in type i, ii and iii, even if the overall analysis may be extended to all the types’ classification. the first step is the classification of a specimen as of type i or of type ii-iii. if the specimen is of type ii-iii a further classification procedure starts in order to decide whether the specimen is of type ii or iii. i a. de santis et alii, frattura ed integrità strutturale, 42 (2017) 231-238; doi: 10.3221/igf-esis.42.25 237 a set of 192n  images of specimens is considered, 64 are of specimens of type i, 64 of specimens of type ii and 64 of specimens of type iii. the images have been previously classified by an expert, manually. to obtain the features a binarization procedure is applied; it has been chosen the binarization by the discrete level set approach [15] and the ten features described in section 2 have been evaluated, thus obtaining three matrices of size 64 10 , collected together in the data matrix d , 192 10 . to deal with data with comparable magnitude, a normalization is applied. the covariance matrix dc of size 10 10 of the data matrix d is evaluated; after evaluating its eigenvalues, by using formula (2) 6pn  principal components are considered, thus preserving the percentage of more than 94% of the original information. the training set trn contains 45 images: 27 of type i, randomly chosen among the set of 64 type i data, and 27 of type ii and iii randomly chosen among the set of 128 images of specimens of these type. the test set is constituted by 20 images, equally distributed between type i and type ii-iii. the 1trn contains 40 elements and the remaining 14 are used for the set 2trn . the number of images of specimens of class 1 (i.e. type i specimens) and of class 2 (i.e. type iiand iii, equally distributed) is the same in the groups involved in training and testing steps to avoid polarization in the result. as said, the parameters  ,h   are determined by the 10-fold cross validation that provides also the optimized value for b . the used svm algorithm libsvm 3.18 is a simple and efficient open source software. the classification accuracy is calculated as the average value of the accuracy evaluated for 20 different random choices of the training and the test sets, to be sure that the results do not depends on lucky choices, obtaining a percentage of success over 99%. with this calculation the off-line step is over. the results over the test set (containing images not used in the training phase) yield a percentage of success of 97.3% 2.7 . the results of the classifier c1 appears satisfactory; moreover it has been also investigated if the classifier c1 makes a mistake more often with images of class 1 (type i data) or with images of class 2 (type ii and iii data), and among the class 2 if more errors are made when testing with images of type ii or iii. this unbundled test on 10 images of each type, repeated 20 times, shows that images of type iii are always correctly classified (percentage of success of 100%), whereas the results on type i and type ii yield percentage of success of 97.5% 5.5 and 94.5% 10.5 , respectively. a possible explanation could be that images of type iii are a little bit more different with respect to the type i, than the images of type ii. for the images classified by the classifier c1 as belonging to class 2 the second classifier c2 must be applied in order to discriminate the images of type ii and those of type iii. also in this case all the results have been repeated for 20 different random choices of the training and test sets. the classifier c2, trained using only images of type ii and type iii, has a classification accuracy of 98.9%. the test accuracy provides a percentage of success of almost 100% on a test set of 10 images belonging to type ii class and of 98.9% 3.15 on a test set of 10 images of type iii. the results of the classifier c2 are even more satisfactory with respect to those of classifier c1, since the training has been more specific. the classifier c2 has the aim of determining the class membership of images of type ii and iii; when applied to an image of type i, for example if the classifier c1 has provided an erroneous classification, in more than 91% the c2 classifier assigns the specimen of type i to the class of type ii images. this is the correct choice, being the images of type ii the more similar to the ones of type i. conclusions and future work n this paper an automatic procedure to support the classification of microstructure of graphite in iron castings is proposed. by training binary support vector machine classifiers it is possible, in an efficient way, to determine the type of the specimen according to the american society for testing and materials guidelines and therefore to proceed in the classification specifying the size, the nodularity and the nodule count. three classes (type i, type ii and type iii) may be identified by the proposed procedure, but it could be extended to as many classes as needed. the choice of using binary classifiers operating sequentially is determined aiming at yielding a simple, efficient and modular procedure. i a. de santis et alii, frattura ed integrità strutturale, 42 (2017) 231-238; doi: 10.3221/igf-esis.42.25 238 the classifier uses features evaluated on the original specimens’ images and successively suitably transformed by principal components analysis that reduces the complexity and yields a more efficient representation of the information. the results appear satisfactory, and future work will be devoted in: classify the images of the specimen with respect to all the properties (size, nodule count,…); determine the most suitable features in order to better characterize each nodule present in the specimen; consider different classification schemes, for example by using polling systems, evaluating their robustness. references [1] labrecque, c., gagne, m., ductile iron: fifty years of continuous development, canadian metallurgical quarterly, 37( 5) (1998) 343–78. [2] bonnet, n., multivariate statistical methods for the analysis of microscope image series: applications in materials science, journal of microscopy, 190 (1998) 2-18. [3] filho, p.p.r., moreira, f.d.l., de lima xavier, gomez, f.g, s.l., dos santos, j.c., freitas, f.n.c, freitas, r.g., new analysis method application in metallographic images through the construction of mosaics via speeded up robust features and scale invariant feature transform, materials, 8 (2015) 3864-3882. [4] papa, j.p., pereiram, c.r., de albuquerque, silva, v.h.c c.c., falcao, a.x, tavares, j.m.r.s., precipitates segmentation from scanning electron microscope images through machine learning techniques, lecture notes in computer science series, 6636 (2011) 456-468. [5] di cocco, v., iacoviello, f., rossi, a., iacoviello, d., macro and microscopical approach to the damaging micromechanisms analysis in a ferritic ductile cast iron, theoretical and applied fracture mechanics, 69 (2014) 26-33. [6] de santis, a., di bartolomeo, o., iacoviello, d., iacoviello, f., quantitative shape evaluation of graphite elements in ductile iron, journal of materials processing and technology, 196 (1-3) (2008) 292-302. [7] astm standard a247 – 16a, standard test method for evaluating the microstructure of graphite in iron castings, (2016) 1-13. [8] decost, b.l., holm, e.a., a computer vision approach for automated analysis and classification of microstructural image data, computational materials science, 110 (2015) 126-133 [9] jolliffe, i.t., principal component analysis, 2nd edition, springer, (2002). [10] cristianini, n., shawe-taylor, j., an introduction to support vector machines and other kernel-based learning methods, cambridge university press, new york, ny, usa, (2000). [11] nguyen, b.p., tay, w.l.,chui, c.k. :,robust biometric recognition from palm depth images for gloved hands, ieee transactions on human-machine-systems, 45 (6) (2015) 799-805. [12] subasi, a., gursoy, m.i., eeg signal classification using pca, ica, lda and support vector machine, expert systems with applications, 37 (2010) 8659-8666. [13] astm standard e2567 – 13a, standard test method for determining nodularity and nodule count in ductile iron, (2013) 1-4. [14] otsu, n.,threshold selection method for gray-level histograms, ieee transactions od systems, man, and cybernetics, 1 (1979) 62-66. [15] de santis, a., iacoviello, d., discrete level set approach to image segmentation, signal, image and video processing, springer-verlag london, 1(4) (2007) 303-320. [16] song, f., guo, z., mei, d., feature selection using principal component analysis, 2010 international conference on system science, engineering design and manufacturing informatization, (2010) 27–30. [17] hsu, c.w., chang, c.c., lin, c.j., a practical guide to support vector classification, bioinformatics, 1 (1) (2003) 1–16. [18] efron, b., estimating the error rate of a prediction rule: improvement on cross-validation, journalsamerican statistical association, 78 (1983) 316–331. [19] chang, c-c, lin, c-j., libsvm: a library for support vector machines,, acm transactions on intelligent systems and technology, 2 (27) (2011) 1-27. software available at http://www.csie.ntu.edu.tw/~cjlin/libsvm. 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/hrv (za stvaranje adobe pdf dokumenata najpogodnijih za visokokvalitetni ispis prije tiskanja koristite ove postavke. stvoreni pdf dokumenti mogu se otvoriti acrobat i adobe reader 5.0 i kasnijim verzijama.) /hun 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can be opened with acrobat and adobe reader 5.0 and later.) >> /namespace [ (adobe) (common) (1.0) ] /othernamespaces [ << /asreaderspreads false /cropimagestoframes true /errorcontrol /warnandcontinue /flattenerignorespreadoverrides false /includeguidesgrids false /includenonprinting false /includeslug false /namespace [ (adobe) (indesign) (4.0) ] /omitplacedbitmaps false /omitplacedeps false /omitplacedpdf false /simulateoverprint /legacy >> << /addbleedmarks false /addcolorbars false /addcropmarks false /addpageinfo false /addregmarks false /convertcolors /converttocmyk /destinationprofilename () /destinationprofileselector /documentcmyk /downsample16bitimages true /flattenerpreset << /presetselector /mediumresolution >> /formelements false /generatestructure false /includebookmarks false /includehyperlinks false /includeinteractive false /includelayers false /includeprofiles false /multimediahandling /useobjectsettings /namespace [ (adobe) (creativesuite) (2.0) ] /pdfxoutputintentprofileselector /documentcmyk /preserveediting true /untaggedcmykhandling /leaveuntagged /untaggedrgbhandling /usedocumentprofile /usedocumentbleed false >> ] >> setdistillerparams << /hwresolution [2400 2400] /pagesize [612.000 792.000] >> setpagedevice microsoft word numero 18 articolo 3.docx s. marfia et alii, frattura ed integrità strutturale, 18 (2011) 23-33; doi: 10.3221/igf-esis.18.03 23 a coupled interface-body nonlocal damage model for the analysis of frp strengthening detachment from cohesive material s. marfia, e. sacco, j. toti department of mechanics, structures and environment, university of cassino, cassino (italy) marfia@uncas.it, sacco@unicas.it, jessica.toti@unicas.it abstract. in the present work, a new model of the frp-concrete or masonry interface, which accounts for the coupling occurring between the degradation of the cohesive material and the frp detachment, is presented; in particular, a coupled interface-body nonlocal damage model is proposed. a nonlocal damage and plasticity model is developed for the quasi-brittle material. for the interface, a model which accounts for the mode i, mode ii and mixed mode of damage and for the unilateral contact and friction effects is developed. two different ways of performing the coupling between the body damage and the interface damage are proposed and compared. some numerical applications are carried out in order to assess the performances of the proposed model in reproducing the mechanical behavior of the masonry elements strengthened with external frp reinforcements. sommario. nel presente lavoro si propone un modello di interfaccia frp-calcestruzzo o frp-muratura, che tiene conto dell’accoppiamento tra il degrado del materiale coesivo ed il distacco del frp; in particolare, si sviluppa un modello di danno non locale accoppiato interfaccia-corpo. si presenta un modello di danno non locale e plasticità per il materiale coesivo ed un modello di interfaccia che tiene conto del modo i, ii e misto di danno, del contatto unilatero e degli effetti dell'attrito. si propongono e confrontano due diversi modi di accoppiamento del danno del corpo e del danno d’interfaccia. si sviluppano applicazioni numeriche per verificare l’efficienza del modello proposto nel riprodurre il comportamento meccanico di elementi in muratura rinforzati con frp. keywords. interface-body damage; detachment phenomenon; nonlocal model. introduction he use of fiber reinforced plastic (frp) materials for the strengthening of existing concrete and masonry elements is growing; in the last twenty years, many structures have been reinforced adopting frp and several experimental and modeling scientific works have been developed [1-9]. the use of frp materials applied on the external surface of concrete or masonry structures aroused new modeling problems. one of the main problem in the use of frp is the detachment phenomenon, which consists in the sudden decohesion of the frp reinforcement from the concrete or masonry surface. indeed, the concrete and the masonry are quasi-brittle materials, whose mechanical response is characterized by damage with softening, which is due to the development of micro-cracks. thus, two damage effects could be presented in the quasi-brittle reinforced structural elements: the body damage, which develops inside the domain of the strengthened element, and the interface damage, which occurs at the frp -concrete or -masonry interface. experimental evidences demonstrate that the detachment of the frp from the support material occurs often with peeling of a thin layer from the t http://dx.medra.org/10.3221/igf-esis.18.03&auth=true http://www.gruppofrattura.it s. marfia et alii, frattura ed integrità strutturale, 18 (2011) 23-33; doi: 10.3221/igf-esis.18.03 24 external surface of the quasi-brittle material; this collapse behavior is due to the fact that the tensile and shear strength of the glue used to apply the frp to the support is generally greater than the strength of the concrete or masonry support. from this observation, it can be deduced that the body damage and the interface damage cannot evolve independently one from the other; in other words, their evolution is coupled [10]. in the present work, a new model of the frp-concrete or masonry interface, that takes into account the coupling occurring between the degradation of the cohesive support material and the frp detachment, is presented. a nonlocal damage and plasticity model is developed for the cohesive support material. an interface model which accounts for the mode i, mode ii and mixed mode of damage and for the unilateral contact and friction effects is developed. two different ways of performing the coupling between the body and the interface damage are proposed. both the approaches assume that the interface damage is influenced not only by the detachment stresses but also by the body damage computed on the bond surface. the first approach ensures that the interface damage is not lower than the body damage evaluated at the bond surface [11]. the second approach is based on simplified micromechanical considerations. some numerical applications are performed in order to assess the performances of the proposed coupled interface models in reproducing the mechanical behavior of the masonry elements strengthened with external frp reinforcements. a coupled body-interface damage model he structural system, schematizing the frp reinforced concrete or masonry element, is studied in the framework of two-dimensional plane stress elasticity, considering small strain and displacement regime. the system, consists in three subsystems: the body 1 , modeling the concrete or masonry element, characterized by a cohesive constitutive law; the body 2 , modeling the frp reinforcement, characterized by a linear elastic behavior; the interface  , modeling the connection between the reinforcement and the cohesive support material, characterized by a damaging behavior with friction and unilateral contact effects. in particular, the interface  is assumed to be constituted by three layers:  the glue, whose mechanical properties are generally much better than those of the support cohesive material;  a thin layer of the support cohesive material in which, during the application of the reinforcement, the glue penetrates the pores, improving its mechanical properties;  a further thin layer of the support cohesive material in which the detachment process occurs. indeed, the first two layers remain joined to the frp after the complete detachment of the reinforcement. the interface damaging process, occurring in the third layer, can be due to the stress induced by the detachment action and also by the degradation of the support cohesive material. as a consequence, the damage occurring in the body 1 influences the behavior and the detachment process of the interface. on the contrary, it can be assumed that the damage of the third layer, generated by the detachment stresses, remains localized in the interface, i.e. it does not influences the body damage. in order to take into account these two possible damaging effects, an interface coupled damage model should be adopted. in fact, the coupling ensures that the damage evolution in the interface depends on the body damage and not vice-versa. the constitutive laws of the body 1 , of the interface  , neglecting the coupling between the body and the interface damage, and of the new proposed interface  , considering two different ways of coupling the body and interface degradation, are presented in the following. body nonlocal damage model for the cohesive material a plastic nonlocal damage model, characterized by the following constitutive law, is considered for the body 1 :      (1 ) sgn ( ) (1 )(1 sgn ( )t cd h tr d h tr           σ σ e e (1) with σ the stress tensor, td  and cd  the damage variables in tension and in compression, respectively, the symbol sgn( ) indicating the sign of the variable  ,  h  the heaviside function, i.e.   1h   if 0  , otherwise   0h   , and σ the effective stress defined as:  p       σ c ε ε c e (2) t http://dx.medra.org/10.3221/igf-esis.18.03&auth=true http://www.gruppofrattura.it s. marfia et alii, frattura ed integrità strutturale, 18 (2011) 23-33; doi: 10.3221/igf-esis.18.03 25 where c is the elastic tensor, ε , p ε and e are the total strain, the plastic strain and the elastic strain tensors, respectively. the following plastic yield function is introduced:          2 2 1 2 1 2y y y yf a b                     ωσ (3) with 1 and 2 the principal stresses of the effective stress tensor ωσ , y the yield stress and a and b material parameters governing the shape of the yield function (a brunch of hyperbola). in particular, it is set a = 0.1 mpa and 100b  . the evolution law of the plastic strain is: p f     ω ω ε σ  (4) which is completed with the classical loading-unloading kuhn-tucker conditions:    0, 0, 0f f    σ σ  (5) the accumulated plastic strain  is introduced as 0 t p dt    ε . as a damage softening constitutive law is introduced, localization of the strain and damage parameter could occur. in order to overcome this pathological problem, to account for the correct size of the localization zone and, also, to avoid strong mesh sensitivity in finite element analyses, a nonlocal constitutive law is considered. in particular, an integral nonlocal model is adopted for the damage in compression and in tension. the evolution of the compressive damage variable is governed by the following law:        3 2 3 2 2 3 max min 1,c c c history u u d d d              (6) with u the final damage threshold in compression and   the nonlocal accumulated plastic strain, evaluated at the point x , as:        1 d d               x x y y x y (7) where y is a typical point of the body 1 and the weight function   x is set as:   2 2 1 r      x y x (8) with r the radius of the nonlocal integration domain and the symbol   denoting the positive part of the number  . the evolution of the tensile damage parameter is governed by an exponential nonlocal law, set as:     0 0 max min 1, eqk eq t t t history eq e d d d                (9) with  eq  x the equivalent nonlocal strain, evaluated at the point x as:        1eq eq d d               x x y y x y (10) and eq  the equivalent strain introduced as [11]: http://dx.medra.org/10.3221/igf-esis.18.03&auth=true http://www.gruppofrattura.it s. marfia et alii, frattura ed integrità strutturale, 18 (2011) 23-33; doi: 10.3221/igf-esis.18.03 26 2 2 1 2eq        (11) with 1 and 2 the local principal strains. moreover, the following condition is introduced: t cd d   (12) in order to prescribe that the damage in tension should not be lower than the damage in compression. interface damage model without coupling a phenomenological interface model based on the micromechanical idea, developed in [13] and [14], is proposed. the displacement fields of the two joined bodies are denoted as 1u and 2u , while the relative displacement at the typical point x on the interface  is defined as      1 2    s x u x u x . at the micromechanical level, the representative area at the point x is considered; in the representative area microcracks could be present, so that it can be modeled in a simplified form splitting the representative area in two parts: the undamaged and damaged part. the damage parameter d is introduced as the ratio between the damaged area with respect to the reference area; it can vary from zero to one: 0d  corresponds to the undamaged state (no microcarcks are present in the representative area), while 1d  corresponds to the completely damaged state (the representative area is completely cracked). the stress-relative displacement relationship is formulated: ( )d         σ k s c p (13) where k is the interface stiffness matrix, c is the unilateral contact vector and p is the sliding friction vector. a local coordinate system on the interface  ,t nx x , where the indices n and t indicate the normal and the tangential directions of the interface, respectively, is introduced. in this coordinate system, the stiffness matrix, the unilateral contact vector and the sliding friction vector are represented as: 0 0 ( ) 0 0 n n n t t k s h s k p                   k c p (14) in order to define the evolution of the inelastic slip relative displacement, the stress given in eq. (13) is rewritten in the following form:  (1 )d d        σ σ k c p (15) defining the contact-frictional stress d σ as:   d d       σ k s c p (16) it is assumed that the stress d σ governs the evolution of the inelastic slip relative displacement. in particular, the classical coulomb yield function is introduced:  d d n dt d n dt         σ (17) where  is the friction coefficient and the symbol d n  denotes the negative part of the contact-frictional stress. the following non-associated flow rule is considered for the evolution of the components of the vector p : http://dx.medra.org/10.3221/igf-esis.18.03&auth=true http://www.gruppofrattura.it s. marfia et alii, frattura ed integrità strutturale, 18 (2011) 23-33; doi: 10.3221/igf-esis.18.03 27 00 dt dt dt d d                         p   (18) together with the khun-tucker conditions:    0, 0, 0d d     σ σ  (19) it can be remarked that the frictional problem can be activated only when the damage is greater than zero. in fact, only in this case the microcracks, in which the unilateral and friction effects can occur, are present at the interface. about the evolution of the damage parameter d , a model which accounts for the coupling of mode i of mode ii of fracture is considered. in fact, the two quantities n and t , defined as the ratios between the first cracking relative displacement 0ns and 0 ts and the full damage relative displacement f ns and f ts , are introduced: 0 0 0 0 0 0 , 2 2 n n n t t t n tf f cn ctn t s s s s g gs s        (20) where 0n and 0 t are the peak stresses corresponding to the first cracking relative displacement and cng and ctg are the specific fracture energies in mode i and mode ii, respectively. then, the parameter  , which relates the two modes of fracture, is defined as follows: 2 2 2 2 n t n t s s     s s  (21) where  tn ts ss . the relative displacement ratios are introduced as: 0 0 n t n t n t s s y y s s   (22) and the equivalent relative displacement ratio is considered: 2 2n ty y y  (23) finally, the damage parameter is assumed to be a function of the history of the relative displacement as follows:      1 max 0, min 1, 1history y d d d y          (24) interface damage models with coupling an interface coupled model, obtained considering different ways of coupling the body and the interface damage, is proposed. denoting with  id x the coupled interface damage evaluated in a point x of the interface ,the coupling between the body damage and the interface damage is performed, in the firs case, ensuring that the interface damage is not lower than the body damage computed on the bond surface [11]:       max ,i td d d x x x (26) in the second case, a representative area a of the interface and, in particular, of the third layer made of cohesive support material, is assumed to be decomposed in two parts, as represented in fig. 1. in fact, when the body damage occurs, it induces the presence of a microfracture in the representative area of the surface, characterized by a corresponding area http://dx.medra.org/10.3221/igf-esis.18.03&auth=true http://www.gruppofrattura.it s. marfia et alii, frattura ed integrità strutturale, 18 (2011) 23-33; doi: 10.3221/igf-esis.18.03 28 ta d a   . because of the presence of the microcrack, the stress wσ in a is equal to zero if the microcrack is open and it is different from zero when it is closed. in the remaining part of the representative area, characterized by an area  1 ta d a   , it is assumed that the mechanical response is governed by the constitutive model described by eqs. (13)(25). thus, the overall constitutive response of the coupled interface is obtained as:  1i wt td d    σ σ σ (27) with σ given by eq. (13) and wσ defined as:   0 n n nw k s c           σ (28) where nc  the normal component of c defined by the second equation of the relations (14). figure 1: representative area of the third layer of the interface. numerical applications umerical procedures for solving the equations governing the mechanical response of the body-interface nonlocal damage models, described in the previous section, are developed. a step by step time integration algorithm is adopted in order to solve the evolutive equations of the proposed body andinterface models. in particular, the time integration is performed adopting a backward-euler implicit procedure. the proposed numerical procedure is implemented in the finite element code feap [15]. in particular, two dimensional plane stress four node quadrilateral elements are adopted to model the bodies 1 and 2 and four node interface elements are developed to model the interface  . some numerical applications are carried out in order to assess the efficiency of the proposed coupled nonlocal damage interface-body model in describing the detachment phenomenon of the frp reinforcement from the cohesive material. in particular, in the following applications model 1 indicates the interface model, in which the coupling is taken into account assuring that the interface damage is not lower than the body damage computed on the bond surface, while model 2 indicates the formulation developed on the basis of a simplified micromechanical analysis. the properties of the materials adopted in the numerical applications are set on the basis of the experimental detachment tests performed on masonry elements reinforced with frp [16]: body 1 1 1 2 0 15300 mpa 0.2 15.0 mm 0.00029 0.0095 n/mm 0.003 20 mpa c u y e r g              (29) body 2 2 2160000 mpa 0.3e   (30) representative area of the third layer of the interface ta d a   1 ta d a   a cohesive support 0td   wσ iσ σ n http://dx.medra.org/10.3221/igf-esis.18.03&auth=true http://www.gruppofrattura.it s. marfia et alii, frattura ed integrità strutturale, 18 (2011) 23-33; doi: 10.3221/igf-esis.18.03 29 interface  3 0 0 270 n/mm 0.5 4.7 mpa 0.34 n/mm n t n t cn ct k k g g           (31) where 1e , 1 , 2e and 2 are the young modulus and the poisson coefficient of the body 1 and 2 , respectively. in particular, first a simple tensile test is performed to show how the response of the interface can be significantly influenced by the damage occurring in the body 1 . then, the maximum detachment force is evaluated for different values of the adhesion lengths and of the initial values of the body damage. tensile test the geometry and loading condition of the scheme considered to perform the tensile test are shown in fig. 2. the geometrical parameters are 500 mm 49 mmb h  and an unit thickness is adopted. figure 2: scheme of the uniaxial test. in order to investigate the influence of the damaging behavior of the body 1 on the tensile mechanical response of the interface and, as a consequence, of the whole structure, three analyses are developed considering different values of the initial threshold damage strain 0 and keeping constant the fracture energy cg ; in particular it is set: case 1: 0 0.00016  case 2: 0 0.00026  case 3: 0 0.00036  the three analyses are performed considering as interface model the two coupled damage approaches previously presented (model 1 and model 2). in fig. 3 and fig. 4, the numerical response obtained adopting the model 1 and the model 2 are shown. the results reported in the graphics of these figures are plotted with a dotted line for case 1, with a dashed line for the case 2 and with a solid line for the case 3. furthermore, the average tensile stress is introduced as q  and the average strain in the body 1 is set as /v h   with v the relative vertical displacement between the two opposite edges of the body 1 . the computations are performed adopting the arc-length technique and considering the relative normal displacement ns at the interface as control parameter. with reference to fig. 3, it can be noted that in the case 3 the mechanical response of the structure is strongly influenced only by the softening behavior of the interface as in this analysis the damage does not occur in the body. in fact, the tensile interface response is equal to the constitutive interface law and the body is subject to the elastic unloading when the interface starts to damage. in the other two cases, the tensile mechanical response of the structure depends on the coupling of the body and interface damage. in fact, after the achievement of the peak stress, which coincides with the tensile strength of the body, the softening branch depends on the evolution of the damage in the body until the interface damage, governed by the relative displacement, becomes higher than the body one at the interface. at this point of the analysis the softening tensile response is due to the development of the interface damage governed by the relative displacement. 2 1  b h h q  http://dx.medra.org/10.3221/igf-esis.18.03&auth=true http://www.gruppofrattura.it s. marfia et alii, frattura ed integrità strutturale, 18 (2011) 23-33; doi: 10.3221/igf-esis.18.03 30 figure 3: numerical results obtained adopting the model 1. a) mechanical response of whole structure; b) mechanical behavior of interface; c) body tensile response. from fig. 4, it is observed that in the case 3 the body does not develop damage and for this reason the softening response of the mechanical system depends only on the evolution of the damage interface. with reference to fig. 3 and fig. 4, it appears evident that in the case 3 the analyses, performed adopting the proposed coupled interface formulations (model 1 and model 2), lead to the same numerical results. in the case 1 and in the case 2, the body damage occurs before the interface one; the maximum tensile stress is lower than the value obtained in the case 3 and it is equal to the tensile strength of the body, as it is achieved in the model 1. in the case 1 and 2 the softening response, obtained adopting the model 1 and 2, presents some significant differences. in fact, the results carried out adopting the model 1, show that the softening behavior is strongly influenced by the evolution of the body damage until the interface damage becomes higher than the body one. from this point of the analysis, the body damage does not increase anymore and the softening behavior is only governed by the evolution of the interface damage. on the other hand, in the results obtained considering the model 2, the softening behavior is strongly influenced by the body damage during the whole detachment process, also when the interface damage becomes to develop and the body damage does not evolve anymore. thus, the degradation process results faster for the model 2 than for the model 1.    v [mm]  [m p a ] 0 0.05 0.1 0.15 0.2 0.25 0 1 2 3 4 5 case 1 case 2 case 3    sn [mm]  [m p a] 0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0 1 2 3 4 5 case 1 case 2 case 3 interface constitutive law   0 0.5 1 1.5 2 2.5 3 3.5 x 10 -3 0 1 2 3 4 5 case 1 case 2 case 3   [m p a ] n a) b) c) http://dx.medra.org/10.3221/igf-esis.18.03&auth=true http://www.gruppofrattura.it s. marfia et alii, frattura ed integrità strutturale, 18 (2011) 23-33; doi: 10.3221/igf-esis.18.03 31 figure 4: numerical results obtained adopting the model 2. a) mechanical response of whole structure; b) mechanical behavior of interface; c) body tensile response. maximum decohesion force the computations are performed considering the scheme and the geometry illustrated in fig. 5. the frp laminate (body 2 ) is bonded to a masonry support (body 1 ) made of two clay bricks separated by an unitary layer of mortar. the frp laminate is subjected to tensile loading. figure 5: scheme of the frp-masonry brick detachment test. v [mm]  [m p a ] 0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0 1 2 3 4 5 case 1 case 2 case 3 0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0 1 2 3 4 5 case 1 case 2 case 3 interface constitutive law sn [mm]  n [m p a ] 0 1 2 3 x 10 -4 0 1 2 3 4 5 case 1 case 2 case 3   [m p a ] a) b) c) f lb40 mm 55 mm 250 mm 250 mm 10 mm 2  1 f lb40 mm 55 mm 250 mm 250 mm 10 mm 2  1 http://dx.medra.org/10.3221/igf-esis.18.03&auth=true http://www.gruppofrattura.it s. marfia et alii, frattura ed integrità strutturale, 18 (2011) 23-33; doi: 10.3221/igf-esis.18.03 32 all computations are developed assuming two interface damage models: the uncoupled model, which does not take into account the interaction between body and interface degradation, and the coupled one, in which the body damage influences the interface damage according to the formulation developed in the model 1. in fig. 6 the value of maxf is plotted versus the adhesion length bl . note that each curve is denoted by a symbol made of a letter and a number. the letter u is used to indicate that the analysis is performed adopting the uncoupled damage model, while the letter c is used to characterize the analysis developed with the coupled damage theory (model 1). the number near the letter indicates the initial damage level uniformly assigned at the body 1 . in particular, the number 1, 2, 3, and 4 corresponds to the damage value equal to 0, 0.5, 0.7, and 0.9, respectively. the numerical results reported in fig. 6 emphasize that, increasing the adhesion length bl , the value of maxf grows till the optimal adhesion length el is reached, after which maxf remains constant. in particular, from the type u curves marked by the discontinuous line, it can be noted that:  for higher values of the damage state of the body 1 the optimal adhesion length el increases;  for higher values of the damage state of the body 1 the maximum value of maxf is quite constant and, in some cases, it tends to increase;  for very high values of the damage state of the body 1 the maximum value of maxf decreases. while the first result is absolutely expected, the second one appears physically unacceptable, as it implies that even if the support material is more damaged, equal or higher values of the forces can be transmitted from 2 to 1 . on the contrary, only when the damage level of the body 1 becomes very high the force decreases. this strange effect is due to the uncoupled damage evolution of the body and of the interface damage state. with reference to the all type c curves marked by the solid line, the following observations can be remarked:  for higher values of the damage state of the body 1 the optimal adhesion length el increases, as in the case of the uncoupled model;  for higher values of the damage state of the body 1 the maximum value of maxf decreases. this last result appears much more reasonable and, as a consequence, more reliable with respect to the one obtained adopting the uncoupled damage model, as it does not suffer from the physical unacceptable effect found in the uncoupled one. figure 6: decohesion force maxf versus adhesion length bl . conclusions n conclusion, it can be remarked that the two different ways of coupling the body and the interface damage present significant differences in the numerical applications. in fact, the results carried out adopting the model 1, show that the softening behavior is strongly influenced by the evolution of the body damage until the interface damage becomes higher than the body one. from this point of the analysis, the body damage does not increase anymore and the 0 50 100 150 200 250 300 350 400 450 0 1000 2000 3000 4000 5000 6000 7000 8000 9000 10000 lb [mm] f m a x [n ] c4 u4 c3 c2 u1 c1 u2 u3 le (c4) u uncoupled theory c coupled theory 1 d 2 d 3 d 4 d i http://dx.medra.org/10.3221/igf-esis.18.03&auth=true http://www.gruppofrattura.it s. marfia et alii, frattura ed integrità strutturale, 18 (2011) 23-33; doi: 10.3221/igf-esis.18.03 33 softening behavior is only governed by the evolution of the interface damage. on the other hand, in the results obtained considering the model 2, the softening behavior is strongly influenced by the body damage during the whole detachment process, also when the interface damage becomes to develop and the body damage does not evolve anymore. thus, the degradation process results faster for the model 2 than for the model 1. moreover, the numerical application show also the differences between the response of the coupled and uncoupled interface model. in particular, the results obtained using the coupled model appears much more reasonable and, as a consequence, more reliable with respect to the one obtained adopting the uncoupled damage model, as it does not suffer from the physical unacceptable effect found in the uncoupled one. references [1] n. plevris, t.c. triantaffilou, d. veneziano, journal of structural engineering asce 121, (1995) 1037. [2] t.c. triantafillou, m.n. fardis, materials and structures, 30 (1997) 486. [3] m. r. valluzzi, m. valdemarca, c. modena, journal of composites for constructions asce (2001) 163. [4] s. marfia, e. sacco, international journal of solids and structures, 38 (2001) 4177. [5] n. galati, g. tumialan, a. nanni, construction and building materials, 20 (2006) 101. [6] b. ferracuti, m. savoia, c. mazzotti, composites: part b, 37 (2006) 356. [7] f. freddi, m. savoia, engineering fracture mechanics, 75 (2008) 1666. [8] e. grande, g. milani, e. sacco, engineering structures, 30 (2008) 1842. [9] f. fouchal, f. lebon, i. titeux, construction and building materials, 23 (2009) 2428. [10] f. freddi, m. fremond, journal of mechanics of materials and structures, 7 (2006) 1205. [11] s. marfia, e. sacco, j. toti, a coupled interface-body nonlocal damage model for frp strengthening detachment, in print on computational mechanics (2011). [12] mazars j, pijaudier-cabot g continuum damage theory: application to concrete. journal of engineering mechanics, asce, 115 (1989) 345. [13] g. alfano, e. sacco, international journal for numerical methods in engineering, 68 (2006) 542. [14] e. sacco, j. toti, international journal for computational methods in engineering science and mechanics, 11 (2010) 354. [15] o.c. zienkiewicz, r. l. taylor the finite element method, 4th edn. mcgraw-hill, london, (1991). [16] e. grande, m. imbimbo, e. sacco, journal of composites part b: engineering, 42 (2011) 330. http://dx.medra.org/10.3221/igf-esis.18.03&auth=true http://www.gruppofrattura.it microsoft word numero_40_art_12 l. zou et alii, frattura ed integrità strutturale, 40 (2017) 137-148; doi: 10.3221/igf-esis.40.12 137 s-n curve modeling method of aluminum alloy welded joints based on the fatigue characteristics domain li zou software institute, dalian jiaotong university, lvshun 116052, china lizou@djtu.edu.cn xinhua yang college of material science and engineering, dalian jiaotong university, dalian, china yangxhdl@foxmail.com jianrong tan department of mechanical engineering and automation, zhejiang university, zhejiang, china yibo sun college of material science and engineering, dalian jiaotong university, dalian, china abstract. the scatter degree of the fatigue samples is reduced when the nodal force based structural method is used for steel welded joints, while it is still high for aluminum alloy welded joints. statistical method and rough set theory is used to fatigue analysis so that fatigue characteristic domains are determined and s-n curves are fitted. experiment results show that fatigue life of the aluminum alloy welded joints is under the influence of some key factors and the fatigue data with the same characteristics distribute in a relatively independent area. accordingly, a novel s-n curve modeling method of aluminum alloy welded joints based on the fatigue characteristics domain is proposed. in the proposed method, the nodal force based structural stress method is used for stress calculation and neighborhood rough set theory is used for character extraction to obtain the key factors. then fatigue characteristics domains are divided and s-n curves are fitted on each fatigue characteristics domain instead of on the whole domain so that a set of s-n curves are obtained. statistical results show that selection of the s-n curve for the aluminum alloy welded joints according to different fatigue characteristic domain is more accurate. keywords. welding; fatigue; structural stress; rough set theory; s-n curve. citation: zou., l., yang, x., tan, j., sun, y., s-n curve modeling method of aluminum alloy welded joints based on the fatigue characteristics domain, 40 (2017) 137-148. received: 09.11.2016 accepted: 10.01.2017 published: 01.04.2017 copyright: © 2017 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. l. zou et alii, frattura ed integrità strutturale, 40 (2017) 137-148; doi: 10.3221/igf-esis.40.12 138 introduction s a traditional processing technique, welding has been widely used in many fields, such as mechanical manufacturing, aerospace, transportation, etc. the fatigue analysis and life prediction of a welding joint are directly related to the stability and safety of the whole structure. currently, the nominal stress method and the nodal based structural stress method are two most commonly used welding fatigue analysis and prediction methods. the nominal stress method is the first routine way to get theoretical and experimental research in fields of engineering fatigue design, strength assessment and life prediction of welded structures. in various industry fields, its method and data has been widely standardized, and it has been maturely applied to the actual project. but because of the existence of various preconditions and regulations, choice of the s-n curves is uncertain in this method. how to accurately select the s-n curve and to calculate the stress are the most important problems which cannot be solved in this method. the nodal force based structural stress method is a new type of fatigue life prediction technology for welded structure proposed by dong [1]. in this method, the finite element technique is used to compute the structural stress through nodal force. currently, the nodal force based structural stress method is one of the most striking engineering technologies for fatigue analysis of welded structures due to its mesh-insensitive hot spot stress calculation, higher fatigue life prediction accuracy and the broad applicability [2]. dong et al. reprocessed thousands of fatigue test data of the steel welded joints in the last 50 years [3]. according to the linear regression analysis, the main s-n curve of fatigue design based on equivalent structural stress (eq. ss) range is determined. in this study, first of all, fatigue data of aluminum alloy welded joints is collected and the fatigue database is obtained from related literatures. then, s-n curves are fitted based on the nodal force based structural stress and the scatter degree of fatigue data is computed. subsequently, neighborhood rough set theory is used for knowledge reduction to find the core among the many factors which influence the fatigue life of aluminum alloy welded joints. finally, the fatigue characteristics domain is established according to the reduction result of neighborhood rough set theory and s-n curves are fitted subsequently in each domain. related works -n curve is the main tool to analyze and predict fatigue lifetime of a metallic material, component or structure. a large number of domestic and foreign scholars have devoted themselves to the study of the s-n curve modeling method. monotonic test based empirical fatigue formulae and a wholer field mathematical model is combined and a new formula for developing full range stress life curves for medium strength steels is proposed [4]. the importance of employing material specific s-n curves with appropriate stress concentration factors for special connection details and correct damage accumulation methods is highlighted. the fatigue crack growth of a double fillet weld with the existence of a semi-elliptical crack is studied [5]. the constant amplitude loading is applied where the influence of the load ratio over the fatigue life is presented. a new probabilistic model is proposed [6], where the model parameters are estimated with an em algorithm for which the maximisation step combines newton-raphson optimization method and monte carlo integrations. a new method that assumes linear change of scatter according to stress levels is developed in [7]. the algorithm derives from maximum likelihood estimation and general newton's method. a study has been carried out to establish which confidence level in the estimation of the characteristic s-n curve from limited data [8].the results of the study provide a new way to optimize fatigue design whenever it is costly or time-consuming to achieve many reliable test data. a unified statistical model which can take into account any number of failure mechanisms and the possible presence of the fatigue limit is presented [9]. the adaptability of the statistical model to the s-n curves proposed in the open literature is demonstrated by qualitative numerical examples. generally speaking, fatigue behavior of welded components is influenced by many factors such as temperature, material type, load type, ratio and etc. up to now, many researchers have devoted themselves to this research and initial achievements have been obtained. for example, plate thickness factor is considered and a new analytical formula of fracture toughness is proposed based on the energy theory and linear elastic mechanics [10], which would significantly reduce the calculation cycle of remaining life of structures in structural integrity assessment of welded structures．crack initiation potential in materials containing defects is investigated numerically by focusing on defect types, size, shape, location, and residual stress influences [11]. results show that the crack initiation potency is higher in case of serious property mismatching between matrix and defects, and higher strength materials are more sensitive to soft inclusions. near-threshold fatigue crack growth tests are conducted at various stress ratios and different pre-cracking locations of a 25cr2ni2mov welded joint by using load-shedding procedure at room temperature to investigate the transition behavior of fatigue crack growth curve [12]. a s l. zou et alii, frattura ed integrità strutturale, 40 (2017) 137-148; doi: 10.3221/igf-esis.40.12 139 results show that there exists a transition point in the fatigue crack growth curve in the near-threshold regime, and the stress intensity range of the fatigue threshold decreases with the increasing of stress ratio. currently, there is still a lack of an objective and comprehensive evaluation of the great many factors which influence the fatigue life of the welded structure. to establish the mathematical model of different influence factors, neighborhood rough set theory is used to find the core factors which influence the fatigue life of the aluminum alloy welded joints based on the data itself rather than on any other prior knowledge. fatigue characteristics domains are then determined according to the key influence factors and the s-n curves are fitted in each domain subsequently. methodology basic principle of the nodal force based structural stress he normal structural stress at each node from elementary structural mechanics theory is given by s m b    (1) /ym f t  (2) 2 6 /xb m t  (3) where / /yy x xf f l m m l, = = is the line force and moment in the weld tow shown as fig. 1, fy is the nodal force, mx is the moment around the weld toe. figure 1: definition of linear force. fracture mechanics is employed to estimate the fatigue life of welded joints. the stress intensity factor in crack propagation theory can be calculated as [2]: * [ ( / ) ( / )], m m b b k t f a t f a t     (4) where a is the crack depth, t* is a ratio of actual thickness t to a unit thickness. ( / ) m f a t and ( / ) b f a t are membrane stress and bending stress as a function of crack growth degree respectively. according to the paris crack growth law, the prediction of the life cycle from an infinitesimally small crack to final failure can be expressed as: / 1 1 2 / 0 * *( / ) 1 ( ) ( ), ( ) ( ) ma t m sn m a t kn t d a t n t i r c m k c         (5) where mkn=k / kn is the notch stress magnification , k represents the total k due to both the far-field stress and the local notch stress effects and kn represents only the far-stress contribution to the stress intensity factor. i(r) is a dimensionless function of r and m is the crack growth exponent, which is set to be 3.6 in asme [13]. a master s-n curve can be established according to eq. 6 based on a set of welding fatigue data. the eq. ss can then be expressed as: 1 2* ( ) ( ) m m s t i r      (6) t f(x) fy2 fy2 x l element fy1 fy1 y l. zou et alii, frattura ed integrità strutturale, 40 (2017) 137-148; doi: 10.3221/igf-esis.40.12 140 where t* is dimensionless the equivalent  retains a stress unit. neighborhood rough set theory founded by pawlak, rough set theory [14] aims to find the inner links of the massive, imprecise, incomplete and uncertain data, it has become an important tool to study granular computing theory nowadays [15]. however, the tradition rough set just works in discrete spaces and it can’t deal directly with the numerical data that widely existed in the practical application. when dealing with the numerical data, discretization is first done to transform the numerical value into the symbol value [16, 17]. this transformation inevitably brings about information loss and the computing results usually depend largely on the effect of discretization algorithm. to deal with this problem, a neighborhood rough set model is proposed based on the definitions of δ neighborhood and neighborhood relations in metric spaces [18, 19]. several foundation definition of neighborhood rough set theory including neighborhood  , lower and upper approximations, dependency degree, significance of the attribute, reduction and core are first introduced here. definition 1 neighborhood  u is a non-empty finite set in the real number space, ix u  , the  -neighborhood of xi is defined as ( ) { , ( , ) }i ix x u x x     (7) where  is a metric function, 1 2 3, ,x x x u  , it satisfied 1 2( , ) 0x x  , 1 2( , ) 0x x  if and only if 1 2x x , 1, 2 2 1( ) ( , )x x x x  and 1, 3 1 2 2 3( ) ( , ) ( , )x x x x x x     . the family of neighborhood granules { ( ) | }i ix x u  forms an element granule system for a given metric space ,u   . we have , ( )i ix u x    and ( ) x u x u   . a neighborhood relation n can be written as a relation matrix ( ) ( )ij n nm n r  , where 1ijr  if ( )j ix x or 0ijr  otherwise. definition 2 lower and upper approximations the lower and upper approximations of x in terms of relation n for a given ,u n  are defined as { | ( ) , },i i inx x x x x u   (8) { | ( ) , },i i inx x x x x u    (9) the boundary region of x is ,bnx nx nx  (10) definition 3 dependency degree the dependency degree of the decision attribute d to the condition attribute b is defined as | | ( ) , | | b b n d d u   (11) it is obvious that 0 ( ) 1b d  . if ( ) 1b d  , we say d completely depend on b otherwise d is  -depend on b. definition 4 significance of the attribute given a neighborhood decision table , , , ,u c d v f  , b⊆c,a∈c-b, the significance of a to b is defined as ( , , ) ( ) ( ),b a bsig a b d d d   (12) definition 5 reduction given a neighborhood decision table , , , ,u c d v f  , b⊆c, we say the subset of attributes b is a reduction of c if ( ) ( )b cd d  and , ( ) ( )b b bb b d d     . definition 6 core l. zou et alii, frattura ed integrità strutturale, 40 (2017) 137-148; doi: 10.3221/igf-esis.40.12 141 given a neighborhood decision table , , , ,u c d v f  , all reductions consist of b1,b2,…bn, the core of is defined as 1 n i i core b   . a kind of forward greedy reduction algorithm is used for the neighborhood decision table in this work, as is shown in the following fig. 2, where ε is the threshold of the significance of attribute and its value is close to 0. figure 2: reduction algorithm. three types of fatigue stress-life relations up to now, there are three types of mathematical expressions to describe the s-n curve, including basquin [20], langer [21] and three parameters stress-life model [22]. among which, basquin model is the most commonly used form, as is shown as ,ms n c (13) where, m and c are constants related to material types. take logarithm on both sides, we get lg lgs a b n  (14) where，a= lg /c m ，b= 1 / m . besides basquin model, langer model and the three parameters model are the other two models commonly used for fatigue analysis. the langer model is shown as eqs. (15) and the three parameters stress-life model is shown as eqs. (16). mse n c (15) ( )mfs s n c  (16) in this work, three types of the fatigue stress-life relations are all used for s-n curve fitting of the aluminum alloy welded joints. then, statistical results of the three relations are compared and the best one is selected. novel s-n curve modeling method establishment of fatigue database fter a review of relevant literature [23, 24], fatigue data of aluminum alloy welded joints is collected and fatigue database is built up. the total number of samples in the database is 64, and s-n curves are fitted on basis of these samples. totally, there are four types of welding methods including mig, gmaw, tig and manual arc, five kinds a l. zou et alii, frattura ed integrità strutturale, 40 (2017) 137-148; doi: 10.3221/igf-esis.40.12 142 of material types including 5083h11, almg4mncr,almgsi1,np5/6 and hp30, four kinds of plate thicknesses including 10mm,2.5mm,3mm and 4.8mm, three kinds of ratio including 0, 0.1 and 0.5, two kinds of load types including 4b and t, three types of joint types including tj:p, lj_ds:p, and sj_ds:p. limited to the space, only part of the experiment data is shown as below in tab.1. it only includes fatigue data of crack initiation from weld toe, excludes that from weld and base metal. material type welding method thickness (mm) ratio load type joint type nominal stress (mpa) eq.structural stress range (mpa) life cycles 5083h11 mig 10 0.1 4b tj:p 120 161 62700 5083h11 mig 10 0.5 4b tj:p 90 121 213750 almg4mncr gmaw 2.5 0.1 t lj_ss:p 45 174 31260 almg4mncr gmaw 2.5 0.1 t lj_ss:p 35 135 52040 almgsi1 tig 3 0 t lj_ds:p 53 160 85920 almgsi1 tig 3 0 t lj_ds:p 32 97 323460 np5/6 manual arc 4.8 0 t sj_ds:p 46 116 188000 np5/6 manual arc 4.8 0 t sj_ds:p 31 77 1250000 hp30 manual arc 4.8 0 t sj_ds:p 62 155 188000 …… table1: part fatigue data of the aluminum alloy welded joints. fitting of s-n curves according to the three fatigue stress-life relations mentioned in the three types of fatigue stress-life relations section, s-n curve fitting results using the nodal force based structural stress are obtained in fig. 3. comparison of goodness-of-fit statistics including sse, r-square, adjusted r-square and rmse is shown in tab. 2. where, sum of squares due to error measures the total deviation of the response values from the fit to the response values. it is also called the summed square of residuals and is usually labeled as sse. 2 1 ( ) , n i i i i sse y y     (17) r-square is the square of the correlation between the response values and the predicted response values. it is also called the square of the multiple correlation coefficients and the coefficient of multiple determinations. r-square is defined as the ratio of the sum of squares of the regression (ssr) and the total sum of squares (sst). ssr is defined as 2 1 ( ) , n i i i ssr y y     (18) sst is also called the sum of squares about the mean, and is defined as 2 1 ( ) , n i i i sst y y    (19) where, sst = ssr + sse. given these definitions, r-square is expressed as r-square= 1 , ssr sse sst sst   (20) r-square can take on any value between 0 and 1, with a value closer to 1 indicating that a greater proportion of variance is accounted for by the model. the adjusted r-square statistic is generally the best indicator of the fit quality when you compare two models that are nested, that is, a series of models each of which adds additional coefficients to the previous model. l. zou et alii, frattura ed integrità strutturale, 40 (2017) 137-148; doi: 10.3221/igf-esis.40.12 143 adjusted r-square= ( 1)1 , ( ) sse n sst    (21) where the residual degrees of freedom  is defined as the number of response values n minus the number of fitted coefficients m estimated from the response values. the adjusted r-square statistic can take on any value less than or equal to 1, with a value closer to 1 indicating a better fit. negative values can occur when the model contains terms that do not help to predict the response. root mean squared error (rmse) is also known as the fit standard error and the standard error of the regression. it is an estimate of the standard deviation of the random component in the data, and is defined as sse rmse mse    (22) similar with sse, an mse value closer to 0 indicates a fit that is more useful for prediction. figure 3: fitting results of the three relations. basquin langer three parameters sse 4.043e+04 4.853e+04 4.03e+04 r-square 0.7661 0.7192 0.7668 adjusted r-square 0.7623 0.7147 0.7592 rmse 25.54 27.98 25.7 table 2: goodness-of-fit statistics. as could be seen from fig. 3 and tab. 2, the fitting effect of langer is the worst thus it isn’t suitable for this group of fatigue data. fitting results of basquin and three parameters are close. from the perspective of higher application security, we choose the basquin model as the fatigue stress-life relation for this group of fatigue data of aluminum alloy welded joints. thus in this paper, basquin model is used and the mean s-n curve is fitted by the least square method based on the nodal force based structural stress according to the collected fatigue data of aluminum alloy welded joints. scatter of fatigue data based on nominal stress and the mean s-n curve based on equivalent structural stress in log-log coordinates are shown in fig. 4 and fig.5. the goodness-of-fit statistics including sse, r-square, adjusted r-square and rmse by using nodal force based structural stress are shown in tab. 3. l. zou et alii, frattura ed integrità strutturale, 40 (2017) 137-148; doi: 10.3221/igf-esis.40.12 144 figure 4: fatigue data scatter based on nominal stress. figure 5: s-n curve based on eq. ss range. mean sse 0.388 r-square 0.772 adjusted rsquare 0.7683 rmse 0.0791 table 3: goodness-of-fit statistics by using eq.ss range. in the eq. ss method, the structural stress is analyzed by nodal forces approach by considering the welded toe structural stress concentration effect. the stress calculation results are insensitive to the finite element type, mesh shape and dimensions in this method, so the welded toe structural stress concentration conditions for different welded joints could be distinguished effectively. the stress parameter relevant to the fatigue lives of welds directly are defined by using the fracture mechanics and the formula for eq.ss transformation is determined subsequently. based on the method of stress calculation and transformation, the fatigue data of aluminum alloy welded joints are analyzed. then the single fatigue design master sn curve, which is necessarily important in the fatigue strength assessment and life prediction, is established as in fig. 5. as could be seen from fig. 4 and fig. 5, the dispersion of the fatigue data has been reduced when eq. structural stress is used compared with using nominal stress. such problems as how to select s-n curves and to accurately calculate the stress existed in the nominal stress method have been overcome when the nodal force based structural stress method is used. features extraction based on neighborhood rough set theory besides the main stress factor, fatigue life of welded joints is also affected by other factors such as the geometry of the welded joints, material types, welding method, load type, ratio, thickness of the plate et al.. while at present, the analysis of the related factors that influence the fatigue life of the welded joints is generally independent and the correlation between each other is rarely studied. we have tried successfully to establish the mathematical model of the influence of related factors on fatigue life by classical rough set theory [25, 26], where attribute discretization algorithm is used for the continuous attribute. due to the use of discretization algorithm for continuous attributes inevitably causes the loss of information, in this work, neighborhood rough set theory is used to deal with the continuous attribute for features extraction, according to which fatigue characteristics domain is determined and s-n curve in each domain is fitted. on basis of the fatigue database established as tab.1, the neighborhood decision table s is built up, which could be expressed as s=(u,c,d,v,f). where u is the data set of all the aluminum alloy welded joints called the universe, a=c∪d is a nonempty finite set of attributes, c is a non-empty finite set of the factors which influence the fatigue life of the aluminum alloy welded joints called condition attributes, and d is the set of the fatigue life called decision attribute. each attribute aa can be viewed as a function that maps elements of u into a set va. the set va is called the value set of attribute a. in the decision table s, each row describes a solder fatigue life test sample of the aluminum alloy welded joints and each column l. zou et alii, frattura ed integrità strutturale, 40 (2017) 137-148; doi: 10.3221/igf-esis.40.12 145 indicates an attribute. considering the advantages of the nodal force based structural stress, take it as the stress factor that influence the fatigue life of the aluminum alloy welded joints in s. thus the fatigue decision system s of the aluminum alloy welded joints is built up in this paper, where the condition attributes of s is c={material type(c1), welding method(c2), thickness(c3,mm), ratio(c4), load type(c5), joint type(c6), eq. structural stress(c7，mpa)}，the decision attribute of s is d={lgn}. part data of the decision table is shown as tab. 4. u condition attributes decision attributes c1 c2 c3 c4 c5 c6 c7 d 1 5083h11 mig 10 0.1 4b tj:p 161 4.7973 2 5083h11 mig 10 0.5 4b tj:p 121 5.3299 3 almg4mncr gmaw 2.5 0.1 t lj_ss:p 174 4.4950 4 almg4mncr gmaw 2.5 0.1 t lj_ss:p 135 4.7163 5 almgsi1 tig 3 0 t lj_ds:p 160 4.9341 6 almgsi1 tig 3 0 t lj_ds:p 97 5.5098 7 np5/6 manual arc 4.8 0 t sj_ds:p 116 5.2742 8 np5/6 manual arc 4.8 0 t sj_ds:p 77 6.0969 9 hp30 manual arc 4.8 0 t sj_ds:p 155 5.2742 …… table 4: part data of the decision table. in the experiment, ( ) ( ) /i ic std c  , 2  , 0.01  .after attributes reduction, the reduction result of the neighborhood decision system of the aluminum alloy welded joints is obtained, namely{ c1(material type), c4(ratio)， c7(eq. structural stress)}. s-n curve modeling based on fatigue characteristics domain in eq. ss method, one master s-n curve is obtained at last thus the uncertain problem of s-n curve choice has been overcome. compared with the nominal stress method, dispersion of the fatigue data samples in the nodal force based structural stress method has been greatly reduced. but from the design point of view, the dispersion degree of the fatigue data samples indicated by the value of rmse is still relatively high, which is about 0.0791 here. in this work, a novel s-n curve modeling method is put forward by using the nodal force based structural stress. in the proposed method, fatigue characteristics domains are divided on basis of the reduction result of the welding fatigue decision system obtained by using rough set granularity theory. subsequently, s-n curves are fitted on each fatigue characteristics domain rather than on the whole domain. as a result, a series of s-n curves instead of only one master s-n curve are obtained at last. in the process of welding fatigue design, we should also design according to each fatigue characteristics domain rather than in the whole fatigue domain. the fatigue characteristics domains of the aluminum alloy welded joints are determined according to the reduction result, that is, {c1(material type), c4(ratio), c7(eq. structural stress)} obtained by using rough set theory. all the fatigue data samples are divided into 6 series from s1 to s6, where s1：{ x∈u∣xc1=5083h11 and xc4=0.1} s2：{ x∈u∣xc1=5083h11 and xc4=0.5} s3：{ x∈u∣xc1 =almg4mncr and xc4=0.1} s4：{ x∈u∣xc1 =almgsi1 and xc4=0} s5：{ x∈u∣xc1 =np5/6 and xc4=0} s6：{ x∈u∣xc1 =hp30 and xc4=0}, among which, each series of fatigue test samples corresponds to a specific fatigue characteristics domain and the determine of the fatigue characteristics domains is shown as fig. 6. fitting the s-n curve in each fatigue characteristics domain and 6 mean s-n curves from mean1 to mean6 are obtained as is shown in fig. 7. as could be seen from fig. 7, fatigue data with the same characteristics scatter in a relatively independent area. for example, the scatter of green asterisk ‘*’ which denote all the fatigue samples whose material name is 5083h11 and ratio is 0.1 in the fatigue experiment are relatively concentrated, corresponding with characteristic domain s1. accordingly, the whole fatigue test samples of aluminum alloy welded joints are divided into six fatigue characteristics domains from s1~s6. the dispersion degree of the fatigue samples are further reduced when s-n curves are fitted according to each series instead of the whole fatigue samples. six mean s-n curves from mean1~mean6 are obtained in the proposed method at last. the coefficients of the basquin equation of mean and mean1~mean6 are shown in tab. 5. l. zou et alii, frattura ed integrità strutturale, 40 (2017) 137-148; doi: 10.3221/igf-esis.40.12 146 figure 6: determine of the fatigue characteristics domains. mean mean1 mean2 mean3 mean4 mean5 mean6 a 3.206 3.369 3.483 2.972 3.268 3.509 3.689 b –0.2139 –0.2398 –0.2626 –0.1844 –0.2213 –0.2607 –0.2866 table 5: coefficients of the basquin equation figure 7: s-n curve modeling based on the fatigue characteristics domain in the process of statistical analysis, the goodness-of-fit statistics including sse, r-square, adjusted r-square and rmse of mean1-mean6 are shown in tab. 6. mean1 mean2 mean3 mean4 mean5 mean6 sse 0.0068 0.0129 0.0648 0.08228 0.0291 0.0013 r-square 0.9465 0.8795 0.7263 0.7877 0.8983 0.9897 adjusted r-square 0.9389 0.8695 0.7053 0.7665 0.8813 0.9871 rmse 0.0312 0.0328 0.0706 0.09071 0.0696 0.0181 table 6: goodness-of-fit statistics of mean1-mean6. l. zou et alii, frattura ed integrità strutturale, 40 (2017) 137-148; doi: 10.3221/igf-esis.40.12 147 experiment results and analysis as could be seen from tab. 3 and tab. 6, the values of sse from mean1 to mean6 based on the fatigue characteristics domain are all smaller than that of the mean in the whole domain. except mean3, the value of r-square of mean1 to mean6 is closer to 1 than mean in the whole domain. each value of adjusted r-square of mean1 to mean6 is closer to 1 than mean in the whole domain. except mean4, the value of rmse of mean1 to mean6 is closer to 0 than mean in the whole domain, which indicates that the scatter degree of the fatigue data is further reduced when fatigue characteristics domain is divided and s-n curves are fitted in each independent domain. thus fatigue life prediction by using s-n curve modeling method based on the fatigue characteristic domains would be more accurate than that by traditional master s-n curve. conclusion n this work, on one hand, nodal force based structural stress is used in the s-n curve modeling method based on the fatigue characteristics domain, thus such problems as how to accurately select the s-n curve and to calculate the stress that existed in the traditional nominal stress method have been overcome in the proposed method. the fatigue characteristics domain is determined by using rough set granularity theory, which can achieve knowledge acquisition relying only on the data itself without depending on the prior knowledge or experience knowledge. on the other hand, the entire fatigue test samples of aluminum alloy welded joints are divided into 6 characteristics domains according to the attributes reduction result of the rough set theory, and the mean s-n curves form mean1 to mean6 are fitted respectively. as could be seen from tab. 6, the value of sse which indicates the dispersion in each fatigue characteristics domain is significantly lower than that of the single master s-n curve obtained in the nodal force based structural stress method. statistical analysis results show that dispersion of the fatigue data is reduced while the proposed sn curve modeling method based on fatigue characteristics domain is used. therefore, compare with the single master s-n curve in the nodal force based structural stress method, to determine the design s-n curve according to the fatigue characteristics domain is more targeted with a lower dispersion degree. thus the fatigue calculation results will be more accurate if the proposed s-n curve modeling method based on the fatigue characteristics domain is used. future work will be concentrated on the aspects of the application of the proposed s-n curve modeling method based on fatigue characteristics domain in the practical engineering practice. acknowledgments he authors would like to thank all the reviewers for their constructive comments. this research was supported by the national natural science foundation of china (51175054), natural science foundation of liaoning province (2015020169), dalian high level talent innovation support plan (2016rq053). references [1] dong, p., a structural stress definition and numerical implementation for fatigue analysis of welded joints, international journal of fatigue, 23 (2001) 865-876. doi: 10.1016/s0142-1123(01)00055-x. [2] dong, p., hong, j. k., osage, d. a., et al., master s-n curve method for fatigue evaluation of welded components, welding research council bulletin, (2002) 1-44. [3] dong, p., prager, m., osage, d., the design master s-n curve in asme div 2 rewrite and its validations, welding in the world le soudage dans le monde, 51 (2007) 53-63. doi:10.1007/bf03266573. [4] bandara, c. s., siriwardane, s. c., dissanayake, u. i., et al., developing a full range s–n curve and estimating cumulative fatigue damage of steel elements, computational materials science, 96 (2015) 96-101. doi: 10.1016/j.commatsci.2014.09.009 [5] benachour, m., benguediab, m., hadjoui, a., et al., fatigue crack growth of a double fillet weld, computational materials science, 44 (2008) 489-495. doi: 10.1016/j.commatsci.2008.04.015. [6] fouchereau, r., celeux, g., pamphile, p., probabilistic modeling of s – n curves, international journal of fatigue, 68 (2014) 217-223. doi: 10.1016/j.ijfatigue.2014.04.015. [7] zhou, y., tang, x., s-n curve modeling for finite life range under the assumption of linearly changing scatter, sae international journal of materials & manufacturing, 7 (2014) 454-464. doi: 10.4271/2014-01-0970. i t l. zou et alii, frattura ed integrità strutturale, 40 (2017) 137-148; doi: 10.3221/igf-esis.40.12 148 [8] ronold, k. o., lotsberg, i., on the estimation of characteristic s – n curves with confidence, marine structures, 27 (2012) 29-44. doi: 10.1016/j.marstruc.2012.03.002. [9] paolino, d. s., chiandussi, g., rossetto, m., a unified statistical model for s-n fatigue curves: probabilistic definition, fatigue & fracture of engineering materials & structures, 36 (2013) 187–201. doi:10.1111/j.1460-2695.2012.01711.x [10] wang, p., liu, x., wang, q., et al., thickness effect on fracture toughness of a7n01p-t5 aluminum alloy, transactions of the china welding institution, (2013) 45-48.(in chinese) [11] zhu, m., xuan, f., fatigue crack initiation potential from defects in terms of local stress analysis, chinese journal of mechanical engineering, 27 (2014) 496-503. [12] yannan, d. u., zhu, m., xuan, f., effect of stress ratio on the transition point of fatigue crack growth curve in the near-threshold regime of a 25cr2ni2mov steel welded joint, journal of mechanical engineering, 51 (2015) 4449.(in chinese) [13] asme, asme boiler and pressure vessel code section viii division 2 part 5: design by analysis requirement, new york, (2007). [14] pawlak, z., rough classification, international journal of man-machine studies, 51 (1984) 469-483. doi:10.1006/ijhc.1983.0315 [15] wang, g. y., yao, y. y., yu, h., a survey on rough set theory and applications, chinese journal of computers, (2009) 1229-1246. (in chinese) [16] wen-hang, l. i., chen, s. b., lin, t., et al., the comparison of discretization method in rough set based modeling method for welding, journal of shanghai jiaotong university, 40 (2006) 1094-1097. (in chinese) [17] wen-hang, l. i., chen, s. b., lin, t., et al., a generalized rough set modeling method for welding process, journal of shanghai jiaotong university, 12 (2007) 319-322. [18] hu, q., yu, d., xie, z., neighborhood classifiers, expert systems with applications an international journal, 34 (2008) 866-876. doi: 10.1016/j.eswa.2006.10.043. [19] li w., huang z., jia x., et al., neighborhood based decision-theoretic rough set models, international journal of approximate reasoning, 69 (2016) 1-17. doi: 10.1016/j.ijar.2015.11.005. [20] nishijima, s., statistical analysis of small sample fatigue data, transactions of the japan society of mechanical engineers a, 46 (1980) 234-245. [21] boiler, a. s. o. m. e., committee, p. v. asme boiler & pressure vessel code: an internationally recognized code , american society of mechanical engineers, (1995). [22] weibull, w. fatigue testing and analysis of results. published for advisory group for aeronautical research and development, north atlantic treaty organization, pergamon press, (1961). [23] sidhom, n., laamouri, a., fathallah, r., et al., fatigue strength improvement of 5083 h11 al-alloy t-welded joints by shot peening: experimental characterization and predictive approach, international journal of fatigue, 27 (2005) 729745. .doi: 10.1016/j.ijfatigue.2005.02.001. [24] beretta, s., sala, g., a model for fatigue strength of welded lap joints, fatigue & fracture of engineering materials & structures, 28 (2005) 257–264. doi: 10.1111/j.1460-2695.2004.00849.x [25] yang, x., deng, w., zou, l., et al., fatigue behaviors prediction method of welded joints based on soft computing methods, materials science & engineering a, 559 (2013) 574-582. doi: 10.1016/j.msea.2012.08.144. 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can be opened with acrobat and adobe reader 5.0 and later.) >> /namespace [ (adobe) (common) (1.0) ] /othernamespaces [ << /asreaderspreads false /cropimagestoframes true /errorcontrol /warnandcontinue /flattenerignorespreadoverrides false /includeguidesgrids false /includenonprinting false /includeslug false /namespace [ (adobe) (indesign) (4.0) ] /omitplacedbitmaps false /omitplacedeps false /omitplacedpdf false /simulateoverprint /legacy >> << /addbleedmarks false /addcolorbars false /addcropmarks false /addpageinfo false /addregmarks false /convertcolors /converttocmyk /destinationprofilename () /destinationprofileselector /documentcmyk /downsample16bitimages true /flattenerpreset << /presetselector /mediumresolution >> /formelements false /generatestructure false /includebookmarks false /includehyperlinks false /includeinteractive false /includelayers false /includeprofiles false /multimediahandling /useobjectsettings /namespace [ (adobe) (creativesuite) (2.0) ] /pdfxoutputintentprofileselector /documentcmyk /preserveediting true /untaggedcmykhandling /leaveuntagged /untaggedrgbhandling /usedocumentprofile /usedocumentbleed false >> ] >> setdistillerparams << /hwresolution [2400 2400] /pagesize [612.000 792.000] >> setpagedevice microsoft word numero_26_art_14 g. fargione et alii, frattura ed integrità strutturale, 26 (2013) 143-155; doi: 10.3221/igf-esis.26.14 143 fatigue characterization of mechanical components in service g. fargione, d. tringale dipartimento di ingegneria industriale e meccanica, università degli studi di catania, viale andrea doria 6, 95125 catania e. guglielmino, g. risitano università degli studi di messina, dipartimento di ingegneria elettronica, chimica e ingegneria industriale, contrada di dio (s. agata), 98166 messina grisitano@unime.it abstract. the quickly identify of fatigue limit of a mechanical component with good approximation is currently a significant practical problem not yet resolved in a satisfactory way. generally, for a mechanical component, the fatigue strength reduction factor (i) is difficult to evaluate especially when it is in service. in this paper, the procedures for crack paths individuation and consequently damage evaluation (adopted in laboratory for stressed specimens with planned load histories) are applied to mechanical components, already failed during service. the energy parameters, proposed by the authors for the evaluation of the fatigue behavior of the materials [1-5], are defined on specimens derived from a flange bolts. the flange connecting pipes at high temperature and pressure. due to the loss of the seal, the bolts have been subjected to a hot flow steam addition to the normal stress. the numerical analysis coupled experimental analysis (measurement of surface temperature during static and dynamic tests of specimens taken from damaged tie rods), has helped to determine the causes of failure of the tie rods. the determination of an energy parameter for the evaluation of the damage showed that factors related to the heat release of the material (loaded) may also help to understand the causes of failure of mechanical components. keywords. mechanical components in service; rrm; fatigue. introduction n this work it has been applied to mechanical components damaged during the working phase, the procedures of damage assessment which have been already adopted in laboratory on the test specimens stressed with programmed loads history. the energy parameters proposed for years by the authors to estimate the materials fatigue behaviour, have been tested on specimens made out of the bolts of a connection flange of high temperature and head steam pipes which have been subjected not only to the usual proof stress, but also to a steam flux caused by a leak of the seal. the numerical and the following experimental analysis carried out through the measurement of the surface temperature during the static and dynamic tests on the specimens made out of by damaged slings allowed to define the causes for the slings breakage. the determination of a reference energy parameter to evaluate also the damage sustained by the material has highlighted again how the factors linked to the material heat release under stress can help to evaluate also the causes of the failure of the mechanical components. i http://dx.medra.org/10.3221/igf-esis.26.14&auth=true http://www.gruppofrattura.it g. fargione et alii, frattura ed integrità strutturale, 26 (2013) 143-155; doi: 10.3221/igf-esis.26.14 144 since 1982 the authors have proposed the energy analysis to evaluate the mechanical characteristics of the materials. risitano and the members of his staff [1-5] have first pointed out how an analysis of the temperature of a stressed specimen (dynamic and also static) is a parameter (the third parameter in association with the stress and the time during the fatigue test) which allows to recognize the birth of irreversible deformations (in general) which generate heat. they have chosen as energy indicator to assess the start of the damage, the surface temperature of the specimen and they have used spread-range instruments (infrared thermographs) to evaluate it on the entire area. they have proposed the use of the temperature integral of the hottest point during the rupture time (φ= ∫tdn) as the energy parameter useful for the evaluation of the energy breaking limit (el) (the energy which is necessary to break the material through dynamic stresses); carrying out some experiments they have verified in several works that the parameter φ is constant for each material (component) as it is constant el, following reliable theories. according to this result it has been proposed a methodology which allows to calculate, using a limited number of specimens (theoretically just one of them), not only the fatigue limit but also the entire fatigue curve. during the last years, according to risitano and his school experiments, different authors [6-13] have applied and confirmed the validity of this methodology, extending it to other materials different from the steels and for which this methodology was born. risitano and the members of his staff have applied the methodology to mechanical components characterizing the fatigue of the components themselves [14], to verify the possibility of estimating a material’s fatigue limit by studying the surface temperature evolution of a specimen loaded with a static axial force [15-19] and to propose a new linear damage model [20-23]. for years and according with the endless application of this methodology, the temperature has been adopted as a damage or a change index of the characteristics of the material. it has been observed that, being the material or the component equal, the surface temperature trend under the same load is different if the component has been previously damaged or not. some authors have recently referred to energetic parameters to evaluate the damage. atzori et al. [24] refers to the heat q released after the material has been stressed for a certain period of time (number of cycles) and with loads which exceed the fatigue limit. on the contrary naderi et al. [25] refer to the entropic status of the material and they use the entropy as an energy parameter. it is clear that both [24] and [25] consider as reference parameter entities which are directly connected with risitano surface temperature because it deals with strong materials with slight volume variations. the surface temperature as the important parameter connected with the stress of the material has been used by risitano as an indicator of the end of the elastic phase and the beginning of local micro plasticizations in single-axle traction tests. the fatigue failure happens when a stress which causes the beginning of the plasticization is applied in repetitive way. therefore, the fatigue limit corresponds to the external stress value (macroscopic), able to produce irreversible local deformation, which is determinable by the slope change of the temperature vs strain curve in a static monotonic traction test. it means that the fatigue limit is coincident with the external stress value (load / area) which, during static traction test, causes micro plasticizations inside the material in order to reach local stresses compatible with the beginning of the irreversible deformation phenomena and heat production consequently. in this work the above mentioned principles have been applied for the assessment of the cause which has caused the breakage of two of the eight tie rods of a measure flange of a steam unit petroleum-processing plant (fig. 1). figure 1: flange of a steam unit petroleum-processing. http://dx.medra.org/10.3221/igf-esis.26.14&auth=true http://www.gruppofrattura.it g. fargione et alii, frattura ed integrità strutturale, 26 (2013) 143-155; doi: 10.3221/igf-esis.26.14 145 materials and methods he need to know the causes of the breakage of two of the eight tie rods of a measure flange during the maintenance operation, suggested the authors to apply, on a material belonging to damaged or broken elements, the procedures applied in to the lab to evaluate the material fatigue characteristics. the visual examination of the broken tie rods has revealed some clear-cut breakages, without huge plastic deformations, near the mean line of the tie rods (fig. 2) and in particularly next to the seal. the integrity (as it seems at a first visual examination) of the residual six tie rods recommends to avoid damaging them, both to support the exercise needs and also to use the first broken one to establish the mechanical characterization of the material. the hypothesis that the leakage of high-temperature (260°c) and high-pressure steam (161 ata) just from one side of the flange should have caused the two tie rods failure due to the steam mechanical effect, has persuaded the present authors to characterize the material of the shorn tie rods. starting from a finite elements analysis which simulate also the steam leakage from the seal, it has been noticed that, in the middle of the tie rod near the seal, the stresses were higher than the usual material strength parameters. the validation of the failure theory has been found examining the conditions of the material of the broken tie rods. the characterization has been achieved with the analysis of the heat releases (thermographic method)of the limited number of the specimens which should be obtained by the two broken tie rods. the tab. 1 reports the characteristics of the tie rods which were totally threaded (iso metric thread with uni 6610-69 fine pitch), while tab. 2 reports the specific characteristics. the tab. 3 reports the steal chemical characteristics. camping element quantity identification mark tie rods m39x3 8 i3 screw material regulations heat treatment 40crmo4 uni 5332-64 quenching screw nut material regulations heat treatment 40crmo4 uni 5332-64 normalized table 1: flange characteristics. identification mark material used temperature [°c] camping element root section [mm2] i3 40crmo4 -10/375 m39x3 980 table 2: identification characteristics c si mn p s al cr 0.44% 0.35% 1.00% 0.035% 0.04% 0.02% 1.2% table 3: 40crmo4 heat-treated steal chemical characteristics. for each of the two tie rods slugs (from now on called a and b) it has been created two clepsydra specimens of 5x15x50 suitable sizes, with a total length of 150 mm, as it is shown in fig. 3. therefore there were four tie rods specimens for a and four tie rods specimens for b. t http://dx.medra.org/10.3221/igf-esis.26.14&auth=true http://www.gruppofrattura.it g. fargione et alii, frattura ed integrità strutturale, 26 (2013) 143-155; doi: 10.3221/igf-esis.26.14 146 figure 2: clear-cut breakages of tie rods. figure 3: for each of the two tie rods slugs it has been created two clepsydra specimens (measures in mm). the realization of the single specimen has been done using cutting and milling mechanical working as it is indicated in fig. 3. it has been realized eight specimen but just one of the tie rod a (specimen 1) and one of the tie rod b ( specimen 2) have been used for the execution of the static tests; the other ones have been used for the fatigue tests. results fe analysis efore examining the characterization of the material of the broken tie rods, it has been done a numerical analysis to value the stresses on the same tie rods during a normal work. after the modelling of the flange-tie rods coupling system (fig. 4), the analysis has been done first using the code marc(r) of msc(r) considering the contact conditions among the different parts ( flange, seal, tie rods, nuts) and it has been pointed out the general stress and deformation states. the fig. 5.a shows the stress reached by the different parts applying the working loads and the fig. 5.b shows the tie rod stresses trend. a second analysis has been done examining the tie rod just with the nuts at the ends: it has applied there the same pressures which they can receive during a normal work. the fig. 6 shows the model and the corresponding calculated stresses. both in the first (complete system) and in the second modelling (pivot and nuts) it has been observed , as expected, that the maximum stresses were near the link to the end nuts and that in the middle section, where the tie rods were broken, the stresses, due to the applied camping values, reached about 220 mpa lower than the material yield load (835 mpa). it can be observed that during the “lighter” second simulation, the deformed stress status was equal to the status obtained using a complex model where the mutual actions among the different connection components (flange, seal, tie rods, nuts) had been considered. therefore, it has been chosen to use a simple model to simulate the tie rod undergone both the onstream forces and the steam jet caused by the seal leakage. b http://dx.medra.org/10.3221/igf-esis.26.14&auth=true http://www.gruppofrattura.it g. fargione et alii, frattura ed integrità strutturale, 26 (2013) 143-155; doi: 10.3221/igf-esis.26.14 147 the fig. 7 shows the tie rod middle section stressed with a temperature of 450 °c and for a length equal to the seal thickness. figure 4: solidworks model of a part of the flanged coupling. (a) (b) figure 5: (a) stress distribution on the model; (b) equivalent stresses on the pivot. figure 6: equivalent stress on the pivot. http://dx.medra.org/10.3221/igf-esis.26.14&auth=true http://www.gruppofrattura.it g. fargione et alii, frattura ed integrità strutturale, 26 (2013) 143-155; doi: 10.3221/igf-esis.26.14 148 figure 7: heat load on the pivot. in tab. 4 it has been reported the characteristics of the material used for the simulation during the temperature variation. temperature [°c] young module [mpa] coefficient of thermal expansion 20 210000 10.0 100 205000 11.1 200 195000 12.1 300 185000 12.9 400 175000 13.5 500 165000 13.9 600 155000 14.1 table 4: characteristics of the material used for the simulation during the temperature variation. the fig. 8 shows the pivot stresses distribution in the middle section caused by the temperature. figure 8: stress distribution on the pivot caused by the temperature. http://dx.medra.org/10.3221/igf-esis.26.14&auth=true http://www.gruppofrattura.it g. fargione et alii, frattura ed integrità strutturale, 26 (2013) 143-155; doi: 10.3221/igf-esis.26.14 149 figure 9: results of fe analysis. the diagram of the fig. 9 reports the material yield load variation with respect to the steam temperature. in the same graph it has been reported the von mises maximum stress value reached in the middle section of the tie rod changing the local temperature and the stress deviation from proportionality at high temperatures. it can be observed that at a 350 °c temperature the stress value is equal to the material yield stress and with a temperature of 450 °c (equal to the steam come out from the flange) the stress is 40% over the material yield stress. experimental analysis in order to determine the mechanical characteristics of the material both static and fatigue tests have been performed. as it has been already said, the static tests have been carried out on 2 of the eight specimens, one belonging to the tie rod a (specimen 1) and another of the tie rod b (specimen 2). the tests have been done using an electrohydraulic machine instron(r) 8501 with a fixed crossrate equal to 1 mm/min. the test has been accompanied by the detection and the acquisition of the surface temperature of the specimens using an ir camera flir(r) 3000 with a frame rate of 1 hz. the fig. 10 reports the deformation stress graph of one of the tested specimen 1. in the same figure it has been reported the temperature trend of the hottest area of the specimen surface showing the unit deformation of the specimen itself. the temperature trend has been deduced examining the following images obtained during the traction test. for a better understanding, in fig. 11 it has been reported the first part of the temperature curve vs strain (till ε = 0.04) of specimen 1. figure 10: stress vs strain curve and temperature trend of specimen 1 mono axial static test. http://dx.medra.org/10.3221/igf-esis.26.14&auth=true http://www.gruppofrattura.it g. fargione et alii, frattura ed integrità strutturale, 26 (2013) 143-155; doi: 10.3221/igf-esis.26.14 150 figure 11: thermal map for the specimen 1. using the method mentioned before the results of the tests and of the acquisitions done for the specimen 2 are reported respectively in fig. 12 and 13. figure 12: stress vs strain curve and temperature trend of specimen 2 mono axial static test. figure 13: thermal map for the specimen 2. http://dx.medra.org/10.3221/igf-esis.26.14&auth=true http://www.gruppofrattura.it g. fargione et alii, frattura ed integrità strutturale, 26 (2013) 143-155; doi: 10.3221/igf-esis.26.14 151 the fig. 11 and 13 allow to point out the surface with a perfect thermoelastic behaviour and where the proportionality between the stress(strain) and temperatures count. after putting on strain the testing machine with the clearance recovery, in fact, it has been noticed in both figures a decreasing linear segment for which it is validthe thermoelasticity law with the costant temperature decreases (a perfect segment) up to spot a slope change for the value ε = 0.010 in fig. 11 and ε = 0.015 in fig. 13. these values are far from 0.02 which conventionally correspond to the yield stress of the material. the tab. 5 and 6 resume the results obtained during the static tests in agreement with [15-19]. in the tables with the caption “material without damage” it has been identified the resistance values provided by the tie rods building firm. yield load breaking loand rp02 [mpa] rm [mpa] material without damage 835 1080 specimen 1 of an old tie rod 759 1063 specimen 2 of an old tie rod 815 105 table 5: results of static test. fatigue limit with alternated symmetric solicitation, 0 [mpa] material without damage 450 specimen 1 of an old tie rod 392 specimen 2 of an old tie rod 420 table 6: results using the [15-19] theory. the fatigue tests have been done using the remaining specimens. in particular the first two of them – one belonging to the tie rod 1 and the other belonging to the tie rod 2 – have been used to define an appropriate test protocol (tab.7) compatible with the values discovered during the static tests. the other 4 (specimen 3, specimen 4) of the tie rod a and of the tie rod b, have been used following the procedure of risitano's rapid method (rrm) to define the thermal maps [45]: it means the determination of the energy parameters (temperature vs cycles, with parameterized applied load) necessary for the following valuation of the fatigue limit and the contouring of the entire fatigue curve (wöhler curve). the tests have been done with almost pulsating load (loading ratio r= 0,1) coherently with the on-stream tie rods loading mode. fig. 14 shows each specimen load history. r (load ratio) [/] starting value (first step) [kn] p (gap between the following steps) [kn] test frequency [hz] cycles for loading steps [cycles] thermal images acquisition[hz] 0,1 36 2 10 10000 1/25 table 7: fatigue test protocol. http://dx.medra.org/10.3221/igf-esis.26.14&auth=true http://www.gruppofrattura.it g. fargione et alii, frattura ed integrità strutturale, 26 (2013) 143-155; doi: 10.3221/igf-esis.26.14 152 figure 14: load history imposed during fatigue test. after having synchronized both the loading application of the testing machine and the images acquisition, the acquisition rate of ir camera has been fixed to 25 s in order to obtain for each load step of 10000 cycles at 10 hz, 40 images to be analyzed. using this procedure it has been obtained during the analysis phase, the specimen temperature every 250 cycles of load application. the following analysis has been done reconstructing the temperature trend of the warmest area of the specimen surface at the different steps in order to have the temperature diagrams as a function of the cycles (curves parameterized according to the applied load). from the fig. 15 to the 18 one it has been reported the thermal maps following the warmest point of the specimen surface revealed during the test. as above mentioned, the temperature data allow to obtain the fatigue limit and the energy parameter φ. figure 15: thermal map of the specimen 3. figure 16: thermal map of the specimen 4. examining the thermal maps and proceeding as indicated in [4-5] it has been obtained the fatigue limit values, the value of the parameter φ and therefore the wöhler curve. it has to remind that the fatigue limit can be estimated directly from the thermal maps (temperature curves) because, being the stress value the same, there aren’t irreversible deformations yet and the temperature variation of the specimen surface is zero in all the points. so, for example, for the specimen 1 the fatigue limit is quite below the first applied load level (36 kn / 480 mpa) (fig. 15). the tab. 8 reports the data related with the two specimen categories. http://dx.medra.org/10.3221/igf-esis.26.14&auth=true http://www.gruppofrattura.it g. fargione et alii, frattura ed integrità strutturale, 26 (2013) 143-155; doi: 10.3221/igf-esis.26.14 153 figure 17: thermal map of the specimen 5. figure 18: thermal map of the specimen 6. fatigue limit 0 [mpa] [°c x cycles] specimen type 3 475 1.44e+05 specimen type 4 460 8.70e+04 specimen type 5 445 8.13e+04 specimen type 6 440 1.85e+05 table 8: results data of fatigue test. using different colours, in fig.19 it has been reported the wöhler curves of each specimen (3, 4, 5, 6). following as it is indicated in [4-5], the number of the breaking cycles nr for a specific load has been obtained as the ratio between the energy parameter φ and the stabilization temperature (the mean value of the detected ones). figure 19: wöhler curves of each specimen in according with rrm [4-5]. http://dx.medra.org/10.3221/igf-esis.26.14&auth=true http://www.gruppofrattura.it g. fargione et alii, frattura ed integrità strutturale, 26 (2013) 143-155; doi: 10.3221/igf-esis.26.14 154 discussion he analysis of the results of the numerical simulations have pointed out that the tie rods failure is not due to the exercise or to the assembling conditions but to the bad performance of the flange seal: when it has broken, in fact, it has allowed that two of the tie rods were hit by a steam jet of 450 °c and a pressure of 160 ata. it has caused a mechanical effect associated with a decay of the material resistance characteristics, quite shearing. the stress values, calculated during the simulation and which consider the steam jet effect , were above the 40% of the material yield limit at that temperature. these values suggested a breakage due to the overcoming of the material resistance characteristics. the quite suddenly breakage (without the plastic deformation) led one to suppose a further decay of the material characteristics due to the high temperature at which it has been subjected in a very limited area. the experimental tests have confirmed the hypothesis of breakage due to the mechanical action of the steam on the tie rod and to the thermal action on the material. the exam of the results of the static tests show a quite different behaviour for both of the specimen under the static traction. the tab. 5 shows a small difference of the breaking and yield loads for the two specimen and which is confirmed by the assessment of the symmetrical stress fatigue limit carried out by the temperature curve of fig. 11 and 13 (392 mpa for the specimen 1 and 420 mpa for the specimen 2) the results of the fatigue curve confirm the trend already noticed through the static analysis. both the values of the fatigue limit and the wohler curves are different for the specimen obtained by the broken bolt a (3 and 4) and the broken bolt b (5 and 6). being bolts made of the same material, the cause of their different behaviour is due to the different stress conditions history. considering the kind of work and the way they have been assembled with controlled draught parameters (use of the torque wrench), it can be justified just with a thermal stress different from the steam loss of the packing flange seal. considering also the characteristics of the same steam it has probably caused structural changes. it can be deduced both from the thermal maps of each specimen and from the resulting fatigue curves for the two specimens (from tie rod a and from tie rod b), in couples completely different. conclusions n the past the static and dynamic analysis examining the thermal release of the stressed material has been adopted to value the failure causes of the mechanical components. in this work it has been conducted a numerical and experimental study to point out the causes which had determined the failure of the tie rods of a measurement flange, for which, during the maintenance two of the eight tie rods sheared in the mean area where the tensions should be lower. the numerical simulation showed as the breakage cause the high steam coming from the irregular seal pressure-tight. the experimental tests have shown a little decay of the material characteristics. considering the limited number of the specimens at our disposal for each type of component (flange tie rods), the analysis has been done detecting the temperatures of the stressed specimens surface. the following analysis of the thermal images which have been collected using a sensor (thermograph at thermal infrared) allowed to point out the characteristics of static and dynamic resistance of the specimens obtained by the two broken bolts. the results of the static tests with the analysis of the superficial temperature and of the fatigue tests according to rrm (based on energy dissipation in heat) have pointed out a different behaviour of the bolts obtained from the two tie rods. this result helped to confirm that the only cause for the failure of the two bolts was the seal behaviour which has allowed that the two bolts were abnormally thermally stressed modifying the resistance characteristics of the bolts steel. the energy study has shown again the opportunity to assess possible damages of the mechanical components. this kind of study, allowing the fatigue characterization through a limited number of specimen, helps to pick out the damage causes necessary for the management and for the future changes and maintenance choices. references [1] geraci, a., la rosa, g., risitano., a, l’infrarosso termico nelle applicazioni meccaniche. ata ingegneria automotoristica, 38 (1985) 8-9. t i http://dx.medra.org/10.3221/igf-esis.26.14&auth=true http://www.gruppofrattura.it g. fargione et alii, frattura ed integrità strutturale, 26 (2013) 143-155; doi: 10.3221/igf-esis.26.14 155 [2] curti, g., la rosa, g., orlando, m., risitano, a., analisi tramite infrarosso termico della “temperatura limite” in prove di fatica, in: proceedings xiv convegno nazionale aias, (1986)211-220. [3] curti, g., geraci, a., risitano, a., un nuovo metodo per la determinazione rapida del limite di fatica. ata ingegneriaautomotoristica, 10 (1989) 634-636. [4] la rosa, g., risitano, a., thermographic methodology for rapid determination of the fatigue limit of materials and mechanical components. int. j. fatigue, 22 (2000) 65–73. [5] fargione, g., geraci, a., la rosa, g., risitano, a., rapid determination of the fatigue curve by the thermographic method. int. j. fatigue, 24 (2002) 11–19. [6] atzori, b., meneghetti, g., energy dissipation in low cycle fatigue of austempered ductile irons, in: proceedings 5th international conference on low cycle fatigue, (2003)147–152. [7] curà, f., curti, g., sesana, r., a new iteration method for the thermographic determination of fatigue limit in steels. int j fatigue, 27 (2005) 453–459. [8] plekhov, o.a., palin-luc, t., saintier, n., uvarov s.v., naimark o., fatigue crack initiation and growth in a 35crmo4 steel investigated by infrared thermography. fatigue fract. eng. mater. struct., 28 (2005) 169–178. [9] meneghetti, g., analysis of the fatigue strength of a stainless steel based on the energy dissipation. int. j. fatigue, 29 (2007)81–94. [10] plekhov o.a., saintier n., palin-luc t., uranov, s.v., naimark, o., theoretical analysis, infrared and structural investigations of energy dissipation in metals under cyclic loading. mater. sci. eng., 462 (2007)367–369. [11] amiri, m., khonsari, m.m., rapid determination of fatigue failure based on temperature evolution: fully reversed bending load. int j fatigue, 32 (2010) 382–389. [12] crupi, v., chiofalo, g., guglielmino, e., using infrared thermography in low-cycle fatigue studies of welded joints. welding journal, 89 (2010) 195-200. [13] crupi, v., chiofalo, g., guglielmino, e., infrared investigations for the analysis of low cycle fatigue processes in carbon steels. journal of mechanical engineering science, in: proceedings of the institution of mechanical engineers part c, 225 (2011) 833–842. [14] clienti, c., la rosa, g., risitano, a., d’andrea, r., proposta di utilizzo di metodologie termografiche per il controllo di qualità di componenti meccanici. frattura ed integrità strutturale, 12 (2010) 37-47. [15] risitano, a., risitano, g., l’importanza del “parametro energetico” temperatura per la caratterizzazione dinamica dei materiali. frattura ed integrità strutturale, 9 (2009) 123-124. [16] clienti, c., fargione, g., la rosa, g., risitano, a., risitano, g., a first approach to the analysis of fatigue parameters by thermal variations in static tests on plastics. engineering fracture mechanics, 77 (2010) 2158–2167. [17] risitano, a., clienti, c., risitano, g., determination of fatigue limit by mono-axial tensile specimens using thermal analysis. key engineering materials 452-453 (2011) 361-364. [18] risitano, g., clienti, c., experimental study to verify the fatigue limit found by thermal analysis of specimen surface in mono axial traction test. key engineering materials, 488-489 (2012) 795-798. [19] risitano, a., risitano, g., determining fatigue limits with thermal analysis of static traction tests. fatigue & fracture of engineering materials & structures, 36 (2013) 631–639. [20] risitano, a., risitano, g., analisi termica per la valutazione del comportamento a fatica di provini soggetti a successive serie di carichi. frattura ed integrità strutturale, 12 (2010) 88-99. [21] risitano, a., risitano, g., cumulate damage evaluation of steel using infrared thermography.theoretical and applied fracture mechanics, 54 (2010) 82-90. [22] risitano, a., risitano, g., corallo, d., cumulative damage by miner's rule and by energetic analysis. sdhm: structural durability & health monitoring, 8 (2012) 91-109. [23] risitano, a., risitano, g., cumulative damage evaluation in multiple cycle fatigue tests taking into account energy parameters. int. j. fatigue, 48 (2013) 214–222. [24] atzori, b., meneghetti, g., ricotta, m., fatigue behaviour of a stainless steel based on energy measurements. key engineering materials, 417-418 (2010) 333-336. [25] naderi, m., amiri, m., khonsari, m.m., on the thermodynamic entropy of fatigue fracture, in: proc r soc a, 466 (2010) 423–438. http://dx.medra.org/10.3221/igf-esis.26.14&auth=true http://www.gruppofrattura.it microsoft word numero_55_art_02_2880 ravikumar m et alii, frattura ed integrità strutturale, 55 (2021) 20-31; doi: 10.3221/igf-esis.55.02 20 focussed on structural integrity and safety: experimental and numerical perspectives experimental studies of different quenching media on mechanical and wear behavior of al7075/sic/al2o3 hybrid composites m. ravikumar department of mechanical engineering, r l jalappa institute of technology, bangalore (r), karnataka, india ravikumar.muk@gmail.com h. n. reddappa department of mechanical engineering, bangalore institute of technology, bangalore, karnataka, india reddyhn.phd@gmail.com r. suresh* department of mechanical and manufacturing engineering, m.s. ramaiah university of applied sciences, bangalore-560058, karnataka, india. sureshchiru09@gmail.com m. sreenivasa reddy department of mechanical engineering, r l jalappa institute of technology, bangalore (r), karnataka, india sreenivasam123@gmail.com abstract. the effects of sic (silicon carbide) al2o3 (aluminium oxide) particle in the al alloy on the mechanical and wear characteristics of stir-casted composites have been reported. the al7075 is reinforced with 2, 4, 6 and 8 wt. % of reinforcements (sic + al2o3) to manufacture the hybrid composite. ceramic particulates were added into al alloy to achieve the low wear rate and improved mechanical properties. hardening of cast specimens was done at 480ºc for the duration of 2 hrs and the specimens were quenched into two different quenching media (water and ice cubes). finally, age-hardening was carried out at the temperature of 160ºc for the duration of 4 hrs and cooled at room temperature. the tensile strength, hardness and wear behaviour of mmcs (metal matrix composites) were evaluated on the un-treated and heat treated composite. the tensile strength and hardness of mmcs increased by incorporating sic-al2o3 particulates. the wear behaviour of the mmcs containing sic-al2o3 particulates revealed high wear-resistance. the heattreatment had considerably improved the properties when compared to the non-heat treated composites. the composites with the highest tensile strength, hardness and enhanced wear resistance were found in the composites quenched in ice cubes. worn-out surfaces of the composite citation: ravikumar, m., reddappa, h.n., suresh, r., sreenivasareddy, m., experimental studies of different quenching media on mechanical and wear behavior of al7075/sic/al2o3 hybrid composites, 55 (2021) 20-31. received: 27.07.2020 accepted: 16.10.2020 published: 01.01.2021 copyright: © 2021 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. https://youtu.be/6thjgx2f1t4 m. ravikumar et alii, frattura ed integrità strutturale, 55 (2021) 20-31; doi: 10.3221/igf-esis.55.02 21 specimens were studied by using sem (scanning electron microscopy) and eds (electron dispersion spectroscopy) analyses. keywords. al 7075; mmcs; heat treatment; tensile; hardness; wear rate. introduction omposites, "materials in which two or more constituents are combined to create a material with properties different from that of either constituent," have been in existence for 1000 of years. al-based mmcs are a valuable addition in the area of newer materials for a high performance application. the composites have better properties than the matrix. the properties include abrasion resistance, improved thermal conductivity, tribology, dimensional stability, creep resistance and good stiffness [1]. interpretation of the materials is generally subjected to optimal choice of reinforcing materials. ceramic particulates can be reinforced into light metal alloys like aluminium (al), copper (cu), zinc (zn), magnesium (mg) and stainless steel for additional weight reduction. the hard ceramic particulates such as al2o3, sic, mgo, sio2 and b4c in the aluminium matrix alloy are frequently used as reinforcement materials to improve its mechanical properties [2]. the possible responses between the ceramic particulates and the al alloy at high temperatures are very essential. this phenomenon has a substantial effect on the stipulations of the interface and second phase. it is clear that, a better bonding at the interface among the reinforcements and the base matrix has a considerable impact on mechanical behaviour of the mmcs [3]. due to its significant strength-to-density, weight ratio, high modulus, wear resistance, strength values, and easy availability, ceramic particles can be used as reinforcement particles in composites [2]. ceramic compounds like sic, al2o3, etc., and carbon allotropes can be used to reinforce al, mg, cu and alloys [4]. among other parameters, wt. % of al2o3 and sic can influence mechanical properties of al mmcs. incorporating of al2o3 to al shows enhancement of mechanical and tribological properties in composites [5]. addition of al2o3, sic and b4c particulates reinforced in al will enhance the mechanical and tribological behaviour and ductility reduces. the wt. % of reinforcements (al2o3 & sic) and heat-treatment for enhancing the mechanical and tribological properties of composites were reported. as compared to monolithic alloy, addition of hard reinforcements such as al2o3, tic, b4c and sic to matrix alloy enhance the hardness and reduces the wear rate [6]. reinforcing al alloys with ceramic particulates such as sic or al2o3 causes a considerable improvement in mechanical properties over conventional al alloys, like improving strength and wear resistance. though, these reinforcements have considerably reduced ductility when compared to alloys [7]. al composite processing method entails using of al as the matrix with adding particles to form mmcs. it is revealed that, the conventional processing methods such as stir casting, powder metallurgy, spray deposition process, vacuum hot pressing and squeeze casting methods can be adopted for the fabrication of composites [1]. the liquid metallurgy method is a good inexpensive technique for fabrication of mmcs. by the various liquid metallurgy procedures stir casting method can be utilized for production of ceramic particulates reinforced hybrid composites [2]. the stir casting technique is chosen because it is simple and economical and also it can be easily monitored [1]. composites fabricated by stir casting method have certain advantages such as faster manufacturing rate and near net shapes can be achieved when compared to solid state methods [8]. subramanya reddy et al. [9] researched on al mmcs produced by the stir casting method with varying wt. % of silicon carbide and boron carbide. mechanical properties were studied and it was revealed that the hybrid mmcs had better properties as compared to pure al due to the existence of the carbide particles in the composite. rajesh and sudhir [10] researched on al-sic reinforced composites. the results concluded that the silicon carbide particles form barricades which hinder the dislocation motion. this supports to enhance the tensile strength and hardness of mmcs. manoj singla et al. [11] researched on the hardness of sic reinforced metal matric composites. various wt. % of sic (5%, 10%, 15%, 20%, 25% and 30%) were adopted to produce mmcs by stir casting method. the outcomes revealed that the hardness in the mmcs enhanced with increase in the wt. % of sic particles. sharma et al [12] studied the effect of sic reinforcement on wear behavior of za27 alloy mmcs. the results revealed that unreinforced alloy have higher wear rate when compared to composites and by increasing wt. % of reinforcements, the wear rate decreased. the increase in hardness and comparatively high percentage of elongation which leads to work hardening seems to be responsible for increase in uts (ultimate tensile strength) of al-al2o3 mmcs [13]. the fabrication of al composites with different weight percentages of al2o3 particles was processed by liquid metallurgy route. it revealed that the al-al2o3 composites have a higher tensile strength than aluminium alloy with reduced ductility. it was found that an increase in the al2o3 content in al alloy contributed to enhancing the hardness of the composites [14]. surappa and rohatgi [13] studied the mechanical properties of al alloy reinforced by al2o3. it was found that the increase in hardness of mmcs might be attributed to the comparatively high hardness of alumina compared with aluminium. yılmaz and buytoz [6] researched on the wear characteristics of al2o3 c ravikumar m et alii, frattura ed integrità strutturale, 55 (2021) 20-31; doi: 10.3221/igf-esis.55.02 22 reinforced aluminum mmcs. the results revealed that the wear rates decreased rapidly by increasing the wt. % of al2o3. abdel-azim et al. [15] in his research, applied vortex method process to produce al-al2o3 composites. it was revealed that the addition of alumina particles improved the wear resistance and also increased the cof (coefficient of friction). the improvement in the wear behaviour of al-al2o3 composites might be due to presence of al2o3 and high hardness [13]. palanisamy pugalenthi et al. [16] researched on al7075 sic al2o3 through stir casting. the result showed that the tensile strength and hardness of the composite increased by increasing the wt. % of reinforcements. the presence of hard particles decreased the wear rate and further the wear rate was reduced by reinforcing with sic-al2o3 [13]. marialaura et al. [17] studied the effect of heat treatment on mechanical properties of alsi3cr alloy. the results revealed that the heat treatment played an important role on intermetallic bonding between the ceramic particles and metal matrix. the mechanical behavior of alsi3cr alloy shows remarkable tensile strength in heat-treated conditions compared to untreated conditions. myriounis et al. [18] investigated the interface effects and heat treatment on the mechanical properties of aluminium matrix composites reinforced with sic-particle. the obtained results indicated the t6 heat-treated mmcs with 20 % wt. of sic particles show the highest strength when compared to the 31 % wt. sic particles composite. this is predictable since the mechanical strength of the mmcs in the t6 condition originates from the development of the mg2si precipitates. prabhu et al. [19] studied the effect of heat-treatment on mechanical strength and wear behaviour of al6061 composites reinforced with sicp. the tensile strength of mmcs composites increases with increasing in sicp. the heat treatment had a significant effect on ultimate tensile strength of composites. further, wear rate of mmcs decreases, by increasing in sicp in the matrix alloy under the tested condition. the heat treatment has a found significant effect on wear behaviour of composites. the detailed literature survey shows that the addition of two different ceramic particulates reinforced in al alloy can improve the mechanical properties and wear resistance of al hybrid mmcs. though, it has been observed that only few research works has been executed to study the influence of two ceramic particulates reinforcement in al mmcs. an effort has been made in the present investigation to produce al composites by adopting stir casting method under various wt. % of reinforcement to obtain better mechanical and wear properties. to improve the mechanical and wear properties of developed al composites reinforced with sic and al2o3 heat treatment process has been introduced. in the present study, the performance of the composites enhanced with different types of quenching processes like as-received, water quenched and ice quenched process were carried out on developed composites. selection of materials and experimental procedures l 7075 having a density 2.7 g/cm3, was used as a matrix material. al2o3 and sic were used as reinforcements. four different weight percentages of sic and al2o3 (2%, 4%, 6% and 8%) were chosen in the experiments. the average particle size was 100 µm al2o3 with ph value of 6.5-7.5. sic of 220 µm mesh size particulates were used in the present investigation. stir casting method was adopted to fabricate the mmcs. the reinforcement particles which were preheated were mixed with al alloy at the time of stirring. degassing process was adopted to remove the gasses present in molten melt. in the present investigation, the stirring was done at 100-125 rpm for the duration of 5 min, later the molten melt was poured in to pre-heated mold box. after solidification, the cast samples were removed from mold box and machined by cnc. the hybrid mmcs with al alloy matrix containing sic and al2o3 were characterized by heat treatment process and thus their material properties can be improved. the process of heat treatment was chosen based on the nature of the materials and its functions, being defined by temperature (ºc), duration and type of cooling medium [20]. quenching formed a significant part of the heat treatment method. the process included cooling the material after the heat treatment in different mediums and at different cooling speeds [21]. the composite specimens were subjected to solutionizing for a duration of 2hrs at a temperature of 480ºc and then quenched separately in two different quenching media such as water and ice cubes. finally, the age-hardening was carried out at a temperature of 160ºc for the duration of 4 hrs and then cooled at room temperature (27ºc). results and discussions tensile strength he specimens were prepared according to astm e8 standard and the tests were performed on the cast composites. tensile tests were performed by subjecting the test specimens to axial or longitudinal load at a particular extension rate of load till failure of the specimen occurred. tests were conducted on the universal testing machine (utm) whose maximum load capacity is 400 kn. fig. 1 shows the tensile strength of sic/al2o3 reinforced hybrid metal matrix a t m. ravikumar et alii, frattura ed integrità strutturale, 55 (2021) 20-31; doi: 10.3221/igf-esis.55.02 23 composites. the result shows clearly that the ultimate tensile strength of the mmcs increased by increase in volume percent sic and al2o3. this outcome is due to the existence of high amounts of ceramic particulates in mmcs [9]. the tensile strength of the mmcs increased due to the resistance of dislocations and therefore the composites strength increased with increase in wt. % of hard ceramic particulates. the nature of hard ceramic particulates is the cause of the enhancement in strength [16]. the ceramic particles correlate with dislocations which lead to improvement in the tensile strength. similar outcomes have been observed by different researchers [22-24]. it was observed that there was an improvement in the tensile strength of heat treated mmcs when compared to as received condition. it is revealed that due to heat treatment there is possibility of development of coherent precipitates. the lattice coherency among the base matrix and the precipitates occur up to a certain degree of temperature beyond which the lattice vibration forms the non-coherent precipitates with the base matrix. it is a known fact that throughout the ageing after the solutionizing treatment fine precipitates are formed on the soft al matrix which results in improving the composite properties [25]. from the results, it was revealed that the tensile strengths of the heat treated composites are higher compared to un-heat treated composites. the improvement in ductility of mmcs can be attributed to the coupling effect of a numerous small hard ceramic particles due to growth restriction and also thermal modification at the time of heat treatment [26]. as shown in fig. 1, maximum tensile strength was found for the composites when the quenched in ice. this marked enhancement in tensile strength of mmcs studied on heat-treatment can be attributed to high extent of development of intermetallic precipitates, generally, which act as the points of obstacles for the pinning down of dislocations. this phenomenon of multiplication of dislocations limits the mobility of dislocations, thus reducing the level of plastic deformation. this leads to major improvement in tensile strength of mmcs [27]. the tensile stress-strain curves of the composite samples fabricated by the stir casting method are shown in fig. 2. stress-strain diagram is plotted for as-received, water quenched and ice quenched samples and all the points are indicated. out of all these composite specimens, the tensile strength is higher for ice quenched specimen. in order to understand the mode of failure during tensile test, fractographic analysis was carried out on the composite specimens after fracture. the fractographic examination shows that increase in the wt. % of the sic & al2o3 changed the kind of failure from ductile to brittle, which could be evidently observed from the dimples and deformed region present within the area of the fracture [16]. with the increased sic-al2o3 content, it is observed that multiple micro cracks have occurred signifying decreased ductility. in general, the topology of the fractured surfaces appears with multiple cracks and voids. formation of voids is caused by the presence of hard ceramic particulates with soft matrix initiating triaxial state of stress in the vicinity of a particle. the void at the interfaces among the particles and matrix increased the crack propagation from their center. the existence of ceramic particles on the fracture surface as well as in micro voids also influenced the mechanical properties by improving the bonding of the matrix and decreased the ductility [28 & 29]. tensile fracture specimens in as-received condition were obtained and showed ductile fracture was seen with micro and macro dimples and also cup and cone fracture have been observed. the fracture surface of composites without heat treatment after tensile test specimen is shown in fig. 3. from the fig. 3, it is observed that the fracture is mainly dimple rupture. generally, this is the normally due to the overload failure and failure by merging of micro-voids process. the numerous cuplike despairs are also observed in fig. 3. formation and coalescence of micro-voids results in the dimples at localized strain regions (grain boundaries). fig. 4 shows the fractured surface of water quenched specimen after tensile test. number of dimples observed is more and in smaller sizes indicating the development of micro-voids. therefore, it is seen that dimples are equally distributed. figure 1: tensile strength for varying wt. % of sic and al2o3. ravikumar m et alii, frattura ed integrità strutturale, 55 (2021) 20-31; doi: 10.3221/igf-esis.55.02 24 figure 2: stress-strain curve for as-received, water quenched and ice quenched samples. figure 3: fracture images of un-heat treated composites. figure 4: fracture images of water quenched composites. m. ravikumar et alii, frattura ed integrità strutturale, 55 (2021) 20-31; doi: 10.3221/igf-esis.55.02 25 figure 5: fracture images of ice quenched composites with different compositions. the fractography of ice quenched composites obtained using sem are as shown in the fig. 5. an investigation of these fracture surface structures as seen in the sem at high magnification was done to study the fracture region, to detect areas of initiation of micro-crack, growth of early crack and the over-loaded area to identify the satisfactory scale fracture features [28]. the dimples size in the fractured surface of the water quenched specimen is smaller when compared to the fractured surface of the untreated composites. similarly, ice quenched specimens show smaller size dimples compared to water quenched specimens. generally, the dimple size shows direct proportional relationship with composite strength. figure 6: vickers hardness with varying content of sic and al2o3. hardness the hardness of composites were tested according to astm e92 standards by using vickers hardness testing equipment with an indenter of 10 mm diamond and the load of 1/2 kg for a period of 10 seconds. the test was conducted at room temperature (27ºc) and the hardness value was evaluated at three different places on the samples to obtain the average value of hardness. the effect of sic and al2o3 on the hardness based on different quenching media is shown in fig. 6. the hardness of the al 7075/sic/al2o3 composite increases by addition of sic and al2o3 content as observed from the fig. 6. generally, the hard ceramic particles avoid the motion of dislocations which leads to improvement in the results of hardness [30]. as the hard ceramic reinforcements are added, the hardness is increased, which exhibits more resistance to plastic deformation with in the composite rendering increase in hardness of the composites [31]. similar outcomes were observed by rajesh kumar bhushan [10] the results conclude that the silicon carbide particles form barricades which hinder the dislocation motion. this causes increase in the hardness of composites. this outcome is in similar agreement with the results ravikumar m et alii, frattura ed integrità strutturale, 55 (2021) 20-31; doi: 10.3221/igf-esis.55.02 26 of yogesh kumar singla et al. [32], resulting the support of the enormous volume of dislocations at the particulates-matrix interface throughout the solidification process due to the low-coefficient of thermal expansion of reinforcing particulates such as sic and al2o3 compared with al is one of the main reasons for increase in hardness values. the influences of quenching media on hardness have been presented in fig. 6. it is observed that heat treated samples exhibit higher hardness as compared to non-heat treated samples. the samples which were quenched in ice, show higher hardness compared to as-received and water quenched samples. the solutionizing treatment shows the formation of intermetallic phase which have been observed to be harder than al leading to higher hardness [20]. in t6 condition of heattreated composites, the thermal mismatching of base matrix and reinforcements thermally promotes the density improvements in dislocation and form towards the advanced resistance to the plastic deformation which leads to better hardness [33]. the ice quenched samples exhibit better hardness which is due to combined effect of improved bonding between the particulates and base matrix due to lower temperature and stabilization of intermetallic phase with in the matrix [20]. high cooling rates caused distortions that might affect the hardness values. this phenomenon affected the distortion which was produced by the dislocation slip and provided the positive effect on the hardness of composites [34]. wear behavior (weight loss) wear behaviour of al 7075-sic-al2o3 composites was conducted by using pin-on-disk wear testing equipment under the load of 3 kg at a sliding speed of 1.66 m/s against the en32 steel disk. composites specimens of 8 mm ϕ and length of 30 mm were prepared by machining process. the initial weight of the wear specimens was measured to a least count of 0.0001 gm. after the each test, the specimens were removed, cleaned by using acetone liquid, dried and weighed to measure the weight loss due to wear. fig. 7 indicates the influence of the weight percentage of sic + al2o3 particles on weight loss based on different quenching media. from the results it is seen that the wear rate of the composites decreases gradually by increasing the weight percentage of sic and al2o3 content. this is evidently due to the existence of the hard ceramic particulates and to their immunization effect which results in the fine grain structure [15]. from the outcomes this observation is made that the existence of hard particles decreases the wear rate and the wear rate of al-sic decreases with increase in of al2o3 particles. when the al2o3 particulates are intensely bonded with al matrix, it helps to protect the surface against destructive action of the counter face which reveals less wear. in case of al composites, the depth of dispersion due to harder asperities of high hardened steel disc is essentially governed by the protruded hard ceramic reinforcements. the major portion of the load applied is carried by sic reinforcement particles. the task of reinforcing particulates is to sustain the contact pressures, preventing from high plastic deformation and graze among the contact surfaces and thus reduce the quantity of wornout materials [13, 35]. the heat treatment of mmcs has a significant effect on the wear resistance of composites as depicted in fig. 7. for a constant load and the steel wheel used, ice as a quenching media has resulted in the high wear resistance of heat treated composites when compared to water quenched and as-received composites [27]. figure 7: wear loss with varying content of sic and al2o3. m. ravikumar et alii, frattura ed integrità strutturale, 55 (2021) 20-31; doi: 10.3221/igf-esis.55.02 27 the water quenched composites exhibit the better wear resistance and further ice quenching reduces the high wear rate as shown in the fig. 7. the heat treated composites show better hardness when compared to the un-heat treated composites. this may be due to the formation of high harder intermetallic phase and quenching with ice further improves the hardness in composites due to the stabilization of the intermetallic phase [20]. nature of wear resistance varies for both the quenching conditions. in the case of water quenching the wear rate has been decreased drastically for the hybrid composites. later, the wear rate has decreased more in composites which were quenched in ice cubes. all these show that the heat treatment has a high influence on the wear behaviour of the composites, which can be understood according to similar observations revealed earlier by various investigations [36]. here, the wear rate of the heat-treated mmcs is less as compared to un-heat treated composites due to the oxide film formed on the composite surface which prevents the metal to metal contact. in heat treated composites, the particles act and restrain severe wear rate [33]. figure 8: sem image of the ice quenched (al 2 % of al2o3 2 % sic) composites figure 9: sem image of the ice quenched (al 8 % of al2o3 8 % sic) composites to understand the wear mechanisms, the wornout surfaces of the composites specimens corresponding to the weight percentage were examined by sem analysis. the sem images of wornout surfaces of the composite specimens with varying wt. % hard particulates are shown in fig. 8 and 9. here, al2o3 particles are observed as whitish phases and the sic particles are observed as dark phases in the composites. the worn morphology of al + 2 % of al2o3 + 2 % sic was revealed scratches and grooves in the deformed areas. the contact between the composite specimen and steel disc was resulting the abrasive wear due to the scratches and parallel grooves on the wornout surfaces. the worn surface of al + 8 % of al2o3 + ravikumar m et alii, frattura ed integrità strutturale, 55 (2021) 20-31; doi: 10.3221/igf-esis.55.02 28 8 % sic was showed high wear resistance than other composites. due to the inter metallic phases the al + 2 % of al2o3 + 2 % sic composites revealed high wear rate. the existence of inter metallic phase have been reduced and ceramic particulates were uniformly distributed in al + 8 % of al2o3 + 8 % sic composite materials. due to the uniform dispersal of ceramic particulates and existence of low inter-metallic phases of al + 8 % of al2o3 + 8 % sic composite revealed better wear resistance [37]. this remarkable observation is evidence with the results of [38, 39] sic/al2o3 particulates are shown to have valuable effects on the wear properties of these mmcs. the sic/al2o3 particles are shown to fracture in the smaller pieces which create wear debris particulates. sic/al2o3 particles may avoid the penetration of the steel disk into the composites and there by protect the aluminum from deforming and finally increase its wear resistance. sic/al2o3 particulates may be crushed into powders which helps to improve the wear resistance, as observed in the results of wear rate. the ceramic particulates are initiated within the cavities and it is seen that few particulates have broken down and some of the particles are pulled away from the face. it indicates the rough wear mechanisms which are fundamentally an influence of hard particles exposed on the wornout region. the micrograph reveals that more number of continuous grooves are present on the wornout surfaces. these parallel grooves are the proof of micro ploughing and comparable wornout surfaces with increased severity were found. wide ploughing can be detected on the wornout surfaces which show prominent wear mechanism in the mmcs. however, in heat-treated mmcs, the wornout surfaces were comparatively smoother with fine grooves and also at the edge of grooves minor plastic deformation was detected in composite. grooves along the sliding direction and material delamination were detected on the wornout surface of the hybrid mmcs. by increasing the hard ceramic reinforcements the grooves were reduced and also some smooth wear tracks can be seen. small size grooves were found with oxide patches [33]. the chance of debonding of the particulates due to the continuous sliding causes the particulates to get loosened from the base matrix and get stuck between the surfaces of sliding whereby it might act as abrader leading to short period of wear. this reveals the enhanced wear rate [20]. to study the chemical composition of the sic/al2o3 reinforced al composites, energy dispersive spectroscopy (eds) studies were carried out by using scanning electron microscope (sem). in fig. 10, the eds analysis shows the main composition of sic/al2o3 reinforced al composites such as mg, si, carbon, fe and al and a small amount of oxygen is also detected. the signals of the oxygen may rise from the presence of the al2o3 particulates. these outcomes indicate that the chemical compositions of the sic/al2o3 reinforced al composites are consistent. the presence of carbon shows the addition of sic, al2o3 particulates with al7075 matrix [40]. figure 10: eds spectrum of wornout surface composite sample (al + 8 % sic + 8 % al2o3) in the chemical compositions of al 7075/sic/al2o3, oxygen (o) content has been found. the content of “o” is due to the presence of al2o3 as the main compound on the composite surface. the silicon peak in the eds analysis confirms the presence of sic in the composites [40-42] conclusions n the investigation, study on the mechanical properties and wear behaviour of al7075/sic/al2o3 were evaluated. the al7075 alloy reinforced by 2, 4, 6 and 8 wt. % of (sic + al2o3) composites was successfully produced using stir casting process. the outputs have been summarized as follows: i m. ravikumar et alii, frattura ed integrità strutturale, 55 (2021) 20-31; doi: 10.3221/igf-esis.55.02 29  the ultimate tensile strength of the mmcs increased by increasing in wt. % of sic and al2o3.  the fractographic studies reveal that the changes in the mode of failure occur from ductile to brittle due to increase in the wt. % of sic & al2o3 content.  the hardness of the hybrid mmcs increased with increasing in wt. % of sic and al2o3 content.  the maximum tensile strength and hardness of composite was found for the samples quenched in ice.  the wear rate (weight loss) of the mmcs gradually decreased with increasing in the weight percentage of sic and al2o3 content. higher wear resistance was found at ice quenched samples compared to water quenched samples.  from the wornout surface, sic/al2o3 particulates are shown to have valuable effects on the wear properties of composites.  eds clearly shows the existence of elemental composition and also revealed the presence of sic and al2o3 content in the composites. references [1] inegbenebor, a. o., bolu, c. a., babalola, p. o., inegbenebor, a. i. and fayomi, o. s. i. (2016). aluminum silicon carbide particulate metal matrix composite development via stir casting processing. silicon, 10, pp. 343-347. doi: 10.1007/s12633-016-9451-7. [2] cao, f., chen, c., wang, z., muthuramalingam, t. and anbuchezhiyan, g. (2019). effects of silicon carbide and tungsten carbide in aluminium metal matrix composites. silicon, doi: 10.1007/s12633-018-0051-6. [3] omid, y., hamid, r. b., ali, r. a. and ermia, a. (2018). development of the properties of al/sic nano-composite fabricated by stir cast method by means of coating sic particles with al. silicon, doi: 10.1007/s12633-018-9867-3. [4] riccardo, c. and maurizio, v. (2014). metal matrix composites reinforced by nano-particles a review. metals, 4, pp. 65-83. doi: 10.3390/met4010065 [5] himanshu, k., mer, k. k. s., sandeep, k. (2014). a review on mechanical and tribological behaviors of stir cast aluminum matrix composites. 3rd international conference on materials processing and characterization (icmpc 2014), hyderabad, india, 1951-1960 march. [6] yılmaz, o. and buytoz, s. (2001). abrasive wear of al2o3-reinforced aluminium-based mmcs. composites science and technology, 61, pp. 2381-2392. [7] belete, s. y., manas, m. m. and pradeep, k. j. (2013). influence of reinforcement type on microstructure, hardness, and tensile properties of an aluminum alloy metal matrix composite. journal of minerals and materials characterization and engineering, 1, pp. 124-130. [8] manu, s., sandeep, r., arshad, n. s. and sachin, m. (2018). investigation on the effects of silicon carbide and cooling medium during multi-pass fsp of al-mg/ sic surface composites. silicon, doi: 10.1007/s12633-018-0037-4. [9] subramanya, r. p., kesavan, r. and vijaya, r. b. (2017). investigation of mechanical properties of aluminium 6061silicon carbide, boron carbide metal matrix composite. silicon, doi: 10.1007/s12633-016-9479-8. [10] rajesh, k. b. and sudhir, k. (2011). influence of sic particles distribution and their weight percentage on 7075 al alloy. journal of materials engineering and performance, 20(2), pp. 317-323. doi: 10.1007/s11665-010-9681-6. [11] manoj, s., deepak, d., lakhvir, s. and vikas, c. (2009). development of aluminium based silicon carbide particulate metal matrix composite. journal of minerals & materials characterization & engineering, 8(6), pp. 455-467. [12] sharma, s. c., girish, b. m., rathnakar, k. and satish, b. m. (1997). effect of sic particle reinforcement on the unlubricated sliding wear behaviour of za-27 alloy composites. wear, 213, pp. 33-40. [13] surappa, m. k. and rohatgi, p. k. (1981). preparation and properties of cast aluminium-ceramic particle composites. journal of materials science, 16, pp. 983-993. [14] madeva, n., bharath, v. and auradi, v. (2013). effect of al2o3 particles on mechanical and wear properties of 6061al alloy metal matrix composites. journal of material sciences & engineering, 2(1), pp. 1-4. [15] abdel, a. a. n., shash, y., mostafa, s. f. and younan, a. (1995). casting of 2024-al alloy reinforced with al2o3 particles. journal of materials processing technology, 55, pp. 199-205. [16] palanisamy, p., murugesan, j. and venkatajalapathy, s. (2019). study of the microstructures and mechanical properties of aluminium hybrid composites with sic and al2o3. materials and technology, 53(1), pp. 49-55. [17] marialaura, t., annalisa p., lorenzo m. and marina. (2017). investigation of mechanical properties of alsi3cr alloy. frattura ed integrità strutturale, 42, pp. 337-351. ravikumar m et alii, frattura ed integrità strutturale, 55 (2021) 20-31; doi: 10.3221/igf-esis.55.02 30 [18] myriounis, d. p., hasan, s. t. and matikas, t. e. (2008). heat treatment and interface effects on the mechanical behavior of sic-particle reinforced aluminium matrix composites. journal of astm international, 5(7), pp. 1-13. [19] prabhu swamy, n. r., ramesh. c. s. and chandrashekar, t. (2010). effect of heat treatment on strength and abrasive wear behaviour of al6061-sicp composites. bull. mater. sci., 33(1), pp. 49-54. [20] reddappa, h. n., suresh, k. r., niranjan, h. b. and satyanarayana, k. g. (2011). effect of cold quenching on wear rate of al6061-beryl composites. international journal of engineering science and technology (ijest), 3(10), pp. 73097315. [21] senthilkumar, p. (2018). effect of quenching media on mechanical properties of 7075 aluminium alloy. international journal of science and research (ijsr), 8(8), pp. 2174-2177. [22] shaik, m. q., suryanarayana, m. b. and pinninti, r. r. (2016). processing and mechanical properties of al2o3 and red mud particle reinforced aa6061 hybrid composites. journal of minerals and materials characterization and engineering, 4, pp. 135-142. [23] jagbir, s., jawalkar, c. s. and belokar, r. m. (2019). analysis of mechanical properties of amc fabricated by vacuum stir casting process. silicon, doi: 10.1007/s12633-019-00338-8. [24] huda, a. a. s., adil, a. m. and hussain, j. a. (2019). mechanical and wear behavior of aa7075 aluminum matrix composites reinforced by al2o3 nanoparticles. nanocomposites, 5(3), pp. 67-73. [25] sanjay, s. and ajay, p. (2014). effect of heat treatment on mechanical behavior and structural response of al-si composite. international journal of advanced mechanical engineering, 4(7), pp. 767-782. [26] vembu, v. and ganesan, g. (2015). heat treatment optimization for tensile properties of 8011 al/15% sicp metal matrix composite using response surface methodology. defence technology, 11, pp. 390-395. [27] prabhu s. n. r., ramesh, c. s. and chandrashekar, t. (2010). effect of heat treatment on strength and abrasive wear behaviour of al6061-sicp composites. bull. mater. sci., 33(1), pp. 49-54. [28] suvarna, r. l. and kumar, a. (2014). influence of al2o3 particles on the microstructure and mechanical properties of copper surface composites fabricated by friction stir processing. defence technology, 10, pp. 375-383. [29] hossain, a. and kurny, a. s. w. (2013). effect of ageing temperature on the mechanical properties of al-6si-0.5mg cast alloys with cu additions treated by t6 heat treatment. universal journal of materials science, 1(1), pp. 1-5. [30] mehdi, r., nader, p. and naser, e. (2010). investigation of particle size and amount of alumina on microstructure and mechanical properties of al matrix composite made by powder metallurgy. materials science and engineering, a527, pp. 1031–1038. [31] dhanalakshmi, s., mohanasundararaju, n. and venkatakrishnan, p. g. (2014). preparation and mechanical characterization of stir cast hybrid al7075-al2o3-b4c metal matrix composites. applied mechanics and materials, 592(594), pp. 705-710. [32] yogesh, k. s., rahul, c., hitesh, b. and anil, k. (2015). wear behavior of aluminum alloy 6061-based composites reinforced with sic, al2o3, and red mud: a comparative study. the minerals, metals & materials society, 67(9), pp. 2160-2169. [33] rajesh a. m., kaleemulla, m. k. and doddamani, s. (2019). effect of heat treatment on wear behavior of hybrid aluminum metal matrix composites. tribology in industry, 41(3), pp. 344-354. doi: 10.24874/ti.2019.41.03.04. [34] hammar, i. a., eko, s., dody, a. and aditya, r. p. (2020). experimental study of quenching agents on al6061-al2o3 composite: effects of quenching treatment to microstructure and hardness characteristics. results in engineering, 6, pp. 1-8. doi: 10.1016/j.rineng.2020.100105. [35] padmavathi, k. r., ramakrishnan, r. and palanikumar, k. (2019). wear properties of sicp and tio2p reinforced aluminium metal matrix composites. indian journal of engineering & materials sciences, 26, pp. 51-58. [36] reddappa, h. n., suresh, k. r., niranjan, h. b. and satyanarayana, k. g. (2012). effect of quenching media and ageing time on al6061-beryl composites. applied mechanics and materials, 110(116), pp. 1374-1379. [37] jaya, p. v., chiranjeevi, r., santosh, k. r., venkata, r. and sunny, k. (2018). effect of sic on mechanical, microstructure and tribological properties of aluminum mmc processed by stir casting. iop conference series: materials science and engineering, 455, pp. 1-9. doi: 10.1088/1757-899x/455/1/012017. [38] altinkoka, n., ozsert, i. and findik, f. (2013). dry sliding wear behavior of al2o3/sic particle reinforced aluminium based mmcs fabricated by stir casting method. acta physica polonica a, 124, pp. 11-19. doi: 10.12693/aphyspola.124.11. [39] umanath, k., selvamani, s.t., palanikumar, k. and dinesh, r. g. (2014). worn surface analysis of hybrid metal matrix composite. advanced materials research, 984(985), pp. 546-550. m. ravikumar et alii, frattura ed integrità strutturale, 55 (2021) 20-31; doi: 10.3221/igf-esis.55.02 31 [40] rajesh, a. m., mohamed, k., saleemsab, d. and bharath, k. n. (2019). material characterization of sic and al2o3reinforced hybrid aluminum metal matrix composites on wear behavior. advanced composites letters, 28, pp. 1-10. doi: 10.1177/0963693519856356. [41] poovazhagan, l., kalaichelvan, k., rajadurai, a. and senthilvelan, v. (2013). characterization of hybrid silicon carbide and boron carbide nanoparticles-reinforced aluminum alloy composites. international conference on design and manufacturing, icondm 2013, 64, pp. 681-689. [42] ravikumar, m., reddappa, h. n. and suresh, r. (2018). study on mechanical and tribological characterization of al2o3/sicp reinforced aluminum metal matrix composite. silicon, 10(6), pp. 2535-2545. doi: 10.1007/s12633-018-9788-1. microsoft word numero_29_art_21 m. marino et alii, frattura ed integrità strutturale, 29 (2014) 241-250; doi: 10.3221/igf-esis.29.21 241 focussed on: computational mechanics and mechanics of materials in italy a finite-element approach for the analysis of pin-bearing failure of composite laminates michele marino università degli studi di roma "tor vergata", department of civil engineering and computer science engineering (dicii), 00133 rome, italy m.marino@ing.uniroma2.it francesca nerilli unicusano università degli studi niccolò cusano telematica roma, 00166 rome, italy fracncesca.nerilli@unicusano.it giuseppe vairo università degli studi di roma "tor vergata", department of civil engineering and computer science engineering (dicii), 00133 rome, italy vairo@ing.uniroma2.it abstract. in this paper, a numerical home-made finite element model for the failure analysis of bolted joints between fiber-reinforced composite laminates is presented. the model is based on an incremental displacementbased approach, it is hinged on the laminate theory and on a progressive material degradation governed by the failure of composite constituents. the model has been applied to a pin-plate system comprising a monodirectional fiber-reinforced laminated plate, and numerical results in terms of the bearing failure load have been successfully compared with available experimental data. aim of this paper is to evaluate the effectiveness of rotem’s and huang’s failure criteria in predicting the pin-bearing failure of bolted joints. the selected criteria act at different material scale: the former operating at the laminate level, while the latter at the constituent’s scale. proposed results seems to suggest that failure criteria accounting for micro-structural stress-strain localization mechanisms (for instance, huang’s criterion) give a more accurate estimate in terms of pin-bearing failure load. keywords. frp composite laminates; bolted joints; progressive damage; pin-bearing failure. introduction he increased use of fiber reinforced polymer (frp) composite materials in civil structural applications, and its corresponding advantages, such as, high specific strength and stiffness, and high corrosion resistance, requires the development of advanced design methods. despite the fact that this type of structural elements have many advantages and potentials, structural joints remain an unavoidable need. joints represent structural discontinuities t m. marino et alii, frattura ed integrità strutturale, 29 (2014) 241-250; doi: 10.3221/igf-esis.29.21 242 associated with stress localization: for many practical applications, structural joining (both adhesive and bolted) could represent a gap for the structural behavior because of their failure mode. failure modes of bolted joints in laminated composite plates under tensile loads usually occur in four basic modes: cleavage, net-tension, shear-out and bearing modes. in detail, local bearing failure modes are characterized by a local laminate compressive failure caused by the bolt diameter which tends to crush the composite material. pin-bearing failure mode of bolted frp joints, locally associated with matrix cracks, is an important design problem that has attracted the interest of the international scientific community, as confirmed by the great number of researches carried out in the last years [1–10]. results of these studies have highlighted that both geometric (e.g., bolt diameter, plate width and thickness, end distance) and material properties (e.g., fiber inclination angle, matrix type and fiber nature, stacking sequence) highly affect the strength and the failure mode of frp-based jointed elements. accordingly, a computational model able to give parametric indications on the mechanical performance of bolted frp joints, as well as able to predict their failure mechanisms, would be a powerful and useful design tool for both civil and mechanical advanced applications. aim of this paper is to develop a numerical model based on a non-linear finite-element formulation for the analysis of the progressive damaging and the failure modes in bolted joints between fiber-reinforced composite laminates. the numerical formulation, applied to a pin-plate system, is based on a plane-stress bidimensional model and on an incremental displacement-based approach driven by the pin position. neglecting friction, the unilateral contact at the pin-plate interface has been treated through a surface-to-surface penalty method. in order to describe the damage evolution, the model implements two failure criteria available in the literature (by rotem [13] and huang [15]), involving different stressstrain measures at different material scales. the obtained results have been successfully compared with the experimental data in [10], allowing to show soundness and accuracy of the proposed formulation, as well as to highlight the effectiveness and/or possible limitations of the considered failure criteria. theoretical background rp composite laminates are made of layers (plies) bonded together to form a plate-like structural element. each ply consists in unidirectional continuous fibers embedded in a polymeric matrix, with a preferred fiber direction. accordingly, each composite ply exhibits a global constitutive response characterized by a transversely isotropic symmetry, with the isotropic plane orthogonal to the fiber direction. in the following, as a notation rule, for each layer the subscript a denotes the direction parallel to the fibers, t the transverse-to-the-fibers direction, and symbols +/discriminate strength material properties in traction and compression, respectively. furthermore the generic constituent is indicated by the subscript c ( c f for fibers and c m for matrix). the fiber’s undamaged material is assumed to be linearly elastic, with symmetry plane orthogonal to the fiber’s axis (with engineering constants afe , t fe , at fg , at f , t f ), and the matrix’s undamaged material is isotropic linearly elastic (with engineering constants me and m ). frp layers and laminated plates are assumed to be planar and characterized by small thicknesses. accordingly, a plane-stress condition is assumed in the following. the ability to predict initiation and growth of damage in bolted frp joints can only be offered by progressive damage modeling techniques. failure analysis of laminate composites are made up of three main ingredients: stress analysis through homogenization theories, failure analysis by means of strength criteria for composite layers, and a material degradation law for describing the failure occurrence in composite constituents. stress analysis in order to determine the mechanical properties of the laminate a refined homogenization procedure, that takes into account localization mechanisms, has been used. accordingly, in agreement with the huang’s indications, the bridging model [14] is herein employed. addressing a single composite layer with mono-directional fiber direction, the 6x6 equivalent homogeneous compliance matrix   [ ]ijs s , expressed in a local coordinate system (a,t,t), results in:        1[ ] [ ]f mf m f ms v s v s a v i v a          (1) f m. marino et alii, frattura ed integrità strutturale, 29 (2014) 241-250; doi: 10.3221/igf-esis.29.21 243 where fv is the fiber volume fraction, 1m fv v  , [ ]i is the identity matrix, [ ] c c ijs s    the compliance matrix for the constituent c , and   [ ]ija a is the bridging matrix. in the case of a plane-stress state [ ]s , [ ] cs and [ ]a reduce to 3x3 matrices, with [ ]a defined component-wise by [14]: 11   m a f e a e  , 22  0.5 1   m t f e a e          , 33 0.5 1   m at f g a g          , 21 31 32 0a a a   (2)   12 12 11 22 12 11 11 f m f m s s a a a s s     , 2 11 1 2113 11 22 12 21 d d a          , 1 22 2 1223 11 22 12 21 d d a          , (3) where  1 13 11 33md s a a  ,      2 23 11 22 33 13 33 12m mf m f md s v v a a a s v v a a     (4) 11 12 12 m fs s   , 12 11 11 m fs s   ,   22 22 12 12m ff mv v a s s    (5)      21 12 12 12 11 22 22f m f mm f mv s s a v v a s s      (6) referring to composite laminated plates comprising mono-directional fiber-reinforced layers, stress analysis is conducted by employing the classical laminate theory [12], where the compliance matrix   k s of each k-th composite layer is obtained from eq. (1), and it is suitably expressed by passing from the local coordinate system (aligned with the fiber direction) to a global reference one. when necessary, a local stress measure for each layer’s constituent can be recovered starting from the homogenized stress field within the layer and by considering as localization matrices [ ]b and [ ][ ]a b for fiber and matrix, respectively, where the 3x3 matrix [ ]a is defined in eqs. (2-6), and the 3x3 matrix [ ]b is defined (in components) as:   11 22 33 /f m f mb v v a v v a    ,   12 12 33 /m f mb v a v v a    , 21 31 32 0b b b   (8)      13 12 23 22 13[ /m m f m mb v a v a v v a v a    ,   22 11 33 /f m f mb v v a v v a    (9)   23 23 11 /m f mb v a v v a    ,   33 22 11 /f m f mb v v a v v a   (10) where    11 22 33f m f m f mv v a v v a v v a     . in detail, referring to an incremental approach, and denoting with kd the increment of the homogenized stress vector within the k-th layer, the corresponding stress increments in fiber and matrix result in:  f kd b d  ,   m kd a b d  (11) failure analysis failure analysis has been based on local criteria. in detail, two approaches differently accounting for micro-mechanical features have been employed to predict degradation of the constituents’ material properties. the first criterion herein considered, provided by rotem [13], operates on the stress state k in the k-th laminate layer, whose increment results from   1k kd s d    , where   k s is computed by eq. (1) and where d is the homogenized strain increment in the laminate. this latter is obtained as the solution of the incremental problem and it is assumed to be constant along the laminate thickness. this criterion is based on the basic assumptions that: a) the failure onset is a localized phenomenon, b) only in-plane stresses are effective (that is, interlaminar stresses do not cause failure), c) the matrix material is weaker and softer than the fibers. in agreement with this approach, it is also assumed that microbuckling does not occur. on the basis of these assumptions the failure criterion actually combines two separate criteria, a failure criterion along the fibers direction and a failure criterion along the tansversal-to-fibers direction. the fibers, being m. marino et alii, frattura ed integrità strutturale, 29 (2014) 241-250; doi: 10.3221/igf-esis.29.21 244 stiffer and stronger than the matrix, can only fail due to loads acting in their axial direction. by omitting the subscript k discriminating different layers and addressing a single frp layer, transversal failure occurs when 2 2 / 1t at att ss                 , (12) where /ts   is the laminate strength (rispectively in tension and compression) in the transverse-to-the-fibers direction, while  ats is the shear laminate strength. on the other hand, the fiber failure criterion is expressed by the following relationships: a as  , a as   (13) where as  and as  are the laminate strengths (respectively in tension and compression) along the fibers direction. the second criterion, provided by huang [15], operates on the stress states in fibers ( )f and matrix ( )m , different in each layer and computed starting from the layer stress state k by employing eq. (11). accordingly, it prescribes tensile failure for the constituent c if ,eq c cs  , (14) where cs  is the tensile strength for the constituent c , and             1 2   1 , 1 2 2   0 0,  1              c c c c c eq c q q q c cc c when when q       (15) cq being a power index accounting for the effects of a biaxial stress state on the bearing capacity, and  1 c ,  2 c are the first (maximum) and the second (minimum) principal stresses in the constituent c . furthermore, a compressive failure of the constituent is assumed to occur if  2  c cs (16) where cs  is the compressive strength for the constituent c . material property degradation in this study, a simple degradation rule is employed by assuming that a damaged constituent reduces its elastic moduli by the factor 1  . when the rotem failure criterion is used, the overall laminate stiffness matrix is locally degraded, while, by using the huang failure criterion, the elastic moduli of fibers or matrix are locally degraded, depending on the damaged component. problem statement he effectiveness of the proposed progressive damage model is verified by addressing as a benchmark the experimental study by ascione et al. [10], carried out on a pin-plate system comprising a glass fiber reinforced polymer (gfrp) laminate with epoxy matrix. this experimental investigation aimed to analyze the influence of the fiber-to-load inclination angle, referred to as  , on the bearing failure load associated to the action of a steel pin (see fig. 1). in particular the experiments in [10] considered three types of laminates, different in the stacking sequences of the plies. herein reference is made to the laminate type denoted in [10] as laminate 1, consisting in a square-shaped plate (500 mm wide) and comprising eight equally-oriented plies of continuous strand mat gfrp material placed between two plies of chopped strand mat (csm), resulting in the plying sequence 4[ / 0 ]scsm . the plate was tighten by two steel plates 500 mm wide and 50 mm thick, with a central circular hole of 300 mm in diameter (see fig. 1). the higher stiffness of the t m. marino et alii, frattura ed integrità strutturale, 29 (2014) 241-250; doi: 10.3221/igf-esis.29.21 245 steel plates with respect to the gfrp laminate allows to regard the testing system as statically equivalent to the central circular region undergoing perfectly fixed conditions on its boundary. at the center of that circular region of the laminated plate a circular hole with diameter d = 20 mm was considered, wherein a steel pin with diameter d d was inserted and acted upon by a testing load parallel to the laminated plate. different values of d were considered in [10]. in the present study, reference has been made to experimental results relevant only to the case d d . the fiber volume fraction for the laminated plate was equal to about 60%, and the plate thickness was equal to 10 mm: 1 mm for each csm layer and 1 mm for each mono-directional layer. this type of laminate is identified in the literature as “mono-directional”, despite the presence of two csm layers, which can be treated as almost isotropic [11]. bearing failure load, defined as the peak in the pin load-displacement curve, has been obtained in [10] for [0 , 90 ]    , observing that it is highly sensitive with  . numerical model n order to simulate the failure mode and to evaluate the pin-bearing load of the laminated plate tested in [10], a 2d numerical model has been developed. a matlab home-made code has been employed for the numerical analysis, with the use of the libraries encoded in the commercial solver comsol multyphysics for the finite-element computations and for managing the non-linear contact problem. the plate external boundary undergoes fully restrained conditions (see fig. 2), in agreement with the experimental setting used in [10]. due to the small thickness-to-side ratio of the plate and since the symmetric plying sequence of the laminate, the plane stress assumption has been enforced. neglecting friction, the unilateral contact at the pin-plate interface has been treated through a surface-to-surface penalty method. figure 1: gfrp composite sample addressed in [10] (dimensions in mm). figure 2: mesh details, loading conditions and laminate plying pattern employed for numerical simulations (on the left, pin is not shown). i m. marino et alii, frattura ed integrità strutturale, 29 (2014) 241-250; doi: 10.3221/igf-esis.29.21 246 the finite-element mesh has been obtained by triangular elements, based on a pure displacement formulation with quadratic displacement shape functions. resulting from a numerical convergence analysis, computational mesh consisted in about 150.000 elements. in order to deal with convergence issues related to contact non-linearities, a mesh refinement around the pin-plate interface, characterized by an average mesh size of about 0.1d, has been employed. as reported in tab. 1, stiffness properties for fiber and matrix constituents are taken from [10]. in tab. 1, strength properties for composite constituents (needed for huang’s criterion and chose from [10]) are also reported. for the sake of simplicity, proposed results are based on the assumption of symmetric tensile/compressive strength of all constituents. moreover, the undamaged csm is treated as an isotropic linearly elastic material (with engineering constants csme and csm ) whose damage is predicted through the von mises criterion (with strengths / csms   ), [17]. finally, the pin is assumed to comprise an isotropic linearly elastic material (with constants pe and p ), and no damage is modeled for it. in tab. 2, the mechanical strength of the gfrp laminate (needed for the rotem’s criterion), experimentally determined in [9], are also provided. fibers: f fs s   2.5 gpa matrix: m ms s   26 mpa a tf fe e 50 gpa me 1.4 gpa m 0.4 a tf f  0.18 pin: pe 210 gpa p 0.3 csm: csm csms s   250 mpa others: q (huang) 5 csme 12.41 gpa  100 csm 0.4 n 20 table 1: undamaged material properties of the layer constituents, csm, pin and other model parameters [10,14,17,16]. laminate: as  222 mpa as  201 mpa ts  71 mpa ts  81 mpa ats 128.17 mpa table 2: mechanical strength of the gfrp laminate [9]. the numerical model is based on an incremental displacement approach driven by the pin position. the plate damage has been evaluated with an iterative numerical procedure, summarized in the flowchart depicted in fig. 3. in detail, after the geometric modeling, equivalent homogenized material properties are locally assigned for each element on the basis of the laminate theory [12] and by adopting the afore-mentioned homogenization technique. at each incremental step, fembased solution allows to compute the increment of the strain field d representing an average measure along the laminate thickness for the overall laminate. by involving the constitutive relationships, the incremental field d is used to compute the increment of the average stress field for the laminate, as well as (if necessary) the increment of the stress field in each layer and in its constituents. accordingly, addressing the actual stress field, obtained by superimposing stress increments, a given failure criterion is employed in order to verify possible damage occurrence. if failure conditions are not detected for undamaged constituents, the geometry of the pin-plate system is updated, fibers packaging is updated on the basis of the computed strain field increment, and the value of pin displacement is increased to perform the analysis of a new incremental step. otherwise, if damage locally occurs, material properties are locally altered by employing the degradation law previously introduced. in order to check if progressive material degradation occurs at that step, the actual incremental step is repeated with the same geometry and under the same boundary conditions until further material failure is no longer detected in the overall computational domain. if this iterative procedure is repeated for a number n of occurrences (see tab. 1), the global failure condition is assumed to be reached and the numerical integral of the m. marino et alii, frattura ed integrità strutturale, 29 (2014) 241-250; doi: 10.3221/igf-esis.29.21 247 distributed reaction force at the external boundary of the plate is considered as a measure of the corresponding failure load. figure 3: flowchart of the incremental numerical procedure implemented in this study. results otem and huang failure criteria are compared in fig. 4 with experimental data proposed in [10]. both criteria describe the qualitative trend experimentally tested, but while the huang’s criterion provides a more accurate quantitative prediction of the failure load, the rotem’s one widely under-estimates (resp., over-estimates) the value of the ultimate load for 90   (resp., 0   ). this result is mainly induced by the simplifying assumption adopted by rotem that fibers only are responsible for longitudinal failure, while matrix only for transverse and shear failure. when fiber direction and pin displacement direction are parallel ( 0   ) the highest components of the average stress field in the plate are along the fiber direction and are associated by the rotem’s criterion entirely to the strength /as   . accordingly, since the fibers’ high longitudinal strength, the failure condition occurs at higher loads than the experimental evidence. in fact, damage, which mostly interests matrix due to its weakness, starts only when fibers locally change their direction due to the pin movement. figure 4: comparison of predicted failure load with experimental data. 0 10 20 30 40 50 60 70 80 90 10 15 20 25 30 35 40 45 50 (°) b ea rin g fa ilu re lo ad (k n ) exp. data (ascione,feo,maceri,2009) rotem huang r m. marino et alii, frattura ed integrità strutturale, 29 (2014) 241-250; doi: 10.3221/igf-esis.29.21 248 0.428  0.571  0.714  0.857  1  0   0.445  0.556  0.667  0.778  0.889  1  45   0.428  0.571  0.714  0.857  1  90   figure 5: progressive damage in the composite laminated plate for 0   , 45 , 90 and for different values of / maxu u  , where u is current pin displacement and maxu is the pin displacement inducing the bearing failure. moreover, daa denotes the equivalent material stiffness of the laminate along the fiber direction. on the other hand, when the pin displacement occurs along the direction orthogonal to the fibers, the rotem’s criterion predicts a damage onset at lower loads than the experiments, since the highest stresses arise in the transverse-to-fiber direction and are entirely associated to the transverse laminate strength ( / ,t ats s   ). m. marino et alii, frattura ed integrità strutturale, 29 (2014) 241-250; doi: 10.3221/igf-esis.29.21 249 as already observed, the huang’s failure criteria gives more accurate results. as long as one of the constituents attains its ultimate stress state, the lamina is considered to fail and its contribution to the overall stiffness matrix of the laminate is reduced. when this micromechanical approach is considered for the evaluation of the failure load, the progressive failure process in the laminate can be more properly understood, and the corresponding failure mode can be straight identified. therefore, the evaluation of localized stress distributions occurring in the composite constituents seems to be extremely important for predicting the onset of damage mechanisms in the laminated plate. accordingly, a refined method accounting for localization mechanisms in matrix and fibers, as the one proposed by huang [14], should be preferred if the aim is the prediction and the analysis of the progressive damaging occurring in bolted frp joints. addressing the huang’s criterion, fig. 5 shows, for different values of  , the evolution of the failure mechanisms within the plate, from the damage onset up to the global failure. proposed results, obtained by a post-processing procedure that involves a slave partition with respect to the finite-element mesh, highlight that damage occurs, as expected, close to the contact zone. in this figure, the spatial distributions of the equivalent material stiffness for the laminate along the fiber direction (denoted as daa) are also provided at different damage levels, aiming to show the damage evolution in terms of material degradation (namely, in the figure blue color indicates the lowest value of the equivalent material stiffness and thereby the damaged region). it is worth pointing out that the proposed model allows to discriminate the constituent within each layer experiencing damage. in the analyzed cases, since the plane stress assumption and the mono-directional plying pattern, damage initiation occurs simultaneously in each frp layer, or in the csm layers, or in both. moreover, the numerical simulations predict a main occurrence of the bearing failure in matrix, in agreement with the experimental results discussed in [10]. finally, it is worth noting also that the procedure is able to predict the onset of different damage mechanisms, as experienced for 90   , where a tensile matrix failure is shown in the direction orthogonal to the pin displacement, suggesting the onset of a net-tension failure mechanism together with the bearing one. conclusions n this paper, a progressive damage model based on a finite-element incremental approach has been proposed, in order to simulate failure mechanisms occurring in bolted joints between fiber-reinforced composite elements. two available failure criteria (namely, by rotem and huang, and differently accounting for micro-structural material features) are employed, and unilateral frictionless contact conditions at the pin-plate interface are included. the model has been applied to study a pin-plate system. proposed numerical results predict a bearing failure mechanism fully in agreement with the experimental evidence discussed in [10]. results in terms of the failure load can be successfully compared with experimental data in a quantitative way only when localization mechanisms in matrix and fibers are suitably accounted for within the formulation of the failure criterion, such as in the huang’s criterion. nevertheless, some significant discrepancies among numerical results and experiments can be highlighted for small values of the angle between the fiber direction and the load one. in order to overcome such a drawback, and as a perspective application, future works will address the development of an ad hoc failure criterion. proposed approach opens towards the possibility of simulating progressive damage mechanisms occurring in bolted joints between fiber-reinforced composite structural elements, allowing to provide useful contributions towards the definition of guidelines for design and analysis of frp bolted joints. acknowledgement his work was partially supported by the italian civil protection department [reluis-dpc 2014-18, cup: e84g14000480007] and it was developed within the framework of the lagrange laboratory, a european research group comprising cnrs, cnr, the universities of rome “tor vergata”, calabria, cassino, pavia and salerno, ecole polytechnique, university of montpellier ii, enpc, lcpc and entpe. references [1] kelly, g., hallstro ̈m, s., pin-bearing strength of carbon fibre/epoxy laminates: effects of bolt-hole clearance, composites part b: engineering, 35 (2004) 331–343. i t m. marino et alii, frattura ed integrità strutturale, 29 (2014) 241-250; doi: 10.3221/igf-esis.29.21 250 [2] counts, w.a., johnson, w.s., bolt pin-bearing fatigue of polymer matrix composites at elevated temperature, international journal of fatigue, 24 (2002) 197–204. [3] xiao, y., ishikawa, t., bearing strength and failure behaviour of bolted composite joints (part i: experimental investigation), composites science and technology: engineering, 65 (2005) 1022–1031. [4] xiao, y., ishikawa, t., bearing strength and failure behaviour of bolted composite joints (part ii: modelling and simulation), composites science and technology: engineering, 65 (2005) 1032–1043. [5] vangrimde, b., boukhili, r., pin-bearing stiffness of glass fibre-reinforced polyester: influence of coupon geometry and laminate properties, composites structures, 58 (2002) 57–73. [6] vangrimde, b., boukhili, r., descriptive relationships between pin-bearing response and macroscopic damage in gfrp bolted joints, composites part b: engineering, 34(8) (2003) 593–605. [7] vangrimde, b., boukhili, r., analysis of the pin-bearing response test for polymer matrix composite laminates: pinbearing stiffness measurements and simulation, composite structures, 56 (2002) 359–374. [8] li, r., kelly, d., crosky, a., strength improvement by fibre steering around a pin loaded hole, composite structures, 57 (2002) 337–383. [9] ascione, f., feo, l., maceri, f., an experimental investigation on the pin-bearing failure load of glass fibre/epoxy laminates, composites part b: engineering, 40 (2009) 197–205. [10] ascione, f., feo, l., maceri, f., on the pin-bearing failure load of gfrp bolted laminates: an experimental analysis on the influence of bolt diameter, composites part b, 41 (2010) 482–490. [11] barbero, e.j., introduction to composite materials design, taylor & francis (1998). [12] kollar, l.p., springer, g.s., mechanics of composite structures, cambridge university press (2009). [13] rotem, a., prediction of laminate failure with the rotem failure criterion, composites science and technology, 58 (1998) 1083–1094. [14] huang, z.m., a bridging model prediction of the ultimate strength of composite laminates subjected to biaxial loads, composites science and technology, 64 (2004) 395–448. [15] huang, z.m., a unified micromechanical model for the mechanical properties of two constituent composite materials, part v: laminate strength, journal of thermoplastic composite materials, 13 (2000) 190–206. [16] grote, k.h., antonsson, e.k., springer handbook of mechanical engineering, springer-verlag (2009). [17] campbell, f.c., structural composite materials, asm international (2010). microsoft word numero_38_art_10 s. hörrmann et alii, frattura ed integrità strutturale, 38 (2016) 76-81; doi: 10.3221/igf-esis.38.10 76 focussed on multiaxial fatigue and fracture the effect of ply folds as manufacturing defect on the fatigue life of cfrp materials s. hörrmann, a. adumitroaie, m. schagerl christian doppler-lab for structural strength control of lightweight constructions, institute of structural lightweight design, johannes kepler university linz, altenberger straße 69, 4040 linz, austria susanne.hoerrmann@jku.at, http://orcid.org/0000-0001-7690-328x adi.adumitroaie@jkt.at, http://orcid.org/0000-0002-0812-5671 martin.schagerl@jku.at abstract. manufacturing defects are inherent to any manufacturing process. however, in composite materials they might be unavoidable, e.g. ply waviness or even folds of plies are present in complex shaped parts during high pressure resin transfer molding of carbon fiber reinforced polymers. in this work, the effect of the ply folds on the fatigue life of the composite material is investigated. folds along fiber direction (as they commonly appear during manufacturing) were artificially introduced in unidirectional non crimp fabric plies. the target of this study is the prediction of damage initiation due to this particular type of manufacturing defect. the folds locally increase the fiber volume fraction and also introduce resin rich areas. fatigue tests in fiber direction and transverse to fiber direction are performed at different load ratios under constant amplitude loading. the influence of the defect geometry on damage initiation and progression is investigated at different scales by non-destructive methods before testing, continuous strain measurement and monitoring the damage progression during testing and fractography analysis after final failure. most of the time, the first damage was observed at the location of the introduced fold for all considered load cases. however, it was also found, that the folds lead to no significant reduction in fatigue life. keywords. manufacturing defects; cfrp; fatigue damage, fold. citation: hörrmann, s., adumitroaie, a., schagerl, m., the effect of ply folds as manufacturing defect on the fatigue life of cfrp materials, frattura ed integrità strutturale, 38 (2016) 76-81. received: 25.05.2016 accepted: 20.06.2016 published: 01.10.2016 copyright: © 2016 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. introduction he high pressure resin transfer molding (hp-rtm) process shows great potential for efficient manufacturing of automotive composite structures in series production. unidirectional or woven fiber mats are preformed and positioned in the mold, resin is injected and cures in the closed mold in less than 10 min. however, manufacturing defects as in-plane or out-of-plane waviness as well as ply folding along or transverse to fiber direction cannot be avoided, t s. hörrmann et alii, frattura ed integrità strutturale, 38 (2016) 76-81; doi: 10.3221/igf-esis.38.10 77 when complex parts are manufactured by hp-rtm. these defects can cause a reduction in static strength or fatigue life. this influence has to be known in order to define if a composite part featuring manufacturing imperfections can be accepted or not. in previous research work the effect of out-of-plane ply waviness in the same material was studied and a reduction in compressive static and fatigue properties was found depending on a defect severity parameter [1]. in this work the influence of ply folding along fiber direction on the fatigue life of a unidirectional laminate is investigated. a ply folding along fiber direction causes a local increase in fiber volume fraction and by this a local increase in the stiffness in fiber direction. effects of local stiffness changes due to gaps and overlaps were already studied in cfrp laminates manufactured through automated fiber placement. a meshing tool for numerical investigation of the effect of defects and their interaction has been developed [2]. however the model has not been validated by test data. an experimental study on the same topic was performed in [3] by static testing of unidirectional and multidirectional material with introduced gaps and overlaps along fiber direction. the conclusion was that ultimate static strength is reduced less than 5% at the lamina level, while at the laminate level the reduction is up to 13 %. this is mainly due to ply waviness induced into the plies surrounding the defect ply. a study on the effect of thickness and fiber volume fraction variations on strain field inhomogeneity under transverse load was done in [4]. in this study it was found that a strain inhomogeneity of up to 10 % is possible for fiber volume fraction variations in a flat part. this is expected to be important for reliability and fatigue behavior. in this work, the effect of ply folding on the fatigue performance of unidirectional cfrp laminates is experimentally assessed. the fold is induced along fiber direction into the extreme top and bottom plies of the laminate, as this is the most common case encountered during manufacturing. the specimens are loaded axially under constant amplitude loading. progressive damage and failure due to the defect are investigated. the results are assessed using sn curves. additionally, the stress states leading to failure for selected load cases are numerically modelled. a defect metric is defined in order to assess the influence of the detailed defect geometry. experimental methods material and specimen configuration est specimens provided by the industry partner were water jet cut out of [0]6 carbon/epoxy plates with a constant thickness of t = 2.23 mm. the specimens feature artificially introduced manufacturing defects. the composite material is manufactured out of a unidirectional automotive non-crimp fabric (ncf) with an areal weight of one ply of ma = 300 g/m². the matrix constituent is epoxy and the manufacturing method is hp-rtm. for production reasons the unidirectional ncf is assembled using transverse glass fiber tows with a spacing of about 2 mm. the average fiber volume fraction of the material without defect is vf,n=6 = 0.45, which is calculated using the formula: f,n a fv =(n m ) / (ρ  t) (1) where n = 6 is the number of plies and ρf = 1.8 g/mm³ is the density of the carbon fibers. tensile and compressive specimens were cut out of the plates along and transverse to fiber direction and aluminum end tabs were bonded on each specimen. the specimen geometries are based on din en iso 527-4 for pure tensile and astm d 3410 for static compression loading; the same specimen configurations are also used for the fatigue load cases [5, 6]. the specimen configurations including the fold position (the black strips) are shown in fig. 1. figure 1: specimen configuration for different loading cases: (a) longitudinal tension; (b) longitudinal compression; (c) transverse tension; (d) transverse compression. t (a) (b) (c) (d) 0° 0° s. hörrmann et alii, frattura ed integrità strutturale, 38 (2016) 76-81; doi: 10.3221/igf-esis.38.10 78 defect configuration the microstructure of the introduced fold defect was investigated by computer tomography of some specimens and optical microscopy of each specimen. the edge of a typical specimen with fold is shown in fig. 2. the computer tomography scan gives the distribution of each ply through the thickness (fig. 2a). the glass fibers between plies used for ncf production give indication of the exact position of each ply, of the fold location and configuration, and of the perturbation induced by the presence of the fold into the neighboring plies, i.e. the modified thickness and the induced waviness of the plies. based on this observation a detailed sketch of the defect configuration is possible (fig. 2b), which is further used for understanding the correlation between the defect geometry and the material strength, and for building the finite element (fe) models of the specimens featuring defects. figure 2: defect configuration of folds; (a) computed tomography scan; (b) schematic sketch; (c) microscopy image of edge. because of the fold presence, there is a local increase in fiber volume fraction at the defect location. two additional plies are added over the laminate thickness within each fold. thus, the average local fiber volume fraction in the folded area can be calculated to vf,n=10 = 0.75. additionally to the local increase in fiber volume fraction, resin pockets in the turning points can be distinguished. the distance c between the two folds is measured using the optical microscopy images of the edges (fig. 2c) for each specimen, such that a possible influence of this parameter on the test results can be identified after the tests. since the folds are introduced along fiber direction in a unidirectional material no fiber waviness is introduced into the composite material, which is a comparable configuration to the laminate configuration in [3]. however, while in [3] the fold in plies located mid-thickness of the laminate, in the present study the folds are located into the surface plies, which is according to the most often encountered situation by our commercial partner, according to their manufacturing process. experimental setup static tension and compression tests, as well as constant amplitude fatigue tests with different load ratios (r = 0.01, r = -1, r = 100) at a frequency of 10 hz are performed. at least ten specimens are tested at each load ratio and defect orientation. the specimens are clamped with hydraulic wedge grips on the aluminum tabs. an in-house designed alignment device is used for all tests in order to guarantee an axial load introduction. strain gauges are applied at the defect location for local strain measurement and an extensometer is used for the tensile specimens, for global strain measurement. results and discussion he results of the different load cases are presented in this section. first the results of tests in fiber direction are given (i.e., the influence of the defect on fiber failure), and then results of tests in transverse to fibers direction are presented (i.e., the influence of the defect on inter fiber failure). t s. hörrmann et alii, frattura ed integrità strutturale, 38 (2016) 76-81; doi: 10.3221/igf-esis.38.10 79 fiber direction various damage mechanisms could be observed and monitored through the use of a camera (resolution = 5 mpx, frame rate = 0.2 fps) during the fatigue loading, and through fractography analysis (optical microscope with magnification factor of max. 63x) after testing: breakage of the longitudinal tows inside of the folds, longitudinal splitting along the folds turning lines (corresponding to the a1 and a2 turning points in fig. 2b), and delamination of the folds along the fold lamination longitudinal plane (corresponding to the fold junction line a1a2 in fig. 2b). all these separate damage mechanisms are initiated at the location of the fold; they are concurrent and coupled (influence each other); they are initiated at approximately the same moment (number of cycles) during the fatigue loading. each of them is a progressive damage mechanism, i.e. longitudinal splitting propagates along longitudinal and through-thickness direction, delamination propagates along longitudinal direction, and more individual tows will break during cyclic loading. to be noted that the same progressive damage mechanisms appear in the material without the fold defect; however, in this case, the damage initiation location can be anywhere along the width of the specimen, while in the case of defect material the onset takes place always at the fold location. by finite element analysis it was found that the increased stiffness within the fold does not lead to a stress concentration by itself. a multiaxial stress state is introduced within the fold by clamping effects and this leads to damage initiation of the folded region nearby the tabs. the longitudinal tows breakage will bring a corresponding stiffness drop, which can be recorded by the strain measurements. what is reported in the present manuscript is the initial stiffness drop, corresponding to the damage onset of the progressive damage events. there will of cause be load carrying capacity after damage onset (which is defined here as the initial longitudinal stiffness drop, found to be around 2 – 8 % of the initial stiffness of the material featuring the fold manufacturing defect before damage initiation. the recorded data for the final failure of the material (defined as the total loss of the load carrying capacity) needs further analysis and understanding, and it will be presented in further reports. in fig. 3, damage onset points of the material with defect are compared to the corresponding onset sn curves of the material without defect. the tension-tension (t-t) results are normalized on the ultimate tensile strength; the tensioncompression (t-c) and compression-compression (c-c) results are normalized on the ultimate compressive strength. the static ultimate strengths for specimens with folds are also included. for the c-c load case no data without defect is available at this moment, further testing is needed for this case. yet, the results of the material without defect under t-c loading (the gray lines in fig. 3c) can be used for preliminary comparison. (a) (b) (c) figure 3: fiber direction loading sn curves, normalized on the static strength. regarding the static results, it can be inferred from fig. 3a that the tensile strength is slightly increased by the presence of the fold, compared to the strength without defect; this is because the additional fibers act as reinforcement for this loading case. the compressive strength with defect is reduced to 80 % of the strength without defect, see fig. 3b,c; the cause of this has to be further investigated and understood. in fiber direction the fold is a local reinforcement, since locally more fibers are present; the reinforcing effect can be noted under tension loading, but not under compression. the distance c did not have a measurable influence on the static results; the same fracture load was measured for different c values. s. hörrmann et alii, frattura ed integrità strutturale, 38 (2016) 76-81; doi: 10.3221/igf-esis.38.10 80 for the fatigue results, the moment of damage initiation was found to be dependent on the distance c (fig. 2c). thus, three ranges of the distance c were defined in order to study its influence on the test results; for folds with a smaller distance c damage initiated earlier for all considered load cases and load ratios. however, for t-t as well as t-c at small c values, failure occurred within the scatter band of the tests without defect. for t-c with c > 3 mm the fatigue life is increased, compared to the material without defect. transverse to fibers direction in the transverse to fibers direction the damage mechanism is inter fiber fracture. in the unidirectional laminate the specimens fail within one load cycle due to fracture through the whole thickness of the laminate; no progressive damage takes place. two different damage mechanisms were observed for the transverse load cases. one is tension failure, corresponding to static tension and fatigue t-t and t-c (the transverse static tension strength is only 30 % of the static compression strength). the transverse tension failure is due to matrix cracking or interfacial debonding between matrix and fibers with a fracture plane perpendicular to the load direction. this fracture plane in most of the cases was located at the turning point of the fold in the resin rich area. figure 4: transverse fracture: (a) at the fold turning point, t-t loading (before and after test); (b) at resin rich area away from fold, t-t loading; (c) at both outer turning points, c-c loading (before and after test). fig. 4a shows the edge of a t-t specimen before and after fracture at the inner turning point of a fold. the two additional plies in the folded area are displayed darker and the crack is indicated by the dashed line. however, for two of the t-t specimens fracture was observed not at the fold area, but within the gauge section away from the fold, where at least three gaps between tows occurred aligned along the same vertical line, see fig. 4b. it follows that in transverse tension additional weak resin rich areas between additional tows at the fold have a higher influence on the static and fatigue strength than the local increase in fiber volume fraction. (a) (b) (c) figure 5: transverse to fiber direction sn curves, normalized on the static strength. s. hörrmann et alii, frattura ed integrità strutturale, 38 (2016) 76-81; doi: 10.3221/igf-esis.38.10 81 the results for the t-c fatigue loading are presented in fig. 5b. here, it can be noted that the specimens with lower c values still fall into the scatter band of the specimens without defect, but a reduced fatigue life is recorded for the specimens with a higher distance c. this is because of the fact that the t-c specimens have to be short (in order to avoid compression buckling) and for high c values the folds are located into the tabs effects area of the specimens. an interaction of stress concentrations at fold and tabs occurs, which reduces the fatigue life of specimens. the second damage mechanism is compression failure, corresponding to static compression and fatigue c-c. in transverse compression the fracture surface is inclined, forming a wedge. by optical microscopy it was observed that, for the material with defect, compression fracture always happened through the triangular resin pockets at the fold, as shown in fig. 4c. in a linear static fe analysis the influence of the fold was modelled by stiffness variation in resin and folded volume, which showed a local increase of the von mises stress in the plies near the resin pockets, and orientation of the higher stress areas corresponding to the fracture lines in experiments. an influence of the distance c could also be observed for c-c fatigue loading (fig. 5c): for smaller distance c the material withstands a reduced fatigue life. conclusions unidirectional carbon fiber reinforced polymer material featuring folds as manufacturing defect has been studied by means of experimental tests and simple numerical fe simulations. the influence on the fatigue life has been investigated under constant amplitude fatigue loading. in fiber direction a dependency on the distance c between the folds was found, where smaller distances lead to higher stress concentrations and lower fatigue life, while in transverse to fibers direction failure usually occurred in resin rich areas nearby the fold without an influence of c. all in all, the studied folds had a minor influence on the fatigue performance and are considered to be allowable in structural parts. however, for multidirectional laminates, waviness might be introduced by the folds in the off-axis plies, which lead to a strength and fatigue life reduction of about 50 % in compression, as was found in a previous study [1]. a combination of these two defects could have a higher influence on the fatigue life, and should be investigated in future work. acknowledgements he financial support by the austrian federal ministry of economy, family and youth and the national foundation for research, technology and development is gratefully acknowledged. the authors are grateful to mr. erich humer for his technical support during the experiments. references [1] hörrmann, s., adumitroaie, a., viechtbauer, c., schagerl m., the effect of fiber waviness on the fatigue life of cfrp materials, int. j. fatigue (submitted 2015). [2] li, x., hallett, s.r., wisnom, m.r. modelling the effect of gaps and overlaps in automated fibre placement (afp)manufactured laminates, sci. eng. compos. mater. 22(2) (2015) 115–129. http://dx.doi.org/10.1515/secm-20130322 [3] croft, k., lessard, l., pasini, d., hojjati, m., chen, j.h., yousefpour, a., experimental study of the effect of automated fiber placement induced defects on performance of composite laminates composites part a, 42 (2011) 484–491. http://dx.doi.org/10.1016/j.compositesa.2011.01.007 [4] jensen, e.m., leonhardt, d.a., fertig iii, r.s., effects of thickness and fiber volume fraction variations on strain field inhomogeneity, composites part a 69 (2015) 178-185. http://dx.doi.org/10.1016/j.compositesa.2014.11.019 [5] din en iso 527-4:1997-07, plastics determination of tensile properties part 4: test conditions for isotropic and anisotropic fibre-reinforced plastic composites, (iso 527-4:1997). [6] astm d3410 / d3410m-03, standard test method for compressive properties of polymer matrix composite materials with unsupported gage section by shear loading, astm international, west conshohocken, pa, 2008. http://dx.doi.org/10.1520/d3410_d3410m-03r08 a t << /ascii85encodepages false /allowtransparency false /autopositionepsfiles true /autorotatepages /none /binding /left /calgrayprofile (dot gain 20%) /calrgbprofile (srgb iec61966-2.1) /calcmykprofile (u.s. web coated \050swop\051 v2) /srgbprofile (srgb iec61966-2.1) /cannotembedfontpolicy /error /compatibilitylevel 1.4 /compressobjects /tags /compresspages true /convertimagestoindexed true /passthroughjpegimages true /createjobticket false /defaultrenderingintent /default /detectblends true /detectcurves 0.0000 /colorconversionstrategy /cmyk /dothumbnails false /embedallfonts true /embedopentype false /parseiccprofilesincomments true /embedjoboptions true /dscreportinglevel 0 /emitdscwarnings false /endpage -1 /imagememory 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/hrv (za stvaranje adobe pdf dokumenata najpogodnijih za visokokvalitetni ispis prije tiskanja koristite ove postavke. stvoreni pdf dokumenti mogu se otvoriti acrobat i adobe reader 5.0 i kasnijim verzijama.) /hun 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can be opened with acrobat and adobe reader 5.0 and later.) >> /namespace [ (adobe) (common) (1.0) ] /othernamespaces [ << /asreaderspreads false /cropimagestoframes true /errorcontrol /warnandcontinue /flattenerignorespreadoverrides false /includeguidesgrids false /includenonprinting false /includeslug false /namespace [ (adobe) (indesign) (4.0) ] /omitplacedbitmaps false /omitplacedeps false /omitplacedpdf false /simulateoverprint /legacy >> << /addbleedmarks false /addcolorbars false /addcropmarks false /addpageinfo false /addregmarks false /convertcolors /converttocmyk /destinationprofilename () /destinationprofileselector /documentcmyk /downsample16bitimages true /flattenerpreset << /presetselector /mediumresolution >> /formelements false /generatestructure false /includebookmarks false /includehyperlinks false /includeinteractive false /includelayers false /includeprofiles false /multimediahandling /useobjectsettings /namespace [ (adobe) (creativesuite) (2.0) ] /pdfxoutputintentprofileselector /documentcmyk /preserveediting true /untaggedcmykhandling /leaveuntagged /untaggedrgbhandling /usedocumentprofile /usedocumentbleed false >> ] >> setdistillerparams << /hwresolution [2400 2400] /pagesize [612.000 792.000] >> setpagedevice microsoft word numero_54_art_11_2851 i. chekalil et alii, frattura ed integrità strutturale, 54 (2020) 153-168; doi: 10.3221/igf-esis.54.11 153 prediction of mechanical behavior of friction stir welded joints of aa3003 aluminum alloy i. chekalil, a. miloudi university of djillali liabes, laboratory of materials and reactive systems (lmsr), sidi bel abbès, algeria chekalil1ismail@gmail.com, miloudidz@yahoo.fr m.p. planche university of technology belfort-montbeliard, carnot de bourgogne interdisciplinary laboratory (icb-lermps), belfort, france marie-pierre.planche@utbm.fr a. ghazi university of mascara, laboratory of materials and reactive systems (lmsr), mascara, algeria ghaziaek@yahoo.fr abstract. friction stir welding (fsw) is an extremely complex process because it depends on the intrinsic and extrinsic factors of the material under consideration. the purpose of the present work is to formulate a set of recommendations concerning the choice of the different factors that are likely to influence the quality of the fsw joint and to find a mathematical model that allows predicting the mechanical behavior of the junction using response surface methodology (rsm). an experimental design was therefore used to highlight the effect of the welding parameters on the behavior of the aluminum alloy 3003 fs-welded joint. three inputs, namely feed rate, tool tilt angle and rotational speed are considered as input parameters and yield stress (ys ), ultimate tensile strength (uts) and rupture strength (rs) are treated as the outputs. the most influential parameters were shown to be in the order of rotational speed, feed rate and tool tilt angle. the study of the interactions between these different parameters made it possible to establish a number of combinations of the different factors, for the purpose of achieving the quality optimization of the fsw joint by obtaining a tensile strength of the weld joint equal to 75% of that of the base metal. keywords. friction stir welding; mathematical model; aluminum alloy 3003; predicting. citation: chekalil, i., miloudi, a., planche, m.p., ghazi, a., prediction of mechanical behavior of friction stir welded joints of aa3003 aluminum alloy, frattura ed integrità strutturale, 54 (2020) 153-168. received: 02.06.2020 accepted: 23.08.2020 published: 01.10.2020 copyright: © 2020 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. https://youtu.be/ggigyc5_v7g i. chekalil et alii, frattura ed integrità strutturale, 54 (2020) 153-168; doi: 10.3221/igf-esis.54.11 154 introduction riction stir welding (fsw) is a complex process that is mainly attributed to thermal, mechanical, metallurgical phenomena, as well as to their combination during welding [1].this would make it very difficult to predict the quality of friction stir welding (fsw). it is interesting to note that the above phenomena depends on several parameters that can be classified into three categories, namely the process parameters, tool parameters and those related to the parts to be welded [2]. numerous studies have investigated the mechanical properties of friction stir-welded joints of aluminum alloys. some of these alloys are those:  suitable for heat treatment. these are alloys of types 2024 [3, 4], 7075 [5], 6061 [6, 7] and 6082 [8-10].  with structural hardening. these are alloys of types 5456 [11] and 5059 [12]. these studies were carried out in order to assess the tensile and fatigue strengths of some aluminum joints. as part of a study on the influence of the rotational speed, feed rate and tool tilt angle, on the mechanical properties of the aa 6061-t6 aluminum joint obtained through friction stir welding (fsw) [13], wasif safeen et al. succeeded in developing some mathematical models to determine these properties. the models developed allowed concluding that the rotational speed was more influential than the feed rate with regard to the tensile strength and ultimate impact resistance. however, the feed rate was shown to have higher effect than the rotational speed when it comes to achieving a good hardness level. they also showed that the optimization of the fsw process parameters makes it possible to obtain a tensile strength of 92% , an impact toughness of 87% and impact hardness of 95% in comparison with the properties of the base metal. as for chetan and al [14], they studied the evolution of the hardness profile for the different tool rotational speeds of 650 700, 800, 900, 1000 and transverse speed of 30, 35, 40 mm / min of aa7075t651 and aa6061t6 aluminum alloy. they found the parameters (800 rpm, 35 mm / min) and (900 rpm, 30 mm / min) give good quality of the weld. on the other hand, singh and kaushik [15] found, during the friction stir welding (fsw) process of aa6061 and aa6082 aluminum alloys, maximum values for the tensile strength ( 236 mpa ) and for micro-hardness ( 115 hv ), under the operating conditions of 1400 rpm for the tool rotational speed, 40   / mm min for feed rate, and 2  for tool tilt angle. however, the tensile strength would drop to a minimum value 165 mpa under the operating conditions of 800 rpm for the rotational speed, 60  /mm min for feed speed, and 2    for tool tilt angle. as for k. ramanjaneyulu et al. [16], they developed some mathematical models using a response surface methodology (rsm) to predict the yield stress (ys), the ultimate tensile strength (uts) and the percent elongation (% el) of friction stirwelded joints of the aa 2014-t6 alloy aluminum. their results suggested that the most influential parameters are in the order of importance the rotational speed, feed rate, tool tilt angle and its profile. these same results indicated that the joints obtained by a hexagonal tool exhibited maximum tensile strength and elongation. on the other hand, a. heidarzadeh et al. [17] used the design of experiments technique to predict the tensile properties of fsw joints in aa 6061-t4 aluminum alloy. in their study, three welding parameters were considered, namely the tool rotational speed, feed rate and axial force. the results obtained showed that the optimal parameters of 920 rpm for the tool rotational speed and 78   / mm min for the feed rate enabled them to obtain high strength values, of the order of 7.2 kn for the axial force. k. elangovan et al. [18] developed a mathematical model to predict tensile strength of the friction stir welded aa6061 aluminum alloy, four fsw parameters were studied: tool profile, rotational speed, welding speed and axial force. response surface method (rsm) has been used to develop the model. the authors concluded that the developed mathematical model can be effectively used to predict the tensile strength of fsw joints at 95% confidence level. recently, srujan manohar and k. mahadevan [19] have predicted mechanical and microstructural behaviors of friction stir welded thin gauge aluminum-copper sheets. weld-process parameters coded for tool-rotational speed, tool-travel speed and tool-plunge depth are examined for predicting better joint characteristics. the authors concluded that the maximum value of uts and ys [191 mpa and 184 mpa] are observed for [1800 rot/min and 80 mm/min]. due to the lack of investigations on the interaction between the tool tilt angle, rotational speed and feed rate of aa 3003 aluminum alloy, the aim of this work is to study the effect of these parameters on the mechanical properties of friction stirwelded joints under tensile loading. the design of experiments technique was applied for the modeling and prediction of the behavior of the friction stir-welded joint of aa 3003 aluminum alloy. response surface method (rsm) has been used to develop the model. in addition, determining the optimum parameters will lead to improved quality of fsw joints. f i. chekalil et alii, frattura ed integrità strutturale, 54 (2020) 153-168; doi: 10.3221/igf-esis.54.11 155 experimental method he friction stir welds were produced on a vertical milling machine using the friction stir welding tool presented in fig. 1. in order to choose the fsw welding tool, preliminary tests were carried out on the tool itself; the geometry adopted is similar to that of a conical pin (  5 d mm and  6.8 d mm , length  1.7 mm with a 19.5 mm diameter flat shoulder), made out of x210cr12 steel with a tensile strength ts = 870 mpa. figure 1: tool geometry two aa 3003 aluminum plates, of dimensions 210 mm x 110 mm and 2 mm thick, were joined along the rolling direction using the friction stir welding process. the initial joint configuration was obtained by securing the plates in position using mechanical clamps. single-pass welding procedure was followed to fabricate the joints (fig. 2-a). the cutting operation of samples on the welded plates is shown in the diagram presented in fig. 2-b, where the geometric dimensions are expressed in mm. figure 2: (a) fsw configuration; (b) cutting of samples on welded plates according to 8 8astm e m (dimensions in mm) the tensile tests were carried out on an instron tensile machine, controlled by the mts software, as shown in fig. 3. the chemical composition and mechanical properties of the base material before welding are reported in tabs. 1 and 2. the chemical composition was obtained by sem-edx (scanning electron microscopy energy dispersive x-ray analysis) method. t i. chekalil et alii, frattura ed integrità strutturale, 54 (2020) 153-168; doi: 10.3221/igf-esis.54.11 156 figure 3: dumbbell-shaped specimen tensile test measured by the extensometer micro hardness (hv) ys (mpa) uts (mpa) rs (mpa) el % ym (gpa) t fusion (°c) 51 110 160 127 5,6 60 650 table 1: mechanical properties of the material before welding element al mn si fe cu ti zn mg cr % 96,7 1,3 0,9 0,9 0,13 0,1 0,03 0 0 table 2: chemical composition of the material before welding fig. 4 displays a typical example of the profile obtained during the tensile test; the important factors of the stress-stain curve of friction stir welding (fsw) joint profile (output experimental results) are summarized in tab. 3. figure 4: typical stress-stain curve of friction stir welding (fsw) joint. i. chekalil et alii, frattura ed integrità strutturale, 54 (2020) 153-168; doi: 10.3221/igf-esis.54.11 157 factors outputs results 1 ys yield stress 2 yss yield stress strain 3 uts ultimate tensile strength 4 utss ultimate tensile strength strain 5 rs rupture strength 6 el elongation table 3: output experimental results the experimental design is used to identify a relationship between the input variables feed rate, tool tilt angle and rotational speed and the output variables (ys, yss, uts, utss, rs and el). in order to predict the mechanical behavior of friction stir welded joints of aa3003 aluminum alloy. the response surface methodology (rsm) is used to develop the non-linear model of the fsw joints of aluminum alloys (aa 3003). the optimization was carried out by a complete factorial plan with three factors, rotational speed n , feed rate s , and tool tilt angle t , at three levels ( 1 , 0 , 1 ). tab. 4 below gives the values of each parameter for each level. the values of these parameters are dictated by the capacity of the machine and the tool wear premature. parameters low level -1 center level 0 high level +1 rotation speed (rot/min) 1000 1500 2000 feed rate (mm/min) 200 300 400 tool tilt angle (°) 0,5 1,5 2,5 table 4: parameter values for each level developing a mathematical model he software modde 5.0 (modeling and design) [20] is used for the model elaboration and the statistical analysis of the experimental design. if there is curvature in the system, then a polynomial of higher degree must be used, such as the second-order model. the model used has the quadratic form given below: 3 3 2 0 1 1 3 1   i i ij j ii i i j i y a a x a x a x e            (1) where a0 is the predicted response value at the center of the experimental domain, ai represents the effect of the factor xi, and aij stands for the interaction between the factor xi and xj. the design of experiments approach was applied to 30 tests, two replicates are considered for each combination of the input variables, which made it possible to define the coefficients summarized in tab. 5. t i. chekalil et alii, frattura ed integrità strutturale, 54 (2020) 153-168; doi: 10.3221/igf-esis.54.11 158 exp n [rot/min] s [mm/min] t [°] ys [mpa] uts [mpa] rs [mpa] fracture location 1 1000 200 0,5 50,2 128,0 76,3 tmaz 2 1500 200 0,5 36,4 123,2 80,2 nugget 3 2000 200 0,5 26,6 123,8 78,7 tmaz 4 1000 300 0,5 40,4 103,7 63,0 tmaz 5 1500 300 0,5 33,8 102,8 78,4 tmaz 6 2000 300 0,5 24,3 97,8 74,6 tmaz 7 1000 400 0,5 58,7 125,9 75,2 tmaz 8 1500 400 0,5 33,8 109,8 87,6 tmaz 9 2000 400 0,5 21,4 98,4 72,0 tmaz 10 1000 200 1,5 36,2 100,3 75,1 tmaz 11 1500 200 1,5 41,9 118,4 90,7 tmaz 12 2000 200 1,5 43,1 121,1 85,0 tmaz 13 1000 300 1,5 34,7 94,7 77,7 nugget 14 1500 300 1,5 40,0 107,4 95,0 tmaz 15 2000 300 1,5 29,5 107,6 79,2 nugget 16 1000 400 1,5 39,4 109,1 88,7 tmaz 17 1500 400 1,5 43,3 115,6 89,1 tmaz 18 2000 400 1,5 38,1 127,8 86,9 tmaz 19 1000 200 2,5 20,5 92,5 65,3 tmaz 20 1500 200 2,5 22,9 100,1 79,7 tmaz 21 2000 200 2,5 43,9 120,1 78,0 nugget 22 1000 300 2,5 12,4 73,1 65,4 nugget 23 1500 300 2,5 32,5 106,8 85,4 tmaz 24 2000 300 2,5 29,2 110,6 72,7 nugget 25 1000 400 2,5 28,7 95,8 88,5 nugget 26 1500 400 2,5 31,7 113,6 95,2 tmaz 27 2000 400 2,5 39,7 120,0 73,0 nugget 28 1500 300 1,5 39,5 108,5 83,3 tmaz 29 1500 300 1,5 40,2 108,2 90,0 tmaz 30 1500 300 1,5 43,5 107,9 86,1 nugget table 5: results of the design of experiments i. chekalil et alii, frattura ed integrità strutturale, 54 (2020) 153-168; doi: 10.3221/igf-esis.54.11 159 the developed mathematical models make it possible to establish a relationship between the input parameters (n, s and t) and the output quantities (yss, ys, utss, uts, el and rs). the polynomials help optimize the welding parameters in order to reach the desired responses. to calculate the coefficients of the models, a regression method based on the least squares criterion is used. the mathematical models suggested by modde 5.0 are: 5 6 2 4 2 2 ys   80, 403 0, 006. 0,199. 17, 805. 5, 72.10 . . 0, 0214. . 0, 0101. . 7,84.10 . 4, 62.10 . 6, 944. n s t n s n t s t n s t               (2) 5 5 2 2 2 uts   217, 617 0, 033. 0, 744. 38, 764. 4,8.10 . . 0, 021. . 0, 048. . 1, 29.10 . 0, 0012. 3, 95. n s t n s n t s t n s t             (3) 5 5 2 4 2 2 rs    9,834 0,146. 0, 208. 16, 76. 7, 58.10 . .   0, 001. . 0, 028. . 3, 96.10 . 5, 08.10 . 7, 585. n s t n s n t s t n s t                (4) 6 6 4 10 7 7 10 2 9 2 5 2 yss   0, 0032 1, 55.10 .n 3, 81.10 .s 7, 013.10 .t 7, 76.10 .n.s 4, 436.10 .n.t 8, 42.10 .s.t 3, 02.10 .n 6, 33.10 .s 8, 73.10 .t                     (5) 5 4 4 7 5 5 8 2 7 2 2 utss   0, 09 8, 03.10 .n 3, 55.10 .s 5, 71.10 .t 1, 29.10 .n.s   1, 269.10 .n.t 6, 626.10 .s.t 4, 03.10 .n 3, 69.10 .s 0, 0022.t                    (6) 5 4 8 5 5 8 2 7 2 2 el   0,1197 6,181.10 . 4,113.10 . 0, 0058. 8, 485.10 . . 1, 463.10 . .   4, 66.10 . . 3,193.10 8. 5, 342.10 . 0, 0026. n s t n s n t s t n s t                    (7) analysis of results ig. 5 gives the true stress true strain curve which illustrates the elastoplastic behavior of aluminum 3003, the experiments are repeated two times, and the mean value is indicated on the graph. 0.00 0.01 0.02 0.03 0.04 0.05 0.06 0 20 40 60 80 100 120 140 160 180 s tr e s s [ m p a ] strain base metal figure 5: true stress true stain curve of 3003 aluminum alloy. f i. chekalil et alii, frattura ed integrità strutturale, 54 (2020) 153-168; doi: 10.3221/igf-esis.54.11 160 fig. 6 presents three combination among the tensile tests carried out, that shows the effect of tool rotational speed on the mechanical behavior of the joint. this figure shows that the tensile strength is maximum when the rotational speed is equal to 1500 tr/min, they reach a low value for a rotational speed equal to 1000 tr/min. this speed must be adjusted in to optimize it. 0.00 0.02 0.04 0.06 0.08 0.10 0 40 80 120 160 s tr e ss [ m p a ] strain 1000 rot/min_ 400 mm/min_ 2,5° 1500 rot/min_ 400 mm/min_ 2,5° 2000 rot/min_ 400 mm/min_ 2,5° figure 6: effect of tool rotational speed on the mechanical behavior of the joint. the values of the coefficients associated with the welding parameters in the mathematical model show the degree of influence of each factor. an example of prediction is given in fig. 7. it is worth mentioning that model (2) may be used to predict the evolution of the elastic limit as a function of the input parameters n, s and t. the central curves represent the predicted values, and the two other curves show the 95% confidence interval of the predicted response. figure 7: evolution of the elastic limit (mpa) as a function of the input data ( n , s and t ) analysis of fig. 7-a suggests that an increase in the rotational speed n involves a slight reduction in the elastic limit. in fact, a 100% increase in the rotational speed leads to a reduction of around 9% in the elastic limit. this elastic limit is maximal when the speed value is equal to 1500 rot/min. consequently, it can be concluded that increasing the rotational speed induces a slight decrease in the elastic limit ys. furthermore, fig. 7-b indicates that the increase in the feed rate leads first to a decrease in the elastic limit, then to its increase beyond 300   / mm min . based on the analysis of these curves, it can be assumed that there is a critical feed rate (    300   / scr mm min ) above which the trends reverse. in this context, mishra et al. [21] studied the effect of the feed rate on the mechanical characteristics of the friction stir-welded joints. they found out that an excessive increase in the feed rate induces internal macropore-type defects and tunnel-shaped defects. these defects can lead to a reduction in the mechanical properties of the welded joints. i. chekalil et alii, frattura ed integrità strutturale, 54 (2020) 153-168; doi: 10.3221/igf-esis.54.11 161 fig. 7-c depicts the variation of the elastic limit as a function of the tool tilt angle. it can be seen that when the tilt angle increases, the elastic limit increases slightly and then starts decreasing thereafter; the maximum value of the elastic limit is obtained for an angle of 1.5  . for the purpose of determining the effect of the rotational speed on the ultimate tensile strength fig. 8-a, it was decided to vary the rotational speed n. it is noted that the ultimate tensile strength increases with increasing rotational speed, which is in good agreement with the results obtained by a. takhakh et al.[22] the ultimate tensile strength is maximum for a rotational speed of  2000   / rot min ; it then begins to decrease until reaching a minimum value for the rotational speed of 1000   / rot min . regarding the impact of feed rate fig. 8-b, it can be noted that when the feed rate s increases, the ultimate tensile strength (uts) decreases at first, then starts increasing to reach a maximum value for the two speed values of 200   / mm min and 400   / mm min . in addition, it can be observed that the uts is maximum for extreme values of s, which is contrary to the results previously published by b. abnar et al. [23], which illustrated through a study the effects of heat input on microstructure and mechanical properties of the welded samples were investigated by changing the ratios of rotational speed (800-1200 r/min) to travel speed (40-100 mm/min), who have indicated that the uts values of the friction stir-welded joints of 3003 18h aluminum are insensitive to the welding parameters n and s. fig. 8-c illustrates the effect of the tilt angle on the ultimate tensile strength (uts). it is clearly noted that the uts is constant within the interval between 0.5  and 1.5  , which is in agreement with the results reported by y. birol et al. [24] in addition, it can be noted that the effect of feed rate (s) and tilt angle (t) on the ultimate tensile strength is similar to that observed on the elastic limit (ys). figure 8: evolution of the ultimate tensile strength (mpa) as a function of the process parameters. this last part focuses on the study of the effect of the welding parameters on the evolution of the rupture strength. fig. 9a shows that an increase in the rotational speed causes the rupture strength to go up from 77 mpa to a maximum value of 88 mpa , and then starts declining. it can therefore be said that there is a critical value of the rotational speed (    1500   / ncr rot min ) above which the rupture strength decreases. the response of the rupture strength predicted by software modde 5.0 is represented on the fig. 9-b in order to illustrate the impact of the feed rate. indeed, an increase in the feed rate s, within the interval between 200 and 300   / mm min , engenders a slight decrease in the rupture strength. beyond the value of 300 mm / min, the tensile strength starts going up to reach a maximum value of 96 mpa . similarly fig. 9-c shows the effect of the tilt angle on the rupture strength. it is clearly seen that, at first, the increase in t leads to an increase in the rupture strength from the value 80 mpa for the angle 0.5  to a maximum value of 87   mpa for 1.5  ; it then goes down to 81 mpa for a maximum angle of 2.5  . moreover, the results obtained show that there is a critical tilt angle    1.5 tcr   beyond which the tensile strength starts decreasing. in this analysis step, it was decided to broaden the scope of our study by taking into account the interaction between two factors. this allows viewing the output parameters on a three dimensional (3d) graph (fig. 10); this graph depicts the variation of ys as a function of the two factors n and s. i. chekalil et alii, frattura ed integrità strutturale, 54 (2020) 153-168; doi: 10.3221/igf-esis.54.11 162 figure 9: evolution of the rupture strength (mpa). figure 10: three-dimensional (3d) variation of ys as a function of n and s the curves in fig. 11, usually called ‘iso curves’, correspond to the projection of the surface on the plane. fig. 11-a shows that the more the rotational speed is reduced, the more the elastic limit rises until reaching a maximum value of 45 mpa . note that this is only valid for a value of n between 1000 and 1200   / rot min , because beyond this value, n has a negative effect on the elastic limit (ys). on the other hand, the low figures of ys were recorded for the maximum values of      2000   / n rot min , and s between 280 and 370   / mm min . it is also worth noting that the best elastic limit values of the weld joint were obtained for a ratio (  / n s ) between 2.5 and 3 . consequently, it may be concluded that to have a high elastic limit (ys), it is necessary to take    400   / s mm min and n between 1000   1200   / and rot min . in fig. 11-b, the quantity s is fixed on 300  /mm min , while t and n are varied. in this type of interactions, the elastic limit (ys) is large while the two factors t and n take minimum values. consequently, in order to increase the elastic limit (ys), it is necessary to decrease n and t. finally, fig. 11-c illustrates the variation of ys as a function of factors t and s. in this case, ys exhibits high values for two intervals; the first interval corresponds to a feed rate (s) equal to 200 mm / min and tilt angle t between 0.8  and 1.52  , i. chekalil et alii, frattura ed integrità strutturale, 54 (2020) 153-168; doi: 10.3221/igf-esis.54.11 163 and the second interval corresponds to    400   / s mm min and t between 1.1  and 1.48  . however, the low values of elastic limit (ys) are recorded for values of s between 220 and 340   / mm min , and t between 2.4  and 2.6 . all these findings turned out to be in good agreement with those obtained by wim van et al. [25] who indicated that the appearance of defects depends on the choice of the tilt angle. they found out that the best mechanical properties are obtained for the optimal tilt angle value of 2  , which makes it possible to obtain the best mechanical properties. in addition, it was found that the best values of the elastic limit (ys) of the welded joint are equal to 53% of those of the base metal. figure 11: variation of ys as a function of the three factors fig. 12-a presents the effect of the two factors n and s acting simultaneously on the ultimate tensile strength (uts), passing from their minimum values to their maximum values while the third factor (t) is kept constant. analysis of the graph in this figure suggests that the more n increases, the more the tensile strength also increases until reaching the maximum value of 121.2 mpa , while s is between 200 and 210   / mm min . in addition, it should also be noted that the uts can reach values closer to the maximum values for maximum s equal to 400   / mm min and for n between 1300 and 2000   / rot min . on the other hand, low uts values are recorded for low values of n around 1000   / rot min . it is also worth mentioning that the best ultimate tensile strength (uts) figures of the weld joint are found equal to 81% of those of the base metal. consequently, it can be concluded from this analysis that a maximum value of uts is obtained for a value of n between 1700 and 2000   / rot min , while keeping the value of s constant and equal to 200   / mm min . this new section aims to present the response surface obtained when the value of s is kept constant, while varying n and t. it can be seen that the ultimate tensile strength (uts) takes maximum values within two interaction intervals; the first interval corresponds to t less than 0.7  and n between 1000 and 1350   / rot min , and the second one is for t between 1.2  and 3  , while n is in the interval from 1700 to 2000   / rot min . it is noted that the best ultimate tensile strength (uts) values of the weld joint are equal to 80% of those of the base metal. on the other hand, fig. 12-c illustrates the variation of the ultimate tensile strength (uts) as a function of s and t. it is found that the simultaneous decrease in s and t leads to an increase in uts; however, the simultaneous increase of s and t leads to a decrease in the magnitude of uts. this effect is more pronounced when t is between 2.3 and 2.6  and s within the interval from 240 to 330   / mm min . figure 12: evolution of uts as a function of the three factors n, s and t i. chekalil et alii, frattura ed integrità strutturale, 54 (2020) 153-168; doi: 10.3221/igf-esis.54.11 164 furthermore, fig. 13 presents the predicted response (rs) as a function of the three factors (n, s and t). analysis of the curve in this figure shows that a maximum value for the rupture strength is obtained when the value of t is between 1.3 and 1.55  , and that of n is within the interval from 1300 to 1650   / rot min , and s is maintained at 400   / mm min . considering all these data, it therefore seems important to study the effect of these different factors on the mechanical properties of the welded joint. first, it is recommended to identify the factors that have the greatest influence and then determine the quantities that react with these factors. figure 13: evolution of uts as a function of the three factors n, s and t figs. 14, 15 and 16 show the most influential parameters on ys, uts and rs, respectively. fig. 14 shows that the factors that have the most influence on ys are in the following order: the tilt angle, then the rotational speed and finally the feed rate. note also that the interaction effect between n and s is the most important, but the interaction effect between s and t is small. we find that the following coefficients n, s and s * t are low compared to the others and will therefore be neglected later in eqn. 2 of the proposed model. this suggests that there are very few linear effects for the parameters n and s. also, we find that increasing the rotational speed and tool tilt angle decreases yield strength. analysis of fig. 15 indicates that the factors that have most effect on uts are in the following order: rotational speed, tilt angle and feed rate. also, it is found that the interactions between the factors are statistically significant, except that between rotational speed and tilt angle. the last interaction study between the dominant factors focuses on the predicted response rs. analysis of fig. 16 indicates that the factors that have most effect on response rs are in the following order of importance: feed rate, rotational speed and tilt angle. in addition, it turns out that the interaction between rotational speed and feed rate, and feed rate and tilt angle have a greater influence on rs, except for the one between n and t. therefore, we find that increasing the rotational speed, tool tilt angle and the feed rate increases rupture strength. it can also be seen that the following coefficients n, s and n * t are weak compared to the others and will therefore be neglected subsequently in eqn. 4 of the proposed model. figure 14: effects of factors on ys and their interaction i. chekalil et alii, frattura ed integrità strutturale, 54 (2020) 153-168; doi: 10.3221/igf-esis.54.11 165 figure 15: effects of factors on uts and their interaction. figure 16: effects of factors on rs and their interaction. the validation of the models is done by comparing the experimental results with those obtained by the proposed models. twenty-seven test cases are generated at random by assigning intermediate values to the process variables and for each combination, by changing the rotational speed (1000-2000 rot/min), travel speed (200-400 mm/min) and tool tilt angle (0.52.5°). fig. 17 shows this comparison, we see that the relative differences obtained are between 0.23 and 6.07 for ys, from 0.13 to 6.35 for uts and from 0.29 to 4.74 for rs. figs. 17-a, 17-b and 17-c show a good correlation between the experimental results and the proposed models. however, the results obtained by the predicted models are closer to reality. tab. 6 below presents the optimized parameter values that allow obtaining the best mechanical properties of a welded joint. these values are achieved through the maximization of ys, uts and rs; they correspond to the values of      1423.93   / n rot min ,    400   / s mm min and    1.2885 t   . the validation of these models is achieved by comparing the suggested optimized welding with those acquired by the predicted models fig. 18, for a rotation speed equal to 1425   / rot min , a feed rate equal to 400   / mm min and a tilt angle of 1.3  . note that the results calculated with the proposed model are in agreement with the experimental ones. this model therefore makes it possible to obtain a better prediction of the mechanical behavior of a welded joint. i. chekalil et alii, frattura ed integrità strutturale, 54 (2020) 153-168; doi: 10.3221/igf-esis.54.11 166 10 20 30 40 50 60 10 20 30 40 50 60 p re d ic te d y s [ m p a ] experimental ys [mpa] (a) 6.07   70 80 90 100 110 120 130 70 80 90 100 110 120 130 p re d ic te d u t s [ m p a ] experimental uts [mpa] 6.35   (b) 60 70 80 90 100 60 70 80 90 100 p re d ic te d r s [ m p a ] experimental rs [mpa] (c) 4.74   figure 17: predicted vs experimental: a) yield strength b) ultimate tensile strength c) rupture strength n [rot/min] s [mm/min] t [°] uts [mpa] ys [mpa] rs [mpa] 1087,13 399,997 0,7508 116,771 49,9487 83,489 1685,85 200,015 1,3552 122,24 41,8872 91,1325 1694,02 200 1,281 122,59 41,7067 91,047 1900 400 2,0999 122,156 39,5626 86.7125 1423,93 400 1,2885 121,186 55,3134 94,6581 1087,13 399,997 0,7508 116,771 49,9487 83,489 1799,9 200 1,4948 122,716 41,8335 89,989 1600 400 1,5 118,225 42,2038 94,8028 table 6: optimal values for the mechanical properties of the welded joint i. chekalil et alii, frattura ed integrità strutturale, 54 (2020) 153-168; doi: 10.3221/igf-esis.54.11 167 0.00 0.05 0.10 0 50 100 s tr e s s [m p a ] strain experimental profile predicted profile figure 18: predicted and experimental values of the stress-strain curve conclusions his work focuses on the friction stir welding (fsw) process of aluminum 3003. this study mainly concentrates on the influence of three parameters, namely rotational speed, feed rate and tool tilt angle. the main purpose of this investigation was to understand and explain the interactions between the three parameters mentioned above, and to highlight the influence of each one of them on the others. the mechanical properties, such as the yield stress, ultimate tensile stress, and rupture strength, of the joints were studied in this context. a mathematical model is proposed to predict the mechanical behavior of the junction using response surface methodology (rsm). this model is used to determine the optimal values of these parameters that are responsible for the better performance of the fsw joint. optimization of the welding process parameters suggests that:  the tensile properties of friction stir-welded joints remain relatively good. in addition, the findings indicate that rupture most often takes place near the thermo-mechanically affected zone (zatm). the most influential parameters are in the order of the rotational speed, feed rate and tool tilt angle.  the model developed by the design of experiments approach made it possible to obtain a better prediction of the mechanical behavior of a welded joint. this model provides an effective tool for selecting the optimal parameters of the friction stir welding (fsw) process.  the optimized parameter values that allow obtaining the best mechanical properties of a welded joint correspond to the values of      1423.93   / n rot min ,    400   / s mm min and  1.2885 t   .  the combinations of the different factors for a better quality of the fsw joint by obtaining a tensile strength of the weld joint equal to 75% of that of the base metal. in continuing the development of these projects. it is interesting to study the effect of these parameters on expected heat input, temperature and material flow. references [1] pashazadeh, h., teimournezhad, j., masoumi, a. (2017). experimental investigation on material flow and mechanical properties in friction stir welding of copper sheets, int. j. adv. manuf. technol., 88(5–8), pp. 1961–1970. https://doi.org/10.1007/s00170-016-8913-9. [2] palanivel, r., mathews, p.k., murugan, n., dinaharan, i. (2012). effect of tool rotational speed and pin profile on microstructure and tensile strength of dissimilar friction stir welded aa5083-h111 and aa6351-t6 aluminum alloys, mater. des., 40, pp. 7–16. http://dx.doi.org/10.1016/j.matdes.2012.03.027. t i. chekalil et alii, frattura ed integrità strutturale, 54 (2020) 153-168; doi: 10.3221/igf-esis.54.11 168 [3] zhang, z.h., li, w.y., li, j.l., chao, y.j. (2014). effective predictions of ultimate tensile strength, peak temperature and grain size of friction stir welded aa2024 alloy joints, int. j. adv. manuf. technol., 73(9–12), pp. 1213–1218. https://doi.org/10.1007/s00170-014-5926-.0 [4] buszta, s., myśliwiec, p., śliwa, r.e., ostrowski, r. (2019). the influence of geometrical parameters and tools material on the quality of the joint made by fsw method in aa2024 thin sheets, arch. metall. mater., 64. doi: 10.24425/amm.2019.127617 [5] rajakumar, s., balasubramanian, v. (2012). predicting grain size and tensile strength of friction stir welded joints of aa7075-t6 aluminium alloy, mater. manuf. process., 27(1), pp. 78–83. doi: 10.1080/10426914.2011.557123 [6] rajakumar, s., muralidharan, c., balasubramanian, v. (2010). establishing empirical relationships to predict grain size and tensile strength of friction stir welded aa 6061-t6 aluminium alloy joints, trans. nonferrous met. soc. china, 20(10), pp. 1863–1872. doi: 10.1016/s1003-6326(09)60387-3 [7] elatharasan, g., kumar, v.s.s. (2013). an experimental analysis and optimization of process parameter on friction stir welding of aa 6061-t6 aluminum alloy using rsm, procedia eng., 64, pp. 1227–1234. doi: 10.1016/j.proeng.2013.09.202 [8] verma, s., misra, j., gupta, m. (2019). study of temperature distribution and parametric optimization during fsw of aa6082 using statistical approaches, sae int. j. mater. manuf, 12(1), pp. 57–72. doi: 10.4271/05-12-01-0005 [9] krasnowski, k., sędek, p., łomozik, m., pietras, a. (2011). impact of selected fsw process parameters on mechanical properties of 6082-t6 aluminium alloy butt joints, arch. metall. mater., 56, pp. 965. [10] krasnowski, k. (2014). fatigue and static properties of friction stir welded aluminium alloy 6082 lap joints using triflute-type and smooth tool, arch. metall. mater., 59(1), pp. 157–62. doi: 10.2478/v10172-011-0106-9 [11] jannet, s., mathews, p.k., raja, r. (2015). optimization of process parameters of friction stir welded aa 5083-o aluminum alloy using response surface methodology, bull. polish acad. sci. tech. sci., pp. 851–855. doi: 10.1515/bpasts-2015-0097 [12] babu, n., karunakaran, n., balasubramanian, v. (2017). a study to estimate the tensile strength of friction stir welded aa 5059 aluminium alloy joints, int. j. adv. manuf. technol., 93(1–4), pp. 1–9. doi: 10.1007/s00170-015-7391-9 [13] safeen, w., hussain, s., wasim, a., jahanzaib, m., aziz, h., abdalla, h. (2016). predicting the tensile strength, impact toughness, and hardness of friction stir-welded aa6061-t6 using response surface methodology, int. j. adv. manuf. technol., 87(5–8), pp. 1765–1781. doi: 10.1007/s00170-016-8565-9 [14] patil, c., patil, h., patil, h. (2016). experimental investigation of hardness of fsw and tig joints of aluminium alloys of aa7075 and aa6061, frat. ed integrità strutt., 10(37), pp. 325–32. doi: 10.3221/igf-esis.37.43 [15] singh, h.n., kaushik, a., juneja, d. (2019). optimization of process parameters of friction stir welded joint of aa6061 and aa6082 by response surface methodology (rsm). doi10.36037/ijrei.2019.3610. [16] kadaganchi, r., gankidi, m.r., gokhale, h. (2015). optimization of process parameters of aluminum alloy aa 2014t6 friction stir welds by response surface methodology, def. technol., 11(3), pp. 209–219. doi: 10.1016/j.dt.2015.03.003 [17] heidarzadeh, a., khodaverdizadeh, h., mahmoudi, a., nazari, a e. (2012). tensile behavior of friction stir welded aa 6061-t4 aluminum alloy joints, mater. des., 37, pp. 166–173. doi: 10.1016/j.matdes.2011.12.022 [18] elangovan, k., balasubramanian, v., babu, s. (2009). predicting tensile strength of friction stir welded aa6061 aluminium alloy joints by a mathematical model, mater. des., 30, pp. 188–193. doi : 10.1016/j.matdes.2008.04.037 [19] srujan manohar, m.v.n., mahadevan, k., (2020). prediction on mechanical and microstructural behaviour of friction stir welded thin gauge aluminium-copper sheets, mater. today: proc. doi: 10.1016/j.matpr.2020.02.742. [20] modde 5.0, modelling and design, umetrics ab, umea, sweden. (1999). [21] mishra, r.s., ma, z.y. (2005). friction stir welding and processing, mater. sci. eng. r reports, 50(1–2), pp. 1–78. doi: 10.1016/j.mser.2005.07.001 [22] takhakh, a.m., abdullah, a.m. (2012). the optimization conditions of friction stir welding (fsw) for different rotational and weld speeds, al-nahrain j. eng. sci., 15(2), pp. 187–96. [23] abnar, b., kazeminezhad, m., kokabi, a.h. (2015). effects of heat input in friction stir welding on microstructure and mechanical properties of aa3003-h18 plates, trans. nonferrous met. soc. china, 25(2147), pp. 2155. doi: 10.1016/s1003-6326(15)63826-2 [24] birol, y., kasman, s. (2013). effect of welding parameters on the microstructure and strength of friction stir weld joints in twin roll cast en aw al-mn1cu plates, j. mater. eng. perform., 22(10), pp. 3024–3033. doi: 10.1007/s11665-013-0607-y [25] van haver, w., stassart, x., de meester, b., dhooge, a. 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/hrv (za stvaranje adobe pdf dokumenata najpogodnijih za visokokvalitetni ispis prije tiskanja koristite ove postavke. stvoreni pdf dokumenti mogu se otvoriti acrobat i adobe reader 5.0 i kasnijim verzijama.) /hun 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can be opened with acrobat and adobe reader 5.0 and later.) >> /namespace [ (adobe) (common) (1.0) ] /othernamespaces [ << /asreaderspreads false /cropimagestoframes true /errorcontrol /warnandcontinue /flattenerignorespreadoverrides false /includeguidesgrids false /includenonprinting false /includeslug false /namespace [ (adobe) (indesign) (4.0) ] /omitplacedbitmaps false /omitplacedeps false /omitplacedpdf false /simulateoverprint /legacy >> << /addbleedmarks false /addcolorbars false /addcropmarks false /addpageinfo false /addregmarks false /convertcolors /converttocmyk /destinationprofilename () /destinationprofileselector /documentcmyk /downsample16bitimages true /flattenerpreset << /presetselector /mediumresolution >> /formelements false /generatestructure false /includebookmarks false /includehyperlinks false /includeinteractive false /includelayers false /includeprofiles false /multimediahandling /useobjectsettings /namespace [ (adobe) (creativesuite) (2.0) ] /pdfxoutputintentprofileselector /documentcmyk /preserveediting true /untaggedcmykhandling /leaveuntagged /untaggedrgbhandling /usedocumentprofile /usedocumentbleed false >> ] >> setdistillerparams << /hwresolution [2400 2400] /pagesize [612.000 792.000] >> setpagedevice microsoft word numero_29_art_10 m. marino, frattura ed integrità strutturale, 29 (2014) 96-110; doi: 10.3221/igf-esis.29.10 96 focussed on: computational mechanics and mechanics of materials in italy an ideal model for stress-induced martensitic transformations in shape-memory alloys michele marino department of civil engineering and computer science engineering (dicii), università degli studi di roma tor vergata, via del politecnico 1, 00133 roma – italy m.marino@ing.uniroma2.it abstract. in this paper, a novel model for stress-induced martensitic transformations in shape-memory alloys is proposed. accordingly, the constitutive pseudo-elastic behavior of these materials is described. the model accounts for the possible co-existence of austenitic/martensitic phases and for asymmetric response in tension and compression (both for transformation and stiffness properties). the model is developed under the assumption of ideal behavior during martensitic transformation, and the predicted response is governed by few parameters, standard in the context of shape-memory alloys' constitutive models, that can be straightforwardly identified from experimental data. moreover, proposed modeling framework opens to the investigation on the effects of non-linear transformation lines in phase diagrams and of temperature-dependent transformation strains. keywords. shape-memory alloys; pseudo-elastic behaviour; constitutive modelling; stress-induced martensitic transformation. introduction hape-memory alloys (smas) are special materials endowed of fascinating properties thanks to possible rearrangements of their thermoelastic lattice microstructure, generally referred to as phase transformations. in fact, objects made of those materials, when significantly deformed, regain their original geometric configuration during heating (one-way shape-memory effect) or, at higher temperature, in the unloading phase (pseudo-elasticity). the intriguing sma thermomechanical properties allow to design smart structures, opening to innovative applications in many engineering fields. proposed designs based on such materials range from aeronautic/mechanical applications (e.g., adaptive smart wings and actuators) and telecommunication devices (e.g., deployment and control mechanisms of satellites and antennas), to biomedical (e.g., self-expanding stents, orthodontic wires, and prostheses) and civil applications (e.g., devices for passive, active and semi-active controls of civil structures) [1, 2]. as proved by the recent wide literature in the field [1, 3-5], there is a great need of constitutive models able to reproduce smas behavior, including a refined description of phase transformation mechanisms. in order to be effectively employed in practical applications, models should be characterized by parameters whose values have to be easily identified from well-established experimental procedures. moreover, since there exists a number of different materials with shapememory and pseudoelastic properties, models should be as flexible as possible in order to be adapted to the wide range of very different thermomechanical features shown through experiments. finally, models should be formulated within a consistent theoretical framework that, in the respect of thermodynamics laws, might be implemented in feasible numerical algorithms for computational analyses. s m. marino, frattura ed integrità strutturale, 29 (2014) 96-110; doi: 10.3221/igf-esis.29.10 97 in this paper, a novel constitutive model for smas is proposed for describing their pseudo-elasticity properties. accordingly, stress-induced transformations (sits) are modeled by addressing isothermal uniaxial tests and by considering direct transformations from a non-oriented lattice arrangement (namely, multi-variant martensite mm or austenite a) to an oriented one (that is, single-variant martensite in its traction and compression variants, ms+ and ms-), and viceversa reverse transformations ms+/ms mm/a,[1]. as a notation rule, quantities referred to ms+ are indicated by the superscript  , and to msby the superscript  , while to direct and reverse transformations by subscripts d (or d ) and r (or r ). denoting with mft and aft the zero-stress martensite-finish and austenite-finish characteristic temperatures (namely, mm is stable at < mft t and a is stable at > aft t ), the typical sma non-linear behavior at high temperature, > aft t , and at low-temperature, < mft t , is addressed. moreover, an intermediate-temperature range, < <mf aft t t , is also considered by admitting the co-existence of mm and a at low stress. present model opens to consider the well-established temperature dependence of transformation strains //d r   (namely, the strain accumulated during sits), [6]. moreover, it is based on a very general phase diagrams with highly non-linear direct/reverse transformation lines // ( )d r t   and without the need of fixing a specific form for the interpolation functions describing the stress-temperature dependence (see fig. 1). in the lack of detailed experimental data, the only assumption on the phase diagram is that there exists a unique temperature value rot , such that < <mf ro aft t t , at which reverse transformations (both from ms+ and ms-) occur at zero stress (that is, the temperature corresponding to = = 0r r    ). the motivations underlying this work, as well as the novelty of the proposed approach with respect to existing modeling approaches, are elucidated in the following. figure 1: left: typical phase diagram in  t plane for smas. the figure shows the direct sit lines to ms+ ( d  ) and to ms( d  ), as well as the reverse ones from ms+ ( r  ) and from ms( r  ). moreover, two loading-unloading paths for uniaxial isothermal traction tests are shown at 1= < mft t t and 2= > aft t t . top right: sma typical   constitutive relationship at 1=t t and 2=t t . bottom right: sma typical relationships between direct ( d  ) and reverse ( r  ) transformation strains and t . state-of-the-art and proposed improvements existing constitutive relationships for smas can be categorized as either micro, micro-macro or macro models [7]. in this paper, phenomenological macro-models are addressed because these are the most effective for engineering applications, being able to describe sma global structural behavior without an explicit modeling of micro-scale behavior. parameters of m. marino, frattura ed integrità strutturale, 29 (2014) 96-110; doi: 10.3221/igf-esis.29.10 98 phenomenological models are usually identified by classical experimental tests and the governing equations are mostly suitable for being implemented into computer programs for structural analyses. a thorough review of the available phenomenological models in specialized literature can be found in [1]. the sequence of thermodynamic states occurring in smas is usually described by introducing additional variables (such as martensite and austenite volume fractions), within the framework of thermodynamics with internal state variables [8]. current sma constitutive models have reached a high level of sophistication accounting for multiple and simultaneous thermomechanical mechanisms [3-5, 9-13]. nevertheless, a common limitation is that most existing models generally assume that phase diagrams governing phase transformations are characterized by piecewise-linear transformation lines, despite of high non-linearities highlighted from experiments [6]. a model overcoming this drawback has been recently addressed by lagoudas and co-workers [14]. moreover, different direct and reverse transformation strains (associated with different transformation kinetics), as well as their dependence on temperature, are generally neglected. furthermore, the implementation of the most effective models is heavy due to:  the costly calibrations of a high number of model parameters, in some case without a clear physical meaning;  the need of introducing iterative schemes for satisfying inequality constraints by means of implicit multi-step redictor-corrector schemes or by introducing equivalent non-linear systems in a large number of unknowns. the last drawback is due to the need of fulfilling the second law of thermodynamics by solving a constrained optimization problem with inequality constraints that derives from the clausius-duhem inequality or, equivalently, from kuhn-tucker conditions, [4]. on the other hand, as shown by j.j. moreau [15], the second law of thermodynamics may be a-priori satisfied within the energy statement of the problem if the constitutive laws for the dissipative part of the static quantities involved in equilibrium equations are defined through the introduction of a pseudo-potential of dissipation. in this case, no iterative numerical schemes are needed for satisfying energy inequality constraints. following this thermodynamical framework, frémond developed a phenomenological sma model based on internal constraints enforced by means of convex analysis arguments [16]. the rationale is standard, successful in modeling many structural mechanical problems involving phase change [17], and characterized by:  a proper choice of state variables;  the formulation of equilibrium equations from the principle of virtual work; if internal variables describing different material phases are introduced as state quantities, equilibrium equations will directly give transformationevolution laws;  the introduction of constitutive laws by splitting static quantities (dual to state variables) in terms of their nondissipative and dissipative term; the former is obtained by the differentiation of the free-energy with respect to state quantities, while the latter by differentiating the pseudo-potential of dissipation with respect to state quantities evolution;  the enforcement of physical restrictions on state quantities and on their evolution through sub-differentiable indicator functions (valued zero or  ) added to both the free-energy and the pseudo-potential of dissipation; accordingly, the evolutions of thermomechanical quantities are obtained by projection on convex hulls defining admissible states. even if qualitative results of frémond's model are good, it does not capture all sma features: no multi-variant martensite volume fraction is considered, the strain-width of the stress-strain loop is proportional to its stress-size, unrealistic softening behavior for strain-driven case arise during direct martensitic transformation in uniaxial isothermal response, austenite and martensite phases have the same material parameters. a further drawback of frémond's model is that the total transformation strain, which is the quantity characterized during experiments, is not a model parameter and it nonlinearly depends on a phase-change viscosity parameter, being of tough determination from experimental data. frémond's rationale inspired baêta-neves and co-authors, [18, 19], whose model introduces some improvements but it is still characterized by softening behavior if not treated with an augmented lagrangian method for convexification of system's energy [20]. accordingly, in order to allow engineers to design shape-memory structures by means of the consistent thermodynamical moreau's framework in which frémond's model is formulated, improvements are still necessary. the constitutive model for the pseudo-elastic behavior of smas proposed in the present work is developed in the lines of the frémond's rationale [16, 17]. obtained results highlight main model features: 1. different kinetics between direct and reverse phase transformations; 2. asymmetric response of transformation mechanisms in tension and compression; 3. admissibility of the co-existence of austenite, multi-variant and oriented martensites; 4. straightforward material parameter identification; m. marino, frattura ed integrità strutturale, 29 (2014) 96-110; doi: 10.3221/igf-esis.29.10 99 5. different elastic moduli in tension and compression. the model is herein developed within a one-dimensional framework by assuming an ideal transformation behavior characterized by no-hardening effects. thanks to the employed generalized energetic framework, the second law of thermodynamics is fulfilled without the need of implicit algorithms. accordingly, thanks to the explicit framework in which present model can be implemented, the model allows to straightforwardly include unconventional sma features such as • non-linear transformation lines in a very flexible phase diagram; • dependence of transformation strains on temperature. following the recent works by lagoudas and co-workers, [14], the possibility to address the non-linear dependence of transformation strains and stresses on temperature is a novelty with respect to many well-established available models. model onsider a one-dimensional (1d) material element of infinitesimal length acted by a self-equilibrated cauchy stress  at constant temperature t . the model is based on an incremental approach in the time variable  . accordingly, the actual value (at time = t ) of the strain measure  is obtained from the superimposition of a reference value  (at time = t ) with an infinitesimal perturbation d (associated with the time increment dt , where =t t dt ), resulting = d   . in order to account for different deformation mechanisms in smas and in agreement with available modeling approaches [5, 12, 21], the mapping from the reference to the actual state is regarded as the superimposition of different thermomechanical mechanisms allowing to identify several deformation variables. accordingly, the infinitesimal strain is split in = e id d d   (1) where subscripts e and i relate the infinitesimal strain with elastic and inelastic mechanisms, respectively. denoting the time derivative (in the sense of left-derivative with respect to the actual time t in agreement with the causality principle) with the dot superscript, let = =k k k k kd dt       (with ={ , }k e i ) be introduced. within a displacement-based approach, the material element is said to undergo loading conditions if > 0d  , and unloading conditions if < 0d  . for describing the alloy composition, quantities j (with {1, 2, 3, 4}j  ) represent respectively the volume fractions of austenite (a), single-variant martensites (ms+ and ms-), and multi-variant martensite (mm). the initial thermodynamical state (at = 0 and denoted by superscript in) is assumed to be physically admissible, that is: 1. austenite is not present at low temperatures  if < mft t , then 1 = 0 in ; 2. multi-variant martensite is not present at high temperatures  if > aft t , then 4 = 0 in ; 3. the alloy is aligned either according to the ms+ or to msconfiguration  2 3 = 0 in in  . phase volume fractions are not independent, since they satisfy some physical properties due to their definitions or to the mechanical properties assumed in the present work. accordingly, quantities j have to respect the following assumptions: 1. they represent volume fractions: [0,1], {1, 2, 3, 4}j j   2. no void can appear in the mixture and no phases interpenetration occurs: 1 2 3 4 = 1      3. the austenite volume fraction cannot increase with respect to its initial value at time = 0 : 1 1 in  under these assumptions, vector 1 2 3= ( , , )  β univocally describes alloy composition because of 4 1 2 3= 1      . accordingly, the state quantities for describing the 1d pseudoelastic behavior of smas are chosen as c m. marino, frattura ed integrità strutturale, 29 (2014) 96-110; doi: 10.3221/igf-esis.29.10 100 ={ , , }e is   β (2) reference state is defined in terms of state quantities values (that is, e , i , and β at time = t ) and state quantities evolutions (that is, e , i , and β in the sense of left-derivative with respect to reference time = t , with =e ed dt  , =i id dt  , and =d dtβ β ). introducing the convex set 31 2 3 1 2 3 1 2 3 1 1:={ = ( , , ) | , , [0,1], 1, } t inc x x x x x x x x x x x     x  (3) physical restrictions in ass. 1, ass. 2 and ass. 3 can be summarized as cβ (4) the ideal pseudo-elastic behavior will be described by introducing few model parameters that can be straightforwardly obtained from experiments: • direct and reverse transformation stresses / // /= ( )d r d r t      ; • direct and reverse transformation strains / // /= ( )d r d r t      ; • young's modulus je of the thj alloy phase, assumed to be isotropic linearly elastic. parameters with the same physical meaning are introduced in many sma available models [1, 4, 5, 9], and thereby can be retained as classical. nevertheless, the possibility to address the non-linear dependence of transformation strains and stresses on temperature is a novelty with respect to most well-established available models, in agreement with the improvements proposed by lagoudas and co-workers, [14]. it is worth pointing out that present approach does not require to fix an a-priori specific form for the interpolation function describing the non-linear dependence of //d r   and / /d r   on t . flow rule the difference between austenite and single-variant martensite is quite small: while the unit cell of austenite is, on average, a perfect cube, the transformation to martensite distorts this cube by interstitial carbon atoms. addressing an uniaxial traction, the unit cell after the transformation can be phenomenologically described as slightly longer in the traction direction and shorter in the orthogonal directions. since multi-variant martensite is a mixture of single-variant configurations, the same can be said for the transformation from non-sheared to sheared lattice configurations in the martensitic phase. in the present one-dimensional framework, the atomic rearrangement occurring during the transformation a/mm  ms+/msis herein kinematically described via a phenomenological way by introducing ori as the elongation-rate of the unit cell, herein defined as 2 3= ( , ) := [ (| |) (| |)] , ori ori d h d h d     β    (5) where ( )h x denotes the heaviside function (such that ( ) = 0h x for 0x  and ( ) = 1h x for > 0x ). results will show that ori   because, thanks to modeling choices, the onset of transformations will never simultaneously imply 2 0d   and 3 0d   . equilibrium equations and constitutive laws denoting virtual quantities with the hat superscript and introducing { , , }e i  b as the set of interior forces dual to s , the increment of virtual work density for external and internal actions are ˆ ˆˆ ˆ ˆ ˆ ˆ ˆ( ) = , ( , , ) =ext int e i e e i idw d d dw d d d d d d          β b β by employing the principle of virtual work ( =int extdw dw for any ˆ ˆ ˆ= e id d d   and for any ˆdβ ), the arbitrariness of virtual quantities êd , îd , and ˆdβ gives the equilibrium relationships: = = , = 0e i   b (6) m. marino, frattura ed integrità strutturale, 29 (2014) 96-110; doi: 10.3221/igf-esis.29.10 101 interior forces are split in non-dissipative (denoted by the superscript nd) and dissipative terms (superscript d). the constitutive laws are chosen by introducing the free-energy = ( )s  (providing the non-dissipative terms) and the pseudo-potential of dissipation = ( )s   (providing the dissipative ones), = = , = = , = =nd d nd d nd de e e i i i e e i i                             b b b β β  (7) the free-energy  of the alloy is chosen as: ( , ) := ( ) ( )e el e ch    β β (8) where: • el is the elastic free-energy contribution: 4 =1 1 ( ) := : : 2 el e el e j j e e j d e d d          where  and el are the reference values at = t of cauchy stress and elastic free-energy, respectively. assuming an undeformed material at the initial configuration, then it results = = 0el  at = 0 . • ch is the free-energy contribution, related to the phase change: ( ) := ( , , ) i ( )ch cβ β r β β     where the indicator function ic ensures condition (4) to be satisfied. moreover, r represents the phase transformation rate vector, defined as: 31 2 3 ( , ) ( ) := ( , ) | |, with , , = ( , , ) ( , ) a t g y x, y, g y x x y v v v g y v r v v v v               phase change activates on the basis of temperature and stress states, being here regulated by activation functions: 3 2( , ) := [1 ( )] ( ) / ( ) ( ) /d d r rg y h v h y h v h y             v 2 3( , ) := [1 ( )] ( ) / ( ) ( ) /d d r rg y h v h y h v h y             v ( , ) := ( , ) ( , )ag y g y g y  v v v transformation strains //d r   as well as transformation stresses //d r   depend on temperature t and they can be straight obtained from experimental data, as reported in fig. 1. since present work addresses isothermal conditions, transformation stresses and strains are here fixed parameters. nevertheless, when non-isothermal conditions are addressed, values of transformation stresses and strains at the reference temperature t (at = t ) can be considered. the pseudo-potential of dissipation  is chosen as: ( , ) := ( ) ( )i ch fr i    β β   (9) where: • ch is the pseudo-potential of dissipation related to the phase change: 2 ( ) := 2 ch β β   • fr is the pseudo-potential of dissipation related to the flow rule: ( ) := i ( )orifr i o i      m. marino, frattura ed integrità strutturale, 29 (2014) 96-110; doi: 10.3221/igf-esis.29.10 102 with io the indicator function of the zero value and := ( , ) ori ori d   β   . it is worth pointing out that dimensional multiplicative unitary coefficients have to be considered in previous relationships, when necessary, in order to respect the unit of measure of the free-energy (namely, work per unit volume) and of the pseudo-potential of dissipation (that is, power per unit volume). these coefficients have been omitted here for the sake of compactness. accordingly, since derivation with respect to a finite quantity (for instance, e ) is formally equivalent to the one with respect to a perturbation (for instance, ed ), constitutive choices (7), (8), and (9) give the interior forces as equal to: 4 =1 = i ( )orie j j e i o i j e d           (10) ( , , ) i ( )cβ r β β 0      (11) governing equations assuming strain  as control variable, the governing equations of the sma thermodynamical problem, obtained from equilibrium relationships (6) and constitutive choices (7), (8), and (9), give the evolution of stress  and alloy composition β . stress  results from: 4 2 3 =1 = with = , = ( (| |) (| |))j j e e i i j e d d d d d h d h d d             (12) alloy composition β is found by means of a single-step prediction-projection procedure. tentative values of volume fractions =j j jd     (with = 1, 2, 3j ) are computed first, where: 1 2 3=d d d       (13) 2 3 2={[1 ( )] ( ) / ( ) ( ) / }| |d d r rd h h h h d                   (14) 3 2 3={[1 ( )] ( ) / ( ) ( ) / }| |d d r rd h h h h d                   (15) and then β is obtained as 1 2 3 = ( , , ) if = , if t pr c c       β β β β β      (16) being 1 2 3= ( , , ) pr pr pr pr t  β the orthogonal projection of β  on c . finally, it is worth pointing out that constitutive choices in eq. (7) and the convexity of the pseudo-potential of dissipation in eq. (9) allow to a-priori satisfy the inequality constraint prescribed by the second law of thermodynamics, [15-17]. figure 2: applied strain  vs. time  . m. marino, frattura ed integrità strutturale, 29 (2014) 96-110; doi: 10.3221/igf-esis.29.10 103 results loading-unloading displacement-based uniaxial test at constant temperature t is simulated. starting from = 0 , a constant strain-rate | |= e  is applied with maximum and minimum strain max  and max  , respectively. accordingly, introducing 1 = /maxt e , applied strain-time law is (see fig. 2). 1 1 1 1 1 for = [0, ] = ( ) = 2 for = ( , 3 ] 4 for = (3 , 4 ] max max e t e t t e t t                     (17) therefore, the material element is loaded for 1[0, ]t  and 1 1[2 , 3 ]t t  , while unloading conditions are addressed for 1 1[ , 2 ]t t  and 1 1[3 , 4 ]t t  . two cases are preliminary distinguished: the high-temperature response for > aft t and the low-temperature one for < mft t . accordingly, in the former case, the alloy is fully austenitic (that is, 1 = 1 in ), while in the latter the alloy is characterized by a multi-variant martensitic lattice arrangement (namely, 4 = 1 in ). moreover, the response of the model at < <mf aft t t , where the co-existence of multi-variant martensite and austenite is admissible, is described. finally, relationships for setting the value of reverse transformation strains in function of experimental residual strains are given. figure 3: stress  vs. strain  predicted by present model in a displacement-driven traction loading-unloading test at the high temperature 2 > aft t . the applied strain is depicted in fig. 2 for 1[0, 2 ]t  . a m. marino, frattura ed integrità strutturale, 29 (2014) 96-110; doi: 10.3221/igf-esis.29.10 104 (a) (b) figure 4: alloy composition predicted by present model for a traction loading-unloading test obtained from applied strain in fig. 2 for 1[0, 2 ]t  . (a) in black, 1 (resp., 4 ) vs.  at the high temperature 2t (resp., low temperature 1t ); in grey, 2 vs.  . (b) evolution of alloy composition in the space of the admissible volume fractions at high and low temperature (dimensions of arrows are not in scale). high-temperature response the stress-strain relationship as well as the alloy composition predicted by present model at high temperature are obtained by construction, considering different time intervals. traction loading-unloading: 1[0, 2 ]t  . for presenting a detailed description of analytical results and denoting with =de edt , it is assumed that there exists natural numbers 1 2 3 4, , , >> 1k k k k such that 1 1 = de k de   , 2 = rk de   , 2 3 =d re k de    , and 4 = rk de   . obtained results in terms of sma stress-strain relationship and alloy composition are described in the following and are reported in figs. 3 and 4. traction loading. for 1[0, ]t  , the material element is loaded with = =d de edt . for the sake of notation, let introduce the following stress and strain values: 1 1 = , = d d d d e de e       the time interval = /d dt e  , and the time values: = , = , = , = d d d d d d d d d d t end end tt t t dt t t t t t t e            (18) where 1< d endt t is assumed. model predicts the following response: m. marino, frattura ed integrità strutturale, 29 (2014) 96-110; doi: 10.3221/igf-esis.29.10 105 • [0, )dt t  . at each step, it results 2 3= = 0d d  and thereby eq. (12) gives = 0id , =ed de , 1= de de     . hence, from eq. (13-15) and (16), it results = = inβ β β . • = dt t . it results = d  and = >d d    , and thereby eq. (13-15) and (16) give (since 2 = 0 ) 1 1 1 2 2 2 3 3 = / = // ( , , ) = / = / = / 0 = 0 = 0 d dd d d d d de dee e d de de d r β                                                    (19) accordingly, it results = (1 / , / , 0)td dde de cβ      and ( ) =tβ β   (see fig. 4). thereby, stress d and the corresponding strain d denote reference stress and strain values at the onset of the direct transformation. moreover, from eq. (12) and since 2 3= = 0d d  , it results = 0id , =ed de , and 1= = d te de   . accordingly, 1= d d t e de   and = d d t de   are the starting stress and the starting strain of the direct transformation, respectively. • [ , )d dt endt t t . at each step, it results 2 > 0d  and 3 = 0d  , and thereby eq. (12) gives =id de , = 0ed , and = = dt   . accordingly, a plateau in the stress-strain response is obtained during the martensitic orientation that occurs at the direct transformation stress dt (see fig. 3). during the overall transformation, the evolution laws for the volume fractions result in 1 2= = / de        as long as 2 < 1 (and thereby 1 > 0 ). accordingly, a complete direct martensitic transformation (corresponding to 2 going from 0 to 1) is obtained in the time interval dt (see fig. 4). thereby, time = =d dend endt t dt t  corresponds to 2 = 1 and 1 = 0 (but 2 > 0d  and 3 = 0d  ), or, in other words, to a complete direct transformation. in this situation and as shown in fig. 4, variations of tentative volume fractions are the same as in eq. (19), and eq. (16) gives / 0 = 1 / = = 1 0 0 d pr d de de cβ β β β                           (20) moreover, actual strain is = dt d    , with the strain produced during the martensitic lattice orientation being fully inelastic, and equal to =i d   (see fig. 3). • 1[ , ] d endt t t . at each step, alloy composition is governed by the projection described in eq. (20). it results 2 3= = 0d d  , and thereby eq. (12) gives =ed de , = 0id , and 2= ( ) d d t d te        (see fig. 3). traction unloading. for 1 1[ , 2 ]t t  , the material element undergoes unloading conditions (in fact, =d de  ). consider the following relevant stress and strain values: 2 2 1 1 2 = = = , = r r d r max r r d de de e de e de e de e                          with 1 2= ( )d r e e de         and 2= ( ) d d max t max d te        . moreover, let introduce the time interval = /r rt e  and the time values: = , = , = , = r r r r r r r r r rmax t end end tt t t dt t t t t t t e             (21) where 1< 2 r endt t is assumed. model predictions are as follows: • 1( , ) rt t t  . at each step, it results 2 3= = 0d d  , and thereby eq. (12) gives = 0id , =ed de  , 2= re de     . accordingly, it results = = (0,1, 0)tβ β . in fact, if > d   , volume fractions follow eq. (20). otherwise, if d   , from eq. (13-15) it results 1 2 3= = = 0d d d      . m. marino, frattura ed integrità strutturale, 29 (2014) 96-110; doi: 10.3221/igf-esis.29.10 106 • = rt t . it results = r  and = <r r    , and eq. (13-15) give (since 2 = 1 and 3 = 0 ) 1 1 2 2 3 3 = / = // ( , , ) = / = / = 1 / 0 = 0 = 0 r rr r r r d de dee e d de de d r β                                                   (22) resulting cβ  and thereby =β β  from eq. (16). accordingly, stress r and the corresponding strain r denote reference stress and strain values at the onset of the reverse transformation. moreover, from eq. (12) and since 2 3= = 0d d  , it results = 0id , =ed de , and 2= = r te de   . accordingly, 2= r r t e de   and = r r t de   are the starting stress and the starting strain of the reverse transformation. • [ , )r rt endt t t . at each step, it results 2 < 0d  and 3 = 0d  , and thereby eq. (12) gives =id de  , = 0ed , and = = rt   . accordingly, a plateau in the stress-strain response is obtained during the martensitic de-orientation, occurring at the reverse transformation stress rt . during the overall transformation, the evolution laws for the volume fractions result in 1 2= = / re       as long as 2 > 0 (and thereby 1 < 1 ). accordingly, a complete reverse martensitic transformation (corresponding to 2 going from 1 to 0) is obtained in the time interval rt . thereby, time = =r rend endt t t dt corresponds to 1 = 1 and 2 = 0 (but 2 < 0d  and 3 = 0d  ) or, in other words, to a complete reverse transformation. in this situation, variations of the tentative volume fractions and alloy compositions are obtained from eq. (13-15) and (16), and therefore 1 2 3 = / 1 / 1 = / = / = = 0 0 0= 0 r r pr r r d de de d de de c d β β β                                         (23) moreover, actual strain is = rt r    , with the strain produced during the martensitic lattice de-orientation (during the time interval [ , ]r rt endt t  ) being fully inelastic and equal to =i r   . accordingly, considering a complete loadingunloading cycle (that is, [0, ]rendt  ), the total inelastic strain at the end of the test is d r    . • 1[ , 2 ] r endt t t . at each step, alloy composition is governed by the projection described in eq. (23). it results 2 3= = 0d d  , and thereby eq. (12) gives =ed de  , = 0id , and 1= e de   . it is worth pointing out that, in the limit 0dt  , it results , , , ,d d d d r r r rt d t d t r t r d r                                  where 1= /d d e    and 1 2= / /r d de e          . in summary, in the limit 0dt  , the obtained constitutive relationship during a tensile traction-release test is (see fig. 3) 1 max 2 if loading ε [0,ε ] : ( ) if < ( ) if > d d d d d d d d d d e e                                        (24) 2 max 1 ( ) if > unloading ε [ε ,0] : ( ) if < if d d d r r r r r r r e e                                        (25) and the corresponding evolution of single-oriented martensitic microstructure 2 is m. marino, frattura ed integrità strutturale, 29 (2014) 96-110; doi: 10.3221/igf-esis.29.10 107 max 2 0 if loading ε [0,ε ] : ( ) if < 1 if > d d d d d d d d                                  (26) max 2 1 if > unloading ε [ε ,0] : ( ) if < 0 if r r r r r r r r                                  (27) with 1 2( ) = 1 ( )    . the behavior of the alloy, as obtained from eq. (24-27), is fully strain-rate independent. moreover, due to the phase diagram in fig. 1, reverse transformation occurs at positive stresses at high-temperature (namely, ( ) > 0r t  for > rot t ), reproducing the characteristic pseudo-elastic behavior of smas in initial austenitic microstructure. compression loading-unloading: 1 1[2 , 4 ]t t  . in this case, the behavior of the alloy in terms of the stress-strain relationship and alloy composition is analogous to the traction behavior. in fact, it can be obtained from previous relationships by replacing 2 with 3 , d  with d  , r  with r  , d  with d  , r  with r  . it is worth pointing out that, in the compressive regime, =d de  is associated with loading conditions, and =d de with un-loading ones. the full sma stress-strain constitutive response, obtained by addressing the traction-compression loading-unloading cycle in eq. (17) for 1[0, 4 ]t  at high temperature 2 > >af rot t t , is depicted in fig. 5a. (a) (b) figure 5: stress  vs. strain  predicted by present model in a tensile-compressive loading-unloading test obtained from applied strain as in fig. 2 at the high temperature 2t (a) and at the low temperature 1t (b). m. marino, frattura ed integrità strutturale, 29 (2014) 96-110; doi: 10.3221/igf-esis.29.10 108 low-temperature response despite the low-temperature response of smas is very different from the high-temperature one, analytical relationships obtained via present model are only slightly different from the ones above described. firstly, due to the multi-variant martensitic lattice arrangement of the alloy, young's modulus 4e should be employed instead of 1e . when > d   , the onset of the direct transformation occurs and the tentative alloy composition is the same as in eq. (19) but, since 1 = 0 in , it results cβ  and eq. (16) gives = = (0, / , 0)pr tddeβ β   with 4 = 1 / dde   . this is clearly shown in fig. 4, where it is also highlighted that analogous projection occurs during the overall direct transformation up to = (0,1, 0)tβ . similarly, model behavior is different also at the reverse transformation, where tentative volume fractions are given by eq. (22) (identical to the high-temperature case), resulting now cβ  . thereby, as shown in fig. 4, alloy composition at the onset of reverse transformation is obtained as = = (0,1 / , 0)pr tddeβ β   [see eq. (16)] with 4 = / dde   . analogous projection occurs during the overall reverse transformation, up to = (0, 0, 0)tβ and 4 = 1 (see fig. 4). the full sma stress-strain constitutive response, obtained addressing the traction-compression loading-unloading cycle in eq. (17) for 1[0, 4 ]t  at the low temperature 1 < <mf rot t t , is depicted in fig. 5b. it is worth highlighting that the phase diagram in fig. 1 determines that the reverse transformation occurs at negative stresses for low-temperature tests (for < rot t ). accordingly, in agreement with experimental evidence, no pseudo-elastic behavior appears at tensile stresses for smas in initial multi-variant martensitic microstructure. intermediate-temperature response the model is able to deal with smas in an initial mixture composition characterized by both multi-variant martensite and austenite lattice arrangement, stable in the temperature range < <mf aft t t . the stress-strain constitutive relationship, obtained by addressing the traction-compression loading-unloading cycle in eq. (17) for 1[0, 4 ]t  , is fully analogous to the ones reported in fig. 5, but employing the transformation stresses values as from experimental phase diagram (see fig. 1) and the initial young's modulus 1 1 4 4= in in ine e e  instead of 1e and 4e . nevertheless, as shown in fig. 6 and due to the initial mixture composition, the evolution of phase volume fractions predicted by present model is significantly different from the ones obtained at high and low temperatures (see fig. 4). figure 6: alloy composition vs. time (left) and in the volume fraction space (right) predicted by present model for a traction loadingunloading test (see applied strain in fig. 2 for 1[0, 2 ]t  ) considering a sma with initial mixture martensitic-austenitic composition with = (0) = (0.7, 0, 0)in tβ β (dimensions of arrows are not in scale). residual strains sometimes it can be easier to describe reverse transformation in terms of experimental data on residual strains res  and res  instead of reverse transformation strains r  and r  . by employing previous analytical results and addressing the traction-compression loading-unloading cycle as in eq. (17), present model allows to derive useful relationships for setting the value of reverse transformation strains in order to obtain = res   (resp., = res res      ) at = 0 at the end of the direct and reverse transformation cycle mm/a  ms+ (resp., mm/a  ms-), m. marino, frattura ed integrità strutturale, 29 (2014) 96-110; doi: 10.3221/igf-esis.29.10 109 32 2 3 ( )( ) = , = inin r d res r d resin in e ee e e e e e                    (28) where = d r       and =| |d r       . conclusions novel constitutive model for the stress-induced martensitic transformations in smas has been proposed, accounting for: different behavior for the transformation laws of direct and reverse lattice rearrangement; asymmetric responses in tension and compression (both for transformation and stiffness properties); the possible co-existence of austenite, multi-variant and oriented martensites. accordingly, the model is suitable for reproducing available experimental data on sma pseudo-elastic properties. the model is formulated in a generalized energetic framework. by introducing a suitable pseudo-potential of dissipation and by formulating transformation-evolution laws from microscopic equilibrium equations, the fulfillment of the second law of thermodynamics is a-priori satisfied, without the need of implicit algorithms. in order to highlight this feature, the model is developed in detail within a fully explicit framework, easy to be implemented for computational analyses. obtained results clearly show this feature, highlighting that material parameter identification is straightforward from experimental data, even accounting for a possible non-perfect pseudo-elastic behavior for sma. the model has been here developed under the assumption of ideal non-hardening behavior. in upcoming works, it will be generalized in order to account for non-linear hardening effects, allowing for an effective comparison with experimental data. moreover, shape-memory effects as well as non-isothermal response will be accounted for. accordingly, the effects of non-linear transformation lines in the phase diagram, as well as of temperature-dependent transformation strains, on sma mechanics will be shown. it is worth pointing out that, within present explicit framework and addressing nonisothermal conditions, the value of //d r   and //d r   at the reference temperature t (at = t ) can be considered in the governing equations at each incremental step. accordingly, present model does not require to fix a specific form of interpolation functions for transformation lines in phase diagram (assumed piecewise-linear in most modeling approaches), as well as for the temperature-dependence of transformation strains, resulting in a very general and flexible tool for describing very different pseudo-elastic behaviors. acknowledgments he author gratefully acknowledges prof. franco maceri, prof. giuseppe vairo and prof. michel frémond for fruitful discussions on this paper. this work was developed within the framework of lagrange laboratory, a european french-italian research group. present research study was supported by miur (prin, grant number f11j12000210001). references [1] shape memory alloys. modeling and engineering applications, lagoudas, d.c. (ed.), springer science+businessmedia, llc, new york, usa, (2008). [2] songa, g., ma, n., li, h.-n., applications of shape memory alloys in civil structures. engineering structures, 28 (2006) 1266-1274. [3] auricchio, f., marfia, s., sacco, e., modeling of sma materials: training and two way shape memory effects, computers and structures, 81 (2003) 2301-2317. [4] auricchio, f., bonetti, e., scalet, g.,ubertini, f., theoretical and numerical modeling of shape memory alloys accounting for multiple phase transformations and martensite reorientation. international journal of plasticity, 59 (2014) 30-54. [5] moumni, z., zaki, w., son, n.-q., theoretical and numerical modeling of solid-solid phase change: application to the description of the thermomechanical behavior of shape memory alloys, international journal of plasticity, 24 (2008) 614-645. a t m. marino, frattura ed integrità strutturale, 29 (2014) 96-110; doi: 10.3221/igf-esis.29.10 110 [6] churchill, c.b., shaw, j.a., iadicola, m.a., tips and tricks for characterizing shape memory alloy wire: part 4 thermo-mechanical coupling, experimental techniques, 34 (2010) 63-80. [7] khandelwal, a., buravalla, v., models for shape memory alloy behavior: an overview of modeling approaches. international journal of structural changes in solids, 1 (2009) 111-148. [8] coleman b.d., m.e. gurtin, thermodynamics with internal state variables. department of mathematical sciences. mellon college of science, (1967) 1-72. [9] bouvet, c., calloch, s., lexcellent c., a phenomenological model for pseudoelasticity of shape memory alloys under multiaxial proportional and nonproportional loadings, european journal of mechanics a/solids, 23 (2004) 37--61. [10] evangelista, v., marfia, s., sacco, e., a 3d sma constitutive model in the framework of finite strain. international journal for numerical methods in engineering, 81 (2010) 761-785. [11] leclercq, s., lexcellent, c., a general macroscopic description of the thermomechanical behavior of shape memory alloys. journal of the mechanics and physics of solids, 44 (1996) 953-980. [12] nguyen, q.s., moumni, z., sur une modélisation du changement de phases solides, comptes rendus de l'académie des sciences. series ii, 321 (1995) 87-92. [13] halphen b., nguyen, q.s., sur les matériaux standard généralisés, journal de mécanique, 14 (1975) 39-63. [14] lagoudas, d., hartl, d., chemisky, y., machado, l., popov, p., constitutive model for the numerical analysis of phase transformation in polycrystalline shape memory alloys, international journal of plasticity, 32-33 (2012) 155183. [15] moreau, j.j., sur les lois de frottement, de viscosité et de plasticité. comptes rendus de l'académie des sciences, 271 (1970) 608-611. [16] frémond, m., phase change in mechanics. lecture notes of the unione matematica italiana. springer-verlag, berlin-heidelberg, (2012). [17] frémond, m., non-smooth thermomechanics. springer-verlag, berlin, (2002). [18] baêta-neves, a.p., savi, m.a., pacheco, p.m.c.l., on the fremond's constitutive model for shape memory alloys. mechanics research communication, 31 (2004) 677-688. [19] savi, m.a., paiva, a., baêta-neves, a.p., pacheco, p.m.c.l., phenomenological modeling and numerical simulation of shape memory alloys: a thermo-plastic-phase transformation coupled model, journal of intelligent material systems and structures, 13 (2002) 261-273. [20] pagano, s., alart, p., maisonneuve, o., solid-solid phase transition modelling. local and global minimizations of nonconvex and relaxed potentials. isothermal case for shape memory alloys, international journal of engineering science, 36 (1998) 1143-1172. [21] zaki, w., moumni, z., a three-dimensional model of the thermomechanical behavior of shape memory alloys, journal of the mechanics and physics of solids, 55 (2007) 2455-2490. [22] ahlers, m., the martensitic transformation, revista matéria, 9 (2004) 169-183. microsoft word numero 24 articolo 8 a.yu. fedorova et alii, frattura ed integrità strutturale, 24 (2013) 81-88; doi: 10.3221/igf-esis.24.08 81 special issue: russian fracture mechanics school a study of the stored energy in titanium under deformation and failure using infrared data a.yu. fedorova, m.v. bannikov, o.a. plekhov institute of continuous media mechanics of the ural branch of the russian academy of sciences, 614013, ac. koroleva street, 1, perm, russia poa@icmm.ru abstract. the work is devoted to the experimental study of heat dissipation caused by plastic deformation and failure processes taking place in a titanium alloy ti-4.2al-1.6mn. to investigate the spatial and time evolution of temperature, a set of experiments has been carried out on plane titanium smooth specimens and specimens with pre-grown centered fatigue cracks. the original mathematical algorithm for experimental data processing has been applied to obtain the rate of heat dissipation generated by plastic deformation and stored energy. it is shown that the stored energy is accumulated in titanium specimens undergoing fatigue tests, and at the time of damage to fracture transition it is equal to zero. keywords. heat dissipation; infrared thermography; stored energy. introduction t is well known that real metals have a complex structure, which is a hierarchy of different scale levels [1, 2]. under deformation, the structural evolution is observed at all scale levels and leads to irreversible deformation and failure that is accompanied by energy accumulation and dissipation. investigation of thermodynamics of deformation and failure is a key issue in solid mechanics. these studies allow one to develop a universal material failure criterion for estimating different stress-strain states (including multi-axial ones) and loading histories. the experimental and theoretical study of the energy balance during deformation is based on an extensive bibliography. the importance of this problem was originally shown by j. h. lambert in 1779 in his work concerning the energy similarity of mechanical and thermal failure processes of solids. the essence of this similarity is that the mechanical failure of metals can occur when the relative deformation in at least one direction reaches a value equal to the linear thermal expansion at the melting point. a substantial contribution to the development of these ideas was made by v.s. ivanova, who proposed the structure-energy theory of metal fracture [3]. a detailed analysis of thermodynamic effects produced by cyclic deformation and failure in metals was carried out by v.t. troshchenko and v.v. fedorov. a review of strength energy criteria was given in [4, 5]. to analyze the thermodynamic characteristics of deformation processes in solids, it is necessary to take into account the fact that the plastic deformation work is converted into two parts: heat energy caused by the movement and annihilation of defects at various structural levels, and hidden (stored) energy of plastic deformation accumulated in the elastic fields of defects. the energy is dissipated in the surrounding environment by conduction, convection and radiation and also stored in the material as thermal energy that increases due to the self-heating effect. the main difficulty encountered in the analysis of deformation and failure processes is a choice of thermodynamic parameters required to determine the exhaustion degree of material deformability. in work [5] published in 1979, it was experimentally shown that an endurance limit can be determined by using almost any thermodynamic characteristics of the process: inelastic deformation per one load cycle, irreversibly consumed energy per one load cycle, self-heating i http://dx.medra.org/10.3221/igf-esis.24.08&auth=true http://www.gruppofrattura.it a.yu. fedorova et alii, frattura ed integrità strutturale, 24 (2013) 81-88; doi: 10.3221/igf-esis.24.08 82 temperature, energy dissipation rate, and energy storage rate. for a more rapid determination of the endurance limits of metals, the author proposed two types of tests: a slowly increasing load (stress) amplitude test and a block amplitude test (used more often today). in the beginning of 1970th, v. fedorov developed an original experimental setup that permitted him to control the heat dissipation and to measure the temperature of the specimen under cyclic loading. the analysis of the experimental studies carried out in ussr in 1970-1980 has led us to the conclusion that the obtained parameters are indirect and thus cannot be used as a basis for the development of the universal material failure criteria. for example, it is experimentally shown [5] that the thermal energy dissipated during the cyclic deformation of specimens made from 40x, 2x10, 25, 45 steels (russian marking) may have very different values [5]. conversely, the value of the stored energy during deformation is independent of loading conditions and correlates, at the time of failure, with the value of enthalpy of the material in a liquid state at melting temperature. with the advent of infrared cameras it became possible to significantly simplify the schemes of experiments and to accelerate the determination of fatigue limits of materials [6-8]. infrared thermography allows one to measure, in real time, the temperature of materials under deformation and to calculate the thermal energy of specimens and the rate of heat dissipation. investigation of the energy accumulation process in metals at different loading conditions was carried out over the entire 20th century. the review of experimental works devoted to the methods of studying the stored energy in the material under deformation and the peculiarities of this process for different materials and load conditions is available in [9]. currently, it has been convincingly shown that the ratio of the energy storage rate to the plastic work rate can reach a value of 0.3-0.4 at the initial stages of plastic deformation process [10, 11]. the aforementioned experimental results indicate the importance of further development of methods for investigation of the thermodynamic parameters of the deformation process. at present, infrared thermography is one of the most promising techniques for thermodynamic measurements; it requires no changes in the standard schemes of mechanical testing. one of the main problems facing scientists today is the development and realization of mathematical methods for experimental data processing, including noise filtering for temperature measurements based on infrared radiation data, elimination of external effects during the experiments (reflection of infrared waves from the metal specimen surface, relative motion of a specimen, etc.), and calculation of heat losses in the course of the experiment. the major goal of such experimental data processing is to provide a solution to the inverse problem and to evaluate the heat source evolution caused by the structure evolution in the material. a comparison of these data with the results of mechanical tests will enable one to determine the value of stored energy and to propose a local material failure criterion. this criterion can be applied for calculation of the stored energy value and determination of the moment at which this parameter is equal to zero, that is, the time of local material failure. in the present paper, the proposed criterion is used in the analysis of stress field and energy dissipation at the fatigue crack tip. materials and conditions of experiment he experimental study of temperature evolution at the fatigue crack tip was carried out on the two types of the plane specimens of titanium alloy. the chemical composition of the material is presented in tab. 1. experiments were made on smooth specimens and specimens weakened by holes to initiate fatigue cracks in the center of the specimen. the specimens were manufactured from a titanium sheet 3 mm thick. the mechanical properties of the materials were determined based on the original experiment. mechanical tests were carried out using a 100 kn servohydraulic machine bi-00-100. the mechanical properties and fatigue loading conditions are presented in tab. 2. the geometry of specimens is shown in fig. 1. al zr si fe o h n c mn 3.68 0.3 0.12 0.3 0.15 0.012 0.05 0.1 1.16 table 1: the chemical composition of titanium alloy(%). modulus of elasticity yield stress ultimate stress fatigue limit fracture toughness pmin pmax stress ratio 64 gpa 800 mpa 900 mpa 460 mpa 75.6 мра√m -18.7 mpa 367 mpa -0.051 table 2: the mechanical properties of ti-4.2al-1.6mn and fatigue loading conditions. t http://dx.medra.org/10.3221/igf-esis.24.08&auth=true http://www.gruppofrattura.it a.yu. fedorova et alii, frattura ed integrità strutturale, 24 (2013) 81-88; doi: 10.3221/igf-esis.24.08 83 the test conditions comply with the conditions of the experiment described in detail in [12]. investigation of the heat source evolution was carried out on the smooth specimens during a quasi-static tensile test. crack propagation was studied at loading frequency of 5 hz and 10 hz. the temperature evolution was recorded by an infrared camera flir sc 5000. the spectral range of the camera is 3-5 mm. the maximum frame size is 320×256 pixels; the spatial resolution is 104 meters. the temperature sensitivity is from 25 mk to 300 k. (a) (b) figure 1: geometry of specimen (a – smooth specimen, b – specimen with a hole). all sizes are in millimeters. experimental data processing and stored energy determination post experimental data processing t the beginning of the data processing procedure, the first frame was subtracted from the film to eliminate the influence of infrared camera lens radiation on the temperature field. to increase data accuracy and to eliminate the influence of random temperature fluctuations, the spatially fixed temperature signal of the smooth specimen was processed using the two-dimensional discrete fourier transform with a standard gaussian kernel [13]. the result of such data processing used to calculate the heat source field is illustrated in fig. 2. the relative motion of the specimen with cracks and the infrared camera lens observed in cyclic tests causes the problem of motion compensation, which should be overcome to obtain the correct temperature data at the given point on the specimen surface. to compensate this relative motion, the algorithm described in detail in [13] was used. the main idea of the algorithm consists in finding a marker zone on the examined surface and searching for this area on the surface in each time step. further, the displacement of every point on the surface is calculated for each time step. the data processing yielded the temperature increment field (fig. 3), which was used to determine the heat source field. (a) (b) figure 2: infrared image of the smooth specimen before data processing (a) and the obtained temperature change field (b). a http://dx.medra.org/10.3221/igf-esis.24.08&auth=true http://www.gruppofrattura.it a.yu. fedorova et alii, frattura ed integrità strutturale, 24 (2013) 81-88; doi: 10.3221/igf-esis.24.08 84 (a) (b) figure 3: infrared image of the specimen with crack before data processing (a) and the obtained temperature increment field (b). calculation of stored energy under quasistatic loading to calculate the specific power of heat source, we have used the finite difference scheme of equation (1) for heat source evolution             ts c t k t (1) where t is the temperature, ρ is the density (4550 kg/m3), c is the heat capacity (600 j/(kg·k)), k is the heat conductivity (6.5 w/(m·k)), s is the unknown specific power of heat source (w/m3), and τ is the constant corresponding to the heat loss due to heat exchange with the surroundings (103 j/(m3·k)). the power of heat source at time close to fracture is shown in fig. 4. the plastic zone is localized on the surface of the smooth specimen (fig. 4a). fig. 4b presents the last moments before fracture of the specimen with crack; one can observe strong plastic deformation at the crack tip, and the plastic zone has the form of a “butterfly”. here we also use the assumption [14, 15] that some of the irreversible plastic work contributes to heat generation, while the rest is stored as the energy of crystal defects accompanying plastic deformation, traditionally known as the stored energy of cold work. (a) (b) figure 4: experimental data for the heat power field near the crack tip at the beginning of unstable crack propagation. for plane specimens without crack the plastic work under quasi-static tensile loading is calculated using the experimental data obtained for the applied force f(t) and the deformation velocity v: http://dx.medra.org/10.3221/igf-esis.24.08&auth=true http://www.gruppofrattura.it a.yu. fedorova et alii, frattura ed integrità strutturale, 24 (2013) 81-88; doi: 10.3221/igf-esis.24.08 85 ( ) ( )quasipw t f t v (2) the power of heat source is integrated over the plastic localization zone, and the heat dissipation energy is defined by the equation 22 1 1 ( ) ( , , )   yx quasi x y q t s x y t dxdy (3) where 1 2 1 2, , ,x x y y are the rectangular coordinates of the plastic deformation zone. the stored energy is determined as a difference between the plastic work and the heat dissipation energy. the results of calculation are presented in fig. 5. 0 20 40 60 80 100 120 -1 0 1 2 3 4 5 6 7 time, sec w p (t ), q (t ), w p (t )q (t ), w plastic work, heat dissipation energy and stored energy, w heat dissipation energy plastic work stored energy figure 5: time dependence of plastic work, heat dissipation energy and stored energy calculated for the smooth specimen. by analyzing the data presented in fig. 5, we can conclude that the stored energy rate tends to zero at the time of failure. this supports the results [5] indicating that the stored energy is a thermodynamic parameter, which can adequately describe the damage evolution in metals under deformation. calculation of stored energy at fatigue crack tip to define the plastic work at the fatigue crack tip, we have used the solution for stress distribution at the crack tip obtained by hutchinson, rice and rosengren (hrr-solution). the specific plastic work in the direction of crack propagation can be written as [16]: 1 0 ( ) ( , ) ( , , ) 1           p n e p n j t nn w r t d n i r (4) where n is the hardening coefficient (in our case, n=4), in is the function of the hardening coefficient, r and θ are the polar coordinates of the point near the crack tip (x=rcosθ, y=rsinθ), σe is the tabulation function, and j(t) is the energy j-integral that is the function of applied cycling loading and crack length. the time dependence of the j-integral is plotted in fig. 6. the stored energy is obtained as a difference between the accumulated plastic work and the accumulated heat dissipation energy calculated in the area near the crack tip at all time moments of the experiment. thus, we have ( , , ) ( , , )  it p p 0 w x y t w x y t dt (5) ( , , ) ( , , )  it 0 q x y t s x y t dt (6) http://dx.medra.org/10.3221/igf-esis.24.08&auth=true http://www.gruppofrattura.it a.yu. fedorova et alii, frattura ed integrità strutturale, 24 (2013) 81-88; doi: 10.3221/igf-esis.24.08 86 0 0.5 1 1.5 2 0 2 4 6 8 x 10 4 time, sec j, p a* m j-integral, pa*m figure 6: time dependence of the energy j-integral under cycling loading. the time dependence of accumulated plastic work, dissipative energy and stored energy calculated for the moving fatigue crack tip is shown in fig. 7. to calculate the parameters presented in fig. 7, the maximum of the temperature field near the crack tip was registered at each step of the experiment, and in equations (4)-(6) the origin of coordinates was displaced to a new position at each time moment. by comparing the time evolution of plastic work and dissipative energy, the deformation process corresponding to the transition from the stable state to the unstable state of crack propagation can be divided into three parts. the first stage lasts for approximately 1.3 second; correlation between two curves is good. from 1.3 second to 5 seconds, the dissipation energy increases slowly compared to the plastic work. over this period, the stored energy is monotonically accumulated in the deformed material and transformed into the potential energy of lattice distortion. at the last moments before fracture, the heat dissipation energy increases jumpwise and reaches the value of plastic work. at this time the rate of plastic work is less than the rate of heat dissipation energy. it can be assumed that the damage accumulation mechanism is changed, and the material approaches the fracture stage, where the role of macroscopic displacements is essential, and the energy dissipation increases significantly. we can suppose that the plastic work at this moment cannot be described by traditional hrr-solution (4), because this model does not agree with the effect of a jumpwise increase in the dissipation energy. so, the stored energy calculated at this moment should be corrected. 0 1 2 3 4 5 6 -0.5 0 0.5 1 1.5 2 2.5 3 x 10 9 time, sec w p , q , w p -q , j/ m 3 plastic work, heat dissipation energy and stored energy, j/m3 accumulated dissipation energy accumulated plastic work stored energy 1 2 3 figure 7: time dependence of plastic work, heat dissipation energy and stored energy at the point near the crack tip (1, 2, 3 – time points for β-distribution in fig. 8). the data obtained for the examined material indicate that the stored energy reaches a critical value, after which the hrr solution is unable to describe the behavior of plastic work near the crack tip. we suppose that the stored energy observed at the last moment before fracture is equal to some constant that indicates the approaching material destruction. http://dx.medra.org/10.3221/igf-esis.24.08&auth=true http://www.gruppofrattura.it a.yu. fedorova et alii, frattura ed integrità strutturale, 24 (2013) 81-88; doi: 10.3221/igf-esis.24.08 87 1 2 3 figure 8: the first coordinate quarter of the space β-distribution at different time moments is shown in fig. 7. the crack propagates along the x-axis. we introduce the parameter β to evaluate the value of stored energy in metals: ( , , ) ( , , ) ( , , ) ( , , )    p p w x y t q x y t x y t w x y t (7) the space distribution of the parameter β at different time points is given in fig. 8. a white pixel is the point of the crack tip where stresses are calculated based on the hrr-solution. therefore, the plastic work has singularity at the crack tip. pictures 1, 2 and 3 correspond to the points shown in fig.7. it is seen that the dissipation energy increases depending on the plastic work, and the images of the space β -distribution are similar (pictures 1, 2). picture 3 indicates that the βdistribution changes, that is, in front of the crack tip an area with zero β appears in the direction of crack propagation. thus, the crack growth can be expected in the area of zero β. the space distribution of the parameter β makes it possible to access the direction of crack motion and to predict its growth up to the specimen failure. this circumstance allows us to use the parameter β as a failure criterion that is based on the thermodynamic laws. conclusion he infrared technique has been applied to investigate the effect of heat dissipation under quasi-static loading and its localization at the crack tip under cyclic loading. the original data processing algorithm developed earlier has allowed us to calculate the values of heat dissipation at the crack tip and to determine the area of plastic deformation localization on the surface of a smooth sample during the tensile test. a method has been developed for determining the stored energy and the parameter β, which could be used as a thermodynamic fracture criterion. the spatial and time distribution of the stored energy has been calculated using the infrared data. the damage parameter is taken as the ratio between the stored energy and the work of plastic deformation. for both the weakened and smooth samples, it has been found that the stored energy is accumulated in titanium specimens undergoing fatigue tests, and the value of stored energy is equal to zero when failure concentration reaches the critical value corresponding to specimen fracture. the obtained results yield information that can be used to develop engineering methods for analyzing the actual state of structures that undergo real loading. acknowledgements his work was supported by the grant of the president of russian federation for support of young russian scientists and leading scientific schools (md-2684.2012.1) and rfbr (grant № 11-01-96005). t t http://dx.medra.org/10.3221/igf-esis.24.08&auth=true http://www.gruppofrattura.it a.yu. fedorova et alii, frattura ed integrità strutturale, 24 (2013) 81-88; doi: 10.3221/igf-esis.24.08 88 references [1] v. e. panin, yu.v. grinyaev, v. v. danilov et al, structural levels of plastic deformation and fracture. novosibirsk: nauka, (1990) 255 (in russian). [2] v. v. rybin, severe plastic deformation and failure of metals. м.:metalurgiya, (1986) 224 (in russian). [3] v. s. ivanova, v. f. terentiev, the nature of the fatigue of metals. moscow «metallurgy», (1975) 456 (in russian) [4] v.t. troshchenko, deformation and fracture of metals under high cyclic loading. kiev: «naukova dumka», (1981) 344 (in russian) [5] v.v. fedorov, thermodynamic aspects of strength and fracture of solids. tashkent: «fan» uz ssr, (1979) 168 (in russian) [6] g. curti, g. la rosa, m. orlando, a. risitano, in: 14th aias italian national conference, catania, italy, (1986) 211 (in italian). [7] g. la rosa, a. risitano, int. journal of f., 22 (2000) 65. [8] m. p. luong, nuclear engineering and design, 158 (1995) 363. [9] m. b. bever, d. l. holt, a. l. tichener, prog. mat. sci., 17 (1973) 1. [10] w. oliferuk, a. korbel, w. bochniak, materials science and engineering a, 319-321 (2001) 250. [11] o. plekhov, n. saintier, t. palin-luc, s. uvarov, a. naimark, material science and engineering a, 462(1) (2007) 367. [12] m. bannikov, a. terekhina, o. plekhov, vestnik permskogo gosudarstvennogo tehnicheskogo universiteta. mehanika, 2 (2011) 14. (in russian). [13] a.yu. fedorova, m.v. bannikov, o.a. plekhov, fracture and structural integrity, 21 (2012) 46. [14] j. hodowany, g. ravichandran, a.j. rosakis, p.rosakis, exp mech, 40(2) (2000) 113. [15] o. plekhov, s. uvarov, o. naimark, strength of materials, 1(391) (2008) 101. [16] yu.g. matvienko, v.g. avramenko, deformation and fracture of materials, 10 (2009) 2. (in russian) http://dx.medra.org/10.3221/igf-esis.24.08&auth=true http://www.gruppofrattura.it microsoft word numero_38_art_27 m.v. karuskevich et alii, frattura ed integrità strutturale, 38 (2016) 198-204; doi: 10.3221/igf-esis.38.27 198 focussed on multiaxial fatigue and fracture multi-purpose fatigue sensor. part 1. uniaxial and multiaxial fatigue m.v. karuskevich, s.r. ignatovich, т.p. maslak national aviation university, kiev, 03680, ukraine a. menou international academy of civil aviation, casablanca, morocco p.о. maruschak ternopil national ivan pul’uj technical university, ternopil, 46001, ukraine maruschak.tu.edu@gmail.com s.v. panin institute of strength physics and materials sciences sb ras, tomsk, 634055, russia national research tomsk polytechnic university, tomsk, 634050, russia f. berto university of padova, vicenza, 36100, italy abstract. the paper describes the key principles and results of preliminary experiments aimed at the development of new technique for the fatigue life prediction under conditions of biaxial cyclic tension. the foundations of the method were developed early by the numerous tests with monitoring the process of surface deformation relief formation, which is proved to be an indicator of accumulated fatigue damage under uniaxial fatigue. the employed phenomenon was early applied for the development of a family of uniaxial loading fatigue sensors. the formation of strain induced relief has been recently taken into consideration as a part of damage accumulation criteria under biaxial fatigue as well. the home-made testing machine has been designed to implement combined bending and torsion loading that simulates loads experienced by an aircraft wing skin. the experimental evidences on formation and evolution of the deformation relief revealed under conditions of combined loading, supports the proposed concept of biaxial fatigue sensor. keywords. defects; fatigue sensors; damage; aviation. citation: karuskevich, m.v., ignatovich, s.r., maslak, т.p., menou, a., maruschak, p.о., panin, s.v., berto, f., multi-purpose fatigue sensor. part 1. uniaxial and multiaxial fatigue, frattura ed integrità strutturale, 38 (2016) 198-204. received: 15.05.2016 accepted: 20.06.2016 published: 01.10.2016 copyright: © 2016 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. m.v. karuskevich et alii, frattura ed integrità strutturale, 38 (2016) 198-204; doi: 10.3221/igf-esis.38.27 199 introduction eing first emerged in aviation, structural health monitoring (shm) systems recently have been spread into the different areas of mechanical engineering applications. among the highly responsible components of shm systems, the fatigue sensor should be considered as a key one. the history of research and developments of metalbased fatigue sensors started together with awareness of the fatigue problem importance. unfortunately, it should be stated that the practical application of metal fatigue sensors remains to be pretty limited even in the spheres were sensors are of high demand. the low level of industrial applications, to our mind is related to the poor scientific basis of many proposed approaches and designs in this area. to an even greater degree this problem is of crucial importance for multiaxial fatigue monitoring. the multiaxial loading is the mostly spread mode for many engineering structures. the complexity of phenomena to develop there has led to numerous theories, models, experimental studies, etc. [1-5]. the papers [6-10] present some recent reviews and approaches for multiaxial fatigue and fracture problems. being general ones for multiaxial fatigue analysis, these criteria might be classified into three groups, being based on fatigue damage parameter used, i.e. stress, strain and strain energy density criteria [11]. each one was described mainly by the critical plane orientation. critical plane concept usually applies different loading parameters within the critical plane whose orientation is determined by i) only shear loading parameters; ii) only normal loading parameters or sometimes iii) mixed loading parameters [12]. the variety of loading conditions gives rise to the development of new concepts, providing rather accurate prediction of the fatigue life. in some cases the unique properties of particular materials might favour a possibility for the prediction their service life. these approaches demand for the obtaining new experimental data. experimental studies of multiaxial fatigue are based on testing specimens of rather complicated shape. the most commonly used specimens have the pipe shapes (similar to ones used in bulge test) as well as cross-shaped (cruciform) ones. in so doing, metal specimens were tested. the available experimental data related to the multiaxial loading of aircraft structure are somehow unavailable. for example, the report on biaxial tests of aircraft component might be found in [10]. the data presented in the paper are the part of investigations aimed at development of the creation for accumulated fatigue damage assessment for structures subjected to multiaxial fatigue. the monitoring of the process was performed with the use of computer aided optical technique based on observation of surface deformation relief of aircraft components made of cladded aluminium alloys [13-15]. since the strain-induced relief results from localized plastic deformation this approach might be referred to as the strain criteria. recently it has been suggested that the deformation relief might be as well taken into consideration within a criterion of the biaxial fatigue damage. loads to act onto aircraft in flight and on the ground ircraft structure is considered as a typical one being subjected to biaxial loading since it experiences the spectrum of loads in air and on the ground. among them are: wind gusts, loads from airdrome unevenness, buffeting motor vibration, acoustic vibration, loads at maneuvers, pressurization, etc. the complexity of analytical and experimental estimation of aircraft components fatigue life is determined by the complexity of their loading patterns, i.e. by irregular (random) character of the loads sequence, multiaxial stress state, etc. the fuselage skin is subjected to the simultaneous action of loadings coming from pressurization, bending and torsion. in the case of airwings the stresses caused by the combined action of bending and torsion are considered as dominant ones. these loads give rise to normal and tangent stresses to act in the bearing components (fig. 1). in doing so, normal stresses are caused by the bending of the wing, while tangent ones result from the shear force and torque moment. the assessment of the accumulated fatigue damage can be performed analytically as well as by instrumental inspection. both approaches need further improvement especially under multiaxial fatigue. deformation relief formation under uniaxial fatigue he aircraft skin is usually made of cladded aluminium (alclad) alloys (2024t3, 7075t6, etc.). the detailed description of the deformation relief nature, its evolution and methods for the analysis can be found in [13-15]. let us point out some key aspects of the nondestructive methods aimed at the analysis of the strain-induced relief. the 2d–optical images of the latter were registered on aluminum alloy specimens under fatigue tests. in order to protect b a t m.v. karuskevich et alii, frattura ed integrità strutturale, 38 (2016) 198-204; doi: 10.3221/igf-esis.38.27 200 them against corrosion, sheets of aircraft alloys are often coated with a layer of pure aluminum (for instance, 2024t3) or with a layer of al doped with 1.0 % of zn (for instance, 7075t6). the depth of cladded layer is varied from 4 to 7 % of the total sheet thickness. aluminum and some of its alloys which are used for the cladding must be persistent slip bands type materials. deformation relief is formed and develops on the surface of the aluminium cladded layer under cyclic loading. the relief consists of persistent slip bands, extrusions, intrusions, etc. the intensity of the relief formation is the function of the stress level, distribution of the stress near the stress concentrator and the number of cycles. figure 1: stresses in the wing components. in order to induce stress localization with further fracture flat specimens with a central hole were tested under cyclic loading. tests were performed under wide spectrum of loads. the procedure of accumulated fatigue damage estimation used in the study included the analysis of digital optical images of the deformation relief registered with the use of a light microscope. the deformation relief was numerically estimated with the use of damage parameter d. it is calculated as the ratio of the surface area covered with extrusion/intrusion structures over the total area under analysis (observation). usually the round shape region with the size of 0.3 mm located near the stress concentrator was analyzed. the characteristic dependence of the parameter d was a function of number of loading cycles. corresponding images of the strain-induced relief under fatigue tests are shown in fig. 2. it should be noticed that besides the damage parameter d, the fractal dimension of the deformation relief clasters were successfully employed for the analysis. figure 2: evolution of the deformation relief under fatigue testing. deformation relief expected under biaxial fatigue t is known that morphology of the deformation relief is determined by the dislocation processes to develop in surface layer. in single crystals one might distinguish preferential gliding (slip) planes. within them the preferential crystallographic directions of dislocation motion might be pointed out (slip directions). the set of slip planes and i m.v. karuskevich et alii, frattura ed integrità strutturale, 38 (2016) 198-204; doi: 10.3221/igf-esis.38.27 201 directions constitutes slip systems. in doing so, dislocations move towards particular directions of planes as the response to shear stresses applied along them. for aluminium, which belongs to the metals with fcc (face centered cubic) lattice the dislocation movement occurs mainly within planes {111} along the direction [110]. the strain hardening, as well as process of plastic deformation in general, depends on the number of actuated slip systems. these, in turn, depend on the level of the resolved shear stress. from this, the number of actuated slip systems depends on the normal stress σy as well as crystallographic orientations. for example, at the loading axis orientation of [011] the total number of equally loaded octahedral slip planes is equal to 2, while for the [001] orientation they make 4. the development of plastic deformation and fatigue processes in polycrystalline metals is more complicated phenomenon. the deformation pattern of a grain there depend on many characteristics, for examples, the size, shape and crystallographic orientation of the grain, the presence of impurities, etc. the straining in neighbouring grains in polycrystalline metals must be compatible in order to maintain continuity and cohesiveness. von mises [16] first showed that a minimum number of active independent slip systems for strain compatibility are equal to five. taylor then suggested [17] that among them only those become active which is require by the least work. because of multiple slip system actuations, polycrystals do not exhibit a stage of easy glide. under the biaxial fatigue, apparently, the additional component of loading, shear or tension/compression increases the number of actuated slip systems or at least alters the order of their involvement. experimental simulation of the wing skin behavior under biaxial loading since the amount of available experimental testing data is very limited it calls for obtaining new original experimental results. commercial biaxial testing systems are complex, expensive, and hence relatively scarce. for this reason the special homemade machine has been designed. it makes possible to investigate some regularities of the fatigue accumulation process. the scheme of the combined “bending-torsion” machine is presented in fig. 3. specimenspecimen a b figure 3: the scheme of the loading: aspecimen end fixed in the loading mechanism; b scheme of combined deformation of the specimen. the simplified design of machine does not provide full spectrum of combinations on torsion and bending components. nevertheless, available regimes allow simulating the stress-strain state in the wing skin components. specimens were made of al clad alloy d16at (2024t3) widely used in ukrainian aviation industry, covered by the layer of pure aluminium. dimensions of the rectangular plata shape specimen with 1 mm diameter central hole (as a stress concentrator where the surface relief was observed) made 140 × 10 × 1.0 mm. normal stresses from the bending moment are determined at the gauge length of the specimen being a function of its deflection. shear stresses are determined by the torque moment, which depends on the displacement of the torsion lever and bending stiffness of the specimen. comparison of the surface deformation relief formed under uniaxial and biaxial loading the deformation relief monitoring was conducted at the points located to the left and to the right from the stress concentrator. the stresses were determined with the use of the common formulas of the strength of materials. in doing so, the stress in the inspected cross section under the bending was equal to σmax = 107.8 mpa. under the combined m.v. karuskevich et alii, frattura ed integrità strutturale, 38 (2016) 198-204; doi: 10.3221/igf-esis.38.27 202 loading the tension stress made σmax = 108 mpa while the shear stress component in the inspected area was equal to τ = 85 mpa. let us compare the pattern of strain induced relief to form under the combined loading with one being developed under applying of the normal stresses. fig. 4 shows typical optical images of the deformation relief being formed under the uniaxial and biaxial loadings. a b figure 4: deformation relief formed under bending (a) and under biaxial loading (b); n=500 000 cycles. 0 0,1 0,2 0,3 0,4 0,5 0,6 0 200000 400000 600000 800000 1000000 1200000 n, cycles d am ag e p ar am et er 1 2 1 1,1 1,2 1,3 1,4 1,5 0 200000 400000 600000 800000 1000000 1200000 n, cycles f ra ct al d im en si o n 1 2 a b figure 5: the evolution of the deformation relief, estimated through calculation of damage parameter d (a) and fractal dimention dp/s (b): 1-uniaxial loading; 2-biaxial loading. all photos were taken at the magnification of ×300. the number of cycles prior to failure of the specimen under bending made 1 450 000 cycles. the specimen subjected to the combined biaxial loading has failured after applying of 512 000 cycles. fig. 5 shows the diagram that characterizes evolution of the deformation relief theough the damage parameter d as well as fractal dimention dp/s. procedures of their calculations were described in [6]. it was experimentally revealed that under uniaxial tests the ultimate value of the parameter d does not exceed the range 0,2 0,25. at the same time under combined biaxial loading it can reach significantly higher values. in doing so, in the current test the ultimate value of d was equal to 0,5. the substantial difference was found in the variation of value of the fractal dimension dp/s. the main reason for the increase of the ultimate intensity of the strain induced relief formation is activating of additional slip systems due to the action of torsion and associated shear stresses [18]. monotonic character of the deformation relief evolution calls for the possibility to monitor fatigue damage by the couple of the parameters employed at evaluating the deformation relief both under uniaxial and biaxial loadings. prospects of the developoment multiaxial fatigue criteria based on deformation relief parameters it is known, that currently used multiaxial fatigue criteria are aimed at the “reduction” of the complex multiaxial loading to an equivalent uniaxial one. experimental results presented in the paper as well as studies previously carried out on the strain-induced relief formation have proved the possibility to monitor damage by calculating the parameters of deformation relief, fig. 6. m.v. karuskevich et alii, frattura ed integrità strutturale, 38 (2016) 198-204; doi: 10.3221/igf-esis.38.27 203 a b figure 6: sensors for fatigue monitoring: a) uniaxial fatigue; b) biaxial fatigue. it is expected that the detailed testing towards these directions will make possible to develop new multiaxial fatigue criteria, being based on the concept of equivalent deformation relief. in concern of practical applications both techniques are of importance: i) direct diagnostic of persistent slip bands; ii) application of fatigue sensors. the latter might be based on the principles proposed for the uniaxial loading, except the design of the sensor shown at the scheme (fig. 6,b). another important problem there is optimization of the sensitivity in concern of real loading conditions. in this sense the geometry of the gauge (sensor) is to be changed. the fe method looks very promising for solving this problem as well. conclusion ircraft structure is very susceptible to the action of fluctuating loading. many components of modern planes are subjected to the multiaxial fatigue. the presented experimental results are aimed at proving the possibility to monitor accumulated biaxial fatigue by the parameters of the surface strain induced relief. it might be implemented through the direct inspection of some airplane components or by application of fatigue sensors. both approaches rely on the phenomenon of formation and evolution of the deformation relief, i.e. conglomerates of persistent slip bands, extrusions and intrusions, etc. further research activity will be directed towards the establishing the relationships between the deformation relief intensity under the uniaxial and multiaxial loading in order to develop the concept of equivalent damage by criteria of equivalent surface relief. basic relationships of relief parameters evolution during the cyclic uniaxial and multiaxial loading have been established. references [1] pan, w.-f., hung, c.-y., chen, l.-l., fatigue life estimation under multiaxial loadings, int. j. of fatigue, 21 (1999) 310. doi:10.1016/s0142-1123(98)00050-4. [2] carpinteri, a., spagnoli, a., multiaxial high-cycle fatigue criterion for hard metals. int. j. of fatigue 23 (2001) 135-145. doi:10.1016/s0142-1123(00)00075-x. [3] papadopoulos, i.v., long life fatigue under multiaxial loading. int. j. of fatigue 23 (2001) 839-849. doi:10.1016/s0142-1123(01)00059-7. [4] jiang, y., a fatigue criterion for general multiaxial loading, fatigue fract. eng. mater. struct., 23 (2000) 19-32. doi: 10.1046/j.1460-2695.2000.00247.x. [5] wang, y.-y., yao, w.-x., evaluation and comparison of several multiaxial fatigue criteria int. j. of fatigue, 26 (2004) 17-25. doi:10.1016/s0142-1123(03)00110-5. [6] karolczuk, a., macha, e., a review of critical plane orientations in multiaxial criteria of metallic materials, int. j. of fracture, 134 (2005) 267-304. doi:10.1007/s10704-005-1088-2. a m.v. karuskevich et alii, frattura ed integrità strutturale, 38 (2016) 198-204; doi: 10.3221/igf-esis.38.27 204 [7] susmel, l., estimating fatigue lifetime of steel weldments locally damaged by variable amplitude multiaxial stress fields, int. j. of fatigue, 32 (2010) 1057-1080. doi:10.1016/j.ijfatigue.2009.12.004. [8] ince, a., glinka, g., innovative computational modeling of multiaxial fatigue analysis for notched components, int. j. of fatigue, 82 (2016) 134-145. doi:10.1016/j.ijfatigue.2015.03.019. [9] ince, a., a novel technique for multiaxial fatigue modelling of ground vehicle notched components, int. j. of vehicle design, 67 (2015) 294-313. doi:10.1504/ijvd.2015.069486. [10] uniaxial and biaxial tests on riveted fuselage lap joint specimens, u.s. department of transportation federal aviation administration, dot/faa/ar-98/33, final report, october 1998. [11] berto, f., lazzarin, p., fatigue strength of structural components under multi-axial loading in terms of local energy density averaged on a control volume, int. j. of fatigue, 33 (2011) 1055-1065. doi:10.1016/j.ijfatigue.2010.11.019. [12] glinka, g., shen, g., plumtree, a., a multiaxial fatigue strain energy density parameter related to the critical fracture plane, fatigue & fracture of engineering materials & structures, 18 (1995), 37-46. doi:10.1111/j.1460-2695.1995.tb00140.x. [13] zasimchuk, e.e., radchenco, a.i., karuskevich, m.v., single-crystals as an indicator of fatigue damage, fatigue & fracture of engineering materials & structures, 15 (1992), 1281-1283. doi:10.1111/j.1460-2695.1992.tb01263.x [14] karuskevich, m., karuskevich, o., maslak, t., schepak, s., extrusion/intrusion structures as quantitative indicators of accumulated fatigue damage, international journal of fatigue, 39 (2012) 116–121. doi:10.1016/j.ijfatigue.2011.02.007. [15] petrasek, m., ignatovich, s., karuskevich, m., maslak, t., surface of metal as an indicator of fatigue damage, adv. in military tech., 8 (2013) 83-91. [16] von mises, r., mechanik der plastischen formanderung von kristallen, z. angew. math. mech., 8 (1928) 161-185. [17] taylor, g.i., plastic strain in metals, j. inst. met., 62 (1938) 307-324. [18] gliha, v., vuherer, t., maruschak, p., yasniy, o., bishchak, r., parameters affecting the fatigue strength of welds, proc. of int. conference "in-service damage of materials, its diagnostics and prediction", tstu, (2009) 154-162. << /ascii85encodepages false /allowtransparency false /autopositionepsfiles true /autorotatepages /none /binding /left /calgrayprofile (dot gain 20%) /calrgbprofile (srgb iec61966-2.1) /calcmykprofile (u.s. web coated \050swop\051 v2) /srgbprofile (srgb iec61966-2.1) /cannotembedfontpolicy /error /compatibilitylevel 1.4 /compressobjects /tags /compresspages true /convertimagestoindexed true /passthroughjpegimages true /createjobticket false /defaultrenderingintent /default /detectblends true /detectcurves 0.0000 /colorconversionstrategy /cmyk /dothumbnails false /embedallfonts true /embedopentype false /parseiccprofilesincomments true /embedjoboptions true /dscreportinglevel 0 /emitdscwarnings false /endpage -1 /imagememory 1048576 /lockdistillerparams 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/hrv (za stvaranje adobe pdf dokumenata najpogodnijih za visokokvalitetni ispis prije tiskanja koristite ove postavke. stvoreni pdf dokumenti mogu se otvoriti acrobat i adobe reader 5.0 i kasnijim verzijama.) /hun 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can be opened with acrobat and adobe reader 5.0 and later.) >> /namespace [ (adobe) (common) (1.0) ] /othernamespaces [ << /asreaderspreads false /cropimagestoframes true /errorcontrol /warnandcontinue /flattenerignorespreadoverrides false /includeguidesgrids false /includenonprinting false /includeslug false /namespace [ (adobe) (indesign) (4.0) ] /omitplacedbitmaps false /omitplacedeps false /omitplacedpdf false /simulateoverprint /legacy >> << /addbleedmarks false /addcolorbars false /addcropmarks false /addpageinfo false /addregmarks false /convertcolors /converttocmyk /destinationprofilename () /destinationprofileselector /documentcmyk /downsample16bitimages true /flattenerpreset << /presetselector /mediumresolution >> /formelements false /generatestructure false /includebookmarks false /includehyperlinks false /includeinteractive false /includelayers false /includeprofiles false /multimediahandling /useobjectsettings /namespace [ (adobe) (creativesuite) (2.0) ] /pdfxoutputintentprofileselector /documentcmyk /preserveediting true /untaggedcmykhandling /leaveuntagged /untaggedrgbhandling /usedocumentprofile /usedocumentbleed false >> ] >> setdistillerparams << /hwresolution [2400 2400] /pagesize [612.000 792.000] >> setpagedevice microsoft word numero_38_art_47 s. bennati et alii, frattura ed integrità strutturale, 38 (2016) 377-391; doi: 10.3221/igf-esis.38.47 377 evaluation of the increased load bearing capacity of steel beams strengthened with pre-stressed frp laminates s. bennati, d. colonna, p.s. valvo università di pisa, dipartimento di ingegneria civile e industriale, largo lucio lazzarino, 56122 pisa, italy s.bennati@ing.unipi.it, p.valvo@ing.unipi.it abstract. we analyse the problem of a simply supported steel beam subjected to uniformly distributed load, strengthened with a pre-stressed fibre-reinforced polymer (frp) laminate. we assume that the laminate is first put into tension, then bonded to the beam bottom surface, and finally fixed at both its ends by suitable connections. the beam and laminate are modelled according to classical beam theory. the adhesive is modelled as a cohesive interface with a piecewise linear constitutive law defined over three intervals (elastic response, softening response, debonding). the model is described by a set of differential equations with suitable boundary conditions. an analytical solution to the problem is determined, including explicit expressions for the internal forces and interfacial stresses. as an application, we consider the standard ipe series for the steel beam and the sika® carbodur® system for the adhesive and laminate. for each considered cross section, we first carry out a preliminary design of the unstrengthened steel beam. then, we imagine to apply the frp strengthening and calculate the loads corresponding to the elastic limit states in the steel beam, adhesive, and laminate. lastly, we take into account the ultimate limit state corresponding to the plasticisation of the mid-span steel cross section and evaluate the increased load bearing capacity of the strengthened beam. keywords. steel beam; frp strengthening; adhesive; beam theory; cohesive-zone model; analytical solution; pre-stressing; ultimate limit state; load bearing capacity. citation: bennati, s., colonna, d., valvo, p.s., evaluation of the increased load bearing capacity of steel beams strengthened with prestressed frp laminates, frattura ed integrità strutturale, 38 (2016) 377-391. received: 15.08.2016 accepted: 08.09.2016 published: 01.10.2016 copyright: © 2016 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. introduction ibre-reinforced polymers (frp) are increasingly used in civil engineering for the strengthening of existing constructions. in such applications, the existing structural elements (made of traditional materials such as, for instance, masonry, wood, concrete, steel, etc.) are strengthened by adhesively bonding frp laminates onto their external surfaces. the type of fibre, shape, thickness, and other characteristics of the laminate vary according to the f s. bennati et alii, frattura ed integrità strutturale, 38 (2016) 377-391; doi: 10.3221/igf-esis.38.47 378 element to be strengthened and the desired level of structural performance [1]. for the strengthening of steel structures, carbon fibre reinforced polymers (cfrp) are preferred because of their superior mechanical properties [2, 3]. furthermore, cfrp laminates can be pre-stressed, which enables more effective use of the composite material, contribution of the strengthening in carrying out the dead load, closure of cracks in concrete [4, 5], and increased fatigue life in steel [6]. the existing structure and frp laminate behave as a composite structure with a key role played by the adhesive layer, which transfers the stresses between the bonded elements. as a matter of fact, debonding of the frp laminate due to high interfacial stresses is a relevant failure mode for this type of interventions. therefore, a wide number of theoretical and experimental studies have been conducted to achieve reliable and accurate evaluation of such interfacial stresses. smith and teng [7] presented a review of the theoretical models for predicting the interfacial stresses and also developed a solution for strengthened beams in bending. al-emrani and kliger [8] determined the interfacial shear stresses in beams strengthened with pre-stressed laminates subjected to mid-span concentrated loads. benachour et al. [9] extended the previous solutions to distributed loads and multidirectional laminates used as strengthening. all the aforementioned models consider the adhesive layer as an elastic interface to obtain simple closed-form solutions. a more realistic modelling of the adhesive can be achieved by introducing a non-linear (or piecewise linear) cohesive law for the interface [10–12]. bennati et al. [13] used a cohesive-zone model to determine the overall non-linear response of an frp-strengthened beam in pure bending. in a preliminary version of the present paper [14], such model has been extended to account for the prestressing of the laminate. the beam is considered simply supported and subjected to uniformly distributed load. according to the assumed application technology, the laminate is first put into tension, then bonded to the beam bottom surface, and finally fixed at both its ends by suitable connections. the beam and laminate are modelled according to classical beam theory. the adhesive is modelled as a cohesive interface with a piecewise linear constitutive law defined over three intervals (elastic response, softening response, debonding). the model is described by a set of differential equations with suitable boundary conditions. here, we determine an analytical solution to the stated problem, including explicit expressions for the internal forces and interfacial stresses. as an application, we consider the standard ipe series [15] for the steel beam and the sika® carbodur® system [16] for the frp strengthening. the latter consists of an epoxy resin adhesive (sikadur-30®) and pultruded carbon fibre-reinforced polymer laminates (carbodur® s). for each considered steel cross section, we first carry out a preliminary design to determine the length and permanent load of the “existing” unstrengthened beam. then, we imagine to apply the frp strengthening and calculate the loads corresponding to the elastic limit states in the steel beam, adhesive, and laminate. lastly, we take into account the ultimate limit state corresponding to the plasticisation of the mid-span steel cross section and evaluate the increased load bearing capacity of the strengthened beam [17, 18]. calculations are carried out according to the eurocodes [19–21] and italian regulations on frp strengthening [22, 23]. figure 1: frp-strengthened steel beam subjected to uniformly distributed load. mechanical model et us consider an i-section steel beam ab of length 2l, simply supported at its ends and subjected to a uniformly distributed load per unit length, p (fig. 1). as better specified in the following, the load p will actually be a combination of the beam self-weight, g1, a permanent load due to non-structural elements, g2, and an imposed load, q. the beam is strengthened by an frp laminate of length 2l adhesively bonded to its bottom surface. as concerns the application technique, we assume that the laminate is first pre-stressed by a suitable axial force, p, then adhesively l s. bennati et alii, frattura ed integrità strutturale, 38 (2016) 377-391; doi: 10.3221/igf-esis.38.47 379 bonded to the beam, and finally fixed at both its end sections, c and d. we denote with a = l – l the distance of the anchor points from the end sections of the beam. we denote with bb and hb respectively the width and height of the steel cross section and with hf the thickness of the flange (fig. 2). furthermore, we indicate with ab, ib, wb, and zb respectively the area, moment of inertia, elastic modulus, and plastic modulus of the cross section of the beam. besides, we denote with bf and tf respectively the width and thickness of the laminate and with ta the thickness of the adhesive layer. lastly, we indicate with af = bf tf the area of the cross section of the laminate. figure 2: cross section of the strengthened beam. thanks to symmetry, the model can be limited to the left-hand half system (fig. 3). the generic cross section of the beam is identified by a curvilinear abscissa, s, measured from the anchor point of the laminate, c. similarly, the generic cross section of the laminate is identified by a curvilinear abscissa, s*, also measured from point c. we denote with wb(s) the axial displacements of points at the beam bottom surface and with wf(s*) the axial displacements of the laminate cross sections. figure 3: mechanical model of the strengthened beam. in the proposed mechanical model, the steel beam is considered as a flexible beam, while the frp laminate is modelled as an extensible strip. an elastic-perfectly plastic behaviour is assumed for steel with young’s modulus es and design yield stress fyd (fig. 4a). the behaviour of frp is assumed elastic-brittle with young’s modulus ef and design tensile strength ffd (fig. 4b). the adhesive layer is represented by a zero-thickness cohesive interface, which transfers shear stresses, , and no normal stresses. the interfacial stresses depend on the relative displacements, w = wf – wb, between the laminate and the bottom surface of the beam. the interface behaviour is assumed linearly elastic for shear stresses up to a limit value,; then, a linear softening stage, corresponding to progressive damage, follows; lastly, debonding occurs. for w ≥ 0, the cohesive interface law is given by the following piecewise linear relationship (fig. 4c): s u u u k w w w w k w w w w w w w 0 0 , 0 (elastic response) ( ) ( ), (softening response) 0, (debonding)                      (1) s. bennati et alii, frattura ed integrità strutturale, 38 (2016) 377-391; doi: 10.3221/igf-esis.38.47 380 where k and ks are the elastic constants for the elastic and softening responses, respectively; w0 and wu are the relative displacements at the elastic limit and start of debonding, respectively. the elastic constant for the elastic response can be taken as k = ga / ta, where ga is the shear modulus of the adhesive. (a) (b) (c) figure 4: constitutive laws: (a) steel, (b) frp, (c) adhesive. structural response o determine the structural response of the frp-strengthened beam, it is necessary to distinguish between different stages of behaviour. in what follows, stage 0 refers to the unstrengthened beam, subjected to its self-weight and permanent loads. in stage 1, the laminate is pre-stressed and fixed to the beam. at this point, there is yet no composite action between the beam and laminate, which however are both stressed and deformed because of the dead load and pre-stressing. in stage 2, the beam and laminate behave as an elastic composite structure under the imposed loads. this stage ends when one of the composing elements – beam, laminate, or adhesive – reaches its elastic limit. in stage 3, non-linear response is expected due to plasticity of the steel beam and/or softening of the adhesive layer. however – as the numerical examples will show – the steel beam turns out to be always the weakest element. therefore, the load bearing capacity of the system is governed by the plasticisation of the steel beam. stage 0 – unstrengthened beam the unstrengthened beam is subjected to its self-weight, g1, and permanent loads, g2, both assumed here as uniformly distributed. such loads will cause both stress and deformation, however within the linearly elastic behaviour regime. at this stage, the axial force, shear force, and bending moment in the beam respectively are b g b g b gn s v s g g l s m s g g a l l a s, , 1 2 , 1 2 1 ( ) 0, ( ) ( )( ), ( ) ( )( )(2 ) 2          (2) with a s l   . when evaluating ultimate limit states, loads in eq. (2) should be suitably factored [19, 21]. in real applications, cambering of the beam is often introduced to compensate for the deflection due to dead loads. for simplicity, here we do not consider any cambering and assume the deformed configuration of the unstrengthened beam as the reference configuration for strains and displacements. stage 1 – pre-stressing and fixing of the laminate during the pre-stressing stage, the laminate is put into tension by an axial force, nf,p = p, applied through the anchor points on the beam bottom surface. simultaneously, the beam is compressed by the same axial force, which produces also bending because of the eccentricity of the load application point with respect to the beam centreline. the internal forces produced by pre-stressing in the strengthened part of the beam ( s l0   ) are b p f p b p b p bn s n p v s m s ph, , , , 1 ( ) , ( ) 0, ( ) 2        (3) the internal forces given by eqs. (3) are to be added to those given by eqs. (2) to obtain the total internal forces in the beam at the end of the pre-stressing stage. all loads should be suitable factored when evaluating ultimate limit states. t s. bennati et alii, frattura ed integrità strutturale, 38 (2016) 377-391; doi: 10.3221/igf-esis.38.47 381 due to pre-stressing, points belonging to the beam bottom surface will move towards the mid-span cross section; conversely, points on the laminate will move towards the anchor point c. from the classic assumption of beam theory, that plane sections remain plane, and the constitutive laws for the beam and laminate, we determine the following (positive) displacement for a point s on the beam bottom surface at the abscissa s:  bb p s b s b h w s p l s e a e i 2 , 1 ( ) 4          (4) and the following (negative) displacement for a point s* of the laminate at the abscissa s*:  f p f f p w s l s e a , ( *) *   (5) on curing of the adhesive, the beam and laminate behave as a composite structure. to determine the interfacial stresses through eq. (1), the relative displacements at the interface should be evaluated with respect to the deformed configuration at the end of the pre-stressing stage. to this aim, we consider that points s and s*, initially not aligned, be placed on the same cross section at the end of the pre-stressing operation (fig. 5). figure 5: displacements of beam and laminate at the end of the pre-stressing stage. alignment of points s and s* after pre-stressing requires that b p f ps w s s w s, ,( ) * ( *)   (6) by substituting eqs. (4) and (5) into (6), we determine the following relationship between s and s*: b b s b s b f f s b s b f f h h l s e a e i e a e a e i p s s e a p 2 21 1 1 1 4 4 * ( ) 1 1                   (7) stage 2 – application of imposed loads – linear response when imposed loads are applied to the strengthened beam, the relative displacement at the interface (with respect to stage 1) turns out to be f q f p b q b pw s w s w s w s w s, , , ,( ) ( *) ( *) ( ) ( )     (8) where wb,q(s) and wf,q(s*) respectively are the axial displacements of the beam bottom surface and laminate produced by the imposed load, q. in eq. (8), the abscissa s* should be calculated through eq. (7). forw ≤ w0, the interface behaves elastically, so that eq. (1) yields the interface shear stress s. bennati et alii, frattura ed integrità strutturale, 38 (2016) 377-391; doi: 10.3221/igf-esis.38.47 382 f q f p b q b ps k w s w s w s w s, , , ,( ) ( *) ( *) ( ) ( )       (9) fig. 6 shows a free-body diagram of an elementary segment of the strengthened beam included between the cross sections at s and s + ds. from static equilibrium, the following equations are deduced: b q f b q b q b q f b f q b q dn s b s ds dv s q ds dm s v s b h s ds n s n s , , , , , , ( ) ( ) ( ) ( ) 1 ( ) ( ) 2 ( ) ( )           (10) where nb,q, vb,q, and mb,q respectively are the axial force, shear force, and bending moment in the beam; nf,q is the axial force in the laminate due to the imposed load. by solving the differential problem defined by eqs. (9) and (10) – as explained in the appendix – the following expressions are obtained for the interfacial shear stress,  s q l s l s( ) exp( )      (11) and internal forces in the beam,     b q f b q b q f b l n s qb s s l s v s q l s l m s q a s l a s qb h s s l s , , , 1 ( ) 1 exp( ) 2 ( ) ( ) 1 1 1 ( ) ( )( 2 ) 1 exp( ) 2 2 2                                     (12) where and  are constant parameters defined by eq. (a10) in the appendix. figure 6: free-body diagram of an elementary beam segment. s. bennati et alii, frattura ed integrità strutturale, 38 (2016) 377-391; doi: 10.3221/igf-esis.38.47 383 stage 3 – application of imposed loads – non-linear response and failure of the system in stage 3, non-linear response is expected due to either plasticity of the steel beam or softening of the adhesive. however, as the numerical examples below will demonstrate, for current material properties and geometry, the steel beam turns out to be the weakest element of the system, while the adhesive behaves elastically up to very high values of the imposed load. a detailed description of the structural response in stage 3 would require considering the progressive plasticisation of the beam at the mid-span and neighbouring cross sections. at the same time, large deformations and displacements are expected to occur, bringing further non-linearity into the problem. for the sake of simplicity, here we do not explicitly analyse the above sketched non-linear response and limit ourselves to consider the ultimate limit state corresponding to the complete plasticisation of the mid-span cross section of the beam. application or illustration purposes, we apply the model to standard ipe steel beams [15]. for each cross section of the series from ipe 120 to ipe 600, we first carry out a preliminary design to determine the span and permanent load of the “existing” unstrengthened beam. then, we imagine to apply the sika® carbodur® frp strengthening system [16] and calculate the loads corresponding to the elastic limit states in the beam, adhesive, and laminate. lastly, we take into account the ultimate limit state corresponding to the plasticisation of the mid-span steel cross section and evaluate the increased load bearing capacity of the strengthened beam. material properties and geometry of structural elements the material properties, factored according to the eurocodes [20, 21] and italian regulations on frp strengthening [22, 23], are the following:  steel (grade s235): young’s modulus, es = 210 gpa; characteristic yield stress, fyk = 235 mpa; partial factor for material, s = 1.05; design yield stress, fyd = fyk / s = 223.81 mpa;  adhesive (sikadur®-30): shear modulus, ga = 4.923 gpa; characteristic strength, k = 15 mpa; environmental conversion factor, a = 0.85; partial factor for material, a = 1.2; design strength, 0 = a k / a = 10.63 mpa;  laminate (carbodur® s): longitudinal young’s modulus, ef = 165 gpa; characteristic tensile strength, ffk = 3100 mpa; partial factor for material, f = 1.1; design tensile strength, ffd = a ffk / f = 2395.45 mpa. concerning the geometry of structural elements, the geometric properties of the steel cross sections are listed in tab. 1. the thickness of the adhesive layer is assumed ta = 1 mm. the laminates have width bf = 60 mm and thickness tf = 1.3 (type s613) or 2.6 mm (type s626), depending on the steel cross section. the distance between the beam supports and laminate anchor points is a = 500 mm for all cross sections. cross section width bb (mm) height hb (mm) flange thickness hf (mm) area ab (mm2) moment of inertia ib (mm4) elastic section modulus wb (mm3) plastic section modulus zb (mm3) ipe 120 64 120 6.3 1321 3178000 52960 60730 ipe 140 73 140 6.9 1643 5412000 77320 88340 ipe 160 82 160 7.4 2009 8693000 108700 123900 ipe 180 91 180 8.0 2395 13170000 146300 166400 ipe 200 100 200 8.5 2848 19430000 194300 220600 ipe 220 110 220 9.2 3337 27720000 252000 285400 ipe 240 120 240 9.8 3912 38920000 324300 366600 ipe 270 135 270 10.2 4595 57900000 428900 484000 ipe 300 150 300 10.7 5381 83560000 557100 628400 ipe 330 160 330 11.5 6261 117700000 713100 804300 ipe 360 170 360 12.7 7273 162700000 903600 1019000 ipe 400 180 400 13.5 8446 231300000 1156000 1307000 ipe 450 190 450 14.6 9882 337400000 1500000 1702000 ipe 500 200 500 16.0 11550 482000000 1928000 2194000 ipe 550 210 550 17.2 13440 671200000 2441000 2787000 ipe 600 220 600 19.0 15600 920800000 3069000 3512000 table 1: geometric properties of steel cross sections. f s. bennati et alii, frattura ed integrità strutturale, 38 (2016) 377-391; doi: 10.3221/igf-esis.38.47 384 pre-sizing of steel beams the span of the “existing” beam, 2l, and permanent load due to non-structural elements, g2, are fixed by assuming that, under the action of dead loads, the maximum stress in the mid-span cross section of the beam is less than 33% of the yield stress and the mid-span deflection is less than 1/800 of the span:   yd b s b g g l f w g g l l e i 2 1 2 41 2 1 ( 2 ) 0.33 8 5 1 ( 2 ) ( 2 ) 384 800        (13) by taking the equal sign in inequalities (13), the maximum theoretical values of 2l and g2 are first determined. then, by rounding down such values to the nearest integer multiples of 500 mm and 0.50 kn/m, respectively, the final values assumed in subsequent calculations are determined (see tab. 2). cross section length 2l (mm) permanent load g2 (kn/m) ipe 120 2000 7.0 ipe 140 2000 7.5 ipe 160 2500 8.0 ipe 180 3000 8.5 ipe 200 3000 9.5 ipe 220 3500 10.0 ipe 240 4000 11.0 ipe 270 4500 11.5 ipe 300 5000 12.0 ipe 330 5500 12.5 ipe 360 6000 13.5 ipe 400 6500 14.0 ipe 450 7500 14.0 ipe 500 8500 14.5 ipe 550 9000 15.0 ipe 600 10000 16.0 table 2: pre-sizing of steel beams. pre-stressing of frp laminates the pre-stressing tensile axial force in the frp laminates is assumed to correspond to 50% of the design tensile strength: fk f f f p a0.50   (14) depending on the steel cross section, one or two laminates carbodur® type s613 or s626 are used, as illustrated in tab. 3. the table also shows the normal stresses at the upper and lower surfaces of the mid-span cross section of the beam, 1and 1, respectively, produced by the dead loads and pre-stressing. by recalling eqs. (2) and (3), such stresses can be computed as follows: s. bennati et alii, frattura ed integrità strutturale, 38 (2016) 377-391; doi: 10.3221/igf-esis.38.47 385 b g b p b g b p b b b b b n l n l m l m l g g l php a w a w 2 , , , , 1 2 1 ( ) ( ) ( ) ( ) ( )1 2            (15) it can be verified that all the computed values are in magnitude less than the design yield stress, fyd. cross section no. and type of laminates width bf (mm) thickness tf (mm) area af (mm2) pre-stressing force p (kn) stress at upper surface 1 (mpa) stress at lower surface 1 (mpa) ipe 120 1 s613 60 1.3 78 109.9 -25.7 -140.7 ipe 140 1 s613 60 1.3 78 109.9 -16.7 -117.1 ipe 160 1 s613 60 1.3 78 109.9 -32.4 -77.0 ipe 180 1 s613 60 1.3 78 109.9 -45.1 -46.7 ipe 200 1 s626 60 2.6 156 219.8 -20.3 -134.0 ipe 220 1 s626 60 2.6 156 219.8 -32.2 -99.5 ipe 240 1 s626 60 2.6 156 219.8 -44.5 -67.8 ipe 270 1 s626 60 2.6 156 219.8 -48.6 -47.1 ipe 300 1 s626 60 2.6 156 219.8 -51.3 -30.4 ipe 330 1 s626 60 2.6 156 219.8 -53.1 -17.1 ipe 360 2 s626 120 2.6 312 439.6 -42.9 -78.0 ipe 400 2 s626 120 2.6 312 439.6 -42.9 -61.2 ipe 450 2 s626 120 2.6 312 439.6 -47.7 -41.2 ipe 500 2 s626 120 2.6 312 439.6 -53.1 -23.0 ipe 550 2 s626 120 2.6 312 439.6 -49.7 -15.7 ipe 600 2 s626 120 2.6 312 439.6 -55.3 -1.1 table 3: pre-stressing of frp laminates. elastic limit state of the system now, we turn to evaluate the imposed load for which the strengthened beam abandons the range of linearly elastic behaviour. this load will be the minimum between the loads corresponding to the elastic limit states in the beam, adhesive, and laminate. we start from the elastic limit state of the adhesive, which occurs when the maximum shear stress in the interface reaches the design strength, . the abscissa, s , where the shear stress is maximum is first determined by differentiating eq. (11) and setting the derivative to zero: d q q l s s l ds 1 exp( ) 0 ln( )               (16) hence, the maximum shear stress value turns out to be   s q l lmax 1( ) 1 ln( )       (17) by putting max 0  , the corresponding imposed load is obtained,   a q q l l 01 1 1 1 ln( )         (18) where q = 1.5 is the partial factor for variable actions [19, 21]. s. bennati et alii, frattura ed integrità strutturale, 38 (2016) 377-391; doi: 10.3221/igf-esis.38.47 386 moving on to consider the elastic limit state of the laminate, we observe that the maximum axial force, nf max, occurs at the mid-span cross section of the beam. by recalling eqs. (3), (10), and (12), we obtain  f p f p q f q p q f l l n n n l p q b l 2 max , , ( ) 1 exp( ) 2                       (19) where p = 1.0 is the partial factor for pre-stressing actions [19, 21]. by putting nf max = ffd af, the corresponding imposed load is obtained,   fd f p f q f f a p q b l l l 2 1 1 1 exp( ) 2           (20) lastly, we consider the elastic limit state of the beam. to this aim, the normal stresses at the upper and lower surfaces of the mid-span cross section of the beam, 2and2, respectively, are computed. by recalling eqs. (2), (3), and (12), we find g b g p b p q b q g b g p b p q b q b b g g b p q f q b b b b n l n l n l m l m l m l a w g g h l l l p q b l l q w a w w , , , , , , 2 2 21 1 2 2 ( ) ( ) ( ) ( ) ( ) ( ) 1 1 1 1 1 1 exp( ) 2 2 2 2                                            (21) where g (equal to g1 = 1.3 for the self-weight, g1, and g1 = 1.5 for the other dead loads, g2) represents the partial factor for permanent actions. hence, by putting 2 = fyd and2 = fyd, respectively, and taking the minimum between the two resulting values of the imposed load, we obtain the imposed load corresponding to the elastic limit state of the beam, g g b yd p b b b b q b f b b b g g b yd p b b b b f b b b g g h f l p w a w q hl l b l l w a w g g h f l p w a w hl l b l l w a w 21 1 2 2 2 21 1 2 2 2 1 1 1 2 21 min ; 1 1 1 1 1 exp( ) 2 2 2 1 1 1 2 2 1 1 1 1 1 exp( ) 2 2 2                                                                 (22) tab. 4 summarises the results obtained by applying eqs. (18), (20), and (22). the weakest element turns out to be always the steel beam, whose yielding stress determines the load corresponding to the elastic limit state of the system. evaluation of increased bearing capacity to evaluate the increase in the load bearing capacity given by the strengthening system, we first calculate the load bearing capacity of the unstrengthened steel beam. the imposed load, qu, corresponding to the complete plasticisation of the midspan cross section of the beam is calculated as follows: g g q p u p g g q g g q l m q q m g g l 2 1 1 2 2 1 1 2 22 1 1 2 ( ) 2                   (23) where mp = fyd zb is the plastic moment of the steel cross section. s. bennati et alii, frattura ed integrità strutturale, 38 (2016) 377-391; doi: 10.3221/igf-esis.38.47 387 cross section limit load for adhesive qa (kn/m) limit load for laminate qf (kn/m) limit load for beam qb (kn/m) ipe 120 878.8 405.8 11.7 ipe 140 1257.1 580.3 18.9 ipe 160 1136.3 353.8 15.1 ipe 180 1122.5 263.8 12.7 ipe 200 785.1 366.2 20.4 ipe 220 795.9 298.6 17.8 ipe 240 838.0 262.9 15.8 ipe 270 935.5 252.3 16.0 ipe 300 1050.2 248.4 16.5 ipe 330 1183.2 249.2 17.3 ipe 360 1390.2 263.9 19.8 ipe 400 1597.5 276.1 21.8 ipe 450 1731.6 253.7 20.4 ipe 500 1909.7 242.8 19.4 ipe 550 2249.1 268.3 22.9 ipe 600 2495.4 264.8 22.2 table 4: imposed loads at elastic limit states. cross section load bearing capacity of unstrengthened beam qu (kn/m) load bearing capacity of strengthened beam qs (kn/m) increase in load bearing capacity q (kn/m) percent increase q / qu (%) ipe 120 11.0 15.9 4.8 43.7 ipe 140 18.8 25.6 6.8 36.4 ipe 160 15.5 21.7 6.1 39.6 ipe 180 13.4 19.0 5.6 42.0 ipe 200 19.6 27.4 7.8 39.8 ipe 220 17.6 24.8 7.2 40.8 ipe 240 16.1 23.1 7.0 43.8 ipe 270 16.7 24.1 7.4 43.9 ipe 300 17.6 25.2 7.5 42.7 ipe 330 18.8 25.7 6.9 36.4 ipe 360 19.8 28.7 8.9 45.0 ipe 400 22.4 32.5 10.2 45.5 ipe 450 21.5 31.7 10.2 47.5 ipe 500 21.0 29.8 8.8 42.0 ipe 550 25.2 33.8 8.7 34.4 ipe 600 24.9 32.5 7.6 30.7 table 5: load bearing capacity of the system. moving on to the strengthened beam, the results of the previous section suggest that the ultimate limit state of the system corresponds to plasticisation of the steel beam and not to debonding of the adhesive or rupture of the laminate. in the strengthened beam, the mid-span cross section is subjected to both axial force and bending moment. according to the s. bennati et alii, frattura ed integrità strutturale, 38 (2016) 377-391; doi: 10.3221/igf-esis.38.47 388 eurocodes [20], eq. (23) can still be used, provided that mp is replaced by mpn, which takes into account a possible reduction of the plastic moment due to the axial force: b p b b b pn b b p b b b n m n a a m n a m n a a 2 1 min 1, , for 1 0.5 1 , for 1                       (24) where, in our notation, b fg b g p b p q b q b b yd b b b hn l n l n l n a f a a , , ,( ) ( ) ( ) and min 1 2 , 0.5             (25) by substituting eqs. (2), (3), and (12) into (23)–(25), and solving for q, the load bearing capacity of the strengthened beam, qs, is determined. tab. 5 summarises the results obtained for the analysed cases, showing the increase in the load bearing capacity of the system, q = qs – qu. the percent increase ranges between 30% and 50%. conclusions e have presented the mechanical model of a simply supported steel beam subjected to uniformly distributed load, strengthened with a pre-stressed frp laminate. an analytical solution has been determined for the differential problem that describes the structural response of the strengthened beam. the model has been applied to study ipe steel beams strengthened by using the sika® carbodur® frp strengthening system. analysis of the elastic limit states in the steel beam, adhesive, and laminate has shown that the steel beam is always the weakest element of the system. the softening response of the adhesive is not reached in practice being preceded by the plasticisation of steel. for the sake of simplicity, however, we have not analysed the non-linear structural response resulting from the progressive plasticisation of the beam at the mid-span and neighbouring cross sections. this behaviour could indeed be the subject of future studies, which should also take into account the expected large deformations and displacements, as well as the possible lateral torsional buckling. here, the complete plasticisation of the mid-span cross section of the steel beam has been assumed as the ultimate limit state of the system. correspondingly, the increased load bearing capacity of the strengthened beam has been evaluated. references [1] bank, l.c., composites for construction, john wiley & sons, new jersey (2006). [2] zhao, x.-l., zhang, l., state-of-the-art review on frp strengthened steel structures, eng. struct., 29 (2007) 1808– 1823. [3] gholami, m., sam, a.r.m., yatim, j.m., tahir, m.m., a review on steel/cfrp strengthening systems focusing environmental performance, constr. build. mater., 47 (2013) 301–310. [4] aslam, m., shafigh, p., jumaat, m.z., shah, s.n.r., strengthening of rc beams using prestressed fiber reinforced polymers – a review, constr. build. materi., 82 (2015) 235–256. [5] haghani, r., al-emrani, m., kliger, r., a new method for strengtheng concrete structures using prestressed frp laminates, in: saha, s., zhang, y., yazdani, s., singh, a. (eds.), proc. 8th international structural engineering and construction conference – isec 2015: implementing innovative ideas in structural engineering and project management, sydney, australia (2015). [6] ghafoori, e., motavalli, m., zhao, x.-l., nussbaumer, a., fontana, m., fatigue design criteria for strengthening metallic beams with bonded cfrp plates, eng. struct., 101 (2015) 542–557. [7] smith, s.t., teng, j.g., interfacial stresses in plated beams. engineering structures, 23(2001) 857–871. w s. bennati et alii, frattura ed integrità strutturale, 38 (2016) 377-391; doi: 10.3221/igf-esis.38.47 389 [8] al-emrani, m., klieger, r., analysis of interfacial shear stresses in beams strengthened with bonded prestressed laminates, compos. part b – eng., 37 (2006) 265–272. [9] benachour, a., benyoucef, s., tounsi, a., adda bedia, e.a., interfacial stress analysis of steel beams reinforced with bonded prestressed frp plate, eng. struct., 30 (2008) 3305–3315. [10] de lorenzis, l., zavarise, g., cohesive zone modeling of interfacial stresses in plated beams, int. j. solids struct., 46 (2009) 4181–4191. [11] cornetti, p., carpinteri, a., modelling the frp-concrete delamination by means of an exponential softening law, eng. struct., 33 (2011) 1988–2001. [12] cornetti, p., corrado, m., lorenzis, l.d., carpinteri, a., an analytical cohesive crack modeling approach to the edge debonding failure of frp-plated beams, int. j. solids struct., 53 (2015) 92-106. [13] bennati, s., dardano, n., valvo, p.s., a mechanical model for frp-strengthened beams in bending, frattura ed integrità strutturale, 22 (2012) 39–55. [14] bennati, s., colonna, d., valvo, p.s., a cohesive-zone model for steel beams strengthened with pre-stressed laminates, procedia structural integrity, 2 (2016) 2682–2689. [15] en 19:1957, ipe beams: i-beams with parallel flange facings. [16] sika® ag, www.sika.com. [17] linghoff, d., al-emrani, m., kliger, r., performance of steel beams strengthened with cfrp laminate – part 1: laboratory tests, compos. part b – eng., 41 (2010) 509–515. [18] linghoff, d., al-emrani, m., performance of steel beams strengthened with cfrp laminate – part 2: fe analyses, compos, part b – eng., 41 (2010) 516–522. [19] en 1990:2002+a1:2005, eurocode: basis of structural design. [20] en 1993-1-1:2005, eurocode 3: design of steel structures – part 1–1: general rules and rules for buildings. [21] ministero delle infrastrutture e dei trasporti, decreto 31 luglio 2012, approvazione delle appendici nazionali recanti i parametri tecnici per l’applicazione degli eurocodici, rome, italy (2013). [22] cnr-dt 200 r1/2013, istruzioni per la progettazione, l’esecuzione ed il controllo di interventi di consolidamento statico mediante l’utilizzo di compositi fibrorinforzati, rome, italy (2005). [23] cnr-dt 202/2005, studi preliminari finalizzati alla redazione di istruzioni per interventi di consolidamento statico di strutture metalliche mediante l’utilizzo di compositi fibrorinforzati, rome, italy (2005). acknowledgements inancial support from the era-net plus infravation 2014 call within the project surebridge (www.surebridge.eu) through subcontract by partner company aice consulting srl (www.aiceconsulting.it) is gratefully acknowledged. appendix formulation of the differential problem he axial strains at the bottom surface of the beam and in the laminate due to the applied load, q, can be defined respectively as f qb q b q f q dw sdw s s s ds ds ,, , , ( *)( ) ( ) and ( *) *    (a1) besides, from navier’s equation and the constitutive laws for the beam and laminate, we have f qb q b q b b q f q s b s b f f nn m h e a e i e a ,, , , ,and 2     (a2) in order to formulate the differential problem through a single equation, we start by differentiating eq. (9) with respect to s: f t s. bennati et alii, frattura ed integrità strutturale, 38 (2016) 377-391; doi: 10.3221/igf-esis.38.47 390 f q f p b q b pdw dw dw dwd ds ds k ds ds ds ds ds ds ds , , , ,* * * *           (a3) then, we differentiate also eq. (7) with respect to s and obtain the following expression, whose numerical values turn out to be approximately equal to 1 for current geometric and material properties: b s b s b f f h p e a e ids ds p e a 21 1 4* 1 1 1      (a4) by substituting eqs. (4), (5), and (a1) into (a3), and considering (a4), we obtain b b q f q s b s b f f hd k p ds e a e i e a 2 , , 1 1 4                    (a5) by further differentiating eq. (a5) and recalling (a2), we have f q f qb q b q b qb s b s b f f d dnd dn dmhd k k ds ds e a ds e i ds e a dsds 2 , ,, , , 2 1 1 2                   (a6) lastly, by substituting eqs. (10) into (a6), after simplification, we obtain the following differential equation for the interfacial shear stress: b b f b q s b s b f f s b h hd kb s k v s e a e i e a e ids 22 ,2 1 1 ( ) ( ) 4 2               (a7) where the shear force is b qv s q l s, ( ) ( ).  (a8) solution of the differential problem the differential problem stated in the previous section can be solved analytically. in fact, the general solution to eq. (a7) for the interfacial shear stress is s c s c s q l s1 2( ) exp( ) exp( ) ( )        (a9) where c1 and c2 are integration constants and the constant parameters b b b f s b s b f f s b f b b s b b f f h h hk kb e a e i e a e i b i h e i a e a 2 2 2 1 1 1 and = = 4 2 2 2                    (a10) are also introduced. by imposing the boundary conditions, l (0) 0 ( ) 0      (a11) s. bennati et alii, frattura ed integrità strutturale, 38 (2016) 377-391; doi: 10.3221/igf-esis.38.47 391 we obtain ql ql c c ql l l 1 20 and 1 exp( 2 ) 1 exp( 2 )                (a12) where the approximations are justified by the values of the exponential functions in practical problems. lastly, we obtain the following final expression for the interfacial shear stress: s q l s ql s( ) ( ) exp( )       (a13) which is equivalent to eq. (11) in the main text above. by substituting eqs. (a8) and (a13) into (10) and integrating, we obtain b q f f b b b q f f l n s qb ls s qb s c h h l m s q b ls s qb s c 2 , 3 2 , 4 1 ( ) ( 2 ) exp( ) 2 1 ( ) (1 )( 2 ) exp( ) 2 2 2                     (a14) where c3 and c4 are integration constants. these are determined by imposing the continuity of the axial force and bending moment at the cross section of the anchor point: b q b q n m qa l a , , (0) 0 1 (0) ( 2 ) 2      (a15) hence, b f f hl l c qb c qa l a qb3 4 1 and ( 2 ) 2 2         (a16) the final expressions for the internal forces in the beam turn out to be b q f f b q f b f b l l n s qb ls s qb s l l m s q a s l a s qb h ls s qb h s 2 , 2 , 1 ( ) ( ) exp( ) 2 1 1 1 1 ( ) ( )( 2 ) ( ) exp( ) 2 2 2 2                         (a17) it can be easily verified that eqs. (a8) and (a17) are equivalent to eqs. 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can be opened with acrobat and adobe reader 5.0 and later.) >> /namespace [ (adobe) (common) (1.0) ] /othernamespaces [ << /asreaderspreads false /cropimagestoframes true /errorcontrol /warnandcontinue /flattenerignorespreadoverrides false /includeguidesgrids false /includenonprinting false /includeslug false /namespace [ (adobe) (indesign) (4.0) ] /omitplacedbitmaps false /omitplacedeps false /omitplacedpdf false /simulateoverprint /legacy >> << /addbleedmarks false /addcolorbars false /addcropmarks false /addpageinfo false /addregmarks false /convertcolors /converttocmyk /destinationprofilename () /destinationprofileselector /documentcmyk /downsample16bitimages true /flattenerpreset << /presetselector /mediumresolution >> /formelements false /generatestructure false /includebookmarks false /includehyperlinks false /includeinteractive false /includelayers false /includeprofiles false /multimediahandling /useobjectsettings /namespace [ (adobe) (creativesuite) (2.0) ] /pdfxoutputintentprofileselector /documentcmyk /preserveediting true /untaggedcmykhandling /leaveuntagged /untaggedrgbhandling /usedocumentprofile /usedocumentbleed false >> ] >> setdistillerparams << /hwresolution [2400 2400] /pagesize [612.000 792.000] >> setpagedevice microsoft word numero 10 art 3 a. pirondi, frattura ed integrità strutturale, 10 (2009) 21-28; doi: 10.3221/igf-esis.10.03 21 failure prediction of t-peel adhesive joints by different cohesive laws and modelling approaches alessandro pirondi university of parma, department of industrial engineering, parco area delle scienze, 181/a 43100 parma, italy alessandro.pirondi@unipr.it riassunto. in questo articolo si è simulato mediante il modello di zona coesiva il cedimento di un giunto tpeel incollato. gli aderendi sono lamiere di acciaio fe360 e sono unite mediante l’adesivo strutturale loctite multibond 330. i parametri del modello di zona coesiva sono stati calibrati sulla base di esperimenti di frattura condotti in precedenza su provini double cantilever beam (dcb) incollati con il medesimo adesivo. la simulazione è stata condotta utilizzando il software di analisi ad elementi finiti abaqus, sviluppando modelli 2-d. il cedimento avviene in uno strato modellato utilizzando elementi di tipo coesivo disponibili nel software. l’analisi è volta ad individuare l’influenza di: i) differenti formulazioni della legge coesiva, ii) la modellazione o meno dello strato di adesivo con le sue proprietà elasto-plastiche. abstract. in this work, cohesive zone modelling (czm) was used to simulate failure of t-peel bonded joints with 1.5mm thick adherends, respectively, bonded toghether with loctite multibond 330 adhesive. the fracture toughness and load-opening behaviour recorded in previous experiments on bonded double cantilever beam (dcb) specimens were taken as reference to calibrate czm parameters. two-dimensional models were analysed using the fe code abaqus. the failing interface was modeled with the cohesive elements available in this software. the influence of: i) different cohesive law shapes, ii) modeling the presence of the adhesive layer explicitly, was studied. keywords. adhesive joints, fracture, cohesive zone modeling. introduction he use of adhesive joining in civil, aerospace and mechanical constructions has considerably increased in the last decades thanks to the advantages over traditional joining techniques such as: i) ability to join dissimilar materials, ii) stress distribution over a wider area, iii) potentially lower weight. however, joint fabrication procedures and component service loads may introduce or initiate defects, whose evolution will control the performance and the reliability of the bonded joint. in those cases, fracture mechanics (fm) can be used to assess the structural integrity of a bonded joint [1]. the fm approach consists in the comparison of a parameter, function of load and geometry of the cracked body (for example the strain energy release rate, g), with the fracture resistance (gc). the simulation of fracture therefore requires to implement a criterion that triggers propagation when g=gc. an attractive way to simulate the effect of a defect on joint strength is to incorporate a model of the rupture process (i.e. the criterion to trigger propagation). in particular, the fracture of bonded joints has been successfully simulated using the cohesive zone model (czm) in [2-7]. according to this approach, the zone in front of the physical crack tip opens and then tears progressively apart following a given traction-separation behaviour. although straightforward methods to evaluate experimentally czm parameters in adhesive joints have been recently presented [8], questions on the physical meaning or, in other words, on the transferability of the parameters to joint geometries different from the one from they were extracted is still an open issue. in particular, studies have been carried t http://www.gruppofrattura.it http://dx.medra.org/10.3221/igf-esis.10.03&auth=true mailto: alessandro.pirondi@unipr.it a. pirondi, frattura ed integrità strutturale, 10 (2009) 21-28; doi: 10.3221/igf-esis.10.03 22 out about the influence of the thickness of the adhesive layer and of the adherends [9-11] that can be seen also as the evaluation of different degrees of constraint. the constraint effect in homogenous materials is well known to arise from the out-of-plane width and from the in-plane interaction of the crack with the boundaries. in the case of a crack in an adhesive joint, the adhesive layer thickness defines the distance of the boundaries (i.e. the adherends) from the crack tip. the flexibility of the boundaries plays of course also an important role in the constraint imparted to the crack. in a previous work [12], 2d czm analyses were carried out to simulate failure of t-peel bonded joints) with 1.5 and 3mm thick adherends, respectively. a trapezoidal cohesive law was used and a cz was introduced using nonlinear springs. the fracture toughness and load-opening behaviour recorded in experiments on bonded dcb specimens [13] were taken as reference to calibrate czm parameters. this work is aimed at extending those results. the failing interface is modeled with the cohesive elements available in this software. the influence of: i) different cohesive law shapes, ii) modelling the presence of the adhesive layer explicitly, is studied. experimental materials he dcb aluminum adherends (e=70gpa, =0.3) were bonded with loctite 330, a modified methacrilate ester supplied as viscous paste plus activator. loctite 330 is a structural adhesive suitable for bonding of metals, wood, ceramics and plastics. its advantage with respect to other structural adhesives is that it does not require specific surface preparation (only degreasing) and the joint can be handled after five minutes, allowing for higher production rates. shear and tensile strength declared by the supplier are about 20mpa. the tensile behavior of the adhesive was modeled as a power law: e 0 (1) 00n 0 (1bis) where e = 878mpa,  = 4.8mpa, n = 0.44 and  = /e were determined by tensile testing of bulk adhesive [13]. the poisson's ratio was 0.15. the t-peel joints were made of italian standard uni fe 360 unalloyed steel, whose properties are typically e=210gpa, =0.3, u=360mpa, =240mpa. dcb tests the specimen dimensions are shown in fig. 1. a four-step procedure was used for surface preparation of the substrates before bonding: i) polishing with sandpaper, ii) degreasing with acetone, iii) rinsing in hot water, iv) drying. the procedure was applied twice, initially using a coarse sandpaper and then a fine sandpaper. the recommended bondline thickness for multibond 330 ranges between 0.05 to 0.5 mm. in all the experiments reported here, a thickness of 0.25 mm was adopted. bond thickness control during specimen preparation was achieved placing two controlled-thickness copper shims between the adherends (see fig. 1a). a 0.05-mm-thick teflon tape was placed just before bonding at mid-thickness of the adhesive layer to obtain a cohesive crack-like defect. the test were performed after at least a 24-hrs curing at room temperature, that is the minimum time to fully develop the mechanical strength according to the datasheet of the adhesive manufacturer. h h t a w b a0 = 40 mm w = 120 mm h = 15 mm t = 0.3 mm b = 30 mm calibrated shims teflon  figure 1: outline of the dcb joint. t http://www.gruppofrattura.it http://dx.medra.org/10.3221/igf-esis.10.03&auth=true a. pirondi, frattura ed integrità strutturale, 10 (2009) 21-28; doi: 10.3221/igf-esis.10.03 23 to account for the elasticity of the adhesive, the dcb specimen can be modeled as a beam on an elastic foundation, where the foundation modulus, k, will depend on the elastic constants of the adhesive (i.e. ea and a) and on the bondline thickness, t. the solution developed in [14] neglecting shear contributions was therefore considered. the load line compliance is given by the following equation:                  32 ' a a 3 2 a2a21 be t2 p c (2) where e’a=ea/(1-a2) is plane strain modulus of the adhesive and e 'e th 6 ei k4 a 3 4  . the strain energy release rate g is given by 2 222 a 1 1 bei ap a c b2 p g                  (3) for the present dcb specimen the term (a)-1 is about 0.25. t-peel tests a series of tensile tests was conducted at the polytechnic of turin [15] on uni fe360 construction steel t-peel joints (fig. 2). figure 2: outline of half of the 1.5mm-thick t-peel joint tested in [15]. a metal sheet thickness of 1.5mm was investigated. the adhesive used is again the loctite 330. a bondline thickness of 0.1mm was obtained in this case. displacement-controlled tests were conducted up to partial or complete separation of the two halves. modelling fe models he 2d fe models corresponding to dcb and t-peel joints are shown in figs. 3a-b. symmetry conditions with respect to the bondline have been applied. plane stress, eight-noded isoparametric elements have been used to simulate the metal adherend. the cohesive zone has been modelled with the cohesive elements available in the fe code abaqus. a convergence analysis was preliminarly conducted to determine the appropriate element size. the presence of the adhesive layer was either included in the cohesive zone (adherend + cohesive zone, acz) or explicitly modelled with four-noded, hybrid, plane strain elements (adherend + adhesive + cohesive zone, aacz), as done for example in [11]. the number of elements along the thickness of the bond was defined so far according to the indications given in [16]. in the case of the t-peel joint, different extensions of the adhesive layer at the fillet were simulated, since they were not known in detail. t 150 1.5 5 0 20 = = 1 0 8 r5 http://www.gruppofrattura.it http://dx.medra.org/10.3221/igf-esis.10.03&auth=true a. pirondi, frattura ed integrità strutturale, 10 (2009) 21-28; doi: 10.3221/igf-esis.10.03 24 cohesive law three different kind of cohesive laws were accounted for: i) trapezoidal, ii) triangular and iii) exponential as shown qualitatively in fig. 4. the relationship between the parameters of the laws is: i)  0 2 1 1 1 2 m c c c     (4) ii) 0 1 2 m c   (5) iii)  0 1 1 1 1 1 m c e                (6) where c1 = 1/c e c2 = 2/c. the cohesive energy 0 was taken equal to the fracture toughness measured in [11], that is 0 = gic = 550j/m2 in the case of the acz kind of models. the parameters of the different laws were tuned until the peak load of the dcb test was achieved, while keeping also a good correspondance with the overall behaviour. (a) f,  f,  cz or acz (b) f,  f,  cz or acz figure 3: fe model of the dcb (a) and of the t-peel (b) joints. ()   c 1 2 () m figure 4: outline of the cohesive zone traction-separation laws (eqns. 4 6). http://www.gruppofrattura.it http://dx.medra.org/10.3221/igf-esis.10.03&auth=true a. pirondi, frattura ed integrità strutturale, 10 (2009) 21-28; doi: 10.3221/igf-esis.10.03 25 results tuning of cz parameters he first step was the tuning of the dcb-acz model on the related experiment performed in [13]. some parameters were pre-calibrated based on the results shown in a previous work [12]. therefore, a value of m=5mpa was adopted in all of the models and in the case of the trapezoidal law, c1=0.2 and c2=0.5 were taken, as tipically found in the literature. it is visible in fig. 5 that with such a cohesive law the propagation phase is well matched and the peak load is only slightly overestimated, but initial slope is quite different. much better results are obtained instead with a triangular law with c1=0.01. a similar agreement (not shown here for the sake of clarity) was found with the trapezoidal law using c1=0.01 and c2=0.02, in fact an almost triangular law. the exponential law was taken with a 1 equal to the 1 defined for the triangular law in order to keep the same initial slope. anyway, this choice resulted in a lower peak load and a different post-failure trend with respect to the triangular law. specifically, it resembles the results that would be obtained using a lower value of m. all of the following simulation were therefore conducted using the triangular law, which incidentally is also easier to handle. figure 5: tuning of acz model on dcb experiment. the value of m=5mpa outcome from the acz tuning is only a bit higher than the yield strength of the adhesive (4.8mpa). the calibration of aacz parameters was attempted using couples of (0, m) lower and higher than the values obtained for the acz model, respectively, as shown in [11]. anyway, since the value of m=5mpa outcome from the acz tuning is only a bit higher than the yield strength of the adhesive (4.8mpa), plasticity within the adhesive layer is not significant and the aacz model did not significantly differ from the acz. simulation of t-peel tests the simulation of t-peel tests was conducted using an acz model with m=12.5 mpa to take into account the higher adesive layer stiffness of the t-peel joints with respect to the dcb due to the different thickness (i.e. 0.1mm against 0.25mm) and m=20.6 mpa, to take into account also the higher strength when joining steel (t-peel) instead of aluminum (dcb), as described in the technical datasheet of the adhesive. the results shown in fig. 6 in the case of a 1.5mmthick tpeel arm exhibit a good correlation with the experiments in the propagation phase but a very poor match in the loading phase, regarding both the slope and the peak load. on the other hand, it is known [11] that in very thin adhesive layers as in the present case plasticity is strongly confined and due to this, the value of m of an acz model increases with decresing adhesive layer thickness. t http://www.gruppofrattura.it http://dx.medra.org/10.3221/igf-esis.10.03&auth=true a. pirondi, frattura ed integrità strutturale, 10 (2009) 21-28; doi: 10.3221/igf-esis.10.03 26 figure 6: comparison between experiment and t-peel simulations (acz model). the simulations done with the aacz kind of model are shown in fig. 7 in the case of 1.5mm-thick peel arm. the use of the parameters determined from dcb (m=5mpa, 0=550j/m2), where acz and aacz were coincident, resulted in a large difference with the experimental behavior. figure 7: comparison between experiment and t-peel simulations (aacz model). from these analyses, it is evident that cz parameters may not be the same for the nucleation and propagation of a crack. besides discrepancies that may arise between the properties of bulk adhesive and joint, and between different joint geometries due to the bonding process, where adhesive and activator cannot be pre-mixed in a fixed ratio, it has been demonstrated that the tearing process is influenced by the local constraint [11]. therefore, a further analysis has been attempted using aacz modeling where: i) the adhesive was extended at the fillet, with the extension length limited by the maximum adhesive thickness that can be polimerized according to the supplier datasheet; ii) the cohesive strength m has been defined as the value of stress in the adhesive normal to the plane of the joint, at the point in the analysis where the uniaxial failure strain was met locally. the distribution of cohesive strength obtained in this way is shown in fig.8. the results of the simulation with the cohesive law input from fig. 8 and 0=550j/m2 reported in fig. 9 show a neat increase of the agreement with the experiment concerning the phase up to the maximum load, while the crack propagation phase is matched well as in the previous analyses. this fact confirms that the crack propagation may be reproduced quite easily tuning the cz parameters on standard fracture experiments, while the nucleation requires specific http://www.gruppofrattura.it http://dx.medra.org/10.3221/igf-esis.10.03&auth=true a. pirondi, frattura ed integrità strutturale, 10 (2009) 21-28; doi: 10.3221/igf-esis.10.03 27 parameters, possibly dependent on the local stress state. in the specific case of the t-peel test it is important also to know the real fillet dimensions. figure 8: distribution of cohesive strength (aacz model) obtained as the value of stress in the adhesive normal to the plane of the joint, at the point in the analysis where the uniaxial failure strain was met locally. conclusions he fracture of adhesively bonded t-peel joints was simulated using a cohesive zone model. the cz parameters were calibrated on fracture tests conducted on a dcb joint bonded with the same adhesive as the t-peels. the explicit modelling of the adhesive layer (aacz) did not give in this case any significant variation of the parameters with respect to the simpler model where the adhesive was included in the cz behaviour (acz). the t-peel test was simulated first using the set of parameters determined from dcb and the acz approach, after a partial recalibration to account for the different thickness of the bondline and for the different metal joined. the results showed a good agreement between experiments and simulations with respect to the propagation phase but the peak load is underestimated and the stiffness is dependent on the modelling of the adhesive at the arm fillet. the simulation with the aacz approach did not give better results using the same set of parameters. a much better agreement was found using a cohesive strength m defined as the value of stress in the adhesive normal to the plane of the joint, at the point in the analysis where the uniaxial failure strain was met locally. this means that the crack propagation may be reproduced quite easily tuning the cz parameters on standard fracture experiments, while the nucleation requires specific parameters, possibly dependent on the local stress state. acknowledgements he author gratefully acknowledge prof. m. rossetto, polytechnic of turin, italy, for the experimental data of tpeel joints. references [1] a. j. kinloch, , adhesion and adhesives, chapman and hall, london, uk, (1986). [2] j. w. hutchinson, a. g. evans, acta mater., 48 (2000) 125. [3] i. mohammed, k.m. liechti, j. mech. phys. solids, 48 (2000) 735. [4] q.d. yang, m.d.thouless, s.m. ward, j. mech. phys. solids, 47 (1999) 1337. [5] w. g. knauss, g. u. losi, j. appl. mech., 60 (1993) 793. [6] h. hadavinia, a.j. kinloch, j.g. williams, in adv. in fract. and damage mech. ii, m. guagliano and m.h. aliabadi eds., hoggar, geneva, (2001) 445. [7] b. f. sorensen, acta mater., 50 (2002) 1053. [8] b. f. sorensen, t. k. jacobsen, eng. fract. mech., 70 (2003) 1841. t t http://www.gruppofrattura.it http://dx.medra.org/10.3221/igf-esis.10.03&auth=true a. pirondi, frattura ed integrità strutturale, 10 (2009) 21-28; doi: 10.3221/igf-esis.10.03 28 [9] i. georgiou, h. hadavinia, a. ivankovic, a. j. kinloch, v. tropsa, j. g. williams, j. adhesion, 79 (2003) 239. [10] b. r. k. blackman, h. hadavinia, a. j. kinloch, j. g. williams, int. j. fract., 119 (2003) 25. [11] t. pardoen, t. ferracin, c. m. landis, f. delannay, j. mech. phys. solids, 53 (2005) 1951. [12] a. pirondi, proc. ecf 15, stockolm, sweden (2004). [13] a. pirondi, g.nicoletto, proc. igf 2000, bari, italy, (2000). [14] s. krenk, , eng. fract. mech., 43-4 (1992) 549. [15] m. rossetto, private communication, polytechnic of turin, turin, italy (2003). [16] k. s. madhusudhana, r. narashiman, eng. fract. mech., 69 (2002) 865. http://www.gruppofrattura.it http://dx.medra.org/10.3221/igf-esis.10.03&auth=true microsoft word numero_56_art_05_2949 a. g. joshi et alii, frattura ed integrità strutturale, 56 (2021) 65-73; doi: 10.3221/igf-esis.56.05 65 investigation on influence of sicp on three-body abrasive wear behaviour of glass/epoxy composites ajith g. joshi dept. of mechanical engineering, canara engineering college, benjanapadavu, mangalore-574219, karnataka, india ajith.joshi.mech@gmail.com s. basavarajappa, s. ellangovan, b.m. jayakumar university b.d.t. college of engineering, davangere -577004, karnataka, india basavarajappas@yahoo.com, ellangovan18@gmail.com, jaikmrbm@gmail.com abstract. the study presents the influence of sicp incorporation on threebody abrasive wear behaviour of glass/epoxy composites. the investigation was carried out using dry sand rubber wheel abrasive wear test apparatus. 2k factorial design of experiments was used to capture the experimental data. the parameters considered are abrading distance, load and speed. the wear rate was found to increase with the increasing values of wear parameters. the applied load has exhibited significant effect on wear rate. incorporation of sicp contributed to enhance wear resistance of glass/epoxy composites. the linear regression was also presented in the study to correlate abrasion parameters with wear rate. sem image analysis of abraded surface revealed the occurrence of ploughing, micro-cutting, matrix removal and fiber breakage. keywords. polymer matrix composites; wear; statistical model; scanning electron microscopy. citation: joshi, a. g., basavarajappa, s., ellangovan, s., jayakumar, b.m..investigation on influence of sicp on three-body abrasive wear behaviour of glass/epoxy composites, frattura ed integrità strutturale, 56 (2021) 6573. received: 09.11.2020 accepted: 06.02.2021 published: 01.04.2021 copyright: © 2020 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. introduction olymer matrix composites (pmcs) are gaining popularity in many engineering applications like chute liners, gears, abrasive pumps, cams, bearings, bushes, bearing cages and other structural applications because of good mechanical and tribological characteristics. abrasive wear plays a vital role in industrial applications like power plant chute liner, mining and earthmoving equipment [1]. the sliding of forced irregularly shaped hard particles against the soft matrix materials causes abrasive wear, which lead to severe damage and removal of the material by ploughing and rubbing mechanisms [2, 3]. during three-body abrasion, abrading medium is entrapped between two bodies which having relative motion between them. the asperities are free to roll and slide. besides with the application of load, abrasive particles penetrate and detach material from the soft surface and produce crater. abrasive particles size, sliding velocity, abrading distance and applied load are important parameters which highly effect the abrasion characteristic of pmcs [2]. abrasive wear resistance increases with the increased fiber volume fraction of pmcs. further, abrasive wear resistance improves with the increase in the modulus of the reinforced fibers almost linearly and polymer matrices within optimal range of volume fraction [4, 5]. wear p https://youtu.be/c1ehomsqn78 a. g. joshi et alii, frattura ed integrità strutturale, 56 (2021) 65-73; doi: 10.3221/igf-esis.56.05 66 behaviour also depends on the orientation of fibers in the composites; fibers perpendicular to the sliding surface presents less abrasion [6]. lee et al. [7] presented physical model for the two-body abrasive wear characteristic of composite materials. the model explains the abrasive wear mechanism possible in two-dimensional with reinforcement effect, but it has a limitation in explaining the mechanism possible in three dimensions. torrance [8] presented a model for the two-body abrasive wear with progress approaching towards real process and concluded that a further development is needed to improve existing models to approach real process. bijwe et al. [6] has reported that the aramid fiber reinforced polyetherimide exhibited good abrasive wear resistance, whereas carbon and glass fibers reinforcement show satisfactory results. vasconcelos et al. [9] studied both reciprocating and abrasive wear of epoxy-based composites and concluded that wear rate decreases with increasing aluminum powder reinforcement, also as a result of reinforcement of carbon and glass fiber. sakthivel et al. [10] presented the work on three body abrasive wear behaviour of sansevieria cylindrica fiber (scf) and e-glass fiber (egf) reinforced polyester (pr) composites. the composite containing 30% scf, 20% egf and 50% pr by weight fraction revealed better wear resistance compared to other studied composite specimens. zhang et al. [11] stated that the wear loss and wear rate of alkali-treated eucalyptus/pvc composites due to three-body abrasion has relatively decreased in comparison to natural eucalyptus fiber. further, micro-cutting and micro-indentations were prominent wear mechanisms of studied materials. addition of fillers into the polymer matrix composites enhances its desired characteristics. cenna et al. [12] concluded that the incorporation of ultra-high-molecular-weight polyethylene (uhmpe) particles in pmcs decreases the wear loss due to abrasion. prehn et al. [13] demonstrated that addition of sicp particles has a positive effect compared to neat peek and epoxy resin material toward enhancement of abrasive wear resistance. suresh and chandramohan [3] reported that the sicp filled composites showed better wear resistance. also, they have illustrated that the graphite filled composites were observed to be not very beneficial. rudresh et al. [14] noticed that pa66/ptfe/short glass fiber composites possess better abrasion resistance. enhanced fracture energy and hardness of composites governed their wear resistance characteristics. suresha et al. [15] investigated the three-body abrasive wear behaviour of high-density polyethylene (hdpe)/ uhmpe composites reinforced with glass fiber and zirconia (zro2). they have also demonstrated that specific wear rate increases with increase in filler/fiber content of composites. jesthi and nayak [16] presented a mathematical model to predict the specific wear rate. the micro-cutting, micro-ploughing and fiber breaking were dominant wear mechanisms of composites. sahin [17] and mondal et al [18] has reported that 2k factorial design of experiments can be employed for describing the abrasive wear behaviour of composites. sahin [17] has employed 23 factorial design of experiments where 3 corresponding to abrading distance, applied load and abrasive size. mondal et. al [18] have employed 22 factorial design of experiments, k=2 corresponding to abrasive particle size and applied load. further, it was inferred from the studied that, factorial design of experiments is useful for establishing the linear relationship to predict the wear behaviour within the selected experimental conditions. the design of experiments by taguchi approach can be adopted successfully to analyze the friction and wear behaviour of composites [19-21]. hemant et al. [22] employ l9 taguchi orthogonal array to study abrasive wear behaviour of hexagonal boron nitride incorporated polyetherketone (pek) composites. the study shown that filler incorporation diminished the wear resistance of pek material under three-body abrasion due to reduction in hardness and impact strength. the retrospection on available literature revealed that the presence of scope for to studying the three-body abrasive wear behaviour of pmcs with varied sicp filler. thus, the current research pays attention on the investigation of three-body abrasive wear behaviour of glass/epoxy composites with varied volume fraction of sicp filler using factorial design of experiments. experimentation materials he medium viscosity epoxy was used as matrix with trade mark of lapox l-12. the curing agent used in the study is polyamine hardener k-6. the reinforcement used was 7-mil e-glass fiber. sicp passed through 400 mesh sieves was used as filler material, since it is hardest and is expected to the improve the abrasive wear resistance of composites. the hand lay-up technique was used to produce specimen as per details provided in tab. 1. the composite laminates were prepared as reported by basavarajappa et al. [23]. the cured laminates were cut to obtain desired specimen of size 76mm×25mm×3mm as per astm g 65 standards [24]. the details of the composite specimens prepared and char tested are given in tab. 1. t a. g. joshi et alii, frattura ed integrità strutturale, 56 (2021) 65-73; doi: 10.3221/igf-esis.56.05 67 matrix volume% reinforcement volume% filler volume% epoxy 50 glass fiber 50 -- epoxy 45 glass fiber 50 sicp 5 epoxy 40 glass fiber 50 sicp 10 epoxy 35 glass fiber 50 sicp 15 table 1. details of samples prepared. plan of experiments the 2k factorial design of experiment was employed in current research, where ‘k’ denotes number of parameters and ‘2’ denotes number of levels. the parameters considered were abrading distance, load and speed. the 2k factorial design of experiments can be successfully employed to capture the experimental data in systematic manner. also, it aids to establish relationship between experimental parameters with responses [17, 18]. eight experimental runs were repeated twice and average reading was analyzed alike in reported literatures [17, 23]. the experiments were conducted as per the experimental design given in each row and corresponding uncoded values of parameters are illustrated in first 3 columns of tab. 3. the regression model of obtained result is expressed as         0 1 2 3 4 5 6 7w a a x a y a z a xy a yz a xz a xyz (1) where w is the wear rate, a0 is the response parameter of wear at base level, with a1, a2 and a3 are correspondingly coefficients of load, speed and abrading distance. abrasive wear three-body abrasive wear experiments were performed on dry sand rubber wheel abrasive wear test (rwat) rig to study the abrasive wear behaviour of composites. the test set up and experiment was conducted according to astm g 65 standards. three-body abrasive wear experiments were performed on dry sand rubber wheel abrasive wear test (rwat) rig in accordance with astm g 65. the chlorobutyl rubber wheel and quartz abrasive particles with approximately 200µm size were employed in experimentation. the flow of abrading particles was attained between rotating wheel and specimen at 372 g/min and the wheel was rotated at desired speed (75rpm and 100rpm). the specimens were cleaned using acetone, the initial and final mass loss were measured with the help of digital balance with an accuracy of 0.1mg. the mass loss was then converted into wear rate using measured density data. further, applied load and abrading distance were varied at two levels viz. 75n and 100n load and 75m and 100m distance respectively. trial no. sliding speed (rpm) abrading distance (m) applied load (n) wear rate (×10-6 mm3/n-m) g-e g-e+ 5%sicp g-e+ 10%sicp g-e+ 15%sicp 1 75 75 75 66.916 49.582 42.951 40.018 2 100 75 75 75.573 62.151 56.622 52.284 3 75 100 75 64.973 50.773 45.320 42.507 4 100 100 75 77.320 54.413 52.093 48.493 5 75 75 100 73.680 52.573 48.093 46.413 6 100 75 100 87.120 56.227 51.667 49.173 7 75 100 100 71.150 45.390 41.680 39.710 8 100 100 100 78.050 47.710 43.290 41.380 table 2: experimental results. result and discussion hree-body abrasive wear behaviour of glass/epoxy composites was investigated with the aim to correlate load, speed and abrading distance with wear loss due to abrasion of composite. the experiments are conducted as per 23 factorial design of experiments. the experiments are repeated twice and average values are considered for the analysis and are shown in tab. 2. t a. g. joshi et alii, frattura ed integrità strutturale, 56 (2021) 65-73; doi: 10.3221/igf-esis.56.05 68 the linear regression model was developed using minitab – r15. the linear regression models are presented as eq. (2) to (5) respectively representing wear equation of unfilled, 5% sicp, 10% sicp and 15% sicp filled glass-epoxy composites.                0 0.537 0.00488 0.00325 0.00027s 0.000016 l d 0.000023 l s 0.000010 d sw l d r-sq. =99.5% r-sq.(adj.)=96.3% (2)                5  1.12 0.00979 0.00926 0.00814s 0.000036 l d 0.000038 l s 0.000038 d sw l d r-sq. =99.3% r-sq.(adj.)=95% (3)                10  1.49 0.0138 0.0109 0.0102s 0.00006 l d 0.000064 l s 0.000034 d sw l d r-sq. =99.8% r-sq.(adj.)=98.6% (4)                15  1.37 0.0135 0.00939 0.00883s 0.000055 l d 0.000061 l s 0.000022 d sw l d r-sq. =99.8% r-sq.(adj.)=98.6% (5) wwhere w0, w5, w10 and w15 represents the wear rate of the composites with unfilled, incorporated with 5%, 10% and 15% sicp respectively. the terms l, s and d represents the applied load, speed and abrading distance parameters. the coefficients of load, abrading distance and speed in the eqns. (2) to (5) are positive, suggesting increased wear rate with increasing values of parameters. the r-sq value indicates the coefficient of determination of respective regression model. the obtained r-sq values for all regression models are above 0.98. it confirms that obtained models give good results within the experimental conditions ranging from 75rpm to 100rpm of sliding speed, 75m to 100m of abrading distance and 75n to 100n load. the constant values of model for unfilled and sicp filled g-e composites are negative. the a0 represents the point of intercept of regression plane and is a mean response value of experimental trials carried out [25 27]. it depends mainly on the important parameters considered in this study and also associated with experimental abnormalities like environmental conditions, machine vibrations, so on. the values of a0 and experimental results illustrates that sicp filled g-e composites have better wear resistance than the unfilled g-e composites. the abrasive wear resistance increases with the increase in the filler volume fraction equal to 10%. further increase in filler volume fraction has not found much effect on the abrasive wear resistance of the composites and there may be chances of detrimental effect. the positive values of the coefficients of load, abrading distance and speed reveal that wear rate increases with increase in the associated parameter. the negative value of coefficients suggests an opposite effect. from the eq. (2)-(5), it is observed that applied load, abrading distance and sliding speed has more effect on the abrasive wear of the composites. however, interaction among the parameters is not statistically significant. the coefficients of associated parameter for applied load possess highest magnitude; it demonstrates that applied load has greater significance followed by abrading distance and least significance was found to sliding speed. hence, wear rate of the composites increases with the increase in applied load and abrading distance and slightly lower for sliding speed in the range of parameters considered in the study. while load is applied on the specimen, it induces high stress on the counterface of the rubber wheel and concurrently stress is transferred to abrading particles. the free-flowing abrasive particles penetrate into soft matrix material, which produces groove. the penetrated abrasive particles execute ploughing of matrix layer, later performs microcutting of high modulus glass fibers. however, the depth of the penetration of abrading medium is subjected to various parameters such as abrasive type, size and hardness of abrasive particles, load environment and matrix material hardness [13]. as a result, greater wear rate of the material is due to the abrasive wear. the increase in sliding distance increases the encounter of specimen surface with abrasive particles and the rubber wheel. successively more stress is transferred from rubber wheel to the abrasive particles. thus, depth of groove increases with the increase in sliding distance. as the sliding speed increases, sliding abrasive particles generates heat at the counterface of rubber wheel and composite which softens the matrix layer. further increase in speed helps the abrasive particle to plough matrix material from the surface. instantaneously glass fibers are subjected to microcutting and however, glass fibers withstand for the increased temperature. in pmcs the penetration of abrasive particles mainly depends on hardness of the surface and on later the modulus of the glass fibers. the plastic deformation of matrix is low and hence less energy is required to plough the matrix layer. the maximum energy is spent during the later stages for microploughing and microcutting of glass fibers. in the presence of sicp filler, the penetration of abrasive particles into matrix is reduced because of the increased hardness. due to continuous abrasion, the abrasive particles penetration is resisted by the incorporated filler materials, thus increases a. g. joshi et alii, frattura ed integrità strutturale, 56 (2021) 65-73; doi: 10.3221/igf-esis.56.05 69 the abrasive wear resistance of the composites. further wear resistance is increased by increasing the filler volume fraction, thus decreases the wear rate of the composite due to wear. the increase in sicp content further would lead to decrease in crosslinking density of the epoxy polymer, thus interfacial bonding strength decreases. the agglomeration of the matrix takes place due to poor adhesion, subsequently filler particles comes out easily [28]. the loose abrasive particles convene with the pulled-out filler particles and together acts as abrasive particles. the increased wear resistance is sufficient for the abrasion of these particles. hence less difference in wear rate was observed between the 10% and 15% filler content specimens. hu et al. [29] reported that increase in volume fraction of reinforcement enhance the wear resistance of the composite. however, there is a critical volume fraction above which the resistance offered by composites decreases. similarly, in the current study there was a critical volume fraction of filler above which relatively less improvement in the abrasive wear resistance was observed. besides, higher sicp content in the matrix forms more interfaces that acts as weak points. it contributes for ploughing of composites and pullout of fibers. hence, it can be concluded that an increase of sicp content in composites has improved its abrasive wear resistance till 10% while a further increase in sicp has not found to be relatively lucrative. the evaluation of the equations was done by conducting the confirmation test. tab. 3 shows experimental conditions used in the confirmation tests and predicted values by the modeled developed and experimental results. the comparison of results obtained from the experiments and the models in eqns. (2) to (5) shows a good agreement with deviation within 5%. hence, eqns. (2) to (5) are demonstrated as feasible within the experimental conditions as similarly stated by previous literatures [12-14, 18-20]. composite applied load (n) abrading distance (m) sliding speed (rpm) wear rate (mm3/n-m) (from expt.) wear rate (mm3/n-m) (from eqn.) %age of error g – e 87.5 87.5 87.5 74.86171 74.66094 0.27 g–e–5%sicp 87.5 87.5 87.5 52.4578 52.38125 0.15 g–e–10%sicp 87.5 87.5 87.5 46.24457 47.73125 3.21 g–e–15%sicp 87.5 87.5 87.5 45.57584 44.8875 1.51 table 3: comparison of obtained results with the experimental results. worn surface morphology n order to investigate the abrasive wear mechanism for filled and unfilled g-e composites, the worn out surfaces at different wear regions were examined using sem. the direction of abrasive particles flow from the upside to the bottom side as depicted in fig. 1. fig. 2(a) depicts the sem features of worn out surface taken at upside of the specimen at low magnification for unfilled ge composite. it indicates that the matrix has relatively greater damage when compared to the glass fibers at upside as same as the bottom side. it perhaps, upside of the specimen is subjected to large contact stress resulting in severe peeling off and damages. the magnified worn microstructure (fig. 2b and c) evinced the occurrence of macro cutting, fiber breakage, matrix removal and ploughing of fibers under compression and shear stress. similar observations were made by suresh et al. [30]. the fibers were fractured into small fragments by the hard-abrasive particles, which were plough out during further abrasion leading to high wear. on the central area of worn surface, the hard asperities have penetrated into the depth of specimen causing the deep craters. in addition, matrix removal phenomenon demonstrated the characteristic of steady state wear. fig. 3(a) has also revealed the formation of many pits attributed to the micro-ploughing action of abrasive particles and pull-out of fibers with larger diameter craters. extensive debris formation with large number of broken fibers were clearly observed through closer inspection (fig. 3b and c). the well dispersion of matrix material was illustrated in fig. 3. on contrary, the worn surface of the bottom side of the specimen is smooth; pulling-out and exposure of the glass fibers are nearly invisible (fig. 4a). at higher magnification (fig. 4b and c), the worn surface was evinced relatively with lesser matrix and fiber removal; associated with phenomenon of more abrasive particle around the fibers. harsha et al. [31] reported that worn surface morphology at the entrance and exit zone were similar and uniform. it was perhaps due to the low pressure applied on abrasives, resulting in rolling action of abrasives instead of penetration or ploughing. i a. g. joshi et alii, frattura ed integrità strutturale, 56 (2021) 65-73; doi: 10.3221/igf-esis.56.05 70 figure 1: schematic diagram of different worn region in abrasive wear figure 2: sem image of unfilled ge composite upside region (a) low magnification, (b) moderate magnification, (c) high magnification. figure 3: sem image of unfilled ge composite central region (a) low magnification, (b) moderate magnification, (c) high magnification. figure 4: sem image of unfilled ge composite bottom region (a) low magnification, (b) moderate magnification, (c) high magnification a. g. joshi et alii, frattura ed integrità strutturale, 56 (2021) 65-73; doi: 10.3221/igf-esis.56.05 71 figure 5: sem image of sicp filled ge composite upside region (a) moderate magnification, (b) high magnification. figure 6: sem image of sicp filled ge composite central region (a) low magnification, (b) moderate magnification, (c) high magnification. figure 7: sem image of sicp filled ge composite bottom region (a) low magnification, (b) moderate magnification, (c) high magnification. the extent of damage to the matrix and fiber was relatively less in sicp filled ge composite compared to unfilled ge composite under similar experimental conditions. worn surface of sicp filled ge composite depicted distinct worn morphologies relative to unfilled ge composite. at low magnification (fig. 5a), worn surface illustrates the occurrence of severe ploughing, cutting action by abrasives. while, wear pattern has revealed that the circumstance associated with relatively reduced particle rolling. perhaps, abrasion particles tend towards sliding instead of rolling. substantially, it indicates that dominant wear regime begin to shift from macro cutting of fibers and debris to micro cutting of fibers and fine debris. although, the surface of filler incorporated composite shown highly damaged regions and ruptured fibers (fig. 5b); the resistance to material removal from its subsurface was enhanced. thus, material pull-out and ploughing due to abrasives penetration was reduced. the worn surface at central region demonstrated less damage to matrix and fibers as shown in fig. 6a. this is due to incorporated hard sicp particles present along with matrix on surface of the composite specimen, which acts as antiwear additive, hence retarded the wear loss. the matrix phase around the sicp particles has evidently worn out with sicp particles (fig. 6b). as a result, substantial sicp particles at this region were exposed directly to abrasives. a. g. joshi et alii, frattura ed integrità strutturale, 56 (2021) 65-73; doi: 10.3221/igf-esis.56.05 72 later, the removal of sicp particles occurs followed by subsequent pulling out of abrasive particles. few craters were also noticed on the worn surface, possibly formed due to the dislodging of sicp particles. at higher magnification (fig. 6c), worn surface pronounced with a distinct evidence of fiber breakage and, also damage to the epoxy resin matrix with sicp particles protruding action. fig. 7a depicts the additionally stepped appearance of glass fibers aided with ploughing marks on the surface, and inclined fracture end of fibers. besides, at higher magnification significant amount of loose wear debris were seen on the surface and filler matrix debonding were also observed (fig. 7b and c). however, it might not have occurred as easily in the case of unfilled ge composite. the wear loss of unfilled ge composite is greater than sicp filler incorporated ge composites. it may be due to the exposure of soft matrix to abrasion. the ge composite exhibited severe matrix wear at the beginning of abrasion. further, hard abrasive particles were in contact with matrix which is softer in nature leading to severe matrix damage, as a consequence wear loss was greater. the improvement in wear resistance of ge composite filled with sicp particles could be attributed to the ability of sicp particles to undertake greater contact stress, as well as to protect the glass fiber from being gouged out during the wear process. conclusions n experimental study of the abrasive wear behaviour of unfilled and filled ge composites was evaluated. the inclusion of sicp filler in the ge composite has significant potential for improving the abrasive wear resistance. further, the study suggests that, applied load and abrading distance are the main factors which are affecting the abrasive wear of composites. the increase of sicp content in composites has improved its abrasive wear resistance till 10%, further increase in sicp has not found to be relatively lucrative. an examination of worn surface morphology suggested that the abrasive wear behaviour of filled and unfilled ge composites was dominated by ploughing, microcutting, matrix removal and fiber breakage. references [1] liu, r., li, d. y. (2001) modification of archard’s equation by taking account of elastic/ pseudoelastic properties of materials, wear, 251, pp. 956-964. doi: 10.1016/s0043-1648(01)00711-6. [2] xian, j., ruofei, l. (2007) two-body free-abrasive wear of polyethylene, nylon1010, epoxy and polyurethane coatings, tribology international, 40, pp. 1276–1283. doi: 10.1016/j.triboint.2007.02.013. [3] suresha, b., chandramohan, g. (2008) three-body abrasive wear behaviour of particulate-filled glass–vinyl ester composites, j. mat. proc. tech., 200, pp. 306-311. doi: 10.1016/j.jmatprotec.2007.09.035. [4] bijwe, j., awtade, s., ghosh ,a. (2006) influence of orientation and volume fraction of aramid fabric on abrasive wear performance of polyethersulfone composites, wear, 260, pp. 401-411. doi: 10.1016/j.wear.2005.02.087. [5] chand, n., ajay, n., somit, n. (2000) three-body abrasive wear of short glass fibre polyester composite, wear, 242, pp. 38–46. doi: 10.1016/s0043-1648(00)00398-7. [6] bijwe, j., indumathi, j., ghosh, a. k. (2002) on the abrasive wear behaviour of fabric-reinforced polyetherimide composites, wear, 253, pp. 768–777. doi: 10.1016/s0043-1648(02)00169-2. [7] gun, y. l., dharan, c. k.. h, ritchie, r. o. (2002) a physically-based abrasive wear model for composite materials, wear, 252, pp. 322–331. doi: 10.1016/s0043-1648(01)00896-1. [8] torrance, a. a. (2005) modelling abrasive wear, wear, 258, pp. 281–293. doi: 10.1016/j.wear.2004.09.065. [9] pedro, v. v., jorge, l. f., baptista, a. m., neto, r. j. l. (2006) tribological behaviour of epoxy-based composites for rapid tooling, wear, 260, pp. 30–39. doi: 10.1016/j.wear.2004.12.030. [10] sakthivel, m., srinivasan, k., kumar, a. g. g. (2019). wear behaviour of sansevieria cylindrica and e-glass reinforced polyester composites, materials testing, 61(3), pp. 239-242. [11] zhang, k., cui, y., yan, w., (2019).thermal and three-body abrasion behaviours of alkali-treated eucalyptus fiber reinforced polyvinyl chloride composites, bioresources, 14(1). [12] cenna, a. a., allen, s., page, n.w., dastoor, p. (2001) a polyethylene-reinforced polymer composite abraded by bulk solids, wear, 249, pp. 663-671. doi: 10.1016/s0043-1648(01)00691-3, [13] prehn, r., haupert, f., friedrich, k. (2005) sliding wear performance of polymer composites under abrasive and water lubricated conditions for pump applications, wear, 259, pp. 693–696. a a. g. joshi et alii, frattura ed integrità strutturale, 56 (2021) 65-73; doi: 10.3221/igf-esis.56.05 73 [14] rudresh, b. m., ravikumar, b. n., madhu, d., lingesh, b. v., (2019). three body abrasive wear behaviour of glassbasalt pa66/ptfe hybrid composites in multi pass condition, tribology in industry. 41(3), pp. 416-425, [15] suresha, b., sriraksha, hemanth, r. (2020). mechanical performance of hdpe/uhmwpe hybrid composites and tribological characterization using taguchi method, materials today: proceedings, 24(2), pp. 1452-1461. [16] jesthi, d. k. and nayak, r. k. (2020). influence of glass/carbon fiber stacking sequence on mechanical and three-body abrasive wear resistance of hybrid composite mater. res. express, 7, 015106, [17] sahin, y. (2003) wear behaviour of aluminium alloy and its composites reinforced by sic particles using statistical analysis, materials and design, 24, pp. 95–103. doi: 10.1016/s0261-3069(02)00143-7, [18] mondal, d. p., das, s., jha, a. k., yegneswaran, a. h. (1998) abrasive wear of al alloy–al2o3 particle composite: a study on the combined effect of load and size of abrasive, wear, 223, pp. 131–148. doi: 10.1016/s0043-1648(98)00278-6, [19] cho, m. h., bahadur, s., pogosian, (2005) friction and wear studies using taguchi method on polyphenylene sulfide filled with a complex mixture of mos2, al2o3, and other compounds, wear, 258, pp. 1825-235. doi: 10.1016/j.wear.2004.12.017, [20] davim, p. j., marques, n. (2004) dynamical experimental study of friction and wear behaviour of bovine cancellous bone sliding against a metallic counterface in a water lubricated environment, j. mat. proc. tech., 152, pp. 389–394. doi: 10.1016/j.jmatprotec.2004.04.420, [21] basavarajappa, s., chandramohan, g. (2006) dry sliding wear behaviour of metal matrix composites: a statistical approach, j. mat. engg. perf., 15, pp. 656-660. doi: 10.1361/105994906x150731, [22] hemanth, g., suresha, b., hemanth, r. (2019). the effect of hexagonal boron nitride on wear resistance under two and three-body abrasion modes of polyetherketone composites, surface topography: metrology and properties, 7(4), 045019. [23] basavarajappa, s., ellangovan, s., arun, k. v. (2009). studies on dry sliding wear behaviour of graphite filled glassepoxy composites, materials and design, 30, pp. 2670-2675. doi: 10.1361/105994906x150731, [24] american society of testing and materials (2004), standard method for measuring abrasion using the dry sand/rubber wheel apparatus, g65, 3.02, pp. 1–12. [25] montgomery, d.c. (1997) design and analysis of experiments, john wiley & sons. [26] sahin, y. (2005) the prediction of wear resistance model for the metal matrix composites, wear, 258, pp. 1717-1722. doi: 10.1016/j.wear.2004.11.024. [27] stachowiak, g. b., stachowiak, g. w. (2001) the effects of particle characteristics on three-body abrasive wear, wear, 249, pp. 201–207. doi: 10.1016/s0043-1648(01)00557-9. [28] suresha, b., chandramohan, g., abraham jawahar m, mohanraj s. (2009) three-body abrasive wear behaviour of filled epoxy composite systems, j. reinf. plast. comp., 28, pp. 225-233. doi: 10.1177/0731684407084247. [29] hu, j., li, d. y., llewellyn, r. (2005) computational investigation of microstructural effects on abrasive wear of composite materials, wear, 259, pp. 6–17. doi: 10.1016/j.wear.2005.02.017. [30] suresha, b., chandramohan, g., samapthkumaran, p., seetharamu, s. (2007) three-body abrasive wear behaviour of carbon and glass fiber reinforced epoxy composites, mat. sci. engg. a., 443, pp. 285–91. doi: 10.1016/j.msea.2006.09.016. [31] harsha, a. p., tewari, u. s., venkatraman, b. (2003) three-body abrasive wear behaviour of polyaryletherketone composites, wear, 254, pp. 680–692. microsoft word numero_42_art_3.doc d. rozumek et alii, frattura ed integrità strutturale, 42 (2017) 23-29; doi: 10.3221/igf-esis.42.03 23 focused on mechanical fatigue of metals fatigue crack growth in 2017a-t4 alloy subjected to proportional bending with torsion d. rozumek, s. faszynka opole university of technology d.rozumek@po.opole.pl, sebastian.faszynka@op.pl abstract. the paper presents the results of tests on the fatigue crack growth for a constant moment amplitude under combined bending with torsion in the aluminium alloy aw-2017a-t4. the tests were performed under different values of the load ratio r. plane specimens with stress concentrators in form of the external one-sided sharp notch were tested. a non-uniform fatigue cracks growth on both lateral surfaces of specimens was observed during experimental tests. fatigue cracks were developing in the specimens in two stages; quarter-elliptic edge cracks were observed at the beginning, then evolving into through cracks. keywords. fatigue crack growth; load ratio; notch; bending with torsion. citation: rozumek, d., faszynka, s., fatigue crack growth in 2017a-t4 alloy subjected to proportional bending with torsion, frattura ed integrità strutturale, 42 (2017) 23-29. received: 31.05.2017 accepted: 07.06.2017 published: 01.10.2017 copyright: © 2017 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. introduction atigue of materials, especially formation of fatigue cracks and their growth belong to the most important problems of solid mechanics, and they have been intensely investigated for many years [1, 2]. these phenomena are extremely important, because they damage components of machines, and in many cases they cause disasters. descriptions of fatigue crack growth under bending with torsion of elements with rectangular cross sections are rarely discussed in the literature. reason behind this is that such elements are less widely used in the industry. in the literature can be found various problems of fatigue crack growth for simple load conditions, such as: tension, torsion or bending [36], as well as for complex load conditions, including: tension with torsion [7], bending with torsion [8], and others [9-11]. the paper [12] the authors described propagation of short cracks and fatigue cracks within threshold range on specimens under three-point bending, during which the researchers initiated crack plane at a certain angle towards bending plane. that allowed obtaining combination of normal and shearing stresses in the crack tip. in ref. [13] presented three-point cyclic bending of specimens with slits for mixed modes i and iii in threshold cracking range. while the performed tests of steel specimens domination of mode i was expected. at the initial stage, changes of mode i were observed, next a fluent rotation of the crack front occurred up to the moment of its perpendicular positioning to the specimen side. the aim of the paper is to describe fatigue cracks growth in specimens with rectangular cross-section made of the aw2017a-t4 aluminium alloy under bending with torsion. f d. rozumek et alii, frattura ed integrità strutturale, 42 (2017) 23-29; doi: 10.3221/igf-esis.42.03 24 experimental procedure material and specimen pecimens with rectangular cross-section and gross size 8 x 10 mm were used in fatigue tests. the specimens were made of the aw-2017a-t4 aluminium alloy and described in the standard pn-en 573 of 1997. mechanical properties of the material are given in tab. 1. the specimens were made of a extruded bar 16 mm in diameter. y (mpa) u (mpa) e (gpa)  382 480 72 0.32 table 1: mechanical properties of the aw-2017a-t4 aluminum alloy. the specimens had an external, unilateral notch, which was a0 = 2 mm long and its radius was  = 0.2 mm (fig. 1). the notches in the specimens were cut with a milling cutter and their surfaces were polished on abrasive paper with decreasing gradation. the theoretical stress concentration factor in the specimen under bending kt = 3.76 was estimated according to ref. [14]. figure 1: shape and dimensions of specimen (in mm). alloys of aluminium with copper and magnesium, that is duralumin, belong to alloys characterised by supreme strength properties. elements of such shape are used, among others, in cars (by renault co.), trucks and tanks (attaching springs) as torsion bars, and as indirect beams used in drilling for oil and natural gas. fig. 2 shows a microstructure of the aw2017a-t4 aluminium alloy. the microstructure heavily dominated by elongated grains of the solid solution α of various sizes, and a width of about 50 μm. between large elongated grains are also visible cluster very small equiaxed α phase grains in the system band. on a background of solid solution α, there are many precipitation of intermetallic phases, particularly al2cu, as well as mg2si, alcumg. precipitations phase al2cu occur mainly in the chain system on grain boundaries of the solid solution, and their size does not exceed 5 mm [15]. figure 2: microstructure of the aw-2017a-t4 aluminum alloy. s d. rozumek et alii, frattura ed integrità strutturale, 42 (2017) 23-29; doi: 10.3221/igf-esis.42.03 25 fatigue tests the test results of fatigue crack growth under proportional bending with torsion were obtained at the laboratory in department of mechanics and machine design in opole university of technology. the tests were performed on the fatigue test stand mzgs – 100 [16, 17], which allows to perform cyclic bending, torsion and synchronous bending with torsion. the tests were conducted under controlled force (in the considered case, the amplitude of bending moment was controlled) with the loading frequency 28.4 hz. the bending with torsion moment was generated by force on the arm 0.2 m in length. fatigue tests were performed in the low cycle fatigue (lcf) and high cycle fatigue regime (hcf). unilaterally restrained specimens were performed with the constant amplitude of moments ma = 7.92 nm and load ratio r = mmin / mmax = 1, 0. the shear stress at the specimen coming from bending takes very small values, below 3% of the maximum applied bending stress and it is neglected in further considerations. in fig. 3 m(t) is the ratio of torsion moment to bending moment was mt(t) / mb(t) = tan = 1. proportional bending with torsion were obtained by rotation of the head by angle  = 45° (see fig. 3). pure bending takes place when the  angle is 0°, and for the  angle 90° we have torsion. figure 3: loading of the specimen under proportional bending with torsion. fatigue crack growth on the specimen lateral surfaces – “a” (active side) and “a*” (passive side) and upper surface “c” (fig. 4) was observed with the portable optical microscope with magnification of 20 times. the fatigue crack increments were measured with the micrometer of accuracy up to 0.01 mm with the corresponding number of loading cycles n. figure 4: crack growth under proportional bending with torsion. experimental results and discussion non-uniform fatigue cracks growth on both lateral surfaces of specimens was observed during experimental tests. fatigue cracks were developing in the specimens in two stages; quarter-elliptic edge cracks were observed first, then evolving into through cracks. experimental test results for proportional bending with torsion are shown as diagrams of crack lengths: a = f (c) (fig. 5a), a = f (a*) (fig. 5b) and a = f (n) (fig. 6). growth period for quarter-elliptic edge cracks at load ratio r = -1 was ca. 27% of specimen lifetime, whereas for through cracks its value reached approximately 73%. for load ratio r = 0 growth period for quarter-elliptic edge cracks was ca. 18% of specimen lifetime, whereas for through cracks it reached approximately 82%. from graphs fatigue cracks growth shown in fig. 5a allowed observing that for load ratio r = -1 the relationship between lengths of cracks a/c had higher values than for ratio r = 0. for example, fig. 5a shows that for ratio r = -1 and c = 7.20 mm (crack depth in specimen upper surface) the a d. rozumek et alii, frattura ed integrità strutturale, 42 (2017) 23-29; doi: 10.3221/igf-esis.42.03 26 relationship between lengths of cracks is: a/c = 0.274, whereas for ratio r = 0 and c = 7.20 mm this relationship is: a/c = 0.174. the results of crack length measurements a = f (c) show higher curvatures for ratio r = -1 than for r = 0. fig. 5b presents experimental test results performed for the same specimen as in fig. 5a, but for further through crack growth. figs. 5a and 5b demonstrate in diagrams non-uniform fatigue cracks growth on both specimen active side and passive side. higher crack growth values were measured for active side than passive side. test results (fig. 5b) allowed observing that for load ratio r = -1 and crack length a = 7.10 mm, the relationship a/a* = 1.203 has higher values than for the ratio r = 0, where a/a* = 1.092. whereas, for r = -1 and a* = 0.15 mm, the relationship a/a* = 14.333 also has higher values than for the ratio r = 0, which is a/a* = 10.133. we may also observe that for a* = 0.15 mm the relationship a/a* is approximately twelve times (r = -1) and nine times higher (r = 0) than for a = 7.10 mm. moreover, experimental test results shown in fig. 5b allow observing that during the final cracking stage, the lengths of cracks on the sides active and passive, for r = 0, are close to each other, and for r = 1 the difference between these lengths is higher. a) b) figure 5: fatigue crack length under bending with torsion for: a) cracks edge quarter-elliptic, b) through cracks on both specimen sides: active and passive. figure 6: fatigue crack length „a” versus number of cycles n (active side specimen). d. rozumek et alii, frattura ed integrità strutturale, 42 (2017) 23-29; doi: 10.3221/igf-esis.42.03 27 fig. 6 shows experimental test results in the form of diagrams the lengths of fatigue cracks “a” in function of the number of cycles n. during the test analysis it has been observed that fatigue life increases more than 14 times, changing ratio value from r = 0 to r = -1. for specimens subjected to oscillatory loads (r = -1), cracking initiation commenced after 90000 cycles (fatigue failure was formed after 251000 cycles), whereas for r = 0 cracking initiation took place already after 9000 cycles (failure was formed after 17500 cycles). the tests were performed for three specimens at each load level. fig. 7 presents experimental test results in the form of diagrams showing fatigue crack growth rate da/dn (dc/dn) in function of changes equivalent stress intensity factor range δkeq. the increase in fatigue crack growth rate da/dn applies to specimen length (active side), whereas dc/dn concerns specimen depth. test results for fatigue crack growth rate in function of equivalent stress intensity factor range were described using paris equation [18]   m eq da dc c k dn dn    (1) a) b) figure 7: comparison of the test results with calculations according to eq. (1) for specimens under bending with torsion: a) r = -1, b) r = 0. in case of proportional loads (bending with torsion), equivalent stress intensity factor range δkeq for mixed cracking mode was computed using the following formula 2 22.64eq i iiik k k     (2) a changes range of the stress intensity factor ki for bending (mode i) and kiii for torsion (mode iii) was calculated from [13]  2 0cosi ik y a a      (3)  0sin cosiii iiik y a a       (4) where  – range of nominal stresses under bending and torsion. the correction coefficients yi for bending [19] and yiii for torsion [20] occurring in eqs. (3) and (4) take the following forms      20 05 / 20 13 / 7 /iy a a h a a h     (5) d. rozumek et alii, frattura ed integrità strutturale, 42 (2017) 23-29; doi: 10.3221/igf-esis.42.03 28      0 02 / tan / 2iiiy h a a a a h   (6) where h – height of the specimen. fig. 7 allows observing that change of ratio r = -1 to r = 0 results in increasing fatigue crack growth rate da/dn (dc/dn). for instance, in case of constant value of stress intensity factor range δkeq = 33 mpa·m1/2, crack growth rate along the length increases from da/dn = 1.69·10-8 m/cycle (r = -1) to da/dn = 2.30·10-7 m/cycle (r = 0). the increase is more than 13 times. whereas, for other example of constant parameter δkeq = 68 mpa·m1/2, crack growth rate along the depth increases from dc/dn = 5.93·10-8 m/cycle (r = -1) to dc/dn = 6.06·10-7 m/cycle (r = 0). the increase exceeds 10 times. coefficients c and m occurring in formula (1), determined on the basis of experimental tests, were computed using the least squares method. they are shown in tab. 2, which also specifies correlation coefficients r. test results for proportional bending with torsion are burdened with relative error not exceeding 13% at significance level α = 0.05. in all cases, correlation coefficients r, have values close to 1, which proves significant correlation of experimental test results and the approved eq. (1). moreover, tab. 2 allows finding that coefficients c and exponents m for r = -1 and r = 0 (da/dn and dc/dn) have different values. differences in the values of coefficients c and m prove that load ratio r affects shift c and inclination m of the curve. figures curves r c, m(mpa·m1/2)-m/cycle m r 7a 7a 1 (depth) 2 (length) -1 -1 5.784·10-12 1.299·10-10 2.201 1.409 0.995 0.985 7b 7b 1 (depth) 2 (length) 0 0 1.131·10-10 7.183·10-9 2.026 0.988 0.991 0.993 table 2: coefficients c and m of eq. (1) and correlation coefficients r for the curves shown in fig. 7. conclusions he following conclusions have been made on the basis of the obtained results fatigue cracks growth:  under proportional bending with torsion was observed two stage fatigue cracks growth, quarterelliptic edge cracks, which then passes through the crack.  it was noticed that the difference in lengths of cracks on both specimen sides is higher for load ratio r = -1 than for r = 0.  the fatigue crack growth rate is higher for dc/dn compared with da/dn under the same value keq.  it has been confirmed that the change of ratio r = 0 to r = -1 results in fatigue life increase exceeding 14 times, while at the same time crack growth rate drops by more than 10 times. references [1] kocańda, s., fatigue failure of metals, wnt, warszawa, (1985). [2] pyrzanowski, p., estimation and consequences of the crack thickness parameter in the assessment of crack growth behaviour of ‘‘squat’’ type cracks in the rail–wheel contact zone, engineering fracture mechanics, 74 (2007) 25742584. [3] rozumek, d., marciniak, z., fatigue properties of notched specimens made of fep04 steel. materials science, 47(4) (2012) 462-469. [4] gadomski, j., pyrzanowski, p., experimental investigation of fatigue destruction of cfrp using the electrical resistance change method, measurement, 87 (2016) 236-245. [5] martins, r. f., ferreira, l., reis, l., chambel, p., fatigue crack growth under cyclic torsional loading, theoretical and applied fracture mechanics, 85 (2016) 56-66. t d. rozumek et alii, frattura ed integrità strutturale, 42 (2017) 23-29; doi: 10.3221/igf-esis.42.03 29 [6] rozumek, d., bański, r., crack growth rate under cyclic bending in the explosively welded steel/titanium bimetals, materials & design, 38 (2012) 139-146. [7] gladskyi, m., fatemi, a., notched fatigue behavior including load sequence effects under axial and torsional loadings, international journal fracture, 55 (2013) 43-53. [8] gasiak, g., robak, g., simulation of fatigue life of constructional steels within the mixed modes i and iii loading, fatigue & fracture of engineering materials & structures, 34 (2011) 389-402. [9] carpinteri, a., brighenti, r., part-through cracks in round bars under cyclic combined axial and bending loading, international journal of fatigue 18, (1996) 33-39. [10] spagnoli, a., carpinteri, a., ferretti, d., vantadori, s., an experimental investigation on the quasi-brittle fracture of marble rocks, fatigue & fracture of eng. mat. & structures, 39 (2011) 389-402. [11] rozumek, d., macha, e., j-integral in the description of fatigue crack growth rate induced by different ratios of torsion to bending loading in alcu4mg1, materialwissenschaft und werkstofftechnik, 40(10) (2009) 743-749. [12] yates, j. r., miller, k. j., mixed mode (i+iii) fatigue thresholds in a forging steel, fatigue & fracture of eng. mat. & structures, 12 (1989) 259-270. [13] pook, l.p., the fatigue crack direction and threshold behaviour of mild steel under mixed mode i and iii loading, int. j. fatigue, 7 (1985) 21-30. [14] thum, a., petersen, c., swenson, o., verformung, spannung und kerbwirkung. vdi, düesseldorf, (1960). [15] rozumek, d., marciniak, z., fatigue crack growth in alcu4mg1 under nonproportional bending with torsion loading, materials science, 46 ( 2011) 685-694. [16] lewandowski, j., rozumek, d., cracks growth in s355 steel under cyclic bending with fillet welded joint, theoretical and applied fracture mechanics, 86 (2016) 342-350. [17] rozumek, d., marciniak, z., control system of the fatigue stand for material tests under combined bending with torsion loading and experimental results, mechanical systems and signal processing, 22(6) (2008) 1289-1296. [18] paris, p. c., erdogan, f., a critical analysis of crack propagations laws, journal of basic engineering, trans, american society of mechanical engineers, 85 (1963) 528-534. [19] picard, a. c., the application of 3-dimensional finite element methods to fracture mechanics and fatigue life prediction, chameleon press ltd, london, (1986). [20] chell, g.g., girvan, e., an experimental technique for fast fracture testing in mixed mode, int. j. fracture, 14 (1978) 81-84. nomenclature a0 notch length a active crack length a* passive crack length c crack depth da/dn fatigue crack growth rate along the length dc/dn fatigue crack growth rate along the depth e young’s modulus kt theoretical stress concentration factor ma amplitude of moments n number of cycles crack growth r load ratio t time  means arctan (mt/mb) of the ratio of the torsional moment to the bending moment  poisson’s ratio u ultimate tensile stress y yield stress keq equivalent stress intensity factor range << /ascii85encodepages false /allowtransparency false /autopositionepsfiles true /autorotatepages /none /binding /left /calgrayprofile (dot gain 20%) /calrgbprofile (srgb iec61966-2.1) /calcmykprofile (u.s. web coated \050swop\051 v2) /srgbprofile (srgb iec61966-2.1) /cannotembedfontpolicy /error /compatibilitylevel 1.4 /compressobjects /tags 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can be opened with acrobat and adobe reader 5.0 and later.) >> /namespace [ (adobe) (common) (1.0) ] /othernamespaces [ << /asreaderspreads false /cropimagestoframes true /errorcontrol /warnandcontinue /flattenerignorespreadoverrides false /includeguidesgrids false /includenonprinting false /includeslug false /namespace [ (adobe) (indesign) (4.0) ] /omitplacedbitmaps false /omitplacedeps false /omitplacedpdf false /simulateoverprint /legacy >> << /addbleedmarks false /addcolorbars false /addcropmarks false /addpageinfo false /addregmarks false /convertcolors /converttocmyk /destinationprofilename () /destinationprofileselector /documentcmyk /downsample16bitimages true /flattenerpreset << /presetselector /mediumresolution >> /formelements false /generatestructure false /includebookmarks false /includehyperlinks false /includeinteractive false /includelayers false /includeprofiles false /multimediahandling /useobjectsettings /namespace [ (adobe) (creativesuite) (2.0) ] /pdfxoutputintentprofileselector /documentcmyk /preserveediting true /untaggedcmykhandling /leaveuntagged /untaggedrgbhandling /usedocumentprofile /usedocumentbleed false >> ] >> setdistillerparams << /hwresolution [2400 2400] /pagesize [612.000 792.000] >> setpagedevice microsoft word numero_41_art_7.docx t. morishita et alii, frattura ed integrità strutturale, 41 (2017) 45-53; doi: 10.3221/igf-esis.41.07 45 focused on multiaxial fatigue evaluation and visualization of multiaxial fatigue behavior under random non-proportional loading condition takahiro morishita postdoctoral researcher, department of mechanical engineering, college of science & engineering, ritsumeikan university, japan morisita@gst.ritsumei.ac.jp fumio ogawa assistant professor, department of mechanical engineering, college of science & engineering, ritsumeikan university, japan ogawa-f@fc.ritsumei.ac.jp takamoto itoh professor, department of mechanical engineering, college of science & engineering, ritsumeikan university, japan itohtaka@fc.ritsumei.ac.jp abstract. in cyclic multiaxial stress/strain condition under nonproportional loading in which principal direction of stress/strain are changed in a cycle, it becomes difficult to analyze stress/strain ranges because of complexity of multiaxial stress/strain states depending on time in cycles. in order to evaluate stress/strain simply and suitably under non-proportional loading, itoh and sakane have proposed a method called as is-method and a strain parameter for life evaluation under non-proportional loading np. in the method, 6-components of stress/strain are converted to an equivalent stress/strain indicating the amplitude and the direction of principal stress/strain as a function of time as well as an intensity of loading nonproportionality fnp. based on is-method, the authors also have developed a tool which enables to analyze multiaxial stress/strain condition with the nonproportionality of loading history and evaluate failure life under nonproportional multiaxial loading. the tool indicates the analyzed results on monitor and users can understand visually not only variation of the stress/strain conditions but also non-proportionality during the cycle, which helps the design of material strength. keywords. multiaxial fatigue; life evaluation; non-proportional loading; analysis tool; cycle counting; additional hardening. citation: morishita, t., ogawa, f., itoh, t., evaluation and visualization of multiaxial fatigue behavior under random nonproportional loading condition, frattura ed integrità strutturale, 41 (2017) 45-53. received: 28.02.2017 accepted: 15.04.2017 published: 01.07.2017 copyright: © 2017 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. t. morishita et alii, frattura ed integrità strutturale, 41 (2017) 45-53; doi: 10.3221/igf-esis.41.07 46 introduction tructural components and materials such as aircrafts and nuclear equipment undergo complex non-proportional multiaxial loadings where directions of stress and strain are changed into various directions under multiaxial stress and strain states. it is difficult for engineers to analyze histories of stress and strain. therefore, development of suitable models for the design of actual components where variation of principal directions of stress and strain vs. time is considered 3-dimensionally is required [1-8]. to evaluate fatigue lives under multiaxial loading condition, multiaxial fatigue models which relate fatigue lives to uniaxial fatigue properties have been established. equivalent strains and stresses based on von mises and tresca are considered as the most common theory. however, they lead to significant overestimation of fatigue lives under non-proportional loadings, thus a few other classical models such as critical plane approaches that correlate stress or strain with multiaxial fatigue lives have been proposed in recent years. however, some disadvantages on these approaches have been reported. therefore, in order to avoid these disadvantages, itoh et al. proposed a strain parameter related to material property and loading path, which are available in both of short-life and long-life fatigue regimes. the parameter takes response to material deformation and is expressed by simple calculation based on strain model [9-15]. based on the is-method proposed by itoh et al., analyses for pipes subjected to cyclic multiaxial/non-proportional loading are performed. under non-proportional loading, it is expected that the reduction of material fatigue life occurs. there are a lot of structural components that are subjected to non-proportional multiaxial loading, but the verification of shortened fatigue life has not been carried out mostly. therefore, in order to have a guarantee for safety and soundness of structural components, an appropriate understanding and damage evaluation under non-proportional multiaxial loading are strongly urged [4-8]. in this study, on the basis of the method of itoh-sakane criterion (is-method) which evaluates the state of stress and strain in a non-proportional multiaxial cyclic loading, the program is developed for the visualization and analysis of stress/strain state and the evaluation of failure life under non-proportional loading with constant or random amplitude was performed. multiaxial fatigue life evaluation models number of multiaxial fatigue models have been proposed based on stress and strain models. stress-based models are more widely used and are suitable for the large class of components that are operated near or below the fatigue threshold. many of the stress-based models can be used successfully in the finite life regime if the plastic strains are small. in a word, stress based multiaxial damage criteria are suitable for infinite or high-cycle finite life evaluation. development of strain-based models started in 1970s, which are more useful for low-cycle fatigue analysis. they may be written in strain alone or some product of stress and strain. when principal directions of strain correspond to axes of coordinates employed, the most common equivalent strain models are [3-8]: maximum normal strain theory 1:  b3a3b2a2b1a11 ,,max  (1) maximum shear strain theory 1:          2 , 2 , 2 max 2 b 3 a 3 b 2 a 2 b 1 a 11 (2) where 1i, 2i, 3i (i=a, b) and 1i, 2i, 3i are principal strains and principal shear strains at arbitrary times a and b in a cycle and ‘max’ takes maximum value in brackets. mises’ equivalent strain theory eq:          21323222122eq 3 2 3 1  (3) s a t. morishita et alii, frattura ed integrità strutturale, 41 (2017) 45-53; doi: 10.3221/igf-esis.41.07 47 these models correlate multiaxial data for certain materials under some loading conditions, but they cannot be considered generally applicable to life evaluation under non-proportional loading. energy models based on the plastic work per cycle are proposed as a parameter for life to crack nucleation. energy is a scalar quantity and does not address the result of the observation where cracks nucleate and propagate along specific planes. critical plane models attempt to correlate fatigue damage with physical observations of the nucleation and growth of cracks. the concept of critical planes was first proposed by brown and miller. the approach defined a failure plane as a critical plane in terms of stage i (shear-type) or stage ii (tensile-type) cracks. firstly, the history of strain on the critical plane is analyzed, and then strain parameters are used to quantify the damage parameters on the critical plane. various terms have been proposed for different materials and experimental results. the brown and miller critical plane approach is expressed as max+s n=c, where max is the maximum shear strain amplitude, n is the amplitude of the normal strain acting on the max plane, and s is a constant. it is reasoned that max governs crack growth and its direction, and that n further assists crack propagation. socie considered that the fatigue life criterion should be based on a physical mechanism. for a material with tensile-type failures, socie modified the smith–watson–topper (swt) parameter by considering that crack growth was perpendicular to the maximum tensile stress. the parameters which control damage were the maximum principal strain amplitude max /2 and the maximum principal stress 1max on the maximum principal strain plane [16-21],     bcb n e n 2f 2 f fff max 1max 1 22 2      (4) where f is the fatigue ductility coefficient and f is the fatigue strength coefficient, while b is the fatigue strength exponent and c is the fatigue ductility exponent. however, some disadvantages on these approaches can be listed as: i) stress based critical plane approach advocated by findley or mcdiarmid is not available for short fatigue lives regime. ii) strain based critical plane approach advocated by brown-miller has no reflection of material behavior, such as nonproportional cyclic hardening. iii) strain-stress based critical plane approach advocated by fetemi-socie or smith-watsontopper is complex on calculating the stresses from the multiaxial strain. therefore, in order to avoid these disadvantages, itoh et al. proposed one strain parameter related to material property and loading path, which are available in both of short-life and long-life fatigue regimes, takes response to material deformation and is expressed by simple calculation based on strain model. multiaxial fatigue life evaluation model: is-method definition of stress and strain n non-proportional multiaxial fatigue, principal directions of stresses and strains vary during a cycle. in such a case, strain and stress ranges and mean strain and stress cannot be easily determined. it is necessary to represent the principal stress/strain and the direction of principal axis as a function of the time. the principal stress/strain vectors at time t are set as si(t), the index i equals to 1, 2 and 3, that is, maximum, median and minimum principal stress or strain vectors, respectively. in addition, s is the symbol denoting either stress () or strain (). fig. 1 illustrates three principal values, si(t), applied to a cube at time t together with xyz-coordinates (spatial coordinates). si(t) is the maximum amplitude of the principal stress or strain at the time t in the is-method [2, 4], which is defined by the following equation.           ttttts 321ii ,,max ssss  (5) the maximum value of si(t) during a cycle is taken as the maximum principal value simax, which is defined as,     tsts i0iaxim max s (6) that is, t0 is the time when |s1(t)| or |s3(t)| takes the maximum value in one cycle. fig. 2 illustrates two rotation angles, (t)/2 and (t), to express the direction change of principal value in xyzcoordinates, where xyz-coordinates are the material coordinates taking x-axis in the direction of simax and the other two i t. morishita et alii, frattura ed integrità strutturale, 41 (2017) 45-53; doi: 10.3221/igf-esis.41.07 48 axes in arbitrary directions. the rotation angle of (t)/2 is the angle between the simax and si(t) directions and the rotation angle of (t) is the angle of si(t) from the y-axis in x-plane. the two angles of (t)/2 and (t) are written as,                       tt ttt i0i i0i1cos 2 ss ss            22 0 t (7)                  yi zi1tan es es t t t    20 t (8) where dots in eqs 7 and 8 denote the inner product, t0 is the time to take simax and ey and ez are the unit vectors in y and z directions, respectively. si(t) is a vector of principal value and the subscript i takes 1 or 3, e.g., i takes 3 when simax =|s3(t0)|. figure 1: principal stress and strain in xyz coordinates. figure 2: definition of principal stress and strain directions in xyz coordinates. definitions of principal stress and strain in polar coordinates fig. 3 shows the trajectory of si(t) in 3d polar coordinates for a cycle where the radius is taken as the magnitude of si(t), and the angles of (t) and (t) are the angles shown in fig. 2. a new coordinate system is used in fig. 3 with the three axes of si1, si2 and si3, where si1-axis directs to the direction of si(t0). the rotation angle of (t) has double magnitude compared with that in the specimen shown in fig. 2 considering the consistency of the angle between the polar coordinates and the physical plane. the figure on the right side in fig. 3 shows the waveform of loading which is the projection value to path length of si(t) projected to si1-axis. the loading waveform represents the magnitude of the normal strain or stress acting on the plane (simax-plane) perpendicular to the direction of si(t0). the maximum range (si) and mean value (simean) can be obtained from fig. 3. si and smean are calculated as follows,      iminimaxiimaxi cosmax ssttsss  (9) x y z s1(t) s1(t) s2(t) s2(t) s3(t) s3(t) x y z (t)/2 (t) si(t) si(t0) ex ey ez simax-plane si(t) si(t0) (t) /2simax=si(t0) t. morishita et alii, frattura ed integrità strutturale, 41 (2017) 45-53; doi: 10.3221/igf-esis.41.07 49  iminimaximean 5.0 sss  (10) as mentioned above, the reference axis (si1) is the direction of maximum principal stress or strain. in the model, it is also possible to use tresca and von mises stress or strain as s. by utilizing the is-method, even complex non-proportional multiaxial cyclic loading can be replaced by simple waveform, similar to uniaxial loading case. figure 3: definition of principal range and mean principal values. strain parameter for life evaluation in order to evaluate the fatigue life of non-proportional multiaxial loading, itoh et al. have proposed life evaluation equation, np, taking into account material dependence and strain paths [1-5].   inpnp 1  f (11) in the equation, i is the principal strain range stated previously as si and  is a material parameter expressing the amount of additional hardening by non-proportional loading, which is defined as the ratio of stress amplitudes between circular loading and push-pull loading. fnp is the non-proportional factor which expresses the severity of non-proportional loading and is defined as,      c r1i pathimax np d 2 st l f ee (12) where, e1 and er are the unit vectors of si(t0) (i(t0)) and si(t) (i(t)), respectively as shown in fig. 3. lpath is the full length of loading path, c is the integration of strain paths, ds is the increase in the strain path, '' shows the cross product. fnp totally evaluates the severity of non-proportional loading in a cycle. therefore, the maximum non-proportionality (fnp=1) occurred in circular straining and the minimum non-proportionality (fnp=0) in proportional loading. evaluation for random loading when loading for life evaluation is random loading, appropriate counting method is required. some counting methods are already proposed, e.g. peak counting, the level crossing counting, the range-pair counting and the rain-flow counting. however, the method for adapting cycle counting method to multiaxial random loading is not established. since multiaxial random loading can be converted to equivalent uniaxial loading by using is-method, the counting methods for uniaxial random loading can be used as they are. fig. 4 shows loading waveform and non-proportionality before and after using cycle counting method. in the figure, the rain-flow method is used and the equivalent strain (i(t)cos(t)) is divided into 2 cycles: o-a-bc’-d-e and b-c-c’. accordingly, non-proportionality (i(t)|e1er|) is split at b and c’. using strain range and non-proportional factor in each cycle, the strain range for evaluation of failure life under non-proportional loading is calculated by eq (11). applicability of this method for life evaluation under non-proportional loading will be discussed further in the future based on the test results. si1 (t) (t) si (t) si(t0) si2 si 3 δ s i 0. 5δ s i s i m ea n simax simin simax e1 e2 e3 er t. morishita et alii, frattura ed integrità strutturale, 41 (2017) 45-53; doi: 10.3221/igf-esis.41.07 50 (a) before using cycle counting method (b) after using cycle counting method figure 4: random loading before and after using counting method. visualization of stress and strain path and life evaluation ased on the definition of stress/strain mentioned above, a program for visualization of stress/strain path and life evaluation under non-proportional loading was developed. c# was used as the programming code. fig. 5 shows a flowchart of the program, that was divided into 8 categories as shown below. figure 5: calculation flow in the program. (1) input data the stress/strain data vs. time is put into the program. the input data consist of the 6 components of stress/strain and time at each column. additional columns such as temperature can be added. fig. 6 is the table of the input data of non-proportional multiaxial random loading formatted for the program. (1) input data (2) calculation of si(t) and simax (3) determination of reference axis (4) calculation of (t) and (t) (5) (6) cycle counting (7) data storage (8) life evaluation （calculate nf from np） figure of stress/strain path in the polar coordinate and waveforms of si(t)cos(t)-t and si(t)sin(t)-t b t. morishita et alii, frattura ed integrità strutturale, 41 (2017) 45-53; doi: 10.3221/igf-esis.41.07 51 figure 6: formatted input data for random loading. (2) calculation of si(t) and simax si(t) and simax are calculated based on is-method. (3) determination of reference axis the reference axis for defining (t) and (t) is determined. although the determination of reference axis is only one kind in the is-method, that can select three methods (method 1, 2, 3) in this program for visualization. in method 1, the reference axis corresponds to the direction of simax as described in section of “definition of stress and strain”. in method 2, the reference axis is determined based on the maximum accumulated damage. accumulated damage k is estimated using following equation, and the reference axis is determined to be the direction where k takes its maximum value.    c dttt ssk )(sin)(sin)(i (13) in method 3, the reference axis can be determined as any direction by users at their request. (4) calculation of (t) and (t) (t) and (t) are calculated in accordance with the is-method. (5) figure of stress/strain path in the polar coordinate and waveforms of si(t)cos(t)-t and si(t)sin(t)-t based on the above-mentioned calculations and analyses, stress/strain path and waveform are calculated. user can understand magnitude and angular variation quantity of loading in the three-dimensional shape. in addition, reference axis can be changed manually in polar coordinate based on these results. fig. 7 shows a graph of input stress as a function of time. in the graph, x, y, z, xy are presented. the magnitude of y is equal to that of z, and the magnitude of xy is equal to that of x, while the phase difference between x and xy is 180o. this waveform of input data is 1 block cycle which consists of 40cycles. fig. 8 shows the waveforms of si(t)cos(t)-t and si(t)sin(t)-t. si(t)cos(t)-t indicates stress/strain waveform, while si(t)sin(t)-t indicates the magnitude of non-proportionality on time. it is apparent that the applied stress path has high non-proportionality. (6) cycle counting (in the case of random loading) in the case of random loading, waveform of stress/strain is analyzed using the rain-flow method, a kind of cycle counting method. it should be noted that damage has to be evaluated by a cumulative damage rule, i.e. miner’s rule. stress/strain waveform under non-proportional loading was already reduced to the simple waveform through categories (1)(5). therefore, the cycle counting and cumulative damage rule used in uniaxial loading can be applied to non-proportional loading. (7) data storage in this step, figures and tables can be graphed and saved to memory. from the figures, users can understand stress/strain range, multiaxiality and non-proportionality of stress/strain state simultaneously. t. morishita et alii, frattura ed integrità strutturale, 41 (2017) 45-53; doi: 10.3221/igf-esis.41.07 52 (8) life evaluation (calculate nf from np) based on the results from categories (1)(7), life evaluation can be performed. in the life evaluation, manson-coffin equation (eq. (14)) obtained from uniaxial proportional loading fatigue test and the is-method are employed with the rain-flow counting method. 6.0 f 12.0 fnp   nbna (14) the result of life evaluation is also presented in fig. 8. in the right side of fig. 8, the name of material used and parameters a and b in manson-coffin are inputted. by comparing eq. (11) and eq. (14), newton method for nonlinear equation was applied for life evaluation. although the detail of the method is omitted here, the solution of eq. (14) was obtained within 5 times of repeated calculations. in this study, the fatigue life obtained by above calculations was 21136 blocks. in the future study, the result of life estimation will be compared with experimental results. in the present paper, visualization and life estimation method was established based on is-method and it was applied for the non-proportional multiaxial random fatigue loading. the method enables the calculation of stress and strain states under non-proportional multiaxial random loading and realizes life estimation under highly non-proportional random fatigue loading. figure 7: stress waveforms of input data. figure 8: output data and life evaluation result. t. morishita et alii, frattura ed integrità strutturale, 41 (2017) 45-53; doi: 10.3221/igf-esis.41.07 53 conclusions software to visually indicate the stress and strain states, the non-proportionality of loading and life evaluation was developed based on the is-method. it was applied for the life evaluation under the multiaxial random fatigue loading, and the theoretical life was estimated based on manson-coffin equation. the software enables researchers and engineers without specific knowledge on multiaxial fatigue loading to assess fatigue strength under nonproportional multiaxial fatigue condition. references [1] fatemi, a., socie, d.f., a critical plane approach to multiaxial fatigue damage including out-of-phase loading, fatigue & fracture of engineering materials & structures, 11 (1988) 149-165. [2] baek, s.h., cho, s.s, joo, w.s., fatigue life prediction based on the rainflow cycle counting method for the end beam of a freight car bogie, international journal of automotive technology, 9 (2008), 95-101. [3] jun, y., cheng-bin, l., shousheng, x., multiaxial fatigue life predication method based on maximum damage critical plane, aviation industry corporation of china, 26 (2011) 2783-2789. [4] han, c., chen, x., kim, k.s., evaluation of multiaxial fatigue criteria under irregular loading, international journal of fatigue, 24 (2002) 913-922. [5] liu, y., mahadevan, s., multiaxial high-cycle fatigue criterion and life prediction for metals, international journal of fatigue, 27 (2005) 790-800. [6] wang, y.y., yao, w.x., evaluation and comparison of several multiaxial fatigue criteria, international journal of fatigue, 26 (2004) 17-25. [7] carpinteri, a., spagnoli, a., vantadori, s., a critical plane-based criterion for high-cycle multiaxial fatigue using averaged princiola stress directions, in: proceedings of the workshop on: “progettazione a fatica in presenza di multiassialità tensionali”, ferrara, italy (2005). [8] carpinteri, a., brighenti, r., spagnoli, a., a fracture plane approach in multiaxial high-cycle fatigue of metals, fatigue & fracture of engineering materials & structures, 23 (2000) 355-364. [9] leyi, d., jun, l., li, c., rain flow count method and its realization in programming, airforce and engine department of engineering college of airforce engineering university, 24 (2004) 38-40. [10] itoh, t., sakane, m., ohnami, m., socie, d.f., nonproportional low cycle fatigue criterion for type 304 stainless steel, trans. asme, j. engineering materials and technology, 117 (1995) 285-292. [11] itoh, t., nakata, t., sakane, m., ohnami, m., nonproportional low cycle fatigue of 6061 aluminum alloy under 14 strain paths, european structural integrity society, 25 (1999) 41-54. [12] itoh, t., yang, t., material dependence of multiaxial low cycle fatigue lives under non-proportional loading, international journal of fatigue, 33 (2011) 1025-1031. [13] itoh, t., sakane, m., shimizu, y., definition of stress and strain ranges for multiaxial fatigue life evaluation under non-proportional loading, journal society material science, japan, 62 (2013) 117-123. [14] itoh, t., sakane, m., ohsuga, k., multiaxial low cycle fatigue life under non-proportional loading, international journal of pressure vessels and piping, 110 (2013) 50-56. [15] socie, d.f., multiaxial fatigue damage models, journal of engineering materials and technology, 109 (1987) 293-298. [16] endo, t., anzai, h., refined rainflow algorithm: p/v difference method, kyushu institute of technology, kitakyushu, the society of materials science, 30 (1981) 89-93. [17] wang, c.h., brown, m.w., life prediction techniques for variable amplitude multiaxial fatigue part 1: theories, journal of engineering material and technology, 118 (1996) 367-370. [19] wang, c.h., brown, m.w., life prediction techniques for variable amplitude multiaxial fatigue part 2: comparison with experimental results, journal of engineering material and technology, 118 (1996) 371-374. [20] chen, x., xu, s., huang, d., a critical plane-strain energy density criterion for multiaxial low-cycle fatigue life under non-proportional loading, 1999 black science ltd. fatigue & fracture of engineering material & structure, 22 (1999) 679-686. [21] farahani, a.v., a new energy-critical plane parameter for fatigue life assessment of various metallic materials subjected to in-phase and out-ofphase multiaxial fatigue loading conditions, international journal of fatigue, 22 (2000) 295-305. a << /ascii85encodepages false /allowtransparency false /autopositionepsfiles true /autorotatepages /none /binding /left /calgrayprofile (dot gain 20%) /calrgbprofile (srgb iec61966-2.1) /calcmykprofile (u.s. web coated \050swop\051 v2) /srgbprofile (srgb iec61966-2.1) /cannotembedfontpolicy /error /compatibilitylevel 1.4 /compressobjects /tags /compresspages true /convertimagestoindexed true /passthroughjpegimages true /createjobticket false /defaultrenderingintent /default /detectblends true /detectcurves 0.0000 /colorconversionstrategy /cmyk /dothumbnails false /embedallfonts true /embedopentype false /parseiccprofilesincomments true /embedjoboptions true /dscreportinglevel 0 /emitdscwarnings false /endpage -1 /imagememory 1048576 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/hrv (za stvaranje adobe pdf dokumenata najpogodnijih za visokokvalitetni ispis prije tiskanja koristite ove postavke. stvoreni pdf dokumenti mogu se otvoriti acrobat i adobe reader 5.0 i kasnijim verzijama.) /hun 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can be opened with acrobat and adobe reader 5.0 and later.) >> /namespace [ (adobe) (common) (1.0) ] /othernamespaces [ << /asreaderspreads false /cropimagestoframes true /errorcontrol /warnandcontinue /flattenerignorespreadoverrides false /includeguidesgrids false /includenonprinting false /includeslug false /namespace [ (adobe) (indesign) (4.0) ] /omitplacedbitmaps false /omitplacedeps false /omitplacedpdf false /simulateoverprint /legacy >> << /addbleedmarks false /addcolorbars false /addcropmarks false /addpageinfo false /addregmarks false /convertcolors /converttocmyk /destinationprofilename () /destinationprofileselector /documentcmyk /downsample16bitimages true /flattenerpreset << /presetselector /mediumresolution >> /formelements false /generatestructure false /includebookmarks false /includehyperlinks false /includeinteractive false /includelayers false /includeprofiles false /multimediahandling /useobjectsettings /namespace [ (adobe) (creativesuite) (2.0) ] /pdfxoutputintentprofileselector /documentcmyk /preserveediting true /untaggedcmykhandling /leaveuntagged /untaggedrgbhandling /usedocumentprofile /usedocumentbleed false >> ] >> setdistillerparams << /hwresolution [2400 2400] /pagesize [612.000 792.000] >> setpagedevice microsoft word numero 9 art 7 finale v. dattoma et alii, frattura ed integrità strutturale, 9 (2009) 64 – 75; doi: 10.3221/igf-esis.09.07 64 verifica a fatica dei giunti saldati sulla base di misure di deformazione locale v. dattoma, r. nobile, f.w. panella università del salento, dipartimento di ingegneria dell’innovazione, lecce; vito.dattoma@unile.it riassunto. lo studio della resistenza a fatica delle giunzioni saldate rappresenta un campo di prova molto interessante dal punto di vista scientifico, con ricadute pratiche altrettanto importanti. si tratta in generale di fornire dei metodi di verifica e progetto deterministici, come è proprio dell’ingegneria, per prevedere il comportamento meccanico di un materiale che, quando è sotto forma di saldatura, cambia le sue proprietà meccaniche e microstrutturali rispetto al materiale base, si dispone in una geometria locale del cordone estremamente variabile e non definibile a priori, è infine affetto da campi di tensione residua non proprio trascurabili. in questo lavoro, partendo da una breve panoramica sui principali indicatori e metodi che sono stati utilizzati nel corso degli anni per la stima dello stato di sollecitazione in un giunto saldato e della vita residua a fatica, si presenta l’approccio basato sulla misura della deformazione locale che è stato seguito da diversi autori nel corso degli anni, evidenziandone i vantaggi ma anche le limitazioni rilevate attraverso le numerose attività sperimentali direttamente eseguite. abstract. fatigue resistance of welded joints represents an interesting and challenging studying field from a scientific point of view, with valuable and important practical consequences. in the specific, the main target is to establish in general the proper quantitative verification and design procedures, based on theoretical achievements. the actual procedures and standard codes are extremely useful for most engineering applications, in which elevated safety factors have to be used. on the other hand the mechanical behavior of welded material is different from the base metal; the weld bead material has different mechanical characteristics because of microstructural changes and other local effects, due to extremely variable weld toe geometry, resulting in notch effects and coupled with relevant residual stresses not to be ignored. in this work, a brief resume of the principal design methods is primarily reported for the estimation of residual life expectancies of welded joints, leading to different engineering approaches; among them, the method based on local deformations measurements is presented as reliable verification tool, already analyzed and modified by several authors in the past. the local deformation approach has been deeply applied and verified by the authors and the main advantage and characteristics are explained, as well as the present limitations to be observed in the frame of many experimental fatigue testing activities. parole chiave. welded joints; fatigue; local strain; design method. introduzione a stima della resistenza a fatica di giunzioni saldate rappresenta un problema particolarmente complesso a causa delle notevoli alterazioni introdotte dal ciclo termico di saldatura. la microstruttura del materiale cambia, favorendo generalmente un comportamento maggiormente fragile; i gradienti termici sviluppati durante il processo originano in maniera complementare campi di tensioni residue o distorsioni e disallineamenti significativi; il materiale depositato sotto forma di cordone, infine, altera la geometria locale del giunto, dando origine a una concentrazione di l http://www.gruppofrattura.it/ http://dx.medra.org/10.3221/igf-esis.09.07&auth=true mailto: vito.dattoma@unile.it v. dattoma et alii, frattura ed integrità strutturale, 9 (2009) 64 – 75; doi: 10.3221/igf-esis.09.07 65 tensione assimilabile ad un intaglio. tutti questi fenomeni, che sono peculiari dei giunti saldati, vanno a complicare un fenomeno già estremamente complesso come il comportamento a fatica. gli effetti di questi parametri sono indistinguibili l’uno dall’altro; se da un lato è abbastanza semplice individuare il tipo di sollecitazione agente globalmente sul giunto, non altrettanto si può dire per la geometria locale dello stesso cordone, che è non definibile a priori e caratterizzata da una variabilità estrema. se è quindi piuttosto ovvio riconoscere nello stato di sollecitazione locale al piede del cordone il principale responsabile della resistenza a fatica di un giunto, il grosso problema diventa determinare tale stato di sollecitazione, o un parametro ad esso legato, basandosi su una geometria non definibile in modo esatto. si corre il rischio di calcolare dei parametri indicativi dello stato di sollecitazione locale relativi sì ad una geometria di riferimento sul cordone, ma in molti casi non rappresentativa della reale situazione. bisognerebbe poi tener conto che in ogni caso un parametro rappresentativo della sollecitazione locale, in quanto espressione del solo campo tensionale e deformativo magari anche residuo, non considera affatto le alterazioni metallurgiche introdotte nel materiale dal processo. in questo lavoro si presenta l’approccio basato sulla misura della deformazione locale, analizzando i dati derivanti da numerose prove di fatica eseguite principalmente su giunti saldati ad arco in acciaio strutturale di varia forma e con diversi spessori delle piastre. si presentano inoltre i primi risultati che sono stati ottenuti per giunti saldati al laser in lega di titanio. metodi principali utilizzati per la resistenza a fatica di giunti saldati i vari approcci che sono stati proposti nel corso degli anni per la valutazione della resistenza a fatica dei giunti saldati possono essere classificati sulla base della tipologia di parametro scelto per rappresentare la gravità dello stato di sollecitazione che porta alla rottura a fatica. la scelta di un parametro affidabile per descrivere quanto accade in giunto saldato sollecitato a fatica è alquanto complicato, come testimoniato dal fatto che tuttora la soluzione adottata in molti casi è rappresentata dalla tensione nominale. le norme internazionali [1-3] individuano infatti un certo numero di dettagli strutturali scelti tra i più significativi nella pratica corrente, fornendo per ognuno di essi un limite di fatica di riferimento espresso proprio in termini di tensione nominale: in altre parole si rinuncia a metodi di calcolo più sofisticati e dettagliati, certificando l’impossibilità di considerare in tutti i suoi aspetti l’effetto della reale geometria del giunto e dello stato di sollecitazione locale al cordone. tradizionalmente, si ritiene che la tensione nominale al piede del cordone venga alterata sia dalla particolare geometria globale del giunto (ossia il dettaglio strutturale codificato dalle norme), sia dagli effetti geometrici locali originati da disallineamenti o distorsioni e dalla geometria locale del cordone [4]. negli approcci tipo hot-spot, l’idea di base è di tralasciare le complicazioni legate alla geometria locale del cordone, ma di considerare le sovrasollecitazioni indotte dalla configurazione geometrica propria del giunto. in pratica, la tensione di hotspot viene a coincidere con la somma della tensione nominale e della componente di flessione ad essa associata. tale tensione di hot-spot può essere valutata numericamente tramite modelli fem della giunzione, o sperimentalmente mediante estensimetri elettrici posizionati in punti prefissati e precisati univocamente dalle procedure proposte [5-7]. partendo da questa base comune, i vari approcci locali si differenziano grandemente per i parametri che vengono considerati: radaj [8, 9] ha proposto di far riferimento ad una concentrazione di tensione elastica, valutata con un modello numerico in cui si assume arbitrariamente al piede del cordone un raggio di raccordo di 1 mm. tali metodi si dimostrano particolarmente efficaci e sono attualmente ben collaudati; in particolare l’iiw ha da tempo emanato una proposta di nuova normativa europea [10], basata appunto sulla determinazione di una tensione “geometrica” di hot spot, da determinarsi sia con modelli fem lineari, sia con misurazioni estensimetriche in due punti lontani dal raccordo sul cordone, con la quale determinare sulle curve di riferimento disponibili per la normativa vigente la vita residua a fatica. tale proposta è estremamente innovativa e valida, nonché meno conservativa della norma ufficiale. più recentemente, si è proposto di considerare una tensione mediata in un volume di riferimento [11] o calcolata ad una particolare distanza critica [12]. un’altra possibile alternativa è far riferimento agli approcci basati sul fattore di intensificazione degli sforzi. la soluzione di williams [13] che descrive il campo tensionale in corrispondenza di intagli a v acuti può essere sfruttata per determinare la gravosità del campo tensionale presente al piede del cordone, sfruttandone la similitudine geometrica con gli intagli a v acuti. tale similitudine, proposta inizialmente da verreman e nie [14], è stata poi portata avanti da altri studi di lazzarin e tovo, atzori e altri [15-17]. diversi studi sono attualmente in corso per generalizzare e standardizzare questi metodi alle diverse tipologie di giunto e di carico. infine, un’ulteriore possibile approccio è quello di considerare comunque presente una cricca al piede del cordone; di conseguenza, la vita a fatica viene ad essere determinata dalle leggi di propagazione delle cricche [18-19]. il fattore di http://www.gruppofrattura.it/ http://dx.medra.org/10.3221/igf-esis.09.07&auth=true v. dattoma et alii, frattura ed integrità strutturale, 9 (2009) 64 – 75; doi: 10.3221/igf-esis.09.07 66 intensificazione degli sforzi, opportunamente modificato da un fattore geometrico, assume quindi il significato di parametro di riferimento per la previsione di vita a fatica. questo approccio ha mostrato di essere molto affidabili nei casi di rinforzi longitudinali e in presenza di incisioni marginali. fattori influenzanti la resistenza a fatica di giunzioni saldate il campo tensionale e deformativo in prossimità del cordone di saldatura è generalmente ritenuto il responsabile del comportamento a fatica del giunto saldato e si è quindi cercato di valutarlo con la maggiore accuratezza possibile [20-21]. gli strumenti a disposizione sono di tipo numerico o sperimentale, ma ognuno di questi ha delle limitazioni che portano ad approssimazioni anche rilevanti. i modelli numerici ad esempio devono far riferimento a geometrie ideali e non possono tenere in conto in maniera appropriata della variabilità imputabile alle distorsioni e ai disallineamenti. la geometria locale del cordone è basata su valori medi statistici di misure sperimentali, la cui variabilità è influenzata in maniera spesso non controllabile dal processo di saldatura, dalla forma geometrica e dall’operatore. di conseguenza, il risultato numerico è formalmente corretto, ma spesse volte si corre il rischio di riferirsi ad una geometria idealizzata troppo lontana dalla realtà. per contro, le simulazioni numeriche rappresentano un potente strumento di calcolo, il cui uso è relativamente facile, veloce e affidabile. inoltre, il risultato ottenuto consiste nell’intero campo tensionale e fornisce in prima approssimazione la sollecitazione locale di riferimento per i calcoli di verifica successivi. l’altro strumento a disposizione, quello delle misure sperimentali, ha la forte limitazione di essere spesso ristretto ad aree di indagine limitate o addirittura puntuali. solo i metodi ottici potrebbero fornire una descrizione completa dello stato tensionale e deformativo sulla superficie, ma la rugosità e le irregolarità superficiali generalmente presenti rappresentano un ostacolo quasi insormontabile. un’altra possibilità è quella di usare estensimetri elettrici per la misura di deformazioni in punti ritenuti significativi e critici. in tal caso il numero di punti di misura è limitato ed in ogni caso la misura non è strettamente puntuale, ma estesa su un’area limitata ma comunque finita e corrispondente alle dimensioni della griglia estensimetrica usata. pertanto le misure sono sempre affette da sorgenti di errore ineliminabili come quelle dovute agli alti gradienti di tensione e ad eventuali fenomeni di plasticizzazione locale. nonostante questi inconvenienti, le misure sperimentali sono in grado di cogliere al meglio gli effetti della geometria globale e locale del giunto, compreso l’effetto dello spessore della piastra principale del giunto e della presenza di disallineamenti [22]. il metodo della deformazione locale metodi basati sulla misura di deformazione locale scelgono come parametro utile ai fini della valutazione della resistenza a fatica la deformazione locale; in particolare, l’ampiezza di deformazione a, misurata da estensimetri in prossimità del piede del cordone sotto carico statico, è considerata il dato più significativo per le verifiche a fatica. la cosiddetta deformazione locale è quindi il risultato di un processo di integrazione su un’area finita corrispondente all’estensione della griglia estensimetrica. di conseguenza, questo parametro può essere significativo per confrontare stati di tensione locali solo se viene standardizzata l’estensione e il posizionamento della griglia stessa rispetto al cordone. in altre parole, per ottenere un parametro ripetitivo, la dimensione della griglia estensimetrica e il suo posizionamento deve essere ben definito. sulla base di esperienze passate [23-24] e della personale esperienza degli autori [25-26], il miglior compromesso tra la necessità di misurare quanto più vicino possibile al piede del cordone e l’affidabilità della misura stessa è rappresentata da estensimetri elettrici aventi una lunghezza di griglia di 3 mm e posizionati con il loro asse trasversale a 2.5 mm dal piede del cordone. in altre parole la misura estensimetrica sarà il risultato dell’integrazione del campo deformativo esistente nella zona tra 1 e 4 mm a partire dal piede del cordone. la fig. 1 riporta alcuni esempi di installazioni estensimetriche eseguite per la validazione del metodo. poiché la rottura a fatica si innesca in maniera casuale in un punto posizionato lungo il piede del cordone, dove presumibilmente il raggio di raccordo assume un valore critico, se ne deduce come l’uso di un valore medio o di un valore fittizio di tale parametro nei modelli numerici possa essere considerata una forzatura. una misura diretta delle deformazioni può fornire una valutazione più affidabile dell’effetto della geometria locale: la misura è infatti sicuramente capace di cogliere gli effetti di disallineamento e, per la sua vicinanza al cordone, risentire almeno in parte degli effetti locali indotti dal raggio di raccordo o dalla presenza di sotto-intagli. infatti, nei giunti testati a fatica la rottura si manifesta quasi sempre dal lato del cordone in cui si rilevano le maggiori deformazioni. la presenza invece di plasticizzazione locale all’apice ha anche una certa influenza, soprattutto nel caso di giunti molto spessi; anche in questo caso, nonostante l’estensione della zona plastica sia molto contenuta nell’arco di 1-2 mm dal piede del cordone, l’estensimetro posto immediatamente accanto riesca a coglierne in parte l’effetto; ciò è dimostrato i http://www.gruppofrattura.it/ http://dx.medra.org/10.3221/igf-esis.09.07&auth=true v. dattoma et alii, frattura ed integrità strutturale, 9 (2009) 64 – 75; doi: 10.3221/igf-esis.09.07 67 sperimentalmente dal fatto che durante l’applicazione sui giunti di carichi elevati si rilevano deformazioni sugli estensimetri che variano in modo non lineare con l’aumentare del carico. figura 1: alcuni esempi dei giunti saldati in acciaio utilizzati per i test di fatica. l’ampiezza di deformazione a deve essere misurata sottoponendo il giunto al ciclo presunto di carico a fatica e può essere messa in relazione al numero di cicli a rottura n in maniera da ottenere curve di resistenza a fatica in termini di ampiezze di deformazione locale, che risultano essere indipendenti dalla tipologia di giunto e dalla modalità di carico. da queste curve, ricavate per giunti di diversa geometria e sottoposti a cicli di carico caratterizzati da diversi valori del rapporto di sollecitazione r, è possibile estrapolare il valore a della deformazione locale in corrispondenza di n = 2 · 106 cicli. la sperimentazione condotta su un gran numero di giunti saldati in acciaio strutturale, differenti per tipologia, spessore e modalità di carico, ha permesso di stabilire che il parametro ampiezza di deformazione locale è abbastanza insensibile alla variabilità di molti dei fattori che incidono sulla resistenza a fatica, rappresentandone una sorta di indicatore riassuntivo di tutto quanto accade al piede del cordone e che riveste una certa importanza ai fini della resistenza a fatica. nei primi lavori [22, 25-29], relativi a giunti saldati con spessore delle piastre superiore a 10 mm, tutti i dati sono stati raggruppati con successo su un’unica curva di resistenza a fatica espressa in termini di ampiezza di deformazione locale. successivamente, le prove condotte su giunti di spessore inferiore ai 10 mm [30-32] hanno evidenziato che questi manifestano una resistenza maggiore se espressa in termini di ampiezza di deformazione locale. il diverso livello di tensioni residue che caratterizza le due classi di spessore dei giunti saldati considerati è stato proposto per spiegare questo comportamento [3334]. in [35] si è voluto valutare l’applicabilità e la coerenza dei dati misurati anche in condizioni estremamente diverse; in tutti i giunti saldati che erano stati studiati fino ad allora l’asse del cordone di saldatura era perpendicolare alla forza applicata. in tale studio si sono invece considerati dei giunti saldati testa a testa aventi il cordone inclinato rispetto all’asse di trazione, incollando questa volta delle rosette al piede del cordone. in questa particolare condizione si ha il dubbio se considerare come ampiezza di deformazione locale quella principale, la cui direzione potrebbe essere incognita a priori, o quella normale al cordone. i dati sperimentali si sono accordati ottimamente a quelli degli altri giunti testati in precedenza, indicando che si può in ogni caso far riferimento alla deformazione misurata in direzione normale al cordone. lo stesso metodo è stato usato anche nel caso di sollecitazioni ad ampiezza variabile considerando un caso industriale reale [36]. in [37] infine è fornita una estesa discussione sulle peculiarità del metodo e sulle linee guida per la sua pratica applicazione. la maggior parte della sperimentazione è stata condotta su giunti saldati in acciaio, ma l’applicabilità del metodo non viene meno cambiando materiale o processo di saldatura. in tal caso ovviamente i valori numerici delle ampiezze di deformazione che determinano una prefissata vita a fatica cambiano ed è quindi necessaria una sperimentazione su ogni materiale si voglia considerare. alcune campagne sperimentali sono state condotte su giunti in lega di alluminio [38-39] e più recentemente gli autori e il gruppo di ricerca del politecnico di bari [40] stanno conducendo un’ampia campagna di prove sperimentali su giunti in lega di titanio. http://www.gruppofrattura.it/ http://dx.medra.org/10.3221/igf-esis.09.07&auth=true v. dattoma et alii, frattura ed integrità strutturale, 9 (2009) 64 – 75; doi: 10.3221/igf-esis.09.07 68 in generale, tutta la sperimentazione eseguita e l’esperienza acquisita nel corso degli anni permettono di affermare che l’uso dell’ampiezza di deformazione locale a come parametro di verifica della resistenza a fatica di giunzione saldate ha mostrato di essere estremamente affidabile come metodo di verifica di giunzioni saldate critiche. correlazione tra geometria globale del giunto e ampiezza di deformazione locale utilizzando la gran mole di dati sperimentali sui giunti saldati in acciaio analizzati in passato a fatica per la validazione del metodo, è possibile avere una base statistica per stabilire qual è l’effetto della geometria globale del giunto sull’ampiezza di deformazione locale. nella tab. 1 riportata di seguito si presentano, limitatamente ai giunti saldati in acciaio strutturale, tutte le prove di fatica eseguite nel corso degli anni per validare il metodo, evidenziando il numero di test a fatica realizzati, lo spessore delle piastre, la modalità di carico e la geometria. per i dettagli delle prove si rimanda alle specifiche pubblicazioni. tali dati sono stati utilizzati per ricavare le curve riportate in fig. 2a e 2b, relativamente al solo rapporto di sollecitazione r=0.1, ottenute a seguito dell’applicazione del metodo della deformazione locale, distinguendo però due classi di spessore principali: giunti di piccolo spessore, fino ad 8 mm, e giunti di spessore medio, tra 10 e 25 mm. e’ interessante notare sui diagrammi di fatica ottenuti l’estrema coerenza dei dati e la loro distribuzione particolarmente contenuta in uno spettro di deformazione basso a numero di cicli fissato. ancora più importante è il fatto che sulla stessa curva di regressione vengono posizionati i dati riferiti a giunti molto diversi tra loro, sia per la loro forma (a croce, a t e di testa) che per gli spessori utilizzati e la modalità di carico principale (trazione o flessione). in entrambi i diagrammi infatti, si riscontrano ottimi valori del coefficiente r di correlazione (r2= 0.89 – 0.69) dei dati. utilizzando tali curve è possibile stimare l’ampiezza di deformazione limite corrispondente alla vita convenzionale di 2 106 cicli, pari rispettivamente a a = 356  per i giunti oltre 10 mm e a = 450 per i giunti fino a 8 mm. tabella 1: riassunto complessivo delle prove di fatica eseguite su giunti in acciaio strutturale tipologia di giunto modalità di carico materiale spessore rapporto di sollecitazione n° di provini 3 -1 5 3 0.5 7 trazione fe510 5 0.1 7 5 0.5 6 10 -1 5 3 -1 6 3 0.1 11 fe510 3 0.5 7 5 -1 7 trazione 5 0.1 12 fe430 17 0.1 12 25 -1 7 fe510 25 -0.25 6 25 0.1 6 e36 8 0.1 7 flessione 3p e560d 8 0.1 8 e36 20 0.1 6 5 -1 5 trazione fe510 15 -1 6 15 0.5 5 trazione incl. cord. 30° fe430 5 0.1 5 http://www.gruppofrattura.it/ http://dx.medra.org/10.3221/igf-esis.09.07&auth=true v. dattoma et alii, frattura ed integrità strutturale, 9 (2009) 64 – 75; doi: 10.3221/igf-esis.09.07 69 e’ necessario sottolineare che i dati sperimentali in termini di ampiezza di tensione a sulle prove di fatica effettuate si dispongono in modo molto diverso se si riferiscono a giunti geometricamente differenti e soprattutto manifestano la classica dispersione molto elevata delle curve di wöhler. ciò obbliga il progettista a dover eseguire un numero di test molto superiore per determinare il limite di fatica della giunzione studiata e nel contempo ad applicare elevati coefficienti di sicurezza per tenere conto dell’elevata variabilità della durata prevista a fatica, calcolabile in seguito ad un regime tensionale imposto. a titolo di esempio infatti si presentano in fig. 3 i dati, espressi questa volta in termini di ampiezza di tensione, relativi agli stessi giunti in acciaio riportati in fig. 2-b. si nota immediatamente l’elevata dispersione dei dati, soprattutto se riferiti a giunti di tipo diverso. nello stesso diagramma viene anche indicata la curva di riferimento secondo normativa eurocode, disposta ben al disotto delle curve sperimentali, proprio a causa dell’incertezza riscontrata. (a) (b) figura 2: curve di resistenza a fatica in termini di ampiezza di deformazione locale di giunti saldati in acciaio: a) spessori 10-25 mm; b) spessori 3-8 mm una limitazione del metodo è invece imputabile proprio al suo approccio sperimentale: una verifica del cordone di saldatura può essere effettuata solo se il componente è stato realizzato, strumentato opportunamente con estensimetri e quindi caricato. questo significa che in fase di progettazione il metodo non potrebbe fornire indicazioni utili al dimensionamento del giunto. per superare questo inconveniente si può stabilire statisticamente, almeno per quelle tipologie di giunto che sono state effettivamente studiate, quanto l’ampiezza di deformazione locale, misurata secondo i dettami del metodo, si discosti da quella nominale che è facilmente calcolabile in modo analitico. in pratica si può definire un coefficiente di amplificazione locale della deformazione ka in questa maniera: http://www.gruppofrattura.it/ http://dx.medra.org/10.3221/igf-esis.09.07&auth=true v. dattoma et alii, frattura ed integrità strutturale, 9 (2009) 64 – 75; doi: 10.3221/igf-esis.09.07 70 noma a ak ,    (1) dovea è l’ampiezza locale di deformazione misurata, mentre a,nom è l’ampiezza nominale di deformazione applicata al giunto, che nel caso di una sollecitazione monoassiale di trazione è immediatamente nota dalla relazione seguente: (2) in cui a è l’ampiezza nominale di carico. i valori medi di questo fattore relativi ai test eseguiti su alcune tipologie di giunti, di cui è riportata anche la numerosità del campione, sono riportati in tab. 2. i dati sono stati calcolati anche nel caso di carico prevalente di flessione e sono classificati non solo in base alla tipologia di giunto ma anche in base allo spessore della piastra principale. figura 3: curve di resistenza a fatica in termini di ampiezza di tensione per giunti saldati in acciaio di vario tipo e normativa di riferimento. tipo di giunto spessore numero di provini noma a ak ,    valore medio deviazione standard giunti a croce 3-5 mm 42 1.740 0.405 giunti a croce 10-25 mm 37 1.312 0.188 giunti testa a testa 3-5 mm 18 2.201 0.497 giunti testa a testa thickness 8 mm 12 1.297 0.156 giunti a t 8 mm 15 0.909 0.070 giunti a t 20 mm 6 1.001 0.039 giunti ad angolo 5 mm 5 0.579 0.010 giunti ad angolo 20 mm 10 0.712 0.080 tabella 2: valore caratteristici del coefficiente di amplificazione locale della deformazione. , a nom e e s e = http://www.gruppofrattura.it/ http://dx.medra.org/10.3221/igf-esis.09.07&auth=true v. dattoma et alii, frattura ed integrità strutturale, 9 (2009) 64 – 75; doi: 10.3221/igf-esis.09.07 71 non per tutte le categorie di giunto si ha una numerosità del campione sufficiente; nonostante questo, si possono dedurre alcune interessanti considerazioni. si può osservare innanzitutto una differenza fra i giunti a seconda se il tipo di sollecitazione prevalente sia la flessione o la trazione. nel caso dei giunti a t per esempio, dove l’unica sollecitazione che interessa il cordone è la flessione, la deformazione locale coincide praticamente con quella nominale: per tali giunti le flessioni spurie dovute ai disallineamenti sono assenti per via del tipo di carico applicato. nei giunti ad angolo invece, in cui il cordone è sollecitato da una trazione eccentrica, la deformazione locale è sensibilmente inferiore all’unità, evidenziando la particolare criticità in termini di resistenza a fatica di quel particolare dettaglio strutturale. un’altra importante osservazione riguarda lo spessore della piastra principale che costituisce il giunto: sia nei giunti testa a testa che in quelli a croce gli spessori minori hanno valori di deformazione locale molto più pronunciati rispetto a quelli nominali, facilmente spiegato con i maggiori disallineamenti, e si risconta anche maggiore variabilità del parametro ka, da cui sono affetti questi giunti. tale parametro può essere classificato in modo univoco in base alla tipologia di giunto considerato, dal momento che tiene conto anche dello spessore delle piastre e della scala geometrica del dettaglio strutturale, diventando così un coefficiente utile al progettista per stimare sulla base di calcoli analitici o fem (in relazione alla complessità della giunzione) la deformazione locale prevista a in seguito ai carichi di progetto, calcolando sulle curve in fig. 2a e 2b la prevista vita residua a fatica. l’influenza della geometria locale sulle misure di deformazione locale la misure di deformazione locale è molto sensibile agli effetti del disallineamento, se è vero che si riduce nel caso di sollecitazioni di flessione. in aggiunta, tale misura riesce a cogliere in parte anche gli effetti della geometria locale del cordone, generalmente associabili con buona approssimazione al valore del raggio di raccordo al piede del cordone. data la loro importanza, questi fattori geometrici sono stati misurati per alcune tipologie di giunti e se ne riportano di seguito i risultati. e’ noto infatti che valori diversi del raccordo r rispetto al modello numerico del giunto alterano sensibilmente le tensioni all’apice dell’intaglio del cordone, mentre valori anche piccoli di disallineamento angolare determinano sovrasollecitazioni spurie che producono talvolta incrementi tensionali superiori ai 100 mpa. il raggio di raccordo è stato misurato in diverse sezioni di 8 giunti testa a testa e 8 giunti a croce con spessore variabile di 5-10 mm ed in alcuni giunti in lega di titanio saldati al laser. e’ stato realizzato un calco del cordone con una resina polimerica siliconica, successivamente sezionato in strati sottili con spessore medio di 1 mm in modo da avere una buona indicazione della variabilità del raggio di raccordo lungo il cordone. tutti i dati relativi al raggio di raccordo sono stati riassunti nelle curve riportate in fig. 4a per i giunti in acciaio e in figura 4b per i giunti in titanio. la variabilità del raggio di raccordo è comunque molto elevata e fortemente dipendente dalla modalità di esecuzione della saldatura; i dati sono ben descritti da una distribuzione normale, seppure con una deviazione standard piuttosto elevata. relativamente ai giunti saldati in acciaio, si è determinato un valore medio di 2.47 mm per i giunti testa a testa e 0.79 mm per i giunti a croce; tali dati sono in accordo con quanto comunemente affermato in letteratura [8-9]. il risultato più evidente è che per giunti in acciaio in genere si prevede un valore del raggio che può con buona probabilità valere da 0.5 fino 4 mm, determinando forti incertezze sui risultati dei calcoli fem o altri metodi analitici. per i giunti testa a testa saldati al laser in lega di titanio si è determinato invece un valore medio del raggio di raccordo pari a 0.98 mm. per quanto riguarda il disallineamento di giunti saldati di testa ed a croce, sono state effettuate circa 80 misure dell’angolo  di disallineamento tra le piastre principali su giunti di vario tipo e di spessore di 5, 10 e 25 mm, successivamente sottoposti a prove di fatica in trazione. in fig. 5 si riassume la distribuzione dei dati provenienti dalle misure di ; i dati presentano una distribuzione asimmetrica, affatto rappresentabile dai valori di media e deviazione standard di una distribuzione normale. in particolare l’angolo assume nella maggior parte dei casi un valore diverso da zero, ma abbastanza contenuto nell’ordine di un grado decimale (la media risulta infatti di circa 1,096°); in altri casi molto meno frequenti si riscontrano angoli molto elevati fino ai 5° per alcuni provini, giudicati eccessivamente poco significativi data la frequenza molto bassa e tenendo conto che la lavorazione manuale dei provini può aver prodotto delle distorsioni non dovute al processo. in fig. 6 si è riportato su un medesimo grafico l’ampiezza di deformazione a, misurata per le prove di fatica, in funzione dell’angolo di disallineamento. naturalmente sono stati considerati solo giunti sottoposti ad un carico di trazione a fatica molto simile, in un intervallo ristretto di tensioni nominali applicate; si noti la mancanza di alcuna correlazione precisa, evidenziando forti variazioni delle deformazioni misurate dagli estensimetri. ciò è una conferma, seppur indiretta, del fatto che la deformazione a non venga influenzata unicamente dal disallineamento ma anche da effetti locali del cordone o http://www.gruppofrattura.it/ http://dx.medra.org/10.3221/igf-esis.09.07&auth=true v. dattoma et alii, frattura ed integrità strutturale, 9 (2009) 64 – 75; doi: 10.3221/igf-esis.09.07 72 comunque caratteristici del giunto esaminato, confermandone la validità come parametro rappresentativo ai fini della valutazione della resistenza a fatica. (a) (b) figura 4: distribuzione del raggio di raccordo: a) giunti in acciaio; b) giunti in titanio. figura 5: distribuzione dei valori misurati dell’angolo di disallineamento . 0 0,1 0,2 0,3 0,4 0,5 0,6 0,7 0 2 4 6r (mm) d is tr ib u z io n e n o rm a le giunti a croce giunti di testa media: 0.79 mm dev. standard: 0.68 media: 2.47 mm dev. standard: 1.28 mis ure di r per giunti di tes ta in titanio 3‐5 mm 0 0,02 0,04 0,06 0,08 0,1 0,12 0,14 0 0,5 1 1,5 2 2,5 r [mm] f re q .  re la ti v a dev. st. : 0.449 dist ribuzione normale 0 0,1 0,2 0,3 0,4 0,5 0,6 0,7 0,8 0,9 1 0 0,5 1 1,5 2 2,5 r medio: 0.982 0 5 10 15 20 25 30 0 1 2 3 4 5 6 7  [°] n ° d i p ro v in i 0 0,05 0,1 0,15 0,2 0,25 0,3 0,35 0 1 2 3 4  [°] d is tr ib u z io n e n o rm a le valor medio: 1,096° dev. standard: 1,328 http://www.gruppofrattura.it/ http://dx.medra.org/10.3221/igf-esis.09.07&auth=true v. dattoma et alii, frattura ed integrità strutturale, 9 (2009) 64 – 75; doi: 10.3221/igf-esis.09.07 73 figura 6: correlazione tra l’ampiezza di deformazione locale a e l’angolo di disallineamento . sperimentazione sulla lega di titanio: primi risultati el presente lavoro si presentano anche i primi risultati ottenuti su giunti in lega di titanio tial6v4, saldati al laser in configurazione testa a testa e aventi uno spessore delle piastre di 3 e 5 mm. in fig. 7 sono stati riportati tutti i dati delle prove eseguite finora, rilevando ancora una volta che la misura di deformazione locale è ben correlata con la vita residua a fatica, come dimostrato dalla bassa dispersione dei dati. i dati riferiti a spessori diversi si dispongono come previsto lungo una stessa curva di fittine e consentono di stimare con buona approssimazione una deformazione limite a pari a circa 769 . trattandosi di materiale diverso, sebbene l’andamento dei dati misurati in funzione del numero di cicli n sia identico a quello dei giunti in acciaio, la posizione della curva di riferimento e la sua pendenza sono rispettivamente più alta e meno inclinata (all’incirca il coefficiente m=7 per il titanio, mentre m=4 i giunti in acciaio); si è verificato quindi che il metodo della deformazione locale è potenzialmente efficace anche per un materiale diverso come la lega di titanio e anche per tecnologie di saldatura totalmente differenti. figura 7: curve di resistenza a fatica in termini di ampiezza di deformazione locale di giunti saldati in titanio. 0 200 400 600 800 1000 1200 1400 0 0,5 1 1,5 2 2,5 3  [°] disallineamento  a tensione nominale da 85 a 100 mpa tensione nominale da 70 a 85 mpa n http://www.gruppofrattura.it/ http://dx.medra.org/10.3221/igf-esis.09.07&auth=true v. dattoma et alii, frattura ed integrità strutturale, 9 (2009) 64 – 75; doi: 10.3221/igf-esis.09.07 74 conclusioni l lavoro eseguito consente di stabilire in modo preciso l’affidabilità e l’efficacia del metodo della deformazione locale per la verifica a fatica dei giunti saldati. sono state ottenute infatti, le curve di riferimento per il calcolo della vita residua in termini di misura dell’ampiezza a, adoperando i risultati da prove di fatica eseguite su diverse tipologie di giunti, con variabile spessore delle piastre ed anche modalità di carico a trazione e flessione. raggruppando tutti i dati disponibili in soli due classi di spessori, i risultati del metodo si dimostrano eccezionalmente coerenti ed offrono una curva di riferimento univoca per la progettazione a fatica in termini di deformazione, che ha carattere globale. gli esperimenti effettuati hanno consentito anche di determinare con certezza l’influenza dei parametri perturbanti sulla metodologia proposta per il dimensionamento a fatica, come ad esempio la variabilità della geometria del raccordo al cordone, la presenza del disallineamento fra le piastre e la geometria globale della classe strutturale del giunto. infine si è dimostrata l’applicabilità del metodo anche su materiale diverso, dal momento che si ottengono delle curve di progetto altrettanto valide, anche se posizionate in un campo differente di valori del numero di cicli. bibliografia [1] eurocode 3 – design of steel structures, env1993-1-1. european committee for standardization (1992). [2] fatigue design and assessment of steel structures, bs7608, british standard institution, london (1993). [3] structural welding code – steel, ansi/aws d1.1-86, american welding society (1986). [4] d. radaj, int. j. of fatigue, 18(3) (1996) 1530. [5] j. l. fayard, a. bignonet, k. dang van, international conference on fatigue welded components and structures, vii international spring meeting. [6] t. partenen, e. niemi, fatigue fract. engineer. material structure, 19(6) (1996) 709. [7] k. iida, annual meeting of international institute of welding, xiii (1983) 1103. [8] d. radaj, design and analysis of fatigue resistant welded structures, abington publishing, cambridge (1990). [9] d. radaj, c.m. sonsino, fatigue assessment of welded joints by local approaches, abington publishers, cambridge (1998). [10] international institute of welding (iiw), iso standard proposal, iiw document xiii-1539-96 / xv-845-96 (1996). [11] g. qylafku, z. azari, n. kadi, m. gjonaj, g. pluvinage, int. j. of fatigue, 21 (1999) 753. [12] d. taylor, p. bologna, k. bel knani, int. j. of fatigue, 22 (2000) 735. [13] m.l. williams, j. of applied mechanics, 74 (1952) 526. [14] y. verreman, b. nie, fatigue, fracture & engineering material structures, (1996) 19. [15] p. lazzarin, r. tovo, fatigue fract. eng. mater. struct., 21 (1998). [16] p. lazzarin, p. livieri, int. j. fatigue, 23 (2001). [17] b. atzori, p. lazzarin, r. tovo, fatigue fract. eng. mater. struct., 22 (1999). [18] j. maddox, advances in fatigue science and technology, cemul, alvor beach algarve, 4-15 april 1988 (1998). [19] j.m. ferreira, a.h. pereira, c.m. branco, thin-walled structures, 21 (1995) 107. [20] k. masubuchi, , analysis of welded structures, pergamon press, usa. [21] t.r. gurney, fatigue of welded structures, cambridge university press (1979). [22] c. pappalettere, r. nobile, notch effects in fatigue and fracture (g. pluvinage and m. gjonanj editors) nato sciences series ii – mathematics, physics and chemistry, kluwer (2000). [23] haibach, proc. of the conference on fatigue on welded structures, the welding institute, abington (uk), 2 (1971). [24] b. atzori, g. blasi, c. pappalettere, experimental mechanics, 25 (1985) 2 [25] v. dattoma, g. demelio, c. pappalettere, proceedings of xxii convegno aias, forlì (1993). [26] v. dattoma, c. pappalettere, j. of strain analysis, 36 (2001) 6. [27] v. dattoma, f.w. panella, c. pappalettere, proceedings of xxix convegno aias, lucca (2000). [28] r. nobile, c. pappalettere, proceedings of xv convegno nazionale del gruppo italiano frattura (igf), bari (2000). [29] r. nobile, verifica ed affidabilità delle strutture saldate, tesi di dottorato, politecnico di bari-université de metz (2001). [30] c. casavola, r. nobile, c. pappalettere, proceedings of xxx convegno aias, alghero (2001). [31] c. casavola, r. nobile, c. pappalettere, new trends in fatigue and fracture, metz (2002). [32] c. casavola, r. nobile, c. pappalettere, new trends in fatigue and fracture ii, hammamet,(2003). i http://www.gruppofrattura.it/ http://dx.medra.org/10.3221/igf-esis.09.07&auth=true v. dattoma et alii, frattura ed integrità strutturale, 9 (2009) 64 – 75; doi: 10.3221/igf-esis.09.07 75 [33] c. casavola, r. nobile, c. pappalettere, society of experimental mechanics (sem) annual conference, charlotte north carolina (usa) (2003). [34] c. casavola, r. nobile, c. pappalettere, sem annual conference and exposition on experimental and applied mechanics, costa mesa (usa), (2004). [35] v. dattoma, r. nobile, f.w. panella, xxxii convegno nazionale dell’associazione italiana per l’analisi delle sollecitazioni (aias) – salerno (2003). [36] c. casavola, u. galietti, m. gismondi, f. pierattini, xxxii convegno nazionale dell’associazione italiana per l’analisi delle sollecitazioni (aias) – salerno (2003). [37] c. casavola, c. pappalettere, int. j. of fatigue, 31 (2009). [38] c. casavola, c. pappalettere, proceedings of sem annual conference and exposition on experimental and applied mechanics, portland (usa), (2005). [39] c. casavola, c. pappalettere, proceedings of the international conference new trends in fatigue and fracture 5, bari (italy), (2005). [40] c. casavola, f. tattoli, c. pappalettere, proceedings of sem annual conference and exposition on experimental and applied mechanics, springfield (usa) (2007). http://www.gruppofrattura.it/ http://dx.medra.org/10.3221/igf-esis.09.07&auth=true microsoft word numero_39_art_25 s. doddamani et alii, frattura ed integrità strutturale, 39 (2017) 274-281; doi: 10.3221/igf-esis.39.25 274 experimental investigation on fracture toughness of al6061–graphite by using circumferential notched tensile specimens saleemsab doddamani department of mechanical engineering, jain institute of technology, karnataka, india, saleemsabdoddamani@gmail.com mohamed kaleemulla department of studies in mechanical engineering, university b.d.t. college of engineering, karnataka, india. abstract. this paper presents the experimental work carried out on the fracture behavior of aluminium 6061 (al6061) and graphite particulate composites. the required specimens are prepared using stir casting method with graphite proportions ranging from 3 to 12 % by weight. the fracture behavior of al6061-graphite particulate composites produced using stir casting method, was investigated by conducting experiments on universal testing machine (utm). circumferential notched tensile (cnt) specimens were utilized to evaluate the fracture toughness of the composites. from the experiment the fracture toughness kic= 15.85mpa m1/2 is obtained for al6061-9% graphite. further, the experimental results revealed that, except 12% graphite, the fracture toughness of al6061-graphite was observed to increases with an increase in weight percentage of graphite. the experimental results reinforce that al6061-graphite particulate mmcs are suitable for automotive and aerospace applications requiring high fracture toughness apart from good wear resistance. keywords. fracture toughness; circumferential notched tensile (cnt) specimens; aluminium graphite particulate composites. citation: doddamani, s., kaleemulla, m., experimental investigation on fracture toughness of al6061–graphite by using circumferential notched tensile specimens, frattura ed integrità strutturale, 39 (2017) 274-281. received: 29.11.2016 accepted: 06.12.2016 published: 01.01.2017 copyright: © 2017 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. introduction etal matrix composites (mmcs) are a widely varied group of materials that consist of a metallic alloy (aluminum, magnesium, and titanium alloys) as matrix and ceramic as reinforcement (alumina (al2o3), silicon carbide (sic), carbon, or graphite) in the form of continuously aligned fibers, short fibers, whiskers, platelets m http://www.gruppofrattura.it/pdf/rivista/numero39/audio/25.mp3 s. doddamani et alii, frattura ed integrità strutturale, 39 (2017) 274-281; doi: 10.3221/igf-esis.39.25 275 and particles. mmcs are used in automobile/aerospace applications, and also in applications requiring thermal management, wear resistance and weight reductions. aluminium alloys is widely used for construction of aircraft structures. there are different cracks being inspected in aircraft wings. different types of cracks inspected are: (1) hairline cracks in the inward wing structure, and (2) cracks at the edges of the vertical web of the feet. if the elevated forces are applied to the fasteners during assembly which are not accounted, the stress arising from the interference fit will possibly lead to cracking [10]. the particular type of aluminium alloy used will also have an effect on the assembly where a balance has to be achieved between stiffness, strength and fracture toughness. the literature survey presents a review of the published material available on the effect of various reinforcement types, their size and volume fraction, ageing behavior with aluminium based mmcs are a combination of two phases, matrix and the reinforcement. aluminium graphite composites for various compositions are prepared by using stir casting method [15], mechanical alloying (mi) and hot extrusion method [16] etc., and the specimens were tested for their hardness, tensile, wear and fracture properties etc. mechanical characterization such as tensile strength and elongation experiments by using universal testing machine (utm) of al/sic has been reported [8] for varying mass fraction of sicp with aluminium. hardness [2], fracture toughness [3, 4], tensile fracture behavior on circumferential notched tensile (cnt) specimens [5,6] on compact tension (ct) test specimen [13, 14] of al/sic was studied by different researchers and most of them compared their results with the unreinforced aluminium alloy. in this research work, a new method of finding the fracture toughness, using circumferential notched tensile (cnt) specimens, is utilized which is a recent advance in fracture toughness testing method is adopted. from the literature it is observed that relatively more work has been done on the tensile and fracture characteristics of aluminium silicon carbide particulate mmcs. however, a significant scope exists for research on the aluminium matrix composites reinforced with graphite particles, particularly in the area of fracture and fatigue in order to improve the strength and fracture characteristics of the material to avoid the cracking. in this backdrop, the current research work is proposed to study the fracture toughness of aluminium 6061 graphite particulate composite at varied weight fractions. the specimen are prepared using stir casting method with graphite proportions of 3 to 12 % by weight. the specific objective of the research work is to study the fracture toughness of the aluminium graphite mmc at varied weight fractions of graphite (3%, 6%, 9%, and 12%) experimentally using circumferential notched tensile (cnt) specimens. also an attempt will be made to compare the results of al6061-graphite composites with the aluminium silicon carbide particulate (al-sicp) composites. materials he material chosen for this research work is aluminium 6061 as matrix and graphite particles as reinforcement. the motivation to use these materials for this research work is the density of two materials involved, which are nearly same for aluminium (2.65g/cc) and graphite (2.2g/cc). the al6061-graphite particulate composites have discontinuously reinforced composite properties which are nearly isotropic and also have outstanding combination of mechanical, structural, thermal and physical properties. figure 1: schematic view of stirring mechanism used in the fabrication of mmc [15]. t s. doddamani et alii, frattura ed integrità strutturale, 39 (2017) 274-281; doi: 10.3221/igf-esis.39.25 276 processing luminium 6061-graphite specimens are prepared at varied weight fractions of graphite (3%, 6%, 9%, and 12%) using stir casting method. the aluminium blocks were melted in the furnace as shown in fig. 1. after melting, molten aluminium was super-heated to desired temperature (about 7500 c). the required amounts of graphite particles were added to the aluminium melts while stirring with stirrer at speed of 550 rpm. the molten aluminium-graphite was poured into a split type permanent mould and it was allowed to solidify. the aluminium-graphite alloy bars were taken out from the mould. the specimens were prepared from as-cast alloys for determination of required properties. experimentation o investigate the fracture toughness, there are different methods. basically american society for testing and materials (astm) standards and recent advances in fracture toughness testing methods are used for testing of aluminium alloys and some of aluminium matrix particulate reinforced composites. astm standard testing methods include fracture toughness testing by single1edge1notch bend (senb) specimen and compact tension (ct) specimen. other testing methods which are getting popular for their ease include fracture toughness by circumferential notched tensile (cnt) specimens, round bar, and indentation techniques. figure 2: schematic representation of the cnt specimen [13]. circumferential notch tensile (cnt) specimen shown in fig. 2 was fabricated for estimation of fracture1toughness, in a manner confirming with alaneme and aluko [3]. the cnt samples were machined for the following dimensions: sample diameter d=12.5mm, notch diameter d =11.24mm, gauge length l =62.5mm, and notch angle α =60°. the test samples were subjected to tensile test on utm for the determination of fracture toughness. the load at fracture (pf) acquired from the cnt specimens load-expansion plots (fig. 3) were utilized to assess the fracture toughness [3] by applying observational relations by dieter: ick f 3/2 p d d 1.72 1.27 d          (1) where, pf = load at fracture, in n d = specimen diameter, in mm and d = notch diameter, in mm. in accordance with nath and das [11], the reliability of the cnt testing method and the achievement of the plane strain condition were evaluated using the relations: ic y k 2 d          (2) a t s. doddamani et alii, frattura ed integrità strutturale, 39 (2017) 274-281; doi: 10.3221/igf-esis.39.25 277 where, σy is the yield strength, in n/mm2 kic is fracture toughness, mpa m½ also, the length of the specimen is taken here for the testing was 4 times the specimen diameter which was the requirement taken into consideration while preparing the cnt specimens. tension test was performed at room temperature on the cnt specimens for the al6061-graphite particulate metal matrix composites of 3%, 6%, 9% and 12% graphite using a utm following standard test procedures in agreement with the astm:e8m – 91 standards [14]. the cnt specimens are allowed for tensile test. the load at fracture (pf) is noted for each specimen of above said weight fractions. the load at fracture (pf) obtained are taken in consideration to calculate the fracture toughness (kic) using the empirical relation (1). evaluation of fracture toughness was investigated for al6061-graphite mmc using cnt specimen testing. from the outcomes it was observed that the crack durability results assessed from the cnt test were justifiable (in plain strain condition) even though the samples were not fatigue pre-cracked. result and discussions racture toughness for the various weight fractions of al6061-grphite particulate mmc are evaluated experimentally and results are shown in tab. 1. fracture toughness of the a6061-grphite composite for 3, 6, 9, 12% graphite is determined using cnt specimens on utm. the plane strain fracture toughness condition was met with the cnt sample diameter of d=12.5 mm using eq. (2) which validates the fracture toughness values obtained from experimentation. sl. no composite fracture load (pf) kn fracture toughness (kic) mpa m1/2 1 al6061-3%gr 12.51 13.92 2 al6061-6%gr 13.70 15.25 3 al6061-9%gr 14.24 15.85 4 al6061-12%gr 14.10 15.69 table 1: experimental fracture toughness of al6061-graphite mmc. from the outcomes it is observed that the fracture toughness results assessed from the cnt test were substantial (in plain strain condition) even though the samples were not fatigue pre-cracked. fracture toughness of the a6061-grphite composite for 3, 6, 9, 12% graphite is determined using cnt specimens on utm. for each composition three specimens are prepared and tested for fracture toughness. load – elongation curve for al-graphite for different weight fractions of graphite is shown in the fig. 3. it is observed that the elongation increases with increase in load. for all specimens there is small difference in change in elongation. fracture load and the maximum elongation of al-3% graphite is pf = 12.51kn and 4.21mm respectively. fracture load and the maximum elongation of al6% graphite is pf = 13.70kn and 4.31mm respectively. fracture load and the maximum elongation of al-9% graphite is pf = 14.24kn and 4.58mm respectively. fracture load and the maximum elongation of al-12% graphite is pf = 14.10kn and 4.55mm respectively. the increase in elnogation is because of the existence of the hard and higher modulus graphite particles embedded in the al6061 matrix, which act as a barricade to oppose plastic flow when the mmc is subjected to an applied load. also, the decreased interparticle spacing, due to the increased weight percent of graphite reinforcement, creates increased resistance to dislocation motion, which gives the improved strength to mmcs. f s. doddamani et alii, frattura ed integrità strutturale, 39 (2017) 274-281; doi: 10.3221/igf-esis.39.25 278 (a) (b) (c) (d) figure 3: load-elongation curve for (a) al-3% graphite (b) al-6% graphite (c) al-9% graphite (b) al-12% graphite. (a) (b) (c) (d) figure 4: sem micrographs of fracture surface of (a) al-3% graphite (b) al-6% graphite (c) al-9% graphite (d) al-12% graphite. s. doddamani et alii, frattura ed integrità strutturale, 39 (2017) 274-281; doi: 10.3221/igf-esis.39.25 279 for studying the nature of crack and bonding of matrix and reinforcement it is essential to examine the fractured surfaces of all the specimens. scanning electron microscope (sem) is used to examine the fractured specimens of al-graphite for the nature of fractured surface either ductile or brittle failure. fractographic inspection was made on the fractured surface of cnt specimens for various al-graphite composites. fig. 4(a-d) show the fractographs of the fractured cnt specimens for various al-graphite composites. from fig. 4 (a-d) the failure of al-graphite composites show dimples which grown through the matrix and are formed by void nucleation. void nucleation cause particle rupture and debonding at the matrix-reinforcement interfaces which in turn cause the crack initiation. these micro cracks propagate from the vicinity of crack tip and passes through the matrix unstructured matrix. from experimental results it was observed that, except 12% graphite, the fracture toughness of al6061-graphite was observed to increase with an increase in weight percent of graphite. this increase in fracture toughness is the effect of graphite particulates which act as barricade to internal cracks in the microstructure. however for 12% graphite there is decrease in the fracture toughness was observed. this decrement may be due to increased particles which causes particle clustering and the surrounding matrix. the maximum fracture toughness was found for al6061-9%gr and the value is 15.85 mpa m1/2. figure 5: fracture toughness of al-gr mmc. fig. 5 shows comparison of fracture toughness of al-gr for all three specimens. from the outcomes it is observed that the fracture toughness results assessed from the cnt specimens were significant. from experimental results it was observed that, except 12% graphite, the fracture toughness of al6061-graphite was observed to increase with an increase in weight percent of graphite. the for specimen 1 maximum fracture toughness was found for al6061-9%gr and the value is 15.85 mpa m1/2. comparison of aluminium silicon carbide with aluminium graphite laneme and aluko [3] utilized the tensile and cnt specimens for tension testing to evaluate, respectively, the tensile properties and fracture toughness of the composite al-sic for 3, 6, 9, and 12 volume percent of sic. from the experimental results obtained for both the tests it concluded that significant improvement in the strength of the al matrix composites is achieved when 9 and 12 vol% of sic is used as reinforcement; and the ductility of the composites is not adversely affected at these compositions in comparison with the monolithic alloy. tab. 2 shows the comparison of fracture toughness of aluminium silicon carbide with aluminium graphite. from the comparison, it is found that the fracture toughness of the aluminium graphite is more compared to aluminium silicon carbide. therefore, aluminium graphite can be considered as a promising material for aerospace and automobile applications where high crack arrest abilities and high strength with reduced weight is required. further, it will contribute to crash worthy design of aircraft/automobile structures. a s. doddamani et alii, frattura ed integrità strutturale, 39 (2017) 274-281; doi: 10.3221/igf-esis.39.25 280 sl.no weight percentage fracture toughness (kic) mpa m1/2 al-sic al-graphite 1 3% 6.61 13.92 2 6% 6.59 15.25 3 9% 5.63 15.85 4 12% 6.71 15.69 table 2: comparison of fracture toughness of al-sic [3] and al-gr. conclusions ased on the experimental study of al6061-graphite mmcs the following conclusions are made. the experimental study of the fracture toughness of the al6061-graphite was conducted in this work. from experimental results it was observed that, except 12% graphite, the fracture toughness of al6061-graphite was observed to increase with an increase in weight percent of graphite. this increase in fracture toughness is the effect of percentage increment of graphite particulates which act as barricade to internal cracks in the microstructure. from the comparison it is found that the fracture toughness of the aluminium graphite is more compared to aluminium silicon carbide. based on the conclusions made here, one can consider the al6061-graphite particulate mmc for automobile applications such as: bearing surfaces, cylinder liners, pistons, cam shafts, brake components, etc., and aerospace applications such as internal aerospace engine components, exhaust systems, wing and fuselage (main body) of aircraft structure. funding his research received no specific grant from any funding agency in the public, commercial, or not-for-profit sectors. references [1] asm international, asm handbook of composites, 21 (2001). [2] saheb, d. a., aluminum silicon carbide and aluminum graphite particulate composites, arpn journal of engineering and applied sciences, 6(10) (2011). [3] alaneme, k.k., aluko, a.o., fracture toughness (kic) and tensile properties of as-cast and age-hardened aluminium (6063)–silicon carbide particulate composites, scientia iranica a, 19 (4) (2012) 992–996. [4] alaneme, k.k., fracture toughness (kic) evaluation for dual phase medium carbon low alloy steels using circumferential notched tensile (cnt) specimens, materials research, 14(2) (2011) 155-160. [5] agboola, o. p., sarioglu, f., kızılors, c., validation of circumferential notched tensile (cnt) test procedure for kiscc determination, proceedings of the world congress on engineering, london, u.k., iii (2013). [6] nath, s. k., kr das, u., effect of microstructure and notches on the fracture toughness of medium carbon steel, journal of naval architecture and marine engineering, (2006). [7] asm international, asm handbook fatigue and fracture, 19 (1996). [8] neelima devi, c, mahesh, v., selvaraj, n., mechanical characterization of al/sic composite, international journal of applied engineering research, dindigul, 1 (4) (2011). [9] anderson, t. l., fracture mechanics-fundamentals and applications, 3rd edition, (2013). [10] european aviation safety agency (easa), the airbus a380 wing cracks: an engineer’s perspective, http://www.theconversation.com. february 10, (2012). b t s. doddamani et alii, frattura ed integrità strutturale, 39 (2017) 274-281; doi: 10.3221/igf-esis.39.25 281 [11] nath, s. k., kr das, u., effect of microstructure and notches on the fracture toughness of medium carbon steel, journal of naval architecture and marine engineering, (2006). [12] rocha-rangel, e., fracture toughness determinations by means of indentation fracture, nanocomposites with unique properties and applications in medicine and industry, (2011). [13] doddamani s., kaleemulla, m., review of experimental fracture toughness (kic) of aluminium alloy and aluminium mmcs, international journal of fracture and damage mechanics, 1(1) (2015) 1-15. [14] astm e8 / e8m-15a, standard test methods for tension testing of metallic materials, astm international, west conshohocken, pa, (2015). [15] begum, y., doddamani, s., mechanical properties of aluminium–graphite particulate composites”, ncerame-2015, international journal of engineering research & technology (ijert), (2015). [16] deaquino-lara, r., soltani, n., bahrami, a., gutiérrez-castañeda, e., garcía-sánchez, e., hernandez-rodríguez, m.a.l., tribological characterization of al7075–graphite composites fabricated by mechanical alloying and hot extrusion, materials and design, 67 (2015) 224-231. << /ascii85encodepages false /allowtransparency false /autopositionepsfiles true /autorotatepages /none /binding /left /calgrayprofile (dot gain 20%) /calrgbprofile (srgb iec61966-2.1) /calcmykprofile (u.s. web coated \050swop\051 v2) /srgbprofile (srgb iec61966-2.1) /cannotembedfontpolicy /error /compatibilitylevel 1.4 /compressobjects /tags /compresspages true /convertimagestoindexed true /passthroughjpegimages true /createjobticket false /defaultrenderingintent /default /detectblends true /detectcurves 0.0000 /colorconversionstrategy /cmyk /dothumbnails false /embedallfonts true /embedopentype false /parseiccprofilesincomments true /embedjoboptions true /dscreportinglevel 0 /emitdscwarnings false /endpage -1 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/hrv (za stvaranje adobe pdf dokumenata najpogodnijih za visokokvalitetni ispis prije tiskanja koristite ove postavke. stvoreni pdf dokumenti mogu se otvoriti acrobat i adobe reader 5.0 i kasnijim verzijama.) /hun 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/pdfxoutputintentprofileselector /documentcmyk /preserveediting true /untaggedcmykhandling /leaveuntagged /untaggedrgbhandling /usedocumentprofile /usedocumentbleed false >> ] >> setdistillerparams << /hwresolution [2400 2400] /pagesize [612.000 792.000] >> setpagedevice microsoft word numero_41_art_49.docx z. li et alii, frattura ed integrità strutturale, 41 (2017) 378-387; doi: 10.3221/igf-esis.41.49 378 residual welding stress of i-section members beyond the limits of width-thickness ratio zhiyuan li chongqing water resources and electric engineering college, yongchuan, chongqing, 402160, china 1628607391@qq.com zhiyun zhao shaanxi architectural design & research institute co., ltd, xi’an, shaanxi, 710018, china 33005652@qq.com abstract. despite the extensive studies on the effect of width-thickness ratio and residual stress on member behavior, few scholars have probed into the residual stress distribution on the i-section members. based on the principle of blind hole drilling, this paper conducts an experimental study of the residual welding stresses of eight welded i-shaped members. through the analysis of the test results, the author draws the following conclusion: it is safe to use i-section members beyond the limits of width-thickness ratio because the residual stress distribution is not severely affected by width-thickness ratio. keywords. steel structure; residual stress; material grade; width-thickness ratio; principle of blind hole drilling; i-shaped members. citation: li, z., zhao, z., residual welding stress of i-section members beyond the limits of width-thickness ratio, frattura ed integrità strutturale, 41 (2017) 378-387. received: 14.03.2017 accepted: 14.05.2017 published: 01.07.2017 copyright: © 2017 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. introduction n many large steel structures, the flexural members are often i-shaped members with excessively high width-thickness ratio. such members fall into the category of large welded components. after welding, residual welding stress will generate inside the components, producing welding deformation or cracks. when members are subjected to external loads, the local regional stress will grow exponentially under the combined effect of welding stress and external stress, leading to plastic deformation, cracking, and even overall fracturing [1-3]. the residual stress distribution and the size of i-shaped members vary significantly as a result of the effect of the residual stress on structural rigidity, stability, strength and stress corrosion cracking. it is therefore necessary to study the relationship between residual stress distribution and width-thickness ratio of such members. many chinese scholars have probed into the effect of width-thickness ratio and residual stress on member behavior. through the analysis of i-section members, shang fan et al. [4] discovered that the residual stress around the weak axis is greatly influenced by the bearing capacity of the component. huan xinyuan et al. [5] adopted segmentation method to cut an i-section member into strips, measured the release of residual strain, and constructed a simplified model that can accurately describe the size of stainless steel isection member and the distribution of residual stress. qu lihua [6] simulated the vibration mode and frequency variation i z. li et alii, frattura ed integrità strutturale, 41 (2017) 378-387; doi: 10.3221/igf-esis.41.49 379 under the influence of residual stress, pointing out that the effect of residual stress on structural mode is too big to be ignored. taking the chunyi bridge on haihe river as an example, ding daiwei et al. [7] expounded the test principle of blind hole method, examined the impact of welding residual stress on the steel box girder bridge, and obtained the distribution and features of the welding residual stress. mo mingchao [8] contoured the internal residual stress in welds by cutting open the vertical welding seam, and conducted contour precision testing and fitting. in the principle of blind hole drilling, this paper aims to measure residual stress, draw residual stress distribution maps, and analyze the influencing factors of welding residual stress, thereby providing a basis for the design of similar components. test overview test materials here are 8 specimens in this research, numbered from ch-1 to ch-8. specimens ch-1~ch-5 are made of the material q235b, while specimens ch-6~ch-8 are made of the material q345b. see tabs. 1 and 2 below for the chemical compositions and mechanical properties of the two types of materials. material chemical composition (%) c si mn p s alt q345b 0.069 0.472 0.86 0.014 0.002 0.021 q235b 0.18 0.029 0.42 0.018 0.003 0.025 table 1: the chemical compositions of test materials material mechanical properties σy/mpa σs/mpa δ/% impact properties/j q345b 460 530 29.5 104 q235b 335 450 33 115 table 2: the mechanical properties of test materials test equipment the hk21b type residual stress detector (fig. 1) and 3-element rosette strain gauge bx120-3ca are adopted for the test. figure 1: hk21b residual stress detector specimen design eight welded i-shaped members (ch-1 ~ ch-8) are prepared for the test. the thickness of the specimens varies: ch-1 ~ ch-3 and ch-6 ~ ch-8 are 6mm thick; ch-4 and ch-5 are 10mm thick. fig. 2 illustrates the specimen sizes and fig. 3 displays the sizes and width-thickness ratios of the specimens. t z. li et alii, frattura ed integrità strutturale, 41 (2017) 378-387; doi: 10.3221/igf-esis.41.49 380 figure 2: specimens sizes specimen b/t hw/tw b/mm hw/mm h/mm ch-1 14.5 75 180 450 462 ch-2 14.5 125 180 750 762 ch-3 24.5 100 300 600 612 ch-4 24.5 75 300 750 770 ch-5 41.2 100 500 1000 1020 ch-6 14.5 75 180 450 462 ch-7 14.5 125 180 750 762 ch-8 24.5 100 300 600 612 table 3: specimen sizes and width-thickness ratios. fundamentals the principle of blind hole residual stress measurement is shown in fig. 3. if a structural member is subjected to a residual stress field and an elastic strain field, the residual stress at any point inside the small blind hole will be released. as the original stress field falls out of balance, there will be a certain amount of strain release around the blind hole so that the original stress field reaches a new equilibrium. the formation of new stress and strain fields at the residual stress measuring points can be measured by the following formulas [9-11].    2 21 31,2 1 3 2 1 3 1 2 4 4a b                (1)  1 21 2 cos 2 2 2 z         (2)    1 3 2 1 3 2 2tg           (3) 2 1 2 1 2 a a e r r    z. li et alii, frattura ed integrità strutturale, 41 (2017) 378-387; doi: 10.3221/igf-esis.41.49 381  2 2 22 1 1 2 2 2 2 1 2 1 2 1 2 1 1 4 a r r r ra b e r r r r           (4) the symbols are explained as below [12]: 1 , 2 and 3 : the relieved strain measured by each of the rosettes in the strain (  ); a, b: the strain release coefficients obtained based on tensile experimental calibration or theoretical calculation formulas based on aperture, hole depth, geometry size of strain rosette and elastic modulus; θ : the clockwise angle between the maximum principal stress and the stress reference axis of 1# rosette; 1 , 2 : the principle stresses (mpa). e: the elasticity modulus; μ : the poisson’s ratio; d, 1r , 2r : the aperture of the blind hole, the distance from the blind hole center to the near end of the strain gauge, and the distance from the blind hole center to the far end of the strain gauge (mm). figure 3: principle of blind hole drilling method residual stress test test methods targeted at measuring the distribution of longitudinal residual stress in the i-section members, the rosettes are arranged along the centerline of the cross-section of each specimen [13-21]. for the sake of simplicity, only the rosettes at the upper flange and web are taken into consideration because the cross-section is symmetrical. the rosette arrangement is shown in figure 3. the spacing between the rosette and the flange is 1/4b; the spacing between the rosette and the web is: 1/6hw (ch-3, ch-4), 1/8hw (ch-5), and 1/4hw (others). the distance from the flange to the edge of the member is 10m, and the distance from the web to the edge of the member is 20mm. (a) paste strain rosettes (b) weld the wires (c) drill the holes figure 4: strain rosettes cementing, wire welding and drilling z. li et alii, frattura ed integrità strutturale, 41 (2017) 378-387; doi: 10.3221/igf-esis.41.49 382 test procedure following the blind hole drilling method, the test procedure goes as: prepare the surface, paste strain rosettes, weld the wires, install the tool, drill the holes, record the drilling, remove the tool and sort out the tool. fig. 4 presents the most important steps in the procedure. test results and analysis test results igs. 5-12 show the distribution of the longitudinal stresses in the specimens. (a) (b) figure 5: longitudinal residual stress distribution of ch-1. (a) flage; (b) web. (a) (b) figure 6: longitudinal residual stress distribution of ch-2. (a) flage; (b) web. (a) (b) figure 7: longitudinal residual stress distribution of ch-3. (a) flage; (b) web. f z. li et alii, frattura ed integrità strutturale, 41 (2017) 378-387; doi: 10.3221/igf-esis.41.49 383 (a) (b) figure 8: longitudinal residual stress distribution of ch-4. (a) flage; (b) web. (a) (b) figure 9: longitudinal residual stress distribution of ch-5. (a) flage; (b) web. (a) (b) figure 10: longitudinal residual stress distribution of ch-6. (a) flage; (b) web. (a) (b) figure 11: longitudinal residual stress distribution of ch-7. (a) flage; (b) web. z. li et alii, frattura ed integrità strutturale, 41 (2017) 378-387; doi: 10.3221/igf-esis.41.49 384 (a) (b) figure 12: longitudinal residual stress distribution of ch-8. (a) flage; (b) web. analysis of test results as shown in figs. 5~12, the residual stress along the centerline in the cross-section obeys symmetric parabolic distribution. in all the specimens, the residual tensile stress descends from the near-weld region to the middle of the member, but the trend is not linear. the residual tensile stress peaks at the centerline of the member. except for specimen ch-5, each of the specimens boasts a peak value of residual tensile stress so large as to exceed the yield strength of the material. the peaks of residual tensile stress at the web occur near the edge of weld instead of the flange. with only a few specimens surpassing the yield strength of the material, the web has a small residual tensile stress that essentially follows symmetric parabolic distribution similar to that of the cross-section of i-section members beyond the limits of width-thickness ratio. the stress distribution is basically linear in the middle of the web. figs. 13, 14 and 15 make pair-wise comparison of residual stress distributions between ch-1 and ch-6, ch-2 and ch-7, as well as ch-3 and ch-8. each pair includes two specimens of the same cross-sectional size but different materials. ch1, ch-2 and ch-3 are made of q345b, while ch-6, ch-7 and ch-8 are made of q235b. figure 13: comparison of residual stress distribution between ch-1 and ch-6. influence of yield strength the material parameters stand for the important influencing factors of welding residual stress. this research mainly emphasizes on the yield strength of q235b and q345b in each pair of specimens. as mentioned above, out of the eight specimens ch-1~ch-8, ch-1~ch-5 are made of q345b, and ch-6~ch-8 are made of q235b. fig. 13 compares the residual stress distributions between ch-1 and ch-6. the two specimens share same cross-sectional size.: 18045066mm. the materials of ch-1 and ch-6 are q345b and q235b, respectively. according to fig. 13, the residual stress distribution of the two specimens are largely the same. the only difference lies in the peak residual stress, which is mainly attributable to the difference in materials. moreover, the peak residual tensile stress at the flange increases from 253.38 mpa in ch-6 to 373.15 mpa in ch-1, up by 47%; the peak residual tensile stress at the z. li et alii, frattura ed integrità strutturale, 41 (2017) 378-387; doi: 10.3221/igf-esis.41.49 385 web rises from 147.10 mpa in ch-6 to 405.53 mpa in ch-1, up by 175%. fig. 14 (comparing ch-2 with ch-7) and fig. 15 (comparing ch-3 with ch-8) show the same trend. therefore, the peak residual stress will increase with the yield strength of the material if the cross-section remains the same. in short, the effect of material grade on residual stress is: for a given width-thickness ratio, the higher the yield strength, the larger the peak value of the residual stress. figure 14: comparison of residual stress distribution between ch-2 and ch-7. figure 15: comparison of residual stress distributions between ch-3 and ch-8. influence of material size fig. 16 compares the peak residual stresses of three groups of specimens. in each group, the specimens share the same material grade but differ in width-thickness ratio. specifically, the first and second groups have different width-thickness ratios at the web; the third group have different width-thickness ratios at the flange. the first group of specimens are ch-1 and ch-2, both of which are made of the same material q345; however, the two specimens differ in width-thickness ratio at the web (75 vs. 125). the second group of specimens are ch-7 and ch-8, both of which are made of the same material q235; however, the two specimens differ in width-thickness ratio at the flange (125 vs. 100). the difference between the two groups of specimens is clearly illustrated in the above figure. for specimens of the same material grade, the peak value of residual stress at the web decreases significantly as the width-thickness ratio increases. for instance, the peak residual stress at the web drops from 405.53mpa in ch-1 to 274.52mpa in ch-2, down by 32%; the peak residual stress at the web falls from 275.23mpa in ch-8 to 251.48mpa in ch-7, down by 9%. z. li et alii, frattura ed integrità strutturale, 41 (2017) 378-387; doi: 10.3221/igf-esis.41.49 386 the first group of specimens are ch-2, ch-4 and ch-5, all of which are made of the same material q345; however, the three specimens differ in width-thickness ratio at the flange, respectively 14.5, 24.5 and 41.2. figure 16: the relationship between the peak residual tensile stress and width-thickness ratio the difference between the third of specimens is also presented in the above figure. for specimens of the same material grade, the peak value of residual stress at the flange plunges with the increase of the width-thickness ratio. in particular, the peak residual stress falls all the way from 564.06mpa in ch-2, 388.09mpa in ch-4 to 31.16mpa in ch-5. the increase in width-thickness ratio means the member is getting thinner and the sectional size (width) is getting larger. the test results reveal the weakening of the effect of residual welding stress on member behavior and the shrinkage of peak residual stress in the cross-section. in other words, the width-thickness ratio has an insignificant effect on the distribution of residual stress in welded i-section members. therefore, it is safe to use large i-section members beyond the limits on width-thickness ratio. conclusion ollowing the blind-hole drilling method, this paper explores the effect of width-thickness ratio on the behavior of isection members. the conclusion are as follows: (1) it is safe to use large i-section members beyond the limits on width-thickness ratio. (2) for a given width-thickness ratio, the higher the yield strength, the larger the peak value of the residual stress. (3) for structural members of the same grade, the larger the width-thickness ratio, the smaller the peak residual stress. acknowledgements he research of this paper is made possible by the generous support from the special fund for construction of key disciplines in shaanxi province, china (no.: e01001, e01003), key research project of chongqing water resources and electric engineering college (no.: k201615), and the science and technology project affiliated to the education department of chongqing municipality (no.: kj1603604). references [1] the ministry of construction of the people's republic of china, gb 50017-2003 code for design of steel structures, beijing: china planning press——steel structure design specification, gb 50017-2003, 2013. [2] teng, t.l., fung, c.p., chang p.h., yang w.c., analysis of residual stresses and distortions in t-joint fillet welds, int. j. pres. ves. pip., 78 (2001) 523-538. doi: 10.1016/s0308-0161(01)00074-6. f t z. li et alii, frattura ed integrità strutturale, 41 (2017) 378-387; doi: 10.3221/igf-esis.41.49 387 [3] park, m.j., yang, h.n., jang, d.y., kim, j.s., jim, t.e., residual stress measurement on welded specimen by neutron diffraction, mater process tech., 155-156 (2004) 1171-1177. doi: 10.1016/j.jmatprotec.2004.04.393. [4] shang, f., zhao m.h., stainless steel overall stability of i-section section axial compression member finite element study, journal of engineering mechanics, 33(3) (2016) 112-119. yuan, h.x., wang, y.q., shi, y.j., the stainless steel welded i-section experimental study the residual stress distribution, journal of building structures, 35(6) (2014) 84-92. [5] qu, l.h., wei, f.f., huang, j.h., at the beginning of bending and residual stress of welding steel i-beam modal effect of numerical simulation, journal of water conservancy and architectural engineering, 11(1) (2013) 105-109. [6] ding d.w., xue j., blind hole method in the application of steel box girder bridge welding residual stress test, journal of urban road and bridge and flood control, 2 (2017) 158-161. [7] mo, m.c., the internal residual stress in weldments was tested based on contour method, journal of low-carbon technologies, 2 (2017) 67-68. [8] american society for testing and materials, standard test method for determining residual stresses by the holedrilling strain-gage method, america: annual book of astm standards, e837-e808, 2008. [9] trebuna, f., simcak, f., bocko, j., sarga, p., trebuna, p., pastor m., mihok, quantification of residual stresses in the weld by the hole-drilling method, metalurgija, 47(2) (2008) 133-137. [10] kamal, b.s., farahaninia, experimental measurement of residual stresses in cold-drawn aluminum tubes, usa: the graduate faculty of texas tech university 13 (1990). [11] wang, n., research on measuring welding residual stress of plate of moderate thickness using blind hole method, dalian university of technology, dalian, (2007). [12] chen, x.r., jiang y.y., zhao z.y., comparison for different circumferential weld-induced imperfections on steel silos. advanced materials research, (2011) 250-253. doi: 10.4271/910191. [13] tsai, c.l., dai, w.l., dickinson, d.w., analysis and development of a real-time control methodology in resistance spot welding, welding research supplement, 70(12) (1991) 339-351. doi: 10.4271/910191. [14] inoue, t., metallo-thermo-mechanics application to phase transformation incorporated processes, pros. theoretical prediction in joining and welding, 12(3) (1996) 89-112. [15] lars-erik, l., lennart k., deformations and stresses in welding of shell structures, international journal for numerical methods in engineering, 25(2) (1998) 635-638. doi: 10.1002/nme.1620250223. [16] teng, t.l., analysis of residual stresses and distortions in t-joint fillet welds, international journal of pressure vessels and piping, 78(8) (2001) 523-538. doi: 10.1016/s0308-0161(01)00074-6. [17] sicot, o., gong, x.l., cherouat, a., lu, j., influence of experimental parameters on determination of residual stress using the incremental hole-drilling method, composites science and technology, 64(2) (2004) 171-180. doi: 10.1016/s0266-3538(03)00278-1. [18] american society for testing and materials. astm e837—08: standard test method for determining residual stresses by the hole-drilling strain-gage method, america: annual book of astm standards, (2008). [19] cui, x.w., ni, w., ren, c., early hydration kinetics of cementitious materials containing different steel slag powder contents, international journal of heat and technology, 34(4) (2016) 590-596. doi: 10.18280/ijht.340406. [20] wang, x.z., wang, c.q., analysis of temperature stress in control of bridge construction, international journal of heat and technology, 34(4) (2016) 715-721. doi: 10.18280/ijht.340423. << /ascii85encodepages false /allowtransparency false /autopositionepsfiles true /autorotatepages /none /binding /left /calgrayprofile (dot gain 20%) /calrgbprofile (srgb iec61966-2.1) /calcmykprofile (u.s. web coated \050swop\051 v2) /srgbprofile (srgb iec61966-2.1) /cannotembedfontpolicy /error /compatibilitylevel 1.4 /compressobjects /tags /compresspages true /convertimagestoindexed true /passthroughjpegimages true /createjobticket false /defaultrenderingintent /default /detectblends true /detectcurves 0.0000 /colorconversionstrategy /cmyk /dothumbnails false /embedallfonts true /embedopentype false /parseiccprofilesincomments true /embedjoboptions true /dscreportinglevel 0 /emitdscwarnings false /endpage -1 /imagememory 1048576 /lockdistillerparams false /maxsubsetpct 100 /optimize true /opm 1 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can be opened with acrobat and adobe reader 5.0 and later.) >> /namespace [ (adobe) (common) (1.0) ] /othernamespaces [ << /asreaderspreads false /cropimagestoframes true /errorcontrol /warnandcontinue /flattenerignorespreadoverrides false /includeguidesgrids false /includenonprinting false /includeslug false /namespace [ (adobe) (indesign) (4.0) ] /omitplacedbitmaps false /omitplacedeps false /omitplacedpdf false /simulateoverprint /legacy >> << /addbleedmarks false /addcolorbars false /addcropmarks false /addpageinfo false /addregmarks false /convertcolors /converttocmyk /destinationprofilename () /destinationprofileselector /documentcmyk /downsample16bitimages true /flattenerpreset << /presetselector /mediumresolution >> /formelements false /generatestructure false /includebookmarks false /includehyperlinks false /includeinteractive false /includelayers false /includeprofiles false /multimediahandling /useobjectsettings /namespace [ (adobe) (creativesuite) (2.0) ] /pdfxoutputintentprofileselector /documentcmyk /preserveediting true /untaggedcmykhandling /leaveuntagged /untaggedrgbhandling /usedocumentprofile /usedocumentbleed false >> ] >> setdistillerparams << /hwresolution [2400 2400] /pagesize [612.000 792.000] >> setpagedevice microsoft word numero 8 art 3 r. ghelichi et alii, frattura ed integrità strutturale, 8 (2009) 30-44; doi: 10.3221/igf-esis.08.03 30 coating by the cold spray process: a state of the art ramin ghelichi, mario guagliano dipartimento di meccanica, politecnico di milano, via la masa 1, 20156 milan, italy riassunto. si descrive il processo di cold-spray per l’ottenimento di rivestimenti di superfici metalliche e non metalliche. la memoria, dopo una parte introduttiva relativa alle applicazioni del processo, intende discutere criticamente le attuali conoscenze al riguardo, principalmente indirizzate all’influenza dei parametri di processo sull’efficienza di deposizione (de). si focalizza l’attenzione su tutti i parametri di interesse ed è indirizzata, in particolare, all’analisi dell’influenza della rugosità della superficie del substrato sul’efficienza di deposizione. vengono poi analizzati i principali effetti del cold-spray sulle proprietà del substrato. infine, sulla base delle attuali conoscenze si tracciano e sottolineano alcuni possibili sviluppi di ricerca in questo settore. abstract. a brief description of cold spray coating process is presented. this paper intends to review some the previous works which are mostly about the influences of the cold spray parameters, mostly the surface of the substrate, on the deposition efficiency (de). almost all the important parameters, with more focus on the roughness of the substrate, on increasing the de are briefly studied; this review also includes a description of application of cold spray and of some important effect of this method on substrate properties. on this basis, some possible development in this field of research are drawn and discussed. keywords: cold spray coating, surface treatments, thermal coating introduction he ever increasing demand to manufacture weight efficient structures that are damage tolerant and can operate at elevated temperatures has fueled the development of novel alloy compositions and radically different processing approaches over the last decades. in recent years, thermal spray technologies have evolved from fairly crude processes that were relatively difficult to control into increasingly precise tools for which the process is tailored to take into account the properties of both the deposited material and the required coatings. the limitation some coating types(for instance hvof process, plasma spray systems, thermal spray technology of coating, etc) seem to be overcome for some materials by the newest thermal spray process-cold spray. cold spray is an allsolid-state process, thus making it suitable for the deposition of oxygen-sensitive materials such as aluminum, copper, or titanium or for temperature sensitive materials such as nanostructured and amorphous powders. furthermore, cold spray is known to present other characteristics that offer unique advantages compared to existing spray technology: the coatings can exhibit wrought-like microstructures with near theoretical density values; the spray trace is small (typically 1-25 mm2) and well defined allowing for precise control on the area of deposition; the coatings can be produced with compressive stresses, thus ultra thick (5-50 m) coatings can be built-up without adhesion failure; coatings can be deposited on temperature-sensitive materials such as glass or polymers[1]. cold gas-dynamic spray (or simply cold spray) is a process of applying coatings by exposing a metallic or dielectric substrate to a high velocity (300–1200 m/s) jet of small (1–50 µm) particles accelerated by a supersonic jet of compressed gas at a temperature that is always lower than the melting point of the material, resulting in coating formation from t http://dx.medra.org/10.3221/igf-esis.08.03&auth=true http://www.gruppofrattura.it r. ghelichi et alii, frattura ed integrità strutturale, 8 (2009) 30-44; doi: 10.3221/igf-esis.08.03 31 particles in the solid state. the general principle of cold spraying has been described elsewhere in more detail [2-4]. this process is based on the selection of the combination of particle temperature, velocity, and size that allows spraying at the lowest temperature possible. as a consequence, the deleterious effects of high-temperature oxidation, evaporation, melting, crystallization, residual stresses, deboning, gas release, and other common problems for traditional thermal spray methods are minimized or eliminated. cold-sprayed coatings can be processed with very low numbers of defects and low oxygen contents, and therefore exhibit bulk like properties with respect to electrical or thermal conductivity that are not attainable by normal thermal spray processes [4]. figure 1: the schematic drawing of cold gas spray apparatuses [3]. application he cold spray cost model was exercised to predict the “should” cost of making deposits of various complexities. sensitivity of these “should” costs to input variables such as powder cost, utility and shop rates, deposition precision, etc., was also carried out. this study showed that manufacturing using the cold spray process attacks many aspects of the value simultaneously. judged against the value stream results, use of this technique accomplished. [5] reduction in material input; elimination of mold and melt pour cost; reduction in rework; reduction in finishing; large increase in material utilization (cold spray has deposition efficiency of 60-95%). these estimated deposition costs were then used to help develop business cases to show that a cost advantage could be obtained by fabricating parts using the cold spray process [5]. cold spray technology can be used to produce both protective coatings and prototyping/freeform fabrication in not only strategic industries such as defense and aerospace, but also in various other general industries such as steel, utilities, paper and pulp, etc. high performance materials such as superalloys, mmcs and nanostructured materials are used to produce complex and intricate components of various high tech industries. established cold spray process can cater to economical and fast prototyping and fabrication of these components. for instance, aluminum and aluminum alloy coatings are being investigated for repair/refurbishment of space shuttle solid rocket boosters and others (aerospace), repair and retrieval of parts and plate stocks used in aircraft structures (aircraft industry), repair/refurbishment of casings (gas turbine), corrosion protection coatings (petrochemicals), brazing/joining (utility) and others. similar to aluminum, it is being pursued with copper (steel, electronics, aerospace), titanium and tantalum (electronics, bioengineering), etc. there are many other applications for cold spray coating some of them as below [5]: corrosion resistant coatings (zn, al) dimensional restoration and repair (ni, stainless steel, titanium, aluminum) wear resistant coatings (crc-nicr, wc-co, wcu) portable units for field repair biomedical – prostheses with improved wear aerospace – fatigue-resistant coatings chemical – improved corrosion resistance mineral processing – improved corrosion and erosion resistance die casting – extending die life electronics – creating a heat sink or superconductive, magnestostrictive surfaces t http://dx.medra.org/10.3221/igf-esis.08.03&auth=true http://www.gruppofrattura.it r. ghelichi et alii, frattura ed integrità strutturale, 8 (2009) 30-44; doi: 10.3221/igf-esis.08.03 32 printing – copper coating on rollers oil and gas – improved corrosion resistance glass – platinum coating. figure 2: an example of the cgds applications [6]. cold spray important parameters deposition efficiency ne of the most important characteristics of cold gas dynamic spray (cgds), as well as of any other methods of powder spray, is deposition efficiency; there are many reasons that make it practically impossible to obtain a deposition efficiency that is equal to unity. first, polydisperse powders are usually used. as the jet during its impingement is spreading along the substrate surface, the finest particles either do not reach the surface at all or impact at acute angles, which deteriorate particle attachment. although the largest particles are incident at a close-to-normal angle (i.e., the angle between the particle impact velocity and the substrate surface is close to 90°), their velocities may be insufficient for particle attachment. second, the particle velocity at the jet periphery can be lower than it must be for particle attachment. in addition, if the velocity is not sufficiently high, the surface should be self-activated by the impacted particles. due to the sufficiently complicated nature of cgds, it is rather difficult to measure the deposition efficiency; first, three main stages (see fig. 3) of the spray process may be identified. at the initial stage, some time is required for surface preparation (i.e., the induction time), when only erosion occurs without any deposition. at the second stage, a thin layer of the particle material (hereinafter referred to as the first layer) is formed on the substrate surface. this stage is characterized by the interaction of particles with the substrate surface, and it depends on the preparation level and properties of the surface material. the third stage, which can be conventionally called the build-up stage, is characterized by the growing thickness of the coating layer. in this case, the particles interact with the surface formed by previously incident particles. thus, it is clear why there is some uncertainty in measuring the powder deposition efficiency. [7] second, adhesion of particles depends on many factors: area of the contact surface, crater depth, plastic strain, yield stress, pressure and temperature at the contact boundary, etc. in turn, these factors are affected by the impact velocity of the particle. therefore, it seems logical to assume that these parameters reach their critical values at velocities close to the critical one or their dependence on velocity becomes different. postulating of some adhesion criterion requires these critical values and conditions to be determined [8]. but in the simplest way the deposition efficiency calculated experimentally as follow: kd = δms/mp (1) where δms is change of weight of a substrate and mp is weight of all particles interacting with a substrate. as it is known up to now, the most important parameter in not only deposition efficiency and also in cold spray procedure per-se is the velocity of the particles. since the particle velocity exceeds the critical value vcr1, the coating o http://dx.medra.org/10.3221/igf-esis.08.03&auth=true http://www.gruppofrattura.it r. ghelichi et alii, frattura ed integrità strutturale, 8 (2009) 30-44; doi: 10.3221/igf-esis.08.03 33 process begins. the deposition efficiency rapidly increases to 50–70% as the particle velocity significantly exceeds the critical value. the other important parameter which has a great influence on deposition it is simply concluded that the particle and substrate temperatures have also a significant effect on the spraying process; as the air temperature in the pre-chamber increases, both the particle velocity and the particle and substrate temperatures increase. during the first stage, the particles interact with the substrate, and this process determines the quality of the interface and coating adhesion. to improve adhesion, sand blasting is commonly used under thermal spraying. however, this method has certain disadvantages including the effect of interface contamination due to penetration of sand blasting particles into the substrate, especially for soft substrate materials. sand blasting is undesirable in many applications, for example, in spraying on parts with thin walls, parts already coated, parts made of brittle materials, etc. in the cold spray process, the sprayed particles are in the solid state, and in some cases they can be used for preliminary treatment and preparation of the substrate, in particular, when the use of sand blasting is unacceptable. the first stage of coating spraying turns out to be more complicated, because it depends on particle and substrate parameters (e.g., roughness, hardness, temperature, etc.) and on the state of the surface, which is obviously changed as the number of particle impacts increases. this change, in turn, leads to changes in conditions of particle–substrate interaction and, consequently, to unsteady growth of the coating [1]. figure 3: the schematic view of different region of particles on substrate [1]. before the first stage there is an induction or delay time is the time between the beginning of surface treatment by the flow of particles and the beginning of particle attachment to the surface. there are three characteristic regions of particle– substrate interaction, divided by two values of particle velocity: vcr1 and vcr2 (fig. 4). in region 1, with vp higher than vcr2 (850 m/s), particles adhere to the initial surface without any delay. as the particle velocity decreases, the situation is changed. in region 2, located between vcr1 and vcr2, particles cannot adhere to the initial (original) surface. they start to http://dx.medra.org/10.3221/igf-esis.08.03&auth=true http://www.gruppofrattura.it r. ghelichi et alii, frattura ed integrità strutturale, 8 (2009) 30-44; doi: 10.3221/igf-esis.08.03 34 adhere to the surface only after some delay, when the surface state is changed because of its treatment by the first impinging particles. in this region, the first particles rebound, thus, preparing the surface ,only after, that does the coating start to form [1]. figure 4: induction (deposition delay) time versus the mean impact velocity of aluminum particles on a polished copper substrate [1]. thus, it is clear that the surface, before the second region, was exposed to a large number of particle impacts before particles start to adhere to the surface. the results presented show that the sprayed particles in the cold spray process can play an important role in the preparation and activation of the substrate surface and this effect can be used in applications when utilization of sand blasting is unacceptable or undesirable. in this case, however, additional effects associated with a delay of spraying of the first layer should be taken into account in the coating formation process analysis. appropriate material polycrystalline solids are classified into isomechanical groups, i.e., groups that possess similar mechanical properties. the most important isomechanical groups of metals are: aluminum, copper, silver, gold, platinum, nickel, and gamma-iron (face-centered cubic (fcc) lattice); tungsten, tantalum, molybdenum, niobium, vanadium, chromium, alpha-iron, and beta-titanium (bulk-centered cubic (bcc) lattice); and cadmium, zinc, cobalt, magnesium, and titanium (hexagonal lattice, which is the densest packing). metals with the fcc lattice have the greatest number of slipping planes, which is responsible for their high plasticity; metals with the hexagonal structure have much fewer slipping planes, which yield a lower plasticity; and metals with the bcc lattice have the lowest plasticity among the three types. groups of tetragonal or trigonal crystalline systems include oxides that are not suitable for cold spray because of their low plasticity (this issue has not been adequately addressed to definitely state inapplicability of all oxides and ceramics for cold spray). if we plot the homological temperature (ratio of temperature to the melting point) on the x axis and the product of the shear modulus and compression modulus on the y axis and mark points corresponding to various metals in the diagram, it turns out that more plastic materials are located in the right side of the diagram close to the x axis, whereas less plastic materials can be found in the left side of the diagram close to the y axis. this positioning allows us to classify materials from the viewpoint of their suitability for cold spray. copper is considered as an almost ideal material, which has a low resistance to strain and a melting point below 1100°c. materials with a low melting point can be readily compacted. in general, cold spray treatment of bcc metals involves more difficulties, because the mobility of spiral dislocations under strains with high rates is limited by peierls stresses [9]. from the viewpoint of material science, the suitability of materials for cold spray could be related to peierls stress. peierls stress is the force, first discovered by rudolph peierls and modified by frank nabarro, needed to move a dislocation within a plane of atoms in the unit cell. the magnitude varies periodically as the dislocation moves within the plane. peierls stress depends on the size and width of a dislocation and the distance between planes. because of this, peierls stress decreases with increasing distance between atomic planes. yet since the distance between planes increases with planar density, slip of the dislocation is preferred on closely packed planes, but available publications are insufficient to draw this conclusion. but based on the results of many researchers, it seems somehow obvious that particle adhesion is primarily related to the readiness of the substrate and particle to deform, and adhesion is assumed to be possible if the particle is substantially more plastic than the substrate. http://dx.medra.org/10.3221/igf-esis.08.03&auth=true http://www.gruppofrattura.it r. ghelichi et alii, frattura ed integrità strutturale, 8 (2009) 30-44; doi: 10.3221/igf-esis.08.03 35 the result of r. gr. maev and v. leshchynsky [10] work shows that the main characteristics of gds such as deposition efficiency and average single pass thickness depend on the kinetics of adiabatic shear band formation following the arrhenius flow law localized plastic deformation at the particle-substrate interface appears to be necessary for the coating formation. for this reason, successful powders and substrates for gds are mostly metals with relatively high plasticity. l. ajdelsztajn et al. [11] show that the localized adiabatic shear instability at the particles boundaries helps the creation of intimate contact between clean surfaces that result in a metallurgical bonding at the particle/particle surfaces. one can speculate that the adiabatic regimen created during the impact could raise particle temperatures close to the glass transition temperature (tg) of the amorphous alloys, leading to particle softening and making it possible to achieve very high densities in the coating. it is proposed that for the soft substrates and hard particles used in this work, the first impacts will primarily confine the deformation to the substrate material, and after the first layer of undeformed hard particles are created the subsequent impacts provide severe plastic deformation on both substrate and impacting particles. the effect of velocity on de for a given material, successful deposition requires a certain minimum particle velocity or “critical velocity,” the value of which depends most significantly on the thermo-mechanical properties of the powder and substrate materials [12-18]; below this critical velocity, impacting particles are generally observed to cause erosion of the substrate. normally, a feedstock powder will contain a range of particle sizes and consequently a distribution of particle velocities a large number of studies have suggested that the particle deposition behavior is influenced significantly by the particle velocity prior to impact with the substrate. particle velocity is a function of the spray process conditions, including gas type, pressure, and temperature, and materials properties, such as particle diameter, density, and morphology [19-21]. the relationships between the deposition efficiencies and particle velocity (fig. 5) were investigated [23, 24]. assadi et al. [26] have used numerical simulation to work out the effect of various material properties on the critical velocity in cold spraying. they summarized these effects into a simple expression for the critical velocity. françois raletz et al [3] present an imaging technique that allows a fast measurement of critical velocity. the measuring method is first evaluated by comparing the critical velocity of copper (sprayed on copper substrate) found in the literature, with the measured one. its accuracy is then tested with other materials and, finally, some improvements of the method are proposed. in development of a generalized parameter window for cold spray deposition tobias schmidt et al calculate the critical velocity based on particles size. they developed a cfd analysis for thermal solution.  figure 5: the effect of particle velocity on deposition efficiency in cgds [22]. papyrin et al. [28] modeled the impact of a plastic particle onto a rigid substrate at velocities that are commonly achieved in the cold spray process. the calculated distribution of the radial component of velocity indicated that metal jetting could take place. however, they also demonstrated that under certain conditions, melting may occur on the surface of the particle in the contact zone but suggested that since this was limited to only a very thin layer, it would not significantly affect the properties of the coating. the modeling of particle impact is used to provide a better understanding of the bonding mechanisms, and to estimate critical velocities for bonding particles of different materials. by means of a so-far widely accepted model, bonding in cold spraying can be explained by the occurrence of local shear instabilities at particlesubstrate and particle-particle interfaces due to thermal softening, as first shown by assadi et al. [29]. based on the concept of bonding by shear instabilities and by combining the results from modeling and experimental investigations, analytical expressions were recently developed to predict the ranges of optimum spray conditions with respect to the mechanical properties of spray materials, spray particle sizes, and particle temperatures [25]. hidemasa takana et al[27] survey a real-time computational simulation on the entire cold spray process by the integrated model of compressible flow field, splat formation model, and coating formation model, in order to provide the fundamental data for the advanced http://dx.medra.org/10.3221/igf-esis.08.03&auth=true http://www.gruppofrattura.it r. ghelichi et alii, frattura ed integrità strutturale, 8 (2009) 30-44; doi: 10.3221/igf-esis.08.03 36 high performance cold gas dynamic spray process with electrostatic acceleration. in this computation, viscous drag force, flow acceleration added mass, gravity, basset history force, saffman lift force, brownian motion, and electrostatic force are all considered in the particle equation of motion for the more realistic prediction of in-flight nano/microparticle characteristics with electrostatic force and also for the detailed analysis of particle-shock-wave-substrate interaction. computational results show that electrostatic acceleration can broaden the smallest size of applicable particle diameter for successful adhesion; as a result, wider coating can be realized. the utilization of electrostatic acceleration enhances the performance of cold dynamic spray process even under the presence of unavoidable shock wave. the surface topography and temperature of the substrate some authors have examined the role of substrate surface topography on the formation of a bond between incoming particles and substrate. tokarev et al. [30] have suggested that particles impacting a substrate in cold spraying first activate the substrate by roughening it; only once this has occurred is a coating able to initiate and grow. it has also been reported that, with a greater roughening of the substrate surface (going from polished to grit-blasted), deposition efficiency of metallic powders increases slightly [7]. j.g. legoux et al surveyed [31] the change in temperature of the substrate during the deposition process was measured by means of a high speed ir camera. the coating formation was investigated as a function of (1) the measured surface temperature of the substrate during deposition, (2) the gun transverse speed, and (3) the particle velocity. both single particle impact samples and thick coatings were produced and characterized. from the results obtained, based on fig. 6 it was quite noticeable that the higher substrate temperature brought about a higher deposition rate of cu particles, even under the condition where particles were kept at room temperature [31].     figure 6: relation between deposition ratio and both substrate temperature and gas pressure [27].   vicek et al. [33] have discussed the bonding of particles in cold spraying primarily on the relative deformability of the particles and the substrate. they indicated that as the substrate deformability decreased, the ease with which particles bond to the surface also decreased. d. zhang et al. [34] have work on spraying aluminum powder a range of substrates. the substrates examined include metals with a range of hardness, polymers, and ceramics. the substrate surfaces had low roughness (ra < 0.1 μm) before deposition of aluminum. it has been shown that initiation of deposition depends critically upon substrate type. a number of phenomena have been observed following spraying onto various substrates, such as substrate melting, substrate and particle deformation, and evidence for the formation of a metal-jet. such phenomena have been related to the processes occurring during impact of the particles on the substrate. metallic substrates which are mostly harder than the aluminum particles generally promoted deposition. initiation was seen to be rapid on hard metallic substrates, even when deformation of the substrate was not visible. it may be concluded that the most successful initiation of bonding of al. particles onto substrates of low roughness by cold spraying requires a metallic surface with hardness higher than that of the particles. the results of their work are completely opposite with the results of vicek et al. [33]. jianhong he et al. [35] worked on the influence of grit blasting, feedstock powder, and thermal spraying technology on the performance near the surface on the substrates side. the experimental results show that both the grit-blasting process and thermal spraying process harden the substrate and microhardness on or near the surface was noticeably increased. grit blasting created deformed regions next to the surface of the substrate and interface between entrapped grits and substrate. when fine ferrite grain regions or pearlite phase were indented, higher hardness were obtained. while coarse ferrite grains created lower hardness value. therefore, a fluctuation of hardness was observed in the hardness profiles. there are always fine grain zones near the surface because of higher cooling rates after hot rolling of the plate. http://dx.medra.org/10.3221/igf-esis.08.03&auth=true http://www.gruppofrattura.it r. ghelichi et alii, frattura ed integrità strutturale, 8 (2009) 30-44; doi: 10.3221/igf-esis.08.03 37   figure 7: the relationship between surface hardness and deposition efficiency in different substrate [34]. stephan siegmann et al. [36] work shows that the topography of a roughened substrate (or bond coat) plays a key role in coating adhesion, and in phenomena which can influence adhesion. it is known that the complex nature of the substrate topographies cannot be adequately characterized over the entire range by conventional methods such as average roughness. the adhesive strength should be expressed as: ha = m (s/a) (m/p) (2) where ha is the adhesive strength, m is a number between 0 and 1 that represents the fraction of the bond sites that are active, s is the characteristic strength of an individual, fundamental bond, a is the characteristic area of an individual, fundamental bond, m is the apparent area of the substrate surface measured at the scale of the characteristic area of an individual bond, and p is the nominal, or projected, area of the surface. the m/p ratio is the relative area at a particular characteristic area or scale, and it is always equal to or greater than 1. the m/p ratio is proposed to be a parameter for relating the texture to the actual adhesive bonding, whereas the droplet impact, spreading and wetting will influence the number of active bond sites, and hence the factor m. in this paper they calculate the adhesion strength for thermal coating based on microstructures. this work shows that the relative area at scales below about 100 μm2 can be a good predictor of adhesive strength. figure 8: tensile adhesive strength as a function of the substrate materials hardness and number of grit blast passes [36]. the adhesive strength as a function of substrate material hardness showed no strong correlation for all grit blast conditions. this means that the surface hardness itself is not a limiting factor for good adhesion, if surface preparation is http://dx.medra.org/10.3221/igf-esis.08.03&auth=true http://www.gruppofrattura.it r. ghelichi et alii, frattura ed integrità strutturale, 8 (2009) 30-44; doi: 10.3221/igf-esis.08.03 38 done properly. adhesive strengths of at least 80 mpa could be achieved for all materials, even for the hardened steel, also it will increase by increasing the number of passes (fig. 8). in [37] which introduce a experimental way to calculate the adhesion strength, the tensile adhesion is rh is the strength obtained in the tension test, calculated from the quotient of the maximum load fm and the cross-section of the specimen at the fractured face. compared to the aisi 304 substrate, extreme roughening was recognized on the a6063 substrate surface. this is simply attributed to the lower hardness of a6063 substrate compared to aisi 304 substrate. from the observation results on the cross-section microstructure for both substrates, it was revealed that the adhered copper particles deformed themselves on the harder aisi 304 substrate while both particles and substrate deformed each other on the softer a6063 substrate surface [31]. on the other hand, the successful building up of coating at high deposition efficiency depends on the design of powder porous structure [39] it was found that the wc-co cermet particles with the porosities of 30% and 44% could be deposited on the substrate of different hardness from 200 to 800 kgf/mm2. the deposition of the particles is mainly attributed to the deformation of powders themselves. the properly designed porous cermet powder with certain hardness is necessary to deposit hard wc-co cermet coating. in hp powders it is evident that the layer becomes more uniform with the increase of substrate hardness. but in mp powders the fracture of powder particles likely occurred compared the spherical morphology of the starting powder with the relative rough one; the deposited particles are relatively complete. lp powder, it was observed that with stainless steel substrate the particles penetrated into the substrate to certain depth, depending on the particle size and subsequently particle velocity. on the other hand, with the ni40 and ni60 substrates only craters were observed on the surface [40]. m. kulmala worked on [42]. a laser-assisted low-pressure cold spraying (lalpcs) is a one-step coating process in which the laser irradiation interacts simultaneously with the spraying spot on the substrate or deposited coating surface in order to improve coating properties. it is expected that the lalpcs could be an effective method to improve a low-pressure cold sprayed coating deposition efficiency and denseness. the results showed that laser irradiation improved the copper coating denseness and also enhanced deposition efficiency. the coating thickness increased mainly in the function of the laser power. z.d. xiang et al. [43] showed that it seems reasonable to expect that the coating would grow faster in a steel surface with a finer grain structure if the coating growth process can be significantly influenced by the diffusion through grain boundaries and microstructural defects. indeed, it has been demonstrated recently that the solid-state diffusion process at low temperatures can be substantially enhanced in the plastically deformed steel surface in which grain sizes are reduced to the range of nanometers and large numbers of microstructure defects are simultaneously generated by a cold working process termed surface mechanical attrition treatment. the shot peened surface would have a microstructure that differs significantly from that of the bulk. it would contain a large number of grain boundaries and lattice defects such as dislocations. t. marrocco et al. [55] shows that the bond strength between a coating (deposited with cti at 29 bar) and substrate, as a function of substrate surface condition, is shown in fig. 9. it can be seen that the grit-blasted surface condition resulted in the lowest bond strength, with an average strength of 8 mpa, while the polished and ground surfaces resulted in higher bond strengths of 22 mpa. figure 9: bar chart showing the effect of substrate condition on the bond strength of deposits sprayed at 29 bar gas pressure using cti powder(course powder) (error bars represent the standard error of the mean)[55]. http://dx.medra.org/10.3221/igf-esis.08.03&auth=true http://www.gruppofrattura.it r. ghelichi et alii, frattura ed integrità strutturale, 8 (2009) 30-44; doi: 10.3221/igf-esis.08.03 39 surface preparation ra , m rz , m rk , m ground 0.21  0.03 1.57  0.16 0.73  0.06 polished 0.046  0.002 0.46  0.09 0.101  0.005 grit blasted 2.66  0.06 17.03  0.39 9.13  0.31 table 1: parameters describing the surface profile of the substrates as a function of surface preparation method [55]. values are the average of three measurements, with standard error of the mean indicated. other important parameters there are many other important parameters which have a great influences on cold spray process. s. barradas et al. [44] developed an experimental simulation of the particle-substrate reactions at the particle impingement. this simulation is based on original flier impact experiments from laser shock acceleration. relevant interaction phenomena were featured and studied as a function of shearing, plastic deformation, phase transformation primarily. they applied a fem analysis for cold spray coating. the ale method provides a suitable way to examine the particle deformation in cold spraying. moreover, the numerical results also show that there exists the similarity for the deformation of particles of different diameters [45]. vicek et al. [33] have examined the impact of a range of powder types onto a range of substrate materials in cold spraying. they explained differences in the ability of particles to deposit in terms of the mechanical properties of the particles and substrate and the specific impulse of the impact. they related bonding primarily to the relative ease of deformation of the substrate and particle, and concluded that if the particle was significantly more deformable than the substrate, then adhesion was not possible. van steenkiste et al. [46] described the deposition of large aluminum particles (> 50 μm) onto a brass substrate by cold spraying; they argued that particle melting does not occur, with bonding resulting from severe deformation and subsequent disruption of oxide films on metallic particles allowing nascent metal surfaces to come into contact. bolesta et al. [47] deposited aluminum by cold spraying onto a nickel substrate. using x-ray diffraction, they detected the formation of ni3al and suggested that the interface phase was in the region of 200 to 500 å in thickness. this indicates that melting may occur as a precursor to the formation of the new phase; such bonding was referred to as a chemisorptional bond. wen-ya li et al. [48]. the microhardness of the as-sprayed and annealed cu coating is shown in fig. 10. the microhardness of the as-sprayed cu coating was about 132 hv0.2, which was consistent with those reported by borchers et al. [49, 50] and mccune et al. [51]. figure 10: the effect of annealing on microhardness of the coated specimen [48].   h. lee et al. [52] worked on the effect of pressure on al coating. in the case of hardness, the coating of al at low pressure condition had higher hardness because of work hardening (peening effect) resulted from bounced-off al particles (0.7 mpa). therefore, it was found that the gas pressure as a processing parameter could have an influence on al coating's properties. the results of their work are shown in fig. 11. eric irissou et al. [47] found out coatings with the starting powder based on the larger al particles are systematically harder than coatings made with the smaller size al powder mixtures. this is likely due to the larger peening effect of the large particles due to their higher kinetic energy. the addition of al2o3 to the al powders helps improving the coating deposition. because al2o3 particles alone cannot form a coating in our experimental conditions, they play only a role of peening and roughening of the layers during deposition. the addition of al2o3 to al powder increased the adhesion of the coating on the substrate. http://dx.medra.org/10.3221/igf-esis.08.03&auth=true http://www.gruppofrattura.it r. ghelichi et alii, frattura ed integrità strutturale, 8 (2009) 30-44; doi: 10.3221/igf-esis.08.03 40 figure 11: a) bond strength against coating al2o3 concentration; b) vickers hardness measurements against al2o3 concentration [52]. t.s. price et al [53] described a method for characterizing the bonding between aluminum and copper particles following deposition by cold spraying. the degree of bonding between particles within cold-sprayed deposits is of great importance as it affects their mechanical and physical properties. this has shown that on impact, high plastic strain rates can occur in the immediate vicinity of the contact zone which lead to adiabatic heating, localized softening of the material and the formation of what are termed shear instabilities. it was found that at inter-particle boundaries oxides were identified that appeared to have originated from the original feedstock. although evidence of ruptured surface oxides was found, which allowed true metal-to metal contact to occur at points along particle interfaces, true metal to metal bonding was incomplete [54] in this respect the occurrence of shear instabilities when high velocity particle impact occurs has a key role in breaking down oxide films and creating intimate metallic contact which will favor atomic level bonding during elevated temperature annealing. the increase in fractional interface coverage with increasing primary gas pressure, which was measured in this work, can presumably be attributed to more extensive breakdown of oxide films at the higher pressure. in this work, it was noted that an increase in bonding pressure increased the area over which intermetallics formed, because of increased oxide break-up. the intermetallic layer development during elevated temperature annealing can be explained in terms of a solute diffusion controlled process. between the other parameters residual stress of coating is more interesting. w.b. choi et al. [41] discuss and evaluate the relationships between the microstructure, properties and residual stresses in cs al coatings, combining indentation, dilatometry, resistivity measurements and neutron diffraction techniques. the results show that: 1) residual stresses in cs al are virtually non-existent and in fact are lower than the peening stresses induced during surface roughening. 2) elastic modulus of cs al is lower than bulk by approximately a factor of 2, attributed to incomplete bonding between particles. annealing might decreased modulus presumably due to weakening of the oxide interphases. this damage is ameliorated during annealing in air, likely due to compression from further oxidation. 3) as-sprayed cs al has a higher flow stress than bulk al, due to hardening of particles. in addition, plastic behavior is brittle, as evidenced by cracking observed underneath indents. annealing softens particles enough to promote ductile behavior, and flow stress is lowered below bulk. the nature of the brittle to ductile transition is interesting and warrants further study. 4) thermal expansion of the coating is increased by oxidation and decreased by the presence of oxides. the only cs coatings that exhibit cte closely matching bulk values were those annealed in argon. 5) electrical resistivity displays some anisotropy (i.e. higher through-thickness than in-plane), as one would expect. annealing in air increases and decreases resistivity for coatings from non-oxidized (spherical) and pre-oxidized (globular) feedstocks, respectively. this is likely due to more oxidation in the former and a greater extent of annealing in the latter coatings. annealing in ar causes an anisotropy reversal in the coatings from pre-oxidized feedstock, presumably due to more ‘‘vertical’’ than ‘‘horizontal’’ micro-damage. http://dx.medra.org/10.3221/igf-esis.08.03&auth=true http://www.gruppofrattura.it r. ghelichi et alii, frattura ed integrità strutturale, 8 (2009) 30-44; doi: 10.3221/igf-esis.08.03 41 the effect of cgds on substrate properties he effect cold spray coating process on many substrate properties specially the fatigue behavior was studied by many authors. t.s. price et al. [56] studied the effect of cold spray deposition of a titanium coating on fatigue behavior. thus, coatings were deposited onto samples with two different surface preparation methods (asreceived and grit-blasted). the fatigue life of the as-received and grit-blasted materials, both before and after coating was measured. a 15% reduction in fatigue endurance limit was observed after application of the coating to the as-received substrate, but no significant reduction was observed on its application to the grit-blasted substrate. it has been shown that cgds titanium coatings have a detrimental effect on the fatigue endurance limit of ti6al4v. compressive stresses found within a coating are usually associated with increased fatigue endurance limits; however, those found within cgds titanium coatings are too low to prevent fatigue crack formation, and these lead to premature fracture. surface finish surface roughness, ra, µm fatigue endurance limit, mpa modulus, gpa as-received 2.7 633 107 as-received and sprayed 8.6 537 20 grit-blasted 3.5 507 107 grit-blasted and sprayed 8.5 512 19 table 2: effect of surface finish on fatigue endurance limit [56].    e. sansoucy et al. [57] work on in particular the bending fatigue and the bond strength, of the al-co-ce coatings. the results show that the al-co-ce coatings improved the fatigue behavior of aa 2024-t3 specimens when compared to uncoated and alclad specimens it is suggested that the increase in the fatigue properties of the specimens can be attributed to the residual compressive stresses induced in the coatings and to the high adhesion strength of the coatings to the substrates. the fatigue results can be rationalized on the basis of two important factors: the existence of residual compressive stresses, and the high adhesion of the coatings to the substrate. the high velocity impacts of particles cause plastic deformation of the underlying layers and generate compressive residual stresses. qiang zhang et al. [58] nanostructured nicraly bond coating was deposited after that a shot-peening treatment was applied to the as-sprayed coating to modify the coating surface morphology. it was found that a uniform oxide layer was formed on the surface of the shot-peened nanostructured nicraly coating during oxidation at temperatures of 900 °c and 1000 °c. the surface geometry of the cold-sprayed mcraly coating must be modified to promote formation of a protective oxide film during oxidation, through application of a post-treatment process such as shot-peening. the surface of as-sprayed coating was very rough, and some protrudings presented on the surface of bond coating, as shown in fig. 12. however, after shot-peening treatment, the surface of bond coating was uniform and smooth, and compacted, as shown in fig. 12. the surface roughness was significantly reduced from ra=5.6±1.2 μm(rz=26.2 ±3.5 μm) at the assprayed state to ra=3.1±0.6 μm (rz=14.1±1.3 μm) at the shot-peened state. figure 12: surface morphology of as-sprayed nicraly bond coating (a) and after shot-peened nicraly bond coating (b)[58]. t http://dx.medra.org/10.3221/igf-esis.08.03&auth=true http://www.gruppofrattura.it r. ghelichi et alii, frattura ed integrità strutturale, 8 (2009) 30-44; doi: 10.3221/igf-esis.08.03 42 and finally the effect of cold spray on residual stress in substrate is shown in fig. 13. this graph displays in-plane stresses in the substrate before deposition and the coating–substrate system after deposition. the bare substrate exhibits ~90 mpa in compression at the surface, presumably due to peening effects of sand blasting. this is partially balanced by a tensile region (max 50 mpa) in the interior. cold spray deposition induces a slight (average 10 mpa) compressive stress through the thickness of the coating, which thus reduces the near-surface substrate stress magnitude [60]. figure 13: residual stress measurement of cs al coating [60]. conclusions any studied have being conducted since ten odd years ago about the cold spray coating and its related parameter. many reviewers, as it is mentioned above, have been trying to survey different factors about cgds such as calculation deposition efficiency, find a way, for example by changing the parameters, to increase the de, critical velocity for different materials, effect of thermal annealing on cold spray, etc. although the authors believe that the most important question remained vague is the main reason of bounding of the particles to the substrate, there are a lot of books and articles in this regard. in this point of view, there is still a field which is missed and it is rarely to find references about the effect of shot peening on cold spray coating. the authors believe that shot-peening which is very famous in increasing the fatigue limit by applying the residual stress on the surface of specimen, might have appreciable effects on the cgds parameters. it seems necessary to find the answers of the following questions: what are the results of applying shot-peening before cold spray coating on substrate on the cgds factors such as deposition efficiency, critical velocity, bounding strength, etc. this answer might be different for different materials, thus it should be experimented for many materials which are suitable for cgds. are the important parameters of substrate (for instance, physical properties of substrate such as electrical and thermal conductivity, fatigue limits which somehow directly related to residual stress on the surface, ductility behavior of substrate) will change by shot-peening before and after the cgds? these questions should be answered by both experimental test and numerical solution. references [1] a.papyrin, v.kosarev, s.klinkov, a.alkhimov,v.fomin, elsevier, (2006). [2] r.c. mccune, a.n. papyrin, j.n. hall, w.l. riggs ii, p.h. zajchowski, houston, asm (1995), 1-5. [3] françois raletz, michel vardelle, guillaume ezo'o , surface & coatings technology 201 (2006) 1942–1947. [4] a.p. alkhimov, s.v. klinkov, v.f. kosarev, a.n. paprin, j. appl. mech. phys. (1997) 176-183. [5] j. karthikeyan,cold spray technology: international status and usa, (2000). [6] us army laboratory webpages, cold spray coating application. [7] t. stoltenhoff, h. kreye, h.j. richter, (2002) 542-550. [8] s.v. klinkov, v.f. kosarev, journal of thermal spray technology, (2006) 364. [9] a.a. deribas, i.d. zakharenko, fisika goreniya i vzryva., (1974) 409–421. m http://dx.medra.org/10.3221/igf-esis.08.03&auth=true http://www.gruppofrattura.it r. ghelichi et alii, frattura ed integrità strutturale, 8 (2009) 30-44; doi: 10.3221/igf-esis.08.03 43 [10] r. gr. maev, v. leshchynsky, journal of thermal spray technology, (2006) 198. [11] l. ajdelsztajn, b. jodoin, p. richer, e. sansoucy, e.j. lavernia, thermal spray technology volume (2006) 495. [12] p.o. kettunen, physical metallurgy. ims tampere university (1995). [13] r.c. mccune, a.n. papyrin, j.n. hall, w.l. riggs ii, p.h. zajchowski, c.c. berndt and s. sampath, (1995) 1-5. [14] r.c. dykhuizen, m.f. smith, d.l. gilmore, r.a. neiser, x. jiang, s. sampath, impact of high j. therm. spray technol., (1999) 559-564. [15] k. sakaki, n. huruhashi, k. tamaki, y. shimizu, e. lugscheider and c.c. berndt, ed., (2002) 385-389. [16] j. vlcek, l. gimeno, h. huber, e. lugscheider, thermal spray (2003) 37-44. [17] v.f. kosarev, s.v. klinkov, a.p. alkhimov, a.n. papyrin, j. therm. spray technol., (2003) 265-281. [18] f. gurtner, c. borchers, t. stoltenhoff, h. kreye, h. assadi, thermal spray (2003) 1-8. [19] k. sakaki, t. tajima, h. li, s. shinkai, and y. shimizu, thermal spray (2004) 358-362. [20] d.l. gilmore, r.c. dykhuizen, r.a. neiser, t.j. roemer, m.f.smith, j. therm. spray technol., (1999) 576-582. [21] r.c. mccune, a.n. papyrin, j.n. hall, p.h. zajchowski, c.c. berndt, s. sampath, (1995) 1-5. [22] d. zhang, p.h. shipway, d.g. mccartney, j. therm. spray technol., (2005) 109-116. [23] frank gurtner, thorsten stoltenhoff, tobias schmidt, heinrich kreye, journal of thermal spray technology (2006) 223. [24] r.c. mccune and a.n. papyrin, j.n. hall, w.l. riggs ii, p.h. zajchowski, (1995). [25] d.l. gilmore, r.c. dykhuizen, r.a. neiser, t.j. roemer, m.f. smith, j. thermal spray technol., (1999) 576-582. [26] t. schmidt, f. gurtner, h. assadi, h. kreye, acta, mater., (2006) 729-742. [27] hidemasa takana, kazuhiro ogawa,tetsuo shoji, hideya nishiyama, journal of fluids engineering, (2008). [28] a.n. papyrin, v.f. kosarev, s.v. klinkov, a.p. alkhimov, dvs (2002) 380-384. [29] t. stoltenhoff, h. kreye, h.j. richter, h. assadi, asm international, (2001) 409-416. [30] a.o. tokarev, metal sci. heat treatment, (1996) 135-139. [31] j.g. legoux, e. irissou, c. moreau, journal of thermal spray technology (2007) 619. [32] m. fukumoto, h. wada, k. tanabe, m. yamada, e. yamaguchi, a. niwa, m. sugimoto, m. izawa, journal of thermal spray (2007) 643. [33] j. vicek, h. huber, h. voggenreiter, a. fischer, e. lugscheider, h. hallén, g. pache, thermal spray, (2001) 417-422. [34] d. zhang, p.h. shipway, d.g. mccartney, j. therm. spray technol., (2005) 109-116. [35] jianhong he, bruce dulin, thomas wolfe , j. thermal spray technology (2008) 214. [36] stephan siegmann, empa thun , thun, switzerland christopher a. brown, surface metrology laboratory, wpi, (1999) 355-360. [37] en 582thermal spraying; determination of tensile adhesive strength (1993-10). [38] junji morimoto, tetuya onoda, yoh sasaki, nobuyuki abe, elsevier (2004) 527–532. [39] pei-hu gao, yi-gong li, chang-jiu li, guan-jun yang, cheng-xin li, journal of thermal spray technology (2008) 742. [40] pei-hu gao, chang-jiu li, guan-jun yang, yi-gong li, cheng-xin li, surface & coatings technology (2008) 384– 390. [41] w.b. choi, l. li, v. luzin, r. neiser, t. gnaupel-herold, h.j. prask, s. sampath, a. gouldstone, acta materialia (2007) 857–866. [42] m. kulmala, p. vuoristo, surface & coatings technology (2008) 4503–4508. [43] z.d. xiang, p.k. datta, scripta materialia (2006) 1151–1154. [44] s. barradas, v. guipont, r. molins, m. jeandin, m. arrigoni, m. boustie, c. bolis, l. berthe, m. ducos , journal of thermal spray technology, (2007) 548. [45] wen-ya li, hanlin liao, chang-jiu li, gang li, christian coddet, xiaofang wang , applied surface (2006) 2852– 2862. [46] t.h. van steenkiste, j.r. smith, r.e. teets, surf. coat. technol., (2002) 237-252. [47] a.v. bolesta, v.m. fomin, m.r. sharafutdinov, b.p. tolochko, nucle. instrum. meth., phys. res. a, (2001) 249-252. [48] wen-ya li, chang-jiu li, hanlin liao, journal of thermal spray technology, (2006) 206. [49] c. borchers, f. gurtner, t. stoltenhoff, h. assadi, h. kreye, appl. phy., (2003) 10064-10070. [50] c. borchers, f. gurtner, t. stoltenhoff, h. kreye, acta mater., (2005) 2991-3000. [51] r.c. mccune, w.t. donlon, o.o. popoola, e.l. cartwright, j. therm. spray technol., (2000)73-82. [52] h. lee, h. shin, s. lee, k. ko, materials letters (2008) 1579–1581. [53] t.s. price, p.h. shipway, d.g. mccartney, e. calla, d. journal of thermal spray technology (2007) 566-570. [54] k. balani, a. agarwal, s. seal, j. karthikeyan, scripta mater., (2005) 845-850. http://dx.medra.org/10.3221/igf-esis.08.03&auth=true http://www.gruppofrattura.it r. ghelichi et alii, frattura ed integrità strutturale, 8 (2009) 30-44; doi: 10.3221/igf-esis.08.03 44 [55] t. marrocco, d.g. mccartney, p.h. shipway, a.j. sturgeon, journal of thermal spray technology, (2006) 263. [56] t.s. price, p.h. shipway, d.g. mccartney, j.of thermal spray technology (2006) 507. [57] e. sansoucy, g.e. kim, a.l. moran, b. jodoin, j. thermal spray technology (2007) 651. [58] qiang zhang, chang-jiu li, cheng-xin li, guan-jun yang, siu-ching lui, surface & coatings technology (2008) 3378–3384. [59] p. bansal, p.h. shipway, s.b. leen, (2006) 5318 – 5327. [60] w. b. choi, l. li, v. luzin, r. neiser, t. gnaupel-herold, h. j. prask, s. sampath. a. gouldstone, , acta materialia 55 (2007) 857-866. http://dx.medra.org/10.3221/igf-esis.08.03&auth=true http://www.gruppofrattura.it microsoft word numero 19 articolo 4.doc l. susmel et alii, frattura ed integrità strutturale, 19 (2012) 37-50; doi: 10.3221/igf-esis.19.04 37 sulla stima di macro, micro e nano-durezza di materiali metallici mediante analisi elasto-plastiche agli elementi finiti estimating macro-, micro-, and nano-hardness of metallic materials from elasto-plastic finite element results luca susmel the university of sheffield, department of civil and structural engineering, sheffield, s1 3jd, uk david taylor trinity college, department of mechanical engineering, dublin 2, ireland riassunto. il lavoro sintetizzato nel presente articolo si pone come obiettivo primario quello di investigare la possibilità di stimare, mediante un approccio elasto-plastico agli elementi finiti, la durezza dei materiali metallici convenzionali, e questo sia a livello macroscopico, che a livello microscopico, che, infine, a livello nanoscopico. per verificare validità e accuratezza della metodologia fem sviluppata, sono state condotte una serie di analisi sperimentali su tre materiali metallici aventi caratteristiche metallurgiche estremamente diverse: una lega d’alluminio (al 7075-t6), un acciaio a basso tenore di carbonio (bs970-en3b) e, infine, un acciaio austenitico (aisi 316l). l’indentazione vickers è stata simulata con analisi elasto–plastiche agli elementi finiti considerando carichi di prova nell’intervallo tra 490 n e 490 µn e calibrando le simulazioni numeriche mediante curve monotone tensione–deformazione ottenute da prove di trazione eseguite utilizzando provini sia di dimensione convenzionale che aventi larghezza della zona calibrata dell’ordine dei 100 µm. la sistematica comparazione tra risultati sperimentali e simulazioni numeriche ha posto in evidenza come l’aumentare del valore della durezza misurata al diminuire della dimensione dell’impronta possa essere imputata al ruolo giocato dalla reale morfologia del materiale, ruolo che diventa predominante sulla plasticità convenzionale quando le dimensioni della superficie indentata diventano comparabili con le dimensioni medie della grana cristallina delle leghe esaminate. tali fenomeni, pertanto, non hanno consentito di estendere l’utilizzo della meccanica del continuo fino ad un livello nanoscopico per determinare correttamente i valori della durezza. alla luce di questi risultati è stata, però, proposta una semplice metodologia di correzione delle stime eseguite mediante gli elementi finiti che si è dimostrata un valido strumento da utilizzarsi in situazioni di interesse pratico per stimare la durezza dei materiali metallici, indipendentemente dalla dimensione della superficie indentata. abstract. this paper summarises an attempt of estimating macro-, micro-, and nano-hardness of metallic materials through conventional elasto-plastic finite element (fe) analyses. in more detail, to verify if the classical fe method can successfully be used for such a purpose, initially a series of hardness testes were carried out on three metallic materials characterised by a different elasto-plastic behaviour, i.e., aluminum alloy 7075t6, low-carbon steel bs970-en3b, and, finally, austenitic steel aisi 316l. subsequently, by making the indentation force vary in the range 490 n-490 μn, vickers hardness was estimated from elasto-plastic fe models done by using, to calibrate the mechanical properties of the investigated metals, the corresponding http://dx.medra.org/10.3221/igf-esis.19.04&auth=true http://www.gruppofrattura.it l. susmel et alii, frattura ed integrità strutturale, 19 (2012) 37-50; doi: 10.3221/igf-esis.19.04 38 monotonic stress-strain curves experimentally determined by testing samples having both conventional size and, for austenitic steel aisi 316l, gauge length size equal to approximately 100 μm. the systematic comparison between experimental results and numerical simulations suggests that the increasing of the measured hardness value with the decreasing of the indenter size may directly be ascribed to the role played by the actual morphology of the material being tested. in particular, it is seen that conventional elastoplastic continuum mechanics is no longer adequate to estimate metallic material hardness as the size of the indented surface approaches the average size of the grains. finally, in order to overcome the above limitation by allowing the classical elasto-plastic fe approach to be used also to estimate nano-hardness, a simple engineering method is proposed and subsequently validated through the generated experimental results. keywords. durezza; nanoindentazione; elementi finiti; plasticità. introduzione e prove di durezza con penetratore sono da più di un secolo ampiamente impiegate nella pratica industriale per misurare in modo rapido ed economico alcune proprietà meccaniche dei materiali (come, ad esempio, per la stima diretta della tensione di snervamento), nonché per valutare le caratteristiche di trattamenti e lavorazioni superficiali. queste metodologie di misura, basate sull’uso di penetratori di geometria standard, permettono l’ottenimento di impronte permanenti (aventi la particolarità di essere geometricamente simili al variare della profondità di penetrazione, ovvero, al variare del carico di prova) la cui estensione superficiale consente il computo diretto del valore di durezza, intesa come pressione media esercitata dal penetratore sull’area dell’impronta, area misurata dopo aver rimosso il carico [1-3]. il forte sviluppo della microelettronica a cui si è assistito negli ultimi decenni (circuiti integrati, microprocessori, ecc.), nonché delle più moderne nanotecnologie (con importanti applicazioni nel campo biomedico), ha di recente portato gli specialisti del settore a rivalutare ulteriormente l’importanza delle prove di durezza basate sull’uso di penetratori. in particolare, viste le ridotte dimensioni di tali componenti, le prove di durezza si sono dimostrate forse le più adatte a rilevare in modo non-distruttivo le proprietà meccaniche dei materiali utilizzati in queste particolari applicazioni. ovviamente, viste le dimensioni assolute dei componenti di cui doveva essere eseguita la misura della durezza, i carichi di prova sono stati ridotti fino ad ottenere profondità di penetrazione compatibili con le dimensioni del componente da testare. uno degli aspetti più interessanti di questo processo di miniaturizzazione delle prove di durezza è stata la progressiva riduzione delle dimensioni assolute dell’impronta, mantenendone, però, inalterata la geometria, con l’evidente vantaggio di poter ottenere misure su diverse scale dimensionali che, almeno dal punto di vista geometrico, potessero essere confrontate in modo diretto. considerando, invece, in modo più generale il problema della dipendenza del valore della durezza dalla dimensione dell’area indentata, è possibile affermare che quando la profondità dell’impronta, ottenuta mediante penetratori conici o piramidali, supera una certo valore di soglia (che varia al variare del materiale), la durezza misurata risulta praticamente indipendente dal valore del carico applicato: questa è la tipica situazione che si osserva nel caso di misure di macro-durezza su materiali metallici. al contrario, quando, invece, la profondità di penetrazione è inferiore al valore di soglia a cui si faceva riferimento poco sopra, le misure di durezza diventano fortemente dipendenti dalle dimensioni dell’impronta stessa, tanto che il valore della misura può risultare anche due o tre volte più alto del valore ottenuto mediante un macro-indentatore (questo fenomeno diventa particolarmente evidente quando si eseguono misure su monocristalli o su materiali policristallini, come chiaramente evidenziato dalla diagramma di fig. 1). il lavoro sintetizzato nel presente articolo si incentra sullo studio delle problematiche legate alla stima della durezza di materiali metallici, quando la durezza viene determinata, su diverse scale dimensionali, mediante l’uso di penetratori di tipo vickers. interessante è subito osservare che quando ci si riferisce a questa particolare geometria di penetratore, come brevemente accennato poco sopra, sembra essere convinzione comune [5] che il valore della durezza, calcolato secondo la formula: 2 2p sin 68 hv d    (1) l http://dx.medra.org/10.3221/igf-esis.19.04&auth=true http://www.gruppofrattura.it l. susmel et alii, frattura ed integrità strutturale, 19 (2012) 37-50; doi: 10.3221/igf-esis.19.04 39 sia indipendente dal carico di prova (dove nella precedente equazione p è la forza applicata e d la dimensione dell’impronta). tale convinzione, ampiamente supportata da sistematiche campagne sperimentali, risulta però valida fintanto che le dimensioni dell’impronta sono sufficientemente grandi rispetto alla grana cristallina, ovvero, tale affermazione è valida solo per prove di macro-durezza. al contrario, alcuni studi [6, 7] hanno evidenziato come esista una forte dipendenza del valore della durezza vickers dalla dimensione dell’impronta quando questa diventa comparabile con la dimensione della grana cristallina. in più, tali studi hanno posto in evidenza come un tale effetto scala non possa essere spiegato invocando unicamente la tradizionale teoria della plasticità, a meno che questa non venga pesantemente modificata onde estenderne la validità anche su scala microscopica. in particolare, si può osservare come l’aumento apparente di durezza a cui si assiste, per uno stesso materiale, passando dal campo macroscopico al campo microscopico, non sembra essere spiegabile solo con considerazioni puramente dimensionali (ovvero, ricorrendo al classico effetto scala): secondo le più moderne interpretazioni, un tale incremento apparente sembra sia legato alla proliferazione di dislocazioni geometricamente necessarie, proliferazione indotta dai gradienti di deformazione che vengono imposti al materiale durante il processo di indentazione [8-10]. più precisamente, deformazioni non uniformi dell’ordine di grandezza del µm producono una densità di dislocazioni geometricamente necessarie che risulta essere comparabile, o a volte anche superiore, alla densità di dislocazioni statisticamente presenti. in altre parole, maggiore è l’ordine di grandezza della deformazione in presenza di forti gradienti, più alta è la densità relativa di dislocazioni geometricamente necessarie e più alto è il loro contributo all’incrudimento: queste rappresentano le basi sui cui è stata recentemente sviluppata la teoria della plasticità fondata sul gradiente della deformazione (strain gradient plasticity) [10]. 0 0.5 1 1.5 2 2.5 0 0.5 1 1.5 2 profondità di indentazione, h [mm] d u re zz a [g p a] singolo cristallo di rame (1 1 1) policristallo di rame lavorato a freddo figura 1: dipendenza della durezza, misurata mediante una punta berkovich, dalla profondità di indentazione di un singolo cristallo di rame e di un agglomerato policristallino di rame lavorato a freddo [4]. figure 1: relationship between berkovich hardness and indentation depth in a single crystal as well as in a cold-rolled polycrystal of copper [4]. partendo dalle problematiche brevemente menzionate poco sopra, il presente lavoro riporta i risultati ottenuti nella previsione, mediante analisi elasto-plastiche agli elementi finiti, di macro-, microe nano-durezza di tre materiali metallici comunemente utilizzati nella realizzazione di componenti meccanici. in particolare, il presente lavoro si pone come obiettivo primario quello di formalizzare una possibile correlazione che leghi misure di durezza ottenute su diverse scale dimensionali mediante l’uso di simulazioni agli elementi finiti e assumendo che il materiale obbedisca ancora alle leggi della meccanica del continuo. la semplice procedura proposta si basa sull’uso di un valore di durezza utilizzato per la calibrazione del modello stesso e sulla curva tensione–deformazione del materiale, curva determinata in campo elastoplastico a mezzo di prove convenzionali di trazione e descrivibile mediante la nota relazione di ramberg-osgood [11]. interessante è osservare che il metodo proposto non solo ha consentito di legare in modo semplice i valori di durezza determinati su scala macro, micro e nano, ma ha permesso anche di individuare il limite di applicabilità della teoria della plasticità convenzionale nella modellazione delle misure di durezza superficiale, suggerendo, allo stesso tempo, che il fenomeno della strain gradient plasticity possa essere tenuto, in un certo qual modo, in considerazione mediante un parametro direttamente legato al comportamento plastico macroscopico del materiale. per concludere, e prima di entrare nel dettaglio della metodologia proposta, è importante sottolineare che, onde restare all’interno del campo di validità della meccanica del continuo, quanto formalizzato nel presente lavoro si basa sulla http://dx.medra.org/10.3221/igf-esis.19.04&auth=true http://www.gruppofrattura.it l. susmel et alii, frattura ed integrità strutturale, 19 (2012) 37-50; doi: 10.3221/igf-esis.19.04 40 assunzione che il materiale sia omogeneo, continuo e isotropo: la dimensione del grano e gli effetti di anisotropia locale dei cristalli non vengono, pertanto, tenuti in alcuna considerazione. modellazione della deformazione plastica dovuta alla indentazione mediante analisi numeriche agli elementi finiti rendendo spunto da quanto già fatto, sia in termini sperimentali che in termini di modellazione, da giannakopoulos et al. [12], è stata messa a punto una procedura adatta a modellare agli elementi finiti il problema dell’indentazione mediante penetratore vickers. tale procedura è stata basata sull’utilizzo, per la determinazione della soluzione numerica, del codice di calcolo commerciale ansys®. inizialmente, e per quanto riguarda la parte di modellazione solida, sfruttando le proprietà di simmetria rispetto a otto piani del penetratore tipo vickers, la geometria del problema in esame è stata fortemente semplificata secondo quanto riportato in fig. 2. si è poi ottenuta una ulteriore semplificazione, considerando il penetratore come un corpo perfettamente rigido e indeformabile (e questo in virtù della elevata rigidezza del diamante comparata a quella dei metalli di cui si doveva eseguire la stima della durezza). figura 2: rappresentazione schematica di un test di durezza eseguito utilizzando un penetratore di tipo vickers. figure 2: schematic sketch of a vickers test. le analisi condotte sono state trattate come problemi isotermi e con applicazione quasi–statica del carico: queste assunzioni hanno permesso di escludere gli effetti dinamici dovuti all’energia cinetica del penetratore. la mesh del solido di cui doveva essere modellata l’impronta generata dal penetratore vickers è stata creata in modo che in corrispondenza, e nei dintorni, dell’area di contatto la dimensione degli elementi fosse piuttosto contenuta, onde determinare correttamente la distribuzione del campo elasto-plastico di tensione. per valutare la bontà della mesh realizzata è stata condotta una accurata e sistematica analisi di convergenza che ha mostrato come il numero di elementi in contatto in condizioni di massimo carico doveva essere almeno pari ad otto in ogni direzione. più lontano dalla zona di contatto, invece, la densità della mesh è stata gradatamente ridotta, visto che tali elementi risultavano essere evidentemente caratterizzati da un valore della deformazione decisamente inferiore. la fig. 3a e, nel dettaglio, la fig. 3b mostrano la distribuzione della mesh utilizzata per condurre le analisi elastoplastiche: il solido su cui doveva essere modellata l’impronta dell’indentatore è stato meshato utilizzando un totale di 22261 nodi e 5219 elementi brick del tipo “solid 186” [13]; inoltre attraverso il “contact wizard” di ansys® è stato creato l’accoppiamento di contatto tra il penetratore e il solido da testare, con l’aggiunta di elementi “target 170” e “contact 174” [13]. per garantire poi un adeguato livello di precisione nella soluzione, precisione che dipendeva dal numero di elementi in contatto sull’area dell’indentazione, mantenendo contemporaneamente i tempi di calcolo a livelli accettabili, lo studio di convergenza ha evidenziato la necessità di scalare, secondo una certa proporzione, le dimensioni sia del provino che dell’impronta generata in funzione del carico di prova. una tale necessità si è in pratica tradotta nel determinare la p http://dx.medra.org/10.3221/igf-esis.19.04&auth=true http://www.gruppofrattura.it l. susmel et alii, frattura ed integrità strutturale, 19 (2012) 37-50; doi: 10.3221/igf-esis.19.04 41 soluzione di modelli geometricamente simili e aventi lo stesso numero di nodi, secondo quanto descritto nel grafico di fig. 4. per quanto riguarda i vincoli applicati, al solido indentato sono state applicate condizioni di simmetria sulle facce laterali, bloccando anche gli spostamenti verticali della sua base. il carico al penetratore, avente direzione coincidente con l’asse di simmetria verticale del problema, è stato applicato seguendo una rampa di carico e scarico (fig. 5): ogni step di carico aveva una durata temporale di 15 secondi, ottenendo, così, la durata totale di una prova vickers standard. infine, si può concludere il presente paragrafo osservando che il comportamento elasto-plastico del materiale su cui veniva eseguita l’indentazione è stato sempre descritto in ambiente ansys® assumendo come criterio di incrudimento un incrudimento di tipo isotropico. (a) (b) figura 3: distribuzione della mesh nella simulazione agli elementi finiti del processo di indentazione eseguita mediante il software ansys®. figure 3: mesh distribution in the fe models used to simulate the vickers test. 0.001 0.01 0.1 1 10 0.1 1 10 100 1000 10000 100000 1000000 carico, p [mn] d im en si o n e d el p ro vi n o , l [m m ] figura 4: criterio utilizzato per determinare la dimensione, l, del provino da modellare in ambiente ansys® al variare del carico applicato all’indentatore. figure 4: definition of dimension l used to do the fe models of the vickers indenters. http://dx.medra.org/10.3221/igf-esis.19.04&auth=true http://www.gruppofrattura.it l. susmel et alii, frattura ed integrità strutturale, 19 (2012) 37-50; doi: 10.3221/igf-esis.19.04 42 0 0.2 0.4 0.6 0.8 1 1.2 0 5 10 15 20 25 30 35 tempo [s] p /p m a x rampa di carico rampa di scarico figura 5: rampa di carico e scarico utilizzata per simulare una prova vickers standard. figure 5: loading and unloading curve used to simulate the vickers test. risultati sperimentali delle misure di macro-, microe nano-durezza e misure di macro-, microe nano-durezza sono state eseguite su tre materiali metallici con caratteristiche metallurgiche alquanto diverse: un acciaio a basso tenore di carbonio (bs970-en3b), un acciaio inossidabile (aisi 316l) e, infine, una lega d’alluminio (7075-t6). le proprietà meccaniche di questi metalli, e in particolare le curve sforzo-deformazione in campo elasto-plastico, sono state ricavate con prove eseguite in accordo alle vigenti normative. come verrà ampiamente descritto nei paragrafi successivi, per investigare in modo più accurato l’influenza della dimensione della superficie indentata sul valore della durezza, le analisi fem relative alle prove condotte sull’acciaio inossidabile aisi 316l sono state calibrate non solo considerando la curva elasto-plastica ottenuta mediante provini di dimensione convenzionale, ma anche mediante quella ottenuta con provini aventi larghezza della zona calibra dell’ordine dei 100 µm, ovvero dell’ordine dei 10 grani [14]. le principali proprietà meccaniche dei materiali investigati sono riassunte nella tab. 1, mentre nel grafico di fig. 6 sono comparate le curve elasto-plastiche ottenute dalle prove di trazione, curve che sono state tracciate in tale diagramma a mezzo delle corrispondenti relazioni di ramberg-osgood [11]: 1 n t t tot el pl e k              (2) materiale e y uts f f k n grain size [mpa] [mpa] [mpa] [mpa] [mpa] [m] 7075-t6 65000 500.5 577 624.3 0.08 709.1 0.048 10 (transv.) bs970 en3b 197400 606.2 638 851.8 0.56 882.7 0.061 13 aisi 316l 177000 298.8 754 986.5 0.39 1238.5 0.251 12 aisi 316l (wire) 150000 315.1 580 1252.3 0.346 12 tabella 1: proprietà meccaniche dei materiali metallici considerati nella presente investigazione. table 1: mechanical properties of the investigated metallic materials. i valori delle costanti della precedente relazione sono riportati, per ogni materiale considerato, in tab. 1. le misure di durezza superficiale sono state eseguite utilizzando tre diversi strumenti di misura: un macro-durometro convenzionale, un micro-durometro mitutoyo mvk–h1 ed un nanoindenter xp-mts, tutti equipaggiati con punte vickers standard. le rilevazioni sperimentali sono state eseguite a temperatura ambiente controllata, e pari a 20°c, su provini preparati in accordo con le normative vigenti e lucidati a specchio con pasta diamantata da 1 µm. i grafici di fig. 7 sintetizzano i risultati delle misure di durezza eseguite sui tre materiali metallici considerati nella presente investigazione: ognuno dei punti sperimentali riportato in tali diagrammi rappresenta il valore medio ricavato da sei misurazioni eseguite per ciascuna condizione di carico considerata. l http://dx.medra.org/10.3221/igf-esis.19.04&auth=true http://www.gruppofrattura.it l. susmel et alii, frattura ed integrità strutturale, 19 (2012) 37-50; doi: 10.3221/igf-esis.19.04 43 0 200 400 600 800 1000 1200 0 0.1 0.2 0.3 0.4 0.5 0.6 deformazione vera,  t t en si o n e v er a ,  t [m p a ] al 7075-t6 bs970-en3b aisi 316l aisi 316l (wire) figura 6: leggi costitutive dei materiali investigati espresse in termini di tensioni e deformazioni vere e tracciate in accordo alla relazione di ramberg-osgood. figure 6: true stress vs. true strain curves of the investigated materials. al 7075-t6 1 10 0.1 1 10 100 1000 10000 100000 1000000 carico, p [mn] d u re zz a , h v [g p a] macro-durezza micro-durezza nano-durezza bs970-en3b 1 10 0.1 1 10 100 1000 10000 100000 1000000 carico, p [mn] d u re zz a , h v [ g p a ] macro-durezza micro-durezza nano-durezza aisi 316l 1 10 0.1 1 10 100 1000 10000 100000 1000000 carico, p [mn] d u re zz a, h v [ g p a] macro-durezza micro-durezza nano-durezza figura 7: risultati delle prove di durezza vickers eseguite sui diversi materiali investigati. figure 7: results of the vickers tests. http://dx.medra.org/10.3221/igf-esis.19.04&auth=true http://www.gruppofrattura.it l. susmel et alii, frattura ed integrità strutturale, 19 (2012) 37-50; doi: 10.3221/igf-esis.19.04 44 si può subito osservare come le macro-prove vickers mostrino, per tutti e tre i materiali, un valore di durezza sostanzialmente indipendente dal carico di prova, e questo ad ulteriore conferma di quanto già da tempo noto [5]. nel zona della microdurezza invece, i valori misurati tendono, per tutti materiali considerati, a crescere al decrescere del carico di prova applicato, e questo incremento diventa chiaramente evidente in corrispondenza dei limiti inferiori di carico delimitanti la zona di utilizzo del micro-durometro. importante è anche osservare che in questa zona dei diagrammi durezza-carico si è sempre osservato un anomalo comportamento dei risultati sperimentali. analisi comparative hanno chiaramente evidenziato che questa anomalia poteva essere imputata ad un problema di cambio di scala nella catena di misura del micro-durometro, cambio di scala che avveniva, per carichi inferiori a 1n, quando la forza al penetratore passava dall’essere applicata mediante contrappesi all’essere applicata per effetto elettromagnetico. fortunatamente la sovrapposizione del campo superiore di utilizzo del nano-durometro con quella inferiore del micro-durometro ha permesso di limitare questo problema, ottenendo così risultati più coerenti. infine, i diagrammi di fig. 7 mostrano che il raggiungimento dei limiti inferiori di carico nel campo delle misure di nanodurezza corrispondeva ad un marcato incremento del valore della durezza rispetto a quella misurata in campo macroscopico (questo trend può essere apprezzato con maggior dettaglio osservando la tab. 2). a conclusione di questo paragrafo, si può da ultimo evidenziare che nel campo delle nano-indentazioni i valori di durezza misurati risultavano sempre caratterizzati da una dispersione statistica, in termini di deviazione standard, più elevata rispetto ai valori di microe macro-durezza, e questo in conseguenza al ruolo fondamentale giocato dalla reale morfologia del materiale in presenza di superfici indentate di estensione inferiore alla dimensione del grano. materiale durezza hv incremento p = 490 n p = 0.49 mn [gpa] [gpa] [%] al 7075t6 1.88 3.25 72.8 bs970 en3b 2.11 3.34 58.3 aisi 316l 1.87 3.75 100.5 tabella 2: incremento delle durezze misurate in campo microscopico rispetto a quelle determinate in campo macroscopico. table 2: comparison between measured microand macroharness. comparazione tra misure sperimentali e simulazioni numeriche a tab. 3 sintetizza i valori dell’errore commesso nello stimare, mediante l’approccio agli elementi finiti discusso in precedenza, la durezza dei tre materiali considerati nella presente investigazione. importante è subito sottolineare come tutte le stime riportate nella sopramenzionata tabella siano state ottenute assumendo che i materiali metallici considerati obbedissero alle leggi della meccanica del continuo e che il loro comportamento elasto-plastico fosse descritto da curve monotone ottenute con provini convenzionali (ovvero, macroscopici). la tab. 3 pone, prima di tutto, in evidenza come i valori ricavati dalle simulazioni di macro-durezza siano tutti in perfetto accordo con le rilevazioni sperimentali. in particolare, il fatto che l’errore massimo sia sempre inferiore al 3%, sembra fortemente supportare l’idea che la durezza in campo macroscopico possa essere efficacemente stimata facendo semplicemente uso della classica meccanica del continuo. i risultati di tab. 3 mostrano poi come al diminuire del carico di prova, ovvero spostandosi dal campo della macrodurezza al campo della micro-durezza, l’errore nella stima rimanga contenuto, ma in evidente tendenza alla crescita. quando, infine, si entra decisamente nel campo della nano-durezza, l’errore nella stima cresce notevolmente, arrivando anche a valori superiori al 50%. interessante è, prima di tutto, osservare come però l’errore commesso nella stima della nano-durezza dell’acciaio da costruzione bs970-en3b sia risultato essere molto basso, ovvero con errori, indipendentemente dall’entità del carico applicato, sempre inferiori all’10%. una tale situazione può essere spiegata con semplicità, osservando che le barre di bs970-en3b da cui erano stati estratti sia i provini per le misure di durezza che i provini per le prove statiche sono state ottenute per rollatura a freddo: il materiale si presentava, pertanto, già fortemente incrudito e questo limitava notevolmente l’effetto della strain gradient plasticity [10] sul valore della durezza, visto che un ulteriore moto delle dislocazioni risultava altamente inibito a causa della precedente lavorazione a freddo. l http://dx.medra.org/10.3221/igf-esis.19.04&auth=true http://www.gruppofrattura.it l. susmel et alii, frattura ed integrità strutturale, 19 (2012) 37-50; doi: 10.3221/igf-esis.19.04 45 materiale scala carico hv errore calcolata misurata [mn] [gpa] [gpa] [%] a l 70 75 -t 6 m ac ro 490000 1.84 1.88 2.2 196000 1.83 1.86 1.6 98000 1.87 1.89 1.1 m ic ro 9800 1.75 1.83 4.6 4900 1.75 1.83 4.6 980 1.59 1.76 10.7 490 1.75 2.01 14.9 245 1.77 2.08 17.5 n an o 98 1.89 2.07 9.5 49 2.07 2.16 4.3 9.8 2.14 2.37 10.7 4.9 2.09 2.5 19.6 0.98 2.13 2.92 37.1 0.49 2.14 3.25 51.9 b s 97 0e n 3b m ac ro 490000 2.07 2.11 1.9 196000 2.08 2.12 1.9 98000 2.08 2.07 -0.5 m ic ro 9800 1.97 2.01 2.0 4900 2.09 2.04 -2.4 980 1.99 2.05 3.0 490 2.25 2.36 4.9 245 2.5 2.63 5.2 n an o 98 2.65 2.8 5.7 49 2.7 2.85 5.6 9.8 2.75 2.87 4.4 4.9 2.94 3.04 3.4 0.98 3.04 3.15 3.6 0.49 3.08 3.34 8.4 a is i 31 6l m ac ro 490000 1.83 1.87 2.2 196000 1.83 1.86 1.6 98000 1.84 1.87 1.6 m ic ro 9800 1.75 1.84 5.1 4900 1.75 1.79 2.3 980 1.75 1.93 10.3 490 1.84 1.77 -3.8 245 1.88 2.22 18.1 n an o 98 2.18 2.41 10.6 49 2.18 2.58 18.3 9.8 2.18 2.59 18.8 4.9 2.19 3.32 51.6 0.98 2.22 3.63 63.5 0.49 2.2 3.75 70.5 tabella 3: comparazione tra i valori di durezza hv ottenuti sperimentalmente e quelli ottenuti mediante analisi numeriche agli elementi finiti. table 3: comparison between the experimental values of the vickers hardness and the corresponding values determined by solving elasto-plastic fe models. http://dx.medra.org/10.3221/igf-esis.19.04&auth=true http://www.gruppofrattura.it l. susmel et alii, frattura ed integrità strutturale, 19 (2012) 37-50; doi: 10.3221/igf-esis.19.04 46 in accordo con quanto riportato in tab. 3, si può, pertanto, affermare che la tendenza evidenziata dall’errore nella stima della durezza (passando dal macroal nano-) sembra fortemente supportare l’idea che la meccanica del continuo possa fornire risultati soddisfacenti fintanto che la dimensione dell’impronta resta maggiore della dimensione media della grana cristallina. al contrario, quando l’impronta presenta una estensione confrontabile, o inferiore, alla dimensione media del grano, è evidente che l’ipotesi di perfetta omogeneità ed isotropia del materiale, ipotesi su cui è basata la meccanica del continuo, risulta essere troppo semplicistica. in altre parole, quando l’area della superficie indentata diventa confrontabile con la dimensione del grano, la reale morfologia del materiale ne influenza troppo il comportamento meccanico per essere completamente trascurata nella modellazione del fenomeno. alla luce delle considerazioni riportate sopra, per verificare se si poteva comunque tenere conto correttamente della influenza della struttura cristallina del materiale restando, però, ancora nell’ambito della meccanica del continuo, la durezza dell’acciaio inossidabile aisi 316l è stata stimata anche a mezzo di analisi fem calibrate mediante la curva monotona del materiale ottenuta a mezzo di provini microscopici, ovvero di provini aventi larghezza della zona calibra pari a circa 100 µm [14]. il diagramma di fig. 6 mostra chiaramente che la curva ottenuta con provini microscopici (wire) differiva dalla corrispondente curva monotona generata con provini di dimensione convenzionale. questa diversità deve essere imputata al fatto che nel caso dei provini microscopici la reale morfologia del materiale nella zona di processo ricopriva un ruolo fondamentale nella definizione del profilo della curva monotona stessa. al contrario, nei macro-provini la reale distribuzione dei grani giocava, invece, un ruolo del tutto marginale a causa dei noti fenomeni di omogeneità ed isotropia di compenso tipica dei materiali metallici. in tab. 4 sono stati sintetizzati gli errori ottenuti nello stimare la durezza dell’acciaio inossidabile aisi 316l, quando i modelli fem venivano calibrati con la curva monotona ottenuta con micro-provini. sfortunatamente, questo tentativo, se pure estremamente attraente da un punto di vista filosofico, non ha dato i risultati sperati, portando ad errori nella stima comunque superiori a quelli che si erano ottenuti calibrando i modelli fem con la curva tensione-deformazione generata con provini macroscopici. materiale scala carico hv errore calcolata misurata [mn] [gpa] [gpa] [%] a is i 31 6l ( w ir e) m ic ro 9800 1.50 1.84 22.7 4900 1.49 1.79 20.1 980 1.32 1.93 46.2 490 1.35 1.77 31.1 245 1.36 2.22 63.2 n an o 98 1.71 2.41 40.9 49 1.67 2.58 54.5 9.8 1.69 2.59 53.3 4.9 1.74 3.32 90.8 0.98 1.76 3.63 106.3 0.49 1.75 3.75 114.3 tabella 4: comparazione tra i valori di durezza hv ottenuti sperimentalmente e quelli ottenuti mediante analisi numeriche agli elementi finiti, calibrando queste ultime mediante la curva monotona ottenuta testando provini di dimensione microscopica. table 4: comparison between the experimental values of the vickers hardness and the corresponding values determined by solving elasto-plastic fe models calibrated through the ramberg-osgood curve generated by testing microscopic samples of aisi 316l. a conclusione di quanto riportato nel presente paragrafo, si può rimarcare come la durezza superficiale dei materiali metallici possa essere stimata correttamente ricorrendo alla sola meccanica del continuo fintanto che la dimensione della superficie indentata risulta essere notevolmente maggiore della dimensione media della grana cristallina. al contrario, per dimensioni dell’impronta comparabili, o inferiori, alla dimensione della grana cristallina, la plasticità classica risulta in una sottostima sia della microche della nano-durezza. da ultimo si può evidenziare che, in accordo alle analisi numeriche e sperimentali condotte sull’aisi 316l, neanche l’impiego di una curva monotona generata con provini di larghezza dell’ordine di pochi grani consente di estendere con successo l’utilizzo della meccanica del continuo fino ad un livello microscopico: in questo scenario così complesso e articolato si comprende, pertanto, il motivo per cui nell’ultimo http://dx.medra.org/10.3221/igf-esis.19.04&auth=true http://www.gruppofrattura.it l. susmel et alii, frattura ed integrità strutturale, 19 (2012) 37-50; doi: 10.3221/igf-esis.19.04 47 decennio gli specialisti della cosiddetta “surface science” abbiano investito così tante risorse nello sviluppare, e validare sperimentalmente, la teoria dello strain gradient plasticity [8-10]. una procedura semplificata per la correzione dei risultati numerici onde incrementare la precisione nella stima di microe nano-durezze el paragrafo precedente, confrontando i risultati sperimentali con i valori ottenuti dalle simulazioni numeriche, si è potuto mettere in luce che l’errore nella previsione aumentava al diminuire della dimensione dell’impronta. in particolare, si è potuto osservare come un approccio agli elementi finiti, e basato sulla teoria della meccanica del continuo, consentisse di prevedere con elevata accuratezza solo il valore della durezza misurata in campo macroscopico, tendendo, sfortunatamente, a diventare sempre meno accurato mano a mano che la dimensione della superficie indentata tendeva a diventare confrontabile con la dimensione media della grana cristallina. in accordo con le più recenti teorie sviluppate nel campo della “surface science”, anche gli autori del presente lavoro ritengono che la via più promettente per tentare di incrementare la precisione nella stima della durezza sia quella di sviluppare algoritmi numerici che siano in grado ti tenere conto in modo efficace dell’effetto della strain gradient plasticity [810] sulla generazione dell’impronta indentata. tuttavia, nonostante questa convinzione, in questo paragrafo si cerca di propone una semplice metodologia ingegneristica adatta a correggere i valori della durezza superficiale quando questi sono stimati con un approccio agli elementi finiti. inizialmente, osservando la tab. 3, si può constatare come l’accuratezza più elevata nella stima della durezza in campo nano-scopico si sia ottenuta considerando i risultati generati dalle prove sull’acciaio al carbonio bs970-en3b. si può poi osservare che la curva monotona di questo materiale (fig. 6) presentava, a causa della lavorazione a freddo con cui erano state ottenute le barre del materiale base, un tratto plastico praticamente orizzontale, ovvero il comportamento di tale materiale poteva, di fatto, essere assimilato ad un comportamento di tipo “perfettamente elastico-perfettamente plastico”. da un punto di vista della fisica del fenomeno, una tale curva denotava, invece, il fatto che il materiale, a causa della lavorazione a freddo, aveva già subito un forte incrudimento: il moto residuo delle dislocazioni risultava alquanto limitato, riducendo gli effetti della strain gradient plasticity sul valore misurato della durezza. alla luce delle osservazioni riportate appena sopra si è formulata allora l’ipotesi che l’effetto della strain gradient plasticity sul valore della durezza rilevata potesse essere assunto come proporzionale ad una sorta di “gradiente equivalente del comportamento plastico macroscopico” definito come: f y f y yf y f e                (3) in base alla definizione (3) un materiale ideale avente un comportamento perfettamente plastico sarebbe caratterizzato, allora, da un rapporto / pari a zero, ovvero, in accordo con le considerazioni esposte sopra, il contributo della strain gradient plasticity sul valore della durezza dovrebbe essere di fatto trascurabile. al contrario, se fosse vero quanto ipotizzato poco sopra, al crescere del valore del rapporto espresso dalla relazione (3), dovrebbe crescere il contributo del gradiente della deformazione sul valore finale della durezza. importante è poi osservare che le costanti del materiale necessarie per la determinazione del rapporto / sono, per come è stato posto il problema, sempre note: tali costanti, infatti, vengono dalla conoscenza della curva monotona del materiale, curva che deve essere nota perché necessaria per eseguire le analisi fem in campo elasto-plastico. in base a quanto ipotizzato, diventa, a questo punto, lecito assumere che il valore misurato sperimentalmente della durezza, hvs, possa essere previsto, noto il corrispondente valore ottenuto dalle simulazione agli elementi finiti, hvfem, e il valore p del carico applicato all’indentatore, mediante la seguente relazione: s fem hv p q cos t hv    (4) una conveniente espressione per l’esponente  è risultata essere la seguente: 510       (5) dove, chiaramente,  è una quantità resa adimensionale dalla costante 10-5 misurata in mpa-1. n http://dx.medra.org/10.3221/igf-esis.19.04&auth=true http://www.gruppofrattura.it l. susmel et alii, frattura ed integrità strutturale, 19 (2012) 37-50; doi: 10.3221/igf-esis.19.04 48 al 7075-t6 1 10 0.1 1 10 100 1000 10000 100000 1000000 carico, p [mn] d u re zz a, h v [ g p a ] sperimentale stimata eq. (7) bs970-en3b 1 10 0.1 1 10 100 1000 10000 100000 1000000 carico, p [mn] d u re zz a , h v [ g p a ] sperimentale stimata eq. (7) aisi 316l 1 10 0.1 1 10 100 1000 10000 100000 1000000 carico, p [mn] d u re zz a , h v [ g p a ] sperimentale stimata eq. (7) figura 8: comparazione tra risultati sperimentali e stime fem corrette a mezzo della metodologia proposta. figure 8: comparison between experimental results and predictions made by correcting the calculated fe values according to the proposed engineering method. il valore della costante q nella relazione (4) può essere determinato considerando una configurazione di riferimento per cui siano noti i valori dei tre parametri hvs, hvfem e p: s fem rif hv q p cos t hv    (6) pertanto per un qualsiasi valore del carico applicato all’indentatore, e una volta calcolato il valore di hvfem mediante un modello agli elementi finiti, la durezza del materiale può essere stimata come: fem s hv hv q p   (7) http://dx.medra.org/10.3221/igf-esis.19.04&auth=true http://www.gruppofrattura.it l. susmel et alii, frattura ed integrità strutturale, 19 (2012) 37-50; doi: 10.3221/igf-esis.19.04 49 i risultati ottenuti applicando la metodologia ingegneristica proposta in questo paragrafo sono riassunti nei diagrammi di fig. 8, dove tali diagrammi sono stati ottenuti assumendo, per tutti i materiali, come configurazione di riferimento per il calcolo della costante q, eq. (6), quella relativa ad una prova di macro-durezza dove il carico applicato all’indentatore era pari a 490 n. si può allora concludere questo paragrafo evidenziando come, in base a quanto mostrato dalla fig. 8, l’approccio proposto, seppure estremamente semplificato, consente di ottenere delle stime della durezza superficiale che sono comunque sufficientemente accurate da un punto di vista ingegneristico e quindi la metodologia di stima sviluppata presenta una indubbia utilità pratica. discussione l lavoro sintetizzato nel presente articolo si poneva come obbiettivo primario quello di verificare se un approccio elasto-plastico agli elementi finiti fosse in grado di stimare in modo ingegneristicamente accurato la durezza dei materiali metallici convenzionali, e questo sia a livello macroscopico, che a livello microscopico, che, infine, a livello nanoscopico. per verificare validità e accuratezza della metodologia fem messa a punto, sono state condotte una serie di analisi sperimentali su tre materiali metallici (al 7075-t6, bs970-en3b e aisi 316l) aventi caratteristiche metallurgiche alquanto diverse. una tale investigazione sperimentale ha inizialmente evidenziato, confermando, d’altra parte, quanto già noto in letteratura, come il valore della durezza vickers (o più ingenerale della durezza misurata a mezzo di un indentatore) tenda a crescere al diminuire della dimensione della impronta: per uno stesso materiale, i valori di durezza misurati in campo nanoscopico sono risultati anche superiori del 100% ai valori determinati in campo macroscopico. una tale diversità può essere imputata al diverso ruolo giocato dalla dimensione del grano sul comportamento meccanico globale del materiale, ovvero al diverso ruolo giocato dalla reale morfologia del materiale sul valore della durezza misurata al diminuire delle dimensioni della superficie indentata. in particolare, e come noto, per i materiali metallici valgono, in campo macroscopico, le ipotesi di omogeneità e di isotropia di compenso grazie alle quali l’influenza della grana cristallina può essere totalmente trascurata nel modellare i fenomeni in presenza di grandi deformazioni plastiche: in questo ambito la meccanica del continuo risulta idonea a descrivere il fenomeno investigato, ovvero analisi fem condotte in campo elasto-plastico, ipotizzando un incrudimento di tipo isotropico, consentono di stimare con estrema accuratezza il valore dell’area della superficie indentata. al contrario, al diminuire della dimensione della superficie indentata, il ruolo della struttura cristallina diventa sempre più importante, tanto che quando l’area dell’impronta diventa confrontabile con la dimensione media del grano, la meccanica del continuo, applicata con metodologie fem, non sembra essere più in grado di modellare correttamente il fenomeno investigato. nel tentativo di verificare se esisteva comunque la possibilità di estendere l’uso della meccanica del continuo anche al campo nanoscopico, si è provato a stimare la durezza superficiale dell’aisi 316l anche utilizzando per la calibrazione dei modelli fem la curva monotona ottenuta testando provini aventi larghezza della zona calibra dell’ordine dei 100µm. questo tentativo prendeva come spunto di partenza l’idea che un approccio agli elementi finiti potesse essere esteso con successo anche a livello nanoscopico, ammesso che per la sua calibrazione si potessero utilizzare proprietà del materiale il più possibile vicine a quelle relative al singolo grano. purtroppo, però, tale tentativo, anche se molto interessante dal punto di vista filosofico/teorico, non ha dato i risultati sperati. a parere degli scriventi, il motivo di un tale insuccesso può essere ricondotto principalmente al fatto che il comportamento meccanico di un agglomerato cristallino, anche se formato da pochi grani, differisce comunque dal comportamento meccanico di un singolo grano. in più, è evidente che quando l’area della superficie indentata risulta essere inferiore alla dimensione del grano le reali proprietà meccaniche/metallurgiche del grano stesso influenzano necessariamente in modo determinante il valore misurato della durezza. a questo livello, l’orientazione delle direzioni preferenziali di scorrimento delle dislocazioni, nonché la possibilità che hanno tali dislocazioni di muoversi in presenza di fenomeni di deformazione così spinti e localizzati, influenza in modo decisivo le caratteristiche dell’impronta generata dall’indentatore. alla luce di queste considerazioni si comprende il motivo per cui la teoria dello strain gradient plasticity [10] sia oggi quella maggiormente utilizzata per spiegare in modo rigoroso e scientifico i fenomeni investigati nel presente lavoro: a livello nanoscopico, il moto delle dislocazioni in presenza di forti gradienti di deformazione gioca il ruolo più importante nella definizione della durezza, quando questa è misurata a mezzo di un indentatore. nonostante questa convinzione però, nel presente lavoro si è comunque tentato di formalizzare una regola pratica, basata sul comportamento plastico del materiale in campo macroscopico, nel tentativo di proporre uno strumento ingegneristico che consentisse di stimare la durezza, i http://dx.medra.org/10.3221/igf-esis.19.04&auth=true http://www.gruppofrattura.it l. susmel et alii, frattura ed integrità strutturale, 19 (2012) 37-50; doi: 10.3221/igf-esis.19.04 50 partendo da un valore stimato mediante gli elementi finiti, indipendentemente dalla dimensione dell’impronta. la comparazione diretta tra stime e risultati sperimentali ha consentito di evidenziare come la metodologia proposta sia, seppure nella sua semplicità, adatta a stimare i valori della durezza sia in campo macroscopico, che in campo microscopico, che, infine, in campo nanoscopico, e questo indipendentemente dalla dimensione assoluta dell’impronta utilizzata per la calibrazione del metodo stesso. un tale approccio, seppure fondato su un forte pragmatismo ingegneristico, ha dato ottimi risultati, dimostrandosi, pertanto, un valido strumento da utilizzarsi in situazioni ingegneristiche di interesse pratico. conclusioni  le prove sperimentali condotte su tre materiali metallici diversi (al 7075-t6, bs970-en3b e aisi 316l) hanno evidenziato un incremento della durezza rilevata al diminuire della superficie indentata;  le simulazioni agli elementi finiti hanno dimostrato di essere attendibili fintantoché si resta nell’ambito di validità della meccanica del continuo, ovvero fintantoché le misure delle impronte hanno dimensione superiore alla dimensione media della grana cristallina;  le proprietà meccaniche ottenute da test di trazione condotti su microprovini si sono rivelate non sufficienti ad estendere con successo l’utilizzo della meccanica del continuo alla simulazione di microe nano-deformazioni (come quelle di interesse in test di microe nano-durezza);  la metodologia ingegneristica proposta si è dimostrata un utile strumento da utilizzarsi, unitamente ai risultati numerici ottenibili con i più comuni codici di calcolo agli elementi finiti, in situazioni di interesse pratico per stimare la durezza dei materiali metallici, e questo indipendentemente dalla dimensione della superficie indentata. bibliografia [1] a. g. atkins, d. tabor, journal of mechanics and physics of solids, 13 (1965) 149. [2] k. l. johnson, journal of mechanics and physics of solids, 18 (1970) 115. [3] c. rubenstein, journal of applied mechanics, 48 (1981) 796. [4] k. w. mcelhaney, j. j. vlassak, w. d. nix, journal of material research, 13 (1995) 1300. [5] d. tabor, the hardness of metals, clarendon press, oxford, uk (1951). [6] n. a. stelmashenko, m. g. wallas, l. m. brown, y. v. milman, acta metallurgica materialia, 41 (1993) 2855. [7] q. ma, d. r. clarke, journal of materials research, 10 (1995) 853. [8] m. f. ashby, philos. mag., 21 (1970) 399. [9] n. a. fleck, g. m. muller, m. f. ashby, j. w. hutchinson, acta metallurgica materialia, 42 (1994) 475. [10] w. d. nix, h. gao, journal of mechanics and physics of solids, 46 (1995) 411. [11] b. atzori, appunti di costruzione di macchine. ed. libreria cortina, padova (2000). [12] a. e. giannakopoulos, p. l. larsson, r. vestergaard, int. j. of solids and structures 31, (1994) 2679. [13] anon., ansys® reference guide, (2011). [14] s. wiersma, d. taylor, fatigue & fracture engn. mater. struct., 28 (2005)1153. http://dx.medra.org/10.3221/igf-esis.19.04&auth=true http://www.gruppofrattura.it microsoft word shana_icmff11_16 a. shanyavskiy et alii, frattura ed integrità strutturale, 49 (2016) 399-404; doi: 10.3221/igf-esis.38.49 399 multiaxial fatigue of in-service aluminium longerons for helicopter rotor-blades a. shanyavskiy state center for civil aviation flight safety, airport sheremetievo-1, po box 54, chimkinskiy state, moscow region, 141426, russia, 106otdel@mail.ru, http://orcid.org/0000-0001-2345-6789 a. toushentsov state center for civil aviation flight safety, airport sheremetievo-1, po box 54, chimkinskiy state, moscow region, 141426, russia, 103otdel@mail.ru, http://orcid.org/0000-0002-2345-6790 abstract. fatigue cracking of longerons manufactured from al-alloy avt-1 for helicopter in-service rotor-blades was considered and crack growth period and equivalent of tensile stress for different blade sections were estimated. complicated case of in-service blades multiaxial cyclically bending-rotating and tension can be considered based on introduced earlier master curve constructed for aluminum alloys in the simple case of uniaxial tension with stress r-ratio near to zero. calculated equivalent tensile stress was compared for different blade sections and it was shown that in-service blades experienced not principle difference in this value in the crack growth direction by the investigated sections. it is not above the designed equivalent stress level. crack growth period estimation in longerons based on fatigue striation spacing or meso-beach-marks measurements has shown that monitoring system introduced designer in longerons can be effectively used for in-time crack detecting independently on the failed section when can appeared because of various type of material faults or in-service damages. keywords. fatigue; multiaxial; longerons; aluminium alloy; crack growth; fractography; stress equivalent. citation: shanyavskiy, a., toushentsov, a., multiaxial fatigue of in-service aluminium longerons for helicopter rotor-blades, frattura ed integrità strutturale, 38 (2016) 399-404. received: 15.07.2016 accepted: 15.08.2016 published: 01.10.2016 copyright: © 2016 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. introduction atigue cracking of longerons manufactured from al-alloy avt-1 for helicopter in-service rotor-blades was considered and crack growth period and equivalent of tensile stress for different blade sections were estimated. complicated case of in-service blades multiaxial cyclically bending-rotating and tension can be considered based on f a. shanyavskiy et alii, frattura ed integrità strutturale, 49 (2016) 399-404; doi: 10.3221/igf-esis.38.49 400 introduced earlier master curve constructed for aluminum alloys in the simple case of uniaxial tension with stress r-ratio near to zero [1]. calculated equivalent tensile stress was compared for different blade sections and it was shown that inservice blades experienced not principle difference in this value in the crack growth direction by the investigated sections. it is not above the designed equivalent stress level. crack growth period estimation in longerons based on fatigue striation spacing or meso-beach-marks measurements has shown that monitoring system introduced designer in longerons can be effectively used for in-time crack detecting independently on the failed section when can appeared because of various type of material faults or in-service damages. a) b) figure 1: scheme (a) of rotor-blade section with numbering “1”-“5” areas for crack origination and pointed out its external loading and (b) cells position for a blade. the pressure gage, installed in the basement portion of the rotor blade, is designed to send a signal of lost excessive pressure to a monitor (a window in that a watcher can see the red cup to appear) once discontinuity arose in the longeron in any section of the propeller blade. according to the service norms, such inspection is to be performed each time before the flight. in-service fatigue cracks nucleated in the longerons in the defect sites that were revealed all over the blade length, from r = 0.085 to r = 0.71, where max( ) / ( )d i dr r r (see fig.1b). in the paper we shall discuss in details the fracture trends of the longerons made of aluminium avt-1 alloy. inspection results of fatigue-cracking behavior of the longerons atigue cracks only nucleated in operating longerons of the rotor-blades if their material was somehow damaged [2, 3]. despite the fact that the defects differed in the sites of location in the cross-section area of the longeron (see fig. 1), all the defects caused failure of the fatigue nature. we can formalize these failure cases according to a general scheme of the fracture surface, fig. 2, as composed of: a fracture-origin exhibits a fracture relief typical of the damage kind and may be located anywhere on the inner or outer surface of the longeron walls; a zone (1) of stable crack growth typically exhibits a smooth fracture surface with distinct mesoscopic or macroscopic (depending of the fracture location) beach-marks of fatigue fracture; a zone (2) of accelerated crack propagation typically shows a wavy fracture surface of the “christmas-tree” or “chevronlike” type; a zone (3) of fast crack propagation when the plastic-shear lips form entirely over the wall-thickness of the longeron. in the zone 1, pseudo-striations pattern forms first (p-region), peculiar to low-rate crack growth in the near-threshold range of the kinetic diagram. the material here experiences extensive shear. as the crack length increases, a pattern of fatigue striations forms or, alternatively, mesoscopic fatigue beach-marks dominate, depending on the blade section in that the crack propagates. formation of fatigue striations alternating with dimpled fracture is typical of the zone 2: here, the crack growth becomes accelerated. purely dimpled relief is typical of the zone 3 of final fracture; here the plastic-shear lips form throughout an entire thickness of the blade wall. having fatigue meso-beach-marks and fatigue striations distinctly visible made it possible to analyze the growth trends of fatigue cracks in the longerons and to determine the growth durations of the cracks and estimate the in-service stress level. f a. shanyavskiy et alii, frattura ed integrità strutturale, 49 (2016) 399-404; doi: 10.3221/igf-esis.38.49 401 furthermore, it made possible to verify if the crack-monitoring alarm gage, installed, by design, in the longeron-basement end, operated efficiently. figure 2: scheme of longerons fracture surfaces for crack origination from the corrosion pitting with indication “1”-“3” different fracture surface areas. consider the data on two cases; in one case the crack was disclosed as it grew not above 25% of the total cross-section area of the longeron and in the other case the longeron failed in flight as the crack occupied 75% of its cross-section. the two helicopters were of the same type and the fracture sites almost coincided. the cases appeared contradicting to one another, i.e., indicated both to the efficient and inefficient operation of the alarm gage. moreover, that fatigue zone, which amounted in total to 25-% of the cross-section of the longeron, occupied equal areas on both sides (top and bottom) of the neutral bending line. consequently, the longeron had the crack partially closed in the qualitatively similar ways whether in flight or in the parked condition. still the gage responded to the drop of pressure in both conditions, which showed its sensitivity as quite high. in such a contradictory situation, when cracks were now revealed and now not revealed, one had to either improve the gage efficiency or discipline the inspecting organizations to use the gage carefully. one could estimate the gage efficiency most correctly using the data on growth duration of fatigue cracks and in-service stresses as applied to the separate blade sections. in so doing, one first should examine the crack-growth patterns in the longerons subjected to bench tests simulating various loading conditions. secondly, one should see to which degree the propagation patterns of fatigue cracks remain similar in the separate longeron sections. initiation and propagation patterns of fatigue cracks in service lades in flight are loaded with the frequency that is determined by the revolution frequency of the rotor and corresponds to the frequency of the single cycles of fatigue damage. accordingly, we calculate the growth period of fatigue cracks based on the measurements of fatigue-striation spacing and assuming that each single fatigue striation is formed as a result of one rotor revolution. this consideration of material damage has accordance with longerons fatigue tests on the special test-device that were performed earlier [2]. we shall compare below these estimations with the crack-growth durations calculated based on the data on fatigue meso-beach-marks (mbm). the area of early crack growth, with typically p-region of fracture, was the largest in the damage site, in the section of relative radius r = 0.085 (beside the blade basement); it measured about 25 mm in length. in all the other sections such crack-growth areas were smaller, though no relation between the fracture region size and the relative radius of a longeron was revealed. for the separate longeron sections (distances from the blade basement), the growth periods of fatigue cracks were estimated based on the data on the fatigue-meso-beach-marks and fatigue-striation spacings. in the region of relative radius r = 0.085 of the longeron fatigue mbm were characteristic of the fatigue damage all over the crack path from the fracture-origin site till the transition to unstable crack growth. this fatigue fracture was initiated owing to the preliminary corrosion cracking of the material. beyond the fracture-origin area mbm geometry is perfect and the meso-beach-mark spacing increases regularly in the crack-growth directions. fatigue striations began to form as the crack increased to 25 mm along the rear wall. plus to them, meso-beach-marks continued to form clearly, which helped to estimate with greater accuracy the crack-growth duration over both in the striation-free (p-region) and striation-bearing portions of the fracture. b a. shanyavskiy et alii, frattura ed integrità strutturale, 49 (2016) 399-404; doi: 10.3221/igf-esis.38.49 402 immediately before the fast-cracking zone began, mbm formed as distinctly as to be visible at quite moderate magnifications (with the use of a light microscope), indicating to quite heavy fatigue damage. we may say that these coarse (macroscopic) fatigue lines formed to respond to the effects of regularly altered applied loads. by the end-rupture time the fatigue crack passed through 45% portion of the longeron cross-section. in these limits (from the origin site till endrupture zone), the crack grew by 120 mm along the bottom wing and by 52 mm along the rear wall. sequentially measured distances between mbm and, then, between the macro-beach-marks confirmed that the recurrence along the crack path is not casual, but regular, indicative of the very blade-loading patterns, regularly repeated with each single flight cycle, fig. 3. therefore, the regularly increasing distances between these marks are indicative of the crackgrowth rate regularly increasing from flight to flight. and the number of these beach-marks corresponds to the number of the helicopter flights accomplished with the fatigue crack propagating in the longeron. a) b) figure 3: spacing of (a) mesoor macro-beach-marks and (b) fatigue striations with number of cycles np against crack length a for two longerons (a) and (b). in case that the distances between the fatigue beach-marks remain unchanged for some periods of crack propagation shows the crack-length increments to obey some scale hierarchy both at the mesoscopic (mbm or fatigue striations) and macroscopic levels. this particular trend again indicates that the blades were loaded in a regular way (each single flight); the latter showed itself through the pattern of regularly advancing fatigue crack. fatigue mbm were counted starting from the area 5.5 mm apart from the crack-origin site (the lines became most distinct here) to find out that the following crack-growth period involved about 210 flights. the inter-mbm distances (and, hence, the crack-length increments) appeared to sequentially increase. for the crack length grown from 5.5 to 7 mm, the average length increment did not exceed 0.056 mm per flight. so, not less than 70 flights were done with the fatigue crack growing in length from 1.5 to5.5 mm. the starting crack length of 1.5 mm was taken a little greater than the depth (1.3 mm) of the stress-corrosion-origin. in total, these estimations give 280 (210 + 70) flight cycles for the period of crack propagation from the corrosion-cracking zone till the beginning point of unstable fracture. of the considered cases of the failure of longerons, the fracture at the site of r =0.7 related to the cases of the deepest fatigue cracks: here, the p-region of early cracking measured as much as 12 mm. the blade fracture began from a nearly spherical cavity as large as about 2 mm in radius, located at the inner surface of the longeron. on both sides of the crack, cavities, similar to the cavity from which the fracture began, were arranged in a file along the longeron axis. the value of striation spacing increased with the crack length in a way indicative of the regular loading pattern of the longeron in service. the spacing of fatigue striations irregularly increasing and decreasing with increasing crack length only appeared immediately before the transition to accelerated crack growth and a chevron-like fracture morphology (see number “2” on fig. 2). the calculations were done according to the following relationships [1, 4]. in so doing, 57000 cycles was thus calculated for crack-growth period in p-region. in average, single-flight duration is close to 30 minutes, and a loading frequency is determined by the revolution frequency (192 revolutions per minute) of the rotor. consequently, the crack growth duration in the longeron must be not less than 49.5 hours (about 100 flights). these figures do not contradict the macroscopic view of the fracture morphology. using a binocular microscope at small magnifications, one could observe indistinct fatigue macro-beach-marks in individual parts of the fracture. such marks were used for estimating the flight number, which then was compared with the flight number acquired from the fatiguestriation patterns. the two estimations appeared to differ not more than by 10%. a. shanyavskiy et alii, frattura ed integrità strutturale, 49 (2016) 399-404; doi: 10.3221/igf-esis.38.49 403 therefore, using predominantly the patterns of mbm and fatigue striations we may estimate the growth durations of fatigue cracks. having compared these estimations, we may see that cracks of fatigue nature grow in the longerons for quite long periods and, hence, inspection and monitoring of their growth in service can be highly efficient. levels of equivalent stress in the longerons of mi-4 and mi-8 helicopters rom the above data one can see that propagation of fatigue cracks in the longerons takes quire a long time. this information, however, should be enlarged to answer how much descriptive are the usually applied calculation methods as concerns the actual stress-strain conditions of the material in various sections of a longeron. having this question answered is especially important, as corrosion-induced damage is well known to occur and, sometimes, be a source of fatigue cracks in the longerons. let us discuss the levels of equivalent stress e with respect to various relative radii of the longerons; the stress levels are estimated in terms of the concept of the single kinetic curve with the use of above-described quantitative-fractography approach to the failure cases of aviation structures. along the longeron, the stress level changes with the distance from the longeron basement. tensile stress diminishes and, simultaneously, bending load increases. this complex loading pattern results in stresses that vary in the level and in the ratio between the torsion and bending components. longerons experience a permanent tensile stress, whose largest value is 60 mpa, and the stress that varies between 10 mpa and 38 mpa. in flight, a longeron is twisted within 3�, and the torsion stress achieves 30 mpa. as follows from the analysis of stressed state of the specimens loaded simultaneously by torsion and tension [5], crackgrowth behavior is predominantly controlled by the value of crack opening normal to the crack-growth direction. in other words, a crack propagates along the normal to the axis of maximum tensile stress, applied to the crack tip. typically, crack-propagation occurs with fatigue striations forming in the fracture area. therefore, we can estimate a crack-growth rate using a synergetic approach, based on the concept of master kinetic curve [1, 4]. striations do not appear in case of out-of-phase loading [6], when the cycle asymmetry r near to zero. though caused by combined uniaxial tension and torsion, fatigue fracture develops as a single phenomenon. therefore, a unified energetic criterion was proposed [6] for describing fatigue-cracking behavior under such combined tension-andtorsion conditions. making use of that criterion helps the calculation of a tension equivalent for stress-intensity factor ke from the following relationships.  1/22 21e i ii iiik k c c     (1) in eq. (3) dimensionless coefficients cii and ciii only depend on the poisson’s ratio and characterize the effects of the crack-opening modes kii and kiii for a pipe-type specimen twisted in the crack plane. eq. (3) relates to the case of using the master curve of fatigue-cracking kinetics for various combinations of shear and tensile components of torsion-andtension loading. here the equivalent stress-intensity factor appears a quantity only dependent on a correction f() for a torsion angle, which value was calculated, typical of all the other cases, for the master kinetics curve [1, 4, 6]. a loading pattern of the rotor-blades repeats quite regularly every flight. so, statistically, we can discuss crack-growth events in various blade sections as relating to the same loading type. the levels of equivalent stress were estimated for various sections and origin sites of fatigue cracks. below, we illustrate the methodological principles of these calculations for the case of fatigue-crack growth at the relative radius r = 0.38 of a longeron. in this section, stresses to be calculated arise from varying stresses and dynamic tension of 59 mpa. in such a case an equivalent stress can be estimated from a relationship    max min max1 / 81.5 1 0.45 60.5e        (2) from the laboratory tests of avt3-1 alloy the value of k1p = 7.9 mpa m1/2 was acquired for border transition from pregion to the stage of fatigue striation formation. for the longeron of interest, this value is achieved as the crack riches 6 mm in length. and using a respective relationship [7], we may estimate a stress-intensity factor for a round crack as f a. shanyavskiy et alii, frattura ed integrità strutturale, 49 (2016) 399-404; doi: 10.3221/igf-esis.38.49 404 1p 0 /ek a   (3) where   1. from eq. (3) we found the equivalent stress e  58 mpa for the crack length a0 = 6 mm. one can see that loading conditions remained the same and no positive or negative deviation occurred from the equivalent-stress level all over the fatigue-striation stage. all these calculations indicate that the fatigue fracture of the longeron was initiated as a result of high stress concentration in the corrosion-cracking site and not because of an overloading event. one can see that, regarding the levels of equivalent stresses, the longeron sections at the r -value 0.7 and 0.5 are close to one another; this finding is consistent with the data on crack-growth durations and stress levels calculated for longerons. in the discussed longeron, initial corrosion cracking (intergranular) reached 0.4-mm depth. then in 5-mm distance predominantly corrosion cracking (transgranular and intergranular) transformed to purely fatigue cracking (transgranular). next to this zone, fatigue crack propagated for quite a long period. here, the value of equivalent stress did not exceed the designed level. therefore, fatigue crack would not nucleate without stress concentration, caused by the corrosion cracking deeper than 0.3 mm from the outer surface of the longeron, as long as the surface layer of such thickness experiences the residual compression stresses greater than the equivalent tensile stress. the monitoring system employed to watch the longeron impermeability of the mi-family helicopters is efficient. conclusion – in cases of nucleation and propagation of fatigue cracks in the longerons of mi-4 and mi-8 helicopters in-service stresses never exceeded the designed levels at any relative radius of the propeller blades; – the longest crack-growth periods are typical of the basement part of the blades; – through fatigue cracks show the growth periods of tens flights for a whichever relative radius of a propeller blade; hence, such cracks can be revealed in good time with the pressure gages, installed in the blades to signal about the loss of their impermeability. references [1] shanyavskiy, a.a., tolerance fatigue cracking of aircraft structures. synergetics in engineering applications. monograph, ufa (russia), (2003). [2] shanyavskiy, a.a., quantitative fractographic analyses of fatigue crack growth in longerons of in-service helicopter rotor-blades. fatigue fract. engng mater struc., 19 (1996) 1129-1141. [3] shanyavskiy, a.a., toushentsov, a.l., effectiveness of safety flight guaranty for helicopters using introduced in longeron rotor-blade device for cracks detecting. science works for investigators society of crashed aircrafts, russia, 11 (1999) 110-128. [4] shanyavskiy, a.a., orlov, e.f., koronov, m.z., fractographic analyses of fatigue crack growth in d16t alloy subjected to biaxial cyclic loads at various r-ratios. fatigue fract. engng mater struc., 18 (1995) 1263-1276. [5] shanyavskiy, a.a., orlov, e.f., grigoriev, v.m., fatigue crack growth in d16 al-alloy sheet subjected to biaxial outof-phase loading. fatigue fract. engng mater struc., 20 (1997) 975-983. [6] chan, k.s., hack, l.e., leverat, g.r. fatigue crack propagation in ni-base superalloy single crystals under multiaxial cyclic loads. met. trans., 17a (1986) 1739-1750. [7] murakami, y. 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/hrv (za stvaranje adobe pdf dokumenata najpogodnijih za visokokvalitetni ispis prije tiskanja koristite ove postavke. stvoreni pdf dokumenti mogu se otvoriti acrobat i adobe reader 5.0 i kasnijim verzijama.) /hun 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can be opened with acrobat and adobe reader 5.0 and later.) >> /namespace [ (adobe) (common) (1.0) ] /othernamespaces [ << /asreaderspreads false /cropimagestoframes true /errorcontrol /warnandcontinue /flattenerignorespreadoverrides false /includeguidesgrids false /includenonprinting false /includeslug false /namespace [ (adobe) (indesign) (4.0) ] /omitplacedbitmaps false /omitplacedeps false /omitplacedpdf false /simulateoverprint /legacy >> << /addbleedmarks false /addcolorbars false /addcropmarks false /addpageinfo false /addregmarks false /convertcolors /converttocmyk /destinationprofilename () /destinationprofileselector /documentcmyk /downsample16bitimages true /flattenerpreset << /presetselector /mediumresolution >> /formelements false /generatestructure false /includebookmarks false /includehyperlinks false /includeinteractive false /includelayers false /includeprofiles false /multimediahandling /useobjectsettings /namespace [ (adobe) (creativesuite) (2.0) ] /pdfxoutputintentprofileselector /documentcmyk /preserveediting true /untaggedcmykhandling /leaveuntagged /untaggedrgbhandling /usedocumentprofile /usedocumentbleed false >> ] >> setdistillerparams << /hwresolution [2400 2400] /pagesize [612.000 792.000] >> setpagedevice microsoft word numero_29_art_7 s. terravecchia et al., frattura ed integrità strutturale, 29 (2014) 61-73; doi: 10.3221/igf-esis.29.07 61 focussed on: computational mechanics and mechanics of materials in italy strain gradient elasticity within the symmetric bem formulation s. terravecchia, t. panzeca, c. polizzotto university of palermo silvioterravecchia@gmail.com, teotista.panzeca@unipa.it, castrenze.polizzotto@unipa.it abstract. the symmetric galerkin boundary element method is used to address a class of strain gradient elastic materials featured by a free energy function of the (classical) strain and of its (first) gradient. with respect to the classical elasticity, additional response variables intervene, such as the normal derivative of the displacements on the boundary, and the work-coniugate double tractions. the fundamental solutions featuring a fourth order partial differential equations (pdes) system exhibit singularities which in 2d may be of the order 41/ r . new techniques are developed, which allow the elimination of most of the latter singularities. the present paper has to be intended as a research communication wherein some results, being elaborated within a more general paper [1], are reported. keywords. strain gradient elasticity; symmetric galerkin bem. introduction fter the pioneering work of mindlin [2], theories of strain gradient elasticity have become very popular, particularly within the domain of nano-technologies, that is, for problems where the ratio surface/volume tends to become very large and there is a need to introduce at least one internal length. however the model introduced by mindlin and then improved by mindlin et al. [3] and wu [4] leads to an excessive number of material coefficients, which at the best for isotropic materials reduce to the number of seven. in the early 1990’s, aifantis [5] introduced a signified material model of strain gradient elasticity which requires only three material coefficients, that is, the lame' constants and one length scale parameter. the latter model was then developed further following the so-called form ii format given by mindlin et al. [3], that is a theory centered on the existence of a free energy function of the (classical) strain and of its first gradient, which leads to the generation of symmetric stress fields (see askes et al. [6] for historical details about the latter formulations and its applications). formulations in the boundary element method based on the strain gradient elasticity were pioneered by polyzos et al. [7], karlis et al. [8], who provide a collocation bem formulation where the simplified constitutive equation by aifantis [5], has been adopted. in latter papers only the fundamental solutions used in the collocation approach to bem are provided. in the case of the symmetric formulation of the bem, somigliana identities (sis) for the tractions and for the double tractions are also needed. these new sis are necessary in order to get, through the process of modeling and weighing, a solving equation system having symmetric operators. in polizzotto et al. [1] all the set of fundamental solutions is derived starting from the displacement fundamental solution given in [7,8]. a s. terravecchia et al., frattura ed integrità strutturale, 29(2014) 61-73; doi: 10.3221/igf-esis.29.07 62 the symmetric formulation is motivated by the high efficiency achieved within classical elasticity by the method in [9] with regard to the techniques used to eliminate the singularities of the fundamental solutions, the evaluation of the coefficients of the solving system and the computational procedures characterized by great implementation simplicity. this has already led to the birth of the computer code karnak sgbem [10] operating in the classical elasticity. the objective of this paper is to experiment new techniques and procedures that, applied in the context of strain gradient elastic materials, may permit one to obtain the related solving system. notation s a rule, a compact notation is used, with vectors and tensors denoted by bold-face symbols. the dot  , the colon products : and :: indicate the simple and higher index contraction. the following notations are also utilized: the gradient operator: grad ( ) ( )   ; the divergence operator : div ( ) ( )   ; the laplacian operator : 2 2 2 ( ) ( ) ( ) ( ) x y              ; the component of the normal derivation of u is denoted as n k kn   g u u ; the quantities with bar superscripts indicate know quantities. other symbols will be specified in the text at their first appearance. basic relations in 2d he class of strain gradient elastic materials herein considered is featured by the following strain elastic energy 21 : : :: ( ) 2 2 tw      ε e ε e ε ε  (1) that is a function of the symmetric 2nd order strains ( 0 ) ( )s  ε ε u and of the strain gradient ( 1)  ε ε , where  is the internal length which relates the microstructure with macrostructure. eq.(1) provides the stress tensors work-coniugate of ( 0 )ε and ( 1)ε respectively ( 0 ) ( 1) 2 2 ( 0 ): ;   σ e ε σ σ (2a,b) where e is the classic isotropic elasticity tensor. by the principle of the virtual work, the indefinite equilibrium equation and the following boundary conditions prove to be in ω  σ b 0 , on γt t , on γr r , on the corner cct t (3a,b,c,d) where the total stresses σ , the tractions t , the double tractions r and the force at the corner p are so defined ( 0 ) 2 2 ( 0 )  σ σ σ , ( ) ( 1)( ) ( )s k      t n σ n n σ , (1):r nn σ , ( 1):c t sn σ    (4a,b,c,d) in eq.(4b), the symbol ( ) ( )s   i nn denotes the tangent gradient on the boundary and ( )sk    n is the curvature on the boundary having normal n ; in eq.(4d) s denotes a unit vector tangent to the two boundary portions convergent in the corner c and the brackets   indicate that the enclosed quantity is the difference between the related values taken on two sides of the corner c. for a more exhaustive understanding of the jump   to see [2]. the constitutive equation relating the total stress σ to the strain is 2 2 )  σ e ε ε:( . (5) a t s. terravecchia et al., frattura ed integrità strutturale, 29 (2014) 61-73; doi: 10.3221/igf-esis.29.07 63 the fundamental solutions he introduction of eq.(5) in (3a) valid in infinity domain  allows to express the latter in terms of displacements only [7,8] and to determine the fundamental solution of the displacements that for 2d solids proves to be 2 22 2 0 22 2 2 4 1 = 16 (1 ) 2 2(3 4 ) [ ] 2 uu r k r r r log r k k r                                                          i g r r      (6) where  0k  and  2k  are bessel functions of the second kind and of order 0 and 2, respectively, and  r ξ x is the distance between effect ξ and cause x points. one can note that the singularity of the fundamental solution uug does not depend on r . indeed, by performing the limit r 0 one obtains  1( ) 2(3 4 ) ln( 2 ) 1 16 (1 ) uu             g ξ x i  (7) where  is the eulero constant and the fundamental solution for isotropic gradient elasticity shows singularity of type ln( ) . in eq.(6) the limit of uug for 0 gives the classic isotropic elasticity solution (kelvin) with singularity of type ln( )r . table 1: fundamental solutions for strain gradient elasticity and relative singularities. by the fundamental solution uug in (6), taking in account eqs.(4b,c,d) and using the well-known procedure given in [11], it is possible, by exploiting the known properties of symmetry of the fundamental solutions, to derive the entire tableau provided in table 1. the fundamental solutions hkg of tab. 1 are characterized by two subscripts: the first indicates the effect at ξ , i.e. displacement for h u , traction for h t , displacement normal derivative for h g , double traction for h r , corner displacement for ch u , corner force for ch t , stress for h  ; whereas the second subscript indicates – through a t s. terravecchia et al., frattura ed integrità strutturale, 29(2014) 61-73; doi: 10.3221/igf-esis.29.07 64 work-conjugate rule – the cause applied at x , i.e. a unit concentrated force for k u , a unit surface relative displacement for k t , a unit concentrated double force for k g , a unit higher order surface distortion for k r , a unit corner force for ck u , a unit corner displacement for ck t , a unit imposed strain for k  . to consider the way in which the fundamental solutions included in the single   and double     brackets to see [2]. while the fundamental solutions represent the response in a point ξ of the unlimited domain caused by unit kinematical or mechanical action imposed at x , the response to the distributed actions is provided by the sis that in [1] are obtained by a generalization of the betti theorem for the gradient elastic materials. a case study s a premise, it should be noted that the theory of strain gradient should be applied to those bodies where the ratio between surface and volume in 3d and between boundary and area in 2d is high. in these cases, the body should be considered as composed of a nucleus, a crust and its boundary. the example we want to meet will show that on the basis of this theory the behavior of the cortex has different characteristics from the classical behavior of the nucleus, and this depends on the presence of new variables such as double traction r and normal derivative g of the displacements. obviously, the body will suffer the effects due to the presence of these new variables. from computational point of view, the fundamental solutions present in the tab. 1 show various orders of singularity, up to 41/ r in the column related to u , up to 31/ r in that related to cu ; furthermore the singularities present in the column cu present an order lower than that of u , relatively to the same effect. in order to investigate the techniques useful to remove the singularities from the blocks of coefficients, a simple application in two-dimensional space is shown, but at this stage involving the study of fundamental solutions having the maximum order of singularity equal to 21/ r . it has to be remembered that in the symmetric bem the coefficients are obtained by a double integration, the first (inner) regarding the modeling of the cause through appropriate shape functions and the second (external) regarding the effect weighing through shape functions, but dual in the energetic sense. x y 1 1 1 1 a b c d ef g 1 2 3 4 567 8 x y h a) b) figure 1: plate: a) geometry and constraints; b) discretization into boundary elements and linear modelling of the boundary quantities. for this purpose, the example shown concerns a plate completely constrained on the boundary, subjected to the simple distortions u , cu and distortions of higher order / n  g u . this example is also used to develop the techniques of rigid motion that could be used in other applications to compute the coefficient blocks in which the techniques available are not sufficient to suppress the residual singularities. for the plate of fig.1a the boundary conditions are u u on u g g on g with u g   (8a,b) let us proceed to write the sis on the boundary a s. terravecchia et al., frattura ed integrità strutturale, 29 (2014) 61-73; doi: 10.3221/igf-esis.29.07 65 , 1 d + d ( )d ( ) ( )d + ( ) 2 u g u g uu ug ut ur u tc c                   u g t g r g u u g g g u   on u (9a) , 1 d + d ( )d ( )d ( )+ ( ) 2 u g u g gu gg gt gr g tc c                   g g t g r g u g g g g u    on g (9b) and, following the compact notation proposed by panzeca et al. [9], the latter equations become 1 [ ] [ ] [ ] ( ) [ ] [ ] 2 cpv c         u u t u r u u u u g u u on u (10a) 1 [ ] [ ] [ ] [ ] ( ) [ ] 2 cpv c         g g t g r g u u g g g u on g (10b) in the sis:  the bar superscripts characterize known quantities;  the apex cpv indicates that the corresponding integral is evaluated as cauchy principal value to which the related free term 1 ( ) 2  is added;  cu is a vector containing only the known displacement of the corner;  [ ]cu u and [ ]c g g u are, respectively, the displacement and normal derivative of displacement distribution on the boundary, computed as the difference between the response to the values of displacement imposed on the two portions of boundary afferent to the corner. introducing the latter sis given in eqs.(10a,b) into the boundary conditions eqs.(9a,b) one has: 1 [ ] [ ] [ ] ( ) [ ] [ ] 2 cpv c         u t u r u u u u g u u 0 on u (11a) 1 [ ] [ ] [ ] [ ] ( ) [ ] 2 cpv c         g t g r g u u g g g u 0 on g (11b) let us now discretize the plate boundary into boundary elements (fig.1b) and introduce the modeling of the quantities on the boundary as functions of the nodal variables through suitable matrices of shape functions hn , with , , ,h t r u g ; ; ; f r u g   t n t r n r u n u g n g (12a,b,c,d) since the vector cu collects nodal quantities to not be modeled, the following identity has to be imposed c cu u (13) in eqs.(12a-d) the quantities t , r , u , g have the meaning of nodal quantities and precisely: force and double traction as unknowns, displacements and normal derivatives of displacements as known quantities. to evaluate the vector g , because the discontinuity of the normal derivative at the corner c, a double node belonging respectively to the two portions of boundary afferent to c has to be considered. introducing the modeling (12a-d) and the relation (13) into eqs.(11a,b) and performing the weighing second galerkin, by using the shape functions in dual form, one writes , 1 + ( ) ( ) 2 ( )+ ( ) u u u g u u u uu ut utug u g u ur u tc t uu t f ug r t ut u t u t ur g t up c                              a a ca a a n g n t n g n r n g n u n n u n g n g n g u 0              (14a) s. terravecchia et al., frattura ed integrità strutturale, 29(2014) 61-73; doi: 10.3221/igf-esis.29.07 66 , + ( ) ( ) 1 ( ) ( ) 2 g u g g g u g g gu gg gt gr g g gr g tc r gu f r gg r r gt u r gr g r g r gp c                               a a a a c a n g n t n g n r n g n u n g n g n n g n g u 0                (14b) and, following the compact notation proposed by panzeca et al. [9], the latter equations become , , ( ) u tcuu ug ut ut ur c gu gu gt gr gr g tc                                      aa a a c at 0u u a a a a cr 0g a        (14c) since some components of the vector u and of the vector cu coincide, it is opportune to introduce the following relation c cu h u (15) where the low rectangular matrix ch is a topological matrix made by 2 2i and 2 20 blocks. the previous relation can be rewritten * , * , ( ) ( ) ( ) g u ut ut u tcuu ug ur gu gu gr gr gt g tc                              k l l a c aa a at 0 u g a a a cr 0a a           (16) where ** , , , ,; u tc u tc c g tc g tc c a a h a a h                   . (17a,b) finally, the solving system is rewritten in compact way with obvious meaning of symbols u g   l k x l l 0  (18) with k symmetric flexibility matrix of the system, x vector of nodal unknowns, ul and gl load vectors due to u e g respectively, being u g l l l the total load vector. in order to evaluate the coefficients of the equation system, the numerical techniques to remove the singularities and the rigid motion strategy have to be employed. observation about rigid motions let the plate of fig.2 be subjected to a) a rigid motion of translation obtained as the sum of constant displacement fields xu and yu (fig.2a), b) a rigid motion of rotation having wideness  around any point (fig.2b), c) a rigid motion of roto-translation obtained as a combination of a) and b). in all these cases the displacement and normal derivative of the displacement fields are entirely known both in the domain and on the boundary of the plate. particularly for the case of rigid motion of translation (fig.2a) s. terravecchia et al., frattura ed integrità strutturale, 29 (2014) 61-73; doi: 10.3221/igf-esis.29.07 67 , 0 , 0 x x x y y y u u c1 g n u u c2 g n             (19a,b,c,d) with c1 and 2c being the wideness of the displacements; for the case of rigid motion of rotation having width f (fig.2b) f  (20a) x x x y y y y x u u f y g f n n u u f x g f n n               (21b,c,d,e) x y x y x u c1= y u c2= f=f a) b) figure 2: rigid motions: a) translation, b) rotation. observations about the load vector as a consequence of the rigid motion 1) if the solid is subject to a rigid motion of translation (fig.2a) having assigned values of the displacements c1 and 2c , one has u 0 and g 0 but the total load vector has to be u g  l l l 0 with * , * , ( ) ( ) ut ut u tc u gt g tc               a c a 0 l u 0a a         (22) ( ) ur g gr gr              a 0 l g a c 0  (23) and as a consequence the solution vector x has to be null. 2) if the solid is subject to a rigid motion of rotation (fig.2a) having assigned rotation vector fφ , in the generic node i one has i i  u r φ 0 i i i    g φ n φ s 0 (24a,b) with ir vector distance between the instantaneous center of rotation and the node i , in e is being respectively the unit normal and tangent vectors to the boundary elements on which the node i lies, but the total load vector has to be u g  l l l 0 with s. terravecchia et al., frattura ed integrità strutturale, 29(2014) 61-73; doi: 10.3221/igf-esis.29.07 68 * , * , ( ) ( ) ut ut u tc u gt g tc               a c a 0 l u 0a a         (25) ( ) ur g gr gr              a 0 l g a c 0  (26) because the solution vector x has to be null. 3) if the solid is subjected to a combination of the rigid motions 1) and 2), the condition u g  l l l 0 has to be always valid. example of coefficient calculation in presence of singularity the greater difficulties consist in removing the singularities when the cause is focused at the corner. the simple observation that the vector u regards all the nodes of the boundary, including the vector cu at the corner, allows to eliminate the higher order singularities after the first integration. indeed, the use of the distribution theory permits to evaluate the effect on the boundary without limit operations and removing the strong singularities through the summing of effects, whereas the remaining ones are eliminated through the second integration. the singularities present in the fundamental solutions used for the plate analysis require shape functions of type ( 0 )c . in order to show how operate to remove singularity in the coefficients of the solving system, we examine the load vector ul and specifically calculate the weighed normal derivative. a) b) figure 3: a) effect: weighed normal derivative ,b yys on the b ; b) cause: vertical displacement on the b and c and corner displacement , 1y cu  . with referring to fig.3, the weighed normal derivative ,b yys is , , b b yy b b yys n g d    (27) where ,b yyg is a normal derivative distribution due to: vertical displacements modeled on boundary elements b and c , having maximum value 1yu  ; corner vertical displacement , 1y cu  . in this case the si of the normal derivative gives ' ' * * * , ( ) ' ' ( ) ' ' , ( )d d b c b yy gt yy b b gt yy c c g tc yyg g n g n g             (28) and, suppressing for simplicity the subscript yy, through the process of weighing one obtains s. terravecchia et al., frattura ed integrità strutturale, 29 (2014) 61-73; doi: 10.3221/igf-esis.29.07 69 ' ' * * * ' ' ' ' ,d d d b b c bc bb bc b b gt b b gt c c g tc b g g g s n g n g n g                              (29) the following contributions bbg , bcg bcg are provided distinguishing between the singular and the regular part ( sing ) ( reg ) ( reg ) 3 4 1 [ ] [1 ] 16(1 ) 1 bb bb bb bbg g g log x log x g x                 (30a) ( sing ) ( reg ) ( reg ) 3 4 3 16(1 ) 1 bc bc bc bcg g g g x             (30b) ( sing ) ( reg ) ( reg ) 3 4 2 16(1 ) 1 bc bc bc bcg g g g x              (30c)  ( sing ) ( sing ) ( sing ) ( reg ) ( reg ) ( reg ) ( reg ) ( reg ) ( reg ) d d d d 3 4 1 ( ) d d d 16(1 ) 2 b b b b b b b b b bb bc bc b b bb b b bc b b bc b b bb b b bc b b bc b s n g g g n g n g n g n g n g n g                                      (31) the sum of the effects in terms of distributions bbg , bcg bcg eliminates the strong singularity 1/ r , while the weak singularity ( )log r present in the bbg distribution is eliminated in the weighing operation by integration by parts. eqn. (31) gives the coefficient in closed form. numerical results let us analyze the two-dimensional plate of fig.1 having the following physical and mechanical characteristics: 1, 0.3, 0.1, 1e s    . y x u x y x g x a) b) figure 4: distribution on the boundary a) xu and b) xg . the plate is subjected to a linear displacement distribution u , including the nodal displacement cu , and to the linear displacement normal derivatives / n  g u , all imposed on the boundary. the displacement and displacement gradient fields imposed on the boundary have the distribution shown in fig.4a,b. the field response is derived by the sis after the solution being obtained. for the example here considered, characterized by the presence of eight nodes on the boundary and four corner (fig. 1b), the know nodal vector u has sixteen components, whereas cu defined by s. terravecchia et al., frattura ed integrità strutturale, 29(2014) 61-73; doi: 10.3221/igf-esis.29.07 70 c c               i 0 0 0 0 0 0 0 0 0 i 0 0 0 0 0 u h u u 0 0 0 0 i 0 0 0 0 0 0 0 0 0 i 0 shows eight components; the vector g collects twenty-four components, due to the presence of the double node belonging respectively to the two portions of boundary afferent to the corners,. two load conditions are considered:  first load condition 1 1 0 x x u at x g        (32) for this condition the vectors of know nodal quantities u , cu and g are  1 0 0 0 1 0 1 0 1 0 0 0 1 0 1 0t    u (33)  1 0 1 0 1 0 1 0tc   u (34)  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0t g (35)  second load condition 1 1 1 x x u at x g         (36) for this condition the vectors of known nodal quantities u , cu and g are  1 0 0 0 1 0 1 0 1 0 0 0 1 0 1 0t    u (37)  1 0 1 0 1 0 1 0tc   u (38)  0 0 0 0 0 0 1 0 1 0 1 0 0 0 0 0 0 0 1 0 1 0 1 0t    g (39) tractions xt , yt , double tractions xr , yr , obtained by analysis, are summarized in tab. 2 and tab. 3. fig.5 and fig.6 show the fields of displacements xu , of standard strain ( 0 ) xx , of high-order strain ( 1) 2 2 ( 0 ) xx xx    ad of total strain ( 0 ) 2 2 ( 0 )xx xx xx      plotted along a line 0.5y  .  comments the diagrams of fig.5,6 show how the distribution of normal derivatives xg imposed on the boundary influence the trend of the displacement field, in particular the slope near the boundary. in the first load conditition the imposed value 0xg  involves zero slope at 1x   for the displacement field and the related field of the standard strain ( 0 )xx show null values at 1x   ; the field of high-order strain show high values at 1x   and values close to zero in the centre of the plate in the second load condition the imposed value 1xg  provides at 1x   the same slope of the displacement field inside the plate; the standard strain ( 0 )xx show constant unit value, whereas the field of the high-order strain is null and the total strain coincides with the standard strain. this is the case in which the imposed value for xg gets the same solution valid for isotropic classic elasticity. s. terravecchia et al., frattura ed integrità strutturale, 29 (2014) 61-73; doi: 10.3221/igf-esis.29.07 71 xt yt xr yr 1a 0.591253 0.673221 1a -0.0391933 -0.00500786 2a -0.188974 0.066697 2a 0.00922674 -0.0104388 2b 0.188974 0.066697 2b -0.00922674 -0.0104388 3b -0.591253 0.673221 3b 0.0391933 -0.00500786 3c 2.05806 -0.371508 3c -0.201115 0.0048963 4c 1.28042 0.246566 4c -0.129643 0.00265313 4d 1.28042 -0.246566 4d -0.129643 -0.00265313 5d 2.05806 0.371508 5d -0.201115 -0.0048963 5e -0.591253 -0.673221 5e 0.0391933 0.00500786 6e 0.188974 -0.066697 6e -0.00922674 0.0104388 6f -0.188974 -0.066697 6f 0.00922674 0.0104388 7f 0.591253 -0.673221 7f -0.0391933 0.00500786 7g -2.05806 0.371508 7g 0.201115 -0.0048963 8g -1.28042 -0.246566 8g 0.129643 -0.00265313 8h -1.28042 0.246566 8h 0.129643 0.00265313 1h -2.05806 -0.371508 1h 0.201115 0.0048963 table 2: results for the first load condition. x t yt xr yr 1a 0.00 0.576923 1a 0.00 0.00 2a 0.00 0.576923 2a 0.00 0.00 2b 0.00 0.576923 2b 0.00 0.00 3b 0.00 0.576923 3b 0.00 0.00 3c 1.34615 0.00 3c 0.00 0.00 4c 1.34615 0.00 4c 0.00 0.00 4d 1.34615 0.00 4d 0.00 0.00 5d 1.34615 0.00 5d 0.00 0.00 5e 0.00 -0.576923 5e 0.00 0.00 6e 0.00 -0.576923 6e 0.00 0.00 6f 0.00 -0.576923 6f 0.00 0.00 7f 0.00 -0.576923 7f 0.00 0.00 7g -1.34615 0.00 7g 0.00 0.00 8g -1.34615 0.00 8g 0.00 0.00 8h -1.34615 0.00 8h 0.00 0.00 1h -1.34615 0.00 1h 0.00 0.00 table 3: results for the second load condition. s. terravecchia et al., frattura ed integrità strutturale, 29(2014) 61-73; doi: 10.3221/igf-esis.29.07 72 figure 5: field mechanical characteristics regarding the first load condition. figure 6: field mechanical characteristics regarding the second load condition. conclusions s. terravecchia et al., frattura ed integrità strutturale, 29 (2014) 61-73; doi: 10.3221/igf-esis.29.07 73 he table of fundamental solutions for isotropic strain gradient elasticity is similar to an analogous table used within classical boundary element method. computational techniques have been pursued in order to eliminate the singularities of order 1/ r , 21/ r , in the blocks of the coefficients related to the corners of the solid and new techniques based on the rigid motion strategy have been introduced in order to test the coefficients of the blocks of the solving system. the displacement and internal deformation fields were obtained. numerical techniques in order to remove the singularity of higher order like 31/ r and 41/ r are in advanced study. references [1] polizzotto, c., panzeca, t., terravecchia, s., a symmetric galerkin bem formulation for a class of gradient elastic materials of mindlin type. part i: theory, (2014). in preparation. [2] mindlin, r.d., second gradient of strain and surface tension in linear elasticity, int. j. solids struct., 1.(1965) 417438. [3] mindlin, r.d., eshel, n.n., on first strain-gradient theories in linear elasticity, int. j. solids struct., 28 (1968) 845858. [4] wu, c.h., cohesive elasticity and surface phenomena, quart. appl. math., l(1) (1968) 73-103. [5] aifantis, e.c., on the role of gradients in the localization of deformation and fracture, int. j. eng. sci., 30 (1992) 1279-1299. [6] askes, h., aifantis, e.c., gradient elasticity in statics and dynamics: an overview of formulations, length scale identification procedures, finite element implementations and new results, int. j. solids struct., 48 (2011) 19621990. [7] polyzos, d., tsepoura, k.g., tsinopoulos, s.v., beskos, d.e., a boundary element method for solving 2-d and 3-d static gradient elastic problems. part.i: integral formulation, comput. meth. appl. mech. engng., 192 . (2003) 28452873. [8] karlis, g. f. , charalambopoulos, a., polyzos, d., an advanced boundary element method for solving 2d and 3d static problems in mindlin's strain gradient theory of elasticity, int. j. numer. meth. engng., 83 (2010) 1407-1427. [9] panzeca, t., cucco, f., terravecchia s., symmetric boundary element method versus finite element method, comp. meth. appl. mech. engrg., 191 (2002) 3347-3367. [10] cucco f., panzeca t., terravecchia s., the program karnak.sgbem release 2.1, (2002) palermo university. [11] polizzotto c., an energy approach to the boundary element method. part.i: elastic solids, comput. meth. appl. mech. engng., 69 (1988) 167-184. t microsoft word numero_42_art_13.docx s. seitl et alii, frattura ed integrità strutturale, 42 (2017) 119-127; doi: 10.3221/igf-esis.42.13 119 focused on mechanical fatigue of metals evaluation of mixed mode i/ii fracture toughness of c 50/60 from brazilian disc test stanislav seitl, petr miarka brno university of technology, faculty of civil engineering, institute of structural mechanics, veveří 331/95, 602 00 brno, czech republic seitl.s@fce.vutbr.cz, http://orcid.org/0000-0002-4953-4324 miarka.p@fce.vutbr.cz abstract. durability and sustainability of structures made from concrete like materials is getting more into an interest of civil engineers. structures are subjected not only to uniaxial load, this means if there is a crack inside the load could be divided into mode i and shear mode ii, but also to a mixed mode i/ii. therefore, it is necessary to perform test, which covers mixed mode loads and could be used for specimen made from concrete core-drill. recommended test specimens used for evaluation of fracture mechanical parameters has usually a prismatic or rectangular shape. the cost of reshaping cylinder into rectangular is expensive and not very efficient, therefore it is very effective to use brazilian disc test specimen with central notch to obtain mixed mode fracture parameters. the contribution deals with numerical support for brazilian disc test to obtain calibration curves for mode i and mode ii, evaluation of experimental results and compare them with data adapted from literature. keywords. fracture mechanics; fracture toughness; centrally cracked brazilian disc; mixed mode i/ii; concrete. citation: seitl, s., miarka, p., evaluation of mixed mode i/ii fracture toughness of c 50/60 from brazilian disc test, frattura ed integrità strutturale, 42 (2017) 119-127. received: 12.06.2017 accepted: 16.06.2017 published: 01.10.2017 copyright: © 2017 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. introduction oday’s trends in civil engineering pushes investors and owners of concrete structures more often into renovation, than into demolition of structures. this fact leads into need for knowledge of material characteristics such as bulk density, young’s modulus of elasticity [1], compressive strength [2], flexural strength [3], etc. some types of civil engineering structures are subjected to mixed mode loading i and ii, therefore the knowledge of fracture mechanical parameters is necessary to predict life-time of concrete structures (bridges, cooling towers). to obtain material sample from considered structure, a core-drill is used, which drills out a cylindrical sample from a structure. this specimen is tested to obtain mechanical properties, but not for fracture mechanical parameters. t s. seitl et alii, frattura ed integrità strutturale, 42 (2017) 119-127; doi: 10.3221/igf-esis.42.13 120 fracture mechanical parameters of cementitious materials are usually obtained from recommended tests such as: three-point (3pbt) and four-point (4pbt) bending test with notch in tested specimen [4], for mixed mode load [5], wedge splitting test (wst) [6-9], or a combination of wst/3pbt [10] and modified compact tension test (mct) [11, 12]. all tests have a predefined prismatic geometry and using them on specimens made from the core-drill is expensive and not very efficient, therefore it is very appropriate to use a brazilian disc test specimen with central notch (circle cut from the core-drill cylinder) [13-16] to determinate fracture parameters of building materials see fig. 1. figure 1: geometry of a typical brazilian disc specimen with load position alongside crack. the main advantage of brazilian disc is, that it could be used for investigation of fracture toughness for mode i, mode ii and mixed mode by rotating the cracked against the load positions. this article compares the measured experimental data with data presented in [17]. theoretical background mechanical properties he unnotched brazilian disc is very often used as an indirect test to determinate tensile strength of rock materials, therefore it is very valuable to use it to obtain tensile strength of concrete [18]. the tensile strength can be evaluated from following equation: 2 t p db    (1) where t is tensile stress, p is compressive load, d is diameter of disc and b is specimen’s thickness. fracture mechanics this contribution is based on a linear elastic fracture mechanics. the linear elastic fracture mechanics concept uses the stress field in the close vicinity of the crack tip described by williams’s expansion [19]. this expansion is an infinite power series originally derived for a homogenous elastic isotropic cracked body, which can be described by a following equation: , ( ) ( ) ( , ) i iii ii i j ij ij ij k k f f o r r r          (2) where ij represents the stress tensor components, ki, kii is the stress intensity factor for mode i respectively mode ii, f iij, fiiij, are known shape functions for mode i and mode ii, oij represents higher order terms and r, θ are the polar coordinates (with origin at the crack tip; crack faces lie along the x-axis). t s. seitl et alii, frattura ed integrità strutturale, 42 (2017) 119-127; doi: 10.3221/igf-esis.42.13 121 the values of the stress intensity factor (sif) for a finite specimen and the polar angle θ = 0° can be expressed in the following form [20-22]: ( / , )i i p a k f a r rb    (3) ( / , )ii ii p a k f a r rb    (4) where p is compressive load, a is a crack length, r is radius of the disc (d/2), b is disc thickness and fi(a/r, ), fii(a/r, ) are dimensionless shape functions (calibration curves) for mode i and mode ii, see figs. 2 and 3. numerical model calibration curves o obtain right calibration curves for each mode of sif a numerical simulation was necessary. the numerical simulation was performed in finite element (fe) software ansys 17.2 [23]. a two-dimensional (2d) numerical model with plane strain boundary condition were used to calculate sif (ki and kii). the numerical model was meshed with element type plane183 taken from ansys’s elements library and command kscon was used to take into account the crack tip singularity. input material properties of concrete used in fe software are following: young’s modulus and possion’s ratio, e = 40 gpa and ν = 0.2, respectively. the geometry of disc has radius r = 50 mm and the relative crack length a/r varied from <0.1; 0.9>, notch angle α varied <0°; 90°> and was loaded with constant force p = 100 n in all calculated cases. in fe software ansys, the following equations are used for calculation of the sif ki and kii for θ = ±180. 2 2 1 i vg k r     (5) 2 2 1 ii ug k r     (6) where u, v are nodal displacements, g shear modulus,  is kolosov’s constant for plane strain respectively plane stress conditions and r is coordinate in cylindrical coordinate system. from brazilian disc geometry, mention above a calibration curves for mode i and ii for various notch angle  and a/r ratio can be determined as a following functions [25, 26]: ( / , ) 1ii k rb a f a r rp a     (7) ( / , ) 1iiii k rb a f a r rp a     (8) from fig. 2, it can be noticed, that for some angle  and a/r, the value of calibration curve for mode i equals zero (fi(a/r,) = 0). this means, that there is only mode ii (pure shear mode). therefore, the fracture toughness for mode ii could be evaluated. t s. seitl et alii, frattura ed integrità strutturale, 42 (2017) 119-127; doi: 10.3221/igf-esis.42.13 122 figure 2: calibration curve fi(a/r,) for mode i. figure 3: calibration curve fii(a/r, α) for mode ii. experiment for material c 50/60 material aterial used in the experimental program was standard concrete c 50/60, maximum aggregate size was 8 mm. specimen’s geometry brazilian disc specimens were prepared from standardized cylindrical specimens used for evaluation of cylindrical compressive strength of concrete [2]. notches were prepared by using water jet cutter. the dimensions of specimens are introduced in tabs. 1 and 2. specimen nmr. diameter d [mm] thickness b [mm] 04 150 28.59 05 150 30.52 06 150 29.90 table 1: dimensions of brazilian disc specimens. m s. seitl et alii, frattura ed integrità strutturale, 42 (2017) 119-127; doi: 10.3221/igf-esis.42.13 123 specimen nmr. a/r [-] diameter d [mm] thickness b [mm] notch length a [mm] 05_4 0.2667 150 31.83 40.06 09_4 0.2667 150 30.68 40.00 04_4 0.2667 150 31.65 40.09 09_6 0.4 150 29.93 60.17 01_6 0.4 150 31.44 60.92 04_6 0.4 150 30.97 60.15 07_6 0.4 150 31.17 59.94 table 2: dimensions of brazilian disc specimens with a center notch. experimental procedure the machine for tests was seidner d7940 with maximum loading capacity 4 000 kn. the load rate was 0.01 kn/s. brazilian disc specimens without notch were tested to obtain the tensile strength. brazilian disc specimens with the notch were tested under the selected angles inclined against loading positions see tab. 3. figure 4: example of specimens used for brazilian disc test without and with notch specimen nmr. a/r [-] inclination angle  [°] 05_4 0.2667 0.0 09_4 0.2667 10.0 04_4 0.2667 27.2 09_6 0.4 0.0 01_6 0.4 0.0 04_6 0.4 10 07_6 0.4 25.2 table 3: the relative length of notch in brazilian disc specimens and angle of used angle position. s. seitl et alii, frattura ed integrità strutturale, 42 (2017) 119-127; doi: 10.3221/igf-esis.42.13 124 results and discussion selected material and mechanical properties nnotched brazilian disc specimens were subjected to compressive load to evaluate tensile strength from eq. 1. the measured forces and calculated tensile strength are showed in tab. 4. specimen nmr. measured force p [kn] tensile strength ft [mpa] 04 34.9 5.18 05 38.8 5.39 06 35.7 5.06 table 4: measured forces and calculated tensile strength from eq. (1) for unnotched brazilian disc. the properties of used concrete are compared with material characteristics of mortar and concrete from hou [17], for detailed information about composition of these materials see [17]. comparison of selected mechanical properties is showed in tab. 5. bulk density ρ [kgm-3] compressive strength fc [mpa] tensile strength ft [mpa] mortar from [17] 2018 25.56 3.6 concrete [17] 2373 34.42 3.1 concrete – present study 2321 55.4 5.21 table 5: comparison of selected mechanical characteristics of used concrete with data adapted from literature [17] fracture mechanical properties fracture mechanical properties of structural concrete were evaluated from eq. (2) and (3). the values of stress intensity factors were evaluated for mode i (specimens 05_4,09_6 and 01_6), for mode ii (specimens 04_4 and 07_6) and for mixed mode i/ii. the evaluated fracture mechanical properties are summed up in tab. 6. specimen nmr. measured force p [kn] ki [mpamm1/2] kii [mpamm1/2] 05_4 26.8 38.069 0.0006 09_4 24.3 30.513 25.906 04_4 25.2 0.0466 54.604 09_6 19.6 36.858 0.0012 01_6 20.0 35.784 0.0012 04_6 17.7 26.104 25.337 07_6 15.8 0.005 44.9745 table 6: measured experimental load p and calculated fracture mechanical parameters ki and kii for each specimen. u s. seitl et alii, frattura ed integrità strutturale, 42 (2017) 119-127; doi: 10.3221/igf-esis.42.13 125 figure 5: comparison of fracture resistance kii/kic (y axis) against ki/kic (x axis) behavior with data from literature [17]. comparison of experimental data experimental results from hou [17] were digitalized and measured forces were used to be compared with data measured in the presented study. the comparison of results is done in two ways. the first one compares fracture resistance values of kii/kiic (y axis) against ki/kic (x axis) which is valuable to see pure mode i and pure mode ii fracture resistance. an envelope curve (a circle with radius ki/kic = 1 and kii/kiic = 1) is plotted in fig. 5. to see effect of mixed mode i/ii failure for each tested specimen (different inclination angle  of notch). the comparison made in fig. 4. is not very often, therefore it is being necessary to made comparison which can be usually seen in literature. fig. 5 compares normative values of kii/kic (y axis) against ki/kic (x axis) which is valuable to see mode ii effects fracture resistance. an envelope curve (an ellipse with radius kii/kic = mean value and ki/kic = 1) is plotted in fig. 6. to see effect of mixed mode failure for each tested specimen (different inclination angle of notch). figure 6: comparison of fracture resistance kii/kic (y axis) against ki/kic (x axis) behavior with data from literature [17]. s. seitl et alii, frattura ed integrità strutturale, 42 (2017) 119-127; doi: 10.3221/igf-esis.42.13 126 conclusions he present paper aims at analyzing the mixed mode fracture in a concrete c50/60 using the brazilian disc test. a finite element analysis of brazilian disc specimen, effects of crack angle rotation are studied based fracture mechanic approach. the following principal conclusions could be derived:  the classical solutions of linear elasticity for the stress fields in the neighborhood of a crack tip in pure mode i or ii can be obtained independently  the solution for the stress field in a combined mode situation is obtained simply by rotation of a initiation crack.  experimentally obtain data for c 50/60 is compared with data from literature. the presented numerical calculation and experimental results (c 50/60) will be used for future two-parameter fracture evaluation on alkali activated concrete [27, 28]. acknowledgment his paper has been worked out under the “national sustainability programme i” project “admas up – advanced materials, structures and technologies” (no. lo1408) supported by the ministry of education, youth and sports of the czech republic. references [1] iso 1920-10, testing of concrete – part 10: determination of static modulus of elasticity in compression, (2015). [2] en 12390-3, testing hardened concrete – part 3: compressive strength of test specimens, (2009). [3] en 12390-5, testing hardened concrete –part 5: flexural strength of test specimens. european committee for standardization, (2009). [4] rilem report 5, fracture mechanics test methods for concrete edited by s. p. shah and a. carpinteri, chapman and hall london, (1991). [5] malikova, l., vesely, v., seitl, s., crack propagation direction in a mixed mode geometry estimated via multiparameter fracture criteria, international journal of fatigue, 89 (2016) 99–107. doi: 10.1016/j.ijfatigue.2016.01.010. [6] linsbauer, h., tschegg, e., fracture energy determination of concrete with cube-shaped specimens, zement beton, 31 (1986) 38–40. [7] brühwiler, e., wittmann, f. h., the wedge splitting test, a new method of performing stable fracture mechanics test, engineering fracture mechanics 35 (1990) 117–125. [8] seitl, s., veselý, v., řoutil, l., two-parameter fracture mechanical analysis of a near-crack-tip stress field in wedge splitting test specimens, computers and structures 89(21-22) (2011) 1852–1858. doi: 10.1016/j.compstruc.2011.05.020. [9] seitl, s., nieto garcía, b., merta i., wedge splitting test method: quantification of influence of glued marble plates by two-parameter fracture mechanics, frattura ed integrita strutturale, 30 (2014) 174–181. doi: 10.3221/igf-esis.30.23. [10] seitl, s., korte, s., de corte, w., boel, v., sobek, j., veselý, v., selecting a suitable specimen shape with low constraint value for setermination of fracture parameters of cementitious composites, 577–578 (2014) 481–484. doi: 10.4028/www.scientific.net/kem.577-578.481. [11] seitl, s., viszlay, v., modified compact tension specimen for experiments on cement based materials: comparison of calibration curves from 2d and 3d numerical solutions, frattura ed integrita strutturale, 11(39) (2017) 118–128. [12] seitl, s., ríos, j.d., cifuentes, h., veselý, v., effect of the load eccentricity on fracture behavior of cementitious materials subjected to the modified compact tension test, solid state phenomena, 258 ssp (2017) 518–521. doi: 10.4028/www.scientific.net/ssp.258.518. [13] li, d., wong, l. n. y., the brazilian disc test for rock mechanics applications: review and new insights, rock mechanics and rock engineering, 46(2) (2013) 269–287. doi: 10.1007/s00603-012-0257-7. [14] atkinson, c., smelser, r. e., sanchez, j., combined mode fracture via the cracked brazilian disk test. international journal of fracture, 18(4) (1982) 279–291. t t s. seitl et alii, frattura ed integrità strutturale, 42 (2017) 119-127; doi: 10.3221/igf-esis.42.13 127 [15] abshirini, m., soltani, n., marashizadeg, p., on the mode i fracture analysis of cracked brazilian disc using a digital image correlation method. optics and lasers in engineering, 78 (2016) 99–105. doi: 10.1016/j.optlaseng.2015.10.006. [16] ayatollahi, m.r., aliha, m.r.m., cracked brazilian disc specimen subjected to mode ii deformation, engineering fracture mechanics, 72 (2005) 493–503, doi: 10.1016/j.engfracmech.2004.05.002. [17] hou, ch., wang, z., liang, w., li, j., wang, z., determination of fracture parameters in center cracked circular discs of concrete under diametral loading: a numerical analysis and experimental results, theoretical and applied fracture mechanics, 85 b (2016) 355-366. doi: 10.1016/j.tafmec.2016.04.006. [18] isrm (1978) suggested methods for determining tensile strength of rock materials, int j rock mech min sci geomech abstr, 15 (3) (1978) 99–103. doi:10.1016/0148-9062(78)90003-7. [19] williams, m. l., on the stress distribution at the base of a stationary crack. asme journal of applied. mechanics, 24 (1957) 109–114. [20] anderson, t. l., fracture mechanics: fundamentals and applications. taylor & francis group, (2005). [21] pook, l. p., linear elastic fracture mechanics for engineers: theory and applications. university college london, united kingdom, (2000). [22] ayatollahi, m. r., pavier, m. j., smith, d. j. determination of t-stress from finite element analysis for mode i and mixed mode i/ii loading. international journal of fracture, 91(3) (1998) 283-298. [23] ayatollahi, m.r., aliha, m.r.m., on the use of brazilian disc specimen for calculating mixed mode i–ii fracture toughness of rock materials, engineering fracture mechanics, 75 (2008). 4631–4641. doi: 10.1016/j.engfracmech.2008.06.018. [24] ansys®, academic research, release 17.2, help system, crack analysis guide. mechanical apdl documentation guide, ansys, (2016). [25] tada, h., paris, p.c., irwin, g.r., the stress analysis of crack handbook, third edition, the american society of mechanical engineering. new york, (2000). [26] haeri, h., shahriar k., fatehimarji. m., moarefvand, p., on the crack propagation analysis of rock like brazilian disc specimens containing cracks under compressive line loading. latin american journal of solids and structures, 11(8) (2014) 1400–1416. [27] bílek, v., hurta, j., done, p., zidek, l., development of alkali-activated concrete for structures-mechanical properties and durability, perspective in science, 7(2016) 190–194. doi: 10.1016/j.pisc.2015.11.031 [28] bílek, v., bonczková, s., hurta, j., pytlík, d., mrovec, m., bond strength between reinforcing steel and different types of concrete, procedia engineering, 190 (2017) 243–247. doi: 10.1016/j.proeng.2017.05.333. << /ascii85encodepages false /allowtransparency false /autopositionepsfiles true /autorotatepages /none /binding /left /calgrayprofile (dot gain 20%) /calrgbprofile (srgb iec61966-2.1) /calcmykprofile (u.s. web coated \050swop\051 v2) /srgbprofile (srgb iec61966-2.1) /cannotembedfontpolicy /error /compatibilitylevel 1.4 /compressobjects /tags /compresspages true /convertimagestoindexed true /passthroughjpegimages true /createjobticket false /defaultrenderingintent /default /detectblends true /detectcurves 0.0000 /colorconversionstrategy /cmyk /dothumbnails false 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can be opened with acrobat and adobe reader 5.0 and later.) >> /namespace [ (adobe) (common) (1.0) ] /othernamespaces [ << /asreaderspreads false /cropimagestoframes true /errorcontrol /warnandcontinue /flattenerignorespreadoverrides false /includeguidesgrids false /includenonprinting false /includeslug false /namespace [ (adobe) (indesign) (4.0) ] /omitplacedbitmaps false /omitplacedeps false /omitplacedpdf false /simulateoverprint /legacy >> << /addbleedmarks false /addcolorbars false /addcropmarks false /addpageinfo false /addregmarks false /convertcolors /converttocmyk /destinationprofilename () /destinationprofileselector /documentcmyk /downsample16bitimages true /flattenerpreset << /presetselector /mediumresolution >> /formelements false /generatestructure false /includebookmarks false /includehyperlinks false /includeinteractive false /includelayers false /includeprofiles false /multimediahandling /useobjectsettings /namespace [ (adobe) (creativesuite) (2.0) ] /pdfxoutputintentprofileselector /documentcmyk /preserveediting true /untaggedcmykhandling /leaveuntagged /untaggedrgbhandling /usedocumentprofile /usedocumentbleed false >> ] >> setdistillerparams << /hwresolution [2400 2400] /pagesize [612.000 792.000] >> setpagedevice microsoft word numero_53_art_23_2821 r. harbaoui et alii, frattura ed integrità strutturale, 53 (2020) 295-305; doi: 10.3221/igf-esis.53.23 295 mechanical behavior of materials with a compact hexagonal structure obtained by an advanced identification strategy of hcp material, az31b-h24 r. harbaoui, o. daghfas, a. znaidi laboratory of applied mechanics and engineering lr-mai university tunis el manar-enit bp37le belvédère,1002, tunis rym.harbaoui@gmail.com, daghfasolfa@yahoo.fr, amnaznaidi@laposte.tn v. tuninetti departament of mechanical engineering, universidad de la frontera, francisco salazar 01145, temuco 4780000, chile. victor.tuninetti@ufrontera.cl abstract. the use of magnesium alloys, in particular az31b-h24, represents an increasingly important aspect in the transport field, as well as in the aeronautical industry. in the forming processes of this material, the shapes of the product are obtained by plastic deformation. therefore, it is important to know the properties of plastic behavior to optimize these shaping processes. the properties of this alloy are strongly influenced by its complex microstructure which can be modified by plastic deformation. for this purpose, in this work an identification strategy is established beginning with the elastoplastic orthotropic law based on the choice of an equivalent stress, a hardening law and a plastic potential. thus, the anisotropic behavior of the magnesium sheet is modeled using cpb06 criterion with four hardening laws then later compared to barlat91 criterion. once the model is validated, it would therefore be useful to study the plastic behavior of az31b-h24 from an experimental database. keywords. magnesium; model; plastic deformation; strategy; anisotropy. citation: harbaoui, r., daghfas, o., znaidi, v. tuninetti a., mechanical behavior of materials with a compact hexagonal structure obtained by an identification strategy, case of study: application on az31b-h2 mg alloy, frattura ed integrità strutturale, 53 (2020) 295-305. received: 07.02.2020 accepted: 14.05.2020 published: 01.07.2020 copyright: © 2019 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. introduction he magnesium alloy has been praised by the greatest number of experts in materials engineering due to its low density, high thermal conductivity and rigidity, excellent mechanical and damping properties as well as excellent flowability [1-3]. in particular, the magnesium alloy material is a promising project in the transport sector. magnesium alloy sheets (az31b) have different mechanical responses than steel and aluminum sheets and have a highly anisotropic behavior due to their compacted hexagonal crystal structure (hcp) and strong basal crystallographic texture t https://youtu.be/bwqof7klbws r. harbaoui et alii, frattura ed integrità strutturale, 53 (2020) 295-305; doi: 10.3221/igf-esis.53.23 296 resulting from the rolling process [4, 5]. it also results in a strong tension / compression asymmetry based on the test data of kelley and hosford [6]. more experience with different loading conditions is required for magnesium alloy sheets to fully understand their complex mechanical behavior. jia and bai [7] carried out a complete series of experiments on the plasticity and fracture of az31b-h24 magnesium under various multiaxial loading conditions. the plasticity and fracture of magnesium is a significant challenge due to its closed hcp structure and its twinning deformation mechanism, which has not yet been properly detailed due to its complexity [7, 8]. to describe the plastic behavior of this material, it is necessary to specify the yield surface defined by an equivalent stress of a plasticity criterion and the hardening law. in previous works, amna et al [9, 10] have shown the ability of the barlat criterion [11] to successfully simulate the plastic behavior in simple tensile test of pure aluminum [10], aluminum alloy 2024 [12] and aluminum alloy 7075 [13] and on the other hand in simple and cyclic shear tests of aluminum alloy 2024 [14]. on the other hand, amna et al [9] have shown that this criterion is insufficient to model the plastic behavior of az31b magnesium alloy sheets under multiaxial loading according to the lankford coefficient. to remedy this insufficiency, rym et al [15] used the casazu criterion [16] which is dedicated to the compact hexagonal structure hcp to identify the plastic behavior of titanium alloy subjected to tensile tests. in this work, the plastic behavior of the az31b-h24 alloy is modeled using an identification strategy that depends on a plastic casazu criterion, an isotropic hardening law (hollomon law, voce law, swift law and ludwick law) and an evolution law. for this purpose, an experimental database [17] corresponds to various hardening curves for tensile and compression tests interpreted as homogeneous and their lankford coefficients is used. thereafter, by smoothing the experimental hardening curves in three loading directions relative to rolling direction, a selection is made in order to choose the most appropriate hardening law for the identification of the az31b-h24 behavior. finally, our identification strategy with a simplex method is validated from lankford coefficients and it is used to conduct the evolution of the load surface for different tests. studied material n this work, an az type magnesium alloy az31 has been studied. its alloying elements are aluminum up to 3%, zinc with 1% and finally 0.4% manganese [18]. the az31b-h24 magnesium alloy has a nominal composition (in wt %) of 3% al and 1% zn. the h24 condition refers to strain hardening and partially annealing (recrystallization without grain growth). this material is treated as having an orthotropic plasticity in three directions: rd (rolling direction), td (transverse direction) and nd (normal direction). al zn mn cu ca ni fe mg o 2.5-3.5 0.7-1.3 0.2 min 0.05 max 0.04 max 0.005 max 0.005 max balance none table 1: composition of az31b-h24 magnesium alloy (wt%) identification model n this study, it is essential to use an identification strategy taking into account: the anisotropic behavior of the material and the sd "strength-differential" effect, the evolution law and the equivalent stress. for the identification step, the following assumptions must be respected [9-15]: identification by "small deformations", the used tests are considered as homogeneous tests, the elastic deformation are neglected; the behavior is considered as rigid plastic incompressible. the plasticity surface evolves homothetically (isotropic hardening) all the tests are carried out in the plane of the sheet resulting in a plane stress condition. the performance criterion can be then written as follows:      ,d dc sf        (1) i i r. harbaoui et alii, frattura ed integrità strutturale, 53 (2020) 295-305; doi: 10.3221/igf-esis.53.23 297 where d is the deviator of the stress tensor of cauchy (incompressible plasticity). the hardening function σs(α) plays the role of the thermodynamic function associated with the internal variable α c ( d ): equivalent stress of the plasticity criterion. function  dc  satisfies the following condition if a > 0 :    d dc ca a    (2) the evolution of the surface load is represented in the spatial deviators of constraints, which are defined as follows: d d d 1 2 3= σ  ;  = σ sinθcos2ψ; = σ sinθsin2ψx cos x x (3) using the special configuration of space deflectors, the general form of the equivalent plane stress is written as follows:      d dc c 1 2 3σ =σ , , = / f θ,2ψx x x  (4) any type of criterion can be written in the following form:  d sf(θ,2ψ)= / σ α (5) the angle  which defines the orientation of d is presented in table2 and ψ the off-axis angle. test expansions equibiaxes (e.e) simple traction (s.t) large traction (l.t) simple shear (s.s) θ 0 π/3 π/6 π/2 table 2: the angle θ respective to four tests [9-10]. first, to identify the hardening curve it is necessary to choose an appropriate analytical law. second, an identification of the parameters that define the material anisotropy is also required. for this step, the cpb06 criterion [19-23] is chosen to identify the behavior of az31b-h24 magnesium alloy. the equivalent stress of cpb06 criterion is defined as follows:   1/3 1 σ m m c i i i q kq          (6) where q1, q2 and q3 are the eigenvalues of the tensor q q = c: σd (7) q : modified stress deviator tensor qi: the principal values of the tensor q. m: the degree of homogeneity also called form coefficient. σd : deviatoric stress tensor (incompressible plasticity) c : 4th order tensor of the linear transformation. the components cij are represented by (voigt notation): r. harbaoui et alii, frattura ed integrità strutturale, 53 (2020) 295-305; doi: 10.3221/igf-esis.53.23 298 c= 11 12 13 12 22 23 13 23 33 44 55 66 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 c c c c c c c c c c c c                    the parameter k may be determined from experimental values of σtr and σcp :           1 1 1 2 2 , 2 21 mm m tr cp tr cp tr cp m m tr cptr cp h k h h                       (8) k: the parameter of the material, the ratio between the uniaxial yield in traction σtr and the uniaxial yield in compression σcp allowing the description of the differential effect of resistance h: is a variable that defines the history of the material to ensure the convexity of the plasticity surface, we fix m ≥1, -1≤ k ≤1 the hardening functions  ps   used are: hollomon law [24] ( holψ°):    np ps k   ) (9) voce law [25] (voce ψ°):     1 expp ps y      (10) swift law [26] (swift ψ°):    0 np p s k     (11) ludwick law [27] (ludwick ψ°) :    0 np p s k     (12) the parameters k and n for hollomon's law the parameters σy , α and β for the voce's law the parameters ε0, k and n for swift's law the parameters σ0, k and n for ludwick's law results and discussion experimental results igs. 1 and 2 respectively represent the uniaxial tensile and compression hardening curves for three different orientations: rd (rolling direction), td (transverse direction) and nd (normal direction). by analyzing the curves in figure 1 and figure 2, we notice an anisotropy translated by the difference between the three directions. on the other hand, this anisotropy in normal direction (nd) for the two tests is different from that of the other directions which translates the phenomenon of asymmetry between traction and compression encountered in magnesium alloys. the yield and flow stresses for nd compression curve followed similar characteristics as in-plane tension at rd and td directions. the yield stresses for rd are lower than those for td and nd. f r. harbaoui et alii, frattura ed integrità strutturale, 53 (2020) 295-305; doi: 10.3221/igf-esis.53.23 299 figure 1: hardening curves of uniaxial tensile [17] . figure 2: hardening curves of uniaxial compression [17]. ψ (°) lankford coefficients 0 1.47 45 2.77 90 3.89 table 3: experimental lankford coefficients. numerical results: identification of the hardening parameters for the identification procedure, we will use the cpb06 model [9] while respecting the assumptions cited above. this step consists of choosing the coefficients of the model while minimizing the squared difference between the theoretical and experimental results. the hardening function σs (α) is identified from the tensile hardening curves in the td and rd directions for the tensile test (figure 1) and of the experimental compression test (figure 2) in the nd direction. in this case, four handening laws are used: hollomon's law, voce's law, swift's law and ludwick's law to best describe the function σs (α) (9)-(12). the experimental results found are the first and only source of data for the implementation of this identification strategy. the identification results are shown in tables 4 and 5. table4, table 5 and table 6 present the identified parameters of the hardening laws for tensile tests in rolling direction, in transverse direction and for compression test in normal direction, respectively. r. harbaoui et alii, frattura ed integrità strutturale, 53 (2020) 295-305; doi: 10.3221/igf-esis.53.23 300 hollomon swift ludwick voce err 0.0205 err 0.0116 err 0.0124 err 0.0372 k 402.605 k 447.0761 σ0 150.6813 σy 1440.8 n 0.1496 ε0 0.0116 k 337.5205 α 0.9 n 0.2015 n 0.3925 β -0.7 table 4: identified parameters of the hardening laws for the tensile test (rd). hollomon swift ludwick voce err 0.0123 err 0.0118 err 0.0118 err 0.0517 k 439.1366 k 445.9781 σ0 51.4125 σy 610.305 n 0.1621 ε0 0.0013 k 401.2347 α 0.662 n 0.1693 n 0.2032 β -2.8943 table 5: identified parameters of the hardening laws for the tensile test (td). hollomon swift ludwick voce err 0.0194 err 0.0076 err 0.0167 err 0.038 k 540.4411 k 490.1859 σ0 -422.981 σy 502.9209 n 0.1427 ε0 -0.0099 k 940.3702 α 0.4453 n 0.0995 n 0.064 β -7.1496 table 6: identified parameters of the hardening laws for the compression test (nd). identification of the hardening curves : in figure 3,4 and 5, the experimental hardening curves (exp) and the identified curves using the four hardening laws are represented for three tests. the identification consists of finding the hardening function σs (α), applying the least squares fitting between the theoretical and the experimental results using the simplex algorithm. thereafter, a comparison between the four hardening laws will be carried out in order to show the most appropriate law for the identification of tensile and compressive hardening curves in plastic deformation. figure 3: identification of the tensile curve for rd with different hardening laws r. harbaoui et alii, frattura ed integrità strutturale, 53 (2020) 295-305; doi: 10.3221/igf-esis.53.23 301 figure 4: identification of the tensile curve for td with different hardening laws figure 5: identification of the compression curve for nd with different hardening laws the identification is made in the area of plastic deformation where the elastic deformation is neglected (as it is indicated above in the hypothesis). it is clearly seen that the swift and voce laws are a little far from identifying az31b in uniaxial deformation. indeed, the ludwick and hollomon laws describe the hardening curves better than those of voce for all the loading directions. on the other hand, ludwick and hollomon laws give very similar results for the td and rd directions for the tensile test compared to the rolling direction especially at the area of the plastic deformation domain. we can therefore conclude that ludwick's law is sufficient to model the plastic behavior of the magnesium alloy in the two cases of monotonic loading: simple tensile and simple compression. in conclusion, the isotropic hardening ludwick's law is chosen in continuation of this work to identify the anisotropic behavior of this alloy. validation : after proving in previous work [9] and [10] that n remains the same for different tests, table 7 and 8 present the identified parameters where n is fixed for ψ=0°. we will therefore choose ‘n’ relating to the tensile test carried out in the rolling direction in addition to that it is the most simple and easy test to perform. by convention, we choose n for tensile test in the rolling direction as a reference. for n = 0.3925, we present different values of k and σ0 (table 7). ludwick00 ludwick td error 0.0124 0.0192 σ0 150.6813 148.4634 k 337.5205 384.4332 table 7: hardening parameters for ludwick law for fixed n=0.3925 r. harbaoui et alii, frattura ed integrità strutturale, 53 (2020) 295-305; doi: 10.3221/igf-esis.53.23 302 figure 6: identified tensile hardening curve with ludwick law for td validation of the compression curve in the normal direction (nd) using the values identified by fixing the coefficient n of the tensile test: ludwick nd ludwick n= n00 error 0.0167 0.0284 σ0 -422.981 217.7096 k 940.3702 428.4957 table 8: hardening parameters for ludwick law for fixed n=0.3925 figure 7: identified compression hardening curve with ludwick law for nd our identification strategy allows us to identify the experimental hardening curve along the two directions td and nd using the identified parameters of the ludwick law according to the rolling direction rd. identification of the anisotropic coefficients of the plasticity model: the second identification step consists in identifying the anisotropic parameters describing the cpb06 criterion using the identified hardening parameters of the ludwick law that is chosen previously. while respecting the initial hypotheses identifying our meta-model, we identify the anisotropy coefficients and the material parameter k which will be represented in the table 9. using the non quadratic cpb06 criterion, the previous identification is followed by an identification of the anisotropy coefficients of the forth order tensor c and the material parameter k, for a fixed degree of homogeneity (shape coefficient m =2) c44=c55=c66=1. r. harbaoui et alii, frattura ed integrità strutturale, 53 (2020) 295-305; doi: 10.3221/igf-esis.53.23 303 table 9: identification of the anisotropy coefficients for a = 2 by cpb06. material behavior study  validation using the lankford coefficient based on the identified anisotropic parameters and the experimental lankford coefficients, the development of the lankford coefficients based on off-axis angles ψ can be represented. in figure 8, the experimental lankford coefficient (exp) and the curves identified by our behavior model using cazacu criterion and the curves identified from model using the barlat criterion (barlat1991) are represented. figure 8: evolution of the experimental lankford coefficient compared to those of cpb06 model and barlat91 model. figure 8 show a good agreement between the identified results using our identification strategy and the experimental results relating to the lankford coefficients. we notice that there is an adjustment (a good agreement) between the experimental results and those obtained from the model using the cpb06 criterion. however, the identification using the barlat91 criterion is not validated by the lankford coefficient. this improvement is exclusive to structure of studied material: the barlat criterion is dedicated to face-centered cubic structure such as aluminum alloys [9-10,12]. on the other hand, the cazacu criterion is developed to model the material behavior with a compact hexagonal structure such as magnesium alloys and titanium alloys [9,15].  load surface after the identification of the model, the evolution of the load surface can be studied when the material is subjected to four solicitations. using the identified anisotropy parameters and based on equations (3)-(5) and table 2, the evolution of the load surface under different stresses (ee, wt, ss, st) is presented in figure 9. figure 9: evolution of the load surface to several tests and solicitations. k c11 c12 c13 c22 c23 c33 error -0. 02 1 0.2283 0.3197 -1.3154 -2.0016 -2.6882 1.1177e-07 -0.3 1 0.1014 0.0521 -0.9734 0.4437 4.8881 1.1394e-10 r. harbaoui et alii, frattura ed integrità strutturale, 53 (2020) 295-305; doi: 10.3221/igf-esis.53.23 304 this allows to represent the load surface f(,2) in space 1 2 3( , , )x x x . using the base of constraint deviators: 22 d x x  σ 33 d x x  σ for the load surface, it is clear that the material is more resistant in simple shear than in uniaxial traction. conclusion n this work, based on an experimental database, we have developed an identification strategy centered on the parameters of plasticity, the hardening law and lankford coefficients in order to raise previously unresolved identification issues. after construction of the model, an identification methodology was presented from the monotonic tensile and compression hardening curves. the first step consists in identifying the tensile and compression curves by the different hardening laws in order to choose the most adequate law to best describes the material behavior, while comparing it with the experimental curves. the second step of the strategy consists in identifying the anisotropy parameters of the material studied by the cpb06 criterion using the ludwick law as a hardening law. the used criterion takes into account the strong anisotropy as well as the sd effect "strength differential" translated by the traction-compression asymmetry. a validation by comparing the model to the experimental database was carried out; the validation of the model is established using the experimental values of the lankford coefficient. a comparison between the cpb06 and barlat criterions were carried out. it is found that the anisotropy evolves in the same way for an identification strategy using the cpb06 criterion as well as the barlat criterion. on the other hand, the validation by the lankford coefficient is well respected by the cpb06 criterion. thus, from the identification results of the anisotropy parameters and the lankford coefficients, it was possible to verify that the identification using the cpb06 criterion gives clearly more efficient results compared to other criteria, in particular barlat91. references [1] yueqian, j. (2011). study on anisotropic plasticity and fracture of lightweight metal sheets, m.s. university of central florida, 2013 b.s. northwestern polytechnical university, china [2] manuel, m., hector, l.g. , verma, r., tong, w. (2006). microstructural effects of az31 magnesium alloy on its tensile deformation and failure behaviors, materials science and engineering, a418, pp. 341–356. [3] roberts c. sheldon (1960). magnesium and its alloys, new york, ny: john wiley and sons [4] yuqian, w., duke, c., yanyao, j. (2019). an experimental study of anisotropic fatigue behavior of rolled az31b magnesium alloy, doi: 10.1016/j.matdes.2019.108266. [5] graff, s., brocks, w., steglich, d. (2007). yielding of magnesium: from single crystal to polycrystalline aggregates , int. j. plast., 23 (12), pp. 1957-1978 [6] kelly, e.w., hosford, w.f.(1968). plane-strain compression of magnesium and magnesium alloy crystals. trans.metall. soc. aime 242, 5–13. [7] yueqian, j, yuanli b. (2016). experimental study on the mechanical properties of az31b-h24 magnesium alloy sheets under various loading conditions, international journal of fracture, 197, pp. 25–48. [8] lou, x.y. , m. li, boger , r.k. , agnew, s.r. , wagoner, r.h. (2007). hardening evolution of az31b mg sheet int. j. plast., 23 (1), pp. 44-86. [9] znaidi, a., daghfas, o., guellouz, s., nasri, r. (2016). theorical study on mechanical properties of az31b magnesium alloy sheets under multiaxial loading, frattura ed integrità strutturale, 38, 135-140; doi: 10.3221/igf-esis.38.18 [10] znaidi, a., daghfas, o., gahbiche, a., et al. (2016). identification strategy of anisotropic behavior laws: application to thin sheets of a5. j. theor. appl. mech, 54, pp. 1147–1156. doi:10.15632/jtam-pl.54.4.1147. i r. harbaoui et alii, frattura ed integrità strutturale, 53 (2020) 295-305; doi: 10.3221/igf-esis.53.23 305 [11] barlat, f., lege, d.j., brem, j.c. (1991). a six-component yield function for anisotropic materials, international. journal of plasticity, 7, pp. 693–712. [12] daghfas, o., znaidi, a. , nasri, r. (2019). plastic behavior laws of aluminum aerospace alloys: experimental and numerical study. journal of the chinese society of mechanical engineers, 40(5), pp. 523-532. [13] daghfas, o., znaidi, a., ben mohamed, a., et al (2017). experimental and numerical study on mechanical properties of aluminum alloy under uniaxial tensile test. frattura ed integrità strutturale 11(39), pp. 263-273. doi: 10.3221/igf-esis.39.24. [14] daghfas, o., znaidi , a., gahbiche, a. , nasri, r. (2019). identification of the anisotropic behavior of an aluminum alloy subjected to simple and cyclic shear tests. proc imeche part c: j mechanical engineering science 2019, 233(3) pp. 911–927. doi: 10.1177/0954406218762947. [15] harbaoui, r., znaidi, a., nasri, r. (2017). modeling of titanium alloys by an identification strategy: biomechanical application. pp. 73-86. doi:https://doi.org/10.3166/rcma.2017.00005. [16] cazacu, o., plunkett, b., barlat, f. (2008). orthotropic yield criterion description of anisotropy in tension and compression of sheet metals. int. j. plasticity, 24, pp. 847-866. [17] nitin ,c., ricardo, a. l. , benoit, r. b. , oana, c. , barlat, f. (2015). combined effects of anisotropy and tensioncompression asymmetry on the torsional response of az31 mg, international journal of solids and structures, 58, pp. 190-200. [18] housh, s., mikucki, b., stevenson, a. (1990). properties of magnesium alloys in metals handbook, 2(10), “properties and selection: nonferrous alloys and special purpose materials”. asm international, materiais park. [19] cazacu, o., ionescu, i. r. , yoon, j. w. (2009). orthotropic strain rate potential for the description of anisotropy in tension and compression of metals. int. j. plasticity. [20] yueqian, j., xiang, l., yuanli, b. (2012). theorical study on mechanical properties of az31b magnesium alloy sheets under multiaxial loading. j automotive safety and energy, 4. [21] cazacu, o., plunkett, b., barlat, f. (2006) orthotropic yield criterion for hexagonal closed packed metals. international journal of plasticity , 22, pp. 1171–1194. [22] cazacu, o. (2015). application of the vpsc model to the description of the stress–strain response and texture evolution in az31, journal of engineering materials and technology. [23] baudard, b.r., cazacu, o. (2016). plasticity-damage coupling in anisotropic titanium and validation by xcmt, xxiv ictam, montreal, canada. [24] hollomon, j.h. (1945). tensile deformation. trans aime. 162, pp. 268–290. [25] voce, e. (1948). the relationship between stress and strain for homogeneous deformations. j inst metals; 74, pp. 537– 562. [26] swift, h.w. (1952). plastic instability under plane stress, journal of the mechanics and physics of solids. 1(1), pp. 1-18. [27] ludwik, p. 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can be opened with acrobat and adobe reader 5.0 and later.) >> /namespace [ (adobe) (common) (1.0) ] /othernamespaces [ << /asreaderspreads false /cropimagestoframes true /errorcontrol /warnandcontinue /flattenerignorespreadoverrides false /includeguidesgrids false /includenonprinting false /includeslug false /namespace [ (adobe) (indesign) (4.0) ] /omitplacedbitmaps false /omitplacedeps false /omitplacedpdf false /simulateoverprint /legacy >> << /addbleedmarks false /addcolorbars false /addcropmarks false /addpageinfo false /addregmarks false /convertcolors /converttocmyk /destinationprofilename () /destinationprofileselector /documentcmyk /downsample16bitimages true /flattenerpreset << /presetselector /mediumresolution >> /formelements false /generatestructure false /includebookmarks false /includehyperlinks false /includeinteractive false /includelayers false /includeprofiles false /multimediahandling /useobjectsettings /namespace [ (adobe) (creativesuite) (2.0) ] /pdfxoutputintentprofileselector /documentcmyk /preserveediting true /untaggedcmykhandling /leaveuntagged /untaggedrgbhandling /usedocumentprofile /usedocumentbleed false >> ] >> setdistillerparams << /hwresolution [2400 2400] /pagesize [612.000 792.000] >> setpagedevice microsoft word numero_41_art_34.docx a. a. ahmed et alii, frattura ed integrità strutturale, 41 (2017) 252-259; doi: 10.3221/igf-esis.41.34 252 focused on crack tip fields on the use of length scale parameters to assess the static strength of notched 3d-printed pla adnan a. ahmed, luca susmel department of civil and structural engineering, the university of sheffield, mappin street, sheffield s1 3jd, uk aaahmed1@sheffield.ac.uk l.susmel@sheffield.ac.uk, http://orcid.org/0000-0001-7753-9176 abstract. this paper aims to investigate the accuracy of the theory of critical distances (tcd) in estimating static strength of notched additively manufactured pla as both notch sharpness and infill angle vary. the tcd takes as its starting point the assumption that the extent of damage under static loading can be assessed successfully by using two different material parameters, i.e. (i) a critical distance whose length is closely related to the material microstructural features and an inherent (i.e., a defect free) material strength. plain and notched specimens of 3d-printed pla were manufactured horizontally by making the deposition angle vary in the range 0-90. using the tcd in the form of the point method, failures were predicted by directly post-processing the linear-elastic stress fields estimated through the well-known analytical solutions due to glinka and newport. independently of the notch sharpness, the estimates being obtained were found to be highly accurate, falling within an error interval of about 20%. this result fully supports the idea that the tcd can successfully be used in situations of practical interest to design against static loading notched components of additively manufactured pla by directly post-processing the results from simple linear-elastic finite element (fe) models. keywords. additive manufacturing; pla; theory of critical distances; static failure; notches. citation: ahmed, a.a., susmel l., on the use of length scale parameters to assess the static strength of notched 3d-printed pla, frattura ed integrità strutturale, 41 (2017) 252-259. received: 28.02.2017 accepted: 03.05.2017 published: 01.07.2017 copyright: © 2017 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. introduction s suggested by astm committee f42 (www.astm.org/committee/f42.htm), additive manufacturing is “the process of joining materials to make objects from 3d-model data, usually layer upon layer, as opposed to subtractive manufacturing methodologies”. in more detail, additive manufacturing is an “additive” process that can be more effective than a a. a. ahmed et alii, frattura ed integrità strutturale, 41 (2017) 252-259; doi: 10.3221/igf-esis.41.34 253 conventional “subtractive” technologies, with this holding true especially in the presence of complex shapes that would be very difficult to be manufactured by using traditional techniques. if attention is focused specifically on plastics, examination of the state of the art suggests that acrylonitrile butadiene styrene (abs) and polylactide (pla) are the two materials that are commonly employed along with low-cost 3d printers, where polymers can be additively manufactured by melting/extruding powders, wires and flat sheets. as mentioned earlier, the unique feature of additive manufacturing is that parts with complex geometries can be fabricated very easily, with the obtained objects being characterized by a remarkable level of accuracy in terms of both shape and dimensions. this makes it evident that 3d-printed objects can contain very complex geometrical features that are likely to act as local stress concentrators. therefore, accurate and simple design methods are needed to allow structural engineers to effectively assess the static strength of 3d-printed materials by taking explicitly into account the presence of stress raisers of all kinds. as far static assessment of notched components is concerned, examination of the state of the art suggests [1-9] that the theory of critical distances (tcd) is the most powerful candidate to be used to design additively manufactured components for the following reasons: (i) the tcd assesses the detrimental effect of notches independently from their shape and sharpness; (ii) it models explicitly the material morphology through ad hoc critical lengths; (iii) the required local stress fields can be estimated without adopting complex non-linear constitutive laws; (iv) the tcd can be applied along with the results from linear-elastic fe models, where the same solid models can be used also to inform the manufacturing process. in this challenging scenario, this paper aims to investigate whether the linear-elastic tcd is successful in performing the static assessment of 3d-printed notched pla subjected to in service static loading. to conclude, it is worth observing that the present investigation was based on pla since this material is a biodegradable, absorbable and biocompatible thermoplastic aliphatic polyester that is widely used to manufacture biomedical components having complex shape [10]. further, thanks to its specific features, pla is one of those polymers that can be additively manufactured at a relatively low-cost by employing commercial 3d-printers. static assessment according to the theory of critical distances ccording to the tcd, the static breakage of notched materials subjected to mode i loading is avoided as long as a critical distance based effective stress, σeff, is lower than the material inherent strength, σ0 [1], i.e.:   0eff (1) an important feature of the tcd is that it assesses static strength by directly post-processing the linear-elastic stress fields damaging the material in the vicinity of the notch being designed, with this holding true independently from the ductility level of the material under investigation [1-4, 6]. this can be done successfully provided that material inherent strength σ0 is determined consistently [3, 4]. the procedure being recommended to be followed to determine σ0 experimentally will be reviewed in what follows. these considerations suggest that the tcd is bi-parametrical design method where the critical distance and the inherent material strength are the two material parameters being used. under static loading, the tcd’s length scale parameter is recommended to be estimated according to this well-known relationship [1, 11]:          2 0 1 ickl (2) where kic is the plane strain fracture toughness. as soon as material length l is known, the required effective stress, σeff, can then be calculated directly according to either the point method (pm) or the line method (lm) as follows [1, 11]:          0, 2 eff y l r point method (pm) (3) a a. a. ahmed et alii, frattura ed integrità strutturale, 41 (2017) 252-259; doi: 10.3221/igf-esis.41.34 254      2 0 1 0, 2 l eff y r dr l line method (lm) (4) figure 1: definition of the local systems of coordinates (a) and effective stress, eff, calculated according to the point method (b) and the line method (c). figure 2: manufacturing direction and orientation of the deposition filaments. the adopted symbols as well as the meaning of the effective stress determined according to definitions (3) and (4) are explained in fig. 1. as to the different formalisations of the tcd, it is worth mentioning here that this powerful theory can be applied also in the form of the area method (am) [1, 12] as well as of the volume method (vm) [1, 13]. in more nom nom  r x y 1 1 eff eff r r point method line method (a) (b) (c) l/2 2l yp x p 45° 45° p filaments reference manufacturing axis build-plate a. a. ahmed et alii, frattura ed integrità strutturale, 41 (2017) 252-259; doi: 10.3221/igf-esis.41.34 255 detail, the am postulates that the effective stress has to be determined by averaging σ1 over a semi-circular area centred at the notch tip and having radius equal to l [1]. in a similar way, the vm calculates σeff by averaging the linear-elastic maximum principal stress over a hemisphere centred at the apex of the stress raiser being assessed and having radius equal to 1.54l [12]. in the present investigation, owing to its simplicity, the accuracy of the tcd in estimating static strength of notched additively manufacture pla will be assessed by applying this theory solely in the form of the pm. the definitions for σeff calculated according to eqs (3) and (4) make it clear that inherent material strength σ0 plays a role of primary importance when the tcd is used to assess static strength of notched components. as far as brittle materials are concerned, much experimental evidence suggests that these materials have inherent strength that is always very close to the ultimate tensile strength, σuts [1-3]. in contrast, when the final breakage is preceded by large scale plastic deformations, σ0 is seen to be somewhat larger than σuts [1, 4, 6]. further, σ0 takes on a value that is higher than σuts also when the plain parent material fails by different mechanisms to those leading to the final breakage in the presence of stress raisers [1]. these considerations should make it evident that the only way to determine σ0 accurately is by running bespoke experiments involving notches whose presence results in different stress distributions in the vicinity of the tested geometrical features [1-6]. figure 3: experimental stress vs. strain curves generated by testing plain samples manufactured by adopting different values for manufacturing angle θp. 0 5 10 15 20 25 30 35 40 45 50 0 0.05 0.1 0.15 0.2 s tr es s [m pa ] strain [mm/mm] p=0 (a) 0 5 10 15 20 25 30 35 40 45 50 0 0.005 0.01 0.015 0.02 s tr es s [m pa ] strain [mm/mm] p=30 (b) 0 5 10 15 20 25 30 35 40 45 50 0 0.005 0.01 0.015 0.02 s tr es s [m pa ] strain [mm/mm] p=45 (c) 0 5 10 15 20 25 30 35 40 45 50 0 0.005 0.01 0.015 0.02 s tr es s [m pa ] strain [mm/mm] p=60 (d) 0 5 10 15 20 25 30 35 40 45 50 0 0.05 0.1 0.15 0.2 s tr es s [m pa ] strain [mm/mm] p=90 (e) a. a. ahmed et alii, frattura ed integrità strutturale, 41 (2017) 252-259; doi: 10.3221/igf-esis.41.34 256 experimental results lain and notched specimens were additively manufactured via 3d-printer ultimaker 2 extended+ by using as parent material new verbatim filaments of white pla with initial diameter of 2.85mm. the values of the adopted manufacturing parameters were as follows: nozzle size=0.4 mm, nozzle temperature=240ºc, build-plate temperature=60ºc, layer height=0.1 mm, shell thickness=0.4 mm, fill density=100%, and print speed=30 mm/s. according to fig. 2, the flat samples being tested were manufactured horizontally on the build-plate by setting angle θp equal to 0º, 30º, 45º, 60º, and 90º. in particular, while the extruded filaments were deposited, layer upon layer, always at ±45º to the axis yp of the build-plate, the angle between the longitudinal axis of the specimens and axis yp was varied in the range 0º-90º (see fig. 2). all samples had thickness, t, equal to 4mm, with the un-notched specimens having net width equal to 15 mm. the sharply u-notched specimens being manufactured had net width, wn, equal to 15.4 mm, gross width, wg, to 24.9 mm, and notch root radius, rn, equal to 0.5 mm. these dimensions returned a value for the net stress concentrator factor, kt, equal to 4.76. the specimens containing the intermediate u-notches had the following average dimensions: wn=15.3 mm, wg=24.9 mm, and rn=1.0 mm (resulting in a kt value equal to 3.51). finally, the dimensions of the bluntly u-notched specimens were as follows: wn=15.2 mm, wg=25.1 mm, and rn=3.0 mm (kt=2.22). for the notched specimens being investigated the corresponding values for the stress concentration factors were estimated using peterson’s diagrams [14]. a number of specimens containing crack-like notches were also additively manufactured in order to determine the fracture toughness for t=4 mm. in particular, the relevant dimensions for these specimens were as follows: wn=16.4 mm, wg=24.9 mm, and rn≈0.01 mm. by setting the displacement rate equal to 2 mm/min, the plain specimens as well as the samples containing both unotches and crack-like notches were tested under quasi-static tensile loading by using a shimadzu universal machine. in the un-notched specimens, the local strains were measured during testing via an axial extensometer with gauge length equal to 50 mm. three different specimens were tested for any geometry/manufacturing configuration that was investigated. (a) (b) (c) figure 4: influence of manufacturing angle θp on e (a), σuts (b), and kc (c). 2000 2500 3000 3500 4000 0 10 20 30 40 50 60 70 80 90 e [ m pa ] manufacturing angle, θp [] +2sd -2sd e=3296 mpa 20 30 40 50 60 0 10 20 30 40 50 60 70 80 90 σ u t s [m p a] manufacturing angle, θp [] +2sd -2sd σuts=42.5 mpa 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 0 10 20 30 40 50 60 70 80 90 k c [m pa ·m 1/ 2 ] deposition angle, θp [] +2sd -2sd kc=3.4 mpa·m 1/2 p a. a. ahmed et alii, frattura ed integrità strutturale, 41 (2017) 252-259; doi: 10.3221/igf-esis.41.34 257 the stress vs. strain diagrams reported in fig. 3 show the mechanical behaviour as measured by testing the un-notched specimens. these charts make it evident that the stress vs. strain response of the additively manufactured material being tested was characterised by a mechanical behaviour that was predominantly linear up to the maximum stress value being recorded during testing. in terms of reference mechanical properties, the results generated by testing the plain samples returned the following average values: young’s modulus, e, equal to 3296 mpa, 0.2% proof stress, σ0.2%, equal to 40.3 mpa and ultimate tensile strength, σuts, equal to 42.5 mpa. the charts reported in figs. 4a and 4b summarise the influence of manufacturing angle θp on both e and σuts. these diagrams make it evident that the infill direction had little effect on the overall mechanical behaviour of the additively manufactured material being investigated. in particular, the experimental results expressed in terms of both e and σuts in figs. 4a and 4b, respectively, are seen to be all within two standard deviations, sd, of the mean. the results generated by testing specimens with crack-like notches are summarised instead in the kc (for t=4 mm) vs. θp diagram of fig. 4c. the values for kc shown in this chart were estimated according to linear elastic fracture mechanics (lefm), i.e. by using the following standard relationship [15]:     c fk a (5) in eq. (5) α is the shape factor (estimated as recommended in ref. [16]), σf is the nominal failure stress referred to the gross area, and a is the crack-like notch depth. since, according to fig. 4c, the experimental values for kc are within two standard deviations of the mean, it is possible to come to the conclusion that also the fracture resistance of the additively manufacture polymer under investigation was marginally affected by manufacturing angle θp. to conclude, it is worth observing that, due to such a high level of consistency, the notched specimens being tested were manufactured by setting angle θp solely equal to 0º, 30º, and 45º. figure 5: linear-elastic stress fields in the incipient failure condition and determination of critical distance l. validation by experimental data y considering notched specimens of polymethylmethacrylate (pmma), in 2004 taylor et al. [17] observed that the inherent strength, σ0, of this material takes on a value that is equal to about 2·σuts. accordingly, the standard formalisation of the tcd considered in the present paper can be used to perform the static assessment of pmma as long the notches being assessed result in stress concentration factors that are larger than σ0/σuts≈2. having recalled these important aspects, in the preliminary investigating summarised in the present paper the accuracy of the tcd in estimating the static strength of notched additively manufactured pla was checked by forming the following simplifying hypotheses: 0 50 100 150 200 250 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1 [mpa] distance, x [mm] linear-elastic stress fields sharp intermediate blunt 0=85.0 mpa error= +20% error= -20% l/2=0.467 mm uts=42.5 mpa b a. a. ahmed et alii, frattura ed integrità strutturale, 41 (2017) 252-259; doi: 10.3221/igf-esis.41.34 258  according to figs. 4b and 4c, the static strength and the fracture toughness of the additively manufactured material being tested were assumed to be independent from manufacturing angle θp;  as per pmma [17], the inherent strength, σ0, of the additively manufactured material under investigation was taken invariably equal to 2·σuts – i.e., σ0=2·σuts=2·42.5 mpa=85 mpa;  the linear-elastic stress fields in the vicinity of the stress concentrators being tested were estimated by simply using the analytical solutions devised by glinka and newport [18]. fig. 5 shows the linear-elastic stress fields determined in the incipient failure condition, where the centre of the adopted system of coordinates was taken coincident with the notch tip (fig. 1a). it is worth observing here also that, for any considered notched geometry, the corresponding stress field was calculated by setting the nominal net stress equal to the average failure stress determined from the nine tests run by using the specimens manufactured with angle θp equal to 0º, 30º, and 45º (fig. 2). as shown in fig. 5, the critical distance value was estimated according to the pm via the point at which the linear-elastic stress-distance curve due to the sharp notch and the horizontal straight line modelling the plain material inherent strength intersected each other [1]. according to fig. 5, this simple procedure returned a value for l of 0.934 mm. fig. 5 makes it evident also that by setting l/2=0.467 mm and σ0=85 mpa, the pm was seen to be very accurate also in estimating the average static strength of the specimens containing both the intermediate and the blunt notches. in order to show the overall accuracy of the pm in performing the static assessment of notched additively manufactured pla, the chart of fig. 6 summarises the error associated with the individual experimental results, with the error being calculated as:         0 0 % 100 eff error (6) according to the error diagram reported in fig. 6, it is possible to conclude by observing that the tcd applied in the form of the pm was seen to be capable of accurately estimating the static strength of notched additively manufactured pla, with its usage returning predictions falling within an error interval of ±20%. figure 6: overall accuracy of the tcd applied in the form of the pm in estimating static strength of additively manufactured pla. conclusions ccording to the analyses summarised in the present paper, the following conclusions can be drawn:  the tcd is successful in predicting static failures in notched additively manufactured pla;  the estimates obtained by applying the tcd in the form of the pm were seen to fall within an error interval of ±20%; -100 -80 -60 -40 -20 0 20 40 60 80 100 0 5 10 15 20 25 30 35 40 45 e rr o r [% ] deposition angle, θp [] point method (pm) kt=4.76 kt=3.51 kt=2.22 error= +20% error= -20% a a. a. ahmed et alii, frattura ed integrità strutturale, 41 (2017) 252-259; doi: 10.3221/igf-esis.41.34 259  satisfactory results were obtained by forming the hypothesis that the mechanical behaviour of additively manufactured pla follows a simple linear-elastic constitutive law;  more work has to be done in this area to systematically check the accuracy and reliability of the tcd when used to predict static failures in additively manufactured materials not only characterised by different elasto-plastic behaviours, but also failing by different mechanisms. references [1] taylor, d. the theory of critical distances: a new perspective in fracture mechanics. elsevier, oxford, uk (2007). [2] taylor, d. predicting the fracture strength of ceramic materials using the theory of critical distances. engng. fract. mech. 71 (2004) 2407-2416. [3] susmel, l., taylor, d. the theory of critical distances to predict static strength of notched brittle components subjected to mixed-mode loading. eng frac mech, 75 3-4 (2008) 534-550. [4] susmel, l., taylor, d. on the use of the theory of critical distances to predict static failures in ductile metallic materials containing different geometrical features. engng. fract. mech. 75 (2008) 4410-4421. [5] susmel, l., taylor, d. the theory of critical distances to estimate the static strength of notched samples of al6082 loaded in combined tension and torsion. part i: material cracking behaviour. engng. fract. mech. 77 (2010) 452–469. [6] susmel l., taylor d. the theory of critical distances to estimate the static strength of notched samples of al6082 loaded in combined tension and torsion. part ii: multiaxial static assessment. engng. fract. mech. 77 (2010) 470–478. [7] susmel, l., askes, h. material length scales in fracture analysis: from gradient elasticity to the theory of critical distances. computational technology reviews 6 (2012) 63-80. [8] susmel, l., askes, h., bennett, t., taylor, d. theory of critical distances vs. gradient mechanics in modelling the transition from the shortto long-crack regime at the fatigue limit. fatigue fract engng mater struct. (2013). [9] askes, h., livieri, p., susmel, l., taylor, d., tovo r. intrinsic material length, theory of critical distances and gradient mechanics: analogies and differences in processing linear-elastic crack tip stress fields. fatigue fract engng mater struct. 36 (2013) 39-55. [10] hamad, k., kaseem, m., yang, h.w., deri, f., ko, y.g.. properties and medical applications of polylactic acid: a review. express polymer letters 9 (2015) 435–455. [11] whitney, j.m., nuismer, r.j. stress fracture criteria for laminated composites containing stress concentrations. j. composite mater. 8 (1974) 253-265. [12] sheppard, s.d. field effects in fatigue crack initiation: long life fatigue strength. transactions of asme, journal of mechanical design 113 (1991) 188-194. [13] bellett, d., taylor, d., marco, s., mazzeo, e., guillois, j., pircher, t. the fatigue behaviour of three-dimensional stress concentrations. int. j. fatigue 27 (2005) 207-221. [14] pilkey, w.d., pilkey, d.f. peterson's stress concentration factors. wiley, usa, (2008). [15] anderson, t.l. fracture mechanics: fundamentals and applications, crc press, usa, (2005). [16] tada, h., paris, p.c., irwin, g.r. stress analysis of cracks handbook, asme press, usa, (2000). [17] taylor, d., merlo, m., pegley, r., cavatorta, m.p. the effect of stress concentrations on the fracture strength of polymethylmethacrylate. materials science and engineering a 382 (2004) 288-294. [18] glinka, g., newport, a. universal features of elastic notch-tip stress fields. int. j. fatigue 9 (1987) 143-150. << /ascii85encodepages false /allowtransparency false /autopositionepsfiles true /autorotatepages /none /binding /left /calgrayprofile (dot gain 20%) /calrgbprofile (srgb iec61966-2.1) /calcmykprofile (u.s. web coated \050swop\051 v2) /srgbprofile (srgb iec61966-2.1) /cannotembedfontpolicy /error /compatibilitylevel 1.4 /compressobjects /tags /compresspages true /convertimagestoindexed true /passthroughjpegimages true /createjobticket false /defaultrenderingintent /default /detectblends true /detectcurves 0.0000 /colorconversionstrategy /cmyk /dothumbnails false /embedallfonts true /embedopentype false /parseiccprofilesincomments true /embedjoboptions true /dscreportinglevel 0 /emitdscwarnings false /endpage -1 /imagememory 1048576 /lockdistillerparams false /maxsubsetpct 100 /optimize true /opm 1 /parsedsccomments true /parsedsccommentsfordocinfo true /preservecopypage 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can be opened with acrobat and adobe reader 5.0 and later.) >> /namespace [ (adobe) (common) (1.0) ] /othernamespaces [ << /asreaderspreads false /cropimagestoframes true /errorcontrol /warnandcontinue /flattenerignorespreadoverrides false /includeguidesgrids false /includenonprinting false /includeslug false /namespace [ (adobe) (indesign) (4.0) ] /omitplacedbitmaps false /omitplacedeps false /omitplacedpdf false /simulateoverprint /legacy >> << /addbleedmarks false /addcolorbars false /addcropmarks false /addpageinfo false /addregmarks false /convertcolors /converttocmyk /destinationprofilename () /destinationprofileselector /documentcmyk /downsample16bitimages true /flattenerpreset << /presetselector /mediumresolution >> /formelements false /generatestructure false /includebookmarks false /includehyperlinks false /includeinteractive false /includelayers false /includeprofiles false /multimediahandling /useobjectsettings /namespace [ (adobe) (creativesuite) (2.0) ] /pdfxoutputintentprofileselector /documentcmyk /preserveediting true /untaggedcmykhandling /leaveuntagged /untaggedrgbhandling /usedocumentprofile /usedocumentbleed false >> ] >> setdistillerparams << /hwresolution [2400 2400] /pagesize [612.000 792.000] >> setpagedevice microsoft word numero 11 art 3 l. giudici et alii, frattura ed integrità strutturale, 11 (2009) 21-35; doi: 10.3221/igf-esis.11.03 21 valutazione della capacità di rientro alla base di un elicottero in presenza di danno balistico ad un albero di trasmissione della linea rotore di coda l. giudici, a. manes, m. giglio politecnico di milano, dipartimento di meccanica,via la masa 1 – 20156 milano, andrea.manes@polimi.it riassunto. nella progettazione di un elicottero militare, destinato ad operare a bassa quota e in ambiente ostile, il danneggiamento di componenti critici, conseguente ad impatto balistico, riveste un ruolo primario nella valutazione delle possibilità di sopravvivenza dell’intera macchina. in questo articolo è quindi proposto uno studio sperimentale, suddiviso in diverse fasi, riguardante la verifica della capacità di un elicottero di portare a termine una missione di rientro alla base a potenza ridotta e in presenza di danneggiamento balistico ad un albero di trasmissione della linea rotore di coda. il lavoro ha richiesto dapprima l’esecuzione, su esemplari del componente in esame, di prove sperimentali di impatto balistico, condotte utilizzando un proiettile calibro 7.62 nato. successivamente su ciascun albero danneggiato sono state eseguite prove torsionali statiche ed a fatica, il cui scopo è stato verificare la resistenza residua del componente all’applicazione di opportuni carichi rappresentativi delle sollecitazioni riscontrate durante la missione di rientro. abstract. in the design of a military helicopter, with the aim to operate at low altitude into enemy territory, the damage of critical components, caused by ballistic impact, plays a primary role in assessing the survival of the entire machine. in this work an experimental study is proposed, concerning the capability of a helicopter to carry out a mission of return to the base at reduced power, in the presence of a tail rotor shaft damaged by ballistic impact of 7.62 nato projectile. in the first part of this study, some specimen representatives of the tail rotor shaft are subjected to experimental ballistic impact tests. subsequently, static and dynamic torsional tests have been performed on the damaged components in order to asses the residual strength under the loads encountered during the mission. parole chiave. elicottero, albero di trasmissione, impatto balistico, proiettile. introduzione o studio sperimentale qui descritto si articola in due parti: inizialmente sugli alberi di trasmissione disponibili sono state condotte delle prove di impatto balistico, utilizzando un proiettile 7.62 nato; in seguito sono state effettuate delle prove di torsione, sia statiche che di fatica, con l’obiettivo di verificare la resistenza degli alberi danneggiati sotto l’azione delle sollecitazioni derivanti dalla missione. tale studio sperimentale rientra nel programma di valutazione del requisito balistico di un componente elicotteristico. il requisito balistico qui considerato, prevede appunto che, in seguito al danneggiamento di un albero di trasmissione della linea rotore di coda, l’elicottero, benché subisca una parziale riduzione delle sue capacità di manovra, sia in grado di portare a termine una missione di rientro alla base “a potenza ridotta” della durata di circa 30 minuti. l http://dx.medra.org/10.3221/igf-esis.11.03&auth=true http://www.gruppofrattura.it l. giudici et alii, frattura ed integrità strutturale, 11 (2009) 21-35; doi: 10.3221/igf-esis.11.03 22 prove sperimentali di impatto balistico descrizione dell’albero entre diversi esperimenti di impatto sono stati condotti su lastre di vari materiali e spessori, sono pochi gli studi pubblicati riguardanti tubi metallici. in [1] e [2] è contenuta una descrizione dettagliata di una vasta gamma di impatti, e sono enunciati alcuni concetti fondamentali di balistica utili alla comprensione del fenomeno. l’albero di trasmissione oggetto di studio è costituito da un tubo cilindrico cavo a parete sottile ai cui estremi sono presenti due flangie atte a consentirne il montaggio. le flange sono saldate mediante tecnologia tig (tungsten inert gas). il componente è realizzato in lega di alluminio 6061 t6, largamente impiegata nel settore aeronautico, in quanto risulta avere ottime prestazioni in termini di saldabilità, resistenza a corrosione, e caratteristiche meccaniche (vedere tab. 1). il disegno dell’albero completo di flangie è rappresentato in fig. 1. tabella 1: proprietà meccaniche della lega al 6061-t6. figura 1: geometria dell’albero di trasmissione oggetto di studio. condizioni di impatto i parametri che concorrono alla definizione delle condizioni di impatto, escludendo la velocità del proiettile legata alle caratteristiche dell’arma da fuoco e del proiettile utilizzati, si riducono essenzialmente ad angolo di impatto e all’offset del proiettile, indicati in fig. 2. trascurando il caso di impatto con imbardata, l’angolo di impatto rappresenta l’angolo formato dalla traiettoria del proiettile con la retta normale all’asse del bersaglio. con offset si intende invece la distanza fra l’asse del bersaglio e la traiettoria del proiettile. sulla base di numerose simulazioni ad elementi finiti dell’impatto balistico di un proiettile calibro 7.62 nato, contro tubi cilindrici cavi, argomento di precedenti studi [3], è stata individuata la condizione più gravosa in termini di danneggiamento. la pericolosità dell’impatto è stata valutata in base alle dimensioni del foro ottenuto ed all’estensione della zona soggetta a sforzi residui, fattori in grado di influenzare rispettivamente la rigidezza dell’albero e la velocità di propagazione delle cricche nucleate sul bordo del foro. considerando le dimensioni geometriche esatte dell’albero, la condizione peggiore, indicata in tab. 2, corrisponde al caso di impatto angolato a 45° con superficie del proiettile tangente a quella del cilindro (definito caso critico): tale condizione origina un singolo foro di forma pressoché ellittica, con asse inclinato di circa 45° e di dimensioni massime. questa condizione costituisce la tipologia di danneggiamento maggiormente gravosa per un albero di trasmissione sollecitato a torsione. le simulazioni, condotte variando l’offset del proiettile, hanno mostrato come una riduzione dell’offset rispetto a quello critico provochi la comparsa di due fori distinti di ingresso ed uscita del proiettile; al contrario m e [mpa] modulo di elasticità longitudinale 70000 ν coefficiente di poisson 0.33 ρ [kg/m3] massa volumica 2700 σsn [mpa] carico unitario di snervamento 289.6 σr [mpa] carico unitario di rottura 310 http://dx.medra.org/10.3221/igf-esis.11.03&auth=true http://www.gruppofrattura.it l. giudici et alii, frattura ed integrità strutturale, 11 (2009) 21-35; doi: 10.3221/igf-esis.11.03 23 aumentando l’offset oltre il valore critico si genera ancora un unico foro di lunghezza gradualmente inferiore, ottenendo talora il rimbalzo del proiettile (ricochet effect). figura 2: parametri che definiscono le condizioni di impatto. tabella 2: condizioni di impatto. set up sperimentale le prove balistiche sono state effettuate presso il poligono di tiro della società oto melara (bs). arma da fuoco, sistema di puntamento e proiettili sono stati forniti dalla stessa società, così come la strumentazione per la misura della velocità iniziale del proiettile. l’arma da fuoco calibro 7.62 nato, dotata di puntatore ottico, è montata su un affusto che dispone di due gradi di libertà di rotazione, in un piano verticale ed orizzontale, definiti rispettivamente alzata e brandeggio. il sistema per la misura della velocità iniziale del proiettile è costituito invece da sorgenti laser e detector fissati ad un supporto trasportabile. tutte le altre attrezzature, necessarie per lo svolgimento delle prove, sono state progettate e realizzate nei laboratori del dipartimento di meccanica del politecnico di milano. la fig. 3 mostra lo schema del set-up sperimentale utilizzato. per il posizionamento degli alberi di trasmissione lungo la linea di tiro, è stato costruito un telaio, utilizzando comuni elementi di carpenteria in acciaio, la cui caratteristica principale è rappresentata dalla possibilità di impostare l’angolo di impatto e l’offset del proiettile. il provino è libero di traslare orizzontalmente e verticalmente grazie a due afferraggi scorrevoli su una struttura tubolare rettangolare, vincolata a due supporti mediante due perni che permettono di regolarne l’inclinazione. l’utilizzo di giunzioni smontabili ha reso possibile la suddivisione del telaio in vari pezzi di peso ed ingombro limitato, facilmente trasportabili anche a mano. come già affermato, il poligono ha fornito i sensori laser atti alla misura della velocità iniziale del proiettile, mentre posteriormente al provino nessuna strumentazione è stata posizionata a causa dei rischi di danneggiamento connessi ad una possibile deviazione del proiettile. figura 3: set-up sperimentale. parametro condizione di massimo danneggiamento angolo di impatto [°] 45 offset del proiettile [mm] 28 http://dx.medra.org/10.3221/igf-esis.11.03&auth=true http://www.gruppofrattura.it l. giudici et alii, frattura ed integrità strutturale, 11 (2009) 21-35; doi: 10.3221/igf-esis.11.03 24 analizzando le metodologie utilizzate in altre indagini sperimentali [4-15] per la misura della velocità residua del proiettile, è stato sviluppato un sistema basato sull’applicazione di due accelerometri a due lamine sottili di alluminio, definito per chiarezza espositiva metodo delle lastre sacrificali: la perforazione delle due lastre genera due segnali distinti che vengono registrati da un sistema di acquisizione in grado di calcolarne l’intervallo temporale di emissione; nota la distanza fra le lastre si determina facilmente la velocità del proiettile. per non compiere una sottostima è stata fatta inoltre una valutazione dell’energia cinetica dissipata per la perforazione di una lastra. il sistema realizzato permette inoltre di stimare la deviazione subita dal proiettile a causa dell’impatto contro il bersaglio, e di valutare la distanza reale percorsa dal proiettile fra le due lastre: ciò può essere compiuto confrontando le posizioni dei fori al termine di ogni test con le posizioni dei fori ottenuti da uno sparo “a vuoto”, cioè senza bersaglio montato. poiché dopo i primi test sono state osservate deviazioni modeste della traiettoria del proiettile, si è ritenuto vantaggioso, al fine di migliorare l’accuratezza della misura della velocità, sfruttare l’indipendenza dei due telai incrementandone la distanza reciproca. analogamente, l’allontanamento della prima lastra dal telaio di supporto degli alberi, ha consentito un più agevole riconoscimento dei fori del proiettile da quelli dovuti all’impatto di eventuali frammenti. la fig. 4 mostra il banco di sostegno dei provini dietro al quale si trova il sistema per la misura della velocità residua del proiettile. in fig. 5 è riportata un’immagine del proiettile 7.62 nato utilizzato. figura 4: banco di sostegno e sistema per la misura della velocità residua figura 5: il proiettile 7.62 nato; inferiormente solo la “pallottola” estratta dal bossolo. la strumentazione per l’acquisizione dei segnali è costituita da: 2 accelerometri pcb piezotronics model 352c23; amplificatore kistler instruments 5122; sistema di acquisizione ni 9215; software labview 8.0; gli accelerometri considerati sono caratterizzati da una banda passante piuttosto ampia: infatti operano correttamente ad una frequenza di 25 khz anche se la loro risposta è migliore sotto i 10 khz . tuttavia ciò che interessa in questa applicazione non è la ricostruzione della risposta in frequenza del fenomeno ma semplicemente l’identificazione dell’intervallo temporale fra gli istanti ai quali si ha il contatto del proiettile su ciascuna delle due lastre sacrificali. il programma labview® permette di realizzare uno strumento virtuale (vi), in grado di calcolare tale intervallo di tempo. risultati delle prove l’esecuzione di prove balistiche a vuoto (con colpo non deviato al centro delle lastre) ha permesso di effettuare una validazione del metodo delle lastre sacrificali, confrontando i risultati con quanto rilevato dai laser/detectors. la corrispondenza fra i risultati appare ottima (si veda la tab. 3); la lieve sottostima della velocità residua commessa mediante questo metodo, è dovuta al fatto che il proiettile deve attraversare una lastra, seppur sottile, di alluminio; quindi per ridurre ulteriormente l’errore è stata valutata l’energia necessaria per la perforazione di tale lastra, utilizzando la teoria espressa in [16]. la velocità iniziale del proiettile è stata ottenuta attraverso la seguente relazione:     2 1 0.02 cf plug dish pet i p e e e e v m       (1) http://dx.medra.org/10.3221/igf-esis.11.03&auth=true http://www.gruppofrattura.it l. giudici et alii, frattura ed integrità strutturale, 11 (2009) 21-35; doi: 10.3221/igf-esis.11.03 25 ricavata attraverso il seguente bilancio energetico:  attrpetdishplugcicf eeeeee  (2) essendo: ecf l’energia cinetica finale nota del proiettile dopo la perforazione; eci l’energia cinetica iniziale incognita del proiettile; attrpetdishplug eeee  l’energia spesa per attraversare una lastra sacrificale, i cui termini si riferiscono rispettivamente al plugging, al dishing, al petaling ed all’attrito. dimostrata quindi la validità del metodo delle lastre sacrificali, questo è stato applicato durante i test di impatto per la misura della velocità residua del proiettile. in questo caso per aumentare l’accuratezza delle misure sono state apportate alcune correzioni che tengono conto non solo dell’energia dissipata dalla perforazione della prima lastra sacrificale, ma anche della traiettoria del proiettile deviato dall’impatto, e del ritardo temporale con cui sono acquisiti i segnali, legato alla velocità di propagazione delle onde all’interno del materiale; in particolare il ritardo sarà differente per i due segnali nel caso in cui il proiettile a causa della deviazione impatti sulle due lastre in posizioni diverse. prove a vuoto laser/detectors [m/s] lastre sacrificali [m/s] lastre sacrificali corretto [m/s] 1 839 816 831 2 838 825 840 3 825 803 817 4 832 810 824 5 846 826 841 6 833 810 824 7 855 830 845 8 848 830 845 9 845 823 838 10 840 820 835 11 845 823 838 12 850 823 838 13 854 826 841 14 847 826 841 15 840 813 828 16 834 813 828 17 852 826 841 18 861 837 852 media 844 821 836 tabella 3: velocità del proiettile rilevata negli spari a vuoto; confronto fra i valori forniti dai laser/detectors e dalle lastre sacrificali. la fig. 6 aiuta a comprendere quanto appena esposto. per la valutazione della traiettoria effettiva del proiettile si sono rilevate le coordinate dei fori sulle due lastre, mentre l’energia assorbita dalla perforazione della prima lastra è stata stimata attraverso il metodo energetico utilizzato in precedenza. le velocità iniziale del proiettile, quella residua (corretta e non), e l’angolo di deviazione del proiettile rilevati in tutte le prove di impatto sono contenuti nella tab. 4. dal punto di vista della forma e delle dimensioni del danneggiamento causato dall’impatto balistico, i test sperimentali presentano una dispersione di risultati non trascurabile: in effetti analizzando tali risultati riportati in tab. 5 è evidente come condizioni di impatto nominalmente identiche portino a risultati macroscopicamente differenti. la scelta di studiare la condizione più gravosa definita in tab. 2 ha avuto infatti un peso rilevante nella determinazione di tale disomogeneità: uno scostamento dalle condizioni critiche ricercate, legato alla variabilità sempre presente in qualche misura in un fenomeno di impatto, anche se di piccola entità, può dare origine ad un danneggiamento caratterizzato da un doppio foro, da un singolo foro di varie lunghezza o in certi casi anche al rimbalzo del proiettile. la fig. 7 mostra le fotografie di due delle principali tipologie di danneggiamento ottenuto. http://dx.medra.org/10.3221/igf-esis.11.03&auth=true http://www.gruppofrattura.it l. giudici et alii, frattura ed integrità strutturale, 11 (2009) 21-35; doi: 10.3221/igf-esis.11.03 26 figura 6: traiettoria del proiettile deviato dall’impatto: il proiettile percorre uno spazio maggiore della distanza fra le lastre; la distanza d determina un ritardo nell’acquisizione del secondo segnale. prova vi [m/s] vr [m/s] vreff [m/s] α [°] 1 859 748 765 1.09 2 853 0.94 3 853 725 741 1.39 4 850 714 730 0.78 5 854 750 767 1.15 6 847 740 757 0.82 7 849 724 740 2.88 8 845 9 849 725 741 0.52 10 859 712 728 2.81 11 862 714 730 3.17 12 844 725 741 1.90 13 855 689 705 1.41 14 852 15 839 709 725 4.76 16 844 711 727 1.25 17 848 685 70 3.34 18 860 754 771 1.11 media 851 728 744 1.83 tabella 4: velocità iniziale del proiettile (v), velocità residua (vr), velocità residua effettiva (vreff ) ed angolo di deviazione (α) rilevati in ogni prova sperimentale. (a) (b) figura 7: principali tipologie di danno balistico osservate al termine dei test: a) singolo foro; b) doppio foro. http://dx.medra.org/10.3221/igf-esis.11.03&auth=true http://www.gruppofrattura.it l. giudici et alii, frattura ed integrità strutturale, 11 (2009) 21-35; doi: 10.3221/igf-esis.11.03 27 i provini sono quindi stati classificati in base alle dimensioni del danno: per i provini con doppio foro sono state misurate, lungo un’elica cilindrica inclinata a 45° rispetto all’asse del tubo, la distanza totale fra gli apici dei due fori e la lunghezza del setto di separazione fra di essi; invece per i singoli fori si è rilevata solo la lunghezza totale della lacerazione. dall’analisi dei risultati ottenuti, si osserva come solamente nel 30 % circa dei casi sia stato ottenuto il danno balistico nominalmente più gravoso. la tab. 5 mostra una classificazione degli alberi, effettuata in base alla tipologia di danneggiamento ottenuto, per ognuna delle quali è stato valutato il valore medio delle velocità iniziale e finale del proiettile misurate durante i test: analizzando i dati contenuti nella tab. 6 si può constatare come la massima riduzione di velocità si sia rilevata nei test che originano un singolo foro a 45°, ai quali è associato il massimo assorbimento energetico. è stata eseguita infine una valutazione dello stato tensionale residuo superficiale lasciato dall’impatto. gli sforzi residui sono stati misurati in vari punti su ciascun provino, sia prima che dopo le prove di impatto, utilizzando un analizzatore di tensione a raggi x stresstech group modello v.1.01. la tab. 7 contiene i valori medi delle tensioni misurate prima e dopo i test. le tensioni rilevate dopo l’impatto ad una distanza massima di 20 mm dagli apici del foro, mostrano in generale andamenti differenti considerando le due zone adiacenti al foro di ingresso e di uscita del proiettile, risultando prevalentemente di trazione nella prima e di compressione nella seconda. tipo di danno ltot [mm] lsetto [mm] lfori [mm] n° provini singolo foro a 45° da 75 a 85 10, 11, 13, 14, 17 doppio foro a 45° da 75 a 85 fino a 20 da 30 a 40 1, 2, 3 da 75 a 85 da 20 a 35 da 20 a 30 5, 6, 16 da 80 a 90 da 35 a 50 da 15 a 25 4, 7, 9, 12 singolo foro imbozzato 45 8 impatto di striscio 21 15 doppio foro a 0° 90 69 da 10 a 11 18 tabella 5: classificazione dei provini in base alla tipologia di danneggiamento. classe di danno vi [m/s] vf [m/s] vfeff [m/s] δv/vi [%] intaglio singolo a 45° 856 700 713 -16,7 doppio foro a 45° setto piccolo 855 737 750 -12,3 setto medio 848 734 747 -11,9 setto grande 848 722 735 -13,2 impatto di striscio a 45° 839 709 722 -13,9 doppio foro a 90° 860 754 768 -10,7 valore medio 851 728 741 -12,9 tabella 6: valori sperimentali medi della velocità incidente e residua effettiva del proiettile relativi alle varie classi di danneggiamento. prima dell'impatto dopo l'impatto in out σi [mpa] σii [mpa] σi [mpa] σii [mpa] σi [mpa] σii [mpa] 89,33 -31,50 114,04 7,37 3,97 -128,40 tabella 7: valore medio delle tensioni residue rilevate prima e dopo le prove di impatto balistico; dopo l’impatto sono state considerate separatamente le zone di ingresso e di uscita del proiettile per evidenziare il differente comportamento osservato nelle due aree http://dx.medra.org/10.3221/igf-esis.11.03&auth=true http://www.gruppofrattura.it l. giudici et alii, frattura ed integrità strutturale, 11 (2009) 21-35; doi: 10.3221/igf-esis.11.03 28 prove torsionali simulanti i carichi della missione di rientro misure effettuate e metodi urante le prove torsionali, che costituiscono l’ultima fase della sperimentazione effettuata, sono state misurate le deformazioni applicando rosette estensimetriche a tre griglie a 0°, 45° e 90°, con compensazione termica, il cui impiego è dettato dalla possibilità di determinare lo stato di sollecitazione principale incognito conoscendo le deformazioni lungo tre direzioni note. sforzi e direzioni principali possono essere calcolati risolvendo il seguente sistema di 3 equazioni nelle 3 incognite i , ii e  :          2 2, 2 1 2 1 i ii a c a b c b e e                  (3) 2 2 b a c a c tg           (4) per acquisire i segnali estensimetrici è stata utilizzata la seguente attrezzatura: chassis national instrument scxi-1000; 3 moduli di acquisizione national instrument scxi-1121 a 4 canali; 3 moduli estensimetrici national instrument scxi-1321 a 4 canali; software di acquisizione dedicato; le rosette sono state applicate sui provini nella zona adiacente al danno balistico, come visibile nella fig. 8. figura 8: posizione delle rosette. durante le prove di fatica torsionale è stata inoltre monitorata la propagazione delle cricche, osservate mediante un microscopio ottico, dotato di hardware e software per l’acquisizione di immagini. nella fig. 9 sono visibili le fotografie ingrandite di una cricca, mentre le fig. 10 e 11 mostrano rispettivamente la strumentazione utilizzata per monitorare le cricche ed il particolare della zona monitorata di un provino. figura 9: fotografie ingrandite di una cricca. d http://dx.medra.org/10.3221/igf-esis.11.03&auth=true http://www.gruppofrattura.it l. giudici et alii, frattura ed integrità strutturale, 11 (2009) 21-35; doi: 10.3221/igf-esis.11.03 29 figura 10: strumentazione utilizzata per monitorare l’avanzamento delle cricche. figura 11: fotografia di un albero danneggiato dopo l’impatto balistico. figura 12: direzione della coppia applicata figura 13: fotografia del provino danneggiato al termine della prova statica. http://dx.medra.org/10.3221/igf-esis.11.03&auth=true http://www.gruppofrattura.it l. giudici et alii, frattura ed integrità strutturale, 11 (2009) 21-35; doi: 10.3221/igf-esis.11.03 30 la rottura nel test effettuato sul provino danneggiato dall’impatto balistico si è verificata a partire dagli apici del foro, lungo un’elica cilindrica inclinata a 45° rispetto all’asse del provino, come visibile nella fig. 13. i risultati di entrambe le prove sono rappresentati nella fig. 14, dalla quale si nota una notevole riduzione della coppia di rottura dell’albero danneggiato rispetto a quello integro. tale differenza sarebbe in realtà ancora superiore dal momento che la rottura sul componente integro si è verificata lungo uno dei due cordoni di saldatura in corrispondenza di una coppia pari a 1360 nm e dunque inferiore al momento di plasticizzazione totale teorico dell’albero pari all’incirca a 1650 nm. come già affermato sono stati valutati gli sforzi e le direzioni principali calcolati a partire dalle deformazioni rilevate da ciascuna rosetta applicata sul provino danneggiato. elaborando i segnali estensimetrici acquisiti si vede, come era lecito attendersi, che la sollecitazione massima si ha in prossimità degli apici del difetto, in cui sono stati rilevati gli sforzi principali più elevati, rappresentati dalle curve blu e viola nelle fig. 15 e 16 e riferiti a rosette posizionate come in fig. 17. figura 14: confronto fra le curve coppia-rotazione ottenute dalle prove effettuate su un provino integro e su un provino con danneggiamento balistico figura 15: andamento dello sforzo principale σi ricavato sulla base dei dati estensimetrici durante la prova statica. figura 16: andamento dello sforzo principale σii durante la prova statica. http://dx.medra.org/10.3221/igf-esis.11.03&auth=true http://www.gruppofrattura.it l. giudici et alii, frattura ed integrità strutturale, 11 (2009) 21-35; doi: 10.3221/igf-esis.11.03 31 figura 17: direzioni principali degli sforzi rilevati durante la prova statica. il proiettile è entrato nel componente in prossimità della rosetta 2 ed è uscito in prossimità della rosetta 1. applicazione degli spettri di carico che simulano la missione di rientro alla base lo scopo di tutta la sperimentazione è verificare che l’elicottero sia in grado di portare a termine una missione di rientro alla base a potenza ridotta, con un albero di trasmissione del rotore di coda danneggiato dall’impatto di un proiettile. ciò si traduce nella verifica della capacità del componente danneggiato di resistere alle sollecitazioni per tutta la durata della missione. da un punto di vista operativo si tratta dunque di applicare all’albero di trasmissione opportuni spettri rappresentativi dei carichi torsionali di manovra (indicati nella tab. 8), e verificare che non si abbia la rottura del componente. in questa sede sono mostrati i risultati di una prova rappresentativa condotta su un provino danneggiato con singolo foro (il caso più gravoso). anche in questo caso, nella zona maggiormente sollecitata, prossima agli apici del difetto, sono state applicate due rosette (si veda la fig. 18). le fig. 19 e 20 mostrano l’andamento degli sforzi principali σi e σii rilevati dalle due rosette durante tutta la prova: in ogni grafico le curve rosse e viola rappresentano il massimo e il minimo dello sforzo σi mentre le curve blu e azzurro il massimo e minimo di σii . spettro mt medio[nm] mt ampiezza [nm] cicli r 1 208 48 2200 0,63 2 38 28 4200 0,15 3 30 24 160000 0,11 tabella 8: spettri di carico rappresentativi delle manovre effettuate in una missione di rientro. figura 18: posizione delle rosette. http://dx.medra.org/10.3221/igf-esis.11.03&auth=true http://www.gruppofrattura.it l. giudici et alii, frattura ed integrità strutturale, 11 (2009) 21-35; doi: 10.3221/igf-esis.11.03 32 figura 19: andamento degli sforzi principali rilevati dalla rosetta 1 in funzione del n° di cicli: le curve di colore rosso/viola e blu/azzurro indicano rispettivamente i valori massimo/minimo degli sforzi principali σi e σii figura 20: andamento degli sforzi principali rilevati dalla rosetta 2 in funzione del n° di cicli: le curve di colore rosso/viola e blu/azzurro indicano rispettivamente i valori massimo/minimo degli sforzi principali σi e σii. figura 21: andamento delle direzioni principali rilevate dalle due rosette. durante la prova, in corrispondenza dell’apice di uscita del proiettile, è stata osservata la formazione di una cricca, il cui avanzamento in funzione del numero di cicli è riportato nella fig. 22: la cricca si è propagata in modo stabile solo durante l’applicazione del primo spettro di carico, contraddistinto da sollecitazioni più elevate, arrestandosi invece nel corso degli altri due spettri. l’esecuzione di altre prove su alberi di trasmissione con stessa tipologia di danneggiamento ha fornito risultati del tutto analoghi. http://dx.medra.org/10.3221/igf-esis.11.03&auth=true http://www.gruppofrattura.it l. giudici et alii, frattura ed integrità strutturale, 11 (2009) 21-35; doi: 10.3221/igf-esis.11.03 33 possiamo dunque affermare che la verifica di resistenza per l’albero danneggiato analizzato è soddisfatta, compatibilmente con la missione definita in precedenza. ne consegue che l’elicottero sarà in grado di portare a termine con successo la missione di rientro alla base in regime di potenza ridotta. figura 22: lunghezza della cricca rilevata in funzione del n° di cicli. definizione di una condizione di propagazione instabile accanto alle prove sperimentali che simulano la missione di rientro sono state effettuate altre due prove con lo scopo di definire degli spettri di carico in grado di determinare una condizione di propagazione instabile con conseguente rottura del componente. dall’analisi dei momenti applicati durante le prove effettuate è stato elaborato un secondo set di carichi (indicato nella tab. 9) ricavato dal primo spettro (spettro 1) del set precedente, mantenendo invariate coppia massima e numero di cicli, ed operando una progressiva riduzione del rapporto di carico r, alla quale consegue un aumento del δk e una maggiore velocità di propagazione della cricca. l’avanzamento della cricca rilevato nel corso di una delle due prove è rappresentato nella fig. 23. la fig. 24 mostra invece l’andamento degli sforzi principali rilevati dalla rosetta applicata in prossimità dell’apice del danneggiamento da cui si è propagata la cricca. nel corso della prova la cricca è avanzata dapprima stabilmente raggiungendo durante l’applicazione dello spettro 3 la condizione di propagazione instabile, a cui è seguito istantaneamente il collasso strutturale del componente. spettro mt med [nm] mt amp [nm] mt max [nm] cicli r 1 208 48 256 2200 0,63 2 166 90 256 2200 0,30 3 141 115 256 2200 0,10 tabella 9: set di carichi derivati dallo spettro n° 1 del set precedente mantenendo invariate coppia massima applicata e numero di cicli e riducendo progressivamente il rapporto di carico r. figura 23: lunghezza della cricca rilevata nel primo test in funzione del n° di cicli: la velocità di propagazione aumenta improvvisamente nel corso del 3°spettro cui corrisponde il minimo rapporto r. http://dx.medra.org/10.3221/igf-esis.11.03&auth=true http://www.gruppofrattura.it l. giudici et alii, frattura ed integrità strutturale, 11 (2009) 21-35; doi: 10.3221/igf-esis.11.03 34 figura 24: andamento degli sforzi principali in funzione del n° di cicli ricavati dalle deformazioni misurate durante il primo test in prossimità dell’apice criccato del danneggiamento: si nota un notevole incremento dello sforzo durante il 3° spettro caratterizzato dal minimo rapporto r conclusioni ono state effettuate alcune prove di impatto balistico, condotte utilizzando un proiettile 7.62 nato, sparato contro provini rappresentativi di un albero di trasmissione sotto ben precise condizioni. i test eseguiti hanno mostrato una dispersione di risultati piuttosto marcata, attribuibile all’estrema criticità che caratterizza il posizionamento reciproco bersaglio-proiettile e ad altri parametri legati alla balistica esterna che sono oggetto di approfondimento attuale. agli alberi danneggiati sono quindi stati applicati degli spettri di carico rappresentativi delle sollecitazioni riscontrate durante la missione di rientro alla base. al fine di contenere la variabilità dei risultati si è testato un campione di provini il più possibile omogenei fra loro e con un danneggiamento di tipo “singolo foro”, che è stato considerato come quello di maggiore pericolosità per un componente sottoposto a carichi torsionali. le prove di torsione effettuate hanno fornito in effetti esiti analoghi, dai quali si può concludere che l’elicottero, benché presenti un componente principale della linea di trasmissione di coda danneggiato da un proiettile, è in grado di portare a termine una missione di rientro alla base a potenza ridotta, dal punto di vista della resistenza strutturale. in relazione agli obiettivi prefissi, la verifica può quindi considerarsi soddisfatta. partendo dagli spettri applicati, e riducendo progressivamente il rapporto di carico r a parità di coppia massima, è stata definita inoltre una condizione di carico più gravosa, in grado di determinare la propagazione instabile della frattura e dunque il collasso strutturale dell’albero. dall’esecuzione di questa seconda serie di test è emerso come il rapporto di carico r rivesta un ruolo decisivo nel determinare la vita residua a fatica del componente. bibliografia [1] m. backmann, w. goldsmith, int engng sci, (1978). [2] w. goldsmith, int. j. impact engng, (1999). [3] d. colombo, progettazione di componenti di elicottero in presenza di cricche e difetti. tesi di dottorato, politecnico di milano, dipartimento di meccanica, (2005). [4] m.j. forrestal, a.j. piekutowsky, int. j. impact engng, (1999). [5] a.j. piekutowsky, m.j. forrestal, k.l. poormon, t.l. warren, int. j. impact engng, (1999). [6] t.l. warren, k. l. poormon, int. j. impact engng, (2001). [7] i.v. roisman, k. weber, a.l. yarin, v. hohler, m.b. rubin, int. j. impact engng, (1999). [8] s. dey, t. borvik, o. s. hopperstad, j. r. leinum., m. langseth, int. j. impact engng, (2004). [9] t. borvik, o.s. hopperstad, m. langseth, k. a. malo, int. j. impact engng, (2002). [10] t. borvik, m. langseth, o.s. hopperstad, k.a. malo, int. j. impact engng, (2000). [11] t. borvik, m. langseth, o.s. hopperstad, k. a. malo, int. j. impact engng, (1999). [12] n. k. gupta, m. a. iqbal, g. s. sekhon, int. j. impact engng, (2005). s http://dx.medra.org/10.3221/igf-esis.11.03&auth=true http://www.gruppofrattura.it l. giudici et alii, frattura ed integrità strutturale, 11 (2009) 21-35; doi: 10.3221/igf-esis.11.03 35 [13] m. zeinoddini, g. a. r. parke, j. e. harding, int. j. impact engng, (2000). [14] n. k. gupta, v. madhu, int. j. impact engng, (1997). [15] l. kezhun, w. goldsmith, int. j. impact engng, (1995). [16] j. ning, w. song, j. wang, acta mech. sinica, (2005). http://dx.medra.org/10.3221/igf-esis.11.03&auth=true http://www.gruppofrattura.it microsoft word numero_26_art_9_finale e. salvati et alii, frattura ed integrità strutturale, 26 (2013) 80-91; doi: 10.3221/igf-esis.26.09 80 mode i stress intensity factors for triangular corner crack nearby intersecting of cylindrical holes fattori di intensificazione delle tensioni per cricche ad angolo triangolari in corrispondenza di intersezione di fori sollecitate a modo i e. salvati, p. livieri, r. tovo dipartimento di ingegneria meccanica, università di ferrara, via saragat 1, 44122, ferrara enrico.salvati@unife.it, paolo.livieri@unife.it, roberto.tovo@unife.it abstract. the paper deals with the stress intensity factor assessment of cracks at the intersection of holes loaded by internal pressure. triangular flaws are considered at the intersection of two holes inside a specific specimen. the research examines the influence of hole diameter ratio d1/d2 and the angle between their axes α. numerical analysis is performed to determine the stress intensity factors (sif) of mode i in many different geometric configurations. the actual shape of a real crack nucleated at the intersection of two cylindrical holes is subject to variable internal pressure and is usually geometrically complex. the stress intensity factor changes along the crack contour and the crack shape development is controlled by its local value, e.g. during a fatigue loading. in general, the estimation of the stress intensity factors of cracks with a complex shape is made by means of numerical methods since closed form solutions in literature are limited. however, in order to solve the problem of crack propagation more quickly, in the case of a crack corner at the intersection between two cylindrical holes, we can assume, in agreement with scientific literature, a symmetrical triangular crack shape and the stress intensity factor are only calculated at the middle of the crack. obviously, this is a strong approximation, but this allows a reduction in the computation effort for crack growth rate assessments and safety evaluation. in this paper, the weight function technique is used by integrating the actual stress field evaluated in the uncracked model. the method of the weight function is of general validity and the weight function is related to the displacement components close to the crack front, as proposed by bueckner and rice. from a computational point of view, the use of the three-dimensional weight function is complex and in scientific literature a weight function of general validity is not available. nevertheless, thanks to the work conducted by petroski and achenbach, shen and glinka, an efficient generalised weight function has been adopted and then developed by sha and yang [9], which considers a series expansion of non-singular terms. in this way, the integration of the weight function, multiplied by a nominal stress, is made along a line and not in a two-dimensional domain. in this preliminary work, according to herz et al., we consider a weight function with three terms by assuming a priori the coefficients of the second and third non-singular terms. this contribution is essentially an extension of a previous paper by herz et al. they only considered the case of d1/d2=1 and =90° (di are the diameters of the two cylindrical holes and a is the angle between their axis). here, we extend the analysis to d1/d2 equal to 2, 4 and 8 with an  of 60 and 45 degrees. http://dx.medra.org/10.3221/igf-esis.26.09&auth=true http://www.gruppofrattura.it e. salvati et alii, frattura ed integrità strutturale, 26 (2013) 80-91; doi: 10.3221/igf-esis.26.09 81 with the aid of three-dimensional modelling, an accurate fe model of a triangular corner crack at different crack depths has been made. subsequently, by using ansys finite element software, it is possible to employ the command kcal that evaluates the stress intensity factors in the middle of the crack. subsequently, a comparison between numerical fe results and the analytical results, giving the values of the unknown coefficients of the weight function (the unknown coefficient is indicated in the paper as m1). as reported in the tables, the accuracy of the weight functions in sif predictions is about 5% despite the strong simplification previously introduced in the model. this result is considerable because it is possible to determine the stress intensity factor of a triangular shaped crack by a line integral of a stress profile in a model without considering the crack. sommario. nel presente lavoro si affronta il problema del calcolo dello stress intensity factors (sif) di cricche di forma triangolare che nucleano in prossimità dell’intersezione di fori cilindrici ad assi complanari. modelli fem tridimensionali sono utilizzati per valutare, nel punto mediano, lo sif di cricche triangolari per poi calcolare la weight function relativa a sollecitazioni di modo i. sono presi in esame il rapporto fra i diametri dei due fori cilindrici e l’angolo formato dai loro assi. la verifica della precisione della weigth function nel calcolare lo sif è mostrata in diversi esempi. infine, lo sif di una cricca triangolare è messo a confronto con quello calcolato per una cricca avente forma simile ad una cricca reale riscontrata in un componente sollecitato a fatica. keywords. weight function; stress intensity factors; intersecting holes; finite element method; fracture mechanics. introduzione ’intersezione di fori in pressione all’interno di componenti meccanici dà luogo ad una intensificazione delle tensioni. questa tipologia di dettaglio strutturale è molto diffusa nell’ambito della moto propulsione dove la necessità di contenere fluidi aventi pressioni sempre più elevate è in continuo aumento. nei collettori che distribuiscono fluido ad elevate pressioni l’innesco di cricche in corrispondenza dell’intersezione di due condotti, è un fenomeno comune [1]. la successiva propagazione può essere arrestata o rallentata qualora fossero presenti tensioni residue derivanti da trattamento di autofrettaggio. test sperimentali a fatica, eseguiti con pressioni pulsanti su dettagli strutturali con due condotti cilindrici intersecanti, hanno dimostrato come l’autofrettaggio può incrementare il limite a fatica di un fattore di circa 2 qualora i fori abbiano ugual diametro e l’angolo  fra gli assi dei cilindri sia di 90° [2]. tale processo di autofrettaggio induce uno stato di tensione residua di compressione che può essere quantificato con analisi fem [3], o in alcuni casi anche per via analitica [4 e 5]. per poter studiare la propagazione per fatica è necessaria la conoscenza del fattore di intensificazione delle tensioni effettivo keff che racchiude in sé le varie componenti di sollecitazione. la forma della cricca che nuclea in corrispondenza di due fori intersecanti soggetti ad una pressione interna variabile non è immediata da calcolare e necessita di una schematizzazione bidimensionale. in generale, i problemi di cricche piane di forma qualunque sono alquanto complessi e per avere soluzioni in forma chiusa direttamente applicabili senza la necessità di dover sviluppare particolari algoritmi di calcolo, è necessario limitare l’analisi ai termini del primo ordine [6 e 7]. tuttavia, per risolvere ingegneristicamente, il problema di una cricca d’angolo nucleata all’incrocio fra due condotti cilindrici, è possibile assumere, in accordo con quanto fatto nel riferimento bibliografico [3], che la cricca abbia una forma triangolare simmetrica concentrando l’attenzione sul valore dello stress intensity factor (sif) in mezzeria della cricca. questo modo di procedere è sicuramente una approssimazione del problema, ma consente di stimare in modo rapido, se il range dello sif imposto dai carichi esterni pulsanti è superiore al relativo valore di soglia del materiale portando ad un aumento della dimensione della cricca. l’obiettivo del seguente contributo, è quello di mettere a disposizione del progettista, una weight function che faciliti il calcolo dello sif noto il rapporto fra i due diametri dei condotti e l’angolo formato dai loro assi. saranno calcolati i coefficienti della weitgh function proposta da shen e glinka [8] considerando uno sviluppo in serie di tre termini [9]. la weight function proposta sarà confrontata, nel calcolo dello sif, con i risultati ottenuti da elaborazioni numeriche di l http://dx.medra.org/10.3221/igf-esis.26.09&auth=true http://www.gruppofrattura.it e. salvati et alii, frattura ed integrità strutturale, 26 (2013) 80-91; doi: 10.3221/igf-esis.26.09 82 analisi fem che vedranno condizioni di carico derivanti da una pressione interna. infine, verrà mostrato il confronto, nella previsione dello sif, fra cricche d’angolo triangolari e quelle aventi forma simile a quella di cricche reali nucleate in corrispondenza di fori cilindrici sollecitati a fatica. il problema della intensificazione delle tensioni nell’incrocio di due condotti in pressione ’intersezione di fori cilindrici comporta una concentrazione delle tensioni tangenziali nella zona di intersezione qualora siano sollecitati da una pressione interna. la fig. 1 riporta una tipica configurazione di due fori complanari con differente diametro e con gli assi di simmetria inclinati di un angolo  ricavati da una matrice di materiale cilindrica che rappresenta in modo schematico il componente meccanico. muovendosi lungo una generatrice, la tensione tangenziale incrementa in modo sensibile fino ad arrivare ad un valore massimo in corrispondenza della zona di intersezione. le fig. 2 e 3 evidenziano il problema della concentrazione delle tensioni qualora i due condotti siano sollecitati da un fluido in pressione. la tensione z, sul piano di taglio, coincide con la tensione tangenziale lungo la generatrice ed incrementa di circa un fattore 6 nel passare da una zona indisturbata al punto di incrocio. figura 1: esempio di una intersezione di due condotti cilindrici. figure 1: example of intersection of two cylindrical hole. figura 2: contour tensione z (p=1 mpa, d1/d2=2, α=45°). figure 2: z contour (p=1 mpa, d1/d2=2, α=45°). l http://dx.medra.org/10.3221/igf-esis.26.09&auth=true http://www.gruppofrattura.it e. salvati et alii, frattura ed integrità strutturale, 26 (2013) 80-91; doi: 10.3221/igf-esis.26.09 83 figura 3: andamento tensione tangenziale (p=1 mpa, d1/d2=2, α=45°) figure 3: hoop stress (p=1 mpa, d1/d2=2, α=45°) il metodo delle funzioni peso per il calcolo dello sif ei componenti meccanici contenenti dei difetti assimilabili a cricche, il calcolo della loro capacità di carico statica o la possibilità di valutare la velocità di crescita del difetto, legata ad un carico variabile nel tempo, è legata al calcolo dello stress intensity factor (sif) della cricca. noto lo sif, il progettista ha modo di garantire la vita di servizio del componente oppure valutare se è raggiunto un certo livello di sicurezza. questi tipi di analisi vengono sviluppati utilizzando modelli di meccanica della frattura e nonostante siano reperibili in vari manuali i valori degli sif [10 e 11] è ancora difficile trovare soluzioni adeguate per molti problemi pratici. l’obiettivo del presente lavoro è quello di valutare lo sif di cricche d’angolo che nucleano in prossimità di un incrocio di due fori cilindrici. in questo lavoro preliminare, si assume che la forma della cricca sia triangolare (fig. 1c) disposta simmetricamente rispetto alla bisettrice dell’angolo  formato dall’incrocio dei due assi dei fori. questa assunzione è in accordo con quanto fatto in [12] dove, oltre ad aver monitorato a posteriori la vera forma della cricca nucleata nel punto di intersezione, è stata proposta tale esemplificazione lineare per agevolare il calcolo dell’allungamento della cricca sotto un carico pulsante. per rendere di validità generale il calcolo dello sif e non legato ad uno specifico tipo di carico, si è deciso di utilizzare il metodo delle weight function [13 e 14] assumendo lo sviluppo in serie di sha e yang [9] troncato al terzo ordine. il modello geometrico di riferimento per la valutazione della weight function è riportato in fig. 4. con il metodo delle weight function il ki è calcolato mediante l’integrazione del prodotto fra la funzione peso m(x,a) e la tensione σz(x), quest’ultima valutata sul componente non criccato in direzione ortogonale al piano nel quale si svilupperà la cricca:       0 ,   a i zk a x m x a dx  (1) nella (1) a rappresenta la dimensione della cricca misurata lungo la bisettrice. ovviamente, con riferimento alla fig. 4c, con la (1) si è in grado di valutare correttamente il valore dello sif nel punto mediano a della cricca, mentre, se è di interesse un altro punto del bordo della cricca, si dovrà modificare la weight function adeguandola di volta in volta. in questo modo si sostituiscono degli integrali di superficie con una serie di funzioni peso ad una sola variabile [15]. il metodo delle weight function è di validità generale e la funzione peso è legata alle componenti di spostamento in prossimità del fronte di cricca come proposto da bueckner [13] e rice [14] nel seguente modo: n http://dx.medra.org/10.3221/igf-esis.26.09&auth=true http://www.gruppofrattura.it e. salvati et alii, frattura ed integrità strutturale, 26 (2013) 80-91; doi: 10.3221/igf-esis.26.09 84   ', r ir ue m x a k a     (2) in cui e’ è il modulo di elasticità per stati piani di tensione, mentre, diventa e’=e/(1-2) per stati piani di deformazione ( modulo di poisson), kir è lo sif di un caso preso a riferimento ed ur è il relativo crack opening displacement. figura 4: geometria di riferimento. figure 4: reference model. la (2) richiede la conoscenza dell’intero campo degli spostamenti sopra la cricca oltre che la conoscenza di un irk di riferimento. grazie al lavoro condotto da petroski e achenbach [16], shen e glinka [8] formularono la scrittura di una efficiente funzione peso scritta generalizzata da sha e yang [9], che considera uno sviluppo in serie di termini non singolari pesati dai parametri mi:     31 2 2 2 1 2 3 2 , 1 1 1 1 1 2 ( ) n n x x x x m x a m m m m a a a aa x                                     (3) in letteratura è stato ampiamente verificato che l’eq. (3) è applicabile ad una vasta gamma di casi di interesse ingegneristico anche per cricche aventi una forma bidimensionale di tipo ellittico [15]. inoltre, in diversi lavori proposti da glinka e shen [17] è stato mostrato che la formulazione con tre termini è sufficientemente accurata comportando errori inferiori all’1%. il problema del calcolo della funzione peso viene perciò spostato alla valutazione dei parametri mi che possono essere calcolati in vari modi. per esempio, se si conoscono tre casi di riferimento relativi a tre differenti distribuzioni di carico agente sopra la cricca, noti i tre sif kiri, è possibile impostare il seguente sistema lineare nelle incognite mi:     31 2 2 1 1 1 2 3 0 2 1 1 1 1 2 ( ) a ir z x x x k x m m m dx a a aa x                                (4)     31 2 2 2 2 1 2 3 0 2 1 1 1 1 2 ( ) a ir z x x x k x m m m dx a a aa x                                (5)     31 2 2 3 3 1 2 3 0 2 1 1 1 1 2 ( ) a ir z x x x k x m m m dx a a aa x                                (6) http://dx.medra.org/10.3221/igf-esis.26.09&auth=true http://www.gruppofrattura.it e. salvati et alii, frattura ed integrità strutturale, 26 (2013) 80-91; doi: 10.3221/igf-esis.26.09 85 nel presente lavoro i kiri saranno calcolati in funzione della geometria con l’ausilio degli elementi finiti costruendo, di volta in volta, dei modelli numerici tridimensionali adeguati alla geometria di fig. 4. calcolo numerico dello sif di cricche bidimensionali razie a simulazioni di tipo numerico è possibile ottenere i fattori di intensificazione delle tensioni sul bordo di una cricca piana bidimensionale posta nel punto di interesse applicando il principio di sovrapposizione di bueckner. sfruttando le potenzialità del software di calcolo agli elementi finiti ansys [18] è possibile utilizzare il comando kcal che permette di ricavare, in modo rapido ed efficiente, i fattori di intensificazione delle tensioni. il modello numerico è stato realizzato infittendo gli elementi in prossimità dell’apice della cricca come mostrato in fig. 5. in ogni porzione di cricca è stato applicato un carico uniforme, mentre sulla rimanente parte di superficie si è imposto una condizione di spostamento nullo in direzione ortogonale al piano di simmetria. figura 5: modello agli elementi finiti usato per il calcolo dello sif del punto a. figure 5: fe model used for sif calculation in point a. il modello solido è suddiviso in diversi sottodomini che facilitano la modifica delle condizioni al contorno al fine di calcolare gli sif per diverse dimensioni a della di cricca. inoltre, viene sfruttata la condizione di simmetria rispetto al piano dove la cricca propaga. il modello è caricato da una pressione unitaria di 1 mpa agente sulla superficie di frattura per le varie profondità considerate. in fig. 6 è possibile notare la zona deformata che coincide, di fatto, con l’area dove è applicato il carico. figura 6: deformata e contour della tensione principale massima per un carico unitario applicato alla superficie della cricca (1 mpa). figure 6: deformed shape and first principal stress for a uniform surface load over the crack (1 mpa). g bordo cricca http://dx.medra.org/10.3221/igf-esis.26.09&auth=true http://www.gruppofrattura.it e. salvati et alii, frattura ed integrità strutturale, 26 (2013) 80-91; doi: 10.3221/igf-esis.26.09 86 calcolo della funzione peso er la cricca triangolare di fig. 4, in virtù di quanto descritto sopra, si decide di utilizzare una funzione di forma avente tre parametri:     31 2 2 1 2 3 2 , 1 1 1 1 2 ( ) x x x m x a m m m a a aa x                             (7) con l’obbiettivo di risolvere il sistema di eq. (4-6) risulta necessario avere a disposizione i fattori di intensificazione delle tensioni per una cricca di profondità stabilita e tre differenti condizioni di carico. recenti lavori eseguiti da herz et al. [12] hanno evidenziato che, per d1/d2=1 e =90°, l’andamento dei parametri m2 ed m3 è stato assunto costante lungo la direzione di propagazione della cricca e pari rispettivamente a 3 e -3. in questo preliminare lavoro, si adotterà tale ipotesi esemplificativa, mantenendo costanti m2 ed m3 relegando così la variabilita dei parametri mi solo su m1. a posteriori, sulla base di un confronto fra risultati numerici fem e i relativi valori calcolati con la (7), sarà verificata la correttezza di tale assunzione al variare delle condizioni di carico. la ricerca della funzione peso dunque si riconduce alla sola determinazione dell’andamento del parametro m1 al variare dalla profondità della cricca. con l’ausilio di un modellatore 3d sono state schematizzate cricche aventi profondità a variabile. successivamente, dal post-processamento di analisi fem sono stati stimati gli im in funzione della geometria dei condotti e della dimensione a della cricca. le configurazioni geometriche analizzate sono riassunte nelle tabelle 1 e 2. per un prefissato rapporto geometrico di diametri, si sono considerate sette differenti profondità di cricca per le quali sono stati calcolati, dai risultati fem, gli sif nel punto mediano. nelle fig. 7-9 sono riassunti gli andamenti di ki per tutte le geometrie analizzate. la risoluzione numerica della (7) permette di ottenere l’andamento del parametro m1. in questo modo, interpolando i valori ottenuti per ogni singola geometria, si ottiene l’andamento del ki in funzione della profondità della cricca. nelle fig. 10-12 è messa in evidenza la variabilità di m1. inoltre, per una fissata dimensione della cricca, la fig. 13 mostra come sia possibile interpolare il valore di m1 per angoli  compresi fra 45 e 90°. n° α [°] 1 2 d d 1 90 1 2 90 2 3 90 4 4 90 8 5 60 1 6 60 2 7 60 4 8 60 8 9 45 1 10 45 2 11 45 4 12 45 8 tabella 1: configurazioni geometriche analizzate. table 1: analysed cases. p http://dx.medra.org/10.3221/igf-esis.26.09&auth=true http://www.gruppofrattura.it e. salvati et alii, frattura ed integrità strutturale, 26 (2013) 80-91; doi: 10.3221/igf-esis.26.09 87 a [mm] 0.1 0.3 0.6 1.0 1.5 2.5 4.0 tabella 2: profondità di cricca analizzate. table 2: crack deep. figura 7: sif per geometria α=90°. figure 7: sif for models with α=90°. figura 8: sif per geometria α=60°. figure 8: sif for models with α=60°. figura 9: sif per geometria α=45°. figure 9: sif for models with α=45°. figura 10: andamento parametro m1 geometria α=90°. figure 10: m1 parameter for models with α=90°. http://dx.medra.org/10.3221/igf-esis.26.09&auth=true http://www.gruppofrattura.it e. salvati et alii, frattura ed integrità strutturale, 26 (2013) 80-91; doi: 10.3221/igf-esis.26.09 88 figura 11: andamento parametro m1 geometria α=60°. figure 11: m1 parameter for models with α=60°. figura 12: andamento parametro m1 geometria α=45°. figure 12: m1 parameter for models with α=45°. figura 13: variabilità di m1 per una prefissata dimensione della cricca. figure 13: m1 parameter for a deep crack of 0.6 mm. http://dx.medra.org/10.3221/igf-esis.26.09&auth=true http://www.gruppofrattura.it e. salvati et alii, frattura ed integrità strutturale, 26 (2013) 80-91; doi: 10.3221/igf-esis.26.09 89 verifica della weight function l fine di verificare la correttezza dell’ipotesi della costanza dei parametri m2 ed m3 della funzione peso nonché i valori di m1 calcolati, risulta necessario prendere in esame differenti tipologie di carico applicate al modello. la modalità di carico utilizzata prevede l’applicazione di una pressione agente unicamente sulle superfici dei condotti cilindrici (non si considera la pressione agente sulla superficie di cricca). tale condizione di carico viene applicata per tutte le configurazioni di α considerate, rapporto fra i diametri dei fori d1/d2 pari a 2 e profondità di cricca a=1.5 mm. la pressione applicata è unitaria (1 mpa). in aggiunta, si considera una condizione di carico mista, limitata ad una sola geometria. tale condizione di carico simula la presenza di un calettamento con interferenza in uno dei due condotti; nell’esempio numerico la pressione nei condotti viene imposta rispettivamente pari ad 1 ed 1.5 mpa. il calcolo numerico mediante il metodo agli elementi finiti, come visto in precedenza, permette di stimare con precisione lo sif (ki,fem) per le varie cicche posizionate come in fig. 4. i valori calcolati, sono stati successivamente confrontati con quelli determinati con la weight function proposta:     31 2 2 , 1 0 2 1 1 3 1 3 1 2 ( ) a z i w x x x x k m dx a a aa x                                (8) nella (8) il valore di m1 sarà letto nei grafici 10-12. la tensione z, relativa ai vari esempi trattati, è riportata in tab. 3. tale tensione fa riferimento alla geometria senza cricca ed ad un materiale lineare elastico. gli errori in percentuale sono risultati nell’ordine del 5% e sicuramente accettabili a fronte delle esemplificazioni introdotte nella weight function. inoltre, è stato verificato che per d1/d2 pari a 4 e con una pressione costante sulla superficie della cricca, è possibile ottenere dalla (2) l’andamento numerico della weight function (angolo  di 60°, dimensione cricca a di 4 mm). tale calcolo è stato possibile grazie alla determinazione, con gli elementi finiti, del crack opening displacement ottenuto senza infittire la mesh rispetto alle analisi viste in precedenza. nella zona in cui la mesh era sufficientemente accurata, la weight function (7), calcolata con i coefficienti numerici delle fig. 10-12, coincideva con la funzione definita dalla (2). calcolo dello stress intensity factors per una cricca avente forma complessa rendendo in considerazione i rilievi sperimentali riportati in [12] e [19], si è costruito un modello tridimensionale in cui la cricca assume forma simile a quella rilevata sperimentalmente qualora i due condotti cilindrici siano sollecitati da una pressione variabile nel tempo (vedere fig. 14). le dimensioni assolute della cricca considerate nell’esempio sono diverse rispetto a quelle riportate nei riferimenti bibliografici [12 e 19] ma rispettano in proporzione la forma del difetto. la geometria di riferimento del modello è quella di fig. 4 con un rapporto fra i diametri dei fori d1/d2 =1 e ad un angolo α di 90°. figura 14: rappresentazione di una cricca reale nucleata all’intersezione di due condotti cilindrici e relativo modello fem tridimensionale. figure 14: actual crack shape at the bore intersection and three-dimensional fe model. a p http://dx.medra.org/10.3221/igf-esis.26.09&auth=true http://www.gruppofrattura.it e. salvati et alii, frattura ed integrità strutturale, 26 (2013) 80-91; doi: 10.3221/igf-esis.26.09 90 descrizione problema risultati errore d1/d2 =1 p1= 1 mpa α=90° , 1.71i femk , 1.60i wk 6% d1/d2 =2 p1= 1 mpa α=90° , 2.12i femk , 2.04i wk 4% d1/d2 =2 p1= 1 mpa α=60° , 3.46i femk , 3.27i wk 5% d1/d2 =2 p1= 1 mpa α=45° , 3.11i femk , 2.98i wk 4% d1/d2 =2 p1= 1 mpa p2= 1.5 mpa α=60° , 3.46i femk , 3.27i wk 5% tabella 3: verifiche con condizione di carico di pressione nei condotti. table 3: check for different pressure inside the bore. allo scopo di verificare l’approssimazione nel calcolare dello sif nel punto h, al variare della dimensione della cricca di forma triangolare, si è costruito il modello fem tridimensionale riportato in fig. 14. successivamente, imponendo una pressione unitaria sulla superficie del difetto, è stato calcolato numericamente lo sif nel punto di controllo h. il p1 p1 p1 p1 p1 p2 http://dx.medra.org/10.3221/igf-esis.26.09&auth=true http://www.gruppofrattura.it e. salvati et alii, frattura ed integrità strutturale, 26 (2013) 80-91; doi: 10.3221/igf-esis.26.09 91 confronto fra i valori ottenuti dello sif per la cricca sagomata di fig. 14 e quello di cricche aventi forma triangolare viene riportato in tab. 4. l’uguaglianza dello sif si ha per un valore di a pari a circa 2.5 mm. in questo caso le aree delle due tipologie di cricca sono di poco discosti fra loro. tabella 4: confronto fra lo sif di cricche di forma triangolare o sagomata (pressione costante sulla superficie della cricca pari ad 1 mpa). table 4: comparison between the sif of a triangular crack and that of a crack with an actual shape (constant pressure on the surface crack equal to 1 mpa). conclusioni el presente lavoro, dopo aver assunto una forma esemplificata di una cricca nucleata nel punto di intersezione di due condotti cilindrici in pressione, si è proposta una weight function per il calcolo dello stress intensity factor (sif) di modo i. il confronto con i dati fem ottenuto mettendo in pressione i due condotti, ha evidenziato errori, in media, del 5 %. la weight function proposta permette di valutare lo sif di una cricca d’angolo in modo estremamente rapido mostrandosi uno strumento di calcolo particolarmente utile per valutare l’influenza delle tensioni residue indotte da un processo di autofrettaggio. ringraziamenti i ringrazia la o.m.t. di torino per il supporto alle attività di ricerca. bibliografia [1] herz, e., hertel, o., vormwald, m., thumser, r., bergmann j.w. , fatigue life of high pressure diesel injection components under variable amplitude loading, in: proc. of the 2nd int. conf. on material and component performance under variable amplitude loading, 2 (2009) 1265-1274. [2] seeger, t., schon, m., bergmann, j., vormwald, m., autofrettage i-dauer – festigkeitssteigerung durch autofrettage, abschluβ bericht heft. 550, forschungsvereiningung verbrennungskraftmaschinen e.v. (fvv), frankfurt, vorhaben 478, (1994). [3] thumser, r., bergmann, j.w., vormwald, m., residual stress field and fatigue analysis of autofrettaged parts, int journal of pressure vessels and piping, 79 (2002) 113-117. [4] livieri, p., lazzarin p., autofrettaged cylindrical vessels and bauschinger effect: an analytical frame for evaluating residual stress distributions, asmejournal of pressure vessel technology, 124 (2002) 38-46. [5] adibi-asl, r., livieri, p., analytical approach in autofrettaged spherical pressure vessels considering the bauschinger effect, asmejournal of pressure vessel technology, 129 (2007) 411-419. [6] livieri, p., segala, f., first order oore-burns integral for nearly circular cracks under uniform tensile loading, international journal of solids and structures, 47(9) (2010) 1167-1176. [7] livieri, p. segala, f., an analysis of three-dimensional planar embedded cracks subjected to uniform tensile stress, engineering fracture mechanics, 77 (2010) 1656-1664. [8] shen, g., glinka, g., weight function for a surface semi-elliptical crack in a finite thickness plates, theoretical applied fracture mechanics, 15 (1991) 247-255. a [mm] profondità cricca area [mm2] cricca triangolare area [mm2] cricca reale [ ]ik mpa mm cricca triangolare eq. (8) [ ]ik mpa mm cricca triangolare fem [ ]ik mpa mm cricca sagomata fem 2.00 4 6.65 1.53 1.54 1.73 2.50 6.3 1.73 1.73 3.39 12.5 2.05 1.97 n s http://dx.medra.org/10.3221/igf-esis.26.09&auth=true http://www.gruppofrattura.it e. salvati et alii, frattura ed integrità strutturale, 26 (2013) 80-91; doi: 10.3221/igf-esis.26.09 92 [9] sha, g. t., yang, c. t., weight function of radial cracks emanating from a circular hole in a plate, astm. – philadelphia, (1986) 573-600. [10] tada, h., paris, p., irwin, g., the stress analysis of cracks handbook, 2nd edition, paris productions incorporated, st. luis, missouri, 8.3 (1985). [11] murakami y., stress intensity factor handbook, pergamon press, oxford (1987). [12] herz, e., hertel, o., vorrmwald m., numerical simulation of plasticity induced fatigue crack opening and closure for autofrettaged intersecting holes, engineering fracture mechanics, 78 (2011) 559-572. [13] h.f. bueckner, a novel principle for the computation of stress intensity factors, zeitschrift angewandte mathematik und mechanik, 50 (1970) 529-546. [14] rice j., some remarks on elastic crack-tip stress field, int. j. of solids struct., 8 (1972) 751-758. [15] niu, x., glinka g., weight function for edge and surface semi-elliptical cracks in flat plates and plates with corners. engng fracture mech., 36 (1990) 459-476. [16] petroski, h. y., achenbach f.d., computation of the weight function from a stress intensity factor, engng. fracture mech., 10 (1978) 257-266. [17] glinka, g. shen g., universal features of weight functions for cracks in mode i, department of mechanics engineering, university of waterloo, waterloo, ontario, canada n2l3g1, engng fracture mech., 40(6) (1991) 11351146. [18] ansys online manuals release 5.5, structural, chapter 10: fracture mechanics (up19980818) http://mostreal.sk/html/guide_55/g-str/gstr10.htm (2013). [19] thumser, r., numerical stability of plane crack paths under mode i loading, crack paths, in: cp2012, gaeta, italy (2012) 943-950. http://dx.medra.org/10.3221/igf-esis.26.09&auth=true http://www.gruppofrattura.it microsoft word numero 17 articolo 3 e. benvenuti et alii, frattura ed integrità strutturale, 17 (2011) 23-31; doi: 10.3221/igf-esis.17.03 23 a brittle fracture criterion for pmma v-notches tensile specimens based on a length-enriched extended finite element approach e. benvenuti, r.tovo, p. livieri università di ferrara abstract. a criterion for the prediction of the static failure loads in tensile pmma specimens with sharp notches is presented. the proposed criterion is based on a regularized version of the extended finite element method (xfem), which has been previously applied to concrete-like materials. the main feature of the proposed approach is that the cracking process is not treated as a local process, but it is modeled by assuming that macro-cracks stem from the interaction of micro-cracks within a finite width process zone. the case of a brittle materials with thin process zone is tackled by assuming one layer of enriched finite elements. preliminary results concerning pmma specimens subjected to mode-one loading are presented. keywords. static failure criteria; pmma; xfem. introduction harp notches in tensile structural elements trigger crack initiation and influence the global load bearing capacity. hence the necessity of formulating reliable and effective static failure criteria for structures with sharp notches emerges. in particular, if the case of notched components made of brittle materials is considered, criteria based on the evaluation of the local maximum value of a stress scalar fail, owing to the presence of infinite values of the stress field components. as argued by neuber [1], effective static fracture criteria can be introduced by assuming that crack initiation is governed by volume, or surface, averages of the local stress scalar field, which is most representative of the expected failure mode. for instance, seweryn [2] proposed a criterion based on the evaluation on the maximum value of the stress scalar, which is obtained by averaging the stress component normal to the crack direction along the crack path. a further extension of this approach can be envisaged in the critical distance criteria proposed by taylor et al. [3]. the introduction of volume averages of stress scalars can be alternatively interpreted as the adoption of a non-local fracture criterion, where the critical value of a certain scalar field at a point depends not only on the local value of that field at the current point, but also on the values that the scalar field reaches at the surrounding points [4, 5]. the non-local continuum concept has been especially exploited in the numerical analysis of components made of elasto-damaging materials. specifically, two variants of non-local models have been intensively used: integral models and gradient models. inspired by the approach proposed by peerlings et al. [6], tovo et al. [7, 8] proposed an implicit gradient static failure criterion which is very reliable, as it can be easily implemented by using standard tools for solving partial differential equations within usual finite element codes. an advantage of the implicit gradient static failure criterion is that the nonlocal equivalent stress can be obtained over the entire spatial domain without a priori assumption of the position of the critical points [7]. an alternative approach to overcome the stress singularity at the crack tip is represented by the adoption of a cohesive crack model [9-11]. in the cohesive crack model, a traction-separation law is introduced along the crack path. the s http://www.gruppofrattura.it http://dx.medra.org/10.3221/igf-esis.17.03&auth=true e. benvenuti et alii, frattura ed integrità strutturale, 17 (2011) 23-31; doi: 10.3221/igf-esis.17.03 24 cohesive crack approach can be extended to rounded notches and makes it possible to deal with non-linear materials. a limitation of the cohesive-crack models is that the crack path has to be placed along the element boundaries. therefore, the crack geometry depends on the mesh topology. this drawback can be overcome by adopting the extended finite element method (xfem) method which has been developed by belytschko and coworkers [12]. xfem makes it possible to consider crack paths, which are embedded within the finite elements. xfem is based on the partition of unity property of the polynomial shape functions, which are used in standard finite element analyses. for instance, in the case of crack problems, where a displacement discontinuity has to be simulated, the standard piecewise continuous approximation of the displacement field is enriched by additional terms, which contain the heaviside function. more recently, enhanced xfem approaches have been proposed were the truncated series of william’s expansion of the displacement field are considered as enrichment functions [13-15]. in quasi-brittle materials, experimental evidence shows that macro-cracks stem from the interaction if micro-cracks distributed within a zone of finite width, called fracture process zone (e.g. [16]). benvenuti et al. [17-19] have proposed a modified xfem approach which is based on the use of regularized enrichment functions. in particular, the discontinuous step function is replaced by a regularized heaviside function where a regularization length is introduced. a cohesive-like stress field emerges along the crack path which is always non singular and smooth. the smoothing effect on the stress field increases for increasing values of the regularization length. in the present study, a static failure criterion based on the regularized xfem approach is applied to the analysis of the tensile pmma specimens previously proposed by seweryn [2]. the pros and cons of the present approach are discussed. basics of the proposed extended finite element formulation et us consider a tensile specimen with a sharp notch. the displacement field is supposed to exhibit a jump  u u across a line ds starting from the notch tip. the vector field n normal to ds is introduced. let us discretize the geometry through en finite elements with nn nodes, and introduce the regularized heaviside function   ( ) /( ( ))(1 )  s x ρh x sign s x exp (1) where ( )s x denotes the signed distance function from the displacement discontinuity defined as ( ):s  x x x if ( ) 0  x x n x and ( )s   x x x if ( ) 0  x x n x . a picture of the regularized heaviside function is given in fig. 2 for various . figure 1: tensile element with a notch. according to the regularized xfem formulation recently proposed by benvenuti et al. [17-19], the displacement field can be expressed as l http://www.gruppofrattura.it http://dx.medra.org/10.3221/igf-esis.17.03&auth=true e. benvenuti et alii, frattura ed integrità strutturale, 17 (2011) 23-31; doi: 10.3221/igf-esis.17.03 25   1 1 ( ) ( ) ( ) ( ) ( )      n n ρ i i i ρ i i i u x n x v x n x h x a x (2) where: in represents the i-th standard polynomial shape function of the usual finite element approximation, iv is the i-th standard degree of freedom representative of the continuous part of the displacement field. finally, ia denotes the i-th enriched degree of freedom. figure 2: regularized heaviside function and corresponding gradient for various . figure 3: micro-cracks density function  obtained by differentiation of h . after collecting the shape functions into the matrix n and the degrees of freedom iv and ia into vectors v and a , the displacement field writes   ( ) ( ) ( ) ρ ρu x n x v n x h x a (3) the compatible strain is calculated by differentiation of displacement ρ u in the following way ( ) ( ) ( ) ( )( ( ) )      ρ ρ ρu n x v n x h x a δ x n n x a (4) where h   n and ( ) ( | ( ) | / ) ρδ x exp s x ρ http://www.gruppofrattura.it http://dx.medra.org/10.3221/igf-esis.17.03&auth=true e. benvenuti et alii, frattura ed integrità strutturale, 17 (2011) 23-31; doi: 10.3221/igf-esis.17.03 26 in particular, the form of the function  , which is displayed in fig. 4, reproduces the distribution of micro-cracks within the process zone which is often recognized in quasi-brittle materials [16]. the presence of a regularization parameter introduces a characteristic length within the present xfem formulation. after introduction of the compatibility operator  b n and n such that ( ( (x) )) n n an a , three distinct strain fields ( ) ( )ε x b x v (5.1) ( ) ( ) ( )ρ ρε x h x b x a (5.2) ( ) ( ) ( )cρ ρε x δ x n x a (5.3) can be introduced. they are kept distinguished because they play a different mechanical role within the model. in particular, the stress field ε is the standard strain field in the absence of the discontinuity. the strain field ρε is related to the spatial variation of the jump intensity, while cρε represents the localized strain field resulting from the micro-cracks distributed within the process zone. independent stress fields are associated with each strain field by means of the following constitutive laws ( ) (1 ) ( ) σ x d e b x v (6.1) ( ) ( )(1 ) ( ) ρ ρσ x h x d e b x a (6.2) ( ) (1 ) ( ) cρ c cσ x d e n x a (6.3) figura 4: microcrack density distribution according to mihashi and nomura [16]. where d and dc are isotropic damage scalar parameters which govern the degradation of the elasticity matrices e and ce . a detailed explanation of the transition strategy from a continuum damage description to the regularized discontinuous description can be found in benvenuti (2011). the key point of the transition procedure is that, as soon as the bulk damage parameter d has reached a critical value, crd , the damage cd is activated. in particular, for a loading history described by the pseudo-time parameter t, the evolution of the damage parameter cd is governed by the following loading unloading conditions , 0, 0, 0      eff c cφ σ r φ d φd (7) the effective stress scalar eff selects the positive value of the maximum principal stress max of the stress field c ρ σ eff maxσ σ (8) http://www.gruppofrattura.it http://dx.medra.org/10.3221/igf-esis.17.03&auth=true e. benvenuti et alii, frattura ed integrità strutturale, 17 (2011) 23-31; doi: 10.3221/igf-esis.17.03 27 the damage is calculated as  0( ),1 ( , ( ) ) [0, )        c cr eff q r d max d r max r max σ t t r (9) where q is an internal variable defined as 0 0 0 0 ( ) ( 2 )     s r r q r r exp h r r r (10) and 0r is an initial threshold, which is set equal to the maximum tensile stress, which can be deduced from the experiments. the variational formulation which has been adopted makes it possible to recover standard cohesive model for vanishing regularization length. moreover, the ductility of the computed structural paths turns out being proportional to  itself. details can be found in previous references [17-19]. figura 5: thin process zone enrichment. the enrichment strategy is general: it can be applied to both the cases of thin and thick process zone. more precisely, the width of the enrichment layer can be larger than a single layer of finite elements. in this case, the model can be seen as an xfem with cohesive crack. alternatively, the width of the enriched volume can be larger than a single layer of finite elements, similarly to what happens in a non-local integral model. the enrichment strategy has been thoroughly discussed in a previous reference [17]. in the present preliminary analysis, the analysis is applied to very brittle materials such as the pmma. to this purpose, only one layer of finite elements has been enriched, as shown in fig. 4, where represents the width of the truncated support of function in the present analyses contributions of gauss points placed at distances larger than 20 were neglected. moreover, the nodes marked with a red square indicate the enriched nodes, while the nodes which are not enriched are indicated by a green circle. the enriched elements have been indicated in light gray. numerical results he pmma tensile specimen experimentally tested by seweryn [2] has been considered (fig. 6).the width w is 109 mm, while the thickness is equal to 4 mm. the notch depth a = 27 mm. in view of the symmetry of both geometry and loading, only one half of the specimen was studied. a plane stress two-dimensional analysis was performed. the constitutive law for the pmma, which is shown in fig. 7 for the one-dimensional case, has been adopted according to the material parameters given in seweryn (1994). in particular, young modulus e=3200 mpa, poisson coefficient equal to 0.4 and a maximum effective stress 105 mpa have been taken. t http://www.gruppofrattura.it http://dx.medra.org/10.3221/igf-esis.17.03&auth=true e. benvenuti et alii, frattura ed integrità strutturale, 17 (2011) 23-31; doi: 10.3221/igf-esis.17.03 28 figure 6: tensile specimen geometry after seweryn (1994). the limit tensile stress which was indicated by seweryn is 105 mpa. as soon as the bulk reaches the critical damage 0.01crd  , the continuous-discontinuous transition is activated. figure 7: constitutive law of the ppma which has been adopted in the numerical tests. the meshes which were adopted are refined in the central zone as shown in fig. 8. a minimal value of the finite element size h=0.1 mm was used for all opening angles (semi-opening angle  = 10, 20, 30, 40, 50, 60, 70 degrees). in the case of a tensile plate made of a softening materials, it was shown in benvenuti [19], that the optimal value of the parameter  which leads to optimal convergence is  = 1/13.33 h which in the present case leads to  = 0.0075 mm. in order to check the ability of the method to effectively approximate the experimental failure loads, a unique value of the ratio between the minimal mesh size h and the parameter  was adopted for all meshes. in order to identify the optimal value of the regularization length  , the following values have been adopted:  = 0.0001, 0.002, 0.0075, 0.01 mm. the critical failure load versus half the opening angle of the notch are displayed in fig. 8. in particular, the value of  = 0.0001 mm leads to divergent results, while the value  = 0.0075 mm leads to the best approximation. fig. 10 shows the computed failure loads for various opening angles and the experimental values from seweryn [2] by using  = 0.0075 mm. http://www.gruppofrattura.it http://dx.medra.org/10.3221/igf-esis.17.03&auth=true e. benvenuti et alii, frattura ed integrità strutturale, 17 (2011) 23-31; doi: 10.3221/igf-esis.17.03 29 figure 8: detail of the mesh refinement for 2=20 deg. figure 9: profiles of the predicted failure loads for variable : divergence for =0.0001mm (red dashed line), green dashed line: =0.01mm, blue dashed dotted =0.0075 mm, ciano continuous line: =0.002mm; circles indicate experimental results. figure 10: comparison of the static failure loads obtained with the present approach (blue continuous line) with the experimental results presented in [2]. http://www.gruppofrattura.it http://dx.medra.org/10.3221/igf-esis.17.03&auth=true e. benvenuti et alii, frattura ed integrità strutturale, 17 (2011) 23-31; doi: 10.3221/igf-esis.17.03 30 for an opening angle 2 20 deg  , fig. 11 displays the map of the total stress component yy in a deformed configuration, which was obtained by using a magnification factor equal to 100. in figs. 12 and 13, respectively, the total stress map and the profiles of the relevant stress components are reported. in particular, the black cross markers indicate the values of the total stress component at the gauss points placed along the crack line, while the regularized stress c are marked with red dots. it can be noted that the total strain attains its maximum value 105 mpa at the notch tip. because, the enrichment extends over a length of 3 mm beyond the notch tip, a new stress singularity is there detected. an extension of the present approach to other non-linear constitutive laws is possible. however, in xfem based approaches, in general, a crack tracking criterion has to be adopted in order to avoid that secondary multiple cracks open. this is a requirement common to embedded discrete-crack approaches. in the implicit gradient approach, instead, no hypotheses on the position of the critical points are necessary, because the effective stress is computed by post-processing the results, which are obtained by means of any standard finite element formulation of a continuum model. an advantage of the present approach over existing cohesive models is that, here, the bulk constitutive law of the material can be directly assumed, because the process zone behavior is not modeled by means of a traction-separation law. instead, the stress and strain fields cσ and c ε are introduced, which can be modeled with same constitutive law of the bulk. figure 11: stress map in the deformed mesh for 2=20 obtained with a magnification factor 100. figure12: total stress map for 2=20. conclusions n the present note, a new approach based on a length-enriched extended finite element method (xfem) has been applied to the evaluation of the failure loads of tensile pmma specimens. in particular, a comparison with the experimental results presented by seweryn [2] has been performed. the present analysis shows that the proposed i http://www.gruppofrattura.it http://dx.medra.org/10.3221/igf-esis.17.03&auth=true e. benvenuti et alii, frattura ed integrità strutturale, 17 (2011) 23-31; doi: 10.3221/igf-esis.17.03 31 method makes it possible not only to avoid stress singularities but also to lead to a satisfying approximation of the experimental failure loads. in order to fully assess the effectiveness of the proposed method, further investigations are required, such as the study of mixed loading modes. the present approach has the same potential of cohesive models without the need of inserting the crack line along the element boundaries. moreover, it can be easily used to deal with general non-linear constitutive laws. figure 13: profiles of the total stress field and the regularized stress c along the crack line for 2=20 deg. references [1] h. neuber, konstruktion, 20 (1968) 245. [2] a. seweryn, engineering fracture mechanics, 47 (1994) 673. [3] l. susmel, d. taylor, international journal of fatigue, 28 (2006) 417. [4] d.g.b. edelen, continuum physics, vol. iv academic press, new york, (1976) 75. [5] c.a. eringen, d.g.b. edelen, international journal of engineering science, 10 (1972) 233. [6] r. h. j. peerlings, m.g.d. geers, r. de borst, w.a.m. brekelmans, int. j. solids structures, 38 (2001) 7723. [7] r. tovo, p. livieri, e. benvenuti, international journal of fracture, 141 (2006) 497. [8] r. tovo, p. livieri, engineering fracture mechanics, 74 (2007) 515. [9] f.j. gomez, m. elices, engineering fracture mechanics, 70 (2003) 1913. [10] j. planas, m. elices, g. v. guinea,f. j.gómez, d. a. cendón, i. arbilla, engineering fracture mechanics, 70 (2003) 1759. [11] a. cornec, i. scheider, k. h. schwalbe, engineering fracture mechanics, 70 (2003) 1963. [12] n. moes, t. belytschko, engineering fracture mechanics, 69 (2002) 813. [13] b. l. karihaloo, q. z. xiao, international journal of fracture, 150 (2008) 55. [14] x. y. liu, q. z. xiao, b. l. karihaloo, international journal for numerical methods in engineering, 59 (2004) 1103. [15] j. réthoré, s. roux, f. hild, international journal for numerical methods in engineering, 81 (2010) 269. [16] h. mihashi, n. nomura, nuclear engineering and design, 165 (1996) 359. [17] e. benvenuti, computer methods in applied mechanics and engineering, 197 (2008) 4367. [18] e. benvenuti, a. tralli, g. ventura, international journal for numerical methods in engineering, 74 (2008) 1097. [19] e. benvenuti, mesh-size-objective xfem for regularized continuous/discontinuous transition, accepted for publication on finite element analysis and design (2011). http://www.gruppofrattura.it http://dx.medra.org/10.3221/igf-esis.17.03&auth=true microsoft word numero_40_art_1 m. a. meggiolaro et alii, frattura ed integrità strutturale, 41 (2017) 1-7; doi: 10.3221/igf-esis.41.01 1 focused on multiaxial fatigue a two-step multiaxial racetrack filter algorithm for non-proportional load histories marco antonio meggiolaro, jaime tupiassú pinho de castro pontifical catholic university of rio de janeiro, puc-rio, r. marquês de são vicente 225, rio de janeiro, 22451-900, brazil meggi@puc-rio.br, jtcastro@puc-rio.br hao wu school of aerospace engineering and applied mechanics tongji university, siping road 1239, 200092, shanghai, p.r.china wuhao@tongji.edu.cn abstract. the recently proposed multiaxial racetrack filter (mrf) is able to deal with general non-proportional multiaxial load histories. while only requiring a single user-defined scalar filter amplitude, the mrf is able to synchronously eliminate non-damaging events from any noisy multiaxial load history without changing the overall shape of its original path, a necessary condition to avoid introducing errors in fatigue damage assessments. the mrf procedures are optimized here by the introduction of a pre-processing “partitioning” step on the load history data, which selects candidates for the reversal points in a robust partitioning process, highly increasing the filter efficiency and decreasing its computational time. the improved mrf is evaluated through the fatigue analyses of over-sampled tension-torsion data measured in 316l stainless steel tubular specimens under non-proportional load paths. keywords. multiaxial racetrack filter (mrf); partitioning operation; multiaxial variable amplitude loading; amplitude filter. citation: meggiolaro, m.a., castro, j.t.p., wu, h., a two-step multiaxial racetrack filter algorithm for non-proportional load histories, frattura ed integrità strutturale, 41 (2017) 17. received: 28.02.2017 accepted: 15.04.2017 published: 01.07.2017 copyright: © 2017 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. introduction atigue load histories measured under actual field conditions usually are noisy, over-sampled, and contain too many non-damaging low-amplitude events that can largely increase the subsequent fatigue damage calculation burden. this problem has long been recognized and properly dealt with in traditional uniaxial analyses, but it is still much more important for multiaxial fatigue damage calculations, which can even become impractical if not properly filtered to remove from the data non-damaging events before performing such complex calculations, in particular under nonproportional (np) loading conditions, so common in practical applications. f m. a. meggiolaro et alii, frattura ed integrità strutturale, 41 (2017) 1-7; doi: 10.3221/igf-esis.41.01 2 consequently, a most important practical issue in multiaxial fatigue analyses is how to reduce a large amount of redundant multiaxial data to a manageable size to decrease their intrinsically high computational cost, while maintaining all the essential features of the load history that contribute to plasticity memory effects. needless to say, this is an unavoidable step to not underestimate fatigue damage, an inadmissible feature in practical applications. uniaxial amplitude filters can be directly implemented in the cycle counting algorithm, usually based on the rainflow method [1-4]. but the original rainflow procedure can only be started after the entire load history is known, increasing even more the computational cost as well as computer memory requirements, which can be quite significant for very long histories. computational cost can be dramatically reduced with ‘‘real-time” rainflow algorithms, such as the pioneer martin–topper–sinclair’s 1971 method [5], which essentially reproduces in real time the uniaxial rainflow algorithm as the load events are provided or measured. the original racetrack filter, proposed by fuchs et al. in 1973 [6], can sequentially filter small amplitudes, but it is limited to uniaxial histories. simplistic amplitude filters based on the uniaxial racetrack are not recommended in multiaxial analyses, because the path between two load reversals is needed to evaluate the path-equivalent stress or strain amplitude associated with each rainflow count, e.g. using a convex-enclosure method [7, 8]. moreover, the reversal points obtained from a multiaxial rainflow algorithm might not occur at the reversal of one of the stress or strain components [9]. in this work, a multiaxial version of the racetrack filter proposed by the authors in [10-13] is reviewed and optimized. while only requiring a single user-defined scalar filter amplitude, it is able to synchronously filter complex loading histories while preserving all key features of the loading path. the filtering process is optimized through the introduction of a pre-processing “partitioning” operation on the load history data, highly increasing its efficiency. over-sampled experimental data from tension-torsion experiments in 316l stainless steel tubular specimens under np load paths are used to verify the efficiency and robustness of the proposed method. the multiaxial racetrack filter (mrf) n the multiaxial racetrack filter (mrf) algorithm originally proposed in [10], the load history path must first be represented in an appropriate stress or strain space. several spaces were proposed in [11], some of them separating the stresses or strains in their deviatoric and hydrostatic components, to allow for a filtering metric based on mises equivalent values or even damage parameters. fig. 1 shows an example of a tension-torsion loading following an elliptical stress path, represented in a normal vs. effective shear stress space x  xy3 through a series of 238 over-sampled points (for each periodic cycle), represented as “” marks. however, spaces with higher dimensions would be necessary for general 6d multiaxial load histories. several of these points could be filtered out without compromising the subsequent multiaxial fatigue life calculations. this amplitude-filtering process is a most desirable step in practical applications, to eliminate unavoidable measurement noise and redundant over-sampled data, as well as small amplitudes that do not cause fatigue damage [12]. but it is important to avoid filtering out important counting points from multiaxial rainflow algorithms, or significant history paths that can affect the calculation of a path-equivalent stress or strain, since all stress or strain components contribute altogether for the reversals that can be eliminated. the mrf requires a user-defined scalar filter amplitude r, which is graphically represented in fig. 1 as the radius of the small dashed circle centered at point 1. in this example, r  80mpa was chosen as the amplitude, which in the x  xy3 space has a clear physical meaning: r is the mises distance between two stress states, due to the adopted 3 scaling factor used in the shear component. the mrf algorithm, thoroughly described in [10-13], was able to reduce the 238 oversampled measurements to only 8, guaranteeing that no filtered-out data lies beyond r  80mpa of the resulting polygonal path 1-2-3-4-5-6-7-8-1. this filtering process results in a dramatic decrease of the computational time needed for further multiaxial fatigue life calculations, especially considering that the original 238 points were from a single elliptical path. more refined outputs can be achieved simply by reducing the user-defined value of the (combined) amplitude filter r. for instance, in the above example, r  5mpa would better describe the elliptical shape of the original stress path, but it would need 31 points instead of 8 to represent it; still, 31 is much better than the original 238 points per cycle. the filter amplitude r can also be varied as a function of the instantaneous normal stresses, to better consider mean and peak-stress effects, as discussed in [12]. moreover, the mrf also works with non-periodic load histories, using the same algorithm. i m. a. meggiolaro et alii, frattura ed integrità strutturale, 41 (2017) 1-7; doi: 10.3221/igf-esis.41.01 3 figure 1: application of the mrf on a tension-torsion x  xy3 history, adopting a filter amplitude r = 80mpa. it is important to note that the mrf does not filter out load reversals, which can be interpreted as sudden changes in path direction of more than 90 degrees. this is a major advantage over simplistic algorithms such as the “peaks procedure” [14], which filters out all points (events) whose components are not peaks or valleys. this non-conservative procedure potentially eliminates important load points that could have the highest mises stresses or strains of the load history, even though each individual load component was not maximized. moreover, the “peaks procedure” stores each and every event that constitutes a peak or valley from any single component, which for (unavoidably noisy) real measurements could result in no events at all being filtered out, even if the noise had very low amplitudes. despite its efficiency and robustness, the mrf can still be optimized to better describe the original path using the same number of sampling points. for instance, in fig. 1 it can be seen that the segment 4-5 faithfully describes the original sampled points, however the segments 6-7 and 7-8 do not reproduce well the originally curved path. one way to improve this issue is to use a smaller filter amplitude, lower than the adopted r = 80mpa, however at a cost of filtering out fewer points, requiring more than 8 to represent the load path in this case. a more efficient way is proposed next, where a preprocessing “partitioning” operation is performed on the original sampled points, resulting in a better description of the path with fewer data points. mrf optimization through partitioning efore applying the mrf algorithm, it is here proposed to perform an improved pre-processing “partitioning” operation on the multiaxial load history data, described as follows. the first step involves choosing the first sample point of the multiaxial load history, tagged with the number 1. for periodic histories, point 1 can be any point from the cyclic load path, see fig. 2(a). then, find the sampled point most distant to 1, labeling it as 2, creating two partitions of the original sample points, defined by the paths {12} and {21}. in the considered tension-torsion example in the x  xy3 space, point 2 results in the one with the highest relative mises stress range with respect to point 1. if more than one point has the same maximum distance from 1, then choose any one of them to become point 2, ignoring the others. note however that, for non-periodic load histories, points 1 and 2 should be simply defined as the first and last ones from the entire history, respectively. -500 0 500 -400 -300 -200 -100 0 100 200 300 400 normal stress (mpa) e ff e c tiv e s h e a r s tr e s s ( m p a ) 1 2 3 4 5 6 7 8 b m. a. meggiolaro et alii, frattura ed integrità strutturale, 41 (2017) 1-7; doi: 10.3221/igf-esis.41.01 4 figure 2: improved partitioning operation on tension-torsion data, showing: (a) joining the previously defined points 1 and 2 of the load history with a straight line; (b) finding the load points 3 and 4 most distant from this line, creating two partitions; (c) finding the points most distant to each segment to subdivide it into additional segments; and (d) continuing the process until reaching the chosen filter amplitude value. the next step of the pre-processing involves joining points 1 and 2 with a straight line, and then finding the load points 3 and 4 most distant from it. note that point 3 lies in the 12 path whereas point 4 lies in the 21, as shown in fig. 2(b). since this maximum distance is higher than the chosen filter amplitude r, create further partitions {13}, {32}, {24} and {41} of the original path, see fig. 2(b). next, look for the load point in the {13} partition that is most distant from the straight line joining 1 and 3; if this maximum distance is higher than r, then create additional two partitions {15} and {53} from {13}, see fig. 2(c). analogously, look for the load point in the {32} partition that is most distant from the straight line joining 3 and 2; if this maximum distance is higher than r, then create two partitions {36} and {62} from {32}. the process continues for the remaining partitions, as long as the associated maximum distance is still higher than r. the pre-processing process continues for all created partitions, ending only when all such maximum distances are not higher than the chosen filter amplitude r. consequently, each of the resulting partitions is such that all points it contains are within a distance r of the straight line joining its extremes. note that the remaining sample points that were not labeled are not yet eliminated, because they could contain load reversions that are not detected in this pre-processing step, as discussed later. -500 -400 -300 -200 -100 0 100 200 300 400 500 -400 -300 -200 -100 0 100 200 300 400 normal stress (mpa) e ff e c tiv e s h e a r s tr e s s ( m p a ) -500 -400 -300 -200 -100 0 100 200 300 400 500 -400 -300 -200 -100 0 100 200 300 400 normal stress (mpa) e ff e c tiv e s h e a r s tr e s s ( m p a ) -500 -400 -300 -200 -100 0 100 200 300 400 500 -400 -300 -200 -100 0 100 200 300 400 normal stress (mpa) e ff e c tiv e s h e a r s tr e s s ( m p a ) -500 -400 -300 -200 -100 0 100 200 300 400 500 -400 -300 -200 -100 0 100 200 300 400 normal stress (mpa) e ff e ct iv e s h e a r s tr e ss ( m p a ) 2 1 2 1 3 4 2 1 3 4 6 5 8 7 2 1 3 4 6 5 8 7 13 9 11 15 12 10 16 14 (a) (b) (c) (d) m. a. meggiolaro et alii, frattura ed integrità strutturale, 41 (2017) 1-7; doi: 10.3221/igf-esis.41.01 5 in the studied tension-torsion example, this partitioning results in the 8 points from fig. 2(c) for r  80mpa. note how the resulting polygonal path better represents the original history than the one from fig. 1, where no pre-processing had been performed, using the same number of points. fig. 2(d) shows the partitioning results if the filter amplitude is refined adopting r  5mpa, resulting in 16 points per cycle, but with a better description of the load path. after (and only after) the pre-processing partitioning ends, the mrf is individually applied to each partition, with a filter surface translation direction [10-12] defined from the extremes of each partition. for instance, for r  80mpa, the partitioning output shown in fig. 2(c) would require the application of the mrf on the points in the {15} path, starting from 1 and with a filter surface translation direction defined by the segment 15; then apply the mrf again in the {53} path, starting from 5 and in the 53 direction; and so on, until processing the segment {81}. in this particular example, all non-labelled sample points ended up filtered out by the mrf, but this might not be the case in more complex paths, as exemplified below. as a result, the output of the mrf will consist of all load points (from all partitions) that did not suffer static or dynamic filtering. this combination of partitioning followed by the mrf is very efficient, resulting in quasi-optimal filtered histories for a given r, without the need to arbitrarily define or optimize the hyper-sphere translation directions [10-12] in higher-dimensional cases. fig. 3 shows a more complex np tension-torsion stress path that needs both partitioning and mrf steps to properly filter its 488 sample points (per cycle) without losing significant load reversions. point 1 is arbitrarily chosen as the initial one in the tension-torsion cycle, and a filter amplitude of r = 80mpa is considered (graphically represented as the radius of the dashed circle around point 1). the pre-processing step then finds point 2 as the most distant from 1. points 3 and 4 are then the ones most distant from the 12 straight line, both with distances greater than r = 80mpa. since all points in the {13} path are within r = 80mpa of the straight segment 13, no further points are selected in this portion. the same applies for the {32}, {24} and {41} portions of the load path, ending the pre-processing step with only 4 identified points, marked with squares in fig. 3. the mrf is then individually applied to each of these portions, using the same filter amplitude r = 80mpa, to be able to identify the important load reversal points 5, 6, 7, 8, 9 and 10, marked with triangles in fig. 3. note that a few load reversal points are purposely not identified, such as the ones in the {41} path, because their associated oscillation amplitudes are smaller than the chosen r = 80mpa, a desirable feature that the simplistic “peaks procedure” [14] would not be able to reproduce. figure 3: tension-torsion load path with 488 sample points per cycle, where the partitioning operation identifies points 1 through 4, followed by the application of the mrf in each partition to identify points 5 through 10, adopting a filter amplitude r = 80mpa. -400 -300 -200 -100 0 100 200 300 400 -300 -200 -100 0 100 200 300 normal stress (mpa) e ff e c tiv e s h e a r s tr e s s ( m p a ) 1 2 3 4 5 6 7 8 9 10 m. a. meggiolaro et alii, frattura ed integrità strutturale, 41 (2017) 1-7; doi: 10.3221/igf-esis.41.01 6 experimental verification o verify the efficiency of the optimized mrf, tension-torsion experiments are performed on annealed tubular 316l stainless steel specimens in an mts 809.25 multiaxial testing machine, shown in fig. 4(a). a relatively thin wall of 2mm is used for the tubular specimens, to avoid having to deal with stress gradient effects across its thickness. engineering stresses and strains are calculated from load/torque cell measurements and from an mts 632.68 axial/torsional extensometer, and then converted to true stresses and strains [13]. the cyclic properties of this 316l steel are obtained from uniaxial tests, resulting in fitted ramberg-osgood uniaxial cyclic hardening coefficient 874mpa and exponent 0.123, with young’s modulus 193gpa, poisson ratio 0.3, and shear modulus 74gpa. (a) (b) figure 4: (a) tension-torsion testing machine and extensometer mounted on a tubular specimen; (b) applied x×xy/3 strain paths. the tests consist of strain-controlled x×xy/3 tension-torsion cycles applied to the tubular specimens, following the very challenging cyclic path sequence oabhaocbdcoedfeoghfgo, see fig. 4(b). fig. 5 shows the resulting experimentally measured stabilized σ×τ3 stress path (samples with  markers), as well as the optimized mrf output including the proposed pre-processing step (square markers) for a filter amplitude r = 15mpa. the measured σ×τ3 stress paths are reduced from 1227 data points per cycle to only 52, showing a very good agreement in both ranges and shape. notice that, despite being highly filtered, the optimized mrf outputs can almost exactly describe the original multiaxial load history, capturing not only all reversal points but also the load path shape, which is a most important feature for path-equivalent range calculations used in fatigue damage assessments. conclusions in this work, an optimized version of the multiaxial racetrack filter (mrf) was proposed, applicable to general nonproportional multiaxial histories. the mrf preserves load order, allowing the synchronous filtering of stress and strain histories, without filtering out important multiaxial load reversal points. the optimized version is based on a preprocessing step that selects candidates for the reversal points, in a robust partitioning process. the filter efficiency was validated from tension-torsion experiments following complex non-proportional histories, without losing information on significant reversals, ranges or load path shapes. x xy / 3 aa a a b a hf o cd e g t m. a. meggiolaro et alii, frattura ed integrità strutturale, 41 (2017) 1-7; doi: 10.3221/igf-esis.41.01 7 figure 5: experimentally measured data points ( markers) and the optimized mrf output (square markers) including the preprocessing partitioning with r = 15mpa. references [1] anthes, r.j., modified rainflow counting keeping the load sequence, int j fatigue, 19 (1997) 529-535. [2] astm e 1049. standard practices for cycle counting in fatigue analysis. astm international. [3] downing, s.d., socie, d.f. simple rainflow counting algorithms. int j fatigue 4 (1982) 31-40. [4] bannantine, j.a., socie, d.f. a variable amplitude multiaxial fatigue life prediction method, fatigue under biaxial and multiaxial loading, esis publ. 10 (1991) 35-51. [5] martin, j.f., topper, t.h., sinclair, g.m. computer based simulation of cyclic stress-strain behavior with applications to fatigue. materials research and standards, mtrsa, 11 (1971) 23-28. [6] fuchs, h.o., nelson, d.v., burke, m.a., toomay, t.l. shortcuts in cumulative damage analysis. sae automobile engineering meeting paper 730565 (1973). [7] dang van, k., papadopoulos, i.v. high-cycle metal fatigue, springer (1999). [8] freitas, m., li, b., santos, j.l.t. multiaxial fatigue and deformation: testing and prediction. astm stp 1387 (2000). [9] meggiolaro, m.a., castro, j.t.p. an improved multiaxial rainflow algorithm for non-proportional stress or strain histories part ii: the modified wang-brown method, int j fatigue 42 (2012) 194-206. [10] meggiolaro, m.a., castro, j.t.p., shortcuts in multiple dimensions: the multiaxial racetrack filter, frattura e integrità strutturale 33 (2015), 368-375. doi 10.3221/igf-esis.33.40. [11] wu, h., meggiolaro, m.a., castro, j.t.p. validation of the multiaxial racetrack amplitude filter, int j fatigue, 87 (2016), 167-179. doi 10.1016/j.ijfatigue.2016.01.016 [12] meggiolaro, m.a., castro, j.t.p., wu, h. incorporation of mean/maximum stress effects in the multiaxial racetrack filter, frattura e integrità strutturale, 38 (2016), 67-75. doi 10.3221/igf-esis.38.09 [13] castro, j.t.p., meggiolaro, m.a. fatigue design techniques, volume 2: low-cycle and multiaxial fatigue. create space 2016. isbn 1530797047. [14] bannantine, j.a. a variable amplitude multiaxial fatigue life prediction method. fcp report n.151, university of illinois at urbana-champaign (1989). << /ascii85encodepages false /allowtransparency false /autopositionepsfiles true /autorotatepages /none /binding /left /calgrayprofile (dot gain 20%) /calrgbprofile (srgb iec61966-2.1) /calcmykprofile (u.s. web coated \050swop\051 v2) /srgbprofile (srgb iec61966-2.1) /cannotembedfontpolicy /error /compatibilitylevel 1.4 /compressobjects /tags /compresspages true /convertimagestoindexed true /passthroughjpegimages true /createjobticket false /defaultrenderingintent /default /detectblends true /detectcurves 0.0000 /colorconversionstrategy /cmyk /dothumbnails false /embedallfonts true /embedopentype false /parseiccprofilesincomments true /embedjoboptions true /dscreportinglevel 0 /emitdscwarnings false /endpage -1 /imagememory 1048576 /lockdistillerparams false /maxsubsetpct 100 /optimize true /opm 1 /parsedsccomments true 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/hrv (za stvaranje adobe pdf dokumenata najpogodnijih za visokokvalitetni ispis prije tiskanja koristite ove postavke. stvoreni pdf dokumenti mogu se otvoriti acrobat i adobe reader 5.0 i kasnijim verzijama.) /hun 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/pdfxoutputintentprofileselector /documentcmyk /preserveediting true /untaggedcmykhandling /leaveuntagged /untaggedrgbhandling /usedocumentprofile /usedocumentbleed false >> ] >> setdistillerparams << /hwresolution [2400 2400] /pagesize [612.000 792.000] >> setpagedevice microsoft word numero_28_art_1 p. valentino et alii, frattura ed integrità strutturale, 28 (2014) 1-11; doi: 10.3221/igf-esis.28.01 1 mechanical characterization of basalt woven fabric composites: numerical and experimental investigation piergiorgio valentino, emanuele sgambitterra, franco furgiuele university of calabria, department of mechanical, energy and management engineering, ponte p. bucci, 44c, 87036 rende (cs), italy marco romano, ingo ehrlich university of applied sciences regensburg, department of mechanical engineering, laboratory for composite technology, galgenbergstrasse 30, 93053 regensburg, germany norbert gebbeken university of the bundeswehr munich, institute for engineering mechanics and structural mechanics, werner-heisenbergweg 39, 85577 neubiberg, germany abstract. basalt fabric composite, with different twill wave reinforcements, i.e. twill 2/2 and twill 1/3, have been studied in this work by means of experimental tests and numerical finite element (fe) simulations. as fabric reinforcements show repeating undulations of warp and fill yarn, simple mixtures law cannot be applied. as a consequence, the mesoscopic scale, lying between the microscopic and the macroscopic one, has to be taken into account to mechanically characterize a fabric reinforced composite. the aim of this work is to evaluate the stiffness of a fabric reinforced composite in warp and fill direction. in particular a numerical fe model, assuming elliptical sections and sinusoidal shape of the yarns, has been implemented and experimental tests have been carried out in order to validate the proposed model. finally, the strength and the failure modes of the composite material, for each analysed structure and textile orientation, have been experimentally investigated. sommario. diverse tipologie di tessuti compositi con fibre di basalto, i.e. tessitura 2/2 e tessitura 1/3 con fibre di basalto sono stati studiati in questo lavoro mediante prove sperimentali e simulazioni agli elementi finiti (fe). poiché i tessuti rinforzanti sono caratterizzati da ondulazioni ripetute di trama e ordito la semplice legge delle misture non può essere applicata. per questo motivo la scala mesoscopica, via di mezzo tra quella microscopica e macroscopica, è utilizzata per la caratterizzazione meccanica di questa tipologia di compositi. scopo del presente lavoro è quello di determinare la rigidezza sia nella direzione della trama che in quella dell’ordito dei compositi rinforzati con tessuti. in particolare è stato implementato un modello numerico agli elementi finiti, (fe) realizzato ipotizzando le sezioni dei fasci di forma ellittica e con andamento sinusoidale e i risultati ottenuti sono stati validati mediante confronto sperimentale. infine, si è investigato sulla resistenza e il modo di cedimento del materiale composito, per ogni struttura analizzata ed orientazione del tessuto. keywords. basalt fibre, basalt fibre reinforced plastic, fabric reinforcement, woven fabric, tensile testing, representative volume element (rve). http://www.gruppofrattura.it http://dx.medra.org/10.3221/igf-esis.28.01&auth=true p. valentino et alii, frattura ed integrità strutturale, 28 (2014) 1-11; doi: 10.3221/igf-esis.28.01 2 introduction oven fabric (wf) composite materials are of particular interest in the scientific community due to their mechanical performances compared to the unidirectional laminates. in particular, textile composites offer better dimensional stability over a large range of temperatures, better impact resistance and tolerance; subtle conformability and deep draw moldability, compared to the common unidirectional laminated composites. the variety of manufacturing methods have made the textile composites cost-competitive, therefore they are used in many application fields and they are being considered for intra and interlaminar strength and damage resistance. among the various textile forms, woven fabrics are the most widely used in composites, they provide more balanced properties in the fabric plane and the interlacing of yarns provides higher out of plane strength, which can take up the secondary loads due to load path eccentricities, local buckling, etc. simplified theoretical approaches to predict the mechanical behaviour of such a kind of composite material are quite little, in fact most of the models are limited to the unidirectional reinforced layers and they use the homogenization technique. several studies, on 2-d and 3-d geometries, have been carried out to model and analyse the mechanical properties of the reinforced composite materials. in particular, barbero et al [1], developed an accurate model of a plain wave fabric in order to evaluate its mechanical properties assuming a sinusoidal shape of the tow fibres. stress and strain averaging procedure has been studied by yiwie jiang et al. [2], for local/global analysis of plain-weave fabric composites, where, within a representative volume cell, using uniform stress and uniform strain assumptions, the constitutive equations are averaged along the thickness direction. chou and ito [3] analysed the strength and failure behaviour of plain weave composites. in particular, the geometrical characteristics of yarn shape, laminate stacking configuration, fibre volume fraction, and yarn packing fraction were investigated using three-dimensional geometrical models. based on the geometrical characteristics, iso-strain approach was developed to predict elastic properties, stress distributions, and strengths under tensile loading. n. k. naik et al. [4] developed a two-dimensional closed-form analytical method for the thermo-elastic analysis of twodimensional orthogonal plain weave fabric laminas, considering the volume fraction of fibres and the possible gap between the two adjacent strands. finally, analytical models of the plain weave laminated composites to evaluate the elastic properties of woven fabric composites are reported in [5]. however, most of these works are related to plain wave fabrics, while not many efforts to study the twill wave type have been carried out. the aim of this work is to evaluate the stiffness of a fabric reinforced composite in warp and fill direction. in particular a numerical fe model, assuming elliptical sections and sinusoidal shape of the yarns, has been implemented and experimental tests have been carried out in order to validate the proposed model. results in terms of stress-strain response and stiffness, for the different analysed structures are reported and discussed. finally, the strength and the failure modes of the composite material, for each analysed structure and textile orientation, have been experimentally investigated. materials and test procedures oven fabric composites made in continuous basalt fibres and polymeric matrix has been investigated. test panels have been produced by placing hand all the constituent layers, as shown in fig. 1, and a curing treatment at room temperature in vacuum bag has been carried out, in order to get the final product. all test panels have been produced using the same epoxy matrix system [6] and two different orientations of the fibres have been considered, as reported in tab. 2. according to the german standard din en 2747 [7], each panel has been processed with the aim to get a thickness of approx. 2 mm. two different fabric types have been used in this investigation, i.e. twill 2/2 and twill 1/3, details are reported in [5]. the corresponding layups and technical data, according to the provided data sheet [12] are listed in tab. 2. tensile test specimens, with plane dimensions of 250 x 25 mm [7], have been obtained by water jet cutting from the panel produced in autoclave as shown in fig. 2. in order to avoid the failure of the specimens near to the gripping zone, due to the local stress concentration, and with the aim to prevent eccentricity of load and limit bending phenomena during the setup, tabs have been bonded to both the ends of each sample, fig. 3. according to [7], they were made of glass fiber reinforced plastics with a ±45°-layup and with dimensions of 25 x 45 x 1.5 mm. w w http://www.gruppofrattura.it http://dx.medra.org/10.3221/igf-esis.28.01&auth=true p. valentino et alii, frattura ed integrità strutturale, 28 (2014) 1-11; doi: 10.3221/igf-esis.28.01 3 the volume fraction of fibre has been evaluated by calculating the mass variation of a sample after heat treatment. in particular, a certain number of specimens, with plane dimensions of 20 x 10 mm, has been collected from the created panels, and each of them has been weighted by using a precision balance mettler toledo 204-s. a heat treatment, needed to completely burn the polymeric matrix without effecting the reinforcement [8-11], has been performed by using a muffle furnace carbolite eml 11/6 for 15 minutes at 620 °c. after cooling, all the treated samples have been weighted again, therefore, the density of the matrix and fibres and, consequently, the fibre volume content, φf , according to the standard din en 2559 [13], has been calculated as below:   f f f f f c c m f c f f m m v v v v v m m m                (1) where the subscripts f, m and c indicate the fibre, matrix and composite properties, respectively, v is the volume, m is the mass and  is the density. figure 1: scheme of the layup used in the processing: 1 sealant tape, 2 vacuum connector, 3 release film, 4 peel ply, 5 composite layup, 6 peel ply, 7 perforated foil, 8 bleeder, 9 vacuum bag. basalt fibres epoxy resin mechanical property value mechanical property value density,  2.75 g/cm3 density,  1.15 g/cm3 young’s modulus, e1 89 gpa young’s modulus, e 2.65 gpa young’s modulus, e2 89 gpa shear modulus, g 0.98 gpa shear modulus,g12 21.7 gpa poisson’s ratio, ν 0.35 shear modulus,g23 21.7 gpa poisson’s ratio,ν12 0.26 poisson’s ratio,ν23 0.26 table 1: mechanical properties of basalt fibres [12] and epoxy resin [6]. fabric type yarn type specific weight in g/m² warp yarns per cm fill yarns per cm layup layers thickness in mm fibre volume content fρ in % twill 2/2 thread of direct roving 11.5 µm 110 tex 334 16 9 [0°/90°]6 6 ~1,8 51.85 twill 2/2 334 16 9 [90°/0°]6 6 ~1,8 47.88 twill 1/3 direct roving 11.5 µm 110 tex 362 18 8 [0°/90°]6 6 ~1,9 49.17 twill 1/3 362 18 8 [90°/0°]6 6 ~1,8 54.75 table 2: types of fabrics, specific weights and layups. http://www.gruppofrattura.it http://dx.medra.org/10.3221/igf-esis.28.01&auth=true p. valentino et alii, frattura ed integrità strutturale, 28 (2014) 1-11; doi: 10.3221/igf-esis.28.01 4 figure 2: typical composite plate after cutting using water jet in order to produce tensile test samples. figure 3: side view of the tensile test specimens with tabs according to german standard din en 2747 [7]. experimental tensile tests, in order to evaluate the mechanical properties of the fabric composites, in terms of stiffness and strength, have been carried out according to [7]. each test has been performed using a universal servo-hydraulic testing machine (instron 8500), at room temperature t=298 k and the strain has been measured by a resistance extensometer with a gauge length of 20 mm. finite-element-analyses representative volume element (rve) of the fabric composite has been geometrically defined and numerically modelled. in order to evaluate the geometric dimensions of the rve, top view of the dry fabric and side view of a crosssection of the test panels have been investigated using an optical microscope. information about length and width have been obtained and they have been properly matched with the geometric dimensions provided in the data sheet. fig. 4 shows a depiction of the cross-section of a single lamina for both of the analysed structures. the height of the rve has been simply obtained by dividing the thickness of the test panel by the number of constituent laminas. the geometry of the rve has been carefully modelled, in different steps, by using a commercial cad software as follows: 1. modeling of warp and fill yarn (corresponds to the dry fabric); 2. separately modeling of the surrounding matrix; 3. assembling of the fabric and matrix in order to get the final geometric model of the rve. fig. 5 shows a 3-dimensional depiction, in wireframe, of the final obtained rves for both of the fabric reinforcements. according to [5], in order to better simulate the real shape of the fabric composite, the trend of the warp and fill yarn have been modelled using a sinusoidal shape which can be expressed as [5, 14] 2 cos x y a c       (2) where a is the amplitude, and c is the pitch of the tow path curve, fig. 6(a). an elliptical shape has been assumed to model the cross-sections of the warp and fill yarn [15, 16]. a http://www.gruppofrattura.it http://dx.medra.org/10.3221/igf-esis.28.01&auth=true p. valentino et alii, frattura ed integrità strutturale, 28 (2014) 1-11; doi: 10.3221/igf-esis.28.01 5 (a) (b) figure 4: schematic depiction of sample cross-sections for the two types of dry fabric reinforcements. (a) twill wave 2/2; (b) twill weave 1/3. (a) (b) figure 5: 3d models of the rve. (a) twill weave 2/2; (b) twill weave 1/3. (a) (b) figure 6: simplifying assumptions for analytical description of the geometry: (a) sinusoidal spline about centreline of an undulated yarn; (b) elliptical cross-section of a yarn. starting from the created geometry, the fem model has been generated by using a commercial finite element software. the mesh distribution, with a proper size, has been generated by means of an automatic option of the fem software and a depiction of the meshed rve for the twill weave 2/2 and twill weave 1/3, respectively, is shown in fig. 7. as a first approach an idealized contact has been obtained by imposing the coincidence of nodes in the matrix-fibres interface, therefore failure mechanisms and friction effects were neglected. furthermore, this assumption results in no relative displacement between the three different regions, i.e. warp yarns, fill yarns and pure matrix. in order to properly assign the mechanical properties of each component of the rve, i.e. matrix and fibres tow, two different reference systems have been considered, respectively. linear elastic properties have been imposed to the yarns, but, in order to simulate the orthotropic behaviour of the material two additional reference systems have been introduced: http://www.gruppofrattura.it http://dx.medra.org/10.3221/igf-esis.28.01&auth=true p. valentino et alii, frattura ed integrità strutturale, 28 (2014) 1-11; doi: 10.3221/igf-esis.28.01 6 the one to assign the mechanical properties of the warp yarns and the other one to assign the fill yarns properties, respectively. isotropic linear elastic properties have been assumed for the matrix and data listed in tab. 1 have been assigned to it. this assumption requires no further specification of the mesh orientation. (a) (b) figure 7: fe models of the rves (a) twill weave 2/2; (b) twill weave 1/3. in order to correctly assign the mechanical properties to the yarns, it has to consider that each tow is characterized by a big percentage of fibres immersed in epoxy matrix. furthermore, the calculation of the material properties should be based on the experimentally determined values of the fibre volume content φf, previously described. however, the latters have been calculated based on a bigger volume of material than the rve, therefore, in order to match the data and to correctly assign the material properties to the yarns, the fibre volume content of the yarns in the rve, φf,y, has been determined by modifying the one experimentally calculated, φf, as below: 1 , rve f y y f y y v v x     (3) where vrve is the rve volume, vy is the tow volume of the rve, x is the relative volume of yarns in the rve. details of the new data are listed in tab. 3. fabric type and test direction φf experimentally determined region in the rve relative volume x in the rve φf,y based on exp. values φf,y standardized to 50 % in the rve twill weave 2/2 51.85 % warp and fill yarns 76.00% 68.22% 65.79% warp polymeric matrix 24.00% twill weave 2/2 47.88 % warp and fill yarns 76.00% 63.00% 65.79% fill polymeric matrix 24.00% twill weave 1/3 49.17 % warp and fill yarns 79.00% 62.24% 63.29% warp polymeric matrix 21.00% twill weave 1/3 54.75 % warp and fill yarns 79.00% 69.30% 63.29% fill polymeric matrix 21.00% table 3: calculated fibre volume content, φf,y, to used in fe-analyses. the new calculated values of the fibre volume content φf,y are based on the relative volumes ratio of the different phase of the rves and on the fibre volume content experimentally calculated, φf. therefore, the geometric dimensions of the yarns, the thickness of the rves [15, 16, 18] as well as the accuracy of the experimental determination of φf, affect this calculation. the yarn is considered as a unidirectional reinforced phase with a transversally isotropic behaviour, therefore, nine elastic constants (five are independent) are required to assign the transversally isotropic properties to the reinforced regions of the rve. the evaluation is described in the following. in particular, in the predominant direction the stiffness can be calculated by means of the mixture law, as below:  1 1, ,   f y f f y me e e    (4) http://www.gruppofrattura.it http://dx.medra.org/10.3221/igf-esis.28.01&auth=true p. valentino et alii, frattura ed integrità strutturale, 28 (2014) 1-11; doi: 10.3221/igf-esis.28.01 7 as the basalt fibre and the polymeric matrix can be considered as homogeneous isotropic materials, the respective shear moduli can be calculated by g=e/2(1+ ν), where the corresponding values are listed in tab. 1. mixture law, according to chamis [19, 22], can be applied in order to calculate three more independent linear-elastic properties of the yarns, namely: 1 2 1 1, m m f y f e e e e e               (5) 12 13 1 1, m m f y f g g g g g               (6)  12 13 1, ,     f y f f y m         (7) the remaining parameters, needed to fully define the material properties of the rve, have been calculated exploiting the maxwell-betti's law, ei νji= ej νij, as below: 2 21 31 12 1   e e     (8) finally, the last independent parameters, i.e. g23, g32, 23 and 32 have been calculated 23 32 23 1 1, , m m f y f g g g g g               (9) 2 23 32 23 1 2   e g           (10) finally, appropriate boundary conditions have been applied to the rve in order to: 1. ensure a purely longitudinal deformation; 2. allow contraction of the cross-sections due to poisson’s effects; 3. avoid twisting and bending effects. results and discussion experimentally and numerically determined stiffness esults, in terms of stress-strain response, for both of the fabric reinforcements, i.e. twill 2/2 and twill 1/3, are reported in fig. 8(a) and fig. 8(b), respectively. figures clearly exhibit an high repeatability of the response in all the cases. this can be attributed to a constant material quality over the whole test panel. however, whereas the 2/2 fabric type shows a clear difference, in terms of stiffness and strength, along the warp and fill direction, the 1/3 fabric type does not show substantial variations. furthermore, the textile exhibits higher stiffness and strength along the warp direction than the fill one for both of the fabric types. using the weighted average method, as a first approximation [21, 22], the stiffness of the specimens have been calculated as secant modulus es.0.5% at a strain value of ε=0.5% and tangent modulus et.0.1% (as a secant modulus at a strain of ε=0.1%) according to german standard din en 2747 [7]. for each textile specimen and layup the average values and standard deviations have been calculated, respectively [23-25]. fig. 9 and fig. 10 show the stiffness related to each textile semi-finished product as secant modulus es.0.5% and tangent modulus et.0.1% with the respective standard deviations. in particular, whereas fig. 9 shows the secant moduli and tangent r http://www.gruppofrattura.it http://dx.medra.org/10.3221/igf-esis.28.01&auth=true p. valentino et alii, frattura ed integrità strutturale, 28 (2014) 1-11; doi: 10.3221/igf-esis.28.01 8 moduli based on the experimentally determined values of the fibre volume content, fig. 10 shows the values standardized to a fibre volume content φf=50%. (a) (b) figure 8: stress-strain diagrams as results of the experimental tensile tests: (a) fabric type twill 2/2 in warp and fill direction; (b) fabric type twill 1/3 in warp and fill direction. figure 9: secant modulus and tangent modulus of the respective textile semi-finished products based on the experimentally determined values of the fibre volume content of φf. figure 10: secant modulus and tangent modulus of the respective textile semi-finished products standardized to a fibre volume content of φf=50%. http://www.gruppofrattura.it http://dx.medra.org/10.3221/igf-esis.28.01&auth=true p. valentino et alii, frattura ed integrità strutturale, 28 (2014) 1-11; doi: 10.3221/igf-esis.28.01 9 the stiffness values, numerically calculated, show good agreement with the corresponding experimental ones in both the considered cases, i.e. experimental and standardized, φf=50%, fibre volume content. in particular, the stiffness determined by the fe-analyses lies in the range of the secant modulus es.0.5% and the tangent modulus et.0.1%. as an exception the numerical results for the stiffness of the twill weave 1/3 in fill direction yield slightly lower values than the experimental ones. experimentally determined strengths and corresponding failure modes tensile strength values σz.b, based on the experimental results, have been calculated, according to [22] and [12], and shown in fig. 12, respectively. in particular the experimental values related to the twill weave 2/2 reinforcement are higher than the ones calculated by the indicated values in the data sheets, while a good agreement has been observed for the twill weave 1/3 reinforcement. with the aim to provide a proper interpretation of the experimental tensile tests a careful analysis on the failure modes and crack path propagation has been carried out. in particular, in fig. 11 is shown a depiction of a typical fracture mode of a specimen with twill weave 2/2 reinforcement. woven fabric with 0°-90° and 90°-0° orientation exhibited analogous failure modes. the crack started in the gauge length and proceeded perpendicularly to the applied load. figure 11: fractured specimen with twill weave 2/2 fabric reinforcement in the warp direction. the area enclosed in the square box show details of the damage mechanism. in fig. 13 is shown a depiction of a typical fracture mode of a specimen with twill weave 1/3 reinforcement. similar to the previous case study, the orientation of the woven fabric did not affect the failure mode and the crack started in the gauge length. however, the crack path is inclined of approx. 45° to the applied load axis. figure 12: calculated tensile strengths of the respective textile semi-finished products standardized to a fibre volume content of φf=50%. http://www.gruppofrattura.it http://dx.medra.org/10.3221/igf-esis.28.01&auth=true p. valentino et alii, frattura ed integrità strutturale, 28 (2014) 1-11; doi: 10.3221/igf-esis.28.01 10 figure 13: fractured specimen with twill weave 1/3 fabric reinforcement in the fill direction. the areas enclosed in the square boxes show details of the damage mechanism leading to sample failure. conclusions asalt fabric composite, with different twill wave reinforcements, i.e. twill 2/2 and twill 1/3, have been studied in this work by means of experimental tests and numerical finite element (fe) simulations. in particular, the mechanical response and the stiffness of a fabric reinforced composite in warp and fill direction has been analysed. the numerical fe model has been properly implemented assuming elliptical sections of the tows and sinusoidal shape of the yarns and particular attention has been applied to generate the rves geometry. the obtained results have been compared with the experimental data in order to validate the proposed model and a good agreement has been observed. therefore the fe-method can be considered an adequate way to predict the stiffness of woven fabric composite with different geometries in the mesoscopic scale or even different kind of fibre reinforcement. finally, the strength and the failure modes of the composite material, for each analysed structure and textile orientation, have been experimentally investigated. acknowledgements ncotelogy ltd. is acknowledged for providing the fabrics of basalt fibres. further thanks go to mr m. eisenried (laboratory for composite technology (lft labor für faserverbundtechnik) at the department of mechanical engineering at the university of applied sciences regensburg) for proofreading and for generating the schematic illustrations in the cadsystem. references [1] barbero, j., trovillion, j., mayugo, j.a., sikkil, k.k., finite element modelling of plain weave fabrics from photomicrograph measurements, composite structures, 73 (2006) 41–52. [2] jiang, y., tabiei, a., simitses, g. j., a novel micromechanics-based approach to the derivation of constitutive equations for local/global analysis of a plain-weave fabric composite, composites science technology, 60 (2000) 1825-1833. [3] ito, m., chou, t.-w., an analytical and experimental study of strength and failure behaviour of plain weave composites, journal of composite materials, 32 (1) (1998) 2-30. [4] naik, n. k., ganesh, v. k., an analytical method for plain weave fabric composites, composites, 26(4) (1995) 281289. b i http://www.gruppofrattura.it http://dx.medra.org/10.3221/igf-esis.28.01&auth=true p. valentino et alii, frattura ed integrità strutturale, 28 (2014) 1-11; doi: 10.3221/igf-esis.28.01 11 [5] niranjan, n. k., woven fabric composites, technomic publication, indian institute of technology, bombay, india (1994). [6] epoxidharz, l., härter, l., technische daten. technical data sheet by r&g, (2011). [7] din en 2747 – luftund raumfahrt – glasfaserverstärkte kunststoffe – zugversuch. normenstelle luftfahrt (nl) im din deutsches institut für normung e.v., beuth verlag, berlin, (1998). [8] jungbauer, b., romano, m., ehrlich, i., reproduzierbare herstellung und definierte vorschädigung von probekörpern aus basaltfaserverstärktem kunststoff zur dämpfungsmessung. bachelor¬thesis, university of applied sciences regensburg, laboratory of composite technology, regensburg, (2012). [9] lauterborn, e., dokumentation ultraschalluntersuchung eingangsprüfung, internal report wiweb erding, erding, (2011). [10] schmid, v., jungbauer, b., romano, m., ehrlich, i., gebbeken, n., diminution of mass of different types of fibre reinforcements due to thermal load. in: proceedings of the applied research conference, regensburg, (2012). [11] schmid, v., jungbauer, b., romano, m., ehrlich, i., gebbeken, n., the influence of different types of fabrics on the fibre volume content and porosity in basalt fibre reinforced plastics. in: proceeding of the applied research conference, regensburg, (2012). [12] quality certificates for fabrics and rovings. incotelogy ltd., bonn, (2012). [13] din en 2559 – luftund raumfahrt – kohlenstoffaser-prepregs – bestimmung des harzund fasermasseanteils und der flächenbezogenen fasermasse. normenstelle luftfahrt (nl) im din deutsches institut für normung e.v., beuth verlag, berlin, (1997). [14] ottawa, p., romano, m., wagner, m., ehrlich, i., gebbeken, n., the influence of ondulation in fabric reinforced composites on dynamic properties in a mesoscopic scale in composites reinforced with fabrics on the damping behaviour, in: proceedings of the 11. ls-dyna forum, ulm, (2012). [15] barbero, e. j., luciano, r., micromechanics formulas for the relaxation tensor of linear viscoelastic composites with transversely isotropic fibers, in: international journal of solid structures, 32 (1995) 1859-1872. [16] ozgen, b., gong, h., yarn geometry in woven fabrics, textile research journal, 81 (2010) 738-745. [17] luciano, r., sacco, e., variational methods for the homogenization of periodic heterogeneous media, european journal of mechanics – a/solids, 17(4) (1998) 599-617. [18] lopresto, v., leone, c., de iorio, i., mechanical characterisation of basalt fibre reinforced plastic, composites: part b, 42(4) (2011) 717-723. [19] chamis, c. c., simplified composite micromechanics equations for hygral, thermal and mechanical properties, sampe quarterly, (1984) 14-23. [20] moser, k., faser-kunststoff-verbund – entwurfsund berechnungsgrundlagen, vdi-verlag, düsseldorf, (1992). [21] schürmann, h., konstruieren mit faser-kunststoff-verbunden, springer-verlag, berlin/heidelberg/new york, (2005). [22] stellbrink, k., micromechanics of composites, hanser-verlag, münchen/wien, (1996). [23] fahrmeir, l., künstler, r., pigeot, i., tutz, g., statistik – der weg zur datenanalyse. 5. auflage, springer verlag, berlin/heidelberg, (2005). [24] din v 65352 – luftund raumfahrt – verfahren zur statistischen auswertung der prüfergebnisse bei der qualifikationsund abnahmeprüfung von faserverbundwerkstoffen. normenstelle luftfahrt (nl) im din deutsches institut für normung e.v., beuth-verlag, berlin, (1987). [25] papula, l., mathematische formelsammlung für naturwissenschaftler und ingenieure, auflage, vieweg-teubner, wiesbaden, (2009) 10. http://www.gruppofrattura.it http://dx.medra.org/10.3221/igf-esis.28.01&auth=true microsoft word numero_42_art_19.docx a. campagnolo et alii, frattura ed integrità strutturale, 42 (2017) 181-188; doi: 10.3221/igf-esis.42.19 181 mode ii brittle fracture: recent developments a. campagnolo department of industrial engineering, university of padova, via venezia 1, 35131, padova, italy s.m.j. razavi, m. peron, j. torgersen, f. berto department of mechanical and industrial engineering, norwegian university of science and technology (ntnu), norway javad.razavi@ntnu.no, mirco.peron@ntnu.no, jan.torgersen@ntnu.no, filippo.berto@ntnu.no abstract. fracture behaviour of v-notched specimens is assessed using two energy based criteria namely the averaged strain energy density (sed) and finite fracture mechanics (ffm). two different formulations of ffm criterion are considered for fracture analysis. a new formulation for calculation of the control radius rc under pure mode ii loading is presented and used for prediction of fracture behaviour. the critical notch stress intensity factor (nsif) at failure under mode ii loading condition can be expressed as a function of notch opening angle. different formulations of nsifs are derived using the three criteria and the results are compared in the case of sharp v-notched brittle components under in-plane shear loading, in order to investigate the ability of each method for the fracture assessment. for this purpose, a bulk of experimental data taken from the literature is employed for the comparison among the mentioned criteria. keywords. fracture strength; sharp v-notch; mode ii fracture; notch stress intensity factor; strain energy density. citation: campagnolo, a., razavi, s.m.j., peron, m., torgesen, j., berto, f., mode ii brittle fracture: recent developments, frattura ed integrità strutturale, 42 (2017) 181-188. received: 28.06.2017 accepted: 25.07.2017 published: 01.10.2017 copyright: © 2017 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. introduction umerous failure criteria have been proposed by scholars dealing with the brittle fracture of v-notches [1]. according to the intensified linear elastic stress at the notch tip, introducing a stress field parameter is useful. considering the linear elastic notch mechanics (lefm) concept, nsifs can be successfully employed for the fracture assessment of brittle materials when weakened by sharp v-notches [2,3]. lazzarin et al. [4] compared two widely employed criteria based on energy considering v-notched components under pure mode i loading; the first criterion is based on the local sed [5] while the second criterion is the so-called ffm approach. two different formulations of the ffm criterion is available in the literature: the first formulation was proposed by leguillon [6,7] and the second one was proposed by carpinteri et al. [8]. the main aim of the current paper is to extend the previous comparison to the case of mode ii loading condition. n a. campagnolo et alii, frattura ed integrità strutturale, 42 (2017) 181-188; doi: 10.3221/igf-esis.42.19 182 the ffm criteria have been recently extended to the mixed mode i/ii and mode ii loading conditions [9-11]. instead, considering the sed criterion, a new formulation for estimating the control radius under in-plane shear loading is proposed here and is compared with results obtained from the expression which is valid for mode i. lazzarin and zambardi [5] proposed the local sed criterion which is based on the strain energy density averaged over a control volume surrounding the notch tip. the size of control volume is dependent on the material property and the loading conditions [12,13]. the average sed value is independent of the mesh size [14]. additionally, a new method for average sed calculations for cracks under mixed mode i+ii loading by adopting very coarse meshes has been recently proposed [15,16] which is based on the maximum stresses obtained from fe analyses. in this paper the analytical formulation of the three compared criteria [5,9-11] is introduced to obtain the critical mode ii notch stress intensity factor using different approaches. after all, the mentioned criteria are applied to sharp v-notched plates subjected to in-plane shear loading, in order to investigate the ability of each method to analysis the fracture behaviour of brittle materials. the experimental data available in the literature were used for the analyses [17]. figure 1: reference system for: (a) averaged sed criterion; (b) leguillon et al. criterion and (c) carpinteri et al. criterion. failure criteria for sharp v-notches under pure mode ii loading averaged strain energy density (sed) criterion ccording to lazzarin and zambardi [5], the fracture of a brittle material takes place when the strain energy density averaged over a control volume characterized by a radius rc (fig. 1a), becomes equal to the critical value wc (eq. 1). in the case of a smooth component under nominal shear loading condition, employing beltrami’s hypothesis, the following expression can be derived:   22 cc c 1 ν ττ w 2g e    (1) where τc is the ultimate shear strength, g the shear modulus and e the young's modulus, while ν represents the poisson’s ratio. considering a v-notched plate subjected to nominal pure mode ii loading, the relationship cww  is verified under critical conditions. accordingly, one can obtain the expression for k2c, which is the critical nsif at failure:        2 2 22 122 22 1 2 1 1              cc c c c c ke k r e e er              (2) the control radius rc can be evaluated by considering a set of experimental data that provides the critical value of the notch stress intensity factor for a given notch opening angle. if the v-notch angle is equal to zero (2α = 0, λ2 = 0.5), the case of a cracked specimen under nominal pure mode ii loading is considered, so that under critical conditions k2c coincides with the mode ii fracture toughness kiic. then, taking advantage of eq. (2), with k2c ≡ kiic, and following the a 2 c r   notch bisector (c) c 2 r  lc (b) notch bisector rc∙ w r c (a) a. campagnolo et alii, frattura ed integrità strutturale, 42 (2017) 181-188; doi: 10.3221/igf-esis.42.19 183 same procedure proposed by yosibash et al. [18] for obtaining the control radius under mode i loading condition, the expression of rc turns out to be:      2 2 2 2 , 1 9 8 9 8( 2 0) (1 ) 8 (1 ) 8 iic iic iic c ii c c c k k ke r                                  (3) moreover, it is useful to express the nsif at failure k2c as a function of the mode i material properties (kic and σc), which are simpler to determine or to find in the literature than mode ii material properties. for this purpose, it is possible to approximately estimate the mode ii fracture toughness (kiic) as a function of kic, according for example to richard et al. [19]. in the same manner, it is possible to approximately estimate the ultimate shear strength (τc) as a function of the tensile one (σc). with reference to brittle materials with linear elastic behaviour (as for example polymethylmethacrylate, graphite,…), it has been observed experimentally [20] that the most appropriate criterion is that of galileo-rankine. accordingly the following expressions are valid: 3 2 iic ick k (4)                     0.80 1.00 on an experimental basisc c     (5) finally, substitution of eqs. (3)-(5) into eq. (2) gives the nsif at failure k2c in a more useful form:     2 22 2 1 2 12 1 2 1 2 2 1 3 9 8 4 8 c ic ck k e                      (6) it should be noted that the control radius rc could be in principle different under mode i and mode ii loading condition, this means that it depends on the material properties but also on the loading conditions. finite fracture mechanics: leguillon et al. formulation by using leguillon et al. criterion, it is thought that at failure an incremental crack of length lc initiates at the tip of the notch. according to leguillon et al. [7,11], two conditions can be imposed on stress components and on strain energy and both are necessary for fracture. they have to be simultaneously satisfied to reach a sufficient condition for fracture. on the basis of the stress condition, the failure of the notched element happens when the singular stress component normal to the fracture direction c is higher than the material tensile stress σc all along the crack of length lc just prior to fracture. on the basis of the condition imposed on strain energy, the failure occurs when the serr   reaches a value higher than c , which is the critical value for the material.   is the ratio between the potential energy variation at crack initiation (δwp) and the new crack surface created (δs). these two conditions can be formalised as follows providing a general criterion for the fracture of components in presence of pointed v-notches. stress criterion:  2 1 ( 2 )2( , )c c c c cl k l        (7a) energy criterion:    22 * 22 22 2 ,     c cp c c k h l dw s l d         (7b) in eqs. (7a,b) the length of the incremental crack is lc (see fig. 1b). λ2 is the mode ii williams’ eigenvalues quantities [21], that is a function of the v-notch opening angle  ( 2 )2   is a function of the angular coordinate  , while d is the a. campagnolo et alii, frattura ed integrità strutturale, 42 (2017) 181-188; doi: 10.3221/igf-esis.42.19 184 thickness of the notched element. finally, *22 ( 2 , )ch   is a “geometrical factor” function of the local geometry (2α) and of the fracture direction ( c ). leguillon et al. criterion requires that conditions (7a) and (7b) must be simultaneously satisfied. the length of the incremental crack can be determined by solving the system of two equations (eqs. (7a,b)), then by substituting it into eq. (7a) or (7b), the fracture criterion can be expressed in the classical irwin form (ki ≥ kic). in this case the critical value of the nsif k2c can be provided as a function of the material properties (σc and c ), the v-notch angle 2α and the critical crack propagation angle c .     2 21 2 1 2 2* ( 2 ) 22       2 , c c c c c k k h                             (8) yosibash et al. [11] have computed the function h22 for a range of values of the notch opening angle 2α and of the fracture direction c , taking into account a material characterized by a young’s modulus e = 1 mpa and a poisson’s ratio ν = 0.36. the function . *22h .for any other young’s modulus e and poisson’s ratio ν can be easily obtained according to the following expression:     2 * 22 22 2 1 1 2 ,   2 ,   1 0.36 c ch h e         (9) a more useful expression for k2c, as a function of the mode i fracture toughness kic and of the ultimate tensile stress σc, can be derived by substituting eq. (9) and the link between c and kic into eq. (8). then, by employing gross and mendelson’s [22] definition for the critical nsif k2c, the following expression can be obtained:       2 2 2 2 1 2 1 2 2 1 2 1 2 ( 2 ) 22 1 0.36 1 2 2 , c ic c c c k k h                                    (10) finite fracture mechanics: carpinteri et al. formulation in a similar manner to leguillon, a fracture criterion for brittle v-notched elements based on ffm concept has been proposed by carpinteri et al. in [8-10]. under critical conditions, a crack of length δ is thought to initiate from the notch tip. again, a sufficient condition for fracture can be achieved from the satisfaction of both a stress criterion and an energy-based one. on the basis of the averaged stress criterion, the failure of the component at the v-notch tip happens when the singular stress component normal to the crack faces, averaged on the crack length δ, becomes higher than the tensile stress σc of the material under investigation. the energy-based condition, instead, requires for the failure to happen that the strain energy released at the initiation of a crack of length δ is higher than the material critical value, which depends on c . by considering the relationship between the serr  and the sifs ki and kii of a crack under local mixed mode i+ii loading, it is possible to derive a more useful formulation. this is valid under plane strain hypotheses and considering that the crack propagates in a straight direction. the contemporary verification of the conditions given by eq. (11a) and (11b) allows to formalize a criterion for the brittle fracture of sharply v-notched elements: average stress criterion:       2 * 2 1 0 0 ,   ( )  2 ii c c c k r dr dr r             (11a) energy criterion:   0 0     ,       p c c dw da a da da          (11b) a. campagnolo et alii, frattura ed integrità strutturale, 42 (2017) 181-188; doi: 10.3221/igf-esis.42.19 185         22 2 * 2 2 1 2 2 212 22 0 0 , ,   2 , 2 ,  i c ii c ii c c ick a k a da k a da k                      in eqs. (11a) and (11b), δ represents the length of the crack initiated at the v-notch tip (see fig. 1c), while λ2 is the mode ii williams’ eigenvalue [21]. (r, θ) are the polar coordinate system centred at the notch tip and a represents a generic crack length. with the aim to employ the energy-based approach, the knowledge of the sifs ki and kii of the tilted crack nucleated at v-notch tip, as a function of the crack length a is strictly required. in order to this, the expressions of the sifs ki and kii derived by beghini et al. [23], on the basis of approximate analytical weight functions, can be used. they are functions of the crack length a, the v-notch angle 2α, the fracture direction θc and the nsif kii*. it is useful to introduce a simplified notation according to eq. (12), in which the relationship between the parameter 22 according to sapora et al. [10] and the parameter h22 according to yosibash et al. [11] is shown, as highlighted also in [9].          22 22 212 22 22 22 2 2 2 , 2 , 2 , 2 2 ,      2 1 0.36 h                   (12) on the basis of carpinteri et al. approach, the fracture of the component happens when both conditions provided by eqs. (11a) and (11b) are simultaneously satisfied. by solving the system of two equations, the length of the initiated crack δ and the critical nsif kiic* can be explicitly found. moreover, by adopting the classical definition of k2c due to gross and mendelson [22], the following expression results to be valid:           22 2 2 2 2 2 11 1 1 2 12 2 1 2 2 2 22 21 2   2 , ( ) c ic c c c k k                                           (13) analytical comparison he criteria taken into consideration in the present contribution, can be compared on the basis of the final relationships of the mode ii critical notch stress intensity factor according to gross and mendelson’s definition [22], see eqs. (6), (10) and (13). the same proportionality relation is common to all criteria:  2 22 1 2 12    c ic ck k    (14) 0.00 0.50 1.00 1.50 2.00 2.50 3.00 0 20 40 60 80 100 p ro po rt io na li ty f ac to rs notch opening angle 2α, [°] sed leguillon et al. carpinteri et al. figure 2: comparison among proportionality factors given by eqs. (6), (10) and (13). t a. campagnolo et alii, frattura ed integrità strutturale, 42 (2017) 181-188; doi: 10.3221/igf-esis.42.19 186 the only difference in the final expressions is represented by the proportionality factor. indeed, the latter is a function of the v-notch angle (2α) in leguillon et al. and carpinteri et al. formulations. on the other hand, the proportionality factor of the sed approach is a function also of the poisson's ratio ν. it should be noted that the v-notch tip singularity (1-λ2), tied to mode ii loading, disappears for opening angles higher than 102 degrees, according to williams [21]. therefore the analytical comparison of eqs. (6), (10) and (13) has been carried out for notch opening angles 2α between 0 and about 100 degrees. the proportionality factors are very similar in their trends (fig. 2). in particular, the factor of leguillon et al. approach is always a bit greater than those obtained by using the other two criteria. the factors according to leguillon et al. and sed criteria assume the same values for 2α= 0 and 100 degrees: 0.87 and 2.27, respectively. the factor based on carpinteri et al. approach, instead, does not match that of the other criteria for any value of 2α. comparison based on experimental data he assessment capability of the considered criteria is compared here by employing experimental data reported in the literature. the data are all relevant to components weakened by sharp v-notches and constituted by polymethylmethacrylate (pmma). the material properties and the experimental details are summarised in the following. a more extended comparison can be found in [15]. the experimental results and the theoretical predictions obtained from eqs. (6), (10) and (13) have been compared on the basis of the critical value of the mode ii nsif, k2c. the critical nsifs are plotted as a function of the notch angle 2α. if not explicitly given in the original contributions, the nsifs to failure k2c were calculated from 2d fe analyses, by adopting fe meshes consisting of eight node solid elements (plane 183) and by applying to the fe models the critical loads experimentally obtained. all fe analyses have been performed by means of ansys®, version 14.5. it should be noted that k2c is coincident with the nsif k2 evaluated on the notch bisector line according to gross and mendelson definition [22] ( 212   2  with  0rk r r      ), provided that the fe model is loaded with the experimental critical load. 0.1 1.0 10.0 100.0 1000.0 0 20 40 60 80 100 n s if t o fa il u re k 2 c, [ m p a m (1 -λ 2 ) ] notch opening angle 2α, [°] experimental data sed leguillon et al. carpinteri et al. figure 3: plot of the nsif to failure k2c (log-scale) and comparison with the experimental data from pmma double v-notched specimens. the considered set of experimental results has been derived from arcan tests carried out by seweryn et al. [3] on pmma double v-notched specimens. the tested v-notched components were characterized by a length l = 200 mm, a width w = 100 mm, a notch depth a = 25 mm and a thickness t = 5 mm. seweryn et al. [3] took into account specimens with four different v-notch angles, 2α = 20, 40, 60 and 80 degrees, being the loading angle to obtain pure mode ii loading equal to ψ = 90 degrees [24]. three pmma samples have been tested for each geometry. the relevant properties of the considered material have been reported in the original contribution [24] as follows: the young’s modulus e was equal to 3000 mpa, the poisson’s ratio equal to 0.30, while the mode i fracture toughness and the critical tensile stress were kic = 1.37 mpa.m0.5 and σc = 115 mpa, respectively. t a. campagnolo et alii, frattura ed integrità strutturale, 42 (2017) 181-188; doi: 10.3221/igf-esis.42.19 187 the experimental results relevant to the pmma v-notched components are shown in fig. 3 in terms of the critical nsif k2c, along with the theoretical predictions based on the fracture approaches under consideration. it can be observed from fig. 3 that the agreement between theoretical predictions and experimental results, in terms of critical mode ii nsif k2c, is very good for all considered criteria. some recent developments dealing with creep stresses are reported in [25]. conclusions hree different fracture criteria for brittle and quasi-brittle materials weakened by sharp v-notches have been considered in the present contribution. the attention has been focused on in-plane shear loading conditions (mode ii). the averaged strain energy density (sed) criterion and two different formulations of the finite fracture mechanics (ffm) theory, according to leguillon et al. and to carpinteri et al. respectively, have been accurately compared. with reference to the criterion based on the averaged sed, a new expression for estimating the control radius rc under pure mode ii loading has been proposed. first, the criteria have been compared analytically by providing the expressions of the critical value of the notch stress intensity factor k2c. the same proportionality relation has been found to exist between k2c and two key material properties: the mode i fracture toughness kic and the ultimate tensile stress σc. the only difference between the analysed criteria is represented by the proportionality factor. finally, the approaches taken into consideration in the present contribution have been adopted for the fracture assessment of brittle v-notched components subjected to pure mode ii loading. this has allowed to investigate the assessment capability of each approach under in-plane shear loading. a set of experimental data reported in the literature has been employed for the comparison. the agreement between experimental data and theoretical predictions has been found very good for all criteria considered in the present investigation. references [1] berto, f., local approaches for the fracture assessment of notched components: the research work developed by professor paolo lazzarin, frattura ed integrita strutturale, 9(34) (2015) 11-26. [2] knesl, z., a criterion of v-notch stability, int. j. fract., 48 (1991) r79–r83. [3] seweryn, a., brittle fracture criterion for structures with sharp notches, eng. fract. mech., 47 (1994) 673–681. [4] lazzarin, p., campagnolo, a., berto, f., a comparison among some recent energyand stress-based criteria for the fracture assessment of sharp v-notched components under mode i loading, theor. appl. fract. mech., 71 (2014) 21– 30. [5] lazzarin, p., zambardi, r., a finite-volume-energy based approach to predict the static and fatigue behavior of components with sharp v-shaped notches, int. j. fract., 112 (2001) 275–298. [6] leguillon, d., a criterion for crack nucleation at a notch in homogeneous materials, c. r. acad. sci. ii b, 329 (2001) 97-102. [7] leguillon, d., strength or toughness? a criterion for crack onset at a notch, eur. j. mech. a solids, 21 (2002) 61–72. [8] carpinteri, a., cornetti, p., pugno, n., sapora, a., taylor, d., a finite fracture mechanics approach to structures with sharp v-notches, eng. fract. mech., 75 (2008) 1736–1752. [9] sapora, a., cornetti, p., carpinteri, a., a finite fracture mechanics approach to v-notched elements subjected to mixed-mode loading, eng. fract. mech., 97 (2013) 216–226. [10] sapora, a., cornetti, p., carpinteri, a., v-notched elements under mode ii loading conditions, struct. eng. mech., 49 (2014) 499–508. [11] yosibash, z., priel, e., leguillon, d., a failure criterion for brittle elastic materials under mixed-mode loading, int. j. fract., 141 (2006) 291–312. [12] berto, f., ayatollahi, m.r., fracture assessment of brazilian disc specimens weakened by blunt v-notches under mixed mode loading by means of local energy, mater. des., 32 (5) (2011) 2858-2869. [13] radaj, d., berto, f., lazzarin, p., local fatigue strength parameters for welded joints based on strain energy density with inclusion of small-size notches, eng. fract. mech., 76 (8) (2009) 1109-1130. [14] lazzarin, p., berto, f., zappalorto, m., rapid calculations of notch stress intensity factors based on averaged strain energy density from coarse meshes: theoretical bases and applications, int. j. fatigue, 32 (2010) 1559–1567. t a. campagnolo et alii, frattura ed integrità strutturale, 42 (2017) 181-188; doi: 10.3221/igf-esis.42.19 188 [15] campagnolo, a., meneghetti, g., berto, f., rapid finite element evaluation of the averaged strain energy density of mixed-mode (i+ii) crack tip fields including the t-stress contribution, fatigue fract. eng. mater. struct., 39 (2016) 982–998. [16] meneghetti, g., campagnolo, a., berto, f., atzori, b., averaged strain energy density evaluated rapidly from the singular peak stresses by fem: cracked components under mixed-mode (i+ii) loading, theor. appl. fract. mech., 79 (2015) 113–124. [17] campagnolo, a., berto, f., leguillon, d., fracture assessment of sharp v-notched components under mode ii loading: a comparison among some recent criteria, theor. appl. fract. mech., 85 (2016) 217–226. [18] yosibash, z., bussiba, a., gilad, i., failure criteria for brittle elastic materials, int. j. fract., 125 (2004) 307–333. [19] richard, h.a., fulland, m., sander, m., theoretical crack path prediction, fatigue fract. eng. mater. struct., 28 (2005) 3–12. [20] berto, f., lazzarin, p., recent developments in brittle and quasi-brittle failure assessment of engineering materials by means of local approaches, mater. sci. eng. r, 75 (2014) 1–48. [21] williams, m.l., stress singularities resulting from various boundary conditions in angular corners of plates in tension, j. appl. mech., 19 (1952) 526–528. [22] gross, b., mendelson, a., plane elastostatic analysis of v-notched plates, int. j. fract., 8 (1972) 267–276. [23] beghini, m., bertini, l., di lello, r., fontanari, v., a general weight function for inclined cracks at sharp v-notches, eng. fract. mech., 74 (2007) 602–611. [24] seweryn, a., poskrobko, sł., mróz, z., brittle fracture in plane elements with sharp notches under mixed-mode loading, j. eng. mech., 123 (1997) 535–543. [25] gallo, p., berto, f., glinka, g generalized approach to estimation of strains and stresses at blunt v-notches under non-localized creep, fatigue fract. eng. mater. struct, 39 (2016) 292-306. << /ascii85encodepages false /allowtransparency false /autopositionepsfiles true /autorotatepages /none /binding /left /calgrayprofile (dot gain 20%) /calrgbprofile (srgb iec61966-2.1) /calcmykprofile (u.s. web coated \050swop\051 v2) /srgbprofile (srgb iec61966-2.1) /cannotembedfontpolicy /error /compatibilitylevel 1.4 /compressobjects /tags /compresspages true /convertimagestoindexed true /passthroughjpegimages true /createjobticket false /defaultrenderingintent /default /detectblends true /detectcurves 0.0000 /colorconversionstrategy /cmyk /dothumbnails false /embedallfonts true /embedopentype false /parseiccprofilesincomments true /embedjoboptions true /dscreportinglevel 0 /emitdscwarnings false /endpage -1 /imagememory 1048576 /lockdistillerparams false /maxsubsetpct 100 /optimize true 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can be opened with acrobat and adobe reader 5.0 and later.) >> /namespace [ (adobe) (common) (1.0) ] /othernamespaces [ << /asreaderspreads false /cropimagestoframes true /errorcontrol /warnandcontinue /flattenerignorespreadoverrides false /includeguidesgrids false /includenonprinting false /includeslug false /namespace [ (adobe) (indesign) (4.0) ] /omitplacedbitmaps false /omitplacedeps false /omitplacedpdf false /simulateoverprint /legacy >> << /addbleedmarks false /addcolorbars false /addcropmarks false /addpageinfo false /addregmarks false /convertcolors /converttocmyk /destinationprofilename () /destinationprofileselector /documentcmyk /downsample16bitimages true /flattenerpreset << /presetselector /mediumresolution >> /formelements false /generatestructure false /includebookmarks false /includehyperlinks false /includeinteractive false /includelayers false /includeprofiles false /multimediahandling /useobjectsettings /namespace [ (adobe) (creativesuite) (2.0) ] /pdfxoutputintentprofileselector /documentcmyk /preserveediting true /untaggedcmykhandling /leaveuntagged /untaggedrgbhandling /usedocumentprofile /usedocumentbleed false >> ] >> setdistillerparams << /hwresolution [2400 2400] /pagesize [612.000 792.000] >> setpagedevice microsoft word numero_43_art_3 f.z. seriari et alii, frattura ed integrità strutturale, 43 (2018) 43-56; doi: 10.3221/igf-esis.43.03 43 fatigue crack growth of composite patch repaired al-alloy plates under variable amplitude loading fatima zohra seriari, mustapha benachour university of tlemcen, ingeniery of mechanical systems and materials laboratory, tlemcen, algeria fsdoctorat@gmail.com, bmf_12002@yahoo.fr mohamed benguediab university of sidi bel abbes, lmpm laboratory, sidi bel abbes, algeria benguediab_m@yahoo.fr abstract. in this paper, fatigue crack growth of edge crack in 2024 t351 aluminum alloy plate repaired with bonded composite patch under constant and variable amplitude loading (val) was predicted. the al-alloy plate was repaired with symmetric patch “boron/epoxy”. additionally to constant amplitude loading (cal), the effects of single overload and band overload were investigated for repaired and unrepaired al-alloy plates. the obtained results confirm the improvement in repair performances by composite patch on fatigue lives and crack growth rates for all applied cycles (cal and val) compared to unrepaired plates. a retardation effect was observed in application of single overload compared to band overload with the same stress ratio (r=0.2) for unpatched plate and characterized by instantaneous delays. however, this retardation effect is increased by the presence of the patch repair which leads to the higher fatigue life. retardation effect was neglected for lower overload ratio (orl>1.8). comparison in fatigue life and crack growth rates under the same overload ratio (orl=2.4) between repaired and unrepaired plates show the supplementary beneficial effects in combination of overloading and patch repair keywords. fatigue crack; composite patch repair; variable amplitude loading; retardation; al-alloy. citation: seriari, f.z., benachour, m., benguediab, m., prediction of fatigue crack growth of composite patch repaired al-alloy plates under variable amplitude loading, frattura ed integrità strutturale, 43 (2017) 4356. received: 08.08.2017 accepted: 03.10.2017 published: 01.01.2018 copyright: © 2018 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. introduction s a consequence, fatigue problems become an important topic for the maintenance of damaged aircrafts structures. bonded composite patch repair presents an advanced technology to reinforce damaged metallic of theses [1-3]. the crack patching bonding technique goes back to the 1980s, when it was successfully applied to a f.z. seriari et alii, frattura ed integrità strutturale, 43 (2018) 43-56; doi: 10.3221/igf-esis.43.03 44 the fracture-critical d6ac steel wing pivot fitting of the f-lli bomber [4]. this technique offers significant advantages over traditional repair methods “riveting, fastening, and welding” [5]. in literature, several studies have investigated this technique, both numerical and experimentally, for different specimen’s dimensions, and which have the following advantages: provides a high structural efficiency and extends the life of cracked structural components at an economical cost, and reduce the stress field near the crack, leads to retardation or complete arrest of the crack growth [3, 5-7], hence, as a result, crack growth is delayed and the service life of the repaired structures is extended. fortunately, the presence of humidity presents harmful effect on fatigue behavior of adhesive joints bonded with aluminium [8]. in patched zone, the composite patch and aluminum alloy present a bi-material, also the interface assembly presents shielding in repaired material [9] and increase the fatigue and decrease the fatigue crack growth rate. sabelkin et al. [10] performed an experimental fatigue investigation on 2024 t3 aluminium alloy reinforced with composite patch boron/epoxy under constant amplitude loading. the results shown that bonded composite patch repair increase fatigue life about fivefold in the case of stiffened panels while it increased about ten fold in the case of unstiffened panels. in absence of patch repair negru and al. [11] have predicted the fatigue life in 2024 t3 aluminium alloy notched specimens (v-notch and semi circular notch) using three method based on finite element method. in the fatigue investigation conducted by salehi-khojin et al. [12] on 6.125 mm cracked 7075 al-alloy without patch repair and repaired with 4-ply boron/epoxy composite patches of several geometries under constant amplitude loading (r=0.1). the results show that the propagation lifetime of the four kinds of patched (repaired) specimens is improved greatly compared to the unpatched al-alloy plate and the fatigue crack growth depends on dimension of patch along the path of crack. the study of fatigue crack growth under constant amplitude loading in repaired aluminium alloy plate 6061 t6 by carbon-epoxy composite patch has shown that the fatigue life has significantly increased. the applied patch has provided about a 100-110% improvement in the fatigue life and a 30-35% decrease in the stress intensity factor [13]. performance for a composite repair patch to prolong the service life of pre-cracked of some aluminium alloys plates under fatigue conditions in a corrosive environment and constant amplitude loading was conducted by schubbe et al. [14]. the boronepoxy used for repairs of all al-alloys plates, showed a positive life improvement comparatively to graphite-epoxy. several experimental research on fatigue crack growth of patched structures were oriented to the fatigue tests under constant amplitude loading including effect of stress ratio, amplitude of loading, number of ply’, geometry of patches…i.e. [15-19]. it is recognized that aeronautics structures were subjected to variable amplitude loading, essentially characterized by overload and underload [20]. research on variable applied loading (val), determined that appreciable crack growth retardation can occur following tensile overloading for unpatched specimens [21, 22]. in recent study, wang et al. [23] have investigated the effect of single and block loading on fatigue crack growth rates of 2024 t4 al-alloy unpatched ct specimen. it is concluded that single tensile overload introduced in the constant amplitude loading causes a significant retardation of crack growth and similar retardation of crack growth occurs for three-step sequence loading. in repaired of crack specimens, few investigations were conducted to shown the simultaneous effects of patch repair and variable amplitude loading (single overload, stepped sequence loading, underload…). albedah et al. [24] have investigated experimentally the associated effects of patch repair of cracks of plate in aluminum alloy 7075 and stepped variable amplitude loading on fatigue life. a small improvement on fatigue life is noticed in decreasing of loading amplitude blocks. recent study on fatigue crack growth of patched 2024 t3 v-notch specimen was conducted by the same authors [25] under applied of two stepped block (increase/decrease and decrease/increase). a retardation effect was observed for decreasing blocks loading in unrepaired (unpatched) specimens. however, this retardation effect is attenuated by the presence of the patch which leads to lower fatigue life for repaired (patched) specimens. in the case of a bonded repair, different mechanisms may be involved in prediction of fatigue crack growth under variable amplitude loading (val) [26, 27]. it is recognized that peak loads might cause debonds under the patch, resulting in an increased crack growth rate. it was concluded that the effects of peak loads on bonded repairs presents a similar effects of peak loads on unrepaired structures; the crack shows retardation, and no debonds after application of the peak loads were found [27]. fatigue crack growth of fibre reinforced metal laminates (glare) under constant amplitude loading following a single overload was studied experimentally by wu and guo [28]. in this investigation, the mechanisms for the effect of a single overload on the crack growth rates and the delamination growth rates were identified. fatigue tests on bonded glare repairs were performed at room temperature in c-5a galaxy fuselage fatigue spectrum [29]. as can be concluded from obtained result with fatigue spectrum, small load cycles are less important for repaired specimens than for unpatched specimens. the present work is aiming at performing a combined experimental fatigue crack growth data of 2024 t351 al-alloy, analytical integrated models of variable amplitude loading (generalized willenborg model) and composite patch repair (ratwani model) for investigation of fatigue behaviour of repaired edge cracked plate. the study of the fatigue behaviour is conducted on al-alloy edge-cracked plate reinforced by a one-side composite patch. applied spectrum characterized by constant amplitude loading, single or band overloading were investigated. f.z. seriari et alii, frattura ed integrità strutturale, 43 (2018) 43-56; doi: 10.3221/igf-esis.43.03 45 theoretical background stress intensity factor alculation of stress intensity factor at the repaired crack tip is need in order to predict the fatigue life or the fatigue life enhancement of bonded patch repaired of structures or tests specimens. the most commonly materials used in bonded patch repair are boron, graphite, and glare. each of these materials has an application in composite patch repair depending on the metallic material thickness, type of load spectrum, and the stress level in the spectrum [30]. it recognized that repair to a cracked structure involves an upper bound on stress intensity [31]. the stress intensity factor after repair of a cracked structure is lower, by an order of magnitude than for other repair. the thickness of the patch can be chosen based on the following equivalent stiffness criterion [32]:  . . r r p p e t s e t (1) where ep is the cracked structure’s young modulus, tp is the cracked structure’s thickness, er is the equivalent young modulus of the patch perpendicular to the crack and tr is the patch thickness. the stress intensity factor for a cracked structure with no repair can is written as:         .i a k a f w (2) where “” is the remote uniform tensile stress, “a” is half crack length and f(a/w) is finite geometrical correction function. in patched specimen, the stress intensity factor depends on presence of composite patch and width of the patch and numbers of plies. evaluation of boundary correction function for evaluation of stress intensity factor is detailed in research of ratwani [33], boyd et al. [30] and ricci et al. [34]. this analysis is based on a green's function method. currently, this developed formulation implemented in afgrow code [35] is only valid for the following conditions: through the thickness cracks, thin structure (<3.17 mm), non-stiffened panels and crack remains under the patch. the stress intensity factor in the cracked structure with repair patch and applied stress of  is kip. the equivalent stress e acting on a sheet with no repair patch and giving stress intensity factor of kip is given by:          .ip e a k a f w (3) kip may be expressed as:   . /ip e ik k the stress transferred to the repair patch is the difference between the remotely applied stress in the repaired structure and the uniform in-plane stress that produces the same stress intensity factor in a single sheet as in the repaired structure. the stress transferred, t, may be written as:    t e (4) then,     /t ip ik k in the case of one sided repairs, ratwani [33] provided a bending correction factor “bc” and the stress intensity factor is expressed by:   1ip ik bc k (5) the bending correction factor is given by: c f.z. seriari et alii, frattura ed integrità strutturale, 43 (2018) 43-56; doi: 10.3221/igf-esis.43.03 46          max. 1 t t tp p r i i ip k bc a y k (6) where i, tp, tr and ymax are respectively the i is the total moment of inertia of the plate repair, thickness of specimen, thickness of patch and ymax is the distance of the outer sheet edge from neutral axis. fatigue crack growth model the forman/mettu equation [36] also called nasgro equation, used by several researchers [37-40] for prediction and investigation of fatigue crack growth of metals and alloys, is given by:                    ' ' im 1 1 1 1 p th n i i q ax crit k kfda c k dn r k k (7) where c, n, p’, and q’ are empirically derived from experimental fatigue crack growth rate for specified material. the others parameters in equation 7 are detailed in afgrow technical manual [37]. beretta and carboni [38] have used nasgro equation in the investigation of the effect constant amplitude loading (r ratio) and spectrum loading on fatigue crack growth of 30nicrmov12 steel. in order to investigate the effect of variable amplitude loading on fatigue crack growth of patched specimens is necessary to account of the interaction of levels of applied load. generalized willenborg model [41] presents the most common load interaction models used in crack growth life prediction. the model is based on early fracture mechanics work performed at wright-patterson afb, oh. the model uses an "effective" stress intensity factor based on the size of the yield zone in front of the crack tip. the formulation of the generalized willenborg retardation model used in fatigue code and integrated in crack growth equation (3) is given below:           max( ) im min( ) im min( ) max( )/ reff ax reff in eff eff eff k k k k k k r k k (8) kr is the residual stress intensity factor due to overload, it is given by the following equation and reff is the effective stress ratio.       im ( ) im ( ) 1 olr ax ol ax y ol a a k k k r (9) factor  expressed by equation 10, define the level of residual stress induced by application of overload.        im1 / / 1th axk k sorl (10) and the yield zone created by overload ry(ol) is expressed by the following equation:          2 im ( ) ( ) 1 . 2 ax ol y ol e k r (11) f.z. seriari et alii, frattura ed integrità strutturale, 43 (2018) 43-56; doi: 10.3221/igf-esis.43.03 47 where “a” is crack length, “aol” crack length at overload, kth threshold value of stress intensity factor at r=0. in patch repair stress intensity factor kip, given by equation 5, is integrated in equation 8. specimen, material & patch repair   he geometry and dimensions of the single edge through crack specimen aluminium specimens investigated in cyclic loading are presented in fig. 1. the nominal thickness of the aluminium alloy plate, tp, is 3 mm. specimen have length lp=320 mm and width wp=160 mm. at the edge of each specimen there is a through thickness initial crack, having length “a=3 mm”. a composite patch was laminated on one of the sides of the specimen, having thickness tr=2 mm, effective length lr=80 mm and width wr=80 mm. the material, used in this study, was 2024-t351 sheet aluminium alloy. the mechanical properties of are presented in table 1. the composite patch used for repair is boron/epoxy. the mechanical properties of this composite patch (boron/epoxy) are presented in table 2 and adhesive film used for patching is fm-73 where shear’s modulus is gxy= 413.68 mpa and thickness t=0.15 mm. the composite patch was composed by four symmetric ply oriented to the direction (±45.02). the maximal applied remote stress on edge-cracked plate with adhesively bonded composite patch for constant amplitude loading is amax=100 mpa. the spectrum forms of applied cyclic stress for variable amplitude loading are given in fig. 2 for single overload and band overload. the main parameters of fatigue crack growth nasgro equation for investigated material at r=0 are given in table 3.   figure 1: edge-cracked plate with adhesively bonded composite patch 0.2 e (gpa) uts kic (mpa.m1/2) kc (mpa.m1/2)  372.31 73.08 469 37.36 74.72 0.33   table 1: mechanical properties of 2024 t351 al-alloy. el(gpa) et (gpa) glt  206.84 193.05 5171 0.33 table 2: mechanical properties of boron/epoxy. t f.z. seriari et alii, frattura ed integrità strutturale, 43 (2018) 43-56; doi: 10.3221/igf-esis.43.03 48 figure 2: applied spectrum form: (a) constant amplitude loading with single overload (b) with band overload.     c n p’ q’ kth at r=0 1.7110-10 3.353 0.5 1 2.857 table 3: parameters of fatigue crack growth according to nasgro equation. results & discussion his section provides and discusses the obtained results including the effects of variable amplitude loading characterized by single overload ratio and band overload on fatigue life and fatigue crack growth rates respectively in cracked unpatched plate and cracked patched composite plate. also, we investigated the effect of patch repair under constant and variable amplitude loading and presented the result in the following subsections. combined effect of overload ratio and patch repair on the crack growth ig. 3 presents the fatigue life response (crack length vs. cycle number) for unpatched 2024 t351 al-alloy specimen, pre-cracked to a length of 3 mm, under spectrum block (fig. 2a) characterized by the presence of single overload and stress ratio r=0.2. from the presented, we notice a no effect for olr = 1.5 [42]. but from orl=1.8 to 2.0, we notice a little effect on fatigue life. at high overload ratio (orl=2.4), we show significant effect on fatigue life compared to the others overloads ratios and constant amplitude loading. the retardation cycles nd between applied spectrums with constant amplitude loading and with single overload ratio is about 1.4104 cycles.   figure 3: overload ratio effect on fatigue life for unpatched 2024 t351 al-alloy t f f.z. seriari et alii, frattura ed integrità strutturale, 43 (2018) 43-56; doi: 10.3221/igf-esis.43.03 49 figure 4: overload ratio effect on fatigue crack growth rate for unpatched 2024 t351 al-alloy the results shown in fig. 5 indicate that the fatigue life of repaired specimens was improved for all overload ratios. it noticed clearly that the fatigue lives for all overloads ratios were affected highly by composite patch repair (fig. 5) compared to the unpatched plate (fig. 3). also, at low overload ratio (orl=1.5) the same effect of overload ratio comparatively to the unpatched plate. at high overload ratio (orl=2.4) with the presence of patch, the fatigue life is increased from 1.18105 cycles for constant amplitude loading to 2.27105 cycles for orl=2.4 witch represents an increasing ratio in fatigue life of 2 times. fig. 6 presents the evolution of the crack growth rate (da/dn) as a function of the crack length “a” for repaired samples under block loading with single overload for the stress ratio r=0.2. at low crack length (a < 7 mm), we show instantaneous delay for orl=2.0 and 2.4. the decrease in fatigue crack growth rate (da/dn) occurs at a length of 5 mm and varies from 8.9510-8 m/cycle in cal to 4.810-8 m/cycle and 1.9010-8 m/cycle respectively for overload ratios “2” and “2.4”. at this stage, patch gives significant rigidity. for orl=2.0 and at crack length “a=7.7 mm”, deferred delay was shown. but for orl=2.4, the presence of retardation is characterized by deferred delay in various crack length (a= 8.66; 11.10; 14.1; 18.0 and 28.37). at crack length “a=28.37”, the maximum crack growth rate does not exceed the value of 1.1210-4 m/cycle at application of overload ratio and decrease to 6.710-8 m/cycle. for orl=1.8, instantaneous delay is predominant until crack length “a=34 mm” with low effect crack growth rate. for all overload ratios, fatigue crack growth rate keep to constant amplitude fatigue crack growth rate from crack length “a=37 mm” and patch repair effect of disappeared. in detail, figs. 7 and 8 present respectively comparison in fatigue life and crack growth rates between repaired and unrepaired 2024 t351 al-alloy plates for overload ratio orl=2.4. in unrepaired plate under application of the spectrum with single overload, the number of delay cycles “nd” due to overload is about 1.25104 cycles and retarded crack length, “ad”, is 2.97 mm. but in repaired al-alloy plate by boron/epoxy, the total number of delayed cycles, “nd”, is about 19.3104 cycles. this result represents a ratio of improvement in fatigue life about 15.5 times in presence of patch repair comparatively to unrepaired plate. also, the retarded crack length, “ad”, is about 26.5 mm influenced conjointly by applied spectrum with single overload and patch repair. additionally to the combined effect of overload ratio and patch repair given in fig. 6, fig. 8 gives comparisons between fatigue crack growth rates in repaired and unrepaired alloy plates under spectrum with single overload (orl=2.4). in unrepaired plate, is noticed a presence of single instantaneous delay at crack length “a=10.9 mm”. fatigue crack growth rate is increased from 9.0210-7 to 5.5210-8 m/cycle. at same crack length “10.9 mm” in repaired plate, the curves in fig. 8 demonstrate that the crack growth rate decrease with differed delay case and leads to 2.2610-8 m/cycle. the ratio in delayed crack growth rate is 2.44 times. in general, a significant reduction in crack growth rate after 5 mm of crack length is shown. crack growth rates ratio between unrepaired and repaired plates in constant amplitude phases varies from 2.5 to 16.6 times. the high percentage of the beneficial effect in fatigue crack growth rate is related to the effect of patch repair characterized by the reduction in stress intensity factor [43] compared to the effect of variable amplitude loading with single overload. f.z. seriari et alii, frattura ed integrità strutturale, 43 (2018) 43-56; doi: 10.3221/igf-esis.43.03 50 figure 5: overload ratio effect on fatigue life for repaired 2024 t351 al-alloy plate. figure 6: overload ratio effect on crack growth rates for repaired 2024 t351 al-alloy plate. the relationships between retard ratio “ d caln n ” and overload ratio “orl” for repaired and unrepaired plate are plotted on a log-log graph in fig. 9. it is seen from the plot that all the points seem to lie on a straight line on the log-log scale for unrepaired plate given by power function [42]. on the others hand, the plot in repaired plate case is given by logarithmic function. the developed equations for the both cases (repaired and unrepaired) are given below:                3.483416.9 10 3.305 1.31 re d cal d cal n orl unrepaired n n ln orl paired n (12) influence of band overloading parameter on patch repair a few investigators have studied the effect of multi overload and band overloading cycles on crack growth retardation. however no attempt has been made to predict fatigue life and fatigue crack growth in multi band overloading case. in the present attempt interaction of multi band overload is investigated. the spectrum of band overloading given by figure 2b is applied and the overload band is characterized by the parameter “q”. f.z. seriari et alii, frattura ed integrità strutturale, 43 (2018) 43-56; doi: 10.3221/igf-esis.43.03 51 figure 7: influence of composite patch repair on fatigue life under variable amplitude loading (orl=2.4) figure 8: influence of composite patch repair on fatigue crack growth rate under variable amplitude loading (orl=2.4) figure 9: retard ratio “ d caln n ” vs overload ratio f.z. seriari et alii, frattura ed integrità strutturale, 43 (2018) 43-56; doi: 10.3221/igf-esis.43.03 52 the results of predicted fatigue life and crack growth rates of repaired plate are presented respectively in figs. 10 and 11 at orl=2.4. it has shown clearly that applied spectrum causes noticeable crack growth delay for “q” equal or less then 100 cycles after constant amplitude compared to constant amplitude loading. figure 10: influence of band overloading parameter “q” on fatigue life for patched crack repair at orl=2.4. figure 11. influence of band overloading parameter “q” on delay ratio nd/ncal in repaired plate. delay in fatigue life decrease with increasing band overloading parameter “q” from 1 to 100. no effect of band overloading at “q=10” is noticed comparatively to the single overload on fatigue life, expected in delayed crack length “ad”. at “q=1 cycle”, the total delayed crack length “ad” is about of 26.82 mm; but for “q=10 cycles”, total delayed crack length is about of 31.51 mm witch presents approximately 4.69 mm in difference. the delay cycles after application of specified spectrum with the presence of patch repair for band overloading cycles “q=100 cycles” is about 1.37105 cycles compared to constant amplitude loading. these delays cycles increases for single overload “q=1” and band overload “q=10” and are respectively, 2.22105 and 2.19105 cycles. also, these delays is attributed to the crack closure effect [44-46] under application of multiple variable spectrums with band overload from “q=1” to “q=100” cycles. the relationship between the retard ratio nd/ncla and band overload “q” is plotted in fig. 12. the developed equation has exponential form and is given below:    1.925 0.005d cal n exp q n (13) f.z. seriari et alii, frattura ed integrità strutturale, 43 (2018) 43-56; doi: 10.3221/igf-esis.43.03 53 in term of crack growth rate, fatigue behavior under application of band overloading is characterized by differed delay for “q” greater than one cycle (single overloading) (fig. 11). crack growth rates are stabilisation at high value after application of band overloading in high stress intensity factor i.e. at high of crack length values with loss of patch rigidity. figure 12: influence of band overloading parameter “q” on crack growth rates of crack patch repair at orl=2.4. conclusion atigue crack propagation predictions were carried out on patched and unpatched 2024 t351 al-alloy plates. performance of composite patch repair was evaluated under constant amplitude and variable amplitude loading conditions. combination of retardation model (modified willenborg model) and patch repair accounting of ratwani model have given good prediction of composite patch repair performances. from the results of the present investigation, we can conclude that:  after application of overload, instantaneous delay is noticed in unrepaired specimens witch theirs levels depends upon the amount of overload.  also, in composite patch repair, differed delays have affected the total fatigue life and crack growth rates  high efficiency is given in fatigue life for repaired specimens.  as the overload ratio (orl) increases, the fatigue life increases for both repaired and unrepaired specimens  the fatigue life is found to be larger if the applied overload was important (orl=2.4) compared to constant amplitude loading in unrepaired and repaired specimens.  the fatigue life increases in each periodic band of overload “q” as compared to constant amplitude loading. also the fatigue life decreases in increasing of band of overload “q”.  finally, experimental studies are needed in order to understanding of the key mechanisms that affect the efficiency of the patch repair under variable amplitude loading effects. references [1] baker, a.a., fatigue crack propagation studies on aluminium panels patched with boron/epoxy composites. in: jones r, miller nj, international conference on aircraft damage assessment and repair, melbourn, australia, (1991) 209-215. [2] baker, a.a., fibre composite repair of cracked metallic aircraft components practical and basic aspects. composites, 18 (1987) 293-308. doi: 10.1016/0010-4361(87)90293-x. [3] baker, a.a., rose, l.r.f., jones, r., advances in the bonded composite repair of metallic aircraft structures. elsevier publisher, amsterdam (2002). f f.z. seriari et alii, frattura ed integrità strutturale, 43 (2018) 43-56; doi: 10.3221/igf-esis.43.03 54 [4] baker, a.a., crack patching: experimental studies, practical applications. in: a.a. baker and r. jones (eds), bonded repair of aircraft structures. dordrecht (nl): martinus nijhoff publishers (1988) 107-173. [5] woerden, h.m., mortier, w.j., guijt, c.b., verhoeven, s., bonded repair patches. in: a. vlot et al. (eds.), fibre metal laminates, kluwer academic publishers (2001). [6] sabelkin, v., mall, s., hansen, m.a., vandawaker, r.m., derriso, m., investigation into cracked aluminum plate repaired with bonded composite patch. composite structures 79 (2007) 55–66. doi: 10.1016/j.compstruct.2005.11.028. [7] tsamasphyros, g.j., kanderakis, g.n., karalekas, d., rapti, d., gdoutos, e.e., zacharopoulos, d., marioli-riga, z.p., study of composite patch repair by analytical and numerical methods. fatigue fract engng mater struct 24 (2001) 631–636. doi: 10.1046/j.1460-2695.2001.00414.x/abstract. [8] costa, m., viana, g., da silva, l.f.m., campillo, r.d.s.g., effect of humidity on the fatigue behaviour of adhesively bonded aluminium joints. latin american journal of solids and structures 14 (2017) 174-187. [9] negru, r., serban, d.a., marsavina, l., magda, a., lifetime prediction in medium-cycle fatigue regime of notched specimens. theoretical and applied fracture mechanics, 84 (august 2016), 140-148. doi: 10.1016/j.tafmec.2016.03.006. [10] sabelkin, v., mall, s. avram, j.b., fatigue crack growth analysis of stiffened cracked panel repaired with bonded composite patch. engineering fracture mechanics 73 (2006) 1553-67. doi: 10.1016/j.engfracmech.2006.01.029 [11] marsavina, l., sadowski, t., knec, m. crack propagation paths in four point bend aluminium–pmma specimens. engineering fracture mechanics, 108 (august 2013), 139-151. doi: 10.1016/j.engfracmech.2013.02.029. [12] salehi-khojin, a., thoreson, a.r., zhong, w.h., stone, j.j., gan, y.x., the effect of patch geometry on the static and fatigue behaviors of defective aluminum panels repaired with a composite patch, journal of adhesion science and technology 20(6) (2006) 537-554. doi: 10.1163/156856106777213311. [13] ricci, f., franco, f., montefusco, n., experimental and numerical analysis of the fatigue behaviour of panels repaired by patches in composite material. key engineering materials, 417-418 (2010) 597-600. doi: 10.4028/www.scientific.net/kem.417-418.597. [14] schubbe, j.j., bolstad, s.h., reyes, s., fatigue crack growth behavior of aerospace and ship-grade aluminum repaired with composite patches in a corrosive environment, composite structures 144 (2016) 44–56. doi: 10.1016/j.compstruct.2016.01.107. [15] klug, c., sun, c.t., large deflection effects of cracked aluminum plates repaired with bonded composites patches, composite structures 42 (1988) 291–296. doi: 10.1016/s0263-8223(98)00018-x. [16] duquesnay, d.l., underhill, p.r., britt, h.j., fatigue failure of adhesively patched 2024-t3 and 7075-t6 clad and bare aluminium alloys, fatigue fract engng mater struct 28 (2005) 381-389. doi: 10.1111/j.1460-2695.2005.00869.x/abstract. [17] hosseini-toudeshky, h., effects of composite patches on fatigue crack propagation of single-side repaired aluminum panels. composite structures 76 (2006) 243–251. doi: 10.1016/j.compstruct.2006.06.028. [18] pastor, m.l., balandraud, x., robert, j.l. grediac, m., lifetime prediction of aluminium structures reinforced with composite patches. international journal of fatigue 31(2009) 850-58. doi: 10.1016/j.ijfatigue.2008.11.009. [19] mall, s., schubbe, j.j., bonded composite patch geometry effects on fatigue crack growth in thin and thick aluminum panels. tech science press, sl: structural longevity 2(1) (2009) 25-47. [20] dawicke, d.s., overload and underload effects on the fatigue crack growth behaviour of the 2024-t3 aluminum alloy. nasa contractor report 201668, dawicke analytical services & materials, inc., hampton, virginia (1997). [21] corbley, d.m., packman, p.f., on the influence of single and multiple peak overloads on fatigue crack propagation in 7075 t6511 aluminum, engineering fracture mechanics 5(1973) 479-497. doi: 10.1016/0013-7944(73)90034-9. [22] kermanidis, a.t., pantelakisn, s.g., prediction of crack growth following a single overload in al-alloy with sheet and plate microstructure. engineering fracture mechanics 78 (2011) 2325-2337. doi: 10.1016/j.engfracmech.2011.05.005. [23] wang, c., wang, x., ding, z., xu, y., gao, z., experimental investigation and numerical prediction of fatigue crack growth of 2024-t4 aluminum alloy, international journal of fatigue 78(2015) 11-21. doi: 10.1016/j.ijfatigue.2015.03.024. [24] albedah, a., khan, s.m.a., benyahia, f., bachir bouiadjra, b., experimental analysis of the fatigue life of repaired cracked plate in aluminum alloy 7075 with bonded composite patch, engineering fracture mechanics 145 (2015) 210220. doi: 10.1016/j.engfracmech.2015.04.008. [25] albedah, a., khan, s.m.a., benyahia, f., bachir bouiadjra, b., effect of load amplitude change on the fatigue life of cracked al plate repaired with composite patch, international journal of fatigue 88 (2016) 1-9. doi: 10.1016/j.ijfatigue.2016.03.002. f.z. seriari et alii, frattura ed integrità strutturale, 43 (2018) 43-56; doi: 10.3221/igf-esis.43.03 55 [26] verhoeven, s., preparation of the spectrum testing of bonded glare repairs for the c-5a galaxy, a study of the interaction effects of peak loads on bonded repairs and a proposal for the modification of c-5a aft crown spectrum data. tz report, delft university of technology, the netherlands (1997). [27] wang, c.h., rose, l.r.f., baker, a.a., modelling of the fatigue growth behaviour of patched cracks. international journal of fracture 88 (1998) l65–l70. [28] wu, x.r., guo, y.j., fatigue behaviour and life prediction of fibre reinforced metal laminates under constant and variable amplitude loading, fatigue fract. engng mat. struct. 25 (2002) 417–432, doi: 10.1046/j.1460-2695.2002.00517.x/abstract. [29] vlot, a., massar, j.m.a., guijt, c.b., verhoeven, s., bonded aircraft repairs under variable amplitude fatigue loading and at low temperatures, fatigue fract. engng mat. struct. 23 (2000) 9-18. doi: 10.1046/j.1460-2695.2000.00250.x/abstract. [30] boyd, k.l. krishnan, s., litvinov, a., eisner, j.h., harter, j.a., ratwani, m.m., glinka, g., development of structural integrity analysis technologies for aging aircraft structures: bonded composite patch repair and weight function methods. analytical services & materials, inc., hampton virginia for wl/fibec, wright-patterson air force base, ohio (1997). [31] baker, a.a., jones, r., bonded repair of aircraft structures. dordrecht, netherlands, martinus nijhoff publisher (1988). [32] royal australian airforce engineering standard c5033, composite materials and adhesive bonded repairs. raaf headquarters logistics command, melbourne, vic., australia (1995). [33] ratwani, m.m., analysis of cracked adhesively bonded laminated structures. aiaa journal 17(9) (1979) 988-994. doi: 10.2514/3.61263. [34] ricci, f., franco, f. montefusco, n., bonded composite patch repairs on cracked aluminum plates: theory, modeling and experiments. in: advances in composites materials ecodesign and analysis. edited by brahim attaf, intech publisher, croatia (2011). [35] harter, j.a., afgrow users guide and technical manual afgrow for windows 2k/xp. version 4.0011.14, air force research laboratory (2006). [36] forman, r.g., mettu, s.r., behavior of surface and corner cracks subjected to tensile and bending loads in ti-6al-4v alloy. fracture mechanics 22nd symposium, vol. 1, astm stp 1131, h.a. ernst, a. saxena and d.l. mcdowell, eds., american society for testing and materials, philadelphia (1992). [37] zhang, w., wang, q., li, x., he, j., a simple fatigue life prediction algorithm using the modified nasgro equation, mathematical problems in engineering, (2016) id 4298507. [38] beretta, s., carboni, m., simulation of fatigue crack propagation in railway axles. journal of astm international 2(5) id jai12040 (2005): 368-381. doi: 10.1520/jai12040. [39] skorupa, m., machniewicz, t., schijve, j., skorupa, a., application of the strip-yield model from the nasgro software to predict fatigue crack growth in aluminium alloys under constant and variable amplitude loading, engineering fracture mechanics 74 (2007) 291–313. doi: 10.1016/j.engfracmech.2006.06.014. [40] maierhofer, j., pippan, r., gänser, h.p., modified nasgro equation for physically short cracks, international journal of fatigue 59 (2014) 200–207. doi: 10.1016/j.ijfatigue.2013.08.019. [41] gallagher, j.p., a generalized development of yield-zone models,” affdl-tm-74-28, air force flight dynamics laboratory, wright-patterson air force base, ohio (1974). [42] kumar, r., prediction of delay cycles due to instant of single overload cycles, engineering fracture mechanics 42(3) (1992) 563-571. doi: 10.1016/0013-7944(92)90174-d. [43] benachour, m, seriari, f.z, benachour, n., benguediab, m., beneficial patch repair effect on fatigue crack growth of al-alloy 7050, applied mechanics and materials 225 (2012) 158-164. doi: 10.4028/www.scientific.net/amm.225.158. [44] černý, i, mikulová, d., evaluation of overloading and crack closure effects on fatigue crack growth in an aircraft 7075-t7351 al-alloy. key engineering materials 577-578 (2014) 325-28. doi: 10.4028/www.scientific.net/kem.577-578.325. [45] topper, t., duquesnay, d., the effects of overloads in service load histories on crack closure and fatigue damage, sae technical paper 2001-01-4079 (2001), doi:10.4271/2001-01-4079. [46] salvati, e., o’connor, s., sui, t., nowell, d., korsunsky, a.m., a study of overload effect on fatigue crack propagation using ebsd, fib-dic and fem methods. engineering fracture mechanics 167 (2016) 210-223. doi: 10.1016/j.engfracmech.2016.04.034. f.z. seriari et alii, frattura ed integrità strutturale, 43 (2018) 43-56; doi: 10.3221/igf-esis.43.03 56 nomenclature a crack length aol crack length at applied overload a0 initial crack length bc bending correction c, n material constants of fatigue crack growth da/dn fatigue crack growth rate ep cracked structure’s young modulus el young modulus of composite patch in longitudinal direction er equivalent young modulus of the patch perpendicular to the crack et young modulus of composite patch in transversal direction f crack closure factor f(a/w) finite geometrical correction function gxy shear’s modulus of adhesive film glt shear’s modulus of composite patch ki stress intensity factor for cracked structures kip stress intensity factor for cracked structures with patch kic critical stress intensity factor for plane strain kc critical stress intensity factor for plane stress ki amplitude of stress intensity factor kth threshold of stress intensity factor kcrit critical stress intensity factor kimax maximal stress intensity factor kmaxeff, kmineff effective stress intensity factor kr residual stress intensity factor lr length of composite patch r stress ratio sorl overload zone factor orl overload ratio cal constant amplitude loading val variable amplitude loading reff effective stress ratio ry(ol) yield zone created by overload nd/ncal retard ratio wp width of plate wr width of composite patch i total moment of inertia tr thickness of patch tp cracked structure’s thickness, ymax distance of the outer sheet edge from neutral axis p’ , q’ constant empirically derived from experimental fatigue crack growth rate p, q length of applied spectrum at constant and variable amplitude amax maximum applied stress  remote 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can be opened with acrobat and adobe reader 5.0 and later.) >> /namespace [ (adobe) (common) (1.0) ] /othernamespaces [ << /asreaderspreads false /cropimagestoframes true /errorcontrol /warnandcontinue /flattenerignorespreadoverrides false /includeguidesgrids false /includenonprinting false /includeslug false /namespace [ (adobe) (indesign) (4.0) ] /omitplacedbitmaps false /omitplacedeps false /omitplacedpdf false /simulateoverprint /legacy >> << /addbleedmarks false /addcolorbars false /addcropmarks false /addpageinfo false /addregmarks false /convertcolors /converttocmyk /destinationprofilename () /destinationprofileselector /documentcmyk /downsample16bitimages true /flattenerpreset << /presetselector /mediumresolution >> /formelements false /generatestructure false /includebookmarks false /includehyperlinks false /includeinteractive false /includelayers false /includeprofiles false /multimediahandling /useobjectsettings /namespace [ (adobe) (creativesuite) (2.0) ] /pdfxoutputintentprofileselector /documentcmyk /preserveediting true /untaggedcmykhandling /leaveuntagged /untaggedrgbhandling /usedocumentprofile /usedocumentbleed false >> ] >> setdistillerparams << /hwresolution [2400 2400] /pagesize [612.000 792.000] >> setpagedevice microsoft word numero_42_art_26.docx a. khitab et alii, frattura ed integrità strutturale, 42 (2017) 238-248; doi: 10.3221/igf-esis.42.26 239 fracture toughness and failure mechanism of high performance concrete incorporating carbon nanotubes anwar khitab, sajjad ahmad mirpur university of science and technology, mirpur ajk, pakistan chairman.ce@must.edu.pk, http://orcid.org/0000-0001-2345-6789 sajjad.ce@must.edu.pk, http://orcid.org/0000-0002-1139-8726 rao arsalan khushnood, syed ali rizwan national university of sciences and technology, islamabad, pakistan arsalan.khushnood@nice.nust.edu.pk, http://orcid.org/0000-0002-9532-4096 syedalirizwan@hotmail.com, http://orcid.org/0000-0001-2345-6789 giuseppe andrea ferro, luciana restuccia politecnico di torino, turin, italy ferro@polito.it, http://orcid.org/0000-0002-2345-6790 luciana.restuccia@polito.it, http://orcid.org/0000-0001-2345-6789 mustajab ali, imran mehmood mirpur university of science and technology, mirpur ajk, pakistan mustajab.ce@must.edu.pk, http://orcid.org/0000-0001-2345-67989 imran.mehmood@must.edu.pk, http://orcid.org/0000-0001-2345-6789 abstract. cement and concrete composites are inherently brittle and exhibit very less tensile/flexural strength capacity as compared to their compressive strength. use of thoroughly dispersed carbon nanotubes in the concrete matrix is one of the possible solution for enhancing mechanical properties in tension/flexure. in the present research work, small fractions of multiwall carbon nanotube (mwcnts) i.e. 0.05 and 0.10 wt% of cement have been integrated into the cement concrete to study their effect on the mechanical properties of the resultant concrete mixtures. the enhanced performance of the whole mix lies on a single point that mwcnts must be thoroughly disperse in the mixture. hence, special arrangement through usage of high energy sonication along with amended acrylic based polymer (performing as a surfactant) was made to have a uniform dispersion of mwcnts in the concrete mix. the testing of concrete samples includes i.e., flexure, splitting tensile and compressive strengths after 3, 7, 28 and 56 days of curing. after having comparison with the control mix cured for 28 days, it was observed that the addition of 0.05 wt% mwcnts increased the splitting citation: khitab, a., ahmad, s., khushnood, r.a., rizwan, s.a., ferro, g.a., restuccia, l., ali, m., mehmood, i., fracture toughness and failure mechanism of high performance concrete incorporating carbon nanotubes, frattura ed integrità strutturale, 42 (2017) 238-248. received: 25.06.2017 accepted: 25.07.2017 published: 01.10.2017 copyright: © 2017 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. a. khitab et alii, frattura ed integrità strutturale, 42 (2017) 238-248; doi: 10.3221/igf-esis.42.26 240 tensile strength by 20.58%, flexural strength by 26.29% and compressive strength by 15.60%. through above results, which verify the increase in concrete mix strength after adding mwcnts, these mwcnts may be incorporated in the treatment of nano/micro cracks completed through process of connecting, branching and pinning. similarly, as proved in threepoint bending tests, mwcnts also enhances the breaking strains as well as the fracture energy of the concrete mixes, besides, imparting increase to the strength. the investigations have shown that incorporating lesser amounts of mwcnts i.e., 0.05 and 0.10 wt% of cement to the concrete mixes after insuring there complete dispersion, unusually improve their properties like mechanical strengths and fracture behavior. keywords. concrete; fracture energy; mwcnts; toughness; critical pullout length; micro cracking. introduction ement and concrete composites are the basic construction materials which are extensively used around the globe [1]. the production of cement involves generation of enormous amounts of anthropogenic carbon dioxide (co2) in the atmosphere, contributing approximately 5.0% co2 generation around the globe. beside this, other environmental concerns are also associated with the use of cement and concrete composites such as depletion of virgin aggregates and its impact on the ecosystem [2]. ordinary cement and concrete composites offer much flexibility and cost effectiveness in their utilization but they are vulnerable to physical and chemical attacks affecting their performance in service life span; therefore, requiring costly repair and maintenance works. construction of super-paves, tunneling, long span structural members and pre-stress technology demand the concretes of ultra-high strength and performance. for effective service life in different situations and under different loading conditions, ordinary concrete is not much beneficial. therefore, the production of modified concrete with exceptional properties in terms of mechanical strength and with minimum amount of cement is highly desired so that economical and sustainable construction may be achieved along with reduction in co2 emissions in the atmosphere [3]. the idea of nanotechnology for the modification of composite properties at nano scale is not new in relation to the construction materials. nanotechnology deals with the synthesis, characterization, utilization and analysis of materials at nano scale [4]. several researchers have explained that the properties of cement and concrete composites may greatly be modified by using nano and micro sized particle inclusions in the matrix [5–12]. the nano level inclusions in concrete have shown improved durability, mechanical strength, porosity reduction and economical construction [13–19]. the nano metric inclusions includes nano silica, graphene, multi walled carbon nano tubes (mwcnts), nano caco3, nano tio2 etc. [20–26]. the studies show that these inclusions not only improve the packing of particles but also produce crack bridging phenomena by densifying the nanostructures [18,27]. nano particles control the c-s-h reaction and improves the concrete durability [28–33]. among above mentioned nano materials, mwcnts possess unique and exceptional characteristics in terms of physical and mechanical properties. mwcnts have tubular structure composed of folded layers of graphene with exceptionally high aspect ratios [34–37]. several researchers have reported the utilization of mwcnts in preparing cement and mortar composites and studied the behavior but limited work is available describing the full-scale utilization of the mwcnts in the concrete matrix. therefore, in the present research, mwcnts were utilized in the preparation of concrete matrix and their influence on the mechanical behavior of concrete is discussed in detail. experimental program materials he concrete mixes were prepared from ordinary portland cement (astm type 1 grade 52.5), having specific gravity of 3.10. locally available sand having fineness modulus of 2.13 and water absorption of 2.87% was utilized. crushed lime stone aggregates confirming to the astm c33 were incorporated in the concrete mix. the c t a. khitab et alii, frattura ed integrità strutturale, 42 (2017) 238-248; doi: 10.3221/igf-esis.42.26 241 characteristics of mwcnts used for the preparation of concrete samples are presented in tab. 1. diameter (nm) length (µm) purity (%) surface area (m2/g) 6-25 10-50 >90% 250-300 table 1: physical characteristics of mwcnts. dispersion of mwcnts the dispersion of mwcnts was achieved with the help of bath sonication in the presence of modified acrylic based surfactant. for attaining good dispersion of mwcnts in water, a solution of surfactant and water was prepared and then the measured amount of mwcnts was added to the solution. the solution was sonicated for 20 min at 25±5oc. the dispersion was assessed qualitatively by filling test tubes with dispersed mwcnts solution and observing the color of solution for next 48 h. the observations revealed that the mwcnts did not settle down in the test tube and remained in the solution indicating effective dispersion of mwcnts. the composition details of solution containing dispersed mwcnts are presented in tab. 2. designation water (g) surfactant (g) mwcnts (g) comments r 100 2.0 0.000 reference mix mix containing 0.00% mwcnts by mass of cement cnt0.05 100 2.0 0.125 mix containing 0.05% mwcnts by mass of cement cnt0.10 100 2.0 0.250 mix containing 0.10% mwcnts by mass of cement table 2: composition of solution containing dispersed mwcnts. mixture proportioning and sample preparation the sand, aggregate and cement were mixed in dry condition as per the required quantities mentioned in tab. 3. after dry mixing half of the water containing mwcnts was added into the mixing machine and mixing was continued for 120 seconds at slow speed. after slow mixing, the machine was stopped for 30 seconds and walls of the machine were cleaned by trowel to separate any material attached to them. then remaining water was added into the mix and the mixing was continued for 120 more seconds at high speed to achieve workable concrete mixture [38]. the mix proportions of concrete containing mwcnts are reported in tab. 3. designation cement (kg/m3) sand (kg/m3) aggregate (kg/m3) water (kg/m3) surfactant (kg/m3) mwcnts (g/m3) r 476 690 1047 190.40 3.81 cnt0.05 476 690 1047 190.40 3.81 238 cnt0.10 476 690 1047 190.40 3.81 476 table 3: mix proportions of concretes containing mwcnts. after complete mixing, the concrete was poured into standard cylinders having 150 mm diameter and 300 mm height and beam molds of 100 mm x 100 mm x 400 mm. the molds were then kept in closed containers having 90% humidity for 24 h. the dried samples were then removed from the molds, labeled, weighed and cured in water at 25±2oc until the day of testing. the beam samples were notched with water cooled diamond saw blade and tested in three-point bending under crack mouth opening displacement (cmod) controlled mode. the rate of cmod was kept at 0.50 mm/min. the schematic diagram of test setup and sample geometry are shown in fig. 1. a. khitab et alii, frattura ed integrità strutturale, 42 (2017) 238-248; doi: 10.3221/igf-esis.42.26 242 figure 1: schematic diagram of (a) test setup; (b) specimen geometry. results and discussion performance evaluation of samples in tension and flexure he cylindrical specimens were tested as per astm c496 for determining their splitting cylinder tensile strengths at 3, 7, 28 and 56 days of curing under constant rate of loading i.e. 0.8 mpa/min. the test results are presented in fig. 2 (a) below. the results revealed that the mixes containing mwcnts exhibit higher tensile strength as compared to the plain concrete samples. maximum enhancement around 26% was observed for cnt0.05 at 56 days of age whereas, it was around 18% for cnt0.10. the overall trend shows that the addition of small amounts of mwcnts produce better results. this behavior may be attributed to the effective dispersion of mwcnts at lower percentage addition. whereas, in case of enhancement of compressive strength of modified samples the direct relation between the amount of mwcnts inclusion and modification of strength was observed. it reveals that the reduction of effective water content ultimately results into the improvement in compressive strength. dispersion concerns and agglomeration sometimes cause a reduction in the strength with increase in the quantity of mwcnts [39]. figure 2: (a) splitting cylinder tensile strength of concrete mixes; (b) modulus of rupture of concrete mixes. the three-point bending tests showed similar trend as produced by the splitting cylinder tensile tests. overall better performance was achieved at 0.05wt.% addition of mwcnts. a typical stress vs. crack mouth opening displacement (cmod) curve is presented in fig. 3, where it can be seen that the mwcnts not only enhances the modulus of rupture but also substantially prolongs the post peak response of the specimens under investigation. the extended post peak behavior of concrete reinforced with mwcnts is due to the crack bridging phenomena of mwcnts, which imparts ductility and toughness. t (a) (b) a. khitab et alii, frattura ed integrità strutturale, 42 (2017) 238-248; doi: 10.3221/igf-esis.42.26 243 figure 3: typical stress vs. cmod curves of concrete specimen with and without mwcnts. performance evaluation of samples in compression the concrete samples were also investigated for their compressive strength at 3, 7, 28 and 56 days of curing to assess the influence of mwcnts addition on compressive behavior of concrete. the results of the compressive strength tests are presented in fig. 4. the results indicate that the mix containing higher amount of mwcnts exhibit higher compressive strength as compared to others. at 56 days of curing, the mix cnt0.10 gives 24.66% higher compressive strength than the control mix whereas; the enhancement was 19.11% for the mix cnt0.05. similar pattern can be observed for strength at other ages. figure 4: compressive strength of concrete mixes with and without mwcnts unlike flexural and tensile behavior, where better performance was observed at 0.05 wt% addition of mwcnts; here in compression, the performance improves with the increase in the mwcnts addition. this behavior may be attributed to the reduction in water content (i.e. effective w/c ratio) in the concrete mix due to the presence of large number of mwcnts. strength activity indices of concrete mixes for relative comparison of the influence of mwcnts addition on the concrete mixes strength activity indices were evaluated and reported in fig. 5 (a, b & c) below. the observations reveal that the concrete mixes containing 0.05 wt% mwcnts perform better in splitting tensile strength and modulus of rupture whereas, concrete containing 0.10 wt% addition of mwcnts perform better in compression as explained earlier. a. khitab et alii, frattura ed integrità strutturale, 42 (2017) 238-248; doi: 10.3221/igf-esis.42.26 244 figure 5: strength activity indices for concrete mixes containing mwcnts (a) splitting tensile strength, (b) flexural strength, and (c) compressive strength. theoretical analysis of composite behavior the mechanical performance of mwcnts reinforced cementitious composites strictly depends upon their volume fraction, level of dispersion and average center-to-center distance in the matrix. according to the fiber spacing theory of romualdi, the center to center distance between the inclusions is inversely related to the resistance offered by the composites to the progression of cracks [40]. this theory has been validated by several researchers and this may explain the phenomena of lower performance of cementitious composites in flexure containing higher amounts of mwcnts [41,42]. when a flexural load is applied on the mwcnts reinforced specimen, the load is transferred to the individual mwcnts making them pull out from the matrix providing improved flexural strength and fracture energy. the improved tensile strength of the reinforced matrix may be computed by using following expression (eq.1) which is further related to flexural strength of concrete specimen as presented in eq.2 [43].  2 /tfc l o c c cl d v    (1) 0.41t bfc fc  (2) where, tfc is the tensile strength of the reinforced composite, l is the coefficient of mwcnts length, o is the orientation coefficient of mwcnts, cl is average mwcnts length, cd is the average mwcnts diameter,  is average bonding strength and cv is the volume fraction of mwcnts in the matrix and b fc is the flexural strength of the mwcnts reinforced concrete. the mwcnts must be embedded in the matrix to some critical length ( critcl ) so that the inclusion may observe full tensile capacity. the critcl may be termed as critical pull-out length which may be evaluated from following expression [44]: / 2critc c c o c fcl l v     (3) (a) (b) (c) a. khitab et alii, frattura ed integrità strutturale, 42 (2017) 238-248; doi: 10.3221/igf-esis.42.26 245 the results of the above expression indicate that the critical pullout length of mwcnts increases with their percentage inclusion in the concrete (fig. 6). the increase in critical length reduces the effective stress that may be developed in the mwcnt bridging a growing crack. fig. 7 represents the stress development in mwcnts as a relation of their embedment lengths. figure 6: relationship of critical pullout length and content of mwcnts in the concrete matrix. figure 7: relationship of embedment length and stress development in mwcnts [44] conclusions n this paper, the remarkable improvement in the mechanical properties of concrete was observed on the inclusion of small fractions (i.e. 0.05 wt% of cement) of mwcnts in concrete matrix. the effects and behavior of mwcnts addition is purely dependent upon the dispersion and content of mwcnts in the mix. many other factors other than dispersion, are also associated with effective outcomes of the inclusion of mwcnts in concrete i.e., size, aspect ratio, purity etc. of mwcnts being utilized in the mix. from the present study, it may be concluded that the same amount of mwcnts may exhibit different behavior in certain mechanical properties of concrete mix i.e. the lower amount of mwcnts is fruitful in case of enhancement of tensile and flexural strength as evident by the theoretical analysis but in case of compressive strength the larger fraction is more effective. i a. khitab et alii, frattura ed integrità strutturale, 42 (2017) 238-248; doi: 10.3221/igf-esis.42.26 246 acknowledgements he authors acknowledge the partial financial support of higher education commission, pakistan for this research. references [1] brandt, a.m., cement based composites; materials, mechanical properties and performance, 2nd ed., taylor & francis, (2009). [2] khitab, a., anwar, w., advanced research on nanotechnology for civil engineering applications, igi global disseminator of knowledge, (2016). [3] khalid, a.r., rizwan, s.a., hanif, u., hameed, m.h., effect of mixing time on flowability and slump retention of self-compacting paste system incorporating various secondary raw materials, arab. j. sci. eng., 41 (2016) 1283–1290. doi:10.1007/s13369-015-1885-5. [4] khitab, a., anwar, w., mansouri, i., tariq, m.k., mehmood, i., future of civil engineering materials: a review from recent developments, rev. adv. mater. sci., 42 (2015) 20–27. [5] raki, l., beaudoin, j., alizadeh, r., makar, j., sato, t., cement and concrete nanoscience and nanotechnology, materials (basel), 3 (2010) 918–942. doi:10.3390/ma3020918. [6] lopez, a., ferro, g.a., jagadale, p., tulliani, j.-m., influence of carbon nanotubes addition onto the mechanical properties of restoration mortars, in: convegno naz. igf xxii, rome, italy, (2013) 278–286. [7] ferro, g.a., tulliani, j.m., lopez, a., jagdale, p., new cementitious composite building material with enhanced toughness, theor. appl. fract. mech., 76 (2015) 67–74. doi:10.1016/j.tafmec.2015.01.005. [8] ahmad, s., khushnood, r.a., jagdale, p., tulliani, j.-m., ferro, g.a., high performance self-consolidating cementitious composites by using micro carbonized bamboo particles, mater. des., 76 (2015) 223–229. doi:10.1016/j.matdes.2015.03.048. [9] khushnood, r.a., rizwan, s.a., memon, s.a., tulliani, j., ferro, g.a., experimental investigation on use of wheat straw ash and bentonite in self-compacting cementitious system, adv. mater. sci. eng., (2014) 1–11. doi:10.1155/2014/832508. [10] khushnood, r.a., ahmad, s., restuccia, l., spoto, c., jagdale, p., tulliani, j.-m., ferro, g.a., carbonized nano/microparticles for enhanced mechanical properties and electromagnetic interference shielding of cementitious materials, front. struct. civ. eng., 10 (2016) 209–213. doi:10.1007/s11709-016-0330-5. [11] ferro, g.a., ahmad, s., khushnood, r.a., restuccia, l., tulliani, j.-m., improvements in self-consolidating cementitious composites by using micro carbonized aggregates, frattura ed integrità strutturale, 30 (2014) 75–83. doi:10.3221/igf-esis.30.11. [12] ahmad, s., tulliani, j.-m., ferro, g.a., khushnood, r.a., restuccia, l., jagdale, p., crack path and fracture surface modifications in cement composites, frattura ed integrità strutturale, 9 (2015) 524–533. doi:10.3221/igf-esis.34.58. [13] lothenbach, b., scrivener, k., hooton, r.d., supplementary cementitious materials, cem. concr. res., 41 (2011) 1244–1256. doi:10.1016/j.cemconres.2010.12.001. [14] lothenbach, b., le saout, g., gallucci, e., scrivener, k., influence of limestone on the hydration of portland cements, cem. concr. res., 38 (2008) 848–860. doi:10.1016/j.cemconres.2008.01.002. [15] wu, z., shi, c., khayat, k.h., wan, s., effects of different nanomaterials on hardening and performance of ultrahigh strength concrete (uhsc), cem. concr. compos., 70 (2016) 24–34. doi:10.1016/j.cemconcomp.2016.03.003. [16] khushnood, r.a., ahmad, s., savi, p., tulliani, j.-m., giorcelli, m., ferro, g.a., improvement in electromagnetic interference shielding effectiveness of cement composites using carbonaceous nano/micro inerts, constr. build. mater., 85 (2015) 208–216. doi:10.1016/j.conbuildmat.2015.03.069. [17] barbhuiya, s., chow, p., memon, s., microstructure, hydration and nanomechanical properties of concrete containing metakaolin, constr. build. mater., 95 (2015) 696–702. doi:10.1016/j.conbuildmat.2015.07.101. [18] abd elrahman, m., hillemeier, b., combined effect of fine fly ash and packing density on the properties of high performance concrete: an experimental approach, constr. build. mater., 58 (2014) 225–233. doi:10.1016/j.conbuildmat.2014.02.024. t a. khitab et alii, frattura ed integrità strutturale, 42 (2017) 238-248; doi: 10.3221/igf-esis.42.26 247 [19] khushnood, r.a., ahmad, s., ferro, g.a., restuccia, l., tulliani, j.-m., jagdale, p., modified fracture properties of cement composites with nano/micro carbonized bagasse fibers, frattura ed integrità strutturale, 9 (2015) 534–542. doi:10.3221/igf-esis.34.59. [20] li, q., liu, j., xu, s., progress in research on carbon nanotubes reinforced cementitious composites, adv. mater. sci. eng. 2015 (2015). doi:10.1155/2015/307435. [21] li, g.y., wang, p.m., zhao, x., mechanical behavior and microstructure of cement composites incorporating surface-treated multi-walled carbon nanotubes, carbon n. y., 43 (2005) 1239–1245. doi:10.1016/j.carbon.2004.12.017. [22] siddique, r., mehta, a., effect of carbon nanotubes on properties of cement mortars, constr. build. mater., 50 (2014) 116–129. doi:10.1016/j.conbuildmat.2013.09.019. [23] wang, b., han, y., liu, s., effect of highly dispersed carbon nanotubes on the flexural toughness of cement-based composites, constr. build. mater., 46 (2013) 8–12. doi:10.1016/j.conbuildmat.2013.04.014. [24] chithra, s., senthil kumar, s.r.r., chinnaraju, k., the effect of colloidal nano-silica on workability, mechanical and durability properties of high performance concrete with copper slag as partial fine aggregate, constr. build. mater., 113 (2016) 794–804. doi:10.1016/j.conbuildmat.2016.03.119. [25] chuah, s., pan, z., sanjayan, j.g., wang, c.m., duan, w.h., nano reinforced cement and concrete composites and new perspective from graphene oxide, constr. build. mater., 73 (2014) 113–124. doi:10.1016/j.conbuildmat.2014.09.040. [26] vulic, t., hadnadjev-kostic, m., rudic, o., radeka, m., marinkovic-neducin, r., ranogajec, j., improvement of cement-based mortars by application of photocatalytic active ti–zn–al nanocomposites, cem. concr. compos., 36 (2013) 121–127. doi:10.1016/j.cemconcomp.2012.07.005. [27] ulm, f.j., nano-engineering of concrete, arab. j. sci. eng., 37 (2012) 481–488. doi:10.1007/s13369-012-0181-x. [28] singh, l.p., bhattacharyya, s.k., shah, s.p., mishra, g., sharma, u., studies on early stage hydration of tricalcium silicate incorporating silica nanoparticles: part ii, constr. build. mater., 102 (2016) 943–949. doi:10.1016/j.conbuildmat.2015.05.084. [29] kong, d., du, x., wei, s., zhang, h., yang, y., shah, s.p., influence of nano-silica agglomeration on microstructure and properties of the hardened cement-based materials, constr. build. mater., 37 (2012) 707–715. doi:10.1016/j.conbuildmat.2012.08.006. [30] hou, p., kawashima, s., kong, d., corr, d.j., qian, j., shah, s.p., modification effects of colloidal nanosio2 on cement hydration and its gel property, compos. part b eng., 45 (2013) 440–448. doi:10.1016/j.compositesb.2012.05.056. [31] fan, y., zhang, s., wang, q., shah, s.p., effects of nano-kaolinite clay on the freeze–thaw resistance of concrete, cem. concr. compos., 62 (2015) 1–12. doi:10.1016/j.cemconcomp.2015.05.001. [32] hu, c., han, y., gao, y., zhang, y., li, z., property investigation of calcium–silicate–hydrate (c–s–h) gel in cementitious composites, mater. charact., 95 (2014) 129–139. doi:10.1016/j.matchar.2014.06.012. [33] wu, z., shi, c., khayat, k.h., influence of silica fume content on microstructure development and bond to steel fiber in ultra-high strength cement-based materials (uhsc), cem. concr. compos., 71 (2016) 97–109. doi:10.1016/j.cemconcomp.2016.05.005. [34] mubarak, n.m., abdullah, e.c., jayakumar, n.s., sahu, j.n., an overview on methods for the production of carbon nanotubes, j. ind. eng. chem., 20 (2014) 1186–1197. doi:10.1016/j.jiec.2013.09.001. [35] broza, g., synthesis, properties, functionalisation and applications of carbon nanotubes: a state of the art review, chem. chem. technol., 4 (2010) 35–45. [36] mamalis, a.., vogtländer, l.o.., markopoulos, a., nanotechnology and nanostructured materials: trends in carbon nanotubes, precis. eng., 28 (2004) 16–30. doi:10.1016/j.precisioneng.2002.11.002. [37] popov, v., carbon nanotubes: properties and application, mater. sci. eng. r reports., 43 (2004) 61–102. doi:10.1016/j.mser.2003.10.001. [38] rizwan, s.a., ahmad, s., bier, t.a., application of packing concepts to high performance self-consolidating mortar (scm) systems, in: am. concr. institute, aci spec. publ., (2012) 299–315. [39] gillani, s.s.-h., khitab, a., ahmad, s., khushnood, r.a., ferro, g.a., kazmi, s.m.s., qureshi, l.a., restuccia, l., improving the mechanical performance of cement composites by carbon nanotubes addition, procedia struct. integr., 3 (2017) 11–17. doi:10.1016/j.prostr.2017.04.003. [40] romualdi, j.p., mandel, j.a., james p. romualdi and james a. mandel, tensile strength of concrete affected by uniformly distributed and closely spaced short lengths of wire reinforcement, in: aci j. proc., (1964) 657–672. doi:10.14359/7801. a. khitab et alii, frattura ed integrità strutturale, 42 (2017) 238-248; doi: 10.3221/igf-esis.42.26 248 [41] armelin, h.s., banthia, n., predicting the flexural postcracking performance of steel fiber reinforced concrete from the pullout of single fibers, aci mater. j., 94 (1997) 18–31. [42] ma, j.x., zhang, m., zhao, g., experimental research on basalt fiber reinforced cementitious composites, appl. mech. mater., 253–255 (2012) 533–536. doi:10.4028/www.scientific.net/amm.253-255.533. [43] hannant, d.j., fibre cements and fibre concrete, john wiley sons. (1978) 231. [44] han, b., zhang, l., zhang, c., wang, y., yu, x., ou, j., reinforcement effect and mechanism of carbon fibers to mechanical and electrically conductive properties of cement-based materials, constr. build. mater., 125 (2016) 479– 489. doi:10.1016/j.conbuildmat.2016.08.063. << /ascii85encodepages false /allowtransparency false /autopositionepsfiles true /autorotatepages /none /binding /left /calgrayprofile (dot gain 20%) /calrgbprofile (srgb iec61966-2.1) /calcmykprofile (u.s. web coated \050swop\051 v2) /srgbprofile (srgb iec61966-2.1) /cannotembedfontpolicy /error /compatibilitylevel 1.4 /compressobjects /tags /compresspages true /convertimagestoindexed true /passthroughjpegimages true /createjobticket false /defaultrenderingintent /default /detectblends true /detectcurves 0.0000 /colorconversionstrategy /cmyk /dothumbnails false /embedallfonts true /embedopentype false /parseiccprofilesincomments true /embedjoboptions true /dscreportinglevel 0 /emitdscwarnings false /endpage -1 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/hrv (za stvaranje adobe pdf dokumenata najpogodnijih za visokokvalitetni ispis prije tiskanja koristite ove postavke. stvoreni pdf dokumenti mogu se otvoriti acrobat i adobe reader 5.0 i kasnijim verzijama.) /hun 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can be opened with acrobat and adobe reader 5.0 and later.) >> /namespace [ (adobe) (common) (1.0) ] /othernamespaces [ << /asreaderspreads false /cropimagestoframes true /errorcontrol /warnandcontinue /flattenerignorespreadoverrides false /includeguidesgrids false /includenonprinting false /includeslug false /namespace [ (adobe) (indesign) (4.0) ] /omitplacedbitmaps false /omitplacedeps false /omitplacedpdf false /simulateoverprint /legacy >> << /addbleedmarks false /addcolorbars false /addcropmarks false /addpageinfo false /addregmarks false /convertcolors /converttocmyk /destinationprofilename () /destinationprofileselector /documentcmyk /downsample16bitimages true /flattenerpreset << /presetselector /mediumresolution >> /formelements false /generatestructure false /includebookmarks false /includehyperlinks false /includeinteractive false /includelayers false /includeprofiles false /multimediahandling /useobjectsettings /namespace [ (adobe) (creativesuite) (2.0) ] /pdfxoutputintentprofileselector /documentcmyk /preserveediting true /untaggedcmykhandling /leaveuntagged /untaggedrgbhandling /usedocumentprofile /usedocumentbleed false >> ] >> setdistillerparams << /hwresolution [2400 2400] /pagesize [612.000 792.000] >> setpagedevice microsoft word numero_54_art_13_2894 p. livieri et alii, frattura ed integrità strutturale, 54 (2020) 182-191; doi: 10.3221/igf-esis.54.13 182 a closed form for the stress intensity factor of a small embedded square-like flaw paolo livieri, fausto segala university of ferrara, department of engineering, italy paolo.livieri@unife.it, fausto.segala@unife.it abstract. in the present work, the stress intensity factor (sif) of a small embedded square-like flaw is calculated by means of a procedure based on the oore-burns integral. an explicit equation is given to evaluate the sif along the two axes of symmetry that correspond to the points where the sif takes its maximum and minimum value on the contour crack. the sif is calculated in accordance with fe numerical results. keywords. weight function; stress intensity factor; three-dimensional crack; weld citation: livieri, p., segala, f., a closed form for the stress intensity factor of a small embedded square-like flaw, frattura ed integrità strutturale, 54 (2020) 182-191. received: 20.08.2020 accepted: 26.08.2020 published: 01.10.2020 copyright: © 2020 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. introduction he analytical evaluation of the stress intensity factor (sif) of three-dimensional cracks is more complicated than cases where the crack is sketched as a straight line in a two-dimensional boundary. few examples of convex threedimensional cracks can be found in textbooks [1–3]. in order to give a general formulation for the sif, bueckner [4] and rice [5] performed the weight function technique. in this way, the calculation is reduced to an integral exactly over the region covered by the crack and this becomes particularly useful in the case of three-dimensional cracks. the exact weight function is known only in few cases.. galin evaluated the exact weight function for the circle but the equation is not simple to manage due to the presence of a singularity typical of the weight function itself (see reference [3]). however, the authors, by means of the oore-burns (ob) weight function, give a simplified formulation of the weight function of the analytical circle where the singularity disappears by means of an appropriate change of variable [6]. this was performed because the ob integral is exact on circles. in others cases, the ob integral is a first level of approximation for the sif in the case of circle-like cracks [7]. usually, for irregular contours, a crack-like elliptical crack can be adopted [8–9]. for example, in flaw characterisation adopted in the fitness-for-service procedure, the flaw is modelled by a simpler geometry such as a trough crack with a straight crack front or with an elliptical or semi-elliptical shape. in this cases, the ob integral should be adopted because the characterisation of a semi-axial ellipse (1, b), when eccentricity e tends to zero, the main contribution of the ob integral t https://youtu.be/kuicf9pkemy p. livieri et alii, frattura ed integrità strutturale, 54 (2020) 182-191; doi: 10.3221/igf-esis.54.13 183 differs from irwin’s analytical solution [11] for a small amount equal to 2 20 e  [12], where e is the eccentricity of the ellipse. the ob integral could also be useful in the fatigue life assessment of materials with small internal defects. in order to obtain an acceptable approximation of the maximum sif kimax, murakami took into account the square root of the crack area ( ,maxik y area  where y is a coefficient that was evaluated as best fitting for numerical and analytical results; see also [13]) of a general crack shape. the internal defect often has rounded corners and an analytical equation for a squarelike flaw could be useful for design purposes. in this paper, we use the oore-burns integral to obtain a closed form solution for a square-like flaw that is intermediate from a circular flaw and a square crack. the results are then compared with the fe results obtained with a fine mesh. weight function for a three-dimensional crack: analytical background ig. 1 shows a two-dimensional crack inside a three-dimensional body subjected to a nominal tensile loading σn(q) that is evaluated without the presence of the crack. q is the inner point of the crack. the crack can be considered as an open bounded simply connected subset ω of the plane. we define: 2 ( ) ( ) ds f q q p s    (1) where ( , )q q x y   , s is the arch-length parameter and point p(s) runs over the boundary  . in their pioneering work in 1980, oore-burns [10] proposed the following expression for the mode i stress intensity factor (sif) for a twodimensional crack of boundary  : 2 ( )2 ( ') , ' ( ) ' n i q k q d q f q q q        (2) under reasonable hypothesis on the function σn(q), the integral (2) is convergent and the proof is based on the asymptotic behaviour of f(q) [14]. figure 1: inner crack. stress intensity factor for a square like-flaw n the case of a square-like flaw, as indicated in fig. 2, the oore-burns integral can be analytically expressed in simplified form at the two points a and b. the oore-burns integral will be approximated by means of riemann sums plus a f i p. livieri et alii, frattura ed integrità strutturale, 54 (2020) 182-191; doi: 10.3221/igf-esis.54.13 184 suitable asymptotic (in terms of mesh size) correction. the equation of a unitary square-like flaw in a cartesian coordinate system x,y is given in the form: 4 4 1x y  (3) figure 2: square-like flaw figure 3: auxiliary cartesian plane u,v at point a the choice to consider a unitary square-like flaw, as in fig. 2, is not restrictive because the final values for the sif can be recovered by multiplying by the square root of the geometrical scale factors. let us consider q’ as the point where the sif is calculated. as a first calculation, we consider q’ as overlapping point a. in order to evaluate the o-b integral, we take into account a new convenient cartesian orthogonal reference system u,v with its origin in q’ with a u axis tangent to  (see fig. 3). the relation between the two reference planes can be summarised as follows:  1/41   2 2 x u v   (4)  1/41   2 2 y u v    (5)   2 x y u   (6) 1/42 2 x y v    (7) a mesh of size δ on  can be considered, where δ divides the length of  . pm in fig. 3 is a point of coordinate mδ with respect to the initial point po. on the x,y plane, the coordinates of pm are equal to (xm, ym)= r(mδ) (cos(mδ), sin(mδ)) with m from 0 to m and 2mδ=2π. from eq. (3) we have:      4 4cos sinr     (8) if we know the polar equation of the crack border ( )r  , it is convenient to discretise the angle α instead of the arc length s. the angle α is equal to mδ. now we consider: p. livieri et alii, frattura ed integrità strutturale, 54 (2020) 182-191; doi: 10.3221/igf-esis.54.13 185 2 2( ) ( ) ' ( )r r     (9) the coordinates of generic point pm = (xm, ym) on the u,v plane become:       1/4 1      cos  sin 2 1      cos  sin 2 2 m m u r m m m v r m m m                (10) we denote by qjk =k (cos(j ) ,sin(jδ)) the generic point on the plane (u,v) of the semi-circular mesh (see fig. 4). in order to establish whether point qjk of the coordinates (u,v) is inside the crack, the following inequality must be verified:    41/4 1/42 2 4u v u v       (11) in this paper, eq. (11) is very simple to use with respect to the general equations proposed in references [15 and 16] for a star domain crack. from eqns. (1) and (2), the sif kia at point a results: 2 jk ia a k d k             +o( ) (12) where 1 22 4 jk jk ma q p m                (13) the sum (12) is made for 1 k n  and 0 / 2j m  . the value of n is calculated in order to obtain a crack inside the mesh as appears in fig. 4. the asymptotic correction term, according to reference [16] is given by: 3 2 2 0.889 0.038 cos 4 4 d                         (14) where    γ max  ,     0, 2     . now we can evaluate the sif also for point b as in fig. 5. eqns. (10)–(14) are replaced with eqns. (15)–(19) and the mesh for riemann sums is shown in fig. 6.        cos    sin 1 m m m u x r m m v r m m          (15)  44 1 1u v   (16) 2 jk ib a k d k             (17) where p. livieri et alii, frattura ed integrità strutturale, 54 (2020) 182-191; doi: 10.3221/igf-esis.54.13 186 1 22 2 jk jk ma q p m                (18) the sum (17) is made for 1 k n  and 0 / 2j m  . 3 2 2 0.889 0.038 cos 2 2 d                         (19) where    γ max  ,     0, 2     . in eqns. (14) and (19), the value of  can be numerically evaluated from fig. 7.  is close to 1.265. figure 4: mesh for riemann sums at point a figure 5: auxiliary cartesian plane u,v at point b u v kꞏδ jꞏδ a qjk p. livieri et alii, frattura ed integrità strutturale, 54 (2020) 182-191; doi: 10.3221/igf-esis.54.13 187 figure 6: mesh for riemann sums at point a figure 7: trend of  along the crack border numerical validation qns. (12) and (17) allow us to numerically evaluate the sif at the two characteristic points a and b of the squarelike crack without any specific computer strategies [17]. in this case, any generic mathematical code can be used to calculate the sif. tabs. 1 and 2 report the value obtained with eq. (12) and (17). the stability of the equation is clear as well as the fundamental rule of asymptotic term c. mastrojannis et al. [18] numerically solved the case of square crack with a small rounded apex. they found that the maximum sif was assumed to be at the middle point of the edge and the maximum shape factor max ,max /( )iy k a  was equal to 0.76. furthermore, for a sharp square crack by means of numerical methods, helsing el al. [19] calculated a value for ymax equal to 0.75, weaver [20] gave 0.74, whereas isida et al. [21] gave 0.76. the results relating to a square-like crack are compared with those obtained by means of the fe code. the percentage of errors are around a few per cent for point b, while they increase up to 10% for point a. figs. 8 and 9 show the model and the mesh used in the numerical fe analysis. the mesh used in this work is accurate as proposed in previous works [22–25]. the dimensions of smaller elements at the tip of the crack were in the order of 10-5 mm. fig. 10 highlights that the slope of stress σz in a double logarithm scale is close to the theoretical value of 0.5 for point b [26]. the y’ axis has the origin at point b. regarding the engineering applications for this topic, the fatigue behaviour of welded joints with internal defects such as pores could be appropriate. for example, the morphology and size distribution of gas pores within the entire weld joints, were examined in references [27-28]. by observing the typical spatial shape of the defects, sometime, the square-like flaw e u v kꞏδ jꞏδ b qjk p. livieri et alii, frattura ed integrità strutturale, 54 (2020) 182-191; doi: 10.3221/igf-esis.54.13 188 appears more appropriate than others shapes when a two-dimensional simplified representation of the defects is requested [13]. the pores show a rounded shape sometime away any ellipse typically used for simplified fatigue assessment [8]. figure 8: three-dimensional model for a square-like crack (a=1 mm, l/a= 100, d/a=20). figure 9: mesh and boundary conditions for a square-like crack of fig. 8. figure 10: stress 𝜎 along the y-direction for the square-like crack of fig. 4 for b on the symmetry axis p. livieri et alii, frattura ed integrità strutturale, 54 (2020) 182-191; doi: 10.3221/igf-esis.54.13 189 i n k y a   m δ y riemann sum y asymptotic term y eq. (12) y fe e% 10 0.628 0.246 0.418 0.664 0.554 -19.8 20 0.314 0.335 0.295 0.630 0.554 -13.7 50 0.126 0.428 0.187 0.615 0.554 -11.0 100 0.063 0.483 0.133 0.616 0.554 -11.1 200 0.031 0.520 0.094 0.614 0.554 -10.8 table 1: shape factor at point a for a nominal tensile loading σn i n k y a   m δ y riemann sum y asymptotic term y eq. (17) y fe e% 10 0.628 0.300 0.398 0.698 0.717 2.6 20 0.314 0.416 0.282 0.698 0.717 2.6 50 0.126 0.537 0.179 0.716 0.717 0.1 100 0.063 0.579 0.127 0.706 0.717 1.5 200 0.031 0.617 0.090 0.707 0.717 1.3 table 2: shape factor at point b for a nominal tensile loading σn conclusions he oore-burns weight function gives us a closed formula for the estimation of the stress intensity factor of a squarelike flaw with a rounded corner. the errors, with respect to the fe results, are around a few per cent in the middle of the side, while they increase up to 10% at the corner. this suggests the need for a corrective procedure in order to significantly improve the oore-burns integral. after careful investigations, it is now clear, without any doubt, that the accuracy of the integral is not satisfactory at the high curvature points of the crack. nomenclature a crack size  size of mesh over crack y shape factor  crack shape  crack border q point of 'q point of crack border  distance between q and  ki mode i stress intensity factor ,x y actual cartesian coordinate system t a a a a a b a a a a p. livieri et alii, frattura ed integrità strutturale, 54 (2020) 182-191; doi: 10.3221/igf-esis.54.13 190 ,u v auxiliary coordinate system  polar radius r polar radius for the square-like flaw s arc length σn nominal tensile stress in ,x y cartesian coordinate system references [1] murakami, y. (chief ed) (2001), stress intensity factors handbook vol. 4, 5, pergamon. press, oxford, u.k. [2] fett, t., munz, d., (1997). stress intensity factors and weight functions, computational mechanics publications. [3] tada, h., paris, c.p., irwin, g.r., (2000). the stress analysis of cracks handbook. third edition, asme press. [4] bueckner, h.f., (1970). a novel principle for the computation of stress intensity factors, zamm 50, pp. 529–546. [5] rice, j.r., (1989). weight function theory for three-dimensional elastic crack analysis. astm stp1020, wei r.p. and gangloff r.p., eds. philadelphia, american society for testing and materials, pp. 29–57. [6] livieri, p., segala, f., (2010). an analysis of three-dimensional planar embedded cracks subjected to uniform tensile stress. engineering fracture mechanics, 77, pp. 1656–1664. [7] livieri, p., segala, f., (2010). first order oore–burns integral for nearly circular cracks under uniform tensile loading. international journal of solids and structures, 47(9), pp. 1167–1176. [8] zerbs, u. t., schödel, m., webster, s., ainsworth, r. (2007). fitness-for-service fracture assessment of structures containing cracks: a workbook based on the european sintap/fitnet procedure, elsevier, 1st ed. oxford, amsterdam, the netherlands . [9] hobbacher, a., (1995). recommendation on fatigue of welded components. iiw document xiii-153995/xv-845-95. [10] oore, m., burns, d.j., (1980). estimation of stress intensity factors for embedded irregular cracks subjected to arbitrary normal stress fields. journal of pressure vessel technology asme, 102, pp. 202–211. [11] irwin, g.r., (1962). crack-extension force for a part-through crack in a plate. asme, journal of applied mechanics, 29(4), pp. 651–654. [12] livieri, p., segala f. (2015). new weight functions and second order approximation of the oore-burns integral for elliptical cracks subject to arbitrary normal stress field, eng. fract. mech. 138, pp. 100–117. [13] murakami, y, (2002). metal fatigue: effects of small defects and non-metallic inclusions, elsevier. [14] ascenzi, o., pareschi, l., segala, f. (2002). a precise computation of stress intensity factor on the front of a convex planar crack. international journal for numerical methods in engineering 54, pp. 241–261. [15] livieri, p., segala, f., (2014). sharp evaluation of the oore-burns integral for cracks subjected to arbitrary normal stress field, fatigue & fracture of engineering materials & structures 37, pp. 95–106. [16] livieri, p., segala, f., (2018). an approximation in closed form for the integral of oore–burns for cracks similar to a star domain. fatigue fract eng mater struct, 41, pp. 3–19. [17] desjardins, j.l., burns, d.j., thompson, j.c., (1991). a weight function technique for estimating stress intensity factors for cracks in high pressure. journal of pressure vessel technology, asme, 113, pp. 10–21. [18] mastrojannis, e.n., keer, l.m., mura, t., (1979). stress intensity factor for a plane crack under normal pressure. international journal of fracture, 15 (3), pp. 247–258. [19] helsing j, jonsson a, peters g. (2001). evaluation of the mode i stress intensity factor for a square crack in 3d, engineering fracture mechanics 68, 605–612. [20] weaver, j., (1997). three-dimensional crack analysis. international journal structures, 13, pp. 321–330. [21] isida, m., yoshida, t., noguchi, h. (1991). a rectangular crack in an infinite solid, a semi-infinite solid and a finitethickness plate subjected to tension. international journal of fracture 52, pp. 79–90. [22] livieri, p., tovo, r., (2009). the use of the jv parameter in welded joints: stress analysis and fatigue assessment. international journal of fatigue, 31(1), pp. 153–163. [23] livieri, p., tovo, r., (2017). analysis of the thickness effect in thin steel welded structures under uniaxial fatigue loading. international journal of fatigue, 101(2), pp. 363–370. [24] livieri, p., segala, s. (2016). stress intensity factors for embedded elliptical cracks in cylindrical and spherical vessels theoretical and applied fracture mechanics 86(1), pp. 260–266. p. livieri et alii, frattura ed integrità strutturale, 54 (2020) 182-191; doi: 10.3221/igf-esis.54.13 191 [25] livieri, p., berto, f., lazzarin, p., (2007). local strain energy approach applied to fatigue analysis of welded rectangular hollow section joints. international journal of materials & product technology, 30(1/2/3), pp. 124–140. [26] aliabadi, m.h., rooke, d.p., (1991). numerical fracture mechanics, southampton, kluwer academic publishers. [27] wu, s.c., yu, c., yu, p.s., buffière, j.y., helfen, l., fu., y.n., (2016). corner fatigue cracking behavior of hybrid laser aa7020 welds by synchrotron x-ray computed microtomography. materials science&engineeringa 651, pp. 604–614. [28] gou, g., zhang, m., chen, h., chen, j., li, p., yang, y.p., (2015). effect of humidity on porosity, microstructure, and fatigue strength of a7n01s-t5 aluminum alloy welded joints in high-speed trains. materials and design 85, pp. 309– 317. << /ascii85encodepages false /allowtransparency false /autopositionepsfiles true /autorotatepages /none /binding /left /calgrayprofile (dot gain 20%) /calrgbprofile (srgb iec61966-2.1) /calcmykprofile (u.s. web coated \050swop\051 v2) /srgbprofile (srgb iec61966-2.1) /cannotembedfontpolicy /error /compatibilitylevel 1.4 /compressobjects /tags /compresspages true /convertimagestoindexed true /passthroughjpegimages true /createjobticket false /defaultrenderingintent /default /detectblends true /detectcurves 0.0000 /colorconversionstrategy /cmyk /dothumbnails false /embedallfonts true /embedopentype false /parseiccprofilesincomments true /embedjoboptions true /dscreportinglevel 0 /emitdscwarnings false /endpage -1 /imagememory 1048576 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can be opened with acrobat and adobe reader 5.0 and later.) >> /namespace [ (adobe) (common) (1.0) ] /othernamespaces [ << /asreaderspreads false /cropimagestoframes true /errorcontrol /warnandcontinue /flattenerignorespreadoverrides false /includeguidesgrids false /includenonprinting false /includeslug false /namespace [ (adobe) (indesign) (4.0) ] /omitplacedbitmaps false /omitplacedeps false /omitplacedpdf false /simulateoverprint /legacy >> << /addbleedmarks false /addcolorbars false /addcropmarks false /addpageinfo false /addregmarks false /convertcolors /converttocmyk /destinationprofilename () /destinationprofileselector /documentcmyk /downsample16bitimages true /flattenerpreset << /presetselector /mediumresolution >> /formelements false /generatestructure false /includebookmarks false /includehyperlinks false /includeinteractive false /includelayers false /includeprofiles false /multimediahandling /useobjectsettings /namespace [ (adobe) (creativesuite) (2.0) ] /pdfxoutputintentprofileselector /documentcmyk /preserveediting true /untaggedcmykhandling /leaveuntagged /untaggedrgbhandling /usedocumentprofile /usedocumentbleed false >> ] >> setdistillerparams << /hwresolution [2400 2400] /pagesize [612.000 792.000] >> setpagedevice microsoft word numero 10 art 4 b. chiaia et alii, frattura ed integrità strutturale, 10 (2009) 29-37; doi: 10.3221/igf-esis.10.04 29 sismabeton: a new frontier for ductile concrete bernardino chiaia, alessandro p. fantilli, paolo vallini politecnico di torino, dep. of structural and geotechnical engineering corso duca degli abruzzi, 24 -10129 torino, italy fantilli@polito.it, vallini@polito.it, chiaia@polito.it riassunto. i calcestruzzi fibrorinforzati ed autocompattanti (definiti sismabeton) manifestano una elevata duttilità non solo in trazione ma anche in presenza di sforzi compressione. ciò e messo in evidenza nel presente lavoro attraverso la misura della risposta meccanica, in regime di compressione triassiale, di calcestruzzi ordinari (nc) ed autocompattanti (sc) con e senza fibre. in strutture semplicemente compresse, la presenza del sismabeton è da sola sufficiente a garantire un confinamento attivo uniforme. abstract. the high ductility of fiber reinforced self-consolidating concrete (called sismabeton) can be developed not only in tension but also in compression. this aspect is evidenced in the present paper by measuring the mechanical response of normal concrete (nc), plain self-compacting concrete (sc) and sismabeton cylindrical specimens under uniaxial and triaxial compression. the post-peak behaviour of these specimens is defined by a non-dimensional function that relates the inelastic displacement and the relative stress during softening. both for nc and sc, the increase of the fracture toughness with the confinement stress is observed. conversely, sismabeton shows, even in absence of confinement, practically the same ductility measured in normal and self-compacting concretes with a confining pressure. thus, the presence of sismabeton in compressed columns is itself sufficient to create a sort of active distributed confinement. keywords. fiber-reinforced concrete, self-compacting concrete, confining pressure, triaxial tests, fracture toughness. introduction everal reinforced concrete (rc) structures fail via concrete crushing in compressed zones. this is the case, for instance, of over-reinforced concrete beams, like those in four point bending tested by mansur et al. [1]. when fiber-reinforced, the post-peak behaviour of such members is remarkably more ductile than that observed in beams having the same geometry, the same steel rebars, and the same bearing capacities, but made of normal concrete (nc) without fiber. thus, when crushing occurs, the type of concrete rules both the mechanical response and the ductility of rc structures. the experimental campaign conducted by khayat et al. [2] on highly confined rc columns, subject to concentric compression, also confirms the influence of the cement-based composites on the structural performances. more precisely, for a given cross-section, the load vs. average axial strain diagrams appear more ductile in the case of columns made of self-compacting concrete (sc) than in nc columns. these experimental observations can be usefully applied to designing rc compressed columns in seismic regions. according to eurocode 8 [3], if a required ductility cannot be attained because concrete strains are larger than 0.35% , a compensation for the loss of resistance due to crushing can be achieved by means of an adequate confinement. such a confinement, usually provided by transversal steel reinforcement (i.e., stirrups), and indicated by the confining pressure 3 (fig.1), allows designers to consider a more ductile stress strain (c-c) relationship in compression. for instance, fig.1 shows the so-called parabola-rectangle diagrams proposed by eurocode 2 [4] for confined and unconfined concretes. s http://dx.medra.org/10.3221/igf-esis.10.04&auth=true http://www.gruppofrattura.it mailto: fantilli@polito.it mailto: vallini@polito.it mailto: chiaia@polito.it b. chiaia et alii, frattura ed integrità strutturale, 10 (2009) 29-37; doi: 10.3221/igf-esis.10.04 30 short steel fibers randomly dispersed in a cement-based matrix can generate confining pressures comparable with that of stirrups. the experimental campaign of ganesan and ramana murthy [5], performed on short confined columns with and without fibers (fig.2a), investigates on this aspect. as shown in fig.2b, the applied loadaverage strain (p-cm) diagram of rc columns, made with ordinary concrete and a transversal reinforcement percentage equal to s=1.6%, is more or less similar (in terms of strength and ductility) to that of fiber-reinforced (frc) columns, made with a reduced quantity of stirrups (s =0.6%) and frc (volume fraction vf = 1.5%, aspect ratio l/ = 70). figure 1: the stress-strain relationship of compressed concrete with and without confinement [4]. figure 2: the columns tested by ganesan and ramana murthy [5]. although fiber-reinforcements have been introduced in order to increase the ductility of cement-based composites in tension, they can also provide a sort of confinement, and therefore higher ductility in compression. for this reason, when a better fiber matrix bond can be achieved, like the fiber-reinforced self-compacting composites [6], higher compressive fracture toughness should be expected. to confirm such a conjecture, the post-peak responses of different cementitious composites under uniaxial and multi-axial compression are here investigated. post-peak response of concrete under compression he stress-strain relationships of concrete and quasi-brittle materials in compression (fig.3a) can be divided into two parts (fig.3b). in the first part, when the stress is lower than the strength fc (and c < c1 ), the specimen can be considered undamaged. in the case of plain concrete, the ascending branch of c-c can be defined by the sargin’s relationship proposed by ceb-fip model code [7]. as soon as the peak stress is reached, localized damage develops and strain softening begins. in this stage, the progressive sliding of two blocks of the cement-based material is evident. in fig.3a, the angle between the vertical axis of the specimen and the sliding surfaces is assumed to be =18°. this value, as measured in many tests, can be also obtained through the mohr-coulomb failure criterion, if the tensile strength is t http://dx.medra.org/10.3221/igf-esis.10.04&auth=true http://www.gruppofrattura.it b. chiaia et alii, frattura ed integrità strutturale, 10 (2009) 29-37; doi: 10.3221/igf-esis.10.04 31 assumed to be 1/10 of compression strength ( fct = 0.1 fc ). the inelastic displacement w of the specimen, and the consequent sliding s of the blocks along the sliding surface, are the parameters governing the average post-peak compressive strain c of the specimen (fig. 3). referring to the specimen depicted in fig. 3a, post peak strains can be defined by the following equation [8]: h w eh w c c celcc      1, (1) where, c1 = strain at compressive strength fc ; c = stress decrement after the peak; h = height of the specimen (see fig. 1b). figure 3: the post-peak response of quasi-brittle materials in compression. according to test measurements [8, 9], the post-peak slope of c-c increases in longer specimens (fig.3b), due to the w/h ratio involved in the evaluation of c [eq.(1)]. the stress decrement c can be defined as:   wfff cccc  1 (2) where, f(w) = non-dimensional function which relates the inelastic displacement w and the relative stress c / fc during softening (fig.3c); fc = compressive strength (assumed to be positive). substituting eq.(2) into eq.(1), it is possible to obtain a new equation for c :    h w e wff c c cc    1 1 for c > c1 (3) eq.(3), adopted for the post-peak stage of a generic cement-based material in compression, is based on the definition of f(w), which has to be considered as a material property [8-9]. in all cement-based composites, this function should be evaluated experimentally on cylindrical specimens, as performed by jansen and shah [9] for plain concrete (fig.3c). fig.4a shows the f(w) relationships proposed by fantilli et al. [10]. it consists of two parabolas and a constant branch:   1 2 wbwa f wf c   a b w   2 0for (4a)   44 4 1 2 2 22                      w b a w b a a b f wf c  a b w a b    2 for (4b)   0 cf wf  a b w for (4c) http://dx.medra.org/10.3221/igf-esis.10.04&auth=true http://www.gruppofrattura.it b. chiaia et alii, frattura ed integrità strutturale, 10 (2009) 29-37; doi: 10.3221/igf-esis.10.04 32 the parabolas are both defined by the same coefficients a, b and have the same extreme point at w = -0.5 b/a , whereas w = b/a (i.e. twice the value at extreme point) is considered the maximum inelastic displacement corresponding to f(w) higher than zero. figure 4: the stress-inelastic displacement relationship proposed by fantilli et al. [10]. in the case of the plain concrete specimens, the values a = 0.320 mm-2 and b = -1.12 mm-1 were obtained by means of the least square approximation of several tests [10]. as observed in fig.4b, the curves defined by eqs.(4) fall within the range of the data experimentally measured by jansen and shah [9]. in the case of multi-axial compression, stress-inelastic displacement relationships, which should reproduce the confined post-peak stage, cannot be found in the existing literature. as is well known, two types of confinement, namely passive and active, can be produced. in compressed columns, passive confinements provided by transversal reinforcement (i.e., stirrups, tubes, strips, spirals, etc.), are only activated by concrete displacements. thus, to define quantitatively this contribution, it is necessary to know the stress-transversal displacement relationship of concrete. active confinement is due to external stresses 3 applied by multi-axial compression tests on cubes in two or three directions, or by triaxial tests on cylinders (see the book by van mier [8] for a review). only a single campaign of triaxial tests, performed by jamet et al. [11] on micro-concrete, is reported in the current literature. in that case, the applied confinement was relatively high (3 >3 mpa), if compared to those produced by stirrups in ordinary rc columns. in accordance with eurocode 2 [4], in columns under concentric compression, transverse reinforcement can develop about 3 = 1mpa [12]. consequently, with the aim of analyzing the equivalent confing pressures produced by a new fiber-reinforced self-consolidating concrete (called sismabeton), the comparison between the results of new triaxial tests on nc, sc and sismabeton cylinders under uniaxial compression are reported. experimental program he post-peak behaviour of cement-based composites under multi-axial compression has been investigated at the department of structural and geotechnical engineering of politecnico di torino (italy) by means of triaxial tests on concrete cylinders (fig.5a). the experimental equipment, named htpa (high pressure triaxial apparatus) and described by chiaia et al. [13], is generally used to test cylindrical specimens made of soft rocks. each triaxial test consists of two stages. a specimen is initially loaded with a hydrostatic pressure σ3 (fig.5b), then deviatoric loads p are applied along the longitudinal direction with a velocity of 0.037 mm per minute (fig.5c). during the second stage of loading, the confining pressure 3 = const. is applied to the lateral surface, whereas the longitudinal nominal stress c becomes: 23 4 d p c    (5) where, p = applied deviatoric load; d = diameter of the cross-section. through a couple of lvdt, local longitudinal displacements, and therefore nominal longitudinal strains c , are also measured (fig. 5a). two confining pressures, namely σ3 = 0 mpa and σ3 = 1 mpa (reached in 10 minutes), are applied to the specimens. during the application of hydrostatic loads (fig.5b), stress increments are electronically recorded every 10 seconds. t http://dx.medra.org/10.3221/igf-esis.10.04&auth=true http://www.gruppofrattura.it b. chiaia et alii, frattura ed integrità strutturale, 10 (2009) 29-37; doi: 10.3221/igf-esis.10.04 33 similarly, in the second stage, when σ3 = const. and p increases, the values of deviatoric load, the relative displacement between the specimen’s ends, and the longitudinal displacement along the lateral surface (taken by the lvdts of fig.5a) are measured. two types of self-consolidating concrete (sc_mix1 and sc_mix2) and a single ordinary concrete (nc) were tested. figure 5: the two stages of triaxial tests on cement-based cylinders. their compositions and strengths are reported in tab. 1. specifically, the self-consolidating concretes have the same unit weight, but different amounts of aggregates. with respect to sc_mix1, in a cube meter of sc_mix2 the content of carbonate filler was increased by 90 n and, contemporarily, the weight of coarse aggregate was reduced by the same quantity. regarding the fiber-reinforced self-consolidated concrete (i.e., simabeton), two specimens were tested, under uniaxial compression (σ3 = 0). as indicated in tab. 1, sismabeton is reinforced with 700 n/m3 of dramix rc 65/35 bn steel fibers having hooked ends (length l = 35 mm, diameter φ = 0.55 mm, volume fraction vf = 0.9%). which were added to the self-consolidating concrete with the higher quantity of filler (i.e., sc_mix2). nc sc_mix 1 sc_mix 2 sismabeton component n/m3 n/m3 n/m3 n/m3 water 1770 1770 1770 1770 superplasticizer (addiment compactcrete 39/t100) 44 44 44 superplasticizer (addiment compactcrete 39/t11) 14 cement (buzzi unicem ii/a-ll 42.5 r) 2840 2450 2450 2450 carbonate filler (nicem carb vg1-2) 0 3240 3730 3730 fine aggregate (0-4 mm) 8830 8930 8930 8930 coarse aggregate (6.3-12 mm) 6380 6380 5890 5890 steel fibers dramix rc 65/35 bn 700 cubic strength -mpa 30.0 31.1 30.4 33.8 table 1: compositions and strengths of nc, sc_mix1, sc_mix2, and sismabeton. the specimens of each concrete mixture were cast simultaneously in polystyrene form, then cured for one week under identical laboratory conditions, and finally tested after one month. three couples of cylinders, with h=140 mm and d=70 mm, were made of nc (nc0 and nc1), sc_mix1 (sc0 and sc1), and sc_mix2 (sc0b and sc1b). the two specimens of http://dx.medra.org/10.3221/igf-esis.10.04&auth=true http://www.gruppofrattura.it b. chiaia et alii, frattura ed integrità strutturale, 10 (2009) 29-37; doi: 10.3221/igf-esis.10.04 34 these couples were tested, respectively, at σ3 = 0 mpa and σ3 = 1 mpa. two sismabeton cylinders (hc0 and hc0b), with h=140 mm and d=70 mm, were tested in uniaxial compression. the properties of each specimen are reported in tab. 2. table 2: mechanical and geometrical properties of the specimens tested in uniaxial and triaxial compression. test results ig. 6 reports the stress-strain relationships obtained from the specimens made respectively with sismabeton (fig.6a), normal concrete (fig.6b) and self-consolidating concrete (fig.6c). the higher the confinement, the higher the values of fc and c1 , which are reported, together with young’s modulus ec , in tab. 3. in all the cases, after the peak stress fc , a remarkable strain softening branch can be observed in the c-c diagrams. although sismabeton is fiber-reinforced, its compressive strength does not differ substantially from those of ordinary and self-consolidating concrete. however, the post peak response of sismabeton appears more ductile. only when the confining pressure 3 increases, does the ductility of nc and sc increase. by comparing all the post-peak branches reported in fig.6, it seems that the post-peak branches of sc and nc specimens in the presence of 3 =1 mpa are more or less the same of sismabeton without any confinement. figure 6: the stress-strain relationships of sismabeton, nc and sc. specimen fc (mpa) c1 (%) ec (mpa) 0nc0 19.4 0.293 24000 0nc1 30.5 0.473 23000 0sc0 20.1 0.479 17000 0sc0b 23.2 0.372 23000 0sc1 36.4 0.604 19000 0sc1b 32.0 0.696 27000 hc0 21.8 0.352 19000 hc0b 22.2 0.534 20000 table 3: mechanical properties measured in the tests. specimen h (mm) d (mm) type of concrete 3 (mpa) nc0 140 70 nc 0 nc1 140 70 nc 1 sc0 140 70 scc mix 1 0 sc1 140 70 scc mix 1 1 sc0b 140 70 scc mix 2 0 sc1b 140 70 scc mix 2 1 hc0 100 50 sismabeton 0 hc0b 100 50 sismabeton 0 f http://dx.medra.org/10.3221/igf-esis.10.04&auth=true http://www.gruppofrattura.it b. chiaia et alii, frattura ed integrità strutturale, 10 (2009) 29-37; doi: 10.3221/igf-esis.10.04 35 however, a direct comparison between the analyzed concretes is not possible in terms of nominal stress and strain, because specimens have different nominal strengths. post-peak comparison in terms of f(w) a more accurate comparison between the post-peak responses of sismabeton, nc and sc under compression can be conducted in terms of f(w) (fig.7). in particular, for a given c  c1, the decrease of compressive stress c = fc-c (and f = c / fc ) can be obtained through the c-c diagrams experimentally evaluated (fig.6), whereas the corresponding w (fig.3a) can be obtained from eq.(3) (fc , c1 , ec and h are known from the tests). the f(w) curves reported in fig.7 are limited to w = 2mm, when compressive strains c are relatively high although, in some cases, stresses are higher than zero. however, in all the tests the relative stress f = c / fc decreases with w. the dashed curves reported in fig.7 represent the behaviour of nc and sc as predicted by eq.(4) in the case of zero confinement. as in the case of 3 = 0 the post-peak responses of the specimens nc0, sc0, sc0b are correctly predicted by eq.(4), and all the tests can be considered consistent [10]. both for nc and sc, fig.7a and fig7b, respectively show the increase of the compressive fracture toughness (within the range w0-2 mm) with the confining pressure 3. however, this phenomenon is also evident in the case of sismabeton, which can show, in absence of confinement, more or less the same f(w) obtained for nc and sc when 3 = 1mpa. figure 7: the post peak behaviour in terms of f(w). figure 8: the active confinement of sismabeton. fig.8a shows the post-peak responses of the specimens hc0 and hc0b, which are closer to those of confined sc and nc (i.e., the range defined by nc1, sc1, sc1b), than to the theoretical f(w) obtained in absence of confinement [10] (the dashed line in fig.8a). within the observed range (w0-2 mm), compressive facture toughness of different concretes can be objectively measured by the area af under the function f(w):   dwwfaf  2 0 (6) http://dx.medra.org/10.3221/igf-esis.10.04&auth=true http://www.gruppofrattura.it b. chiaia et alii, frattura ed integrità strutturale, 10 (2009) 29-37; doi: 10.3221/igf-esis.10.04 36 in fact, as f(w) is a relative stress normalized with respect to the compressive strength fc , a comparison between all the cement-based composites, under uniaxial and multi-axial compression, is possible. higher values of af are attained in concretes capable of maintaining high loads after failure (i.e., in the case of ductile materials). obviously, the maximum ductility af,max = 2mm is reached in the case of plastic behaviour [f(w) = 1= const.]. the areas af computed by eq.(6) for the tested specimens (tab. 2) are also reported in the histogram of fig. 8b. in all cases, af is between af,max = 2 mm and the lower limit af,min = 0.61 mm, corresponding to the normal and selfconsolidating concretes without any confinement (fig.8b). to be more precise, af,min is obtained by substituting eqs.(4) (with a = 0.320 mm-2 and b = -1.12 mm-1 ) into eq.(6). at 3 = 1mpa, for the specimens made of sc and nc (i.e., nc1, sc1, sc1b) the values of af range between 1.39 mm and 1.46 mm (fig.8b), and do not differ substantially from those measured for sismabeton (af 1.56 mm) without confinement. conclusions rom the results of an experimental campaign performed on nc, sc and sismabeton cylinders under uniaxial and multi-axial compression, the following conclusion can be drawn: in normal and self-consolidating concrete, fracture toughness in compression increases in the presence of an active confinement. during the post-peak stage, the ductility of sismabeton is comparable with that of nc or sc at 1mpa of confining pressure. in compression, the performance of fiber-reinforced composites can be quantified by the distributed confining pressure generated by the fibers. the presence of an active confinement can improve the mechanical behaviour of concrete and, consequently, its durability. thus, further researches should be developed in order to introduce new sustainability indexes, which take into account fracture toughness, both in tension and compression. acknowledgements he authors wish to express their gratitude to the italian ministry of university and research (prin 2006) and to fondazione cassa di risparmio di alessandria for financing this research work, and also to buzzi unicem s.p.a. for its technical support. references [1] m. a. mansur, m. s. chin, t. h. wee, aci structural journal, 94-6 (1997) 663. [2] k. h. khayat, p. paultre, s. tremblay, aci materials journal, 98-1 (2001) 371. [3] uni en 1998-1:2005. eurocodice 8 – design of structures for earthquake resistance part 1: general rules, seismic actions and rules for buildings, (1998) 229 [4] uni en 1992-1-1:2005. eurocodice 2design of concrete structurespart 1-1: general rules and rules for building, (1992) 225. [5] n. ganesan, j. v. ramana murthy, aci materials journal, 87-3 (1990) 221. [6] g. pons, m. mouret, m. alcantara, j. l. granju, materials and structures, 40-2 (2007) 201. [7] ceb (comite euro-international du beton), “ceb-fip model code 1990”, bulletin d'information n°203-205, thomas telford, london, uk (1993). [8] j. g. m. van mier, , fracture processes of concrete: assessment of material parameters for fracture models. crc press, (1996) 448. [9] d. c. jansen, s. p. shah, asce journal of engineering mechanics, 123-1 (1997) 25. [10] a. p. fantilli, h. mihashi, p. vallini, aci materials journal, 104-5 (2007) 501. [11] p. jamet, a. millard, g. nahas, int. conference on concrete under multiaxial conditions, toulouse (1984) 133. [12] s. j. foster, j. liu, s. a. sheikh, asce journal of structural engineering, 124-12 (1998) 1431. f t http://dx.medra.org/10.3221/igf-esis.10.04&auth=true http://www.gruppofrattura.it b. chiaia et alii, frattura ed integrità strutturale, 10 (2009) 29-37; doi: 10.3221/igf-esis.10.04 37 [13] b. chiaia, a. p. fantilli, p. vallini, in 3rd north american conference on the design and use of self-consolidating concrete (scc), chicago (2008). http://dx.medra.org/10.3221/igf-esis.10.04&auth=true http://www.gruppofrattura.it microsoft word numero_38_art_17 m. a. meggiolaro et alii, frattura ed integrità strutturale, 38 (2016) 128-134; doi: 10.3221/igf-esis.38.17 128 focussed on multiaxial fatigue and fracture a unified rule to estimate multiaxial elastoplastic notch stresses and strains under in-phase proportional loadings marco antonio meggiolaro, jaime tupiassú pinho de castro, luiz fernando martha pontifical catholic university of rio de janeiro, puc-rio, r. marquês de são vicente 225, rio de janeiro, 22451-900, brazil meggi@puc-rio.br, jtcastro@puc-rio.br, lfm@tecgraf.puc-rio.br luiz fernando nazaré marques federal university of south and southeast of pará, unifesspa, av. dos ipês s/n, marabá, 68500-000, brazil lfernando@unifesspa.edu.br abstract. several methods can be used to estimate elastoplastic (ep) notchtip stresses and strains from linear elastic calculations, providing ep stress and strain concentration factors. for uniaxial load histories, neuber’s and glinka’s rules are perhaps the most used. for non-proportional multiaxial histories, such corrections require incremental plasticity calculations to correlate stresses and strains at the notch root, a quite challenging task. however, for in-phase proportional multiaxial histories, where the principal directions do not change and the load path in a stress diagram follows a straight line, approximate methods can be used without requiring an incremental approach. most of these methods are based on neuber’s rule, so they usually result in conservative predictions, especially in plane strain-dominated cases associated with sharp notches. in this work, a unified notch rule (unr) is proposed for uniaxial and in-phase proportional multiaxial histories. the unr can reproduce neuber’s or glinka’s rules, interpolate their notch-tip behaviors, or even extrapolate them for notches with increased constraint. moreover, the unr also allows a non-zero normal stress perpendicular to the free-surface. the proposed method predictions are compared with elastoplastic finite element calculations on notched shafts. keywords. multiaxial fatigue; in-phase proportional loadings; unified notch rule; finite element. citation: meggiolaro, m. a., castro, j.t.p., martha, l. f., marques, l. f. n., a unified rule to estimate multiaxial elastoplastic notch stresses and strains under in-phase proportional loadings, frattura ed integrità strutturale, 38 (2016) 128-134. received: 18.05.2016 accepted: 12.06.2016 published: 01.10.2016 copyright: © 2016 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. introduction irection-sensitive materials like most metallic alloys tend to initiate a single dominant microcrack under fatigue loadings. under multiaxial loading conditions this behavior tends to be well modeled by critical-plane fatiguedamage models, which search for the material plane at the critical point where the corresponding accumulated damage parameter is maximized. d m. a. meggiolaro et alii, frattura ed integrità strutturale, 38 (2016) 128-134; doi: 10.3221/igf-esis.38.17 129 to calculate elastoplastic (ep) strains from a given multiaxial stress history, it is usually necessary to adopt an incremental plasticity formulation, which integrates non-linear differential equations to obtain the stress-strain behavior [1]. in the presence of notches, a much simpler approach is to perform a single linear elastic (le) finite element (fe) calculation on the entire piece for a static unit value of each applied loading. the resulting values at the notch root are called pseudostresses and pseudo-strains, which are fictitious quantities calculated using the theory of elasticity at the critical point of the piece, while assuming that the material follows hooke’s law [2]. these pseudo values are represented here with a “~” symbol on top of each variable. under in-phase proportional loadings, approximate models to obtain the stress and the strain concentration factors kand kcan be used to avoid computationally-intensive incremental plasticity calculations. they provide notch corrections that try to correlate pseudo and notch-tip values using a scalar parameter such as the mises equivalent stress. the main ep notch models for in-phase proportional histories are the constant ratio [3], hoffmann-seeger's [4-5], and dowling's [6] models. these models require some variable definitions, namely:  i and i : pseudo principal stresses and strains at the notch tip, where i 1, 2, 3.  i and i : actual elastoplastic principal stresses and strains at the notch tip.  2 and 3: biaxiality ratios between the principal stresses, 2 2/1 and 3 3/1, both assumed between 1 and 1.  2 and 3: biaxiality ratios between principal strains, where2 2/1 and 3 3/1, also assumed between 1 and 1; and   : effective poisson ratio, with 0.5   in the ep case, where  is the (le) poisson ratio. dowling’s model [6] assumes that the principal stresses1 and 2 act on the free surface of the critical point (thus 3 0), but it considers that both 2 and 2 are constant, estimating them from the pseudo-stresses and pseudo-strains: 2 2 2 2 2 2 2 2 1 1 2 1 1 2 , 1 1                               (1) the model then directly correlates1 and 1 using effective ramberg-osgood parameters e* and hc*: hc ce h 1 1 1 1 **           (2) hc c c hc e e h h ( 1)/22 2 2 2** 2 2 1 (1 ) , 1 (1 / 2)                  (3) in notched components, assuming that the principal directions of the ep stresses and pseudo-stresses are equal, a reasonable supposition, then a variation of neuber’s rule [7] could be used to calculate the ep notch-tip 1 (and then 1) from the pseudo 1 : hc ce e h 1 1 1 1 1 1 1 1 1 1* * *                                (dowling) (4) the above equation does not require a plastic term on the left hand side, because the pseudo-stresses and pseudo-strains are, by definition, le. finally, the other notch-tip ep principal stresses and strains are then obtained from 1 and 1: e 2 2 1 3 2 1 2 2 1 3 1 * 12 , 0 1 , 0.5 ( 0.5 ), 1                        (5) m. a. meggiolaro et alii, frattura ed integrità strutturale, 38 (2016) 128-134; doi: 10.3221/igf-esis.38.17 130 the uniaxial unified notch rule (unr) oting that glinka’s rule [8] usually underestimates while neuber’s rule [7] overestimates notch-tip stresses and strains, when compared to experimental results and fe analyses, a unified incremental rule (unr) has been proposed by ye et al. in [9], which returns values in-between them. for a monotonic uniaxial loading in the x direction, it states that x x ed x x ed x x x xd d d d(1 ) (1 )                  (6) where 0  ed  1 was called the energy dissipation coefficient, assumed in [9] as a material parameter, estimated based on an energy argument as ed  (12hc)/(1hc), where hc is the cyclic exponent of ramberg-osgood’s equation. however, ed might depend not only on the material but also on the notch geometry and constraint factor. this coefficient ed can also be regarded as a fitting parameter if experimental data or reliable ep fe analyses are available for its calibration. to extend the unr rule to multiaxial problems, a deviatoric version of eq. 6 is proposed in this work: x x u x x u x x x xs de e ds s de e ds( ) ( 2 )          (7) where x x y zs ( 2 ) 3     and x x y ze ( 2 ) 3     are the deviatoric stresses and strains in the x direction at the notch tip, while uc  (1ed) is called the notch constraint factor, with values1  u  2 to interpolate the incremental neuber rule [10-11] (for which u  1) and a similar incremental glinka rule (which has u  2). as the deviatoric stresses sx, sy and sz are linearly-dependent, since sx  sy  sz  0, it is possible to reduce the deviatoric stress and strain space dimensions using: y y z y zz x x s s s s s1 2 3 , 3 3 2 2 2 2            (8) y z y z y z x x e e e e e1 2 3 , 3 3 2 2 2 2              (9) assuming that eq. 7 is valid for the transformed deviatoric stresses and strains from eqs. 8 and 9, then u u u u s de e ds s de e ds s de e ds s de e ds 1 1 1 1 1 1 1 1 2 2 2 2 2 2 2 2 ( ) ( 2 ) ( ) ( 2 )                          (10) where, as explained before, the symbol “~” is used for pseudo-values calculated from le analyses. the unified notch rule (unr) proposed in this work can then be obtained from the integration of eq. 10, which can be used for both uniaxial and in-phase proportional histories. for uniaxial histories, this integration results in the scalar unr: hc u che e 1/ 2                  , u c uu c h h ( 2 ) 1        (unr) (11) where u is the effective notch constraint factor. this equation can reproduce neuber for u 1 and thus u 1  , or glinka’s rule for u 2 and thus 2 (1 )u ch   . although conceptually different, u shares some similarities with newman’s constraint factor [12], varying from 1.0 under plane stress conditions (where neuber’s rule is recommended) to usually more than 3.0 under plane strain. thus, both u and newman’s reflect increased stress-state constraint and associated plasticity decrease at the critical point, however using u at notch tips and newman’s at crack tips. n m. a. meggiolaro et alii, frattura ed integrità strutturale, 38 (2016) 128-134; doi: 10.3221/igf-esis.38.17 131 the multiaxial unified notch rule he multiaxial version of the unr assumes in-phase proportional loading under free-surface conditions, supposing xz = yz = 0, but allows the presence of a surface normal z ≠ 0, where the z axis is assumed perpendicular to the surface, and the x and y axes are aligned with the remaining principal directions, with x in the direction of the maximum absolute principal stress. therefore, the principal notch tip stresses x  1, y  2, and z  3 are assumed to satisfy|x|  |y| and |x|  |z| during the entire load history. the involved variables are the same as the ones defined before, in addition to an elastic and plastic separation of the strain biaxiality ratios, through:  2el and 3el: biaxiality ratios between principal elastic strains, where 2el 2el/1el and 3el 3el/1el are both assumed between 1 and 1; and  2pl and 3pl: same definition, but for plastic strains (for pressure-insensitive materials, where 1pl 2pl3pl0, it follows that 12pl 3pl 0 and thus 2pl 3pl1). since the multiaxial loading history is assumed here to be proportional, the deviatoric stress increment is always parallel to the plastic straining direction, so the prandtl-reuss plastic flow rule [1] gives, for the normal deviatoric strain components, x xy z y zpl pl pl y z y zpl pl d d d d d dde de d d d dp 1 2 ( ) 2 ( ) 21 ( ) 3 2 ( ) 3 2                                      (12) where p is called the generalized plastic modulus (proportional to the slope of the stress vs. plastic strain curve at the current stress state), and all shear increments are zero since x, y, and z are defined in the principal directions. integrating the above equation using the plastic biaxiality ratio definitions, then pl plx xpl x xpl pl pl d d p 2 3 2 3 0 0 2 3 2 3 1 ( ) 2 1 ( ) 21 ( ) 3 2 ( ) 3 2                                    (13) neglecting the isotropic hardening transient, let’s assume that the material follows ramberg-osgood with cyclic constant hc and exponent hc. moreover, assuming that this proportional loading is balanced, i.e. it does not cause ratcheting or mean stress relaxation, then a mróz multi-surface hardening model can be adopted [1] (instead of the more general non-linear kinematic hardening models). to improve accuracy, let’s adopt an infinite number of hardening surfaces, as discussed in [13], see fig. 1. from the calibration of the mróz model, the generalized plastic modulus p pi for the hardening surface with radius ri becomes   hcc c i cip h h r h 1 1 ( 2 3)    (14) consider a monotonic proportional loading departing from the origin of the deviatoric stress space, as shown in fig. 1, assuming x, y and z as principal directions. in this case, the radius ri of the current active surface from the mróz model is equal to the norm (and thus the mises equivalent value) of the current stress state. replacing the values of p  pi and ri into eq. 13, and using the plastic strain incompressibility condition 2pl 3pl 1, it follows that hc u che e 1 11 1 1 1 ** *                       (15) e e* 2 3[1 ( )]      , hc c c hc h h ( 1)/22 2 * 2 3 2 3 2 3 2 3 [1 ( ) ( ) ] [1 ( ) / 2 ]                  (16) t m. a. meggiolaro et alii, frattura ed integrità strutturale, 38 (2016) 128-134; doi: 10.3221/igf-esis.38.17 132   hcel pl c el pl el el pl pl el el pl pl e h 1/* * 1 1 1 1 1 1 1 2 2 1 3 3 1 2 2 1 2 1 3 3 1 3 1 , , , ,                                           (17) pl pl 2 3 3 2 2 3 2 3 2 3 0.5 (1 ) 0.5 (1 ) , 1 0.5 ( ) 1 0.5 ( )                         (18) el el 2 3 3 2 2 3 2 3 2 3 (1 ) (1 ) , 1 ( ) 1 ( )                             (19) figure 1: mróz infinite-surface hardening model for a monotonic proportional loading. dowling’s model for in-phase proportional loadings is a particular case of the more general in-phase proportional unr, setting u 1  (to reproduce neuber’s rule) and also 3 0 (free-surface with 3 0), assuming as well that2pl 2el based on, and that 3pl 3el based on an effective poisson ratio  . both dowling’s and unr models assume the nominal section (away from the notch) remains le. in other words, they are valid even under general yielding of the net cross section, but they do not account for yielding of the gross cross section. to perform this correction, the pseudo principal stress 1 is represented as the product of a le stress concentration factor kt multiplied by a nominal stress n1, i.e. n tk1 1 /   , where n1 is assumed to follow ramberg-osgood, giving h hc c nn t u un c c k h he e 1 1 2 1 11 1 1 1* ** *                                      (20) verification of the unr with elastoplastic finite elements he proposed unr and dowling’s classic notch rule are checked against elastoplastic (ep) finite element (fe) calculations, for multiaxial in-phase proportional tension-torsion problems. the comparison is based on the calculation of the peak ep stresses and strains at a notched solid shaft with largest diameter 50.8 mm and a semicircular u-notch with a sharp radius 0.254 mm. the shaft is assumed made of a heat-treated 1070 steel with young modulus t m. a. meggiolaro et alii, frattura ed integrità strutturale, 38 (2016) 128-134; doi: 10.3221/igf-esis.38.17 133 e  210gpa, poisson ratio0.3, and ramberg-osgood parameters hc 1736mpa and hc = 0.199, using data reported in [14]. for the ep calculations all simulations were carried out using ansys software, using the solid186 3d elements with 20 nodes each and 3 degrees of freedom per node. the model used for the ep fe simulations is illustrated in fig. 2, and its notch tip grid is depicted in fig. 3. figure 2: the fe model for the sharply notched shaft. figure 3: the grid around the notch tip. figure 4: predicted and fe-calculated ep strain and stress. 0 0.5 1 1.5 2 0.5 1 1.5 2 σ̃m ises/sy σ (� ) m is e s / σ̃ (�̃ ) m is e s ε − non−deviatoric neuber α u = 1 ε − non−deviatoric glinka α u = 2 ε − non−linear fe σ − non−deviatoric neuber α u = 1 σ − non−linear feσ − non−deviatoric glinka α u = 2 ε − deviatoric unr α u = 1.979 σ − deviatoric unr α u = 1.979 k tσ = 6.70 k tτ = 3.75 r τσ = 1.73 m. a. meggiolaro et alii, frattura ed integrità strutturale, 38 (2016) 128-134; doi: 10.3221/igf-esis.38.17 134 fig. 4 shows the ratio between the ep and the pseudo mises strain  mises mises and stress  mises mises for a particular case of a tension-torsion multiaxial loading assuming a proportionality stress ratio between equivalent shear and normal nominal stresses   3r .the le stress concentration factors for this sharply notched shaft are ktσ = 6.70 for normal stresses and ktτ = 3.75 for pure shear stresses. the two solid lines for both strains and stresses show the numerically obtained ep results obtained from the fe simulations, which are overestimated by both neuber’s (u1, the rule adopted in dowling’s multiaxial model) and glinka’s rules (u 2). the third dashed lines also for both strains and stresses are the better estimates obtained from the proposed unr, calibrated for u 1.979. these results show that the proposed rule is able to improve significantly the traditional estimates from neuber’s and glinka’s models, in particular for notched components with high transversal constraints around the notch tip, the case of the studied sharply notched shaft. finally, as expected, all predictions tend to the       1mises mises mises mises under low stresses. conclusions n this work, a unified notch rule (unr) was proposed to predict elastoplastic stresses and strains at a notch roots from linear elastic calculations, for uniaxial and in-phase proportional multiaxial histories. the unr can interpolate between neuber’s and glinka’s rules using its u parameter calibration to account for the magnitude of the transversal constraint around the notch tip, or even to extrapolate them to better reproduce increased constraint effects around sharp notch tips. moreover, the proposed unr allows biaxiality ratios 3 3/1  0, an improvement over dowling’s model, which always assume 3 = 0. even though the derivation of the unr model assumed an integration for a monotonic load, the resulting equations could be applied to cyclic loadings, as long as they are also in-phase and proportional, and the appropriate biaxiality ratios can be assumed constant. references [1] castro, j.t.p., meggiolaro, m.a., fatigue design techniques: vol. ii low-cycle and multiaxial fatigue. createspace publishing company, scotts valley, ca, usa, (2016). [2] köettgen, v.b., barkey, m.e., socie, d.f., fatigue fract eng mat struct, 18 (1995) 981-1006. [3] socie, d.f., marquis, g.b., multiaxial fatigue, sae, (2000). [4] hoffmann, m., seeger, t., a generalized method for estimating multiaxial elastic plastic notch stresses and strains, part i: theory, j eng mat tech, 107 (1985) 250-254. [5] hoffmann, m., seeger, t., a generalized method for estimating multiaxial elastic-plastic notch stresses and strains. part 2: application and general discussion, j eng mat tech, 107 (1985) 255-260. [6] dowling, n.e., brose, w.r., wilson, w.k., in: fatigue under complex loading: analysis and experiments, ae-6, sae, (1977). [7] neuber, h., theory of stress concentration for shear-strained prismatic bodies with arbitrary nonlinear stressstrain law, j appl mech, 28 (1961) 544-551. [8] molski, k., glinka, g., a method of elastic-plastic stress and strain calculation at a notch root, mat sci eng, 50 (1981) 93-100. [9] ye, d., hertel, o., vormwald, m., a unified expression of elastic-plastic notch stress-strain calculation in bodies subjected to multiaxial cyclic loading, int j solids struct, 45 (2009) 6177-6189. [10] kujawski, d., on energy interpretations of the neuber's rule, theor appl fract mech, 73 (2014) 91-96. [11] ince, a., glinka, g., a numerical method for elasto-plastic notch-root stress–strain analysis, j strain analysis eng design, 48 (2013) 229-224. [12] newman, j.c. jr, crews, j.h., bigelow, c.a., dawicke, d.s. astm stp 1244 (1995) 21-42. [13] chu, c.c., the analysis of multiaxial cyclic problems with an anisotropic hardening model, int j solids struct, 23 (1987) 567-579. [14] jiang, y.r., sehitoglu, h., materials engineering – mechanical behavior report #413, university of illinois, urbana, illinois, (1992). i microsoft word numero_38_art_11 m. kepka et alii, frattura ed integrità strutturale, 38 (2016) 82-91; doi: 10.3221/igf-esis.38.11 82 focussed on multiaxial fatigue and fracture structure service life assessment under combined loading using probability approach miloslav kepka, miloslav kepka jr. university of west bohemia in pilsen, regional technological institute – research center of the faculty of mechanical engineering, univerzitni 8, 306 14 pilsen, czech republic kepkam@rti.zcu.cz, http://www.rti.zcu.cz/00-42037763-8700 kepkami1@rti.zcu.cz, http://www.rti.zcu.cz/00-42037763-8736 jan chvojan, jaroslav václavík research and testing institute pilsen, tylova 1581/46, 301 00 pilsen, czech republic chvojan@vzuplzen.cz, http://www.vzuplzen.cz/00-420-37985-2193 vaclavik@vzuplzen.cz, http://www.vzuplzen.cz/00-420-37985-2162 abstract. this article presents a basic research approach for probabilistic assessment of vehicle structure fatigue endurance under multiaxial loading. one representative welded structural detail of the bottom joint plate of an articulated bus was selected for the case study. the character of the loading on the joint during a service test is analyzed and discussed. the methodology for estimation of the damage level in the joint builds on deterministic procedures for railway vehicle assessment based on shear, longitudinal and transverse stress components. this approach based on the equivalent stress and particular load capacity factors was expanded to include the probabilistic perspective. keywords. service life; combined loading; damage; vehicle; probabilistic approach. citation: kepka, m.., kepka, m. jr., chojan, j., václavík, j., structure service life assessment under combined loading using probability approach, frattura ed integrità strutturale, 38 (2016) 82-91. received: 16.05.2016 accepted: 22.06.2016 published: 01.10.2016 copyright: © 2016 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. introduction n-service loads acting on components and structural details in vehicles tend to be complex and, in most cases, multiaxial and time-variable. the stress response to such loads can (but need not) be multi-axial. critical locations in vehicle structures are subjected to fatigue loading which can lead to initiation of fatigue cracks, fatigue crack propagation and, sometimes, to final failure. even today, sizing and assessment of such critical locations often involves the deterministic approach. this means that both loading and strength are represented by their mean values for which adequate safety factors are sought. in the following, a description is given of fatigue lifetime assessment of a welded joint operating under relatively complex loading in an articulated bus. the engineering approach which is normally used in technical practice has been expanded i m. kepka et alii, frattura ed integrità strutturale, 38 (2016) 82-91; doi: 10.3221/igf-esis.38.11 83 into a reliability analysis which gives a more accurate description of the risk of fatigue failure in the critical location of the structural detail. service life assessment using probability approach aterials subjected to time-varying loads suffer damage caused by the fatigue process. their load response can be described in terms of time-varying strain and stress, and the cumulative fatigue damage can be found using an appropriately chosen rule. in order to evaluate the service fatigue life of a structure, one needs not only information about its service loading but also some data on the structure’s fatigue strength. the resistance of a structure to high-cycle fatigue damage is described by the s-n curve. the s-n curve can be constructed using fatigue data from a sufficient number of test pieces representing the structural detail under examination. however, it can also be determined by estimate or obtained from one of the standards for design of structures. fatigue life assessment is often based on the deterministic approach which relies on mean values of load-bearing capacity and load, and a set of factors of safety. if, however, the values of the safety factors are not chosen correctly, the load and the fatigue resistance of the material may prove to be mismatched under real-world service conditions, which may lead to fatigue damage or even failure of the part. probabilistic approach, on the other hand, uses distributions of random input variables for finding the fatigue life distribution function, i.e. the probability that the material enters its limit state with respect to strength after a certain period in service. fatigue life estimates are based on cumulative fatigue damage rules. conformity to the life requirement may be formulated as the part’s reliability. this means that over the required life treq the probability of fatigue failure does not exceed the allowable value pallow. statistical characteristics of input variables are obtained from measurement and tests (service loading measurement, fatigue testing), determined from experience, or derived from standards and codes. important to the life estimates are the relationships between input variables, e.g. in the form of cumulative fatigue damage rules, and the mean stress of loading cycles. comparison can be done using several different rules. this, however, enlarges the variance of the lifetime estimate. structures are normally designed to the guaranteed design life tg and failure probability pg. these values are guaranteed with certain margins δtg and δpg, and therefore tg >treq, pg < pallow (fig. 1). figure 1: schematic illustration of the probabilistic approach to life estimation – position of the point of design life of the structural detail with respect to the fldf while material properties of parts of equipment are given before it is put into operation, the actual service loads can only be estimated for an already-known steady-state process. changes to the loading conditions or out-of-standard load states affect the form and position of the fatigue life distribution function (fldf). they may shorten the life margin δtg and m pallow 0 pg a d a m a g e p ro b a b ili ty p stress time history t tres, act tres, req δtg δ p g tact treq tg service life t m. kepka et alii, frattura ed integrità strutturale, 38 (2016) 82-91; doi: 10.3221/igf-esis.38.11 84 even lead to a loss of reliability at δtg < 0. such occurrences must be prevented by identifying and signaling the onset of hazardous states. the way to achieve that is to continuously monitor the service loads on critical locations of the structure and track (calculate) the fatigue damage in them. to find the fatigue life distribution function, one needs the following input information. a) service loads on the critical location. continuous stress-time histories can be obtained from appropriate monitoring devices, for instance. typical input into fatigue damage calculation is represented by a two-parameter histogram of cycle frequencies, reflecting cycle amplitudes and mean stress levels. most often, this histogram (also referred to as “load spectrum”, “stress spectrum”, and otherwise) is obtained by the rain flow method but other techniques can be used as well. signals obtained from the monitoring sometimes show trends (changes in variance with time, shifting mean value, and others) which can be accounted for in the fatigue damage predictions. b) material properties. the input into the calculation is an experimentally measured and statistically evaluated s-n curve, or more precisely, an implicit representation of its left-sided tolerance limits for various failure probabilities. the probabilistic evaluation of service fatigue life of a structural detail of a road vehicle which was carried out in the present case study was based on the segmentation of random loading processes proposed by kliman [5, 6]. random loading process the loading process of interest is analysed by appropriately segmenting a sufficiently long in-service measurement record from a critical location of the relevant part of a vehicle. a load record of certain length represents a random portion of a vehicle’s service. obviously, another measurement carried out at another time will be different due to the random nature of the load. if a loading process record of adequate length σ(t) is segmented appropriately, it can be substituted for repeated measurement runs. in-service loads will thus be represented by a set of records – process segments σ(t). in order to calculate a faithful fldf, one has to find the minimum acceptable length of the process segment. in practice, this means finding such length, at which the standard deviation and mean value of the calculated fldf become stable (i.e. they do not change substantially with further increases of the segment length). the segment length is understood as a certain portion of the service run represented by time, mileage or otherwise. the procedure is as follows. the stress-time history is analyzed using the rain flow method applied to a series of segments of a constant length where the overlap between these consecutive segments (“windows”) is 95 %. for each “window”, the fatigue life is calculated. mean value and standard deviation are calculated for each set of lifetimes obtained with a certain segment length. the procedure starts with the shortest segment length and continues by increasing the length. an example of such procedure is illustrated in fig. 2 which also shows the chosen optimal segment length. the set of lifetimes obtained for the optimal segment length determined by the above procedure will be input into the fldf calculation. lifetime is calculated using an appropriate cumulative fatigue damage rule and the theory of accounting for the effect of the mean component of cycles. 0.0e+00 5.0e+05 1.0e+06 1.5e+06 2.0e+06 2.5e+06 3.0e+06 3.5e+06 4.0e+06 0 10 20 30 40 50 60 s e rv ic e l if e l [ k m ] segment length [km] mean std solution 27 km figure 2: example of determination of minimum segment length m. kepka et alii, frattura ed integrità strutturale, 38 (2016) 82-91; doi: 10.3221/igf-esis.38.11 85 random nature of materials properties low-cycle or high-cycle fatigue properties of materials are described by the cyclic stress-strain curve, the lifetime curve or the s-n curve. these (or their coefficients) can be determined on the basis of fatigue tests. however, one can also estimate their values using various empirical formulas or find them in certain standards and codes. statistical evaluation of fatigue tests can provide confidence intervals and tolerance limits for the chosen probability of a particular curve and the corresponding coefficients. such limits are often difficult to define analytically by means of simple equations. they can be somewhat simplified by using linear relationships. this is common practice with fatigue curves for typical structural details listed in various categories in standards. there, the left-sided limits of tolerance are simply expressed in the form of the residual standard deviation and the d quantile for the probability in question. kliman’s methods requires that the parameters of the left-sided limits of tolerance of the lifetime curve are calculated for the probabilities p = 1 through 99 % in steps of 1 % (fig. 3). figure 3: schematic illustration of the method of finding materials parameters – standardized fatigue curves. figure 4: schematic procedure for calculating the fldf. m. kepka et alii, frattura ed integrità strutturale, 38 (2016) 82-91; doi: 10.3221/igf-esis.38.11 86 determination of resulting fatigue life distribution function the resulting fatigue life distribution function (fldf) is to account for the random nature of loading, as well as the random nature of material properties. the input to the process of its determination consists of the quantity s of constantlength segments of the loading process, and 99 lifetime curves for individual failure probability levels. hence, a total of k = s×99 combinations of loads and material properties are available. the resulting fldf is obtained by finding a set of distribution curves through process segmentation, using the lifetime curve for p = 1 %, then 2 %, and so forth until 99 % is reached. finally, 99 distribution curves are obtained from which the resulting fldf is generated for individual corresponding probability levels. demonstration example he chosen demonstration example concerns a welded joint in an articulated bus which is located at the base of the fixed bracket of the articulated joint on the rear section (fig. 5). in fact, some vehicles exhibited fatigue damage in this location. the purpose of the measurement was to assess the stresses in this structural detail, redesign it and validate this modification through another measurement run. for this case study, stress analysis has been carried out for the location of the r1 strain gauge rosette which is a place where two welded joints meet. engineering strain time histories from this rosette were used for evaluating the components of principal, longitudinal, vertical and shear stresses. road tests involved running a demanding route of approximately 13 kilometers in urban and suburban traffic: four times with the vehicle empty and four times with the vehicle loaded, although without real passengers. on this route, the frequency of failures occurring in buses was the highest. along this route, the road is uneven with large differences in height which causes vertical excitation in the vehicle. in addition, there are many curves and upward and downward slopes which were expected to contribute to twisting loads on the joint. figure 5: the joint of the rear section of an articulated bus – a schematic drawing and the strain gauge rosette r1. time histories analysis generally, the approach for multiaxial fatigue problems depends on the type of loading involved. the solution is less complicated for structural details under proportional loading. this is the type of loading in which the ratio of principal stresses (biaxiality ratio) a = σ2 / σ1 and the directions of the principal stresses remain constant. non-proportional loading involves principal stresses whose directions rotate or undergo stepwise changes. the critical location of interest – the strain gauge rosette r1 – was studied using the ncode software. the figures below show results of the analysis for one of the stress-time histories obtained from the road test of the empty vehicle in real traffic. fig. 6 shows the dependence of the absolute maximum principal stress on its angle to the x direction. the graph indicates that the directions of principal stresses remain constant at all stress levels, except the very low ones. this is the necessary condition for considering proportional loading conditions. the other graph in fig. 6 from the same measurement run shows the dependence of the absolute maximum principal stress on the biaxiality ratio. at higher stresses, the biaxiality ratio fluctuates about 0.25 and approaches the poisson’s ratio, which is an indication of near-plane strain loading. t m. kepka et alii, frattura ed integrità strutturale, 38 (2016) 82-91; doi: 10.3221/igf-esis.38.11 87 figure 6: absolute maximum principal stress against the angle to the x direction, absolute maximum principal stress vs. biaxiality ratio. used methodology he assessment of the endurance of the welded detail in question relied on a methodology which is used for rail vehicle testing in germany. allowable stresses were determined on the basis of nominal values and estimated notch factors according to iiw [1] and fkm [2] standards. using the measured stress-time series in the location of the strain gauge rosette, stress components perpendicular to the weld σ, parallel to the weld σii, and shear stress components τxy were calculated. a similar approach is used for demonstrating the fatigue life of railway vehicles on test rigs [3, 4]. decomposition of these series by means of the rainflow technique yields a matrix of stress amplitude rates and mean values of the cycle. the resulting matrices are combined into a single macro block on the basis of representative samples of service runs. in our case, the matrices were combined from four half-hour runs of an empty vehicle and four runs of a vehicle fully-loaded with a 1:1 passenger-equivalent load. the resulting matrix is converted to a single-parameter histogram of amplitude rates, accounting for the sensitivity to the mean value by using the coefficient m = 0.15 for normal stresses and m = 0.09 for shear stresses, as expressed in eq. (1) a ef i a i mm, , ,     (1) using notch factors, the measured stress values are transformed to notch stress values. notch factors can be found in various sources. here, they follow the principle used in the femfat software for the notch radius of r = 1 mm. the slope of the s-n curve for weldments is set as m = 3 for normal stresses and m = 5 for shear stresses. the characteristic stress amplitude for n = 2·106 and for the base material s355, which is the material of the structural detail in question, and for normal stresses and a completely reversed cycle is σa,r=-1 = 150 mpa, whereas for shear stresses and a completely reversed cycle it is τa,r=-1 = 87 mpa (√3·σa,r=-1). these values are derived with respect to the iiw standard which has been developed for the stress ratio of r = 0.5. the s-n curve has no inflection point. it has been extended all the way to half the amplitude achieved upon n = 5 million cycles. this approach is more conservative than that used by the fkm standard. the allowable fatigue damage is d = 1. the above approach relies on the calculation of load capacity factors a. fig. 7 explains the calculation. an aggregate macro block is determined from individual load matrices. this macro block is converted to equivalent stress amplitude which would cause the same amount of damage as the entire macro block. the ratio of this equivalent stress amplitude σa,ef and the allowable stress amplitude σa,bk for the given number of cycles nd is the load capacity factor a. for each stress amplitude component σa,, σa,ii, τxy, the local load capacity factor a is calculated using eqs. (2) through (4). finally, a complex load capacity factor involving all three components (5) is determined in order to account for the multiaxial state of stress in a manner similar to yield criteria. if this factor is less than 1, sufficient fatigue strength of the detail in question has been demonstrated. t m. kepka et alii, frattura ed integrità strutturale, 38 (2016) 82-91; doi: 10.3221/igf-esis.38.11 88 figure 7: the relations between the effective stress amplitude σa,ef, the limit stress amplitude σa,bk and the load capacity factor a with respect to the s-n curve and the total number of cycles nd. k kj a ii bk d d ri n a n 1 , , , 11                    (2) k kj a ii bk d d ri n a n 1 , , , 11                    (3) k kj a ii bk d d ri n a n 1 , , , 11                    (4) tot bk bk bk bk bka a a a a a 2 2 2 , , , , ,             (5) probability approach for evaluation of combined loading he methodology outlined above represents the deterministic approach. in a probability-oriented assessment, the random nature of the loading, as well as the random nature of materials properties must be taken into account. a load record of certain length represents a random portion of a vehicle’s service. obviously, another measurement carried out at another time will be different due to the random nature of the load. if a process record of adequate length σ(t) is segmented appropriately, it can be substituted for repeated measurement runs. in-service loads will thus be represented by a set of records – process segments [5]. by this method, the segment length for a representative lifetime assessment and the variance of load spectra used in the lifetime calculation can be determined. in fig. 8, this procedure is applied to the complex load capacity factor based on (5) which is calculated within a moving window of l size. in the figure, mean values and standard deviations for the set of values atot obtained are plotted for the expanding interval l. the segment length, at which the value of atot ceases to change significantly, is used for calculating the load capacity factor distribution function. in the present case, a distance of 21 km has been used. the random nature of materials properties is reflected in the tolerance limits of the s-n curve. the variability of the number of cycles to failure n is expressed through the standard deviation s(log n) for the quantile d, depending on failure t m. kepka et alii, frattura ed integrità strutturale, 38 (2016) 82-91; doi: 10.3221/igf-esis.38.11 89 probability. for this purpose, a median s-n curve must be obtained first – by shifting the curve defined in the standards for 97.5 % failure probability. the s-n curve equation is as follows i a in c m d s n1 ,log log log (log )     (6) the actual probabilistic assessment of fatigue strength is carried out using an ms excel sheet. first, the distributions of individual components of the load capacity factor for corresponding tolerance limits of s-n curves are found. then, the distribution of the combined load capacity factor is calculated. the real distributions are approximated by lognormal distributions figure 8: determination of the moving window for the probabilistic characterization of the vehicle run. obtained results discussion he above procedure was applied to the measured location of the articulated joint (fig. 5). distributions of individual components of the load capacity factor were determined. fig. 9 shows example plots of their distribution functions using the median s-n curve. in this case, the random nature has been accounted for on the part of the load only. figure 9: probability distribution of particular loading factor components ax, ay and aτxy. t m. kepka et alii, frattura ed integrità strutturale, 38 (2016) 82-91; doi: 10.3221/igf-esis.38.11 90 the largest damage is caused by the longitudinal component of the load (bending load acting on the articulated joint). fig. 10 shows plots of the distribution function of the complex load capacity factor for three design lifetimes of the bus. these distributions indicate the following outcomes. the probability that atot at the design lifetime of l = 1 mil. km will be less than 1 is lower than 30 %. there is a high probability of p = 97.5 % that the value atot will be less than 1 only at the lifetime of l = 250 000 km. figure 10: distribution functions of the complex loading factor for three values of design service life. conclusion he objective of this paper was to use an articulated joint of a bus for demonstrating the engineering approach for fatigue life assessment of welded parts operating under multiaxial loads, and expand this approach by incorporating the probabilistic perspective. the assessment of the resistance to fatigue damage is based on distribution functions of the complex load capacity factor which has been calculated from three load components acting on the welded joint by using a formula analogous to yield criteria calculations. this paper illustrates the following benefits of this approach. if this structural detail was examined using no other than the deterministic approach, taking into account only the normal stress component which is perpendicular to the welded joint, and the median s-n curve, the detail would be found to meet the design lifetime requirement (fig. 9, component ax). even though the stress component perpendicular to the welded joint dominates in this case, the combined assessment of the weld shows that the probability of meeting the design lifetime is no more than 30 %. the variance of in-service loading conditions has a milder effect on the life than the variance of material properties, provided that the lifetime estimates are based on a sufficiently long record of the loading process (21 km in our case). at half running distance, the variance doubles, which would broaden the distribution functions plotted in fig. 10. in the redesigned structural detail, the stresses in the welded joint were found to be substantially lower, as confirmed by repeated measurement. acknowglements his paper is a result of the collaboration between the regional technological institute and research and testing institute pilsen under the project no. lo1502 entitled development of the regional technological institute funded from the national sustainability programme i (ministry of education of the czech republic). t t m. kepka et alii, frattura ed integrità strutturale, 38 (2016) 82-91; doi: 10.3221/igf-esis.38.11 91 references [1] iiw-richtlinie xiii-1539-96/xv-845-96, (1996). [2] fkm-richtlinie, rechnerischer festigkeitsnachweis für maschinenbauteile, 4. erweiterte ausgabe (2002). [3] tests to demonstrate the strength of railway vehicles. regulations for proof test and maximum permissible stresses. erri b 12/rp 60, (1995). [4] gestaltung und dauerfestigkeitsbewertung von schweißverbindungen an stählen im schienenfahrzeugbau, dvs 1612, (2009). [5] kliman, v., füleky, p., jelemnská, j., advances in fatigue lifetime predictive techniques, 3 (1996) 305-327. [6] kliman, v., kepka, m., václavík, j., influence of scatter of cyclic properties of material on operational endurance of construction, kovove mater., 48 (2010) 367–378. doi: 10.4149/km 2010 6 367. << /ascii85encodepages false /allowtransparency false /autopositionepsfiles true /autorotatepages /none /binding /left /calgrayprofile (dot gain 20%) /calrgbprofile (srgb iec61966-2.1) /calcmykprofile (u.s. web coated \050swop\051 v2) /srgbprofile (srgb iec61966-2.1) /cannotembedfontpolicy /error /compatibilitylevel 1.4 /compressobjects /tags /compresspages true /convertimagestoindexed true /passthroughjpegimages true /createjobticket false /defaultrenderingintent /default /detectblends true /detectcurves 0.0000 /colorconversionstrategy /cmyk /dothumbnails false /embedallfonts true /embedopentype false /parseiccprofilesincomments true /embedjoboptions true /dscreportinglevel 0 /emitdscwarnings false /endpage -1 /imagememory 1048576 /lockdistillerparams false /maxsubsetpct 100 /optimize true 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/hrv (za stvaranje adobe pdf dokumenata najpogodnijih za visokokvalitetni ispis prije tiskanja koristite ove postavke. stvoreni pdf dokumenti mogu se otvoriti acrobat i adobe reader 5.0 i kasnijim verzijama.) /hun 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can be opened with acrobat and adobe reader 5.0 and later.) >> /namespace [ (adobe) (common) (1.0) ] /othernamespaces [ << /asreaderspreads false /cropimagestoframes true /errorcontrol /warnandcontinue /flattenerignorespreadoverrides false /includeguidesgrids false /includenonprinting false /includeslug false /namespace [ (adobe) (indesign) (4.0) ] /omitplacedbitmaps false /omitplacedeps false /omitplacedpdf false /simulateoverprint /legacy >> << /addbleedmarks false /addcolorbars false /addcropmarks false /addpageinfo false /addregmarks false /convertcolors /converttocmyk /destinationprofilename () /destinationprofileselector /documentcmyk /downsample16bitimages true /flattenerpreset << /presetselector /mediumresolution >> /formelements false /generatestructure false /includebookmarks false /includehyperlinks false /includeinteractive false /includelayers false /includeprofiles false /multimediahandling /useobjectsettings /namespace [ (adobe) (creativesuite) (2.0) ] /pdfxoutputintentprofileselector /documentcmyk /preserveediting true /untaggedcmykhandling /leaveuntagged /untaggedrgbhandling /usedocumentprofile /usedocumentbleed false >> ] >> setdistillerparams << /hwresolution [2400 2400] /pagesize [612.000 792.000] >> setpagedevice microsoft word numero 8 art 4 k. g. kodancha et alii, frattura ed integrità strutturale, 8 (2009) 45-51; doi: 10.3221/igf-esis.08.04 45 variation of stress intensity factor and elastic t-stress along the crack-front in finite thickness plates k. g. kodancha, s. k. kudari department of mechanical engineering, b. v. b. college of engineering & technology, hubli 580 031, india abstract. non-singular terms in the series expansion of the elastic crack-tip stress fields, commonly referred to as the t-stress. the t-stress is as an additional stress field characterizing parameter to stress intensity factor (k) in the analysis of cracked bodies. t-stress is used as an important constraint parameter in the fracture analysis. in this investigation, three-dimensional finite element analyses have been conducted to compute the elastic t-stress considering a single edge notched tensile (sent) specimen with varied thickness and a/w ratio. the results indicate that the t-stress depends on the specimen thickness and significantly varies along the crackfront from surface to centre of the specimen. the t-stress results obtained in the present analysis together with corresponding ki values can be used for analysis of constraint effects in a fracture specimen. keywords: elastic t-stress; stress intensity factor; finite element method; constraint issue. introduction he elastic t-stress, or the second term of the williams [1] series expansion for linear elastic crack-tip fields, represents the stress acting parallel to the crack plane. the t-stress can strongly affect the magnitude of hydrostatic triaxiality in the near crack-tip elastic–plastic fields. it is well known that the sign and magnitude of tstress can substantially alter the level of crack-tip stress triaxiality [2-4], hence influence crack-tip constraint. positive tstress strengthens the level of crack-tip stress triaxiality and leads to high crack-tip constraint; while negative t-stress reduces the level of crack-tip stress triaxiality and leads to the loss the crack-tip constraint. several researchers [5-8] have shown that the t-stress, in addition to the k or j-integral, provides an effective two-parameter characterization of plane strain elastic–plastic crack-tip fields in a variety of crack configurations and loading conditions. the application of twoparameter fracture mechanics to include the constraint effect in the failure assessment procedure is becoming more and more established. in order to apply the two-parameter fracture mechanics methodology, it is important to provide tstress solutions for the crack configuration under consideration. many earlier investigators [9, 11] have provided t-stress solutions for 2d cracked bodies. however, study on variation of t-stress along the crack-front is very limited. recently, qu and wang [12] using quarter-elliptical corner cracks have shown that the magnitude of t-stress varies along the quarter-elliptical corner crack-front. but dependence of t-stress along the crack-front in fracture specimens is not available. hence, in the present investigation, detailed three-dimensional finite element analyses have been conducted to study the variation of the t-stress and ki along the crack-front considering a sent specimen geometry having varied thickness and crack length to width ratio (a/w) subjected to tension load. finite element analysis series of 3d stress analyses by finite element method have been made on sent specimen using abaqus 6.5 [13] finite element software. the geometry of the specimen considered in this analysis is shown in fig.1. finite element computations were carried out considering only one half of the specimen due to the symmetry. the analysis domain is descritized using 20-noded isoparametric 3d solid reduced integration elements. these types of t a http://dx.medra.org/10.3221/igf-esis.08.04&auth=true http://www.gruppofrattura.it k. g. kodancha et alii, frattura ed integrità strutturale, 8 (2009) 45-51; doi: 10.3221/igf-esis.08.04 46 elements in abaqus are referred as c3d20r. this kind of elements is used in the work of qu and wang [12] for computation of t-stress. in this analysis, to model the ( 1 / r ) singularity of stress/strain at the crack-front, the nodes of crack front elements are shifted to quarter point as shown in fig.2. the number of elements in the analysis domain varied with the thickness of the specimens. it is noted that for specimen with thickness 2 mm the number of elements used are 5625 (number of nodes, 25,536) and for 20 mm thick specimen the number of elements used were 7875 (number of nodes, 35, 456). the number of elements in the analysis domain increases with increase in the specimen thickness to maintain the mesh refinement. for specimen with thickness between 2 and 20 mm the numbers of elements were between 5625 – 7875. a typical mesh used in the analysis is shown in fig.3. the stress distribution and the magnitude of ki and t-stress were obtained by abaqus post processor. the method of computation of ki and t-stress from abaqus are detailed in the following section. the variation of stress components, t-stress and ki along the crack-front has been studied for varied specimen thickness and crack length to width ratio (a/w=0.4-0.6). the normal stress () applied on the specimen as shown in fig.1 is considered = 50 mpa, which is ≈1/3rd of yield stress to keep the analysis domain approximately under lefm. the specimen thicknesses (b) considered in this analysis are 2 to 20 mm (b/w=0.11.0) in steps of 2 mm. in these calculations, the material considered is interstitial free steel (if) possessing yield strength (y) of 155 mpa and elastic modulus of 197 gpa [14]. computation of ki and t-stress the computation of stress intensity factor (ki) is carried out by maximum tangential stress criterion [15] as available in abaqus. the t-stress extracted by abaqus post processor is as given below. consider a 3d crack front with a continuously turning tangent as shown in fig. 4a. assume a line-load of magnitude fk = fk(s) to be applied along the crack front as illustrated in fig. 4b. in the figure, k(s) defines the direction normal to the crack front and in the plane of the crack at point s. the solution for this problem is the case of a plane strain semi-infinite crack with a point force f applied at the crack tip in the direction parallel to the crack. using superscript ‘l’ to designate the stress and displacement fields, the analytical solution [16] gives: stress field: s q p = 311 cos , l f r s q q p = 222 cos sin , l f r s n q p =33 cos , l f r s s= =13 23 0 l l s q q p = 212 sin cos , l f r (1) and displacement field : n q p n ì üæ öï ïï ï÷ç= +í ý÷ç ÷çï ïè ø -ï ïî þ 2 2 1 1 sin ln 2(1 ) l f ru e d { } n n q q q p + = -2 1 (1 2 ) cos sin 2 l fu e =3 0 lu (2) employing the stress field and displacement field solutions given in eqns. (1) and (2) as an auxiliary field, kfouri [17] has extracted the t-stress for 2d crack problems by introducing an interaction j-integral. nakamura and parks [18] extended this method of extraction of t-stress to 3d crack problems and provided the domain integral formulations in the form given below: s s s e ì üæ öï ï¶ ¶ ¶ ¶÷ï ïç ÷= + -çí ý÷ç ÷çï ï¶ ¶ ¶ ¶è øï ïî þ ò ( ) 1 ( ) l l li i k k ij ij ij ij c k k j kv s u u q q i s dv a x x x x (3) where v(s) is a domain, which encloses the crack front segment between (s-) and (s+) (refer fig. 4c), qk(s) defines the virtual extension of the crack front segment (s-) ≤ s ≤ (s+) and ac is the increase in crack area generated by the virtual http://dx.medra.org/10.3221/igf-esis.08.04&auth=true http://www.gruppofrattura.it k. g. kodancha et alii, frattura ed integrità strutturale, 8 (2009) 45-51; doi: 10.3221/igf-esis.08.04 47 crack advance; ij, ij and ui are the stress, strain and displacement components of the 3d crack problem under consideration; s ,lij e l ij and l iu are the corresponding components in the line-load auxiliary solution given by eqns. (1) and (2). nakamura and parks [18] have shown that the crack-tip t-stress is related to the integral, i(s) as given below: ne u ì üï ïï ï= +í ý ï ïï ïî þ 332 ( ) ( ) ( ) 1 e i s t s s f (4) where 33(s) is the extensional strain at point s in the direction tangential to the crack front. the computation of the domain integral, eqn. (3), is readily compatible with finite element formulations. in this analysis, t-stress is computed from eqn. (4) based on the domain integral i(s) (refer eqn. (3)) using five contours. in this finite element analysis it is observed that last four contours give almost path independent values of i(s). hence, in this study, the average value of t-stresses is obtained using the results from the outer four contours. figure1: geometry of the specimen considered in the analysis. figure 2: a typical finite element used at crack-front. http://dx.medra.org/10.3221/igf-esis.08.04&auth=true http://www.gruppofrattura.it k. g. kodancha et alii, frattura ed integrità strutturale, 8 (2009) 45-51; doi: 10.3221/igf-esis.08.04 48 figure 3: a typical finite element mesh used in the analysis. figure 4: a schematic diagrams of elements used in the definition of the interaction integral: (a) crack front and contour, (b) line load applied along the crack front and (c) volume v(s) encloses the crack front segment. results and discussion nitially, two dimensional elastic plane stress fe analysis is conducted on the sent specimen with a/w=0.4, 0.5 and 0.6 and applied load 50 mpa for validation of 2d t-stress results obtained in the present study with results available in the literature [9,10]. the t-stress values are converted to bi-axial stress (b) from the relation: s = i t a b k (5) the magnitudes of b vs. a/w is plotted in fig.5 along with the results of levers and randon [9] and paulino and kim [10]. this figure indicates that the present results on biaxial stress obtained in the fe analysis are in excellent agreement with the similar results available in literature [9, 10]. this analysis provides the validation of the present fe computation in 2d. a series of 3d fe stress analyses have been carried out on sent specimens with varied thickness and a/w ratio, to study the variation of t-stress along the crack-front (effect of thickness).the obtained t-stress results are normalized with respect to applied stress (). a typical variation of normalized t-stress (t/) along the crack-front is shown in fig.6. fig. 6 demonstrates that t-stress strongly varies with distance along the crack-front and depends on the thickness of the specimen. it is interesting to find that the magnitude of normalized t-stress is higher at the centre of the specimen than on the surface. it is observed in fig.6 that for specimen with higher thickness, the magnitude of normalized t-stress decreases for a short distance from the specimen surface and again increases at the centre of the specimen thickness. this nature of variation of normalized t-stress could not be explained clearly at this stage, but it can be attributed to the effect i http://dx.medra.org/10.3221/igf-esis.08.04&auth=true http://www.gruppofrattura.it k. g. kodancha et alii, frattura ed integrità strutturale, 8 (2009) 45-51; doi: 10.3221/igf-esis.08.04 49 of crack-tip plasticity. the magnitude of normalized t-stress for sent specimen (a/w=0.5) obtained in 2d analysis reported by sherry et al. [11] is -0.4 (shown by dotted line in fig.6). in the present 3d analysis it is found that normalized t-stress for specimen having a/w=0.5, varies between -0.6 to -0.1 depending on the thickness of the specimen. as tstress is used as constraint parameter, this result demonstrates that the constraint parameter is not a unique value; it varies along the thickness of the specimen. it is known that the magnitude of t-stress depends on the a/w ratio [11] of the specimen. the 2d results of sherry et al. [11] shows that normalized t-stress is positive (0.1) for a/w=0.6. the fe results of variation of t-stress along the thickness of specimen with a/w =0.6 along with 2d results [11] is shown in fig.7. it is interesting to know from this figure that the t-stress is negative on the surface of the specimens with higher thickness and vice versa. figure 5: variation of b vs. a/w figure 6: variation of normalized t-stress along the crack-front for various specimen thicknesses figure 7: variation of normalized t-stress along the crack-front for various specimen thicknesses. figure 8: variation of normalized t-stress along the crack-front for various a/w ratio and specimen thickness 10 mm. a typical variation of normalized t-stress (t/) along the crack-front for various a/w ratio and specimen thicknesses 10 mm along with 2d result [11] is shown in fig.8. this figure shows the effect of a/w ratio on variation of t-stress along the crack-front. this analysis demonstrates that the studies on constraint issues based on t-stress estimated by 2d analysis leads to considerable error. hence, it is required to conduct 3d analysis to completely assess the constraint issues in a fracture specimen having finite thickness. in this work, the variation of stress intensity factor along the crack-front is also studied. a typical plot of variation of ki along the crack-front along with theoretical magnitude of ki for a specimen with a/w=0.5 is shown in fig.9. this figure indicates that the magnitude of ki is higher at the centre of the specimen than on the surface compared to theoretical magnitude. the nature of variation of ki shown in fig.9 is in good agreement with the similar results presented by http://dx.medra.org/10.3221/igf-esis.08.04&auth=true http://www.gruppofrattura.it k. g. kodancha et alii, frattura ed integrità strutturale, 8 (2009) 45-51; doi: 10.3221/igf-esis.08.04 50 fernandez et al. [19]. the effect of variation of ki for specimens with a/w=0.4, 0.5 and 0.6 are also studied. a typical plot of effect of a/w ratio on variation of ki for specimen thickness 10 mm is shown in fig.10. this figure illustrates that the nature of variation of ki along the crack-front is almost similar for various a/w ratios. but, the magnitude of difference in ki (ki) estimated by 2d and 3d analyses measured at the centre of the specimen thickness is found to vary with respect to specimen thickness. for the similar applied load it is observed that (ki) is higher for a/w=0.6, which indicates that the specimen experience high crack-tip constraint at the centre than other specimens with a/w < 0.6. the t-stress results obtained in the present analysis together with corresponding ki values can be used for analysis of constraint effects in a fracture specimen. the 3d results indicate that the magnitude of t-stress and ki are lesser on the surface than the centre of the specimen. compared to 2d results one can infer from these results that the crack-tip constraint is very high at the centre of the specimen than at the surface. the constraint effect on the surface is referred as in-plane constraint and at the centre is referred as out of plane constraint [20]. due to higher out of plane constraint the material at the centre of the specimen thickness fails earlier than on the surface. the constraint also depends on the specimen a/w ratio. the present results infer that the specimen with higher a/w ratio experiences highest crack-tip constraint. the 3d results obtained in this study can also be used to formulate/correct two parameter characterization of crack-tip fields proposed by betegon and hancock [5]. figure 9: variation of ki along the crack-front for various specimen thicknesses. figure 10: variation of ki along the crack-front for various a/w ratio and specimen thickness 10 mm. conclusions ollowing conclusions are made from the present study: the magnitude of t-stress and ki varies along the crack-front; the variation depends on the specimen thickness and a/w ratio of the specimen. crack-tip constraint is very high at the centre of the specimen than at the surface because of higher magnitude of tstress and ki at the centre of the specimen. due to higher out of plane constraint the material at the centre of the specimen thickness fails earlier than that on the surface. acknowledgement uthors gratefully acknowledge the computational facilities provided by research center, b. v. b. college of engineering & technology, hubli, and prosim, bangalore. f a http://dx.medra.org/10.3221/igf-esis.08.04&auth=true http://www.gruppofrattura.it k. g. kodancha et alii, frattura ed integrità strutturale, 8 (2009) 45-51; doi: 10.3221/igf-esis.08.04 51 references [1] m. l. williams, asme journal of applied mechanics, 24 (1957) 109–114. [2] s. g. larsson, a. j. carlsson, journal of mechanics and physics of solids, 21 (1973) 263–277. [3] j. r. rice, journal of mechanics and physics of solids, 22 (1974) 17–26. [4] b. a. bilby, g. e. cardew, m. r. goldthorpe, i. c. howard. size effect in fracture. london: mechanical engineering publications limited, (1986) 37–46. [5] c. betegon, j. w. hancock, asme journal of applied mechanics, 58 (1991) 104–110. [6] z.z. du, j.w. hancock, journal of mechanics and physics of solids, 39 (1991) 555–567. [7] n. p. o_dowd, c. f. shih, journal of mechanics and physics of solids, 39 (1991) 989–1015. [8] y. y. wang, astm stp, 1171. american society for testing and materials, (1993), 120–38. [9] p.s. levers, j.c. randon, international journal of fracture, 19 (1982) 311-325. [10] g.h.paulino, j.h.kim, engineering fracture mechanics, 71 (2004) 1907-1950. [11] a.h. sherry, c.c. france, l. edwards, fatigue and fracture of engineering materials and structures, 18 (1995) 141155. [12] jie qu, xin wang, international journal of pressure vessels and piping, 83 (2006) 593–606. [13] abaqus user’s manual. version 6.5. hibbitt, karlsson & sorensen, inc., (2004). [14]. s.k. kudari, ph.d thesis, (2004), iit, kharagpur, india. [15]. f. erdogan, g. c. sih, journal of basic engineering, 85 (1963) 519-527. [16]. s. p. timoshenko, j.n. goodier, theory of elasticity, mcgraw-hill (1970). [17]. a. p. kfouri, international journal of fracture, 30 (1986) 301–315. [18]. t. nakamura, d.m parks. international journal of solids and structures, 29 (1992) 1597–1611. [19] z.d. fernandez, j.f. kalthoff, c.a. fernandez, a. canteli, j. grasa, m. doblare, ecf-15 (2005). [20] h. yuan, w. brocks, journal of mechanics and physics of solids, 46 (1998) 219-241. http://dx.medra.org/10.3221/igf-esis.08.04&auth=true http://www.gruppofrattura.it microsoft word numero_37_art_44 g. cricrì et alii, frattura ed integrità strutturale, 37 (2016) 333-341; doi: 10.3221/igf-esis.37.44 333 modelling the mechanical behaviour of metal powder during die compaction process g. cricrì, m. perrella university of salerno –department of industrial engineering, via giovanni paolo ii 132, 84084. fisciano (sa), italy, gcricri@unisa.it; mperrella@unisa.it abstract. in this work, powder compaction process was investigated by using a numerical material model, which involves mohr-coulomb theory and an elliptical surface plasticity model. an effective algorithm was developed and implemented in the ansys finite element (fem) code by using the subroutine usermat. some simulations were performed to validate the proposed metal powder material model. the interaction between metal powder and die walls was considered by means of contact elements. in addition to the analysis of metal powder behaviour during compaction, the actions transmitted to die were also investigated, by considering different friction coefficients. this information is particularly useful for a correct die design. keywords. cap-cone model; die compaction process; fem simulation; residual strain. introduction deep knowledge of metal powder behaviour during compaction stage is necessary to predict the final shape and density distribution of formed products, and to avoid damages and breakages, which may occur during the subsequent sintering phase. the design of die and of compaction process should be supported by an adequate simulation analysis of the mechanical behaviour of compacted material during the process steps. in literature, several constitutive, phenomenological and micromechanical models, based on the continuum mechanics approach, have been proposed to this aim. in general, most used constitutive models for compaction consider the powder material as granular or as porous. soil composed primarily of coarse-grained sand or gravel is an example of granular material, whose behaviour is strongly influenced by the friction phenomenon. instead, constitutive equations for modelling porous materials are usually extensions of the von mises plasticity model, satisfying conditions of symmetry and convexity of plasticity theory. in particular, extensions of plastic flow theory, by introducing additional state variables, are used for modelling different kinds of phenomena, from creep [1] to ductile fracture [2]. for porous materials, the limit function differs from the classical one of von mises criterion because of incompressibility of porous solid particles during the compaction stage. thus, the plastic flow of porous particles is considered function of two terms, at least: the hydrostatic tensor and the second principal invariant of the stress deviator tensor. for these models, the general form of the limit surface is as follows:        2 22 1ijf a j b i c k         (1) a g. cricrì et alii, frattura ed integrità strutturale, 37 (2016) 333-341; doi: 10.3221/igf-esis.37.44 334 in equation (1), i1 is the first invariant of cauchy stress tensor, j2 is the second invariant of deviatoric tensor, k is a limit stress of base material, which takes account of the hardening effect due to plastic flow, and a, b and c are model parameters, function of variable density ρ. the simplest constitutive model combines a rule of plastic flow with an isotropic hardening law. its basic hypothesis is to consider the powder grains only affected by plastic strains whilst their rearrangement is negligible. kuhn, green, shima, doraivelu, fleck and many other authors [3-16] have presented material models characterized by a yield surface function of i1 and j2, as described in (1). however, according to biswas [17] these relationships, developed omitting grains rearrangement mechanism, are not suitable for modelling initial stages of compaction process, at lower density levels. therefore, in this work a material model with two limit surfaces (cap-cone model) is presented in order to simulate all the die compaction steps of powders whose behaviour is both porous and granular. in such a way, it is possible to overcome the drawback highlighted by biswas. a plastic flow law combined with friction mechanism is implemented in the finite element (fem) commercial code ansys by means of the usermat subroutine written in fortran. moreover, several numerical simulations were performed to investigate the entire die compaction process, considering different friction coefficients between metal powders and die walls and punches. friction parameters play a crucial role in the evaluation of loads applied to the die and consequently in the proper estimation of die strength and residual strains in the formed object therefore, these analyses are helpful for a correct die design and final recognition of formed objects’ dimensions [18-20]. material model he material model used in this study consists of two limit surfaces [21] f1 and f2: the former, f1(σ), θ is related to the mohr-coulomb criterion (cone surface); the latter, f2(σ, σc), is related to a yield elliptical surface (cap surface) where σc represents a hardening parameter, function of volumetric plastic strain. such a formulation is suitable for modelling metal powders with extremely different relative density (from 0.2r  to 1.0r  ). the f1 and f2 limit surfaces are expressed in equations (2) and (3), respectively.   21 1 2 1 sin cos sin sin cos 0 3 3 j f i j c          if m c   (2)     2 22 2 2, 0 tan c m c c c f j m                      if m c   (3) in these equations, i1 is the first stress invariant, j2 is the second invariant of the deviatoric stress tensor and σm is the hydrostatic stress, defined as σm= i1/3. the yield surface f1 is obtained from the mohr-coulomb criterion, as a function of normal stress n and shear stress : 1 cos sin cosnf c       . (4) the parameters c and  are respectively the cohesion and the angle of internal friction of metal powder. the angle of internal friction  represents the angle of shearing resistance during compression, i.e. a measurement of resistance to relative sliding of grains. the cohesion c defines the shear strength of powder when no normal loads are applied to. let the principal stresses be with magnitudes 1 2 3    , the equation for the surface (4) can be rewritten as (5).    1 1 3 1 3 1 1 sin cos 2 2 f c          (5) the principal stresses and invariants  1 2, ,i j  depend on the relationships: t g. cricrì et alii, frattura ed integrità strutturale, 37 (2016) 333-341; doi: 10.3221/igf-esis.37.44 335       1 2 1 2 3 sin 2 3 1 2 sin 1 33 sin 2 3 1 j i                                  (6) by using (6), the relation (5) can be expressed as a direct function of the stress invariants i1 and j2 and of the angle of lode θ, which describes the projection of the stress state into the deviatoric plane. in the limit function f2, the parameter σc controls the dimensions of the elliptical cap surface (figure 1) whilst the parameter m represents the slope of the mohr-coulomb yield surface, in the same plane. as highlighted in figure 1, the factor σc locates in the plane  '2 , mj  both the centre of ellipse and the ordinate of intersection of the two curves that model the overall yield surface. figure 1: cap-cone material model. the factor m is a function of the angles  and , as reported in eq. (7). 1 sin cos sin sin 3 m            (7) the critical stress σc follows a hardening law, function of volumetric plastic strain p v :   0 p v p c v cf e         (8) where 0c is the initial hydrostatic stress of compaction, which is obtained from considerations on the final filling of dies and assumed to be uniform, and χ defines the plastic hardening coefficient, which is derived from a uniaxial compression/relaxation test. thus, the limit surface has a direct dependence from plastic strain value. the constitutive equations (cap-cone model) were implemented in a user defined material subroutine usermat of ansys software. the developed algorithm provides, for each increment of strain tensor, with updated stress and current constitutive tensor. both outputs also depend on the values of state variables of constitutive law, among which the most important is the volumetric plastic strain. it controls the shape of the critical surface f2 through the hardening factor c and other parameters. when balance convergence is satisfied for a step increment of imposed strain, all state variables’ values are updated before the beginning of a new load step. in addition to relations (2)-(8), variability of elastic constants is also considered, as a function of density, and then of volumetric plastic strain, as specified in the next paragraph. -m √j’2 c c+ c/tan() c/tan()  dp dp cap surface: f2(c)=0 cone surface: f1)=0 g. cricrì et alii, frattura ed integrità strutturale, 37 (2016) 333-341; doi: 10.3221/igf-esis.37.44 336 numerical simulation of die compaction process model parameters etal powders properties are influenced by manufacturing process and chemical composition. powders can be characterized by several parameters, including size, shape and distribution of grains, size of surface as well as flowability that influences uniform powder distribution in dies. among powder properties, density plays a crucial role in compaction steps and affects all the parameters listed above. it can be expressed in terms of apparent (bulk) density ρa, defined as mass per unit volume of free flowing powder, or in terms of tapped density ρt, which is an increased bulk density attained after mechanically tapping a container containing the powder sample. another parameter most used in die compaction process is relative density, ρr, i.e. degree of densification, defined as the ratio between the density of the material at a given state ρ and the density of the fully dense material ρs: r s     where 0 exp( ) p v    (9) pavier and doremus [7] showed how young’s modulus, for different powder materials, highly increases as a function of relative density. they modelled such a behaviour through an exponential law. the proposed model allows calculating bulk modulus k with the following relationship: 1 2 3 1 1 2 1 exp if 0 if 0 p vc c c ik c c i            (10) in particular, in this work the properties of metal powder distaloy ae by höganäs, mixed with 1% of hoecht wax and 0.5% of c are used in numerical simulations. bulk modulus k was obtained by imposing c1= 9.79 gpa, c2 = 19.35 pa and c3 = 24.36in eq. (10). successively, knowing bulk modulus k and poisson’s ratio , young’s modulus is calculated by the following relationship:  3 1 2e k  basic material properties of metal powder distaloy ae are listed in table 1. material e [mpa] ν k ρ0 [kg/cm3] ρs [kg/cm3]  c0 [mpa]  [rad] distaloy ae 15000 0.3 12500 3.04 7.33 0.154 0.866 0.523 table 1: material properties of the simulated metal powder (initial values). in powders compaction processes, shape changes are obtained by means of pressure exerted on base material by punches, which are obviously much more rigid than the material to be formed. for this reason, there is a great difference between deformations of punches and rough material. this produces a relative motion on contact surface, depending on geometry and boundary conditions at interface. the role of friction in fem modelling of compaction is important for a proper estimation of density distribution, and even crucial in assessment of loads by pressed compact acting on dies. friction phenomenon was evaluated considering two values of friction coefficient between metal powder and die walls: μ = 0.1, corresponding to the average value in absence of lubricant, and μ = 0.05, matching the average value in presence of lubricant. demonstration example as a demonstration example, numerical analysis of the stress-strain relations was performed for double action pressing process of metal powder distaloy ae. the 2d axialsymmetric geometry considered in the calculation represents an object composed of two solid cylinders with different diameter, filleted in the middle (figure 2). m g. cricrì et alii, frattura ed integrità strutturale, 37 (2016) 333-341; doi: 10.3221/igf-esis.37.44 337 the compaction step was simulated by using a die and two rigid punches, located at the top and bottom of the sample, which move simultaneously with different rates, in order to obtain a formed product of almost uniform density. such working condition was considered in the numerical simulations by imposing a ratio between punches displacements that maintains average volumetric density approximately equal in upper and lower cylinder. figure 2: geometry considered in numerical simulations. metal powder area was modelled with about 5000 quadratic elements plane183 (figure 3). the action of punches and the friction resulting from contact both between punches and powder and between die walls and formed object were investigated by a non linear contact analysis. die walls were modelled through targe169 elements whilst conta175 elements were used to model the perimeter of compacted component. of course, the former elements were considered rigid respect to the latter ones. 1 x y z jul 15 2011 14:03:05 elements figure 3: axialsymmetric fe model mesh. the trend of axial stress σy in different compaction stages is shown in figures 4-5. it is possible to highlight that material properties and friction between metal powders and die walls cause a non-uniform stress distribution inside the specimen, with stress concentration in the filleted zones of die, as expected. moreover, stress values become very high only in the final phase of compaction process. for the same reasons, axial stress tends to null value during the unloading step, but for the zones close to die fillets (figure 5). loads transferred to dies from pressed powder is a critical factor in the compaction die design. moreover, this information is helpful in a double way: 1) to evaluate the strain state of ejected workpiece; 2) to modify dies geometry in order to prevent errors in tolerances of formed object. g. cricrì et alii, frattura ed integrità strutturale, 37 (2016) 333-341; doi: 10.3221/igf-esis.37.44 338 1 mn mx x y z -10.117 -9.621 -9.124 -8.627 -8.13 -7.633 -7.136 -6.639 -6.142 -5.645 jul 18 2011 19:34:24 nodal solution step=2 sub =113 time=2 sy (avg) rsys=0 dmx =1.5 smn =-10.117 smx =-5.645 1 mn mx x y z -29.77 -28.172 -26.574 -24.976 -23.378 -21.78 -20.182 -18.585 -16.987 -15.389 jul 18 2011 19:33:52 nodal solution step=4 sub =105 time=4 sy (avg) rsys=0 dmx =3 smn =-29.77 smx =-15.389 1 mn mx x y z -100 -93.333 -86.667 -80 -73.333 -66.667 -60 -53.333 -46.667 -40 jul 18 2011 19:33:18 nodal solution step=5 sub =105 time=5 sy (avg) rsys=0 dmx =4 smn =-74.449 smx =-39.655 1 mn mx x y z -732.132 -696.128 -660.123 -624.119 -588.115 -552.11 -516.106 -480.102 -444.097 -408.093 jul 18 2011 19:26:29 nodal solution step=6 sub =105 time=6 sy (avg) rsys=0 dmx =6 smn =-732.132 smx =-408.093 figure 4: axial stress σy[mpa] at different steps of compaction process (loading phase). 1 mn mx x y z -147.778 -140.463 -133.148 -125.833 -118.518 -111.203 -103.888 -96.573 -89.258 -81.943 jul 18 2011 19:34:41 nodal solution step=7 sub =105 time=7 sy (avg) rsys=0 dmx =5.88 smn =-147.778 smx =-81.943 1 mn mx x y z -105.222 -95.333 -85.444 -75.555 -65.667 -55.778 -45.889 -36 -26.112 -16.223 jul 18 2011 19:34:57 nodal solution step=8 sub =105 time=8 sy (avg) rsys=0 dmx =5.856 smn =-105.222 smx =-16.223 figure 5: axial stress σy[mpa] at different steps of compaction process (unloading phase). in figures 6-7 numerical results of pressure exerted by metal powder on die walls are shown, considering the step of maximum loading exerted by punches and friction coefficient equal to  = 0.1 and = 0.05, respectively. contact pressure distribution is not uniform along surfaces of punches and die walls, because of powder mechanical behaviour, strongly influenced by local and global friction. contact pressure exerted on upper and lower punches reaches a peak in the edges close to die walls, where friction stress is maximum, whilst presents a mean value of 570 mpa in the zones far from edges. specifically, peak values are equal to an increase by 15% and 7% than mean outcome, when friction coefficient is = 0.1 and  = 0.05 respectively. g. cricrì et alii, frattura ed integrità strutturale, 37 (2016) 333-341; doi: 10.3221/igf-esis.37.44 339 contact pressure applied by metal powder to the horizontal wall of die is almost equal to that exerted on punches. this is a confirmation of correct ratio of punches’ displacements. pressure on vertical walls of die varies from 290 mpa to 390 mpa (corresponding to about 50-70% of punches pressure), showing a trend almost independent of friction coefficient value. instead, friction stress is not negligible and is strongly dependent of friction factor between powder and walls, reaching the maximum values of 57 mpa and 28 mpa when = 0.1 and  = 0.05 respectively. 1 mn mx x y z 285 326.111 367.222 408.333 449.444 490.556 531.667 572.778 613.889 655 jul 29 2011 16:50:43 nodal solution step=6 sub =105 time=6 contpres (avg) dmx =6 smn =295.49 smx =651.511 1 mn mx x y z -42 -31 -20 -9 2 13 24 35 46 57 jul 29 2011 16:53:23 nodal solution step=6 sub =105 time=6 contsfri (avg) dmx =6 smn =-42.066 smx =56.115 figure 6: contact pressure and friction stress, respectively, at final stage of compaction process, just after the loading phase ( = 0.1). 1 mn mx x y z 285 326.111 367.222 408.333 449.444 490.556 531.667 572.778 613.889 655 jul 20 2011 11:38:57 nodal solution step=6 sub =105 time=6 contpres (avg) dmx =6 smn =286.16 smx =614.57 1 mn mx x y z -42 -31 -20 -9 2 13 24 35 46 57 jul 29 2011 16:56:12 nodal solution step=6 sub =105 time=6 contsfri (avg) dmx =6 smn =-19.619 smx =28.728 figure 7: contact pressure and friction stress, respectively, at final stage of compaction process, just after the loading phase ( = 0.05). the mechanical behaviour of a pressed product is function of density obtained during compaction process. indeed, defects and failures may occur most probably in components with lower density. moreover, for several formed elements, such as filters, the compaction level is closely connected to their correct operation. figure 8 shows the plot of relative density r in the final compaction scenario. the value of relative average density obtained in numerical simulations is equal to 1.075, corresponding to a final density s = 7.88 kg/cm3. the bulk and young’s moduli after compaction are k = 156 gpa and e = 189 gpa respectively. around the corners between punches and die and in the zone of object fillets numerical analyses provide with maximum and minimum density, which are about -5.8% and + 3.5% of average density (with  = 0.1) respectively. figure 9 depicts the variation of the minimum, maximum, and average density during the loading and unloading phases, for both considered friction coefficients. average density is not significantly influenced by variation of friction coefficient, whilst the deviation of maximum and minimum density from the average is lower in the case with  = 0.05 respect to the simulation with  = 0.1. specifically, the previously mentioned deviation of maximum and minimum density is equal to 4.2% and +1.9% respectively. g. cricrì et alii, frattura ed integrità strutturale, 37 (2016) 333-341; doi: 10.3221/igf-esis.37.44 340 1 mn mx x y z 1.032 1.042 1.052 1.062 1.071 1.081 1.091 1.101 1.11 1.12 jul 19 2011 16:59:06 nodal solution step=6 sub =105 time=6 svar10 (avg) dmx =5.996 smn =1.032 smx =1.12 figure 8: relative density, r at final step of compaction process ( = 0.1). 0 0.2 0.4 0.6 0.8 1 1.2 0 100 200 300 400 500 600 r el a ti v e d en si ty  r loading pressure [mpa] maximum rel. density minimum rel. density average rel. density 0 0.2 0.4 0.6 0.8 1 1.2 0 100 200 300 400 500 600 r el a ti ve d en si ty  r loading pressure [mpa] maximum rel. density minimum rel. density average rel. density figure 9: relative maximum, minimum and average density vs loading pressure ( = 0.1 and  = 0.05) conclusions n the present work, the behaviour of metal powder during die compaction process is described, by using a cap-cone model of yield surfaces in order to simulate material strain hardening capability. material model was implemented in ansys fem code by subroutine usermat. several numerical simulations were performed considering a simple 2d axialsymmetric geometry to evaluate the forces acting on the die walls, in addition to metal powder behaviour analysis. the obtained outcomes were used to describe an adequate characterization of the pressed object, in terms of stress and density distribution. in particular, fem analyses highlighted that increasing friction coefficient the density gradient becomes higher and higher whilst the stress field of the compacted powders grows slowly. although the presented constitutive material model has provided with satisfactory results, comparable with those available in literature relating to similar tests, it may be subject to further developments that make it possible to consider the relation between relative density and other parameters, such as cohesion and internal friction. references [1] calì, c., cricrì, g., perrella, m., an advanced creep model allowing for hardening and damage effects, strain, 46-4 (2010) 347-357. doi: 10.1111/j.1475-1305.2009.00682.x i g. cricrì et alii, frattura ed integrità strutturale, 37 (2016) 333-341; doi: 10.3221/igf-esis.37.44 341 [2] cricrì, g., a consistent use of the gurson-tvergaard-needleman damage model for the r-curve calculation, frattura ed integrità strutturale, 24 (2013) 161-174. doi: 10.3221/igf-esis.24.17 [3] green, r.j., a plasticity theory for porous solids, int. j. mech. sci. 14 (1972) 215-224. [4] kuhn, h.a., downey, c.l., deformation characteristics and plasticity theory of sintered powder materials, int. j. powder metall., 7-1 (1971) 15-25. [5] doraivelu, s.m., gegel, h.l., gunasekera, j.s., malas, j.c., morgan, j.t., thomas jr., j.f., a new yield function for compressible pm materials, int. j. mech. sci., 26-9/10 (1984) 527-535. [6] shima, s., oyane, m., plasticity theory for porous metals, int. j. mech. sci. 18 (1976) 285-291. [7] pavier, e., doremus, p., triaxial characterisation of iron powder behaviour, powder metallurgy, 42-4 (1999) 345-352. [8] fleck, n.a., kuhn, l.t., mcmeeking, r. m., yielding of metal powder bonded by isolated contacts, j. mech. phys. solids, 40-5 (1992) 1139-1162. doi: 10.1016/0022-5096(92)90064-9 [9] carnavas, p.c., page, n.w., elastic properties of compacted metal powders, journal of materials science, 33 (1998) 4647-4655. [10] jonsèn, p., häggblad, h-å., modelling and numerical investigation of the residual stress state in a green metal powder body, powder technology, 155 (2005) 196-208. doi: 10.1016/j.powtec.2005.05.056 [11] lewis, r.w., khoei, a.r., a plasticity model for metal powder forming processes, international journal of plasticity, 17 (2001) 1659-1692. doi: 10.1016/s0749-6419(00)00096-6 [12] khoei, a.r., numerical simulation of powder compaction processes using an inelastic finite element analysis, materials and design, 23 (2002) 523-529. [13] chtourou, h., guillot, m., gakwaya, a., modelling of the metal powder compaction process using the cap model. part. i. experimental material characterization and validation, international journal of solids and structure, 39 (2002) 1059-1075. doi: 10.1016/s0020-7683(01)00255-4 [14] park, s.j., han, h.n., oh, k.h., lee, d.n., model for compaction of metal powders, international journal of mechanical sciences, 41 (1999) 121-141. [15] smith, l.n., midha, p.s., graham, a.d., simulation of metal powder compaction, for the development of a knowledge based powder metallurgy process advisor, journal of materials processing technology, 79 (1998) 94-100. [16] bocchini, g.f., criteri di classificazione del grado di complicazione delle forme dei componenti sinterizzati, la metallurgia italiana, 7 (2008) 37-44. [17] biswas, k., comparison of various plasticity models for metal powder compaction processes, j. of material processing technology, 166 (2005) 107-115. doi: 10.1016/j.jmatprotec.2004.08.006 [18] bocchini, g.f., cricrì, g., esposito, r., influence of operating temperature on shrink fitting pressure of pm dies, powder metallurgy, 39-3 (1996) 195-206. [19] armentani, e., bocchini, g.f., cricrì, g., esposito, r., short dies and thin walled inserts for room temperature or warm compaction numerical determination of design features, powder metallurgy, 45-2 (2002) 115-133. [20] armentani, e., bocchini, g.f., cricrì, g., esposito, r., metal powder compacting dies: optimised design by analytical or numerical methods, powder metallurgy, 46-4 (2003) 349-360. [21] lewis, r.w., khoei, a. r., numerical modelling of large deformation in metal powder forming, comput. methods appl. mech. engrg., 159 (1998) 291-328. << /ascii85encodepages false /allowtransparency false /autopositionepsfiles true /autorotatepages /none /binding /left /calgrayprofile (dot gain 20%) /calrgbprofile (srgb iec61966-2.1) /calcmykprofile (u.s. web coated \050swop\051 v2) /srgbprofile (srgb iec61966-2.1) /cannotembedfontpolicy /error /compatibilitylevel 1.4 /compressobjects /tags /compresspages true /convertimagestoindexed true /passthroughjpegimages true /createjobticket false /defaultrenderingintent /default /detectblends true /detectcurves 0.0000 /colorconversionstrategy /cmyk /dothumbnails false /embedallfonts true /embedopentype false /parseiccprofilesincomments true /embedjoboptions true /dscreportinglevel 0 /emitdscwarnings false /endpage -1 /imagememory 1048576 /lockdistillerparams false /maxsubsetpct 100 /optimize true /opm 1 /parsedsccomments true 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can be opened with acrobat and adobe reader 5.0 and later.) >> /namespace [ (adobe) (common) (1.0) ] /othernamespaces [ << /asreaderspreads false /cropimagestoframes true /errorcontrol /warnandcontinue /flattenerignorespreadoverrides false /includeguidesgrids false /includenonprinting false /includeslug false /namespace [ (adobe) (indesign) (4.0) ] /omitplacedbitmaps false /omitplacedeps false /omitplacedpdf false /simulateoverprint /legacy >> << /addbleedmarks false /addcolorbars false /addcropmarks false /addpageinfo false /addregmarks false /convertcolors /converttocmyk /destinationprofilename () /destinationprofileselector /documentcmyk /downsample16bitimages true /flattenerpreset << /presetselector /mediumresolution >> /formelements false /generatestructure false /includebookmarks false /includehyperlinks false /includeinteractive false /includelayers false /includeprofiles false /multimediahandling /useobjectsettings /namespace [ (adobe) (creativesuite) (2.0) ] /pdfxoutputintentprofileselector /documentcmyk /preserveediting true /untaggedcmykhandling /leaveuntagged /untaggedrgbhandling /usedocumentprofile /usedocumentbleed false >> ] >> setdistillerparams << /hwresolution [2400 2400] /pagesize [612.000 792.000] >> setpagedevice microsoft word numero_41_art_8 a. s. cruces et alii, frattura ed integrità strutturale, 41 (2017) 54-61; doi: 10.3221/igf-esis.41.08 54 focused on multiaxial fatigue evaluation of new multiaxial damage parameters on low carbon steel a. s. cruces, p. lopez-crespo, b. moreno department of civil and materials engineering, university of malaga, c/dr ortiz ramos s/n, 29071 malaga, spain plopezcrespo@uma.es a. lopez-moreno department of materials science and metallurgy engineering, university of jaen, campus las lagunillas, 23071 jaen, spain s. suman research center, environmental solution group, dover corporation, fort payne, al, 35967, usa abstract. most mechanical components are subjected to the complex fatigue loading conditions, where both amplitude and direction of loading cycles change over the time. the estimation of damage caused by these complex loading scenarios are often done by simplified uniaxial fatigue theories, which ultimately leads to higher factor of safety during the final design considerations. critical plane-based fatigue theories have been considered more accurate for computing the fatigue damage for multiaxial loading conditions in comparison to energy-based and equivalent stress-based theories. two recently developed fatigue theories have been evaluated in this work for the available test data. test data includes significant amount of biaxial load paths. keywords. critical plane approach; biaxial fatigue; fatemi-socie damage parameter. citation: cruces, a. s., lopez-crespo, p., moreno, b., lopez-moreno, a., suman, s., evaluation of new multiaxial damage parameters on low carbon steel, frattura ed integrità strutturale, 41 (2017) 54-61. received: 28.02.2017 accepted: 15.04.2017 published: 01.07.2017 copyright: © 2017 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. introduction ver the years, the analysis of complex multiaxial fatigue loading has mainly been done with the simplified uniaxial approach. this has led to the large amount of knowledge generated in this area, both from experimental [1,2] and numerical [3,4] points of view. advanced experiments have allowed a number of features to be characterized, including surface and bulk behavior [5,6], crack-closure mechanisms [7,8], evolution of the process zone thru the thickness [9,10], crack branching processes [11], effect of variable amplitude loads such as crack acceleration [12] o a. s. cruces et alii, frattura ed integrità strutturale, 41 (2017) 54-61; doi: 10.3221/igf-esis.41.08 55 or retardation [13,14] or mixed-mode local changes in the volume [15]. however, uniaxial approach does not represent the real world scenario and computation of fatigue life thru these approach often results either in under prediction or over prediction of fatigue life for the machine component. because of the complexities and computational cost involved with the multiaxial fatigue tests, very limited amount of fatigue data are publicly available [16]. among several other fatigue models, critical plane-based fatigue models provide more accurate prediction of fatigue lives. critical plane-based fatigue models are based upon the determination of the location of fatigue crack initiation and microcrack –propagation [17]. the damage is computed at the plane where crack initiates, and this plane is called critical plane, however; the definition of critical plane is still controversial among the fatigue researchers. some researchers define this plane as the plane of maximum fatigue damage, whereas other group of researchers believe that considering the plane of maximum shear stress as critical plane will be more logical and computationally cheaper. fatigue data from the multiaxial test on st52-3n steel specimen have been analyzed in this paper by using new fatemisocie model [18] and suman-kallmeyer model [19]. it is well known fact that the shear stresses at the critical plane provokes the fatigue crack initiation whereas, presence of tensile stress in combination of shear stress creates condition for the microcrack to propagate. both of the damage parameters [18,19] discussed in this paper consider the interaction of normal and shear stress at the critical plane. both of these damage parameters [18,19] have been used to predict the fatigue life of the test specimen, and the correlation between experimental and predicted fatigue life has been analyzed. materials and methods aterial and test data have been taken from the previous biaxial fatigue test program at the university of malaga [20]. the material that has been considered for this paper is st52-3n. the chemical composition for this steel is: 0.17% c, 1.235% mn, 0.225% si, 0.010% p, 0.0006% s, 0.032% al, 0.072% cr, 0.058% ni and 0.016% mo. this is a low carbon steel, and has been widely used in the structural applications in the construction, manufacturing, ship building and offshore industries [21] that combines good fatigue resistance with low environmental impact for applications where no energy is consumed during the use phase of the component [22]. monotonic tension, compression and torsion tests were conducted to evaluate the monotonic properties of the st52-3n steel (tab. 1). tension tests were conducted on the solid specimens, whereas, compression and torsion tests were conducted on the tubular specimens [23]. fig 1 shows the geometry and dimensions of the tubular specimen. yield stress, σy 386 mpa ultimate tensile stress, σu 639 mpa young’s modulus, e 206 gpa shear modulus, g 78 gpa critical buckling stress, σcr 348 mpa table 1: monotonic properties of st52-3n steel. figure 1: geometry of the tubular hollow specimen used in the experiments. all dimensions are in mm. m a. s. cruces et alii, frattura ed integrità strutturale, 41 (2017) 54-61; doi: 10.3221/igf-esis.41.08 56 the cyclic elastic-plastic material properties were obtained from the cyclic uniaxial tests. the properties obtained from the cyclic uniaxial tests have been listed in tab. 2 & tab. 3. astm standard was followed to conduct these tests. cyclic strength coefficient, k’ 630.6 mpa cyclic hardening exponent, n’ 0.10850 cyclic yield strength, σ’y 321.3 mpa fatigue strength coefficient, σ’f 564.4 mpa fatigue strength exponent, b -0.0576 fatigue ductility coefficient, ɛ’f 0.1554 fatigue ductility exponent, c -0.4658 table 2: monotonic properties of st52-3n steel. cyclic strength coefficient, k’ɤ 593.8 mpa cyclic hardening exponent, n’ ɤ 0.1553 cyclic yield strength, τ’y 594.2 mpa fatigue strength coefficient, τ’f 486.9 mpa fatigue strength exponent, b ɤ -0.0668 fatigue ductility coefficient, ɤ’f 0.0662 fatigue ductility exponent, c ɤ -0.3191 table 3: torsional properties of st52-3n steel. biaxial tests require both torsional and longitudinal extensometer. it also needs a technician with good skill to place four pins of these devices [24]. as per the astm, load was also recommended to be applied at relatively low frequency (normally less than 4 hz) because the weak connection between extensometer pins and the sample is preserved. a series of in-phase biaxial tests were conducted with the strain levels that were chosen with an intension to fail the samples between 104 and 106. the design of these bi-axial fatigue tests was done on the basis of the previous uniaxial test results. tab. 4 shows the applied axial strain amplitudes (ɛa), and shear strain amplitudes (ɤa) data for these tests. the corresponding axial stress amplitudes (σa) and shear stress amplitudes (τa) are also shown in tab. 4 with corresponding fatigue life. total of 13 samples were tested for this test program. all the load path for these bi-axial tests were kept proportional (tab. 4). critical plane approaches fatemi-socie damage parameter ii (fsdp-ii) atemi-socie has recently modified their earlier developed fatigue model [25]. the previous fatemi-socie model was based on the concept that the range of shear strain is primary reason to initiate the fatigue crack and the tensile normal stress creates secondary effects of opening the crack face. fatemi-socie also introduced the normal stress component to account for the rotation of principle plane axis at the critical plane. fatemi-socie have recently modified their damage parameter and introduced a shear stress range term to account for the interaction of normal and shear stress at the critical plane. fatemi & socie model resorts on the ratio of maximum normal stress and the range of shear stress to model the interaction. a material dependent parameter k has also been introduced in the parameter. modified fatemisocie fatigue damage parameter has been shown in eq. 1 [18].                 , 1 2 ' 2 2 δ b cfn maxmax f f fk n n g (1) f a. s. cruces et alii, frattura ed integrità strutturale, 41 (2017) 54-61; doi: 10.3221/igf-esis.41.08 57                                      ' ' ' ' ' ' 2 2 1 2 1 2 1 2 b cf f f f y b b cf f f e f p f f n n gk n n n e (2) sample ɛa ɤa σa (mpa) τa (mpa) nf ip1 0.0015 0.0032 198 156 36,147 ip2 0.0015 0.0028 238 151 141,938 ip3 0.0015 0.0028 234 151 103,138 ip4 0.0015 0.0026 238 148 162,119 ip5 0.0011 0.0032 177 176 179,628 ip6 0.0011 0.0032 180 185 72,011 ip7 0.0011 0.0028 183 165 179,446 ip8 0.0011 0.0028 178 163 268,051 ip9 0.0011 0.0026 185 154 662,706 ip10 0.0009 0.0032 146 184 248,009 ip11 0.0009 0.0032 143 183 188,219 ip12 0.0009 0.0028 151 172 624,521 ip13 0.0009 0.0026 152 162 870,886 table 4: strain and stress conditions for in-phase strain conditions and the obtained fatigue life in number of cycles. suman & kallmeyer damage parameter (skdp) the importance of interaction of normal and shear stress on the critical plane has recently been investigated by suman & kallmeyer [19]. they have used the product of normal and shear stress at the critical plane to model this interaction. the product term in suman & kallmeyer model represents the maximum value of the product of normal and shear stress at the critical plane. by considering this product term, suman & kallmeyer were able to overcome the ambiguity caused by the non-proportional loading where both normal and shear stress peaks do not occur at the same time point. this product term can model the interaction effects for wide range of in-phase and out of phase fatigue data. apart from that, this formulation (eq 3) also has significantly less number of material dependent parameter in comparison to the model previously developed by the same group of researchers, and provides excellent correlation between experimental and predicted fatigue lives of the steel and titanium specimen. suman & kallmeyer fatigue model also captures the effect of strain hardening due to lcf loading and the mean shear stress at the critical plane.                 w 1 w max max 2 0 σ τ dp g γ τ 1 k σ (3) results n this study, most of the load path used are proportional and sinusoidal. due to the proportionality, both shear and normal stress peaks in these tests happened at the same time point. the critical plane stresses for the test ip1 (tab. 4) are presented in fig 2 and fig 4. the peaks of normal and shear stresses are presented by solid and dashed lines respectively, and the damage parameter values are presented by the green solid line (damage parameter is obtained with the maximum load). i a. s. cruces et alii, frattura ed integrità strutturale, 41 (2017) 54-61; doi: 10.3221/igf-esis.41.08 58 fatemi-socie damage parameter ii it can be observed from the plots in fig 2 that the maximum value of fatemi-socie damage parameter and the maximum value for shear stress range is not at the same time point, which implies that the plane of maximum shear and plane of maximum damage parameter is far apart. figure 2: ip 1 – σ, τ and fsdp-ii at max peak cycle (a) and min peak cycle (b). fsdp-ii was computed for all the test data shown in tab. 4, and the damage parameter value was presented against the cycles to failure. the plot is shown in fig 3, and it can be noticed that the fsdp-ii models most of the lcf fatigue behavior data but it produces significant scatter in the hcf data range. figure 3: fatigue life correlation for st52-3n steel based on fatemi ii model suman-kallmeyer damage parameter in contrast to fatemi-socie damage parameter, the difference in the location of maximum shear stress range plane and the plane where the value of suman & kallmeyer damage parameter value is maximum is much smaller. while computing the damage parameter for the proportional load path, computation of maximum shear plane was comparatively easy. a. s. cruces et alii, frattura ed integrità strutturale, 41 (2017) 54-61; doi: 10.3221/igf-esis.41.08 59 figure 4: ip 1 – σ, τ and skdp at max peak cycle (a) and min peak cycle (b) skdp was computed for the test data shown in tab. 4, and the material dependent parameters were optimized with a dual power law fit line. after several iterations of computations to optimize these damage parameter, it was observed that fit was good for larger w & k values for this data set. the direction of shear stress in this parameter is not taken into the account because both positive and negative shear stress create same crack initiation phenomenon. the damage parameter vs cycles to failure for the suman-kallmeyer damage parameter is shown in fig 5, and it can be observed from the curve that both lcf and hcf data have collapsed very well along the fitting line. comparison of fig 3 and fig 5 appears to indicate that the suman-kallmeyer damage parameter provided better correlation for the test data. figure 5: fatigue life correlation for st52-3n steel based on sandip model (k=2.1, w=1.1). life-life plots were also created for the test data by using both fatemi-socie ii [18] damage parameter and the damage parameter proposed by suman-kallmeyer [19]. red square in fig 6 represent the life predicted by fsdp ii, and green triangles represent the life predicted by skdm model. by observing this plot (fig 6) and the data, the fsdp ii tends to overestimate the fatigue life and the skdp tends to underestimate the fatigue life. similar level of correlation is observed on both damage parameters. the two new theories give overall good predictions for the test data under study. a. s. cruces et alii, frattura ed integrità strutturale, 41 (2017) 54-61; doi: 10.3221/igf-esis.41.08 60 figure 6: predicted vs. experimental life for st52-3n using fatemi ii model and sandip model. conclusion wo recently developed fatigue theories have been studied on experimental data. the experimental data were acquired on biaxial tests combining tension-compression and torsion under proportional load. the two fatigue theories were based on the critical plane approach. one of them is an enhanced formulation of the fatemi-socie damage parameter. the other theory uses the product of the normal and the shear stress at the critical plane. both theories provided an overall good prediction for the loading cases analyzed. while the new fatemi-socie damage parameter tended to overestimate the fatigue life preditions, the suman-kallmeyer tended to underestimate the life preditions. acknowledgements uthors would like to acknowledge financial support of junta de andalucía thru proyectos de excelencia grant reference tep-3244, campus de excelencia internacional del mar (ceimar) and ministerio de economía y competitividad thru grant reference mat2016-76951-c2-2-p. references [1] christopher cj, lu y, patterson ea. local crack plasticity and its influences on the global elastic stress field. int j fatigue 2013;46:4–15. [2] zanganeh m, lopez-crespo p, tai yh, yates jr. locating the crack tip using displacement field data: a comparative study. strain 2013;49:102–15. [3] branco r, antunes fv. finite element modelling and analysis of crack shape evolution in mode-i fatigue middle cracked tension specimens. eng fract mech 2008;75:3020–37. doi:10.1016/j.engfracmech.2007.12.012. [4] lopez-crespo p, pommier s. numerical analysis of crack tip plasticity and history effects under mixed mode conditions. j solid mech mater eng 2008;2:1567–76. [5] rodopoulos ca. fatigue damage from surface to bulk. in: sih gc, editor. multiscale fatigue crack initiat. propag. eng. mater. struct. integr. microstruct. worthiness fatigue crack growth behav. small large bodies, dordrecht: springer netherlands; 2008, p. 113–31. doi:10.1007/978-1-4020-8520-8_6. t a a. s. cruces et alii, frattura ed integrità strutturale, 41 (2017) 54-61; doi: 10.3221/igf-esis.41.08 61 [6] lopez-crespo p, mostafavi m, steuwer a, kelleher jf, buslaps t, withers pj. characterisation of overloads in fatigue by 2d strain mapping at the surface and in the bulk. fatigue fract eng mater struct 2016;39:1040–8. [7] pippan r, grosinger w. fatigue crack closure: from lcf to small scale yielding. int j fatigue 2013;46:41–8. [8] pippan r, hohenwarter a. fatigue crack closure: a review of the physical phenomena. fatigue fract eng mater struct 2017;40:471–95. doi:10.1111/ffe.12578. [9] skorupa m, skorupa a, schijve j, machniewicz t, korbut p. effect of specimen thickness and stress ratio on fatigue crack growth after a single overload cycle on structural steel. eur. conf. fract. ecf 13, san sebastian: 2000. [10] camas d, lopez-crespo p, gonzalez-herrera a, moreno b. numerical and experimental study of the plastic zone in cracked specimens. eng fract mech 2017. doi:10.1016/j.engfracmech.2017.02.016. [11] lu s, bao r, zhang t, fei b. a link-up resulted fatigue crack branching in al–cu–mg alloy. int j fatigue 2016;92:459–69. doi:10.1016/j.ijfatigue.2016.02.036. [12] zitounis v, irving p. fatigue crack acceleration effects during tensile underloads in 7010 and 8090 aluminium alloys. int j fatigue 2007;29:108–18. doi:10.1016/j.ijfatigue.2006.02.048. [13] lopez-crespo p, steuwer a, buslaps t, tai yh, lopez-moreno a, yates jr, et al. measuring overload effects during fatigue crack growth in bainitic steel by synchrotron x-ray diffraction. int j fatigue 2015;71:11–6. [14] salvati e, o’connor s, sui t, nowell d, korsunsky am. a study of overload effect on fatigue crack propagation using ebsd, fib–dic and fem methods. eng fract mech 2016;167:210–23. doi:10.1016/j.engfracmech.2016.04.034. [15] toda h, sinclair i, buffière j-y, maire e, khor kh, gregson p, et al. a 3d measurement procedure for internal local crack driving forces via synchrotron x-ray microtomography. acta mater 2004;52:1305–17. doi:10.1016/j.actamat.2003.11.014. [16] wang yy, yao wx. evaluation and comparison of several multiaxial fatigue criteria. int j fatigue 2004;26:17–25. [17] socie df, marquis gb. multiaxial fatigue. warrendale, pa (usa): society of automotive engineers, inc.; 2000. [18] gates nr, fatemi a. interaction of shear and normal stresses in multiaxial fatigue damage analysis. frat ed integrità strutt 2016;37:160–5. doi:10.3221/igf-esis.37.22. [19] suman s, kallmeyer a, j s. development of a multiaxial fatigue damage parameter and life prediction methodology for non-proportional loading. frat ed integrità strutt 2016;38:224–30. doi:10.3221/igf-esis.38.30. [20] lopez-crespo p, garcia-gonzalez a, moreno b, lopez-moreno a, zapatero j. some observations on short fatigue cracks under biaxial fatigue. theor appl fract mech 2015;80:96–103. [21] mokhtarishirazabad m, lopez-crespo p, moreno b, lopez-moreno a, zanganeh m. optical and analytical investigation of overloads in biaxial fatigue cracks. int j fatigue 2017. doi:10.1016/j.ijfatigue.2016.12.035. [22] chaves v. ecological criteria for the selection of materials in fatigue. fatigue fract eng mater struct 2014;37:1034–42. doi:10.1111/ffe.12181. [23] lopez-crespo p, moreno b, lopez-moreno a, zapatero j. study of crack orientation and fatigue life prediction in biaxial fatigue with critical plane models. eng fract mech 2015;136:115–30. [24] lopez-crespo p, moreno b, lopez-moreno a, zapatero j. characterisation of crack-tip fields in biaxial fatigue based on high-magnification image correlation and electro-spray technique. int j fatigue 2015;71:17–25. [25] fatemi a, socie df. a critical plane approach to multiaxial fatigue damage including out-of-phase loading. fatigue fract eng mater struct 1988;11:149–65. << /ascii85encodepages false /allowtransparency false /autopositionepsfiles true /autorotatepages /none /binding /left /calgrayprofile (dot gain 20%) /calrgbprofile (srgb iec61966-2.1) /calcmykprofile (u.s. web coated \050swop\051 v2) /srgbprofile (srgb iec61966-2.1) /cannotembedfontpolicy /error /compatibilitylevel 1.4 /compressobjects /tags /compresspages true /convertimagestoindexed true /passthroughjpegimages true /createjobticket false /defaultrenderingintent /default /detectblends true /detectcurves 0.0000 /colorconversionstrategy /cmyk /dothumbnails false /embedallfonts true /embedopentype false /parseiccprofilesincomments true /embedjoboptions true /dscreportinglevel 0 /emitdscwarnings false /endpage -1 /imagememory 1048576 /lockdistillerparams false /maxsubsetpct 100 /optimize true /opm 1 /parsedsccomments true 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can be opened with acrobat and adobe reader 5.0 and later.) >> /namespace [ (adobe) (common) (1.0) ] /othernamespaces [ << /asreaderspreads false /cropimagestoframes true /errorcontrol /warnandcontinue /flattenerignorespreadoverrides false /includeguidesgrids false /includenonprinting false /includeslug false /namespace [ (adobe) (indesign) (4.0) ] /omitplacedbitmaps false /omitplacedeps false /omitplacedpdf false /simulateoverprint /legacy >> << /addbleedmarks false /addcolorbars false /addcropmarks false /addpageinfo false /addregmarks false /convertcolors /converttocmyk /destinationprofilename () /destinationprofileselector /documentcmyk /downsample16bitimages true /flattenerpreset << /presetselector /mediumresolution >> /formelements false /generatestructure false /includebookmarks false /includehyperlinks false /includeinteractive false /includelayers false /includeprofiles false /multimediahandling /useobjectsettings /namespace [ (adobe) (creativesuite) (2.0) ] /pdfxoutputintentprofileselector /documentcmyk /preserveediting true /untaggedcmykhandling /leaveuntagged /untaggedrgbhandling /usedocumentprofile /usedocumentbleed false >> ] >> setdistillerparams << /hwresolution [2400 2400] /pagesize [612.000 792.000] >> setpagedevice microsoft word numero 9 art 8 finale t. marin et alii, frattura ed integrità strutturale, 9 (2009) 76 84; doi: 10.3221/igf-esis.09.08 76 fatigue design of welded joints using the finite element method and the 2007 asme div. 2 master curve t. marin, g. nicoletto university of parma, department of industrial engineering, italy, marin@ied.unipr.it riassunto. lo studio della fatica nei giunti saldati è solitamente basata sugli approcci della tensione nominale, quella di hot spot o quella di intaglio, i quali però presentano svariate limitazioni quando sono associati ad analisi mediante il metodo degli elementi finiti. in questo lavoro viene presentata una definizione più recente di tensione strutturale e la sua implementazione in un postprocessore per codici fem. essa permette un efficace utilizzo dei risultati delle simulazioni per valutare la resistenza a fatica di strutture anche complesse. le applicazioni presentate confermano le principali caratteristiche del metodo, ossia l’insensibilità alla mesh e stime accurate della vita a fatica e del punto di propagazione delle cricche. abstract. fatigue design of welded structures is primarily based on a nominal stress; hot spot stress methods or local approaches each having several limitations when coupled with finite element modeling. an alternative recent structural stress definition is discussed and implemented in a post-processor. it provides an effective means for the direct coupling of finite element results to the fatigue assessment of welded joints in complex structures. the applications presented in this work confirm the main features of the method: mesh-insensitivity, accurate crack location and life to failure predictions. keywords. welded joints; structural stress; fatigue assessment; finite element analysis. introduction elding is the most widespread joining technique for metallic structures due to its applicability to many geometric configurations. the principal failure mode in welds is fatigue cracking, [1], therefore many efforts have been put in the study of the strength of welded joints and in the definition of design guidelines, [2]. as the finite element method has become the favorite tool in structural analysis, there is an unquestionable need for a direct connection of the fatigue assessment approaches to the simulations. in this work, after a brief review of some well established techniques in section 2, a novel approach developed at battelle institute, and recently entered in the asme standards, is described in sections 3-4. some applications to experimental tests are then presented in section 5. this method allows a relaxation of some finite element modeling difficulties, mainly the mesh sensitivity, and grants the possibility of using alternatively solid and shell elements to model welded joints. the results of the fe analysis are then used in combination to a fatigue master curve that consolidates a large number of welded joint configurations. approaches to fatigue assessment of welded joints t is common practice to separate the approaches to fatigue assessment of welded joints into “global” and “local” families, [3-4]. the former consists of the long standing nominal stress method, which is still the most used for its simplicity and is the basis of all standards and design codes in use. with nominal stress approach no attempt is made w i http://www.gruppofrattura.it/ http://dx.medra.org/10.3221/igf-esis.09.08&auth=true mailto: marin@ied.unipr.it t. marin et alii, frattura ed integrità strutturale, 9 (2009) 76 84; doi: 10.3221/igf-esis.09.08 77 of taking into account the stress concentrations due to macroand micro-geometric effects of the joints. it employs several empirical s-n curves that are associated with detail categories and corrective factors. the selection of a detail class for a welded joint type and loading mode is often subjective and, in many common situations, difficult even for a skilled engineer. this is especially true when the geometry of the structure is complex or when the stress state is not reducible to a simple main component. moreover it must be added that the real structures can develop cracks in locations different to those indicated in the details present in the standards so this method has severe limitations. the group of “local” methods comprises many different strategies, ranging from the notch stress and notch strain approaches to the fracture mechanics approach. a brief generalization of them is not possible since they differ in the local parameter (being a stress, a strain or a stress intensity factor) and in the phase of the fatigue damage where they can be applied (for example local notch stress is suitable for the crack initiation while fracture mechanics is ideal for crack propagation), [5]. even if these approaches are sophisticated and have a significant theoretical foundation, the applicability is very often confined to specific cases and therefore they cannot be easily generalized to cover the variety of situations typically found in engineering. this is the main reason why they have not seen a straightforward acceptance in the standard codes, [3]. an intermediate approach between “global” and “local” methods uses a definition of a representative stress, in proximity of the weld toes, which is based on an idealized stress distribution in the thickness of the joined members. different terms have been adopted for this stress depending on the field of application and on the way it is calculated (geometric stress, structural stress, hot-spot stress). here the term structural stress is adopted. the fundamental idea is to consider the stress component orthogonal to the weld line and to reduce it to a linearized distribution, fig. 1a. the structural stress approach is suited for the assessment of fatigue failures occurring at the weld toes; accordingly it is the stress component normal to the crack plane, i.e. normal to the weld line that is the driver for crack propagation (fig. 1b). figure 1: a) decomposition of the through thickness stress at the weld toe; b) stress component acting normal to the weld fillet. the structural stress can be inferred by surface measurements and extrapolations, leading to the traditional hot-spot technique. the procedure can be replicated by numerical simulations using finite element models and is present in standard codes (i.e. eurocode3). linearization of the stress over the section thickness can be achieved only through fe simulations and usually interrogating nodal stresses. such practiced has also been introduced in pressure vessel standard en 13445. as a result of the linearization, the structural stress s at the weld toe is composed by a membrane part m, constant in the thickness, and a bending part b, as depicted in figure 1a. the remaining self-equilibrated non-linear nl is not considered; therefore the structural stress includes only the effects of gross structural discontinuities but disregards the local notch effect due to the weld geometry. the notch-induced complex stress state at the weld toe can then be simplified and only the two components m and b are taken into account. the finite element simulations required for this approach are linear elastic and the fatigue assessment is performed using structural stress s-n curves that are in limited number with respect to the nominal stress s-n curves. structural stress approach based on nodal forces he finite element framework allows the calculation of a structural stress based on forces and moments at the nodes of the mesh. this method has the distinctive advantage of providing a structural stress fairly insensitive to the mesh features (element size and element type) in the areas corresponding to the weld toes. the typical meshdependence that is found in the traditional surface extrapolation method and in the through thickness linearization, is t http://www.gruppofrattura.it/ http://dx.medra.org/10.3221/igf-esis.09.08&auth=true t. marin et alii, frattura ed integrità strutturale, 9 (2009) 76 84; doi: 10.3221/igf-esis.09.08 78 therefore overcome. elemental stresses or stresses extrapolated to the nodes are in fact influenced by the element formulation and by the geometric characteristics of the finite elements, whereas nodal forces directly derive from the equilibrium of the structure. nodal forces (and moments) for each element are calculated from the stiffness matrix and the nodal displacements (and rotations). the displacements are the primary output of displacement-based fe codes and the equilibrium at each node in the mesh is satisfied regardless of the element size and element formulation. a few different variants of this approach have been proposed and they mainly stem from the automotive field for either spot or seam welds, see for example fermer and co-workers [6]. the literature reports also a recent implementation of a similar approach in the commercial code femfat, [7]. researchers, headed by p. dong at battelle institute, have formulated an effective procedure for the calculation of the structural stress from forces and moments at the nodes of a finite element mesh, based on work-equivalence considerations, [8]. in dong’s method, first distributed line forces (and moments) are determined along the edges of the weld toe lines starting from balanced nodal forces (and moments), then at each node the structural stress is calculated as: 2 6 t m t f xy bms    (1) where t is the section thickness of the plate, fy is the line force in the local y direction orthogonal to the weld line and in the plane of the shell; mx is the line moment in the local x direction tangent to the weld line. forces and moments have to be preliminarily rotated into local coordinate systems defined at the nodes of the weld line. the resulting line forces (and moments) are continuous along the weld toe lines and so is the structural stress. the detailed procedure is described in several publications, for example [8-9]. even if these concepts can be applied to solid elements (2d and 3d), the approach is particularly suited for shell elements. thus, since shell and plates are often the preferred choice for modeling the response of engineering structures that are obtained using welding (for example truck frames, ships, cranes, bridges, etc.), the potential applications of the method are many. it must be emphasized that the finite element simulations have to be linear elastic therefore a fatigue assessment of the welded joints in the components can be a precious additional outcome of a standard stress analysis. the only specific requirement concerns the modeling of the welds because the fillets must be explicitly included to correctly represent the stiffness of the joints. this can be done using inclined elements, as shown in fig. 2a which reports an example of a t-joint connection between two tubular parts. several strategies for a realistic modeling of partial and complete penetration seam welds are collected in fig. 2b. the authors acknowledge that the manual creation of the elements in the welds is a tedious and time consuming part of the procedure and the automation of the welds definition has to be pursued. note in fig. 2a how for a given fillet both the two toe lines have to be analyzed since a priori it is not know which one is the most prone to fatigue propagation and where. figure 2: a) tubular connection (t-joint) modeled with shell elements; b) fillet welds with partial and complete penetration. the mesh-insensitivity of the structural stress claimed above, is demonstrated through the illustrative numerical example of figure 3. here a curved thin profile is joined on the outer side to a flat plate by a full penetration fillet weld. the main dimensions of the flat panel are 100x100 mm, the two sides of the curved plate are 50 mm long and the thickness is 5 mm. a uniform traction is applied longitudinally to the curved profile and transverse loading acts on the top edge as shown in fig. 3a; top and bottom nodes of the flat plate are pinned. three different meshes are studied, the first one is shown in fig. 3a together with the resulting v.mises stress on the visible surfaces of the shells. this is a rather coarse http://www.gruppofrattura.it/ http://dx.medra.org/10.3221/igf-esis.09.08&auth=true t. marin et alii, frattura ed integrità strutturale, 9 (2009) 76 84; doi: 10.3221/igf-esis.09.08 79 mesh but regularly spaced and with a low aspect ratio in the rows of elements corresponding to the two weld toes. the second case considered, fig. 3b, has weld toes characterized by distorted elements having a wide spectrum of shape metrics. fig. 3c shows the third mesh with a regular and fine discretization. any experienced finite element analyst would prefer the last one for a local stress investigation but such level of refinement may not be necessary for a fatigue analysis based on the present procedure. the proof comes from figure 4 where the structural stress (s), the membrane (m ) and bending (b) components are plotted along the weld toe lines 1 and 2 indicated in fig. 3a. the results from the three meshes are drawn with different line styles (refined mesh: continuous lines, distorted mesh: dashed lines, coarse mesh: dash-dot lines) but they are barely distinguishable since they are closely overlapped. the distorted mesh plots have few little jerks in correspondence of some elements but the trends are completely captured and so are the peak values and positions. even the coarse mesh does not fail in revealing the maximum values. these graphs give also useful information about the relative magnitude of the structural stress components, membrane and bending, so the analyst has a clear picture of the loading mode in each point along the weld toes. in the example discussed here there is a strong predominance of bending stress in most parts of the toe lines. figure 3: curved profile welded to a flat plate: a) shell model using a coarse regular mesh at the toes; b)-c) close views of the fillet for the irregular mesh and the refined regular mesh. figure 4: a) comparison of the structural stress and its membrane and bending components along the weld toes of fig. 3. fm: fine mesh mesh, cm: coarse mesh, dm: distorted mesh. (a) (b) (c) http://www.gruppofrattura.it/ http://dx.medra.org/10.3221/igf-esis.09.08&auth=true t. marin et alii, frattura ed integrità strutturale, 9 (2009) 76 84; doi: 10.3221/igf-esis.09.08 80 the mesh sensitivity of the nodal stresses extrapolated to the nodes on the toe line is obvious in fig. 5. these are the normal stresses to the weld, calculated as weighted average of the stresses (extrapolated to the nodes) given only by the elements in the toe. the convergence of the mesh is evident since the coarse mesh provides lower stresses but, even if the finer mesh provides higher stresses, these values are still far from the structural stress calculated based on nodal forces. figure 5: comparison of the normal stress to the weld calculated from nodal stresses and the structural stress obtained from nodal forces (toe 1 in fig. 3). one of the major drawbacks of the structural stress approaches in their basic forms is that they usually take into account only the stress component normal to the weld line. in analogy with eq. (1), a structural shear stress along the fillet could be calculated as: 2 6 t m t f yx bms    . (2) as of now only few studies on multiaxial fatigue and structural stress are found in the literature, [10], so a complete understanding of the correct combination of s and s is yet to be available. the whole procedure has been implemented by the authors in matlab routines which act as a post-processor to the fe software abaqus. together with the calculations described above, the code detects the toes for all the fillets in the shell mesh of a structure or a component, thus offering an automatic, quick and complete analysis of the welded joints. the asme master s-n curve ccording to this approach, the structural stress defined in equation 1 is consistent with the far-field stress typically used in fracture mechanics to compute the stress intensity factors k for a given crack shape and size. since the life of welded joints is dominated by crack propagation, the structural stress and its components correlate the actual geometry and loading of any joint to simplified fracture mechanics configurations where crack growth models can be applied. as a result of the analytical procedure developed in [9] for a two-stage growth model, an equivalent structural stress parameter can be defined as: mmm s s rit s /12/)2( )(     (3) where the structural stress range s is modified by a loading mode function i(r) and by a thickness correction factor. the polynomial i(r)1/m is a function of the ratio r : a http://www.gruppofrattura.it/ http://dx.medra.org/10.3221/igf-esis.09.08&auth=true t. marin et alii, frattura ed integrità strutturale, 9 (2009) 76 84; doi: 10.3221/igf-esis.09.08 81 bm br      (4) that represents the content of bending stress over the total structural stress, t is the section thickness of the plate and m=3.6 represents the slope of a paris-like crack propagation curve. it has been shown in several publications by dong and co-workers that, using this procedure, it is possible to define a single s-n curve for many different weld geometries and loading configurations, therefore proving its robustness. this master s-n curve, which has also been incorporated in the asme boiler and pressure vessel codes (2007) section viii division 2 as an alternative prediction method, has the following form: h s ncs  (5) where c and h are parameters of the material and are tabulated for different prediction intervals. contrary to most of the standards, this norm does provide neither a cut-off limit (fatigue strength for infinite life) nor any knees in the curve: all the cycles (after rainflow filtering) are considered damaging. this is consistent with the recommendations given in [11]. the equivalent structural stress is the parameter that provides the estimate of the life via eq. (5). these concepts can again be applied to the example from section 3. accepting that the combined loading is proportional and in-phase, and assuming that the load history is constant amplitude with a stress ratio r=0, the structural stress range is s=s. the number of cycles to failure is then obtained through eq. (3)-(5) and the results are given in the graphs of figure 6. the point with the maximum ss is the location where the fatigue cracks would most probably propagate in the through thickness of the plate. in this case the plots suggest that a fatigue crack would take place at 0.4*l of the toe 1 (l: total length of the toe line) and that the failure of the part would occur after about 4.0e+6 cycles based on the mean master sn curve. figure 6: life prediction (with different scatter bands) and equivalent structural stress range ss for the weld toes in fig. 3. applications ome experimental tests were performed in this work to further validate the structural stress approach and asme master s-n curve. several specimens of three different geometries were subjected to pulsating tensile constant amplitude loading (stress ratio r=0). to assess the predictive capabilities of the method, the maximum load was set to values corresponding to a given number of cycles. from the target life, the structural stress was deduced using eq. (3)(5) and compared to the maximum structural stress found in a finite element simulation of the specimen subjected to the known load. the linearity of the solution then allowed an easy scaling of the applied load to determine the force required in the test. the target life of this experimental campaign ranged from n=1.0e+5 to n=5.0e+5. s http://www.gruppofrattura.it/ http://dx.medra.org/10.3221/igf-esis.09.08&auth=true t. marin et alii, frattura ed integrità strutturale, 9 (2009) 76 84; doi: 10.3221/igf-esis.09.08 82 the specimens consisted of plates (thickness t=8 or 10mm, width w=50mm, length l ranging from 250 to 300mm) with attachments on the top surface. the attachments were h-shaped, t-shaped and a solid cubic block (“h”, “t”, “b” types in the following). the specimen types “h” and “t” had 5 mm thick attachments that were centered and aligned with the longitudinal direction, while the solid block (37x37x30mm) was not symmetrically positioned on the top of the plate. the material was a typical structural steel fe510. the failure criterion adopted was the complete propagation of the fatigue cracks through the plate thickness, so the tests were continued until final fracture had occurred and the total number of cycles could be determined. a detailed presentation of the computed structural stress is provided for type “t” specimen. fig. 7 shows two finite element models constructed using shell elements. because of the particular geometry, the t-shaped attachment is completely wrapped by the inclined elements forming the fillet. the simplified toe line in fig. 7b is continuous and smooth except in two points where there is an abrupt change in direction and a 90° angle. at these points (marked with a p in the figure) some disturbance in the structural stress distribution has to be expected. figure 7: a) specimen with the t-shaped attachment; b)-c) shell models with different mesh size. the v.mises stress is normalized by the nominal tensile stress. figure 8: structural stress and its components along the fillet weld of type “t” specimen. cm: coarse mesh, fm: fine mesh. the results of the post-processed simulations are illustrated in fig.8 for two mesh sizes. the graph has in the x-axis the position of the nodes on the toe line with respect to a curvilinear abscissa with origin on the tip of the “t” and running along the whole fillet. the continuous lines refer to the coarse mesh while the dashed lines correspond to the fine mesh. the structural stress values are normalized by the nominal stress in the section (nom= f/a, f: applied force, a: area of http://www.gruppofrattura.it/ http://dx.medra.org/10.3221/igf-esis.09.08&auth=true t. marin et alii, frattura ed integrità strutturale, 9 (2009) 76 84; doi: 10.3221/igf-esis.09.08 83 the transverse section). these stresses are to be intended as located on the upper surface of the plate and at the intersection of the weld elements and plate elements. the graph shows that there is an obvious symmetry due to the geometry, and, above all, that the fine mesh and coarse mesh plots are consistently overlapped with differences substantially negligible almost everywhere. there are some sensible discrepancies only close to the points p as discussed before. it is evident from the graph that the membrane content is dominant as could have been expected since the specimen is loaded in tension. the macro-geometric notch effect caused by the attachment is responsible for the bending component. peak values are reached at the tip of the “t” (point y in fig. 8) and in the middle point of the top leg of the “t” (point q in fig. 8). these are actually the locations of the fatigue failures, the choice between y and q being dictated by the local weld quality. along the sides of the “t”, which are parallel to the load direction, the structural stress is close to zero because only the stress component normal to the weld fillet is considered. figure 9: finite element model using 3d elements and real specimen with the solid block. analogous plots are obtained for type “h” specimens and for sake of brevity are not reported. the presence of the massive block in type “b” specimens prevents the use of shells so for that case solid 3d elements are employed, fig. 9. it is important to note that the failure location is always in correspondence with the highest value of the structural stress so these tests confirm the ability of the method to take into account the main features of fatigue failure in a simplified but correct way. the fatigue data for the all the specimen types are inserted into the 2007 asme div. 2 master curve as shown in fig. 10. all the data, independently of the specimen geometry, fall within the ±2 s-n curves, therefore demonstrating that the predictions using the presented calculation approach are quite accurate. figure 10: 2007 asme div.2 master s-n curve and experimental results. http://www.gruppofrattura.it/ http://dx.medra.org/10.3221/igf-esis.09.08&auth=true t. marin et alii, frattura ed integrità strutturale, 9 (2009) 76 84; doi: 10.3221/igf-esis.09.08 84 conclusions he work presented a structural stress approach to fatigue assessment of welded joints that integrates well with finite element modeling. the implementation in a post-processor program was successful and showed the potential for becoming a useful tool for the design and assessment of welded structures subjected to fatigue. the mesh-insensitivity was confirmed: even coarse meshes provide adequate structural stress estimates so the method can be used in modeling complex structures. the procedure was applied to three different specimen geometries subjected to constant amplitude loading and predicted the correct location of the fatigue cracks. finally, the use of the asme master s-n curve proved to give accurate fatigue life predictions. references [1] d. radaj design and analysis of fatigue resistant welded structures, abington publishing, cambridge (1990). [2] w. fricke, marine structures, 16 (2003) 185. [3] d. radaj, c.m. sonsino, w. fricke fatigue assessment of welded joints by local approaches (2nd ed.), woodhead publishing, cambridge (2006). [4] a. hobbacher, recommendations of iiw joint working group xiii – xv, woodhead publishing (1996). [5] b. atzori, p. lazzarin, r. tovo, fatigue and fracture of engineering materials and structures, 22 (1999) 369. [6] m. fermer, m. andreasson, sae technical paper 982311(1998). [7] s. zhang, daimlerchrysler ag research report gr/vmb-07-001 (2007). [8] p. dong, int. j. of fatigue, 23 (2001) 865. [9] p. dong, j. k. hong, z. cao, int. j. of fatigue, 25 (2003) 811. [10] p. dong, j. k. hong, international institute of welding: iiw doc. xiii-2036-04/xv-1173-04 [11] t. gurney, cumulative damage of welded joints, woodhead publishing, cambridge (2006). t http://www.gruppofrattura.it/ http://dx.medra.org/10.3221/igf-esis.09.08&auth=true microsoft word numero_54_art_04_2848 e.m. strungar et alii, frattura ed integrità strutturale, 54 (2020) 56-65; doi: 10.3221/igf-esis.54.04 56 mathematical data processing according to digital image correlation method for polymer composites elena m. strungar, dmitrii s. lobanov perm national research polytechnic university, russia cem.spaskova@mail.ru, http://orcid.org/0000-0002-2246-8638 cem.lobanov@gmail.com, http: //orcid.org/0000-0003-1948-436x abstract. the paper analyses the numerical algorithms for experimental data processing using a contactless video system vic-3d, designed for threedimension analysis of displacement and strain fields, and digital image correlation method. the authors considered methodological issues of conducting an experiment using a video system. they suggested recommendations on the choice of parameters of calculation of correlation, the size of subset and step during the analysis of non-homogeneous displacement and strain fields in polymer composite materials through laminated fiberglass composite. the efficient parameters of mathematical data processing are identified according to digital image correlation method on the basis of building fields for one frame on the surface of laminated fiberglass reinforced plastic at various subset values and at fixed step value. the paper shows the impact of step value on the strain fields detail degree. the authors have identified the relation of the chosen parameters of experimental data processing using digital image correlation method with the scaled levels of consideration of composite materials strain processes. to evaluate the strains at various scale levels, the paper uses supplementary video system instruments: “virtual extensometer”, “rectangular area” and “line”. the authors obtained a longitudinal strain profile that allows evaluating the location of strain peak areas on the composite object surface. keywords. the method of digital image correlation; composite material; scale level; mathematical parameters of correlation analysis; structurally heterogeneous material. citation: strungar, e. m., lobanov, d. s., mathematical data processing according to digital image correlation method for polymer composites, frattura ed integrità strutturale, 54 (2020) 56-65. received: 02.06.2020 accepted: 29.06.2020 published: 01.10.2020 copyright: © 2020 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. introduction ue to high specific physical-mechanical properties the polymer composites are widely used in all fields of aviation and automobile industry, power industry and machine building which provides a number of benefits as compared to metals [1-5]. experimentally proven correlation between microand macroscales in composite d https://youtu.be/fo36um9_pki e.m. strungar et alii, frattura ed integrità strutturale, 54 (2020) 56-65; doi: 10.3221/igf-esis.54.04 57 materials is of special importance because it provides the establishment of true multiscale structure during the composite materials study. composite materials possess significant structural non-homogeneity, besides, scientific literature points out the structure complexity, therefore, the defects should be considered at various levels and stages of manufacture of components, materials and products [1,6,7]. multiscale structures can bring the most efficient and realistic models, which, in turn, will improve understanding of mechanical behavior of composite materials. the approaches based on experimental studies, that show the relation of strain measurement on the reinforcing element strain level with the macroscale material response are poorly reflected in scientific literature. it is necessary to study the complex interactions between the reinforcing fibers and the matrix, homogenization algorithms should be performed at carefully selected volume (or surface) of material which is low enough to cover the impact of each individual component and at the same time large enough to represent the global response of the material [8-13]. such promising methods as ultrasonic testing, x-ray tomography, thermography, acoustic emission (ae), fiber-optic methods etc. are used to study the defects, fissures, delaminations that occur in composite materials [6,7,14-18]. a prospective trend of experimental mechanics is the simultaneous use of the methods presented. contactless optical methods are widely used to analyze the stress-strained condition of the deformed elements of composite structures with significant structural non-homogeneity in the process of mechanical properties study. the digital images correlation (dic) method is one of the prospective experimental methods of displacement and strain fields study. the development of a new method for solution of tasks of deformed solids mechanics calls for complex studies of the efficacy of using this experimental mechanics “instrument” as applied to the analysis of mechanical behavior of solids of various structures at implementation of complex modes of external exposures. nevertheless, there are some problems related to the use of dic at small scales for essentially structurally non-homogeneous materials [12, 19]. to evaluate the structural features of material, to study the processes of origination and development of defect structures and destructions using dic method, special attention should be paid to the selection of correlation processing parameters, in particular, the choice of subset size and step value [15]. the main objective of the paper is the analysis of specific features of testing process using the digital optical system, and substantiation of the choice of efficient parameters of data processing using dic method as applied to composite materials objects.     methodology and methods of research igital image correlation method is a contactless optical method for recording the displacement and strain fields on the object surface. all information is contained in the structure (pixel distribution) on the surface of the test object with varying degrees of brightness of black-and-white image. during digital images processing by dic method, displacement vectors are calculated not at each individual image point (in the pixel), but by discretizing the study area into small local subsets, or, in other words, correlation areas x × x pixels in size (fig. 1). the subset size significantly affects the accuracy of correlation analysis, the degree of detail of displacement and strain fields along the surface of the studied object, as well as the size of the edge zone that occurs on the edge or near the stress concentrators (holes, inclusions, fissures, defects). the step value sets the distance between the points (central pixels of the subset) analyzed during the mathematical processing in pixels. figure 1: discretization of the area of study into subsets. d e.m. strungar et alii, frattura ed integrità strutturale, 54 (2020) 56-65; doi: 10.3221/igf-esis.54.04 58 the choice of the subset value  and step  depends on the conditions of the shooting performed, the results of the video system calibration, as well as on the geometric parameters of the study object and the structural features of the sample material. even under almost perfect experimental conditions, the differences between the intensities of images recorded at different times will exist. these changes can be caused by various reasons, for example, changes in lighting, changes in the sample reflectivity due to deformation, or changes in the sample orientation. the procedure of identification of the image sections is carried out by calculating the coefficient of correspondence of images and the search for its minimum. in this paper, we use the criterion of the normalized sum of squared differences with a zero mean, because it is the least sensitive to changes in lighting during the test. the subset value is acceptable if the value of the correlation coefficient does not exceed a≤0.01. in scientific literature [19], the correlation coefficient value is indicated as σ; in this paper, we changed the indication into “a” to avoid misinterpretation of the well-known stress indication. in the course of post-processing by vic-3d system, the deformation components were calculated in this paper using the finite strain tensor in the sense of lagrange [19]. the software vic-3d provides the recording of strain using a video system instrument “virtual extensometer”. the principle of its action is similar to resistance strain gauge, it consists in tracking the mutual displacement between two points of the surface of the samples according to the applied force. the main advantages of the use of the “virtual extensometer” are the contactless registration of deformations, which eliminates mechanical impact on the surface of the sample. in addition, additional video system tools were used in the work: the “rectangular region” and “line” to determine the average deformations in the region and along the averaging line, respectively. to implement the tool "rectangular area" in the working area of the sample area was allocated in the form of a rectangle. the line tool is a line drawn on the surface of the sample along which strain averaging occurs. it is worth noting that the strain assessment is carried out already at the post-processing stage by the specialized vic-3d program, after the test. equipment, technique and material xperimental studies were carried out using the large-scale research facilities «complex of testing and diagnostic equipment for studying properties of structural and functional materials under complex thermomechanical loading» pnrpu modernized with funds by the ministry of science and higher education of the russian federation, unique project identifier rfmefi61920x0017. the uniaxial tensile of a structural fiberglass specimen will be considered as an example of digital image processing using dic method. experimental studies were conducted at an electromechanical system instron 5989 at normal temperature. the movable grip speed was 2 mm/min. the deformations on the surface of the samples were recorded using the vic-3d contactless optical video system and dic method. the video system preciseness was determined by technical characteristics of objectives and digital cameras, in particular, matrix sensibility, resolving power and the possible framing frequency. the strain process video recording was performed using cameras with 35 mm objective. the shooting speed was 3 frames per second with the set cameras resolution of 16.0 mp. the optical recording systems synchronization with the test system controllers in the process of testing was provided by analog-to-digital converter unit (ni usb-6251) (fig. 2). the strain experiments were performed in compliance with astm d3039 recommendations using strip samples 25 mm wide, 5 mm thick with 120 mm working part. the material used in the study is the general purpose construction fiberglass laminate stef. it is laminated reinforced fiberglass obtained by hot pressing of fiberglass cloth impregnated with thermoreactive compound based on combined epoxide and phenolformaldehyde resins. fig. 3. (a) presents the image of a composite sample surface with a marked structural element , obtained using a stereomicroscope carl zeiss stereo discoverу v12. the size of the structural element  means the width of interlacing cell, for this material it is =4 mm. to implement dic method, a finely dispersed coating should be applied on the surface before testing, prior to the object stressing (fig. 3. (b)). the coating provides reliable identification of displacements and improves the fine detail resolution of the surface studied. there are various methods of application of such coating, for example, with laser speckles [20]. in this study the black and white dots were applied on the specimen surface by means of aerosol paint. the finely dispersed coating significantly affects the image correlation preciseness which is reflected in the paper [21]. numerous recommendations on application of the coating were taken into account in this study [22], they were not analyzed separately.  e e.m. strungar et alii, frattura ed integrità strutturale, 54 (2020) 56-65; doi: 10.3221/igf-esis.54.04 59 figure 2: test pattern together with the non-contact optical video system and the acoustic emission recording system: 1—test machine, 2—specimen installed in the grips, 3—test system controller, 4—pc from which the machine is controlled, 5— synchronization unit, 6— pc from which the video system is controlled, 7—cameras mounted on the support, 8—lighting system. figure 3: the image of the specimen before (а) and after (b) application of contrast finely dispersed coating on its surface. methodical problems of data processing using digital image correlation method o evaluate the effect of correlation processing parameters on non-homogeneous strain fields, the authors conducted a series of construction of fields for one frame on the surface of laminated reinforced fiberglass at various values of subset and the interval of =3563 and at fixed step value =3 pixels. the results are provided in tab. 1, where maximal amax , average amean and minimal correlation amin coefficient values are presented. t e.m. strungar et alii, frattura ed integrità strutturale, 54 (2020) 56-65; doi: 10.3221/igf-esis.54.04 60 x, п amean amax amin x, п amean amax amin 35 0.0040 0.0194 0.0015 51 0.0026 0.0108 0.0012 39 0.0035 0.0169 0.0014 53 0.0025 0.0100 0.0012 43 0.0031 0.0148 0.0014 55 0.0024 0.0093 0.0012 45 0.0030 0.0137 0.0013 57 0.0023 0.0087 0.0011 47 0.0028 0.0126 0.0013 59 0.0022 0.0081 0.0011 49 0.0027 0.0117 0.0013 63 0.0021 0.0071 0.0011 table 1: the results of image correlation processing at various subset values and fixed step value =2. figure 4: the fields of transversal, shear and longitudinal strain at the fixed value of subset and various step values. following the calculation it is observed that the chosen subset size 51×51 pixels possesses sufficient uniqueness of pixels distribution to provide unique identification of local areas based on the image amean=0.0026, amax=0.0108 and amin=0.0012. at smaller size of subset χ<51 unacceptable values of correlation coefficient a are observed. after the choice of the suitable subset value, it is necessary to match the step value , by which the degree of detail of displacement and deformation fields vary. for this purpose a correlation processing of one image for laminated reinforced e.m. strungar et alii, frattura ed integrità strutturale, 54 (2020) 56-65; doi: 10.3221/igf-esis.54.04 61 fiberglass sample at step values at the interval of =115 pixels and at the fixed value of subset x=5151 pixels. as we can see from the fig. 4, the smaller the step value =1,2,3 pixels, the more detailed is the strain field due to the increase of calculation points number. as the parameter =6,10,15 pixels increases, the non-homogeneity smoothens, the maximal and minimal values, registered on the sample surface, average, the composite material structural features blur and the edge area increases. the non-homogeneous fields of transversal, shear and longitudinal strain at the fixed value of subset =51 and various step values =115 are obtained as a result of the study (fig. 4). to assess the structural features of the material, to study the processes of origination and development of defective structures and destruction, to analyze the behavior in stress concentration areas, it is necessary to establish a step size comparable to the size of the structural non-homogeneity δ. therefore, it has been established that for the studied material, =2 is a suitable step size because this size makes it possible to take into account the structural features of stef fiberglass. the fiber bundles size coincides with the size of the field non-homogeneity. the fig. 5 presents the images of the material structure obtained using a stereo microscope with superimposed non-homogeneous strain fields at a fixed step size =2. in view of the fact that the numerical image processing parameters significantly affect the results of building of the displacement and strain fields, when presenting the results obtained using the dic method, it is necessary to indicate the subset size x, the step size x, and the size of the composite material structural element . figure 5: the images of the material structure with superimposed non-homogeneous strain fields at a fixed step size. scale levels of deformation registration aking into consideration the size of the structural non-homogeneity of the material, it is possible to affect the scale level of strain registration. to measure the structural deformations, it is necessary to set a smaller step. the structural level h is the level of structural non-homogeneity. its scale is smaller than the characteristic size of the inclusion particle or fiber diameter. in this case, deformation changes are recorded on the structural element. the next level is the macroscopic h, at which hh but less than the characteristic size of the product or the distance at which the averaged stresses and strains distinctly change. based on the results of the studies conducted, the following recommendations for selection of suitable dic calculation parameters during the analysis of non-homogeneous deformation fields of composite materials are identified. choosing the step value , it is necessary to take into consideration the objective of the study, in particular, when the video system is used as a “virtual extensometer” to determine the general characteristics of the material, when there is no need to take into account the structural features of the material, it is necessary to choose greater values of the step . the deformation is calculated at the macroscopic level h. to assess the structural features of the material, to study the t e.m. strungar et alii, frattura ed integrità strutturale, 54 (2020) 56-65; doi: 10.3221/igf-esis.54.04 62 processes of origination and development of defective structures and destruction, to analyze the behavior in stress concentration areas, it is necessary to establish a step size , comparable to the size of the structural non-homogeneity δ. the deformations are calculated at structural level h. an interesting aspect of non-homogeneous strain fields analysis is the location of local strain peaks. for this purpose the fig. 6 presents the plot of the distribution of longitudinal strains along the width of the sample along a line drawn through the geometric center of the sample perpendicular to the load application. according to fig. 6 it has been found that the places of greatest deformations are located in the fiber bundles. on the other hand, it has been found that the smallest strain values are located in the narrow regions located mainly at the intersection of longitudinal and transverse fiber beams. these results were obtained using the supplementary video system instrument “line”. figure 6: the plot of longitudinal strains superposed on real fiberglass structure.  it is supposed that the strain process in the inner layers of the woven composite is the same as on the surface. to assess the deformations at various scale levels we used a supplementary video system instrument “rectangular area (r)”, for which a rectangular site in the form of rectangle was assigned in the specimen working area. the rectangular area а×b mm is first applied in the center of the specimen working area and is subsequently enlarged (fig. 7). the schematic picture of the increasing sizes of the “rectangular area” used for local deformation averaging is presented in fig. 7. the values of axial strain of all the integrity of data points located inside this square, are averaged, and the resulting average value is indicated as local. the error related to calculation of local is calculated as: 100 global local global error             (1) where εglobal is the total (macroscale) longitudinal deformation obtained along the specimen surface. the fig. 7 shows the dependence of the of longitudinal deformation mean value εlocal on the size of the “rectangular area (r)”. the sizes of the “rectangular area (r)” increase proportionally, the number of data points in it increases, and the error is estimated for each corresponding size of the “rectangular area (r)”. it can be supposed that the errors value will become smaller at greater sizes of “rectangular areas (r)” [11,12]. if the established convergence criterion for all cases is 2%, the error is much higher at the smallest size of the “rectangular area (r0)” (tab. 2). rectangular area r0 r1 r2 r3 r4 area size, mm2 2.86 30.50 161.84 533.01 1160.70 amount of points, item 49 845 5580 15281 32072 error, % 3.16  0.27 0.09 0.09 0.09 table 2: characteristics of “rectangular areas (r)”. e.m. strungar et alii, frattura ed integrità strutturale, 54 (2020) 56-65; doi: 10.3221/igf-esis.54.04 63 figure 7: the diagram of dependence of the longitudinal deformation mean value on the “rectangular area” size, schematic picture of increasing size of the “rectangular area” used for local deformation averaging. it should be noted that the least size of the “rectangular area (r0)” is 2.86 mm2, which is much smaller than the size of the structural element [23] of the material =16 mm2, but the error in the case surpasses 2%. there is no need to take into consideration the obtained deformation values in the further study. considering the next size of the “rectangular area r1” 30.5 mm2, approximately 2 structural elements are taken into consideration, the error value is acceptable, but supplementary results convergence analysis is necessary. depending of the way the “rectangular area r” of r1 size was applied, the minimal, maximal of mixed strain field areas may be found in the area of the sample deformation identification. if maximal deformations are found in the area, the former will be too high in comparison with the average ones, if they are found in the minimal area, they will be too low. the sizes of “rectangular areas r2, r3, r4”, for which the error is also acceptable, must be theoretically sufficient to present the strain reaction at macroscale. the error in the regions r2, r3 and r4 is the same, it is proposed to use the region r2. the calculation of this area requires the least computational resources. since the number of calculation points (5580) is the smallest, comparing these three areas. conclusions   he authors have conducted a series of experiments for uniaxial strain on construction fiberglass sample. a series of building the fields for one frame on the surface of laminated reinforced fiberglass at various subset values and at fixed step value was performed to assess the impact of correlation processing on non-homogeneous strain fields. to assess the deformations, the authors used a video system for 3d analysis of displacement and strain fields vic-3d, based on digital image correlation (dic) method. such supplementary video system instruments as “virtual extensometer”, “rectangular area” and “line” were used for this purpose. therefore, according to the study results it has been found that the selection of correlation analysis parameters should consider the size of structural non-homogeneity of the material; in view of this fact, in become possible to select the scale level of deformation recording. to assess the structural features of the material, to study the processes of origination and development of defective structures and destruction, to analyze the behavior in stress concentration areas, it is necessary to establish a step size comparable to the size of the structural non-homogeneity of the material. in the paper the authors have analyzed the non-homogeneous strain fields on the surface of the composite samples of the studied structure. the options of averaging the deformations in the working area of the tested samples have been analyzed using the supplementary instruments of vic-3d system. the analysis of displacement and strain fields by digital image correlation data is generally performed along the entire surface of the studied object. the study conducted has proven that the values of composite deformations at smaller sizes differ from the macroscale deformations. t e.m. strungar et alii, frattura ed integrità strutturale, 54 (2020) 56-65; doi: 10.3221/igf-esis.54.04 64 acknowledgements he work is carrying out in perm national research polytechnic university with financial support of grant of president of russian federation for government support of young russian scientists (grant no mk-1222.2020.8.) references [1] lobanov, d.s., wildemann, v.e., spaskova, e.m., chikhachev, a.i. (2015). experimental investigation of the defects influence on the composites sandwich panels strength with use digital image correlation and infrared thermography methods. pnrpu mechanics bulletin, 4, pp. 159-170. doi: 10.15593/perm.mech/2015.4.10 [2] babushkin, a.v., babushkina, a.v., strungar, e.m., staroverov, o.a., lobanov, d.s., temerova, m.s., feklistova, e.v. (2019). phenomenological characteristics structural features research obtained at fibrous plastics standard tests, procedia structural integrity, 17, pp. 658–665. doi: 10.1016/j.prostr.2019.08.088. [3] fedulov, b.n., fedorenko, a.n., kantor, m.m., lomakin, e.v. (2018). failure analysis of laminated composites based on degradation parameters, meccanica, 53(1-2), pp. 359–372. doi: 10.1007/s11012-017-0735-9. [4] rajak, d.k, pagar, d.d., kumar, r., pruncu, c.i. (2019). recent progress of reinforcement materials: a comprehensive overview of composite materials, journal of materials research and technology, 8(6), pp. 6354-6374. doi: 10.1016/j.jmrt.2019.09.068 [5] panin, s.v., byakov, a.v., lyubutin, p.s., bashkov, o.v., grenke, v.v., shakirov, i.v., khizhnyak, s.a. (2011). study of deformation and fracture using data of acoustic emission, correlation of digital images and strain-gauging, industrial laboratory. material diagnostics, 77(9), pp. 50‒59. [6] hadjem-hamouche, z., derrien, k., héripré, e., chevalier, j.p. (2018). in-situ experimental and numerical studies of the damage evolution and fracture in a fe-tib2 composite, materials science and engineering: a, 724, pp. 594-605. doi: 10.1016/j.msea.2018.03.108. [7] damaskinskaya, e., panteleev, i., gafurova, d., frolov, d. (2018). defect structure of deformed heterogeneous materials: acoustic emission and x-ray microtomography, procedia structural integrity, 13, pp. 298-303. doi: 10.1016/j.prostr.2018.12.050. [8] mishnaevsky, l., brondsted, p. (2009). micromechanical modeling of damage and fracture of unidirectional fiber reinforced composites: a review, computer material science, 44(4), pp. 1351-1359. doi: 10.1016/j.commatsci.2008.09.004 [9] ansar, m., xinwei, w., chouwei, z. (2011). modeling strategies of 3d woven composites: a review, composite structure, 93(8), pp. 1947-1963. doi: 10.1016/j.compstruct.2011.03.010. [10] dixit, a., singh mali, h. (2013). modeling techniques for predicting the mechanical properties of woven-fabric textile composites: a review, mech composite material, 49(1), pp. 1-20. doi: 10.1007/s11029-013-9316-8. [11] koohbor, b., ravindran, s., kidane, a. (2018). a multiscale experimental approach for correlating global and local deformation response in woven composites, composite structures, 194, pp. 328-334. doi: 10.1016/j.compstruct.2018.04.016. [12] koohbor, b., ravindran, s., kidane, a. (2017). experimental determination of representative volume element (rve) size in woven composites, optics and lasers in engineering, 90, pp. 59-71. doi: 10.1016/j.optlaseng.2016.10.001. [13] mehdikhani, m., aravand, m., sabuncuoglu, b., callens, m.g., lomov, s.v., gorbatikh, l. (2016). full-field strain measurements at the micro-scale in fiber-reinforced composites using digital image correlation, composite structures, 140, pp. 192-201. doi: 10.1016/j.compstruct.2015.12.020. [14] wildemann, v.e., spaskova, e.v., shilova, a.i. (2016). research of the damage and failure processes of composite materials based on acoustic emission monitoring and method of digital image correlation problems of deformation and fracture in materials and structures, solid state phenomena, 243, pp. 163-170. doi: 10.4028/www.scientific.net/ssp.243.163. [15] tretyakova, t.v., dushko, a.n., strungar, e.m., zubova, e.m., lobanov, d.s. (2019). comprehensive analysis of mechanical behavior and fracture processes of specimens of three-dimensional reinforced carbon fiber in tensile tests, pnrpu mechanics bulletin, no. 1, pp. 173-183. doi: 10.15593/perm.mech/2019.1.15. t e.m. strungar et alii, frattura ed integrità strutturale, 54 (2020) 56-65; doi: 10.3221/igf-esis.54.04 65 [16] panteleev, i.a., bayandin, yu.v., naimark, o.b. (2016). spatio-temporal regularities of damage evolution in deformed fiberglass composite laminate by acoustic emission data, physical mesomechanics, 19(4), pp. 64-73. [17] djabali, a., toubal, l., zitoune, r., rechak, s. (2019). fatigue damage evolution in thick composite laminates: combination of x-ray tomography, acoustic emission and digital image correlation, composites science and technology, 183, 107815. doi: 10.1016/j.jnucmat.2014.08.043. [18] nozawa, t., ozawa, k., asakura, y., kohyama, a., tanigawa, h. (2014). evaluation of damage accumulation behavior and strength anisotropy of nite sic/sic composites by acoustic emission, digital image correlation and electrical resistivity monitoring, journal of nuclear materials, 455(1–3), pp. 549-553. doi: 10.1016/j.jnucmat.2014.08.043. [19] sutton, m.a., orteu, j.-j., schreier, h. (2009). image correlation for shape, motion and deformation measurements. – university of south carolina, columbia, sc, usa, 364 p. [20] zheng, o., mashiwa, n., furushima, t. (2020) evaluation of large plastic deformation for metals by a non-contacting technique using digital image correlation with laser speckles, materials & design, 191. doi: 10.1016/j.matdes.2020.108626. [21] park, j., yoon, s., kwon, t., park, k. (2017). assessment of speckle-pattern quality in digital image correlation based on gray intensity and speckle morphology, optics and lasers in engineering, 91, pp. 62-72. doi: 10.1016/j.optlaseng.2016.11.001. [22] pan, b., lu, z., xie, h. (2010). mean intensity gradient: an effective global parameter for quality assessment of the speckle patterns used in digital image correlation, optics and lasers in engineering, 48(4), pp 469-477. doi: 10.1016/j.optlaseng.2009.08.010. [23] strungar, e.m., yankin, a.s., zubova, e.m. babushkin, a.v., dushko, a.n. 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/hrv (za stvaranje adobe pdf dokumenata najpogodnijih za visokokvalitetni ispis prije tiskanja koristite ove postavke. stvoreni pdf dokumenti mogu se otvoriti acrobat i adobe reader 5.0 i kasnijim verzijama.) /hun 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can be opened with acrobat and adobe reader 5.0 and later.) >> /namespace [ (adobe) (common) (1.0) ] /othernamespaces [ << /asreaderspreads false /cropimagestoframes true /errorcontrol /warnandcontinue /flattenerignorespreadoverrides false /includeguidesgrids false /includenonprinting false /includeslug false /namespace [ (adobe) (indesign) (4.0) ] /omitplacedbitmaps false /omitplacedeps false /omitplacedpdf false /simulateoverprint /legacy >> << /addbleedmarks false /addcolorbars false /addcropmarks false /addpageinfo false /addregmarks false /convertcolors /converttocmyk /destinationprofilename () /destinationprofileselector /documentcmyk /downsample16bitimages true /flattenerpreset << /presetselector /mediumresolution >> /formelements false /generatestructure false /includebookmarks false /includehyperlinks false /includeinteractive false /includelayers false /includeprofiles false /multimediahandling /useobjectsettings /namespace [ (adobe) (creativesuite) (2.0) ] /pdfxoutputintentprofileselector /documentcmyk /preserveediting true /untaggedcmykhandling /leaveuntagged /untaggedrgbhandling /usedocumentprofile /usedocumentbleed false >> ] >> setdistillerparams << /hwresolution [2400 2400] /pagesize [612.000 792.000] >> setpagedevice microsoft word numero_41_art_50.docx x. wu et alii, frattura ed integrità strutturale, 41 (2017) 388-395; doi: 10.3221/igf-esis.41.50 388 carbon nano-tubes in improving the mechanical property of cement-based composite materials xu wu, li dai institute of architecture and civil engineering, nantong institute of technology, nantong, jiangsu, 226000, china wxlrgwu@163.com abstract. carbon nano-tubes as a kind of novel nanometer material have been extensively applied in cement-based composite materials to improve their properties. this study prepared carbon nano-tubes cement based composite materials by evenly scattering carbon nano-tubes in cement materials using ultrasonic method and emphatically investigation the improvement of the mechanical property. the results demonstrated that, the addition of carbon nano-tubes could significantly relieve the mechanical properties of cement based composite materials. when the mixing amount of carbon nano-tubes reached the optimal value, i.e., 0.1%, the improvement of the mechanical property of the carbon nano-tubes cement based composite materials was the best. the microstructure analysis using scanning electron microscope suggested that, carbon nano-tubes produced bridging and pullout effects in the cement-based materials, which enhanced the damage resistance of the cement based materials. keywords. carbon nano-tubes; cement-based composite material; mechanical property. citation: wu, x., dai, l., carbon nano-tubes in improving the mechanical property of cement-based composite materials, frattura ed integrità strutturale, 41 (2017) 388-395. received: 11.04.2017 accepted: 15.05.2017 published: 01.07.2017 copyright: © 2017 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. introduction ith the rapid development of modern society, requirements for the mechanical property of cement concrete whose demand is the largest and which is the most widely used construction material has become stricter and stricter. the traditional cement materials have been far from enough to satisfy the requirements on material properties in special occasions such as earthquake and temperature stress effect in dam body. how to improve the mechanical property of cement concrete and then perform effective test has been an issue concerned by the world [1]. relevant studies [2-4] suggested that, the addition of an appropriate amount of carbon materials in cement base can not only enhance the mechanical property and crack resistance, but also impart a favorable voltage-sensitive property. carbon nano-tubes, a kind of tubular nano carbon material containing graphite crystal, has nearly perfect mechanical performance compared to the traditional carbon fibres. it is the fibre material with the best comprehensive performance so far. carbon nano-tubes can be typed into single-wall carbon nano-tubes and multiple-wall carbon nano-tubes according to the layers of w x. wu et alii, frattura ed integrità strutturale, 41 (2017) 388-395; doi: 10.3221/igf-esis.41.50 389 carbon atoms. single-wall carbon nano-tubes which was expensive is generally applied in the fields of field emission panel display and sensors. multiple-wall carbon nano-tubes which is low in cost and has achieved scale production and extensive application is usually applied in the study of reinforced composite materials. base materials such as polymer base, metal base and ceramic base are frequently studied, while few studies concern cement-based composite materials [5-9]. in 2003, campillo i. et al. [10] from spain reported the reinforcement of cement-based composite materials using carbon nano-tubes for the earliest and found single-wall carbon nano-tubes and multiple-wall carbon nano-tubes could improve the compressive strength of cement paste for 6% and 30% respectively in 14 days and that effective control of the structure of multiple-wall carbon nano-tubes in cement base could significantly enhance its strength. in 2008, kowald t. et al. [11] from suegen in germany investigated the effects of unprocessed and oxidized multiple-wall carbon nano-tubes on cement hydration products taking pure c3s as the simplified model system as well as the effects of multiple-wall carbon nano-tubes on the micro-mechanical properties of cement hydration products using nanoindentation technology. the unprocessed multiple-wall carbon nano-tubes increased the number of low-density c-s-h in composite materials and oxidized multiplewall carbon nano-tubes increased the high-density c-s-h. they also pointed out that multiple-wall carbon nano-tubes could enhance the performance of ultra high performance concrete as the regulation phase of cement hydration product. since 2008, studies on carbon nano-tubes cement-based composite materials has began around the world. luo j.l. et al. [12] analyzed the correlation between the electrical resistivity of carbon nano-tubes cement-based composite materials and the mixing amount of carbon nano-tubes and further analyzed its voltage-sensitive property. morsy m.s. et al. [13] found adding multi-walled carbon nano-tubes whose mass was 0.02% that of cement could enhance its compressive strength. for material researchers, it is urgent to study on the application of carbon nano-tubes in cement-based materials.the breakthrough of production and application of carbon nano-tubes are bound to motivate the development of nanotechnology and the emergence of related high-tech industries, which may induce a new scientific reformation and bring huge benefits to the whole society. in this study, carbon nano-tubes were evenly scattered in water solution by ultrasonic method using cetyl trimethyl ammonium bromide (ctab), and then the solution was added into cement paste to investigate mechanical and endurance performance of the carbon nano-tubes cement-based composite materials. test profile raw materials for test arbon nano-tubes which was prepared by chemical vapor deposition and purchased from a nanometer material enterprise in shandong, china was used; its physical parameters are shown in tab. 1, and the structure diagram is shown in fig. 1. p·o 42.5 ordinary portland cement produced by qingdao, shandong, china was used, and its physical properties and mineral composition are shown in tab. 2. ctab, white chemical powder, was used. the water reducing agent used was polycarboxylate superplasticizer (solid content: 20%; water-reducing rate: 30%; jiangsu bote new material co., ltd., china). purity/% external diameter/nm length/μ m specific surface area/(m2/g) ash content/% electric conductivity/(s/cm) -cooh content/% >95 10-20 10-30 40-300 <1.5 100-1000 2.00 table 1: the basic physical parameters of carbon nano-tubes. specific surface area/(m2/kg) setting time/min stability rupture strength/mpa compressive strength/mpa mineral composition/% initia l set final set 3d 28d 3d 28d c3s c2s c3a c4af so3 330 191 247 qualified 5.2 8.1 31.2 65.2 48.12 24.03 9.88 11.02 2.24 table 2: the physical properties and mineral composition of the cement. c x. wu et alii, frattura ed integrità strutturale, 41 (2017) 388-395; doi: 10.3221/igf-esis.41.50 390 figure 1: the schematic diagram of carbon nano-tubes structure. specimen moulding and testing carbon nano-tubes were added into the solution of ctab. the mass ratio of ctab to carbon nano-tubes was 10:1. ultrasonic dispersion processing was performed using a ultrasonic apparatus, for 60 min, to ensure carbon nano-tubes evenly distributing in the water solution to form carbon nano-tubes suspension. then the carbon nano-tubes suspenion was poured into a cement mixer along with the cement; the water cement ratio was 0.30. the stirring lasted for 6 min; the ratio of duration of stirring at the low speed to duration of stirring at the high speed was 2:1. the mixture of carbon nano-tubes and cement paste in the mixing pot was rapidly poured into a standard test mould in a specification of 40mm×40 mm×160 mm and another one in a specification of 40 mm×40 mm×40 mm at the end of stirring. it was vibrated to be dense mechanically. the moulds were removed after 24-h standard maintenance. each test specimen was numbered and then put into water at the temperature of (20±1) � for maintenance [14-16]. the mix proportion of the test specimens and the mixing amount are shown in tab. 3. the microstructures of some specimens are shown in fig. 2. sample water to cement ratio (w/c) mix proportion/wt% mwcnts ctab water reducer no.0 0.30 0 0 0.1 no.1 0.30 0.05 0.5 0.1 no.2 0.30 0.10 1.0 0.1 no.3 0.30 0.15 1.5 0.1 no.4 0.30 0.20 2.0 0.1 no.5 0.30 0.25 2.5 0.1 table 3: the mix proportion of carbon nano-tubes cement-based composite materials figure 2: the microstructures of some specimens (the mixing amount of multiple-wall carbon nano-tubes in (a) (d) is 0.05%, 0.1%, 0.2% and 0.25% respectively). x. wu et alii, frattura ed integrità strutturale, 41 (2017) 388-395; doi: 10.3221/igf-esis.41.50 391 property characterization effects of carbon nano-tubes on the bending strength of cement-based composite materials were investigated by performing a bending strength test with a dkz-5000 antifracture test machine based on method of testing cements-determination of strength gb/t 17671-1999 which was formulated according to iso 679:1989 (cement testing method strength determination) whose main content is completely consistent with iso 769; but some points of gb/t 17671-1999 were modified according to the actual condition of china, and the comprehensive strength testing results based on gb/t 176711999 are equal to those based on iso 679:1989. effects of carbon nano-tubes on the compressive strength of cement-based composite materials were investigated by performing a compressive strength test with a why microprocessor controlled fully automatic press machine. the morphology of carbon nano-tubes cement-based composite materials was characterized using a su-70 thermal field emission scanning electron microscope, and the mechanism of interaction between carbon nano-tubes and cement was initially explored. result discussion mechanical properties he testing results of the mechanical properties of carbon nano-tubes cement-based composite materials after seven days of maintenance are shown in fig. 3. fig. 3 suggests that, the bending and compressive strength of carbon nanotubes cement-based composite materials was significantly improved compared to the blank group, 10% mostly. when the mixing amount of carbon nano-tubes was 0.10 wt% that of cement, the bending strength improved for 25.36%, i.e., 6.96 mpa, and the compressive strength improved for 21.8%, i.e., 40.94 mpa. the variation tendencies of bending and compressive strength of the test specimens were the same, increasing at first and decreasing after reaching the maximum value. it could be concluded that a small amount of carbon nano-tubes could produce a great influence on the mechanical properties of cement-based composite materials, but the changes in the strength were little when the mixing amount of carbon nano-tubes exceeded a certain value, i.e., excessive carbon nano-tubes might reduce the compressive and bending strength instead of improving the strength. figure 3: mechanical properties of cement-based composite materials test specimens which were mixed with different amount of carbon nano-tubes after seven days of maintenance. the testing results of the mechanical properties of carbon nano-tubes cement-based composite materials after 14 days of maintenance are shown in fig. 4. fig. 4 demonstrates there were changes in the variation tendencies of the bending and compressive strength of the test specimens; the bending strength fluctuated greatly with the increase of carbon nano-tubes amount, increasing first and then decreasing. the optimal values of the bending and compressive strength of cement-based composite materials were different. when the mixing amount of carbon nano-tubes was 0.10% that of cement, the bending strength reached the maximum value, 8.14 mpa, suggesting an improvement of 15.67%. when the mixing amount of carbon nano-tubes was 0.15%, the compressive strength reached the maximum value, 58.27 mpa, suggesting an improvement of 17.59%. t x. wu et alii, frattura ed integrità strutturale, 41 (2017) 388-395; doi: 10.3221/igf-esis.41.50 392 figure 4: the mechanical properties of cement-based composite materials test specimens which were mixed with different amount of carbon nano-tubes after 14 days of maintenance. the testing results of the mechanical properties of carbon nano-tubes cement-based composite materials after 14 days of maintenance are shown in fig. 5. fig. 5 shows that the compressive and bending strength of carbon nano-tubes cementbased composite materials was significantly improved (10% mostly) compared to the blank group after 28 days of maintenance. when the mixing amount of carbon nano-tubes was 0.10% that of cement, the bending strength reached the maximum value, 9.07 mpa, which was 12.56% higher than the blank controls. when the mixing amount of carbon nanotubes was 0.05%, the compressive strength reached the maximum value, 72.44 mpa, suggesting an improvement of 13.01%. when the mixing amount of carbon nano-tubes was 0.10wt%, the variation of the compressive strength was not obvious but the variation of the bending strength was. the variation tendencies of the compressive and bending strength changed. the bending strength fluctuated significantly with the increase of carbon nano-tubes amount, increasing first and then decreasing. regardless of no.0 blank sample, the curve showed unilateral slow drop. figure 5: the mechanical properties of cement-based composite materials test specimens which were mixed with different amount of carbon nano-tubes after 28 days of maintenance. the variation of the compressive and bending strength of the cement-based composite material test specimens which were mixed with different amount of carbon nano-tubes following the changes of age is shown in fig. 6 and 7. the two figures demonstrated that the compressive and bending strength of the test specimens which was mixed with carbon nano-tubes tended to increase with the changes of age, and the increase amplitude decreased progressively. when the mixing amount of carbon nano-tubes was 0.10%, the improvement of the bending strength was optimal; the bending strength of the aforementioned test specimen was 9.07 mpa after 28 days of maintenance, which was 12.56% higher than that of the blank test specimen. as to the compressive strength, the cement-based composite material test specimen whose content of carbon x. wu et alii, frattura ed integrità strutturale, 41 (2017) 388-395; doi: 10.3221/igf-esis.41.50 393 nano-tubes was 0.05% was the best (72.44mpa), suggesting an improvement of 13.01% after 28 days of maintenance. the improvement of the compressive and bending strength was obvious in the early stage, which indicated carbon nano-tubes could effectively improve the strength of cement in the early stage. with the changes of carbon nano-tubes amount, the compressive and bending strength of the test specimens showed similar tendencies, i.e., increasing first and then decreasing, but the fluctuation of the bending strength was more obvious. according to the results after 7, 14 and 21 days of maintenance, the improvement of the compressive and bending strength was better when the mixing amount of carbon nano-tubes was 0.10%. figure 6: the variation of the bending strength of carbon nano-tubes cement-based composite materials test specimens along with the change of age. figure 7: the variation of the compressive strength of carbon nano-tubes cement-based composite materials test specimens along with the change of age. analysis using scanning electron microscope to further verify the mechanism of carbon nano-tubes in enhancing the mechanical properties of cement-based composite materials, the cross surface of the product was analyzed using a scanning electron microscope (sem); the results are shown in fig. 8. as shown in fig. 8, carbon nano-tubes play a bridging role in the cement base. because of the bridging effect, carbon nano-tubes could bear certain external force and consume external stress damages, which could help inhibiting the further growth of cracks and enhance the strength and toughness of the composite materials. with the growth of crack size or the increase of tensile stress, carbon nano-tubes could inhibit the expansion of cracks and shoulder most of external force. if local fracture occurred, a long and thin carbon tube would form at the fracture site of the cement material, and x. wu et alii, frattura ed integrità strutturale, 41 (2017) 388-395; doi: 10.3221/igf-esis.41.50 394 moreover carbon tubes would consume part of energy in the form of energy consumption in pullout, which could help improving breaking energy and overcoming fragility. figure 8: the observation results of carbon nano-tubes under a sem. conclusions he mixing of a certain amount of carbon nano-tubes can enhance the mechanical properties of cement-based composite materials. after analyzing the condition in the 7th, 14th and 28th d, it was found that the mixing of 0.10 wt% carbon nano-tubes had the best effect in improving the mechanical properties of cement-based composite materials; the bending and compressive strength improved for 12% approximately. in the analysis using sem, it was found that, carbon nano-tubes produced bridging and pullout effects in the cement-based materials and absorbed more damage energy to ensure the integrity of composite materials and protect the cement-based materials from external damages. acknowledgement eneral program of university natural science research of education department of jiangsu, no: (16kjb560011). references [1] lo, t.y., cui, h.z., li, z.g. influence of aggregate pre-wetting and fly ash on mechanical properties of lightweight concrete. waste management, 24(4) (2004) 333-338. [2] hunashyal, a.m., sundeep, g.v., quadri, s.s., et al. experimental investigations to study the effect of carbon nanotubes reinforced in cement-based matrix composite beams. proceedings of the institution of mechanical engineers, part n: journal of nanoengineering and nanosystems, 225(1) (2011)17-22. [3] konsta-gdoutos, m.s., metaxa, z.s., shah, x.p. multi-scale mechanical and fractural characteristics and early-age strain capacity of high performance carbon nanotubes/cement nanocomposites. cemnet and concrete composites, 32(2) (2010) 110-115. [4] chaipanich, a., nochaiya, t., wongkeo, w., torkittikul, p. compressive strength and microstructure of carbon nanotubes-fly ash cement composites. materials science and engineering: a, 527(4-5) (2010) 1063-1067. [5] lahiri, i., seelaboyina, r., hwang, j.y., et al. enhanced field emission from multi-walled carbon nanotubes grown on pure copper substrate. carbon, 48 (2010) 1531-1538. [6] yang, w., thordarson, p., gooding, j.j., et al. carbon nanotubes for biological and biomedical applications. nanotechnology, 41 (2007) 412001-1-8. [7] yan, j., liu, j., fan, z., et al. high-performance supercapacitor electrodes based on highly corrugated grapheme sheets. carbon, 50 (2012) 2179-2188. t g x. wu et alii, frattura ed integrità strutturale, 41 (2017) 388-395; doi: 10.3221/igf-esis.41.50 395 [8] kuznetzov, a.a., lee, s.b., zhang, m., et al. electron field emission from transparent multiwalled carbon nanotube sheets for inverted field emission displays. carbon, 48 (2010) 41-46. [9] kauffman, d.r., sorescu, d.c., schofield, d.p., et al. understanding the sensor response of metal-decorated carbon nanotubes. nano letters, (10) (2010) 958-963. [10] campillo, i., dolado, j.s., porro, a. high-performance nanostructured materials for construction. speciai, publicationroyal society of chemistry, 292 (2004) 215-226. [11] kowald, t., trettin, r., dorbaum, n., et al. influence of carbon nanotubes on the micromechanical properties of a model system for ultra-high performance concrete. proc.2nd international symposium on ultra high performance concrete, (2008) 129-134. [12] luo, j.l., duan, z.d., zhao, t.j. properties of electrical resistivity of fiber-reinforced cement composites with multiwalled carbon nanotubes. journal of harbin institute of technology, 42(8) (2010) 1237-1241. [13] morsy, m.s., alsayed, s.h., aqel, m. hybrid effect of carbon nanotube and nano-clay on phsico-mechanical properties of cement mortar. construction and building materials, 25 (2011) 145-149. [14] cwirzen, a., habermehl-cwirzen, k., penttala, v. surface decoration of carbon nanotubes and mechanical properties of cement/carbon nanotube composites. advances in cement research, 20 (2008) 65-73. [15] yang, z.g., li, y.f., zhou, j., li, y.t. mechanical properties of carbon nanotubes cement-based composites. water power, 8 (2014) 129-132. [16] li, g.y., wang, p.m., zhao, x. mechanical behavior and microstructure of cement composites incorporating surfacetreated multi-walled carbon nanotubes. carbon, 43 (2005) 1239-1245. << /ascii85encodepages false /allowtransparency false /autopositionepsfiles true /autorotatepages /none /binding /left /calgrayprofile (dot gain 20%) /calrgbprofile (srgb iec61966-2.1) /calcmykprofile (u.s. web coated \050swop\051 v2) /srgbprofile (srgb iec61966-2.1) /cannotembedfontpolicy /error /compatibilitylevel 1.4 /compressobjects /tags /compresspages true /convertimagestoindexed true /passthroughjpegimages true /createjobticket false /defaultrenderingintent /default /detectblends true /detectcurves 0.0000 /colorconversionstrategy /cmyk /dothumbnails false /embedallfonts true /embedopentype false /parseiccprofilesincomments true /embedjoboptions true /dscreportinglevel 0 /emitdscwarnings false /endpage -1 /imagememory 1048576 /lockdistillerparams false /maxsubsetpct 100 /optimize true /opm 1 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/hrv (za stvaranje adobe pdf dokumenata najpogodnijih za visokokvalitetni ispis prije tiskanja koristite ove postavke. stvoreni pdf dokumenti mogu se otvoriti acrobat i adobe reader 5.0 i kasnijim verzijama.) /hun 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/pdfxoutputintentprofileselector /documentcmyk /preserveediting true /untaggedcmykhandling /leaveuntagged /untaggedrgbhandling /usedocumentprofile /usedocumentbleed false >> ] >> setdistillerparams << /hwresolution [2400 2400] /pagesize [612.000 792.000] >> setpagedevice microsoft word numero_51_art_14_2636 b. zaoui et alii, frattura ed integrità strutturale, 51 (2020) 174-188; doi: 10.3221/igf-esis.51.14 174 finite element analysis of the thermomechanical behavior of metal matrix composites (mmc) zaoui bouchra, baghdadi mohammed, serier boualem, belhouari mohammed university of djillali liabes, laboratory of mechanics physics of materials (lmpm laboratory), sidi bel abbes, algeria. zaouibouchra55@yahoo.com, mohbagh0@gmail.com , boualems@yahoo.fr, belhouari@yahoo.com abstract. in this work the finite element method (fem) was used to analyze the mechanical behavior of the composite materials subjected to the mechanical loading. this behavior is studied in terms of stress intensity factor variation as a function of the applied stress intensity. the residual stresses induced in the composites, during the elaboration of these composites are taken into consideration in this study. the superimposition of these types of stresses (residuals and commissioning) is simulated here by thermomechanical stresses. the results obtained show that in the vicinity very close to the fibermatrix interface and under the effect of this loading type, the matrix cracks propagate in modes i, ii and iii, and far from the interface, in mode i. the propagation kinetics is slowed down by the interface-crack interaction. the effects of the crack size, the orientation and propagation of the crack, commissioning stresses, the elaboration temperature, fiber physical properties, matrix stiffness and thermomechanical stresses have been highlighted in this work. keywords. composites; crack growth; fem; residual stresses; stress intensity factor (sif); interface. citation: zaoui, b., baghdadi, m., serier, b., belhouari, b., finite element analysis of the thermomechanical behavior of metal matrix composites (mmc), 51 (2020) 174-188. received: 15.09.2019 accepted: 22.11.2019 published: 01.01.2020 copyright: © 2019 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. introduction he composite materials are assembled materials, usually two immiscible components whose mechanical properties complement each to other. this design makes it possible to improve the mechanical characteristics (rigidity, lightness, corrosion, etc.) and to cope with increasingly stringent commissioning conditions, to cope with the conditions of commissioning more and more severe. this explains, the increasing use of the composite material in the industrial sector and especially in the aeronautic domain, aerospace domain, maritime domain, automotive domain and civil engineering domain etc. nevertheless, these materials have a major disadvantage. in fact, during the elaboration process, a residual stress develops during the cooling of the elaboration temperature to ambient temperature. these stresses are generally due to the difference in stiffness materials and the thermal expansion coefficient, between the reinforcing material (fiber) and the matrix, the main constituents of composite materials. t http://www.gruppofrattura.it/va/51/2636.mp4 b. zaoui et alii, frattura ed integrità strutturale, 51 (2020) 174-188; doi: 10.3221/igf-esis.51.14 175 this difference weakens the adhesion between these two components and therefore promotes the initiation and propagation of fatigue microcracks. in fact, the fatigue sub-interfacial microcracks can be initiated in one of these two constituents, and their propagation leads to the ruin of the composite. the initiation of interface cracks may be due either to a poor mechanical attachment, or to the existence of internal shear stresses at the reinforcement-matrix interface. the level of these stresses and the energy of fiber-matrix adhesion, condition the composite rupture behavior. added to commissioning stresses, these stresses (residual stresses) can be fatal for composites. several works have been devoted to the analysis of the composite rupture behavior. thus, hahn chooa and al [1], have shown that, in the case of ni-al metal matrix reinforced by unidirectionally al2o3 alumina fibers, the relaxation of the residual stress, induced during the cooling or heating of the material, depends on the elastic or plastic properties, creep and the volume fraction of the fibers. abou msallem [2], based on thermomechanical and thermokinetic models, they have evaluated the residual stresses using the finite element method (fem), and they have used also, the elastic limit of the resin (matrix) as a criterion for the residual stresses presence. an experimental approach based on the peel-layer method makes it possible to deduce these residual stresses by measuring the moments and the induced curvatures, the residual stresses through the thickness estimated by this method are compared with those calculated from a thermoelastic model and a variational approach. sellam and al [3], using the finite element method (fem), they have analyzed the crack growth and their interaction with the defects. they show that, the propagation in modes i and ii in the composites depends on the cracks location and the defects nature .using the same method (fem), metehri and al [4] have shown that the level and distribution of residual stresses, in polymer matrices, are closely related to the fiber-matrix, fiber-fiber and fiber-interphase interaction. boutabout and al [5] they analyzed numerically also, by the finite element method (fem), the residual stresses developed in the copper-alumina and zirconia-alumina composite materials, they showed that these stresses are closely related to the gap between thermal expansion coefficients of these two constituents. put the interface in shear. mecirdi and al [6] using the finite element method (fem) have highlighted the areas, exposed to the damage risk by a residual stress, developed in the composite which consists of soda-lime matrix and sic fiber. wang and al [7] have shown that the extended finite element method (xfem), is an effective modeling technique for analyzing the initiation and propagation of a crack in composites. a method for evaluating the initial and progressive failure of composite laminates was proposed by chi-seung and al [8], based on the damage criterion and that of puck, respectively. these authors used the puck damage criterion to analyze the crack initiation and propagation in the fiber and the matrix. this latter determines the predominant mode of composite failure, they also show that the presence of defects in the crack propagation direction accelerates its instability. węglewski and al [9], they analyzed experimentally, by neutron diffraction and numerically by the finite element method (fem), the effect of alumina particle size (al2o3) on the level of the residual stresses generated during the processing cooling of the temperature, by sintering the metal matrix composite (chromium) at ambient temperature after cooling the elaboration temperature, this study allowed the development of numerical model of microcracking, induced by the residual stresses allowing the prediction of the effective young modulus of the damaged composite. prabha and sirinivasan [10], using the stresses generated in the fiber and matrix, from direct tests on these two individual materials, have analyzed the degradation of the fiber and the matrix separately, they show that the damage phenomenon is different in these two constituents. jin and al [11] have shown that, the delamination leads to both, a drop in macroscopic elastic stiffness and the mechanical strength of composites, these authors also analyzed the effect of the inclusion size on the macroscopic behavior of composites, they conclude that the inclusions of important size minimize the risk of interface disbanding and reduce the damage threshold. safarabadi [12], analyzed the factors responsible for the formation of the residual stresses in composites and their effects on the fiber and matrix properties, this author presented, in this study, the analytical, numerical and experimental methods for the prediction of thermal residual stresses. mecirdi and al [13], have shown, using the finite element method (fem), that the behavior of the matrix cracks depends on the fiber volume fraction, the fiber-matrix interaction, the crack-inclusion interactions, microcavity and interface cracks. yi zeng and al [14], used the finite element analysis, they showed that the presence of carbide in the c/c composites leads to a significant increase in residual stresses in the pyc near the carbide, which explains why this compound could modify the distribution and the level of these stresses in these composites. zhenyi and al [15], proposed a multiscale model allowing the prediction of residual stresses developed during the process of hardening (polymerization) of the composites and the correlation of the residual stresses at the microscopic and macroscopic scale. they showed that, there is too great gap in the calculation of micro-residual stresses by introducing the multiscale model effect. nelson and al [16] based on a simplified approach to residual stresses modeling in composites, they developed a model (modeling), the experimental results obtained on bimaterial type composites were used to validate the modeling, they conclude that the experimental results are in very good agreement with those obtained from the simulation approach. zhang and al [17] taking into account oriented curved fibers and the rule of change of fiber angles and determining the residual stresses using abaqus, have proposed a mathematical model of stratified composites with variable rigidity for the residual stresses b. zaoui et alii, frattura ed integrità strutturale, 51 (2020) 174-188; doi: 10.3221/igf-esis.51.14 176 prediction induced during the polymerization process, they showed that the residual stresses induced in composites with variable stiffness are reduced by increasing the final angle of the fiber path during the hardening process. kati and al [18], using x-ray diffraction (xrd), they analyzed the residual stresses induced in biphasic composite types ce9gdo1-bla6sr4co2fe8o3-6 (gdc-lscf) obtained by sintering at 1250 °c and used for the manufacture of oxygen transport membranes, they showed that theses stresses put on compression the gdc and in tension the lscf. the scanning electron microscopy has shown that these two compounds crystallize in cubic and rhombohedral spatial groups respectively. this work fits into this context and aims to highlight the residual stresses and their effect on the performance of metal matrix composites. this latter is analyzed, in terms of the stress intensity factor variation (sif) in opening modes (mode i) and in shear modes (modes ii and iii). the majority of the latest scientific work realized until now, do not take into account the residual stresses, induced during the elaboration of the composite strongly localized in the fiber-matrix interface vicinity, in the prediction of the composite damage. the originality of this work lies therefore in the prediction of the rupture behavior of the composite materials subjected to the superposition of these residual stresses to the commissioning stresses. on the other parts, a matrix crack initiated perpendicular to the tensile forces propagates in mixed mode i, ii and iii. the abaqus calculation code, based on the finite element method, was used to achieve this objective. for this purpose, a three-dimensional numerical model has been developed. geometric model developed in this work he finite element method (fem) was used to analyze the matrix cracks behavior in composite materiel subjected to mechanical stresses, thermal stresses and thermomechanical stresses. this last (thermomechanical stresses) simulates the superposition of the residual stresses to those of commissioning stresses. to do this, the abaqus software version 6.11 [19] was used. for this purpose, a three-dimensional model has been developed, this last regroup a metal matrix of parallelepiped shape, having two capillaries, along its main axis, in which two cylindrical fibers are inserted (fig. 1). the latter constitutes an elementary cell of a unidirectional composite. a crack of size "a", initiated in the matrix perpendicular to the main axis of the fiber, and then oriented at an angle "ɵ", relative to the longitudinal axis of the fiber (fig. 1), this crack propagates to the reinforcing material. this structure is subjected to uniaxial tension stresses (fig. 2a). due to the symmetry of the developed model, only half of it has been taken into consideration. for this purpose, the imposed boundary conditions are: uy = urx = urz = 0 (condition of symmetry relative to y) (fig. 2a). figure 1: the analyzed structure. the three-dimensional model developed in this work was meshed globally using the elements of the type c3d8. (an 8node linear brick) (fig. 2). to obtain a correct representation of the displacement field near the crack, the elements called singular are used (elements type barssoum.), as suggested by the abaqus software documentation. the type of singularity 1/√r, for the stress fields are obtained by moving all the intermediate nodes of the elements around the crack heads to a t b. zaoui et alii, frattura ed integrità strutturale, 51 (2020) 174-188; doi: 10.3221/igf-esis.51.14 177 quarter of a distance from the nodes belonging to the considered crack head. the mesh of the crack head was exclusively refined using this special type element (fig. 2). figure 2: the finite elements model. a) boundary conditions, b) total mesh of structure, c) refined mesh in the vicinity of the crack heads. the side sizes of an element, far from the crack and in the crack vicinity, were represented in tab. 1, these sizes and types of mesh, remains the same for all the simulations in this study, to avoid any influence of the mesh on the results. the different components of the analysed structure numbers of elements sizes of elements metal matrix 115200 0.001mm crack front 280 0.001mm fibres 104000 0.001mm composite material globally 219480 0.001mm table 1: numbers and sizes of the mesh elements. reinforcement materials are assumed to be elastic linear isotropic and the matrix is elastic linear isotropic also, whose mechanical and physical characteristics are grouped in tab. 2. the criterion to predict the angle at which a pre-existing crack is propagate used in this work, is the maximum energy release rate criterion (merr), it is based on the work of hussain et al. (1974), nuismer (1975), palaniswamy and knauss (1978), as well as wu (1978). this criterion proposed in abaqus documentation. b. zaoui et alii, frattura ed integrità strutturale, 51 (2020) 174-188; doi: 10.3221/igf-esis.51.14 178 materials young modulus e (mpa) poisson coefficient υ expansion thermal coefficient α(10-6 k-1) nickel (ni) 207000 0.31 13 silicon carbide (sic) 450000 0.17 2.8 silver (ag) 76000 0.37 20 bromine (br) 400000 0.21 4.5 copper (cu) 124000 0.33 17 alumina (al2o3) 350000 0.25 8 table 2: mechanical and physical properties of the constituents of the composites used (serier [20]). results and discussion effect of the elaboration temperature intensity omposites are elaborated at relatively high temperatures. these temperatures promote mechanical bonding between the fiber and the matrix and ensure good adhesion between these two constituents. the adhesion energy, conditioning the fiber-matrix charge transfer, is all the stronger as the elaboration temperature is higher. nevertheless, this last (elaboration temperature) induces in these two components residual stresses in the vicinity very close of the fiber-matrix interface due to the difference between the thermal expansion coefficient of the fiber and the matrix. in fact, at the elaboration temperature of the composite, the metal matrix retracts much more than the ceramic fiber; this phenomenon resulting shear stresses at the matrix-fiber interface due to the equalization of the elastic deformations of the matrix and the fiber: 0 0( ) and ( )m m f ft t t t       (1) αm and αc are the thermal expansion coefficients of the matrix and the fiber respectively. with δα = αmαc. δt = (t-t0) is the temperature gap from the reference temperature. these internal stresses are a function not only of the gap between the thermal expansion coefficients of the matrix and the fiber, of the gap between the temperature at which the thermoelastic deformation disappears and the elaboration temperature but also of the elastic modulus of the two constituents (fiber and matrix). for a long-fiber unidirectional composite, in the axial middle phase matrix, the thermal residual stresses induced during the elaboration process of composite material 〈σth33〉m, and in fiber, 〈σth 33〉f, are expressed by (withers and al [21]): 33 m m fth f f f m m f e e t f e f e          (2) 33 f m fth m f f m m f e e t f e f e         (3) fm and ff are the volume fractions of the matrix and the fiber respectively, em and ef their respective elastic modulus. in some cases, the residual stresses of thermal origin are critical to facilitate the transfer of stresses from one phase to another. in fact, in a composite material of long fiber, the clamping of the fibers by the matrix during its cooling of the elaboration temperature, determines the level of the frictional stress necessary to pull the fiber out of the matrix. for a long, insulated fiber in a unidirectional metal matrix composite (mmc), the radial residual stress of matrix-fiber clamping is expressed by (withers and al [21]): c b. zaoui et alii, frattura ed integrità strutturale, 51 (2020) 174-188; doi: 10.3221/igf-esis.51.14 179 (1 ) (1 ) m fth n m f f m e e t e e           (4) νm and νf are the poisson coefficients of the matrix and the fiber respectively. this component, of the residual stresses, reinforces the adhesion between the matrix and the fiber and disadvantages the delamination of the composites. generally, the metal matrix composites are composed of matrices whose a thermal expansion coefficient is much higher than that of the fiber, which generates more intense residual stresses. the highly localized residual stresses at the matrix-fiber interface can constitute a barrier for charge transfer, from the ductile metal matrix to the rigid fiber. on the other hand, added to the commissioning stresses, these stresses (residual stresses) can be responsible for the composites damage by initiation and propagation of fatigue cracks. these stresses are generated during the cooling of the elaboration temperature, initially high, to ambient temperature. according to the relations (1), (2) and (3), this temperature generates more intense residual stresses in unidirectional metal matrix composite (mmc). therefore, the analysis of this temperature effect is of great use, in other words, is of great value for the performance of the cmm. to do this, we chose a nickel matrix composite "ni" reinforced by unidirectional silicon carbide fibers "sic" elaborated at given temperatures. to simulate the residual stress effect, a fatigue crack of size "a" is initiated in the matrix. far from the crack, under elastic residual stress effect, the fibers are axially in compression and the matrix in tension, as shown by metahri and al [4]. the result obtained, clearly defined that, under the effect of these stresses and in the vicinity very close of the fiber-matrix interface, the matrix crack propagates in mixed modes i, ii, and iii (fig. 3).it is these non-zero values of stress intensity factors obtained in the simulation in three modes that are characteristic of such growth. these ruptures criteria are all the more important as the composites are elaborated at high temperatures. the residual tensile stresses in the matrix act as a crack opening stresses. in mode i, the stress intensity factor values increase with the crack size and with the temperature, after then drop as the crack front, approach the interface (fig. 3a). it is the crack-interface interaction that is responsible for the decreasing of the matrix crack propagation speed to the fiber. in fact, the interaction of strongly localized stress fields at the crack fronts and at the fiber-matrix interface leads to a reduction of the stress intensity factor in the mode i. for this purpose, in the vicinity very close of the fiber-matrix interface, the crack propagates essentially under the action of highly concentrated residual stresses at the interface. when the crack fronts crosses the interface, this parameter drops abruptly. in the fiber, the residual stresses deal as compression stresses which act as closure stresses of the crack (fig. 3a). the negative values of the stress intensity factor at the crack head are characteristic of this closure (fig. 3a). this behavior clearly shows that the propagation of the matrix crack is being finally stopped by the fiber and whatever the elaboration temperature of the composite. the crack propagation, in modes ii and iii, intervenes only when the front of the matrix crack tends towards the interface (a = 13μm) and crossed the interface (a = 15μm) (fig. 3b and 3c), beyond this size the crack propagates in the fiber is in pure mode i. the propagation kinetics is all the stronger as the composite is elaborated at high temperatures. this kinetics are defined in terms of stress intensity factor variation in shear modes (mode ii and mode iii) (fig. 3b and 3c). far from the fiber, no propagation in these two modes is observed, the stress intensity factors characteristic of these modes are of zero values (fig. 3b and 3c). this behavior clearly illustrates that matrix crack initiated far from the interface propagates in pure opening mode (mode i). its development towards the fiber is done both, by shearing and by the opening of its lips. it is the residual stress, of tension in the matrix and the compression in the fiber that is responsible for such propagation. the results illustrated in fig. 3 show that the propagation kinetics is even stronger than the composite is elaborated at high temperatures. the crack propagation, in mode i, towards the fiber is broken by the compression residual stresses induced in this component. but, by penetrating the fiber, the crack propagates in mixed mode ii and iii by shearing of its lips (fig. 3b and 3c). this clearly illustrates that, under residual stress effect, the crack propagation mode in the matrix and in the fiber is different. it is the fiber-matrix interaction that is responsible for crack growth in shear modes (mode ii and iii).the results obtained in this part of the work show that under the residual stress effect, a crack, initiated in the matrix, propagates in pure mode i when its front is located relatively far from the interface with the fiber and in mixed modes i, ii and iii when his front approaches towards this interface. in the latter case, the crack propagates preferentially in the open mode (mode i). the very high values of stress intensity factors are characteristic of such predominance (fig. 3a). the stress intensity factors at the heads of a matrix crack increase with the increase of its size and with the increase of the elaboration temperature of the composite; by penetrating the fiber (the crack penetrates the fiber), the matrix crack propagates only by shear of its lips in modes ii and iii. this elaboration temperature of the composite material is a determining parameter of the fiber-matrix adhesion; its increase leads to high adhesion energies between these two b. zaoui et alii, frattura ed integrità strutturale, 51 (2020) 174-188; doi: 10.3221/igf-esis.51.14 180 constituents of the composite and ensures a better resistance to the disbanding phenomenon. however, this temperature resulting a residual stress that can lead to the initiation and propagation of fatigue cracks and a premature damage to the composite. 0,0000 0,0025 0,0050 0,0075 0,0100 0,0125 0,0150 0,0175 -200 -150 -100 -50 0 50 100 150 200 k i ( m p a. m m 1/ 2 ) a (mm) t= 400°c t = 600°c t = 800°c matrix fiber a) 0 100 200 300 400 500 600 700 800 900 -1 0 1 2 3 4 5 6 7 8 9 k i i ( m p a. m m 1/ 2 ) t(°c) a = 0.004 mm a = 0.008 mm a = 0.012 mm a = 0.013 mm a = 0.016 mm b) 0 100 200 300 400 500 600 700 800 900 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 a = 0.004 mm a = 0.008 mm a = 0.012 mm a = 0.013 mm a = 0.016 mm k i ii ( m p a. m m 1/ 2 ) t(°c) c) figure 3: variation of the stress intensity factors. a) in mode i, b) in mode ii, c) in mode iii, according to the elaboration temperature and the crack size. effect of physical properties (thermal expansion coefficient) relations (1), (2) and (3) show that for a given elaboration temperature, the difference between the thermal expansion coefficients of the two constituents of the composite (fiber and matrix) conditions the thermoelastic deformations and therefore the thermally induced stresses. in this part, the effect of this physical parameter on the behavior of matrix cracks is analyzed. the results obtained in the fig. 4 shown that the crack is all the more unstable in mode i, ii and iii when this difference, between the thermal expansion coefficients of the fiber and matrix, is more important, and that the predominant mode is the opening mode (fig. 4). in fact, the values of the relative stress intensity factor in this mode (opening mode) are much higher than those corresponding to modes ii and iii (shearing modes). b. zaoui et alii, frattura ed integrità strutturale, 51 (2020) 174-188; doi: 10.3221/igf-esis.51.14 181 0,0 2,5 5,0 7,5 10,0 12,5 15,0 17,5 20,0 22,5 25,0 -20 -10 0 10 20 30 40 50 60 k ( m p a. m m 1/ 2 )  (10-6 k-1) k i ( mode i ) k ii ( mode ii ) k iii ( mode iii ) figure 4: variation of the stress intensity factor in modes i, ii and iii as a function of the gap of the thermal expansion coefficients of the matrix and the fiber: a = 13mm, δt = 800 ° c. 0,000 0,005 0,010 0,015 0,020 0,025 -450 -400 -350 -300 -250 -200 -150 -100 -50 0 50 100 150 200 k i ( m p a. m m 1/ 2 ) a (mm) t = 400°c t = 600°c t = 800°c fiber matrix a) 0,000 0,005 0,010 0,015 0,020 0,025 -1 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 a (mm) k i i ( m p a. m m 1/ 2 ) t = 400°c t = 600°c t = 800°c matrix fiber b) 0,000 0,005 0,010 0,015 0,020 0,025 -25,0 -22,5 -20,0 -17,5 -15,0 -12,5 -10,0 -7,5 -5,0 -2,5 0,0 2,5 k i ii ( m p a. m m 1/ 2 ) a (mm) t = 400°c t = 600°c t = 800°c matrix fiber c) figure 5: effect of elaboration temperature of the composite on the matrix crack propagation. a) in mode i, b) in mode ii, c) in mode iii. b. zaoui et alii, frattura ed integrità strutturale, 51 (2020) 174-188; doi: 10.3221/igf-esis.51.14 182 effect of crack propagation (crack sizes) under the same simulation conditions of the previous study, the effect of the elaboration temperature of the composite, on the crack propagation, initiated in the matrix perpendicular to the main axis of the fiber, is analyzed. to do this, this crack propagates in the direction of the fiber (fig. 5a, b and c). the results obtained showed that, in mode i, the crack propagates only in the matrix. in this case, the stress intensity factor increases with the advance of the crack and with the increase of the elaboration temperature of the composite .the normal compressive residual stresses induced in the fiber cause the crack lips to close (fig. 5a).the negative values of the stress intensity factor are characteristic of this closure. this crack does not propagates in mixed modes (mode ii and iii) only if its heads tends towards the interface (fiber-matrix interface), in this zone of the composite, the stress intensity factors values in these modes (mode ii and iii) reach their maximum values in the matrix and in the fiber (fig. 5b and 5c).in other words, in this zone the crack propagates in mixed mode i, ii and iii; far from this zone, this crack develop in mode i in the matrix and in modes ii and iii in the fiber (fig. 5a, b and c).the crack crossing the fiber by shearing its lips (modes ii and iii). the crack propagation kinetics in the composite is all the stronger as the fibers are jointly bonded to the matrix at high temperatures. 0,000 0,005 0,010 0,015 0,020 0,025 -200 -175 -150 -125 -100 -75 -50 -25 0 25 50 75 100 k i ( m p a. m m 1/ 2 ) a (mm) t = 400°c t = 600°c t = 800°c matrix fiber a) 0,000 0,005 0,010 0,015 0,020 0,025 -40 -30 -20 -10 0 10 20 30 40 50 60 70 80 90 100 k i i ( m p a. m m 1/ 2 ) a (mm) t = 400°c t = 600°c t = 800°c matrix fiber b) 0,000 0,005 0,010 0,015 0,020 0,025 -14 -12 -10 -8 -6 -4 -2 0 2 4 6 8 k i ii ( m p a. m m 1/ 2 ) a (mm) t = 400°c t = 600°c t = 800°c matrix fiber c) figure 6: variation of the stress intensity factor of the crack oriented at 45 ° according to its size and the composite elaboration temperature. a) in mode i, b) in mode ii, c) in mode iii. b. zaoui et alii, frattura ed integrità strutturale, 51 (2020) 174-188; doi: 10.3221/igf-esis.51.14 183 effect of crack orientation the residual stresses of thermal origin effect on the behavior of a matrix crack, oriented at 45 ° with respect to the longitudinal axis of the fiber, are analyzed in the following (fig. 6). it is clearly shown that such a crack propagates in the matrix in mixed modes i, ii and iii and in the fiber in shear modes ii and iii (fig. 6a, b and c). it is these non-zero values of the stress intensity factors in these three modes that are characteristic of this mode of growth. these rupture parameter values are all the more important as the ni / sic composite is elaborated at relatively high temperatures. in opening mode and under the residual stress effect, the crack propagates only in the matrix; in the fiber these stresses act as closing stresses (fig. 6a). this crack propagates by shearing of its lips (modes ii and iii) only when its front tends towards the fiber-matrix interface (fig. 6b and 6c). the crack is all the more unstable as the composite is elaborated at high temperatures. our results show that under the residual stress effect, the a matrix crack, oriented at 45 ° propagates in the matrix, far from the interface with the fiber in pure mode i, and in the close vicinity of this interface in mixed modes i, ii and iii and in the fiber in mixed mode ii and iii. in mode i (opening mode), the residual compression stresses induced in the fiber, act as crack closure stresses, which explains the negative values of the stress intensity factor. effect of commissioning stresses (applied stress intensity) under the same simulation conditions, the behavior of the same structure as previously analyzed, is subject to commissioning stresses of varying amplitude, to put in the cracking conditions, the structure containing a matrix crack is solicited in uniaxial tension along the fiber (fig. 1).such a loading leads to a crack propagation in pure mode i (opening mode) whose stress intensity factor increases with its advance towards the fiber, its threshold value is reached when its front approaches the fiber-matrix interface (fig. 7).from this zone, this failure criterion drops, and then increases rapidly when this crack front crosses the interface and propagates in the fiber. it is the strong crack-interface interaction that is responsible for this drop. more severe commissioning conditions, defined by more intense applied stresses, lead to a high instability of the crack, defined by the high values of the stress intensity factor. it is clearly defined that the speed of cracks propagation is strongly slowed down in the matrix in the vicinity of the interface (fig. 7). remember, that the values of the stress intensity factors in mode ii and iii are extremely low and will not be discussed here. 0,0000 0,0025 0,0050 0,0075 0,0100 0,0125 0,0150 0 5 10 15 20 25 30 35 40 45 k i ( m p a. m m 1/ 2 ) a (mm)  = 50 mpa  = 80 mpa  = 120 mpa matrix fiber figure 7: variation of the stress intensity factor in mode i, as a function of the commissioning stresses intensities and the matrix crack size. for a better analysis of the intensity of the commissioning stresses effect, the fig. 8 shows, as a function of the crack size, the evolution of stress intensity factor in the mode i from the matrix to the fiber. in this case, the matrix crack, initiated perpendicular to the direction of traction, crosses the matrix, the interface and the fiber with a non-uniform propagation speed. in fact, it is slow in the matrix and accelerated in the fiber. thus, the increase of the curve slope of the matrix b. zaoui et alii, frattura ed integrità strutturale, 51 (2020) 174-188; doi: 10.3221/igf-esis.51.14 184 towards the fiber is characteristic of this propagation kinetics variation of the crack. when the crack crosses the entire fiber and tends towards the second interface, this speed is again slowed down by the strong crack-interface interaction. this behavior is all the more marked as the commissioning stress is more intense. 0,000 0,005 0,010 0,015 0,020 0,025 0 10 20 30 40 50 60 70 80 k i ( m p a. m m 1/ 2 ) a (mm)  = 50 mpa  = 80 mpa = 120 mpa matrix fiber figure 8: effect of the commissioning stress intensities on matrix crack propagation in mode i. 0,000 0,005 0,010 0,015 -200 -150 -100 -50 0 50 100 150 k i ( m p a. m m 12 ) a (mm) t = 400°c,  = 120 mpa t = 600°c,  = 80 mpa t = 800°c,  = 50 mpa matrix fiber a) 0,000 0,005 0,010 0,015 0 2 4 6 8 10 t = 400°c,  = 120 mpa t = 600°c,  = 80 mpa t = 800°c,  = 50 mpak i i ( m p a. m m 1/ 2 ) a (mm) matrix fiber b) 0,000 0,005 0,010 0,015 -3,0 -2,5 -2,0 -1,5 -1,0 -0,5 0,0 0,5 1,0 t = 400°c,  = 120 mpa t = 600°c,  = 80 mpa t = 800°c,  = 50 mpa fibermatrix k i ii ( m p a. m m 12 ) a (mm) c) figure 9: variation of the stress intensity factor according to applied thermomechanical stresses intensities. a) in mode i, b) in mode ii, c) in mode iii. b. zaoui et alii, frattura ed integrità strutturale, 51 (2020) 174-188; doi: 10.3221/igf-esis.51.14 185 effect of thermomechanical stresses thermomechanical stresses simulate, here, is the superposition of commissioning stresses and thermal residual stresses. this energy accumulation, in the case of composite materials, is largely responsible for their premature damage by initiation and propagation of fatigue cracks. for this purpose, the demonstration of the superposition effect on the behavior of a matrix crack is of great importance for the performance of metal matrix composites. to do this, the same conditions of solicitations and simulations as those used previously were retained. under the superposition effect, the crack propagates in the matrix is of pure mode i (opening mode) and in the vicinity very close to interface, in mixed modes i, ii and iii and in the fiber in shear modes ii and iii (fig. 9b and 9c).in mode i, in the fiber, the commissioning stresses of tension are retrenching from the residual stresses of compression, these last act like closing forces, this last (closing forces) is defined by the negative values of the stress intensity factor (fig. 9a).in the matrix the commissioning stresses and the residual stresses are added, which makes the matrix vulnerable to damage by cracking. under the thermomechanical stress effect, the matrix crack, penetrates and propagates in the fiber by shearing its lips (fig. 9b and 9c). thus, and in mode i (fig. 9a), this superposition leads to a high instability of the matrix crack, defined by the strong values of the stress intensity factor. for this purpose, this stresses accumulation can lead to the initiation and propagation of fatigue cracks, may cause premature damage of mmc, at stresses well below the rupture threshold of this material. as mentioned above, a crack initiated perpendicularly to the longitudinal axis of the fiber and subjected to tension stresses along this axis, propagates in pure opening mode. the crack propagates in modes ii and iii, results from the residual stresses alone (fig. 9b and 9c).these results show that this mode (modes ii and iii) of rupture is preponderant only when the tip of this crack is localized, in the matrix or the fiber, very close to their interface (fiber-matrix interface).this behavior is all the more marked as the composite elaborated at high temperatures. our results clearly show that, the composites elaborated at high temperatures generate in the matrix and in the fiber, in the vicinity very close of their interface, a residual stress of high intensities. these stresses are the main causes of the matrix cracks instability, and especially when they are superimposed on commissioning stresses. this superposition is often responsible for the premature damage of the fibers, by the initiation and propagation of fatigue cracks. it is clear that, the fiber and the matrix are perfectly bonded only at too high temperatures. at these temperatures, the fiber-matrix bonds are too strong, and promote the charge transfer from the matrix to the fiber. nevertheless, as our results show that, these temperatures weaken the composite by the introduction of residual stresses. this latter, can be partially relaxed by the interposition, between the matrix and the fiber, of an interphase whose thermal expansion coefficient of intermediate value between the two components of the composites. 0,0000 0,0025 0,0050 0,0075 0,0100 0,0125 0,0150 -60 -50 -40 -30 -20 -10 0 10 20 30 40 50 60 70 80 k i ( m p a. m m 1/ 2 ) a(mm) fiber al 2 o 3 fiber bore fiber sic matrix fiber a) 0,0000 0,0025 0,0050 0,0075 0,0100 0,0125 0,0150 -200 -175 -150 -125 -100 -75 -50 -25 0 25 50 75 100 125 150 k i ( m p a. m m 1/ 2 ) a (mm) fiber al 2 o 3 fiber bore fiber sic matrix fiber b) figure 10: variation of the stress intensity factor, in mode i according to the nature of the fiber and the intensity of the applied thermomechanical stresses. a) δt = 400 ° c, σ = 120 mpa, b) δt = 800 ° c, σ = 50 mpa. effect of the nature of the matrix and the fiber as we have shown previously, the nature of the matrix and the fiber, defined in the thermomechanical loading by their young’s modulus and their thermal expansion coefficients, determine the level of the stresses originally mechanical and thermal. in this part, we analyze this nature effect on the matrix crack behavior as a function of the intensity of the applied thermomechanical stresses and the crack size (fig. 10 and 11). the matrix chosen for this study is nickel. b. zaoui et alii, frattura ed integrità strutturale, 51 (2020) 174-188; doi: 10.3221/igf-esis.51.14 186 in mode i, in the matrix, the stress intensity factor increases with the decrease of the thermal expansion coefficients of the fiber and with the crack size (fig.10a).compared to this factor resulting from commissioning stresses and residual stresses originally thermal separately, this propagation parameter (sif) resulting from the thermomechanical stresses is more important (fig.10). the comparative analysis of the results, illustrated in figs. 10a and 10b, show that, in mode i, the crack is all the more unstable as the intensity of the applied thermomechanical stresses is greater. in the fiber, this type of stress leads to the stability of the crack by the closing of its lips. the results in fig. 11, shows the stress intensity factor variation in mode i as a function of the matrix nature reinforced by the sic fiber and the intensity of the applied thermomechanical stresses. in the matrix, this factor increases with the size of the crack (fig. 11a) and the intensity of the applied thermomechanical stresses (fig. 11b). 0,0000 0,0025 0,0050 0,0075 0,0100 0,0125 0,0150 -50 -40 -30 -20 -10 0 10 20 30 40 50 60 70 80 90 100 110 120 matrix ni matrix cu matrix ag k i ( m p a. m m 1/ 2 ) a (mm) fibermatrix a) 0,0000 0,0025 0,0050 0,0075 0,0100 0,0125 0,0150 -200 -175 -150 -125 -100 -75 -50 -25 0 25 50 75 100 125 150 175 matrix ni matrix cu matrix ag k i ( m p a. m m 1/ 2 ) a (mm) fibermatrix b) figure 11: variation of the stress intensity factor, in mode i according to the nature of the matrix and the intensity of the applied thermomechanical stresses. a) δt = 400 ° c, σ = 120 mpa, b) δt = 800 ° c, σ = 50 mpa. conclusion he results obtained in this study explicitly show that: under the residual stress effect, a matrix crack propagates at the heart of the matrix in pure mode i, in the vicinity very close of the fiber-matrix interface in mixed modes i, ii and iii, and in the fiber in mixed shear modes ii and iii. the opening mode is the predominant mode. residual stresses in the matrix are responsible for opening the crack lips (mode i), and compression in the fiber cause it to close; in mode i, the propagation kinetics of the matrix crack is all the stronger as the composite is elaborated at high temperatures. in the vicinity very close of the fiber-matrix interface, this propagation kinetics is slowed down. the lower values of the stress intensity factor are characteristic of this slowdown; under the residual stress effect, a matrix crack, oriented, with respect to the axis of the fiber, propagates in the heart of the matrix and in the vicinity very close to the fiber-matrix interface, in mixed modes i, ii and iii. such a crack crosses the fiber-matrix interface by shearing of its lips (modes ii and iii). the instability of the crack grows with the increase of the temperature of composite elaboration; under the effect of tension commissioning stress of the composite, the matrix crack develops in pure mode i and penetrates the fiber by opening its lips. the propagation kinetics is strongly slowed down when its front approaches very close to the fiber-matrix interface and then grows rapidly in the fiber. this behavior is all the more accentuated as these stresses are more severe; under the superposition action of the residual stresses to the commissioning stresses, the matrix crack propagates more quickly under the effect of these two stresses taken separately. the high stress intensity factor values in modes i, ii and iii are characteristic of this strong instability of the crack. the commissioning tension stresses add to the residual stresses in the matrix accelerates the propagation velocity of the crack in this matrix and makes this component vulnerable to damage t b. zaoui et alii, frattura ed integrità strutturale, 51 (2020) 174-188; doi: 10.3221/igf-esis.51.14 187 by cracking. in the fiber, the commissioning tension stresses retract the residual stresses of compression and lead to the mode i closure of the crack. for this purpose, the crack propagates, in the matrix, in mixed modes i, ii and iii, the opening mode (mode i) is predominant, and in the fiber in shear modes ii and iii. references [1] hahn, ch., a.m. bourke, m. and r. daymond, m. (2001). a finite-element analysis of the inelastic relaxation of thermal residual stress in continuous-fiber-reinforced composites. composites science and technology, 61, pp. 17571772. doi: 10.1016/s0266-3538(01)00075-6. [2] msallem, y.a. (2008). caractérisation thermique et mécanique d'un matériau composite aéronautique pendant le procédé d'élaboration : contribution à l'estimation des contraintes résiduelles. thèse en partenariat avec institut de recherche en génie civil et mécanique et de école centrale de nantes. [3] sellam, s., serier, b., bouafia, f., bachir bouidjra, b. and sardar, s. h. (2013). analysis of the stresses intensity factor in alumina–pyrex composites. journal computational materials science, 72, pp. 68–80. doi: 10.1016/j.commatsci.2013.01.030 [4] metehri, a., serier, b., bachir bouiadjra, b., belhouari, m. and mecirdi m.a.(2009). numerical analysis of the residual stresses in polymer matrix composites. materials and design journal, 30, pp. 2332-2338. doi: 10.1016/j.matdes.2008.11.009. [5] boutabout, b., serier, b., mecirdi, m.a. and chama, m. (2008). analyse numérique des contraintes résiduelles dans les bimatériaux céramique/métal. revue des composites et des matériaux avancés, 18, pp.325-335. doi:10.3166/rcma.18.325-335. [6] boutabout, b., bouafia, f., mecirdi, m a. and bourdim s. m. (2010). modélisation tridimensionnelle par éléments finis des contraintes résiduelles dans un composite à matrice en verre. revue des composites et des matériaux avancés, 20, pp.7-23. doi: 10.3166/rcma.20.7-23. [7] wang, h.w., zhou, h.w., ji, h.w. and zhang, x.c. (2014). application of extended finite element method in damage progress simulation of fiber reinforced composites. journal materials & design, 55, pp.191–196. doi: 10.1016/j.matdes.2013.09.071. [8] chi-seung, l., jeong-hyeon, k., seul-kee, k., dong-man, r. and jae-myung, l. (2015). initial and progressive failure analyses for composite laminates using puck failure criterion and damage-coupled finite element method. journal composite structures, 121, pp.406-419. doi: 10.1016/j.compstruct.2014.11.011. [9] węglewski, w., basista, m., manescu, a., chmielewski, m., pietrzak, k. and schubert, th. (2014). effect of grain size on thermal residual stresses and damage in sintered chromium–alumina composites: measurement and modeling. composites part b: engineering, 67, pp. 119-124. doi: 10.1016/j.compositesb.2014.06.027. [10] prabha, m. and srinivasan, m. s. (2014). a constituent-behavior-motivated model for damage in fiber reinforced composites. computational materials science, 94, pp. 163-172. doi: 10.1016/j.commatsci.2014.03.048. [11] jin, c.f., zhu, q.z. and shao j.f. (2014). a numerical analysis of interface damage effect on mechanical properties of composite materials. mechanics research communications, 62, pp.18-24. doi: 10.1016/j.mechrescom.2014.08.003. [12] safarabadi, m. (2014). understanding residual stresses in polymer matrix composites. in book: residual stresses in composite materials, pp. 197–232. doi: 10.1533/9780857098597.2.197. [13] mecirdi, m.a. and serier b. (2015). calcul des facteurs d'intensité de contraintes (fic) pour les fissures interfaciales dans les composites fibreux. revue des composites et des matériaux avancés, 25, pp.311-325. doi :10.3166/rcma.25.311-325. [14] zeng,yi., xiong, x., wang, d. and liang w. (2015). residual thermal stresses in carbon/carbon–zr–ti–c composites and their effects on the fracture behavior of composites with different performs. carbon, 81, pp. 597-606. doi: 10.1016/j.carbon.2014.09.094. [15] zhenyi, y., yongjun, w., guigeng, y., aofe,i t., zhenchao, y., shujuan, l., yan, l. and danlong, s.(2018). evolution of curing residual stresses in composite using multi-scale method. composites part b: engineering , 155, pp. 49-61. doi: 10.1016/j.compositesb.2018.08.012. [16] nelson, s., hanson, a., briggs, t. and werner b. (2018). verification and validation of residual stresses in composite structures. composite structures, 194, pp. 662-673. doi: 10.1016/j.compstruct.2018.04.017. [17] zhang, g., wang, j., ni, a. and li, sh. (2018). process-induced residual stress of variable-stiffness composite laminates during cure. composite structures, 204, pp. 12-21. doi: 10.1016/j.compstruct.2018.07.040. b. zaoui et alii, frattura ed integrità strutturale, 51 (2020) 174-188; doi: 10.3221/igf-esis.51.14 188 [18] kati, r., seyoung, k., ji haeng, yu., soo-hyun, kim., young-hoon, s. and in-sub, h.(2018). rietveld refinement and estimation of residual stress in gdc–lscf oxygen transport membrane ceramic composites. ceramics international, 44, pp. 10293-10298. doi: 10.1016/j.ceramint.2018.03.036. [19] simulia, dassault systems. abaqus software. version 6.11. (2011). [20] serier, b. (1991). eude et caractérisation des liaisons céramique-métal élaborées par thermocompression: application au couple ag/al2o3 .thèse de doctorat en sciences. génie des matériaux, ecole centrale de lyon. [21] withers, philip j. and matthew, j. roy. 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can be opened with acrobat and adobe reader 5.0 and later.) >> /namespace [ (adobe) (common) (1.0) ] /othernamespaces [ << /asreaderspreads false /cropimagestoframes true /errorcontrol /warnandcontinue /flattenerignorespreadoverrides false /includeguidesgrids false /includenonprinting false /includeslug false /namespace [ (adobe) (indesign) (4.0) ] /omitplacedbitmaps false /omitplacedeps false /omitplacedpdf false /simulateoverprint /legacy >> << /addbleedmarks false /addcolorbars false /addcropmarks false /addpageinfo false /addregmarks false /convertcolors /converttocmyk /destinationprofilename () /destinationprofileselector /documentcmyk /downsample16bitimages true /flattenerpreset << /presetselector /mediumresolution >> /formelements false /generatestructure false /includebookmarks false /includehyperlinks false /includeinteractive false /includelayers false /includeprofiles false /multimediahandling /useobjectsettings /namespace [ (adobe) (creativesuite) (2.0) ] /pdfxoutputintentprofileselector /documentcmyk /preserveediting true /untaggedcmykhandling /leaveuntagged /untaggedrgbhandling /usedocumentprofile /usedocumentbleed false >> ] >> setdistillerparams << /hwresolution [2400 2400] /pagesize [612.000 792.000] >> setpagedevice microsoft word numero_42_art_4.docx r. pawliczek et alii, frattura ed integrità strutturale, 42 (2017) 30-39; doi: 10.3221/igf-esis.42.04 30 focused on mechanical fatigue of metals modeling of the stress-strain relationship for specimens made of s355j0 steel subjected to bending block loading with mean load r.pawliczek, c.t lachowicz opole university of technology, mikołajczyka 5, 45-271 opole, poland r.pawliczek@po.opole.pl, c.lachowicz@po.opole.pl abstract. the paper presents results of calculation for modelling of the stressstrain relationship in the case of block loads with mean load value. a model, based on the stable hysteresis loops, was assumed and modified to use for block loading analysis. for stress history calculation, the proposed model and two other constitutive models were used. results of fatigue test of specimens made of s355j0 steel subjected to bending block loading with mean load value are presented and used to verify the proposed model. in the tests, the mean load was increased and decreased in subsequent blocks. the changes of strain recorded during the tests shown in the paper indicate a different behavior of the material. damage accumulation degree for block sequence was used to compare the results of calculations. it was shown, that stress history parameters (stress amplitude and mean stress value in this case) are similar for all investigated models. keywords. stress-strain relationship; block loading; mean load. citation: pawliczek r., lachowicz c.t., modeling of the stress-strain relationship for specimens made of s355j0 steel subjected to bending block loading with mean load, frattura ed integrità strutturale, 42 (2017) 3039. received: 31.05.2017 accepted: 08.06.2017 published: 01.10.2017 copyright: © 2017 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. introduction bservation of the relation between strains of the structural materials and loading applied to the structure allow assessing the phenomena which occurs during fatigue of materials [1, 2]. for given material the value of load is a parameter which decides about strain-stress relationship. the area of the stress-strain hysteresis loop is identified with the plastic strain energy density. this energy parameter is widely used in so called energy based criteria to describe and predict the fatigue life of material, eg. [3, 4] as well for unnotched and notched components eg. [5]. in the case of complex load, during operation of the structures, some changes of the shape and location of the hysteresis loop are observed. it has to be considered in the algorithm of the fatigue life calculation, where the influence of the different load parameters on the strain-stress relationship is important. using a proper combination of cyclic loading blocks it is possible to realize complex load histories as laboratory tests. also the mean stress influence can be investigated – in this case, a constant component should be added to the generated blocks of variable amplitude loading. the load sequence can change the final fatigue life of materials and components, because damage accumulation is changed. the most important load sequences are these, which are strongly different with their parameters – amplitude and mean stress. usually the hi-lo or lo-hi sequences are used [1]. studying papers on that problem, we can find that there is no standard procedure for fatigue life calculation and some researchers obtained completely opposite results [6]. most of those considerations were o r. pawliczek et alii, frattura ed integrità strutturale, 42 (2017) 30-39; doi: 10.3221/igf-esis.42.04 31 based on experimental results which were obtained for different materials, loading conditions, applied stress levels. it is possible to describe a proper damage accumulation rule for such cases only. fatemi and yang [7] present a wide number of different cumulative fatigue damage and life prediction theories. they conclude that none of them is widely accepted. each damage model can only account for one or several phenomenological factors, such as load dependence, multiple damage stages, nonlinear damage evolution, load sequence and interaction effects, over load effects, small amplitude cycles below the fatigue limit and mean stress. the tests presented by chiou and yip [8] shows the effect of the mean load based on the example of research on aisi 316 alloy steel subjected to uniaxial loads of constant amplitude and the saw-toothed waveform. curve parameters of cyclic strengthening were determined for a fixed value of the mean strain of εm= 0.1%; 0; 0.2%; 0.4% resulting in the following values: k’=745.594; 722.571; 693.080; 587.699 mpa and n’=0.1572; 0.1507; 0.1424; 0.1170 [8], respectively. in the case of block loads involving different mean values in each load blocks, distinct changes of fatigue life are observed. the authors memon at al. [9] shows the results of fatigue tests under conditions of two-stage block loads in lo-hi and hi-lo sequences (fig. 1) for different sequences of amplitude and the mean stressess. a) b) figure 1: the sequence of blocks according to [8]: a) lo-hi, b) hi-lo. the algorithm of fatigue life calculation, proposed by the authors, uses lemaitre’s model of kinematics hardening and also additional stress-strain analysis based on mes method. final degree of damage accumulation was calculated with the use of linear palmgren-miner rule. the results present good agreement between calculations and tests in the cases, where amplitudes of the load in analyzed sequences were on similar level and maxi-mum stresses were near the yield limit. bigger difference be-tween amplitudes of the loading in the block sequence strongly influences on the level of the degree of damage accumulation for hi lo and lo-hi cases. the effect of block loads on the fatigue life is shown by pawliczek and lachowicz [10], which have involved bending of specimens from s355j0 steel to certain maximum stress levels. in the case of loads at yield point, a difference in fatigue life has been observed depending on the direction of increase of the mean load, and fatigue life was twice lower if the highest mean load value occurred in the beginning of the load sequence. similar tests were performed by pawliczek [11]. the paper describes the research on the relationship between stress and strain under bending block loads where the mean value of the load varied for each block segment. a significant impact of such a load on strains generated in the material, and consequently on the fatigue life, is shown. it can be seen, that analyze of the stress-strain relation is an important part of block loading fatigue tests where mean load is applied. such investigations allow considering that effect and verifying the influence of the mean load on it. the aim of this paper is to create an algorithm for stress history parameters definition and its application for calculations of accumulation damage degree. model for stress history parameters definition he model for stress amplitude and mean stress value calculation bases on the model of the hysteresis loop presented by chiou and yip [8]. i was assumed that the shape of the stable hysteresis loop remains unchanged under the same strain amplitude and different mean strain level conditions. additionally, the stable hysteresis loop shifts in accordance with the value of the mean strain. this results in symmetry of the hysteresis loop according to the point described by mean strain εm and mean stress σm (fig. 2).  t1min 1max 2max 2min block 1 n1 cycles block 2 n2 cycles  t1min 1max 2max 2min block 1 n1 cycles block 2 n2 cycles t r. pawliczek et alii, frattura ed integrità strutturale, 42 (2017) 30-39; doi: 10.3221/igf-esis.42.04 32 figure 2: description of the stable hysteresis loop [7]. the parameters on the fig. 2 are as follow: εmax, σmax – maximum strain and stress at point a respectively, εmin, σmin – minimum strain and stress at point b respectively, εm, σm – mean strain and stress in the point respectively, εa, σa – amplitude of strain and stress in the point respectively, εapl, εael – plastic strain and elastic strain at point a respectively. for situation presented in fig. 2 the most conservative case exists. all calculations are performed for known strain history ε(t) registered during the test, so all strain parameters in fig. 2 are available. take into account geometry of the stress-strain relation based on the presented assumptions and using standard ramberg-osgood formula for its mathematical description, the strain amplitude εa can be expressed as: 1 max max n a e k          (1) where: σmax – maximum stress at point a, e – young modulus, k’ = k’(εm ) cyclic strength coefficient, n’ = n’(εm ) – cyclic fatigue exponent. assuming additionally, that cyclic strength coefficient and cyclic fatigue exponent values depend on the actual value of the mean strain, it should be noted, that coefficients k’ and n’ are defined for actual mean strain εm [8]. eq. (1) allows calculating stress at point a. considering, that εm+εa= εapl+εael and σmax=σa+σm (fig. 2) max m am a apl apl e e e             (2) where stress amplitude σa is unknown. from hysteresis loop and ramberg-osgood relationship, we can use the amplitudes of elastic εael and plastic εapl strains: aa ael apl apl e         (3) substituting elastic part in eq.(2) using eq.(3), after transformation, the mean stress σm can be calculated from the following formula: m m apl apl e       (4) a (max, max) a a m m a apl ael   b (min, min)   r. pawliczek et alii, frattura ed integrità strutturale, 42 (2017) 30-39; doi: 10.3221/igf-esis.42.04 33 this form of equation (young modulus) suggests that mean stress is responsible for elastic part of deformation. however, the parameter εapl in eq.(4) is still undefined. also to solve this problem, the ramberg-osgood equation can be used. bearing in mind, that the shape of the stable hysteresis loop does not change for the same strain amplitude and different mean strains we can calculate stress amplitude σa using relation 1 n a a a e k          (5) it is very important to use coefficients k’ = k’(εm=0) and n’ = n’(εm=0) obtained for standard, symmetric loading (εm=0 and σm=0) in the case of eq.(4). all the equations presented above are adequate for cyclic load with the mean load, where load conditions are constant during the test. however, it was mentioned before, for block loading location of the hysteresis loop can be different for each segment of block. some researches of this problem [11] allows observing, that changing the men load during test a new, stable location of the hysteresis loop is registered. strong flow of the mean strains along strain axis usually arises at the end of life of the specimen, so it can be assumed, that each, new position of the hysteresis loop stabilises at new levels of mean strain and stress (fig.3). figure 3: location of the hysteresis loops for the next sequence in the block load. after first block, where strain εm1 and stress σm1 exists a new position of the hysteresis loop is observed and described by parameters εm2(measured) and σm2. notation “measured” means mean strain of the measured strain history. it should be noted, that after first sequence some value of permanent deformation εapl1 exists in material after unloading (fig.3). this part of strains participates as the initial state of the material for next stage of loads. in the case, for which the second block will have zero mean load value it leads to situation, that presented algorithm will resulting with non-zero mean stress, what is not corresponds to the real stress conditions. the strain εapl1 as the “starting” point for each sequence must be taken into account in calculations. the algorithm for stress history calculation aving regard to the considerations presented above the following algorithm for stress history calculation can be defined, where all the steps must be repeated for each sequence in the block load for whole registered time history of the strain: m1 m2 m1 m2(measured) m2(real)apl1   h r. pawliczek et alii, frattura ed integrità strutturale, 42 (2017) 30-39; doi: 10.3221/igf-esis.42.04 34 1. input data: εmax εmin εa εm 2. calculation of σmax where k’(εm) and n’(εm) are defined for actual mean strain value: 1 max max n a e k          3. calculation of εapl: max maxapl e     4. calculation of σa where k’(εm=0) and n’(εm=0): 1 n a a a e k          5. calculation of εapl: a a apl e     6. calculation of the mean stress σm: ( )m m ap aple      7. calculation of the damage accumulation degree for given stresses (σa, σm) and the fatigue life can be predicted. additionally, in order to define the stress history parameters, some kinematic models of cyclic deformation were used. usually, those criteria base on the von mises’s plasticity surface as the yield criterion. for such calculation then the flow rule for a plastic strain increment calculation must be specified. additionally, during computation with use of the constitutive equations it is important to define the way the plasticity surface is translated. translation can be described by some hardening rules. during numerical tests it was found that the best results of calculations were obtained for garud-mroz [12] and chu [13] models of the constitutive equations of the cyclic plasticity description. these cyclic plasticity models are used very often for energy based criteria for fatigue life estimation, eg. lachowicz [14], to describe stress-strain state and to calculate energy dissipated in material. fatigue tests the fatigue tests conducted included subjecting the samples made of s355j0 steel to fatigue loads with including the mean load values. the tab. 1 presents properties of the tested materials. e gpa σy mpa σu mpa ν n’ k’ mpa 210 357 535 0.30 0.2074 1323 c mn si p s cr ni cu fe 0.20 1.49 0.33 0.023 0.024 0.01 0.01 0.035 others table 1: strength properties and chemical composition (%) of s355j0 steel. the tests were performed under bending loads applied in blocks with different mean load values. two paths of the change in the mean load value in blocks were applied (fig.4): a) mean load was increased from zero to maximum value for the following sequences in blocks of loading, b) mean load was decreased from maximum to zero value in successive blocks of loading. the mean value of the load was as follow: 1: σm = 0, 2: σm = ⅓σa, 3: σm = σa. the whole number of cycles nb in block was divided to three equal parts n1=n2=n3=⅓nb. the block applied in the tests had a length nb=15000 cycles. r. pawliczek et alii, frattura ed integrità strutturale, 42 (2017) 30-39; doi: 10.3221/igf-esis.42.04 35 a) b) figure 4: block loading applied in fatigue tests: a) for increasing mean load value, b) for decreasing mean load value. the view of the fatigue tests stand mzgs100 is presented in fig. 5a. the stand allows realizing tests under cyclic bending with mean load value, which is applied by spring actuator. the applied loads and observed deformations (strains) of the specimens were measured during the tests. the strain bridge ni usb9237 and the author’s software (fig. 5b) were used. it was possible to observe on-line the time courses of loading (amplitude and mean value of the bending moment) and strains and additionally moment-strain curve was displayed. a) b) figure 5: fatigue tests: a) the view of the fatigue tests stand, b) software’s user interface. an example time histories of bending moment and corresponding strains are shown in fig. 6. figure 6: registered moment and strains history. n1 n2 n3 nb n  1 32 n1 n2 n3 nb n  3 12 0 0.02 0.04 0.06 0.08 0.1 t, s -25 -20 -15 -10 -5 0 5 10 15 20 -0.004 -0.002 0 0.002 0.004 m n.m r. pawliczek et alii, frattura ed integrità strutturale, 42 (2017) 30-39; doi: 10.3221/igf-esis.42.04 36 then, the registered signals were used to define the changes of the moment-strain relation for both of applied block load paths. the results of fatigue test are presented in fig. 7 and fig. 8 for the load paths shown in fig. 4a and fig. 4b. figure 7: hysteresis loops at the increasing mean load value. in the case of fig. 7 higher value of the moment amplitude in the first phase of fatigue testing resulted with strain amplitude εa=0.3% after 2000 cycles. the increase in the mean value of load in each sequence resulted in a shift of the loop towards the average value of εm=0.35%. when ma=mm=10n·m, the increase of the mean strain value to εm=0.45% was observed but the variable strains are in the elastic range (curves 5 and 6 in fig. 7). the maximum strain of εmax=0.6% and the mean strain εm(max)=0.47% were recorded. figure 8: hysteresis loops at the decreasing mean load value. for the case shown in fig. 8 in the initial phase of the test the highest value of the mean moment was applied. in the case where ma=15n·m and mm=5 n·m (curves 3 and 4 in fig. 8), there is no increase plastic strain as compared to the corresponding case (curves 3 and 4 in fig. 7) with the increase of the mean load value. this may indicate the strengthening of the material caused by the mean load at the beginning of the block. the reduction in the mean moment value to zero in -0.004 0 0.004 0.008  -25 -20 -15 -10 -5 0 5 10 15 20 25 m n.m 1 2 3 4 5, 6 1: ma=20n.m mm= 0 n=2000; 2: ma=20n.m mm= 0 n=5000 3: ma=15n.m mm=5n.m n=7000; 4: ma=15n.m mm=5n.m n=10000 5: ma=10n.m mm=10n.m n=12000; 6: ma=10n.m mm=10n.m n=15000 -0.004 0 0.004 0.008  -20 -15 -10 -5 0 5 10 15 20 25 m n.m 1,2 3,4 5 6 1: ma=10n.m mm=10n.m n=2000; 2: ma=10n.m mm=10n.m n=5000 3: ma=15n.m mm=5n.m n=7000; 4: ma=15n.m mm=5n.m n=10000 5: ma=20n.m mm= 0 n=12000; 5: ma=20n.m mm= 0 n=15000 r. pawliczek et alii, frattura ed integrità strutturale, 42 (2017) 30-39; doi: 10.3221/igf-esis.42.04 37 the last block enlarged the area of the hysteresis loop and a little shift of the hysteresis loop after 3000 load cycles is observed. at the same time, the mean load εm=0.2% was recorded that remained after the strain (curves 5 and 6 in fig. 5). the maximum strain of εmax=0.5% and the mean strain εm(max)=0.15% were recorded. results of calculations or registered histories of the strains the proposed algorithm and two kinematic models (garud-mroz and chu) of cyclic deformation were used to calculate the stress history parameters: stress amplitude and mean stress value in this case. figs. 9 and 10 presents hysteresis loops as stress-strain relationship calculated by the use of garud-mroz model. form of the graphs corresponds to the measurement results presented in fig. 8 and fig.9, respectively. figure 9: stress-strain loops at the increasing mean load value calculated with the use of garud-mroz model. figure 10: stress-strain loops at the decreasing mean load value calculated with the use of garud-mroz model. -0.004 0 0.004 0.008  -400 -300 -200 -100 0 100 200 300 400  mpa 1 2 3 4 5, 6 1: n=2000; 2: n=5000 3: n=7000; 4: n=10000 5: n=12000; 6: n=15000 -0.004 0 0.004 0.008  -400 -300 -200 -100 0 100 200 300 400 500  mpa 5,6 3,4 2 1 1: n=2000; 2: n=5000 3: n=7000; 4: n=10000 5: n=12000; 6: n=15000 f r. pawliczek et alii, frattura ed integrità strutturale, 42 (2017) 30-39; doi: 10.3221/igf-esis.42.04 38 it can be seen, that for curves 5 and 6 of fig. 9 some compression stresses reordered. the same effect is visible for curves 1 and 2 on the diagram for the case of decreased mean load (fig. 10). the aim of performed calculations is to establish a parameters of the stress history (stress amplitude σa and mean stress σm in this case) for each sequence of the applied block loads respecting both paths of changes of the mean load using proposed model, garud-mroz proposal and chu also. results of these investigations are presented in the fig. 11 for increased mean load value and in the fig. 12 for decreased mean load value. 2000 5000 7000 10000 12000 150002000 5000 7000 10000 12000 15000 n, cycle 0 100 200 300 400  , m p a s355 a: garud-mroz m: garud-mroz a: chu m: chu a: proposed model m: proposed model figure 11: comparison of the stress history parameters calculated by proposed model and models of garud-mroz and chu for increased mean load value. figure 12: comparison of the stress history parameters calculated by proposed model and models of garud-mroz and chu for decreased mean load value comparing all analyzed models it can be seen, that stress amplitude are very close to each other for all cases, however for mean stress the proposed model gives results with higher values: about 40% for 7000 and 10000 cycles (second sequence in block load) and 80% for 12000 and 15000 cycles (third sequence in block load). it will generate higher level of damages – then lower, predicted fatigue life will be calculated for such load sequence. in general, such observations are indicated in the research. 2000 5000 7000 10000 12000 150002000 5000 7000 10000 12000 15000 n, cycle 0 100 200 300 400  , m p a s355 a: garud-mroz m: garud-mroz a: chu m: chu a: proposed model m: proposed model r. pawliczek et alii, frattura ed integrità strutturale, 42 (2017) 30-39; doi: 10.3221/igf-esis.42.04 39 summary and conclusions he algorithm of the stress history parameters calculation is presented in this paper and its application to the block loads with influence of the mean load value is described. the sequences in block load differ with values of the mean load for each sequence of the block. taking into account results of the test and calculations the following conclusions can be drawn: – fatigue tests present significant changes of the strain develop in material for both analyzed load path. if the hysteresis loop is moving along strain axis for the load with increased mean load values (fig. 4a) in the case of decreasing mean load value it is observed, that after first sequence with higher mean load value some hardening effect occurs, – garud-mroz and chu cyclic plasticity models gives very similar results of calculations of stress amplitude and mean stress value for both analyzed cases of the load path (fig. 11 and fig.12), – proposed model is more sensitive for mean value in the block loads in the case of increased mean load value for following sequences in the block comparing to the cyclic plasticity models (fig. 11), where for second case of loads similar results for all of three analyzed models were obtained (fig. 12). references [1] kocańda, s., szala, j., basis for the calculation of fatigue, pwn, warszawa (1989) (in polish). [2] kocańda, s., kocańda, a., low cycle fatigue strength of metals, pwn, warszawa (1989) (in polish). [3] morrow, j., cyclic plastic strain energy and fatigue of metals. international friction, damping and cyclic plasticity, astm stp, philadelphia (1965). [4] łagoda, t., macha, e., będkowski, w., a critical plane approach based on energy concepts: application to biaxial random tension-compression high-cycle fatigue regime, international journal of fatigue, 21 (1999) 431-443. [5] łagoda, t., robak, g., słowik, j., fatigue life of steel notched elements including the complex stress state, fatigue life of steel notched elements including the complex stress state, materials and design, 51 (2013) 935–942. [6] van paepegem, w., degreck, j., effect of load sequence and block loading on the fatigue response of fibre-reinforced composites, mechanics of advanced materials and structures, 9(1) (2002) 19-35. [7] fatemi, a., yang, l., cumulative fatigue damage and life prediction theories: a survey of the state of the art for homogeneous materials, international journal of fatigue, 20(1) (1998) 9-34. [8] chiou, y.c., yip, m.c, effect of mean strain level on the cyclic stress-strain behavior of aisi 316 stainless steel, materials science and engineering, a354 (2003) 270-278. [9] memon, i., zhang, x., cui, d., fatigue life prediction of 3-d problems by damage mechanics with two-block loading, international journal of fa-tigue, 24 (2002) 9-37. [10] pawliczek, r., lachowicz, c.t., the mean stress effect on fatigue behavior of constructional steels subjected to variable amplitude bending, 2nd inter-national conference on material and component performance under variable amplitude loading, eds c.m.sonsino and p.c mckeighan, dvm, berlin (2009) 1095-1102. [11] pawliczek, r., influence of the mean load value in fatigue block loading on strains, key engineering materials, trans tech publi-cations, switzerland, 598 (2014) 195-200. [12] garud, y. s., a new approach to the evaluation of fatigue under multiaxial loadings, trans asme j. of pressure vessel technol., 103 (1981) 118-125. [13] chu, c. c., a three dimensional models of anisotropic hardening in metals and its application to the analysis of sheet metal formability, journal of the mechanics and physics of solids, 32 (1984) 197-212. [14] lachowicz, c. t., energy based method for analysis of the fatigue life of materials, machines components and structures, printing house of opole university of technology, opole (2013) (in polish). t << /ascii85encodepages false /allowtransparency false /autopositionepsfiles true /autorotatepages /none /binding /left /calgrayprofile (dot gain 20%) /calrgbprofile (srgb iec61966-2.1) /calcmykprofile (u.s. web coated \050swop\051 v2) /srgbprofile (srgb iec61966-2.1) /cannotembedfontpolicy /error /compatibilitylevel 1.4 /compressobjects /tags /compresspages true /convertimagestoindexed true /passthroughjpegimages true /createjobticket false /defaultrenderingintent /default /detectblends true /detectcurves 0.0000 /colorconversionstrategy /cmyk /dothumbnails false /embedallfonts true /embedopentype false /parseiccprofilesincomments true /embedjoboptions true /dscreportinglevel 0 /emitdscwarnings false /endpage -1 /imagememory 1048576 /lockdistillerparams false /maxsubsetpct 100 /optimize 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/hrv (za stvaranje adobe pdf dokumenata najpogodnijih za visokokvalitetni ispis prije tiskanja koristite ove postavke. stvoreni pdf dokumenti mogu se otvoriti acrobat i adobe reader 5.0 i kasnijim verzijama.) /hun 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can be opened with acrobat and adobe reader 5.0 and later.) >> /namespace [ (adobe) (common) (1.0) ] /othernamespaces [ << /asreaderspreads false /cropimagestoframes true /errorcontrol /warnandcontinue /flattenerignorespreadoverrides false /includeguidesgrids false /includenonprinting false /includeslug false /namespace [ (adobe) (indesign) (4.0) ] /omitplacedbitmaps false /omitplacedeps false /omitplacedpdf false /simulateoverprint /legacy >> << /addbleedmarks false /addcolorbars false /addcropmarks false /addpageinfo false /addregmarks false /convertcolors /converttocmyk /destinationprofilename () /destinationprofileselector /documentcmyk /downsample16bitimages true /flattenerpreset << /presetselector /mediumresolution >> /formelements false /generatestructure false /includebookmarks false /includehyperlinks false /includeinteractive false /includelayers false /includeprofiles false /multimediahandling /useobjectsettings /namespace [ (adobe) (creativesuite) (2.0) ] /pdfxoutputintentprofileselector /documentcmyk /preserveediting true /untaggedcmykhandling /leaveuntagged /untaggedrgbhandling /usedocumentprofile /usedocumentbleed false >> ] >> setdistillerparams << /hwresolution [2400 2400] /pagesize [612.000 792.000] >> setpagedevice microsoft word numero_38_art_28 m.v. karuskevich et alii, frattura ed integrità strutturale, 38 (2016y) 205-214; doi: 10.3221/igf-esis.38.28 205 focussed on multiaxial fatigue and fracture multi-purpose fatigue sensor. part 2. physical backgrounds for damages accumulation and parameters of their assessment m.v. karuskevich, s.r. ignatovich, т.p. maslak national aviation university, kiev, 03680, ukraine a. menou international academy of civil aviation, casablanca, morocco p.о. maruschak ternopil national ivan pul’uj technical university, ternopil, 46001, ukraine maruschak.tu.edu@gmail.com s.v. panin institute of strength physics and materials sciences sb ras, tomsk, 634055, russia national research tomsk polytechnic university, tomsk, 634050, russia f. berto university of padova, vicenza, 36100, italy abstract. the characteristic informative parameters for defect detection to be used in fatigue sensors have been established. their development is interpreted in terms of scale levels of deformation and fracture. damage accumulation of the sensor’s surface tends to exhibit the self-organization nature. it is accompanied by formation of "folded" strain-induced relief on the surface. the mechanisms of damage accumulation under cyclic deformation were analyzed with the use of the multiscale approach. keywords. defects; fatigue sensors; damage; aviation. citation: karuskevich, m.v., ignatovich, s.r., maslak, т.p., menou, a., maruschak, p.о., panin, s.v., berto, f., multi-purpose fatigue sensor. part 2. physical backgrounds for damages accumulation and parameters of their assessment, frattura ed integrità strutturale, 38 (2016) 205-214. received: 16.05.2016 accepted: 10.06.2016 published: 01.10.2016 copyright: © 2016 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. m.v. karuskevich et alii, frattura ed integrità strutturale, 38 (2016y) 205-214; doi: 10.3221/igf-esis.38.28 206 introduction here is a number of physical backgrounds that explain the nature of an ordered surface relief formation including ones based on the principle of self-ordering [1-3]. one of the most well-known concepts is underlined by the effect of "chessboard" (ordered pattern) of normal compressive/tensile stresses and strains distribution in surface layers and interfaces of solids to occur under the impact of external loading (mechanical, thermal, electrical, etc.). this physical phenomenon is related to the strain incompatibility of two interfaced media and occurs in various multilevel systems: at the "surface layer bulk material" interfaces, in "coating substrate" compositions, in multilayered or thin film materials, at grain boundaries (triple joints) in polycrystals [4], etc. it is known that accumulation of defects in surface layers takes place under the cyclic loading that is followed by the material self-organization there that is exhibited in the form of dissipative structure and microextrusions [5-7]. it should be noticed that depending on the mechanical impact on the material the structure of surface damages will be varied. this numerously experimentally proved evidence testifies for the fact that surface layer of the material is the most "sensitive" in order to be used for characterization the kinetics of damage accumulation at various loading modes [8, 9]. these above mentioned properties of material self-organization are widely used at development of instrumental techniques for fatigue fracture diagnostics of aircraft structures [10-12]. a big number of automated methods for monitoring parts made of cladded aluminum alloys are available. in particular, a nondestructive computerized optical-digital inspection technique is based on determination of damage parameter of strain– induced surface relief of fatigue sensors for aircraft structures was described in [13-14]. in doing so the peculiarity of using the strain induced relief as a measure of damage accumulation is related to the fact that the latter is already formed after a few loading cycles and keeps developing till fatigue crack nucleation. this makes possible to run the diagnostic and prediction of the mechanical state and residual life-time of structure elements from the early damaging stage till approaching their limit state. currently, various parameters which are used for describing strain induced surface relief in structural aluminum cladded alloys being formed under cyclic loading are employed. they typically depend on the nature and accumulation mechanisms of deformation structures at the material surface. recently, various irregular structures of natural origin are effectively quantitatively described with the use of the following parameters: fractal dimension, shannon entropy, etc. [7, 10, 12]. in our opinion, the accuracy of the assessment of the critical state approaching in the optical inspection application may be attained by attracting modern techniques of strain induced relief analysis based on calculation of several informative parameters. the aim of the study is establishing the basic principles of damage accumulation on the fatigue sensor surface under cyclic bending and “bending + torsion” loading schemes. techniques and material for fatigue sensor investigation 16at aluminum alloy which is widely used in aviation was selected for the research. this alloy has a cladded layer made of pure aluminum for anti-corrosion protection. in doing so, the strain induced relief is formed [7] under the fatigue process. flat specimens with dimension of 140 × 10 × 1.0 mm were employed for cyclic cantilever bending as well as "bending + torsion" tests. the stress concentrator in the form of a central hole with 1.0 mm diameter was drilled. these allowed us to reveal the basic regularities of strain induced relief evolution under various schemes of the loading. experiments were conducted with the help of testing machine (home made in the national aviation university in kiev) at the stress level of σmax = 107.8 mpa under the cyclic bending. when complex loading pattern "bending + tension" was used the tensile stress component made σmax = 108 mpa while the shear one –  = 85 mpa. the parameters described were constant at the region where surface relief was examined. surface relief images were captured after certain operating times at the left and at the right from the stress concentrator. in doing so, the optical magnification made × 300. the calculation and comparative analysis of the surface damaging parameters in the regions under observation were performed with the help of automated image analysis. algorithm for image analysis according to data of our recent studies on fatigue sensors behavior the image of regions with accumulated microdefects differ from non-damaged ones by brightness intensity [6, 8]. this is related to the changing sensor surface relief to take place under the loading. the former is responsible for the changing optical properties of the polished surface. in so doing, with the increasing the number of loading cycles, the number and area occupied with plastically deformed surface regions are enlarged [15]. in this response, the following potential informative parameters that might be used for the assessment t d m.v. karuskevich et alii, frattura ed integrità strutturale, 38 (2016y) 205-214; doi: 10.3221/igf-esis.38.28 207 of the fatigue sensor state were selected: area of regions being microplastically deformed, as well as the information shannon entropy. they should indicate the deviation of the surface image of the damaged material from the initial (nondeformed) state (being characterized by low value of the entropy) [16]. to calculate the area of microplastically damaged material the following algorithm was employed. it comprises the following steps: illumination alignment, converting an image into the grayscale one, threshold binarization, computation of the relative area of the "dark" fragments over the total surface region under observation [17]. since the surface image was registered with the help of the optical microscope equipped with a directed illumination source the “raw” (initial) images were non-uniformly illuminated. this gave rise to the heterogeneity of the background level in various image regions (that affects pattern of microplastically deformed surface). by applying the procedure of the illumination alignment the nonuniformity of the surface illumination was corrected. by converting the image into the grayscale pattern one can substantially reduce the amount of information to be computed as well as to simplify the image processing algorithm. at the next step the aligned illumination image was subjected to the threshold binarization. this operation is aimed at obtaining an image with regions of two types: the light ones (corresponding to the background) and dark ones (corresponding to the damaged regions). the relative area of the damaged regions smda was calculated as the ratio of dark pixels nb over the total number of pixels in the image nt: b mda t n s n 100%  (1) the shannon information entropy was calculated by the formula [6, 8]:    h h i i i i i h mn mn 255 2 0 log    (2) where i – pixel brightness, i 1, 255 ;  hi i – image brightness histogram i (the frequency of pixels with brightness); m, n –width and height of the image, measured in pixels, respectively. the information entropy characterizes the degree of uncertainty in the brightness distribution over the image pixels. it is known that the entropy possesses the maximum value when uniform brightness distribution takes place (i.e., for a rectangular pattern of the image histogram). the entropy of the totally monochrome image has the minimum value. since the pixel’s brightness of damaged regions and the background are different, the parameter h will depend on the number and size of microplastically deformed regions the image, as well as on their contrast over the background [17]. experimental results t is known that fatigue sensors are strain gauges of integral type which are used in aviation. they are mounted onto bearer carrying structural elements of aircrafts. since these structures are deattachable they are periodically removed for the aim of automated analysis in the laboratory conditions [8, 12]. although application of these sensors does not allows gaining information in real-time due to absence of connection to electrical circuits and related communication devices; however their relative simplicity and informativeness makes their use possible not only for aircrafts inspection but for bridge and other building structures as well [7, 8]. cyclic bending optical aided investigations of the d16at alloy surface after cyclic loading suggest that the latter give rise to nucleation of surface damages, formation of strain induced relief (extrusions, intrusions, sliding traces, etc.). the mechanism of damage formation on the sensor surface is related to the intragranular sliding. in doing so, sliding traces becomes visible within individual grains already after several thousand loading cycles [18]. with the increasing of cyclic loading the larger number of grains are involved into the sliding process, while the formed lines (traces) broaden and unite to form the "spots". these spots are the places of plastic deformation localization. they might be considered as dispersed damages being accumulated within certain grains resulting from relaxation of mechanical microscale stresses [12]. it is the evolution of the strain induced relief during the cyclic loading that allows considering it as an indication for accumulated strain damages. the formation and accumulation of the spots is actively developed especially under long-term operation. i m.v. karuskevich et alii, frattura ed integrità strutturale, 38 (2016y) 205-214; doi: 10.3221/igf-esis.38.28 208 а b c d e f і k figure 1: the surface images of strain induced relief found on the structure-sensitive fatigue gauge under bending (a-d) (n = 5000 cyles (a); 150000 (f); 100000 (i); 1000000 (k)), σmax =110 mpa and “bending + torsion” (e-k) loadings: (n = 5000 cyles (a); 25000 (f); 100000 (i); 512000 (k)). cyclic "bending + torsion" complex loading pattern gives rise to the activation of additional sliding planes in grains that, in turn, increases surface damaging at the same comparable number of loading cycles [19]. in doing so, the multiplicative sliding mechanisms are activated, which, in addition to conventional ones, involve sliding systems, which are not active at uniaxial straining [20]. three or even more slip planes are additionally involved into the cyclic deformation process when a multiplicative sliding takes place. this results in the reciprocal slippage along adjacent grain boundaries (slipping, translation, rotation). mutual slippage of adjacent grains provides activation of the surface microrelief formation that, in turn, calls for increase of the damage accumulation intensity. thus, the kinetics of damage accumulation on the fatigue sensor surface in the d16at aluminum alloy under investigation at various cyclic loading schemes is different by their physical nature. this specificity should be taken into account when assessing the operating time as well as residual life-time of aircraft components including the use of the digital-optical inspection. graphs of cyclic damage accumulation bending he following data were obtained at the region under inspection located from different sides from the stress concentrator. it was revealed that dependences of damaged area (s) (fig. 2, a) and the shannon entropy (h) versus the number of loading cycles have nearly the same shape. this testifies for the sensitivity of these parameters to the accumulation of defects within the surface regions under observation, fig. 2. "vertical portion" is formed as a result of intensive accumulation of deformed structures. in doing so, strain develops within individual grains. the tendency of the material to the “easiness” of strain development is determined by the crystallographic orientation of individual grains [21]. the diagram portion responsible for the individual defects being united into the groups is manifested through a gradual increase in the relative area of damaging with signs of microplastic deformation. it gives rise to uniting of the deformation “cluster” and changing of their shape. dispersed and localized surface damages on the bright surface of the aluminum sensor appear as multiple bands and partially merged spots. the diagram portion responsible for the uniting of the damages (saturation). significant reduction of the material resistance to cyclic deformation is characteristic for this part of the curve. formation and development of "spots" in the regions of their concentration result in the height growth of extrusion and increase of their number [7]. damage accumulation in d16at aluminum alloy change in a monotonous manner during running time range is illustrated in fig. 3. this also t m.v. karuskevich et alii, frattura ed integrità strutturale, 38 (2016y) 205-214; doi: 10.3221/igf-esis.38.28 209 proves the possibility of their successful application for the sake of technical diagnostic procedures. the curve to characterize the dependence of the damaged area (s) versus the shannon entropy (h) exhibit a non-linear character that is related to the difference in their nature as well the background to affect these parameters. 4·105 s, % n, cycles 0 2 4 6 8 10 12 14 16 18 8·105 0 1 2 i ii iii 4·105 h n, cycles 8·105 0 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 i ii iii а b figure 2: dependence of the deformed (damaged) area (s) –(a), and the shannon entropy (h) – (b) vs the number of cycles. 0 2·105 4·105 6·105 0 10 20 30 40 s, % n, cycles 1 2 i ii iii а 0 2·105 4·10 5 6·105 n, cycles 0 0.2 0.4 0.6 0.8 1.0 h i ii iii b s, % 0 5 10 15 20 25 30 35 40 0 0.2 0.4 0.6 0.8 1.0 h c figure 3: dependence of the damaged area (s) – (a) and the shannon entropy (h) – (b) versus the number of cycles and the s – to h ration under cyclic bending. images were taken from the right (1) and left (2) sides from the stress concentrator m.v. karuskevich et alii, frattura ed integrità strutturale, 38 (2016y) 205-214; doi: 10.3221/igf-esis.38.28 210 bending + torsion much like the previous case, the damaging at both sides from the stress concentrator exhibits the 3-stage pattern, fig. 3. it should be noticed that under "bending + torsion" loading the portion responsible for joining of individual defects into groups is more pronounced as compared to the upper case. the curves to characterize the damaged area and the shannon entropy are almost identical to ones shown in fig. 2. by combined analysis of these parameters one can gain deeper understanding on the nature of defect joining as well as prove the self-organization character of processes under investigation. the shape and size of damaged areas testifies for the higher damaging effect of the complex scheme of the loading. however, the stage pattern of damage development on the sensor surface is kept; this allows us to carry out a correct comparative analysis of these curves. lower degree of nonuniformity of fatigue damaging distribution on the sensor surface during cyclic loading under "bending + torsion" scheme as well as higher intensity of grouping individual defect into larger size conglomerates allows one to determine by a first approximation the loading scheme of a structure at the point of its fixation. the "bending + torsion" loading scheme gave rise to the formation of "concentrated" (localized) black "spots", while the uniaxial loading scheme ensures more uniform distribution of surface defects and the less intensity of damage accumulation. in the case of more complex cyclic deformation the spots had darker appearance and more pronounced shape. it is these parameters that are crucial at formation of the defect domain structure. the attained physical regularities are confirmed by the relative changing of damaging if judging by the both studied parameters: λh= (hc – hb)/hc×100%, where hb, hc – the shannon entropy values for the bending and "bending + torsion" loading schemes, respectively. generalized parameters of specimen’s surface damaging being plotted in relative coordinates for different deformation schemes are shown in fig. 4. the effect of cyclic loading onto the sensor damaging was estimated with the use of a relative factor which allows to analyze the peculiarities of particular combination of the surface damaging parameters (the damaging area of and the shannon entropy). it is found that at 5 * 105 loading cycles the value of λs is reduced from 0.90 down to 0.55, while the value of λs drops form 0.80 down to 0.35. this indicates the fact that the difference of sensor surface damaging under the bending and "bending + tension" loading schemes has decreased with increasing cyclic operating time. however the difference in the damaging accumulation kinetics is large enough when judging by the smda parameter (area of damaged regions). at the same time the value of the shannon entropy testifies for the faster increasing of localized deformation regions disorientation as compared to the area of the damaged regions. n, cycles 0 200000 400000 600000 0.3 0.4 0.5 0.6 0.7 0.8 λh λ, % λs figure 4: dependence of the relative damage indicators λs and λh versus the number loading cycles of the sensor. thus, under the "bending + tensile" scheme more active accumulation of the dispersed defects takes place as compared to the "pure bending" scheme. in so doing, they are much more disordered. according to our opinion, the sensitivity of the material (d16at aluminum alloy) to the loading scheme as well as proper choice of the informative parameters for damaging analysis allows to discuss design of the gauges with controllable sensitive to the amplitude of cyclic straining. the sensitivity of the sensor might be changed by varying their thickness within the region under analysis. m.v. karuskevich et alii, frattura ed integrità strutturale, 38 (2016y) 205-214; doi: 10.3221/igf-esis.38.28 211 discussion et us analyze the obtained results within the concept of scale levels of deformation and fracture. in contrast with traditional phenomenological interpretation of the results of cyclic damaging of the sensor surface the main characteristic feature of this approach is consideration a solid as a hierarchical system where deformation and fracture processes are self-consistent and develop at the micro-, mesoи macroscale levels [22]. microscale level. the force affecting the surface layer of the specimen gives rise to changing the stress-strain state of its local volumes, generation, accumulation and annihilation of point defects [23-25]. however, the main relaxation processes are carried due to formation of microscale shear strains. during further cyclic deformation quite damaged surface layer is gradually degraded by accumulating local structural heterogeneities and dispersed damages [24]. the microscale level is characterized by shear processes to develop within the grains experiencing micro-plastic flow, as well as structural changes of the loaded material. generalization of surface damage mechanisms in the sensor is shown in tab. 1. mesoscale level i. within the plastically deformed surface layer as well as resulting from mechanical-structural heterogeneity some intrusions occur there which initiate corrugating processes. the latter is accompanied by formation of transverse mesoscale wrinkles to emerge on the material surface. it should be noticed that the described deformation processes do not cover the entire surface, and are concentrated within localized shear bands. with the deformation process development the stress-strain state is changed [25]. this gives rise to the strain redistribution on the surface. as a matter of fact the accumulation processes are terminated in some regions while other ones are activated that is followed by the formation of the relief structures (folds) on the surface. mesoscale level ii. stress oscillations occur due to cyclic deformations to develop at the "surface underlayer" interface that results in additional straining of the surface and subsurface layers [24]. local deformations substantially exceed the average ones over the specimen which provides activation of sliding processes on the surface and contributes to emergence of additional stress concentrators (in the form of corrugating). in doing so, localized plastically deformed regions are formed. macroscale level. the main reason for the nucleation of "spots" on the surface of the fatigue sensor is cyclic deformation and displacement of grain conglomerates. this is proved by the literature data [7, 8, 23] where strain localization and appearance of "spots" on the sensor surface are discussed. the types of damages and their scale level the mechanisms of the origin and growth of defects for various schemes of loading bending bending + torsion spots (macroscale level) shears and displacements of grain conglomerates in different planes shear and rotation deformation mechanisms shear bands, united in individual spots (mesoscale level ii) increasing sizes and width of the surface regions covered by extrusions uniting of extrusions into "packages", increasing of their height, microscale wrinkling mesoscale wrinkles (mesoscale level i) formation of predominantly individual extrusion and increasing of their width formation of multiple single and adjacent (neighboring) extrusions localized shear deformation within individual grains (microscale level) formation of shear bands in individual grains shears in grains, increasing surface microroughness table 1: scale levels and mechanisms of damage origin. in a number of previous studied based on the multiscale approach [1] the mathematical modeling techniques to simulate strain induced relief formation at various types of temperature-force impacts on material surface have been developed. the results obtained there make a background for the development of the algorithms for data processing on surface relief formation under cyclic loading [27, 28]. this allows running statistical-based analysis of the surface relief parameters of local spatial regions with taking into account the cyclic, stochastic and localized location pattern of regions with spatial self-organization of surface relief formations. the above described mechanisms are confirmed by the analysis of operating loading conditions of the d16at aluminum alloy. the analysis of the localization geometry of the strain spots and data on the optical-digital inspection allow concluding on the nonuniformity of the damaged zone development. this is l m.v. karuskevich et alii, frattura ed integrità strutturale, 38 (2016y) 205-214; doi: 10.3221/igf-esis.38.28 212 supported by data [1-3] where the accumulation of damages as a sequence of stages of strain localization is considered. in our case, the activation of additional sliding planes at the complex “bending + torsion” loading scheme increases the formation intensity as well as localization in comparison with the bending loading scheme. 0 0.2 0.4 0.6 0.8 1.0 0 0.3 0.6 0.9 1 2 h ‾ n figure 5: dependence of the shannon entropy values versus the relative number of loading cycles of the fatigue sensor: bending (1) and ʺbending + torsionʺ (2) loading schemes. in order to compare the data on sensor damaging at various loading schemes the dependence of the shannon entropy versus the relative operating time n was analyzed. in doing so, a larger cyclic running time (nc) that is characteristic feature for the bending loading was taken as equal to 1. it is also worth mentioning that the specimens simulating the sensor operation under simple bending have longevity by 1.95 times higher and damaging of 1.42 times lower (at the comparable number of loading cycles). also, the kinetics of damage accumulation on the surface of the sensor of both types differs mostly in the range of n = 0.01-0.1 while after, the contrast in mechanisms of damage accumulation has gradually reduced, fig. 5. the above considered issues on the complex analysis of the fatigue sensor damaging at various loading schemes provide an insight into the mechanisms of dispersed damage accumulation and their uniting into the "spots". this is responsible for stage pattern of the process and helped us to justify the application of the proposed approach for the evaluation of residual life of aircraft parts. conclusion he basic regularities of damage accumulation in specimen simulating the operation conditions of the fatigue sensors made from d16at aluminum alloy are revealed. with the use of the automated data processing of digital images to illustrate the damaged surface the curves describing the kinetics of damage accumulation under bending and "bending + torsion" loading schemes were constructed. sensitivity of the fatigue sensor surface to the changing of the loading scheme was established during the study at both sides of the stress concentrator. two parameters – the damaging area and the shannon entropy were employed to describe the kinetics of damage accumulation. the dependence curves of each parameter versus the number of operating cycles possess the same shape and stage pattern. it is found that in the aircraft structure these parameters are sensitive to the deformation conditions and peculiarities of dispersed and localized defect accumulation on the surface of the cladded layer of the specimens. the joint use of these parameters was tested and substantiated. references [1] panin, v.e., elsukova, t.f., egorushkin, v.e., vaulina, o.yu., pochivalov, yu.i., nonlinear wave effects of curvature solitons in surface layers of high-purity aluminum polycrystals under severe plastic deformation. i. experiment, phys. mesomech., 11 (2008) 63-72. doi:10.1016/j.physme.2008.11.009. t m.v. karuskevich et alii, frattura ed integrità strutturale, 38 (2016y) 205-214; doi: 10.3221/igf-esis.38.28 213 [2] panin, v.e., elsukova, t.f., angelova, g.v., mechanism of deformation and nucleation of fatigue cracks in aluminum polycrystals under alternating bending, doklady phys. 47 (2002) 67-71. doi:10.1134/1.1450665. [3] panin, v.e., elsukova, t.f., vaulina, o.yu., pochivalov, yu.i., nonlinear wave effects of curvature solitons in surface layers of high-purity aluminum polycrystals under severe plastic deformation. ii. the role of boundary conditions, interfaces, and nonequilibrium of a deformed state, phys. mesomech., 11 (2008) 299-307. doi:10.1016/j.physme.2008.11.009. [4] zinovieva, o., romanova, v., balokhonov, r., shakhijanov, v., emelyanova, t., a numerical analysis of formation of the surface relief: a single inclusion model, aip conf. proc., 1623 (2014) 667-670. doi:10.1063/1.4899033. [5] panin, v.e., elsukova, t.f., popkova yu.f., pochivalov, yu.i., sunder r., effect of structural states in near-surface layers of commercial titanium on its fatigue life and fatigue fracture mechanisms, phys. mesomech., 18 (2015) 1-7. doi:10.1134/s1029959915010014. [6] panin, v.e., panin, a.v., elsukova, t.f., popkova, yu.f., fundamental role of crystal structure curvature in plasticity and strength of solids, phys. mesomech., 18 (2015) 89-99. doi:10.1134/s1029959915020010. [7] ignatovich, s.r., menou, a., karuskevich, m.v., maruschak, p.o., fatigue damage and sensor development for aircraft structural health monitoring, theor. and appl. fract. mech., 65 (2013) 23-27. doi:10.1016/j.tafmec.2013.05.004 [8] burkov, m., panin, s., lyubutin, p., eremin, a., maruschak, p., menou, a. aluminum foil based fatigue sensor for structural health monitoring of carbon fiber composites, proc. tech., 19 (2015) 307-312. doi:10.1016/j.protcy.2015.02.044. [9] zinovieva, o., romanova, v., balokhonov, r., zinoviev, a., kovalevskaya, zh. numerical study of the influence of grain size and loading conditions on the deformation of a polycrystalline aluminum alloy, j. of appl. math. and phys. 2 (2014) 425-430. doi:10.4236/jamp.2014.26051. [10] panin, s.v., burkov, m.v., lyubutin, p.s., altukhov, yu.a., shakirov, i.v., fatigue damage evaluation of carbon fiber composite using aluminum foil based strain sensors, eng. frac. mech., 129 (2014) 45-53. doi:10.1016/j.engfracmech.2014.01.003. [11] luo, h., hanagud, s., pvdf film sensor and its applications in damage detection, j. aerospace eng. 12 (1999) 23-30. doi:10.1061/(asce)0893-1321(1999)12:1(23). [12] zasimchuk, e.e., gordienko, yu.g., gontareva, r.g., zasimchuk, i.k., equidimensional fractal maps for indirect estimation of deformation damage in nonuniform aircraft alloys, j. of materials engineering and performance, 12 (2003) 68-76. doi:10.1361/105994903770343501. [13] romanova, v.a., balokhonov, r.r., schmauder, s., numerical study of mesoscale surface roughening in aluminum polycrystals under tension, materials science and engineering a 564 (2013) 255-263. doi:10.1016/j.msea.2012.12.004. [14] wang, p., takagi, t., takeno, t., miki, h., early fatigue damage detecting sensors-a review and prospects, sensors and actuators a: physical, 198 (2013) 46-60. doi:10.1016/j.sna.2013.03.025. [15] yoshida, s., muhamed, i., pardede, m., widiastuti, r., muchiar, siahaan, b., kusnowo, a., optical interferometry applied to analyze deformation and fracture of aluminum alloys, theor. and appl. fract. mech., 27 (1997) 85-98. doi:10.1016/s0167-8442(97)00010-4. [16] li, h., bao, y., ou, j., structural damage identification based on integration of information fusion and shannon entropy, mechanical systems and signal processing, 22 (2008) 1427-1440. [17] maruschak, p., konovalenko, i., guzanová, a., sydor, p., panin, s., defectometry analysis of surface condition damaged with corrosion pitting, mat. sci. forum, 818 (2015) 153-157. doi:10.4028/www.scientific.net/msf.818.153. [18] sierra-pérez, j., torres-arredondo, m.a., güemes, a., damage and nonlinearities detection in wind turbine blades based on strain field pattern recognition. fbgs, obr and strain gauges comparison, composite structures, 135 (2016) 156-166. doi:10.1016/j.compstruct.2015.08.137. [19] le, v.-d., morela, f., belletta, d., saintier, n., osmond, p., multiaxial high cycle fatigue damage mechanisms associated with the different microstructural heterogeneities of cast aluminium alloys, materials science and engineering a, 649 (2016) 426-440. doi:10.1016/j.msea.2015.10.026. [20] maruschak, p., konovalenko, i., brezinová, j., zakiev, i. investigation of statically deformed aluminum alloy surface, mat. sci. forum 818 (2015) 83-88. doi:10.4028/www.scientific.net/msf.818.83. [21] deve, h., harren, s., mccullongh, c., asaro, r.j. micro and macroscopic aspects of shear band formation in internally nitrided single crystals of fe-ti-mn alloys, acta met., 36 (1988) 341-365. doi:10.1016/0001-6160(88)90011-9. m.v. karuskevich et alii, frattura ed integrità strutturale, 38 (2016y) 205-214; doi: 10.3221/igf-esis.38.28 214 [22] yoshida, s., rourks, r.l., mita, t., ichinose, k., physical mesomechanical criteria of plastic deformation and fracture, phys. mesomech., 12 (2009) 249-253. doi:10.1016/j.physme.2009.12.006. [23] ignatovich, s.r., yutskevich, s.s., monitoring of the d16at alloy according to the characteristics of deformation surface pattern, mat. sci., 47 (2011) 636-643. doi:10.1007/s11003-012-9438-5. [24] arul kumar, m., kanjarla, a.k., niezgoda, s.r., lebensohn, r.a., tomé, c.n., numerical study of the stress state of a deformation twin in magnesium, acta mat., 84 (2015) 349-358. doi:10.1016/j.actamat.2014.10.048. [25] zhang, t., jiang, j., shollock, b.a., britton, t.b., dunne, f.p.e., slip localization and fatigue crack nucleation near a non-metallic inclusion in polycrystalline nickel-based superalloy, materials science and engineering a, 641 (2015) 328–339. doi:10.1016/j.msea.2015.06.070. [26] cikalova, u., kroening, m., schreiber, j., vertyagina, ye., evaluation of al-specimen fatigue using a "smart sensor", phys.mesomech., 5-6 (2011) 308-315. doi:10.1016/j.physme.2011.12.009. [27] lytvynenko, i., maruschak, p., lupenko, s., panin, s.v., segmentation and statistical processing of geometric and spatial data on self-organized surface relief of statically deformed aluminum alloy, appl mech and materials, 770 (2015) 288-293. doi:10.4028/www.scientific.net/amm.770.288. [28] karuskevich, m.v., karuskevich, o.m., maslak, t.p., schepak, s.v., extrusion/intrusion structures as quantitative indicators of accumulated fatigue damage, international journal of fatigue 39 (2012) 116–121. doi:10.1016/j.ijfatigue.2011.02.007. << /ascii85encodepages false /allowtransparency false /autopositionepsfiles true /autorotatepages /none /binding /left /calgrayprofile (dot gain 20%) /calrgbprofile (srgb iec61966-2.1) /calcmykprofile (u.s. web coated \050swop\051 v2) /srgbprofile (srgb iec61966-2.1) /cannotembedfontpolicy /error /compatibilitylevel 1.4 /compressobjects /tags /compresspages true /convertimagestoindexed true /passthroughjpegimages true /createjobticket false /defaultrenderingintent /default /detectblends true /detectcurves 0.0000 /colorconversionstrategy /cmyk /dothumbnails false /embedallfonts true /embedopentype false /parseiccprofilesincomments true /embedjoboptions true /dscreportinglevel 0 /emitdscwarnings false /endpage -1 /imagememory 1048576 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/hrv (za stvaranje adobe pdf dokumenata najpogodnijih za visokokvalitetni ispis prije tiskanja koristite ove postavke. stvoreni pdf dokumenti mogu se otvoriti acrobat i adobe reader 5.0 i kasnijim verzijama.) /hun 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can be opened with acrobat and adobe reader 5.0 and later.) >> /namespace [ (adobe) (common) (1.0) ] /othernamespaces [ << /asreaderspreads false /cropimagestoframes true /errorcontrol /warnandcontinue /flattenerignorespreadoverrides false /includeguidesgrids false /includenonprinting false /includeslug false /namespace [ (adobe) (indesign) (4.0) ] /omitplacedbitmaps false /omitplacedeps false /omitplacedpdf false /simulateoverprint /legacy >> << /addbleedmarks false /addcolorbars false /addcropmarks false /addpageinfo false /addregmarks false /convertcolors /converttocmyk /destinationprofilename () /destinationprofileselector /documentcmyk /downsample16bitimages true /flattenerpreset << /presetselector /mediumresolution >> /formelements false /generatestructure false /includebookmarks false /includehyperlinks false /includeinteractive false /includelayers false /includeprofiles false /multimediahandling /useobjectsettings /namespace [ (adobe) (creativesuite) (2.0) ] /pdfxoutputintentprofileselector /documentcmyk /preserveediting true /untaggedcmykhandling /leaveuntagged /untaggedrgbhandling /usedocumentprofile /usedocumentbleed false >> ] >> setdistillerparams << /hwresolution [2400 2400] /pagesize [612.000 792.000] >> setpagedevice microsoft word numero_39_art_26 s. harzallah et alii, frattura ed integrità strutturale, 39 (2017) 282-290; doi: 10.3221/igf-esis.39.26 282 numerical study of eddy current by finite element method for cracks detection in structures s. harzallah, m. chabaat, k. chabane university built environmental research lab., civil engineering faculty, university of sciences and technology houariboumediene, b.p 32 el alia bab ezzouar, algiers 16111 algeria. sharzallah@usthb.dz, m.chabaat@usthb.dz, kahinachabane91@yahoo.fr abstract. in this paper, we try to use the finite element method of 2-d axisymmetry to solve problems in eddy current testing problems where the main idea is detecting crack's shape using the ndt-ec. results are given for a simple eddy current problem using the finite element method as a tool to control cracks and defects in materials and eventually, to study their propagation as well as their shape classification. these latest can be described as the task of reconstructing the cracks and damage in a tube’s profile of an inspected specimen in order to estimate its material properties. this is accomplished by inverting eddy current probe impedance measurements which are recorded as a function of probe position. this approach has been used in the aircraft industry to control cracks. besides, it makes it possible to highlight the defects of parts while preserving the integrity of the controlled products. keywords. non destructive testing; sensor eddy currents; differential mode; stress intensity factor. citation: harzallah, s., chabaat, m., chabane, k., numerical study of eddy current by finite element method for cracks detection in structures, frattura ed integrità strutturale, 39 (2017) 282-290. received: 13.10.2016 accepted: 09.12.2016 published: 01.01.2017 copyright: © 2017 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. introduction here are often sharp breaks that cause bad consequences because of existing defects (cracks, micro-cracks, crazes etc…) inside or outside parts [1]. on the other hand, usual calculations of continuum mechanics cannot predict fracture because it requires the absence of any failure or the development of fracture mechanics, defined as the science studying a structure with defects [2]. it is characterized by irreversible separation of a continuous medium into two parts on either side of a geometrical surface called crack created by damage under the effect of a biasing or default prepared when setting. it also controls the evolution of the crack, [3]. in the aircraft industry as well as in the majority of industries of transport, the non-destructive tests (ndt) can make the difference between life and death. non-destructive examination using inductive sensors is a relatively common method in the industry (aviation, automotive, nuclear power, etc…). its development is primarily due to the advanced technology provided. the ndt aims to detect cracks while preserving the integrity of the product. this definition is rather broad and t http://www.gruppofrattura.it/pdf/rivista/numero39/audio/26.mp3 s. harzallah et alii, frattura ed integrità strutturale, 39 (2017) 282-290; doi: 10.3221/igf-esis.39.26 283 related particularly to the health of the matter [1, 2]. the non-destructive testing of materials became a tool impossible to circumvent for the improvement of safety (at the time of the uniform), and of quality (during the development) [3]. eddy current sensor devices have been used for over a century in the control of conductive parts including metal parts. nowadays, the theory of eddy current sensors is already largely developed. we find its applications in various industrial fields, ranging from the measurement of the properties of matter to the detection of flaws in metal parts. due to their sensitivity to defects (fatigue cracks, inclusions or corrosion effects) [4] their implementation, easy and robust, is widespread in the context of industrial use. however, the growing need for reliability and rapidity of checking operations lead to the development of new sensors [5]. detection and characterization of a crack in a plate at its initial stage (before propagation), is a real industrial challenge and a major element in safety especially in high-risk areas. it is on the basis of these characterizations that engineers have the means to analyze such crack behavior, predict its spread and eventually assess its harmfulness as well as the life of the inspected body, [6]. in this paper, a numerical model for the assessment of eddy currents in materials, for the detection and characterization of defects is considered. we first describe the physical and geometrical properties of used materials and then, we present, through an example, results of eddy currents obtained using a numerical model that we have developed. the most promising numerical technique for computation of eddy current fields is the fem. this method has proven usefulness in demonstrating the feasibility of flaw detection under given inspection conditions. the problems studied in this work of this paper are the ndt by ec of ferromagnetic materials. these materials are largely used in various industrial fields, such as aeronautics, metallurgy and rail transport. basic equations istribution of the magnetic field and the currents induced in a conducting material, and possibly magnetic, is governed by the fundamental laws of the electromagnetism whose most general formulation is given by the maxwell's equations [7]: 0 0 0 0 s ρ  .e   ε  .  b  0  b   e      t  e     b   μ ε  μ j  t                           (1) where, b   is the magnetic induction and. e  represents the electrical field. the quantities ρ and sj  are the volume charge density and the electrical current density (flux) of any external charges, respectively. proposed model ddy current testing systems consist of configurations that are present in fig. 1 such as the conductor sensor in which c , nk represent the sample conducting region and cracks area (a damage region), respectively. on the other hand; k refers to the conductor region with its normal vector n . in a multi-conductor sensor, a high coupling is considered from the sensor and the tube as a sample. the primary field resulting from the current source ik includes contribution to the flow of all conductors k which interact entirely all due to proximity effect. in another mode, every conductor interacts with the secondary field produced by the eddy current induced in the sample. for the massive conductor  k and  s ki the interaction from the primary and secondary fields are weak because all considerations on the effects of skin and proximity [8]. d e s. harzallah et alii, frattura ed integrità strutturale, 39 (2017) 282-290; doi: 10.3221/igf-esis.39.26 284 mathematical division may be achieved by the following partial differential equation. the fem for ec phenomena 2d revolution has been developed in numerous works. for axisymmetric geometries set equations to 2d. we suggest that two-dimensional cylindrical coordinates are considered in order to study these system components of the current density   0, 0, ,s sj j r z . the magnetic vector potential   0, 0, ,a a r z and the two-dimensional cylindrical components of the magnetic vector potential (mvp) diffusion are related as follows;         c k 1 0 in in 1 1 1 1 in in nc sk k k ncoils s k kk j ra r ra ra i nr r r z r z s i n s                                              (2) where, j is the complex number, is the angular frequency, ski , k k s ds    [9].applying the galerkine’s method, with approximation functions of the magnetic vector potential (mvp), and using dirichlet boundary conditions, we can write every mesh nodes into discrete forms as follows;   c 1 1 1 0 in . in 1 in nc n m n j j n sm n j k m k kj k ncoil s k m kk j n n d a in n d a n n d s i n n s                                         k in s kd                 (3) where nn is the approximation function at node n, nm is the shape function for all nodes in a given region. then, we get the following algebraic equations [10] c k 1 0 in [ ][ ] in [ f] in [ ] [ ] in nc k ncoils k j k a m f                (4) where 1 mn m nm n n d                 (5) . .mn m n kk n n d    (6) sk m m k k i f n n d s     (7) s. harzallah et alii, frattura ed integrità strutturale, 39 (2017) 282-290; doi: 10.3221/igf-esis.39.26 285 impedance analysis etection of the change in the resulting magnetic fields is based on two basic methods: the ndt differential mode represented by two separate coils linked magnetically and supplied by the same current and the nde absolute mode which makes use of only one coil. the impedance variation is obtained from comparison with the reference impedance. the impedance variation z is a complex number. the imaginary part is computed with the magnetic energy (wm) in the whole meshed domain and the real part is computed with the joule losses in the conductive media and the imaginary part is computed with the magnetic energy in the whole meshed domain [11]. the coil impedance with an excited current at a frequency f is obtained by the following expression [12]:       2 22 f c jl z   i 1          j j d σ re re z             (8) and,       m 2 22 f c ω w   z   i 1   z    b b  μ im im               (9)   2 2 j1    ( d  j2 πf  b.h  d σi z r jx z            (10) where, z is the impedance given as a complex number, jl represents the joule losses and wm corresponds to the magnetic energy. i is the current source and h is the magnetic field. besides, jf , j and bf, b are the current density field and the magnetic induction field, respectively. these parameters are calculated with and without a defect and are both software post-treatment quantities. figure 1: sensor-tube geometrical configuration. simulation sensor – tube without a crack he inspection of tubes is usually carried out by using the eddy currents testing through the analysis of the impedance variations. the considered device is shown in fig. 1. for the first application, we tested a non-magnetic tube without any crack and characterized by a permeability equal to the unit, a high conductivity 36.7 106 ms, d t s. harzallah et alii, frattura ed integrità strutturale, 39 (2017) 282-290; doi: 10.3221/igf-esis.39.26 286 excited by a sinusoidal current of density of current j = 2.67 106 a/m and a frequency of 10 khz. here, the crack size length is taken to be 4mm. results interpretations results of a simulation obtained for the case of a non-magnetic tube without defects are illustrated in the following figures: fig. 2 represents the distribution of the potential of the vector. it exposes a great power of concentration of the potential to the level of the inductor and of weak in values from where the high use of the frequency. figs. 3 and 4 show the orientation of the field lines. this field concentrates on the level of the probe and its degree penetration depth in the tube remains very weak. besides, the effect of the penetration depth on a side is crucial for a high frequency and depends on other dimensions as well as the nature of the non-magnetic target representing the homogeneous part. figure 2: representation of the potential vector. figure 3: circulation of the field lines. fig. 5 gives lines of equipotential of the real part (the source) and the imaginary part (the part induced in the load) of the magnetic potential vector with a zero value of the magnetic potential on l axis of symmetry of the two reels. fig. 6 indicates the distribution of magnetic induction. that explains the strong concentration of the vectors of magnetic induction on the level of the inductor without the possibility to penetrate inside the tube due to the characteristics of the material and the effect of the frequency. it represents the vectors of magnetic inductions which turn around the two inductors in contrary directions because of the reverses excitation of the two inductors. 0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.1 0.04 0.05 0.06 0.07 0.08 0.09 0.1 s. harzallah et alii, frattura ed integrità strutturale, 39 (2017) 282-290; doi: 10.3221/igf-esis.39.26 287 figure 4: representation of the vector of induction b. fig. 7 represents the distribution of the currents induced on the surface of target. it is noticed that their values are high because the conductivity of the non-magnetic target is considerable (j = σ.2π.f.a) but are relatively weak compared to the primary currents. it is known that the complex impedance has two parts, a real part given by resistance and an imaginary part given by the reluctance. in the analysis of fig. 8, we remark that more the frequency is high and more the impedance z, given by the difference between the two impedances constituting the sensor, increases. this increase is due to the effect of skin being very important and also, to an existing crack. figure 5: representation of the real and imaginary part of the potential. figs. 9 and 10 represent the evaluation of resistance and reactance of the sensor (ω). 0.04 0.045 0.05 0.055 0.06 0.04 0.045 0.05 0.055 bxx , byy 0.04 0.06 0.04 0.045 0.05 0.055 0.06 0.065 0.07 -3 -2 -1 0 1 2 3 x 10 -6 0.04 0.06 0.04 0.045 0.05 0.055 0.06 0.065 0.07 -4 -3 -2 -1 0 1 2 3 4 x 10 -7 s. harzallah et alii, frattura ed integrità strutturale, 39 (2017) 282-290; doi: 10.3221/igf-esis.39.26 288 figure 6: representation of the magnetic induction. figure 7: density of induced currents. . figure 8: ∆z for f =10, 100 and 240 khz. figure 9: the imaginary part impedance z (ω). figure 10: the real part impedance z (ω). effects between dimensions of a defect and the sensors in this research, we consider two cases of shape’s geometries. each one includes three different defects and for each system, we obtain results after the execution of the program. these values are represented in the form of curves of the impedance δz. in fig. 11 and 12, when the width decreases, the value of impedance δz decreases. the width of the defect has a great influence on the variation of impedance. the variation depth of the defect has a light influence on δz. it is noticed that the difference of impedance δz has a relationship with the width of the defect. whenever the width of defect increases, δz automatically increases and vice versa. consequently, the depth of defect has an influence on impedance. the variation depth of the defect has a light influence on δz. it is noticed that the difference of impedance δz correlates with the width of the defect. it is noticed that the difference of impedance δz has a dependency on the width of the defect and the depth of a defect has a great influence on the impedance. 0.025 0.03 0.035 0.04 0.045 0.05 0.055 0.06 0.065 0.07 0.04 0.045 0.05 0.055 0.06 0.065 0.07 0.5 1 1.5 2 2.5 3 x 10 -3 0.025 0.03 0.035 0.04 0.045 0.05 0.055 0.06 0.065 0.07 0.04 0.045 0.05 0.055 0.06 0.065 0.07 0 2 4 6 8 10 12 14 16 x 10 -3 -0.025 -0.02 -0.015 -0.01 -0.005 0 0.005 0.01 0.015 0.02 0.025 -0.5 -0.4 -0.3 -0.2 -0.1 0 0.1 0.2 0.3 0.4 0.5 -0.025 -0.02 -0.015 -0.01 -0.005 0 0.005 0.01 0.015 0.02 0.025 -2.5 -2 -1.5 -1 -0.5 0 0.5 1 1.5 2 s. harzallah et alii, frattura ed integrità strutturale, 39 (2017) 282-290; doi: 10.3221/igf-esis.39.26 289 figs. 13-16 represent the evaluation of resistance and reactance of the sensor versus the crack depth and width. we notice that when the width decreases, the value of resistance and the reactance decrease in a proportional way. figure 11: impedance z vs. crack width. figure 12: impedance z vs. crack depth. conclusion t is shown through this research work that obtained results are identified by a variation of impedance of the magnetic currents values. these values agreed with the previous results that lead us to determine the mechanical properties of fracture of materials. the new approach has been useful in the study of expansion and crack propagation in materials. it can easily predict afuture damage of mechanical parts. besides, this technique can be benefit in the treatment of materials rather than changing parts. it gives accurate results and high performance for parts of materials. herein, a possible prediction of cracks propagation through the determination of parameters sif and j-integral using eddy currentby detecting crack tip opening displacement is described. similar results are obtained for both parameters kand jintegral using variation of the impedance. notice that this method is widely used in industrial application because of its precision (minimal error) and its low costs. figure 13: evaluation of resistance and reactance sensor vs. crack depth. figure 14: evaluation of resistance and reactance sensor vs. crack width. 0.04 0.045 0.05 0.055 0.06 0.065 0 20 40 60 80 100 120 width=1.4mm width=1.2mm width=1 mm 0.04 0.045 0.05 0.055 0.06 0.065 0 20 40 60 80 100 120 depth=3mm depth=2mm depth=1mm -100 -80 -60 -40 -20 0 20 40 60 80 100 -250 -200 -150 -100 -50 0 50 100 150 200 250 reactance(v/i) r e s is t a n c e ( v /i ) w=1mm w=2mm w=3mm w=4.5mm -100 -50 0 50 100 150 -250 -200 -150 -100 -50 0 50 100 150 200 250 risistance z r e a c t a n c e x l=1mm l=2mm l=3mm i s. harzallah et alii, frattura ed integrità strutturale, 39 (2017) 282-290; doi: 10.3221/igf-esis.39.26 290 figure 15: evaluation of the reactance of the sensor vs. crack width. figure 16: evaluation of resistance of the sensor vs. crack depth. references [1] horan. p, underhill. p. r., krause. t. w., pulsed eddy current detection of cracks in f/a18 inner wing spar without wing skin removal using modified principal component analysis, ndt&e international, 55 (2013) 21-27. [2] hamia, r., dolabdjian, c., eddy-current non-destructive testing system for the determination of crack orientation, ndt & e international, 61 (2014) 24–28. [3] uchimoto, t., takagi, t., ichihara, t., dobmann, g., evaluation of fatigue cracks by an angle beam emat–et dual probe, ndt & e international, 72 (2015) 10–16. [4] zaoui, a., menana, h., feliachi, m., berthiau, g., inverse problem in nondestructive testing using arrayed eddy current sensors.sensors, 10(9) (2010) 8696-8704. [5] skarlatos, a., pichenot, g., lesselier, d., electromagnetic modeling of a damaged ferromagnetic metal tube via a volume integral formulation,ieee trans. mag, 44 (2008) 623-632. [6] garcia-martin, j., gomez-gil, j., vazquez-sanchez, e., non-destructive techniques based on eddy current testing, sensors, 3 (2011) 2525-2565. [7] harzallah, s., chabaat, m., nondestructive technique for the determination of cracks parameters by eddy current in differential mode, journal of applied mechanics & materials, 532 (2014) 81-89. [8] harzallah, s., chabaat, m., benissad, s., formulation for stress intensity factors and j-integral calculation by eddy current testing, international journal of key engineering materials, 660 (2015) 225-230. [9] harzallah, s., chabaat, m., benissad, s., inverse problems using neural networks for cracks characterization in materials, international journal of key engineering materials, 660 (2015) 361-365. [10] harzallah, s., chabaat, m., eddy current sensor modeling for the nondestructive evaluation of stress intensity factor, journal aasriprocedia, elsevier ltd., 9 (2014) 57–63. [11] harzallah, s., chabaat, m., bin muhammad, b.f., eddy current modeling by finite element method for evaluation of mechanical properties of the structure cracked in absolute probe, aip conference proceedings, 1637(1) (2014) 1416. [12] harzallah, s., chabaat, m., bin muhammad, b.f., non destructive technique for cracks detection by an eddy current in differential mode for steel frames, aip conf. proc., 1637 (2014) 1406. 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can be opened with acrobat and adobe reader 5.0 and later.) >> /namespace [ (adobe) (common) (1.0) ] /othernamespaces [ << /asreaderspreads false /cropimagestoframes true /errorcontrol /warnandcontinue /flattenerignorespreadoverrides false /includeguidesgrids false /includenonprinting false /includeslug false /namespace [ (adobe) (indesign) (4.0) ] /omitplacedbitmaps false /omitplacedeps false /omitplacedpdf false /simulateoverprint /legacy >> << /addbleedmarks false /addcolorbars false /addcropmarks false /addpageinfo false /addregmarks false /convertcolors /converttocmyk /destinationprofilename () /destinationprofileselector /documentcmyk /downsample16bitimages true /flattenerpreset << /presetselector /mediumresolution >> /formelements false /generatestructure false /includebookmarks false /includehyperlinks false /includeinteractive false /includelayers false /includeprofiles false /multimediahandling /useobjectsettings /namespace [ (adobe) (creativesuite) (2.0) ] /pdfxoutputintentprofileselector /documentcmyk /preserveediting true /untaggedcmykhandling /leaveuntagged /untaggedrgbhandling /usedocumentprofile /usedocumentbleed false >> ] >> setdistillerparams << /hwresolution [2400 2400] /pagesize [612.000 792.000] >> setpagedevice microsoft word numero_30_art_11 g. ferro et alii, frattura ed integrità strutturale, 30 (2014) 75-83; doi: 10.3221/igf-esis.30.11 75 focussed on: fracture and structural integrity related issues improvements in self-consolidating cementitious composites by using micro carbonized aggregates giuseppe andrea ferro, sajjad ahmad, rao arsalan khushnood, luciana restuccia department of structural, geotechnical and building engineering, politecnico di torino, c.so duca degli abruzzi, 24-10129, torino, italy ferro@polito.it, sajjad.ahmad@polito.it, rao.khushnood@polito.com, luciana.restuccia@polito.it jean marc tulliani department of applied science and technology, politecnico di torino, c.so duca degli abruzzi, 24-10129, torino, italy jeanmarc.tulliani@polito.it abstract. there is growing interest in the use of self-consolidating cementitious systems in construction industry. the present research was conducted to enhance the mechanical performance of cement composites by the utilization of micro-sized inert particles. this paper deals with the synthesis of micro-sized inert carbonized particles from hemp hurds. the synthesized carbonized particles were characterized by field emission scanning electron microscope (fesem). these particles were further used as additive in self-consolidating cement composites. total of four different wt% additions (i.e. 0.08, 0.20, 1.00 and 3.00 by wt% of cement) were investigated. the cement composites containing carbonized particles inclusions were characterized by three point bending and compression tests. the results indicate that the carbonized particles additions enhanced the flexural and compressive strengths of the cement composites. it was also observed that the fracture properties and the energy absorption capability of the cement composites were enhanced substantially. keywords. self-consolidating cement composites; pyrolysis; hemp hurds; fracture energy; toughness indices. introduction oncrete is the most produced and utilized manmade composite in the world. it is majorly composed of cement, aggregate and sand [1]. in recent years, production of cement has reached to 4.0 billion metric ton [2]. the production of ordinary portland cement (opc) is an energy intensive process and a major cause of anthropogenic production of co2 in the atmosphere [3]. for the standpoint of eco-efficiency and sustainability, it is highly desirable to improve the mechanical performance of the cement composites. high performance of cement composites can be achieved by good proportioning of the mix quantities i.e. cement, sand, water and mineral or chemical additives. various types of powders/fillers such as fly ash, silica fume, metakaolin, limestone, glass, ground granulated blast furnace slag, bentonite, rice husk ash, coconut shell ash have already been investigated by the researchers for the production of high performance cement composites [4–12]. the utilization of the nano/micro-sized fillers improves the mechanical performance due to the secondary hydration, heterogeneous nucleation and/or due to the filling effect of small particles c g. ferro et alii, frattura ed integrità strutturale, 30 (2014) 75-83; doi: 10.3221/igf-esis.30.11 76 [13]. in the present research, a novel micro-sized material has been synthesized by the pyrolysis of hemp hurds and afterwards has been utilized in the production of cement composites. history of hemp cultivation and use dates back to twelve thousands years. in the 16th century hemp was considered as a necessary crop for the production of cloth, food, oil and ropes [14]. in the beginning of nineteenth century its importance was reduced due to the development of cotton and synthetic fibers; however the interest of farmers has been revived by the use of hemp as insulation material, energy recovery and feedstock for paper [15]. currently hemp is cultivated over an area of 41,246 hectare around the world producing 53,495 metric ton of hemp tow waste [16]. hemp belongs to the cannabis family of plants. it is a fast growing plant with a maturity age of 3 to 4 months. the plant usually grows in a single and slender stem of around 20 mm thickness and height can range up to 5 meters at maturity [17]. the stem tissues inside the bark are referred as hemp or bast fiber. the fibers are composed of disordered arrangement of cellulose fibrils that are held together by the complex organic matrix of hemicellulose, lignin and proteins [18]. the inner woody portion that is surrounded by the hemp fibers contains the pith and xylem vessels and is referred as hurd or hemp hurd (fig. 1) [17]. the hemp hurds (hh) have wood like structure and makes about 70% of the mass of stem [19]. figure 1: transverse section of hemp stem major portion of hemp hurd (hh) is generally used for inferior applications such as animal bedding etc. being economically available, hemp hurds have been successfully tried with cement composites for producing light weight concrete or hempcrete, in epoxy composites and in magnesium oxide composites for producing thermal insulation panels [20]. there is nothing in the literature so far concerning its use in carbonized form in self-compacting cementitious systems. in the current study, hemp hurds have been investigated in a novel way to enhance the mechanical performance and fracture properties of self-compacting cementitious composites. materials and methods materials ement composite samples were prepared with general purposes ordinary portland cement type-1 (buzzi unicem 52.5r). high range water reducer mapei dynamon sp-1 was used to provide fluidity or workability to the cement composites. general properties of cement and admixture are reported in tab. 1 and 2 [21, 22]. hemp hurds were obtained from the piedmont region of italy and in house synthesis of inert carbonized particles was carried out in the department of applied science and technology (disat) of politecnico di torino. details of the synthesis are given in following text. physical characteristics standard average values density 2,800 kg/m3 specific surface area uni en 196-6 480 m2/kg color light grey chemical composition cao sio2 al2o3 fe3o4 so3 mgo k2o % content 44 9.5 26.5 2.5 12 1.3 0.6 table 1: physical and chemical properties of cement [21]. c g. ferro et alii, frattura ed integrità strutturale, 30 (2014) 75-83; doi: 10.3221/igf-esis.30.11 77 feature value appearance amber specific gravity 1.090 ph value 6.5 9.0 solid content 30.50% recommended dosage 1.5 wt% of cement table 2: properties of super plasticizer [22]. synthesis of inert carbonized particles the as obtained hemp hurds (fig. 2) were dried in oven for 24 hours at 105±5oc. the dried hemp hurds were carbonized in a small air-tight quartz reactor under inert atmosphere. the inert atmosphere was obtained by the constant flow of argon gas under a pressure of 0.2 bar. the heating ramp of the furnace was fixed at 1oc/sec. the hemp hurds were carbonized at 850oc for 1 hour. after the completion of carbonization process, the carbonized hemp hurds were cooled and then removed from quartz reactor. the carbonized material was grinded by mortar and pestle and passed through astm sieve #120 (aperture size of 125µm). the sieved powder was then ball milled by using 10 mm diameter agate beads for 120 hours. the particle size was determined by means of a laser granulometer after ball milling and the average particle size was less than 14 µm. then, the size of ground material was further reduced with the help of attrition milling. attrition milling was carried out for 1 hour by using 2 mm alumina balls and distilled water as grinding media. after the attrition milling the powder was dried in oven and stored in air tight container for further use. figure 2: (a) as obtained hemp hurds (b) carbonized and grinded hemp hurds. material characterization the synthesized inert carbonized particles were observed by means of “supra-40 carl zeiss” field emission scanning electron microscope (fesem) for their microstructure and morphology. the fesem micrographs are reported in fig. 3. fesem micrographs of ground-carbonized particles show their smooth texture and glossy surface. the edges of particles are sharp and highly angular indicating their brittleness. the size of particles varies from several nanometers (approx. 200 nm) to few micrometers (approx. 3 µm). raman analysis of ground powder was carried out by using “renishaw ramanscope” operating at 514.5 nm wavelength. the results of analysis are represented in fig. 4. in raman spectra, two distinct peaks occurring at 1352 cm-1 & 1578 cm-1 are related to d-band & g-band, respectively. g-band refers to the graphitic structure of the carbon material and it is used as a measure of material’s quality. d-band is the defect band indicating the presence of defects in the crystal structure of material. the intensity peak ratio of d & g-bands (id/ig) of carbonized hemp powder is 0.66 indicating degree of structural defects concentration in the ground carbonized hemp hurds. g. ferro et alii, frattura ed integrità strutturale, 30 (2014) 75-83; doi: 10.3221/igf-esis.30.11 78 figure 3: fesem micrographs of carbonized and ground hemp hurds. figure 4: raman analysis of carbonized hemp powder. preparation of composite samples five cement composites were prepared: four with various contents of inert carbonized particles and one without any inclusion to be used as reference. composition details of cement mixes are reported in tab. 3. notation inert carbonized particles weight (%) weight (mg) cem 0 0 cem +0.08% hh 0.08 171 cem +0.20% hh 0.20 428 cem +1.00% hh 1.00 2140 cem +3.00% hh 3.00 6420 *for each mix 214 g cement, 75 g water and 3.21 g hrwra were used. table 3: composition of cement composites. procedure followed for the preparation of the cement composite samples is given below: a. the inert carbonized particles were added in to the solution of water and superplasticizer, b. the mixture was then sonicated for 15 minutes, c. after sonication the mixture was transferred into the mixing bowl and mixer was started, d. mixer speed was kept at 440 rpm and the cement was added gradually in the mixing bowl within 60 seconds, e. after the addition of cement the mixing was carried out for another 60 seconds at constant speed (i.e. 440 rpm), f. then, the speed was increased to 630 rpm and mixing was done for 2 more minutes, hence making the total mixing time of 4 minutes, g. after completion of the mixing, the paste was transferred into the acrylic molds of 20 20 75  mm3, h. the molds were then kept in air tight boxed having humidity level of 90%, i. after the completion of 24 hours of sample preparation, the samples were removed from molds and kept in water for immersed water curing of 28 days, j. at the completion of curing period the samples were removed and 2 mm thick and 6 mm deep u shaped notches were made, testing methods the cured and notched cement composite samples were tested for their strengths in flexure and compression. for flexural strength the cement samples were analyzed in three point bending according to the astm c348 [23] by using a single column zwick-line z010 testing machine. the crack mouth opening displacement (cmod) controlled mode was 0 500 1000 1500 2000 2500 3000 3500 2d 2d' d d+g in te n si ty ( a .u .) raman shift (cm -1 ) g g. ferro et alii, frattura ed integrità strutturale, 30 (2014) 75-83; doi: 10.3221/igf-esis.30.11 79 selected for all the specimens and displacement rate was fixed at 0.003 mm/min. the portions of broken prisms were tested in compression according to astm c349 [24]. for compression, the displacement rate was kept at 0.50 mm/min and 0.80 mm/min for loading and unloading the specimens. typical test setup for flexural and compression test is shown in fig. 5(a) and 5(b). figure 5: test setup for: (a) flexural strength test & (b) compressive strength test small broken pieces of specimens from compression tests were analyzed by fesem for their microstructure. fesem images are shown in fig. 6. figure 6: fesem images of cement composite containing inert carbonized particles results and discussions he notched specimen were tested in three point bending. minimum three specimens were tested for each composition and their average modulus of rupture (mor) was evaluated according eq. (1): 2 2  3     2 max max f l wh   (3) where f is the maximum force in the load deflection curve, l is the span length, w is the specimen width, h is the specimen height. t g. ferro et alii, frattura ed integrità strutturale, 30 (2014) 75-83; doi: 10.3221/igf-esis.30.11 80 typical load-cmod curves and fracture surfaces as experimentally recorded for cement composite specimens with and without micro carbonized inerts are shown in fig. 7 and 8. the comparison of average modulus of rupture of cement composite mixes is given in fig. 9. (a) (b) figure 7: typical load vs. cmod curves for (a) cement (b) cement with 0.08 wt% carbonized hemp hurds figure 8: fracture surface of cement composite samples (a) cement (b) cement with 0.08wt% carbonized hemp hurds figure 9: comparison of flexural strength of cement composites containing various wt% of carbonized hemp hurds the analysis of flexural strength results demonstrated some sort of mixed trend of increase and decrease in proportion to increase in the content of carbonized particles inclusions. a slight increase of 7% in mor was achieved on addition of 0.08 wt% hh but there was noticeable decrease on further addition up to 3%. the fracture surfaces are highly affected by the inert particles inclusion. it seems that carbonized particles act as a heterogenic obstacle in the way of crack tip and (a) (b) g. ferro et alii, frattura ed integrità strutturale, 30 (2014) 75-83; doi: 10.3221/igf-esis.30.11 81 either forced it to deflect or to transform it into multiple cracks (fig. 6). as a result, several times increase was observed in the area of fracture surface as compared to the cross section of reference cement specimen. the load deflection curves were further analyzed and fracture toughness parameters were evaluated as per standard set forth in astm c1018 [25]. based on eq 2(a & b) toughness indices i5 and i10 were evaluated for all the compositions with and without micro-carbonized particles. related results of i5 and i10 are given in fig 10 & 11 respectively:        &         3    1     5        &         1     st st area under the force cmod curve up to times the crack cmod i area under the force cmod curve up to crack cmod  (2a)        &         5.5    1     10          &         1     st st area under the force cmod curve up to times the crack cmod i area under the force cmod curve up to crack cmod  (2b) evaluated toughness indices (i5 & i10) of the cement composites clearly demonstrate that the addition of hh (in microcarbonized form) significantly increase the fracture toughness. the rate of increase in flexural toughness is non-linearly related to the added content of micro-carbonized hh. it is believed that presence of high number of irregular shaped carbonized particles control the cracks by increasing their lengths. this phenomenon considerably increases the energy required for crack propagation and resultantly enhances the overall fracture toughness of cement composites. figure 10: comparison of toughness index i5 of cement composites containing various wt% of carbonized hemp hurds. figure 11: comparison of toughness index i10 of cement composites containing various wt% of carbonized hemp hurds. compression tests were carried out by using the broken pieces of the prisms from flexural test. the results of compressive strength tests are reported in fig. 12. the results showed increasing trend up to 1 wt% carbonized particles inclusion and then decrease in strength. the maximum compressive strength enhancement was about 58% at 1 wt% inclusion. this strength enhancement may be attributed to the filling action of inert particles inclusion in the cement matrix and resulting in higher packing density. figure 12: comparison of compressive strength of cement composites containing various wt% of carbonized hemp hurds g. ferro et alii, frattura ed integrità strutturale, 30 (2014) 75-83; doi: 10.3221/igf-esis.30.11 82 conclusions n this work micro-carbonized particles were prepared from hemp hurd by controlled pyrolysis. these particles were found quite effective in enhancing compressive strength and fracture toughness of cement matrix composites. it is believed that irregular shaped micro particles contouring by the crack and crack pinning are the mechanisms, which can explain the increase of toughness in the composite samples. acknowledgements he authors are grateful to dr. guastella salvatore for fesem and edx analysis, to mr. felice giraudo (assocanapa) for hemp hurds supplying, to dr. stefano broggio (mapei s.p.a.) for superplasticizer providing and to dr. fulvio canonico (buzzi unicem s.p.a.) for cement providing. sajjad ahmad and rao arsalan khushnood wish to acknowledge the phd study grant of higher education commission pakistan (ref no. hrdiuestps/hec/2012/36). references [1] gambhir, l., concrete technology, 3rd ed. tata mcgraw-hill publishing cny, (2004). [2] van oss, h. g., usgs, cement statistics, u.s. geological survey, mineral commodity summaries, (2014). http://minerals.usgs.gov/minerals/pubs/commodity/cement/mcs-2014-cemen.pdf. [3] worrell, e., price, l., martin, n., hendriks, c., meida, l. o., carbon dioxide emissions from the global cement industry, annu. rev. energy environ., 26 (2001) 303–329. [4] khatib, j. m., performance of self-compacting concrete containing fly ash, constr. build. mater., vol. 22, no. 9, pp. 1963–1971, sep. 2008. [5] oertel, t., hutter, f., helbig, u., sextl, g., amorphous silica in ultra-high performance concrete: first hour of hydration, cem. concr. res., 58 (2014) 131–142. [6] grilo, j., santos silva, a., faria, p., gameiro, a., veiga, r., velosa, a., mechanical and mineralogical properties of natural hydraulic lime-metakaolin mortars in different curing conditions, constr. build. mater., 51 (2014) 287–294. [7] rashad, a. m., metakaolin as cementitious material: history, scours, production and composition – a comprehensive overview, constr. build. mater., 41 (2013) 303–318. [8] baldino, n., gabriele, d., lupi, f. r., seta, l., zinno, r., rheological behaviour of fresh cement pastes: influence of synthetic zeolites, limestone and silica fume, cem. concr. res., 63 (2014) 38–45. [9] aly, m., hashmi, m. s. j., olabi, a. g., messeiry, m., hussain, a. i. ,effect of nano clay particles on mechanical , thermal and physical behaviours of waste-glass cement mortars, mater. sci. eng. a, 528(27) (2011) 7991–7998. [10] sharmila, p., dhinakaran, g., influence of nano slag on micro-structure, capillary suction and voids of high strength concrete, int. j. chemtech res., 6(4) (2014) 2521–2528. [11] memon, s. a., arsalan, r., khan, s., lo, t. y., utilization of pakistani bentonite as partial replacement of cement in concrete, constr. build. mater., 30 (2012) 237–242. [12] antiohos, s. k., papadakis, v. g., tsimas, s., rice husk ash (rha) effectiveness in cement and concrete as a function of reactive silica and fineness, cem. concr. res., 61–62 (2014) 20–27. [13] lawrence, p., cyr, m., ringot, e., mineral admixtures in mortars: effect of inert materials on short-term hydration, cem. concr. res., 33(12) (2003) 1939–1947. [14] luginbuhl, a. m., industrial heinp ( cannabis savita l ): the geography of a controversial plant, calif. geogr., 41 (2001) 1–14. [15] finnan, j., styles, d., hemp: a more sustainable annual energy crop for climate and energy policy, energy policy, 58 (2013) 152–162. [16] faostat agriculture data, food and agriculture organization of united nations; hemp area, yield and production, (2012). http://faostat3.fao.org/faostat-gateway/go/to/download/q/qc/e (2014). [17] olsen, j., information paper on industrial hemp (industrial cannabis), department of primary industries, queensland, (2004). i t g. ferro et alii, frattura ed integrità strutturale, 30 (2014) 75-83; doi: 10.3221/igf-esis.30.11 83 [18] stevulova, n., kidalova, l., junak, j., cigasova, j., terpakova, e., effect of hemp shive sizes on mechanical properties of lightweight fibrous composites, procedia eng., 42 (2012) 496–500. [19] beaugrand, j., nottez, m., konnerth, j., bourmaud, a., multi-scale analysis of the structure and mechanical performance of woody hemp core and the dependence on the sampling location, ind. crops prod., 60 (2014) 193– 204. [20] sassoni, e., manzi, s., motori, a., montecchi, m., canti, m., novel sustainable hemp-based composites for application in the building industry: physical, thermal and mechanical characterization, energy build., 77 (2014) 219– 226. [21] buzzi unicem, buzzi unicem next, user manual, http://www.buzziunicem.it/online/download.jsp?iddocument=2327&instance=1, (2014) [22] mapei spa, mapei; adhesives, sealants, chemical products for buildings, material safety data sheet (msds), http://www.mapei.com/public/com/products/671_dynamon_sp1_gb.pdf, (2014) [23] astm, astm c348-02 standard test method for flexural strength of hydraulic cement mortars, (2002) 7. [24] astm, astm c349-02 standard test method for compressive strength of hydraulic cement mortars (using portions of prisms broken in flexure), (2002) 4. [25] astm, astm c1018-97 standard test method for flexural toughness and first-crack strength of fiber reinforced concrete (using beam with third-point loading), (1997) 7. microsoft word numero_39_art_17 m. shariati et alii, frattura ed integrità strutturale, 39 (2017) 166-180; doi: 10.3221/igf-esis.39.17 166 investigation of stress intensity factor for internal cracks in fg cylinders under static and dynamic loading mahmoud shariati ferdowsi university of mashhad, mashhad, iran mshariati44@um.ac.ir, http://orcid.org/0000-0001-8742-2975 masoud mahdizadeh rokhi shahrood university of technology, shahrood, iran mmrokhi@shahroodut.ac.ir, http://orcid.org/ 0000-0001-6973-8431 hassan rayegan university of birjand, birjand, iran hassanrayegan@yahoo.com abstract. this paper investigates the variations of mode i stress intensity factor (ki) for inner penny-shaped and circumferential cracks in functionally graded solid and hollow thick walled cylinders, respectively with the changes of crack geometry, material gradation and loading conditions. the functionally graded material of cylinders consists of epoxy and glass. it is assumed that the mechanical properties vary with a power law in the radial direction of cylinders. micromechanical models for conventional composites are used to estimate the material properties of functionally graded cylinders. the equations of motion obtained from the extended finite element discretization are solved by the newmark method in the time domain. the interaction integral method is employed to calculate the mode i stress intensity factor (ki). the matlab programming environment was implemented to solve the problem. keywords. stress intensity factor; functionally graded cylinders; pennyshaped cracks; circumferential cracks; extended finite element method; rotational speed. citation: shariati, m., mahdizadeh rokhi, m., rayegan, h., investigation of stress intensity factor for internal cracks in fg cylinders under static and dynamic loading, frattura ed integrità strutturale, 39 (2017) 166-180. received: 12.06.2016 accepted: 11.10.2016 published: 01.01.2017 copyright: © 2017 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. introduction unctionally graded materials (fgms) are a new class of composite materials in which their composition and structure gradually change resulting in a corresponding change in their properties. these materials are used extensively in applications such as thermal barrier coatings are exposed to severe stress gradients induced by f http://www.gruppofrattura.it/pdf/rivista/numero39/audio/17.mp3 m. shariati et alii, frattura ed integrità strutturale, 39 (2017) 166-180; doi: 10.3221/igf-esis.39.17 167 thermal and/or mechanical loading [1]. fgms can be used in the construction of tanks and cylindrical furnace such as cement kiln. circumferential cracks are occasionally developed in cylindrical structures during service or production. these cracks are threats to the safety and reliability of these structures. subsequent fracture and fatigue analysis of such cracks is of great interest, and requires the determination of stress intensity factors. the stress intensity factor (sif) is an important parameter to determine the safety of a cracked part. although several stress intensity factor handbooks have been published, the available solutions of stress intensity factors for pressure vessels are not always adequate for particular engineering applications. [2] solutions to the problem concerning a circumferential crack in a circular cylinder made of homogeneous or composite materials are relatively few. closed form stress intensity factor of an arbitrarily located inner-surface circumferential crack in an edge-restraint homogeneous cylinder under linear radial temperature distribution derived by meshii and watanabe [3]. chen [4] evaluated stress intensity factors in a cylinder with a circumferential crack using the computing compliance and the finite difference methods to solve the boundary value problem. lee [5] analyzed the stress distribution in a long circular cylinder of isotropic elastic material with a circumferential edge crack under uniform shearing stress and determined the stress intensity factor. jones [6] applied the impulse response method to the analysis of the thermally striped internal surface of a hollow cylinder containing a circumferential crack on this surface. he calculated stress intensity factor and strain energy density factor ranges as functions of crack depth for various sinusoidal striping frequencies. moulick and sahu [2] derived weight functions for the surface and the deepest point of an internal semi elliptical crack in a thick-wall cylinder. tran and geniaut [7] developed an extended finite element method (x-fem) axisymmetric model and employed it to compute stress intensity factors for cracked industrial specimens and components. they used the x-fem model to assess the integrity and durability of a cracked rotor coil retaining ring during the power plant operation. wu et al. [8] described a three-dimensional domain integral method for extracting mixed-mode stress intensity factors. predan et al. [9] calculated the stress-intensity factor for the circumferential semielliptical surface cracks in a hollow cylinder cross section under torsion using a finite element technique. sharma [10] et al. used the extended finite element method to evaluate the stress intensity factors of a semi-elliptical part through thickness axial/circumferential crack. the pipe or pipe-bend having a crack on the outer surface was subjected to internal pressure or opening bending moment in their research. seifi [11] determined the stress intensity factors for internal surface cracks in autofrettaged functionally graded cylinders. eshraghi and soltani [12] obtained stress intensity factors for functionally graded cylinders with internal circumferential cracks using the weight function method for different combinations of cylinder geometry, crack depth, and material gradation. in this paper, two problems are considered; the first is the determination of the stress intensity factor (ki) of an inner penny-shaped crack in a fg rod loaded by uniform axial tension and the second problem is the calculation of the sif for an inner circumferential crack in a fg thick walled cylinder under uniform axial tension. both problems are solved under static and dynamic loading conditions. the extended finite element method is used in this study, to compute the stress and displacement fields necessary for determining the stress intensity factor. stress intensity factors are obtained using the interaction integral method. the newmark time integration scheme is used to solve the dynamical system of matrix equations obtained from the spatial discretization of equations of motion. the effects of crack radius, rotational speed of cylinders and material gradation on sifs are studied. the programming is done in matlab. modeling of functionally graded cylinder n the present study, we assume that the material properties change along the radius of the cylinder and the volume fraction of inclusion iv follows a simple power function, iv r r r w r r r w p / , (2-1) where r and w are inner radius and thickness of cylinder, respectively. p is the power exponent determining the volume fraction profile. the volume fraction of matrix mv is obtained as below. m iv r v r1 (2-2) i m. shariati et alii, frattura ed integrità strutturale, 39 (2017) 166-180; doi: 10.3221/igf-esis.39.17 168 we assume that the functionally graded cylinder is made of epoxy-phase and glass-phase. in this study, micromechanical models for conventional composites [13, 14] are employed to calculate the properties of functionally graded cylinder. according to these models, the shear modulus of rigidity ( ) and bulk modulus ( k ) of fgm cylinder are obtained by the following equations. i i m m m i m m m m m m m v v k k 1 9 8 6 2 (2-3) i i m m m i m m m v k k k k v k k k 1 4 / 3 (2-4) in these equations subscript i and m refer to inclusion and matrix, respectively. young’s modulus ( e ), poisson’s ratio ( ) and density of fgm cylinder are calculated as follows. e k k9 / 3 (2-5) k k3 2 / 2 3 (2-6) i i m mv v (2-7) to incorporate these formulas into the extended finite element model, the value of each material property is computed at each individual node based on micromechanical models. utilizing the generalized isoparametric graded finite elements, introduced by kim and paulino [15], material properties gradation is considered in an element. in this method, material properties such as elastic modulus ( e ), poisson’s ratio ( ), and mass density ( ) at gauss points can be interpolated using shape functions from their nodal point values as follows [15]: h h h i i i i i i i i i e n e n n h ne 1 1 1 , , , 1, 2, , (2-8) general problem formulation ith regard to the geometry of cracked cylinders and loading conditions, considered problems are axisymmetric. in this kind of problems, material properties and forces are constant in circumferential direction; also, displacement along -axis (u ) vanishes. the general governing equations are the equations of motion in cylindrical coordinates, which are simplified as follows for axisymmetric problems [16]. rzr r r r u r rf r r z t 2 2 (3-1) rz z z z r u r rf r r z t 2 2 (3-2) w m. shariati et alii, frattura ed integrità strutturale, 39 (2017) 166-180; doi: 10.3221/igf-esis.39.17 169 where in these equations r , , u , f , t , and are radius, density, displacement, body force, time, normal and shear stress, respectively. subscripts r and z refer to radial and longitudinal directions of cylinders, respectively. also, in axisymmetric problems we have [17] r z u0 , 0 , 0 (3-3) to solve equations of motion, discontinuous-galerkin-based extended finite element method is employed. the extended finite element model of the problem is obtained by discretizing the solution domain into a number of arbitrary elements. the formulation of the xfem for displacement components can be written as [18] n n n n n n all nodes n ncr u r z t n r z a t n r z h r z h r z b t, , , , , , (3-4) n m m n n nm m n ntip n r z f r f r c t, ,ˆ ˆ , where crn is the set of nodes that the discontinuity has in its influence domain, while tipn is the set of nodes inside a predefined area around the crack tip (fig. 1). h r z, is heaviside eichment function and mf represents crack tip enrichment functions [19]. r̂ and are the usual crack-tip polar coordinates. also, na , nb and nmc are vectors of the nodal unknowns. tu w n n na t a t a t, , tu w n n nb t b t b t, , tu w nm nm nmc t c t c t, (3-5) figure 1: selection of enriched nodes for crack. circled nodes are enriched by the discontinuity function whereas the squared nodes are enriched by the crack tip enrichment functions. displacement components for the element (e) with n nodal points are approximated by compact forms as follows u u u h h h h hm hmu n r z a t r z b t r z c t, , , (3-6) w w w h h h h hm hmw n r z a t r z b t r z c t, , , (3-7) h = 1, 2, …, ne and m = 1, 2, 3, 4, where ne is the number of nodes in an element. also and exhibit the enriched parts of displacements related to crack path and crack tip enrichment, respectively [20]. applying the weighted residual integral to the equations of motion with respect to the weighting functions ls r z, , the formal galerkin approximations reduce to m. shariati et alii, frattura ed integrità strutturale, 39 (2017) 166-180; doi: 10.3221/igf-esis.39.17 170 l l l r l rz r v e s s r u s s dv f l ns r r z ¨ 1, 2, 3, , (3-8) l l l rz z z v e s s r w s dv f l ns r z ¨ 1, 2, 3, , (3-9) where ns is the number of shape functions of the element e and ls is the component of the vector s . m m m ms n n n n1 2 3 4 1 2 3 4 1 2 3 4, , , , , , , , , , , (3-10) for axisymmetric problems in cylindrical coordinates relations between the stresses and displacements can be expressed in the form below [21]. r z rz u u w u r r z r u u w u r r z r u u w w r r z z u w z r 2 2 2 (3-11) by substituting eqs. (3.11) into eqs. (3.8) and (3.9) we have l l l r v e v e l s su u w u u u w u r r r z r r r r z r r u s dv r dv f s u w z z r l ns ¨ 2 2 1, 2, 3, ..., (3-12) l l l z v e v e s su w u u w w r w s dv r dv f l ns r z r z r r z z ¨ 2 1, 2, 3, , (3-13) by substituting displacements (eqs. (3-6) and (3-7)) into eqs. (3-12) and (3-13), and some manipulations, equations are obtained which we can assemble them to a matrix form as below. m k f (3-14) in this equation m and k are the mass and stiffness matrices, respectively. also and f are the nodal displacements and force vectors, respectively. generally, for the fictional element e which is enriched with both heaviside and crack tip enrichment functions, these matrices and vectors can be written as follows: m. shariati et alii, frattura ed integrità strutturale, 39 (2017) 166-180; doi: 10.3221/igf-esis.39.17 171 t v e m r s s dv1 1 (3-15) t v e k r s d s dv2 2 (3-16) u w u w u w h h h h hm hma a b b c c, , , , , h , m =1,2,3,4 (3-17) t r zf f f, (3-18) matrices s1 and s2 are derived as follows: n n s n n 1 4 1 4 1 1 4 0 0 0 0 0 0 (3-19) 11 44 1 4 11 44 0 0 0 0 0 0 x x y y r r y y x x x y y yx y x x n n n n s n n r r n n n n 1, 4 , 1, 4 , 1 1, 1 4 1, 4 1, 4 , 2 1/ 4/ 1 , 1, 4 ,, 4 , 1, 4 , ... 0 ... 0 ... 0 ... 0 0 ... 0 ... 0 ... ... ... 0 ... 0 ... 0 ... 0 ... ... ... . / .. / (3-20) x x y y x xy y r r 11, 44 , 11, 44 , 4411 11, 11,11, 44 , 0 0 0 0 0 0 the material stiffness matrix d for axisymmetric problems is defined as below [22]. e d 1 0 1 0 1 01 1 2 0 1 2 / 20 0 (3-21) we use the newmark method to solve equations of motion. the newmark family is the most widely used family of direct methods for solving the equation of motion which consists of the following equations [23]. n n n n n n n n n n n n m k f t t t t t 1 1 1 2 2 1 1 1 1 1 1 2 1 (3-22) m. shariati et alii, frattura ed integrità strutturale, 39 (2017) 166-180; doi: 10.3221/igf-esis.39.17 172 the newmark family includes many widely used methods. the average acceleration method is one of them for structural dynamics applications, which is unconditionally stable. in this method, and are equal to 0.5 and 0.25, respectively. we choose the mean acceleration method in this study. interaction integral and sif computations he general form of domain integral for axisymmetric problems, introduced by moran and shih [24] is as follows: t c i r da r 1 :q p p q (4-1) where, cr is the crack tip radial coordinate, rq r z e,q , lj lj ij i lp w u , is the energy-momentum tensor and w is summation of strain and kinetic energy. in this work, the interaction integral method is used to compute the mode i stress intensity factor (ki). by superimposing the actual and auxiliary fields on the domain integral, in the absence of thermal strains the general axisymmetric form of interaction integral ( mi ) in local cartesian coordinate systems on crack tip (fig. 2) for fgms is obtained as below. aux aux aux aux aux auxr r ir i r ir i r ij ij r ij ij c a aux aux iz r iz i r z aux aux aux aux aux auxr r ijkl r kl ij i i i r ij j i r ir i r u u q mi u u q r r r r u u q u u c u b u u u r r , , , * 1, , , , , , , , 1 aux ir i ru r q da, / (4-2) where q is a weight function varying from unity at the crack tip to zero on boundary of domain a* . for a stationary crack in axisymmetric state, the relation between the m-integral and the sif is identical to its relation in plane strain state [25]. figure 2: local (r, z) coordinate system. tip aux aux tip mi k k k k e 2 i i ii ii 2 1 (4-3) t m. shariati et alii, frattura ed integrità strutturale, 39 (2017) 166-180; doi: 10.3221/igf-esis.39.17 173 where tipe and tip denote young’s modulus and poisson’s ratio at crack tip, respectively. consequently, k i and k ii are computed by replacing k kaux auxi ii1, 0 and k k aux aux i ii0, 1 in eq. (4-3), respectively. validation of the xfem axisymmetric model n order to validate the results of the xfem code, four problems were solved and their results were compared with reported values in previous researches. in the first problem, a homogeneous solid cylinder with a central penny-shaped crack under uniform tensile load of 10 mpa, was modeled using the xfe model described in this work. the radius and length of cylinder are 50 mm and 100 mm, respectively. the central crack radius is 5 mm. the obtained sif solution for this crack geometry is compared with the analytical and numerical solutions given by eshraghi and soltani [12] in tab. 1. in the second example, a penny-shaped crack embedded in a homogeneous steel cylinder was considered. the ratio of crack radius to cylinder radius and the ratio of crack radius to cylinder height were selected to 0.2 and 0.1, respectively. the cylinder was under a uniform tensile stress of 1 mpa. the calculated sif (ki) is compared with the computational and analytical stress intensity factors reported by tran and geniaut [7], in tab. 1. previous problem under the loading condition of a uniform tensile stress of 1 mpa and rotation of 150 rpm was considered as the third example. in the fourth example, a complete circumferential surface crack at the inner wall of a hollow cylinder under constant axial tension of 105 mpa was studied. the values of the inner and outer radius of the cylinder were chosen to 50 mm and 55 mm, respectively with a crack length of 2.5 mm. the material was assumed to be linear elastic with values of the young’s modulus and the poisson’s ratio of e = 200 mpa and = 0.3. the computed sif (ki) is compared with the stress intensity factor reported by grebner and ustrathmeier [26], in tab. 1. problem no. reported results present work percent difference analytical numerical 1 25.27 [12] 25.23 [12] 24.12 4.6 2 1.596 [7] 1.656 [7] 1.536 3.8 3 ---22.035 [7] 23.076 4.7 4 ---520 [26] 530.63 2 table 1: comparison of ki values obtained by numerical simulation with those reported in the literature. it seems that the obtained results based on the xfem method agree very well with that reported in the literature. numerical examples penny-shaped crack embedded in a fg cylinder under static loading n this example, an epoxy/glass functionally graded cylinder with a central penny-shaped crack (fig. 3) under static uniform tensile load of 1 mpa is analyzed. the values of the radius and height of the cylinder are chosen to r 0.1 m and h 0.2 m, respectively. the material gradient parameter in eq. (2-1) is chosen to p 0.2 . the outer surface of the cylinder is made of the glass. the properties of the epoxy and glass are presented in tab. 2 [27]. a 55 × 105 four-node rectangular element is used for meshing the models. a domain of 4 × 4 elements is used to calculate the interaction integral and sif. i i m. shariati et alii, frattura ed integrità strutturale, 39 (2017) 166-180; doi: 10.3221/igf-esis.39.17 174 figure 3: (a) schematic plot of a transparent circular solid cylinder with central penny-shaped crack. (b) a finite element mesh for an axisymmetric cross section used in the xfem models. material young’s modulus (gpa) poisson’s ratio density (kg/m 3) epoxy 3.2 0.34 1175 glass 70 0.23 2500 table 2: the properties of the epoxy and glass [27] the obtained stress intensity factors ki for different values of crack radius are plotted in fig. 4. as expected, it is shown that increasing the crack radius increases the stress intensity factor, since the stresses near the crack tip increase with increasing the crack radius (fig. 5). the deformed mesh and the von mises stress contours for an axisymmetric cross section are illustrated in fig. 5. note that a 7000 times larger scale for displacements was used to plot fig 5(a). figure 4: stress intensity factor versus ratio of crack radius to cylinder radius. penny-shaped crack embedded in a fg cylinder under dynamic loading an epoxy/glass functionally graded cylinder with the same dimensions as the cylinder in the previous section (fig. 3) including a central penny-shaped crack with various radiuses under uniform impulsive tensile stress of 1 mpa is analyzed in this section. the time step and the material gradient parameter are chosen to t 1 s and p 0.2 , respectively. the impulsive tensile stress at time t 1 s is applied to the upper surface of the cylinder and the stress intensity factors are obtained at given time steps. the curves of sif versus time for different crack radius are plotted in fig. 6. before reaching the stress wave to the crack tip, the sif is zero and as the wave approaches to the crack tip, the m. shariati et alii, frattura ed integrità strutturale, 39 (2017) 166-180; doi: 10.3221/igf-esis.39.17 175 sif dramatically increases. after passing the wave through the crack tip, the stress intensity factor reduces. wave arrival time to the crack tip decreases with increasing crack radius. a = 0.05 m a = 0.04 m a = 0.06 m a = 0.09 m figure 5: deformed mesh and von mises stress contours for the axisymmetric cross sections with various crack length. a =0.09 a =0.07 a =0.05 figure 6: plots of sif vs. time for penny-shaped crack with various radiuses embedded in a fg cylinder under impulsive tension. figure 7: schematic plot of a transparent hollow cylinder with internal circumferential crack. fg hollow cylinder with internal circumferential crack under static loading in this section, first an epoxy/glass functionally graded hollow cylinder with an inner circumferential crack with various radiuses (fig. 7) under static uniform tensile load of 1 mpa is analyzed. the values of the height, inner and outer radius of the cylinder are chosen to h 0.2 m, ir 0.1 m and or 0.2 m, respectively. m. shariati et alii, frattura ed integrità strutturale, 39 (2017) 166-180; doi: 10.3221/igf-esis.39.17 176 the influence of the change in the material gradient parameter p on the value of stress intensity factor ki is considered. the values of sif for different crack length are plotted (in fig. 8) versus p . for p 0 the constituent material of the cylinder is pure epoxy. fig. 8 shows that for large cracks the stress intensity factor decreases with increasing p , while for cracks which their lengths are less than half of the wall thickness of the cylinder, the sif curves are downward for p 0.5 approximately, and for larger values of p the sif curves are upward. a =0.01 a =0.03 a =0.05 a =0.07 figure 8: sif vs. p curves for different values of circumferential crack length. to study the effect of the rotational speed of cylinder on the sif of circumferential crack, cylinders with different circumferential crack length under various rotational speed are considered. for this purpose, the stress intensity factors are calculated for different values of rotational speed of cylinders, which vary from 100 to 1900 rpm. in these analysis the value of material gradient parameter is selected to p 0.2 . the sif vs. rotational speed of cylinder curves for different values of crack length are illustrated in fig. 9. as expected, the stress intensity factor increases with increasing rotational speed because the radial component of body force is proportional to the square of rotational speed of cylinder. a =0.09 a =0.07 a =0.05 a =0.03 a =0.01 figure 9: sif vs. rotational speed of cylinder curves for different values of circumferential crack length. the longitudinal displacement and stress contours for an axisymmetric cross section of a hollow cylinder with a circumferential crack of length 0.05 m under rotational speed of 1800 rpm are illustrated in fig. 10. m. shariati et alii, frattura ed integrità strutturale, 39 (2017) 166-180; doi: 10.3221/igf-esis.39.17 177 von mises stress (pa) longitudinal stress (pa) longitudinal displacement (m) figure 10: stress and displacement contours for the axisymmetric cross sections of a cylinder with a circumferential crack of length a = 0.05m at rotational speed of 1800 rpm. for investigating the effect of the inner radius of the cylinder on the sif, hollow cylinders with three different circumferential crack lengths under static uniform tensile load of 1 mpa are analyzed. in this analysis, the values of the height and thickness of the cylinders are chosen to 0.2 m and 0.1 m, respectively. in addition, the material gradient parameter is considered to be 0.2. the results are presented in fig. 11. it is observed that ki increases with increasing the inner radius of hollow cylinder. for small crack sizes, the curve rises gradually. these behaviors have been reported in reference [12]. a =0.01 a =0.03 a =0.05 figure 11: plots of sif vs. inner radius of hollow cylinder under uniform axial tension for p 0.2 . fg hollow cylinder with internal circumferential crack under dynamic loading according to the previous section, an epoxy/glass functionally graded hollow cylinder with an inner circumferential crack (fig. 7) under impulsive tensile load is analyzed. the values of the height, inner and outer radius of the cylinder are chosen to h 0.2 m, ir 0.1 m and or 0.2 m, respectively. in addition, the material gradient parameter is chosen to p 0.2 for this example. a uniform impulsive tension 1 mpa at time t 1 s is applied to the upper and lower surfaces of cylinder and the stress intensity factors are obtained at specified time steps ( t s1 ). the sif vs. time curves for different crack sizes are plotted in fig.12. the stress wave arrival time to the circumferential crack tip decreases with increasing crack radius similar to a pennyshaped crack. fig. 12 shows that the maximum value of sif in dynamic loading condition is so much larger than its value m. shariati et alii, frattura ed integrità strutturale, 39 (2017) 166-180; doi: 10.3221/igf-esis.39.17 178 at static loading condition. the von mises stress and longitudinal displacement contours for an axisymmetric cross section of a hollow cylinder with a circumferential crack of length 0.05 m at time t s26 is illustrated in fig. 13. a =0.09 a =0.07 a =0.05 a =0.03 a =0.01 figure 12: plots of sif vs. time for circumferential crack with various depths embedded in a fg cylinder under impulsive tension. von mises stress (pa) longitudinal displacement (m) figure 13: stress and displacement contours for the axisymmetric cross section of a cylinder with a circumferential crack of length a = 0.05 m under impulsive tension at time t s26 . to investigate the effect of the material gradient parameter p on the sif of circumferential crack in dynamic loading condition, some functionally graded hollow cylinders composed of epoxy/glass with different values of parameter p under impulsive tensile load are analyzed. the impulsive tension 1 mpa at time t 1 s is applied to the upper surface of cylinders and the stress intensity factors are obtained at specified time steps ( t s1 ). sif curves in term of time are plotted in fig. 14. it is concluded from fig. 14 that increasing the material gradient parameter p decreases the maximum sif value so long as p 1 while for p 1 the maximum sif value increases with increasing p . in addition, the speed of stress wave decreases with increasing p . m. shariati et alii, frattura ed integrità strutturale, 39 (2017) 166-180; doi: 10.3221/igf-esis.39.17 179 figure 14: plots of sif vs. time for circumferential crack embedded in an epoxy/glass cylinder under impulsive tension. conclusions n this study, equations of motion in cylindrical coordinate system were solved using the xfe and newmark’s methods in functionally graded materials. the stress intensity factors for penny-shaped and circumferential cracks in the epoxy/glass circular cylinders under static and dynamic loading conditions were computed using the interaction integral method. finally, the following results were obtained from this research: 1increasing the crack radius increases the stress intensity factor. 2wave arrival time to the crack tip decreases with increasing crack radius. 3for hollow cylinders with large circumferential crack sizes ( o ia r r/ 0.5 ), the stress intensity factor decreases with increasing the material gradient parameter p (increasing glass inclusion). 4for hollow cylinders with circumferential cracks which their lengths are less than half of the wall thickness of the cylinder, the sif curves are downward for p 0.5 approximately, and for larger values of p the sif curves are upward. 5increasing the rotational speed of the cylinder increases the stress intensity factor. 6the sif increases with increasing the inner radius of hollow cylinder. however, for small crack sizes, the effect of inner radius on sif value is small. 7. for epoxy/glass hollow cylinders with circumferential cracks under impulsive tension, increasing the material gradient parameter p decreases the maximum sif value so long as p 1 while for p 1 the maximum sif value increases with increasing p . in addition, the speed of stress wave decreases with increasing p . references [1] walters, m.c., paulino, g.h.; robert, h.d.jr., computation of mixed-mode stress intensity factors for cracks in three-dimensional functionally graded solids, j. eng. mech., 132(1) (2006) 1-15. doi: 10.1061/(asce)0733-9399(2006)132:1(1). [2] moulick, s.k., sahu, y.k., stress intensity factor for internal cracks in thick walled pressure vessels using weight function technique, national conference on innovative paradigms in engineering & technology (ncipet), proceedings published by international journal of computer applications (ijca), 10 (2012) 6-12. [3] meshii, t., watanabe, k., closed form stress intensity factor of an arbitrarily located inner-surface circumferential crack in an edge-restraint cylinder under linear radial temperature distribution, eng. frac. mech., 60(5) (1998) 519527 doi: 10.1016/s0013-7944(98)00046-0. i m. shariati et alii, frattura ed integrità strutturale, 39 (2017) 166-180; doi: 10.3221/igf-esis.39.17 180 [4] chen, y.z., stress intensity factors in a finite length cylinder with a circumferential crack. international journal of pressure vessels and piping, 77 (2000) 439-444. doi: 10.1016/s0308-0161(00)00047-8. [5] lee, d-s., a long circular cylinder with a circumferential edge crack subjected to a uniform shearing stress, international journal of solids and structures, 39 (2002) 2613–2628. doi: 10.1016/s0020-7683(02)00150-6. [6] jones, i.s., impulse response model of thermal striping for hollow cylindrical geometries, theoretical and applied fracture mechanics, 43(1) (2005) 77–88. doi:10.1016/j.tafmec.2004.12.004. [7] tran, v-x., geniaut, s., development and industrial applications of x-fem axisymmetric model for fracture mechanics, eng. frac. mech. 82(2012) 135–157. doi:10.1016/j.engfracmech.2011.12.002. [8] wu, l., zhang, l., guo, y., extended finite element method for computation of mixedmode stress intensity factors in three dimensions, procedia engineering 31 (2012) 373 – 380. doi: 10.1016/j.proeng.2012.01.1039. [9] predan, j., mo ilnik, v., gubeljak, n., stress intensity factors for circumferential semi-elliptical surface cracks in a hollow cylinder subjected to pure torsion, eng. frac. mech., 105 (2013) 152–168. doi: 10.1016/j.engfracmech.2013.03.033. [10] sharma, k., singh, i.v., mishra, b.k., bhasin, v., numerical modeling of part-through cracks in pipe and pipe bend using xfem, procedia materials science 6 (2014) 72 – 79. doi: 10.1016/j.mspro.2014.07.009. [11] seifi, r., stress intensity factors for internal surface cracks in autofrettaged functionally graded thick cylinders using weight function method, theoretical and applied fracture mechanics, 75 (2015) 113–123. doi: 10.1016/j.tafmec.2014.11.004. [12] eshraghi, i., soltani, n., stress intensity factor calculation for internal circumferential cracks in functionally graded cylinders using the weight function approach, eng. frac. mech., 134 (2015) 1–19. doi: 10.1016/j.engfracmech.2014.12.007. [13] hatta, h., taya, m., equivalent inclusion method for steady state heat conduction in composites, int. j. eng. scie., 24(1986) 520–524. doi: 10.1016/0020-7225(86)90011-x. [14] mori, t., tanaka, k., average stress in matrix and average elastic energy of materials with misfitting inclusions, acta materialia, 21 (1973) 571–574. doi: 10.1016/0001-6160(73)90064-3. [15] kim, j-h., paulino g.h., isoparametric graded finite elements for nonhomogeneous isotropic and orthotropic materials, asme j. appl. mech., 69 (2002) 502–514. doi: 10.1115/1.1467094. [16] rao, s.s., the finite element method in engineering, fifth edition, butterworth-heineman, london, (2010). [17] sadd, m.h., elasticity: theory, applications and numerics, second edition, academic press, san diego, (2009). [18] rokhi, m.m., shariati, m, coupled thermoelasticity of a functionally graded cracked layer under thermomechanical shocks, arch mech, 65(2) (2013) 71–96. [19] mohammadi, s., extended finite element method, blackwell, london, (2008). [20] rokhi, m.m., shariati, m., implementation of the extended finite element method for coupled dynamic thermoelastic fracture of a functionally graded cracked layer. j braz soc mech sci eng, 35 (2013) 69–81. doi: 10.1007/s40430-013-0015-0. [21] lai, w.m., rubin, d.h., rubin, d., krempl, e., introduction to continuum mechanics, butterworth-heinemann, london, (2009). [22] logan, d., a first course in the finite element method, cengage learning, boston (2011) [23] hughes, t.j., the finite element method: linear static and dynamic finite element analysis, courier dover publications, new york, (2000). [24] moran., b., shih, c.f., crack tip and associated domain integrals from momentum and energy balance, engineering fracture mechanics 27(6)(1987) 615-642. doi: 10.1016/0013-7944(87)90155-x. [25] gosz, m., moran, b., an interaction energy integral method for computation of mixed-mode stress intensity factors along non-planar crack fronts in three dimensions, eng. frac. mech., 69(3) (2002) 299-319 doi: 10.1016/s0013-7944(01)00080-7. [26] grebner, h., ustrathmeier, u., investigation of different isoparametric axisymmetric crack tip elements applied to a complete circumferential surface crack in a pipe. computers & structures, 21(6) (1985) 1177-l180. doi: 10.1016/0045-7949(85)90172-5. [27] kirugulige, m.s., a study of mixed-mode dynamic fracture in advanced particulate composites by optical interferometry, digital image correlation and finite element methods. dissertation, auburn university, (2007). << /ascii85encodepages false /allowtransparency false /autopositionepsfiles true /autorotatepages /none /binding /left /calgrayprofile (dot gain 20%) /calrgbprofile (srgb iec61966-2.1) /calcmykprofile (u.s. web coated \050swop\051 v2) /srgbprofile (srgb iec61966-2.1) /cannotembedfontpolicy /error /compatibilitylevel 1.4 /compressobjects /tags /compresspages true /convertimagestoindexed true /passthroughjpegimages true /createjobticket false /defaultrenderingintent /default /detectblends true /detectcurves 0.0000 /colorconversionstrategy /cmyk /dothumbnails false /embedallfonts true /embedopentype false /parseiccprofilesincomments true /embedjoboptions true /dscreportinglevel 0 /emitdscwarnings false /endpage -1 /imagememory 1048576 /lockdistillerparams false 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can be opened with acrobat and adobe reader 5.0 and later.) >> /namespace [ (adobe) (common) (1.0) ] /othernamespaces [ << /asreaderspreads false /cropimagestoframes true /errorcontrol /warnandcontinue /flattenerignorespreadoverrides false /includeguidesgrids false /includenonprinting false /includeslug false /namespace [ (adobe) (indesign) (4.0) ] /omitplacedbitmaps false /omitplacedeps false /omitplacedpdf false /simulateoverprint /legacy >> << /addbleedmarks false /addcolorbars false /addcropmarks false /addpageinfo false /addregmarks false /convertcolors /converttocmyk /destinationprofilename () /destinationprofileselector /documentcmyk /downsample16bitimages true /flattenerpreset << /presetselector /mediumresolution >> /formelements false /generatestructure false /includebookmarks false /includehyperlinks false /includeinteractive false /includelayers false /includeprofiles false /multimediahandling /useobjectsettings /namespace [ (adobe) (creativesuite) (2.0) ] /pdfxoutputintentprofileselector /documentcmyk /preserveediting true /untaggedcmykhandling /leaveuntagged /untaggedrgbhandling /usedocumentprofile /usedocumentbleed false >> ] >> setdistillerparams << /hwresolution [2400 2400] /pagesize [612.000 792.000] >> setpagedevice microsoft word numero_37_art_32 y. wang et alii, frattura ed integrità strutturale, 37 (2016) 241-248; doi: 10.3221/igf-esis.37.32 241 focussed on multiaxial fatigue and fracture estimation of fatigue lifetime for selected metallic materials under multiaxial variable amplitude loading yingyu wang key laboratory of fundamental science for national defense-advanced design technology of flight vehicle, nanjing university of aeronautics and astronautics, nanjing, 210016, china yywang@nuaa.edu.cn luca susmel department of civil and structural engineering, the university of sheffield, sheffield s1 3jd, uk l.susmel@sheffield.ac.uk abstract. this paper initially investigates the accuracy of two methods, i.e., the maximum variance method (mvm) and the maximum damage method (mdm), in predicting the orientation of the crack initiation plane in three different metallic materials subjected to multiaxial variable amplitude loading. according to the validation exercise being performed, the use of both the mvm and the mdm resulted in a satisfactory level of accuracy for selected three metals. subsequently, three procedures to estimate the fatigue lifetime of metals undergoing multiaxial variable amplitude loading were assessed quantitatively. procedure a was based on the mdm applied along with fatemi-socie’s (fs) criterion, bannantine-socie’s (bs) cycle counting method and miner’s linear rule. procedure b was based on the mvm, fs criterion, bs cycle counting method and miner’s linear rule. procedure c involved the mvm, the modified manson coffin curve method (mmccm), the classical rainflow cycle counting method and miner’s linear rule. the results show that the usage of these three design procedures resulted in satisfactory predictions for the materials being considered, with estimates falling within an error band of three. keywords. multiaxial fatigue; variable amplitude loading; critical plane; life prediction. introduction ince the beginning of the last century, devising a sound method to estimate the fatigue lifetime of a component subjected to variable amplitude (va) multiaxial loading has been the goal of numerous experimental/theoretical investigations. there are four aspects that need to be considered to estimate fatigue lifetime under multiaxial variable amplitude fatigue loading, i.e., the cyclic stress-strain model, the cycle counting method, the damage model and the damage accumulation model. [1] in addition, also the following aspects should be considered under multiaxial variable amplitude load histories: determining the orientation of the critical plane and calculating the amplitude and mean value of the stress/strain components relative to the critical plane. [2] s y. wang et alii, frattura ed integrità strutturale, 37 (2016) 241-248; doi: 10.3221/igf-esis.37.32 242 fatigue criteria based on the concept of the critical plane are generally considered to be more accurate for multiaxial fatigue life estimation [1]. as far the low/medium cycle fatigue regime is concerned, the most successful criteria are seen to be those proposed by smith, watson and topper [3], brown & miller [4, 5], fatemi & socie [6], and susmel [7, 8]. as to the determination of the orientation of the critical plane, the mvm and the mdm are widely discussed in refs [911]. the mvm assumes that the damage in any material plane can be related to the variance of the stress/strain signal in that plane. the plane on which the variance of the resolved shear stain/stress reaches its maximum value is defined as the critical plane. the mdm postulates that the critical plane is that material plane which experiences the maximum extent of fatigue damage. the rainflow cycle counting method [12] has been most widely and successfully used under uniaxial loading. among the methods dealing with va multiaxial loading histories, bannantine and socie’s (bs) method [13] and wang and brown’s method [14, 15] deserve to be mentioned explicitly. formalising an appropriate damage accumulation model is another tricky problem to be addressed properly in order to estimate fatigue damage under va multiaxial loading [16,17]. miner’s linear damage rule [18] is still the most used rule. in this paper, the accuracy of the mvm and the mdm in predicting the orientation of the critical plane is assessed. the accuracy of three procedures suitable for estimating multiaxial fatigue lifetime of metallic materials is checked against experimental data taken from the literature. the considered design procedures are as follows: (a) procedure a: fs criterion applied with mdm, bs cycle counting method and miner’s linear rule; (b) procedure b: fs criterion applied with mvm, bs cycle counting method and miner’s linear rule; (c) procedure c: mmccm applied with mvm, rainflow counting method and miner’s linear rule. fatigue criteria fs criterion atemi and socie [6] proposed a shear-strain based multiaxial fatigue criterion that can be expressed as follows:     00 cff b f f y maxn, n2n2 g k1 2                (1) where /2 is the shear stain amplitude relative to the critical plane, n,max is the maximum normal stress, k is a material constant, andy is the material yield strength. mmccm criterion the mmccm [7, 8] postulates that the degree of multiaxiality and non-proportionality of the stress state at the critical location can be quantified through the following stress ratio: a maxn, a n,an,m       (2) wherea denotes the shear stress amplitude relative to the critical plane, n,m and n,a are the mean value and the amplitude of the stress normal to the critical plane, respectively, and n,max is the maximal normal stress relative the critical plane. for a given value ofthe profile of the corresponding modified manson–coffin curve can be described by using the following general relationship:          cff b f f a n2)('n2 g )(' (3) where ’f(), b(), ’f(), and c() are fatigue constants that can be determined from the fully-reversed uniaxial and torsional fatigue curves [7, 8]. f y. wang et alii, frattura ed integrità strutturale, 37 (2016) 241-248; doi: 10.3221/igf-esis.37.32 243 bs cycle counting method annantine and socie [13] have proposed a method based on the critical plane concept and the rainflow cycle counting method. this method makes use of a major channel and some auxiliary channels. for those materials whose fatigue breakage is shear governed, the major channel is the shear strain history. for those materials characterised by a mode i dominated cracking behaviour, the major channel is the normal strain history. the rainflow cycle counting method is used to post-process the master channel. the normal stress signal is the auxiliary channel for fs criterion. the schematic of bs cycle counting method is shown in fig.1. figure 1: schematic of bs cycle counting method. experimental evaluations number of experimental data were selected from the technical literature [19, 20] to check the accuracy of the considered procedures in estimating multiaxial fatigue lifetime. the summary of the static and fatigue properties of the investigated materials are reported in tabs. 1 and 2. when the material constants listed in tabs. 1 and 2 were not directly available in the original sources, they were estimated as follows [1]: 3 ' ' ff   ; ff '3'  ; bb0  ; cc0  the required stress component was calculated from the strain load histories being provided by using the model proposed by jiang and sehitoglu [21, 22]. the hardening effect under non-proportional loading was taken into account by making the following assumption [1]: k25.1'k np  ; 'n'n np  material ref. e (gpa) g (gpa) y (mpa) k in fs s45c [19] 186 70.6 496 1 1050 qt steel [20] 203 81 1009 0.6 304l stainless steel [20] 195 77 208 0.15 table 1: static properties of the investigated materials b a y. wang et alii, frattura ed integrità strutturale, 37 (2016) 241-248; doi: 10.3221/igf-esis.37.32 244 material ref. k' (mpa) n' 'f 'f (mpa) b c 'f 'f (mpa) b0 c0 s45c [19] 1215 0.217 0.359 923 -0.099 -0.519 0.198 685 -0.12 -0.36 1050 qt steel [20] 1558 0.123 2.01 1346 -0.062 -0.725 3.48 777 -0.062 -0.725 304l stainless steel [20] 2841 0.371 0.122 1287 -0.145 -0.394 0.211 743 -0.145 -0.394 table 2: fatigue properties of the investigated materials  /√3  /√3  /√3  /√3  /√3 path av path tv path pv path at path e1  /√3  /√3  /√3  /√3    /√3   path e2 path r01 path r02 path fr path pi figure 2: investigated loading paths the investigated loading paths are shown in fig. 2. the stress and strain associated with any material plane can be obtained by coordinate transformation. figure 3: comparison of observed and predicted orientation of crital plane by the mvm y. wang et alii, frattura ed integrità strutturale, 37 (2016) 241-248; doi: 10.3221/igf-esis.37.32 245 figure 4: comparison of observed and predicted orientation of crital plane by the mdm. critical plane orientation the predicted orientation of the critical plane versus experimental orientation of stage i crack plane for s45c steel, 1050 qt steel and 304l steel is reported in figs 3 and 4. as it can be seen from these figures, the predictions made through the mvm and the mdm are characterised by the same level of accuracy, with 90% of the data falling within an error band of 20%. figure 5: comparison of observed and predicted fatigue lives by procedure a. y. wang et alii, frattura ed integrità strutturale, 37 (2016) 241-248; doi: 10.3221/igf-esis.37.32 246 figure 6: comparison of observed and predicted fatigue lives by procedure b figure 7: comparison of observed and predicted fatigue lives by procedure c y. wang et alii, frattura ed integrità strutturale, 37 (2016) 241-248; doi: 10.3221/igf-esis.37.32 247 fatigue lifetime prediction the predicted versus experimental fatigue lifetime diagram determined via procedure a is reported in fig. 5. the predicted vs experimental fatigue lifetime diagram obtained through procedure b is reported in fig. 6. finally, fig. 7 shows the predicted vs experimental fatigue lifetime diagram determined using procedure c. as it can be seen from figs. 5, 6 and 7, all the data fall within an error scatter band of 3. conclusions 1. both the mvm and the mdm can predict the orientation of the critical plane satisfactorily. the mvm is more efficient from a computation point of view. 2. satisfactory fatigue lifetime predictions are obtained by using procedure a, b and c. 3. the mvm can be applied with fs criterion successfully to predict fatigue lifetime for metallic materials undergoing va multiaxial fatigue loading. acknowlegements he aviation science funds of china (no.: 2013za52008) and the national natural science foundation of china (no.: 10702027) are acknowledged for supporting the present research work. references [1] socie, d.f., marquis, g.b., multiaxial fatigue, sae, warrendale, pa. (2000). [2] wang, y., susmel, l.,critical plane approach to multiaxial variable amplitude fatigue loading, fracture and structural integrity, 33(2015) 345-356. [3] smith, k.n., watson, p., topper, t.h., a stress-strain function for the fatigue of metals, j. mater., 5(1970) 767-776. [4] [2] brown m.w., miller k.j., a theory for fatigue under multiaxial stress-strain conditions, in: proc institution of mechanical engineering, 187 (1973)745-56. [5] kandile, f.a., brown, m.w., miller, k.j., biaxial low-cycle fatigue fracture of 316 stainless steel at elevated temperature, met. soc. lond., 280 (1982) 203-210. [6] fatemi a., socie d.f., a critical plane approach to multiaxial fatigue damage including out-of-phase loading, fatigue fract eng mater struct, 11 (1988) 149-65. [7] susmel l., meneghetti g., atzori b., a simple and efficient reformulation of the classical manson-coffin curve to predict lifetime under multiaxial fatigue loading-part i: plain materials, journal of engineering materials and technology, 131 (2009) 021009-1-021009-9. [8] wang, y., susmel, l., the modified manson-coffin curve method to estimate fatigue lifetime under complex constant and variable amplitude multiaxial fatigue loading, int. j. fatigue, 83(2016) 135-149. [9] marciniak, z., rozumek, d., macha, e., verification of fatigue critical plane position according to variance and damage accumulation methods under multiaxial loading, int. j. fatigue, 58 (2014) 84-93. [10] susmel l., a simple and efficient numerical algorithm to determine the orientation of the critical plane in multiaxial fatigue problems, int. j. fatigue, 32 (2010) 1875-1883. [11] susmel, l., tovo, r., socie, d.f., estimating the orientation of stage i crack paths through the direction of maximum variance of the resolved shear stress, int. j. fatigue, 58 (2014) 94-101. [12] matsuishi, m., and endo, t., fatigue of metals subjected to varying stress, presented at japan society of mechanical engineers, fukuoka, japan, (1968). [13] bannantine, j.a., socie, d.f., a multiaxial fatigue life estimation technique, in: m.r. mitchel, r.w. landgraf (eds.), astm symposium on advances in fatigue lifetime predictive techniques, astm stp 1122, american society for testing and materials, philadelphia, (1991) 249-75. [14] wang c.h., brown m.w., life prediction techniques for variable amplitude multiaxial fatigue – part i: theories, trans. asme, j. eng. mater. technol., 118 (1996) 367–70. t y. wang et alii, frattura ed integrità strutturale, 37 (2016) 241-248; doi: 10.3221/igf-esis.37.32 248 [15] wang, c.h., brown, m.w. life prediction techniques for variable amplitude multiaxial fatigue – part ii: comparison with experimental results, trans. asme, j. eng. mater. technol., 118 (1996) 371-374. [16] fatemi, a., yang, l., cumulative fatigue damage and life prediction theories: a survey of the state of art for homogeneous materials, int. j fatigue, 20 (1998) 9–34. [17] wang, y., zhang, d., yao, w., fatigue damage rule of ly12cz aluminum alloy under sequential biaxial loading, sci. china – phys., mech. & astro, 57 (2014) 98-103. [18] miner, m.a., cumulative damage in fatigue, j appl mech, 67 (1945) ai59–64. [19] kim, k.s., park, j.c., lee, j.w., multiaxial fatigue under variable amplitude loads, trans asme j. eng. mater. technol.,121 (1999) 286-93. [20] shamsaei, n., fatemi, a., socie, d.f., multiaxial fatigue evaluation using discriminating strain paths. int. j. fatigue, 33 (2011) 597-609. [21] jiang, y., sehitoglu, h., modeling of cyclic racheting plasticity, part : development of constitutive equations, journal of applied mechanics, 63 (1996) 720-725. [22] jiang y., sehitoglu h., modeling of cyclic racheting plasticity, part ii: comparison of model simulations with experiments, journal of applied mechanics, 63 (1996) 726–733. << /ascii85encodepages false /allowtransparency false /autopositionepsfiles true /autorotatepages /none /binding /left /calgrayprofile (dot gain 20%) /calrgbprofile (srgb iec61966-2.1) /calcmykprofile (u.s. web coated \050swop\051 v2) /srgbprofile (srgb iec61966-2.1) /cannotembedfontpolicy /error /compatibilitylevel 1.4 /compressobjects /tags /compresspages true /convertimagestoindexed true /passthroughjpegimages true /createjobticket false /defaultrenderingintent /default /detectblends true /detectcurves 0.0000 /colorconversionstrategy /cmyk /dothumbnails false /embedallfonts true /embedopentype false /parseiccprofilesincomments true /embedjoboptions true /dscreportinglevel 0 /emitdscwarnings false /endpage -1 /imagememory 1048576 /lockdistillerparams false /maxsubsetpct 100 /optimize true /opm 1 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/hrv (za stvaranje adobe pdf dokumenata najpogodnijih za visokokvalitetni ispis prije tiskanja koristite ove postavke. stvoreni pdf dokumenti mogu se otvoriti acrobat i adobe reader 5.0 i kasnijim verzijama.) /hun 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/pdfxoutputintentprofileselector /documentcmyk /preserveediting true /untaggedcmykhandling /leaveuntagged /untaggedrgbhandling /usedocumentprofile /usedocumentbleed false >> ] >> setdistillerparams << /hwresolution [2400 2400] /pagesize [612.000 792.000] >> setpagedevice microsoft word numero_41_art_38.docx v.shlyannikov et alii, frattura ed integrità strutturale, 41 (2017) 285-292; doi: 10.3221/igf-esis.41.38 focused on crack tip fields 285 the effect of creep damage formulation on crack tip fields, creep stress intensity factor and crack growth assessments v. shlyannikov kazan scientific center of the russian academy of sciences, russia shlyannikov@mail.ru, http://orcid.org/0000-0001-2345-6789 a. tumanov kazan scientific center of the russian academy of sciences, russia tumanoff@rambler.ru, http://orcid.org/0000-0002-2345-6790 abstract. fields of stress, strain rate and process zone of a mode i creep crack growth are analyzed by employing damage evolution equations. damage models for fracture of process zone represented by stress based formulation. two expressions are presented to describe the stress-sensitive nature of multiaxial rupture behavior. both damage free and defective creeping solids have been studied. the variation of creep stress and the crack-tip governing parameter in the form of creep in-integral with time and the evolution of creep damage were analyzed by using the fe-model. the effect of the introduced creep stress intensity factor as a function of creep time through the continuum damage mechanics of the creep crack growth are discussed in detail. keywords. creep damage; creep sif; multi-axial stress function. citation: shlyannikov, v., tumanov, a., the effect of creep damage formulation on crack tip fields, creep stress intensity factor and crack growth assessments, frattura ed integrità strutturale, 41 (2017) 285-292. received: 28.02.2017 accepted: 03.05.2017 published: 01.07.2017 copyright: © 2017 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. introduction he high temperature damage accumulation and growth that occurs under creep conditions unites of changes in material microstructure, void nucleation, interaction and growth on grain boundaries leading to creep rupture. a number of approaches have been proposed in the literature for the damage analysis and the estimation of stressstrain rate variation at the crack tip in creeping solids [1-8]. some of them take into account the effect of multi-axial states of stress in the form of stress and ductility based models [1,2,8]. the authors analyzed the influence of creep damage on crack tip fields under small-scale and extensive creep conditions by the use of an asymptotic analyses [5,6] and finite element method [7]. in this paper, attention is directed on defective solids behavior in which stress-strain state changed as a result of the damage accumulation at the crack tip for steady state secondary creep conditions. the multi-axial stress function and continuum damage model are discussed and developed in order to assess the creep crack growth on the basis of a creep stress intensity factor. t v.shlyannikov et alii, frattura ed integrità strutturale, 41 (2017) 285-292; doi: 10.3221/igf-esis.41.38 286 multi-axial rupture behavior he many experimental results of uniaxial tension creep rupture tests of structural materials different properties show that the stress rupture time behavior can be accurately described by power-law equation  t a (1) where a and  are constants independent of stress for a given material. values of  for a variety of materials tested at different temperatures described by an approximate relationship with the norton equation exponent  = 0.7n. it has been shown by hayhurst [1] that under multi-axial loading conditions the constant a should be a function of the stress invariants        1 2mpt a j j (2) where mp is the maximum principal tensile stress, j1 is the first stress invariant, 2j is the second deviatoric stress invariant, ,  and  are constants ( +  +  = 1). in terms of principal stresses j1 and 2j are given by     1 1 2 3j ,                    2 22 2 1 2 2 3 3 1 1 6 j (3) the most general multi-axial creep rupture criterion is obtained by pisarenko-lebedev [2], which unites the limiting state theories in the form of the maximum principal tensile stress and the von mises condition         21eff mp j (4) in which  is the experimental material constant that is determined as the ratio of uniaxial tensile to compression strength =t/c. for brittle fracture =0, while for ductile fracture =1. hayhurst [1] have mentioned that a general representation of multi-axial creep rupture behavior must exhibit the sensitivity of micro-structural changes to the maximum principal tensile stress and express the stress sensitivity of different materials to final collapse or failure mechanism. the preceding review of creep rupture equations indicates that a general formulation of stress function which satisfies these requirements can be consists two parts:  in the tension-tension quadrant the behavior can be approximated by combination of the maximum hydrostatic stress and an octahedral shear stress criteria              1 2 1 21 1fd j j fj f j (5)  in the tension-compression quadrant the behavior can be approximated by combination of the maximum principal tensile stress and an octahedral shear stress criteria in the form of the pisarenko-lebedev limiting state theory [2]                2 21 1mp mpfd j f f j (6) where    1 f ,   1f (7) by substituting eq.(3) into (4) and (5) and writing    2 1 , the stress function can be represented in the normalized form:  plane stress                    21 1 1mpfd (8)                 21 1mpfd (9) t v.shlyannikov et alii, frattura ed integrità strutturale, 41 (2017) 291-298; doi: 10.3221/igf-esis.41.39 287  plane strain                                2 21 1 1 1 1 1mpfd (10)                          2 21 1 1 1mpfd (11) figure 1: rupture loci computed from multi-axial stress functions. by writing    0i i where 0 is uniaxial rupture stress, the magnitudes of the biaxial stresses can be determined for different values of the governing material parameter . in fig.1, the results of calculations are shown for plane stress and plane strain conditions using eqs.(8-11). for constant rupture time the particular forms (8-11) of general relationships (5,6), show a marked sensitivity to stress biaxiality and material constant . it would clear therefore that in order to obtain material constants that govern the behavior of general stress function in the form of eqs.(5,6) two sets of standard tests should be conducted: first set to determine the uniaxial tensile rupture characteristics, a second set carried out under uniaxial compression. the tests carried out under uniaxial compression, as it shown in fig.1, are the most sensitive in their response to the material behavior under multi-axial stress conditions. creep damage function et  denote the measure of damage with  = 0 denoting the undamaged state and  = 1 the fully damaged state. an equation describing the evolution of damage under a multi-axial stress state has been proposed by hayhurst [1]                    1 2 1 1 mpa j j (12) similarly, we introduce a function for rate of accumulation of creep damage as follows                 1 m fd c (13) l v.shlyannikov et alii, frattura ed integrità strutturale, 41 (2017) 285-292; doi: 10.3221/igf-esis.41.38 288 where c and m are material constants and multi-axial stress function    fd described by eqs.(5,6). by assuming that the creep strain rate is governing by the equivalent von mises stress, the damage accumulation constitutive equation in multiaxial state of stress is used in the form given by kachanov [9]            1 n eqv eqv b (14) where b and n are constants of the norton power law equation. creep stress intensity factor n [10] one unified parameter in the form of a plastic stress intensity factor (sif) is introduced based on the asymptotic elastic-plastic stress and strain the crack tip fields which gives more accurate the characterization of fracture resistant properties materials and structures under static and cyclic loading than the wide spread twoparametric theories. the plastic sif takes into account both the in-plane and out-of-plane constraint effects at fracture. generally, the creep crack-tip singular asymptotic fields in the terms of a creep sif's under the secondary extensive creep conditions can be modified to obtain a stress, strain and displacement rate for elastic-nonlinear-viscous material properties as the follows [11]              1 1* 0 0 ; n cr n c k i l  , n cr crk k (15) for a crack of length 2a in an infinite body and subject to a remote stress , c* for the plane strain problem is given by [4]               1 * 0 0 0 3 2 n c a n (16) where 0 and 0 are reference stress and strain rate, respectively. equations for the crack tip asymptotic stress-strain fields for three-dimensional creeping solids through amplitude factor (eq.15) are a function of a governing parameter in the form of creep in-integral. the numerical method was introduced by the authors [11] to determine the in-integral for power-law creeping materials. according to this approach, the dimensionless angular stress  femij and displacement rate iu functions are directly determined from the fea distributions          , , ( , , )fem femni t n t n d (17)                                                              1 , , cos sin 1 1 cos 1 fem femnfem fem fem fem fem femr e rr r r fem fem fem fem rr r r du dun t n u u n d d u u n (18)                                               01 0 0 0 1 n n nnfem fem n fem fem fem fem fem fem i i e i e i en i n fem fem femfem e e ecr u u u du u r l l dt lbl k (19) i v.shlyannikov et alii, frattura ed integrità strutturale, 41 (2017) 291-298; doi: 10.3221/igf-esis.41.39 289 where t is creep time, e is the mises equivalent stress and    0 fem fem e e . as is usual in mathematical analysis a dot over a displacement quantity denotes a time differentiation. the numerical parameter in-integral and the -variation angular functions of the suitably normalized functions ij and iu depend on the creep exponent n. in the сontrary to the traditional models for creep crack growth prediction that the in-integral is a function only the creep exponent, in the present work it will be demonstrated that this governing parameter depends on the creep damage function and the creeping crack tip stress-strain fields. results and discussion lane strain finite element analysis was performed based on ansys fe-code for study of the creep damage effect on the nonlinear crack tip stress-strain fields for center cracked plate (ccp) subjected to a uniform tensile stress of magnitude =50 mpa. the ccp configuration contains an internal crack of length 2a=20mm (a/w =0.01, where w is plate width). the 2d plane strain eight-node isoparametric elements were applied to ccp geometry. to consider the details of large deformation and blunting of the crack tip, a typical fe-mesh was used with the initial notch root radius /a =0.01. for creeping undamaged and damaged materials we consider five stages of creep time which is varied from t = 1 hrs up to t = 103 hrs. the creep properties of analyzed material at the elevated temperature of 550c are summarized in table 1. e [gpa]  b [1/(mpa^nhr)] n c [1/(mpa^mhr)] 200 0.3 110-14 5.0 110-10 table 1: the creep properties of material. employing the constitutive equations (13,14) directly into the fem rate-dependent formulation and using an explicit time integration procedure leads to a standard runge-kutta integration scheme in which the finite element stiffness matrix is derived from elastic moduli. after the solution of a nonlinear problem, the ansys output file is used as an input data for special code developed to determine dimensionless stress-strain angular distributions, damage contour and creep stress intensity factor. note that for creeping material, the damage evolution depends generally on the creep time, magnitude of the applied loading, crack geometry and material properties. due to complexities we consider in the present study different creeping stages. in this case it is useful to normalize a current creep time t by the characteristic time tt for transition from smallscale creep to extensive creep which is given as [7]        2 21 1 1t t n ect t k (20) where k1 is elastic stress intensity factor,  is the poisson's ratio, e is the young's modulus and c -integral is given by eq.(16). in our case the transition time for given nominal stress  =50 mpa and crack length a =10mm is tt = 21.88 hrs. in order to explore the effects of damage formulation, comparisons for  =50 mpa and creep time t /tt = 45.7 are made in fig.2 between the hrr-field, undamaged creep field and defective fields at the crack tip in creeping solids. near the crack tip the influence of the damage degree is evident and the sufficient difference between the hrr and creep damage fields is observed. the data presented in fig.2 demonstrate the effect of creep damage behaviour on the crack tip fields. furthermore, it is no longer true that  -variations of the stresses are independent of creep damage parameter . a fracture damage zone (fdz) or fracture process zone (fpz) local to the crack tip is defined as a core where microstructure damage accumulates until crack growth takes place at the macroscopic scale level. microstructure damages can include void nucleation, growth and coalescence and it is assumed that local fracture will occur at the crack tip when the creep ductility of the material is exhausted there. this process is governed by combination of the maximum principal stress mp and the stress invariants j1 and 2j . once these stress invariants have been determined during fem procedure the creep damage distribution or the fpz shape and size are obtained by a numerical integration of eq.(13). in fig.3 p v.shlyannikov et alii, frattura ed integrità strutturale, 41 (2017) 285-292; doi: 10.3221/igf-esis.41.38 290 shown contours of damage zones around the crack tip at =50mpa and creep time t/tt = 45.7 for material different properties defined by the value of constant =t/c. contours in fig.4 demonstrated process of the crack tip damage accumulation as a function of creep time. figure 2: von mises equivalent stress angular distributions for different solids states. figure 3: contours of damage around crack tip at =50mpa and creep time t/tt =45.7. figure 4: contours of damage around crack tip as a function of creep holding time. the important factor in the present study is the influence of state of stress on the damage process. to this end a plane strain analysis of a plate containing an internal crack of relative length a/w =0.01 which is loaded by remote tension was also carried out. in fig.5 the numerical results for the maximum size of creep damage zone behavior are shown as a function of creep time. it follows from these data, in essence, maximum damage size is sensitive to the maximum principal stress or to the hydrostatic stress through effective stress function formulation by eqs.(5,6). an increase in hydrostatic stress with  < 1, then increases the damage zone leading to failure at lower strains and lower times. as in the case of the dimensionless stress angular distributions ij (fig.2), the main effect of damage parameter  or material properties  on the dimensionless displacement rate components iu arises through the normalizing factor in the form of creep in -integral (eqs.17-19). figure 6,a represents variation of the in -integral distributions through the creep stage for different values of the governing parameter  for material behavior constitutive equation. it should be noted that the values for creep in -integral do not coincide with those of the hrr elastic-plastic field hrr ni = 5.024 at the same hardening exponent n = 5. furthermore, in the frame of creeping solids formulation, in -integral distributions as a function of creep time for undamaged and defective materials are different and these distinctions increase with increasing of the holding time. it is obvious that in creeping solids the behavior of the governing parameter of crack-tip field with elapsed time beyond t/tt > 1 is very sensitive to the material constant  = t/c variation. v.shlyannikov et alii, frattura ed integrità strutturale, 41 (2017) 291-298; doi: 10.3221/igf-esis.41.39 291 figure 5: crack tip damage zone maximum size as a function of creep time. figure 6: in-factor (a) and (b) creep stress intensity factor behavior as a function of creep time. finally fig.6,b represents the corresponding numerical results for creep stress intensity factor behavior as a function of creep time according to eq.(15). the curve concerns to the undamaged material for the steady state of secondary creep solution is also shown in this figure. the creep damage rate dependence of creep stress intensity factor arises from the time dependence of the in-integral. again it is clear that the effect of damage evolution appears at the extensive creep condition behind of the small-scale state when the transition time t/tt > 1. it should be note that as recommended by corresponding astm standards, the description of the crack growth rate under creep and creep-fatigue conditions should be given in the terms of c(t) or c*-integral. however, this parameter a-priory may not take into account the effect of the accumulation and growth of damage. unlike the definition for the elastic stress intensity factor and c-parameters, the creep stress intensity factor approach gives the possibility to obtain the crack growth rate as a function of creep damage. to this end, it was necessary to calculate the in-integral distribution for each crack front position corresponds to a certain combination crack length and creep time and as consequence accumulated creep damage. recall that in the present study all calculations carried out for the stationary crack under steady state secondary creep conditions. going back to the crack growth interpretation it should be noted that the effect of the creep damage accumulation on the creep crack growth rate may be scaled through the corresponding value of the creep stress intensity factor. in addition, an inherent property of the creep sif is their dependence on the multi-axial state of stress through the equation for the damage function (13). under certain circumstances, this numerical solution may also have application to creeping solids which undergo damaging near the crack tip. thus, the creep sif may by identified as damage sensitive high temperature fracture parameter for correlating crack growth under multi-axial stress of state conditions. v.shlyannikov et alii, frattura ed integrità strutturale, 41 (2017) 285-292; doi: 10.3221/igf-esis.41.38 292 conclusions he effects of material damage on the stress field, shape and size of fracture process zone of a mode i creep crack were investigated on the basis of continuum damage mechanics by using multi-axial stress function. two cases of continuum solids state, i.e. undamaged creeping material and defective material with different degree of creep damage, were examined. a governing parameter of damage field for creeping solids under multi-axial stress state represented by the experimental constant in the form of ratio uniaxial tensile rupture strength to compression at an appropriate test temperature. it has been shown that the creep holding time and multi-axial states of stress may be combined to produce a method on the basis of creep stress intensity factor for quantifying the damage effects on creep crack growth rate. acknowledgments he author gratefully acknowledges the financial support of the russian science foundation under the project 1719-01614. references [1] hayhurst, d.r., creep rupture under multi-axial states of stress, j. mech. phys. solids, 20 (1972) 381–390. [2] pisarenko, g. s., lebedev, a.a., deformation and strength of materials under complex state of stress, naukova dumka, kiev, (1976). [3] hutchinson, j.w., constitutive behavior and crack tip fields for materials undergoing creep-constrained grain boundary cavitation, acta metall., 31 (1983) 1079–1088. [4] he, m.y., hutchinson, j.w., in: elastic-plastic fracture, v.1, astm stp 803, american society for testing and materials, philadelphia, (1983) 227–290. [5] qinghua meng, zhenqing wang, asymptotic solutions of mode i steady growth crack in materials under creep conditions, acta mech. solida sinica, 28 (2015) 578–591. [6] murakami, s., hirano, t., liu, y., asymptotic fields of stress and damage of a mode i creep crack in steady-state growth, int. j. solids struct., 37 (2000) 6203–6220. [7] li, f.z, needleman, a., shih, c.f., characterization of near tip stress and deformation fields in creeping solids, int. j. fract., 36 (1988) 163–186. [8] budden j.p., ainsworth, r.a., the effect of constraint on creep fracture assessments, int. j. fract., 87 (1997) 139–149. [9] kachanov, l.m., introduction to continuum damage mechanics, martinus-nijhoff, dordrecht, (1986). [10] shlyannikov, v.n., tumanov, a.v., characterization of crack tip stress fields in test specimens using mode mixity parameters, int. j. fract., 185 (2014) 49–76. 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can be opened with acrobat and adobe reader 5.0 and later.) >> /namespace [ (adobe) (common) (1.0) ] /othernamespaces [ << /asreaderspreads false /cropimagestoframes true /errorcontrol /warnandcontinue /flattenerignorespreadoverrides false /includeguidesgrids false /includenonprinting false /includeslug false /namespace [ (adobe) (indesign) (4.0) ] /omitplacedbitmaps false /omitplacedeps false /omitplacedpdf false /simulateoverprint /legacy >> << /addbleedmarks false /addcolorbars false /addcropmarks false /addpageinfo false /addregmarks false /convertcolors /converttocmyk /destinationprofilename () /destinationprofileselector /documentcmyk /downsample16bitimages true /flattenerpreset << /presetselector /mediumresolution >> /formelements false /generatestructure false /includebookmarks false /includehyperlinks false /includeinteractive false /includelayers false /includeprofiles false /multimediahandling /useobjectsettings /namespace [ (adobe) (creativesuite) (2.0) ] /pdfxoutputintentprofileselector /documentcmyk /preserveediting true /untaggedcmykhandling /leaveuntagged /untaggedrgbhandling /usedocumentprofile /usedocumentbleed false >> ] >> setdistillerparams << /hwresolution [2400 2400] /pagesize [612.000 792.000] >> setpagedevice microsoft word numero 24 articolo 12 y. petrov et alii, frattura ed integrità strutturale, 24 (2013) 112-118; doi: 10.3221/igf-esis.24.12 112 special issue: russian fracture mechanics school temporal peculiarities of brittle fracture of rocks and concrete y. petrov, i. smirnov, a. evstifeev, n. selyutina st. petersburg state university, universitetsky prospekt, 28, peterhof, 198504, st. petersburg (russian federation) yp@yp1004.spb.edu; ivansmirnov@math.spbu.ru abstract. when we want to compare the strength of two materials, we compare the table values of quasistatic strength. however results of some experiments show that the strength ratio of the materials can change with increase in rate of loading. such "substitution effect" of material strength at different strain rates is studied in this paper. it is shown that one material can have a lower dynamic strength for a higher static strength compared to the other material. tests of two different materials, tests of mortar and concrete, and tests of concrete with different water content are considered. it is shown that load-carrying capacity of materials and the substitution effect of material strength in a wide range of loading rates can be predicted by the incubation time criterion. keywords. static strength; dynamic strength; incubation time; substitution effect. introduction n selecting a material of construction an engineer is usually guided by the values of mechanical parameters obtained in quasi-static tests. a construction material is selected on the basis of its ability to withstand a certain stress (as one of the defining parameters). there is a set of test standards governing determination of the ultimate strength of a material under quasi-static tension, compression, bending, etc. however tests under dynamic loading conditions show essential differences of dynamic strength characteristics in comparison with those of quasi-static tests. these differences relate to the dependence of the mechanical characteristics on the history (duration, intensity, shape of the stress pulse, etc.) and method of loading [1]. a critical value can be considered as a material constant only under quasistatic loading conditions. under dynamic loading, the critical properties are characterized by very strong instabilities and can vary by several orders of magnitude. as a result, the dynamic system behaviour often appears unpredictable. importance of studying rocks and concrete dynamic strength is not in doubt. these materials are highly suitable materials for building structures in the energy sector, for instance solar energy storage water tanks, nuclear containment vessels, etc. however, such civil and military infrastructures (e.g. buildings, barracks, bridges, tunnels, containment structures for hazardous, toxic and inflammable materials, etc) are susceptible to catastrophic failure under intense sudden overloading (e.g. due to blasts, explosions) for which they are not designed. a correct and rational analysis of dynamically loaded structures requires an understanding of the behaviour of the mechanical properties of materials at high strain rates. therefore a study of the behaviour of rocks and concrete at high rates of deformation and fracture is necessary. dependence of rocks on the extraction quarry, as well as numerous admixtures of concrete makes the research of strength characteristics a complex task. moreover, various heterogeneity and impurity content can lead to various dynamic effects of fracture. one of such effects is the change of the dominant strength between the two materials. a material, which has a lower strength compared to another material in quasi-static tests, can have greater strength under dynamic loading. i http://dx.medra.org/10.3221/igf-esis.24.12&auth=true http://www.gruppofrattura.it y. petrov et alii, frattura ed integrità strutturale, 24 (2013) 112-118; doi: 10.3221/igf-esis.24.12 113 in this paper we consider such "substitution effect" of strength of two materials in three cases: tests of two different materials; tests of mortar and concrete; tests of concrete under different environmental conditions. as experimental data we used the results of [2-5]. the theoretical analysis is based on the criterion of the incubation time of fracture [1, 6, 7]. this criterion provides correct transition between quasi-static and dynamic loadings. introduction of the additional measured characteristic of strength (the incubation time) to the already known "quasi-static" parameter of strength (limit stress) allows us to build dependences of maximal fracture stress on a loading (deformation) rate without numerous experiments for any type and character of loading. the incubation time criterion he criterion of fracture based on the concept of incubation time, proposed in [6-8], makes it possible to predict the unstable behaviour of the dynamic-strength characteristics observed in experiments on the dynamic fracture of solids. the fracture criterion can be written in the following general form: α'( )1 1 t ' ct f t dt f          (1) here, f(t) is the intensity of the local force field causing the fracture (or structural transformation) of the medium, fc is the static limit of the local force field, and τ is the incubation time associated with the dynamics of the relaxation processes preceding the fracture. it actually characterizes the strain (stress) rate sensitivity of the material. the fracture time t* is defined as the time at which equality sign is reached in eq. (1). the parameter α characterizes the sensitivity of the material to the intensity (amplitude) of the force field causing the fracture (or structural transformation). often, α = 1 gives a good agreement with test data. one of the possible means of interpreting and determining the parameter  is proposed here on the example of the mechanical rupture of a material. let us assume that a standard test specimen made of the material in question is subjected to tension and is broken into two parts under a stress p arising at a certain time t = 0: f(t) = ph(t), where h(t) is the heaviside step function. in the case of quasi-brittle fracture, the material would unload, and the local stress at the break point would decrease rapidly (but not instantaneously) from p to 0. in this case, a corresponding unloading wave is generated which propagates over the sample and can be detected by standard (e.g., inter-ferometry) methods. the stress variation at the break point can be conditionally represented by the relation σ(t) = p – pf(t), where f(t) varies from 0 to 1 (fig. 1) within a certain time interval t. figure 1: schematic of fracture kinetics at the place of rupture. the case f(t) = h(t) corresponds to the classical strength theory. in other words, according to the classical approach, rupture occurs instantaneously (t = 0). in practice, the rupture of a material (sample) is a process in time, and the function f(t) describes the microscale level kinetics of the transition from a conditionally defect-free state (f(0) = 0) to a completely broken state at the given point f(t*) = 1 that can be associated with the macro-fracture event. on the other hand, application of the fracture criterion (1) to macro-level situation (f(t) = ph(t)), gives the time to fracture t* = t = τ at p = fc. in other words, the incubation time introduced above is equal to the duration of the fracture process after the stress in the material has reached the static strength on the given scale level [9]. this duration can be measured experimentally by statically fracturing the samples and controlling the rupture process by different possible methods, e.g., by measuring the time of t http://dx.medra.org/10.3221/igf-esis.24.12&auth=true http://www.gruppofrattura.it y. petrov et alii, frattura ed integrità strutturale, 24 (2013) 112-118; doi: 10.3221/igf-esis.24.12 114 the increase in pressure at the unloading wave front based on the recorded velocity profile of points (by interferometry) on the sample boundary. below, we apply the general fracture criterion eq. (1) to three problems. calculation procedure et us consider application of the criterion (1) for calculation of carrying capacity of a material for different strain rate. note that we understand the carrying capacity as the maximum stress that the material can withstand without fracture. however according to the criterion of incubatory time, dynamic strength is characterized by the incubatory time, but not the maximum stress. (a) (b) figure 2: test results of cardifrc in dynamic splitting [2]. a) typical stress diagram (σ* is the maximum stress; t* is the fracture time). b) maximum stress vs stress rate. for simplicity of understanding, we consider simple test methods, such as the split hopkinson bar test (the kolsky method) [10-12] and the spall test [13]. such tests allow to carry out calculations in one-dimensional statement. for example, fig. 2 shows the results of dynamic splitting of cardifrc (fibre reinforced concrete) [14], which were carried out in the laboratory of material mechanics at the nizhny novgorod state university [2]. the initial part of the loading branch (fig. 2a) corresponds to the growth of the stress and strain. after the stress in the specimen reaches a limiting value, the material begins to fail rapidly accompanied by the formation of micro and macro cracks leading to a significant reduction in the stress with increasing strain. in spite of the scatter in the data, it is reasonable to conclude that the maximum stress increases with increasing stress rate. the observed time dependence of the maximum stress can be predicted on the basis of the incubation time criterion (1), which in this particular case of fracture takes the form: 1 ( ) t c t t dt       (2) where σ(t) is the time dependence of stress in point of fracture (the average stress in the specimen in case of the shpb test); σc is static strength of the material for given type of loading; τ is the fracture incubation time of the material. for the well-known formulae from the strength of materials we can get a fairly simple relation to calculate the rate dependence of strength. these formulae allow engineers to obtain the values of the material strength, for a given character of loading and specimen geometry, without resorting to lengthy and laborious calculations. in our case, a simple analytical rate dependence of the limit stress can be obtained in the following manner. according to fig. 2a an increase in the tensile stress with strain rate can be assumed to be linear until it reaches the maximum value σ*, so that ( ) ( ) ( )t t h t e t h t         (3) where  and  are the rates of growth of the stress and strain respectively, which we assume to be constant, e is the modulus of elasticity, and h(t) is the heaviside function. stress rate determines as the ratio of the maximum stress to the fracture time. we substitute this function into the stress criterion eq. (2) and find the value of the time to failure t* (using the equality sign) and get l http://dx.medra.org/10.3221/igf-esis.24.12&auth=true http://www.gruppofrattura.it y. petrov et alii, frattura ed integrità strutturale, 24 (2013) 112-118; doi: 10.3221/igf-esis.24.12 115 * * * / 2 / , 2 / , c c t t t                    which yields the following expression for the limiting stress: * * * * / 2 ( ) 2 c c t t t                         (4) the incubation time of fracture τ can be determined by a semi-empirical method. the semi-empirical method consists in fitting of the calculated dependence * ( )  to the experimental dependence * ( )  by means of τ variation. the different algorithms (gauss-newton method, the steepest descent method, etc.) can be used to adjust the parameter values in the iterative procedure. the standard way of finding the best fit is to choose the parameters that would minimize the deviations of the theoretical curve(s) from the experimental points. thereby nonlinear fitting was made to estimate the incubation time values which best describe the data. it is clear that the experimental values of the studied parameters can deviate from this simple dependence as a result of a scatter. note that more complex schemes of loading (non-linear loading, three-dimensional problem, etc.) will lead to more complicated analytical expressions. it is more convenient to consider such problems numerically [15]. strength of two different materials n this part, we compare the strength of gabbro-diabase and fibre reinforced concrete (cardifrc). gabbro-diabase is dense, solid, homogeneous rock, characterized by a low degree of resistance to abrasion, frost resistance, and durability. cardifrc [14] is an ultra high performance fibre reinforced cement based composite characterised by high compressive and flexural strengths and high toughness. the tests have been performed using the modification of kolsky method for dynamic splitting (the brazil test) [16]. detailed schemes of tests and results were presented in [3] for gabbro-diabase and in [2] for cardifrc. fig. 3 summarizes the split tests of the fibre reinforced concrete and gabbro-diabase under quasi-static and high strain rates on a semi-logarithmic scale. the curves in fig. 3 correspond to the calculation by eq. (2) with the following parameter values: σc = 23 mpa and τ = 15 μs for concrete and σc = 18 mpa and τ = 70 μs for gabbro-diabase. it is clear from the picture that carrying capacity of both materials increases with the growth of loading rate. however although cardifrc has a higher quasi-static split strength than that of gabbro-diabase, its dynamic carrying capacity in splitting is lower at high stress rates (>102.5). 10 -4 10 -3 10 -2 10 -1 10 0 10 1 10 2 10 3 10 4 10 15 20 25 30 35 40 45 50 55 60 test results for cardifrc test results for gabbro-diabase calculation for cardifrc calculation for gabbro-diabase m a x im u m s tr es s (m p a ) stress rate (gpa/s) figure 3: the split tests of cardifrc and gabbro-diabase; black squares are the experimental values for cardifrc [2]; black line is predictions of eq. (2) for cardifrc (σc = 23 mpa and τ = 15 μs); red triangles are the experimental values for gabro-diabase [3]; and red dashed is predictions of eq. (2) for gabbro-diabase (σc = 18 mpa and τ = 70 μs). i http://dx.medra.org/10.3221/igf-esis.24.12&auth=true http://www.gruppofrattura.it y. petrov et alii, frattura ed integrità strutturale, 24 (2013) 112-118; doi: 10.3221/igf-esis.24.12 116 strength of mortar and concrete he experimental study of the behavior of concrete and mortar at high strain rates in compression were conducted in [4]. application of techniques of the split hopkinson bar (shpb) and plate impact have allowed us to consider a range of loading rates of 102-104 s-1 with an amplitude of pulses up to 1.5 gpa. both materials have the same processing conditions, and the pure mortar has the same composition as the mortar phase in the concrete. the parameters of the test materials are shown in tab. 1. the quasi-static compressive strength was determined according to the standard astm c39-96. the tests by the kolsky method were carried out only for mortar. the results of these experiments are shown in fig. 4. the curves correspond to the calculation of the maximum stress by the criterion (2). the value of the incubation time τ can be determined by eq. (4) (see table 1). we received the same incubation time for the mortar and concrete. however, despite the lower quasi-static strength compared with that of the mortar, the concrete can show greater strength under dynamic loading (at a given strain rate). ρ, kg/m3 ν e, gpa σcompс , mpa τ, μs concrete 2100 0.2 20 46 6.5 pure mortar 2600 0.29 45 30 6.5 table 1: parameters of concrete and mortar. 10 -4 10 -3 10 -2 10 -1 10 0 10 1 10 2 10 3 10 4 10 5 10 6 10 7 0 400 800 1200 1600 2000 2400 test results for mortar test results for concrete calculation for mortar calculation for concrete m a x im u m s tr es s (m p a ) strain rate (1/s) figure 4: dependence of limit compression stress on strain rate. black squares are the experimental values for concrete [4]; black line is predictions of eq. (2) for concrete; red triangles are the experimental values for mortar [4]; and red line is predictions of eq. (2) for mortar. the authors of the experiments [4] explain this effect by existence of hydrostatic pressure in a sample at high speeds of loading that leads to "compression" of microdefects and microcracks in material structure. as concrete can contain many defects (voids, cracks between the cement and the inclusion, etc.), its carrying capacity increases by limiting of the development of defects. nevertheless, this effect can be explained with a simple argument, without assumptions about the mechanisms of deformation and fracture. since the load is linear (see eq. 3), at high strain rates the limit stress will depend on the modulus of elasticity, that is, the quasi-static strength does not affect on the strength under dynamic loading. thus, we can set the carrying capacity of concrete by the elasticity of fillers. t http://dx.medra.org/10.3221/igf-esis.24.12&auth=true http://www.gruppofrattura.it y. petrov et alii, frattura ed integrità strutturale, 24 (2013) 112-118; doi: 10.3221/igf-esis.24.12 117 strength of dry and saturated concrete n the paper [5] the influence of relative humidity of concrete subjected to a large range of stress rate was analyzed and discussed. the hopkinson bar bundle (hbb) was realized to study the high loading rate tensile properties of plain concrete cubes. the experiments were carried out on concrete cured at three different curing conditions (drying at 50 ˚c; 20 ˚c 50% rh; and saturated) and tested at three strain rates. the results showed that level of free water inside the concrete has an important influence on the carrying capacity of concrete. 10 -6 10 -5 10 -4 10 -3 10 -2 10 -1 10 0 10 1 10 2 2 4 6 8 10 dry concrete 50% rh curing concrete saturated cocrete calculation for dry concrete calculation for 50% rh curing concrete calculation for saturated cocrete m a x im u m s tr es s (m p a ) strain rate (1/s) figure 5: strain rate effect on maximum tensile stress of concrete with three different curing states. black squares are the experimental values for dry concrete [5]; black line is predictions of eq. (2) for dry concrete; red triangles are the experimental values for 50% rh curing concrete [5]; and red dash line is predictions of eq. (2) for 50% rh curing concrete; blue circles are the experimental values for saturated concrete [5]; blue dash-dot line is predictions of eq. (2) for saturated concrete. dry concrete 50% rh curing concrete saturated concrete σc, mpa 3.3 3.5 3 τ, μs 12 22 44 table 2: parameters of concrete at different curing conditions. the results of experiments (points) and the prediction of these results by eq. (2) (curves) are shown in fig. 5. the calculations were performed on the basis of the parameters in table 2. it is clearly seen that the saturated concrete has a lower static strength (limit stress in statics) of the three materials, but one has a higher dynamic strength (the incubation time of fracture). humidity increases the carrying capacity of concrete at high strain rates and vice versa in statics. conclusions n this paper, we have analyzed the "effect of substitution" of load-carrying capacity of materials at different strain (stress) rate. the substitution effect means that in spite of the fact that static strength of one material is smaller than that of another one, its dynamic strength measured in terms of incubation time can be essentially higher. the analysis was conducted based on the incubation time approach, which allows one to separate static strength (limit stress in statics) and dynamic strength (the incubation time of fracture). as the incubation time is a material parameter, i i http://dx.medra.org/10.3221/igf-esis.24.12&auth=true http://www.gruppofrattura.it y. petrov et alii, frattura ed integrità strutturale, 24 (2013) 112-118; doi: 10.3221/igf-esis.24.12 118 independent of the loading history, we can estimate and compare load-carrying capacity of materials in a wide range of loading rates. three cases of the substitution effect were examined. in the first case, two different materials were compared. it is shown that the fibre reinforced concrete (cardifrc) has a lower dynamic strength for a higher static strength compared to the gabbro-diabase. in the second case, mortar and concrete were considered. it is shown that the substitution effect is also in this case. moreover the difference between load-carrying capacity of concrete and mortar can depend on the elasticity of aggregate in concrete. in the third case, concrete with different water saturation was studied. it is shown that saturated concrete has a greater dynamic strength than dry concrete. thus, humidity can increase the carrying capacity of concrete under dynamic loads, and vice verse under quasi-static loads. thus, one of the central problems in testing of dynamic strength properties of rocks and concrete can be associated with measurements of the incubation time parameter. studies of strain rate (loading rate) phenomenon provide an effective opportunity to examine the incubation stage of the fracture process that is important for predicting critical parameters of external action in a wide range of loading conditions. references [1] n.f. morozov, y.v. petrov, dynamics of fracture. berlin-heidelberg-new york: springer-velrag (2000). [2] a.m. bragov, b.l. karihaloo, yu.v. petrov, a.yu. konstantinov, d.a. lamzin, a.k. lomunov, i.v. smirnov, j. of applied mechanics and technical physics, 53(6) (2012) 926. [3] a.m. bragov, a.p. bolshakov, n.n. gerdyukov, a.k. lomunov, s.a. novikov, i.v. sergeichev, in: international conference "v kharitonov thematic scientific reading" (sarov, vniief, 2003). [4] d.l. grote, s.w. park, m. zhou, int. j. of impact eng., 25 (2001) 869. [5] e. cadoni, k. labibes, c. albertini, m. berra, m. giangrasso, materials and structures, 34 (2001) 21. [6] y.v. petrov, a.a. utkin, material science, 25 (1989) 153. [7] y.v. petrov, n.f. morozov, asme j. appl. mech., 61 (1994) 710. [8] y.v. petrov, dokl. phys., 49 (2004) 246. [9] y.v. petrov, b.l. karihaloo, v.a. bratov, a.m. bragov, int. j. of engng. sci., 61(1) (2012) 3. [10] a.c. ross, e.y. thompson, j.w. aci mater. j., 86(5) (1989) 475. [11] p.h. bischoff, s.h. perry, mater. struct., 24 (1991) 425. [12] f. akopov, a.m. bragov, p. demenko, l. kruszka, a.k. lomunov, v. mineev, l.v. sergeichev, j. de physique iv, 110 (2003) 225. [13] t. antoun, l. seaman, d.r. curran, g.i. kanel, s.v. razorenov, a.v. utkin, spall fracture. springer-verlag new york (2003). [14] s.d.p. benson, b.l. karihaloo, magazine concrete research, 57 (2005) 347. [15] v. bratov, n. morozov, y. petrov. dynamic strength of continuum. st.-petersburg university press (2009). [16] t. rodriguez, c. navarro, v. sanchez-galvez, journal de physique iv, 4(c8) (1994) 101. [17] a.m. bragov, b.l. karihaloo, a.yu. konstantinov, d.a. lamzin, a.k. lomunov, bulletin of nizhny novgorod university n. lobachevsky, 4 (2011) 123. (in russian) http://dx.medra.org/10.3221/igf-esis.24.12&auth=true http://www.gruppofrattura.it microsoft word numero_28_art_2 m. malnati, frattura ed integrità strutturale, 28 (2014) 12-18; doi: 10.3221/igf-esis.28.02 12 a method for calculation of finite fatigue life under multiaxial loading in high-cycle domain m. malnati ruag aerospace services gmbh ruag aviation, claude-dornier-str., 82231 wessling, germany mario.malnati@ruag.com , mario.malnati@yahoo.fr abstract. a method for fatigue life assessment in high-cycle domain under multiaxial loading is presented in this paper. this approach allows fatigue assessment under any kind of load history, without limitations. the methodology lies on the construction at a macroscopic level of an “indicator” in the form of a set of cycles, representing plasticity that can arise at mesoscopic level throughout fatigue process. during the advancement of the loading history new cycles are created and a continuous evaluation of the damage is made. keywords. high-cycle multiaxial fatigue; metal fatigue; multiaxial rainflow counting; crack initiation; nonproportional loading; continuous damage. introduction umerous methods for multiaxial fatigue analysis exist in literature (see e.g. [1]) and they are widely applied in different industrial contexts. nevertheless many of them are limited to specific loading conditions typically proportional loading: see [2, 3] for a review or intended only for an evaluation of the unlimited fatigue life (see [1, 2, 4]). the motivation of the method presented in this paper comes from the need felt during years by the author in the fatigue assessment of industrial structures, to conceive a simple and easily applicable tool capable to estimate finite life crack initiation under any kind of loading, in the domain of high-cycle fatigue (hcf). every type of variable amplitude multiaxial stress history can be treated without presenting incorrect filtering of significant cycling events. general presentation of the method t is a widely recognized and well accepted phenomenon [5] that the fatigue damage in the hcf domain is related to the amount of plasticity created at least in some grains under a macroscopically elastic stress history. the ref. [5] gives for instance a synthetic understanding: “…the common principal mechanism responsible of the crack initiation is the plastic strains and the damage developed in the grains due to irreversible dislocations motion. the essential difference between hcf and lcf regimes is that the scale of the plastic localization in a material volume is mesoscopic and respectively macroscopic”. some criteria for the calculation of the fatigue life are actually based on the evaluation of the plasticity amount. they can be either direct as described for instance in [6] and [7], where a computational crystal plasticity model is used at a refined microstructural scale or indirect, like for example the work of jabbado and maitournam [8] where a macro-meso relationship is used. n i http://www.gruppofrattura.it http://dx.medra.org/10.3221/igf-esis.28.02&auth=true m. malnati, frattura ed integrità strutturale, 28 (2014) 12-18; doi: 10.3221/igf-esis.28.02 13 similarly, the methodology proposed in the present paper has its foundation on a plasticity approach, since usage is made of “yield surfaces” created in the stress space during the advancement of the stress history. but on the other side, the description remains here merely in the stress space: no explicit use of the mesoscopic plastic strain is made, but the equivalent fatigue stress is calculated directly on each created stress cycle. the yield surfaces used in the present approach just represent a way to describe at the macroscopic level the underlying phenomenon related to the plasticity arising at a mesoscopic level. from a more general point of view, the present work follows the same scope of the initial work of jabbado [3] to extend the endurance criterion of dang van [9] to a finite life assessment using a continuous damage evaluation. nevertheless, differently from [3] a notion of stress cycle is used here, even though the cycles are not counted and extracted from the global sequence as it is done in a rainflow method (see e.g. [1]) but they are simply created and updated in a continuous way while the stress history advances. this continuous damage approach has the same viewpoint of the cited work of jabbado [3] or for example of the methodology proposed by stefanov [10]. on the other hand, the principle to adapt a multi-surface concept to fatigue assessment by creating the stress cycles during the stress history advancement has some similarities with the work of herbland [11]. construction of the stress cycles he basic ingredient of the present approach is the geometrical creation of closed surfaces in the stress space while the stress point is moving on its path, in a way identical to the classical plasticity theory (see e.g. [12, 13]). each created yield surface is afterward associated to an amount of fatigue damage, evaluated using the basic fatigue material properties. this usage of the yield surfaces is analogous to what is done for the stress cycles after their extraction by a classical cycle-counting, like the rainflow method. for this reason, the terms “yield surface” and “stress cycle” will be used hereafter as synonyms. the rules described here below resume the stress cycles creation.  the equation defining a yield surface in the stress space has the form fp( – xc) = y (1) where fp is a scalar function that in accordance with the hypothesis used by jabbado [3] and by many classical multiaxial criteria (see [1, 4]) takes the von mises equivalent stress: fp() =      2 2 2 1 2 [ ]i ii ii iii iii i          (2) where i, ii, iii are the principal stresses of . let us note explicitly that fp is function of the only deviatoric part s of the stress tensor : fp() = fp(s) (3) s = dev  =  ph i where ph = tr() / 3 (4) hence each yield surface is a von mises hypersphere fully described by its centre xc (back-stress tensor) and its size y.  in the same way of a classical plasticity criterion, when the current stress state moves along the stress history a yield surface is hardened if the stress lies on the surface itself and is moving outwards. these conditions will be integrated in the eqs. (5.a), (5.b) and (12.a), (12.b) written below. as a consequence the stress point will be always inside or exactly on – a yield surface, but never outside.  a multi-surface model is used, inspired to the one proposed by mroz and described e.g. in [12]. in such a model, more than one yield surface can exist at the same time. however a significant dissimilarity with the concept of mroz is that intersections between surfaces are allowed in the present approach. as a consequence the existing surfaces are not necessarily all nested inside each other: this issue in the frame of multi-surface plasticity models is discussed for instance in ref. [14].  the following hardening rules are used. when the deviatoric part s of the stress tensor  has an increment ds, among the surfaces that are hardened at a given instant the one having maximum y is hardened by the following superposed isotropic / kinematic hardening law: t http://www.gruppofrattura.it http://dx.medra.org/10.3221/igf-esis.28.02&auth=true m. malnati, frattura ed integrità strutturale, 28 (2014) 12-18; doi: 10.3221/igf-esis.28.02 14 dxc = 1 2 h(p) <ds : n> n (5.a) dy = 1 2 h(p) 2 3 <ds : n> (5.b) where: h(x) = 1 if x ≥ 0, h(x) = 0 if x < 0 (6) <x> = x h(x) i.e. <x> = x if x ≥ 0, <x> = 0 if x < 0 (7)  p(s; xc, y) = fp(s – xc) y (8) and n is the local outward vector normal to the surface in the deviatoric stress space, having unit length in the following sense: n : n = 1 (9) the symbol : in eqs. (5.a), (5.b) and (9) designates the following scalar product in the stress space, between two tensors sa, sb: sa : sb = 3 aij bij i,j 1 s s   (10) since von mises stress is used, it is possible as done in [3] to give to n the following explicit form: n = 3 2 (s – xc) / fp(s – xc) (11) if at a given instant the same maximum y belongs to two or more yield surfaces contemporarily then the one to be hardened according to the eqs. (5.a) and (5.b) is chosen conservatively as the one having the maximum value of the scalar product ds : n. additionally, if two or more surfaces have not only the same maximum y but also the same maximum ds : n, then the choice for the one to be hardened according to the eqs. (5.a) and (5.b) becomes physically arbitrary: we simply choose the one which had been previously created firstly. the other surfaces that are hardened at a given instant because the stress point lies on the surface and is moving towards the outside simply move rigidly with a pure kinematic hardening (y remain constant) defined by: dxc = h(p) <ds : n> n (12.a) dy = 0 (12.b) actually only the yield surface selected by the criteria illustrated above is considered to be plastically active and it is called “active surface”. the other hardened surfaces having a pure kinematic hardening expressed by the eqs. (12.a) and (12.b) are not directly considered in the current global computation of the fatigue damage, but their updated position will have an influence on the subsequent response in fatigue. they are designated as “transported surfaces”. a third category is given by those surfaces that are not moving at a current instant: they are denoted as “resting surfaces” since the stress point moves internally. the presence of the transported and resting yield surfaces represents a memory effect in the fatigue process, since they can be activated in the subsequent stress history. as already remarked above, all the existing surfaces do not form obligatorily a set of nested surfaces but they can intersect each other.  an increment of plastic deformation at the grain scale can be by hypothesis created at each instant under a deviatoric stress variation. to take into account this, if the stress point is moving in such a way that none of the already existing yield surfaces are hardened then a new surface is created starting from the size y = 0 and obeying to the hardening law for the active surface expressed by eqs. (5.a) and (5.b). of course a first surface is immediately created at the start of the stress history. a problem arises when a surface is created: its normal n is not defined since the surface is collapsed in a point (y = 0). this problem is bypassed by defining, at the instant where a yield surface is created, a normal driven by the stress variation ds: http://www.gruppofrattura.it http://dx.medra.org/10.3221/igf-esis.28.02&auth=true m. malnati, frattura ed integrità strutturale, 28 (2014) 12-18; doi: 10.3221/igf-esis.28.02 15 n = d d :d s s s for y = 0 (13) once the rules for the creation of the stress cycles are defined, a “deviatoric fatigue equivalent stress” y is calculated for the yield surfaces by means of the following equations: deq = fp(dxc) + dy for the active surface (14.a) deq = 0 for all the other surfaces (14.b) the eqs. (14.a) and (14.b) affirm that an increment of deq is applied to the active surface only and not to the other surfaces: for both transported and resting surfaces the value of eq does not change at a given instant. at each instant of the stress history the result is thus the presence of a certain number of yield surfaces, each one with a related value of eq. the following figures show the concept illustrated above. they are intended only as a geometric plane representation of the stress cycles creation process, with pure explanation scope. the function fp used here is the cartesian distance in the plane, so that the yield surfaces are circles. during the stress advancement, the size and the center of the surfaces are determined by the same differential hardening laws defined above: eqs. (5.a), (5.b) for the active surface and eqs. (12.a), (12.b) for transported and resting surfaces. a closed stress sequence is given, defined by the points numerated from 1 to 10 and represented by thick continuous line. at four different instants, the stress cycles already created by the moving stress point are sketched with thin continuous lines. a dashed line represents the smallest circle enclosing all the points of the sequence, which is used in the dang van criterion for unlimited endurance [9]. figure 1: the stress point is moving between states ‘1’ and ‘2’. only one stress cycle has been created. figure 2: created stress cycles when the stress point is moving between states ‘5’ and ‘6’. figure 3: created stress cycles when the stress point is moving between states ‘7’ and ‘8’. figure 4: stress cycles at final instant of the sequence: the stress point has reached the instant ‘10’. http://www.gruppofrattura.it http://dx.medra.org/10.3221/igf-esis.28.02&auth=true m. malnati, frattura ed integrità strutturale, 28 (2014) 12-18; doi: 10.3221/igf-esis.28.02 16 effect of the hydrostatic pressure t is necessary to take into account the effect of the hydrostatic pressure, since the deviatoric fatigue equivalent stress eq calculated on the fatigue cycles as defined in the previous paragraph cannot entirely describe the fatigue damage process. this is due to the fact that the function fp describing the yield surfaces depends on the deviatoric part only of the stress tensor. several possibilities arise. it is chosen here to give to the hydrostatic pressure effects a formulation inspired by the classical hypothesis of sines (see e.g. [1, 4]) in which the average hydrostatic pressure during a load cycle is used. but it is important to remark that this hypothesis is not the only possible in the frame of this methodology: by introducing it, we do not loose generality regarding the possibility to use other mechanisms of hydrostatic pressure influence. let us consider firstly that during the advancement of the stress history the deviatoric fatigue equivalent stress eq for a given stress cycle ‘j’ is a monotonic non-decreasing function going from 0 at the initial instant to its final maximum value eq,j thus the evolution of the hydrostatic pressure hp can be regarded as a function of eq,j, so that it is possible to calculate for the considered stress cycle ‘j’ the average value h,jp in the following way: eq,jτ h,j h eq,j eq,j 0 eq,j 1 p p (τ )dτ τ    (15) let us remark explicitly that h,jp is different for each stress cycle. the quantity h,jp is then used in combination with eq,j in order to evaluate the fatigue damage of the cycle itself. to this scope in the frame of the present method it is required to have for a given material a relationship which provides, for an uniaxial tension/compression fatigue problem under constant amplitude (ca) cycles, the fatigue equivalent stress as a function of the stress amplitude sa and of the average stress s , as follows: seq = seq(sa , s ) (16) when such an equation is not available for a material, then it is necessary to do a hypothesis to describe the influence of the average stress for uniaxial ca cycles. an “equivalent fatigue stress” eq,j for each of the yield surfaces is then calculated by applying the same law of eq. (16) on the calculated eq,j and 3 h,jp : eq,j = seq(eq,j , 3 h,jp ) (17) this can be better illustrated by a simple example: in the “mmpds” handbook [15] the expression of the equivalent stress for uniaxial ca cycles is given by the following formula: seq = smax (1-r)q (18) where r is the cycle ratio r = smin/smax. conformingly to the eq. (16) this equation can be rewritten in terms of sa and s : seq = 1 q ass 2       saq (19) the application of eq. (17) gives for a given stress cycle ‘j’:  eq,j = 1 q eq,j h,j τ 3p 2        eq,j q (20) the so-calculated equivalent fatigue stress eq,j can be then entered directly in a seq-n curve available for a material, in order to calculate the damage made by a single stress cycle. however, an important remark must be made: in the evaluation of their damage, the yield surfaces obtained by the procedure described above must be considered as half-cycles (or stress-reversals) and not as entire cycles. this can be well i http://www.gruppofrattura.it http://dx.medra.org/10.3221/igf-esis.28.02&auth=true m. malnati, frattura ed integrità strutturale, 28 (2014) 12-18; doi: 10.3221/igf-esis.28.02 17 understood when thinking that in the present approach, when the stress point goes forth and back on a segment from a point to a second point and then back to the initial point then two identical yield surfaces are created. explicitly: if a seq-n curve is available in which n has the meaning of number of complete cycles (from peak to peak), then the damage dj associated to the yield surface ‘j’ calculated with the present method will be: dj = j 1 2n (21) where nj is the number of cycles on the seq-n curve corresponding to eq,j. using the palmgren-miner law, the total damage d at a given instant of the complete stress history is given by: d = j j d (22) preliminary validation of the methodology he approach presented in this paper needs obviously at least firstly a robust numerical implementation and secondly a wide validation, by comparison with data coming from test or literature. this activity is in progress, in order to reach a comprehensive substantiation of the methodology. it is the intention of the author to present the complete results in a forthcoming publication. at the present time, the main purpose of the paper is to submit, in a first time, this methodology to the judgment of the community working in the field of the fatigue analysis and dealing with the necessity of treating complicated spectra and non-proportional loading in a hcf multiaxial context. nevertheless, a first important element of the validation process is presented here: the scope is to prove that for an uniaxial closed sequence having variable amplitude (va) cycles, the present methodology is equivalent to a classical 1-d rainflow counting (see e.g. [1]) in the sense that the size eq of the yield surfaces is equal to the amplitude of the 1-d stress cycles extracted by the rainflow. this has been tested by comparison between the present procedure and the rainflow counting prescribed in [16]: namely, a set of 10 uniaxial stress sequences has been created, each one made of 50 stress points randomly generated with probability uniformly distributed between -100 and +100 mpa. the stress points have been preliminarily discretized using a step of 1 mpa. the cycles extracted from both the rainflow procedure [16] and the present approach have been compared in terms of stress amplitude and they have been found to be strictly identical. the figure below gives for one of the sequences the stress points as well as the cycles extracted with the two methods. figure 5: stress points of a test-sequence and amplitude of extracted cycles. conclusions n the previous paragraphs a general approach for multiaxial hcf crack initiation assessment has been presented. as mentioned in the preliminary validation of the methodology paragraph, its validation by comparison with available experimental data is in progress and will be enclosed in a future publication. t i http://www.gruppofrattura.it http://dx.medra.org/10.3221/igf-esis.28.02&auth=true m. malnati, frattura ed integrità strutturale, 28 (2014) 12-18; doi: 10.3221/igf-esis.28.02 18 regarding the evolution of this work a first significant enhancement should be the extension to yield surfaces more general than the only von mises hypersphere, namely the possibility to use non-smooth surfaces based for example on the tresca equivalent stress. references [1] pinho de castro, j.t., meggiolaro, m.a., fadiga técnicas e práticas de dimensionamento estrutural sob cargas reais de serviço: volume i iniciação de trincas, isbn-13: 978-1449514709, createspace (2009). [2] weber, b., fatigue multiaxiale des structures industrielles sous chargement quelconque, phd thesis, insa lyon (1999). [3] jabbado, m., fatigue polycyclique des structures métalliques: durée de vie sous chargements variables, phd thesis, école polythechnique (2006). [4] papadopoulos, i.v., davoli, p., gorla, c., filippini, m., bernasconi, a., a comparative study of multiaxial high-cycle fatigue criteria for metals. international journal of fatigue, 19(3) (1997) 219–235. [5] charkaluk, e., constantinescu., a., dissipation and mean stress effect in hcf and lcf, in: 12th international conference on fracture, (2009). [6] manonukul, a., dunne, f. p. e., highand low-cycle fatigue crack initiation using polycrystal plasticity, in: proc. r. soc. lond. a, 460 (2004) 1881-1903. [7] musinski, w.d., mcdowell, d.l., microstructure-sensitive probabilistic fatigue at notches in in100. pratt & whitney progress report for the period 8/15/08-12/31/10 (2010). [8] jabbado, m., maitournam, m.h., a high-cycle fatigue life model for variable amplitude multiaxial loading. fatigue & fracture of engineering materials & structures, 31(1) (2008) 67–75. [9] dang van, k., griveau, b., message, o., on a new multiaxial fatigue limit criterion: theory and applications, biaxial and multiaxial fatigue, in: egf 3, ed. m. w. brown and k. j. miller, mechanical engineering publications, london, (1989) 479–496. [10] stefanov, s. h., integration of damage differentials (idd) for fatigue life assessment under any loading, phd thesis, ltu sofia (2011). [11] herbland, t., une méthode de correction élastoplastique pour le calcul en fatigue des zones de concentration de contraintes sous chargement cyclique multiaxial non proportionnel, phd thesis, école des mines de paris (2009). [12] lemaitre, j., chaboche, j.l., mechanics of solid materials, cambridge university press, (1990). [13] lubliner, j., plasticity theory, macmillan publishing company, new york (1990). [14] puzrin, a. m., houlsby, g. t., on the non-intersection dilemma in multiple surface plasticity, géotechnique, 51(4) (2001) 369-372. [15] metallic materials properties development and standardization (mmpds) handbook, faa, u.s. dept. of transportation (2003). [16] a 03-406 produits métalliques fatigue sous sollicitations d'amplitude variable méthode rainflow de comptage des cycles afnor (association française de normalisation), (1993). http://www.gruppofrattura.it http://dx.medra.org/10.3221/igf-esis.28.02&auth=true microsoft word numero_38_art_3 r. shravan kumar et alii, frattura ed integrità strutturale, 38 (2016) 19-25; doi: 10.3221/igf-esis.38.03 19 focussed on multiaxial fatigue and fracture stress-state dependent cohesive model for fatigue crack growth r. shravan kumar, i.s. nijin, m. vivek bharadwaj, g. rajkumar, anuradha banerjee department of applied mechanics, indian institute of technology madras, chennai-36, india anuban @ iitm.ac.in abstract. in the cohesive framework, a stress-state dependent cohesive model, combined with an irreversible damage parameter has been used in simulation of fatigue crack growth initiation and continued growth. the model is implemented as interface elements and plane strain simulations of crack initiation and growth under cyclic loading are performed. the stressstate of neighboring continuum elements is used in the traction-separation behavior of the cohesive elements. the model is shown to be able to reproduce the typical initiation life as well as fatigue crack growth curves. further, the effect of the cohesive fatigue parameter on the initiation life and crack growth rates is established. keywords. cohesive zone model; fatigue; triaxiality; stress state. citation: shravan kumar, r., nijin, i. s., vivek bharadwaj, m., rajkumar, g., anuradha banerjee, stress-state dependent cohesive model for fatigue crack growth, frattura ed integrità strutturale, 38 (2016) 1925. received: 15.05.2016 accepted: 15.06.2016 published: 01.10.2016 copyright: © 2016 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. introduction rogressive growth of microstructural damage under sub-critical loads makes fatigue one of the most critical modes of failure. over the years, diverse approaches have been adopted with the objective of better prediction of fatigue failure. classical approaches such as paris law that are based on finding empirical relations between the amplitude of the stress intensity factor and the crack growth rate, firstly, are predictive only for crack growth under very idealized conditions but also lack the ability to predict the initiation life of a fatigue crack near a stress-concentrator. safe operation and life assessment of ageing components and structures, thus, require not only a better understanding of the factors that influence the initiation and growth of damage under cyclic loading but also development of predictive models that account for these effects. as an alternative to classical fracture mechanics based characterization of fatigue crack growth, the cohesive zone model (czm) has been receiving increasing attention for modeling fatigue damage growth ahead of a macroscopic crack [3-5]. more recently, a stress-dependent model that is able to incorporate the dominant role of stress-states in prediction of failure due to fatigue damage has been proposed [2]. in this model, the constitutive behavior of the process zone was described by a stress-state dependent traction-separation law that was combined with an irreversible damage parameter, whose evolution was based on continuum damage laws requiring two fatigue model parameters. while the model was able to capture the typical features of fatigue failure under uniaxial and proportionate bi-axial loads, the implementation of the model, determination of the model parameters and its validation with experimental data on fatigue crack growth was left as a future task. p r. shravan kumar et alii, frattura ed integrità strutturale, 38 (2016) 19-25; doi: 10.3221/igf-esis.38.03 20 in the present work, the stress state dependent model along with an irreversible damage parameter is implemented as cohesive element. a cohesive model for a plane strain modified ct specimen analyzed for fatigue failure is presented for an aluminum alloy material. the mechanical properties and the corresponding cohesive properties for the monotonic nature of the traction separation law are taken from monotonic fracture properties of aluminum. the fatigue crack growth predictions of the model for different fatigue parameters are presented. the effect of the cohesive fatigue parameters on crack growth curves is established. stress-state dependent cohesive model for fatigue n the present work, the simulation of fatigue crack initiation in a modified compact test specimen and its continued growth is based on the fatigue cohesive model proposed by jha and banerjee [2]. the model assumes that the damage mechanisms that lead to failure are localized in a thin layer (process zone). the constitutive behavior of this thin layer is represented by a triaxiality dependent cohesive law that is updated with an irreversible damage parameter to account for the progressive cyclic damage. the triaxiality dependent relation between the traction, nt , and the normalized separation, n , are taken to have three distinct expressions to represent linear, hardening and softening behavior for increasing separation between the bounding surfaces as: n ot ,   = (1+  eff n e h 2 3  )   3      0 < n ≤ n1 = (1+ effh3  ) y 3   n n y e2 3           n1 ≤ n ≤ n 2 =    n n max n exp 4 2 2       0.01                 n 2 ≤ n ≤ n 210 where n1 = y e 3 2  and n 2 = 3 2 h yeffce e 1.5       . here, effh   is an effective triaxiality parameter defined to incorporate the effects of triaxiality [7], and c and s are model parameters that are used to define upper and lower bounds on the equivalent plastic strain required for failure during monotonic fracture respectively. to incorporate the accumulation of incremental damage due to cyclic loading, a damage evolution law proposed by roe and siegmund [1] was used. the accumulation of damage parameter was taken to start once a deformation measure, accumulated separation ( n ), is greater than a critical magnitude ( o ), which is implemented through heaviside function. the accumulated separation is calculated by n n dt ˙      and the critical magnitude ( o ) is the separation at maximum stress ( max ). the increment of damage is related to the increment of deformation weighted by the current load level while the incremental deformation is normalized by accumulated cohesive length ( ). also, the model assumes that there exists an endurance limit, f , which is a stress level below which cyclic loading can proceed infinitely without failure. the evolution equation for the damage parameter is taken to be: n n nf c max max o o t d h ˙ ˙ , | |     1                      cohesive endurance limit, f and accumulated cohesive length,  are two fatigue parameters of this model. max is the current maximum stress that can be taken by the process zone after the onset of damage accumulation. it is calculated by max =  max o cd,   1  . then the damage is translated as the degradation of the process zone by updating its constitutive i r. shravan kumar et alii, frattura ed integrità strutturale, 38 (2016) 19-25; doi: 10.3221/igf-esis.38.03 21 behavior. the current traction is calculated by  n n o ct t d, 1    . here it is assumed that, the tangential separation is less significant when compared to normal separation, therefore the contribution of shear traction on damage is ignored in the proposed model. a description of the cohesive zone behavior under unloading and reloading is provided by a linear function similar to the linear part of tsl, modified to retain opening displacement continuity and use the current elastic modulus as:              n n eff c n net t t t t h d t t t2    1   3 1 ( 3           during unloading, to avoid interpenetration of cohesive surfaces, which is physically unrealistic, higher stiffness is incorporated for negative normal separation. in the present model, the frictional interactions have been ignored. the cohesive model is implemented as a user-element through a user-subroutine (uel) in abaqus v6.10. the cohesive element formulation as per gao and bower [6] is modified to include the stress-state dependence, fatigue damage evolution and criteria for failure of a cohesive element representing crack growth. the damage in every increment is calculated according to the evolution equation depending on the incremental separation. the damage calculated in every increment over one cycle is accumulated using an additional damage variable ( dd ). to avoid longer computational times, it is assumed that the damage accumulated in each cycle is similar valued to next (n-1) cycles, where ’n’ is a chosen number of cycles that is significantly smaller than the number of cycles taken from initiation of crack to final failure. as a consequence, after every thi  cycle the damage is updated to be ic cd d n dd 1 *  and the total number of cycles, in n n1  . failure of cohesive element is taken to occur under two conditions. the first condition is based on traction, where if the traction of cohesive element is less than a specified low value of traction. the second condition is based on the accumulated damage, when the damage accumulated within a cohesive element reaches a threshold value the element is considered to have failed. figure 1: (a) fem model (b) mesh around the crack tip. a modified compact tension (ct) specimen geometry with a width, w =74 mm and thickness, b =22 mm is used for analysis as shown in fig. 1. a plain strain finite element mesh based on the specimen geometry was created and the cohesive elements are inserted along the process zone. the elastic-plastic mechanical properties used in this investigation are that of aluminum alloy (e=70000 mpa, ν=0.33) and the model parameters are taken as, s=4.32 and c=0.432 as per faizan and banerjee [9]. mode-1 fatigue loading with an amplitude range of 1-8 kn is applied on the plain strain fem model. fatigue crack growth curve predictions of the model were generated for different model parameters. a crack growth curve prediction of the model with parameters f =0.25,  =10, th = 1 is shown in fig. 2 (a) and the corresponding damage evolution of the first five elements ahead of the crack tip is shown in fig. 2 (b). it is observed that the element 3 attains the threshold damage (d=0.002) first followed by element 2 and then element 1, which eventually leads to the crack propagation causing the further elements to fail in the similar manner. the stress field ahead of the crack tip is shown in fig. 3. the plastic wakes forming locally along the crack path is shown in fig. 4. the formation of r. shravan kumar et alii, frattura ed integrità strutturale, 38 (2016) 19-25; doi: 10.3221/igf-esis.38.03 22 these regions could be correlated with the instabilities observed in the crack growth curves as the regions with localized plastic strains in the wake correspond to the cycles that have low crack growth rate while the cycles having fast crack growth rate resulted in virtually no plastic strain in the wake. figure 2: a) fatigue crack growth curve (1-8 kn) b) damage evolution in the elements ahead of crack tip. figure 3: stress contour ( yy ) ahead of the crack tip. figure 4: contour of equivalent plastic strain. r. shravan kumar et alii, frattura ed integrità strutturale, 38 (2016) 19-25; doi: 10.3221/igf-esis.38.03 23 results and discussion parametric study was carried out to establish the effect of stress state on crack growth kinetics and determine the effect of model parameters on fcg curves. the effect of the parameters cohesive length ( ), threshold ( th ) and cohesive endurance limit (f ) are discussed in detail in this section. the effect of cohesive length (δς) parameter on the crack growth curve the effect of the cohesive length parameter,  , in the model is established by keeping the other parameters cohesive endurance limit (f ) and threshold ( th ), constant for the cohesive length ranging between 2 2n and 20 2n . figure 5: effect of cohesive length (δς) parameter on the fatigue crack growth curve. in the crack growth curves, as seen in fig. 5 for the chosen set of parameters, with increasing cohesive length, the accumulation of damage is slower and thus the initiation of crack as well as the rate of crack growth is comparatively slower. the effect of threshold parameter (δth) parameter on the crack growth curve the effect of the threshold parameter, th , in the model is seen by keeping the parameters cohesive endurance limit (f ) and cohesive length ( ) constant and varying the threshold ( th ). in fig. 6, it is observed that threshold ( th ) has a strong influence on the crack initiation, for th = (1.25δn2) the crack initiation is delayed by almost 4000 cycles when compared to th = (1.0 2n ). the effect of the threshold parameter on the rate of crack growth, however, is comparatively less significant. the effect of cohesive endurance limit (f) parameter on the crack growth curve the effect of the cohesive endurance limit parameter, f , in the model is established by keeping the other parameters cohesive length ( ) and threshold ( th ) constant and varying the cohesive endurance limit values. as shown in fig. 7, it is observed that cohesive endurance limit (f ) shows significant influence on the crack initiation. as the cohesive endurance limit is increased, there is a delay in crack initiation. it also shows a significant effect on the crack growth rate. as observed, lower the cohesive endurance limit faster is the crack growth rate. a r. shravan kumar et alii, frattura ed integrità strutturale, 38 (2016) 19-25; doi: 10.3221/igf-esis.38.03 24 figure 6: effect of threshold ( th ) parameter on the fatigue crack growth curve. figure 7: effect of cohesive endurance limit (σf) parameter on the fatigue crack growth curve. concluding remarks stress-state dependent cohesive model for fatigue is used in simulation of fatigue crack initiation and growth in a representative aluminum alloy. the model was shown to be capable of predicting both initiation and propagation reasonably well compared to as observed in the experiments [8]. from the parametric study it is observed that increase in the parameter, cohesive endurance strength (f ), is causing a delay in the crack initiation with significantly lower crack growth rates. a similar effect of the parameter, a r. shravan kumar et alii, frattura ed integrità strutturale, 38 (2016) 19-25; doi: 10.3221/igf-esis.38.03 25 threshold ( th ), is observed where higher the threshold value, more the delay in the crack initiation. however the effect of threshold parameter on crack growth rates is negligible. the parameter accumulated cohesive length ( ) with increase in its value exhibits slower crack growth rate and delay in the initiation of the fatigue crack. references [1] roe, k.l., siegmund, t., an irreversible cohesive zone model for interface fatigue crack growth simulation, engineering fracture mechanics, 70 (2002) 209-32. [2] jha, d., banerjee, a., a cohesive model for fatigue failure in complex stress-states, international journal of fatigue, 36 (2011) 155-62. [3] nguyen, o., repetto, e.a., ortiz, m., radovitzky, r.a., a cohesive model of fatigue crack growth, international journal of fracture, 110 (2001) 351-69. [4] yang, b., mall, s., ravi-chandar, k., a cohesive zone model for fatigue crack growth in quasibrittle materials, international journal of solids and structures, 38 (2001) 3927-44. [5] ural, a., krishnan, v.r., papoulia, k.d., a cohesive zone model for fatigue crack growth allowing for crack retardation, international journal of solids and structures, 46 (2009) 2453-62. [6] gao, y.f., bower, a.f., a simple technique for avoiding convergence problems in infinite simulations of crack nucleation and growth on cohesive interfaces, modeling and simulation in material science and engineering, 12 (2004) 453-63. [7] banerjee, a., manivasagam, r., triaxiality dependent cohesive zone model, engineering fracture mechanics, 76 (2009) 1761-70. [8] bharadwaj, v. m., banerjee, a., effect of mode-mixity on fatigue crack growth, procedia engineering, 86 (2014) 653-61. [9] faizan md rashid, banerjee, a., simulation of ductile fracture of aluminum alloy using a triaxiality dependent cohesive zone model. 4th international conference on computational modeling of fracture and failure of materials and structures (cfrac-2015), ecole normale superieure de cachan, paris, france (2015). << /ascii85encodepages false /allowtransparency false /autopositionepsfiles true /autorotatepages /none /binding /left /calgrayprofile (dot gain 20%) /calrgbprofile (srgb iec61966-2.1) /calcmykprofile (u.s. web coated \050swop\051 v2) /srgbprofile (srgb iec61966-2.1) /cannotembedfontpolicy /error /compatibilitylevel 1.4 /compressobjects /tags /compresspages true /convertimagestoindexed true /passthroughjpegimages true /createjobticket false /defaultrenderingintent /default /detectblends true /detectcurves 0.0000 /colorconversionstrategy /cmyk /dothumbnails false /embedallfonts true /embedopentype false /parseiccprofilesincomments true /embedjoboptions true /dscreportinglevel 0 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/hrv (za stvaranje adobe pdf dokumenata najpogodnijih za visokokvalitetni ispis prije tiskanja koristite ove postavke. stvoreni pdf dokumenti mogu se otvoriti acrobat i adobe reader 5.0 i kasnijim verzijama.) /hun 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can be opened with acrobat and adobe reader 5.0 and later.) >> /namespace [ (adobe) (common) (1.0) ] /othernamespaces [ << /asreaderspreads false /cropimagestoframes true /errorcontrol /warnandcontinue /flattenerignorespreadoverrides false /includeguidesgrids false /includenonprinting false /includeslug false /namespace [ (adobe) (indesign) (4.0) ] /omitplacedbitmaps false /omitplacedeps false /omitplacedpdf false /simulateoverprint /legacy >> << /addbleedmarks false /addcolorbars false /addcropmarks false /addpageinfo false /addregmarks false /convertcolors /converttocmyk /destinationprofilename () /destinationprofileselector /documentcmyk /downsample16bitimages true /flattenerpreset << /presetselector /mediumresolution >> /formelements false /generatestructure false /includebookmarks false /includehyperlinks false /includeinteractive false /includelayers false /includeprofiles false /multimediahandling /useobjectsettings /namespace [ (adobe) (creativesuite) (2.0) ] /pdfxoutputintentprofileselector /documentcmyk /preserveediting true /untaggedcmykhandling /leaveuntagged /untaggedrgbhandling /usedocumentprofile /usedocumentbleed false >> ] >> setdistillerparams << /hwresolution [2400 2400] /pagesize [612.000 792.000] >> setpagedevice microsoft word numero_29_art_22 f. tornabene et alii, frattura ed integrità strutturale, 29 (2014) 251-265; doi: 10.3221/igf-esis.29.22 251 focussed on: computational mechanics and mechanics of materials in italy the strong formulation finite element method: stability and accuracy francesco tornabene, nicholas fantuzzi, michele bacciocchi university of bologna francesco.tornabene@unibo.it, nicholas.fantuzzi@unibo.it, michele.bacciocchi@studio.unibo.it abstract. the strong formulation finite element method (sfem) is a numerical solution technique for solving arbitrarily shaped structural systems. this method uses a hybrid scheme given by the differential quadrature method (dqm) and the finite element method (fem). the sfem takes the best from dqm and fem giving a highly accurate strong formulation based technique with the adaptability of finite elements. the present study investigates the stability and accuracy of sfem when applied to 1d and 2d structural components, such as rods, beams, membranes and plates using analytical and semi-analytical well-known solutions. the numerical results show that the present approach can be very accurate using a small number of grid points and elements, when it is compared to standard fem. keywords. strong formulation finite element method; differential quadrature method; finite element method; free vibration analysis; static analysis; numerical stability. introduction his manuscript illustrates a general view of a class of methods which approximates functions at points, called collocation or sampling points. the complete review of the present methodology can be found in the previous works by the authors [1-6] and in the book by the authors [7]. the name which comprehends all this approaches is termed strong formulation finite element method and it has its basis in the differential quadrature (dq) method (dqm) [8-12] as far as the numerical solution is concerned and in the finite element concept [13] as far as element connection is considered. the dq method is part of a more general family of methods called spectral methods (sms) [14-16] with the advantage of considering a free collocation once certain basis functions are set. however, dqm is not always stable increasing the number of collocation points. for this reason generalized differential quadrature (gdq) method was introduced by shu [17]. shu followed the former studies of quan and chang [10, 11], who developed a mathematical procedure for the definition of the weighting coefficients in exact form, thus the accuracy and stability is not lost increasing the number of grid points. other papers that used the mapping technique for strong form based formulations can be found in [18, 19]. it should be mentioned that, the authors in their previous papers gave explicit formulae for the corner point conditions [1-6] that are an extension of the conditions given by other researchers. the following sections expose the mathematical basics of the dq and gdq methods. only some details are given for the sake of conciseness, nevertheless for further details the interested reader can read the references [18-34]. in the numerical applications, the stability, reliability and accuracy of the strong formulation finite element method (sfem) and the weak formulation finite element method (wfem) are shown through several figures. t f. tornabene et alii, frattura ed integrità strutturale, 29 (2014) 251-265; doi: 10.3221/igf-esis.29.22 252 lagrange polynomials (pdq) lagrange trigonometric polynomials (hdq)                     1 1 1 1, , , , 1, 2,..., , j j j j n n k j j k k k j k l r l r r j n r r l r l r r r l r r r                                  1 1 1 1, , 0, 2 , 1, 2,..., sin 2 sin , sin 2 2 j j j j n n j kk j k k j k s r s r r j n r r s r r rr r s r s r                               jacobi polynomials (jac) legendre polynomials (leg)               , 1 1 1 2 ! 1 1 1,1 , 1, 2,..., , , 1 j j j j j j jj d j r r r drj r r r j n                             21 12 ! 1,1 1, 2,..., j j j j j j j d p r r j dr r j n           chebyshev polynomials (i kind) (cheb i) chebyshev polynomials (ii kind) (cheb ii)     cos arccos , 1,1 , 1, 2,...,j jt r j r r j n                  sin 1 arccos , 1,1 , 1, 2,..., sin arccos j j j r u r r j n r          chebyshev polynomials (iii kind) (cheb iii) chebyshev polynomials (iv kind) (cheb iv)         2 1 arccos cos 2 , 1,1 , 1, 2,..., arccos cos 2 j j j r v r r j n r                             2 1 arccos sin 2 , 1,1 , 1, 2,..., arccos sin 2 j j j r w r r j n r                     power or monomial polynomials (power) exponential polynomials (exp)   , , , 1, 2,...,jj jm r r r j n             1 , , , 1, 2,...,j rj je r e r j n          hermite polynomials (her) laguerre polynomials (lague)      2 21 , , , 1, 2,..., j j r r j j j d h r e e r j n dr                1 , 0, , 1, 2,..., ! j j r j j r j d g r r e r j n j e dr           bernstein polynomials (bern) fourier polynomials (fourier)          1 1 ! 1 1 ! ! 0,1 , 1, 2,..., n jj j j n b r r r j n j r j n                 1 1 cos for even 2 1, 1 sin for odd 2 0, 2 , 2,3,..., j j j j f r r j f r j f r r j r j n                            lobatto polynomials (lob) sinc function (sinc)     1 , 1,1 , 1, 2,...,j j jda r p r r j n dr                  sin 1 1 0,1 , 1, 2,..., j j j j n r r sinc r n r r r j n              table 1: list of several basis functions j and their definition interval used in structural mechanics applications. differential and integral quadrature enerally an unknown sufficiently smooth function  f x can be approximated by a set of basis functions  j x for 1, 2, ,j n  , where n is the total number of collocation points in a closed definition interval. a polynomial set uniformly converges to the unknown function when the number of grid points tends to infinity and the unknown function is smooth in a closed interval. hence, the approximate solution of a function  f x can be g f. tornabene et alii, frattura ed integrità strutturale, 29 (2014) 251-265; doi: 10.3221/igf-esis.29.22 253 found in the form     1 n j j j f x x     (1) these polynomials constitute a linear vector space nv and are used for the approximation (1) [7, 17]. a list of several basis functions is given in tab. 1 and it should be used as a reference for the present manuscript. it should be mentioned that tab. 1 presents the polynomials in their definition interval indicated by r . the functional approximation is performed using the cartesian coordinates, as indicated by eq. (1). the approximation can be done if the domain is discretized in n discrete points, such as kx for , , ,1 2 k n . tab. 2 reports the most common grid point distributions that can be found in literature. it is assumed that every grid is defined in the interval  0,1k  . in addition, some cases need extra points for the enforcement of the boundary conditions, known also as  -point technique [9, 12]). hence, a grid distribution  0,1k  without  -points can be defined as , for , 1, 2, ...,k k m n k n    (2) whereas considering  -points it takes the following aspect 1 2 1 10, , 1 , 1, , for 2, 2, 3, ..., 1n n k k m n k m                  (3) the stretching formulation [7, 17] can be defined using the previous definitions (2)-(3), a grid distribution  0,1k  (tab. 2) and a non-zero constant  , as   2 31 3 2 , for 1, 2, ...,k k k k k n         (4) this technique takes the points in the  0,1k  domain and stretches them into the domain  0,1k  . the parameter  cannot take any value because for some entries the distribution  0,1k  (see for more details [140]). finally, the collocation points in dimensionless form  0,1k  must be transformed into the physical interval  ,kx a b , thus, a general coordinate transformation [7] can be used as   , for 1, 2,...,k k b a x c a k n d c        (5) where  ,k c d  is a dimensionless discretization. using the so-called differentiation matrix procedure [7, 10, 11, 17], the approximation (1) for the one-dimensional case can be written in matrix form as f a λ (6) where      1 2, , , t nf x f x f x   f  is the vector of the unknown function values, λ is the vector of the unknown coefficients j and the components of the coefficient matrix a are given by  ij j ia x for , 1, 2, ,i j n  . if a structural component is described in the interval  0,kx   , where  is the domain length, the transformation (5) corresponds to , for 1, 2, ...,k kx k n  (7) expression (1) can be derived for the general n -th order polynomial and the derivative is transferred to the functions  j x , because the unknown coefficients j do not depend on the variable x     1 , for 1, 2, ..., 1 nn n j jn n j d xd f x n n dx dx       (8) expression (8) can be written in matrix form as follows f. tornabene et alii, frattura ed integrità strutturale, 29 (2014) 251-265; doi: 10.3221/igf-esis.29.22 254            with for , 1, 2, ..., i n jn n n n ij j in x d x a x i j n dx     f a λ (9) where         1 2 , , , n t n n n n n n n x x x d f x d f x d f x dx dx dx         f is the vector which contains the derivative of the function  f x at all the discrete points ix . in order to perform the derivation, the matrix a should be invertible. this property depends on the basis functions  j x and on the location of the grid points. the unknown parameters vector λ can be evaluated from eq. (6) by simply inverting the matrix a , such as 1λ a f (10) subsequently, substituting expression (10) into (9), one obtains      1n n n f a a f d f (11) the differentiation matrix  nd is found as a matrix product between the inverse of the matrix a containing the values of the basis functions  j ix in all the grid points and the derivatives of the same functions     n j ix contained in the  na matrix. all the steps presented above are valid for any derivative order n . in general, eq. (11) takes the form             1 1 with for , 1, 2,..., i n n n n n n ij j ij ijn ij jx d f x d f x d i j n dx        a a (12) in conclusion, a generic n-th order derivative can be expressed by the following relation       1 i n n n ij jn jx d f x f x dx    (13) although eq. (12) is valid for any basis function and grid point distribution, the coefficient matrix a , since it is like the vandermonde matrix, can become ill-conditioned when the number of grid points n is large. it is important to note that, when the lagrange polynomials  jl x , lagrange trigonometric polynomials  js x or the sinc function  jsinc x are chosen as a basis of the linear vector space nv , the coefficient matrix a becomes an identity matrix  ia (14) this is due to the fact that, the three previous basis functions have the following properties       0 for 1 forj i j i j i i j l x s x sinc x i j       (15) in all these three cases eq. (12) becomes             1 with for , 1, 2,..., i n n n n n n ij j ij ij ijn jx d f x d f x d i j n dx       a (16) the important consequence that derives from relations (14) and (15) is that the matrix a i is always invertible ( 1  ia ) and thus the ill-conditioning drawback does not occur when the lagrange polynomials  jl x , lagrange trigonometric polynomials  js x or the sinc function  jsinc x are chosen. further details about the weighting coefficients of the previously reported methodologies can be found in [7]. f. tornabene et alii, frattura ed integrità strutturale, 29 (2014) 251-265; doi: 10.3221/igf-esis.29.22 255 a) b) figure 1: a) static analysis for single element structural components varying the number of points n for a cc rod, ss eb beam with  -points (1/2) and a cc tim beam using pdq basis functions and che-gau-lob grid distribution. b) static analysis for structural components varying the number of elements en with 7n  for a cc rod, ss eb beam with  -points (1/2) and a cc tim beam using pdq basis functions and che-gau-lob grid distribution. a) b) figure 2: a) static analysis for structural components using weak formulation (wfem) varying the number of elements en with 7n  for a cc rod and a cc tim beam using pdq basis functions and leg-gau-lob grid distribution. b) dynamic discrete spectra for single element structural components with 151n  for a cc rod, a ss eb beam with  -points (1/2) and a cc tim beam using pdq basis functions and che-gau-lob grid distribution. a) b) figure 3: a) dynamic discrete spectra for various structural components with 7n  and 100en  for a cc rod, a ss eb beam with  -points (1/2) and a cc tim beam using pdq basis functions and leg-gau grid distribution. b) dynamic discrete spectra for several structural components using weak formulation (wfem) with 7n  and 100en  for a cc rod and a cc tim beam using pdq basis functions and leg-gau-lob grid distribution. f. tornabene et alii, frattura ed integrità strutturale, 29 (2014) 251-265; doi: 10.3221/igf-esis.29.22 256 uniform (unif) chebyshev-gauss-lobatto (che-gau-lob) 1 , 1, 2,..., 1 k k k m m      1 1 1 1 , cos , 1, 2,..., , 1,1 1 k k m k m r r k r k m r r r m                  quadratic (quad) (only for m odd) extended chebyshev (extd cheb) or (cheb i) 2 2 1 1 2 1, 2,..., 1 2 1 1 1 2 4 1, 1,..., 1, 1 1 2 k k k m k m k k m k m m m m                                     1 1 , roots of , 1, 2,..., , 1,1kk k m m r r r t r k m r r r          extrema chebyshev (extr cheb) or (cheb ii) approximate legendre (app leg)  1 1 , roots of , 1, 2,..., , 1,1kk k m n r r r u r k m r r r          1 1 2 3 1 1 1 4 1 , 1 cos , 8 8 4 2 1, 2,..., , 1,1 k k m k m r r k r r r m m m k m r                         legendre-gauss (leg-gau) legendre-gauss-radau (leg-gau-rad)   1 1 1 2 , 1, 1, roots of , 2,3,..., 1, 1,1 k k m m k m r r r r r r r p r k m r                   1 1 1 , roots of , 1, 2,..., , 1,1 k k k m m mr p r r r p r r k m r r             chebyshev-gauss (cheb-gau) legendre-gauss-lobatto (leg-gau-lob)   1 1 1 1 2 3 , 1, 1, cos , 2 2 2,3,..., 1, 1,1 k k m m k m r r k r r r r r m k m r                        11 1 1 , 1, 1, roots of , 2,3,..., 1 1,1 mk k m k m dp rr r r r r r r dr k m r                hermite (her) laguerre (lague)  1 1 , roots of , 1, 2,..., , , k k k m m r r r h r r r k m r             1 1 , roots of , 1, 2,..., , 0, k k k m m r r r g r r r k m r           jacobi (jac) chebyshev-gauss-radau (cheb-gau-rad)    ,1 1 , roots of , 1, 2,..., , 1,1 k k k m m r r r j r r r k m r             1 1 1 2 1 , cos , 2 1 1, 2,..., , 1,1 k k m k m kr r r r r m k m r                  jacobi-gauss (jac-gau) ding et al. [37] distribution    ,1 1 2 1 , 1, 1, roots of , 2, 3,..., 1, 1,1 k k m k m m r r r r r j r r r k m r                 1 1 1 2 cos , 1, 2,..., 2 4 2 1 k k k m m               chebyshev iii (cheb iii) chebyshev iv (cheb iv)  1 1 , roots of , 1, 2,..., , 1,1kk k m n r r r v r k m r r r           1 1 , roots of , 1, 2,..., , 1,1kk k m n r r r w r k m r r r          radau i (rad i) radau ii (rad ii)     1 1 1 11 2, 1, roots of , 1, 2,..., 1, 1,1 m m k k m k m r r r r p r p r r r k m r                      11 2 1 , 1, roots of , 1, 2,..., 1, 1,1 k m mk m k m r r r r r p rp r r k m r                table 2: list of several grid distributions used in structural mechanics applications. f. tornabene et alii, frattura ed integrità strutturale, 29 (2014) 251-265; doi: 10.3221/igf-esis.29.22 257 a) b) figure 4: a) relative error of the first frequency for various structural components with 7n  for a cc rod, a ss eb beam with  points (1/2) and a cc tim beam using pdq basis functions and leg-gau grid distribution. b) effect of the grid point number inside each element for the static analysis of a cc rod using sfem with pdq basis functions and leg-gau grid distribution, wfem and sem with pdq basis functions and leg-gau-lob grid distribution and fem with linear and quadratic shape functions. however, when a domain decomposition method is taken into account, it could not be necessary to use a polynomial of high degree inside each element, because a good approximation might be captured with a number of points less than 13n  . it has been demonstrated in [8, 9] that the vandermonde matrix becomes ill-conditioned when 13n  . thus, if a limited number of points is considered the matrix inversion (12) can be used for the evaluation of the weighting coefficients. it is also noted that considering a limited number of points any polynomial basis (tab. 1) within any distribution (tab. 2) can be taken into account for the evaluations of the weighting coefficients using the presented general scheme (12). on the contrary, when a single element is taken into account the weighting coefficients in exact form must be used to avoid ill-conditioning problems. the present work also illustrates some applications related to the weak formulation finite element method (wfem), where an integration procedure based on the weighting coefficients of the gdq method is developed. the present technique has been described in the works [7, 17]. this approach has been termed the generalized integral quadrature (giq) method. a) b) figure 5: a) dynamic discrete spectra with 100en  for a cc rod using sfem with pdq basis functions and leg-gau grid distribution, wfem and sem with pdq basis functions and leg-gau-lob grid distribution and fem with linear and quadratic shape functions. b) relative error of the first frequency varying the number of elements en for a cc rod using sfem with pdq basis functions and leg-gau grid distribution, wfem and sem with pdq basis functions and leg-gau-lob grid distribution and fem with linear and quadratic shape functions. in general, the numerical integration of a function  f x over a domain  ,a b can be defined as     1 b n k k ka f x dx w f x    (17) 1 2 1 4 6 810 1 1 1 1 6 1 10 1 10 f. tornabene et alii, frattura ed integrità strutturale, 29 (2014) 251-265; doi: 10.3221/igf-esis.29.22 258 where kw are the weighting coefficients. the integral of  f x over a given domain can be generally approximated by a linear combination of all the functional values in the whole domain as     1 j i x n ij k k kx f x dx w f x    (18) the limits ix , jx of eq. (18) can be changed. when ia x and jb x eq. (18) becomes a conventional integral (17). the giq weighting coefficients can be computed as ij k jk ikw w w  (19) the weighting coefficients for the integral are evaluated by inverting the matrix   1(1)   w , which depends on the matrix of the weighting coefficients of the first order derivative [7, 17] and they can be calculated by the following relations        1 1 1 1 1for , foriij ij ij ii j i x c i j i j x c x c             (20) a) b) figure 6: a) static analysis for single element structural components varying the number of points n for a membrane, a kl plate with  -points ( 510 ) and a rm plate using pdq basis functions and che-gau-lob grid distribution. b) static analysis for structural components varying the number of elements en with 7n  for a membrane and a rm plate using pdq basis functions and leggau grid distribution. a) b) figure 7: a) dynamic discrete spectra for single element structural components with 31n  for a membrane, a kl plate with  points ( 510 ) and a rm plate using pdq basis functions and che-gau-lob grid distribution. b) dynamic discrete spectra for various structural components with 7n  and 64en  for a membrane and a rm plate using pdq basis functions and leg-gau grid distribution. f. tornabene et alii, frattura ed integrità strutturale, 29 (2014) 251-265; doi: 10.3221/igf-esis.29.22 259 it is important to note that c is an arbitrary constant and can be set equal to 1010nc x   in order to obtain stable and accurate results. it must be pointed out that in the applications, the coordinate transformation from an interval  1 ,k nc d     to another one  1 ,k nx a x b x   should be defined, especially when different basis functions are used for the definitions of the weighting coefficients. thus, the transformation of the giq weighting coefficients 1nkw allows to switch from the interval  ,c d to a generic one  ,a b . recalling eq. (5), the following relation can be written           1 1 1 1 1 1 1 1 where b d n n k k ka c n n n n n n k k k k k k k k b a b a b a b a f x dx f c a d w f c a d c d c d c d c b a b a b a w f c a w f x w w d c d c d c                                                 (21) it is noted that 1nkw are the weighting coefficients in the shifted interval  ,c d and the 1nkw are the ones in the physical interval  ,a b . applications and results n the present section the static and dynamic behaviors of 1d and 2d structural components, summarized in tab. 3 and 4, are reported. in all the computations an isotropic material with elastic modulus 210 gpae  , poisson ratio 0.3  and density 37800 kg/m  has been considered. the one-dimensional problems (rod, eb and tim beams) have a length 2 ml  and a squared cross section / .20 0 1 m  b h l . the two-dimensional applications (membrane, kl and rm plates) are squared with .., the membrane has a constant tension 1 ns  , the kl plate has a thickness 0.01 mh  and the rm plate has a thickness 0.08 mh  . in all the static calculations the uniform applied load for both 1d and 2d problems is taken equal to 100 paq  . the convergence, stability and reliability of the sfem varying the basis functions, collocation, number of grid points and number of elements are discussed in the following. the spacing of floating point numbers, due to the machine in use, is 52 162 10cpu    . the static and dynamic convergence and stability of rods, euler-bernoulli (eb) and timoshenko (tim) beams are shown. for the present studies the basis functions, the grid point distributions, the number of points in each domain and the number of elements for the domain decomposition can be selected. the eb beam has the additional parameter given by the  -points location. the authors defined a new way of inserting the  -points other than the classic one [9, 12]. this new approach consists in adding the  -points as functions of the first and third (last and two-before the last) points. the  -points location is indicated in brackets “( )”. as far as the classic  -points technique is concerned, the extra points locations are directly reported as ( 510 ), whereas for the second approach the distance between the first and the third points is indicated. for instance, if (1/2) is used the  -points are the mid-points of the first and the third ones. in the following applications the gdq method based on pdq basis functions is considered. the reader can find the complete nomenclature of the grid point locations in tab. 2. the one dimensional tests are divided into static and dynamic analysis. for the static benchmarks, the l2-norm of the absolute error of the displacement field is taken into account, since comparing a displacement of a single point of the domain can rise numerical instabilities. for the dynamic cases, the discrete spectra and the relative error on the first natural frequency will be shown in the following. fig. 1a shows the l2-norm of the absolute error of the displacement for several structural elements composed of a single finite element varying the number of points n . the error given by the eb beam model is higher than the one exhibited by the rod and tim beam, because extra points have to be added in order to enforce the boundary conditions. the che-gau-lob grid distribution is chosen within pdq basis functions. for the eb beam model  -points are taken as (1/2), showing the best accuracy with respect to the classic value ( 510 ). the present method has been demonstrated to be stable even for 151n  . fig. 1b studies the accuracy of the domain decomposition by varying the number of elements with 7n  in each element. the same basis functions and grid distribution of the previous case was used. increasing the number of grid points or the elements, the same trends are obtained when fig. 2a and 1b are compared. in the following the free vibration problems of the rod, eb and tim beams are reported in fig. 2b, 3, 4a. in the computations dn represents the total number of degrees of freedom i f. tornabene et alii, frattura ed integrità strutturale, 29 (2014) 251-265; doi: 10.3221/igf-esis.29.22 260 and mn indicates the mode number which is plotted in the discrete spectra. it is remarked that  2d en n n  for the rod,  2 2d en n n  for the tim beam and  4d en n n  for the eb beam. moreover   2 2d en n n  for the membrane,  23 2d en n n  for the rm plate and   2 4d en n n  for the kl plate. fig. 2b and 3a illustrate the dynamic discrete spectra by following the same analyses of fig. 1a and 1b. firstly a single element of high degree ( 151n  ) is investigated. secondly the same structural elements are divided into 100en  of low degree ( 7n  ). the dynamic discrete spectra give a very close picture of the complete dynamic behavior given the total number of degrees of freedom. the percentage error with respect to the exact solution is plotted against the mode number. globally in fig. 2b, the accuracy is around 60% (for the rod and the eb beam) and 50% (for tim beam), when a single element is taken into account. however, it is uncommon to use a single element with many points in it. thus, the sfem approach is investigated in fig. 3a where 100en  and 7n  . the  -points for the eb beam are taken as (1/2) and the global accuracy results to be good until 30% of the modes, whereas the other rod and tim beam models reach the 60% and 40% respectively. these plots report some discrete jumps through the whole spectrum that were not investigated in the present paper. hence, these aspects will be deeply exhibited in a following work. finally the dynamic discrete spectra of the wfem are represented in fig. 3b for the rod and the tim beam. it can be noted that the curves start to detach from the horizontal line with respect to fig. 3a where sfem approach is presented. in fact, rod and tim beam are accurate until the 20% of the modes. fig. 4a reports the convergence rate of the sfem in the double logarithmic plot of the relative error of the first frequency versus the number of elements. in the study the degree of the approximating polynomials is 6 ( 7n  ) and the number of element varies from 1 to 100. pdq basis functions and leg-gau grid distribution are taken into account. it is remarked that the rod and the tim beam have a rate of convergence higher than the eb beam due to the fact that fourth order differential equations need extra points for the imposition of the boundary conditions, hence 2 grid points (per boundary) are lost for the imposition of the boundary conditions. furthermore, the maximum accuracy that can be reached by the rod is around 1510 and the tim beam is around 1210 , on the contrary the eb beam reaches 910 . for the sake of comparison, the interested reader can refer to the works [36, 37] where the free vibrations of rods and eb beams are investigated within the isogeometric analysis (iga). for instance fig. 10-12 of reference [37] show the convergence rates of a rod with different polynomial orders. as expected, the convergence rate changes from 1/4 to 1/8 increasing the polynomial order. nevertheless for all three cases the author shows only four points for the rod convergence. in fact fig. 10 and 11 consider 10en  , 20en  , 30en  , 40en  , whereas fig. 12 5en  , 10en  , 15en  , 20en  . the author is assuming that the minimum convergence is reached, hence no more elements are needed. nevertheless, the machine error noise is never shown throughout the paper. ultimately, it is noted that the results proposed by [37] are in perfect agreement with the ones presented by the authors in fig. 4a. the only exception is given by eb beams with  -points, because a lower trend 1/6 occurs together with a lower accuracy 910 . the interested reader can find more details about the so-called round-off error in the book by boyd [15]. in conclusion, fig. 4b, 5a, 5b exhibit a summary of the rod structure behavior using four different numerical approaches: sfem, wfem, sem (spectral element method) and fem. the first solves the strong form and uses 1c compatibility conditions, the second solves the weak form and uses 1c compatibility conditions, the third and the fourth solve the weak form with 0c continuity, but the former with a general polynomial degree (lagrange polynomials) and the latter with well-known linear and quadratic functions. fig. 4b shows that increasing the polynomial order inside each element the error increases. in fact the sfem error with 7n  is higher than the fem one with 2n  . nevertheless, the maximum error is always below the machine working precision (black dashed line). a comparison in terms of dynamic discrete spectra in shown in fig. 5a. it can be noticed that sfem offers the best accuracy in terms of percentage of accurate modes and the maximum errors are always more limited than all the other techniques. fig. 5b shows several convergence rates with respect to the first natural frequency. obviously, increasing the polynomial degree the convergence rate passes from 1/2 to 1/10. linear fem ( 2n  ) has the same trend (1/2) of the ones obtained by sfem and wfem with 3n  and 1c continuity. the strong formulation requires a higher derivation order with respect to a variational or weak formulation. considering the second order rod problem, for a given basis function of order n the strong form derives the approximate solution two times, whereas the weak form only one. therefore, the strong form solution becomes of order 2n  and the weak form is 1n  . moreover, since the 1c continuity is considered in the strong form the boundary points are excluded from the computation due to the kinematic condensation. f. tornabene et alii, frattura ed integrità strutturale, 29 (2014) 251-265; doi: 10.3221/igf-esis.29.22 261 constants definition: 3 30 0 2, 5 6 , , 12, 12a bh k a a i h i bh i h        axially-loaded beam, bar or rod problem static analysis dynamic analysis 2 2 0 d u ea pb dx   2 2 02 0 d u ea bi u dx   boundary conditions clamped-clamped (cc)    0 0, 0u u l  clamped-clamped (cc)    0 0, 0u u l  exact solutions     2 pb u x l x x ea   0 02 n n n ea n ea f l bi l bi      euler-bernoulli (eb) beam static analysis dynamic analysis 4 4 0 d w ei qb dx   4 2 04 0 d w ei bi w dx   boundary conditions simply supported-simply supported (ss)         2 2 2 2 0 0, 0 0, 0, 0 d w d w w w l l dx dx     simply supported-simply supported (ss)         2 2 2 2 0 0, 0 0, 0, 0 d w d w w w l l dx dx     exact solutions   4 4 3 4 3 2 24 qbl x x x w x ei ll l         2 2 2 2 2 0 02 n n n ei n ei f bi bil l       timoshenko (tim) beam static analysis dynamic analysis 2 2 2 2 0 0 d w d g qb dxdx d dw ei g dxdx                      2 2 02 2 2 22 0 0 d w d g bi w dxdx d dw ei g bi dxdx                         boundary conditions clamped-clamped (cc)        0 0, 0 0, 0, 0w w l l     simply supported-simply supported (ss)        0 0, 0 0, 0, 0d dw w l l dx dx       exact solutions     2 4 2 2 2 2 2 3 3 2 3 2 24 2 2 3 12 qbl x x qbl x x w x ei l g ll l qbl x x x x ei ll l                           2 2 4 4 2 2 2 4 0 0 , 1 , bi biei n ei n p q r g g bi bil l             table 3: list of one dimensional static and dynamic exact solutions. f. tornabene et alii, frattura ed integrità strutturale, 29 (2014) 251-265; doi: 10.3221/igf-esis.29.22 262 constants definition:  3 2 30 0 212 1 , 5 6 , , 12eh k gh gh i h i h          membrane (mem) or poisson problem static analysis dynamic analysis 2 2 2 2 sin sin 0 w w x y s q x y a b            2 2 2 02 2 0 w w s i w x y            boundary conditions: clamped (cccc)        0, 0, , 0 0, , 0, , 0w y w x w a y w x b           0, 0, , 0 0, , 0, , 0w y w x w a y w x b    exact solutions   2 2 4 , sin sin 1 1 q x y w x y a b s a b                     2 2 0 1 2 nm n m s f a b i              kirchhoff-love (kl) thin plate problem static analysis dynamic analysis 4 4 4 4 2 2 4 2 sin sin 0 w w w x y q x x y y a b                 4 4 4 2 04 2 2 4 2 0 w w w i w x x y y                 boundary conditions: completely simply-supported (ssss)                 2 2 2 2 2 2 2 2 0, 0, 0, 0, , 0, , 0 , 0 0, , 0 0, , 0, , 0 w w w y y w a y a y x x w w w x x w x b x b y y                                 2 2 2 2 2 2 2 2 0, 0, 0, 0, , 0, , 0 , 0 0, , 0 0, , 0, , 0 w w w y y w a y a y x x w w w x x w x b x b y y                 exact solutions   2 2 2 6 , sin sin 1 1 q x y w x y a b a b                     2 2 02 nm n m f a b i                   reissner-mindlin (rm) thick plate problem static analysis dynamic analysis 2 2 2 2 22 2 2 2 2 2 2 2 2 sin sin 0 1 1 0 2 2 1 1 0 2 2 yx yx x x y y x y w w x y q x y x y a b w x y x y x w y x x y y                                                                               2 2 2 02 2 2 2 2 2 22 2 2 2 2 2 22 2 0 1 1 0 2 2 1 1 0 2 2 x y x x y x x y y x y y w w i w x y x y w i x y x y x w i y x x y y                                                                                       boundary conditions: completely simply-supported (ssss)                                 0, , 0, 0, , 0, , 0, 0, , 0 , , 0, , , , , 0, , , 0 , 0, 0, , 0, 0, 0, , 0, , 0 , , 0, , , 0, , , , , 0 yx y yx y y x x y x x w y t y t y t y t x y w a y t a y t a y t a y t x y w x t x t y t y t y x w x b t x b t x b t x b t y x                                                                                       0, 0, 0, 0, 0, 0, 0 , 0, , , 0, , 0 , 0 0, , 0 0, 0, 0, 0 , 0, , 0, , , 0 x y y x y y y x x y x x w y y y y x y w a y a y a y a y x y w x x y y y x w x b x b x b x b y x                                                    exact solutions 2 2 2 2 2 2 2 2 2 2 2 2 11 12 13 22 23 332 2 2 2 2 2 1 1 1 , , , , , 2 2 2 n m n m n m n m n m s s s s s s a b a b a b a b a b                                            11 11 12 13 12 22 23 11 13 23 33 11 , sin sin 0 , cos sin 0 , sin cos nm x x nm x y nm y y x y w x y w a bs s s w q x y s s s x y a b s s s x y x y a b                                         11 12 13 0 2 12 22 23 2 13 23 33 2 0 0 0 0 0 0 2 0 0 0 nm x nm nm nm nm y nm s s s i w s s s i f s s s i                                                 table 4: list of two dimensional static and dynamic exact solutions. f. tornabene et alii, frattura ed integrità strutturale, 29 (2014) 251-265; doi: 10.3221/igf-esis.29.22 263 in conclusion, in order to have the same accuracy trend sfem or wfem with 1c compatibility conditions should have a higher number of grid points with respect to sfem or sem with 0c compatibility conditions. remark that the first point of the curves in fig. 5b refer to a single element mesh. the comparison between sfem and the other weak methods is meaningless for this case because, excluding the boundary conditions, the sfem has an 1n  order with respect to the others due to the strong formulation (second order derivatives with respect to first order ones). it should be also noted that not only sfem and wfem but also sem has the increasing error machine effect when the maximum accuracy is reached (around 1210 ). fig. 6-8 show some results related to the static and dynamic stability and accuracy of membranes, kirchhoff-love (kl) and reissner-mindlin (rm) plates. fig. 6a is analogous to fig. 1a where the number of grid points n varies from 5 to 31 using pdq basis functions and che-gau-lob grid distribution. the kl plate model is considered with  -points ( 510 ). note that when 15n  the error is stable increasing the number of points (round-off plateau). fig. 6b collects the static convergence behavior of a single domain decomposed into several regular elements (no mapping is involved). the number of grid points is fixed 7n  and the number of elements is variable 1, 4, 9, 16, 25, 36, 49, 64. for the present cases the pdq basis functions and leg-gau grid distribution are considered. as expected the error decreases increasing the number of elements. the dynamic convergence of several structural components is shown in fig. 7 and 8. fig. 7a shows the dynamic discrete spectra of the membrane, the kl and the rm plates using pdq basis functions and che-gau-lob grid distribution with 31n  using a single element. the membrane and kl plate calculate accurate modes until the 25% of total modes, whereas the rm plate gets 10% of accurate modes due to the comparison with a semi-analytical solution. an analogous plot using pdq basis functions and leg-gau grid distribution with 7n  and 64en  is shown in fig. 7b for the membrane and the rm plate. due to the element decomposition the accuracy decreases both for the membrane and the rm plate. however, the error is limited within the 5% for the 40% and 50% of the modes of the membrane and the rm plate, respectively. in conclusion a comparison in terms of dynamic discrete spectra for structured and distorted meshes is presented in fig. 8 for the membrane and rm plate, respectively. different number of grid points is considered, in order to get the same number of degrees of freedom changing the number of elements. as expected the modes are more accurate when the mesh is structured, whereas a lower accuracy is observed when irregular meshes are considered. a) b) figure 8: a) dynamic discrete spectra using different meshes (structured and distorted) of a membrane using pdq basis functions and leg-gau grid distribution. b) dynamic discrete spectra using different meshes (structured and distorted) of a rm plate using pdq basis functions and leg-gau grid distribution. conclusions and remarks he present paper references the dqm and other methods that, according to the authors’ knowledge, represent similar techniques. the paper aims to present a general view on strong formulation methods. the main novelty of this manuscript is given by the presentation in several forms of the stability and accuracy of the sfem technique when applied to simple 1d and 2d models and compared to exact solutions (or semi-analytical ones as far as rm plate is concerned). this work should help researchers, of the computational mechanics community, to understand the advantages and disadvantages of a strong formulation approach and, in particular, to the ones who are keen on weak (or t f. tornabene et alii, frattura ed integrità strutturale, 29 (2014) 251-265; doi: 10.3221/igf-esis.29.22 264 variational) formulation based approaches. although it seems that dqm has been widely developed for several engineering problems, some aspects are still in a developing stage (e.g. boundary conditions in a domain decomposition approach using 1c conditions). in a future paper the authors want to expose in detail the boundary conditions implementation from the mathematical point of view, giving all the formulae in discrete form. moreover, the numerical results will be compared to classical fem and sem solutions. acknowledgements he authors want to thank the school’s central library “gian paolo dore” and the engineering and architecture’s library “giovanni michelucci” for providing some of the books, theses and articles that were used and cited in the manuscript. the research topic is one of the subjects of the center of study and research for the identification of materials and structures (cimest)-”m. capurso” of the university of bologna (italy). references [1] viola, e., tornabene, f., vibration analysis of damaged circular arches with varying cross-section, sid-sdhm, 1 (2005) 155-169. [2] viola, e., dilena, m., tornabene, f., analytical and numerical results for vibration analysis of multi-stepped and multi-damaged circular arches, j. sound vib., 299 (2007) 143-163. [3] viola, e., tornabene, f., fantuzzi, n., generalized differential quadrature finite element method for cracked composite structures of arbitrary shape, compos. struct., 106 (2013) 815-834. [4] fantuzzi, n., tornabene, f., viola, e., generalized differential quadrature finite element method for vibration analysis of arbitrarily shaped membranes, int. j. mech. sci., 79 (2014) 216-251. [5] fantuzzi, n., tornabene, f., strong formulation finite element method for arbitrarily shaped laminated plates i. theoretical analysis, adv. aircraft space. sci., 1 (2014) 125-143. [6] fantuzzi, n., tornabene, f., 2014, “strong formulation finite element method for arbitrarily shaped laminated plates ii. numerical analysis”, adv. aircraft space. sci., 1 (2014) 145-175. [7] tornabene, f., fantuzzi, n., mechanics of laminated composite doubly-curved shell structures. the generalized differential quadrature method and the strong formulation finite element method, esculapio, bologna, (2014). [8] bellman, r., casti, j., differential quadrature and long-term integration, j. math. anal. appl., 34 (1971) 235-238. [9] bert, c.w., malik, m., differential quadrature method in computational mechanics, appl. mech. rev., 49 (1996) 1-27. [10] quan, j.r., chang, c.t., new insights in solving distributed system equations by the quadrature method i. analysis, comput. chem. eng., 13 (1989) 779-788. [11] quan j.r., chang, c.t. , new insights in solving distributed system equations by the quadrature method ii. numerical experiments, comput. chem. eng., 13 (1989) 1017-1024. [12] striz, a.g., chen, w.l., bert, c.w., static analysis of structures by the quadrature element method (qem), int. j. solids struct., 31 (1994) 2807-2818. [13] reddy, j.n., mechanics of laminated composites plates and shells, 2nd edition, crc press, new york, (2004). [14] gottlieb, d., orszag, s.a., numerical analysis of spectral methods. theory and applications, cbms-nsf regional conf. ser. in appl. math., siam, (1977). [15] boyd, j.p., chebyshev and fourier spectral methods, dover publications, (2001). [16] canuto, c., hussaini, m.y., quarteroni, a., zang, t.a., spectral method. fundamentals in single domains, springer, (2006). [17] shu, c., differential quadrature and its application in engineering, springer, (2000). [18] chen, c.-n., discrete element analysis methods of generic differential quadratures, springer, (2006). [19] zong, z., zhang, y.y., advanced differential quadrature methods, crc press, (2009). [20] viola, e., tornabene, f., dynamical analysis of spherical shell structural elements using the first order shear deformation theory, mechanical vibration: where do we stand?, cism, 488 (2007) 17-41, springer-wien, new york. [21] tornabene, f., 2-d gdq solution for free vibrations of anisotropic doubly-curved shells and panels of revolution, compos. struct., 93 (2011) 1854-1876. [22] tornabene, f., free vibrations of anisotropic doubly-curved shells and panels of revolution with a free-form meridian resting on winkler-pasternak elastic foundations, compos. struct., 94 (2011) 186-206. t f. tornabene et alii, frattura ed integrità strutturale, 29 (2014) 251-265; doi: 10.3221/igf-esis.29.22 265 [23] tornabene, f., liverani, a., caligiana, g., laminated composite rectangular and annular plates: a gdq solution for static analysis with a posteriori shear and normal stress recovery, compos. part b eng., 43 (2012) 1847-1872. [24] tornabene, f., liverani, a., caligiana, g., general anisotropic doubly-curved shell theory: a differential quadrature solution for free vibrations of shells and panels of revolution with a free-form meridian, j. sound vib., 331 (2012) 4848-4869. [25] tornabene, f., ceruti, a., free-form laminated doubly-curved shells and panels of revolution resting on winklerpasternak elastic foundations: a 2-d gdq solution for static and free vibration analysis, world j. mech., 3 (2013) 125. [26] tornabene, f., and ceruti, a., mixed static and dynamic optimization of four-parameter functionally graded completely doubly-curved and degenerate shells and panels using gdq method, math. problem. eng., 2013 (2013) 133, article id 867079. [27] tornabene, f., reddy, j.n., fgm and laminated doubly-curved and degenerate shells resting on nonlinear elastic foundations: a gdq solution for static analysis with a posteriori stress and strain recovery, j. indian inst. sci., 93 (2013) 635-688. [28] tornabene, f., viola, e., static analysis of functionally graded doubly-curved shells and panels of revolution, meccanica, 48 (2013) 901-930. [29] tornabene, f., viola, e., fantuzzi, n., general higher-order equivalent single layer theory for free vibrations of doubly-curved laminated composite shells and panels, compos. struct., 104 (2013) 94-117. [30] viola, e., tornabene, f., fantuzzi, n., general higher-order shear deformation theories for the free vibration analysis of completely doubly-curved laminated shells and panels, compos. struct., 95 (2013) 639-666. [31] viola, e., tornabene, f., fantuzzi, n., static analysis of completely doubly-curved laminated shells and panels using general higher-order shear deformation theories, compos. struct., 101 (2013) 59-93. [32] tornabene, f., fantuzzi, n., viola, e., ferreira, a.j.m., radial basis function method applied to doubly-curved laminated composite shells and panels with a general higher-order equivalent single layer theory, compos. part b eng., 55 (2013) 642-659. [33] tornabene, f., fantuzzi, n., viola, e., carrera, e., static analysis of doubly-curved anisotropic shells and panels using cuf approach, differential geometry and differential quadrature method, compos. struct., 107 (2014) 675–697. [34] tornabene, f., fantuzzi, n., viola, e., reddy, j.n., winkler-pasternak foundation effect on the static and dynamic analyses of laminated doubly-curved and degenerate shells and panels, compos. part b eng., 57 (2014) 269-296. [35] ding, h., shu, c., yeo, k.s., xu, d., numerical computation of three-dimensional incompressible viscous flows in the primitive variable form by local multiquadric differential quadrature method, comput. meth. appl. mech. eng., 195 (2006) 516-533. [36] cottrell, j.a., hughes, t.j.r., bazilevs, y., isogeometric analysis. toward integration of cad and fea, john wiley & sons, (2009). [37] reali, a., an isogeometric analysis approach for the study of structural vibrations, j. earthq. eng., 10 (2006) 1-30. microsoft word numero_42_art_20.docx p. ferro et alii, frattura ed integrità strutturale, 42 (2017) 189-195; doi: 10.3221/igf-esis.42.20 189 the fatigue behavior of v-notches in presence of residual stresses: recent developments and future outcomes p. ferro department of engineering and management, university of padova, stradella s. nicola 3, 36100, vicenza (italy) ferro@gest.unipd.it m. peron, s.m.j. razavi, f. berto, j. torgersen department of mechanical and industrial engineering, norwegian university of science and technology (ntnu), richard birkelands vei 2b, 7491, trondheim, norway. mirco.peron@ntnu.no, javad.razavi@ntnu.no, filippo.berto@ntnu.no, jan.torgersen@ntnu.no abstract. residual stresses, arising from welding processes or nonhomogeneous plastic deformations, broadly influence the high cycle fatigue behavior of mechanical components. the presence of v-notches leads to singular residual stresses ahead of the notch tip and the asymptotic stress field can be described by the notch stress intensity factor (nsif). however, plastic effects induce redistribution of residual stresses during cyclic loading and this variation is accounted in several numerical models developed for the calculation of the residual nsifs. due to the development of these models, the fascinating issue of predicting the fatigue strength of pre-stressed notched components has gained widely attention by the researchers and new approaches were recently developed and some of them are here reviewed. keywords. high cycle fatigue; residual stress; v-notch; fatigue strength. citation: ferro, p., peron, m., razavi, s.m.j, berto, f., torgesen, j., the fatigue behavior of v-notches in presence of residual stresses: recent developments and future outcomes, frattura ed integrità strutturale, 42 (2017) 189-195. received: 15.06.2017 accepted: 21.07.2017 published: 01.10.2017 copyright: © 2017 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. introduction t is widely reported that static and fatigue strength is affected by geometric variations, especially by sharp v-notches [1-5]. starting from williams’ research [6], several works were written about the effect of local stress field rising from singularities, especially on fatigue strength of welded joints, that can be quantified by means of local strain energy density criterion (sed) averaged over a control volume of a critical radius rc [7-11] or notch stress intensity factor criterion (nsifs) [12-16]. intensity and distribution of residual stresses are difficult to be quantified near the weld toe, and, moreover, residual stresses are related to welding parameters, geometry, clamping conditions, applied stress and number of cycles. as a consequence of these drawbacks, works reported just above include residual stress effects in reference curves built up from several experimental data. despite of these complications, several numerical models were developed in order to describe the residual stress field near the weld toe, but ferro et al. [17] were the firsts to reveal the asymptotic nature of residual stresses. they described how stationary and transient thermal loads affected thermal and residual stress fields, i p. ferro et alii, frattura ed integrità strutturale, 42 (2017) 189-195; doi: 10.3221/igf-esis.42.20 190 reporting that both of them are singular near a v-notch tip and the singularity degree matches the elastic [6] or the elasticplastic solution [18,19], depending on the magnitude of the thermal loads and clamping conditions. ferro [20] and ferro and petrone [21] investigated deeply the influence of clamping conditions and phase transformation effects (specific volume change, transformation plasticity [22] on residual stress field and they reported that phase modifications affect the sign of residual asymptotic stress distribution, leading to an enhancement or to a decrease of the fatigue strength by means of stress-relief heat treatment, depending on the material to be welded. during low-cycle regime loading, i.e. where plastic effects are not negligible as they are instead in high-cycle regime (small scale yielding hypothesis) [23], a redistribution/relaxation occurs in the first cycle and it remains stable going ahead with fatigue cycling [23]. reliable numerical models can provide the calculation of the residual and stationary nsif and the residual asymptotic stress field can be seen as a ‘mean stress’ field as reported by ferro [24]. the aim of this work is to review some recent improvements. asymptotic residual stress field efore any model is developed which quantify the influence of residual stresses on fatigue strength of pre-stressed notched components, the distribution of residual stress near a ‘geometric singularity’ has to be first studied. consider the problem of the elastic equilibrium in the presence of a v-shaped notch with an opening angle 2β (fig. 1). figure 1: domain ω for the sharp v-notch problem. if the material is homogeneous and isotropic, under the hypothesis of linear, thermo-elastic theory and plane-strain conditions, the equations representing the stress field near the v-notch, are independent of the thermal terms and match the solution obtained by williams in [6] ([17]). whatever the load applied (thermal or mechanical), under linear-elastic hypothesis and plane-stress or plane-strain conditions, the induced stress field near the notch tip (by relating only to the first term of the williams’ solution and mode i of v-notch opening), is described by the following asymptotic equation:     , 1    ( , , ) i th m i ij ij k g i j r r         (1) where gij(θ) are the angular functions, λi is the first eigenvalue obtained from eq. (2),    sin 2 sin 2 0    (2) and ,th mik is the nsif due to a thermal (th) or mechanical (m) symmetrical load (opening mode i). according to gross and mendelson’s definition [25]: , 1 0 2 lim      ( , 0)ith mi n k r r        (3) b p. ferro et alii, frattura ed integrità strutturale, 42 (2017) 189-195; doi: 10.3221/igf-esis.42.20 191 the first eigenvalue depends only by the v-notch angle (2β) and varies in the range between 0.5 and 1. the eigenvalue is 0.5 in the crack case (2β = 0), and increases to 0.674 and 0.757 when the notch opening angles are equal to 135 and 150 degrees, respectively. by simulating the solidification of a fusion zone (fz) near the tips of a double v-notched plate (2β = 135°), the asymptotic nature of residual stresses is revealed (fig. 2). figure 2: (a) in-plane distribution of residual stresses (radial component, σr) near the notch tip; (b) tensile residual stresses along the bisector of the v-notch (2β=135°), ( si rek =135 mpa.mm0.3264) (material: astm 11 sa 516, free edges) [24]. influence of phase transformation on residual stress field more in depth investigations were carried out in order to evaluate the influence of phase transformations on residual stresses. during solidification and cooling of a multi-phase material, the variation of the specific volume and the ‘transformation plasticity’ [22] associated to phase transformation, influence the thermal and residual stresses induced by thermal loads. it was shown that such effects are so high that any numerical model of welding process that doesn’t take into account phase transformation effects fails in calculating the thermal and residual stress filed [26]. when the scale of observation is focused on about one tenth of the notch depth, it was observed that phase transformation changes the sign of residual stresses if compared to the results obtained in a simplified mono-phase material [20]. this means that stress relief heat treatments may decrease the fatigue strength at high-cycle regime when the sign of the asymptotic residual stress is negative. fig. 3 shows the asymptotic residual stress fields (θ component) along the bisector of the v-shaped weld toe calculated by taking into account phase transformation effects, volume change only and no phase transformations. as a general rule it was found that as-welded mono-phase materials, such as austenitic or ferritic stainless steels, are characterized by a compressive singular residual stress field, while multi-phase material such as carbon steels shows a tensile asymptotic residual stress field (under free-edge clamping condition). p. ferro et alii, frattura ed integrità strutturale, 42 (2017) 189-195; doi: 10.3221/igf-esis.42.20 192 figure 3: (a) mesh of the numerical model and fusion zone dimension and shape (butt-welded joint); (b) phase transformation effects on residual stresses along the bisector of the v-notch (2β =135°) (material: astm 11 sa 516, free edges). residual stresses redistribution it is well known that residual stresses redistribute during cyclic load due to plastic effect. however, such redistribution is completed after few cycles and a residual nsif (r-nsif) stationary value is reached. it was found that the residual stress redistribution under fatigue loading is negligible in the high-cycle regime since the zone that experiments plastic deformation is restricted to about one tenth of the zone dominated by the elastic asymptotic residual stress distribution (small scale yielding hypothesis) [24]. on the other hand, stress redistribution increases as the remotely applied stress increases. at high stress amplitudes, plasticity ‘erases’ the pre-existing residual stress field so that there is not difference between the fatigue strength of a stress-relieved joint and an as-welded joint. this means that the superposition property can be applied only in the high-cycle regime where the experimental results show that fatigue strength is sensitive to pre-existing residual stresses. in this case the r-nsif can be summed to the stress-induced nsif as shown in fig. 4a. it can be noted that in that case, residual stresses are negative (single-phase material, aa 6063) so that they decrease the maximum transverse stress filed (fig. 4a). fig. 4b shows that at high remotely applied stress amplitude, the plastic effects make the maximum transverse stress filed almost insensitive to the pre-existing residual stress field. (a) (b) figure 4: maximum transverse stress field of stress-relief and as-welded joint after ten cycles at different values of the remotely applied stress amplitude (δσn) (a) δσn = 25 mpa; (b) δσn = 120 mpa; 2β =135°, l ik = nsif induced by load, s i rek = nsif induced by the solidification of the fz: aa 6063, free edges [23]. p. ferro et alii, frattura ed integrità strutturale, 42 (2017) 189-195; doi: 10.3221/igf-esis.42.20 193 quantification of the influence of residual stresses on fatigue strength of welded joints n the basis of the above mentioned developments, a model which quantifies the influence of residual stresses on fatigue strength of welded joints or pre-stressed notched components was finally developed [24], and experimentally validated [23]. the model uses the concept of strain energy density (sed) averaged over a control volume of radius rc [7,8,11], which under plane strain conditions and mode i loading takes the form: 2 , 1 i th m i i c e k w e r         (4) in eq. (4), the parameter ei depends on v-notch opening angle (2β), poisson’s ratio (ν) of the material and failure hypothesis. under beltrami failure hypothesis (total strain energy density) and plane strain conditions, ν = 0.34 (aluminum alloy aa 6063) and 2β = 135°, ei is equal to 0.111. the control radius (rc) is a material characteristic length that for alalloy welded joints was found to be equal to 0.12 mm [8,11]. now, residual stresses have the effect of modifying the local load ratio (r). as a matter of fact, the following relationships hold true: max min min min max min max     0   m m i i m res i i m res i im res i i m i m i k k k k k r k k k k k r k                    (5) max min   0 0 m res m resi i i i k k k k k r        (6) where si rek is the r-nsif which characterizes the residual stress field. rm and r correspond to the local load ratio of the nominal and real cycle, respectively. starting from eqs (4-6), for r = 0, the following equation is obtained (details about the analytical frame employed are published in [24]): 1/21/ 1 1 1   i i i z c res i i n i i e c r e n k k t k t                  (7) where δσn (= σn,max) is the nominal stress amplitude. similarly, for r>0 the following relationship is obtained:          1/2 1/ 2 max 1 1 1   1   1 1i i m z res i m res im i m m i i r e c k e nr k k t r k t r                   (8) where c is a constant and z is the slope of the fatigue data expressed in terms of local strain energy density experimentally calculated 1 2 2 1 log( / ) / ( / )d d d dz n n log w w   , subscripts d1 and d2 indicate two points of the curve ( )w n ; ki is a non-dimensional coefficient, analogous to the shape functions of cracked components calculated by using the following equation: o p. ferro et alii, frattura ed integrità strutturale, 42 (2017) 189-195; doi: 10.3221/igf-esis.42.20 194 1 imi i nk k t   (9) where σn is the remotely applied stress, and t is a geometrical parameter of the plate, according to [16]. eqs. (7,8) are applied in high-cycle fatigue regime where the redistribution of the pre-existing residual stresses is considered negligible [24]. by using experimental results of fatigue strength of butt-welded stress-relieved and as-welded joints in aa 6063 [27], the model was validated in[23]. under the condition   0 min m res i ik k  , fig. 5 shows an estimation of the fatigue resistance of the stress-relieved and as-welded component predicted by means of the proposed model, eq. (7). due to the negative value of the r-nsif, an improvement of fatigue strength of as-welded joints is observed experimentally and predicted by the model compared to the fatigue strength of the stress-relief specimens. it is worth mentioning that in this model the fatigue strength of as-welded joints in the low-cycle regime was set equal to that of stress-relieved specimens according to the redistribution/relaxation induced by high remotely applied stress amplitudes (fig. 4b). some extensions related to creep are also possible [28]. figure 5: residual stress influence on fatigue strength of the aa 6063 butt-welded joint predicted by eq. (7). conclusions tarting from 2006, the asymptotic residual stress fields in notched components have been studied extensively with the aim to develop a model which quantifies the influence of residual stresses on fatigue strength of welded joints. such asymptotic residual stress fields were found strongly influenced by mechanical constraints, geometry, process parameters and material. in particular, the sign of the residual stress field depends on phase transformations effects such as volume changes and transformation plasticity. for this reason, these effects cannot be neglected in any reliable numerical model of welding process. furthermore, residual stresses redistribute during the fatigue load application because of the plastic deformation that occurs near the weld toe at high remotely applied stress amplitudes. on the contrary, when such remotely applied stress amplitudes are low, the stress redistribution is not expected and the superposition principle can be applied. in such conditions, the residual stress field near the notch tip works in the same way as a mean stress and its influence on fatigue strength is quantified by the proposed model. references [1] berto, f., lazzarin, p., ayatollahi, m. r., brittle fracture of sharp and blunt v-notches in isostatic graphite under torsion loading, carbon n. y., 50 (2012) 1942–1952. s p. ferro et alii, frattura ed integrità strutturale, 42 (2017) 189-195; doi: 10.3221/igf-esis.42.20 195 [2] berto, f., ayatollahi, m. r., fracture assessment of brazilian disc specimens weakened by blunt v-notches under mixed mode loading by means of local energy, mater. des., 32 (2011), 2858–2869. [3] maragoni, l., carraro, p. a., peron, m., quaresimin, m., fatigue behaviour of glass/epoxy laminates in the presence of voids, int. j. fatigue, 95 (2017) 18–28. [4] da silva, b. l., ferreira, j. l. de a., araújo, j. a., high-cycle notch sensitivity of alloy steel astm a743 ca6nm used in hydrogenator turbine components, fract. struct. integr., 14 (2010), 36-44. [5] brotzu, a., felli, f., pilone, d., effects of the manufacturing process on fracture behaviour of cast tial intermetallic alloys, fract. struct. integr., 27 (2013) 66-73. [6] williams, m. l., stress singularities resulting from various boundary conditions in angular corners of plates in extension, j. appl. mech, 19 (1952) 526–528. [7] lazzarin, p., zambardi, r., a finite-volume-energy based approach to predict the static and fatigue behavior of components with sharp v-shaped notches, int. j. fracture, 112 (2001) 275–298. [8] livieri, p., lazzarin, p., fatigue strength of steel and aluminium welded joints based on generalised stress intensity factors and local strain energy values, int. j. fracture, 133 (2005) 247–276. [9] radaj, d., berto, f., lazzarin, p., local fatigue strength parameters for welded joints based on strain energy density with inclusion of small-size notches, eng. fract. mech., 76 (2009) 1109–1130. [10] lazzarin, p., comportamento a fatica dei giunti saldati in funzione della densità di energia di deformazione locale: influenza dei campi di tensione singolari e non singolari, fract. struct. integr., 9 (2009) 13-26. [11] berto, f., lazzarin, p., a review of the volume-based strain energy density approach applied to v-notches and welded structures. theor. appl. fract. mec., 52(3) (2009) 184-194. [12] atzori, b., meneghetti, g., fatigue strength of fillet welded structural steels: finite elements, strain gauges and reality, int. j. fatigue, 23 (2001) 713–721. [13] atzori, b., lazzarin, p., tovo, r., from the local stress approach to fracture mechanics: a comprehensive evaluation of the fatigue strength of welded joints, fatigue fract. eng. m., 22 (1999) 369–381. [14] lazzarin, p., campagnolo a., berto, f., a comparison among some recent energyand stress-based criteria for the fracture assessment of sharp v-notched components under mode i loading, theor. appl. fract. mech., 71 (2014) 21– 30. [15] lazzarin, p., livieri, p., notch stress intensity factors and fatigue strength of aluminium and steel welded joints. int. j. fatigue, 23 (2001) 225–232. [16] lazzarin, p., tovo, r., a notch intensity approach to the stress analysis of welds, fatigue fract. eng. m., 21 (1998) 1089–1104. [17] ferro, p., berto, f., lazzarin, p., generalized stress intensity factors due to steady and transient thermal loads with applications to welded joints, fatigue fract. eng. m., 29 (2006) 440–453. [18] hutchinson, j. w., singular behaviour at the end of a tensile crack in a hardening material, j. mech. phys. solids, 16 (198) 13–31. [19] rice, j. r., rosengren, g. f., plane strain deformation near a crack tip in a power-law hardening material, journal of the mechanics and physics of solids, 16 (1968) 1-12. [20] ferro, p., influence of phase transformations on the asymptotic residual stress distribution arising near a sharp v notch tip, model. simul. mater. sci. eng., 20 (2012). [21] ferro, p., petrone n., asymptotic thermal and residual stress distribution due to transient thermal loads. fatigue fract. eng. m., 32 (2009) 936-948. [22] leblond, j. b., devaux, j. c., mathematical modelling of transformation plasticity in steels: i. case of ideal-plastic phases, international j. plasticity, 5 (1989) 551–572. [23] ferro, p, berto, f, james, m.n., asymptotic residual stresses in butt-welded joints under fatigue loading, theor. appl. fract. mec., 83 (2016) 114–124. [24] ferro, p, the local strain energy density approach applied to pre-stressed components subjected to cyclic load, fatigue fract. eng. m., 37 (2014) 1268–1280. [25] gross, r., mendelson, a., plane elastoplastic analysis of v-notched plates, int. j. fracture, 8 (1972) 267-276. [26] ferro, p., porzner, h., tiziani, a., bonollo, f., the influence of phase transformation on residual stresses induced by the welding process—3d and 2d numerical models, model. simul. mater. sci. eng., 14 (2006) 117–136. [27] bertini l., fontanari v., straffellini g., influence of post weld treatments on fatigue behaviour of al-alloy welded joints, int. j. fatigue, 20 (1998) 749–755. [28] gallo, p., berto, f., glinka, g generalized approach to estimation of strains and stresses at blunt v-notches under non-localized creep, fatigue fract. eng. mater. struct., 39 (2016) 292-306. << /ascii85encodepages false /allowtransparency false /autopositionepsfiles true /autorotatepages /none /binding /left /calgrayprofile (dot gain 20%) /calrgbprofile (srgb iec61966-2.1) /calcmykprofile (u.s. web coated \050swop\051 v2) /srgbprofile (srgb iec61966-2.1) /cannotembedfontpolicy /error /compatibilitylevel 1.4 /compressobjects /tags /compresspages true /convertimagestoindexed true /passthroughjpegimages true /createjobticket false /defaultrenderingintent /default /detectblends true /detectcurves 0.0000 /colorconversionstrategy /cmyk /dothumbnails false /embedallfonts true /embedopentype false /parseiccprofilesincomments true /embedjoboptions true /dscreportinglevel 0 /emitdscwarnings false /endpage -1 /imagememory 1048576 /lockdistillerparams false /maxsubsetpct 100 /optimize true 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/hrv (za stvaranje adobe pdf dokumenata najpogodnijih za visokokvalitetni ispis prije tiskanja koristite ove postavke. stvoreni pdf dokumenti mogu se otvoriti acrobat i adobe reader 5.0 i kasnijim verzijama.) /hun 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can be opened with acrobat and adobe reader 5.0 and later.) >> /namespace [ (adobe) (common) (1.0) ] /othernamespaces [ << /asreaderspreads false /cropimagestoframes true /errorcontrol /warnandcontinue /flattenerignorespreadoverrides false /includeguidesgrids false /includenonprinting false /includeslug false /namespace [ (adobe) (indesign) (4.0) ] /omitplacedbitmaps false /omitplacedeps false /omitplacedpdf false /simulateoverprint /legacy >> << /addbleedmarks false /addcolorbars false /addcropmarks false /addpageinfo false /addregmarks false /convertcolors /converttocmyk /destinationprofilename () /destinationprofileselector /documentcmyk /downsample16bitimages true /flattenerpreset << /presetselector /mediumresolution >> /formelements false /generatestructure false /includebookmarks false /includehyperlinks false /includeinteractive false /includelayers false /includeprofiles false /multimediahandling /useobjectsettings /namespace [ (adobe) (creativesuite) (2.0) ] /pdfxoutputintentprofileselector /documentcmyk /preserveediting true /untaggedcmykhandling /leaveuntagged /untaggedrgbhandling /usedocumentprofile /usedocumentbleed false >> ] >> setdistillerparams << /hwresolution [2400 2400] /pagesize [612.000 792.000] >> setpagedevice microsoft word numero_55_art_18_2951 m. m. konieczny et alii, frattura ed integrità strutturale, 55 (2021) 241-257; doi: 10.3221/igf-esis.55.18 241 research of stress distribution in the cross-section of a bimetallic perforated plate perpendicularly loaded with concentrated force mateusz marcin konieczny, henryk achtelik, grzegorz gasiak opole university of technology, poland mateuszmarcinkonieczny@wp.pl, kmpkm@po.edu.pl, g.gasiak@po.edu.pl abstract. the paper presents the stress distribution along the plate thickness in a bimetallic steel – titanium circular perforated plate produced in the technological process of explosion welding. the steel layer is the layer that transfers the load in the plate, while the titanium layer is used to improve the properties of the plate, e.g. corrosion resistance, thermal transmittance, etc. in the plate. two cases of fastening were considered, i.e. a freely supported and fixed plate. such plates are used in various engineering structures, e.g. simply supported plates can be used in loose material screens, while plates are fixed in heat exchangers. the load was assumed as a concentrated force applied perpendicularly to the plate surface. the results obtained numerically using the finite element method were compared with the results calculated according to the analytical equations. it has been shown that the difference in the results of equivalent von mises stress calculations does not exceed 13%. the research results presented in the paper can be used by engineers to design bimetallic perforated plates perpendicularly loaded to their surface. keywords. bimetallic perforated plate; concentrated force; stress analysis; analytical calculations; numerical calculations citation: konieczny, m. m., achtelik, h., gasiak, g., research of stress distribution in the cross-section of a bimetallic perforated plate perpendicularly loaded with concentrated force, frattura ed integrità strutturale, 55 (2021) 241-257. received: 13.11.2020 accepted: 17.12.2020 published: 01.01.2021 copyright: © 2019 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. introduction n engineering structures, structural elements consisting of many layers [1, 2] and of many materials [3] are often used plated elements called metallic composites [4, 5]. metallic composites (plating) are obtained by so-called explosive welding. explosive welding, or bonding, makes it possible to join together many groups of construction materials by means of the energy released during the detonation of the explosive [6]. the unquestionable advantage of the explosive technology is the possibility of joining together materials that currently cannot be permanently joined by conventional methods such as: soldering, gluing or welding. however, the key benefit of using metal composites is the ability to significantly reduce the cost of making a given structure by reducing the amount of expensive materials with unique properties. an example of this type of material is bimetal steel titanium, which, when used in engineering structures, maintains the assumed strength and anti-corrosion parameters, ensuring work safety, while reducing the amount of expensive titanium used. i https://youtu.be/k24shmryuyw m. m. konieczny et alii, frattura ed integrità strutturale, 55 (2021) 241-257; doi: 10.3221/igf-esis.55.18 242 the main applications of steel – titanium plated materials include high-pressure tanks and highly specialized elements of process equipment, e.g. heat exchanger tube sheets (fig. 1). elements made of bimetal steel – titanium are most often used due to the improvement of physical properties, thermal properties, chemical properties (e.g. corrosion resistance) as well as mechanical parameters of a given structure in which such elements are present. in heat exchangers, an important issue is the analysis of the complex effect of the perforated plate on the connected shell of the chemical apparatus and the associated stress distribution in the shell, in the tubes and in the perforated plate itself [7, 8, 9]. contemporary engineering structures, compared to their predecessors, are characterized by a reduced safety factor. therefore, the precise calculation of temporary strength, stiffness and stability, in particular of thin-walled structural elements, is of increasing importance. literature studies indicate the widening perspective of the use of plated materials [10, 11, 12, 13]. the paper proposes an analytical and numerical approach to determining the value of stresses along the plate thickness in a bimetallic circular axially symmetrical perforated plate, freely supported at the edge and fixed at the edge and centrally loaded with a concentrated force p perpendicular to the plate surface. the research conducted at work was carried out on the basis of the finite element method (fem) and the analytical method according to mathematical formulas. a novelty in this work is the development and application of the analytical method to determine the stress state in the transition zone between the titanium layer and the steel layer in a bimetallic perforated plate loaded with e.g. a concentrated force. figure 1: model of bimetallic perforated plate. figure 2: model of bimetallic perforated plate consisting of steel thickness perforated plate h and titanium perforated plate thickness a containing holes with diameters d1,…,d5 and sections t1 and t2. m. m. konieczny et alii, frattura ed integrità strutturale, 55 (2021) 241-257; doi: 10.3221/igf-esis.55.18 243 material and geometry he calculation was based on a bimetallic circular axisymmetric perforated plate with dimensions: diameter d = 300 mm and comprising two layers, i.e. the base layer b in the form of structural steel with a thickness of h = 10 mm and the applied layer (plating) in the form of titanium with the thickness of a = 2.5 mm. 100 holes with different radii located on the plate. these holes were arranged in five circles with 20 holes in each circle. on the first outer circle, the plate had holes d1 = 20.5 mm in diameter and on the fifth, inner circle holes d5 = 9.5 mm in diameter (fig. 2). steel plate grade s355j2 was adopted as the base material, and titanium sheet was adapter as the applied material with the following mechanical and material parameters (tab. 1) [14]. the materials used in the work, titanium and steel included in the bimetallic perforated plate, were modeled as elastic materials. s355j2 steel and titanium applied layer a titanium re [mpa] rm [mpa] e [gpa] v [-] g [gpa] a5 [%] 189-215 308-324 100 0.37 36.5 43-56 c fe h n o ti 0.10 0.20 0.015 0.03 0.18 99.5 base layer b s355j2 steel re [mpa] rm [mpa] e [gpa] v [-] g [gpa] a5 [%] 382-395 598-605 220 0,30 84,6 24-34 c si mn p s cu fe 0.22 0.55 1.60 0.025 0.025 0.45 all table 1: strength properties and chemical composition of s355j2 steel and titanium, where: re – yield strength [mpa], rm – tensile strength [mpa], e – young’s modulus [gpa], v – poisson’ s ratio [-], a5 – tensile elongation [%]. analytical method nlike the classical form of plate bending theory [15], in which the analysis is concerned with the state of equilibrium of internal forces acting on the separated full plate element, in this case the state of equilibrium of the plate element containing the halves of the holes is considered (fig. 2) [16] and described in the cylindrical coordinate axis system r, θ, z. the following variables can be found in fig. 3: 1m , 2m – circumferential torque intensity in the steel and titanium parts, respectively; 1r m , 2r m – radial torque intensity in the steel and titanium parts, respectively;  1 ,  2 – circumferential stress in the steel and titanium parts;  1r ,  2r – radial stress in the steel and titanium parts; e1 , e2, 1v , 2v – young's modules and poisson's ratios for steel and titanium parts respectively; h1, h2 – values determining the position of the inert layer in the cross-section of the plated plate; h – total thickness of the plate; t(r) – intensity of transverse force acting in cross-sections of the plated plate. the conditions of equilibrium of internal forces presented in fig. 3 result in the following form of a differential equation [15] describing the state of plate effort: t u m. m. konieczny et alii, frattura ed integrità strutturale, 55 (2021) 241-257; doi: 10.3221/igf-esis.55.18 244      r r dm m m t r dr r (1) the intensity of moments mr1, mr2, mθ1, mθ2 in a bimetallic perforated plate are expressed by the respective relations [16]:         1 2 * ** r r r r d m m m c b b dr r (2)             1 2 ** *dm m m c b b dr r (3) where:  – is the angle of inclination tangential to the curved central surface of the plate.  * 1 2b b b  ** 1 1 2 2b v b v b       3 31 1 1 22 13 1 e b h h v ;         3 32 2 2 22 23 1 e b h a h v ; – bending strength of the steel and titanium layer, respectively. figure 3: wedge element cut from a bimetallic perforated plate in a state of static equilibrium. the rc , c coefficients determine the degree of weakening of the cross-section due to the existence of discontinuities in the form of perforations (fig. 2) in the radial and circumferential direction. they were adopted in the respective form [16]:     δ δ r r d c r ;    δ δ r d c r (4) where: δr , δ – finite increments of radial coordinate r and circumferential one θ; d diameter of the perforation. after introducing compounds (2), (3) into eqn. (1), the following form was obtained: the equilibrium of internal forces acting on the element of the bimetallic circular perforated plate (fig. 3): m. m. konieczny et alii, frattura ed integrità strutturale, 55 (2021) 241-257; doi: 10.3221/igf-esis.55.18 245                   2 ** 2 * 2 * 1 1 1 r r r t rc cd b d c r dr cdr b r c b (5) where the function of the transverse force intensity t(r) for the most common methods of plate support was assumed to take the form [16]:      221 3 k t r k r k r r (6) where: k1, k2, k3 – lateral force function coefficients. the solution to eqn. (5) is given by the function of the plate deflection angle  (r):                            1 2 43 λ λ31 2 1 2* 1 2 1 2 1 2 1 3 λ 3 λ 1 λ 1 λ 4 λ 4 λr k rk r k r r d r d r c b (7) in which 1λ and 2λ are roots of the characteristic equation:          ** 2 * λ 1 λ 0 r r c cb c cb (8) in function (7), which is the general integral of the differential eqn. (5), the constant coefficients k1, k2, k3 depend on the load method, while d1 and d2 are integration constants whose numerical values are determined on the basis of the boundary conditions given in this study. after determining the function φ(r) from compounds (2) and (3), the intensities of radial and circumferential moments in the base material (steel) mr1, mθ1 and in the plating layer (titanium) mr2, mθ2 are determined. the deflection of the bimetallic perforated plate with the plating layer is determined by the relationship:       3w r r dr d (9) where d3 – integration constant. the stress in the cross-sections of the bimetalic perforated plate (fig. 3) is derived on the basis of the compounds: 1) radial stress  r: a) in the base material of the plate (steel)  1r :      1 1 3 3 1 2 3 r r r m z c h h , dla   1 2h z h (10) b) in the applied layer of the plate (titanium)  2r :         2 2 3 3 1 2 3 r r r m z c h a h , dla    2 2h z h a (11) 2) circumferential stress   : a) in the base material of the plate (steel)  1 :         1 1 3 3 1 2 3m z c h h , dla   1 2h z h (12) m. m. konieczny et alii, frattura ed integrità strutturale, 55 (2021) 241-257; doi: 10.3221/igf-esis.55.18 246 b) in the applied layer of the plate (titanium)  2 :            2 2 3 3 2 2 3m z c h a h , dla    2 2h z h a (13) the equivalent von mises stress was determined from the relationship: a) for the steel layer:        1 1 1 1 1 2 2 red r r (14) b) for the titanium layer:        2 2 2 2 2 2 2 red r r (15) in the formulas for determining the intensity of bending moments in the radial direction (2) and circumferential direction (3) as well as in the formulae applied for determining the stresses in the radial direction (10) and (11) and circumferential directions (12) and (13) h1 and h2 determine the position of the layer inert sections of the plate (fig. 3):      2 2 1 2 2 1 22 e h e a h e h e a (16)  1 2h h h (17) where: h1, h2 – values determining the state of the inactive layer in the cross section of the steel plate; e1 , e2 – young's modules for the steel and titanium parts; h, a – thickness of steel and titanium plate, respectively. inactive layer of the plate – it is a layer in which the deformations are equal to zero [15, 16]. bimetallic perforated plate freely supported on the perimeter and loaded with a concentrated force p acting perpendicular to the surface in the first case, the analysis the state of stress in a bimetallic perforated plate loaded with a concentrated force applied perpendicularly to the surface with the value p = 10 kn was presented below. the geometry of the plate is presented in fig. 2. the concentrated force p was applied centrally to the pressure stamp with a diameter of b1 = 14 mm. a free support of the plate on the outer perimeter was assumed. the method of support and loading the plate is shown in fig. 4. the boundary conditions are assumed to take the following form (fig. 4): a) for the radius r – ½ b = 6 mm – plate deflection angle φ = 0; b) for the radius r = ½ d = 150 mm – radial moment strength  0rm . in this case, the coefficients k1, k2, k3 inside the function of the lateral force intensity t(r) (6) are equal to, respectively: k1 = 0; k2 = 2 p ; k3 = 0 the roots of the eqn. (8) 1λ and 2λ are:   1λ 1.127  ;    2λ 1.065  m. m. konieczny et alii, frattura ed integrità strutturale, 55 (2021) 241-257; doi: 10.3221/igf-esis.55.18 247 integration constants d1 and d2 in the eqn. (7) are equal to:    71 21.21545 * 10  d k mm ;    52 25.1032 * 10  d k mm ; cross-section weakening coefficients (4) c and rc in the analyzed plate are respectively:    0.590 c ;   0.496 rc ; figure 4. bimetallic perforated plate freely supported on the perimeter and loaded with a concentrated force p acting perpendicular to the surface. for calculations it was assumed: p = 10 kn – load in the form of concentrated force distributed around the circumference of the hole with a diameter; b = 12 mm – hole diameter; b1 – 14 mm – pressure stamp diameter; d = 300 mm – outer diameter of the plate; h = 10 mm – base layer thickness (steel plate); a = 2.5 mm – applied layer thickness (titanium plate); h1 = 5.64 mm (fig. 2); h2 = 4.36 mm (fig. 2); the mechanical properties of the steel plate and titanium plate are taken from tab. 1. on the basis of the eqns. (10) – (15), values of radial stresses  ar and circumferential  a and equivalent von mises stresses  ared were determined for the adopted geometry of the bimetallic perforated plate given in fig. 4. for example, in fig. 5 the values of the circumferential stress  a , radial stress  ar and equivalent von mises stresses  a red are plotted along the thickness h of the bimetallic perforated plate in sections t1 and t2, i.e. on the radius r = r5 = 60 mm and r = 130 mm (fig 2), loaded from the side of the titanium layer with a concentrated force applied perpendicularly to the center of the plate p = 10 kn. bimetallic perforated plate fixed supported on the perimeter and loaded with a concentrated force p acting perpendicular to the surface in the second case, the analysis the state of stress in a bimetallic perforated plate loaded with a concentrated force applied perpendicularly to the surface with the value p = 10 kn was presented below. the geometry of the plate is presented in fig. 2. the concentrated force p was applied centrally to the pressure stamp with a diameter of b1 = 14 mm. a fixed of the plate on the outer perimeter was assumed. the method of support and loading the plate is shown in fig. 6. the boundary conditions are assumed to take the following form (fig. 6): a) for the radius r – ½ b = 6 mm – plate deflection angle φ = 0; b) for the radius r = ½ d = 150 mm – plate deflection angle φ = 0. m. m. konieczny et alii, frattura ed integrità strutturale, 55 (2021) 241-257; doi: 10.3221/igf-esis.55.18 248 figure 5. stress distribution, respectively:  a ,  ar , and  a red in the cross-section of a bimetallic perforated plate freely supported and loaded with a concentrated force with the value p = 10 kn: a) in the section t1 on the radius r = 5r = 60 mm; b) in the section t2 on radius r = 130 mm (fig. 2). figure 6. bimetallic perforated plate fixed on the perimeter and loaded with a concentrated force p acting perpendicular to the surface in this case, the coefficients k1, k2, k3 inside the function of the lateral force intensity t(r) (6) are equal to, respectively: k1 = 0; k2 = 2 p ; k3 = 0 the roots of the eqn. (8) 1λ and 2λ are:   1λ 1.127  ;    2λ 1.065  integration constants d1 and d2 in the eqn. (7) are equal to:    71 21.322 * 10  d k mm ;    52 23.219 * 10  d k mm m. m. konieczny et alii, frattura ed integrità strutturale, 55 (2021) 241-257; doi: 10.3221/igf-esis.55.18 249 cross-section weakening coefficients (4) c and rc in the analyzed plate are respectively:    0.590 c ;   0.496 rc ; data as in the above case were adopted for the calculations. on the other hand, the mechanical properties of the steel plate and the titanium plate were taken from tab. 1. on the basis of the eqns. (10) – (15), values of radial stresses  ar and circumferential  a and equivalent von mises stresses  ared were determined for the adopted geometry of the bimetallic perforated plate given in fig. 6. for example, in fig. 7 the values of the circumferential stress  a , radial stress  ar and equivalent von mises stresses  a red are plotted along the thickness h of the bimetallic perforated plate in sections t1 and t2, i.e. on the radius r = r5 = 60 mm and r = 130 mm (fig 2), loaded from the side of the titanium layer with a concentrated force applied perpendicularly to the center of the plate p = 10 kn. figure 7. stress distribution, respectively:  a ,  ar , and  a red in the cross-section of a bimetallic perforated plate fixed and loaded with a concentrated force with the value p = 10 kn: a) in the section t1 on the radius r = 5r = 60 mm; b) in the section t2 on radius r = 130 mm (fig. 2). numerical method he subject of numerical calculations was the stress distribution in a bimetallic circular perforated plate, in the first case freely supported (fig. 4) and in the second case fixed (fig. 6) and loaded with a concentrated force applied perpendicular to the center of the plate. the free support of the plate was realized by designing a ring support on which a bimetallic perforated plate was placed. minimal friction contact is applied between the plate and the support. on the other hand, the plate was fixed by removing all degrees of freedom from the finite elements located on the outer contour of the perforated plate. t m. m. konieczny et alii, frattura ed integrità strutturale, 55 (2021) 241-257; doi: 10.3221/igf-esis.55.18 250 the three-dimensional 3d computational model of the bimetallic circular axially-symmetrical perforated plate was created and discretized by the possibility of modeling and creating a finite element mesh in ansys [17]. the finite elements used for discretization were solid186 finite elements. the calculation model contained the total number of 3379707 finite elements, while the total number of nodes was 7027927. the entire plate had 25 layers of finite elements (20 layers of base plate and 5 layers of applied layer) (fig. 8). figure 8. finite elements of a bimetallic circular perforated plate in ansys program. the base layer of the b – steel plate is combined with the applied layer of the a – titanium plate by using the "connections" function, providing the option to bond two or more elements [17]. it was assumed that the combination of the titanium layer and the steel layer of the plates is excellent. modeling the connection of these two layers, contact was used in the form of inseparable bonding – as both layers were bonded permanently. bimetallic perforated plate freely supported on the perimeter and loaded with a concentrated force p acting perpendicular to the surface for example, the distribution of equivalent von mises stress in the cross section of the plate is presented in fig. 9. the figure illustrates the distribution of equivalent von mises stress in a bimetallic perforated plate loaded with a force of p = 10 kn in the applied layer a – titanium, in the applied transition zone a’titanium, in the based transition zone b’ – steel and based layer b steel determined for the radius r = r5 = 60 mm. the following numerical calculation results (fig. 9) demonstrate the places where the equivalent von mises stress values occur, i.e. point ap’ – the place of maximum equivalent m. m. konieczny et alii, frattura ed integrità strutturale, 55 (2021) 241-257; doi: 10.3221/igf-esis.55.18 251 von mises stress near the hole in the titanium transition zone, bp’ – the value of the maximum equivalent von mises stress near the hole in the transition zone of structural steel, ap– the place of maximum equivalent von mises stress near the hole in the titanium layer, bp – the value of the maximum equivalent von mises stress near the hole in the structural steel layer. the maximum equivalent von mises stress around the hole and its coordinates in the vicinity of the hole were respectively: red maxσ 97.997 mpa in a layer, where ap [x = 6.0 mm, y = 68.51 mm, z = 0.0 mm], red maxσ 168.83 mpa in b layer, where bp [x = 6.0 mm, y = 68.81 mm, z = 12.5 mm], while red maxσ 66.417 mpa in a’ zone, where ap’ [x = 6.0 mm, y = 68.51 mm, z = 2.49 mm] and red maxσ 130.27 mpa in b’ zone, where bp’ [x = 6.0 mm, y = 68.51 mm, z = 2.51 mm]. figure 9. distribution of equivalent von mises stress  nred in the cross section of the plate determined on the radius r = r5 = 60 mm. whereas in fig. 7 the values of the circumferential stress  a , radial stress  ar and equivalent von mises stresses  a red are plotted along the thickness h of the bimetallic perforated plate in sections t1 and t2, i.e. on the radius r = r5 = 60 mm and r = 130 mm (fig 2), loaded from the side of the titanium layer with a concentrated force applied perpendicularly to the center of the plate p = 10 kn. bimetallic perforated plate fixed supported on the perimeter and loaded with a concentrated force p acting perpendicular to the surface for example, the distribution of equivalent von mises stress in the cross section of the plate is presented in fig. 11. the figure illustrates the distribution of equivalent von mises stress in a bimetallic perforated plate loaded with a force of p = 10 kn in the applied layer a – titanium, in the applied transition zone a’titanium, in the based transition zone b’ – steel and based layer b steel determined for the radius r = r5 = 60 mm. the following numerical calculation results (fig. 11) demonstrate the places where the equivalent von mises stress values occur, i.e. point ap’ – the place of maximum equivalent von mises stress near the hole in the titanium transition zone, bp’ – the value of the maximum equivalent von mises stress near the hole in the transition zone of structural steel, ap– the place of maximum equivalent von mises stress near the hole in the titanium layer, bp – the value of the maximum equivalent von mises stress near the hole in the structural steel layer. the maximum equivalent von mises stress around the hole and its coordinates in the vicinity of the hole were respectively: red maxσ 51.155 mpa in a layer, where ap [x = 8.88 mm, y = -54.81 mm, z = 0.0 mm], red maxσ 91.816 mpa in b layer, where bp [x = 8.88 mm, y = -54.81 mm, z = 12.5 mm], while red maxσ 32.258 mpa in a’ zone, where ap’ [x = 8.88 mm, y = -54,81 mm, z = 2.49 mm] and red maxσ 71.527 mpa in b’ zone, where bp’ [x = 8.88 mm, y = -54.81 mm, z = 2.51 mm]. m. m. konieczny et alii, frattura ed integrità strutturale, 55 (2021) 241-257; doi: 10.3221/igf-esis.55.18 252 figure 10. stress distribution, respectively:  n ,  nr , and  n red in the cross-section of a bimetallic perforated plate freely supported and loaded with a concentrated force with the value p = 10 kn: a) in the section t1 on the radius r = 5r = 60 mm; b) in the section t2 on radius r = 130 mm (fig. 2). figure 11. distribution of equivalent von mises stress  nred in the cross section of the plate determined on the radius r = r5 = 60 mm. m. m. konieczny et alii, frattura ed integrità strutturale, 55 (2021) 241-257; doi: 10.3221/igf-esis.55.18 253 whereas in fig. 12 the values of the circumferential stress  a , radial stress  ar and equivalent von mises stresses  a red are plotted along the thickness h of the bimetallic perforated plate in sections t1 and t2, i.e. on the radius r = r5 = 60 mm and r = 130 mm (fig 2), loaded from the side of the titanium layer with a concentrated force applied perpendicularly to the center of the plate p = 10 kn. figure 12. stress distribution, respectively:  n ,  nr , and  n red in the cross-section of a bimetallic perforated plate fixed and loaded with a concentrated force with the value p = 10 kn: a) in the section t1 on the radius r = 5r = 60 mm; b) in the section t2 on radius r = 130 mm (fig. 2). results of the research he problem of the stress analysis on the plate thickness, taken up in the paper, enables the appropriate selection of the base layer of the steel plate as well as the layer of the applied plate – titanium. the base layer is the layer that carries the load in the plate, in this case it is the steel layer of the plate. however, in this case, the titanium layer of the plate is used due to the improvement of the plate properties, e.g. corrosion resistance, thermal permeability, etc. the thickness of the applied layers, depending on the type of use of the plated plate, may be from 1.5–15% of the thickness of the base plate. taking into account the thickness of the layer of the applied plate during design also affects the strength of the bimetallic perforated plate. for example, fig. 13 shows the values equivalent von mises stresses obtained numerically by the finite element method  nred and analytically  ared in a bimetallic circular perforated plate freely supported on the edge and loaded centrally with a concentrated force p = 10 kn perpendicular to the plate surface and the percentage difference between the results obtained for these cases red . for example, fig. 14 presents the values of equivalent von mises stresses obtained numerically using the finite element method  nred and analytically  a red in a bimetallic circular perforated plate fixed at the edge and loaded centrally with a concentrated force p = 10 kn acting perpendicular to the plate surface and the percentage difference between the results obtained for these cases red . apart from numerical calculations the state of stress using the finite element method, an attempt was made to develop analytical equations allowing to determine the stress values in a bimetallic perforated plate subjected to a normal load in the form of a concentrated force. the results the state of stress calculations obtained according to the analytical method were t m. m. konieczny et alii, frattura ed integrità strutturale, 55 (2021) 241-257; doi: 10.3221/igf-esis.55.18 254 compared with the results obtained by the finite element method according to the ansys program. the results of these comparisons are presented in fig. 13 – in the case of freely supported plate and in fig. 14 – in the case of fixed edges, respectively. fig. 13 shows that the maximum difference in the stress values is equivalent von mises stress   7.49%ared . on the other hand, fig. 14 shows that the maximum difference in the stress values is equivalent von mises stress   12.34%ared . the calculations carried out in the work with the analytical and numerical method using the ansys program show that the maximum difference in the results obtained with these methods in the case of equivalent von mises stress is  ared = 12.34%. (around 13%), i.e.:    σ σ *100% σ a n a red red red a red where:  nred ,  n red –equivalent vo mises stress determined by analytical and numerical methods, respectively. figure 13: comparison of equivalent von mises stress  red determined analytically and numerically in the cross-section of the bimetallic perforated plate freely supported and loaded with a concentrated force p = 10 kn determined on the radius r = r5 = 60 mm. figure 14: comparison of equivalent von mises stress  red determined analytically and numerically in the cross-section of the bimetallic perforated plate fixed and loaded with a concentrated force p = 10 kn determined on the radius r = r5 = 60 mm. m. m. konieczny et alii, frattura ed integrità strutturale, 55 (2021) 241-257; doi: 10.3221/igf-esis.55.18 255 a significant difference in the results obtained with the analytical method and the finite element method results from the fact that the bimetallic plate has a perforation, which causes a significant heterogeneity of the material, which was fully taken into account in the analytical solution. therefore, it is believed that the error of about 13% is the discrepancy between the results obtained by the analytical method and the results obtained with the ansys program. the paper shows that the ansys program allows to determine the state of stress in a sufficiently accurate state in a bimetallic perforated plate at any point, i.e. on the bridge between the holes, around the holes, along the thickness of the titanium layer and the steel layer. it also enables the determination of stress concentration zones, and thus the location of dangerous places in the designed plate. knowing the coordinates of stress concentration points, it is possible to predict the zones of crack initiation and propagation in bimetallic perforated plates. despite significant differences in the stress values determined by the analytical method, it is believed that the analytical solution of the state of stress in a bimetallic perforated plate may be helpful for engineers to estimate the effort of the designed multilayer structures of the perforated plate type. it should be mentioned that the use of analytical solutions when designing bimetallic perforated plates allows to obtain the stress values in the structure relatively quickly. the paper shows that the method of supporting a bimetallic perforated plate has a significant impact on its state of stress. tabs. 2 and 3 show that for the same load, the stresses in the plate freely supported along the perimeter are higher in relation to the plate fixed at the edge. the graphs in figs. 5, 7, 10 and 12 show that both the analytical method and the ansys program, engineers can present the curves of the circumferential stress  , radial stress r , equivalent von mises stress  red distributions along the plate thickness, both in the applied layer – titanium, the base layer – steel and in the transition zone between the overlay and the edge layer. the existence of a significant difference in the stress values in the transition zone between the applied layer a’ titanium and the base layer b’ – steel. figs. 9 and 11 show as an example the location of points along the plate thickness, where we plate with the maximum values of equivalent von mises stresses obtained by the ansys program. the analytical method does not provide such possibilities. conclusions he following conclusions can be drawn from the above analysis: 1) the attempt to use the analytical method to determine the state of stress in a bimetallic perforated plate resulted in the discrepancy of the calculation results in the equivalent von mises stress values in comparison with the finite element method, up to approximately 13%; 2) it is proposed that the analytical method be recommended to design engineers as a tool for the estimation of the state of stress of multilayer perforated plates; 3) it was shown that in the transition zone of the plate between the applied layer – titanium and the base layer – steel, there is a step change in stress values. references [1] cheng wu, x.j. (1999). a higher order theory for plane stress conditions of laminates consisting of isotropic layers, journal of applied mechanics, 66, pp. 95-100. [2] jafari, m., mounssavian, h. and chaleshtari, m.h. (2018). optimum design of perforated orthotropic and laminated composite plates under in–plane loading by genetic algorithm, structural and multidisciplinary optimization, 57, pp. 341-357, doi: 10.1007/s00158-017-1758-5. [3] shaikh, e.n., panchal, k.c. and patel, d.b. (2015). stress analysis of an infinite plate with different shaped cutouts in composite plate, international journal of science technology and management, 4 (1), pp. 307-317. [4] kosturek, r., wachowski, m., śnieżek, l. and gloc, m. (2018). the influence of the post weld heat treatment on the microstructure of inconel 625/carbon steel bimetal joint obtained by explosive welding, www.preprints.org., pp. 115. [5] konieczny, m., achtelik, h. and gasiak, g. (2020). stress distribution in plated perforated plate loaded centrally with concentrated force, zmęczenie materiału w eksploatacji maszyn roboczych, po, 2, pp. 47-62 (in polish). [6] walczak, w. (1989). metal explosion welding. wtn, warsaw (in polish). t m. m. konieczny et alii, frattura ed integrità strutturale, 55 (2021) 241-257; doi: 10.3221/igf-esis.55.18 256 [7] konieczny, m., achtelik, h. and gasiak, g. (2020). finite element analysis (fea) and experimental stress analysis in circular perforated plates loaded with concentrated force, frattura ed integrità strutturale, 51, pp. 164-173, doi: 10.3221/igf-esis.51.13. [8] konieczny, m., achtelik, h. and gasiak, g. (2019). research of maximum stresses zones in circular perforated plates made of s235jr steel loaded with concentrated force, materials engineering, 2 (228), pp. 39-46, doi: 10.15199/28.2019.2.4. [9] konieczny, m., achtelik, h. and gasiak, g. (2020). analysis of reduced stress distribution in circular perforated plates, fundamentals of machine design: selected problems, military university of technology, pp. 133-145. [10] kurek, a., niesłony, a. and szulc, z. (2013). design of process equipment made from explosively cladded materials, including the imposed material thickness in calculations, przegląd mechaniczny, 12, pp. 22-27. [11] karolczuk, a., kowalski, m., bański, r. and żok, f. (2013). fatigue phenomena in explosively welded steel – titanium clad components subjected to push-pull loading, international journal of fatigue, 48, pp. 101-108, doi: 10.1016/j.ijfatigue.2012.10.007 . [12] karolczuk, a. and kowalski, m. (2013). residual stress determination based on the hole drilling method in explosively welded bimetallic composite, third international conference on material modelling, warsaw, p. 140. [13] konieczny, m., achtelik, h. and gasiak, g. (2021). location of stress concentration zones in a two-layer axially symmetrical perforated plate with force applied normally to its surface, engineering structures, 226 , pp. 1-14, doi: 10.1016/j.engstruct.2020.111355. [14] data from explomet company research (z.t.w. explomet, gałka, szulc, sp. j. ul. oświęcimska 100h, 45-641 opole, poland). [15] timoshenko, s. and woinowsky – krieger, s. (1959). theory of plates and shells, 2nd ed. new york, mcgraw – hill book company, pp. 62-85. [16] achtelik, h., gasiak, g. and grzelak, j. (2008). strength tests of axially symmetric perforated plates for chemical reactors: part 1 the simulation of stress state, international journal of pressure vessels and piping, 85, pp. 248-256, doi: 10.1016/j.ijpvp.2007.08.009. [17] user’s guide ansys 2020 r1, ansys, inc., usa. nomenclature h, a – thickness of steel and titanium plate, respectively; h – thickness of plate; d – diameter of the circular axially-symmetrical plated perforated plate; b – diameter of the hole in the central part of the plate; b1 – pressure stamp diameter; cr, cθ – coefficients of weakening of the plate cross-section due to the existence of discontinuities in the form of holes in the radial and circumferential directions, respectively; b*, b** plate stiffness coefficients;    r – tilt angle of the tangent to the curved central surface of the plate; k1, k2, k3 – coefficients of the lateral force function; mθ1, mθ2 – circumferential torque intensity in the steel and titanium parts, respectively; mr1, mr2 – radial moment intensity in the steel and titanium parts, respectively; 1λ , 2λ – roots of the characteristic equation for the differential equation of the perforated plate balance; d1, d2, d3 – integration constants; , r – radial and peripheral coordinates of the plate;  1 ,  2 – circumferential stress in the steel and titanium parts, respectively;  1r ,  2r – radial stress in the steel and titanium parts, respectively; e1 , e2, 1v , 2v – young's modules and poisson's coefficients for steel and titanium parts; h1, h2 – values determining the position of the inactive layer in the cross-section of the plated plate; 1b , 2b – bending stiffness of the steel and titanium layer, respectively; t(r) – intensity of the transverse force acting in the cross-sections of the plated plate; w = w(r) – deflection of the perforated plate; m. m. konieczny et alii, frattura ed integrità strutturale, 55 (2021) 241-257; doi: 10.3221/igf-esis.55.18 257  1red ,  2red – equivalent von mises stress in steel and titanium parts, respectively; rn – radius of the circles on which the holes on the plate are arranged; dn – diameter of the holes; p – load in the form of concentrated force; r – radius of the circles on which the measuring points are located; t1, t2 – sections; b – base (steel) layer of the plate; b’ – basic transition zone (from the steel side) of the plate; a’ – transition zone applied (from the titanium side) to the plate; a – applied (titanium) layer of the plate. microsoft word numero_39_art_2 f. hokes et alii, frattura ed integrità strutturale, 39 (2017) 7-16; doi: 10.3221/igf-esis.39.02 7 focussed on modelling in mechanics selecting the objective function during the inverse identification of the parameters of a material model of concrete f. hokes, j. kala faculty of civil engineering, brno university of technology, veveri 331/95 brno 60200 hokes.f@fce.vutbr.cz, http://www.fce.vutbr.cz kala.j@fce.vutbr.cz, http://www.fce.vutbr.cz abstract. selecting the correct objective function is the critical precondition for a successful optimization task. the validity of this condition is also required when optimization algorithms are needed for the inverse identification of the unknown parameters of nonlinear material models of concrete, where experimentally measured load-displacement curves can be conveniently applied. in such cases, the objective function expressions can be formulated as the difference between the functional values of the curves or via comparing the characteristic features, which comprise the area under the curve and also the maximum functional value. the proposed article brings a study of the influence of the different formulations of the objectives functions to achieving optimum in the inverse analysis using genetic algorithm. the numerical part of the study was performed in the ansys computational system with use of multiplas library of elasto-plastic material models from which the model based on formulations of menetrey and willam was chosen. keywords. identification; objective function; rmse; optimization; sensitivity analysis. citation: hokes, f., kala, j., selecting the objective function during the inverse identification of the parameters of a material model of concrete, frattura ed integrità strutturale, 39 (2017) 7-16. received: 11.07.2016 accepted: 21.09.2016 published: 01.01.2017 copyright: © 2017 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. introduction he application of advanced nonlinear constitutive models of building materials can be described as the approximation of mathematical modelling methods to the real behaviour of structures. such efforts are, however, often complicated by the existence of a wide set of input parameters for such nonlinear models. interest in the phenomenon of nonlinear behavior of concrete is in order of a wide range of use of this material in scope of many researchers. however, the construction of a correct constitutive relationship which is able to express this nonlinear behaviour for various types of loading appears to be problematic [1]. one of the basic problems which arise when formulating a material model for concrete is the different responses of the material to tensile and compressive load [2]. for this reason, several approaches are used for the mathematical description of the behaviour of concrete. one of these approaches involves the use of theory of plasticity [3]. applications of theory of plasticity to the description of the t http://www.gruppofrattura.it/pdf/rivista/numero39/audio/2.mp3 f. hokes et alii, frattura ed integrità strutturale, 39 (2017) 7-16; doi: 10.3221/igf-esis.39.02 8 behaviour of plain concrete can be found in the work of authors in [4], willam and warnke [5], bazant [6], dragon and mroz [7], schreyer [8], chen and buykozturk [9], onate [10], pramono and willam [11], etse and willam [12], menetrey and willam [13], and grassl [14]. the use of pure plasticity theory is not sufficient due to the gradual decrease in the stiffness of concrete due to the occurrence of cracks [1]. this problem can be removed when damage theory is used, i.e. by using an adequate damage model. however, as grassl claims [15], independent damage models are not sufficient when the description of irreversible deformations and the inelastic volumetric expansion of concrete is required. despite the above-mentioned limitations of both approaches, there are advantages to using both of them in mutual combination, and they can be combined further with other approaches formulated within the framework of nonlinear fracture mechanics. however, the use of combined material models results in a problem in real life in the form of the large amount of parameters which need to be known for the selected material model before the launch of the numerical simulation itself. unfortunately, not all data regarding these parameters, which can be both mechanico-physical and fracture-mechanical in nature, may be available in advance. this problems can be resolved with use of other advanced mathematical approaches like optimization analysis. the varied spectrum of possibilities characterizing the use of optimization methods includes, among other options, the above mentioned inverse identification of the unknown parameters of the nonlinear material models utilized in numerical analyses performed with the finite element method. the optimization algorithms exploited in the inverse analysis of unknown material parameters, described within references [16, 17], constitute a counterpart to methods based on the training of artificial neural networks as discussed by novak and lehky [18]. however, both in cases where optimization is applied to the identification problem and during any classic use of the optimization methods presented in [19], the decisive factor to support a successful optimization process consists in selecting the appropriate algorithm and correctly formulating the relevant objective function. the actual need of such a function becomes even more prominent in identification using optimization modules implemented within ansys workbench [20], where the definition and computation of the objective function value have to be performed with an external program or script. the task embodying the inverse identification of unknown material parameters consists in utilizing the experimentally measured curves that characterize the relationship between the load l and the deformation d (l-d curves). during the actual identification, this reference pattern is compared with the l-d curves produced by the nonlinear numerical simulations within the corresponding experiment. the basis of the comparison then rests in calculating the similarity ratio, which is represented by one or more numerical values and also prescribes the objective function. with respect to the formulation of the objective function, the optimization task is, in a given case, defined as the minimization of the similarity ratio. for the discussed purpose, it appears advantageous to employ the rmse (root-mean-square error) ratio, an instrument that, according to [21], enables us to compare the differences between the values measured and those generated via a mathematical model; in this context, the authors of reference [22] analyze the application of the rmse ratio within disciplines such as meteorology, economics, and demography. considering the shape of the l-d curves, it is then possible, as shown in study [23], to exploit them in comparing the value of the surface below the loading curve with the maximum load value. importantly, if the second one of the described variants is used, we also have to select a correct and robust algorithm to facilitate the optimization including multiple objective functions; this problem can be further encountered in the computation of more rmse ratios for partial sections of the curve, whose positive impact is embodied in the analysis of the individual parameters‘ sensitivity to specific sections of the loading curve. with respect to the above-outlined conditions, the present article examines the effect exerted by different formulations of the objective function in a given identification task. for the identification proper, we chose the l-d curve measured during a three point bending test on a notched concrete beam, according to [24]. the numerical simulation of the experiment was performed with ansys via a nonlinear, multi-parametric material model of concrete adopted from the multiplas library [25]. generally, the paper aims to describe the applicability of the above-mentioned possibilities of formulating the objective function; the computation of the individual options was enabled by scripts created in python. input data n order to analyze the suitability of the selected objective functions, we chose one l-d curve associated with the set of fracture tests published by zimmermann et al. [24]. the specimen, a notched concrete beam manufactured from class c25/30 concrete and having the length l equal to 360 mm, height h of 120 mm, width w corresponding to 58 mm, and notch height of 40 mm, was configured for three point bending test; the vertical deformation d was measured in the middle of the span of 300 mm at the bottom side of the specimen. the cited article presented experimental and numerical research where the identification procedure based on utilization of neural network was used. the identification i f. hokes et alii, frattura ed integrità strutturale, 39 (2017) 7-16; doi: 10.3221/igf-esis.39.02 9 process was aimed to finding values of basic mechanic-physical and fracture-mechanical properties of concrete specimens: modulus of elasticity ec, tensile strength ft and fracture energy gft. the resultant statistical values of these properties were: modulus of elasticity ec = 38,9 gpa, tensile strength ft = 2,76 mpa and fracture energy gft = 215,6 j/m2. figure 1: the testing configuration. geometry and mesh of the computational model he computational model and the nonlinear computation of the fracture experiment task were performed using ansys workbench. to reduce the computing time, the geometry of the computational model was covered with a mesh of 2d finite elements (plane182) having the edge length of 6 mm, and the problem was solved as a plane stress task with the element thickness of w = 58 mm. the real support provided by steel bearings was, in the computational model, idealized via strain boundary conditions, where the vertical deformation was prevented at the location of the support, and the horizontal deformation was – with respect to the solvability of the task – restrained in the middle of the span at the upper side; such an arrangement then corresponded to the position of the introduced load. the notch was modeled in a simple manner, using a pair of parallel lines having a common node at the top of the notch. figure 2: the computational model. t f. hokes et alii, frattura ed integrità strutturale, 39 (2017) 7-16; doi: 10.3221/igf-esis.39.02 10 material model o ensure both the nonlinear behavior and the identification of the corresponding material parameters, we selected a material model from the multiplas database; this model is based on the plasticity surface derived by willam and warnke [5] and then modified by menétrey [26], menétrey and warnke [13], and klisinsky [27]. further, the applied material model represents the evolutionary branch of nonlinear material models of concrete that exploit plasticity theory combined with instruments of nonlinear fracture mechanics to form a single model. this product then ranks among the group of models with non-associated plastic flow rule and is formulated such that it considers the invariants of the stress tensors and the deviatoric stress tensors; thus, the plasticity surface edges are softened, and the definition fidelity of the nonlinear behavior of concrete improves [10]. the formula for the yield surface as found in the programme manual [10] has the following form:  mw b f a r e 2 2 , ( , ) 0 ( , )             σ κ σ κ (1) with the elliptic function r(θ,e) developed by klisinsky [27] on the basis of willam and warnke´s findings [5] and where ω(σ,κ) is a hardening/softening function with a work-hardening law and a, b, c, d are model parameters containing basic mechanico-physical properties of concrete (uniaxial compressive strength fc, uniaxial tensile strength ft and biaxial compressive strength fb) whose form is given by the following relationships: b t t b c f f a f f f 2 1 1 1 6          (2) c b f 2 3 2  (3) c e 21  (4) d e2 1  (5) with         b c t t b c b c t t b c f f f f f f e f f f f f f 2 2 2 2 2 2 2 22        (6) the eq. (1) also contains coordinates of haigh-westergaard cylindrical space, where χ represents the height, ρ the radius and θ the azimuth. these coordinates are functions of the above mentioned invariants of stress tensor and can be written in the following manner: i 3 3   (7) j 22  (8) j j 3 3 2 3 3 cos 3 2   (9) the formula for the plastic potential takes the following form: mwq x y 2     (10) t f. hokes et alii, frattura ed integrità strutturale, 39 (2017) 7-16; doi: 10.3221/igf-esis.39.02 11 where parameters x and y are again related to uniaxial compressive strength fc, uniaxial tensile strength ft, biaxial compressive strength fb and the so-called dilatancy angle ψ. c t f f x 2 tan 2 3(1 2 tan )      (11) t fx y 2 2 3   (12) and where t c f f 1 arctan arctan 2 2   . as regards using the finite element method, the model utilizes the concept of smeared cracks [28], and, thanks to exploiting bazant’s crack band theory [29], it does not exhibit a negative dependence on the size of the finite element mesh. with respect to the above-described material model formulation consisting in a combination of several theoretical approaches, the total of 12 mechanico-physical and fracture-mechanical parameters were required to ensure the functionality of the model; a description of these parameters is presented in tab. 1 [30]. parameter unit description e [pa] young’s modulus of elasticity ν [-] poisson’s ratio fc [pa] uniaxial compression strength ft [pa] uniaxial tension strength k [-] ratio between biaxial compressive strength and uniaxial compressive strength ψ [ ͦ ] dilatancy angle (friction angle) εml [-] plastic strain corresponding to the maximum load gfc [nm/m2] specific fracture energy in compression ωci [-] relative stress level at the start of nonlinear hardening in compression ωcr [-] residual relative stress level in compression gft [nm/m2] specific fracture energy in tension ωtr [-] residual relative stress level in tension table 1: the material model parameters. inverse identification he lack of knowledge of the input parameter values constitutes, together with the continuous theoretical development in the given field, a basic problem affecting the actual performance of advanced nonlinear material simulations of concrete structures. however, such knowledge deficiency can be advantageously eliminated via inverse analysis and experimental research. yet the use of optimization techniques to identify the discussed parameters t f. hokes et alii, frattura ed integrità strutturale, 39 (2017) 7-16; doi: 10.3221/igf-esis.39.02 12 still poses questions concerning the choice of a correct formulation for the relevant objective function. the inverse identification within this paper was carried out with an optimization module implemented in ansys workbench; using such a computing system nevertheless required us to create external scripts in python, and these were called during the batch calculation to compute the relevant objective function values. the whole process of inverse identification consisted in sensitivity analysis of the input material parameters to shape of the l-d curve and optimization itself which was used for minimization of the difference between the numerical and experimental l-d curves. the optimization algorithm was used for varying values of the material parameters and the parameters belonging to the curve with the lowest value of the objective function could be then considered as the sought material parameters. the calculation was performed automatically via adpl macro that prepared geometry and mesh of the computational model, set up the material model with appropriate values of the material parameters, solved the task and called external python script for calculation the of the objective function. description of the selected objective functions the basic objective function giving the difference between two curves was embodied in the rmse ratio. the calculation of this function could not be performed directly, because the distribution of points on the reference and numerical curves was invariably different due to the varied runs of the solver. the mapping of the points on the numerical curve according to the reference curve was, within the script, resolved via linear interpolation. after aligning the points on the curves, we calculated the rmse ratio according to the formula  i iy y n 2* rmse   (13) where yi* was the value of the force at the i-th point of the curve, and yi denoted the value of the force calculated using the nonlinear material model at the i-th point of the curve. within the second optimization task, five optimization functions were created, formulated as the rmse ratios calculated in five sectors evenly distributed along the curves. the prescription of these functions was identical with that shown in eq. (1), the only difference being the number of points n, which corresponded to the number of points in the given sector. the third optimization task exploited two optimization functions. the former function was defined as the difference between the area δald,ref under the reference l-d curve and the surface δald,num below the numerically calculated l-d curve: ld ld ref ld numa a a, ,   (14) the latter function, then, was defined similarly, as the difference between the maximum loading values lmax,ref and lmax,num in the form ref numl l lmax max, max,   (15) sensitivity analysis the actual identification of the material model parameters was invariably preceded by a sensitivity analysis aimed at mapping the space of the design variables and determining the sensitivity of the individual material parameters to the value of the objective function. for each identification task, we conducted 250 simulations, and uniform covering of the design space was ensured via the lhs method. the sensitivity of the individual material parameters to the output parameters was expressed using the spearman correlation coefficient rs. the sensitivity analysis for the option with one rmse optimization function showed that the highest sensitivity rate could be found in the elasticity modulus e, uniaxial tensile strength ft, and specific tensile fracture energy gft. the high sensitivity rate of these parameters can be explained by the very basis of the examined problem: the simulated task is one with tensile bend. very interesting results were obtained from the sensitivity analysis involving the subdivision of the material parameters into l-d curve sectors represented by 5 values of the rmse ratio. in the given case, we identified that the first sector is f. hokes et alii, frattura ed integrità strutturale, 39 (2017) 7-16; doi: 10.3221/igf-esis.39.02 13 utterly dominated by the sensitivity to the elasticity modulus e; the second portion is governed by the tensile strength ft; and the last part exhibits major influence of the specific tensile fracture energy gft. in the analysis of the parameter sensitivity to the values δald and δlmax, only the sensitivities to the tensile strength ft and the specific fracture energy gft were revealed, which nevertheless cannot be considered correct with respect to the character of the task. the values of the spearman correlation coefficient rs for the individual analyses are summarized in tab. 2. output par. rs(e) [%] rs(ft) [%] rs(gft) [%] version 1 rmse 24.38 32.61 88.60 version 2 rmse – 1 96.74 24.55 0.00 rmse – 2 43.31 84.92 0.00 rmse – 3 0.00 41.78 86.44 rmse – 4 0.00 -18.21 97.62 rmse – 5 0.00 -29.26 92.81 version 3 δald 0.00 19.91 97.23 δlmax 0.00 63.37 0.00 table 2: the spearman correlation coefficient rs. optimization the actual identification of the material parameter values was carried out via direct optimization using a genetic algorithm, and, considering the results of the sensitivity analysis, it was performed in a space of three variables. the reduced design vector then assumed the form  tt fte f g, ,redx (16) as already indicated above, the identification in its entirety was performed three times; in the second and third tasks, however, two optimization variants were carried out. the actual process comprised only a minor formulation change, where the first phase involved minimizing the objective function values, and the second one consisted in seeking the zero value of the relevant objective function. results o present and compare the results, we selected the rmse ratio, which was then computed in all calculation options. within the initial identification task, the optimization algorithm generated 76 design vectors in total, and the minimum exhibiting the value of rmse = 144.92 n was achieved with the 33rd iteration. the second optimization task, or, more concretely, its variant that sought the minima of the rmse ratio values within the l-d curve sectors, eventually generated 58 design vectors, and the minimum having the total value of rmse = 160.39 n was obtained during the 10th iteration. the second version of this identification task produced the minimum with the total value of rmse = 136.92 n in the 165th out of 188 iterations the material parameter identification conducted with the objective functions defined as the differences between δald and δlmax proved the applicability of the given manner of formulating the objective function, though only at the cost of the longest computational time (compared to the related options). in the minimization variant, we obtained the minimum exhibiting the total value of rmse = 143.13 n during the 85th out of 122 iterations, while the associated version provided the minimum at rmse = 178.39 n in the 254th out of 415 iterations. comparative diagrams representing the resulting l-d curves and the history of the objective function values within the optimization process are shown in figs. 1(a) to 1(c). t f. hokes et alii, frattura ed integrità strutturale, 39 (2017) 7-16; doi: 10.3221/igf-esis.39.02 14 (a) the history of the rmse values for version 1. (b) the history of the rmse values for version 2. (c) the history of the rmse values for version 3. (d) the resulting l-d curves. figure 3: the results. conclusion he results obtained within the presented research indicate that a successful identification can be performed with both an objective function defined as the rmse ratio and an objective function formulated as the differences between the characteristic signs of the l-d curves: the surface under the δald and δlmax curves. however, it can be also claimed that the best optical agreement was achieved with the objective function defined as the rmse ratio along the entire l-d curves. by extension, the outcome of the research then points to the fact that the actual formulation of the objective function is influenced by whether or not the given function is only minimized or a zero value is sought. even though the use of the variant seeking the zero value of the objective function was accompanied by increased computational time requirements, both of the above-characterized methods can be recommended for practical computation; now, however, it is also necessary to consider the fact that, besides the selection of the correct objective function, the choice of a suitable algorithm constitutes a major, decisive aspect within the discussed procedures. acknowledgement he research presented within this paper was supported from project ga14-25320s titled "aspects of the use of complex nonlinear material models“ and guaranteed by czech science foundation. the authors also wish to acknowledge the assistance provided by the project no. fast-j-16-3562, “implementation of material models of concrete in ansys and their experimental verification”, associated with the specific university research programme of brno university of technology. t t f. hokes et alii, frattura ed integrità strutturale, 39 (2017) 7-16; doi: 10.3221/igf-esis.39.02 15 references [1] cicekli, u., voyiadjis, g.z., al-rub, r.k.a., a plasticity and anisotropic damage model for plain concrete, int. j. of plasticity, 23 (2007) 1874-1900. doi: 10.1016/j.ijplas.2007.03.006. [2] hokes, f., the current state-of-the-art in the field of material models of concrete and other cementitious composites, applied mechanics and materials, 729 (2015) 134-139. doi: 10.4028/www.scientific.net/amm.729.134. [3] chen, w.f., han, d.j., plasticity for structural engineers, springer-verlag, new york, (1988). [4] chen, a.c.t., chen, w.f., constitutive relations for concrete, j. of the engineering mechanics division, 101 (1975) 465–481. [5] willam, k., warnke, e., constitutive model for the triaxial behavior of concrete, in international assoc. for bridge and structural engineering, 19 (1975) 1–30. [6] bazant, z.p., endochronic inelasticity and incremental plasticity, int. j. of solids and structures, 14 (1979) 691–714. [7] dragon, a., mroz, z., a continuum model for plastic-brittle behaviour of rock and concrete, int. j. of engineering science, 17 (1979) 121–137. [8] schreyer, h.l., a third-invariant plasticity theory for frictional materials, j. of structural mechanics, 11 (1973) 177– 196. [9] chen, e.s., buyukozturk, o., constitutive model for concrete in cyclic compression, j. of engineering mechanics, 111 (1985) 797–814. [10] onate, e., oller, s., oliver, j., lubliner, j., a constitutive model for cracking of concrete based on the incremental theory of plasticity, engineering computations, 5 (1988) 309–319. [11] pramono, e., willam, k., fracture energy-based plasticity formulation of plain concrete, j. of engineering mechanics, 115 (1989) 1183–1204. [12] etse, g., willam, k., fracture energy formulation for inelastic behavior of plain concrete, j. of engineering mechanics, 120 (1994) 1983–2011. [13] menetrey, p., willam, k., triaxial failure criterion for concrete and its generalization, aci structural journal, 92 (1995) 311–318. [14] grassl, p., lundgren, k., gylltoft, k., concrete in compression, int. j. of solids and struct., 39 (2002) 5205–5223. [15] grassl, p., jirasek, m., damage-plastic model for concrete failure, int. j. of solids and struct., 43 (2006) 7166–7196. [16] vaz, m., cardoso e.l., munoz-rojaz, et al., identification of constitutive parameters optimization strategies and applications. materialwissenschaft und werkstofftechnik, 46 (2015) 477-491. doi: 10.1002/mawe.201500423. [17] hokes, f., kala, j., krnavek, o., nonlinear numerical simulation of a fracture test with use of optimization for identification of material parameters. international journal of mechanics, 10 (2016) 159-166. [18] novak, d., lehky, d., ann inverse analysis based on stochastic small-sample training set simulation. engineering applications of artificial intelligence, 19 (2006) 731-740. doi: 10.1016/j.engappai.2006.05.003. issn 0952-1976. [19] fedorik, f., kala, j., haapala, a., malaska, m., use of design optimization techniques in solving typical structural engineering related design optimization problems. structural engineering and mechanics, 55 (2015) 1121-1137. doi: 10.12989/sem.2015.55.6.1121. [20] ansys inc. ansys mechanical theory reference: release 15.0. canonsburg pa, usa, (2014). [21] root-mean-square deviation. in: wikipedia: the free encyclopedia [online]. san francisco (ca): wikimedia foundation, 2016 [cit. 2016-04-04]. available from: https://en.wikipedia.org/wiki/root-mean-square_deviation. [22] hyndman, r. j., koehler, a. b., another look at measures of forecast accuracy. international journal of forecasting, 22 (2006) 679-688. doi: 10.1016/j.ijforecast.2006.03.001. issn 0169-2070. [23] kveton, j., elias, j., identification of material parameters for nonlocal model of concrete fracture, in: kruis, j., tsompanakis, topping, b. h. v., proceedings of the fifteenth international conference on civil, structural and environmental engineering computing, united kingdom: civil-comp press, (2015). [24] zimmerman, t., strauss, a., lehky, d., novak, d., kersner, z., stochastic fracture-mechanical characteristics of concrete based on experiments and inverse analysis. construction and building materials, 73 (2014) 535-543. doi: 10.1016/j.conbuildmat.2014.09.087. [25] dynardo. multiplas: user’s manual release 5.1.0 for 15.0. weimar, (2014). [26] menetrey, p., numerical analysis of punching failure in reinforced concrete structures. lausane, (1994). phd thesis. epfl. [27] klisinsky, m., degradation and plastic deformation of concrete [mimeo]. polish academy of sciences, iftr report 38, (1985). f. hokes et alii, frattura ed integrità strutturale, 39 (2017) 7-16; doi: 10.3221/igf-esis.39.02 16 [28] polling, r., eine praxisnahe, schädigungsorienten materialbeschreibung von stahlbeton für strukturanalysen. bochum, (2000). phd thesis. ruhr-universität. [29] bazant, z. p., oh, b. h., crack band theory for fracture of concrete. matériaux et constructions, 16 (1983) 155-177. doi: 10.1007/bf02486267 [30] hokes, f., selected aspects of modelling of non-linear behaviour of concrete during tensile test using multiplas library. transactions of the všb – technical university of ostrava, 15 (2015). doi: 10.1515/tvsb-2015-0009. << /ascii85encodepages false /allowtransparency false /autopositionepsfiles true /autorotatepages /none /binding /left /calgrayprofile (dot gain 20%) /calrgbprofile (srgb iec61966-2.1) /calcmykprofile (u.s. web coated \050swop\051 v2) /srgbprofile (srgb iec61966-2.1) /cannotembedfontpolicy /error /compatibilitylevel 1.4 /compressobjects /tags /compresspages true /convertimagestoindexed true /passthroughjpegimages true /createjobticket false /defaultrenderingintent /default /detectblends true /detectcurves 0.0000 /colorconversionstrategy /cmyk /dothumbnails false /embedallfonts true /embedopentype false 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/hrv (za stvaranje adobe pdf dokumenata najpogodnijih za visokokvalitetni ispis prije tiskanja koristite ove postavke. stvoreni pdf dokumenti mogu se otvoriti acrobat i adobe reader 5.0 i kasnijim verzijama.) /hun 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/pdfxoutputintentprofileselector /documentcmyk /preserveediting true /untaggedcmykhandling /leaveuntagged /untaggedrgbhandling /usedocumentprofile /usedocumentbleed false >> ] >> setdistillerparams << /hwresolution [2400 2400] /pagesize [612.000 792.000] >> setpagedevice microsoft word numero 10 art 5 a.namdar et alii, frattura ed integrità strutturale, 10 (2009) 38-42; doi: 10.3221/igf-esis.10.05 38 numerical analysis of soil bearing capacity by changing soil characteristics abdoullah namdar mysore university, mysore, india, sina_a_n@yahoo.com mehdi khodashenas pelko amirkabir university, tehran, iran abstract. in this research work by changing different parameters of soil foundation like density, cohesion and foundation depth and width of square foundation at angle of friction of 0 to 50 with increment of 5, numerically safe bearing capacity of soil foundation is calculated and it is attempted to assess economical dimension of foundation as well as understanding variation range of bearing capacity at different degree. it could help of civil engineering in design of foundations at any situation. keywords. safe bearing capacity, density, cohesion of soil (c), angle of friction (φ) and dimension of foundation introduction mprovement of soil foundation is a method to disabling earthquake forces and stabilization of soil foundation. for achieving this aim designing a series of foundations by changing gradually the main parameters of soil is the shortest way to better understanding soil characteristics. it has been reported the effect of soil confinement on the behavior of a model footing resting on sand under eccentric – inclined load [1]. rea and mitchell conducted a series of model plate loading tests on circular footings supported over sand-filled square-shaped paper grid cells to identify different modes of failure and arrive at optimum dimensions of the cell [2]. mahmoud and abdrabbo presented an experimental study concerning with a method of improving the bearing capacity of strip footing resting on sand sub-grades utilizing vertical non-extensible reinforcement. they found out this type of reinforcement increases the bearing capacity of sub-grades and modify the load–displacement behavior of the footing [3]. the investigations also made on the laboratory-model tests for the bearing capacity of a strip foundation supported by a sand layer reinforced with layers of geo-grid [4]. research on the ultimate bearing capacity of strip and square foundations supported by sand reinforced with geo-grid has also been performed [5]. das and omar presented the ultimate bearing capacity of surface strip foundations on geo-grid-reinforced sand and un-reinforced sand [6]. dash et al. investigated the use of vertical reinforcement along with horizontal reinforcement. the reinforcement consisted of a series of interlocking cells, constructed from polymer geo-grids, which contain and confine the soil within its pockets [7]. schimizu and inui carried out load tests on a single six-sided cell of geo-textile wall buried in the subsurface of the soft ground [8]. mandal and manjunath used geo-grid and bamboo sticks as vertical reinforcement elements and studied their effect on the bearing capacity of a strip footing [9]. rajagopal et al have studied the strength of confined sand and the influence of geo-cell confinement on the strength and stiffness behavior of granular soils [10]. dash et al. performed an experimental study on the bearing capacity of a strip footing supported by a sand bed reinforced with a geo-cell mattress [11]. study of bearing capacity of footing without reinforcement under eccentric inclined loads by many researchers has been carried out [12-15]. nearly 340 foundations by adopting terzaghi method have been calculated and the results presented in form of tables and graphs, the result helps better understanding of improving of soil foundation bearing capacity. i http://dx.medra.org/10.3221/igf-esis.10.05&auth=true http://www.gruppofrattura.it mailto: sina_a_n@yahoo.com a. namdar et alii, frattura ed integrità strutturale, 10 (2009) 38-42; doi: 10.3221/igf-esis.10.05 39 methodology and experiments y adopting of terzaghi method and altering characteristics of soil such density, cohesion, angle of friction of soils and dimension of foundation safe bearing capacity of soil foundation has been evaluated. here three hundred forty one problems by assuming various soil properties have been solved and results of them in form of table and graph have been considered. for all models, safe bearing capacity considered to assess soil foundation improvement thorough the interpreting of the suggested results. formulas for calculation of safe bearing capacity are the following: qf = 1.3c nc + γdnq + 0.4 γbnγ (1) qnf = qf qnf = qf-γd (2) qs =(qnf /f)+ γd (3) also nq, nc and nγ are the general bearing capacity factors and depend upon 1) depth of footing 2) shape of footing 3) φ, have been used from suggestion by the terzaghi calculation method [16]. results and discussion mprovement of any site could be possible, if soil characteristics of site were clearly identified [17]. increasing cohesion of the soil has more effect on bearing capacity when degree of friction is low (tab. 1 and fig. 1). changing of soil density at any level of friction has constant effect on bearing capacity (tab. 2 and fig. 2). increasing depth of the foundation has more effect on bearing capacity when degree of friction is low (tab. 3 and fig. 3). increasing width of the foundation has less effect on bearing capacity when friction is low (tab. 4 and fig. 4). it could be suggested when a soil has low friction, increasing depth of foundation is the best way of increasing bearing capacity or increasing cohesion of soil by adding clay mineral to the soil foundation, this technique could be done by employment of mixing soil technique. in a soil with high friction, increasing width of foundation could be best way to increase its bearing capacity. in general decreasing depth of foundation leads to a weak bearing capacity, and appeared maximum declination in soil foundation stability. soil density is acting like gravity force to holding foundation in stable conditions, decreasing that is deduction of holding gravity force of foundation. sl. no φ qs if c=0 (kn/m2) qs if c=1 (kn/m2) qs if c=2 (kn/m2) qs if c=3 (kn/m2) qs if c=4 (kn/m2) qs if c=5 (kn/m2) 1 0 21.00 23.47 25.94 28.41 30.88 33.35 2 5 27.53 30.70 33.86 37.02 40.19 43.35 3 10 38.50 42.66 46.82 50.98 55.14 59.30 4 15 56.47 62.06 67.65 73.24 78.83 84.42 5 20 89.13 96.80 104.47 112.14 119.81 127.48 6 25 148.17 159.04 169.92 180.80 191.67 202.55 7 30 263.43 279.55 295.67 311.79 327.91 344.03 8 35 501.67 526.71 551.76 576.81 601.85 626.90 9 40 1051.63 1093.10 1134.57 1176.04 1217.51 1258.98 10 45 2615.43 2690.10 2764.76 2839.42 2914.09 2988.75 11 50 8301.30 8451.88 8602.47 8753.05 8903.63 9054.22 table 1: safe bearing capacity of soil when cohesion of soil (c) is varied, soil density is 14 kn/m3 and width and depth of foundation are equal to 1.5 and 2.5 m, respectively. b i http://dx.medra.org/10.3221/igf-esis.10.05&auth=true http://www.gruppofrattura.it a.namdar et alii, frattura ed integrità strutturale, 10 (2009) 38-42; doi: 10.3221/igf-esis.10.05 40 figure 1: safe bearing capacity vs angle of friction of soil sl. no φ qs if =14 (kn/m3) qs if =15 (kn/m3) qs if =16 (kn/m3) qs if =17 (kn/m3) qs if =18 (kn/m3) qs if =19 (kn/m3) qs if =20 (kn/m3) 1 0 21.00 22.50 24.00 25.50 27.00 28.50 30.00 2 5 27.53 29.50 31.47 33.43 35.40 37.37 39.33 3 10 38.50 41.25 44.00 46.75 49.50 52.25 55.00 4 15 56.47 60.50 64.53 68.57 72.60 76.63 80.67 5 20 89.13 95.50 101.87 108.23 114.60 120.97 127.33 6 25 148.17 158.75 169.33 179.92 190.50 201.08 211.67 7 30 263.43 282.25 301.07 319.88 338.70 357.52 376.33 8 35 501.67 537.50 573.33 609.17 645.00 680.83 716.67 9 40 1051.63 1126.75 1201.87 1276.98 1352.10 1427.22 1502.33 10 45 2615.43 2802.25 2989.07 3175.88 3362.70 3549.52 3736.33 11 50 8301.30 8894.25 9487.20 10080.15 10673.10 11266.05 11859.00 table 2: safe bearing capacity of soil when soil density () is varied, cohesion is zero and width and depth of foundation are equal to 1.5 and 2.5 m, respectively. figure 2: safe bearing capacity vs angle of friction of soil. http://dx.medra.org/10.3221/igf-esis.10.05&auth=true http://www.gruppofrattura.it a. namdar et alii, frattura ed integrità strutturale, 10 (2009) 38-42; doi: 10.3221/igf-esis.10.05 41 sl. no φ qs if d=0.7 (m) qs if d=0.8 (m) qs if d=0.9 (m) qs if d=1 (m) qs if d=1.1 (m) qs if d=1.2 (m) qs if d=1.3 (m) qs if d=1.4 (m) qs if d=1.5 (m) 1 0 9.80 11.20 12.60 14.00 15.40 16.80 18.20 19.60 21.00 2 5 14.09 15.77 17.45 19.13 20.81 22.49 24.17 25.85 27.53 3 10 20.95 23.15 25.34 27.53 29.73 31.92 34.11 36.31 38.50 4 15 32.57 35.56 38.55 41.53 44.52 47.51 50.49 53.48 56.47 5 20 54.04 58.43 62.81 67.20 71.59 75.97 80.36 84.75 89.13 6 25 93.29 100.15 107.01 113.87 120.73 127.59 134.45 141.31 148.17 7 30 171.97 183.40 194.83 206.27 217.70 229.13 240.57 252.00 263.43 8 35 339.64 359.89 380.15 400.40 420.65 440.91 461.16 481.41 501.67 9 40 740.65 779.52 818.39 857.27 896.14 935.01 973.89 1012.76 1051.63 10 45 1960.98 2042.79 2124.59 2206.40 2288.21 2370.01 2451.82 2533.63 2615.43 11 50 6744.13 6938.77 7133.42 7328.07 7522.71 7717.36 7912.01 8106.65 8301.30 table 3: safe bearing capacity of soil when depth of foundation (d) is varied, cohesion is zero, width of foundation is 2.5 m and soil density () is 14 kn/m3. figure 3: safe bearing capacity vs angle of friction of soil sl. no φ qs if w=1.7 (m) qs if w=1.8 (m) qs if w=1.9 (m) qs if w=2.0 (m) qs if w=2.1 (m) qs if w=2.2 (m) qs if w=2.3 (m) qs if w=2.4 (m) qs if w=2.5 (m) 1 0 21.00 21.00 21.00 21.00 21.00 21.00 21.00 21.00 21.00 2 5 26.79 26.88 26.97 27.07 27.16 27.25 27.35 27.44 27.53 3 10 36.71 36.93 37.16 37.38 37.60 37.83 38.05 38.28 38.50 4 15 52.73 53.20 53.67 54.13 54.60 55.07 55.53 56.00 56.47 5 20 81.67 82.60 83.53 84.47 85.40 86.33 87.27 88.20 89.13 6 25 133.68 135.49 137.30 139.11 140.92 142.73 144.55 146.36 148.17 7 30 234.01 237.69 241.37 245.05 248.72 252.40 256.08 259.76 263.43 8 35 438.35 446.26 454.18 462.09 470.01 477.92 485.84 493.75 501.67 9 40 901.70 920.44 939.19 957.93 976.67 995.41 1014.15 1032.89 1051.63 10 45 2171.17 2226.70 2282.23 2337.77 2393.30 2448.83 2504.37 2559.90 2615.43 11 50 6579.19 6794.45 7009.72 7224.98 7440.24 7655.51 7870.77 8086.04 8301.30 table 4: safe bearing capacity of soil when width of foundation (w) is varied, cohesion is zero, depth of foundation is 1.5 m and soil density () is 14 kn/m3. http://dx.medra.org/10.3221/igf-esis.10.05&auth=true http://www.gruppofrattura.it a.namdar et alii, frattura ed integrità strutturale, 10 (2009) 38-42; doi: 10.3221/igf-esis.10.05 42 figure 4: safe bearing capacity vs angle of friction of soil. conclusion by understanding all factors, which effected to the soil, could be starting way of the improvement of any soil. some element have linear and some of them nonlinear effect on soil bearing capacity. unit weight has linear correlation with bearing capacity at any degree of angle of friction, cohesive of soil and width and depth of foundation have nonlinear correlation with bearing capacity at any angle of friction. data has been produces in this paper could make clear economical design of any foundation. increasing of bearing capacity in a soil with low angle of friction is not same, as a soil with high level of angle of friction, at any of them should apply proper technique. references [1] v. k. singh, a. prasad, r.k. agrawal, ejge, 12 e(2007) 1. [2] c. rea, j.k. mitchell, proc. symposium on earth reinforcement, pittsburg, asce (1978) 644. [3] m. a. mahmoud, f.m. abdrabbo, canadian geotechnical journal, 26 (1989) 154. [4] k. h. khing, , b.m. das, v.k. puri, e.e. cook, s.c. yen, , geotextiles and geomembranes, 12 (1993) 351. [5] v. k. puri, k.h. khing, b.m. das, e.e. cook, s.c. yen, geotextile and geomembrane, 12 (1993) 351-361. [6] b. m. das, m.t. omar, geotechnical and geological engineering, 12 (1994) 133. [7] s. dash, k. rajagopal, n. krishnaswamy, geotextile and geomembrane, 19 (2001) 529. [8] m. schimizu, t. inui, proc. 4th international conference on geotextiles, geomembranes and related products, 1 (1990) 254. [9] j.m. mandal, v.r. manjunath, construction and building material, 9-1 (1995) 35. [10] k. rajagopal, n. krishnaswamy, g. latha, geotextile and geomembrane, 17 (1999)171. [11] s. dash, n. krishnaswamy, k. rajagopal, geotextile and geomembrane, 19 (2001) 535. [12] g. g. meyerhof, 3rd icsmfe, zurich, 1 (1953) 1. [13] g. g. meyerhof, canadian geotechnical journal, 1-1 (1963) 16. [14] g. g. meyerhof, j. of smfd, asce, 91 sm2 (1965) 21. [15] s. prakash, s. saran, j. of smfe div, asce, sm1 (1971) 95. [16] b. c. punmia, soil mechanics and foundations, madras, 1988. [17] a. namdar, g. s. gopalakrishna, modern applied science, 3-5 (2009). http://dx.medra.org/10.3221/igf-esis.10.05&auth=true http://www.gruppofrattura.it microsoft word numero_29_art_11 n.a. nodargi et alii, frattura ed integrità strutturale, 29 (2014) 111-127; doi: 10.3221/igf-esis.29.11 111 focussed on: computational mechanics and mechanics of materials in italy state update algorithm for associative elastic-plastic pressure-insensitive materials by incremental energy minimization n.a. nodargi, e. artioli, f. caselli, p. bisegna department of civil engineering and computer science university of rome “tor vergata”, via del politecnico 1, 00133 rome, italy {nodargi, artioli, caselli, bisegna}@ing.uniroma2.it abstract. this work presents a new state update algorithm for small-strain associative elastic-plastic constitutive models, treating in a unified manner a wide class of deviatoric yield functions with linear or nonlinear strain-hardening. the algorithm is based on an incremental energy minimization approach, in the framework of generalized standard materials with convex free energy and dissipation potential. an efficient method for the computation of the latter, its gradient and its hessian is provided, using haigh-westergaard stress invariants. numerical results on a single material point loading history and finite element simulations are reported to prove the effectiveness and the versatility of the method. its merit turns out to be complementary to the classical return map strategy, because no convergence difficulties arise if the stress is close to high curvature points of the yield surface. keywords. plasticity; hardening; incremental energy minimization; dissipation; state update algorithm; haigh-westergaard coordinates. introduction he solution of inelastic structural boundary value problems in a typical finite element implementation requires the integration of the material constitutive law at each gauss point. the complexity of hardening elastic-plastic constitutive equations requires their time discretization and numerical integration on a sequence of finite time steps. this procedure is referred to as the state update algorithm. the most traditional way to formulate the associative plasticity constitutive law is based on the assumption of a convex yield function and the adoption of a normality law to determine the plastic flow. a widely used class of constitutive updates exploiting this framework is the so-called return mapping algorithms. while the basic idea dates back to the work of wilkins [1], all the return mapping algorithms share the use of an elastic-predictor, plastic-corrector strategy. in particular, in a first step the algorithm checks whether the elastic trial state is plastically admissible. if such is not the case, a solution for the time-discrete plastic evolution equations is sought for in the plastic corrector step. from a geometric standpoint, the return map algorithm amounts to finding the closest point projection, in a suitable norm, of the elastic trial state on the yield domain. to this purpose, a typical method pursued among others in [2-6] consists in the iterative t n.a. nodargi et alii, frattura ed integrità strutturale, 29 (2014) 111-127; doi: 10.3221/igf-esis.29.11 112 solution by a newton-raphson scheme. that strategy appears to be attractive because of the quadratic rate of convergence of newton method, preserved by the adoption of an algorithmically consistent tangent operator. details on the subject can be found in several recent textbooks, e.g. [7-11]. however, in many cases of practical interest, the localconvergence characteristic of newton schemes does not guarantee global convergence [12-14]. for instance, convergence may not be attained for elastic trial stress in the neighborhood of high curvature points of the yield surface [15]. in the literature, various techniques have been proposed to avoid this drawback, as the use of line search methods, sub-stepping, adaptive sub-stepping, or other ad-hoc integration algorithms, see for example [16-21]. an alternative approach is to set the elastic-plastic problem in the framework of normal-dissipative standard media in the sense of halphen and nguyen [22]. the evolution of internal variables is assumed to be governed by a convex scalar dissipation function which is the support function of the elastic domain (e.g., [23]). consequently, the flow law results in a statement of the classical postulate of maximum plastic dissipation [7]. exploiting this formulation, several state update algorithms have been proposed, either at local level [24-26] or at finite element level [27, 28]. conceptually, the underlying basic idea is that the evolution of internal variables in a finite time step incrementally minimizes a suitable convex functional, given by the sum of the internal energy and the dissipation function. this paper focuses on the incremental energy formulation, for elastic-plastic hardening materials characterized by isotropic deviatoric yield function and associative flow law, in the framework of infinitesimal deformation. a two-step algorithm is proposed to perform the material state update. in the first step, an elastic prediction of the updated material state is carried out. in case it is not plastically admissible, the newton-raphson method is adopted to solve the constitutive variational problem. an efficient strategy to compute the dissipation function is proposed. in particular, adopting the haigh-westergaard representation (e.g. see [29-31]), the problem is reduced to a non-linear scalar equation. moreover closed-form expressions of the gradient and of the hessian of haigh-westergaard coordinates, as well as of the dissipation function, are presented. with the aim of proving the robustness and stability of the proposed algorithm, numerical tests on a single integration point and fe simulations are provided. this numerical approach appears to be complementary to the classical return map strategy, because no convergence difficulties arise if the stress is close to points of the yield surface with high curvature. the paper is organized as follows: a first part is concerned with a brief discussion on the incremental energy minimization in hardening elastoplasticity. then the computation algorithm of dissipation function and the proposed state update algorithm are extensively treated. finally a selected number of numerical tests are reported. incremental energy minimization formulation et nε  be the total strain at a fixed point x  of a solid dimn  , in practice a gauss point in a typical finite element solution. in the case of infinitesimal deformation, the total strain ε , i.e. the symmetric part of the displacement gradient, is additively decomposed as: e p ε ε ε (1) where eε and pε are the elastic and plastic parts, respectively. the kinematic description of the material state is completed by a set of strain-like internal variables nα  . the corresponding conjugated stress-like variables are the stress nσ  and the stress-like internal variables nq  , respectively. by standard thermodynamic arguments, the stress-like variables are derived from an helmholtz free energy function  e , . ε α assuming the latter to be strictly convex, the constitutive equations follow    e e e, , ,  αεσ ε α q ε α (2) where (•) is the sub-differential operator of non-smooth convex functions (see [22, 32] and references therein). in the context of elastic-plastic materials, the generalized stresses σ , q are constrained to belong to an admissible set, denoted as elastic domain and introduced by means of the yield function  ,f σ q :     , : , 0n n fk     σ q σ q  (3) hereafter we suppose the yield function to be convex; consequently the elastic domain is convex itself. l n.a. nodargi et alii, frattura ed integrità strutturale, 29 (2014) 111-127; doi: 10.3221/igf-esis.29.11 113 the model is supplemented by the evolution law of plastic strain pε and strain-like internal variables α . with the assumption of normal-dissipative or standard material behavior, i.e. of associative plastic flow, it is customary to introduce a scalar dissipation function defined as the support function of the elastic domain      p p , , sup k d      σ q ε α σ ε q α    (4) and to express the evolution law in the form:    p p p,, ,d d αεσ ε α q ε α     (5) it is worth noting that the dissipation function is convex, non-negative, zero only at the origin and positively homogeneous of degree one; moreover it is nondifferentiable at the origin, where its sub-differential set coincides with the elastic domain [7]. substituting the decomposition (1) in the constitutive law (2) and adding the result to (5), the constitutive differential equations are obtained:         p p p p p p , , , , d d           ε ε α α ε ε α ε α 0 ε ε α ε α 0         (6) often referred to as biot’s equation of standard dissipative systems, see [22, 24, 33] for instance. we now proceed with the numerical approximation of the rate eq. (6). in particular, we adopt a backward euler integration scheme and assume that plastic strain pε and strain-like internal variables α vary linearly in each time step 1 ][ ,n ntt  . consequently, by exploiting the degree-one positive homogeneity of the dissipation function, the incremental form of (6) follows:         p p p p p 1 p p p 1 , , , , n n n n n n d d                            ε ε α α ε ε ε α α ε α 0 ε ε ε α α ε α 0   (7) with the notation    • • | nt tn   ,     11 • • | nt tn   ,       1 • • • n n    . eq. (7) represent the euler-lagrange first order conditions associated to the incremental minimization problem        p e,trial p trial p 1 1 , inf , ,n n d             ε α ε ε α α ε α (8) where e,trial p1 1n n n  ε ε ε , trial 1n n α α define the elastic trial state, i.e. the material state corresponding to no plastic evolution. therefore, the incremental minimization problem (8) determines the internal state of the material for finite increments of time. we remark that the present formulation is similar to the one proposed in [24], under the assumption of rateindependent evolution and linear variation in time of plastic strain pε and strain-like internal variables α . computation of the dissipation function inematic and isotropic hardening are distinguished by assuming that the yield function can be represented as  k i,f qσ q , where kq [resp., iq ] is the stress-like kinematical [resp., isotropic] hardening variable. accordingly, the dissipation function is given by         k i k i p p k i k k i i , , , 0 , , sup q f q d q             σ q σ q ε α σ ε q α (9) where kα [resp., i ] is the strain-like kinematical [resp., isotropic] hardening variable. setting  k σ σ q , it results       k i i p p p k i k k i i { , , } ( , ) 0 , , sup ( ) q f q d q               σ q σ ε α σ ε q ε α (10) k n.a. nodargi et alii, frattura ed integrità strutturale, 29 (2014) 111-127; doi: 10.3221/igf-esis.29.11 114 whence it follows that pk  α ε (11) and         i i p p i i i ˆ , ˆ , 0 ˆ, sup q f q d q         σ σ ε σ ε (12) with the assumption that the yield function is isotropic, it can be represented, with a slight abuse of notation, as  ˆ ˆ ˆ i, , ,f q  σ σ σ , where ˆσ , ˆ 0 σ ,  ˆ 0, 3 σ are the haigh-westergaard coordinates of σ̂ (see appendix a). since the maximum of the scalar product of two symmetric tensors is attained when they are coaxial (see, e.g., [34]), in (12) it is possible to assume that σ̂ is coaxial with pε and to express their scalar product making use of the haigh-westergaard representation. accordingly, the dissipation function is given by        p p p ˆ ˆ ˆ i ˆ ˆ ˆ i p ˆ ˆ ˆi i i , , , , , , 0 , sup cos( ) q f q d q                          σ σ σ σ σ σ σ σ σε ε ε ε (13) where pε , p 0 ε ,  p 0, 3  ε are the haigh-westergaard coordinates of pε . deviatoric yield function, perfect plasticity or kinematic hardening the yield function is assumed to be of the form     0ˆ ˆ ˆ ˆ ˆ y , ,f g c      σ σ σ σ σ (14) where g is a 2c , positive, even, periodic function with period 2 3 , such that 0g g  . the latter condition guarantees that curves of polar equation  ˆ ˆ constg  σ σ are convex. moreover, 0y and c are positive constants; usually, 2 3c  : in that case, 0y  can be interpreted as the initial yield limit in tension if  0 1g  , or in compression if  3 1g   . according to (14), the dissipation function is given by         p p p ˆ ˆ ˆ ˆ ˆ y0 p ˆ ˆ ˆ , , sup cos g c d                     σ σ σ σ σ σ σ σε ε ε ε (15) this implies:    p p p 0 p y0, d c d       ε ε εε  (16) where       p p ˆ ˆ ˆ ˆ ˆ ˆ { , } 1 sup cos g d              σ σ σ σ σ σε ε  (17) or, equivalently,         p p ˆ ˆ ˆ cos supd g               σ σ ε ε σ  (18) it is worth noting that d is the support function of the convex set of polar coordinates     ˆ ˆ ˆ ˆ, : 1g    σ σ σ σ . because the supremum is attained on the boundary of that set, a simple computation yields        p pˆ ˆ ˆ ˆsin cos 0g g         σ σ σ σε ε (19) which can be recast as: n.a. nodargi et alii, frattura ed integrità strutturale, 29 (2014) 111-127; doi: 10.3221/igf-esis.29.11 115     p ˆ ˆ ˆ arctan g g        σσ ε σ (20) this is a scalar equation in the unknown  ˆ 0, 3 σ , which implicitly defines a function  pˆ σ ε . by applying dini’s theorem, its first derivative turns out to be:  p 2 2 ˆd d g g g g g       σ ε (21) where g and its derivatives are computed at  pˆ σ ε . noting that pˆ σ ε can be assumed to belong to  3, 3  , by (20) it follows that    p pˆ ˆ 2 2 2 2 cos , sin g g g g g g               σ σε ε (22) whence, recalling (18) and (21), p( )d    and its first and second derivatives with respect to p easily follow:         p p p 4 2 2 3 2 2 2 2 3 2 2 21 , , g g g g g g d d d g g g g g g g g g g                        ε ε ε    (23) where the derivatives on the right-hand sides of (23) are performed with respect to ˆσ and computed at  pˆ σ ε . finally the gradient and the hessian of  pd ε are straightforwardly obtained from (16):   p p p 0 p p p p p p p p p p 0 y y d c d d d c d d d d                                                      ε ε ε ε ε ε ε ε ε ε ε ε        (24) simple expressions for the gradient and the hessian of pε and p are given in appendix a. the same argument holds if kinematic hardening is present. deviatoric yield function, isotropic hardening the yield function is assumed to be       0ˆ ˆ ˆ ˆ ˆi y i , , ,f q g c q       σ σ σ σ σ (25) whence the dissipation function follows:           p p p ˆ ˆ ˆ i ˆ ˆ y i0 p ˆ ˆ ˆi i i , , , , sup cos q g c q qd σ σ σ σ σ σ σ σε ε ε ε                           (26) this implies:         p p p 0 i y0 p i y i i i0, , sup q d c q d q                   ε ε ε ε  (27) accordingly, the dissipation function turns out to be:         p p 0 p p p p 0 y i i p i y i if , if otherwise c d d c d c d                               ε ε ε ε ε ε ε    (28) n.a. nodargi et alii, frattura ed integrità strutturale, 29 (2014) 111-127; doi: 10.3221/igf-esis.29.11 116 whence it is finite provided that  p pi 0c d     ε ε . in case of hardening material, recalling (25), the solution 0i y q  of the supremum in (27) is unfeasible. hence it can be assumed that (16) prevails, complemented with    p p 0 p i y 1 c d d         ε ε ε (29) the same treatment holds if also kinematic hardening is present. state update algorithm n this section, under the assumption of deviatoric yield function, we introduce a reduced formulation for the incremental minimization problem (8) and discuss the state update algorithm proposed for its solution. the following common choice for the free energy function e( , ) ε α is made:      e e, w  ε α ε α (30) where w and  , respectively, denote the elastic and hardening potentials, and may account for nonlinear elastic and/or hardening behavior. the contributions from kinematic and isotropic hardening are distinguished in the latter, as follows:      k k i i α α   (31) as a consequence, substituting kα [resp., i ] from (11) [resp.(29)], the incremental energy problem (8) is transformed into:            0p p e,trial p trial p trial p p 1 k k , 1 i i , 1 y 0 inf n n nw d d                     ε ε ε ε α ε ε ε   (32) under isotropy assumption, the elastic potential is decomposed as:      e e esph devtrw w w ε ε e (33) where sphw and devw denote the spherical and deviatoric parts of w , ee denotes the deviatoric part of eε , and tr denotes the trace operator. moreover, without loss of generality, the kinematic hardening potential is assumed to depend only on the deviatoric part of k .α therefore the incremental energy problem (32) is further reduced to:               0pe,trial e,trial p trial p trial p psph 1 dev 1 k k , 1 i i , 1 ytr infn n n nw w d d               eε e e α e ε e   (34) where pe is the deviatoric part of pε . recalling that the dissipation function  pd e is singular at the origin p e 0 , the state update algorithm first computes an elastic predictor. in case the corresponding state is plastically admissible, the step is elastic and the infimum in (34) is attained at the origin. conversely, having excluded the singularity, a smooth incremental energy minimization problem can be solved. by introducing the linear projector operator on the deviatoric tensor subspace dev / 3  i i  , the euler-lagrange equation of (34) is:          0 0e,trial p trial p trial p pdev dev 1 k k , 1 i i , 1 y y ,1t n n nw d d                  e e α e e e 0  (35) where the gradients of devw , k , and d are taken, respectively, with respect to ee , kα , and pe . eq. (35) is solved by the newton-raphson method, using the consistent tangent:                 0 0 0 0 e,trial p trial p trial p p dev dev 1 k k , 1 i i , 1 y y trial p 2 p p i i , 1 y y dev 1 . t n n n n w d d d d d                                   e e α e e e e e e       (36) i n.a. nodargi et alii, frattura ed integrità strutturale, 29 (2014) 111-127; doi: 10.3221/igf-esis.29.11 117 a convenient initial guess is computed by substituting p p p ,     e e e u with deviatoric unit peu , in (34). exploiting the degree-one positive homogeneity of the dissipation function, the taylor expansion about p 0 e of the corresponding euler-lagrange condition results in a scalar algebraic equation for the lode angle p  e u . once computed pe satisfying (35), the algorithmic consistent elastoplastic tangent is given by:  ep 1sph dev dev dev devtw w w     i i     (37) remark. the present formulation, when specialized to particular choices of yield function and elastic/hardening potentials, gets simplified. as an example, we consider a linear elastic and hardening behavior with von mises criterion. the helmoltz free energy and the hardening potentials are given by: e e 2 e 2 2 2k k k k i i i i 1 1 1 ( ) (tr ) g , ( ) , ( 2 ) 32 k h k h k     ε ε e α α    (38) the yield function and the relevant dissipation function are given by:     0 p p ˆ ˆ ˆ ˆi y i y0, ( ),,,f cq dq c       σ σ σ σ ε ε  (39) the euler-lagrange eq. (35) becomes:       0 p e,trial p trial p trial p 1 k k , 1 i i , 1 y y0 p 2 2 1 3 n n ng k k c c                   e e e α e ε 0 e     (40) introducing the deviatoric trial back-stress trial e,trial trial 1 1 k k , 122 3 ,n n ng k   s e α  noting that the latter results to be parallel to pe and multiplying (40) by p p e e  , the following solution for pe is obtained:   trial trial pp 1trial y0 i i , 1p p 1trial k1 , ( 2 2 3) n n n n c k c g k                 s εe e s e s           (41) as a consequence, the well-known expression (see, e.g., [35]) for the algorithmic consistent elastoplastic tangent results: trial trialp p 1 1ep devtrial trial trial trial2 k i1 1 1 1 2 1 2 2 2 2 2 3 n n n n n n g g g g g k c k k                            e e s s i i s s s s                   (42) numerical tests n this section we assess the numerical reliability and robustness of the proposed state update algorithm. its convergence properties are explored by a single increment test and compared with the performances of the classical return mapping approach. the numerical results prove that the two strategies have complementary convergence properties. then, we consider the integration of a non-proportional stress-strain loading history of a material point, and finite element simulations. single increment test in [17] armero and pérez-foguet assess the converge properties of return mapping algorithms by using the following single increment test. assuming the initial state to be virgin, a total strain ε (coinciding with the elastic trial strain e,trialε ) is applied to the gauss point. the total strain is defined in terms of its haigh-westergaard coordinates in the deviatoric plane, namely ε and ε . a von mises–tresca yield function with 20m  (see appendix b) is adopted and this choice corresponds to a yield surface with high curvature points close to °, 00 6 ° σ and low curvature in between. because of the symmetry of the resulting yield surface, only lode angle °, °0 0 ][ 3 ε need to be considered. isotropic linear elastic constitutive law, with bulk modulus 164.206 gpak  and shear modulus 89.1938 gpag  , and perfect plasticity, with yield stress y0 0.45 gpa  , are considered. i n.a. nodargi et alii, frattura ed integrità strutturale, 29 (2014) 111-127; doi: 10.3221/igf-esis.29.11 118 fig. 1 compares the performances of the return mapping and incremental energy minimization algorithms in terms of number of iterations needed for convergence. in fig. 1(a) it is clear that when the elastic trial state in stress space is close to high curvature points of the yield surface, i.e. for 0   σ ε , the return mapping algorithm has convergence difficulty. as depicted in fig. 1(b), for the same elastic trial state the proposed state update algorithm needs 1-3 iterations to reach convergence. a converse situation happens around 30   σ ε . this result is explained observing that high curvature points in the yield surface correspond to low curvature points in the graph of the dissipation function, and viceversa (see appendix b). (a) (b) figure 1: single increment test. number of iterations needed for convergence for von mises–tresca yield surface (m=20) by: (a) return mapping algorithm [17]; (b) proposed incremental energy minimization algorithm. pointwise mixed stress-strain test in order to explore the algorithm effectiveness, we consider a pointwise mixed stress-strain test as reported in [36]. in particular, a non-proportional stress-strain history is adopted. the two controlled strain components, x and xy , follow the loading history described in tab. 1, whereas the four controlled stress components, y , z , xz , yz , are held identically equal to zero. the strains are varied proportionally to the first yielding value in a uniaxial loading history y0 . isotropic linear elastic constitutive law with young modulus 100 mpae  and poisson coefficient 0.3  is assumed. we consider a von mises yield function (see appendix b) characterized by yield stress y0 15 mpa  , linear kinematic and isotropic with hardening modulus k 10 mpah  and i 10 mpah  respectively. in fig. 2 the numerical solution, expressed in terms of the stress-strain history, proves to be in perfect agreement with the analytical one (for example, see [35]). time unit 0 1 2 3 4 5 6 7 x y0/  0 5 5 -5 -5 5 5 0 xy y0/  0 0 5 5 -5 -5 0 0 table 1: pointwise mixed stress-strain test. controlled strain history: in between two next time units, strain components vary linearly. n.a. nodargi et alii, frattura ed integrità strutturale, 29 (2014) 111-127; doi: 10.3221/igf-esis.29.11 119 figure 2: pointwise mixed stress-strain test. comparison between analytic and numerical solution for von mises yield surface. a) u c) 0 0.04 0.08 0.12 0.16 0 0.5 1 1.5 2 2.5 3 3.5 r ea ct io n [k n ] deflection [mm] present reference b) figure 3: stretching of a perforated rectangular plate. (a) geometry, boundary conditions and finite element mesh; (b) comparison of reaction-deflection diagram between the proposed algorithm and reference solution [10]; (c) contour plot of accumulated equivalent plastic strain pε at load level 15%, 45%, 75%, 100%. n.a. nodargi et alii, frattura ed integrità strutturale, 29 (2014) 111-127; doi: 10.3221/igf-esis.29.11 120 stretching of a perforated rectangular plate a classical benchmark for the implementation of plasticity models is the stretching of a thin perforated plate along its longituindal axis (see [10], for instance). this problem is solved under the usual assumption of plane stress, which is straightforwardly imposed within the present formulation. to this end, it suffices to minimize the incremental energy functional in (34) also with respect to the total strain component normal to the stress plane. the plate is 20 mm wide, 36 mm high, 1 mm thick and presents a circular hole of radius 10 mm at its center. the geometry and boundary conditions are depicted in fig. 3(a). the material is supposed to be isotropic linear elastic, with young modulus 70 gpae  and poisson coefficient 0.2  . a von mises yield criterion (see appendix b), with yield stress y0 0.243 gpa  and linear isotropic hardening of modulus i 0.2 gpah  , is adopted. because of the symmetry, only one quarter of the plate is considered in the analysis by applying the appropriate boundary condition on the symmetry edges. the finite element mesh adopted is constituted by 576 opt triangular elements (see [38], for instance), with a total number of 325 nodes. the analysis is conducted under displacement control, assigning a vertical displacement on the top constrained edge. in fig. 3(b) the diagram of the total reaction force versus the prescribed displacement is reported. the numerical solution is in good agreement with the reference one [10]. in fig. 3(c) the evolution of the accumulated equivalent plastic strain p p 0 2 3 t dt ε ε corresponding to different load levels is shown. figure 3: pinching of a cylindrical shell with diaphragms. (a) geometry, boundary conditions and finite element mesh; (b) deformed configuration; (c) comparison of load-displacement diagram between the proposed algorithm and reference solution (see [39]). pinching of a cylindrical shell with diaphragms in this section we consider the application of the proposed state update algorithm to a geometrically nonlinear problem. in particular, we refer to the problem of a cylindrical shell, constrained by rigid diaphragms at end-sections, and pinched by concentrated forces in the mid-section [39]. the cylinder has radius of 300 consistent units (c.u.), while its total length is of 600 c.u. the initial shell thickness is 3 c.u. fig. 4(a) shows the geometry and boundary conditions (we assume that the presence of rigid diaphragms constrains the in-plane degrees of freedom of the cylinder end sections). we assume the material to be isotropic linear elastic, with young modulus 3000e  c.u. and poisson coefficient 0.3  . a von mises yield criterion (see appendix b), with yield stress y0 24.3  c.u. and linear isotropic hardening of modulus i 300h  c.u., is adopted, under plane-stress assumption. due to symmetry, only one-eighth of the cylinder is considered in the analysis by applying appropriate boundary conditions on the symmetry edges. the geometrical nonlinearity is treated by a corotational approach [40, 41], and the n.a. nodargi et alii, frattura ed integrità strutturale, 29 (2014) 111-127; doi: 10.3221/igf-esis.29.11 121 finite element mesh is constituted by 24×24 opt-dkt triangular elements (see [38, 42], for instance). the analysis is conducted under displacement control, up to a total displacement of 300 c.u., coinciding with the cylinder radius. fig. 4(b) depicts the deformed configuration at the final load level, while in fig. 4(c) load-displacement diagram is plotted. the numerical solution appears to be in good agreement with the reference one [39]. the slight difference at high displacement values may be attributed to different finite-element types used in the computations. conclusions new state update algorithm for small-strain associative elastic-plastic constitutive models was presented. it is set within the theoretical framework of generalized standard materials with internal variables, under the assumption of rate independence. the evolution of internal variables in a finite time step obeys an incremental minimization principle involving a suitable convex functional, given by the sum of internal energy and dissipation function. an efficient strategy to compute the latter and its gradient and hessian is proposed, using haigh-westergaard stress invariants, for an ample class of isotropic deviatoric yield functions with linear or nonlinear strain-hardening. numerical results proved the effectiveness and the versatility of the methodology on a single material point state update, for a given loading history under mixed stress/strain control, and showed its reliability as an efficient constitutive solver in conjunction with finite element simulations. the proposed algorithm turned out to be complementary to the classical return mapping strategy, because no convergence difficulties arise if the stress is close to points of the yield surface with high curvature. hence it may improve the robustness of available plastic solvers through a hybrid approach. future work will involve the modeling of pressure-sensitive yield surfaces and non-associative plastic flow rules, and the testing of the solution algorithm on extensive large-scale fe simulations of engineering-relevant problems. acknowledgment he financial support of prin 2010-11, project “advanced mechanical modeling of new materials and technologies for the solution of 2020 european challenges” cup n. f11j12000210001 is gratefully acknowledged. references [1] wilkins, m.l., calculation of elastic-plastic flow, methods of computational physics, academic press, new york, 3 (1964). [2] simo, j.c., taylor, r.l., consistent tangent operators for rate-independent elastoplasticity, comput. meth. appl. mech. eng., 48 (1985) 101–118. [3] simo, j.c., taylor, r.l., a return mapping algorithm for plane stress elastoplasticity, int. j. numer. methods eng., 22 (1986) 649–670. [4] ortiz, m., popov, e.p., accuracy and stability of integration algorithms for elastoplastic constitutive relations, int. j. numer. methods eng., 21 (1985) 1561–1576. [5] ortiz, m., simo, j.c., an analysis of a new class of integration algorithm for elastoplastic constitutive relations, int. j. numer. methods eng., 23 (1986) 353–366. [6] ortiz, m., martin, j.b., simmetry-preserving return mapping algorithms and minimum work paths: a unification of concepts, int. j. numer. methods eng., 28 (1989) 1839–1853. [7] han, w., reddy, b.d., plasticity: mathematical theory and numerical analysis, interdisciplinary applied mathematics: mechanics and materials, vol. 9. springer, new york, (1999). [8] simo, j.c., hughes, t.j.r., computation inelasticity, springer, new york, (1998). [9] simo, j.c., numerical analysis of classical plasticity, in handbook for numerical analysis, ciarlet pg, lions jj (eds.), vol. iv, elsevier, amsterdam, (1998). [10] de souza neto, e.a., perić, d., owen, d.r.j., computational methods for plasticity: theory and applications, john wiley & sons, ltd, chichester, (2008). a t n.a. nodargi et alii, frattura ed integrità strutturale, 29 (2014) 111-127; doi: 10.3221/igf-esis.29.11 122 [11] borja, r.i., plasticity – modeling & computation, springer, berlin, (2013). [12] bićanić, n., pearce, c.j., computational aspects of a softening plasticity model for plain concrete, mechanics of cohesive and frictional materials, 1 (1996) 75–94. [13] de souza neto, e.a., perić, d., owen, d.r.j., a model for elastoplastic damage at finite strains: algorithmic issues and applications, eng. comput., 11 (1994) 257–281. [14] pérez-foguet, a., rodríguez-ferran, a., huerta, a., consistent tangent matrices for substepping schemes. comput. meth. appl. mech. eng., 190 (2001) 4627–4647. [15] armero, f., pérez-foguet, a., on the formulation of closest-point projection algorithms in elastoplasticity. part i: the variational structure, int. j. numer. methods eng., 53 (2002) 297–329. [16] abbo, a.j., sloan, s.w., an automatic load stepping algorithm with error control, int. j. numer. methods eng., 39 (1996) 1737–1759. [17] armero, f., pérez-foguet, a., on the formulation of closest-point projection algorithms in elastoplasticity. part ii: globally convergent schemes, int. j. numer. methods eng., 53 (2002) 331–374. [18] dutko, m, perić, d, owen, drj, universal anisotropic yield criterion based on superquadratic functional representation: part i. algorithmic issues and accuracy analysis, comput. meth. appl. mech. eng., 109 (1993) 73–93. [19] owen, d.r.j., hinton, e., finite elements in plasticity, pineridge press, swansea, (1980). [20] sloan s.w., substepping schemes for the numerical integration of elastoplastic stress-strain relations, int. j. numer. methods eng., 24 (1987) 893–911. [21] rosati, l., valoroso, n., a return map algorithm for general isotropic elasto/visco-plastic materials in principal space, int. j. numer. methods eng., 60 (2004) 461–498. [22] halphen, b., nguyen, q.s., sur les matériaux standards généralizés, journal de mécanique, 14 (1975) 39–63. [23] eve, r.a., reddy, b.d., rockafellar rt, an internal variable theory of plasticity based on the maximum plastic work inequality, q. appl. math., 48 (1990) 59–83. [24] miehe, c., schotte, j., lambrecht m., homogenization of inelastic solid materials at finite strains based on incremental minimization principles. application to texture analysis of polycrystals, j. mech. phys. solids, 50 (2002) 2123–2167. [25] mosler, j., variationally consistent modeling of finite strain plasticity theory with non-linear kinematic hardening, comput. meth. appl. mech. eng., 199 (2010) 2753–2764. [26] petryk, h, incremental energy minimization in dissipative solids, c. r. mec., 331 (2003) 469–474. [27] comi, c., perego, u., a unified approach for variationally consistent finite elements in elastoplasticity, comput. meth. appl. mech. eng., 121 (1995) 323–344. [28] reddy, b.d., martin j.b., algorithms for the solution of internal variable problems in plasticity, comput. meth. appl. mech. eng., 93 (1991) 253–273. [29] nayak, g.c., zienkiewicz, o.c., convenient forms of stress invariants for plasticity, proceedings of the asce journal of the structural division, 98(st4) (1972) 949–953. [30] matzenmiller, a., taylor, r.l., a return mapping for isotropic elastoplasticity, int. j. numer. methods eng., 37 (1994) 813–826. [31] panteghini, a., lagioia, r., a fully convex reformulation of the original matsuoka-nakai failure criterion and its implicit numerically efficient integration algorithm, int. j. numer. anal. methods geomech., 38 (2014) 593–614. [32] moreau, j.j., on unilateral constraints, friction and plasticity, springer, berlin (1974). [33] biot, m.a., mechanics of incremental deformations, wiley, new york (1965). [34] piccolroaz, a., bigoni, d., yield criteria for quasibrittle and frictional materials: a generalization to surfaces with corners, int. j. solids struct., 46 (2009) 3587–3596. [35] wriggers, p., nonlinear finite element methods, springer, berlin, (2008). [36] artioli, e., auricchio, f., beirão da veiga, l., a novel ‘optimal’ exponential-based integration algorithm for vonmises plasticity with linear hardening: theoretical analysis on yield consistency, accuracy, convergence and numerical investigations, int. j. numer. methods eng., 67 (2006) 449–498. [37] klinkel, s., govindjee, s., using finite strain 3d-material models in beam and shell elements, eng. comput., 19 (2002) 254–271. [38] felippa, c.a., a study of optimal membrane triangles with drilling freedoms, comput. meth. appl. mech. eng., 192 (2003) 2125–2168. [39] areias, p., garção, j., pires, e.b., infante barbosa j, exact corotational shell for finite strains and fracture, comput. mech., 48 (2011) 384–406. n.a. nodargi et alii, frattura ed integrità strutturale, 29 (2014) 111-127; doi: 10.3221/igf-esis.29.11 123 [40] caselli, f., bisegna, p., polar decomposition based corotational framework for triangular shell elements with distributed loads, int. j. numer. methods eng., 95 (2013) 499–528. [41] caselli, f., bisegna, p., a corotational flat triangular element for large strain analysis of thin shells with application to soft biological tissues, comput. mech., (2014) doi: 10.1007/s00466-014-1038-9. [42] batoz, j.l., bathe k.j., ho l.w., a study of three-node triangular plate bending elements, int. j. numer. methods eng., 15 (1980) 1771–1812. [43] del piero, g., some properties of the set of fourth-order tensors, with application to elasticity, j. elast., 9 (1979) 245–261. [44] lode, w., versuche über den einfuss der mittleren hauptspannung auf das fliessen der metalle eisen kupfer und nickel, zeitung phys., 36 (1926) 913–939. [45] asensio, g., moreno, c., linearization and return mapping algorithms for elastoplasticity models, int. j. numer. methods eng., 53 (2002) 331–374. appendix a: haigh-westergaard coordinates and their derivatives he analysis of isotropic yield functions can be pursued by disregarding the orientation of the stress/strain principal axes and using three isotropic invariants. the most common invariants are: 2 3 1 2 3 1 1 tr , tr , tr 2 3 i j j  ε e e (a1) where ε is a symmetric second-order tensor and e is its deviatoric part , defined by: 1 1 3 3 i         e ε i i i ε (a2) i is the second-order identity tensor,  is the usual dyadic product between second-order tensors, and  is the fourthorder identity on second-order symmetric tensors. the gradients and the hessians of those invariants are given by:   1 1 2 2 2 2 3 3 , 1 , 3 2 2 , 3 3 i i j j j j j                     i e i i e i e i i e e i i e    (a3) here (•) denotes the derivative with respect to ε ,  is the fourth-order null tensor,  denote the square tensor product between second-order tensors [43]. the analysis presented herein is however greatly simplified by using another set of invariants, known as haighwestergaard coordinates [29, 44], defined by: 31 2 3/2 2 1 3 3 , 2 , arccos 3 23 ji j j             (a4) the gradients and hessians of  and  are straightforwardly derived: 2 2 2 2 3 , 3 , j j j j                     i  (a5) whereas the derivation of  and  is somewhat more involved. to this end, the argument in [45] is briefly sketched, and the trihedron 1 2 3{ , , }f f f of second-order symmetric tensors is introduced: 1 2 3, ,        f f f (a6) using (a4), (a5) and (a3), it turns out that: t n.a. nodargi et alii, frattura ed integrità strutturale, 29 (2014) 111-127; doi: 10.3221/igf-esis.29.11 124 31 2 21 2 3 2 cos 3 6 , , sin 3 sin 33 3 ji j j                i e f f f (a7) the latter equation yields by (a3) and (a4): 23 2 2 1 6 6 cos 3 3 sin 3 6 3            f f f f (a8) whence  follows by (a6). on the other hand, eq. (a7) can be recast as 33 2 2 6 sin 3 cos 3 j       f f (a9) and, by differentiating with respect to ε , it leads to:   3 33 2 3 2 2 3 6 2 6 sin 3 cos 3 3 cos 3 sin 3 j j                    f f f f (a10) noting that by (a9), (a3) and (a7) it turns out that:     2 3 3 2 3 1 2 2 1 1 2 2 1 sin 3 cos 3 6 2 3 3 j j                   f f f f f f f f f f  (a11) and by (a6), (a5) and (a3) it turns out that:  2 1 1 2 2 3 1 ,                   f f f f f f (a12) it is a simple matter to verify that (a10) yields:  1 2 2 12 1 cos 3 3 2 sin 3 ij i j           f f f f f f  (a13) where cos 3 2 2 0 2 2 cos 3 3sin 3 0 3sin 3 3cos 3                    (a14) alternative expressions for  and  , more effective from a computational point of view, are:   3 22 23 2 2 22 2 3 2 2 3 3 2 3 3 3 4 1 cos 3 6 sin 3 1 1 cos 3 6 cos 3 2 cos 3 5 sin 3 sin 3 3 6 18 cos 3 j j j j j j j j j j j j                                                           (a15) the expressions for  and  derived in (a8), (a6) and (a13), or the alternative expressions in (a15), get greatly simplified when computed in an orthonormal basis of eigenvectors of ε . the tensor 1f is spherical, thus it is represented by  diag 1;1;1 3 where  diag • denotes the diagonal matrix with the enclosed eigenvalues. recalling (a7), 2f is n.a. nodargi et alii, frattura ed integrità strutturale, 29 (2014) 111-127; doi: 10.3221/igf-esis.29.11 125 represented by  1 2 3diag ; ,;e e e  where i , 1, ..., 3ie  are the eigenvalues of e , which are the roots of the characteristic polynomial of e : 3 2 3 0j j     (a16) using (a4), it is a simple matter to verify that those roots are  2 3 cos 2 3 ,k    0, -1,1 .k  as a consequence, 2f is represented by:     2 cos 0 0 2 0 cos 2 3 0 3 0 0 cos 2 3                f (a17) in passing, it is noted that  may be assumed to belong to [0, 3] , implying that the eigenvalues of e are sorted in descending order. substituting 1f and 2f into (a8), it turns out that 3f is represented by:     3 sin 0 0 2 0 sin 2 3 0 3 0 0 sin 2 3                 f (a18) analogously, substituting the above representations into (a13), the representation of  is obtained. the only nonzero terms turn out to be:                                   21111 2233 3322 22222 3311 1133 23333 1122 2211 22323 2332 3223 3232 23131 3113 1331 1313 2 sin 2 3 2 2 sin 2 3 3 2 2 sin 2 3 3 1 cot 2 1 cot 2                                                                                   21212 1221 2112 2121 2 3 1 2 cot 2 3                            (a19) expressions (a18) was reported in [45]; to the best of authors’ knowledge, (a19) is new. it is emphasized that the singularity of  at integer multiples of 3 , due to the sin3 term in the denominator of (a8) or (a15), turns out to be removable, because it disappears in (a18). on the other hand, the “shear components” of  are indeed singular at integer multiples of 3 , as apparent by (a19). however,  only appears in (24), multiplied by d . using (23) and recalling that 'g vanishes at integer multiple of / 3 , it turns out that the product d  has removable singularities there, thus allowing for a stable numerical computation of d . appendix b: gallery of deviatoric yield functions von mises yield function eferring to the form reported in (14) and (25), the von mises yield function is obtained by assuming (see [45], for instance):  ˆ 1g  σ (b1) r n.a. nodargi et alii, frattura ed integrità strutturale, 29 (2014) 111-127; doi: 10.3221/igf-esis.29.11 126 figure 5: von mises yield function. (a) yield surface; (b) dissipation function graph. figure 6: von mises–tresca ( 20m  ) yield function. (a) yield surface; (b) deviatoric section of the yield surface; (c) dissipation function graph; (d) unitary level set of the dissipation function. fig. 5 shows the corresponding yield surface and dissipation function graph. it is worth noting that the dissipation function results convex, non-negative, zero only at the origin and positively homogeneous of degree one. the latter feature is clear from its cone-like graph. von mises–tresca yield function the von mises–tresca yield function corresponds to the choice (see [17] and references therein): (a) (b) (a) (b) (c) (d) n.a. nodargi et alii, frattura ed integrità strutturale, 29 (2014) 111-127; doi: 10.3221/igf-esis.29.11 127       1 2 1 22 2 2 ˆ 1 2 3 2 2 3 3 m m mm m mdg d d    σ (b2) where            ˆ ˆ ˆ ˆ ˆ2 ˆ1 3cos cos 2 3 , cos 2 3 cos 2 3 , cos 2 3 cosd d d                σ σ σ σ σ σ (b3) the material parameter m determines the shape of the yield surface. in particular in the limit of 0m  [ resp., m   ] the von mises circle [resp. the tresca hexagon] is recovered. high curvature of the yield surface corresponds to high values of the parameter m . for 20m  the discrepancy between this yield surface and the tresca hexagon is less than 2 per cent [17]: fig. 6 depicts the von mises–tresca yield surface and the corresponding dissipation function graph. fig. 6(b,d) show that high curvature points in the yield surface correspond to low curvature points in the graph of the dissipation function, and vice-versa. microsoft word numero_53_art_31_2824 e. m. strungar et alii, frattura ed integrità strutturale, 53 (2020) 406-416; doi: 10.3221/igf-esis.53.31 406 inelastic deformation and destruction of fiber-laminated polymer composites in stress concentration zones elena m. strungar, valery e. wildemann perm national research polytechnic university, russia cem.spaskova@mail.ru, http://orcid.org/0000-0002-2246-8638 wildemann@pstu.ru, http: //orcid.org/0000-0002-6240-4022 abstract. the article is devoted to the experimental study of the laws of inelastic deformation of structural polymer composites in the presence of macroinhomogeneous fields. the work uses a three-dimensional optical system and a method of digital image correlation, thermoscanning equipment. the relationship between the selected parameters of the correlation analysis and the scale level of the deformation processes is shown. experimental data were obtained confirming the presence of a large-scale effect of strength in a certain range of structural parameter values, data on the features of the deformation of composites with various reinforcement schemes, as well as in the presence of technological defects. recommendations on the use of a video system for calibration and sensitivity assessment of integrated fiberoptic sensors are presented. keywords. experimental mechanics; the method of digital image correlation; stress concentrator; fiber-laminated polymer composites; the scale effect of strength citation: strungar, e. m., wildemann, v. e., inelastic deformation and destruction of fiber-laminated polymer composites in stress concentration zones, frattura ed integrità strutturale, 53 (2020) 406-416. received: 19.05.2020 accepted: 24.05.2020 published: 01.07.2020 copyright: © 2020 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. introduction ue to their high specific physical and mechanical properties fiber-laminated polymer composite materials are widely used in critical aviation structures. experimental studies that provide the assessment of evolution of displacement and strain fields in stress concentration zones as well as the specific features of composites behavior in these zones, are necessary for improvement of inelastic behavior models, the development of calculation models and designing the critical structure elements [1-9]. alongside with various geometry concentrators, in particular, the holes, the structure defects that occur in the process of manufacture or operation may become prospective concentrators [10-14].  the method of digital image correlation (dic) is one of promising experimental displacement and strain fields analysis methods. the development of a new method for solution of deformable solid mechanics tasks calls for complex studies of efficacy of the use of experimental mechanics “instrument” with reference to the analysis of mechanical behavior of solids of various geometry and structures during implementation of complex external impact modes [15-21]. this work d https://youtu.be/4z8ehizagai e. m. strungar et alii, frattura ed integrità strutturale, 53 (2020) 406-416; doi: 10.3221/igf-esis.53.31 407 aimed at obtaining new experimental data about the regularities of evolution of displacement and strain fields in the zones of composite elements stress concentration at inelastic behavior by means of digital image correlation method appears relevant.  despite the significant achievements of experimental composite mechanics, the issues that need extra studies include complex theoretical and experimental study of damage accumulation process regularities, defects development, structural and macro-damage of structural polymer composite materials operating under the conditions of non-homogeneous strain fields in the parts with various geometry concentrators. it is noted that the composite materials structure complexity results in the necessity of consideration the defects at various levels, and finding the damage development stages [22-24]. the objective of this work is the experimental study of regularities of inelastic deformation, the processes of damage accumulation and structure polymer composite materials damage under the condition of non-homogeneous strain fields.      methodology and methods of research his work was carried out in perm national research polytechnic university using unique scientific equipment «complex of testing and diagnostic equipment for studying properties of structural and functional materials under complex thermomechanical loading» . registration and analysis of evolution of non-homogeneous strain fields and the temperatures on the surface of structurally non-homogeneous material provided the joint use of in-situ optical methods of experimental mechanics: the highly efficient method of digital images correlation (dic) on the basis of three-dimensional digital optical system vic-3d (correlated solutions) and infra-red tomography method flir sc7700m with thermal imaging system with mct (mercury-cadmium telluride) cooled detector. the quantitative comparison of the images in dic method is provided by means of computation of image conformity factor according to one the criteria and the search for its extremum. this work uses the criteria of normed sum of squared differences with zero mean [15]. in the process of data processing, we establish the surface points displacement fields, and the transition to deformation is performed by means of finite strain tensor in the sense of lagrange [15]. the analysis of composite material damage due to macro-fissure development, the study of developmental prototype fracture surfaces was performed with the use of stereomicroscope carl zeiss stereo discoverjу.v12. the study of inelastic deformation processes, the accumulation of damages and development of defects in composite objects depending of stress conditions and modes provided the performance of mechanical tests at quasi-static loading at multipurpose electromechanical test system instron 5882 (100 кn), instron 5989 (600 кn) as well as at cyclic loading with various cycle parameters at servohydraulic two-axis (tensile-and-compression/torsion) test system instron 8850 (100 кn/1000 nm) [8]. methodical specifics of the use of digital images correlation and digital optical systems method at composite materials testing he paper considers the methodical issues of conducting the experiment with the use of digital optical system for 3d analysis of displacement and strain fields. the method dic suggests the selection of correlation analysis parameters, in particular, the subarea size  and the step value . during the correlation processing of digital images the displacement vectors computation is performed not at each individual image point (pixel), but through the study area discretization into small local study areas or sub-areas. the step is another parameter to be set in the algorithm of building the displacement vector fields, its size determines the procedure of search and identification of image sections. the step value sets the distance between the points analyzed in the process of mathematical processing in pixels [15]. in view of the fact that composite materials possess significant structural non-homogeneity, which is not considered in the method dic, the authors performed a number of calculations of deformation fields on the surface of dimensionally laminated carbon composite for one frame at various values of subarea in the interval of =989 pixels and at the fixed step value =5. the authors have built a diagram of dependence of the subarea size impact on the results of correlation ratio calculation fig. 1). the paper takes into account the recommendation of literature sources [15], that the subarea size is acceptable if correlation ration does not exceed σ≤0.01 [15]. the selected subarea size 49×49 has sufficient uniqueness of pixels t t e. m. strungar et alii, frattura ed integrità strutturale, 53 (2020) 406-416; doi: 10.3221/igf-esis.53.31 408 distribution for the possibility of conclusive identification of local areas from the image. at smaller parameter size , the unaffordable correlation ratio values are observed. based on the study conducted it is observed that the selection of parameters should be performed in consideration of the size of structural non-homogeneity of the material; in view of this fact, the scale level of deformation registration is selected. to assess the structural specificity of the material, to study the processes of origin and development of defect structures and damage, the analysis of behavior in the stress concentration zones it is necessary to establish the step value consistent with the structural non-homogeneity size [21].   figure 1: the effect of subarea size on the results of calculation of correlation ratio; non-homogeneous longitudinal strain fields at a fixed size of subarea and various step values. due to the fact that the video-system precision is not a fixed value but depends on various mathematical parameters, the authors conducted a study to confirm the precision of the measurements obtained using a three-dimensional optical system, a series of tests for uniaxial stretching of a fiberglass flat sample was carried out using amounted extensometer instron 2620-601 and additional vic-3d software module of “virtual extensometer” (fig. 2). the characteristics of the extensometer instron 2620-601 are as follows: the maximal possible deviation from the measured value is 0.15%. the measuring base of the mounted extensometer is 50 mm.  figure 2: longitudinal strain-time diagram. according to the test results, it was concluded that the use of a digital optical system makes it possible to determine the deformation values on a fixed basis, with the accuracy consistent with the data of the mounted longitudinal strain gauge  e. m. strungar et alii, frattura ed integrità strutturale, 53 (2020) 406-416; doi: 10.3221/igf-esis.53.31 409 the analysis of the mechanisms of inelastic deformation and the composites destruction in the concentrators zones in consideration of structural parameters n the process of creation of structures, it is often necessary to make the holes of various size in their elements due to the process considerations. the following part of the paper presents the results of experimental studies of mechanical behavior of a fiber-laminated composite material in the vicinity of stress concentrators. the authors tested the fiberglass samples for uniaxial tension with different values of through hole diameter. fig. 3 presents the comparative analysis of the descending sections of the diagram for diameters d1-d5. with the increase of diameter, the descending sections extend, the degree of implementation of the supercritical stage rises. the angle (slope modulus) of the curves changes as well. figure 3: load diagram for samples with different hole diameters during uniaxial tensile tests; the comparative analysis of the descending sections of the diagram. the analysis of the composite material damage due to macro-fissure development was carried out using a stereo microscope carl zeiss stereo discoverjу.v12 in the upper layers. in large deformation areas, the fiber breakage is observed around the holes on both sides, the evidence of this fact is shown in the image of the sample surface (fig. 4). due to the results obtained, the geometrically similar samples are of special interest; the program of assessment of the effect of structural parameters of the composite samples with the tension concentrator included mechanical tests for uniaxial tension of three groups of strip samples with different hole diameters 3, 6 и 9 mm. figure 4: the images of fiberglass structure after the destruction of the sample on the upper layer. when selecting the width and length of the working part of the sample, the similarity of geometric dimensions was observed: the hole diameter d (mm), the width of the working part h=6d (mm), the length of the working part l=14d (mm), the speed of movement l0.01 (mm/min) of the movable grabber provided similar strain rate in the working areas of all samples (1.710-4 s-1). the average stress value was determined by the formula σ = p/(5dh). fig. 5 shows the characteristic deformation diagrams. the destruction occurred due to the formation of the fiber breakage band, besides, the formation of extensive delamination regions was recorded. in the course of study the authors found a large-scale effect, the bearing capacity decreased with the increase of the hole diameter. the detected scale effect can be attributed to the fact that, depending on the hole size, various volumes of a structurally non-homogeneous medium are involved in the work. i e. m. strungar et alii, frattura ed integrità strutturale, 53 (2020) 406-416; doi: 10.3221/igf-esis.53.31 410 figure 5: the diagram of samples deformation at uniaxial tensile test. the work deals with structurally non-homogeneous solids, and a change in the size of the sample and the hole affects the bearing capacity, it can be assumed that it is attributed to the material structure. in this regard, a diagram of dependence of the limiting value of the average stress on non-homogeneity parameter was obtained for samples with different hole diameters (fig. 6). figure 6: the diagram of dependence of the limiting value of the average stress on non-homogeneity parameter and the image of destroyed sample with fiber breakage and matrix delamination areas. non-homogeneity parameter was introduced for quantitative analysis, it depends on the hole diameter and the size of the structural element and is calculated by the formula ξ=d/δ. the size of the structural element for this material was δ = 4 mm (weave width). the dependence of the specific strength characteristics on the specified parameter is shown in fig. 6. it is seen, that a critical value of non-homogeneity parameter can be introduced ξcritical = 1,5. conditionally, the diagram in fig. 6 can be divided into two sections: section i (ξ ≤ ξcritical) and section ii (ξ < ξcritical). when the values of the structural nonhomogeneity parameter are less than the critical value, the limiting values of the average stress decreased (section i); the obtained data indicate the presence of a scale effect. when the structural non-homogeneity parameter is greater than the critical value for the specific material, there is practically no change in the limiting values of the average voltage (section ii), while there is no scale effect. the use of the video-system makes it possible to use the deformation fields in the vicinity of the concentrator. the analysis of longitudinal strain (εyy) distribution on the surface, along the line l drawn from the hole to the edge of the plate e. m. strungar et alii, frattura ed integrità strutturale, 53 (2020) 406-416; doi: 10.3221/igf-esis.53.31 411 is performed for composite samples. strain diagram are built at particular level of strain (σ) 150, 250, 350 mpa for a sample with the hole diameter d=3, 6, 9 mm (fig. 7).  figure 7: longitudinal strain diagrams d=3,6,9 mm on the sample surface with diameter size at various strain level; a thermogram of unloaded sample before the test d=6 mm.  it has been found that in the process of inelastic deformation the maximal values of longitudinal strain at extension of the sample displace from the boundary of the hole. it is possible to assume that such peculiarity of mechanical conduct is related to the presence of defects in the vicinity of the hole. to confirm this fact, thermal scanning is performed after short-term heating. the corresponding results are provided in fig. 7. a local heating is found in the area of the opening which indirectly confirms the supposition of a defect area. structural and deformational properties determining the composite’s behavior at shear, belong to important characteristics of any composite. the study of these properties of materials is associated with specific methodic difficulties [25,26]. the paper considers iosipescu method astm d5379. there are various international standards for these mechanical tests. the paper shows that these standards need adjustment for a number of structures. the authors suggested recommendations for obtaining and mathematical processing of experimental data using contactless optical video-system. to determine shear deformations, astm d5379 recommends to use resistance strain gauges with 1.5mm basis situated at the angle of ±45о to the loading area in the working area of the sample (between v-shaped cutout), but the video-system software makes it possible to simulate the resistance strain gauges using supplementary virtual instruments. based on the tests, deformation fields were built for each of the 10 samples in their working areas in consideration of the structural properties. fig. 8 shows the analyzed options of averaging the deformations in the working area of spatially reinforced samples using such video-system elements as “virtual extensometer t” and “rectangular area r” [28]. in the course of deformation fields study it was found that shear deformations distribution is of non-homogeneous nature, depending on non-homogeneity areas location, the data values may vary by shear module by more than 1.6 times, by nominal shear strength – by 1.4 times, by strength limit – by 1.1 times [28]. it should be pointed out that experimental studies were conducted at 8 spatially reinforced structures, but only two structures have such peculiarity for determination of shear deformations for spatially reinforced structures according to astm d5379, a video-system has advantages over resistance strain gauges and is more preferable to use because it provides the full pattern of shear deformations distributions on sample surface [28]. the analysis of deformation and damage accumulation processes in composite objects with stress concentrators of process and maintenance origin he previously provided results illustrate deformation fields in consideration of sizes of the sample concentrators and structure elements. defects, fissures, healing areas may also be the possible concentrators. the next part of the work is devoted to it. the process of manufacture of the sample with imbedded process defects of “delamination” type is based on the use of fluoroplastic film laid between the layers. t e. m. strungar et alii, frattura ed integrità strutturale, 53 (2020) 406-416; doi: 10.3221/igf-esis.53.31 412 for experimental study of deformation processes and accumulation of damages in carbon fiber composite samples with internal defects under complex stressed conditions the authors implemented mechanical tests at proportional extension/compression with torsion at k=0.028 (k=u/φ). to assess the internal defect development the tests were conducted with three unloadings and repeated loadings. in the event of internal defect development in the process of loading the change of deformation fields pattern is recorded (fig. 9) [13,14].  figure 8: the diagrams of sample deformation using the instruments “virtual extensometer t” and “rectangular area r” to determine shear deformations. figure 9: non-homogeneous longitudinal strain fields on the sample surface with the defect size 10 х 10 mm. figure 10: longitudinal strain fields evolution and the corresponding thermograms depending on the number of performed loading cycles. e. m. strungar et alii, frattura ed integrità strutturale, 53 (2020) 406-416; doi: 10.3221/igf-esis.53.31 413 special attention is paid to analysis of deformation fields pattern evolution for assessment of development of the healed reach-through breakdown defects and formation of macro-damage conditions in three-layer composite fiberglass laminate panels. the authors suggested a method of study of the defect effect on residual strength of the elements of composite structures based on the joint use of the systems of deformation fields and temperatures registration. they assessed the effect of cyclic tests on behavior of defect-containing composites with the following parameters: asymmetry coefficient r= -0.25; cycle amplitude na = 25kn; sinus wave shape; frequency – 0.25hz; the number of cycles n=200. the minimal values at loading constituted -10kn, the maximal ones – 40kn (fig. 10). it is shown that the bearing capacity of a sample with a defect applied is 30% lower than that of a defectless sample. cyclic loadings under the above-discussed modes resulted in another strength reduction by 10% [12]. the use of digital image correlation method for solution of fiber optic technology tasks mong the present-day and promising diagnostic instruments, the monitoring systems based on the introduction of fiber optic deformation sensors (fods) which are effective both under production conditions and during operation of various purposes products and objects, are of special interest. introducing fods into the composite structure, it is necessary to solve a number of technical and scientific problems. one of the trends of the use of dic method may be the use of this instrument to solve the problems of fiber optic technologies [14,27]. the final part of the paper shows that the use of video systems for three-dimensional analysis of the displacement and deformation fields makes it possible to develop recommendations for location and calibration of built-in fiber optic deformation sensors fods (taking into account the calibration coefficient provides the increase of precision of deformations recorded by fods by 25%), and assess the sensitivity to loading modes [27]. besides, the paper studied the organization of the equilibrium fissure growth mode. this study provides the results of experiments on registration of deformations under cyclic loading, and the development of recommendations on registration the damages based on the results of measuring the deformations during cyclic loading. in this case, we provided not an instant development of the damage area, but its development with a rate that allows us to speak about significant effect of the number of cycles on destruction. to analyze the deformation fields and determine the locations of the optical sensors to record the origin and development of damage in the polymer composite material, we implemented a multi-stage cyclic loading according to fig. 11 diagram. the transition from one stage to another was carried out with the decrease in the value of the load amplitude pa by more than 5%. a sample with a lateral cutout was used as the study object, it served as a stress concentrator, in the vicinity of which the damages first occur under loading. the longitudinal deformation fields and the corresponding images obtained using a microscope are shown in fig. 12[14].  figure 11: staged strain mode. similarly, this technique was applied to carbon fiber composite samples; a loading-time diagram with the marked points corresponding to longitudinal strain fields is shown in fig. 13. the criterion for transition from one stage to another was the change in the value of the loading amplitude pa by 3, 10, 50%. in the course of a staged cyclic loading necessary for recording the origin and development of damages in the polymer composite material, a more equilibrium fissure growth is observed for fiberglass samples, than for carbon fiber composite samples. the presented technique is necessary for determining the locations of optical sensors during registration of origin and development of damages in a polymer composite material  a e. m. strungar et alii, frattura ed integrità strutturale, 53 (2020) 406-416; doi: 10.3221/igf-esis.53.31 414 figure 12: evolution of longitudinal strain fields during a fissure growth for a fiberglass samples. figure 13: evolution of longitudinal strain fields during a fissure growth for a fiberglass samples. conclusions   herefore, the paper analyzes numerical algorithms for processing the experimental data using the digital image correlation method. the authors suggested recommendations on selection of calculation parameters for analysis of non-homogeneous displacement and strain fields in composite products taking into account the structural nonhomogeneity of materials. they have shown the correlation between the selected parameters of the correlation analysis and the scaled level of the consideration of strain processes. since there is a correlation between the selected processing parameters and the characteristic size of the strain averaging region, the selection of building the vector fields predetermines the possibility of identifying the features of strain localization at various scales. the authors conducted experimental studies of the mechanical behavior of fiber-laminated composite materials in the vicinity of stress concentrators under quasistatic loading. the results of assessment of the effect of the hole size in relation to the characteristic size of the composite material structure on the processes of inelastic deformation and breakage have been obtained. the data confirming the presence of a scale effect of strength in a certain range of values of material structural heterogeneity parameter have been obtained. t e. m. strungar et alii, frattura ed integrità strutturale, 53 (2020) 406-416; doi: 10.3221/igf-esis.53.31 415 recommendations on obtaining and mathematical processing of experimental data for determining the mechanical characteristics of composites under shear, using a contactless optical video system have been suggested. to analyze the regularities of mechanical behavior of materials in the areas of process and operational imperfections, the processes of strain and accumulation of damage in sandwich composite objects with pre-embedded defects have been experimentally studied. the authors analyzed the evolution of strain field patterns to assess the development of defects in composite samples. they suggested a technique for studying the effect of defects on the residual strength of composite structural elements based on the joint use of strain fields and temperatures recording systems. experimental data on assessment of the effect of defects on the residual strength of structurally similar composite structural elements have been obtained. the load-bearing capacity of coarse-grained panels with the damages under cyclic and quasi-cyclic impacts has been assessed. the paper provides a complex study of usability of digital images correlation method for solution of fiber optic technology tasks. it is shown that the use of video-systems for three-dimensional analysis of the displacement and strain fields makes it possible to develop recommendations for location and calibration of built-in fiber optic sensors, and assess the sensitivity to loading modes.  acknowledgements xperimental studies were carried out using the large-scale research facilities «complex of testing and diagnostic equipment for studying properties of structural and functional materials under complex thermomechanical loading» pnrpu modernized with funds by the ministry of science and higher education of the russian federation, unique project identifier rfmefi61920x0017. references [1] staniera, d., radhakrishnana, a., genta, i., shankhachur roy, s., hamertona, i., potlurib, p., scarpa, f., shaffer, m., ivanov, d. s. (2019). matrix-graded and fibre-steered composites to tackle stress concentrations, composite structures, 207, pp. 72–80. doi: 10.1016/j.compstruct.2018.09.019. [2] fedulov, b. n., fedorenko, a. n., kantor, m. m., lomakin, e. v. (2018). failure analysis of laminated composites based on degradation parameters, meccanica, 53(1-2), pp. 359–372. doi: 10.1007/s11012-017-0735-9. [3] hadjem-hamouche, z., derrien, k., héripré, e., chevalier, j. p. (2018). in-situ experimental and numerical studies of the damage evolution and fracture in a fe-tib2 composite, materials science and engineering: a, 724, pp. 594-605. doi: doi.org/10.1016/j.msea.2018.03.108 [4] junshan, h., kaifu, z., hui, c., ping, l., peng, z., danlong, s. (2017) stress analysis and damage evolution in individual plies of notched composite laminates subjected to in-plane loads, chinese journal of aeronautics, 30(1), pp. 447–460. doi: 10.1016/j.msea.2018.03.108. [5] krzyzak, d., robak, g., lagoda, t. (2015). determining fatigue life of bent and tensioned elements with a notch, with use of fictitious radius, fatigue & fracture of engineering materials & structures, 38(6), pp. 693-699. doi: 10.1111/ffe.12276. [6] lagattu, f., lafarie-frenot, m.c., lam, t.q., brillaud, j. (2005). experimental characterisation of overstress accommodation in notched cfrp composite laminates, composite structures, 67(3), pp. 347-357. doi: 10.1016/j.compstruct.2004.01.016. [7] tretyakova, t.v., vildeman, v.e. (2017). influence the loading conditions and the stress concentrators on the spatialtime inhomogeneity due to the yield delay and the jerky flow: study by using the digital image correlation and the infrared analysis, frattura ed integrità strutturale, 11(42), pp. 303-314. doi: 10.3221/igf-esis.42.32. [8] wildemann, v.e. at all. (2011). the mechanics of materials. methods and means of experimental research. perm: publishers inc. pnrpu, 165 p. [9] wildemann, v.e. (2012). experimental studies of the properties of materials under complex thermomechanical effects. м.: fizmatlit, 204 p. [10] emery, t.r., dulieu-barton, j.m. (2010). thermoelastic stress analysis of damage mechanisms in composite materials, composites part a: applied science and manufacturing, 41, pp. 1729–1742. doi: 10.1016/j.compositesa.2009.08.015. e e. m. strungar et alii, frattura ed integrità strutturale, 53 (2020) 406-416; doi: 10.3221/igf-esis.53.31 416 [11] tashkinov, m. a. (2017). modelling of fracture processes in laminate composite plates with embedded delamination, 11 (39), pp. 248-262. doi: 10.3221/igf-esis.39.23. [12] lobanov, d.s., wildemann, v.e., spaskova, e. m., chikhachev, a.i. (2015). experimental investigation of the defects influence on the composites sandwich panels strength with use digital image correlation and infrared thermography methods. pnrpu mechanics bulletin, no. 4, pp. 159-170. doi: 10.15593/perm.mech/2015.4.10. [13] wildemann, v. v., tretyakova, t. v., strungar, e. m., tretyakov, m. p. (2018). deformation and failure of carbon fiber composite specimens with embedded defects during tension-torsion test, frattura ed integrità strutturale, 12(46), pp. 295-305. doi: 10.3221/igf-esis.46.27. [14] lobanov, d.s., strungar, e.m., zubova, e.m., wildemann, v.e. (2019). studying the development of a technological defect in complex stressed construction cfrp using digital image correlation and acoustic emission methods, russian journal of nondestructive testing, 55, pp. 631-638. doi: 10.1134/s1061830919090031. [15] sutton, m.a., orteu, j.-j., schreier, h. (2009). image correlation for shape, motion and deformation measurements. – university of south carolina, columbia, sc, usa, 364 p. [16] huh, y.-h., kim, j., hong, s., park, j. h. (2015). measurement of hole damage characteristics in the glass fibre reinforced plastic composite using digital image correlation technique, material wissenschaft und werkstofftech, 46(4–5), pp. 446-453. doi: 10.1002/mawe.201500420. [17] khechai, a., tati, a., guerira, b., guettal,a a., mohite, p.m. (2018). strength degradation and stress analysis of composite plates with circular, square and rectangular notches using digital image correlation, composite structures, 185, pp. 699-715. doi: 10.1016/j.compstruct.2017.11.060. [18] mehdikhani, m., aravand, v., sabuncuoglu, b., callens, m. g., lomov, s.v., gorbatikh, l. (2016). full-field strain measurements at the micro-scale in fiber-reinforced composites using digital image correlation, composite structures 140, pp. 192-201. doi: 10.1016/j.compstruct.2015.12.020. [19] tretyakova, t. v., spaskova, е.м. (2013). experimental study of limit stress-strain state quasi-brittle material using correlation techniques digital images. pnrpu mechanics bulletin, 2, pp. 186-198. [20] wildemann, v.e., spaskova, e.v., shilova, a.i. (2016). research of the damage and failure processes of composite materials based on acoustic emission monitoring and method of digital image correlation problems of deformation and fracture in materials and structures, solid state phenomena, 243, pp. 163-170. doi: 10.4028/www.scientific.net/ssp.243.163. [21] tretyakova, t.v., dushko, a.n., strungar, e.m., zubova, e.m., lobanov, d.s. (2019). comprehensive analysis of mechanical behavior and fracture processes of specimens of three-dimensional reinforced carbon fiber in tensile tests, pnrpu mechanics bulletin, 1, pp. 173-183. doi: 10.15593/perm.mech/2019.1.15. [22] camanho, p.p., maimı, p., dávila, c.g. (2007). prediction of size effects in notched laminates using continuum damage mechanics, compos sci technol, 67, pp. 2715-2727. doi: 10.1016/j.compscitech.2007.02.005. [23] frantziskonis, g., deymier, p. (2006). surface effects at the nanoscale significantly reduce the effects of stress concentrators, probabilistic engineering mechanics. 21(3), pp. 277-286. doi: 10.1016/j.probengmech.2005.10.004. [24] green, b.g., wisnom, m.r., hallet, s.r. (2007). an experimental investigation into the tensile strength scaling of notched composites, composites—part a, 38, pp. 867-878. doi: 10.1016/j.compositesa.2006.07.008. [25] babushkin, a.v., babushkina, a.v., strungar, e. m., staroverov, o. a., lobanov, d. s., temerova, m.s., feklistova e.v. (2019). phenomenological characteristics structural features research obtained at fibrous plastics standard tests, procedia structural integrity, 17, pp. 658–665. doi: 10.1016/j.prostr.2019.08.088. [26] strungar, e. m., feklistova, e.v., babushkin, a.v., lobanov, d. s. (2019). experimental studies of 3d woven composites interweaving types effect on the mechanical properties of a polymer composite material, procedia structural integrity, 17, pp. 965–970. doi: 10.1016/j.prostr.2019.08.128. [27] anoshkin, a. n., voronkov, a. a., kosheleva, n. a., matveenko, v. p., serovaev, g. s., spaskova, e. m., shardakov, i. n., shipunov, g. s. (2016). measurement of inhomogeneous strain fields by fiber optic sensors embedded in a polymer composite material, mechanics of solids, 51(5), pp. 542-549. doi: 10.3103/s0025654416050058. [28] strungar, e.m., yankin, a.s., zubova, e.m., babushkin, a. v., dushko, a. n. 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/hrv (za stvaranje adobe pdf dokumenata najpogodnijih za visokokvalitetni ispis prije tiskanja koristite ove postavke. stvoreni pdf dokumenti mogu se otvoriti acrobat i adobe reader 5.0 i kasnijim verzijama.) /hun 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can be opened with acrobat and adobe reader 5.0 and later.) >> /namespace [ (adobe) (common) (1.0) ] /othernamespaces [ << /asreaderspreads false /cropimagestoframes true /errorcontrol /warnandcontinue /flattenerignorespreadoverrides false /includeguidesgrids false /includenonprinting false /includeslug false /namespace [ (adobe) (indesign) (4.0) ] /omitplacedbitmaps false /omitplacedeps false /omitplacedpdf false /simulateoverprint /legacy >> << /addbleedmarks false /addcolorbars false /addcropmarks false /addpageinfo false /addregmarks false /convertcolors /converttocmyk /destinationprofilename () /destinationprofileselector /documentcmyk /downsample16bitimages true /flattenerpreset << /presetselector /mediumresolution >> /formelements false /generatestructure false /includebookmarks false /includehyperlinks false /includeinteractive false /includelayers false /includeprofiles false /multimediahandling /useobjectsettings /namespace [ (adobe) (creativesuite) (2.0) ] /pdfxoutputintentprofileselector /documentcmyk /preserveediting true /untaggedcmykhandling /leaveuntagged /untaggedrgbhandling /usedocumentprofile /usedocumentbleed false >> ] >> setdistillerparams << /hwresolution [2400 2400] /pagesize [612.000 792.000] >> setpagedevice microsoft word numero_41_art_35.docx f. berto et alii, frattura ed integrità strutturale, 41 (2017) 260-268; doi: 10.3221/igf-esis.41.35 260 focused on crack tip fields review of the influence of non-singular higher order terms on the stress field of thin welded lap joints and small inclined cracks in plates f. berto norwegian university of science and technology ntnu, department of mechanical and industrial engineering, trondheim, 7491, norway filippo.berto@ntnu.no m.r. ayatollahi fatigue and fracture lab., centre of excellence in experimental solid mechanic and dynamics, school of mechanical engineering, iran university of science and technology, narmak, 16846, tehran, iran. s. vantadori, a. carpinteri dept. of civil-environmental engineering and architecture, university of parma, parco area delle scienze 181/a 43124 parma, italy abstract. in stress analysis of cracked plates, alongside the stress intensity factor which quantifies the singular stress component perpendicular to the crack plane, the role played in crack growth by the constant term parallel to the crack plane, called the t-stress, has been widely investigated by many researchers. there are, however, cases of practical interest where the influence on the stress field of the higher order terms in the series expansion for the crack tip stress field, is not negligible. the main aim of the present investigation is to present and apply a set of equations able to describe more accurately the stress components for those cases where the mode i and mode ii stress intensity factors used in combination with the t-stress are unable to characterise with sufficient precision the complete stress field ahead the crack tip. the starting point is represented by the williams’ solution (williams, 1957) where stresses as expressed in terms of a power series. an example is investigated of a thin-thickness welded lap joint characterized by various joint width to thickness ratios, in the range of d/t ranging from 0.5 to 5. the present paper indicates that the local stresses as well as the strain energy averaged over a control volume which embraces the slip tip, can be evaluated with satisfactory precision only by taking into account a further four terms besides ki, kii and t-stress. keywords. crack; stress intensity factors; t-stress; higher order terms; strain energy. citation: berto, f., ayatollahi, m.r., vantadori, s., carpinteri, a., review of the influence of non-singular higher order terms on the stress field of thin welded lap joints and small inclined cracks in plates, frattura ed integrità strutturale, 41 (2017) 260-268. received: 28.02.2017 accepted: 03.05.2017 published: 01.07.2017 copyright: © 2017 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. f. berto et alii, frattura ed integrità strutturale, 41 (2017) 260-268; doi: 10.3221/igf-esis.41.35 261 introduction s a part of a more general two-dimensional study on sharp v-notches in plates, the specific case of a zero angle vnotch, or crack, was carried out by williams [1] to supplement previous results by inglis (1913), griffith (1921), and westergaard (1939). for the crack case williams demonstrated that the stress function can be expressed as a series expansion, being the coefficients of each term undetermined and depending on the loading conditions. williams also underlined that for practical cases when the plate has finite dimensions, higher order eigenfunctions should be used to determine a solution in the large. the stress associated with the symmetric and skew-symmetric singular terms in combination with the constant term were finally presented by williams, neglecting the other terms proportional to r1/2, r, r3/2. today, after larsson and carlsson and rice, the constant stress term is commonly called t-stress [2, 3]. by using a boundary collocation technique, a procedure to determine mode i and mode ii stress intensity factors was proposed by gross and mendelson [4]. the collocation technique was later used also by carpenter [5] to determine the coefficients associated both to singular and non-singular stress terms. carpenter presented some examples where the main aim was to handle the complex coefficients of higher order terms. however, after williams up to now, classical theories of fracture mechanics generally assume that the near-crack-tip stresses can be characterized by the stress intensity factors but extensive studies in the last two decades have shown that also the t-stress is important for describing the states of stress and strain near the crack tip [6-10]. the role of the t-stress in brittle fracture for linear elastic materials has been emphasized by ayatollahi et al. [6] who proposed a modified erdogan-sih’s criterion (erdogan, sih, 1963). their generalized maximum tensile stress criterion is based on the mode i and ii stress intensity factors, ki and kii, the t-stress and a fracture process zone parameter, rc.. several closed form solutions of t-stress in plane elasticity crack problems in an infinite plate are investigated using the complex potential theory [7]. a rigorous derivation for t-stress in line crack problem is presented by chen et al. (2010). similar to the edge crack case, this paper provides the t-stress dependence on loading with the dirac delta function property [11].dealing with mixed mode loading a particular weight function method is used to determine the stress intensity factors (sifs) and t -stresses for offset double edge cracked plates under mixed mode loading [12]. beyond the t-stress, the problem related to the different role played by the higher order terms remain open. ramesh et al. [13, 14] presented an over-deterministic least squares technique to evaluate the mixed-mode multi-parameter stress field by photoelasticity underlining the fact that the use of a multi-parametric representation is not just an a academic curiosity but a necessity in some cases of engineering interest. this fact is underlined also by ayatollahi and nejati [15] who provided a specific algorithm for a fast determinations of the unknown parameters. a method for the direct determination of sif and higher order terms by a hybrid crack element has been developed in the past also by xiao et al. [16] proving the versatility and accuracy of the element for pure mode i problems and for mode ii and mixed mode cracks. an overview of a hybrid crack element and determination of its complete displacement field has been carried out by xiao and karihaloo [17]. a novel mathematical model of the stresses around the tip of a fatigue crack, which includes the t-stress and considers the effects of plasticity through an analysis of their shielding effects on the applied elastic field was developed by christopher et al. [8, 9]. the ability of the model to characterize plasticity-induced effects of cyclic loading and on the elastic stress fields was demonstrated using full field photoelasticity. the effects due to overloads have been also discussed [10]. the model can be seen as a modified linear elastic approach, to be applied outside the zone where nonlinear effects are prevailing. two logarithmic terms are added to the williams’ solution and three new stress intensity factors kf, kr and ks are proposed to quantify shielding effects ahead of the crack tip and on its back. the present authors have been recently interested in the fatigue strength of welded lap joints and they have paid particular attention to thin plates characterized by a thickness equal or lower than 5 mm [18, 19]. in that study, the tstress was considered together with ki and kii to describe the stress field. the closed form expressions involving only these three parameters was found to be inadequate to accurately describe the actual stress fields in thin welded lap joints as well as the mean value of the strain energy density on a control volume embracing the slit tip. decreasing the plate thickness of the welded joint, the zone controlled by the first order terms became smaller than the characteristic control volume of the welded material. the effect of the higher order terms will be object of the present contribution and a demarcation line between linear elastic and elastic-plastic analyses will be drawn on the basis of the local strain energy density creating also a bridging with the recent model proposed by christopher et al. [8, 9]. a f. berto et alii, frattura ed integrità strutturale, 41 (2017) 260-268; doi: 10.3221/igf-esis.41.35 262 analytical background ollowing williams’ approach a generic term of the stress function expressed as a series expansion can be written in the following form [1]:                                             2/ 2 1 χ( r,θ) r sin 1 θ sin 1 θ cos 1 θ cos 1 θ 2 2 2 2 2 i j n n n n nn a a n (1) by explicitly writing the terms of the series (1), the stress function becomes:                                                                 2 23/2 2 1 2 3 3 5/2 4 5 23 6 7 7/2 8 9 4 θ θ θ ( r, ) r sin sin 3 cos 2 r sinθ 3 2 2 2 4 θ θ 5 r 3 2 cosθ sin cos cos θ 5 2 2 2 4 r sinθ sinθ 3 cosθ 3 3 3 7 3 7 r sin θ sin θ cos θ cos θ 2 7 2 2 2 a a a a a a a a a                          24 10 11 9/2 12 13 2r sinθ sin 2θ 1 2 cos 2θ 5 5 9 5 9 r sin θ sin θ cos θ cos θ 2 9 2 2 2 a a a a (2) here a1, a2, a3, a4, etc. are the undetermined parameters whereas  is the angle shown in fig. 1 (with . as well known, there is a precise link between the three first coefficients of eq. (2) which control the stress intensity factors (ki kii) and the t-stress acconding to the expressions:    1 2 3/ 2 / 2 / 4i iia k a k a t (3) in the contribution by williams (1957), although fundamental and pioneering, some typos were present where higher order terms were presented by splitting into even and odd parts the initial stress function (ibid. eqs 8 and 9). in order to avoid misunderstandings, all stress components are determined here by directly using the stress function approach, according to which:                                2 2 2 2 1 1 r,ψ r,ψ 1 1 r,ψ rr r r r r rr r r (4) the generic n-th terms of the stress distributions are then as follows:                                                             /2 1 2 2r,ψ,n ( 2)sin ( 2)cos 4 2 2 2 2 6 sin 6 cos 2 2 n rr i j i j n n n r a n a n n n a n a n (5a) f f. berto et alii, frattura ed integrità strutturale, 41 (2017) 260-268; doi: 10.3221/igf-esis.41.35 263                                                             /2 1 2 2r,ψ,n ( 2)sin ( 2)sin 4 2 2 2 2 2 cos 2 cos 2 2 n i i j j n n n r a n a n n n a n a n (5b)                                                              /2 1 2 2r,ψ,n ( 2)cos ( 2)cos 4 2 2 2 2 2 sin 2 sin 2 2 n r i i j j n n n r a n a n n n a n a n (5c) for n=1 the subscripts are i=1 and j=2; for n=2 we have here only j=3 (because the correspondent terms containing ai disappear). finally, for n>2, the subscripts are i=2n  2 and j=2n1. eqs. 5a-c are given also in [13, 14] where they are splitted into symmetric and skew-symmetric terms. analogous equations are given also in [15-17] with inclusion of the terms linked to the rigid translation of the slit tip and the rigid body rotation with respect to the same point. by considering the first 13 parameters (a1,…, a13) of the williams’ series, the stress field can be explicitly derived:                                        2 1 1 2 2 31/2 1/2 4 4 5 5 2 6 7 7 3/2 8 8 9 9 ψ ψ1 3 3 cos ψ 5 cos 3 sin ψ 5 sin 4 cosψ 2 2 2 24 r ψ ψr 5 5 9 cos 3 cos ψ 9 sin 15 sin ψ 4 2 2 2 2 8 cosψ sinψ 2 cosψ 6 cos 3ψ r 3 7 3 7 5 cos ψ 15 cos ψ 5 sin ψ 35 sin ψ 4 2 2 2 2 rr a a a a a a a a a r a a a a a a a                2 10 11 5/2 12 12 13 13 r 6 sin 4ψ 12 cos 4ψ r 5 9 5 9 7 cos ψ 35 cos ψ 7 sin ψ 63 sin ψ 4 2 2 2 2 a a a a a a (6a)                                                     3 2 2 1 2 31/2 3 3 1/2 4 4 5 5 3 2 6 7 3/2 8 8 9 ψ ψ ψ1 cos 3 sin cos 4 sinψ 2 2 2r ψ ψ ψ15 15 5 r 9 cos 6 cosψ cos sin sin ψ 2 2 4 2 4 2 r 8 sinψ 24 sinψ cosψ r 3 7 3 35 cos ψ 15 cos ψ 35 sin ψ 4 2 2 2 a a a a a a a a a a a a                          9 2 2 22 10 11 11 5/2 12 12 13 13 7 35 sin ψ 2 r 24 sinψ sin 2ψ 24 sinψ 48 sinψ cos 2ψ r 5 9 5 9 63 cos ψ 35 cos ψ 63 sin ψ 63 sin ψ 4 2 2 2 2 a a a a a a a a (6b) along the bisector line the stress components turn out to be: f. berto et alii, frattura ed integrità strutturale, 41 (2017) 260-268; doi: 10.3221/igf-esis.41.35 264         1/2 3/2 2 5/21 3 4 7 8 11 121/2 4 3r 8 r 5 r 12 r 7 rr rr a a a a a a a (7a)       1/2 3/2 5/21 4 8 121/2 3r 5 r 7 r r a a a a (7b)      1/2 3/2 5/22 5 9 131/2 3r 5 r 7 r r r a a a a (7c) along the direction  , the unique non vanishing stress component is the radial stressrr:         1/2 3/2 2 5/22 3 5 7 9 11 131/2 2 4 6r 8 r 10 r 12 r 14 r r rr a a a a a a a (8) it is important to underline that, for the welded lap joint shown in fig. 1, the polar angle  providing the maximum tangential stress  and the corresponding provisional crack propagation angle is close to /2 due to the high contribution due to mode ii in this kind of geometry. in the light of this consideration the expression of the stress components in that direction are of particular interest. along the direction  we have:             1/2 1/2 3/24 5 81 2 1/2 1/2 3/2 2 5/2 5/29 1312 11 3 3 53 r r r 2 2 2 2 2 22 2r 2 2r 15 3521 r 12 r r r 2 2 2 2 2 2 rr a a aa a a aa a (9a)               1/2 1/24 51 2 3 61/2 1/2 3/2 3/2 2 5/2 5/28 9 1312 11 9 153 4 r r 8 2 2 2 22 2r 2 2r 25 35 6349 r r 24 r r r 2 2 2 2 2 2 2 2 a aa a a ra a a aa a (9b)              1/2 1/2 3/24 5 81 2 71/2 1/2 3/2 2 5/2 5/29 1312 10 3 9 15 r r 8 r 2 2 2 2 2 22 2r 2 2r 25 4935 r 12 r r r 2 2 2 2 2 2 r a a aa a ra a aa a (9c) stress field at the slit tip of a thin welded lap joint he geometry of lap joint subjected to tensile-shear loading is shown in fig. 1. the initial value of the thickness is t=1 mm, whereas the ratio d/t ranges from 0.5 to 5.0. the applied load f results in a membrane nominal stress f/t = 10 mpa. on the slit edge side of point o, the membrane stress (10 mpa) and the bending stress (30 mpa) are superimposed, resulting in a total nominal stress of 40 mpa. parameters a1, a2, a3 are derived directly from ki, kii and the t-stress respectively by means of eq. (3). the original values of ki, kii and t stress match those reported in lazzarin et al. (2009). the parameters a4, a5, a7 are set by imposing the condition that numerical values of the stress components rr, r coincide with theoretical prediction along the slit ligament far from the tip. this distance varied as a function of the ratio d/t. dealing with the ratio d/t=1, a4 and a5 have been directly determined along the bisector line by a condition on andr at a distance r=0.1 mm and r=0.4 mm, respectively. the parameter a7 has been then derived by a condition t f. berto et alii, frattura ed integrità strutturale, 41 (2017) 260-268; doi: 10.3221/igf-esis.41.35 265 on  at r = 0.4 mm and finally the parameter a6 has been obtained by a condition on  at r = 0.1 mm along the direction . stress components along the slit ligament as determined from the finite element model with t=1 mm and d/t=1 are shown in fig. 2. the stress components are plotted along the direction =0° over a distance less than or equal to 1.0 mm. the fe results are compared with eqs (7a-c) along the slit bisector line considering the first seven parameters, from a1 to a7, see tab. 1. the plot of rr along the direction =180° is also documented as well as the theoretical stress fields limited figure 1. geometry of the welded lap joint to ki, kii and the t-stress, which are reported for comparison. the figure shows that the agreement between analytical frame and numerical results is satisfactory only by using of a multi-parameter stress field equation. it is important to note that the parameters a5 and a7 in eq.( 8) for the radial stress component at =180° were determined by involving parameters set in the other directions as explained above. in fig. 3 the stress components are plotted along the direction =90° where the only parameter set at =90° is a6 which is obtained by imposing a condition on . the agreement between finite element results and theoretical stresses is very good also for the stress components not directly involved in the determination of the parameters a4, a5 a6 and a7. a slightly larger discrepancy between numerical and theoretical results is shown in fig. 4 for the direction 90°. in this case the stress components present an intensity lower than in the other directions. the improvement introduced by considering the higher order terms with respect to the solution based on ki, kii and the t-stress is evident. d/t t= 1 a1 mpa mm0.5 a2 mpa mm0.5 a3 mpa a4 mpa mm-0.5 a5 mpa mm-0.5 a6 mpa mm-1 a7 mpa mm-1 1 1.73 4.10 4.87 4.02 1.00 3.50 1.02 ki=4.35 kii= 10.28 t=19.5 table 1. parameters of the stress field, overlap joints influence on strain energy density of higher order terms he sed approach was later extended to thin welded lap joints (lazzarin et al., 2009) considering two values of the control radius, r0 = 0.15 and r0 = 0.28 mm. together with the sed values directly determined from the fe models, that paper documented also the sed values determined on the basis of the mode 1 and mode 2 nsifs, ki and kii, the t-stress which plays an essential role in the case of thin welded joints. the deviation values k ,k ,t* fe fei iiδ  ( ) /w w w , showed that for the sheet thickness t=5 mm, the maximum deviation with respect to the fe results was 3.6% for r0=0.15 mm and 3.1% for r0=0.28 mm (lazzarin et al., 2009). when t = 1 mm, the deviation increased up to 25.0% for r0=0.28 mm and up to 9.6% for r0=0.15 mm (see tab. 3). this means that in the presence of a sheet thickness t ≤ 1 mm and r0=0.28 mm, the sed depends not only ki, kii and t-stress but also on other nonsingular stress components. the averaged sed can be easily determined directly from the fe model. alternatively, a complex expression based on eq (6a-c), involving the first seven terms has been derived and reported herein for sake of brevity. a comparison between the sed from fe models and that obtained considering the parameters a1, a2, …a7 already reported in tab. 1, is shown in tab. 2. the deviation values hot fe feδ ( ) /w w w is less than 3%. t t d t l > 100 d t=1 ft o f   r o  x y slit 0 mm r0 f. berto et alii, frattura ed integrità strutturale, 41 (2017) 260-268; doi: 10.3221/igf-esis.41.35 266 r0=0.28mm, =0 mm t=1mm few (10 3) w hot (103)  *t,k,k iiiw (10 3)  (mj/m3) (mj/m3) (%) (mj/m3) (%) d/t=0.5 1.412 1.453 2.9 1.765 25.0 1 1.208 1.214 0.5 1.509 25.0 3 1.181 1.193 1.0 1.443 22.2 table 2. mean values of the strain energy density over the control volumes for welded lap joints, with f/(t1)=10 mpa; values based on t* determined on the ligament, close to the point of singularity, r  0.03 mm figure 2: stress field along the ligament line for the case d/t=1 and t=1 mm. figure 3: stress field along the direction =90° for the case d/t=1. 0 1 10 100 1000 0.001 0.010 0.100 1.000 r [mm] t=1mm d/t=1 = 0° and 180° s tr es s co m p o n en ts [ m p a]  (= 0°) rr (= 0°) r (= 0°) fe results rr (= 180°) theoretical solution considering the parameters a1,…, a7 theoretical solution considering the parameters ki, kii and t-stress 1 10 100 1000 0.001 0.010 0.100 1.000r [mm] s tr es s co m p o n en ts [ m p a]  rr r t=1mm d/t=1 = +90° theoretical solution considering the parameters a1,…, a7 theoretical solution considering the parameters ki, kii and t-stress fe results range of valitidy of ki, kii, t-stress based solution f. berto et alii, frattura ed integrità strutturale, 41 (2017) 260-268; doi: 10.3221/igf-esis.41.35 267 figure 4: stress field along the direction =-90° for the case d/t=1.  (mpa) ew x 10 3 (mj/m3) pw x 10 3 (mj/m3) 10 1.120 1.120 20 4.481 4.485 40 17.93 18.07 80 71.72 79.68 110 135.5 171.8 table 3: mean values of sed as determined from linear elastic and elasto-plastic analyses (control volume r0=0.28 mm). limitations to the linear elastic approach et us assume for the material the ramberg-osgood law, according to which the uniaxial tensile strain  is related to the uniaxial stress  according to the expression:           ' ' n e k (10) where 1  n’  . the analyses were carried out under plane strain conditions by introducing into the stress-strain curve e, k’ and n’=6.66. tab. 3 summarizes the values of the sed parameter as a function of the applied t is interesting to observe that for values of < 40 mpa the elastic and elastic-plastic values are close each other. when mpa,that is a typical value for this kind of joints at 105 cycles to failure, the sed under elastic conditions is significantly different from the elastic-plastic case. the different role played by plasticity at different number of cycles can also be used as justification of the different slope shown by thin lap joints under shear loading and welded joints under tensile loading. 1 10 100 1000 0.001 0.010 0.100 1.000r [mm] t=1mm d/t=1 = 90° s tr es s co m p on en ts [ m p a]  rr r fe results theoretical solution considering the parameters a1,…, a7 theoretical solution considering the parameters ki, kii and t-stress l f. berto et alii, frattura ed integrità strutturale, 41 (2017) 260-268; doi: 10.3221/igf-esis.41.35 268 conclusions he present investigation is aimed to present and apply a useful set of equations able to describe accurately the stress components also in those cases where the mode i and mode ii stress intensity factors used in combination with the t-stress, fail to describe the complete stress field ahead the slit tip. a practical example of a thin-thickness welded lap joint characterized by different jointing face width to thickness ratio, ranging d/t from 0.5 to 3, is investigated. the stress field and the strain energy averaged over a control volume can be evaluated with satisfactory precision only taking into account further four other terms besides ki, kii and t. references [1] williams, m.l., on the stress at the base of a stationary crack, j. appl. mech., trans. asme, 24 (1957) 109-114. [2] rice, j.r., limitations to the small scale yielding approximation for crack tip plasticity, j. mech. phys. solids, 22 (1974) 17-26. [3] larsson, s.g., carlsson, a.j., influence of nonsingular stress terms and specimen geometry on small scale yielding at crack tips in elastic-plastic materials, j. mech. phys. solids, 21 (1973) 263–277. [4] gross, r., mendelson, a., plane elastostatic analisys of v-notched plates, int. j. fract. mech., 8 (1972) 267-276. [5] carpenter, w.c., the eigenvector solution for a general corner of finite opening crack with further studies on the collocation procedure, int. j. fract., 27 (1985) 63-74. [6] ayatollahi, m.r., pavier, m.j., smith, d.j., determination of t-stress from finite element analysis for mode i and mixed mode i/ii loading, int. j. fract., 91 (1998) 283–298. [7] chen, y.z., closed form solutions of t-stress in plane elasticity crack problems, int. j. solids struct., 37(11) (2000) 1629–1637. [8] fett, t., stress intensity factors and t-stress for single and double-edge-cracked circular disks under mixed boundary conditions, engng. fract. mech., 69 (2002) 69-83. [9] christopher, c.j., james, m.n., patterson, e.a., tee, k.f., towards a new model of crack tip stress fields, int. j. fract., 148 (2007) 361-371. [10] colombo, c., du, y., james, m.n., patterson, e.a., vergani l., on crack tip shielding due to plasticity-induced closure during an overload, fatigue fract. eng. mater. struct., 33(12) (2010) 766–777. [11] chen, y.z., lin, x.y., wang, z.x., a rigorous derivation for t-stress in line crack problem, eng. fract. mech., 77 (2010) 753–757. [12] ramesh, k., gupta, s., srivastava, a.k., equivalence of multi-parameter stress field equations in fracture mechanics, int. j. fract., 79 (1996) r37-r41. [13] ramesh, k., gupta, s., kelkar, a.a., evaluation of stress field parameters in fracture mechanics by photoelasticityrevisited, engng fract. mech., 56(1) (1997) 25-45. [14] ayatollahi mr, nejati m. an over-deterministic method for calculation of coefficients of crack tip asymptotic field from finite element analysis fatigue fract. engng mater. struct., 34 (3) (2011) 159–176. [15] xiao, q.z., karihaloo, b.l., liu, x.y., direct determination of sif and higher order terms of mixed mode cracks by a hybrid crack element, int. j. fract., 125(3-4) (2004) 207–225. [16] xiao, q.z., karihaloo, b.l., an overview of a hybrid crack element and determination of its complete displacement field, eng. fract. mech., 74 (2007) 1107-1117. [17] lazzarin, p., berto, f., radaj, d., fatigue-relevant stress field parameters of welded lap joints: pointed slit tip compared with keyhole notch. fatigue fract. eng. mater. struct., 32 (2009) 713–735. [18] berto, f. and lazzarin, p. 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/hrv (za stvaranje adobe pdf dokumenata najpogodnijih za visokokvalitetni ispis prije tiskanja koristite ove postavke. stvoreni pdf dokumenti mogu se otvoriti acrobat i adobe reader 5.0 i kasnijim verzijama.) /hun 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can be opened with acrobat and adobe reader 5.0 and later.) >> /namespace [ (adobe) (common) (1.0) ] /othernamespaces [ << /asreaderspreads false /cropimagestoframes true /errorcontrol /warnandcontinue /flattenerignorespreadoverrides false /includeguidesgrids false /includenonprinting false /includeslug false /namespace [ (adobe) (indesign) (4.0) ] /omitplacedbitmaps false /omitplacedeps false /omitplacedpdf false /simulateoverprint /legacy >> << /addbleedmarks false /addcolorbars false /addcropmarks false /addpageinfo false /addregmarks false /convertcolors /converttocmyk /destinationprofilename () /destinationprofileselector /documentcmyk /downsample16bitimages true /flattenerpreset << /presetselector /mediumresolution >> /formelements false /generatestructure false /includebookmarks false /includehyperlinks false /includeinteractive false /includelayers false /includeprofiles false /multimediahandling /useobjectsettings /namespace [ (adobe) (creativesuite) (2.0) ] /pdfxoutputintentprofileselector /documentcmyk /preserveediting true /untaggedcmykhandling /leaveuntagged /untaggedrgbhandling /usedocumentprofile /usedocumentbleed false >> ] >> setdistillerparams << /hwresolution [2400 2400] /pagesize [612.000 792.000] >> setpagedevice shot peening processes to obtain nanocrystalline surfaces in metal alloys: j. toribio et alii, frattura ed integrità strutturale, 41 (2017) 62-65; doi: 10.3221/igf-esis.41.09 62 focused on multiaxial fatigue influence of crack micro-roughness on the plasticity-induced fatigue propagation in high strength steel j. toribio, j.c. matos, b. gonzález fracture and structural integrity research group (fsirg), university of salamanca (usal) e.p.s., campus viriato, avda. requejo 33, 49022 zamora, spain toribio@usal.es, jcmatos@usal.es, bgonzalez@usal.es abstract. this article deals with the locally multiaxial fatigue behaviour of high strength steel. to this end, the influence of the cracking path deflections (at the micro level) on the plasticity-induced fatigue crack growth is analyzed. with regard to this, a modelling by means of the finite element method was performed for a given stress intensity factor in the paris regime, considering the existence of micro-roughness in the crack path (local micro-deflections with distinct micro-angles as a function of the microstructure of the material). the numerical results allow one to obtain the fatigue crack propagation rate and compare it with that for the same material in the absence of microroughness (with no micro-crack deflections, i.e., uniaxial fatigue behaviour). keywords. crack tip; micro-roughness; crack deflection; plasticity-induced fatigue crack propagation; finite element method. citation: toribio, j., matos, j.c., gonzález, b., influence of crack micro-roughness on the plasticity-induced fatigue propagation in high strength steel, frattura ed integrità strutturale, 41 (2017) 62-65. received: 28.02.2017 accepted: 15.04.2017 published: 01.07.2017 copyright: © 2017 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. introduction atigue cracks exhibit surface micro-roughness caused by material microstructure, e.g., pearlitic steel shows continuous deflections in the fatigue crack path [1]. the non-linear crack configuration should be taken into account in the matter of crack-morphological aspects in fracture mechanics [2], since variations in crack deflection features influence considerably the fatigue crack propagation rates and threshold stress intensity factor range [3]. elasticplastic finite element simulations of growing fatigue cracks are used to study the plastic crack advance and the so-called crack closure phenomenon. with regard to plastic crack advance, the laird-smith mechanism of propagation by cyclic blunting and re-sharpening, which transfers material from the crack tip towards its flanks, is visualized in [4]. with this sort of modeling procedure, the rate per cycle reproduced common trends of the fatigue cracking dependence on loading range and overload [5]. paris-like equations obtained from the numerical modeling of plastic crack advance showed good agreement with experimental results [6]. in the matter of plasticity-induced fatigue crack closure, a strong controversy still does exist, with researchers raising doubts about its mere existence [4,5], and others obtaining it as a numerical result [7], although the total length of closed crack at minimum load in plane strain is shown to be a small fraction of the total crack length [8]. f j. toribio et alii, frattura ed integrità strutturale, 41 (2017) 62-65; doi: 10.3221/igf-esis.41.09 63 numerical procedure or the study of fatigue propagation by plastic crack advance, a numerical simulation by the finite element method (fem) under small scale yielding (ssy) was performed using the msc.marc software (nonlinear finite element code). material was characterized as elastic–perfectly-plastic and the von mises yield criterion was employed to define the plastic zone in the vicinity of the crack tip. large strains and large geometry changes were used with an updated lagrangian formulation. material properties (young’s modulus e=200gpa, yield strength σy=600mpa and poisson coefficient ν=0.3) were those associated with a typical high-strength steel. the geometry used in the computations is a symmetric double-edge-cracked panel under remote tension fatigue (fig. 1). the undeformed crack was a parallel-flanks slot, where the kink length l0 (representing 0.0012 times the total crack length) is deflected an angle α0 (fig. 2) and exhibits a semicircular shape (smooth blunting [9]) with b0=5µm, i.e., 0.055l0. fournode isoparametric quadrilateral elements (for plane strain applications) were used. finally, a convergence study was performed to determine the optimal finite element mesh size and the most adequate number of steps required in the computations. (a) (b) figure 1: finite element mesh: (a) general view; (b) crack tip. figure 2: scheme and dimensions of the deflected crack kink. the key variable analyzed in this research work is the deflection angle of the kink in relation to the main crack. the four values α0=0, 15, 30 and 45º were used. the stress intensity factor (sif) range used in the numerical procedure was δk=25mpam1/2 (associated with the paris regime of fatigue crack propagation). numerical results ig. 3 shows the cumulative equivalent plastic strain in the deformed geometry of the cracked solid with the deflected crack kink after the main crack. the initial geometry of the solid before loading (initial crack profile) is also shown. results are obtained after applying 20 loading cycles (fatigue) with δk=25mpam1/2. it is observed how the crack, independently of the deflection angle, tends to propagate in mode i when subjected to remote mode i (opening) tensile loading. in addition, the distribution of cumulative equivalent plastic strain becomes more non-symmetric and exhibits more elevated values as the kink deflection angle increases. the crack deflection provokes a retardation effect in fatigue crack growth in global mode i, this effect being more pronounced for elevated deflection angle, as shown in fig. 4. l α 0 0 b 0 f f j. toribio et alii, frattura ed integrità strutturale, 41 (2017) 62-65; doi: 10.3221/igf-esis.41.09 64 (a) (b) (c) (d) figure 3: cumulative equivalent plastic strain for δk=25mpam1/2: (a) α0=0º; (b) α0=15º; (c) α0=30º; (d) α0=45º. -1.556e-004 1.374e+000 2.748e+000 4.121e+000 5.495e+000 6.869e+000 8.243e+000 9.617e+000 1.099e+001 1.236e+001 1.374e+001 j. toribio et alii, frattura ed integrità strutturale, 41 (2017) 62-65; doi: 10.3221/igf-esis.41.09 65 0.0 5.0 10-8 1.0 10-7 1.5 10-7 2.0 10-7 2.5 10-7 3.0 10-7 3.5 10-7 0 15 30 45 da /d n ( m /c ic lo ) α 0 (º) figure 4: fatigue crack growth rate as a function of the deflection angle of the kink. conclusions racks with a deflected kink in a plate subjected to remote tensile loading exhibit plastic crack advance in mode i with retarded fatigue crack growth when compared with a fully straight crack (with no kink). the increment of the crack deflection angle increases the retardation effect. acknowledgement he authors wish to acknowledge the financial support provided by the following spanish institutions: micyt (grant mat2002-01831), mec (grant bia2005-08965), micinn (grant bia2008-06810), mineco (grant bia2011-27870) and jcyl (grants sa067a05, sa111a07 and sa039a08). references [1] toribio, j., matos, j.c., gonzález, b., a macroand micro-approach to the anisotropic fatigue behaviour of hot-rolled and cold-drawn pearlitic steel, eng. fract. mech., 123 (2014) 70–76. doi: 10.1016/j.engfracmech.2014.02.004. [2] kitagawa, h., yuuki, r., ohira, t., crack-morphological aspects in fracture mechanics, eng. fract. mech., 7 (1975) 515–529. doi: 10.1016/0013-7944(75)90052-1. [3] suresh, s., crack deflection: implications for the growth of long and short fatigue cracks, metall. mater. trans. a, 14 (1983) 2375–2385. doi: 10.1007/bf02663313. [4] toribio, j., kharin, v., simulations of fatigue crack growth by blunting–re-sharpening: plasticity induced crack closure vs. alternative controlling variables, int. j. fatigue, 50 (2013) 72–82. doi: 10.1016/j.ijfatigue.2012.02.019. [5] toribio, j., kharin, v., large crack tip deformations and plastic crack advance during fatigue, mater. lett., 61 (2007) 964–967. doi: 10.1016/j.matlet.2006.06.025. [6] toribio, j., kharin, v., ayaso, f.j., gonzález, b., matos, j.c., vergara, d., lorenzo, m., numerical and experimental analyses of the plasticity-induced fatigue crack growth in high-strength steels, constr. build. mater., 25 (2011) 3935– 3940. doi: 10.1016/j.conbuildmat.2011.04.025. [7] tvergaard, v., on fatigue crack growth in ductile materials by crack–tip blunting, j. mech. phys. solids, 52 (2004) 2149–2166. doi: 10.1016/j.jmps.2004.02.007. [8] mcclung, r.c., thacker, b.h., roy, s., finite element visualization of fatigue crack closure in plane stress and plane strain, int. j. fract., 50 (1991) 27–49. doi: 10.1007/bf00035167. [9] handerhan, k.j., garrison jr., w.m., a study of crack tip blunting and the influence of blunting behavior on the fracture toughness of ultra high strength steels, acta metall. mater., 40 (1992) 1337–1355. doi: 10.1016/09567151(92)90435-h. c t da /d n (m /c yc le ) microsoft word numero_41_art_2_.docx g. meneghetti et alii, frattura ed integrità strutturale, 41 (2017) 8-15; doi: 10.3221/igf-esis.41.02 8 focused on multiaxial fatigue crack initiation life in notched ti-6al-4v titanium bars under uniaxial and multiaxial fatigue: synthesis based on the averaged strain energy density approach giovanni meneghetti, alberto campagnolo university of padova, department of industrial engineering, padova (italy) giovanni.meneghetti@unipd.it alberto.campagnolo@unipd.it filippo berto university of padova, department of management and engineering, vicenza (italy) ntnu, department of engineering design and materials, trondheim, (norway) berto@gest.unipd.it keisuke tanaka meijo university, department of mechanical engineering, nagoya (japan) ktanaka@meijo-u.ac.jp abstract. the fatigue behaviour of circumferentially notched specimens made of titanium alloy, ti-6al-4v, has been analysed. to investigate the notch effect on the fatigue strength, pure bending, pure torsion and multiaxial bending-torsion fatigue tests have been carried out on specimens characterized by two different root radii, namely 0.1 and 4 mm. crack nucleation and subsequent propagation have been accurately monitored by using the direct current potential drop (dcpd) technique. based on the results obtained from the potential drop technique, the crack initiation life has been defined in correspondence of a relative potential drop increase v/v0 equal to 1%, and it has been used as failure criterion. doing so, the effect of extrinsic mechanisms operating during crack propagation phase, such as sliding contact, friction and meshing between fracture surfaces, is expected to be reduced. the experimental fatigue test results have been re-analysed by using the local strain energy density (sed) averaged over a structural volume having radius r0 and surrounding the notch tip. finally, the use of the local strain energy density parameter allowed us to properly correlate the crack initiation life of ti-6al-4v notched specimens, despite the different notch geometries and loading conditions involved in the tests. keywords. titanium alloy; fatigue notch effect; potential drop method; crack initiation; averaged sed. citation: meneghetti, g., campagnolo, a., berto, f., tanaka, k., crack initiation life in notched ti-6al-4v titanium bars under uniaxial and multiaxial fatigue: synthesis based on the averaged strain energy density approach, frattura ed integrità strutturale, 41 (2017) 8-15. received: 10.03.2017 accepted: 15.04.2017 published: 01.07.2017 copyright: © 2017 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. g. meneghetti et alii, frattura ed integrità strutturale, 41 (2017) 8-15; doi: 10.3221/igf-esis.41.02 9 introduction n the recent literature [1–6], an unexpected notch-strengthening phenomenon was found in circumferentially notched specimens under pure torsion or combined tension-torsion multiaxial fatigue loadings. the fatigue life of notched bars resulted longer than that of smooth ones, the higher the stress concentration factor under the same load amplitude. this notch-strengthening effect has been observed by fatigue testing cylindrical specimens made of austenitic stainless steels [1–3], nicrmo steel [4], pure titanium [5], but it was not found in carbon steels [3,7,8]. as recently discussed by tanaka [6], this effect can be explained on the basis of different morphologies of the fracture surfaces: in circumferentially notched bars under torsion fatigue loadings, factory-roof type fracture surfaces have been found; consequently, the sliding contact and the meshing between crack surfaces cause the retardation of crack propagation [9–13]. in this context, the fatigue behaviour of circumferentially notched specimens made of titanium grade 5 alloy, ti-6al-4v, has been analysed in the present contribution. to investigate the effect of the notch geometry and the loading condition on the fatigue strength of the titanium alloy, pure bending, pure torsion and multiaxial bending-torsion fatigue tests have been carried out on specimens characterised by two different notch root radii , namely 0.1 and 4 mm. in all cases, the nominal load ratio r has been kept constant and equal to -1. crack initiation and subsequent propagation have been accurately monitored by using the matelect® dcm-2 direct current potential drop (dcpd) method, which allows to define the crack initiation life in correspondence of an increase of the electrical potential drop. the experimental fatigue results have been re-analysed by using the local strain energy density (sed) averaged over a structural volume having radius r0 surrounding the notch tip, as proposed by lazzarin and zambardi [14] and lazzarin and berto [15]. according to a recent contribution [16], to exclude all extrinsic mechanisms acting during the fatigue crack propagation phase, such as sliding contact, friction and meshing between mating crack surfaces, the crack initiation life has been considered. for the sake of brevity and the experimental fatigue tests being ongoing, in this contribution the preliminary experimental fatigue results only relevant to pure bending loading will be discussed and reanalyzed. experimental fatigue tests he geometry of the fatigue tested bars, made of ti-6al-4v titanium alloy, is reported in fig. 1, along with details of the circumferential notches characterized by different values of the notch tip radius . figure 1: geometry of the circumferentially notched specimens (dimensions are in mm). the experimental fatigue tests have been carried out by means of a flexible test bench: with the experimental arrangement shown in fig. 2a it has been possible to execute fatigue tests under pure bending, pure torsion and combined bendingtorsion loadings by properly setting the external loads applied to the specimen by two independent hydraulic actuators. a nominal load ratio r equal to -1 has been adopted in all fatigue tests. in all fatigue tests, the matelect® dcm-2 direct current potential drop method, sketched in fig. 2b, has been adopted to monitor in detail both fatigue crack initiation and propagation phases. two specimens have been used: one was the fatigue i t 150 ϕ24 90°  4  = 0.1 90°  g. meneghetti et alii, frattura ed integrità strutturale, 41 (2017) 8-15; doi: 10.3221/igf-esis.41.02 10 tested specimen, while the other one was the reference unloaded specimen. the specimens were connected in series so that a 30-a-constant-current (i in fig. 2a) flowed through both of them. during each experimental fatigue test, the electrical potential drops v, for the tested specimen, and v0, for the reference one (see fig. 2b), have been measured between two 3-mm-diameter copper pins, glued close to the notch edges by using ag-filled epoxy. accordingly, the technical fatigue crack initiation life can be defined as the number of loading cycles at which the normalized electrical potential v/v0 shows a given increase, assumed here about equal to 1%. figure 2: (a) flexible test bench adopted for pure bending fatigue tests and (b) experimental setup of the adopted electrical potential drop measurement system. calibration curves of the potential drop method ccording to the pioneering contributions by ritchie and bathe [17] and aronson and ritchie [18], the finite element method (fem) is an accurate tool to derive the calibration curves of the electrical potential drop method, i.e. the potential drop as a function of the initiated crack depth in a specific specimen geometry, which is more simple and fast than experimental or theoretical calibrations. the calibration curves relevant to ti-6al-4v notched specimens (reported in fig. 1) have been derived by means of electrical fe analyses. the numerical analyses have been carried out using ansys® code, by adopting a 3d, 10-node, tetrahedral, electric solid element (solid 232 of ansys® element library). the boundary conditions have been applied to the fe model following the procedure extensively described in a previous contribution [19], which is not repeated here. however, in this case due to application of bending loadings in the fatigue tests, the fatigue crack has been assumed to initiate and subsequently to propagate with a semi-elliptical shape from the circumferential notch toward the center of the bar, and not concentrically as assumed in [19], in which axial and torsion loadings were considered. the results obtained by employing a full 3d fe analysis relevant to ti-6al-4v notched specimens are reported in figs. 3a in terms of ratio v/v0 as a function of the normalized crack depth a/rnet, rnet being the radius of the net-section. a range of the ellipse semi-axes ratio c/a has been analysed, since it could be not the same in all specimens and it could also change during crack propagation as highlighted by doremus et al. [20]. however, it is worth of mentioning that a saturation effect occurs on the calibration curves with increasing the c/a ratio, so that ratios higher than 4 have not been considered. the calibration curves reported in fig. 3a were used to define the crack initiation life in an operational manner, i.e. at a relative potential drop increase v/v0 equal to 1.01. such operational definition is consistent with that adopted by a 40 a 16 δv0 δv imposed electrical current matelect® dcm-2 dcpd crack growth monitor fatigue tested specimen i reference specimen i screw for current i/o (b) matelect ® dcm-2 dcpd crack growth monitor fatigue tested specimen reference specimen hydraulic actuators (a) g. meneghetti et alii, frattura ed integrità strutturale, 41 (2017) 8-15; doi: 10.3221/igf-esis.41.02 11 figure 3: (a) calibration curves δv/δv0 obtained numerically as a function of the normalized crack depth a/rnet, for ti-6al-4v notched specimens. δv0 represents the electrical potential of the reference un-cracked specimen (a = 0). (b) definition of crack initiation life in terms of electrical potential drop. tanaka [6]. according to the zoom reported in fig. 3b, it is seen that a ratio v/v0 equal to 1.01 corresponds to a crack depth a in the range 0.8÷1.4 mm. averaged strain energy density approach he strain energy density (sed) averaged over a control volume, the radius of which is thought of as a material property according to lazzarin and zambardi [14], proved to efficiently account for notch effects both in static [14,21] and fatigue [14,22,23] structural strength problems. the idea is reminiscent of the stress averaging to perform along a material-dependent microstructural length, according to the approach proposed by neuber. such a method was formalized and applied first to sharp, zero radius, v-notches [14] and later extended to blunt u and vnotches [15]. when dealing with sharp v-notches, see for example the case with = 0.1 mm in fig. 1, the control volume is a circular sector of radius r0 centered at the notch tip [14] as shown in fig. 4a. for a blunt v-notch, see for example the case with = 4 mm in fig. 1, the volume assumes the crescent shape shown in fig. 4b [15], where r0 is the depth measured along the notch bisector line. the outer radius of the crescent shape is equal to r0 + r0, where r0 depends on the notch opening angle 2 and on the notch root radius  according to the following expression:    q 1q r0 (1) with q defined as:    22 q (2) the control radius r0 for fatigue strength assessment of notched components made of titanium grade 5 alloy has been previously estimated by berto et al. [24] by equating the averaged sed in two situations, i.e. the fatigue limit (or the highcycle fatigue strength) of un-notched and notched specimens, respectively. therefore, r0 combines two material properties: the high-cycle fatigue strength of smooth specimens, referred to na = 2·106 cycles, and the value of the notch stress intensity factor (nsif) range for sharp v-notches with opening angle equal to 90 degrees, referred to the same number of cycles na, according to eqs. (3) and (4) derived in [4,14]. berto et al. obtained the following values for the t 1,00 1,01 1,02 0,00 0,05 0,10 0,15 0,20 0,25 δ v /δ v 0 a/rnet c/a = 2 c/a = 3 c/a = 4 c/a = 2 c/a = 3 c/a = 4 i = const. = 30 a rnet = 6 mm = 0.1 mm = 4 mm crack initiation life → δv/δv0 ≈ 1.01 crack initiation life → 0.14 < a/rnet < 0.24 (b) 1,00 1,10 1,20 1,30 0,00 0,30 0,60 0,90 δ v /δ v 0 a/rnet c/a = 2 c/a = 3 c/a = 4 c/a = 2 c/a = 3 c/a = 4 i = const. = 30 a rnet = 6 mm = 0.1 mm = 4 mm (a) g. meneghetti et alii, frattura ed integrità strutturale, 41 (2017) 8-15; doi: 10.3221/igf-esis.41.02 12 control radius r0 of ti-6al-4v [24] dealing with tension (mode i) and torsion (mode iii) loadings, respectively, with a load ratio r = -1: mm051.0 mpa950 mmmpa452 146.02 k e2r 545.01 1 455.01 1 a a,i 1i,0 1                  (3) mm449.0 mpa776 mmmpa1216 3.01 310.0k 1 e r 666.01 1 333.01 1 a a,iii3 iii,0 3                          (4) it should be noted that the control radius r0 for fatigue strength assessment of ti-6al-4v notched components assumes extremely different values under mode i and mode iii, so that the energy contributions related to the two different loadings should be averaged in control volumes of different size [4]. the idea of a control volume size dependent on the loading mode has been proposed for the first time in [4] dealing with the multiaxial fatigue strength assessment of notched specimens made of 39nicrmo3 steel, then it has been successfully applied also for the fatigue strength assessment of notched components made of aisi 416 [25] and cast iron en-gjs400 [26] subjected to combined tension and torsional loading. figure 4: control volume for specimens weakened by (a) sharp [14] and (b) blunt v-notches [15]. once the size of the control volume is properly defined, the averaged sed can be evaluated directly from the fe results, w , by summation of the strain-energies wfem,i calculated for each i-th finite element belonging to the control volume v (or area a in two-dimensional problems, as shown in fig. 4): v w cw v i,fem w   (5) where the coefficient cw accounts for the effect of the nominal load ratio r [27], when the range value of the nominal stress is applied to the fe model. it is equal to 1 for r = 0 and to 0.5 for r = 1. eq. (5) represents the so-called direct approach to calculate the averaged sed. according to a recent contribution of lazzarin et al. [28], very coarse fe meshes can be adopted within the control volume (see fig. 5). r0  r0  notch bisector line r0 + r0 a   notch bisector line r 0 a (a) (b) g. meneghetti et alii, frattura ed integrità strutturale, 41 (2017) 8-15; doi: 10.3221/igf-esis.41.02 13 sed-based reanalysis of crack initiation and total life experimental data he local sed values, averaged over the control volume relevant to mode i loadings (r0,i = 0.051 mm), have been calculated using the direct approach, w , according to eq. (5) (with about 50 finite elements inside the control volume). due to application of non axis-symmetric loadings, i.e. pure bending, 3d fe analyses of the cylindrical specimens were needed to evaluate the averaged sed. to obtain the 3d mesh, first, a 2d free mesh pattern of quadrilateral 8-node plane 183 elements has been generated; after that, the 2d fe mesh has been extruded about y axis by using 3d 20-node brick elements (solid186 of the ansys® element library) and by setting a proper extrusion step size in order to obtain a control volume v having both radius and depth equal to r0,i, as suggested for 3d applications of the sed approach [21,23]. an example of the adopted fe mesh along with a detail of the structural volume for averaged sed calculation is reported in fig. 5. it should be noted that only a quarter of each specimen has been modelled, taking advantage of the anti-symmetry on the yz plane and of the symmetry on the xy plane (see fig. 5). to properly simulate the loads and restraints applied by the adopted test bench (see fig. 2a), the cylindrical surface highlighted in gray in fig. 5a was fixed, while bending loading was applied by means of concentrated forces at the opposite end. figure 5: (a) coarse fe mesh (about 50 fe inside the control volume) adopted in the 3d numerical analyses. the y-axis coincides with the axis of the specimen. (b) details of the fe mesh inside the control volume v. considered case: sharp v-notched specimen ( = 0.1 mm) under pure bending loading, r0,i = 0.051 mm. the preliminary experimental fatigue results presented in terms of local sed and relevant to pure bending fatigue loading are reported in fig. 6a, where the operational definition of crack initiation life (v/v0 = 1.01 according to fig. 3b) has been applied. in a recent contribution of the present authors [16], it has been highlighted that a physical definition of the crack initiation life in relation to the sed-approach could be defined when the crack depth a equals the structural volume size r0, that is the initiated crack depth leads to the structural volume failure. dealing with the present results, it should be noted that: (i) given a crack depth a, the potential drop method is less sensitive to the initiation of an elliptical crack than to the initiation of a circumferential one (calibration curves of fig. 3 should be compared with those reported in [19]); (ii) the control radius r0,i for fatigue strength assessment of ti-6al-4v notched components is equal to 0.051 mm. therefore, the physical definition of the crack initiation life (a =r0,i) corresponds to a relative potential drop increase v/v0 lower than 1‰ (fig. 3b): such a reduced v/v0 value is not applicable to the present case due to the un-sufficiently high sensitivity of the adopted dcpd crack growth monitor device. t fixed region v notch bisector r 0,i r 0,i f/8 x y z f/8 (a) (b) g. meneghetti et alii, frattura ed integrità strutturale, 41 (2017) 8-15; doi: 10.3221/igf-esis.41.02 14 leaving aside the physical definition of crack initiation, fig. 6a shows that the ratio between crack initiation life according to the operational definition (open markers) and total life (filled markers) is equal to approximately 0.50÷0.60 for the sharp v-notch (= 0.1 mm), while it is equal to about 0.90 for the blunt notch (= 4 mm). fig. 6b shows a comparison between the averaged sed-based scatter-band calibrated previously by berto el al. [24] on about 160 uniaxial and multiaxial experimental data obtained from sharp v-notched ti-6al-4v specimens and the new fatigue results relevant to pure bending loading, obtained in the present contribution and expressed in terms of total fatigue life. it can be observed from fig. 6b that all new data fall within the sed-based scatter band showing a good agreement between theoretical estimations and experimental results. however, it should be noted that the averaged sedbased scatter-band reported in fig. 6b is characterized by a rather wide scatter (tw = 2.50, i.e. an equivalent stress-based scatter index t = wt = 1.58), being calibrated on experimental data expressed in terms of total fatigue life. it is worth noting that fig. 6a suggests that the scatter index could be reduced if the averaged sed-based scatter-band was calibrated on crack initiation data rather than total fatigue life data. figure 6: (a) crack initiation (open markers) and fatigue life to failure (filled markers) of ti-6al-4v notched specimens expressed in terms of averaged sed. (b) comparison of new fatigue data in terms of total fatigue life with the averaged sed-based scatter-band calibrated previously [24] on about 160 uniaxial and multiaxial experimental fatigue results obtained from sharp v-notched specimens. conclusions n the present contribution, some preliminary experimental fatigue results, obtained from circumferentially notched specimens made of titanium alloy, ti-6al-4v, with different notch root radii and subjected to pure bending fatigue loadings, have been reanalysed by means of the averaged strain energy density (sed) approach. agreement has been found between new fatigue data and a sed-based scatter band previously calibrated on uniaxial and multiaxial fatigue results in terms of total fatigue life. however, if the crack initiation life had been considered, even though defined in an operational manner, reduction of scattering in the sed-based synthesis of notches of different severity is likely to be obtained and it will be the subject of future investigations. references [1] tanaka, k., hashimoto, a., narita, j., egami, n., fatigue life of circumferentially notched bars of austenitic stainless steel under cyclic torsion with and without static tension, j. soc. mater. sci. jpn., 58 (2009) 1044–1050. [2] tanaka, k., small fatigue crack propagation in notched components under combined torsional and axial loading, procedia eng., 2 (2010) 27–46. doi: 10.1016/j.proeng.2010.03.004. [3] ohkawa, c., ohkawa, i., notch effect on torsional fatigue of austenitic stainless steel: comparison with low carbon steel, eng. fract. mech., 78 (2011) 1577–1589. doi:10.1016/j.engfracmech.2011.01.015. [4] berto, f., lazzarin, p., yates, j.r., multiaxial fatigue of v-notched steel specimens: a non-conventional application of the local energy method, fatigue fract. eng. mater. struct., 34 (2011) 921–943. i 0,5 5,0 50,0 1,00e+04 1,00e+05 1,00e+06 1,00e+07 s e d r an g e, δ w [ m j/ m 3 ] number of cycles to failure 0.1 mm 4 mm r0,i = 0.051 mm δwa,50% = 3.08 mj/m 3 na = 2 ∙10 6 cycles scatter index (10%-90%): tw = 4.87/1.95 = 2.50 slope k = 5.90 ti-6al-4v: scatter band calibrated in [24] mm mm 4.87 1.95 3.08 run out (b) 1,0 10,0 1,00e+04 1,00e+05 1,00e+06 1,00e+07 s e d r an g e, δ w [ m j/ m 3 ] number of cycles 0.1 mm innesco 4 mm innesco 0.1 mm 4 mm mm mm run out (a) r0,i = 0.051 mm mm mm fatigue crack initiaton life total fatigue life g. meneghetti et alii, frattura ed integrità strutturale, 41 (2017) 8-15; doi: 10.3221/igf-esis.41.02 15 [5] okano, t., hisamatsu, n., effect of notch of torsional fatigue property of pure titanium, proc. 31 symp. fatigue, soc. mater. sci. japan, 31 (2012) 129–133. [6] tanaka, k., crack initiation and propagation in torsional fatigue of circumferentially notched steel bars, int. j. fatigue, 58 (2014) 114–125. doi: 10.1016/j.ijfatigue.2013.01.002. [7] atzori, b., berto, f., lazzarin, p., quaresimin, m., multi-axial fatigue behaviour of a severely notched carbon steel, int. j. fatigue, 28 (2006) 485–493. doi: 10.1016/j.ijfatigue.2005.05.010. [8] tanaka, k., ishikawa, t., narita, j., egami, n., fatigue life of circumferentially notched bars of carbon steel under cyclic torsion with and without static tension, j. soc. mater. sci. jpn, 60 (2011). [9] ritchie, r.o., mcclintock, f.a., nayeb-hashemi, h., ritter, m.a., mode iii fatigue crack propagation in low alloy steel, metall. trans. a, 13 (1982) 101–110. doi: 10.1007/bf02642420. [10] tschegg, e.k., a contribution to mode iii fatigue crack propagation, mater. sci. eng., 54 (1982) 127–136. doi: 10.1016/0025-5416(82)90037-4. [11] tschegg, e.k., the influence of the static i load mode and r ratio on mode iii fatigue crack growth behaviour in mild steel, mater. sci. eng. 59 (1983) 127–137. doi:10.1016/0025-5416(83)90094-0. [12] tanaka, k., akiniwa, y., nakamura, h., j-integral approach to mode iii fatigue crack propagation in steel under torsional loading, fatigue fract. eng. mater. struct., 19 (1996) 571–579. doi: 10.1111/j.1460-2695.1996.tb00993.x. [13] yu, h., tanaka, k., akiniwa, y., estimation of torsional fatigue strength of medium carbon steel bars with a circumferential crack by the cyclic resistance-curve method, fatigue fract. eng. mater. struct., 21 (1998) 1067–1076, doi: 10.1046/j.1460-2695.1998.00105.x. [14] lazzarin, p., zambardi, r., a finite-volume-energy based approach to predict the static and fatigue behavior of components with sharp v-shaped notches, int. j. fract., 112 (2001) 275–298. doi:10.1023/a:1013595930617. [15] lazzarin, p., berto, f., some expressions for the strain energy in a finite volume surrounding the root of blunt vnotches, int. j. fract., 135 (2005) 161–185. doi: 10.1007/s10704-005-3943-6. [16] campagnolo, a., meneghetti, g., berto, f., tanaka, k., crack initiation life in notched steel bars under torsional fatigue: synthesis based on the averaged strain energy density approach, int. j. fatigue, 100 (2017) 563-574. doi: 10.1016/j.ijfatigue.2016.12.022. [17] ritchie, r.o., bathe, k.j., on the calibration of the electrical potential technique for monitoring crack growth using finite element methods, int. j. fract., 15 (1979) 47–55, doi: 10.1007/bf00115908. [18] aronson, g., ritchie, r., optimization of the electrical potential technique for crack growth monitoring in compact test pieces using finite element analysis, j. test. eval., 7 (1979) 208. doi: 10.1520/jte11382j. [19] campagnolo, a., meneghetti, g., berto, f., tanaka, k., averaged strain energy density-based synthesis of crack initiation life of notched titanium and steel bars under uniaxial and multiaxial fatigue, fatigue 2017, cambridge, uk: (2017). [20] doremus, l., nadot, y., henaff, g., mary, c., pierret, s., calibration of the potential drop method for monitoring small crack growth from surface anomalies – crack front marking technique and finite element simulations, int. j. fatigue, 70 (2015) 178–185. doi: 10.1016/j.ijfatigue.2014.09.003. [21] berto, f., lazzarin, p., recent developments in brittle and quasi-brittle failure assessment of engineering materials by means of local approaches, mater. sci. eng. r reports, 75 (2014) 1–48. doi: 10.1016/j.mser.2013.11.001. [22] livieri, p., lazzarin, p., fatigue strength of steel and aluminium welded joints based on generalised stress intensity factors and local strain energy values, int. j. fract., 133 (2005) 247–276. doi: 10.1007/s10704-005-4043-3. [23] berto, f., campagnolo, a., chebat, f., cincera, m., santini, m., fatigue strength of steel rollers with failure occurring at the weld root based on the local strain energy values: modelling and fatigue assessment, int. j. fatigue, 82 (2016) 643–657. doi: 10.1016/j.ijfatigue.2015.09.023. [24] berto, f., campagnolo, a., lazzarin, p., fatigue strength of severely notched specimens made of ti-6al-4v under multiaxial loading, fatigue fract. eng. mater. struct., 38 (2015) 503–517. [25] berto, f., lazzarin, p., fatigue strength of structural components under multi-axial loading in terms of local energy density averaged on a control volume, int. j. fatigue, 33 (2011) 1055–1065. doi: 10.1016/j.ijfatigue.2010.11.019. [26] berto, f., lazzarin, p., tovo, r., multiaxial fatigue strength of severely notched cast iron specimens, int. j. fatigue, 67 (2014) 15–27. doi: 10.1016/j.ijfatigue.2014.01.013. [27] lazzarin, p., sonsino, c.m., zambardi, r., a notch stress intensity approach to assess the multiaxial fatigue strength of welded tube-to-flange joints subjected to combined loadings, fatigue fract. eng. mater. struct., 27 (2004) 127–140. [28] lazzarin, p., berto, f., zappalorto, m., rapid calculations of notch stress intensity factors based on averaged strain energy density from coarse meshes: theoretical bases and applications, int. j. fatigue, 32 (2010) 1559–1567. doi: 10.1016/j.ijfatigue.2010.02.017. << /ascii85encodepages false /allowtransparency false /autopositionepsfiles true /autorotatepages /none /binding /left /calgrayprofile (dot gain 20%) /calrgbprofile (srgb iec61966-2.1) /calcmykprofile (u.s. web coated \050swop\051 v2) /srgbprofile (srgb iec61966-2.1) /cannotembedfontpolicy /error /compatibilitylevel 1.4 /compressobjects /tags /compresspages true /convertimagestoindexed true /passthroughjpegimages true /createjobticket false /defaultrenderingintent /default /detectblends true /detectcurves 0.0000 /colorconversionstrategy /cmyk /dothumbnails false /embedallfonts true /embedopentype false /parseiccprofilesincomments true /embedjoboptions true /dscreportinglevel 0 /emitdscwarnings false /endpage -1 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/hrv (za stvaranje adobe pdf dokumenata najpogodnijih za visokokvalitetni ispis prije tiskanja koristite ove postavke. stvoreni pdf dokumenti mogu se otvoriti acrobat i adobe reader 5.0 i kasnijim verzijama.) /hun 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/pdfxoutputintentprofileselector /documentcmyk /preserveediting true /untaggedcmykhandling /leaveuntagged /untaggedrgbhandling /usedocumentprofile /usedocumentbleed false >> ] >> setdistillerparams << /hwresolution [2400 2400] /pagesize [612.000 792.000] >> setpagedevice microsoft word numero_43_art_5 f. majid et alii, frattura ed integrità strutturale, 43 (2018) 79-89; doi: 10.3221/igf-esis.43.05 79 continuum damage modeling through theoretical and experimental pressure limit formulas fatima majid, mohamed elghorba university of hassan ii, national superior school of electricity and mechanics casablanca (ensem), lccmms, morocco majidfatima9@gmail.com, http://orcid.org/0000-0001-8909-8232 abstract. in this paper, we developed a mathematical modeling to represent the damage of thermoplastic pipes. on the one hand, we adapted the theories of the rupture pressure to fit the high density polyethylene (hdpe) case. indeed, the theories for calculating the rupture pressure are multiple, designed originally for steels and alloys. for polymer materials, we have found that these theories can be adapted using a coefficient related to the nature of the studied material. the hdpe is characterized by two important values of pressure, deduced from the ductile form of the internal pressure’s evolution until burst. for this reason, we have designed an alpha coefficient taking into account these two pressures and giving a good approximation of the evolution of the experimental burst pressures through the theoretically corrected ones, using faupel’s pressure formula. then, we can deduce the evolution of the theoretical damage using the calculated pressures. on the other hand, two other mathematical models were undertaken. the first one has given rise to an adaptive model referring to an expression of the pressure as a function of the life fraction, the characteristic pressures and the critical life fraction. the second model represents a continuum damage model incorporating the pressure equations as a function of the life fraction and based on the burst pressure’s static damage model. these models represent important tools for industrials to assess the failure of thermoplastic pipes and proceed quick checks. keywords. continuum damage; hdpe; burst pressure; life fraction. citation: majid, f., elghorba, m., continuum damage modeling through theoretical and experimental pressure limit formulas, frattura ed integrità strutturale, 43 (2018) 79-89. received: 25.09.2017 accepted: 03.11.2017 published: 01.01.2018 copyright: © 2018 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. introduction olymers have changed all facets of the industrial life and are almost a part of all fields, including the medical and food industries. universities, organizations and industrial companies are getting deeply concerned about these materials. they are contributing to the advance and the prosperity of several industries such as petrochemicals, gas, water networks and slurries’ transport. this multitude of applications explains the huge number of product ranges, which have been produced. many researches were interested to the extreme environmental conditions, the manufacturing methods p f. majid et alii, frattura ed integrità strutturale, 43 (2018) 79-89; doi: 10.3221/igf-esis.43.05 80 and the technological advances of polymer’s applications [1–5]. in this context, several discoveries have been recorded in the history of plastic materials starting with pvc in 1913, plexiglas in 1924, polystyrene in 1933, polyethylene in 1935, teflon in 1938, abs in 1946 and polypropylene in 1954. the polymers are generally classified into three main categories, which are thermosetting, thermoplastic and elastomer. for our case, the high density polyethylene (hdpe) materials have gained a huge importance in the industrial field because of their durability and high performances. to contribute to these advances, we led many simplifying approaches of failure assessment and prediction of hdpe pipes [14-16]. all the developed concepts have been based on experimental tensile and burst tests. indeed, our aim is to assess the degradations through the damage modelling by referring only to static tests and models instead of tedious and very costly dynamic ones therefore, we are using the results of the burst tests of hdpe pipes for a mathematical modeling of burst pressure evolution and damage evaluation. for that reason, we evaluated the characteristic pressures of these pipes, obtained from the internal pressure curve, which have been integrated in theoretical equations leading to the damage assessment. in this paper, new concepts based on the limit pressure formulas such as faupel one [6] and continuum equation of pressure have been introduced. these formulas led to three ways of damage modeling of hdpe pipes: • a theoretical model based on the faupel formula applying a corrective coefficient α; • an adaptive model using the pressure formulation, p (β), as a function of the life fraction and the critical life fraction and assuming that the applied pressure corresponds to the calculated pressure p (β) corresponding to the last experimental life fraction (86%); • a continuum damage model d (β), which takes values as a function of the life fraction β and the constant α and η and assumes an applied pressure equivalent to the experimental one (11.9 bar). this modeling is considering the theoretical calculations of the hdpe pipe’s burst pressure, for different notches’ depths, by either the faupel or p (β) formulas. therefore, we consider the burst pressure of a neat pipe as the ultimate rupture pressure, maximum pressure, while the other pressures, related to the notched pipes, are considered as the residual ones for both the theoretical and the adaptive damage models. for the continuum damage, it is taking into consideration the different pressures of the hdpe pipes as a function of the intervals of β. these approaches are validated and compared to the model of static damage obtained through the experimental burst pressures in order to evaluate their accuracy. material and method o determine the experimental burst pressures of the studied pipes, we used a hydrostatic tester allowing the control of the internal pressure until burst, fig. 1. this test allowed us to determine the hdpe pipes’ resistance through their burst pressure. thus, undamaged hdpe pipes and notched pipes, with a groove of 100 mm length, 5 mm width, and a variable depth from 1 to 5 mm, have been exposed to an increasing pressure until burst for the ultimate and residuals burst pressures determination. the specimens have been chosen according the astm code d1599 that requires a specimen with a length that should not exceed five times the diameter of the pipe. the specimens are prepared and conditioned at the room temperature (23 ° c) prior to pressurization. the burst pressures were evaluated, according to the notches’ depths experimentally and theoretically, as explained by the methodology shown in the fig. 2. then, the experimental burst pressures have been obtained and recorded, tab. 1. it is having a proportional drop according to the increase of the notch depth. figure 1: bursting of hdpe pipes and the specimen and notch dimensions. t pn 16 bar pe 100 thickness = 5.8 mm ultimate stage of failure 1 0 0 m m 5 n o tc h f. majid et alii, frattura ed integrità strutturale, 43 (2018) 79-89; doi: 10.3221/igf-esis.43.05 81 this paper highlight a new and simplified approach for the industrials to get through the fastidious checks required by the different codes. on the one hand, we propose two ways to get fast to this purpose. the first approach is an accelerated damage creation through notches in hdpe pipes. from the latter, ultimate and residual pressures have been measured and used in a static damage model obtained through the eq. (3). the establishment of the corresponding graph give rise to the prediction of the damage behavior of hdpe pipes. on the other hand, the same thing, which has been done through experimental burst tests, can be done only by theoretical calculations through rupture pressure formulas or the newly developed formulas presented in this paper. from then, we get to the theoretical static damage evaluation and to the plot of the damage curves, which tells about the material behavior. figure 2: damage building methodology. notch depth (mm) life fraction (β) burst pressure (bar) 0 0 63.2 1 0.17 57.8 1.5 0.26 49.7 2 0.34 47.5 2.5 0.43 42.3 3 0.52 37.5 3.5 0.60 23.5 4 0.69 20.4 4.5 0.78 18.2 5 0.86 11.9 table 1: burst pressure evolution in function of the life fraction. theory rupture pressure theories everal theories have been developed to predict the rupture of a cylinder under pressure by determining the limit loads. hill, in 1950, developed a theory predicting the pressure at boundary load conditions. it gives the evolution of the internal pressure at break as a function of the value of the stress σy, the internal diameter d0 and the external diameter di [7]. for the same purpose, nadai proposed calculating the burst pressure using the ultimate stress instead of the yield s f. majid et alii, frattura ed integrità strutturale, 43 (2018) 79-89; doi: 10.3221/igf-esis.43.05 82 stress [8]. in 1953, faupel developed a formula that takes into account the ultimate stresses and the internal and external diameters of a pipe, eq. (1) [6]. lately in 2006, klever developed a relationship based on thickness, mean diameter and ultimate stress [9]. more recently, brabin has presented in his works a new formula using the same data as faupel in addition to a parameter λ, which depends on the characteristics of the studied material [10]. finally, in 2010, the dnv standards simplified the formulas proposed in the literature by introducing a new formula based only on the yield stress, the thickness and the mean diameter [11].                02 2 ln 3 y y uts i d p d (1) • d0 and di are the external and internal diameters of the cylinder ; • σy is the yield stress ; • σuts is the ultimate stress. static damage kachanov formulated the approach of continuum damage mechanics in 1958 [12]. from a physical point of view, the author considered the initiation of damage as an internal phenomenon of progressive deterioration of the material reflected by the presence of cavities and micro-cracks under the effect of repetitive loadings generating the reduction of the area of the cross section [13]. chaboche who proposed a law of fatigue damage with nonlinear evolution took up this approach to quantify the level of damage. the damage value d takes imposed values varying from zero, for the undamaged material, to a value equal to one corresponding to the appearance of a detectable crack or rupture. these damage theories, developed in the literature, are elaborated based either on the concepts of palmgren, langer and kommers or on kachanov's continuum damage approach. the most common and used model, adopted by the international codes like asme and iso, is the linear damage model which is directly proportional to the life fraction. miner has presented the damage as equal to the life fraction. this law is expressed as below: d=β=n/nf (2) the life fraction presented by miner is referring to the ratio between the instantaneous number of cycles under an applied stress (n) and the total number of cycles at the rupture (nf) in the fatigue case. in this paper, as per the fatigue phenomenon, the notch level is considered as the preloading for fatigue because it is consuming a number of cycle of the material that corresponds to the level of weakening of it. therefore, the ratio between the thickness fluctuation, which is measuring the notch impact and the thickness, which represents the full strength of the hdpe pipe, can be considered as the life fraction for the material. in this paper, we evaluated the damage through a combined theory using the static damage of the unified theory [14–16] and burst pressure equations herein developed. indeed, we exposed neat and notched hdpe pipes to an increasing internal pressure until rupture (burst). each notch level is corresponding to a life fraction calculated through the thickness fluctuation. this fluctuation is influencing the burst pressure of the pipes. therefore, each (β) is corresponding to a burst pressure. for the neat pipe, this pressure is considered as the ultimate one (pu), while they are considered as the ultimate residual pressures (pur1, pur2, …, pa) for the others.    1 1 ur u s a u p p d p p (3) where, • pur is the burst pressure for damaged pipes ; • pu is the burst pressure for a neat pipe ; • pa is the pressure just before rupture f. majid et alii, frattura ed integrità strutturale, 43 (2018) 79-89; doi: 10.3221/igf-esis.43.05 83 results and discussions theoretical damage based on corrected faupel formula he theoretical burst pressures obtained by the formula (1), and those obtained experimentally, tab. 1, are shown in fig. 3. they have a decreasing trend according to the life fraction (β). figure 3: theoretical and experimental burst pressures as a function of the life fraction. the observed difference at the small notch depths can be explained by the ductile behavior of the studied material, which is not taken into account by the theoretical burst pressure formulas. in order to correct this discrepancy, the formula (1) is corrected by a new coefficient α that represents the ratio between the maximum pressure pmax and the pressure at break pr. then, the approximate corrected equation of faupel is given by:                  02 2 ln 3 y y uts i d p d (4) where:   max r p p (5) α is a parameter that depends on the studied material. pmax and pr represent the maximum pressure and rupture pressure of an hdpe pipe as shown in fig. 4. afterwards, the corrected pressures obtained by the eq. (4) and (5) is represented as shown in fig. 5. the corrected theoretical damage model is obtained by combining the static damage, based on the rupture pressures, to the corrected burst pressures formula of faupel for different life fractions. therefore, we obtain the ultimate pressure (pu), the ultimate residual pressures (pur) and the applied pressure, which corresponds to the life fraction just before rupture (pa). then, these pressures were integrated in the static damage eq. (3), to obtain the corrected model. finally, we represent the theoretical damage and the experimental damage in comparison as shown in fig. 6. we note from this figure that these damages have the same tendencies. therefore, we deduce that the corrected theoretical damage can be adopted as a simple and an efficient tool to represent the damage of hdpe pipes by bursting a neat pipe only. 0 10 20 30 40 50 60 0 0,2 0,4 0,6 0,8 1 b u rs t p re ss u re (b ar ) β=δe/e experimental burst pressure theoretical burst pressure t f. majid et alii, frattura ed integrità strutturale, 43 (2018) 79-89; doi: 10.3221/igf-esis.43.05 84 figure 4: internal pressure evolution as a function of the time. figure 5: the theoretically corrected pressure versus the experimental one as a function of the life fraction. figure 6: theoretical and experimental damage as a function of the life fraction. 63,2 35 49,8 40,1 0,6 0 10 20 30 40 50 60 70 34 39 44 49 p re ss ur e( b ar ) time (s) pressure pr pmax rupture necking f. majid et alii, frattura ed integrità strutturale, 43 (2018) 79-89; doi: 10.3221/igf-esis.43.05 85 adaptive and continuum damage based on burst pressure formula p (β) in this part, we developed a new formula for burst pressure calculations, which takes into account the intervals of the life fraction and the characteristic pressures shown in the first part of this paper. this equation is independent of the limit pressure’s equations such as faupel one. it is conditioned by the critical life fraction as shown by the eq. (6) and (7):                        max max ( ) * ; 0, ( ) * * ; ,1 r c r p p p c p p p c (6) taking into account the parameter α, we obtain:                           ( ) ( ) ; 0, ( ) 1 * * ; ,1 r c r p p c p p c (7) the model presented above is an adaptive tool for estimating the burst pressure through a burst test of a neat hdpe pipe only as shown in fig. 7: figure 7: theoretically corrected and adaptive estimation of burst pressure. starting from the expression of the pressure p (β), we have developed two ways to calculate the damage. the first consists of a model of damage inspired from the experimental static damage. in fact, we calculate the adaptive pressures through the p(β) equation for the same life fractions as the experimental case. consequently, we consider that the pressure is ultimate (pu) for a neat pipe (β = 0). for the other intermediate life fractions, we obtain the residual ultimate pressures (pur). the applied pressure (pa) corresponds to the last pressure before the rupture corresponding to the last possible loading level (β = 0.86). furthermore, the integration of these pressures into the burst pressure static damage model allows us to obtain the adaptive damage that is shown in fig. 8. the second consists of the creation of a continuum damage model that supports the characteristic pressures of hdpe, pr and pmax, represented by the coefficient α and a non-dimensional coefficient representing the ratio of the applied pressure (pa) and the rupture pressure (pr), η. in fact, this model presents a continuum function represented according to three intervals of β.calculations of the damage are possible by choosing the iteration of the desired life fraction and by knowing the various experimental parameters such as the applied pressure (pa) corresponding to the last experimental pressure before the rupture of 11.9 bar for the studied hdpe. the continuum static damage is expressed by: f. majid et alii, frattura ed integrità strutturale, 43 (2018) 79-89; doi: 10.3221/igf-esis.43.05 86                                                max max max ( * ) 1 ( ) ; 0, ; 1 * * 1 ( ) ; , 1 ( ) 1; ,1 r u u a u c r u pa a u p a p p p d c p p p p p p p d c p p d (8) so:                                     max max max max max max ( * ) ( ) ; 0, ; * * ( ) ; , ( ) 1; ,1 r u a c r pa a pa p p p d c p p p p p d c p p d (9) so:                                  max max max max * ( ) ; 0, ; * * ( ) ; , ( ) 1; ( ),1 r u a c r pa a a p d c p p p p p d c p p d p (10) in addition:                                          ( ) ; 0, ; : * ( ) ; , ( ) 1; ,1 a r c p a p a p d c p d c d (11) f. majid et alii, frattura ed integrità strutturale, 43 (2018) 79-89; doi: 10.3221/igf-esis.43.05 87 the coefficient α, β and η represent respectively the ratio of the ductile rupture pressures, the life fraction and the nondimensional ratio of the applied pressure and the rupture one. βpa is the life fraction corresponding to the pressure before rupture. the representation of the adaptive model is given in fig. 8: figure 8: approximate theoretical damage, through corrected faupel, adaptive and experimental damages according to the life fraction. the representation of the continuum damage model is almost the same as the one given by the adaptive damage model as illustrated in fig. 8. the difference is explained by taking into account the applied experimental pressure (pa = 11.9 bar) for the continuum damage model independently of the theoretical equations. figure 9: approximate theoretical damage, through corrected faupel, adaptive, continuum d (β) and experimental damages as a function of the life fraction. . we observe from the damage curves of figs. 8 and 9 that the theoretical damage is linear as the damage of miner, while the experimental damage clearly shows three phases of evolution. the first phase is characterized by slow evolution under the theoretical damage up to the life fraction of 17%. in the second phase, we observe a steady increase of the latter up to the 65% of life fraction. in the third phase, a significant acceleration of the damage to reach the unit was registered. concerning the adaptive damage, we found that the developed model traces perfectly the model of static damage obtained f. majid et alii, frattura ed integrità strutturale, 43 (2018) 79-89; doi: 10.3221/igf-esis.43.05 88 experimentally. the same evolution was observed for continuum damage model, which has the same tendency as the adaptive one, fig. 9. conclusion he assessment and establishment of the damage of hdpe pipes can’t be considered as a simple task. on the one hand, we propose a new approach based on the calculated pressures through the faupel formula. this theoretical pressure can substitute the experimental burst pressures of the hdpe pipes, which are exposed to an increasing internal pressure until burst. nevertheless, the calculations obtained by the faupel formula must take into account the specificities of the used material since they were originally proposed for metals (steels). in this perspective, we have developed a modified equation based on a factor α that depends strongly on the behavior of the internal pressure used for the bursting of the neat studied pipes. indeed, we have highlighted the effect of elongation of the pipe during the elastic phase to reach a maximum pressure. after that, the pipe reaches a phase of large strains before getting to another pressure peak representing the pressure of rupture. in the used static damage models presented in this paper, we substitute the experimental pressures by the calculated and modified ones. then, we obtain a close approximate model more representative of the experimental model. the latter represents a powerful and rapid tool that can be used by manufacturers to launch audits and fast checks by knowing just the value of the coefficient α deduced from the evolution of the internal pressure of a neat pipe. moreover, we have shown another powerful tool, adaptive damage model, perfectly reproducing the experimental static damage through a single burst test of a neat hdpe pipe. therefore, if we want to calculate the burst pressure and subsequently the corresponding damage, we simply replace the value of the life fraction in the set of eq. (6) or (7) knowing that the parameters pr, pmax and βc are constants that depend on the thermoplastic material and on the class of the pipeline. for the hdpe pe100 pn16 63 mm x 5.8 mm, we found that the values of these parameters are respectively 49.8 bar, 63.2 bar and 0.52. a theoretical modeling of the damage giving rise to a continuum damage model, eqs. (8) to (11), showed that the latter could be evaluated by knowing the values of the coefficients α and η. these coefficients are constants of the studied material depending respectively on the pressures pr and pmax for the first and on the applied experimental pressure pa and the rupture pressure pr for the second as well as the critical life fraction. the continuum model is represented as a function of the theoretical life fraction by choosing an iteration for its evolution according to the wanted accuracy. references [1] abedini, a., rahimlou, p., asiabi, t., ahmadi, s.r., azdast, t., effect of flow forming on mechanical properties of high density polyethylene pipes, j. manuf. process., 19 (2015) 155–162. doi:10.1016/j.jmapro.2015.06.014. [2] krishnaswamy, r.k., analysis of ductile and brittle failures from creep rupture testing of high-density polyethylene (hdpe) pipes, polymer (guildf). 46 (2005) 11664–11672. doi:10.1016/j.polymer.2005.09.084. [3] grigoriadou, i., paraskevopoulos, k.m., chrissafis, k., pavlidou, e., stamkopoulos, t.g., bikiaris, d., effect of different nanoparticles on hdpe uv stability, polym. degrad. stab. 96 (2011) 151–163. doi:10.1016/j.polymdegradstab.2010.10.001. [4] zhang, s.h., chen, x.d., wang, x.n., hou, j.x., modeling of burst pressure for internal pressurized pipe elbow considering the effect of yield to tensile strength ratio, meccanica, 50 (2015) 2123–2133. doi:10.1007/s11012-015-0148-6. [5] choi, b.h., chudnovsky, a., paradkar, r., michie, w., zhou, z., cham, p.m., experimental and theoretical investigation of stress corrosion crack (scc) growth of polyethylene pipes, polym. degrad. stab., 94 (2009) 859–867. doi:10.1016/j.polymdegradstab.2009.01.016. [6] faupel, j., furbeck, a., influence of residual stress on behavior of thick-wall closed-end cylinders, trans. asme. (1953). [7] hill, r., the mathematical theory of plasticity oxford university press london google scholar, (1950). [8] nadai, a., plasticity of metals, (1950). [9] klever, f., formulas for rupture, necking, and wrinkling of octg under combined loads, spe annu. tech. conf. exhib. (2006). [10] brabin, a., christopher, t., investigation on failure behavior of unflawed steel cylindrical pressure vessels using fea, multidiscipline, (2009). [11] veritas, d., offshore standard dnv-os-f101, submar. pipeline syst. (2000). t f. majid et alii, frattura ed integrità strutturale, 43 (2018) 79-89; doi: 10.3221/igf-esis.43.05 89 [12] bathias, c., pineau, a., fatigue of materials and structures, (2013). doi:10.1002/9781118616994. [13] lemaitre, j., desmorat, r., engineering damage mechanics, (2005). doi:10.1007/b138882. [14] majid, f., elghorba, m., hdpe pipes failure analysis and damage modeling, eng. fail. anal. (2017). [15] majid, f., nattaj, j., elghorba, m., pressure vessels design methods using the codes, fracture mechanics and multiaxial fatigue, 38 (2016) 273–280. doi:10.3221/igf-esis.38.37. [16] majid, f., ouardi, a., barakat, m., elghorba, m., prediction of ppr and hdpe polymers through newly developed nonlinear damage-reliability models, procedia struct. integr., 3 (2017) 387–394. doi:10.1016/j.prostr.2017.04.043. nomenclature δe thickness fluctuation of each created notch (groove). e thickness of the pipe. n instantaneous number of cycles under an applied stress. nf total number of cycles at the rupture. β life fraction representing the thickness fluctuation over the pipe’s thickness (β = δe/e). βc critical life fraction. βpa life fraction corresponding to the pressure before rupture. p burst or limit pressure. pu ultimate pressure corresponding to a neat hdpe specimen. pmax maximum pressure of the internal pressure curve of neat hdpe pipes pr rupture pressure of hdpe pipes. pur ultimate residual burst pressure of notched pipes. pa pressure just before the rupture corresponding to the last possible notch. pur1, pur2, , pa ultimate residual burst pressure of notched pipes according to the notch level. α parameter depending on the studied material (α = pmax/pr). η parameter depending on the applied pressure corresponding to the notch just before rupture (η =pa/pr). d0, di external and internal diameters of a cylinder. σy yield stress. σuts ultimate stress p (β) continuum burst pressure as a function of the life fraction β, d (β) continuum damage as a function of the life fraction β. ds static damage based on burst pressures of hdpe pipes. d linear damage of miner. << /ascii85encodepages false /allowtransparency false /autopositionepsfiles true /autorotatepages /none /binding /left /calgrayprofile (dot gain 20%) /calrgbprofile (srgb iec61966-2.1) /calcmykprofile (u.s. web coated \050swop\051 v2) /srgbprofile (srgb iec61966-2.1) /cannotembedfontpolicy /error /compatibilitylevel 1.4 /compressobjects /tags /compresspages true /convertimagestoindexed true /passthroughjpegimages true /createjobticket false /defaultrenderingintent /default /detectblends 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/pdfxoutputintentprofileselector /documentcmyk /preserveediting true /untaggedcmykhandling /leaveuntagged /untaggedrgbhandling /usedocumentprofile /usedocumentbleed false >> ] >> setdistillerparams << /hwresolution [2400 2400] /pagesize [612.000 792.000] >> setpagedevice microsoft word numero_54_art_14_2901 v. shlyannikov et alii, frattura ed integrità strutturale, 54 (2020) 192-201; doi: 10.3221/igf-esis.54.14 192 strain-gradient effect on the crack tip dislocations density valery shlyannikov, andrey tumanov, ruslan khamidullin frc kazan scientific center of russian academy of sciences, russia shlyannikov@mail.ru, http://orcid.org/0000-0003-2468-9300 tymanoff@rambler.ru, ruslankhamidullin94@mail.cru abstract. in this study, the influence of a material’s plastic properties on the crack tip fields and dislocation density behavior is analytically and numerically analyzed using the conventional mechanism-based strain-gradient plasticity (cmsgp) theory established using the taylor model. the material constitutive equation is implemented in a commercial finite element code by a user subroutine, and the crack tip fields are evaluated with novel parameters in the form of the intrinsic material length, characterizing the scale over which gradient effects become significant. as a consequence of the strain-gradient contribution, fe results show a significant increase in the magnitude of the stress fields of cmsgp when the material length parameter is considered. it is found that the density of geometrically necessary dislocations (gnd) is large around the crack tip, but it rapidly decreases away from the crack tip. on the contrary, the density of statistically stored dislocations (ssd) is not as large as geometrically necessary dislocations around the crack tip, but it decreases much slower than gnd away from the crack tip. a couple effect of material work hardening and the crack tip distance is identified. keywords. strain gradient; crack tip; dislocations density. citation: shlyannikov, v., tumanov, a., khamidullin, r., strain-gradient effect on the crack tip dislocations density, frattura ed integrità strutturale, 54 (2020) 192-201. received: 04.08.2020 accepted: 27.08.2020 published: 01.10.2020 copyright: © 2020 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. introduction he last quarter of a century witnessed increasing attention being drawn to problems of gradient plasticity. this is attributed to the established effects of measuring characteristics on small scales with respect to the structure of the material, leading to a sufficient increase in true local stresses. several experiments, including micro-indentation hardness and micro-torsion tests, have shown that metallic materials demonstrate a strong size effect at the micron and sub-micron scales. these size effects are attributed to geometrical dislocations induced by non uniform plastic deformation and strain gradients. constitutive models of classical plasticity theories do not take into account the intrinsic material lengths, and thus cannot describe size-dependent material behavior at the micron scale. fleck and hutchinson [1,2] and fleck et al. [3] developed a phenomenological gradient theory of the plasticity of materials and structures whose dimensions control plastic deformation, in the range of approximately a tenth of a micron to tens of microns. they have been applied to numerous problems where strain gradient effects are expected to play significant roles in the behavior of the material, including in the analysis of stress fields at the crack tip (huang et al.[4,5], xia and hutchinson [6]). to enable t https://youtu.be/4dxtpa0o1mk v. shlyannikov et alii, frattura ed integrità strutturale, 54 (2020) 192-201; doi: 10.3221/igf-esis.54.14 193 dimensional matching, characteristic length l was introduced to scale the components of the rotational gradient of coupled stresses (fleck and hutchinson,[1], fleck et al., [3]). this length scale was considered as an internal parameter of the material structure associated with the dislocation density. an analysis by nix and gao [7] partially elucidated the property embodied by the characteristic length l of the material, introduced by fleck and hutchinson [1] and indicated the need to further refine the gradient theory of plasticity by an experimental law based on an analysis of the dominant deformation mechanisms. nix and gao [7] used the taylor model to clarify the relationship between the shear strength and dislocation density of a material and identified a characteristic parameter of the material structure, which was introduced in the original formulation of the theory of gradient plasticity by fleck and hutchinson [1,2]. subsequently, gao et al. [8] supplemented the formulation which is referred to as the mechanism-based theory of strain gradient plasticity (msg), where the characteristic length of the material structure corresponds to the scale at which the effects of the gradients are comparable with the strain values. in the presence of a large strain gradient, the total dislocation density is considered as the sum of the statistical and geometric components. the msg theory is an attempt to establish the relationship between continuum mechanics and material science. this relationship is realized through fundamental length scales, which are combinations of elasticity and plasticity constants in combination with the burgers vector. recently, huang et al. [9] presented a simplified formulation of the gradient theory of plasticity by eliminating high-order terms associated with rotational components, naming the formulation the conventional mechanism-based strain gradient (cmsg) plasticity theory. it is likewise based on the taylor dislocation model and preserves the structure of the classical j2 theory of plasticity. in the past two decades, applications of the cmsg gradient plasticity theory were subject to intense development to solve problems of fracture mechanics. the finite element analysis showed that the stress level in the dominant gradient plasticity zone is two to three times higher than in the classical hrr field, and the stress singularity is higher than 1/2, indicating that stresses are more singular than not in the hrr solution as well as in the classical solution with elastic stress intensity factors [10-12]. martínez-pañeda et al. [12-16] quantitatively determined the ratio between the parameters of the material and the physical length at which gradient effects significantly increase stresses at the crack tip. the plasticity at the crack tip is found to be suppressed when the characteristic taylor parameter of the material structure is of the order of the size of the plastic zone, which is determined by the elastic stress intensity factor. gao and huang [17] paid attention on the role of geometrically necessary dislocations in the development of continuum plasticity theories with an intrinsic material length scale. following to this work, the purpose of our study is to investigate the crack tip dislocation behavior in cmsg plasticity. constitutive equations of conventional mechanism-based strain gradient plasticity he conventional theory of mechanism-based strain gradient plasticity (cmsg) developed by huang et al. [9] is employed in the present study owing to the following reasons. several authors have asserted that strain gradient plasticity theories can be classified into higher-order and lower-order theories. the first framework involves higher-order stress and therefore requires more boundary conditions; it includes the theory of mechanism-based strain gradient (msg) plasticity established using the taylor dislocation model. the second framework involves lower-order theories, such as the conventional theory of mechanism-based strain gradient plasticity (cmsg), which does not include a higher-order stress, where the strain gradient effect comes into play via the incremental plastic module. this is also based on the taylor dislocation model, where the plastic strain gradient appears only in the constitutive model, and the equilibrium equations and boundary conditions are the same as those in conventional continuum theories. according to the cmsg, the stress-strain relation in uniaxial tension is given by   n n yp p ref y y e f e                      , (1) where ref is a reference stress in uniaxial tension  nref y ye   , (2) t v. shlyannikov et alii, frattura ed integrità strutturale, 54 (2020) 192-201; doi: 10.3221/igf-esis.54.14 194 and f is a nondimensional function of plastic strain determined from the uniaxial stress-strain curve, which for most ductile materials can be written as a power law relation      n p p yf e    . (3) in eqns. (1–3),y denotes the initial yield stress, and n is the plastic work hardening exponent (0 n <1). the cmsg plasticity is based on the taylor (1938) dislocation model b   , (4) where  is the shear flow stress,  is the shear modulus, b the burgers vector,  is an empirical coefficient ranging from 0.3 to 0.5, and  is the dislocation density. the dislocation density  is composed of the density s for statistically stored dislocations (ssds), which accumulate by trapping each other in a random manner, and density g for geometrically necessary dislocations (gnds), which are required for compatible deformation of various parts of the material, i.e., s g    . (5) the ssd density is related to the flow stress and the material stress-strain curve in uniaxial tension   2 p s ref f m b       (6) the gnd density is related to the curvature of plastic deformation, or the effective plastic strain gradient p, by p g r b    , (7) where r is the nye factor, which is around 1.90 for face-centered-cubic polycrystals. the measure of the effective plastic strain gradient p was reported by gao et al. [8] in the form of three quadratic invariants of the plastic strain gradient tensor to represent p, and the coefficients were determined by three models of gnds, i.e., p dt    ; 1 4 p p p ijk ijk     ; , , , p p p p ijk ik j jk i ij k         . (8) where pij is the tensor of the plastic strain rate. the tensile flow stress is related to the shear stress by p flow sm m b r b        . (9) because the plastic strain gradient p vanishes in uniaxial tension, the density s for ssds is described by eqn. (6), and the flow stress becomes  2 p pflow ref f l     , (10) where v. shlyannikov et alii, frattura ed integrità strutturale, 54 (2020) 192-201; doi: 10.3221/igf-esis.54.14 195  2218 yl b   (11) is the intrinsic material length in the strain gradient plasticity based on parameters of elasticity (shear modulus ), plasticity (reference stress ref), and atomic spacing (burgers vector b). for metallic materials, the internal material length is indeed on the order of microns, consistent with the estimate by fleck and hutchinson [2]. to avoid the uses of higher-order stresses, huang et al. [9] proposed a viscoplastic formulation of the cmsg plasticity in the form of the following constitutive equations  2 m m p e e p p flow ref f l                            (12) 3 2 2 m e ij kk ij ij ij e flow k                           , (13) where e is the effective stress, ij is the deviatoric strain rate, and m is the rate-sensitivity exponent. notably, huang et al. [9] compared cmsg with the higher-order theory of mechanism-based strain gradient plasticity (gao et al.,[8]) established from the same taylor dislocation model. the stress distributions predicted by the lower and higher-order theories are only different within a thin boundary layer, whose thickness is approximately 10nm. cmsg, along with other continuum plasticity theories must have lower limits and cannot be applied down to the nanometer scale. this is because the continuum plasticity theories represent the collective behavior of discrete dislocations, and therefore the strain gradient effects are significant at a scale larger than the average dislocation spacing, such that continuum plasticity is still applicable. this lower limit, however, is not a fixed constant, and it may vary for different materials. however, such a lower limit exists, below which cmsg and other continuum plasticity theories are not applicable. there is no upper limit of cmsg, as the strain gradient term pl becomes negligible at the large scale. cmsg then naturally degenerates to classical plasticity. subject for consideration and loading conditions for numerical fem analyses he geometry considered in this study is the compact tension (ct) specimen. the ct configuration is applied conventionally for the numerical and experimental studies in fracture mechanics. the load is prescribed by imposing a displacement on the pins. we model the contact between the pins and the specimen by using a surface to surface contact algorithm with finite sliding (fig.1). the principal feature of our study is the evaluation of coupling material properties and strain gradient plasticity effects. to this end, the wide range of plastic work hardening exponent n for the elastic-plastic solids at a specified value of the intrinsic material length parameter l, have been used in our calculations. in the numerical results to be considered, the comparative analysis is based on assuming different values of the normalized, remotely applied elastic stress intensity factor (sif) 1 yk l . different pure mode i loading conditions are obtained for considered configuration by combinations of the nominal stress level and the initial crack length. in the following, stresses ij are normalized by the yield stress y in uniaxial tension, while the distance r to the crack tip is normalized by the internal material length l in cmsg plasticity. it must be pointed out that the internal material length l has been used to normalize r and k1, and this intrinsic material length parameter enters the constitutive equation for dimensional consistency. the value of l can be obtained by fitting micro-scale experiments and typically ranges between 1 μm and 10 μm. the cmsgp model recovers the conventional plasticity solution when l = 0. the crack faces for considered subject remain traction-free. the elastic stress intensity factor, k1, of the remotely applied field increases monotonically, such that there is no unloading. t v. shlyannikov et alii, frattura ed integrità strutturale, 54 (2020) 192-201; doi: 10.3221/igf-esis.54.14 196 figure 1: compact tension specimen. the numerical results for the ct specimen presented in this study concern the following sets of loading conditions and material properties: /y e =0.002, plastic work hardening exponents are n = 0.1, 0.2; the intrinsic material lengths is l = 5 μm, external applied loads are 1 1 yk k l = 10.87, 21.73 and the poissons' ratio is  = 0.3. unlike the higher-order theory of mechanism-based strain gradient plasticity, cmsg is a lower-order theory, which does not involve a higher-order stress, such that its governing equations are essentially the same as those in classical plasticity theories. existing finite element programs can be easily modified to incorporate the plastic strain gradient effect. the framework presented in section 2 is numerically implemented by using the ansys program [18]. specifically, we implemented the constitutive relations (eqns.1,12,13) of cmsg in the finite element program ansys via its usermaterial subroutine umat. it only differs from classical plasticity in that the plastic strain gradient must be evaluated in umat. fortran modules are used to store the plastic strain components across the gaussian integration points, and the plastic strain gradient is computed by numerical differentiation within the element. this is accomplished by interpolating the plastic strain increment εp within each element via the values at gaussian integration points in isoparametric space, and subsequently determining the gradient of the plastic strain increment via differentiation of the shape function. figure 2: crack tip finite element mesh. we model an ct specimen (fig.1) of width w = 50 mm and initial crack length a0= 23.65 mm. in the finite element models, an initial crack tip is defined as a notch with finite curvature radius  = 0.06m. with the aim of accurately characterizing the influence of the strain gradient, a highly refined mesh is used near the crack tip. after a mesh sensitivity analysis, the size of the elements is on the order 5 nm; the typical number of quadrilateral quadratic plane strain elements v. shlyannikov et alii, frattura ed integrità strutturale, 54 (2020) 192-201; doi: 10.3221/igf-esis.54.14 197 is approximately 550 000. as shown in fig. 2, a very refined mesh is used near the crack tip to accurately capture the influence of plastic strain gradients. efforts are made to ensure that the elements have an aspect ratio close to one. mesh refinement and a comparison of different elements can ensure that the numerical results are accurate. numerical results and discussion the compact tension specimen is analyzed by the two-dimensional plane strain finite element method. fig. 3 shows the effective stress e /y, normalized by the uniaxial yield stress y, versus the nondimensional distance to the crack tip, r/l, ahead of the crack tip predicted by cmsg theory, where l is the internal material length in the strain gradient plasticity. the remotely applied stress intensity factors depict the ct specimen 1k =10.87 and 1k =21.73, while the plastic work hardening exponents are n =0.2 and 0.4. the corresponding stress distribution in the classical hrr plasticity (without strain gradient effects) is also shown in fig. 3. and the horizontal line of 1eqv y   represents plastic yielding. for the specified value of l =5m, the above result indicates that the strain gradient effects are significant within a zone of approximately 0.3r/l. this is in agreement with the xia and hutchinson’s [6] estimate of the size of dominance zone for the asymptotic and jiang et al. [10] numerical crack tip fields in strain gradient plasticity. once the distance to the crack tip is less than 0.3r/l, the effective stress predicted by cmsg plasticity increases considerably more rapidly than its counterpart in conventional hrr plasticity, which is dependent on the applied stress intensity factor level 1k and the plastic work hardening exponent n value. at a relatively small remote stress intensity factor 1k =10.87, the equivalent stress accounting for the strain gradient effect is approximately five times higher and more than that in classical plasticity. figure 3: effective stress distributions at crack tip in ct specimen. a) b) figure 4: comparison ssd and gnd behavior versus crack tip distance as a function of work hardening exponent n. v. shlyannikov et alii, frattura ed integrità strutturale, 54 (2020) 192-201; doi: 10.3221/igf-esis.54.14 198 figs. 4a and b show the distributions of the densities ρg and ρs of geometrically necessary dislocations and statistically stored dislocations as a function of the nondimensional crack tip distance r/l ahead of the crack tip at polar angle  = 0. here ρs and ρg are related to the uniaxial stress-plastic strain relation and the effective plastic strain gradient and by   2 p s ref f m b       and   p g r b  , according to eqns.(6) and (7), respectively. it can be seen in fig. 4 that the density ρg of geometrically necessary dislocations is large around the crack tip, but it rapidly decreases away from the crack tip. on the contrary, the density ρs of statistically stored dislocations is not as large as ρg around the crack tip, but it decreases much slower than ρg away from the crack tip. this suggests that both ρs and ρg are important near the crack tip, which is consistent with the conclusion established from fig. 3 that the significant increase in stress near the crack tip is due to the geometrically necessary dislocations. a) b) figure 5: (a) ssd and (b) gnd density radial distributions for different loading conditions and plastic material properties. figs. 5a and b provides a separate comparison ahead of the crack tip distributions of the densities ρg and ρs of geometrically necessary dislocations and statistically stored dislocations for different loading conditions and plastic material properties described by applied stress intensity factors level 1k and the plastic work hardening exponent n value. as expected, the dislocation density increases with increasing sif 1k , with higher densities corresponding to a more ductile material at n=0.2. once the distance to the crack tip is less than 0.01r/l, the statistically stored dislocations (ssd) density ρs predicted by cmsg plasticity rapidly increases (fig.5a), while the density ρg of geometrically necessary dislocations (gnd) is monotonously decreases away from the crack tip (fig.5b). a) b) figure 6: contour plots of dislocation densities (a) ssd and (b) gnd. figs. 6a and b show the contour plots of the densities ρs and ρg of statistically stored dislocations and geometrically necessary dislocations as a function of the specified the crack tip distance values that is normalized by the internal material length l . dimension plots of  can be shown by considering 𝑥 cos𝜃 and 𝑦 sin𝜃. first, fig. 6 shows the angular v. shlyannikov et alii, frattura ed integrità strutturale, 54 (2020) 192-201; doi: 10.3221/igf-esis.54.14 199 stress variations at different r/l values. angular plots are shown for four different dimensionless values of the crack tip distance ranging from 0.04 to 0.72. the applied stress intensity factor is 1 10.87k  , the intrinsic parameter value is l =5 m, and the plastic work hardening exponents is n =0.2. in fig.6a, the angular statistically stored dislocations densities ρs distributions show a very small sensitivity to the crack tip distance. fig. 6b shows how the contour plots of the geometrically necessary dislocations densities ρg change shape and decrease in size with a gradual increase in the crack tip distance r/l. a) b) figure 7: comparison of contour plots for ssd and gnd densities. recall that fig. 3 shows that strain gradient effects become important within a dominated zone at the distance ranging from 0.003(r/l) to 0.3(r/l) of the crack tip, depending on the strain hardening exponent. therefore, it is useful to analyze behavior of the dislocation density within this dominated zone. to this end fig.7 represents a comparison of the contour plots of the ssd and gnd densities ρs and ρg as a function of the dimensionless crack tip distance r/l. in fig.7a the dislocation density distribution within a small distance to the crack tip r/l≤ 0.12 indicates that the density ρg of gnd around a crack tip is significantly larger than the density ρs of ssds along all contours. this is because the strain gradient becomes more singular than the strain near the crack tip and dominates the contribution to the flow stress. however, as it follows from fig.7b, when as r/l gets larger than 0.1 the effect of the plastic strain gradients leads to situation when the densities ρs and ρg of statistically stored dislocations and geometrically necessary dislocations being the same order of magnitude. interestingly, the results shown in fig. 7b, indicates that in the plane ahead of the crack tip (𝜃 0∘) the density ρs of ssd is larger than the density ρg gnds. a) b) figure 8: contour plots of gnd densities as a function of plastic work hardening exponent and crack tip distance. v. shlyannikov et alii, frattura ed integrità strutturale, 54 (2020) 192-201; doi: 10.3221/igf-esis.54.14 200 the sensitivity of the angular geometrically necessary dislocations density distributions to the plastic material properties is investigated in fig. 8. the calculated angular distributions of the gnd density ρg are plotted in fig. 8 for plastic work hardening exponents of n = 0.2 and 0.4 for the dimensionless crack tip distance r/l = 0.04 and 0.12. the applied stress intensity factor is 1 10.87k  , the intrinsic parameter value is l =5 m. figs. 8a and b show that the difference between the contour plots in strain-gradient plasticity is significant, especially for n =0.2, and this difference gradually disappears with an increase in the degree of hardening in the order of transition from plasticity to elasticity. focusing on the cmsg plasticity results, it is evident that the dislocation density behavior at the crack tip is the result of the combined influence of plastic strain gradients and plastic material properties of the material. the comparison of these the gnd density ρg variations to each other as a function of the radial coordinate r/l conform very strong sensitivity to the crack tip distance, in agreement with expectations. during the past two decades it is found that, conventional plasticity lacks an intrinsic length scale and hence cannot predict the size effects observed in experiments. therefore, it was pointed out the importance of the mesoscale plasticity concepts based on the taylor model of dislocation hardening and the need to develop a strain gradient plasticity theory with an intrinsic material length scale. this is a significant challenge and should be collectively tackled by wide spread both experimental and numerical investigations. the analysis of the ssd and gnd densities ρs and ρg contributions according to the flow stress constitutive eqn. (10) presented in this study defines the interrelated participation of a set of governing parameters such as n, l, r/l and 1k in achieving the general effect of increasing stresses within the framework of the theory of gradient plasticity as compared to the conventional approach. conclusions s a consequence of the strain-gradient contribution, fe results show a significant increase in the magnitude and the extent of the difference between the crack tip stress fields of cmsgp and conventional hrr theories when the material length parameter is considered. the stress level in this field is three or more times higher than that in the hrr field within a zone on the order of microns around the crack tip. the contour plots of the dislocation densities clearly indicate that both geometrically necessary dislocations and statistically stored dislocations are important around the crack tip. the strain gradient effect associated with geometrically necessary dislocations is responsible for the significant stress increase around the crack tip. the sensitivity of the considered parts of dislocation densities to the coupled effects of the plastic work hardening exponent 𝑁 and the crack tip distance normalized by material length scale 𝑙 is established. acknowledgment he authors gratefully acknowledge the financial support of the russian science foundation under the project 2019-00158. references [1] fleck, n.a., hutchinson, j.w. (1993). a phenomenological theory for strain-gradient effects in plasticity, j. mech. phys. solids, 41, pp. 1825–1857. doi:10.1016/0022-5096(93)90072-n. [2] fleck, n.a., hutchinson, j.w. (1997). strain gradient plasticity, adv. appl. mech., 33, pp. 295–361. doi:10.1016/s0065-2156(08)70388-0. [3] fleck, n.a., muller, g.m., ashby, m.f., hutchinson, j.w. (1994). strain gradient plasticity: theory and experiment, acta metal. mater., 42, pp. 457–487. doi:10.1016/0956-7151(94)90502-9. [4] huang, y., zhang, l., guo, t.f., hwang, k.c. (1995). near-tip fields for cracks in materials with strain gradient effects, proc. iutam symposium on nonlinear analysis of fracture (edited by j.r.wills), kluwer academic publishers, cambridge, england, pp. 231–242. [5] huang, y., zhang, l., guo, t.f., hwang, k.c. (1997). mixed mode near-tip fields for cracks in materials with strain gradient effects, j. mech. phys. solids., 45, pp. 439–465. doi:10.1016/s0022-5096(96)00089-0. a t v. shlyannikov et alii, frattura ed integrità strutturale, 54 (2020) 192-201; doi: 10.3221/igf-esis.54.14 201 [6] xia, z.c, hutchinson, j.w. (1996). crack tip fields in strain gradient plasticity, j. mech. phys. solids., 44, pp. 1621– 1648. doi:10.1016/0022-5096(96)00035-x. [7] nix, w.d., gao, h. (1998). indentation size effects in crystalline materials: a law for strain gradient plasticity, j. mech. phys. solids., 46, pp. 411–425. doi:10.1016/s0022-5096(97)00086-0. [8] gao, h., huang, y., nix, w.d., hutchinson, j.w. (1999). mechanism-based strain gradient plasticity-i, theory. j. mech. phys. solids., 47, pp. 1239-1263. [9] huang, y., qu, s., hwang, k.c., li, m., gao, h. (2004). a conventional theory of mechanism-based strain gradient plasticity, int. j. plast., 20, pp. 753–782. doi:10.1016/j.ijplas.2003.08.002 [10] jiang, h., huang, y., zhuang, z., hwang, k.c., 2001. fracture in mechanism-based strain gradient plasticity. j. mech. phys. solids 49, 979 – 993. doi: 10.1016/s0022-5096(00)00070-3 [11] shi, m., huang, y., jiang, h., hwang, k.c., li, m. (2001). the boundary-layer effect on the crack tip field in mechanism-based strain gradient plasticity, int. j. fract., 112, pp. 23–41. doi: 10.1023/a:1013548131004. [12] qu s, huang y, jiang h, liu c. (2004). fracture analysis in the conventional theory of mechanism-based strain gradient (cmsg) plasticity, int. j. fract., pp. 199–220. doi: 10.1023/b:frac.0000047786.40200.f8 [13] martínez-pañeda, e., betegon, c. (2015). modeling damage and fracture within strain-gradient plasticity, int. j. solids struct., 59, pp. 208 –215. doi:10.1016/j.ijsolstr.2015.02.010 [14] martínez-pañeda, e., niordson, c.f. (2016). on fracture in finite strain gradient plasticity, int. j. plast., 80, pp. 154167. doi: 10.1016/j.ijplas.2015.09.009 [15] martínez-pañeda, e., natarajan, s., bordas, s. (2017). gradient plasticity crack tip characterization by means of the extended finite element method, comp. mech., 59, pp. 831–842. doi: 10.1007/s00466-017-1375-6 [16] martínez-pañeda, e., fleck, n.a. (2019). mode i crack tip fields: strain gradient plasticity theory versus j2 flow theory, europ. j. mech.a solids., 75, pp. 381 –388. doi: 10.1016/j.euromechsol.2019.02.009 [17] gao, h., huang, y. (2003). geometrically necessary dislocation and size-dependent plasticity, scripta materialia., 48, pp. 113-118. doi: 10.1016/s1359-6462(02)00329-9 [18] ansys mechanical apdl theory reference release 14.5, ansys, inc. southpointe, 275 technology drive, canonburg, pa 2012. << /ascii85encodepages false /allowtransparency false /autopositionepsfiles true /autorotatepages /none /binding /left /calgrayprofile (dot gain 20%) /calrgbprofile (srgb iec61966-2.1) /calcmykprofile (u.s. web coated \050swop\051 v2) /srgbprofile (srgb iec61966-2.1) /cannotembedfontpolicy /error /compatibilitylevel 1.4 /compressobjects /tags /compresspages true /convertimagestoindexed true /passthroughjpegimages true /createjobticket false /defaultrenderingintent /default /detectblends true /detectcurves 0.0000 /colorconversionstrategy /cmyk /dothumbnails false /embedallfonts true /embedopentype false /parseiccprofilesincomments true /embedjoboptions true /dscreportinglevel 0 /emitdscwarnings false /endpage -1 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can be opened with acrobat and adobe reader 5.0 and later.) >> /namespace [ (adobe) (common) (1.0) ] /othernamespaces [ << /asreaderspreads false /cropimagestoframes true /errorcontrol /warnandcontinue /flattenerignorespreadoverrides false /includeguidesgrids false /includenonprinting false /includeslug false /namespace [ (adobe) (indesign) (4.0) ] /omitplacedbitmaps false /omitplacedeps false /omitplacedpdf false /simulateoverprint /legacy >> << /addbleedmarks false /addcolorbars false /addcropmarks false /addpageinfo false /addregmarks false /convertcolors /converttocmyk /destinationprofilename () /destinationprofileselector /documentcmyk /downsample16bitimages true /flattenerpreset << /presetselector /mediumresolution >> /formelements false /generatestructure false /includebookmarks false /includehyperlinks false /includeinteractive false /includelayers false /includeprofiles false /multimediahandling /useobjectsettings /namespace [ (adobe) (creativesuite) (2.0) ] /pdfxoutputintentprofileselector /documentcmyk /preserveediting true /untaggedcmykhandling /leaveuntagged /untaggedrgbhandling /usedocumentprofile /usedocumentbleed false >> ] >> setdistillerparams << /hwresolution [2400 2400] /pagesize [612.000 792.000] >> setpagedevice microsoft word numero_38_art_18 a. znaidi et alii, frattura ed integrità strutturale, 38 (2016) 135-140; doi: 10.3221/igf-esis.38.18 135 focussed on multiaxial fatigue and fracture theorical study on mechanical properties of az31b magnesium alloy sheets under multiaxial loading a. znaidi, o.daghfas, s.guellouz, r.nasri lr-mai-enit bp37, national school of engineers of tunis, université de tunis manar 1002, tunisie amna.znaidi@laposte.net, daghfasolfa@yahoo.fr, sameh.guellouz@laposte.net, rachid.nasri@enit.rnu.tn abstract. numerical simulation by plastic deformation of the shaping processes currently has a large industrial interest. it allows you to shorten the time of design and construction related products and tools to analyze and to optimize processes. an essential part of simulation tools is the constitutive law used to describe the material used. the activity of characterization and modeling of material behavior of the plastic deformation shaping remains a very important research field of activity; the objective of proposing laws of behavior used in computer codes, essentially based on finite element is sufficiently to represent the real behavior of materials. considering the nature of the materials used and the stresses they experience the behavior laws account for several requirements which make them increasingly complicated. among these requirements, we cite in particular plastic anisotropy, the great transformations, the complexity and diversity of loads, etc. the complexity of these laws makes them more difficult to implement and in particular to identify: the classic tests are no longer sufficient for identification. the objective of this work is based on two essential points: suggest a construction strategy, particularly of identifying laws elastoplastic behavior anisotropic operational for the numerical simulation of plastic deformation shaping processes with particular attention to sheet metal magnesium. magnesium sheet metal manufacturing process involves rolling operation. in a cost-cutting goal, this operation now takes place cold, implying a very marked anisotropy of the material at the output of the mill. keywords. mechanical behavior; tensile test; loading direction; lankford coefficient; identification. citation: znaidi, a., daghfas, o., guellouz, s., nasri, r., theorical study on mechanical properties of az31b magnesium alloy sheets under multiaxial loading, frattura ed integrità strutturale, 38 (2016) 135-140. received: 30.05.2016 accepted: 25.06.2016 published: 01.10.2016 copyright: © 2016 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. a. znaidi et alii, frattura ed integrità strutturale, 38 (2016) 135-140; doi: 10.3221/igf-esis.38.18 136 introduction large majority of the metal parts are obtained by forming during which the material is plastically deformed. these forming processes are optimized to reduce cost; this requires manufacturers to increasingly use numerical simulation and therefore need to describe the material behavior. these simulations are often flawed by a simplified description of the plastic behavior of the material; particularly the anisotropy of rolled sheets [1-3]. therefore, it is important to accurately model the plastic behavior of metals in large deformation in order to better predict the behavior of the part during the forming. the formulation of the anisotropic elasto-plastic behavior in large deformations is well understood now: using the formalism of rotating frame ensures the objectivity of the behavior law regardless of the constitutive model functions, [2-5]. to describe the plastic behavior of the material, it is necessary to clarify two concepts: (i) a load surface related to a plasticity criterion [6] that indicates the conditions of plastic flow, (ii) an anisotropy evolution. the experimental determination of these areas through various mechanical testing and mathematical modeling has been the subject of many research efforts such as using the von mises criterion: due to its implementation in most commercial finite element analysis codes. this criterion is called energy criterion in which the elastic deformation energy of the material must not exceed a limit value in order to remain within the elastic range. in the case sheet metal, the material is treated as having orthotropic plasticity where retained three preferred directions used in the expression of the hill criterion. also, in order to describe the asymmetric behavior in tension and compression such as the anisotropy of a structure of a sheet metal cazacu, barlat and al proposed in a new orthotropic criterion [7-11]. the objective of this work is to provide a model for the numerical simulation of forming processes by plastic deformation of thin metal sheets. hence, the importance of developing a general framework for elasto-plastic orthotropic models (initial orthotropic and isotropic hardening) based on the choice of an equivalent stress, a hardening law and a plastic potential [12-14] and a model identification strategy using and experimental database [15]. this database consists of various hardening curves from various tests interpreted as homogeneous [2] and their lankford coefficients. these plates are obtained from a hot-rolling process. at this point, the identification of constitutive parameters of the material behavior laws is an important step. a new identification strategy with its validation using barlat's criterion will be presented. anisotropic elasto-plastic constitutive laws n this work, we are interested in a plastic hardening behavior. the materials are treated as incompressible with negligible elastic deformations. the plastic hardening constitutive laws that we have to study fall within the following framework:  f ( , ) 0,    σ q (1) with q the transformation tensor between the initial time t0 and the current time t. α represents the internal hardening variable. h( , )   σd (2) . 1( , )    σ (3) with λ plastic multiplier that can be determined from the consistency condition . f and d is the plastic strain rate tensor. this work is limited to plastic orthotropic behavior. models are formulated for standard generalized materials with an isotropic hardening described by an internal hardening variable, a law of evolution and an equivalent deformation. the material is initially orthotropic and remains orthotropic; isotropic hardening is assumed to be captured by a single scalar internal hardening variable denoted by . in particular, we will assume that the elastic range evolves homothetically, the yield criterion is then written as follows: a i a. znaidi et alii, frattura ed integrità strutturale, 38 (2016) 135-140; doi: 10.3221/igf-esis.38.18 137 d d c sf ( , ) ( ) ( )    σ σ (4) dσ is the deviator of the cauchy stress tensor (incompressible plasticity). using the special setup of the space deviators, the general form of the equivalent orthotropic plan stress, is thus: d d f1 2 3c c( ) ( x , x , x ) / ( , 2 )    σ σ (5) with d d d 1 2 3x cos ; x sin cos2 ; x sin sin2      σ σ σ any type of criterion (4) can be written in the form: d sf ( , 2 ) / ( )    σ (6) where  is the angle that defines the test and  the off-axis angle [12-14]. test expansions equibiaxes (e.e) simple traction (s.t) large traction (l.t)     table 1: values of θ relative to the various tests identification procedures n this section we focus on the phenomenology of plastic behavior; especially modeling plasticity and hardening based on experimental data represented as families of hardening curves, and lankford coefficient data. in order to simplify our identification process, the following assumptions are adopted: identification through “small perturbations” process, the tests used are treated as homogeneous tests, we neglect the elastic deformation; the behavior is considered rigid plastic incompressible, the plasticity surface evolves homothetically (isotropic hardening)and all tests are performed in the plane of the sheet resulting in a plane stress condition. the identified model is defined by an equivalent stress σc (a: σd) when σc is an isotropic function; it is assumed that the shape is defined by coefficient of the form m, a is the 4th order orthotropic tensor defined by anisotropy coefficients f, g, h, n’ and the hardening curve s (). knowing that hardening’s curve ( )   is determined from experimental tests as r ( ). we can also begin our identification procedures using the lankford coefficient; as determined from the tensile test by: . . . . 2 3 1 2r / -1/ (1 / )       (7) we can notice that the lankford coefficient is independent of . this coefficient is equal to one in the case of isotropy, and remains constant in the case of transverse isotropy. however, in the case of orthotropy, it varies depending on the off-axis angle . this coefficient completely characterizes the anisotropy of the sheet when loaded in its plane. results and discussions his identification strategy requires:  experimental database.  criterion for anisotropic plasticity. i t a. znaidi et alii, frattura ed integrità strutturale, 38 (2016) 135-140; doi: 10.3221/igf-esis.38.18 138  validation strategy in the particular case of magnesium sheets where anisotropy is present, the identification of this constitutive law requires the identification of the hardening function, the anisotropy coefficients, the form factor m and r ( ) the lankford coefficient. using as a hardening function a hollomon law: n s k   (8) and as a plasticity criterion using the barlat model [6]: m mmm c q q q q q q1 2 2 3 1 3        (9) where q1, q2 and q3 are the eigenvalues of the tensor q c s ai i(q) ( ) 0. where (a ) : thus (a ) :      q a q aσ (10) using the simplex algorithm and using the plastic barlat model and respecting the assumptions, the identification of the thin magnesium sheet is equivalent to choosing the model coefficients while minimizing the squared difference between the theoretical and experimental results. ψ k n 00° 408.5 0.102 22.5° 410.6 0.096 45° 425.6 0.101 67.5° 432.5 0.0901 90° 437.1 0.0873 table 2: identification of the constants of hardening law for different tractions tests. knowing that the coefficient n is the same for all tests as demonstrated at the beginning of this work, by convention we choose n for traction in direction ψ = 00° as reference. for n=0.102, we present different values of k (see tab. 3). ψ k 00° 418.1 22.5° 418.1 45° 427.1 67.5° 447.3 90° 455 table 3: identification of the constant hardening law for fixed n. in fig.1, the experimental hardening curve (exp) and the curve identified from a model (iden) using an average value of n are represented. for tensile tests, the models (iden) give a clear fit between the theoretical and experimental results. our second identification step amounts to determining the coefficients of anisotropy (f, g, h, n’) and the shape coefficient m (tab. 4), considering the non-quadratic barlat's criterion (9). a. znaidi et alii, frattura ed integrità strutturale, 38 (2016) 135-140; doi: 10.3221/igf-esis.38.18 139 figure 1: identification of the hardening curve:  =00°. f g h n’ m 0.137 0.0992 1.4889 3.104 1.1999 table 4: identification of anisotropic coefficients and a shape coefficient m in fig. 2 the model (ident) allows us to study the load surface on each test. we note that this material is resistant to simple shear like simple traction. figure 2: evolution of the load surface in the deviatory plan  x x2 3, . figure 3: evolution of the anisotropy. 0,5 0,7 0,9 1,1 0 0,4 0,8 1,2 1,6       a. znaidi et alii, frattura ed integrità strutturale, 38 (2016) 135-140; doi: 10.3221/igf-esis.38.18 140 using the identified anisotropic coefficients, we represent in fig. 3 the evolution of the anisotropy based on off-axis angles; using the barlat's criterion this material is very anisotropic at  =45°. conclusion in this work we show that identification strategy results can be extracted. this identification has focused both on plastic material parameters of the constitutive law and lankford coefficient. thus, the plastic behavior model: hollomon law and barlat criterion with 5 parameters are identified. a validation by comparing model / to experiment data was performed.the model using the barlat's criterion is in good agreement with experimental results relating to lankford coefficients. following this strategy, we observed very pronounced anisotropy of az31bmagnesium and the load surface for different tests at the end of this identification. with this strategy, we can study in a more precise way the anisotropy of the magnesium model by integrating barlat in integrating the model hill. references [1] ghouati, o., gelin, j.c., a finite element based identification method for complex metallic material behavior, computational materials science, 68 (2001) 2157. [2] znaidi, a., plasticity orthotrope in large deformation, phd thesis at the faculty of sciences of tunis (2004). [3] znaidi, a., gahbiche a., identification of the plastic behavior of orthotropic thin plates based on non-quadratic yield criterion. 6th national conference of physics research hammamet (1999). [4] boubakar, l., boisse, p., anisotropic elastoplastic behavior for numerical analysis of thin shells in great transformations. européene review mechanics, 7(6) (1998). [5] manget, b., perre, p., a large displacement formulation for anisotropic constitutive laws, european journal of mecanique, 18(5) (1999). [6] barlat, f., brem, d. l. j., a six components yield function for anisotropic materials, int. j. plasticity, 7 (1991) 693712. [7] gronostajsk, z., the constitutive equations for fem analysis. journal of material processing technology, 106 (2000) 40-44. [8] hill, r., a theory of the yielding and plastic flow of anisotropic metals, proc. roy. soc of london, a93 (1948) 281297. [9] cazacu, o., ionescu, i. r., yoon, j. w., orthotropic strain rate potential for the description of anisotropy in tension and compression of metals, int. j. plasticity, (2009). [10] cazacu, o., plunkett, b., barlat, f., orthotropic yield criterion description of anisotropy in tension and compression of sheet metals, int. j. plasticity, 24 (2008) 847-866. [11] plunkett, b., cazacu, o., barlat, f., orthotropic yield criterion for hexagonal closed packed metals, int. j. plasticity, 22 (2006) 1171-1194. [12] daghfas, o., znaidi, a., nasri, r., anisotropic behavior of mild steel subjected to isotropic and kinematic hardening, in: 6th international conference on advances in mechanical engineering and mechanics (icamem2015), hammamet, (tunisia) (2015) 128. [13] baganna, m., znaïdi, a., kharroubi, h., nasri, r., identification of anisotropic plastic behavior laws for aluminum 2024 after heat treatment materials from off-axis testing, toulouse, (2010). [14] znaidi, a., daghfas, o., toussaint, f., nasri, r., strategy for the identification of anisotropic behavior laws for ti40 sheets, ampt2015 madrid, (2015). [15] yueqian, j., xiang, l., yuanli, b., theorical study on mechanical properties of az31b magnesium alloy sheets under multiaxial loading, j. automotive safety and energy, 4 (2012). << /ascii85encodepages false /allowtransparency false /autopositionepsfiles true /autorotatepages /none /binding /left /calgrayprofile (dot gain 20%) /calrgbprofile (srgb iec61966-2.1) /calcmykprofile (u.s. web coated \050swop\051 v2) /srgbprofile (srgb iec61966-2.1) /cannotembedfontpolicy /error /compatibilitylevel 1.4 /compressobjects /tags /compresspages true /convertimagestoindexed true /passthroughjpegimages true /createjobticket false /defaultrenderingintent /default /detectblends true /detectcurves 0.0000 /colorconversionstrategy /cmyk /dothumbnails false /embedallfonts true /embedopentype false /parseiccprofilesincomments true /embedjoboptions true /dscreportinglevel 0 /emitdscwarnings false /endpage -1 /imagememory 1048576 /lockdistillerparams false /maxsubsetpct 100 /optimize true /opm 1 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can be opened with acrobat and adobe reader 5.0 and later.) >> /namespace [ (adobe) (common) (1.0) ] /othernamespaces [ << /asreaderspreads false /cropimagestoframes true /errorcontrol /warnandcontinue /flattenerignorespreadoverrides false /includeguidesgrids false /includenonprinting false /includeslug false /namespace [ (adobe) (indesign) (4.0) ] /omitplacedbitmaps false /omitplacedeps false /omitplacedpdf false /simulateoverprint /legacy >> << /addbleedmarks false /addcolorbars false /addcropmarks false /addpageinfo false /addregmarks false /convertcolors /converttocmyk /destinationprofilename () /destinationprofileselector /documentcmyk /downsample16bitimages true /flattenerpreset << /presetselector /mediumresolution >> /formelements false /generatestructure false /includebookmarks false /includehyperlinks false /includeinteractive false /includelayers false /includeprofiles false /multimediahandling /useobjectsettings /namespace [ (adobe) (creativesuite) (2.0) ] /pdfxoutputintentprofileselector /documentcmyk /preserveediting true /untaggedcmykhandling /leaveuntagged /untaggedrgbhandling /usedocumentprofile /usedocumentbleed false >> ] >> setdistillerparams << /hwresolution [2400 2400] /pagesize [612.000 792.000] >> setpagedevice microsoft word numero_27_art_1 l. vergani et alii, frattura ed integrità strutturale, 27 (2014) 1-12; doi: 10.3221/igf-esis.27.01 1 focussed on: infrared thermographic analysis of materials a review of thermographic techniques for damage investigation in composites laura vergani, chiara colombo, flavia libonati politecnico di milano, department of mechanical engineering, via la masa 1, 20156 milano laura.vergani@polimi.it abstract. the aim of this work is a review of scientific results in the literature, related to the application of thermographic techniques to composite materials. thermography is the analysis of the surface temperature of a body by infrared rays detection via a thermal-camera. the use of this technique is mainly based on the modification of the surface temperature of a material, when it is stimulated by means of a thermal or mechanical external source. the presence of defects, in fact, induces a localized variation in its temperature distribution and, then, the measured values of the surface temperature can be used to localize and evaluate the dimensions and the evolution of defects. in the past, many applications of thermography were proposed on homogeneous materials, but only recently this technique has also been extended to composites. in this work several applications of thermography to fibres reinforced plastics are presented. thermographic measurements are performed on the surface of the specimens, while undergoing static and dynamic tensile loading. the joint analysis of thermal and mechanical data allows one to assess the damage evolution and to study the damage phenomenon from both mechanical and energetic viewpoints. in particular, one of the main issues is to obtain information about the fatigue behaviour of composite materials, by following an approach successfully applied to homogenous materials. this approach is based on the application of infrared thermography on specimens subjected to static or stepwise dynamic loadings and on the definition of a damage stress, d, that is correlated to the fatigue strength of the material. a wide series of experimental fatigue tests has been carried out to verify if the value of the damage stress, d, is correlated with the fatigue strength of the material. the agreement between the different values is good, showing the reliability of the presented thermographic techniques, to the study of composite damage and their fatigue behaviour. keywords. ir-thermography; damage; composite; fatigue. introduction omposite materials, widely used in structural applications for their well-known favourable strength-to-weight ratio, generally present a variety of defects or imperfections related to their heterogeneous nature and depending on the manufacturing process. their mechanical properties, especially those of stiffness and strength, that are important in structural design, are connected to the presence defects. dealing with cyclic loading, thus with fatigue problems, the assessment of structures and the prediction of residual life still remain an open issue in the literature. also, the existence of a strength, which can be defined as fatigue limit for composite materials, is not even univocal. some authors [1] do not find drastic change between low cycle fatigue and high cycle fatigue behaviour in composites, unlike in metals. on the c http://dx.medra.org/10.3221/igf-esis.27.01&auth=true http://www.gruppofrattura.it l. vergani et alii, frattura ed integrità strutturale, 27 (2014) 1-12; doi: 10.3221/igf-esis.27.01 2 other side, other authors [2, 3] evidenced an infinite life region, where damage mechanisms are either arrested or prevented by a rather slow propagation rates to cause failure for large number of cycles. all these problems dealing with fatigue of composites are complex, also because different kinds of damage can occur in these materials, leading to many kinds of failure modes: matrix cracking, fibre-matrix interfacial bond failure, fibre breakage, void growth, matrix crazing and delamination [4]. in order to detect damages in composite structures and to monitor their location and evolution during loading, adequate experimental techniques are therefore necessary. in the present review, among the available non-destructive techniques, infrared (ir) thermography is adopted. ir-thermography is a non-contact and non-destructive experimental methodology, based on the concept of surface temperature scanning during the application of a mechanical or thermal load on a structural component. in the following, the paper gives an overview of the principles and methodologies at the basis of thermography as experimental non-destructive technique, especially dealing with composites. different methods have been developed in the literature, initially applied to homogeneous materials, and recently applied also to composite structures. the attention is focused on the correlation between the thermal response of composites under mechanical loads, either static or dynamic, and the fatigue behaviour of the studied materials: the idea is to discuss thermographic methods and their applications in order to relate variations in thermal response to fatigue limit of composites. infrared thermography: principles and applications nfrared (ir) thermography is a non-destructive technique, widely applied for quick inspection of large components. laying on the principle that a grey body emits electromagnetic radiation due to its thermal conditions, irthermography allows performing contactless measurements of the surface temperature variation of the emitting body. this technique can be applied in a passive or active mode: the former is generally applied on materials, which experience a different temperature than the surrounding materials, the latter, instead needs an external stimulus to induce a surface temperature variation. the external stimulus can be a mechanical or a heat source. passive thermography is rather qualitative, whereas active thermography allows both qualitative and quantitative analyses to be performed [5]. as qualitative analyses, this technique allows the detection of damages of various nature on different types of materials, e.g. fibre–matrix debonding and delamination in composites, moisture ingress in honeycomb sandwich materials, interfacial debonding in adhesive joints, crack-like defects in metals [6]. an example of thermography-based quantitative analysis instead, is the thermoelastic stress analysis (tsa), which is an experimental method of stress measurement based on the thermoelastic effect [7-12]. the thermoelastic effect, first described by lord kelvin [13] consists in the reversible temperature variation, occurring in a solid when it is deformed in the elastic field, and due to volume variation. this is summarized by the experimental equation of thermoelasticity, which states a linear relationship between the stress state of a homogeneous isotropic material in adiabatic conditions and its temperature variation: 0 0 t k t      (1) where t0 is the average temperature of the solid, k0=λ/ρcp is the thermoelastic constant, λ is the linear thermal expansion coefficient, ρ the mass density, cp the specific heat at constant pressure δσ=δ(σ1+σ2+ σ3) is the variation of the first stress invariant. this equation, formulated for a homogeneous isotropic material, has also been extended to orthotropic materials, by considering different thermoelastic constants in each direction, due to the anisotropy [14]. indeed tsa, largely used for homogeneous materials, has also recently found application to orthotropic materials [10, 15]. however, in particular cases, such as for polymer composite materials, according to salerno et al. [11] the thermoelastic constants have shown to be affected by the presence of a surface resin rich layer as well, which is few microns thick and creates a frequency dependence, by damping the thermal waves generated in the fibres. nevertheless, surface temperature variations in materials do occur not only for thermoelastic effect, but also for irreversible transformations (i.e. damage, plastic deformation, and change in the microstructure). i http://dx.medra.org/10.3221/igf-esis.27.01&auth=true http://www.gruppofrattura.it l. vergani et alii, frattura ed integrità strutturale, 27 (2014) 1-12; doi: 10.3221/igf-esis.27.01 3 recent thermographic systems generally use an infrared detector, endowed with a sensor array, to measure the small reversible temperature changes, induced in a component, due to external stimuli, such as loads (e.g. in the case of tsa), or heat sources, such as pulsed light (e.g. in the case of pulsed thermography). thermographic techniques applied to composite materials many thermographic approaches are present in the literature to study behaviour of different composites, and to relate their thermal response to fatigue life, from almost 40 years. in the past, thermocouples were used, while, more recently, applications by means of ir-cameras connected with laptops for data acquisition have been developed. moreover, dedicated softwares for thermal maps (matrices where the observed surface temperature is stored) handling have also been developed. considering tensile static loads, composites, as all other homogeneous materials, experience an initial decrease in surface temperature: this is due to the well-known thermoelastic effect [13] and it is related to the variation in volume during the elastic stage. generally, after the initial decrease in temperature, while load increases, temperature deviates from linearity, till a minimum, then it starts to increase. a schematic of the classic stress trend and temperature trend is given in fig. 1. figure 1: schematic representation of the typical stress and temperature trends as a function of time, during a static tensile test. from these experimental observations, some authors related the end of the thermoelastic stage to the fatigue limit of homogeneous materials [16], or to composite fatigue strength. this value of stress was named σd, where d stands for damage initiation. this idea was developed for glass [17, 18] and for basalt fibre reinforced composites [19]. in both these cases, if the applied load is lower than σd, defects present in the materials do not propagate and the global temperature trend during tensile static tests is linear. this was also confirmed by sem analyses on glass-fibre reinforced specimens tested at various load levels [18] and by measurements of stiffness reduction in interrupted static tests charaterised by two loading-unloading cycles. together with this application of thermography to static tensile tests, also dynamic loads can be taken into account, and considerations on surface temperature changes can be proposed. from experimental observations [20], it was clear that during fatigue the surface temperature of the loaded specimens tends to reach a constant value, characteristic of the stress level. also, the initial thermal response to cyclic (dynamic) loads, that is the increase of temperature (δt) during cycling (δn), thus the ratio δt/δn, is a typical feature of each tested material and it can be related to the applied stress. according to the literature, values of δt/δn, plotted as a function of different applied stresses, present a double linear trend [20]. the intercept between these two lines (i.e. the breakup point) identifies a stress level, which was experimentally found to be close to the fatigue limit. this experimental observation was confirmed not only for homogeneous materials, but also for composites [17, 19]. a schematic of the trend δt/δn vs. maximum stress amplitude is given in fig. 2. a third method, based on progressively increased stress amplitudes and on energetic observations, was also proposed in the literature [21]. it is well known that dissipation of heat, thus energy, occurs when the material starts being damaged. this irreversible loss of energy is related to friction inside the material or to irreversible damage evolution. in [21], a new digital processing technique, called d-mode, is proposed to evaluate the dissipated energy. this technique can be performed with lock-in thermographic systems [22]. it extracts non-linear coupled thermo-mechanical effects during cycling. dissipated energy is much smaller than thermo-elastic source and, therefore, the measure of this quantity requires a high sensitive thermal imaging camera. its evaluation also requires a dedicated algorithm, which separates the dissipated energy from the thermo-elastic source and filters signals, neglecting the background noise. according to experimental http://dx.medra.org/10.3221/igf-esis.27.01&auth=true http://www.gruppofrattura.it l. vergani et alii, frattura ed integrità strutturale, 27 (2014) 1-12; doi: 10.3221/igf-esis.27.01 4 observations by brémond [21], in case of progressively increased stress amplitudes, the dissipated energy shows a bi-linear trend. when the stress amplitude is low, the dissipated energy as a function of applied stress shows an almost flat trend, thus no energy is dissipated by irreversible mechanisms. then, a rapid increase in the slope occurs for higher stress amplitudes, as schematically shown in fig. 3, where a classic d-mode signal vs. stress amplitude trend is given. the author proposed that this breakup stress in the dissipated energy trend corresponds to a different behaviour in the material damage and indicates damage initiation in the material subject to dynamic loads. thus it could be correlated with the material fatigue limit. this consideration has recently been validated also for carbon fibre reinforced composites [23, 24].  t / n stress amplitude d -m o d e stress amplitude figure 2: schematic representation of the classic δt/δn trend with respect to the stress amplitude. figure 3: schematic representation of the typical d-mode trend as a function of the stress amplitude. materials n our research studies we considered different materials, to investigate different damage types. indeed, in the case of composite materials, it is interesting to probe the effects of the material internal organization on the mechanical response and on the damage modes. we mainly focused on fibre-reinforced composites (frc) made of natural or synthetic fibres, impregnated into polymer matrix, and arranged in different stacking sequences. in particular, in [18] we considered two e-glass/epoxy laminates with a 50% wt. of e-glass fibres (600 mg/m2), obtained by manual lamination: one laminate made of unidirectional (i.e. ud) fibreglass, and one plate made of non-crimp fabrics (ncfs), with the following layup [±45°]10. from the composite plates we cut rectangular specimens and we placed gfrp adhesively bonded tabs at the specimen ends, as required by the standards [25, 26], ensuring a correct load transfer and avoiding any stress concentration due to the pressure applied in the grip zone. the dimensions of the specimens were also chosen according to the standards. we cut the ud-plate in two orthogonal directions, to get [0°]10 and [90°]10 stacking sequences. also, to study the influence of defects in composites, we considered another plate of ncf-e-glass/[±45°]10 and we included a teflon (ptfe) sheet, during the manufacturing process, to simulate a delamination damage and possible damage initiation sites [27]. teflon layer was placed in correspondence of the middle layer: in this case, thermography was applied in order to localize a pre-existent damage and monitor its evolution during static or dynamic loads, as well as to evidence its influence on the surrounding regions. for this series of specimens, fibre content is 55% wt. another example of the application of thermography to composite materials is described in [19] and deals with basalt fibre reinforced plastics. in this work, basalt biaxial fabrics were used to manufacture laminated plates by vacuum infusion process and an epoxy resin, with stacking sequence [0°/90°/+45°/-45°]2s and a fibre content of 50% vol. methods efore performing thermal analyses we characterized all the materials under static loading conditions to determine the mechanical properties. then, we used a thermal camera to monitor most of the performed tests. the camera is a flir titanium ir-thermal camera, working in the waveband 2-5mm, with a 320·256 focal plane array sensor, insb cooling system and a 25mk thermal sensitivity. the adopted ir-camera is also endowed with a lock-in amplifier, i b http://dx.medra.org/10.3221/igf-esis.27.01&auth=true http://www.gruppofrattura.it l. vergani et alii, frattura ed integrità strutturale, 27 (2014) 1-12; doi: 10.3221/igf-esis.27.01 5 which amplifies the signal and filters the background noise, and a lock-in software, which operates a fourier transform of the signals. this module is useful in case of a sinusoidal source, either mechanical or thermal. indeed, by analysing a sequence of thermal images, acquired during a modulated cycle, it allows the measurement of the peak-to-peak temperature change, in terms of phase and amplitude, with respect to the modulated input cycle. during the ir-monitored tests, we placed the ir-camera approximately 300mm far from the specimen surface. we scanned the central area of the specimens, since the heat transfer from the grips could have affected the upper and lower parts of the specimen. we connected the camera to a computer, for data analysis, and to the testing machine, to have a reference signal. then we used altair, the software of the thermal camera, to post-process the data. this software allows one to have full field thermal maps of the scanned surface, hence a quick damage detection, and to perform a pixel by pixel analysis of the temperature data. besides static and dynamic characterizations of the above described materials, we carried out different types of tests, under static and dynamic loading, coupled with thermal measurements. in particular, we performed: i) static tests under monotonic loading, ii) static tests with interrupted loading, iii) stepwise dynamic tests. for the static tests we followed the standards astm d3039/d 3039m-08 [25] for ud specimens and astm d 3518/d3518m-94 [26] for the specimens with ±45° fibres. tests were performed in displacement control mode, under monotonic loading, using an mts alliance rf150 universal tensile testing machine with a 150 kn load cell. we chose a crosshead speed of 2 mm/min. during the tests, the surface temperature of the specimens was recorded by using the previously described thermal camera. the data acquisition frequency was set at 5 hz for stress-strain data, and at 1 hz for the temperature data. we also performed interrupted static tests, by stopping the load at different previously defined values. for these tests we used the same tensile testing machine used for the monotonic static tests, and the above described ir-camera for the thermal measurements. the data acquisition frequency was set at 5 hz for stress-strain data, and at 1 hz for the temperature. we performed two loading-unloading cycles and we measured, after each test, the stiffness reduction, defined as d, to have a first damage parameter: 2 1 1 % e e d e   (2) in eq. (2), d is the damage, e1 is referred to the stiffness measured during the first load cycle and e2 is referred to the stiffness measured in the second load cycle. we also performed interrupted static tests, at previously defined load values, with a single loading-unloading cycle. after the tests we cut the specimens and we analysed the cross sections by means of a scanning electron microscope (sem) to assess the internal damage due to the applied load. stepwise dynamic tests consists of dynamic tests with an increased applied load. a schematic of the load history is given in fig. 4a. these tests were performed in load control mode, with a stress ratio equal to 0.1, and the specimen surface temperature was monitored with the ir-camera. in this case we used an mts 810 hydraulic machine with a 100 kn load cell. the load frequency was set at 20 hz and the thermal data acquisition at 80 hz. the stress range, the step height, the step length, and the number of steps depend on the studied material. we carried out two types of stepwise dynamic tests: i) characterized by short steps (i.e. 103 cycles for each load step), and ii) characterized by longer steps (i.e. 6·103 cycles for each load step) for the case of glass/epoxy specimens with ±45° oriented fibres. in both cases we increased the amplitude stress by 2 mpa steps. in the short-step tests, the data were analysed by using the dissipation mode (i.e. d-mode), a tool of the thermal camera to measure the energy dissipated by the material under cyclic loading. indeed, the thermographic system is endowed with full radiometric software for lock-in applications, allowing the heat dissipation of a component, under dynamic loads, to be assessed. these measurements can give important information regarding the involved damage mechanisms. in long step tests, besides performing a d-mode analysis, the temperature was also measured. the aim of these tests, characterized by longer loading steps, was to find the stabilization temperature [20] of the material for different applied loads and the initial slope δt/δn for each applied stress. indeed according to la rosa and risitano, in homogeneous materials subjected to cyclic loads, it is possible to recognize a repeating temperature trend, characterized by three phases: an initial temperature increase, a plateau region and then a final further increase in temperature. this characteristic trend is given in fig. 4b (represented with a continuous black line), along with a bi-linear trend consisting of phase i and ii (represented with a black dashed line), characteristic of composites [17, 19]. http://dx.medra.org/10.3221/igf-esis.27.01&auth=true http://www.gruppofrattura.it l. vergani et alii, frattura ed integrità strutturale, 27 (2014) 1-12; doi: 10.3221/igf-esis.27.01 6 (a) (b) figure 4: a) stepwise loading history. the characteristics of each interval (i.e. maximum applied stress and length of the interval) depend on the tested material. b) thermal profile in each interval: the temperature characterized by an initial linear increasing region (i), represented with a black continuous line, then followed by a second linear region –represented by a back dashed lineor by a plateau region (region ii, represented by a continuous black line) and a final increasing region (region ii, represented by a continuous black line). for basalt fibre reinforced composite in epoxy matrix, specimens were tested and subjected to blocks of 10000 cycles per step, and increasing stress amplitude of 10 mpa. tests were stopped when the specimen failed. as mentioned above, we also performed a fatigue characterization of the studied materials, by carrying out load-controlled dynamic tests according to the standard astm d 3479 [28]. for these tests we used an mts 810 hydraulic machine with a 100 kn load cell, we set a stress ratio equal to 0.1 and a load frequency equal to 10 hz. we carried out tests at different load levels, to determine the σmax-logn curve. in our initial studies we chose 5·106 cycles as the runout value, chosen as an average value from the literature. in a more recent study we also performed an hcf characterization, by setting the runout value at 107. then, in view of the obtained results, we made estimations about the materials damage initiation and growth, the materials failure mode, and the life of the materials. case studies n this section, we show a series of case studies. we investigated the damage behaviour on glass fibreand basalt fibrereinforced composite materials; for the glass-frc we also considered the effect of delamination. here the results are shown on the basis of the type of performed test and analysis. generally with ir-thermography it is possible to perform both qualitative and quantitative analyses. indeed, in our study by observing the thermal maps it was possible to locate damage, which appeared as the hottest region. the analysis of the thermal map during an entire test also allowed one to make hypotheses on the failure modes. for instance, during the tests some flashes of lighting were barely visible and oriented like the fibres of the tested materials, hence representing the energy release, due to debonding, at the fibre-matrix interface. we also performed quantitative analyses, by accurately post-processing the thermal data. the temperature can be considered an important energetic parameter, strictly correlated to the damage state of the material. in our data analyses we measured the surface temperature and we averaged the temperature over the scanned area of each specimen, mainly corresponding to the central part of the specimen. indeed, in our calculations we avoided the upper and lower parts of the specimen surface for the local influence due to the grips, and the external borders for the edge effect. we should stress that the selection of the area, where to average the temperature data, has no influence on the results of the temperature trends. indeed, we performed some trials, but the trends were globally similar, though upper or lower shifted on the temperature scale. static tests (continuous and interrupted) and microscopic analyses the results of the static tests were repeatable for all the studied materials. static tests allowed the determination of the mechanical properties of the materials. the thermal analyses allowed the study of the material behaviour from an energetic viewpoint. in particular, a characteristic thermal trend has been found for all the materials and it is characterized by three regions: i http://dx.medra.org/10.3221/igf-esis.27.01&auth=true http://www.gruppofrattura.it l. vergani et alii, frattura ed integrità strutturale, 27 (2014) 1-12; doi: 10.3221/igf-esis.27.01 7 1. an initial region, where the mechanical behaviour of the material is completely elastic, the mechanical energy is elastically stored by the material, and the temperature is approximately linearly decreasing. 2. a middle region, where the mechanical behaviour of the material is elastic from a macroscopic point of view, energy is absorbed in large part, and the temperature is nonlinearly decreasing, till a minimum. it is very likely that this region corresponds to the formation of local micro-damages, from pre-existent defects. this was also confirmed by micrographic analyses by means of an sem, as shown in a previous work (libonati and vergani 2013). 3. a final region, where damage is propagating and leading to final failure. here the thermal trend is nonlinear: at beginning there is a damage localization and a local temperature increase, then as damage is growing and spreading over the sample surface, a general rise in surface temperature occurs. being the increase in temperature correlated with the energy release due to damage, the increase rate is strictly correlated with the damage mode. indeed, we observed a net increase for more brittle behaviour (e.g. the case of gfrp material with ud glass fibres parallel or orthogonal to the applied load) [18], whereas a more progressive increase in temperature (i.e. energy release) occurred for materials showing a more progressive failure mode (e.g. the case of gfrp material with glass fibres oriented at ±45° with respect to the loading direction) [18]. a schematic of the characteristic temperature curve, showing the three above described regions, is given in fig. 5, along with a characteristic stress-time curve. indeed, by overlapping the two curves in the same graph we could find the stress levels corresponding to significant damage (i.e. temperature) events. the first phase is characterized by a linear trend, and the data were fitted with a regression line, in all the studied cases. in the regression analyses we chose the experimental data to get the maximum regression coefficient. the temperature level, which represents the deviation from the linearity, coincides with the beginning of the second region. in our studies we correlated the end of the first region, from the energetic point of view, to the end of the linear thermoelastic behaviour of the material, whereas from the physical viewpoint, it could represent the beginning of the first micro-damages, probably originated from pre-existing defects, in the studied materials. indeed, there was no defect visible by bare eyes, and considering the stress-time curve, it was difficult to define the range where the material has a completely elastic behaviour. by considering the temperature-time curves we were able to define the end of the linear thermoelastic region, for all the studied materials, and by overlapping the temperature-time curve to the stress-time curve, we could determine the stress value, corresponding to the end of the linear thermoelastic phase. in our previous work, this stress value was defined as damage stress, σd [17-19]. the average values of σd, obtained per each sample type are reported in tab. 1, along with the mechanical properties (e.g. uts and fatigue stress). figure 5: schematic representation of stress and temperature trends and the three temperature regions, highlighetd with grayscale colors. in region i, the temperature data are fitted with a line, allowing the determination of the damage stress, σd, which corresponds to σi, the first stress level used in the interrupted static tests. in the graph, also σii and σiii are highlighted, the former corresponding to the minimum temperature and to the end of region ii, and the latter corresponding to the increasing temperature region (i.e. region iii). also, σii and σiii are used as stress levels for the interrupted static tests. the results of static tests, characterized by interrupted loading, were also interesting. the specimens were loaded until stress values corresponding to the end of the first and second temperature regions, and to a load level corresponding to the third region, in order to evaluate the material damage from a mechanical and physical point of view and to correlate the stress value corresponding to each temperature region with a mechanical damage parameter and an empiric observation. a schematic representation of these stress values (σi, σii, and σiii) and the three temperature regions is given in http://dx.medra.org/10.3221/igf-esis.27.01&auth=true http://www.gruppofrattura.it l. vergani et alii, frattura ed integrità strutturale, 27 (2014) 1-12; doi: 10.3221/igf-esis.27.01 8 fig. 5. in two loading-unloading cycle tests we determined the stiffness reduction as a mechanical damage parameter and we found that the damage parameter is negligible only when a specimen is loaded until a stress level smaller than the damage stress. indeed, according to the results presented in [18], the tested material (i.e. e-glass/epoxy [±45°]10) seems not to be affected by the load application, until a certain load level, which corresponds to the damage stress, whereas for stress larger than the damage stress, non-negligible micro-damages are created into the material, leading to a deviation from the linearity in the temperature curve. these micro-damages, indeed, affect the mechanical performance, leading to a non-negligible stiffness reduction, in loading-unloading interrupted static tests. the material is macroscopically in the elastic field, but according to the thermal analysis, it is very likely that small damages originate from pre-existing defects. in single loading-unloading cycles we investigated the damage state by analysing the cross sections of tested specimens by means of an sem. also these observations confirmed the hypotheses of the authors: stresses smaller than the damage stress σd cause a negligible damage, as stated by the small value of the damage parameter and by the sem micrographic images, showing no stress-induced damage. the loading-unloading curves and the sem images are given in [18]. dealing with specimens of the same nature, reinforced in glass fibres oriented at ±45°, we observed that the presence of a delamination in the thickness does not induce variation in the mechanical properties, leading to an estimation through thermographic static method very similar to the one above described for undamaged specimens. moreover, thermography applied following this approach did not lead to a clear localization of the defect. decrease/increase in temperature is uniform on the specimen surface during the static test. also, magnifications at the optical microscopy identified a uniform damage occurring in the specimens thickness [27]. for basalt reinforced, in [19] results dealing with basalt reinforced specimens in epoxy resin were reported, plotting temperature and stress data as a function of test time. a clear initial trend of the temperature was detected, till a minimum, which corresponds to a stress value very close to the one causing final failure. for the case of basalt fibre reinforced composites in epoxy matrix, the end of the temperature linearity corresponds to 69 mpa (σd). it is likely that this value of stress, if compared to the fatigue results, indicates the fatigue limit of the material. for a full comparison of the thermo-mechanical behaviour of these materials, in the present review all the results dealing with the previously discussed composites are reported, and a final plot is presented in fig. 6. this graph shows, as a summary of all the presented test cases, a comparison among thermal answers of these different materials, as a function of the applied stress. these experimental data can be fitted by a line, thus identifying a ratio (slope) characteristic of each material. considering these slopes, glass fibre composites resulted the ones cooling less quickly. this consideration is valid both for undamaged and delaminated specimens. figure 6: temperature vs stress for fibre reinforced composites: glass/epoxy, glass/epoxy with induced delamination, and basalt/epoxy. in this graph, only the data related to the linear temperature region (region i) are reported, along with the corresponding regression line. on the abscissa, the damage stresses of each tested material (d-ge for glass/epoxy, d-ge,del for glassy/epoxy with induced delamination, and d-be for basalt/epoxy) are highlighted. taking into account, instead, epoxy resin reinforced in basalt, the slope is higher and clearly different with respect to the cases of glass fibre composites. moreover, in case of fibreglass the linear region ends up very early, while basalt composite presents a completely different behaviour showing higher estimation of fatigue performances (σd) [19]. this kind of plot, shown in fig. 6, can be used to compare the global thermo-mechanical response of different materials. even if it is obtained from experimental observations on static tests, this plot is extremely useful for mechanical design, http://dx.medra.org/10.3221/igf-esis.27.01&auth=true http://www.gruppofrattura.it l. vergani et alii, frattura ed integrità strutturale, 27 (2014) 1-12; doi: 10.3221/igf-esis.27.01 9 since it can offer quick information about fatigue behaviour of the materials, and in particular to their fatigue limit, or to a stress level corresponding to a different damage mechanism. dynamic tests (stepwise and fatigue) the post-processing of the results obtained from the dynamic stepwise tests confirmed the hypotheses put forth, by observing the results of static tests. in the case of e-glass/epoxy material, [±45°]10, the results obtained by stepwise dynamic tests, characterized by shorter and longer steps, were respectively analysed by measuring the d-mode signal and the δt/δn. in particular, by plotting the results of δt/δn-σmax and d-mode-σmax we get a bilinear trend, similar to the characteristic trends reported in fig. 2 and fig. 3, respectively. the breakup point was found to be 36 mpa. in tab. 1 the average value of σd, (34) obtained from static and dynamic thermographic methods, is reported. instead, a net variation in the thermo mechanical response specimens is detected in delaminated samples tested by stepwise dynamic tests [27]. for these specimens, indeed, fatigue behaviour is deeply influenced by the presence of the localized damage in the thickness. this is clearly visible from experimental fatigue tests (fig. 7). fig. 7 shows all the fatigue data available for the considered materials in a normalised s-n curve. in order to have comparable values along vertical axis for all the composites, the ratio between applied stress amplitude and ultimate tensile strength for each material is taken into account. experimental fatigue data are fitted by means of straight lines, one for each material, to describe the finite life region. considering the final part of the curve, related to the high cycle fatigue, thus fatigue limit, data of broken and runout specimens of all the considered composites show a flattening trend at approximately 20% of the ultimate tensile strength. this ratio seems a feature for all the composites, able to describe their fatigue strength. figure 7: normalized fatigue curves for all the materials. a linear interpolation is added in the finite life region, and the fatigue limit is plotted in the infite life region. table 1: characteristics and mechanical properties of the tested materials. damage stress is the average value among those obtained from the different thermographic methods, except for e-glass/epoxy [0°]10 and [90°]10 where only the static thermographic method has been applied. material layup fibre content uts fatigue strength damage stress σd/uts % e-glass/epoxy [0°]10 50% wt. 388±4 226 58 e-glass/epoxy [90°]10 50% wt. 59±10 33 56 e-glass/epoxy [±45°]10 50% wt. 142±3 35 34 24 e-glass/epoxy* [±45°]10 55% wt. 155±5 40 37 24 basalt/epoxy [0°/90°/+45°/-45°]2s 50% vol. 409±9 74 18 *teflon insert in the mid-section of the material layup to mimic delamination. http://dx.medra.org/10.3221/igf-esis.27.01&auth=true http://www.gruppofrattura.it l. vergani et alii, frattura ed integrità strutturale, 27 (2014) 1-12; doi: 10.3221/igf-esis.27.01 10 in fig. 7, focusing the attention on the finite life region, we can notice a larger decrease in the mechanical properties of delaminated specimens, if compared with the undamaged ones. indeed this kind of specimens clearly shows different mechanical fatigue properties with respect to the other undamaged materials. instead, as previously mentioned, its high cycle fatigue limit is approximately the same: in [27] it is hypothesized that, at high cycling, active mechanisms of fatigue damage are different than for finite life region. delamination is active only in this finite stage of s-n curve, while its presence is not influencing mechanical fatigue behaviour at low stress amplitudes. from microscopy magnifications, moreover, it is clear that the teflon layer is active for the performed tests and cracks start their evolution in the composite from the two edges of this induced damage. the results from the application of thermographic techniques evidenced, for both δt/δn-σmax and d-mode-σmax plots, a similar value of fatigue limit (σd), for the cases of delaminated fiberglass. this value, moreover, is very similar to the same undamaged material: this supports the thesis that the presence of delamination does not influence the fatigue limit, which can be defined as a characteristic feature of the material. the results of stepwise dynamic tests, carried out on basalt reinforced specimens, lead to a clear bi-linear trend in both the considered plots (i.e. δt/δn-σmax and d-mode-σmax graphs) based on thermal observations. however, the δt/δn-σmax method appeared underestimating the fatigue limit, while σd value from d-mode and energetic technique appeared to be more realistic as fatigue limit of the basalt reinforced composite [19]. concluding remarks n this review, we presented the application of ir-thermography to different composite materials, in order to relate the thermal response of these materials to their mechanical behaviour, and in particular to the fatigue limit. glass and basalt fibre reinforced composites were considered and a review of thermographic approaches was discussed. according to the literature, three main thermographic methods are applied to composites to quantify, through this technique, fatigue performances of these materials. one is related to thermographic observations during static tests, while the other two deal with the application of dynamic load, and are based on thermal and energetic considerations. in the present review, applications of this techniques are discussed and compared for the different materials (glass fibre reinforced composites, without and with an induced delamination, and basalt fibre reinforced composites). thermography is therefore proposed as a valid experimental technique able to quickly estimate mechanical fatigue properties through thermal response of the materials. nomenclature cp specific heat at constant pressure d damage parameter, defined in eq. (2) e elastic modulus (stiffness) frc fibre-reinforced composites ir infrared k0 thermoelastic constant t0 average surface temperature of solid tsa thermoelastic stress analysis n number of cycles ncf non-crimp fabrics ud unidirectional δt variation in surface temperature with respect to the initial temperature, t0 λ linear thermal expansion coefficient ρ mass density σd damage stress, from thermographic observations σmax maximum applied stress during fatigue cycling σ1, σ2, σ3 principal stresses σi, σii, σiii stress as defined in fig. 5 i http://dx.medra.org/10.3221/igf-esis.27.01&auth=true http://www.gruppofrattura.it l. vergani et alii, frattura ed integrità strutturale, 27 (2014) 1-12; doi: 10.3221/igf-esis.27.01 11 references [1] bathias, c., an engineering point of view about fatigue of polymer matrix composite materials, international journal of fatigue, 28 (2006) 1094-1099. [2] gamstedt, e. k., talreja, r., fatigue damage mechanisms in unidirectional carbon-fibre-reinforced plastics, journal of materials science, 34 (1999) 2535-2546. [3] keller, t., tirelli, t., zhou, a., tensile fatigue performance of pultruded glass fiber reinforced polymer profiles, composite structures, 68 (2005) 235-245. [4] wu, y., polymer microscopy. third edition. eds: l.c. sawyer, d.t. grubb, g.f. meyers. springer, new york; (2008). isbn 978-0-387-72627-4. microscopy and microanalysis, 15 (2009) 265-265. [5] maldague, x., theory and practice of infrared technology for nondestructive testing, wiley (2001). [6] armstrong, k. b., bevan, l. g., cole, w. f., care and repair of advanced composites. sae international (2005). [7] dulieu-barton, j. m., stanley p., development and applications of thermoelastic stress analysis, the journal of strain analysis for engineering design, 33 (1998) 93-104. [8] quinn, s., dulieu-barton, j. m., langlands, j. m., progress in thermoelastic residual stress measurement, strain, 40 (2004) 127-133. [9] dulieu-barton, j. m., emery, t. r., quinn, s., cunningham, p. r., a temperature correction methodology for quantitative thermoelastic stress analysis and damage assessment, measurement science and technology, 17 (2006) 1627. [10] emery, t. r., dulieu-barton, j. m., thermoelastic stress analysis of damage mechanisms in composite materials, composites part a: applied science and manufacturing, 41 (2010) 1729-1742. [11] salerno, a., costa, a., fantoni, g., calibration of the thermoelastic constants for quantitative thermoelastic stress analysis on composites, review of scientific instruments, (2009) 80. [12] greene, r., patterson, e., rowlands, r., thermoelastic stress analysis. in: springer handbook of experimental solid mechanics, ed. w. n. sharpe, jr., (2008) 743-768. [13] thomson, w., on the thermoelastic, thermomagnetic, and pyroelectric properties of matter. philosophical magazine series 5, 5 (1878) 4-27. [14] stanley, p., chan w. k., the application of thermoelastic stress analysis techniques to composite materials, the journal of strain analysis for engineering design, 23 (1988) 137-143. [15] emery, t. r., dulieu-barton, j. m., earl, j. s., cunningham, p. r., a generalised approach to the calibration of orthotropic materials for thermoelastic stress analysis, composites science and technology, 68 (2008) 743-752. [16] clienti, c., fargione, g., la rosa, g., risitano a., risitano g., a first approach to the analysis of fatigue parameters by thermal variations in static tests on plastics, engineering fracture mechanics, 77 (2010) 2158-2167. [17] colombo, c., libonati, f., vergani, l., fatigue damage in gfrp, international journal of structural integrity, 3 (2012) [18] libonati, f., vergani, l., damage assessment of composite materials by means of thermographic analyses, composites part b: engineering, 50 (2013) 82-90. [19] colombo, c., vergani, l., burman, m., static and fatigue characterisation of new basalt fibre reinforced composites. composite structures, 94 (2012) 1165-1174. [20] la rosa, g., risitano, a., thermographic methodology for rapid determination of the fatigue limit of materials and mechanical components, international journal of fatigue, 22 (2000) 65-73. [21] brémond, p., ir imaging assesses damage in mechanical parts: determining the fatigue limit of real structures under real operating conditions saves time. photonics spectra (2004). [22] breitenstein, o., langenkamp, m., lock-in thermography: basics and use for functional diagnostics of electronic components. springer (2003). [23] montesano, j., fawaz, z., bougherara, h., use of infrared thermography to investigate the fatigue behavior of a carbon fiber reinforced polymer composite, composite structures, 97 (2013) 76-83. [24] minak, g., on the determination of the fatigue life of laminated graphite-epoxy composite by means of surface temperature measurement, journal of composite materials, (2010). [25] astm d3039/d3039m-08, standard test method for tensile properties of polymer matrix composite materials, (2008). [26] astm d3518m-94, standard test method for in-plane shear response of polymer matrix composite materials by tensile test of a ±45° laminate, (2007). http://dx.medra.org/10.3221/igf-esis.27.01&auth=true http://www.gruppofrattura.it l. vergani et alii, frattura ed integrità strutturale, 27 (2014) 1-12; doi: 10.3221/igf-esis.27.01 12 [27] colombo, c., vergani, l., influence of delamination on fatigue properties of a fibreglass composite, composite structures, 107 (2014) 325-333. [28] astm d3479m-96, standard test method for tension-tension fatigue of polymer matrix composite materials, (2007). http://dx.medra.org/10.3221/igf-esis.27.01&auth=true http://www.gruppofrattura.it microsoft word numero_38_art_12 t. sawada et alii, frattura ed integrità strutturale, 38 (2016) 92-98; doi: 10.3221/igf-esis.38.12 92 focussed on multiaxial fatigue and fracture effect of molding processes on multiaxial fatigue strength in short fibre reinforced polymer takahiko sawada, hiroshi aoyama research & development group, hitachi, ltd., takahiko.sawada.dy@hitachi.com,hiroshi.aoyama.ra@hitachi.com abstract. this study concerns the multiaxial static and fatigue strength properties. short-glass-fibre-reinforced phenolic-resin composites (sgp) molded by injection and compression processes were subjected to tensiontorsion combined static and fatigue tests at room temperature under various test conditions. tension – torsion combined static strength well agreed with tsai-hill failure criteria without depending on processes. relationships between the maximum principal stress, σp1, max, and the number of fracture cycles, nf, were approximately linear in the whole range of up to 106 cycles. for a unified evaluation of multiaxial fatigue life for sgp, non-dimensional effective stress, σ*, defined by modifying tsai-hill failure criteria was applied. the slopes of σ*nf curves according to baskin’s law were almost identical to the injection (n = 26.3) and compression (n = 26.2). we finally confirmed that the multiaxial fatigue life of sfrp could be predicted by using σ* with a unique wöhler curve without relying on molding processes. keywords. short-fibre reinforced plastics; multiaxial; fatigue; tsai-hill. citation: sawada, t., aoyama, h., effect of molding processes on multiaxial fatigue strength in short fibre reinforced polymer, frattura ed integrità strutturale, 38 (2016) 9298. received: 27.06.2016 accepted: 26.07.2016 published: 01.10.2016 copyright: © 2016 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. introduction hort fibre reinforced thermo-set plastic (sfrp) has been mainly applied to automobiles and electrical industries owing to its superior mechanical properties and lower weight. however, a machine designer often faces difficulties using sfrp or predicting its mechanical properties. sfrp generally shows complex fracture behaviours combined with a matrix crack, fibre break, fibre pull-out, and others, and these make product design difficult. therefore, a machine designed using sfrp often requires a production test and a strength test to be repeated until its reliability is confirmed. because reducing the number of test repetitions decreases the cost of development, high-reliability strength evaluation methods will be required to meet the increase in products that will use sfrp in the future. further, multiaxial stress generally occurs in a structure subjected to an external force. in the literature, moosbrugger et al. [1, 2] experimentally investigated and calculated the multiaxial fatigue behaviour of sfrp. they conducted some tensiontorsion combined fatigue tests and estimated the fatigue life on the basis of the failure criterion of laminate. gaier et al. [3] established a simulation process for the multiaxial fatigue life prediction of orthotropic sfrp. they combined the resin flow simulation, finite element analysis, and fatigue analysis. the fatigue damage of a belt pulley was predicted by s t. sawada et alii, frattura ed integrità strutturale, 38 (2016) 92-98; doi: 10.3221/igf-esis.38.12 93 comparing experimental and simulation results. although some additional papers [4-7] have focused on investigating the multiaxial strength for sfrp, little attention has been paid to the effect of manufacturing process on that property. this study is concerned with the multiaxial fatigue evaluation in short-glass-fibre reinforced phenolic resin (sgp) among various volume fractions. round-bar specimens molded by injection and compression processes were subjected to static and fatigue tests in room temperqature to clarify the effect of molding processes on the multiaxial strength. tension torsion combined tests were conducted with various stress ratio parameters described as the ratio of torsion and tension stress as α = τ / σ. experimental details ab. 1 details the configuration of sgp. thermosetting phenolic resin was used as the matrix. the reinforcement was a short e-glass fibre 10 mm long and 10 μm in diameter. 0.0vf, 0.2vf, and 0.5vf described at the first row means that the fiber volume fraction vf is 0%, 20%, and 50%. test specimens with three-types vf were molded by compression (c-sgp) and injection (i-sgp) respectively. in the compression molding, 300-mm-square and 30-mm-thick bulk plates were manufactured, and then test pieces were cut from the bulk plate to the dimensions as shown in fig. 1. edges of the sample surface were not polished. a machining surface roughness was confirmed by using a roughness tester to be approximately the same in each specimen. compression molding temperature was 160 °c, press pressure was 20 mpa, and curing time was 250 seconds. in contrast, in injection molding, test specimens were directly manufactured to specimen shapes described as fig.1. injection mold temperature was 140-160 °c, injection pressure was 80 mpa, and curing time was 20 seconds. component 0.0vf 0.2vf 0.5vf glass fibre [%] 0 20 50 phenolic resin [%] 70~85 55~65 30~35 phenol [%] 1 1 1 hexamethylene etramine [%] 3 3 3 rock wool [%] 10~20 10~20 10~20 zinc stearate [%] 1.0~2.0 1.0~2.0 10~20 table 1: configuration of sgp material. 6 9 50 127 axia l force torsion torque figure 1: tension-torsion test specimen dimensions. multiaxial test procedure in this study, we conducted multiaxial static and fatigue tests at room temperature to compare strength properties in different manufacturing processes. all the tests were performed by combining tension-torsion electro-hydraulic servo systems under axial-loads up to ± 25 kn with standard displacements of ± 50 mm and torsion-torques up to 220 n･m with total rotations of 270°. tension-torsion combined tests were performed by using the specimen as shown in fig. 1. tension stress σ1 is given by eq. 1, where f is tension load and d is diameter at the gauge section. torsion stress τ12 is given by eq. 2, where t is torque. t t. sawada et alii, frattura ed integrità strutturale, 38 (2016) 92-98; doi: 10.3221/igf-esis.38.12 94 f d 1 2 4     　 (1) t d 12 3 16     (2) axial-tension stress σ1 was loaded in proportion to torsion stress τ12 in accordance with a combined stress ratio α, which is defined in tab. 2, on the gauge section surface. static tests were controlled by eq. 3 so as to achieve the stress loading speed ( ,  ) of 10 mpa/sec. fatigue tests were conducted at the stress ratio r defined as the ratio of minimum stress to maximum stress of 0.1 and applied sinusoidal waves combined between axial-tension stress and torsion stress with cyclic frequency f of 2 hz. axial-tension stress was loaded to the specimen so as to be in the same phase with torsion stress in accordance with defined the combined stress ratio α in tab. 2. τ12 σ1 α=τ12/σ1 1 0 1/0 (pure torsion) 1 1 1/1 1 2 1/2 0 1 0/1 (pure tension) table 2: definitions of combined stress ratio α. 2 2 10 [ mpa / sec]    　 (3) test results and discussion multiaxial static strength evaluation xternal load acting on a structure is commonly considered to be not only a uni-axial stress but also a multiaxial stress state. therefore, we discuss a multiaxial strength criterion in terms of the axial tension strength and the torsional shear strength in this chapter. from the micro observation and frequency analysis for fibre orientation in c-sgp and i-sgp, we deduced that they will have an orthotropic property. then, we assumed the sgp multiaxial failure was followed by tsai-hill failure criterion given by eq. 4 [8]. l s 2 2 1 12 2 2 1       (4) where σl and τs are tension and torsional strength in material reference axes, and σ1, and τ12 are applied axial stress and torsional stress on the specimen surfaces. suffixes 1 and 12, which are written in subscript to the right of strength parameters σ and τ, indicate the axial-stress direction and the torsional-stress direction, respectively. σl and τs are the material strengths determined by the static test on the basis of the experimental results in α = 0 / 1 and α = 1 / 0 in tab. 2. fig. 2 shows the static strength criterion for sgp in the multiaxial stress state, which is plotted on σl τs plane. the white and gray plots on each chart indicate the strength data of c-sgp and i-sgp, respectively. the solid lines on the σ τ plane represent the failure criterion given by eq. 4 for each vf. broken lines represent α given in tab. 2. as c-sgp is molded by pressuring and heating after raw materials described at tab. 1 are filled into the die, a microscopic void tends to be easily retained as a manufacturing defect in c-sgp. furthermore, the authors [9] previously suggested that the strength properties of sgp depend on both short-fibres orientation and manufacturing defects in matrices. from these perspectives, we deduced that these manufacturing defects affected experiment variations in sgp. considering such manufacturing defects, the static fracture strength of c-sgp approximately accords with the tsai-hill failure theory criteria in eq. 4. e t. sawada et alii, frattura ed integrità strutturale, 38 (2016) 92-98; doi: 10.3221/igf-esis.38.12 95 (a) 0.0vf (b) 0.2vf (c) 0.5vf figure 2: multiaxial static strength evaluation with tsai-hill failure rule. fatigue strength properties fatigue strength in uni-axial loading is generally evaluated by using the s-n diagram. s-n diagrams are associated with the relationships among the number of cycles to failure and stress range, stress amplitude, or maximum stress in uni-axial loading. however, we have to deal with stress states of combined axial stress and torsion stress in this paper. therefore, sn diagrams are organized by using principal stress applied on specimen surfaces σp1, and the number of cycles to fracture nf. σp1 was calculated as follows: 2 21 1 p1 12 2 2           　 (5) where σ1 and τ12 are the axial stress and shear stress applied. figs 3 and 4 show the relationships between σp1,max as cyclic maximum principal stress and nf as fracture cyclic numbers on a double logarithmic chart obtained as s-n diagrams. arrows in the diagrams show that the fatigue tests were terminated after reaching 1×106 cycles. figure 3: relationships between σp1, max and nf with various α in c-sgp. since the value of the fatigue life in c-sgp are scattered widely, fatigue life in c-sgp can no longer be expected to sort in vf and α by using the s-n diagram. meanwhile, s-n diagram in i-sgp indicates the characteristic to decrease σp1, max with increasing nf without dependence on fatigue test conditions. comparing the fatigue properties in molding processes, they 0 25 50 75 100 125 0 25 50 75 100 t o rs io n s tr en gt h τ s [m p a ] axia l strength σl [mpa ] 0 25 50 75 100 125 0 25 50 75 100 t o rs io n s tr en gt h τ s [m p a ] axia l strength σl [mpa ] 0 25 50 75 100 125 0 25 50 75 100 125 t o rs io n s tr en gt h τ s [m p a ] axia l strength σl [mpa ] α = 2/1 α = 1/1 α = 1/2 α = 0/1 α = 1/0 α = 2/1 α = 1/1 α = 1/2 α = 0/1 α = 1/0 α = 2/1 α = 1/1 α = 1/2 α = 0/1 α = 1/0 10 100 0 1 10 100 1000 10000 100000 1000000 p ea k s tr es s σ p 1 , m ax [m p a ] fracture cycles nf [cycles] 0.5vf, α=1/0 0.5vf, α=2/1 0.5vf, α=1/1 0.5vf, α=0/1 0.2vf, α=1/0 0.2vf, α=2/1 0.2vf, α=1/1 0.2vf, α=0/1 0.0vf, α=1/0 0.0vf, α=2/1 0.0vf, α=1/1 0.0vf, α=0/1 101 102100 103 104 105 10610-1 sta tic strength t. sawada et alii, frattura ed integrità strutturale, 38 (2016) 92-98; doi: 10.3221/igf-esis.38.12 96 do not seem to agree despite these properties being made of the same materials. vf, α, and molding processes strongly affect the multiaxial fatigue properties, hence those effects have to be removed from s-n diagrams to evaluate fatigue with high accuracy. figure 4: relationships between σp1, max and nf with various α in i-sgp. definition of unified equivalent stress we confirmed multiaxial fracture strengths well agreed with the tsai-hill failure criteria with dependence on processes and fibre volume fractions vf as shown in fig. 2. meanwhile, multiaxial fatigue properties are not able to be organized by the relationships between σp1,max and nf because of being affected the dependence on the molding process, α, and vf. then, due to the static strength behaviours described above, the fatigue strength will be represented by expanding the tsai-hill failure rule [10]. hence, non-dimensional equivalent stress σ* was defined by modifying the tsai-hill failure rule as shown in eq. 6 to evaluate the multiaxial fatigue behaviour without dependence on molding process effects. 2 2 *1 12 2 2 l s          　 (6) figs 5 and 6 show the relationships between σ* and nf on double logarithmic charts in c-sgp and i-sgp. σ*nf correlation is approximately determined by baskin’s law [11] with the broken line in fig. 6. baskin’s law is presented by eq. 7 as follows;  nfn c*  　 (7) where n and c are presented as material constants for a slope of σ*nf correlation on the double logarithmic chart. the slopes of σ* nf curves represented by baskin’s law were almost identical for the c-sgp (n = 26.2) and i-sgp (n = 26.3). comparing σ*-nf curves among the manufacturing processes, fatigue strengths in c-sgp are widely fluctuated than that of i-sgp. fig. 7 shows typical fracture surface observation image in c-sgp by scanning electron microscopy. manufacturing defects like a cavity were able to be observed on the fracture surface area, and it is deduced that they became the origin of the fatigue failure. therefore it is considered that the manufacturing processes were affected on the strength distribution. although c-sgp shows wider fatigue life distributions than i-sgp, we are practically able to predict fatigue life by using σ* considering the strength variation that depends on the manufacturing defects. the proposed method is expected to be applied to the fatigue life estimation as a unified evaluation method in sgp without depending on manufacturing processes. therefore, σ* nf correlation is synthetically able to evaluate the multiaxial fatigue properties without dependence on molding processes, fibre volume fraction, and combined stress ratio α. 10 100 0.1 1 10 100 1000 10000 100000 1000000 p ea k s tr es s σ p l, m ax [m p a ] fra cture cycles nf [cycles] 0.5vf, α=0/1 0.5vf, α=2/1 0.5vf, α=1/1 0.5vf, α=1/0 0.2vf, α=0/1 0.2vf, α=2/1 0.2vf, α=1/1 0.2vf, α=1/0 0.0vf, α=0/1 0.0vf, α=2/1 0.0vf, α=1/1 0.0vf, α=1/0 101 102100 103 104 105 10610-1 sta tic strength t. sawada et alii, frattura ed integrità strutturale, 38 (2016) 92-98; doi: 10.3221/igf-esis.38.12 97 figure 5: relationships between σ* and nf with various α in c-sgp. figure 6: relationships between σ* and nf with various α in i-sgp. figure 7: a typical tensile fracture surface situations with scanning electron microscopes in c-sgp. (05vf) 0.1 1.0 0 1 10 100 1000 10000 100000 1000000 e q u iv a le n t e ff ec ti v e st re ss σ * [ ] fra cture cycles nf [cycles] 0.5vf, α=1/0 0.5vf, α=2/1 0.5vf, α=1/1 0.5vf, α=0/1 0.2vf, α=1/0 0.2vf, α=2/1 0.2vf, α=1/1 0.2vf, α=0/1 0.0vf, α=1/0 0.0vf, α=2/1 0.0vf, α=1/1 0.0vf, α=0/1 101 10210-1 103 104 105 106100 sta tic strength (σ*)n･nf= c n=26.2 0.1 1.0 0.1 1 10 100 1000 10000 100000 1000000 e q u iv a le n t e ff ec ti v e st re ss σ * [ ] fra cture cycles nf [cycles] 0.5vf, α=0/1 0.5vf, α=2/1 0.5vf, α=1/1 0.5vf, α=1/0 0.2vf, α=0/1 0.2vf, α=2/1 0.2vf, α=1/1 0.2vf, α=1/0 0.0vf, α=0/1 0.0vf, α=2/1 0.0vf, α=1/1 0.0vf, α=1/0 101 10210-1 103 104 105 106100 (σ*)n･nf= c n=26.3 sta tic strength t. sawada et alii, frattura ed integrità strutturale, 38 (2016) 92-98; doi: 10.3221/igf-esis.38.12 98 conclusions ultiaxial fatigue evaluation in sgp among the various volume fractions was investigated in this paper. roundbar specimens molded by injection and compression processes were subjected to static and fatigue tests in room temperature to clarify the effect of molding processes on the multiaxial strength. tension torsion combined tests were conducted with various combined stress ratio parameters described as α = τ / σ. general conclusions of this study are as follows. 1. tsai-hill failure criteria can be applied to evaluate tension-torsion static strength in sgp with dependence on the molding process and vf. 2. the non-dimensional equivalent stress σ* is defined to evaluate multiaxial fatigue strength by modifying tsai-hill failure criteria. 3. the slopes of σ*nf curve for i-sgp (n = 26.3) is almost identical to that for c-sgp (n = 26.2). 4. the relationship between σ* and nf explains the tension-torsion fatigue properties on the double logarithmic chart without depending on a molding process, combined stress ratios α, and fibre volume fraction vf especially for i-sgp. references [1] sonsino, c.m., moosbrugger, e., fatigue design of highly loaded short-glass-fibre reinforced polyamide parts in engine compartments, int. j. fatigue, 30 (2008) 1279-1288. [2] moosbrugger, h., demonte, m., multiaxial fatigue behavior of a short-fiber reinforced polyamide–experiments and calculations, mat.-wiss. u. werkstofftech, 42 (2011) 950-957. [3] gaier, c., unger, b., dannbauer, h., multiaxial fatigue analysis of orthotropic materials, revue de metallurgie, 107 (2010) 369-375. [4] quaresimin, m., susmel, l., talreja, r., fatigue behaviour and life assessment of composite laminates under multiaxial loading, int. j. fatigue, 32 (2010) 2-16. [5] launay a., maitournam m.h., marco y., raoult i., multiaxial fatigue models for short glass fiber reinforced polyamide – part i: nonlinear anisotropic constitutive behavior for cyclic response, int. j. fatigue, 47 (2013) 382-389. [6] launay, a., maitournam, m.h., marco, y., raoult, i., multiaxial fatigue models for short glass fibre reinforced polyamide. part ii: fatigue life estimation, int. j. fatigue, 47 (2013) 390-406. [7] klimkeit, b., nadot, y., castagnet, s., nadot-martin, c., dumas, c., bergamo, s., multiaxial fatigue life assessment for reinforced polymersoriginal, int. j. fatigue, 33 (2011) 766-780. [8] tsai, s.w., strength characteristics of composite materials, nasa cr-224, (1965). [9] sawada, t., aoyama, h., effect of molding process on mechanical properties of glass short fiber/phenolic resin composite, trans. soc. mech. eng. a japan, 76 (2009) 672-674. [10] kawai, m., yajima, s., takano, y., off-axis fatigue and its damage mechanics modeling for unidirectional carbon fiber-reinforced composite at room and high temperatures, trans. soc. mech. eng. a japan, 64 (1998) 2838-2864. [11] basquin, o. h., the experimental law of endurance tests, proceedings of astm, 10 (1910) 625-630. m << /ascii85encodepages false /allowtransparency false /autopositionepsfiles true /autorotatepages /none /binding /left /calgrayprofile (dot gain 20%) /calrgbprofile (srgb iec61966-2.1) /calcmykprofile (u.s. web coated \050swop\051 v2) /srgbprofile (srgb iec61966-2.1) /cannotembedfontpolicy /error /compatibilitylevel 1.4 /compressobjects /tags /compresspages true /convertimagestoindexed true /passthroughjpegimages true /createjobticket false /defaultrenderingintent /default /detectblends true /detectcurves 0.0000 /colorconversionstrategy /cmyk /dothumbnails false /embedallfonts true /embedopentype false /parseiccprofilesincomments true /embedjoboptions true /dscreportinglevel 0 /emitdscwarnings false /endpage -1 /imagememory 1048576 /lockdistillerparams false /maxsubsetpct 100 /optimize true /opm 1 /parsedsccomments true /parsedsccommentsfordocinfo true /preservecopypage true 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/hrv (za stvaranje adobe pdf dokumenata najpogodnijih za visokokvalitetni ispis prije tiskanja koristite ove postavke. stvoreni pdf dokumenti mogu se otvoriti acrobat i adobe reader 5.0 i kasnijim verzijama.) /hun 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can be opened with acrobat and adobe reader 5.0 and later.) >> /namespace [ (adobe) (common) (1.0) ] /othernamespaces [ << /asreaderspreads false /cropimagestoframes true /errorcontrol /warnandcontinue /flattenerignorespreadoverrides false /includeguidesgrids false /includenonprinting false /includeslug false /namespace [ (adobe) (indesign) (4.0) ] /omitplacedbitmaps false /omitplacedeps false /omitplacedpdf false /simulateoverprint /legacy >> << /addbleedmarks false /addcolorbars false /addcropmarks false /addpageinfo false /addregmarks false /convertcolors /converttocmyk /destinationprofilename () /destinationprofileselector /documentcmyk /downsample16bitimages true /flattenerpreset << /presetselector /mediumresolution >> /formelements false /generatestructure false /includebookmarks false /includehyperlinks false /includeinteractive false /includelayers false /includeprofiles false /multimediahandling /useobjectsettings /namespace [ (adobe) (creativesuite) (2.0) ] /pdfxoutputintentprofileselector /documentcmyk /preserveediting true /untaggedcmykhandling /leaveuntagged /untaggedrgbhandling /usedocumentprofile /usedocumentbleed false >> ] >> setdistillerparams << /hwresolution [2400 2400] /pagesize [612.000 792.000] >> setpagedevice microsoft word numero_50_art_45_2620 d. triantis et alii, frattura ed integrità strutturale, 50 (2019) 537-547; doi: 10.3221/igf-esis.50.45 537 focused on the research activities of the greek society of experimental mechanics of materials fracture precursor phenomena in marble specimens under uniaxial compression by means of acoustic emission data dimos triantis university of west attica, department of electrical and electronic engineering, laboratory of electronic devices and materials, 250 thivon avenue, campus 2, 122 44, athens, greece triantis@uniwa.gr, http://orcid.org/0000-0003-4219-8687 stavros k. kourkoulis national technical university of athens, school of applied mathematical and physical sciences, department of mechanics, laboratory for testing and materials, 5 heroes of polytechnion avenue, theocaris bld., zografou campus, 157 73 athens, greece stakkour@central.ntua.gr, https://orcid.org/0000-0003-3246-9308 abstract. marble specimens are subjected to a specially designed stepwise loading protocol, in an attempt to detect fracture precursor phenomena taking advantage of acoustic emission (ae) data. the analysis is carried out in terms of the number of acoustic hits recorded and the time evolution of the improved b-value (ib-value), the cumulative energy of the acoustic signals and the f-function. during the stage of increasing load, intense acoustic activity is detected as the corresponding stress reaches the transitional phase from the linear to the nonlinear mechanical response of the material. when the stress is stabilized at levels exceeding 95% of the material’s compressive strength, the acoustic activity is drastically reduced. during the first seconds of the stress stabilization stage the reduction follows an exponential law. special attention is paid to the phases, where the occurrence of ae hits shows a strong increase. during these phases acoustic signals of low frequency and high ra are recorded, indicating that the micro-cracking process is of shear rather than of opening mode. keywords. acoustic emission; marble; compression; ib-value; f-function; micro-cracking classification. citation: triantis, d., kourkoulis, s.k. fracture precursor phenomena in marble specimens under uniaxial compression by means of acoustic emission data, frattura ed integrità strutturale, 50 (2019) 537-547. received: 21.01.2019 accepted: 18.05.2019 published: 01.10.2019 copyright: © 2019 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. introduction he mechanical response of brittle heterogeneous materials under compressive loading and the damage accumulation within their mass, which unavoidably accompanies the loading procedure, are of great interest in a wide range of engineering applications. of particular interest are the quantitative description of the damage mechanisms activated and the early prediction of upcoming catastrophic failure. in this direction, series of damage assessment techniques have t http://www.gruppofrattura.it/va/50/2620.mp4 d. triantis et alii, frattura ed integrità strutturale, 50 (2019) 537-547; doi: 10.3221/igf-esis.50.45 538 been long ago proposed and are being continually developed since then. among them, the acoustic emission (ae) technique is perhaps the one most widely applied worldwide. although the ae technique is introduced many decades ago, it is still developed and refined and today it is a flexible tool for monitoring and understanding the dynamic processes taking place within the mass of mechanically loaded structural elements. moreover, the ae technique is considered as a unique tool providing warning signals about impending failure, especially for brittle materials [1-3]. acoustic emissions (aes) are detected as series of short impulse energy packets, sequentially released when damage accumulation exceeds some critical limits leading to micro-cracking within the mass of materials subjected to mechanical loads. the detection of aes is nowadays widely used for the spatiotemporal damage localization as well as for the assessment of the damage level (or in other words of the remaining load carrying capacity) in brittle materials such as concrete and rocks [4-7]. it is known that mechanical loading of rocks and rock-like materials generates a stress field, which is responsible for the activation of various micro-mechanisms, such as dislocation activity and formation of micro-cracks, which in turn are responsible for the release of elastic energy, traveling in the form of elastic waves and detected in the form of acoustic signals. the fracture process starts by the nucleation of micro-cracks, which grow and coalescence forming cracks leading to catastrophic fracture. micro-cracking is the most important source of aes at least for brittle materials, such as rocks [8]. initially, tiny cracks are produced, which are gradually growing, reaching eventually a critical size, beyond which coalescence of the micro-cracks starts generating macro-cracks. in general, aes are generated at different spatial and temporal scales. it should be noted that the release of seismic waves related to an earthquake and the aes detected in specimens of solids during their fracture process have remarkable similarities. the initial correlation of aes and seismology was attempted by ono and ohtsu [9-11], who employed techniques used for earthquake data processing to elaborate laboratory aes data. as a result, quite a few techniques applied in seismology from the civil engineering point of view are nowadays employed in the field of analysis of aes data. the number of incoming signals is a basic parameter when monitoring the acoustic activity. as the stress level increases approaching that causing failure of specimens or structural members, the number of ae hits recorded starts increasing at an increasing rate, depending on the material and the loading mode. therefore, the rate of ae hits (dn/dt), can provide direct information on the frequency of micro-cracking activity in rocks. graphical representation of dn/dt versus time provides information about the various stages or phases of micro-cracking activity in rocks. for further analysis of the failure mode, two additional ae parameters are widely used: the average frequency (af) of the acoustic signals, defined as the number of counts divided by their duration, and the ra parameter (rise time/amplitude) [12, 13]. it is accepted that cracks generating signals of relatively high af and low ra are related to tensile cracking (mode-i) while shear cracking (mode-ii) corresponds to lower af and higher ra. moreover, researchers in the field of rock mechanics use the so-called improved b-value analysis to quantify damage and describe the respective fracture processes [1, 3, 14]. in this work, rock samples (marble) are subjected to uniaxial compression until fracture. the analysis of the aes data focuses on how the acoustic activity evolves, especially in phases near the catastrophic fracture of the specimens. for this purpose, a special loading protocol of four successive steps is implemented, as it is described in next section. for the representation and analysis of the acoustic activity, besides the above mentioned parameters, a recently proposed f-function is used [7], which reflects the mean occurrence of ae hits, in a predefined time window of n consecutive hits. τhe material and the experimental protocol rismatic specimens made of dionysos marble, of dimensions 40 x 40 x 100 mm3 were used. dionysos marble is exclusively used for the restoration of the athenian acropolis monuments. its composition is 98% calcite, 0.5% muscovite, 0.3% sericite, 0.2% quartz and 0.1% chlorite. detailed characteristics of the material are given by exadaktylos et al. [15]. during a preliminary experimental protocol with standardized specimens, the strength of the specific material’s batch under monotonic uniaxial compression was determined, and it was found varying between 62.5 mpa and 65.1 mpa, with an average of about 63.8 mpa. an instron dx 300 loading frame was used for the main experimental protocol. the strain developed was measured using kyowa strain gauges attached on the microlink-770, 120 ω resistor bridge. an acoustic sensor was attached in the central cross section of the specimens with the aid of vacuum grease. preamplifier with 40 db gain and analogue band-pass filters in the 20-400 khz range was also used. the ae equipment and software were by mistras group, inc. the specimens were subjected to uniaxial compression until fracture, following a specially designed protocol of four discrete consecutive stages [16]: during the first stage (a), the load was applied at a constant rate, resulting to a stress rate of 0.44 mpa/s, up to a stress level of 60.5 mpa. during the second stage (b), the duration of which was equal to about 120 s, the stress was kept constant at 60.5 mpa. at the end of stage b the stress level was increased slightly at 63.5 mpa of p d. triantis et alii, frattura ed integrità strutturale, 50 (2019) 537-547; doi: 10.3221/igf-esis.50.45 539 (stage c), with the same rate with that used in stage a (0.44 mpa/s). finally, during the last stage (d) the stress level was again kept constant at 63.5 mpa, until the fracture of the specimens. the time evolution of the stress during all four stages, for a characteristic specimen, is depicted in fig.1, in juxtaposition to the respective evolution of the axial strain (as it was recorded by the strain gauge) for the whole loading procedure until the fracture of the specimen. the respective stress-strain curve is shown in fig.2. it is noted that for the major portion of stage a the material’s response is perfectly linear (excluding the unavoidable non-linearity accompanying the very early loading steps during uniaxial compression) until the stress reaches the level of 57 mpa, corresponding to about 90% of the fracture stress (point k in fig.1)). the modulus of elasticity determined from this linear region of the stress-axial strain curve is equal to about 74 gpa (fig.2), in good agreement with previous experimental protocols by kourkoulis et al. [17]. in stage b, i.e., under constant stress of 60.5 mpa, the axial strain appears almost constant. however, thorough study of the respective data indicates that the strain during stage b is actually increasing (although imperceptibly), though at a gradually decreasing rate. in stage d, i.e., under constant stress of 63.5 mpa, the strain is increasing, at rates much higher compared to those of stage b. the time variation of the axial strain rate during stages b and d, namely the stages during which the stress is kept constant, is plotted in fig.3. it is very interesting to emphasize the significant increase of the axial strain rate during the last steps of stage d, which eventually leads to the fracture of the specimen under constant stress (!), about 60 seconds after the stabilization of the stress level (or, equivalently, 25 seconds before the fracture of the specimen). 0 25 50 75 0 50 100 150 200 250 300 time (sec) st re ss ( m p a) 0.0000 0.0005 0.0010 0.0015 0.0020 st ra in strain series3 series4 stress stage a stage b stage c stage d a x ia l s tr es s [m p a ] a x ia l s tr a in time [s] k toto strain stress figure 1: stress and strain versus time. the four loading stages of the loading scheme are clearly visible. 0 25 50 75 0 0.0002 0.0004 0.0006 0.0008 0.001 0.0012 0.0014 0.00 st re ss ( m p a) stage a stage b stage c stage d slope=74gpa 75 50 25 0 a x ia l s tr es s [m p a] 0 4 8 12 16 slop e: 74x109 stage a stage b stage c stage d slope=74g stage a stage b stage c stage d stage a stage b stage c stage d axial strain [x10-4] figure 2: axial stress versus axial strain for a typical experiment. the colour code is used to distinguish the four stages of the loading protocol exhibited in fig.1. d. triantis et alii, frattura ed integrità strutturale, 50 (2019) 537-547; doi: 10.3221/igf-esis.50.45 540 1.e-07 1.e-06 1.e-05 1.e-04 0 20 40 60 80 100 time (s) a ve ra g e s tr a in r a te stage b stage d 1e-04 1e-05 1e-06 1e-07 a ve ra g e st ra in r at e [s -1 ] 0 20 40 60 80 100 time [s] stage b stage d stage b stage d stage b stage d figure 3: time evolution of the average strain growth rate <δε/δt>, in stages b and d. experimental results and discussion analysis in terms of the ib-value and the cumulative energy of the acoustic signals he number of ae hits recorded during uniaxial compression tests on rocks is usually large with inconsistent shapes of the respective waveforms and with parameters varying within wide limits. in the present study ae hits with duration less than 10 μs and count number less than 2 were ignored [18], in order to exclude from the analysis ae hits that would probably be of parasitic nature. the number of ae hits, of amplitude equal or higher than 40 db that were finally used after the above filtering, was equal to about 3500. for the specific experiment discussed in previous section, this number was equal to 3335. the allocation of these hits to each one of the four stages of the loading protocol is shown in table 1, together with the average amplitude, the average energy and average duration of the hits of each stage. stage ae hits number average amplitude (db) average energy (aj) average duration (μs) a 893 49.3 3098 4734 b 730 48.0 621 1966 c 174 50.9 7027 11112 d 1538 49.7 25095 5645 table 1: statistical data for the ae parameters. to further explore the details of the acoustic activity, an improved b-value (denoted from here on as ib-value) analysis is carried out, as it was already discussed for the specific protocol by triantis [16]. in this direction, the total number of ae hits was divided into groups of sequential hits. each group included 100 hits and the sliding step was set equal to 1. this means that the first group (providing the first value of ib) includes the first 100 hits (i.e., the hits with order from i=1 to i=100), the second group (providing the second value of ib) includes the hundred hits with order from i=2 to i=101, etc. the ib-values were then calculated using the familiar equation:       1 2 1 2      log logn n ib          (1) in eq.(1) μ is the mean amplitude, σ is the standard deviation and α1, α2 are constants the numerical value of which is usually set equal to 1 [1]. then, each ib-value was paired to a time instant corresponding to the mean value of the time instants of occurrence of the hundred sequential hits of each group. the results of the above procedure are shown in fig.4, in which the time evolution of the ib-value is plotted for all four stages of the loading protocol, in juxtaposition to the respective evolution of the cumulative energy of the acoustic signals. the abrupt reductions of the ib-values, towards levels approaching the critical limit of 1, observed in fig.4, are always accompanied by strong increase of the cumulative energy of the acoustic signals. this is observed as one approaches the end of stage a (when the stress exceeds about 90% of the fracture stress), during stage c and, finally, at the end of stage d during t d. triantis et alii, frattura ed integrità strutturale, 50 (2019) 537-547; doi: 10.3221/igf-esis.50.45 541 1e+03 1e+04 1e+05 1e+06 1e+07 1e+08 0 25 50 75 100 125 150 175 200 225 250 275 300 325 cu m m ul at iv e en er gy ( aj ) 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 ib -v al ue cum m ulative energy ib-value stage a stage c stage d stage b c u m u la ti v e en er gy [a j] ib -v a lu e time [s] cumula tive energy ib-va lue stage a stage b stage d stage c ib=1 figure 4: time evolution of the cumulative energy and the ib-values during the four stages of the loading scheme. during the very last seconds before the macroscopic fracture of the specimen. the as above behaviour could be considered as corresponding to a transitional phase, from the stage of cracks formation to that of the final fracture of the specimen. at the end of this transitional phase preliminary crack-coalescence is possible. special attention is next paid to the time evolution of the cumulative energy (ce) of the acoustic signals in stages b and d, i.e., the stages of constant stress level. for both stages, it appears that the time evolution of the specific parameter is governed by a power law of the following form:  ( )moce l t t (2) in eq.(2) l and m are constants while to corresponds to the time instant of onset of each constant stress stage (see fig.1). plotting eq.(2) on log-log scales (fig.5a) indicates that the time evolution of the cumulative energy (ce) of the acoustic signals during the constant stress stage b consists, in fact, of two distinct branches of different values of the exponent m. the first branch is of relatively limited duration (t-to<1 s) and corresponds to an exponent value m=0.70. the second branch (t-to>1 s), corresponds to an exponent value m=0.31. attention is drawn to the fact that the starting point for calculating and drawing the time evolution of the cumulative energy is the time instant to (the beginning of stage b), while the starting point of the horizontal axis (t=to) corresponds, also, to the onset of stage b. stage b 1e+03 1e+04 1e+05 1e+06 0.01 0.1 1 10 100 slope=m=0.70 slope=m=0.31 c u m u la ti v e en er gy [a j] t to [s] stage d 1e+03 1e+04 1e+05 1e+06 1e+07 1e+08 0.01 0.1 1 10 100 ( ) slope=m=0.94 slope=m=0.29 40s t to [s] c u m u la ti v e en er gy [a j] m=0.31 m=0.70 m=0.29 m=0.94 40 (a) (b) figure 5: time evolution of the cumulative energy in stages b (a) and d (b). d. triantis et alii, frattura ed integrità strutturale, 50 (2019) 537-547; doi: 10.3221/igf-esis.50.45 542 a similar pattern prevails in stage d with exponent values m=0.94 and m=0.29, respectively (fig.5b). deviation from the law of eq.(2) is only observed in this stage for t-to>40 s with the cumulative energy increasing quite rapidly. this deviation is obviously correlated to the fact that at this time instant the average rate of strain growth starts increasing rapidly (see fig.3) indicating entrance of the system (specimen) into a state of impending failure, and providing thus a potentially interesting pre-failure indicator. frequency of occurrence of ae hits analysis in terms of the f-function [7] in this section, a new way of exploring details of the acoustic activity is employed, based on the recently introduced f function, which represents an average frequency of the ae hits, in a window of n successive hits [7]. to compute and plot the f-function the inter-event times of a sufficient number of ν (ν>10) consecutive hits are used, in conjunction to the “sliding window” technique. each value of the f-function is paired to an average time instant of the time instants of the n successive hits used to calculate the specific value of the f-function. analytic description of how the f-function is determined can be found in refs. [7, 19]. this approach appears to be advantageous, since it allows for a continuous representation of the acoustic activity in a given time period rather than for a quantized presentation of the respective data, which characterizes the familiar plots of hits per second. this presentation is particularly useful when intense ae activity is recorded within a very short time interval. it offers, also, valuable information concerning the time evolution of the acoustic activity just before the failure of the samples, providing direct information on the frequency of micro-cracking activity within the specimen. quite a few research teams worldwide are already using the f-function to study various aspects of the acoustic activity, especially in brittle materials [20-23]. the way according to which the f-function varies throughout the experiment discussed in previous sections is shown in fig.6. the first significant and abrupt increase of the value of the f-function is observed in stage a and, in particular, after the 125th second (denoted from here on as t*). this time instant corresponds to the transition phase from the linear to the non-linear response of the material (see point k, fig.1). moreover, at the beginning of stage c, the f-function increases, also, considerably. at the beginning of stages b and d (stages of constant stress level), the f-function exhibits a rapid decrease and re-establishes low values, due to the sparse occurrence of ae. in particular, in stage d, the f-function, after a short period with low values, shows a gradual increase attaining a maximum value just a few seconds prior to the macroscopic fracture of the specimen, providing another interesting pre-failure indicator. due to its increased importance the behaviour of the f-function during the last seconds of stage d will be discussed thoroughly in next paragraphs. 0 20 40 60 0 50 100 150 200 250 300 tim e (sec) st re ss ( m p a) 0 50 100 150 f -f un ct io n ( 1/ se c) stress f function stage a stage b stage c stage d t* f -f u n ct io n [s -1 ] time [s] a x ia l s tr es s [m p a ] a x ia l s tr es s [m p a ] figure 6: time evolution of f-function during the experiment. the time evolution of the f-function and the respective one of the ib-values exhibit several qualitative similarities, as it is shown in fig.7. more specifically, the sharp decrease of the ib-values observed at the end of stages a and d, as well as during stage c, is combined with the corresponding intense increase of the acoustic activity expressed by the f-function. furthermore, the intense decrease of the f-function at the beginning of stages b and d is combined with the gradual increase of the ib-values. special attention must be paid to the last seconds of stage d, at which an abrupt decrease of the ib-values, to levels approaching 1, is observed. at the same time, as far as the f-function is concerned, a strong increase is recorded, leading to a local peak, which designates and presages the upcoming failure of the specimen [7]. d. triantis et alii, frattura ed integrità strutturale, 50 (2019) 537-547; doi: 10.3221/igf-esis.50.45 543 0 50 100 150 0 50 100 150 200 250 300 f -f un ct io n ( 1/ se c) 0 1 2 3 4 ib -v al ue f function ib-value f -f u n ct io n [s -1 ] time [s] ib -v a lu e figure 7: time evolution of the f-function in juxtaposition to that of the ib-value. considering now the systematic reduction exhibited by the f-function at stages b and d, further analysis of the experimental results was undertaken, indicating that during the first two (2) seconds after the stabilization of the stress level, the f-function decreases following a power law of the form:       ( ) exp t f t a  (3) the above law is plotted in fig.8 for both stages b (fig.8a) and d (fig.8b) using logarithmic scale for the values of the ffunction. in this figure, the origin of the time scale (i.e., t=0) corresponds to the time instant to (for each stage) at which the stress attains its maximum value and is then stabilized, practically corresponding to the time instant at which the maximum values of the f-function are attained. the values of the parameter a and the time constant τ of eq.(3), as obtained by means of proper curve fitting, are equal to a=128.7 s-1, τ=0.98 s for stage b and a=141.6 s-1, τ=1.23 s, for stage d. as it is expected, the highest value of the time constant τ is observed in stage d due to the considerably increased acoustic activity that is recorded in this stage (recall that, after a while, fracture of the specimen occurred). y = 128.71e-1.02x 1 10 100 1000 0 2 4 6 8 time (sec) f f un ct io n (1 /s ec ) stage b y = 141.56e-0.81x 1 10 100 1000 0 2 4 6 8 time (sec) f f un ct io n (1 /s ec ) stage d f -f u n ct io n [s -1 ] time [s] f -f u n ct io n [s -1 ] time [s] (a) (b) figure 8: restoration of the f-function during the first seconds following stress stabilization in stages b (a) and d (b). as a last step, it is worth studying the time evolution of the f-function during the very last seconds prior to the failure of the specimen (i.e., the very last time interval of stage d). in a recent paper by triantis and kourkoulis [7], it was indicated that the f-function exhibits a peak just before the fracture, while before the occurrence of this peak there is a sharp increase of the f-function, which in terms of the time-to-failure parameter, tf-t, is governed by a power law of the form: d. triantis et alii, frattura ed integrità strutturale, 50 (2019) 537-547; doi: 10.3221/igf-esis.50.45 544    nff c t t (4) where tf is the time instant corresponding to the fracture of the sample and t, n are numerically obtained constants. a similar response is observed in the present experimental protocol. this is clearly seen in fig.9, in which the f-function is plotted versus the (tf-t) parameter on log-log scales. plotting the f-function versus the specific parameter offers a “magnified” picture of what happens during the very last instants before macroscopic fracture. it is observed from fig.9 that from the critical time instant at which the f-function starts increasing (i.e., about 40 s before the specimen’s macroscopic fracture) the law of eq.(4) prevails, with an exponent value equal to n=1.4, close enough to the value of n=1.2 determined in the protocol described in ref. [7] for marble specimens under monotonic uniaxial compression. from this time instant on, i.e., for (tf-t)<5 s, the f-function exhibits a stabilisation trend at relatively high values. finally, during the very last tenths of a second before macroscopic fracture (i.e., (tf-t)<0.7 s) the values of the f-function are reduced, as a consequence of the high values of the respective inter-event times, due to the fact that long-duration acoustic hits are recorded (again in accordance with the behaviour observed in ref. [7]). y = 1042.10x-1.44 1 10 100 1000 0.1 1 10 100 tf t (sec) f f un ct io n ( 1/ se c) 1000 100 10 1 f -f u n ct io n [s -1 ] 0.1 1 10 100 y=1042.10x 1.4 tf t [s] figure 9: the f-function versus the (tf-t) parameter on a log-log scale, during the last seconds before the sample failure (i.e., during the last time interval of stage d). classification of the cracking modes by correlating average frequency and ra values to the values of the f-function the ae technique is already widely used to classify the cracking modes according to the rilem tc 212-acd recommendation, with very satisfactory results, for example in concrete [24]. according to the specific recommendation, the classification of micro-cracking in mode-i or mode-ii is achieved through the correlation of the parameter ra (rise time/amplitude) of the acoustic signals to their average frequency (af). in order to investigate how the average values of ra and af are correlated in the various loading stages of the experimental protocol considered here, in which both high and low acoustic activity is observed, the following procedure is followed: as a first step, the maximum value fmax of the f-function is determined. for the specific experiment, considered in previous sections, the time instant at which the f-function was maximized was found equal to about t=319 s and the corresponding value of the f-function was fmax=145.7 s-1. for each one of the four stages of the loading protocol the acoustic hits were classified into three categories: the first one includes the hits that are recorded when the acoustic activity is low or, equivalently, the normalized function f=f/fmax varies in the 0<f<0.1 range. the second category includes the hits recorded when 0.1≤f<0.5 (i.e., the acoustic activity is of moderate intensity), and the third one includes the hits recorded when f≥0.5 (i.e., the acoustic activity is intense). as a second step, for each one of these three categories and for each stage of the loading protocol the average values of ra and af are calculated. in fig.10 the mean value of the af is plotted against the respective mean value of the ra for all three categories and all four stages. α straight line of slope equal to k=0.5 khz·mv/μs is plotted, starting from point (0, 0), in order to study the ratio between the ra and af values and properly classify the cracking modes within the marble volume. it is noted here that the appropriate slope of this line is an open issue for research, as there is not a generally accepted rule. in general, it is believed that this slope is to be determined taking into account the type of the material and the type of the experiment [25]. d. triantis et alii, frattura ed integrità strutturale, 50 (2019) 537-547; doi: 10.3221/igf-esis.50.45 545 stage a 0 10 20 30 40 0 20 40 60 80 mode mode ii stage b 0 10 20 30 40 0 20 40 60 80 mode i mode ii stage c 0 10 20 30 40 0 20 40 60 80 mode i mode ii stage d 0 10 20 30 40 0 20 40 60 80 mode ii mode i m ea n v al u e of a f [ k h z] mean value of ra [μs/mv] mean value of ra [μs/mv] m ea n v al u e of a f [ k h z] m ea n v al ue o f a f [ k h z] mean value of ra [μs/mv] mean value of ra [μs/mv] m ea n v al ue o f a f [ k h z] stage a stage b stage dstage c mode i figure 10: classification of cracking modes according to the rilem tc 212-acd recommendation (i.e., with the aid of the relation between the af and ra parameters), in the four stages of the loading protocol ((a), (b), (c), (d) correspond to the stages a, b, c, d, respectively (see fig.1)). the blue squares correspond to f<0.1, the green ones to 0.1≤f<0.5 and the red ones to f≥0.5. the red star in fig.10d (i.e., for stage d) corresponds to the average values of af and ra during the last 5 seconds before the catastrophic fracture of the specimen (see fig.9). for f≥0.5 in all four stages, the mean values of ra and af correspond to gradients k<0.5 khz·mv/μs. this leads to the conclusion that, at least for the specific material, when the acoustic activity is intense, the shear type of cracking (mode-ii) is dominant. in contrast, when the acoustic activity is low (f<0.1), it is clear that all acoustic signals are classified as modei ones. particularly, during the last 5 seconds before the final fracture of the sample, the f-function shows a stabilization trend but with strong fluctuations (f=110±35) s-1 (see fig.9), and the shear type of micro-cracking (mode-ii) is prominent. the mean values of ra and af at this time interval are depicted fig.10d with the aid of a red star. a more detailed description of the results of classification of cracking modes according to the characteristics of the ae hits in the four stages of the experiment discussed here is presented in table 2. again, it is seen from this table that when the acoustic activity is high (f>0.5) the mode-ii cracking is dominant (exceeding 50%) for all four stages of the loading scheme. on the contrary, for f<0.5 the majority of ae hits corresponds to mode-i cracking. the shear mode exists also but it corresponds to a relatively low proportion ranging from about 6% to about 31%. stage f>0.5 f<0.5 mode-i mode-ii mode-i mode-ii a 22% 78% 85% 15% b 25% 75% 94% 6% c 44% 56% 87% 13% d 35% 65% 69% 31% table 2: classification of αε hits. d. triantis et alii, frattura ed integrità strutturale, 50 (2019) 537-547; doi: 10.3221/igf-esis.50.45 546 conclusions he experimental protocol described here was designed in order to gather data regarding the response of rock-like materials under stepwise uniaxial compression, at load levels closely approaching those causing fracture. as a first step, the acoustic activity was analyzed in terms of the improved b-value (ib-value) and the cumulative energy of the acoustic signals. it was demonstrated that, when the acoustic activity is weak, the ib-value varies in the 2<ib<3 interval. however, as the acoustic activity is intensified, the ib-value drops rapidly, attaining values close to the critical value of 1, i.e., to the limit designating the onset of formation of macro-cracks. as far as it concerns the cumulative energy of the acoustic signals, it was observed that during the stages of constant stress level, its time evolution is governed by a power law with two distinct branches. however, during the last seconds before fracture it exhibits an abrupt increasing trend, in spite of the fact that the stress is constant. the detection of signals that could play the role of pre-failure indicators was also considered. this was attempted it terms of the time evolution of the ib-value, the cumulative energy of the acoustic hits and the f-function. it was definitely indicated that all three parameters just mentioned provide interesting and clear indices which could be considered as timely warning signals designating entrance of the system (specimen) into the stage of impending failure. especially the f-function, well before macroscopic fracture is visible, exhibits an increasing trend which is governed by a power law. then, a few seconds (or even tenths of a second) before the onset of macroscopically visible fracture, it reaches a maximum value and starts decreasing. concerning the stages at which the specimen is under constant externally applied stress, the mean frequency of the ae hits, as it is expressed by the f-function, exhibits an exponential decrease (during the first one or two seconds of the constant stress stage). then, it shows a stabilization tendency at fairly low values. an exception is the stage at which the stress is stabilized at levels closely approaching its ultimate value (i.e., the compressive strength of the material). in this stage, after a time interval of about 40 seconds (almost 25 s before fracture), the f-function exhibits a sharp increase (under constant stress), thus presaging the final macroscopic collapse of the specimen. finally, the standardized approach for the classification of the damage process in terms of the ra-af pair (which in fact determines the ratio of each type of damage, i.e., mode-i or mode-ii micro-cracking), based on the rilem tc 212-acd recommendation, was applied. the classification showed that, for the phases with weak acoustic activity, mode-i crackingh type appears as the dominant one, while, when the acoustic activity is intense, the majority of the acoustic signals corresponds to the mode-ii type of cracking. references [1] rao, m.v.m.s. and lakschmi, p.k.j. (2005). analysis of b-value and improved b-value of acoustic emissions accompanying rock fracture, curr. sci. india, 89, pp. 1577–1582. [2] colombo, i.s., main, i. and forde, m.c. (2003). assessing damage of reinforced concrete beam using ‘‘b-value’’ analysis of acoustic emission signals, j. mater. civil. eng., 15, pp. 280–286. [3] cox, s.j.d. and meredith, p.g. (1993). microcrack formation and material softening in rock measured by monitoring acoustic emissions, int. j. rock mech. min., 30, pp. 11–24. [4] aggelis, d.g., mpalaskas a.c. and matikas, t.e. (2013). investigation of different fracture modes in cement-based materials by acoustic emission, cement concrete res., 48, pp. 1–8. [5] stanchits, s., dresen, g. and vinciguerra, s. (2006). ultrasonic velocities, acoustic emission characteristics and crack damage of basalt and granite, pure appl. geophys., 163, pp. 975–994. [6] lockner, d. (1993). the role of acoustic emission in the study of rock fracture, int. j. rock mech. min., 30, pp. 883– 899. [7] triantis, d. and kourkoulis, s. k. (2018). an alternative approach for representing the data provided by the acoustic emission technique, rock mech. rock eng., 51, pp. 2433–2438. [8] ono, k. (1979). fundamentals of acoustic emission, in: fundamentals of acoustic emission, ono, k. (ed.), los angeles, usa, ucla publ. [9] ohtsu, m., shigeishi, m., iwase, h. and koyanagi, w. (1991). determination of crack location, type and orientation in concrete structures by acoustic emission, mag. concrete res., 155, pp. 127–134. [10] ono, k. (1993). trends of recent acoustic emission literature, j. acoustic emission, 12, pp. 177–198 [11] ohtsu, m. (1994). new trends in non-destructive and in-place testing of concrete structures, in: proc. concrete technology: new trends, industrial applications, aguado a., gettu r. and shah, s.p. (eds), london, e&fn spon. t d. triantis et alii, frattura ed integrità strutturale, 50 (2019) 537-547; doi: 10.3221/igf-esis.50.45 547 [12] ohtsu, m. and tomoda, y. (2008). phenomenological model of corrosion process in reinforced concrete identified by acoustic emission, aci mater. j., 105, pp. 194–199. [13] aggelis, d.g., soulioti, d.v., sapouridis, n., barkoula, n.m., paipetis, a.s. and matikas, t.e. (2011). acoustic emission characterization of the fracture process in fibre reinforced concrete, constr. build. mater., 25, pp. 4126–4131. [14] main, i.g. (1989). a reinterpretation of the precursory seismic b-value anomaly from fracture mechanics, geophys. j., 96, pp. 131–138. [15] exadaktylos, g.e., vardoulakis, i. and kourkoulis, s.k. (2001). influence of nonlinearity and double elasticity on flexure of rock beams – ii. characterization of dionysos marble, int. j. solids struct. 38(22-23), pp. 4119–4145. [16] triantis, d. (2018). acoustic emission monitoring of marble specimens under uniaxial compression. precursor phenomena in the near-failure phase, procedia structural integrity 10, pp. 11–17. [17] kourkoulis, s.k., exadaktylos, g.e. and vardoulakis, i. (1999). u-notched dionysos-pentelicon marble in three point bending: the effect of nonlinearity, anisotropy and microstructure., int. j. fracture, 98, pp. 369–392. [18] calabrese, l., campanella, g. and proverbio, e. (2012). noise removal by cluster analysis after long time ae corrosion monitoring of steel reinforcement in concrete, constr. build. mater., 34, pp. 362–371. [19] triantis, d., stavrakas, i., pasiou, e. d. and kourkoulis, s.k. (2019). assessing the acoustic activity in marble specimens under stepwise compressive loading, mat. design process comm., doi:https://doi.org/10.1002/mdp2.100. [20] zhang, j-z., zhou x-p., zhou, l-s. and berto, f. (2019). progressive failure of brittle rocks with non-isometric flaws: insights from acoustooptic-mechanical (aom) data, fatigue fract. eng. mater. struct., 42, pp. 1787–1802. [21] zhou, x-p., zhang, j-z., qian, q-h. and niu, y. (2019). experimental investigation of progressive cracking processes in granite under uniaxial loading using digital imaging and ae techniques, j. struct. geol., 126, pp. 129–145. [22] wang, x., wang, e., liu, x. (2019). damage characterization of concrete under multi-step loading by integrated ultrasonic and acoustic emission techniques, constr. build. mater., 221, pp. 678–690. [23] niu y., zhou x-p., zhou l-s. (2019). fracture damage prediction in fissured red sandstone under uniaxial compression: acoustic emission b-value analysis, fatigue fract. eng. mater. struct., doi: 10.1111/ffe.13113. [24] ohtsu, m. (chairman) (2010). recommendations of rilem technical committee 212-acd: acoustic emission and related nde techniques for crack detection and damage evaluation in concrete: 3. test method for classification of active cracks in concrete structures by acoustic emission, mater struct. 43, pp.1187–1189. [25] aggelis, d.g. 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/hrv (za stvaranje adobe pdf dokumenata najpogodnijih za visokokvalitetni ispis prije tiskanja koristite ove postavke. stvoreni pdf dokumenti mogu se otvoriti acrobat i adobe reader 5.0 i kasnijim verzijama.) /hun 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/pdfxoutputintentprofileselector /documentcmyk /preserveediting true /untaggedcmykhandling /leaveuntagged /untaggedrgbhandling /usedocumentprofile /usedocumentbleed false >> ] >> setdistillerparams << /hwresolution [2400 2400] /pagesize [612.000 792.000] >> setpagedevice microsoft word numero 9 art 9 finale g. meneghetti, frattura ed integrità strutturale, 9 (2009) 85 94; doi: 10.3221/igf-esis.09.09 85 utilizzo della tensione di picco per la verifica a fatica dei giunti saldati d’angolo con il metodo degli elementi finiti g. meneghetti università di padova, dipartimento di ingegneria meccanica, giovanni.meneghetti@unipd.it riassunto. in questo lavoro viene applicato il metodo della tensione di picco per l’analisi della resistenza a fatica di giunti saldati con cordone d’angolo limitatamente al caso di rottura al piede del cordone di saldatura. il metodo è un’applicazione ingegneristica dell’approccio locale basato sul fattore di intensificazione delle tensioni per intagli (notch-stress intensity factor, n-sif) di modo i, che assimila il profilo del piede del cordone di saldatura ad un intaglio a v con raggio di raccordo pari a zero. inoltre si basa sull’utilizzo della tensione di picco singolare calcolata al piede del cordone mediante un’analisi agli elementi finiti lineare elastica con elementi aventi una prefissata dimensione, assunta pari a 1 mm in questo lavoro. la relativa semplicità di utilizzo e la robustezza del metodo lo rendono adatto all’applicazione in ambito industriale. abstract. the paper presents the so-called peak stress method applied to the analysis of the fatigue strength of fillet-welded joints failing from the weld toe. such method is an engineering application of the local approach based on the mode i notch stress intensity factor (n-sif), which assumes the weld toe profile as a sharp vshaped notch having a toe radius equal to zero. according to the peak stress method, the design stress is the elastic peak stress calculated at the point of singularity by means of a finite element analysis, where the element size has a fixed value, for example equal to 1 mm in the present work. due to its simplicity, the peak stress method proved to be convenient in practical applications. keywords. fatigue design, local approaches, notch-stress intensity factors, fillet welded joints, finite element analysis, coarse mesh, peak stress method. introduzione ’approccio locale basato sui fattori di intensificazione delle tensioni per intagli (notch-stress intensity factors, n-sifs) è stato applicato con successo all’analisi della resistenza a fatica di giunti saldati, sia in acciaio che in lega leggera, con rottura al piede del cordone di saldatura [1-3]. l’assunzione di base è che il profilo geometrico del piede del cordone di saldatura si possa assimilare ad un intaglio acuto a v con angolo di apertura che nella maggior parte dei casi si può ritenere prossimo a 135°, come rappresentato in figura 1. questa assunzione è ragionevole in quanto il valore minimo del raggio di raccordo in giunti saldati d’angolo e testa-testa con tecnologie tradizionali varia notevolmente anche lungo uno stesso cordone di saldatura e i valori sono compresi tipicamente tra 0.05 mm e 0.6 mm [4]. la variabilità dei valori medi del raggio di raccordo è ancora maggiore e pertanto sarebbe poco rappresentativa la definizione di un valore caratteristico del raggio di raccordo per effettuare un’analisi a fatica. assunta la geometria di figura 1, la distribuzione locale delle tensioni in un’analisi piana lineare elastica è descritta dagli nsifs di modo i e ii, vik and v iik , rispettivamente, che quantificano l’intensità della distribuzione asintotica delle tensioni in accordo alla soluzione teorica di williams [5]. la definizione degli n-sifs di modo i e ii [6] è la seguente:   r)(lim2k 110 0r v i     (1a)   r)(lim2k 210r 0r v ii     (1b) l http://www.gruppofrattura.it/ http://dx.medra.org/10.3221/igf-esis.09.09&auth=true mailto: giovanni.meneghetti@unipd.it g. meneghetti, frattura ed integrità strutturale, 9 (2009) 85 94; doi: 10.3221/igf-esis.09.09 86 figura 1: modello geometrico di un giunto saldato d’angolo e sistema di riferimento polare con origine al piede del cordone. nelle precedenti definizioni, r e  sono le coordinate polari mostrate in fig. 1, 1, 2 sono gli autovalori di williams per modo i e ii, rispettivamente. quando l’angolo di apertura è pari a 135°, l’esponente (1-1) risulta 0.326 mentre (1-2) risulta –0.302. le componenti dello stato di tensione si possono infine esprimere nella forma [1]:                                                 )(f )(f )(f kr )(f )(f )(f kr r,2 r,2 ,2 v ii 302.0 r,1 r,1 ,1 v i 326.0 r rr (2) dove le funzioni f sono espressioni trigonometriche note. le espressioni (2) mostrano che, essendo 2=135°, solamente la distribuzione di modo i è singolare. la fig. 2 mostra come esempio il campo di tensione locale lungo la lamiera principale di un giunto saldato d’angolo con doppio irrigidimento. è evidente che solo il contributo di modo i allo stato di tensione locale è singolare, mentre il contributo di modo ii tende a zero. nella figura è anche riportato per confronto il risultato ottenuto con un’analisi piana lineare elastica agli elementi finiti. utilizzando i risultati dell’analisi agli elementi finiti ottenuti lungo la bisettrice dell’intaglio e applicando la definizione (1a) è possibile calcolare vik , parametro da cui dipende la resistenza a fatica. infatti esprimendo in sintesi l’approccio locale, è possibile affermare che due giunti saldati che in una prova di fatica sperimentano lo stesso range di variazione di vik avranno la stessa vita a fatica, qualunque sia la loro geometria e la loro dimensione assoluta. tuttavia la fig. 2 mostra che la densità della mesh necessaria per calcolare la distribuzione asintotica del campo locale, e quindi il fattore di intensificazione di modo i, è elevata. pertanto le fasi di preparazione della mesh, di calcolo e di analisi dei risultati risultano dispendiose in termini di tempo. si nota che in fig. 2 la dimensione degli elementi più piccoli utilizzati è una frazione di micron. l’analisi agli elementi finiti risulta inoltre ancora più complicata per giunti aventi geometria tridimensionale come ad esempio i giunti con attacchi longitudinali. 0.001 0.01 0.1 1 10 100 0.1 1 10 modo i modo iimodo i+ii fem r (mm) rr/n t l h r l/t = 1 t = 12 mm h = 10 mm figura 2: confronto fra risultati analitici e numerici nella valutazione dello stato tensionale lungo la superficie di un giunto saldato. http://www.gruppofrattura.it/ http://dx.medra.org/10.3221/igf-esis.09.09&auth=true g. meneghetti, frattura ed integrità strutturale, 9 (2009) 85 94; doi: 10.3221/igf-esis.09.09 87 il metodo della tensione di picco supera questi problemi di applicazione dell’approccio n-sif nell’analisi della resistenza a fatica dei giunti saldati, sostituendo al parametro vik la tensione di picco singolare calcolata a piede cordone, che risulta più facile da calcolare con un’analisi agli elementi finiti. pertanto dopo aver presentato le basi teoriche del metodo, ne verrà mostrata l’applicazione all’analisi della resistenza a fatica di giunti d’angolo aventi geometria semplice. questa analisi consente di tarare due curve di resistenza a fatica in termini di tensione di picco, valide per giunti saldati d’angolo in acciaio e in lega leggera, rispettivamente, senza trattamenti post-saldatura. successivamente queste curve di resistenza a fatica di progetto verranno utilizzate per stimare la resistenza a fatica di giunti aventi geometria più complessa. il metodo della tensione di picco uando si considera un componente contenente punti di singolarità, ad esempio l’apice di una cricca o di un intaglio aperto a spigolo vivo, la tensione calcolata all’apice con un’analisi lineare elastica agli elementi finiti dipende dalla fittezza della mesh, in modo che la tensione è tanto più elevata quanto minore è la dimensione degli elementi utilizzati. pertanto la tensione singolare calcolata con gli elementi finiti non ha significato. tuttavia nisitani e teranishi [7] hanno mostrato che la tensione singolare peak calcolata all’apice di una cricca con un’analisi lineare elastica agli elementi finiti è in rapporto costante con il fattore di intensificazione delle tensioni ki (ki/peak = costante), purché sia mantenuta costante la dimensione e il tipo di elemento utilizzato. recentemente, è stata data una giustificazione teorica al metodo della tensione di picco (psm) [8] ed il suo utilizzo è stato esteso a casi diversi da quelli considerati in origine da nisitani e teranishi. in particolare il psm è stato esteso a casi di intagli aperti a v a spigolo vivo ed è stato valutato l’effetto della dimensione degli elementi utilizzati per l’analisi. la fig. 3 mostra diverse geometrie contenenti punti di singolarità dovuti a cricche o intagli a spigolo vivo. per ognuna di queste geometrie è stata fatta variare la profondità dell’intaglio o della cricca a parità di dimensione di elemento oppure la dimensione dell’elemento a parità di dimensione di intaglio o cricca. le analisi agli elementi finiti lineari elastiche sono state fatte con il codice ansys utilizzando gli elementi quadrangolari a quattro nodi plane 42. la mesh è stata generata automaticamente dal software una volta imposta la dimensione dell’elemento d con il comando ‘global element size’. nessun altro controllo sulla forma e dimensione degli elementi è stato utilizzato. figura 3: geometrie contenenti punti di singolarità tensionale utilizzate per validare il metodo della tensione di picco (dimensioni in mm) [8]. q http://www.gruppofrattura.it/ http://dx.medra.org/10.3221/igf-esis.09.09&auth=true g. meneghetti, frattura ed integrità strutturale, 9 (2009) 85 94; doi: 10.3221/igf-esis.09.09 88 i risultati sono riportati nella fig. 4, che mostra, al variare del rapporto tra la dimensione di riferimento a del componente e la dimensione d dell’elemento, il parametro adimensionale *fek : 11 peak v i* fe d k k   (3) calcolato per ogni geometria presa in considerazione. la fig. 4 mostra che non appena a/d è maggiore o uguale a 3, il parametro *fek è pressoché costante e pari a 1.38, con risultati numerici raccolti in una ristretta banda definita dal +-3% rispetto a tale valore. in [8] è fornita anche un’espressione analitica per calcolare il parametro *fek . scelta quindi una certa dimensione di elemento d da utilizzare nelle analisi agli elementi finiti, la fig. 4 e l’eq. (3), dove 38.1k*fe  , mostrano che il rapporto peak v ik  è costante e quindi la tensione di picco peak può sostituire l’n-sif vik nelle analisi di resistenza a fatica con notevole riduzione dei tempi e semplificazione delle procedure di calcolo. è necessario tener presente che il metodo della tensione di picco così come presentato è valido sotto le seguenti condizioni: elementi lineari quadrilateri a quattro nodi (plane 42, della libreria del codice ansys 8.0); pattern di elementi come quello riportato nella successiva fig. 5; intagli a v con angolo di apertura compreso tra 0° e 135°. 1 1.2 1.4 1.6 1.8 2 1 10 100 a/d * fek  3% 2.2 fig. 6a, a=variabile, d=1 mm fig. 6b, a=variabile, d=1 mm fig. 6b, a=10 mm, d=variabile fig. 6c, 2=135°, a=10 mm, d=variabile fig. 6c, 2=90°, a=5 mm, d=variabile fig. 6c, 2=90°, a=10 mm, d=variabile fig. 6c, 2=90°, a=15 mm, d=variabile fig. 6d, a/b/t=13/10/8, d=variabile fig. 6d, a/b/t=100/50/16, d=variabile valore medio limiti di validità del psm 3 figura 4: parametro adimensionale * fek ottenuto da 61 analisi agli elementi finiti delle geometrie riportate in fig. 5. la linea continua rappresenta il valor medio pari a 1.38 [8]. definizione di curve di resistenza a fatica di progetto per giunti saldati d’angolo in acciaio e in lega leggera a possibilità di definire bande di resistenza a fatica unificate, al variare della geometria e delle dimensioni assolute, per giunti in acciaio e in lega leggera saldati d’angolo in termini di range di variazione di vik , v ik , è già stata verificata in passato [1, 3]. essendo valida l’eq. (3) con 38.1k*fe  e una volta scelta la dimensione di elemento utilizzata nell’analisi agli elementi finiti, è quindi possibile definire delle curve di progetto di resistenza a fatica in termini di range della tensione di picco peak. a tale scopo sono stati utilizzati i dati di maddox [9], gurney [10, 11], kihl and sarkani [12, 13] pubblicati negli articoli originali in termini di tensione nominale. i dettagli sulle geometrie, i materiali e le condizioni di carico sono riportati in [8]. in sintesi, i dati si riferiscono a giunti in acciaio da costruzione (con tensione di snervamento variabile tra 360 e 670 mpa) e in leghe leggere della serie 5000 e 6000 (con tensione di snervamento variabile fra 250 e 304 mpa) sollecitati a trazione o flessione con rapporto nominale di ciclo r (definito come rapporto fra la tensione nominale minima e quella massima applicata) prossimo a zero. tutti i giunti hanno semplice configurazione a t o a croce con saldature d’angolo e sono stati sottoposti a prova senza alcun trattamento post-saldatura. i giunti in acciaio l http://www.gruppofrattura.it/ http://dx.medra.org/10.3221/igf-esis.09.09&auth=true g. meneghetti, frattura ed integrità strutturale, 9 (2009) 85 94; doi: 10.3221/igf-esis.09.09 89 hanno spessore del piatto principale variabile fra 6 e 100 mm con rapporto tra gli spessori saldati compreso fra 0.03 e 8.8, mentre quelli in lega leggera fra 3 e 24 mm con rapporto tra gli spessori saldati variabile fra 0.25 e 1. figura 5: mesh free utilizzata per le analisi agli elementi finiti di giunti saldati d’angolo con elementi di dimensione pari a 1 mm. n. cicli a rottura     4 5 205 108 d, 50% 6 7 pendenza k = 3.00 t = %7.97,a %3.2,a   =1.90 d, 50% = 149 mpa r 0   p ea k [ m p a] figura 6: resistenza a fatica di giunti saldati d’angolo in acciaio da costruzione in termini di tensione di picco lineare elastica calcolata con la mesh riportata in fig. 5. banda di dispersione relativa al valor medio  due deviazioni standard [8]. n. cicli a rottura 4 5 94 52 d, 50% 6 7 pendenza k = 3.80 t = %7.97,a %3.2,a   =1.81 r 0   pe ak  [ m p a]       figura 7: resistenza a fatica di giunti saldati d’angolo in lega leggera in termini di tensione di picco lineare elastica calcolata usando elementi di 1 mm di dimensione come riportato in fig. 5. banda di dispersione relativa al valor medio  due deviazioni standard [8]. le analisi numeriche sono state fatte con il software ansys usando mesh di tipo free con elementi di dimensione di 1 mm come riportato in fig. 5 e imponendo una tensione nominale pari a 1 mpa. calcolando la tensione massima principale (peak) nel punto di singolarità è stato possibile esprimere i risultati originali in termini di range di tensione di picco anziché x y z d = 1 mm nodo in cui calcolare la tensione massima principale (peak) http://www.gruppofrattura.it/ http://dx.medra.org/10.3221/igf-esis.09.09&auth=true g. meneghetti, frattura ed integrità strutturale, 9 (2009) 85 94; doi: 10.3221/igf-esis.09.09 90 range di tensione nominale. i risultati sono riportati in fig. 6 e 7 per i giunti in acciaio e in lega leggera, rispettivamente. le bande di dispersione riportate si riferiscono a probabilità di sopravvivenza del 97.7% e il parametro t che ne quantifica l’ampiezza risulta confrontabile con i valori trovati in termini di n-sif [3]. considerando ulteriormente i giunti in acciaio e calcolando il parametro t per probabilità di sopravvivenza del 10% e 90% si trova 1.51 in ottimo accordo con il valore di 1.50 relativo alla banda unificata proposta da haibach [14]. pertanto è possibile concludere che le bande riportate nelle fig. 6 e 7 si possono ritenere bande unificate per la progettazione a fatica di giunti saldati d’angolo in acciaio da costruzione e lega leggera, rispettivamente, senza trattamenti post-saldatura e per rotture innescate a piede cordone. applicazione del metodo della tensione di picco a giunti complessi e curve di resistenza a fatica riportate nelle fig. 6 e 7 sono state utilizzate per stimare la resistenza a fatica di giunti saldati d’angolo aventi geometria complessa presenti in letteratura. le tab. 1 e 2 riportano le geometrie di giunto analizzate per acciai e leghe leggere, rispettivamente, mentre per i dettagli riguardo ai materiali e ai riferimenti ai lavori originali si rimanda a [15]. le geometrie dei giunti sono del tipo con irrigidimento longitudinale, single-lap o tubolare come riportato nelle tab. 1 e 2. per quanto riguarda i giunti in acciaio, i materiali impiegati sono acciai da costruzione con tensione di snervamento compresa fra 309 e 780 mpa, gli spessori variabili fra 3 e 12.5 mm, mentre il rapporto di ciclo è compreso fra 0 e 0.7. per quanto riguarda i giunti in lega leggera, i materiali impiegati sono leghe della serie 5000 e 6000 aventi tensione di snervamento compresa fra 245 e 290 mpa, gli spessori sono variabili fra 3 e 12 mm, mentre il rapporto di ciclo è compreso è prossimo a zero. le analisi agli elementi finiti dei giunti bidimensionali, come ad esempio i giunti single-lap, sono state condotte utilizzando la mesh riportata in figura 5, mentre per calcolare la tensione di picco nel caso di giunti tubolari è stata utilizzata la procedura a due step dettagliata in [15, 16] e riassunta dalla fig. 8. nel primo step di analisi è stato definito un modello ad elementi shell (modello principale). nel secondo step di analisi si è immaginato di fare una sezione longitudinale del giunto reale in corrispondenza del punto di innesco della rottura a fatica del giunto con un piano che nel caso di fig. 8 stacca sulla superficie del modello principale le due linee spesse. si ottiene così il sottomodello riportato in fig. 8 che riproduce lo spessore degli elementi saldati e il profilo a v a spigolo vivo del piede del cordone. i risultati dell’analisi sul modello principale, a cui sono applicate le condizioni al contorno, sono trasferiti al sottomodello imponendo una condizione di congruenza, ovvero gli spostamenti calcolati lungo le linee spesse del modello principale vengono imposti alle corrispondenti linee spesse del sottomodello. questa operazione è effettuata automaticamente in ambiente ansys utilizzando il comando ‘shell-to-solid’ submodeling. le fig. 9 e 10 riportano il confronto fra i risultati sperimentali e le curve di progetto riportate nelle fig. 6 e 7, rispettivamente, per i giunti in acciaio e in lega leggera. dal confronto si nota la validità delle curve di progetto, fatta eccezione per i giunti di più piccolo spessore, che meritano ulteriori approfondimenti [15]. nelle strutture reali i percorsi di propagazione possono essere multipli oppure particolarmente lunghi, in modo tale da rendere significativa la quota parte di vita a fatica spesa per la propagazione di cricche al di fuori del piccolo volume di materiale in cui lo stato di tensione è controllato dagli n-sifs. in questi casi le curve di progetto riportate nelle figure 6 e 7 vanno utilizzate per stimare la vita fatica a innesco, mentre per la fase di propagazione è valido il classico approccio basato sulla meccanica della frattura lineare elastica. si ritiene infine che utilizzando il metodo della tensione di picco unitamente alla procedura di calcolo descritta, l’approccio n-sif per la progettazione a fatica dei giunti saldati possa essere implementato in un contesto industriale. conclusioni l metodo della tensione di picco (psm) è stato applicato all’analisi della resistenza a fatica di giunti saldati d’angolo in acciaio e in lega leggera senza trattamenti post-saldatura con rottura al piede del cordone di saldatura. il metodo proposto è un’applicazione ingegneristica dell’approccio locale basato sugli n-sif, che assimila il profilo geometrico del piede del cordone di saldatura ad un intaglio a v a spigolo vivo con angolo di apertura tipicamente pari a 135°. il metodo della tensione di picco utilizza come tensione di progetto la tensione di picco singolare calcolata al piede cordone con un’analisi agli elementi in cui la dimensione degli elementi sia prefissata, pari a 1 mm in questo lavoro. la tecnica di analisi è presentata nelle figure 5 e 8 per giunti aventi geometria riconducibile a modelli bidimensionali e tridimensionali, rispettivamente. le curve di resistenza a fatica da utilizzare per le verifiche sono riportate nelle figure 6 e 7, rispettivamente, per giunti in acciaio e in lega leggera. l i http://www.gruppofrattura.it/ http://dx.medra.org/10.3221/igf-esis.09.09&auth=true g. meneghetti, frattura ed integrità strutturale, 9 (2009) 85 94; doi: 10.3221/igf-esis.09.09 91 geometria tipo di carico geometria tipo di carico tabella 1: geometria e condizioni di carico per i giunti saldati d’angolo in acciaio considerati (n: range della tensione nominale considerata negli articoli originali; dimensioni in mm) [15]. http://www.gruppofrattura.it/ http://dx.medra.org/10.3221/igf-esis.09.09&auth=true g. meneghetti, frattura ed integrità strutturale, 9 (2009) 85 94; doi: 10.3221/igf-esis.09.09 92 geometria tipo di carico tabella 2: geometria e condizioni di carico per i giunti saldati d’angolo in lega leggera considerati (n: range della tensione nominale considerata negli articoli originali; dimensioni in mm) [15]. http://www.gruppofrattura.it/ http://dx.medra.org/10.3221/igf-esis.09.09&auth=true g. meneghetti, frattura ed integrità strutturale, 9 (2009) 85 94; doi: 10.3221/igf-esis.09.09 93 figura 8: tecnica di analisi agli elementi finiti di giunti tridimensionali per calcolare la tensione di picco (peak) a piede cordone [15]. 100 1000 5000 1.e+04 1.e+05 1.e+06 1.e+07 n. cicli a rottura  peak [mpa] giunti a croce n-l-c (3 mm < t < 10 mm) t nlc (t=5 and 6 mm) giunti a croce lc (t= 3 and 6 mm) lap joint (t= 3.2 mm) attacchi longitudinali (6 mm < t < 12 mm) tubo-su-flangia (5 mm < t < 8 mm) giunti tubolari a croce (t=12.5 mm) simboli pieni: prove run-out banda di dispersione proposta (cfr fig. 6) figura 9: confronto fra la banda di dispersione proposta in fig. 6 e i risultati sperimentali in termini di range di tensione di picco per giunti saldati d’angolo in acciaio (n-l-c: cordoni non portanti; lc: cordoni portanti) [15]. punto di innesco cricca ( piede cordone ) primo step: analisi del ‘modello principale ’ . gli elementi shell vengono generati sulla superficie media punto di innesco cricca virtuale gli spostamenti calcolati lungo la linea evidenziata nel ‘modello principale ’ sono trasferiti nelle corrispondenti posizioni del ‘ sottomodello ’ . secondo step: analisi del ‘sottomodello ’ . mesh standard con elementi da 1 mm sulla sezione longitudinale del giunto peak (nel punto di innesco) punto di innesco cricca virtuale http://www.gruppofrattura.it/ http://dx.medra.org/10.3221/igf-esis.09.09&auth=true g. meneghetti, frattura ed integrità strutturale, 9 (2009) 85 94; doi: 10.3221/igf-esis.09.09 94 20 100 1000 1.e+04 1.e+05 1.e+06 1.e+07 n. cicli a rottura  peak [mpa] giunti a croce nlc (t=8 mm) t nlc (t=3 mm and 8 mm) lap joint (3 mm < t < 8 mm) attacchi longitudinali (t= 8 mm and 11 mm) simboli pieni : prove run-out rhs-to-rhs (t= 3 mm) banda di dispersione proposta (cfr fig. 7) figura 10: confronto fra la banda di dispersione proposta in fig. 6 e i risultati sperimentali in termini di range di tensione di picco per giunti saldati d’angolo in lega leggera (n-l-c: cordoni non portanti; lc: cordoni portanti; rhs-to-rhs: giunto realizzato con elementi tubolari a sezione rettangolare) [15]. bibliografia [1] p. lazzarin, r. tovo, fatigue fract. engng. mater. struct., 21 (1998)1089. [2] b. atzori, g. meneghetti, int. j. fatigue, 23(8) (2001) 713. [3] p. lazzarin, p. livieri, int. j. fatigue, 23 (2001) 225. [4] a. seto, y. yoshida, a. galtier, fatigue fract. engng. mater. struct., 27 (2004) 1147. [5] m. l. williams, j. appl. mech., 19 (1952) 526. [6] r. gross, a. mendelson, int. j. fract. mech., 8 (1972) 267. [7] h. nisitani, t. teranishi, engng. fract. mech., 71 (2004) 579. [8] g. meneghetti, p. lazzarin, fatigue fract. engng. mater. struct., 30 (2007) 95. [9] s. j. maddox, the effect of plate thickness on the fatigue strength of fillet welded joints, abington publishing, abington, cambridge (1987). [10] t. r. gurney, the fatigue strength of transverse fillet welded joints, abington publishing, abington, cambridge (1991). [11] t. r. gurney, fatigue of thin walled joints under complex loading, abington publishing, abington, cambridge (1997). [12] d. p. kihl, s. sarkani, int. j. fatigue, 19 (1997) s311. [13] d. p. kihl, s. sarkani, probab. eng. mech. , 14 (1999) 97. [14] e. haibach service fatigue-strength – methods and data for structural analysis, dusseldorf, vdi (1989). [15] g. meneghetti, fatigue fract. engng. mater. struct., 31 (5) (2008) 346. [16] g. meneghetti, f. righetto, atti del xxxv convegno nazionale aias, ancona (2006). http://www.gruppofrattura.it/ http://dx.medra.org/10.3221/igf-esis.09.09&auth=true microsoft word numero 15 articolo 4 d h ni un nzu ab (pb hu per wa rel the aci gas tem ma ke in atte low obs into dev th sin bet is c am pro car a design a high tem icola zulia niversity of tri uliani@units. bstract. h bi) polymer midification rformance. t ater managem ate to the d e main desig id membran s mixture si mperature di anagement. t eywords. h ntroductio fuel-ce density sources ention becaus w temperatur stacles hinde olerance to c velopment of here are sever gle phase of w tween the fue considerably i mongst all typ omising. they rbon monoxid a and expe mperatu ani ieste, departm it high temper r and phosp n is not requ this is what ment proble development gn features a nes. perform mulating a istribution a this could s high tempe on ell power-sou y, ergonomics s. amongst a se of their hig e (< 100 °c) er their wides co usually co f pem fuel c ral advantages water need to el cell stack an increased ther pes of ht pe y can be oper de (co) cont eriment ure pem ment of mechan rature proto phoric acid, uired and co t makes ht ems are avo t and charac nd the perfo mance curves typical steam analysis sugg simplify stack rature pem urce system s and enviro all types of f gh power den ) and are co spread comm ontained in t ells that can s in operating o be consider nd the coolan reby allowing em, the ones rated at temp tent up to 2% n. zuli tal chara m fuel c nical engineer on exchange can be ope o content up t pem very oided. till n cterization o ormance cur s refer to the m reformer gest that cat k design and m fuel cells; 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[7] e types of ref could operate authors of th 9-12], but on ow lower per niform distrib with the aim performance c emperature di good results ell contains a the active ar of 860 µm. t latinum cataly built by the °c [16]. each erpentine pat lates, fixed w nd the stack w of the 25 cells department of presented in k temperatur . reactants fl air circuit and ents tti ld on the nation ts flows, tem ent and mode studied the p formates, con e with good p his paper for ly some stud rformance wh ution of reac m of experim curves of a 2 istribution. during a pre a commercial rea and the re the membran yst loading is authors, usin h plate contai ttern with fiv with eight all t was tightened ht pem stac f the university fig. 3. two re is measured flow rates we d a bronkhor 300 electron nal instrumen mperature) an elling of the h performance ntaining up to performance w a single fuel dies relate to hen compare ctants inside e mental analyze 25 cells ht p evious single l pbi basf f eactant manif ne is about 60 0.75 mg/cm ng sigracet b ins the flow f ve square sec threaded tie r d to a maxim ck designed at t y of trieste. baumer pres d using 6 kre measured rst el-flow f nic load mod nts compactr nd to acquire high of a o 5% with cell the d to each e an pem cell fuel folds 0 µm m2 on pp4 field ction rods mum the sure type and f201 dule, rio the http://www.gruppofrattura.it http://dx.medra.org/10.3221/igf-esis.15.04&auth=true gau th con inp usi a a ex (o con cur typ unt tem infr a figure 3: sche uge, 6-valve, 7he compactr nfigured with put, analog ou ng a ni crio agema therm xperiment start u degrada °c usin cv) and purg ntrolled, using rves were coll pical steam re til the lowest mperature di frared camera figure 4: a ematic represen -solenoid valve rio hardware h modules de utput for mas o 9201 and n movison 570 in tal proced up and shutd ation. during ng an externa ged with nitro g an on/off a lected operat eforming refo t stack cell v stribution wa was pointing : polarization c ntation of the t e, 8-hydrogen c e, consisting edicated to sp ss flow contro ni crio 920 nfrared came dure down proced g the start-up al hot air blow ogen, on both algorithm. th ting the stack ormate: h2 56 voltage reach as observed o g the top side curves and pow stack a [v ] n. zuli test bed (1-air cylinder, 9-pre of the ni cr pecific tasks: ols and digita 6 analog inpu era. dure were im procedure th wer. during t h anode and c he control sys at 160°c wit 6.35%, co 0. h about 0.3 v operating the e of the stack. wer density var and single cell 0,3 0,4 0,5 0,6 0,7 0,8 0,9 1,0 0 200 [ ] single fuel 25 cells sta single fuel 25 cells sta iani, frattura ed filter, 2-air com ssure regulator rio 9004 rea analog input al output for t ut modules. s mplemented in he fuel cell sta the shut-down cathode sides stem acted on th two differe .5%, co2 43. v. single cel stack with pu riations with lo mean tempera 400 [ma/cm2] cell voltage ack mean cell voltage cell power density ack mean cell voltage d integrità struttu mpressor, 3-flo r, 10-nitrogen al time contr t for voltage temperature c stack tempera n order to a ack is heated n procedure, s. at normal o n the hot air ent fuels: pur .15 %. stack lls voltages w ure hydrogen oad for the 25 ature: 160°c. f 600 800 0 50 10 15 20 25 30 35 40 urale, 15 (2011) owmeter, 4-pre cylinder, 11-th roller and the and current control. singl ature distribu avoid water c up from roo the stack wa operation, the blower or on re hydrogen a voltage was were measure n at 400 ma/ cells stack and fuel: h2. 0 00 50 00 50 00 50 00 [m w /c m 2 ] ) 29-34; doi: 10 essure transmit hermocouple, 1 e ni crio 9 measurement le cell voltage tion has been condensation om temperatu as set in open e stack mean n the cooling and a gas mix measured sta ed at 200 an cm2 current d d for a single fu .3221/igf-esis.1 tter, 5pressur 12-electronic lo 9104 chassis, ts, thermocou es were measu n measured u n and membr ure to at least n circuit vol temperature fan. polariza xture simulatin arting from o nd 400 ma/c density load. uel cell [8]. 15.04 31 re oad). was uple ured using rane 120 ltage was ation ng a ocv cm2. the http://www.gruppofrattura.it http://dx.medra.org/10.3221/igf-esis.15.04&auth=true n. 32 st cell 0.4 dec mw the th the 2], imp st hy to inv an per obs     l f f zuliani, frattur tack perfo ig. 4 sho hydrogen fuel cell l voltage, cor 46 v mean ce creases as loa w/cm2 for th e stack (14 % his behaviour e end plates c cell voltages proving perfo tack perfo ydrogen an ig. 5 sho hydrogen of fuels a some extend vestigated. fu n important as rformance of servation can stack voltag stack voltag fig. 8; 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of the stack n the stack is distribution at 2 mperature 160 (h2 56.35%, c 5 9 1 cell n h2 200 m sim. reform h2 400 m sim. reform with load ope variation with ower of 365 w ack power ha mance. perform for the single fuel cell and 2 ds the heat di ces depend on perature non for the stack fferences bet o reformate o e a single fu as load incre owest voltage m2 and 400 m temperature fuelled with r 200 ma/cm2 a °c. fuels: h2 a co 0.5%, 43.15 13 17 21 number ma/cm2 mate 200 ma/cm2 ma/cm2 mate 400 ma/cm2 erating with p h load for a si w at 0.5 v m as been 433 w mance differe fuel cell and 292 mw/cm2 spersion thro n temperatur uniformity t k operating w tween the 2 ty operation are o uel cell has b ease [17]. cell will limit ma/cm2. sev profile show reformate. and 400 ma/c and simulated 5 % co2). 25 pure ingle mean w at ence 162 2 for ough e [1, thus with ypes only been t the veral wn in cm2. http://www.gruppofrattura.it http://dx.medra.org/10.3221/igf-esis.15.04&auth=true th to t cell th effe low wit st tem nam the cat c f current densit [ma/cm2] 200 400 580 table 1: p he voltage dist the temperatu ls could be re he voltage non fect is strongl west voltage d th reformate f tack tempe ig. 7 and mean te central a mperature beh med t1, t2 a e stack middl thode air cool figure 7: th current density f ty me volt 0 0 0 performance d tribution follo ure dependen elated to the d n-uniformity ly associated due to the co fuels stack tem erature di d fig. 8 show emperature an and end sta haviour. it is and t3 (fig. 7 le reaching 2 ling effect. in hermal image o y 400 ma/cm2 fuel: pur f ean cell tage [v] 0.63 0.56 0.50 differences at 2 ows a parabo nt performanc different reac becomes eve to cell tempe ombined effe mperature dis istribution w the temper nd 400 ma/ ack parts (ab s also possibl 7 and fig. 9). 25°c between n fact, reactan of the 25 cells 2, mean stack te re hydrogen. figure 9: simpl n. zuli hydrogen mean cell pow density [mw/cm2] 126 223 292 200 and 400 ma olic pattern th ce of the sing tant distribut en more notic erature [17]. i ct of co con stribution is c n rature distribu /cm2 current bout 20°c). le to observe . t1 temperat n t1 and t2 nt air enters th htpem stack emperature 16 lification schem iani, frattura ed wer ] stac pow [w 157 279 36 a/cm2 for the hat is similar t gle pbi/h3po tion along the ceable when f in this case th ntent in the f crucial in orde ution along th density load the heat di e the temper ture is the low 2. this tempe he stack from k. 60°c, me of the air p °c d integrità struttu ck wer w] me volt 7 0 9 0 5 stack operatin to the stack t o4 based fuel e stack. fuels containi he first stack fuel and low er to obtain b he stack ope d. there is a ispersion thr rature differen west compare erature behav m the t1 sectio figure 8: sta 400 ma/ path through th 60 80 100 120 140 160 180 200 0 c urale, 15 (2011) ean cell tage [v] 0.60 0.51 ng with hydrog emperature p l cell. voltage ing co are us k cell (see red cell temperat best performa rating with p a marked tem rough the en nces amongs ed to t3 and viour could b on and leave ack temperatur /cm2, mean sta fuel: pure h he fuel cell stac 50 100 ) 29-34; doi: 10 reformate mean cell pow density [mw/cm2] 119 204 gen and reform profile (see fi e differences b sed. in fact th d arrow in fig ture. in the c ance. pure hydrogen mperature dif nd plates co st the 3 secti t2. differen be explained from the t3 re profile. curr ck temperature hydrogen. ck. 0 150 mm .3221/igf-esis.1 wer ] stac pow [w 14 25 mate as fuel. ig. 8). this is between adja he co poison g. 6) presents case of opera n at 160°c s fference betw ould explain ions of the s nces are highe referring to (fig. 9). rent density e 160 °c, 200 t1 t2 t3 15.04 33 ck wer w] 9 5 due cent ning s the ating tack ween this tack er at the http://www.gruppofrattura.it http://dx.medra.org/10.3221/igf-esis.15.04&auth=true n. 34 th tem sin sim com co of th rea stac des pur re [1] [2] [3] [4] [5] [6] [7] [8] [9] [10 [11 [12 [13 [14 [15 [16 [17 i zuliani, frattur his simple inv mperature and gle blower c mplification co mplex balanc onclusion n this pape the stack with reform a single fuel c he stack volta ach the best p ck temperatu sign improve rpose. eferences j. zhang, z j. of power q. li, j. o. d. f. chedd k. scott, s. o. shamard m.k. daleto a. r. korsg r. taccani, application h. tang, z. 0] j. hu, h. zh ] z. qi, s. bu 2] a.d. modes 3] j. scholta, m 4] s. j. andrea 5] t. j. schmid 6] sigracet bpp 7] q. f. li, r. i ra ed integrità st vestigation s d reach a bet could be used ould not easy e of plant. ns er the main d can deliver a mate stack pe cell system. a age and temp performance ure distributio ement could s z. xie, y. tan sources, 160 jensena, r. f die, n. d.h. m pilditch, m. m dina, a. chert ou, n. gourd gaard, r. refs , r. radu, z ns, efc 09-17 . qi, m. rama hanga, y. zh uelte, j. of pow stov, m.r. ta m. messersch asen, s. k. kæ dt, j. baurmei p datasheet, h. he, j. a. trutturale, 15 (20 uggests the ter temperatu d for cathodi y apply to a lo design charact about 350 w erformance de as expected st perature distri particularly on noticeably lead to a sim ng, c. song, t 0 (2006) 872. f. savinell, n. munroe, j. of mamlouk, j. o tovich, a.a. k doupi, j.k. k shauge, m. p. z. nicola, a 7056 (2009). ani, j. f. elte haia, g. liua, b wer sources, arasevich1, v midt, l. jöris ær, int. j. of h ister, j. of po eisenhuth g gao, j. o. je 011) 29-34; do opportunity ure distributio ic air supply ow temperatu teristics and a at 0.5 v mea ecreases only tack performa ibution analy when operat suggesting th mpler bop a t. navessin, . j. bjerrum, p f power sour of appl. elec kulikovsky, a kallitsis, j. of m nielsen, m. a. damnjano r, j. of power b. yia, int. j. 161 (2006) 1 v.ya. filimono ssen, ch. har hydrogen en ower sources, gmbh, (2004) nsen, n. j. b oi: 10.3221/igf-e of using ca on. additiona y and coolant ure pem fuel an experimen an cell voltag y slightly. this ance is lower ysis reveal tha ting with refo he opportuni as only a sin z. shi, d. so progress in p rces, 160 (200 ctrochem., 37 a.r. khokhlo membrane sc banga, s. k. ovic, in: pro r sources, 158 of hydrogen 126. ov, n.m. zag rtnig, j. of pow nergy, 33 (200 176 (2008) 4 ). jerrum. j. ele esis.15.04 athodic air as ally, the bop t purpose. it cell based sys ntal analysis o ge when oper s performanc than single c at temperatur ormates. it h ty to use it fo ngle blower c ong, h. wang polymer scien 06) 215. 7 (2007) 1245. ov, int. j. of h cience, 252 (2 kæra, j. of p oceedings of 8 (2006) 1306 n energy, 31 gudaeva, elec wer sources, 08) 4655. 428. ectrochem. so s coolant in p of the syste t is significan stem where h of a 25 cells h rated with pu ce behaviour h cell performan re manageme has been obse or temperatur could be use g, d. p. wilki nce, 34 (2009) . hydrogen en 005) 115. power sources the europe 6. (2006) 1855. ctrochimica a 190 (2009) 8 oc., 150 (2003 order to m em can be sim nt to highligh humidification ht pem stac ure hydrogen has been foun nce. ent has a key erved that ca re manageme d for air sup inson, z. s. l 449. nergy, 30 (200 s, 162 (2006) an fuel cell acta, 54 (2009 3. 3) 1600. manage the s mplified as on ht that this b n requires a m ck are presen . when oper nd similar to y role in orde athode air aff ent purpose. t pply and coo liu, s. holdcr 09) 1. 239. l technology 9) 7121. tack nly a bop more nted. rated that er to fects this oling roft, y & http://www.gruppofrattura.it http://dx.medra.org/10.3221/igf-esis.15.04&auth=true microsoft word numero_41_art_39.docx a.s. chernyatin et alii, frattura ed integrità strutturale, 41 (2017) 293-298; doi: 10.3221/igf-esis.41.39 293 focused on crack tip fields the effect of residual stress on the nonsingular t-stresses a.s. chernyatin, yu.g. matvienko, i.a. razumovsky mechanical engineering research institute of the russian academy of sciences, moscow, russia cas@inbox.ru, http://orcid.org/0000-0002-2708-8132 matvienko7@yahoo.com, http://orcid.org/0000-0003-2367-0966/ murza45@gmail.com abstract. the effect of residual stresses on surface fatigue crack propagation and fracture mechanics parameters of intersecting orthogonal cracks is discussed. mutual influence of intersecting cracks and biaxiality affects the nonsingular parameters txx and tzz. at the same time, the effect on the stress intensity factor is negligible. two-parameter fracture mechanics is employed for an analysis of fatigue crack propagation taking into account residual stresses. the final configuration of the crack front is close to the semi-elliptical configuration. keywords. residual stress; fatigue surface crack; t-stresses; intersecting cracks; finite element simulation. citation: chernyatin, a.s., matvienko, yu.g., razumovsky, i.a., the effect of residual stress on the nonsingular t-stresses, frattura ed integrità strutturale, 41 (2017) 293-298. received: 28.02.2017 accepted: 03.05.2017 published: 01.07.2017 copyright: © 2017 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. introduction n analysis of propagation of surface cracks is considered in a number of publications [1-5], where the results of the experimental and numerical analysis of a flat semi-elliptical crack growth under cyclic loading are presented. the paris formula or some subsequent modifications is used for calculations of fatigue crack increment. for assessment of the crack front configuration, the principle of self-similarity is used in most investigations. in this paper, the numerical method and the appropriate program realization are presented for the analysis of the surface crack growth in weld joint of a pipeline, including the calculation of changes in the crack front configuration due to action of the active cyclic loading, influence of no uniformly distributed residual stresses and the t-stress. it should be noted that the results of the mutual influence of intersecting perpendicular cracks on the parameters of fracture mechanics are not enough presented in the literature [6]. it is clear that the effect of the t-stress can be significant and the two-parameter fracture mechanics should be employed. the analysis of mutual influence intersecting cracks on the values and distribution of singular (the stress intensity factor) and nonsingular (the t-stress) components of the stress field along the crack fronts of intersecting cracks are also presented. a a.s. chernyatin et alii, frattura ed integrità strutturale, 41 (2017) 293-298; doi: 10.3221/igf-esis.41.39 294 fatigue crack propagation under cyclic loading and residual stress crack propagation low he method is based on the modified forman expression which includes the nonsingular t-stress        max 1 mt c c qdl k kdn k (1) where   max mink k k is the stress intensity factor (sif) range and  min maxr k k is the sif ratio. the correction function qt can be represented taking into account the t-stress as follows [3]          1 t ct y tq e (2) the constants c, m, ct, as well as the critical stress intensity factor kc and yield strength σy are the properties of the material. it should be noted that in this case, the sif ratio varies along the crack front (here, it is not a characteristic of external loads) due to the effect of the residual stress (rs). since, the fatigue crack increment occurs when load is increased to maximum values at the cycle, the t-stress in eq. (2) should be determined as tmax. therefore, eq. (1) becomes       max max, mdl c k t k dn (3) numerical simulation of three-dimensional planar cracks can be constructed as a gradual process of crack increments (after finite number of the cycles δn) in a limited set of the crack front points, the position of which will be characterized by a dimensionless local coordinate s that runs along the crack front from one external points to other. an infinitely small value dn can be replaced by a finite cycle increment δn and dl replaced by δl in eq. (1). so, the crack increment at the current crack front configuration (after n cycles) can be calculated according to the follow equation               max max, , , , , m l n s c k n s t n s k n s n (4) for the successful solution of the crack propagation problem under the action of residual stresses and taking into account the constraint along the crack front by means implementation of eq. (4), the principle of remeshing procedure of finite elements in the vicinity of the crack front is proposed. adaptive parametric finite elements model with varying crack configuration the parametric finite element model (fe-model) of crack area in the form of a prismatic region is developed in ansys software. the model includes the regions with different structures of the element mesh and its sizes. embedding the crack volume into the fe-model is carried out by means of the macro "crack" which contains the following features [7]: configuration of the crack front as a line can be arbitrary, but must have smoothness; an mapped mesh of the singular elements is created along the crack front. crack front may pass through several geometric volumes. it is especially convenient for modeling of cracks intersection. numerical procedure of the sif and t-stress determination the elastic crack-tip displacement and stress fields of mode i crack can be represented as follows [8] t a.s. chernyatin et alii, frattura ed integrità strutturale, 41 (2017) 293-298; doi: 10.3221/igf-esis.41.39 295 (5) where r, θ and x, y are local polar and cartesian coordinates related to the crack tip, the plane x0y is perpendicular to the crack front line; κ is the parameter of the stress state. it should be noted that  1 2ik a ,  24т а . the program in the matlab environment, so called "williams", in conjunction with macro "crack" provides the calculation of the coefficients of stress field expansion terms (eq. (5) in the vicinity of the crack tip. the "williams" interacts with the macro in ansys software, which enables collection of the displacements and stresses at measuring points surrounding the crack tip in plane x0y. the determination of the coefficients of expansion (5) is carried out by means of least squares method that provides comparison of these data and data calculated via expression (5). these calculations are performed in many planes which are perpendicular to the crack front for estimation of the sif and tstress distribution along front. algorithm of numerical crack propagation simulation control program (with gui) that provides collaboration between program elements of ansys and matlab software is developed in matlab. a schematic diagram of its implementation is given in fig. 1. the data files with special structures are formed at the beginning for initialization of different data, namely, sizes and geometry of the model, the crack, elements, material properties, options of loading (minimum and maximum value of cyclic loading and residual stresses distribution along thickness) and other data. the solution begins with the start of the control program and "williams". next step is the launching of ansys in the background mode for creation of the fe-model and solution of minimum and maximum values for the loading cycle. the collected data in the analyzed points are transiting to "williams". figure 1: the algorithm of numerical solution for the crack propagation problem. after computing the coefficients of william’s expansion for the minimum and maximum loads per cycle (as well as kmin, tmax, kmax), the control program calculates values of the fatigue crack increment at each points of the crack front in accordance with eq. (4). the new configuration of the crack front is formed and saved in the data file for the "crack" macro. this specified sequence of procedures in ansys and matlab are executing repeatedly. a.s. chernyatin et alii, frattura ed integrità strutturale, 41 (2017) 293-298; doi: 10.3221/igf-esis.41.39 296 internal surface crack propagation in weld joint of a pipeline let consider a welded zone of the pipe with outer diameter 1420 mm and wall thickness 18.7 mm. the pipeline internal pressure is 10.6 mpa and it leads to the active axial and circumference stress 200 mpa and 400 mpa, respectively. note that axial direction is perpendicular to the plane of the weld joint. in operation, there are additional axial stresses that occur because of bending and thermal loading. the axial stresses in conjunction with the pressure pulsation lead to cyclic loading. the following parameters of the loading cycle are accepted in the work: average stress is 200 mpa, the minimum and maximum values are 133 mpa and 267 mpa, respectively. in addition, there are residual stresses in the zone of welding. distribution of axial residual stresses (rs) along the thickness was accepted in accordance with the results of well-known experimental study of a full-scale pipeline (fig. 2). a) b) figure 2: loading condition of the pipe (a) and the axial residual stress distribution along pipe thickness (b) taking into account the small curvature of the pipe, the region with the crack is considered as thick plate. the initial front geometry of the crack located in the weld joint plane on the inner pipe surface is assumed in form of a semicircle with radius of 4 mm. ten terms in the williams expansion are kept to estimate the sif and the t-stress at points of the fatigue crack front after discrete cycles δn = 105. the total number of cycles, at which a calculation stop was occurred, (if previously sif did not reach the critical value) is n=107. the results of calculations in the form of finite configurations of the crack front at various conditions are shown in fig. 3. figure 3: final configuration of the crack front (half) under different loading conditions. it should be noted that independently of the initial crack geometry, final configuration of the crack front is close to the semi-elliptical. as expected, the stress t>0 leads to decreasing of the crack growth rate. this fact allows concluding about the conservatism of classic paris and forman formulas (not taking into account the effect of constraint and the residual stress). otherwise, the residual stress (rs) affects on the rate of crack growth. stress intensity factor distribution along the crack front strives for a constant value during crack size growing in absent of the rs. presence of the rs leads to quite complex distribution of the sif along the crack front. in contrast to the sif, distribution and values of the t-stress along the crack front are weakly dependent on the rs. a.s. chernyatin et alii, frattura ed integrità strutturale, 41 (2017) 293-298; doi: 10.3221/igf-esis.41.39 297 intersecting cracks in pipeline with residual stress racture mechanics parameters for intersecting surface cracks in the weld joint of pipeline are analyzed bellow. the pipe has the following dimensions, namely, outer diameter is 325 mm; wall thickness is 16 mm. the material is corrosion-resistant austenitic steel. the circular crack (crack a) with depth of 6 mm is assumed to be formed on the inner side of the pipe in the plane of welding zone. the semi-elliptical crack is located in the meridional section (crack b). these cracks are intersected perpendicular each other (fig. 4). dimensions of the elliptical crack are 8 mm (crack depth) and 12 mm (length). figure 4: intersecting cracks on inner surface of the pipe. the active circumferential stress is 67.6 mpa and axial stress is 108.8 mpa (taking into account not only pressure, but other loading factors). in addition, there are residual stresses occurred during the welding process. it is assumed that the axial residual stress is linearly varying through the pipe thickness. the residual stress reaches the yield strength on the inside surface near the weld root and a similar value with the opposite sign on the outer surface. the circumferential residual stress is also equal to the yield strength and this stress is constant through the thickness (they are varying along the pipe). a) b) figure 5: distribution of ki, txx, tzz along the crack front a (a) and crack front b (b) under different loading conditions. the computed results are summarized in fig. 5. note that sa and sb are dimensionless local coordinates (fig. 4) transiting along a front of the crack a and b, respectively. distributions of the tzz-stress [9] as well as the sif and the txx-stress are determined by means of the program "williams" for only active external stress ("act") as well as in combination with the residual stress ("res"). an analysis of fracture mechanics parameters allows concluding the following. the axial crack (b) has a great influence on the txx-stress and the tzz-stress. the values of txx and especially tzz are decreasing (staying more f a.s. chernyatin et alii, frattura ed integrità strutturale, 41 (2017) 293-298; doi: 10.3221/igf-esis.41.39 298 negative). strong influence of the rs on the sif of the crack a is not observing. however, the residual stress acts on sif values in more manner then on t-stress values of crack a. the distribution of fracture parameters and the effect of the rs for the crack b are more complex. the sif has an almost constant value along the crack front, whereas t-stresses have values great varied. it should be noted that there is the influence of the crack a on the state of the crack. conclusions he effect of residual stresses on surface fatigue crack propagation and fracture mechanics parameters of intersecting orthogonal cracks in the pipeline is discussed. the method on the basis of modified foreman equation and program software for realization of gradual remeshing of the finite element model during incremental crack growth is developed. it is implemented for an numerical analysis of fatigue surface crack propagation in welded area of pipeline taking into account nonlinear distributed residual stress and constraint effect in the crack tip employing two-parameter fracture mechanics. in spite of the fact that the residual stress and the nonsingular t-stress have a significant influence on the crack growth rate. final configuration of the crack front is close to the semi-elliptical configuration. mutual influence of intersecting surface cracks and biaxiality effects on the nonsingular parameters txx and tzz is observed. at the same time, their effect on the stress intensity factor is negligible. acknowledgments he authors acknowledge the support of the russian science foundation (project n 14-19-00383). references [1] zhao, c.y., huang, p.y., zhou, h., zheng, x.h., numerical analysis of ki of semi-elliptical surface crack in steel structure strengthened with frp under tensile load, j. app. mech. mat., 137 (2012) 42–49. [2] roychowdhury, s., dodds, r.h., three-dimensional effects on fatigue crack closure in the small scale yielding regime a finite element study, j. fat. fract. eng. mat. struct., 8 (2003) 663–673. [3] hamam, r., pommier, s., bumbieler, f. mode i fatigue crack growth under biaxial loading, int. j. fatigue, 27 (2005) 1342–1346. [4] hoshide, t, tanaka, k., stress-ratio effect of fatigue crack propagation in a biaxial stress field, j. fat. fract. eng. mat. struct., 4 (1981) 355–366. [5] forman, r. g., study of fatigue crack initiation from flaws using fracture mechanics theory, j. eng. fract. mech., 2 (1972) 333–345. [6] chen, y.z., evaluation of t-stresses in multiple crack problems of finite plate, j. fat. fract. eng. mat. struct., 35 (2012) 173–184. [7] razumovskii, i.a., chernyatin, a.s., experimental numerical method of loading estimation for structures with surface cracks, j. machinery manufacture and reliability, 38-3 (2009) 247–253. [8] williams, m.l., on the stress distribution at the base of a stationary crack, j. appl. mech., 24 (1957) 109–114. 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can be opened with acrobat and adobe reader 5.0 and later.) >> /namespace [ (adobe) (common) (1.0) ] /othernamespaces [ << /asreaderspreads false /cropimagestoframes true /errorcontrol /warnandcontinue /flattenerignorespreadoverrides false /includeguidesgrids false /includenonprinting false /includeslug false /namespace [ (adobe) (indesign) (4.0) ] /omitplacedbitmaps false /omitplacedeps false /omitplacedpdf false /simulateoverprint /legacy >> << /addbleedmarks false /addcolorbars false /addcropmarks false /addpageinfo false /addregmarks false /convertcolors /converttocmyk /destinationprofilename () /destinationprofileselector /documentcmyk /downsample16bitimages true /flattenerpreset << /presetselector /mediumresolution >> /formelements false /generatestructure false /includebookmarks false /includehyperlinks false /includeinteractive false /includelayers false /includeprofiles false /multimediahandling /useobjectsettings /namespace [ (adobe) (creativesuite) (2.0) ] /pdfxoutputintentprofileselector /documentcmyk /preserveediting true /untaggedcmykhandling /leaveuntagged /untaggedrgbhandling /usedocumentprofile /usedocumentbleed false >> ] >> setdistillerparams << /hwresolution [2400 2400] /pagesize [612.000 792.000] >> setpagedevice microsoft word numero_30_art_12 s. baragetti et alii, frattura ed integrità strutturale, 30 (2014) 84-94; doi: 10.3221/igf-esis.30.12 84 focussed on: fracture and structural integrity related issues scc and corrosion fatigue characterization of a ti-6al-4v alloy in a corrosive environment – experiments and numerical models s. baragetti university of bergamo – dept. of engineering – viale marconi 5, 24044 dalmine (bg) gitt – centre on innovation management and technology transfer – university of bergamo – via salvecchio 19, 24129 bergamo sergio.baragetti@unibg.it f. villa university of bergamo – dept. of engineering – viale marconi 5, 24044 dalmine (bg) francesco.villa@unibg.it abstract. in the present article, a review of the complete characterization in different aggressive media of a ti-6al-4v titanium alloy, performed by the structural mechanics laboratory of the university of bergamo, is presented. the light alloy has been investigated in terms of corrosion fatigue, by axial fatigue testing (r = 0.1) of smooth and notched flat dogbone specimens in laboratory air, 3.5% wt. nacl–water mixture and methanol–water mixture at different concentrations. the first corrosive medium reproduced a marine environment, while the latter was used as a reference aggressive environment. results showed that a certain corrosion fatigue resistance is found in a salt water medium, while the methanol environment caused a significant drop – from 23% to 55% in terms of limiting stress reduction – of the fatigue resistance of the ti-6al-4v alloy, even for a solution containing 5% of methanol. a stress corrosion cracking (scc) experimental campaign at different methanol concentrations has been conducted over slightly notched dog-bone specimens (kt = 1.18), to characterize the corrosion resistance of the alloy under quasi-static load conditions. finally, crack propagation models have been implemented to predict the crack propagation rates for smooth specimens, by using paris, walker and kato-deng-inoue-takatsu propagation formulae. the different outcomes from the forecasting numerical models were compared with experimental results, proposing modeling procedures for the numerical simulation of fatigue behavior of a ti-6al-4v alloy. keywords. ti6al4v; corrosion fatigue; stress corrosion cracking; crack propagation; fem. introduction he titanium high strength-to-mass ratio ti-6al-4v alloy is one of the most widespread materials in advanced engineering applications, especially when high resistance is required for critical, low-weight components. for this reason, the ti-6al-4v alloy is hence extremely valuable for aerospace, automotive and marine high performance structural applications [1], and it has been widely applied to the biomedical sector, due to its biocompatibility and its favorable interaction with the body environment [2]. another reason which explains the high diffusion of this particular alloy in the most demanding applications is motivated by its high resistance to a wide spectrum of corrosive environments, with respect to other titanium based alloys, due to its inclination to form protective surface oxides [3, 4]. sanderson et al. underlined this aspect, by concluding that the ti-6al-4v alloy is not susceptible to stress corrosion cracking (scc) in seawater, if considering the results of u-bend specimens [5]. in another work by sanderson et al. [6], on the same specimen geometry and test procedures, a significant scc effect was found for ti-6al-4v alloy in pure methanol t s. baragetti et alii, frattura ed integrità strutturale, 30 (2014) 84-94; doi: 10.3221/igf-esis.30.12 85 and methanol-hcl solutions. the authors observed a 30 hours fracture time for pure methanol, and a 0.3÷0.6 hours for the methanol-hcl combination. in this latter case however, water addition easily passivated the reaction. some critical service failures were observed in the apollo rocket ti-6al-4v tanks, filled with n2o4 and methanol, promoting several tests in different aggressive environments to investigate on the susceptibility of this alloy. the results, found by nasa investigations presented in the works of johnston et al. [7], and johnson et al. [8] for static and fatigue loading of methanol filled pressurized tanks, show a high sensitivity from the methanol environment in both loading cases, as can be seen in tab. 1. brown [9] has collected a wide review of most of the work conducted in the late 60’s on scc of titanium alloys and high strength steels, proposing similar conclusions. apart from the work from nasa [7,8], which reports a direct correlation between load and the aggressive methanol environment, the other literature results [5, 6, 9, 10] are based only on static or u-bend corrosion tests, reported in terms of hours to failure, thus avoiding a direct correlation between the applied load and the corrosive environment. an example of this kind of results in a methanol-water-hcl mixture is reported in fig. 1, from [10]. test type static fatigue environment load [mpa] time to failure [min] load [mpa] cycles to failure air 827 >4463 (no failure) 48-965 1385 methanol 17 86 table 1: comparison between ti-6al-4v specimens in air and methanol environment, for static and fatigue loading, from [7] figure 1: time to failure for u-bend ti-6al-4v specimens in x wt.% methanol – 0.17 wt.% hcl – y wt. % water, from [10]. it is hence mandatory to investigate further into the mechanisms which reduce the material strength in corrosive environments, since it is well known from literature that the high corrosion resistance of the ti-6al-4v alloy is linked to the quick oxidation of its surface, protecting the base material from the interaction with the external environment [3,4,6]. the mechanical loading, both in the tensile and fatigue cases, may compromise the effectiveness of the external oxidation passivating layer, depending also on the dynamics of the applied load, as reported in [3]. in [6], a removal of the oxide layer, both in the proximity of scc cracks and in other regions not stress interested, was observed in the methanol-hcl solution. a study of the mechanical behavior of ti-6al-4v in aggressive environments, both under quasi-static and fatigue loading is hence essential to understand the possible insurgence of scc or corrosion fatigue behavior for this material, due to the effects that various loading conditions can impose on the alloy oxide based protection system. in the last years, the authors research group has conducted several studies on the corrosion fatigue performances of the ti-6al-4v alloy in air and sea water (3.5 % wt. nacl) [11] and on the corrosion fatigue in methanol environment at different concentrations [12]. in the present work, the most relevant results obtained by these campaigns are discussed, highlighting the effect of s. baragetti et alii, frattura ed integrità strutturale, 30 (2014) 84-94; doi: 10.3221/igf-esis.30.12 86 the environment on different loading conditions, in terms of fatigue strength reduction. the results of an experimental campaign on the quasi-static scc characterization of the ti-6al-4v alloy in methanol at different concentrations are reported, and a comparison with the fatigue data is drawn. a numerical model for the crack propagation rate for the ti6al-4v alloy is proposed, in order to provide a tool to decouple the mechanical effects from the chemical driving forces. materials and methods he specimens for the corrosion fatigue characterization in air, 3.5 wt. % nacl water mixture, methanol water mixture [11] and for the quasi-static testing in methanol water mixture were obtained from the same ti-6al-4v raw plate supply. the flat dogbone specimens were machined with a reasonable notch, according to the geometry presented in fig. 2, in order to obtain failure in the test section with inferior loads. the test section area was of 45 mm2, while the local stress concentration factor kt was 1.18, as obtained by a linear elastic fe simulation with plane-stress elements. the specimens were machined so that the load axis was transversal to the rolling direction of the raw ti-6al-4v supply plate. the chemical composition, tensile properties and successive heat treatments are reported in tab. 2. 260 ±0,5 80 ±0,215 3 ±0,05 30 figure 2: specimen geometry. chemical composition al [%] v [%] fe [%] o [%] c [%] ti [%] 5.97 4.07 0.20 0.1885 0.03 bal. raw plate mechanical characterization heat treatments rp,02 [mpa] rm [mpa] e [mpa] 1. solution treatment 2. overaging 3. stress relieving after machining 1’050 1’100 130’000 925 °c – 1 h 700 °c – 2 h table 2: ti-6al-4v chemical and mechanical characteristics – including thermal treatments. axial fatigue loading (r = 0.1) was imposed in the corrosion fatigue testing [11,12] in air, 3.5 wt. % nacl water mixture and methanol water mixture at different wt. % methanol concentrations. the corrosive environment surrounded the test area of the specimens, by means of a containment device that allowed environment recirculation by means of a pump. the specimens were loaded using rolling bearing grips in order to avoid parasite bending moments during testing. a picture of the test device is reported in fig. 3, while the tested environments are reported in tab. 3. step-loading technique, validated by bellows et al. [12] and lanning et al. [13], was adopted to obtain fatigue limits at 200’000 cycles. the 200’000 cycles number was selected by observing the s-n fatigue data of sadananda et al. [14], where it is found that the r = -1 specimens reach a constant limit, and the steepness of the r = 0.1 test results decreases significantly. specimens were tested at a given maximum stress, and if they reached the end of the cycles block without a failure, the load was increased and the test was restarted. the final fatigue limit was obtained by a linear interpolation between the failed load block and the previous not failed block, according to the formula: t s. baragetti et alii, frattura ed integrità strutturale, 30 (2014) 84-94; doi: 10.3221/igf-esis.30.12 87  , ffl n pb fb pb n n       where σfl,n is the fatigue strength limit at n cycles, σfb is the applied load during the failed cycle block, nf is the number of cycles at which failure is reached during the failed block, and σpb is the applied load during the previous, not failed block. two specimens were tested for every environmental configuration, in order to confirm the results. figure 3: corrosion fatigue test setup: (a) specimen mounted on hinge grips to avoid parasite bending; (b) aggressive environment containment system. adapted from [11]. test type fatigue environments air, 3.5%wt nacl-water solution, methanol-water solution methanol wt. % conc. tested 5%, 25%, 50%, 95% table 3: test environments for corrosion fatigue testing, from [11]. a quasi-static stress corrosion campaign was conducted on the same specimen geometry and material, in order to decouple the mechanical effects from the chemical driving forces, quantifying the contribution of the different load application. the tests were performed in air and in methanol environment, using the same methanol concentrations adopted in the fatigue tests, as well as other intermediate concentrations to improve the resolution and confidence on the obtained results. the environmental test conditions are reported for both corrosion fatigue and quasi-static scc tests in tab. 4, while the test setup for the quasi-static campaign is depicted in fig. 4. the specimens were loaded by means of a threaded road tensile system, and mounted on similar rolling bearing hinge grips to avoid parasite moments. to control the effectiveness of the procedure, strain-gages were mounted on the front and rear faces of each specimen, and correlated by means of fe analysis to the actual throat stress. a direct placement of the strain gages in the test section was avoided, since it would have required to remove the oxide layer, thus modifying the test conditions. the applied load was measured by means of a load cell applied on the rod. the load was augmented every hour by a value of 5 mpa. the mean deformation velocity was hence calculated as 8 11.23 10 s e t             the aggressive environment was placed in a containment system near the specimen test section, granting continuous full immersion of the specimen throat, as in the corrosion fatigue tests. methanol was added during the tests, and removed whenever the tests were paused. s. baragetti et alii, frattura ed integrità strutturale, 30 (2014) 84-94; doi: 10.3221/igf-esis.30.12 88 figure 4: experimental setup for the quasi static scc tests: (a) specimen mounted on hinge grips; (b) methanol containment system and applied strain gages. test type static environments air, methanol-water solution methanol wt. % conc. tested 25%, 50%, 75%, 85%, 90%, 92.5%, 95%, 97.5%, 99.8% (maximum purity) table 4: test environments for quasi-static scc testing. experimental results corrosion fatigue data he corrosion fatigue σmax data, obtained by the results of [11] by using the haigh diagram with r = 0.1, are presented in fig. 5, showing the effect of aggressive environment compared with testing in laboratory air. the cycles number adopted for the step-loading technique was selected at 200’000. the data related to fatigue testing in methanol, compared with the results for air and 3.5% wt. nacl-water solution, identify a dramatic decrease of fatigue strength even from the least concentrated (5%) methanol solution. the detrimental effect of methanol increases then with concentration. the effect of mechanical loading in this case seems to improve the corrosion effects even for very light methanol concentrations: a 24% maximum stress loss is detected for the 5% methanol solution, against a 56% loss for the 95% methanol concentration. these data indicate that, with respect to the u-bend ti-6al-4v specimens, which showed a marked scc behavior only for very high methanol concentrations [10], there is a strong influence of the mechanical stress effects in the corrosion fatigue process. figure 5: corrosion fatigue test results for air, 3.5 % wt. nacl water mixture and different wt. % methanol water mixture at 200’000 cycles, adapted from [11]. t a) b) s. baragetti et alii, frattura ed integrità strutturale, 30 (2014) 84-94; doi: 10.3221/igf-esis.30.12 89 quasi-static scc data the results of the quasi-static testing campaign in air and methanol at different concentrations are reported in fig. 6. figure 6: quasi-static experimental data and interpolations with confidence bands for ti-6al-4v specimens tested in air and methanol water solution at different concentrations, in terms of maximum nominal stress in the test section. the quasi-static results indicate that the scc behavior show a reduction of the failure stress starting from a 90% wt. methanol concentration in water. the overall drop is limited for pure methanol, with a -25% in terms of nominal stress applied to the test section. however a marked methanol effect is recognizable even for a 92.5 % methanol concentration, if compared to higher results from literature [10]. comparison between corrosion fatigue and quasi-static scc data the results in terms of maximum stress drop in function of methanol concentration have been extracted from the experimental data presented in this work, and compared between the fatigue and quasi-static tests. the chemical driving forces in the two different cases have been highlighted by extracting the difference from the mechanical failure stress, according to the following relations:     , , , , chem qs mech qs qs met chem f mech f f met x x           the direct comparison is presented in fig. 7. fig. 7 remarks the difference in terms of the material strength behavior in an aggressive methanolic media for the ti-6al4v alloy for different loading conditions. it must be recognized that a dynamic loading causes an onset of corrosive effect even from mild methanol concentrations, while a methanol concentration over 90% is needed in a quasi-static scc condition. the different loading conditions may affect the protective role of the surface oxide of the alloy showed in [3,4,6]. in particular, fatigue loading may induce premature cracking of the substrate oxide, resulting in an enhanced susceptibility of the material to the external environment, while quasi-static conditions require higher methanol concentrations to damage the external film. further analyses at different loading conditions, number of cycles and frequencies are needed in order to evaluate the mechanical loading effects on the corrosion protection characteristics of the ti-6al-4v alloy. s. baragetti et alii, frattura ed integrità strutturale, 30 (2014) 84-94; doi: 10.3221/igf-esis.30.12 90 figure 7: corrosion effects in terms of mechanical and chemical stress contributions in different load conditions. numerical models elastic stress intensity factor field n order to deepen the investigation on the mechanical effects involved in the process, a fe simulation procedure was developed to predict the fatigue crack propagation rate for a ti-6al-4v alloy. the model was based on the experimental da/dn – δk results obtained by lee et al. [15] for the same alloy. the fe model of a flat smooth fatigue specimen was realized using linear plane stress elements, the geometry being compatible with the one reported in [16]. the crack was modeled in the throat section starting from an initial length of 5 µm, and propagated by a finite step δa until the value of kic was obtained. the value of the first mode stress intensity factor field ki is hence obtained from the half crack tip opening displacement in the longitudinal, tensile direction uy, by using the following relations [17]:   2 ( , ) 1 i e u k r r f         2sin 1 2 cos 2 2 f                     with 3 4   for plane strain and    3 / 1     for plane stress state. the presented ki model is valid in the elastic field of the material. in the presence of a sharp notch, the stresses may rise above the yielding stress. however, according to milella [18], if the plastic zone is inferior to 1 mm, small scale yielding (ssy) conditions are reached, and the linear stress field relations can be used for fatigue crack propagation. due to the very high yielding stress of the considered ti-6al-4v alloy, a ssy condition is very likely to be reached in our case, and the [17] relations are thus adopted. to obtain ki, a value of e equal to 113000 mpa and a ν of 0.342 for the ti-6al-4v alloy were adopted, and a plane stress state was considered, coherently with the fe modeling and with the actual load situation. the vertical displacement uy, as well as the coordinates r and θ have been taken from the first and second node away from the crack tip, and the corresponding value of the applied δk was obtained by extrapolating linearly the ki value to the crack tip. the adopted coordinate system and an example of the stress distribution map for the smooth specimen, at a crack propagation depth of 50 µm, are displayed in fig. 8. the applied nominal tensile load was of 548 mpa, while the measured stress concentration factor kt in the linear elastic field, prior to the crack introduction, was of 1.18. i s. baragetti et alii, frattura ed integrità strutturale, 30 (2014) 84-94; doi: 10.3221/igf-esis.30.12 91 a) b) figure 8: fe model for the crack propagation model: (a) coordinate system for the elastic stress intensity factor field calculation; (b) σy stress field around the crack tip for a propagation depth of 50 µm. crack propagation models once the model for the determination of the ki field has been defined, a propagation law for the crack front is needed. in the present work, three models have been applied to the case. the models of paris [17], walker [19] and kato et al. [20] have been proposed and applied to the obtained stress intensity factors for the two considered fe models. the first, most common adopted model for the crack propagation growth rate is the paris model [17], which simply assumes a power-law dependence of the growth rate from the stress intensity factor, thus describing only the stable propagation rate. paris’ law takes the form:  nda c k dn   where δk is the applied stress intensity factor, defined as δk =(1 r)kmax [15], with kmax obtained from the fe model. for the ti-6al-4v alloy, the paris constants are assumed as c = 3.8·10-8 [(mm/cycle) / (mpa√m)n] and n = 3.11, from [21]. the paris model reconstructs the stable propagation region as a straight line in a log-log diagram, not considering the effect of the load ratio r as well as other properties of the material. a more sophisticated relation is proposed in the walker model [19], which takes into account the effect of the load ratio, with the empirical law:     1 1 1 1 1 m m cda k dn r     where c1 and m1 are the same as paris’ law, γ is a an additional parameter which gives an offset to the log-log stable propagation rate curve. a more detailed model is the one proposed for case carburized steel spur gears from kato et al. [20], which includes a relation to obtain the threshold crack propagation stress intensity δkth, as well as a description of both the quasi-static crack propagation region and the stable crack growth propagation region, thus defining a transition stress intensity factor kc. the model consists in two crack propagation rate laws, one for the initial and the other for the stable growth region:       1 1 n n th th cn n n ic c icnn ic da c k k for k k k dn da c k k for k k k dn k k                          with  1 2,th c th ic ic k k k k k      s. baragetti et alii, frattura ed integrità strutturale, 30 (2014) 84-94; doi: 10.3221/igf-esis.30.12 92 the authors of [20] propose an experimental correlation between the threshold δkth value, the model parameters c and n and the fracture toughness kic which takes into account the material hv hardness. the model was developed to describe case carburized steel gears with hardness profiles variable with the depth, while in our case a constant measured hardness of 350 hv was used. the experimental relations are: 3 1 3 5 2 2 5 2 2.45 3.41 10 3.64 141 1.64 10 83.6 4.31 8.66 10 1.17 10 log( ) 10.0 1.09 10 1.40 10 th ic k h mpa m k h mpa m n h h c h h                           numerical results the three different models have been adopted to reconstruct the da/dn – δk curve for a r = 0.1, to be compared directly with the data obtained by lee et al. for the same alloy and load conditions [15], as shown in fig. 9. the stress data of the fe model have been inserted in the three models at different discrete intervals of a, obtaining a da/dn curve covering the whole interval from δkth to kic, as taken directly from the kato et al. model [20]. since the value obtained by the model proposed in [20], i.e. kic = 83.6 mpa√m, is quite high for a ti-6al-4v alloy, a comparison with literature data for sta annealed ti-6al-4v [22] is also shown, the proposed value being kic lit =43 mpa√m. from the results, it can be seen that the paris model provides a suitable description of the constant growth rate region, although the walker model reaches a better correlation. the kato model shows a good resemblance with the material behavior in the proximity of the threshold value, describing correctly the initial growth phase, in contrast with the other two models. the threshold result obtained by this model has proved to be in good correspondence with the experimental data, as in fig. 9. figure 9: comparison between the proposed propagation models of paris, walker, kato, based on actual fe results, and the experimental data from lee et al. [15]. each solid point represents the da/dn value obtained by a single fe simulation. conclusions n the present work, an overview of the recent results of the authors research group on the corrosion behavior of the ti-6al-4v alloy in different loading conditions and various aggressive environment conditions is presented. the considered alloy has shown good corrosion fatigue resistance properties in a 3.5 wt.% nacl-water mixture, while a significant drop of fatigue performance (-56% σmax loss) is found at high methanol concentrations. the corrosion fatigue σmax drop persisted, even if with reduced intensity (-24%), for the minimum 5 wt.% methanol concentration. a different behavior was observed for quasi-static scc tests, where the effect of the aggressive solution was not observed below a 92.5 wt. % concentration of methanol in water. the maximum quasi-static drop for the reagent grade (≥ 99.8 wt. %) i s. baragetti et alii, frattura ed integrità strutturale, 30 (2014) 84-94; doi: 10.3221/igf-esis.30.12 93 methanol maximum concentration observed in this case was of -25% in terms of nominal applied stress. a direct dependence of the degradation of the mechanical characteristics of the alloy from the loading conditions was found. this dependence may be explained by the different damage mechanisms occurring on the protective oxides on the alloy surface. the chemical driving forces have been decoupled from the mechanical contribution in air, and an environmental effect in terms of chemical stresses σchem has been isolated for different loading conditions. finally, a fe model to describe the mechanical effects in terms of crack propagation for smooth fatigue specimens has been developed, by comparing different crack propagation laws to literature data. this model will be useful to improve the study of the mechanical effects involved in the corrosion fatigue process, by providing a chemical free simulation of the crack advancement, to be compared with experimental results in air and aggressive environments. acknowledgments he authors wish to thank eng. marco giustinoni and mr. marco ceresoli for the help in the test setup and in the fe models realization. references [1] lütjering, g., williams, j.c., titanium, second ed., springer, berlin (2007). [2] dimah, m.k., devesa albeza, f., amigó borrás, v., igual muñoz, a., study of the biotribocorrosion behavior of titanium biomedical alloys in simulated body fluids by electrochemical techniques, wear, 294–295 (2012) 409–418. [3] codaro, e.n., nakazato, r.z, horovistiz, a.l., ribeiro, l.m.f., ribeiro, r.b., hein, l.r.o., an image analysis study of pit formation on ti-6al-4v, mater. sci. eng. a, 341 (2003) 202–210. [4] gurrappa, i., characterization of titanium alloy ti-6al-4v for chemical, marine and industrial applications, mater. charact., 51 (2003) 131– 139. [5] sanderson, g., powell, d.t., scully, j.c., the stress-corrosion cracking of ti alloys in aqueous chloride solutions at room temperature, corros. sci., 8 (1968) 473–481. [6] sanderson, g., scully, j.c., the stress-corrosion cracking if ti alloys in methanolic solutions, corros. sci., 8 (1968) 541–548. [7] johnston, r.l., johnson, r.e., ecord g.m., castner w.l., stress-corrosion cracking of ti-6al-4v alloy in methanol, nasa technical note tn d-3868 (1967). [8] johnson, r.e., nasa experiences withti-6al-4v in methanol, dmic memorandum 228 (1967) 2–7. [9] brown, b.f., stress-corrosion cracking in high strength steels and in titanium and aluminum alloys, first ed., naval research laboratory, washington (1972). [10] chen, c.m., kirkpatrick h.b., gegel h.l., stress corrosion cracking of titanium alloys in methanolic and other media, technical report afml-tr-71-232, usaf materials laboratory, wright-patterson afb (1972). [11] baragetti, s., corrosion fatigue behaviour of ti-6al-4v in methanol environment, surf. interface anal., 45 (2013) 1654–1658. [12] bellows, r.s., muju, s., nicholas, t., validation of the step test method for generating haigh diagrams for ti–6al– 4v, int. j. fatigue, 21 (1999) 687–697. [13] lanning, d.b., haritos, g.k., nicholas, t., influence of stress state on high cycle fatigue of notched ti-6al-4v specimens, int. j. fatigue, 21 (1999) s87–s95. [14] sadananda, k., sarkar, s., kujawskj, d., vasudevan, a.k., a two-parameter analysis of s-n fatigue life using δσ and σmax, int. j. fatigue 31 (2009) 1648–1659. [15] lee, e.u., vasudevan, a.k., sadananda, k., effects of various environments on fatigue crack growth in laser formed and im ti–6al–4v alloys, int. j. fatigue 27 (2005) 1597–1607. [16] baragetti, s., notch corrosion fatigue behavior of ti-6al-4v, materials 7 (2014) 4349–4366. [17] anderson, t.l., fracture mechanics, third ed., taylor & francis, boca raton (2005). [18] [milella, p.p., fatigue and corrosion in metals, first ed., springer verlag italia, milan (2013). [19] beden, s.m., abdullah s., ariffin a.k., review of fatigue crack propagation models for metallic components, eur. j. sci. res., 3 (2009), 364–397. t s. baragetti et alii, frattura ed integrità strutturale, 30 (2014) 84-94; doi: 10.3221/igf-esis.30.12 94 [20] kato, m., deng, g., inoue, k., takatsu, n., evaluation of the strength of carburized spur gear teeth based on fracture mechanics, jsme int. j., ser. c, 36(2) (1993) 233–240. [21] carpinteri, a., paggi, m., self-similarity and crack growth instability in the correlation between the paris’ constants, eng. fract. mech., 74 (2007) 1041–1053. [22] matweb: www.matweb.com, (2014). microsoft word numero_55_art_05_2924 s. merdaci et alii, frattura ed integrità strutturale, 55 (2021) 65-75; doi: 10.3221/igf-esis.55.05 65 analytical solution for static bending analysis of functionally graded plates with porosities slimane merdaci university of sidi bel abbes, faculty of technology, civil engineering and public works department, bp 89 cité ben m’hidi 22000 sidi bel abbes, algeria. slimanem2016@gmail.com , http://orcid.org/0000-0001-8221-3760 adda hadj mostefa university of rélizane, institut des sciences & technologie, rélizane, algeria. hadj9510@gmail.com youcef beldjelili, mohamed merazi, sabrina boutaleb, hadjira hellal university of sidi bel abbes, faculty of technology, civil engineering and public works department, algeria. beldjelili.youcef@gmail.com, merazi@hotmail.com, sabrinasbouta@gmail.com, hadjiramhell@gmail.com abstract. the paper examines a static bending of porous functional plates (fgp) and rectangular plate solutions, based on an underlying high-order shear deformation theory. the proposed high-order shear deformation theory, as opposed to other theories, includes four unknowns. for this reason, a new shear strain function is considered. the technique of navier is used in closed-form fgp solutions. results of deflections and stresses are presented for simply supported border conditions. current figures are contrasted with the non-poreous plate deflecting solutions and the literature's stresses. effects of different parameters, including thickness, gradient index and porosity of fgm plates, are discussed. keywords. fgp; static bending; power-law; porosity factor; high-order theory. citation: merdaci, s., hadj mostefa, a., beldjelili, y., merazi, m., boutaleb, s., hellal, h., analytical solution for static bending analysis of functionally graded plates with porosities, frattura ed integrità strutturale, 55 (2021) 65-75. received: 12.09.2020 accepted: 15.10.2020 published: 01.01.2021 copyright: © 2021 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. introduction hese materials are generally recognized and produced in many foreign science labs, and one of the most widely used composites gives various fields such as engineering, the aeronautics, chemical, nuclear energy, electronics , optics, civil engineering, biomaterials, etc. [1-4]. the materials used in this field are functionally graded materials (fgms). the material compositions of fgms are assumed to vary smoothly and continuously in all gradient directions. in the mid 1980s, japanese scientists developed the earliest fgms as high-temperature-resistant materials for aerospace applications. during the sintering process and in the production of fgm porosity, materials may occur. this porosity is t https://youtu.be/jnde8ldvllg s. merdaci et alii, frattura ed integrità strutturale, 55 (2021) 65-75; doi: 10.3221/igf-esis.55.05 66 because of the large temperature coagulation difference between the material components [5]. the porosities in ref [6] are identified in lateral fgm samples with multi-stage sequence filtration. it is thus critical that the porosity effect is taken into account when designing fg dynamic load components. the most popular of these theories are classic platform theory (cpt), the theory of first plate order (fsdt) and refined plate theory (rpt). the kirchhoff love hypothesis is based on the classical plate theory (clpt) [7-9], an extension of the traditional plate theory (cpt), this model is provides acceptable results for the analysis of plates thin and neglect normal deformation and transverse shear results. both reissner [10] and mindlin [11] used the fsdpt (first-order sharp deformation theories) and accounted for the cross-sectional shear effects through simple linear differences in in-ground thickness shifts. the correction factor is not appropriate for this model, refined plate theory (rpt) and higher order theories of shear deformation (hsdt) are responsible for shear deformation effects and stress-free boundary conditions. for decades, a large number of rpt and hsdts have been proposed with a particular number of unknowns [12-20]. a great number of analysis and complex platform hypotheses were recently suggested to study the conduct of mechanical fgm plates. information concerning the study of static bending is especially important for the optimal design of structures. a new, higher order sharp theory of deformation (hsdt) is used in the study of the bending and free vibration of multi-layered panels and coats [21]. the rectangular bending motion on plate, which is supported only on four sides (fgm), has been studied more and more during recent years, subject to transverse static loading, with a refined shear deformation theory in high order [22-26]. it is proposed to study twin (2d) and quasi-3d (sometimes 3d) functionally graded plates to bend and free vibration using hyperbolic hsdt function [27]. the literature reviews on porosity effect are presented by several researchers in the recent works on porosity effect of fgm plates and beams. the effect of porosity is therefore important to consider in the design of static and bending plates made of functionally graded materials fgm [28-33] and sandwich plates fgm with porosity usage [33-35] of a high-order shear-deformation theory. consequently, studies focused more and more on the dynamic and free vibration of plate made of functionally graded fgm materials in recent years [37-47]. the dynamic fracture behavior of homogeneous and functionally graded materials under dynamic loading [48] and the investigating damage of functionally graded particulate materials by means of a multiscale approach based on micromechanics principles [49]. this paper aims to present a research solution for the performance of static porosity-grading plates analysis using highorder shear deformation theory. during the manufacture of these plates, defects such as porosities may appear, considering the porosities that can occur inside the functionally graded materials (fgm) plates. the board is called a porous board according to the power law on volume fractions of the platform elements, the poisson ratio is constant. the navier solution in closed-form is used to correct the limit conditions of simply supported fg pourer boards. the navier solution is also used. this theory removes the effect of shear correction factors on the plates and follows the equilibrium conditions of the porous fgm layer. the results of the current theory of the porous fgm plates are studied as well as the effect of the aspect ratio, the thickness ratio, the scaled exponent factor, and the deflection and stress porosity. in the assessment of deflations and stress distribution of functionally classified material plates, the impact of porosity on shave deformation has been increased. theory and formulations onsider a rectangular, wide fg-platform with length (a), width (b) and thickness (h) of a given functional material as shown in fig. 1. figure 1: geometry and fg porous plate coordinates. c s. merdaci et alii, frattura ed integrità strutturale, 55 (2021) 65-75; doi: 10.3221/igf-esis.55.05 67 the fgm plate is subjected to a transverse load q(x, y) for deformation analysis of the plate and a rectangular cartesian x and y co-ordinates are attached. the analysed plate is bounded by coordination levels (x = 0, a) and (y = 0, b). let the present platform be transformed by exponential or polynomial law from lower to upper surfaces .first and foremost, we will look at a non-homogeneity material with a porosity volumetric function, namely, ξ (0 ≤ ξ ≤ 1). the functional relation for the ceramic and metal fgm plates between e(z) is assumed.               1 ( ) 2 2 p c m m c m z e z e e e e e h (1) when ec and em are the corresponding ceramic and metal elements, and "p" is an exponent volume fraction that takes values greater or equal to zero. the above power law theory demonstrates a simple blending rule used to achieve the efficient characteristics of a ceramic metal platform. the theory of shear deformation plates is ideal for displacements in this study:                 0 0 ( , , ) ( , ) ( ) ( , , ) ( , ) ( ) ( , , ) ( , ) ( , ) b s b s b s w w u x y z u x y z f z x x w w v x y z v x y z f z y y w x y z w x y w x y (2) in the present theory, this function f(z) is considered:         ( ) sin 2 z f z z z h h (3) with the small strain assumptions, the strain-displacement relation is given by the following equation:           0 0 ( ) , ( ) , 0b s b sx x x x y y y y zz k f z k z k f z k (4a)          0 ( ) , ( ) , ( ) b s s sxy xy xy xy yz yz xz xzz k f z k g z g z (4b)                                                                                                            2 2 0 2 2 0 2 2 0 0 2 2 0 2 2 0 0 , , 2 2 b s b s x x x b sb s y y y b s xy xy xy b s w wu x xx k k v w w k k y y y k ku v w w y x x y x y                                ( ) , , ( ) 1 s s yz s sxz w df zy g z dzw x (5) the constituent relationships can be written as elastic and isotropic fgms                                                11 12 44 12 22 55 66 0 0 0 , 0 0 0 x x yz yz y y zx zx xy xy q q q q q q q (6) using the material properties, the coefficients of stiffness, qij, can be expressed s. merdaci et alii, frattura ed integrità strutturale, 55 (2021) 65-75; doi: 10.3221/igf-esis.55.05 68              11 22 12 44 55 662 2 ( ) ( ) ( ) , , 2 11 1 e z e z e z q q q q q q (7) the static equations can be solved by virtual displacement. it may be classified as analysis                                /2 /2 0 h x x y y xy xy yz yz xz xz h d dz q w d (8) the top surface. where the results of stress n, m and s are described by:                            /2 /2 , , 1 , , , , , ( ), , x y xy h b b b x y xy x y xy hs s s x y xy n n n m m m z dz f zm m m (9a)         /2 /2 , , ( ) h s s xz yz xz yz h s s g z dz (9b) the stress result is given as                              , s b s b s s s s s s n a b b m a d d k s a m b d h k (10)        , , , , , , , ,t tt b b b b s s s sx y xy x y xy x y xyn n n n m m m m m m m m (11a)           0 0 0, , , , , , , ,t t tb b b b s s s sx y xy x y xy x y xyk k k k k k k k (11b)                               11 12 11 12 11 12 12 22 12 22 12 22 66 66 66 0 0 0 0 , 0 , 0 0 0 0 0 0 0 a a b b d d a a a b b b d d d a b d (11c)                                      11 12 11 12 11 12 12 22 12 22 12 22 66 66 66 0 0 0 0 , 0 , 0 0 0 0 0 0 0 s s s s s s s s s s s s s s s s s s b b d d h h b b b d d d h h h b d h (11d)                 44 55 0 , , , , 0 s t ts s s xz yz xz yz s a s s s a a (11e) where aij , bij , etc is defined as plate stiffness s. merdaci et alii, frattura ed integrità strutturale, 55 (2021) 65-75; doi: 10.3221/igf-esis.55.05 69                                /2 2 /2 /2 2 /2 /2 2 /2 , , 1, , , 1, 2, 6 , , ( ), ( ), ( ) , 1, 2, 6 ( ) , , 4, 5 h ij ij ij ij h h s s s ij ij ij ij h h s ij ij h a b d z z q dz i j b d h f z z f z f z q dz i j a g z q dz i j (12a)              13 2( ) 11 44 552 1 ( ) ( ) , ( ) 2 11 n n h n s s n h e z e z q a a g z dz (12b) thus the balance equations associated with the newest shear deformation theory can be obtained,       : 0 xyx nn u x y (13a)        : 0 xy yn n v x y (13b)           2 22 2 2 : 2 0 b bb xy yx b m mm w q x yx y (13c)                 2 22 2 2 : 2 0 s s s ss xy y xz yzx s m m s sm w q x y x yx y (13d) fg plates analytical solutions n the side edges of the fg plate are placed the following easily endorsed boundary conditions:             0 0 0, b sb sb s x x x w w v w w n m m and x a y y (14a)             0 0 0, b sb sb s y y y w w u w w n m m and y b x x (14b) the external force can be expressed as per the navier solution:         1 1 ( , ) sin( )sin( )mn m n q x y q x y (15) where λ= mπ/a and μ= nπ/b, « m » and « n » are mode numbers. where q0 represents the intensity of the load at the plate center. for the case of a sinusoidal distributed load, we have   11 0 , 1q q m n (16) o s. merdaci et alii, frattura ed integrità strutturale, 55 (2021) 65-75; doi: 10.3221/igf-esis.55.05 70 we consider the following solution form (u, v, wb, ws), following the navier solution protocol, to satisfy the boundary conditions                                    cos( )sin( ) sin( )cos( ) sin( )sin( ) sin( )sin( ) mn mn b bmn s smn u u x y v v x y w w x y w w x y (17) where the parameters umn, vmn, wbmn and wsmn are arbitrary. first order equations system as:      k f (18) where the {∆}and {f}columns are referred to            , , , , 0, 0, ,t tmn mn bmn smn mn mnu v w w f q q (19)               11 12 13 14 12 22 23 24 13 23 33 34 14 24 34 44 a a a a a a a a k a a a a a a a a (20) the elements aij = aji of the coefficient matrix [k]. numerical results and discussions umerical results for changes and stresses in functionally graded porosity plates are given in this section in order to confirm the exactness of the present formulation. the material properties of the fg plates are aluminum and alumina: • metal (aluminum, al): em = 70 gpa, ν = 0.3 . • ceramic (alumina, al2o3): ec = 380 gpa, ν = 0.3. the following non-dimensional parameters are used for simplicity:                       2 2 2 00 0 10 10 , , , , , 0, , 0 2 2 2 2 2 2 c x xzx xz he a b h a b h h b w w aqa q a q (21) thicknesses coordinate  /z z h . tab. 1, dimensionalless deflection (a/h = 10), normal square fg plate transverse stress (a=b=1) and separate power-law index values p , higher-order shear deformation theory four uncertain predictions in relation to the theory of zenkour [50] and refined plate theory (rpt) hadj henni et al [20] in the literature. the inclusion of the coefficient of porosity (ξ=0) is not included in tab. 1. displacements and stresses resulting from the new theory are found to be in excellent agreement with zenkour [50] and hadj henni et al [20] rpt theories. furthermore, tab. 1 indicates that the shifts increase with the increase of the power-law indices when the plates are made from either fully ceramic (p = 0) or fully metal (p = ∞) normal stress and transverse normal stress are similar. this is due to the increased power law index, which makes fg plate more flexible, that is to say decreases its rigidity. fig. 2 shows non-dimensional displacement differences for two thickness ratios (a / h=10 and a / h=20) based on the power and law index "p" for the perfect floor (ξ = 0) and the three porosity values (ξ = 0.1, 0.2 and 0.3) from this curve, n s. merdaci et alii, frattura ed integrità strutturale, 55 (2021) 65-75; doi: 10.3221/igf-esis.55.05 71 it can be concluded that the dimensional transition is the with the rise in the force law index. moreover, increasing the porosity coefficient increases the dimensional displacement of the two thickness ratios. p w  x  xz zenkour[50] rpt[20] present zenkour[50] rpt[20] present zenkour[50] rpt[20] present ceramic 0.2960 0.2961 0.29603 1.9955 1.9943 1.9955 0.246 2 0.238 6 0.2205 1 0.5889 0.5890 0.58891 3.0870 3.0850 3.0850 0.246 2 0.238 6 0.2369 2 0.7573 0.7573 0.75733 3.6094 3.6067 3.6067 0.226 5 0.218 6 0.2249 3 0.8377 0.8375 0.83768 3.8742 3.8709 3.8709 0.210 7 0.202 4 0.2105 4 0.8819 0.8816 0.88187 4.0693 4.0655 4.0655 0.202 9 0.194 4 0.1984 5 0.9118 0.9112 0.91183 4.2488 4.2447 4.2447 0.201 7 0.193 0 0.1898 10 1.0089 1.0085 1.00892 5.0890 5.0849 5.0849 0.219 8 0.211 4 0.1986 metal 1.6070 1.6074 1.60702 1.9955 1.9943 1.9943 0.246 2 0.238 6 0.2205 table 1: functionally graded plate fg with non-dimensional deflections and stresses on various power law index. figure 2: displacement variation as a function of the power index “p” and the volume fraction of porosity of a fg plate. figure 3: displacement variation depending on the thickness ratio (a/h) for various porosity factor values ξ. s. merdaci et alii, frattura ed integrità strutturale, 55 (2021) 65-75; doi: 10.3221/igf-esis.55.05 72 fig. 3 illustrates the influence of the aspect ratio (a/h) for the fluidization of the fg plate for perfect plate size (ξ = 0), and three values of the imperfect plates of the porosity coefficient (ξ = 0.1, 0.2 and 0.3). it is assumed the power-law index to be constant, p = 2. the increase in dimensional displacements, explained through the effect of material rigidity, i.e. the rise of the value of the porosity coefficient (ξ) is seen in this figure, leads to an increase in plate displacements. the impact of porosity on the bending of a plate has also been shown to increase with the larger values of the ratio of thickness to length. figure 4: displacement variance as a geometric ratio feature (a / b) for different porosity factor values (ξ). in fig. 4, we study a dimensionless displacement variation function as a geometric ratio of square (a=b=1) and rectangular (a≠b) fgp, as well as of the different porosity coefficient values (ξ=0.1, 0.2 and 0.3), with equal density ratio (a / h = 10) and a material index p = 2. we found a decrease in that ratio reduces displacement. figure 5: the thickness of fgp axial stress distribution for different porosity factor (ξ) (a/h=10 and p=2). fig. 5 took account of the effect of the porosity of the fgp by adding the coefficient (ξ). therefore, four values are maintained (ξ = 0, 0.1, 0.2 and 0.3). the increase in the porosity index (ξ) can be observed to contribute to increased stress. this can be explained by the reduction of the rigidity of the plate by the porosity. the stresses are tensile above the middle plane and compressed under the middle plane. it should be remembered that the overall stress based on the magnitude of the volume fraction exponent. fig. 6 indicates shear stresses through the transverse thickness distribution. s. merdaci et alii, frattura ed integrità strutturale, 55 (2021) 65-75; doi: 10.3221/igf-esis.55.05 73 this figure shows the remarkable direct impact of the porosity effect; this occurs at a point in the fgp middle plane and lowers transverse shear stress. figure 6: via the thickness distributions of the fg shear stress (a/h=10 and p=2). conclusion he paper is intended to analyses the static bending effect of functionally labeled plates with porosities that can occur inside of this type of plates based on the concept of high order shear deformation. analytical solutions with realistic grades for porous and rectangular plates are given. this paper supports study and the analysis of various parameters, such as the material parameter, volume fraction, appearance ratio, surface thickness and coefficient of porosity. the control equations are resolved with the navier-style closed-form solution for sinusoidal fg plates. the material characteristics vary in the thickness direction of the sheet according to the rules of the mixture and are reformulated to approximate the material characteristics in the phased porosity. the results from the static bending study for this test are fully validated by the observations present and those present in the literature. there is discussion of the use of graded and porosity parameters. from this work, we can say that the current and simple theory of the resolution of the mechanical behavior of porosity fgm plates that defect factories. references [1] suresh, s., mortensen, a. (1998). fundamental of functionally graded materials. london: maney. [2] hadj mostefa, a., merdaci, s., and mahmoudi, n. (2018). an overview of functionally graded materials «fgm», proceedings of the third international symposium on materials and sustainable development, isbn 978-3-31989706-6, pp. 267–278. [3] paulino, g. h., and nelli silva, e. c. (2005). design of functionally graded structures using topology optimization, materials science forum 492-493, pp. 435-440. doi: 10.4028/www.scientific.net/msf.492-493.435. [4] paulino, g.h., jin, z.-h. and dodds, jr.r.h. (2003). failure of functionally graded materials, comprehensive structural integrity, volume 2, (isbn: 0-08-044156-4), pp. 607–644. [5] zhu, j., lai, z., yin, z., jeon, j., lee, s. (2001). fabrication of zro2–nicr functionally graded material by powder metallurgy, mater chem phys, 68, pp. 130–135. [6] wattanasakulpong, n., prusty, b.g., kelly, d.w., hoffman, m. (2012). free vibration analysis of layered functionally graded beams with experimental validation, mater des, 36, pp. 182–190. [7] reissner, e., and stavsk, y. (1961). bending and stretching of certain types of heterogeneous aelotropic elastic plates, asme j applmech, 28, pp. 402-428. [8] timoshenko, s.p., and gere, j.m. (1972). mechanics of materials, new york: d.van nostrand company. t s. merdaci et alii, frattura ed integrità strutturale, 55 (2021) 65-75; doi: 10.3221/igf-esis.55.05 74 [9] reddy, j.n., wang, c.m. (2000). an overview of the relationships between solutions of the classical and shear deformation plate theories, compos. sci. technol, 60, pp. 2327–2335. [10] reissner, e. (1945). the effect of transverse shear deformation on the bending of elastic plates. trans. asme j. appl. mech, 12, pp. 69–77. [11] mindlin, r.d. (1951). influence of rotary inertia and shear on flexural motions of isotropic, elastic plates,trans. asme j. appl.mech, 18, pp. 31–38. [12] reddy, j.n. (1984). a simple higher-order theory for laminated composite plates, trans. asme j. appl. mech, 51, 745–752. [13] ren, j.g. (1986). a new theory of laminated plate, compos. sci. technol, 26, pp. 225–239. [14] kant, t., pandya, b.n. (1988). a simple finite element formulation of a higher-order theory for unsymmetrically laminated composite plates, compos. struct, 9, pp. 215–264. [15] mohan, p.r., naganarayana, b.p., prathap, g. (1994), consistent and variational correct finite elements for higherorder laminated plate theory, compos. struct, 29, pp. 445–456. [16] kim, s.e., thai, h.t., lee, j. (2009). atwo variable refined plate theory for laminated composite plates, compos. struct, 89, pp. 197–205. [17] merdaci, s., tounsi, a., houari, m.s.a., mechab, i., hebali, h., benyoucef, s. (2011). two new refined shear displacement models for functionally graded sandwich plates, arch appl mech, 81, pp. 1507-1522. [18] reissner, e. (1944). on the theory of bending of elastic plates, j. math. phy, 23, pp. 184–191. [19] reddy, j.n., wang, c.m., lee, k.h. (1997). relationships between bending solutions of classical and shear deformation beam theories, international journal of solids and structures, 34 (26), pp. 3373–338. [20] hadj henni, a., ait atmane, h., mechab i., boumia l., tounsi a., adda bedia e.a. (2011). static analysis of functionally graded sandwich plates using an efficient and simple refined theory, chinese journal of aeronautics, 24, pp. 434-448. doi: 10.1016/s1000-9361(11)60051-4 [21] zine, a., tounsi, a., draiche, k., sekkal, m., and mahmoud, s.r. (2018). a novel higher-order shear deformation theory for bending and free vibration analysis of isotropic and multilayered plates and shells, steel compos. struct, 26(2), pp. 125-137. [22] merdaci, s., benyoucef, s., tounsi, a., adda bedia, .e.a. (2013). etudes a la flexion statique des plaques epaisses en materiaux a gradients de proprietes « fgm », revue communication science & technologie « cost », 12, pp. 34-41. [23] merdaci, s., boutaleb, s., hellal, h., benyoucef, s. (2019). analysis of static bending of plates fgm using refined high order shear deformation theory, j. build. mater. struct, 6(1), pp pp. 32-38. doi: 10.5281/zenodo.2609306. [24] reddy, j. n. (1984). a simple higher-order theory for laminated composite plates, journal of applied mechanics, 51(4), pp. 745-752. [25] shi, g. (2007), a new simple third-order shear deformation theory of plates, international journal of solids and structures, 44(13), pp. 4399-4417. [26] shimpi, r. p., & patel, h. g. (2006). a two variable refined plate theory for orthotropic plate analysis, international journal of solids and structures, 43(22-23), pp. 6783-6799. [27] younsi, a., tounsi, a., zaoui, .f.z., bousahla, a., mahmoud, .s.r. (2018). novel quasi-3d and 2d shear deformation theories for bending and free vibration analysis of fgm plates, geomechanics and engineering, 14(6), pp. 519-532. [28] merdaci, s. (2018). analysis of bending of ceramic-metal functionally graded plates with porosities using of high order shear theory, advanced engineering forum; 30, pp. 54-70. [29] merdaci, s., belghoul, h. (2019). high order shear theory for static analysis functionally graded plates with porosities, comptes rendus mécanique, 347(3), pp. 207-217. [30] merdaci, s. (2018). analysis of bending of functionally graded plates with porosities using of high order shear theory, algerian journal of research and technology (ajrt), 2(1), pp. 54-69. [31] behravan, r. a. (2018). static analysis of non-uniform 2d functionally graded auxeticporous circular plates interacting with the gradient elastic foundations involving friction force, aerosp sci technol, 76, pp. 315–339. [32] karama m., afaq, k.s., mistou, s. (2003). mechanical behaviour of laminated composite beam by the new multilayered laminated composite structures model with transverse shear stress continuity, int. j. solids structures, 40 (6), pp. 1525-1546. [33] kaddari, m., kaci, a., bousahla, a.a., tounsi, a., bourada, f., tounsi, a., adda bedia, e.a., al-osta,m.a. (2020) a study on the structural behaviour of functionally graded porous plates on elastic foundation using a new quasi-3d model: bending and free vibration analysis, computers and concrete, 25(1), pp. 37-57. doi: 10.12989/cac.2020.25.1.037 s. merdaci et alii, frattura ed integrità strutturale, 55 (2021) 65-75; doi: 10.3221/igf-esis.55.05 75 [34] merdaci, s., hadj mostefa, a. (2020). influence of porosity on the analysis of sandwich plates fgm using of high order shear-deformation theory, frattura ed integrità strutturale, 51, pp. 199-214. doi: 10.3221/igf-esis.51.16 [35] medani, m., benahmed, a., zidour, m., heireche, h., tounsi, a., bousahla, a.a., tounsi, a., mahmoud, s.r. (2019). static and dynamic behavior of (fg-cnt) reinforced porous sandwich plate using energy principle, steel and composite structures, 32(5), pp. 595-610. doi: 10.12989/scs.2019.32.5.595 [36] draoui, a., zidour, m., tounsi, a., and adim, b. (2019). static and dynamic behavior of nanotubes-reinforced sandwich plates using (fsdt), j. nano res, 57, pp. 117-135. [37] merdaci, s., belmahi, s., belghoul, h., hadj mostefa, a. (2019). free vibration analysis of functionally graded plates fg with porosities, international journal of engineering research & technology (ijert), 8 (3), pp. 143-147. doi: 10.17577/ijertv8is030098 [38] merdaci, s. (2019). free vibration analysis of composite material plates "case of a typical functionally graded fg plates ceramic/metal" with porosities, nano hybrids and composites (nhc), 25, pp. 69-83. [39] merdaci, s (2019). analytical solution for free vibration analysis of plates functionally graded fgp with porosities, recueil de mécanique, 4(2), pp. 397–408. doi: 10.5281/zenodo.3738699. [40] merdaci, s., belghoul, h., hadj mostefa, a., merazi, m., hellal, h., boutaleb, s. (2020). free vibration analysis of advanced composite plates with porosities, algerian journal of research and technology, (ajrt), 4(2), pp. 13-22. https://www.asjp.cerist.dz/en/presentationrevue/538 [41] merdaci, s., hadj, m.a., merazi, m., belghoul, h., hellal, h., boutaleb, s. (2020). effects of even pores distribution on vibrational behavior of functionally graded plate porous rectangular and square, procedia structural integrity, 26, pp. 35-45. [42] mojahedin, a., farzaneh, j.e., jabbari, m. (2014). thermal and mechanical stability of a circular porous plate with piezoelectric actuators, acta mech, 225, pp. 3437–3452. [43] shojaeefard, m.h., googarchin, h.s., ghadiri, m., mahinzare, m. (2017). micro temperature dependent fg porous plate: free vibration and thermal buckling analysis usi modified couple stress theory with cpt and fsdt, appl math model, 50, pp. 633–655. [44] chen, d., yang, j., kitipornchai, s. (2017). nonlinear vibration and postbuckling of functionally graded graphene reinforced porous nanocomposite beams, compos sci technol, 142, pp. 235–245. [45] kitipornchai. s., chen, d., yang, j. (2017). free vibration and elastic buckling of functionally graded porous beams reinforced by graphene platelets, mater des, 116, pp. 656–665. [46] yang, j., chen, d., kitipornchai, s. (2018). buckling and free vibration analyses of functionally graded graphene reinforced porous nanocomposite plates based on chebyshev-ritz method, compos struct, 193, pp. 281–294. [47] bhimaraddi, a., stevens, l.k. (1984). a higher order theory for free vibration of orthotropic, homogeneous and laminated rectangular plates, trans. asme j. appl. mech, 51, pp. 195–198. [48] zhang, z., paulino, g.h. (2005). cohesive zone modeling of dynamic failure in homogeneous and functionally graded materials, international journal of plasticity, 21, pp. 1195–1254. doi: 10.1016/j.ijplas.2004.06.009. [49] paulino, g. h., yin, h. m. and sun, l. z. (2006). micromechanics-based interfacial debonding model for damage of functionally graded materials with particle interactions, international journal of damage mechanics, pp. 1-22. doi: 10.1177/1056789505060756. [50] zenkour, a.m. (2006). generalized shear deformation theory for bending analysis of functionally graded plates. appl. math. model, 30, pp. 67–84. microsoft word numero_38_art_29 f. berto et alii, frattura ed integrità strutturale, 38 (2016) 215-223; doi: 10.3221/igf-esis.38.29 215 focussed on multiaxial fatigue and fracture averaged strain energy density-based synthesis of crack initiation life in notched steel bars under torsional fatigue filippo berto university of padova, department of management and engineering, vicenza (italy) ntnu, department of engineering design and materials, trondheim, (norway) berto@gest.unipd.it alberto campagnolo, giovanni meneghetti university of padova, department of industrial engineering, padova (italy) alberto.campagnolo@unipd.it, giovanni.meneghetti@unipd.it keisuke tanaka meijo university, department of mechanical engineering, nagoya (japan) ktanaka@meijo-u.ac.jp abstract. the torsional fatigue behaviour of circumferentially notched specimens made of austenitic stainless steel, sus316l, and carbon steel, sgv410, characterized by different notch root radii has been recently investigated by tanaka. in that contribution, it was observed that the total fatigue life of the austenitic stainless steel increases with increasing stress concentration factor for a given applied nominal shear stress amplitude. by using the electrical potential drop method, tanaka observed that the crack nucleation life was reduced with increasing stress concentration, on the other hand the crack propagation life increased. the experimental fatigue results, originally expressed in terms of nominal shear stress amplitude, have been reanalysed by means of the local strain energy density (sed) averaged over a control volume having radius r0 surrounding the notch tip. to exclude all extrinsic effects acting during the fatigue crack propagation phase, such as sliding contact and/or friction between fracture surfaces, crack initiation life has been considered in the present work. in the original paper, initiation life was defined in correspondence of a 0.1÷0.4-mm-deep crack. the control radius r0 for fatigue strength assessment of notched components, thought of as a material property, has been estimated by imposing the constancy of the averaged sed for both smooth and cracked specimens at na = 2 million loading cycles. keywords. torsional fatigue; notch effect; crack initiation; averaged sed; electrical potential drop. citation: berto, f., campagnolo, a., meneghetti, g., tanaka, k., averaged strain energy density-based synthesis of crack initiation life in notched steel bars under torsional fatigue, frattura ed integrità strutturale, 38 (2016) 215-223. received: 14.05.2016 accepted: 12.06.2016 published: 01.10.2016 copyright: © 2016 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. f. berto et alii, frattura ed integrità strutturale, 38 (2016) 215-223; doi: 10.3221/igf-esis.38.29 216 introduction ealing with torsional and multiaxial fatigue, an anomalous phenomenon of the notch-strengthening effect was observed in circumferentially notched specimens made of austenitic stainless steels [1–3]. the fatigue life of notched specimens resulted longer than that of smooth ones, and increased with increasing stress concentration factor under the same amplitude of the nominal shear stress. this notch-strengthening effect was also observed in nicrmo steel [4], pure titanium [5], but it was not found in carbon steels [3,6,7]. in circumferentially notched bars subjected to torsion fatigue loadings, factory-roof type fracture surfaces are obtained under low stress amplitudes and the sliding contact of the fracture surfaces causes the retardation of crack propagation [8–12]. at high stress amplitudes, instead, flat fracture surfaces are observed and the crack retardation due to sliding contact is reduced. the presence of a superimposed static tensile stress also reduces the crack surfaces contact [11]. recently, tanaka [13] has deeply investigated this phenomenon dealing with the fatigue behaviour of notched bars made of austenitic stainless steel, sus316l, and carbon steel, sgv410, subjected to torsion loadings and characterized by different notch tip radii. in the present work, the experimental fatigue results have been reanalysed by means of the averaged strain energy density (sed) approach, first proposed by lazzarin and zambardi [14]. the crack initiation life has been considered, in such a way to exclude all extrinsic effects acting during the fatigue crack propagation phase, such as sliding contact and/or friction between fracture surfaces. experimental fatigue results he materials tested in [13] were an austenitic stainless steel (sus316l) and a carbon steel (sgv410) for structural use in nuclear power plants. the yield strength and tensile strength of sus316l were 260 and 591 mpa, and those of sgv410 were 275 and 470 mpa. fig. 1 reports the geometry of the cylindrical specimens weakened by circumferential notches with three different root radii. the specimens with a notch radius  equal to 4.5, 1.07, and 0.22 mm are named na, nb, and nc, respectively. the elastic stress net-section concentration factor for the shear stress under torsion for na, nb, and nc specimens calculated by the finite element method (fem) was 1.17, 1.55, and 2.54, respectively, while that for the tensile stress was 1.50, 2.50, and 5.07, respectively. figure 1: geometry of the cylindrical notched specimens [13] (dimensions are in mm). d t f. berto et alii, frattura ed integrità strutturale, 38 (2016) 215-223; doi: 10.3221/igf-esis.38.29 217 the experimental fatigue test results were obtained by adopting a nominal load ratio r equal to -1. the applied shear stress amplitude was expressed in terms of nominal stress calculated elastically from the applied torque for the minimum cross section. the fatigue tests under torsion loadings were conducted with and without superimposed static tension. in the first case, the applied static tensile stress (m) equaled the applied shear stress amplitude (a). tanaka [13] employed a dc electrical potential method to monitor the fatigue crack initiation and propagation phases. the initiation life was defined in correspondence of a 0.1÷0.4-mm-deep crack. it was observed that the total fatigue life of the austenitic stainless steel (sus316l) increases with increasing stress concentration factor for a given applied nominal shear stress amplitude. in particular, tanaka [13] observed that the crack nucleation life was reduced with increasing stress concentration; on the other hand the crack propagation life increased. the notch-strengthening effect has been attributed to the retarded propagation promoted by the crack surfaces contact, which occurs especially for the sharper notches. indeed, the superposition of static tension on the fatigue torsion loading resulted in a notch-weakening behaviour, being the contact between the crack surfaces reduced. the notch strengthening effect was not observed in the sgv410 carbon steel. on the basis of fracture surfaces and crack paths analyses [13], the difference in the notch effect on the fatigue behaviour of sus316l and sgv410 appeared to be tied to different crack path morphologies of small cracks and three-dimensional fracture surface topographies observed by using scanning electron microscopy (sem). more details about the experimental results, expressed in terms of nominal shear stress amplitude, and the fracture surfaces analysis can be found in the original paper [13]. averaged strain energy density approach he strain energy density (sed) averaged over a control volume, thought of as a material property according to lazzarin and zambardi [14], proved to efficiently account for notch effects both in static [14–16] and fatigue [14,17,18] structural strength problems. the idea is reminiscent of the stress averaging to perform inside a material dependent structural volume, according to the approach proposed by neuber. such a method was formalized and applied first to sharp, zero radius, v-notches [14] and later extended to blunt u and vnotches [19]. when dealing with sharp v-notches, the control volume is a circular sector of radius r0 centered at the notch tip [14]. for a blunt v-notch, instead, the volume assumes the crescent shape shown in fig. 2 [19], where r0 is the depth measured along the notch bisector line. the outer radius of the crescent shape is equal to r0 + r0, where r0 depends on the notch opening angle 2 and on the notch root radius  according to the following expression:    q 1q r0 (1) with q defined as:    22 q (2) the control radius r0 for fatigue strength assessment of notched components has been defined by equalling the averaged sed in two situations, i.e. the fatigue limit of un-notched and cracked specimens, respectively [4,20]. therefore r0 combines two material properties: the plain material fatigue limit (or the high-cycle fatigue strength of smooth specimens) and the threshold value of the sif range for long cracks. the following expressions have been derived under plane strain hypothesis [4,20] dealing with tension (mode i) and torsion (mode iii) loadings, respectively:    2 0 th,i 2 0 th,i 1i,0 k 4 851k e2r                     (3) 2 0 th,iii3 iii,0 k 1 e r            (4) t f. berto et alii, frattura ed integrità strutturale, 38 (2016) 215-223; doi: 10.3221/igf-esis.38.29 218 it should be noted that, in principle, the control radius r0 could assume different values under mode i and mode iii, so that the energy contributions related to the two different loadings should be averaged in control volumes of different size [4]. the idea of a control volume size dependent on the loading mode has been proposed for the first time in [4] dealing with the multiaxial fatigue strength assessment of notched specimens made of 39nicrmo3 steel, then it has been successfully applied also for the fatigue strength assessment of notched components made of aisi 416 [21], cast iron en-gjs400 [22] and titanium grade 5 alloy ti-6al-4v [23] subjected to combined tension and torsional loading. it is important to underline that using a poisson’s coefficient = 0.30, eq. (3) (being valid under plane strain hypothesis) can be re-written as follows [20,17]: 0 2 0 th,i i,0 a85.0 k1 85.0r            (5) therefore, r0 in fig. 2 results on the order of the el haddad-smith-topper length parameter [24]. figure 2: control volume for specimens weakened by rounded v-notches [19]. once the control volume is properly defined, the averaged sed can be evaluated directly from the fe results, w , by summation of the strain-energies wfem,i calculated for each i-th finite element belonging to the control area (a in figs. 24): a w cw a i,fem w   (6) where the coefficient cw accounts for the effect of the nominal load ratio r [25], when the range value of the nominal stress is applied to the fe model. it is equal to 1 for r = 0 and to 0.5 for r = 1. equation (6) represents the so-called direct approach to calculate the averaged sed. according to a recent contribution of lazzarin et al. [26], very coarse fe meshes can be adopted within the control volume a (see fig. 4). sed-based synthesis of crack initiation experimental data he fatigue properties of the considered materials have been taken from [12,27] and are reported in table 1. all parameters are expressed in terms of range, defined as maximum minus minimum value. the control radii r0,i and t f. berto et alii, frattura ed integrità strutturale, 38 (2016) 215-223; doi: 10.3221/igf-esis.38.29 219 r0,iii have been calculated from eqs. (3) and (4), respectively, where parameters e1 and e3 equal 0.133 and 0.414, respectively, for a poisson’s ratio ν = 0.3. material 0 (mpa) i,th (mpa m0.5) r0,i (mm) 0 (mpa) iii,th (mpa m0.5) r0,iii (mm) sus 316l 442 10.30 0.144 266 9.86 0.438 sgv 410 436 10.60 0.157 270 12.80 0.716 table 1: mechanical properties the averaged sed values were calculated using the direct approach, w , according to eq. (6) (with about 500 finite elements inside the control volume). fe analyses have been carried out by means of ansys® software and by adopting free mesh patterns consisting of two-dimensional, harmonic, 8-node linear quadrilateral elements (plane 83 of ansys® element library), as shown in figs. 3-4. the adopted finite element enables to analyse axis-symmetric components subjected to external loads that can be expressed according to a fourier series expansion. therefore, it can be employed for modelling three-dimensional axis-symmetric components under axial, bending or torsional loadings, keeping the advantage of treating two-dimensional fe analyses. figure 3: (a) refined fe mesh (about 500 fe inside the control volume) adopted in the numerical analyses to evaluate the exact sed value. the y-axis coincides with the axis of the specimen. (b) details of the fe mesh inside the control volume and (c) sed contour lines. considered case: nb specimen made of sgv 410 steel, with  = 1.07 mm, r0,iii = 0.716 mm, r0 = 0.428 mm. f. berto et alii, frattura ed integrità strutturale, 38 (2016) 215-223; doi: 10.3221/igf-esis.38.29 220 figure 4: (a) coarse fe mesh (about 50 fe inside the control volume) adopted in the numerical analyses producing a reduced error of 1%. the y-axis coincides with the axis of the specimen. (b) details of the fe mesh inside the control volume. considered case: nb specimen made of sgv 410 steel, with  = 1.07 mm, r0,iii = 0.716 mm, r0 = 0.428 mm. the results of the synthesis based on the local strain energy density are reported in fig. 5. with the aim to exclude all extrinsic effects acting during the fatigue crack propagation phase, such as sliding contact and/or friction between fracture surfaces, crack initiation life, defined by tanaka [13] in correspondence of a crack depth in the range of 0.1÷0.4 mm, has been considered in the present reanalysis. moreover, it is important to underline that the range of the averaged strain energy density, w , has been taken into account, so that the constant energy contribution of static tensile stresses has been neglected. this engineering approximation might be acceptable if crack initiation life, and not the total life, is considered, since the static tensile stress contributes more to the crack growth behaviour (i.e. sliding contact and friction between the mating surfaces) than to the crack initiation phase. the control radius r0,i has been calculated and reported in table 1 only for comparison purposes. it can be observed that in the case of sus 316l steel, the crack initiation experimental results are well summarized in a scatter-band (fig. 4a), characterized by an equivalent stress-based scatter index t (= t ) equal to 1.23; this value is practically coincident with the intrinsic scatter of the original data expressed in terms of nominal stresses, which was found equal to t = 1.24. however, the effects of sliding contact and/or friction between fracture surfaces during the propagation phase are evident, because the experimental results in terms of total fatigue life (see the smaller symbols: the black ones are related to pure torsion fatigue loading, while the gray ones are for torsion fatigue loading with superimposed static tension) are characterized by a high scatter, due to the difference between the fatigue lives of specimens tested with and without static tensile stress. in the case of sgv 410 steel (fig. 4b) the crack initiation experimental data are more scattered, t being higher and equal to 1.51, while the intrinsic scatter of the original data expressed in terms of nominal stress resulted equal to t = 1.17. however, in this case, the influence of extrinsic effects is almost negligible and the experimental data in terms of total fatigue life fall within the scatter-band determined using crack initiation data. conclusions n the present contribution, some recent experimental fatigue test results, obtained from circumferentially notched specimens made of stainless and carbon steels, with different notch root radii and subjected to torsional fatigue loadings, have been reanalysed by means of the averaged strain energy density (sed) approach. crack initiation life has been taken into account to exclude all extrinsic effects acting during the crack propagation phase, particularly of severely notched specimens made of stainless steel. the synthesis based on the local sed allowed to correlate fairly well the notch fatigue data for each tested material. i r0,iii r0 a x y  f. berto et alii, frattura ed integrità strutturale, 38 (2016) 215-223; doi: 10.3221/igf-esis.38.29 221 figure 5: averaged sed-based scatter-band calibrated on the crack initiation experimental fatigue results for (a) sus 316l and (b) sgv 410 steels. the smaller symbols indicate the total fatigue life for comparison purposes: the black ones are for pure torsion loading, while the gray ones are for torsion loading with superimposed static tension. references [1] tanaka, k., hashimoto, a., narita, j., egami, n., fatigue life of circumferentially notched bars of austenitic stainless 0,1 1,0 1,e+03 1,e+04 1,e+05 1,e+06 1,e+07 s e d r an g e, δ w [ m j/ m 3 ] number of cycles to crack initiation na nb nc na nb nc r0,iii = 0.438 mm δwa,50% = 0.280 mj/m 3 na = 2 ∙10 6 cycles scatter index (10%-90%): tw = 0.346/0.227 = 1.52 slope k = 5.27 torsion fatigue loading, r = -1 torsion fatigue loading, r = -1 with superimposed static tension σm = τa 2.0 0.346 0.280 0.227 na sus 316l (a) 0,01 0,10 1,00 1,e+03 1,e+04 1,e+05 1,e+06 1,e+07 s e d r an g e, δ w [ m j/ m 3 ] number of cycles to crack initiation na nb nc na nb nc torsion fatigue loading, r = -1 torsion fatigue loading, r = -1 with superimposed static tension σm = τa r0,iii = 0.716 mm δwa,50% = 0.145 mj/m 3 na = 2 ∙10 6 cycles scatter index (10%-90%): tw = 0.220/0.096 = 2.29 slope k = 5.01 2.00 sgv 410 na 0.220 0.145 0.096 (b) f. berto et alii, frattura ed integrità strutturale, 38 (2016) 215-223; doi: 10.3221/igf-esis.38.29 222 steel under cyclic torsion with and without static tension, j soc mater sci., 58 (2009) 1044–1050. [2] tanaka, k., small fatigue crack propagation in notched components under combined torsional and axial loading, procedia eng., 2 (2010) 27–46. doi:10.1016/j.proeng.2010.03.004. [3] ohkawa, c., ohkawa, i., notch effect on torsional fatigue of austenitic stainless steel: comparison with low carbon steel, eng. fract. mech., 78 (2011) 1577–1589. doi:10.1016/j.engfracmech.2011.01.015. [4] berto, f., lazzarin, p., yates, j.r., multiaxial fatigue of v-notched steel specimens: a non-conventional application of the local energy method, fatigue fract. eng. mater. struct., 34 (2011) 921–943. doi:10.1111/j.1460-2695.2011.01585.x. [5] okano, t., hisamatsu, n., effect of notch of torsional fatigue property of pure titanium, proc. 31 symp. fatigue, soc. mater. sci. japan., 31 (2012) 129–133. [6] atzori, b., berto, f., lazzarin, p., quaresimin, m., multi-axial fatigue behaviour of a severely notched carbon steel, int. j. fatigue, 28 (2006) 485–493. doi:10.1016/j.ijfatigue.2005.05.010. [7] tanaka, k., ishikawa, t., narita, j., egami, n., fatigue life of circumferentially notched bars of carbon steel under cyclic torsion with and without static tension, j soc mater sci. 60 (2011). [8] ritchie, r.o., mcclintock, f.a., nayeb-hashemi, h., ritter, m.a., mode iii fatigue crack propagation in low alloy steel, metall. trans. a., 13 (1982) 101–110. doi:10.1007/bf02642420. [9] tschegg, e.k., a contribution to mode iii fatigue crack propagation, mater. sci. eng. 54 (1982) 127–136. doi:10.1016/0025-5416(82)90037-4. [10] tschegg, e.k., the influence of the static i load mode and r ratio on mode iii fatigue crack growth behaviour in mild steel, mater. sci. eng., 59 (1983) 127–137. doi:10.1016/0025-5416(83)90094-0. [11] tanaka, k., akiniwa, y., nakamura, h., j-integral approach to mode iii fatigue crack propagation in steel under torsional loading, fatigue fract. eng. mater. struct., 19 (1996) 571–579. doi:10.1111/j.1460-2695.1996.tb00993.x. [12] yu, h., tanaka, k., akiniwa, y., estimation of torsional fatigue strength of medium carbon steel bars with a circumferential crack by the cyclic resistance-curve method, fatigue fract. eng. mater. struct., 21 (1998) 1067–1076. doi:10.1046/j.1460-2695.1998.00105.x. [13] tanaka, k., crack initiation and propagation in torsional fatigue of circumferentially notched steel bars, int. j. fatigue, 58 (2014) 114–125. doi:10.1016/j.ijfatigue.2013.01.002. [14] lazzarin, p., zambardi, r., a finite-volume-energy based approach to predict the static and fatigue behavior of components with sharp v-shaped notches, int. j. fract., 112 (2001) 275–298. doi:10.1023/a:1013595930617. [15] berto, f., lazzarin, p., recent developments in brittle and quasi-brittle failure assessment of engineering materials by means of local approaches, mater. sci. eng. r reports, 75 (2014) 1–48. doi:10.1016/j.mser.2013.11.001. [16] campagnolo, a., berto, f., leguillon, d., fracture assessment of sharp v-notched components under mode ii loading: a comparison among some recent criteria, theor. appl. fract. mech., (2016) in press. doi:10.1016/j.tafmec.2016.02.001. [17] livieri, p., lazzarin, p., fatigue strength of steel and aluminium welded joints based on generalised stress intensity factors and local strain energy values, int. j. fract., 133 (2005) 247–276. doi:10.1007/s10704-005-4043-3. [18] berto, f., campagnolo, a., chebat, f., cincera, m., santini, m., fatigue strength of steel rollers with failure occurring at the weld root based on the local strain energy values: modelling and fatigue assessment, int. j. fatigue, 82 (2016) 643– 657. doi:10.1016/j.ijfatigue.2015.09.023. [19] lazzarin, p., berto, f., some expressions for the strain energy in a finite volume surrounding the root of blunt vnotches, int. j. fract., 135 (2005) 161–185. doi:10.1007/s10704-005-3943-6. [20] lazzarin, p., berto, f., from neuber’s elementary volume to kitagawa and atzori’s diagrams: an interpretation based on local energy, int. j. fract., 135 (2005) l33–l38. doi:10.1007/s10704-005-4393-x. [21] berto, f., lazzarin, p., fatigue strength of structural components under multi-axial loading in terms of local energy density averaged on a control volume, int. j. fatigue, 33 (2011) 1055–1065. doi:10.1016/j.ijfatigue.2010.11.019. [22] berto, f., lazzarin, p., tovo, r., multiaxial fatigue strength of severely notched cast iron specimens, int. j. fatigue, 67 (2014) 15–27. doi:10.1016/j.ijfatigue.2014.01.013. [23] berto, f., campagnolo, a., lazzarin, p., fatigue strength of severely notched specimens made of ti-6al-4v under multiaxial loading, fatigue fract. eng. mater. struct., 38 (2015) 503–517. [24] el haddad, m.h., topper, t.h., smith, k.n., prediction of non propagating cracks, eng. fract. mech., 11 (1979) 573– 584. doi:10.1016/0013-7944(79)90081-x. [25] lazzarin, p., sonsino, c.m., zambardi, r., a notch stress intensity approach to assess the multiaxial fatigue strength of welded tube-to-flange joints subjected to combined loadings, fatigue fract. eng. mater. struct., 27 (2004) 127–140. doi:10.1111/j.1460-2695.2004.00733.x. [26] lazzarin, p., berto, f., zappalorto, m., rapid calculations of notch stress intensity factors based on averaged strain energy density from coarse meshes: theoretical bases and applications, int. j. fatigue, 32 (2010) 1559–1567. f. berto et alii, frattura ed integrità strutturale, 38 (2016) 215-223; doi: 10.3221/igf-esis.38.29 223 doi:10.1016/j.ijfatigue.2010.02.017. [27] tanaka, k., akiniwa, y., yu, h., the propagation of a circumferential fatigue crack in medium-carbon steel bars under combined torsional and axial loadings. in: mixed-mode crack behaviou, in: k. miller, d. mcdowell (eds.), mix. crack behav. astm 1359, west conshohocked, pa, (1999) 295–311. << /ascii85encodepages false /allowtransparency false /autopositionepsfiles true /autorotatepages /none /binding /left /calgrayprofile (dot gain 20%) /calrgbprofile (srgb iec61966-2.1) /calcmykprofile (u.s. web coated \050swop\051 v2) /srgbprofile (srgb iec61966-2.1) /cannotembedfontpolicy /error /compatibilitylevel 1.4 /compressobjects /tags /compresspages true /convertimagestoindexed true /passthroughjpegimages true /createjobticket false /defaultrenderingintent /default /detectblends true /detectcurves 0.0000 /colorconversionstrategy /cmyk /dothumbnails false /embedallfonts true /embedopentype false /parseiccprofilesincomments true /embedjoboptions true /dscreportinglevel 0 /emitdscwarnings 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can be opened with acrobat and adobe reader 5.0 and later.) >> /namespace [ (adobe) (common) (1.0) ] /othernamespaces [ << /asreaderspreads false /cropimagestoframes true /errorcontrol /warnandcontinue /flattenerignorespreadoverrides false /includeguidesgrids false /includenonprinting false /includeslug false /namespace [ (adobe) (indesign) (4.0) ] /omitplacedbitmaps false /omitplacedeps false /omitplacedpdf false /simulateoverprint /legacy >> << /addbleedmarks false /addcolorbars false /addcropmarks false /addpageinfo false /addregmarks false /convertcolors /converttocmyk /destinationprofilename () /destinationprofileselector /documentcmyk /downsample16bitimages true /flattenerpreset << /presetselector /mediumresolution >> /formelements false /generatestructure false /includebookmarks false /includehyperlinks false /includeinteractive false /includelayers false /includeprofiles false /multimediahandling /useobjectsettings /namespace [ (adobe) (creativesuite) (2.0) ] /pdfxoutputintentprofileselector /documentcmyk /preserveediting true /untaggedcmykhandling /leaveuntagged /untaggedrgbhandling /usedocumentprofile /usedocumentbleed false >> ] >> setdistillerparams << /hwresolution [2400 2400] /pagesize [612.000 792.000] >> setpagedevice microsoft word numero_37_art_34 d. angelova et alii, frattura ed integrità strutturale, 37 (2016) 258-264; doi: 10.3221/igf-esis.37.34 258 focused on fracture mechanics in central and east europe on fatigue behaviour of two spring steels. part ii: mathematical models d.angelova, r. yordanova, t. lazarova, s. yankova university of chemical technology and metallurgy, bulgaria donkaangelova@abv.bg, r.yordanova@uctm.edu abstract. symmetric fatigue in two spring steels is investigated in three groups of specimens. one of the groups (steel en10270-1sh/ din 17223c – c 0.82%, mn 0.76%, si 0.26%) has experienced rotating-bending fatigue in air, and the other two groups (steel bs250a53/ din 55si7 – c 0.56%, mn 0.81%, si 1.85%), torsion fatigue in-air and corrosion environment. all experiments include testing to fracture, applying acetate-foil replication technique, replica monitoring of short crack surface growth, length measuring of propagating cracks, a, at the corresponding number of fatigue cycles, n. data obtained from replica monitoring are presented in plots “crack lengths, a – cycles, n”, and used for calculating fatigue crack growth rates, da/dn, and graphical presentations “crack growth rates, da/dn – crack lengths, a”. a mathematical description of da/dn – a is presented by introducing a parabolic-linear model in different versions for each of the steels. the model versions are verified through comparing the experimental fatigue lifetimes with those calculated by the proposed model version. keywords. rotating-bending fatigue; torsion fatigue; short fatigue-cracks; modeling of crack-growth rate. introduction t is well known that fatigue life of technical components made of high-strength materials, and subjected to high-cycle fatigue, can be dominated up to 90% by stages of initiation and propagation of microstructurally short cracks. this supports the significance of quantitative analyses of all physical mechanisms being responsible for local stress concentration, plastic deformation and, eventually, the initiation and propagation of short fatigue cracks which are very different from traditionally investigated long fatigue cracks [1, 2]. the early propagation mechanisms of short fatigue cracks are strongly related to the local microstructural features. only when the sizes of these features become small than the crack length, predictions of crack propagation rates can be made on the basis of linear-elastic fracture mechanics. fatigue long/short crack growth characteristics are normally expressed by the relation between crack growth rate and stress intensity factor range/short crack length, which involves two very different methods (by nature) for data obtaining based on different kind of specimens when observing and registering different physical cracks long cracks, and physically small and short cracks [2, 3], also the two methods concerning long and short cracks use different technical standards [4]. experimental work material and specimens. testing. n the present study, fatigue in two spring steels are investigated: (i) steel en10270-1sh/ din 17223c (steel a) for conducting own fatigue experiments, [5, 6], and proposing new mathematical models of short fatigue crack growth; and (ii) bs250a53/din 55si7 (steel b) for using some already published results, [7], describing those results by the i i d. angelova et alii, frattura ed integrità strutturale, 37 (2016) 258-264; doi: 10.3221/igf-esis.37.34 259 newly-proposed mathematical models of short fatigue crack growth, and making comparative analysis with steel a. the microstructure, chemical compositions and slightly different hour-glass shape of specimens of steel a and steel b are presented in [6, 7]. steel a. twelve hourglass-shaped specimens were subjected to symmetric cyclic rotating-bending fatigue (rbf) at different stress ranges (δσ = 800, 1000, 1200, 1400, 1500 mpa), frequency of f=11 hz and air environment. steel b. fourteen hourglass-shaped specimens were exposed to fully reversed torsion fatigue (tf), and frequency f=5 hz for two sets of stress ranges δτ = (915, 1080, 1106 mpa in air), (404, 601, 815, 900 mpa in corrosion). for both steels a traditional replication technique was used; all details are given in [6]. fatigue crack growth modeling since the beginning of the last two decades it has been well established that the fatigue behaviour of metals can be described by three distinct regimes microstructurally short cracks (msc), physically small cracks (psc) and long cracks (lc). each type of crack requires different analytical approach characterizing its behaviour, i.e. microstructural fracture mechanics (mfm), elastic-plastic fracture mechanics (epfm) and linear elastic fracture mechanics (lefm), respectively. in terms of driving stresses there exist two basically different forms of crack, a stage i crack developed by shear stresses, and a stage ii crack developed by tensile stresses. the limits of the transition zone between a propagating stage i shear crack and a continuously growing stage ii tensile crack (the psc zone) are emphasized by miller [8] as two fundamentally different threshold conditions (or barriers d1 and d2) representing a "microstructural-dependant state" and "mechaniical stress-strain-dependant state". the barrier d1 is defined by short fatigue crack experiment and d2 by long fatigue crack experiment using the same material. based upon the experimental data for short fatigue crack behaviour there are a few basic models describing it, the most known of which are those of hobson and brown [9] h-b and akid and murtaza[10] a-m, which present crack growth rate as a combined parabolic (stage i of msc) and linear (stage ii of psc and lc) functions of crack length. the h-b model (for symmetrical push-pull fatigue) consist of one parabola and one line, considering one barrier of type d1 and one, d2. the a-m model (for tf) includes four barriers of type d1 and one of type d2 for in-air fatigue; and two barriers d1 and one d2 for corrosion fatigue. the h-b and a-m models are revised by angelova [11] becoming h-b-a and a-m-a who introduces a special modelling of psc zone between a stage i shear crack and a stage ii tensile crack. in this way two important tasks were solved: a more precise description of psc behaviour; and finding the barrier of type d2 from the same short fatigue crack experiment. the complicated defining of the barriers d1 and d2, and the parabolic functions in h-b-a and a-m-a models was replaced with simplified methodic by yordanova [12] which is more convenient for practical use and a quick (express) evaluation of fatigue at keeping the basic concept for separated description of msc (parabolic function), psc (parabolic function) and lc (linear function) and conducting only short fatigue crack experiment. the new model is presented in eq.1: m(a):                iii d liips ims ndaaddndalcnddadadaddndapsc ndaadadaddndamsc ;;/:;;,;/: ;;,;/: 272165 2 4 1032 2 1 8 (1) where:      nnnnn nnaadnda   111 // is the crack growth rate da/dn; di, i=1-8 – materials constants; iiiiii nnn ,, – the corresponding number of cycles to crack regimes, msc, psc, ls; d1 and d2 – the microstructural barriers analytically determined after yordanova's methodic, described in detail in[12]. this model is supported by the comparison of the fatigue lifetime predicted by eq. (2), mfn , , and the actual fatigue lifetime, exp,fn : iiiiiifmf nnnnn  0, or in more detail, [12]: 0, fmf nn  dadnda ms d a )/(/1 1 0    dadnda ps d d )//(1 2 1 dadnda l a d f )//(1 2  (2) where 0fn is the number of cycles to crack initiation, a0 – the initial crack length and af – the final crack length. the following formulae   %,/100 exp,exp,, ffmf nnn  is used as an evaluation of the adequacy of the proposed new model and if its value is in the error band  25 %, the mathematical description is accepted as adequate. d. angelova et alii, frattura ed integrità strutturale, 37 (2016) 258-264; doi: 10.3221/igf-esis.37.34 260 results and discussion data obtained for steel a and published for steel b a and n are presented in figs. 1a, b,c respectively, and dependences “crack length, a – numbers of cycles, n”, “a–n”, plotted in the same figures. the steel a curves “a–n” for rbf, fig.1a, show that both major cracks (for δσ = 1200 and 1400 mpa) have originated first. it can be seen that the major crack in the family "major crack secondary cracks", "mc-sc", at δσ = 1400 mpa has initiated in an earlier stage in comparison with the initiation stages of all secondary cracks. at the same time the major crack and the secondary cracks in the family "mc-sc" at δσ = 1200 mpa show small difference at the number of cycles to initiation, close propagation (in terms of cycles) and a kind of competition between the secondary cracks for merging their propagation paths with that of the major crack. the surface of whole working area shows (by observation after specimen's fracture) unusual roughness, probably due to specimen polishing [5,6], confirming the strong influence of the surface-condition factor on fatigue behaviour. the curves “a–n” for steel b (tf) are plotted in fig. 1b,c. they show a major crack and only a few secondary cracks in each family "mc-sc" corresponding to a given stress range. an exception is the family "mc-sc" at δτ = 900 mpa in corrosion with several secondary cracks. the family "mc-sc" at δτ = 817 mpa in corrosion has more secondary cracks than those at δτ = 404 and 601 mpa. then the two families "mc-sc" at δτ = 817 and 900 mpa having more secondary cracks are located very closely (in terms of cycles), which shows that above δτ = 817 mpa the surface short cracks propagation and paths look like those of the family "mc-sc" of steel a at δσ = 1200 mpa. this means that nature of material is of great importance, but varying with fatigue loading and kind of scheme, environment and surface condition, it is possible to observe a similar short fatigue crack behaviour of different materials. a b c figure 1: plots “crack length, a – numbers of cycles, n” and lines d1 and d2 defining psc regime for steels: (a) a rbf; (b) & (c) b – tf an interesting fact can be mentioned. during the transition regime of psc some specific events take place: (i) as a crack grows longer at a constant cyclic stress range, its plastic zone size controlling crack growth rate, increases. d. angelova et alii, frattura ed integrità strutturale, 37 (2016) 258-264; doi: 10.3221/igf-esis.37.34 261 however, the actual onset and extent of crack tip plasticity are functions of the cyclic stress-strain curve, and its well known that normally materials having a high yield strength and exhibiting cyclic strain hardening behaviour have a small plastic zone size at crack tip, and smaller crack growth rate compared with a lower yield strength materials that cyclically soften originally mentioned by [13]. it has been shown that for a cyclic hardening material, the hardening rate is lower than the critical value which renders a continuously increasing plastic zone size relative to crack length discussed for the first time by navarro et al. [14]. (ii) during the psc regime, microstructural barriers between grains are located in both tangential and normal directions to the advancing crack front. as the crack advances past the first dominant structural barrier it will still be decelerating as it approaches subsequent barriers, but to a lesser extent, before finally accelerating as it escapes the influence of barriers at a > d2. in addition to that, at some conditions as increased stress range, rough surface, aggressive environment, the cyclic plastic behaviour of materials can be exhausted quickly, in fact there is not time enough for plasticity realization. the cases of psc regimes of steel a at δσ = 1200 mpa and steel b at δτ = 817 mpa and 900 mpa can be treated in the above mentioned way. steels a and b show a high yield strength and appearance of many secondary cracks initiating in narrow cycle interval in msc regime (stage i) of the major crack. later on these secondary cracks probably help with plasticity exhaustion in psc regime stage ii (described by epfm), influencing the behaviour of the major crack, figs. 1a, b, c. after the plasticity exhaustion and still in psc regime, the major crack transforms from shear mode into tensile mode; also do the secondary cracks. (in figs. 1a, b, c the psc regime is defined by lines showing barriers d1 and d2.) in lc regime (stage ii) some of the secondary cracks merge with the major crack. crack growth rates da/dn are calculated and presented versus crack lengths a for steel a in figs. 2, 3a, and for steel b, in fig. 4. applying the parabolic-linear model, plm, of [12], eq.1, to these data leads to obtaining of dependences “crack growth rate, da/dn – crack length a”. for steel a the values of coefficients d are shown in tab. 1, and the values of all the other fatigue characteristics, in tab. 2. a b figure 2: new parabolic-linear model “crack growth rate, da/dn – crack length a” for steel a: (a) l version, δσ=1400 mpa;.(b) comparison between l, m and n versions, δσ = 1200 mpa a b figure 3: steel a tested at δσ = 1200 mpa (l, m and n versions) and δσ =1400 mpa (l version): (a) comparison between the new parabolic-linear model; (b) comparison between experimental and predicted fatigue lifetimes and the corresponding error bands in percentages. d. angelova et alii, frattura ed integrità strutturale, 37 (2016) 258-264; doi: 10.3221/igf-esis.37.34 262 steel a. the graphical presentation of the applied plm from eq. 1 to the experimental data at δσ = 1400 mpa can be seen in fig. 2a. in this case the basic model is applied only to the major crack and is marked as version l of it. the secondary cracks have not been taken into consideration. at the same time the graphical presentation of the applied plm from eq. 1 to the experimental data at δσ = 1200 mpa is shown in fig. 2b in three versions, and is very different from that in fig. 2a stage d 1200 mpa 1400mpa 1 2 3 4 5 6 l version m version n version l version psc d4 -2.2e-05 -1.3e-05 -9.9e-06 -7. 5e-05 1 2 3 4 5 6 d5 1.4e-02 8.5e-03 6.2e-03 4.5e-02 msc d1 -2.3e-06 -5.1e-06 -3.2e-06 -9.1e-06 d6 -2.0e+0 -1.2e+0 -8.8e-01 6.5e+00 d2 7.3e-04 1.3e-03 9.7e-04 2.7e-03 lc d7 2.0e-06 2.7e-06 1.7e-06 6.5e-05 d3 -1.7e-02 -2.3e-02 -2.0e-02 -6.5e-02 d8 1.6e+00 1.6e+0 1.7e+00 1.2e+00 table 1: values of coefficients d in eq. 1 at δσ = 1200 & 1400 mpa, steel a. the version l presents crack growth rate only of the major crack. the version m shows a different behaviour of the major crack while influenced by the secondary cracks merging with it. δσ, mpa a0, μm d1, μm d2, μm af, μm n0, cycles nf,exp, cycles nf,m, cycles (nf,m – nf,exp)100/nf,exp, % 1200 l version 30 220 385 4395 20790 37840 49654 31.2 m version 41867 10.6 n version 44149 16.7 1400 l version 30 250 360 5835 4840 17380 19310 11.1 table 2: fatigue characteristics of steel a for msc, psc, lc growth and some numbers of cycles during specimen fatigue lifetime. the version n presents the major crack propagation involving all the secondary cracks. the three versions l, m and n are analytically described by eq. 1 and tabs. 1, 2. it is important to mention that for modeling different stages of the major crack propagation (msc, psc, lc), there are used only those data da/dn, a of the secondary cracks initiated or developed in the corresponding regimes of the major crack growth. the comparison between the three versions (l, m, n) of the basic plm at 1200 mpa (curves l, m and n), shown in fig. 2b, can be used for usefulinteresting discussions. the curve m shows acceleration of crack growth rates for msc and lc regimes in comparison with l and n curves, due to interaction and merge of the secondary cracks with the major crack. however in psc regime the curve m is located below the curve l although very close to it. it is connected with the multitude of secondary cracks initiated easily due to the observed surface roughness and helping with plasticity exhaustion of steel a in psc regime of the major crack; also it is connected with the specific events taking part in psc and described in 3.3. transition regime psc for steels a and b. so, we can conclude that at 1200 mpa, the version m of the basic plm most realistically represents the fatigue behaviour of steel a. at 1400 mpa there are registered only a couple of secondary cracks which merge with the major crack, figs. 1a, 2a; their influence is exerted during the third stage (lc) and practically does not affect the major crack growth behaviour; in this case the version l of plm takes place. the versions l, m, n at δσ = 1200 mpa and version l at δσ = 1400 mpa are shown together in fig. 3a. the highest crack growth rates correspond to the highest stress range. at the same time the final length of the major crack at δσ = 1200 mpa is 75% from the length of the major crack at δσ = 1400 mpa. this can be explained as a result of both, a full and quick consumption of specimen plasticity at δσ = 1200 mpa and a high degree of energy dissipation, due to initiation and development of many and more secondary cracks at that stress range, interacting and merging with the major crack. steel b. the graphical presentation of the applied plm from eq. 1 to the experimental data of steel b (subjected to tf inair and corrosion environment) can be seen in fig. 4, and the version m of plm is shown by thick line. the original model of murtaza (having 4/2 microstructural barriers of type d1 characterizing tf for in-air/corrosion environment, and d. angelova et alii, frattura ed integrità strutturale, 37 (2016) 258-264; doi: 10.3221/igf-esis.37.34 263 one of type d2) is plotted by dashed line in fig. 4, too. in fact at corrosion condition da/dn increases, figs. 4b, c; also the higher stress range plays the same role, leading to higher da/dn. as illustrated in figs. 2b, 3a, 4, a reasonable agreement can be seen when comparing experimental da/dn and theoretical ones using the new analytical model m described by eq. 1 and tabs. 1, 2 (the case when many secondary cracks have initiated and influenced the growth of major crack). the proposed new model m is supported by the comparison of predicted nf,m , eq. 2, and actual nf,exp fatigue lifetimes presented in figs. 3b and 5. a b c figure 4: fatigue crack growth curves for steel b: (a) air; (b), (c) corrosion. conclusions hort fatigue crack behavior of two spring steels was investigated and analytically modeled: steel en10270-1sh/ din 17223c (steel a) for own fatigue experiment; and bs250a53/din 55si7 (steel b) with already published fatigue data and for comparison with steel a. steel a is subjected to symmetric rotating bending fatigue in air, and steel b to fully reversed torsion fatigue in air and in corrosion environment. for steel a two cases of loading are discussed, δσ = 1200 mpa and δσ = 1400 mpa. in both cases the major surface crack originates first and develops in three regimes of propagation: msc, psc, lc. the major crack at δσ = 1400 mpa s d. angelova et alii, frattura ed integrità strutturale, 37 (2016) 258-264; doi: 10.3221/igf-esis.37.34 264 has initiated in an earlier stage than the secondary cracks and is well separated from them; it merges with only a couple of secondary cracks . at the same time the major crack at δσ = 1200 mpa propagates at condition of interaction between and with many secondary cracks in its vicinity at no big difference between their initiation stages; it leads to exhaustion of local plasticity in psc regime, crack merging (six secondary cracks merge with the major crack) and complete failure. for steel b some fatigue tests data of major and secondary cracks propagation are studied in-air and corrosion environment, considering specific features of the three regimes of major crack growth: msc, psc, lc. for both steels short fatigue crack growth behaviour is modeled on the base of hobson-brown-angelova, akid-murtazaangelova and yordanova models. three new versions of yordanova model are proposed and approved at different conditions of loading, environment and specimen surface state; a special attention has been given to psc regime of major crack propagation. the three proposed model versions are additionally supported by the comparison between the predicted and actual fatigue lifetimes. references [1] miller, k. j., metal fatigue – past, current and future. proc. inst. mech. engrs, london. (1991). [2] suresh, s., fatigue of materials. cambridge univ. press, cambridge, uk, (1998). [3] krupp, u., fatigue crack propagation in metals and alloys, wiley-vch gmbh and co. kgaa. (2007) [4] dowling ,n., mechanical behaviour of materials, prentice-hall, new jersey, usa, (2006). [5] angelova d., yordanova r., nikolova l., yankova sv., investigation on fatigue behavior and fatigue crack growth of a spring steel. part ii: mathematical description an analyses, scientific proceedings, xxi, 2(139) (2013) 244-248. [6] angelova, d., yordanova, r., lazarova, ts., yankova, sv., on fatigue behavior of two spring steels. part i: wöhler curves and fractured surfaces, 20th european conference on fracture, 30th june – 04th july, 2014, trondheim, norway. [7] murtaza, g., corrosion fatigue short crack growth behaviour in a high strength steel. phd thesis-university of sheffield, (1992). [8] miller, k. j., the two threshold of fatigue behaviour. fatigue fract. engng mater. struct., 16 (1993) 931-939. [9] hobson, p., brown, m., de los rios, e., short fatigue cracks. in: egp publication 1, mechanical engineering publications, london, (1986) 441-459. [10] murtaza, g., akid, r., modelling short fatigue crack growth in a heattreated low alloy steel. int. j. fatigue, 17 (1995) 207-214. [11] angelova, d., akid, r., a note on modelling short fatigue crack growth behaviour, fatigue & fracture of engineering materials &structures, 21 (1998) 771-779. [12] yordanova, r., modeling of fracture process in low-carbon 09mn2 steel on the bases of short fatigue crack growth experiments. comparative analyses on the fatigue behavior of other steels, phd thesis, university of chemical technology and metallurgy, bulgaria (2003). [13] miller, k. j, materials science perspective of metal fatigue resistance, mater.sci. tech., 9 (1993) 453-462. [14] navarro, a., de los rios, e., fatigue crack growth modelling by successive blocking of doslocations. proc r. soc. lond. a, 437 (1992) 375-390. << /ascii85encodepages false /allowtransparency false /autopositionepsfiles true /autorotatepages /none /binding /left /calgrayprofile (dot gain 20%) /calrgbprofile (srgb iec61966-2.1) /calcmykprofile (u.s. web coated \050swop\051 v2) /srgbprofile (srgb iec61966-2.1) /cannotembedfontpolicy /error /compatibilitylevel 1.4 /compressobjects /tags /compresspages true /convertimagestoindexed true /passthroughjpegimages true /createjobticket false /defaultrenderingintent /default /detectblends true /detectcurves 0.0000 /colorconversionstrategy /cmyk /dothumbnails false /embedallfonts true /embedopentype false /parseiccprofilesincomments true /embedjoboptions true /dscreportinglevel 0 /emitdscwarnings false /endpage -1 /imagememory 1048576 /lockdistillerparams false /maxsubsetpct 100 /optimize true /opm 1 /parsedsccomments true 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/hrv (za stvaranje adobe pdf dokumenata najpogodnijih za visokokvalitetni ispis prije tiskanja koristite ove postavke. stvoreni pdf dokumenti mogu se otvoriti acrobat i adobe reader 5.0 i kasnijim verzijama.) /hun 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can be opened with acrobat and adobe reader 5.0 and later.) >> /namespace [ (adobe) (common) (1.0) ] /othernamespaces [ << /asreaderspreads false /cropimagestoframes true /errorcontrol /warnandcontinue /flattenerignorespreadoverrides false /includeguidesgrids false /includenonprinting false /includeslug false /namespace [ (adobe) (indesign) (4.0) ] /omitplacedbitmaps false /omitplacedeps false /omitplacedpdf false /simulateoverprint /legacy >> << /addbleedmarks false /addcolorbars false /addcropmarks false /addpageinfo false /addregmarks false /convertcolors /converttocmyk /destinationprofilename () /destinationprofileselector /documentcmyk /downsample16bitimages true /flattenerpreset << /presetselector /mediumresolution >> /formelements false /generatestructure false /includebookmarks false /includehyperlinks false /includeinteractive false /includelayers false /includeprofiles false /multimediahandling /useobjectsettings /namespace [ (adobe) (creativesuite) (2.0) ] /pdfxoutputintentprofileselector /documentcmyk /preserveediting true /untaggedcmykhandling /leaveuntagged /untaggedrgbhandling /usedocumentprofile /usedocumentbleed false >> ] >> setdistillerparams << /hwresolution [2400 2400] /pagesize [612.000 792.000] >> setpagedevice microsoft word numero_39_art_18 h. xiao et alii, frattura ed integrità strutturale, 39 (2017) 181-190; doi: 10.3221/igf-esis.39.18 181 experimental analysis on physical and mechanical properties of thermal shock damage of granite he xiao institute of geotechnical engineering, chongqing jiaotong university, chongqing, 400074, china. school of geographical sciences, southwest university, chongqing, 400715, china. hhexiao123@163.com li qing school of geographical sciences, southwest university, chongqing, 400715, china. chen hongkai, tang hongmei, wang linfeng institute of geotechnical engineering, chongqing jiaotong university, chongqing, 400074, china. abstract. the purpose of this study was to explore the changes of mechanical and physical properties of granite under different thermal loading effects. uniaxial compression experiments studying the rules of the influence of temperature load on mechanical properties of granite were carried out. after high-temperature heating at above 600 °c, granite tended to have stronger ductility and plasticity as well as declined peak stress and compressive strength. thermogravimetry differential scanning calorimetry (tg-dsc) analysis results showed that, thermal load at different temperatures induced reactions such as water loss, oxidation and crystallization in the microstructure of granite, which led to physical changes of granite. hence it is concluded that, heating can significantly weaken the mechanical performance of granite, which provides an important support for the optimization of heating assisted processing of granite. it also reveals that, heating assisted cutting technique can effectively lower energy consumption and improve processing efficiency. keywords. granite; damage; differential scanning colorimetry analysis; uniaxial compression thermogravimetry analysis. citation: xiao, h., qing, l., hongkai, c., hongmei, t., linfeng, w., experimental analysis on physical and mechanical properties of thermal shock damage of granite, frattura ed integrità strutturale, 39 (2017) 181-190. received: 25.08.2016 accepted: 10.10.2016 published: 01.01.2017 copyright: © 2017 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. introduction ranite, a kind of highly hard and brittle material, is featured by high strength and stable physical and chemical performance. granite products, which look elegant and beautiful, have been widely applied in fields such as architectural ornament, precision machine tool manufacture, etc [1-3]. currently, the processing of granite g http://www.gruppofrattura.it/pdf/rivista/numero39/audio/18.mp3 h. xiao et alii, frattura ed integrità strutturale, 39 (2017) 181-190; doi: 10.3221/igf-esis.39.18 182 becomes more precise and artistic and stone machining industry develops rapidly. however, stone material is a nonrenewable resource. under the tendency that the society appeals to save industrial resources and protect environment, how to exploit and utilize stone materials efficiently has become a bottleneck in stone material industry [4-6]. ogilvie sr [7] analyzed the microstructure of granite under the condition of uniaxial compression using image analysis method and found stronger aeolotropy of internal structure. by using different test specimens, it was found that, larger anisotropy inside specimens resulted in more significant directional property in the shape of micro-grains and the grain size had a remarkable influence on macroscopic strength of specimens. under different thermal loads, real-time changes happen to temperature field and stress filed inside granite, which can result in the changes of structure and mechanical performance of granite. this study explored the rules of temperature load influencing the physical performance of granite by carrying out a thermal load difference experiment and a uniaxial compression experiment. physical properties under thermal loading n the actual grinding processing of granite, the intensive friction between cutter and workpiece generates a large amount of heat, due to the high hardness of granite. diamond crystals may lose cutting ability at the temperature above 800 °c due to carbonization. hence cutter needs to be cooled using water [8, 9]. in this experiment, the cutter was cooled using water after high-temperature heating up to 800 °c. experimental equipment and methods the workpiece used was granite g630 with a size of 100 mm × 50 mm × 20 mm. after the determination of the specification, two types of treatment named plan a and b were performed in the following. eight specimen groups were set up for each plan. in each group, five granite rectangle blocks were used. the temperature for the groups was set as 100 °c, 200 °c, 300 °c, 400 °c, 500 °c, 600 °c, 700 °c and 800 °c. heating stopped after 30 min at constant temperature. granite specimens of plan a were cooled with water for 5 min and then dried with air for 24 h, while granite specimens of plan b were cooled under natural conditions. the experimental set up is shown in fig. 1. figure 1: experimental set up. analysis of experimental results quality changes of granite after water and air cooling are shown in fig. 2. when the temperature was not higher than 400 °c, heating dried up the water stored on the surface or in the gap of the granite. when the temperature was higher than 400 °c, weight loss became more obvious. it was because that, micro-damage generated and micro-cracks increased in rocks under stress, which resulted in the evaporation of the water on the surface of rock cracks. through comparing the data of the groups treated by air cooling and thermal shock, we found that, when the temperature was lower than 500 °c, the weight loss of the granite processed by air cooling was less remarkable than that of the granite processed by water cooling. it was because that, water entered into the cracks of the workpiece during water cooling and then was stored inside after cracks closed with the decreasing of temperature. when the temperature was higher than 600 °c, the weight lost in air cooling was less than the weight lost in water cooling. it was because of the excessive loss of crystal water caused by the sharp increase of micro-cracks of the granite. i h. xiao et alii, frattura ed integrità strutturale, 39 (2017) 181-190; doi: 10.3221/igf-esis.39.18 183 figure 2: mass changing rate after heating. figure 3: volume changing rate after heating. figure 4: density changing rate after heating. grains with different compositions, structures and coefficients of linear expansion expand when the granite is heated at certain temperature. as a result, the stress inside the rock exceeds yield strength limit of grains, thus causing damage on crystal. therefore, cracks grow in the place where stress concentrates or preexisting defects generate and expand. when the temperature exceeds 400 °c, the internal stress increases sharply and the number and length of cracks increase faster, which indirectly results in the expansion of the granite. h. xiao et alii, frattura ed integrità strutturale, 39 (2017) 181-190; doi: 10.3221/igf-esis.39.18 184 it can be noted in fig. 3 that, when the temperature exceeded 400 °c, the volume expansion rate of the granite processed by water cooling was higher than that of the granite processed by air cooling. it was because that, the sharp decreasing of temperature outside rocks led to the significant temperature gradient inside and outside rocks, and cracks expanded when the stress inside grains exceeded the yield limit. the above findings suggest that, increasing temperature gradient can promote the expansion of cracks and the generation of new cracks, which is beneficial to refine grains. it can be noted in fig. 4 that, when the thermal temperature was not higher than 400 °c, the rock density declined slightly. it was because of the evaporation of both free water in granite cracks and the expansion of micro-cracks of the granite. when the temperature exceeded 400 °c, micro-cracks further expanded, a large number of preexisting defects generated and expanded, and some crystal water was separated out, leading to the further decrease of density. uniaxial compression test experimental equipment and methods his experiment was carried on an electro-hydraulic servo universal testing machine [10, 11]. the selected hydraulic cylinder had a maximum axial output of 2000 kn and a piston movement speed of 0 ~ 85 mm/min. the axial loading of the cylinder sample which was cooled down after high temperature heating was controlled by the displacement generated by the hydraulic cylinder. axial loading was performed on cylinder samples by means of hydraulic cylinder displacement control. an axial compression load was exerted under a constant displacement speed up to 0.001 mm/s till samples collapsed and lost the weight-carrying ability. then a force-displacement curve was output. after numerical conversion, a stress-strain curve and parameters such as elastic modulus were obtained. experimental procedure the heating processing and heating speed of the uniaxial compression test were the same as those of the thermal load difference experiment. the heating temperature was set as 200 °c, 400 °c, 600 °c and 800 °c. after temperature preservation for 30 min, the granite was taken out and then cooled with normal temperature water for 5 min. then the granite specimens were dried up with air at normal temperature for 24 h. there were totally five groups. in each group, there were three cylinder granite specimens. a uniaxial compression test was performed on the fully cooled samples. the experimental process is shown in fig. 5. figure 5: experimental process. analysis of experimental results fig. 6 shows the axial stress-strain curve of the cylinder granite processed by different heating temperatures. the stressstrain curve of the granite could be divided into five stages. (a) compression stage (oa) in this stage, most of the preexisting defects except cracks, whose initial arrangement direction was parallel to axial stress, were compressed to close and the slope of the axial strain curve increased gradually. compression deformation in this stage was nonlinear: the structure and properties of the rock had no reversible changes and were at an equilibrium state when loading and unloading experiments were carried out in this area. whether this stage was distinct or not depends on the density and initial distribution direction of preexisting defects. (b) elastic stage (ab) as most of the preexisting defects were compressed in the last stage, the stress in this stage, though, could promote relative sliding between crack surfaces, but was not large enough to promote the expansion of cracks. therefore, rock samples could be regarded as linear and isotropous elastic deformation bodies. the slope of axial strain and horizontal t h. xiao et alii, frattura ed integrità strutturale, 39 (2017) 181-190; doi: 10.3221/igf-esis.39.18 185 strain remained unchanged. in this stage, there was no macro irreversible process and the deformation state was uniform. hence the elastic stage was at an equilibrium state. (c) initial growth stage (bc) with the increase of stress, new cracks developed in the site where the tip and local stress of the preexisting defects concentrated. the stress in this stage was 20% ~ 40% of the peak stress. but as the number of cracks was limited, the deformation of the specimens was still approximate to elastic deformation. (d) stable growth stage (cd) with the increase of load, some cracks which had closed began to open and even expand when the stress was 36% ~ 90% of peak stress. some weak grain boundaries generated new cracks. both the original cracks and the new cracks expanded towards the direction parallel (or approximately) to the maximum major stress. in this stage, horizontal strain curve deviated from the original direct line and the growth speed of horizontal strain was faster than that of axial stress. therefore, volume growth speed slowed down, which meant that dilatation occurred. cyclic loading and uploading experiments suggested that, the generated permanent deformation could be ignored when axial stress was loaded to a level higher than 90% of the peak stress and then unloaded. such a phenomenon could be observed under different confining pressures. hence, it was considered that, the granite was still in a state of elastic deformation in the stable growth stage of cracks, but elastic modulus and poisson ratio had been deteriorated due to the stable expansion of micro-cracks. (e) post-peaking stage (de) the micro-fracture surface inside rocks developed into a connective structural surface. when the exerted load was larger than the bearing capacity of rock samples, deformation became severer and friable rocks might even burst. as shown in fig. 6, when the heating temperature was set between normal temperature and 400 °c, the stress-strain curve of samples suggested that, the deformation was similar to elastic deformation. when the load reached the peak stress, stress sharply declined, leading to the crushing of the rock body. nearly no plastic deformation happened. when the temperature was between 600 °c and 800 °c, the rock body showed obvious plastic deformation; the samples at that moment still had certain bearing ability, but became soften when the stress slowly declined and the strain rapidly increased. finally, the samples were damaged after severe deformation. with the increase of thermal loading temperature, the compressive strength of the granite gradually declined. combining with the heating processing results, we found the increase of micro-cracks of rocks resulted in the reduction of overall bonding area of grains, and intergranular cracks were more likely to generate during loading, considering the decline of strength. figure 6: stress-strain curves of granite specimens heated at different temperatures in uniaxial compression test. through comparing the stress-strain curves of granite specimens heated at different temperatures, it can be noted that, with the increase of heating temperature, the strain capacity of the granite increased, peak stress decreased, overall elasticbrittle performance weakened and ductile-plastic performance strengthened. when the heating temperature was lower h. xiao et alii, frattura ed integrità strutturale, 39 (2017) 181-190; doi: 10.3221/igf-esis.39.18 186 than 400 °c, the stress-strain curve of samples was similar to the curve of deformation of brittle materials. brittle damage occurred to rock samples when stress reached the peak value, and the stage of elastic deformation did not last long. when the temperature was higher than 600 °c, the rock body showed significant plastic deformation and strengthened ductility. strain of rock samples increased rapidly after the stress reached the peak value, and then the stress decreased slowly. eventually, the deformation similar to plastic deformation happened. effects of temperature on peak stress-strain and elastic modulus changes of microstructure of granite heated at different temperatures were reflected as the decrease of both macro-peak stress and elastic modulus and the increase of strain. (1) changes in peak stress of granite fig. 7 shows the changes of uniaxial compressive strength of granite σbc along with the increase of heating temperature. results with relatively large deviation caused by personal error, instrumental error and calculation error were removed; the average values of the remaining peak stress points were calculated and connected with a line. it can be noted in fig. 7 that, when the temperature was not higher than 200 °c, compressive strength was above 90 % of compressive strength of granite at normal temperature, showing no obvious reduction. it suggested that, internal thermal stress and thermal damage were small and compressive strength showed no significant decreasing when the temperature was lower than 200 °c. when the temperature reached 400 °c, compressive strength decreased from 98 mpa to 78 mpa. when the temperature reached 600 °c or 800 °c, compressive strength sharply decreased to 62 mpa and 30 mpa respectively, and consequently the compressive strength was 64% and 30% that of granites at normal temperature, respectively. when the temperature was higher than 400 °c, mineral grains inside samples expanded and cracks rapidly grew under the effect of internal stress, which resulted in the remarkable decrease of compressive strength. figure 7: relationship between compressive strength and heating temperature. (2) changes of peak strain of granite fig. 8 shows the curve for the relationship between compressive peak strain of granite and heating temperature after water cooling. the average peak strain value of temperature gradient in different groups was calculated and then a curve was drawn. with the increase of heating temperature, peak strain of granite tended to be higher. when the temperature was not higher than 200 °c, mineral grains inside rocks expanded and preexisting defects gradually closed. when the temperature was higher than 200 °c and continued to increase, thermal expansion became more and more intensive. due to the different compositions and forms of grains, coefficient of linear expansion was also different. therefore, interaction generated between grains promoted the intensive expansion of preexisting defects at the point where stress concentrated. when the temperature was lower than 400 °c, peak strain increment was relatively small; but when temperature exceeded 400 °c, peak strain increment suddenly increased. peak strain increment at temperature 600 °c and 800 °c was 66.7% and 94.5%, respectively. on one hand, higher temperature resulted in stronger thermal motion of molecules inside rocks and the active molecular motion weakened the combination of grains, which led to high risks of sliding deformation of grains and generation of more intergranular micro-cracks. on the other hand, with the increase of temperature, the action force between grains strengthened, leading to the increase of stress concentration points which exceeded grain ultimate strength and sharp increase of transgranular cracks. as a result, the number and area of micro h. xiao et alii, frattura ed integrità strutturale, 39 (2017) 181-190; doi: 10.3221/igf-esis.39.18 187 crack inside rocks increased rapidly and peak strain increment during uniaxial compression became larger, generating an increase of compressive deformation of rock samples at macro level. figure 8: the relationship between peak strain and heating temperature. (3) changes of elastic modulus of granite elastic modulus, e, could be obtained by fitting approximate straight line segment on the stress-strain curve before peak stress. the elastic modulus of granite against the increase of temperature is shown in fig. 9. such a figure suggests that, elastic modules of granite gradually declined with the increase of temperature. when the temperature was not higher than 200 °c, such a decreasing was not remarkable, but when the temperature was higher than 400 °c, elastic modulus declined rapidly. at 400 °c and 600 °c, elastic modulus reduced by 50% and 75% respectively. elastic modulus of granite heated at above 800 °c was only 10% that of elastic modulus of granite at normal temperature. the above curve indicates that, high temperature had a significant influence on the elastic modulus of granite, reflected as decreased rigidity and strengthened plasticity. figure 9: the relationship between elastic modulus and heating temperature. granite contains multiple mineral components. different thermal expansion coefficients of various mineral particles and different thermoelastic properties of different crystalline orientations of anisotropic grains induce uncoordinated thermal expansion across grain boundary, which results in tensile stress or pressure stress between grains or inside grains. the generated stress promotes the generation of micro-cracks. during high temperature heating, both constraining force promoting and inhibiting deformation between mineral grains lead to the increase of micro-cracks in granite. structure thermal stress induced by temperature can cause damages to rock structure and thus weaken rock strength. in these tests, g603 cylinder granite with a diameter of 60 mm and a height/diameter (h/d) of 2 was used. diameter of 50 mm and h/d of 2 are usually regarded as the calculation basis of tests in most studies in china and abroad. therefore, h. xiao et alii, frattura ed integrità strutturale, 39 (2017) 181-190; doi: 10.3221/igf-esis.39.18 188 we applied size amend coefficient kd in the calculation of standard elastic modulus value of the sample. standard size amend coefficient of diameter of 60 mm was 1.033. standard elastic modulus could be obtained by amending elastic modulus measured, as shown in tab. 1. temperature t/°c elastic modulus e[mpa] 20 17.18 200 14.37 400 8.95 600 4.33 800 1.64 table 1: standard elastic modulus obtained after amendment. thermal analysis of granite hermal analysis is defined as a technology for analyzing the relationship between physical properties of substances and temperature by international confederation for thermal analysis (ic-ta). thermal analysis includes therogravimetry (tg), derivative thermogravimetry (dtg), differential thermal analysis (dta), differential scanning calorimetry (dsc), thermomechanic analysis (tma), evolved gas analysis (ega) and thermal expansion analysis. among them, tg, dta and dsc are the ones commonly used. the theory of thermal analysis can be simplified as: p f t( ) (1) where t refers to temperature which is a function of time, and p stands for a physical property (function of temperature) of tested samples. dsc [12-14] and tg were used in this experimental campaign. tg [12-14] is mainly used for analyzing the relationship between substance quality and temperature. tg can be used for understanding thermal reaction of substance, for example, loss of crystal water and quality changes induced by changes of structure or crystalline state in thermal decomposition reaction. dsc [15, 16] is a technology used for measuring the relationship between the power difference of substance and reference compound and temperature. the deviation of curve from baseline represents the speed of heat absorption or heat release (unit mj/s). the area surrounded by peak or valley in a curve represents changes of heat. in this test, a differential thermal analyzer was used to make thermal analysis on powder particles of granite, with which, tg curve and dsc curve can be obtained. performance index of the analyzer was: sensitivity < 0.2 µg. room temperature during heating was about 1500 °c. in the test, grey white granite grains were used. the granite was grinded into even fine powder, with an initial weight of 13.1 mg and the weight turned to be 12.6 mg when the powder was heated from 20 °c to 1000 °c with an increasing speed of 10 k/min. it can be seen from fig. 10 that, the dsc curve and tg curve had three obvious heat absorption valleys and three obvious weight loss steps. the first heat absorption valley of the dsc curve appeared at 55 °c; when the temperature was 55 °c, water adhered on the surface of micro-crack of granite evaporated under the effect of heat, and weight loss rate was 0.21%. the second heat absorption valley appeared at 200 °c; water adhered on the surface of micro-cracks of granite evaporated under the effect of heat and the weight loss rate was 0.69 %. moreover, interlayer water of granite was dehydrated in this stage. heat release peak at temperature from 250.4 °c and 466.7 °c was smooth and heat release peak at temperature 264.7 °c was the highest; the weight loss rate was 1.49% in this stage. crystal water of mineral crystal lattice lost when the temperature was between 590.7 °c and 670.4 °c; a weight loss rate of 3.87% appeared though there was no significant heat exchange. when the temperature exceeded 800 °c, mineral crystal lattice was damaged and showed phase change. a heat absorption valley appeared at 890 °c on the dsc curve. t h. xiao et alii, frattura ed integrità strutturale, 39 (2017) 181-190; doi: 10.3221/igf-esis.39.18 189 we can know from physical and chemical changes of granite during heating that, absorbed water and interlayer water on the surface or in the cracks of granite evaporated when the heating temperature was between 100 °c and 200 °c. microcrack inside granite lost support and closed due to the loss of interlayer water, which led to increased density and stronger mechanical performance of the granite. when the temperature was between 200 °c and 466.7 °c, oxidation and crystallization reaction occurred to granite, i.e., granite released heat and lost much weight. when the temperature was between 466.7 °c and 800 °c, granite lattice lost crystal water and thus much weight lost; temperature had a large span in this stage, but there was no obvious thermal exchange. moreover, in this stage, macro-mechanical performance of granite significantly decreased, cracks of grains grew rapidly and severe thermal damage generated. when the temperature exceeded 800 °c, silica grains inside granite showed phase changes, mica melted, the structure of granite was severely damaged, and mechanical performance intensively declined. figure 10: dsc-tg curve of granite. conclusion n this study, on the premise of not considering homogeneous polycrystal, mechanical performance under different temperatures was obtained through carrying out heat processing experiment and uniaxial compression experiment. the increase of temperature resulted in lower density, volume expansion, decrease of compressive strength and elastic modulus and increase of peak strain. with the increase of temperature, more weight of granite lost, cracks grew and crack volume increased due to the concentration of internal stress, leading to the permanent expansion of macro-volume and a density decrease. when the heating temperature exceeded 600 °c, the ductility and plasticity of granite strengthened, peak stress declined and compressive strength of granite declined. tg-dsc analysis showed that, thermal load induced reactions such as water lost, oxidation and crystallization in the microstructure of granite specimens, resulting in the changes in physical properties of rocks. the research results of this study reveal that, heating can significantly lower mechanical performance of granite, which provides an important data support for the optimization of heating assisted processing of granites. moreover, heating assisted cutting technology is proved to be effective in reducing energy consumption and improving processing efficiency. acknowledgement ational sciences foundation of china (no: 51378521, 51408084); fundamental research funds for the central universities (no: xdjk2015c069, xdjk2012b004); doctoral foundation of southwestern university (no. swu111058). i n h. xiao et alii, frattura ed integrità strutturale, 39 (2017) 181-190; doi: 10.3221/igf-esis.39.18 190 references [1] yarmolyuk, v.v., kozlovsky, a.m., sal’nikova, e.b., et al., contribution of alkaline granite magmatism to the formation of the khangai batholith: geological and geochronological evidence, journal of clinical investigation, 305(20) (2011) 2069-2070. [2] palin, r.m., searle, m.p., waters, d.j., et al., a geochronological and petrological study of anatectic paragneiss and associated granite dykes from the day nui con voi metamorphic core complex, north vietnam: constraints on the timing of metamorphism within the red river shear zone. journal of metamorphic geology, 31(4) (2013) 359–387. [3] li, x.c., fan, h.r., santosh, m., et al., hydrothermal alteration associated with mesozoic granite-hosted gold mineralization at the sanshandao deposit, jiaodong gold province, china. ore geology reviews, 53(8) (2013) 403421. [4] mezadre, s.d.b.b., bianco, m.d.f., polishing knowledge: a study of marble and granite processing. bar brazilian administration review, 11(3) (2014) 302-322. [5] abreu, c.m., covelo, a., díaz, b., et al., electrochemical behaviour of iron in chlorinated alkaline media. the effect of slurries from granite processing. journal of the brazilian chemical society, 18(6) (2007) 1158-1163. [6] guillén, j., tejado, j.j., baeza, a., et al., environmental impact of a granite processing factory as source of naturally occurring radionuclides. applied geochemistry, 47(8) (2014) 122-129. [7] ogilvie, s.r., glover, p.w.j., the petrophysical properties of deformation bands in relation to their microstructure. earth & planetary science letters, 193(s 1–2) (2001) 129-142. [8] rao, z., wang, s., zhang, g., simulation and experiment of thermal energy management with phase change material for ageing lifepo 4 power battery. energy conversion & management, 52(12) (2011) 3408-3414. [9] strunz, p., gilles, r., mukherji, d., et al., dependence of small-angle neutron scattering contrast on the difference in thermal expansions of phases in two-phase alloys. journal of applied crystallography, 42(6) (2007) 981–989. [10] wang, c.g., liang, y.s., liu, x.j., et al., electro-hydraulic servo system modeling and dynamic performance analysis of mechanics of rock materials testing machine. advanced materials research, 765-767 (2013) 1867-1872. [11] zhang, t.j., yu, s.h., ren, j.h., et al., the emd analysis ae signals of rock failure under uniaxial compression. applied mechanics & materials, 571-572 (2014) 845-852. [12] schick, c., differential scanning calorimetry (dsc) of semicrystalline polymers. analytical & bioanalytical chemistry, 395(6) (2009) 1589-1611. [13] arockiasamy, a., german, r.m., wang, p., et al., dsc analysis of al6061 aluminium alloy powder by rapid solidification. journal of thermal analysis & calorimetry, 100(1) (2010) 361-366. [14] alves, m.b., umpierre, a.p., santos, v.o., et al., the use of differential scanning calorimetry (dsc) to characterize phase diagrams of ionic mixtures of 1-n-butyl-3-methylimidazolium chloride and niobium chloride or zinc chloride. thermochimica acta, 502 (2010) 20-23. [15] parthasarathy, p., narayanan, k.s., arockiam, l., study on kinetic parameters of different biomass samples using thermo-gravimetric analysis. biomass & bioenergy, 58(5) (2013) 58-66. [16] rekondo, a., irusta, l., fernández-berridi, m.j., characterization of silanized poly (ether-urethane) hybrid systems using thermogravimetric analysis (tg). journal of thermal analysis & calorimetry, 101(1) (2010) 331-337. << /ascii85encodepages false /allowtransparency false /autopositionepsfiles true /autorotatepages /none /binding /left /calgrayprofile (dot gain 20%) /calrgbprofile (srgb iec61966-2.1) /calcmykprofile (u.s. web coated \050swop\051 v2) /srgbprofile (srgb iec61966-2.1) /cannotembedfontpolicy /error /compatibilitylevel 1.4 /compressobjects /tags /compresspages true /convertimagestoindexed true /passthroughjpegimages true /createjobticket false /defaultrenderingintent /default /detectblends true /detectcurves 0.0000 /colorconversionstrategy /cmyk /dothumbnails false /embedallfonts true /embedopentype false /parseiccprofilesincomments true /embedjoboptions true /dscreportinglevel 0 /emitdscwarnings false /endpage -1 /imagememory 1048576 /lockdistillerparams false 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can be opened with acrobat and adobe reader 5.0 and later.) >> /namespace [ (adobe) (common) (1.0) ] /othernamespaces [ << /asreaderspreads false /cropimagestoframes true /errorcontrol /warnandcontinue /flattenerignorespreadoverrides false /includeguidesgrids false /includenonprinting false /includeslug false /namespace [ (adobe) (indesign) (4.0) ] /omitplacedbitmaps false /omitplacedeps false /omitplacedpdf false /simulateoverprint /legacy >> << /addbleedmarks false /addcolorbars false /addcropmarks false /addpageinfo false /addregmarks false /convertcolors /converttocmyk /destinationprofilename () /destinationprofileselector /documentcmyk /downsample16bitimages true /flattenerpreset << /presetselector /mediumresolution >> /formelements false /generatestructure false /includebookmarks false /includehyperlinks false /includeinteractive false /includelayers false /includeprofiles false /multimediahandling /useobjectsettings /namespace [ (adobe) (creativesuite) (2.0) ] /pdfxoutputintentprofileselector /documentcmyk /preserveediting true /untaggedcmykhandling /leaveuntagged /untaggedrgbhandling /usedocumentprofile /usedocumentbleed false >> ] >> setdistillerparams << /hwresolution [2400 2400] /pagesize [612.000 792.000] >> setpagedevice shot peening processes to obtain nanocrystalline surfaces in metal alloys: j.-f. he et alii, frattura ed integrità strutturale, 42 (2017) 263-271; doi: 10.3221/igf-esis.42.28 263 study on the abrasion property of the anvil inside a hydraulic dth hammer fitted with horizontal oriented sliders jiang-fu he state key laboratory of coal mine disaster dynamics and control, college of resources and environmental science, chongqing university, chongqing 400030, china post-doctoral research station of mineral engineering, chongqing university, chongqing 400030, china hejf2016@cqu.edu.cn; http://orcid.org/ 0000-0002-6581-9709 qi-lei yin*, kun yin college of construction engineering, jilin university, no. 6 ximinzhu str., chaoyang district, changchun, 130021,china yinql_jlu@126.com, yinkun@jlu.edu.cn abstract. hydraulic hammers have been extensively applied to horizontal directional well drilling in hard rock formations. however, the service life of a hydraulic hammer is still unsatisfactory due to the heavy wear or abrasion of the horizontal anvil, which leads to the failure and the reduction of service life in directional well drilling. in order to improve the performance life of a hydraulic hammer, the new type of anvil with a horizontal oriented slider has been designed. the abrasion property of the horizontal oriented slider have been numerically simulated and analyzed by finite element analysis. simulation and experimental results have shown that the abrasion rate exponentially varies with the mass of the anvil and the friction coefficient of horizontal oriented slider, nevertheless the abrasion rate of horizontal anvil is almost logarithmically varies with moving velocity of oriented slider. the maximum abrasion rate of horizontal oriented sliders will exceed 4% while moving velocity of the horizontal anvil is larger than 3m/s. while the mass of the anvil is 100kg, the maximum abrasion rate of horizontal oriented slider is 7.5‱. however, the maximum abrasion rate of a horizontal oriented slider will be up to 16.5% while the friction coefficient is more than 0.2. keywords. horizontal oriented slider; hydraulic hammer; anvil; abrasion rate; directional well drilling. citation: he, j.-f., yin,.q., yin, k., study on the abrasion property of a hydraulic hammer with horizontal oriented sliders, frattura ed integrità strutturale, 42 (2017) 263-271. received: 20.05.2017 accepted: 13.08.2017 published: 01.10.2017 copyright: © 2017 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. introduction s a percussive and rotary drilling tool, the hydraulic dth hammer with a fluidic amplifier has been extensively applied to geological core drilling, hydrological well drilling, trenchless drilling, oil and gas well drilling [1, 2]. due to the high penetration rate, low occurrence of drilling accidents and excellent borehole quality in drilling, the a j.-f. he et alii, frattura ed integrità strutturale, 42 (2017) 263-271; doi: 10.3221/igf-esis.42.28 264 hydraulic hammer with a fluidic amplifier has also been regarded as the most efficient drilling tool in hard rock or complicated formations [3-5]. with the rapid development of drilling technology, the application of hydraulic hammers with a fluidic amplifier has been extended to horizontal directional well drilling in recent years, which contributes to the development of trenchless drilling technology of oil-gas pipeline construction in hard rock and complicated formations. unlike the conventional vertical hole drilling with hydraulic hammers, horizontal directional well drilling demands the anvil horizontally impact the drill bit while the hydraulic dth hammer is in operation, which aggravates the abrasion of hydraulic hammer and leads to the reduction of service life of hydraulic dth hammers. in order to improve the penetration rate and drilling cost of hard rock formations, the hydraulic hammer has been initially proposed and designed in former soviet union, and a proven efficiency of 40% has been achieved with new generation of hydraulic hammer. afterwards, yuri and andrei conducted relevant field tests to improve the efficiency of the hammer in us, which leads to the development of hydraulic hammer [6]. allowing for the cost reduction and technological advantages in deep or medium-to-hard rock formations, d. pixton and d. hall have proposed the advanced mud hammer system, and the prototype of the hammer system have also been developed and reported [7]. however, no extra introduction of this mud-actuated hammer has been reported with respect to the field application results and service life time. therefore, the new type of hydraulic dth hammer with a horizontal oriented slider has been urgently designed and applied to horizontal directional well drilling in order to improve the service life of hydraulic dth hammers. moreover, the abrasion property of hydraulic dth hammers with horizontal oriented sliders should be intensively studied with respect to the application of hydraulic dth hammers to horizontal directional well drilling. while in horizontal directional well drilling with hydraulic dth hammers, the piston is actuated by powered muds, which drives the hammers horizontally and reciprocally impact the drill bit. however, the service life of hydraulic dth hammers is unsatisfactory due to the reciprocating motion of anvil with high frequency, which deteriorates the performance of hydraulic dth hammers in horizontal directional oil-gas well drilling [8]. in order to improve the service life of hydraulic dth hammers in horizontal directional well drilling, a specialized anvil with horizontal oriented sliders has been designed, as shown in fig. 1. the material of slider has been optimized, and totally 6 sliders are embedded into the anvil, which contributes to reducing the abrasion of hydraulic dth hammer. furthermore, the abrasion property of horizontal oriented slider has numerically analyzed by finite element analysis, which indicates the design and optimization of hydraulic hammers in horizontal directional well drilling. figure 1: structure of hydraulic dth hammers with horizontal oriented slider. in previous studies, the service life of a hydraulic dth hammer has been analyzed by drilling crews and researchers while in vertical or up-down drilling. c.w. li has analyzed the effect of material property of hydraulic hammer on its service life time in 2002, and numerical models of damage mechanism are established [9]. ding daipo has improved the service life of hydraulic dth hammers up to 120h while in oil-gas well drilling [10]. meanwhile, series of experiments on abrasion property of hydraulic dth hammers in vertical well drilling have been conducted by he liu in 2014 on the basis of finite element analysis (fea), which numerically and practically contributes to improving the service life of hydraulic dth hammers [4]. in addition, the abrasion process of abrasive particle is numerically analyzed by wu jinghua et al., which could theoretically illustrate the behavior of abrasive impacting [11]. furthermore, li weitao has optimized the hydraulic dth hammer by numerical analysis on the fluidic amplifier in order to improve the service life of hydraulic dth hammers [10]. some other related work has been finished with different experiments and apparatus in order to improve the service life of hydraulic hammers in various drilling conditions [13, 14]. j.-f. he et alii, frattura ed integrità strutturale, 42 (2017) 263-271; doi: 10.3221/igf-esis.42.28 265 however, there are no corresponding researches on the improvement of service life of hydraulic dth hammer in horizontal directional well drilling since the numerical modelling technique in drilling engineering has been popularized throughout the world [15]. in addition, no new type of hydraulic hammer with anti-abrasive slider has been existed in horizontal directional well drilling or trenchless drilling. thus, the research on anti-abrasive property of hydraulic dth hammers should be conducted in order to improve the service life of hydraulic hammers while in horizontal directional well drilling. the study of hydraulic dth hammers on the abrasion property of a horizontal oriented slider is an efficient way to improve the service life time of hydraulic hammers, including numerical simulation and experimental analysis. in this paper, numerical models of the anvil inside hydraulic dth hammers have been developed with several groups of oriented sliders, and different friction coefficients (different material of oriented slider) of horizontal oriented sliders, various mass and moving velocity of the anvil have been denoted as the variables in fea simulation. in end, the abrasion rate of oriented slider in hydraulic hammers has been obtained by fea, which promotes the improvement of service life time of hydraulic hammers with a horizontal oriented slider while in directional well drilling. methodology and abrasion theory nlike vertical well drilling or up-down well drilling, the working principle of hydraulic dth hammers with oriented sliders in horizontal directional well drilling is distinguished. meanwhile, the abrasion theory of oriented sliders has also been presented. working principle of hydraulic hammers with horizontal oriented slider while drilling a horizontal directional well with a hydraulic dth hammer, the operation principle of the hydraulic hammer with horizontal oriented sliders is shown as fig 2. figure 2: schematic diagram of a hydraulic hammer with the horizontal anvil. c, e: discharge channel; d, f: controlled flow channel the pumped mud with high pressure and velocity was initially delivered to the nozzle through the drilling pipe, which is termed as the pressure inlet. then the mud is sprayed by the nozzle to generate a wall-attachment effect with high mud speed. it has been provided that the mud is attached to the back chamber (as shown in yellow pipe line), thus the piston then is actuated by high pressure mud to horizontally impact the drill bit. in the meantime, the controlled channel f is stimulated by a pressure pulse while the piston with the anvil moves to the right dead point, simultaneously the discharge channel of high pressure mud is shifted from channel e to channel c, and the mud is instantaneously pumped into the ante-chamber of the cylinder (as shown in green pipe line), which actuates the piston to move back to return strokes. the whole working process of the hydraulic hammer rapidly and periodically completes in hundreds of a second. therefore, the reciprocating impact energy transmission can be obtained by the periodic exchange of pumped mud in ante-chamber and back chamber. in addition, the circulating mud in back chamber and ante-chamber will be discharged through the channel c and channel e, which is termed as the pressure outlet. then it will be discharged to the annular space between the cylinder and drilling pipes. u j.-f. he et alii, frattura ed integrità strutturale, 42 (2017) 263-271; doi: 10.3221/igf-esis.42.28 266 abrasion theory the complete abrasion theory was proposed by archard, and was optimized by rowe in 1995 [16-18]. while the hydraulic dth hammer is operated in horizontal directional well drilling, the oriented slider is reciprocally abraded by external cylinder with high frequency. the volumetric wearing capacity v can be derived from eq. 1, which is closely related to the friction coefficient, lubrication coefficient and the load. β αµ= + 2(1 )m wl v k h (1) where, mk , α denotes the constant, dimensionless; β denotes the lubrication coefficient, dimensionless; µ denotes the friction coefficient, dimensionless; w denotes the applied load of oriented slider, mpa, and h denotes the brinell hardness, hbw. the formula of abrasion theory is feasible to the wear of horizontal oriented sliders, thus the friction coefficient, applied load and the moving velocity of oriented slider were employed as the variables while in the simulation of abrasion property of the anvil with horizontal oriented slider. fea simulation here are totally 3 variables used in the simulation, which are friction coefficient, moving velocity and applied load, respectively. each variable has at least 5 models in numerical simulation. in order to obtain the abrasion rate of the anvil inside hydraulic dth hammers with horizontal oriented slider, the numerical modelling, meshing and solving process are successfully completed. numerical modelling and meshing as shown in fig. 3, the numerical model of the anvil with oriented sliders was developed by software ansys 2014 according to the parameter of a 203mm hydraulic dth hammer. the material models of external cylinder and oriented slider were defined as 35crmo and teflon with carbon fiber, respectively. there are totally 6 horizontal oriented sliders are evenly distributed along the outer circle of the anvil, and the parameter of oriented slider is ×80 36mm mm . in end, 3 groups of material models are established in whole, as shown in tab. 1. figure 3: numerical model and meshes of a hydraulic dth hammer with horizontal oriented sliders. the numerical model was quarterly symmetric in order to reduce the computational time. in addition, the deformation of oriented slider and external cylinder is defined as plane strain problem. the numerical model was meshed with 3d structure cell solid 185, and the contact cells between oriented slider and external cylinder are defined as contact 174. furthermore, the grids of contact region should be refined, which contributes to the improvement of simulation results. thus the grids type of contact region was defined as surface-to-surface contact, which is termed as target 170 in ansys, as shown in fig. 4. the cells of horizontal oriented slider are in red, and the cells of external cylinder are in blue. t j.-f. he et alii, frattura ed integrità strutturale, 42 (2017) 263-271; doi: 10.3221/igf-esis.42.28 267 materials (slider/external cylinder) applied load (mpa) friction coefficient (m/s) temperature (℃) 35crmo/ptfe 50～70 0.01～0.03 -180～250 35crmo/pom 50～70 0.15～0.35 -180～260 35crmo/p-ni 0～715 0.1 -180～200 table 1: property of numerical models of hydraulic hammers with horizontal oriented sliders. there are totally 42318 elements in each of numerical model, and the meshed grids are hexahedrons, which are obtained by sweep meshing of ansys. all of the meshed grids are volume grids with a maximum diameter of 3mm, and the grid coordination is excellent. the maximum grid deviation is 5%, which guarantees the accuracy of simulation results. the meshed elements of a horizontal oriented slider are shown as fig. 3. boundary conditions and solver settings in order to reduce the computational time, the numerical model was simplified with horizontal friction force, and other extra loads were ignored, such as hydraulic pressure, fluids resistance and buoyance of drilling mud. moreover, the boundary condition of contact region between horizontal oriented slider and external cylinder is simplified as wetting boundary conditions. in addition, the initial load on oriented sliders was applied with 1kn, and friction coefficient between oriented slider and external cylinder is denoted as 0.02. once all numerical models were finishing computing, the abrasion rate of hydraulic hammer has been obtained, which is helpful to optimize the structure design of hydraulic dth hammers with horizontal oriented sliders. figure 4: contact cells between horizontal oriented slider and external cylinder. with regard to the solver settings of numerical simulation with horizontal oriented sliders, there are totally 1000 time steps were set. the details of solver settings are as shown in tab. 2. thus the abrasion property of hydraulic hammers with horizontal oriented sliders can be obtained with various material models and boundary conditions. results and discussions he abrasion property of a hydraulic hammer with horizontal oriented sliders has been numerically modeled by fea simulation. especially the moving velocity of the anvil, the mass of anvil or applied load, and the friction coefficient of horizontal oriented sliders have been separately analyzed with various numerical models. meanwhile, t j.-f. he et alii, frattura ed integrità strutturale, 42 (2017) 263-271; doi: 10.3221/igf-esis.42.28 268 the related experiments are conducted in order to improve the service life of hydraulic dth hammers while in horizontal directional well drilling. in end, the abrasion rate of hydraulic hammer with horizontal oriented sliders is obtained, and the abrasion property of horizontal oriented sliders is discussed according to numerical simulation results. meshes no. 42318 friction coefficient 0.02 applied loads (kn) 1 total steps 1000 time step 2 convergence coefficient 0.5 moving velocity of hammer (m/s) 3 table 2: details of boundary condition and solver settings. effects of hammer mass on abrasion property of hydraulic hammer with oriented sliders as shown in fig. 5, the von-mises stress of oriented sliders has been obtained. while the mass of the anvil is 60kg, the main stress of oriented sliders is approximately 6mpa. it can be implied that the main stress of horizontal oriented sliders is nearly linearly increasing with the raise of anvil mass. while the mass of the anvil exceeds 100kg, the main stress of oriented sliders will exceed 9mpa, which will reduce the working performance of hydraulic hammer with horizontal oriented sliders. thus the abrasion between horizontal oriented sliders and external cylinder has been increased while the applied stress of oriented sliders is increasing. therefore, the mass of anvil should be less than 100kg while in horizontal directional well drilling with hydraulic hammer, which contributes to improvement and optimization on the design of hydraulic hammer with horizontal oriented sliders. figure 5: effect of anvil mass on the von-mises stress of hydraulic hammer with horizontal oriented sliders. meanwhile, the variation of anvil mass on the abrasion property of hydraulic hammer with horizontal oriented sliders is shown as fig. 6. the lighter the impact hammer is, the abrasion rate of oriented sliders will be, and the service life of hydraulic hammer with horizontal oriented sliders will be longer. it can be concluded that the abrasion rate of oriented sliders is approximately exponentially increasing the augment of hammer mass. the maximum abrasion rate of horizontal oriented sliders is 7.5‱, which meets the requirements of impact energy of hydraulic hammer while in horizontal j.-f. he et alii, frattura ed integrità strutturale, 42 (2017) 263-271; doi: 10.3221/igf-esis.42.28 269 directional well drilling. in addition, the maximum abrasion rate deviation of horizontal oriented sliders with various mass of anvil is less than 1‱, thus the effects of anvil mass on the abrasion property of the hydraulic hammer is acceptable. figure 6: variation of anvil mass on the abrasion property of hydraulic hammer with horizontal oriented sliders. effects of moving velocity of the anvil on abrasion property of horizontal oriented sliders as shown is fig. 7, the abrasion property of a horizontal oriented slider is affected by the moving velocity of the anvil, which is corresponding to the specification of impact energy of hydraulic hammer. it can be concluded that the abrasion rate of a hydraulic hammer with horizontal oriented sliders is almost logarithmically varies with the moving velocity of the anvil. while the moving velocity of the anvil and horizontal oriented slider is 1m/s, the minimum abrasion rate of oriented slider is nearly 1.8%. the abrasion rate of horizontal oriented slider sharply varies with the increase of moving velocity. while the moving velocity of the anvil and oriented slider exceeds 3m/s, the maximum abrasion rate of horizontal oriented sliders will be up to 4%, which would have a significant effect on the service life of hydraulic hammers with horizontal oriented sliders. figure 7: variation of moving velocity on the abrasion property of hydraulic hammer with horizontal oriented sliders. the actual simulation results are slightly different with the fitted abrasion rates. the maximum deviation between simulation results and the logarithmically fitted abrasion rate is less than 2%, which is tolerable in real time operation of hydraulic hammers with horizontal oriented sliders. meanwhile, the abrasion rate of horizontal oriented sliders is smaller, j.-f. he et alii, frattura ed integrità strutturale, 42 (2017) 263-271; doi: 10.3221/igf-esis.42.28 270 the longer service life of the hydraulic hammer will be. in order to improve the service life of hydraulic hammer with horizontal oriented sliders, the moving velocity of the anvil should be less than 4m/s, thus the abrasion rate of oriented sliders in horizontal directional or vertical well drilling is acceptable. according to the filed application results of the hydraulic hammer with horizontal oriented sliders, the abrasion of the anvil inside the hydraulic hammer will be dramatically aggravated while the moving velocity of the anvil exceeds 3m/s [19]. thereby the simulation results have shown extraordinary agreements with the actual cases of hydraulic hammer in directional well drilling. it can be suggested that the moving velocity of the anvil with horizontal oriented sliders should be significantly controlled in horizontal directional well drilling, which contributes to the improvement of service life of hydraulic hammer with horizontal oriented sliders. effects of friction coefficient on the abrasion property of horizontal oriented sliders the effect of friction coefficient of the anvil on abrasion rate of horizontal oriented slider has been numerically analyzed by fea method. as shown in fig. 8, it can be concluded that abrasion rate of oriented sliders is approximately exponentially increases with the friction coefficient of oriented sliders. while the friction coefficient between oriented sliders and external cylinder exceeds 0.2, the maximum abrasion rate of oriented slider will be up to 16.5%, which seriously reduce the service life of hydraulic hammers in horizontal directional well drilling. while the friction coefficient of horizontal oriented sliders is less than 0.05, the minimum abrasion rate of oriented sliders is much more considerable. therefore the design of hydraulic hammers with oriented sliders is qualified due to the friction coefficient of ptfe with carbon fiber is 0.02. figure 8: variation of friction coefficient on the abrasion property of hydraulic hammer with horizontal oriented sliders. the service life of hydraulic hammers is severely influenced by friction coefficient of oriented sliders in horizontal directional well drilling. once the horizontal oriented sliders are abraded, the horizontal alignment among piston, the anvil and oriented sliders will be damaged, which will lead to the failure of hydraulic hammer with oriented sliders in horizontal direction well drilling. thereby the friction coefficient of horizontal oriented sliders must be controlled in order to reduce the abrasion rate of hydraulic hammer with horizontal oriented sliders. conclusions have been drawn that the friction coefficient of oriented sliders should be less than 0.2 in order to improve the service life of the hydraulic hammer with oriented sliders in horizontal directional well drilling. conclusions 1) hydraulic hammer with horizontal oriented sliders have been designed, and corresponding numerical models have been developed to investigate the effects of anvil mass, friction coefficient and moving velocity of the anvil on abrasion rate of oriented sliders. j.-f. he et alii, frattura ed integrità strutturale, 42 (2017) 263-271; doi: 10.3221/igf-esis.42.28 271 2) the maximum abrasion rate of horizontal oriented sliders is 7.5‱ while the anvil mass is 100kg, otherwise the abrasion rate will be up to 4% while the moving velocity of the anvil inside hydraulic hammers exceeds 3m/s. 3) the service life of hydraulic hammers is severely influenced by friction coefficient of horizontal oriented sliders, and the friction coefficient must be less than 0.2 while in horizontal directional well drilling. 4) new type of hydraulic hammer with oriented sliders is qualified in horizontal directional well drilling, which contributes to the improvement on service life of hydraulic dth hammers. acknowledgments he authors thank to the supports from the project funded by china postdoctoral science foundation (project no. 2017m612916) and the china pipeline research institute of cnpc, china petroleum natural gas pipeline bureau (project no. 2014220101001321), which are gratefully acknowledged. the authors also express their thanks to hou-ping liu and yanli liu for their precious help. references [1] yin, k., wang, m, et al., percussive and rotary drilling, geological publishing press, beijing, (2010). [2] li, s.-z., drilling and exploring technology, geological publishing press, beijing, (1989). [3] han, g., bruno, m., lao, k., percussion drilling in oil industry: review and rock failure modeling, the aade national technical conference and exhibition, houston, usa, (2005). [4] liu, h., yin, k., peng, j.m., yin, q.l., fracture failure analysis of baseplates in a fluidic amplifier made of wc-11co cemented carbide, rattura ed integrità strutturale, 27 (2014) 53-65. [5] melamed, y., kiselev, a., gelfgat, m., dreesen, d., blacic, j., hydraulic hammer drilling technology: developments and capabilities, j. energ. resour. technol., 122(1) (2000) 1-8. [6] melamed, y., kiselev, a., gelfgat, m., et. al., hydraulic hammer drilling technology: developments and capabilities. journal of energy resources technology, 122(01) (2003). [7] pixton, d., hall, d., advanced mud hammer system. novatec. inc. 2185 south larsen parkway, provo, ut. [8] he, j., zhao, x., kun, y. et al., application of a fluidic amplifier to horizontal directional well drilling. asia-pacific energy equipment engineering research conference, atlantis press, 60-63 (2015). [9] chuanwu, l., fadong, l., hai, r. j., applications of hydraulic operated hammers in pilot hole drilling of kezuan-1 well, petroleum drilling techniques, 30(5) (2002). [10] daipo, d., research on the working life of key accessory of oil drilling impacting machine, master thesis, jilin university, (2008). [11] jinghua, w., wencheng, t., liyi, z., numerical analysis of impacting behavior of abrasive particle, machine tool and hydraulics, 36(9) (2008) 2-77. [12] weitao, l., the experiment and research on the working life of the liquid jet amplifier of the hydraulic hammer, master thesis, jilin university, (2004). [13] qingyan, w., kun, y., et al., development and application of hydrokinetic hammer’s simulation technique, petroleum drilling technique, 36(1) (2008) 45-49. [14] tesar, v., hung, c.-h., zimmerman, w. b., no-moving-part hybrid-synthetic actuator, sensors and actuators a: physical, 125 (2006) 159-169. [15] xingkun, g., zhengyi, s., hongxuan, l., application and prospect of computer simulation technique in drilling engineering, (2007) 118-121. [16] ting, j., huaping, y., hui, y., numerical simulation of the process of friction and wear, lubrication engineering, 38(12) (2013) 88-92. [17] huaisong, c., study of numerical simulation on reciprocating wear under boundary lubrication condition, master’s theses, technical university of wuhan, (2005). [18] zhongyong, g., wubin, x., et al., experimental study and analysis of wear and abrasion of rails, steel, 37(8) (2002) 5357. [19] he, j., theoretical and experimental research on hydraulic hammer with application to horizontal directional well drilling in hard rocks, thesis, jilin university, china, (2016). t microsoft word numero 9 notiziario frattura ed integrità strutturale, 9 (2009) notiziario igf 153 n. 20 luglio 2009 in questo numero 1) editoriale del presidente igf; 2) verbale dell’assemblea annuale dei soci 2008; 3) verbali dei consigli di presidenza; 4) resoconto delle attività igf 2008-09 5) resoconto delle attività tc-esis 2008-09; 6) prossime attività igf; 7) calendario congressi internazionali ; 8) esis procedures and documents (www.esisweb.org) 9) modulo di iscrizione igf-esis. editoriale del presidente l gruppo italiano frattura compie quest’anno 26 anni e festeggia a torino, dove è nato nel lontano 1981 presso uno studio notarile nelle vicinanze del politecnico di torino, il 20 congresso nazionale. l’associazione in tenera età ha avuto e prosperato spinta non solo dal fervore di colleghi universitari, ma soprattutto dall’entusiasmo di molti ricercatori provenienti dal mondo della ricerca industriale, quasi scomparsa oggi in italia. un forte stimolo allora veniva certamente posto dal nucleare con le problematiche relative alla sicurezza strutturale e alle quali la meccanica della frattura poteva fornire validi strumenti e nuove certezze. da allora si sono succeduti 5 presidenti, prima del sottoscritto, ed a parte la finestra della presidenza reale, dal 1994 al 1998, si è vista una presenza al vertice igf dal 1988 ad oggi di colleghi del politecnico di torino. il mio primo approccio all’igf è datato 1994, l’allora decimo congresso igf tenutosi anche in quella circostanza a torino. la mia elezione in consiglio di presidenza è avvenuta due anni dopo, in occasione del 12° congresso a parma. da allora, per ben tredici anni ho cercato di aiutare il gruppo spinto soprattutto da un forte entusiasmo. un grosso impegno per il gruppo è stato quello di organizzare il congresso mondiale icf, sempre a torino nel 2005, anno in cui sono succeduto alla presidenza del gruppo ad alberto carpinteri. il post congresso è stato uno dei periodi più cupi del gruppo. risultava difficile ripartire con attività routinarie dopo la sbronza di un evento di tale importanza, che aveva drenato praticamente tutte le attenzioni per sette anni. la mia acclamazione a presidente (senza votazione in quel di bologna nel 2004) è stata forse motivata dalla necessità di trovare qualcuno con l’esperienza acquisita all’interno di igf e che potesse in tale frangente far ripartire l’associazione con un consiglio di presidenza fortemente rinnovato. le prime riunioni sono state invero abbastanza strane. del vecchio consiglio eravamo rimasti in 4: il sottoscritto, lo storico del gruppo, donato i presidente igf giuseppe ferro politecnico di torino dipartimento di ingegneria strutturale e geotecnica corso duca degli abruzzi, 24, 10129, torino tel. 011-5644885, fax 011-5644899; ferro@polito.it segretario igf – curatore notiziario francesco iacoviello università di cassino dipartimento di meccanica, strutture, ambiente e territorio via g. di biasio 43, 03043 cassino (fr) tel./fax 07762993681; iacoviello@unicas.it mailto: ferro@polito.it mailto: iacoviello@unicas.it http://www.gruppofrattura.it frattura ed integrità strutturale, 9 (2009) notiziario igf 154 firrao, la colonna portante degli ultimi credo 20 anni, angelo finelli, e stefano beretta, mio compagno di avventura nell’esis. i nuovi: franco furgiuele, francesco iacoviello, roberto frassine, francesca cosmi e lorenza barsanti ci guardavano con aria un pò perplessa per capire quali obiettivi porci e come organizzare il lavoro. i primi tre anni (20042007) come detto sono stati veramente duri. nel secondo biennio, nel quale a lorenza è subentrato mario guagliano abbiamo inserito il turbo. il consiglio (mi verrebbe di chiamarlo il gruppetto) di presidenza si è amalgamato in modo perfetto, e anche se l’impegno profuso dai singoli non sia stato omogeneo, la serenità e la fiducia reciproca instauratasi ha permesso agli stacanovisti (iaco e angelo fra i più) di poter lavorare a fondo per raggiungere dei livelli e degli obiettivi onestamente non molto credibili agli inizi. fra le varie attività che mi onoro di aver portato a termine (con il durissimo, costante ma a detta dell’interessato, giocoso lavoro del segretario iaco) spicca la rivista “frattura e integrità strutturale”, rivista completamente online, tra le prime in italia e forse in assoluto e che ha superato i 9000 downloads dalla sua nascita. non è da meno il sito del gruppo (gruppofrattura.it), all’interno del quale siamo riusciti a inserire gli atti di tutti i congressi igf e dagli ultimi due anche tutte le presentazioni video, collezionando circa 800 papers. alcuni di questi, soprattutto i più antichi, hanno a mio avviso anche una certa valenza storica. in particolare i giovani ricercatori possono desumere da essi quali passi avanti ci siano stati elativamente alle basi teoriche della meccanica della fattura, ma anche quali siano stati i progressi da un punto di vista dell’informatica. nei prossimi anni l’igf si troverà ad affrontare due sfide cruciali: il ritorno del nucleare in italia che aprirà scenari nuovi e probabilmente con opportunità mai avute nel recente passato e icm-11 (international conference on materials) che si terrà a como nel giugno del 2011, che costituisce uno dei più importanti congressi nell’ambito dei materiali, portato in italia dai colleghi milanesi e che vedrà l’igf come al solito protagonista nell’organizzazione dell’evento. davanti a questo scenario, visti i miei pressanti impegni sia come segretario esis, sia come vice rettore del politecnico e visto il mio crescente impegno in qualità di esperto che sto ricoprendo da qualche tempo al consiglio superiore dei lavori pubblici, impegni che non mi hanno permesso di svolgere con il consueto rigore e disponibilità di tempo, il mio impegno come presidente igf, sentiti i colleghi del consiglio di presidenza, ho deciso che sia meglio per l’igf lasciare la presidenza. tale decisione è stata anche motivata dall’idea che una più rapida rotazione delle cariche sociali eviti una fossilizzazione dei ruoli e un maggior coinvolgimento dei membri del consiglio di presidenza alla vita dell’associazione. credo che sia importante far capire anche all’esterno che il gruppetto di consiglieri che ha operato nella fase di ricostruzione dell’igf sia formato da un gruppo di amici, dove non esiste una gerarchia precostituita e dove solo con l’impegno di tutti ci si può porre più ambiziosi obiettivi, primo fra tutti quello della rivista internazionale, “acta fracturae”, che da anni ho in mente ma che solo con il lavoro di un gruppo molto coeso può vedere la luce. auguro un futuro radioso per il gruppo, e spero di poter contribuire con qualche consiglio di vecchio saggio ai futuri successi. alè igf. avanti così e in bocca al lupo al futuro presidente. il presidente igf giuseppe ferro verbale assemblea dei soci del 5 novembre 2008 la riunione ha inizio alle ore 15.15 presso il politecnico di torino, con il seguente ordine del giorno: approvazione ordine del giorno; approvazione del verbale dell’assemblea dei soci del 2 luglio 2007; comunicazioni del presidente; relazione annuale del presidente; relazione del tesoriere ed approvazione del bilancio consuntivo 2007; relazione dei revisori dei conti; indirizzi dell’attività dell’associazione nell’anno 2008-09; previsione finanziaria e quota associativa 2009; varie ed eventuali risultano presenti i seguenti consiglieri: cosmi, ferro (presidente), finelli, furgiuele, firrao, guagliano, iacoviello . sono presenti i seguenti soci: bagheri fard, carboni, di cocco, piacente, valentini, http://www.gruppofrattura.it frattura ed integrità strutturale, 9 (2009) notiziario igf 155 punto 1 all’o.d.g.: approvazione ordine del giorno. l’assemblea dei soci approva l’ordine del giorno punto 2 all’o.d.g.: approvazione del verbale dell’assemblea dei soci del 2 luglio 2007 l’assemblea dei soci approva il verbale dell’assemblea dei soci del 2 luglio 2007. punto 3 all’o.d.g.: comunicazioni del presidente il presidente non ha comunicazioni. punto 4 all’o.d.g.: relazione annuale presidente il presidente presenta all’assemblea l’attività svolta durante il 2008. questa ha visto: l’organizzazione presso l’università di trieste dal 21 al 24 luglio 2008 della prima summer school igf elasticity and stress contentration a new way of thinking (relatore il prof. yukitaka murakami), con oltre 50 partecipanti. contestualmente a tale evento, sono state anche presentate le attività dei dottorandi. i lavori sono stati raccolti in un volume digitale dal titolo giovani ricercatori igf 2008. l’organizzazione a torino della giornata igf dal titolo “fatica ad altissimo numero di cicli” il 5 novembre con circa 70 partecipanti; lo sviluppo del sito web igf con quasi 700 paper inseriti; l’implementazione del sito in un formato “open access” harvestabile, ovvero non solo disponibile su web, ma effettivamente reperibile: il risultato è l’inserimento del database igf all’interno di oltre 40 biblioteche digitali; l’implementazione di una webtv igf. al momento sono stati inseriti gli ultimi 4 eventi igf con oltre 70 videoregistrazioni (lezioni e presentazioni scientifiche) la pubblicazione del numero 6 della rivista ufficiale igf on-line frattura ed integrità strutturale. punto 5 all’o.d.g.: relazione del tesoriere ed approvazione del bilancio consuntivo 2007 il tesoriere angelo finelli da lettura della relazione, con data 30 aprile 2008: l’anno trascorso ha finalmente portato ossigeno alle casse del gruppo. l’organizzazione di framcos-6 infatti, grazie al volontariato degli addetti ai lavori ed all’oculatezza nelle spese, ha fruttato un attivo di circa 50 mila euro che saranno divisi fra i cinque organizzatori dell’evento. voglio qui rimarcare che il successo economico di questo evento è stato realizzato a fronte di un numero di partecipanti non certo elevato (270 paganti a vario titolo) e senza minimamente lesinare sulle spese di catering ed ospitalità. relativamente al framcos-6 rimangono ancora pendenti la redistribuzione dei 4/5 dell’attivo ai coorganizzatori e, non ancora contabilizzata ma già inserita nel calcolo dell’attivo, una “donazione” di € 3000 a “international association for fracture of concrete structures”. questo successo ha permesso di saldare il debito con esis, fare fronte ai costi iniziali per la realizzazione del nuovo sito web del gruppo e, non da ultimo, coprire le spese necessarie alle varie gabelle per la registrazione della nostra rivista. un sostanziale pareggio ha invece registrato il convegno igf 19 magistralmente organizzato dal nostro vice-presidente presso il politecnico di milano. come ormai di abitudine, l’andamento del mercato borsistico, ha, ancora una volta, sconsigliato il realizzo dei fondi investito in titoli. su decisione dell’assemblea di catania del 2002, a bilancio viene comunque riportato il capitale inizialmente versato a cui viene detratto il valore di un prelievo effettuato nel 2003. il conto profitti o perdite verrà quantificato al momento di un eventuale completo realizzo. come si può notare dal rendiconto economico, l’anno finanziario 2007 pur con i limiti dovuti alle partite framcos-6 ancora in atto, porta il capitale del gruppo da € 61.106,88 a € 93.183,20 il giro di affari della gestione 2007, rilevabile dal bilancio consuntivo, è stato invece di € 427.955,52. un’ultima considerazione di tipo economico (what else): l’utilizzo della posta elettronica per l’invio della newsletter, del notiziario e degli avvisi relativi agli eventi ha permesso di eliminare spese di stampa e postali non indifferenti. queste però sono state in gran parte sostituite da altre spese necessarie alla manutenzione ed aggiornamento del sito web che rappresenta per noi, in questo momento, un significativo ed insperato strumento di visibilità attivo anche a livello internazionale. il poter continuare su questa strada necessita pertanto ancora delle nostre idee e delle nostre iniziative che dovranno essere sostenute sia dalla capacità di reperire sponsorizzazioni, sia dalla volontà di lavorare assieme per il conseguimento dei risultati sperati. l’assemblea dei soci approva all’unanimità. punto 6 all’o.d.g.: relazione dei revisori dei conti il segretario francesco iacoviello da lettura della relazione dei revisori dei conti, v.m. sglavo e g. demelio, con data 30 aprile 2008: il bilancio 2007 chiude con entrate per € 194.416,29 e uscite per € 162.340,97. tenendo conto dell'avanzo di € 61.106,88 della gestione precedente, la presente gestione si chiude con un avanzo di € 93.183,20 che è stato iscritto alla voce bilancio del giornalmastro all'inizio dell'anno 2008 nel corso dell'anno 2007 abbiamo verificato che la contabilità del gruppo è stata tenuta regolarmente e che gli adempimenti fiscali del gruppo http://www.gruppofrattura.it frattura ed integrità strutturale, 9 (2009) notiziario igf 156 sono stati regolarmente ottemperati. riteniamo pertanto che il bilancio rifletta conti sinceri in accordo con la realtà dell'associazione e vi invitiamo ad approvarlo. l’assemblea dei soci approva all’unanimità punto 7 all’o.d.g.: indirizzi dell’attività dell’associazione nell’anno 2008-09 per quanto riguarda le attività previste nel prossimo anno, il presidente propone le date del 22, 23 e 24 giugno 2009 per lo svolgimento a torino, presso il castello del valentino del prossimo congresso nazionale igf xx. l’assemblea dei soci approva all’unanimità. il 9 ed il 10 marzo 2009 è previsto a forni di sopra (ud) il workshop dal titolo “progettazione a fatica di giunzioni saldate (...e non)”. l’organizzazione è già in fase avanzata, con la data limite dell’invio dei sommari per il 15 novembre 2008. guagliano ha proposto una giornata di studio sul tema "trattamenti superficiali e tensioni residue nella progettazione meccanica", da tenersi nella prima metà di novembre 2009 presso il campus bovisa del politecnico di milano. l’assemblea dei soci approva all’unanimità. punto 8 all’o.d.g.: previsione finanziaria e quota associativa 2009 l’assemblea approva all’unanimità di lasciare immutata la quota associativa anche per il 2009 (ammontante a 30 €, comprensiva della quota iscrizione esis). punto 9 all’o.d.g.: varie ed eventuali non essendovi varie ed eventuali, il presidente scioglie l’assemblea alle ore 17.00. verbali dei consigli di presidenza consiglio di presidenza del 27 gennaio 2009 la riunione ha inizio alle ore 14.00 del 27 gennaio 2009 presso la sede di metallurgia dell’università di roma “sapienza”, via eudossiana 18, con il seguente ordine del giorno: comunicazioni workshop “forni di sopra” convegno nazionale torino organizzazione sessione tematica nella prossima “conferenza nazionale sulle prove non distruttive, monitoraggio, diagnostica” (roma 15-17 ottobre) organizzazione sessione congiunta del prossimo congresso aias (torino 9-11 settembre) oppure aitem (7-9 settembre) attività igf 2010 varie ed eventuali risultano presenti i seguenti consiglieri: ferro (presidente), beretta, cosmi, finelli, firrao, frassine, furgiuele, iacoviello. partecipa inoltre luca susmel in qualità di organizzatore della prossima giornata igf. punto 1 all’o.d.g.: comunicazioni il tesoriere finelli comunica al consiglio il rendiconto economico 2008. cosmi trasmette al consiglio il pieghevole del prossimo “8th youth symposium on experimental solid mechanics”, che si terrà in ungheria il prossimo 20-23 maggio, per l’inserimento nel calendario del sito igf. contestualmente comunica al consiglio che la nona edizione (2010) si terrà a trieste e che lei coordinerà il comitato organizzatore locale. guagliano, via mail, ricorda al consiglio la disponibilità ad organizzare una giornata dal titolo provvisorio “frattura, fatica e sforzi residui” nel mese di novembre 2009. punto 2 all’o.d.g.: workshop “forni di sopra” luca susmel descrive al consiglio le attività intraprese fino al momento. sono previste 25 memorie, di cui tre invitate (lazzarin, sonsino e james). tre aziende contribuiscono sponsorizzando l’evento per un ammontare complessivo di 2400 euro. si propone di distribuire i lavori mediante penne usb, oltre ovviamente alla loro pubblicazione nel sito istituzionale. susmel e iacoviello raccoglieranno preventivi per penne da 1 e 2 gb, da utilizzare anche in occasione del prossimo convegno nazionale. iacoviello provvederà alla produzione del volume digitale ed alla sua pubblicazione nel sito. punto 3 all’o.d.g.: convegno nazionale igf xx (torino) http://www.gruppofrattura.it frattura ed integrità strutturale, 9 (2009) notiziario igf 157 il consiglio stabilisce all’unanimità le date relative al prossimo convegno nazionale igf di torino: 17.03.2009: invio abstract 15.04.2009: accettazione abstract 18.05.2009: invio memorie 24-26 giugno 2009: convegno 25 giugno: assemblea dei soci le memorie invitate saranno tenute da david taylor e da franz-josef ulm. punto 4 all’o.d.g.: organizzazione sessione tematica nella prossima “conferenza nazionale sulle prove non distruttive, monitoraggio, diagnostica” (roma 15-17 ottobre) iacoviello da lettura della mail inviata da marco sarti contenente la proposta per l’igf di organizzare una sessione tematica per il prossimo congresso aipnd (roma 15-17 ottobre). il consiglio aderisce alla proposta, delegando beretta all’organizzazione di detta sessione. punto 5 all’o.d.g.: organizzazione sessione congiunta del prossimo congresso aias (torino 9-11 settembre) oppure aitem (7-9 settembre) iacoviello da lettura della mail inviata da renzo capitani contenente la proposta per l’igf di organizzare una sessione congiunta all’interno dei prossimi eventi aias (torino 9-11 settembre) oppure aitem (torino 7-9 settembre). il consiglio decide di proporre a renzo capitani l’organizzazione di una sessione congiunta all’interno del prossimo convegno aias. punto 6 all’o.d.g.: attività igf 2010 giornata igf su “frattura, fatica e sforzi residui”: considerato il fitto calendario degli impegni previsti per il 2009, il consiglio decidere di chiedere a guagliano la disponibilità a spostare l’organizzazione di detta giornata ai primi mesi del 2010. scuola estiva 2010: francesca cosmi conferma la disponibilità della sede di trieste ad organizzare la scuola estiva anche nel 2010 e propone di associare l’evento “giovani ricercatori igf 2010” al convegno “9th youth symposium on experimental solid mechanics” di cui sarà organizzatrice. il consiglio approva unanimamente la proposta. punto 9all’o.d.g.: varie ed eventuali. non ci sono varie ed eventuali. il presidente scioglie il consiglio alle ore 16.30. consiglio di presidenza del 7 maggio 2009 la riunione ha inizio alle ore 11.00 del 7 maggio 2009 presso i locali del castello del valentino, politecnico di torino, via mattioli 39, con il seguente ordine del giorno: comunicazioni organizzazione convegno nazionale torino, 24 – 26 giugno 2009 organizzazione sessione tematica nella prossima “conferenza nazionale sulle prove non distruttive, monitoraggio, diagnostica” (roma 15-17 ottobre) organizzazione sessione congiunta del prossimo congresso aias (torino 9-11 settembre) attività igf 2010 varie ed eventuali risultano presenti i seguenti consiglieri: ferro (presidente), beretta, finelli, firrao, furgiuele, guagliano, iacoviello. punto 1 all’o.d.g.: comunicazioni guagliano ricorda al consiglio la disponibilità ad organizzare una giornata dal titolo provvisorio “frattura, fatica e sforzi residui” nel periodo febbraio-marzo 2009. punto 2 all’o.d.g.: organizzazione convegno nazionale torino, 24 – 26 giugno 2009 iacoviello riferisce che ad oggi sono stati ricevuti 32 sommari, relatori invitati compresi. il programma del convegno viene quindi articolato come segue: 24 giugno 17.00 – 18.00 registrazione 18.00 – 18.40 memoria invitata (ulm) 18.40 – 20.15 sessione 20.15 – 21.30 cena presso il castello del valentino 21.30 – 22.30 fuochi d’artificio in onore di san giovanni 25 giugno 9.00 – 10.00 registrazione 10.00 – 10.15 saluti http://www.gruppofrattura.it frattura ed integrità strutturale, 9 (2009) notiziario igf 158 10.15 – 11.00 memoria invitata (taylor) 11.00 – 13.00 sessione 13.00 pranzo 14.30 – 17.10 sessione 17.10 – 17.30 coffee break 17.30 – 19.30 assemblea dei soci 20.00 cena sociale 26 giugno 9.00 – 9.45 memoria invitata (firrao) 9.45 – 11.00 sessione 11.00 – 11.15 coffee break 11.45 – 13.00 sessione 13.00 – 13.15 chiusura lavori e’ stata quindi contattata la locale caffetteria per il pranzo del 15, delegando ferro e finelli per gli accordi finali. e’ stato delegato ferro per organizzare i coffee break, la cena del 14 nel castello e la cena sociale. per quanto riguarda la sessione serale, è stata contattata la persona che gestisce i locali del castello che ha garantito la presenza del tecnico e del portiere per la serata del 24 giugno. considerato il successo riscosso dalla distribuzione degli atti durante l’ultima giornata igf di forni di sopra (penne usb da 2 gb), il consiglio decide di non procedere alla stampa cartacea degli atti, ma continuare a distribuirli con dette penne (sia con formato sfogliabile che come pdf) ed utilizzando il sito web istituzionale. iacoviello fa notare che il formato b5 utilizzato fino a questo momento per gli atti dei convegni igf non si presta ad una comoda visualizzazione mediante pc. l’assemblea decide quindi di utilizzare il formato a4, conservando una impaginazione simile a quella già adottata per la rivista igf. punto 3 all’o.d.g.: organizzazione sessione tematica nella prossima “conferenza nazionale sulle prove non distruttive, monitoraggio, diagnostica” (roma 15-17 ottobre) beretta riferisce che al momento sono pervenute 4 memorie per la sessione igf. punto 4 all’o.d.g.: organizzazione sessione congiunta del prossimo congresso aias (torino 9-11 settembre) beretta e furgiuele comunicano che al momento sono previste 10 memorie per la sessione igf. il consiglio ringrazia beretta e furgiuele per l’impegno, prevedendo un forte supporto durante dette sessioni al fine di pubblicizzare al meglio l’igf e le sue attività. punto 5 all’o.d.g.: attività igf 2010 giornata igf dal titolo “sforzi residui” guagliano conferma la disponibilità ad organizzare detta giornata nei primi mesi del 2010. il consiglio approva, delegando guagliano a definire al più presto la data possibile al fine di iniziare al più presto la pubblicizzazione dell’evento. giornate igf beretta e finelli comunicano la possibilità di organizzare due differenti giornate igf da tenersi nel 2010. il consiglio li delega a definire ulteriormente i termini dell’organizzazione, identificando al più presto il soggetto ed un possibile programma. scuola estiva 2010 nel calendario delle attività igf del 2010 è già presente la scuola estiva “giovani ricercatori igf 2010”, da organizzare a trieste associata al convegno “9th youth symposium on experimental solid mechanics” di cui sarà organizzatrice cosmi. sono da definire al più presto le date in modo da poter iniziare la pubblicizzazione. punto 6 all’o.d.g.: varie ed eventuali. non ci sono varie ed eventuali. il presidente scioglie il consiglio alle ore 15.00. resoconto delle attivita’ igf 2008-09 giornata igf “fatica ad altissimo numero di cicli”, torino 5 novembre 2008 sei relatori, numerosi partecipanti fra cui molti dottorandi, la giornata ha consentito sia di produrre un volume di atti digitalizzato, che di ampliare la disponibilità della webtv igf. http://www.gruppofrattura.it frattura ed integrità strutturale, 9 (2009) notiziario igf 159 workshop igf “progettazione a fatica di giunzioni saldate (… e non)”, forni di sopra (ud) 9-10 marzo 2009 oltre venti presentazioni, più di cinquanta iscrizioni, il successo dell’iniziativa è sicuramente dovuto all’impegno degli organizzatori locali, bruno atzori e luca susmel. gli atti sono stati distribuiti utilizzando come supporto delle penne da 2 gb. oltre al volume degli atti disponibile nel sito, ed all’ampliamento della disponibilità della webtv igf, il workshop ha permesso di ottenere un numero dedicato della rivista igf (luglio 2009). sito igf in quest’ultimo anno sono aumentati notevolemente i contenuti del sito. i lavori disponibili e reperibili in pdf sono prossimi ad ottocento, mentre, per quanto riguarda i video disponibili in streaming, i lavori registrati durante il xx convegno igf consentono di superare ampiamente la soglia di cento. il numero di accesi è costantemente in crescita, sia dall’italia che dall’estero, ed i principali motori di ricerca inseriscono i contenuti del sito fra le prime dieci risposte per molte chiavi di ricerca (ad esempio, “frattura” oppure “integrità strutturale”). rivista igf “frattura ed integrità strutturale” la rivista è arrivata al numero 9 (luglio 2009), ed è disponibile on line secondo tre diferenti formati: singolo pdf, portfolio pdf e versione sfogliabile. gli articoli pubblicati nell’ultimo anno sono venticinque. da segnalare che diversi autori non sono soci igf, ed altri ancora sono stranieri. resoconti delle attivita’ tc-esis 2008-09 ecf17 17th european conference on fracture multilevel approach to fracture of materials, components and structures the 17th european conference on fracture (ecf17) took place in brno, czech republic, in september 2-5, 2009 (the official website ecf17.fme.vutbr.cz). the conference chairmen were prof. jaroslav pokluda from the brno university of technology and dr. petr lukas from the institute of materials physics, czech academy of sciences in brno. the co-organizer of this periodical conference, traditionally held under the auspices of the european structural integrity society (esis), was the czech chapter of esis in brno. more than 400 participants from 42 countries all over the world presented 280 oral and 63 poster contributions in 9 parallel sections during the whole conference time. scientific program a number of high-level contributions dealing with a multi-scale modeling of deformation and fracture as well as experimental works introducing facilities of extreme resolutions and unique capabilities have been presented. the plenary key-notes were given by world leaders in fracture and fatigue: z. p. bazant (evanston), l. botvina (moscow), y. estrin (melbourne), t. kitamura (kyoto), a. j. mcevily (storrs), y. murakami (fukuoka), j. newman (mississippi state), j. petit (futuroscope), t. palin-luc and p. c. paris (talence cedex), k. wallin (espoo), g. williams (london) and m. zehetbauer (vienna). other 12 invited talks were given as section key-notes. all presentations were published in the book of abstracts and the proceedings (cd rom). the best sixty papers were selected for a possible publication in special issues of the scientific journals engineering fracture mechanics, international journal of fatigue and engineering failure analysis that will be devoted to ecf17. these special issues are under preparation and will appear in autumn 2009. accompanying sessions in the frame of ecf17, a number of important meetings of international scientific authorities took place as, for example, the esis council, the esis executive committee, the icf executive committee and esis technical committees. moreover, sessions of editorial boards of several scientific journals published in elsevier, springer and willey-blackwell have been in progress during the conference time. thus, many very important personalities exercising over the field of fracture and fatigue were present, e.g. prof. k. ravi-chandar, prof. e. gdoutos, prof. d. taplin, prof. a. carpinteri, dr. m. elboujdaini, prof. r. v. goldstein, prof. k-h. schwalbe, prof. l. bank sills, prof. a. neimitz, prof. g. ferro, prof. s. beretta, etc. social events three social events were organized during the conference evenings. the first one, the welcome party, was associated with registration of arriving participants. the second one, the banquet, was aimed as the opportunity to meet the local political leaders. the attendants could also enjoy the beautiful voices of singers of the vox iuvenalis choir. the conference dinner http://www.gruppofrattura.it http://www.ecf17.fme.vutbr.cz frattura ed integrità strutturale, 9 (2009) notiziario igf 160 was held in the reconstructed vannieck gallery. during the dinner, the conference chairman and the esis president traditionally passed the esis awards on c. m. sonsino (the wöhler medal), a. carpinteri (the griffith medal), r. a. ainsworth (the honorary membership) and e. gdoutos (the award of merit). the music band jazz archive dulcified the atmosphere of both the ceremony and the following free entertainment. final assessment according to reactions of many participants and authorities during and after the conference, the ecf17 very successfully continued the old tradition of primary esis conferences. esis awards esis president prof. gdoutos and ecf17 chaimen conferred the esis awards during the social dinner: griffith medal to prof a. carpinteri, “for his outstanding theoretical results achieved in the field of fracture mechanics and their successful applications, especially those devoted to the improvement of structural integrity in civil engineering”; wöhler medal to prof. c. m. sonsino, “for his outstanding contributions to the field of fatigue, especially those devoted to the multiaxialand variable amplitude loading”; award of merit to prof. e. gdoutos, “for his outstanding research in the field of fracture mechanics and for hiswork devoted to the advancement of the european structural integrity society”; honorary membership to dr. r. a. ainsworth, “for his outstanding contributions to the fields of fracture and structural integrity design as well as for his work devoted to the advancement of the european structural integrity society”. further informations about esis activities can be found at: www.structuralintegrity.eu. esis awards conferred at ecf17 (from left): j. pokluda (ecf17 co-chaiman), c.m. sonsino (wohler medal), e. gdoutos (award of merit), a. carpinteri (griffith medal), r.a. ainsworth (honorary membership), p. lukas (ecf17 co-chaiman). esis – tc3 activity professor andrea carpinteri (parma), professor les p. pook (london) and professor andrea spagnoli (parma) : guest editors of a special issue on “crack paths” of the international journal “engineering fracture mechanics”, vol.75, no.3-4, 297-900, 2008, with papers selected from those presented at the international conference on “crack paths (cp 2006)”, held in parma, italy, 14th to 16th september, 2006. professor bruno atzori (padua), professor andrea carpinteri (parma), professor paolo lazzarin (padua) and professor les p. pook (london): chairmen of the 3rd international conference on “crack paths (cp 2009)”, to be held in vicenza (60 km from venice), italy, 23rd to 25th september, 2009. professor andrea carpinteri (parma), professor les p. pook (london) and professor cetin morris sonsino (darmstadt): chairmen of the 9th international conference on multiaxial fatigue and fracture (icmff9), to be held in parma, italy, 7th to 10th june, 2010. http://www.gruppofrattura.it frattura ed integrità strutturale, 9 (2009) notiziario igf 161 esis tc24 activity meeting of esis tc4 on polymers, adhesives and composites 11th -12th september 2008 at the eurotel, les diablerets, switzerland. minutes present bamber blackman, imperial college (uk) roy moore (uk) antonio martinez, u. catalunya, (es) lluisa maspoch, u. catalunya, (es) andrea pavan, politecnico di milano (i) alicia salazar, u. rey juan carlos, (es) orlando santana, u. polit. cat (es) andreas brunner, empa (ch) jesus rodriguez, u. rey juan carlos, (es) silvia agnelli, u. brescia, (i) stefano pandini, u. brescia, (i) laurent warnet. u. twente, (nl) alessandro pegoretti, u. trento, (i) luigo franchino, polimeri europa (i) leonardo castellani, polimeri europa (i) francesco caimmi, politecnico di milano (i) andrea calzolari, ceast (i) hugh macgillivray, imperial college (uk) luca andena, politecnico di milano (i) manuela boggio, politecnico di milano (i) claudia marano, politecnico di milano (i) paul lambert, intertek msg, (uk) denis cartié, cranfield (uk) theonis ricco, u. brescia (i) francesco baldi, u brescia (i) helge steininger, basf, (d) gilles orange, rhodia r & d (f) gordon williams, imperial college (uk) takashi kuriyama, u. yamagata, (j) marta rink, politecnico di milano (i) neal murphy, u. college dublin (ire) tony kinloch, imperial college (uk) welcome gordon williams welcomed attendees to the committee meeting and the agenda was confirmed. 1. essential work of fracture: marta rink a review of the results from the previous round-robin were presented. it was apparent that the test results are very sensitive to the sharpness of the initial notch and there was much discussion of this issue. there was a presentation of results from one lab where razor notching had been compared with laser ablation notching. a drawback was that laser ablation costs €60 per specimen. actions: future work will focus on notching and the statistical analysis of the test result (marta). 2. jc testing: helge steininger helge reviewed the results of some tests performed at basf and the issues of crack front shape and the accuracy of the various compliance measurements were discussed. actions: a final version of the protocol to be written with comments on suitability (helge). application of the load-separation criteria to be evaluated (helge). cutting and scratch testing: gordon williams gordon summarised the development of the new analysis schemes, which had been presented in the conference paper two days earlier. two additional analyses were now available and had been trialled at imperial college. there was a presentation of data from intertek, where a new cutting rig had been developed. the cutting method appears to offer a route for gc determination in polymers for which it would be impossible to obtain values from conventional g or j tests. actions: new analysis methods to be added to protocol. dave wyeth (u. reading) to send details of his experimental method to gordon. labs to try new analysis methods. laminates testing (and structural adhesives): fatigue (andy brunner for gerald pinter): andy presented the essential features of the tc4 delamination fatigue protocol which has been developed. a new roundrobin was proposed, with carbon-fibre laminate being provided by u. leoben. the status of the astm round-robin was discussed. actions: labs agreeing to take part in new round-robin: empa, dublin, leoben, oviedo, brecia, imperial college (bamber to confirm). round-robin to be initiated (gerald). high rate: denis cartié denis reviewed the results from the current high speed delamination round-robin. the crack length correction factor appeared to introduce scatter in the results obtained using the load-independent method. this required some further refinement. denis reported that he was leaving cranfield in december and would be unlikely to continue with his tc4 involvement. actions: a new leader was required for this activity (bamber to advise). http://www.gruppofrattura.it frattura ed integrità strutturale, 9 (2009) notiziario igf 162 mode ii (laminates and structural adhesive joints): bamber blackman bamber reviewed the protocol developed by tc4 to determine giic for composite laminates using a calibrated end-loaded split (c-els) test. this was a development of the original tc4 els test method and used an effective crack length approach to determine g. the first round-robin was complete and a second round robin was underway. bamber reported that graham sims (npl, uk) had submitted the 4-enf test method to iso as a new work item, and in discussions with graham it had been agreed that the c-els protocol would also be submitted as an alternative document. actions: tests to be completed at cranfield (denis) and empa (andy) and results to be sent to bamber. c-els test protocol to be sent to graham sims for presentation at the iso meeting in sept 2008 (bamber). peel of flexible laminates: neal murphy neal presented the results of a detailed study into the results obtained by various workers using the tc4 peel protocol. results were compared to values obtained from lefm. a two part rejection criterion was proposed as an attempt to ensure invalid results were not obtained using the method. there was a discussion of the criteria proposed. actions: further consideration of the rejection criteria (neal). tony kinloch (imperial college) agreed to run a follow-on msc project this year. short fibre composites at 1m/s: andrea pavan a round-robin had been completed using the short fibre amendment to iso-13586 (but without the size criteria) with testing at 1m/s. the main difficulty had been in the determination of crack initiation in the presence of pop-in effects. andrea presented details of two requirements to formalise the identification. it was agreed that these should be added, and that the new text be proposed as an amendment to iso-17281 (at 1m/s), which is now due for review. actions: andrea to prepare the text for the amendment to iso-17281. environmental stress cracking: gordon williams the possibility of the committee starting work in this area had been previously discussed. it was agreed that the procedure should be suitable for brittle polymers, probably in three point bending and in a water environment. a procedure will be written in time for the next meeting. actions: an activity to be launched at the next meeting (gordon). labs to indicate their interest in participating to gordon. conference assessment the committee reviewed the 5th international tc4 conference which had just taken place in the village and it was widely felt that this had been a great success. a detailed assessment of the conference was presented by committee members and this was to be passed to the conference organisers. the papers were to appear as a special issue of engineering fracture mechanics, and the review procedures were discussed and agreed. actions: bamber to prepare the committee assessment and pass to claire norris at elsevier. aob some dissatisfaction was expressed concerning the dates of the may meeting as they clash with the main european holiday. bamber was in discussion with the hotel regarding possible alternative dates. post meeting note, the date of the next meeting has been changed, see below. dates of future meetings (all to be held at the eurotel in les diablerets) are now confirmed as:  13th-15th may 2009 (committee meeting)  30th sept-2nd oct 2009 (committee meeting) esis tc24 activity on 13-14 october 2008, prof. beretta hosted a tc24 workshop dedicated to the “damage tolerance of railway axles”. the workshop was the opportunity to discuss some of the results obtained in different cooperative projects in europe. the complete list of the presentations, that were delivered to an audience of 70 participants from different european countries, is: "broken axles: moving to solutions of a long standing problem" r. smith imperial college, uk “uk axle: service loads in axles and their effects on the axle life” m. beagles, deltarail, uk “damage tolerance investigations on railway axles” u. zerbst, m. schodel – gkss, germany "deufrako: crack propagation behavior on thirdand full-scale railway axles" a. esderts, k lütkepoh tu clausthal, germany http://www.gruppofrattura.it frattura ed integrità strutturale, 9 (2009) notiziario igf 163 “damage tolerance of tgv axles” f. cocheteaux, sncf, france “deufrako: effect of specimen geometry on fatigue crack growth rates in an a4t material” i. varfolomeyev, m. burdack, m. luke iwm, germany “widem: estimation of load spectra for integrity assessment of an high speed train wheelset” s. bruni, f. braghin, f. resta polimi, italy s. cervello lucchini rs, italy m. grosse-hovest – lbf, germany “the effect of steady torsion on small crack initiation and propagation under rotating bending: multiaxial fatigue and mixed-mode cracking” m. de freitas, instituto superior técnico, technical university of lisbon, portugal “widem: damage tolerance and design review for the axles of an high speed train” s. beretta, m. carboni polimi, italy j. rudlin, l. wei twi, uk "numerical investigations on an engineering approach for analysis of fretting fatigue in press-fits" t. bruder, l. voigt – lbf, germany “deufrako: fatigue crack growth behaviour in railway axle materials under constant and variable amplitude loading” m. luke, m. burdack, i. varfolomeyev, iwm, germany “longitudinal cracking of railway axles” n. gubeljac university of maribor, slovenia “investigations on fatigue crack growth under variable amplitude loading in wheelset axles” h. richard, m. sander – university of paderborn, germany "an effect of strength of railway axle steels on fatigue resistance under press fitting" v. linhart, i. černý, svum, czech the working days were closed by two round table discussions: “determination of ut pod curves for railway axles” by m. carboni – polimi, italy; “sif solutions in railway axles” by m. madia – polimi, italy. remarks the workshop was very successful; it provided an excellent opportunity for the dissemination of the eu 6th framework project widem results. it also brought together the leading european intellectual experts in railway wheelsets for a review of contemporary work which, clearly, was state of the art. the workshop demonstrated that there is a high level of interest in the subject which has a very high level of economic value to industry. as a consequence industry is very enthusiastic in its support for academic research in the problem fundamentals. in addition to the important widem work, significant new developments were unveiled during the workshop. there is a great deal of attention focussed on to contemporary problem areas of railway axle design. although not linked to specific axle designs, difficulties in dealing with crack initiation in axle radius transitions received a great deal of attention. prof. stefano beretta of polimi led presentations of the widem work. the widem project, because of technical difficulties in the experimental work, was delayed and did not achieve all of its ambitious objectives. nonetheless, important progress has been made in understanding the crack initiation problems referred to above, predicting crack growth rates and in understanding the probability of detecting cracks in railway axles. the progress made by widem, together with other presented activities at the workshop, suggests that a complete understanding of all of the engineering fundamentals of the structural integrity may soon be achieved. prossime attivita’ igf sessione tematica durante il prossimo convegno aias (associazione italiana analisi sollecitazioni; torino dal 9 all’11 settembre 2009) dal titolo “integrità strutturale”. il coordinatore di questa sessione sarà il prof. franco furgiuele, cui potete far riferimento per aderire (furgiuele@unical.it); http://www.aiasonline.org/default.asp http://www.gruppofrattura.it http://www.aiasonline.org/default.asp mailto: furgiuele@unical.it frattura ed integrità strutturale, 9 (2009) notiziario igf 164 sessione tematica durante il prossimo convegno aipnd (associazione italiana prove non distruttive; roma dal 15 al 17 ottobre 2009). il coordinatore di questa sessione sarà il prof. stefano beretta, cui potete far riferimento per aderire all’iniziativa (stefano.beretta@polimi.it). http://www.aipnd.it/ l’igf è fra le associazioni che supportano il prossimo ninth international seminar on experimental techniques and design in composite materials (dal 30 settembre al 2 ottobre 2009 a vicenza). http://www.gest.unipd.it/etdcm9/ calendario congressi internazionali 12-17 luglio 2009: icf 12thinternational conference on fracture, ottawa, canada http://www.icf12.org 8-10 settembre 2009: 8th international conference on fracture and damage mechanics, malta http://fdm.engineeringconferences.net/new/ 23-25 settembre 2009: international conference on crack paths (cp2009), vicenza. http://www.cp2009.unipr.it/ 23-28 maggio 2010: 7th international conference on fracture mechanics of concrete and concrete structures & post-conference workshops, seogwipo kal hotel, jeju, korea. http://www.framcos7.org 7-10 giugno 2010: the ninth international conference on multiaxial fatigue & fracture, parma http://www.icmff9.unipr.it. 30 agosto – 3 settembre 2010: ecf 18 european conference on fracture, dresda, germania http://www.esisweb.org http://www.gruppofrattura.it http://www.esisweb.org http://www.icmff9.unipr.it http://www.framcos7.org http://www.cp2009.unipr.it/ http://fdm.engineeringconferences.net/new/ http://www.icf12.org http://www.gest.unipd.it/etdcm9/ http://www.aipnd.it/ mailto: stefano.beretta@polimi.it frattura ed integrità strutturale, 9 (2009) notiziario igf 165 esis procedures and documents (www.esisweb.org) two kinds of documents are produced by esis technical committees with the following designatory system: esis p2-92 or esis p4-92d, where: 1) p means "procedure", and 2 and 4 are the current numbers, while 92 is the year of issue. 2) d following the year (eg: 92d) means "draft", ie: not yet approved, while 3) d prior to the year (eg: d1-92) means "document" other than test methods. p1-92 esis recommendations for determining the fracture resistance of ductile materials. responsible body: tc1 subcommittee on fracture mechanics testing standards. p2-92 esis procedure for determining the fracture behaviour of materials. responsible body: tc1 subcommittee on fracture mechanics testing standards. p3-03d draft unified procedure for determining the fracture behaviour of material. responsible body: tc1 subcommittee on fracture mechanics testing standards (under preparation not available). p4-92d esis recommendations for stress corrosion testing using pre-cracked specimens. responsible body: tc10 committee on environmental-assisted cracking. p5-00/vamas procedure for determining the fracture toughness of ceramics using the sevnb method . responsible body: tc6 committee on ceramics. p6-98 esis procedure to measure and calculate material parameters for the local approach to fracture using notched tensile specimens. responsible body: tc8 committee on numerical methods. p7-00 esis procedure for dynamic tensile tests responsible body: tc5 subcommittee on dynamic testing at intermediate strain rates. p8-99d esis draft code of practice for the determination and interpretation of cyclic stress-strain data. responsible body: tc11 committee on high temperature mechanical testing. p9-02d guidance on local approach of rupture of metallic materials. (under preparation not available). p10-02 a code of practice for conducting notched bar creep rupture tests and interpreting the data. responsible body: tc11 high temperature mechanical testing committee. p11-02 technical recommandations for the extreme value analysis of data on large nonmetallic inclusions responsible body: tc20 committee on inclusions. d1-92 fracture control guidelines for stress corrosion cracking of high strength alloys. responsible body: tc10 committee on environmental assisted cracking. d2-99 fracture toughness of ceramics using the sevnb method; round robin, test programme. the esis tc6 and vamas twa3 developed a test method and conducted a round robin for its validation. d2-99 presents a detailed documentation of this activity. the final form of the test method has appeared as p5-00. responsible body: tc6 committee on ceramics. http://www.gruppofrattura.it microsoft word numero_38_art_4 l. cui et alii, frattura ed integrità strutturale, 38 (2016) 26-35; doi: 10.3221/igf-esis.38.04 26 focussed on multiaxial fatigue and fracture crack initiation behavior of notched specimens on heat resistant steel under service type loading at high temperature lu cui school of mechanical engineering, xi’an shiyou universityuniversity institut für werkstoffkunde, technische universität darmstadt cuiluxa@hotmail.com peng wang borgwarner turbo systems engineering gmbh institut für werkstoffkunde, technische universität darmstadt wp168@hotmail.com abstract. cracks at notches deserve special consideration in the design of steam turbine components. this work is addressed to investigate the crack initiation behavior a 10%cr rotor steel with the help of notched specimens under service-type loading. a significant drifting down of the peak-values of axial deformation under constant amplitude load was observed. crack initiation was evaluated with the help of the relationship between irreversible deformation energy and cycle number. further, metallographic examinations were employed to characterize the superposition of creep and fatigue damage mechanisms. both neuber-hypothesis and von mises equivalent strain at notch root were applied for lifetime prediction. finally, the effectiveness of both methods is validated by comparing with experimental results. keywords. 10%cr steel; notched; lifetime; neuber; von mises. citation: cui, l., wang, p., crack initiation behavior of notched specimens on heat resistant steel under service type loading at high temperature, frattura ed integrità strutturale, 38 (2016) 26-35. received: 14.05.2016 accepted: 20.06.2016 published: 01.10.2016 copyright: © 2016 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. introduction team turbine components are subjected to quasi-static primary loading due to steam pressure superimposed by variable secondary loading due to temperature transients in start-up and shut-down processes. the difference between the surface temperature and the average core temperature leads to compression strains during start-up and tension strains during shut-down (fig. 1). at stationary service, the turbine temperature reaches quasi-balance, and the compression and tension stresses relax during the hold time. due to stress concentration, notches lead to a further decrease of lifetime [1]. s l. cui et alii, frattura ed integrità strutturale, 38 (2016) 26-35; doi: 10.3221/igf-esis.38.04 27 in previous studies, notch behavior on rotor steel of x12crmowvnbn10-1-1 was investigated by conventional low cycle fatigue tests without dwell time (lcf-cycles) and creep fatigue tests with hold times at maximum and minimum load on notched specimens [2]. however the knowledge gained from those experiments are still insufficient to exploit the full potential of this steel. this requires experiments on notched specimen to understand the practical implications of applying such an approach to a service situation. figure 1: three stage service-type strains cycling at heated surface of power plant components a phenomenological lifetime estimation method which was developed for a multistage service-type creep fatigue loading, specially demonstrates the applicability of rules for synthesis of stress strain path and relaxation including an internal stress concept, as well as mean stress effects. further, a modified linear damage rule for creep-fatigue life estimation was employed, and a creep fatigue interaction concept covering a wide range of creep dominant loading as well as fatigue dominant loading was also developed. to describe multiaxial stress state at notch, the neuber hypothesis was applied. in addition, the service-type loading was also analyzed with finite-element-calculation and an equivalent loading is determined. in the end, the lifetime estimation model was validated with the experiments performed in this study. experimental material he tested material is a modern ferritic-martensitic stainless steel of type 10cr-1mo-1w-v-nb (german grade x12crmowvnbn10-1-1), which is proposed to be suitable for high temperature applications up to 600°c/300bar. chemical composition and heat treatment of the material are introduced in [3] and listed in tab. 1. test specimens were manufactured from the same heat. because the maximal thermal damage occurs on the heated surface of a rotor, the specimens were taken from locations close to the periphery of production forging with a longitudinal orientation with respect to the axis of the rotor. c cr mo w ni v nb n mn si p x12crmowvnbn10-1-1 0.12 10.7 1.04 1.04 0.76 0.16 0.05 0.06 0.42 0.1 0.007 manufacturing segment of a rotor diameter 400 mm x 6500 mm, weight 6000 kg, forged heat treatment austenitization 1050°c 7h / oil + 570°c 10.25 h / air + 690°c 10h / air table 1: chemical composition (weight %) and heat treatment of x12crmowvnbn10-1-1 t l. cui et alii, frattura ed integrità strutturale, 38 (2016) 26-35; doi: 10.3221/igf-esis.38.04 28 experimental details experiments were carried on an electric-mechanical servo machine with a maximum force capacity of ±100kn (fig. 2a). the specimen was heated with a controlled three-zone-convention-furnace, which keeps homogeneous temperature distribution advantageously. the temperature was measured by a ptrh-pt thermocouple of type s at mid gauge section during testing. two extra thermocouples were fixed on the both tension rods (fig. 2b) in order to control the temperature homogeneity. the temperature variations at control thermocouple positions were held to within ±3°c. the deformation was measured by inductive distance sensor with analog output (fig. 2b). fig. 3 illustrates the geometry of the specimen. extensometer rods were placed on locations indicated with a. all tests were carried out at 600°c. the stress-controlled test cycle was based on the service-type strain cycles [1], which is a three-stage strain collective with 1 cold start, 3 warm starts and 16 hot starts (fig. 1). the sum of hold times amounts to one hour. nominal stress rate subject to service condition was chosen according to an equivalent strain rate of ca. 10-5/s (fig. 4). figure 2: equipment for testing of notched specimens, (a) electric mechanical testing system and (b) used measurement device of the axial deformation at the edge of the notch as well as the thermocouple to measure the temperature. figure 3: specimen and dimensions of the used notched specimen (mm). figure 4: force controlled loading on notched specimens with a three-stage service-type loading. l. cui et alii, frattura ed integrità strutturale, 38 (2016) 26-35; doi: 10.3221/igf-esis.38.04 29 experimental results tab. 2 summarizes the test results of creep-fatigue lives under the 3-stage service-type loading at temperature 600°c performed in this study, where nominal stresses are normalized in  and in its proportion because of data protection. the stress amplitude /2 is just below the yield strength rp,0.2%,600c at 600c. the total hold time ∑th represents the summation of dwell periods within a single cycle. the number of cycles to crack initiation ni corresponds to crack depth δa≈0.5-1mm, which is determined by analyzing the relationship between irreversible deformation energy w and the number of cycles n. here, the procedure is introduced by example with the experiment ua16kb63 (fig. 5). at first, crack depth is plotted against the deformation energy w. crack depth after tests was measured though metallographic investigations. it is assumed that the initial crack depth at the end of linear behavior of deformation energy w is zero. in fig. 5a, it is observed that irreversible deformation energy w increases linearly up to ca. ¾ of the test duration. the deformation energy w by crack depth of 0.5mm was resulted from a linear interpolation in fig. 5b, and with this value, the number of cycles of crack initiation ni was determined in fig. 5a. test piece id t (°c) ∑th (h) δσn,c /δσn,w /δσn,h (mpa) nia) (-) tia) (h) ua16kb60 600 1 2.78/2.35/2.00 441 523 ua16kb61 600 1 2.36/2.00/1.70 801 928 ua16kb62 600 1 2.08/1.76/1.50 2733 3000 ua16kb63 600 1 1.39/1.17/ 7547 8284 a) crack initiation, crack depth 0.5-1 mm table 2: summary of the test results under service-type loading on notched specimens the numbers of cycles to fracture nf and to crack initiation ni in relationship to nominal stress range δσn are summarized in fig. 6, where the nominal stress range of hot start cycles δσn,h is applied to represent the 3-stage service-type cycles. the solid line was generated from uniaxial push-pull tests without dwell time [2][3]. the both dashed lines represent creep fatigue lifetime with 1h and 3h dwell time [2, [3] at maximum and minimum load on notched specimens with the same specimen type used in this paper (fig. 3). the four life data performed in this paper are shown as filled circles in fig. 6. endurances to crack initiation of service-type with total dwell time of 1h are similar to life of fracture from 1h/1h pushpull test results (dashed line). the difference between life of fracture nf and life of crack initiation ni is estimated about 10%. in general, increasing loading period leads to a reduction of lifetime due to high influence of the creep damage during the dwell time. this is caused by the high ductility of the examined 10%cr-steel and the high influence of the creep damage during the hold times. the four life data performed in this paper are subordinated to prior results. the lower load rate, which induces more creep damage, is also another reason to reduce lifetime. figure 5: (a) irreversible deformation energy w against number of cycles n and (b) crack depth δa against irreversible deformation energy w, specimen ua16kb63. l. cui et alii, frattura ed integrità strutturale, 38 (2016) 26-35; doi: 10.3221/igf-esis.38.04 30 figure 6: characteristic lines of experiments without and with dwell time at maximum and minimum nominal stress [2][3] as well as the service-type data on notched specimens. fig. 7 correlates an overview of measured maximum and minimum peak-values of axial deformations as well as mean values of the 3-stage service-type experiments in relation to the number of cycles. the peak-values of axial deformation are drifting down with a constant rate at the beginning of the tests. the peak-values of specimens of ua16kb60 and ua1kb61 decrease after that quickly (fig. 7 a, b). the both specimens were loaded under relative high nominal stress, whose amplitudes are substantially higher than yield strength rp,0.2%,600°c. in contrast, the axial deformation peak-values of specimens of ua16kb62 and ua16kb63 decrease after that slowly until the cycle number to about 2000 (fig. 7 c,d). after that, the peak-values drift up against the number of cycles with an increase of deformation range, which indicate the initiation of micro cracks in microstructure. figure 7: measured maximal amplitude of axial deformations, minimal amplitude of axial deformations and mean deformations of service-type experiments on notched specimens against number of cycles according to tab. 2. l. cui et alii, frattura ed integrità strutturale, 38 (2016) 26-35; doi: 10.3221/igf-esis.38.04 31 metallographic examination fter tests, significant plastic deformation was observed at notch roots by macroscopic investigation (fig. 8). the higher the stress range or the longer the dwell time is, the larger the deformation is. this leads to change the form factor kt determined from notch geometry before testing. thus it is difficult to estimate lifetime with neuberhypothesis. cracks on notch root specimens of ua16kb60 and ua16kb61 (fig. 8a, b) are initiated obviously through extrusions in correspondence with the drifting of axial deformation peak-values into press (fig. 7a,b). typical fatigue dominant damage is shown by transgranular cracks which initiate from the surface along the notch shape (fig. 8ato d). main crack moves sometimes along grain boundaries during its course (fig. 8e to h) representing intergranular cracking and a typical creep fatigue interaction. a complex damage was observed underneath the notch root surface (crack tips). figure 8: crack after 3-stage service-type loading at 600°c (a) to (d) and details of the 4 marked location (e) to (h), notched specimens, x12crmowvnbn10-1-1. stress strain analyses constitutive material model viscoplastic constitutive material model in accordance with lemaitre and chaboche with a few changes for a better adaptation to high temperature material behaviors is applied for the stress strain analysis [4, 5]. an equivalent stress f: d df 3 ( ) : ( ) 2   t x t x (1) is derived from the deviator of the difference between the stress tensor t and the back stress tensor of kinematic hardening x, where the operator (...)d denotes deviator of a tensor. the accumulated plastic strain s is used in the model, and its evolution is described as: m da ffs e    (2) with four material parameters m, η, a and d. the power law was modified with the term dfae  according to [6] for better conformance to a wide stress range. a a l. cui et alii, frattura ed integrità strutturale, 38 (2016) 26-35; doi: 10.3221/igf-esis.38.04 32 the plastic strain flow rule is given as: d p s f ( )3 2   t x e  (3) the evolution equation of the kinematic hardening variable y follows the armstrong–frederick hardening rules with an additional static recovery term and can be written as: pc b b s p   x e x x   (4) where b, p and c are material parameters. a scalar function b b sb s b b e 21 1( ) (1 )     (5) represents accumulated plastic strain s; parameters b1 and b2 are applied to the dynamic recovery term describe cyclic softening behavior. all of the above mentioned material parameters m, η, a, b, d, p, c, b1 and b2 were determined by uniaxial creep tests and push pull tests with analytical fits at 600°c. the material model was implemented in the finite element analysis program abaqus by means of a user subroutine umat, in which the differential equations of the material model are numerically integrated using the runge-kutta method [5]. figure 9: comparing of axial deformation between two positions a marked in fig.3, fe – calculation (material model from [4][6]) in comparison with experiment. finite-element analysis nonlinear finite-element calculations were performed in order to determine the stress-strain behavior at notch during 3stage service-type loading. according to axis symmetry of the specimen shape a quarter of the specimen was modeled by a fe mesh. an axisymmetric mesh with quad elements was employed. l. cui et alii, frattura ed integrità strutturale, 38 (2016) 26-35; doi: 10.3221/igf-esis.38.04 33 plotting the axial deformation vs. testing time, the simulation provides an acceptable agreement with experimental values for the first 20 sub-cycles in all 4 tests (fig. 9). in tests with larger stress amplitudes, which means that the maximum nominal stress is bigger than 0.2% yield strength at the testing temperature, the displacement drifts into compression domain with an increasing number of cycles (fig. 9a, b). the ratcheting effect is overestimated by the material model for the tests ua16kb60 and ua16kb61. the influence of material damage on the deformation was considered in the fea. however, the impact of damage in the first cycle of sequence plays no significant role, therefore it is not the reason for overestimating ratcheting. in contrast, the simulation describes the deformation of the experiments with lower nominal stress (ua16kb62 and ua16kb63) pretty well (fig. 9c, d). the maximum of the equivalent loading is located at the notch root in accordance with the fea, thus the simulation results at the corresponding node is applied for lifetime prediction. lifetime estimation phenomenological lifetime estimation approach developed for service-type loading (fig.1) was based on rules for synthesis of stress strain path, wherein mean stress effect and creep fatigue interaction are include. for life estimation under service-type creep fatigue loading, the life fraction rule proposed by robinson/taira [7] was implemented in the approach. crack initiation is determined by the summation of fatigue damage df representing a cyclic fraction and creep damage dc representing a time fraction summing up to the number of cycles to crack initiation ni: n j k n k n c f u k n io j t d d d t n , , , ,1 1 1 1             (6) the creep damage for one hold phase is calculated as the accumulation of the ratio of time increments δtk,n to rupture time tu,k,n during the hold phase. the rupture time tu,k,n is carried out according to the instantaneous acting load and temperature from rupture characteristic curves, which were generated by data of static creep tests. the fatigue damage df is calculated by a reference number of cycles to crack initiation nio, which is determined under consideration of creep fatigue interaction and mean stress effect. the creep fatigue interaction was developed in a previous paper according to metallographic damage [8]. the material-specific mean creep fatigue damage of 0.68 for the material x12crmowvnbn10-1-1 determined by uniaxial service-type tests [8] was used as a critical damage value dcrit in this paper. phenomenological life time calculation requires scalar stress and strain values. hence the maximum principal stress 1 and the von mises equivalent stress v were calculated for one point at the surface of the notch root with the help of the constitutive material model introduced above. the maximum principal stress 1 is equal to the stress in axial direction 22. the hysteresis loop 22 (22) represents a corresponding uniaxal loading. in fig. 9 the signed equivalent stress σv,1 gets its sign form the maximum principal stress σ1: v v sign,1 1( )    with d d v 3 2   t t and 1 22  (7) the directions of the elastic equivalent strain εve and the plastic equivalent strain εvp are also associated with the sign of the maximum principal stress 1: t v v ve vp s sign dt e ,1 ,1 ,1 ,1 1 0 ( )           (8) the equivalent strain range δεv is used for estimation of the fatigue damage with the uniaxial low cycle fatigue curve representing a hold time of th = 1h. the equivalent stress is used for estimation of the creep damage. for stress-controlled loading the mean stress is constant and the mean strain varies during testing. as fig. 10 observed, a significant drifting of the mean axial deformation is observed. therefore, the smith-waston-topper parameter pswt [8] is modified as follows: a l. cui et alii, frattura ed integrità strutturale, 38 (2016) 26-35; doi: 10.3221/igf-esis.38.04 34 swt mp e, 2 2              (9) with δ as constant stress range and m as mean strain. as an alternative to the approach described above, the neuber-hypothesis can be used to determinate the maximum stress and strain by using cyclic tensile curves. however the hypothesis is not applicable on the experiments ua16kb60 and ua1kb61, because the high nominal stress leads to significant plastic deformation. by simulating the experiments with the material model, the mean strain cannot be described satisfactorily, which leads to a very conservative lifetime estimation (fig.10). thus, the mean strain is read from measured value at half-life cycle to represent the “saturated” material state. by considering the mean strain effect, the lifetime can be predicted within a scatter band of factor 2 (fig. 10). to summarize, lifetime estimation without considering mean strain is conservative. the neuber hypothesis has its strength in its easy applicability. but its application is limited to the elastic domain and it leads to strong conservatism in lifetime estimation. the application of equivalent stress and equivalent strain determined with fe analysis based on the material model of type chaboche [6] appears relatively expensive in terms of parameter identification from current level of technology. however, it has more potential on describing complex loading because it can better represent the deformation under the complex loading. figure 10: correlation between estimated life n*i and measured life ni. concluding remarks ervice-type experiments were carried out on notched specimens of the x12crmowvnbn10-1-1 rotor steel under cyclic creep fatigue loading at service temperature 600°c. the peak-values of deformation decrease quickly if the loaded nominal stress is higher than the material’s 0.2% yield strength at the testing temperature. at lower nominal stress, the peak-values decrease slowly and almost linearly until about 2000 cycles and then they increase again. according to metallographic investigations on the 4 tested specimens, cracks are perpendicular to the direction of loading and propagate from the surface of the notch root. crack initiations are transgranular and clearly through extrusions on the surface. the main transgranular cracks ramified during its propagation. the lifetime of the 4 test specimens was estimated with a phenomenological lifetime prediction method by using neuber hypothesis and equivalent stress/strain in the gauge part of the specimens. the uniaxial equivalent stress was determined with von mises from finite-element-analysis according to constitutive material model of type chaboche. the estimated life and experiment are predicted in a scatter band of factor 2, while the results are conservative by using neuber hypothesis if the effect of mean strain on lifetime estimation is not considered. s l. cui et alii, frattura ed integrità strutturale, 38 (2016) 26-35; doi: 10.3221/igf-esis.38.04 35 acknowledgement hanks are due to the forschungsvereinigung der arbeitsgemeinschaft der eisen und metall verarbeitenden industrie e.v. (avif-no. a232) and national natural science foundation of china (no. 51305348) for financial support. references [1] samir, a., simon a., scholz a., berger c., service-type creep-fatigue experiments with cruciform specimens and modelling of deformation, international journal of fatigue, 28(5-6) (2006) 643-651. [2] schwienheer, m., scholz, a., haase, h., berger, c., influences of hold times and notches on life time under service type creep fatigue loading, proceedings of fifth international conference on low cycle fatigue, lcf 5, berlin, dvm, (2003) 245-250. [3] schwienheer, m., hochtemperaturverhalten der 600°c-dampftubinenstähle (g)x12crmowv-nbn10-1-1, dissertation tu-darmstadt, d17 (2004). [4] simon, a., scholz a., berger c., validation of creep fatigue lifetime calculation methods for the application to steam turbine rotors, variable amplitude loading, darmstadt, proceedings, dvm, i (2009), 505-516. [5] tsakmakis, c., reckwerth, d., the principle of generalized energy equivalence in continuum damage mechanics, deformation and failure in metallic materials, springer verlag (2003). [6] wang, p., cui, l., scholz, a., linn, s., multiaxial thermomechanical creep-fatigue analysis of heat-resistant steels with varying chromium contents, international journal of fatigue, 67(2014) 220-227. [7] taira, s., lifetime of structures subjected to varying load and temperature, in creep in structure, j. ed. academic press, new york (1960) s. 96/124. [8] scholz, a., berger, c, deformation and life assessment of high temperature materials under creep fatigue loading, mat.-wiss. u. werkstofftechn. 36(11) (2005) 722–730. t << /ascii85encodepages false /allowtransparency false /autopositionepsfiles true /autorotatepages /none /binding /left /calgrayprofile (dot gain 20%) /calrgbprofile (srgb iec61966-2.1) /calcmykprofile (u.s. web coated \050swop\051 v2) /srgbprofile (srgb iec61966-2.1) /cannotembedfontpolicy /error /compatibilitylevel 1.4 /compressobjects /tags /compresspages true /convertimagestoindexed true /passthroughjpegimages true /createjobticket false /defaultrenderingintent /default /detectblends true /detectcurves 0.0000 /colorconversionstrategy /cmyk /dothumbnails false /embedallfonts true /embedopentype false /parseiccprofilesincomments true /embedjoboptions true /dscreportinglevel 0 /emitdscwarnings false /endpage -1 /imagememory 1048576 /lockdistillerparams false /maxsubsetpct 100 /optimize true /opm 1 /parsedsccomments 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can be opened with acrobat and adobe reader 5.0 and later.) >> /namespace [ (adobe) (common) (1.0) ] /othernamespaces [ << /asreaderspreads false /cropimagestoframes true /errorcontrol /warnandcontinue /flattenerignorespreadoverrides false /includeguidesgrids false /includenonprinting false /includeslug false /namespace [ (adobe) (indesign) (4.0) ] /omitplacedbitmaps false /omitplacedeps false /omitplacedpdf false /simulateoverprint /legacy >> << /addbleedmarks false /addcolorbars false /addcropmarks false /addpageinfo false /addregmarks false /convertcolors /converttocmyk /destinationprofilename () /destinationprofileselector /documentcmyk /downsample16bitimages true /flattenerpreset << /presetselector /mediumresolution >> /formelements false /generatestructure false /includebookmarks false /includehyperlinks false /includeinteractive false /includelayers false /includeprofiles false /multimediahandling /useobjectsettings /namespace [ (adobe) (creativesuite) (2.0) ] /pdfxoutputintentprofileselector /documentcmyk /preserveediting true /untaggedcmykhandling /leaveuntagged /untaggedrgbhandling /usedocumentprofile /usedocumentbleed false >> ] >> setdistillerparams << /hwresolution [2400 2400] /pagesize [612.000 792.000] >> setpagedevice microsoft word numero_28_art_4 b. ye et alii, frattura ed integrità strutturale, 28 (2014) 32-41; doi: 10.3221/igf-esis.28.04 32 quantitative estimating size of deep defects in multi-layered structures from eddy current ndt signals using improved ant colony algorithm bo ye, ming li, gefei qiu, jun dong, fang zeng faculty of electric power engineering, kunming university of science and technology yeripple@hotmail.com, kingttlly@foxmail.com, tsugefei@foxmail.com, yn_dj@tom.com fanger1119@163.com tanghua yang, biao bai puer power supply bureau, yunnan power grid corporation aiyi2001@sina.com, baibiao2014@hotmail.com abstract. detection and quantitative estimation of deep defects in multi-layered structures is an essential task in a range of technological applications, such as maintaining the integrity of structures, enhancing the safety of aging aircraft, and assuring the quality of products. a novel approach to accurately quantify the two-dimensional axisymmetric deep defect size from eddy current nondestructive testing (ndt) signals is presented here. the method uses a finite element forward model to simulate the underlying physical process and an improved ant colony algorithm (iaca) to solve the inverse problem. experiments are carried out. the performance comparison between the iaca method and the least square method is shown. the comparison results demonstrate the feasibility and validity of the iaca method. between them, the iaca method gives a better estimation performance than the least square method at present. keywords. eddy current nondestructive testing; finite element method; ant colony algorithm; multi-layered structures; defect measurement. introduction ulti-layered structures are widely used in many different structural systems, such as nuclear structures, composite aircraft structures, and other civil engineering structures [1]. structural integrity is one of the prime requirements for multi-layered structures in working condition. the continuous operation of multi-layered structures leads to the loss of its material due to defect generation [2, 3]. the generation of defects in the structure does not mean that structure is at the end of its service life; it becomes necessary to check the multi-layered structure integrity to ensure optimal utilization to its service life. to check the multi-layered structures, various nondestructive testing (ndt) techniques are used, such as visual inspection, eddy current (ec) technique, ultrasonic technique, x-rays, etc. among these ndt techniques, the eddy current nondestructive testing (ecndt) method is a useful technique for detecting defects in conductive materials, especially in multi-layered structures. when using the other ndt techniques [4-8], it is widely recognized as being both a complex and critical problem. m http://www.gruppofrattura.it http://dx.medra.org/10.3221/igf-esis.28.04&auth=true b. ye et alii, frattura ed integrità strutturale, 28 (2014) 32-41; doi: 10.3221/igf-esis.28.04 33 in ecndt, one of the principal challenges is to determine the size of deep defects in the multi-layered structures based on information contained in the signal representing the change in impedance of the coil as it scans over the specimen. for single-layered structure materials, the high degree of accuracy of some numerical simulation techniques has been demonstrated and several fast computational methods have been presented [9-11]. however, the quantitative estimating size of deep defects in multi-layered structures still poses a major challenge and remains to be dealt with [12]. in this paper, we propose a method of inversing eddy current ndt signals to quantify deep defect size using an iterative improved ant colony algorithm (iaca). the forward problem is calculated via the finite element method (fem). this method simplifies the inversion process and can be used more easily for complicated defects owing to the flexibility of finite elements. the accuracy and robustness of two-dimensional (2d) estimation results for a deep defect in the twolayered structures demonstrate the potential of implementing the algorithm. problem description he arrangement for the detection problem of the two-layered structures using the ecndt technique is shown in fig. 1. the typical deep defect investigated in this work is assumed to be a regular rectangle defect with different values of length, height and depth, representing the model of a real inner deep defect increasing in time and size. the ecndt system taken into account here has been developed in our laboratory. the right-cylindrical air-cored coil probe scans over the surface of the structures from left to right under testing. (a) (b) figure 1: schematic diagram of the detection system. (a) sectional view; (b) top view. in order to describe and calculate the defect size conveniently, cartesian coordinates are used. the global coordinates are o (x, y, z) and the origin lies in the upside of the two-layered structure surface. the local coordinates of the coil are o1 (x1, y1, z1) and the origin o1 is (0, 0, ½(l2−l1)) in the global coordinates. (l2−l1) is the length of the coil, l2, l1 respectively represent the global coordinates of the upper and lower side of the coil. the local coordinates of the defect are o2 (x2, y2, z2) and the origin o2 is assumed the geometry centre of the defect. forward problem he ec problem can be described mathematically by the partial differential equations in terms of the magnetic vector potential. the fem based on variation principles can obtain the numerical solution of magnetic field by transforming the partial differential equations into the liner algebraic equations, which are built by combining the boundary conditions and the minimum energy functional [12]. t t http://www.gruppofrattura.it http://dx.medra.org/10.3221/igf-esis.28.04&auth=true b. ye et alii, frattura ed integrità strutturale, 28 (2014) 32-41; doi: 10.3221/igf-esis.28.04 34 the energy functional of magnetic vector potential (step a) for simplifying analysis, we assume the existing current of coil uniformly distributes at its window, not considering the harmonic component. the conductivity and permeability can vary from layer to layer, but are constant in each one. after magnetic vector potential a (b=×a) is introduced, the maxwell equation is 2a+k2a=−μjs (1) where a represents magnetic vector potential, k2=−jωμ(σ+jωε), j is an imaginary unit, ω is the angular frequency of excitation current (rad), ω=2πf, f is the frequency of excitation current (hz), js is the density of excitation current (amp/m2), σ is the electrical conductivity (s/m), μ is the magnetic permeability of the media involved (h/m), and ε is dielectric constant (f/m). to simplify the eddy current scanning detective problem into a two-dimension axisymmetric problem, and using cylindrical coordinates o (ρ, θ, z) shown in fig. 2, the laplace expression 2a of the vector function a is figure 2: the cylindrical coordinates and triangle unit subdivision. 2 2 2 2 2 2 2 2 2 2 2 a a a a a a1 a a a a1 z z                                          (2) omitting the suffix θ of aθ, eq. (2) can be predigested to 2 2 2 2 2 a 1 a a a asj j z                 (3) according to eq. (3) the energy functional is 2 2 21 a a a a a a 2 2 ( ) d ds r j f j z z                        (4) where, r is the solution region. the solution region (step b) the solution region is shown in fig. 3. this is a two-layered aluminium alloy structure (region 2 and 4). there is a rectangle defect 3 in the two-layered aluminium alloy structures. its boundary is efgh supposing the air in it. the probe is placed on the surface of the aluminium alloy structures in the ec detection and scans from left to right. in order to compute accurately in fem, region 5 is assumed air and must be taken into account. http://www.gruppofrattura.it http://dx.medra.org/10.3221/igf-esis.28.04&auth=true b. ye et alii, frattura ed integrità strutturale, 28 (2014) 32-41; doi: 10.3221/igf-esis.28.04 35 figure 3: the solution region of fem: 1-probe 2-aluminum plate 3-defect 4-aluminum plate 5-air region. region boundary condition (step c) the solution region boundary ab, bc, ad and cd are the first boundary. ab is the symmetric axis and the source current is opposite on both sides. the magnetic vector potential a equals to zero along the symmetric axis ab. the boundary of region 5 bc, ad and cd are independent boundary whose magnetic vector potential a is given to zero. the solution region discretization (step d) several principles of triangle subdivision are as follows: 1) avoiding triangle aspect ratio oversize; 2) only one species of media in one triangle region, subdivision element is incapable of spanning boundary in the defect region 3 whose boundary is efgh; 3) subdivision region denser in the large gradient field, while more sparse in the small gradient field. inside any unit shown in figure 2, adopting linear interpolation function, the magnetic vector potential ap(ρ, z) of any point p(ρ, z) can be represented using the magnetic vector potential al, am and an of the triangle peak points l, m and n.      a s s s a a a s a( , ) t t p z l m n l m n e   (5) where, ap(ρ, z) is the magnetic vector potential of any point p, the t and e of [a]et respectively represent transpose and the finite element, si is basic interpolation function, namely form function, i=l, m, n, δ is triangular unit area. the minimum of energy functional and the finite element equations of magnetic vector potential (step e) by the first order partial derivative of eq.5 inside the element, it is expressed: a a 1 1 a b a 2 2 a a a 1 1 a c a 2 2 a ( ) [ ][ ] ( ) [ ][ ] l t l m n m e n l t l m n m e n b b b c c c z                                  (6) based on eqs. (4), (5) and (6), the energy functional fe(a) of every element is:                 22 21 1 1 1 a c a b a s a s a s a 2 2 2 2 ( ) d d e t t t t te e e e e e j f j z                            (7) if the whole solution region is dispersed to m triangular element, the total energy functional of solution region is 1 a a( ) ( ) m e e f f   (8) http://www.gruppofrattura.it http://dx.medra.org/10.3221/igf-esis.28.04&auth=true b. ye et alii, frattura ed integrità strutturale, 28 (2014) 32-41; doi: 10.3221/igf-esis.28.04 36 the computation of fem equations (step f) the step a to step e above is the solution procedure of the ritz law finite element analysis for the ec detection forward problem. from the method, we can obtain the approximate solution of the vector [a] and then the probe impedance changes. the multi-turn coil, if its density is nc and cross-section is dispersed to k unit element, the impedance of coil is: 2 1 1 2 2 a a k k c ck k ck ck k ck k k j n j j z r r i i            (9) where, δk is triangular element area of the coil interface, rck is distance from the element centroid to symmetric axis, ack is the a at centroid, and j=nci is current density of coil. in this way, on the basis of magnetic vector potential of each node, we can compute the impedance changes of probe. inverse problem and improved ant colony algorithm uring the last decades, some optimization algorithms, such as artificial neural network, genetic algorithm and artificial immune algorithm, have been successfully applied to solve complex optimization problems in ecndt. ant colony algorithm is another heuristic search algorithm succeeding artificial neural network, genetic algorithm and artificial immune algorithm. it is a bionic natural optimization algorithm based on research of foraging behaviors of a real ant colony. it has characteristics of probability seeking and adopts the catalytic mechanism of parallelism and positive feedback. ant colony algorithm has strong robustness and an excellent distributed computing mechanism. it is easy to combine with artificial neural networks, genetic algorithm, artificial immune algorithm and particle swarm optimization algorithm. however, when solving the continuous domain optimization problems, ant colony algorithm has the disadvantages of slow convergence and is time consuming in the process of evolution [13, 14]. this paper presents an improved ant colony algorithm (iaca) and proposes the use of iaca to quantitative estimate defect size from ec inspection signals. the iaca has more global search capability and robustness, and ease of implementation. in order to use iaca, the first step is object discretization as shown in figure 4. every vertical line represents a parameter variable. all vertical lines are divided into n equal divisions. the discretization nodes represent the specific values of the parameter variable. ants walk from the node “start” and pass through the node of every parameter variable. after reaching the node “end”, the iaca completes one cycle and gets a combination of values of all parameter variables. assuming (r, i) is the ith node of parameter r, xr, j is the value of (r, i). (r +1, j) is the jth node of parameter r +1. [( r, 1) , ( r + 1) , j] represents the line connecting node (r, i) and node (r + 1, j). the amount of ants is m. in the process of evolution, ant k (k=1,2, …, m) selects the walk direction according to the pheromone of each path. at time t, the probability of ant k from position (r, i) to position(r + 1, j) is 1 1 1 0[( , ),( , )] [( , ),( , )] arg max {[ ( )] [ ( )] } otherwise rj m r i r j r i r j t t q q s s             (10) where, mr+1 is the allowable range of the r + 1th parameter, 1[( , ),( , )]( )r i r j t  is the intensity of pheromone trace on path [( r, i), ( r + 1), j] at time t. initially, the intensity of pheromone of each path is equal. 1 0[( , ),( , )]( )r i r j c   , c is constant. 1[( , ),( , )]( )r i r j t  is visibility of pheromone trace on path [( r, i) , ( r + 1) , j]. it’s is 1 1 1 1 1 [( , ),( , )] min ( ) ( , ) ( ) r i r j t j r j j r        (11) where, j(r + 1, j) is the heuristic function value of different node, jmin (r +1) is the minimum of j(r + 1, j) in jmr+1. when the ant selects the path, α is the important degree index of the intensity of pheromone trace, while β is the important degree index of the visibility of pheromone trace. α≥0, β≥ 0. q is random number, q[0, 1 ]. q0 is a parameter, 0≤q0≤1. s is the next node selected according to the probability shown in eq.12. d http://www.gruppofrattura.it http://dx.medra.org/10.3221/igf-esis.28.04&auth=true b. ye et alii, frattura ed integrità strutturale, 28 (2014) 32-41; doi: 10.3221/igf-esis.28.04 37 1 1 1 1 1 1 1 [( , ),( , )] [( , ),( , )] [( , ),( , )] [( , ),( , )] [( , ),( , )] [ ( )] [ ( )] ( ) [ ( )] [ ( )] r r i r j r i r jk r i r j m r i r j r i r j j t t p t t t                  (12) in the process of creating solution, ants visit each node and update the pheromone using local pheromone along the path. 1 1 11 new old [( , ),( , )] [( , ),( , )]( )r r j r i r j          (13) where, ρ is the decay parameter of pheromone, 0<ρ< 1. letbe δτ=τ0=c, τ0 is the initial pheromone. after all ants walk through all nodes, the global pheromone is updated as: 1 1 1 1 1 1 1 [( , ),( , )] min gb [( , ),( , )] [( , ),( , )] ( ) ( ) if[( , ),( , )] global-best-tour ( ) otherwise r i r j r i r j r i r j f r i r j                         (14) where fmin gb is the value of objective function at the beginning of iteration. in addition, for continuous domain object, stochastic search leads to low solution efficiency and solution result dispersion. this paper combines the stochastic search and the deterministic search. after each iterating, ants need to move using the deterministic search strategy. they will then gradually move to the optimal solution. if the solution is worse at this node, the distance of the deterministic moving is longer. at time t, the deterministic moving principle of node (r, i) is: 1 best , , , , best , , , if if t t r i r i r i rt r i t t r i r i r i r x x x x x x x x x           (15) min ( , ) , max min r i r r i r r f f x e f f     (16) where bestrx is the optimal solution of parameter r at present, e is step size, f(r, i) is the minimum value finding in the process of passing through the node (r, i). when the feasible scheme is not obtained, min( , )r i rf f . min rf is the minimum value of all nodes for parameter r, while maxrf is the maximum value of all nodes for parameter r. by the nodes moving, nodes will gradually move to the optimal solution. the precision of search results is improved. until to all r, , , t t r i r jx x e  , that is to say the distance of arbitrary two nodes of all parameters is less than e, which shows that the algorithm is convergence. at that time, the search range has focused near the optimal solution. the optimal solution of parameter r is bestrx . the iteration will stop. in addition when the cumulative times t of search moving is greater than the maximum moving times tmax the algorithm will stop iteration. in the process of iteration, the deterministic search continuously modified the moving path. it will be helpful to overcome the disadvantage of result discretization and improve the global optimization capability. therefore, the iaca can obtain the high precision results and need not to set too large n. its application to large-scale optimization problems can be easily implemented on parallel machines resulting in a significant reduction of required time. in common, the iaca is conducted according to the following procedure: step 1 parameter initialization, parameter equal division (n). step 2 m ants walk from the node “start”. according to eq.10 and eq.12, every ant individually computes the transition probability and creates the parameter scheme. step 3 compute and save the object function value of feasible scheme, and save the optimal scheme at present. step 4 update the pheromone according to eq.13 and eq.14 using the path of the ant associated with the feasible scheme. step 5 each node deterministically moves according to eq.16. step 6 1t t  , if to every parameter r, , , t t r i r jx x e  , or t≥tmax, then output the optimal scheme. otherwise, return to step 2. http://www.gruppofrattura.it http://dx.medra.org/10.3221/igf-esis.28.04&auth=true b. ye et alii, frattura ed integrità strutturale, 28 (2014) 32-41; doi: 10.3221/igf-esis.28.04 38 in ecndt, the problem of quantifying defect size from probe signals is formulated as an optimization problem, which seeks a set of defect size by minimizing an objective function, representing the difference between the models predicted signal and the measured signal. the inversion process iteratively attempts to estimate a set of defect size so that the corresponding model predicted signal matches the measured signal. such method presented by this paper is based on the underlying physical process. a time-varying current flowing into an exciting coil placed near to the specimen induces eddy current in the specimen under testing. the induced eddy current, depending on the spatial values of the resistivity and magnetic permeability, affects the signal detected by the surrounding pick-up coils or magnetic sensors. then, changes in impedance of the coil are used as a basis for detecting the presence of discontinuities in the specimen by inversion of the measured data. the inversion process is shown in fig. 4. figure 4: the flowchart of quantitative estimating size of deep defects in multi-layered structures from ecndt signals using iaca. the measured signal at the position of the defect is assumed the target signal. a set of randomly generated initial defect parameters are given to the finite element model to predict the eddy current coil responses associated with these defects. then, the model predicted signals are compared with the measured signal and the corresponding value of the objective function is evaluated. if the value of the objective function is less than a predefined threshold, the iterative process is terminated. otherwise the iaca correct the defect parameters. then the process is iterated until the error becomes less than the predefined threshold. numerical and experimental results o use iaca in optimization, it is essential to settle the configuration of many parameters. parameter equal division number (n), ant number (m) and maximum moving times (tmax) are heuristically determined and dependent on the optimization problem. in the method with the help of iaca applied to determinate the parameters of the defect, the length, the height and the depth of the defect are expressed as: x=[l, h, d] (17) where, l is the length of the defect, h is the height of the defect; d is the depth of the defect. the object function is: 2 1 1 1 ' g i ii f a z z     (18) where, a is a constant, zi is the model predicted coil impedance at scanning position i, and zi’ is the corresponding probe impedance from actual measurement. g is the number of scanning positions. the object function is calculated by comparing the signals of the measurement with those of the prediction by fem forward model. updating the pheromone and deterministically moving are operated based on the object function value. after a lot of iteration, the ant with the highest object function value is expected to indicate the defect size. the other features of iaca which are used in this paper are shown in tab. 1. the structure parameters are shown in tab. 2 and the coil parameters are shown in tab. 3. t n predicted signal stop initial defect parameters numerical simulate fem forward model δz≤ε ? stop criterion? y measured signal modified defect parameters http://www.gruppofrattura.it http://dx.medra.org/10.3221/igf-esis.28.04&auth=true b. ye et alii, frattura ed integrità strutturale, 28 (2014) 32-41; doi: 10.3221/igf-esis.28.04 39 configuration operation n 50 m 20 ρ 0.1 α 1 β 2 q0 0.1 c (8×40038.5) −1 tmax 500 e 0.01 table 1: iaca configuration. structures conductivity σ ms/m permeability μ thickness t mm layer 1 18.5 μ0 1 layer 2 18.5 μ0 2 defect 0 μ0 table 2: structure parameters. item quantity number of turns n 330 inside radius r1 mm 3.0 outside radius r2 mm 5.11 length l mm 20.70 inductance l0 mh 1.02 resistance r0 ω 19.84 frequency f0 hz 400 liftoff l1 mm 0.0 table 3: coil parameters. in the actual computing process, we find the method needs a long computing time to find the global optimum, when the estimation of the objective function requires a field analysis by means of the fem. so, we propose a novel method with a signal database consisting of impedance signals of different size computed by fem in advance, applied to the optimization of defect inspection, to reduce the computing time for the whole optimization. the identification results using iaca are shown in tab. 4. at the same time, the identification results using the least square method are shown in tab. 5. group 1 group2 group 3 group 4 true length (mm) 16 17 18 19 true height (mm) 0.8 1 0.8 1 true depth (mm) 1.2 1.7 1.2 1.7 estimated length (mm) 16.26 17.16 17.83 18.74 estimated height (mm) 0.84 1.04 0.77 1.04 estimated depth (mm) 1.22 1.73 1.15 1.66 length error (%) 1.63 0.94 -0.94 -1.37 height error (%) 5 4 -3.75 4 depth error (%) 1.67 1.76 -4.17 -2.35 table 4: identification of defect using iaca. http://www.gruppofrattura.it http://dx.medra.org/10.3221/igf-esis.28.04&auth=true b. ye et alii, frattura ed integrità strutturale, 28 (2014) 32-41; doi: 10.3221/igf-esis.28.04 40 group 1 group2 group 3 group 4 true length (mm) 16 17 18 19 true height (mm) 0.8 1 0.8 1 true depth (mm) 1.2 1.7 1.2 1.7 estimated length (mm) 16.65 17.25 17.74 19.53 estimated height (mm) 0.91 0.94 0.83 1.08 estimated depth (mm) 1.17 1.65 1.3 1.78 length error (%) 4.06 1.47 -1.44 2.79 height error (%) 13.75 -6 3.75 8 depth error (%) -2.5 -2.94 8.33 4.71 table 5: identification of defect using the least square method. comparing tab. 4, using iaca, and tab. 5, using the least square method, the results show that the former has higher precision and robustness than the latter. conclusion n iterative improved ant colony algorithm has been implemented with fem to determine the defect size in ecndt. defect size is automatically obtained and material parameters of the structure can be obtained more effectively than the existing ecndt method. the main advantage of this method is its easy implementation. particularly, the resolution of fem has been pre-calculated. the only work is to write a few lines of code in order to define parameters to be optimized, the objective function and the constraints. the improved fast inverse method with the database computed in advance distinctly reduces the computing time of the whole optimization. the possibility of quantifying size of deep defects in multi-layered structures is demonstrated. a decrement in human errors and faster inspections can be expected by completely automatic inspection. acknowledgment his work is supported by the national natural science foundation of china grant no. 51105183, the research fund for the doctoral program of higher education of china grant no. 20115314120003, the applied basic research programs of science and technology commission foundation of yunnan province of china grant no. 2010zc050, the foundation of yunnan educational committee grant no. 2013z121, the national college student innovation training program funded projects grant no. 201210674014, the science and technology project of yunnan power grid corporation grant no. k-yn2013-110. references [1] takagi, t., huang, h., fukutomi, h., tani, j., numerical evaluation of correlation between crack size and eddy current testing signal by a very fast simulator, ieee trans. magn., 34 (1998) 2581–2584. [2] auld, b.a., moulder, j.c., review of advances in quantitative eddy current nondestructive evaluation, j. nondestr. eval., 18 (1999) 3-36. [3] ye, b., cai, j., huang, p., fan, m., gong, x., hou, d., zhang, g., zhou, z., automatic classification of eddy current signals based on kernel methods, nondestruct. test. eva., 24 (2009) 19-37. [4] mandache, c., khan, m., fahr, a., yanishevsky, m., numerical modelling as a cost-reduction tool for probability of detection of bolt hole eddy current testing, nondestruct. test. eva., 26 (2011) 57-66. [5] shubochkin, a.e., eddy-current testing of the quality of railway wheels, russ. j. nondestruct. test., 41 (2005) 189192. [6] kojima, f., fujioka, t., quantitative evaluation of material degradation parameters using nonlinear magnetic inverse problems, int. j. appl. electrom., 25 (2007) 57-163. a t http://www.gruppofrattura.it http://dx.medra.org/10.3221/igf-esis.28.04&auth=true b. ye et alii, frattura ed integrità strutturale, 28 (2014) 32-41; doi: 10.3221/igf-esis.28.04 41 [7] fitzpatrick, g.l., thome, d.k., skaugset, r.l., shih, e.y.c., shih, w.c.l., magneto-optic/eddy current imaging of aging aircraft: a new ndi technique, mater. eva., 51 (1993) 1402-1407. [8] thollon, f., lebrun, b., burais, n., jayet, y., numerical and experimental study of eddy current probes in ndt of structures with deep flaws, ndt&e int., 28 (1995) 97-102. [9] chomsuwan, k., yamada, s., iwahara, m., improvement on defect detection performance of pcb inspection based on ect technique with multi-sv-gmr sensor, ieee trans. magn., 43 (2007) 2394-2396. [10] edward, p., manson, j., the application of dual-frequency eddy current inspection to aircraft structures, insight, 44 (2002) 141-145. [11] zenzinger, g., bamberg, j., satzger, w., carl, v., thermographic crack detection by eddy current excitation, nondestruct. test. eva., 22 (2007) 101-111. [12] huang, l., he, r., zeng, z., an extended iterative finite element model for simulating eddy current testing of aircraft skin structure, ieee trans. magn., 48 (2012) 2161–2165. [13] dorigo, m., gambardella, l.m., ant colony system: a cooperative learning approach to the traveling salesman problem, ieee trans. evolut. comput., 1 (1997) 53-66. [14] mohan, b.c., baskaran, r., a survey: ant colony optimization based recent research and implementation on several engineering domain, expert syst. appl., 39 (2012) 4618-4627. http://www.gruppofrattura.it http://dx.medra.org/10.3221/igf-esis.28.04&auth=true microsoft word numero_42_art_6.docx m. olzak et alii, frattura ed integrità strutturale, 42 (2017) 46-55; doi: 10.3221/igf-esis.42.06 46 focused on mechanical fatigue of metals numerical analysis of the influence of liquid on propagation of a rolling contact fatigue crack mirosław olzak, janusz piechna warsaw university of technology, institute of aeronautics and applied mechanics, poland zpk-mo@meil.pw.edu.pl, jpie@meil.pw.edu.pl paweł pyrzanowski warsaw university of technology, institute of aeronautics and applied mechanics, poland pyrzan@meil.pw.edu.pl, http://orcid.org/0000-0003-1015-7645 abstract. numerical investigations of the propagation of rolling contact fatigue crack filled by the liquid have been conducted. two models of fluid – crack interaction have been considered. in the first model called “hydrostatic” the assumption of incompressible, inviscid and weightless liquid was accepted. it was also assumed that due to the wheel load the trapped liquid could not get outside the crack and its volume remained constant until the rising pressure would open up the crack mouth again. on this assumption the analysis has a steady-state character. in the second model it has been assumed that the crack is filled by the viscous, incompressible fluid and the fluid motion as well as the resulting pressure distribution can be represented by one-dimensional form of the reynolds equation. the method for solving the problem of the coupled motion of liquid and crack faces has been developed and series of calculation were made. the method has been employed for the predicting of crack deformation in the course of wheel rolling. keywords. rolling contact fatigue; fluid viscosity; stress intensity factor. citation: olzak, m., piechna, j., pyrzanowski, p., numerical analysis of the influence of liquid on propagation of a rolling contact fatique crack, frattura ed integrità strutturale, 42 (2017) 46-55. received: 31.05.2017 accepted: 08.06.2017 published: 01.10.2017 copyright: © 2017 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. introduction he research presented in the paper is part of more comprehensive investigations aimed at understanding the propagation mechanisms of rolling contact fatigue cracks in railway rails. liquid penetrating the crack interior may be considered as a very important factor affecting the crack propagation. the effect of liquid influence has been already investigated; e.g., m. kaneta and y. murakami [1] considered a 3d model representing a semi-elliptical surface crack situated in the elastic half space. the load had a form of the hertz stress of t m. olzak et alii, frattura ed integrità strutturale, 42 (2017) 46-55; doi: 10.3221/igf-esis.42.06 47 ellipsoidal distribution moving along the half space. the effect of liquid presence in the crack was considered in terms of stress the magnitude of which was equal to the pressure acting on the crack mouth. variations of non-dimensional stress intensity factors as functions of the load position were analysed. the contact between the crack faces was neglected, therefore the negative values of ki factor appeared. a.f. bower [2] analysed a 2d model of a surface crack situated in the elastic half space using a dislocation distributions finding analytical method. the hertz stress replaced the wheel action. the model considered included the contact effect and the tangential component of interaction between the crack faces as well as the tangential loads acting on the surface. the liquid interaction was considered using the following three different ways: (a) reducing the value of friction coefficient on the crack faces; (b) introducing a hydraulic pressure of the magnitude equal to the pressure acting on the crack mouth; (c) assuming a constant volume of the crack interior after the pressure acting on the crack mouth has closed it. variations of stress intensity factors were analysed as functions of different parameters of the model and the direction of load motion. in this paper the authors have once again attempted to define the role of liquid in the development of rolling contact fatigue (rcf) cracks in railway rails. the effect of liquid has been represented as a crack face pressure distribution. this distribution has been determined taking the following two ways (a) a hydrostatic approach in which a constant volume of liquid is assumed to be trapped in the crack interior and (b) a hydrodynamic approach based on the equations of viscous fluid motion. additionally, both the wheel and rail have been modelled as finite, linear elastic solid bodies. the authors used a unique algorithm that employs the flexibility matrices of the bodies in contact, which were determined using fem [3]. the algorithm employed allows for solving 2d and 3d problems of the wheel-rail contact taking into account the contact between the crack faces well as introducing many other phenomena, like pressure of the liquid filling the crack, wheel loads acting upon the contact zone, thermal loads, residual stresses in the rail, rail bending, variable friction coefficients over the contact surface and different types of the crack faces interaction [4, 5]. the model description art of the analysis reported here was based on considerations of the 2d model, in which a rectangular prism with an oblique crack represented a rail head segment with a crack, and a cylinder represented the rail wheel. the value of cylinder radius was equal to that of the wheel. the magnitude of normal load r was selected in the way ensuring that maximal magnitudes of pressure in the cylinder-prism contact zone (remote from the crack) be equal to about 870 mpa, i.e. the magnitude revealed in the real wheel-rail contact zone. the values of young modulus and poisson’s ratio assumed were equal to those revealed by steel. the boundary conditions for the prism are shown in fig. 1. the conditions of plane strain-state were imposed on the model. in the course of investigations presented below the crack had a length of a = 5.81 mm and was inclined at α = 25. the existence of tangential forces was assumed in the contact zones, determined by the friction coefficients μp in the prism-cylinder contact zone and μs at the crack faces, respectively. figure 1: scheme of the 2d model of a rail with the crack of together with the rail wheel. the current position of cylinder was represented by the coordinate x and the value x = 0 corresponded to the point at which the crack intercepted the rail raceway. on the diagrams the cylinder position is represented by the non-dimensional parameter x/b, where b = 6.7 mm is half of the contact length calculated using the hertz formulae for a cylinder and a half space. a r tx x 140 3 8 r450y  p m. olzak et alii, frattura ed integrità strutturale, 42 (2017) 46-55; doi: 10.3221/igf-esis.42.06 48 the investigations conducted have proved that as the cylinder comes closer to the crack its mouth tends to open allowing the liquid to penetrate the crack interior (fig. 2a) when the rolling wheel closes the crack mouth the space is formed in which the liquid is entrapped (fig. 2b). a) b) figure 2: part of a deformed fem mesh representing the prism with the crack for two positions of the cylinder: a) x/b = -1.2 – corresponding to the maximum crack opening; b) x/b = -0.9 corresponding to the position at which the crack mouth is closed liquid models ne of the main problem is the use of a suitable fluid model. this model should provide high compatibility with reality and, on the other hand, be easy to solve. there are usually two main groups of models: hydrostatic and hydrodynamic. hydrostatic model the first attempt the authors made at investigations, in which the liquid presence in the crack was considered dates back to 1993 [6, 7]. in the analysis carried out the assumption of incompressible, inviscid and weightless liquid was accepted. it was also assumed that after the crack mouth had closed due to the wheel load the entrapped liquid could not get outside the crack and its volume remained constant until the rising pressure would open up the crack mouth again. this assumption was rather unrealistic since the real crack faces reveal rough surfaces making a tight closing impossible, the analysis however aimed at the determination of the limit of pressure and amplitudes of stress intensity factor variations that might be affected by the liquid presence in the crack. the aforementioned assumptions forced the quasi-static nature of the analysis, i.e. the time was not a parameter of the model. for that reason the authors called their model the hydrostatic one. additionally, zero pressure at the crack mouth was assumed, and in the “bubble”, i.e. in the closed space with no contact, the magnitude of pressure was independent of a position, while along the contact zone in the crack interior the pressure magnitude was changed linearly from zero value to that in the “bubble”. similar models are still used in the calculations by different authors for their simplicity and quick calculation time. they assume a pressure distribution between a cylinder and a prism calculated according to the hertzian theory [8 11] or, like in the authors’ solution, pressure distribution during rolling is calculated on an ongoing basis [12]. despite the fact that the assumption accepted for the hydrostatic model make it not very realistic and the results obtained cannot be fully reliable, one can get, however, an impression of how strongly the liquid could affect the propagation of crack. hydrodynamic model the authors have decided to apply the model in which the liquid filling the crack interior is represented in a more realistic way i.e. with its viscosity included. a similar approach was used at work [13]. since the crack height is very small as compared to its length a 1d model was assumed for representation of a liquid flow in the crack. as the crack front is closed changes appearing in the crack height due to the wheel rolling generate a flow along the crack. the velocities of the crack faces directed along the crack were neglected. on the assumption that the crack is filled with incompressible liquid one can represent a pressure distribution using the reynolds equations in the form: p h3h 12η s s t          (1) o m. olzak et alii, frattura ed integrità strutturale, 42 (2017) 46-55; doi: 10.3221/igf-esis.42.06 49 where: p – liquid pressure h – local crack height η coefficient of dynamic viscosity s – coordinate directed along the crack t – time the equation is completed by the following boundary conditions:  p pambs 0  dp 0 s lds  it can be easily seen that the pressure distribution depends on the crack height and the speed at which the crack faces come closer to each other. the pressure magnitude at the crack mouth equals to the ambient pressure pamb while its value at the crack front results from the condition of zero pressure gradient that should be satisfied there. since the applied algorithm for solving the contact problems deals with discrete systems it would be more convenient to transform the reynolds equation also to a discrete form. using the planes perpendicular to the crack plane one can divide it into the segments that correspond to those employed in the algorithm for solving the contact problems (fig. 3). figure 3: part of the fem mesh showing the way the crack vicinity is divided into finite elements. the grid used in flow analysis is the same as boundary fem nodes the sectional planes bear the numbers within (1, n). all quantities appearing in a given section have the indices equal to the plane number (fig. 4). the section position is determined by the s-coordinate measured along the crack length. figure 4: the way of crack discretisation by means of its sectional division using n perpendicular planes after replacing the derivatives in eq (1) with the corresponding finite quantities the reynolds equation has the form 1 2 3 nn-1ii-1 i+1 s 0 ss s li-1 i+1i h i pi m. olzak et alii, frattura ed integrità strutturale, 42 (2017) 46-55; doi: 10.3221/igf-esis.42.06 50 p p p p3 3i 1 i i i 1h h1 1s s s si i δhi 1 i i i 1 i2 2 12 s s δti 1 i 1 2            (2) where: h hi 1 ih 1i 22   ; h hi i 1h 1i 22    ; after transformation and substitution for δhivi δt  being the velocity of crack faces motion we have   3 3 3 3h h h h1 1 1 1i i i i 2 2 2 2p p p 6 η v s si 1 i i 1 i i 1 i 1s s s s s s s si i 1 i 1 i i i 1 i 1 i                                  (3) the discrete boundary conditions have the form p1 = pamb pn = pn-1 after writing eq (3) for all sections of the crack we obtain the following set of linear equations with a 3-diagonal matrix pb a d11 1 1 pc b a d22 2 2 2 c b a dpn 1 n 1 n 1 n 1n 1 c b dn n npn                                                              (4) where: 3a hi 1i 2   3c hi 1i 2   3 3b h hi 1 1i i 2 2             d 6 η v s si i i 1 i 1       and from the boundary conditions we have m. olzak et alii, frattura ed integrità strutturale, 42 (2017) 46-55; doi: 10.3221/igf-esis.42.06 51 a1 = 0 b1 = 1 d1 = pamb bn = 1 cn = -1 dn = 0 for the sake of simplicity the ambient pressure pamb = 0 was assumed in calculations. if the vector of crack heights [h] = {h1, h2, ..., hn} is known ( i.e. the values hi are known for all sections) together with the crack faces velocity vector [v] = { v1, v2, ..., vn} one can determine the pressure vector [p] = { p1, p2, ..., pn} using eq (4). in the case of crack in elastic material the pressure change [p] affects the height change [h] and the crack faces velocity change [v], respectively. therefore, when dealing with the problem of a wheel rolling along a rail with a crack filled with liquid one should use iterative methods for calculation of the pressure distribution along the crack. the scheme of solution to the aforementioned problem is given below (the index in brackets represents the current iteration number while the index with no brackets stands for the section number). wheel path is divided into small fragments x small enough to fulfill assumption that the pressure can be treated as constant during motion along it. at the beginning of a new segment x pressure distribution along the crack and the crack height distribution are described by the vectors [p(0)] and [h(0)]. a new pressure distribution vector [p(i)] at i-th iteration is calculated in following way: a) taking the pressure distribution vector [p(i-1)], the crack height distribution vector [h(i)] is calculated for the wheel position at the end of segment x b) first vector of crack faces transversal velocity [v(i)] is calculated from following formula: [h ] [h ](i) (0) [v ](i) δt   where: t is the time of wheel passing distance x c) then by the help of eqs. (4), using vectors [v(i)] and [h(i)] vector describing the pressure distribution [p’(i)] is defined d) then modified pressure vector [p(i)] is calculated m 1 1 [p ] [p ] [p ](i) (i 1) (i)m m     where: m – natural number from the range 10001000000 chosen experimentally (lower mfaster convergence, higher m – better stability) modified pressure vector have been used to assure convergence of described iterative algorithm iterative process is repeated until in all crack face nodes the pressure difference between actual pressure [p’(i)] and modified pressure [p(i)] is less than the arbitrary chosen value peps = 0.002 mpa, i.e. . p max{[p ] [p ]}eps (i) (i)   . if presented condition is fulfilled the pressure vector for the next wheel position is calculated. in presented calculation segments x equal 0.025mm have been used. two times reduction of the segment length x hasn’t had any significant influence on the pressure distribution inside the crack. the following assumptions were accepted in the model with liquid: liquid is weightless and incompressible liquid fills the whole crack interior even when subject to a negative pressure initial clearance between the crack faces changes linearly taking the value of 0.005 mm at the crack mouth and 0 at its front (existence of clearance have been find during investigation of real cracks) plane strain conditions tangential forces in the contact zones are neglected (μp = μs = 0) boundary conditions for the prism are shown in fig.2. the following values of parameters were assumed: speed of wheel rolling 30 m/s (108 km/h) ambient pressure pamb) = 0 m. olzak et alii, frattura ed integrità strutturale, 42 (2017) 46-55; doi: 10.3221/igf-esis.42.06 52 crack length a = 5.81mm angle of the crack inclination α = 25 for the material of prism and cylinder the young modulus e = 210000 mpa and poisson’s ratio ν = 0.3 (the values for steel) cylinder radius r = 450 mm load acting upon the cylinder r = 9 kn/mm. coefficient of dynamic viscosity η = 0.01 [ns/m2] the dynamic viscosity of the pure water at a temperature of 20c has the value of η = 0.001 [ns/m2]. but η varies increasing as the pressure increases and temperature decreases [14]. additionally, the water filling the crack can be oil contaminated. therefore, to ensure that the calculated stress intensity factors are not underestimated, a slightly higher value of viscosity has been accepted in calculations. results comparison between the hydrostatic and the hydrodynamic model o find out to how the form of the model used affects the obtained values of amplitudes of stress intensity factors the calculations were performed once again for the hydrostatic model, neglecting the tangential forces in contact zones and introducing a clearance between the crack faces and for hydrodynamic model. the results are presented on fig. 5. in both cases the tangential forces in contact zones were neglected (friction coefficients μp = μs = 0.0) and a clearance between the crack faces changed linearly assuming the value of 0.005 mm at the crack mouth and 0 at its front, respectively -3 -2 -1 0 1 2 3 4 5 x/b -12 -8 -4 0 4 8 12 16 20 24 28 k [ m p a  m ] ki hydrostatic model ki hydrodynamic model kii hydrostatic model kii hydrodynamic model figure 5: distributions of the stress intensity factors in the process of cylinder rolling along a prism with the crack filled with viscous liquid (hydrodynamic model) and inviscid liquid (hydrostatic model), respectively. the value of amplitude ki obtained from the hydrodynamic model with viscous liquid was almost two times higher than the value obtained from the hydrostatic model with inviscid liquid while the value of amplitude kii remained unchanged. substantial reduction in ki value observed when neglecting the tangential forces in the hydrostatic model and introducing at the same time a clearance in the crack resulted from both a smaller volume of liquid entrapped in the crack interior and reduction in the magnitude of wheel load acting on the rail. when the clearance appears in the crack its deflection arises due to a cylinder action and the load is transferred to the areas ahead of and behind the crack, respectively. t m. olzak et alii, frattura ed integrità strutturale, 42 (2017) 46-55; doi: 10.3221/igf-esis.42.06 53 results for the hydrodynamic model fig. 6 show the distributions of pressure, crack heights and liquid flow along the crack, respectively, for different cylinder positions obtain using hydrodynamic model. a) b) c) d) figure 6: distributions of: a) pressure (p); b) crack height (h); c) crack faces velocity (v); d) flow rate (q), respectively, along the crack (s) for different load positions (x/b). at the starting point of the analysis, i.e., when the cylinder is located ahead of the crack at a distance of x/b = -2.832, zero values of the pressure, crack faces speed and flows, respectively, are assumed. despite the fact that the distance between the cylinder and the crack mouth equals almost 3b (18.975 mm) the crack height at its mouth due to the cylinder action reaches the value of about 10 μm. as the cylinder comes closer to the crack its faces open generating the negative pressure (down to -1.63 mpa) and the liquid is sucked into the crack interior. the process terminates when the cylinder comes into contact with the end of the wedge-shaped raceway part behind the crack. the process of crack mouth closing starts at that moment manifesting through high negative values of crack faces speed close to the crack mouth. as the cylinder moves on and the wedge-shaped raceway part behind the crack deflects the raceway points situated more far away from the crack come into contact with cylinder, while those close the crack mouth loos the contact, so the position at which the closing velocity of crack faces is highest (i.e. most negative) moves into interior of the crack. reduction of volume filled by liquid causes the pressure increase and induces the motion of liquid in direction of lowering pressure. whereas, volume growth causes pressure decreases and makes possible of fluid inflow. due to the use in calculation of simplified model of liquid omitting the cavitation (liquid evaporation), calculated pressure can drop down to values lower than zero. such situation can be noticed in crack at wheel position equal x/b  -1.0 . wheel, reducing the crack height near the crack mouth increases pressure in central crack segment and due to induced outward faces motion near the crack tip forces the dramatic pressure drop. due to the viscosity of fluid the inflow of liquid to the low-pressure area is restrained and the pressure difference increases. when the cylinder is situated at the point x/b = -0.593 the pressure at the crack front reaches its minimum of -449 mpa. starting from that point the pressure rises along the whole crack length and the growth is most rapid at the crack front, where it takes positive values as the cylinder comes as close as x/b = -0.556. the crack height reduces continuously at the crack mouth starting at the moment at which the cylinder comes into contact with the wedge-shaped part of raceway behind the crack (x/b = -1.146) and at the same time the flow rate of the liquid flowing out of the crack reduces, despite the pressure growth in the crack interior (near the crack front). the crack height reduces until the cylinder reaches the point x/b = 0.44, at which its value comes down to 0.32 μm at a distance of 0.33 mm from the crack mouth. m. olzak et alii, frattura ed integrità strutturale, 42 (2017) 46-55; doi: 10.3221/igf-esis.42.06 54 at the point x/b = 0.701 the liquid pressure attains its maximal value equal to 907.8 mpa. as the cylinder rolls on the liquid pressure drops and the process is most rapid from the crack mouth side. it is caused by the process of crack mouth opening as the cylinder-prism contact zone rolls on behind the crack. when the cylinder crosses the point x/b  1.5 the opening rate of the crack mouth is high enough to enable generation of low negative pressure and the liquid flow into the crack (positive q value at the crack mouth) while, at the crack front the faces come closer to each other and the pressure reaches the value of 700 mpa. the crack mouth opens until the cylinder-prism contact zone moves behind the crack (x/b  1.8) and then the crack height reduces. as the cylinder comes far away from the crack the pressure at the crack front drops, the velocities at which the crack faces come closer to each other reduce and the flows in the crack interior reduce as well. the analysis terminates at the cylinder position x/b = 5.224. during the rolling process the crack faces do not come into contact at any point. conclusions n all the cases that have been investigated so far, with no liquid present in the crack, the amplitude of kii changes (kii ) dominates, while the value of ki remains low exerting only a weak influence on the fatigue crack propagation [2-5]. the liquid presence in the crack causes a substantial growth of ki value, despite the model considered. the value of amplitude ki obtained from the hydrodynamic model with viscous liquid was almost two times higher than the value obtained from the hydrostatic model with inviscid liquid while the value of amplitude kii remained unchanged (fig. 7). the tangential forces in the contact zones were neglected in both the models considered. it is known (see [5]) that the aspherities of the crack faces may come into contact creating a kind of shape joints that block the crack faces motion relative to each other, limiting therefore considerably the value of kii. if the liquid presence in the crack is considered ki may dominate and the crack may propagate by means of tearing of the crack front i.e. mode i of crack propagation may arise. it occurred in practice, however that the algorithm presented above reveals unsatisfactory convergence. when the cylinder is situated at a point far from the crack a few up to several dozen thousand of pressure iterations are required for the position change x = 0.025 mm. but when the cylinder comes above the crack the required number of pressure iterations grows up to several hundred thousand or even reaches a million. in view of the above it seems quite unreasonable to consider models of cracks filled with liquid with the tangential forces in the contact zones introduced into the model since a solution to the contact problem posed that way needs iterative procedures. to calculate the tangential forces and slips one should make several hundred up to several thousand iterations for each position change x. when using the model with the liquid and tangential forces introduced, after each iteration of tangential forces a smaller number of liquid pressure iterations is required than for the corresponding model with no tangential forces introduced, of course for the same cylinder position change x. one should, however, be conscious of the necessity for longer calculation time, even by over a dozen times. it should be noted that the analysis presented above still reveals some shortages. no limits imposed on negative pressure formation in liquid are introduced and as a result the negative pressure arising close to the crack front the magnitude of which reaches 449 mpa. the presence of negative pressure opens up the possibility that the phenomenon of cavitation may arise in the crack interior. limiting the negative pressure value to -0.08mpa, i.e. the value at which water of a temperature of about 20 c starts to boil may restrain substantially the process of crack filling with liquid at the phase when the wheel comes closer to the crack. a smaller amount of liquid present in the crack results in a lower value of ki . moreover, at the pressure of 800 mpa the liquid cannot be assumed as incompressible. taking into account the liquid compressibility would probably result in additional reduction of the value of ki. it should be noted that however the zero value of ambient pressure was assumed in the presented analysis, one should rather assume the hydrodynamic pressure that might be generated over the wheel-rail contact zone e.g. under wet weather conditions. in the future, the liquid model used here can be used to calculate the development of real cracks with geometry measured on real object. an example of such measurements can be found at work [15]. i m. olzak et alii, frattura ed integrità strutturale, 42 (2017) 46-55; doi: 10.3221/igf-esis.42.06 55 references [1] kaneta, m., murakami, y., propagation of semi-elliptical surface cracks in lubricated rolling/sliding eliptical contact, journal of tribology, transaction of the asme, 113 (1991) 270-275. doi: 10.1115/1.2920616. [2] bower, a.f., the influence of crack face friction and trapped fluid on surface initiated rolling contact fatigue cracks, journal of tribology, transaction of the asme, 110 (1988) 704-711. doi: 10.1115/1.3261717. [3] olzak, m., stupnicki, j, wójcik, r., numerical analysis of 3d crack propagation in raill-wheel contact zone, proc. of int. conf. on rail quality and maintenance for modern railway operation, deft, (1992) 385-395. doi: 10.1007/978-94-015-8151-6_31. [4] stress analysis of rail rolling contact fatigue – the european raill research institute, utreht, the netherlands, final raport, rp no 19 (1996). [5] olzak, m., stupnicki, j., numerical study of stress intensity factors for cracks in raceways with the experimentally determined interaction between crack faces, computational methods in contact mechanics v, witpress, (2001) 253-262 [6] rail rolling contact fatigue – the european rail research institute, utreht, the netherlands, annual report –1993. [7] bogdański, s., olzak, m.. stupnicki, j., influence of liquid interaction on propagation of rail contact fatigue cracks, proc. of the 2nd mini conference on contact mechanics and wear of rail/wheel systems, budapest, (1996) 134143. [8] glodež, s., potočnik, r., flašker, j., zafošnik, b., numerical modelling of crack path in the lubricated rolling–sliding contact problems, engineering fracture mechanics, 75 (2008) 880–891. doi:10.1016/j.engfracmech.2007.02.001. [9] fletcher, d.i, hyde, p., kapoor, a., modelling and full-scale trials to investigate fluid pressurisation of rolling contact fatigue cracks, wear 265 (2008) 1317–1324. doi:10.1016/j.wear.2008.02.025. [10] makino, t., kato, t., hirakawa, k., the effect of slip ratio on the rolling contact fatigue property of railway wheel steel, international journal of fatigue, 36 (2012) 68–79. doi:10.1016/j.ijfatigue.2011.08.014. [11] dallago, m., benedetti, m., ancellotti, s., fontanari, v., the role of lubricating fluid pressurization and entrapment on the path of inclined edge cracks originated under rolling–sliding contact fatigue: numerical analyses vs. experimental evidences, international journal of fatigue, 92 (2016) 517–530. doi:10.1016/j.ijfatigue.2016.02.014. [12] ancellotti, s., benedetti, m., dallago, m., fontanari, v., fluid pressurization and entrapment effects on the sifs of cracks produced under lubricated rolling-sliding contact fatigue, procedia structural integrity, 2 (2016) 3098–3108. doi: 10.1016/j.prostr.2016.06.387. [13] balcombe, r., fowell, m.t., olver, a.v., ioannides, s., dini, d., a coupled approach for rolling contact fatigue cracks in the hydrodynamic lubrication regime: the importance of fluid/solid interactions, wear, 271 (2011) 720– 733. doi:10.1016/j.wear.2011.02.005. [14] tribology handbook, edited by m.j.aeale, butterworths, london, (1973). [15] pyrzanowski, p., estimation and consequences of the crack thickness parameter in the assessment of crack growth behaviour of "squat" type cracks in the rail-wheel contact zone, engineering fracture mechanics, 74(16) (2007) 25742584. doi: 10.1016/j.engfracmech.2006.11.017. << /ascii85encodepages false /allowtransparency false /autopositionepsfiles true /autorotatepages /none /binding /left /calgrayprofile (dot gain 20%) /calrgbprofile (srgb iec61966-2.1) /calcmykprofile (u.s. web coated \050swop\051 v2) /srgbprofile (srgb iec61966-2.1) /cannotembedfontpolicy /error /compatibilitylevel 1.4 /compressobjects /tags /compresspages true /convertimagestoindexed true /passthroughjpegimages true /createjobticket false /defaultrenderingintent /default /detectblends true /detectcurves 0.0000 /colorconversionstrategy /cmyk /dothumbnails false /embedallfonts true /embedopentype false /parseiccprofilesincomments true /embedjoboptions true /dscreportinglevel 0 /emitdscwarnings false /endpage -1 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can be opened with acrobat and adobe reader 5.0 and later.) >> /namespace [ (adobe) (common) (1.0) ] /othernamespaces [ << /asreaderspreads false /cropimagestoframes true /errorcontrol /warnandcontinue /flattenerignorespreadoverrides false /includeguidesgrids false /includenonprinting false /includeslug false /namespace [ (adobe) (indesign) (4.0) ] /omitplacedbitmaps false /omitplacedeps false /omitplacedpdf false /simulateoverprint /legacy >> << /addbleedmarks false /addcolorbars false /addcropmarks false /addpageinfo false /addregmarks false /convertcolors /converttocmyk /destinationprofilename () /destinationprofileselector /documentcmyk /downsample16bitimages true /flattenerpreset << /presetselector /mediumresolution >> /formelements false /generatestructure false /includebookmarks false /includehyperlinks false /includeinteractive false /includelayers false /includeprofiles false /multimediahandling /useobjectsettings /namespace [ (adobe) (creativesuite) (2.0) ] /pdfxoutputintentprofileselector /documentcmyk /preserveediting true /untaggedcmykhandling /leaveuntagged /untaggedrgbhandling /usedocumentprofile /usedocumentbleed false >> ] >> setdistillerparams << /hwresolution [2400 2400] /pagesize [612.000 792.000] >> setpagedevice microsoft word numero 24 articolo 17 g. cricrì, frattura ed integrità strutturale, 24 (2013) 161-174; doi: 10.3221/igf-esis.24.17 161 a consistent use of the gurson-tvergaard-needleman damage model for the r-curve calculation gabriele cricrì department of mechanical engineering, university of salerno, italy gcricri@unisa.it abstract. the scope of the present work is to point out a consistent simulation procedure for the quasi-static fracture processes, starting from the micro-structural characteristics of the material. to this aim, a local nineparameters gurson-tvergaard-needleman (gtn) damage law has been used. the damage parameters depend on the micro-structural characteristics and must be calculated, measured or opportunely tuned. this can be done, as proposed by the author, by using an opportunely tuned gtn model for the representative volume element simulations, in order to enrich the original damage model by considering also the defect size distribution. once determined all the material parameters, an mt fracture test has been simulated by a fe code, to calculate the r-curve in an aeronautical al-based alloy. the simulation procedure produced results in a very good agreement with the experimental data. keywords. gtn model; ductile fracture; cell calibration; r-curve. introduction luminium alloys are widely used in aircraft structures, transportation industries and civil engineering due to their relative lightness and versatility. in particular, the fuselage skin, which thickness ranges from 1 to 3 mm, is often made of aluminium alloys capable of fully ductile behaviour. thus, in order to better take advantage from the material metallurgical characteristics, the damage tolerance design concept is often used in the aircraft structures sizing. following this approach, the presence of macroscopic cracks during the ordinary service life can be tolerated, as long as they are under control. for this reason, in this field the study of both the static and the dynamic response of cracked panels in ductile regime, in terms of residual strength it assumes a relevance that can hardly be overestimated [1]. the socalled r-curve, that represents the critical stress intensity factor versus the crack length for a given structure, is a widely used tool to design by following the above criteria. unfortunately the r-curve behaviour depends both from material and geometrical properties and then it changes as the test set-up changes [2, 3]. a reliable calculation model of the r-curve is, for this reasons, very important for the design purposes, in order to drastically decrease the amount of the very expensive physical tests. from a micro-mechanical point of view, ductile failure is typically characterized by three coupled stages: nucleation, growth and coalescence of voids, which are induced in the metal alloy matrix by the presence of a variety of microscopic defects. in order to consider the effects of these voids evolution on the stress-carrying capability of a mechanical continuum during simulations, damage mechanics models are often used. many models for ductile fracture growth have been proposed in the past [4 11] and, for their relative simplicity and efficiency the gurson-tvergaard-needleman (gtn) model and many of its variants are proposed by several authors and also included in some public fe codes, like warp3d [12]. these kinds of models for ductile fracture include the micro-mechanical effects of void nucleation, growth, and coalescence of micro-voids in the constitutive equation used to describe the mechanical continuum. the coalescence mechanism, in particular, induces a strain softening at the large-scale material response. therefore, the a http://dx.medra.org/10.3221/igf-esis.24.17&auth=true http://www.gruppofrattura.it g. cricrì, frattura ed integrità strutturale, 24 (2013) 161-174; doi: 10.3221/igf-esis.24.17 162 material becomes susceptible of bifurcations, instabilities and localized deformation modes. this is because the governing equations become hyperbolic in some unknown area of the continuum and make ill-posed the boundary value problem. as a consequence, numerical solutions chronically suffer from mesh dependency [13 15]. a popular and well proven in literature way to avoid this problem is the use some nonlocal formulations of the damaged material model. this is done by replacing the local variables denoting stress and strain fields, as well as the damage variables and the other internal ones, with nonlocal variables, which are space-weighted averages of the local ones. the averaging volume is related to a characteristic length lc depending from the failure evolution at the micro-structural scale. the nonlocal formulations are capable to regularize ill-posed problems associated with damage, but require a very large increasing of the computational amount with respect to the local damage formulations [16 19]. from the computational point of view, the regularization is strictly related to the characteristic length; in fact, with lc a constraint to the material law is introduced in addition to the large scale material behavior [20]. also the local models can be regularized, and the easiest way to do this in a fe analysis is introducing the characteristic length not at the material model level, but more roughly at the element level. in other words, the element dimension will be strictly related to the characteristic length lc. in many works the latter computational strategy is adopted [21 24]. they typically present many free parameters that should be calibrated and fixed in a physically consistent way in order to make the calculation procedure effective. in the present work, a complete procedure to calculate the r-curve starting from a local form of the gtn model is presented and a numerical application on a widely used aeronautical alloy, 2024a-t351, is reported, using material and test data provided by industrial research offices. differently from the purely phenomenological approach that is usually employed to calculate all the model parameters, a procedure to consistently calculate some of these parameters on the basis of objective micro-structural data has been performed. in order to enrich the original damage model also the defect size distribution has been considered. with such methodology, the arbitrariness of the parameters tuning is strongly reduced, and a double result is attained: the number of the fe run needed to simulate the r-curve behaviour drastically decreases, and the transferability of the whole methodology to different geometries and boundary conditions is improved. once determined all the material parameters, to calculate the r-curve an mt fracture test has been simulated by the free fe code warp3d. the gtn model for ductile fracture n a homogeneous ductile metal model, the total strain amount usually leaves unchanged the volume, because the plastic part of the strain is dominant with respect to the elastic one. on the other hand, in a material model containing voids which matrix phase is ductile, the volume can globally change, due to the local plastic flow arising around the voids boundary and, consequently, the void volume change. then, the material model response to an imposed global strain will be a stress-strain curve presenting a softening curve, nevertheless the matrix material model have hardening behaviour. in such model, the voids can grow until the global load carry capability becomes negligible. the gurson-tvergaard (gt) model is able to explain the local strength decreasing during the fracture process of ductile metals in the intermediate phase between the nucleation and the coalescence of voids. standing this characteristic, in the void growth model the number of voids is kept constant. nucleation and coalescence are taken into account before the homogenization of the material model, applying some opportune corrections, originally proposed by needleman et al., directly to the stress-strain cell response. updated in this way the gt model, it is usually named gtn model. gurson-tvergaard model the homogenization technique is based on the stress-strain characterization of a representative volume element (rve), that can be roughly defined as the minimum material volume containing all the micro-structural information of a heterogeneous material, related to the specific problem under investigation (see, e.g., [25 27]). in the gurson-tvergaard void growth model, the rve of the material is considered as a cubic volume with a single void, yet existing in the virgin material. the initial void volume fraction f0 should be chosen as the ‘equivalent’ volume fraction corresponding to the physical distribution of voids inside the rve (fig.1). the resulting homogenized material model was defined by modifying the analytical solution of the single void cell (fig. 1) performed by gurson and limited to a rigid-plastic material model of the matrix. the corrections take into account for the hardening of the matrix material and for the presence of void cell array instead of a single void cell. they are represented by the coefficients q1, q2, q3 in the critical surface definition, originally introduced by tvergaard. i http://dx.medra.org/10.3221/igf-esis.24.17&auth=true http://www.gruppofrattura.it g. cricrì, frattura ed integrità strutturale, 24 (2013) 161-174; doi: 10.3221/igf-esis.24.17 163 figure 1: physical vs. equivalent voids distribution (plane representation). the homogenized constitutive law is defined by (tensors are indicated with bold characters):     2 22 1 3 3 , , , 2 1 0 2 eq m eq m q f q fcosh q f                       (1) pd d      ε σ (2)  1 :pdf f d  ε i (3) (1 ) : pf d d     (4)  p σ c ε ε (5) 1 0 0 0 0    0 0 n n if and d d otherwise                    (6) where: eq. (1) defines the plastic surface; eq. (2) is the plastic flow rule; eq. (3) is the void growth rate definition; eq. (4) imposes the equivalence between micro and macro-mechanical plastic work; eq. (5) is the global stress-strain relationship; eq. (6) is the plastic hardening power law for the matrix material. further, the symbols indicate:  : stress tensor; p : total and plastic strain tensors; c : constitutive elastic law; eq : von mises equivalent global stress; m : global mean stress;  : current matrix flow stress (internal variable of the model);  : current matrix equivalent strain (internal variable); f : voids volume fraction (internal variable); n : hardening coefficient; 00 : yield equivalent stress and strain; q1, q2, q3 : tvergaard correction coefficients. http://dx.medra.org/10.3221/igf-esis.24.17&auth=true http://www.gruppofrattura.it g. cricrì, frattura ed integrità strutturale, 24 (2013) 161-174; doi: 10.3221/igf-esis.24.17 164 voids nucleation model the nucleation of the first void in an array of cells is implicit in the above model. with the increasing load, further voids can nucleate in the rve, and this fact is indirectly taken into account in the homogenized material law by increasing the void growth rate defined in eq. (3). in the present study the following relation is used:  nucdf a d  (7) where:   2 1 22 n n nn f a exp ss                 (8) the corrected void growth rate becomes:    1 :pdf f d a d   ε i (9) the expressions (7-9) relate the voids growth rate due to the nucleation process to the internal equivalent strain rate d . this acceleration is driven by the parameter a and it is limited to an internal strain condition in which  is quite close to a certain value n, representing the matrix strain value where the nucleation takes place. three new parameters are so introduced in the constitutive law (1-6): fn : magnitude of the volume fraction rate increasing; n : main value of the internal strain for which the nucleation takes place sn : standard deviation of the gaussian distribution. the void nucleation law completes the analytical description of the gtn model. cell dimension it is well known that the undefined equilibrium problem in a material domain which constitutive law has softening branches loses ellipticity near the critical point and then it is hill-posed [27]. if the finite element method is used to search a solution, disregarding the above problem, the resulting discrete equation can be solved, but the solution is chronically mesh dependent and the convergence can’t be reached. this occurs because near the softening condition the strain field would become discontinuous and, correspondently, in the discrete problem the strain tends to concentrate in a small zone, which size depends on the elements size. smaller the element size, smaller the zone affected by the strain concentration. this behaviour is commonly named strain localization. if the softening law derives from a physical model of the material, the incongruence can be explained noting that, at the micro-structural scale, the material domain can’t be longer be considered homogeneous, so the softening at the large scale material law can be attributed to the micro-structural geometric changes. apparently, the consequence of this fact is that we can’t use local homogenization techniques if the global material law presents a softening behaviour. in practice, using a local fe model, we can avoid the mesh dependence by keeping fix the element dimensions in the fracture zone, regardless with the macroscopic geometry of the domain. in particular, the dimension d0 to be mandatory controlled is the cell length in the direction perpendicular to the crack plane. the correct value of the element dimension depends on the scale of the local fracture process related to the particular material under consideration. in this way, the element dimension becomes a further parameter of the material constitutive law. in other words, we couldn’t use a local homogenized law because the analytical equilibrium problem is hill-posed, but the error that cannot be eliminated in the fe solution of this problem can be driven in order to reach a numerically correct result. voids coalescence in the constitutive law (1-6) the internal strain state is represented by a unique variable  . this simplification can be accepted only in the early phases of the void growth, in which the internal strain (and stress) distribution doesn’t vary too much. in the following load phase the matrix material model becomes unrealistic. in fact, in this phase the fracture advances between two consecutive voids (coalescence) and then the rve model with the single equivalent void itself becomes unrealistic. the voids coalescence, and the consequent crack advancing, is modelled in the fe code by eliminating the corresponding element (named killed element) when a critical volume fraction value fc is reached. many studies have demonstrated that http://dx.medra.org/10.3221/igf-esis.24.17&auth=true http://www.gruppofrattura.it g. cricrì, frattura ed integrità strutturale, 24 (2013) 161-174; doi: 10.3221/igf-esis.24.17 165 the critical value should be much less than 1, which is the value rigorously provided by the theory. for many ductile materials the critical volume fraction can be set-up between 0.15  0.25, and a phenomenological correlation furnishes the following empirical law [21, 22]: fc = 0.15 + 2f0 (10) along the crack plane, the element traction forces are still present in this condition (f = fc) and they are gradually decreased until zero is reached, using a multiplicative coefficient , related to the cell dimension d0 and depending from a further parameter , to be set. 0 1         0 1c d d d         (11) in eq. (11) d and dc indicates respectively the actual and the critical value of d0, averaged over the cell volume. cell calibration he material model described above needs the calculation, the measurement or the phenomenological tuning of (at least) 13 parameters:  the internal plastic-hardening parameters n, 0, 0.  the tvergaard correction coefficients q1, q2, q3.  the nucleation parameters fn , n , sn .  the cell height d0.  the initial and critical void volume fractions f0 , fc .  the force release parameter . critical void volume fraction and force release parameter these parameters are related to the coalescence phase. for the present calibration they have been chosen as mean values from the ones present in literature [21, 22]. fc = 0.2;  = 0.1 notwithstanding the above position, the release forces parameter  contributes to form the energy released in the element extinction process, so it can’t be rigorously considered a merely calculation parameter. the coefficient defined in (11) depends on the component of the strain orthogonal to the crack plane. in fact, we can write: 0 0 0 / / exp( ) exp( ) 1 1 1c c c d d d d d d d                rel c  where rel is the stress value present during the force release process (coalescence). thus, the corresponding energy density w released in the coalescence phase can be evaluated, for small , c: | 0 2 2 c c c c w w d               where c is the stress corresponding to the critical strain c (reached when f = fc). then, the parameter  is related to the energy released during the coalescence process. cell height and initial void volume fraction both the cell height d0 and the initial void volume fraction can be estimated considering as a starting point the defect size distribution. t http://dx.medra.org/10.3221/igf-esis.24.17&auth=true http://www.gruppofrattura.it g. cricrì, frattura ed integrità strutturale, 24 (2013) 161-174; doi: 10.3221/igf-esis.24.17 166 2024a-t351 all three directions equivalent diameter (m) volume fraction (%) standard deviation nearest neighbour (m) nearest neighbour standard deviation (m) minimum separation distance (m) minimum separation distance standard deviation (m) average diam of particles in size category (m) all sizes 0.76 0.33 10.61 8.01 8.55 8.09 1.75 1:2 0.13 0.06 16.14 12.11 14.65 12.39 1.41 2:3 0.10 0.05 35.18 26.48 32.82 27.30 2.41 3:4 0.07 0.04 62.38 46.78 59.61 48.71 3.41 4:6 0.12 0.07 58.90 40.68 53.76 42.22 4.87 6:8 0.11 0.08 93.54 64.45 86.12 66.44 6.88 8:10 0.09 0.09 130.27 96.68 122.14 101.91 8.86 10+ 0.14 0.21 126.95 97.90 111.94 99.72 13.23 tabella 1: defects size distribution. as shown above, the cell dimension, and in particular the cell height, is a fundamental parameter because, when the strain localization occurs, the cell height coincides with the localized strip of material. so, from this point, the most of the energy released is proportional to this parameter. on the other side, in the present model the energy released is also influenced by the coalescence parameters and by the shape of the stress-strain curve (that depends on the nucleation and tvergaard parameters). then, the correct cell height should be chosen taking into account the influence of all the above parameters in the fracture process. if we consider the cell as a representative volume element (as it is usually done) it should contain a sufficiently representative voids distribution. of course, a greater rve contains more micro-structural information, but it is less useful in the present model because the strain would localize in a strip with fixed height. in conclusion, the cell height can’t be precisely defined without a critical consideration of all the constitutive law parameters influence. as an approximated evaluation, we can consider the bigger defects above the last 20% of the total volume fraction as it were the driving defects of the localization process. in this way, with reference to the tab.1, an rve, which dimension is coincident with the cell height, will contain one defect with 10+ m diameter and the appropriate number of minor defects as deduced from the size distribution (tab. 2). category volume fraction average diameter (m) spherical average diameter (m) volume (m3) density (defects/ mm3) defects in the rve 1:2 0.0013 1.41 1.79 3.00 433000 904 2:3 0.0010 2.41 3.07 15.1 66200 138 3:4 0.0007 3.41 4.34 42.8 16300 34 4:6 0.0012 4.87 6.20 125 8810 18 6:8 0.0011 6.88 8.50 322 3410 7 8:10 0.0009 8.86 11.3 752 1200 2 10+ 0.0014 13.23 17.7 2920 479 1 tabella 2: defects distribution in the rve (from tab. 1 data rearranging). the cell height and the initial void volume fraction can be finally estimated: d = (10+ category density) 1/3≈ 130 m; f0 = 0.0014 the d value is in good agreement with the literature values that range between 80÷200 m. http://dx.medra.org/10.3221/igf-esis.24.17&auth=true http://www.gruppofrattura.it g. cricrì, frattura ed integrità strutturale, 24 (2013) 161-174; doi: 10.3221/igf-esis.24.17 167 this procedure can appear quite arbitrary. in fact, if the categories were chosen in a different way (for instance the last category could be 8+ or 12+), the resulting d and f0 parameters were different. on the other side, this can be avoided if we consider for all the distribution, as stated above, the bigger defects above the last 20% of the total volume fraction; in this case, is arbitrary the 20% value. as discussed above, a certain degree of arbitrariness is un-eliminable because the cell height (and consequently the initial volume fraction) has the double role of dimension of the rve and dimension of the strain localization zone. then, once established the cell height on the basis of a reasonable rve choice, the effect of the strain localization should be taken into account by tuning both the nucleation parameters (that can be considered responsible for the minor defects growth) and the coalescence parameters fc , . as an example, in the pictures below (fig. 2) is reported the equivalent strain distribution inside two different twodimensional rves with the same initial volume fraction (see fig.1 for the unstrained configurations). the first, is the simplified gurson rve with a single void; the second, has a void distribution compatible with the tab. 2 distribution. figure 2: equivalent strain distribution inside two rve. 0.00 0.10 0.20 0.30 0.40 0.50 0.00 200.00 400.00 600.00 800.00   single void distribution figure 3: global cell response. it can be deduced that the localization zone dimension is larger in the first that in the second rve. this fact influences the global cell response (fig. 3). a more general discussion on this topic can is presented in [28]. supposing that the second rve represents a sufficiently accurate evaluation of the material behaviour, the pre-defined cell height seems too large in relation to the ‘true’ localization zone, as it results comparing the different entity of energy involved in the load process. once established a compromise value d = 100 m < 130 m, the residual difference should be taken into account by tuning, as written above, the nucleation and the coalescence parameters. tvergaard correction coefficients the correction coefficients q1, q2, q3 can be calculated from a single void rve model. the global cell behaviour has been calculated for two different load conditions: http://dx.medra.org/10.3221/igf-esis.24.17&auth=true http://www.gruppofrattura.it g. cricrì, frattura ed integrità strutturale, 24 (2013) 161-174; doi: 10.3221/igf-esis.24.17 168 1) imposed global strain x > 0 and free surface condition for y and z direction. 2) imposed global strain x > 0 and y = z = 0.2x . in the following pictures 4-5 are presented the cell mesh and the resulting strain distribution in the x direction for the two considered load cases. figure 4: fe model of the single void cell. figure 5: strain (x) distribution for the two load cases. it can be noted that in the first case the x-direction strain is about uniform, but in the second there is a consistent strain concentration on the void boundary. this agrees with the constitutive law (1-6), that attributes the void volume fraction growth to the mean stress (eq. 3) that in the first case is much lower than in the second one. the global rve responses have to be compared with the eq. (1-6) stress-strain curves resulting from an equivalent load process. this comparison allows to determine the tvergaard correction coefficients. in the present work, the analytically derived relation is adopted [23], that: 23 1q q in the subsequent refinement of the model calibration the parameter q3 could be left free. the two remaining free parameters q1, q2 are determined by imposing on the homogenized law the condition that the characteristic values: 0 ;    c max cw d      are equal to that resulting from the fem calculation. the first load case (uniaxial strain) is quite insensitive to the parameter variation, due to the very slow void growth rate present in this condition, so the calibration has been done with reference to the second load case. finally, the resulting values are: http://dx.medra.org/10.3221/igf-esis.24.17&auth=true http://www.gruppofrattura.it g. cricrì, frattura ed integrità strutturale, 24 (2013) 161-174; doi: 10.3221/igf-esis.24.17 169 q1 = 1.25; q2 = 0.98; q3 = 1.56 in fig. 6, the comparison between the fe model of the cell and the homogenized law (1-6) stress-strain curve is reported for the two load cases. 0.00 0.20 0.40 0.60 0.00 400.00 800.00   cell result homogenized law 0.00 0.05 0.10 0.15 0.20 0.25 0.00 500.00 1000.00 1500.00 2000.00   cell result homogenized law figure 6: global cell response compared with eq. (1-6) for the two load cases. nucleation parameters in the present work, the nucleation parameters have been considered as correction parameters, not directly related to the microstructure. then, the parameters fn, n , sn have been used to fit the experimental-numerical results in the residual strength curve, and their values are reported in the following section. in fig. 7 the coalescence law (11) has been included into the constitutive law, with the imposed values fc = 0.2 for the starting point, and  = 0.1 for the curve slope, as established before. it is shown that the energy related to the coalescence process is a non negligible part of the total cell energy. 0.00 0.05 0.10 0.15 0.20 0.25 0.00 500.00 1000.00 1500.00 2000.00   cell result homogenized law cohalescence figure 7: global cell response compared with eq. (1) and the coalescence law. r-curve determination he r-curve calculation procedure has been tested on an m(t) specimen model, which experimental results have been published in [2]. the m(t) specimen used for the residual strength results is made by a 1.28 mm thick 2024 sheet material. the t http://dx.medra.org/10.3221/igf-esis.24.17&auth=true http://www.gruppofrattura.it g. cricrì, frattura ed integrità strutturale, 24 (2013) 161-174; doi: 10.3221/igf-esis.24.17 170 panel width is h = 500 mm and the initial half crack length is a0 = 49.78 mm. testing and data evaluation were done according to astm specification e561-86 for r-curve determination. the residual strength tests were done under displacement control. mesh generation the fem mesh has been generated within the ansys code pre-processor module. all the elements are eight nodes brick, in order to be allowable for the subsequent calculations with the warp3d [12] solver. the specimen has been modelled taking into account the three symmetry conditions. along the crack plane, all the elements are cubic with length d0 = 106.667 m (see the calibration section). along the thickness t, six elements have been generated, so that t/2 = 0.64 mm = 6d0. in fig. 8 some particulars of the mesh generation are reported. it should be noted that, as shown in the last picture, there the row of elements before the initial crack front is not present. further, the elements that will be killed during the crack advance simulation are indicated with a different colour, that indicates two different materials. in fact, for computational reasons, the killable elements have to be separated from the non-killable ones; otherwise, the solver can try to kill the above elements in contrast with the crack plane definition. this contrast will produce a program error (the limitation is related only to the force-release kill procedure). the elements immediately before the initial crack front have been deleted in order to avoid an undesired ‘collaboration’ to the initial crack strength. the as generated mesh, and the boundary conditions have been ‘translated’ into the corresponding warp3d commands by using a fortran routine. figure 8: mesh generation. results: load vs. crack length curve from the experimental test data, the following material parameters have been chosen for the numerical analysis: e = 71100 mpa y = 366 mpa u = 482 mpa f = 0.173 http://dx.medra.org/10.3221/igf-esis.24.17&auth=true http://www.gruppofrattura.it g. cricrì, frattura ed integrità strutturale, 24 (2013) 161-174; doi: 10.3221/igf-esis.24.17 171 so, the internal stress parameters are: 0 = y = 366 mpa o = y / e = 0.00515 f,log = log(1 + f) = 0.1596 u,true = u (1 + f ) = 565 mpa n = log(f,log /o) / log(u,true /0) = 8.0 the other constitutive law parameters values, calculated in the above section, are: q1 = 1.25 q2 = 0.98 q3 = 1.56 f0 = 0.0014 d = 0.107 mm fc = 0.2  = 0.1 after the solution has been calculated, by using a fortran routine, the warp3d output file can be read and interpreted. for every step, the total reaction value ry in the traction direction and the total number of killed elements nk are stored. then, with simple data manipulations, the gross stress s and the half crack length a are pointed out: s = ry / (t·h/4) a = nk / (t/2)·d 2 the resulting curve s(a) has to be compared with the experimental curve in order to perform the tuning of the nucleation parameters. nucleation parameters tuning from the afore cited experimental test data, the following experimental stress vs. crack length curve results (fig. 9). by varying the nucleation parameters n, sn, fn, different curves have been calculated . the parameter fn gets down the curve when it is increased; sn has the opposite effect, with a little influence on the shape of the curve; the increasing of n can slightly move the curve maximum value versus the increasing a. the best nucleation parameter values are: n = 0.09 sn = 0.09 fn = 0.2 0.00 20.00 40.00 60.00 80.00 100.00 150.00 200.00 250.00 300.00 s a a 0 figure 9: experimental stress vs. crack length curve. final results and r-curve the astm specification e561-86 for r-curve determination imposes that the curves have to be expressed in terms of equivalent stress intensity factor and equivalent crack length, in order to take into account for the plastic deformation around the crack tip. for the m(t) central crack specimen, the equivalent sif is defined by: http://dx.medra.org/10.3221/igf-esis.24.17&auth=true http://www.gruppofrattura.it g. cricrì, frattura ed integrità strutturale, 24 (2013) 161-174; doi: 10.3221/igf-esis.24.17 172  eqeq eq eq eq a k sec s a a s a h            (12) the equivalent crack length has two alternative definitions: the one, based on the crack opening displacement in the traction direction of the centre of the crack; the other, which has been adopted in the present work, based on the plastic radius evaluation. the plasticity contribution to the equivalent crack length is done by: 2 1 2 eq p y k r           (13) then, the equivalent crack length is defined by: 0;  δeq p eq eqa a r a a a    (14) the plastic radius definition (13) contains the equivalent sif and, vice-versa, the expression (12) contains the equivalent crack length. it is then necessary to calculate iteratively the two expressions (12), (13-14) up to the convergence is reached. the current plastic radius value is then done, in an iterative formulation by:       2 2 1 11 1;    2 2 i i p pi p p y y a r s a r a s a r r                          the convergence is reached when the (i+1)-th value of the plastic radius differs from the i-th value for a small enough quantity. by using the s(a) values calculated before, and after the above descript transformation (s, a)  (keq, aeq), we can compare the calculated and experimental r-curves, as reported in fig. 10. as a result, the calculated r-curve is in very good agreement with the experimental test. 40.00 80.00 120.00 160.00 200.00 0.00 2000.00 4000.00 6000.00 8000.00 keq [nmm ]-1.5 aeq experimental calculated figure 10: comparison between calculated and experimental r-curve. in the following pictures, some results from the fe solution are reported. the warp3d solution data stored during the calculation has been ‘translated’ in ansys commands with a fortran routine, in order to use its postprocessor module. in fig. 11 the calculated stress distribution in the traction direction (y) for the half-crack length increasing a = 25 mm is reported for the whole model and near the crack front. it is possible to appreciate the thorough-the-thickness distribution (remember that symmetry conditions have been imposed). in the following fig. 12, the crack front shape is pointed out. it results from the elements extinction procedure described above. http://dx.medra.org/10.3221/igf-esis.24.17&auth=true http://www.gruppofrattura.it g. cricrì, frattura ed integrità strutturale, 24 (2013) 161-174; doi: 10.3221/igf-esis.24.17 173 figure 11: calculated stress distribution in the traction direction (y) for a = 25 mm. figure 12: crack front shape resulting from elements extinction. in fig. 13, the enhanced deformed configuration is reported, for a = 25 mm. in the first picture, the deformation around the crack tip is pointed out and it is possible to appreciate the strain localization effect. in the last picture, the residual strain near the initial crack length is shown. considering that the crack surface is stress free, the deformation is totally plastic. further, the difference between the residual strain on the symmetry surface (the visible surface) and the external one is shown, were for the external surface (near the plane stress condition) the plastic strain is much higher. figure 13: deformed configuration near the crack tip and the initial crack length. http://dx.medra.org/10.3221/igf-esis.24.17&auth=true http://www.gruppofrattura.it g. cricrì, frattura ed integrità strutturale, 24 (2013) 161-174; doi: 10.3221/igf-esis.24.17 174 conclusions complete procedure for the r-curve calculation has been presented, tested on a mt test specimen simulation reproducing a widely used aeronautical alloy, 2024a-t351, which gives results in a very good agreement with the experimental tests. the algorithm was based on the local form of the gurson – tvergaard –needleman damage model and, differently from the purely phenomenological approach that is usually employed to calculate all the model parameters, it uses a preliminary rve definition, partially based on microstructural information on the material, to determine most of the continuum-scaled model. in order to enrich the original damage model also the defect size distribution has been considered. only few parameters are tuned on the basis of an experimental test: they are the nucleation parameters fn, n, sn. they are related to the material behaviour, nor to the geometry of the test specimen. for this reason, they can reasonably be determined with a single test result, as is done in the present work, and the same values can be used for different geometries, as the design process requires. references [1] r. citarella, g. cricrì, advances in engineering software, 40 (2009) 363–377. [2] office of aviation research residual strength test on stiffened panels with multiple-site damage, technical report, washington, d.c. 20591 [www.tc.faa.gov/its/act141/reportpage.html]. [3] t. v. pavankumar, m. k. samal, j. chattopadhyay, b. k. dutta, h. s. kushwaha, e. roos, m. seidenfuss, int. j. of pressure vessels and piping, 82 (2005) 386. [4] b. dodd, b. yilong, ductile fracture and ductility, academic press inc. ldt., orlando, florida, (1987). [5] m. li, int. j. mech. science, 42 (2000) 907. [6] l. xia, c. fong shih, j. w. hutchinson, j.mech. phys. solids, 43(3) (1995) 389. [7] l. xia, c. fong shih, j.mech. phys. solids, 43(2) (1995) 233. [8] l. xia, c. fong shih, j.mech. phys., solids, 43(12) (1995) 1953. [9] l. xia, c. fong shih, j.mech. phys., solids, 44(4) (1996) 603. [10] c. ruggieri, t. l. panontin, r. h. jr. dodds, int. j. of fracture, 82 (1996) 67. [11] l. malcher, f. m. andrade pires, j. m. a. césar de sá, int. j. of plasticity, 30-31 (2012) 81. [12] a. s. gullerud, k. c. koppenhoefer, a. roy, r. h. jr. dodds. warp3d–release 13.9 department of civil engineering, university of illinois at urbana–champaign urbana, illinois, (2000), issn: 0069–4274. [13] h. l. schreyer, m. k. neilsen, int. j. numer. methods engrg., 39 (10) (1996) 1721. [14] g. cricrì, r. luciano, simulation modelling practice and theory, elsevier, 11 (2003) 433. [15] g. cricrì, m. perrella, c. calì, composites part b: engineering, 45(1) (2013) 1079. [16] s. d’hers, e. n. dvorkin, in: mecánica computacional, buenos aires, argentina, xxix (2010) 5189. [17] m. k. samal, m. seidenfuss, e. roos, b. d. dutta, h. s. kushwaha, in: proceedings of the institution of mechanical engineers, part c: journal of mechanical engineering science (2009) 223. [18] x. lu, j. p. bardet, m. huang, comput. methods appl. mech. engrg., 198 (2009) 3702. [19] g. hütter, t. linse, u. mühlich, m. kuna, int. j. of solids and structures, 50(5) (2013) 662. [20] p. j. sanchez, a. e. huespe, j. oliver, int. j. of plasticity, 24 (2008) 1008. [21] j. faleskog, x. gao, c. f. shih, int. j. of fracture, 89 (1998) 355. [22] x. gao, j. faleskog, c. f. shih, int. j. of fracture, 89 (1998) 375. [23] z. l. zhang, c. thaulow, j. odegard, engineering fracture mechanics, 67 (2000) 155. [24] p. negre, d. steglich, w. brocks, engineering fracture mechanics, 71 (2004) 2365. [25] g. cricrì, e. garofalo, f. naddeo, l. incarnato, j. of polymer science part b: polymer physics, 50(3) (2012) 207. [26] m. hori, s. nemat-nasser, mech. of materials, 31 (1999) 667. [27] j. f. ganghoffer, l. j. sluys, r. de borst, eur. j. mech. solids, 18 (1999) 17. [28] h. fei, k. yazzie, n. chawla, h. jiang, j. of electronic materials, 41(2) (2012) 177. a http://dx.medra.org/10.3221/igf-esis.24.17&auth=true http://www.gruppofrattura.it microsoft word numero_52_art_22_2637 m. fouzia et alii, frattura ed integrità strutturale, 52 (2020) 281-298; doi: 10.3221/igf-esis.52.22 281 optimization design based approach for the determination and minimization of the displacement under tensile load in hybrid composite joint fouzia merabbi laboratory of mechanics of structures and solids (lmss) mechanical engineering department-faculty of technology, university of sidi bel abbès bp 89, cité ben m’ hidi sidi belabbes 22000 – algeria merabbi-f@hotmail.fr abdelkader lousdad, abdelkader megueni laboratory of mechanics of structures and solids (lmss) mechanical engineering department-faculty of technology, university of sidi bel abbès bp 89, cité ben m’ hidi sidi belabbes 22000 – algeria a_lousdad@yahoo.com, a_megueni@yahoo.fr abderahmane sahli mechanical engineering department-faculty of technology, university of sidi bel abbès bp 89, cité ben m’ hidi sidi belabbes 22000 – algeria mail:sahliabderahmen@yahoo.fr abstract. composite materials are most often used for lengthier and thin structures susceptible to buckle. the optimization is often carried out taking into consideration the resistance to buckling and tensile loads for minimum displacement i.e maximization of the tensile load for composite assembly joint. it well known that nowadays that composite material in structural mechanics is widely used in many industrial sectors such as in aerospace and aeronautic, automobile, marine industries as well as in and civil engineering. composite materials are attractive due to their advantages and performance i.e: lighter weights, high resistance to thermal and mechanical loads, resistance to corrosion and wear. in this paper an investigation is focused on the problem of hybrid assembly joint (bolted –bonded) composite structures. the aim is the optimization of the main influencing parameters. a bonded assembly has only one advantage which is its lightness; on the other hand bolted assembly has the inconvenient of increasing the weight of the structure and stress concentrators. in practice certain structural designs require the use of hybrid assembly for safety and reliability. the objective of this study is to optimize the influencing factors using both genetic algorithm and design of experiments for high mechanical performance of hybrid composite assembly. keywords. hybrid composite joint; composite structure; adhesive; genetic algorithm; optimization. citation: fouzia, m., abdelkader, l., abdelkader, m., abderahmane, s., optimization design based approach for the determination and minimization of the displacement under tensile load in hybrid composite joint, 52 (2020) 281-298. received: 15.09.2019 accepted: 10.03.2020 published: 01.04.2020 copyright: © 2020 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. https://youtu.be/znguemzpi4y m. fouzia et alii, frattura ed integrità strutturale, 52 (2020) 281-298; doi: 10.3221/igf-esis.52.22 282 introduction he bonding assembly methods are more and more used in aeronautics due to the important use of composite materials. the bonded joints have the advantage of being rigid and lighter. moreover, the drilling of holes for bolts in composite structures is costly and may locally compromise the resistance of the structure by delamination. thus, when it is possible to use bonded joints it is more feasible than the use of bolted joints [3]. however, the certification standards do not always allow only bonded joints. in some circumstances bolts and rivets may be added or coupled to the bonded joints for the purpose of increasing rigidity allowing then the certification of the product. these additional mechanical fasteners are often placed in a way to assure the certification but do not always allow an improvement in mechanical performance of the joint since the two assembly processes do not work in synergy. first of all, it is important to know the works done in the domain of hybrid joints. for this aim a literature review is made in this subject in the following sections. behavior of a single lap hybrid joint under tensile load secondary deflection ig.1 illustrates the way a single lap hybrid joint is deformed under tensile load. in this type of joint the load is eccentric with respect to the neutral axes of the substrates. this causes a secondary deflection in the joint which leads to peeling stresses in the adhesive as shown in fig.2. for composite material joints, it is possible to reduce the secondary deflection by positioning the oriented plies in the direction of the load near the joint plane. this allows reducing the eccentricity between the load transfer lines of the two substrates [1]. the increase of the thickness of the substrates also allows the reduction of the secondary deflection by increasing the rigidity [2]. figure 1: deflection of a single lap hybrid joint under tensile load figure 2: principal stresses in an hybrid joint: 1) peeling in the adhesive, 2) shear of the adhesive 3), matting in the substrates, 4) normal force in the substrates. t f m. fouzia et alii, frattura ed integrità strutturale, 52 (2020) 281-298; doi: 10.3221/igf-esis.52.22 283 transfer of loads according to [3, 12, 14], the bolts do not participate in the transfer of loads in an hybrid joint as long as the adhesive remains intact. this conclusion was obtained via an analytical study made on stepped joint as shown in fig. 3 using seven rows of bolts and an adhesive having a high rigidity. fig. 4 illustrates the role and process of bolt transfer load. the existence of a radial gap between the bolt diameter and the hole in the laminates prevents the bolt from participating to the load transfer as long as the relative displacement between the two laminates has not fill the radial clearance [3, 13]. this situation is different from the case of bolted joints where the friction between the parts allows to the bolts to transfer the load even if there is contact between the bolt and the parts. the presence of the adhesive makes such that there is no friction between the parts. the bolt load transfer decreases when the rigidity of the adhesive increases. according to [2], for a high rigidity adhesive the load transferred by the bolt is about 2% while it can reach 35% for less rigid adhesive figure 3: different configuration of bonded joints figure 4: effect of radial clearance between the bolt diameter and the hole in hybrid joint fig. 5 shows the behavior of a single lap joint subjected to tensile load. the figure shows the comparison between a bonded joint and hybrid joint using an adhesive whose behavior displays an elastic-plastic curve. when the applied load is low the two joints behave in similar manner. however, when the applied is sufficiently higher to cause plastic deformation in the adhesive, the rigidity of the bonded joint decreases. in the case of hybrid joint this decrease in the rigidity of the adhesive leads to an increase of the rate of transfer of load by the bolts. in consequence, the types of joints offer similar rigidity for lower applied loads while the hybrid joint presents a greater rigidity when the applied load is higher as found by [4, 5, 16]. according to kelly’s works [2], and those of [6], the transfer of the load of the bolts is influenced by many parameters other than the rigidity of the adhesive. an increase in the thickness of the adhesive layer leads to an increase in the relative m. fouzia et alii, frattura ed integrità strutturale, 52 (2020) 281-298; doi: 10.3221/igf-esis.52.22 284 displacement between the subtracts for the same level of the external applied load which results in higher load transfer of the bolts. figure 5: comparison between stress-strain curves of a bonded joint and hybrid joint [4, 16]. an increase in the overlap length increases the stiffness of the bonded joint due to the increase in area. however, this increase in the stiffness leads to the reduction of the load transfer of the bolts. for the same reason, an increase in the distance between bolts reduces the load transfer due to the increase of length of the joint [2]. according to ganji [6], the properties of the materials used for the substrates have a significant effect on the load transfer. the results obtained show an increase in load transfer when the axial stiffness of substrates decreases. resistance of the hybrid joints the resistance of hybrid joint is highly affected by the joint parameters. lee‘s works [7] have showed the complexity in analyzing hybrid joints. in their works the authors carried out destructive testing on hybrid joint al-composite using stiffer adhesive. the following conclusion where drawn: only 3% of the external applied load was transferred by the bolts. at the final rupture the maximum measured load is identical for both the bonded joint and hybrid joint. this indicates that the resistance of the equivalent bonded joint is greater than the resistance to the matting of the equivalent bolted joint. this indicates that at the moment the adhesive is completely broken the load transferred to the bolt is already greater than its maximum resistance. theoretical considerations ifferent approaches and modeling are used in investigating hybrid assemblies. according to hart-smith [7] the combination of the two assembly techniques for aerospace applications does not present any significant improvement with respect to bonding or bolting. this is due to the use of very rigid adhesives which do not allow a uniform distribution of the loads between the adhesive and the fixation clamping. the adhesive supports most part of the load. the application of hybrid junctions appears to be effective for repairing or for decreasing the adhesive load at the end of the joint by introducing the fixations to counter peeling. lunsford [15] investigated theoretically three different types of bonded joints metal-metal intended for lokheed missiles and space company in order to develop theoretical tools to design bonded metal-metal junction to replace costly experimental testing. d m. fouzia et alii, frattura ed integrità strutturale, 52 (2020) 281-298; doi: 10.3221/igf-esis.52.22 285 the third of the three types is design such as the load is transferred by a series of fixations and by a film of glue working in shear. this type of junction is not yet called hybrid. fig. 6 illustrates this type of junction used by lunsford as well, as the notation and boundary conditions figure 6: lunsford’s model geometry and notation of the junction. bloc a is subjected to a tensile load fa at x= d while bloc b is subjected to a compression load fb at x= d in elastic domain under plane strain conditions along a longitudinal axis. only the shear stresses in the adhesive and the normal stresses in the substrates are taken in consideration. the flexion of the substrates was not taken into account. the author assumed a uniform distribution in the substrates at the clamping line. the author determined the equations of the stress distribution of the gluing film in the bloc a and b [15]. by using volkerson’s classical approach and the maximum stress in the film at x=l. the following expression is obtained: τmax=f g{e1e1+e2e2[cosb(ην(l – d)+tangb(ην d) sinb(ην(l – d))]} –1/(e ην e1e2e1e2[sinb(ην(l – d)+tangb(ην d) cosb(ην(l – d))]) (1)   1 12 /  g ee e   (2) where:  f : load, g the adhesive shear modulus,  e : young’s modulus of the substrates,    e : substrates thickness  l : bonded length,    d : abscissa the author reaches an expression which do not contain any load transfer ratio as well as the rigidity of the fixations yamaguchi and amano’s analysis yamaguchi and amano in [9] investigated combined junctions from bolted assemblies and bonded assemblies. it is possible to assemble parts using the combination of these two assembly modes which can be either in series or in parallel referred to as hybrid junctions. the authors investigated these combinations in parallel in particular for single overlap joint. the junction is assumed in equilibrium with n lines of fixations in linear elastic conditions. the volkersen’s bonding approach is used [10]. the fixation of the subtracts is not taken into consideration. a tensile load is applied to the junction with two components: f fa f b  (3) with fa the force applied on the adhesive and f b the force applied on the bolts m. fouzia et alii, frattura ed integrità strutturale, 52 (2020) 281-298; doi: 10.3221/igf-esis.52.22 286 by noting   moy a being the mean shear stress deformation of the adhesive, amoyl the mean shear displacement of the adhesive,  ag the adhesive shear modulus and φ the diameter of the fixations, we have:   2/   / 4moy af bl n    (4) and              2 2 2        / 4       / 4     ( /     / 4 a moy a moya a a moy a f bl n g bl n g l e bl n                (5) the authors considering that the bolts are deformed only by shearing at the joint plane. noting gb the shear modulus if the bolt, tb the uniform stress of the bolt and δlb the shear deformation of the bolt we have: 2/ ( ( ) / 4 )b bf n  (6) and     2 2/ / 4 4 b b b moy n f l en      (7) by noting:     b moy a l k l    (8) we obtain:     2      ) /     / 4b b moy af g k l e n   (9) thus:       2 2(   1 /       / 4     / 4moy a baf l e g bl n kg n       (10) by defining α as the tress concentration factor expressed by:  /  total moy al l    (11) and considering        /   max a total a moy aa g l e g     (12) where (τmax)a is the maximum stress at the adhesive, we obtain :     2 21/       / 4      / 4  a b totalf e g bl n kg n l        (13) m. fouzia et alii, frattura ed integrità strutturale, 52 (2020) 281-298; doi: 10.3221/igf-esis.52.22 287 the experimental results are in a good agreement with this equation. the authors analyzed in a decoupled manner the (association of the two assembly modes. moreover, the distribution of the transferred load in the substrates along the lap as well as in the fixation lines was not given. the analysis gives the average portion of the resisting load by the adhesive layer and the average portion of the resisting load supported by n fixation lines. furthermore, by noting ch the global stiffness and considering the last eqn. (10) we have:      2 2      / 4     / 4 /h a bc g bl n kg n e     (14) the parameter can be determined analytically, the parameter can be rewritten as:             /   / /       ^ 2 / 4         ^ 2 / 4 /  u a a uk f c ef g bl n g bl n ec     (15) where cu is the stiffness of the bolt. we thus note that it is possible to use and test the different formulations of the calculation of the stiffness of the fixations in combination with the different analytical approaches of the bonding, to determine the global stiffness of the hybrid assembly. eqn. (13) is used as the objective function. problem statement his study is an investigation on the behavior of hybrid joint assembly when subjected to applied external load. an analysis is carried out on an hybrid bonded-bolted joint model by means of finite element method (fem) using abaqus software. this method has been selected because it allows predicting the deformations of the joint components as well as visualizing the stress distribution inside the joint. moreover, it also permits considering all the parameters of the joint. in the first part the geometric model and the mesh are presented followed by the application of the boundary conditions as well as the modeling of the contact zones will be introduced. finally, the results obtained from the model will be compared with the experimental results obtained by paroissien [11] for validation. geometric model of the hybrid assembly we consider a single lap bolted –bonded assembly with two fixations and a lap length l. this junction three bonded intervals loaded in tension by force f at one end and fixed in the other extremity as shown in fig. 7. first of all, we develop the parametric tools using abaqus computer programming in order to determine the global mechanical behavior. a campaign of statistical testing is carried out then the results obtained are compared and validated. secondly, an optimization is carried for determining the parameters in improving the hybrid joint performance. the joint parameters are given in tab. 1. figure 7: geometric model of the hybrid joint t m. fouzia et alii, frattura ed integrità strutturale, 52 (2020) 281-298; doi: 10.3221/igf-esis.52.22 288 parameters value fixations diameter d(mm) 9.52 substrates thickness (mm) 5 width b(mm) 38 adhesive thickness (mm) 0.7 distance from the free end of the bolts (mm) 19 distance between the bolts(mm) 38 width of the non-bonded part (mm) 115 table 1: the joint parameters. materials and adhesives used the two subtracts are composite materials of type [0,+45,-45,90]s2 with organic carbon/epoxy matrix. the adhesive selected is a poligrip7400/7410 and the bolts are made of ti-6al-4v. the mechanical properties of the materials used are given respectively in tabs. 2,3 and 4. table 2: material properties of the substrates. material properties of the poligrip 7400/7410 (adhesive) value e (mpa) 620 σe(mpa) 3 σr(mpa) 24 ν 0.24 material properties of the bolts ti-6al-4v value e (mpa) 114000 σe(mpa) 1100 σr(mpa) 1170 ν 0.33 table 3: material properties of the adhesive poligrip 7400/7410. table 4: material properties of the bolts. material properties of the substrates value exx(gpa) 140 eyy(gpa) 10 ezz(gpa) 5.2 νxy 0.3 νxz 0.3 νyz 0.5 gxy(gpa) 5.3 gxz(gpa) 5.2 gyz(gpa) 3.9 m. fouzia et alii, frattura ed integrità strutturale, 52 (2020) 281-298; doi: 10.3221/igf-esis.52.22 289 boundary conditions and meshing the upper substrate is fixed at one end which is the far away from the lap zone. the conditions at the extremities are only applied on the nodes of the contact areas of the clamps. for the first substrate the three translations are blocked at the fixed end. for the second substrate the transversal translations (y, z) are blocked. the external load is applied on the second substrate with an imposed displacement at the nodes in contact with the clamps along the longitudinal direction (x). figure 8: model boundary conditions meshing the meshing of the substrates and the adhesive is made using abaqus with an 8 nodes linear brick c3d8r type with reduced integration hourglass control. the meshing is shown in fig. 9(a) and (b) respectively for the adhesive and the substrates. these elements are of 8 nodes 3d solid elements of tetrahydric type representing 83642 elements. they are generally used for structural analysis. (a) (b) (c) (d) figure 9: meshing of the assembly elements. (a)mesh of the adhesive; (b)mesh of the substrates; (c) nut mesh; (d) bolt mesh. comparison with paroisien and kelly’s experimental results n order to validate the results obtained with the model a comparative study is carried out. fig. 10(a) shows the stress –strain plot of the clamps for hybrid joint with pilogrip 7400/7410 adhesive. the results of the finite element model agree quite well with kelly’s experimental results kelly [2]. i m. fouzia et alii, frattura ed integrità strutturale, 52 (2020) 281-298; doi: 10.3221/igf-esis.52.22 290 figure 10(a): comparison the stress –strain plot of the clamps for hybrid joint [2]. the slight difference shown between the two curves is due to the difference between the experimental and analytical results figure 10(b): comparison the stress –strain plot of the clamps for hybrid joint [11]. analysis of the stress distribution in the substrates ig.11 (a) illustrates the substrates longitudinal stress distribution in the lapping zone under the applied external load (matting). the stress is maximum at the holes at the joint and at the limit of the adhesive. moreover fig.11 (b) shows the secondary bending caused by the joint geometry leading to an important stress gradient inside the subtract thickness. stress distribution in the adhesive fig.12 shows the peeling and shear stress distribution in the adhesive. in both cases there is a high stress gradient at the joint extremity. the peeling stress reaches a minimum at the vicinity of the bolts. the bolt heads limit the separation of f m. fouzia et alii, frattura ed integrità strutturale, 52 (2020) 281-298; doi: 10.3221/igf-esis.52.22 291 the parts at these locations resulting in a minimum peeling stress zone. the shearing is lesser with the presence of the bolts. figure 11(a): longitudinal stress distribution (s12). figure 11(b): joint bending (a) (b) figure 12: stress distribution in the adhesive under 14kn applied load. (a) peeling stress ( s33) in the adhesive; (b) shear stress in the adhesive (s13) optimization using genetic algorithm ga he objective of the optimization is to minimize the total displacement δl in the substrates of the hybrid assembly due to an applied tensile stress f. the objective function is then the displacement which is calculated by yamaguchi and amano’s theory [12]. the total displacement ∆𝑙 is given by:     2 2    . . /   . . / 4    . . . / 4.  total a bl f e g b l n k g n        (16) with      2    / 4 /  a uk g bl n ec  (17) t m. fouzia et alii, frattura ed integrità strutturale, 52 (2020) 281-298; doi: 10.3221/igf-esis.52.22 292     . / 2.tanh . l l    (18) and     1 1  2. / . .  ag e e e   (19) the parameters of the hybrid assembly are given in the following tab. 5. table 5: parameters of the hybrid assembly figure 13(a): optimum for tensile load f=1250n using matlab software an unconstrained optimization is carried out with continuous variable parameters of 50 generations and a population of 100. fig.13(a) and fig.13(b) show respectively the convergence of the minimum displacement as well as the histogram of the most influencing factors namely the thickness of the adhesive, young’s parameters notation dimension transversal modulus in the adhesive (mpa) ga 218.30 transversal modulus in the jonction (mpa) gb 4285.71 thickness of the adhesive (mm) e parameter variable0.3≤e≤0.7 thickness of the subtrate (mm) e1 5 width of the adhesive (mm) b parameter variable 38≤b≤100 bonded length (mm) l 76 number of bolts n 2 bolts diameter (mm) φ 9.52 applied force (n) f [1250 ;3875 ;15000] stifness of the bolts (kn/mm) cu 70 young’s modulus of the substrates e1 parameter variable 7000≤e1≤13400 m. fouzia et alii, frattura ed integrità strutturale, 52 (2020) 281-298; doi: 10.3221/igf-esis.52.22 293 modulus of the substrates and their width with an applied tensile force of 1250n. similarly, fig.14 and fig.15 give the same information respectively for the applied forces of 8750n and 14000n. figure 13 (b): effects of the factors we notice that the most influential factor is the young’s modulus of substrates but for the other factors are not significant and cannot be observed on the graph. that’s why we used a design of experiments approach. figure 14: optimum for tensile load f=8750n. m. fouzia et alii, frattura ed integrità strutturale, 52 (2020) 281-298; doi: 10.3221/igf-esis.52.22 294 figure 15: optimum for tensile load f=14000n. table 6: parameters of the hybrid assembly optimization by design of experiments he objective of the optimization is to minimize the total displacement δl in the substrates of the hybrid assembly due to an applied tensile stress f. the objective function is then this displacement which is calculated by yamaguchi and amano’s theory [12]. parameters notation dimension transversal modulus in the adhesive (mpa) ga 218.30 transversal modulus in the jonction (mpa) gb 4285.71 thickness of the adhesive (mm) e parameter variable0.3≤e≤0.7 thickness of the substrate (mm) e1 5 width of the adhesive (mm) b parameter variable 38≤b≤100 bonded length (mm) l 76 number of bolts n 2 bolts diameter (mm) φ 9.52 applied force (n) f [1250 ;3875 ;15000] stiffness of the bolts (kn/mm) cu 70 young’s modulus of the substrates e1 constant parameter e1 t m. fouzia et alii, frattura ed integrità strutturale, 52 (2020) 281-298; doi: 10.3221/igf-esis.52.22 295 the parameters of the hybrid assembly are given in tab. 6. in this design of experiment optimization two factors are considered namely the thickness of the adhesive ea and the width of the subtracts w. we have two factors with two levels which give 22 experiments. tab. 7 shows the values of the factors and the corresponding response value of the displacement. n0 of experiment thickness of the adhesive width of the substrates displacement δl 01 0.3 38 4.981 02 0.3 100 4.93 03 0.7 38 5.501 04 0.7 100 5.44 table 7: values of the factors and the response coded values of the factors and interactions are given in the matrix of experiments tab. 8. factors ea width ea* width displacement ea 1 0 0 0.994094 width 0 1 0 -0.108096 ea* width 0 0 1 -0.00965127 displacement 0.994094 -0.108096 -0.00965127 1 table 8: matrix of experiments (coded values). the predicted model is a first order model with respect to each factor expressed as: 0 1 1 2 2 12 1 2y a a x a x a x x    (20) where: y is the response corresponding to the displacement xi represents the level given to factor i. a0 is the average value at the center of the design study plan. a1 is the coefficient of factor 1. a2 is the coefficient of factor 2. a12 is the interaction of the two factors 1 and 2. the coefficients of the model are obtained using the design of experiments software moode. coefficients value average a0 5.213 a1 coefficient ea 0.297335 a2 coefficient the width of substrates -0.0323316 a12 interaction ea* width -0.00333319 table 9: the coefficient of the model m. fouzia et alii, frattura ed integrità strutturale, 52 (2020) 281-298; doi: 10.3221/igf-esis.52.22 296 the obtained model is given by: 1 2 1 25.213 0.297335 0.0323316 0.00333319y x x x x    (21) figure 16: effects of the factors and their interaction results and discussion ig.16 (a) shows respectively the effects of the thickness of the adhesive and the width of the substrates on the displacement. the effect of the thickness is equal to 0.29 mm for a variation of 0.033 of the width of the subtracts. the displacement can be minimized by reducing the thickness of the adhesive. the effect of the width of the substrates is -0.033 mm for a variation of 31 mm. thus, it is concluded that to optimize the displacement, the width of the substrates should be increased. fig.16(b) shows the effect of the most influencing factors. significant effect is due to the thickness of the adhesive followed by the width of the substrates and the interaction fig. 16(c) shows the iso curves illustrating the effects of the factors on the displacement. figure 16(a): effects of the thickness of the adhesive and the width of the substrates on the displacement f 0.00 0.10 0.20 0.30 e p a la r e p a *l a r investigation: opti1 (pls, comp.=1) scaled & centered coefficients for allongement n=4 df=0 q2=0.447 conf. lev.=0.95 m. fouzia et alii, frattura ed integrità strutturale, 52 (2020) 281-298; doi: 10.3221/igf-esis.52.22 297 figure 16(b): the most influencing factors. figure 16(c): iso curves of the factors effect on the displacement. conclusion n this paper the behavior of an hybrid assembly (bonded – bolted) is investigated. the study has been carried out using genetic algorithm for the optimization of the factors namely the thickener of adhesive, the of the substrates and young’s modulus on the displacement secondly, in order to optimize the parameter of the assembly a design of experiment method has been used by considering two factors with two levels namely thickness, width and their interaction. the results obtained are:  the optimum thickness is 0.33mm  the young’s modulus is 13248n/mm2  the width is 99.995mm. references [1] stewart, m. and stewart, m. (1997). an experimental investigation of composite bonded and/or bolted repairs using single lap joint designs. in 38th structures, structural dynamics, and materials conference, pp. 1339. [2] kelly, g. (2005). load transfer in hybrid (bonded/bolted) composite single-lap joints. composite structures, 69(1), pp. 35-43. [3] hart-smith, l. (1985). bonded-bolted composite joints. journal of aircraft, 22(11), pp. 993-1000. [4] kelly, g. (2006). quasi-static strength and fatigue life of hybrid (bonded/bolted) composite single-lap joints. composite structures, 72(1), pp. 119-129. [5] paroissien, e. (2006). contribution aux assemblages hybrides (boulonnés/collés)-application aux jonctions aéronautiques (doctoral dissertation). [6] ganji, n. (2007). parametric study of load transfer in two-bolted single lap hybrid (bonded/bolted) shear joints (doctoral dissertation). [7] lee, y. h., lim, d. w., choi, j. h., kweon, j. h., and yoon, m. k. (2010). failure load evaluation and prediction of hybrid composite double lap joints. composite structures, 92(12), pp. 2916-2926. [8] johnson, r. p., and tait, c. j. (1981). the strength in combined bending and tension of concrete beams with externally bonded reinforcing plates. building and environment, 16(4), pp. 287-299. i m. fouzia et alii, frattura ed integrità strutturale, 52 (2020) 281-298; doi: 10.3221/igf-esis.52.22 298 [9] yamaguchi, y., and amano, s. (1985). mechanical behaviour of a combined joint composed of mechanical fastening and adhesive bonding. international journal of adhesion and adhesives, 5(4), pp. 193-199. [10] volkersen, o. (1938). die nietkraftverteilung in zugbeanspruchten nietverbindungen mit konstanten laschenquerschnitten. luftfahrtfor schung, 15, pp. 41-47. [11] paroissien, e. (2006). contribution aux assemblages hybrides (boulonnés/collés)-application aux jonctions aéronautiques (doctoral dissertation). [12] supian, a. b. m., sapuan, s. m., zuhri, m. y. m., zainudin, e. s., and ya, h. h. (2018). hybrid reinforced thermoset polymer composite in energy absorption tube application: a review. defence technology, 14(4), pp. 291-305. [13] valentino, p., sgambitterra, e., furgiuele, f., romano, m., ehrlich, i., and gebbeken, n. (2014). mechanical characterization of basalt woven fabric composites: numerical and experimental investigation. frattura ed integrità strutturale, 8(28), pp. 1-11. [14] shishesaz, m., and hosseini, m. (2018). a review on stress distribution, strength and failure of bolted composite joints .journal of computational applied mechanics, 49(2), pp. 415-429. [15] lunsford l.r. (1966) stress analysis of bonded joints, applied polymer symposia, 3, pp. 57-73 [16] ouellet, m. (2013). conception axiomatique des joints hybrides à recouvrement simple en matériaux composites (mémoire de maîtrise, école polytechnique de montréal). https://publications.polymtl.ca/1153/. << /ascii85encodepages false /allowtransparency false /autopositionepsfiles true /autorotatepages /none /binding /left /calgrayprofile (dot gain 20%) /calrgbprofile (srgb iec61966-2.1) /calcmykprofile (u.s. web coated \050swop\051 v2) /srgbprofile (srgb iec61966-2.1) /cannotembedfontpolicy /error /compatibilitylevel 1.4 /compressobjects /tags /compresspages true /convertimagestoindexed true /passthroughjpegimages true /createjobticket false /defaultrenderingintent /default /detectblends true /detectcurves 0.0000 /colorconversionstrategy /cmyk /dothumbnails false /embedallfonts true /embedopentype false /parseiccprofilesincomments true /embedjoboptions true /dscreportinglevel 0 /emitdscwarnings false /endpage -1 /imagememory 1048576 /lockdistillerparams false /maxsubsetpct 100 /optimize true /opm 1 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can be opened with acrobat and adobe reader 5.0 and later.) >> /namespace [ (adobe) (common) (1.0) ] /othernamespaces [ << /asreaderspreads false /cropimagestoframes true /errorcontrol /warnandcontinue /flattenerignorespreadoverrides false /includeguidesgrids false /includenonprinting false /includeslug false /namespace [ (adobe) (indesign) (4.0) ] /omitplacedbitmaps false /omitplacedeps false /omitplacedpdf false /simulateoverprint /legacy >> << /addbleedmarks false /addcolorbars false /addcropmarks false /addpageinfo false /addregmarks false /convertcolors /converttocmyk /destinationprofilename () /destinationprofileselector /documentcmyk /downsample16bitimages true /flattenerpreset << /presetselector /mediumresolution >> /formelements false /generatestructure false /includebookmarks false /includehyperlinks false /includeinteractive false /includelayers false /includeprofiles false /multimediahandling /useobjectsettings /namespace [ (adobe) (creativesuite) (2.0) ] /pdfxoutputintentprofileselector /documentcmyk /preserveediting true /untaggedcmykhandling /leaveuntagged /untaggedrgbhandling /usedocumentprofile /usedocumentbleed false >> ] >> setdistillerparams << /hwresolution [2400 2400] /pagesize [612.000 792.000] >> setpagedevice microsoft word numero_29_art_24 r. serpieri et alii, frattura ed integrità strutturale, 29 (2014) 284-292; doi: 10.3221/igf-esis.29.24 284 focussed on: computational mechanics and mechanics of materials in italy bond-slip analysis via a cohesive-zone model simulating damage, friction and interlocking r. serpieri, l. varricchio dipartimento di ingegneria, università degli studi del sannio, benevento, italy rserpier@unisannio.it, luigi.varricchio@ingpec.eu e. sacco dipartimento di ingegneria civile e meccanica, cassino, università di cassino e del lazio meridionale, (fr), italy sacco@unicas.it g. alfano school of engineering and design, brunel university, uxbridge, uk giulio.alfano@brunel.ac.uk abstract. a recently proposed cohesive-zone model which effectively combines damage, friction and mechanical interlocking has been revisited and further validated by numerically simulating the pull-out test, from a concrete block, of a ribbed steel bar in the post-yield deformation range. the simulated response is in good agreement with experimental measurements of the bond slip characteristics in the post-yield range of deformed bars reported in the literature. this study highlights the main features of the model: with physically justified and relatively simple arguments, and within the sound framework of thermodynamics with internal variables, the model effectively separates the three main sources of energy dissipation, i.e. loss of adhesion, friction along flat interfaces and mechanical interlocking. this study provides further evidence that the proposed approach allows easier and physically clearer procedures for the determination of the model parameters of such three elementary mechanical behaviours, and makes possible their interpretation and measurement as separate material property, as a viable alternative to lumping these parameters into single values of the fracture energy. in particular, the proposed approach allows to consider a single value of the adhesion energy for modes i and ii. keywords. fracture energy; friction; interlocking; thermodynamics with internal variables; interface elements; mixed-mode delamination. introduction ohesive‐zone models (czms) are widely used to simulate initiation and propagation of cracks along structural interfaces. they represent an effective alternative approach to fracture-mechanics-based methods for a wide variety of problems at very different scales, such as crack growth in dams, mortar-joint failure in brick masonry, bond-slip response of reinforcing bars in concrete, debonding of adhesive joints, delamination or fibre‐matrix debonding in composites, among many others. many of such problems entail combination of de-cohesion and frictional sliding, c r. serpieri et alii, frattura ed integrità strutturale, 29 (2014) 284-292; doi: 10.3221/igf-esis.29.24 285 which is often accompanied by dilatancy, in turn associated with the interlocking effect created by the asperities of the fracture surface. therefore, in order to formulate models that properly account for the underlying physics of the problem it is essential to capture the distinct types of dissipation due to fracture and friction, the influence of the geometry of the asperities on the interlocking effect. several interface models accounting for damage-friction coupling have been proposed in literature, see e.g. del piero and raous [1] and references therein. some of them are based on nonassociative softening plasticity, as for the multidissipative interface model proposed by cocchetti et al. [2] and the contributions given by bolzon and cocchetti [3] and by červenka et al. [4] in the field of concrete dams analysis, and by giambanco et al. [5]. a different strategy was followed by alfano and sacco [6], alfano et al. [7] and, more recently, sacco and toti [8], where interface damage and friction have been combined in a cohesive zone model based on a simplified micromechanical formulation. the main idea was to consider a representative area at a micromechanical scale, which is assumed to be additively decomposed into an undamaged and a fully damaged part; moreover, it is supposed that friction occurs only on the latter. the evolution of damage is assumed to depend on the elastic energy in the undamaged part while the frictional behaviour is governed by a coulomb law. to simulate dilatancy and interlocking this approach was adopted by serpieri and alfano [9], within a multi-scale framework in which, at a small scale, the asperities of the interface are represented in the form of a periodic arrangement of distinct inclined planes, denominated representative interface area (ria). on each of these planes the interaction is governed by the formulation proposed in alfano and sacco (2006). the above formulation by serpieri and alfano was recently revisited by serpieri et al. [10], where it was shown that use of a single damage variable, combined with the choice of having a threshold damage function only depending on the damage variable itself and an equivalent displacement norm, requires coincidence of fracture energies in modes i and ii to preserve thermodynamic consistency. furthermore, it was shown that the enhancement of the model to account for friction and interlocking, based on the formulation proposed by serpieri and alfano [9], results in retrieving the experimental evidence that the measured fracture energy in mode ii is typically quite higher than in mode i. for mixedmode loading, with positive (opening) mode i, the proposed model predicts an increase of the total fracture energy with increasing mode ii loading component. both facts are well supported by good agreement between experimental and numerical results. in this paper the model formulated in refs. [9, 10] is revisited and applied to the study of the pull-put test of a ribbed steel bar from concrete specimen, in which the interface model is used to simulate the interaction between steel and concrete within a two-dimensional axisymmetric simulation. the ‘bond-slip’ interaction between steel and concrete has been widely investigated in the last decades, both theoretically and experimentally [11-14]. many studies have revealed the significant role played by complex mechanisms including the progressive development of primary transversal and secondary inclined cracks [15], the influence of stress triaxiality on the formation of inclined struts in the concrete surrounding the steel bar [16], the fact that with increasing confinement the failure mode changes from being more brittle (splitting) to more ductile (pull out) [17]. all these studies also revealed that, for ribbed bars (the only ones nowadays used), interlocking is the predominant mechanism of stress transfer between concrete and steel with respect to adhesion and friction (the latter intended as the theoretical friction that would be obtained if the fracture surfaces were flat). all these complex mechanisms are influenced by aspects that are not limited to the point-wise interaction between concrete and steel at the interface but include other structural details. for this reason, all the models developed somehow depend on details such as the diameter of the bars, the type of confinement, the cyclic nature of loading, among many others, and typically include a number of corrective coefficients that need to be empirically determined and are of difficult, if not impossible, physical interpretation for the practicing engineer. hence, the aim of this paper is to show that very accurate prediction of the bond-slip interaction between concrete and steel bars can be achieved through a physically well justified model, developed within a general and thermodynamically consistent framework in which each contribution to the overall energy dissipation on the interface is accounted for with a simplified, yet effective multiscale description of the microscale. to show the effectiveness of the formulation, the model is validated by simulating the pull-out test of a steel bar from a concrete specimen and comparing the numerical results with the experimental ones reported by shima [18]. these have been chosen as benchmark test data because the relatively large dimensions of the concrete specimen, as well as the insertion of a clay sleeve with very small adherence in an initial part at the loaded end of the steel bar, prevents the formation of splitting cracks and results in rather negligible concrete damage or plasticity, except in a thin region immediately adjacent to the steel bar and its ribs, whose progressive damage is indeed incorporated in the cohesive-zone model. therefore, the nonlinear response up to failure during the test is predominantly the result of the interface interaction, which is the focus of this investigation and is simulated by the proposed cohesive-zone model. this makes calibration of the model easier and gives more confidence in the robustness of the validation. r. serpieri et alii, frattura ed integrità strutturale, 29 (2014) 284-292; doi: 10.3221/igf-esis.29.24 286 cohesive-zone model derivation multiscale formulation n this section the fundamental ideas behind the frictional cohesive-zone model proposed in refs. [9, 10] are reported and discussed. for all the details of the derivation of the model and its implementation within an incremental nonlinear finite-element formulation, the reader is referred to the above references. an interface  is considered between two parts 1 and 2 f a body  . in this paper we will focus on two-dimensional problems whereby  is represented by a line. the model considers two scales: a macroscale where the interface is assumed to be smooth (fig. 1(a)) and a microscale where the asperities of the fracture surface are considered (fig. 1(b)). the terms microscale and macroscale are here used with aim to distinguish the smaller from the larger scale. in the context of the finite-element method, which is considered here, this implies the use of smooth interface elements to model the macroscale, whereby the details of the asperities do not have to be captured by the spatial discretization. instead, at each integration point of each interface element, the cohesive law, which relates the relative displacement vector s to the interface stress σ , is determined by resolving a microscale problem for a representative interface area (ria). figure 1: multi-scale approach linking a smooth interface at the (a) macro-scale level to the (b) ria characterized by a periodic arrangement of microplanes. the ria is assumed to be large enough to capture the details of the asperities. if the actual microscale is periodic, the repeating unit of the interface defines the ria. in case it is not periodic or not perfectly periodic, the ria can be taken large enough and with a geometry rich enough so that the response of the ria can be considered statistically representative of the response of an ‘infinitesimally small’ area at the macroscale. in turn, this implies the assumption of ‘separation of scales’, which is typically required in multiscale homogenization [19]. while the approach could be theoretically implemented by representing the asperities through a curved profile, it is assumed that such profile is defined by a finite number n of microplanes. a further assumption that is made in the model is that the two sides of the interface profile within the ria are infinitely rigid. in other words, the deformation of the asperities, as well as their damage, wear and fracture, are not considered. this means that a single vector s characterizes the relative displacement between the two sides of the ria. on the kth microplane a local reference system     ,n tk k is defined,  n k and  t k representing the local normal and tangential directions, respectively. hence, the relative displacement vector is decomposed on the kth microplane into its local mode-i component,   s n kkis , and mode-ii component,   s t kkiis . thermodynamical formulation of the model on each microplane, the stress is obtained implementing the model developed by alfano and sacco [7]. the main idea behind such model is that an infinitesimal area da of microplane can be decomposed into an undamaged part, whose i r. serpieri et alii, frattura ed integrità strutturale, 29 (2014) 284-292; doi: 10.3221/igf-esis.29.24 287 area is  1 kd da , and a damage part, whose area is kd da , kd being a damage parameter ranging from zero, in the case of no damage, to unity in the case of complete damage (fig. 2). figure 2: decomposition of each infinitesimal area of microplane into damaged and undamaged parts. assuming a linear elastic relationship for the undamaged part and a coulomb-type frictional-contact relationship on the damaged part, the following expression of the free energy is obtained:                  1 1 1 1 1 , , , , , , 1       2 2                    s k s s k s s s sf f d f d fk k k k k k k ks s s s n k k k k d d s s d d s s (1) where  k s the ratio between the area of the kth microplane and the sum of all such areas while, denoting with x  the negative part of x i.e.   / 2x x x   , it results:                   0 0 0 ki kii i ii ki kii f k s s k k s s s s                                      s n s r s s t k s s k k kk k d f k k s s s s s s (2) in (local) modes i and ii and fks denotes the frictional slip on the kth microplane. note that all microplanes are characterized by the same stiffness. the interface stress is obtained as the derivative of the free energy with respect to the relative displacement s:     1 1                σ r k s k s s t d k k k k n k k k k d d (3) the frictional slip on each microplane is obtained through a non-associate coulomb-type relationship defined by:          ,      sign      s  fk i ki ii kii k k kiis k s k s s s s sf f fk k ks s s (4)    0                  , 0                   , 0     s s k k k ks sf fk k (5) where k represents the slip-onset function and  denotes the friction coefficient. the evolution of damage variable kd , for each microplane, is defined to recover the two classical bilinear cohesive-laws in pure modes i and ii depicted in fig. 3, for the relevant local stress-displacement relation: in such relationships 0 is and 0 iis represent the values of the relative displacements corresponding to the onset of damage in modes i and ii, respectively, while cis and ciis represent the ‘critical values’ corresponding to the attainment of complete damage. furthermore, 0 i and 0 ii denote the strengths in modes i and ii, respectively, and it is easy to r. serpieri et alii, frattura ed integrità strutturale, 29 (2014) 284-292; doi: 10.3221/igf-esis.29.24 288 recognize that 0 0/i i ik s and 0 0/ii ii iik s . finally, the areas under the bilinear curves in each mode represent the fracture energies in pure modes i and ii and are denoted by cig and ciig , respectively. figure 3: decomposition of each infinitesimal area of microplanes into damaged and undamaged parts. the assumption is then made that 0 0/ /i ci ii ciis s s s and the following ‘ductility’ parameter  is introduced: 0 01 1    i ii ci cii s s s s (6) according to [6], the evolution of the damage variable kd is given by: 1 max 0, min 1, 1                   k k k d (7) where     2 2 0 0 max 1 ki kii k history i ii s s s s                 s s (8) the above evolution law for the damage variable kd could allow to consider different values of the fracture energies [11] in modes i and ii, cig and ciig . however, it is shown in [10] that thermodynamically consistency is more ‘neatly’ achieved if these two values are taken to be equal. in fact, there is an ongoing debate in the scientific community concerning the underlying physical justification for a mode-mixity dependent fracture energy, that for zero or positive mode-i opening typically increases from the lowest value in pure mode i to the highest value in pure mode ii, to the point that many authors have questioned whether the mode-ii fracture energy can be considered as a true material property at all [20]. in this aspect lies one of the primary strengths of the proposed approach, because the different contributions to the energy dissipation, i.e. to the measured fracture energy, are accounted for separately in the model and with a simple, yet physically sound, approach. in particular, the fracture energies cig and ciig only represent here the energy dissipation due to the rupture of bonds; regardless of any theoretical reason on how thermodynamic consistency can be ensured, physical arguments suggest that such energy should be equal. numerical simulations of a pull-out test experimental set up and finite element model he model briefly described in the previous section has been implemented in a finite-step algorithm, providing the solution of the interface law at the integration points of interface elements, and coded in a user-subroutine (umat) for the finite-element code abaqus. to validate the efficiency of the model in capturing the concretesteel interface interaction against experimental results published in the literature, the pull-out test of s sd30 steel bar from a cylindrical block of concrete, studied by shima et al. [18] has been numerically simulated. the experimental apparatus devised by shima et al. is reported in fig. 4(a). the diameter d of the steel bar is 19.5mm, and the set-up and specimen geometry are such that an initial 10 195d mm long unbonded region in the vicinity of the loaded end of the bar is created. these features have been purposefully designed by shima and coworkers in order to move the stress concentration well inside the concrete block and therefore avoid concrete damage and splitting at the top end of the concrete block. to this end, an initial 195mm long clay sleeve surrounding the bar in this region was inserted. t r. serpieri et alii, frattura ed integrità strutturale, 29 (2014) 284-292; doi: 10.3221/igf-esis.29.24 289 the load has been applied by prescribing the displacement of the top end of the bar up to a maximum value of 5.2 mm, with an applied strain rate of 10-4 min-1, the strain being measured at the top end of the bar and reaching a maximum value of 0.032. the strain along the bar has been measured using pairs of 5mm strain gauges, each pair placed on the bar diametrically opposite to each other, and at a distance of 49mm from the next pairs along the bar. a two-dimensional axisymmetric finite-element model has been used for the simulation employing a structured mesh. both the steel bar and the concrete block have been discretized with 4-node fully integrated axisymmetric elements (named cax4 in abaqus), with a size of 5mm in the concrete and 2.5mm in the steel bar. on the interface, 4-node axisymmetric interface elements (named cohax4 in abaqus) have been used. details of the geometry, mesh and constraints employed in the fe model are reported in fig. 4(b). on the region unbonded by the clay sleeve no interface elements have been inserted on account of the prevented adhesion, and also because no data on the clay material properties were provided. the overall length of the bar and of the concrete cylinder is equal to 975mm. the concrete and steel material properties used in the simulation are reported in tab. 1. for the concrete, a linear elastic material model was used due to the negligible damage and plasticity evidenced in the experimental results. since the average cylindrical strength fc reported in [18] is 19.6 mpa, the value of the young’s modulus ce in tab. 1 was obtained using the following correlation suggested by the italian code of practice [21]: c   22000 10 c f e (9) 5 0 0 m m 4 0 0 m m 3 0 0 m m support shoe center hole load cell reaction platebolt center hole jack support plate steel bar support ring free end slip displacement meter concrete specimen 10d unbonded regionsteel bar casting direction 9.75 mm 50 mm 1.0 mm 139.25 mm 50mm 10d unbonded region steel bar (3x325 cax4 elms) bonded region interface (156 cohax4 elms) 1 9 5 m m 7 8 0 m m 9 7 5 m m c o n c r e t e c o n c r e t e b o u n d b y r in g c o n c r e t e support ring simmetry axis prescribed vertical displacement concrete specimen (48x195 cax4 elms) (a) (b) figure 4: pull-out test: (a) experimental set up [18] and (b) details of the geometry and the mesh of the finite element model. the poisson’s ratio of concrete c has been taken in accordance with values typically reported in the literature in the case of linear elastic behaviour. for the steel, the values of the young modulus se , the poisson ratio  s , the first yield strength yf and the total strain h corresponding to the onset of hardening after the initial plateau are those reported in [18]. for the steel a j2 small-strain von mises elasto-plastic model with nonlinear isotropic hardening has been used. the isotropic hardening curve in tab. 2 relating the hardened yield strength  y to the equivalent plastic strain  p eq has been given in accordance with the uni-axial stress-strain curve reported in [18]. ce (mpa) c se (gpa) s yf (mpa) h 2621.0 0.2 190.0 0.3 350.0 1.65 table 1: input parameters for concrete and steel. r. serpieri et alii, frattura ed integrità strutturale, 29 (2014) 284-292; doi: 10.3221/igf-esis.29.24 290 y (mpa) peq 350.0 0 350.0 0.0164 390.0 0.0206 410.0 0.0242 427.0 0.0278 444.0 0.0314 450.0 0.0352 460.0 0.038 table 2: hardening curve for the sd30 steel. figure 5: ria geometry. the geometry of the ria has been taken as shown in fig. 5. the three microplanes are all equal in length, resulting in a value of 0.333 k for all 1, 2, 3k . one of them has zero inclination and the remaining two are symmetric and have an inclination angle equal to 1 3 5.5    deg. this value has been determined through a sensitivity analysis reported in fig. 6. the properties of the interface have been determined through calibration and are reported in tab. 3. the strengths in modes i and ii have been taken equal to those determined by serpieri and alfano [9] for a similar problem, as they are known to have a limited effect on results. the same values of fracture energies have been taken for modes i and ii in accordance with the observations made at the end of the previous section. their value has been calibrated through a sensitivity analysis, whose results are provided in fig. 7 and falls well within the range typically found for the adhesion between steel and concrete. the ductility parameter  has been taken very close to 1 because this results in values of the stiffness parameters i iik k high enough to well simulate the initial response when the interface is undamaged, yet not too high to avoid ill conditioning. in this range of values the sensitivity of the analysis to  is known to be negligible [22]. the value selected for  has been taken as a mid-value in the range 0.7 and 1.4 recommended by the aci code of practice [23] for the friction coefficient of concrete surfaces. oi (mpa) oii (mpa) cig (n/mm) ciig (n/mm)   1 3   (deg) 2 1 2 3    1.5 1.5 0.7 0.7 0.999 1.1 5.5 0 0.333 table 3: input parameters for the interface model. numerical results and comparison with experimental data fig. 6 shows the interface tangential stress against the distance from the loaded end for varying microplane inclination 1 3    , compared to the curve experimentally determined. the latter have been obtained in [16] based on the strains measured in the bars. it can be noted that with increasing  the peak value of the tangential stress in the vicinity of the loaded end increases, which is expected because of the increase in the mechanical interlocking with increasing microplane inclination. fig. 7 shows the influence of the fracture energy c ci ciig g g  and reveals that this parameter has a limited influence on the tangential stress profile, whose values tend to decrease at the loaded end of the bar and to increase at the free end with increasing cg . fig. 8 reports the axial stress obtained in the fe simulation at the centre of the bar cross section against the distance from the loaded end, compared with the experimentally determined curve. in the fe model the axial force in the bar is completely withstood by the bar in the first 195mm, because of no adherence between steel and concrete in this part. instead, the experimental results reveal that some adherence is actually present. this explains the initial, relatively small discrepancy in the curve, after which the agreement between numerical and experimental results is good. similar considerations can be made for fig. 9, where the numerical and experimental axial strain profile along the same path have been reported. both curves report a steep change at the point separating the two parts of the bar in the plastic and elastic ranges. r. serpieri et alii, frattura ed integrità strutturale, 29 (2014) 284-292; doi: 10.3221/igf-esis.29.24 291 figure 6: interface tangential stress vs. the distance from the loaded end for varying microplane inclination 1 3    nd comparison with experimental results in [18]. figure 7: interface tangential stress vs. the distance from the loaded end for varying fracture energy ci ciig g nd comparison with experimental results in [18]. figure 8: vertical direct stress in the bar vs the distance from the loaded end: comparison of the simulation results with the experimental results in [18]. figure 9: vertical direct (total) strain in the bar vs the distance from the loaded end: comparison of the simulation results with the experimental results in [18]. conclusions he cohesive-zone model proposed in [9, 10], which combines elastic damage, friction and dilatancy due to mechanical interlocking, has been revisited in this paper and further validated by simulating the pull-out test conducted by shima et el. and reported in [16], obtaining good agreement between experimental and numerical results. the relatively large dimensions of the concrete block and the clay sleeve inserted at the top of the steel-concrete interface, which moves the stress concentration well inside the block, result in negligible damage and plasticity in the concrete block. this gives more significance and robustness to the presented validation because the only significant source of nonlinearity are the concrete-steel interface interaction and the plasticity in the mild-steel bar, with values of the plastic strains in the bar exceeding the end of the plateau of the stress-strain curve of the steel. the latter aspect is also significant because it has been observed that the deformation of steel bars affects the experimentally measured bond-slip law, particularly when reaching the plastic range [16]. the main strength of the proposed model is that it effectively separates the total dissipated energy per unit of new crack surface, i.e., the measured mode-mixity dependent fracture energy, into the sum of three contributions. a first one is the rupture of bonds, which is mode-mixity independent and is therefore given by one single value of the fracture energy ci ciig g nd, for each microplane, this translates in a single variable kd easuring the evolution of damage. a second contribution is given by the frictional dissipation that would be present even if, at the microscale, the interface presented no asperities, i.e. if it was completely flat. for the kth microplane this dissipative mechanism is related to the evolution of the inelastic slip s fk finally, the third contribution, which has a predominant influence on the bond-slip relationship between concrete and ribbed steel bars, is given by the interlocking effect, which is here modelled through the above described multiscale approach and the definition of a pattern of microplanes in the ria. t r. serpieri et alii, frattura ed integrità strutturale, 29 (2014) 284-292; doi: 10.3221/igf-esis.29.24 292 the remaining small discrepancies between the numerical and experimental results obtained in the presented validation can be partly attributed to the need of including some adherence between steel and concrete in correspondence of the clay sleeve. on the other hand, these can also be due to some aspects of the underlying physics that have not yet been included in the model, namely the finite size of the asperities in the ria at the microscale, their deformation, wear, damage and failure and a more representative statistical distribution of their dimensions and geometry. these aspects will be investigated in the continuation of this research. references [1] del piero, g., raous, m., a unified model for adhesive interfaces with damage, viscosity and friction, eur j. mech. a/solids. 29 (2010) 496-507. [2] cocchetti, g., maier, g., shen., x.p., piecewise linear models for interfaces and mixed mode cohesive cracks, comp model. eng. sci., 3(2002) 279–298. [3] bolzon, g., cocchetti, g., direct assessment of structural resistance against pressurized fracture, int. j. num. anal. meth. geomech., 27 (2003) 353–378. [4] červenka, j., chandra kishen, j.m., saouma, v.e., mixed mode fracture of cementitious bimaterial interfaces; part ii: numerical simulation, eng. frac. mech. 60 (1998) 95–107. [5] giambanco, g., rizzo, s., spallino, r., numerical analysis of masonry structures via interface models, comp. meth. appl. mech. eng., 190 (2001) 6493–6511. [6] alfano, g., sacco, e., combining interface damage and friction in a cohesive-zone model, int. j. num. meth. eng., 68 (2006) 542-582. [7] alfano, g. marfia, s., sacco, e., a cohesive damage-friction interface model accounting for water pressure on crack propagation, comp. meth. appl. mech. eng., 196 (2006) 192-209. [8] sacco, e., toti, j., interface elements for the analysis of masonry structures, int. j. comp. meth. eng. sci. mech, 11 (2010) 354-373. [9] serpieri, r., alfano, g., bond-slip analysis via a thermodynamically consistent interface model combining interlocking, damage and friction, int. j. num. meth. eng. 85 (2011) 164-186. [10] serpieri, r., sacco, e., alfano, g., a thermodinamically consistent derivation of a frictional-damage cohesive-zone model with different mode i and mode ii fracture energies, submitted to eur j. mech. a/solids. [11] federation internationale du bèton (fib), bond of reinforcement in concrete, bulletin no. 10, state of art report t.g. 4/2 bond models, fib, lausanne, switzerland, (2000). [12] tassios, t.p., properties of bond between concrete and steel under load cycles idealizing seismic actions, in proc. aicap-ceb symposium, rome, ceb, bulletin d’information 131 (1979) 67-122. [13] tassios, t.p., koroneos, e.g., local bond-slip by means of the moiré method, aci struct. j., 81 (1984) 27-34. [14] gambarova, p.g., rosati, g.p., bond and splitting bar in pull-out: behaviour laws and concrete cover role, magaz. concr. res., 49 (1997) 99–110. [15] goto, y., cracks formed in concrete around deformed tension bars. aci journal, proceedings, 68 (4) (1971) 501. [16] tepfers, r., cracking of concrete cover along anchored deformed reinforcing bars, magaz. concr. research, 31(106) (1979) 3-12. [17] rehm, g., the basic principles of the bond between steel and concrete., transl. 134 cement concr. association, london, (1968). [18] shima, h., chou, l.l., okamura, h. micro and macro models for bond reinforced concrete, reprinted from journal of the faculty of engineering, the university of tokio, 39, (1987). [19] geers, m.g.d., kouznetsova, v.g., brekelmans, w.a.m., multi-scale computational homogenization: trends and challenges, j. comp. appl. math., 234 (2010) 2175-2182. [20] carpinteri, a., valente, s., ferrara, g., melchiorri, g., is mode ii fracture energy a real material property?. comp. struct. 48 (1993), 397-413. [21] ntc2008 nuove norme tecniche per le costruzioni g. u. n. 29, 04.02.2008 – supplemento ordinario n. 30 (in italian). [22] alfano, g., crisfield, m.a., finite element interface models for the delamination analysis of laminated composites: mechanical and computational issues, int. j. num. meth. engin., 50 (2001) 1701-1736. [23] american concrete institute. building code requirements for structural concrete (aci 318-05) and commentary (aci 318r-05), (2005). microsoft word numero_53_art_27_2825 s. kirin et alii, frattura ed integrità strutturale, 53 (2020) 345-352; doi: 10.3221/igf-esis.53.27 345 risk based analysis of rhpp penstock structural integrity snežana kirin, lazar jeremić innovation center of the faculty of mechanical engineering, belgrade, kraljice marije 16, serbia snezanakirin@yahoo.com, laki991@hotmail.com aleksandar sedmak university of belgrade, faculty of mechanical engineering, kraljice marije 16, 11020 belgrade 35, serbia asedmak@mas.bg.ac.rs igor martić, simon sedmak, ivana vučetić innovation center of the faculty of mechanical engineering, belgrade, kraljice marije 16, serbia simonsedmak@yahoo.com tamara golubović innovation center of the faculty of technology and metallurgy, belgrade, karnegijeva 4, serbia simonsedmak@hotmail.com abstract. risk based analysis of reverse hydro power plant penstock structural integrity is performed using fracture mechanics parameters. to assess its structural integrity, extensive testing of the full-scale prototype had been performed, including hydrostatic over-pressurizing, during the design phase. more recently, the failure assessment diagram has been used to evaluate probability, whereas phenomenological analysis has been used to estimate consequence, in the scope of common risk estimation. it is shown that over-pressuring has potential detrimental effect on pipeline safety, i.e. structural integrity. keywords. over-pressure; pipeline; structural integrity; risk matrix. citation: kirin, s., jeremić, l., sedmak, a., martić, i., sedmak, s., vučetić, i., golubović, t., risk based analysis of rhpp penstock structural integrity, frattura ed integrità strutturale, 53 (2020) 345-352. received: 12.05.2020 accepted: 31.05.2020 published: 01.07.2020 copyright: © 2020 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. introduction eversible hydro power plant (rhpp) “bajina basta” is in operation since 1982, [1, 2]. taking into account that the failure of its most critical part, the penstock, fig. 1, would cause water overflow of the surge hub in the surrounding area, and the collapse of the entire plant, it is clear that special attention is still needed to prove its structural integrity. r https://youtu.be/2o838dsbi2w s. kirin et alii, frattura ed integrità strutturale, 53 (2020) 345-352; doi: 10.3221/igf-esis.53.27 346 this is especially important when it comes to the proof testing, now scheduled for 2022, since it has been shown that overpressure can cause significant damage and bring no benefit, [3]. therefore, the basic aim of this paper is to make risk based analysis of the penstock structural integrity with focus of overpressure effect. toward this aim, a simple engineering tool will be used to estimate probability, [4-10], and simple reasoning will be used to estimate consequence, [7, 11], so that risk will be evaluated as the product of these two. this approach is also adopted in the scope of esis tc12 activities, [12]. figure 1: disposition of penstock (upper and lower pipeline) “bajina bašta”. figure 2: the full-scale model: l-longitudinal, c-circular; maw – shielded manual arc welding; saw-submerged arc welding s. kirin et alii, frattura ed integrità strutturale, 53 (2020) 345-352; doi: 10.3221/igf-esis.53.27 347 rhpp bajina basta – penstock design and testing aving in mind the importance of the penstock, special design procedure has been used, combined with extensive testing of the full-scale prototype, fig. 2, including static, dynamic and fracture mechanics testing, based on the request to construct only one pipeline, made of steel with yield strength significantly higher than for the common structural steels. therefore, sumiten ht80 was chosen, quenched and tempered weldable high strength low alloyed (hsla) steel, with nominal yield strength (ys) above 700 mpa, and tensile strength (ts) cca 800 mpa. anyhow, welded joints made of such steels are well known for their susceptibility to cracking, making three stages hydrostatic proof testing of the model inevitable: 1. loading from 0 to 3 mpa to check the measuring system. 2. loading from 0 to 9.02 mpa, to reach the service stress. 3. overloading (33.3%) from 0 to 12.05 mpa, as required by the regulation. full-scale model strains were measured by strain gages (sg) and moiré grids, as described in details in [1,2]. in the base metal (bm) response was dominantly elastic, whereas plastic strain (0,24%) was registered in welded joint ls1 (sg2, sg34), indicating non-uniform, even strange behavior due to stress concentration and weld mismatching, as shown in [4]. potential consequences event frequency people property environment reputation a b c d e negligible low moderate medium large 0 no injuries no losses no damage no harm 1 insigni ficant injuries loss up to 10 k€ minor damage to environment insignificant consequences. employees and population awareness. 2 minor injuries loss from 180 k€ to 540 k€ minor consequence and damage to environment. small costs.. mild consequences. there is a concern at the local level. 3 serious injuries loss from540 k€ to 1,8 m€ moderate consequence. short-term damage to environment.. minor consequences. there is a concern at the regional level 4 perma nent incapabilit y loss from 1,8 k€ to 50 m€ major consequences. big damage to environment. large costs. moderate consequenes. there is a concern at the national level. 5 death loss over 50 m€ dire consequences. longterm and big damage. huge costs. dire consequence. concern and reaction at the international level. table 1: descriptive risk matrix, taken from [11]. h s. kirin et alii, frattura ed integrità strutturale, 53 (2020) 345-352; doi: 10.3221/igf-esis.53.27 348 risk matrix hen observing the risk, possible consequences for the people, property, environment and reputation of the company should be considered. in the suggested model, we proposed a combination of qualitative and quantitative approach to the assessment of potential consequences, as given in tab. 1 in the form of risk matrix, [7, 11]. other aspects of risk based structural integrity assessment is given in [3-11]. as already shown in the case of pressure vessels that would cause air strike and significant damage, probably with fatalities, [7, 11], this is the case also with eventual penstock failure. the indirect damage would be the total stoppage of a reversible hydroelectric power plant for long period of time. therefore, potential consequence in the case of penstock failure is certainly the highest one, category 5, since it would cause the collapse of the entire power plant. anyhow, the approach adopted here will not consider event frequency when probability is evaluated, since it has no relevance to the case considered. instead, engineering approach will be applied, based on fracture mechanics concept, i.e. failure assessment diagram (fad), as described for different applications in [3-11]. failure assessment diagram application ailure assessment diagram, in its simplest form, i.e. level 1 as shown fig. 3, enables one of the most efficient ways to assess structural integrity of a cracked component made of elastic-plastic material, such as hsla steel. basically, fad indicates safe and unsafe position of a point corresponding to a given stress state for a cracked component, divided by so-called limit curve, fig. 3: 1/ 2 2 8 ln sec 2 r r rk s s             (1) where sr=sn/sc and kr=ki/kic, sn stands for stress in net cross section, sc for the critical stress (yield strenght, tensile strength or any value in-between), ki for the stress intensity factor and kic for its critical value, i.e. fracture toughness. figure 3: failure assessment diagram, including assessment points for edge cracks. using experience and results of previous testing of the prototype, [1,2], two axial surface cracks are analysed here, both with length 90 mm, one with depth 11.75 mm (¼ of penstock thickness, 47 mm), and the other one with depth 23.5 mm (½ of penstock thickness). two loading cases are analysed, one being 9.02 mpa (design pressure), and the other one 12.05 mpa (hydrostatic proof testing pressure, 33.3% higher). conservative assumption would be to consider cross-section as being just where the crack is, i.e. 90 mm wide and 47 mm deep (minus the crack depths), i.e. ¾ or ½ of the original value, and use formulas for an edge crack, whereas sc is taken as average value of ys and ts, i.e. 750 mpa:  sn is taken as 536 mpa, for „1/4“ crack and 804 mpa for „1/2“ crack, with remote stress 402 mpa for p=9.02 mpa and 536 mpa for p=12.05 mpa.  sr=sn/sc=536/750=0.71 for p=9.02 mpa, 0.95 for p=12.05 mpa and „1/4“ crack. w f s. kirin et alii, frattura ed integrità strutturale, 53 (2020) 345-352; doi: 10.3221/igf-esis.53.27 349  sr=sn/sc=804/750=1.07 for p=12.05 mpa, 1.43 for p=12.05 mpa and „1/2“ crack.  ki=1.39(pr/t)a=1.39·402··11.75=3402 mpamm for p=9.02 mpa and a/t=0.25 or 4536 mpamm for p=12.05 mpa and a/t=0.25.  ki=2.71(pr/t)a=2.71·402··23.5=9380 mpamm for p=9.02 mpa and a/t=0.5 or 12507 mpamm for p=12.05 mpa and a/t=0.5.  kic=(ejic/(1-ν2)=8548 mpamm (jic=316.6 n/mm [13]).  kr=ki/kic=3402/8548=0.40 (p=9.02, ¼), 4536/8548=0.53 (p=12.05, 1/4), 9380/8548=1.08 (p=9.02, 1/4), 12507/8548=1.44 (p=12.05, ½). therefore, the fad coordinates obtained for cracks treated as through thickness cracks with depths being ¼ and ½ half of thickness, are as follows, fig. 1: for ¼ crack, p=9.02 (0.71, 0.40), p=12.05 (0.95, 0.53). for ½ crack, p=9.02 (1.07, 1.08), p=12.05 (1.43, 1.44). clearly, this is overconservative estimation since both material and crack geometry are presented in conservative way. anyhow, even this simple analysis indicates detrimental effect of over-pressurizing, since the points corresponding with it are way out of the safe region (1/2 crack), or very close to the limit curve (1/4 crack), fig. 3. less conservative assumption would be to consider cracks as they are, i.e. treat them as surface cracks. in that case reduction of cross-section is negligible, so sn and sr are calculated as follows:  sn=pr/t= 9.02x2.1/0.047=402 mpa,  sn=pr/t=12.05x2.1/0.047=536 mpa.  sr=sn/sc=402/750=0.54  sr=sn/sc=538/750=0.72 stress intensity factor for surface edge crack in a plate can be evaluated using the following procedure from [14]. plate is taken as better approximation than thin cylinder, since the ratio b/ri is just 47/2100=0.023, i.e. much closer to 0 than to 0.1, which is the lowest value for cylinders in [14]. geometry parameters f and q are calculated for tensile plate with a surface crack (a/2c=0.13 for ¼ crack and ≤1) at the point of maximum stress intensity factor (φ=900) as follows: 1.65 1 1.464 1.08 c q a         for ¼ crack and 1.22 and for ½ crack, 2 4 1 2 3 1.102w a a f m m m gf f t t                      for ¼ crack and 1.033 and for ½ crack, 1 1.13 0.09 1.106 c m a            for ¼ crack and 1.108 and for ½ crack, 2 0.89 0.54 1.39 1 / m a c     for ¼ crack and 0.7 and for ½ crack, 24 3 1 0.5 14 1 0.589 0.65 a m a c c            for ¼ crack and -0.355 and for ½ crack,   2 3 1 0.08 0.15 1 cos 1 c g t                 1 1 2 4 2 2 2sin cos 1, sec 1 2 w c c a f f a w t                              s. kirin et alii, frattura ed integrità strutturale, 53 (2020) 345-352; doi: 10.3221/igf-esis.53.27 350 now, for a/t=0.25 one can calculate ki=2837 mpamm for p=9.02 mpa and 3777 mpamm for p=12.05 mpa, whereas for a/t=0.5 ki=4012 mpamm for p=9.02 mpa and 5341 mpamm for p=12.05 mpa. finally, assessment points coordinates in fad are, fig. 4: for ¼ crack, p=9.02 (0.54, 0.33), p=12.05 (0.54, 0.46). corresponding probablities are 0.58 and 0.62. for ½ crack, p=9.02 (0.72, 0.44), p=12.05 (0.72, 0.62). corresponding probablities are 0.75 and 0.82. figure 4: failure assessment diagram, including assessment points for surface cracks now, one can get risk matrix in usual way, as presented in tab. 2, indicating shift from high (0.58) to very high risk (0.62), for 1/4 crack, or from very high (0.75) to extremely high risk (0.82) for 1/2 crack. consequence category 1 – very low 2 low 3 medium 4 high 5 very high risk legend p ro b ab lit y ca te go ry ≤0.2 very low very low 0.2-0.4 low low 0.4-0.6 medium 1/4 crack p=9.02 mpa medium 0.6-0.8 high 1/4 crack p=12.05 mpa 1/2 crack p=9.02 mpa high 0.8-1.0 very high 1/2 crack p=12.05 mpa very high table 2: risk matrix for ¼ crack and ½ crack, p=9.02 mpa and 12.05 mpa. discussion he approach so far presented is the simplest one which takes into account crack geometry and material behaviour. being the simplest it is not the most accurate one, lacking precise stress distribution, especially in weld joint zones. namely, as shown previously, [1,2], stress concentration can cause local plastic deformation in welded joints made by saw, in the case of overpressure, since they have the lowest ys (687 mpa). to take into account such effects, more sophisticated approach is needed, e.g. japp vs. j-r curve analysis, based on more complex analytical solutions for j, [1,2]. here, such an analysis is briefly presented, as shown in fig. 5. corresponding critical values (0.91·ys for wm and 0.92·ys for bm in the case of ¼ crack, or 0.82·ys for wm and 0.85·ys for bm in the case of ½ crack, can be taken as inverse of t s. kirin et alii, frattura ed integrità strutturale, 53 (2020) 345-352; doi: 10.3221/igf-esis.53.27 351 probability, but this is beyond the scope of this approach since its basic advantage, simplicity, would be lost. anyhow, one can notice that overpressure in weld metal can reach the critical state, since only 563 mpa would cause unstable crack growth in saw weld metal with ½ crack, whereas operating pressure would not jeopardize penstock integrity even in that case. figure 5: crack driving force vs. j-r curves for bm and wm. conclusions ased on the results shown here, one can conclude the following  risk based analysis using fracture mechanics parameters, as presented here, is efficient engineering method to assess structural integrity of a cracked component, especially if its geometry is relatively simple.  effect of over-pressure is detrimental from the point of view of structural integrity since it can cause unnecessary damage of welded joints, as the most crack sensitive regions. both simple engineering method, as presented here, and previously performed more complex fracture mechanics analysis, lead to that conclusion. references [1] sedmak, s., sedmak, a. (2005) integrity of penstock of hydroelectric power plant, structural integrity and life 5, pp. 59-70 [2] sedmak, s., sedmak, a. (1995). experimental investigation into the operational safety of a welded penstock by a fracture mechanics approach, fatigue and fracture of engineering materials and structures 18, pp. 527-538 [3] martić, i., sedmak, a., mitrović, n., sedmak, s., vučetić, i. (2019). effect of over-pressure on pipeline structural integrity, technical gazette, 26(3), pp. 852-855 [4] golubović, t., sedmak, a., spasojević brkić, v., kirin, s., rakonjac, i. (2018). novel risk based assessment of pressure vessels integrity. technical gazette, 25(3), pp. 803-807. [5] sedmak, a., algool, m., kirin, s., rakicevic, b., bakic, r. (2016). industrial safety of pressure vessels structural integrity point of view, hemijska industrija, 70(6), pp .685-694 [6] golubović, t., sedmak, a., spasojević brkić, v., kirin, s., veg, e. (2018). welded joints as critical regions in pressure vessels – case study of vinyl-chloride monomer storage tank, hemijska industrija, 72(4), pp. 177-182. [7] vučetić, i., kirin, s., sedmak, a., golubović, t., lazic, m. (2019). risk management of a hydro power plant – fracture mechanics approach, technical gazette 26, pp. 428-432. [8] pilić, v., mihajlović, v., stanojević, p., anđelković, a., baloš, d. (2019). application of innovative risk assessment methodology for damage mechanisms identification on part of amine regeneration unit, structural integrity and life, 19(1), pp.29–35. b s. kirin et alii, frattura ed integrità strutturale, 53 (2020) 345-352; doi: 10.3221/igf-esis.53.27 352 [9] pilić, v., stanojević, p., mihajlović, v., baloš, d. (2019). damage mechanism and barrier identification on hydrogen production unit using innovative methodology for risk assessment, structural integrity and life, 19(2), pp.131–137. [10] zaidi, r., sedmak, a., kirin, s., grbovic, a., li, w., lazic vulicevic, l., sarkocevic, z. (2020). risk assessment of oil drilling rig welded pipe based on structural integrity and life estimation, engineering failure analysis, 112, 104508. [11] vučetić, i., kirin, s., vučetić, t., golubović, t., sedmak, a. risk analysis in the case of air storage tank failure at rhpp bajina bašta, structural integrity and life, 18 (1), pp. 3-6. [12] correia, j.a.f.o., de jesus, a.m.p., muniz-calvente, m., sedmak, a., moskvichev, v., calçada, r. (2019). the renewed tc12/esis technical committee risk analysis and safety of large structures and components (editorial), engineering failure analysis, 105, pp. 798-802. [13] petrovski, b. (1985). determination of residual strength of pressure vessel with a surface crack (in serbian), ph.d. thesis, university of belgrade. 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/hrv (za stvaranje adobe pdf dokumenata najpogodnijih za visokokvalitetni ispis prije tiskanja koristite ove postavke. stvoreni pdf dokumenti mogu se otvoriti acrobat i adobe reader 5.0 i kasnijim verzijama.) /hun 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can be opened with acrobat and adobe reader 5.0 and later.) >> /namespace [ (adobe) (common) (1.0) ] /othernamespaces [ << /asreaderspreads false /cropimagestoframes true /errorcontrol /warnandcontinue /flattenerignorespreadoverrides false /includeguidesgrids false /includenonprinting false /includeslug false /namespace [ (adobe) (indesign) (4.0) ] /omitplacedbitmaps false /omitplacedeps false /omitplacedpdf false /simulateoverprint /legacy >> << /addbleedmarks false /addcolorbars false /addcropmarks false /addpageinfo false /addregmarks false /convertcolors /converttocmyk /destinationprofilename () /destinationprofileselector /documentcmyk /downsample16bitimages true /flattenerpreset << /presetselector /mediumresolution >> /formelements false /generatestructure false /includebookmarks false /includehyperlinks false /includeinteractive false /includelayers false /includeprofiles false /multimediahandling /useobjectsettings /namespace [ (adobe) (creativesuite) (2.0) ] /pdfxoutputintentprofileselector /documentcmyk /preserveediting true /untaggedcmykhandling /leaveuntagged /untaggedrgbhandling /usedocumentprofile /usedocumentbleed false >> ] >> setdistillerparams << /hwresolution [2400 2400] /pagesize [612.000 792.000] >> setpagedevice microsoft word numero_41_art_36.docx s. beretta et alii, frattura ed integrità strutturale, 41 (2017) 269-276; doi: 10.3221/igf-esis.41.36 269 focused on crack tip fields stress intensity factor calculation from displacement fields s. beretta, l. patriarca, s. rabbolini politecnico di milano, department of mechanical engineering, via la masa 1, 20156, milano, italy stefano.beretta@polimi.it, luca.patriarca@polimi.it, silvio.rabbolini@polimi.it abstract. in the last two decades, visual image techniques such as digital image correlation (dic) enabled to experimentally determine the crack tip displacement and strain fields at small scales. the displacements are tracked during loading, and parameters as the stress intensity factor (sif), opening and closing loads, t-stress can be readily measured. in particular, the sifs and the t-stress can be obtained by fitting the analytical equation of the williamstype expansion with the experimentally-determined displacement fields. the results in terms of fracture mechanics parameters strictly depend on the dimension of the area considered around the crack tip in conjunction with the crack length, the maximum sif (and thus the plastic tip radius), and the number of terms to be considered in the williams-type expansion. this work focuses in understanding the accuracy of the sif calculation based on these factors. the study is based on finite element analysis simulations where purely elastic material behavior is considered. the accuracy of the estimation of the sif is investigated and a guide-line is provided to properly set the dic measurements. the analysis is then experimentally validated for crack closure measurements adopting the sent specimen geometry. keywords. stress intensity factor; digital image correlation; crack-tip displacement fields. citation: beretta, s.., patriarca, l., rabbolini, s., stress intensity factor calculation from displacement fields, frattura ed integrità strutturale, 41 (2017) 269-276. received: 28.02.2017 accepted: 03.05.2017 published: 01.07.2017 copyright: © 2017 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. introduction he digital image correlation (dic) technique is nowadays largely adopted as a reliable, non-destructive, low-cost technique to measure real-time local displacements on a flat surface of the specimens [1, 2]. the full-field displacement and strain measurements found several engineering applications as, for example, in the study of the crack tip fields and in the characterization of the typical fracture mechanics parameters such as the stress intensity factor (sif). however, the adoption of displacement measurements to calculate the sifs is critical, and special attention is required to properly select the dic measurements. for example, the choice of the area of interest in front the crack tip (field-of-view) strictly depends on to the type of the analytical model selected for the fitting of the displacement field. it turns out that the accuracy of the sifs measurements from full-field dic displacement fields is a technical issue which t s. beretta et alii, frattura ed integrità strutturale, 41 (2017) 269-276; doi: 10.3221/igf-esis.41.36 270 still requires attention even though the rich literature growing in the last decades [3-5]. in fact, real crack tip displacement fields are affected by several factors that cannot be easily controlled during dic displacement measurements. crack tip plasticity, crack closure, correlation parameters (field of view, subset size) have shown to profoundly influence the sif calculation. in order to clarify and to provide a guideline on the sif measurements, in this work we analyze the displacement field calculated according finite element (fe) simulations of two typical cracked body geometries: the center cracked tension (cct) and single-edge notched tension (sent) specimens. starting from the displacement fields obtained from the fe simulations, this work shows the comparison with the sif predicted by the numerical analyses focusing specifically on the parameters that are required to be properly set to obtain an accurate sif measurement during dic measurements. the methodology was successively experimentally implemented for the measurement of the opening stress for a crack propagating in a sent specimen. figure 1: geometries considered in this study: center cracked tension (cct) and single-edge notched tension (sent) specimens. the regressions of the displacement fields in front of the crack tip are based on the williams expansion [6]. the williams expansion is herein written for the displacements v in the direction perpendicular to the crack surfaces in three different versions based on the number of terms involved:                        2sin 1 2 cos cos 2 2 2 2 i v k r v k ar b (1)                                    2sin 1 2 cos sin 3sin cos 2 2 2 2 8 i v k r t v k r k ar b (2)                                                              2 3/2 13 sin 1 2 cos sin 3sin 2 2 2 2 8 1 3 3 sin sin cos 2 2 2 2 2 i v k r t v k r k r a k ar b (3) the terms a and b account the contributions of the specimen rotation and translation on the displacement field. s. beretta et alii, frattura ed integrità strutturale, 41 (2017) 269-276; doi: 10.3221/igf-esis.41.36 271 the cct and sent geometries are shown in fig.. 1. the field-of-view dimension is herein indicated as d, while the crack length in indicated as a and the specimen width as w. numerical analyses ig. 2 illustrates the preliminary fe analysis performed to set the dimension of the finite element in proximity of the crack tip necessary to model the stress singularity determining the sif. for a crack length of a=0.9mm, and a ratio a/w=0.3, the fe simulations show convergence of the stress fields for element sizes in proximity of the crack tip of, respectively, 3.6µm and 2.5µm. figure 2: convergence analysis for finite element model according to finite element sizes of 3.6µm and 2.5µm in proximity of the crack tip. the stress plot indicates that the dimension of the elements chosen provides the same stress distribution. following the fe model definition, a set of fe analyses was implemented. the crack lengths analyzed range from a/w=0.05 to a/w=0.5. fig. 3 shows the results of the regression of the fe displacement fields for different number of terms included in the williams expansion. the regression adopting only the first term (k) yields to precise sif estimations only for very restricted field-of-view dimension d (less than 0.01mm). however, the real material behavior shows local plasticity in front of the crack tip which includes the small area where the k regression provides accurate results. in addition, performing dic measurements with such small field-of-view is a challenging task and it would involve other problems with out-of-plane displacements that affect the dic quality. it turns out that the regression based only on the first term of the williams expansion is not pursued, and the additional terms are required to be fitted. the sif measurement based on the 2-terms regression is also observed to provide generally inaccurate sif values. in particular, only for field-of-view dimensions lower than d<0.2mm the sif calculated shows a 10% discrepancy with the fe solution. the 3-terms regression is shown to be the most accurate and stable for field-of-view dimensions raging from d>0.2mm to d=1.4mm giving an accuracy of less than 5% on the sif estimation. f s. beretta et alii, frattura ed integrità strutturale, 41 (2017) 269-276; doi: 10.3221/igf-esis.41.36 272 figure 3: precision of sif calculation depending on the crack length and the dimension of the regression region for the cct specimen. the regression based only on the k term is always overestimating the sif and only for very small regression regions it gives accurate sif solutions; the solution including the k term and the t-stress tends to underestimate the sif, even though the solution is accurate for relative for dimensions of the regression area up to 0.2 mm. the 3-terms regression results in the most stable and accurate sif estimations. in particular, it requires regression dimensions higher than d>0.2mm which can be adopted in dic measurements. s. beretta et alii, frattura ed integrità strutturale, 41 (2017) 269-276; doi: 10.3221/igf-esis.41.36 273 figure 4: precision of sif calculation depending on the crack length and the dimension of the regression region for the sent specimen. the regression based only on the k term is not accurate for most of the crack lengths investigated, and it gives accurate predictions only for small regression regions d<0.05mm which requires high dic resolutions. the most accurate solutions are given by the 3-terms regression. s. beretta et alii, frattura ed integrità strutturale, 41 (2017) 269-276; doi: 10.3221/igf-esis.41.36 274 similar trends can be observed for the analyses performed for the sent geometry, fig. 4. for field-of-view dimensions lower than d<0.2mm the most accurate sif estimations are given by the single and 2-terms regressions. again, the regressions presented refer to an idealized linear elastic continuum and do not consider the local plasticity arising from the crack tip. the 3-terms regression is providing also for the sent geometry the most accurate results for field-of-views larger than d>0.2mm. the adoption of larger number of terms to fit the williams expansion do not improve further the sif accuracy as already shown by m. mokhtari and coauthors [1]. experiments he experimental set-up adopted in the present work is shown in fig. 5a. a leica dfc290hd camera was used in conjunction with optem lens in order to capture real-time in-situ dic images. the specimens were machined by electrical discharge machining (edm) to a dog-bone geometry with gauge section of 6mm x 3mm and a lateral notch with 1mm depth. the specimen surfaces in proximity of the notch tip were prepared for dic measurements. initially, the target surface was polished with abrasive paper up to a grit of p2500. successively, a fine speckle pattern was produced using an iwata airbrush and black paint. a very refined pattern is required for the present analysis, and this was accomplished by using the airbrush with a 0.18mm wide needle. the image resolutions available with this speckle pattern range from 2.13µm/px to 0.53µm/px. the tested alloy is a quenched and tempered high strength 30nicrmov12 steel with young’s modulus equal to 207 gpa, yield stress σy=945mpa and ultimate tensile stress σu=1023mpa. figure 5: experimental set-up for dic measurements: a) the optical microscope, the hydraulic load frame, and the specimen geometry adopted for the present study; b) the crack propagation is affected by the crack closure, the analysis is based on the effective sif range δkeff. the specimens were cyclically loaded by means of a servo-hydraulic mts landmark 810 load frame. the load ratio r was set to 0.05. initially, the specimens were pre-cracked to a crack length of 1.7mm. successively, the crack was grown from 1.7mm to a final crack length of 2.58mm and different dic measurements were performed at different crack advancements (tab. 1). a [mm] ktheo [mpa√m] kopen [mpa√m] (2-terms) kopen/ktheo (2-terms) kopen [mpa√m] (3-terms) kopen/ktheo (3-terms) 1.70 18.65 7.46 0.4 8.01 0.43 1.83 20.25 7.49 0.37 8.50 0.42 1.95 21.83 7.86 0.36 8.30 0.38 2.17 25.09 9.78 0.39 9.53 0.38 2.58 33.77 13.85 0.41 14.18 0.42 table 1: sif measurements by dic displacement field measurements during crack advance. fig. 5b depicts the dic acquisition strategy performed at different crack lengths. the images were acquired during two load cycles. the reference image for correlation is selected as the image captured at minimum load. the images captured t s. beretta et alii, frattura ed integrità strutturale, 41 (2017) 269-276; doi: 10.3221/igf-esis.41.36 275 successively were correlated using a commercial software (vic 2d) and the displacement field for each load increment was successively used to calculate the sif. the sif evolution with the load p is then plotted and compared with the sif calculated analytically. it is important to observe that, since the sif is calculated based on the displacement fields calculated from the reference image captured at the minimum load, the measured sif is interpreted as a variation δk form the reference condition. since the crack propagation is also influenced by crack closure, we also provide an analysis of the measured effective δkeff. the plot in fig. 5b shows that the measured sif remains approximately zero before crack opening which occurs at point 3” where it can be defined the opening sif as the kopen. the ratio between the opening sif and the maximum sif calculated analytically kopen/ktheo is used to quantify the crack closure effect. this approach has been already successfully adopted by carroll and co-authors [7]. figure 6: dic measurements and regression of the displacement field: a) contour plot of the dic displacement field; b) analysis of the displacement fields by the 3-terms regression; c) δk calculation and comparison with the analytical solution for the 2-terms regression and for the d) 3-terms regression. in order to precisely measure the sifs, the area adopted for the two regressions are different according the analysis performed in the first part of the paper, for more details refer to the text. fig. 6 shows the main results of the experiment conducted on the sent specimen. contour plot in fig. 6a shows the vertical displacement field as calculated from the dic algorithm for a defined load step. fig. 6b indicates the vertical displacement field (blue lines) and the displacement field calculated from the fitting of the william expansion adopting a correlation basted on the first 3 terms (red lines). accordingly, fig. 6c and 6d include the analyses of the variation of the sif during loading for the same crack length but different number of terms in the regression. in particular, fig. 6c shows the sif variation according the 2-terms regression calculated using a dic regression area of 0.03 mm2 which corresponds to a field-of-view dimension of d=0.17mm. the crack length at this test interruption was a/w=0.4. according to these parameters, fig. 4 shows that the sif calculated should provide accurate results. as a comparison, fig. 6d shows the 3terms regression. in this case, the numerical analysis (fig. 4) suggests that, for a crack length of a/w=0.4, the regression performed with 3 terms provides accurate sif values when the field-of-view dimension is between d=0.2mm and d=0.6mm. the dic regression area was then selected to be 0.18 mm2 which corresponds to a field-of-view dimension d=0.42mm. comparing the results in terms of sif values it is observed a good agreement between the two types of regressions. this results also in the correct estimation of the closure levels of approx. kopen/ktheo=0.4 for both the types of regressions. s. beretta et alii, frattura ed integrità strutturale, 41 (2017) 269-276; doi: 10.3221/igf-esis.41.36 276 final remarks his work focused on the analysis of the field-of-view influence in the sif calculation from displacement fields measured using the dic technique. in the first part of the work, numerical analyses on cct and sent geometries were designed aiming to reproduce the displacement fields in the crack tip area. the results of the fe simulations enabled to study the influence of the number of terms in the regression of the displacement fields based on the area investigated (field-of-view). this study provides a guideline to properly select the field-of-view dimension and the number of terms in the williams expansion to obtain accurate sif evaluation from dic measurements. experimentally, a crack was grown in a notched dog-bone specimen (sent geometry), and the displacement fields were measured with real-time dic acquisitions for specific crack advancements. the sifs were determined using 2-terms and 3-terms regressions and compared. following the first part of the work, two different field-of-views were selected depending on the number of terms selected in the williams expansion giving a difference in the sifs estimations within 5%. references [1] mokhtari, m., lopez-crespo, p., moreno, b., zanganeh, m., some experimental observations of crack-tip mechanics with displacement data, frattura ed integrita� strutturale, (33) (2015) 143. [2] hild, f., roux, s., measuring stress intensity factors with a camera: integrated digital image correlation (i-dic), comptes rendus mécanique 334(1) (2006) 8-12. [3] réthoré, j., gravouil, a., morestin, f., combescure, a., estimation of mixed-mode stress intensity factors using digital image correlation and an interaction integral, international journal of fracture, 132(1) (2005) 65-79. [4] sutton, m.a., orteu, j.-j., schreier, h. w., image correlation for shape, motion and deformation measurements: basic concepts, theory and applications, (2009). [5] pan, b., qian, k., xie, h., asundi, a., two-dimensional digital image correlation for in-plane displacement and strain measurement: a review, measurement science and technology, 20(6) (2009) 062001. [6] williams, m., on stress distribution at base of stationary crack., journal of applied mechanics 24 (1957) 109. [7] carroll, j., efstathiou, c., lambros, j., sehitoglu, h., hauber, b., spottswood, s., chona, r., investigation of fatigue crack closure using multiscale image correlation experiments, engineering fracture mechanics, 76(15) (2009) 23842398. t << /ascii85encodepages false /allowtransparency false /autopositionepsfiles true /autorotatepages /none /binding /left /calgrayprofile (dot gain 20%) /calrgbprofile (srgb iec61966-2.1) /calcmykprofile (u.s. web coated \050swop\051 v2) /srgbprofile (srgb iec61966-2.1) /cannotembedfontpolicy /error /compatibilitylevel 1.4 /compressobjects /tags /compresspages true /convertimagestoindexed true /passthroughjpegimages true /createjobticket false /defaultrenderingintent /default /detectblends true /detectcurves 0.0000 /colorconversionstrategy /cmyk /dothumbnails false /embedallfonts true /embedopentype false /parseiccprofilesincomments true /embedjoboptions true /dscreportinglevel 0 /emitdscwarnings false /endpage -1 /imagememory 1048576 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/hrv (za stvaranje adobe pdf dokumenata najpogodnijih za visokokvalitetni ispis prije tiskanja koristite ove postavke. stvoreni pdf dokumenti mogu se otvoriti acrobat i adobe reader 5.0 i kasnijim verzijama.) /hun 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/pdfxoutputintentprofileselector /documentcmyk /preserveediting true /untaggedcmykhandling /leaveuntagged /untaggedrgbhandling /usedocumentprofile /usedocumentbleed false >> ] >> setdistillerparams << /hwresolution [2400 2400] /pagesize [612.000 792.000] >> setpagedevice microsoft word numero_56_art_06_2955 m.i boulifa et alii, frattura ed integrità strutturale, 56 (2021) 74-83; doi: 10.3221/igf-esis.56.06 74 study of the influence of alloying elements on the mechanical characteristics and wear behavior of a ductile cast iron mohammed iliasse boulifa university of el oued, fac. technology, dept. mechanical engineering 39000 el oued, algeria foundry laboratory, faculty of engineering sciences, badji mokhtar university 23000 annaba, algeria biliasse@gmail.com, http://orcid.org/0000-0001-5131-8551 ali hadji foundry laboratory, faculty of engineering sciences, badji mokhtar university 23000 annaba, algeria hadji.lrf@gmail.com, http://orcid.org/0000-0001-6673-6967 abstract. in the present work, the influence of alloying elements, on the mechanical characteristics and wear behavior by modification of the chemical composition of the ductile iron was studied, to improve these characteristics for the manufacture of agricultural tractors parts in particular front and rear axles, ploughshares, gear crankcase, pinions, transmission shafts, crankshafts, etc... the cast iron investigated was prepared in an induction furnace at 1500°c and inoculated by a ferro-silicon-magnesium to 45% si and 10% mg. the specimens were casted into self-hardening sand moulds at 1450°c, after an addition of alloying elements, manganese (0.6%), nickel (0.5%), molybdenum (0.2%), and vanadium(0.1%) in the base spheroidal graphite cast iron produced. various techniques including, optical microscopy, microhardness, hardness, tensile strength, impact resistance, and wear tests (wear resistance and friction coefficient) were used to characterize these specimens. the obtained results show that the tested samples have ductile iron structures formed by ferrite and pearlite. moreover, mechanical and wear tests prove that the alloyed cast iron has improved characteristics compared to unalloyed cast iron and shows the positive effect of alloying elements on these characteristics. keywords. ductile iron; ferrite-pearlitic matrix; mechanical characteristics; wear resistance; friction coefficient. citation: boulifa, m. i., hadji, a., study of the influence of alloying elements on the mechanical characteristics and wear behavior of a ductile cast iron, frattura ed integrità strutturale, 56 (2021) 74-83 received: 24.11.2020 accepted: 16.02.2021 published: 01.04.2021 copyright: © 2021 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. introduction uctile iron is a cast iron with spheroidal graphite, so-called spheroidal graphite cast iron. it has mechanical properties that are similar to those of some steels [1]. more favourably, in contrast to cast steels, ductile iron has many technical and manufacturing advantages. these include excellent damping ability, increased wear resistance, d https://youtu.be/zmqfr6dgqqo m.i boulifa et alii, frattura ed integrità strutturale, 56 (2021) 74-83; doi: 10.3221/igf-esis.56.06 75 20-40% lower production costs and reduced volume shrinkage during solidification. besides, it is superior in cost, antifrictional and damping characteristics to steel. as a result, it has been successfully used to manufacture several types of mechanical components, based on the combination of good mechanical properties and casting abilities of ductile cast iron. especially in the automotive industry, such as gears, camshafts, connecting roads, crankshafts, gearboxes, front wheel spindle supports and truck axles, and also used for a wide variety of industrial applications, such as like pipes, flanges, pump housings, turbine components, that before had been made of steel [2-6]. in ductile iron, graphite is precipitated as spheroids rather than flakes by controlled processing of the molten iron. the graphite's circular form reduces the risk of the material to crack and helps avoid the spread of cracks. graphite flakes serve as stress risers that initiate and propagate cracks in gray cast iron, rendering the material weaker [7-9]. ductile iron's chemical and metallurgical characteristics make it the strongest and hardest cast iron, and also with the highest maximum durability. [10-12]. a study of the production of iron makes it simple to understand the advantages of ductile iron. in a matrix of ferrite and pearlite, ferrite-pearlitic ductile iron has graphite spheroids. pearlite is a fine ferrite and cementite (fe3c) lamellar aggregate. with moderate ductility and high strength, the alloy is relatively hard [4,13-15]. during the design of a new material that is going to be used for structural application, mechanical properties need to be well taken into account. the development of spheroidal cast iron has reached an important place in the mechanical components industry due to its mechanical properties. the main factors that influence the mechanical properties of a ductile iron are the microstructure, the morphology of the graphite (size and nodularity), and the casting defects (shrinkage and inclusions). the alloying elements are related to the microstructure, the matrix microstructure and mechanical properties are defined by many of these elements. up in a particular way, the matrix microstructure affects the hardness of the cast [16,17]. the contents of alloying elements have a very important influence on the structure of the cast iron and of course on the mechanical properties. the role of alloying elements in ductile iron can be interpreted differently depending on the behavior of each element, because these elements influences mechanical properties in the same cast in a different manner. if heat treatment is not taken into account, the appropriate balance of the alloying elements must be treated carefully. talking about the different alloying elements in terms of the properties they confer on iron is a tradition. the ability of alloying elements to promote the formation of a certain phase or to stabilize it is a property of great importance. these elements are grouped as elements that form austenite, ferrite, carbide, and nitride [18]: elements may encourage formation of graphite from the carbide. before forming graphite, only a small proportion of these elements can be added to the iron. silicon, nickel, cobalt, and aluminum are elements that facilitate the formation of graphite; alloying elements may go into solid solution in the iron, such silicon, molybdenum, chromium, nickel, and magnesium improve strength; elements which tend to form carbides include chromium, tungsten, titanium, columbium, vanadium, molybdenum, and manganese; austenite stabilizing elements include manganese, nickel, cobalt, and copper. these increase the range over which austenite is stable; elements, which tend to stabilize ferrite, include chromium, tungsten, molybdenum, vanadium, and silicon. they decrease the quantity of carbon soluble in the austenite and thus increase the quantity of free carbide in the iron at a given carbon content. recent research works [13,15,19-24] have shown that, si, mn, ni, mo, v, cu, ti, nb, w, sn… are the typical alloying elements used to control ferrite and pearlite contents and increases mechanical properties in ductile iron as-cast grades. mn and cu are used to promote pearlite, si is used to promote ferrite and to strengthen it. when producing the pearlitic grades, si is usually must be below 2.5% and when developing ferritic grades, it is between 2.5 and 2.8%. when making pearlitic grades, the rate of mn is generally between 0.4 and 0.6% and below 0.3% when making ferritic grades. according to these research works, it can noted that: silicon is considered as an alloying element if its content exceeds 3%, it easily forms solid solutions with cast iron. it has a certain effect to avoid grain enlargement. silicon alloyed with iron, widens ferrite phase domain. it increases the stability, wear resistance, and the yield strength, as it greatly increases the fluidity of the cast iron. manganese greatly reduces the critical cooling rate. it thus increases the hardness, yield strength, and tensile strength, decreasing elongation and improving toughness. if its content varies from 5 to 12%, it favors the formation of martensitic structure. if its content exceeds 12%, then the structure becomes austenitic. nickel gives the metal a set of remarkable properties so that it is used in all kinds of applications. the effect of nickel only occurs when it is used together with other elements. it allies completely with the austenite, forming a m.i boulifa et alii, frattura ed integrità strutturale, 56 (2021) 74-83; doi: 10.3221/igf-esis.56.06 76 continuous series of solid solutions. addition of ni improves hardness. nickel has a similar behavior to manganese. its fundamental interest is to lower the temperature of critical points. molybdenum is used in combination with ni and/or cu. it improves hardenability and decreases the critical cooling rate. it increases the yield strength, tensile strength, and wear resistance. it improves machinability, impact resistance, and fatigue resistance properties. mo gives the cast iron good fluidity. the improvement in properties, due to molybdenum, is also because it lowers the temperature of critical points. vanadium is a powerful generator of carbides, hence it increases wear resistance. it is an element, which has the effect of stabilizing the carbides. it is used to compensate, in certain alloyed cast irons, containing elements encourage formation of graphite from the carbide (nickel-titanium). vanadium is a deoxidizing element, it is used in order to obtain very healthy cast irons. copper dissolves in the ferrite, the addition of copper has not a direct influence on the hardness, only if the dimensions of the parts are not important. it increases tensile strength and yield strength. cu contents superior at 0.30% may cause structural hardening improving hardenability. titanium has grain refining properties, which increases the value of mechanical characteristics and causes a reduction of the austenite zone. titanium has a very noticeable effect on graphite it makes it very thin. niobium is a very powerful generator of carbides and ferrite while reducing the austenite zone. it increases hardness, tensile strength, yield strength, and refines the grains. as is known, many factors can affect the wear performance of a material. the microstructure and the nature of the material are extremely important among these factors. depending on the composition, the matrix structure of ductile iron can be ferritic, pearlitic, bainitic, or martensitic [13-16]. one of the most commonly encountered industrial problems is wear, particularly through abrasion, leading to frequent replacement of components. abrasive wear occurs when hard particles or asperities penetrate a softer surface and displace material in the form of elongated chips and slivers. during the wear process, the hard particles can be formed inside the tribosystem itself or they can be contaminated by the environment. wear resistance is not an intrinsic material property, but relies on the tribological mechanism, such as material microstructure properties, abrasive grit size, test condition, equipment, and environment [25-27]. friction and wear are subject to many mechanical components, which makes this iron very interesting from the point of view of tribological behavior. several researchers have studied the sliding wear action of cast iron. the wear resistance of the ductile iron under dry sliding conditions is superior than that of the same steels of the same hardness. they have also reported that the wear loss is related to the original hardness (before the wear test) under dry sliding conditions using the pin-on-disk machine [28,29]. during these last few years, ductile iron is the subject of a wide variety of studies, both on transformation theory, on the fields of application, and on the mechanical properties. currently, research efforts on this cast iron are mainly concentrated on possible improvements in its mechanical properties. the problems to be studied are the thermal and thermo-mechanical stability of the structure, the influence of alloying elements on the mechanical properties, the influence of heat treatment parameters on the structure, and on the state of the residual stresses… the main objective of the present research is to improve the properties of this cast iron, also to investigate the correlation between microstructure and these properties. this is why we took as research axes, the choice of alloying elements to be added, their contents, and their influence on the mechanical properties and wear resistance. in other words, this research has been done with the aim of analyzing the behavior of the casting from the variation of the chemical composition and its effect on the mechanical properties and wear behavior. with it, we want to reaffirm the role and the importance that the appropriate control of each alloying element introduced in the spheroidal graphite cast iron. this last is characterized by the end zones of solidification less rich in silicon, where there are the porosities, first responsible sites at initiation of fatigue cracks. the base metal (unalloyed cast iron) presented in this research is an industrial ductile cast iron actually used for the production of mechanical parts, in an agricultural tractor society, which has well-defined mechanical properties. the best mechanical properties such as microhardness, hardness, yield strength, tensile strength, elongation, impact resistance and wear resistance were found based upon various structural and mechanical characterizations based upon alloying elements such as mn, ni, mo and v added in the base metal. many of these elements define the matrix microstructure and mechanical properties. these alloying elements added to nodular irons are of particular interest for the manufacturing of mechanical parts, because of benefits to the resulting mechanical properties. ductile iron constitutes alloyed ferrite and perlite in the matrix, this microstructure confers a high strength with favourable hardness. m.i boulifa et alii, frattura ed integrità strutturale, 56 (2021) 74-83; doi: 10.3221/igf-esis.56.06 77 experimental procedures casting procedure n this experimental work, the specimens used to study the ductile cast iron were obtained in an industrial foundry, by casting the melt in cold self-hardening sand moulds at 1450°c, in form of 50 mm y-blocks according to dimensions specified in iso 1083-76 standard [30]. for 100 kg of base metal (ductile iron) heats comprising of 70 kg of pig iron, 20 kg returns and 10 kg of steel scrap were prepared in an induction furnace with a maximum capacity of 3000 kg at 1500 °c. the spheroidization process was performed by the sandwich method using a fe–si–mg alloy (45% si and 10% mg). from the base composition, an alloyed material was studied: 0.6 % mn, 0.50% ni, 0.20% mo, and 0.10% v. the rate of mn added (element which tends to form carbides) is to stabilize austenite, increase the hardenability, favour the formation of precipitates, and consequently improving the mechanical properties and wear behavior. concerning the level of ni (element may encourage formation of graphite from the carbide and go into solid solution in the iron), this is to stabilize austenite on one side, neutralize the adverse effect of mn notably graphite degeneration and the formation of the white structure on the other side. molybdenum and vanadium were introduced to stabilize ferrite and increase strength. the chemical composition analysis of the unalloyed (base metal) and alloyed cast irons was determined using a fluorescence spectrometer x. the results of this analysis are shown in tab. 1. table 1: chemical composition of experimented cast irons (wt. %). microstructural examination the microstructure analysis was carried out using an optical microscope (nikon eclipse lv100nd type). the samples were polished and chemically attacked at 3% nital. mechanical tests the specimens were cut from y-blocks to different shapes according to the test type. a vickers microhardness tester "zwick/roell zhv10" type was used. the tests were carried out using 0.1 kg load and 15 second period of loading. the method used for measuring hardness was "hrb". six tests were performed for each specimen of microhardness and hardness and the average was taken. tensile tests were performed at a strain rate of 8×10− 3 s− 1 on a "zwick / roell z100" testing machine. three samples were tested for each cast iron and the average was taken. the tests were carried at 20°c according to the iso 1083-76 standard. impact resistance was measured by charpy impact test using a "sintco" type machine. tests were carried at 20°c using notched specimens according to the iso 1083-76 standard. three experimental tests were carried out for each sample. the calculated average of these three measures reflected the impact resistance. wear tests the sliding wear tests were carried out using a pin-on-disc method at room temperature according to the astm-g99 standard. the weight loss of material was determined after a passage of the specimen on a disk, on which a silicon carbide abrasive paper (800 grit) was fixed. it travels a total distance of 420 m at 80 rotations per minute. the test was performed using an applied normal load of 12 n. 6 mm diameter and 10 mm long specimens were used for the test. after an initial run of 6 min for each specimen, the weight was measured using a 0.1 mg precision scale. after wear test, each specimen was weighed to determine the weight loss. three experimental tests for each sample were carried out. the weight loss was represented by the calculated average of these three tests [31,32]. the variation of friction coefficient test was carried out on the prepared specimens, two wear tests were performed using a ball-on-disk apparatus under two loads (5 n and 10 n) at 0.5 m/s sliding speed and 100 m sliding distance. the ball specimen was made of steel (100cr6) with a diameter of 6 mm and hardness of 61 hrc. before the test, the samples were ground with abrasive paper (2400 grit), polished and cleaned with alcohol [33]. i cast irons c (%) si (%) mn (%) p (%) s (%) ni (%) mo (%) v (%) unalloyed 3.39 2.175 0.08 0.008 0.0018 0.007 0.00 0.06 alloyed 3.39 2.175 0.638 0.008 0.0018 0.507 0.20 0.16 m.i boulifa et alii, frattura ed integrità strutturale, 56 (2021) 74-83; doi: 10.3221/igf-esis.56.06 78 results and discussion microstructural analysis he metallographic study shows that the structure of the unalloyed cast iron (fig. 1) is formed by ferrite and pearlite where the ferrite surrounds graphite nodules. this structure has a ferrite rate more important than that the pearlite. the morphology of graphite nodules is wholly spherical. figure 1: microstructures of unalloyed cast iron in the cast condition. the alloyed cast iron (fig. 2) has a ferrite-pearlitic structure. compared to the unalloyed cast iron, the alloyed cast iron structure exhibits an increase in the quantity of pearlite. this is due to high rates of ni (0.5%) and mn (0.6%). the morphology of graphite nodules in the microstructure of the cast iron is entirely spherical, it is not influenced by carbideforming elements. the refining effect of alloying elements (mn and ni) is also observed compared to unalloyed cast condition. ni delays the coarsening of austenite grains and so refines the microstructure. concerning the graphite, the morphology of nodules in the microstructure of the cast iron always remains entirely spherical. figure 2: microstructures of alloyed cast iron in the cast condition. microhardness the results obtained show sufficiently the influence of alloying elements on cast irons produced in a positive manner, because of the change in structure on the one hand and increase the properties on the other hand (tab. 2). microhardness measurements of microstructural constituents of the unalloyed cast iron have given a ferrite of 132 hv (the standard deviation is 1.41 hv) and perlite of 214 hv (the standard deviation is 1.41 hv). for alloyed cast iron, the microhardness of the ferrite is 166 hv (the standard deviation is 1.41 hv) and 282 hv for pearlite were the standard deviation is 2.16 hv. an increase in the microhardness of various microstructural constituents is observed in alloyed cast iron, compared with unalloyed cast iron. this can be explained by a manganese content introduced (0.6%) and that of nickel (0.5%). t m.i boulifa et alii, frattura ed integrità strutturale, 56 (2021) 74-83; doi: 10.3221/igf-esis.56.06 79 hardness the hardness results obtained show the influence of alloying elements on cast irons elaborated in a positive manner because of the remarkable increase of this property after addition of the alloying elements. the results are presented in tab. 2. the hardness of the unalloyed cast iron is 95 hrb (the standard deviation is 1.41 hrb). after the addition of alloying elements in this cast iron, there is a remarkable increase in hardness (99 hrb with a standard deviation is 1.82 hrb). compared to the unalloyed cast iron, the hardness of alloyed cast iron is greater, this is due to the addition of mn, 0.6% and ni, 0.5%. the increase of the hardness is probably due to structural hardening following the dissolution of the alloying elements in the solid solutions or by the formation of precipitates. cast irons microhardness (hv) hardness (hrb) ferrite pearlite unalloyed 132 214 95 alloyed 166 282 99 table 2: microhardness and hardness results. tensile proprieties the results of the young's modulus, yield strength, tensile strength and elongation are shown in tab. 3. the young's modulus of unalloyed cast iron is 171 gpa with a standard deviation is 2.16 gpa and that of alloyed cast iron is 175 gpa with a standard deviation is 2.94 gpa. the yield strength of the unalloyed cast iron is 530 mpa were the standard deviation is 2.16 mpa. an increase (560 mpa with a standard deviation is 7.11 mpa) is observed for alloyed cast iron following the addition of ni (0.5%), mn (0.6%), mo (0.2%) and v (0.1%). the tensile strength of the unalloyed cast iron is 710 mpa (the standard deviation is 3.55 mpa). the growth of the resistance of alloyed cast iron to 750 mpa (the standard deviation is 7.25 mpa) is due to the addition of 0.6% mn and 0.5%ni. these two elements improve the hardenability of cast iron and therefore promote this increase. the results of elongation of the different cast iron experimented shows that this property of the unalloyed cast iron is higher (4.63% with a standard deviation is 0.17%). the elongation of alloyed cast iron (3.0% with a standard deviation is 0.71%) has decreased relative to the unalloyed cast iron. this shows that the elevation of the different elements favoured a structural hardening, which explains this clear regression in ductility. the increase in young's modulus, yield strength, tensile strength and the decrease in elongation observed in alloyed cast iron compared to unalloyed cast iron can be explained by the structural hardening. this is as in the case of hardness, following the dissolution of the alloying elements in the solid solutions or by the formation of precipitates. impact resistance the results of the impact resistance of ductile cast iron are illustrated in tab. 3. the unalloyed cast iron has an impact resistance of 6.12 j/cm2 (the standard deviation is 0.17 j/cm2). this characteristic achieved 8.5 j/cm2 (the standard deviation is 0.50 j/cm2) for alloyed cast iron is due to the addition of 0.2% mo and 0.1% v. these elements create precipitates that cause structural hardening. cast irons young’s modulus (gpa) yield strength (mpa) tensile strength (mpa) elongation (%) impact resistance (j/cm2) unalloyed 171 530 710 4.63 6.12 alloyed 175 560 750 3.0 8.5 table 3: tensile proprieties and impact resistance results. wear behavior: wear resistance the wear tests were conducted on both of cast irons. the weight loss results presented in tab. 4, show that the weight loss of the unalloyed sample is 0.043 g (the standard deviation is 0.004 g), while for the alloyed cast iron sample is 0.025 g (the m.i boulifa et alii, frattura ed integrità strutturale, 56 (2021) 74-83; doi: 10.3221/igf-esis.56.06 80 standard deviation is 0.003 g). this result is explained by an improvement of the wear resistance of the studied cast iron. alloying elements favours the formation of an enriched solid solution and different precipitates, which increase the hardness and the wear behavior of the cast iron under study. the wear mechanism occurs in this case is based on three factors. the first one is the applied load. increasing of the latter leads to an acceleration of the sliding wear of the iron. the second factor is related to the microstructure and the properties of the cast iron. the presence of ferrite in the matrix, ductile phase decrease the hardness of the cast iron and increases its wear rate. the last factor is the graphite, this phase is known for its less resistance to elastic strain caused by wear stresses [31,32]. wear behavior: friction coefficient the friction coefficient presented in tab. 4 of the unalloyed cast iron is 0.388 (standard deviation is 0.067) for 5 n and 0.426 (standard deviation is 0.093) for 10 n. while for the alloyed cast iron is 0.303 (standard deviation is 0.097) for 5 n and 0.324 (standard deviation is 0.099) for 10 n. it is noticed that the friction coefficient increases with the applied load for the two cast irons (unalloyed and alloyed). the coefficient of friction of alloyed cast iron is lower than that of unalloyed cast iron for both loads 5 n and 10 n. also, the alloyed cast iron is more resistant to friction compared to unalloyed cast iron for both forces. this decrease is explained by the refinement of the structure, caused by the addition of alloying elements in the alloyed cast iron compared to the unalloyed cast iron. a fine structure favours a high resistance to friction, which reduces the friction coefficient. the ferrite, which surrounds the graphite in the alloyed cast iron is finer than that formed in the unalloyed cast iron coarser. the graphs of the unalloyed cast iron (fig. 3) are more fluctuated for the two applied loads (5 and 10 n). this is due to the heterogeneity of the microstructure of this metal. the formation of a coarse perlite phase distributed heterogeneously in the structure, leads to more of fluctuations. on the other hand, the friction coefficient of the alloyed cast iron (fig. 4) presents less fluctuations compared to the unalloyed cast iron, this is explained by the enrichment of the perlite with manganese, nickel, molybdenum and vanadium, which hardened it. cast irons weight loss (g) friction coefficient 5 n 10 n unalloyed 0.043 0.388 0.426 alloyed 0.025 0.303 0.324 table 4: weight loss and friction coefficient results. figure 3: friction coefficient of unalloyed cast iron; a: 5 n, b: 10 n. m.i boulifa et alii, frattura ed integrità strutturale, 56 (2021) 74-83; doi: 10.3221/igf-esis.56.06 81 figure 4: friction coefficient of alloyed cast iron; a: 5 n, b: 10 n. conclusion uctile cast iron alloyed to manganese (0.6%), nickel (0.5%), molybdenum (0.2%) and vanadium (0.1%)) was produced aiming to replace the unalloyed ductile iron. the effect of alloying elements on the mechanical characteristics and wear behavior (wear resistance and friction coefficient) was studied. according to this study, it can be concluded that: 1. the optical microscope observation shows that the samples have structures formed of ferrite and pearlite. the alloyed cast iron structure shows an improvement in the amount of pearlite relative to the unalloyed cast iron. 2. the results of mechanical tests and wear behavior show in the whole that the cast irons studied achieve higher properties. hardness and microhardness are increased in a remarkable way for alloyed cast iron, compared to the unalloyed cast iron. 3. the sample of the alloyed cast iron has reached a higher tensile strength than that of the unalloyed cast iron with an important ductility. the same ascertainment can be made for the impact resistance. 4. for the wear tests, it is noted that the weight loss and the friction coefficient decrease with the addition of the alloying elements compared to the unalloyed cast iron. it thus influenced in a positive way by the addition of these elements. 5. alloyed ductile cast iron formed by ferrite-pearlitic structures. there are therefore several advantages to using this cast iron in many fields of engineering. acknowledgement uthors gratefully acknowledge agricultural tractor society (etrag constantine) for permitting to conduct the melting and casting. in addition, we thanks pr. touhami med zine, pr. mechachti said, dr. maouche hichem, and dr. ayadi souad (metallurgy and materials engineering department, university of annaba) for their assistance in characterization of specimens. references [1] xiang ru, c., qi jie, z., han, d., bao hua, d. and hardy m. (2020). molybdenum alloying in cast iron and steel, adv. manuf., 8, pp. 3–14. doi: 10.1007/s40436-019-00282-1. d a m.i boulifa et alii, frattura ed integrità strutturale, 56 (2021) 74-83; doi: 10.3221/igf-esis.56.06 82 [2] bok gyu l., kyong ho s., and ryong chol k. (2018). effect of sb–ba–ce–si–fe post inoculants on microstructural and mechanical properties of as-cast pearlitic ductile iron, steel research int., 90(5), pp. 1-6. doi: 10.1002/srin.201800530. [3] mohd nadeem, b., afzal khana, d.m. and singh, k.k. (2018). effect of inoculation and nodularisation treatment temperature on recalescence and eutectic undercooling temperature in spheroidal graphite (sg) cast iron, international journal of cast metals research, 31(5), pp. 261-268. doi: 10.1080/13640461.2018.1434987. [4] rodolfo, g.m., urko de la, t., andré, e., jacques, l. and jon, s. (2018). effects of high silicon contents on graphite morphology and room temperature mechanical properties of as-cast ferritic ductile cast irons. part ii–mechanical properties, materials science & engineering a 712, pp. 803-811. doi: 10.1016/j.msea.2017.11.051. [5] moritz, r., hergen groß, s., bjo¨rn, p., and andreas, b.p. (2018). influence of carbide-promoting elements on the pearlite content and the tensile properties of high silicon ssdi ductile iron, inter metalcast, 12, pp. 106-112. doi: 10.1007/s40962-017-0146-7. [6] costanzo, b., vittorio di, c., gregory, f., francesco, i. and luca, s. (2019). ductile cast irons: microstructure influence on the fatigue initiation mechanisms, fatigue and fracture of engineering materials structure, 42(9), pp. 1-11. doi: 10.1111/ffe.13100. [7] jacques, l. (2017). trace elements and graphite shape degeneracy in nodular graphite cast irons, inter metalcast, 11(1), pp. 44-51. doi: 10.1007/s40962-016-0115-6. [8] gorka, a., doru, m. s., esther de la, f., pello, l. and ramon, s. (2018). the influence of trace elements on the nature of the nuclei of the graphite in ductile iron, materials science forum, 925, pp. 78-85. doi:10.4028/www.scientific.net/msf.925.78. [9] wolfram, b. (2020). chunky graphite in ferritic spheroidal graphite cast iron: formation, prevention, characterization, impact on properties: an overview, inter metalcast, 14, pp. 454-488. doi: 10.1007/s40962-019-00363-8. [10] jose florentino, a. a. and juan, a.l. (2017). optimization of the mechanical behaviour under tensile stress of spheroidal cast iron with ferritic matrix used in the manufacture of wind turbine hubs, inter metalcast, 11, pp. 513522. doi: 10.1007/s40962-016-0100-0. [11] wolfram, s., herbert, l., gert, g. and peter, s. (2014). solution strengthened ferritic ductile cast iron properties, production and application, inter metalcast, 8(2), pp.35-40. doi: 10.1007/bf03355580. [12] murcia, s.c., paniagua, m.a. and ossa, e.a. (2013). development of as-cast dual matrix structure (dms) ductile iron, materials science & engineering a 566, pp. 8-15. doi: 10.1016/j.msea.2012.12.033. [13] laura, n.g., alfredo, j.t., fernando, d.c. and roberto, e.b. (2019). identification of cu-rich precipitates in pearlitic spheroidal graphite cast irons, materials science and technology, 35(18) pp. 2252-2258. doi: 10.1080/02670836.2019.1668999. [14] kalle, j., jarkko, l., joona, v., tero, f. and juhani, o. (2020). investigation on dynamic strain aging behaviour of ferritic-pearlitic ductile cast irons, materials science and technology, 36(2), pp. 160-167. doi: 10.1080/02670836.2019.1685760. [15] hartung, c., eivind, hoel, g., emmanuelle, o., logan, r., andy, p. and david, w. (2020). research on solution strengthened ferritic ductile iron (ssfdi) structure and properties using different treatment and inoculation materials, inter metalcast, 14, pp. 1195–1209. doi: 10.1007/s40962-020-00469-4. [16] jarkko, l., vaara, j., jalava, k., soivio, k. and orkas, j. (2020).the mechanical properties of ductile iron at intermediate temperatures: the effect of silicon content and pearlite fraction, inter metalcast, doi: 10.1007/s40962-020-00473-8. [17] regordosa, a., de la torre, u., loizaga, a., sertucha, j. and lacaze, j. (2020) microstructure changes during solidification of cast irons: effect of chemical composition and inoculation on competitive spheroidal and compacted graphite growth, inter metalcast, 14, pp. 681-688. doi: 10.1007/s40962-019-00389-y. [18] mok, c.m. (2008). effect of steel alloying elements, in: effects of alloying elements on iron carbon alloy, usa, ndt solution, pp. 58-93. [19] bakhshinezhad, h., honarbakhshraouf, a., and abdollah-pour, h. (2019). a study of effect of vanadium on microstructure and mechanical properties of as-cast and austempered ductile iron, physics of metals and metallography, 120(5), pp. 441-446. doi: 10.1134/s0031918x19050016. [20] abdul, r., jian-xin, z., talib, h., zhi-xin, t., ya-jun, y., xiao-yuan, j., gen, x., and xu, s. (2019). effect of alloying elements w, ti, sn on microstructure and mechanical properties of gray iron 220, research & development, 16(6), pp. 393-398. doi: 10.1007/s41230-019-9035-4. [21] branko, b., ivana mihalic, p., mitja, p. and primož, m. (2018). effect of si and ni addition on graphite morphology in heavy-section spheroidal graphite iron parts, materials science forum, 925, pp. 70-77. doi: 10.4028/www.scientific.net/msf.925.70. m.i boulifa et alii, frattura ed integrità strutturale, 56 (2021) 74-83; doi: 10.3221/igf-esis.56.06 83 [22] barnabas, a.a., oyetunji, a. and seidu, s.o. (2019). microstructural characterization of antimony modified carbidic austempered ductile iron, journal of materials science research, 8(2) pp.36-48. doi:10.5539/jmsr.v8n2p36. [23] nikša, č., dražen, ž. and zvonimir, d. (2018). the effects of molybdenum and manganese on the mechanical properties of austempered ductile iron, tehnički vjesnik (technical gazette), 25(2), pp. 635-642. doi: 10.17559/tv20170124120729. [24] sining, p., fanzheng, z., nanguang, s. and zhaokun, x. (2020). the effect of niobium addition on the microstructure and properties of cast iron used in cylinder head, j mater res technol., 9(2) pp. 1137-2610. doi: 10.1016/j.jmrt.2019.11.076. [25] ahmet, a. (2019). an experimental study on comparison of wear properties of cast irons with compacted graphite and spheroidal graphite, trans indian inst met, 72, pp. 2257-2262. doi: 10.1007/s12666-019-01673-5. [26] laguna-camacho, j.r., juárez-morales, g., calderón-ramón, c., velázquez-martínez, v., hernández-romero, i., méndez-méndez, j.v. and vite-torres, m. (2015). a study of the wear mechanisms of disk and shoe brake pads, engineering failure analysis, 56, pp. 348-359. doi: 10.1016/j.engfailanal.2015.01.004. [27] lyu, y. (2019). abrasive wear of compacted graphite cast iron with added tin. metallogr. microstruct. anal. 8, pp. 67-71. doi: 10.1007/s13632-018-0504-8. [28] kim, k., yoon, m. j. (2015). characterisation of friction behaviour of flake, spheroidal, and compacted vermicular graphite cast irons, int j surf sci eng, 9(1), pp.1-12. doi: 10.1504/ijsurfse.2015.067035. [29] bedolla-jacuinde, a., guerra, f.v., rainforth, m., mejía, i. and maldonado, c. (2015). sliding wear behavior of austempered ductile iron microalloyed with boron, wear, 330-331, pp. 23-31. doi: 10.1016/j.wear.2015.01.004. [30] romany, r.m., amer, e. a., ragab k. a., mohamed n. e. (2019). an investigation into mechanical properties of ductile cast iron with different heat treatment processes, periodica polytechnica mechanical engineering, 63(3), pp. 183–187. doi: 10.3311/ppme.13672. [31] boulifa, m i. and hadji, a. (2015). effect of alloying elements on the structure and mechanical properties of austempered ductile irons, metall. res. technol. 112(4), 404 pp.1-9. doi: 10.1051/metal/2015022. [32] boulifa, m.i. and hadji, a. (2015). effect of alloying elements on the mechanical behavior and wear of austempered ductile iron, mechanics & industry 16(3), 304 pp. 1-6. doi: 10.1051/meca/2015002. [33] ayadi, s. and hadji, a. (2019). effect of heat treatments on the microstructure and wear resistance of a modified hadfield steel. metallofiz. noveishie tekhnol 41(5), pp. 607-620 doi: 10.15407/mfint.41.05.0607. microsoft word numero_41_art_10.doc a. carpinteri et alii, frattura ed integrità strutturale, 41 (2017) 66-70; doi: 10.3221/igf-esis.41.10 66 focused on multiaxial fatigue joined application of a multiaxial critical plane criterion and a strain energy density criterion in low-cycle fatigue andrea carpinteri, giovanni fortese, camilla ronchei, daniela scorza, sabrina vantadori department of engineering and architecture, university of parma parma, italy filippo berto department of engineering design and materials, ntnu trondheim, norway abstract. in the present paper, the multiaxial fatigue life assessment of notched structural components is performed by employing a strain-based multiaxial fatigue criterion. such a criterion, depending on the critical plane concept, is extended by implementing the control volume concept reated to the strain energy density (sed) approach: a material point located at a certain distance from the notch tip is assumed to be the verification point where to perform the above assessment. such a distance, measured along the notch bisector, is a function of both the biaxiality ratio (defined as the ratio between the applied shear stress amplitude and the normal stress amplitude) and the control volume radii under mode i and mode iii. once the position of the verification point is determined, the fatigue lifetime is assessed through an equivalent strain amplitude, acting on the critical plane, together with a unique material reference curve (i.e. the manson-coffin curve). some uniaxial and multiaxial fatigue data related to v-notched round bars made of titanium grade 5 alloy (ti-6al-4v) are examined to validate the present criterion. keywords. critical plane approach; control volume; notched components; multiaxial low-cycle fatigue; strain-based criterion. citation: carpinteri, a., berto, f., fortese, g., ronchei, c., scorza, d., vantadori, s., joined application of a multiaxial critical plane criterion and a strain energy density criterion in low-cycle fatigue, frattura ed integrità strutturale, 41 (2017) 66-70. received: 28.02.2017 accepted: 15.04.2017 published: 01.07.2017 copyright: © 2017 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. introduction n situation of practical interest, metallic structural components often contain geometrical irregularities (such as notches, fillets and key-seats) because of the design requirements. the above irregularities result in stress/strain concentration phenomena which have to be properly take into account during the design process in order to avoid catastrophic in-service failures [1]. the presence of stress/strain concentrators gives rise to a multiaxial stress/strain state close to the geometrical irregularities even if the applied loading is uniaxial. moreover, the complexity of the stress/strain state is further increased by the presence of multiaxial fatigue loadings as those experienced by structural components during in-service operation. i a. carpinteri et alii, frattura ed integrità strutturale, 41 (2017) 66-70; doi: 10.3221/igf-esis.41.10 67 since the pioneering work by neuber [2], a big effort has been made by the scientific community in order to devise suitable criteria for accurately assessing the fatigue strength/life of structures weakened by either blunt or sharp notches, subjected to complex time-varying loading. nowadays, a universally accepted criterion does not exist yet, and hence the multiaxial fatigue analysis of notched components is a research topic still open. reviews of the most promising fatigue criteria for fatigue assessment of notched metallic components can be found in refs [3,4]. several multiaxial fatigue criteria available in the literature represent a reformulation of their counterparts for smooth components, by considering the detrimental effect of the stress/strain concentration phenomena on the material fatigue strength. such criteria usually reduce the complex multiaxial stress/strain state to an equivalent uniaxial condition: they are stress-based in high-cycle fatigue (hcf), whereas they are strain-based in low-cycle fatigue (lcf). according to the above remarks, the present authors have recently proposed a strain-based multiaxial fatigue criterion in order to estimate the fatigue life of severely notched specimens under lcf [5]. such a criterion is an extension of the critical plane-based multiaxial fatigue criterion proposed by carpinteri et al. for smooth specimens [6,7] to the case of notched ones. the above extension is formulated by implementing the concept of the control volume, related to the strain energy density (sed) criterion proposed by lazzarin et al. [8,9]. more precisely, the fatigue life assessment is performed by taking into account the strain state at a material point (named verification point) located at a certain distance from the notch tip, depending such a distance on both the biaxiality ratio  (remote shear stress amplitude over remote normal stress amplitude) and the control volume radii under loading conditions of mode i and mode iii. the goal of the present paper is to discuss the accuracy and reliability of the joined application of the strain-based criterion together with the control volume concept [5] in estimating multiaxial fatigue lifetime of structural components weakened by notches. in particular, the results obtained by employing the criterion proposed in ref. [5] are compared with some experimental data recently published [10], related to circumferentially v-notched round bars made of titanium grade 5 alloy (ti-6al-4v) under both uniaxial and multiaxial fatigue loadings. criterion formulation for notched components n order to check the accuracy of the strain-based multiaxial fatigue criterion together with the control volume concept (related to the sed criterion) in estimating fatigue life of notched components, we briefly outline the analytical basis of such a criterion (details may be found in ref. [5]). the fatigue life assessment is carried out at a verification point (point p ), which is distant r from the notch tip. such a distance r , measured along the notch bisector line, is a function of both the biaxiality ratio  and the control volume radii provided by the sed criterion [8,9]:     1.484 0.221 11.3m mr r r (1) where mr is the mean control volume radius, computed by averaging the control volume radius related to mode i, 1r , and that related to mode iii, 3r . according to the sed criterion, such radii depend on the mean values of mode i and mode iii notch stress intensity factors (nsifs) ranges, and on mode i and mode iii hcf strengths of both smooth specimens and the notch geometry. once the position of the verification point p is determined according to eq. (1), the strain tensor at such a point is obtained from a finite element analysis by examining a tridimensional model. after the strain state at point p is deduced, the averaged directions of the principal strain axes can be determined on the basis of their instantaneous directions by means of the averaged values of the principal euler angles. the orientation of the critical plane is linked to the above averaged directions through the off-angle  :                    2 3 1 1 45 2 2 1 a a eff (2) where eff is the effective poisson ratio, and a and  a are defined by the well-known tensile and torsional mansoncoffin equations, respectively. i a. carpinteri et alii, frattura ed integrità strutturale, 41 (2017) 66-70; doi: 10.3221/igf-esis.41.10 68 then, the fatigue strength is assessed by means of an equivalent strain amplitude together with a unique material reference curve (i.e. the tensile manson-coffin curve). more precisely, the above equivalent strain amplitude is expressed by a combination of the amplitudes of both the normal,  , n a , and tangential,  , c a , displacement vectors acting on the critical plane:                2 2 2 , , , a eq a n a c a a (3) by equating eq. (3) with the tensile manson-coffin equation, the number fn of loading cycles to failure can be worked out through an iterative procedure. fatigue experimental campaign he strain-based multiaxial fatigue criterion formulated in conjunction with the control volume concept is here applied to a set of data recently published [10]. in particular, uniaxial and multiaxial fatigue tests have been carried out on circumferentially v-notched round bars made of ti-6al-4v titanium alloy. each specimen presented a v-notch depth equal to 6 mm, an opening angle equal to 90 and a notch root radius equal to about 0.1 mm. the experimental fatigue tests have been performed by means of an mts 809 servo-hydraulic biaxial machine. all tests have been conducted under load control at a frequency from 5 to 10 hz, depending on the applied load. details of the loading conditions being examined are reported in ref. [10]. according to the notch geometry and the material properties (that is, the values of nsifs ranges and hcf strengths), the control volume radius 1r is equal to 0.051 mm, whereas the control volume radius 3r is equal to 0.837 mm. the above difference in the values of control volume radii is not only due to the different behaviour in the crack propagation under tension or torsion loading, but also to the higher plasticity around the notch tip experienced under torsion loading with respect to tension loading. criterion validation ll experimental data being examined (see the previous section) are characterised by fatigue life between 310 and  56 10 loading cycles and nominal load ratio equal to 1 . in particular, we consider six different fatigue test series on v-notched specimens: (1) one series of tests under pure tension fatigue loading and one series under pure torsion fatigue loading; (2) two series of tests under combined in(   0 ) and out-of-phase (   90 ) tension and torsion loading, with a constant biaxiality ratio,  , equal to 0.6 ; (3) two series of tests under combined in(   0 ) and out-of-phase (   90 ) tension and torsion loading, with a constant biaxiality ratio,  , equal to 2.0 . different values of the distance r to determine the verification point position are computed according to eq. (1): (a) for pure tension loading, i.e.   0 , r is equal to 1.9 mr ; (b) for pure torsion loading, i.e.    , r is equal to 11.3 mr ; (c) for combined inand out-of-phase tension and torsion loading characterised by   0.6 , r is equal to 7.5 mr ; (d) for combined inand out-of-phase tension and torsion loading characterised by   2.0 , r is equal to 10.8 mr . note that eq. (1) has been obtained through a best-fit procedure by taking into account some values of  related to the experimental data reported in refs [5,10]. the values of the material parameters related to the manson-coffin curves, required for the application of the criterion, are reported in ref. [11]. the effective poisson ratio, eff , is assumed to be equal to the elastic poisson ratio (that is,   0.3 ). t a a. carpinteri et alii, frattura ed integrità strutturale, 41 (2017) 66-70; doi: 10.3221/igf-esis.41.10 69 the comparison between experimental, , expfn , and theoretical, ,f caln , fatigue life for both uniaxial and multiaxial loadings is shown in figs 1(a) and 1(b), respectively, where the solid line indicates , , expf cal fn n , the dashed lines correspond to , , expf cal fn n equal to 0.5 and 2.0 (scatter band 2), and the dash-dot lines correspond to , , expf cal fn n equal to 0.3 and 3.0 (scatter band 3). in particular, the following remarks can be made: for uniaxial fatigue loading (that is, pure tension or pure torsion loading, fig. 1(a)), 71% of fatigue life calculation results are included into the scatter band 3 ; for multiaxial fatigue loading (that is, combined tension and torsion loading with different values of biaxiality ratio, fig. 1(b)), 76% of fatigue life calculation results are included into scatter band 3 . moreover, better estimations are obtained by examining multiaxial fatigue data characterised by   0.6 , since all the theoretical fatigue lives fall within the scatter band 3. n f, ex p [c yc le s] nf,cal [cycles] 103102 104 106 102 104 105 106 uniaxial loadings  0.0  105 103 (a) nf,cal [cycles] 103102 104 106 02 03 04 05 06 multiaxial loadings   0.6 0° 2.0 90° 105 (b) figure 1: comparison between theoretical and experimental fatigue life: (a) uniaxial loadings; (b) multiaxial loadings. figures 2(a) and 2(b) show the experimental fatigue life, , expfn , plotted against the equivalent strain amplitude  ,eq a (see eq. (3)) for uniaxial and multiaxial fatigue loading, respectively. the solid curves are related to the experimental tensile manson-coffin equation. a good agreement is in general observed since the experimental results lie very close to the theoretical curves, and this holds true independent of the applied loading conditions (i.e. for both uniaxial and multiaxial fatigue tests).  a ,e q 2*nf,exp , [cycles] 10-1 10-2 10-3 10-4 103 104 105 106 uniaxial loadings  0.0  (a) 2*nf,exp , [cycles] -1 -2 -3 -4 103 104 105 106 multiaxial loadings   0.6 0° 2.0 90° (b) figure 2: fatigue life experimental data plotted in terms of the equivalent normal strain amplitude (eq. (3)): (a) uniaxial loadings; (b) multiaxial loadings. the solid lines refer to the tensile manson-coffin equation. a. carpinteri et alii, frattura ed integrità strutturale, 41 (2017) 66-70; doi: 10.3221/igf-esis.41.10 70 conclusions n the present paper, the multiaxial fatigue life assessment of notched structural components has been performed by employing a strain-based multiaxial fatigue criterion in conjunction with the concept of control volume, related to the sed approach proposed by lazzarin and co-workers. in particular, the above assessment is carried out at a verification point, which is located at a certain distance from the notch tip, depending such a distance on both the biaxiality ratio and the control volume radii under mode i and mode iii. some uniaxial and multiaxial fatigue data, recently published in the literature, have been analysed to evaluate the effectiveness of the present criterion. the agreement between experimental and theoretical fatigue lives is quite satisfactory. in conclusion, the present criterion appears to be a promising tool to estimate fatigue lifetime of notched structures, although further investigations are needed by performing experimental tests characterised by fatigue ratio values different from 1 and different notch geometries. references [1] susmel, l., taylor, d., a novel formulation of the theory of critical distances to estimate lifetime of notched components in the medium-cycle fatigue regime, fatigue fract. engng. mater. struct., 30 (2007) 567-581. doi: 10.1111/j.1460-2695.2007.01122.x. [2] neuber, h., theory of notch stresses: principles for exact calculation of strength with reference to structural form and material, second ed., springer verlag, berlin, (1958). [3] nieslony, a., sonsino, c.m., comparison of some selected multiaxial fatigue assessment criteria, l.b.f. report, no. fb-234 (2008). [4] fatemi, a., shamsaei, n., multiaxial fatigue: an overview and some approximation models for life estimation, int. j. fatigue, 33 (2011) 948–958. doi: 10.1016/j.ijfatigue.2011.01.003. [5] carpinteri, a., berto, f., campagnolo, a., fortese, g., ronchei, c., scorza, d., vantadori, s., fatigue assessment of notched specimens by means of a critical plane-based criterion and energy concepts, theor. appl. fract. mech., 84 (2016) 57-63. doi: 10.1016/j.tafmec.2016.03.003. [6] carpinteri, a., ronchei, c., spagnoli, a., vantadori, s., lifetime estimation in the low/medium-cycle regime using the carpinteri–spagnoli multiaxial fatigue criterion, theor. appl. fract. mech., 73 (2014) 120–127. doi: 10.1016/j.tafmec.2014.06.002. [7] carpinteri, a., ronchei, c., scorza, d., vantadori, s., fatigue life estimation for multiaxial low-cycle fatigue regime: the influence of the effective poisson ratio value, theor. appl. fract. mech., 79 (2015) 77–83. doi: 10.1016/j.tafmec.2015.06.013. [8] berto, f., lazzarin, p., yates, j.r., multiaxial fatigue of v-notched steel specimens: a non-conventional application of the local energy method, fatigue fract. eng. mater. struct., 34 (2011) 921–943. doi: 10.1111/j.14602695.2011.01585.x. [9] berto, f., lazzarin, p., tovo, r., multiaxial fatigue strength of severely notched cast iron specimens, int. j. fatigue, 67 (2014) 15–27. doi: 10.1016/j.ijfatigue.2014.01.013. [10] berto, f., campagnolo, a., welo, t., local strain energy density to assess the multiaxial fatigue strength of titanium alloys, frattura ed integrità strutturale, 10 (2016) 69-79. doi: 10.3221/igf-esis.37.10. [11] basan, r., franulovic, m., prebil, i., crnjaric-žic, n., analysis of strain-life fatigue parameters and behaviour of different groups of metallic materials, int. j. fatigue, 33 (2011) 484–491. doi: 10.1016/j.ijfatigue.2010.10.005. i << /ascii85encodepages false /allowtransparency false /autopositionepsfiles true /autorotatepages /none /binding /left /calgrayprofile (dot gain 20%) /calrgbprofile (srgb iec61966-2.1) /calcmykprofile (u.s. web coated \050swop\051 v2) /srgbprofile (srgb iec61966-2.1) /cannotembedfontpolicy /error /compatibilitylevel 1.4 /compressobjects /tags /compresspages true /convertimagestoindexed true /passthroughjpegimages true /createjobticket false /defaultrenderingintent /default /detectblends true /detectcurves 0.0000 /colorconversionstrategy /cmyk /dothumbnails false /embedallfonts true /embedopentype false /parseiccprofilesincomments true /embedjoboptions true /dscreportinglevel 0 /emitdscwarnings false /endpage -1 /imagememory 1048576 /lockdistillerparams 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can be opened with acrobat and adobe reader 5.0 and later.) >> /namespace [ (adobe) (common) (1.0) ] /othernamespaces [ << /asreaderspreads false /cropimagestoframes true /errorcontrol /warnandcontinue /flattenerignorespreadoverrides false /includeguidesgrids false /includenonprinting false /includeslug false /namespace [ (adobe) (indesign) (4.0) ] /omitplacedbitmaps false /omitplacedeps false /omitplacedpdf false /simulateoverprint /legacy >> << /addbleedmarks false /addcolorbars false /addcropmarks false /addpageinfo false /addregmarks false /convertcolors /converttocmyk /destinationprofilename () /destinationprofileselector /documentcmyk /downsample16bitimages true /flattenerpreset << /presetselector /mediumresolution >> /formelements false /generatestructure false /includebookmarks false /includehyperlinks false /includeinteractive false /includelayers false /includeprofiles false /multimediahandling /useobjectsettings /namespace [ (adobe) (creativesuite) (2.0) ] /pdfxoutputintentprofileselector /documentcmyk /preserveediting true /untaggedcmykhandling /leaveuntagged /untaggedrgbhandling /usedocumentprofile /usedocumentbleed false >> ] >> setdistillerparams << /hwresolution [2400 2400] /pagesize [612.000 792.000] >> setpagedevice microsoft word numero_43_art_6 p. zampieri et alii, frattura ed integrità strutturale, 43 (2018) 90-96; doi: 10.3221/igf-esis.43.06 90 fatigue strength of corroded bolted connection paolo zampieri, andrea curtarello, carlo pellegrino department of civil, environmental and architectural engineering, university of padova, via marzolo, 9 35131 padova, italy paolo.zampieri@dicea.unipd.it, http://orcid.org/0000-0002-4556-5043 emanuele maiorana omba impianti & engineering spa, via della croce 10, 36040 torri di quartesolo (vi), italy abstract. this note summarizes some recent investigation results on the behavior of corroded steel bolted joints under uniaxial fatigue loading. fatigue test specimens, were made up using s355 structural steel plates joined together with preloaded m12 bolts of class 10.9 with a geometry that corresponds to the δσ = 112 mpa ec3 detail category. the accelerated corrosion process was accomplished using an electrolyte consisting of an aqueous 5% nacl solution whereby the specimens were treated. in particular, during the corrosion process specimens were repeatedly immersed for 2 minutes in the electrolyte and then removed keeping them 60 minutes long in free air at 35 °c. an atmospheric corrosion in marine-industrial environment is wellrepresented through corrosion test. fatigue loading tests and surface morphology measurement of uncorroded and corroded specimens were performed and the results were compared. keywords. fatigue strength; corrosion; bolted connections; steel bridge. citation: zampieri, p., curtarello, a., pellegrino, c., maiorana, e., fatigue strenght of corroded bolted connection, frattura ed integrità strutturale, 43 (2018) 90-96. received: 08.08.2017 accepted: 30.10.2017 published: 01.01.2018 copyright: © 2018 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. introduction n civil engineering, the structures most affected by mechanical fatigue are steel railway bridges that are subjected to a large number of traffic load cycles during their service life. in this type of structures, the most critical elements from the point of view of fatigue strength are the connections between the members; the irregularity of the connections geometry is one of the factors that affect the fatigue life of these structural elements. the fatigue life assessment of structural details is widely studied in the recent years [1, 2]. another important factor of great influence on the fatigue strength of bridge structure is the material degradation [3-5]. in particular, corrosion phenomenon is perhaps one of the problems that most affects the integrity of metal structures in all countries. in this context, understanding the corrosion effects on the fatigue life of steel structures is becoming a topic on which research is investing. many studies were conducted on the corrosion and fatigue phenomena, however there are few publications regarding their interaction in steel bridges. researches are carried out in fields different than the civil sector, e.g. structures working in the i p. zampieri et alii, frattura ed integrità strutturale, 43 (2018) 90-96; doi: 10.3221/igf-esis.43.06 91 seawater like offshore structures and pipelines [6]. typically to study the interaction of corrosion and fatigue, it is used a model of pre-corroded samples and then the cyclic loads are applied to them. there are few cases where electrochemical and mechanical stresses act at the same time. fatigue crack initiation and growth from artificial pits was modelled by rokhlin et al. [7]. the authors find good agreement with the experimental data: they described fatigue crack initiation and growth from pits and obtained the relationship between reduction of fatigue life and artificial pits size. other studies focused the attention on the pits shape characterization [8, 9]. shan-hua xu et al. [10] estimated the effects of corrosion pits on the fatigue life of steel plates. they defined three different pit shapes and concluded that corrosion causes a significant decrease in fatigue life as the pit depth increases and the surface roughness is a crucial factor to assess the fatigue strength. they also found that the start of the crack could trigger from a single pit or by the interaction and coalescence of multiple pits. similar studies were conducted also by acuna et al. [11] and by kondo et al. [12]. some researches were proposed as regards the fatigue corrosion interactions in steel bridges. the proposed approaches for corrosion fatigue life assessment are based on the use of s-n curves and cumulative damage laws. sharifi et al. [13] studied the notch factor in steel bridges due to corrosion and proposed two functions which could represent fatigue notch factor in terms of average corrosion penetration and time of weathering exposure to compare it with the one obtained for various classes of structural detail as classified in bs 5400. they concluded that the fatigue notch factor could well quantified the effect of corrosion on the fatigue life of steel bridge members. aim of this paper is to investigate the influence of the corrosive phenomenon on the fatigue strength of a friction type joint made of high strength preloaded bolts (m12 class 10.9). to work out these analyses the fatigue behavior of virgin bolted joints (without any degradation effect) and the behavior of the same joints, (having the same geometric and material properties) after corrosion effects were compared. to make so, an accelerated corrosion process was carried out on a lot of n. 10 specimens. at the end of the procedure, it was possible to perform fatigue tests (r=0) to plot the s-n fatigue curve of uncorroded and corroded specimens. figure 1: geometry of the bolted joints. p. zampieri et alii, frattura ed integrità strutturale, 43 (2018) 90-96; doi: 10.3221/igf-esis.43.06 92 accelerated corrosion process material and geometric properties of the specimens he structural detail under investigation is a slip resistant bolted joint made with high strength preloaded bolts (with geometry carried out from berto et al 2016) [3-4]. in particular, two plates of 10mm thickness, 40mm width and 229.5mm length are longitudinally joined by means of two cover plates and n.6 m12 class 10.9 bolts tightened with a torque of 91nm (fig. 1). the plates are made of s355 structural steel with drilled holes. all the plates were treated with a sa3+ sandblasting process that guarantees a white metal cleaning and consequently a quite uniform friction coefficient equal to 0.5. in regard the friction, between the bolt shank, the nut and the bolt washers, the manufacturer’s technical data sheet was considered, which provides a friction coefficient value equal to 0.128. (a) (b) figure 2: equipment used for the corrosion process: (a) phase of samples immersion; (b) phase of samples exposure on air. accelerated corrosion treatment the accelerated corrosion process was applied on n. 10 specimens. the procedure was set up by referring to iso 11130 norm. the process consists in submitting samples to a sequence of immersion and drying cycles, without interruption for the duration of 672h (corresponding to 4 weeks). every cycle is made up of two minutes long immersion step in a distilled water solution with 5% nacl followed by a sixty minutes long drying step made with dry air at a temperature of about 35°c. the equipment used to carry out the corrosion cycles consists of the following parts:  two tanks for the specimens immersion named v1 and v2: samples are completely immersed in saline solution in v1 tank; v2 tank allows to empty the v1 volume and to let samples on air at the controlled temperature of 35°c for the drying phase;  two immersion pumps named p1 and p2: p1 pump, located inside v1 tank, allows to empty the tank to expose specimens to the air during the drying phase; the p2 pump, located inside the v2 tank, allows to move the solution from v2 to v1 and to immerse the specimens;  two electromagnetic sensors called s1 and s2: both inside v1 tank. the s1 sensor is positioned at a higher level than that of the samples; it has the function of detecting the maximum level of the solution in the v1 tank and therefore sending the pumping interruption signal to p2 pump (which was transferring the solution from v2 to v1 tank). the s2 sensor, positioned at a lower level than that of the samples, sends to p1 pump the pumping signal (it allows to transfer the solution from v1 to v2 tank).  an electric panel to power to the pumps and sensors, and a simple control system (made by a couple of timers) having the function of managing the tanks filling and emptying steps;  a third tank v3 placed above the v1 and used as an hermetic closure; an heating device positioned on the top of the v3 tank has the purpose to keep the air temperature at a constant value of 35°c. the outline of the equipment is shown in fig. 2. prior to initiating the accelerated corrosion process, samples were weighed with an electronic scale to be able to estimate the mass drop caused by the oxidative phenomenon. every 168 hours of t p. zampieri et alii, frattura ed integrità strutturale, 43 (2018) 90-96; doi: 10.3221/igf-esis.43.06 93 treatment mass drop measurements were conducted taking off the specimens from the tank and performing the following steps:  cleaning of the tanks and replacing the solution with a new one; this operation was carried out to ensure that the corrosive liquid was as untouched as possible by external agents and to restore the quantities of water and nacl lost due to evaporation;  samples surface cleaning;  samples weighing to measure mass losses. (a) (b) figure 3: a) corroded specimens (672h); b) mean mass losses interpolation of the corroded specimens (g/cm2). in fig. 3, the curve resulting from the interpolation of the mean mass losses (g/cm2) measured every 168 hours is reported. as can be seen from the chart, the maximum mass loss at the end of the corrosion process is approximately equal to 0.06g/cm2. (a) (b) figure 4: a) fatigue test setup with mts810; b) failure section of the specimen n. 2 set b. 0 0.01 0.02 0.03 0.04 0.05 0.06 0 168 336 504 672 m as s lo ss [ g/ cm 2 ] time [h] p. zampieri et alii, frattura ed integrità strutturale, 43 (2018) 90-96; doi: 10.3221/igf-esis.43.06 94 fatigue tests atigue tests were conducted using a mts810 hydraulic test system with a load capacity of 250kn (fig. 4 a). stress cycles were performed setting a sinusoidal load control signal (constant amplitude, r=0, 5 hz frequency). all fatigue tests were made at room temperature. two sets of samples were tested: set a composed of 8 uncorroded specimens and set b composed of 10 corroded specimens (fig. 4 b). the results obtained from fatigue tests for both sets in terms of stress range δσ and number of cycles to failure n were reported in a bi-logarithmic chart and interpolated by a regression curve calculated by the least squares method. in addition, the s-n curve with ps (probability of survival) 97.7%, 10% and 90% were computed by student’s distribution. the expression used for the s-n curve provided by the ec3 [15] is shown below: 62 10k k rr r cn      (1) where k is the inverse slope of the s-n curve, δσc is the stress range at 2 million cycles of the detail category, δσr is the stress range (independent variable) and nr is the number of cycles (dependent variable). in fig. 5 the data obtained from fatigue tests on uncorroded specimens and the corresponding s-n curves with ps = 10%, 50%, 90% e 97.7% are reported. in fig. 6 the data obtained from fatigue tests on corroded specimens and the corresponding s-n curves with ps = 10%, 50%, 90% e 97.7% are shown. the two different s-n curves (ps 97.7%) obtained from the experimental tests presented in this paper have about the same slope but the curve representative of corroded specimens moves downward respect to the curve of virgin samples. figure 5: test results with ps 10-50-90-97.7% of not corroded joints. figure 6: test results with ps 10-50-90-97.7% of corroded joints. 10 100 1000 1.00e+04 1.00e+05 1.00e+06 1.00e+07 s tr es s ra n g e [n /m m 2 ] number of cycles ps 50% ps 97.7% ps 10-90% 10 100 1000 1.00e+04 1.00e+05 1.00e+06 1.00e+07 s tr es s ra ng e [n /m m 2 ] number of cycles ps 50% ps 97.7% ps 10-90% f p. zampieri et alii, frattura ed integrità strutturale, 43 (2018) 90-96; doi: 10.3221/igf-esis.43.06 95 moreover, as already noted by other researchers [14], the inverse slope k of the s-n curve obtained from experimental tests is substantially greater (between 8 and 9) than the one proposed by the ec3 standard for the detail category 112. the inverse slopes and δσ at 2 million cycles with ps = 90% and 97.7% are reported in tab. 1. specimens k δσ90 [n/mm2] δσ97.7 [n/mm2] not corroded 8.29 155.9 144.0 corroded 9.05 127.7 113.7 difference [%] 8.00 22.0 27.0 table 1: summary of fatigue tests. conclusions n this paper, experimental tests were performed on a bolted joint (category 112 of the ec3 standard) by fatigue cyclic tests on virgin samples and on degraded samples obtained by an accelerated corrosion process. from the test results statistical reanalysis, the s-n curve (with ps 97.7%) obtained from uncorroded samples has an inverse slope of 8.29, approximately equal to 9.05 that is the one relative to the s-n curve derived from corroded tests results, however the last curve (of corroded specimens) is moved down with respect to the not corroded curve. the results confirm that the accelerated corrosion process applied to the specimens caused a not negligible reduction of the fatigue strength of this kind of joints. acnowledgments he authors would thank to prof. m. quaresimin, eng. n. de rossi, prof. g. concheri and eng. g. savio for their contribution. references [1] correia, j.a.f.o., huffman, p.j., de jesus, a.m.p., cicero, s., fernandez-canteli, a., berto, f., glinka, g. unified twostage fatigue methodology based on probabilistic damage model applied to structural details. [2] sampayo, l.m.c.m.v., monteiro, p.m.f., correia, j.a.f.o., xavier, j.m.c., de jesus, a.m.p., fernandez-canteli, a., calcada, r.a.b. 2015. probabilistic s-n field assessment for notched plate made of puddle iron from the eiffel bridge with an elliptical hole. 1st icsi. 114 (2015) 691-698. [3] razavi, s.m.j., peron, m., torgersen, j., berto, f., mutignani, f. effect of hot dip galvanization on the fatigue strength of steel bolted connections, frattura ed integrita strutturale, 41 (2017) 432-439. doi: 10.3221/igf-esis.41.5. [4] berto, f., mutignani, f., guido, e. effect of hot dip galvanization on the fatigue behaviour of steel bolted connections, international journal of fatigue, 93 (2016) 168-172. doi: 10.1016/j.ijfatigue.2016.08.02. [5] berto, f., mutignani, f., tisalvi, m. notch effect on the fatigue behavior of a hot-dip galvanized structural steel strength of materials, 47 (5) (2015) 719-727. doi: 10.1007/s11223-015-9709-0 [6] horstmann, m., gregory, j.k., schwalbe, k.h. 1995. geometry effects on corrosion fatigue in offshore structural steels. international journal of fatigue, 17 (1995) 293–299. [7] rokhlin, s.i., kim, j.y., nagy, h., zoofan, b., effect of pitting corrosion on fatigue crack initiation and fatigue life. engineering fracture mechanics, 62 (1999) 425-444. [8] ernst, p., newman, r.c. pit growth studies in stainless steel foils. i. introduction and pit growth kinetics, corrosion science, 44 (2002) 927-941. [9] liu, y.m., mahadevan, s. probabilistic fatigue life prediction using an equivalent initial flaw size distribution, international journal of fatigue, 31 (2009) 476-487. [10] shan-hua, x., you-de, w., estimating the effects of corrosion pits on the fatigue life of steel plate based on the 3d profile. international journal of fatigue, 72 (2015) 27-41. i t p. zampieri et alii, frattura ed integrità strutturale, 43 (2018) 90-96; doi: 10.3221/igf-esis.43.06 96 [11] acuna, n., gonzalez-sanchez, j., ku-basulto, g., dominguez, l., analysis of the stress intensity factor around corrosion pits developed on structures subjected to mixed loading, scripta mater, 55 (2006) 363–366. [12] kondo, y., prediction of fatigue crack initiation life based on pit growth. corrosion, 45 (1999) 7–11. [13] sharifi, y., rahgozar, r., archives of civil and mechanical engineering, 9(4) (2009) 75-83. [14] abílio, m.p. de jesus, antónio, l.l. da silva, josé, a.f.o. correia, fatigue of riveted and bolted joints made of puddle iron – a experimental approach. journal of constructional steel research, 104 (2015) 81-90. 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can be opened with acrobat and adobe reader 5.0 and later.) >> /namespace [ (adobe) (common) (1.0) ] /othernamespaces [ << /asreaderspreads false /cropimagestoframes true /errorcontrol /warnandcontinue /flattenerignorespreadoverrides false /includeguidesgrids false /includenonprinting false /includeslug false /namespace [ (adobe) (indesign) (4.0) ] /omitplacedbitmaps false /omitplacedeps false /omitplacedpdf false /simulateoverprint /legacy >> << /addbleedmarks false /addcolorbars false /addcropmarks false /addpageinfo false /addregmarks false /convertcolors /converttocmyk /destinationprofilename () /destinationprofileselector /documentcmyk /downsample16bitimages true /flattenerpreset << /presetselector /mediumresolution >> /formelements false /generatestructure false /includebookmarks false /includehyperlinks false /includeinteractive false /includelayers false /includeprofiles false /multimediahandling /useobjectsettings /namespace [ (adobe) (creativesuite) (2.0) ] /pdfxoutputintentprofileselector /documentcmyk /preserveediting true /untaggedcmykhandling /leaveuntagged /untaggedrgbhandling /usedocumentprofile /usedocumentbleed false >> ] >> setdistillerparams << /hwresolution [2400 2400] /pagesize [612.000 792.000] >> setpagedevice microsoft word numero_39_art_4 p. konecny et alii, frattura ed integrità strutturale, 39 (2017) 29-37; doi: 10.3221/igf-esis.39.04 29 focussed on modelling in mechanics effect of cracking and randomness of inputs on corrosion initiation of reinforced concrete bridge decks exposed to chlorides p. konecny, p. lehner všb – technical university of ostrava, faculty of civil engineering, department of structural mechanics, l. podeště 1875, 708 33 ostrava-poruba, czech republic petr.konecny@vsb.cz, http://orcid.org/0000-0001-6667-7522 petr.lehner@vsb.cz, http://orcid.org/0000-0002-1478-5027 abstract. the paper is aimed at the indicative evaluation of the effect of random scatter of input parameters in case of durability of reinforced concrete bridge deck. the time to onset of corrosion of steel reinforcement of concrete bridge deck exposed to chloride is evaluated. the effect of cracking in concrete onto chloride ingress is considered. the selected steel reinforcement protection strategies are: unprotected steel reinforcement, epoxy-coated steel reinforcement and water-proof barrier bellow asphalt overlay. the preliminary model for damage effect on chloride ion ingress through water proof membrane under penetrable asphalt overlay is used. 2-d finite element chloride ingress model is combined with monte carlo simulation technique. the innovative crack effect modeling via highly penetrable elements is applied. deterministic and probabilistic calculations are compared. keywords. concrete; crack; steel reinforcement; bridge deck; corrosion initiation; probability. citation: konecny, p., lehner, p., effect of cracking and randomness of inputs on corrosion initiation of reinforced concrete bridge decks exposed to chlorides, frattura ed integrità strutturale, 39 (2017) 29-37. received: 15.07.2016 accepted: 21.09.2016 published: 01.01.2017 copyright: © 2017 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. introduction he random scatter of input parameters is important feature of many engineering tasks. thus considering randomness in the numerical modeling via distribution functions of significant parameters is suitable approach in probabilistic reliability assessment even in case of public infrastructure. typical example of the civil engineering structure of interest is reinforced concrete (rc) bridge structure. the durability of such structure is, in many cases, predetermined by durability of steel reinforcement as proven by many structures requiring premature repairs or replacement. need for repairs results from defects caused by e.g. the effect of environment or the long term actions of loads including chemical actions. shortened lifespan leads to increased life cycle costs of the structure thus contributing indirectly to higher burden on public budgets. the production of more durable construction systems and higher quality concrete mixes can help to reduce the overall costs of the structure (see e.g. [1] and [2]). it is assumed that higher durability can be achieved with increased knowledge t http://www.gruppofrattura.it/pdf/rivista/numero39/audio/4.mp3 p. konecny et alii, frattura ed integrità strutturale, 39 (2017) 29-37; doi: 10.3221/igf-esis.39.04 30 of the progress of the degradation process caused by the long term actions of environmental and structural loading. (see e.g. [3-10]). however, models that aims to investigate durability of bridge deck with cracks or even waterproof membrane both from deterministic, not mentioning probabilistic, standpoint are still under intensive development. moreover, information about the scatter or uncertainty of model parameters are of particular interest. for example, one of probabilistic 1d models of ideal bridge deck without cracks [4] applied description of variability of diffusion coefficient, surface chloride concentration, reinforcement depth in the form of frequency histogram. histogram were based on measurements from real bridges in the northwestern united states [11]. there are also other studies dealing with input parameters for chloride affected bridge deck steel reinforcement corrosion. the effect of steel protection reinforcement is presented in [12]. surface chloride concentration and is part of the study dealing with epoxy-coating protection effect [13]. this study also provides data for the epoxy-coating defects. there are also attempts to codify the model and description of probability density function. fib model code [5] contains description of the 1d chloride ingress model with aging effect including recommendation for probability density functions of input parameters. joint committee for structural safety has prepared draft of the chapter 2.19 environmental attack. however, this chapter is not publicly available [14]. since the concrete is brittle material where cracking occurrence is accepted thus crack effect on the chloride ion penetration shall be considered. there were attempts to reflect the need for the crack effect modeling. the finite element analysis (fea) of chloride ingress into concrete with crack was considered in [6] and [15]. both models were based on the second fick’s law of diffusion. the aggressive chloride exposure was applied as boundary conditions of a concentration of chlorides applied directly in nodes relevant to surface as well as to crack position. in contrast, the authors in [16] model the effect of cracks in the form of changes in the material parameters in the area of the crack. moreover the crack width effect important for the chloride ion penetration into concrete is discussed in [17]. presented work aims on the indicative evaluation of the effect of randomness of input parameters on two examples: directly exposed bridge decks and bridge decks protected by waterproof insulation (see fig. 1). the possibilities of innovative crack effect modeling, presented briefly also in [18], are discussed more in depth here in. the results of deterministic and probabilistic assessment of the selected bridge decks are compared. reinforced concrete slab reinforcement protected with an epoxide coating asphalt overlay waterproof membrane reinforced concrete slab unprotected reinforcement figure 1: the rc bridge deck scheme with epoxide protection of reinforcement typical for the north east part of the usa (left) and waterproof insulation typical for central europe (right). 2d fea diffusion model taking into account the effects of cracks he fea model [18] applied herein focusses on the transport of chloride ions through a rc bridge deck with a transverse crack and on an estimation of the concentration of chlorides at the reinforcement level or in places with damage to the epoxide coating of the reinforcement. besides the capability of the modeling the cracking effect feature, the model also allows for simplified description of the damage to the waterproof insulation under the asphalt coating. the durability evaluation of selected bridge deck protection strategies is based on the work [4] and [6]. it is enriched by introducing the effects of the aging of concrete via time varied diffusion coefficients [19]. model allows for chloride ingress modeling and corrosion initiation analysis. the available model is supplemented with a special description of the effect of cracks in the directly exposed bridge deck. the crack is applied in the form of introducing a highly permeable area [16-18]. the crack area is formed as narrow elements with width of crack. this approach allows for rather fast computation even though the irregularity of element t p. konecny et alii, frattura ed integrità strutturale, 39 (2017) 29-37; doi: 10.3221/igf-esis.39.04 31 shape is of concern. focus on the model precision is another part of ongoing research. the crack effect is modelled via change of diffusion coefficient in the respective area of the crack. the calculation of the diffusion coefficient in the elements representing the crack is computed based on the work [17] as: dc,cr = (dc,cr,max dc,28)/50×(crckw 30) + dc,28, (1) where dc,28 is diffusion coefficient for an undisturbed sample [m2/s]. dc,cr,max is the coefficient of the media in the crack, dc,cr,max =14×10-10 [m2/s]. dc,cr is the diffusion coefficient in the crack [m2/s] and crckw is width of the crack in the range of 30 < crckw <80 [µm]. if the crack width is too low than the diffusion coefficient in crack dc,cr has the same value as for the intact material dc,28. if the crack width is higher than the limiting value then the diffusion coefficient in respective elements has value similar to the one of porous media dc,cr,max. figure 2: the sample contour plot of concentration of chloride ions in a concrete bridge deck with a crack. deterministic solution for an exposure period t = 20 years shows the fea meshed elements and concentration in the form of contours. deterministic application and the brief description of crack modeling approach were discussed in [18]. illustrative probabilistic example of the model of a rc bridge deck from ordinary concrete with steel reinforcement protected by waterproof insulation under an asphalt cover is discussed in [20]. the finite element model with resulting concentration is shown in fig. 2 and fig. 3. 0 0.2 0.4 0.6 0.8 1 1.2 -0.2 -0.1 0 time [years] : 20 0.2 0.3 0.4 0.5 figure 3: the sample isolines plot of concentration of chloride ions in a concrete bridge deck with a crack. assessment of durability the main inputs to the durability assessment are the response of the structure to loading et and resistance r. the expression respecting the durability of bridge deck compares chloride concentration at most exposed spot of steel reinforcement cxz,t with chloride threshold cth when corrosion is initiated. their mutual interaction can be analyzed by using typical reliability function: txztt ccerrf ,th  (2) the inherent variability of studied problem is suitable for the application of probabilistic assessments. the probabilistic methods allow us to capture the random interaction between mutually contradictory parameters (see for example [21], [22] or [14]). in case of the rc bridge decks, the random interaction between cracks in concrete, defects in epoxide coatings and damage to waterproofing under an asphalt surface is of the interest. the level of reliability is expressed as the probability of given limit state exceedance: 0)p(0)p(pf,  ttt rfer (3) p. konecny et alii, frattura ed integrità strutturale, 39 (2017) 29-37; doi: 10.3221/igf-esis.39.04 32 the reliability of the structure is generally analyzed by comparison with the probability of failure pf,t at particular age of the structure t and the design probability of failure pd. in the case of parametric studies, it is also advantageous to compare the reliability of individual alternatives with the aid of computed failure probability pf without a direct reliability assessment. available probabilistic approaches when considering probabilistic methods for the reliability assessment, it is possible to select from tools analytic, simulation-based or numerical. an overview of available tools and methods can be found e.g. in [22] or [23]. direct monte carlo simulation [24] is robust but the computation costs may be rather high in case of low probability events. thus variation reduction techniques may be used in order to reduce the simulation time. these tools include for instance: importance sampling [25, 26]. stratified sampling and latin hypercube sampling [27, 28]. these approaches can lead to a reduction of computational burden which is necessary for large highly nonlinear tasks even nowadays. another approach for the optimization of computation costs is so called “directly optimized probabilistic calculation” (doproc, [29, 30]). this method is on the boundary between combinatory and numerical integration. sbra probabilistic method the simulation-based reliability assessment method (sbra, see [21]) is implemented. this method is based on the limit state design principle and on the application of a monte carlo simulation [24] for the calculation of probability of failure pf,t in time. this method applies bounded histograms for description of probability density functions. since the direct monte carlo method is applied, the question of precision arises. a very large number of steps is necessary particularly in case of tasks related to the limit state of carrying capacity with the expected probabilities of failure in order of one in one hundred thousand. in case of an analysis of corrosion initiation, the expected accuracy is in the range of single percentage. with the selection of thousand simulation steps, the monte carlo method induced error can be estimated with the aid of the common statistics. the estimation of probability in order of one percent falls with 90% certainty, into the interval pf = 0.01±0.0052 [20]. this precision is reasonable for given task. it is worth mentioning that the precision of the resulting probabilities estimates comparing with approaches that use continues mathematical models instead is a matter of discussion. moreover, the opinion of the authors is that if is the resulting probability treated as measure of reliability useful for comparison of different scenarios then the difference in probability evaluation with procedures such as jcss [14] does not play significant role. application of durability assessment urability assessment is computed without the variation of input parameters as well as with consideration of their randomness. an estimation of the period to the initiation of corrosion for the selected alternatives of rc bridge decks for the deterministic as well as for the probabilistic analysis uses the 2d finite element model. the probabilistic framework extends the work [26] and calls a fea macro with a description of a specific type of an rc bridge deck. there are two main steel reinforcement protection strategies considered as discussed in the following two sections. the period to the onset of corrosion as well as respective probabilities are evaluated using a model prepared in an environment compatible with octave or matlab. the probabilistic solution of this macro is carried out repeatedly as part of a monte carlo simulation and always with randomly generated input variables according to the assigned histogram. the resulting probabilities are referenced to a 1x1 m square and the area of the damaged bridge structure can then be later calculated by a simple multiplication of the probability obtained by the area of the bridge deck. the change of the diffusion coefficient due to the concrete aging is respected. the respective equation was introduced in [32] and reformulated to shape (4) in [31]. the approach for generating random values of the diffusion coefficient in time is given in (5). thus the first step is a calculation of the nominal value of the diffusion coefficient over time t: m t t d t d          28 c,28nom,c, (4) where is dc,nom,t nominal diffusion coefficient for a selected age [m2/s]. concrete age is t [years] while t28 [years] is reference period of measurement for an age of 28 days. aging factor is m [-]. the scatter of diffusion coefficient in time is possible to generate while respecting the dispersion change in time with: d p. konecny et alii, frattura ed integrità strutturale, 39 (2017) 29-37; doi: 10.3221/igf-esis.39.04 33 dc,t = dc,nom,t + dc,var×dc,nom,t (5) where dc,nom,t is diffusion coefficient [m2/s] for the selected age t [years]. dc,var is respective distribution [m2/s]. reinforced concrete bridge deck with a crack the durability is expressed in the form of the period to the onset of corrosion. the analysis of a directly exposed rc bridge deck with unprotected steel reinforcement and consideration of crack effect is denoted as p1b. the model also contains a module for the reinforcement with an epoxide coating protection. this protection strategy is denoted as p1e. the input parameters are similar to black bar computation (p1b) with the special description of the spot on the epoxy coated steel reinforcement, called holidays, where the chloride concentration is evaluated. a summary of the parameters applied in alternative p1b and p1e is given in tab. 1. the summary considers both random variables as well as the deterministic ones. the selection of distribution function is based on the available research studies as well as engineering judgment. if the distribution were available than the reference to literature source is given otherwise the engineering judgment is applied. it needs to be noted that there is a minor difference between deterministic and probabilistic calculation in case of aging coefficient t. it is assumed that the difference has very low impact on the resulting time to corrosion initiation. table 1: the random variables and deterministic input parameters for ordinary concrete and a directly exposed reinforced concrete bridge deck with a crack (p1b unprotected steel reinforcement, p1e steel reinforcement protected by an epoxide coating). the parameters that belong exclusively to p1e are marked in the table. analysis with a defect in the waterproof insulation and a crack in a reinforced concrete bridge deck by adding waterproof membrane under the penetrable asphalt overlay on the surface of alternative p1b, the corner stone of the model for a typical bridge deck in the czech republic (alternative p2b) is introduced. however, the parameters of the waterproof membrane damage are based on the initial engineering judgment. parameter name deterministic probabilistic solution solution range/value probability density function diffusion coefficient (opc) dc,28. [10-12m2/s] 5.59×10-12 5.59×10-12 constant [2] aging coefficient m [-] 0.26 0.284 constant [2] variation of the diffusion coefficient dc,var [-] -0.116-0.482 gumbel distribution (µ=0, s=1)×0.043 [33] depth of reinforcement (cover) rebd [m] 0.05 0.04-0.11 histogram [11] chloride threshold for corrosion initiation cth [%] 0.2 0.09-0.51 histogram [12] depth of cracks crckdpt [m] 0.025 0.0-depth histogram expon1.dis crack spacing crcks [m] 2.4-3.6 bounded normal distribution. n(3,0.1) crack width crckw [mm] 0.3 0.035-0.565 bounded normal distribution, n(0.3,0.05) relative spacing of the first cracks crcks,i 0.5 0-1 uniform distribution frequency of defects in the reinforcement coating mashn [m-1] 5 0-10 histogram [13] (p1e) relative spacing of the first defect in the reinforcement coating mashi 0.05 0-1 uniform distribution (p1e) concentration of chlorides at the surface c0 [%] 0.6 0.21-1.63 histogram [13] initial concentration of chlorides in concrete cb %] 0 0 constant monitored life span t [years] 100 100 constant depth of rc slab depth [m] 0.23 0.23 constant p. konecny et alii, frattura ed integrità strutturale, 39 (2017) 29-37; doi: 10.3221/igf-esis.39.04 34 in the case of reinforcement protected by epoxide, the alternative marked as p1e becomes with the addition of waterproof insulation under the asphalt overlay alternative p2e. deterministic as well as random variable parameters for waterproof insulation alternative are given in tab. 2. the asphalt is considered as totally permeable for simplification of the problem herein. the waterproof insulation is assumed to contain defects that allow chlorides to penetrate through. the area of defects in the modeled water proof barrier is assumed to grow linearly every year. parameter name deterministic probabilistic solution solution range/value probability density function crack spacing in waterproof insulation crckhis [m] (0.46-1.53) bounded normal distribution n(1,0.1) width of the cracks growth in the waterproof membrane crckhiw [mm/year] 10 (1.15-18.85) bounded normal distribution n(10,1.65) first defect in waterproof insulation crckshi,i [m] 0.4 0-1 uniform distribution table 2: the modification of random input variables and deterministic input parameters for ordinary concrete and a reinforced concrete bridge deck with a crack under damaged waterproof insulation (p2b unprotected steel reinforcement, p2e steel reinforcement protected by an epoxide coating). other parameters of the model are given in tab. 1. results he prepared models allow for indicative comparison of the behavior of the steel reinforcement protection strategies (black bar vs. epoxy-coated reinforcement). at the same time, variants are studied from the point of view of the use of a waterproof membrane. the results of the growth of the probability initiation of corrosion during a simulated period of 100 years are shown on fig. 4 including results from deterministic analysis [18]. probabilities corresponding to time to deterministic onset of corrosion are indicated in graph as well. the resulting times to the initiation of corrosion for deterministic solution [18] and selected probability levels [20] are given in tab. 3 on the next page. 0 20 40 60 80 100 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 corrosion initiation n: 1000, 30x32-20150429 t i [years] p ro b ab il it y p t[ m -2 ]  [24.1 , 0.03]  [16.4 , 0.078]  [46.9 , 0.018]  [44 , 0.103] p 1e p 1b p 2e p 2b figure 4: probability of corrosion initiation ti for the variants considered by type of reinforcement protection. b unprotected reinforcement, e epoxy-coated steel reinforcement; and the bridge deck type. 1 directly exposed bridge deck with a crack, 2 ordinary concrete and a bridge deck with a crack protected by waterproof insulation under an penetrable asphalt overlay. fig. 4 shows that unprotected steel reinforcement marked p1b has the value of computed deterministic time to onset of corrosion ti =16.4 years that correspond to 7.8 percent of corrosion initiation likelihood in probabilistic solution. if the epoxy coating was used than the onset of corrosion started almost two times later (ti =24.1 years) and it was related to probability of corrosion initiation pf =3.0 percent. t p. konecny et alii, frattura ed integrità strutturale, 39 (2017) 29-37; doi: 10.3221/igf-esis.39.04 35 the computation with initial attempt to model waterproofing with progressively widening insulating membrane defect (case p2b) showed that the risk of corrosion at the beginning of structural lifespan is almost mitigated. however due to the progressive growth of cracks the modelled effect of waterproof insulation is lost with time and this alternative follows the variant without concrete protection. the delay between cases p1b and p2b is ranging from 20 to 30 years for deterministic results. the onset of corrosion of unprotected steel reinforcement embedded in concrete under the water proof membrane is ti =44.0 years that corresponds to probability of corrosion initiation pf =10.3 percent. if epoxy-coated reinforcement is combined with waterproof insulation p2e then a highest durability is obtained herein (ti =46.9 years, pf = 1.8 percent). addition of water proof membrane on top of the epoxy-coating protection has less significant effect comparing to unprotect steel reinforcement because it is second protection strategy in such case. fea mesh: 30×32 time to corrosion initiation ti [years] deterministic solution probability of corrosion initiation pf [%] 5 10 25 p1b 16.4. 10.5 21.2 50.6 p1e 24.1 28.6 59.3 100.0 p2b 44.0 29.8 43.1 83.9 p2e 46.9 87.9 100.0 100.0 table 3: period to the initiation of corrosion ti [years] for a selected probability of the initiation of corrosion for selected variants according to type of reinforcement protection: b unprotected steel reinforcement, e reinforcement covered with epoxide; the bridge deck construction: 1 ordinary concrete and a directly exposed bridge deck with a crack, 2 ordinary concrete and a bridge deck with a crack protected by waterproof insulation under an penetrable asphalt overlay. comparison of deterministic and probabilistic results deterministic analysis of steel reinforcement protected by epoxy-coating yields lower time to corrosion initiation comparing to probabilistic analysis in both cases: directly exposed bridge deck surface (p1e), as well as bridge deck with waterproof membrane under the penetrable asphalt overlay (p2e). if the uncoated reinforcement in directly exposed bridge deck is evaluated (p1b, ti =16.4 years) than the deterministic results compared with the fifth percentile yielded lower time to corrosion initiation (ti,05 = 10.5 years) while the tenth percentile yielded higher time (ti,10 = 21.2 years). if the bridge deck is covered by waterproof membrane (p2b, ti =44.0 years) than fifth percentile yielded lower time to corrosion initiation (ti,05 = 29.8 years) while the tenth percentile yield similar time (ti,10 = 43.1 years). conclusions and discussion he indicative durability assessment of reinforced concrete bridge deck exposed to chloride ingress is applied considering 2d finite element model of chloride ion ingress with crack and simplified ability to describe the waterproof membrane effect. moreover, the implementation of a continuous model of crack effect is discussed and applied. the monte carlo simulation is utilized for probabilistic evaluation. the description of the basic input parameters is based on the available research data. however, the description of the crack frequency and depth in reinforced concrete bridge deck as well as description of waterproof membrane damage are based on the preliminary engineering judgment. from the conducted analysis it is shown, that the worst protected is, as expected, the steel reinforcement without an epoxy-coating in the directly exposed bridge deck with a crack. when an epoxide coating was used on steel reinforcement then the model calculations significantly reduced the risk of the occurrence of corrosion. the comparison of deterministic and probabilistic assessment of chloride ingress related durability of selected bridge decks with enhanced crack effect consideration is conducted. the effect of two protection strategies with respect to durability of reinforced concrete bridge deck is discussed, namely waterproof membrane under penetrable asphalt overlay and epoxy coating steel reinforcement protection. it was observed that the application of random input parameters variation increased time to onset of corrosion on probability levels of 10 and 25 percentiles comparing to deterministic solution. it is assumed that it was caused by lower likelihood of simultaneous encountering of following phenomena: crack in bridge deck, problem in waterproof membrane and/or defect in epoxy-coating. this observation is more significant in cases with epoxy-coating where more random variables are involved. t p. konecny et alii, frattura ed integrità strutturale, 39 (2017) 29-37; doi: 10.3221/igf-esis.39.04 36 the presented models describe the initial attempt to encounter for the effect of the water proof membrane and cracking. however, it needs to be noted that the selection of model parameters as well as probability distribution significantly affects the time to onset of corrosion, so the results reflect considered simplifications and assumptions. thus further research is necessary in order to improve the input parameters description and model assumptions. moreover, addressing the input parameters with respect to proposed codified approaches shall be of special interest as well. acknowledgements inancial support from všb-technical university of ostrava by means of the czech ministry of education, youth and sports through the institutional support for conceptual development of science, research and innovations for the year 2016 is gratefully acknowledged. references [1] tikalsky, p.j., scheetz, b.e., tepke, d.g., task 6 final report statewide high performance concrete initiative, penndot research, state college, pa, usa, pennsylvania state university, (2007). [2] ghosh, p., tran, q., correlation between bulk and surface resistivity of concrete, international journal of concrete structures and materials, 9(1) (2014) 119-132. doi 10.1007/s40069-014-0094-z. [3] keršner, z., novák, d., teplý, b., bohdanecký, v., concrete carbonation, reinforcing steel corrosion and cooling tower durability, sanace, 4 (1996) 21-23. [4] tikalsky, p.j., pustka, d., marek, p. statistical variations in chloride diffusion in concrete bridges, aci struct. j., 102 (2005) 481-486. [5] fib bulletin 34: model code for service life design, (2006). [6] konečný, p., tikalsky, p.j., tepke, d.g., performance evaluation of concrete bridge deck affected by chloride ingress: simulation-based reliability assessment and finite element modeling, transportation research record, 2028 (2007) 3-8. doi: 10.3141/2028-01. [7] novák, d., vořechovský, m., teplý, b., freet: software for the statistical and reliability analysis of engineering problems and freet-d: degradation module, adv. eng. softw., 72 (2014) 179-192. doi:10.1016/j.advengsoft.2013.06.011. [8] konečný, p., brožovský, j., ghosh, p. evaluation of chloride influence on the cracking in reinforced concrete using korozeeneck software. in: transactions of the všb – technical university of ostrava, civil engineering series, 11(1) (2011) 1–7. doi: 10.2478/v10160-011-0006-y. [9] teplý, b., vořechovská, d., reinforcement corrosion: limit states, reliability and modelling, j. adv. conc. technol., 10 (2012) 353-362. doi: 10.3151/jact.10.353. [10] sýkora, m., holický m., marková, j., verification of existing reinforced concrete bridges using the semiprobabilistic approach. eng. struct., 56 (2013) 1419-1426. doi: 10.1016/j.engstruct.2013.07.015. [11] sohanghpurwala, a.a., scannell. w.t.,verification of effectiveness of epoxy-coated rebars. final report to pennsylvania department of transportation, project no. 94-05. ashburn, va [usa]: concorr, (1998). [12] darwin, d., browning, j., o’reilly, m., xing, l., ji, j., critical chloride corrosion threshold of galvanized reinforcing bars, aci mat. j., 106 (2009) 176-183. doi: 10.14359/56465. [13] weyers, r.e., pyc, w., springel, m.m., estimating the service life of epoxy-coated reinforcing steel, aci mat. j., 95 (1998) 546-557. [14] jcss probabilistic model code, http://www.jcss.byg.dtu.dk/publications/probabilistic_model_code.aspx, (2016). [15] marsavina, l., audenaert, k., de schutter, g., faur, n., marsavina, d., experimental and numerical determination of the chloride penetration in cracked concrete. in: constr. build. mater., 23 (2009) 264-274. doi: 10.1016/j.conbuildmat.2007.12.015. [16] bentz, d.p., garboczi, e.j., lu, y., martys, n., sakulich, a.r., weiss, j.w, modeling of the influence of transverse cracking on chloride penetration into concrete, cement concrete comp., 38 (2013) 65-74. doi: 10.1016/j.cemconcomp.2013.03.003. [17] djerbi, a., bonnet, s., khelidj, a., baroghel-bouny., v., influence of traversing crack on chloride diffusion into concrete, cement concrete res., 38 (2008) 877-883. doi: 10.1016/j.cemconres.2007.10.007. f p. konecny et alii, frattura ed integrità strutturale, 39 (2017) 29-37; doi: 10.3221/igf-esis.39.04 37 [18] konečný, p., lehner, p., durability assessment of concrete bridge deck considering waterproof membrane and epoxy-coated reinforcement. perspectives in science, 7 (2016) 222-227. doi:10.1016/j.pisc.2015.11.036. [19] lehner, p., konečný, p., ghosh, p., tran, q., numerical analysis of chloride diffusion considering timedependent diffusion coefficient, international journal of mathematics and computers in simulation, 8 (2014) 103106. [20] konečný, p., lehner, p., probabilistic evaluation of concrete bridge performance considering waterproof membrane and epoxy-coated reinforcement, in: proceedings of the 13th international probabilistic workshop, (2015). http://rpsonline.com.sg/rps2prod/ipw2015/pdf/089.pdf. [21] marek, p., guštar, m., anagnos, t., simulation-based reliability assessment fo structural engineers, boca raton, fl, usa, crc press, (1995). [22] melchers, r., structural reliability analysis and prediction (civil engineering) west sussex, england, wiley, (1999). [23] haldar, a., mahadevan, s., probability, reliability, and statistical methods in engineering design, new york, usa, john wiley, (2000). [24] metropolis, n., ulam, s.,the monte carlo method. journal of american statistical association, 44(247) (1949) 335341. [25] schueller, g.i., pradlwarter, h.j., bucher, c.g. efficient computational procedures for reliability estimates of mdof systems. int. j. nonlin. mech., 26 (1991) 961-974. [26] praks, p., numerical aspects of simulation based reliability assessment of systems, international colloquium eurosibram’2002, prague, itam cas czech republic, ii (2002). [27] iman, r.l., conover, w.j., a distribution-free approach to inducing rank correlation among input variables, commun. stat. simulat., 11 (1982) 311-334. doi: 10.1080/03610918208812265. [28] vořechovský, m., novák, d., correlation control in small-sample monte carlo type simulations, in: a simulated annealing approach. prob. eng. mech., 24 (2009) 452-462. doi:10.1016/j.probengmech.2009.01.004. [29] janas, p., krejsa m., krejsa, v., using the direct determined fully probabilistic method (ddfpm) for determination of failure, briš, r., c.g. soares a s. martonell. reliability, risk and safety: theory and applications, in: proceedings of the european safety and reliability conference, esrel 2009, prague, czech republic, 7-10 september crc press, (2009) 1467-1474. [30] krejsa, m., janas, p., yilmaz, i., marschalko, m., bouchal, t., the use of the direct optimized probabilistic calculation method in design of bolt reinforcement for underground and mining workings, scientific world journal, 2013 (2013) 267593. doi: 10.1155/2013/267593. [31] thomas, m.d.a., bamforth, p.b., modelling chloride diffusion in concrete effect of fly ash and slag, cement concrete res., 29 (1999) 487–495. doi: 10.1016/s0008-8846(98)00192-6. [32] mangat, p., molloy, b., prediction of long term chloride concentration in concrete. mater. struct. 27 (1994) 338–346. doi: 10.1007/bf02473426. [33] konečný, p., vyhodnocení trvanlivosti železobetonových mostovek s ohledem na vliv chloridů a na rozptyl vstupních parametrů (evaluation of the durability of reinforced concrete bridge decks with respect to the actions of chlorides and scatter of input parameters). habilitation thesis, všb-technical university of ostrava (2015). << /ascii85encodepages false /allowtransparency false /autopositionepsfiles true /autorotatepages /none /binding /left /calgrayprofile (dot gain 20%) /calrgbprofile (srgb iec61966-2.1) /calcmykprofile (u.s. web coated \050swop\051 v2) /srgbprofile (srgb iec61966-2.1) /cannotembedfontpolicy /error /compatibilitylevel 1.4 /compressobjects /tags /compresspages true /convertimagestoindexed true /passthroughjpegimages true /createjobticket false /defaultrenderingintent /default /detectblends true /detectcurves 0.0000 /colorconversionstrategy /cmyk /dothumbnails false /embedallfonts true /embedopentype false /parseiccprofilesincomments true /embedjoboptions true 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can be opened with acrobat and adobe reader 5.0 and later.) >> /namespace [ (adobe) (common) (1.0) ] /othernamespaces [ << /asreaderspreads false /cropimagestoframes true /errorcontrol /warnandcontinue /flattenerignorespreadoverrides false /includeguidesgrids false /includenonprinting false /includeslug false /namespace [ (adobe) (indesign) (4.0) ] /omitplacedbitmaps false /omitplacedeps false /omitplacedpdf false /simulateoverprint /legacy >> << /addbleedmarks false /addcolorbars false /addcropmarks false /addpageinfo false /addregmarks false /convertcolors /converttocmyk /destinationprofilename () /destinationprofileselector /documentcmyk /downsample16bitimages true /flattenerpreset << /presetselector /mediumresolution >> /formelements false /generatestructure false /includebookmarks false /includehyperlinks false /includeinteractive false /includelayers false /includeprofiles false /multimediahandling /useobjectsettings /namespace [ (adobe) (creativesuite) (2.0) ] /pdfxoutputintentprofileselector /documentcmyk /preserveediting true /untaggedcmykhandling /leaveuntagged /untaggedrgbhandling /usedocumentprofile /usedocumentbleed false >> ] >> setdistillerparams << /hwresolution [2400 2400] /pagesize [612.000 792.000] >> setpagedevice microsoft word numero_38_art_19 s. fu et al, frattura ed integrità strutturale, 38 (2016) 141-147; doi: 10.3221/igf-esis.38.19 141 focussed on multiaxial fatigue and fracture ratcheting of 316l stainless steel thin wire under tension-torsion loading sichao fu, dunji yu, gang chen, xu chen school of chemical engineering and technology, tianjin university fu_sc126@126.com, djyu@tju.edu.cn, agang@tju.edu.cn, xchen@tju.edu.cn abstract. a series of cyclic tension-torsion tests under symmetric shear strain and asymmetric axial stress control in various loading paths are conducted on 100 μm-diameter 316l steel wires applying a micro tensiontorsion fatigue testing apparatus. the ratcheting strain of the thin wire increases with increasing axial mean stress and decreases in a sequence of linear, rhombic and circular paths. the macro-scale based cyclic plastic constitutive models with kinematic hardening rules of the ohno-wang (ow) and the chen-jiao-kim (c-j-k) are evaluated for the thin wire. comparing with the o-w, the c-j-k predicts more accurately under high axial stress. while the loading path effects on ratcheting for wire specimens are basically simulated, the macro-based models tend to under-estimate the effect of phase difference between axial and torsional loadings and the ratcheting evolution in the initial 50 cycles. keywords. thin wire; tension-torsion; ratcheting; 316l stainless steel. citation: fu, s., yu, d., chen, g., chen, x., ratcheting of 316l stainless steel thin wire under tension-torsion loading, frattura ed integrità strutturale, 38 (2016) 141-147. received: 30.05.2016 accepted: 25.06.2016 published: 01.10.2016 copyright: © 2016 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. introduction yclic mechanical behaviors under multiaxial loading conditions at small-scale are key issues in the design of durable micro-devices as well as crucial aspects in characterizing mechanical properties of materials. while the issues at macro-scale have been widely studied for decades, research on multiaxial mechanical properties at micro-scale is quite limited. most researches on this issue have focused on the biaxial cyclic tensile behaviors of thin films on substrates [1, 2]. another fundamental multiaxial property, the tension-torsional cyclic behavior, is barely studied experimentally at micro-scale because of the technological problems of precise loading control and measurements. recently, a novel tensiontorsional fatigue apparatus for micro-scale components has been developed [3] and enables the biaxial cyclic tests on thin wires. in this study, a series of cyclic tension-torsion tests under various loading paths are conducted on 100 μm-diameter 316l stainless steel wires. the material is widely used in micro-devices such as cardiovascular stents. in service, small-scale components may undergo multiaxial loading with tensile stress due to low structural stiffness, leaving multiaxial ratcheting c s. fu et al, frattura ed integrità strutturale, 38 (2016) 141-147; doi: 10.3221/igf-esis.38.19 142 one concern in the design of stents. the low level ratcheting under biaxial loading is observed and simulated by means of macro-scale based kinematic hardening rules of the ohno-wang (o-w) and chen-jiao-kim (c-j-k). experimental procedure micro tension-torsional fatigue apparatus for thin wires, as shown in fig. 1, is applied in this study. the coupled tensile and torsional loading at the scale of 100 n-102 μnm is achieved by a tensile and a torsional load frame that actuated and measured independently without interfering with each other. a wire specimen is clamped between the frames that have been aligned by an x-y translation stage. a linear motor connected with a load cell is applied in the tensile frame, which allows for the precise control of axial force and the free axial movement of specimen. the micro-torque of the specimen in test is loaded by a dc micro motor and measured by a high precision torque transducer through the transference of a thrust air bearing. the axial deformation of the wire specimen in tension-torsion tests is measured by a grating sensor built in the linear motor and corrected based on data acquired by a non-contact displacement detection system (ndds) in uniaxial tension tests. more details about this apparatus can be found elsewhere [3]. figure 1: schematic illustration of the tension-torsional fatigue apparatus for micro-scale components. the material used in this study is 316l stainless steel soft tempered wire, in nominal diameter of 100 μm, annealed with pure hydrogen. the chemical composition of the material is (wt%): c 0.03%, cr 16.93%, ni 12%, mn 0.95%, p 0.63%, s 0.21%, mo 2.39%, si 1%. the actual diameters of specimens were measured before testing by using a scanning electron microscope (sem). the gauge lengths of the specimens were denoted as the distance between the edges of clamps, which was set to be around 6 mm for all tests. uniaxial tension tests and torsion tests were conducted to derive the basic mechanical properties. the cyclic tension-torsion tests were conducted at room temperature under load control for axial loading and angle control for torsional loading. the loading paths in the axial stress-shear strain plane (σ-γ plane) are illustrated in fig. 2, and test conditions are given in tab. 1. in all cases the shear strain amplitude is 0.55%. as the strains in this study are small and consist of low level of plasticity, the shear stress is derived with the hypothesis of linear distribution in the cross section. the shear strain and stress are calculated as follows: d l    (1) t d3 16    (2) where  is the shear strain,  is the shear stress,  is the twisting angle, t is the corrected torque, and d and l are the diameter and gauge length of wire specimen, respectively. in addition, a completely reserved torsional test with shear strain amplitude of 2% was performed to characterize the isotropic softening behavior of the material. a minimum axial stress of a s. fu et al, frattura ed integrità strutturale, 38 (2016) 141-147; doi: 10.3221/igf-esis.38.19 143 26 mpa was persisted during the test in order to avoid buckling of the wire specimen. all tests were conducted at a shear strain rate of 0.002/s. figure 2: loading paths in cyclic tension-torsion tests. path / 2 (%) mean (%) / 2 (mpa) mean (mpa) case 1 0.55 0 0 128 case 2 0.55 0 0 77 case 3 0.55 0 0 26 case 4 0.55 0 51 77 case 5 0.55 0 51 77 case 6 0.55 0 51 77 table 1: multiaxial ratcheting testing of 316l wire under various loading paths experimental results ig. 3 shows the experimental results of case 4 under linear path. the shear hysteresis loop exists as shown in fig. 3(a). the accompanied tensile stress, reversed between 26 and 128 mpa and far below the 0.2% yield strength, contributes to an asymmetric stress state (fig. 3(d)) that leads to ratcheting in the axial direction. the remarkable axial strain accumulation is demonstrated in the axial stress-strain curve (fig. 3(b)) as well as the strain path (fig. 3(c)). the evolution of ratcheting under various loading paths are displayed in fig. 4. the ratcheting strain is defined as the maximum strain per cycle. with increasing cycle number, the ratcheting strain sharply rises in the beginning and then is slowly suppressed until a stable rate of increment is reached. case 1 with constant axial stress of 128 mpa displays the highest level of ratcheting. as reducing the axial mean stress, the ratcheting strain decreases and the rate of stable increment after 100 cycles slightly changes. the effect of loading path on ratcheting is demonstrated by case 4-6 with the same range of cycling axial stress. the linear path in case 4 leads to larger ratcheting than the rhombic path in case 5 and the circular path in case 6. the ratcheting behaviors of the rhombic and the circular paths are similar, with the latter slightly lower in value. the deviation caused by loading path is consistent with the multiaxial ratcheting behavior of steels at macro-scale, which is related with the non-proportionality of certain loading path and the resulted additional hardening [6, 7]. f s. fu et al, frattura ed integrità strutturale, 38 (2016) 141-147; doi: 10.3221/igf-esis.38.19 144 figure 3: experimental results of case 4, (a) shear stress-strain curve in cycle 200, (b) axial stress-strain curve, (c) strain path and (d) stress path in cycle 200. figure 4: evolution of ratcheting strain under various loading path evaluation of macro-scale based cyclic plasticity he macro-scale based cyclic plasticity with the assumption of rate-independent material’s behavior is phenomenologically described by three parts: yield criterion, plastic flow rule and the kinematic hardening rule. the kinematic hardening rule is the central part of the constitutive modelling of cyclic plasticity. it defines the translation of yield surface in stress space during plastic deformation, which is the most important feature for the multiaxial ratcheting simulation. two of the most successful kinematic hardening rules are evaluated for the ratcheting simulation of 316l thin wires: the nonlinear ohno and wang (o-w) [8] and the chen-jiao-kim (c-j-k) [6] rules. o-w: m ia a1 ,  mi i i i i i p p i i i a a da r d d a r a 2 3                (3) c-j-k: mi i i i i i i i p p i ii i a a a da r d n d a ra a 2 3                  (4) t s. fu et al, frattura ed integrità strutturale, 38 (2016) 141-147; doi: 10.3221/igf-esis.38.19 145 where ia is the ith component of back stress a , ia is the magnitude of ia , p is the plastic strain tensor, i , ir and im are material constants (i = 1, 2, … m), n is the direction of plastic strain rate or the normal vector of yield surface, i is a multiaxial parameter. is the macauley bracket: a a if a 0 , a 0 otherwise. the total back stress in this study is decomposed into 8 components for the o-w and c-j-k rules. all the i and ir components in the o-w are determined from a torsion test by the scheme discussed by bari and hassan [9]. im is determined from a tension-torsion test which is low in stress ratio max max/  . the i introduced in the c-j-k is selected by calibrating with a tension-torsion test with low axial stress. the values of the parameters are: 0  200 mpa; 1~8  5000, 1000, 311.7, 161.6, 51.3, 15.2, 5.2, 3.2; r1~8  180, 90, 140, 18, 7.6, 48.7, 200, 132 mpa; im i( 1 ~ 8) 10  ; i i( 1 ~ 8) 3   ;. the predicted cyclic stress-strain response of case 4 in linear path by the c-j-k is illustrated in fig. 5. the o-w and the c-j-k rule predict similar response of shear stress and axial strain in this case. obvious shear hysteresis loop and axial ratcheting behavior is appropriately simulated. figure 5: predicted results of case 4 under linear path by the c-j-k, (a) shear stress-strain curve, (b) axial stress-strain curve, (c) strain path and (d) stress path. the ratcheting responses obtained by the o-w and the c-j-k models as well as experimental data are presented in fig. 6. the o-w and the c-j-k predicted similar ratcheting evolutions with small errors for cases 2-6. in terms of case 1 with relatively high axial mean stress, the o-w obviously over-predicts as the non-proportionality of loading increases. by taking into account the non-coaxiality of plastic strain rate for reducing dynamic recovery, the c-j-k successfully suppresses the ratcheting under relatively high non-proportional hardening in case 1. comparing with simulations for cases 1-3 with constant axial stresses, the c-j-k or the o-w model predicted with more errors for cases 4-6 with loading-unloading axial stress, especially for cases 5, 6 with phase differences of tensile and torsional loading. while the models under-estimate the ratcheting evolution under linear path in case 4, they over-predict ratcheting under rhombic path in case 5 and circular path in case 6. thus it is suggested that the phase difference of loading in two directions has more influence on ratcheting than that predicted by the models. deficiency of simulation also exists in the initial ratcheting stage with high but sharply decreased strain rate. the experimental ratcheting evolves more dramatically with larger decreasing rate in this stage than simulation, which results in the under-predictions within about 50 cycles in most cases. the quickly retarded ratcheting may implies some additional hardening related with plastic strain gradients that prominent in small-scale components undergoing inhomogeneous deformation such as torsion or bending. under an applied torque, while one dislocation of a dipole moves outward and escape or annihilated, another dislocation moves inward under stress gradients and piles up around the wire center, which results in polarized dislocations (or gnds) with non-uniform density [10]. the inhomogeneous spatial distribution of gnds, or the resulted plastic strain gradients, can lead to a strong back stress [5] and may suppress the multiaxial ratcheting of thin wire. further work on the microstructure observation is needed to clearly explain the multiaxial ratcheting behavior s. fu et al, frattura ed integrità strutturale, 38 (2016) 141-147; doi: 10.3221/igf-esis.38.19 146 at small-scale. and the models may be modified to give phenomenological predictions for ratcheting in engineering applications. though certain difference exists between simulation and experimental data, the effects of loading paths on ratcheting is basically described by both models, that is, the ratcheting strain increases with increasing mean stress and reduces with nonproportionality in a sequence of linear>rhombic>circular paths. figure 6: ratcheting strain predicted by the o-w and the c-j-k models, (a) cases 1-3 under constant axial stress, (b) case 4 under linear path, (c) case 5 under rhombic path, (d) case 6 under circular path. conclusion he ratcheting strain of 100 μm-diameter 316l wire increases with increasing axial mean stress and decreases in a sequence of linear, rhombic and circular paths, which suggests similar effect of loading paths on ratcheting of the micro-scale components with that of bulk material. the c-j-k predicts more accurately than the o-w under relatively high axial stress. both models basically simulate the loading path effect on ratcheting for wire specimens. however, the models tend to under-estimate the effect of phase difference between axial and torsional loadings. and the experimental ratcheting strain evolves more dramatically with larger decreasing rate than prediction in the initial 50 cycles, which may imply some additional hardening related with plastic strain gradients. acknowledgments he authors are grateful for the financial support from the national natural science foundation of china (nos. 11372215 and 51435012). references [1] alaca, b. e., selby, j. c., saif, m. t. a., sehitoglu, h., biaxial testing of nanoscale films on compliant substrates: fatigue and fracture, rev. sci. instrum., 73 (2002) 2963. [2] baker, s. p., keller-flaig, r. m., shu, j. b., bauschinger effect and anomalous thermomechanical deformation induced by oxygen in passivated thin cu films on substrates, acta mater., 51 (2003) 3019-3036. t t s. fu et al, frattura ed integrità strutturale, 38 (2016) 141-147; doi: 10.3221/igf-esis.38.19 147 [3] fu, s., wang, l., chen, g., yu, d., chen, x., a tension-torsional fatigue testing apparatus for micro-scale components, rev. sci. instrum., 87 (2016) 015111. [4] yang, x., gao, q., he, g., cai, l., on nonproportional cyclic properties of type 316 stainless steels, acta metallurgica sinica, 32 (1996) 15-22. [5] liu, d., he, y., shen, l., lei, j., guo, s., peng, k., accounting for the recoverable plasticity and size effect in the cyclic torsion of thin metallic wires using strain gradient plasticity, mater. sci. eng. a, 647 (2015) 84-90. [6] chen, x., jiao, r., kim, k.s., on the ohno-wang kinematic hardening rules for multiaxial ratcheting modeling of medium carbon steel, int. j. plasticity, 21 (2005) 161-184. [7] hamidinejad, s.m., varvani-farahani, a., ratcheting of 304 stainless steel under multiaxial step-loading conditions, int. j. mech. sci., 100 (2015) 80-89. [8] ohno, n., wang, j.-d., kinematic hardening rules with critical state of dynamic recovery, part i: formulation and basic features for ratcheting behavior, int. j. plasticity, 9 (1993) 375-390. [9] bari, s., hassan, t., anatomy of coupled constitutive models for ratcheting simulation, int. j. plasticity, 16 (2000) 381409. [10] liu, d., he, y., dunstan, d. j., zhang, b., gan, z., hu, p., ding, h., toward a further understanding of size effects in the torsion of thin metal wires: an experimental and theoretical assessment, int. j. plasticity, 41 (2013) 30-52. << /ascii85encodepages false /allowtransparency false /autopositionepsfiles true /autorotatepages /none /binding /left /calgrayprofile (dot gain 20%) /calrgbprofile (srgb iec61966-2.1) /calcmykprofile (u.s. web coated \050swop\051 v2) /srgbprofile (srgb iec61966-2.1) /cannotembedfontpolicy /error /compatibilitylevel 1.4 /compressobjects /tags /compresspages true /convertimagestoindexed true /passthroughjpegimages true /createjobticket false /defaultrenderingintent /default /detectblends true /detectcurves 0.0000 /colorconversionstrategy /cmyk /dothumbnails false /embedallfonts true /embedopentype false /parseiccprofilesincomments true /embedjoboptions true /dscreportinglevel 0 /emitdscwarnings false /endpage -1 /imagememory 1048576 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can be opened with acrobat and adobe reader 5.0 and later.) >> /namespace [ (adobe) (common) (1.0) ] /othernamespaces [ << /asreaderspreads false /cropimagestoframes true /errorcontrol /warnandcontinue /flattenerignorespreadoverrides false /includeguidesgrids false /includenonprinting false /includeslug false /namespace [ (adobe) (indesign) (4.0) ] /omitplacedbitmaps false /omitplacedeps false /omitplacedpdf false /simulateoverprint /legacy >> << /addbleedmarks false /addcolorbars false /addcropmarks false /addpageinfo false /addregmarks false /convertcolors /converttocmyk /destinationprofilename () /destinationprofileselector /documentcmyk /downsample16bitimages true /flattenerpreset << /presetselector /mediumresolution >> /formelements false /generatestructure false /includebookmarks false /includehyperlinks false /includeinteractive false /includelayers false /includeprofiles false /multimediahandling /useobjectsettings /namespace [ (adobe) (creativesuite) (2.0) ] /pdfxoutputintentprofileselector /documentcmyk /preserveediting true /untaggedcmykhandling /leaveuntagged /untaggedrgbhandling /usedocumentprofile /usedocumentbleed false >> ] >> setdistillerparams << /hwresolution [2400 2400] /pagesize [612.000 792.000] >> setpagedevice microsoft word numero_40_art_3 m. sakane et alii, frattura ed integrità strutturale, 41 (2017) 16-23; doi: 10.3221/igf-esis41.03 16 focused on multiaxial fatigue cracking directions in multiaxial low cycle fatigue at high and room temperatures masao sakane, takamoto itoh department of mechanical engineering, ritsumeikan university, 1-1-1, nojihigashi kusatsu shiga, 525-8577, japan sakanem@se.ritsumei.ac.jp, itohtaka@fc.ritsumei.ac.jp abstract. cracking direction in multiaxial low cycle fatigue is an important research subject because crack initiation and propagation behavior is a physical background for developing an estimation method of multiaxial low cycle fatigue lives. however, there are a few open questions on cracking direction in multiaxial low cycle fatigue because cracking direction in multiaxial low cycle fatigue is complex and changes depending on stress multiaxiality, strain range, notch and material. this paper overviews cracking directions in tension-torsion low cycle fatigue of low alloy steels and nickel base superalloys. two types of cracking directions in these materials, maximum shear direction and maximum principal direction, are discussed in relation with strain multiaxiality and an existence of notch and precrack. the two cracking directions in torsion low cycle fatigue of sus 304 stainless steel are also discussed in relation with strain range. detailed micro crack observations are finally presented to discuss the two cracking directions in torsion low cycle fatigue of a sus 304 unnotched specimen. keywords. multiaxial fatigue; crack mode; notch; fatigue life; torsion. citation: sakane, n., itoh, t., cracking directions in multiaxial low cycle fatigue at high and room temperatures, , frattura ed integrità strutturale, 41 (2017) 16-24. received: 28.02.2017 accepted: 15.04.2017 published: 01.07.2017 copyright: © 2017 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. introduction wo types of cracking directions have been reported in multiaxial low cycle fatigue (lcf); stage i cracking and stage ii cracking. stage i cracking is the cracking on maximum shear plane (shear crack) and stage ii cracking is that on principal plane (principal crack). in a uniaxial push-pull low cycle fatigue of ductile materials, shear cracks initiate and they turn to be principal cracks as they grow, one of them forming a main crack to bring failure of specimen [1]. however, in multiaxial lcf, cracking direction is not so simple as in the uniaxial case, and cracking direction is influenced by several factors. numerous papers have discussed influential factors on cracking direction but still some of their effects seem to be conflicting. major factors influencing cracking direction are strain/stress multiaxiality, type of material, notch and precrack, material anisotropy, strain/stress range, oxidation and so on. t m. sakane et alii, frattura ed integrità strutturale, 41 (2017) 16-23; doi: 10.3221/igf-esis41.03 17 the objective of this paper is to overview factors influencing cracking direction under multiaxial lcf. the factors that this paper overviews are stress/strain multiaxiality, notch and precrack and stress/strain range. this paper discusses the strain range dependency of cracking directions in torsion lcf in more detail. in torsion lcf, shear cracking occurs at high strain ranges but principal cracking at low strain ranges. the reason of the transition of cracking direction depending on strain range has not been well understood so that this paper discusses this topic from micro crack observations on specimens fatigued in torsion. ϕ        scale main crack 1 mm sub crack 0.1 < 2a < 1.0 mm 0.1 mm micro crack 2a < 0.1 mm 0.05 mm axial direction figure 1: crack observation in tension-torsion lcf of sus304 stainless steel at 923k. influential factors to crack direction multiaxial strain/stress states ultiaxial strain/stress state has an evident influence on cracking mode and many papers discuss this factor. a systematic research of the author’s [2] on cracking mode in tension-torsion lcf of a sus 304 austenitic stainless steel is shown in fig.1. in the figure, cracking directions are classified according to crack length into three categories. the main crack is a crack that brings specimen to failure, the sub-crack a crack having a length between 0.1 mm and 1 mm, and the micro-crack a crack with a length less than 0.1 mm. fig.2 depicts the crack angle at failure against the principal strain ratio ( =3/1) and the strain ratio ( =/ ) as a summary of the observations shown in fig.1. the crack angle is the angle from the longitudinal direction of specimen axis,  the shear strain amplitude and  the axial normal strain amplitude. the  =0.5 test corresponds with the tension test and  =1.0 with the torsion test, assuming that the poisson’s ratio being 0.5 in lcf region. the main cracks at the three strain ranges propagated at an angle of 90 degrees (principal crack) in tension tests ( =0.5 test) but they at an angle of 45 degrees (shear crack) in torsion tests ( =1.0 test). the transition of the cracking mode from principal crack to shear crack occurred at the principal strain ratio of about 0.74. the cracking mode of sub-cracks is the same as that of the main crack. however, the cracking mode of the micro-crack is different from that of the main and sub-crack, and both principal and shear cracking modes were found in the principal strain ratios of 0.86 and 1.0. principal strain ratios at which the tension-torsion crack transits from the principal mode to the shear mode with decreasing principal strain ratio are listed in tab. 1 for several materials listed in the table together with testing temperatures. the table indicates that the principal strain ratio at transition does not significantly depend on material and takes the value around 0.70 whereas a slightly smaller value is found in sus 304 stainless steel at 823 k. materials listed in tab. 1 range over wide types of materials, austenitic stainless steel, low alloy ductile steels, conventional cast superalloy, and directional solidified super alloys. considering that the steels and the conventional cast superalloy are an isotropic material but the directionally solidified superalloys have a strong anisotropy due to the crystallographic texture the result in the table means that texture and material anisotropy has a weak effect on the principal strain ratio at the transition. m m. sakane et alii, frattura ed integrità strutturale, 41 (2017) 16-23; doi: 10.3221/igf-esis41.03 18 figure 2: cracking modes in tension-torsion lcf of sus304 stainless steel at 923k. table 1: principal strain ratio at which crack changes propagation plane. note that the above discussion does not hold for all materials listed in the table. cracks of inconel 738lc conventional cast superalloy remain on the principal strain plane in all principal strain ratios. tab. 1 mainly summarizes the crack transition in elevated temperature lcf so that oxidation may bring some influence on cracking direction [2,3] but this paper is not discuss the oxidation effect in more detail because there are conflicting reports on the oxidation effect on cracking direction [2–4]. material anisotropy also has some influence on the cracking direction as seen in the literature [10]. cracking direction is a physical background for developing a multiaxial lcf damage model and therefore studying the relationship between cracking direction and fatigue life is meaningful. the relationship of the three materials is shown in fig.3 [7]. the ordinate of the figure is the life ratio obtained by dividing the multiaxial lcf life by the uniaxial lcf life in a test with the same von mises strain amplitude. the dashed lines indicate a factor of two band from unity value of the ordinate. as stated earlier, inconel 738lc showed principal cracking in all principal strain ratios and most of all fatigue lives fall into the factor of two band. fatigue lives of sus 304 and 1cr-1mo-1/4v steels with principal cracking also fall materials temperature, k  =3/1 ref. 1cr-1mo-1/4v 838 0.79 [3] 1cr-1mo-1/4v* 293 0.74 [3] 1cr-1mo-1/4v** 823 0.74  0.70 [4] sus 304 923 0.74 [2] sus 304 823 0.64 [5] aisi 316 673 0.74 [3] mild steel r.t. 0.74 [6] inconel 738lc 1123 n. t. [7] rene’80h ds 1173 0.70 [8] mar-m247lc ds 1173 0.70 [9] *   1.2 %, **   1.2 %, n.t. no transition (shear crack), ds directionally solidified superalloy m. sakane et alii, frattura ed integrità strutturale, 41 (2017) 16-23; doi: 10.3221/igf-esis41.03 19 into the factor of two band but those of the two steels with the shear cracking exceed the band. this result suggests that a fatigue life with shear cracking is slightly longer than that with principal cracking at the same von mises strain condition. figure 3: cracking mode and transition angle of main crack for three materials. notch and pre crack notch and precrack also have evident but complex influences on cracking direction in multiaxial lcf. sakane et al. [12] reported effects of a notch and precracks on cracking direction in torsion lcf of a sus 304 stainless steel. the geometry of the notch and precracks is shown in fig.4. the diameter of the notch is 0.6 mm and the notch was machined with a drill to penetrate a 1.5 mm wall thickness of tube specimen. two types of precracks were provided by applying high cycle fatigue cyclic loading for type i precrack with tension loading and for type ii precrack with torsion loading. the length of the precracks is 1.0 mm including the notch hole for type i and type ii precracks. 0.2 0.6 0.2 type i type ii s pe ci m en a xi s figure 4: schematic of two precrack directions. fig.5 shows cracking directions of smooth, notched and precracked specimens in torsion lcf loading. the cracking direction of the smooth specimen, fig.5 (a) [12] , is the shear direction that is commonly observed cracking direction at high strain/stress ranges. however, the cracking direction of the notched specimen with a 0.6 mm diameter is the principal directions as shown in fig.5 (b) [12]. putting the notch hole changes the cracking direction. to induce shear cracking, the specimen with shear precrack (type i crack) in fig.4 was fatigued but the cracking direction was the principal directions as shown in fig.5 (c) [12]. type ii precracked specimen also yielded the principal crack. however, notch and precrack do not always bring the principal crack. the influence of the notch may change depending on the notch size and material. the 1crmov specimen with a through hole with 0.2 mm diameter in fig.5 (d) [11] showed shear cracking as well as the smooth specimen. furthermore, the sus 304 specimen with a surface hole with 0.1 mm diameter and 0.1 mm depth yielded a short principal cracking followed by a shear cracking, fig.5 (e) [13]. the last two results, shown in fig.5 (d) and fig.5 (e), presumably indicate that the notch effect on cracking direction may change depending on the geometry of notch and material. m. sakane et alii, frattura ed integrità strutturale, 41 (2017) 16-23; doi: 10.3221/igf-esis41.03 20 specimen axis 1 mm figure 5: cracking direction in torsion tests of unnotched, notched and precracked specimens. strain range dependency of cracking direction in torsion low cycle fatigue cracking direction in torsion lcf is also influenced by strain range, shear cracking at high strain ranges and principal cracking at low stain ranges shown in fig.6 [14] as a typical case for a sus 304 stainless steel, but the mechanism of the transition of cracking direction is still an open question whereas many researchers discussed this topic. the strain ranges with shaded area are the strain ranges at which crack transits its direction. micro-cracks on the specimen fatigued until a half-life shown with the solid circles in the figure were observed in detail with a scanning electron microscope. figure 6: torsion low cycle fatigue life and cracking mode of sus 304 stainless steel. four type of cracks were observed on the specimen surface shown in fig.7 [14]. they are classified according to the propagation behavior as shown in fig.8 schematically. type 1 and type 2 cracks extended in the shear direction in some (a) unnotched specimen of sus 304 stainless steel at 923 k (δσ*=329 mpa, nf=4694) (b) notched specimen of sus 304 stainless steel at 923 k (δσ*=314 mpa, nf=1500) (c) precracked specimen of sus 304 stainless steel at 923 k (δσ*=314 mpa, nf=1320) (d) notched specimen (0.2 mm through hole) of 1crmov at 823 k (e) notched specimen (0.1 mm diameter, 0.1 mm depth) of sus 304 stainless steel at 823 k 0.2 mm specimen axis m. sakane et alii, frattura ed integrità strutturale, 41 (2017) 16-23; doi: 10.3221/igf-esis41.03 21 distance and branched into the principal directions. type 3 crack propagated in the principal directions and type 4 crack is the crack that only propagated in the shear direction. more than 400 cracks were observed on each specimen. type 1 and type 2 cracks were most frequently found and type 3 and type 4 cracks are scarcely found. this result indicates that the coalescence of micro cracks is not a major mechanism of the shear cracking at high strain ranges and of the principal cracking at low strain ranges because the number of shear cracks should be dominant at high strain ranges and that of principal cracks should be dominant at low strain ranges if the coalescence of cracks is a major mechanism of failure. (a) δ=1.73%, type 1 (b) δ=3.46%, type 2 (c) δ=1.73%, type 3 (d) δ=3.46%, type 4 a xi al di re ct io n figure 7: four crack type in torsion low cycle fatigue of sus 304 stainless steel. figure 8: schematic of four crack types in torsion low cycle fatigue of sus 304. shear crack lengths before branching to principal cracks for type 1 and type 2 cracks (critical crack length) were measured and the average values of the critical crack lengths (average crack length) against shear strain ranges are plotted in fig.9 [14]. the averaged crack length was obtained by observing 1956 cracks within a gage length of the intermitted specimens. the figure clearly indicates that the average crack length has constant values at the low and high low strain ranges. the transition of the average crack length is found in the shear strain range between 2.0% and 2.5%. this transition strain range well corresponds with the transition strain range of main cracks shown in fig.6. the correspondence of the transition strain range implies that one of the mechanisms of the crack direction change results from that both a macro shear crack and a macro principal crack microscopically propagate zigzag in the respective directions but the propagation length in shear direction is longer at high strain ranges and that in the principal directions longer at low strain ranges. makabe et al. [15] made a similar discussion but on the notched specimen. they reported that the critical crack length before branching increased momentously with shear strain range. to investigate the reason of the two propagation directions, aspect ratios of a shear crack and a principal crack were measured by continuing stepwise polishing off the material from the specimen surface and measuring the removed depth and crack length on a respective new surface. the observations are shown in fig.10 [14]. the figure clearly indicates that the shear crack has a small aspect ratio while the principal crack a large aspect ratio, the shear crack mainly propagating near the specimen surface but the principal crack extending deep into the specimen. m. sakane et alii, frattura ed integrità strutturale, 41 (2017) 16-23; doi: 10.3221/igf-esis41.03 22 figure 9: variation of average crack length with strain range in torsion low cycle fatigue of sus 394 stainless steel. figure 10: aspect ratio of principal and shear cracks in torsion low cycle fatigue of sus 304 stainless steel. considering that a crack propagates in a direction to release strain energy most, elastic-plastic strain energy release by a crack formation was analyzed by a finite element method for three models. the three models have a same cracked area but the cracking direction is changed. two models have a deep semi-circular crack, 2 mm surface length and 1 mm depth, one directing to principal orientation (model a) and the other to shear orientation (model b). the third model has a shear shallow crack with 5 mm surface length and 0.4 mm depth directing to shear direction (model c). the energy release of model c is larger than that of model b at high strain ranges but the latter showed larger energy release than the former at low strain ranges. the results of the energy release well accounts for the transition of crack direction depending on strain range from an energy release viewpoint. the graphical representation of this discussion is not presented from the shortage of the space of the paper. the cracking direction in torsion lcf depends on material and the discussion on this topic is made in the literatures [16,17] in detail. m. sakane et alii, frattura ed integrità strutturale, 41 (2017) 16-23; doi: 10.3221/igf-esis41.03 23 conclusions (1) strain multiaxiality dependence of cracking direction in tension-torsion multiaxial low cycle fatigue is discussed. the transition of cracking direction occurred at the principal strain range of about 0.70 for low alloy steels of sus 304, sus 316 and crmov and directionally solidified superalloy of mar-m247 and rene’80. only conventional cast superalloy of inconel 738 showed shear cracking in all principal strain ratios. (2) the specimen with the principal cracking showed slightly smaller low cycle fatigue life than that with the shear cracking fatigued at the same von mises strain amplitude. (3) notches and precracks changed the cracking direction in torsion low cycle fatigue. the specimen with large through hole and through precrack yielded principal cracks in the testing condition that the smooth specimen yielded shear crack. however, the specimen with a small through hole and a surface hole had a shear crack. (4) the strain ranges at which macro cracks transit the direction between the shear direction and the principal direction corresponded to the transition strain range at which the average crack length increase. (5) the aspect ratio of the shear crack was smaller compared with the principal crack. finite element analysis revealed that the strain energy release of the shear crack was larger at high strain ranges but that of the principal crack was larger at low strain ranges. references [1] forsyth, p.j.e., a two stage process of fatigue crack growth, proc crack propag. symp cranfield, (1961) 74–91. [2] sakane, m., ohnami, m., sawada, m., fracture modes and low cycle biaxial fatigue life at elevated temperature, j. eng. mater. technol., 109 (1987) 236–243. [3] brown, m.w., miller, k.j., initiation and growth of cracks in biaxial fatigue, fatigue fract. eng. mater. struct., 1 (1979), 231–246. [4] sakane, m., ohnami, m., sawada, m., biaxial low cycle fatigue of unaged and aged 1cr-1mo-1/4v steels at elevated temperature, j. eng. mater. technol., 113 (1991) 244–253. [5] nitta, a., ogata, t., kuwabara, k., relationship between fracture mode and fatigue life under biaxial loading at 550c in sus 304 stainless steel, j. soc. mater. science, japan, 37 (1988) 334–339. [6] cox, h.l., field, j.e., the initiation and propagation of fatigue cracks in mild steel pieces of square section, aeronaut. q., 4 (1954) 1–18. [7] isobe, n., multiaxial creep-fatigue life evaluation for inconel 738lc nickel base super alloy, master theses ritsumeikan univ., 1992. [8] hirose, t., multiaxial creep-fatigue life evaluation for rene80 directionally solidified nickel base super alloy, master theses ritsumeikan univ., 1993. [9] shirafuji, n., shimomizuki, k., sakane, m., ohnami, m., tension-torsion multiaxial low cycle fatigue of marm247lc directionally solidified superalloy at elevated temperature, j. eng. mater. technol., 120 (1998) 57–63. [10] ohji, k., ogura, k., harada, s., ohyama, s., torsional fatigue behavior of anisotropic rolled steel plate in middle and high cycle fatigue ranges, j. soc. mater. scinece, japan, 25 (1976) 836–841. [11] sakurai, s., fukuda, y., isobe, n., kaneko, r., micro-crack growth and life prediction of a 1crmov steel under axialtorsional low cycle fatigue at 550c, fatigue fract. eng. mater. struct., 17 (1994) 1271–1279. [12] sakane, m., ohnami, m., hamada, n., biaxial low cycle fatigue for notched, cracked, and smooth specimens at high temperatures, j. eng. mater. technol., 110 (1988) 48–54. [13] ogata, t., nitta, a., blass, j.j., propagation behavior of small cracks in 304 stainless steel under biaxial low-cycle fatigue at elevated temperature, in: d.l. mcdowell, j.r. ellis (eds), advances in multiaxial fatigue, astm stp 1191, (1993) 313–325. [14] sawada, m., bannai, k., sakane, m., crack propagation direction of type 304 stainless steel in torsion low cycle fatigue, j. soc. mater. science, japan, 54 (2005) 615–621. [15] makabe, c., socie, d.f., crack growth mechanism in precracked torsional fatigue specimens, fatigue fract. eng. mater. struct., 24 (2001) 607–615. [16] bannantine, j, socie, df., observations of cracking behavior in tension and torsion low cycle fatigue, in: h.d. solomon, g.r. halford, j.r. kaisand, b.n. leis (eds), low cycle fatigue, astm stp 942 (1988) 899–921. [17] hiyoshi, n., sakane, m., nose, h., crack propagation direction under reversed torsion test for sus304 stainless/scm435 steels and al 1050 alloy, trans. japan soc. mech. eng. a, 68 (2002) 81–87. << /ascii85encodepages false /allowtransparency false /autopositionepsfiles true /autorotatepages /none /binding /left /calgrayprofile (dot gain 20%) /calrgbprofile (srgb iec61966-2.1) /calcmykprofile (u.s. web coated \050swop\051 v2) /srgbprofile (srgb iec61966-2.1) /cannotembedfontpolicy /error /compatibilitylevel 1.4 /compressobjects /tags /compresspages true /convertimagestoindexed true /passthroughjpegimages true /createjobticket false /defaultrenderingintent /default /detectblends true /detectcurves 0.0000 /colorconversionstrategy /cmyk /dothumbnails false /embedallfonts true /embedopentype false /parseiccprofilesincomments true /embedjoboptions true /dscreportinglevel 0 /emitdscwarnings false /endpage -1 /imagememory 1048576 /lockdistillerparams false /maxsubsetpct 100 /optimize true 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/pdfxoutputintentprofileselector /documentcmyk /preserveediting true /untaggedcmykhandling /leaveuntagged /untaggedrgbhandling /usedocumentprofile /usedocumentbleed false >> ] >> setdistillerparams << /hwresolution [2400 2400] /pagesize [612.000 792.000] >> setpagedevice microsoft word numero_42_art_21.docx m. peron et alii, frattura ed integrità strutturale, 42 (2017) 196-204; doi: 10.3221/igf-esis.42.21 196 notch stress intensity factors under mixed mode loadings: an overview of recent advanced methods for rapid calculation m. peron, s.m.j. razavi, f. berto, j. torgersen department of mechanical and industrial engineering, norwegian university of science and technology (ntnu), richard birkelands vei 2b, 7491, trondheim, norway. mirco.peron@ntnu.no, javad.razavi@ntnu.no, filippo.berto@ntnu.no, jan.torgersen@ntnu.no abstract. recently some methods for the rapid calculation of notch stress intensity factors (nsifs) have been developed and three of them are compared in this work. first, the criteria proposed by lazzarin et al. and treifi et al. have been reviewed. the former is based on the calculation of the mean value of sed on two different control volume (characterized by two different radius values) centred at the stress singularity point, whereas the latter takes advantage of the strain energy density averaged within two control volumes (semi-circular sector) centred at the notch tip. then, a new method based on the evaluation of the total and deviatoric sed averaged in a single control volume has been proposed. finally, plate specimens weakened by different notch geometries have been subjected to the application of the above mentioned methods and the obtained values of the nsifs have been compared with those derived according to gross and mendelson. keywords. nsifs; sed; control volume; mixed mode; fe analysis. citation: peron, m., razavi, s.m.j., berto, f., torgersen, j., notch stress intensity factors under mixed mode loadings: an overview of recent advanced methods for rapid calculation, frattura ed integrità strutturale, 42 (2017) 196-204. received: 02.07.2017 accepted: 29.07.2017 published: 01.10.2017 copyright: © 2017 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. introduction ecause of the detrimental effects played by notches on mechanical behavior [1-3] , several criteria have been proposed in literature for the assessment of material strength of components [4,5]. concerning brittle and quasibrittle materials, notch stress intensity factor (nsif) has been reported to be an effective criterion for the evaluation of static strength [6], and also for high cycle fatigue strength of structural materials weakened by sharp vnotches [7] and of welded joints [8,9]. gross and mendelson [10] expressed mode i and mode ii nsifs, which define the intensity of the asymptotic stress field ahead of the sharp v-notch tip. (1) (2)    111 002 limrk r               212 002 lim rrk r            b m. peron et alii, frattura ed integrità strutturale, 42 (2017) 196-204; doi: 10.3221/igf-esis.42.21 197 where r and θ is the radial and angular coordinate of a polar coordinate system centred at the notch tip (fig. 1), σθθ and τrθ are the stress components according to the coordinate system and the mode i and mode ii first eigenvalues in william’s equations [11] are denoted respectively as λ1 and λ2. the main drawback exploiting nsif criterion for the calculation of (1) and (2) is that very refined meshes are needed using finite element (fe) analysis, and this requirement holds also for cracked component [12-17]. figure 1: polar coordinate system centred at the notch tip. however, an approach based on the determination of the total elastic strain energy density (sed) averaged over a control volume of radius r0 surrounding the points of stress singularity has been developed [18] and it has broadly gained interest in the last years, since it allows to exploit course meshes overcoming the main drawback of nsif criterion both for static static [19-24] and fatigue [1, 25-27] strength evaluation. moreover, some approximate methods for the rapid calculation of the nsifs, based on the averaged strain energy density, are available in literature and, referring to mixed mode loading, they required the solution of a system of two equations in two unknowns (k1 and k2). in this work, two of these methods, one proposed by lazzarin et al. [28] and the other by treifi and oyadiji [29], have been reviewed, and, afterwards, a new method based on the evaluation of the total and deviatoric sed averaged in a single control volume has been proposed, allowing also in this case the determination of the sifs, ki and kii, of cracks under mixed mode loading by means of two independent equations, one linked to the total sed and the other to the deviatoric one. approximate methods lazzarin et al. approach he first method has been proposed by lazzarin et al. [28] and it is based on the evaluation of the averaged sed on two different control volumes (circular sectors) centred at the notch tip and characterized by the radii ra and rb (fig. 2a). known the sed values ( aw and bw ), by means of a fe analysis, and defined the control radii (ra and rb), it is possible to obtain a system of two equations in two unknowns (k1 and k2):         1 2 1 2 2 2 2 21 1 2 2 , 1 22 1 2 1 1 2 2 2 2 21 1 2 2 , 1 22 1 2 1 1 2 1 2 2 2 1 2 2 2 a fe a a a a b fe b b b b i k i k w c k d k e r r i k i k w c k d k e r r                                          (3) where is the young’s modulus of the material while i1 and i2 are the integrals of the angular stress functions [18], which depend on the notch opening angle, 2α = 2π 2γ, and the poisson's ratio ν. this method cannot be applied to a crack subjected to mixed mode loading, since an indeterminate system of equations would be obtained. solving the system of equations, the values of the nsifs can be determined: t m. peron et alii, frattura ed integrità strutturale, 42 (2017) 196-204; doi: 10.3221/igf-esis.42.21 198 (4) (5) figure 2: control volumes in the lazzarin et al. approach (a) and in the treifi et al. approach (b). treifi et al. approach the second method has been proposed by treifi et al. [29] and it is based on the evaluation of the averaged sed on two different control volumes (semi-circular sectors with a central angle equal to γ) centred at the notch tip and characterized by a radius r (fig. 2b). known the sed values ( aw and bw ) by means of a fe analysis, and defined the control radius (r), it is possible to obtain a system of two equations in two unknowns (k1 and k2):         1 21 2 1 21 2 2 2 1, 2, 12, 2 21 2 1 2 , 1 2 1 222 1 2 1 1 2 1 2 2 2 1, 2, 12, 2 21 2 1 2 , 1 2 1 222 1 2 1 1 2 1 2 21 2 ( ) 21 2 ( ) s s s a fe s s s b fe i i ik k k k w mk nk qk k e rr r i i ik k k k w mk nk qk k e rr r                                                      (6) where i1,s, i2,s and i12,s are the integrals of the angular stress functions [29], which depend on the notch opening angle, 2α, the angle defined by the semi-circular sector, γ, and the poisson's ratio ν. in this case also the contribution of the mixed term (k1.k2 is present because the integration for the strain energy evaluation is not performed on a control volume symmetrical with respect to the notch bisector line (fig. 2b). due to the presence of the mixed term it is possible to decouple the contributions of the loading modes, obtaining a solution of the system even in the crack case. solving the system of equations, the values of the nsifs can be determined:       2 2 , , , , , , 2 1 4 4 a fe b fe a fe b fe a fe b fe mn w w w w w w q k m       (7) , , 2 12 a fe b few wk qk   (8) new approach based on the deviatoric sed in the present contribution a new method is proposed. it is based on the evaluation of the total and deviatoric sed averaged in a single control volume (circular sector) centred at the notch tip and characterized by a radius r (fig. 3a). two independent equations can be obtained: one linked to the total sed and the other to the deviatoric one. in this way it is possible to obtain a solution of the system even in the case of a crack. , , 1 a b fe b a fe a b b a d w d w k d c d c    2 , 1 2 a fe a a w c k k d   m. peron et alii, frattura ed integrità strutturale, 42 (2017) 196-204; doi: 10.3221/igf-esis.42.21 199 as previously, knowing the sed values ( and ), by means of a fe analysis, and defining the control radius (r), it is possible to obtain a system of two equations in two unknowns (k1 and k2): (9) where i1,dev and i2,dev are the integrals of the angular stress functions related to the deviatoric strain energy density [18], which depend on the notch opening angle, 2α, and the poisson's ratio ν. solving the system of equations, the values of the nsifs can be determined: (10) (11) figure 3: control volumes in the new approach (a) and in the modified version of the new approach (b). as discussed earlier, the total sed can be derived directly from nodal displacements, so that also coarse meshes are able to give sufficiently accurate values for it. on the other hand, the calculation of the deviatoric sed by means of a fe code is based on the von mises equivalent stress averaged within the element [18]. this quantity is more sensitive to the refinement level of the adopted mesh, so the new proposed method could not be mesh-insensitive. with the aim to improve the results obtained from the application of the new method (based on the deviatoric sed) in the case of coarse meshes, a modified version is proposed. the approach is similar to the previous but it is applied to a control volume consisting of a circular ring (fig. 3b). being the calculation of the deviatoric sed by means of a fe code based on the von mises equivalent stress averaged within the element, that is a parameter sensitive to the refinement level of the adopted mesh, it could be useful to exclude from the calculation the area characterized by the highest stress gradient (i.e. the region close to the notch tip) in the case of coarse meshes. the control volume results to be constituted by a circular ring characterized by an outer radius ra and by an inner radius rb (fig. 3b). as before, knowing the sed values (w and devw ), by means of a fe analysis, and defining the control radii (ra and rb), it is possible to obtain a system of two equations in two unknowns (k1 and k2):     1 1 2 2 1 1 2 2 2 2 1 1 2 2 2 2 2 22 2 1 2 2 2 1, 1 2, 2 , 2 2 2 22 2 1 2 1 1 1 1 1 2 22 1 1 1 1 1 2 23 fe a b a ba b dev dev dev fe a b a ba b i k i k w r r r re r r i k i k w r r r re r r                                                                   (12) solving this system of equations, as already shown in the previous cases, the values of the nsifs can be determined. w devw         1 2 1 2 2 2 2 21 1 2 2 1 22 1 2 1 1 2 2 2 1, 2, 2 21 2 , 1 22 1 2 1 1 2 1 2 2 2 1 3 2 2 fe dev dev dev fe dev dev i k i k w sk tk e r r i ik k w s k t k e r r                                           , 1 dev fe dev fe dev dev tw t w k ts t s    2 , 1 2 dev fe dev dev w s k k t   m. peron et alii, frattura ed integrità strutturale, 42 (2017) 196-204; doi: 10.3221/igf-esis.42.21 200 results he methods described above have been applied to five different geometries of notched plates subjected to mixed mode i+ii loading. for each geometry k1 and k2 have been first calculated according to gross and mendelson (eqs. 1 and 2), by means of fe analyses adopting very refined meshes in the close neighbourhood of the notch tip (size of the smallest element of the order of 10-5 mm). afterwards the approximate methods have been applied, taking into consideration three different values of the control radius r0 (0.1, 0.01 and 0.001 mm) and by using coarse and refined fe meshes. the mesh has been performed by means of 8-nodes elements (plane 183), using the fe code ansys® 14.5. in the fe analyses a poisson’s ratio ν equal to 0.3 and a young’s modulus e equal to 206 gpa have been adopted. in the summary tables the normalized nsifs are reported, according to the definition: , 1 i i i normalized k k a     (13) case studies: geometries and results the geometries taken into consideration (fig. 4) consist in notched finite or infinite plates subjected to mixed mode i+ii loading. the geometry of the finite plates is characterized by equal width and height, 2w = h = 10 mm, while plates of infinite extension are characterized by 2w = h = 10 mm. diamond shape notches (fig. 4a) are characterized by a projected notch depth 2a = 2 mm and a notch inclination angle φ = 45o. two different notch opening angle 2 have been analysed: 45° and 30°. the obtained results and the comparison between the different approaches are reported in table 1 and table 2. the square hole (fig. 4b) is characterized by a projected notch depth 2a = 2 mm and a notch opening angle 2α = 90o. the obtained results and the comparison between the different approaches are reported in table 3. figure 4: case studied for the application of the method: diamond shape notch (a), square hole (b), central tilted crack in a finite plate (c) and central tilted crack in a plate of infinite extension (d). discussion abs. 1-5 show the results obtained from different geometries of notched plates subjected to mixed mode i+ii loading, by adopting coarse and refined meshes for the application of the approximate methods. all the considered approaches allow to obtain very good approximations when refined meshes are adopted in the fe analyses, being the deviations, with respect to the values calculated according to gross and mendelson [10], lower than 1% in most of the cases. the obtained results become more interesting when coarse meshes, which require shorter calculation time, are adopted in the fe analyses. it can be observed that the approach of lazzarin et al. [28] enables to obtain very good approximations, being the deviations lower than 1% in most of the cases analyzed in the present contribution. it should be noted that this method has not been applied to cracks subjected to mixed mode loading (tables 4, 5), since an indeterminate system of equations would be obtained. the percentage error increases to about 3-6% in the case of treifi et al. approach [29], which reaches a maximum percentage deviation of 12-18% in the case of tilted cracks (table 5). t t m. peron et alii, frattura ed integrità strutturale, 42 (2017) 196-204; doi: 10.3221/igf-esis.42.21 201 the new proposed method, based on the evaluation of the total and deviatoric sed, allows to obtain a percentage error close to that observed in the case of treifi et al. [29]. the deviation still remains greater than that observed in the case of lazzarin et al. [28], because of the dependence of the deviatoric sed on the mesh size. this problem is overcome by the modified version of the new method that, through a control volume consisting of a circular ring, enables to exclude the region characterized by the highest stress gradient making the method less sensitive to the refinement level of the adopted mesh. the new method, particularly the modified version, provides very good approximations and a greater applicability than the approach of lazzarin et al. [28] and [30], so it could be useful for rapid calculation of the nsifs. coarse mesh (64 finite elements) refined mesh (3128 finite elements) r0 [mm] method k1 k2 δk1 (%) δk2 (%) k1 k2 δk1 (%) δk2 (%) gross and mendelson 0.656 0.911 0.1 and 0.075 lazzarin et al. 0.650 0.919 -0.91 0.88 0.650 0.919 -0.91 0.88 0.1 treifi et al. 0.694 0.878 5.79 -3.62 0.693 0.878 5.64 -3.62 0.1 new method 0.681 0.891 3.81 -2.20 0.666 0.905 1.52 -0.66 0.1 new modified method 0.664 0.908 1.22 -0.33 0.01 and 0.0075 lazzarin et al. 0.657 0.909 0.15 -0.22 0.655 0.912 -0.15 0.11 0.01 treifi et al. 0.665 0.895 1.37 -1.76 0.663 0.897 1.07 -1.54 0.01 new method 0.671 0.883 2.29 -3.07 0.657 0.909 0.15 -0.22 0.01 new modified method 0.656 0.911 0.00 0.00 0.001 and 0.00075 lazzarin et al. 0.659 0.901 0.46 -1.10 0.656 0.909 0.00 -0.22 0.001 treifi et al. 0.658 0.907 0.31 -0.44 0.657 0.908 0.15 -0.33 0.001 new method 0.671 0.856 2.29 -6.04 0.658 0.901 0.30 -1.10 0.001 new modified method 0.658 0.905 0.30 -0.66 table 1: comparison between approximate methods for nsifs evaluation of diamond-shaped notch (2α = 45°). coarse mesh (64 finite elements) refined mesh (3063 finite elements) r0 [mm] method k1 k2 δk1 (%) δk2 (%) k1 k2 δk1 (%) δk2 (%) gross and mendelson 0.654 0.813 0.1 and 0.075 lazzarin et al. 0.648 0.818 -0.92 0.62 0.650 0.817 -0.61 0.49 0.1 treifi et al. 0.670 0.803 2.45 -1.23 0.681 0.796 4.13 -2.09 0.1 new method 0.686 0.792 4.89 -2.58 0.663 0.808 1.38 -0.62 0.1 new modified method 0.660 0.810 0.92 -0.37 0.01 and 0.0075 lazzarin et al. 0.657 0.811 0.46 -0.25 0.655 0.813 0.15 0.00 0.01 treifi et al. 0.621 0.847 -5.05 4.18 0.638 0.829 -2.45 1.97 0.01 new method 0.677 0.789 3.52 -2.95 0.657 0.811 0.46 -0.25 0.01 new modified method 0.656 0.812 0.31 -0.12 0.001 and 0.00075 lazzarin et al. 0.660 0.807 0.92 -0.74 0.656 0.811 0.31 -0.25 0.001 treifi et al. 0.673 0.784 2.91 -3.57 0.660 0.805 0.92 -0.98 0.001 new method 0.675 0.779 3.21 -4.18 0.659 0.807 0.76 -0.74 0.001 new modified method 0.658 0.809 0.31 -0.49 table 2: comparison between approximate methods for nsifs evaluation of diamond-shaped notch (2α = 30°). m. peron et alii, frattura ed integrità strutturale, 42 (2017) 196-204; doi: 10.3221/igf-esis.42.21 202 coarse mesh (48 finite elements) refined mesh (2206 finite elements) r0 [mm] method k1 k2 δk1 (%) δk2 (%) k1 k2 δk1 (%) δk2 (%) gross and mendelson 0.618 1.209 0.1 and 0.075 lazzarin et al. 0.613 1.229 -0.81 1.65 0.613 1.229 -0.81 1.65 0.1 treifi et al. 0.604 1.249 -2.27 3.31 0.632 1.184 2.27 -2.07 0.1 new method 0.635 1.175 2.75 -2.81 0.625 1.200 1.13 -0.74 0.1 new modified method 0.629 1.196 1.78 -1.08 0.01 and 0.0075 lazzarin et al. 0.617 1.205 -0.16 -0.33 0.617 1.210 -0.16 0.08 0.01 treifi et al. 0.617 1.211 -0.16 0.17 0.618 1.200 0.00 -0.74 0.01 new method 0.601 1.394 -2.75 15.30 0.617 1.212 -0.16 0.25 0.01 new modified method 0.618 1.192 0.00 -1.41 0.001 and 0.00075 lazzarin et al. 0.618 1.166 0.00 -3.56 0.618 1.182 0.00 -2.23 0.001 treifi et al. 0.618 1.213 0.00 0.33 0.617 1.202 -0.16 -0.58 0.001 new method 0.627 1.167 1.46 -3.54 0.618 1.178 0.00 -2.56 0.001 new modified method 0.619 1.130 0.16 -6.53 table 3: comparison between approximate methods for nsifs evaluation of diamond-shaped notch (2α = 90°). coarse mesh (64 finite elements) refined mesh (3395 finite elements) r0 [mm] method k1 k2 δk1 (%) δk2 (%) k1 k2 δk1 (%) δk2 (%) gross and mendelson 0.655 0.638 0.1 treifi et al. 0.636 0.642 -2.90 0.63 0.660 0.637 0.76 -0.16 0.1 new method 0.697 0.620 6.41 -2.82 0.639 0.645 -2.44 1.10 0.1 new modified method 0.639 0.645 -2.44 1.10 0.01 treifi et al. 0.613 0.654 -6.41 2.51 0.635 0.647 -3.05 1.41 0.01 new method 0.708 0.616 8.09 -3.45 0.653 0.640 -0.31 0.31 0.01 new modified method 0.653 0.640 -0.31 0.31 0.001 treifi et al. 0.624 0.651 -4.73 2.04 0.644 0.644 -1.68 0.94 0.001 new method 0.712 0.615 8.70 -3.61 0.662 0.636 1.07 -0.31 0.001 new modified method 0.657 0.639 0.31 0.16 table 4: comparison between approximate methods for nsifs evaluation of central tilted crack (2α = 0°) in a plate of finite extension. conclusions n the present contribution three methods for the rapid calculation of the nsifs, based on the averaged strain energy density, are compared. the first method, proposed by lazzarin et al., is based on the calculation of the sed averaged in two different control volumes centred at the notch tip. this approach cannot be applied to notch with zero opening angle (cracks) subjected to mixed mode loading. the second method, presented by treifi et al., overcomes this problem taking advantage of the strain energy density averaged within two control volumes (semi-circular sector) centred at the notch tip. then a new method based on the evaluation of the total and deviatoric strain energy density has been proposed. i m. peron et alii, frattura ed integrità strutturale, 42 (2017) 196-204; doi: 10.3221/igf-esis.42.21 203 coarse mesh (64 finite elements) refined mesh (3395 finite elements) r0 [mm] method k1 k2 δk1 (%) δk2 (%) k1 k2 δk1 (%) δk2 (%) gross and mendelson 0.595 0.595 0.1 treifi et al. 0.667 0.564 12.10 -5.21 0.703 0.547 18.15 -8.07 0.1 new method 0.649 0.572 9.08 -3.87 0.596 0.595 0.17 0.00 0.1 new modified method 0.598 0.594 0.50 -0.17 0.01 treifi et al. 0.582 0.599 -2.18 0.67 0.603 0.592 1.34 -0.50 0.01 new method 0.649 0.571 9.08 -4.03 0.597 0.594 0.34 -0.17 0.01 new modified method 0.598 0.594 0.50 -0.17 0.001 treifi et al. 0.575 0.602 -3.36 1.18 0.593 0.595 -0.34 0.00 0.001 new method 0.649 0.571 9.08 -4.03 0.612 0.588 2.86 -1.18 0.001 new modified method 0.598 0.594 0.50 -0.17 table 5: comparison between approximate methods for nsifs evaluation of central tilted crack (2α = 0°) in a plate of infinite extension. the described methods have been applied to plates subjected to mixed mode i+ii loading and weakened by different vnotch geometries. the values of the nsifs derived according to gross and mendelson have been compared with those obtained by means of the approximate methods taking into consideration three different values of the control radius r0 (0.1, 0.01 and 0.001 mm) and by using coarse and refined fe meshes. the comparison of the results shown that the new proposed method provides the best combination between the degree of approximation and the level of applicability, so it could be useful for rapid calculation of the nsifs. central tilted cracks in a plate of finite (fig. 4c) or infinite (fig. 4d) extension are characterized by a projected crack length 2a = 2 mm and a crack inclination angle φ = 45o. the obtained results and the comparison between the different approaches are reported in tables 4, 5. it is worth noting that the case of the infinite plate has been modelled as a finite plate characterized by width and height two orders of magnitude greater than the crack length. references [1] lazzarin, p., comportamento a fatica dei giunti saldati in funzione della densità di energia di deformazione locale: influenza dei campi di tensione singolari e non singolari, frattura ed integrita strutturale, 9 (2009) 13-26. [2] maragoni, l., carraro, p. a., peron, m., quaresimin, m., fatigue behaviour of glass/epoxy laminates in the presence of voids, int. j. fatigue, 95 (2017) 18–28. [3] brotzu, a., felli, f., pilone, d., effects of the manufacturing process on fracture behaviour of cast tial intermetallic alloys, frattura ed integrita strutturale, 27 (2013) 66-73. [4] askes, h., susmel, l., gradient enriched linear-elastic crack tip stresses to estimate the static strength of cracked engineering ceramics, frattura ed integrita strutturale, 25 (2013) 87-93. [5] susmel, l., on the overall accuracy of the modified wöhler curve method in estimating high-cycle multiaxial fatigue strength, frattura ed integrita strutturale, 16 (2011) 5-17, [6] seweryn, a., brittle fracture criterion for structures with sharp notches, eng. fract. mech., 47 (1994) 673–681. [7] boukharouba, t., tamine, t., niu, l., chehimi, c., pluvinage, g., the use of notch stress intensity factor as a fatigue crack initiation parameter, eng. fract. mech., 52 (1995) 503–512. [8] lazzarin, p., tovo, r., a notch intensity factor approach to the stress analysis of welds, fatigue fract. eng. mater. struct., 21 (1998) 1089–1103. [9] atzori, b., meneghetti, g., fatigue strength of fillet welded structural steels: finite elements, strain gauges and reality, int. j. fatigue, 23 (2001) 713–721. m. peron et alii, frattura ed integrità strutturale, 42 (2017) 196-204; doi: 10.3221/igf-esis.42.21 204 [10] gross, b., mendelson, a., plane elastostatic analysis of v-notched plates, int. j. fract. mech., 8 (1972) 267–276. [11] williams, m. l., stress singularities resulting from various boundary conditions in angular corners on plates in extension, j. appl. mech., 19 (1952) 526–528. [12] lazzarin, p., campagnolo a., berto, f., a comparison among some recent energyand stress-based criteria for the fracture assessment of sharp v-notched components under mode i loading, theor. appl. fract. mech., 71 (2014) 21– 30. [13] ayatollahi, m.r., razavi, s.m.j., rashidi moghaddam, m., berto, f., mode i fracture analysis of polymethylmetacrylate using modified energy—based models, phys. mesomec., 18 (2015) 53-62. [14] ayatollahi, m.r., rashidi moghaddam, m., razavi, s.m.j., berto, f., geometry effects on fracture trajectory of pmma samples under pure mode-i loading. eng. fract. mech., 163 (2016) 449–461. [15] ayatollahi, m.r., razavi, s.m.j., sommitsch, c., moser, c., fatigue life extension by crack repair using double stophole technique, mater. sci. forum, 879 (2017) 3-8. [16] razavi, s.m.j., ayatollahi, m.r., sommitsch, c., moser, c., retardation of fatigue crack growth in high strength steel s690 using a modified stop-hole technique, eng. fract. mech., 169 (2017) 226–237. [17] rashidi moghaddam, m., ayatollahi, m.r., razavi, s.m.j., berto, f., mode ii brittle fracture assessment using an energy based criterion, phys. mesomec. (in press). [18] lazzarin, p., zambardi, r., a finite-volume-energy based approach to predict the static and fatigue behavior of components with sharp v-shaped notches, int. j. fract., 112 (2001) 275–298. [19] berto, f., lazzarin, p., recent developments in brittle and quasi-brittle failure assessment of engineering materials by means of local approaches, mater. sci. eng. r., 75 (2014) 1–48. [20] lazzarin, p., campagnolo, a., berto, f., a comparison among some recent energyand stress-based criteria for the fracture assessment of sharp v-notched components under mode i loading, theor. appl. fract. mech., 71 (2014) 21– 30. [21] torabi, a. r., campagnolo, a., berto, f., local strain energy density to predict mode ii brittle fracture in brazilian disk specimens weakened by v-notches with end holes, mater. des., 69 (2015) 22–29. [22] torabi, a. r., campagnolo, a., berto, f., experimental and theoretical investigation of brittle fracture in key-hole notches under mixed mode i/ii loading, acta mech. 226, (2015) 2313–2322. [23] berto, f., ayatollahi, m. r., fracture assessment of brazilian disc specimens weakened by blunt v-notches under mixed mode loading by means of local energy, mater. des., 32 (2011) 2858–2869. [24] berto, f., barati, e., fracture assessment of u-notches under three point bending by means of local energy density, mater. des., 32 (2011) 822–830. [25] livieri, p., lazzarin, p., fatigue strength of steel and aluminium welded joints based on generalised stress intensity factors and local strain energy values, int. j. fract., 133 (2005) 247–276. [26] berto, f., campagnolo, a., lazzarin, p., fatigue strength of severely notched specimens made of ti-6al-4v under multiaxial loading, fatigue fract. eng. mater. struct., 38 (2015) 503–517. [27] berto, f., croccolo, d., cuppini, r., fatigue strength of a fork-pin equivalent coupling in terms of the local strain energy density, mater. des., 29 (2008) 1780–1792. [28] lazzarin, p., berto, f., zappalorto, m., rapid calculations of notch stress intensity factors based on averaged strain energy density from coarse meshes: theoretical basis and applications, int. j. fatigue, 32 (2010) 1559–1567. [29] treifi, m., oyadiji, s. o., strain energy approach to compute stress intensity factors for isotropic homogeneous and bi-material v-notches, int. j. solids struct., 50 (2013) 2196–2212. [30] gallo, p., berto, f., glinka, g generalized approach to estimation of strains and stresses at blunt v-notches under non-localized creep, fatigue fract. eng. mater. struct, 39 (2016) 292-306. << /ascii85encodepages false /allowtransparency false /autopositionepsfiles true /autorotatepages /none /binding /left /calgrayprofile (dot gain 20%) /calrgbprofile (srgb iec61966-2.1) /calcmykprofile (u.s. web coated \050swop\051 v2) /srgbprofile (srgb iec61966-2.1) /cannotembedfontpolicy /error /compatibilitylevel 1.4 /compressobjects /tags /compresspages true /convertimagestoindexed true /passthroughjpegimages true /createjobticket false /defaultrenderingintent /default /detectblends true /detectcurves 0.0000 /colorconversionstrategy /cmyk /dothumbnails false /embedallfonts true /embedopentype false /parseiccprofilesincomments true /embedjoboptions true /dscreportinglevel 0 /emitdscwarnings false /endpage -1 /imagememory 1048576 /lockdistillerparams false /maxsubsetpct 100 /optimize true 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can be opened with acrobat and adobe reader 5.0 and later.) >> /namespace [ (adobe) (common) (1.0) ] /othernamespaces [ << /asreaderspreads false /cropimagestoframes true /errorcontrol /warnandcontinue /flattenerignorespreadoverrides false /includeguidesgrids false /includenonprinting false /includeslug false /namespace [ (adobe) (indesign) (4.0) ] /omitplacedbitmaps false /omitplacedeps false /omitplacedpdf false /simulateoverprint /legacy >> << /addbleedmarks false /addcolorbars false /addcropmarks false /addpageinfo false /addregmarks false /convertcolors /converttocmyk /destinationprofilename () /destinationprofileselector /documentcmyk /downsample16bitimages true /flattenerpreset << /presetselector /mediumresolution >> /formelements false /generatestructure false /includebookmarks false /includehyperlinks false /includeinteractive false /includelayers false /includeprofiles false /multimediahandling /useobjectsettings /namespace [ (adobe) (creativesuite) (2.0) ] /pdfxoutputintentprofileselector /documentcmyk /preserveediting true /untaggedcmykhandling /leaveuntagged /untaggedrgbhandling /usedocumentprofile /usedocumentbleed false >> ] >> setdistillerparams << /hwresolution [2400 2400] /pagesize [612.000 792.000] >> setpagedevice microsoft word numero_41_art_51.docx ch. f. markides et alii, frattura ed integrità strutturale, 41 (2017) 396-411; doi: 10.3221/igf-esis.41.51 396 parametric study of the deformation of transversely isotropic discs under diametral compression christos f. markides, stavros k. kourkoulis national technical university of athens, school of applied mathematical and physical sciences, department of mechanics, 5 heroes of polytechnion avenue, theocaris bld., zografou campus, 157 73 athens, greece stakkour@central.ntua.gr abstract. the displacement field in a circular disc made of a transversely isotropic material is explored in a parametric manner. the disc is assumed to be loaded by a parabolic distribution of compressive radial stresses along two finite arcs of its periphery in the absence of any tangential (frictional) stresses. advantage is here taken of a recently introduced closed-form analytic solution for the displacement field developed in an orthotropic disc under diametral compression which was achieved adopting the complex potentials technique for rectilinear anisotropic materials as it was formulated in the pioneering work of s.g. lekhnitskii. the analytic nature of this solution permits thorough, indepth exploration of the influence of some crucial parameters on the qualitative and quantitative characteristics of the deformation of transversely isotropic circular discs compressed between the jaws of the devise suggested by the international society for rock mechanics for the standardized implementation of the brazilian-disc test. the parameters considered include the anisotropy ratio (i.e., the ratio of the two elastic moduli characterizing the disc material), the angle between the loading axis and the planes of transverse isotropy and the length of the loaded arcs. strongly non-linear relationships between these parameters and the components of the displacement field are revealed. keywords. rectilinearly anisotropic materials; transverse isotropy; anisotropy ratio; brazilian-disc test; displacement field. citation: markides, ch.f., kourkoulis, s.k., parametric study of the deformation of transversely isotropic discs under diametral compression, frattura ed integrità strutturale, 41 (2017) 396-411. received: 21.05.2017 accepted: 31.05.2017 published: 01.07.2017 copyright: © 2017 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. introduction he configuration of a circular disc squeezed between two either plane or curved jaws is quite familiar to engineers, since it is widely used in practical applications (in the standardized form of the brazilian-disc test [1, 2]) for the estimation of the tensile strength of brittle materials. although the stress and displacement fields developed in a circular disc under the as above loading scheme are quite complicated and by no means uniaxial, it is widely accepted that, under specific restrictions and limitations [3-7], the fracture load recorded by such an experiment can be used to determine the material tensile strength (according to the simplified formulae proposed by carneiro [8], akazawa [9] and hondros [10]), assuming that fracture starts from the disc center. t ch. f. markides et alii, frattura ed integrità strutturale, 41 (2017) 396-411; doi: 10.3221/igf-esis.41.51 397 at this point, it is emphatically underlined that the analytic solutions, which have been used for the derivation of the as above classical formulae, are valid exclusively for linearly-elastic isotropic materials. in spite of this strict restriction, the as above formulae are quite often used, also, for the determination of the tensile strength of transversely isotropic materials, although it is well known that for non-isotropic materials the tensile strength is not a unique constant but rather it is a function of the orientation of the loading axis with respect to the anisotropy axes [11]. the main reason for this “compromise” is the fact that generally accepted analytic solutions for the stress and displacement fields developed in a finite circular disc made of a material characterized by even the simplest kind of anisotropy, i.e., transverse isotropy, are not as yet available. indeed, the respective mathematical problem, i.e., that of a finite disc made of transversely isotropic material that is subjected to diametral pressure is extremely complicated and the analytic solutions available for the stress and displacement field are based on quite a few simplifying assumptions which unavoidably restrict seriously their applicability [12, 13]. among these assumptions, the one perhaps most distanced from experimentally reality, is the simulation of the loading scheme by either a pair of diametral point forces or by a distribution of uniform radial pressure acting along two very “small” arcs of the disc periphery, symmetric with respect to the disc center, of arbitrarily predefined length. in the direction of relieving some of these restrictions, an analytic, closed-form solution was recently introduced [14] considering an orthotropic disc loaded by a parabolic distribution of radial stresses acting along two finite arcs of the disc periphery. the specific loading scheme is very close to the actual distribution of radial stresses [15, 16] developed along the disc-jaw contact arcs, when an intact isotropic disc is compressed between the curved jaws of the device suggested by the international society for rock mechanics (isrm) [1], in which case the length of these arcs is not constant but rather it is a function of the load level imposed and the relative stiffness of the disc and jaws materials, as it is expressed by the ratio of the respective elastic moduli [17]. the problem of the orthotropic disc [14] was solved with the aid of lekhnitskii [18] complex potentials technique whereas regarding a first approximation of the loading scheme and contact length previously mentioned formulae [16], based on muskhelishvili formalism for isotropic bodies [19], were properly modified. in the work described here, advantage is taken of the above mentioned solution [14], in an effort to enlighten and quantify the influence of some crucial material and geometric parameters on the displacement field developed in a disc made of a transversely isotropic material. among the parameters considered here is the degree of anisotropy, or in other words the ratio δ of the two elastic moduli characterizing a transversely isotropic material (recall that δ=1 corresponds to an isotropic material while increasing δ-values indicate stronger anisotropy). the role of the specific parameter is studied in-depth in order to quantify the limit of δ for which the use of analytic solutions developed for isotropic materials could be, perhaps, considered satisfactory approximations, also for transversely isotropic materials. the second parameter, the role of which is explored, is the inclination of the loading axis (in fact the axis of symmetry of the parabolic distribution) with respect to the axis of anisotropy. the role of the specific parameter is decisive since it governs the magnitude of shear deformation developed at the disc center in case the material layers are neither normal nor parallel to the loading direction. in other words, it dictates the shear stresses developed at the center of the disc, which in turn modify the fracture mechanism (with respect to that of the isotropic disc) rendering the validity of the brazilian-disc test questionable in case of anisotropy. the last parameter studied here is the length of the loaded arcs. although it is generally accepted that the specific quantity plays a rather minor role concerning the stress and strain fields at the center of the disc, it is known that it strongly influences the disc deformation in the immediate vicinity of the disc-jaw contact area [15, 16]. from this point of view it is definitely concluded that ignoring the length of the contact arc could yield erroneous results, since it is quite possible that fracture starts from the disc-jaw interface rather than from the center of the disc. the results of the study indicate that the dependence of the strain and displacement fields on the as above parameters (and especially on the degree of anisotropy) is strongly non-linear and the room for maneuver (i.e., using solutions for isotropic discs to approximately describe the tensile strength of transversely isotropic materials) is rather limited. it is therefore concluded that there is a demanding need for novel standards for the determination of the tensile strength of the specific type of materials which should lie on analytical solutions capable to properly describe the stress and displacement fields in a transversely isotropic finite circular disc under parabolic diametral compression. the displacement field in a transversely isotropic disc under diametral compression circular disc of radius r and thickness d, made of a transversely isotropic material (or for brevity “transtropic” material, a term quoted in [18]) is in equilibrium, in the absence of any kind of friction, between two curved jaws, compressed against each other by a force pframe (fig.1). the radius of curvature of the jaws ranges from 1.5r (case corresponding to the isrm standardization for implementing the brazilian-disc test [1]) to infinity (case for the relevant astm standardized experimental procedure [2], i.e., plane loading platens). pframe acts in the disc cross-section, which, a ch. f. markides et alii, frattura ed integrità strutturale, 41 (2017) 396-411; doi: 10.3221/igf-esis.41.51 398 normally intersected by the planes of isotropy, is a plane of elastic symmetry. for the specific purely plane strain configuration, the present study is concerned with a thorough parametric investigation of the displacement and strain fields developed all over the disc cross-section. figure 1: a disc made of a transversely isotropic material compressed between metallic jaws of radius ranging from 1.5r to infinity: configuration of the analytic problem and definition of symbols. in this context, a cartesian co-ordinate system {o; x; y; z} is considered at the disc center so that the xz-plane to be parallel to the planes of isotropy, the so-called strong direction, and the xy-plane to be parallel to the disc cross-section, known as the week direction. the strong direction is characterized by a young modulus e, a poisson ratio ν and a shear modulus g=e/(2(1+ν)); for the week direction the respective engineering constants are e΄, ν΄ and g΄(actually, ν΄ characterizes dilatation/contraction in xz-planes of isotropy for compression/tension along y-direction). the force pframe exerted by the loading frame to the disc through the metallic jaws forms an arbitrary angle ϕo with respect to x-axis, i.e., the strong direction (fig.1). in addition, and taking advantage of the isotropic disc-jaw contact problem, it is here assumed, in a first approximation, that pframe is parabolically distributed along two finite arcs of the disc periphery l, according to the law [16]:    2 21 sin sinc o op p        (1) in eq.(1) it is assumed that p(θ)>0 so that the pressure on the loaded rim will be σr= – p(θ). moreover, it holds that pc=max{p(θ)} and angle ωo corresponds to the half loaded arc. these two quantities may equally well be defined in two different ways at one convenience. namely, assuming without loss of generality that the jaw radius is equal to 1.5r and resorting to the isotropic disc-jaw contact problem, one may postulate [14]:   6 ( ) 3 1( ) 1 ( ) sin , , ( ) 32 ( ) 4 4 o frame frame jo o o c o o o j k p p arc p k rd k rd g΄ g                (2) where, assuming plane strain conditions, it holds that [14]: xz-planes of isotropy ε, v, g xy-plane of elastic symmetry e΄, ν΄, g΄ d x 2ωο y z pframe o r 2ωο ϕο z=reiθ r θ σr = – p(θ) – pframe l upper jaw lower jaw guide pin half-ball bearing ch. f. markides et alii, frattura ed integrità strutturale, 41 (2017) 396-411; doi: 10.3221/igf-esis.41.51 399 2 2 2 2 ( ) 3 4 ( ) 3 4 cos sino o e ΄ e΄             (3) in the above formulae, κ is muskhelishvili constant [19] while index j indicates the jaw. alternatively, ignoring the contact problem, one may fix arbitrarily the length of the loaded arc, i.e., the value of ωο, in which case (keeping pframe constant) [16] it would be written:   22 sin sin 2 2 cos 2 frame o c o o o p p rd       or 3 4 sin frame c o p p rd   (4) (the two expressions of eq.(4) are equivalent, especially for small to moderate ωο-values, with the latter, however, being the most adequate one in the complex form representation of the resultant force in [19]). under the above considerations and assuming, also, that both the displacement and rigid body rotation of the disc center arte equal to zero, the displacement field on any point of the “transtropic” disc cross-section was recently obtained [14] by employing lekhnitskii formalism [18, 20]. according to that solution [14], the cartesian components of the displacement field were found to be described by the following equations (where  indicates the real part):                 0 0 066 11 12 1 3 13 1 1 1 2 3 23 2 2 2 5,7,9,... 5,7,9,... , 2 2 x y xy m m m m m m u x y x y p a p z a p z p b p z b p z                                         (5)                 0 0 066 12 22 1 3 13 1 1 1 2 3 23 2 2 2 5,7,9,... 5,7,9,... , 2 2 x y xy m m m m m m v x y y x q a p z a p z q b p z b p z                                         (6) in the above formulae, zj, j=1,2, are the so-called complicated complex variables (in contrast with the ordinary complex variable z=x+iy=reiθ, fig.1), defined as: 1 1 2 2,z x i y z x i y     or 1 1 2 2cos sin , cos sin , 0z r i r z r i r r r           (7) where:       2 12 66 12 66 11 221 1 2 2 11 2 2 4 , 2                     (8) and βij are the so-called reduced elastic constants defined as: 2 2 11 12 22 66 1 1 1 1 , , 1 ,΄ ΄ e e΄ e΄ e΄ g΄                     (9) moreover, 2 2 1 11 1 12 2 11 2 12 1 12 1 22 1 2 12 2 22 2, , ,p p q q                     (10) with μj, j=1,2 being the so-called complex parameters reading as: 1 1 2 2,i i     (11) ch. f. markides et alii, frattura ed integrità strutturale, 41 (2017) 396-411; doi: 10.3221/igf-esis.41.51 400 in addition, with m=3,5,7,9,…,                                         2 2 2 2 2 2 2 1 2 1 1 2 2 1 2 1 1 2 1 1 1 1 1 1 2 1 2 1 1 2 2 1 2 1 1 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 m m m m m m m m m m m m m m m m m m m m m m m m m m m m m m m m m m t a t b t a t b a i t t t t t t t t t a t b t a t b b i t t t t t t t t                                                          (12) where    1,2 1,2 1,21 1t i i    (13) and , , ,m m m ma b a b    are the real and imaginary parts of the following constants (as coefficients of the fourier series representation of the boundary conditions on l): (14) what is more, and again for m=3,5,7,9,…,        2 2 2 2 2 21 ,2 1,2 1,2 1,2 1,2 1,2 1,2 1,2 1,2 1 1 1 1 m m m m mm p z z z r z z r r i                            (15) finally,                  0 0 01 1 1 1 1 1 1 1, ,x y xyb b ri a a r a a ri b b r           (16) indicate constant stresses throughout the disc cross-section [20], where the respective coefficients of fourier series representation of the boundary conditions on l read as [14]: 2 1 2 2 2 1 1 2 sin 2 sin 2 cos 2 2 sin 2 sin 2 2 22 sin 2 sin i o ic o o o oo o o o o o o a p r e e b i                                     (17)     3 2 2 3 2 2 2 2 1 sin 2 cos 2 sin 41 sin 2 sin 2 6 2 42 sin sin 4 2 cos 2 sin 4 sin 2 cos 4 2 32 sin 1 sin 1 sin 11 2 1 2 sin ic o o o o o o o o i o io o o o o o o m oc m o a p r e b i e e a m mp r b i m m                                                                                          1 2 2 2 1 1 cos 2 sin 1 2 sin 2 cos 1 1 cos 4 1 1 sin 1 sin 11 5, 7, ... 2 1 12 sin 1 cos 2 sin 1 2 sin 2 cos 1 1 cos 4 1 o i mo o o o o o oc o i mo o o o m m m m m e m m mp r m i m m m m m m m e m                                                             1 o ch. f. markides et alii, frattura ed integrità strutturale, 41 (2017) 396-411; doi: 10.3221/igf-esis.41.51 401 the role of critical parameters on the deformation of “transtropic” discs aking now advantage of the closed-form expressions for the displacements presented in previous section it is possible to explore crucial features of the deformation induced on a “transtropic” disc under parabolic pressure. as it was mentioned the parameters that will be considered include the anisotropy ratio δ, the inclination of the loading with respect to the planes of transverse isotropy and the length of the two loaded arcs. before analytic data are presented attention is drawn to the following issues:  the anisotropy ratio δ is defined as δ=ε/ε΄ and it is assumed that δ>1 since e corresponds to the strong anisotropy direction.  the term “material” represents, in fact, a specific combination of the values assigned to the material properties characterizing a transversely isotropic material, namely e, ν, e΄, ν΄ and g΄. various combinations of these values (mainly of e and e΄) are considered, in order for the analysis to cover the broadest possible range of rocks and rock-like materials. these materials, when do not correspond to a specific natural material, are denoted as “fictitious” materials. it is underlined that when considering various combinations of the values assigned to e, ν, e΄ and ν΄, attention must be paid to fulfill the necessary condition: xy e ΄ e΄   (18) characterizing the magnitude of dilatation in y-direction due to compression in x-direction, dictated by the symmetry of the strain tensor  under the term “actual material” a serpentinous schist with e=58 gpa, ν=0.34, e΄=27 gpa, ν΄=0.12 [11] is implied.  in all applications use is made of an approximating formula between the material properties which was proposed by lekhnitskii [18] and is valid for a relatively wide class of rocks:  1 2 ee΄ g΄ e ΄ e΄   (19)  allthough eqs.(5, 6) refer to the points z1 and z2, all results obtained on the disc cross-section and on l, refer to the point (x, y) or (r, θ), through eqs.(7). the role of the anisotropy ratio, δ and the load inclination angle ϕo in order for a global overview of the deformation imposed on the “transtropic” disc under parabolic radial pressure to be obtained, it was decided as a first step to pay attention at the immediate vicinity of the disc center, given that this is the point where fracture is expected (or where fracture “must” start), for the results of the brazilian-disc test to be reliable. in this direction, the components of the strain tensor are plotted in figs.2 and 3 versus the anisotropy ratio δ, for a series of “fictitious” “transtropic” materials. the values assigned to δ vary from δ=1 (which corresponds to a disc made of an isotropic material) to δ=5, covering well the range of anisotropy ratios that can be met in real rocks and rock-like materials. the mechanical properties of the materials considered are recapitulated in tab. 1. the radius of the disc was set equal to 50 mm and its thickness (length) equal to 10 mm. a constant overall load equal to pframe=20 kn was exerted on the discs. angle ϕo, i.e., the inclination of the axis of symmetry of the parabolic distribution of radial stresses with respect to x-axis, was set equal to ϕo=0 o, 15 o, 30 o, 45 o, 60 o, 75 o and 90o. the dependence of the normal radial strain component εrr (i.e., that along the loading axis) and the normal transverse strain component εθθ (i.e., that normal to the loading axis) on the anisotropy ratio δ is shown in figs.2(a, b) for all ϕovalues. it is observed from fig.2a that the normal radial strain εrr is negative (contractive) for all δ-values, as it is obviously expected. for relatively low δ-values (δ<1.3) εrr decreases rapidly, reaching a minimum value for δ≈1.3 for all ϕo-values without any exception. for higher δ-values εrr increases smoothly. the dependence of εrr on the inclination ϕo of the anisotropy planes with respect to the loading line is smooth and monotonous. the respective behaviour of the transverse strain component εθθ is somehow “symmetric” to that of εrr (fig.2b): it is positive (dilatative) for all δand ϕo-values, it exhibits a clear maximum (again for δ≈1.3) and its dependence on angle ϕo is also smooth and monotonous. of higher importance is the variation of the shear strain γrθ against the anisotropy ratio δ which is shown in fig.3. contrary to what happens at the center of an isotropic (δ=1) disc (where γrθ is constantly zero for obvious symmetry reasons), t ch. f. markides et alii, frattura ed integrità strutturale, 41 (2017) 396-411; doi: 10.3221/igf-esis.41.51 402 -0.0025 -0.0020 -0.0015 -0.0010 -0.0005 1 2 3 4 5 n o rm al a st ra in ε rr (a lo n g th e lo ad in g ax is ) δ = e / e' ϕo=0o 15o 30o 45o 60o 75o 90o 0.0003 0.0006 0.0009 0.0012 1 2 3 4 5 n o rm al tr an sv er se s tr ai n ε θθ (p er p en d ic ul ar to th e lo ad in g ax is ) δ = e / e' ϕo=0o 15o 30o 45o 60o 75o 90o materials e [gpa] e΄ [gpa] ν΄ (=νyx) νxy (<0.5) δ “fictitious” isotropic 75 75 0.30 0.30 1 “fictitious” “transtropic” 1 20 15 0.30 0.12 1.33 2 25 0.10 1.67 3 30 0.10 2.00 4 35 0.10 2.33 5 40 0.10 2.67 6 45 0.10 3.00 7 50 0.10 3.33 8 55 0.10 3.67 9 60 0.10 4.00 10 65 0.10 4.33 11 70 0.10 4.67 12 75 0.10 5.00 table 1: the mechanical properties of the materials considered. (a) (b) figure 2: the dependence of the normal radial εrr (a) and transverse εθθ (b) strain on the anisotropy ratio δ for a series of ϕo-values. ch. f. markides et alii, frattura ed integrità strutturale, 41 (2017) 396-411; doi: 10.3221/igf-esis.41.51 403 -0.0012 -0.0009 -0.0006 -0.0003 0.0000 1 2 3 4 5 sh ea r st ra in γ rθ δ = e / e' ϕo=0o, 90o 15o 30o 45o 60o 75o γrθ figure 3: the dependence of the shear strain γrθ on the anisotropy ratio δ for a series of ϕo-values. in the case of “transtropic” discs γrθ is non-zero (excluding the limiting values ϕo=0o, ϕo=90o, for which symmetry imposes zeroing of γrθ) and the deformation in the immediate vicinity of the disc center becomes both distortive and dilatational rather than purely dilatational. the magnitude of γrθ increases constantly with increasing δ for ϕo-values in the 0o< ϕo<45o range. on the contrary, for ϕo-values in the 45o< ϕo<90o range γrθ increases for low δ-values and then it reaches a plateau. the dependence of the magnitude of γrθ on the angle ϕo is non-monotonous exhibiting its maximum value around ϕo≈30o. for the differences of the deformation between an isotropic and a “transtropic” disc to become more evident, and in order to highlight the loss of some symmetries which are “familiar” in case of isotropic materials, the deformed shape of an element (δr, δθ)=(15πr/180, 15πr/180) of the disc cross-section, oriented along the loading line, is drawn in figs.4(a, b). this element is located in the immediate vicinity of the disc-jaw contact arc, i.e., in the area where the deformation field is extremely amplified due to the “direct” action of the external loading scheme (see the sketches embedded in figs.4). both the undeformed element (black dashed line) and the respective deformed ones are drawn: the deformed element for the isotropic configuration is drawn with green line while that for the “transtropic” one with red line. two geometries were considered, one for ϕo=20o (fig.4a) and a second one for ϕo=60o (fig.4b). the materials considered correspond to rocks with relatively low stiffness in order for the deformation to be clearly visible. for the “fictitious” isotropic material it is assumed that e=e΄=4 gpa, ν=ν΄=0.34 while for the “fictitious” “transtropic” one it is assumed that e=4 gpa, ν=0.34, e΄=2 gpa, ν΄=νyx=0.2 (and it follows that νxy=0.40<0.50). again for clarity reasons the value of the load imposed is rather “unrealistic” (pframe=100 kn). given that the analysis introduced is linearly elastic, it is obvious that the magnitude of the load imposed will only quantitative influence the results; from a qualitative point of view the conclusions drawn are not influenced by the specific parameter. finally, it is mentioned that the length of the loading arc (2ωo) is not constant but rather it is obtained with the aid of the solution of the respective isotropic disc-jaw contact problem. as a result it depends both on the inclination of the loading axis with respect to the anisotropy planes, ϕo, and also on the properties of the disc materials. in this context, for the configuration with ϕo=20o (fig.4a) it is calculated that ωο(ϕo=20o)=23.05o for the “fictitious” “transtropic” disc while for the same configuration for the “fictitious” isotropic material it is calculated that ωο(ϕo=20o)=24.52o. similarly for the configuration with ϕo=60o (fig.4b) it is determined that ωο(ϕo=60o)=22.29o for the “fictitious” “transtropic” disc and ωο(ϕo=60o)= 24.52o for the “fictitious” isotropic disc (obviously for the isotropic disc the length of the contact arc does not depend on the inclination angle ϕo of the loading axis with respect to x-axis of the reference system (see fig.1)). the most important conclusion drawn from figs.4(a, b) (besides the expected differences between the “transtropic” and the isotropic disc in the “rigid body” translation and rotation of the element in question, as intermediate steps from the unstrained to its final strained state), is the evident asymmetry detected in the variation of shear deformation in case of “transtropic” materials, at symmetric points, i.e., of the corner points of the element in question, even when located along the loaded radius. indeed, while for the isotropic material γrθ(r, θ)=γrθ(r, θ+δθ) all along the loaded radius, this is by no means ch. f. markides et alii, frattura ed integrità strutturale, 41 (2017) 396-411; doi: 10.3221/igf-esis.41.51 404 the case for the “transtropic” material for which clearly γrθ(r, θ)≠γrθ(r, θ+δθ). moreover, it is observed that the differences in deformation between the particular “fictitious” isotropic and “transtropic” discs are more pronounced for ϕo=60o. (a) (b) figure 4: deformed vs. undeformed (black dashed line) configuration of an element (δr, δθ) (oriented along the loading axis and normally to it), for an isotropic (green line) and a “transtropic” (red line) disc, when the loading direction is ϕo=20o (a) and ϕo=60o (b). the role of the length of the contact arc, 2ωo the specific parameter, i.e., the length of the loaded arc, is in general disregarded in practical applications of the braziliandisc test, since it is considered that the stress state at the disc center can be simulated as a biaxial stress field with a con ch. f. markides et alii, frattura ed integrità strutturale, 41 (2017) 396-411; doi: 10.3221/igf-esis.41.51 405 stant biaxiality ratio k, equal to k=σcompressive/σtensile=3, independently of the actual boundary conditions which prevail along the loaded arcs of the disc. this was suggested, perhaps for the first time, by peltier [21], who arrived at the conclusion that, as long as the loaded arc is not “too large” (indicatively, he mentioned as an upper limit for the length of the loaded arcs a value less than one fifth of the disc diameter), the tensile stresses remain uniform almost all along the length of the loaded diameter. barenbaum and brodie [22] as well as rudnick et al. [24] drew similar conclusions. however, the fact that the stress field at the disc center is more or less insensitive to the actual conditions along the loaded arcs is by no means a necessary and sufficient condition for the validity of the results provided by the brazilian-disc test: it has been indicated by many researchers that depending on the actual stress field in the immediate vicinity of the loaded arcs it is quite possible that fracture could start far from the disc center, unless certain precautions are taken, rendering the results of the test erroneous [3-7, 24-26]. in the direction of minimizing the as above risk, mellor and hawkes [5] suggested, for the first time, the use of curved jaws (instead of plane loading platens) of radius exceeding that of the specimens, suggestions which were the seed for the respective isrm standard [1]. it is therefore evident that, in spite of the insensitivity of the stress field at the disc center to the actual boundary conditions, the reliability of the final outcomes of the brazilian-disc test strongly depends on the actual conditions prevailing along the disc loaded arcs and on their length. as a result, one should consider, at least qualitatively, the role of the specific parameter (length of the contact arc), independently of whether the disc is made of isotropic or “transtropic” material. given that the problem for isotropic materials was recently considered thoroughly [17], a first attempt is described here to explore the role of the loaded arcs’ length on the displacement field in case of “transtropic” discs. this attempt is possible because the displacement field in a “transtropic” disc under parabolic pressure is, for the first time, provided here in terms of analytic, closed-form expressions. in this direction, a disc made of a serpentinous schist (with e=58 gpa, ν=0.34, e΄=27 gpa, ν΄=0.12) [11] was considered, compressed between the isrm jaws, by an overall load equal to pframe=20 kn, which is kept constant for all ωο-values assigned to the contact semi-arc. given now that the length of the two contact arcs (2ωο) is arbitrarily prescribed (rather than being determined from the respective contact problem) the amplitude of the parabolic distribution must be determined through eqs.(4) (it is here recalled that the two formulae of eq.(4) are almost equivalent, especially for relatively small ωo-values). as a first step, it was decided to plot the components of the displacement field along the disc loaded diameter, which is, perhaps, the locus of utmost importance for practical applications. a relatively wide interval of ωo-values was studied, ranging from a very small one equal to ωo=2o (which in fact approaches the diametral compression by a pair of “point” forces, or equivalently to compression of very stiff discs which are not significantly deformed at the disc-jaw interface) to a rather very high one equal to ωo=30o (which corresponds to diametral compression of discs with extremely low stiffness). concerning angle ϕo, three characteristic values were studied, namely ϕo=0o (loading parallel to the planes of isotropy, or equivalently x-axis parallel to the loading line), ϕo=90o (loading normal to the planes of isotropy, or equivalently x-axis normal to the loading line) and ϕo=30o (corresponding to the geometry for which the shear strain at the disc center is maximized independently of the anisotropy ratio, δ (fig.3)). the results of the analysis are shown in figs.5(a, b, c), in which the polar components ur and uθ of the displacement field are plotted along the loaded diameter from r=0 (the center of the disc) to r=r (or in other words to the point where the disc is in contact to the loading jaw). as it is expected, both for ϕo=0o and ϕo=90o the transverse (tangential) component of the displacement field is zero for obvious symmetry reasons. in addition, as it was also expected, the magnitude of the non-zero component of the displacement, i.e., ur, increases with increasing ϕo (for the same point and the same ωο-value) since for ϕo=0o loading is exerted along the strong anisotropy axis (characterized by high value of the elastic modulus or equivalently by increased stiffness) while for ϕo=90o loading is exerted along the weak anisotropy axis (characterized by low value of the elastic modulus or equivalently by decreased stiffness). in accordance to similar conclusions for isotropic discs [15, 16], it is also here concluded that the influence of angle ωo on the displacement (and therefore on the strainand stress-fields) is definitely negligible at the disc center. the role of ωo becomes significant only for r→r. the lower limit of r for which ωo plays some role on the displacement field appears very sensitive to the value of angle ϕo. from a quantitative point of view, it can be seen from fig.5a that for ϕo=0o and r=r it holds that ur=6.5x10-5 for ωο=2o while for ωο=30o the respective value is ur=3.5x10-5. in other words, increasing ωο from 2o to 30o results to a decrease of the radial displacement in the vicinity of the loaded arc by more than 45%. similar conclusions are drawn also for ϕo=90o and ϕo=30o. in general, increasing the length of the loading arc weakens the intensity of the displacement field. concerning the influence of angle ωο on the transverse (tangential) component of the displacement field, it can be said that it is almost negligible all along the loaded radius. indeed, as it can be seen from fig.5b only for r>0.45r some differences can be detected, which are much lower compared to the respective ones of ur. ch. f. markides et alii, frattura ed integrità strutturale, 41 (2017) 396-411; doi: 10.3221/igf-esis.41.51 406 (a) (b) (c) figure 5: the distribution of the polar-displacement components, ur, uθ, along the loaded radius 0≤r≤r, for ϕo=0o (a), ϕo=30o (b) and ϕo=90o (c) for various values of the contact semi-arc ωo equal to ωo=2o, 5o, 10o, 15o, 20o, 25o and 30o. ch. f. markides et alii, frattura ed integrità strutturale, 41 (2017) 396-411; doi: 10.3221/igf-esis.41.51 407 discussion and concluding remarks he displacement field developed in a transversely isotropic disc under diametral compression was determined analytically and in closed form. the main advantage of the present solution is the nature of the analytic expressions, which are relatively easily programmable, providing an overview of the deformed shape either of an element of the disc (see figs.4(a, b)) or for the disc as a unit. to highlight the specific feature of the solution the deformed shape of a “fictitious” “transtropic” disc is plotted in figs.6(a, b, c), in juxtaposition to the respective isotropic one, for three characteristic configurations, i.e., ϕo=30o (fig.6a), ϕo=45o (fig.6b), and ϕo=60o (fig.6c). in all cases the transtropic disc is characterized by e=40 gpa, ν=0.30, e΄=10 gpa, ν΄=νyx=0.12, νxy=0.48 and the isotropic one by e=e΄=40 gpa, ν=ν΄=0.30. again the length of the contact arcs is determined from the respective contact problem and the magnitude of the load imposed is “unrealistically” high for the deformed shape to be clearly distinguished from the undeformed one. it is again easily concluded that the deformation of the “transtropic” disc is asymmetric with respect to the loading line. this “degree of asymmetry” depends both on the anisotropy ratio, δ, and also on the value of angle ϕo, although this dependence is extremely complicated and by no means monotonous. moreover, it is interesting to emphasize the fact that for the “transtropic” disc the diameters parallel and normally to the loading direction do not remain linear segments after deformation, but rather they become curved segments, contrary to what happens for the isotropic disc, for which the specific diameters (as expected) remain linear segments. the curvature of the deformed diameters depends (according to an extremely complicated manner) on quite a few parameters, the most important of which are: the orientation of the diameter with respect to the loading line, the distance from the disc center, and (obviously) on the orientation of the load with respect to the planes of isotropy (angle ϕo). analogous conclusions are drawn for the diameters (symmetrically placed with respect to the loaded diameter) connecting the starting and ending points of the loaded arcs. namely, while in the case of the isotropic disc these diameters exhibit completely symmetric deformation, for the “transtropic” disc the deformation is asymmetric following the general distortion of the deformed configuration as a whole. moreover, worth mentioning is the diversification in the values of ωo (corresponding to the half-contact length) between the isotropic and the “transtropic” disc, as well as, among the three deformed configurations of the “transtropic” disc itself; namely, while for the isotropic disc ωο is constantly equal to 40.04o for all three values of angle ϕo (30o, 45o, 60o), this is not the case for the “transtropic” disc where the relevant values of ωο read respectively as 58.46o, 63.89o and 72.22o (due to the successive decrease of the “transtropic” disc stiffness for increasing ϕo-values). (a) figure 6: (a) deformed versus undeformed (black dashed line) configuration of a circular disc under parabolic diametral compression, for an isotropic(green line) and a “transtropic”(red line) material, for ϕo=30o. t ch. f. markides et alii, frattura ed integrità strutturale, 41 (2017) 396-411; doi: 10.3221/igf-esis.41.51 408 (b) (c) figure 6 (continued): deformed versus undeformed (black dashed line) configuration of a circular disc under parabolic diametral compression, for an isotropic(green line) and a “transtropic”(red line) material, for ϕo=45o (b) and ϕo=60o (c). besides the above mentioned characteristic, related to the “convenient” and “easy-to-use” (or “easy-to-program”) nature of the expressions for the displacement components, the solution introduced cures some critical drawbacks of existing ch. f. markides et alii, frattura ed integrità strutturale, 41 (2017) 396-411; doi: 10.3221/igf-esis.41.51 409 solutions. the first one is related to the kind of the loading scheme considered (i.e., the parabolic distribution of radial stresses), which approaches closely the actual distribution developed along the disc-jaw interface when the brazilian-disc test is implemented according to the isrm standard [1]. in fact the specific distribution is of “cyclic” nature [15, 27], however, it is quite accurately simulated by a parabolic one, like the one adopted here. in any case the parabolic distribution is much closer to experimental reality compared to either a “uniform” one or to a loading scheme consisting of “point” diametral forces. the second advantage of the present solution is the fact that the loaded arc is not arbitrarily prescribed but rather it is determined from the solution of the respective disc-jaw contact problem. as a result, the present solution takes into account the relative stiffness of the disc and jaw materials, providing, in a first approximation, realistic values for the length of the contact arc. to make the importance of the specific issue clear, it is mentioned characteristically that, depending on modulus of elasticity of the disc material, the length of the contact arc varies within extremely broad limits, ranging from 2o to 3o (for very stiff discs made, for example, of dionysos marble) [16, 28] to 20o or even 30o (for discs of low stiffness made, for example, of shell-stones) [16, 29]. another issue that should be thoroughly discussed (also in future studies) is the “suitability” of the anisotropy ratio, δ, to act as a proper parameter that could properly describe the dependence of the strain-field, developed in a “transtropic” disc, on the anisotropy degree of the disc material. to make this point clear, the variation of the shear strain γrθ, developed at the disc center, θ= ϕo =30ο, is plotted in fig.7 against an “average stiffness” of the “transtropic” disc material. this “average stiffness” is here defined as the mean value eav=(e+e')/2 of the two elastic moduli characterizing a “transtropic” material. to draw fig.7 a series of fictitious “transtropic” materials were considered with constant anisotropy δ equal to δ=2. the modulus of elasticity along the “strong” anisotropy axis ranges from e=4 gpa to e=80 gpa, while that along the “weak” anisotropy axis ranges from e'=2 gpa to e'=40 gpa in such a way that δ is kept constant equal to δ=2. for the poisson ratios it is considered (for all combination of e and e΄) that ν=0.30, and ν'=0.15. an average external load equal figure 7: the dependence of the shear strain γrθ at the disc center on the “average stiffness” (e+e')/2, i.e., on the mean value of the two elastic moduli characterizing “transtropic” materials. to pframe=20 kn is imposed on the discs for all materials’ combinations. the non-linear nature of the dependence shown in fig.7 is quite striking, indicating that, even for materials with the same δ-value, the shear strain does not decrease linearly with linearly increasing “average stiffness” of the disc material (the term “average stiffness” is a “neologism” and is introduced in an attempt to somehow quantify the stiffness of materials which are characterized by more than one elastic moduli). before concluding some limitations, restricting the general applicability of the present solution, should be mentioned. the assumption of zero shear stresses along the loaded arc (in other words the assumption of perfectly smooth interface) is, perhaps, the most critical one. it is widely accepted that these stresses do not influence the stress field at the disc center, however, under specific conditions they could be responsible for premature fracture in the vicinity of the loaded arc, jeopardizing, thus, the validity of the results of the brazilian-disc test [30-32]. although it is an extremely complicated -5.0e-03 -4.0e-03 -3.0e-03 -2.0e-03 -1.0e-03 0.0e+00 0 15 30 45 60 γ r θst ra in a t th e d is c' s ce n tr e (ε+ε΄)/2 ϕo=30o ch. f. markides et alii, frattura ed integrità strutturale, 41 (2017) 396-411; doi: 10.3221/igf-esis.41.51 410 problem, it is absolutely necessary for the role of these stresses to be thoroughly explored. along the same lines, and despite a first attempt made here to approximately obtain the length of the contact arc of the “transtropic” disc compressed between the isrm jaws [1] (by properly modifying the relevant formulae of the isotropic disc-jaw contact problem (eqs.(2), (3))), use of the latter should be also made with consciousness, until further analytical and experimental results are available. references [1] isrm, suggested methods for determining tensile strength of rock materials, international journal of rock mechanics and mining sciences and geomechanics abstracts, 15(3) (1978) 99-103. [2] astm, standard test method for splitting tensile strength of intact rock core specimens, d3967-08, astm volume 04.08 soil and rock (i): d420 d5876 (2014). [3] hobbs, d.w., an assessment of a technique for determining the tensile strength of rock, british journal of applied physics, 16 (1965) 259-269. [4] fairhurst, c., on the validity of the ‘brazilian’ test for brittle materials, international journal of rock mechanics and mining sciences and geomechanics abstracts, 1 (1964) 535-546. [5] mellor, m., hawkes, i., measurement of tensile strength by diametral compression of discs and annuli, engineering geology, 5 (1971) 173-225. [6] hooper, j.a., the failure of glass cylinders in diametral compression, journal of mechanics and physics of solids, 19 (1971) 179-200. [7] markides, ch.f., pazis, d.n., kourkoulis, s.k., closed full-field solutions for stresses and displacements in the brazilian disk under distributed radial load, international journal of rock mechanics and mining sciences, 47(2) (2010) 227237. [8] carneiro, f.l.l.b., a new method to determine the tensile strength of concrete (in portuguese), in: proceedings of the 5th meeting of the brazilian association for technical rules, 3d. section, 16 september (1943) 126-129. [9] akazawa, t., new test method for evaluating internal stress due to compression of concrete (the splitting tension test) (part1), journal of japan society of civil engineers, 29 (1943) 777-787. [10] hondros, g., the evaluation of poisson’s ratio and the modulus of materials of a low tensile resistance by the brazilian (indirect tensile) test with particular reference to concrete. australian journal of applied sciences, 10 (1959) 243-268. [11] barla, g., innaurato, n., indirect tensile testing of anisotropic rocks, rock mechanics, 5 (1973) 215-230. [12] amadei, b., importance of anisotropy when estimating and measuring in situ stresses in rock, international journal of rock mechanics and mining sciences & geomechanics abstracts, 33(3) (1996) 293-325. [13] exadaktylos, g.e., kaklis, k.n., applications of an explicit solution for the transversely isotropic circular disc compressed diametrically, international journal of rock mechanics and mining sciences, 38(2) (2001) 227-243. [14] markides, ch.f., kourkoulis s.k., the displacement field in an orthotropic disc under parabolic pressure. application to the case of transverse isotropy, procedia structural integrity, 3 (2017) 334-345. [15] markides, ch.f., kourkoulis, s.k., chatzistergos, p.e., the standardized brazilian disc test as a contact problem, international journal of rock mechanics and mining sciences, 57 (2012) 132-141. [16] markides, ch.f., kourkoulis, s.k., the stress field in a standardized brazilian disc: the influence of the loading type acting on the actual contact length, rock mechanics & rock engineering, 45(2) (2012) 145-158. [17] markides, ch.f., kourkoulis, s.k., the influence of jaws’ curvature on the results of the brazilian-disc test, journal of rock mechanics and geotechnical engineering, 8(2) (2016) 127-146. [18] lekhnitskii, s. g., theory of elasticity of an anisotropic body, mir, moscow (1981). [19] muskhelishvili, n. i., some basic problems of the mathematical theory of elasticity, noordhoff, groningen, the netherlands (1963). [20] lekhnitskii, s. g., anisotropic plates (english translation by tsai, s. w.), gordon and breach, new york (1968). [21] peltier, r., étude théorique de l'essai brésilien, rilem bulletin, 19 (1954) 29-69. [22] barenbaum, r., brodie, i., measurement of the tensile strength of brittle materials, british journal of applied physics, 10(6) (1959) 281-287. [23] rudnick, a., hunter, a.r., holden, f.c., an analysis of the diametral compression test, materials research and standards, 3(4) (1963) 283-289. [24] addinall, e., hackett, p., tensile failure in rock-like materials. in: spokes, e.m., christiansen, c.r. (eds), proceedings of the 6th symposium on rock mechanics. rolla: university of missouri at rolla, (1964) 515–538. ch. f. markides et alii, frattura ed integrità strutturale, 41 (2017) 396-411; doi: 10.3221/igf-esis.41.51 411 [25] kourkoulis, s.k., markides, ch.f., hemsley, j.a., 2013. frictional stresses at the disc-jaw interface during the standardized execution of the brazilian disc test. acta mechanica 224(2) 255-268. [26] markides, ch.f., pazis, d.n., kourkoulis, s.k., the brazilian disc under non uniform distribution of radial pressure and friction, int. j rock mech. mining sci., 50 (2012) 47-55. [27] timoshenko, s.p., goodier, j.n., theory of elasticity, mcgraw-hill, new york, 3rd edition (1970). [28] exadaktylos, g.e., vardoulakis, i., kourkoulis, s.k., influence of nonlinearity and double elasticity on flexure of rock beams – ii. characterization of dionysos marble, international journal of solids and structures, 38(22-23) (2001) 41194145. [29] vardoulakis, i., kourkoulis, s.k., zambas, c., modeling of the mechanical behaviour of a conchyliates shellstone, 2nd int. symposium on hard soils soft rocks, naples, italy, 12-14 october 1998. published in: the geotechnics of hard soils-soft rocks, evangelista, a., picarelli l. (eds.), a. a. balkema: rotterdam, the netherlands, (1998) 911922. [30] markides, ch.f., pazis, d.n., kourkoulis, s.k., the brazilian disc under non uniform distribution of radial pressure and friction, international journal of rock mechanics and mining sciences, 50 (2012) 47-55. [31] kourkoulis, s.k., markides, ch.f., hemsley, j.a., frictional stresses at the disc-jaw interface during the standardized execution of the brazilian disc test, acta mechanica, 224(2) (2013) 255-268. [32] markides, ch.f., kourkoulis, s.k., an alternative analytic approach to the brazilian disc test with friction at the disc jaw interface, archive of applied mechanics, 83(5) (2013) 743–763. << /ascii85encodepages false /allowtransparency false /autopositionepsfiles true /autorotatepages /none /binding /left /calgrayprofile (dot gain 20%) /calrgbprofile (srgb iec61966-2.1) /calcmykprofile (u.s. web coated \050swop\051 v2) /srgbprofile (srgb iec61966-2.1) /cannotembedfontpolicy /error /compatibilitylevel 1.4 /compressobjects /tags /compresspages true /convertimagestoindexed true /passthroughjpegimages true /createjobticket false /defaultrenderingintent /default /detectblends true /detectcurves 0.0000 /colorconversionstrategy /cmyk /dothumbnails false /embedallfonts true /embedopentype false /parseiccprofilesincomments true /embedjoboptions true /dscreportinglevel 0 /emitdscwarnings false /endpage -1 /imagememory 1048576 /lockdistillerparams false /maxsubsetpct 100 /optimize true /opm 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can be opened with acrobat and adobe reader 5.0 and later.) >> /namespace [ (adobe) (common) (1.0) ] /othernamespaces [ << /asreaderspreads false /cropimagestoframes true /errorcontrol /warnandcontinue /flattenerignorespreadoverrides false /includeguidesgrids false /includenonprinting false /includeslug false /namespace [ (adobe) (indesign) (4.0) ] /omitplacedbitmaps false /omitplacedeps false /omitplacedpdf false /simulateoverprint /legacy >> << /addbleedmarks false /addcolorbars false /addcropmarks false /addpageinfo false /addregmarks false /convertcolors /converttocmyk /destinationprofilename () /destinationprofileselector /documentcmyk /downsample16bitimages true /flattenerpreset << /presetselector /mediumresolution >> /formelements false /generatestructure false /includebookmarks false /includehyperlinks false /includeinteractive false /includelayers false /includeprofiles false /multimediahandling /useobjectsettings /namespace [ (adobe) (creativesuite) (2.0) ] /pdfxoutputintentprofileselector /documentcmyk /preserveediting true /untaggedcmykhandling /leaveuntagged /untaggedrgbhandling /usedocumentprofile /usedocumentbleed false >> ] >> setdistillerparams << /hwresolution [2400 2400] /pagesize [612.000 792.000] >> setpagedevice microsoft word numero 10 art 6 m. paggi, frattura ed integrità strutturale, 10 (2009) 43-55; doi: 10.3221/igf-esis.10.06 43 a dimensional analysis approach to fatigue in quasi-brittle materials marco paggi politecnico di torino, dep. of structural and geotechnical engineering, corso duca degli abruzzi 24, 10129 torino, italy marco.paggi@polito.it riassunto. nel presente lavoro si propone uno studio di analisi dimensionale del fenomeno della fatica nei materiali quasi-fragili. esso costituisce una generalizzazione della metodologia pionieristica proposta da barenblatt e botvina e si prefigge di interpretare le deviazioni dalle leggi di potenza classiche usate per caratterizzare il comportamento a fatica dei materiali. in base a questo approccio teorico, gli effetti dovuti alla dimensione microstrutturale (correlabile al contenuto volumetrico di fibre nei calcestruzzi fibrorinforzati), alla dimensione delle fessure e alla scala strutturale sulla legge di paris e sulle curve di wöhler sono discussi in un contesto matematico unificato. il modello teorico è confermato dal confronto con rilevanti risultati sperimentali disponibili in letteratura, usati per determinare i valori degli esponenti di autosimilarità incompleta. le informazioni fornite da questa teoria possono essere particolarmente utili per guidare la progettazione di nuovi esperimenti, dal momento che viene chiarito il ruolo delle diverse variabili adimensionalizzate che governano il fenomeno della fatica. abstract. in this study, a generalized barenblatt and botvina dimensional analysis approach to fatigue crack growth is proposed in order to highlight and explain the deviations from the classical power-law equations used to characterize the fatigue behaviour of quasi-brittle materials. according to this theoretical approach, the microstructural-size (related to the volumetric content of fibres in fibre-reinforced concrete), the crack-size, and the size-scale effects on the paris’ law and the wöhler equation are presented within a unified mathematical framework. relevant experimental results taken from the literature are used to confirm the theoretical trends and to determine the values of the incomplete self-similarity exponents. all these information are expected to be useful for the design of experiments, since the role of the different dimensionless numbers governing the phenomenon of fatigue is herein elucidated. keywords. fatigue; quasi-brittle materials; fibre-reinforced concrete; dimensional analysis; incomplete selfsimilarity. introduction he assessment of the fatigue behaviour of quasi-brittle materials, such as plain or fibre-reinforced concrete (frc), is particularly important from the engineering point of view. concrete pavements for highways are in fact subjected to millions of cycles of repeated axial loads of high stress amplitude due to passing vehicles. airport pavements are also subjected to a number of loading cycles during their design life, ranging from about several thousand to several hundred thousand. concrete structures supporting dynamic machines may also fail due to repeated loadings causing complex stress states. to make the problem even more complex, very often failure is the result a steady decrease in the stiffness of the structural element, rather than by the propagation of a single macroscopic crack [1]. from the design point of view, the classical methods used to assess the fatigue performance of concrete are mainly empirical and are based on the cumulative fatigue damage approach, well-established for the analysis of the fatigue t http://dx.medra.org/10.3221/igf-esis.10.06&auth=true http://www.gruppofrattura.it mailto: marco.paggi@polito.it m. paggi, frattura ed integrità strutturale, 10 (2009) 43-55; doi: 10.3221/igf-esis.10.06 44 behaviour of metals [2,3]. hence, the empirical s-n curve, relating the fatigue life or cycles to failure, n, to the applied stress range,  or s, is often used both for plain [4-6] and fibre-reinforced concretes [7-12]. a schematic representation of the wöhler’s diagram is shown in fig. 1a, where the cyclic stress range, max min     , is plotted as a function of the number of cycles to failure, n. in this diagram, we introduce the range of stress at static failure, max min min (1 )u u ur            , where u is the material tensile strength, and we define the endurance or fatigue limit, fl , as the stress range that a sample will sustain without fracture for 71 10n   cycles, which is a conventional value that can be thought of as “infinite” life. with the advent of fracture mechanics, a more ambitious task was undertaken, i.e., to predict, or at least understand, the propagation of cracks. plotting the crack growth rate, da/dn, as a function of the stress-intensity factor range, max mink k k   , most of the experimental data can be interpreted in terms of a power-law relationship, i.e., according to the so-called paris’ law [13,14]. in spite of the fact that this approach requires a more elaborate testing procedure than for the s-n curves, it has also been applied to plain concrete [15-17] (see a schematic representation of the paris’ curve in fig. 1b). note that the power-law representation presents deviations for very high values of k approaching cr ic(1 )k r k   [18], where ick is the material fracture toughness, or for very low values of k approaching the threshold stress-intensity factor range, thk [19]. again, in close analogy with the concept of fatigue limit, the fatigue threshold is defined in a conventional way as the value of k below which the crack grows at a rate of less than 91 10 m/cycle. (a) (b) figure 1: schemes of the (a) wöhler and (b) paris’ curves with the related fatigue parameters. yet, the fatigue behaviour of quasi-brittle materials in bending or even in compression is not completely understood in terms of all the influential variables, such as the type of the loading cycle, cycling rate, structural size, crack length and, perhaps most important of all for frc, fibres parameters. for instance, it has been experimentally shown in [15-17] that the coefficients entering the paris’ law depend on the material composition, on the structural size, and on the crack length, potentially explaining the large scatter in the reported values available in the literature. this result has also the fundamental implication that the paris coefficients cannot be treated as true material constants. similarly, the s-n curves are found to be dependent on the size of the tested specimen [11], on the loading conditions [1], as well as on the material composition [8]. from the modelling point of view, an important research effort towards simulating s-n curves of plain concrete and frc in cyclic bending was put forward in [11,20]. this required the use of nonlinear fracture mechanics theories coupled with a damage law for modelling the degradation of the concrete cohesive crack stresses and of the fibres bridging in the process zone due to cyclic loading. however, in spite of the useful predictive capabilities of these models, their complex mathematical formulation limits their applicability to design purposes and confines them to the research environment. moreover, although the damage model can be tuned on the basis of experimental data as proposed in [10], other choices for the expression of the damage variable are also possible (see e.g. [21]) and the connection existing between the evolution of damage and the outcome of the fatigue simulation has not yet been completely clarified. http://dx.medra.org/10.3221/igf-esis.10.06&auth=true http://www.gruppofrattura.it m. paggi, frattura ed integrità strutturale, 10 (2009) 43-55; doi: 10.3221/igf-esis.10.06 45 following an independent line of research, the use of the concepts of dimensional analysis and incomplete self-similarity originally proposed by barenblatt and botvina [22,23] seems to be very promising in understanding the phenomenon of fatigue. applying these concepts to metals, the present author has determined the relationship between the paris’ law parameters c and m on the basis of theoretical arguments [18]. then, the barenblatt and botvina’s analysis of the sizescale effects on the paris’ law parameter m has been extended in [24] to the paris’ law parameter c. finally, a dimensional analysis of the cumulative fatigue damage and of the damage tolerant approaches has been proposed in [25], interpreting the observed deviations from the paris and wöhler regimes within a unified theoretical framework. this approach promises to bring simplicity in what has been up to now considered as an unexplained set of data, putting into evidence the role of the most influential variables on the fatigue behaviour of materials. the aim of the present study is to extend the dimensional analysis approach to quasi-brittle materials, determining the main dimensionless numbers influencing the d d/a n k and the s-n curves. more specifically, the possibility of incomplete self-similarity in the dimensionless numbers related to the microstructural size, the crack size and the structural size is explored in details. as a result, different aspects that have always been so far treated separately are herein interpreted within a unified mathematical framework. the corresponding incomplete self-similarity exponents and their dependencies on the dimensionless numbers are also quantified on the basis of relevant experimental data taken from the literature. the new proposed correlations provide useful information for design purposes. generalized mathematical representations of fatigue the generalized paris law ccording to the pioneering work by barenblatt and botvina [22], the following functional dependence can be put forward for the analysis of the phenomenon of fatigue crack growth:  ic th d , , ; , , , , , ;1 , d u a f k k k h d a e r n      (1) where the governing variables are summarized in tab. 1, along with their physical dimensions expressed in the lengthforce-time class (lft). variable definition symbol dimensions ultimate tensile strength u 2fl fracture toughness ick 3/ 2fl frequency of the loading cycle  1t stress-intensity factor range k 3/ 2fl threshold stress-intensity factor range thk 3/ 2fl stress range  2fl fatigue limit fl 2fl structural size h l microstructural size (aggregate or fibre size) d l crack length a l elastic modulus e 2fl loading ratio r  table 1: governing variables of the fatigue crack growth phenomenon. a http://dx.medra.org/10.3221/igf-esis.10.06&auth=true http://www.gruppofrattura.it m. paggi, frattura ed integrità strutturale, 10 (2009) 43-55; doi: 10.3221/igf-esis.10.06 46 considering a state with no explicit time dependence, it is possible to apply the buckingham’s  theorem [26] to reduce the number of parameters involved in the problem (see also [27-29] for the application to the quasi-static case). as a result, we have:   2 2 2 2 ic th 2 2 2 ic ic ic ic ic 2 ic d , , , , , ;1 d u u u u u i u k ka k e h d a r n k k k k k k                              (2) where i ( 1, , 7)i   are dimensionless numbers. note that 3 corresponds to the square of the dimensionless number z introduced by barenblatt and botvina [13] and to the inverse of the square of the brittleness number s introduced by carpinteri [17-19]. the number 5 was firstly considered by spagnoli [8] for the analysis of the crack-size dependence of the paris’ law parameters. here, it has to be noted that, according to irwin, the ratio  2ic / uk  , which is used to made dimensionless the variables h , d and a , is proportional to the plastic zone size, pr . the number 4 is related to the microstructural length scale and has been introduced in [24] in order to interpret the effect of the grain size in metals on the coefficient c of the paris’ law according to the experimental findings by chan [30]. as far as plain concrete is concerned, this microstructural length scale should correspond to the average size of the aggregates. for frc, the variable d should correspond to the fibre diameter and eq. (2) can be rewritten in order to put into evidence the fibre volumetric content. this parameter is computed as the ratio between the total area of fibres contained in a transversal cross-section of the specimen and the cross-section area of the specimen itself,    2/ 100 /f fv a a f d h   . here, the function f represents a shape function which depends on the transversal cross-section of the fibres and on their amount. for a square specimen cross-section of side h and for circular fibres we have 100 / 4ff n   , where fn is the total number of crossed fibres. in this case, instead of considering the dimensionless representation (2), where all the variables with a physical dimension of a length are made dimensionless using the plastic zone size, it is more convenient to use the following alternative form:   2 2 2 ic th 2 2 ic ic ic ic 2 ic d , , , , , , ;1 d u u u u i u k ka k d l e h a r n k k k h k d k                             (3) where the dimensionless number 4 has been replaced by * 4 4 3/ / /fd h v f      . moreover, the number 6 /l d  (fibre length/fibre diameter) has also been suitably introduced in eq. (3) and it corresponds to the fibre aspect ratio. at this point, we want to see if the number of quantities involved in the relationships (2) or (3) can be reduced further from seven (or height). this can occur either in the case of complete or incomplete self-similarities in the corresponding dimensionless numbers. in the former situation, the dependence of the mechanical response on a given dimensionless number, say i , disappears and we can say that i is non essential for the representation of the physical phenomenon. in the latter situation, a power-law dependence on i can be proposed, which usually characterizes a physical situation intermediate between two asymptotic behaviours. considering the dimensionless number 1 ic/k k   , it has to be noticed that it rules the transition from the asymptotic behaviours characterized by the condition of nonpropagating cracks, when thk k   , to the pure griffithirwin instability, when crk k   . moreover, incomplete self-similarity in 1 would correspond to a power-law http://dx.medra.org/10.3221/igf-esis.10.06&auth=true http://www.gruppofrattura.it m. paggi, frattura ed integrità strutturale, 10 (2009) 43-55; doi: 10.3221/igf-esis.10.06 47 dependence of the crack growth rate on the stress-intensity factor range, which is experimentally confirmed by the use of the paris’ law for concrete [15-17]. therefore, complete self-similarity in 1 cannot be accepted and the assumption of incomplete self-similarity holds whenever k is far lower than ick , i.e., for 1 1  . as far as 3 is concerned, this number is expected to be particularly important in quasi-brittle materials, since it compares the structural size-scale h with the plastic zone size. as regards 4 (or * 4 for frc), we know that, in metals, incomplete self-similarity is attained for p/ 1d r  , i.e., for 4 1  [25,30]. a similar reasoning applies for 5 , that is incomplete self-similarity in this number is expected when the crack length is comparable with the process zone size [17]. as regards 8 , a dependence on r is very often observed and therefore incomplete self-similarity in 8 is expected for 80 1   . hence, assuming incomplete self-similarity in the dimensionless variables 1 , 3 , 4 , 5 and 8 , the following generalized representation of fatigue crack growth is derived starting from eq.(3):     1 2 43 5 3 51 2 4 3 1 2 3 4 2 3 4 2 2 2 ic 1 2 6 72 2 ic ic ic 1 2 6 7 2 2 2 2 2(1 ) ic d (1 ) , , d , , (1 ) fu u u f u vka k h a r n k k f k k h v a r f k                                                                   (4) where the exponent i and, consequently, the dimensionless function 1 , cannot be determined from considerations of dimensional analysis alone. moreover, it is important to remark that the exponents i may depend on the dimensionless numbers i . eq. (4) can be regarded as a generalized paris’ law (see the classical expression d d ma n c k  superimposed to fig. 1b), in which the main functional dependencies of the parameter c have been now explicitated. figure 2: the effect of incomplete self-similarity in 3 , 4 , 5 and 8 on the paris’ curves. in this mathematical framework, it emerges that the incomplete self-similarity exponent 1 simply corresponds to the paris’ law parameter m that can be evaluated as the slope of the bilogarithmic d da n vs. k curve (see fig. 2). usually, m varies from 5 up to 30 in quasi-brittle materials [31], a value particularly high as compared to metals, where m ranges between 2 and 4. for 1k  , the intercept of the straight line with the vertical axis provides the logarithm of the multiplicative parameter c (see fig. 2). under the assumptions of incomplete self-similarity discussed above, c is no longer a true constant, but it is rather a power-law function of h , fv and a . regarding the exponents 2 and 3 , it is reasonable to expect them less than zero, with a reduction of c by increasing either the size of the specimen or the amount of fibres. in fact, this would imply a shift of the vertical asymptote corresponding to max ick k towards http://dx.medra.org/10.3221/igf-esis.10.06&auth=true http://www.gruppofrattura.it m. paggi, frattura ed integrità strutturale, 10 (2009) 43-55; doi: 10.3221/igf-esis.10.06 48 higher values of k . this trend is consistent with the common observation that the fracture toughness of concrete is an increasing function of the size of the tested sample [32] and of the fibre volumetric content [10]. on the contrary, short cracks are expected to grow faster than long cracks [19] and therefore the exponent 4 is expected to be positive valued. the same reasoning holds for the loading ratio. it is important to note that the above scaling law has been derived by considering the stress-intensity factor range as the driving parameter for crack growth. however, in quasi-brittle materials, where the cohesive crack model is routinely applied to describe crack propagation, it is also possible to find numerical results relating the crack growth rate to the range of energy release rate, g . power-laws of the paris form relating the crack growth rate to g still hold [33] and eq. (1) could be replaced by the following expression:  f th d , , ; , , , , , ;1 d u a f g g g h d a e r n      (5) where the fracture energy, fg , has been suitably introduced instead of the fracture toughness ick and the existence of a threshold range of energy release rate, thg , has been postulated. hence, eq. (3) would become: thf f f f f d , , , , , , ;1 d u u u u gga g d l e h a r n g g g h g d             (6) where we recognize that the dimensionless number governing the size-scale effects is no longer equal to 2 2 ic1/ /us h k as in eq. (3), but it is now represented by the inverse of the energy brittleness number, e f1/ /us h g . however, it is possible to demonstrate that eq. (6) implies eq. (3) and viceversa. therefore, the dimensionless representation in eq. (3) is equivalent to that in eq. (6) and no additional dimensionless numbers have to be introduced. recalling the irwin’s relationship between the stress-intensity factor and the energy release rate, it is possible to recast eq. (6) in terms of stress-intensity factors. in doing that, we note that the energy brittleness number es is equal to the stress brittleness number s times the inverse of the dimensionless number / ue  [34], i.e.,  2e / / us s e  . therefore, es is nothing but a linear combination of two dimensionless numbers already defined in eq. (3). hence, considering plane stress conditions, eq. (6) can be rewritten as follows: 2 ic th 2 2 ic ic ic ic d , , , , , , ;1 d u u u u k k e ea k d l e h a r n e k k k h k d             (7) which can be further manipulated by replacing the young’s modulus with the tensile strength, since the value of the ratio between these two variables is already taken into consideration by the dimensionless number / ue  . therefore, after such a substitution, eq. (7) becomes identical to eq. (3). the inverse implication is straightforward and can be gained by applying the inverse of the irwin’s relationship. the generalized wöhler representation o far, the crack growth rate has been chosen as the main output parameter characterizing the phenomenon of fatigue crack growth. however, it is also possible to consider the number of cycles, n, as the parameter representative of fatigue. following this alternative route, we postulate again the following functional dependence:  ic, , ; , , , , , ;1u fln f k h d a e r       (8) where the definition of the governing variables is provided in tab. 1. considering a state with no explicit time dependence, it is possible to apply the buckingham’s  theorem [26] to reduce the number of parameters involved in the problem: s http://dx.medra.org/10.3221/igf-esis.10.06&auth=true http://www.gruppofrattura.it m. paggi, frattura ed integrità strutturale, 10 (2009) 43-55; doi: 10.3221/igf-esis.10.06 49   2 2 2 2 ic ic , , , , , , ;1 fl u u i u u u d l e n h a r k h k d                  (9) where  is a dimensionless function. note that eq. (9) has been derived from eq. (8) by choosing u , ick and the plastic zone size as the main variables whose suitable combination provides a dimensionless number. at this point, we want to see if the number of quantities involved in the relationship (9) can be reduced further from height. in close analogy with the procedure carried out for the paris’ law, we assume incomplete self-similarity in 1 , 3 , 4 , 5 and 8 (the same conditions apply to the dimensionless numbers as in the derivation of eq. (4)), obtaining:           1 2 43 5 531 2 4 2 3 43 1 2 3 4 2 2 2 2 6 72 2 ic ic 2 2 6 7 2 2 2 2 ic 1 , , , , 1 fu u u f u v n h a r k f k h v a r f k                                                          (10) eq. (10) represents a generalized wöhler relationship of fatigue and encompasses the empirical s-n curves as limit cases. for instance, the s-n curve in fig. 1a can be approximated by the basquin power law: 1 n n nu fln n k        (11) where u is the range of stress at static failure, fl is the fatigue limit corresponding to a conventional fatigue life of 71 10n   cycles,  is the stress range corresponding to a fatigue life n and k is a constant. equating the first and the third terms in eq. (11), we obtain he following power-law equation:  1n n nuu n r n           (12) hence, the basquin power law is predicted as a limit case of eq. (10) when 1 n   , 2 3 4 0     and 5 n  . figure 3: the effect of incomplete self-similarity in 3 , 4 , 5 and 8 on the s-n curves. therefore, in this framework, the incomplete self-similarity exponent 1 simply corresponds to basquin parameter n that can be evaluated as the slope of the  vs. n curve in a bilogarithmic diagram (see fig. 3). for 1n  , the http://dx.medra.org/10.3221/igf-esis.10.06&auth=true http://www.gruppofrattura.it m. paggi, frattura ed integrità strutturale, 10 (2009) 43-55; doi: 10.3221/igf-esis.10.06 50 intercept of the straight line with the vertical axis provides the logarithm of the multiplicative parameter u (see fig. 3). under the assumptions of incomplete self-similarity discussed above, we expect 2 less than zero, with a reduction of u by increasing the size of the specimen. note that this trend is fully consistent with the well-known size-scale effects on the tensile strength of quasi-brittle materials [32] and with the recent findings in [35]. similarly, we expect 4 0  as for metals [36]. as regards the fibre volumetric content and the loading ratio, an opposite trend is expected, with 3 and 5 positive valued (see fig. 3). application to quasi-brittle materials n this section, the generalized paris and wöhler representations of fatigue are applied to plain concrete and frc, providing a dimensional analysis interpretation to some of the most relevant experimental trends found in the literature. more specifically, the effect of the microstructural size (fibre diameter), of the crack size and of the structural size are carefully discussed. the effect of the microstructural size as shown in section generalized mathematical representations of fatigue, the use of fibres is beneficial from the fatigue standpoint, since an increase in fibre diameter (or, equivalently, in volumetric content) corresponds to a decrease in crack growth rate for a given value of k and to an increase in the cycles to failure for a given value of  . the quantify such an effect, the experimental flexural fatigue data by johnston and zemp [8] can be profitably used. they tested square concrete beams in cyclic bending without fibres or with smooth wire fibres with different volumetric contents ( fv  0.5, 1.0 and 1.5%). all the fibres have an aspect ratio / 75l d  . the original s-n results are reported in the bilogarithmic diagram of fig. 4, along with the best-fitting power-law regression curves. according to eq. (10), the exponent of n corresponds to 11/  and we note that it is almost independent of the fibre volumetric content, ranging from 0.0218 to 0.0249 . for this type of fibres, the average value of 1 is then equal to 43 . on the other hand, the multiplicative coefficient of the variable n corresponds to u and this parameter is significantly affected by the presence of fibres. plotting the values of u vs. the volumetric content in fig. 5 and determining the best-fitting power-law equation, we find 0.266.37u fv  . according to eq. (10) evaluated in correspondence of 1n  , the exponent of fv is equal to 3 1/  , leading 3 10.26 11.3    . figure 4: the effect of the fibre volumetric content, fv , on the s-n curves as a result of incomplete self-similarity in 4 (experimental data from [8], aspect ratio / 75l d  ). i http://dx.medra.org/10.3221/igf-esis.10.06&auth=true http://www.gruppofrattura.it m. paggi, frattura ed integrità strutturale, 10 (2009) 43-55; doi: 10.3221/igf-esis.10.06 51 figure 5: determination of the incomplete-self-similarity exponent 3. as pointed out by johnston and zemp [8], the fibre aspect ratio has an important effect on the fatigue behaviour of frc, whereas the fibre type (smooth wire, surface deformed wire, melt-extract and slit sheet) is of secondary importance. to show this effect in terms of dimensional analysis arguments, let us consider the experimental results by singh et al. [12]. they tested frc beams under fatigue loading with different volumetric content of fibres ( 1.0, 1.5fv  and 2.0% ). however, instead of using a single fibre type as in [8], 50% of their total weight has an aspect ratio of / 20l d  and the remainder has an aspect ratio of / 40l d  . again, as for the previous case, the higher the volumetric content, the higher the fatigue life for a given applied stress range (see fig. 6). however, now the s-n curves have an average slope equal to 0.030 , corresponding to an exponent 1 33   . this value is significantly higher than 43 found in the case of a higher aspect ratio equal to 6 / 75l d   . according to dimensional analysis, this difference has to be ascribed to the different value of the aspect ratio and to the fact that the power-law exponent 1 depends on 6 . from the engineering point of view, the use of longer fibres is clearly advantageous, since it increases the fatigue life of the specimen for a given applied stress range, reducing the exponent 1 . figure 6: s-n curves of beams tested in flexural fatigue with 50% of fibres with / 20l d  and the remainder with / 40l d  (experimental data taken from [12]). the effect of the crack size modified paris’ laws taking into account the effect of the crack size have been proposed both for metals and for quasibrittle materials. for metals, several researchers have questioned the validity of the similitude hypothesis, which states that http://dx.medra.org/10.3221/igf-esis.10.06&auth=true http://www.gruppofrattura.it m. paggi, frattura ed integrità strutturale, 10 (2009) 43-55; doi: 10.3221/igf-esis.10.06 52 “two different sized cracks embedded into two different sized bodies subjected to the same stress-intensity factor range should grow at the same rate”. as a support to the theories against the similitude hypothesis, we mention the experimental results by newman et al. [37], who observed that “in the threshold regime there is something missing in the (closure) model”, and those by forth et al. [36], revealing that similitude does not hold in region i (the near-threshold region) and also in the lower portion of region ii. to overcome this problem, molent et al. [39] and jones et al. [40] have recently proposed a generalized frost and dugdale crack growth law, assuming that the crack growth rate is proportional to the accumulated plastic strain, averaged over a characteristic length ahead of the crack tip, ' (1 '/ 2) 'd / d m ma n c a k  , where c’ and m’ are regarded as material constants. this equation states that d / da n is not only a function of the stressintensity factor range, but also of the crack length. such a generalized frost and dugdale crack growth equation was successfully used to predict the growth of near micron sized cracks in both coupon and full scale aircraft fatigue tests and interpret a large amount of experimental data that could not be modelled using the paris’ law. for concrete, a detailed experimental examination of crack propagation in flexural fatigue [17] has shown that the crack growth rate is not a monotonic increasing function of the crack length. for cracks shorter than the crack length at peak load in quasi-static monotonic loading, a deceleration stage was found, where da/dn is a decreasing function of a. afterwards, an acceleration stage takes place and da/dn can be well approximated according to the classical paris’ law [17]. to model the deceleration stage, kolloru et al. [17] proposed an empirical relationship between da/dn and the crack length, apparently independent of the paris’ law. actually, it can be interpreted as a particular case of our proposed generalized paris’ law, simply allowing a crack-size dependence of the coefficient c , i.e., setting 1 2( / 2)n nc a  4 1 2( / 2)n n   , where 1n and 2n are the power-law exponents for the two regimes found in [17]. the effect of the structural size the effect of the structural size can be highlighted by considering the experimental data by bažant and xu [15] for normal strength concrete and by bažant and shell [16] for high strength concrete, subsequently re-examined by spagnoli [41]. from their experimental results on self-similar beams tested in cyclic bending, the computed paris’ law exponent 1m  was found to be dependent on the structural size. plotting m vs. 3 in fig. 7, we recognize that m is a linear decreasing function of 3 for each type of concrete. the effect of the ultimate tensile strength is also important, since it affects the dimensionless number 7 / ue   . for normal strength concrete we have 7 9686  , whereas for high strength concrete we have 7 4303  and the slope of the linear relationship between m and 3 turns out to be an increasing function of 7 (see fig. 7). figure 7: size-scale effects on the paris’ law exponent 1m  for normal and high strength concrete (experimental data from [15,16] reinterpreted in [41]). http://dx.medra.org/10.3221/igf-esis.10.06&auth=true http://www.gruppofrattura.it m. paggi, frattura ed integrità strutturale, 10 (2009) 43-55; doi: 10.3221/igf-esis.10.06 53 the experimental data by bažant and xu [15] for normal strength concrete and by bažant and shell [16] for high strength concrete can also be used to assess the hypothesis of incomplete self-similarity in 3 and therefore the size-scale effect on the parameter c . plotting the paris’ law coefficient c vs. 3 in a bilogarithmic diagram and computing the bestfitting power-law regression curves, we find 2 4.7  for normal strength concrete and 2 1.1  for high strength concrete (see fig. 8). figure 8: size-scale effects on the paris’ law coefficient c (evaluated using k in mpa m and da/dn in m/cycle) as a result of incomplete self-similarity in 3 for normal and high strength concretes (experimental data from [15,16] reinterpreted in [41]). incomplete self-similarity in 3 is also expected to occur in the wöhler regime, as recently put into evidence for metals in [35] on the basis of fractal concepts. for concrete specimens, the experimental data by zhang and stang [9] and murdock et al. [42] show that the s-n curves corresponding to two different sizes are almost parallel to each other and translate vertically. in particular, the larger the beam size, the lower stress range at static failure (see fig. 8). this result is in perfect agreement with the present theoretical predictions and with the numerical findings by zhang et al. [11]. in this case, however, it is not possible to compute the incomplete self-similarity exponent 2 , since we have only two values of ( 1) un     for different beam depths. figure 9: the effect of the structural size on the s-n curves (experimental data taken from [9,42]). http://dx.medra.org/10.3221/igf-esis.10.06&auth=true http://www.gruppofrattura.it m. paggi, frattura ed integrità strutturale, 10 (2009) 43-55; doi: 10.3221/igf-esis.10.06 54 conclusions n the present paper, a generalized barenblatt and botvina dimensional analysis approach to fatigue crack growth has been proposed in order to highlight and explain the deviations from the classical power-law equations used to characterize the fatigue behaviour of quasi-brittle materials. it has been theoretically demonstrated that both the parameters entering the paris’ law and the wöhler equation are microstructural-size, crack-size and size-scale dependent. from the theoretical point of view, these anomalous dependencies are due to incomplete self-similarities in the corresponding dimensionless numbers. more specifically, as far as the paris’ law is concerned, it has been shown that the higher the structural size or the volumetric content of fibres, the lower the crack growth rate for a given stress-intensity factor range. conversely, the higher the initial crack size or the loading ratio, the higher the crack growth rate. regarding the s-n curves, the higher the structural size or the initial crack length, the lower the fatigue life for a given stress range. the opposite trend is noticed for the volumetric content of fibres and the loading ratio. finally, we have also shown that the slopes of the s-n curves are dependent on the fibre aspect ratio. similarly, the slope of the paris’ curve is found to be dependent on the size of the specimen and on the ratio between the elastic modulus of concrete and its tensile strength. all these information are expected to be extremely useful for the design of experiments, since the role of the different dimensionless numbers governing the phenomenon of fatigue has been elucidated. references [1] d. a. hordijk, heron, 37 (1992) 1. [2] a. wöhler, z. bauwesen (1860) 10. [3] o. h. basquin, proc. astm, 10 (1910) 625. [4] j. w. murdock, c. e. kesler, aci j., 55 (1959) 221. [5] r. tepfers, aci j., 76 (1979) 919. [6] j. e. butler, strain, 26 (2008) 135. [7] v. ramakrishnan, g. oberling, p. tatnall, sp-105-13, aci special publication, aci, detroit (1987) 225. [8] c. d. johnston, r. w. zemp, aci mater. j., 88 (1991) 374. [9] j. zhang, h. stang, aci mat. j., 95 (1998) 58. [10] j. zhang, h. stang, v.c. li, asce j. mat. in civ. engrg., 12 (2000) 66. [11] j. zhang, v.c. li, h. stang, asce j. mater. civil engng., 13 (2001) 446. [12] s.p. singh, y. mohammadi, s.k. madan, j. zhejiang university science a, 7 (2006) 1329. [13] p. paris, m. gomez, w. anderson, 13 (1961) 9. [14] p. paris, f. erdogan, j. basic eng. trans. asme, 58d (1963) 528. [15] z.p. bažant, k. xu, aci mater. j., 88 (1991) 390. [16] z.p. bažant, w.f. shell, aci mater. j., 90 (1993) 472. [17] s.v. kolloru, e.f. o’neil, j.s. popovics, s.p. shah, asce j. engng. mech., 126 (2000) 891. [18] al. carpinteri, m. paggi, engng. fract. mech., 74 (2007) 1041. [19] m. paggi, al. carpinteri, chaos, solitons and fractals, 40 (2009) 1136. [20] t. matsumoto, v.c. li, cement & concrete composites, 21 (1999) 249-261. [21] k. l. roe, t. siegmund, engng. fract. mech., 70 (2003) 209. [22] g. i. barenblatt, l. r. botvina, fat. fract. engng. mater. struct., 3 (1980) 193. [23] g. i. barenblatt, scaling, self-similarity and intermediate asymptotics. cambridge: cambridge university press, (1996). [24] m. ciavarella, m. paggi, al. carpinteri, j. mech. phys. solids, 56 (2008) 3416. [25] al. carpinteri, m. paggi, int. j. fatigue, in press, doi: 10.1016/j.ijfatigue.2009.04.014 [26] e. buckingham, asme trans., 37 (1915) 263. [27] al. carpinteri, rilem mat. struct., 14 (1981) 151. [28] al. carpinteri, engng. fract. mech., 16 (1982) 467. [29] al. carpinteri, rilem mat. struct., 16 (1983) 85. [30] k. chan, scripta metal. mater., 32 (1995) 235. [31] n. a. fleck, k. j. kang, m. f. ashby, acta metall. mater., 42 (1994) 365. [32] al. carpinteri, mech. mater., 18 (1994) 89. i http://dx.medra.org/10.3221/igf-esis.10.06&auth=true http://www.gruppofrattura.it m. paggi, frattura ed integrità strutturale, 10 (2009) 43-55; doi: 10.3221/igf-esis.10.06 55 [33] y. xu, h. yuan, proc. of the 12th international conference on fracture, ottawa, canada, (2009). [34] al. carpinteri, in: size-scale effects in the failure mechanisms of materials and structures (proceedings of a iutam symposium, torino, italy, 1994), ed. a. carpinteri, e & fn spon, london, (1996) 3. [35] an. carpinteri, a. spagnoli, s. vantadori, int. j. fatigue, 31 (2009) 927. [36] j.c. newman, jr., e.p. phillips, m.h. swain, int. j. fatigue, 21 (1999) 109. [37] j.c. newman, jr., a. brot, c. matias, engng. fract. mech., 71 (2004) 2347. [38] s.c. forth, w.m. johnston, b.r. seshadri, proc. 16th european conf. fracture, alexandroupolis, greece, (2006). [39] l. molent, r. jones, s. barter, s. pitt, int. j. fatigue, 28 (2006) 1759. [40] r. jones, l. molent, s. pitt, int. j. fatigue 29, (2007) 1658. [41] a. spagnoli, mech. mat., 37 (2005) 519. [42] j.w. murdock, c.e. kesler, aci j., 55 (1959) 221. http://dx.medra.org/10.3221/igf-esis.10.06&auth=true http://www.gruppofrattura.it microsoft word numero_51_art_20_2622 m. s. bennouna et alii, frattura ed integrità strutturale, 51 (2020) 254-266; doi: 10.3221/igf-esis.51.20 254 numerical investigation of the effect of constrained groove pressing process on the mechanical properties of polyamide pa66 mohammed salah bennouna university of kasdi merbah ouargla, algeria bennouna_ms@yahoo.fr, http://orcid.org/ 0000-0002-3694-9993 sadek kaddour, aour benaoumeur labab laboratory, enporan, algeria sadekkaddour@gmail.com, ben_aour@yahoo.fr damba nadir university of adrar, algeria boudjmaa.damba@yahoo.fr abstract. this research is a numerical study of the effect of the constrained groove pressing (cgp) process and its impact on a thermoplastic polymer (polyamide pa 66). a simulation is performed using a finite element tool. the effect of the process conditions and the tool geometry on the mechanical properties is noted. the results are significant, the equivalent strain and von mises stress have been progressed accordingly to the number of cycles and the tool geometry. concluding remarks on the alteration of the microstructure have been proclaimed at the end of this paper. keywords. fea method; polymer; stress; strain; cgp; spd. citation: bennouna, m. s., kaddur, s., aour, b., damba, n.,. numerical investigation of the effect of constrained groove pressing process on the mechanical properties of polyamide pa66, frattura ed integrità strutturale, 51 (2020) 254-266. received: 30.08.2019 accepted: 26.11.2019 published: 01.01.2020 copyright: © 2020 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. introduction any research works have been carried out on several super plastic deformation (spd) processes to introduce a large plastic deformation into bulk materials to give them an ultra-fine grained structure. these processes are used in the industry as metal forming processes but in this work we are using one of these processes (cgp) on polymeric materials to improved mechanical and physical properties which destine them for a wide commercial use such as biomechanical materials. m http://www.gruppofrattura.it/va/51/2622.mp4 m. s. bennouna et alii, frattura ed integrità strutturale, 51 (2020) 254-266; doi: 10.3221/igf-esis.51.20 255 nowadays it is evident that the numerical approach completes the experimental one in the research activity. in this context comes the present study which completes a detailed experimental study of the effect of cgp on polymer (pa66) was carried out and published by bennouna et al [1]. note that the cgp process is performed with two tools, a corrugating one for applying intense plastic deformation to material and a straightening one to restore the straight shape of the sample. this study applies the fem (finite element method) approach which is widely applied by researchers. among the most successful applications this method we find the modeling of the deformation of material [2-5]. noting that deformation, rate of deformation and chemical composition are parameters which have a significant effect on the mechanical properties of the material [6, 7]. many phenomenological models have been used to simulate the intense plastic deformation of polymeric materials such as those used by bardenhagen et al [8], frank and brockman [9], colak [10] and which has been by several researchers such as aour et al. [11-13], mitsak [14] and draï and aour [15] and that used by estrin et al and improved by mckenzie et al [16] and also by hosseini and kazminezhad [17]. simulating intense deformations such as those induced by the cgp process using finite element is a very complex operation that those of small deformations because introducing simple definitions such as isotropic hardening or perfectly plastic conditions do not lead to precise results to see acceptable [ 18]. to describe the plastic deformation behavior of polymeric materials many constitutive models have been used by searchers to simulate semi crystalline polymers with a finite element tool such as abaqus. in general these models are based on the additive decomposition of the strain rate tensor d into an elastic part de and a viscoplastic part dvp: d = de + dvp note that a single pressing of cgp process yields a shear strain of =h/h =1 (where h is the groove wide) at deformed region. this is equivalent to an effective strain εeff = 2 4 2 3       = 0.58 but the present simulation was carried out by injecting into the modeling; the true parameters extracted from the experimental tests and corrected using the correction factor of the machine which leads to engineering values. for this reason, experimental tensile tests were performed on pa66 samples to obtain the stress-strain curve shown in fig. 1 [1]. figure 1: stress-strain curve obtained from a tensile test on pa66 polyamide [1]. m. s. bennouna et alii, frattura ed integrità strutturale, 51 (2020) 254-266; doi: 10.3221/igf-esis.51.20 256 figure 2: different phases that the sample undergo during the tensile test. fig. 1and fig.2 show that the deformation of the material passes through three different phases: the first (i) is a phase of elastic deformation, the second (ii) is a phase of plastic deformation with a low strain hardening, and in the third phase (iii), a softening was noted (stress drop) which results of the high ductility of this polymer, which determines a fast lowering stress, but this is due to the use of engineering strains. data of this experimental curve are used for the numerical simulation. material and methods he simulations were run using abaqus, an fe tool. the initial dimensions of the pa66 sample used are the same as those used in the experimental study carried out and published by bennouna et al (87 × 45 × 3 mm), (2018) [1]. the same boundary conditions were also used with a mesh of 4935 4-node quadrilateral elements of the cpe4r type (fournode plane strain element) (fig. 3). note that true strains values are used for the simulation and not nominal values. figure 3: finite element discretization of samples. as shown in fig. 4 pure shear occurs in the inclined areas of the sample but some regions remain undeformed, which means that the microstructure has certain heterogeneity (fig 5). to overcome this disadvantage and introduce a uniform deformation in the workpiece, the sample is placed on the right side of tool during one cycle and then pushed to the left side during the next cycle. the friction metal/polymer was considered in the simulation although the surfaces of the dies and samples were polished to reduce it. t m. s. bennouna et alii, frattura ed integrità strutturale, 51 (2020) 254-266; doi: 10.3221/igf-esis.51.20 257 figure 4: illustration of the plastic deformation zones during the cgp process. figure 5: sample after plastic deformation of the cgp process. result and discussion influence of the number of cycles o demonstrate how the number of cycles affects the equivalent strain that different surfaces of the samples undergo (fig.6) the process was repeated three times (cycles). the results obtained for the different cycles are illustrated in figs. 7 to 12. fig.7 illustrates the evolution of voe mises during three different cycles of cgp. figure 6: different paths selected for study. t m. s. bennouna et alii, frattura ed integrità strutturale, 51 (2020) 254-266; doi: 10.3221/igf-esis.51.20 258 (a) one cycle (b) two cycles (c) three cycles figure 7: distribution of von mises constraints for different numbers of cycles. figure 8: influence of the number of cycles on the evolution of the plastic strain at the level of the upper surface. m. s. bennouna et alii, frattura ed integrità strutturale, 51 (2020) 254-266; doi: 10.3221/igf-esis.51.20 259 case of a path of the upper face the equivalent strain on the upper surface increases progressively with the number of cycles, the maximum value goes from 1.25 in the first cycle to 4.5 in the third cycle (fig. 8). case of a path of the middle face as for the upper surface, the value of the equivalent plastic strain induced by the median path increases with the number of cycles applied but with less values than those induced by the upper surface. indeed, the maximum value of the equivalent plastic strain does not exceed 0.81 in the third cycle (fig. 9). figure 9: influence of the number of cycles on the evolution of the plastic strain at the level of the median surface of the sample. case of a path of the lower face the equivalent plastic strain at the bottom surface of the sample increases gradually with the number of cycles. indeed, the maximum value goes from 0.9 for the first cycle to 3.45 for the third cycle (fig. 10). figure 10: influence of the number of cycles on the evolution of the plastic strain at the level of the upper surface. fig. 11 presents a comparison between the evolutions of the equivalent plastic strain introduced by the number of cgp cycles at the different paths selected in the sample. it is clear that the equivalent plastic strain increases progressively with the number of cycles for the three types of selected paths. we can also see that the equivalent plastic strain in the middle of the sample is very small compared to the other two surfaces for the case of the three cycles and that the lower surface keep the same value of equivalent plastic strain during the second and the third cycles. m. s. bennouna et alii, frattura ed integrità strutturale, 51 (2020) 254-266; doi: 10.3221/igf-esis.51.20 260 figure 11: evolution of maximal equivalent plastic strain along the selected paths, for different numbers of cycles. influence of the groove angle in this section, we will evaluate the influence of the dimensions of the groove of the tool on the equivalent plastic strain at the level of the different paths. for this reason, we selected three different values (30 °, 45 ° and 60 °) for the angle β as shown in fig. 12. figure 12: illustration of the different values of the angle β of the tool groove. the depth of the groove was fixed to 7mm. the results of the third cycle obtained for the three different selected trajectories (lower, middle and upper) are presented respectively in figs. 13, 14 and 15. case of a path of the upper face according to fig. 13, it is the tool of 60 ° which ensures a higher equivalent plastic strain for the upper surface with a maximum value equal to 2.4, whereas, the weakest values are obtained at an angle of 30°. case of a path of the middle face in this case, we note that the angle of 60 ° is the one which ensures the maximum of equivalent plastic strain with a value of 2.4 (fig.14), whereas, the low values are obtained with the angle 30°. m. s. bennouna et alii, frattura ed integrità strutturale, 51 (2020) 254-266; doi: 10.3221/igf-esis.51.20 261 figure 13: evolution of the equivalent plastic strain for a path of the upper surface using different angles of grooves. figure 14: evolution of the equivalent plastic strain for a trajectory in the median of the sample using different angles of grooves. case of a path of the lower face fig. 15 illustrates the evolution of the equivalent plastic strain along the lower path for different angles of the groove of the dies. it may be noted that the angle of 45 ° is the one which ensures the maximum of plastic strain on this surface of the sample with a maximum value equal to 1.8, while the low values are obtained with the angle of 60 °. it is visibly clear that the angle of 60 ° ensures higher plastic strain than the ones of 30 ° and 45 ° for the upper surface and the middle surface of the sample. for the lower surface, it is the angle of 45 ° which ensures a maximum value of equivalent plastic strain. it can also be seen from fig. 16 that the value of the deformation increases progressively with the value of the angle with the exception of the lower surface. influence of the depth of the groove to evaluate the influence of the groove depth on the process results, the value of the angle β was fixed to 45 ° by varying the value of the depth of the groove h. three different values were used (3mm, 5mm and 8mm) as shown in fig. 17. m. s. bennouna et alii, frattura ed integrità strutturale, 51 (2020) 254-266; doi: 10.3221/igf-esis.51.20 262 figure 15: evolution of the equivalent plastic strain for a path of the lower surface using different groove angles. figure 16: evolution of maximum equivalent plastic deformations for different angles of the die groove. case of a path of the upper face fig. 18 shows the evolution of equivalent plastic strain along a path on the upper surface for different values of the depth of the groove. it can be noted that the highest level of plastic strain is obtained with a depth h = 5 mm, whereas the lowest level of plastic strain is obtained by the depth of 8 mm. m. s. bennouna et alii, frattura ed integrità strutturale, 51 (2020) 254-266; doi: 10.3221/igf-esis.51.20 263 figure 17: illustration of three configurations of the matrices by varying the depth of the groove: (a) h = 3mm, (b) h = 5mm, (c) h = 8mm. figure 18: evolution of the equivalent plastic deformation along a path on the upper surface, using different groove depths. case of a path of the middle face the evolution of the equivalent plastic strain along a trajectory in the middle of the sample using different groove depths is illustrated in fig. 19. it can be observed that the highest plastic deformations are obtained by a depth of 8 mm, whereas, the lowest values are obtained by h = 5 mm. case of a path of the lower face fig. 20 shows the evolution of equivalent plastic strain along a path on the lower surface for different values of the depth of the groove. it can be noted that the highest level of plastic strain is obtained with a depth h = 5 mm, whereas the lowest level of plastic deformation is obtained by the depth of 3 mm. m. s. bennouna et alii, frattura ed integrità strutturale, 51 (2020) 254-266; doi: 10.3221/igf-esis.51.20 264 figure 19: evolution of equivalent plastic deformation along a path on the middle of the sample using different groove depths. figure 20: evolution of the equivalent plastic deformation along a path on the lower surface, using different groove depths fig. 21 summarizes the different results of the maximum values of equivalent plastic strain for different depth values of the groove. it can be noted that the highest values are obtained at the lower and upper surfaces with a depth h = 5 mm while the lowest values are obtained in the middle of the sample. for this surface the maximum equivalent strain is obtained by a groove with depth of 8 mm. m. s. bennouna et alii, frattura ed integrità strutturale, 51 (2020) 254-266; doi: 10.3221/igf-esis.51.20 265 figure 21: evolution of maximum equivalent plastic deformations for different depths of the die groove. conclusion he objective of this work was devoted to the numerical study of the cgp process for a typical semi-crystalline polymer which is polyamide (pa66). the effects of the main parameters, such as, the number of cycles, the angle of the groove and its depth have been highlighted. from the results obtained, we can draw the following conclusions:  in the general case, the equivalent plastic strain induced in the samples increases with the increase in the number of cycles applied.  the maximum values of the equivalent plastic strain on the paths of the upper and lower surfaces are much greater than that of the path taken in the middle of the sample.  the angle of inclination of the groove of the cgp dies significantly influences the evolution of the equivalent plastic strain. indeed, to obtain a relatively high level of plastic strain with a good homogeneity of distribution, it is recommended to use a 45 ° angle.  the groove depth of the cgp dies has a remarkable influence on the pa 66 equivalent plastic deformation. for a 3 mm thick plate, we found that a depth of 5 mm ensures the highest level of plastic deformation. high on the upper and lower surfaces. in the middle of the sample, it is the depth of 8 mm that achieves the highest level of plastic deformation. references [1] bennouna, m. s., aour, b., bouaksa, f., hamzaoui, s. (2018). experimental investigation of mechanical behavior of a polyamide before and after constrained groove pressing process, international journal of engineering research in africa, pp. 25-36. doi: 10.4028/www.scientific.net/jera.36.25. [2] yang, h., wang, m., guo, l.g., sun, z.c. (2008). 3d coupled thermo-mechanical fe modeling of blank size effects on the uniformity of strain and temperature distributions during hot rolling of titanium alloy large rings. comput mater sci, pp. 611–621. doi: 10.1016/j.commatsci.2008.04.026. [3] lee, j.w., park, j.j. (2002). numerical and experimental investigations of constrained groove pressing and rolling for grain refinement, j mater proc technol, pp. 208–213. doi: 10.1016/s0924-0136(02)00722-7. t m. s. bennouna et alii, frattura ed integrità strutturale, 51 (2020) 254-266; doi: 10.3221/igf-esis.51.20 266 [4] lee, h.r., sutcliffe, m.p.f. (2004). finite element modelling of the evolution of surface pits in metal forming processes, j mater proc technol, pp. 391–396. doi: 10.1016/s0924-0136(02)00722-7. [5] kim, t.s., kuwamurab, h. (2007). finite element modeling of bolted connections in thin-walled stainless steel plates under static shear. thin-walled struct, pp.407–421. doi: 10.1016/j.tws.2007.03.006 [6] lopesa, a.b., barlatb, f., gracioc, j.j., duarted, j.f.f., rauch,e e.f. (2003). effect of texture and microstructure on strain hardening anisotropy for aluminum deformed in uniaxial tension and simple shear. int j plast, pp.1–22. doi: 10.1016/s0749-6419(01)00016-x. [7] prasad g.v., goerdeler m., gottstein g. (2005). work hardening model based on multiple dislocation densities, mater sci eng, pp. 231–233. doi: 10.1016/j.msea.2005.03.061. [8] bardenhagen, s.g., stout, m.g., gray, g.t. (1997). three-dimensional, finite deformation, viscoplastic constitutive models for polymeric materials, mechanics of materials, pp. 235-253. doi: 10.1016/s0167-6636(97)00007-0. [9] frank, g.j., brockman, r.a. (2001). a viscoelastic-viscoplastic constitutive model for glassy polymers, international journal of solids and structures, pp. 5149-5164. doi: 10.1016/s0020-7683(00)00339-5. [10] colak, o.u. (2005). modelling deformation behaviour of polymers with viscoplasticity theory based on overstress, international journal of plasticity, pp. 145-160. doi: 10.1016/j.ijplas.2004.04.004. [11] aour, b. (2007). investigation of ecae process of semi crystalline polymers by a finite element and a coupled boundary element-finite element approach, thesis of doctorat in mechanical engineering, université des sciences et de la technologie d'oran, algérie. [12] aour, b., zairi, f., nait-abdelaziz, m., gloaguen, j.m., rahmani, o., lefebvre, j.m. (2008). a computational study of die geometry and processing conditions effects on equal channel angular extrusion of a polymer, international journal of mechanical sciences, pp. 589-602. doi: 10.1016/j.ijmecsci.2007.07.012. [13] aour, b., mitsak, a. (2016). .analysis of plastic deformation of semi-crystalline polymers during ecae process using 135° die, journal of theoritical and applied mechanics, 54(1), pp. 263-275. doi: 10.15632/jtam-pl.54.1.263. [14] mitsak, a. (2017). contribution à la modélisation du comportement des polymères solides au cours du processus d’extrusion angulaires à égales sections, thesis of doctorat in mechanical engineering enporan algeria [15] draï, a., aour, b. (2013). analysis of plastic deformation behavior of hdpe during high pressure torsion process, engineering structures, pp. 87–93. doi: 10.1016/j.engstruct.2012.06.033. [16] mckenzie, p.w.j., lapovok, r., estrin, y. (2007). the influence of back pressure on ecap processed aa 6016: modeling and experiment, acta mater, pp. 2985–2993. doi: 10.1016/j.actamat.2006.12.038. [17] hosseini, e., kazeminezhad, m. (2008). a hybrid model on severe plastic deformation of copper, compute mater sci, pp. 1107–1115. doi: 10.1016/j.commatsci.2008.07.024. [18] aretz, h., luce, r., wolske, m., kopp, r., goerdeler, m., marx, v. (2000). integration of physically based models into fem and application in simulation of metal forming processes, modell simul mater sci eng, pp.881–891. doi: 10.1088/0965-0393/8/6/309. << /ascii85encodepages false /allowtransparency false /autopositionepsfiles true /autorotatepages /none /binding /left /calgrayprofile (dot gain 20%) /calrgbprofile (srgb iec61966-2.1) /calcmykprofile (u.s. web coated \050swop\051 v2) /srgbprofile (srgb iec61966-2.1) /cannotembedfontpolicy /error /compatibilitylevel 1.4 /compressobjects /tags /compresspages true /convertimagestoindexed true /passthroughjpegimages true /createjobticket false /defaultrenderingintent /default /detectblends true /detectcurves 0.0000 /colorconversionstrategy /cmyk /dothumbnails false /embedallfonts true /embedopentype false /parseiccprofilesincomments true /embedjoboptions true /dscreportinglevel 0 /emitdscwarnings false /endpage -1 /imagememory 1048576 /lockdistillerparams false /maxsubsetpct 100 /optimize true /opm 1 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/hrv (za stvaranje adobe pdf dokumenata najpogodnijih za visokokvalitetni ispis prije tiskanja koristite ove postavke. stvoreni pdf dokumenti mogu se otvoriti acrobat i adobe reader 5.0 i kasnijim verzijama.) /hun 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/pdfxoutputintentprofileselector /documentcmyk /preserveediting true /untaggedcmykhandling /leaveuntagged /untaggedrgbhandling /usedocumentprofile /usedocumentbleed false >> ] >> setdistillerparams << /hwresolution [2400 2400] /pagesize [612.000 792.000] >> setpagedevice microsoft word numero 9 art 10 finale a. pirondi et alii, frattura ed integrità strutturale, 9 (2009) 95 104; doi: 10.3221/igf-esis.09.10 95 simulazione della propagazione di difetti a fatica mediante il modello di zona coesiva a.pirondi, f.moroni università degli studi di parma, dipartimento di ingegneria industriale , v.le g.p. usberti 181/a, 43100 parma; alessandro.pirondi@unipr.it riassunto. le giunzioni incollate guadagnano sempre più mercato, nel campo delle costruzioni in genere, dove è necessario un alleggerimento delle strutture. nel caso di geometrie di giunto semplici il dimensionamento avviene attraverso relazioni analitiche che restituiscono il valore massimo delle tensioni, il quale deve essere inferiore al limite di utilizzo dell’adesivo stesso. quando le geometrie sono complesse l’approccio analitico diventa impraticabile, di conseguenza si provvede a verificare la correttezza della soluzione mediante analisi agli elementi finiti (ef). l’introduzione del modello di zona coesiva nell'analisi ef permette di simulare il danneggiamento ed il cedimento del giunto in condizioni quasi-statiche e impulsive. in questo articolo si vuole implementare il modello per la simulazione della propagazione a fatica di difetti, utilizzando il software agli elementi finiti abaqus assieme a subroutine esterne interagenti con il modello ef stesso. un punto focale dell'implementazione sarà il calcolo automatico del tasso di rilascio di energia g in modo indipendente dalla geometria del difetto stesso. i parametri del modello ricavati da prove di tenacità a frattura e propagazione di difetti a fatica in modo i, saranno utilizzati come riferimento per la convalida dell'implementazione. abstract. this work deals with the prediction of the fatigue crack growth of bonded joints. traditionally cohesive zone model is used for the simulation of failure of bonded joint under quasi-static and impact conditions. on the other hand fracture mechanics concepts are used for the prediction of fatigue crack growth in bonded joint. in this work a modified cohesive damage model, accounting for the fatigue crack growth, was implemented in the commercial software abaqus. the fatigue damage evolution in the cohesive element is related to the number of cycles through the experimental fatigue crack growth behavior. an automated procedure, valid for any from the geometry and load distribution, was also defined to compute the strain energy release rate, the necessary input to define the instantaneous fatigue crack growth rate. the model is validated by comparing the simulation to fatigue crack growth tests. parole chiave. fem; modello di zona coesiva; giunti incollati; fatica; propagazione difetti. introduzione fenomeni che portano un giunto incollato al collasso possono sia essere dovuti a carichi quasi statici che a carichi affaticanti. a seconda dei casi, le metodologie utilizzate per la previsione della resistenza del giunto possono consistere in: i) previsioni basate su modelli analitici; ii)simulazioni agli elementi finiti (ef). in entrambi i casi si può valutare quindi se riferirsi semplicemente alle tensioni nell'adesivo o se adottare un approccio più generale di meccanica della frattura. in quest'ultimo caso, la simulazione ef con il modello di zona coesiva [1, 2] è un metodo efficace per la previsione di cedimento in condizioni quasi-statiche e impulsive [3 – 11]. in particolare il modello di zona coesiva prevede un legame tra le tensioni che si possono avere in prossimità dell’apice del difetto e l'apertura e/o scorrimento dello stesso. questo modello di comportamento può essere mutuato per simulare il danneggiamento legato a fenomeni di fatica [12-17]. nella maggior parte di questi lavori i parametri del modello vengono i http://www.gruppofrattura.it/ http://dx.medra.org/10.3221/igf-esis.09.10&auth=true mailto: alessandro.pirondi@unipr.it a. pirondi et alii, frattura ed integrità strutturale, 9 (2009) 95 104; doi: 10.3221/igf-esis.09.10 96 opportunamente tarati in modo da riprodurre prove di propagazione a fatica di difetti, mentre in [12] la degradazione a fatica della zona coesiva è legata direttamente al rateo di avanzamento ciclico del difetto attraverso un modello di omogeneizzazione del danno (transizione micro-macroscala). il limite del lavoro effettuato in [12] è rappresentato dalla mancanza di generalità nel calcolo del valore del tasso di rilascio di energia, g, da cui dipende la velocità di avanzamento del difetto. in questo articolo si vuole implementare un modello per la simulazione della propagazione di difetti a fatica basato sul lavoro presentato in [12]. l'implementazione sfrutterà il software agli elementi finiti abaqus attraverso l’utilizzo di subroutine esterne interagenti con il modello ef stesso. un punto focale dell'implementazione sarà il calcolo automatico di g in modo indipendente dalla geometria del difetto stesso. i parametri del modello ricavati da prove di tenacità a frattura e propagazione di difetti a fatica in modo i, saranno utilizzati per come riferimento per la convalida dell'implementazione. aspetti teorici l modello di zona coesiva è un modello ampiamente studiato e utilizzato, in cui la frattura viene descritta come un fenomeno di progressiva separazione lungo una porzione di materiale, detta appunto zona coesiva, nella quale agiscono trazioni all’interfaccia delle superfici di frattura, come schematicamente mostrato in fig.1. figura 1: modello di zona coesiva. si può quindi definire un legame tra l’apertura del difetto e la tensione esercitata, come ad esempio riportato in fig. 2. figura 2: legame tensioni-apertura per il modello di zona coesiva. la prima parte è puramente elastica, mentre superato δ0, il comportamento è caratterizzato da un danno d che agisce degradando la rigidezza rispetto a quella iniziale, fino a δc in cui non viene esercitata più alcuna tensione all’interfaccia. si può quindi pensare l’interfaccia come una zona in grado di assorbire un energia  pari all’area sottesa dal triangolo, pari a (1) questo valore г rappresenta un energia per unità di superficie ed è sostanzialmente rappresentato dalla tenacità a frattura gc del materiale. il modello di zona coesiva è un modello implementato nella maggior parte dei solutori fem, e risulta essere molto flessibile. infatti, una volta tarati i parametri per un determinato materiale, questi possono essere utilizzati per qualsivoglia geometria di giunto. i c max2 1 http://www.gruppofrattura.it/ http://dx.medra.org/10.3221/igf-esis.09.10&auth=true a. pirondi et alii, frattura ed integrità strutturale, 9 (2009) 95 104; doi: 10.3221/igf-esis.09.10 97 d’altro canto la vita a fatica può essere analizzata secondo metodologie basate sulla meccanica della frattura e la legge che lega la velocità di avanzamento a fatica del difetto in regime stazionario al carico applicato (legge di paris [18]) è: (2) in cui da è l’avanzamento areale del difetto, δg la variazione del tasso di rilascio di energia unitario e c ed m caratteristiche dell'adesivo. per utilizzare il modello di zona coesiva nel caso di carichi ciclici, il danneggiamento non deve essere solo legato all’apertura, ma anche alla velocità di propagazione del difetto, funzione della sollecitazione affaticante. basandosi su precedenti esperienze degli autori si è scelto di riferirsi ad una semplice legge di tipo triangolare, considerando per il momento il solo modo i. aumentando l’apertura da una valore nullo, dopo un iniziale comportamento lineare, superato δ0, il modello cerca di rappresentare la formazione di vuoti o microdifetti, fino ad arrivare in corrispondenza di δc in cui le superfici di frattura sono completamente formate. si può quindi definire la perdita di rigidezza in funzione dell’apertura secondo la relazione (3) figura 3: definizione del danneggiamento in termini energetici. secondo quanto postulato in [12], si può quindi definire una seconda variabile di danno d che rappresenta il rapporto tra la sezione danneggiata ad e la sezione resistente iniziale ae di un elemento di volume rappresentativo dei processi di danneggiamento (evr). nell'analisi ef ae coincide con la sezione associata al punto d'integrazione di un elemento coesivo. questo rapporto può essere legato al rapporto tra l’energia già consumata durante il danneggiamento (δг) e l’energia inizialmente disponibile (г). ne risulta quindi (4) attraverso semplici relazioni si può legare il danneggiamento in termini di perdita di rigidezza alla variabile di danno in termini energetici (5) e sostituendo l’apertura δ con la sua relazione in funzione del danno d risulta (6) per quel che riguarda la modellazione del danneggiamento a fatica si mettono in relazione grandezze tipiche della meccanica della frattura con il danneggiamento stesso; in particolare si lega la variabile di danno d, con l’avanzamento del difetto nd ad . entrando nel dettaglio la variazione del danno con il numero di cicli può essere espressa attraverso mda c gdn= d    0 0      f f d   ae add ( ) ( )0 00 1 1 1 f f f k k d d d k d d d d d dd d = = ( ) 0 01f dad ae d d d d d = + http://www.gruppofrattura.it/ http://dx.medra.org/10.3221/igf-esis.09.10&auth=true a. pirondi et alii, frattura ed integrità strutturale, 9 (2009) 95 104; doi: 10.3221/igf-esis.09.10 98 (7) dove a sua volta il termine dad dd può essere ricavato derivando l’eq. (6). (8) il termine dn dad invece può essere ricavato formulando un'ipotesi di distribuzione del danno negli evr dove si sta sviluppando e conoscendo g, c, ed m. in particolare, se il giunto viene sollecitato per un numero di cicli δn, l’ampiezza della zona danneggiata all’apice del difetto aumenterà di δad, che può essere ritenuto rappresentate ad un avanzamento del difetto equivalente pari a δa. l’avanzamento del difetto può quindi essere ritenuto pari alla somma della variazione di area danneggiata di tutti gli elementi che appartengono alla zona di processo acz. (9) la zona di processo viene considerata come quella zona in cui avviene il danneggiamento per fatica, ed in particolare è l’area corrispondente a punti di integrazione che hanno un livello di apertura maggiore di δth, il quale viene a sua volta determinato conoscendo δgth. in letteratura [12-14], acz è stimata attraverso relazioni analitiche, mentre in questo caso sarà automaticamente calcolata come uno dei risultati dell’analisi fem. supponendo che il valore medio della variazione dell’area danneggiata, per gli elementi facenti parte la zona di processo, sia pari a nd dad , si può riscrivere la relazione precedente come (10) dove ncz è il numero di elementi che appartengono alla zona di processo. esplicitando la variazione di area danneggiata con il numero di cicli si ottiene (11) dove a sua volta il numero di elementi appartenenti alla zona di processo può essere scritto come il rapporto tra l’area della stessa, acz, e la dimensione media degli elementi in tale zona ae. sostituendo le relazioni trovate nell’eq. (7) si trova la relazione (12) in cui nd da è rappresentato dall’eq. (2). aspetti pratici – implementazione nel sofware ef i è scelto di implementare la procedura sopra illustrata sfruttando le potenzialità degli elementi coesivi, limitandosi per ora al caso bidimensionale. il danneggiamento è stato assegnato come una variabile di stato, la quale va ad agire sulla rigidezza del materiale costituente lo strato di elementi coesivi. inoltre per quel che riguarda tensioni, spostamenti e danno si è sempre fatto riferimento ai punti di integrazione, che nel caso di elementi coesivi bidimensionali sono due. per valutare l’avanzamento a fatica è necessario, come indicato in precedenza, conoscere il valore di δg durante la propagazione. questo viene valutato a partire dal calcolo di g, a sua volta effettuato secondo la definizione : (13) quindi per pervenire a questo valore è necessario il calcolo dell’energia interna u e del lavoro delle forze esterne w, oltre che alla variazione dell’area del difetto a. sebbene questa teoria sia di semplice applicazione il suo utilizzo è reso critico s dd dd dad dn dad dn= ( ) 2 0 0 1f f d d dd dad ae d d d d é ù+ê úë û= i i acz d a dad d n dn î = å i cz i acz d a dad dadnd n dn dn î = =å 1 cz aedad da da dn dn dnn acz = = ( ) 2 0 0 1f f d d dd da d n d na cz d d d d é ù+ê úë û=  d w u g da    http://www.gruppofrattura.it/ http://dx.medra.org/10.3221/igf-esis.09.10&auth=true a. pirondi et alii, frattura ed integrità strutturale, 9 (2009) 95 104; doi: 10.3221/igf-esis.09.10 99 dalla valutazione dell’area del difetto. infatti nei casi in cui la variazione dell’area del difetto, incremento per incremento è ridotta, gli errori numerici vedono i loro effetti amplificati e si possono avere errori sulla valutazione di g. d’altra parte variazioni eccessive del danneggiamento incremento per incremento possono condurre ed errori legati alla linearizzazione di relazioni più complesse e anche a problemi di convergenza. a tal proposito si definisce una valore d massimo di incremento del danno d che può essere consumato all’interno di un incremento. al fine di validare la metodologia che conduce al calcolo di g e conseguentemente di δg, si sono eseguiti confronti dell’andamento del tasso di rilascio unitario di energia g con la lunghezza del difetto a, per giunti double cantilever beam (dcb), in cui come termine di confronto si sono assunti: i) la soluzione analitica [19] (14) ii) l’integrale di contorno j valutato medianti analisi fem lineari elastiche (in (14) p rappresenta il carico applicato, a la lunghezza del difetto, b lo spessore del giunto, e il modulo elastico degli aderendi, i il modulo di inerzia della sezione degli aderendi, λσ un fattore correttivo dipendente dalla geometria del giunto e dai materiali in gioco). il confronto è mostrato in fig. 4 per un giunto dcb in acciaio con aderendi di lunghezza 120mm, larghezza 30mm e spessore 25mm a cui è applicata una forza di 1625n avente un difetto iniziale di 45mm. si nota come i tre metodi siano praticamente equivalenti per il primo tratto di propagazione. oltre ai 15 mm l’integrale di contorno e il tasso di rilascio di energia unitario si differenziano dall’andamento analitico: questo è prevedibile in quanto l’eq.14 ha validità solo per condizioni in cui si può considerare l’incollaggio infinitamente lungo (per la geometria a ci si riferisce in fig. 4 significa a < 60mm, cioè un avanzamento del difetto < 15mm). figura 4: valori di g calcolati mediate la subroutine e l’eq. (13) in funzione all’avanzamento del difetto, confrontati con l’andamento analitico (eq. 14) l’integrale di contorno ottenuto mediante una simulazione fem lineare elastica. in ogni caso l’integrale di contorno e il tasso di rilascio di energia unitario ottenuto mediante la subroutine esterna continuano ad avere andamenti pressoché identici anche per propagazioni molto maggiori. si ritiene quindi valida la metodologia numerica sviluppata per il calcolo di g. l’analisi viene svolta globalmente in quattro passi successivi: i) nel primo passo non viene considerato alcun danneggiamento e si carica il giunto fino al carico massimo da utilizzare nella propagazione a fatica; ii) nel secondo passo il giunto viene scaricato, assegnando contemporaneamente un valore d=1 al punto di integrazione più sollecitato nello step precedente, in modo da creare un avanzamento virtuale del difetto mediante il quale può essere calcolato il valore di δg iniziale per la simulazione dell’avanzamento a fatica del difetto. iii) nuovo caricamento del giunto con calcolo dell'eventuale danno statico dovuto alla rampa di carico; iv) simulazione dell’avanzamento a fatica del difetto in cui il carico viene mantenuto costante. in quest'ultimo passo, ricavato il δg applicato si verifica che questo sia maggiore del limite di fatica δgth. se tale condizione è soddisfatta parte il loop per la previsione dell’avanzamento del difetto (fig. 5). per ogni punto di integrazione, conoscendo il danno d accumulato fino a quel momento, viene calcolato il danno d . si impone quindi l’aumento di danno d e si calcola il nuovo valore d  : questo sarà assunto pari a se stesso se risulta essere minore di 1, ( ) 22 1 1 p a g b e i a sl æ ö÷ç ÷= +ç ÷ç ÷çè ø http://www.gruppofrattura.it/ http://dx.medra.org/10.3221/igf-esis.09.10&auth=true a. pirondi et alii, frattura ed integrità strutturale, 9 (2009) 95 104; doi: 10.3221/igf-esis.09.10 100 oppure pari all’unità in caso contrario. per ogni punto di integrazione si hanno quindi un valore iniziale e finale di d. integrando l’eq. 12 tra questi due valori si identifica un numero di cicli per ogni punto dei integrazione, e si assume come numero di cicli dell’incremento il minore tra tutti questi. mediante questo numero di cicli si aggiorna il danno d di ogni elemento integrando nuovamente l’eq. 12, al fine però di trovare il nuovo valore di danno. figura 5: schema di funzionamento della subroutine. questa operazione è quindi ripetuta fino all’incremento in cui il valore di g raggiunge il valore critico gc. ad ogni incremento corrisponde quindi una sollecitazione δg, un numero di cicli δn, ed un avanzamento del difetto δa (calcolato come la somma delle aree danneggiate ad di ogni elemento). i primi due step permettono anche la determinazione di δth. questo viene assunto pari al valore massimo di apertura tra tutti i punti di integrazione dello strato di adesivo, quando il δg applicato eguaglia il valore di soglia δgth (vedi fig. 6). figura 6: determinazione del valore di δth. parametri del modello er lo svolgimento dell’analisi sono necessari i parametri della zona coesiva, cosi come i parametri della legge di paris dell’adesivo. per quel che riguarda i primi si sono determinati dalla simulazione di prove di frattura su giunti dcb [21], che hanno portato alla definizione di una legge coesiva triangolare con le caratteristiche riportate in tab. 1. per quel che riguarda invece i parametri della legge di paris si sono ottenuti da prove di propagazione di difetti sempre su provini dcb [22]. in tab. 2 sono riportati i coefficienti della regressione a legge di potenza (rapporto di carico r=0.1). p http://www.gruppofrattura.it/ http://dx.medra.org/10.3221/igf-esis.09.10&auth=true a. pirondi et alii, frattura ed integrità strutturale, 9 (2009) 95 104; doi: 10.3221/igf-esis.09.10 101 parametro valore г [n/mm] 0.6 σmax [mpa] 30 δ0 [mm] 0.004 δc [mm] 0.04 tabella 1: parametri del modello di zona coesiva. parametro valore c 5.19 m 3.64 tabella 2: coefficienti della legge di paris. risultati e discussione l fine di verificare la validità dell'implementazione i risultati della simulazione sono stati confrontati con i dati sperimentali [22]. i risultati mostrati in fig. 7sono stato ottenuti con un incremento massimo del danno d pari a 0.05 per ogni incremento dell'analisi. figura 7: confronto tra risultati sperimentali e previsione del modello ottenuto con eq. 12. si nota come i risultati delle simulazioni rientrino nel campo di quelli ottenuti sperimentalmente anche se si può notare una pendenza inferiore. tale differenza può viene evidenziata anche nei risultati delle analisi svolte in [12] (fig. 8) dove la pendenza della curva ottenuta per via numerica è inferiore rispetto a quella ottenuta dalla regressione di dati sperimentali. questo fenomeno si ritiene sia legato al criterio di omogeneizzazione del danno rappresentato dalle eq. 4 e 10. esaminando l’eq. (12) si può notare che, definito un rateo di avanzamento del difetto nd da , il rateo di aumento del danno per i punti di integrazione con danno pari 0, sta in un rapporto circa pari a 2 0         f rispetto al rateo di aumento di danno dei punti di integrazione con danno prossimo a 1. nel caso in cui il valore di 0 sia molto minore del valore di f (e nel caso in esame c’è un rapporto di circa 1/10) questo porta gli elementi lontani dall’apice del difetto a danneggiarsi molto più velocemente degli elementi prossimi all’apice stesso (nel caso in esame il rapporto è prossimo a 100). legando invece il danno a livello microscopico ai suoi effetti sulla rigidezza [20], cioè (15) a 0 1 ad k d ae k    http://www.gruppofrattura.it/ http://dx.medra.org/10.3221/igf-esis.09.10&auth=true a. pirondi et alii, frattura ed integrità strutturale, 9 (2009) 95 104; doi: 10.3221/igf-esis.09.10 102 e svolgendo di nuovo tutti i passaggi mostrati nella sezione precedente si arriva ad un legame (16) in questo legame non vi è alcuna dipendenza dal valore del danno, ovvero tutti gli elementi appartenenti alla zona di processo acz presentano il medesimo rateo di aumento del danno. svolgendo una analisi identica alla precedente in cui viene utilizzata l’eq. (17) al posto della (12), si arriva al risultato mostrato in fig. 9. si nota come i punti della simulazione siano decisamente più allineati a quelli sperimentali rispetto a fig. 7, anche se la simulazione continua a sovrastimare la velocità di avanzamento nella fase iniziale dell’analisi. figura 8: confronto tra risultati sperimentali e previsione del modello da [12]. figura 9: confronto tra risultati sperimentali e previsione del modello ottenuto con eq. (16). un ulteriore modifica, in fase di implementazione, è una legge di omogeneizzazione del danno diversa dalla semplice ripartizione in parti uguali dell'avanzamento del difetto sugli elementi compresi in acz rappresentata dall’eq. (10). si è inoltre valutata l’influenza sul risultato della dimensione della mesh degli elementi coesivi. fig. 10 mostra il valore del coefficiente m della regressione ottenuta dai risultati delle analisi per varie dimensioni degli elementi coesivi. per una maggiore chiarezza si sono normalizzati i dati rispetto ad una dimensione di 0.4mm che è quella utilizzata per i precedenti risultati. 1 cz dd da dn dna = http://www.gruppofrattura.it/ http://dx.medra.org/10.3221/igf-esis.09.10&auth=true a. pirondi et alii, frattura ed integrità strutturale, 9 (2009) 95 104; doi: 10.3221/igf-esis.09.10 103 figura 10: influenza della dimensione della mesh sulla pendenza della regressione dei risultati delle simulazioni. si può notare come da mesh molto fitte (0.01mm) fino a 2 mm, non vi sia una grossa differenza dei risultati. aumentando ancora la mesh si nota invece come i risultati si discostino sempre di più. figura 11: distribuzione della variabile di danno d in funzione della distanza dall’apice del difetto. fig. 11 mostra l’andamento della variabile danno in funzione della distanza dell’apice del difetto originale, quando la zona coesiva è completamente sviluppata: questo mostra come la zona coesiva interessi una dimensione circa 8mm noto ciò e nota l’influenza della mesh sui risultati, si può quindi identificare un numero minimo di elementi che devono essere presenti all’interno della zona coesiva, quando questa è completamente sviluppata, pari a 4. questo è necessario per permettere di descrivere in modo accurato le tensioni e i relativi spostamenti all’apice del difetto. si è infine valutata l’influenza di d . il grafico in fig. 12 mostra come varia la vita a fatica di un giunto (la geometria è la medesima cui si riferisce fig. 4) in funzione della variazione massima del danno. figura 12: influenza del valore di dδ sulla previsione di vita a fatica. http://www.gruppofrattura.it/ http://dx.medra.org/10.3221/igf-esis.09.10&auth=true a. pirondi et alii, frattura ed integrità strutturale, 9 (2009) 95 104; doi: 10.3221/igf-esis.09.10 104 diminuendo tale limite da 0.5 fino ad un valore di 0.01 si nota come le durate vadano diminuendo asintoticamente. questa differenza può essere spiegata analizzando l’eq. (12), in cui la derivata del danno d rispetto al numero di cicli è funzione del danno stesso. di conseguenza tanto più sono piccoli gli intervalli su cui tale equazione viene integrata, tanto più accurati saranno i risultati. la diminuzione di d porta però a tempi di calcolo via via crescenti, ed al fine di ottimizzare la procedura è conveniente fare una sorta di analisi di convergenza cosi come viene di norma svolto per quanto riguarda la dimensione della mesh. conclusioni i è eseguita l’implementazione di una procedura per la previsione della propagazione di difetti a fatica attraverso una subroutine esterna interagente con il software abaqus. in questo modo si è anche reso possibile il calcolo automatico dei valori della variazione del tasso di rilascio di energia applicato e della dimensione della zona di processo. la simulazione di propagazione di difetti in modo i in giunti dcb, ha mostrato risultati caratterizzati da una pendenza dell'andamento della velocità di propagazione in funzione di g inferiore a quello sperimentale, come riscontrato anche in [12]. al fine di individuare il motivo di tale scostamento e cercare di limitarlo, viene proposta una nuova legge di omogeneizzazione del danno, che permette di ridurre le differenze, senza però eliminarle. sviluppi futuri interesseranno l’identificazione di differenti leggi di omogeneizzazione del danno in modo da ripercorrere in modo più fedele i dati sperimentali. inoltre il modello sarà esteso anche per sollecitazioni agenti in modo ii in modo da poter ampliare la varietà di giunti analizzabili. bibliografia [1] g. barenblatt, adv. appl. mech., 7 (1962) 55. [2] d. dugdale, j. mech. phys. solids., 8 (1960) 100. [3] i. mohammed, k.m. liechti, j. mech. phys. solids, 48 (2000) 735. [4] q.d. yang, m.d. thouless, s. m. ward, j. mech. phys. solids, 47 (1999) 1337. [5] w. g. knauss, g. u. losi, j. appl. mech., 60 (1993) 793. [6] h. hadavinia, a. j. kinloch, j. g. williams, in adv. in fract. and damage mech. ii, (m. guagliano, m.h. aliabadi eds.), hoggar, geneva, (2001) 445. [7] b. f. sorensen, , acta mater., 50 (2002) 1053. [8] b. f. sorensen, , jacobsen, t.k., eng. fract. mech., 70 (2003) 1841. [9] i. georgiou, h. hadavinia, a. ivankovic, a.j. kinloch, v. tropsa, j.g. williams, j. adhesion, 79 (2003) 239. [10] b.r.k. blackman, h. hadavinia, a.j. kinloch, j.g. williams, int. j. fract., 119 (2003) 25. [11] t. pardoen, t. ferracin, c.m. landis, f. delannay, j. mech. phys. solids, 53 (2005) 1951. [12] turon, costa, camanho, dàvila, composites, 38 (2007) 2270. [13] k.l. roe, t. siegmund, eng. fract. mech., 70 (2003) 209. [14] s. maiti, p.h. geubelle, eng. fract. mech., 72 (5) (2005) 691. [15] a. abdul-baqi, p.j.g. schreurs, m.g.d. geers, int. j. of solids and structures, 42 (2005) 927. [16] j.j. munoz, u. galvanetto, p. robinson, int. j. fatigue, 28 (2006) 1136. [17] m. erinc, p.j.g. schreurs, m.g.d. geers, international journal of solids and structures, 44 (2007) 5680. [18] p. paris, f. erdogan, j. basic eng 85 (1961) 528. [19] s. krenk, eng. fracture mech. 43 (1992) 549. [20] j. lemaitre, j. of engn. mat. and tech., 107 (1985) 83. [21] a. pirondi, d. fersini, e. perotti, f. moroni, atti del xix convegno nazionale igf, milano (2007). [22] a. pirondi, f. moroni, m. vettori, atti del xxxvi convegno nazionale aias, ischia (2007). s http://www.gruppofrattura.it/ http://dx.medra.org/10.3221/igf-esis.09.10&auth=true microsoft word numero_29_art_12 a. castellano et alii, frattura ed integrità strutturale, 29 (2014) 128-138; doi: 10.3221/igf-esis.29.12 128 focussed on: computational mechanics and mechanics of materials in italy geometric numerical integrators based on the magnus expansion in bifurcation problems for non-linear elastic solids a. castellano, p. foti, a. fraddosio, s. marzano, m. d. piccioni politecnico di bari – dipartimento di scienze dell’ingegneria civile e dell’architettura anna.castellano@poliba.it, pilade.foti@poliba.it, a.fraddosio@poliba.it, s.marzano@poliba.it, m.d.piccioni@poliba.it abstract. we illustrate a procedure based on the magnus expansion for studying mechanical problems which lead to non-autonomous systems of linear ode’s. the effectiveness of the magnus method is enlighten by the analysis of a bifurcation problem in the framework of three-dimensional non-linear elasticity. in particular, for an isotropic compressible elastic tube subject to an azimuthal shear primary deformation we study the possibility of axially periodic twist-like bifurcations. the approximate matricant of the resulting differential problem and the first singular value of the bifurcating load corresponding to a non-trivial bifurcation are determined by employing a simplified version of the magnus method, characterized by a truncation of the magnus series after the second term. keywords. nonlinear elasticity; bifurcation; geometric numerical integrators; magnus expansion. introduction n the framework of three-dimensional non-linear elasticity, a number of “small on large” bifurcation problems lead to the analysis of a system of linear second order ode’s with varying coefficients. it is a common practice to reduce the system of linear second order ode’s to a simpler non-autonomous first order linear ode system. nevertheless, the resulting differential system may be somewhat complex and only numerically tractable; thus, it is crucial to adopt an adequate strategy for obtaining an accurate numerical solution for determining the critical load and the corresponding bifurcation deformation field. for example, approximate expressions of the matricant of non-autonomous linear ode systems, based either on the multiplicative integral of volterra or on the truncated peano expansion, have been recently proposed for bifurcation problems analyzed by means of the stroh approach within the so-called sextic formalism [1-3]). in section 2, we discuss an alternative numerical method – based on the magnus expansion [4] – which furnishes an approximate exponential representations of the matricant of first order linear ode systems. the magnus expansion belongs to the so-called geometric numerical integrators, based on lie-group methods [5 -7] for appropriate references). to our knowledge, the applications of this method are not widespread in continuum mechanics, but it has been shown in [8] that for problems involving singularities, bifurcations and wave propagation the geometric numerical integrators may be useful and accurate. in particular, the magnus expansion may be very efficient for a number of bifurcation analyses, since it leads to the determination of approximate solutions that preserve at any order of approximation the same qualitative properties of the exact (but unknown) solution; moreover, this method exhibits an improved accuracy with respect to other frequently used numerical schemes. as an application of the magnus method, in an application of the magnus method in solid mechanics: periodic twist-like deformations bifurcating from the azimuthal shear of a circular tube we investigate the possibility for a compressible hollow cylinder subject to i a. castellano et alii, frattura ed integrità strutturale, 29 (2014) 128-138; doi: 10.3221/igf-esis.29.12 129 azimuthal shear to support axially periodic twist-like bifurcation modes similar to the taylor-couette axially periodic cellular patterns observed when the flow of a viscous fluid confined in the gap between two rotating concentric cylinders becomes unstable. here, the hollow cylinder is made of a levinson-burgess isotropic compressible elastic material. by restricting our attention to a class of incremental displacements characterized by three unknown scalar functions of the radial coordinate and having an axial periodic structure, we then study the related incremental boundary-value problem. this leads to a somewhat complex non-autonomous homogeneous system of six first order linear ode’s with homogeneous boundary conditions, whose analysis is performed by a numerical approach. we show that a procedure based on the magnus method outlined in an overview of geometric numerical integrators with special reference to the magnus expansion reveals very effective either for approximating the matricant of the resulting differential problem or for determining the first singular value of the bifurcating load corresponding to a non-trivial twist-like solution. an overview of geometric numerical integrators with special reference to the magnus expansion number of problems in scientific and engineering areas, ranging from quantum mechanics, optics, electromagnetism and molecular physics to control theory and bifurcation, require the resolution of systems of differential equations with varying coefficients. besides some very special cases, for which a fundamental matrix solution is explicitly available, the analysis of the problem usually requires the construction of an approximate representation of the solution of the non-autonomous differential system. in the last decade, this issue has attracted many scientists and has also represented a field of intense research activity; in particular, recent studies have shown that in many cases the so-called geometric numerical integration methods may offer better approximation schemes compared to perturbative procedures or to standard numerical integrators. the magnus method belongs to the class of geometric numerical integrators, based on lie-group methods (see [6, 7] for appropriate references), which, although not yet diffused in continuum mechanics, have recently found many applications in areas of molecular physics [9], electromagnetism [10] and celestial mechanics [11]. in this section, we first give a brief overview of geometric numerical integrators and then we deal with the magnus method as a particular case. geometric numerical integration concerns the development of numerical approximations to the solution of an ode system with the main goal of preserving at any order of approximation the qualitative properties of the exact (but unknown) solution and thereby of exhibiting an improved accuracy with respect to other numerical methods. although such methods apply also for nonlinear matrix differential equations, for the purposes of bifurcation problems here we consider geometric numerical integrators based on the magnus expansion for the special case of homogeneous nonautonomous first order linear ode systems of the form         6x6r r r , r 0, 0   y a y y i (1) where the unknown 6x6 matrix  ry , usually referred as the matricant of the cauchy initial-value problem (1), is the 6dimensional identity matrix when the real independent variable r is equal to zero. generally speaking, these new numerical approaches involve lie-group methods, which are based on lie groups and their associated lie algebras. we recall that a lie group corresponds to a differential manifold which is endowed with a group structure; the corresponding lie algebra, defined as the tangent space to the lie group at the identity, is a linear space endowed with the lie bracket commutation operation and a natural mapping. since the unknown matricant of a first order ode system like (1) must be an invertible 6x6 matrix with variable entries, the setting for finding solutions of (1) is a 6x6 matrix lie group. in this case, the above general definition of a lie algebra implies that the 6x6 matrix  ra governing (1) is an element of a matrix lie algebra. moreover, in this setting the associated matrix lie algebra is endowed with the matrix commutation law  , := a b ab ba (2) where  , a b is commonly called the matrix commutator. finally, for these special matrix lie groups the matrix exponential function plays the role of the natural mapping. we emphasize that in the theory of lie groups the role of the exponential mapping is crucial. indeed, within the context of differential geometry, the matrix exponential maps an element belonging to a matrix lie algebra into an invertible matrix belonging to its corresponding lie group; in other words, the exponential mapping allows to recapture the local a a. castellano et alii, frattura ed integrità strutturale, 29 (2014) 128-138; doi: 10.3221/igf-esis.29.12 130 group structure from the corresponding lie algebra. thus, for a first order ode system like (1), it is natural to attempt to construct the solution as a matrix exponential with exponent given by a matrix which belongs to the associated lie algebra. this peculiarity of the exponential mapping probably inspired the idea developed by magnus [4], who proposed to express the exponent by a matrix series expansion made of infinite terms, each of them belonging to the lie algebra corresponding to the lie group of the unknown matricant. in detail, with reference to the differential problem defined in (1) the magnus method assumes the matricant to be of exponential form with the exponent given by the following series expansion, called the magnus expansion:            6x6 k k=1 r exp r 0 , 0 , r r       y y o    (3) here we do not report the analytical procedures for determining the terms of the series expansion in (3). we address the reader to the seminal paper [5] where, in view of (1) and (3), and according to the notions of the first derivative of a matrix exponential map and of its inverse (see formulae (33) and (38) in [5]), it is clearly showed how it is possible to construct all the terms of the magnus series. for our purposes, we report here only the first two terms of the series:           1r r 1 1 1 2 1 1 2 2 0 0 0 1 r d , r d , d 2             a a a  (4) where [. , .] is the matrix commutator (2) and  a is the governing matrix of (1). notice that each of the remaining terms (here not reported) contains nested matrix commutators of the form (2) involving the matrix operator  ra . it is worth to note that only if the commutative condition        1 2 2 1 1 2r r r r for each r , ra a a a (5) holds, then, in view of (3), (1) and (4), the matricant of (1) takes the exponential form     r 0 r exp d          y a (6) which is analogous to the classical exponential solution for a scalar linear ode. clearly, (6) yields the solution of (1) if the entries of the matrix a governing (1) are independent of r. obviously, (5) holds only in special cases because the matrices in general do not commute (this is closely related to the structure of the commutation law (2) which characterizes matrix lie algebras). a crucial aspect of the magnus method related to its pertinence when seeking approximate solutions of differential problems like (1) emerges from the analysis of (3) and (4). by the above discussion, we recall that the matrix  ra in (1) belongs to a matrix lie algebra for all r; thus, in view of (4) we see that any term of the magnus expansion belongs to the same lie algebra. this implies that any truncation of the magnus series will also belong to the same lie algebra and therefore the exponential map of any truncation will necessarily stay in the corresponding lie group. this is basically the main reason why an approximated solution obtained by truncating the magnus expansion at any order preserves the same qualitative features of the exact solution. another major issue concerns the conditions on the matrix  ra which guarantee the convergence of the magnus series. this problem has been studied in [12], where it is shown that a sufficient condition for the local convergence of the magnus series in a certain interval  20, r is given by :   2r 2 0 r dr   a (7) where the integrand function in (7) is the spectral norm of  ra , i.e., the square root of the maximum eigenvalue of the product    tr ra a . moreover, the fulfilment of the inequality (7) determines the range of the independent variable r for which it is possible to write the solution in the form (3). however, in many applicative cases it happens that the convergence condition (7) does not hold for the whole integration interval  20, r . in these cases, as usual for numerical a. castellano et alii, frattura ed integrità strutturale, 29 (2014) 128-138; doi: 10.3221/igf-esis.29.12 131 integration methods, it is common dividing the interval  20, r into n subintervals  i+1 ir , r such that the magnus series converges in each of them. given such a subinterval  i+1 ir , r , in view of (3) we may write:       i+1 i+1 ir exp r ry y (8) wherein  i+1r is expressed by the infinite magnus series. consequently, the matricant of (1) evaluated on the whole domain of interest  20, r takes the form      n 2 i+1 i=1 r exp r        y  (9) as it usually occurs when constructing approximate solutions, a crucial issue is that of choosing an appropriate order of truncation for  i+1r which guarantees a suitable level of accuracy. to this aim, we recall the efficient procedure suggested in [7], which may be summarized in the following three steps: first, the series  i+1r is truncated at a suitable order in each subinterval wherein the convergence is guaranteed. then, the integrals appearing in each truncated series are approximated by appropriate quadrature rules. finally, the exponential of the matrix  i+1r is evaluated. the qualified literature on this issue contains a number of proposals which correlate the level of accuracy of the method to the order of truncation of the magnus series. we recall the paper [6] for an overview on this problem. finally, the accurate calculation of the exponential of a matrix is still an open problem, as one may infer from the paper [13]. in the spirit of geometric numerical integration methods, the consequence of an inaccurate computation of the exponential matrix due, for example, by the replacement of the exponential map with one of its analytic (for example rational) approximants may lead to a solution not belonging to the desired lie group, thus rendering the main advantages of geometric numerical integration ineffective. here, we report two references on this issue, namely the splitting method proposed in [14] and the scaling and squaring with a padè approximation method summarized in [13]. notice that the command matrixexp of the widely used software mathematica employs the padè approximation method for the calculation of the exponential matrix. we conclude by observing that the non-trivial evaluation of the exponential matrix may be circumvented when the unknown matrix of a differential problem belongs to special lie groups. one of these cases involves a group commonly occurring in mechanical problems, namely the orthogonal group, that is the group of 3x3 matrices q such that t 3x3 .qq i unlike many other lie-group solvers, they do not require the evaluation of matrix exponentials because, as outlined in [15], the back translation from the lie algebra to the corresponding lie group may be obtained by using the cayley transform. an application of the magnus method in solid mechanics: periodic twist-like deformations bifurcating from the azimuthal shear of a circular tube n the present section, we introduce a bifurcation problem set within the context of the nonlinear theory of elastic solids. in particular, the last part of the following analysis contains an explicit application of the magnus method based on the procedure outlined in the previous section. the fundamental azimuthal shear equilibrium deformation we consider a homogeneous, isotropic, compressible, elastic tube which occupies the region   1 2r, , z 0 < r r r , 0 2 , 0 z h          (10) in its natural reference configuration.  r, , z denote the cylindrical coordinate of a point x in a cylindrical coordinate system with orthonormal basis  r z, , e e e . the boundary of  is divided into two disjoint complementary parts:      , 1 1 2 2r, , z r = r or r = r r, , z z = 0 or z = h           (11) i a. castellano et alii, frattura ed integrità strutturale, 29 (2014) 128-138; doi: 10.3221/igf-esis.29.12 132 a deformation        : = r, , z r, , z    f x x f x f  of  is assumed to be a smooth function with gradient    : f x f x . since the tube is elastic and isotropic, the general form of the strain energy function is given by    w w i , ii , iiif b b b , where         22 2 22 t1 1i tr , ii tr tr tr , iii det det 2 2               b f f b b f f ff b fb b b (12) are the orthogonal principal invariants of t : b f f ; thus, the piola stress takes the form       t1 2 3 dw w w i w iii 2 2 2     s f f f f bf fb b (13) with 1 2 3 w w w w : , w : , w : i ii iii         b b b (14) we assume that the inner cylinder is kept fixed, whereas the outer is subject to a uniform angular displacement 0  around its axis. on the bases of  only tangential displacements are admitted. this leads to the following mixed boundary-value problem:  div = in s 0f  (15)            1 r 2 2 1 z 1 2 2 1 2, 0 at r = r = r cos 1 at r = r 0 at r = r = on r sin at r = r = 0 at r = r r                f x x e f x x e f x x e  (16)       2 = 0, = on      f x x e s e e 0f  (17) for the equilibrium problem (15)-(17), we consider the possibility of an azimuthal shear deformation f defined by  r r, r , z z       (18) where  , the angular displacement field, is assumed to be a smooth function satisfying    1 2r 0, r 0      1on   (19) consequently, in view of (18) we have     2 2r r rr r , r r                   i e i f e b e e e e e e (20) where the prime denotes differentiation with respect to r and  r z, , e ee is the deformed cylindrical orthonormal basis at  r, , z . notice that the azimuthal shear is an isochoric deformation whose principal invariants (12) are given by 2 2 , i ii 3 r ii 1i     b b b (21) moreover, (18) trivially satisfies the displacement boundary conditions (16)-(17)1 and, in view of (13) and (20), it is easily seen that also the traction boundary condition (17)2 holds. it remains to study the equilibrium field eq. (15). the explicitly evaluation of (15) by means of (13) and (20) yields an over-determined system of two ode for the single unknown function  r . in particular, here we consider the class c2 levinson-burgess strain energy function a. castellano et alii, frattura ed integrità strutturale, 29 (2014) 128-138; doi: 10.3221/igf-esis.29.12 133            21 2 1 2= 1 4 1i 3 1 j 3 2 1 2 iii 1 2 iii 1 2 1 2 w                       f b b b b (22) where and are the referential shear modulus and referential poisson’s ratio, respectively, and  0, 1 is a dimensionless material parameter. for the constitutive class (22), the piola stress takes the form        1 2 1 2-1 -t -t4 1 1 1 2 2 iii 1 iii 1 2                            b bs f f b f f (23) by following a result contained in [16], it is possible to generate classes of strain energy functions such that the azimuthal shear satisfies both the two equilibrium ode; in particular, for the present case of a levinson-burgess material, deformations of the form (18) are allowed only if the following condition on the material parameters holds: 3 4   (24) finally, in view of (23), (19)-(21) and (24), after a non-trivial calculation we obtain from (15) a single ode, whose solution is      2 2 2 2 2 22 1 1 2r r r r r r 1 r,           (25) periodic twist-like bifurcations we now consider the possibility of deformations which bifurcate from the primary equilibrium pure circular shear (18) as the loading parameter (angle)  increases from 0 (natural state). a condition (only necessary) for the occurrence of a local branch of bifurcating solutions at a fixed  is the existence of a non-trivial solution of the homogeneous linearized equilibrium problem which corresponds to an adjacent equilibrium state. such solutions superposed to the primary azimuthal shear must satisfy the adjacent equilibrium eq. (26) and the incremental boundary conditions (27)-(28), obtained by linearizing (15)-(17) around the fundamental deformation  x f x , which is conveniently assumed as the independent variable:     gradr, div in  0 uf  (26) 1 on u 0  (27)    gradr, z 2z z= 0, = on  u e e e 0 uf  (28) in particular,   3: u x  represents an incremental displacement field, “div” and “grad” are the divergence and gradient operators with respect to x, respectively, and  is the fourth-order instantaneous elasticity tensor, given by:           r, r, r, r, 2 t: d , w lin          hh hf f f f (29) for the constitutive class (22), it follows from (29), (20)-(21) and (24) that                   r, t t1 1 t grad 1 grad grad grad 4 3 2 1 grad grad grad 4 1 2 2                        u b b u u u b i u i u     uf (30) where b is given by (20)2. we now restrict our analysis to the class           3 r 1 2 z 3 1 2 : : u v r cos z, u v r cos z, u v r sin z, n , n 0, 1, 2, .., r r h                       u u u  0   (31) a. castellano et alii, frattura ed integrità strutturale, 29 (2014) 128-138; doi: 10.3221/igf-esis.29.12 134 of periodic bifurcating displacements which are reminiscent of the instability patterns observed in the classical taylorcouette shear flow of viscous fluids. a more detailed discussions on such a choice, together with an exhaustive analysis of problems closely related to the one here presented, are developed in [17], [18]; in particular, in [17] one may also find stability issues based on [19] and partly on [20]. this allows us to skip here the description of certain analytical developments, for which we refer to the works above mentioned. notice that (31) models the occurrence of an axially periodic cellular pattern in the gap between the inner and outer cylinders (n represents the number of possibly forming cells in the axial direction); in particular, inside each of the n possible forming cells, (31) describes a twist-like displacement perpendicular to the e -direction of primary annular shear, so that the vector lines of the incremental displacement u are similar to the streamlines of the twisting taylor-like effects for fluids. we easily check from (31) that the displacement incremental boundary condition (28)1 trivially holds, whereas (27) holds provided the smooth scalar functions  1v r ,  2v r ,  3v r for r in  1 2r , r are such that                    1 1 1 1 2 2 21 2 3 2 3 21r : r r r rv , v , v v , v , v: r r r 0 0, , 0    v v 0 (32) for what concerns the traction boundary condition (28)2 and the field eq. (26), we first observe by (31) that     1 1 1 r r 2 r 2 r 1 3 z z 1 r z 2 z 3 z r grad v v r v v r v v cos z sin z v v                             u e e e e e e e e e e e e e e e e (33) and by (20)2 that z z b e e ; thus, in view of (30)-(31), condition (28)2 immediately holds. finally, by evaluating the divergence of (30) with the aid of (20)2 and (33), after some non-trivial calculation and also by employing separation of variables allowed by the choice (31) of the displacement field, we reduce the partial differential problem (26)-(28) to the following system of three homogeneous second-order ode (see also (32)):                   t 1 2 1 2 r, r, r, , r, , r, , r, , r r r r r                           p v p r r v r q v v v 0 0 (34) where  1 2 3v , : v , vv (we have omitted the dependence on r) and       rrrr rr r rr rrr rrzz rrr r r r rr rzz zrzr zrrz zr z 2 2 rzrz r rz z z r a r a 0 a a r a r, r a r a 0 , r, , a a r a 0 0 r a r a r a 0 1 1 a r a a r a a r r r, ,                                                          p r q z 2 2 r zrz r r z z r zz 2 zz zzr zzzz 1 1 a r a a r a a r r a a r a                                    (35) are non-constant matrices determined by the components    ijhk h k i j hkij:    e e e e   of the symmetric fourthorder tensor  in the coordinate system (r, , z). here, we do not report the explicit expression of such components, which may be obtained by (30), (20)2 and (26). we only observe that  r, p and  r, , q are symmetric, since  is symmetric; moreover, for the constitutive class (22)  r, p is always invertible. the latter property of  r, p is crucial. indeed, a common practice is that of transforming the set of three linear second order ordinary differential equations like (34) into a system of six linear first order ordinary differential equations, for a. castellano et alii, frattura ed integrità strutturale, 29 (2014) 128-138; doi: 10.3221/igf-esis.29.12 135 which well-known existence theorems and procedures for constructing the solutions are available in the literature. with this aim, once introduced the 3x3 matrices                 1 1 t : r, r, , r, , : r, r, r, , r, ,                        t p r q k p p r r (36) we rewrite (34) in the form     1 2 1 2 , r r r r r          v tv kv v v 0 (37) then, by setting 6x1 6x6 6x6 6x6 : , : : , :                                   v o i y a v t k i o o o m n o o i o (38) we easily see that (37) is equivalent to the linear homogeneous first order ode boundary-value problem       1 2 1 2 6x1 r for r r r r r                  y a y my ny 0 0 (39) observe that in the notation above we have dropped the dependence of the basic parameters (the inner and outer radii, the height of the tube, the material moduli and the angular displacement  ), usually assumed as prescribed. we only maintain explicit the dependence on r, in order to emphasize that the linear ode system is non-autonomous. now, by following elementary results on systems of linear ode's, we may write a solution of (39) in the form (see (38)1 and (37)2)           1 1 6x1 r r r r r           y y y y v 0 (40) where  1ry is an unknown constant vector and               1 2 1 2 1 1 2 6x66x6 r r r , with det r 0, for r < r < r and r r r                  i ou u y y y o iu u (41) is a particular fundamental matrix solution for (39)1, usually called matricant. then, substitution of (40) into (39)2 yields      1 2 1r r r             0 my ny y 0 (42) which, in view of (38)3-4 , (41) and (40), is equivalent to the homogeneous system of three algebraic equations    2 2 1r r u v 0 (43) for which non-trivial solution  1rv 0  are possible if and only if  2 2det r 0u (44) a. castellano et alii, frattura ed integrità strutturale, 29 (2014) 128-138; doi: 10.3221/igf-esis.29.12 136 finally, a solution of the primary ode problem (34) can be written in the following form      2 1r r rv u v (45) which clearly satisfies the boundary conditions (34)2 (see (41) and (43)). the above analysis shows that the possibility of determining non-trivial solutions for the bifurcation differential problem (34) is strictly related to the knowledge of the 3x3 matrix  2 ru , which represents the “north-east” block of the 6x6 matricant (41) of the cauchy initial-value problem         1 2 1 6x6 r r r for r r r r              y a y i o y o i (46) since (46) has the same structure of the cauchy initial-value problem (1), in the following we illustrate a strategy based on the magnus method for determining the solution of (46). a strategy for determining the bifurcating load through the magnus method the theoretical preliminaries in an overview of geometric numerical integrators with special reference to the magnus expansion combined with the bifurcation analysis of subsections the fundamental azimuthal shear equilibrium deformation periodic twist-like bifurcations allow us to describe a strategy for determining the critical value cr of the primary angular displacement, that is the lowest value of the angle  for which the tube may support (during a loading process) a non-trivial twist-like bifurcation of the form (31) from the fundamental azimuthal shear deformation. the magnus method is now the key ingredient for approximately determining the matricant of (46), whereas (44) plays the role of bifurcation condition. following the steps outlined in the section 2, we first fix the radii r1 and r2, the height h, the referential shear modulus  and the referential poisson’s ratio  (recall that 3 / 4  by (24)). then, we: fix the number n of twisting cells in the axial direction (by (31) this is equivalent to fixing  ) starting from n =1; fix the value of the loading parameter  starting from zero; compute the matrices (35), which now depend only on r, and then compute  ra in (38) by means of (36); divide the interval  1 2r , r into n subintervals i+1 ir , r such that the magnus series converges in each of them (see the convergence condition (7)); employ for simplicity a fourth-order method by truncating the magnus series  i+1r after the second term in each subinterval (see (4)) and by approximating the integrals using a gauss quadrature rule. this allow us to write                2 1 2 1 2 i+1 i i i i h h 3 r r r r , r 2 12        a a a a (47) where    1 2 2 1 i ii i r r1 3 1 3 r r h, r r h , with h = 2 6 2 6 n                   (48) are two gauss points in correspondence of which  ra and its employed linear approximation agree. compute the matrix exponential of  i+1r using the function matrixexp in the software mathematica; evaluate the matricant of (46) at the external radius r2 = r2 by (8) and (9); compute the “north-east” block of the matricant at r2 = r2 , that is the 3x3 matrix  2 2ru ; compute the determinant of  2 2ru and check if the bifurcation condition (44) holds. following this procedure, we define ncr as the smallest value of  which satisfies the bifurcation condition (44) corresponding to the fixed value of n. of course, when one repeats the above procedure by varying the number of possible axial cells, the corresponding critical load ncr varies. we have performed a large number of computations which show that as n increases, the corresponding ncr determined by (44) decreases until a critical value of n above which (44) a. castellano et alii, frattura ed integrità strutturale, 29 (2014) 128-138; doi: 10.3221/igf-esis.29.12 137 definitively does not hold for any  . in correspondence, a load cr corresponding to crn is determined, and this is the critical value of the circular angle of shear which allows for the occurrence of a non-trivial axial periodic deformation of the form (31). fig. 1 reports the bifurcation curve for a referential shear modulus 1  mpa, referential poisson’s ratio 0.25  , 3 / 4  and h/r1=1. it shows the critical load cr as a function of the ratio 2 1r /r between the outer and the inner radius of the tube. we may easily infer, as expected, that twist-like bifurcation may be more easily supported in thin tubes. figure 1: cr vs. r2/r1, for  = 1,  = 3/4,  = 0.25, h/r1=1. conclusions e have studied a bifurcation problem concerning the possibility of periodic twits-like deformations superposed to a primary azimuthal shear state for a levinson-burgess isotropic elastic tube. the procedure proposed for determining approximate solutions of the resulting non-autonomous systems of linear ode’s is based on the magnus method, which represents an innovative numerical scheme belonging to the more general class of geometric numerical integrators. we have the feeling that these new methods, already employed in many scientific areas, may find interesting applications also in the field of continuum mechanics. in the future we are going to further explore the applicability and the advantages of the magnus method by studying other bifurcation problems yielding non-autonomous ode systems like, for example, a taylor-couette type bifurcation for a sheared incompressible annular tube modeled by an extended version of the gent constitutive equation. acknowledgments he authors gratefully acknowledge the research projects miur-prin 2010-2011: “dinamica, stabilità e controllo di strutture flessibili” and miur pon-rec: “massime” – sistemi di sicurezza meccatronici innovativi (cablati e wireless) per applicazioni ferroviarie, aerospaziali e robotiche. references [1] goriely, a., vandiver, r., destrade, m., nonlinear euler buckling, proc. r. soc. a, 464 (2008) 3003 – 3019. [2] shuvalov, a. l., a sextic formalism for the three-dimensional elastodynamics of cylindrically anisotropic radially inhomogeneous materials, proc. r. soc. lond., 459 (2003) 1611–1639. [3] shuvalov, a. l., poncelet, o., deschamps, m, general formalism for plane guided waves in transversely inhomogeneous anisotropic plates, wave motion, 40 (2004) 413 – 426. w t a. castellano et alii, frattura ed integrità strutturale, 29 (2014) 128-138; doi: 10.3221/igf-esis.29.12 138 [4] magnus, w., on the exponential solution of differential equations for a linear operator, comm. pure appl. math., vii (1954) 649 – 673. [5] blanes, s., casas, f., oteo, j.a., ros, j., the magnus expansion and some of its applications, physics reports, 470 (2009) 151 – 238. [6] iserles, a., munthe-kaas, h.z., norsett, s.p., zanna, a., lie-group methods, acta numer., 9 (2000) 215 – 365. [7] iserles, a., norsett, s.p., on the solution of linear differential equations in lie groups, phil. trans. r. soc. a, 357 (1999) 983 – 1019. [8] budd, c. j., piggott, m.d., the geometric integration of scale-invariant ordinary and partial differential equations, j. of comput. and appl. mathematics, 128 (2001) 399 – 422. [9] schek, i., jortner, i., sage, m.l., application of the magnus expansion for higher-order multiphoton excitation, chem. phys., 59 (1981) 11 – 27. [10] botchev, m.a., verwer, j.g.., numerical integration of damped maxwell equations, technical report cwi amsterdam (2008). [11] viswanath, d., symbolic dynamics and periodic orbits of the lorenz attractor, nonlinearity, 16 (2003) 1035 – 1056. [12] moan, p.c., niesen, j., convegence of the magnus series, found. comput. math., 8 (20089 291 – 301. [13] [13] moler, c. b., van loan, c. f., nineteen dubious ways to compute the exponential of a matrix, twenty-five years later, siam review, 45 (2003), 3 – 49. [14] celledoni, e., iserles, a., approximating the exponential from a lie algebra to a lie group, math. comput., 69 (2000) 1457 – 1480. [15] iserles, a., on cayley-transform methods for the discretization of lie-group equations, found. comput. math., 1 (2000) 129 – 160. [16] haughton d.m., circular shearing of compressible elastic cylinders, q. jl. mech. appl. math., 46 (1993) 471 – 486. [17] fosdick r., foti p., fraddosio a., marzano s., shear driven planar couette and taylor-like instabilities for a class of compressible isotropic elastic solids, zamp, 61 (2010) 537 – 554. [18] fosdick r., foti p., fraddosio a., marzano s., piccioni, m. d., taylor-like bifurcations for a compressible isotropic elastic tube, mathematics and mechanics of solids (mms), published on line (2013) issn: 1081-2865, doi: 10.1177/1081286513496576. [19] fosdick, r., foti, p., fraddosio, a., piccioni, m.d., lower bound estimate of critical loads for isotropic elastic solids, cont. mech. and thermodynamics (cmt), 22 (2010) 77 – 97. [20] fosdick r., foti p., fraddosio a., marzano s., piccioni, m. d., a lower bound estimate of the critical load in bifurcation analysis for incompressible elastic solids, mathematics and mechanics of solids (mms), invited contribution on the special number in honor of k.r. rajagopal, (2014). [21] pease iii, m.c.. methods of matrix algebra, academic press, new york and london, (1965). microsoft word numero 3 art 2.doc m. zappalorto et al., frattura ed integrità strutturale, 3 (2008) 11-17; doi: 10.3221/igf-esis.03.02 11 1 introduzione nella letteratura recente è stato ampiamente dimostrato come la resistenza a fatica di giunzioni saldate ad arco in acciaio da costruzione o in lega leggera possa essere sintetizzata in termini di fattori di intensificazione delle tensioni o "notch stress intensity factors” (n-sifs) [1-3]. il problema della variabilità dei raggi di raccordo al piede e alla radice dei cordoni di saldatura viene superato nell’approccio n-sif modellando i cordoni come intagli acuti a v; le distribuzioni di tensione in corrispondenza dei punti critici presentano quindi un carattere asintotico e gli n-sif quantificano proprio la loro intensità. poiché le distribuzioni sono sensibili alle dimensioni assolute del giunto, l’effetto scala è interamente conglobato nel valore dell’n-sif [1-3]. quando l’angolo di apertura 2α dell’intaglio è abbastanza grande da rendere il modo ii non singolare (2α>102°, condizione generalmente soddisfatta in tutti i giunti con cordoni d’angolo), il comportamento a fatica in presenza di sollecitazioni di trazione o flessione dipende solo dal fattore di intensificazione di modo i, δk1 [1-3]. tale parametro, che era naturale pensare idoneo a controllare la fase di innesco delle cricche di fatica, è invece risultato efficace anche nell’operare una sintesi della vita finale dei giunti saldati; ciò accade perché nei campioni testati in laboratorio la maggior parte della vita a fatica è spesa come innesco e propagazione di cricche corte, localizzate all’interno della zona di singolarità governata dai campi asintotici iniziali [3]. gli n-sif permettono di superare il complesso problema legato alla propagazione di cricche multiple e della loro possibile interazione su piani diversi, fenomeni variabili in funzione del tipo di sollecitazione e delle irregolarità presenti al piede dei cordoni. la fig. 1 riassume numerosi dati sperimentali in funzione del fattore di intensificazione delle tensioni di modo i. la sintesi riguarda giunti a croce e a t, soggetti a trazione o a flessione e caratterizzati da uno spessore dei piatti principali variabile tra 3 e 100 mm. la variabilità dei piatti traversali risulta ancora più pronunciata, con uno spessore variabile tra 3 e 220 mm. le rotture si manifestavano sempre al piede dei cordoni di saldatura, in presenza di un angolo apertura di 135° tra piatti principali e superficie inclinata dei cordoni. dal punto di vista teorico, la banda di dispersione riportata in fig. 1 non può essere estesa a giunzioni saldate che manifestano rotture alla radice dei cordoni, né a giunzioni densità di energia di deformazione locale e resistenza a fatica di giunti saldati di geometria complessa m. zappalorto, f. berto, p. lazzarin università di padova, dipartimento di tecnica e gestione dei sistemi industriali, stradella san nicola 3, 36100 vicenza e-mail: zappalorto@gest.unipd.it, plazzarin@gest.unipd.it riassunto. un recente criterio basato sul valore medio della densità di energia di deformazione (sed) in un volume di controllo è applicato a diverse serie di dati sperimentali tratti dalla letteratura, relativi a giunti saldati di geometria complessa realizzati in acciaio. il volume di controllo è rappresentato da un settore circolare di raggio pari a 0.28 mm, centrato sul piede o sulla radice dei cordoni di saldatura. entrambe le regioni sono modellate come intagli v non raccordati con differenti angoli di apertura. la densità di energia di deformazione viene valutata direttamente da modelli agli elementi finiti tridimensionali. i dati sperimentali, riconvertiti in termini energetici, si posizionano all’interno di una banda di dispersione recentemente proposta in letteratura. la banda sintetizzava più di 650 dati sperimentali relativi a giunti saldati con cordone d’angolo, con rotture innescate indifferentemente al piede o alla radice dei cordoni di saldatura. abstract. a recent criterion based on the local strain energy density (sed) averaged over a given control volume is applied to well-documented experimental data taken from the literature, all related to steel welded joints of complex geometry. this small size volume embraces the weld root or the weld toe, both regions being modelled as sharp (zero notch radius) v-notches with different opening angles. the sed is evaluated from three-dimensional finite element models by using a circular sector with a radius equal to 0.28 mm. the data expressed in terms of the local energy fall in a scatter band recently reported in the literature, based on about 650 experimental data related to fillet welded joints made of structural steel with failures occurring at the weld toe or at the weld root. parole chiave. notch stress intensity factor, energia di deformazione, giunti saldati, resistenza a fatica http://dx.medra.org/10.3221/igf-esis.03.02&auth=true http://www.gruppofrattura.it http://www.gruppofrattura.it m. zappalorto et al., frattura ed integrità strutturale, 3 (2008) 11-17 12 con angoli di apertura al piede sensibilmente diversi da 135°. questo è dovuto al fatto che le unità di misura degli n-sif cambiano proprio in funzione dell’angolo di apertura. il problema è stato superato in recenti lavori [4-9] usando come parametro rappresentativo della resistenza a fatica il valore medio della densità di energia di deformazione δw calcolata in un volume finito centrato sul piede o sulla radice dei cordoni. in linea di principio tale energia è funzione dei fattori di intensificazione di modo i e di modo ii nei casi piani [4], di modo i, ii e iii nel caso di sollecitazioni multiassiali [6, 9]. una banda in termini di δw è stata inizialmente proposta nelle referenze [4, 5] sulla base di circa 300 dati sperimentali relativi ad acciai da costruzione saldati ed è stata successivamente verificata utilizzando altri 400 dati che si sono resi disponibili nel tempo [7]. la stessa banda è risultata valida non solo per i giunti con cordoni d’angolo ma anche per i giunti saldati testa a testa [8]. una sintesi parziale è presentata in fig. 2 relativamente a giunti realizzati con acciai da costruzione, interessati da rotture al piede e alla radice dei cordoni di saldatura [7-8]. l’indice tw che fornisce la larghezza di banda riferita a valori medi +/due deviazioni standard vale 3.3. passando dal range di densità di energia di deformazione a un range di tensione locale equivalente e ai livelli di probabilità di sopravvivenza del 10-90%, l’indice scende a tσ= figura 1. resistenza a fatica di giunti saldati in acciaio e lega leggera in funzione del fattore di intensificazione delle tensioni di modo i. geometrie a croce e a t, con cordone portante. angolo di apertura di 135°; t spessore dei piatti principali; banda di dispersione relativa a valori medi ± 2 deviazioni standard (ps=2.3-97.7%). la figura è tratta dal riferimento [7]. figura 2. resistenza a fatica in funzione del valore medio della densità di energia di deformazione presente in un settore semicircolare di raggio rc centrato sull’apice dell’intaglio a v [7-8]. nel caso di giunti saldati realizzati con acciai da costruzione il raggio critico rc vale 0.28 mm.   cicli a rottura, n 104 105 106 107 99 74 132 211 155 287 100 1000 6-100 3-24 t [mm] pendenza k=3.0 steels al alloys r ≈ 0.1 r ≈ 0 ref. [2,6] ref. [13] pendenza k=4.0 ferritic and high strength steels 6-32 3 high strength steel 2000 300 600 δ k 1 [m pa m m 0. 32 6 ]   0.01 0.1 1 10 104 107 numero di cicli a rottura, n 106 105 r0=0.28 mm rottura al piede dei cordoni rottura alla radice dei cordoni pendenza k = 1.5 rapporto nominale r≈0 650 dati a fatica vari acciai da costruzione v al or e m ed io d el la d em si tà d i e ne rg ia d i d ef or m az io ne δ w [n m m /m m 3 ] 0.192 0.105 0.058 δw tw=3.3 m. zappalorto et al., frattura ed integrità strutturale, 3 (2008) 11-17 13 1.50, valore che caratterizza la banda normalizzata s-n di haibach [10]. l’obiettivo del presente lavoro è quello estendere l’uso del criterio dell’energia locale a un elevato numero di dati sperimentali tratti dalla letteratura [11-13] relativi a giunti saldati in acciaio con geometrie tridimensionali complesse e di confrontarli con la banda di dispersione già citata. 2 premesse analitiche il grado di singolarità 1-λi dei campi di tensione in prossimità di intagli a v non raccordati varia in funzione dell’angolo di apertura (fig. 3), riducendosi progressivamente rispetto al caso di una cricca dove il grado di singolarità è 0.5 per i modi di sollecitazione i e ii [1, 14]. l’intensità delle distribuzioni di tensione asintotiche presenti di fronte all’apice dell’intaglio a v non raccordato è generalmente espressa in funzione degli n-sif. in un sistema in coordinate polari (r, θ) avente l’origine centrata sull’apice (fig. 4), le distribuzioni lineari elastiche delle tensioni possono essere espresse in forma generale come: modo i 1)1(ij n 1 )1( ij 1r)(~k),r( −λ⋅θ⋅=θσ σ (1) modo ii 1)2(ij n 2 )2( ij 2r)(~k),r( −λ⋅θ⋅=θσ σ dove n1k e n 2k , sono gli n-sif di modo i e ii, )(θθσ~ij sono le funzioni angolari e, infine, λ1 e λ2 gli autovalori del problema lineare elastico. vale per gli n-sif la seguente definizione [15]: [ ] [ ] )0,(lim2 )0,(lim2 2 1 -1 0→ 2 -1 0→ 1 λ θ λ θθ σπ σπ rrk rrk r r n r n + + = = (2) nell’ipotesi di deformazione piana, l’energia di deformazione mediata su un settore circolare di raggio rc che abbraccia l’apice dell’intaglio può essere espressa mediante la relazione [4-9]: figura 3. grado di singolarità 1-λ dei campi di tensione in prossimità di intagli a v non raccordati in funzione dell’angolo di apertura. figura 4. sistema di coordinate polari centrato sull’apice dell’intaglio. 2α/π γ/π λ1 λ2 i1 i2 0 1 0.5000 0.5000 0.8450 2.1450 3/4 5/8 0.6736 1.3021 0.6201 1.1505 tabella 1. valore dei parametri presenti nelle equazioni (1-3) ottenuti con l’ipotesi di beltrami e con un coefficiente di poisson ν=0.3.   0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40 0.45 0.50 0 20 40 60 80 100 120 140 160 180 modo i modo ii 2α [gradi] 1λ i (1-λ1) (1-λ2) 2α   σ θθ σ rr σ r θ θ γ 2α r m. zappalorto et al., frattura ed integrità strutturale, 3 (2008) 11-17 14 ⎪⎭ ⎪ ⎬ ⎫ ⎪⎩ ⎪ ⎨ ⎧ ⎥ ⎦ ⎤ ⎢ ⎣ ⎡ δ λ γ +⎥ ⎦ ⎤ ⎢ ⎣ ⎡ δ λ γ δ = λ λ 2 1c n 2 2 2 2 1c n 1 1 w 1 1 2r k 4 i r k 4 i e c w (3) dove il coefficiente cw permette di tenere conto dell’influenza del rapporto nominale di ciclo r nel solo caso di giunti soggetti a distensione post-saldatura. tutti gli altri parametri in gioco sono riportati in tab. 1 con riferimento al criterio della densità di energia totale di deformazione (ipotesi di beltrami) e a un coefficiente di poisson ν=0.3. il parametro cw, definito in condizioni lineari elastiche, può essere ottenuto per mezzo delle seguenti relazioni [6]: ( ) ( ) ( )⎪ ⎪ ⎩ ⎪ ⎪ ⎨ ⎧ ≤ ≤ ≤ < + = se 0 r 1 1-r 1-r se -1 r 0 1-r 1 r c r 2 2 2 2 w (4) passando da r=0 a r=-1, cw scende da 1.0 a 0.5; ad un dimezzamento della densità di energia locale corrisponde un aumento della resistenza a fatica in termini di tensione locale di un fattore 1/.707=1.41, simile al coefficiente empirico 1.33 suggerito dalla cnr uni 10011. ovviamente, se i giunti non subiscono alcun trattamento di distensione post-saldatura, la dipendenza dal rapporto nominale di ciclo r scompare e il parametro cw deve considerarsi unitario. e’ noto infatti che nelle strutture reali soggetti ad elevati stati di tensioni residue la resistenza a fatica è sostanzialmente indipendente dal rapporto nominale di ciclo [16]. 3 resistenza a fatica di giunti saldati di geometria complessa basata sulla densita’ di energia di deformazione locale sono stati riconsiderati alcuni dati sperimentali relativi a particolari strutturali saldati in acciaio tratti da precedenti lavori [11-13]. i principali parametri geometrici così come le condizioni di carico e di vincolo erano perfettamente definite nei lavori originali e sono rappresentati schematicamente in fig. 5. (a) (b) (c) (d) figura 5. geometrie dei giunti saldati analizzati. i dati originali sono relativi ai riferimenti [11-13]. tutte le dimensioni sono in mm.   8 38 150 12.7 150 800 12.7 maddox, 1982 mild steel bs 4360 grade 50 s70 qt445a   740 100 t=5, 8 40 600 8 300 lihavainen e marquis, 2003 s355 steel 34 r25   r30 <12> 4 4 120 260 220 60 0 12 80 fricke e doerk, 2006   <12> r50 30 70 <12> 185 15 4 4 <12> 100 70 40 0 10 0 fricke e doerk, 2006 m. zappalorto et al., frattura ed integrità strutturale, 3 (2008) 11-17 15 3.1 dati di maddox. la prima serie rianalizzata riguarda i dati di resistenza a fatica già discussi da maddox [11]. i componenti utilizzati nelle prove sperimentali consistono in giunti con un irrigidimento longitudinale saldato su un solo lato del piatto principale, avente uno spessore di 12.7 mm (fig. 5a) e realizzati in quattro differenti tipologie di acciai (i.e. mild steel, bs 4360 grade 50, s70 and qt445a). i componenti sono stati testati a trazione in condizioni as-welded utilizzando cinque differenti rapporti nominali di carico: r=-∞, -1, 0, 0.5 e 0.67. tutti i componenti sono stati portati a completa rottura, fatta eccezione per il caso r=-∞ in cui la velocità di propagazione manifestava un decremento al propagare delle cricche di fatica; per questa serie i test erano stati arrestati prima del completo cedimento. in tutti i casi considerati la nucleazione delle cricche di fatica avveniva in corrispondenza del piede del cordone. 3.2 dati di lihavainen e marquis. i giunti ad irrigidimento longitudinale non portante già analizzati da lihavainen e marquis [12] sono rappresentati in fig. 5b. i giunti erano realizzati in acciaio s355 j0 utilizzando piatti principali di spessore 5 mm e 8 mm. le prove di fatica erano state condotte a trazione con un rapporto di ciclo pari a r=0.1. per tutti i componenti considerati la nucleazione delle cricche di fatica avveniva in corrispondenza del piede del cordone. 3.3 dati di fricke e doerk. l’ultima serie di dati sperimentali riguarda i giunti saldati sottoposti a sperimentazione da fricke e doerk [13] e rappresentati in fig. 5c-d. i dati di resistenza a fatica erano stati ottenuti con prove di trazione (fig. 5c) e di flessione a tre punti (fig. 5d). i dettagli saldati erano stati testati sia in condizioni as-welded (con due differenti rapporti nominali di carico, r=0 and r=0.5), che stressrelieved (con r=0). figura 6. esempio di modellazione del giunto ad irrigidimento longitudinale già analizzato da maddox [11] (a) e del giunto cruciforme già analizzato da fricke e doerk [13] (b); modelli complessivi e particolari relativi alla modellazione del volume strutturale.   (a)   (b) m. zappalorto et al., frattura ed integrità strutturale, 3 (2008) 11-17 16 i componenti di fig. 5c testati in condizioni as-welded esibivano un comportamento a rottura anomalo; in molti casi infatti le cricche di fatica innescavano alla radice del cordone di saldatura, in corrispondenza della zona centrale del piatto principale, nonostante lo stato tensionale non fosse massimo in quel punto. nei componenti stress-relieved invece, la nucleazione avveniva sia al piede che alla radice del cordone di saldatura. infine, la maggior parte dei componenti rappresentati in fig. 5d manifestava prevalentemente una nucleazione alla radice. per riconvertire i dati sperimentali in termini energetici la densità di energia di deformazione è sempre stata valutata su un volume di controllo che abbraccia le zone di innesco delle cricche di fatica indicate dagli autori nei lavori originali. la densità di energia di deformazione è stata ottenuta mediante analisi tridimensionali agli elementi finiti eseguite con il software ansys 9.0®, modellando il volume di controllo come un settore circolare tridimensionale di raggio rc=0.28 mm, posizionato al piede o alla radice del cordone di saldatura (fig. 6). poiché i dati fanno riferimento sia a giunti sottoposti a trattamento di distensione delle tensioni residue (stressrelieved) con r=0, sia a giunti testati allo stato as-welded con differenti rapporti nominali di carico (-∞<r<0.67), nella sintesi il coefficiente correttivo cw è sempre stato posto pari al valore unitario. nella fig. 7 i dati sperimentali riconvertiti in termini energetici sono confrontati con una banda di dispersione già riportata nel riferimento [5]; l’accordo è molto soddisfacente, tranne per alcuni dati relativi alle serie già analizzate da maddox [11] e caratterizzati da un rapporto di ciclo pari a r=-∞ (pura compressione). l’indice di dispersione tw relativo alle probabilità di sopravvivenza ps=2.3% e 97.7% è risultato pari a 3.3 e se riconvertito in termini di tensione locale equivalente e probabilità di sopravvivenza ps=10% e 90% risulta 1.5, in perfetto accordo con la banda normalizzata suggerita da haibach [10]. 4 conclusioni nel presente lavoro sono state considerate diverse serie di dati di resistenza a fatica tratti dalla letteratura e relativi a unioni saldate in acciaio di geometria complessa. per tali serie risultavano precisati tutti i parametri che consentono di descrivere con precisione la geometria locale in corrispondenza del piede e della radice dei cordoni di saldatura. i dati sperimentati sono stati rianalizzati utilizzando un criterio locale basato sul valore medio della densità di energia di deformazione, criterio già messo a punto e applicato a giunti di geometria diversa, soggetti a trazione o flessione. il metodo energetico consente di sintetizzare dati di resistenza a fatica indipendentemente dal punto di innesco delle cricche e dall’angolo di apertura al piede dei cordoni. i dati di resistenza a fatica, riconvertiti in termini di densità di energia locale, sono stati confrontati con una banda di sintesi recentemente proposta in letteratura. l’accordo con la banda di sintesi è risultato soddisfacente. l’indice di dispersione, se riconvertito in termini di tensione media locale, piuttosto che in termini di densità media di energia locale, appare perfettamente in linea con le indicazioni fornite dalla banda normalizzata di haibach. 5 bibliografia [1] p. lazzarin, r. tovo, a notch stress intensity approach to the stress analysis of welds. faigue and frac figura 7. resistenza a fatica di giunti saldati in acciaio strutturale di geometria complessa in termini di densità di energia locale; i dati originali sono riportati nei riferimenti [11-13]. confronto con la banda di dispersione proposta da lazzarin et al. [5] (ps=2.3-97.7).   0.01 0.1 1 1 0 104 105 106 107 cicli a rottura, n lihavainen e marquis, 2003; r=0.1 (as-welded) fricke e doerk, 2006; r=0, 0.5 (as-welded) fricke e doerk, 2006; r=0 (stress-relieved) maddox, 1982; -1<r<0.67 (as-welded) maddox, 1982; zero-compression (as-welded) k=1.5 134 dati δ w [ n ⋅m m /m m 3 ] rc=0.28 mm tw=3.3 α να= 2×10 6 cicli: δw = 0.105 [n⋅mm/mm3] m. zappalorto et al., frattura ed integrità strutturale, 3 (2008) 11-17 17 ture of engineering materials and structures, 21 (1998) 1089-1103. [2] b. atzori, p. lazzarin, r. tovo, from the local stress approach to fracture mechanics: a comprehensive evaluation of the fatigue strength of welded joints. fatigue and fracture of engineering materials and structures, 22 (1999) 369-382. [3] p. lazzarin, p. livieri, notch stress intensity factors and fatigue strength of aluminium and steel welded joints. international journal of fatigue, 23 (2001) 225232. [4] p. lazzarin, r. zambardi, a finite-volume-energy based approach to predict the static and fatigue behaviour of components with sharp v-shaped notches. international journal of fracture, 12 (2001) 275-298. [5] p. lazzarin, t. lassen, p. livieri. a notch stress intensity approach applied to fatigue life predictions of welded joints with different local toe geometry. fatigue and fracture of engineering materials and structures, 26 (2001) 49-58. [6] p. lazzarin, c.m. sonsino, r. zambardi. a notch stress intensity approach to predict the fatigue behaviour of t butt welds between tube and flange when subjected to in–phase bending and torsion loading. fatigue and fracture of engineering materials and structures, 27 (2004) 127-141. [7] livieri p, lazzarin p. fatigue strength of steel and aluminium welded joints based on generalised stress intensity factors and local strain energy values. international journal of fracture, 133 (2005) 247-276. [8] lazzarin p, berto f, radaj d. uniform fatigue strength of butt and fillet welded joints in terms of the local strain energy density. proc. fatigue 2006, atlanta, usa. [9] p. lazzarin, p. livieri, f. berto, m. zappalorto. engineering fracture mechanics. 2007; in press (available on line). [10] e. haibach. service fatigue strength – methods and data for structural analysis. springer verlag, berlin, 2002. [11] s.j. maddox. influence of tensile residual stresses on the fatigue behavior of welded joints in steel. astm stp.,776 (1982) 63-96. [12] v.m. lihavainen, g. marquis. fatigue strength of a longitudinal attachment improved by ultrasonic impact treatment. iiw. 2003; document xiii-1990-03. [13] w. fricke, o. doerk. simplified approach to fatigue strength assessment of fillet-welded attachment ends. international journal of fatigue, 28 (2006) 141-150. [14] m.l. williams. stress singularities resulting from various boundary conditions in angular corners of plates in extension. asme journal of applied mechanics, 19 (1952) 526-528 [15] r. gross, a. mendelson. plane elastostatic analysis of v-notched plates. international journal of fracture mechanics, 8 (1972) 267-327. [16] b. atzori. trattamenti termici e resistenza a fatica delle strutture saldate. rivista italiana della saldatura, 1 (1983) 3-16. microsoft word numero_27_art_2 l. marsavina et alii, frattura ed integrità strutturale, 27 (2014) 13-20; doi: 10.3221/igf-esis.27.02 13 focussed on: infrared thermographic analysis of materials a review of using thermoelasticity for structural integrity assessment l. marsavina department strength of materials, politehnica university of timisoara,blvd. m. viteazu, nr.1, timisoara 300222 romania. msvina@mec.upt.ro r.a. tomlinson department of mechanical engineering, university of sheffield, mappin street, sheffield s1 3jd, uk. r.a.tomlinson@sheffield.ac.uk abstract. the advances in the use of thermoelastic stress analysis (tsa) for fracture mechanics assessment are reviewed. the development of techniques to determine stress intensity factor is presented followed by the application of these techniques to fatigue crack growth, crack closure and the study of mixed mode cracks. keywords. thermoelastic stress analysis; crack; fatigue; stress intensity factor range. introduction hermoelastic stress analysis (tsa) has been developed over last two decades to be a useful method for structural integrity assessment, harwood and cummins [1]. using a sensitive infra-red detector, minute temperature changes due to the thermoelastic effect are detected from around the tip of a crack under cyclic load. the signal from the detector, s, is related to the first stress invariant by the following equation: 1 2( ) a s    (1) where a is a calibration constant. an expression for this first stress invariant in the region of the crack tip can be derived from stress field equations and used to determine the stress intensity factors. a typical un-calibrated thermoelastic map from a crack of 15 mm length loaded in mixed mode with kii/ki = 1 is shown in fig. 1. figure 1: thermoelastic data around a 15 mm crack loaded in mixed mode with applied mixed mode ratio kii/ki = 1. t http://dx.medra.org/10.3221/igf-esis.27.02&auth=true http://www.gruppofrattura.it l. mardavina et alii, frattura ed integrità strutturale, 27 (2014) 13-20; doi: 10.3221/igf-esis.27.02 14 the stress intensity factor value obtained from thermoelastic analysis is equal to the range of the stress intensity factor, δk, which occurs at the crack tip due to the applied cyclic load. this allows the actual crack driving force to be experimentally determined rather than being inferred from maximum and minimum stress intensity factors, which is the case with other experimental techniques. the direct determination of δk makes the technique ideal for use in structural integrity assessment. further advantages over other experimental methods are that thermoelasticity is a non-contacting method, with minimal surface preparation required, which may be used to study cracks in both real components and models. this paper will review the advances made in thermoelastic fracture mechanics in recent years. an outline of the experimental issues which need to be considered for determining stress intensity factors using thermoelasticity was presented by tomlinson and olden [2] and this paper adds to that. methods to determine the stress intensity factor at crack tips using thermoelastic stress analysis are explored, starting from selected line techniques using the westergaard equations to the most recent methods which utilise the full array of data available together with complex stress field equations. crack path analysis and interaction of cracks will be explored in addition to fracture mechanics investigation of a range of materials. in order to obtain accurate results a number of areas of experimental procedure need to be considered and these are discussed in detail. the paper will present the progress made on determination of stress intensity factors for fatigue cracks, tracking the location of the crack tip during propagation under cyclic loading, and also in investigating the crack closure effect. recently, risitano et al. [3], utilizing the thermographic method, made an estimations very close of the real values of stress concentration factor and fatigue-stress concentration factor. the determination of stress intensity factors for sharp notches evaluation of mode i stress intensity factors for sharp notches here are primarily five methods available to determine the stress intensity factor of a crack using thermoelastic equipment. the techniques proposed by stanley and chan [4], stanley and dulieu-smith [5], lesniak [6], tomlinson et al. [7] and lin et al. [8] are detailed in the following sections. in 1986 the thermoelastic technique was first used to determine ki, the opening mode stress intensity factor, by stanley and chan [4] who used a spate (stress pattern analysis by thermal emission) system to record the thermoelastic signal, s. using the first two terms of the westergaard equations for the elastic stresses in the vicinity of a crack under mode i and mode ii loading it was shown that the stress intensity factor of a crack could be related to the spate signal recorded using the following relationship: 2 2 cos sin 2 22 2 i iik kas r r         (2) thus the spate signal around the crack tip, s, when multiplied by a calibration factor, a, could be used to calculate stress intensity factors from points located at distances (r,) from the crack tip. this equation provides the basis of determining both single-mode stress intensity factors, and also mixed-mode. for the latter case it was explained that ki would first be generated from data along the line  = 0, before kii could be calculated from a general line. emphasis was placed by the authors on the likelihood of large errors if a single point value were used, as it would not be clear whether data had been recorded from the region of validity for the westergaard equations, and also it would be necessary to know the exact location of the crack tip. the region of validity of the westergaard equations is discussed in a later section. stanley and chan [4] also describe a graphical method to determine the opening mode stress intensity factor of a fatigue crack. this used a series of line scans either perpendicular or parallel to the crack line. in the parallel case the stress intensity factor is determined using: 24 3 3 i a gr k    (3) where gr. is the gradient of the linear region from a graph of 1/smax2 against distance y. typical data points from which the gradient was obtained are shown in fig. 2. the non-linearity observed close to the crack tip and also at the extremities was attributed to crack tip plasticity and finite plate size respectively. remote stresses in a finite width specimen are higher than in an infinite specimen, for which the westergaard equations were derived. for the fatigue cracks studied all experimental results were found to be within 10 % of the theoretical solutions. t http://dx.medra.org/10.3221/igf-esis.27.02&auth=true http://www.gruppofrattura.it l. marsavina et alii, frattura ed integrità strutturale, 27 (2014) 13-20; doi: 10.3221/igf-esis.27.02 15 this technique was further developed on mode ii fatigue cracks, stanley and chan, [9]. (a) (b) (c) figure 2: a typical set of data points from a thermoelastic scan of a crack (stanley and chan [2]). a study of simulated inclined edge and centre cracks by stanley and dulieu-smith [10] showed that the isopachic contour in the crack tip region generally took the form of a cardioid curve, centred on the crack tip. by determining the area and orientation of a typical cardioid, ki and kii were calculated. using eq. (2) the following equation was derived: 2 2 2 2 (1 cos( 2 ))i ii k k r a s          (4) where  = tan-1(ki/kii). for a constant value of s, eq. (4) represents a closed curve in (r,) co-ordinates which represent a cardioid or “apple” shape. in the experimental investigation a series of line scans parallel to the crack line were used to construct a curve by recording the location(s) on each line scan where a particular value of thermoelastic signal was measured. hand fitting a cardioid shape to experimental data did not result in a perfectly symmetrical curve and scatter in the results was noted. the agreement between experimental and theoretical ki/kii values was concluded to be no better than moderate. in a later paper the omission of the non-singular stress term in the calculation of stress intensity factors in the original work of stanley and dulieu-smith [10] was discussed. a method was suggested for including this factor and determining its value from a map of thermoelastic data. however, no results were presented to indicate whether experimental values were closer to theoretical predictions for ki and kii when account was taken of the non-singular stresses. the cardioid curve method was extended to allow inclusion of all the data from around the crack tip (fulton et al. [11], dulieu-barton et al. [12]). a computer program is used to calculate the area and orientation of nine cardioid curves of constant thermoelastic signal. a potential source of error in the method was highlighted as being its sensitivity to an exact knowledge of pixel size in the map of thermoelastic data. this technique was further developed to greater accuracy by dulieu-barton and worden, [13] using a curve fitting routine based on a genetic algorithm to generate the cardioid curves from thermoelastic data, which were subsequently used to determine the stress intensity factor. an alternative approach for determining stress intensity factors for cracks subject to mixed-mode loading which had previously been used in photoelastic analysis, was developed by tomlinson et al. [7]. a newton-raphson iteration combined with a least squares approach was used to fit the equations describing the stress field around the crack tip, based on mushkelishvili’s approach, to the experimental data. this approach allows different applied stress fields to be described which may include non-uniform stress fields. the computerised analysis method required the map of data obtained from each spate scan to be interrogated at a number of points on lines radiating from the crack tip between an inner and an outer radius in the "singularity dominated zone". the co-ordinates of these points and the spate signal value were input into a new computer program which calculates ki and kii. the mean and variance of the least-squares fit of the solution to the data points are also calculated in order to give an indication of the accuracy of the results. a further data array method was developed by lesniak [6] where the airy stress function was fit to the array of thermoelastic data using a least squares method. the method uses the complete stress function, rather than just the singularity term, and therefore can account for the boundaries of a component. it is also very fast, since multiple terms of the stress field can be least-squares fit in seconds, which gives the potential to perform live crack growth analyses. the procedure gave errors of 3% for mode i cases when compared to analytical solutions. a mixed-mode example has also been published but with less accurate results, lesniak et al. [14]. http://dx.medra.org/10.3221/igf-esis.27.02&auth=true http://www.gruppofrattura.it l. mardavina et alii, frattura ed integrità strutturale, 27 (2014) 13-20; doi: 10.3221/igf-esis.27.02 16 the above methods require thermoelastic data to be taken from close to the crack tip in order to determine the stress intensity factor, since these approaches use the principles of linear elastic fracture mechanics. in such methods there are restrictions on the areas of data collection due to localised plasticity and tri-axial stress effects near the crack tip. in order to overcome these problems, a hybrid method has been developed which is based on equilibrium, compatibility and the j integral and uses far-field thermoelastic data to determine the stress intensity factor, lin et al. [8]. the value of the procedure is that it is not restricted to isotropic materials and was demonstrated by determining the stress intensity factor for cracks in both orthotropic composites and isotropic plates. the proposed methods by tomlinson et. al. [7], lesniak et al. [14], dulieu barton et al. [12], diaz et al. [15] which have been developed to determine stress intensity factors at crack tips have taken advantage of computing power and data processing available on a standard personal computer. these methods have been shown to give more accurate results than previous manual methods when compared to theoretical solutions, and it is believed this work will advance in a number of areas in the near future. evaluation of mixed mode solutions for sharp notches shiratori et al. [16] used a method of stress intensity factor calculation based on the westergaard equations and applied the spate technique to three different specimen types. the first specimen type was a compact tension specimen which was notched but had no fatigue crack. results for three notch lengths showed that spate results were in fairly close agreement with the findings of a finite element analysis, except within 5 mm of the crack tip where they were much lower. the authors suggested that this was due to the smoothing of the data by the spate equipment, leading to an underestimation of the stress value in regions where the stress gradient is high. in the smoothing the value of stress at a pixel is determined from the average stress value at a pixel and also the surrounding pixels. therefore it was recommended that the minimum load range that could be applied to obtain a clear stress plot should be used to minimise the stress gradient at the crack tip. the other specimens analysed by the authors were a surface notched specimen and also a fatigue crack at the end of a slanted through-wall crack. on the basis of the results from the three specimens it was concluded that stress intensity factors for various crack types could be calculated to within 10-20% using spate equipment. this was considered to be suitably accurate for use in the analysis of cracks in the complicated members of real structures where computational methods cannot be reliably used due to unknowns such as loads, crack length and other boundary conditions. the method of tomlinson et al. [8] was experimentally assessed using angled slots of various lengths in centre cracked specimens. an array of up to 100 discrete points was used to provide spate signal values to be input into the analysis. mode i and ii stress intensity factors for slots at both 90 and 45 to the loading were on average within 6.6% of theoretical solutions. large differences in solutions for the shortest crack length at the 45 angle were explained as possibly being due to interaction of the crack tips. although for 30 cracks mode i results were close to a theoretical solution, this was not the case for kii, where it was suggested that in fact the theory may not be reliable for the geometry. spark eroded slots loaded at 45 were found to give excellent results by dulieu-barton et al. [12] when compared to theoretical solutions, although those for 60 slots were less accurate. the paper also included an interesting comparison with the results obtained from previous investigations. marsavina and tomlinson [17] presented a study of mixed mode stress intensity factors investigating a biaxial specimen with a 45 inclined notch produced by spark erosion. by changing the loads on the two axes a large range of mode mixities where created from pure mode i to predominantly mode ii. using the staring array deltatherm system and the algorithm of tomlinson el al. [8] they obtained experimental values for stress intensity factors range in good agreement with the theoretical solution 4.5 % error forki and 6.5 % for kii. determination of stress intensity factors from fatigue cracks mode i stress intensity factors he previous section outlines the main improvements and variations on methods to determine stress intensity factors using thermoelasticity. other researchers have made contributions, particularly in the area of fatigue crack studies. both real cracks and spark eroded slots were examined in the experimental investigation of dulieu-barton et al. [12]. there was evidence of crack closure occurring when a fatigue crack was studied under a number of different stress ranges. the ratio of ki recorded using spate equipment to the value of the theoretical solution was found to decrease as the t http://dx.medra.org/10.3221/igf-esis.27.02&auth=true http://www.gruppofrattura.it l. marsavina et alii, frattura ed integrità strutturale, 27 (2014) 13-20; doi: 10.3221/igf-esis.27.02 17 stress range increased. results for the real fatigue cracks with no crack closure agreed with theoretical values to within 11%. as the error was not consistently this high, it was suggested that for the worst case this error may have been due to geometric irregularities of real cracks. an improvement in the methodology for monitoring fatigue crack growth and inferring the stress intensity factor from thermoelastic data is presented by diaz et al. [15]. the approach is based on a multipoint over-deterministic method but uses a new fitting algorithm based of the downhill simplex method to fit the equations describing the stress field around the crack tip to thermoelastic data, where the crack tip was considered as a variable to be optimised. initially the accuracy was checked with images generated based on westergaard’s stress field equations. for the stress fields dominated by the mode i component, the new algorithm yielded mode i results within 1% of the value used to generate the image. for the mixed mode cases, the difference between the inferred sif and the one employed in generating the images is 6% for the mode i sif and 10 % for mode ii. processing experimental data obtained for real mode i cracks shows that the methodology is sensitive to the crack closure effect. in an experimental study of real cracks in compact tension specimens by olden [18] it was found that the technique of tomlinson et al. [8] was very sensitive to errors in the crack tip location,. this problem was easily overcome by locating the correct crack tip position by moving the relative position of the crack tip to the data points to give the smallest mean of the least-squares fit. a similar method was proposed by lesniak et al. [14], where the crack tip location was estimated by the user and was then optimised automatically by a search routine. diaz et al. [19] showed that the presence of high stress gradients or local plasticity at the crack tip leads to a loss of adiabatic conditions, and consequently conduction through the specimen takes place. investigating the phase map of the thermoelastic signal they concluded that any deviation from zero of the phase is due to the presence of non-adiabatic conditions. on all phase thermoelastic maps they observed a region surrounding the crack tip and ahead of the crack where the phase becomes negative, that is the thermal response lags behind the loading cycle. this fact can be seen in the phase profile along the crack line. this behaviour is due to the lack of adiabatic conditions and could be due to heat generation and conduction as a consequence of plastic work at the crack tip. the initial estimate of the crack tip is taken to be at the point where the phase changes from positive to negative. in contrast, the simpler method of stanley and chan [4] did not require any knowledge of the crack tip location and therefore appears to be more applicable for the study of fatigue cracks. mixed mode cracks stress intensity measurements of a mixed-mode fatigue crack have been published by lesniak [6], but very little detail of the experiment was supplied. only one example was given and the crack was predominantly mode i with a kii/ki ratio of 0.6. although ki was within 5% of the analytical solution, kii differed by 20.8%, therefore these results were no better than those determined from machined slots. dulieu-barton et al. [12] have performed tests by growing mode i cracks in large specimens, then cutting sections out of the plates to produce a specimen in which axial loading gave mixed-mode conditions at the crack tip. the experimental results for central 30 and 45 inclined cracks show good agreement with the theoretical solution within 6%. however when edge cracks were investigated the experimental values are with 20 – 30 % higher than the theoretical ones. they also pointed out the importance of the frictional effects between the two crack surfaces. figure 3: the loads applied to each axis of the load machine for the successive load cycle for crack growth under biaxial load, where kii/ki = 2 (1 – mode i loading; 2 – mode ii loading), and the sinusoidal load cycle used for data collection, where kii/ki = 2 (3 – sinusoidal loading). the most complete research program in investigating mixed mode cracks was published by tomlinson and marsavina [20]. they grow real mixed mode cracks under successive loading using method developed by bold et al. [21] and then http://dx.medra.org/10.3221/igf-esis.27.02&auth=true http://www.gruppofrattura.it l. mardavina et alii, frattura ed integrità strutturale, 27 (2014) 13-20; doi: 10.3221/igf-esis.27.02 18 record thermoelastic data under a reduced sinusoidal load range, e.g. in fig. 3, ensuring that the crack did not grow during the data collection. they investigate the effects of the applied mixed mode and the r=min/max. the reported data at higher r (>0.5) ratios and predominantly mode i loading kii/ki = 0.45, when the effect of crack closure on the values of the stress intensity factors is minimised since the crack is fully open, were obtained with an average difference between experiment and analytical solutions of 4.3% and 5% for ki and kii respectively which is comparable to the accuracy obtained for the specimens containing slots and also comparable to the results obtained by dulieu-barton et al. [11] for central crack. crack closure and propagating crack studies thermoelasticity is an ideal method for the study of crack closure, since k is determined directly from the thermoelastic data. yet very little work has been done in this area using this technique, probably due to the inaccuracy of manual data processing techniques in the past. fulton et al. [12] have used their new computer technique to perform a study where experimentally determined stress intensity factors were found to decrease with respect to theoretical values with increasing stress range. this was stated to be possibly due to the effect of crack closure. other tests have been performed using thermoelasticity by batchelor [22] using the method developed by tomlinson et al. [8], where crack closure was studied by measuring the effects on the stress intensity factor of cutting out the wake of a fatigue crack. this was found to be a useful technique, but only one crack was studied and further tests need to be carried out to give greater confidence in the results. tomlinson et al. 1997 also concluded that if a spatial field of thermoelastic data is used, crack closure effects can be detected. diaz et al. [19] studying the crack propagation in single edge notched specimens found that the ki values obtained from thermoelasticity are lower than theoretical ones. the decrease in this difference at high r – ratios pointed to crack closure. using the compliance change method for determining the opening load for a fatigue crack they found that the stress intensity factor range from thermoelastic data matched perfectly with the effective sif calculated by compliance change. marsavina et al. [23] evaluated the effective stress intensity factors for a mixed mode crack, propagated using a successive loading cycle, using thermoelasticity and surface replicas. a sinusoidal loading cycle with applied kii/ki=0.45 was used in order to record the thermoelastic data around a crack for determining the stress intensity factors ranges. fig. 4 shows the results normalized with a theoretical solution for the mode i sif range. it can be observed that the thermoelastic and surface replica results are lower than the theoretical ones for lower values of r-ratio, and for r > 0.5 the experimental tsa results and the replica ones are in very good agreement with the theoretical values. they concluded that the results for the stress intensity factor range obtained by tsa represent the crack driving force. recent application of thermoelastic fracture mechanics has been done by yates et al. [24] in the investigation of techniques for tracking the crack path as it grows and evaluating the strength of the mixed mode crack tip stress field. they demonstrate the suitability of tsa techniques to explore the hypothesis that the direction of fatigue cracks may be governed more strongly by directionality of crack tip plasticity rather than by the magnitude of the elastic stress field. figure 4: theoretical, experimental tsa and replica ki values against r – ratio. conclusions his review has shown the development of methods to determine stress intensity factors from thermoelastic data. with the availability of new, faster thermoelastic systems it is likely that thermoelasticity will continue to be widely used for crack tip studies. the technique has many advantages over other full-field stress analysis methods t http://dx.medra.org/10.3221/igf-esis.27.02&auth=true http://www.gruppofrattura.it l. marsavina et alii, frattura ed integrità strutturale, 27 (2014) 13-20; doi: 10.3221/igf-esis.27.02 19 including minimal specimen preparation, equipment relatively unaffected by test environment, and perhaps most importantly it is able to provide a direct measurement of the crack driving force k. this will undoubtedly mean that the technique will be beneficial in studying crack closure effects, mixed-mode and propagating cracks. nomenclature a calibration constant [mpa/signal] ki, kii mode i, ii stress intensity factors [mpa m] r polar coordinate [mm] r stress ratio [ ] s thermoelastic signal [signal]  variation (maximum minimum)  mode mixity [rad]  polar angle [rad]  principal stresses [mpa] references [1] harwood, n., cummings w. m., thermoelastic stress analysis, edited by, adam hilger, new york, (1991). [2] tomlinson, r.a., olden, e.j., thermoelasticity for the analysis of crack tip stress fields – a review, strain, (1999) 49 – 55. [3] risitano, a., fargione, g., experimental method for the determination of the under-stress first-plasticization process parameters. proc. of igf xxii, rome, italy, (2013) 370-382. [4] stanley, p., chan, w. k., the determination of stress intensity factors and crack tip velocities from thermoelastic infra-red emissions, proc. of international conference on fatigue of engineering materials and structures, c262, imeche, (1986) 105-114. [5] stanley, p., dulieu-smith, j. m., progress in the thermoelastic evaluation of mixed-mode stress intensity factors, proc. of the sem spring conference on experimental mechanics, dearborn, usa, (1993) 617-626. [6] lesniak, j. r., differential thermography for extreme-environmental structural integrity measurements, asc/naf report f33657-93-c-2230, (1994). [7] tomlinson, r. a, nurse, a. d., patterson, e. a., on determining stress intensity factors for mixed-mode cracks from thermoelastic data, fatigue fract. engng. mater. struct., 20 (1997) 217-226. [8] lin, s. t., feng, z., rowlands, r. e., thermoelastic determination of stress intensity factors in orthotropic composites using the j-integral, engng. fract. mech., 56 (1997) 579-592. [9] stanley, p., chan, w. k., mode ii crack studies using the ‘spate’ technique, proc. of sem spring conference on experimental mechanics, new orleans, (1986) 916-923. [10] stanley, p., dulieu-smith, j. m., the determination of crack tip parameters from thermoelastic data, exp. techniques, 20, (1996), 21-23. [11] fulton, m. c., dulieu-barton, j. m., stanley, p., improved evaluation of stress intensity factors from spate data, proc. of the 11th international conference in experimental mechanics, oxford, (1998) 1211-1216. [12] dulieu–barton, j.m., fulton, m.c., stanley, p., the analysis of thermoelastic isopachic data from crack tip stress fields, fatigue fract. engng. mater. struct., 23 (2000) 301-313. [13] dulieubarton, j m, worden, k, genetic identification of crack-tip parameters using thermoelastic isopachics, meas. sci. & tech., 14 (2003) 176-183. [14] lesniak, j.r., bazile, d. j., boyce, b. r., zickel, m. j., cramer, k. e., welch, c. s., stress intensity measurement via infra-red focal plane array, proc. of astm non-traditional methods of sensing stress, strain and damage in materials and structures, orlando, (1996) stp 1318. [15] diaz, f.a., yates, j. r., patterson, e.a., some improvements in the analysis of fatigue cracks using thermoelasticity, int. j. fatigue, 26 (2004) 365–376. [16] shiratori, m., miyoshi, t., nakanishi, t., noda, hanada, t., detection of cracks and measurement of stress intensity factors by infrared video system, jsme international journal, series i, 33 (1990) 400-408. http://dx.medra.org/10.3221/igf-esis.27.02&auth=true http://www.gruppofrattura.it l. mardavina et alii, frattura ed integrità strutturale, 27 (2014) 13-20; doi: 10.3221/igf-esis.27.02 20 [17] marsavina, l., tomlinson, r. a., the use of infra – red detectors for determination of the fracture mechanics parameters, j. optoelectronics and advanced materials, 6 (2004) 1323 – 1329. [18] olden, e. j., the application of experimental stress analysis techniques to the study of cracks around cold-expanded holes, phd. thesis, university of sheffield, (1998). [19] diaz, f.a., patterson, e.a., tomlinson, r.a., yates, j. r., measuring stress intensity factors during fatigue crack growth using thermoelasticity, fatigue fract. engng. mater. struct., 27 (2004) 571-583. [20] tomlinson, r a, marsavina, l., thermoelastic investigations for fatigue life assessment, exp. mech., 44 (2004) 487 – 494. [21] bold, p. e., brown, m. w., allen, r j., shear mode crack growth and rolling contact fatigue, wear, 144 (1991) 307317. [22] batchelor, h., measurement of fatigue crack closure using thermoelastic stress analysis, m.sc. thesis, the university of sheffield, (1996). [23] marsavina, l., tomlinson, r. a., patterson, e.a., yates, j. r., investigation of crack closure by using thermoelastic stress analysis, cd-rom proc. of the 16th european conference of fracture, alexandroupolis, (2006), #236_mar. [24] yates, j.r., zanganeh, m., tomlinson, r.a., diaz garrido, f.a., crack paths under mixed mode loading, eng. fract. mech., 75 (2008) 319-330. http://dx.medra.org/10.3221/igf-esis.27.02&auth=true microsoft word numero_30_art_13 b. tyson et alii, frattura ed integrità strutturale, 30 (2014) 95-100; doi: 10.3221/igf-esis.30.13 95 focussed on: fracture and structural integrity related issues elastic compliance of single-edge-notched tension se(t) (or sent) specimens b. tyson1 canmetmaterials, hamilton, on, canada btyson@nrcan.gc.ca p. ding, x. wang carleton university, ottawa, canada pingding@cmail.carleton.ca, xwang@mae.carleton.ca abstract. there has been a trend recently to use specimen geometries for toughness measurement that are more representative of actual flaw geometries in service. a prominent example is the use of single-edge-notched tension specimens for assessment of surface flaws in pipelines. to obtain a resistance (r) curve, i.e. j-integral or ctod as a function of crack growth, it is necessary to monitor the crack size as a function of j or ctod. to facilitate obtaining these data from a single specimen, the elastic cmod unloading compliance c has been used in several testing programs to estimate crack size. c is a function of several variables in addition to crack size – notably, specimen constraint (plane stress or plane strain). in this paper, the dependence of c on these variables will be discussed. keywords. sent; se(t); constraint; compliance; r-curve. introduction: se(t) testing haracterization of resistance to fracture of the materials used in construction of engineering structures such as pipelines is a vital step in design. conventionally, this has been done by using a test that gives a conservative material property (the “fracture toughness”) that can be compared with the estimated maximum crack driving force of a plausible flaw in service, and ensuring that the material selected has adequate toughness to prevent fracture. this is a safe way to proceed, but because of the high degree of conservatism in some cases it can lead to uneconomic design. in particular, for thin-walled structures such as pipe, the lower degree of constraint experienced by surface flaws can enable the material to withstand much higher driving force than in a highly-constrained test specimen. the logical response to this is to reproduce the actual service geometry and loads as closely as possible in the toughness test set-up. the resistance displayed by the material in this arrangement may not be a lower bound for the material, i.e. it may be “geometry-dependent”, but it will be the appropriate toughness to use in assessing the defect tolerance of the structure being simulated. the procedure for engineering critical assessment of circumferential surface flaws (i.e. weld defects) in line pipe is a case in point. it is well known that the constraint for such flaws is substantially lower than the constraint in the standard threepoint-bend test geometry. to generate toughness measurements more representative of the service conditions, tests with 1 © her majesty the queen in right of canada, as represented by the minister of natural resources, 2014. c b. tyson et alii, frattura ed integrità strutturale, 30 (2014) 95-100; doi: 10.3221/igf-esis.30.13 96 specimens of the same thickness as the pipe, notched in the same orientation as the surface flaws being assessed and loaded in tension to simulate service loads, have been developed. several variants of the test, using single-edge-notched specimens loaded in tension (sent or se(t)), are in existence. the first, rp-f108 published by det norske veritas [1], uses multiple specimens. the rp-f108 specimens are of preferred cross-section 2bxb (thickness x width: the dimension b here refers to specimen width, which is the pipe wall thickness in this case; normally, b refers to the specimen thickness, but there is no confusion for bxb cross-section specimens which will be the focus of the remainder of this paper), and “daylight” (distance between grips) of h=10b (i.e. 10w), tested in tension. in the years since rp-f108 appeared, many papers dealing with sent testing have been published as well as two test methods in draft standard form, i.e. canmet’s recommended procedure [2] and exxonmobil’s procedure for measurement of ctod using sent specimens [3]. the latter two tests report single-specimen methods relying on a crack-mouth-opening (cmod) unloading compliance (uc) technique to monitor crack size during the test. the intent of the present report is to discuss details of the uc method. to estimate crack size using uc, a relationship between crack size and compliance is required. estimation of this relationship is straightforward using standard linear-elastic finite element methods available in several software codes, and has been performed in many laboratories around the world. however, there are some subtleties in application of the results that should be recognized, in particular the relationship between plane strain and plane stress and which of these is the closest approximation to the actual test constraints. estimation of crack size plain stress/strain he most straightforward procedure to obtain stress and displacement using finite element analysis (fea) is to use a two-dimensional (2d) plane strain model. plane stress constraints are difficult to simulate, and resort is normally made to a “generalized plane stress” formulation for this case. the resulting compliance data can be expressed in terms of a parameter u (sometimes called the “normalized compliance”): u=1/(√(bce´)+1) (1) where b=specimen width, c=cmod compliance (displacement/load), and e´ is the “effective modulus”. for planestrain compliance calculations, the appropriate “effective modulus” is the “plane-strain modulus” e´=e/(1-ν2) where ν is poisson’s ratio for the material. the actual specimen constraints are, of course, not plane strain but rather something between plane strain and plane stress (see, for example, [4]). to obtain the plane stress compliance from eq. (1), the “plane stress modulus” e´=e should be used, where e is young’s modulus for the material. in practice, the relationship between a/w and u is first found from plane-strain fea calculations, and expressed in a convenient form, normally a polynomial for a/w as a function of u. then, to estimate a/w from compliance, the value of u using the “effective modulus” appropriate to the constraint of the test specimen is calculated from the measured compliance. then, a/w is calculated from the polynomial for a/w as a function of u. polynomial expressions for a/w have been published in a number of papers. it has become conventional to use a “daylight” h between grips of 10w and fixed-grip (clamped) load application, and most use a bxb cross-section geometry; all of the results discussed here are for this condition. all previously published results are in essential agreement. according to shen et al. [2], a/w = 2.044 15.732u + 73.238u2 – 182.898u3 + 175.653u4 + 60.930u5 – 113.997u6 – 113.031u7 + 8.548u8 + 142.840u9 (2) this expression is rather cumbersome, but since the equation is intended to be valid over the extended range of a/w between 0.05 and 0.95, to maintain accuracy it was found necessary to include ten terms in the polynomial. another polynomial was published earlier by cravero and ruggieri [5]: a/w = 1.6485 9.1005u + 33.025u2 78.467u3 + 97.344u4 47.227u5 (3) this equation contains only six terms, as it is valid only over the range 0.1≤a/w≤0.7. this is the relevant range for practical testing, and in that range it agrees well with eq. (2). for purposes of the test standard then, eq. (3) is adequate. fig. 1 shows a comparison of cravero’s eq. (3) with shen’s fea data [2] and with data calculated in the present study. note that cravero’s equation (shown as a solid curve in fig. 1) provides an excellent fit to shen’s and the present results over the range 0.1≤a/w≤0.7, even up to a/w=0.8. there is a slight discrepancy for a/w=0.05 and a/w=0.9 and 0.95; however, these values of a/w are outside of the range expected to be used in practical tests. the conclusion is that cravero’s equation is suitable for estimating crack size from cmod compliance over the range 0.1≤a/w≤0.8. t b. tyson et alii, frattura ed integrità strutturale, 30 (2014) 95-100; doi: 10.3221/igf-esis.30.13 97 to demonstrate the influence of constraint, fig. 2 shows the cmod compliance (multiplied by the specimen thickness b; e was taken as 207 gpa) calculated from cravero’s equation using plane strain and plane stress moduli. also shown in the figure is the plane strain, stress (represented by one value at a/w=0.6) and 3d compliance calculated using fea in the present study. figure 1: normalized compliance as a function of a/w. the 3d compliance is substantially larger than the plane strain compliance, and almost identical to the plane stress compliance. this is shown more clearly in the expanded portion of fig. 2 shown in fig. 3. moreira and donato [6] have confirmed for se(t) specimens with w/b=0.5, 1, and 2 and a/w=0.1 to 0.7 that the 3d compliance is correctly predicted by the plane stress model, although their results are for h/w=6 and so are not directly comparable to the data in this paper for h/w=10. donato has also confirmed (private communication) that the fea plane stress and plane strain compliances are the same function of u when u is normalized by the modulus e´=e for plane stress and by e´=e/(1-ν2) for plane strain. figure 2: variation of cmod compliance with a/w. figure 3: expanded portion of fig. 2. validation anmet has recently completed a round robin designed to assess the viability of the single-specimen method developed earlier [2]. the results have been published recently [7]. participants reported both calculated values (from unloading compliance) and measured values (from nine-point optical size measurements on the fracture surface) of the crack size. the results are shown in fig. 4 and in tab. 1. c b. tyson et alii, frattura ed integrità strutturale, 30 (2014) 95-100; doi: 10.3221/igf-esis.30.13 98 figure 4: comparison of calculated crack size with measured size. table 1: results of canmet round robin: a0q and a0 are initial calculated and measured crack size values respectively, and af is the final crack size. lab spec. a0q, mm   0 0 qa a af, mm fcalc meas a a     f f 0 0 9 r -curve point   qa a aa calc. meas. calc. meas. a ht-1 6.92 6.95 0.996 9.32 9.44 0.987 0.964 ht-3 7.13 7.13 1.001 9.69 9.79 0.989 0.963 ht-5 7.07 7.08 0.998 8.50 8.63 0.985 0.925 ht-7 7.37 7.36 1.000 10.23 10.43 0.981 0.937 d 5108 6.93 7.02 0.987 9.35 9.99 0.936 0.960 5208 6.63 6.85 0.967 9.72 9.99 0.973 0.933 5407 7.80 8.04 0.970 9.94 10.29 0.966 0.896 5409 6.77 6.65 1.017 9.67 9.41 1.028 1.004 e rr5102 7.99 7.77 1.027 10.69 10.82 0.988 0.977 rr5109 6.20 5.82 1.066 8.76 8.61 1.017 0.915 rr5308 7.09 7.09 1.000 9.80 9.98 0.982 0.936 rr5410 7.21 7.06 1.022 10.08 10.36 0.973 0.869 i 5103 7.50 6.81 1.101 8.83 8.62 1.025 0.646 5205 7.50 6.73 1.114 9.99 9.03 1.106 0.841 5406 7.28 6.59 1.104 8.84 8.35 1.059 0.840 j 5504 6.38 6.59 0.968 7.75 8.16 0.950 0.873 5505 6.22 6.46 0.963 7.59 7.99 0.950 0.901 5507 6.38 6.70 0.952 7.65 8.10 0.944 0.901 5509 6.70 7.01 0.956 7.95 8.43 0.943 0.880 l 5401 7.34 7.36 0.997 9.55 9.48 1.007 1.025 5104 7.27 7.20 1.009 9.22 9.11 1.012 1.027 5101 7.91 7.88 1.004 10.85 11.04 0.983 0.928 5508 7.30 7.25 1.007 9.24 9.07 1.019 1.061 n 5408 7.59 7.48 1.016 8.15 8.04 1.014 0.875 5105 7.26 7.17 1.013 7.82 7.76 1.008 0.956 5201 7.43 7.36 1.008 8.02 7.99 1.004 0.921 5202 7.06 6.97 1.013 7.61 7.68 0.991 0.938 o rrt01 6.849 6.184 1.108 8.32 7.61 1.094 1.035 rrt02 6.842 6.213 1.101 8.45 7.62 1.109 1.142 rrt03 6.784 5.974 1.136 8.22 7.21 1.140 1.161 rrt04 6.582 5.963 1.104 7.92 7.24 1.094 1.125 avg. 1.023 1.008 0.947 std. devn. 0.053 0.053 0.100 b. tyson et alii, frattura ed integrità strutturale, 30 (2014) 95-100; doi: 10.3221/igf-esis.30.13 99 as shown in the last row of the table, the calculated and measured initial values agree on average within 2.3%, with a standard deviation of individual estimates of 5.3%. calculated final values are accurate (i.e. agree with measured values) to within 0.08%, with a standard deviation of individual measurements of 5.3% (fortuitously identical to the standard deviation of initial crack size values). the estimate of crack growth, being the difference between final and initial crack sizes, is more sensitive to errors in size measurement; as shown in the last column, the calculated crack growth is accurate to 94.7% of measured values, with a standard deviation of individual measurements of 10%. it should be noted that a correction for rotation is required to use the uc method for a se(t) specimen because the alignment of the specimen changes during crack growth. the specimen rotates so that the load line moves closer to the centre of the ligament, and the compliance changes accordingly. a correction factor derived by shen and tyson [8] is incorporated in the canmet procedure [2] and was applied in the round robin. the correction is not large; for a deep crack (a/w≈0.5) the measured compliance is smaller by about 9% when the ligament is fully yielded than it would be for a straight specimen (to which the uc crack size equation applies), and the correction increases the calculated crack size by about 3%. observation of specimens removed from the testing machine showed that yielding was confined to the ligament; the deduction is that rotation occurred by elastic deformation of the arms of the specimen. conclusions and discussion he principal conclusions of this study are: 1) for se(t) specimens with h=10w and bxb cross section, the parameters reported by cravero and ruggieri [5] represent well the relation between crack size and compliance; and 2) the effective modulus e´ used in the normalized compliance u should be the “plane stress modulus” e. conclusion 2 is consistent with the approach in astm e1820-11e [9], in which e rather than e/(1-ν2) is used in the uc equation for crack size as a function of u in for se(b) specimens. at first glance it may seem strange that the plane stress modulus should be used for calculations in a test designed to measure the plane strain toughness. however, it is readily appreciated that the compliance is a function of displacements everywhere in the specimen and not just near the crack tip. the crack tip may well be in a state close to plane strain, especially if side grooves are used, and this justifies the use of the plane strain modulus in calculations relating the stress intensity factor k and the j-integral j, i.e. j=k2/e´. however, the constraint for the bulk of the specimen, especially in tension-loaded specimens, is closer to plane stress than to plane strain. acknowledgements he authors are grateful to the staff of canmetmaterials, notably dr. g. shen, who performed the initial experiments and fea calculations on which the se(t) procedures in this paper are based, and d.-y. park who applied the procedures successfully under a variety of conditions. we are also grateful to the participants in the canmet round robin for their diligence in applying the recommended procedure and for supporting the development of an se(t) standard. references [1] det norske veritas, fracture control for pipeline installation methods introducing cyclic plastic strain, recommended practice dnv-rp-f108 (2006). [2] shen, g., gianetto, j. a., tyson, w.r., development of procedure for low-constraint toughness testing using a singlespecimen technique, canmet report no. 2008-18(tr) (2008). [3] exxonmobil, measurement of crack-tip opening displacement(ctod) fracture resistance curves using single-edge notched tension (sent) specimens, exxonmobil upstream research company, houston (2010). [4] barber, j.r., elasticity, kluwer academic publishers, dordrecht, the netherlands (1992). [5] cravero, s., ruggieri, c., estimation procedure of j-resistance curves for se(t) fracture specimens using unloading compliance, eng. fracture mech., 74 (2007) 2735-2757. t t b. tyson et alii, frattura ed integrità strutturale, 30 (2014) 95-100; doi: 10.3221/igf-esis.30.13 100 [6] moreira, f., donato, g.h.b., compliance solutions including 3-d and side-groove effects applicable to crack size estimation using c(t), se(b) and clamped se(t) specimens, in: 68th abm international congress, belo horizonte, mg, brazil (2012). [7] tyson, w.r., gianetto, j.a., low-constraint toughness testing: results of a round robin on a draft se(t) test procedure, in: proc. asme 2013 pressure vessels & piping division conference pvp2013, paris, paper pvp201397299 (2013). [8] shen, g., tyson, w.r., crack size evaluation using unloading compliance in single-specimen single-edge-notched tension fracture toughness testing, jour. of testing and evaluation, astm, 37 (4) (2009) id jte102368. [9] astm e1820-11e, standard test method for measurement of fracture toughness, american society for testing and materials, conshohocken, pa (2011). microsoft word numero_38_art_13 h. wu et alii, frattura ed integrità strutturale, 38 (2016) 99-105; doi: 10.3221/igf-esis.38.13 99 focussed on multiaxial fatigue and fracture application of the moment of inertia method to the critical-plane approach hao wu school of aerospace engineering and applied mechanics, tongji university, siping road 1239, 200092, shanghai, p.r.china wuhao@tongji.edu.cn marco antonio meggiolaro, jaime tupiassú pinho de castro pontifical catholic university of rio de janeiro, puc-rio, r. marquês de são vicente 225, rio de janeiro, 22451-900, brazil meggi@puc-rio.br, jtcastro@puc-rio.br abstract. the moment-of-inertia (moi) method has been proposed by the authors to solve some of the shortcomings of convex-enclosure methods, when they are used to calculate path-equivalent ranges and mean components of complex non-proportional (np) multiaxial load histories. in the proposed 2d version for use with critical-plane models, the moi method considers the non-proportionality of the projected shear-shear history on each candidate plane through the shape of the load path, providing good results even for challenging non-convex paths. the moi-calculated path-equivalent shear stress (or strain) ranges from each counted load event can then be used in any shear-based critical-plane multiaxial fatigue damage model, such as findley’s or fatemi-socie’s. an efficient computer code with the shear-shear version of the moi algorithm is also provided in this work. keywords. multiaxial fatigue; non-proportional loadings; equivalent ranges; critical-plane approach. citation: wu, h., meggiolare, m.a., de castro, j.t.p., application of the moment of inertia method to the critical-plane approach, frattura ed integrità strutturale, 38 (2016) 99-105. received: 12.05.2016 accepted: 15.06.2016 published: 01.10.2016 copyright: © 2016 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. introduction irection-sensitive materials like most metallic alloys tend to initiate a single dominant microcrack under fatigue loadings. under multiaxial loading conditions this behavior tends to be well modeled by critical-plane fatiguedamage models, which search for the material plane at the critical point where the corresponding accumulated damage parameter is maximized. although in general any plane can be a candidate at the critical point, bannantine and socie [1] narrowed down the search space for the critical plane at the critical point of the structural component when it is under free-surface conditions, as usual, classifying the most common microcracks into three types, which depend on the fatigue damage mechanism: case a tensile or case a shear microcracks, which grow at the critical point along planes perpendicular to the free surface; and d h. wu et alii, frattura ed integrità strutturale, 38 (2016) 99-105; doi: 10.3221/igf-esis.38.13 100 case b shear microcracks, which grow on planes that make an angle  = 45o with the free surface, see fig. 1. to compact and hopefully clarify the critical plane notation in this work, case a tensile planes are represented as a90(t), case a shear as a90(s), and case b shear as b45(s), where 90 or 45 come from their  angles in degrees with respect to the free surface. a90(t) or a90(s) microcracks only involve one normal and one shear stress/strain component, so normal or shear ranges are quite easy to calculate under variable amplitude loading (val) conditions using classic uniaxial rainflow procedures. however, b45(s) microcracks involve in general two shear components, an in-plane stress a (or strain a) and an out-ofplane b (or b), see fig. 1, which must be properly combined to evaluate their joint effect on fatigue damage. figure 1: non-proportional shear strain path b  a (or shear stress path b  a) acting on a b45 candidate plane (at 45o from the free surface), for a general loading history. the combination of both usually non-zero b and a ranges may cause the initiation of a combined mode ii-iii b45(s) microcrack, with b mainly contributing to increase its depth while a is mainly tending to increase its width. the combination of b and a into an equivalent range  is not a trivial step under general np loadings, where the b and the a histories may be (and usually are) out of phase. this process requires first a 2d rainflow algorithm such as the modified wang brown method [2] to identify every load event from the b  a (or b  a) history. then, for each identified load event, its path segments are used to calculate a path-equivalent shear stress  (or strain ) range. the simplest approach for the b  a diagram is to assume a pathequivalent a b 2 2       for each identified load event, as discussed in [3]. however, this simple equivalent range expression would not be able to tell apart e.g. a rectangular from a less damaging cross-shaped b  a path with same b and a, because both would wrongfully generate the same equivalent shear stress range . hence, this path-equivalent range is not a suitable solution to solve these problems in practical applications. another possible approach is to use the so-called convex-enclosure methods, which try to find circles, ellipses, or rectangles that circumscribe the load-event path in such 2d b  a or b  a diagrams. for instance, dang van’s pioneer minimum ball method [4] searches for the circle with minimum radius that circumscribes each identified load path; the minimum ellipse methods [5-6] search for an ellipse with semi-axes a and b that circumscribes the entire path with minimum area ab or minimum “ellipse norm” [a2 + b2]0.5; and the maximum rectangular hull methods search for a minimum rectangle that circumscribes the path with maximum area or maximum diagonal [7]. the value of the pathequivalent  or  would be assumed as the circle diameter, the ellipse norm, or the rectangle diagonal, which is then used for fatigue damage calculation purposes. however, such convex-enclosure algorithms do not consider the actual shape of the loading path. instead they substitute the actual load path by some convex enclosures associated with them. therefore, an infinite number of loading paths associated with different fatigue lives could have the same convex enclosure, wrongfully predicting the same damage if such simplified path-equivalent algorithms are used to calculate it. this issue has been solved with the moment-of-inertia (moi) method, which has been proposed in [8-9] to estimate path-equivalent stress and strain ranges, as well as their mean components, considering the influence of the shape of the h. wu et alii, frattura ed integrità strutturale, 38 (2016) 99-105; doi: 10.3221/igf-esis.38.13 101 multiaxial loading path, not only its convex enclosure. the general 6d version of the moi is reviewed next, followed by its application in critical-plane models, proposed in this work. further details on how the moi works, and on its main advantages over concurrent convex-enclosure methods are studied in the aforementioned references. the moment-of-inertia (moi) method n the moi method, the stress or strain path is assumed to be represented by a homogeneous wire with unit mass, whose center of mass (centroid) is used to estimate the location of the mean component of the load path. then, the mass moment of inertia (moi) of this hypothetical wire with respect to its centroid is calculated, which gives a measure of how much the path stretches away from its mean component. the path-equivalent range of the true stress or strain path is finally calculated as a function of this moi, which is a physically sound approximation, since paths with larger amplitudes would be associated with wider wires with increased moi. the moi method has been applied to tension-torsion [10] and to general 6d histories [11], following a fatigue damage calculation approach based on stress invariants. for 6d histories, the history must first be represented in a 5d deviatoric stress or strain space, using the 5d vectors s  and e  , defined as t t y y zz x xy xz yz y z y z xy xz yz x s s s s s s e e e e e e s s s e e 1 2 3 4 5 1 2 3 4 5 1 2 3 4 5 1 2 3 4 5 [ ] and [ ] , 3, 3, s 3, s 3 2 2 , e 3, e 3, e 3, 3 2 2 2 2 2                                         (1) these deviatoric stress and strain spaces are used because they have a significant advantage over all other choices: their euclidean norms |s |  and e| | (1 )  are equal to the von mises equivalent stresses and strains, where  is an effective poisson ratio. for 2d tension-torsion histories with stress paths defined by the normal and shear components x and xy, then y  z  xz  yz 0, while y  z   ∙x and xz  yz  0. in this case, x xys s s1 2 3 4 5, 0, 3, s 0, s 0      (2) y z y z xy x xe e1 2 3 4 5(1 ), e 3 0, e 3, e 0 2 2 2                     (3) since only s1, s3, e1, and e3 are not null, the stress or strain paths of such tension-torsion histories can be represented in the 2d deviatoric diagrams s1  s3 or e1  e3, as shown in fig. 2. figure 2: stress path of a 2d tension-torsion load history in the deviatoric s1  s3 diagram (left) and its corresponding strain path in the e1  e3 diagram (right), both assumed as homogeneous wires with unit mass. i h. wu et alii, frattura ed integrità strutturale, 38 (2016) 99-105; doi: 10.3221/igf-esis.38.13 102 the tension-torsion version of the moi method assumes that the 2d load path, which is represented by a series of points (s1, s3) or (e1, e3) that describe the stress or strain variations along it, is analogous to a homogeneous wire with unit mass. the mean component of the path is assumed to be located at the center of gravity of this hypothetical homogeneous wire shaped as the load history path. its center of gravity is located at the perimeter centroid (s1m, s3m) or (e1m, e3m) of the stress or strain paths, calculated from contour integrals along it m s m s ss p s ds s p s ds p ds1 1 3 3(1 ) | |, (1 ) | |, | |              (4) m e m e ee p e de e p e de p de1 1 3 3(1 ) | |, (1 ) | |, | |              (5) where ds| |  and de| |  are the lengths of infinitesimal segments of the stress and strain paths, while ps and pe are the respective path perimeters, see fig. 2. the moi method calculates the path-equivalent range of a stress or strain path from the mass moment of inertia (moi) of its corresponding unit-mass homogeneous wire. however, instead of using the axial moi of the analogous wire, which is calculated about an axis, the polar moi (pmoi) is adopted instead, which represents the distribution of the wire (or load) path about a single point, its perimeter centroid. the pmoi of the stress or strain path about the perimeter centroid is then obtained from the contour integral of the square of the distance rm between each point in the path and the path centroid, see fig. 2, resulting in p m m m m s e r rm m i s s s s ds e e e e de p p 2 2 2 2 1 1 3 3 1 1 3 3 2 2 1 1 ( ) ( ) | | or ( ) ( ) | |                   (6) the path-equivalent ranges are assumed proportional to the radius of gyration of the path, which is equal to the square root of the pmoi of the unit-mass wire. this hypothesis is physically sound, since path segments of the load history further away from their mean components contribute more to the path-equivalent range, in the same way that wire segments further away from the perimeter centroid contribute more to the pmoi of an imaginary homogeneous wire. the path-equivalent stress and strain ranges become then mises mises pi or (1 ) 12        (7) the moi method for the critical-plane approach he moi method has been shown experimentally to effectively estimate path-equivalent ranges [10-11]. for convex stress or strain paths, it essentially reproduces the good predictions from the maximum rectangular hull method [7]. moreover, for non-convex paths such as cross or star-shaped paths, the moi method results in better pathequivalent ranges than any convex-enclosure method. the 6d generalization of the moi method can be directly used with invariant-based multiaxial fatigue damage models like sines and crossland. however, models based on stress or strain invariants like von mises should not be used to make multiaxial fatigue damage predictions for directional-damage materials, like most metallic alloys, which fail due to a single dominant crack. according to the critical-plane approach, the moi method would lead to significant errors if directly applied to the original np deviatoric histories, because the resulting ranges would be calculated on different planes at different points in time, not on the critical plane where the microcrack is expected to initiate under multiaxial fatigue loads. instead of projecting the original 6d stress or strain history onto 5d deviatoric spaces, it should be projected onto the several candidate planes before proceeding with the fatigue damage analysis. as discussed before, for directional-damage materials, the moi method would only be needed for a b45(s) microcrack subjected to mixed mode ii-iii loading, in the search for the angle of a candidate plane (, = 45o) loaded by a projected np history combining in-plane shear stresses a(, 45o) or strains a(, 45o) and out-of-plane shear stresses b(, 45o) or strains b(, 45o). to do so, the load history of the two shear stresses or strains acting parallel to each b45 t h. wu et alii, frattura ed integrità strutturale, 38 (2016) 99-105; doi: 10.3221/igf-esis.38.13 103 candidate plane first needs to be represented in a 2d b  a or b  a diagram, see fig. 3, where a 2d rainflow followed by the 2d moi method can be applied. for each rainflow-counted path, the path perimeters p or p, the mean shear components (bm, am) or (bm, am), the associated pmoi ip, and the resulting path-equivalent ranges  and  from the moi method become a b a bp d d p d d 2 2 2 2,          (8) bm b a b am a a bp d d p d d 2 2 2 2(1 ) , (1 )                 (9) bm b a b am a a bp d d p d d 2 2 2 2(1 ) , (1 )                 (10) p b bm a am a b p b bm a am a b i d d p i d d p 2 2 2 2 2 2 2 2 1 ( ) ( ) or 1 ( ) ( )                                   (11) pi or 12     (12) figure 3: stress path of a 2d shear-shear load history on a candidate plane (left) and its corresponding strain path (right), both assumed as homogeneous wires with unit mass. for a polygonal path such as the one in fig. 4, which is usually the case in discrete computational implementations of the moi method, the above equations could be applied by changing the integrals into summations, and infinitesimal increments db, da, db, or da into finite bi, ai, bi, or ai. if each polygon side i has length bai ai bi 2 2       or bai ai bi 2 2       , centered at (bmi, ami) or (bmi, ami), and associated with a mean normal mi or mi, then bai baii i p p,        (13) bm bmi bai am ami baii i p p(1 ) , (1 )             (14) bm bmi bai am ami baii i p p(1 ) , (1 )             (15) h. wu et alii, frattura ed integrità strutturale, 38 (2016) 99-105; doi: 10.3221/igf-esis.38.13 104 m mi bai m mi baii i p p(1 ) , (1 )                (16) p bai bmi bm ami am baii p bai bmi bm ami am baii i p i p 2 2 2 2 2 2 1 12 ( ) ( ) or 1 12 ( ) ( )                                     (17) which are calculated adding all path-segment contributions of a given cycle (or half-cycle), whose path-equivalent range is then obtained from eq. (12). a computer implementation of the critical-plane version of the moi method for polygonal paths is shown in the appendix, based on the matlab environment [12]. further details about such procedures can be found in [13]. figure 4: polygonal shear-shear stress (left) or strain (right) paths on a candidate plane. conclusions n this work, a critical-plane version of the moi method has been presented to allow the calculation of pathequivalent shear ranges for projected shear-shear stress or strain histories on candidate planes, in multiaxial fatigue problems that must be treated by critical-plane approaches. the combination of both out-of-plane (b or b) and inplane (a or a) shear components into an equivalent range ( or ) is fundamental to correctly account for shear damage on b45(s) candidate planes. the moi method is a computationally-inexpensive and robust procedure to calculate the initiation lives of microcracks under combined in-plane and out-of-plane shear loads. the moi method can estimate both path-equivalent ranges and mean components with a much better coherence than any convex-enclosure method. moreover, since it accounts for the contribution of every single segment of the path, the moi method can deal with arbitrarily shaped multiaxial load histories without losing information about such shapes. references [1] bannantine, j.a., socie, d.f., a variable amplitude multiaxial fatigue life prediction method, in: k.f. kussmaul, d.l. mcdiarmid, d.f. socie (eds.), fatigue under biaxial and multiaxial loading, esis publication 10, london, (1991) 35-51. [2] meggiolaro, m.a., castro, j.t.p., an improved multiaxial rainflow algorithm for non-proportional stress or strain histories – part ii: the modified wang–brown method, int. j. fatigue, 42 (2012) 194-206. i h. wu et alii, frattura ed integrità strutturale, 38 (2016) 99-105; doi: 10.3221/igf-esis.38.13 105 [3] castro, f.c., araújo, j.a., mamiya, e.n., pinheiro, p.a., combined resolved shear stresses as an alternative to enclosing geometrical objects as a measure of shear stress amplitude in critical plane approaches, int. j. fatigue, 66 (2014) 161-167. [4] dang van, k., griveau, b., message, o., on a new multiaxial fatigue limit criterion: theory and application, in: m. w. brown, k. j. miller (eds.), biaxial and multiaxial fatigue egf3, mechanical engineering publications, london, (1989) 479-496. [5] li, b., santos, j.l.t., freitas, m., a unified numerical approach for multiaxial fatigue limit evaluation, mech. struct. mach., 28 (2000) 85-103. [6] zouain, n., mamiya, e.n., comes, f., using enclosing ellipsoids in multiaxial fatigue strength criteria, european j. mech.a/solids, 25 (2006) 51-71. [7] araújo, j.a., dantas, a.p., castro, f.c., mamiya, e.n., ferreira, j.l.a., on the characterization of the critical plane with a simple and fast alternative measure of the shear stress amplitude in multiaxial fatigue, int. j. fatigue, 33 (2011) 1092-1100. [8] meggiolaro, m.a., castro, j.t.p., an improved multiaxial rainflow algorithm for non-proportional stress or strain histories – part i: enclosing surface methods, int. j. fatigue, 42 (2012), 217-226. [9] meggiolaro, m.a., castro, j.t.p., prediction of non-proportionality factors of multiaxial histories using the moment of inertia method, int. j. fatigue 61, (2014) 151-159. [10] meggiolaro, m.a., castro, j.t.p., the moment of inertia method to calculate equivalent ranges in non-proportional tension–torsion histories, j. mat. res. tech., 4 (2015) 229-234. [11] meggiolaro, m.a., castro, j.t.p., wu, h., on the use of tensor paths to estimate the non-proportionality factor of multiaxial stress or strain histories under free-surface conditions, acta. mech. in press (2016). [12] matlab, the mathworks inc., natick, ma, (2016). [13] castro, j.t.p., meggiolaro, m.a., fatigue design techniques (in 3 volumes), createspace, scotts valley, ca, usa (2016). appendix atlab implementation of the moi method for a shear-shear stress history. for shear-shear strain histories, it is enough to replace all shear stress with shear strain data. %inputs: taua = [0 100 100 0 0]; %single event, e.g. rectangular path in mpa taub = [0 0 50 50 0]; perimeter = 0; tauam = 0; taubm = 0; iorigin = 0; %initialize variable for i = 1:(size(taua,2)-1) %for all elements of load path dtaua = (taua(i+1)-taua(i)); %increment of shear a dtaub = (taub(i+1)-taub(i)); %increment of shear b dtau = sqrt(dtaua^2+dtaub^2); %length of the shear increment perimeter = perimeter + dtau; %perimeter of the entire shear path tauac = (taua(i+1)+taua(i))/2; %centroid of the shear a segment taubc = (taub(i+1)+taub(i))/2; %centroid of the shear b segment tauam = tauam + dtau*tauac; %mean of the shear a path taubm = taubm + dtau*taubc; %mean of the shear b path iorigin = iorigin + dtau*(dtau^2/12 + tauac^2 + taubc^2); %pmoi end iorigin = iorigin/perimeter; %polar moi requires division by perimeter tauam = tauam/perimeter; %mean component of the shear a path taubm = taubm/perimeter; %mean component of the shear b path i = iorigin (tauam^2 + taubm^2); %pmoi with respect to path mean %outputs: mean_component = [tauam taubm] %output mean component of 2d shear path equivalent_range = sqrt(12*i) %output equivalent range m << /ascii85encodepages false /allowtransparency false /autopositionepsfiles true /autorotatepages /none /binding /left /calgrayprofile (dot gain 20%) /calrgbprofile (srgb iec61966-2.1) /calcmykprofile (u.s. web coated \050swop\051 v2) /srgbprofile (srgb iec61966-2.1) /cannotembedfontpolicy /error /compatibilitylevel 1.4 /compressobjects /tags /compresspages true /convertimagestoindexed true /passthroughjpegimages true /createjobticket false /defaultrenderingintent /default /detectblends true /detectcurves 0.0000 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/hrv (za stvaranje adobe pdf dokumenata najpogodnijih za visokokvalitetni ispis prije tiskanja koristite ove postavke. stvoreni pdf dokumenti mogu se otvoriti acrobat i adobe reader 5.0 i kasnijim verzijama.) /hun 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can be opened with acrobat and adobe reader 5.0 and later.) >> /namespace [ (adobe) (common) (1.0) ] /othernamespaces [ << /asreaderspreads false /cropimagestoframes true /errorcontrol /warnandcontinue /flattenerignorespreadoverrides false /includeguidesgrids false /includenonprinting false /includeslug false /namespace [ (adobe) (indesign) (4.0) ] /omitplacedbitmaps false /omitplacedeps false /omitplacedpdf false /simulateoverprint /legacy >> << /addbleedmarks false /addcolorbars false /addcropmarks false /addpageinfo false /addregmarks false /convertcolors /converttocmyk /destinationprofilename () /destinationprofileselector /documentcmyk /downsample16bitimages true /flattenerpreset << /presetselector /mediumresolution >> /formelements false /generatestructure false /includebookmarks false /includehyperlinks false /includeinteractive false /includelayers false /includeprofiles false /multimediahandling /useobjectsettings /namespace [ (adobe) (creativesuite) (2.0) ] /pdfxoutputintentprofileselector /documentcmyk /preserveediting true /untaggedcmykhandling /leaveuntagged /untaggedrgbhandling /usedocumentprofile /usedocumentbleed false >> ] >> setdistillerparams << /hwresolution [2400 2400] /pagesize [612.000 792.000] >> setpagedevice microsoft word numero 9 art 1 finale c. m. sonsino, frattura ed integrità strutturale, 9 (2009) 3-12; doi: 10.3221/igf-esis.09.01 3 structural durability assessment of welded offshore k-nodes by different local design concepts c.m. sonsino fraunhofer institute for structural durability and system reliability lbf, darmstadt, germany; c.m.sonsino@lbf.fraunhofer.de abstract. the structural durability design of complex welded structures should not rely only on one single design method but should apply different methods for assuring the reliability of the assessment. in this context the application of the structural stress concept, notch stress concept and crack propagation concept are discussed through the example of k-nodes used in energetic offshore constructions like oil platforms or wind power plants, presenting the state of the art. keywords. welded joints; steel; design concept. introduction he most important parameters controlling the durability of welded structures are the service loadings, mechanical as well as environmental, the geometry to be realized according to the required service function, the material and the manufacturing process, fig. 1 [1]. these interactive parameters are matched together by reliability and safety concepts while in this paper, the relation between reliability and safety in fatigue design, fig. 2, will be highlighted through the example of k-nodes used in energetic offshore constructions, fig. 3 and 4. design concepts for offshore k-nodes and prerequisites he most commonly applied fatigue design concepts [2] for the assessment of welded joints, are displayed in fig. 5. design prerequisites for evaluating the durability of k-nodes, such as geometry, spectrum, experimental results, allowable stress ranges, fracture mechanics data, fe-model, and the fe-calculation of hot-spot and notch stresses, will be presented. after this, the evaluation of the experimental results by selected concepts will be carried out. figure 1: influencing parameters of durability of welded structures. t t http://www.gruppofrattura.it/ http://dx.medra.org/10.3221/igf-esis.09.01&auth=true mailto: c.m.sonsino@lbf.fraunhofer.de c. m. sonsino, frattura ed integrità strutturale, 9 (2009) 3-12; doi: 10.3221/igf-esis.09.01 4 figure 2: reliability and safety aspects in fatigue design. figure 3: offshore wind power plant (repower systems ag). figure 4: offshore oil platform. figure 5: overview of fatigue design concepts for welded joints. as for the fatigue critical areas of the k-nodes, fig. 6, at the chord-sided weld seam a nominal stress cannot be defined and as the notch strain concept is not yet sufficiently mature for application, only the hot-spot stress concept, the notch stress concept and the crack propagation concept will be compared, based on experimental results obtained with gas metal arc welded k-nodes, fig. 6, from the fine grained structural steel fe 355 [3]. the tests were carried out under constant and variable amplitude loading under artificial sea-water. the straight line spectrum for variable amplitude loading (common http://www.gruppofrattura.it/ http://dx.medra.org/10.3221/igf-esis.09.01&auth=true c. m. sonsino, frattura ed integrità strutturale, 9 (2009) 3-12; doi: 10.3221/igf-esis.09.01 5 load sequence, colos) was derived from sea-state observations in the north sea. one sequence with the size ls = 4.95 x 105 cycles corresponds to one year of service, fig. 7. figure 6: geometry of welded k-nodes. figure 7: colos spectrum. all of the tested tubulars were instrumented in the critical areas with strain gauges and two failure criteria were defined for presentation of the test results: fatigue life to the initiation of a crack with a depth of a  1.00 mm, detected by dc potential drop technique, and the fatigue life to break-through, fig. 8. crack propagation between these two incidents was also registered. the nominal stress range on the ordinate of fig. 8 is valid only for the braces of the k-nodes and not related to the chord side of the weld seams. as the failures occure on the chord side, for which a nominal stress cannot be defined, the nominal stress concept is not applicable for the assessment of the investigated k-nodes. the calculations of the hot-spot and notch stress ranges will be explained later. fig. 8 includes, as well as the mean curves with the probability of survival ps = 50% for the break-through criterion, also the fatigue life curve for variable amplitude loading with ps = 97.7 %, which is the assigned probability to fatigue life curves in the iiw-recommendations [4]. this curve is obtained by reducing the mean curve by the factor of j = 1.37 resulting from the assumed scatter t = 1:1.50 and a gaussian log-normal distribution. for assessment of the accuracy of the hot-spot and local concepts, the iiw-design curves (allowable stresses) fat 90 and fat 225 (ps = 97.7%) were used. the curves were corrected for thickness and the sea-water corrosion was considered according to gl-design rules [5]. in the case of the local stress concept, as the load dependent notch stresses were http://www.gruppofrattura.it/ http://dx.medra.org/10.3221/igf-esis.09.01&auth=true c. m. sonsino, frattura ed integrità strutturale, 9 (2009) 3-12; doi: 10.3221/igf-esis.09.01 6 calculated for the reference radius rref = 1.00 mm, fig. 9, according to von mises, the fat value 225 mpa, which is a principal stress, was transformed into a von mises stress of 200 mpa [6], tab. 1. this table contains also allowable values for the reference radius rref = 0.05 mm to be applied for thin sheets with t  5mm. figure 8: results presented by load ranges versus fatigue life. figure 9: principle of applying reference radii. all given allowable stress ranges loc are in mpa for n = 210 6 , r = 0.5 , ps= 97.7% ; k = 3.0 , nk = 110 7 , k* = 22.0 , k‘ = 5.0 rref [mm] 1.00 1.00 0.05 0.05 hypothesis psh von mises psh von mises steel 225 200 630 560 aluminium 71 63 180 160 magnesium 28 25 71 63 table 1: fat-values according to the notch stress concept for different reference radii and strength hypotheses (psh: principal stress hypothesis). with regard to cumulative damage, fig. 10, the fatigue life assessment for spectrum loading was carried out according to the palmgren-miner rule keeping the slope k’ = k after the knee point [7] and using the allowable damage sum dal = 0.5 [8]. for the crack propagation calculations, the paris-erdogan curve for steel in salt water with r = 0 and ps = 50 %, fig. 11, was used. http://www.gruppofrattura.it/ http://dx.medra.org/10.3221/igf-esis.09.01&auth=true c. m. sonsino, frattura ed integrità strutturale, 9 (2009) 3-12; doi: 10.3221/igf-esis.09.01 7 figure 10: modification of the sn-curve and calculation of fatigue life (schematically). figure 11: crack propagation law for steel in air and seawater. the crack propagation calculations were carried out using the single edge model, fig. 12. the effect of possible tensile residual stresses was covered conservatively using the crack propagation data with r = 0 [9] even though the tests were carried out with r = -1. the fe-modelling of the critical area of the brace-chord connection was carried out to determine the hot-spot stresses and the modelling of the weld toe for the calculation of the local stresses for the reference radii rref = 0.5 and 1.00 mm, fig. 13. the hot-spot stress (von mises) was calculated for the critical crack initiation region ( = 105°) by a fe-model in the program system marc using curved four-node “thick” shell elements. the stiffening effect of the weld seam on chord wall bending itself was not modelled. the notch stress was calculated by a plane cross sectional model (in finite elements) subject to prescribed end displacements (including end notations) taken from the three dimensional tubular joint model. the linear-elastic stress was determined for the plane strain condition for measured minimum weld toe radius of r = 0.5 2105.1  3104  cycles mm stress intensity δk artificial seawater (f = 1 hz) air (f = 1-10 hz) kｪc,air c ra ck p ro pa ga tio n ra te d a/ dn 10-2 10-3 10-4 10-5 10-6 1033 1.56 n/mm3/2 28.3m 105.7c 86.2m 103.5c 1.0r )k(c dn da sea 14 sea air 13 air m         material: fe e 355 http://www.gruppofrattura.it/ http://dx.medra.org/10.3221/igf-esis.09.01&auth=true c. m. sonsino, frattura ed integrità strutturale, 9 (2009) 3-12; doi: 10.3221/igf-esis.09.01 8 mm with the flank angle  = 45° as well as for the reference radius of rref = 1.00 mm. principal stresses, as well as appertaining von mises stresses (eq, von mises = 0.89 x 1), are given in fig. 13 [10]. figure 12: crack propagation in the chord of a k-node. figure 13: hot-spot and weld local notch stresses in the critical area of the weld seam. the accuracy of the notch stress cannot be verified by strain measurements whereas that of the hot-spot stresses can. in table 2, calculated and measured values are compared. the calculated stresses differ from the measured ones within a range of ± 15%. the differences result from manufacturing dependent inaccuracies from the ideal geometry assumed for the calculations. thus, the modelling can be considered as reliable. with regard to modelling of welded structures for application of the hot-spot and local stress concepts also the iiw-recommendations [4] and the appertaining guidelines [11] should be taken into consideration. http://www.gruppofrattura.it/ http://dx.medra.org/10.3221/igf-esis.09.01&auth=true c. m. sonsino, frattura ed integrità strutturale, 9 (2009) 3-12; doi: 10.3221/igf-esis.09.01 9 ca: constant amplitude loading, va variable amplitude loading *) retested run-out (brace 1), **) retested run-out (brace 2) no. load f [mn] measured hotspot stress hs [mpa] local stress rf = 1 mm loc,v.mises = 3.14 hs [mpa] n1 (a  1 mm, 2l  20mm) n3 (breakthrough) site of crack initiation (°) brace calculated hs [mpa] calculated loc,v.mises [mpa] 6, ca 1.5 150 471 1.60 105 3.95 105 90 95 1 163.5 514 7 * ) , ca 1.0 108 339 6.00 105 1.92 106 105 1 109 343 7 * * ) , ca 1.0 97 305 8.05 105 1.92 106 270 1 109 343 1, va 3.0 346 1086 5.93 105 2.22 106 90 2 327 1028 10, va 3.0 294 920 8.00 105 3.96 106 225 1 327 1028 13, va 1.7 218 685 7.42 106 1.46 107 120 235 1 185 583 3, va 2.0 208 653 2.82 106 1.29 107 120 135 1, 2 218 685 2, va 2.0 205 644 1.20 106 6.30 106 90 1 218 685 table 2: test and calculation results obtained with welded k-nodes. assuming the soundness of quality of the welds, of the fatigue data and of the calculated local stresses provided, the comparison of the calculated and experimental fatigue lives will reveal the accuracy and reliability of the three concepts. comparison of calculations with experiments according to selected concepts he assessments are carried out with calculated hot-spot and local notch stresses. as the differences between the real and calculated stresses are tolerable, the consideration of the real stresses (which are not known in the design stage) will not change the results, which will be discussed in the following. the assessment by the hot-spot concept is displayed in fig. 14 and by the notch stress concept in fig. 15. the calculated fatigue life curves for both concepts, which are valid for the failure criterion total rupture and ps = 97.7 %, cover all results for the comparable failure criterion break-through. even the results for the criterion crack initiation of a crack with the depth of a  1.00 mm are on the safe side with one exception. the curves with ps = 97.7 % for the experimental results are derived from the experimental mean curves with ps = 50 % using the factor j = 1.37 as explained in fig. 8. as the insertion of the particular experimental curves with ps = 97.7 % into the figs. 14 and 15 would overload them, they are not presented here but used later for the comparison of the calculated fatigue lives with the experimental ones. figure 14: application of the hot-spot concept for the evaluation of welded k-nodes. t http://www.gruppofrattura.it/ http://dx.medra.org/10.3221/igf-esis.09.01&auth=true c. m. sonsino, frattura ed integrità strutturale, 9 (2009) 3-12; doi: 10.3221/igf-esis.09.01 10 figure 15: application of the notch stress concept with rref = 1.0 mm for the evaluation of welded k-nodes. the crack propagation lives, calculated as well as measured from a crack depth of a  1.00 mm to break-through, are presented in fig. 16. as the calculations were carried out with the paris-erdogan law for the probability of survival of ps = 50 %, fig. 11, they are compared with the experimental mean curves. here also, the calculations lie on the safe side. besides this, they reveal that the cracks propagate slowly and permit their detection by inspections before break-through. figure 16: comparison of experimental and calculated crack propagation lives. the accuracy of the concepts can be evaluated by the ratio between the calculated and experimental fatigue lives, fig. 17. on the basis of the assumptions and prerequisites described already, the hot-spot and crack-propagation concepts reveal the same accuracy. however, the notch stress concept with the reference radius rref = 1.00 is more conservative. but this may result from the modelling of the weld. also for the crack propagation concept, it has to be mentioned again that the crack propagation was calculated with r = 0 conservatively. nevertheless, all three concepts do not exaggerate on the safe side and are reliable. http://www.gruppofrattura.it/ http://dx.medra.org/10.3221/igf-esis.09.01&auth=true c. m. sonsino, frattura ed integrità strutturale, 9 (2009) 3-12; doi: 10.3221/igf-esis.09.01 11 figure 17: accuracy of fatigue life estimations according to different concepts by the example of welded k-nodes. conclusions and summary he applied local concepts show similar results. the observed differences in the results are certainly due to the particular assessments but still tolerable and support the overall evaluation of the structural durability behaviour of the k-nodes, i.e. for assessing the safety of a structure the parallel application of different concepts, their reliably provided, assures the evaluation. in this context good balance between calculations, experimental verifications and feedbacks from field service, fig. 18, lead to a reliable design. figure 18: knowledge interaction for reliable design. references [1] c.m. sonsino, mat.-wiss.u. werkstofftech. 38-1 (2007) 9. [2] d.radaj, c.m. sonsino, w. fricke, fatigue assessment of welded joints by local approaches woodhead publishing, cambridge, (2006) 2nd edition. [3] corrosion fatigue of welded tubular joints and cast-steel compound tubular joints in large size scale report no. eur 14316 de, brussels, european coal and steel commission (1993). [4] a.hobbacher (ed.), recommendations for fatigue design of welded joints and components iiw doc. no. xiii1823-07 (update july 2008). [5]. rules for classification and construction offshore technology, part 2 offshore installations structural design, section 3 g: fatigue germanischer lloyd, hamburg (1990). [6] c.m. sonsino, suggested allowable equivalent stresses for fatigue design of welded joints according to the notch stress concept with the reference radii rref = 1.00 and 0.05 mm iiw-doc. no. xiii-2216-08 / xv-1285-08, graz (2008). t http://www.gruppofrattura.it/ http://dx.medra.org/10.3221/igf-esis.09.01&auth=true c. m. sonsino, frattura ed integrità strutturale, 9 (2009) 3-12; doi: 10.3221/igf-esis.09.01 12 [7] e. haibach, betriebsfestigkeit: verfahren und daten zur bauteilberechnung springer-verlag, düsseldorf (2003) 2nd edition. [8] c .m. sonsino, int. j. fatigue 29 (2007) 1080. [9] c.m. sonsino, m. vormwald, geschweißte offshore – rohrknoten (anwendungsbeispiel) in: bruchmechanischer festigkeitsnachweis für maschinenbauteile (fkm), frankfurt (2004) 81. [10] d. radaj, c.m. sonsino, d. flade, int. j. fatigue 20-6 (1998) 471. [11] w. fricke, guideline for the fatigue assessment by notch stress analysis for welded structures iiw-2240r1-08 / xv-1289r1-08 (2008). http://www.gruppofrattura.it/ http://dx.medra.org/10.3221/igf-esis.09.01&auth=true microsoft word numero_37_art_35 d. angelova et alii, frattura ed integrità strutturale, 37 (2016) 265-271; doi: 10.3221/igf-esis.37.35 265 focused on fracture mechanics in central and east europe on monitoring of mechanical characteristics of hot rolled s355j2 steel d. angelova, r. yordanova, a. georgiev, s. yankova university of chemical technology and metallurgy, bulgaria donkaangelova@abv.bg, r.yordanova@uctm.edu abstract. hot rolling normalization technology for producing sheets from a low-carbon steel, steel s355j2, used in the bulgarian metallurgical plant “stomana industry sa” is under investigation. a newly introduced automatic application optimization procedure in this technology is an important step that leads to avoiding of traditional heat treatment, improving of steel mechanical characteristics, increasing of production efficiency, all resulting in high quality final products. on the basis of the final mechanical rolled-sheet characteristics yield strengths, re, ultimate tensile strengths, rm, absorbed energies in impact tests, k, and elongations after fracture some energy-stress and energy-stress-elongation constructions-spaces have been plotted. these spaces can be used for general evaluation of the applied rolling technology and for prediction of steel-sheet mechanical behaviour. keywords. hot rolling; low-carbon steel s355j2; rolled-sheet; prediction of steel-sheet mechanical behaviour introduction evelopment of modern metallurgy and engineering is characterized not only by increasing production volume and enriching production range, but by sufficient improve in quality increase of metal-product’s service life in combination with high reliability of structures machines and devices [1-3]. industrial processing of metals (forming) by plastic deformation is one of the major and most important industries in the global economy. high quality metal product features a constant chemical composition, microand macrostructure, geometric shapes and sizes and guaranteed physical and mechanical properties. the quality of metal products depends primarily on their mechanical properties, their behavior in processing and exploitation, and their microstructure [1-5]. experimental work and results conventional hot rolling technology for producing thick sheets hick sheets (30 mm and 40 mm) from a low-carbon steel, steel s355j2+n, have been produced by normalization rolling in the bulgarian metallurgical plant “stomana industry sa” for more than 60 years [6-7]. the aim of this work is to investigate and control the technological process of forming of hot-rolled steel plate (sheet) of steel s355j2+n in attempt to improve mechanical characteristics of the final product. d t d. angelova et alii, frattura ed integrità strutturale, 37 (2016) 265-271; doi: 10.3221/igf-esis.37.35 266 standard chemical composition and mechanical properties steel s355j2+n is low-carbon, low-alloy structural steel with chemical composition shown in tab. 1 and mechanical properties presented in tab. 2, both accordingly the standard en 10025-2:2004 "hot rolled products of structural steel". c mn si p s cr ni cu mo as al v ti 0.160.18 1.101.16 0.200.26 0.0080.014 0.0020.010 0.0400.120 0.0600.150 0.1800.320 0.0090.031 0.0080.027 0.0250.040 0.0310.042 0.0220.037 table 1: chemical composition of steel s355j2+n (weight %) yield strength, re, mpa tensile strength, rm, mpa total elongation, а, % impact test*, к, j 345 430 470 630 min 20 – 22 % min 27 * * test piece with v-figurative notch; т= 20ос table 2: mechanical properties of hot-rolled sheet’s steel s355j2+n with nominal thickness 30 and 40 mm equipment and technological experiments according to en 10025-2:2004, 40 experiments have been carried out – two groups of 20 experiments to obtain two different thicknesses of the finished product (final plate/sheet), respectively of 30 mm and 40 mm. rolling mill used is schematically represented in fig. 1 as a complex of mechanical components and equipment for hot rolling of heavy plates/sheets, their further processing and transportation. the mill consists of a reverse roll mill type "quarto", and equipment for straightening, cutting and marking of finished products [6-7]. figure 1: scheme of quarto reversing rolling stand for hot-rolled steel plates/sheets in the bulgarian metallurgical plant “stomana industry sa”. d. angelova et alii, frattura ed integrità strutturale, 37 (2016) 265-271; doi: 10.3221/igf-esis.37.35 267 to adjust the parameters of the rolling mill for receiving quality products with desired properties by total thickness of 30 mm and 40 mm, there were developed and experimentally tested two speed-temperature-deformation regimes regime a and regime b. each profile size (30mm and 40mm) is obtained, performing deformation process in these two regimes; 10 pieces from each thickness are tested. specific features of the different rolling regimes regime a. rolling process is carried out when the parameters of the rolling mill are set up as follows: large rolling forces (up to 75% of the maximum for the mill or up to 16,000 kn); high torque (running over to the equipment nominal value); large difference between the initial and the final thickness of the metal concerning each pass, h [mm], respectively a high degree of deformation (reduction in thickness into each pass about 20%). speed-temperature-deformation normalization rolling for regime a is designed with 21 passes. regime b. normalization rolling process is performed with new setting of the parameters of the rolling stand, providing less stress (up to 68%), a low torque, small difference between the initial and the final thickness of the metal concerning all passes ( h is between 13 and 16 mm) and decreased deformation, respectively to maximum 16-20%. all this leads to an increase in the number of passes to 25. under these initial conditions and using an automatically applied optimization program, regime b has been developed as a more efficient one. testing after rolling, 40 specimens were machined for standard mechanical testing – 20 for regime a and 20 for regime b, of which 10 specimens for the final thickness of 30 mm and the same quantity for the thickness of 40 mm. data obtained from testing concern mechanical (tensile strength, yield strength) and plastic (elongation) behaviour (of the final product), as well as impact energy providing information about impact strength. they (the data) are presented in fig. 2. discussion and analyses he data presented in fig. 2 show that the final products obtained in regime b have improved mechanical behaviour, corresponding to the standard en 10025-2:2004, when the plates obtained by using regime a cannot satisfy the requirements of this standard. this means that the rolling process of regime a is unstable in comparison to the stable one under regime b, wherein the rolling process is controlled, which leads to a sufficient improve of all mechanical properties and their steady reproduction. usually mechanical testing results have the standard presentation as can be seen in fig. 2, following by standard analysis. but these results can be presented in a new different way as it has been done in fig. 3a and 3b. the fig. 3 visualizes energy-stress constructions-spaces mnlqq1m1n1l1 for 30 mm and 40 mm plates/sheets (obtained under regime b including automatic application of the mentioned above optimization procedure), which are built by using the final mechanical rolled-plate characteristics yield strengths, re, ultimate tensile strengths, rm, absorbed energies in impact tests, k. (elongations after fracture are included in similar constructions-spaces in fig. 5.) these constructions-spaces bring additional information about rolling technology and energy-mechanical properties of the finished/final products. the complicated three-dimensional energy-stress surface mnlq in fig. 3a and 3b shows that although the minimum values of yield strength and tensile strength are above the minimum set by the standard, it is worth looking for further improvement of the speed-temperature-deformation regime of rolling that will make this surface smoother, meaning further (even higher) stabilization of technology and energy-mechanical properties of the finished/final product. at the moment surface mnlq looks smoother for 30 mm plates/sheets than that for 40 mm ones. in fig. 4a and 4b complex pyramidal spaces stut1s1p have been built, each by: the straight lines pu and s1t1 of the average values of yield strengths and tensile strengths respectively, corresponding to the 10 tests for each thickness; and the broken line st, obtained from the average energy of impact tests and the stresses (rm,av – re,av)/2 (corresponding to the same 10 tests). it is easy to build a line corresponding to the average value of the stresses from the broken line st. thus the visualization of the pyramidal spaces stut1s1p makes it possible to predict dispersion of all stresses from the range between the yield strength and the tensile strength, enabling us to do some preliminary comparisons with the exploitation stress requirements. t d. angelova et alii, frattura ed integrità strutturale, 37 (2016) 265-271; doi: 10.3221/igf-esis.37.35 268 a. b. figure 2: comparative analysis of mechanical properties of hot-rolled plate/sheet, obtained by strain–speed–temperature regimes a and b; a. – plate/sheet with final thickness 30 mm; b. – plate/sheet with final thickness 40 mm. 0 100 200 300 400 500 600 700 1 2 3 4 5 6 7 8 9 10 sheet mark number t e n s il e s tr e n g th , r m , м р а 470 мра (еn 10025-2:2004) 630 мра (еn 10025-2:2004) 0 100 200 300 400 500 600 1 2 3 4 5 6 7 8 9 10 sheet mark number y ie ld s tr e n g th , r e , m p a 345 мра (еn 10025-2:2004) 430 мра (еn 10025-2:2004) 0 10 20 30 40 50 1 2 3 4 5 6 7 8 9 10 sheet mark number e lo n g a ti o n a ft e r fr a c tu re а , % min 20% (еn 10025-2:2004) 0 50 100 150 200 250 1 2 3 4 5 6 7 8 9 10 sheet mark number v -n o tc h i m p a c t e n e rg y к , j min 27j (еn 10025-2:2004) 0 100 200 300 400 500 600 700 1 2 3 4 5 6 7 8 9 10 sheet mark number t e n s il e s tr e n g th , r m , м р а 470 мра (еn 10025-2:2004) 630 мра (еn 10025-2:2004) 0 100 200 300 400 500 600 1 2 3 4 5 6 7 8 9 10 sheet mark number y ie ld s tr e n g th , r e , m p a 345 мра (еn 10025-2:2004) 430 мра (еn 10025-2:2004) 0 10 20 30 40 50 1 2 3 4 5 6 7 8 9 10 sheet mark number e lo n g a ti o n a ft e r fr a c tu re а , % min 20% (еn 10025-2:2004) 0 50 100 150 200 250 1 2 3 4 5 6 7 8 9 10 sheet mark number v -n o tc h i m p a c t e n e rg y к , j min 27j (еn 10025-2:2004) d. angelova et alii, frattura ed integrità strutturale, 37 (2016) 265-271; doi: 10.3221/igf-esis.37.35 269 a. b. figure 3: energy-stress constructions-spaces mnlqq1m1n1l1, expressing mechanical behaviour of: a. 30 mm plates/sheets; and b. 40 mm plates/sheets. a. b. figure 4: pyramidal spaces stut1s1p, presenting a basis for predicting mechanical behaviour of: a. 30 mm plates/sheets; and b. 40 mm plates/sheets. on the basis of fig. 3, energy-stress-elongation construction-space mvzqq1m1v1z1 has been plotted and shown in fig. 5. it includes elongation after fracture, plotted for all stresses of the broken line nl, which moves the line nl to its new position, the broken line vz. the construction-space mvzqq1m1v1z1 includes all energy, stress and elongation characteristics of the final product and can be used as an instrument for general evaluation of the applied rolling technology and for prediction of steel-sheet mechanical behaviour, including plasticity, under exploitation conditions [3, 4]. transition from the space mnlqq1m1n1l1 to the space mvzqq1m1v1z1 can be done through the plotted in fig. 5, stress-elongation area nvzl. d. angelova et alii, frattura ed integrità strutturale, 37 (2016) 265-271; doi: 10.3221/igf-esis.37.35 270 figure 5: energy-stress-elongation constructions-space mvzqq1m1v1z1, expressing mechanical behaviour, including plasticity, of 30 mm plates/sheets conclusion he technological process of obtaining hot-rolled steel plates/sheets of steel s355j2 + n has been investigated aiming at improving mechanical characteristics of the final product. two different regimes of normalization rolling have been studied (carrying out 20 experiments per regime) – the basic regime a and a newly designed regime b (including automatic application optimization procedure) – and regime b is found and proved to be the more efficient one. using standard test data characterizing mechanical (tensile strength, yield strength) and plastic (elongation) behaviour of the final product, as well as impact energy providing information about impact strength, some energy-stress and energystress-elongation constructions-spaces have been built. these spaces can be used as an instrument for general evaluation of the applied rolling technology and for prediction of steel-sheet mechanical behaviour under exploitation conditions. transition from one space to the other can be done through a specific stress-elongation area, including the elongation after fracture. acknowledgements his paper has been produced with the financial assistance of the european social fund, projects number bg051po001-3.3.06-0014 and bg051po001-3.3.06-0038. the authors are responsible for the content of this material, and under no circumstances can be considered as an official position of the european union and the ministry of education and science of bulgaria. references [1] dieter, e. g., mechanical metallurgy, mcgraw-hill book company (1988). [2] angelova, d., kolarov, d., philipov, к. , yordanova, r., metal science and metal forming handbook, part 5, sofia, bulgaria: academic publishing house “м. drinov”, (2009) (in bulgarian) t t d. angelova et alii, frattura ed integrità strutturale, 37 (2016) 265-271; doi: 10.3221/igf-esis.37.35 271 [3] dowling, n., mechanical behavior of materials. engineering methods for deformation, fracture, and fatigue, prentice hall, (2006) [4] angelova, d., yordanova, r., georgiev, a., yankova, s., investigation of possibilities for improving mechanical characteristics of a low-carbon hot rolled steel, scientific proceedings, xxi, 2(139) (2013) 249-253. [5] yordanova, r., georgiev, a., yankova, s., angelova, d., improved quality of sheets of a low -carbon hot rolled steel as a result of a new technology, scientific proceedings, xxii, 1 (150) (2014) 122-125. [6] courtney, t., mechanical behavior of materials, international edition, mcgraw-hill publishing company, (1990). [7] smallman, r., bishop, r., modern physical metallurgy and materials engineering. science, process, applications, 6th edition, butterworth-heinemann, oxford, (1999). << /ascii85encodepages false /allowtransparency false /autopositionepsfiles true /autorotatepages /none /binding /left /calgrayprofile (dot gain 20%) /calrgbprofile (srgb iec61966-2.1) /calcmykprofile (u.s. web coated \050swop\051 v2) /srgbprofile (srgb iec61966-2.1) /cannotembedfontpolicy /error /compatibilitylevel 1.4 /compressobjects /tags /compresspages true /convertimagestoindexed true /passthroughjpegimages true /createjobticket false /defaultrenderingintent /default /detectblends true /detectcurves 0.0000 /colorconversionstrategy /cmyk /dothumbnails false /embedallfonts true /embedopentype false /parseiccprofilesincomments true /embedjoboptions true /dscreportinglevel 0 /emitdscwarnings false /endpage -1 /imagememory 1048576 /lockdistillerparams false /maxsubsetpct 100 /optimize true /opm 1 /parsedsccomments true 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can be opened with acrobat and adobe reader 5.0 and later.) >> /namespace [ (adobe) (common) (1.0) ] /othernamespaces [ << /asreaderspreads false /cropimagestoframes true /errorcontrol /warnandcontinue /flattenerignorespreadoverrides false /includeguidesgrids false /includenonprinting false /includeslug false /namespace [ (adobe) (indesign) (4.0) ] /omitplacedbitmaps false /omitplacedeps false /omitplacedpdf false /simulateoverprint /legacy >> << /addbleedmarks false /addcolorbars false /addcropmarks false /addpageinfo false /addregmarks false /convertcolors /converttocmyk /destinationprofilename () /destinationprofileselector /documentcmyk /downsample16bitimages true /flattenerpreset << /presetselector /mediumresolution >> /formelements false /generatestructure false /includebookmarks false /includehyperlinks false /includeinteractive false /includelayers false /includeprofiles false /multimediahandling /useobjectsettings /namespace [ (adobe) (creativesuite) (2.0) ] /pdfxoutputintentprofileselector /documentcmyk /preserveediting true /untaggedcmykhandling /leaveuntagged /untaggedrgbhandling /usedocumentprofile /usedocumentbleed false >> ] >> setdistillerparams << /hwresolution [2400 2400] /pagesize [612.000 792.000] >> setpagedevice microsoft word numero_28_art_5 d. gentile et alii, frattura ed integrità strutturale, 28 (2014) 42-50; doi: 10.3221/igf-esis.28.05 42 experimental measurement and model validation of cod in pipe under bending with off-centered circumferential crack d. gentile, g. iannitti, n. bonora department of civil and mechanical engineering, university of cassino and southern lazio (italy) gentile@unicas.it abstract. the leak area of circumferential through-thickness crack in pipe under bending depends on the position of the crack with respect to the bending plane. in leak-before-break (lbb) analysis, the assumption that the crack is symmetrically placed with respect to the bending plane is not necessarily conservative. in this work, the crack opening of circumferential cracks, off-centered with respect to the bending plane, was investigated experimentally. here, three pipe geometries and two crack lengths were investigated. for each crack, the centred and two off-centered configuration were examined. the crack opening displacement (cod) distribution along the crack length was measured for two selected bending load levels using digital image correlation (dic) technique. these measurements have been used for verifying the solution provided by the hodograph cone method (hcm) as proposed by bonora [1]. sommario. in una tubazione con difetto passante circonferenziale soggetta a carico di moment flettente, l’area di efflusso o area di leakage dipende dalla posizione del difetto rispetto al piano di momento. nell’analisi leakbefore-break (lbb), l’assunzione che il difetto sia sempre posizionato simmetricamente rispetto al piano di momento non è necessariamente un’ipotesi conservativa. in questo lavoro, l’effettiva apertura di difetti circonferenziali, in tubazioni soggette flessione e non posizionati simmetricamente rispetto al piano di momento flettente, è stata determinata attraverso opportuna indagine sperimentale. sono stati analizzati tre geometrie di tubazione e due lunghezze di difetto. per ogni configurazione di difetto sono state poi esaminate tre posizioni: una in asse e due fuori asse. il cod, ovvero l’apertura del difetto lungo tutta la lunghezza del difetto, è stato misurato per mezzo di estensimentria senza contatto con tecnica speckle (digital image correlation –dic).le misure sono state utilizzate per verificare l’accuratezza della soluzione ottenuta con il metodo del cono odografo (hcm) proposta da bonora [1]. keywords. crack; pipe; bending; cod; off-axis; hodograph cone method. introduction eak before break criteria (lbb) provide a design route to assess if a crack can critically affect the structural integrity of a pipe or pressure vessel [2]. in this approach, the leak rate, the shape and size of the leak area (coa), or alternatively the crack opening displacement (cod) distribution along the flaw length under the acting load, is needed to estimate the associated crack size [3]. a reference configuration for the structural integrity assessment of flawed pipe is the through-thickness circumferential crack under bending and/or internal pressure load [4]. here, the crack is l http://www.gruppofrattura.it http://dx.medra.org/10.3221/igf-esis.28.05&auth=true d. gentile et alii, frattura ed integrità strutturale, 28 (2014) 42-50; doi: 10.3221/igf-esis.28.05 43 always assumed to be placed symmetrically with respect to the bending plane because the maximum crack opening and coa occur for this configuration [5]. in the literature, based on finite element analyses, several solutions for the maximum crack opening have been reported and the coa is calculated assuming an elliptical distribution of the cod along the crack length. an example of these solutions can be found in design code such as ge-epri [4, 6]. in real cases and for many reasons, such as fabrication imperfections, vibrations, load transient, etc., the crack can be offcentered and located in different positions around the pipe circumference. in these conditions, for leak rate and applied load identical to that of symmetrical centered crack, these solutions lead to: 1. a smaller crack opening area that drive to a larger detectable flaw size (detrimental effect). 2. a higher pipe capability to carrying load (beneficial effect). therefore, finite element analysis becomes mandatory to determine the effective leak area for a generic off-centered crack configuration [7]. when the crack is off-centered with respect to the bending plane, the coa is reduced with respect to that of the reference centered configuration and the shape of the cod distribution along the crack is no longer elliptical. bonora [1] proposed the hodograph cone method (hcm) in which the cod distribution (shape and amplitude) and the leak area are predicted, as a function of the crack length and off-center angle, only by means of geometrical considerations. later, rahman et al. [8] performed further numerical investigations on off-centered crack configurations, and firmature and rahman [9] investigated the behavior of off-center cracks in elastic-plastic regime. at the present, the hcm method is the only available solution that does not require extensive use of finite element simulation and allows quick estimation of the cod distribution and associated coa, given the crack length and the offaxis angle, and the maximum cod for the prescribed load in the centered crack configuration. for this reason, it is attractive for its potential use in design-by-analysis procedures. this model has been validated by means of finite element simulation on selected flawed pipe configurations [10]. more recently, experimental measurements of the cod profile for off-centered circumferential crack under bending have been presented [11]. in this work, an extensive experimental work, to investigate the evolution of cod profile with the offcenter angle in different pipe configurations (diameter and thickness) under bending, was carried out. these results have been used to provide a physical evidence for the qualification of the hcm. material and methods n this study, the pipe selected for the cod measurement were made of two materials: fe360 steel for the pipe 3.4 mm thick, and st52 for 2mm and 5mm thick pipes. three mean pipe radius/thickness ratios have been investigated. these ratios were selected to compare the results with the ge-epri solution which has the following limit 5<r/t<20. a summary of the pipe geometries, off axis angle and selected load is given in tab. 1. test configuration mean radius [mm] t [mm] rm/t a/ off-axis angle  (°) load [n] 250t2 29 2 14.5 0.139 0 30 60 500 2 90t2 29 2 14.5 0.25 0 30 60 500 2 90t3.4 28.3 3.4 8.32 0.25 0 30 60 500 2 50t5 27.5 5 5.5 0.139 0 30 60 1500 2 90t5 27.5 5 5.5 0.25 0 30 60 1500 table 1: test configuration: three different rm/t and two different crack length. pipe used in this work were obtained by cold drawing ensuring constant thickness and small ovalization. on each pipe the cracks was machined using a circular saw which generate a squared crack tip with an initial opening of 1.0 mm. no fatigue pre-cracking was performed to sharp the tip radius since the interest is in the cod distribution along the crack length. however, preliminary 3d fem analysis was performed in order to verify if an initial blunting could influence the cod i http://www.gruppofrattura.it http://dx.medra.org/10.3221/igf-esis.28.05&auth=true d. gentile et alii, frattura ed integrità strutturale, 28 (2014) 42-50; doi: 10.3221/igf-esis.28.05 44 profile. results showed that the cod profile is not affected by the shape of the initial blunting since the initial crack opening, due to the cut, scales the overall opening displacement [10]. each pipe was loaded under four point bending. tests were performed with instron 300kn electromechanical testing machine, and the cod was measured for two applied load values: 500n and 1500n. a pre-load of 40n was used in order to compensate loading fixture compliance, fig. 1. the measure of the cod distribution along the crack length was performed by means of digital image correlation (dic). the system used is aramis by gom, which ensures an accuracy on strain measurements of 0.01%. in order to proceed with dic, the pipe surface is initially sprayed with white coating and successively sprayed with black coating to produce the reference speckle surface. two calibrated cameras were used in order to account for the 3d nature of the measurement. in fig. 2 an example of the acquired and processed images from dic is shown. for each flawed pipe configuration, the cod profile was measured initially for the in-axis (symmetric) position with respect to the bending moment. successively, the measure was repeated, at the same prescribed load, rotating the pipe around its longitudinal axis by an off-axis angle. figure 1: four point bend test set-up. a) b) c) figure 2: example of processed dic images: a) in green the analysis area red dots are the virtual clip gauge ends; b) in blu the crack and green squares shows the grid for strain measurements; c) the resulting strain map. the crack opening displacement was measured defining a series of virtual clip gauges applied on the computational grid generate by aramis software. since the cod profile is a 3d curve in the coordinate space, two cameras were used to determine the coordinates of the physical points, which are mapped onto the image pixels, to obtain deformation and strain comparing digital images at different times. http://www.gruppofrattura.it http://dx.medra.org/10.3221/igf-esis.28.05&auth=true d. gentile et alii, frattura ed integrità strutturale, 28 (2014) 42-50; doi: 10.3221/igf-esis.28.05 45 the hodgraph cone method he hodograph cone method (hcm) is a geometry approach for the estimation of the cod profile for a generic circumferential part-through crack in a pipe under bending and/or internal pressure. the method and the derivation of the solution is given in details elsewhere [1]. in the following the hcm is summarized. according to the hcm, the geometrical representation of the cod of a circumferential crack in a pipe can be seen as the intersection of two surfaces: a cylindrical surface, representative of the pipe, and a cone, with elliptical base and the vertex insisting on the cylinder circumference. the base of the cone is an ellipse with its minor axis equal to the maximum crack opening displacement for the in axis configuration. the cone has an opening angle that is half of the physical crack opening angle. a sketch of the hcm is shown in fig. 3. figure 3: geometric representation of the hodograph cone for the reference in-axis configuration. for the centered crack configuration, the intersection of the cone and the cylinder return in the 3d space the cod profile as the elliptical profile projected onto the pipe surface. for the off-centered crack, the cod profile can still be obtained as the intersection of the cylinder and the shifted cone, moving its vertex along the cylinder circumference by the same off axis angle , fig. 4. for a circumferential crack length 2r and a generic off-centered angle , the cod curve in the 3d space can is given as:                 2 1 222 2 2 / * cos cos sin sin tan sin cos y x r z r                        (1) where  ;     and * is the maximum cod at the center crack length for the in axis configuration. off course this value is function of the pipe geometry and load and can be determined either by fem or estimated according to geepri or similar solutions. according to this, crack closure stars when the crack goes in the compression region that is predicted to occurs at an angle that depends on the crack length according to,   1 2     (2) t http://www.gruppofrattura.it http://dx.medra.org/10.3221/igf-esis.28.05&auth=true d. gentile et alii, frattura ed integrità strutturale, 28 (2014) 42-50; doi: 10.3221/igf-esis.28.05 46 therefore, provided the pipe reference radius (inner, outer or thickness average), the crack opening angle , and the maximum cod at the center of the crack for the in axis configuration, eqn. 1 provides the equation of the cod in the 3d space. figure 4: hcm for the generic off-center crack configuration. results and discussion n fig. 5 the comparison of the measured and calculated cod profile for the centered crack configuration and two different pipe thicknesses is shown. here, experimental data could be obtained only for half of the crack length since in the centered crack configuration the crack length was exceeding the dic cameras window. however, it was possible to measure the cod beyond the point for which the maximum opening occurs to confirm the symmetry of the cod profile. the maximum cod was measured for the centered crack configuration also for 2=90° and for the three pipe thicknesses. these results have been used to validate available solutions based on fem such as those reported in the ge-epri. it was found that in some cases, these solutions do not agree well with present experimental results. the hcm assumes that, given the maximum cod for the center crack, the cod distribution for the off-center crack configuration is given by              1 222 20 2 / cos cos sin sin tan           (1.1) this solution overestimates the effective maximum opening for given off-axis angle. it has been found that applying the following correction usually leads to much better agreement between the hcm and fem results,  0 0 0 * cos /    where 0 is a factor that depends on the amplitude of the applied bending and crack length and it is equal to the ratio of half crack angle  and the off center angle  for which there is half closure of the crack. this correction is applied only for half crack angle greater than 45°. in fig. 7-fig. 11 the comparison of the hcm and the measured cod profile for the off-axis configuration is shown. in all the cases, the agreement is very good indicating that the hcm is accurate enough to predict the effective modification of the cod profile with the increasing off-axis angle even for very large cracks. in tab. 2, the comparison between the measured cod and calculated values determined with ge-epri solution for the centered crack configuration, [6] is given. it is interesting to note that for smaller thickness and shorter crack length, the difference is larger. a possible explanation is that ge-epri numerical simulation were performed using shell elements which do not correctly take into account 3d effects and rotation of the through-thickness crack faces. much better agreement is found when using 3d finite element models as shown in by the author in [10]. i http://www.gruppofrattura.it http://dx.medra.org/10.3221/igf-esis.28.05&auth=true d. gentile et alii, frattura ed integrità strutturale, 28 (2014) 42-50; doi: 10.3221/igf-esis.28.05 47 -1 -0.5 0 0.5 1 0 1 2 3 4 5 x 10 -3 dimensionless angle c o d /2 ( m m ) model thickness 5mm thickness 2mm figure 5: cod distribution for specimen in the canonical configuration, (=0°), crack length 250°. -1 -0.5 0 0.5 1 0 0.002 0.004 0.006 0.008 0.01 dimensionless angle c o d /2 ( m m ) model thickness 2mm thickness 5mm thickness 3.4mm figure 6: cod distribution for pipe with different thickness: crack length 290°. -1 -0.5 0 0.5 1 0 1 2 3 4 x 10 -3 dimensionless angle c o d /2 ( m m ) model  50  60  50  30 figure 7: t=2 mm crack length 2(0°) and (0°). http://www.gruppofrattura.it http://dx.medra.org/10.3221/igf-esis.28.05&auth=true d. gentile et alii, frattura ed integrità strutturale, 28 (2014) 42-50; doi: 10.3221/igf-esis.28.05 48 -1 -0.5 0 0.5 1 0 2 4 6 8 x 10 -3 dimensionless angle c o d /2 ( m m ) model  90  30  90  60 figure 8: t=2 mm crack length 2(0°) and (0°). -1 -0.5 0 0.5 1 0 0.5 1 1.5 2 2.5 3 3.5 x 10 -3 dimensionless angle c o d /2 ( m m ) model  50  60  50  30 figure 9: t = 5mm; crack length 2(0°) and (0°). -1 -0.5 0 0.5 1 0 2 4 6 x 10 -3 dimensionless angle c o d /2 ( m m ) model  90  60  90  30 figure 10: t = 5mm; crack length 2(0°) and (0°). http://www.gruppofrattura.it http://dx.medra.org/10.3221/igf-esis.28.05&auth=true d. gentile et alii, frattura ed integrità strutturale, 28 (2014) 42-50; doi: 10.3221/igf-esis.28.05 49 -1 -0.5 0 0.5 1 0 0.5 1 1.5 2 2.5 3 3.5 x 10 -3 dimensionless angle c o d /2 ( m m ) model 50  30  50  60 figure 11: t = 3.4mm; crack length 2(0°) and (0°). configuration ge-epri[6] [mm] experimental measure [mm] error % 2 50t2 4.9e-3 7.2e-3 32 2 90t2 1.5e-3 1.8e-3 17 2 90t3.4 2 50t5 5.4e-3 6.5e-3 14 2 50t5 1.4e-3 1.5e-3 7 table 2: comparison between maximum cod calculated by ge-epri and the experimental values. conclusions n this work, an experimental investigation on the shape of the cod profile for off-centered circumferential crack in bended pipe was carried out. cod measures were performed on pipes with different thickness, different crack length, and for different values of the off-crack angle. these measures have been used to validate the hodograph cone method which provided a geometrical solution for the determination of the cod modification as a function of the pipe geometry, crack length and off-axis angle. the comparison of the hcm solution and present cod measures indicates that the hcm is very accurate and rubout tools for predicting the cod for off-centered crack configuration suggesting its use as valid alterative to extensive finite element analysis in lbb analysis. the measures of the maximum cod for the centered crack configuration were compared with ge-epri solutions. it was found that for the selected r/t pipe ratio and crack opening angle, the ge-epri provides always a maximum ctod that is larger than that measured in the experiments. this difference, although conservative, becomes larger when considering shorter crack length and thinner pipe. references [1] bonora, n., cod of off-centred cracks in pipes under bending load: a geometrical solution, international journal of fracture, 75(1) (1996) 1-18. [2] the nuclear regulators' working group task force on leak before break, "european safety practices on the application of leak before break (lbb) concept," no. eur 18549 en (2000). [3] wilkowski, g., leak-before-break: what does it really mean?, journal of pressure vessel technology, 122 (2000) 267-272. i http://www.gruppofrattura.it http://dx.medra.org/10.3221/igf-esis.28.05&auth=true d. gentile et alii, frattura ed integrità strutturale, 28 (2014) 42-50; doi: 10.3221/igf-esis.28.05 50 [4] klecker, r., brust, f., wilkowski, g. m., nrc leak-before-break (lbb.nrc) analysis method for circumferentially through-wall cracked pipes under axial plus bending loads, no. nureg/cr-4572, us nuclear regulatory commission, washington dc (1986). [5] rahman, s., brust, f., ghadiali, n., choi, y. h., krishnaswamy, p., moberg, f., brickstad, b., wilkowski, g. m., refiniment and evaluation of crack-opening area analyses for circumferential through-wall cracks in pipes, nureg/cr-6300, nuclear regulatory commission (1995). [6] kishida, k., zahoor, a., crack-opening area calculations for circumferential throughwall pipe cracks, np-5959-sr, electric power research institute, palo alto, ca. usa, (1998) [7] kumar, v., german, m., wilkening, w., andrews, w., delorenzi, h., mowbray, d., advances in elastic-plastic fracture analysis, epri final report np-3607, electric power research institute, palo alto, ca., usa, (1984). [8] rahman, s., ghadiali, n., wilkowski, g. m., bonora, n., effects of off-centered cracks and restraint of induced bending caused by pressure on the crack-opening-area analysis of pipes, nuclear engineering and design, 167(1) (1996) 55-67. [9] firmature, r., rahman, s., elastic-plastic analysis of off-center cracks in cylindrical structures, engineering fracture mechanics, 66(1) (2000) 15-39. [10] iannitti, g., bonora, n., gentile, d., assessment of an engineering approach to the evaluation of the cod of offcentered crack in pipes under bending for lbb design, engineering fracture mechanics, 81 (2012) 69-79. [11] gentile, d., iannitti, g., bonora, n., cod of off-centered cracks in pipes under bending: experimental measures and model validation, in: proc. asme 2013 pressure vessels & piping division / k-pvp conference, asme, ed., asme pp. pvp2013-97347 (2013). http://www.gruppofrattura.it http://dx.medra.org/10.3221/igf-esis.28.05&auth=true microsoft word numero_38_art_30 s. suman et alii, frattura ed integrità strutturale, 38 (2016) 224-230; doi: 10.3221/igf-esis.38.30 224 focussed on multiaxial fatigue and fracture development of a multiaxial fatigue damage parameter and life prediction methodology for non-proportional loading sandip suman research center, environmental solution group, dover corporation, usa ssuman@doveresg.com alan kallmeyer north dakota state university, fargo, nd, usa, alan.kallmeyer@ndsu.edu john smith research & validation, environmental solution group, dover corporation, usa, josmith@doveresg.com abstract. most of the prior studies on the prediction of fatigue lives have been limited to uniaxial loading cases, whereas real world loading scenarios are often multiaxial, and the prediction of fatigue life based upon uniaxial fatigue properties may lead to inaccurate results. a detailed exploration of multiaxial fatigue under constant amplitude loading scenarios for a range of metal alloys has been performed in this study, and a new methodology for the accurate prediction of fatigue damage is proposed. a wide variety of uniaxial, torsional, proportional and non-proportional load-paths has been used to simulate complex, real-world loading scenarios. test data have been analyzed and a critical-plane based fatigue damage parameter has been developed. this fatigue damage parameter contains stress and strain terms, as well as a term consisting of the maximum value of the product of normal and shear stresses on the critical plane. the shear-dominant crack initiation phenomenon and the combined effect of shear and tensile stresses on micro-crack propagation have been modeled in this work. the proposed formulation eliminates many of the shortcomings of the earlier developed critical-plane fatigue damage models. it is mathematically simple with substantially fewer material dependent constants, and provides design engineers with a tool to predict the fatigue life of machine parts with minimal computational effort. this life prediction methodology is intended for a wide variety of lcf and hcf loadings on machine parts made of metals including advanced alloys. keywords. multiaxial; fatigue damage parameter; non-proportional loading. citation: suman, d., kallmeyer, a., smith, j., development of a multiaxial fatigue damage parameter and life prediction methodology for non-proportional loading, frattura ed integrità strutturale, 38 (2016) 224-230. received: 11.06.2016 accepted: 10.07.2016 published: 01.10.2016 copyright: © 2016 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. s. suman et alii, frattura ed integrità strutturale, 38 (2016) 224-230; doi: 10.3221/igf-esis.38.30 225 introduction atigue is one of the most prolific phenomena responsible for the failure of machine parts. very often, the fatigue related damage stays undiagnosed, and by the time a visible fatigue crack is detected, the structure is left with a very small number of cycles required to propagate this crack until catastrophic fracture. therefore, it is very important to understand this phenomenon, and consider it during the very early stages of the design process. although it is very convenient to assume uniaxial loading conditions and perfect machine parts with no defects or irregularities, in practice this is seldom the case, and many cyclic loading conditions create some multiaxial stress states. thus, the modeling of fatigue phenomena and the development of suitable damage methodologies is very challenging for engineers and researchers in the fatigue and fracture community. extensive review of several multiaxial fatigue theories [1-18] leads to three broad categorizations of fatigue analysis methodologies, namely equivalent stress-based, energy-based and critical plane-based models. efforts have been made by several researchers [1-4] to represent the multiaxial stress state by an equivalent uniaxial stress value using von mises or tresca type equations. however, this approach fails to adequately account for many complexities like lcf-hcf interactions and the effects of non-proportional loading. equivalent stress-based parameters often result in highly conservative fatigue life predictions with large factors of safety. unlike equivalent-stress based models, energy-based fatigue theories compute the damage by estimating the strain energy within each fatigue cycle [5-9]. critical plane-based fatigue theories [10-17] support the observation that the fatigue damage computation should be based upon the estimation of location and orientation of the crack. this approach is more convincing because it allows designers to determine the exact orientation of the fatigue crack plane to accurately make any design changes in the parts. findley [10] was one of the earliest researchers to put forth the concept of the critical plane approach; however; the findley model [10] is stress-based and thus often produces significant errors within the lcf regime. other researchers [7-9] have proposed energy based-critical plane fatigue models, but it is difficult to exactly estimate the total energy of fatigue cycles that have mean stresses [11]. brown & miller [15] developed a strain-based fatigue model, and fatemi & socie [16] developed a critical plane model that included a normal stress term for non-proportional loading. the extra hardening and softening caused by multiple normal stress subcycles on the critical plane was addressed by erickson et al. [17]. the critical-plane concept for the prediction of fatigue life of steel and titanium alloys has further been explored in this paper through a series of additional uniaxial and multiaxial fatigue tests under a wide variety of load paths. special attention has been given to the need of a strain term, and a parameter to model the interaction of shear stress and normal stress on the critical plane. the erickson et al. [17], findley [10] and fatemi-socie [16] damage parameters have also been assessed for their complexity and ability to accurately estimate the fatigue damage, and a comparatively simpler formulation has been proposed. material and methods everal material data sets were used to evaluate the accuracy of the new damage parameter, including a titanium alloy (ti-6al-4v) and nickel-based steel alloys (718 steel and rene 104). these alloys have been used extensively in gas turbine engines for military and commercial applications, and also have many applications in the automotive and electronics industries. these data sets included both uniaxial and biaxial (axial/torsion) data subjected to a wide variety of cyclic load paths. much of data were generated as part of a us air force program on high cycle fatigue, while other data sets were generated by industrial sources or taken from the literature [18]. additional details about the materials can be found in erickson et al [17]. tests were conducted using both solid and tubular specimens with highly polished inner and outer surfaces. the majority of the tests were conducted in strain control on servo-hydraulic tension/torsion load frames. some of the long-life tests were switched to load control after cyclic stabilization had occurred in order to accelerate the tests. an elastic-plastic stress strain analysis was performed using fem to calculate the stresses on the outer surface of the specimens, using measured strains as input. this analysis utilized cyclically stabilized stress-strain curves for each material, which were generated from the half-life hysteresis loops recorded from the uniaxial fatigue tests. separate curves were generated for both r = -1 and r = 0 loading conditions. a wide variety of cyclic load paths were used in generating the fatigue data sets, including uniaxial, torsion, and combined axial/torsion. the biaxial tests included both proportional and non-proportional load paths, as illustrated schematically in fig. 1. when both axial and shear stresses (strains) remain linearly proportional to one another throughout the cycle, the f s s. suman et alii, frattura ed integrità strutturale, 38 (2016) 224-230; doi: 10.3221/igf-esis.38.30 226 loading is considered proportional. in contrast, under non-proportional loading, the axial and shear stresses (strains) do not maintain a constant ratio during the load cycle. this causes the principle stress planes to rotate during the cycle, which has been observed to cause additional cyclic hardening or softening in some metals [16]. such load paths also make the prediction of fatigue life more challenging. the non-proportional load paths shown in fig. 1 were designed to provide discriminating test conditions for evaluating the critical plane parameters. specifically, the “check” path and “box” path simulated actual loading scenarios experienced in aircraft engine components, whereas the “triangle” path, “s” path, and “double check” path were designed to produce varying combinations of normal-stress “subcycles” on the shear-based critical plane. the critical-plane stresses are discussed in more detail in the following sections. figure 1: multiaxial load paths considered in this study. damage parameter development for life estimation critical plane analysis s previously mentioned, the critical plane method allows designers to compute the fatigue damage on the crack plane; however, the identification of the critical plane is dictated by several factors including load level, load type, load path, and the behavior of the material. similarly, the definition of the critical plane itself may vary among different researchers, and various proposals can be found throughout the literature. many researchers define the critical plane as the plane possessing the maximum value of the damage parameter, whereas others have used the plane on which a particular stress or strain component (such as the normal or shear stress range) is maximized. in this work, the latter definition was adopted, with the maximum shear stress range used to identify the orientation of the critical plane. this definition was established after thorough analysis of a large amount of uniaxial and multiaxial fatigue data from high strength steel and titanium alloys. in comparing the correlation of the data sets from different parameters (described below) calculated on the maximum shear plane and the plane of maximum damage parameter, the differences were found to be very small. additionally, using the maximum shear plane as the critical plane significantly reduces the mathematical computation (as it is easier to identify), and also makes optimization of the material constants needed by each parameter much simpler. it should also be noted that the critical plane definition proposed in this paper is for constant amplitude fatigue cycles, and may not be appropriate for variable amplitude loading cases because the orientation of the critical plane may change from cycle to cycle. critical plane damage computations several well-accepted damage parameters were initially used to model the fatigue damage in the data sets mentioned above; however, the findley parameter [10], fatemi & socie parameter [16], and erickson et al. parameter [17] were found to provide better correlations between experimental and predicted fatigue lives for all the data sets, and thus are presented in detail in this paper. these damage parameters are expressed in the equations below: findley (eq. 1), fatemi & socie (eq. 2), and erickson et al. (eq. 3). a maxdp τ  kσ  (1) max max n y γ σ dp 1 k 2 σ          (2) a s. suman et alii, frattura ed integrità strutturale, 38 (2016) 224-230; doi: 10.3221/igf-esis.38.30 227 ww w21 3 max minmin min max 2 max max y max k σ k στ σ dp τ 1 1 k σ 1 τ σ σ                       (3) for each model, the stress and strain values on the surface of the specimen were taken from the finite element analysis and considered as the values on the zero degree plane. these values were rotated in 1-degree increments onto all possible planes to identify the critical (maximum shear) plane. the material constants required by each model were optimized using a leastsquares process to minimize the error between predicted and experimental lives for each data set. a double power-law type of formulation was assumed to relate the dp value to the fatigue life, n, as shown in eq. 4. b ddp an cn  (4) the initial model evaluations were performed using a large set of uniaxial and biaxial ti-6al-4v fatigue data. the resulting correlations of the data set using each model are shown in fig. 2. (a) findley [10] (b) fatemi & socie [16] (c) erickson et al. [17] figure 2: correlation of ti-6al-4v fatigue data using three different models. it can be observed that the best correlation of all the uniaxial, proportional and non-proportional fatigue data has been achieved by computing the damage with the erickson et al. model. the findley parameter and fatemi & socie parameter provided good correlation for most of the uniaxial and proportional test data; however, both of these parameters failed to collapse some of the non-proportional fatigue data along the best-fit curve. it is to be noted that the fatemi & socie parameter has a shear strain term which allows it to better account for the plasticity in the short-life (lcf) regime, relative to the findley parameter. similarly, erickson et al.’s model accounts for the strain-hardening effects, as well as the damage caused by multiple normal-stress “subcycles” on the critical plane, by summing the damage caused by these subcycles. this parameter was clearly superior in its ability to correlate the non-proportional test data. development of new damage parameter while all three damage parameters possess both normal and shear components to model the fatigue damage, the erickson et al. [17] formulation (eq. 3) contains extra terms in an effort to account for additional subtleties that may arise in nonproportional load paths. the first term, comprised of maximum and minimum values of shear stress, can account for the effect of mean shear stresses. the second term is designed to model the effect of the normal stress on the critical plane, while the third term has been introduced to capture the additional damage from multiple normal-stress subcycles on the critical plane. despite the fact that this parameter captures many factors that contribute towards the nucleation of a fatigue crack, this model is very complex and has altogether six material dependent constants. the optimization of these constants requires extensive computations and a large volume of data. in an effort to better understand the effects of normal-stress subcycles on the critical (maximum shear) plane, a series of specialized tests were designed to vary the number and timing of these subcycles, relative to the major shear cycle. the tests were designed in such a way that after rotating the stresses onto the critical plane, they produced identical shear stress cycles and one or more normal stress subcycles. these tests were performed on a different material, da 718, for which a significant amount of uniaxial and proportional fatigue data was also available. s. suman et alii, frattura ed integrità strutturale, 38 (2016) 224-230; doi: 10.3221/igf-esis.38.30 228 proportional, nf = 36,078 s-path, nf = 34,816 triangle path, nf = 176,559 check path, nf = 168,803 double check, nf = 141,421 figure 3: critical plane stresses for the tests conducted on da 718. the critical-plane shear and normal stresses from these specialized tests are shown in fig. 3, along with the resulting fatigue lives. note that for all the tests, the shear stress cycles and normal stress cycles were nearly identical in magnitude; consequently, the differences in fatigue lives can be attributed to the number and positioning of the normal stress subcycles on the critical plane. of particular interest is the fact that the proportional and s-path tests had similar lives, despite the fact the s-path contained three subcycles in comparison to one in the proportional test. this would indicate that the number of subcycles is of less importance than the magnitude. in comparing the triangle, check, and double-check tests, it is evident these tests also had similar lives (within expected scatter), but the lives were over four times longer than the proportional and s-path tests even though the normal stress cycles were similar in magnitude. the difference in the three latter tests was that the peak normal stress did not occur at the same time as the peak shear stress; i.e., the normal and shear cycles were offset. this again indicates a negligible effect from the number of subcycles, but a very large influence from the timing of a subcycle. in other words, when the normal stress cycle peaks simultaneously with the shear cycle, significantly more damage occurs, resulting in a shorter life. based on these observations, it was concluded that the erickson parameter does not accurately model the fatigue damage in complex, multiaxial load paths. specifically, the subcycle summation term is unnecessary. however, a different term is needed to model the interaction between the shear and normal stresses on the critical plane. a new critical-plane parameter that eliminates many of the shortcomings of the previous models is shown in eq. 5. this parameter makes use of the shear strain range (  ) multiplied by the maximum shear stress in order to capture the effects of strain hardening in the lcf regime and mean shear stresses in the hcf regime. the effect of the interaction between normal and shear stresses on the critical plane is accounted for by the product of these stresses in the secondary multiplicative term. the value of σo in this equation is arbitrary, and simply used to maintain unit consistency. note also that the parameter contains only two material-dependent constants (k and w), relative to the six required by the erickson model. thus, this parameter requires substantially less computational effort to fully implement in comparison to the erickson model.      w 1 w max max 2 o σ τ dp =  g γ τ 1 k σ          (5) the application of this new parameter to the ti-6al-4v data set referenced in fig. 2 is shown below in fig. 4(a). in comparing this plot with the one shown in fig. 2(c), it is evident the new parameter provides a similarly excellent correlation of both the uniaxial and multiaxial fatigue data throughout the full lcf/hcf spectrum. a second set of fatigue data, taken s. suman et alii, frattura ed integrità strutturale, 38 (2016) 224-230; doi: 10.3221/igf-esis.38.30 229 from the thesis of morrow [18], is shown in fig. 4(b). this data set includes uniaxial, torsional, proportional and nonproportional multiaxial data from an in 718 alloy. it can be seen that the new parameter also collapses this data set extremely well to a single curve, providing further evidence of its ability to predict fatigue lives in a variety of materials and load paths. (a) (b) figure 4: proposed damage parameter applied to (a) ti-6al-4v and (b) in 718 [18]. conclusion new critical-plane damage parameter for the prediction of fatigue life under multiaxial loading has been presented. this new parameter has been evaluated using a significant amount of fatigue data from several high strength titanium and steel alloys, and found to provide excellent correlation of the data. the parameter can account for strain hardening in the lcf regime, and the effect of mean stresses in the hcf regime. the parameter is computationally inexpensive and requires determination of only two material constants. references [1] gough, h.j., polland, h.v., clenshaw, w.j., some experiment on the resistance of metals under combined stress, aeronautical research council report and memoranda no. 2522, hmso, london, (1951). [2] stulen, f.b., cummings h.n., a failure criterion for multiaxial fatigue stresses, proc. of astm, 54 (1954) 822-830. [3] sines, g., waisman, j.l., metal fatigue, mcgraw-hill, new york, (1959). [4] stephens, r.i., fatemi, a., stephens, r.r., fuchs, h.o., metal fatigue in engineering, second ed., john wiley & sons, new york, (2001). [5] garud, y.s., a new approach to the evaluation of fatigue under multiaxial loadings, j. eng. mater. technol., 103 (1981) 118-125. [6] ellyin, f., valaire, b., high-strain multiaxial fatigue, j. eng. mater. technol. 104 (1982) 165-173. [7] glinka, g., wang, g., plumtree, a., mean stress effect in multiaxial fatigue, fatigue fract. eng. mater. struct., 18 (1995) 755-764. [8] farahani, a.v., a new energy-critical plane parameter for fatigue life assessment of various metallic materials subjected to in-phase and out-of-phase multiaxial fatigue loading conditions, int. j. fat., 22 (2000) 295-305. [9] pan, w.f., hung, c.y., and chen, l.l., fatigue life estimation under multiaxial loading, int. j. fat., 21 (1999) 3-10. [10] findley, w.n., a theory for the effect of mean stress on fatigue of metals under combined torsion and axial load or bending, j. eng. ind., (1959) 301-306. [11] findley, w.n., effect of range of stress on fatigue of 76s-t61 aluminum alloy under combined stresses which produce yielding, j. appl. mech., (1953) 365-374. [12] mcdiarmid, d.l., a general criterion for high cycle multiaxial fatigue failure, j. fat. fract. eng. mater. struct., 14 (1991) 429-453. [13] matake, t., explanation of fatigue limit under combined stress, bulletin of the jsme, 20 (1977) 257-264. a s. suman et alii, frattura ed integrità strutturale, 38 (2016) 224-230; doi: 10.3221/igf-esis.38.30 230 [14] carpinteri, a., spagnoli, a., multiaxial high cycle fatigue criterion for hard metals, int. j. fat., 23 (2001) 135-145. [15] brown, m., miller, k., a theory for fatigue failure under multiaxial stress-strain condition, proc. of ime 187, (1973) 745-755. [16] fatemi, a., socie, d., a critical plane approach to multi-axial fatigue damage including out-of-phase loading, j. fat. fract. eng. mater. struct., 11 (1988) 149-165. [17] erickson, m., kallmeyer, a.r., vanstone, r.h., kurath, p., development of a multiaxial fatigue damage model for high strength alloys using critical plane methodology, j. eng. mater. technol., 130 (2008) 1-9. 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can be opened with acrobat and adobe reader 5.0 and later.) >> /namespace [ (adobe) (common) (1.0) ] /othernamespaces [ << /asreaderspreads false /cropimagestoframes true /errorcontrol /warnandcontinue /flattenerignorespreadoverrides false /includeguidesgrids false /includenonprinting false /includeslug false /namespace [ (adobe) (indesign) (4.0) ] /omitplacedbitmaps false /omitplacedeps false /omitplacedpdf false /simulateoverprint /legacy >> << /addbleedmarks false /addcolorbars false /addcropmarks false /addpageinfo false /addregmarks false /convertcolors /converttocmyk /destinationprofilename () /destinationprofileselector /documentcmyk /downsample16bitimages true /flattenerpreset << /presetselector /mediumresolution >> /formelements false /generatestructure false /includebookmarks false /includehyperlinks false /includeinteractive false /includelayers false /includeprofiles false /multimediahandling /useobjectsettings /namespace [ (adobe) (creativesuite) (2.0) ] /pdfxoutputintentprofileselector /documentcmyk /preserveediting true /untaggedcmykhandling /leaveuntagged /untaggedrgbhandling /usedocumentprofile /usedocumentbleed false >> ] >> setdistillerparams << /hwresolution [2400 2400] /pagesize [612.000 792.000] >> setpagedevice microsoft word numero_41_art_40.docx g. meneghetti et alii, frattura ed integrità strutturale, 41 (2017) 299-306; doi: 10.3221/igf-esis.41.40 299 focused on crack tip fields the heat energy dissipated in a control volume to correlate the crack propagation rate in stainless steel specimens g. meneghetti, m. ricotta university of padova, italy giovanni.meneghetti@unipd.it, http://orcid.org/0000-0002-4212-2618 mauro.ricotta@unipd.it, http://orcid.org/0000-0002-3517-9464 abstract. metallic materials dissipate thermal energy when subjected to fatigue. some of them, due a favorable combination of thermo-physical material properties, exhibit a significant temperature rise, which can be easily measured in-situ by means of thermocouples or infrared cameras. the heat energy dissipated in a unit volume of material per cycle (the q parameter) has proven to be effective as a fatigue damage index in case of aisi 304l plain and notched specimens. originally conceived and applied as a point-related quantity, recently q has been averaged at the tip of propagating fatigue cracks (the q* parameter) in order to correlate crack growth data gathered from fracture mechanics tests. the use of q* seems interesting because (i) it can be evaluated in-situ from infrared temperature maps and (ii) crack acceleration due to excessive plasticity is likely to be accounted for. keywords. fracture mechanics; crack tip plasticity; energy methods; fatigue; temperature. citation: meneghetti, g., ricotta, m., the heat energy dissipated in a control volume to correlate the crack propagation rate in stainless steel specimens, frattura ed integrità strutturale, 41 (2017) 299-306. received: 28.02.2017 accepted: 03.05.2017 published: 01.07.2017 copyright: © 2017 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. introduction n the last years the authors proposed [1] to use the heat energy to rationalise the fatigue behaviour of plain and bluntly notched specimens made of aisi 304l stainless steel subjected to push-pull, constant amplitude [2,3] and two load level [4] fatigue tests. the mean stress influence in fatigue has also been taken into account [5]. the proposed approach assumes the heat energy dissipated in a unit volume of material per cycle, q, as a fatigue damage index, that can be readily evaluated by means of temperature measurements performed at the crack initiation point. originally conceived and applied as a point-related quantity, q can hardly correlate fatigue test results generated from cracked specimens. rather, it should be averaged inside a material dependent structural volume vc [6]. the approach is sketched in fig. 1a. in a previous paper it was demonstrated that the specific energy per cycle dissipated as heat is approximately equal to the plastic strain hysteresis energy, which drives fatigue crack propagation according to ref. [7]. i g. meneghetti et alii, frattura ed integrità strutturale, 41 (2017) 299-306; doi: 10.3221/igf-esis.41.40 300 figure 1: a propagating fatigue crack and the assumed shape of the structural volume vc where the heat energy is to be averaged (a) and time-variant temperature for i-th pixel (b). the averaged heat energy generated inside the structural volume can be evaluated as follows:   cdc s cd clv c c * dsh vf dvq v q 11 (1) where h is the heat flux existing at a point along the boundary of vc, scd, through which heat energy is extracted by conduction. it is worth noting that eq. (1) is valid under the hypothesis that the heat is extracted from vc only by conduction, which is not true, strictly speaking. however, it has been demonstrated that conduction is by far the most active heat dissipation mechanism in standard laboratory testing conditions [8]. the heat flux can be evaluated from the thermal gradients calculated from infrared temperature maps; therefore, referring to a two-dimensional problem, eq. (1) can be written as follows [8]:                  * ( , )1 m c l c r rc t r q z r d f v r (2) tm(r,) being the mean temperature, measured when the thermal equilibrium with surroundings is reached. fig. 1b reports a typical temperature vs time acquisition at a point of a specimen or component after a fatigue test has started. if the temperature field is monitored by means of an infrared camera, fig. 1b is the pixel-by-pixel temperature vs time history and it shows that temperature increases until the mean temperature level stabilizes, while the alternating component due to the thermoelastic effect still exists. if we consider a sampling window taken after thermal equilibrium with the surroundings is achieved (between ts and t* in fig. 1b), the mean temperature tim for i-th pixel is defined as follows:    max 1 max n i j ji m t t n (3) where tji are the temperature data acquired at a sampling rate facq and nmax= facq·(t*ts) is the number of picked-up samples between the time ts (j=1) and the time t* (j=nmax). eq. (2) is based on the radial temperature gradient, therefore it has been referred as spatial gradient technique. an alternative method to evaluate q* has also been proposed, which is based on the cooling gradient measured after the machine test has been stopped and therefore it has been referred as cooling gradient technique [8]. however, the latter method has not been applied here. the aim of the present paper is to use the parameter q* to correlate crack growth data generated from tensioncompression axial fatigue tests on specimens machined from 4-mm-thick, hot-rolled aisi 304l steel plates. the plan of t ji time tim thermoelastic oscillations ts t* tia nmax/facq (b)(a) g. meneghetti et alii, frattura ed integrità strutturale, 41 (2017) 299-306; doi: 10.3221/igf-esis.41.40 301 the paper is as follows: to estimate the structural volume size rc, to present the crack growth experiments and temperature measurements and finally to use q* as crack driving force. material and testing methods pecimens were prepared from 4-mm-thick, hot-rolled aisi 304l stainless steel specimens. the mechanical properties and the chemical composition are reported in tab. 1. rp0.2% (mpa) rm (mpa) a (%) a-1 (mpa) hb c (%) mn (%) si (%) cr (%) ni (%) p (%) s (%) n (%) 279 620 57 202 170 0.026 1.470 0.370 18.100 8.200 0.034 0.001 0.058 table 1: mechanical properties and chemical composition of the aisi 304l stainless steel. the specimens’ geometry is reported in fig. 2a-b, which shows the crack starter, consisting of a sharp, 8-mm-deep vnotch. both specimens’ surfaces were polished by means of emery papers starting from grade 80 up to grade 4000; afterwards, a black paint was applied to one specimen’s surface in order to increase the emissivity in view of the infrared thermal measurements. push-pull (r=-1), constant amplitude, load controlled crack propagation tests were conducted on a servo-hydraulic schenck hydropuls psa100 fatigue test machine equipped with a triosistemi rt3 digital controller (load capacity 100 kn). load frequencies ranging between 4 and 40 hz were adopted, depending on the applied stress level. after a fatigue test started, a crack initiated at the notch tip and it was propagated to a total initial crack length of approximately a=9 mm (according to fig. 1a). afterwards, crack growth experiments started. the temperature field was measured by means of a flirsc7600 infrared camera, having a 50-mm focal lens and equipped with an analog input interface, which was used to synchronize the force signal coming from the load cell with the temperature signal measured by the infrared camera. the infrared camera had a spectral response range from 1.5 to 5.1 m, a noise equivalent temperature difference (netd) < 25 mk, and operated at a frame rate facq equal to 200 hz. a 30-mm spacer ring was adopted to improve the spatial resolution up to 20 or 23 m/pixel. as a result, the field of view (fov) was reduced to 320x256 pixels, which corresponds to a minimum of 6.4 mm x 5.1 mm and a maximum of 7.4 mm x 5.9 mm. figure 2: specimen’s geometry (rn=0.1 mm for 2=45°, rn=0.15 mm for 2=90°; thickness is 4 mm; dimensions in mm) (a,b) and aisi 304l austenitic microstructure (c). in order to evaluate q* at a given crack length during the fracture mechanics experiments, a trigger signal was manually sent to the infrared camera to start the acquisition of the thermal images at a frame rate facq=200hz for a duration of 5s, translating into 1000 acquired images. such temperature maps were first processed by using the flir motionbyinterpolation tool to allow for the relative motion compensation between the fixed camera lens and the moving specimen subject to cyclic loads (the displacements to compensate ranged from 6 to 20 pixels within the fov, depending on the stiffness of the specimen). to perform successfully the motion compensation, the force signal coming from the load cell must be sampled synchronously with the thermal images. after that, the spatial distribution of the mean temperature tm(r,) was calculated by averaging the available 1000 temperature maps according to eq. (3) and by means of the altair 5.90.002 commercial software; finally, the q* parameter was evaluated by applying eq.(2). the crack length was measured by means of a am4115zt dino-lite digital microscope operating with a magnification ranging from 20x to 220x. the microscope and the infrared camera monitored the opposite surfaces of the specimens; in s 2 150 2l=90 machine grip machine grip 8 w = 46 a (a) rn 2 + (b) 50 m (c) g. meneghetti et alii, frattura ed integrità strutturale, 41 (2017) 299-306; doi: 10.3221/igf-esis.41.40 302 particular, the microscope images were used to single-out the crack tip position, which was subsequently reported in the infrared thermal images. a total number of 10 specimens was fatigue tested. the structural volume size vc he experimental procedure to evaluate the structural volume size rc (see fig. 1a) was a tricky point, which was tackled in [9] and is summarized here. the underlying concept to evaluate the structural volume size rc, thought of as a material property for a given applied nominal load ratio, is widely adopted in notch fatigue [6,10-14] and, if formalized in the present case, it states that the averaged energy q* must be the same at the conventional fatigue limit, whatever the geometrical features involved. alternatively stated, the characteristic energy q* at the fatigue limit of a plain and a notched (either blunt or severe) specimen must be the same. figure 3: temperature field for a specimens having a 9.803-mm-long crack (see crack length definition ‘a’ in fig. 1a), loaded at k=32.7 mpa·m0.5, fl=35 hz (a), and microscope image of the fatigue crack taken on the opposite surface (b). figure 4: radial temperature profile (a) and specific heat flux distribution measured along the boundary of vc (b), during tensioncompression fatigue test with a=9.803 mm, k=32.7 mpa·m0.5, fl=35 hz. unfortunately, at the fatigue limit of the present cracked specimens, the thermal rise close to the crack tip was vanishingly small in relation to the thermal accuracy of the available infrared camera. therefore, calibration of rc was performed at a fixed finite-life, rather than at the fatigue limit. the chosen reference fatigue life was on the order of 105 cycles and the calibration procedure is explained in the following with reference to a single fatigue test. a specimen was pre-cracked to obtain a total crack length a=9.803 mm (according to fig. 1a). fig. 3a shows the temperature field calculated by averaging the 1000 available frames, after the motion compensation algorithm has been applied. the crack tip position (see fig. 3b) could be determined from the digital microscope image captured on the opposite surface. the number of cycles to 308,8 309 309,2 309,4 309,6 309,8 310 0,000 0,001 0,002 0,003 0,004 t m [k ] r [m] -51.9 k/m r=rc 0° rc = 5.2·10 -4 m fl = 35 hz  16 w/(m·k) k = 32.7 mpa·m0.5 (a) -90.0° -112.5° -135.0° -157.5° 180.0° 157.5° 135.0° 112.5° 90.0° 67.5° 45.0° 22.5° 0.0° -22.5° -67.5° -45.0° h [w/m2] 102 10 103 104 105 t (a) (b) 1 mm  2rc (b) crack tip g. meneghetti et alii, frattura ed integrità strutturale, 41 (2017) 299-306; doi: 10.3221/igf-esis.41.40 303 separate the specimen starting from the configuration shown in fig. 3 was nf=69840 cycles. the relevant temperature profile evaluated at =0° and the heat flux h calculated along the boundary of vc are reported in fig. 4a and fig. 4b, respectively. for the same fatigue life, the characteristic energy of plain specimens made of the same material and loaded with the same load ratio can be found in ref. [15], to which the reader is referred, and is equal to q=q*=0.66 mj/(m3•cycle). as a final step, the control radius rc was iteratively varied in fig. 3a until the averaged heat loss q* calculated inside vc by means of spatial gradient technique – eq. (2) was equal to the characteristic value 0.66 mj/(m3•cycle). the result was rc=0.65 mm. by repeating such a procedure using additional three specimens, the results reported in tab. 2 were obtained, where a mean value rc=0.52 mm was calculated. a(1) (mm) nf (/) q*(2) (mj/(m3 cycle)) k (mpa√m) rc(1) (mm) 9.803 69840 0.66 32.7 0.65 19.035 82001 0.61 33.0 0.45 14.969 62221 0.69 35.0 0.42 8.475 46263 0.80 38.0 0.55 mean value 0.52 (1) see fig. 1a; (2) from eq. (2) table 2: experimental value of the structural volume size of the aisi 304l stainless steel tested in uniaxial tension-compression fatigue. fig. 5 shows, as an example, the distribution of the specific energy flux per cycle q measured along the boundary of vc (rc=0.52 mm) at different applied k values; q is obtained by simply dividing h by fl.. figure 5: distribution of the specific energy flux per cycle q along the boundary of structural volume vc at different k values (specimen v_45_r01_17). crack growth data ig. 6a shows a typical crack configuration captured by the digital microscope during a fatigue test. the raw crack propagation data are shown in fig. 6b. having the crack length vs the number of cycles, the crack growth rate da/dn was calculated. the peak stress method [16] was adopted to evaluate the mode i stress intensity factor -90.0° -112.5° -135.0° -157.5° 180.0° 157.5° 135.0° 112.5° 90.0° 67.5° 45.0° 22.5° 0.0° -22.5° -67.5° -45.0° dk= 40.86 dk= 51.03 dk= 92.88 105 q [j/(m2cycle)] 10 103 104 k=40.9 mpa·m k=51.3 mpa·m k=92.9 mpa·m f g. meneghetti et alii, frattura ed integrità strutturale, 41 (2017) 299-306; doi: 10.3221/igf-esis.41.40 304 (sif) range, k=kmax-kmin, for different crack lengths. in view of this, linear elastic, two-dimensional, finite element analyses were performed by using the 4-node solid182 element of ansys® commercial code. to account for the machine grip effect, displacements were applied in the numerical model to the appropriate lines shown in fig. 2a. figure 6: a fatigue crack observed during the tension-compression fatigue tests, (a=25.60 mm, k=61.77 mpa·m0.5, fl=30 hz) (a) and crack propagation data (b). figure 7: crack growth rates vs k (a) and q* evaluated by using rc=0.52 mm (b). fig. 7a shows the paris curve of aisi 304l stainless steel, along with the 10%-90% scatter band and the crack growth rate scatter index tda/dn (tda/dn=4.00), calculated under the hypothesis of log-normal distribution of da/dn. in the same figure, a vertical band defined by two dashed vertical lines is reported, on the left hand side of which all data points satisfy the conditions of applicability of the lefm according to eq.4 [17], while on the right hand side of the band they do not:            2 ' ,02 4 ,( ), 2 p k a w a l (4) where a is the crack length, w the specimen width (w=46 mm, see fig. 2a), 2l the specimen length (2l=90 mm, see fig. 2a) and 'p,02 the cyclic engineering proof stress equal to 265 mpa [9]. the data that did not satisfy the condition of applicability of the lefm were not included in the statistical analysis reported in fig. 7a. one can note that on the right 8 10.5 13 15.5 18 20.5 23 25.5 28 30.5 33 35.5 38 1.e+02 1.e+03 1.e+04 1.e+05 1.e+06 a [m m ] n, number of cycles v_45_r01_14 v_45_r01_16 v_45_r01_17 v_45_r01_18 v_90_r015_3 v_90_r015_4 v_90_r015_5 v_90_r015_6 v_90_r015_7 v_90_r015_8 (b) 10 100 da /d n [ m /c yc le ] k [mpa ·m0.5] comply with lefm, eq. 4 do not comply with lefm, eq. 4 10-8 10-7 10-6 10-5 10-4 500 tda/dn=4.00 (a) 0.1 1 10 100 1000 da /d n [ m /c yc le ] q* [mj/(m3·cycle)] comply with lefm, eq. 4 do not comply with lefm, eq. 4 10-8 10-7 10-6 10-5 10-4 tda/dn=3.34 (b) rc=0.52 mm (a) 2 mm g. meneghetti et alii, frattura ed integrità strutturale, 41 (2017) 299-306; doi: 10.3221/igf-esis.41.40 305 hand side of the band included by the vertical lines, crack acceleration occurs, which was interpreted as the effect of the excessive plasticity around the crack tip [18]. synthesis based on the averaged dissipated energy q* he same crack growth data previously plotted in fig. 7a are shown in fig. 7b. in this case, q*, calculated using rc=0.52 mm combined with the spatial gradient technique eq. (2), was assumed as driving force for crack propagation. fig. 7b reports the mean curve, the 10%-90% survival probability scatter bands and the scatter index tda/dn. the crack growth rates can be rationalized with a higher level of accuracy using the averaged heat energy q*, rather than the range of the linear elastic mode i sif k. conclusions n this paper, the specific heat energy per cycle averaged in a structural volume surrounding the crack tip, q*, was used as a fatigue parameter to correlate the crack growth data generated from 4-mm-thick, hot rolled aisi 304l stainless steel specimens, tested in fully reversed tension-compression fatigue . the size of the structural volume was defined by equaling the averaged heat energy in cracked and smooth specimens for the same fatigue life and it was found equal to 0.52 mm. the crack growth data were plotted in terms of range of the linear-elastic mode i stress intensity factor, k, as well as q*. when presented in terms of k, a 10%-90% survival probability scatter band calibrated on crack growth data complying with the conditions of applicability of the lefm was determined; however, as it is well known, crack acceleration is observed at progressively higher applied k values. conversely, by using the averaged heat energy q*, all crack growth data (irrespective of the applied k) fall within a single 10%-90% survival probability scatter band having the same scatter index of the k-based one. this outcome is interpreted with the intrinsic nature of the energy q*, which accounts for crack acceleration due to excessive plasticity occurring at increasingly higher applied k values. acknowledgments his work was carried out as a part of the project code cpda145872 of the university of padova. the authors would like to express their gratitude for financial support. references [1] meneghetti, g., analysis of the fatigue strength of a stainless steel based on the energy dissipation, int. j. fatigue, 29 (2007) 81–94. doi: 10.1016/j.ijfatigue.2006.02.043. [2] meneghetti, g., ricotta, m., the use of the specific heat loss to analyse the lowand high-cycle fatigue behaviour of plain and notched specimens made of a stainless steel. eng. fract. mech., 81 (2012) 2–17. doi: 10.1016/j.engfracmech.2011.06.010. [3] meneghetti, g., ricotta, m., atzori, b., a synthesis of the push-pull fatigue behaviour of plain and notched stainless steel specimens by using the specific heat loss. fatigue fract. eng. mater. struct., 36 (2013) 1306-1322. doi: 10.1111/ffe.12071. [4] meneghetti, g., ricotta, m., atzori, b., experimental evaluation of fatigue damage in two-stage loading tests based on the energy dissipation. proc imeche part c: j mechanical engineering science, 229 (2015) 1280-1291. doi: 10.1177/0954406214559112. [5] meneghetti, g., ricotta, m., atzori, b., a two-parameter, heat energy-based approach to analyse the mean stress influence on axial fatigue behaviour of plain steel specimens. int j fatigue, 82 (2016) 60-70. doi: 10.1016/j.ijfatigue.2015.07.028. [6] neuber, h., über die berücksichtigung der spannungskonzentration bei festigkeitsberechnungen. konstruction 20 (1968) 245-251. t i t g. meneghetti et alii, frattura ed integrità strutturale, 41 (2017) 299-306; doi: 10.3221/igf-esis.41.40 306 [7] klingbeil, nw., a total dissipated energy theory of fatigue crack growth in ductile solids. int j fatigue, 25 (2003) 117– 128. [8] meneghetti, g., ricotta, m., evaluating the heat energy dissipated in a small volume surrounding the tip of a fatigue crack. int. j. fatigue, 92 (2016) 605-615. doi: 10.1016/j.ijfatigue.2016.04.001. [9] meneghetti, g., ricotta, m., rigon, d., the heat energy dissipated in a control volume to correlate the fatigue strength of severely notched and cracked stainless steel specimens. proceedings of fatigue 2017, 3-5 july 2017, cambridge (uk). [10] peterson, re., notch sensitivity, in: g. sines and j. l. waisman (eds.) metal fatigue, macgraw-hill, new york, (1959) 293-306. [11] tanaka, k., engineering formulae for fatigue strength reduction due to crack like notches. int j fract, 22 (1983) r39– 46. [12] sheppard, sd., field effects in fatigue crack initiation: long life fatigue strength. trans asme, journal of mechanical design, 113 (1991) 188-94. [13] taylor, d., geometrical effects in fatigue: a unifying theoretical model. int j fatigue 21 (1999) 413–20. [14] lazzarin, p., zambardi, r., a finite-volume-energy based approach to predict the static and fatigue behavior of components with sharp v-shaped notches, int j fract 112 (2001) 275–98. [15] meneghetti, g., ricotta, m., atzori, b., the heat energy dissipated in a control volume to correlate the fatigue strength of bluntly and severely notched stainless steel specimens, structural integrity procedia, 2 (2016) 2076-2083. [16] meneghetti, g., lazzarin, p., significance of the elastic peak stress evaluated by fe analyses at the point of singularity of sharp v-notched components, fatigue fract. eng. mater. struct, 30 (2007) 95-106. doi: 10.1111/j.1460-2695.2006.01084.x [17] dowling, n.e., mechanical behavior of materials, pearson prentice hall (2007). [18] tanaka, k., takahash, h., akiniwa, y., fatigue crack propagation from a hole in tubular specimens under axial and torsional loading, int j fatigue 28 (2006) 324-334. doi: 10.1016/j.ijfatigue.2005.08.001 nomenclature a: notch depth plus notch-emanated crack length [mm] a%: percent deformation after fracture facq: sample rate of the infrared camera [hz] fl: load test frequency [hz] h: specific heat flux [w/m2] hb: brinell hardness k, k: stress intensity factor, its range [mpam] q: specific energy flux per cycle [j/(m2·cycle)] q, q*: specific heat energy per cycle, its average value inside vc [j/(m3·cycle)] rn: notch radius [mm] r: nominal stress ratio (ratio between the minimum and the maximum applied nominal stress) rc: radius of structural volume vc [m] rp,02: engineering proof stress [mpa] rm: engineering tensile strength [mpa] scd: external surface of control volume through which heat q is transferred by conduction [m2] ta: amplitude of temperature oscillations [k] tm: material temperature averaged over time [k] vc: structural volume [m3] z: specimen thickness [m]  notch opening angle [rad] : material thermal conductivity [w/(mk)] a-1: plain material fatigue limit for r=-1 [mpa] (obtained from a stair-case sequence at 107 cycles)  ' ,02p : cyclic engineering proof stress [mpa] << /ascii85encodepages false /allowtransparency false /autopositionepsfiles true /autorotatepages /none /binding /left /calgrayprofile (dot gain 20%) /calrgbprofile (srgb iec61966-2.1) /calcmykprofile (u.s. web coated \050swop\051 v2) /srgbprofile (srgb iec61966-2.1) /cannotembedfontpolicy /error /compatibilitylevel 1.4 /compressobjects /tags /compresspages true /convertimagestoindexed true /passthroughjpegimages true /createjobticket false /defaultrenderingintent /default /detectblends true /detectcurves 0.0000 /colorconversionstrategy /cmyk /dothumbnails false /embedallfonts true /embedopentype false /parseiccprofilesincomments true /embedjoboptions true 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/hrv (za stvaranje adobe pdf dokumenata najpogodnijih za visokokvalitetni ispis prije tiskanja koristite ove postavke. stvoreni pdf dokumenti mogu se otvoriti acrobat i adobe reader 5.0 i kasnijim verzijama.) /hun 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can be opened with acrobat and adobe reader 5.0 and later.) >> /namespace [ (adobe) (common) (1.0) ] /othernamespaces [ << /asreaderspreads false /cropimagestoframes true /errorcontrol /warnandcontinue /flattenerignorespreadoverrides false /includeguidesgrids false /includenonprinting false /includeslug false /namespace [ (adobe) (indesign) (4.0) ] /omitplacedbitmaps false /omitplacedeps false /omitplacedpdf false /simulateoverprint /legacy >> << /addbleedmarks false /addcolorbars false /addcropmarks false /addpageinfo false /addregmarks false /convertcolors /converttocmyk /destinationprofilename () /destinationprofileselector /documentcmyk /downsample16bitimages true /flattenerpreset << /presetselector /mediumresolution >> /formelements false /generatestructure false /includebookmarks false /includehyperlinks false /includeinteractive false /includelayers false /includeprofiles false /multimediahandling /useobjectsettings /namespace [ (adobe) (creativesuite) (2.0) ] /pdfxoutputintentprofileselector /documentcmyk /preserveediting true /untaggedcmykhandling /leaveuntagged /untaggedrgbhandling /usedocumentprofile /usedocumentbleed false >> ] >> setdistillerparams << /hwresolution [2400 2400] /pagesize [612.000 792.000] >> setpagedevice microsoft word numero_55_art_09_2903 f.k. fiorentin et al, frattura ed integrità strutturale, 55 (2021) 119-135; doi: 10.3221/igf-esis.55.09 119 focussed on structural integrity and safety: experimental and numerical perspectives fatigue behaviour of metallic components obtained by topology optimization for additive manufacturing f.k. fiorentin, b. oliveira, j.c.r. pereira, j.a.f.o. correia, a.m.p. de jesus inegi/faculty of engineering, university of porto, portugal ffiorentin@inegi.up.pt, https://orcid.org/0000-0002-7352-8637 jcpereira@inegi.up.pt, https://orcid.org/0000-0002-0412-8728 jacorreia@fe.up.pt, http://orcid.org/0000-0002-4148-9426 ajesus@fe.up.pt, https://orcid.org/0000-0002-1059-715x f. berto ntnu norwegian university of science and technology, norway filippo.berto@ntnu.no, https://orcid.org/0000-0002-4207-0109 abstract. the main goal of the present research is to propose an integrated methodology to address the fatigue performance of topology-optimized components, produced by additive manufacturing. the main steps of the component design will be presented, specially the methods and parameters applied to the topology optimization and the post-smoothing process. the simp method was applied in order to obtain a lighter component and a suitable stiffness for the desired application. in addition, since residual stresses are intrinsic to every metallic additive manufacturing process, the influence of those stresses will be also analysed. the laser powder bed fusion was numerically simulated aiming at evaluating the residual stresses the workpiece during the manufacturing process and to investigate how they could influence the fatigue behaviour of the optimized component. the effect of the built orientation of the workpiece on the residual stresses at some selected potential critical points are evaluated. the final design solution presented a stiffness/volume ratio nearly 6 times higher when compared to the initial geometry. by choosing the built orientation, it is possible impact favourably in the fatigue life of the component. keywords. metallic additive manufacturing; topology optimization; building strategy; residual stress; fatigue life prediction; multiaxial criterion. citation: fiorentin, f.k., oliveira, b., pereira, j.c.r., correia, j.a.f.o., jesus, a.m.p., berto, f., fatigue behavior of metallic components obtained by topology optimization for additive manufacturing, frattura ed integrità strutturale, 55 (2021) 119-135. received: 25.08.2020 accepted: 20.10.2020 published: 01.01.2021 copyright: © 2021 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. https://youtu.be/l3-s4gyucgu f.k. fiorentin et al, frattura ed integrità strutturale, 55 (2021) 119-135; doi: 10.3221/igf-esis.55.09 120 introduction dditive manufacturing (am) processes are creating new design opportunities for structural components, allowing structural optimization to be explored without traditional manufacturing restrictions. am processes allow a massive autonomy of design, which may result in significant reductions of weight, while maintaining the main function of the component. however, this geometrical design may have repercussions in the fatigue strength due to stress concentrations and residual stresses promoted by the thermal effects during the am process. many efforts are being dedicated to reach mechanical properties on additive manufactured components close to the conventional counterparts. right now, the am has much to evolve in order to meet the industry requirements. therefore, problems associated with costs, production speed, mechanical performance, surface quality and homogeneous microstructures have to be addressed [1]. structural optimization improves additive manufacturing benefits, since there is a perfect symbiosis between these two methods. both of these methods aim at providing freedom to the designers or engineers. the topology optimization algorithms are adapted to simulate structures with complex shapes, optimizing them to meet the desired mechanical performance. lightweight designs are a reality when these technologies are combined, reducing the amount of manufacturing operations required, but increasing the importance of the product development. fig. 1 illustrates this new product development outlook [2]. figure 1: product development process [2]. additive manufacturing does not cover a single, but a range of different technologies. these technologies can explore not only the freedom of new designs but can also process parts using several different materials. currently, am has been mostly used with polymers and metals, despite composites and ceramics are increasing their relevance too. the current processes for metals encompass methods such as binder jet, powder bed fusion (pbf), sheet lamination (sl) and directed energy deposition (ded) processes. powder bed fusion is one of the most popular mam processes. it uses a heat source to selectively melt thin layers of metal powder, welding one layer to the previous, forming a solid component. the heat source, laser or electron beams, differentiates this category into selective laser melting (slm) or selective laser sintering (sls) or laser powder bed fusion (lpbf) and electron beam melting (ebm) [3]. selective laser melting offers the opportunity to generate components with complex shapes and provides one of the best surface qualities among the am processes. during this process, a layer of powder is deposited onto a substrate and is spread by a re-coater. after that, a laser beam melts this powder according to specific process parameters (laser power, beam diameter, modulation and scan strategy). afterwards, the melted material solidifies and retracts. subsequently, a new powder layer is deposited. this process is repeated layer upon layer until the part is completed. the remaining (un-melted) powder is removed from the building chamber and most of the times it will be recycled [4][5][6]. due to the described intrinsic characteristics of the process, residual stresses are typically developed within the part, which contributes to the part distortion and would disturb the stress fields due to the external loads applied into the part. investigations related to the mechanical properties of the am parts [7] show that, comparing the microstructure of parts produced by slm with the wrought material, the elongation for wrought is usually a little bit higher. parts produced by slm are near full density and have good mechanical properties, the thermal stresses that these parts are subjected to may cause distortions and micro-cracks. during slm, the trapped gases, un-melted powder and oxidized particles lead to porosity in the component. these defects inside the material and in the surface may favour crack propagation and lead to premature failure of the component under dynamic/fatigue loads. slm process allows a wide range of materials processing, such as titanium alloys (e.g.ti-6al-4v), stainless steel, nickel-based alloys (inconel) and aluminium alloys [8][9]. the fatigue characterization of am materials has been received intensive research focus in the recent years [10–13]. nevertheless, the research about the fatigue behaviour of real components has deserved little attention, most likely due to yet limited knowledge about am material fatigue behaviour and the complex interaction between the manufacturing conceptual design topology opt. possibly shape & size opt. cad stress analysis final design a f.k. fiorentin et al, frattura ed integrità strutturale, 55 (2021) 119-135; doi: 10.3221/igf-esis.55.09 121 parameters and the structural performance of the components (e.g. residual stresses, defects, anisotropy, distortions, surface finish). in the current investigation, an integrated methodology (full process digital twin) from design to structural fatigue performance assessment is proposed and illustrated for a typical bracket part often presented in the literature as a case study for topological optimization and additive manufacturing [14][15]. the proposed design methodology will involve a first stage of topological optimization, followed by process additive manufacturing simulation and finally fatigue assessment based on process simulated residual stresses combined with stress field from external load application. methods he current section presents the problem definition and the objectives are presented which will support the presentation of the proposed methodology. in addition, the necessary analytical and numerical formulations are described, encompassing the methodologies applied for topology optimization, the residual stresses computation resulting from additive manufacturing and the formulation for the fatigue damage assessment. problem definition the proposed methodology will be demonstrated using a case study from aerospace industry, consisting of a holding support element, commonly called “bracket”. in particular, a bracket developed through topological optimization and produced thru am for the airbus a350 xwb [14][15], as shown in fig. 2, was considered in this study. this element makes part of the suspension of the flight crew rest compartments, which is attached to the primary structure of the aircraft [14][15]. this component was selected as a reference in this work for topological optimization, additive manufacturing simulation and fatigue analysis. the selection of an existing part was important, once it allows the comparison between the proposed optimization solution and the existing one for the bracket. the part dimensions, as well as the forces and boundary conditions applied, were obtained from kranz [14] and are summarized in tab. 1. despite the original bracket was built it was decided to establish the 316l stainless steel as the working material. this material presents good mechanical properties and is popular in am applications, mainly because of its excellent corrosion resistance resulting from the nickel and molybdenum contents in the alloy and excellent stability during processing [12]. the elastic and plastic hardening behaviours of the material were based on literature data, the respective parameters being presented in the tab. 2. this data was used in numerical analysis (on both the am simulations and structural analysis under cyclic load), allowing to reproduce the elastoplastic behaviour of the material, combining the isotropic and cyclic hardening of the material. however, for the optimization analysis, only the elastic analysis was used. figure 2: airbus alm/3d printing fcrc cabin bracket installation [14][15]. besides the original part has been built in aluminium alloy, it was decided to establish the 316l stainless steel as the working material. this material presents good mechanical properties and is popular in am applications, mainly because of its excellent corrosion resistance resulting from the nickel and molybdenum contents in the alloy and excellent stability during processing [16]. the elastic and plastic hardening behaviours of the material were based on literature data, the respective parameters being presented in the tab. 2. this data was used in numerical analysis (on both the am simulations and structural analysis under cyclic load), allowing to reproduce the elastoplastic behaviour of the material, combining the isotropic and cyclic hardening of the material. however, for the optimization analysis, only the elastic analysis was used as previously referred. t f.k. fiorentin et al, frattura ed integrità strutturale, 55 (2021) 119-135; doi: 10.3221/igf-esis.55.09 122 as regards the fatigue study, the relation of the applied stress range and the number of cycles to failure is described by means of the sn curve estimated for a stress ratio of r=-1, shown in fig. 3 [17]. this curve will be used later to estimate the fatigue life of the optimized part taking into account the effect of residual stresses promoted by additive manufacturing process and service load. figure 3: s-n curve of the 316l (11 hz) [17]. designation function material dimensions (mm) weight (g) fcrc-bracket load transfer al 7075 ρ=2.8g/cm3 160.56565.5 (y, z, x) 226 table 1: technical data of the original bracket component [14]. young modulus e (gpa) poisson ratio yield stress 0 (mpa) kinematic hardening parameters isotropic hardening parameters c (mpa)  q (mpa) b 200 0.3 211 57.81 619.04 42.3 21.6 table 2: properties of the 316l stainless steel adopted in this study [18]. the boundary conditions adopted for the bracket are illustrated in fig. 4. the load direction is specified together with the displacement constraints at base plane. while the load is to be applied thru a spherical bearing, the displacement constraints are applied thru 10 bolts. the optimization domain for the bracket is illustrated in the fig. 5. the boundary condition used was “encastre” of the bottom of the bushing connector to simulate the bolts tightening and a longitudinal symmetry plane was used in order to reduce the computational cost (once it reduces the number of required elements by half). this model encompasses the stiffness of the bolt in several directions. it was assigned local seeds to the regions of the fasteners and to the hole where the load was applied. the loading during working conditions was applied at the centre of the ring, as shown in fig. 5b. a reference point was used, the load was applied to this point and distribute around the internal surface at the ring. all degrees of freedom between these nodes and the reference point were constrained, expect the rotation around the bearing axis, z-axis (since it was a bearing, the shaft was supposed to rotate freely around its axis). the initial mass of this part was 2.10 kg. a mesh refinement study was performed for a static analysis and the final mesh approximate global element size chosen was 1.5 mm. topology optimization the topology optimization methods are based on results of finite element analysis (fea), which are applied in order to evaluate how a structure behave to different actions like forces, vibration, heat, fluid flow and so forth. fea requires a mesh to divide the part into finite elements, which have material properties assigned to them. the importance of the mesh is f.k. fiorentin et al, frattura ed integrità strutturale, 55 (2021) 119-135; doi: 10.3221/igf-esis.55.09 123 undeniable on fem and topology optimization. however, the mesh has a high impact on computation time. this impact gains even more relevance because topology optimization is computationally expensive by itself. for three-dimensional topology optimization, the most common elements are the tetrahedral and hexahedral. since the tetrahedral allows an easily mesh generation in less computation time, it is usually more convenient. however, in some situations, the hexahedral elements are more suitable [19]. figure 4: boundary conditions and coordinate system applied to the bracket [14]. a) b) c) figure 5: 3d part for topology optimization: a) geometry and dimensions in mm of starting geometry; b) coupling constraint to simulate the spherical bearing; c) finite element mesh of solid block. f.k. fiorentin et al, frattura ed integrità strutturale, 55 (2021) 119-135; doi: 10.3221/igf-esis.55.09 124 according to the well-established theory of bendsoe and sigmund [20], most of the optimization methods are applied to find and solve a minimum strain energy design (also called compliance method) with a volume constraint, and this was applied to the present study. the objective function to be minimized is:         0 1 1 min   ρ n n pt e e e e e e e e c u ku u k u u k u (1) where the c represents the strain energy, k means the global stiffness matrix, u is displacement vector, ρe is the relative element density (being 1 the solid element and 0 a “void”), ue is the element displacement vector, ke is the element stiffness matrix after density interpolation and k0 is the initial stiffness matrix [21]. the constraint was the maximum volume, which for this case could not exceed the 12% of the initial optimization domain. it is important to emphasize that not the entire workpiece was inside the optimization domain, the regions around the load application and the fasteners were selected to be outer of optimization domain (therefore they were not changed during the optimization loop). the constraint can be written as:   * 1  v  ρ 0 n e e e v (2) where v* represents the constraint volume, n is the total number of elements and ve is the volume of the element. it can be also stipulated a minimum density, ρmin, for the element, this is a good practice once it does not allow elements with very low stiffness to be created. on the other hand, if a very high ρmin is used, usually the code is “discouraged” to create new elements paths and the optimization might not converge well to a satisfactory minimum. the minimum density law can be written as:   emin 0  ρ  ρ 1 (3) solid isotropic material with penalization (simp) is the approach that offer inherent simplicity and favourable complexity and it is abundantly used in modern topology optimization problems. simp is a soft-kill method and it is used to discretize the design domain dividing it into a grid of n elements (isotropic solid microstructures) each element having a fractional material density [22]. with the density function varying between 1 and 0, it will create a variable density gradient in the new domain. the solid isotropic microstructure with penalization approach represents the intermediate density material with a tensor:    0ρ pijkl ijklk k (4) where the original stiffness tensor of solid material 0ijklk is penalized by a density factor. the penalization factor p forces the algorithm to converge to a solution that contains only a solid or a void by lowering the participation of fractional density elements, encouraging the development of elements with densities close to 1 or 0. usually the proportional stiffness model is used, where the penalized density will be essential to define the new penalized stiffness, which can be written as:     0 ,  1pijkl ijklk x x k p (5) the penalty function heavily influences on density and consequently on the penalized stiffness. for p>1 the stiffness will be very low for low density values and it is not recommended. the topology optimization procedure has been carried out in abaqus with the simp algorithm. the workflow of the optimization loop is shown in fig. 6. the initial stage of the simulation is a structure with 100% density elements. at each loop, a structural simulation is performed. for each step (with a known density of elements) a sensitivity analysis is developed, where the influence of the elements density on the objective function is evaluated. after the optimization procedure is concluded, it is possible to extract the optimized geometry; a threshold called iso value is usually set to regulate which elements are displayed. the iso value must be between zero and one. if the iso value is very high, the part surface f.k. fiorentin et al, frattura ed integrità strutturale, 55 (2021) 119-135; doi: 10.3221/igf-esis.55.09 125 will shift toward the inside of the model decreasing its volume. for example, for an iso value of 0.5, the results only show the elements with densities above 50 %. the most recommended values for this parameter is iso=0.3-0.5 [23,24]. figure 6: flow chart of simp algorithm [22]. figure 7: topology optimization workflow. after extracting the corresponding stl file resulted from the optimization process, which only describes the surface geometry of a three-dimensional object, it is critical to remove/smooth potential areas that can promote stress concentration. reengineer the part is also important, once it is necessary to interpret the shape of the geometry obtained taking into account the functional conditions of the part. it should be noted that the optimization process leads to an initial approach of the final part. in fact, if there is a significant hole that is an interface of the component or if it is found a lack of material in certain areas, it is essential to correct it in order to avoid weak regions and/or without potential stress concentration. the post-processing of the optimized component was done manually, the flow chart containing the steps of the process and the software used can be seen in fig. 7. residual stresses in additive manufacturing for simulating the additive manufacturing process of this part from a case study, a commercial software was used, the esi additive manufacturing. simulating the manufacturing procedure is a complex task, especially for the powder bed fusion process, which encompasses different fields of study. looking at the metallurgical component of the process, it involves melting and solidification of the material, in some cases multiphase materials, several grain sizes depending on the cooling rate, porosity and other defects and so on. the heat transfer of the process is also complex, a moving heat source is present, properties like conductivity, absorptivity, emissivity and specific heat are temperature dependent, the powder and the bulk material present very different properties. in addition, the process involves huge cooling rates and temperatures gradients, where conductivity, convection and radiation take an important role. therefore, to make it possible to simulate the manufacturing process, some assumptions and hypothesis are required. for the present numerical analysis, the material properties used were constant (average values from properties at melting and room temperature were used). also, the “full-layer” strategy was used. this strategy ignores the laser path and assumes that an entire layer is solidified at once. this simplification makes it possible to simulate the process without having to perform a heat transfer analysis, coupled with a structural simulation. for every new layer, a mechanical analysis is performed. the initial temperature for this new layer is the melting temperature and the final temperature for it is the f.k. fiorentin et al, frattura ed integrità strutturale, 55 (2021) 119-135; doi: 10.3221/igf-esis.55.09 126 chamber temperature. the other layers and baseplate are always at the chamber temperature. in other words, for every new layer, a structural problem where a layer cool-down form solidus temperature to chamber temperature is solved, which can be summed as a thermal contraction problem. for a unidirectional problem, the governing equation is:   0 l l t (6) where δl is the difference between final length, α is the linear expansion coefficient, 0l is the initial length and t is the difference between final and initial temperatures. as the new layer wants to contract, the previous layers and baseplate will provide resistance, generating residual stresses. using a mechanical analysis, the applied load will be equivalent to the thermal strain supplied by the process (due to the thermal contraction/expansion). previous works were able to successfully estimate the workpiece distortion (and, consequently, the residual stresses) using similar approaches, validating the numerical results by experimental measurements [25]. fig. 8 shows the three stages of the process simulation. the first stage is the building of the workpiece, it starts only with the baseplate and ends up with the part completely built. during the building process, the baseplate is clamped to the machine structure. the second stage is the release of the baseplate from the machine. finally, the last stage is the removal of the workpiece, where the supports and baseplate were detached. the residual stresses presented during the working conditions are the same as the ones from the last building stage, therefore this will be used to perform the fatigue assessment. it can be noticed that a workpiece with the same final form can present different residual stress fields if some parameters are changed, like its building orientation. at this study, three building orientations were simulated and their respective effect on the residual stress field. therefore, the full part simulation was used instead of taking advantage of the longitudinal symmetry plane used in the topology optimization simulation. the am simulations considered elastic-plastic properties of the material (see tab. 2). in addition, the solidification temperature of 1673.15 k was assumed with an expansion coefficient of 1.9910-5. a) b) c) figure 8: stages of the simulation: (a) building process, (b) releasing build plate from the machine, (c) removal of the workpiece from the base plate. fatigue assessment concerning the fatigue assessment, firstly a cyclic stress analysis of the optimized component, without residual stresses, and a load ratio, r=1 was conducted in abaqus®, allowing estimating the evolution of the stresses and the identification of potential critical locations. from the cyclic elastoplastic analysis, the alternating and mean stresses required for fatigue analysis are computed. due to the applied load ratio, the referred analysis would lead to null mean stresses (minimum and maximum stress values are symmetrical). however, this result could lead to the wrong assumption that the workpiece is absent from mean stresses. as the workpiece was designed to be additive manufactured, it will present significant residual stresses, which will effectively act as the mean stress during external loads. this leads to another conclusion different locations of the workpiece will present different residual stress, resulting on different mean stresses, which would impact in fatigue damage. in addition, construction parameters, including build direction, will influence the residual stresses and the fatigue behaviour. a fatigue model sensitive to the mean stress is therefore needed for the present study. in addition, the load applied to the optimized bracket would lead to multiaxial stress fields that need to be addressed by a convenient multiaxial proportional fatigue damage model. a cyclic quasi-static analysis was performed on the workpiece, applying the working load as the external force. after this analysis, the most critical regions were selected to be further studied. from these nodes, the alternating stresses were extracted. however, the geometry covered in this work is complex, and it presents multiaxial stresses fields. so, this stress state must be represented into a scalar. the octahedral shear stress theory (von mises) was used to find this scalar, and is calculated as: f.k. fiorentin et al, frattura ed integrità strutturale, 55 (2021) 119-135; doi: 10.3221/igf-esis.55.09 127             2 2 2 1 2 2 3 3 1 1 2 qa a a a a a as s s s s s s (7) where 1as , 2  as and 3as are the principal stress amplitudes. for several applications, the octahedral shear stress theory can be applied with success, but in the case of mean stress effect on fatigue, it is not suitable. the main reason is that it removes the information about the stress being compressive or tractive. for the fatigue analysis, this information makes all the difference, a workpiece under compression will not fail due to cyclic loads, and a workpiece under tensile loads will have a premature failure. to solve these issue, one may consider the sum of the principal mean normal stresses [26]:    1 2 3qm m m ms s s s (8) where qms is the equivalent mean stress, 1ms , 2ms and 3ms are respectively the first, second and third principal mean stresses. according to the formulation of eqn. (8), the mean stress can be either positive and negative, which better represents the beneficial effect of compressive mean stress and the adverse effect of tensile mean stress on fatigue behaviour. coupling the information about the alternating stress (due to the loading conditions) and the mean stress (resultant from the building process), it is necessary to combine these two formulations. one of the most used approaches in this case is the sines method [27], which is represented as:                2 2 21 1 2 3 3 1 1 2 3 2 a a a a a a m m m nfs s s s s s m s s s s (9) where m is the coefficient of mean stress, normally 0.5 [26]. since the formulations for both alternating and mean stress were proposed, it is necessary to identify the regions of interest. the critical regions for the alternating stress may not (and most likely will not) be the same as the ones for residual stresses (mean stress). also, depending on the building orientation chosen for am process, the residual stress will change, and the critical regions as well. in order to encompass both the most critical points for residual stress and alternating stress, 6 points have been choosing, being 3 of them selected based on the alternating stress field and 3 of them based on the residual stress. for the cyclic analysis, the 3 points chosen will be designated simply as “point 1”, “point 2” and “point 3”. since these points are only based on the working load (alternating stress), changing the building orientations will have no effect on their alternating stress, therefore these points will be studied in all building orientations. regarding the critical regions associated to the highest residual stresses, 3 building orientations were studied. for each orientation, the 3 most critical points for residual stress were chosen (and their location may be different for each building orientation studied). they will be called “point 4”, “point 5” and “point 6” for building orientation 1; “point 7”, “point 8” and “point 9” for orientation 2 and “point 10”, “point 11” and “point 12” for orientation 3. summing up, 6 points for each orientation will be studied, add up to 12 points, being 3 of them common to all building orientations. at the following section, the locations for these points and their results will be discussed. the final goal is performing the estimative about the number of cycles to failure in each point, according to each orientation, and it can be obtained by the application of the sn curve of the material, shown in fig. 3, as:    mnfs c n (10) where n is the number of cycles, and the values used for c were 1139.1 mpa and for m was -0.101 [17]. results and discussion hrough the numerical procedure described on subsection topology optimization, an optimized geometry was reached. the obtained design is shown in fig. 9. it is important to emphasize that the presented geometry only shows elements of densities higher than 50% (iso-value=0.5), and it was used merely as a plot tool. as it can be seen in fig. 9 and fig. 10, the obtained geometries presented some sharp edges and irregular surfaces, most of them related to the mesh refinement (since the topology optimization is very computationally expensive, a very fine mesh would be impractical) t f.k. fiorentin et al, frattura ed integrità strutturale, 55 (2021) 119-135; doi: 10.3221/igf-esis.55.09 128 and the imposed boundary conditions. the structural fe analyses performed after the optimization using this geometry have shown that these locations presented peak stresses. therefore, a post-processing based on smoothing and repairing operations on these surfaces was performed using the netfabb software. the final workpiece is presented on fig. 11 and it can be seen that the previous critical regions are much smoother, resulting on more homogeneous stress fields. the mass was reduced to 12.53 % of the initial mass. this value is different from the constraint in topology optimization. this discrepancy can be explained because the workpiece was submitted to reverse engineering (post-processing) that added material to the part as well as regions around the interface of the part were excluded from the optimization domain. in order to investigate the stiffness of the bracket, a static analysis for both geometries (before and after the optimization) was performed. the displacement magnitude of the reference point (located at the centre of the hole) was extracted for both analysis and divided by the load magnitude. the stiffness achieved for both geometries had a difference of 23% and since for stiffness-to-weight ratio, only the mass changes significantly, this ratio is significantly higher for the final geometry, compared to the initial one. the mass properties, stiffness and stiffness-to-mass ratio are presented in tab. 3. using the final design, it has been possible to simulate the workpiece performance under cyclic loads. fig. 12 shows the von mises stresses field of the component, for the current image the peak load of 34155n was used. it can be seen that the higher stresses are below 400 mpa, being most of the regions under 150 mpa. it is important to emphasize that this analysis does not encompass the residual stresses, being presented only the influence of the working/external cyclic loads. later, these results will be combined with the residual stress promoted by the am process and estimates about the fatigue behaviour of the component will be performed. design stage mass (g) stiffness (nmm-1) stiffness to weight ratio (nmm-1g-1) initial 2100 1.96105 93 final 263 1.52105 578 table 3: initial and final mass and stiffness of the bracket. figure 9: extracted geometry from to (iso-value=0.5). f.k. fiorentin et al, frattura ed integrità strutturale, 55 (2021) 119-135; doi: 10.3221/igf-esis.55.09 129 with the final bracket geometry defined, it was also possible to simulate the am process of it and compute the residual stress and distortions during and after the manufacturing process. three building orientations were studied; this was performed in order to identify which building orientation was the most suitable for the final goal of the workpiece. in other words, the best orientation would be the one which presented lower residual stress on critical points, improving the number of cycles that the component can handle before failure. preferably, compressive residual stresses at hot spots would be desirable. figure 10: topology optimization result before smoothing. figure 11: final geometry of the case-study part after smoothing operation. fig. 13 presents the residual stress for orientation 1. it can be observed that residual stress are not negligible, once they create regions of the workpiece under plastic deformation. the residual stress presented here are the ones existing after the baseplate removal; this was performed because this is the residual stress field the workpiece will be subjected to during the working conditions assuming there will be not extra post-processing applied to the part. fig. 14 presents the residual stresses for orientation 2. it is possible to see that the maximum values are similar to the previous orientation. however, it is important to notice that they happen in different locations, and this is relevant because if these regions are not critical during the working load, they will not reduce the fatigue life of the component (the actual stress during the operation is a superposition of the stresses originated by the loads and the residual stresses). the results for the third orientation are shown on fig. 15. once more, the maximum stresses are around the same value as the previous orientations. combining both the stress results from external cyclic loads applied thru the spherical bearing and the ones originated by the manufacturing process (residual stresses), it is possible to combine these results and perform a fatigue assessment. as referred earlier the 6th most critical points were evaluated, being 3 of them originated from the working loads and the remaining points taking according to the residual stress. fig. 16 illustrates the selected points. it is important to notice that all points were located at the surface. this happened for several reasons; first of all the surface is the region where the tensile residual stress are usually located; secondly, during the load conditions, the nodes at the surface were the ones with higher stresses; finally, for the fatigue assessment, the surface is very important, mainly because there is where the cracks initiation happens, most of the times. f.k. fiorentin et al, frattura ed integrità strutturale, 55 (2021) 119-135; doi: 10.3221/igf-esis.55.09 130 figure 12: static analysis of the final optimized component (von mises stress field for peak load of 34155 n): global overview and details around spherical bearing and gripping holes. figure 13: residual stress distribution for orientation 1. f.k. fiorentin et al, frattura ed integrità strutturale, 55 (2021) 119-135; doi: 10.3221/igf-esis.55.09 131 figure 14: residual stress distribution for orientation 2. figure 15: residual stress distribution for orientation 3. figure 16: potential critical points provided by high stress areas resulting from to and am simulations. f.k. fiorentin et al, frattura ed integrità strutturale, 55 (2021) 119-135; doi: 10.3221/igf-esis.55.09 132 based on the s-n curve presented in fig. 3, it was possible to insert the equivalent stress computed at each selected potential critical point for an applied load of 34155 n (r=1). fig. 17 presents the fatigue results for the orientation 1. the group of points called “no residual stress” are the ones where only the cyclic load is present, and since the load ratio on this study is -1, they result on a null mean stress, therefore are located exactly on the s-n curve. accounting the effect of the residual stress, it can be noticed that it has a detrimental effect on fatigue behavior for all points. the tensile residual stress obtained from am simulation process for the purpose locations and taking into account the referred orientation have led to a reduction on the estimated number of cycles. consequently, it can be stated that for the present orientation the residual stress due to manufacturing process will reduce the fatigue life of the component, from 1.1105 cycles to 2.0104 cycles as can be observed in the fig. 17. figure 17: sn curve considering the alternating stress points and the mean stresses for build orientation 1. for the second studied building orientation, the results are presented in fig. 18. this manufacturing orientation presented an interesting and promising effect. ignoring the residual stresses, the most critical point for fatigue was the point 2 (the same as in orientation 1). however, this point presented compressive residual stresses, which are beneficial for fatigue. hence, taking into account the residual stresses, the fatigue behaviour of this region was improved. due to the residual stress originated by the am, the overall fatigue life of the component was improved, increasing from 1.1105 cycles to 5.0105 cycles. in addition, the region of failure was no longer around point 2, moving to the point 1. figure 18: sn curve considering the alternating stress points and the mean stresses for build orientation 2. 1e+04 1e+05 1e+06 1e+07 1e+08 1e+09 100 200 300 400 500 a lt e rn a ti n g  s tr e ss  [ m p a ] number of cycles no residual stress with residual stress (am) σa 1e+04 1e+05 1e+06 1e+07 1e+08 1e+09 1e+10 1e+11 1e+12 1e+13 1e+14 1e+15 1e+16 1e+17 1e+18 9 100 200 300 500 a lt e rn a ti n g  s tr e ss  [ m p a ] number of cycles no residual stress with residual stress (am) σa f.k. fiorentin et al, frattura ed integrità strutturale, 55 (2021) 119-135; doi: 10.3221/igf-esis.55.09 133 concerning the third building orientation, fig. 19 illustrates the fatigue results. the results where similar to the ones on orientation 1, i.e. the residual stresses are all tractive at selected potential critical points, significantly reducing the strength of the component under cyclic loads. one may figure out that the build orientation may have an impact on fatigue resistance of the component, being the build orientation 2 the most favourable since it induced compressive residual stresses at the most critical point under external loading. therefore, the am process parameters may be selected to produce favourable residual stresses. in addition, it is clear that the residual stresses at the surface are generically positive (tensile), therefore post-processing techniques aiming at residual stresses relief would be beneficial towards the global fatigue performance of the part. it is worth mentioning that besides the residual stresses, the build direction also influences the surface roughness, which need to be accounted in fatigue assessment. nevertheless, this surface geometric feature cannot be conveniently modelled with fea. figure 19: sn curve considering the alternating stress points and the mean stresses for build orientation 3. conclusions he optimization methodology proposed was able to find an efficient geometry, fulfilling the design requirements. the present case study was based on a well-known case study picked from literature, which allowed the validation of some stages of the methodology namely the topology optimization stage. the main conclusion for the proposed study are summarized below: the optimization methodology applied on the present work was proved to be efficient. the volume (and the mass) of the optimized component was only 12.53% of the initial domain. the stiffness to mass ratio was almost 6 times higher than the initial value. the post-processing approach on the geometry resulted in more homogenous stress field. sharp edge and abrupt changes in surface were smoothed, resulting in lower stresses concentration on these locations. the residual stresses due to the am process presented a significant effect on fatigue. therefore, when it must be considered during the design stage of parts subjected to cyclic loads. the fatigue performance of a component showed to be strongly dependent on the building orientation. build orientation 2 presented the highest fatigue life. compressive residual stresses shift the critical point to an alternative location. thus, component design may account for construction parameters in order to produce beneficial residual stresses. besides the built direction, other manufacturing parameters such as the scanning strategy, layer thickness and laser power could be handled to produce favourable residual stresses. nevertheless, this investigation would require accurate process simulation tools allowing a truly digital twin of the process. future challenges would be to demonstrate the proposed methodology based on experimental program. also, residual stresses are one variable affecting the fatigue damage, but surface roughness and internal defects, which also depends on the manufacturing parameters, would influence the fatigue damage as well. 1e+04 1e+05 1e+06 1e+07 1e+08 1e+09 80 90 100 200 300 400 500 a lt e rn a ti n g  s tr e ss  [ m p a ] number of cycles no residual stress with residual stress (am) σa t f.k. fiorentin et al, frattura ed integrità strutturale, 55 (2021) 119-135; doi: 10.3221/igf-esis.55.09 134 acknowledgments he projects add.strength entitled "enhanced mechanical properties in additive manufactured components" (reference ptdc/eme-eme/31307/2017) and “mamtool machinability of additive manufactured parts for tooling industry” (reference ptdc/eme-eme/31895/2017) funded by the programa operacional competitividade e internacionalização, and programa operacional regional de lisboa funded by feder and national funds (fct) are acknowledged. references [1] dilberoglu, u.m., gharehpapagh, b., yaman, u., dolen, m. (2017). the role of additive manufacturing in the era of industry 4.0, procedia manuf., 11, pp. 545–554, doi: 10.1016/j.promfg.2017.07.148. [2] holmberg, e. (2013). stress and fatigue constrained topology optimization. linköping univeristy, 2013. [3] gibson, i., rosen, d., stucker, b. (2015). additive manufacturing technologies: 3d printing, rapid prototyping, and direct digital manufacturing, second edition. additive manufacturing technologies: 3d printing, rapid prototyping, and direct digital manufacturing, second edition, new york, springer, pp. 1–498. [4] tripathy, s., chin, c., london, t., ankalkhope, u., oancea, v. (2017). process modeling and validation of powder bed metal additive manufacturing. nafems world congress 2017. [5] yap, c.y., chua, c.k., dong, z.l., liu, z.h., zhang, d.q., loh, l.e., sing, s.l. (2015). review of selective laser melting: materials and applications, appl. phys. rev., 2(4), pp. 041101, doi: 10.1063/1.4935926. [6] yang, l., hsu, k., baughman, b., godfrey, d., medina, f., menon, m., wiener, s. (2017). additive manufacturing of metals: the technology, materials, design and production, springer. [7] bhavar, v., kattire, p., patil, v., khot, s., gujar, k., singh, r. (2017). a review on powder bed fusion technology of metal additive manufacturing. additive manufacturing handbook, crc press, pp. 251–253. [8] kurzynowski, t., chlebus, e., kuźnicka, b., reiner, j. (2012).parameters in selective laser melting for processing metallic powders. in: beyer, e., morris, t., (eds.), p. 823914. [9] zumofen, l., beck, c., kirchheim, a., dennig, h.-j. (2018). quality related effects of the preheating temperature on laser melted high carbon content steels. industrializing additive manufacturing proceedings of additive manufacturing in products and applications ampa2017, cham, springer international publishing, pp. 210–219. [10] nicoletto, g., konečna, r., frkan, m., riva, e. (2020). influence of layer-wise fabrication and surface orientation on the notch fatigue behavior of as-built additively manufactured ti6al4v, int. j. fatigue, 134, pp. 105483, doi: 10.1016/j.ijfatigue.2020.105483. [11] nicoletto, g. (2020).an efficient test method for the quantification of technology-dependent factors affecting the fatigue behavior of metallic additive manufacturing components. structural integrity of additive manufactured parts, 100 barr harbor drive, po box c700, west conshohocken, pa 19428-2959, astm international, pp. 484–506. [12] nicoletto, g. (2020). influence of rough as-built surfaces on smooth and notched fatigue behavior of l-pbf alsi10mg, addit. manuf., 34, pp. 101251, doi: 10.1016/j.addma.2020.101251. [13] nicoletto, g. (2019). smooth and notch fatigue behavior of selectively laser melted inconel 718 with as-built surfaces, int. j. fatigue, 128, pp. 105211, doi: 10.1016/j.ijfatigue.2019.105211. [14] kranz, j. (2017). methodik und richtlinien für die konstruktion von laseradditiv gefertigten leichtbaustrukturen, . [15] sander, p. (2016). on the way to additive manufacturing chances & challenges for the future design , industrial production emerging technologies & concepts. world pm2016 congress and exhibition, hamburg. [16] zhong, y., rännar, l.e., liu, l., koptyug, a., wikman, s., olsen, j., cui, d., shen, z. (2017). additive manufacturing of 316l stainless steel by electron beam melting for nuclear fusion applications, j. nucl. mater., 486, pp. 234–245, doi: 10.1016/j.jnucmat.2016.12.042. [17] angelova, d., yordanova, r., lazarova, t. (2014). on factors influencing fatigue process in steel 316l used in hydrogen energy technologies, j. chem. technol. metall., 49(1), pp. 29–34. [18] roy, s.c., goyal, s., sandhya, r., ray, s.k. (2012). low cycle fatigue life prediction of 316 l(n) stainless steel based on cyclic elasto-plastic response, nucl. eng. des., 253, pp. 219–25, doi: 10.1016/j.nucengdes.2012.08.024. [19] nikolas taillieu. (2016). a topology optimization framework for additively manufactured materials under mechanical load. 2016. [20] bendsøe, m.p., sigmund, o. (2004). topology optimization, berlin, heidelberg, springer berlin heidelberg. t f.k. fiorentin et al, frattura ed integrità strutturale, 55 (2021) 119-135; doi: 10.3221/igf-esis.55.09 135 [21] liu, j., ma, y. (2016). a survey of manufacturing oriented topology optimization methods, adv. eng. softw., 100, pp. 161–175, doi: 10.1016/j.advengsoft.2016.07.017. [22] cazacu, r., & grama, l. (2014). overview of structural topology optimization methods for plane and solid structures, ann. univ. oradea, fascicle manag. technol. eng., 23(3), pp. 1583–1591. [23] johnsen, s. (2013). structural topology optimization: basic theory, methods and applications. [24] ansys. (2017). topology optimization r18.0 feature and usage highlights: additive manufacturing application. [25] desmaison, o., p-a. pires, levesque, g., peralta, a., sundarraj, s., makinde, a., jagdale, v. and megahed, m. (2017). influence of computational grid and deposit volume on residual stress and distortion prediction accuracy for additive manufacturing modeling. in proceedings of the 4th world congress on integrated computational materials engineering (icme 2017), pp. 365-374. springer, cham. [26] stephens, r.i. (ralph i., fuchs, h.o. (henry o. (2001). metal fatigue in engineering. [27] gough, h.j., sines, g. (1959). behavior of metals under complex static and alternating stresses, sines g, waisman jl, ed. met. fatigue. met. fatigue, 1, pp. 145–69. microsoft word numero 19 articolo 3.doc m. paggi, frattura ed integrità strutturale, 19 (2012) 29-36; doi: 10.3221/igf-esis.19.03 29 structural integrity of hierarchical composites marco paggi politecnico di torino, department of structural and geotechnical engineering, corso duca degli abruzzi 24, 10129 torino, italy marco.paggi@polito.it abstract. interface mechanical problems are of paramount importance in engineering and materials science. traditionally, due to the complexity of modelling their mechanical behaviour, interfaces are often treated as defects and their features are not explored. in this study, a different approach is illustrated, where the interfaces play an active role in the design of innovative hierarchical composites and are fundamental for their structural integrity. numerical examples regarding cutting tools made of hierarchical cellular polycrystalline materials are proposed, showing that tailoring of interface properties at the different scales is the way to achieve superior mechanical responses that cannot be obtained using standard materials keywords. hierarchical composites; fracture mechanics; finite element method; cohesive zone model. introduction significant advancement in the field of strength of materials has been achieved with the advent of composites. combining different materials together allows us to realize structures with enhanced mechanical properties. fiber reinforced materials are just one of these successful examples. the matrix contributes to the toughness and the density of the material, whereas fibers significantly increase the strength. notable applications regard metal matrix composites used for aerospace applications, as well as fiber reinforced concrete for civil engineering purposes [1]. similar strategies are accomplished with laminates and sandwich structures, where superior mechanical properties are achieved through the suitable combination of the individual material constituents [2]. in this context, the mechanical behaviour and the overall performance of composites are usually not limited by bulk properties, but by the interface characteristics. debonding between matrix and reinforcement develops from early stage of deformation under monotonic and cyclic loading [3]. this damage affects the tensile strength, the fatigue strength, the fracture toughness, as well as the main mechanical properties. therefore, to understand the effect of the interface properties upon the mechanical response, several theoretical, numerical and experimental studies have been put forward in the last decades. although research progresses are evident, especially from the computational point of view, a lot of work has still to be done to understand the mechanics of interfaces and their effect on the global structural response. in general, interfaces are commonly considered as defects, i.e., weak points of the material microstructure that limit the achievement of the maximum theoretical strength. this way of thinking, in conjunction with the difficulty of defining appropriate physical and mathematical models for interfaces, leads to a passive design approach. the attention is therefore focused on preserving the structural integrity by remaining in the elastic regime, covering all the modelling uncertainties with severe safety coefficients. a different approach, leading to an active design, could however be pursued. once suitable models are developed for characterizing the mechanics of interfaces, then structural analysis should pay attention to the failure modes, optimizing the material microstructure and the structural component performance through a suitable tailoring of the interface properties. a http://www.gruppofrattura.it http://dx.medra.org/10.3221/igf-esis.19.03&auth=true m. paggi, frattura ed integrità strutturale, 19 (2012) 29-36; doi: 10.3221/igf-esis.19.03 30 this way of thinking is clearly inspired by biological structures, where interfaces play an active role in the realization of an optimized structured by using individual constituents of relatively poor mechanical properties [4]. for instance, bone tissue undergoes microcracking as a result of repeated daily loading cycles. fracture toughness capabilities are related to the osteonal structure. a ductile osteon-matrix interface promotes crack initiation, but, at the same time, it reduces the velocity of crack propagation in compact bone by blunting the crack tip and trapping it within the lamellar structure [4]. therefore, design of biological structures suggests not to avoid microcracks and defects, but rather include them as an important parameter for the optimization of the material microstructure. recent research on this field has focused on the characterization of biological interfaces, which is considered nowadays as a topic of extreme importance. the investigation of the constituent materials organization and distribution is also a compelling need. preliminary results show that the realization of hierarchical microstructures is the way how biological materials achieve superior material properties. robust and reliable adhesion systems of geckos are obtained through a hierarchical assembly of fibrils [5]. similarly, toughness and defect tolerance of biological hard tissues are the result of hierarchical microstructures ranging over several length scales, from nano to macro [6]. the outcome of this research may contribute to a future development of new nanocomposite materials, mimicking the structures of biological materials. a pioneering effort in this direction is given by cellular polycrystalline materials recently designed by fang et al. [7]. extruded single fibers were packed together and put through a further extrusion process. the result is a honeycomb microstructure as sketched in fig. 1, in which the cores are of polycrystalline diamond (pcd) and the cell walls are of wc/co. toughness and hardness of these new materials are considerably higher than those of standard homogeneous pcd, as also analytically predicted in [8]. this seems to be primarily attributed to the cell boundary material, which deters crack propagation and absorbs fracture energies, while the high hardness of the cell material provides wear resistance. in this context, to understand the role of the process variables on the mechanical response, it is urgent to move from real experiments to virtual (numerical) simulations. in this paper, an example of active design is proposed, where it is shown that the interfaces in hierarchical cellular materials are determinant for the realization of desired material responses. figure 1: scheme of a functionally designed cellular microstructure (adapted from [9]). fracture mechanics of hierarchical cellular materials the effect of the upper scale interfaces on crack growth et us consider a bimaterial component where an external layer composed of polycrystalline cells is bonded to a substrate (see fig. 1). this is for instance the case of the bit of a cutting tool, where the external layer is usually made of polycrystalline diamond (pcd) and the substrate is hardmetal. this composite structure is then joined to a steel support (for more details about geometry and material properties, please refer to [10,11]). when subjected to repeated loadings, as during cutting operations, different failure modes (micro-, mesoand macro-chipping) may occur, depending on the initiation point of a crack on the vertical side in tension. different failure mechanisms (brittle crack propagation, fatigue crack growth) may also occur. in general, chipping leads to a premature failure of the bit ad therefore to a reduced lifetime of the tool. l http://www.gruppofrattura.it http://dx.medra.org/10.3221/igf-esis.19.03&auth=true m. paggi, frattura ed integrità strutturale, 19 (2012) 29-36; doi: 10.3221/igf-esis.19.03 31 in case of a standard pcd layer, where the size of the polycrystals is much smaller than the size of the layer, the material can be considered as homogeneous from the modelling point of view. as a consequence, crack propagation takes place under prevailing mode i conditions and the crack path is curvilinear, as shown in fig. 2. figure 2: sketch of a pcd bit used in cutting tools [10]. the critical impact load is denoted by pc and different possible failure modes ranging from microto macro-chipping are sketched. if heterogeneous cellular materials are used instead of a homogeneous layer, then a different crack path can be obtained. more specifically, considering the mechanical stress field due to a horizontal force acting at the tool tip, a magnification of the crack path for macro-chipping is shown in fig. 3. figure 3: fracture of a cutter with a cellular microstructure: scheme of the compact bit (left) and magnification of the crack path in the region inside the rectangular dashed box (right). this result is obtained by performing a finite element analysis of the bimaterial structure using linear elastic fracture mechanics as in [10]. the simulations are carried out exploiting the interface fracture mechanics features of franc2d [13]. more specifically, the fracture parameters of the bimaterial interfaces are assumed equal to the average value of those of the neighboring materials. the rod diameter is equal to 200 m and the thickness of the binder between the cells is 50 m (see [9] for more details about the geometry of the material microstructure). the critical load for crack propagation, pc, which corresponds to the condition of i ick k at the crack tip, is shown in fig. 4 vs. the crack length a. the load p* represents the average load typically experienced during experimental tests and amax is the final crack length, when the crack meets the hardmetal substrate. at the beginning of the simulation, the crack propagates into a pcd road, and therefore there is no difference with respect to a standard homogeneous material, at http://www.gruppofrattura.it http://dx.medra.org/10.3221/igf-esis.19.03&auth=true m. paggi, frattura ed integrità strutturale, 19 (2012) 29-36; doi: 10.3221/igf-esis.19.03 32 least in 2d simulations. interestingly, when the crack tip meets the bi-material interface, delamination of the rod cell takes place (path a-b). since the interface fracture energy is higher than that of the pcd, the external applied load required for crack propagation has to be significantly increased with respect to the homogeneous case. subsequently, crack deviates again into the rod (path b-c). a second peak is finally observed when the crack propagates through the binder between the cells (path c-d). figure 4: dimensionless critical load for brittle crack propagation vs. dimensionless crack length. the response of a cellular microstructure is compared with that of a homogeneous layer. these results are important for two reasons. first, a crack would arrest its propagation at the first interface if the dimensionless applied load is lower than 2.0. this situation is substantially different from the case of a homogeneous layer, where the critical dimensionless load is a monotonic decreasing function of the crack length. therefore, when the dimensionless applied load exceeds 1.5, then the crack cannot be arrested. therefore, the use of a cellular microstructure acts as a crack-arrester, controlling the evolution of chipping failure modes. on the other hand, interfaces tougher than the rods is not always a desirable situation. in case of micro-chipping, weak interfaces may promote crack propagation along the rod boundaries. this would be suitable to activate a self-resharpening process of the tool tip, which progressively loses its cutting efficiency due to wear. therefore, the optimal material microstructure would correspond to cellular rods embedded into a tougher matrix, with interface properties depending on the vertical coordinate on the cutting edge. the effect of a hierarchical assembly of interfaces it is also possible to quantify the effect of structural hierarchy by simulating the mechanical behaviour of a cellular microstructure using the finite element method and nonlinear fracture mechanics. to this purpose, let us consider the material microstructure depicted in fig. 5. figure 5: cross-section of cellular rods with bright cells and dark grey cell boundaries (adapted from [9]). http://www.gruppofrattura.it http://dx.medra.org/10.3221/igf-esis.19.03&auth=true m. paggi, frattura ed integrità strutturale, 19 (2012) 29-36; doi: 10.3221/igf-esis.19.03 33 each exagonal rod (mesostructure) is composed of a standard polycrystalline material (microstructure). at the microscopic scale (called level 1 in this work), polycrystalline grains are separated by interfaces. such polycrystals compose the material mesostructure (level 2), which is represented by the exagonal rods. such rods are also separated from each others by interfaces, much thicker and with different composition with respect to the interfaces of level 1. as proposed in [13,14] interface fracture can be modelled by simplifying the real material microstructure and considering zero-thickness interface elements between the grains. then, a suitable cohesive zone model (czm) which takes into account the properties of finite thickness interfaces has to be used. in the present study, we consider the nonlocal czm recently proposed by paggi and wriggers [13,14]. a sketch of the interfaces of a standard polycrystalline material is shown in fig. 6. ideal exagonal shapes are considered for the polycrystals. the constitutive model of each interface is described by a mixed mode stress-separation relation, given by the nonlocal czm [13,14]. figure 6: 2d model of a polycrystal (czm interface elements are shown in red with a suitably amplified thickness, for visual representation). to model the present materials processing, we remark that each rod is realized first through sintering of polycrystalline materials as those shown in fig. 6. then, the individual roads are joined together using high pressure and temperature conditions, such that the interfaces of level 2 develop. this configuration is sketched in fig. 7, where yellow interfaces define the boundaries of the rod cells. a direct comparison between figs. 6 and 7 clearly shows that the two microstructures are not physically similar, if different constitutive laws are used for the interfaces at the two levels. as an example, let us consider interfaces at the second level tougher than those of the first level. in particular, we select 2 1 ic ic/ 5 l lg g  . keeping constant the czm parameters of the interfaces of level 1, different czm shapes are considered for the interfaces of level 2, as shown in fig. 8 in case of pure mode i deformation. here, 1max l denotes the peak cohesive stress of the interfaces of level 1, and 1lncg is the critical relative opening displacement corresponding to vanishing cohesive stresses for the interfaces of level 1. considering virtual tensile tests, imposing a monotonic horizontal displacement to the nodes on the vertical right side of the material microstructure, the homogenized response of the representative volume element of the hierarchical material is determined. the peak stresses for the various simulations are plotted in fig. 9 vs. 2 1max max/ l l  . these peak stresses are made dimensionless using the mode i fracture energy of level 1 and the grain size diameter of the polycrystals composing the rods, 1ld . in this diagram, the response of a standard polycrystalline material without structural hierarchy, as that shown in fig. 6, is represented by the red dot in correspondence of 2 1max max/ 1 l l   . the results clearly show that the tensile strength of the material can be significantly increased by using a hierarchical microstructure. the interfaces of the level 2 act as crack-arresters for the microcracks propagating into level 1. the main effect of material hierarchy is therefore to increase the ability of a heterogeneous material to tolerate defects. http://www.gruppofrattura.it http://dx.medra.org/10.3221/igf-esis.19.03&auth=true m. paggi, frattura ed integrità strutturale, 19 (2012) 29-36; doi: 10.3221/igf-esis.19.03 34 figure 7: 2d model of a hierarchical polycrystal (czm interface elements are shown in yellow and red, at the different scales). figure 8: shapes of the czms of the interfaces between the rods (level 2 or mesostructure). figure 9: dimensionless tensile strength vs. czm peak stress ratio between levels 2 and 1. http://www.gruppofrattura.it http://dx.medra.org/10.3221/igf-esis.19.03&auth=true m. paggi, frattura ed integrità strutturale, 19 (2012) 29-36; doi: 10.3221/igf-esis.19.03 35 the peak stresses for the various simulations are plotted in fig. 9 vs. 2 1max max/ l l  . these peak stresses are made dimensionless using the mode i fracture energy of level 1 and the grain size diameter of the polycrystals composing the rods, 1ld . in this diagram, the response of a standard polycrystalline material without structural hierarchy, as that shown in fig. 6, is represented by the red dot in correspondence of 2 1max max/ 1 l l   . the results clearly show that the tensile strength of the material can be significantly increased by using a hierarchical microstructure. the interfaces of the level 2 act as crack-arresters for the microcracks propagating into level 1. the main effect of material hierarchy is therefore to increase the ability of a heterogeneous material to tolerate defects. conclusions n this paper it has been shown that functionally designed microstructures can offer enhanced mechanical properties as compared to traditional heterogeneous materials. tailoring the interfaces properties allows us to enforce crack propagation along desired paths. in this way, self-resharpening effects can be achieved. structural hierarchy is also particularly important. in this study it has been demonstrated that the interaction of interfaces with different properties at the different hierarchical levels may explain the experimental results in [7]. further work has to be done in this direction, especially for the 3d simulation of crack propagation in polycrystalline materials. finite element analyses should also consider coupled thermo-elastic problems, an issue particularly important in cutting technology due to the high temperature conditions. the present study has been limited to a two-level hierarchical composite material. more hierarchical level should be investigated in the future research. however, due to very different length scales involved in the problem, ranging from the size of the sample to the size of the smallest heterogeneity, modelling the mechanical behaviour is a challenging task and multiscale computational methods should be invoked [15]. one possibility is to define representative volume elements (rve) that provide a homogenized constitutive relationship to be used at the upper level. however, although such an approach is very appealing and has been pursued by several authors [16], some aspects require special attention. for instance, the definition of a rve is not obvious, especially in case of localized phenomena, like crack nucleation and propagation. moreover, the condition of scales separation has to be checked with care, otherwise the risk is to exclude coupling effects between length scales that may influence the mechanical response of the material. acknowledgements he support of the italian ministry of education, university and research (miur), ateneo italo-tedesco, and the deutscher akademischer austausch dienst (daad) to the vigoni project "3d modelling of crack propagation in polycrystalline materials" is gratefully acknowledged. references [1] k.k. chawla, composite materials: science and engineering, springer-verlag, berlin, (1987). [2] i.m. daniel, e.e. gdoutos, k.a. wang, j.l. abot, int. j. dam. mech. 11 (2002) 309. [3] a. carpinteri, m. paggi, g. zavarise, int. j. solids struct., 45 (2008) 129. [4] r. de santis, l. ambrosio, f. mollica, p. netti, l. nicolais, modeling of biological materials (chapter 6), f. mollica, l. preziosi, k.r. rajagopal eds., birkhäuser, boston, (2007). [5] h.m. yao, h.j. gao, j. mech. phys. solids, 54 (2006) 1120. [6] z. zhang, y.-w. zhang, h. gao, in: proc. r. soc. b, in press, doi:10.1098/rspb.2010.1093 [7] z.k. fang et al., int. j. refractory metals & hard materials, 19 (2001) 453. [8] a. carpinteri, m. paggi, chaos, solitons and fractals, 42 (2009) 2546. [9] functional design puts the bite into hard and refractory metals. mpr technical trends in metal-powder, 26 (2003) 20. [10] a. carpinteri, m. paggi, finite elements in analysis design, 43 (2007) 941. [11] s.g. moseley, k.-p. bohn, m. goedickemeier, int. j. refractory metals & hard materials, 27 (2009) 394. i t http://www.gruppofrattura.it http://dx.medra.org/10.3221/igf-esis.19.03&auth=true m. paggi, frattura ed integrità strutturale, 19 (2012) 29-36; doi: 10.3221/igf-esis.19.03 36 [12] a.r. ingraffea, p.a. wawrzynek, discrete modeling of crack propagation: theoretical aspects and implementation issues in two and three dimensions, report 91-5, school of civil and env. engng., cornell university, (1991). [13] m. paggi, p. wriggers, computational materials science, 50 (2011) 1625. [14] m. paggi, p. wriggers, computational materials science, 50 (2011) 1634. [15] m. paggi, p. wriggers, in: proceedings of the iv european conference on computational mechanics, on cd-rom, paris, france, (2010) no. 158. [16] t. zohdi, p. wriggers, int. j. solids struct., 36 (1999) 2507. http://www.gruppofrattura.it http://dx.medra.org/10.3221/igf-esis.19.03&auth=true microsoft word numero_55_art_06_2925 l. vigna et alii, frattura ed integrità strutturale, 55 (2021) 76-87; doi: 10.3221/igf-esis.55.06 76 an innovative fixture for testing the crashworthiness of composite materials lorenzo vigna, iman babaei, ravin garg, giovanni belingardi, davide salvatore paolino department of mechanical and aerospace engineering, politecnico di torino, italy lorenzo_vigna@polito.it, https://orcid.org/0000-0002-5913-253x iman.babaei@polito.it, https://orcid.org/0000-0002-6471-5094 ravin.garg@polito.it, https://orcid.org/0000-0001-5473-7436 giovanni.belingardi@polito.it, https://orcid.org/0000-0003-1378-1902 davide.paolino@polito.it, https://orcid.org/0000-0002-4231-4580 andrea calzolari, giuseppe galizia itw test and measurement italy, italy andrea_calzolari@instron.com, https://orcid.org/0000-0002-2605-7203 giuseppe_galizia@instron.com, https://orcid.org/0000-0002-9837-286x abstract. despite the growing diffusion of composite materials in automotive and aerospace sectors, a standard procedure for testing their crashworthiness has not been developed yet. at present, the international standards for testing composite materials under impact conditions are not adequate to test their crush behavior. in this paper, a procedure for measuring the energy absorption due to the compressive crushing of a composite flat specimen along its mid plane is proposed. the experimental setup requires a fixture to hold the specimen and to avoid its buckling and an instrumented drop weight tower to obtain the force-displacement curves with the aim of calculating the specific energy absorption. the paper describes the adopted test procedure and some of the features of the newly developed experimental setup. the effectiveness of the procedure is demonstrated by testing several glass fiber-epoxy specimens under different impact energies. keywords. crashworthiness; specific energy absorption; impact response. citation: vigna l., babaei i., garg r., belingardi g., paolino d.s., calzolari a., galizia g., an innovative fixture for testing the crashworthiness of composite materials, frattura ed integrità strutturale, 55 (2021) 7687. received: 16.09.2020 accepted: 29.10.2020 published: 01.01.2021 copyright: © 2021 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. introduction he growing diffusion of composite materials in the automotive and aerospace sectors is mainly due to the excellent mechanical properties combined with low density. other features like the possibility to design the material properties choosing the right combination of matrixes, fibers, curing cycles and manufacturing processes have made composites the best choice for those applications where high performances are needed. t https://youtu.be/4thk9wxpdxm l. vigna et alii, frattura ed integrità strutturale, 55 (2021) 76-87; doi: 10.3221/igf-esis.55.06 77 the numerous studies carried out in last decades have built up a wide knowledge of composite materials, of their properties and of the manufacturing processes. today this knowledge makes the design process of a composite structure quite easy, also thanks to the numerous tools and software that can be used for the design. nevertheless, the crashworthiness of composite materials is a field in which the research is still evolving due to the difficulty of prediction of the failure of a composite structure during crash and to the absence of a standard test method for the characterization of the specific energy absorption (sea) [1]. the term “crashworthiness” provides a measure of the ability of a structure to protect the occupants in survivable crashes. when an impact occurs, structures must deform irreversibly in a short period of time (milliseconds) to absorb the crash energy in a controllable manner. the typical strategy to achieve this objective is to include in the chassis of the vehicle some elements specifically designed to absorb a large part of the kinetic energy in a controlled way [2]. the components designed as crash absorbers are typically made of ductile metals, that can absorb a high quantity of energy before their final failure. the prediction of the behavior of this kind of structure is quite easy with current simulation algorithms, that allow to model the damage progression of metals with good accuracy. it is well-known in the literature that composite materials have good energy absorption capabilities and offer even better performance than metals in terms of specific energy absorption [3]. however, the simulation of the crash phenomenon in composite materials is extremely difficult because several failure mechanisms can occur, and each of them has a proper efficiency in terms of energy absorption [4]. there are several factors that can influence the failure mechanisms, such as the geometry, the matrix and the fibers utilized, the layup design and the manufacturing process. the failure modes can be subdivided in some categories, even if a proper categorization with widely accepted nomenclature has not yet been developed. the main studies on the failure modes of composites under crash have been carried out by farley and jones [4] and hull [5], that have divided the failure modes in four main categories: tearing or transverse shearing with crack growth inside the fabric layer, causing the rupture of both matrix and fibers splaying, lamina bending or foiling, characterized by the separation of two layers of the laminate that bend in two opposite directions. the energy is mostly dissipated in matrix breaking due to the delamination brittle fracturing or fragmentation that causes the formation of small fragments and cracks inside the fiber’s fabric local buckling or progressive folding characterized by the local bending of the structure, similar to what happens during plastic folding of ductile metals. a composite structure subjected to crash usually involves a combination of failure modes, and it is difficult to foresee which failure mode will occur in a structure before performing a test. furthermore, every failure mechanism has a proper capability to absorb energy through deformation and rupture. a more detailed description of the failure modes of composite materials can be found in the literature [4,5]. several studies have been carried out to predict through numerical simulations the crash behavior of complex composite components but, at present, there are no standard experimental procedures available in the literature [6–10]. the availability of a standard testing procedure to assess the material properties required by material cards used in simulation software would certainly increase the efficiency of the design process and reduce the related costs. focusing on impact tests, existing standards like the puncture tests (astm d3763 [11], astm d5628 [12], iso 6603 [13,14]) and the compression after impact test (astm d7136 [15] and d7137 [16], iso 18325 [17]) are not adequate to provide a measure of the crashworthiness of the material. indeed, in the available standards, impact loads are applied in the direction perpendicular to the laminate plane (out-of-plane loading condition) and not parallel to the plane (in-plane loading condition), as it typically occurs on crash absorbers during crash events. in long fiber composite materials subjected to crash the most typical failure modes are tearing and splaying. the splaying failure mode is typical of parts designed as crash absorbers. these components usually have a tube or a box-like geometry to avoid buckling and to guarantee a certain length of crushable material and are widely used in automotive and aerospace sectors. while some tearing can occur in small areas of these components when subjected to crash, most of the material shows delamination according to the splaying failure mode. for this reason, the study of the splaying is of particular interest. several studies have been carried out in the past 30 years to measure the energy absorption of plain composite specimens, that can easily show splaying if their buckling is avoided through a proper testing fixture. the design of the fixture is extremely important to obtain the desired failure mode of the specimen. the first fixture designed to test the crashworthiness of composite flat specimens was developed by nasa in the early 90’s [18]. this fixture was made of four vertical columns acting as anti-buckling system, and two horizontal plates through which the load was applied to the specimen. the load-displacement curves obtained were similar to those measured with samples l. vigna et alii, frattura ed integrità strutturale, 55 (2021) 76-87; doi: 10.3221/igf-esis.55.06 78 of different shapes, like tubes and cones. however, the specific energy absorption was higher than expected because of the over-constraint of the specimen provided by the anti-buckling system. several fixtures were developed in the following years to overcome the problems raised by the nasa fixture. one of the most interesting was built by feraboli [19]. with this fixture in 2009 several carbon fiber specimens were successfully crashed under quasi static load, obtaining the desired failure mode. the key element of this fixture is the anti-buckling system: it maintains a part of the specimen unsupported, decreasing the constraining effect of the fixture and leaving enough space to crush and eliminate the debris. the results obtained from flat specimens were also compared with those obtained from complex shape elements like square and l-shape elements that give different failure modes. a relation was found between curvature and specific energy absorption [20]. an interesting progress in the field of crashworthiness of composite materials has been proposed by the company engenuity [21]. it consists of an experimental setup similar to that of feraboli, but with the addition of some features able to induce other failure modes in the specimen (such as tearing) if desired. engenuity worked as well on the simulation software to predict the crush behavior of structures, getting good agreement with experimental tests [21]. the engenuity’s fixture was successfully used under dynamic and impact load [22]. other researchers have designed similar devices for testing flat specimens with good results both in quasi-static and dynamic load conditions, showing the effectiveness of using a plane specimen to characterize the material [23–26]. nevertheless, none of the reported testing setups is considered as a standard for the measurement of the sea. the present paper reports the design of an innovative fixture for testing the crashworthiness of flat composite specimens under dynamic load. the device is designed to be fully integrated in a drop tower testing system to replicate the dynamic effects that occur during a crash, that only few studies have addressed using a flat specimen [10,22,24]. the work represents a first step in the process of defining a standard testing procedure for the assessment of crash properties of composite materials through in-plane impact loads. experimental setup and testing procedure he aim of the present testing procedure is to measure the crushing force and the absorbed energy of a plane composite specimen. this allows to calculate the specific energy absorption (sea), which is commonly used as an indicator of the specific amount of energy that the material can absorb during a crash event:         e fdx sea a a , (1) where e is the energy absorbed during the crash event,  is the density of the material, a is the cross section of the specimen,  is the length of the crushed part of the specimen, and f is the force measured during the crash. the crash event should be obtained through an appropriate equipment in order to get the desired failure mode under the required load condition. for the present tests, the load is applied as a falling weight of known mass and velocity, dropped by a drop tower. all tests have been carried out in an instron 9450 drop weight tower, using an instrumented striker equipped with a 222 kn load cell and an acquisition system operating with a sampling frequency of 1 mhz. all tests have been performed using a total falling mass of 60.2 kg and potential energy varying from 400 j to 700 j, obtained through different drop heights. with this equipment it is possible to acquire a time-force curve and calculate the displacement of the falling mass by double integration of the force signal with respect to time. the calculation is numerically performed by the acquisition system according to:                   2 0 0 0 02 t t f tgt t v t dt dt m , (2) where δ0 and v0 are the initial displacement and velocity, t is the time, m is the falling mass and g the acceleration of gravity. from the displacement-force signal is then possible to obtain the energy absorbed during the crushing of the specimen. the tests were recorded using a photron fastcam mini ax high speed camera with a resolution of 1024x1024 pixels at 6400 fps to observe the failure mode(s) and track the displacement of the specimen during the test. t l. vigna et alii, frattura ed integrità strutturale, 55 (2021) 76-87; doi: 10.3221/igf-esis.55.06 79 figure 1: glass fiber plain specimen for crashworthiness test (dimensions in mm): (a) picture of the specimen, (b) overall dimensions of the specimen, (c) detail of the trigger geometry. material tests have been carried out on specimens made of glass fiber woven coated with epoxy resin. the material is a nema fr4 laminate with thickness of 3 mm, made of a 0°/90° glass fiber fabric coated with epoxy resin according to the standard nema li-1 [27]. the fiber content is 60% in weight. it is a widely used material with the mechanical properties listed in tab. 1. a flat specimen was chosen because considered to be the best choice to obtain delamination without occurring in other failure modes like tearing. a flat specimen is also low-cost and easy to manufacture. the chosen dimensions of the plate are the same used for the compression after impact test (astm d7136 [15] and d7137 [16]), i.e. a rectangular plate with dimensions 150 mm and 100 mm (fig. 1b). a trigger feature is machined on one of the shorter sides in order to initiate the progressive crush of the specimen. a sawtooth trigger is chosen to correctly initiate the delamination in the desired part of the specimen (fig. 1) and combined with the flat shape of the specimen selected to avoid undesired failure modes like tearing or buckling. nema fr4 density 2.07 kg/dm3 elastic modulus (iso 178) 24 gpa tensile strength (iso 527) 300 mpa flexure strength (iso 178) 500 mpa compressive strength parallel to laminate (iso 604) 350 mpa compressive strength perpendicular to laminate (iso 604) 500 mpa table 1: mechanical properties of nema fr4 laminates. the density was measured by the authors, while the other properties are given by the supplier of the material [28]. fixture to avoid buckling, it has been decided to use lateral supports that permit to have a long enough crushable length. the designed anti-buckling fixture (figs. 2a and 2b) consists of four vertical columns that, if sustained by a sufficiently stiff l. vigna et alii, frattura ed integrità strutturale, 55 (2021) 76-87; doi: 10.3221/igf-esis.55.06 80 structure, completely avoid the buckling of the specimen [19]. the columns leave an unsupported height in the lower part of the specimen, where the failure takes place, to avoid over-constraining of the specimen and to leave enough space to remove debris and foils. the specimen must be positioned with the trigger in the lower part in order to have the initiation of the failure in the unsupported part. the unsupported height is constant during the test, but it can be modified to get different testing configurations. the columns are connected to the lower part of the fixture trough an aluminum structure. the lateral stiffness required to avoid the buckling of the specimen is given by the structure that surrounds the specimen, whose parts are connected using four screws. a certain care should be taken when fastening the screws not to have too much friction between the specimen and the supporting columns, resulting in an overestimation of the crush force. in all tests the four screws have been fastened with a 1 nm torque, which is the lowest torque capable to provide enough lateral stiffness: in tests with lower values of torque, whose results are not reported in this paper, the specimen showed lateral oscillations due to presence of a clearance between the specimen and the anti-buckling columns. another critical feature of the support consists of the way the load is transmitted to the specimen. the fixture has been designed to allow two possible configurations. the first one consists of a thick steel plate in contact with the upper part of the specimen (fig. 2a). the striker impacts on the crushing plate on the top of the fixture, that transmits the load to the specimen. in the second configuration, the upper plate is removed, and the striker’s hemispherical head is substituted by a special insert with shape of a flat disk that hits the upper part of the specimen (fig. 2b). the fixture allows to test specimens with thicknesses from 1 mm to 10. (a) (b) figure 2: fixture for crashworthiness test in two different configurations: (a) fixture with crushing plate on top, (b) fixture with crushing insert on the striker, and crushing plate removed. methods the acquired data consists of a force-time curve: fig. 3 shows two representative force versus displacement curves, obtained from force-time data with the testing fixture in the two different configurations described above (fig. 2). l. vigna et alii, frattura ed integrità strutturale, 55 (2021) 76-87; doi: 10.3221/igf-esis.55.06 81 the force-displacement curve is particularly useful to make comparisons between different materials and to calculate the specific energy absorption (sea). this curve can be divided in three parts. the first part is related to the first contact between the falling mass and the specimen. when the crushing plate on the fixture is used (blue dash-dot curve in fig. 3), the plot shows a high peak immediately followed by a part with null force, due to the inertia of the crushing plate and to the dynamic behavior of the system, as found also in literature [24]. when the crushing plate is removed (red solid curve in fig. 3) and the dropped mass gets directly in contact with the specimen the initial peak disappears, leaving space for a smoother growth of the force in time with a lower peak, in agreement with the literature [20]. the oscillations of the signal in this part of the curve are evident and are due to the dynamics of the system, which is excited by the impact. the sea calculated in the first part of curve is not correct because the acquired force cannot be referred to the cross section of the specimen because of the presence of the trigger, which is required to initiate the progressive crushing. the first part of curve is then discarded in the post-processing of results. the second part of the curve is more stable and is characterized by the progressive crushing of the specimen. this part is not influenced by the trigger but can still have some oscillations that can be due to the dynamics of the system and to irregularities in the behavior of the material. the mean value of the force is a parameter that well characterizes the material, and consequently the specific energy absorption can be calculated in a defined interval comprised by this part of curve. the third portion of the curve, corresponding to the last few millimeters of displacement, is quite unstable and significantly rises the scatter of the results. the last millimeters of displacement of the striker are characterized by a drop of the force signal due to the interruption of the movement at the complete absorption of the kinetic energy of the falling mass. it is possible to notice a decrease of the displacement value due to the rebound of the impactor caused by the release of the elastic energy of the undamaged part of the specimen. this part of curve is discarded for sea computation. to verify the effectiveness of the testing procedure, the accuracy of the calculated displacement has been verified in two ways. first, the final calculated displacement has been compared with the one measured on the crushed specimen at the end of the test (fig. 4). second, the whole displacement-time curve has been compared with the one obtained by image tracking from a high-speed video recorded during the crash event (fig. 5). since the displacement is obtained from the double integration of the force signal in time, good agreement of the two different displacement signals implies that force signal is correct. the high-speed video is also important to verify if the failure mode of the specimen is the desired one. figure 3: comparison between results obtained in the configuration with crushing plate on the fixture (blue dash-dot curve) and with crush insert on the striker (red solid curve) during a test with impact energy of 600 j and dropped mass of 60.2 kg. l. vigna et alii, frattura ed integrità strutturale, 55 (2021) 76-87; doi: 10.3221/igf-esis.55.06 82 figure 4: measurement of the crushed length of a specimen after the test. figure 5: tracking of the displacement of the specimen during the crush test from the high-speed video using the photron pfa software. experimental results he specimens tested showed a failure mode in line with expectations. the trigger caused the initiation of the failure in the lower part of the specimen, and failure observed after the test consists of two large foils in the lower part of the specimen with the addition of a high quantity of debris of smaller dimensions originated during the crush (fig. 6). even though both testing configurations (i.e. crushing plate on fixture and crushing insert on striker) gave good results in terms of failure mode, the curves obtained with the crushing insert on the striker are preferred because they are more similar to those obtained in quasi-static tests reported in literature [4,19,29]. t l. vigna et alii, frattura ed integrità strutturale, 55 (2021) 76-87; doi: 10.3221/igf-esis.55.06 83 observing the high-speed videos and focusing on the area where the failure takes place, it is possible to observe several failure modes in different moments of the same test or in different tests. the material shows a good crush behavior with a relatively high energy absorption, but the failure mode is not constant during the test. delamination, fragmentation and local buckling of some layers are visible in different areas of the failure and in different moments of the same test as shown in fig. 7. this is probably one of the causes of the oscillations in the force signal (fig. 3), given that different failure modes have been observed to absorb different amounts of energy [4]. figure 6: detail of the crushed part of a glass fiber specimen as visible in fig. 7, delamination of the layers that compose the material is the most evident failure mechanism, but not the only one. the superficial layers sometimes show buckling in some points while bending toward the outside of the support, while the central layers alternate phases of buckling, bending and fragmentation. several fragments are found after the test, showing that the fragmentation of both matrix and fibers occurs during the test. the dimensions of the fragments vary from barely visible dust to fragments of laminate with dimensions of some centimeters, with the addition of the two large foils in fig. 6. (a) (b) figure 7: identification of the failure modes in different moments of the same test on glass fiber specimens, as recorded through the highspeed camera at the beginning of the test (a) and at the end of the test (b). the failure mode is a combination of splaying, fragmentation and local buckling. l. vigna et alii, frattura ed integrità strutturale, 55 (2021) 76-87; doi: 10.3221/igf-esis.55.06 84 figure 8: linear correlation between impact energy and final crushed displacement calculated from the acquired force data. crushing plate on fixture crushing insert on striker slope estimated coefficient 0.031766 0.0353961 p-value 8.42e-12 8.27e-10 other regression results multiple r2 0.999 0.9964 adjusted r2 0.9989 0.9959 f-statistic 7174 1930 p-value 8.419e-12 8.272e-10 table 2: regression results for the two linear models with null intercept plotted in fig. 8, where the final displacement is expressed as a function of the impact energy. the test results show a linear increase of the final displacement at the end of the test with respect to the impact energy (fig. 8). two linear models, one for each testing configuration, were estimated with software r (tab. 2). the behavior of the two testing configurations is similar, with the crushing plate on the fixture responsible of a slightly lower displacement at the end of the test, probably due to the friction between the crushing plate and its guiding columns, that dissipates a part of the kinetic energy. a linear dependence between the impact energy and the volume of crushed material indicates that the sea of this material is not depending on the impact energy, and consequently on the impact velocity because the falling mass was kept constant during these tests. at a first glance this could disagree from what is shown in fig. 9, that reports that the sea as a function of the impact energy is not constant. however, the sea reported in fig. 9 does not take in account the full test, but only the central part of the force-displacement curve (between 40% and 90% of the final displacement of each test), where the crash behavior of the material has been observed to be more stable. the increase of the impact energy (and velocity) seems then to determine a decrease of the specific energy absorption of the material in both testing configurations (i.e. crushing plate on the fixture and crushing insert on the striker). the decreasing behavior of the sea can be explained by taking into account the segment of the force-displacement curve that has been considered for the sea computation. in high-energy impacts the segment completely falls in the part of curve that shows a plateau. on the other hand, in low-energy impacts the segment falls in the region that shows a peak, causing l. vigna et alii, frattura ed integrità strutturale, 55 (2021) 76-87; doi: 10.3221/igf-esis.55.06 85 higher values of sea. therefore, for the investigated material, only tests carried out at impact energies equal or higher than 600 j provide a correct sea value, related to steady crush conditions. the peak force, instead, has very different behaviors in the two testing configurations (fig. 10). the crushing plate on the top of the specimen causes high peak forces whose values increase with the impact speed. on the other hand, peak forces are lower and constant with the crushing insert on the striker. this is also confirmed by the two regression models implemented in r for the two testing configurations (tab. 3). figure 9: specific energy absorption of the material as a function of the impact energy at constant falling mass of 60.2 kg. figure 10: peak force during the test as a function of the impact energy with constant falling mass of 60.2 kg. crushing plate on fixture crushing insert on striker slope estimated coefficient 99.29 5.973 p-value 0.000148 0.559017 intercept estimated coefficient 12582.93 40671.419 p-value 0.103480 0.000303 other regression results multiple r2 0.9229 0.05992 adjusted r2 0.91 -0.09675 f-statistic 71.79 0.3825 p-value 0.0001478 0.559 table 3: regression results for the two linear models plotted in fig. 10, where the peak force is expressed as a function of the impact energy. conclusions new testing procedure to measure the crashworthiness of composite materials has been proposed. the procedure is based on impact tests of flat coupons of material, using a drop weight testing machine, and requires a device to hold the specimen and avoid buckling during the impact. the crush force is measured during the test and allows to calculate the value of specific energy absorption (sea) of the material, that characterizes the behavior of the material during a crash. a l. vigna et alii, frattura ed integrità strutturale, 55 (2021) 76-87; doi: 10.3221/igf-esis.55.06 86 several tests have been carried out with different impact energies, obtaining a linear correlation between the impact energy and the final crushed length of the specimen. the test setup worked well with glass fiber-epoxy specimens, obtaining an average value of sea between 40 kj/kg and 60 kj/kg, that decreases with impact energy. the high speed video recorded during the test showed the failure of the specimen, that appeared to be a complex mixture of foiling, local buckling and fragmentation. this points out the need of further investigation on the relationship between material, failure modes and crush energy absorption. of the two testing configurations proposed, the one with crushing insert on the striker seems to be the most useful because it reduces the dynamic effects given by the testing equipment and provides a more accurate force acquisition during the full test. the testing procedure demonstrated to be useful for the experimental evaluation of the crush force and sea of flat specimens, but further investigation is necessary to compare the results with other testing methods and specimen geometries. tests are also necessary to verify the applicability of the presented testing procedure to other materials. in addition, further investigation is required to assess the possibility to use the acquired results as input data for fem simulations. references [1] feraboli, p., deleo, f., garattoni, f. (2007). efforts in the standardization of composite materials crashworthiness energy absorption, am. soc. compos. 22nd tech. conf. am. soc. compos. 2007 compos. enabling a new era civ. aviat., 1, pp. 741–759. [2] cmh-17. (2012).crashworthiness and energy management. composite materials handbook (cmh-17), vol. 3. [3] lukaszewicz, d.h. ‐j. a. (2013). automotive composite structures for crashworthiness. in: elmarakbi, a. (ed.), advanced composite materials for automotive applications: structural integrity and crashworthiness, chichester, uk, john wiley & sons, ltd, pp. 99–127. [4] farley, g.l., jones, r.m. (1989). energy-absorption cabability of composite tubes and beams. nasa technical memorandum 101634 . [5] hull, d. (1991). a unified approach to progressive crushing of fibre-reinforced composite tubes, compos. sci. technol., 40, pp. 377–421. [6] bisagni, c., di, g., fraschini, l., terletti, d. (2005). progressive crushing of fiber-reinforced composite structural components of a formula one racing car, 68, pp. 491–503, doi: 10.1016/j.compstruct.2004.04.015. [7] obradovic, j., boria, s., belingardi, g. (2012). lightweight design and crash analysis of composite frontal impact energy absorbing structures, compos. struct., 94(2), pp. 423–430, doi: 10.1016/j.compstruct.2011.08.005. [8] joosten, m.w., dutton, s., kelly, d., thomson, r. (2011). experimental and numerical investigation of the crushing response of an open section composite energy absorbing element, compos. struct., 93(2), pp. 682–689, doi: 10.1016/j.compstruct.2010.08.011. [9] liu, z., xia, y. (2019). development of a numerical material model for axial crushing mechanical characterization of woven cfrp composites, compos. struct., 230(july), pp. 111531, doi: 10.1016/j.compstruct.2019.111531. [10] dalli, d., varandas, l.f., catalanotti, g., foster, s., falzon, b.g. (2020). assessing the current modelling approach for predicting the crashworthiness of formula one composite structures, compos. part b eng., doi: 10.1016/j.compositesb.2020.108242. [11] (2018). astm d3763 − 18: standard test method for high speed puncture properties of plastics using load and displacement sensors. [12] (2018). astm d5628 − 18: standard test method for impact resistance of flat, rigid plastic specimens by means of a falling dart (tup or falling mass). [13] (2000). iso 6603-1: plastics determination of puncture impact behaviour of rigid plastics part 1 : non-instrumented impact testing. [14] (2000). iso 6603-2: plastics — determination of puncture impact behaviour of rigid plastics — part 2: instrumented puncture testing. [15] (2015). astm d7136/d7136m − 15: standard test method for measuring the damage resistance of a fiberreinforced polymer matrix composite to a drop-weight impact event. [16] (2017). astm d7137/d7137m − 17: standard test method for compressive residual strength properties of damaged polymer matrix composite plates. [17] (2009). iso 18352:2009 carbon-fibre-reinforced plastics — determination of impact properties at a specified impactenergy level. l. vigna et alii, frattura ed integrità strutturale, 55 (2021) 76-87; doi: 10.3221/igf-esis.55.06 87 [18] lavoie, j.a., morton, j. (1993). design and application of a quasistatic crush test fixture for investigating scale effects in energy absorbing composite plates. nasa contractor report 4526. [19] feraboli, p. (2009). development of a modified flat-plate test specimen and fixture for composite, j. compos. mater., 43(19), pp. 1967–1990, doi: 10.1177/0021998309343025. [20] feraboli, p., wade, b., deleo, f., rassaian, m. (2009). composites : part a crush energy absorption of composite channel section specimens, compos. part a, 40(8), pp. 1248–1256, doi: 10.1016/j.compositesa.2009.05.021. [21] lescheticky, j., barnes, g., schrank, m. (2013). system level design simulation to predict passive safety performance for cfrp automotive structures, sae tech. pap., 2, doi: 10.4271/2013-01-0663. [22] aitharaju, v., kia, h.g., aashat, s., pulugurtha, v.c. (2016). modeling of crush behavior of carbon fiber composites, proc. am. soc. compos. thirty-first tech. conf. [23] israr, h.a., rivallant, s., bouvet, c., barrau, j.j. (2014). finite element simulation of 0 ° / 90 ° cfrp laminated plates subjected to crushing using a free-face-crushing concept, compos. part a, 62(july), pp. 16–25, doi: https://doi.org/10.1016/j.compositesa.2014.03.014. [24] duong, a.v., rivallant, s., barrau, j.j., petiot, c., malherbe, b.î. (2010).influence of speed on the crushing behavior of composite plates. 7th asian-australasian conference on composite materials 2010, accm 2010, 1, pp. 678–681. [25] ueda, m., nishimura, t. (2010). compressive failure of unidirectional cfrp plate under progressive crushing, 25th tech. conf. am. soc. compos. 14th us-japan conf. compos. mater., 2, pp. 1658–1668. [26] cauchi savona, s., hogg, p.j. (2006). effect of fracture toughness properties on the crushing of flat composite plates, compos. sci. technol., 66(13), pp. 2317–2328, doi: 10.1016/j.compscitech.2005.11.038. [27] national electrical manufacturers association. (1998). nema li-1-1998 (r2011): industrial laminated thermosetting products. [28] demezzi sas. vetro epossidico nema fr4. available at: http://www.demezzi.it/termici/fr4.php. [accessed october 13, 2020]. [29] carruthers, j.j., kettle, a.p., robinson, a.m. (1998). energy absorption capability and crashworthiness of composite material structures: a review, appl. mech. rev., 51(10), pp. 635–649, doi: 10.1115/1.3100758. microsoft word numero_29_art_37 s.k. kudari et alii, frattura ed integrità strutturale, 29 (2014) 419-425; doi: 10.3221/igf-esis.29.37 419 technical note a new formulation for estimating maximum stress intensity factor at the mid plane of a senb specimen: study based on 3d fea s. k. kudari, k. g. kodancha research centre, department of mechanical engineering, b. v. b. college of engineering and technology, hubli 580 031, karnataka, india. s.kudari@rediffmail.com abstract. in this investigation, three-dimensional elastic finite element analyses have been conducted to compute the stress intensity factor (ki) in a senb specimen with varied thickness (b) and crack-length to width ratio (a/w). the results indicate that the magnitude of ki depends on b, and significantly varies along the crackfront from surface to the center of the specimen. the maximum value of ki is found at mid plane of the specimen. based on the present 3d finite element calculations an effort is made to propose the new analytical relationship between maximum ki and specimen a/w, which helps to estimate maximum ki by only knowing specimen geometry and applied load. keywords. senb specimen; finite element analysis; maximum stress intensity factor. introduction n fracture analysis, two-dimensional approach of lefm is popular because of its simplicity in mathematical formulation and numerical analysis. in two-dimensional structural analyses, plane strain is governed by case where deformation is highly constrained for example plates with larger thickness, and plane stress is used for thin plates. several methods have been developed in past, to compute the ki for engineering problems with complex geometry and loading [1]. fett [2] has used boundary allocation method to compute ki solutions for components containing internal cracks. chen and lin [3] investigated the dependence of the ki from the imposed boundary conditions in a rectangular cracked plate. based on the asymptotic solution of the singular stress field, and the common numerical solution (stresses or displacements) obtained by finite element method, a simple and effective numerical method is developed by yihua liu et al. [4] to calculate stress intensity factors. due to complexity of the solution, the stress field around the crack-front in 3d continua is limited. kwon and sun [5] given the detailed literature review about the efforts in computating 3d stress intensity factor and presented 3d fe analyses to investigate the stress fields near the crack tip. the authors [5] suggested a simple technique to determine 3d ki at the mid plane of a specimen by knowing 2d ki and poison’s ratio (v). moreira et al. [6] studied the 3d effects in a central cracked plate by numerical determination of the stress field and ki variation through the thickness. as single edge notch bend (senb) specimen is more preferred for fracture tests hence, it is essential to have such study on this specimen. the aim of this investigation is to study the variation of ki along the crack-front considering a senb specimen geometry having varied thickness (b) and crack length to width ratio (a/w). to calculate the maximum ki at mid plane of any fracture specimen, it is essential to conduct complex 3d fea. hence, it is always very difficult for a structural engineer to conduct 3d fea for estimating ki at the mid plane of a specimen. hence, based on the present 3d fe calculations, an attempt is made to propose a new analytical relationship between ki at the mid plane, a/w and applied i s.k. kudari et alii, frattura ed integrità strutturale, 29 (2014) 419-425; doi: 10.3221/igf-esis.29.37 420 stress ratio (/y) which shall be a great help in estimating maximum magnitude of ki in a senb specimen without complex 3d fe analysis. finite element analysis series of 3d finite element analyses have been made on senb specimens using abaqus 6.5 [7] finite element software. the dimensions of senb specimen has been computed according to astm standard e1290 [8] considering width of the specimen w=20mm. figure1 shows the geometry of the senb specimen used in this analysis. finite element computations were carriedout considering only one-half of the specimen due to the geometric and loading symmetry. the analysis domain is descritized using 20-noded quadratic brick finite elements using reduced integration. this kind of elements were used in the work of moreira et al. [6], qu and wang [9], kim et al. [10], courtin et al. [11], kudari and kodancha [12]. in this analysis, the number of elements in the analysis domain varied with the thickness (b) of the specimen. the specimen thickness modeled by considering 11 layers in the thickness direction. a typical mesh used in the analysis for specimen thickness b=4 mm is shown in fig. 2. the stress distributions in the specimen and magnitudes of ki have been extracted by using abaqus post processor. the variation of stress components and ki along the crack-front has been studied for different specimen thickness and crack length to width ratio (a/w=0.45-0.70). figure 1: the geometry of the senb specimen used in the analysis (w=20 mm). figure 2: 3d specimen fe mesh used for the analysis. in this work the magnitude of applied stress () is computed using the relation [13]: 2)(2 3 wb ps  (1) where, p is applied load, b is thickness of the specimen, w is width of the specimen, s=4w, the span of the specimen. the specimen thicknesses (b) considered in this analysis is 2 to 20 mm (b/w=0.1-1.0) in steps of 2 mm. in these finite a s.k. kudari et alii, frattura ed integrità strutturale, 29 (2014) 419-425; doi: 10.3221/igf-esis.29.37 421 element calculations, the material behaviour has been considered to be multi-linear kinematic hardening type pertaining to an interstitial free (if) steel possessing yield strength of 155 mpa, elastic modulus of 197 gpa, poison’s ratio=0.30, and ramberg-osgood constants n=3.358 and =19.22 [14]. results and discussion 2d stress intensity factor (ki) n this study, initially 2d elastic plane-stress fe analysis has been conducted on the senb specimen with a/w=0.450.70 to extract the ki. the magnitude of ki computed by theoretical formulation [15] as given in eq. (2) and present 2d fe analysis is plotted against a/w in fig. 3. )(yaki  (2) where,  is applied stress, a is crack length and y is geometric factor. the fig. 3 indicates that the present fe results of 2d ki are in excellent agreement with the results obtained by theoretical eq. (2). these analyses provide the validation of the fe computation of ki in 2d. figure 3: variation of ki vs. a/w obtained by eq. (2) ref [15] and 2d fea. 3d stress intensity factor (ki) a series of 3d fe stress analyses have been carried out on senb specimen with varied b, a/w and normalized applied stress (/y) to study the variation of ki along the crack-front. the applied stress () in this analysis is computed using the analytical formulation provided in the work of sherry et al. [13]. the details of extraction of magnitudes of ki are discussed elsewhere [16]. a typical variation of ki for b=10mm with a/w=0.55 for various loading (/y=0.08 to 0.80) is shown in the fig.4. this figure indicates that the magnitude of ki is higher at the centre of the specimen than on the surface. this is due to variation of stress tri-axiality along the specimen thickness. the nature of variation of ki shown in fig.4 is in good agreement with the similar results presented by fernandez et al. [17]. further, the effect of a/w on variation of ki is also studied. a typical variation of ki along the crack-front for specimen having various a/w and b=10 mm for /y=0.56 is shown in fig. 5. this figure illustrates that for the similar applied load the magnitude of ki at the centre and the surface of the specimen increases as a/w increases. this kind of variation of ki along the crack front is not possible to study analytically. the 2d magnitude of ki can be computed by well-known analytical formulation eq. (2). the eq. (2) do not consider the effect of specimen thickness, and provide the magnitude of ki less than that at the center of the specimen as shown in fig. 5 (typically for a/w=0.60). from this result, one can infer that the analytical estimates of ki (estimated by eq. (2)) are not suitable for the analysis of fracture in case of specimens with higher thickness (plane strain). earlier, nakamura and parks [18] have used degree of plane strain to demonstrate the plane strain behavior in 3d cracked plate. the degree of plane strain, dp, a parameter that measures the variation of the constraint factors needs the computed values of stress variation in all three directions as [18]: i s.k. kudari et alii, frattura ed integrità strutturale, 29 (2014) 419-425; doi: 10.3221/igf-esis.29.37 422 )( 2211 33     pd (3) figure 4: variation of ki along the crack-front for various loading. figure 5: variation of ki along the crack-front for b=10 mm and various a/w. this dp is quite complex to compute and analysis. the above limitations in fracture analysis demand the 3d analysis of fracture specimen to find the ki at the center (maximum) of the specimen. one can observe from fig.5 that there exists a considerable difference in the magnitudes of ki between center and surface of the specimen. a typical variation of difference between the magnitude of ki at the center and on the surface (ki) for a specimen having b=10mm for /y=0.56 and various a/w is shown in the fig. 6. this figure indicates that ki of the specimen increases as a/w increases, which infers that higher magnitude of specimen a/w ratio provides maximum outof-plane constraint. the magnitude of ki are also extracted for b=2 to 20 mm (b/w=0.1 to 1) and a/w=0.45 to 0.70 for loading /y=0.08 to 0.80. a typical variation of ki for thicknesses b=2mm, 10mm and 20mm for a/w=0.50 and /y=0.56 is shown in fig 7. this figure clearly demonstrates an interesting finding that the magnitude of ki at the center of the specimen is independent of specimen thickness (b). figure 6: variation of ki for various a/w ratios. figure 7: variation of ki along the crack-front for b=2 mm, 10 mm and 20 mm with a/w=0.50 fig. 4 to 7 show that ki strongly varies with distance along the crack-front and depends on the specimen thickness. figure 4 to 7 show that the magnitude of ki is higher at the centre of the specimen than on the surface. this nature of variation s.k. kudari et alii, frattura ed integrità strutturale, 29 (2014) 419-425; doi: 10.3221/igf-esis.29.37 423 of ki is in agreement with the result presented by kwon and sun [5]. based on their fe results, kwon and sun [5] have proposed a formulation to obtain the highest magnitude of 3d ki (at the centre of the specimen) based on magnitude of ki obtained by 2d analysis as: 2 2 3 1 1   d d k k (4) where  is poisson’s ratio of the material. the highest magnitude of the ki (at the center of the specimen) extracted by the present 3d fe analysis for various a/w ratios is plotted in fig. 8 along with the 3d ki values estimated by the formulation, eq. (4) using 2d results shown in fig. 3. the 2d computation of ki were made in order to verify the possible use of the formula (eq. (4)) proposed by kwon and sun [5]. the fig.8 shows that there is an acceptable agreement of 3d ki at the center of the specimen and the computations made by the formulation given by kwon and sun [5] using present 2d fe results. as magnitude of ki is found to be maximum at the centre of the specimen, it becomes important to do the fracture analysis of material based on the value of ki estimated at the center of the specimen. this demands 3d fe analysis of fracture specimen, which is difficult and time consuming for any fracture analyst. hence, in this study an effort is made to propose a simple relation to estimate ki at the center of the specimen, without any numerical computations. further, the magnitude of ki at the center of specimen having various b (b=2 to 20mm) and /y=0.08 to 0.80 and a/w=0.45 to 0.70 are extracted from 3d fe analysis. a typical plot of ki at center against /y and b for a/w=0.50 is plotted in fig.9. figure 8: variation of ki for various a/w ratios obtained by present 3d fea and kwon and sun [5] figure 9: a typical plot of ki at specimen centre against / y  for various b. it is interesting to know from this figure that the variation of ki vs. /y is linear for various specimen thicknesses (b) and is independent of b. this nature of the variation of ki vs. /y allows us to obtain the relation between ki and /y for particular a/w. next, the slope of ki vs. /y is evaluated by fitting a straight-line equation to all the values of ki estimated at the centre of the specimen shown in fig. 9. now, it is required to find the variation of ki / (/y) with the specimen thickness (b) for various a/w. ki / (/y) against normalized thickness (b/w) for various a/w are plotted in fig. 10. the plot indicates that the slopes are almost independent of normalized specimen thicknesses (b/w). the average slope values of b=2 to 20mm (b/w=0.1-1.0) are computed for a respective a/w. the plot between average slope value of ki / (/y) and a/w is shown in fig 11. this figure is used to obtain the relation between ki / ( /y) and a/w, in which ki is the only unknown. as relation between ki / (/y) and a/w is nonlinear, we have tried to fit the data with a suitable polynomial. in such exercise, we found a polynomial equation of third order fits the data with least error (coefficient of determination, cod=0.99885), which is superimposed in fig.11. from this third order polynomial fit, the relation between ki, (a/w) and (/y) can be expressed as:   2 3 2824 35 23133 54 50651 70 41421 48. . . . / i y k a a a w w w                       (5) s.k. kudari et alii, frattura ed integrità strutturale, 29 (2014) 419-425; doi: 10.3221/igf-esis.29.37 424 using eq. (5) for various (a/w) and applied stress ratio (/y), the value of ki can be easily computed. to validate the formulation, eq. (5), the computed values of ki using eq. (5) for typically, a/w=0.50 for b=10mm is compared with present 3d fe results and results of kwon and sun [5] in fig.12. the figure shows that the results computed by eq. (5) are in excellent agreement with the results of kwon and sun [5]. the maximum percentage of error estimated in use of eq. (5) for b=2 to 20mm, a/w=0.45 to 0.70 and /y=0.08 and 0.80 is 2.17%. hence, the above proposed analytical formulation (eq. (5)) is much capable and easy to use to compute maximum ki in a specimen by knowing only specimen a/w and applied stress ratio (/y). this formulation is much improved and simple to the one given by kwon and sun [5], which demands 2d ki results. using the proposed new approximate analytical eq. (5) one can estimate the magnitudes of maximum ki at mid plane of the senb specimen without complex numerical solutions. the proposed eq. (5) can encourage the practicing engineers to estimate the realistic value of ki as compared to eq. (2). figure 10: variation of ki/  / y  against normalized thickness (b/w) for various a/w figure 11: variation of average slope value of ki/  / y  vs. a/w figure 12: comparison of ki estimated using eq.(5) for typically, a/w=0.50 and b=10mm is with present 3d fe results and results of kwon and sun [5]. concluding remarks (i) the magnitude of ki varies along the crack-front and is found to be maximum at the centre of the specimen (ii) the magnitude of ki is observed to be independent of b at the center of the specimen s.k. kudari et alii, frattura ed integrità strutturale, 29 (2014) 419-425; doi: 10.3221/igf-esis.29.37 425 (iii) the proposed formulation, eq. (5) is more simple than the one proposed by kwon and sun [5] given in eq. (4), which needs magnitude of k computed by 2d fe analysis. the proposed equation can be readily used to evaluate the maximum ki in a senb specimen by knowing only applied stress, specimen thickness (b) and a/w acknowledgement uthors gratefully acknowledge the computational facilities provided by research center, b. v. b. college of engineering & technology, hubli, and prosim, bangalore. references [1] murakami, y., stress intensity factors hand book, pergamon press, oxford, (1987). [2] fett, t., stress intensity and tstresses for internally cracked circular disks under various conditions, engineering fracture mechanics, , 68 (2001) 1119-1136. [3] chen, y.z., lin, x.y., on dependence of the stress intensity factor and t-stress from imposed boundary conditions in a rectangular cracked plate, computational materials science, 42 (2008) 149-55. [4] yihua, l., zhigen, w., yongcheng, l., xiaomei, l., numerical methods for determination of stress intensity factors of singular stress field, engineering fracture mechanics, 75 (2008) 4793–4803. [5] kwon, s.w., sun, c.t., characteristics of three-dimensional stress fields in plates with a through –the-thickness crack, international journal of fracture, 104 (2000) 291-315. [6] moreira, p.m.g.p., pastrama, s.d., castro, p.m.s.t., three-dimensional stress intensity factor calibration for a stiffened cracked plate, engineering fracture mechanics, 76 (2009) 2298–2308. [7] abaqus user’s manual. version 6.5-1. hibbitt, karlsson & sorensen, inc. (2004). [8] astm standard e1820-13, standard test method for measurement of fracture toughness, american society for testing and materials, philadelphia, pennsylvania (2013). [9] jie, q., xin, w., solutions of t-stresses for quarter-elliptical corner cracks in finite thickness plates subject to tension and bending, international journal of pressure vessels and piping, 83 (2006) 593–606. [10] kim, y., zhu, x.k., chao, y.j., quantification of constraint on elastic-plastic 3d crack front by the j-a2 three-term solution, engineering fracture mechanics, 68 (2001) 895-914. [11] coutin, s., gardin, c., bezine, g., ben hadj hamouda, h., advantages of the j-integral approach for calculating stress intensity factors when using the commercial finite element software abaqus, engineering fracture mechanics, 72 (2005) 2174-2185. [12] kudari, s.k., kodancha, k.g., effect of specimen thickness on plastic zone, in: 17th european conference on fracture (ecf-17), (2008). [13] sherry, a.h., france, c.c., edwards, l., compendium of t-stress solutions for two and three dimensional geometries, fatigue and fracture of engg mat and structures, 18 (1995) 141-155. [14] kudari, s. k., maiti, b., ray, k. k., the effect of specimen geometry on plastic zone size: a study using the j integral. journal of strain analysis, 42 (2007) 125-136. [15] saxena, a., nonlinear fracture mechanics for engineers, crc press, boca raton, florida (1997), pp. 51–52 [16] kodancha., k.g., kudari., s. k., variation of stress intensity factor and elastic t-stress along the crack-front in finite thickness plates. frattura ed integrità strutturale, 8 (2009) 45-51. [17] fernandez, z.d., kalthoff, j.f., fernandez, c.a., canteli, a., grasa , j., doblare, m., three dimensional finite element calculations of crack-tip plastic zones and kic specimen size requirements, in: 15th european conference on fracture (ecf-15), (2005). [18] nakamura, t., parks, d.m., three-dimensional stress field near the crack -front of a thin elastic plate, journal of applied mechanics, 55 (1988) 805-813. a microsoft word numero_41_art_4.docx m. kurek et alii, frattura ed integrità strutturale, 41 (2017) 24-30; doi: 10.3221/igf-esis.41.04 24 focused on multiaxial fatigue determination of the critical plane orientation depending on the fatigue curves for bending and torsion marta kurek, tadeusz łagoda university of technology opole, poland ma.kurek@po.opole.pl, t.lagoda@po.opole.pl abstract. this paper contains a proposition setting out a new way of determining an orientation angle of the critical plane. the applied method involves an analysis of fatigue life results’ scatter of several selected materials on the basis of a new criterion of multiaxial fatigue. the expression for the equivalent stress was derived on the basis of pure bending and pure torsion. the paper also contains a verification of the effectiveness of the proposed model by analyzing scatter bands and the value of the ratio of normal to shear stresses. keywords. critical plane; fatigue life; equivalent stress; scatter analysys. citation: kurek, m., łagoda, t., determination of the critical plane orientation depending on the fatigue curves for bending and torsion frattura ed integrità strutturale, 41 (2017) 24-30. received: 28.02.2017 accepted: 15.04.2017 published: 01.07.2017 copyright: © 2017 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. introduction he literature contains a number of propositions including models for fatigue life assessment [1-4]. the work aimed at finding an algorithm for predicting fatigue life accompanying random loads was undertaken by macha in 1979 [5], who applied the notion of stress for this purpose. over the successive years, the propositions were improved and modified, and each of them accounted for one or a few aspects of the fatigue life. with the time passing, the strain model was established [6], followed by the one based on energy [7], which applied the parameter of strain energy density parameter acting on the critical plane. despite the large number of propositions, there is still a need to modify the existing models. the justification for the adopted foundations is based on the scatter of the gained calculation results of the fatigue [8]. they form an important factor used for verifying the effectiveness of the proposed way of assessing fatigue strength. the objective of this paper is to present a new model applicable for assessment of fatigue life on the basis of a concept of the critical plane accompanied by the analysis of the scatter of the results. t m. kurek et alii, frattura ed integrità strutturale, 41 (2017) 24-30; doi: 10.3221/igf-esis.41.04 25 the algorithm of fatigue life evaluation he proposed algorithm of predicting fatigue life was formulated on the basis of a concept by carpintieri [9]. the principal way of modifying the concept by carpintieri involves a new relation that is established for the angle defining the critical plane orientation, as it plays a critical role in the assessment of fatigue strength. calculations were done using multiaxial fatigue criterion, based on the critical plane concept. the coefficients b and k in formulas for equivalent stress are calculated according to typical fatigue limits for pure bending and pure torsion. the general form of the equivalent stress [10] according to the criteria on critical plane is expressed as: ( ) ( ) ( )t b t keq s t     (1) authors use criterion (1) where weighing factors b and k [11] using pure bending and pure torsion can be defined as: 2 2 2 sin(90 2 ) cos sin 2 sin(90 2 ) cos(90 2 ) 2 cos o o o b b             (2) 2 sin 2 2 2 222 cos b af k b af         (3) 2 af b af    (4) ση(t) is the normal stress and τηs(t) is the shear stress, both acting on the critical plane: 2( ) ( )cos ( )sin 2xx xyt t t      (5) 1 ( ) ( )sin 2 ( )cos 2 2 s xx xyt t t       (6) where     (7) being αη the angle defined by the direction of the maximum normal stress if the above damage accumulation method is applied and β is 2 ( )1 3 1 3 (4 ) 22.5 22.5 ( ) 2 ( ) 2 a fi fi a fi n ctg b n n                        (8) the proposition (8) was derived on the basis of the variability of calculated fatigue strength depending on angle β for several selected materials [11-13]. we can note here that formula (4) is based on the ratio of the fatigue life boundaries. in the proposition (8), this coefficient is relative to the number of cycles, and can be stated the following form ( ) ( )2 ( ) na fi b n fi na fi    (9) t m. kurek et alii, frattura ed integrità strutturale, 41 (2017) 24-30; doi: 10.3221/igf-esis.41.04 26 a graphical interpretation of formula (8) is presented in fig. 1, whereas the broken line marks the proposition developed by carpintieri (10). 22 2 2 3 1 3 1 1 45 ( ) 1 45 2 2 ( ) fi fi b n b b n                             (10) figure 1: the relationship between the angle β and the parameter b2 according to different models. the final step is the calculation of the fatigue strength. for constant amplitude cyclic loading, the fatigue strength is evaluated by using basquin’s fatigue characteristics ( a and m ) in compliance with the relevant astm standard [14]. the formula for strength calculation under cyclic loading is expressed as follows: ,lg10 eq acal a m n   (11) where ,eq a is the amplitude of the equivalent stress related to the critical plane (eq.(1)) , a, m coefficients of regression equation for oscillatory bending. fatigue strength scatter analysys he proposition in eq. (8) presented in fig. 1 was developed on the basis of the results of a study involving several materials and requires verification. an analysis of the scatter of the results of fatigue life depending on the proposed angle and value of the ratio of the normal to shear stress was undertaken for this purpose. the analysis applied the values of the scatter bands for the particular materials just as it was calculated in [8] for angle β in the range <0°, 45°>. fig. 2 presents the methodology followed during the analysis of the proposed expression (8) with regard to the relation of angle β and scatter t. the values of angles β were calculated so that the scatter t is in the range <tmin, 1.1tmin>. on this basis, βopt ϵ <βmin, βmax>. fig. 3 illustrates relationship between scatter values t and the angle β for d30 [15]. t m. kurek et alii, frattura ed integrità strutturale, 41 (2017) 24-30; doi: 10.3221/igf-esis.41.04 27 figure 2: the methodology of presented calculations. figure 3: relationship between scatter values t and the angle β for d30. in addition, calculations were performed with regard to the relation of the ratio of normal stress to shear one depending on angle β. the study took into consideration the level of error of 10%. accordingly, it was adopted that the ratio is established with the probability level of ± 5% 0.95 1.05a a a a a a         . one of the characteristics of fatigue tests is that the results demonstrate a considerable degree of scatter. this paper is based on an assumption that the error is at a level of 10%, which is sufficient during calculations of fatigue life with regard to loads. the results that were gained, were subsequently plotted onto the diagram representing the relation of angle β depending on the ratio of normal to shear stresses (fig. 4). m. kurek et alii, frattura ed integrità strutturale, 41 (2017) 24-30; doi: 10.3221/igf-esis.41.04 28 figure 4: exemplary analysis of material d30. the hatched field is the area for which the results of the fatigue life are the same or differ insignificantly. such analysis was performed for all test materials. fig. 5 shows the distribution of the scatter results for gts45 material [16]. figure 5: relationship between scatter values t and the angle β for gts45. the subsequent analysis for exemplary materials is presented in figs. 6-7. from the analysis of fig. 7, we can note down that the model also applies to materials, which are not covered by the proposed function (e.g. d30). in the future, it would be necessary to perform a more comprehensive static analysis involving the determination of fatigue characteristics with regard to pure bending and pure torsion for the respective materials. m. kurek et alii, frattura ed integrità strutturale, 41 (2017) 24-30; doi: 10.3221/igf-esis.41.04 29 figure 6: exemplary analysis of selected materials. figure 7: exemplary analysis of selected materials. concusions n the basis of the analysis of the experiments as well as calculations and simulations, we can draw the following conclusions: 1. the proposed model has been developed on the basis of relations for materials in elastic-brittle state (galileo’s hypothesis) and in elastic-plastic state (hmh hypothesis). these states are nevertheless not limiting like in case of the carpinteri’s model. 2. the proposed model accounts for a wider range of the ratio of normal to shear stresses than the carpintieri model. 3. the presented analysis is indispensable for the verification of the foundations and effectiveness of the new model. 4. taking into consideration the scatter of the determined β angle and also the ratio of the fatigue limits for bending and torsion in may be noticed, that most of the materials coincide with the proposed model. 5. in the future more materials should be analyzed in order to continue the verification of the proposed model or to look for an evet better suiting model for experimental tests. o m. kurek et alii, frattura ed integrità strutturale, 41 (2017) 24-30; doi: 10.3221/igf-esis.41.04 30 acknowledgments roject financed by the national science centre. decision number: 2016/21/d/st8/02007 references [1] carpinteri, a., fortese, g., ronchei, c., scorza, d., spagnoli, a., vantadori s., fatigue life evaluation of metallic structures under multiaxial random loading, international journal of fatigue, 90 (2016) 191-199. doi: 10.1016/j.ijfatigue.2016.05.007. [2] skibicki, d., pejkowski, ł., low-cycle multiaxial fatigue behaviour and fatigue life prediction for cuzn37 brass using the stress-strain models, international journal of fatigue, 102 (2017) 18–36. [3] wanga, y., susmel, l., the modified manson–coffin curve method to estimate fatigue lifetime under complex constant and variable amplitude multiaxial fatigue loading, international journal of fatigue, 83 (2016) 135–149. [4] karolczuk, a., kluger, k., łagoda, t., a correction in the algorithm of fatigue life calculation based on the critical plane approach, international journal of fatigue, 83 (2016) 174-183. [5] macha, e., modele matematyczne trwałości zmęczeniowej materiałów w warunkach losowego złożonego stanu naprężenia, seria: monografie, wrocław, 13 (1979) 100 (in polish). [6] macha, e., generalization of strain criteria of multiaxial cyclic fatigue to random loadings, fortschr. – ber. vdi, reiche 18, nr 52, vdi-verlag, dusseldorf, (1988) 102. [7] łagoda, t., macha, e., generalization of energy multiaxial cyclic fatigue criteria to random loadings, multiaxial fatigue and deformation: testing and prediction, astm stp 1387, american society for testing and materials, west conshohocken, pa, (2000) 173. [8] walat, k., łagoda, t., lifetime of semi ductile materials through the critical plane approach, international journal of fatigue, 67 (2014) 73-77. [9] carpinteri, a., spagnoli, a., vantadori, s., multiaxial fatigue assessment using a simplified critical plane-based criterion, international journal of fatigue, 33(8) (2011) 969-976. doi: 10.1016/j.ijfatigue.2011.01.004. [10] macha, e., generalization of fatigue fracture criteria for multiaxial sinusoidal loadings in the range of random loadings, in: biaxial and multiaxial fatigue, egf 3, (edited by m.w. brown and k.j. miller), mechanical engineering publications, london, (1989) 425–436. [11] carpinteri, a., kurek, m., łagoda, t., vantadori, s., estimation of fatigue life under multiaxial loading by varying the critical plane orientation, international journal of fatigue, (2016). doi: 10.1016/j.ijfatigue.2016.10.028. [12] mrzygłód, m., kurek, m., łagoda, t., the application of the criteria of multiaxial fatigue in the critical plane for the topology optimization, application of the fictitious radius for the calculation of the fatigue life using the elastic-plastic body model, aip conference proceedings, 1780, fatigue failure and fracture mechanics xxvi, (2016) 030003-1-6. [13] kurek, m., łagoda, t., including of ratio of fatigue limits from bending and torsion for estimation fatigue life under cyclic loading, procedia materials science, 12 (2016) 30-35. [14] astm e 739–91, standard practice for statistical analysis of linearized stress–life (s–n) and strain life fatigue data, in: annual book of astm standards, philadelphia, 03.01 (1999) 614–628. [15] nishihara, t., kawamoto, m., the strength of metals under combined alternating bending and twisting, memoirs of the college of engineering, kyoto imperial university, japan, (1941). [16] muller, a., zum festigkeitsverhalten von mehrachsig stochastisch beanspruchten gußeisen mit kugelgraphit und tempergu. fraunhofer institut fur betriebsfestigkeit, darmstadt, (1994). p << /ascii85encodepages false /allowtransparency false /autopositionepsfiles true /autorotatepages /none /binding /left /calgrayprofile (dot gain 20%) /calrgbprofile (srgb iec61966-2.1) /calcmykprofile (u.s. web coated \050swop\051 v2) /srgbprofile (srgb iec61966-2.1) /cannotembedfontpolicy /error /compatibilitylevel 1.4 /compressobjects /tags /compresspages true /convertimagestoindexed true /passthroughjpegimages true /createjobticket false /defaultrenderingintent /default /detectblends true /detectcurves 0.0000 /colorconversionstrategy /cmyk /dothumbnails false /embedallfonts true /embedopentype false /parseiccprofilesincomments true /embedjoboptions true /dscreportinglevel 0 /emitdscwarnings false /endpage -1 /imagememory 1048576 /lockdistillerparams false /maxsubsetpct 100 /optimize true /opm 1 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/hrv (za stvaranje adobe pdf dokumenata najpogodnijih za visokokvalitetni ispis prije tiskanja koristite ove postavke. stvoreni pdf dokumenti mogu se otvoriti acrobat i adobe reader 5.0 i kasnijim verzijama.) /hun 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can be opened with acrobat and adobe reader 5.0 and later.) >> /namespace [ (adobe) (common) (1.0) ] /othernamespaces [ << /asreaderspreads false /cropimagestoframes true /errorcontrol /warnandcontinue /flattenerignorespreadoverrides false /includeguidesgrids false /includenonprinting false /includeslug false /namespace [ (adobe) (indesign) (4.0) ] /omitplacedbitmaps false /omitplacedeps false /omitplacedpdf false /simulateoverprint /legacy >> << /addbleedmarks false /addcolorbars false /addcropmarks false /addpageinfo false /addregmarks false /convertcolors /converttocmyk /destinationprofilename () /destinationprofileselector /documentcmyk /downsample16bitimages true /flattenerpreset << /presetselector /mediumresolution >> /formelements false /generatestructure false /includebookmarks false /includehyperlinks false /includeinteractive false /includelayers false /includeprofiles false /multimediahandling /useobjectsettings /namespace [ (adobe) (creativesuite) (2.0) ] /pdfxoutputintentprofileselector /documentcmyk /preserveediting true /untaggedcmykhandling /leaveuntagged /untaggedrgbhandling /usedocumentprofile /usedocumentbleed false >> ] >> setdistillerparams << /hwresolution [2400 2400] /pagesize [612.000 792.000] >> setpagedevice microsoft word numero_39_art_19 m. a. lepore et alii, frattura ed integrità strutturale, 39 (2017) 191-201; doi: 10.3221/igf-esis.39.19 191 from test data to fe code: a straightforward strategy for modelling the structural bonding interface m. a. lepore, m. perrella department of industrial engineering, university of salerno, via giovanni paolo ii, 132 84084 fisciano (sa), italy malepore@unisa.it, mperrella@unisa.it abstract. a straightforward methodology for modelling the cohesive zone (czm) of an adhesively bonded joint is developed, by using a commercial finite element code and experimental outcomes from standard fracture tests, without defining a damage law explicitly. the in-house developed algorithm implements a linear interpolated cohesive relationship, obtained from literature data, and calculates the damage at each step increment. the algorithm is applicable both to dominant mode i or dominant mode ii debonding simulations. the hypothesis of unloading stages occurrence is also considered employing an irreversible behaviour with elastic damaged reloading. a case study for validation is presented, implementing the algorithm in the commercial finite element method (fem) software abaqus®. numerical simulation of dominant mode i fracture loading provides with satisfactory results. keywords. finite element method; mode i crack; fracture toughness; cohesive law; adhesive bonding. citation: lepore, m. a., perrella, m., from test data to fe code: a straightforward strategy for modelling the structural bonding interface, frattura ed integrità strutturale, 39 (2017) 191-201. received: 10.06.2016 accepted: 10.10.2016 published: 01.01.2017 copyright: © 2017 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. introduction owadays, structural bonding is widely used as joining technique in many engineering fields. safety requirements are often to be satisfied, as for example in civil applications where frp laminates are anchored to beams for strengthening purposes and seismic retrofitting [1]; in superconducting systems where insulating composite wraps are bonded to superconducting cables subjected to lorentz forces [2]; in aeronautical and automotive structures for repairing process [3]. there are numerous advantages with respect to traditional mechanical fastening methods: homogeneous distribution of stresses throughout the union, reduction of the joint weight, sealing function and protection against corrosion, excellent fatigue strength, free design of the joint, and so on. however, the application of this technique to high-technology industry requires the satisfaction of a large number of requirements especially about the adhesive joining durability and reliability. thus, a proper description of mechanical behaviour, and the prediction of fracture propagation at the interface is necessary in order to realize a correct design phase of adhesively bonded structures. continuum damage mechanics (cdm) offers suitable tools for facing this issue, in coupling with the fe methodology. using such approach the proper definition of a representative volume element (rve) is crucial because its dimension relates the relevant scales in which the fracture process and the softening behaviour take place. a careful choice of the n http://www.gruppofrattura.it/pdf/rivista/numero39/audio/19.mp3 m. a. lepore et alii, frattura ed integrità strutturale, 39 (2017) 191-201; doi: 10.3221/igf-esis.39.19 192 rve dimension makes this approach versatile enough to deal with a plenty of practical problems, among which, as examples, we can cite the homogenization of an rve as a step for multiscale modelling [4]; the damage and failure modelling of inhomogeneous micro-structured materials under quasi static load [5]; the damage evolution and failure modelling of homogeneous materials under creep conditions [6]. the cohesive zone modelling (czm) approach can be considered as a special case of the cdm methodology in which the softening behaviour is confined to an interface domain and the rve dimension is implicitly taken into account by the material law. among the methodologies for studying decohesion processes, the czm approach is relevant in many engineering applications, from the simple debonding of a cantilever beam [7], to the three-dimensional delamination modelling in a cracked fml full scale aeronautic panel [8]. this method is based on the definition of a cohesive zone law, i.e. the traction-separation relationship at the bonded surface of the joint. for basic modes of debonding, the czm can be estimated with experimental data from suitable test campaigns. once defined, both in a direct or indirect way, it can be implemented in a finite element code for simulating the debonding phase. many cohesive traction-separation laws are reported in literature by using experimental, theoretical, and computational techniques. among them, a large number concerns the response in normal (mode i) and shearing (mode ii and iii) direction with respect to the interface and under mixed mode i-ii loading condition, whilst pure mode iii or mixed mode ii-iii are less investigated. in order to evaluate experimentally the constitutive, peel, properties of adhesive and adherends, both metallic and composite, several standard test methods use the double cantilever beam (dcb) specimen under mode i fracture loading. olsson et al. [9] developed an analytical solution for the determination of the constitutive properties of thin interphase layers, which provides with reliable results for non rigid adherends. sorensen et al. [10] presented a traction-separation relation, based on the j-integral approach, for dcb. valoroso et al. [11] proposed a deterministic identification of mode i cohesive parameters for bonded interfaces that overcomes the difficulties and limitations of iso 25217 standard test. stigh et al. [12] proposed an alternative experimental method to determine the complete cohesive relation of a thin adhesive layer loaded in peel with the same dcb specimen. shen et al. [13], instead, implemented digital image correlation (dic) technique to measure displacements at the crack tip in order to evaluate fracture parameters and determine cohesive relationships. fernandes et al. [14] analysed mode ii cohesive relationship of carbon–epoxy composite bonded joints using dic and the direct method applied to the end notched flexure (enf) test. mode ii and mixed mode i-ii testing were also analysed in [15, 16]. a mode iii traditional test methodology was presented in [17]. cricrì et al. [18] presented a methodology, based on an innovative test device, for studying bonded elements subjected to pure mode iii loading condition. the present work describes a straightforward strategy for modelling the structural bonding interface of a joint using a commercial fem code, assuming that the loading modes are uncoupled. such an approach is implemented in an algorithm and a validation study case is presented by using the software abaqus. theoretical background n a 2d problem, the traction vector t, whose components  and , respectively acting on the interface along normal n and tangential s direction, can be expressed in matrix form as: nn ns n sn ss s k k k k                         t k u (1) where knn, and kss are stiffness terms, while n and s are normal and tangential separations, respectively. in particular, separations are numerically equal to the jump displacements of the cohesive elements. the initial (undamaged state) stiffness components of knn and kss are respectively equal to the ratio between young’s modulus and adhesive thickness and the ratio between shear modulus and adhesive thickness whereas ksn = kns = 0. in general, during the phase of interface opening, the stiffness parameters vary, decreasing their values with damage increasing. therefore, the damage law defines the stiffness terms. when  and are considered uncoupled, the mixed elastic terms in eq. (1), kns and ksn, are set to null values. many effective traction-separation laws valid for pure loading modes or uncoupled cohesive behaviours are available in literature. among these, one of the simplest, sometimes also available in commercial fem codes, is the bilinear (linear softening) relationship. three points of the traction-separation curve define this model (origin, maximum and final points) whilst the area under the curve represents the critical fracture energy gc (fig. 1). in the first section of the curve, two i m. a. lepore et alii, frattura ed integrità strutturale, 39 (2017) 191-201; doi: 10.3221/igf-esis.39.19 193 hypothesis are assumed: there is no damage at the material interface (adhesive) and displacements and strains are elastic. in the second section, instead, the adhesive undergoes progressive damage up to the reaching of a limit value, corresponding to the occurrence of the maximum allowable deformation. in this section, the stress, normal respect to the displacement direction, decreases. beyond this limit value, the stress has null values.  nc m 0 figure 1: bilinear traction-separation relationship for mode i loading condition. the vertex, corresponding to the ending point of linear elastic section, represents the starting point of damage process. the damage function, which relates the separation within the cohesive elements to the corresponding tractions, is initially set to zero and reaches its maximum value, equal to one, in correspondence of the maximum displacement at the interface, i.e. the point of maximum damage. the cohesive law for mode i (or mode ii) fracture process is defined by only three parameters: 1) the initial stiffness k0, which physically is the slope of the elastic section; 2) the traction 0 at the interface or the separation c within the cohesive elements, in correspondence of which the damage process starts; 3) the critical energy release rate gc or the displacement at the failure m. the mathematical formulation of bilinear cohesive law is the following:     n n c n m c n m c m n m k0 0 ,  0 ,   0,                             (2) c mg 0 1 2   tvergaard et al. [19] proposed a tri-linear relationship, more accurate for ductile adhesives. as previously, the first section grows linearly reaching the damage initiation process in correspondence of a critical separation c1. the traction remains constantly equal to its maximum value in the range [c1, c2] and then decreases after the critical separation c2. the shape of trapezoidal function is shown in fig. 2, while it is mathematically expressed as follows:     n n c c c n c n m c n m c m n m 0 1 1 0 1 2 0 2 2 ,  0 ,   ,   0,                                       (3)  c m c cg 0 2 1 1 2       m. a. lepore et alii, frattura ed integrità strutturale, 39 (2017) 191-201; doi: 10.3221/igf-esis.39.19 194  nc1 m 0 c2 figure 2: trilinear traction-separation relationship for mode i loading condition. another often used traction-separation model is the exponential relationship (fig. 3), proposed by needleman et al. [20].  nc m 0 figure 3: exponential traction-separation relationship for mode i loading condition. this model consists of a continuous and smooth exponentially decaying function, having the following formulation: n c c c g e 2      (4) in the exponential model, the damage process begins with the displacement n 0  , whereas in the previously described laws the damage initiation starts after the reaching of a critical separation value or of the corresponding maximum stress occurrence. for all the above models, a damage variable d is also defined, depending on the maximum separation currently achieved, max. such variable can be conveniently expressed in terms of current versus initial stiffness, as:  max max d k 0 1 1      (5) proposed methodology n this work, a new approach in the damage fe implementation of interfaces is proposed. first, it is not explicitly defined a damage law. indeed, this relation is calculated at each step by using the experimental cohesive relationship, which is generated by interpolating some inputted points. these points are sampled from a traction-separationcurve, obtained from previous (mode i or ii) decohesion tests, and are inserted in an array named parx. the damage d is evaluated at each step increment and is updated from the beginning of the loading process (when the decohesion displacement is yet null). the present tool allows to define damage variables that are independent for each fracture mode (i.e. anisotropic damage formulation). for the sake of simplicity, we hereby describe only the analytical formulation of mode i cohesive law because the mode ii cohesive relationship can be similarly defined. thus, the components of the traction vector t of dominant mode i loading conditions are expressed by the following equations: i m. a. lepore et alii, frattura ed integrità strutturale, 39 (2017) 191-201; doi: 10.3221/igf-esis.39.19 195   n n n n n n d k k 0 0 1 ,   0 ,   0           (6)   s sd k 01   (7) where d is the damage function and the initial stiffness kn0 and ks0 are the slope of the first segment of mode i and mode ii cohesive curve, respectively. the structure of the algorithm requires the displacement jump u and its relative increments du as data input, whilst provides as output with ,  and its derivative respect to the displacement jump components. for each integration step, the value of displacement jump across the interface n is compared with the state variable max, which is associated with the current damage (5), reported here:     max t0,  max       where t is the variable time. when separation is greater than previous max, i.e. the point (curr, curr) is located on the effective limit curve  nf  (fig. 4), the damage d is increasing according to the relationship ncurr n k d k 0 1    (8) being curr equal to the updated max , the current stiffness is  max ncurr n max f k        (9) whilst the initial stiffness  nk f0 0  (10) then, the stress field is recalculated according to eqs. (6)-(7).  nmax(t) curr(t) f(curr) kcurr p1 p2 pi pn figure 4: interpolated cohesive law – opening of the interface. m. a. lepore et alii, frattura ed integrità strutturale, 39 (2017) 191-201; doi: 10.3221/igf-esis.39.19 196 the stress increment processed in fe iterations is equal to   n n n n n n n n dd d k kd d d k 0 0 0 1 ,   0 ,   0              (11) s d d 0    n d d 0    (12)   s s s s s s s s dd d k kd d d k 0 0 0 1 ,   0 ,   0              where      n n n n max n n n f f ddd f d otherwise 2 1 ,   , 0 0 0,                         (13) s dd d 0   a null derivative of damage with respect to separation n implies that damage is considered constant and equal to the last estimated value when opening displacement at the interface is decreasing orn < max. for this reason, if the current value of normal separation is less than previous max, the corresponding point (curr, curr) is located inside the area under the effective limit curve and the damage d is considered unchanged (fig. 5). the stress field is calculated using eqs. (6)-(7).  nmax(t)curr(t) curr f(max) kcurrk0 ddn p1 p2 pi pn ddn figure 5: interpolated cohesive law – closing of the interface. m. a. lepore et alii, frattura ed integrità strutturale, 39 (2017) 191-201; doi: 10.3221/igf-esis.39.19 197 a simplified flowchart of the proposed methodology in presented in fig. 6. displacements at interface and their increments u, du experimental traction-separation curve points (parx) shear modulus g updating of the state variable damage (d) if convergence condition is satisfied in the previous step: d_trial  d calculation of damage: d_curr = f(parx) d_trial = max(d, d_curr) calculation of stress state: (u, d_trial) dd/du , d(u, d_trial, du)/du figure 6: overall schematic of algorithm, to be repeated until the convergence over u is achieved. although the stress field calculated using (6)-(7) is considered as obtained from a mode i fracture loading condition, i.e. the separation normal to the interface dominates the slip tangent to the interface, the developed algorithm can also evaluate the tangential stress (mode ii) by means of a shear stiffness, function of d. therefore, the stress field for a dominant mode ii condition is obtained from the following equations:   s s s s s s d k k 0 0 1 ,   0 ,   0           (14)   n nd k 01   (15) m. a. lepore et alii, frattura ed integrità strutturale, 39 (2017) 191-201; doi: 10.3221/igf-esis.39.19 198 where scurr s k d k 0 1    . (16) the tangential slip distance is a numerical input from each fe iteration. when the dominant mode ii loading condition is analysed, an experimental cohesive law shearseparation s is to be used whilst the methodology follows the same scheme. case study he proposed cz model is implemented into the abaqus fem code through the user subroutine uinter. a validation of the algorithm is presented simulating a case study, whose 2d geometry consists of a t-beam bonded to a clamped edge plate. the adopted case study is representative of all the main aspects and critical issues involved in debonding phenomenon of adhesive layer. four different boundary conditions on displacements (see fig. 7) are sequentially imposed to the web edge of the t-beam: 1) opposing displacements to apply a clockwise moment; 2) opposing displacements to apply an anticlockwise moment; 3) null displacement (unloading step); 4) tensile displacement. figure 7: boundary conditions on web edge displacements: step 1, step 2 and step 4, respectively. the beam and the plate are considered made of steel, whilst the simulated adhesive is corresponding to the epoxy resin araldite® 2015. their elastic properties are listed in tab. 1. material e [gpa]  steel 210 0.30 araldite® 2015 1.85 0.33 table 1: adherend and adhesive mechanical properties. the bonded joint is modelled with about 3000 cps4 elements (fig. 8). the adhesive interface is modelled using cohesive elements with zero thickness; the considered czm initial stiffness values are listed in tab. 2. nnk ssk ttk 6476 2496 0 table 2: czm initial stiffness values set in fe simulations. t m. a. lepore et alii, frattura ed integrità strutturale, 39 (2017) 191-201; doi: 10.3221/igf-esis.39.19 199 figure 8: fe model mesh. the experimental points used for the built up of the piecewise linear cohesive law, as explained in the methodology paragraph, are taken from the mode i decohesion test outcomes in [21]. results and discussion he plots of deformed bonded joint at different steps are shown in fig. 9. the debonding phenomenon occurs since the application of first loading condition. the relationship between traction and separation of representative points at the interface is depicted in fig. 10. it is possible to highlight a cohesive behaviour, which includes the phases of damage propagation complete debonding, and constant damage. figure 9: deformed mesh plots at step 1, step 2 and step 4, respectively. in particular, in the representative point p1, a complete debonding is reaching during step 1 (fig. 9-a), when a clockwise moment is applied, strictly following the cohesive behaviour as expressed by the experimental law. the normal separation, after the debonding, reaches the value of about 0.06 mm maintaining the stress equal to zero. subsequently, when an anticlockwise moment is applied to the specimen, the trend of normal displacement highlights the interface closure of the upper part of flange (fig. 9-b) and the cohesive stress increases in compression, following the slope of kn0, up to the value of about 19 mpa. during the step 3, there is the unloading phase of the entire specimen and stress and separation return to zero. finally, when a tensile displacement is applied to the bonded joint for highlighting the interface opening (fig. 9-c), the corresponding cohesive traction remains equal to zero nevertheless the separation increases up to the value of about 0.045 mm. moreover, the hypothesis of case study under dominant mode i load condition is confirmed comparing the components of the traction vector. indeed, as verifiable in fig. 10, the value of tangential traction is negligible during the entire load spectrum with respect to the traction normal to the interface. t p1 a) b) c) m. a. lepore et alii, frattura ed integrità strutturale, 39 (2017) 191-201; doi: 10.3221/igf-esis.39.19 200 figure 10: traction-separation curves (n and s) of the representative point p1 at the interface. the damage evolution is evaluated from the beginning of the loading process, trying to better simulate the real process of decohesion. although the tabular definition of damage as function of displacement is available in abaqus, there is no possibility to use uncoupled damage functions, which refer to different fracture modes. with the proposed tool, instead, it is possible to define a specific damage function for each fracture mode. finally, good convergence properties of the algorithm have been shown during fem simulations, allowing the authors to consider the described methodology to be efficient and robust. conclusions he cohesive zone modelling of an adhesively bonded joint is analyzed by using an innovative straightforward methodology implemented into a commercial finite element code. experimental results from standard fracture tests, in terms of traction-separation law, are used as an input for the algorithm but no damage law has to be explicitly defined. in such a way, the in-house developed algorithm calculates the damage at each step increment, from the beginning of loading process, when decohesion opening displacement is yet null, up to the complete debonding of the joint. a case study for validation is presented by using the software abaqus. the cohesive behaviour in the interface elements of bonded joint is shown over all different loading conditions (damage propagation, constant damage and complete debonding), providing with satisfactory results. references [1] ascione l., berardi v.p., anchorage device for frp laminates in the strengthening of concrete structures close to beam-column joints, composites part b: engineering, 42(7) (2011) 1840-1850. [2] corato v., affinito l., anemona a., besi vetrella u., della corte a., di zenobio a., fiamozzi zignani c., freda r., messina g., muzzi l., perrella m., reccia l., tomassetti g., turtù s., detailed design of the large-bore 8t superconducting magnet for the nafassy test facility, superconductor science and technology, 28(3) (2015) 034005. doi:10.1088/0953-2048/28/3/034005. [3] campilho r.d.s.g., de moura m.f.s.f., domingues j.j.m.s., using a cohesive damage model to predict the tensile behaviour of cfrp single-strap repairs, international journal of solids and structures, 45 (2008) 1497-1512. [4] cricrì, g., luciano, r., homogenised properties of composite materials in large deformations, composite structures, 103 (2013) 9-17. [5] cricrì, g., a consistent use of the gurson-tvergaard-needleman damage model for the r-curve calculation, frattura ed integrità strutturale, 24 (2013) 161-174. [6] calì, c., cricrì, g., perrella, m., an advanced creep model allowing for hardening and damage effects, strain, 46(4) (2010) 347-357. t m. a. lepore et alii, frattura ed integrità strutturale, 39 (2017) 191-201; doi: 10.3221/igf-esis.39.19 201 [7] valoroso n., de barros s., adhesive joint computations using cohesive zones, applied adhesion science, 1 (2013) 19. doi:10.1186/2196-4351-1-8. [8] citarella, r., cricrì, g., three-dimensional bem and fem submodelling in a cracked fml full scale aeronautic panel, applied composite materials, 21(3) (2014) 557-577. [9] olsson p., stigh u., on the determination of the constitutive properties of thin interphase layers an exact inverse solution, international journal of fracture, 41 (1989) 71-76. [10] sørensen b.f., jacobsen t.k., determination of cohesive laws by the j integral approach, engineering fracture mechanics, 70 (2003) 1841-1858. [11] valoroso n., sessa s., lepore m., cricrì g., identification of mode-i cohesive parameters for bonded interfaces based on dcb test, engineering fracture mechanics, 104 (2013) 56-79. [12] stigh u., andersson t., an experimental method to determine the stress-elongation relation for a structural adhesive loaded in peel, european structural integrity society, 27 c (2000) 297-306. [13] shen b., paulino g.h., direct extraction of cohesive fracture properties from digital image correlation: a hybrid inverse technique, experimental mechanics, 51 (2011) 143-163. [14] fernandes r.m.r.p., chousal j.a.g., de moura m.f.s.f., xavier j., determination of cohesive laws of composite bonded joints under mode ii loading, composites: part b, 52 (2013) 269-274. [15] leffler, k., alfredsson, k.s., stigh, u., shear behaviour of adhesive layers, international journal of solids and structures, 44(2) (2007) 530-545. [16] högberg, j.l., sørensen, b.f., stigh, u., constitutive behaviour of mixed mode loaded adhesive layer, international journal of solids and structures, 44(25-26) (2007) 8335-8354. [17] khoshravan, m.r., moslemi, m., investigation on mode iii interlaminar fracture of glass/epoxy laminates using a modified split cantilever beam test, engineering fracture mechanics, 127 (2014) 267-279. [18] cricrì g., perrella m., sessa s., valoroso n., a novel fixture for measuring mode iii toughness of bonded assemblies, engineering fracture mechanics, 138 (2015), 1-18. doi: 10.1016/j.engfracmech.2015.03.019. [19] tvergaard v., hutchinson j.w., the relation between crack growth resistance and fracture process parameters in elastic-plastic solids, journal of the mechanics and physics of solids, 40 (1992) 1377-1397. [20] needleman, a., an analysis of decohesion along an imperfect interface, international journal of fracture, 42 (1990) 21-40. [21] de moura m.f.s.f., gonçalves j.p.m., magalhães a.g., a straightforward method to obtain the cohesive laws of bonded joints under mode i loading, international journal of adhesion and adhesives, 39 (2012) 54-59. << /ascii85encodepages false /allowtransparency false /autopositionepsfiles true /autorotatepages /none /binding /left /calgrayprofile (dot gain 20%) /calrgbprofile (srgb iec61966-2.1) /calcmykprofile (u.s. web coated \050swop\051 v2) /srgbprofile (srgb iec61966-2.1) /cannotembedfontpolicy /error /compatibilitylevel 1.4 /compressobjects /tags /compresspages true /convertimagestoindexed true /passthroughjpegimages true /createjobticket false /defaultrenderingintent /default /detectblends true /detectcurves 0.0000 /colorconversionstrategy /cmyk /dothumbnails false /embedallfonts true /embedopentype false /parseiccprofilesincomments true /embedjoboptions true /dscreportinglevel 0 /emitdscwarnings false /endpage -1 /imagememory 1048576 /lockdistillerparams false /maxsubsetpct 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/hrv (za stvaranje adobe pdf dokumenata najpogodnijih za visokokvalitetni ispis prije tiskanja koristite ove postavke. stvoreni pdf dokumenti mogu se otvoriti acrobat i adobe reader 5.0 i kasnijim verzijama.) /hun 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can be opened with acrobat and adobe reader 5.0 and later.) >> /namespace [ (adobe) (common) (1.0) ] /othernamespaces [ << /asreaderspreads false /cropimagestoframes true /errorcontrol /warnandcontinue /flattenerignorespreadoverrides false /includeguidesgrids false /includenonprinting false /includeslug false /namespace [ (adobe) (indesign) (4.0) ] /omitplacedbitmaps false /omitplacedeps false /omitplacedpdf false /simulateoverprint /legacy >> << /addbleedmarks false /addcolorbars false /addcropmarks false /addpageinfo false /addregmarks false /convertcolors /converttocmyk /destinationprofilename () /destinationprofileselector /documentcmyk /downsample16bitimages true /flattenerpreset << /presetselector /mediumresolution >> /formelements false /generatestructure false /includebookmarks false /includehyperlinks false /includeinteractive false /includelayers false /includeprofiles false /multimediahandling /useobjectsettings /namespace [ (adobe) (creativesuite) (2.0) ] /pdfxoutputintentprofileselector /documentcmyk /preserveediting true /untaggedcmykhandling /leaveuntagged /untaggedrgbhandling /usedocumentprofile /usedocumentbleed false >> ] >> setdistillerparams << /hwresolution [2400 2400] /pagesize [612.000 792.000] >> setpagedevice microsoft word numero_38_art_5 d. marhabi et alii, frattura ed integrità strutturale, 38 (2016) 36-46; doi: 10.3221/igf-esis.38.05 36 focussed on multiaxial fatigue and fracture prediction of the critical stress to crack initiation associated to the investigation of fatigue small crack d. marhabi h.e.i 13 rue de toul 59046 lille-cedex france driss.marhabi@hei.fr n. benseddiq, g. mesmacque university lille 1 villeneuve d’ascq france noureddine.benseddiq@univ-lille1.fr gerard.mesmacque@univ-lille1.fr z. azari labps, enim, 1 route d’ars laquenexy, 57070 metz, france azari@enim.fr j.m. nianga h.e.i 13 rue de toul 59046 lille-cedex france jean-marie.nianga@hei.fr abstract. fatigue design is of vital importance to avoid fatigue small crack growth in engineering structures. this study shows that the critical fatigue design stress can be defined below the usual endurance limit, considered in rules and codes. the material constitutive behaviour is using linear isotropic elasticity. lassere and pallin-luc [1-2] use the elastic energy and over-energy under uniaxial load (tension and rotating bending). the authors deduce the influencing critical stress value corresponding to σ*. it’s a linear approach. we propose an over-energy under dissymmetrical rotating bending and expressed in the ellipse axes. an asymptotic approach is transformed the over-energy in polynomial function of critical stress. unknown depend on experimental service conditions, endurance limit of tension and rotating bending of specimen. the fatigue database of 30ncd16 steel studied by froustey and dubar [3-13] is used. critical stresses are evaluated (fig. 2). the research done by manning and all [4] has shown the small crack effect to be as large as 0.3 mm. small crack and critical stress are illustrated here in as resulting from pure bending approach expressed by bazant law [7]. it’s reproduces well the kitagawa diagram [6] (fig. 3). when the short cracks are hidden in the material, we shows that the number citation: marhabi, d., benseddiq, n., mesmacque, g., azari, z., nianga, j.m., prediction of the critical stress to crack initiation associated to the investigation of fatigue small crack, frattura ed integrità strutturale, 38 (2016) 36-46. received: 12.05.2016 accepted: 20.06.2016 published: 01.10.2016 copyright: © 2016 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. d. marhabi et alii, frattura ed integrità strutturale, 38 (2016) 36-46; doi: 10.3221/igf-esis.38.05 37 cycles during small crack growth be significantly higher (fig. 4) than the corresponding cycles of large cracks growth (oni’s fatigue test) for the same physically crack size. indeed its evolution can be blocked by a microstructural barrier (grain boundary, for example). hence, the considerations of small crack growth are strongly influencing the fatigue life of a component or structure. keywords. tensile; dissymmetrical rotating bending; over-energy; critical stress; small crack; fatigue cycle. introduction ue to fatigue loading cracks can initiate in material. they can exist as a consequence of manufacturing process such as (deep machining marks, voids in welds) or of metallurgical and geometrical discontinuities. small cracks have been thoroughly studied aerospace, nuclear, and the ground vehicle industries. in order to predict defects and/or transverse cracks under service conditions, different cracking process have to be noted and explained in terms of the fatigue small crack effect. the first part of this paper is dedicated to analyze the over-energy under dissymmetrical rotating bending and expressed in the ellipse support. an asymptotic approach associated to critical stress function predict and evaluate the unknown stresses σ*. the second part proposes the small crack size effect using pure bending approach and bazant law. we confirm that the curve trend reproduces well the kitagawa diagram. the last part is considering the applicability of linear elastic fracture mechanics (lefm) for physically small crack. the integral calculus of number cycles required for small crack is determined. however, the small crack has faster growth rates than long crack. the influencing stress in the fatigue in the fatigue initiation crack s proposed by palin-luc, lasserre and banvillet [1-2] to predict the effect on the fatigue under a uniaxial load in the component. an area influencing fatigue crack initiation s* is considered. from fully reversed fatigue, these authors show that a stress σ* can be defined below the endurance limit σ-1. the critical stress limit σ* is associated to no damage crack. the elastic energy and over-energy in this study we assume that the material’s behaviour law is linear isotropic elasticity. for a given elementary area of material, the energy density per loading cycle is: ij ij t m t m t dt t 1 1 w ( , ) ( , ) 2    (1a) the energy wte and wrb distributions are axisymmetric in tensile and rotating bending. these sinusoidal loadings are taking as a reference to identify the critical stress * . s* is the area influencing fatigue crack initiation. s c p x y around c so that w p w c** ( ) ( , ) ( ) ( )         (1b) the over-energy c( ) allows initiating short cracks around the critical point c d a d. marhabi et alii, frattura ed integrità strutturale, 38 (2016) 36-46; doi: 10.3221/igf-esis.38.05 38 w m w c s cs c c ds** ( ( ) ( ))* ( )( ) 1( )  (1c) at the endurance limit, this quantity c( ) is supposed to be constant. if we note d uniax  as being its value at the endurance limit for any uniaxial stress our criterion is: dc uniax ( )  (1d) postulate: the quantity  is an intrinsic size in the material (noted uniax  ) thus it does not depend on the loading type. we can identify their energy to satisfy the equation: uniax te rb pb rb dw w w w w ,    (2a) d uniax te rb pb rb d,         (2b) uniaxial energy associated to critical stress by reference to an homogenous fully reversed uniaxial stress and the energy analyses by palin-luc, lasserre and banvillet (eqs. 1a and 1c). the authors deduce the influencing critical stress value corresponding to σ* in the fatigue initiation crack: eq eq te eq rb * 2 2 , ,2    (3) from (eqs. 1a and 1c) and value at the endurance limit for (eq. 3) it easy to prove that *uniaxw is given by (4b); d uniax can be calculated by (4c). eq te rb te rb uniax rb ted uniax w e e a b c * 2 2 , 1 , 1 2 2 , 1 , 1* 2 2 , 1 , 1 2( ) ( ) 2( ) ( ) 4 ( ) ( ) 4 (4 ) (4 ) (4 )                           energy under dissymmetrical rotating bending he service stress (fig. 1 (5a) (b)) on a straight section by a cylindrical specimen: y r t trb d m rb rbr r ( ) sin, ,      (5a) the energy density given to each elementary under dissymmetrical rotating bending is: m rb rb rb d y r e r e r 2 2 22 , ,w 4 4             (5b) t (4a) (4b) (4c) d. marhabi et alii, frattura ed integrità strutturale, 38 (2016) 36-46; doi: 10.3221/igf-esis.38.05 39 the energy value corresponding to σ* for fatigue initiation crack is represented by: m rb te rbrb uniax y r w e r e r e 2 22 2 22* * , , 1 , 1* * rb,d 2( ) ( ) w 4 4 4                     (5c) the iso-energy (eq. 5c) is an ellipse on the cross-section of the specimen (fig. 1). eq. 5a eq. 5c figure 1: dissymmetrical rotating bending (eq. 5a) and line iso-energy *w (eq. 5c). the large half axis a * and the small half axis b* defined by (eq. 5c) are the ellipse axes: te rb rb m rb b r 2 2 2* , 1 , 1 2 2 , 2            (6a) te rb rb a r 2 2 2* , 1 , 1 2 2( ) ( )           (6b) over-energy under dissymmetrical rotating bending (d.r.b) in the ellipse axes this part is dedicated to analyze the over-energy expressed in the ellipse support is: rb d te rb rb d eb a r r r w ds is ce w uniax s , , 1 , 1 , 2 22 * * 4 2 1 * * *                            (7a) the member term i ce is given by: rb d rb di w y r d dr w y r d dr i iy ysc sece c e, , ( , ) ( , )     (7b) sc and se are respectively the circular and the elliptical section (fig. 1 (5c)) the integral transformation in elliptical section gives d. marhabi et alii, frattura ed integrità strutturale, 38 (2016) 36-46; doi: 10.3221/igf-esis.38.05 40 eq rbrb b a bm rb rb r rr b a u dud r re e r a b a b r r e r r e i e 3 3 222 * * * * , 22 2* * * 1 , 2 3 4 2 2* *1 2 2cos cos sin 0 ) 8                                                                                     (7c) the integral transformation in circular section evaluated by m rb rb ui c e e r m rb rbdud e e 2 2 1 1, 3(1 cos 2 ) (1 sin 2 ) 4 2 2 221 2 2, 80 2                                (7d) the over-energy (7a) under dissymmetrical rotating bending when a r * 1 , gives: m rb rb rb eq rb te rb rb d a b a b r r r r eb ae r r , , , 1 , 1 , 3 3* * * *2 2 2 2( 2 ) 2 22 4* * 8 1                                                                        (8) for us, this result is necessary to identify critical crack in the cylindrical specimen. an asymptotic method and over-energy expressed by critical stress the basic concept in the influence area of no damage crack is expressed by * *w wrb,dte  we allow writing two limits equations near the small half axis and the large half axis of the ellipse (fig. 1). with this asymptotic method, we have: b for eq eq rb r a for eq rb r 2*2* 20, ( ), 2*2* 2, ( ) 2                               (9) the equality (8) and (9) are considered to define the critical stress eq. (10). it can be deduced by the application of the postulate (eq. 2b):    eq rb eq rb rb d te rb b ca , 2* 2 * 2 0      (10a) d. marhabi et alii, frattura ed integrità strutturale, 38 (2016) 36-46; doi: 10.3221/igf-esis.38.05 41 eq rb eq tete rb rb eq te te rb eq rb rb eq rb rb rb rb rb a b c , ,, 1 , 1 , , 1 , 1 , , 6 2 2 24 * [( 2 ) ( ) ( )] 2 22 2 2[4 * [( ) (2 ) ]( )                          (10b) from the eq. (10a) according to the postulate energy and (eq. 9) we define: m rb rb rb rb rb rbte eq m te rb te rb database b b a cmpa ampa mpa mpa , , , 1 , 1 2 2 4427 * 2290 658 560                                                      (11) prediction of the critical stress our proposal consists to study an analytical model and predict the critical stress:    2* * 2 * 2( )eq rb eq rb eq rba b c     (12) we use the fatigue database of 30ncd16 steel [3-13]. the endurance limit d dte fr, 1 , 1,   and various stresses values rb m rb and ,   identify the roots by (eq.12). figure 2: over-energy (d.r.b) for various stress values of 30ncd16 steel. the critical stresses of any curve in tab. 1 are situated between σ* and σ-1 and designed respectively by the stress of small crack σ*min and the stress of the smallest crack σ*max. the over-energy allows for the critical stress and requires a vigilance on the fatigue design in engineering structures. d. marhabi et alii, frattura ed integrità strutturale, 38 (2016) 36-46; doi: 10.3221/igf-esis.38.05 42 specimen 1 specimen 2 specimen 3 specimen 4 bending stress (mpa) rb m  rb m  rb m  rb m 517 280 494 245 435 205 405 172 critical stress σ*min 289.57 293.29 278.02 253.03 critical stress σ*max 566.83 545.97 514.46 508.80 table 1: critical stress in a smooth cylindrical specimen. fatigue small crack associated to critical stress n 1976, kitagawa [6] presented a schematic comparison between stress range and crack length a, on a log-log scale. in this part, we approximate the small crack size for various stress σ* under pure bending and expressed by bazant’s law [7]. small crack effect and critical stress under a pure bending the elasticity theory [5] evaluate the crack size under influencing stress σ*: thk 2 * a 1.99        (13a) the fatigue limit ratios is based on the mises criterion n * 3 5    . indeed, the crack length a under a pure bending (fig. (5a)) is: th rb k 2 5 a 3 1.99         (13b) we hold the service conditions values from database of froustey and dubar. bazant’s law for small crack if critical stress cannot lead to long crack growth prediction, the method used is bazant’s law for cracked material. since the process is controlled by critical stress σ*, the fatigue limit ratios is 5 3 and the normal stress effect law proposed is:   1 25 a * 1 3 a n th thk a a                       (13c) according to tanaka [8] and livieri [9], most of experimental data is situated between two corresponding curves in γ = 1.25 and γ = 8. the threshold stress in the literature for 30ncd16 steel have average values between 4.3 mpam and 6 mpam. in our analyses we used kth = 6 mpam and a mmth 0.1 . the representation of (eqs. 13b and 13c) gives: the small crack effect is illustrated here in as resulting from bazant’s law and reproduces well the kitagawa diagram. we show also that the curve predicted by (eq. 13b) is significantly bounded by the bazant curves (eq. 13c). the small crack a0 length below which the linear elastic fracture mechanics (lefm) considered is the first point where the bazant curve (γ = 8) detaches from the endurance line. the initiation crack length predicted (fig. 3) is a0 = 40.e-6 m i d. marhabi et alii, frattura ed integrità strutturale, 38 (2016) 36-46; doi: 10.3221/igf-esis.38.05 43 figure 3: small crack effect for 30ncd16 steel under critical stress. prediction of the fatigue cycles and lefm analyses he initiation behavior of small crack is more complex than long crack propagation. based on the general classification of small fatigue cracks as defined in astm standard e647 [10], small cracks are defined as follows: microstructurally small if their length is comparable to the microstructural scale, mechanically small if their length is small compared to the scale of local plasticity, physically small if their length is typically between 0.1 and aℓ = 2mm [4-10]. we consider the applicability of (lefm) for physically small crack when a0 ≤ a ≤ aℓ. paris-erdogan law and parameters (c, m) in kinetics region i the pure bending approach (eq. 13b) suggests the existence of small crack under critical stress in high strength steel 30ncd16 used in the aerospace industry. it is therefore important to predict the number cycles of such defects in kinetics region i under shear stress * . the paris-erdogan law is:   da m c k dn    (da/dn in m/cycles et k in mpam ) (14a) where k ath a 1 2 k (1 ( ) )th         and  is a function of a [6] a k a max * ( ) 3 5     the relationship (eq. 14a) between the rate small crack and the stress intensity factor is: m akda thc dn aa 1 max 2. k (1 ( ) )th5 * 3                    (14b) for this situation, the integration is usually necessary using either computer programs. the fatigue henaff’s [11] test result for 30ncd16 steel in the first part of kinetics region i enable us to calculate the parameters c and m: t d. marhabi et alii, frattura ed integrità strutturale, 38 (2016) 36-46; doi: 10.3221/igf-esis.38.05 44 da k dn ,      c m, 1t point: (2.8, 8 10-11) [1.028 10-13 , 6.468] 2d point: (3, 1.25 10-10) 1t point: (3, 3 10-10) [5.718 10-12, 3.594] 2d point: (3.25, 4 10-10) 1t point: (3.5, 6 10-10) [1.626 10-12, 4.716] 2d point: (3.9, 10-9) table 2: the parameters c and m in kinetics region i. prediction of numbers cycles for physically small crack the relationship (eq. 14b) is integrated in interval [a0, ap] when ap ≤ aℓ (p=1, 2, ... , n). the number cycles of small crack growth is:   mm a ap m thn a daf ac k a * 1 5 2(1 ( ) ) 3 k 0max th                (15) a0: defines the intergranular initial crack length in the specimen. aℓ: defines the upper limit of physically small cracks. the analysis for the fatigue life use the parameter γ = 6. the crack grows under the fracture toughness of the material kmax = 18 mpam. the thresholds stress intensity used in this analyze is: kth = 6 mpam and a mmth 0.1 . the parameters c and m of tab. 2 in kinetics region i are used. the mean defect (inclusion whose size is a0 = 40x10-6 m) was assumed to exist in the specimen. however, we compute the number cycles nf (eq. 15) in mathematica. the results are presented in (fig. 4) figure 4: number cycles for small crack and oni’s long crack for 30ncd16 steel fatigue propagation notes of oni [12, 14] give 0.25x106 cycles for crack length 2 mm. our prediction for the same crack size when it can be blocked by a microstructural barrier (grain boundary, for example) gives nf = 2.91x106 cycles. this is of paramount importance for components, such as gas turbine engine and blades, where fatigue life is dominated by physically small crack growth can be long under critical stress σ*. d. marhabi et alii, frattura ed integrità strutturale, 38 (2016) 36-46; doi: 10.3221/igf-esis.38.05 45 conclusion he following results of the critical stress * and fatigue small crack effect are:  an over-energy under dissymmetrical rotating bending is used to predict the fatigue critical stress below the endurance limit.  we show that these critical stress and small crack are governed in good agreement with kitagawa diagram trend.  the physically small crack, usually nucleate on planes of shear stress, can significantly reduce the fatigue life of the engineering structures. nevertheless the capabilities of this method are very promising. further investigations will aim to validate these results by experimental processes and microscopic observations. references [1] palin-luc, t., lasserre s., berard, j.y., experimental investigation on the significance of the conventional endurance limit of a spheroidal graphite cast iron, fat. & fracture of eng. mat. & str, 21 (1988) 191-200. [2] banvillet, a., palin-luc, t., lasserre, s., a volumetric energy based high cycle multiaxial fatigue criterion. int. j. fatigue, 25 (2003) 755-769. [3] froustey, c., lasserre, s., multiaxial fatigue endurance of 30ncd16 steel. int. j. fatigue, 113 (1989) 169-175. [4] manning, s.d., yang, j.n., advanced durability analysis, volume i analytical methods. afwal-tr-86-3017, air force wright aeronautical laboratories (1987). [5] stephens r.i., fatemi, a., stephens, r.r., fuchs h.o., metal fatigue in engineering, 2d edition, wiley inter-science publication, (2001). [6] kitagawa, h., takahashi, s., applicability of fracture mechanics to very small cracks or the cracks in the early stage. proceeding of the second int. conf. on mechanical behavior of materials, american society for metals, metal park, oh, (1976) 627-702. [7] bazant, z.p., scaling of quasi brittle fracture: asymptotic analysis. int. j. fracture, 83 (1997) 19-40. [8] tanaka, k., nakai, y., yamashita, y., fatigue growth threshold of small cracks, int. j. fracture, 17 (1981) 519-533. [9] livieri, p., tovo, r., fatigue limit evaluation of notches, small and defects: an engineering approach. fatigue & fracture of engineering materials & structures, 27 (2004) 1037-1049. [10] standard test method for measurement of fatigue crack growth rates, astm e647, 03.01, astm, west conshohocken, pa, (2000) 591 [11] hénaff, g., petit j., bouchet, b., environmental influence on the near-threshold fatigue crack propagation behaviour of a high-strenth steel. int. j. fatigue, 14 (1992) 211-218. [12] oni, o., bathias, c., a comparison of near-threshold fatigue crack propagation in two high strength steels, fatigue & fracture of engineering materials & structures, 13 (1990) 585–596. [13] dubar, l., froustey, c., multiaxial fatigue of 30ncd16 steel, passage of the endurance to the limited endurance and taking into account of the geometrical accidents. phd thesis, ensam bordeaux, france (1992). [14] oni, o., bathias, c., contribution à l’étude des fissures courtes se propageant en fatigue dans les aciers. phd u.t.c compiègne france, (1986). nomenclature m te, ; te tensile mean stress and dynamic amplitude; eq te m te te 2 2 2 , ,    equivalent stress under tensile loading; tew ; teω energy density and over-energy on the area s* under tensile loading m rb, ; rb rotating bending mean stress and dynamic amplitude; eq rb m rb rb 2 2 2 , ,    equivalent stress under rotating bending; t d. marhabi et alii, frattura ed integrità strutturale, 38 (2016) 36-46; doi: 10.3221/igf-esis.38.05 46 rbw ; rbω energy density and over-energy on the area s* under rotating bending * critical stress and their effect on physically small crack; *w energy supplied to the material at the critical stress; eq m te * 2 2 *2 ,    equivalent critical stress under axial loading; te , 1  ; rb , 1   endurance limit under fully alternate tensile and rotating bending d uniax over-energy 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can be opened with acrobat and adobe reader 5.0 and later.) >> /namespace [ (adobe) (common) (1.0) ] /othernamespaces [ << /asreaderspreads false /cropimagestoframes true /errorcontrol /warnandcontinue /flattenerignorespreadoverrides false /includeguidesgrids false /includenonprinting false /includeslug false /namespace [ (adobe) (indesign) (4.0) ] /omitplacedbitmaps false /omitplacedeps false /omitplacedpdf false /simulateoverprint /legacy >> << /addbleedmarks false /addcolorbars false /addcropmarks false /addpageinfo false /addregmarks false /convertcolors /converttocmyk /destinationprofilename () /destinationprofileselector /documentcmyk /downsample16bitimages true /flattenerpreset << /presetselector /mediumresolution >> /formelements false /generatestructure false /includebookmarks false /includehyperlinks false /includeinteractive false /includelayers false /includeprofiles false /multimediahandling /useobjectsettings /namespace [ (adobe) (creativesuite) (2.0) ] /pdfxoutputintentprofileselector /documentcmyk /preserveediting true /untaggedcmykhandling /leaveuntagged /untaggedrgbhandling /usedocumentprofile /usedocumentbleed false >> ] >> setdistillerparams << /hwresolution [2400 2400] /pagesize [612.000 792.000] >> setpagedevice microsoft word numero_42_art_7.docx s. seitl et alii, frattura ed integrità strutturale, 42 (2017) 56-65; doi: 10.3221/igf-esis.42.07 56 focused on mechanical fatigue of metals comparison of fracture toughness values of normal and high strength concrete determined by three point bend and modified disk-shaped compact tension specimens stanislav seitl academy of sciences of the czech republic, institute of physics of materials, v. v. i., žižkova 22, 616 62 brno, czech republic seitl@ipm.cz, http://orcid.org/0000-0002-4953-4324 josé d. ríos, hector cifuentes grupo de estructuras, etsi, universidad de sevilla, camino de los descubrimientos s/n, 41092 sevilla, spain. jdrios@us.es, bulte@us.es, http://orcid.org/0000-0001-6302-418x abstract. the modified disk shaped compact tension test is a configuration derived from standard compact tension test that is used for measuring fracture mechanical properties of primarily metallic materials. the compact tension configuration is commonly used for measurement fracture mechanical properties as e.g. fracture toughness, young’s modulus, work of fracture etc. the modified compact tension tests imply significant modifications of the specimen morphology in order to avoid premature failure. the modified compact tension test is not proper for quasi-brittle materials due to its complicated shape (steel-concrete interface), but it is easily extracted from drill core and we do not need large amount of material for obtaining fracture properties as we need for e.g. threeor fourpoint bend test. since it is a new test method, a wide range of tests is needed to be done before it can be applied. in the paper the selected outputs of the experiments performed on normal and high strength concrete will be processed and the values of fracture mechanical parameters will be discussed. keywords. concrete; stress intensity factor; t-stress; compact tension test; fracture behavior; fracture mechanics; constraint. citation: seitl, s., ríos, j.d., cifuentes, h. comparison of fracture toughness values of normal and high strength concrete determined by three point bend and modified disk-shaped compact tension specimens, frattura ed integrità strutturale, 42 (2017) 56-65. received: 31.05.2017 accepted: 08.06.2017 published: 01.10.2017 copyright: © 2017 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. introduction he assessment of residual life of existing concrete structures has been an attractive topic for the researchers for decades. this could be carried out to regularly monitor the health of old/important concrete structures and/or to evaluate damaged concrete structures to conserve the structural integrity and for constructional issues i.e. repair and t s. seitl et alii, frattura ed integrità strutturale, 42 (2017) 56-65; doi: 10.3221/igf-esis.42.07 57 modification. the importance of rehabilitating the concrete structures has become obvious especially in some regions of the world that have been suffering from e.g. earthquakes, flooding, military conflict, terrorist attacks etc. repairing these structures instead of destroying and rebuilding them could save time and finance from the one side and save the nature (do not need preparation of new concrete etc.) from the other side. the structural assessment is carried out by evaluating the concrete quality indicate by e.g. compressive strength, fracture toughness, fracture energy, young’s modulus, tensile splitting strength, etc. for evaluation of all fracture mechanical properties of materials like concrete, standardized methodology is not published yet. there are norms: aci [1] and [8] for compressive strength, [9] for flexural strength of test specimens, tensile splitting strength [10], young’s modulus [7], recommendations for fracture energy determination for three-point-bend (tpb) specimen in rilem [24] and for wedge splitting test (wst) specimen in [18] or tensile strength and fracture toughness [33]. in literature we can found that researchers used various geometries for measurement of concrete fracture properties , e.g. tpb [13,17], wst [4, 21], the combination of tpb and wst [29-30], disk shaped compact tension [14, 32] and another configurations can be found in handbooks e.g. [22, 28]. (a) (b) figure 1: schemes of modified compact tension (a) and three-point bend test (b) with the characteristic dimensions widely used testing procedure for measuring the fracture properties of diverse types of materials is a compact tension (ct) test see in astm standard e-399 [2], plastics (astm standard d5045-14) or composite materials with limited orthotropy [23]. nevertheless, tests applied to concrete samples have not attained satisfactory results leading to the failure prematurely. wagoner et al. [32] carried out the ct test on concrete specimens and the premature failure was attained in 50% tested cases at the pulling load holes. modify compact tension (mct) test is a different version of ct test to reliably obtain the fracture properties of quasi-brittle materials (like the concrete). the specimen morphology is adapted to avoid premature failures during testing procedure. the load holes are replaced for two longitudinal steel bars, inserted in the specimen during its casting stage, to avoid generation of local fracture at load holes, the geometry of mct and tpb specimens are shown schematically in fig. 1.a and b, respectively. for fracture analysis of a test specimen, the major parameters that characterize the stress and strain fields around the crack tip should be known for the test specimen. as mct test is a very recent methodology of calculus, detailed studies must be carried out to deepen on the reliability of the results. in this way, seitl and viszlay [26] provided calibration curves corresponding to four fracture mechanical parameters (stress intensity factor, ki, t-stress, crack opening displacement, cod, and crack mouth opening displacement, cmod) for cement based materials varying the elasticity modulus (e). so significant amount of evaluations is measured by means of finite element model of the mct test developed for them. the results were determined from the aforementioned model for 2d and 3d simulations and discussed the obtained values. in this paper, experimental measured data from tests performed by cifuentes et al. [5, 6] to assess the use of mct test for measuring the fracture energy (gf) on normal-strength concrete (nsc) and high-strength concrete (hsc) will be processed and analyzed for various crack length to width ratios and the values of fracture mechanics parameters (ki and t-stress) will be evaluated and discussed using the outputs-calibration curvesfrom previous performed numerical simulations. afterwards, an assessment of all procedures used to calculate fracture parameters will be performed. the rest of this paper is organized as follows. details of experimental campaign, normal and high strength concrete mechanical properties and dosages are shown in section 2. the numerical simulations and related calibration curves s. seitl et alii, frattura ed integrità strutturale, 42 (2017) 56-65; doi: 10.3221/igf-esis.42.07 58 accounted on this work to calculate fracture parameters, are presented in section 3. the values of fracture parameters obtained through the empirical and numerical calibration curves are shown and discussed in section 4. finally, the conclusions of this work are given in section 5. experimental campaign he experimental data used to obtain the two fracture parameters, ki and t-stress, by means of calibration curves from numerical simulations, presented in next section, were attained in a previous paper by cifuentes et al. [5]. that paper was focused on the reliability of mct test for measuring the fracture energy (gf) on normal-strength (nsc) and high-strength concrete (hsc) comparing the results with those achieved from three-point bend (tpb) test. the fracture parameters will be calculated for the aforementioned normal strength concrete (nsc) and high strength concrete (hsc) whose constituents and mix proportions are shown in tab. 1. constituents nsc content [kg/m3] hsc content [kg/m3] cement 376 500 micro-silica 75 coarse aggregate (crushed limestone) <10 mm 580 990 sand < 2 mm 739 660 limestone powder < 2 mm 192 134 water 545 105 super-plasticizer 3.0 18.4 flow spread (mm) 710 695 t500 (s) 3.1 3.4 table 1: constituents and mix proportions for nsc and hsc. the specimen geometry for mct and tpb test are listed in tab. 2. three different types of mct specimens were casted. from mct1 to mct3, the distance from the load axis to the backside of the specimen, w, measures 112.5 mm. for each type, specimens with three different relative notch length, α, (0.1, 0.3 and 0.5) were tested. regarding tpb test, two type of specimens were accounted with a relative notch length, α, of 0.05 and 0.5. all specimens were manufactured for nsc and hsc to analyse the influence of testing on two different concrete strengths.   specimen mct1 mct2 mct3 specimen tpb1 tpb2 φcs (mm) 153 153 153 d (mm) 100 100 φsb (mm) 8 8 8 b (mm) 100 100 w (mm) 112.5 112.5 112.5 s (mm) 400 400 b (mm) 60 60 60 l (mm) 440 440 e (mm) 4 4 4 a0 (mm) 5 50 alig (mm2) 6075 4725 3375 alig (mm2) 9714 5213 table 2: dimensions of mct and tpb specimens experimentally tested. to determine the mechanical properties of nsc and hsc the following tests were carried out. the compressive strength is determined from cube specimens of 100 mm side in accordance with une en 12930-3:2009 [8]. the indirect tensile strength is obtained from splitting tests using 100 mm diameter by 200 long cylinders, according to une en 12930-6:2010 [10]. the young’s modulus is determined according to une en 12390-13:2014 [7]. the mechanical properties for nsc t s. seitl et alii, frattura ed integrità strutturale, 42 (2017) 56-65; doi: 10.3221/igf-esis.42.07 59 are the following: an average value on compressive strength of 36.8 ± 2% mpa, splitting tensile strength of 3.8 ± 9% mpa and young’s modulus of 24.4 ± 4% gpa and for hsc, compressive strength of 97.0 ± 3% mpa, splitting tensile strength of 5.7 ± 4% mpa and young’s modulus of 41.3 ±3%, detail see in [5]. the experimentally obtained maximum values of load for various notch length are shown in tab. 3.   specimen mct1 mct2 mct3 tpb1 tpb2  [-] 0.1 0.3 0.5 0.05 0.5 pmax, nsc [n] 3667 2956 1168 6329 1987 pmax, hsc [n] 7178 3584 2148 9581 3754 table 3: crack length ratio for each specimen and experimental values of maximum load on nsc and hsc. calibration curves for mct or this work are used the results presented by seitl and viszlay [26] for mct tests through 2d and 3d finite element model of steel bars and cement based materials. in their contribution, four mechanical fracture parameters (stress intensity factor, t-stress, crack opening displacement – cod and crack mouth opening displacement – cmod) are evaluated by means of two finite element models, one of them 2d and the another 3d. all cases (2d and 3d model) were carried out for concrete with five various young’s modulus (e = 5, 20, 25, 60, 100 gpa) and the same poisson ratio 0.2. the material was assumed to be homogeneous, isotropic with linear elastic behavior. the finite element software ansys was used for numerical analysis. for this paper, the calibration curves for e = 40 gpa were calculated. obtained calibration curves used here for normalized stress intensity factor (b1) and t-stress, as b2, are follows: for stress intensity factor, ki: 2 3 4 5 1_ 2 ( 25, ) 4.4888 157.35 992.61 2913.2 3845.6 1937.8db e              (1)   2 3 4 51_ 2 40,    12.87 314.45 1992.3 5711.8 7387.7 3597.5db e             (2) 2 3 4 5 1_ 3 ( 25, ) 19.17 437.74 2795.2 7977.5 10259 4936.2db e              (3) for parameter t-stress: 2 3 4 2 _ 2 ( 25, ) 0.352 2.6238 2.2014 9.8235 7.4131db e            (4)   2 3 42 _ 2 40,    0.2776 1.8433 4.7557 13.039 8.8474db e           (5) 2 3 4 2 _ 3 ( 25, ) 0.2905 2.2439 2.305 8.4968 6.315db e            (6) evaluation of measured data the fracture properties, we focused in the article, are critical values of stress intensity factor and of t-stress. the eqs. (7) and (8) were used to calculate the stress intensity factor and t-stress, respectively, for all cases according [16]. i 1k a b  (7) 2ik bt a  (8) f s. seitl et alii, frattura ed integrità strutturale, 42 (2017) 56-65; doi: 10.3221/igf-esis.42.07 60 where a is a crack length, b1 and b2 are calibration curves for sif a t-stress and  is applied stress for tpb, stress is calculated through following equation, see [28]: 2 3 2 ps bd   (9) and for ct and mct specimen is calculated through following equation, see [16]. p b w   (10) for evaluation of measured data, the calibration functions for tpb and ct specimens are well known and are taken from handbook, e.g. [28], [16].for stress intensity factor and t-stress are follow: tpb for s/d=4 2 3 4 5 1( ) 0.4487 17.782 156.01 533.83 768.03 400.1b            (11)   2 3 4 2 ( ) 0.6016 2.2111 2.2529 0.4647 1.7727b           (12)   and for ct 2 3 4 5 1( ) 2.5552 183.27 1544.2 5315.4 7728.2 4060.3b             (13) 2 3 4 2 ( ) 0.5804 4.1331 18.206 28.239 15.294b          (14) note that used geometries of measured tpb and mct specimens are shown in tab. 2 and their values of maximum loads, pmax, can be seen in tab. 3. now, tab. 4 shows the evaluated data from experimental measurement performed on two kinds of concrete, values of sif and t-stress for each experiment. evaluation of mct data for nsc is done by using tree different calibration curves, the first one for ct specimen eqs. (13) and (14), second one for mct2d eqs. (1) and (4) and mct3d eqs. (3) and (6). evaluation of mct data for hsc is done by using two different calibration curves, the first one for ct specimen eqs. (13) and (14) and second one for mct2d eqs. (2) and (5). calibration function nsc – ki [mpa m1/2] hsc – ki [mpa m1/2] α 0.05 0.1 0.3 0.5 0.05 0.1 0.3 0.5 ct 0.552 0.826 0.560 1.080 1.001 1.031 mct2d 0.705 0.872 0.582 1.258 0.910 1.193 mct3d 0.666 0.863 0.582 tpb 0.472 0.664 0.710 1.254 nsc – t-stress [mpa] hsc – t-stress [mpa] ct 1.359 0.695 0.715 2.660 0.842 1.315 mct2d -0.319 1.170 1.034 -0.321 1.176 2.185 mct3d -0.181 1.092 1.025 tpb -1.786 0.198 -2.700 0.373 table 4: values of stress intensity factor and t-stress versus relative crack length for mct and tpb specimens made from nsc and hsc. mct values are evaluated for three different calibration curves ct, mct2d and mct3d. s. seitl et alii, frattura ed integrità strutturale, 42 (2017) 56-65; doi: 10.3221/igf-esis.42.07 61 discussion wo mixtures of (normal and high strength) concrete were evaluated from experimental measurement. the experiment was prepared on geometrically different (mct and tpb) specimens with various initial notch length. results of nsc stress intensity factor, ki, for each type of test and relative crack length, α, are shown in fig. 2. the first row, marked ct, is measured value on modified compact tension specimen but evaluated by using calibration curve for ct (geometry similar), that is very easily find in literature e.g. [2, 16, 22]. the ct values are different from mct2d and mct3d values the application of loads on ct and mct is not exactly equal and consequently stress-field in the material is differently distributed. therefore, the calibration curves for mct has to be surely calculated. the values of sif for mct2d and mct3d, for each relative crack length, are very similar and we do not need for evaluation relatively demanding 3d calculation. note that the tpb test are recommended by rilem [24] for obtaining fracture properties, in recommendation is written that relative crack length has to be equaled 0.5. therefore, the obtain values for tpb test is compared with another results. from literature, the constraint effect is known, especially for metallic materials [19, 20, 25]. note that for brittle materials, depending on the geometry and loading configurations, the t-stress in real engineering components can vary significantly under their service conditions, see in contributions published by ayatollahi et al. [3] or by zhao [35] and literature review by gupta et al. [12]. figure 2: stress intensity factor, ki, values for each used procedure and crack length ratio, α, on nsc (e=24.4 gpa). figure 3: t-stress values for each used procedure and crack length ratio, α, on nsc (e=24.4 gpa). t s. seitl et alii, frattura ed integrità strutturale, 42 (2017) 56-65; doi: 10.3221/igf-esis.42.07 62 in fig. 3, it can be seen the results of t-stress for each test and relative crack length, α. in this case, there is barely difference on mct2d and mct3d results, as it occurs for sif values. the t-stress values are in interval -2 mpa to 2 mpa. similar trends are shown in fig. 4 and 5 for sif and t-stress evaluated for hsc. the t-stress values of hsc for each analyzed test and different relative crack length is shown in fig. 5. the necessary stress intensity factor values to obtain the t-stress are those correspond to fig. 4 and previously calculated. the results follow a trend like that for nsc, where the main extreme values were achieved for lower relative crack length. to analyse the influence of both stress intensity factor and t-stress parameters in the material, it has been plotted these data for mct and tpb tests in fig. 6. t-stress is dimensionless in fig. 6.a to obtain a trend without variability of this property. both values are dimensionless to not include the influence of the material in fig. 6.b. in fig. 7.a and b was performed the same analyses for hsc regarding the relation between sif and t-stress, previously carried out for nsc. as it can be seen, both parameters follow a linear tendency, so when the t-stress is higher the sif increases. figure 4: maximal values of stress intensity factor, ki, values for each used procedure and crack length ratio, α, on hsc (e=41.3 gpa). figure 5: t-stress values for each used procedure and crack length ratio, α, on hsc (e=41.3 gpa). there is a slight variation among ct, mct2d and tpb values. the explanation to these differences were given for nsc. it is worth noticing the remarkable higher values for hsc compared to nsc results. s. seitl et alii, frattura ed integrità strutturale, 42 (2017) 56-65; doi: 10.3221/igf-esis.42.07 63 the tendency line of nsc and hsc, for dimensionless sif and t-stress, are plotted in fig. 8. as it can be seen the two curves are practically the same, as it can be proved from their linear equation shown in fig. 8. the coefficient of correlation reveal that the data are significantly scattered because they are used to obtain the linear tendency mct and tpb tests. in spite of this, the results show reliable and useful behaviour. the dominant role for evaluation of data is played by geometry [35]. (a) (b) figure 6: tendency curve of evolution of t-stress/ft related to ki on nsc. the t-stress value for mct specimen is positive for relative crack length 0.5 and we could recommend this test for obtaining fracture toughness from core drill specimen. (a) (b) figure 7: tendency curve of evolution of t-stress/ft related to ki on hsc.  figure 8: comparison of tendency curve of evolution of t-stress/ft related to ki (dimensionless) on nsc and hsc. s. seitl et alii, frattura ed integrità strutturale, 42 (2017) 56-65; doi: 10.3221/igf-esis.42.07 64 conclusions he outputs of the experiments have been processed and the values of fracture mechanics parameters (maximal value of stress intensity factor, kic, and t-stress) have been obtained and discussed using the outputs-calibration curves from previous and newly performed numerical simulations. the following conclusions are drawn: using ct-calibration function leads to not very reliable results compared with calibration functions calculated for mct2d and mct3d. t-stress results achieved their more extreme values for smaller crack length ratios for any type of test – it is recommended to measured data from relative crack length 0.3. for the evaluation of experimentally obtained data, the mct2d calibration curves can be used instead of mct3d, because the obtained results by both ways provide reliably similar values and it is save the numerical time. dimensionless sif and t-stress/ft follow a remarkable linear trend for nsc and hsc and with similar linear equations, this leads to the geometrical shape of specimen plays dominant role. the mct specimen can be recommended as a favourite test sample from core drill to obtain information about concrete fracture toughness by considering the contribution of t-stress. acknowledgment he authors acknowledge the support of czech sciences foundation project no. 16-18702s, ministry of economy and competitiveness of spain bia2013-48352-p. the research was conducted in the frame of ipminfra supported through project no. lm2015069 of meys. references [1] aci 318-1 building code requirements for reinforced concrete, american concrete institute 20111, detroit, michigan, usa. [2] astm e399-90. standard test method for plane-strain fracture toughness testing of high strength metallic materials. philadelphia: amer. soc. for testing and mater; (1990). [3] ayatollahi, m.r., sedighiani, k., a t-stress controlled specimen for mixed mode fracture experiments on brittle materials, european journal of mechanics, a/solids, 36 (2012) 83–93. doi:10.1016/j.euromechsol.2012.02.008. [4] cifuentes, h., karihaloo, b.l., determination of size-independent specific fracture energy of normal and high-strength self-compacting concrete from wedge splitting tests, construction and building materials, 48 (2013) 548–553. doi: 10.1016/j.conbuildmat.2013.07.062. [5] cifuentes, h., lozano, m., holusova, t., medina, f., seitl, s., canteli, a., applicability of a modified compact tension specimen for measuring the fracture energy of concrete, anales de mecánica de la fractura, 32 (2015) 208–213. [6] cifuentes, h., lozano, m., holušová, t., medina, f., seitl, s., fernández-canteli, a., modified disk-shaped compact tension test for measuring concrete fracture properties, international journal of concrete structures and materials, (2017). doi:10.1007/s40069-017-0189-4 [7] en 12390-13: testing hardenes concrete – part 13: determination of secant modulus of elasticity in compression, aenor n.d. [8] en 12390-3 testing hardened concrete – part 3: compressive strength of test specimens [9] en 12390-5 testing hardened concrete – part 5: flexural strength of test specimens [10] en12390-6. testing hardened concrete – part 6: tensile splitting strength of test specimens, aenor n.d. [11] guinea, g.v. elices, m. planas j., stress intensity factors for wedge–splitting geometry, int. j fracture, 81 (1996) 113– 124. doi: 10.1007/bf00033177. [12] gupta, m., alderliesten, r.c., benedictus, r., a review of t-stress and its effects in facture mechanics, engineering fracture mechanics, 134 (2015) 218–241. doi :10.1016/j.tafmec.2015.02.001. [13] havlíková, i., majtánová, r.v., šimonová, h., láník, j., keršner, z., evaluation of three-point bending fracture tests of concrete specimens with polypropylene fibres via double-k model, key engineering materials, 592-593 (2014) 185– 188. doi: 10.4028/www.scientific.net/kem.592-593.185. t t s. seitl et alii, frattura ed integrità strutturale, 42 (2017) 56-65; doi: 10.3221/igf-esis.42.07 65 [14] holušová, t., seitl s., cifuentes, h., fernandez-canteli, a., a numerical study of two different specimen fixtures for the modified compact tension test — their influence on concrete fracture parameters, frattura ed integrita strutturale, 10 (35) (2016) 242–249. doi: 10.3221/igf-esis.35.28. [15] karihaloo, b.l., fracture mechanics and structural concrete, usa: longman scientific and technical publishers, (1995) 346. [16] knésl, z. bednář, k., two–parameter fracture mechanics: calculation of parameters and their values, institute of physics of materials academy of science of the czech republic, (1998). [17] korte, s., boel, v., de corte, w., de schutter, g., static and fatigue fracture mechanics properties of self–compacting concrete using three–point bending tests and wedge–splitting tests. construction and building materials, 57 (2014) 1– 8. doi: 10.1016/j.conbuildmat.2014.01.090 [18] linsbauer, h.n., tschegg, e.k, fracture energy determination of concrete with cube shaped specimens, zement und beton, 31 (1986) 38–40. [19] matvienko, y.g., two approaches to taking nonsingular t-stress into account in the criteria of fracture mechanics for bodies with notches, journal of machinery manufacture and reliability 40(5) (2011) 494–498. doi: 10.3103/s105261881104011x. [20] matvienko, y.g., two-parameter fracture mechanics in contemporary strength problems, journal of machinery manufacture and reliability, 42(5) (2013) 374–381. doi: 10.3103/s1052618813050087. [21] merta, i., tschegg, e.k., fracture energy of natural fibre reinforced concrete, construction and buildings materials 40 (2013) 991–997. doi: 10.1016/j.conbuildmat.2012.11.060. [22] murakami, y., stress intensity factors handbook, elmsford ny (usa) pergamon books, (1987) 1566. [23] pinho, s.t., robinson, p. iannucci, l., fracture toughness of the tensile and compressive fibre failure modes in laminated composites. composites science and technology, 66(13) (2006) 2069–2079. [24] rilem 106, determination of the fracture energy of mortar and concrete by means of three-point bend tests on notched beams, (1985) 285–290. [25] seitl, s., hutař, p., fatigue crack propagation near threshold region in framework two-parameter fracture mechanics, journal materials and technology, 41(3) (2007) 135–138. [26] seitl, s., viszlay, v., modified compact tension specimen for experiments on cement based materials: comparison of calibration curves from 2d and 3d numerical solutions. frattura ed integrità strutturale, 39 (2017) 118–128. doi: 10.3221/igf-esis.39.13. [27] seitl, s., viszlay, v., cifuentes, h., fernández-canteli, a., effects of specimen size and crack depth ratio on calibration curves for modified compact tension specimens, transactions of the všb –technical university of ostrava, civil engineering series, 15(2) (2015) 23. doi: 10.1515/tvsb-2015-0023. [28] tada, h., paris, p.c., irwin, g.r., the stress analysis of crack handbook, third ed., the american society of mechanical engineers three park avenue, new york, (2000). [29] veselý, v. frantík, p. sobek, j., malíková, l. seitl, s., multi-parameter crack tip stress state description for evaluation of nonlinear zone width in silicate composite specimens in component splitting/bending test geometry, fatigue and fracture of engineering materials and structures, 38(2) (2015) 200–214. doi: 10.1111/ffe.12170. [30] veselý, v., merta, i., šimonová, h., schneemayer, a., seitl, s., keršner, z., component wedge-splitting/bending test of notched specimens with various crack-tip constraint conditions: experiments and simulations, 9th international conference on fracture mechanics of concrete structures framcos-9, (2016) 1–12. doi: 10.21012/fc9.086. [31] veselý, v., sobek, j., frantík, p., štafa, m., šestáková, l., seitl, s., estimation of the zone of failure extent in quasibrittle specimens with different crack-tip constraint conditions from stress field, key engineering materials, 592-593 (2014) 262–265. doi: 10.4028/www.scientific.net/kem.592-593.262. [32] wagnoner, m.p., buttlar, w.g., paulino, g.h., disk-shaped compact tension test for asphalt concrete fracture, experimental mechanics, 45(3) (2005) 270–277 . [33] wang, y., hu, x.. liang, l., zhu, w., determination of tensile strength and fracture toughness of concrete using notched 3-p-b specimens, engineering fracture mechanics 160 (2016) 67–77. doi: 10.1016/j.engfracmech.2016.03.036 [34] williams, m.l., on the stress distribution at the base of stationary crack, asme journal of applied mechanics, 24 (1957) 109–114. [35] zhao, y. xu, b., effect of t-stress on the mode-i fracture toughness of concrete, c. r. mecanique 342 (2014) 490– 500. doi: 10.1016/j.crme.2014.03.001. << /ascii85encodepages false /allowtransparency false /autopositionepsfiles true /autorotatepages /none /binding /left /calgrayprofile (dot gain 20%) /calrgbprofile (srgb iec61966-2.1) /calcmykprofile (u.s. web coated \050swop\051 v2) /srgbprofile (srgb iec61966-2.1) /cannotembedfontpolicy /error /compatibilitylevel 1.4 /compressobjects /tags /compresspages true /convertimagestoindexed true /passthroughjpegimages true /createjobticket false /defaultrenderingintent /default /detectblends true /detectcurves 0.0000 /colorconversionstrategy /cmyk /dothumbnails false /embedallfonts true /embedopentype false /parseiccprofilesincomments true /embedjoboptions true /dscreportinglevel 0 /emitdscwarnings false /endpage -1 /imagememory 1048576 /lockdistillerparams false /maxsubsetpct 100 /optimize true /opm 1 /parsedsccomments true 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/hrv (za stvaranje adobe pdf dokumenata najpogodnijih za visokokvalitetni ispis prije tiskanja koristite ove postavke. stvoreni pdf dokumenti mogu se otvoriti acrobat i adobe reader 5.0 i kasnijim verzijama.) /hun 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can be opened with acrobat and adobe reader 5.0 and later.) >> /namespace [ (adobe) (common) (1.0) ] /othernamespaces [ << /asreaderspreads false /cropimagestoframes true /errorcontrol /warnandcontinue /flattenerignorespreadoverrides false /includeguidesgrids false /includenonprinting false /includeslug false /namespace [ (adobe) (indesign) (4.0) ] /omitplacedbitmaps false /omitplacedeps false /omitplacedpdf false /simulateoverprint /legacy >> << /addbleedmarks false /addcolorbars false /addcropmarks false /addpageinfo false /addregmarks false /convertcolors /converttocmyk /destinationprofilename () /destinationprofileselector /documentcmyk /downsample16bitimages true /flattenerpreset << /presetselector /mediumresolution >> /formelements false /generatestructure false /includebookmarks false /includehyperlinks false /includeinteractive false /includelayers false /includeprofiles false /multimediahandling /useobjectsettings /namespace [ (adobe) (creativesuite) (2.0) ] /pdfxoutputintentprofileselector /documentcmyk /preserveediting true /untaggedcmykhandling /leaveuntagged /untaggedrgbhandling /usedocumentprofile /usedocumentbleed false >> ] >> setdistillerparams << /hwresolution [2400 2400] /pagesize [612.000 792.000] >> setpagedevice microsoft word numero_38_art_20 x. yu et alii, frattura ed integrità strutturale, 38 (2016) 148-154; doi: 10.3221/igf-esis.38.20 148 focussed on multiaxial fatigue and fracture fatigue crack growth of aluminium alloy 7075-t651 under non-proportional mixed mode i and ii loads xiaobo yu aerospace division, defence science and technology group, 506 lorimer street, fishermans bend, vic 3207, australia xiaobo.yu@dsto.defence.gov.au, http://www.dsto.defence.gov.au ling li, gwénaëlle proust school of civil engineering, faculty of engineering & it, the university of sydney, nsw 2006, australia lili1626@uni.sydney.edu.au, gwenaelle.proust@sydney.edu.au abstract. this study aims to investigate fatigue growth behaviour in aa7075-t651 under non-proportional mixed mode i and ii loads. fatigue tests were performed under cyclic tension and torsion using a thin-walled tubular specimen with a key-hole style crack starter. after the generation of a single-side mode i pre-crack, varied forms of mixed mode loads were applied, which in most cases led to a short distance coplanar growth followed by a long and stable crack path deviation. it was found that under most of the non-proportional mixed mode load cases, the direction of the deviated crack path could not be reasonably predicted using the commonly accepted maximum tangential stress criterion. meanwhile, in some cases, the crack path directions could be approximately predicted using the maximum shear stress criterion. it was also confirmed for the first time that a long, stable and noncoplanar shear mode fatigue crack growth could be produced in aa7075t651 under non-proportional mixed mode i and ii loads. ©2016 commonwealth of australia keywords. fatigue crack growth; non-proportional; mixed mode; aluminium alloy; 7075-t651. citation: yu, x., li, l. proust, g., fatigue crack growth of aluminium alloy 7075-t651 under non-proportional mixed mode i and ii loads, frattura ed integrità strutturale, 38 (2016) 148-154. received: 12.05.2016 accepted: 15.06.2016 published: 01.10.2016 copyright: © 2016 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. introduction atigue of aircraft structures is traditionally managed based on the assumption of uniaxial loads. this is a simplified and acceptable approach for most fatigue critical locations where the local stress field is predominantly uniaxial due to loading path restrictions. nevertheless, as evidenced in recent durability analysis of a new type of f x. yu et alii, frattura ed integrità strutturale, 38 (2016) 148-154; doi: 10.3221/igf-esis.38.20 149 surveillance aircraft, severe multiaxial loads may exist at some of the primary structural locations. multiaxial fatigue analysis, including fatigue crack growth (fcg) analysis under non-proportional mixed mode i and ii loads, is needed for these locations. at present, experimental fcg investigations are predominantly undertaken for mode i or proportional mixed mode loads. only a few studies [1-8] focus on non-proportional mixed mode loads. limited results on a106-93 mild steel [3] reveal that a long and stable shear mode fcg – which is significantly different from the commonly understood open mode fcg – could be produced by non-proportional loads. to illustrate this difference, fig. 1 compares the fcg behaviour under two load cases: (i) proportional load case td1, under which, the fcg deviated into a direction that can be approximately predicted by the maximum tangential stress (mts) criterion [9], and striations were found along the deviated crack path; (ii) non-proportional load case td2, under which the fcg deviated to a direction that is about 60° off the mts prediction, and dimples were found along the deviated crack path. for this particular case, the deviation angle is approximately predictable by the maximum shear stress (mss) criterion [10]. the shear mode fcg as shown in fig. 1 (d) is more than 8mm long along the deviated path. thus, it is not a shortdistance propagation in shear mode occurring in an early stage of crack growth as discussed in [7]. nor is it a transient behaviour occurring at a short-distance coplanar growth following the change of load mixture as reported in [11]. the persistence of the shear mode fcg as presented in fig. 1 (d) indicates the complexity of underlying mechanism under non-proportional loads. it means that a stage ii fatigue crack can propagate in other than open mode growth, and in such a case, the crack path is absolutely unpredictable by the commonly accepted mts criterion. nevertheless, the above finding is so far only based on experimental results for a106-93 mild steel. it is not clear whether this finding also applies to other materials, such as aluminium alloy (aa) 7075-t651, which is typically used for aircraft structures, as no similar tests have been reported for the latter in the open literature. hence, the purpose of this study is to investigate fcg behaviour in aa7075-t651 under non-proportional mixed mode i and ii loads. in particular, it aims to clarify whether the long and stable shear mode fcg also occurs. for the sake of comparison, the specimen design and majority of the mixed-mode load cases used in the present study are the same as reported in [3]. figure 1: fcg from a mode i pre-crack, under proportional (a-c), and non-proportional (d-f), mixed-mode loads [3, 12]. (ssy in the figure refers to small scale yielding). specimen and test procedures he fatigue tests of the present study were performed on an instron 8500 servo-hydraulic tension-torsion biaxial fatigue test machine with a capacity of ±250 kn and ±2000 nm. the test machine is located in the structural laboratory, school of civil engineering at the university of sydney. this is the same test machine as the one that t x. yu et alii, frattura ed integrità strutturale, 38 (2016) 148-154; doi: 10.3221/igf-esis.38.20 150 was used in [3], except that the electronic test controllers have been upgraded prior to the present study. the design of the specimen is the same as previously used in [3]. a schematic illustration of the specimen is given in fig. 2, which includes a notched thin-walled tube and two solid plugs. both the tube and plugs were machined from 2.5″ aa7075-t651 solid bars, and the tight tolerance between the plugs and the tube was filled with araldite epoxy adhesive. the plugs are reusable and their main function is to provide support to the tube under hydraulic grippers. the tube has a large diameter-to-thickness ratio of 38, which helps to suppress the effects of uneven shear stress distribution through the thickness. the crack starter notch has a keyhole shape, and was introduced via drilling and electronic discharge machining. figure 2: (a) illustration of a tubular specimen for fcg test under cyclic tension and torsion. (b) the crack start notch with a singlesided mode i pre-crack. (after [3]). the tension and torsion loads are described using  and  , which are the nominal tensile and shear stresses in an uncracked and un-notched tube. the positive direction of  and  , are shown in fig. 2(a). ten specimens were tested. for each specimen, the fatigue test was performed in two phases. during phase 1 of the test, only tension was applied which cycled at 10hz between 25 mpa and 125 mpa. a single-sided circumferential crack, here noted as pre-crack and illustrated in fig. 2(b), was produced. the phase 1 procedure completed when the total crack length, 2a, reached between 7.5mm and 9mm approximately. during phase 2 of the test, both tension and torsion were applied according to the  - curves as illustrated in fig. 3. the time-histories of tension and torsion feedback were monitored, and when needed load frequency was reduced to around 2hz, to ensure that the target shape of the  - curve was achieved. each specimen was subject to a single load case, except for one specimen where three load cases (lc8, 9 and 10) were applied in a sequential order. at the pre-crack tip, the applied and produce mode i and mode ii stress intensities, respectively, when the crack is fully opened. strictly speaking, load cases lc1 to lc4 should be catalogued as proportional mixed mode loads. nevertheless, they are here included for comparison. it is noted that all the load cases, except lc13, have been previously tested for a106-93 mild steel [3], and that the load cases lc4 and lc5 depicted in fig. 3 are identical to td1 and td2 in fig. 1. all the fatigue tests were performed at room temperature in the laboratory environment. fatigue crack growth was monitored using a portable optimal microscope and still images were taken at given intervals of cycles. results and analysis or all ten specimens, the fatigue cracks produced by the end of the tests are shown in fig. 4. these images were taken at the outer surface of the tubular specimens while the cracks were kept open under applied load in the test machine. the main interest here is the fcg behaviour under mixed mode loads, in particular the crack directions, as defined in fig 4. tab. 1 compares the measured crack directions with those predicted by the mts [9] and mss [10] criteria, which are expressed in eqs. 1 and 2, respectively: mts criterion: 2 2 0 and 0             (1) mss criterion: r r 2 2 0 and 0             (2) f 200 65 41 plug plug 65 2  5 4. 5  5 7. 5  5 7 .3 notch notched tube (a) (b)     2 0.5 1 .7 5 2 a pre-crack x. yu et alii, frattura ed integrità strutturale, 38 (2016) 148-154; doi: 10.3221/igf-esis.38.20 151 figure 3: load cases applied during the phase 2 of the fatigue tests. 75  = 25   (mpa)  = 75  = 100  = 50 lc1 lc2 lc3 lc4 lc5 lc6 lc8 lc9 lc10 lc11 lc12 lc13 0 50 0 50 0 50 125 25 125 25 125 25 125 25 125 25     x. yu et alii, frattura ed integrità strutturale, 38 (2016) 148-154; doi: 10.3221/igf-esis.38.20 152 load case pre-crack length (mm) coplanar fcg before branching crack direction (θ) length (mm) cycle as measured mts criterion mss criterion lc1 8.3 1.3 3200 -66.1° -70.5° 0° lc2 7.8 4.5 1850 +10.1° -70.5° 0° lc3 8.3 no growth n/a n/a -70.5° 0° lc4 8.1 0.54 650 -27.3° -40° +28.5° lc5 8.0 0.4 750 +41° -40° +28.5° lc6 8.4 0 411 +8° -25.5° +44° lc8 7.5 0.6 4928 -52.5° -61.5° +8° lc11 7.7 0.4 1832 +18.4° -40° +28.5° lc12 9.1 0.8 568 -43.2° -40° +28.5° lc13 8.3 0.3 1500 -19.9° -40° +28.5° table 1: fatigue crack growth behaviour under mixed mode loads. where,  and r are tangential and shear stress calculated using eq. 3 which is simplified from [13]. at the pre-crack tip, the mode i and mode ii stress intensity factors were calculated as ik a  and iik a  , respectively. the effects of crack surface interference [14, 15] were not considered in this study. i ii r k k r r 2 2 2 cos 3sin cos 2 2 2cos 22 2 sin cos cos (1 3sin ) 2 2 2 2                                              (3) the results given in tab. 1 shows that only four of the measured crack directions, or two of the six non-proportional load cases, can be approximately (with less than ±15° error) predicted using the mts criterion. meanwhile, three of the directions can be approximately predicted by the mss criterion. it is noted that the maximum and minimum values of  and  are all identical across five of the load cases, including lc4, 5, 11, 12 and 13. nevertheless, the crack paths that were produced in the tests are all very different. the comparison between lc4 and lc5 is here elaborated. under lc4 (proportional  - variation), the crack path turns into a -27.3° direction, which is close to the mts prediction. meanwhile, under lc5 (non-proportional  - variation), the crack path turns into a +41° direction, which is close to the mss prediction. these two directions are more than 60° apart, showing the dependency of crack path, and hence the crack growth mechanism, on the relative phases between the  and  variations. a similar dependency was previously observed for a106-93 mild steel [3] as shown in fig. 1. it means that for both the mild steel [3] and aa7075-t651 (this study), a long and stable shear mode fcg can be produced by applying non-proportional mixed mode load. the comparison between lc11 and lc12 is also worth noting. for these two load cases, the  - curves are the same except that one follows a clockwise direction, and the other follows an anti-clockwise direction. the crack paths as measured on the specimens are +18.4° and -43.2°, respectively, again more than 60° apart. the load cases lc1, lc2 and lc3 tested here are similar to those achievable using a fixed-grip-shear specimens [16], where a static tensile (mode i) load was superimposed onto a cyclic shear (mode ii) load. for the load case lc3 of the present study, no growth was observed from the pre-crack tip, which can be attributed to the severe crack closure and shear attenuation as the applied static tension is only one-fifth of the maximum  applied during the pre-cracking phase. under the load cases lc1 and lc2, nominal iik at the pre-crack tip were 5.7mpa·m1/2 and 8.3mpa·m1/2, respectively; and the fcg turned into -66.1° (close to mts prediction) and +10.1° (close to mss prediction) directions, respectively. it means that, under the cyclic  plus static  load conditions shear mode fcg can be produced under a higher iik for aa7075-t651. similar observations were reported in [16] for aa7075-t6. however, under the same load case as lc2, no x. yu et alii, frattura ed integrità strutturale, 38 (2016) 148-154; doi: 10.3221/igf-esis.38.20 153 shear mode fcg was observed for a106-93 mild steel [3]. this result reconfirms an earlier review finding [3] that under cyclic mode ii loads, a shear mode fcg is more likely in aluminium alloys than in steels. figure 4: fatigue cracks at the outer surface of tubular specimens at the end of tests. coplanar fcg was also observed under almost all load cases as summarised in tab. 1. nevertheless, for the loading cases where both  and  were cyclically applied, the coplanar growth was a transient behaviour, typically less than 1mm long, after which the fcg turned into the direction as discussed above. θ x. yu et alii, frattura ed integrità strutturale, 38 (2016) 148-154; doi: 10.3221/igf-esis.38.20 154 it is noted that under most loading cases, a second crack also emanated from the far edge of the circular hole. however, the second crack only emerged after more than 4000 cycles of the applied mixed mode load. therefore, their effect on crack path deviation was ignorable in this study. conclusion his study clarifies that for aa7075-t651, the fcg under non-proportional mixed mode i and ii loads is significantly different from the open mode fcg commonly expected under mode i or proportional mixed mode loads. similarly to previous results for mild steel, a long and stable shear mode fcg can be produced in aa7075t651 under non-proportional loads. the commonly accepted mts criterion does not apply under most non-proportional load cases. further investigations are needed to gain sufficient understanding, including those under in-service multiaxial loading spectra, to better support durability assessment of primary aircraft structures subjected to severe non-proportional multiaxial loads. references [1] nayeb-hashemi, h., taslim, m.e., effects of the transient mode ii on the steady state crack growth in mode i, engng fract mech, 26(6) (1987) 789-807. doi:10.1016/0013-7944(87)90029-4. [2] wong, s.l., bold, p.e., brown, m.w., allen, r.j., a branch criterion for shallow angled rolling contact fatigue cracks in rails, wear, 191 (1-2) (1996) 45-53. doi: 10.1016/0043-1648(95)06621-7 [3] yu, x., phd thesis, the university of sydney, australia, (1999). [4] doquet, v., pommier s., fatigue crack growth under non-proportional mixed-mode loading in ferritic-pearlitic steel fatigue fract engng mater struct, 27(11) (2004) 1051-1060. doi: 10.1111/j.1460-2695.2004.00817.x. [5] highsmith, s., jr., phd thesis, georgia institute of technology, usa (2009). [6] doquet, v., abbadi, m., bui, q. h., pons, a., influence of the loading path on fatigue crack growth under mixedmode loading, int j fract, 159 (2009) 219-232. doi: 10.1007/s10704-009-9396-6. [7] shamsaei, n., fatemi, a., small fatigue crack growth under multiaxial stresses. int j fatigue, 58 (2014) 126–135. doi: 10.1016/j.ijfatigue.2013.02.002. [8] zerres, p., vormwald, m., review of fatigue crack growth under non-proportional mixed-mode loading, int j fatigue, 58 (2014) 75-83; doi: 10.1016/j.ijfatigue.2013.04.001. [9] erdogan, f., sih, g.c., on the crack extension in plates under plane loading and transverse shearj basic engng, 85(4) (1963) 519-525. doi:10.1115/1.3656897. [10] otsuka, a., mori, k., miyata t., the condition of fatigue crack growth in mixed mode conditions, engng fract mech, 7(3) (1975) 429-439; doi:10.1016/0013-7944(75)90043-0. [11] smith, m.c., phd thesis, university of cambridge, uk, (1984). [12] yu, x., on the fatigue crack growth analysis of spliced aircraft wing panels under sequential axial and shear loads, engng fract mech, 123 (2014) 116-125. doi: 10.1016/j.engfracmech.2014.03.018. [13] anderson, t.l. (1995) fracture mechanics: fundamentals and applications, 2nd edition, crc press, inc. [14] yu, x., abel, a., mixed-mode crack surface interference under cyclic shear loads, fatigue fract engng mater struct, 23(2) (2000) 151-158. doi: 10.1046/j.1460-2695.2000.00236.x. [15] yu, x., abel, a., modelling of crack surface interference under cyclic shear loads, fatigue fract engng mater struct, 22(3) (1999) 205-213; doi: 10.1046/j.1460-2695.1999.00152.x. [16] otsuka, a., mori, k., ohshima, t., tsuyama, s., mode ii fatigue crack growth in aluminium alloys and mild steel, in: advances in fracture research, fracture 81, icf5, francois, d. 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can be opened with acrobat and adobe reader 5.0 and later.) >> /namespace [ (adobe) (common) (1.0) ] /othernamespaces [ << /asreaderspreads false /cropimagestoframes true /errorcontrol /warnandcontinue /flattenerignorespreadoverrides false /includeguidesgrids false /includenonprinting false /includeslug false /namespace [ (adobe) (indesign) (4.0) ] /omitplacedbitmaps false /omitplacedeps false /omitplacedpdf false /simulateoverprint /legacy >> << /addbleedmarks false /addcolorbars false /addcropmarks false /addpageinfo false /addregmarks false /convertcolors /converttocmyk /destinationprofilename () /destinationprofileselector /documentcmyk /downsample16bitimages true /flattenerpreset << /presetselector /mediumresolution >> /formelements false /generatestructure false /includebookmarks false /includehyperlinks false /includeinteractive false /includelayers false /includeprofiles false /multimediahandling /useobjectsettings /namespace [ (adobe) (creativesuite) (2.0) ] /pdfxoutputintentprofileselector /documentcmyk /preserveediting true /untaggedcmykhandling /leaveuntagged /untaggedrgbhandling /usedocumentprofile /usedocumentbleed false >> ] >> setdistillerparams << /hwresolution [2400 2400] /pagesize [612.000 792.000] >> setpagedevice microsoft word numero_42_art_31.docx d. v. orlova et alii, frattura ed integrità strutturale, 42 (2017) 293-302; doi: 10.3221/igf-esis.42.31 293 macroscopic criteria for the deformation and fracture of iron based alloys dina v. orlova, alexey g. lunev, lidiya v. danilova, lev b. zuev institute of strength physics and materials science sb ras, 2/4 akademicheskii ave., 634055 tomsk, russia dvo@ispms.tsc.ru abstract. in the article the deformation of different steels is analyzed using the autowave theory of plasticity. the article considers the possible use of an autowave model to formulate criteria for the structural strength of materials and elastic-plastic transition. the time and place of future fracture for steel samples are shown can be predicted before visible necking takes place by using the kinetic dependencies of localized plasticity domains at the prefracture stage. the results show that during elastic-plastic transition in lowcarbon steel, there is the break of the curve for the ultrasound velocity versus deformation, which can serve as an acoustic criterion of irreversible deformation for the pressure treatment of metals, the operation and nondestructive testing of products and structures. keywords. steels, ductile fracture; ultrasound velocity; digital speckle photography. citation: orlova, d.v., lunev, a.g., danilova, l.v., zuev, l.b., macroscopic criteria for the deformation and fracture of iron based alloys, frattura ed integrità strutturale, 42 (2017) 293-302. received: 04.07.2017 accepted: 15.08.2017 published: 01.10.2017 copyright: © 2017 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. introduction t present, the critical parts and structures of many hazardous production facilities operate under mechanical loads which initiate the occurrence and accumulation of damages leading to the fracture of equipment. these damages can be timely identified and eliminated if appropriate technical means and methods are available. in this connection, special attention is paid to the problem concerning the objective and reliable estimation of the mechanical condition and the prediction of the resource for critical elements and structures in the long operation. since the localized development of a plastic flow has a significant effect on the strength and plastic characteristics of structural steel products, it is of importance to describe the kinetics of a plastic flow and the transition from deformation to ductile fracture. the progressive development of the dislocation theory using high-resolution techniques, mainly electron microscopy, allowed a number of efficient models to be developed for the strain and impurity hardening of metals, as well as for the micromechanics of fracture [1-9]. nevertheless, the kinetics of a plastic flow was not insufficiently described. it is difficult to add the time factor to the equations of plasticity. for example, the taylor-orowan equation obtained for this purpose a d. v. orlova et alii, frattura ed integrità strutturale, 42 (2017) 293-302; doi: 10.3221/igf-esis.42.31 294 is valid only for certain chaotic distributions of dislocations, when their density is considered to be independent of coordinates [10]. that is, beginning with the griffith’s [9] hypothesis about the existence of places for the initiation of cracks, deformation criteria consider local characteristics for the development of cracks and the structural parameters of materials. also, the microscopic approach was mainly used to consider the physics of material fracture. therefore, the complete description of a plastic flow only on the basis of micromechanisms is impossible. thus, inefficient dislocation models in the physics of strength and plasticity were replaced with the complex concept of a multilevel approach. a multiscale approach to the problems of plastic deformation and fracture was developed due to the works of domestic and foreign researchers [11-19] and currently is used by the scientific community. thus, at present a deformable material is considered to be a nonlinear medium, an appropriate description of which is impossible without the approach based on the concepts for the mechanics of nonlinear media, synergetics and nonlinear acoustics. so, using the synergetic approach describing the self-organization of highly nonequilibrium systems, the authors of this article and coworkers found a new type of wave processes in a solid. any plastically deformed object is known to be under nonequilibrium conditions [20]. in order to describe strain, it is proposed to consider a deformed macroobject to be an active medium that includes two factors: activator and inhibitor. moreover, localized shear processes are considered to be an activator, and the redistribution of local stresses connected with these processes is considered to be an inhibitor. this was the basis for the autowave model for the evolution of localized macrodeformation [21-24]. in contrast to ordinary waves described by hyperbolic equations, autowaves are the solutions of parabolic equations, an important feature of which is the presence of a time derivative, which determines their applicability for the description of reversible processes [25-26]. autowaves are formed only in the media with energy dissipation and when there are external nonperiodic effects. from this point of view, the strain of any object represents the evolution of autowaves during different type deformation. the change in the type of autowaves is determined by the law of strain hardening, that is, it depends on the stages of the strain flow curve (rule of correspondence). thus, the movement of a solitary deformation front is observed within the yield plateau (the work hardening coefficient 0  ) along the sample, the so-called autowave excitation or switching. at the linear stage ( const  ) there is the coordinated movement of localization zones (phase autowaves). the stationary structure of zones (stable dissipative systems) corresponds to the stages of parabolic hardening  1 2 1 2~ , ~     . a stationary high-amplitude zone (domain) of localized plasticity is formed in the sample at the place of future fracture at the final stage of the deformation process (pre-fracture stage), and the movement of other localized plasticity domains is nonuniform but self-coordinated. this article is devoted to deep studying the macrolocalization of plastic deformation at this stage. in addition, the authors of this article believe that a complex approach based on a combined analysis of the plastic flow localization during the deformation process and supplemented by the simultaneous measurement of small changes in the velocity of ultrasound propagation should be applied to the problem concerning the reliable estimation of the mechanical condition and the prediction of the resource for structures in the long operation. this will allow us to determine the exact location of the places with damages and find a connection with a localized plastic flow. recently, an acoustic analysis of materials under loading has been developed in the field of plastic deformation in theoretical and experimental studies by kobayashi [27, 28], maurel [29], zuev [30]. at present, individual groups of researchers only start developing such an approach, mainly by using idealized simple model media. for real materials used in technological production and materials with a complex structure, such an integrated approach has not been developed yet. thus, the aim of the work is to study the stage of pre-fracture for iron based alloys and analyze the possible use of an autowave model to formulate criteria for the structural strength of materials and elastic-plastic transition. the last fact will allow an important technological problem to be solved and the behavior of structural materials to be controlled before the initiation of irreversible plastic deformation. since the inhomogeneity or localization of deformation is manifested not only in the accumulation of defects during the operation of constructions, but also in many technological processes connected with pressure treatment, drawing, etc., the estimation of material plasticity is an urgent problem for these processes. materials and experimental procedures teel of different composition was chosen as test materials. heat-resistant stainless steel (aisi 420), cryogenic structural steel (321n), carbon steel (g10080), and electrical steel (alloy of iron and silicon) were used. these iron based alloys are widely used not only in industry, but in experimental studying the physics of plasticity and strength. s d. v. orlova et alii, frattura ed integrità strutturale, 42 (2017) 293-302; doi: 10.3221/igf-esis.42.31 295 for example, silicon iron chosen by amelinckx and hull [31, 32] is a traditional material for investigating the mechanisms of plastic flow and fracture. the elemental composition of the test steels is given in tab. 1. the samples were obtained using sheet semi-fabricated products subjected to pressing and recrystallization annealing. in the mechanical tests, flat samples were in the form of a double blade 21050 mm in size. steels c cr ni si mn cu aisi 420 0.35-0.45 12-14 ≤0.6 ≤0.8 ≤0.8 ≤0.3 321h ≤0.12 17-19 9-11 ≤0.8 ≤2.0 ≤0.3 g10080 0.05-0.11 0.1 ≤0.25 0.05-0.17 0.35-0.65 ≤0.25 fe-si alloy 2.8-3.8 table 1: chemical compositions of experimental steels, in wt.%. the samples were subjected to uniaxial loading at room temperature and a constant velocity of 6.67·10-5 s-1 by using the one universal testing machine head (walter + bai, switzerland), the second testing machine head was fixed. the initial load curves of all materials    were recalculated into true stresses s and strain e, the relationship between which was described by the ludwik's equation   0 ns e s ke  [33], where k is the work hardening coefficient, and n is the hardening exponent. to determine the stages of the plastic flow, the dependence  s e was taken in the logarithmic form. the sections corresponding to the stages of the plastic flow are easily separated when the curve  s e is transformed into the coordinates  0ln lns s e  , and represented by the straight lines for k = const and n = const. the hardening exponent n = 0 corresponds to the yield plateau, n = 1 corresponds to the linear stage, and n = 0.5 corresponds to the parabolic stage of strain hardening. the continuous pre-fracture stage, for n < 0.5, was observed for all materials (tab. 2). the stress-strain state of objects in the real time mode, visualization of deformation and fracture localization zones were investigated by speckle interferometry, described in detail in [34, 35]. the method allows the patterns of plastic deformation localization to be recorded by fixing the displacement fields of points for a deformed sample. the use of a two-exposure speckle photograph and the analysis of the speckle structure for the images of deformed objects are very promising for investigating the features of plastic deformation at the macroscale level. this technique is successfully used in solving similar problems [36, 37]. the method is valid in the field of vision about 100 mm in size and has a measuring accuracy of 1 μm for displacement vectors. a series of sequential specklegrams reflecting the displacement field of the sample points for an increase in the total strain of 0.2% was recorded within the yield plateau for the steel (g10080) and at the pre-fracture stage for all the materials studied. using the data on the displacement fields and numerical coordinate differentiation, all components for the tensor of the plastic material distortion can be determined for the plane case: local narrowing, local elongation, shift and rotation. then, the data on the displacement fields for the points of a deformed sample are transformed into the distributions of local elongations хх, where the localized plasticity domains are clearly separated. the propagation velocity of ultrasonic rayleigh waves was used as an acoustic informative parameter at a frequency of 5 mhz. using this type of waves allows the propagation of ultrasound velocity in the sample to be kept constant during experiments. to measure the propagation velocity of rayleigh waves, a transmit-receive sensor was used, which contained transmitting and receiving piezoelectric transducers installed in the same enclosure and based on piezoceramics (cts-19) with a resonance frequency of 5 mhz. piezoelectric transducers are installed at an angle of 56 to the normal to the incidence plane of an acoustic wave, which provides the formation of a surface acoustic wave (rayleigh wave) in iron based alloys. the distance between the transducers (the length of the acoustic path in the test object) without considering the length of the sensor waveguide was 32 mm. the propagation velocity of rayleigh waves was determined by the ratio between the path length of a wave in the sample and the delay time for the signal of the receiving transducer relative to the transmitting one. the delay time was measured using an oscillogram recorded with a digital oscilloscope at a sampling frequency of 2 ghz. the measurement accuracy was 104 – 105. d. v. orlova et alii, frattura ed integrità strutturale, 42 (2017) 293-302; doi: 10.3221/igf-esis.42.31 296 experimental results and discussions stress-strain curves and propagation of elastic surface rayleigh waves ig. 1 and 2 show the stress-strain curves of the test materials. it is seen that these curves are parabolic and can be used to determine the stages in accordance with the law of strain hardening. the fracture is ductile, and there is well visible necking in the samples. the mechanical characteristics and length of the section with the n < 0.5 are given in tab. 2. the exception is the σ-ε curve for carbon steel g10080 (fig.2). the feature of this curve is the presence of a tooth and a yield plateau typical for carbon steels [38]. the length of the yield plateau is 0.013 < e < 0.047 (3.4%). the strain within the yield plateau is known to be in the form of the luders band [39]. steels σy, mpа σ0.2, мpа δ,% pre-fracture stage, n < 0.5 aisi 420 1183 420 6.0 0.033 < e < 0.05 (1.7 %) 321h 178 512 55 0.45 < e < 0.55 (10 %) g10080 310 210 40 0.25 < e < 0.35 (10 %) fe-si alloy 590 320 25 0.064 < e < 0.22 (15.6 %) table 2: mechanical properties of the samples and the length of the pre-fracture stage. figure 1: stress-strain curves of the test materials. figure 2: stress and relative sound velocity versus the strain of steel (g10080). the measurement of acoustic characteristics within the yield plateau is of great interest. the position of the luders bands and the change in the propagation velocity of ultrasonic rayleigh waves in steel (g10080) within the yield plateau were recorded simultaneously with the deformation of the sample. in fig. 3, the σ-ε loading diagram is plotted by a light gray line, and the yield plateau is accompanied by the formation of the luders band front near the lower testing machine head. the position of the luders band fronts is plotted in the form of black circles (black lines). the deformation is accompanied by the propagation of the two luders band fronts at a velocity of 0.052 mm/s and 0.038 mm/s. the region of the sample in which the change in the velocity of ultrasonic waves is recorded is indicated by two horizontal dashed lines. red markers indicate the entry of the luders band fronts in the ultrasonic velocity measurement area. it should be noted that the formation of the luders band out of the acoustic measurement area is accompanied by the increase in the velocity of ultrasonic waves. when the fronts move to the area of acoustic measurements, a maximum is formed on the v(ε) curve and the ultrasound velocity starts decreasing, since the front moves inside the acoustic measurement area. during plastic deformation, two types of stresses has an effect on the propagation velocity of ultrasonic waves: macrostresses caused by an external applied load [40] and microstresses caused by the evolution of the dislocation structure [27-29, 41]. the formation of the luders band leads to the fact that the stresses in the sample are localized in the luders band, and the stresses in the remaining volume of the sample are decreased. this leads to an increase in the ultrasound velocity. the propagation of the localized deformation front is accompanied by the increase in the dislocation 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0 200 400 600 800 1000 1200  , m p a  fe-si alloy aisi 420 321h 0.0 0.1 0.2 0.3 0.4 0.988 0.990 0.992 0.994 0.996 0.998 1.000 1.002 1.004 0 100 200 300 400 v /v 0  , m p a  f d. v. orlova et alii, frattura ed integrità strutturale, 42 (2017) 293-302; doi: 10.3221/igf-esis.42.31 297 density and, as a consequence, by the decrease in the ultrasound velocity, which is observed when the luders fronts move in the acoustic measurement area. figure 3: propagation of the luders band within the yield plateau in steel (g10080) and the change in the velocity of ultrasonic rayleigh waves. development of localized plastic deformation at the pre-fracture stage n <0.5 fig. 4 shows localized deformation versus time for all test alloys. the position of the localized deformation domains is indicated by colored symbols. the time sequence of the localized plasticity domains allows the number of macrostrain zones and their rate to be determined using the slope of curves (displacement coordinate time (x-t)). thus, 4 movable deformation zones and one fixed maximum of deformation localization are formed in steel (g10080) at the pre-fracture stage (fig. 4a). such a stationary zone of localized plasticity has the highest amplitude. fig. 5 shows the distribution of local strain εxx along the sample at the beginning and at the end of the pre-fracture stage. at the pre-fracture stage, when the index of strain hardening is n < ½, the localized plasticity domains start moving along the tension axis, approaching the high-amplitude zones mentioned above, which were stationary before fracture. during the movement of localized plasticity domains, the values of their velocities become mutually consistent. the farther the localization zone is located from a stationary zone, the higher its velocity is (tab. 3). this leads to the fact that all zones reach simultaneously the stationary zone of localization, and the graphs for the positions of the movable zones versus time create the bundle of straight lines with the center coordinates of *x and *t . often, the extrapolation of the dependence  x t is required for large time to determine *x and *t . according to the experimental data of all the materials studied, the location of the sample fracture also coincides with the position of the stationary localization zone. thus, the question concerning the stationary zone position and, consequently, the pole of the zone movement at the prefracture stage acquires a special meaning. for the quantitative description of the kinetics for the zones at the pre-fracture stage, it is reasonable to combine the origin of coordinates with the stationary localization zone. in this case, the coordinate of an arbitrary zone i is determined by 0i ix x   , (1) where 0x and ix are the coordinates of the stationary localization zone and arbitrary zone in the laboratory coordinate system, the origin of which coincides with the fixed testing machine head. in the reference system chosen in this way, the zone movement graphs form a sheaf of straight lines with a single pole, when the velocities of the zones are linearly dependent on their coordinates i , that is the following relation is met: 0( )i iv     (2) where  and 0 are the empirical constants. 0.00 0.01 0.02 0.03 0.04 0.05 0.06 0 10 20 30 40 50 0.998 0.999 1.000 1.001 1.002 1.003 1.004  0.052 mm/s 0.038 mm/s x l ()  v() x , m m v /v 0 d. v. orlova et alii, frattura ed integrità strutturale, 42 (2017) 293-302; doi: 10.3221/igf-esis.42.31 298 (a) (b) (c) (d) figure 4: movement of localized plasticity domains at the stage n <0.5: a for steel (g10080); b for steel (aisi 420); c for silicon iron; d for steel (321h). for the obtained dependences  x t , the pole is not always identified. however, the position of poles can always be shown if the linear dependence (2) is met. let us consider the calculation for steel (g10080). it is seen that the pole is reached at the moment of time 5978 s, and the self-consistent movement of the zones begins at t0 = 4003 s (fig. 4a). the coordinate of the stationary localization zone for steel (g10080) is хs.z. = 35.85 mm from the stationary testing machine head. according to the data in tab. 3, the velocity of deformation zones was obtained versus the initial coordinates vaw(ξ) (fig. 6). the constants α and 0 are determined experimentally by the method of least squares, in this case 0 = 0.0018 and  = 4.98·10-4. fig. 6 also shows that the dependence  v  obtained for all test alloys is linear. domain, № 1 2 3 4 5 ξi, mm 26.47 20.58 15.19 6.48 0 vi×106, m·s-1 0.15 0.11 0.1 0.07 0.0031 table 3: velocities of the deformation zones at the pre-fracture stage for steel (g10080). 3500 4000 4500 5000 5500 6000 5 10 15 20 25 30 35 40 5 4 3 2 1 t exp c o o rd in a te ( m m ) time (s) * 500 550 600 650 700 750 5 10 15 20 25 30 35 40 c o o rd in a te ( m m ) time (s) 1200 1400 1600 1800 2000 2200 2400 15 20 25 30 35 40 45 c o o rd in a te ( m m ) time (s) 5300 5400 5500 5600 5700 5 10 15 20 25 30 35 40 45 c o o rd in a te ( m m ) time (s) d. v. orlova et alii, frattura ed integrità strutturale, 42 (2017) 293-302; doi: 10.3221/igf-esis.42.31 299 the analysis of the  and 0 coefficients showed that 0 1 t  , where t is the time for the movement of zones at the pre-fracture stage, and the ratio * 0   is the deviation of the pole from a stationary zone. then, in the laboratory reference system the location of the pole and the time required for reaching the pole by the localization zones are given by: * * 0 0 0/x x x      (3a) * 0 1/t t   (3b) where 0t is the time when a pre-fracture stage is formed. the position of the pole and the time required for reaching the pole, calculated according to (3a) and (3b) for steel (g10080), were *x = 39.5 mm and *t = 6011 s. in fact, the sample was fractured in 5978 s after deformation at a distance of 38 mm from the fixed testing machine head. it can be seen that the space-time coordinates of the pole and the experimental values of location and fracture time are in satisfactory agreement. tab. 4 shows the calculated values of location and fracture time for other materials. the calculated values obtained were compared with the real coordinates and fracture time of different materials. it is seen that the difference does not exceed 11%. thus, the kinetic characteristics obtained for the autowaves of localized plasticity at the pre-fracture stage, which can be found experimentally, allow the space-time coordinates of the object fracture to be predicted long before the occurrence of external fracture signs. this can be used as a macroscopic criterion for the plasticity of structural steels and alloys. (a) (b) figure 5: three-dimensional image of εxx at the beginning (a) and end (b) of the pre-fracture stage for steel (g10080). fracture time material fracture coordinate t٭exp, с t٭calc, с t٭exp/t٭calc x٭exp, mm x٭calc, mm x٭exp/x٭calc 5978 6011 0.99 g10080 38 39.5 0.96 6620 5895 1.11 321h 25 27 0.93 4014 3679 1.09 fe+3%si 35 35.5 0.99 930 871 1.07 aisi 420 43 42 1.02 table 4: comparison of the experimental and calculated coordinates and the fracture time of the samples. xx x, mm y, mm xx x, mm y, mm d. v. orlova et alii, frattura ed integrità strutturale, 42 (2017) 293-302; doi: 10.3221/igf-esis.42.31 300 figure 6: dependencies of ( )awv  : for 321h ( ); for g10080 ( ); for aisi 420 ( ); for silicon iron ( ). conclusions he deformation of metals and alloys is locally developed at all stages of a plastic flow, including elastic-plastic transition. during transition, dislocations actively move and spread in localization zones, and the density of dislocations is increased. this leads to a change in the characteristics for the propagation of acoustic waves. thus, during the transition to the region of a plastic flow, there is the break of the curve for the velocity of ultrasonic rayleigh waves versus the magnitude of deformation, and the increase is replaced with a drop. the break of the curve can serve as an acoustic criterion of irreversible deformation for the pressure treatment of metals, the operation and non-destructive testing of products and structures. for large deformation, at the pre-fracture stage of iron based alloys, the deformation process is gradually stopped in the entire volume of the material, except the part of the material that directly adjoins the place of necking and a ductile crack. in terms of self-organization, there is the autowave collapse of localized plastic deformation [21]. the kinetic characteristics of the autowave collapse at the pre-fracture stage, which can be found experimentally, allow the space-time coordinates of the object fracture to be predicted long before the occurrence of external signs. the work conducted contributes to the creation of a database on the mechanical and acoustic characteristics of alloys and steels both for elastic-plastic transition and large plastic deformations. this is necessary for the development of algorithms for predicting the resource of plasticity in the operation and manufacturing of parts and structures. acknowledgments he work was supported by the russian foundation for basic research (project no. 16-19-10025). references [1] cottrell, a.h., bilby, b.a., dislocation theory of yielding and strain ageing in iron, proc. phys. soc. a, 62 (1949) 1-40. [2] kuhlmann-wilsdorf, d., dynamic effects in the mesh length theory of workhardening, acta metall., 37 (1989) 32173223. -25 -20 -15 -10 -5 0 5 10 15 20 25 30 35 -0.025 0.000 0.025 0.050 0.075 0.100 mm v , m m /s , t t d. v. orlova et alii, frattura ed integrità strutturale, 42 (2017) 293-302; doi: 10.3221/igf-esis.42.31 301 [3] johnston, w.g., gilman, j.j., dislocation velocities, dislocation densities, and plastic flow in lithium fluoride crystals, j. appl. phys., 30 (1959) 129 – 134. [4] kubin, l.p., estrin, y., strain nonuniformities and plastic instabilities, rev. phys .appl., 23 (1988) 573 – 583. [5] burgers, j.m., geometrical considerations concerning the structural irregularities to be assumed in a crystal, proc. phys. soc., 52 (1940) 23-33. [6] read, w.t., shockley, w., dislocation models of crystal grain boundaries, phys. rev., 78 (1950) 275 – 289. [7] estrin, y., toth, l.s., molinari, a., brechet, y., a dislocation-based model for all hardening stages in large strain deformation, acta mater., 46 (1998) 5509-5522. [8] armstrong, r.w., dislocation viscoplasticity aspects of material fracturing, eng. fract. mech., 77 (2010) 1348-1359. [9] griffith, a.a., the phenomena of rupture and flow in solids, philos. trans. r. soc., 221 (1921) 163–198. [10] orowan, e., dislocations in metals, aime, new york, (1954). [11] panin, v.e., egorushkin, v.e., panin ,a.v., the plastic shear channeling effect and the nonlinear waves of localized plastic deformation and fracture, phys. mesomech., 13 (2010) 215-232. [12] panin ,v.e., egorushkin, v.e., deformable solid as a nonlinear hierarchically organized system, phys. mesomech., 14 (2011) 207-223. [13] ning, j., aifantis, e.c., on the description of anisotropic plastic flow by the scale invariance approach, int. j. plasticity, 11 (1995) 183-193. [14] zaiser, m., glazov, m., lalli, l.a., richmond, o., on the relations between strain and strain-rate softening phenomena in some metallic materials: a computational study, comp. mater. sci., 15 (1999) 35-49. [15] zaiser, m., avlonitis, m., aifantis, e., stochastic and deterministic aspects of strain localization during cyclic plastic deformation. acta mater., 46 (1998) 4143-4151. [16] chrysochoos, a., louche, h., an infrared image processing to analyse the calorific effects accompanying strain localisation, int. j. eng. sci., 38 (2000) 1759-1788. [17] inal, к., wu, p.d., neale, k.w., instability and localized deformation in polycrystalline solids under plane-strain tension, int. j. solid. struct. 39 (2002) 983-1002. [18] benallal, a., berstad, t., børvik, t., clausen, a.h., hopperstad, o.s. dynamic strain aging and related instabilities: experimental, theoretical and numerical aspects, eur. j. mech, a-solid, 25 (2006) 397–424. [19] sarmah, r., ananthakrishna ,g., influence of system size on spatiotemporal dynamics of a model for plastic instability: projecting low-dimensional and extensive chaos, phys. rev. e, 87 (2013) 052907. [20] haken, h., information and self-organization, springer, berlin, (1988). [21] zuev, l.b., on the waves of plastic flow localization in pure metals and alloys, ann. phys., 16 (2007) 286–310. [22] zuev, l.b., barannikova, s.a., experimental study of plastic flow macro-scale localization process: pattern, propagation rate, dispersion, int. j. mech. sci., 88 (2014) 1-7. [23] danilov, v.i., orlova, d.v., zuev, l.b. on the kinetics of localized plasticity domains emergent at the pre-failure stage of deformation process, mater. design, 32 (2011) 1554 – 1558. [24] zuev, l.b. regularities of the localized plastic flow viewed as consequences of elastoplastic invariant of strain, metallofiz.noveishie tekhnol., 38 (2016) 1335-1349. [25] evers, l.p., brekelmans, w.a.m., geers, m.g.d., scale dependent crystal plasticity framework with dislocation density and grain boundary effect, int. j. solid struct., 41 (2004) 5209-5230. [26] billingsley, j.p., the possible influence of the de broglie momentum-wavelength relation on plastic strain ‘autowave’ phenomena in ‘active materials’, int. j. solid. struct., 38 (2001) 4221-4234. [27] kobayashi, m., ultrasound nondestructive evaluation of microstructural changes under plastic deformation, int. j. plasticity, 19 (2003) 511-522. [28] kobayashi, m., analysis of deformation localization based on the proposed theory of ultrasonic wave velocity propagation in plastically deformed solids, int. j. plasticity, 26 (2010) 107-125. [29] maurel, a., pagneux, v., barra, f., lund, f., ultrasound as a probe of plasticity? the interaction of elastic waves with dislocations, int. j. bifur. chaos, 19 (2009) 2765-2781. [30] barannikova, s., lunev, a., li, yu., zuev, l., use of acoustic parameter measurements for evaluating the reliability criteria of machine parts and metalwork, key eng. mater., 743 (2017) 486-489. [31] amelinckx, s., the direct observation of dislocations, academic press., new york, (1964). [32] hull, d., effect of grain size and temperature of slip, twining and fracture in 3% silicon iron, acta met., 9 (1961) 191-204. [33] honeycombe, r.w.k., the plastic deformation of metals, edward arnold ltd., new york, (1968). [34] zuev, l.b., danilov, v.i., a self-excited wave model of plastic deformation in solids, philos. mag., 79 (1999) 43-57. d. v. orlova et alii, frattura ed integrità strutturale, 42 (2017) 293-302; doi: 10.3221/igf-esis.42.31 302 [35] jones, r., wykes, c., holographic and speckle interferometry, cambridge univ. press., cambridge, (1983). [36] hudson, r.r., setopoulos, d.d. ,speckle interferometric method for the determination of time-dependent displacement and strain. strain., 11 (1975) 126-132. [37] aebischer, h.a., waldner, s.. strain distribution made visible with image-shearing speckle pattern interferometry, opt. laser. eng., 26 (1997) 407-420. [38] shioya, t., shiroiri, j., elastic–plastic analysis of the yield process in mind steel, j. mech. phys. solid, 24 (1974) 187– 204. [39] mazière, m., luisb, c., maraisa, a., foresta, s., gaspérini, m., experimental and numerical analysis of the lüders phenomenon in simple shear, int. j. of solid and struct., 106–107 (2017) 305–314. [40] riichi, m., kazuhiro, m., development of a non-contact stress measurement system during tensile testing using the electromagnetic transducer for a lamb wave, ndt & e int., 39 (2006) 299-303. [41] granato, a.v., lucke, k., theory of mechanical damping due to dislocations, j. appl. phys., 27 (1956) 583-593. << /ascii85encodepages false /allowtransparency false /autopositionepsfiles true /autorotatepages /none /binding /left /calgrayprofile (dot gain 20%) /calrgbprofile (srgb iec61966-2.1) /calcmykprofile (u.s. web coated \050swop\051 v2) /srgbprofile (srgb iec61966-2.1) /cannotembedfontpolicy /error /compatibilitylevel 1.4 /compressobjects /tags /compresspages true /convertimagestoindexed true /passthroughjpegimages true /createjobticket false /defaultrenderingintent /default /detectblends true /detectcurves 0.0000 /colorconversionstrategy /cmyk /dothumbnails false /embedallfonts true /embedopentype false /parseiccprofilesincomments true /embedjoboptions true /dscreportinglevel 0 /emitdscwarnings false /endpage -1 /imagememory 1048576 /lockdistillerparams false /maxsubsetpct 100 /optimize true /opm 1 /parsedsccomments true /parsedsccommentsfordocinfo true /preservecopypage 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/hrv (za stvaranje adobe pdf dokumenata najpogodnijih za visokokvalitetni ispis prije tiskanja koristite ove postavke. stvoreni pdf dokumenti mogu se otvoriti acrobat i adobe reader 5.0 i kasnijim verzijama.) /hun 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/pdfxoutputintentprofileselector /documentcmyk /preserveediting true /untaggedcmykhandling /leaveuntagged /untaggedrgbhandling /usedocumentprofile /usedocumentbleed false >> ] >> setdistillerparams << /hwresolution [2400 2400] /pagesize [612.000 792.000] >> setpagedevice microsoft word numero_43_art_7 f. majid et alii, frattura ed integrità strutturale, 43 (2018) 97-105; doi: 10.3221/igf-esis.43.07 97 residual life prediction of defected polypropylene random copolymer pipes (ppr) abderazzak ouardi, fatima majid, nadia mouhib, mohamed elghorba university of hassan ii, national superior school of electricity and mechanics casablanca (ensem), lccmms, morocco majidfatima9@gmail.com, http://orcid.org/0000-0001-8909-8232 abstract. the polypropylene random copolymer (ppr) is a thermoplastic material generally used for the transport of water under pressure, especially hot water. ppr pipes are exposed to severe conditions in terms of pressure and temperature, hence the need to characterize their fracture behavior in order to avoid the design risks. sudden overpressure is one of the most common problems in piping. it can affect the security of goods and the safety of people. in this context, we have performed tests of overpressures at the laboratory scale according to astm d1599 standard, on virgin and notched pipes, to characterize mechanically the fracture behavior of ppr pipes. afterwards, we identify experimentally the evolution of their damage. the calculation of the damage, by experimental damage models, have led to determine the three stages of evolution of the damage, which are the initiation, the progression and the acceleration of it. therefore, the concept of reliability is used to specify the critical life fraction relative to the notch depth (βc) of a defect modeled as an external longitudinal groove on the ppr pipe. a comparison of ppr and hdpe pipes damage and reliability has been done. moreover, a theoretical reassessment of the damage level was done through a judicious adaptation of the theoretical model proposed by the unified theory. from the latter, we proved that theoretical and experimental results show good agreement and correlations. keywords. mechanical characterization; ppr themoplastic pipes; damage; reliability; burst pressure. citation: ouardi, a., majid, f., mouhib, n., elghorba, m., residual life prediction of defected polypropylene random copolymer pipes (ppr), frattura ed integrità strutturale, 43 (2018) 97-105. received: 16.10.2017 accepted: 03.10.2017 published: 01.01.2017 copyright: © 2018 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. introduction he polypropylene random copolymer (ppr) is a thermoplastic material made by copolymerizing propylene and small quantity of ethylene (usually less than 7 %). in fact, the role of ethylene co-monomer is to disrupt the crystallization of the main chain of propylene by introducing irregularities leading to a decrease of the crystallinity, rigidity, melting point and glass-transition temperature [1-2]. thanks to their good physical, chemical and mechanical characteristics along with the low cost of the installation and maintenance, ppr pipes becomes quickly one of the most used polymers in the market. their application merged from transport of hot and cold water, to system of air-conditioned, and various industrial and medical applications. a complete range of fittings that can be welded to create well tight systems, even under most severe conditions [3], improved ppr pipes system. t f. majid et alii, frattura ed integrità strutturale, 43 (2018) 97-105; doi: 10.3221/igf-esis.43.07 98 several researchers have studied the behavior of ppr pipes. zgoul et al [3] evaluated the convenience of two types of thermoplastic pipes to transport industrial and domestic hot water by a comparative study of polypropylene random copolymer (ppr) and cross-linked polyethylene (pex) pipes in terms of melting temperature and mechanical strength. authors used differential scanning calorimetry (dsc), uniaxial tensile tests and hydrostatic pressure. poduska et al were interested in the determination of residual stresses, and the fusion temperature of ppr pipes [4]. geertz et al have put ppr pipes under hydrostatic pressure for a long time, which the purpose was to analyze an antioxidant diffusion named irganox1010 (phenolic stabilizer) using infrared microscopy technique [5]. litvinov and soliman reported the effect of storage under hydrostatic pressure and high temperature on morphology, molecular mobility and behavior at the fracture of ppr tubes using the differential analyses of x-ray diffraction (xrd) and differential scanning calorimetry (dsc) [6]. in the framework of damage mechanics, researchers developed theoretical expressions of damage like miner, starkey and shanly. bui-quoc has developed the unified theory of metal fatigue and suggested expressions of damage that allows a quantification of the damage according to the initial and present fatigue limits [7]. in order to use this model for polymers’ characterize, through static tests, needs a judicious adaptation taking into account different parameters. however, makadir et al [8] used the normalized damage to characterize an acrylonitrile-butadiene styrene (abs) polymer plate under uniaxial loading. to highlight the influence of the notch on the behavior of polyvinyl chloride (pvc) pipes, arid et al [9] used normalized damage formulation on notched plat specimens. in this paper, we have used the normalized damage to define the different stages of the damage development within defected ppr pipes subjected to burst pressure tests. furthermore, the calculation of the reliability allows the determination of the critical depth (βc) of a defect modeled as an external longitudinal groove on the ppr pipe. method and material he chosen pipes for the study are manufactured by extrusion from ppr material. they were prepared according to the astm d1599 standard [10], which requires samples of 450 mm length. the fig. 1 shows dimensions of the used pipes in this work. in order to study the notch effect on the strength of the ppr pipes under pressure, eight pipes were notched using a universal milling machine with grooves of 6 mm width, 100 mm length and a depth from 2.42 mm to 14.5 mm. the life fraction β is defined as the ratio between the notch depth (a) and the total thickness of the pipe (t). fig. 2 and tab. 1 show the notched samples dimensions. the experimental test bench is constituted of a tank filled with water and a hydraulic pump for the pressurization. the pump is equipped with a screen to display the pressure inside the pipe. in order to prevent any leakage, caps were fixed at the ends of pipes and strongly tightened through bolts; those caps are connected to a hydraulic pump through a pressurizing hose. after fixing the caps, pipes were immersed in the tank filled with water. then, the hydraulic pump applies a gradient of pressure until their burst. the goal of this test is the determination of the residual ultimate pressures according to each life fraction β. figure 1: specimen dimensions. t diameter: 90 mm length: 450 mm thickness: 15 mm f. majid et alii, frattura ed integrità strutturale, 43 (2018) 97-105; doi: 10.3221/igf-esis.43.07 99 figure 2: groove notch preparation and dimensions. table 1: burst pressure evolution in function of the life fraction. figure 3: rupture of ppr pipes. number of specimens d (mm) l (mm) β = a/t neat 6 100 0 1 6 100 0.16 2 6 100 0.32 3 6 100 0.43 4 6 100 0.54 5 6 100 0.71 6 6 100 0.80 7 6 100 0.90 8 6 100 0.97 f. majid et alii, frattura ed integrità strutturale, 43 (2018) 97-105; doi: 10.3221/igf-esis.43.07 100 theory damage theories n this paper, we led burst tests over notched pipes for both hdpe and ppr materials. thus, we prepared standard specimens according the astm 1599. then, we created multi-level grooves in the produced specimens. after that, we exposed neat and notched pipes to an increasing internal pressure until the rupture through a hydrostatic burst tester. the studied specimens of hdpe and ppr have seemingly the same dimensions. moreover, the internal pressure evolution according to time have been registered for the neat pipe and the notched ones. besides, the burst pressure and the time of burst have been also got from the hydrostatic tester display. these pressures are considered as the main parameters used in this paper to quantify the damage evolution. on the one hand, we interpreted the internal pressure evolution and the way it is representing the ductile behavior of the thermoplastic materials. on the other hand, the representation of the burst pressure according to the life fraction, which have been chosen as the ratio of the thickness and its fluctuation, have been detailed. the static damage of the unified theory based on the burst pressures has been developed to predict the damage evolution and the artificial preloading impact, which is represented by the notch depth [14, 15]. static damage the static damage model is presented in the eq. (1). this model is justified by the proportionality between the stress and the rupture pressure.    1 1 ur u a u p p d p p (1) unified theory damage by correlation to the expression of the unified theory damage developed by bui-quoc, a relationship describing the evolution of the damage depending on the life fraction and pressure is given by eq. (2):                            _ 1 1 m u d (2) with: β: life fraction. m: empirical constant depending on material (m=1 for our case). /u u ap p  : parameter reflecting the strength of the material in a virgin state. /ur ap p  : parameter characterizing the effect of the damage on the mechanical characteristics of the material. reliability estimation reliability analysis is an essential part of any safety study. originally, reliability was related to high-tech systems (nuclear power plants, aerospace). today, reliability has become a key parameter of quality and decision-making in the study of most components, products and processes for transport, energy, buildings, electronic components and mechanical components. many industrialists are working to evaluate and improve the reliability of their products during their life cycle, from design to operation in order to develop their knowledge of the report cost / reliability and control failure causes [11]. i f. majid et alii, frattura ed integrità strutturale, 43 (2018) 97-105; doi: 10.3221/igf-esis.43.07 101 in fact, reliability is defined as the probability of survival of systems during their operation at a given time. this parameter may be considered as the compliment to 1 of the damage. the relation between these two parameters is given by eq. (3) [12]:     1r d   (3) by using this equation, the evolution of these two quantities can be studied at the same time as shown in fig. 6. results and discussions residual burst pressures he variation of the ultimate internal pressure of the pipes in function of the life fraction β is presented by the fig. 4 and fig. 5. undamaged pipes can withstand an ultimate pressure of about 129 bars. in addition, the notch had caused a drop of the ultimate pressure of the notched pipes compared to neat one. the increase in depth of the notches leads to a depletion of residual ultimate pressures of notched ppr pipes. figure 4: internal pressure evolution for neat and notched ppr pipes. figure 5: ultimate pressure evolution in function of life fraction β static damage the hdpe and ppr polymers are relatively different materials. in this paper, we led a study of their performances by focusing over their mechanical behavior under an internal pressure until rupture. however, we were able to compare the internal pressure evolution and the way it is representing ductility of these materials. we showed that the impact of the internal pressure depends on the necessary time for burst and the duration of each stage (preloading, elastic, plastic and 0 20 40 60 80 100 120 140 0 0,2 0,4 0,6 0,8 1 p re ss u re  ( b a rs ) life fraction  β=a/t t f. majid et alii, frattura ed integrità strutturale, 43 (2018) 97-105; doi: 10.3221/igf-esis.43.07 102 rupture). moreover, the damage-reliability curves, fig. 6, allowed us to define precisely the critical life fraction for both of them. indeed, the critical life fractions are 52% and 58% for both hdpe and ppr respectively. the damage stages of them are different. therefore, the first stage limit is 20% and 38%, the second one 75% and 78% and third over the last values for hdpe and ppr respectively. the performance of hdpe and ppr have a similar performance regarding the damage behavior and the criticism of thickness reduction. however, the two materials are very different considering the elastic and the rupture limits and the time to failure. in fact, the neat ppr reaches the burst pressure of 135 bars in 14 s. meanwhile, the hdpe reaches the burst pressure of 69.5 bars at 49 s. the range of each pipe can explain the discrepancies of these values, the ppr pipes are pn20 and those of hdpe are pn16, and the thickness differences. in fact, we used the existing pipes in the market. furthermore, we were able to validate previous researches done over hdpe, by comparing the hdpe and ppr performances and developing the modified version of the static damage model based on the burst pressures instead of the stresses as published in the literature [7,14]. unlike the damage, reliability begins with the value of one, corresponding to the absence of damage, and decreases gradually as the notch depth increases; the total failure of the material is indicated by the zero value. the superposition of damage and reliability curves defines the life fraction at 52% and 58% of reliability for hdpe and ppr respectively. this point is located at the end of stage ii and allows the maintenance department to decide on the time of reparation or even the change of the defected pipe. figure 6: ppr and hdpe’s damage-reliability evolution in function of the life fraction. unified theory damage the variation of the unified theory damage in function of the fraction life  is given in the fig. 7. the unified damage is indicated by a set of curves associated with a constant pressure ratio /u u ap p  ( up =129.3bars and ap =20bars) and variable parameter /ur ap p  . therefore, each curve is associated with a separate level of applied pressure. in the direction of increasing of γ, the curves of the unified theory damage grow to reach the linear tendency for high loading levels. comparison of static and unified theory damages fig. 8 shows the variation of experimental and unified theory damages ( 6.46u  ) and that proposed by miner in function of the β the life fraction. for low life fractions (0% <β<16%), experimental damage and unified theory damage at a loading level γ = 1.27 are similar. with the increase of the life fraction β, the curve of static damage approaches tend to reach the unified damage corresponding to the loading level γ = 1.9 until they overlay at the end of stage i. then, in the beginning f. majid et alii, frattura ed integrità strutturale, 43 (2018) 97-105; doi: 10.3221/igf-esis.43.07 103 of stage ii and up to a life fraction β equal to 60%, the experimental damage is below the theoretical damage corresponding to γ = 1.9. then it exceeds the curve of this loading level and overlaps in this time with the curve of the unified damage at a loading level γ = 2.55 at the end of stage ii. in stage iii curves of static damage and unified theory damage for γ = 1.9 return back similar. both graphs of the two types of damage remain below the damage given by miner. figure 7: unified theory damage variation in function of the life fraction β. figure 8: experimental, unified and miner damages comparaison. conclusion he polypropylene random copolymer (ppr) is a thermoplastic material used for the transport of under pressure water, especially hot waters. in the industrial conditions, ppr pipes are exposed to severe conditions in terms of pressure and temperature. in order to characterize the behavior of the ppr at failure we have performed tests of overpressures at the laboratory scale according to astm d1599 standard, on virgin and notched pipes. according experimental and theoretical results. many results have been found: • the notch had caused a drop of the ultimate pressure of the notched pipes compared to the undamaged ones. the increase in depth of the notch leads to a depletion of residual ultimate pressures of ppr notched pipes. • the calculation of the damage, by the experimental damage formulation, have led to determine the three stages of evolution of the damage initiation, progression and acceleration of damage. t f. majid et alii, frattura ed integrità strutturale, 43 (2018) 97-105; doi: 10.3221/igf-esis.43.07 104 • the use of experimental damage ensures an optimization of maintenance costs for defective pipes by predicting low values of damage in comparison with that one gives by miner’s model. • the calculation of the reliability allows the defining the depth β=a/t of external longitudinal groove in a ppr pipe that corresponding to 50% of reliability. • in the framework of the preventive maintenance, at a value of 70% of the total depth of a longitudinal external groove, it is recommended to repair or change the defective pipe before that defect becomes unstable and causes costly fractures. • the comparison of the unified theory damages calculated for different load levels revealed that the loading level γ = 1.9 gives the best results with respect to the static damage, it seems most realistic to properly describe the progression of the damage of the tubes ppr with defects in the form of external longitudinal grooves. references [1] papageorgiou, d.g., papageorgiou, g.z., bikiaris d.n., chrissafis k., cristallization and melting of polypropyleneethylene random copolymers. homogeneous nucleation and β-nucleationg agents, european polymer journal, 49 (2013) 1577-1590. [2] yu, l., wu, t., chen, t., yang, f., xiang, m., polypropylene random copolymer in pipe application: performance improvement with controlled molecular weight distribution. thermochimica acta, 578 (2014) 43-52. [3] zgoul, m.h., habali, s.m., an invistigation into pipes as hot water transporters in domestic and industrial applications, jordan journal of mechanical and industrial engineering, 2 (4) (2008) 191 – 200. [4] poduska, j., kucera, j., hutar, j.p., sevcik, m., krivanek, j., sadilek, j., nhalik, l., residual stress distribution in extruded polypropylene pipes, polymer testing, 40 (2014) 88-98. [5] geertz, g., brull, r., maria j.r., wenzel, m., engelsing, k., wust, j., bastian, m., rudscuck, m., stabiliser diffusion in long-term pressure tested polypropylene pipesanalysed by ir microscopy, polymer degradation and stability, 94 (2009) 1092-1102. [6] litvinov, m., soliman, m., the effect of storage of polypropylene pipes under hydrostatic pressure and elevated temperatures on the morphology molecular mobility and failure behaviour, polymer, 46 (2005) 3077–3089. [7] el ghorba, m., evolution of the damage and the crack propagation under cyclic loading of the steel a36 and the aluminum 6351-t6, master thesis, montreal university, canada, (1985). [8] makadir, i., barakat, m., el ghorba, m. study of damage to abs specimens submitted to uniaxial loading, the international journal of engineering and science, 4 (1) (2015) 05-08. [9] arid g., makadir, i., naji, a., chergui, m., el ghorba, m. comparative study of the mechanical behavior of polymer materials betwin abs and pvc, the international journal of engineering and science, 4 (4) (2015) 55-60. [10] astm international d1599, standard test method for resistance to short-time hydraulic pressure of plastic pipe, tubing, and fittings. annual book of standards, astm international, west conshohocken, pa, 8.04 (2009). [11] meksem, a., probabilistic approach and experimental characterization of the behavior of wire rope hoist. ph.d. thesis, ensem, hassan 2 casablanca university. morocco, (2010). [12] chouairi, a., optimization by the reliability of the life of a hoisting wire rope at its damage. master’s thesis, ensem, hassan 2 casablanca university, morocco, (2009). [13] majid, f., elghorba, m., hdpe pipes failure analysis and damage modeling, eng. fail. anal., 71 (2017) 157-165. [14] majid, f., nattaj, j., elghorba, m., pressure vessels design methods using the codes, fracture mechanics and multiaxial fatigue, frattura ed integrità strutturale38 (2016) 273–280. doi:10.3221/igf-esis.38.37. [15] majid, f., ouardi, a., barakat, m., elghorba, m., prediction of ppr and hdpe polymers through newly developed nonlinear damage-reliability models, procedia struct. integr., 3 (2017) 387–394. doi:10.1016/j.prostr.2017.04.043. nomenclature  /ur ap p parameter characterizing the effect of the damage on the mechanical characteristics of the material. u /u ap p parameter reflecting the strength of the material in a virgin state. n is the instantaneous number of cycles under an applied stress. nf is the total number of cycles at the rupture. f. majid et alii, frattura ed integrità strutturale, 43 (2018) 97-105; doi: 10.3221/igf-esis.43.07 105 pur is the ultimate residual pressure. pu is the ultimate pressure corresponding to an undamaged hdpe specimen. pa is the pressure just before the rupture. p0 is the endurance limit’s corresponding pressure. σθ is the circumferential stress. r is the radius of the pipe specimen. t is the thickness of the pipe specimen. a is the notch depth d is 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can be opened with acrobat and adobe reader 5.0 and later.) >> /namespace [ (adobe) (common) (1.0) ] /othernamespaces [ << /asreaderspreads false /cropimagestoframes true /errorcontrol /warnandcontinue /flattenerignorespreadoverrides false /includeguidesgrids false /includenonprinting false /includeslug false /namespace [ (adobe) (indesign) (4.0) ] /omitplacedbitmaps false /omitplacedeps false /omitplacedpdf false /simulateoverprint /legacy >> << /addbleedmarks false /addcolorbars false /addcropmarks false /addpageinfo false /addregmarks false /convertcolors /converttocmyk /destinationprofilename () /destinationprofileselector /documentcmyk /downsample16bitimages true /flattenerpreset << /presetselector /mediumresolution >> /formelements false /generatestructure false /includebookmarks false /includehyperlinks false /includeinteractive false /includelayers false /includeprofiles false /multimediahandling /useobjectsettings /namespace [ (adobe) (creativesuite) (2.0) ] /pdfxoutputintentprofileselector /documentcmyk /preserveediting true /untaggedcmykhandling /leaveuntagged /untaggedrgbhandling /usedocumentprofile /usedocumentbleed false >> ] >> setdistillerparams << /hwresolution [2400 2400] /pagesize [612.000 792.000] >> setpagedevice microsoft word numero_40_art_3 i. stavrakas, frattura ed integrità strutturale, 40 (2017) 32-40; doi: 10.3221/igf-esis.40.03 32 focussed on recent advances in “experimental mechanics of materials” in greece acoustic emissions and pressure stimulated currents experimental techniques used to verify kaiser effect during compression tests of dionysos marble ilias stavrakas laboratory of electronic devices and materials, technological educational institute of athens, 12210, athens, greece ilias@ee.teiath.gr, http://research.ee.teiath.gr/ abstract. the damage development due to externally applied mechanical stress is a hot topic of interest involving several applications of everyday life, like civil engineering, monument restoration, construction evaluation and health monitoring. repetitive loadings of brittle materials cause internal damages that gradually extend, leading to inevitable failures. such processes are studied under the concept of the materials’ mechanical memory effect that is widely known as kaiser effect. the kaiser effect states that a structure will only suffer further internal damaging when exposed to applied stresses higher than previously encountered. certain conditions lead to a violation of the kaiser effect, known as the felicity effect, quantitatively measured using the felicity ratio. this work presents the experimental results when repetitive mechanical load loops are applied on marble specimens, while concurrent acoustic emission (ae) and pressure stimulated currents (psc) measurements are conducted. the collected ae and psc data are studied in combination with the mechanical data, like mechanical stress and strain, under the frame of the kaiser effect. it is clearly seen that the felicity ratio strongly depends on the stress range the material is subjected to, with regard to the elastic or plastic deformation region. keywords. acoustic emissions; pressure stimulated currents; dionysos marble; kaiser effect; felicity ratio. citation: stavrakas, i., acoustic emissions and pressure stimulated currents experimental techniques used to verify kaiser effect during compression tests of dionysos marble., frattura ed integrità strutturale, 40 (2017) 3240. received: 05.01.2017 accepted: 06.02.2017 published: 01.04.2017 copyright: © 2017 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. introduction he scientific literature reports several studies and recordings of ae that are attributed to mechanical stresses adequate to cause microcracking phenomena in rocks [1]. towards this direction, the experimental technique of ae detection has been evaluated and developed in order to constitute a valuable tool for the monitoring and t i. stavrakas, frattura ed integrità strutturale, 40 (2017) 32-40; doi: 10.3221/igf-esis.40.03 33 interpretation of the underlying physical mechanisms of mechanical dynamic processes and the detection of an upcoming event of mechanical failure [2]. further than the ae, the detection and recording of low-level electric signals provide reliable information, regarding the development of damage processes. such electric signals are detected due to fracture processes in quasi-brittle materials following microcracks formation and growth. it is known that transient electric phenomena are often appearing when solid materials are subjected to stress and mechanical effects are taking place [3, 4]. since 2000, the detection of the electric signals that are related to weak electric current emissions is conducted through an innovative experimental technique rendered under the term pressure stimulated currents technique, while the recorded electrical currents are known as pressure stimulated currents (psc) [5]. the psc are detected through the recording of a weak (low-level) electric current using a sensitive electrometer, when a pair of electrodes is attached properly on the specimen that is subjected to mechanical tests. the above-described experimental technique was initially applied when marble materials were subjected to axial compressive mechanical stress [6, 7]. the kaiser effect is an ae phenomenon briefly defined as the absence of detectable acoustic emissions until the previously applied stress level is exceeded. this effect is based on the experimental discovery by kaiser (1950), that metallic materials had the capability to remember the previous maximum stress level. the existence and the experimental verification of the kaiser effect was also discovered in rocks and described in other works [8-10] and since then, the kaiser effect is used to detect and assess the amount of damage that has been developed in rocks [11, 12]. the breakdown of the kaiser effect can be represented quantitatively by the felicity ratio (fr) that is defined as the ratio of the ae-onset stress to the maximum stress of the previous cycle. it may be taken as a measure of the quality of the rock [13]. a high felicity ratio means that the rock is of good quality. regarding the psc emissions, several works in the past demonstrate the ability of a marble specimen to “remember” previous mechanical loadings [5, 6, 14-16]. specifically, the main properties of the psc signal, which are affected by the existence of memory, converge to an inertial attitude of the material to the same stimuli and they are quite common with the properties of other fracture induced signals (i.e. ae). namely, they are the following: (a) the psc peak evolution over loading cycles is a changing signal property, with respect to the time interval between loadings, (b) the decrease of the dissipated electric energy during cyclic loading tests, (c) the psc slower relaxation in each loading, quantified by the relaxation process parameters evolution, (d) the psc signal initiates to show up at higher stress level after each next loading cycle. the aim of this work is to conduct a laboratory experimental investigation and verification of the kaiser effect on dionysos marble specimens combining the ae and psc recordings. the specimens are subjected to compressive loading loops where the first loading is in the region where the material leaves the elastic region and enters the plastic deformation i.e., the stress-strain curve deviates from linearity. test facilities and arrangement he marble specimens were subjected to three loading-unloading loops (see fig. 1). the maximum stress level during the 1st and the 2nd loading was approximately 60 mpa, a value that corresponds to the 70% of the ultimate compressive strength of the material and leads to a young’s modulus of 72 gpa (see fig. 2). this stress level, according to preliminary tests on similar specimens, corresponds to the region that the material gradually enters the nonlinear region regarding its stress-strain behaviour and initial plasticity effects take place, which is in accordance, also, to previously published data [17-19]. during the unloading processes the stress level was maintained at a value of 15 mpa, approximately. a third loading was attempted during which the specimen failed at a stress level of 82.7 mpa. the compressive stress was applied following load control at a rate of 320 kpa/s. fig. 1 shows the temporal variation of the loading path until the failure of the specimen and fig. 2 shows the stress-strain curve during the complete cyclic loading. it must be noted that during the 1st loading the linear region was estimated to last up to a stress level of 58 mpa approximately. the specimens (i.e. dionysos marble) were prismatic with dimensions 35mm×35mm×75mm. the physical and chemical properties of this kind of marble have already been presented in bibliography [6, 20, 21]. the strain was measured using kyowa strain gauges attached on the microlink-770, 120ω resistor bridge (see fig. 3). during the tests the ae events were monitored using a physical acoustic corporation (pac) mistras systems. the aes transducer was the model r6 sensor provided from the mistras s.a. that obtains a wide frequency range and was attached in the middle of the specimen’s height (see fig. 3). the ae threshold for detecting acoustic events was set at 40 db. concerning the psc technique, the measuring system consisted of an ultra-sensitive programmable electrometer (keithley, 6517a) resolving currents ranging from 0.1 fa to 20 ma in 11 ranges. the data of the electrometer were stored t i. stavrakas, frattura ed integrità strutturale, 40 (2017) 32-40; doi: 10.3221/igf-esis.40.03 34 in a computer using a gpib interface. the sensing system consisted of a pair of gold plated electrodes, installed in the middle of the specimen’s height (see fig. 3), enabling the collection of electric emissions as close as possible to any potential source of electric current (or equivalently to any point where damage occurs). further details on the monitoring of the αε and psc are described in earlier papers [22, 23]. figure 1: temporal variation of the mechanical stress (black line), and the corresponding behaviour of the mechanical strain (gray line) during the complete cyclic loading. figure 2: the stress-strain behaviour during the two loading / unloading loops as well as the final loading during which the specimen failed. i. stavrakas, frattura ed integrità strutturale, 40 (2017) 32-40; doi: 10.3221/igf-esis.40.03 35 figure 3: the schematic diagram of the experimental setup showing the physical locations of the sensors on the specimen, the geometry as well as the data communication interfaces. verification of the kaiser effect acoustic emission (ae) recordings he ae activity during the complete experimental procedure is illustrated in fig. 4. specifically, the ae events per second are shown with respect to time. in the same figure, the temporal variation of the normalized applied mechanical stress is also presented. it may be clearly seen that ae were continuously detected during the entire process. specifically, high ae rate is observed during the loading procedures while low ae rate is observed during the unloadings. it must be noted that despite the fact that the experimental apparatus is well isolated from external ae noise and the configuration of the ae hardware system significantly reduces the probability to record noise as ae events (i. preamplifier filters were applied and ii. background noise was continuously recorded and subtracted) the low values of ae rate may be attributed to such an external influence. during the first loading loop, a total number of 978 ae events is recorded while a significantly smaller number of ae events (289 ae events) were recorded during the second loading loop. it is noticeable that during the second loading of the specimen, practically no ae events were recorded until the load reached the 68% of the compressive strength (i.e. only 24 low amplitude ae events were recorded). the most of the ae events (i.e. 90% of the detected ae events) were recorded in the region between 68% and 73% of the compressive strength. this region corresponds to the upper limit of the linear behaviour of the material regarding its stress-strain curve. during the 3rd loading and before the stress reached the level of the previously applied stress, only 45 ae events were recorded while the 36 of them were recorded when the applied stress was in the region between 71% and 73% of the compressive strength. when the stress exceeded these values, 1237 ae events were recorded until the failure of the specimen. the ae records of the entire experimental procedure are plotted in a cumulative form, as shown in fig. 5. these experimental results are in good agreement with the existing literature and specifically works published in [8-12]. during the 2nd and the 3rd loading-unloading loops the felicity ratio (fr) can be calculated to be equal to 0.66 and 0.8 approximately, correspondingly (see fig. 5). the fr values were calculated according to the following formula: loadatonsetof significant aeevent fr previousmaximumload  t i. stavrakas, frattura ed integrità strutturale, 40 (2017) 32-40; doi: 10.3221/igf-esis.40.03 36 the deviation from the optimum value of fr=1, may be justified due to the fact that the maximum stress values of the 1st and 2nd loading loops was selected to lay in the limits of the linear and non-linear region, regarding the stress-strain behaviour of the marble, and additionally to the quality of the used marble. it must be noted that during each loading loop the fr clearly depends on the maximum stress of the previous loop and decreases as the value of the maximum stress increases [13]. this fact clearly is not the case for the described loading protocol of this work since the fr seems to increase rather than decrease during each next loading. such a behaviour may be attributed to two main reasons. firstly, the two initial loadings were performed up to the same stress value, a fact that is not typical for the fr development and secondly the selected stress value of 60 mp lays in the limits between the linear and non-linear region of the stress-strain curve, so no further damages may be caused during the second loading leading, as expected at a higher fr value. figure 4: the mechanical stress temporal development during the complete experimental procedure (gray line) and the corresponding per second ae event rate (black bars). figure 5: the behaviour of the cumulative number of the ae events with respect to the normalized value of the mechanical stress applied on a typical specimen. pressure stimulated current (psc) recordings concurrently to the above described observations, psc emission recordings were conducted. fig. 6 shows the temporal variation of the recorded psc with respect to the temporal variation of the mechanical stress. observing the behaviour of the psc, it may be clearly seen that during the first loading, where the mechanical stress reached a maximum value of 60mpa approximately, a strong psc emission was recorded reaching a maximum value of 40pa approximately, while a i. stavrakas, frattura ed integrità strutturale, 40 (2017) 32-40; doi: 10.3221/igf-esis.40.03 37 gradual decay back to the background level occurs when the mechanical stress is relieved. it must be noted that the maximum value of the applied stress (i.e. 70% of the maximum stress) enters the specimen into the early nonlinear region regarding its stress-strain behaviour. during the second loading the applied mechanical stress reached approximately the level of the mechanical stress of the 1st loading (i.e. 60mpa) while the recorded psc reached a maximum of 10pa which is significantly lower than the recorded psc of the first loading. such a behaviour may be attributed to the underlying physical mechanisms of the psc generation and specifically the moving charged dislocations model [4]. since the psc variation is attributed to the damage generation and extension it is expected that when a brittle specimen, like marble, is subjected to a mechanical stress in sequential loading cycles new damages occur only during the initial application of the stress. during each following stress application only minor extension of the already created damages is produced and consequently only weak psc emissions are expected. the third loading was scheduled to lead the specimens to failure, and the mechanical stress was applied at the same rate of the two initial loadings. during this third loading a strong psc emission was detected reaching a peak psc value of the order of 100pa. it is worth noticing that a short time (i.e. 5 seconds) before the stress drop (due to the specimen’s failure) the characteristic psc decrease [5, 6] was observed clearly indicating the upcoming failure. the above experimental results are in good agreement with the corresponding results presented in other works [5, 6, 14-16]. figure 6: the temporal variation of the mechanical stress during the complete experimental procedure and the corresponding behaviour of the psc emission. the inset figure constitutes a zoom in at the final stage before fracture making clear the characteristic psc drop before the failure of the specimen. fig. 7 demonstrates the behaviour of the psc emission in logarithmic scale with respect to the mechanical stress during each loading cycle. specifically, the blue, the green and the light grey lines correspond to the load increase from 0 mpa to 60 mpa of the first, the second and the third loading, respectively. the black line shows the behaviour of the psc with respect to the mechanical load during the third loading, when the applied stress becomes higher than 60 mpa exceeding this way any previously applied level of stress. observing fig. 7 it is clear that during the three loadings and while the stress is below 60 mpa, the recorded psc becomes significantly lower for each next loading. when the mechanical stress exceeded 60 mpa during the third loading, the psc emission significantly increases reaching a peak of 100 pa, few seconds before fracture. the black line in fig. 7 supports the dominance of the kaiser effect during the experimental procedure and in addition that psc may also be used to detect that a sample has suffered significant mechanical stress at earlier times and it “remembers” such a fact. another observation is that during the second and the third loading the detected psc and the corresponding psc energy are both at the same low levels up to a stress value of 45 mpa. beyond that point of stress and during the third loading the recorded psc is maintained at a very low level. during the third loading and when stress becomes higher than 60 mpa strong psc emissions and rapid increase is detected. i. stavrakas, frattura ed integrità strutturale, 40 (2017) 32-40; doi: 10.3221/igf-esis.40.03 38 figure 7: the behaviour of the psc, shown in logarithmic scale, with respect to the value of the mechanical stress. figure 8: the behaviour of the psc cumulative energy, shown in logarithmic scale, with respect to the value of the mechanical stress. fig. 8 shows the behaviour of the released cumulative energy of the psc in logarithmic scale with respect to the mechanical loading during the experimental procedure. the square of psc adjusted amplitude psc(t), expresses an energy quantity [24] and may be calculated according to:    2psc i ie t psc t where it corresponds to the time instance of each psc recorded sample. the cumulative psc energy pscce during each loading is calculated according to the following formula: i. stavrakas, frattura ed integrità strutturale, 40 (2017) 32-40; doi: 10.3221/igf-esis.40.03 39   1 n psc psc i i ce e t    where n corresponds to the number of the recorded psc values in the examined mechanical stress region. it may be clearly seen that during the first loading a significant amount of energy is released (blue line). additionally it is clear that the psc emission initiated from early mechanical stress levels which means that the psc is emitted even in low stress levels. during the second and the third loadings (green and gray lines respectively) the psc energy initiates only when stress becomes higher than 15mpa approximately, while their cumulative energy levels are significantly lower than the corresponding of the first loading. finally, during the third loading and when the mechanical stress became higher than the 60 mpa a significant increase of the released cumulative energy is recorded. this fact that also manifests kaiser effect dominates the psc emissions and the corresponding psc cumulative energy. concluding remarks uring the present experimental protocol two sequential compressive loadings and unloadings were applied on marble prismatic specimens up to a stress level that corresponds to early non-linear region regarding the stressstrain behaviour. during the third loading, the stress was not relieved but instead it was further increased until the sample mechanically failed. concurrently to the loading ae and psc emissions were recorded. the aim was to investigate and correlate the fingerprint of the kaiser effect on the ae recordings and the psc emissions as well as the corresponding cumulative energy. the tests were performed on series of marble prismatic specimens and representative experimental results of the carried out tests are presented herein. additionally, regarding the ae recordings, it is experimentally verified that for marble specimens the felicity ratio (fr) obtains high values (i.e. 0.66 and 0.8 approximately) during the two loading/unlading cycles when the applied stress lays in the region where the material is still near the limits of linear region regarding its stress-strain behaviour. regarding the behaviour of the ae events the number recorded is significantly large during the first loading while the number of ae events becomes fewer during the second load. ae events practically disappear during the third loading and more specific when the applied stress is in the range of the two previous loadings. when the stress was further increased significant ae events are recorded until the fracture of the sample. regarding the psc emissions it is observed that the maximum value of the psc emission becomes significantly lower during each next loading while the applied mechanical stress varies in the same stress limits. it is also important to notice that detectable psc emissions show up at higher stress levels during the second and the third loading. during the third loading and while the applied mechanical stress becomes higher than the corresponding values of the previous loadings, intense psc emissions are detected. the characteristic drop of the psc is detected when the sample approaches failure. all the above manifest that both ae and psc emissions may be used to detect and qualitatively approach the kaiser effect phenomena when dionysos marble samples are subjected to mechanical stress. combining the experimental findings after applying the ae and the psc experimental techniques when marble specimens are subjected to compressive mechanical stress it is observed that both experimental techniques may be used in order to detect an upcoming specimen failure. further on qualitative comparison shows that the use of psc and ae provide similar information regarding the existence of the kaiser effect. specifically, it was seen that when applying sequential loadings and unloadings on marble specimens the emitted psc becomes lower during each loading cycle and the recorded ae events rate start to increase only when the applied mechanical stress gets values higher than the corresponding stress values during the previous loadings. quantitative comparison is not yet possible and further experimental work is required in order to attempt such an approach. references [1] tonolini, f., sala, a., villa, g., general review of developments in acoustic emission methods, international journal of pressure vessels and piping, 28(1)(1987) 179–201. [2] rao, m.v.m.s., lakschmi, p.k.j., analysis of b-value and improved b-value of acoustic emissions accompanying rock fracture. current science, 89 (2005) 1577-1582. [3] enomoto, j., hashimoto, h., emission of charged particles from indentation fracture of rocks, nature, 346 (1990) 641–643. d i. stavrakas, frattura ed integrità strutturale, 40 (2017) 32-40; doi: 10.3221/igf-esis.40.03 40 [4] vallianatos, f., triantis, d., tzanis, a., anastasiadis, c., stavrakas, i., electric earthquake precursors: from laboratory results to field observations, physics and chemistry of the earth, 29 (2004) 339-351. [5] stavrakas, ι., triantis, d., agioutantis, z., maurigiannakis, s., saltas, v., vallianatos, f., pressure stimulated currents in rocks and their correlations with mechanical properties, natural hazards and earth system sciences, 4 (2004) 563567. [6] stavrakas, ι., anastasiadis, c., triantis, d., vallianatos, f., piezo stimulated currents in marble samples: precursory and concurrent – with – failure signals, natural hazards and earth system sciences, 3 (2003) 243-247. [7] triantis, d., stavrakas, i., anastasiadis, c., kyriazopoulos, a., vallianatos, f., an analysis of pressure stimulated currents (psc), in marble samples under mechanical stress, physics and chemistry of the earth, 31 (2006) 234-239. [8] lavrov, a., the kaiser effect in rocks: principles and stress estimation techniques, international journal of rock mechanics & mining sciences, 40 (2003) 151–171. [9] lavrov, a., kaiser effect observation in brittle rock cyclically loaded with different loading rates, mechanics of materials, 33 (2001) 669-677 [10] kurita, k., fuji, n., stress memory of crystalline rocks in acoustic emission, geophys. res. lett., 6(1) (1979) 9-12. [11] holcomb, d.j., costin, l.s., detection damage surfaces in brittle materials using acoustic emissions. trans, asme., 53 (1986) 536-544. [12] holcomb, d.j., stone, c.m., costin, l.s., combining acoustic emission locations and a microcrack damage model to study development of damage in brittle materials. in: hustrulid, w.a., johnson, g.s. (eds) proc., 31st u.s. symposium, rock mechanics contributions and challenges, balkema, rotterdam, (1990) 645-651. [13] li, c., nordlund, e., experimental verification of the kaiser effect in rocks. rock mech. eng., 26-4(1993) 333-351. [14] anastasiadis, c., triantis, d., hogarth, c.a., comments on the phenomena underlying pressure stimulated currents in dielectric rock materials, j mater sci., 42-8 (2007) 2538-2542. doi:10.1007/s10853-006-0690-7. [15] kyriazis, p., anastasiadis, c., triantis, d., vallianatos, f., wavelet analysis on pressure stimulated currents emitted by marble samples, nat. hazards earth syst. sci., 6 (2006) 889–894. [16] kyriazis, p., stavrakas, i., anastasiadis, c., triantis, d., stonham, j., memory effects on mechanically stimulated electric signal; diversification of stimuli impact on material memory and comments on the observed features, geophysical research abstracts, egu2010-12994, 12 (2010). http://meetingorganizer.copernicus. org/egu2010/egu2010-12994.pdf. [17] kourkoulis, s.k., exadaktylos, g.e., vardoulakis, i., unotched dionysos-pentelicon marble beams in three point bending: the effect of nonlinearity, anisotropy and microstructure, int. j. fracture, 98 (1999) 369–392. [18] exadaktylos, g.e., vardoulakis, i., kourkoulis, s.k., influence of nonlinearity and double elasticity on flexure of rock beams i. technical theory, international journal of solids and structures, 38(22-23) (2001) 4091-4117. [19] exadaktylos, g.e., vardoulakis, i., kourkoulis, s.k., influence of nonlinearity and double elasticity on flexure of rock beams ii. characterization of dionysos marble, international journal of solids and structures, 38(22-23) (2001) 41194145. [20] kourkoulis, s.k., prassianakis, i., agioutantis, z., exadaktylos, g.e., reliability assessment of the ndt results for the internal damage of marble specimens, international journal of material and product technology, 26(1/2) (2006) 35-56. [21] kourkoulis, s.k., ganniari-papageorgiou, e., mentzini, m., dionysos marble under bending: α contribution towards understanding the fracture of the parthenon architraves, engineering geology, 115(3-4) (2010) 246-256. [22] stergiopoulos, c., stavrakas, i., hloupis, g., kyriazopoulos, a., triantis, d., anastasiadis, c., stonham, j., monitoring acoustic emissions and electrical signals during three-point bending tests performed on cement mortar specimens, viii international conference on fracture mechanics of concrete and concrete structures, framcos-8, toledo (spain), 2013. http://www.framcos.org/framcos-8/p591.pdf [23] stergiopoulos, c., stavrakas, i., hloupis, g., triantis, d., vallianatos, f., electrical and acoustic emissions in cement mortar beams subjected to mechanical loading up to fracture, engineering failure analysis, 35 (2013) 454–461. [24] vallianatos, f., triantis, d., scaling in pressure stimulated currents related with rock fracture, physica a, 387 (2008) 4940-4946. << /ascii85encodepages false /allowtransparency false /autopositionepsfiles true /autorotatepages /none /binding /left /calgrayprofile (dot gain 20%) /calrgbprofile (srgb iec61966-2.1) /calcmykprofile (u.s. web coated \050swop\051 v2) /srgbprofile (srgb iec61966-2.1) /cannotembedfontpolicy /error /compatibilitylevel 1.4 /compressobjects /tags /compresspages true /convertimagestoindexed true /passthroughjpegimages true /createjobticket false /defaultrenderingintent /default /detectblends true /detectcurves 0.0000 /colorconversionstrategy /cmyk /dothumbnails false /embedallfonts true /embedopentype false /parseiccprofilesincomments true /embedjoboptions true /dscreportinglevel 0 /emitdscwarnings false /endpage -1 /imagememory 1048576 /lockdistillerparams false /maxsubsetpct 100 /optimize true /opm 1 /parsedsccomments true /parsedsccommentsfordocinfo 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can be opened with acrobat and adobe reader 5.0 and later.) >> /namespace [ (adobe) (common) (1.0) ] /othernamespaces [ << /asreaderspreads false /cropimagestoframes true /errorcontrol /warnandcontinue /flattenerignorespreadoverrides false /includeguidesgrids false /includenonprinting false /includeslug false /namespace [ (adobe) (indesign) (4.0) ] /omitplacedbitmaps false /omitplacedeps false /omitplacedpdf false /simulateoverprint /legacy >> << /addbleedmarks false /addcolorbars false /addcropmarks false /addpageinfo false /addregmarks false /convertcolors /converttocmyk /destinationprofilename () /destinationprofileselector /documentcmyk /downsample16bitimages true /flattenerpreset << /presetselector /mediumresolution >> /formelements false /generatestructure false /includebookmarks false /includehyperlinks false /includeinteractive false /includelayers false /includeprofiles false /multimediahandling /useobjectsettings /namespace [ (adobe) (creativesuite) (2.0) ] /pdfxoutputintentprofileselector /documentcmyk /preserveediting true /untaggedcmykhandling /leaveuntagged /untaggedrgbhandling /usedocumentprofile /usedocumentbleed false >> ] >> setdistillerparams << /hwresolution [2400 2400] /pagesize [612.000 792.000] >> setpagedevice microsoft word numero_27_art_3 p. hou et alii, frattura ed integrità strutturale, 27 (2014) 21-27; doi: 10.3221/igf-esis.27.03 21 focussed on: infrared thermographic analysis of materials the application of the infrared thermography on titanium alloy for studying fatigue behavior p. hou, j. fan, q. guo, x. guo state key laboratory of structural analysis for industrial equipment, dalian university of technology, dalian 116024, china xlguo@dlut.edu.cn, fanjunling@mail.dlut.edu.cn abstract. the infrared thermography is an attractive tool for studying the fatigue behavior of materials. based on two theoretical models of fatigue damage indicators, this work studied the fatigue properties of the virgin ti6al-4v alloy. according to the two damage indicators and the energy theory, the relationship between the macro-phenomenon and the micro-structural evolution during fatigue process was discussed. the fatigue limit of the titanium alloy was rapidly determined based on the measured temperature increment signals. the capability of the infrared thermographic method on the evaluation of fatigue properties was validated. keywords. thermography; fatigue indicator; ti-6al-4v alloy; fatigue limit. introduction n practical applications, fatigue failure occurs everywhere including automobiles, airplanes, and vessels, etc. this often leads to disastrous damage to human beings. as a consequence, fatigue properties of materials should be well known before mechanical designs. however, it is difficult to obtain the fatigue properties of materials due to the time-consuming and expensive costing of the traditional fatigue tests. during the fatigue evolution process, most of the plastic work dissipates into the surroundings as heat energy, and simultaneously generates a heterogeneous temperature field on the surface of materials and components. the measurement of the thermal signals makes it possible to visibly detect the appearance of fatigue damage and to predict the fatigue parameters of materials. there are many measuring methods used to monitor the temperature field evolution [1]. however, the infrared thermography is more promising due to the high accuracy and rapid response of the infrared camera [2, 3]. over the last 30 years, the infrared thermography, as a non-destructive, full-field and non-contact measuring method, has been widely and successfully used to study the fatigue behavior of materials and components [4-7]. the infrared thermographic method was first proposed by g. curti et al. [5] by using the surface temperature increment signals as the major fatigue indicator. and also some efficient methods based on the infrared thermographic analysis have been developed to correlate the temperature signal evolution with the corresponding fatigue parameter. luong et al. [4] proposed to use the dissipated thermal energy under a given number of cycles to get the fatigue limit. la rosa et al. [8] analyzed the temperature signals of the external surface during the application of cyclic loading to evaluate the dynamic behavior of an element and to determine the fatigue limit. kim and jeong [9] found a linear correlation between the temperature increment squared and the logarithm of the fatigue life. similarly, a modified thermographic method using the iterative algorithm was presented and confirmed by curà et al. [10], and the method could give more accurate prediction of the fatigue limit. meneghetti [11] defined a theoretical model in order to derive the specific heat loss per cycle from the temperature measurements during fatigue tests, and the fatigue strength of smooth and notched specimens was analyzed by this model. i http://dx.medra.org/10.3221/igf-esis.27.03&auth=true http://www.gruppofrattura.it p. hou et alii, frattura ed integrità strutturale, 27 (2014) 21-27; doi: 10.3221/igf-esis.27.03 22 fatigue failure will occur once the accumulated energy due to the micro-plastic deformation reaches a constant threshold value. based on this physical hypothesis, fargione et al. [6] confirmed the connection between the fatigue limit and the quantity of heat dissipation by testing a given element to failure. the development of the energetic method facilitates the application of this infrared thermography in predicting the fatigue behavior of materials. pastor et al. [12] and fan et al. [13,14] associated the infrared thermographic method with the intrinsic dissipation and accumulated energy to investigate metallic fatigue behavior, including fatigue limits, s/n endurance curves, and to identify the initiation of a fatigue crack and its location. in addition, ummenhofer and medgenberg [15] investigated the fatigue damage by a specialized data processing method and developed the infrared thermographic method. risitano et al. [16-18] investigated the cumulate fatigue damage by infrared thermographic method. the results demonstrated accordance with the traditional test rather well. the purpose of the present work is to rapidly study the fatigue behavior of ti-6al-4v alloy by using different fatigue damage indicators provided by the infrared thermography. at the same time, the fatigue crack initiation and propagation were observed, and the relationship between the internal microstructures and mechanical properties was discussed by analyzing the evolution of the fatigue damage indicators. theoretical models relative temperature increment atigue damage is known as energy dissipation process accompanied by the temperature signal variation. the temperature signals linked with the energy dissipation enable us to understand the energy transformation, toughness reduction and damping vibration of materials. therefore, the fatigue process can be qualitatively evaluated by using the relative temperature increment signals. during fatigue tests, to avoid any possible errors induced by the environmental perturbation and the experimental system sensitivity, the relative temperature increment δt on the hot-spot zone of the specimen surface is used to describe the fatigue damage status: m 0t t t   (1) where tm is the maximum temperature signal on the zone, and t0 is the initial temperature signal. standard deviation of stress micro-cracks often initiate from local points due to the stress concentration effect in the micro-size. the fatigue damage distribution is not uniform when a material is subjected to cyclic/random loadings. the distribution of the local stress levels can be described by the standard deviation. the stress state on the hot-spot zone, due to the localized high stress, enables us to qualitatively identify the critical location responsible for the final fracture. accordingly, the economic losses caused by the sudden fatigue fracture might be greatly decreased by analyzing this damage indicator. the stress level used here is the thermoelastic stress calculated by the equation below: p a t t c        (2) where a is the coefficient of linear expansion; cp is the specific heat capacity; ρ is the material density; t is the absolute temperature; δσ is the change of the sum of principal stresses; δt is the change of temperature. the stress pattern can be visibly obtained using the infrared camera, and each pixel stands for a point in the selected zone ω. thus, the standard deviation of the stress can be written as: 2 sds m , 1 ( ( , ) ) x y x y n       (3) f http://dx.medra.org/10.3221/igf-esis.27.03&auth=true http://www.gruppofrattura.it p. hou et alii, frattura ed integrità strutturale, 27 (2014) 21-27; doi: 10.3221/igf-esis.27.03 23 where σm denotes the average stress in the zone ω; σ(x, y) denotes the stress value at the point (x, y); n denotes all the points in the zone ω. experiment material and specimen he material used in the present research is ti-6al-4v alloy. the chemical composition of this alloy (in wt.%) is given in tab. 1 [19]. fig.1 shows the dimension of the tested specimens. the tested specimens were made from a sheet of titanium alloy. ti al v fe o n h bal. 6.27-6.32 4.15-4.19 0.18-0.20 0.18-0.19 0.012-0.014 0.0041 table 1: chemical composition of ti-6al-4v alloy (wt.%). figure 1: size of the specimen (unit: mm). experimental procedures fatigue tests were carried out at room temperature without disturbance of the external heat resource. the testing system is composed of mts810 system, infrared thermographic system, lock-in module, and controlling computers [2, 3]. before fatigue tests, all the specimens were polished with fine grit papers, and then painted the specimens black to improve the heat radiation and reduce the heat reflection. the stress ratio was set as r=σmin/σmax=-1.0 with a low frequency of f=20hz. the successive stepwise loading procedure was applied to the same specimen [2]. to minimize fatigue damage accumulation, the cyclic stress was applied from 300mpa with steps of 50mpa until the final fracture. the thermal images on the hot-spot zone were recorded simultaneously by the infrared camera to perform the subsequent data analysis, as shown in fig.2. figure 2: hot-spot zone evolution. t http://dx.medra.org/10.3221/igf-esis.27.03&auth=true http://www.gruppofrattura.it p. hou et alii, frattura ed integrità strutturale, 27 (2014) 21-27; doi: 10.3221/igf-esis.27.03 24 results and discussion qualitative identification of the fatigue damage emperature evolution is mainly attributed to the thermo-elastic effect, inelastic effect and heat conduction effect. the fluctuating temperature signals are attributed to the thermo-elastic effect. the cyclic temperature amplitude increases with the increasing cyclic loading amplitude. however, the thermo-elastic effect has no contribution to the average temperature increment [20]. fig.3 presents the relative temperature evolution at different stress levels. figure 3: temperature increment at different stress amplitude. the elastic stress controls the mechanical responses of the tested specimens when the stress level is lower than the fatigue limit of ti-6al-4v alloy. during this period, the specimen mainly takes place elastic deformation, and the temperature signal variation is mainly induced by the non-plastic effects, i.e. viscosity effect etc. if the stress level is higher than the fatigue limit, micro-cracks would initiate from the specimen boundaries, such as the corner and the free surface. the fatigue cracks initiated along the axial direction of 45o, and then coalesced to form a main macro-crack. the main crack propagated perpendicular to the principal stress direction. the plastic strain energy continues to accumulate during the fatigue evolution process. most of the mechanical energy was dissipated as heat energy heating up the specimen. fig.4 shows variations of the stress standard deviation of the material. there is no obvious plastic deformation when the applied stress is lower. however, if the stress is higher than the fatigue limit, it sets to increase sharply in the localized zone due to the stress concentration effect. the break point indicates that the mechanisms related to fatigue failure have changed into plastic effect. local stress concentration, due to pores and impurities, governs the stress distribution. the damage status can be qualitatively identified by the standard deviation to avoid the sudden fracture. from fig.4, the standard deviation of the ti-6al-4v alloy is small when the fatigue stress amplitude is lower than the fatigue limit. however, the standard deviation of the ti-6al-4v continues increasing with the increasing stress. figure 4: standard deviation of stress at different stress amplitude. t http://dx.medra.org/10.3221/igf-esis.27.03&auth=true http://www.gruppofrattura.it p. hou et alii, frattura ed integrità strutturale, 27 (2014) 21-27; doi: 10.3221/igf-esis.27.03 25 fatigue limit prediction in [21], the interpolated fatigue limit of ti-6al-4v alloy at 106 cycles was reported as 451 mpa. this value would be used to compare with the infrared thermographic results, and then the errors between the predicted parameter σp and the traditional parameters σf would be presented in following section. the temperature increment signals on the hot-spot zone were considered as a fatigue damage indicator for the fatigue behavior analysis. the asymptotic temperature increments were used to determine the fatigue limit stress. based on the couples of (δts, σa2), a good linear correlation was plotted between the applied stress range squared and the asymptotic temperature increment in fig.5. the fatigue limit σp was determined as 423 mpa by extrapolating the straight line down to zero at the abscissa axis. figure 5: fatigue limit stress by the infrared thermographic method. discussion the error of the fatigue limit σf by traditional method and predicted fatigue limit σp were obtained by the following formula, presented in tab. 2: f p f % 100        (5) the difference between these two results is 6.21%. the low value of error δ% demonstrates that the thermographic method is applicable for the evaluation of the fatigue limit in practical engineering. method σf (mpa) error traditional thermography 451 423 / 6.21% table 2: comparison. the above fatigue tests can be divided into three phases. at lower stress stage, which is that the temperature increases slowly, and the intrinsic dissipation is practically null. the internal microstructure evolution is reversible under the elastic stress. however, when the stress is close to the fatigue limit, the local stress may be beyond the yield limit due to the stress concentration in micro-scale. consequently, the slip band begins to form, and numerous micro-cracks initiate here. fatigue damage sets to accumulate continuously. if the stress is higher than the fatigue limit stress, all the above damage indicators will increase drastically. conclusions (1) the infrared thermographic method enables us to qualitatively and quantitatively evaluate the fatigue behavior of titanium alloy. http://dx.medra.org/10.3221/igf-esis.27.03&auth=true http://www.gruppofrattura.it p. hou et alii, frattura ed integrità strutturale, 27 (2014) 21-27; doi: 10.3221/igf-esis.27.03 26 (2) all the fatigue damage indicators can describe the fatigue damage evolution process. the macro-phenomenon and internal microstructure evolution are associated by the energy theory. (3) the low error between the predicted fatigue limit and the traditional value demonstrates the reliability of the infrared thermographic method in predicting fatigue parameters of materials and components. (4) it is a fast and accurate technique for fatigue evaluation using various damage indicators resorting to the infrared technique. consequently, the method may be used to identify fatigue damage status of structures in service in the future work. acknowledgements he financial support of the natural science foundation of china (grant no.11072045) is gratefully acknowledged. moreover, j. fan would like to thank the china scholarship council for his research at purdue university of usa. nomenclature r stress ratio ρ material density cp specific heat capacity a coefficient of linear expansion k heat conduction coefficient ψ helmholtz free energy ε strain tensor α internal variables γe external heat resource d intrinsic dissipation σα stress amplitude σm average stress σ(x, y) stress value at the point (x, y) σsds standard deviation of stress σp predicted fatigue limit stress σf fatigue limit stress δt temperature increment t0 initial temperature tm average temperature δts stationary temperature increment references [1] zhang, l., liu, x. s., wu, s. h., et al., rapid determination of fatigue life based on temperature evolution, int j fatigue, 54 (2013) 1-6. [2] fan, j., guo, x. l., wu, c. w., a new application of the infrared thermography for fatigue evaluation and damage assessment, int j fatigue, 44 (2012) 1-7. [3] fan, j., guo, x., wu, c., et al., influence of heat treatments on mechanical behavior of fv520b steel, exp techniques, (2013) doi: 10.1111/ext.12019. [4] luong, m. p., fatigue limit evaluation of metals using an infrared thermographic technique, mech mater, 28 (1998) 155-163. [5] curti, g., la rosa, g., orlando, m., et al., analisi tramite infrarosso termico della temperatura limite in prove di fatica, conference proceedings: 14th aias italian national conference, catania, italy, (1986). [6] fargione, g., geraci, a., la rosa, g., et al. rapid determination of the fatigue curve by the thermographic method, t http://dx.medra.org/10.3221/igf-esis.27.03&auth=true http://www.gruppofrattura.it p. hou et alii, frattura ed integrità strutturale, 27 (2014) 21-27; doi: 10.3221/igf-esis.27.03 27 int j fatigue, 24 (2002) 11-19. [7] crupi, v., chiofalo, g., guglielmino, e., using infrared thermography in low-cycle fatigue studies of welded joints, weld j, 89 (2010) 195s-200s. [8] la rosa, g., risitano, a., thermographic methodology for rapid determination of the fatigue limit of materials and mechanical components, int j fatigue, 22(1) (2000) 65-73. [9] kim, j., jeong, h. y., a study on the hysteresis, surface temperature change and fatigue life of sm490a, sm490aweld and fc250 metal materials, int j fatigue, 32 (2010) 1159-1166. [10] cura, f., curti, g., sesana, r., a new iteration method for the thermographic determination of fatigue limit in steels. int j fatigue, 27 (2005) 453-459. [11] meneghetti, g., analysis of the fatigue strength of a stainless steel based on the energy dissipation, int j fatigue, 29(1) (2007) 81-94. [12] pastor, m. l., balandraud, x., grediac, m., et al., applying infrared thermography to study the heating of 2024-t3 aluminium specimens under fatigue loading, infrared phys. techn., 51 (2008) 505-515. [13] fan, j. l., guo, x. l., wu, c. w., et al., research on fatigue behavior evaluation and fatigue fracture mechanisms of cruciform welded joints, mater sci eng a, 528 (2011) 8417-8427. [14] fan, j. l., guo, x. l., wu, c. w., fatigue performance assessment of welded joints using the infrared thermography, struct eng mech, 44(4) (2012) 417-429. [15] ummenhofer, t., medgenberg, j., on the use of infrared thermography for the analysis of fatigue damage processes in welded joints, int j fatigue, 31 (2009) 130-137. [16] risitano, a., risitano, g., cumulative damage evaluation of steel using infrared thermography, theor appl fract mech, 54(2) (2010) 82-90. [17] risitano, a., corallo, d., risitano, g., cumulative damage by miner's rule and by energetic analisys, struct durability health monitor, 8(2) (2012) 91-109. [18] risitano, a., risitano, g., cumulative damage evaluation in multiple cycle fatigue tests taking into account energy parameters, int j fatigue, 48 (2013) 214-222. [19] nalla, r. k., altenberger, i., noster, u., et al. on the influence of mechanical surface treatments-deep rolling and laser shock peening-on the fatigue behavior of ti-6al-4v at ambient and elevated temperatures, mater sci eng a, 355 (2003) 216-230. [20] boulanger, t., chrysochoos, a., mabru, c., et al., calorimetric analysis of dissipative and thermoelastic effects associated with the fatigue behavior of steels, int j fatigue, 26 (2004) 221-229. [21] lanning, d. b., nicholas, t., haritos, g. k., on the use of critical distance theories for the prediction of the high cycle fatigue limit stress in notched ti-6al-4v, int j fatigue, 27(1) (2005) 45-57. http://dx.medra.org/10.3221/igf-esis.27.03&auth=true http://www.gruppofrattura.it microsoft word numero_52_art_05_2639 b. e. sobrinho et alii, frattura ed integrità strutturale, 52 (2020) 51-66; doi: 10.3221/igf-esis.52.05 51 differential evolution algorithm for identification of structural damage in steel beams brunno e. sobrinho, gilberto gomes, welington v. da silva, ramon s. y. r. c. silva, luciano m. bezerra university of brasilia, brazil brunno.emidio@aluno.unb.br, https://orcid.org/0000-0003-4407-7213 ggomes@unb.br, http://orcid.org/0000-0002-8385-9042 welington.vital@aluno.unb.br, ramon@unb.br, lmbz@unb.br erwin u. l. palechor university of cariri juazeiro do norte, ceará, brazil erwin.lopez@ufca.edu.br abstract. problems involving errors and uncertainties from the use of numerical and experimental responses of beams using optimization processes have been studied by many researchers. in this field, to simulate the real behavior of structures, especially in problems involving damage, it is required to have reliable experimental results in order to adjust a numerical model. these difficulties may be associated for example to the modeling of the connection stiffness, support conditions, or relevant parameters in structures involving damages. this paper proposes a new methodology to detect damage in steel beams using the differential evolution technique based on experimental and numerical data. the results show a great potential of the methodology to solve damage detection problems. keywords. steel beams; optimization; damage identification; differential evolution. citation: sobrinho, b., gomes, g., v. silva, w., silva, r., bezerra, l, palechor, e. differential evolution algorithm for identification of structural damage in steel beams, frattura ed integrità strutturale, 52 (2020) 51-66. received: 19.09.2019 accepted: 17.01.2020 published: 01.04.2020 copyright: © 2020 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. introduction n recent years researchers have dedicated considerable attention to optimization procedures. the real behavior of structures is not easy to be simulated due to the complexity in modeling the stiffness of connections, support conditions and other parameters. therefore, the damage identification process becomes more difficult. on the other hand, the inverse problems area has a great potentiality to deal with damaged structures. according to [1], the damage identification is done by numerical methods, which seek the identification of geometric parameters of a model adopted for damage, from the structural response (static, dynamic, electrical, thermal excitation, among others). a powerful i https://youtu.be/d_q4wn0pcfu b. e. sobrinho et alii, frattura ed integrità strutturale, 52 (2020) 51-66; doi: 10.3221/igf-esis.52.05 52 and well-known technique used to detect damage in structures is based on wavelet transform, which can be applied using the damaged condition of the structure; see for example [2, 3, 4]. the inverse problem to find and to identify damage in a structure, as seen in [5], is solved by two different and independent approaches, one based on optimization (using a genetic algorithm) and the other one based on a parameter identification (using a neural network). in [6], it is pointed out that the optimization algorithms have a flexibility of implementation because the evaluation scheme customizes the algorithm for a specific purpose. this paper proposes a new methodology in the context of the structural health monitoring methods, using differential evolution to detect damage in steel beams on the basis of numerical and experimental results. optimization algorithms differential evolution algorithms ccording to [7], the main goal of the optimization algorithms is to find the ideal solution for a given problem, whereas it can achieve the objectives that have been established with the least cost and / or maximum efficiency. the differential evolution (de) method, proposed by [8], is a heuristic approach for minimizing possibly nonlinear and non-differentiable continuous space functions. the de method has been presented with a simple, but powerful numerical optimization algorithm for global optimal solution search and has been successfully applied in complex optimization problems. the de method uses algorithms that are based on population of individuals. each individual represents a search point in the space of potential solutions to a given problem and imitates nature principles to create optimization procedures. this method has selection procedures based on the individual fitness, crossover and mutation operators. fig. 1 shows the flowchart of de algorithms presented in [9]. the main procedure of de includes four phases, such as initiation, mutation, crossover and selection. figure 1: differential evolution (de) method flowchart [9]. in [10], other mechanisms that can be used to finish the evolutionary process are referred: the processing time, the evaluations number of the objective function, the final value of the objective function and own user monitoring. it must be emphasized that it seems always to converge with a low computational effort using numerical evaluations of objective functions. the optimization problem the optimization algorithms involve well-defined mathematical formulations, in which a set of variables describes the system, called design variables. both the objective function and project restrictions can have features of analyses or synthesis of design, for example, minimizing the mass of a structure in order to find a specified stress limit. as defined in [11], the optimization problem, or determining the minimum, is composed as follows:  objective function: it is the mathematical function f(p) to be optimized;  design variables: these are the independent variables that appear in the objective function; a crossover objective function evaluation selection convergence? started population (beginning) objective function evaluation minimum point (end) yes no diferential mutation b. e. sobrinho et alii, frattura ed integrità strutturale, 52 (2020) 51-66; doi: 10.3221/igf-esis.52.05 53  restrictions: these are the limits imposed to the system, or established by natural laws that govern the system, subjected to the design variables;  search region: it is the space region defined by the variable of project and delimited by the restrictions, where the interior or border locates the optimal objective function. a general scheme of an optimization problem is shown in fig. 2, in which can observe that the method intends to find the minimum local points. figure 2: general schemes of an optimization problem: (a) optimization method; (b) constraint; (c) objective function. structural damage formulation he identification, localization and quantification of stiffness loss of a system from the static or dynamic response of the structure are important indicators to damage detection procedure. the natural frequencies tend to decrease as the damage increases its dimensions [12], and the modal amplitude values at damaged positions also tends to decrease. the effect of a structural damage can be classified as linear and non-linear. the first case is a situation where the structure is initially in the linear elastic domain and remains in this same domain after the damage appearance. for the second case, the initial behavior of the structure is linear and after a high level of damage the behavior becomes nonlinear, as in the case of fatigue cracks due to cyclic loads or after the plastification of certain elements due to a crash, for example [13]. in a static analysis, the basic formulation used is presented in following eqn. (1). ([k][x]) [ ]p (1) t b. e. sobrinho et alii, frattura ed integrità strutturale, 52 (2020) 51-66; doi: 10.3221/igf-esis.52.05 54 where “k” is the stiffness matrix; “x” is the static displacements vector and “p” are the nodal loads. it is important to remember that the differences with specific elements of the matrices make possible the damages evaluation. the hypothesis that the mass matrix is constant is considered when the internal damage does not result in material loss. these parameters can be related, in the stiffness matrix, to a series of variables, as following eqn. (2). k [k(a, , , , , , )]t l e i g j (2) where “a” is the area, “t” is thickness, “l” is the length, “e” is the young’s modulus, “i” represents the longitudinal moment of inertia, “g” is transverse elasticity modulus and “j” is the torsional moment of inertia. parameter [k] shown in eqn. (2) is identified and used for the static equilibrium equation. this research is limited to the use of only static responses in terms of displacement which is the variable that changes its value due to the damage presence. this variable, named “di”, minimizes the objective scalar function “f” that represents the difference between the analytical response (intact structure) and the experimental one (damaged structure). the following eqn. (3) contemplates:  2ij ijm a i j f y y  , (3) where ijmy are the static displacements measured (intact structure), ij ay are the static displacements obtained analytically (damaged structure), “i” is the degree of freedom and “j” is the static shipment condition in a particular case. the stiffness matrix of each beam element was modified to incorporate the damage variable, as the expression of the beam element. for a beam element, though the following eqn. (4), the stiffness matrix establishes how the physical and material properties are stored and also how each beam is modified to incorporate the variable damage.    2 2 2 2 3 2 2 2 2 6 6 0 0 0 0 0 12 6 0 12 6 1 0 6 4 0 6 2 0 0 0 0 0 12 6 0 12 6 0 6 2 0 6 4 i j x al al i il i il e d il il il il k l al al i il i il il il il il                          , (4) where [di] is the variable design vector and, the variable design vectors “di” shown in eqn. (4), could assume values between 0 (intact element) and 1 (damaged element). experimental program n this section, the considered experimental program, based on the results obtained by [15] is presented. two simply supported i steel beams characterized by two different loading schemes, as illustrated in fig. 3 were simulated. the beam properties are presented in tab. 1. (a) beam 1 (v3e) (b) beam 2 (v5e) figure 3: schematic models of the beams analyzed. i b. e. sobrinho et alii, frattura ed integrità strutturale, 52 (2020) 51-66; doi: 10.3221/igf-esis.52.05 55 *characteristic value american i profile – steel: 102.0 x 11.4 h (cm) h0 (cm) tf (cm) t0 (cm) c (cm) b (cm) area (cm2) ix (cm4) e (mpa) 10.16 8.68 0.74 0.483 1.59 6.76 14.50 252 200 lengt h (m) wx (cm³) ix (cm) iy (cm4) wy (cm³) iy (cm) zx (cm³) zy (cm³) fy* (mpa) 6.00 49.70 4.17 31.70 9.37 1.48 56.220 17.414 250 table 1: beam geometric, mass, and mechanical properties. according to [14], the load stages used for evaluation with the optimization methods refer to those immediately before the maximum load. damage was induced through notches transverse to the longitudinal axis of the beams (fig. 4b). it is worth noticing that the adoption of these open vertical cracks can be caused by diverse demands, such as behaviors found in buildings with metallic structural elements. (a) (b) figure 4: beams overview: (a) 16 element beam subdivision and (b) induced damage 2 cm [15]. the beams tested were divided into 16 parts (see fig. 4a) and one linear variable differential transformer (lvdt) was positioned in each element. fig. 5 shows the 15 internal points and lvdt’s positions. figs. 6 and 7 report details of the support conditions and the loading arrangement, respectively. the loading was applied in a vertical upward direction in loading steps, taking into account the maximum load value supported by the intact beam so as not to suffer local buckling. these load values chosen for the application of the proposed damage identification method were lower than the calculated maximum load value. the loads were chosen in service stage. the maximum load that can be applied to the intact beam (undamaged) in the middle of the span so that the beam does not buckle locally was 4373n, as summarized in tab. 2. b. e. sobrinho et alii, frattura ed integrità strutturale, 52 (2020) 51-66; doi: 10.3221/igf-esis.52.05 56 figure 5: lvdt’s positions (16 parts) [15]. (a) (b) figure 6: support conditions of the steel beam specimen [15]. figure 7: loading details of the steel beam specimen [15]. lateral buckling limits loads web maxp =903kg flange maxp =903kg torsion maxp =438kg 4373n table 2: beam limits loads. for the maximum load calculation, the intact beam data were considered, since the size and location of the damage is initially unknown. considering the calculated maximum load, it can be analyzed in relation to a lower load due to the presence of imperfections in the beam (geometric and material imperfections) that can lead the part to reach the plastic regime. for this reason it was very important to apply in the structure load increments values immediately smaller than the maximum load. b. e. sobrinho et alii, frattura ed integrità strutturale, 52 (2020) 51-66; doi: 10.3221/igf-esis.52.05 57 numerical model umerical analyses were developed using the ansys© (2007) software [14] in order to reproduce the same conditions of the above described experimental program. the elements adopted, beam3 or shell63, have three and six degrees of freedom by node, respectively, as illustrated in fig. 8a and 8b. (a) (b) figure 8: from ansys© (2007) library [15]: (a) beam3; (b) shell63 elements. in order to simulate damage, the area and moment of inertia of the element cross section were reduced in beam3 model (fig. 9), while and some elements were deleted for shell63 model (fig. 10). the numerical models in fig. 9 and 10 consider the same measurement points used in experimental test carried out by [15]. figure 9: damage simulation: beam3 element. figure 10: damage simulation: shell63 element. n b. e. sobrinho et alii, frattura ed integrità strutturale, 52 (2020) 51-66; doi: 10.3221/igf-esis.52.05 58 proposed methodology ne way to validate an analytical model is to compare its results with experimental ones. problems of systems identification, also denominated as inverse problems, have applications in many areas of engineering, medicine and science in general. in these problems the fundamental properties are determined by observing the behavior of the system. some responses are related to variables which is possible to use to verify the agreement between the results of the analytical model and the experimental measures. the objective function used is measured by least squares of the difference between the values obtained in the numerical model and in the experimental tests, see eqn. (5) as follows:      2 0 t mf x t x t dt  (5) where x (t) is obtained by the analytical model and xm (t) is the response measured experimentally in the time domain t in a time interval [0, t]. these parameters were adjusted to minimize the f function. in the identification of structural systems, normally mode shapes, natural frequencies and static displacements are selected as parameters to be used for identification of model. thus, the best results will be obtained when the values of the objective function are closer to zero. the proposed methodology is based on the use of a well-known differential evolution technique using numerical and experimental data of intact and damaged steel beams, see fig. 11 and 12. figure 11: flowchart analyses of beam 1 (v3e). it can be observed in the flowcharts (fig. 11 and 12) the association of the de method with the numerical and experimental data. for the beam 1 (v3e) the numerical response (shell63 element) of the intact beam was used. for the beam 2 (v5e) the numerical and experimental response of the intact structure was used. elements/ analysis beam3 shell63 euler bernoulli experimental intact damaged better analytical model better experimental model better parameter de damage identification o b. e. sobrinho et alii, frattura ed integrità strutturale, 52 (2020) 51-66; doi: 10.3221/igf-esis.52.05 59 figure 12: flowchart analyses of beam 2 (v5e). results he models of the two beams are schematized in fig. 13 and 14, in which the de method was applied to different situations of beams with constant elements. in these different situations were used experimental static displacement results. the measured data were simulated by introducing two damaged elements (low stiffness) in finite element analyses and an elastic analysis was assumed. in fig. 13, the damage location occurs at 1.80m and 4.20m from left support, with damage of 2cm length (45%) in each side, in correspondence of an applied load of 4350n in the middle of the span. in fig. 14, damage is located at the middle of the span (3.00m), for an applied load of 2000n in both beam sides. beam 1 (v3e): load 4350n the plot of displacements of intact and damaged beam 1 (v3e) is presented in fig. 15, which reports the displacements obtained along the beam length generated by applying a load of 4350n. the exam of this diagram can help to analysis the coherence of the elements used in the analytical method, as well as to verify the experimental model, in terms of intact and damaged situations. figure 13: damaged beam 1 (v3e). elements/ analysis beam3 shell63 euler bernoulli intact damaged better numerical model better experimental model better parameter de damage identification better analytical model experimental t b. e. sobrinho et alii, frattura ed integrità strutturale, 52 (2020) 51-66; doi: 10.3221/igf-esis.52.05 60 figure 14: damaged beam 2 (v5e). figure 15: plot of displacements for the intact and damaged beam 1 v3e (load 4350n). in the following numerical results obtained from simulations with beam3 and shell63 elements, euler-bernoulli theory, as well as through a proposed simulation that relates the intact model to the damaged experimental model, whose goal is to identify damaged elements in the structure, are presented in tab. 3. item beam load (n) elements / analyses iterations damaged elements % of damage objective function minimum 1 beam 1 (v3e) 4350 beam3 50th 5 and 12 45% 0.72466525 shell63 50th 5 and 12 45% 2.01215635 euler-bernoulli 50th 5 and 12 45% 183.19207908 experimental 100th 5 and 12 45% 148.31064460 table 3: results for the beam1 (v3e). fig. 16 shows the analyses of the problem solution using the beam3 element, which provides values in agreement with the considered problem, finding few residues. in fig. 17, using the shell63 element, it is verified that the damaged values of the elements are in agreement with the considered problem, where there are some distortions, probably, due to not null displacements close to supports. fig. 18 shows the analyses of the problem solution and the damage values of the elements obtained by using euler-bernoulli theory. these values are in agreement with the problem proposed with minor variations, but with good results. in fig. 19, the results obtained from the proposed numerical simulation of the intact beam are compared to those obtained by the experimental damaged beam. these comparisons between the intact plot analyses and the damaged (experimental) one are provided in terms of displacements along beam length for beam 1 (v3e), in correspondence of a load application of 4350n. b. e. sobrinho et alii, frattura ed integrità strutturale, 52 (2020) 51-66; doi: 10.3221/igf-esis.52.05 61 figure 16: damage identification: beam 1 v3e, load 4350n (beam3). figure 17: damage identification: beam 1 v3e, load 4350n (shell63). figure 18: damage identification: beam 1 v3e, load 4350n (euler-bernoulli). b. e. sobrinho et alii, frattura ed integrità strutturale, 52 (2020) 51-66; doi: 10.3221/igf-esis.52.05 62 figure 19: intact (numerical) and damaged (experimental) displacements for the beam 1 v3e (load 4350n). this attempt of damage identification analysis is already possible because the displacements obtained in the ansys© (2007) intact numerical analysis by means of the shell63 element have values lower than those obtained in the damaged analysis through the experimental model, demonstrating possibilities of coherence in the analysis. it can be explained by the fact that this element presents simulation conditions near to what was applied in the experimental analysis. this simulation of the fourth approach intends to obtain result values in the intact numerical analyses of the ansys© (2007), through element shell63 together with the experimental damaged analysis, used to identify a damaged element in the structure. in this analyses were only considered static displacements values of beam elements. fig. 20 presents the analysis of the problem solution results. the element's damage values are in agreement with the proposed problem, even if at the beginning and end of damage analyses appeared some distortions probably due to not null displacements close to supports. figure 20: damage identification: beam 1 v3e, load 4350n (numerical x experimental). the damage identification analyzed in this example was restricted to the displacements obtained in the intact and damaged numerical analyses using a small number of iterations that generate the presence of residues of damages identification in other elements. mainly where there were large displacement differences (whether negative results), the presence of point loads, the area next to supports or even next to damaged regions, nevertheless the damage values of the elements follow the proposed problem. it is emphasized that the increase in the number of iterations, in some cases, helps to solve the problem of local minimum approximation. b. e. sobrinho et alii, frattura ed integrità strutturale, 52 (2020) 51-66; doi: 10.3221/igf-esis.52.05 63 in the analyses of beam 1 (v3e), it can also be pointed out that a big number of displacements information also would help in the optimizing procedure. the answers had relatively fast characteristics of convergence, considering the small amount of involved iterations. even so, the tool attended to the localization capacity and damage quantification in any element of the structure in study. beam 2 (v5e): load 2000n in the intact and damaged analyses according to beam 2 (v5e), displacements plots are presented in fig. 21, where the xaxis (abscissa) corresponds to the length of the beam (6.00 m) and the y-axis (ordinate) correspond to displacements generated by application of 2000n load. this demonstration is necessary again to establish an analysis of the coherence of the elements used, as well as the analytical method, without the verified experimental model, but always in terms of intact and damaged situations, verifying the de method potential in the numerical analyses. figure 21: intact and damaged analyses corresponding to the displacements for the beam 2 v5e (load 2000n). for the beam 2 (v5e) analyses, the obtained results for the considered problem solutions are showed in tab. 4. item beam load (n) elements / analyses iterations damaged elements % of damage objective function minimum 1 beam 2 (v5e) 2000 beam3 100th 9 45% 0.18006354 shell63 100th 9 45% 0.51703227 euler-bernoulli 100th 9 45% 50.86801964 table 4: results for the beam 2 (v5e). fig. 22 shows the analyses of the problem solution using the element beam3 that is in agreement with the considered problem. the proposed simulations in the second approach was carried out using shell63 element. fig. 23 shows the problem solution result. only the values of the static displacements of the beam elements were again considered, with the damage values of the elements in agreement with the considered problem. the results of the third approach with euler-bernoulli theory are show in fig. 24 the result of the problem solution. this case presented damaged values in agreement to the considered problem. in the analyses with beam3 element, there are some damage residues close to the damaged element, still with close values. in the case of shell63 element, at the beginning and end of damage analyses some residues were observed, probably due to non-zero displacements close to supports. anyway, good results were achieved, due to a big number of iterations. finally, the analyses with euler-bernoulli, presented some perturbations, but with the values of damages of the elements in agreement with the problem considered good results were obtained, although the minimum of the objective function for being a little big. b. e. sobrinho et alii, frattura ed integrità strutturale, 52 (2020) 51-66; doi: 10.3221/igf-esis.52.05 64 figure 22: damage identification: beam 2 v5e, load 2000n (beam3). figure 23: damage identification: beam 2 v5e, load 2000n (shell63). figure 24: damage identification: beam 2 v5e, load 2000n (euler-bernoulli). b. e. sobrinho et alii, frattura ed integrità strutturale, 52 (2020) 51-66; doi: 10.3221/igf-esis.52.05 65 the damage identification analyses in this example was restricted to the displacements obtained in intact and damaged numerical analyses. with the analyses of beam 2 (v5e), it can also be affirmed that a big number of displacements information also would assist in the optimizing procedure. the answers had relatively fast characteristics of convergence, considering the small amount of involved iterations. even so, the tool was able to localize and quantify damage in any element of the structure in study. conclusions he structural responses of steel beams under different loading conditions were used in conjunction with de method in order to detect structural damage. the design variables considered in the objective function minimization problem were the intact and damaged structural responses. these variables were continuously changed in order to allow the response obtained by the analytical model to approximate the experimental response. the differential evolution method turned out to be a good method for solve problems of damage identification, since it converges to a correct solution in all cases. the euler-bernoulli beam model was used because it is a simplification of the linear theory of elasticity that provides a way to calculate the deflection characteristics of a beam subjected to bending under a given load (static or dynamic). it is an ideal theory for use in beams with lower heights, such as the cases studied in this research. the consistency of the results obtained from static displacements with the other methods and the experimental results was also one of the determining factors of this use of euler bernoulli's theory. the characteristic of the difference distribution vector could be analyzed as a convergence parameter and it was possible to find localized solutions at regions where there is a minimum point. all these aspects were considered in the present research and at hence the results were validated since the damages were detected successfully. acknowledgments he authors thank the graduate program in structural engineering and civil construction of the department of civil and environmental engineering at the university of brasilia, brazil. references [1] rus, g. and gallego, r. (2002). optimization algorithms for identification inverse problems with the boundary element method. engineering analysis with boundary elements, 26, pp. 315-327. doi: 10.1016/s0955-7997(02)00008-5. [2] pnevmatikos, n. g., blachowski, b., hatzigeorgiou, g. d. and swiercz, a. (2016). wavelet analysis based damage localization in steel frames with bolted connections, smart structures and system, 18(6), pp.1189-1202. doi: 10.12989/sss.2016.18.6.1189. [3] pnevmatikos, n. g. and hatzigeorgiou, g. d. (2016). damage detection of frame structures subjected to earthquake excitation using discrete wavelet analysis, bulletin of earthquake engineering, 15(1), 227-248. doi: 10.1007/s10518-016-9962-z. [4] palechor, e. u. l., silva, r. s .y. r. c., bezerra, l. m. and bittencourt, t. n. (2014). damage detection in beams using experimental data. key eng. materials, v. 607, 21-29. doi: 10.4028/www.scientific.net/kem.607.21. [5] lopes, p. s. (2010). inverse problem modeling of damage detection by parameter identification and optimization techniques. doctoral thesis – federal university of itajubá, brazil (doctoral thesis). [6] vigdergauz, s. (2003). combined upper bounds on the effective moduli of a perforated elastic plate. numerical assesment by genetic algorithm. mathematics and mechanics of solids. doi: 10.1177/1081286505040404. [7] barbosa, h. j., bernardino, h. s. and barreto, a. m. (2013). using performance profiles for the analysis and design of benchmark experiments. in advances in metaheuristics, 21-36. springer, new york. doi: 10.1007/978-1-4614-6322-1_2. t t b. e. sobrinho et alii, frattura ed integrità strutturale, 52 (2020) 51-66; doi: 10.3221/igf-esis.52.05 66 [8] storn, r. and price, k. (1997). differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. j. global optimiz., 11, pp. 341–359. [9] suveges, j. m. c. (2014). study on detection of damage in structures via optimization method. master thesis, federal university of itajubá, brazil (masters dissertation). [10] santos, g. f. (2009). identification of structural damages using optimization techniques. master thesis – rio de janeiro state university, rio de janeiro, brazil (masters dissertation). [11] kleinermann, j. p. (2000). identification parametrique et optimization des procèdès de mise a forme par problemes inverses. unpublished doctoral dissertation. university of liege. liege, belgium (doctoral thesis). [12] cury, a., borges, c. and barbosa, f. (2011). a two-step technique for damage assessment using numerical and experimental vibration data, structural health monitoring, 10, pp. 417-428. doi: 10.1177/1475921710379513. [13] alves, v. n. (2012). study of new strategies for identifying structural damage from vibrational data. master thesis, federal university of ouro preto, brazil. (masters dissertation). [14] ansys (2007). structural analysis guide – release 11.0. in: ansys©. [15] palechor, e. u. l. 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/hrv (za stvaranje adobe pdf dokumenata najpogodnijih za visokokvalitetni ispis prije tiskanja koristite ove postavke. stvoreni pdf dokumenti mogu se otvoriti acrobat i adobe reader 5.0 i kasnijim verzijama.) /hun 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can be opened with acrobat and adobe reader 5.0 and later.) >> /namespace [ (adobe) (common) (1.0) ] /othernamespaces [ << /asreaderspreads false /cropimagestoframes true /errorcontrol /warnandcontinue /flattenerignorespreadoverrides false /includeguidesgrids false /includenonprinting false /includeslug false /namespace [ (adobe) (indesign) (4.0) ] /omitplacedbitmaps false /omitplacedeps false /omitplacedpdf false /simulateoverprint /legacy >> << /addbleedmarks false /addcolorbars false /addcropmarks false /addpageinfo false /addregmarks false /convertcolors /converttocmyk /destinationprofilename () /destinationprofileselector /documentcmyk /downsample16bitimages true /flattenerpreset << /presetselector /mediumresolution >> /formelements false /generatestructure false /includebookmarks false /includehyperlinks false /includeinteractive false /includelayers false /includeprofiles false /multimediahandling /useobjectsettings /namespace [ (adobe) (creativesuite) (2.0) ] /pdfxoutputintentprofileselector /documentcmyk /preserveediting true /untaggedcmykhandling /leaveuntagged /untaggedrgbhandling /usedocumentprofile /usedocumentbleed false >> ] >> setdistillerparams << /hwresolution [2400 2400] /pagesize [612.000 792.000] >> setpagedevice microsoft word numero_29_art_13 l. facchini et alii, frattura ed integrità strutturale, 29 (2014) 139-149; doi: 10.3221/igf-esis.29.13 139 focussed on: computational mechanics and mechanics of materials in italy an efficient bouc & wen approach for seismic analysis of masonry tower luca facchini, michele betti department of civil and environmental engineering (dicea), university of florence luca.facchini@unifi.it, mbetti@dicea.unifi.it abstract. the assessment of existing masonry towers under exceptional loads, such as earthquake loads, requires reliable, expedite and efficient methods of analysis. these approaches should take into account both the randomness that affects the masonry properties (in some cases also the distribution of the elastic parameters) and, of course, the nonlinear behavior of masonry. considering the need of simplified but effective methods to assess the seismic response of such structures, the paper proposes an efficient approach for seismic assessment of masonry towers assuming the material properties as a stochastic field. as a prototype of masonry towers a cantilever beam is analyzed assuming that the first modal shape governs the structural motion. with this hypothesis a nonlinear hysteretic bouc & wen model is employed to reproduce the system response which is subsequently employed to evaluate the response bounds. the results of the simplified approach are compared with the results of a finite element model to show the effectiveness of the method. keywords. bouc & wen model; masonry towers; nonlinear dynamics; perturbation methods. introduction he analysis of the structural response of slender masonry towers, especially in case of seismic loading, should take into account both the randomness that affects the masonry material (even the elastic parameters distribution along the height of the beam) and the specific nonlinear masonry behavior (the small tensile strength). several methods have been proposed in recent years to analyze the structural response of such structural systems. betti et al. [1] analyzed the response of a slender masonry wall under turbulent wind proposing an approach based on the modal reduction (more: modal reduction). the material was assumed as no tensile resistant (ntr), but the mechanical properties were assumed as deterministic. an analysis method to solve this typology of mechanical problems, assuming the properties of the material as a stochastic field, was further proposed by facchini et al. [2] based on a galerkin approach. additional possible approaches are the perturbation methods, originally proposed by liu et al. [3]. to offers an insight on this background, the paper proposes an expeditious and effective method to assess the seismic response of slender masonry towers where the masonry is assumed as a random material by means of an approach based on a nonlinear hysteretic bouc [4] & wen [5, 6] model. the bouc & wen hysteretic model has been found great interest in nonlinear stochastic dynamics being a smooth and multipurpose hysteresis model that allows for explicit form calculation of the linearization terms. the versatility of the bouc & wen model is also demonstrated by the large number of applications reported in the scientific literature concerning, f.i., steel and concrete [7] and wood structures [8]. despite the spreading of the model only few case studies, to the authors’ knowledge, are reported concerning applications with masonry structures. t l. facchini et alii, frattura ed integrità strutturale, 29 (2014) 139-149; doi: 10.3221/igf-esis.29.13 140 in the following, a masonry cantilever beam, as a prototype of masonry towers, is analyzed assuming that the first modal shape governs the structural motion. with this hypothesis the nonlinear hysteretic bouc & wen model is employed to reproduce the system response, which is subsequently employed to evaluate the bounds of the structural response through a perturbation approach. the results of the proposed approach are compared with the results of a finite element (fe) model to show the effectiveness of the method. identification of bouc & wen model for the tower he bouc [4] & wen [5, 6] model (in the following bw for short) has been extensively employed to model the dynamic behavior of hysteretic systems. as masonry is a no-tensile resistant material, it may on occasion exhibit such kind of behavior. to assess the employability of the bw model as an efficient approach for seismic analysis of masonry towers the paper analyzes the clarifying example of a masonry cantilever beam. to identify the bw model parameters several methods have been proposed. herein the tuning of the bw parameters is performed by comparing the behavior of the bw model with the response of the masonry cantilever beam acted upon by a static transversal force as evaluated through a fe analysis. figure 1: the curve “applied force – computed displacement” (ansys analysis under cyclic loading). numerical fe modeling as a reference case the structural behavior of a cantilever masonry beam with dimensions 10 (length) × 40 (height) × 1 (thickness) m was investigated by the ansys fe code [9]. the behavior of the masonry tower under seismic loads was analyzed by means of both static nonlinear pushover analysis and dynamic nonlinear analysis. to model with the ansys code the nonlinear behavior of masonry, a proper combination of two failure domains was employed. on the one hand the drucker-prager (dp) plasticity criterion [10], originally proposed for geo-materials, was employed. the material parameters required to define the plasticity model, the cohesion c and the internal angle of friction φ, were introduced in such a way that the circular cone yield surface of the dp model corresponds to the outer vertex of the hexagonal mohr-coulomb yield surface. the dp criterion was combined with the willam and warnke (ww) failure criterion, originally proposed for concrete [11], which accounts for both cracking and crushing failure modes through a smeared model. with these assumptions the masonry is modeled as an isotropic continuous medium capable to exhibit plastic deformation, to crack by traction and to crush by compression. the assignment of the mechanical parameters required by the dp and ww criterion requires a careful calibration [12, 13], especially if a macro-element approach is used. in the present study, being the analyses aimed to assess the effectiveness of a disordered bw system, these parameters were assumed on the basis of available literature results for stone masonry walls [14]. the final three-dimensional model consisted of 902 joints and 400 solid elements corresponding to 2,640 degrees of freedom (dofs). the nonlinear system of equations was solved by an incremental newton-raphson method. details of the t l. facchini et alii, frattura ed integrità strutturale, 29 (2014) 139-149; doi: 10.3221/igf-esis.29.13 141 analyses are reported in [15]. if for instance the force is harmonic, then the top displacement of the cantilever beam exhibits a slight hysteretic behavior, as shown in fig. 1. adopted simplifications from the results of the structural analyses performed by means of ansys (fig.1), it can be inferred that the dynamic behavior of the cantilever beam can be modeled accurately enough by means of its first modal shape. therefore, a nonlinear single degree of freedom (sdof) system can be defined whose stiffness is determined by means of the performed nonlinear numerical analyses. the analysis performed with ansys applying a horizontal displacement on the top of the masonry cantilever beam, in such a way to obtain the first-loading curve and the successive unloading curve, was hence employed to approximate the system behavior with the bw model, as reported in the following. approximation of the tower response with bouc & wen oscillator within the first part of the research, the simplified sdof bw model for the restoring force of the cantilever beam was identified. the behavior of the oscillator is described by an incremental equation of the form:        mx t cx t kg t f t           1  g t x t z t    (1)         nz t x t a z sign x sign z        ∣∣ this model represents the restoring g(t) function with a linear combination of a linearly elastic force and a historydependent term: z(t). the variable x(t) represents the displacement of the top of the cantilever beam. the first set of parameters that must be identified is composed by k, , a, n,  and γ. it can be shown [15] that parameter a in eq. (1) is redundant, and hence in the following it will be considered as unitary: a=1. the tangent stiffness of the oscillator can be obtained by deriving the nonlinear restoring function g(t) with respect to the displacement x, obtaining:    1 1t g z z k k k k x x x                         (2) being the parameter a assumed unitary without loss of generality, parameter k reduces to the initial stiffness of the system and the initial stiffness can be computed substituting initial conditions z(0)=0 in eq. (2), obtaining:    00 0 1i t zz k k k k         ∣ (3) and asymptotically (according marano and greco [16] the post-elastic stiffness is given as fk k ): 0 f t f i k z k k k k        (4) when the maximum displacement is reached, and the unloading process begins, following expression holds:         1/ 1/ γ β β γ    α 1 α 1 β γ1;    ˆ 1 n u z z k k sgn z sgn x                        (5) and:  1 /β γ β γ 1 α u i u i f k k k k k k        (6) finally, the elastic limit displacement can be expressed, according to cunha [17], as: β γ nyx   . the ratio / affects the transitions from the loading curve to the unloading one. therefore, only one parameter, n, or alternatively  or  , remain undetermined. it is possible to observe that the parameter n influences the transition from elastic to post-elastic behavior and the distance of the unloading path from the first loading. l. facchini et alii, frattura ed integrità strutturale, 29 (2014) 139-149; doi: 10.3221/igf-esis.29.13 142 as a first attempt, imposing the exponent n=5 and the limit elastic displacement yx = 90 mm, the behavior shown with a red line in fig. 2 is obtained. from the numerical analyses carried out by means of ansys, an initial stiffness of ki = 5654 n/mm and a ratio α = kf / ki = 0.1395 can be estimated (tab. 1). it is possible to observe that n=5 reproduce correctly the transition from the elastic to the post-elastic branch, but the overall behavior of the oscillator is very poor. figure 2: comparison of the identified bw model with the ansys results (1st attempt). figure 3: comparison of the identified bw model with the ansys results (2nd attempt). as a second attempt, n and the unloading initial stiffness ku were both lowered (tab. 1), obtaining the behavior reported in fig. 3. these choice gave better results, with an energy dissipation cycle close to the one obtained with the fe code. i k (n/mm) fk (n/mm) uk (n/mm) yx (mm) n α β γ k (n/mm) 1st 5654 789 1171 90 5.0 0.1395 1.627  10-10 6.656  10-12 5654 2nd 5654 789 793 90 4.0 0.1395 1.523  10-8 6.646  10-12 5654 table 1: bw model parameters identification. once the restoring function was modeled, the mass m and the damping c in eq. (1) are two further parameters that need to be evaluated. a “hint” can be drawn from the fe model which has a participating mass of 165 tons. assuming these l. facchini et alii, frattura ed integrità strutturale, 29 (2014) 139-149; doi: 10.3221/igf-esis.29.13 143 values, the dynamic response of the identified bw oscillator was compared with the dynamic response of the cantilever beam evaluated with ansys, and the comparison is showed in fig. 4 (to perform the dynamic nonlinear analyses the el centro 1940 earthquake was employed). it can be seen that the sdof bw oscillator compares well enough with the more complex and computational demanding models elaborated with ansys (fig. 4); however the worst error committed on the response peaks is about 20%. to encompass this error, a possibility is to identify mass and damping of the bw system by means of the analysis of the seismic response of the cantilever beam. according to this approach, the system mass m and damping c are optimized in order to minimize the difference between the cantilever beam response computed with ansys and the response of the bw oscillator. results of this optimization are reported in fig. 5. figure 4: displacement time history: comparison between bw identified model and ansys results (2nd attempt). figure 5: displacement time history: comparison between bw identified model and ansys results (optimization of mass and damping of the bw sdof system). influence of random stiffness on bw response fter calibration of the bw oscillator parameters (k, , a, n, , γ, m and c), the bw model was employed to analyze the behavior of the disordered oscillator. masonry mechanical parameters, such as young’s modulus, are often difficult to estimate, especially for monuments and historical buildings. possibilities can be in-situ tests by means of flat jacks and even laboratory tests on small samples of the examined masonry, but the results can only a l. facchini et alii, frattura ed integrità strutturale, 29 (2014) 139-149; doi: 10.3221/igf-esis.29.13 144 give an estimate of the parameters, which are necessarily affected by a more or less pronounced randomness. hence the problem has significant impact on seismic assessment. being one of the aims of the research to determine the influence of the material parameters (e.g. resistance, stiffness etc.) on a tower response, the liu et al. [3] approach (successively developed by chiostrini and facchini [18]) was employed and a variation of material stiffness was considered. based on this perturbative approach both the system response x(t) and the history-dependent term z(t) were approximate by means of a series expansion on the random parameter k:             2 2 , 1/ 2 , 1/ 2 k kk k kk x t k x k k x k k x z t k z k k z k k z           (7) the kx and kz represent the sensitivity vectors, and must be computed with their derivatives. the solving equations are the derivatives of the equation of motion with respect to the random parameter k:        0mx t cx t kg t f t           0 α 1 αg t x t z t   (8)         1 β γnz t x t z sign x sign z       ∣∣                                        1 0 1 ˙ ˙ ˙ 1 α 1 α 1 β γ 1 β γ β γ k k k k n kk n k n k mx t cx t kg t g t g t x t z t t t sign sign t n sign sign sign d sign si z x z x z x z z z x z z x zgn                                  ∣∣ ∣∣ ∣∣ (9) the computation of the sensitivity vectors requires the solving of eq.. (8)-(9), where a derivative of the signum function appears: it implies differentiation with respect to k of a product of two signum functions, which involves considerable numerical difficulties. to overcome this problem, the signum function was approximated with    12 tan π s x cx with c=5.5 10-4. figure 6: comparison of the identified bw model with the ansys results (signum function approximated with s ) l. facchini et alii, frattura ed integrità strutturale, 29 (2014) 139-149; doi: 10.3221/igf-esis.29.13 145 it can be seen that the replacement of the signum function with  s x causes the cycle of the bw oscillator to enlarge (fig. 6), thus missing the match with the reference response (fig. 1); on the other hand, it was seen that the reintroduction of the condition upon the unloading stiffness brought back the cycle of the bw system to match the reference response again ((fig. 7). a final check was made taking into account the dynamic response of this modified version of bw system to the el centro 1940 earthquake, and the comparison with the fe results is shown in fig. 8. figure 7: comparison of the identified bw model with the ansys results. figure 8: displacement time history: comparison between bw identified model and ansys results (el centro 1940 earthquake). taking into account the proposed approximation for the signum function, eq. (8)-(9) can be written as follows:                         1 2 1 2 1 2 2 1 2 , α 1 α 1 , where :     , , β γn mx t cx t kg f t g x x x x z t x t h x z h x x x s x s x x z                    ∣ ∣ (10) l. facchini et alii, frattura ed integrità strutturale, 29 (2014) 139-149; doi: 10.3221/igf-esis.29.13 146                    1 2 , , 1 , , , , , k k k k k k k k mx t cx t kg z g z z t x t h x z x t h x z zzh x x x x                      (11) figure 9: response  x t evaluated for  k e k . figure 10: sensitivity of the response  kx t . moreover, a further differentiation with respect to k gives the equation of motion of the second derivative of bw response to the earthquake, as follows:                                 1 2 2 2 11 12 22 1 2 , 2 , 1 , 2 , , , , , , 2 , , , , , , , , kk kk kk kk k k kk kk k k k k k k k kk kk mx t cx t kg z g z z t x t h x z x t h x z x h x z z x t h x z x h x z x z h x z z h x z x h x x x z z                                      (12) l. facchini et alii, frattura ed integrità strutturale, 29 (2014) 139-149; doi: 10.3221/igf-esis.29.13 147 by means of the integration of eq. (10)-(11)-(12), that constitute a set of coupled deterministic nonlinear equations, it is possible to obtains the sensitivity vectors and to estimate: i) the response  x t evaluated for  k e k (fig. 9); ii) the sensitivity of the response  kx t (fig. 10) and iii) the derivative of the sensitivity  kkx t (fig. 11). figure 11: derivative of the sensitivity  kk tx . and eventually, the approximations for the expected value of the response and its standard deviation are obtained considering a second-order expansion for the mean displacement and a first-order expansion for the variance, by:           21/ 2  σ σ σ kk k x k k x xe x t t t txt      (13) the expected response, together with the 3σ bounds, is shown in fig. 12. figure 12: expected response and bounds of the disordered bw system. conclusions he paper showed the application of a simplified methodology for the seismic analysis of masonry towers. the method is based on the assumption that such response is mainly due to the first modal shape of the tower, and takes into account the randomness of the tower parameters. with this assumption, the behavior of the first modal t l. facchini et alii, frattura ed integrità strutturale, 29 (2014) 139-149; doi: 10.3221/igf-esis.29.13 148 shape is modeled by means of a nonlinear hysteretic bouc & wen model, where the parameters of the model are identified on the results of a numerical computation. the paper demonstrates that the tower seismic response can be efficiently approximated by a sdof bouc & wen system, provided that a proper identification of the parameters is performed. the influence of a random initial stiffness of the bouc & wen model on its seismic response is subsequently analyzed by means of a perturbation approach, and the bounds of the response of the system are computed. it is possible to comment that such approach works well with a single accelerogram, but it cannot be applied with a seismic stochastic process yet. further improvements of the proposed approach can take into account the response of the disordered system to a stochastic process, instead of only one accelerogram, and the dependence of the response on the randomness of other parameters, such as the yielding point. acknowledgements he authors kindly acknowledge the region of tuscany that financially supported the research (theme par fas 2007-2013 cipe n°166/2007 line 1.1.a.3: science and technology for the preservation and enhancement of cultural heritage). references [1] betti, m., biagini, p., facchini, l., comparison among different techniques for reliability assessment of no-tensile structures under turbulent wind, proceedings of the fourth european-african conference on wind engineering, eacwe4 2005 (2005). [2] facchini, l., betti, m., biagini, p., vignoli, a., rbf – galerkin approach for the dynamics of simple disordered masonry structures, atti del xvii congresso nazionale aimeta di meccanica teorica ed applicata, aimeta 2005 (2005). [3] liu, w.k., belytschko, t., mani, a., probabilistic finite elements for nonlinear structural dynamics, computer methods in applied mechanics and engineering, 56(1) (1986) 61-81. [4] bouc, r., forced vibration of mechanical systems with hysteresis, in: proceedings 4th international conference nonlinear oscillations, prague, cz (1967). [5] wen, y.k., method for random vibration of hysteretic systems, asce journal of the engineering mechanics division, 103(2) (1976) 249-263. [6] wen, y.k., equivalent linearization for hysteretic systems under random excitation, asme j. appl. mech., 47 (1980) 150-154. [7] wen, y.k., eliopoulos, d., method for nonstationary random vibration of inelastic structures. probabilistic engineering mechanics, 9 (1994) 115–123. [8] foliente, g.c., hysteresis modeling of wood joints and structural systems, journal structural engineering, 121(6) (1995) 1013–1022. [9] ansys inc. users’s manual (rev. 5.0). swanson analysis systems, inc. (1992). [10] drucker, d.c., prager, w., soil mechanics and plastic analysis or limit design, quarterly of applied mathematics, 10(2) (1952) 157–165. [11] willam, k.j., warnke, e.d., constitutive model for the triaxial behaviour of concrete, in: proceeding international association for bridge and structural engineering iabse 1975 (1975). [12] betti, m., vignoli a., modelling and analysis of a romanesque church under earthquake loading: assessment of seismic resistance. engineering structures, 30(2) (2008) 352-367. [13] betti, m., orlando, m., vignoli, a. static behaviour of an italian medieval castle: damage assessment by numerical modelling, computers and structures, 89(21-22) (2011) 1956-1970. [14] chiostrini, s., galano, l., vignoli, a., in-situ tests and numerical simulations on structural behaviour of ancient masonry, in: proceedings workshop on seismic performance of monuments (1998). [15] facchini, l., betti, m., biagini, p., seismic analysis of masonry towers, meccanica dei materiali e delle strutture, 1(3) (2012) 90-20. [16] marano, g.c., greco, r., damage and ductility demand spectra assessment of hysteretic degrading systems subject to stochastic seismic loads, journal of earthquake engineering, 10(5) (2006) 615-640. t l. facchini et alii, frattura ed integrità strutturale, 29 (2014) 139-149; doi: 10.3221/igf-esis.29.13 149 [17] cunha, a.m.f., the role of the stochastic equivalent linearization method in the analysis of the nonlinear seismic response of building structures, earthquake engineering and structural dynamics, 23 (1984), 837-857. [18] chiostrini, s. facchini, l., response analysis under stochastic loading in presence of structural uncertainties, int. j. numer. meth. engng., 46 (1999) 853-870. microsoft word numero 10 art 7 g. bolzon et alii, frattura ed integrità strutturale, 10 (2009) 56-63; doi: 10.3221/igf-esis.10.07 56 mechanical characterization of metal-ceramic composites g. bolzon, m.bocciarelli, e.j. chiarullo politecnico di milano , dipartimento di ingegneria strutturale, bolzon@stru.polimi.it riassunto. i compositi metallo-ceramici rappresentano una classe di materiali per uso strutturale che richiede una adeguata caratterizzazione meccanica. le difficoltà ed i costi associati con la produzione e la lavorazione di questi compositi scoraggiano l’esecuzione di prove meccaniche tradizionali, che richiedono l’impiego di un numero statisticamente significativo di provini di dimensioni e geometria proibitivi in questo contesto. risulta invece indicata la prova di indentazione strumentata, rapida ed economica, abbinata a tecniche di analisi inversa che combinano l’informazione sperimentale con la simulazione del comportamento del materiale durante la prova, come si mostra in questo contributo basato sull’esperienza acquisita nell’ambito del network di eccellenza su ‘knowledge-based multi-component materials for durable and safe performance’ (kmm-noe). abstract. metal-ceramic composites represent a class of quasi-brittle materials for advanced structural applications that require adequate mechanical characterization. difficulties and costs associated with material production and specimen extraction prevent the execution of a statistically meaningful number of standard laboratory tests. parameter calibration methodologies based on instrumented indentation and inverse analysis represent fast and reliable identification procedures in the present context, as shown by the present contribution, based on some experience achieved in the framework of the european network of excellence on ‘knowledge-based multi-component materials for durable and safe performance’ (kmm-noe). keywords. metal-ceramic composites; constitutive models; quasi–brittle fracture; mechanical characterization; instrumented indentation; parametric identification; inverse analysis. introduction etal-ceramic composites represent a class of advanced materials of growing interest for their application in several technological fields, ranging from energy production and biomechanics as witnessed, e.g., by the website www.kmm-noe.org. significant dimensional stability, reduced thermal expansion, increased wear and damaging resistance at high temperature, good mechanical strength (mainly in compression) make these composites interesting replacement of metals as structural components and protective coatings in high demanding applications. main limitations concerning their usage consist of: difficult processing; high production costs; strong influence on the overall material properties of micro-structural details; brittle behaviour, though mitigated by the metal phase when compared with pure ceramics. the composition and the production process of these composites are usually designed in order to optimize their effective thermo-mechanical response, which require to carefully control the possible presence and the evolution of local damages and defects. the estimation of macroscopic properties is often based on homogenization techniques, which often neglect microstructural details playing a significant role for brittle and quasi-brittle materials [1-8]. a proper experimental validation of the mechanical properties is therefore mandatory. on the other hand, difficulties and costs associated with specimen production prevent the execution of a statistically meaningful number of standard laboratory investigations. a practical methodology for material characterization is based on instrumented indentation, which represents a fast and economical test, which can be performed at different scales on small material portions, even directly on the structural m http://dx.medra.org/10.3221/igf-esis.10.07&auth=true http://www.gruppofrattura.it mailto: bolzon@stru.polimi.it g. bolzon et alii, frattura ed integrità strutturale, 10 (2009) 56-63; doi: 10.3221/igf-esis.10.07 57 components. the combination of experimental information with the test simulation and inverse analysis [9] represents the envisaged approach to material characterization as the properties to be determined becomes numerous and less amenable to direct separate measurement, as in the present context. this approach can return the bulk and fracture properties of metal-ceramic composites in a robust and reliable manner, by exploiting experimental data relevant to both the traditional indentation curves and the mapping of the residual displacement field, as shown e.g. in [10-16] and illustrated in the next sections with the aid of some meaningful application example. indentation tool ndentation test represents a practical methodology for the characterization of traditional and innovative materials. with respect to more traditional experimental investigation, indentation can be performed on small material portion, does not require to extract laboratory specimens, can be performed even in situ, directly on the structural component, to continuous monitoring and diagnosis purposes. the outcome of instrumented indentation, namely the curves that represent the relationship between the penetration depth and the force exerted on the equipment tip, see fig. 1, reflect constitutive and fracture properties of the sampled material, though in an indirect way. quantitative calibration of parameters entering the selected constitutive model can then be returned by inverse analysis procedures, which combine experimental data and the simulation of the laboratory test as shown, e.g., in [9, 17, 18]. the inverse analysis problem can be formulated as the minimisation, with respect to the unknown parameters, of a norm that quantifies the overall discrepancy between the measured quantities and the corresponding values computed through a mathematical or numerical model. indentation test can be analysed in the large deformation regime by finite element (fe) approaches, as already done in previous analyses [10-16] or by alternative numerical techniques, like in [19, 20]. numerical simulation represents an useful tool also to the purpose of designing the experimental test, and selecting the most appropriate measurements, e.g. by sensitivity analysis [21]. figure 1: comparison between the experimental mean indentation curves obtained from conical (rockwell) tests on an al/tib2 specimen with 50% tib2 weight content and the corresponding curves recalculated by a fe model of the test, supplemented by the identified material parameter set. let the indentation forces if (i=1, …, n) and the corresponding penetration depth mid represent the experimental information collected from the mean indentation curves, visualised in fig. 1. for any given value if , numerical analysis returns the corresponding penetration depth ( )cid z as a function of the constitutive parameters contained in the selected material or fracture model (elastic moduli, yield limits, fracture energy, …), here collected by vector z. the discrepancy between quantities gathered from the experimental apparatus and from the simulation of the test can then be defined by the norm: i http://dx.medra.org/10.3221/igf-esis.10.07&auth=true http://www.gruppofrattura.it g. bolzon et alii, frattura ed integrità strutturale, 10 (2009) 56-63; doi: 10.3221/igf-esis.10.07 58 2 1 ( ) ( ) n ci mi i i d d w         z z (1) where iw represent weights on the displacement components mid , assumed to be proportional to the variances which quantifies the measurement discrepancies, also visualised in fig. 1. the optimum value of the sought parameters is represented by the entries of vector optz , which corresponds to the minimum discrepancy. these values can be returned by a number of numerical methods implemented in widely available optimisation tools [22]. in this kind of application, the discrepancy function ( ) z is expected to be non-convex and to admit multiple minimum points, often almost equivalent from the engineering point of view, in the sense that the corresponding parameter values approximate to the same extent the available experimental data and return comparable representation of the real material behaviour, consistently with the selected constitutive model. the optimisation algorithm is hence run several times, starting from different initial parameter sets or, alternatively, evolutionary search techniques like genetic algorithms or soft computing methodologies are exploited; see, e.g., the review paper [20]. the computational efficiency of the simulation tool represents, hence, an important issue in this context. bulk material properties ccording to a popular approach developed by tamura et al. [23] for metal alloys and applied to different composite systems by a proper calibration of a characteristic ‘stress transfer’ parameter, the overall mechanical response of metal-ceramic composites is governed by the metal phase. pressure-insensitive elastic-plastic laws, like the classical hencky–huber–mises (hhm) model, are therefore mostly considered at the macro-scale [24-26] and supplemented by constitutive parameters (elastic modulus, yield limit, hardening coefficients), evaluated on the basis of some mixture theory that depends on volume fractions. in the proposal by bocciarelli et al. [15], volume fractions govern the transition from hhm model toward drucker–prager (dp) constitutive law, capable to describe the mechanical behaviour of ceramics [14]. the elastic domain defined by the traditional dp yield criterion with linear isotropic hardening is represented by: 1 1 ' ' 0 2 ij ijf i k h       (2) where: 'ij denote the components of the deviatoric stress tensor; 1i represents the first stress invariant, i.e. the trace of the tensor collecting the stress components ij ; λ (>0) is the cumulative multiplier of the plastic deformations, which develop as 0f  and 0f  (the superimposed dot denotes a rate quantity); α, k and h are constitutive parameters. internal friction α and initial cohesion k depend on the initial tensile and compressive yield limits, 0t and 0c , respectively, as follows:     0 0 0 0 0 0 0 0 2 3 , 3 c t c t c t c t k           (3) while parameter h governs material hardening. hhm criterion can be recovered from dp model as the value of the internal friction coefficient α is set equal to zero. the plastic rate components pij of the strain tensor are assumed to develop orthogonally to a potential surface ( )ijg  as follows: 1 1 , ( ) ' ' 2 p ij ij ij ij ij g g i           (4) where β represents the dilatancy coefficient. a http://dx.medra.org/10.3221/igf-esis.10.07&auth=true http://www.gruppofrattura.it g. bolzon et alii, frattura ed integrità strutturale, 10 (2009) 56-63; doi: 10.3221/igf-esis.10.07 59 parameters governing dp constitutive law have been inferred from available experimental information gathered from conical rockwell indentation of al/tib2, al/zro2 and cu/al2o3 with about 40 to 50% weight metal content. associative plasticity has been then introduced as reasonable hypothesis, so that α=β in relations (4). poisson’s ratio has been a priori fixed due to the expected low influence of this parameter on indentation results; see [10, 14] and references therein. then, the unknown overall material parameters to be returned by inverse analysis are: the elastic modulus e; the initial compression yield stress 0c ; the internal friction angle α and the hardening modulus h. results listed in tab. 1 concern the case of an al/tib2 sample with 50% tib2 weight content produced by spark plasma sintering in a joint research project with inasmet-tecnalia (san sebastian, spain), partner of the kmm noe [8]. the identified parameter values are given in terms of the average and of the standard deviation of several converged optimization solutions, which returned small similar values of ( )opt z starting from different initial z vectors. the scatter on the value of the internal friction angle returned by the exploited inverse analysis procedure is relatively large, nevertheless α values were found much larger than zero in all considered situations, thus indicating that hydrostatic stress component plays a significant role in controlling the mechanical response of the considered metal-ceramic composites. the accuracy of the selected material model and of the optimal parameter set obtained from the present identification procedure can be appreciated by the comparison between the experimental information and the corresponding recalculated curves, drawn in fig. 1. elastic modulus e [gpa] initial yield limit in compression 0c [mpa] internal friction angle arctan(α) [°] hardening modulus h [mpa] al/tib2 57.9 (±3.7) 240.4 (±36.5) 10.7 (±4.3) 1032 (±91) table 1: identified material properties after different initializations of the discrepancy minimisation algorithm for an al/tib2 sample with 50% tib2 weight content. the results of this research work showed that the overall material properties are strongly influenced by embedded defects and local damages, as earlier observed for different material systems [6]. classical homogenization rules and mixture laws, which do not consider micro-structural details, fail in returning reliable quantitative prediction of constitutive parameters even in the elastic range. fracture properties he brittleness of the composite materials under investigation is mitigated by the ductility of their metal phase. in fact, during fracture processes, large plastic deformations produce metal ligaments which bridge crack surfaces as shown e.g. in fig. 2. this image is relevant to a fracture experiment performed at the technical university darmstadt (tud), partner of the kmm network, on a cu/al2o3 composite with interpenetrating network structure [13]. fracture can be induced in a brittle material sample to parameter identification purposes by the sharp corners of a vickers pyramidal tip, as shown in fig. 3 for the case of a pure zirconia (zro2) specimen. semi-empirical formulae based on linear elastic fracture mechanics (lefm) permit to correlate the material toughness to the length of the cracks, measured from the centre of the imprint left by indentation [27, 28] which can be observed after unloading. however, experimental investigations show a systematic dependence of such estimated toughness values on the level of the applied indentation load. this result, inconsistent with lefm assumptions, is likely originated by various error sources like the experimental difficulties in getting reliable measurement of the actual crack length and the influence of possible residual stresses, besides the existence of a crack-bridging zone at the crack tip [1, 4]. furthermore, indentation results of brittle and quasibrittle materials are affected by big scatters and influenced by microstructure [29, 30]. these limitations can be mitigated by an identification approach based on inverse analysis, as introduced above, comparing results gathered from the experiment and from the test simulation. material separation during fracture propagation can be introduced in fe simulation of the indentation tests by interface elements, as shown e.g. in fig. 4 and 5. the relationship between displacement discontinuities and the cohesive tractions transmitted across the fracture surface of metal-ceramic composites can be described by relatively simple and t http://dx.medra.org/10.3221/igf-esis.10.07&auth=true http://www.gruppofrattura.it g. bolzon et alii, frattura ed integrità strutturale, 10 (2009) 56-63; doi: 10.3221/igf-esis.10.07 60 computational effective cohesive model originally proposed for mode i fracture for metals and bimetallic interfaces by rose et al. [31], further extended in [32, 33] and widely employed in different application fields; see, e.g., [12, 14, 16, 37] and references therein. figure 2: detail of a fracture experiment on a cu/al2o3 composite (courtesy of tud) figure 3: result of vickers indentation on a zro2 specimen. figure 4: simulation result of vickers indentation on a zro2 specimen. http://dx.medra.org/10.3221/igf-esis.10.07&auth=true http://www.gruppofrattura.it g. bolzon et alii, frattura ed integrità strutturale, 10 (2009) 56-63; doi: 10.3221/igf-esis.10.07 61 figure 5: contour map of the crack opening displacements of the half-penny shape fracture surface produced by indentation (simulation results) according to this popular formulation, the normal cohesive stress σ transferred during progressive mode i fracture processes can be described by the relationship: ( ) c c c w w w w e we    (5) where: e is the neper number; c is the maximum cohesive normal traction; w represents the opening displacement and cw is a characteristic value of it, associated to the fracture energy fg of the material by the formula: 0 ( )f c cg w dw e w      (6) in mixed model fracture formulation, the opening displacement w is replaced by a scalar measure of the displacement jump vector across the interface and a further parameter is introduced to describe the shear strength of the interface [32, 33]. preliminary studies have shown that the indentation curve, the geometry of the residual imprint and the crack length reflect to different extent fracture properties like c and fg , entering relation (5) and (6). the biggest sensitivity to a change in these parameters is shown by the fracture length but, in turn, the actual position of the crack tip is rather difficult to establish with the required precision. for this reason, information about the geometry of the residual imprint and in-plane displacement components on the specimen surface after fracture propagation can be acquired by several kinds of microscopes nowadays available on the market, possibly endowed with suitable image correlation tools, see e.g. [35, 36]. these data can be exploited to enhance the identification of fracture properties through indentation test [12, 14, 16], including them in the discrepancy function (1), compared to the corresponding computed quantities. the application, now in progress, of reliable and robust identification procedures should also allow to verify the range of applicability of approaches based on modified mixture laws, proposed for fracture properties of metal-ceramic composites by jin et al. [37], in analogy with [23]. closing remarks he envisaged increasing use of metal-ceramic composites for structural applications in the near future require adequate mechanical characterization, which can be better based on instrumented indentation and inverse analysis rather than on standard laboratory tests, due to difficulties and costs associated with material production and specimen extraction processes. recently developed parameter calibration methodologies, gathering experimental information from the measurement of the residual deformed configuration of the specimen after the test, besides from the indentation curves, are generally bound to enhance the identification of both bulk and fracture parameters. t http://dx.medra.org/10.3221/igf-esis.10.07&auth=true http://www.gruppofrattura.it g. bolzon et alii, frattura ed integrità strutturale, 10 (2009) 56-63; doi: 10.3221/igf-esis.10.07 62 the application of these novel fast and reliable identification techniques can assist the selection of the constitutive models better suited to describe the behaviour of these composites and permits to appreciate the influence of micro-structural details on the overall mechanical characteristics. in fact, left porosity and micro defects generated by the production processes, generally neglected by material parameter prediction approaches based on classical homogenization rules, have strong influence on the properties of these quasi-brittle composites. acknowledgement u financial support to the project ‘knowledge-based multi-component materials for durable and safe performance’ (kmm-noe, nmp3-ct-2004-502243) is gratefully acknowledged. references [1] h. prielipp, m. knechtel, n. claussen, s.k. streiffer, h. muellejans, m. ruehle, j. roedel., mater. sci. eng., a197 (1995) 19. [2] r.j. moon, m. tilbrook, m. hoffman, a. neubrand, j. am. ceramic soc., 88 (2005) 666. [3] s. skirl, r. krause, s.m. wiederhorn, j. roedel, journal of the american ceramic society, 84 (2001) 2034. [4] m. basista, w. węglewski, j. theor. appl. mech., 44 (2006) 455. [5] z. poniznik, v. salit, m. basista, d. gross, computat. mater. sci., 44 (2008) 813. [6] h.a. bruck, r.h. rabin, j. mater. sci., 34 (1999) 2241. [7] a.m. klaska, t. beck, a. wanner, d. lohe, mater. sci. eng. a 501 (2009) 6. [8] g. bolzon, e.j. chiarullo, p. egizabal, c. estournes, mechanical modelling and characterization of aluminium-based metal matrix composites produced by spark plasma sintering, submitted. [9] g. stavroulakis, g. bolzon, z. waszczyszyn, l. ziemianski, in comprehensive structural integrity, b. karihaloo, r.o. ritchie, i. milne (eds), elsevier science ldt, 3 (2003) 685-718. [10] g. bolzon, g. maier, m. panico, int. j. solids struct., 41 (2004) 2957. [11] m. bocciarelli, g. bolzon, g. maier, mech. mat., 37 (2005) 855. [12] g. maier, m. bocciarelli, g. bolzon, r. fedele, int. j. fract., 138 (2006) 47. [13] m. bocciarelli, g. bolzon, mater. sci. engng a, 448 (2007) 303. [14] g. bolzon, m. bocciarelli, e.j. chiarullo, in applied scanning probe methods xii characterization, b. bhushan, h. fuchs (eds), springer-verlag, heidelberg, (2008) 85. [15] m. bocciarelli, g. bolzon, g. maier, computat. mater. sci., 43 (2008) 16. [16] m. bocciarelli, g. bolzon, int. j. fract., 155 (2009) 1. [17] h.d. bui. inverse problems in the mechanics of materials: an introduction, crc press, boca raton, fl (1994). [18] z. mroz, g. stavroulakis, eds. parameter identification of materials and structures, springer-verlag, berlin (2004). [19] z. ostrowski, r.a. bialecki, a.j. kassab, inv. problems sci. eng., 16 (2008) 705. [20] g. maier, g. bolzon, v. buljak, t. garbowski, b. miller, in: computer methods in mechanics lectures of the cmm 2009, springer verlag, eidelberg (2009). [21] m. kleiber, h. antúnez, t.d. hien, p. kowalczyk, parameter sensitivity in non-linear mechanics. theory and finite element computations, john wiley & sons, chichster (1997). [22] the math works inc. matlab user’s guide and optimization toolbox, release 6.13, natick, ma, usa (2004). [23] i. tamura, y. tomota, h. ozawa, proc. of the third international conference on strength of metals and alloys, volume 1, institute of metals, cambridge (1973) 611. [24] t. nakamura, t. wang, s. sampath, acta mater., 48 (2000) 4293. [25] a.e. giannakopoulos, int. j. solids structures, 39 (2002) 2495. [26] y. gu, t. nakamura, l. prchlik, s. sampath, j. wallace, mat. sci. eng. a, 345 (2003) 223. [27] b.r. lawn, a.g. evans, d.b. marshall, j. am. ceram. soc., 63 (1980) 574. [28] b.r. lawn. fracture of brittle solids. cambridge university press, cambridge (1993). [29] c. ullner, a. germak, h. le doussal, r. morrell, t. reich, w. vandermeulen, j. eur. ceramic soc. 21 (2001) 439. [30] l.l. mishnaevsky jr., acta materialia, 52 (2004) 4177. [31] j.h. rose, j. ferrante, j.r.smith, phys. rev. letters, 47 (1981) 675. e http://dx.medra.org/10.3221/igf-esis.10.07&auth=true http://www.gruppofrattura.it g. bolzon et alii, frattura ed integrità strutturale, 10 (2009) 56-63; doi: 10.3221/igf-esis.10.07 63 [32] x.p. xu, a. needleman, modelling sim. mat. sci. eng., 1 (1993) 111. [33] m. ortiz, s. suresh, asme j. of appl. mech., 60 (1993) 77. [34] p. liu, y.w. zhang, k.y. zeng, c. lu, k.y. lam, eng. fract. mech., 74 (2007) 1118. [35] d. vogel, a. gollhardt, b. michel, sensors and actuators a, 99 (2002) 165. [36] f. hild, s. roux, strain, 42 (2006) 69. [37] z. h. jin, g.h. paulino, r.h. dodds jr., eng. fract. mech., 70 (2003) 1885. http://dx.medra.org/10.3221/igf-esis.10.07&auth=true http://www.gruppofrattura.it microsoft word numero_39_art_5 p. král et alii, frattura ed integrità strutturale, 39 (2017) 38-46; doi: 10.3221/igf-esis.39.05 38 focussed on modelling in mechanics inverse identification of the material parameters of a nonlinear concrete constitutive model based on the triaxial compression strength testing petr král, petr hradil, jiří kala brno university of technology, faculty of civil engineering, veveří 331/95, 602 00 brno, czech republic kral.p@fce.vutbr.cz, hradil.p@fce.vutbr.cz, kala.j@fce.vutbr.cz abstract. the aim of this paper is to perform the inverse identification of the material parameters of a nonlinear constitutive model intended for the modeling of concrete which is known as the karagozian & case concrete model. at present, inverse analysis is frequently used because it allows us to find the optimum parameter values of nonlinear material models. when applying such parameters, the resulting response of the structure obtained from a computer simulation is very similar to the real response of the structure based on the related experimental measurement. this condition then undoubtedly constitutes one of the progressive steps to refine the current numerical approaches. for the purposes of the inverse analysis performed in this paper the experimental data was obtained from the triaxial compression strength tests carried out on the concrete cylinders. keywords. inverse analysis; optimization; objective function; numerical simulation; nonlinear concrete material model; experimental data. citation: král, p., hradil, p., kala, j., inverse identification of the material parameters of a nonlinear concrete constitutive model based on the triaxial compression strength testing, frattura ed integrità strutturale, 39 (2017) 3846. received: 11.07.2016 accepted: 22.09.2016 published: 01.01.2017 copyright: © 2017 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. introduction sing nonlinear material models of concrete to examine the behavior of concrete structures exposed to static or dynamic loading currently constitutes a major move within the effort to approach the real character of and processes in the material during computer simulations. current modern computing systems based on the finite element method, such as ansys [1], ls-dyna [2], and atena [3], offer a comparatively wide variety of nonlinear material models to simulate different conditions across the entire spectrum of materials. according to their respective properties, these models are applicable in both static [4-7] and dynamic [8-12] numerical simulations. the actual utilization of nonlinear material models of concrete within tasks of continuum mechanics nevertheless poses certain difficulties. one of such complications, forming the main subject of this paper, lies in the fact that the resulting computer simulation-based response of the structure is heavily dependent on the entered parameter values of the relevant nonlinear model of concrete. thus, in any case where the parameter values of the employed material model were entered inappropriately, the eventual, computer-simulated response of the structure completely differs from the real response, and this condition constitutes an undesired effect in the given respect. to function properly, a large number of nonlinear u http://www.gruppofrattura.it/pdf/rivista/numero39/audio/5.mp3 p. král et alii, frattura ed integrità strutturale, 39 (2017) 38-46; doi: 10.3221/igf-esis.39.05 39 models of concrete also require multiple material parameters, some of which carry only a mathematical meaning and therefore remain difficult to acquire due to the lack of a physical substance or can be acquired only via special testing. such aspects then render the use of certain material models rather problematic; however, modern computing technology enables us to solve the above-mentioned drawbacks by means of inverse analysis, or, in other words, the inverse identification of material parameters. the inverse analysis combines the numerical and experimental approaches with optimization procedures, and it advantageously facilitates finding the optimum parameter values of the employed material model in such a manner that the computer simulation-based response of the structure is as close as possible to the structure’s real response obtained from the related experimental measurement. at present, the set of the most widely preferred techniques for the inverse identification of material parameters includes, among other tools, optimization methods based on the training of artificial neural networks [13]. considering commercial computing systems, a very powerful instrument to perform inverse analysis currently appears to consist in the optislang program [14], which offers a robust algorithm comprising a broad spectrum of optimization procedures suitable for the inverse identification of material parameters [15, 16]. the aim of the research characterized in this paper is to execute the inverse identification of the material parameters of a nonlinear constitutive model, namely, the karagozian & case (k & c) concrete model [17]. the relevant inverse analysis is carried out exploiting a load-displacement curve, one experimentally measured during the triaxial compression strength testing of concrete cylinders. within the inverse analysis process, we utilize the interaction of nonlinear numerical simulations performed using ls-dyna software (an explicit solver of the finite element method), with the optimization procedures implemented in the optislang program. experimental analysis enerally, the entire inverse analysis process requires us to define the input data. in the inverse identification of the material parameters of nonlinear models, the basic input information consists in experimental data, which are most often formed by a loading curve defining the response of the real structure to static or dynamic loading. triaxial compression strength testing of concrete cylinders within this paper, the experimental data consisted in a load-displacement curve obtained from the multiple triaxial compression strength tests presented by the authors of reference [18]. such testing of cylindrical concrete specimens is one of the methods to examine and verify the physical-mechanical properties of concrete. the dimensions of the concrete cylinders applied in each test were, invariably, 304.8 mm (height) and 152.4 mm (base diameter). the established ultimate uniaxial compressive strength of the concrete used to produce the test cylinders corresponded to 45.4 mpa. during the testing, each cylinder was compressed at a constant velocity, and the loading had a quasi-static character. for this paper, we chose the results for the temporally constant transverse pressure (confinement) of 7 mpa, from which the triaxial stress was induced. figure 1: the experimentally-measured load-displacement curve. g p. král et alii, frattura ed integrità strutturale, 39 (2017) 38-46; doi: 10.3221/igf-esis.39.05 40 evaluation of the experimental results the load-displacement curve based on the above-discussed triaxial compression strength tests of concrete is shown in fig. 1. the curve indicates that, during the compressive loading, the concrete cylinder first exhibited linearly elastic behavior and then elasto-plastic behavior, respectively; further, it is also evident that, after the cylinder had reached its ultimate strength in triaxial compression, compressive strain softening began to occur. this process resulted from cracks disrupting the structure of the relevant concrete cylinder; however, due to the action of the temporally constant transverse pressure of 7 mpa, the total response of the concrete cylinder was very ductile. nonlinear numerical analysis ithin the process of the inverse identification of material parameters, the nonlinear numerical analysis was carried out using the ls-dyna computing system based on the explicit finite element method. to describe the nonlinear behavior of concrete, we selected the k & c concrete material model, whose parameters were identified. the setting of the computational model, the parameters of the selected nonlinear model of concrete, the solver, and other settings required for the execution of calculations were all written with relevant keywords [17] into the ls-dyna input file carrying the suffix *.k. following the formerly defined experimental data, this file embodied the second part of the input information necessary for performing the inverse analysis in the optislang program. computational model during the real triaxial compression strength test of a concrete cylinder, the cylindrical specimen was invariably positioned in a triaxial test chamber, between the pressure plates of the test press. for the purposes of the numerical simulations presented within this paper, the boundary conditions were simplified as follows:  the actual modeling involved only the test cylinder, excluding the pressure plates, and was performed via eight-node 3-d structural finite elements (bricks) designated for an explicit analysis (see fig. 2);  the nodes of the lower base of the finite element model of the cylinder were pre-assigned zero displacements in all the directions (see fig. 2);  the nodes of the upper base of the finite element model of the cylinder were pre-assigned zero displacements in the horizontal directions (x and y) and linearly increasing displacements in the vertical direction (z), as is shown in fig. 2. the vertical displacements of the base nodes then simulated the compression of the cylinder at a constant velocity;  a temporally constant transverse surface pressure was applied directly to the model of the cylinder (see fig. 2). figure 2: the computational model. the initial stiffness of the cylinder established from the numerical simulations at simplified boundary conditions corresponded to the initial stiffness of the real cylinder during compression loading, and the assumed simplification thus w p. král et alii, frattura ed integrità strutturale, 39 (2017) 38-46; doi: 10.3221/igf-esis.39.05 41 could be considered correct. the material characteristics in the computational model were defined by means of the k & c concrete material model. karagozian  case concrete model the k & c concrete model [19] is a three-invariant constitutive model based on three shear failure surfaces: an initial yield surface, a maximum shear failure surface and a residual failure surface. the shear failure surfaces are mutually independent, and their generalized mathematical notation can be expressed as follows [20]: 0 1 2 ( )i i i i p f p a a a p    (1) where the index i = y (initial yield surface), m (maximum shear failure surface), or r (residual failure surface). the variables aji (j = 0, 1, 2) are the parameters calibratable from the experimental data, and p denotes the pressure which depends on the first invariant of the stress tensor (p = -i1/3). the resulting failure surface is, within the model, interpolated between the maximum shear failure surface and either the initial yield surface or the residual failure surface according to the formulas: 1 2 3 3( , , ) ( )[ ( )( ( ) ( )) ( )] for m y y mf i j j r j f p f p f p       (2) 1 2 3 3( , , ) ( )[ ( )( ( ) ( )) ( )] for m r r mf i j j r j f p f p f p       (3) where i1 is the first invariant of the stress tensor, j2 and j3 are the second and third invariants of the deviatoric stress tensor, λ denotes the modified effective plastic strain, η(λ) represents the function depending on the modified effective plastic strain λ, and r(j3) is the scale factor in the form of the willam-warnke equation [21]. the model is implemented in the ls-dyna software and enables us to consider the failure and various physicalmechanical properties of the material; thus, it is well-suited for the modeling of concrete. within its parameters, the model facilitates considering also the effect of strain rate on the state of stress; however, this capability can be neglected in the model, making the model’s response temporally independent. it then follows from this fact that the k & c concrete model is suitable for simulating the response of a structure to not only fast dynamic but also quasi-static loading, and this property was utilized in the numerical analysis presented within this paper. to ensure the correct functioning of the material model, the numerical values of 48 model parameters have to be defined, together with the values of 34 parameters of the equation of state [17]. the appropriate use of the model thus requires us to define the numerical values of 82 parameters, which, with respect to the character of some of the parameters, constitutes a rather difficult task. no. parameter unit description 1 ro [mg/mm3] mass density. 2 pr [-] poisson’s ratio. 3 sigf [mpa] maximum principal stress for failure. 4 a0 [mpa] cohesion. 5 a2 [mpa-1] pressure hardening coefficient. 6 a0y [mpa] cohesion for yield. 7 a2y [mpa-1] pressure hardening coefficient for yield limit. 8 a2f [mpa-1] pressure hardening coefficient for failed material. 9 b1 [-] damage scaling factor. 10 18 p2 p10 [mpa] pressure 2 pressure 10. 19 28 bu1 bu10 [mpa] bulk unloading modulus 1 bulk unloading modulus 10. table 1: the identified parameters of the k & c concrete model. p. král et alii, frattura ed integrità strutturale, 39 (2017) 38-46; doi: 10.3221/igf-esis.39.05 42 a significant number of the model parameters remain constant despite alterations in the physical-mechanical properties of the material; thus, these parameters need not to be identified, and we utilized this condition within the research discussed herein. however, even after omitting the constant parameters, the numerical values of 28 parameters still wait to be defined, and as they change according to the physical-mechanical properties of the material, this step too is somewhat problematic to perform, especially in view of the character of certain parameters. a survey of these 28 parameters, including the applied units, is given in tab. 1. within this paper, these parameters were identified to find, in the available range of options, the most accurate approximation of the experimental data via numerical simulation. inverse analysis he inverse identification of material parameters was performed using the optislang program and comprised two stages; within the former one, we analyzed the sensitivity of the identified material parameters to the required reference response, and the latter stage was then focused on the optimization. sensitivity analysis as already indicated by its name, the procedure [22, 23] was aimed at analyzing the sensitivity of the variable input parameters to the required reference response, and, subsequently, at reducing the number of the parameters in the design vector to the necessary minimum. the variable input parameters consisted of the identified material parameters of the k & c concrete model, and the reference response comprised points lying on the experimentally-measured loaddisplacement curve. fig. 3 shows the load-displacement curves obtained via numerical simulations for the boundary values of the identified material parameters from their initial range of the variability. these curves constituted the upper and lower bounds, meaning that they enclosed the experimentally-measured load-displacement curve (see fig. 3), and both of them were based on the test calculations. the above-mentioned initial range of the variability of the individual input variables was also modified within the sensitivity analysis. figure 3: the boundary load-displacement curves. the actual sensitivity analysis was carried out via the alhs (advanced latin hypercube sampling) statistical method [24]; based on this procedure, we generated 500 random realizations of the design vector, which sufficiently covered the given design space. the results produced by the sensitivity analysis indicated that only 9 identified material parameters out of the total of 28 exerted major influence on the resultant form of the load-displacement curve. the initial design vector, which comprised all the original 28 identified parameters, expressed as:  , , , 0, 2, 0 , 2 , 2 , 1, 2 10, 1 10 tro pr sigf a a a y a y a f b p p bu bu  origx (4) could eventually be reduced for the subsequent optimization process, assuming the form: t p. král et alii, frattura ed integrità strutturale, 39 (2017) 38-46; doi: 10.3221/igf-esis.39.05 43  , , 0, 2, 2 , 1, 2, 3, 1 tpr sigf a a a f b p p buredx (5) the design vector reduction was then utilized during the optimization process as it shortens the computational time and saves the hard disk space without significantly affecting the achievement of the desired results. the reduced design vector xred already included only the 9 parameters having a marked impact on the numerical simulation results. the values of the pre-optimized material parameters and objective function (lsm) obtained from the best random realization generated within the sensitivity analysis are presented in tab. 2. no. parameter unit sensitivity analysis evolutionary algorithm 1 ro [mg/mm3] 2.46810-9 2.40010-9 2 pr [-] 0.1632 0.1677 3 sigf [mpa] 3.4787 3.2092 4 a0 [mpa] 13.2501 13.9527 5 a2 [mpa-1] 1.75510-3 1.84610-3 6 a0y [mpa] 10.613 10.130 7 a2y [mpa-1] 5.56810-3 5.67010-3 8 a2f [mpa-1] 2.71510-3 2.82010-3 9 b1 [-] 1.5425 1.4752 10 p2 [mpa] 23.1475 22.7979 11 p3 [mpa] 49.659 49.170 12 p4 [mpa] 80.662 93.030 13 p5 [mpa] 170.923 176.750 14 p6 [mpa] 232.417 266.590 15 p7 [mpa] 372.124 378.220 16 p8 [mpa] 527.117 578.620 17 p9 [mpa] 3362.560 3378.180 18 p10 [mpa] 4812.750 5166.940 19 bu1 [mpa] 16147.867 18220.000 20 bu2 [mpa] 15205.699 17719.000 21 bu3 [mpa] 16277.413 17967.000 22 bu4 [mpa] 19149.825 18871.000 23 bu5 [mpa] 20935.411 22450.000 24 bu6 [mpa] 24486.102 26047.000 25 bu7 [mpa] 28990.083 29627.000 26 bu8 [mpa] 32188.319 32338.000 27 bu9 [mpa] 65782.085 72755.000 28 bu10 [mpa] 81950.750 88596.000 lsm [kn2] 10312.759 6601.210 table 2: the resulting identified material parameter values of the k & c concrete model, obtained from the inverse analysis. p. král et alii, frattura ed integrità strutturale, 39 (2017) 38-46; doi: 10.3221/igf-esis.39.05 44 optimization the aim of the optimization process consisted in finding such identified parameter values at which the value of the objective function was minimal. the objective function utilized within the entire inverse analysis process was defined as a sum of squares by the formula:  2* 1 n i i i lsm y y    (6) where, for yi, we substituted the loading force values obtained from the numerically-simulated load-displacement curve at the given deformations, and yi* was substituted with the loading force values obtained from the experimentally-measured load-displacement curve at the same deformations. as already mentioned, the objective function was minimized during the optimization process (lsm  min), meaning that we sought such material parameter values at which the loaddisplacement curve obtained from the numerical simulation exhibited the smallest possible deflection from the reference load-displacement curve produced by the experiment; in other words, we sought such values at which the sum of squares was minimal. it then follows from this description that the inverse analysis was based on minimizing the sum of squares (the least squares minimization) [15]. as pointed out above, the optimization involved only those material parameters that were part of the reduced design vector. the remaining parameters were defined by the constant values from their initial range of the variability. the optimization of the parameters was performed using the optimization procedure known as evolutionary algorithm (ea) [14], an optimization approach that exploits processes inspired by biological evolution, including, for example, reproduction, mutation, and recombination. more concretely, we utilized in this context the evolutionary algorithm used for global optimization, with the 10 best realizations acquired within the sensitivity analysis serving as the starting point for the discussed algorithm. the values of the identified material parameters provided by the best generation of the evolutionary algorithm are, together with the relevant minimum value of the objective function, presented in tab. 2. fig. 4 below compares the load-displacement curve obtained via the numerical simulation, in which we applied the optimized parameter values of the k & c concrete model from the evolutionary algorithm (ea), with the experimentally-measured load-displacement curve. it is then obvious from the representation that the parameters of the selected material model were identified very accurately because the results of the numerical simulation ensure a very good approximation of the experimental data. figure 4: the load-displacement curve for the optimized parameter values compared with the experimental load-displacement curve. conclusion his paper was based on performing an inverse analysis to identify the material parameters of the karagozian & case concrete constitutive model. the inverse analysis was carried out utilizing the load-displacement curve experimentally measured during the triaxial compression strength testing of concrete cylinders. the actual results t p. král et alii, frattura ed integrità strutturale, 39 (2017) 38-46; doi: 10.3221/igf-esis.39.05 45 of the inverse analysis conducted by the authors of this paper showed that the k & c concrete model is a suitable tool to describe the nonlinear behavior of concrete in triaxial compression, and they also indicated that, in any case where the parameters of the model are conveniently selected and entered, we can obtain a very good approximation of the experimental data. importantly, this claim is proved by the outcome of the numerical simulation performed using the resulting identified parameter values of the material model. the discussed results then approximated the applied experimental data with a high degree of accuracy. advantageously, the product of the procedure can be exploited for further research concerning the nonlinear numerical response of concrete structures. although the experimental data approximation yielded very good accuracy, it has to be pointed out that there still is the possibility of reaching an even better performance rate via operations such as local optimization, the application of an optimization procedure different from that characterized in this paper, increasing the number of the design vector generations, or using a non-reduced design vector within the optimization process. these aspects, which could further improve the accuracy of experimental data approximation and thus lead us towards obtaining more refined values of identified material parameters, will be examined within future research planned by the authors of this paper. acknowledgment he research presented within this paper was supported from project ga14-25320s "aspects of the use of complex nonlinear material models" provided by czech science foundation. financial assistance was also received via project fast-j-16-3744 "optimization of the parameters of nonlinear concrete material models for explicit dynamics"; this instrument was structured and guaranteed by brno university of technology to support the specific university research. references [1] ansys, ansys mechanical theory reference release 15.0, (2014). [2] ls-dyna, theory manual, livemore software technology corporation, livemore, california, (2016). [3] atena program documentation, cervenka consulting ltd., (2013). [4] kala, j., hradil, p., bajer, m., reinforced concrete wall under shear load – experimental and nonlinear simulation, international journal of mechanics, 9 (2015) 206-212. [5] hradil, p., kala, j., analysis of the shear failure of a reinforced concrete wall, applied mechanics and materials, 621 (2014) 124-129. [6] hokeš, f., selected aspects of modelling of non-linear behaviour of concrete during tensile test using multiplas library, transactions of the všb technical university of ostrava, civil engineering series, 2(15) (2015). [7] sucharda, o., brozovsky, j., numerical modelling of reinforced concrete beams with fracture-plastic material, frattura ed integrita strutturale, 30 (2014) 375-382. doi: 10.3221/igf-esis.30.4 [8] kala, j., hušek, m., improved element erosion function for concrete-like materials with the sph method, shock and vibration, 2016 (2016) 1-13. [9] wu, m., chen, z., zhang, c., determining the impact behavior of concrete beams through experimental testing and meso-scale simulation: i. drop-weight tests, engineering fracture mechanics, 135 (2015) 94-112. [10] král, p., kala, j., hradil, p., verification of the elasto-plastic behavior of nonlinear concrete material models, international journal of mechanics, 10 (2016) 175-181. [11] cichocki, k., domski, j., katzer, j., ruchwa, m., static and dynamic characteristics of waste ceramic aggregate fibre reinforced concrete, transactions of the všb technical university of ostrava, civil engineering series, 2(15) (2015). [12] králik, j., králik jr., j., seismic analysis of reinforced concrete frame-wall systems considering ductility effects in accordance to eurocode, engineering structures, 31(12) (2009) 2865-2872. doi: 10.1016/j.engstruct.2009.07.029. [13] lehký, d., novák, d., inverse reliability problem solved by artificial neural networks, in: safety, reliability, risk and life-cycle performance of structures and infrastructures, new york, usa, (2013) 5303-5310. [14] optislang, methods for multi-disciplinary optimization and robustness analysis, dynardo gmbh, weimar, germany, (2014). [15] most, t., identification of the parameters of complex constitutive models: least squares minimization vs. bayesian updating, reliability conference in münchen, (2010). t p. král et alii, frattura ed integrità strutturale, 39 (2017) 38-46; doi: 10.3221/igf-esis.39.05 46 [16] hokeš, f., kala, j., krňávek, o., nonlinear numerical simulation of a fracture test with use of optimization for identification of material parameters, international journal of mechanics, 10 (2016) 159-166. [17] ls-dyna, keyword user's manual, livemore software technology corporation, livemore, california, (2016). [18] joy, s., moxley, r., material characterization, wsmr-5 3/4-inch concrete, report to the defense special weapons agency, usae waterways experiment station, vicksburg, ms, (1993) (limited distribution). [19] malvar, l. j., crawford, j. e., wesevich, j. w., simons, d., a plasticity concrete material model for dyna3d, international journal of impact, 19 (1997) 847-873. [20] youcai, w., crawford, j. e., magallanes, j. m., performance of ls-dyna concrete constitutive models, 12th international ls-dyna users conference, detroit, (2012). [21] chen, w. f., han, d. j., plasticity for structural engineers, springer-verlag, new york, (1988). [22] kala, z., kala, j., škaloud, m., teplý, b., sensitivity analysis of the effect of initial imperfections on the (i) ultimate load and (ii) fatigue behaviour of steel plate girders, journal of civil engineering and management, 11 (2005) 99-107. [23] tvrdá, k., optimal design, reliability and sensitivity analysis of foundation plate, transactions of the všb technical university of ostrava, civil engineering series, 2(15) (2015). [24] huntington, d. e., lyrintzis, c. s., improvement to limitations of latin hypercube sampling, probabilistic engineering mechanics, 13 (1998) 245-253. << /ascii85encodepages false /allowtransparency false /autopositionepsfiles true /autorotatepages /none /binding /left /calgrayprofile (dot gain 20%) /calrgbprofile (srgb iec61966-2.1) /calcmykprofile (u.s. web coated \050swop\051 v2) /srgbprofile (srgb iec61966-2.1) /cannotembedfontpolicy /error /compatibilitylevel 1.4 /compressobjects /tags /compresspages true /convertimagestoindexed true /passthroughjpegimages true /createjobticket false /defaultrenderingintent /default /detectblends true /detectcurves 0.0000 /colorconversionstrategy /cmyk /dothumbnails false /embedallfonts true /embedopentype false /parseiccprofilesincomments true /embedjoboptions true /dscreportinglevel 0 /emitdscwarnings false /endpage -1 /imagememory 1048576 /lockdistillerparams false /maxsubsetpct 100 /optimize true /opm 1 /parsedsccomments true 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can be opened with acrobat and adobe reader 5.0 and later.) >> /namespace [ (adobe) (common) (1.0) ] /othernamespaces [ << /asreaderspreads false /cropimagestoframes true /errorcontrol /warnandcontinue /flattenerignorespreadoverrides false /includeguidesgrids false /includenonprinting false /includeslug false /namespace [ (adobe) (indesign) (4.0) ] /omitplacedbitmaps false /omitplacedeps false /omitplacedpdf false /simulateoverprint /legacy >> << /addbleedmarks false /addcolorbars false /addcropmarks false /addpageinfo false /addregmarks false /convertcolors /converttocmyk /destinationprofilename () /destinationprofileselector /documentcmyk /downsample16bitimages true /flattenerpreset << /presetselector /mediumresolution >> /formelements false /generatestructure false /includebookmarks false /includehyperlinks false /includeinteractive false /includelayers false /includeprofiles false /multimediahandling /useobjectsettings /namespace [ (adobe) (creativesuite) (2.0) ] /pdfxoutputintentprofileselector /documentcmyk /preserveediting true /untaggedcmykhandling /leaveuntagged /untaggedrgbhandling /usedocumentprofile /usedocumentbleed false >> ] >> setdistillerparams << /hwresolution [2400 2400] /pagesize [612.000 792.000] >> setpagedevice microsoft word numero_30_art_14 t. voiconi et alii, frattura ed integrità strutturale, 30(2014) 101-108; doi: 10.3221/igf-esis.30.14 101 focussed on: fracture and structural integrity related issues the notch effect on fracture of polyurethane materials t. voiconi, r. negru, e. linul, l. marsavina, h. filipescu university politehnica timisoara, romania liviu.marsavina@upt.ro abstract. this paper investigates the fracture properties and notch effect of pur materials with four different densities. the asymmetric semi-circular bend specimen was adapted to perform mixed mode fracture toughness tests. this semi-circular specimen with radius r, which contains an edge crack of length a oriented normal to the specimen edge, loaded with a three point bending fixture, was proved to give wide range of mixed modes from pure mode i to pure mode ii, only by changing the position of one support. different types of notched specimens were considered for notch effect investigations and the theory of critical distances was applied. it could be seen that the critical distances are influenced by the cellular structure of investigated materials. keywords. polyurethane materials; notch effect; fracture toughness; theory of critical distances. introduction olyurethane (pur) materials are polymers composed of a chain of organic units joined by urethane links. low density polyurethanes (30 200 kg/m3), having closed cell foam structure, are used to manufacture flexible, highresilience seating; rigid foam insulation panels; microcellular foam seals and gaskets, high durable elastomeric wheels and tires, automotive suspension bushings, [1]. while for higher density polyurethanes (> 200 kg/m3), with a porous solid structure, the main applications are fixtures and gauges, master and copy models, draw die moulds, hard parts for electronic instruments. the properties of these materials are influenced by the properties of solid material, by the cellular structure topology and the relative density, [2, 3]. cellular and porous materials crush in compression, while in tension fail by propagating of single crack. most of the rigid polymeric foams have a linear – elastic behavior in tension up to fracture, and a brittle failure, [4]. components made of cellular or porous materials may have micro-structural defects like cracks, filled cells or missing walls holes induced by manufacturing process, [5]. on the other hand macro-structural notches or holes may be introduced in design of components. the influence of notches on the strength of the structures is an important issue, which should be considered on the design stage. up to now there are only few studies investigating notch effect on foam and porous materials mainly regarding metallic foams [6 8] and polymeric foams [6, 9]. the notch effect was experimentally investigated [6, 9], but also computational studies [7, 8] were performed. the theory of critical distances (tcd) was proved to be an useful engineering tool to predict the failure of notched components for different types of materials [10 12]. this paper proposes the use of tcd approach to quantify the notch effect in cellular and porous materials. a correlation of characteristic length and inherent stress to microstructure dimensions and ultimate tensile stress of the material is proposed, which could be used in design to quantify the notch effect of cellular and porous materials. p t. voiconi et alii, frattura ed integrità strutturale, 30(2014) 101-108; doi: 10.3221/igf-esis.30.14 102 materials olyurethane (pur) materials of four different densities (100, 145, 300 and 708 kg/m3) manufactured by necumer gmbh, germany under commercial designation necuron (100, 160, 301 and 651) were investigated. at low densities 100 and 145 kg/m3 the materials have a closed cellular structure, while the pur materials of higher densities show a porous solid structure. the microstructures of the investigated materials (at 1000x magnification) were obtained using quantatm feg 250 sem and are presented in fig. 1. the results of statistic analysis of microstructures are shown in table 1 together with the experimentally determined values of the densities according with astm d 162208 [13]. necuron 100 160 301 651 cell diameter, [m] 104.5±9.4* 83.8±9.6* 68.5±33.9* 49.1±30.2* cell wall thickness, [m] 2.9-5.8 5.1-13.1 3.8-21.8 4.7-37.6 density (determined), [kg/m3] 100.35±0.25* 145.53±0.22* 300.28±1.38* 708.8±3.45 table 1: characteristics of the microstructure and determined densities. (* standard deviation values) a) necuron 100 b) necuron 160 c) necuron 301 d) necuron 651 figure 1: microstructures of the investigated materials. p t. voiconi et alii, frattura ed integrità strutturale, 30(2014) 101-108; doi: 10.3221/igf-esis.30.14 103 the microstructures of all low density pur materials show a closed cell structure, while the high density materials highlighted a porous solid structure. for all pur materials a circular shape of cells or pores could be considered with cell diameter and thickness of cell walls as microstructure parameters. the statistical analysis of the microstructure shows a decrease of cell diameter and an increase of cell wall thickness with increasing density. tensile tests were performed using dog bone specimens with a gage length of 50 mm and a cross section in the calibrated zone with 10 mm width and 4 thickness, according to en iso 527 [14]. the test specimens were cut from pur panels in flow direction. four specimens were tested for each material at room temperature and with a loading rate of 2 mm/min using a zwick/roell z005 testing machine with a 5 kn loading cell. mode i and mode ii fracture toughness were determined using asymmetric semi-circular bend (ascb) specimens [15]. this semi-circular specimen with radius r=40 mm and thickness t=10 mm, which contains an edge crack of length a=20 mm oriented normal to the specimen edge, loaded with a three point bend fixture, was proved to give a wide range of mixed modes from pure mode i (s1=s2=30 mm) to pure mode ii (s2=2.6 mm), only by changing the position of one support, ayatollahi et al. [16], marsavina et al. [17], negru [18]. table 2 summarizes the mechanical and fracture properties of the investigated materials. necuron 100 160 301 651 ultimate tensile stress, σu [mpa] 1.16±0.024* 1.87±0.036* 3.86±0.092* 17.40±0.32* young's modulus, e [mpa] 30.18±1.75* 66.89±1.07* 281.39±2.92* 1250±15.00* mode i fracture toughness, kic [mpa m0.5] 0.087±0.003* 0.131±0.003* 0.372±0.014* 1.253±0.027* mode ii fracture toughness, kiic [mpa m0.5] 0.050±0.002* 0.079±0.004* 0.374±0.013* 1.376±0.047* table 2: mechanical and fracture properties of pur materials. (* standard deviation values) from table 2 it could be observe that at low densities kic is higher than kiic while at higher densities kiic > kic. notched specimen tests he experimental tests were performed on 5 kn zwick/roell z005 testing machine at room temperature in displacement control at a crosshead speed of 2 mm/min. fig. 2 presents the notch shapes and the geometrical parameters of specimen used for tensile tests. for each type of notch three specimens were tested. a) lateral v-notches b) lateral u-notches c) circular hole figure 2: notch shapes and geometrical parameters of used specimens. t t. voiconi et alii, frattura ed integrità strutturale, 30(2014) 101-108; doi: 10.3221/igf-esis.30.14 104 typical load displacement curves for the necuron 651 material and different notch shapes are shown in fig. 3.a, while fig 3.b presents the influence of density on mechanical properties for lateral rounded v-notches. it could be observed from fig. 3.a that the maximum load was obtained for circular hole specimen, while the v-notch specimen give the lower value of maximum load. also, the maximum load increase with increasing pur material density, fig. 3.b. 0.0 0.5 1.0 1.5 2.0 2.5 3.0 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 lo ad [n ] displacement [mm] v-notch u-notch circular hole 0.0 0.5 1.0 1.5 2.0 0.0 0.5 1.0 1.5 2.0 2.5 3.0 lo ad [n ] displacement [mm] necuron 100 necuron 160 necuron 301 necuron 651 a) influence of notch shapes b) influence of density figure 3: load-displacement curves. for all tested specimens a linear load-displacement behavior was obtained with an abrupt drop of load to zero after reaching the maximum load and brittle fracture was observed. the linear elastic behavior was confirmed during the tests when no plastic deformations remain after finishing the test. the maximum load values resulted from experimental tests are listed in table 3. necuron fmax,[n] 100 160 301 651 v-notch 166.7 143.1 149.1 194.0 186.8 209.1 392.7 376.94 398.5 1827.0 1786.9 1869.1 u-notch 216.1 181.3 190.6 260.9 256.8 270.3 432.88 484.0 452.5 2137.3 2104.7 2177.6 circular hole 190.5 178.6 159.0 239.0 252.9 295.3 487.38 472.5 471.5 2144.1 2631.8 2047.1 table 3: the maximum load values. evaluation of notch effect using tcd ccording to [10] the theory of critical distances (tcd) represents a group of four methods (point method, line method, area method and volume method) which have a common approach, i.e. they use the characteristic length l and the inherent stress σ0 as material parameters. the tcd postulates that brittle fracture in notched components can be predicted by using the linear-elastic stress field acting in the area of the notch tip. concerning the mode i loading, the point method assumes that brittle fracture occurs when the maximum principal stress σ1 at the critical distance l/2 from the notch tip, along the bisector, reaches the inherent stress σ0: 1 0, 0 2 l r         (1) where r and θ are the polar coordinates. unfortunately, the inherent stress σ0 is a material property whose definition varies as the type of material to be assessed changes, [11]. for the situations where the material presents a linear-elastic behavior up to fracture (e.g. ceramics, a t. voiconi et alii, frattura ed integrità strutturale, 30(2014) 101-108; doi: 10.3221/igf-esis.30.14 105 composites and other brittle or quasi-brittle materials), inherent stress σ0 is equal to ultimate tensile strength σu and the characteristic length l can be determined as follows: 2 0 1 ickl          (2) kic representing the plane strain fracture toughness. in those situations in which the final fracture is preceded by a limited amount of plastic deformation (metals tested at low temperature) or the fracture of the plain specimens occurs by different mechanisms to those governing fracture of notched components (polymers), the inherent stress σ0 is larger than σu. in these cases the l and σ0 material constants can be determined by using two experimental results obtained under mode i loading for specimens having different geometrical features, [12]. thus, plotting at fracture condition the linearelastic stress-distances curves for a relatively blunt notch and a sharp notch, the intersection point allows the determination of the material constants l and σ0. following this strategy, the linear-elastic stress-distances curves were plotted for all four polyurethane materials, using the experimental results presented in table 3. as is recommended in [12], the circular hole and the rounded v-notch were used as different stress concentrators in order to obtain accurate estimations for material constants l and σ0. the stressdistance curves along the notch bisector for maximum principal stress σ1 were obtained through a linear-elastic finite element analysis. the abaqus 6.13 software was used to generate the quarter finite element models, using the symmetric boundary conditions. the models were meshed using cps8r plane 8-node bi-quadratic elements with a suitably high mesh density in the area of the notch tip. the mean values of critical fracture forces were applied as a tensile stress at the ends of the specimens. the results are presented in fig. 4, and are summarized in table 4. 0.395 2.32 0 2 4 6 8 10 0 0.1 0.2 0.3 0.4 0.5  1 [m p a] distance [mm] circular hole rounded v-notch 0.355 3.08 0 2 4 6 8 10 12 0 0.1 0.2 0.3 0.4 0.5  1 [m p a] distance [mm] circular hole rounded v-notch a) necuron 100 b) necuron 160 0.297 6.02 0 5 10 15 20 0 0.1 0.2 0.3 0.4 0.5  1 [m p a] distance [mm] circular hole rounded v-notch 0.259 24.05 0 10 20 30 40 50 60 70 80 0 0.1 0.2 0.3 0.4 0.5  1 [m p a] distance [mm] circular hole rounded v-notch c) necuron 301 d) necuron 651 figure 4: determination of l and σ0 material constants. t. voiconi et alii, frattura ed integrità strutturale, 30(2014) 101-108; doi: 10.3221/igf-esis.30.14 106 necuron 100 145 300 651 length, l [mm] 0.790 0.710 0.594 0.518 inherent stress, σ0 [mpa] 2.32 3.08 6.02 24.05 table 4: summarized data for material constants l and σ0. an attempt to relate the material constants to the cell diameter and ultimate tensile stress of the cellular and porous materials was carried out. fig. 5.a presents the variation of characteristic length l versus the cell diameter, and fig. 6.b shows the plot of inherent stress with ultimate tensile stress. both representations show a linear variation, and indicate an easy way to estimate the material constants (l and 0) based on material microstructure (cell diameter) and mechanical properties (ultimate tensile stress). y = 5.098x + 0.263 r² = 0.982 0.0 0.2 0.4 0.6 0.8 1.0 0.00 0.02 0.04 0.06 0.08 0.10 0.12 le n gt h l [m m ] cell diameter [mm] y = 1.341x + 0.721 r² = 0.999 0 5 10 15 20 25 30 0 5 10 15 20 in h er en t s tr es s  0 [m p a] ultimate tensile stress u [mpa] figure 5. influence of the relative density on material constants l and σ0. validation of these material constants was performed on other notched geometry, respectively lateral u notches. starting from the stress-distance curves obtained for an applied tensile stress equal cu 1 [mpa], the failure forces were predicted by simply rescaling these curves until the maximum principal stress σ1 reaches the inherent stress 0 value at the critical distance l/2. the predictions, as can be seen in fig. 6, are in agreement with the experimental results, the relative errors falling between ±15 [%], which represents a reasonable engineering approximation. 0 500 1000 1500 2000 2500 100 160 301 651 f m ax [n ] necuron experimental results tcd prediction figure 6. failure force predictions for u-notched specimens. t. voiconi et alii, frattura ed integrità strutturale, 30(2014) 101-108; doi: 10.3221/igf-esis.30.14 107 conclusions our pur materials having a cellular and porous microstructure were considered for the study of the notch effect. three different types of notches were used: circular hole, symmetric lateral u-notch and v-notch. the theory of critical distance was employed and the characteristic length and inherent stress were determined from the circular hole and v-notch geometry. to validate the results these material characteristics were used to predict maximum load for the u-notch geometry. the estimated values are in good agreement with the experimental ones. also were proposed linear correlations between characteristic length and cell structure diameter, respectively inherent stress and ultimate tensile stress. acknowledgments r. t. voiconi was supported by the strategic grant posdru/159/1.5/s/137070 (2014) of the ministry of national education, romania, co-financed by the european social fund – investing in people, within the sectoral operational programme human resources development 2007-2013. the experimental work was carried out in the framework of the grant from the romanian national authority for scientific research, cncs – uefiscdi, project pn-ii-id-pce-2011-3-0456, contract number 172/2011, which also supported the authors e. linul and l. marsavina. references [1] http://www.necumer.com/index.php/en/produkte-2/board-materials.html, (2014). [2] gibson, l.j., ashby, m.f.,. cellular solids, structure and properties, second edition, cambridge university press, (1997). [3] ashby, m.f., cellular solids scaling of proprieties. in scheffler, m., colombo p. (eds), cellular ceramics, structure, manufacturing, properties and applications, wiley-vch verlag gmbh & co, (2005) 3-17. [4] marsavina, l., fracture mechanics of cellular solids, in: h. altenbach, a. ochsner (eds.), cellular and porous materials in structures and processes, springer, wien, (2010) 1-46. [5] andrews, e.w., gibson, l.j., the influence of cracks, notches and holes on the tensile strength of cellular solids, acta mater. 49 (2001) 2975-2979. [6] fleck, n.a., olurin, o.b., chen, c., ashby, m., the effect of hole size upon the strength of metallic and polymeric foams, j. mech. phys. solids, 49 (2001) 2015-2030. [7] combaz, e., rossoll, a., mortensen, a., hole and notch sensitivity of aluminium replicated foam, acta mater., 59 (2011) 572–581. [8] mangipudi, k.r., onck, p.r., notch sensitivity of ductile metallic foams: a computational study, acta mater. 49 (2001) 7356-7367. [9] legan, m.a., kolodezev v.e., sheremet a.s., quasi-brittle fracture of foam-polystyrene plates with hole, strength, fracture and complexity, 3 (2005) 217-225. [10] taylor, d., the theory of critical distances. a new perspective in fracture mechanics, 1st ed., elsevier bv, london, (2007). [11] susmel, l., taylor, d., the theory of critical distances as an alternative experimental strategy for the determination of kic and δkth, engng. fract. mech., 77 (2010) 1492-1501. [12] susmel, l., taylor, d., on the use of the theory of critical distances to predict static failures in ductile metallic materials containing different geometrical features, engng. fract. mech., 75 (2008) 4410-4421. [13] astm d 1622-08. standard test method for apparent density of rigid cellular plastics. [14] en iso 527:2012, plastics-determination of tensile properties. [15] marsavina, l., constantinescu, d.m., linul, e., apostol, d.a., voiconi, t., sadowski, t., evaluation of mixed mode fracture for pur foams, procedia materials science, 3 (2014) 1342–1352. [16] ayatollahi, m.r., aliha, m.r.m., aghafi, h., an improved semi-circular bend specimen for investigating mixed mode brittle fracture, engineering fracture mechanics 78 (2011) 110-123. f m t. voiconi et alii, frattura ed integrità strutturale, 30(2014) 101-108; doi: 10.3221/igf-esis.30.14 108 [17] marsavina, l., constantinescu, d.m., linul, e., apostol, d.a., voiconi, t., sadowski, t., refinements on fracture toughness of pur foams, eng. fracture mech. in press, http://dx.doi.org/10.1016/j.engfracmech.2013.12.006. [18] negru, r., marsavina, l., filipescu, h., pasca, n., investigation of mixed mode i/ii brittle fracture using ascb specimen, int j fract, 18 (2013) 155-161. microsoft word numero_42_art_22.docx m. peron et alii, frattura ed integrità strutturale, 42 (2017) 205-213; doi: 10.3221/igf-esis.42.22 205 local strain energy density for the fatigue assessment of hot dip galvanized welded joints: some recent outcomes m. peron, s.m.j. razavi ,f. berto, j. torgersen, f. mutignani department of mechanical and industrial engineering, norwegian university of science and technology (ntnu), richard birkelands vei 2b, 7491, trondheim, norway. mirco.peron@ntnu.no, javad.razavi@ntnu.no, filippo.berto@ntnu.no, jan.torgersen@ntnu.no abstract. since in literature only data about the effect of the hot-dip galvanizing coating on fatigue behavior of unnotched specimens are available, whereas very few for notched components and none for welded joints, the aim of this paper is to partially fill this lack of knowledge comparing fatigue strength of uncoated and hot-dip galvanized fillet welded cruciform joints made of structural steel s355 welded joints, subjected to a load cycle r = 0. 34. the results are shown in terms of stress range δσ and of the averaged strain energy density range w in a control volume of radius r0 = 0.28 mm keywords. hot-dip galvanized steel; high cycle fatigue; fillet welded cruciform joint; sed. citation: peron, m., razavi, s.m.j., berto, f., torgersen, j., mutignani, f., local strain energy density for the fatigue assessment of hot dip galvanized welded joints: some recent outcomes, frattura ed integrità strutturale, 42 (2017) 205-213. received: 15.07.2017 accepted: 31.07.2017 published: 01.20.2017 copyright: © 2017 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. introduction orrosion is one of the main issue affecting metallic materials such as iron and steel, and several technique to prevent corrosion are available in literature, especially surface treatments. among all, hot-dip galvanizing has been widely used, with great successes in a large amount of worldwide applications. hot-dip galvanization involves the coating of the base material with a zinc layer and several works investigate the influence of different bath composition on mechanical properties [1, 2] and the effect of this protective film on static and fatigue behavior. whilst tensile properties are not greatly affect, except for the yield stress, fatigue strength is reported to be reduced when the coating thickness exceed a threshold value [3], calculated employing the kitagawa–takahashi diagram. moreover, bergengren and melander [4], found an increase in the detrimental effect on fatigue life increasing the zinc layer thickness, but, nevertheless, contrasting results were obtained by browne et al., [5], and nilsson et al., [6], that did not find any correlation in terms of loss of the fatigue strength due to the coating thickness. furthermore, hot-dip galvanization is still an attractive topic, as proved by several recent studies, such as [7-10]. however, the works just mentioned refer to unnotched specimens and very few results are available for notched components. in fact, at the best of author’s knowledge the only data available in literature for notched components are due to huhn and valtinat [11], that examined s 235 jr g2 plates with holes and bearing-type connections with punched and drilled holes. besides this lack of c m. peron et alii, frattura ed integrità strutturale, 42 (2017) 205-213; doi: 10.3221/igf-esis.42.22 206 experimental results on notched components, that represents a great gap since notches greatly affect the mechanical behavior [12–15] , the detrimental effect of the zinc layer on the fatigue strength cannot be quantified yet, neither in [11], since a direct comparison between uncoated and hot-dip galvanized notched specimens was not performed. furthermore, though hot-dip galvanization is widely used to enhance the corrosion resistance of welded joints, none researchers have interested in assessing the effect of this surface treatment on their fatigue behavior. thus, the aim of this work is to fill these lacks, by means of experimental fatigue tests on uncoated and hot-dip galvanized fillet welded cruciform joints made of structural steel s355. the results report the harmful effect of the presence of zinc layer on fatigue strength both in terms of stress range δσ and of the averaged strain energy density range w in a control volume of radius r0 = 0.28 mm. figure 1: geometry of the fillet welded cruciform specimen and typical fracture surface. experimental details he steel plates used to fabricate the samples were 10 mm in thickness, while the complete specimen had a global length of 250 mm. the complete geometry of the specimen can be seen in fig. 1. fatigue tests have been conducted on transverse non-load carrying fillet welded joints, made of s 355j2+n structural steel. welding beads have been made by means of automatic mag (metal active gas) technique. one of the two series of welded joints has been later hot dip galvanized. tests have been performed on a servo-hydraulic mts 810 test system with a load cell capacity of 250 kn at 10 hz frequency, in air, at room temperature. all samples have been tested using a sinusoidal signal in uniaxial tension (plane loading) and a load ratio r = 0, under remote force control. regarding the galvanized series, the coating treatment has been carried out at a bath temperature of 452 oc and the immersion time was kept equal to 4 minutes for all the specimens. as a consequence, the coating thickness resulted in a range between 96 and 104 μm. results atigue tests results are here presented in terms of the stress range δσ = σmax σmin versus the number of cycles to failure, in a double logarithmic scale. the stress range is referred to the nominal area (400 mm2). failure has always occurred at the weld toe, as expected, with a typical fracture surface as that shown in fig. 1. the results from the tests were statistically elaborated by using a log-normal distribution. the ‘run-out’ samples, over two million cycles, were not included in the statistical analysis and are marked in the graphs with an arrow. fig. 2 refers to uncoated and coated series, while fig. 3 shows all the data elaborated together: in addition to the mean curve relative to a survival probability of ps = 50%, (wöhler curve) the scatter band defined by lines with 10% and 90% of probability of survival (haibach scatter band) is also plotted. the mean stress amplitude values corresponding to two million cycles, the inverse slope k value of the wöhler curve and the scatter index tσ (the ratio between the stress amplitudes corresponding to 10% and 90% of survival probability) are provided in the figure. for the complete listing of the results of the fatigue tests, please refer to tab. 1. t f m. peron et alii, frattura ed integrità strutturale, 42 (2017) 205-213; doi: 10.3221/igf-esis.42.22 207 it can be noted, comparing the uncoated and coated series (fig. 2), that the scatter index reduces from 1.6 to 1.3. this value is reasonably low both for the uncoated series and the galvanized one. moreover also in terms of fatigue strength the effect of the galvanization is found to be negligible with a reduction, at n = 2×106 and ps = 90%, from 83 to 82 mpa. furthermore, from the data summarised in fig. 3, it is possible to see that the fatigue strength at n = 2×106 and ps = 90% is 75 mpa: this value is comparable with the fatigue stress range (from 71 to 80 mpa) given for the corresponding detail category in eurocode 3. figure 2: fatigue behaviour of bare (left) and galvanized (hdg, right) welded steel at r = 0. figure 3: fatigue behaviour of both uncoated and galvanized welded steel at r = 0. strain energy density approach n averaged strain energy density (sed) criterion has been proposed and formalized first by lazzarin and zambardi ([16]), and later has been extensively studied and applied for static failures and fatigue life assessment of notched and welded components subjected to different loading conditions [17]. according to this volumebased criterion, the failure occurs when the mean value of the strain energy density over a control volume with a well-w a m. peron et alii, frattura ed integrità strutturale, 42 (2017) 205-213; doi: 10.3221/igf-esis.42.22 208 defined radius r0 is equal to a critical value wc, which does not depend on the notch sharpness. the critical value and the radius of the control volume (which becomes an area in bi-dimensional problems) are dependent on the material [17]. figure 4: polar coordinate system and critical volume (area) centered at the notch tip. uncoated specimens coated specimens δσ [mpa] n [cycles] w [n.mm/mm3] δσ [mpa] n [cycles] w [n.mm/mm3] 260 168750 0.5692 140 494000 0.1650 320 81500 0.8622 120 1079000 0.1212 260 181484 0.5692 100 4800000 run out 0.0842 220 445750 0.4075 260 85000 0.5692 180 572333 0.2728 140 436500 0.1650 140 5000000 run out 0.1650 120 978200 0.1212 160 803000 0.2155 220 96820 0.4075 160 523983 0.2155 120 905500 0.1212 140 804960 0.1650 110 1125546 0.1019 140 556990 0.1650 100 3800000 run out 0.0842 160 645140 0.2155 110 1500000 0.1019 320 45000 0.8622 110 4500000 run out 0.1019 120 5000000 run out 0.1212 110 4000000 run out 0.1019 220 173000 0.4075 260 101200 0.5692 220 205616 0.4075 170 195000 0.2433 170 250000 0.2433 110 1940000 0.1019 320 42000 0.8622 220 115000 0.4075 table 1: fatigue results from uncoated and coated (hdg) welded specimens. the sed approach was formalized and applied first to sharp, zero radius, v-notches ([16]), considering bi-dimensional problems (plane stress or plane strain hypothesis). the volume over which the strain energy density is averaged is then a circular area ω of radius r0 centred at the notch tip, symmetric with respect to the notch bisector (fig. 4), and the stress m. peron et alii, frattura ed integrità strutturale, 42 (2017) 205-213; doi: 10.3221/igf-esis.42.22 209 distributions are those by williams [18], written according to lazzarin and tovo formulation ([19]). dealing with sharp vnotches the strain energy density averaged over the area ω turns out to be: 1 2 2 2 1 1 2 2 1 1 0 0 e k e k w e r e r                (1) where e is the young’s modulus of the material, λ1 and λ2 are williams’ eigenvalues [18], e1 and e2 are two parameters dependent on the notch opening angle 2α and on the hypothesis of plane strain or plane stress considered. those parameters are listed in tab. 1 as a function of the notch opening angle 2α, for a value of the poisson’s ratio ν = 0.3 and plane strain hypothesis. k1 and k2 are the notch stress intensity factors (nsifs) according to gross and mendelson [20]:         1 2 1 1 0 1 2 0 2 lim , 0 2 lim , 0 r r r k r r k r r                       (2) the sed approach was then extended to blunt uand v-notches ([21,22]), by means of the expressions obtained by filippi et al. [23] for the stress fields ahead of blunt notches, and to the case of multiaxial loading [24], by adding the contribution of mode iii. table 2: values of the parameters in the sed expressions valid for a poisson’s ratio ν = 0.3 (beltrami hypothesis) it is widely demonstrated that the sed criterion is a reliable approach for the strength determination in a wide range of materials and notch geometries [25-28], in particular it has been successfully applied to the fatigue assessment of welded joints and steel v-notched specimens. considering a planar model for the welded joints, the toe region was modelled as a sharp v-notch. a closed form relationship for the sed approach in the control volume can be employed accordingly to eq. (1), written in terms of range of the parameters involved. in the case of an opening angle greater than 102.6o, as in transverse non-load carrying fillet welded joints (fig. 4), only the mode i stress distribution is singular. then the mode ii contribution can be neglected, and the expression for the sed over a control area of radius r0, centred at the weld toe, can be easily expressed as follows: 1 2 1 1 1 0 e k w e r          (3) the material parameter r0 can be estimated by equating the expression for the critical value of the mean sed range of a butt ground welded joints, / 2c aw e   , with the one obtained for a welded joint with an opening angle 2α > 102.6o. the final expression for r0 is as follows [16]: 1 1 1 1 1 0 2 a a e k r          (4) 2α [rad] γ [rad] λ1 λ2 λ3 e1 plane strain e2 plane strain e3 axis-sym. 0 π 0.5000 0.5000 0.5000 0.13449 0.34139 0.41380 π/6 11π/12 0.5014 0.5982 0.5455 0.14485 0.27297 0.37929 π/3 5π/6 0.5122 0.7309 0.6000 0.15038 0.21530 0.34484 π/2 3π/4 0.5445 0.9085 0.6667 0.14623 0.16793 0.31034 2π/3 2π/3 0.6157 1.1489 0.7500 0.12964 0.12922 0.27587 3π/4 5π/8 0.6736 1.3021 0.8000 0.11721 0.11250 0.25863 m. peron et alii, frattura ed integrità strutturale, 42 (2017) 205-213; doi: 10.3221/igf-esis.42.22 210 in eq. (4) 1 ak is the nsif-based fatigue strength of welded joints (211 mpa.mm0.326 at na = 5×106 cycles with nominal load ratio r = 0) and δσa is the fatigue strength of the butt ground welded joint (155 mpa at na = 5×106 cycles r = 0) [29]. introducing these values into eq. (4), r0 = 0.28 mm is obtained as the radius of the control volume at the weld toe for steel welded joints. for the weld root, modelled as a crack, a value of the radius r0 = 0.36 mm has been obtained by [29], re-writing the sed expression for 2α = 0. therefore it is possible to use a critical radius equal to 0.28 mm both for toe and root failures, as an engineering approximation [29]. it is useful to underline that r0 depends on the failure hypothesis considered: only the total strain energy density is here presented (beltrami hypothesis), but one could also use the deviatoric strain energy density (von mises hypothesis) ([30]). the sed approach was applied to a large bulk of experimental data: a final synthesis based on 900 fatigue data is shown in fig. 5 [17], including results from structural steel welded joints of complex geometries, for which fatigue failure occurs both from the weld toe or from the weld root. also fatigue data obtained for very thin welded joints have been successfully summarized in terms of the sed ([31]). recently, the sed approach has been extended to the fatigue assessment of notched specimens made of ti-6al-4v under multiaxial loading [32] and to high temperature fatigue data of different alloys [33]–[35]. a new method to rapidly evaluate the sed value from the singular peak stress determined by means of numerical model has been presented by meneghetti et al. [36]. some recent applications to creep are reported in [37]. results in terms of sed e analyses of the transverse non-load carrying fillet welded joint have been carried out applying as remote loads on the model the experimental values used for the fatigue tests. a control volume with a radius equal to 0.28 mm was realized in the model, in order to quantify the sed value in the control volume having the characteristic size for welded structural steel. the diagram of the sed range value w versus the number of cycles to failure n was plotted in a double logarithmic scale, summarizing the fatigue data for both bare and hot-dip galvanized specimens. with the aim to perform a direct comparison, the scatter band previously proposed for welded joints made of structural steel and based on more than 900 experimental data, fig. 5, has been superimposed to the results of the present investigation (fig. 6). for the detailed list of the sed values for both bare and hdg specimens corresponding to the stress ranges used in the fatigue tests, please refer to the last columns of tab. 1. it can be noted that hot-dip galvanized specimens have a lower fatigue strength than the bare specimens, but both bare and hdg data fall within the scatter band previously proposed in the literature for welded structural steel. figure 5: fatigue strength of welded joints made of structural steel as a function of the averaged local strain energy density. f m. peron et alii, frattura ed integrità strutturale, 42 (2017) 205-213; doi: 10.3221/igf-esis.42.22 211 figure 6: fatigue behaviour of uncoated and galvanized welded steel at r = 0 as a function of the averaged local strain energy density. scatter band of 900 experimental data of welded joints made of structural steel is superimposed. acknowledgments he authors wish to remember with great gratitude professor paolo lazzarin, master of science and life, under whose leadership the research presented in this paper has been planned. finally they want to express sincere thanks to ing. emiliano guido of zincherie valbrenta for his active and valuable collaboration. references [1] di cocco, v., sn and ti influences on intermetallic phases damage in hot dip galvanizing, frattura ed integrità strutturale, 22 (2012) 31-38. [2] di cocco, v., zortea, l., influence of dipping time on cracking during bending of hot dip galvanized coatings with sn and ti contents, frattura ed integrità strutturale, 14 (2010) 52-63. [3] vogt, j. b., boussac, o., foct, j., prediction of fatigue resistance of a hot-dip galvanized steel, fatigue fract. eng. mater. struct. 24 (2001), 33–39. [4] bergengren, y., melander, a., an experimental and theoretical study of the fatigue properties of hotdip-galvanized high-strength sheet steel, int. j. fatigue, 14 (1992) 154–162. [5] browne, r. s., gregory, n., harper, s., the effects of galvanizing on the fatigue strengths of steels and welded joints, proceedings of a seminar on galvanizing of silicon-containing steels, (1975) 246 – 264. [6] nilsson, t., engberg, g., trogen, h., fatigue properties of hot-dip galvanized steels, scand. j. metall., 18 (1989) 166175. [7] jiang, j. h., ma, a. b., weng, w. f., fu, g. h., zhang, y. f., liu, g. g., lu, f. m., corrosion fatigue performance of pre-split steel wires for high strength bridge cables, fatigue fract eng m, 32 (2009) 769–779. [8] yang, w. j., yang, p., li, x. m., feng, w. l., influence of tensile stress on corrosion behaviour of high-strength galvanized steel bridge wires in simulated acid rain, mater corros, 63 (2012) 401–407. [9] berchem, k., hocking, m. g., the influence of pre-straining on the high-cycle fatigue performance of two hot-dip 0.01 0.10 1.00 10.00 1.00e+04 1.00e+05 1.00e+06 1.00e+07 a v er ag ed s tr ai n e n er g y d en si ty δ w ( n m m /m m 3 ) number of cycles to failure, n δw 2.3% δw 50% δw 97.7% bare hdg 0.192 k=1.5 ps = 97.7 % ps = 2.3% 0.058 0.105 s355r = 0 scatter index tw = 3.3 w50% = 0.105 nmm/mm3 (n = 2 ∙ 106) rc = 0.28 mm t m. peron et alii, frattura ed integrità strutturale, 42 (2017) 205-213; doi: 10.3221/igf-esis.42.22 212 galvanised car body steels, mater. charact., 58 (2007) 593–602. [10] maaß, p., peißker, p., handbook of hot-dip galvanization, wiley-vch verlag gmbh & co. kgaa, weinheim, (2011). [11] valtinat, g., huhn, h., bolted connections with hot dip galvanized steel members with punched holes, proceedings of connections in steel structures v, (2004) 297–310. [12] lazzarin, p., comportamento a fatica dei giunti saldati in funzione della densità di energia di deformazione locale: influenza dei campi di tensione singolari e non singolari, frattura ed integrità strutturale, 9 (2009) 13-26. [13] maragoni, l., carraro, p. a., peron, m., quaresimin, m., fatigue behaviour of glass/epoxy laminates in the presence of voids, int. j. fatigue, 95 (2017) 18–28. [14] brotzu, a., felli, f., pilone, d., effects of the manufacturing process on fracture behaviour of cast tial intermetallic alloys, frattura ed integrità strutturale, 27 (2013) 66-73. [15] nilsson, t., engberg, g., trogen, h., fatigue properties of hot-dip galvanized steels, scand. j. metall., 18 (1989) 166– 175. [16] lazzarin, p., zambardi, r., a finite-volume-energy based approach to predict the static and fatigue behavior of components with sharp v-shaped notches, int. j. fract., 112 (2001) 275–298. [17] berto, f., lazzarin, p., recent developments in brittle and quasi-brittle failure assessment of engineering materials by means of local approaches, mater. sci. eng. r., 75 (2014) 1–48. [18] williams, m. l., stress singularities resulting from various boundary conditions in angular corners on plates in extension, j. appl. mech., 19 (1952) 526–528. [19] lazzarin, p., tovo, r., a notch intensity factor approach to the stress analysis of welds, fatigue fract. eng. mater. struct., 21 (1998) 1089–1103. [20] gross, b., mendelson, a., plane elastostatic analysis of v-notched plates, int. j. fract. mech. 8 (1972), 267–276. [21] lazzarin, p., berto, f., elices, m., gómez, j., brittle failures from uand v-notches in mode i and mixed, i + ii, mode: a synthesis based on the strain energy density averaged on finite-size volumes, fatigue fract. eng. m., 32 (2009) 671–684. [22] lazzarin, p., berto, f., some expressions for the strain energy in a finite volume surrounding the root of blunt vnotches, int. j. fracture, 135 (2005) 161–185. [23] filippi, s., lazzarin, p., tovo, r., developments of some explicit formulas useful to describe elastic stress fields ahead of notches in plates, int. j. solids struct., 39 (2002) 4543–4565. [24] lazzarin, p., livieri, p., berto, f., zappalorto, m., local strain energy density and fatigue strength of welded joints under uniaxial and multiaxial loading, eng. fract. mech., 75 (2008) 1875–1889. [25] berto, f., lazzarin, p., ayatollahi, m. r., brittle fracture of sharp and blunt v-notches in isostatic graphite under torsion loading, carbon n. y., 50 (2012) 1942–1952. [26] berto, f., ayatollahi, m. r., fracture assessment of brazilian disc specimens weakened by blunt v-notches under mixed mode loading by means of local energy, mater. des., 32 (2011) 2858–2869. [27] berto, f., croccolo, d., cuppini, r., fatigue strength of a fork-pin equivalent coupling in terms of the local strain energy density, mater. des., 29 (2008) 1780–1792. [28] berto, f., barati, e., fracture assessment of u-notches under three point bending by means of local energy density, mater. des., 32 (2011) 822–830. [29] livieri, p., lazzarin, p., fatigue strength of steel and aluminium welded joints based on generalised stress intensity factors and local strain energy values, int. j. fract., 133 (2005) 247–276. [30] lazzarin, p., lassen, t., livieri, p., a notch stress intensity approach applied to fatigue life predictions of welded joints with different local toe geometry, fatigue fract. eng. m., 26 (2003) 49–58. [31] lazzarin, p., berto, f., atzori, b., a synthesis of data from steel spot welded joints of reduced thickness by means of local sed, theor. appl. fract. mec., 63-64 (2013) 32–39. [32] berto, f., campagnolo, a., lazzarin, p., fatigue strength of severely notched specimens made of ti-6al-4v under multiaxial loading, fatigue fract. eng. mater. struct., 38 (2015) 503–517. [33] gallo, p., berto, f., lazzarin, p., high temperature fatigue tests of notched specimens made of titanium grade 2, theor. appl. fract. mech., 76 (2015) 27–34. [34] berto, f., gallo, p., lazzarin, p., high temperature fatigue tests of a cu-be alloy and synthesis in terms of linear elastic strain energy density, key eng. mater., 627 (2015) 77–80. [35] gallo, p., berto, f., influence of surface roughness on high temperature fatigue strength and cracks initiation in 40crmov13.9 notched components, theor. appl. fract. mech., 80 (2015) 226–234. m. peron et alii, frattura ed integrità strutturale, 42 (2017) 205-213; doi: 10.3221/igf-esis.42.22 213 [36] meneghetti, g., campagnolo, a., berto, f., atzori, b., averaged strain energy density evaluated rapidly from the singular peak stresses by fem: cracked components under mixed-mode (i+ii) loading, theor. appl. fract. mech., 79 (2015) 113–124. [37] gallo, p., berto, f., glinka, g generalized approach to estimation of strains and stresses at blunt v-notches under non-localized creep, fatigue fract. eng. mater. struct, 39 (2016) 292-306. nomenclature 2α notch opening angle γ supplementary angle of α: γ = π – α ν poisson’s ratio δσ stress range δσa fatigue strength in terms of stress range at na cycles δk1,2,3 mode 1, 2 and 3 notch stress intensity factor range δk1a fatigue strength in terms of notch stress intensity factor range at na cycles w averaged strain energy density (sed) cw critical value of the sed range λ1,2,3 mode 1, 2 and 3 williams’ eigenvalues e young’s modulus e1,2,3 mode 1, 2 and 3 functions in the sed expression f frequency k1,2,3 mode 1, 2 and 3 notch stress intensity factor (nsif) k inverse slope of the wöhler curve n number of cycles ps survival probability r load cycle ratio r0 radius of the control volume for the calculation of the averaged sed value tσ scatter index referred to the stress range tw 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can be opened with acrobat and adobe reader 5.0 and later.) >> /namespace [ (adobe) (common) (1.0) ] /othernamespaces [ << /asreaderspreads false /cropimagestoframes true /errorcontrol /warnandcontinue /flattenerignorespreadoverrides false /includeguidesgrids false /includenonprinting false /includeslug false /namespace [ (adobe) (indesign) (4.0) ] /omitplacedbitmaps false /omitplacedeps false /omitplacedpdf false /simulateoverprint /legacy >> << /addbleedmarks false /addcolorbars false /addcropmarks false /addpageinfo false /addregmarks false /convertcolors /converttocmyk /destinationprofilename () /destinationprofileselector /documentcmyk /downsample16bitimages true /flattenerpreset << /presetselector /mediumresolution >> /formelements false /generatestructure false /includebookmarks false /includehyperlinks false /includeinteractive false /includelayers false /includeprofiles false /multimediahandling /useobjectsettings /namespace [ (adobe) (creativesuite) (2.0) ] /pdfxoutputintentprofileselector /documentcmyk /preserveediting true /untaggedcmykhandling /leaveuntagged /untaggedrgbhandling /usedocumentprofile /usedocumentbleed false >> ] >> setdistillerparams << /hwresolution [2400 2400] /pagesize [612.000 792.000] >> setpagedevice shot peening processes to obtain nanocrystalline surfaces in metal alloys: y.d. shou et alii, frattura ed integrità strutturale, 53 (2020) 434-445; doi: 10.3221/igf-esis.53.34 434 experimental and analytical investigation on the coupled elastoplastic damage model of coal-rock yundong shou* school of civil engineering, wuhan university, china shouyundong@whu.edu.cn, https://orcid.org/0000-0001-7424-4006 jianwei zhang school of civil engineering, chongqing university, china 20076188@cqu.edu.cn filippo berto norwegian university of science and technology, norway filippo.berto@ntnu.no abstract. in this paper, a novel coupled elastoplastic damage model for coal-rock is proposed to predict the deformation and potential disaster in coal mining. the conditions of small deformation and thermodynamic potential are considered, as well as the coupling of damage evolution process with the plastic deformation and the plastic hardening of coal-rock. based on the theory of damage mechanics, the formulas of damage evolution, plastic yield and plastic potential of coal-rock are deduced theoretically. in addition, triaxial compression tests of coal-rock under the different confining stresses are conducted to reveal the law of deviatoric stress and strain. based on the experimental data, the control parameters of the coupled elastoplastic damage model of coal-rock are determined. the theoretical results obtained from the coupled elastoplastic damage model for coal-rock agree well with those from the experiment. the proposed model is reasonable to predict the deformation of coal-rock. keywords. coal-rock; coupled elastoplastic damage model; damage mechanics; triaxial compression tests; the deformation prediction of coalrock. citation: shou, y.d., zhang, j.w., berto, f., experimental and analytical investigation on the coupled elastoplastic damage model of coal-rock, frattura ed integrità strutturale, 53 (2020) 434-445. received: 23.04.2020 accepted: 05.06.2020 published: 01.07.2020 copyright: © 2020 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. introduction wo types of inelastic behaviors generally exist in most rock materials: plastic deformation, related to sliding mechanisms inside the microstructure of rock matrix; and damage to rock materials, induced by spreading microcracks[1-2]. in the case of semi-brittle rocks, for instance, limestone and porous sandstone, plastic deformation t https://youtu.be/x0c-hyzm5eg y.d. shou et alii, frattura ed integrità strutturale, 53 (2020) 434-445; doi: 10.3221/igf-esis.53.34 435 and damage are usually coupled. therefore, it is necessary to develop a coupled elastoplastic damage model to better understand the mechanical behaviors of these semi-brittle geomaterials. coal is a complex fractured geological medium containing numerous randomly distributed micro holes and cracks [3]. its mechanical properties are important essential parameters for the mining design, roadway support and some other underground coal engineering [4-5]. therefore, the constitutive relation and damage model of coal-rock is still a major issue to be solved urgently. several elastoplastic models have been proposed for coal-rock in the past, thus providing the standard framework for contemporary models [6-9]. the last two decades of geomechanic research have led to an active discussion of damage models for geomaterials, to better address microcracks. a series of isotropic and anisotropic damage models have been proposed. these approaches can be classified into two groups: (macroscopic) phenomenological and micromechanical models. the phenomenological damage models can be easily implemented in computer codes, which then provide an efficient tool for progressive failure analysis of coal-rock mass structures under complex loading conditions. additionally, the phenomenological damage models generally take the thermodynamics of irreversible processes into account; they make use of different orders of tensorial internal variables to represent the distribution and nucleation and growth of microcracks [10-13]. however, in these coupled models, the choice of damage variables and thermodynamic potential is somewhat arbitrary, because it is based on mathematical conveniences, rather than the physical interpretation of microcracks. moreover, most of the previous coupled elastoplastic damage models are isotropic, rather than anisotropic, models. but in fact, the anisotropic features of geomaterials are observable in triaxial and uniaxial compressive tests. the micromechanical damage mechanics approach leads to an improved understanding of the underlying physical processes. in the micromechanical approach, researchers study the growth, nucleation, and coalescence of microcracks and their influence on the mechanical properties, which is reflected in the constitutive relation in certain ways [9, 14-17]. among these, the most widely used models are the dilute-concentration method (dcm), the self-consistent method [18-20], the differential method (dm) [21, 22], the generalized self-consistent method (gscm) [23], and finally, the effective selfconsistent method [24]. however, the micromechanical damage mechanics model is often difficult to implement in engineering applications, because of its proclivity to cause 3d problems. therefore, the phenomenological approach is adapted in the new model. this article proposes a novel coupled elastoplastic damage model for coal-rock to discuss the plastic deformation and induced damage found in coal mine. in section 2, reconstituted coal samples were manufactured in size of 50 mm × 100 mm by compressing machine. then triaxial compression tests of coal-rock under four confining stresses of 0mpa, 5 mpa, 10 mpa and 15 mpa are conducted. the complete deviatoric stress-strain curves of the coal-rock under the different confining stress conditions are obtained. moreover, in section 3, a novel coupled elastoplastic damage model for coal-rock is proposed to predict the deformation. the conditions of small deformation and thermodynamic potential are considered, as well as the coupling of damage evolution process with the plastic deformation and the plastic hardening of coal-rock. based on the theory of damage mechanics, the formulas of damage evolution, plastic yield and plastic potential of coal-rock are deduced theoretically. in section 4, the theoretical results obtained from the coupled elastoplastic damage model for coal-rock agree well with those from the experiment. it is demonstrated that the proposed model is reasonable to predict the deformation of coal-rock. experiment study on and result of the triaxial compression deformation of coal and rock sample preparation n this paper, reconstituted coal samples were used to investigate the mechanical property of coal-rock. the pulverized coal was collected from songzao coal mining area in chongqing. then in laboratory, the pulverized coal and water were mixed first and stirred evenly, as shown in fig. 1 (a). the reconstituted coal samples were made by compressing machine, as shown in fig. 1(b). the compression of the pulverized coal was stress-controlled with a loading rate of 200 n/s until the axial load reached 150kn. the diameter and length of coal sample were 50mm and 100mm, respectively. four groups (each group contained 5 samples) coal samples were prepared for the triaxial compression test with different confining stresses. the samples were dried in a thermostat at 28°c for 30 days. the reconstituted coal sample is shown in fig. 1(c). experimental apparatus in this paper, the triaxial compression test of coal-rock were conducted using the servo-controlled rock mechanical test system mts815, as shown in fig. 2(a) and fig. 2(b). the axial stress, the axial displacement and the circumferential displacement under different confining stresses can be obtained using mts815. the triaxial compression tests of coal-rock i y.d. shou et alii, frattura ed integrità strutturale, 53 (2020) 434-445; doi: 10.3221/igf-esis.53.34 436 have four confining stresses of 0mpa, 5 mpa, 10 mpa and 15 mpa. all tests were conducted under displacement-controlled conditions at average loading rate of 0.01 mm/min until the coal-rock sample is failure. figure 1: the preparation of coal samples. (a) the pulverized coal collected from songzao coal mining area in chongqing; (b) the stresscontrolled compressing machine for manufacture the coal samples; (c) the reconstituted coal sample. figure 2: the rock mechanical triaxial test system. (a) the servo-controlled rock mechanical test system mts815; (b) the installation of the coal samples. experimental results according to the experimental data, the complete deviatoric stress-strain curves of the coal-rock under the different confining stress conditions can be obtained, as shown in figs 3-6. it is found from figs 3-6 that the overall trends of the complete deviatoric stress–strain curves are similar. the characteristics of the complete deviatoric stress–strain curves can be divided into three stages, which are the linear elastic stage, the elastic damage stage and the plastic damage stage. as shown in fig. 3, the peak deviatoric stress 1 3 − of the coal-rock is 4.576 mpa and the corresponding axial strain 1 is 0.518% when the confining stress is 0 mpa. as shown in fig. 4, the peak deviatoric stress 1 3 − of the coal-rock is 9.442 mpa and the corresponding axial strain 1 is 1.765 % and the corresponding transverse strain 3 is -0.956% when the confining stress is 5 mpa. as shown in fig. 5, the peak deviatoric stress 1 3 − of the coal-rock is 12.832 mpa and the corresponding axial strain 1 is 3.146 % and the corresponding transverse strain 3 is -1.771% when the confining stress is 10 mpa. as shown in fig. 6, the peak deviatoric stress 1 3 − of the coal-rock is 13.521 mpa and the corresponding y.d. shou et alii, frattura ed integrità strutturale, 53 (2020) 434-445; doi: 10.3221/igf-esis.53.34 437 axial strain 1 is 3.583% and the corresponding transverse strain 3 is -1.872% when the confining stress is 15 mpa. the elastic modulus of coal-rock is 957 mpa and the poisson's ratio of coal-rock is 0.36. figure 3: the deviatoric stress versus axial strain under the confining pressure of 0 mpa. figure 4: the deviatoric stress 1 3 − versus axial strain 1 and transverse strain 3 under the confining pressure of 5 mpa. figure 5: the deviatoric stress 1 3 − versus axial strain 1 and transverse strain 3 under the confining pressure of 10 mpa. y.d. shou et alii, frattura ed integrità strutturale, 53 (2020) 434-445; doi: 10.3221/igf-esis.53.34 438 figure 6: the deviatoric stress 1 3 − versus axial strain 1 and transverse strain 3 under the confining pressure of 15 mpa. elastoplastic damage coupled model of coal-rock ontinuum damage mechanics is investigated based on macro phenomenological theory, which deals with dissipative systems. in the dissipative systems, the whole damage process is irreversible and always accompanied by internal energy dissipation. in the study of irreversible processes, some basic principles (such as conservation of mass, conservation of momentum moment, conservation of momentum, etc.) must be satisfied. for irreversible processes, there is always energy dissipation within the system. the irreversible phenomenon of energy dissipation within the system is related to internal state variables. the basic state variables can be taken as thermodynamic temperature and strain. in continuum damage mechanics, the internal state variables involve the elastic strain tensor e  , the plastic strain tensor p  , the cumulative inverse strain p  and the damage variable d and so on. mechanical characteristics of coal-rock firstly, elastic modulus, poisson's ratio, tensile strength, internal cohesion and internal friction angle of coal-rock are the basic mechanical properties of coal. according to the experimental results above, the mechanical properties of coal-rock are low modulus of elasticity, low strength and high poisson's ratio. moreover, it is easy to produce plastic deformation. the axial failure stress and modulus of coal-rock are related to confining stress closely. secondly, many micro-cracks, micro-pores and weak structural planes exist in coal-rock, as shown in fig. 7. the existence of these micro-cracks determines the internal structure of coal-rock, which lead to the heterogeneity and anisotropy of coalrock. therefore, coal-rock is a typical geotechnical material with internal defects. because the stress concentration at the cracks or the micro-pores will occur in the process of loading, the coal-rock will be destroyed. figure 7: the micro-pores and micro-cracks in coal-rock [25]. the elastoplastic coupled damage model of coal-rock in this paper, an elastoplastic coupling model is proposed to describe the mechanical properties of coal and rock. under the isothermal conditions, the state variables are composed of the elastic strain tensor e , the plastic strain tensor p  , the c y.d. shou et alii, frattura ed integrità strutturale, 53 (2020) 434-445; doi: 10.3221/igf-esis.53.34 439 damage variable d and the cumulative inverse strain p  . the total strain  are divided into two parts, namely the elastic strain e and the plastic strain p  . e p  = + and e p d d d  = + (1) where d is the incremental total strain, ed is the incremental elastic strain e d is the incremental plastic strain. as stated by shao et al. [9], the damage process is coupled with plastic deformation and plastic hardening. therefore, the thermodynamic potential can be expressed as ( ) ( ) 1 : ( ) : ( , ) 2 p p p pc d d     = − − +  (2) where ( )c d is the fourth-order elastic stiffness tensor of the damaged coal-rock and ( , )p p d is the closed plastic potential of the damaged coal-rock related to plastic hardening. then, the equation of state can be obtained by deriving the elastic strain e from the thermodynamic potential as [9] ( )( ) : pe c d     = = −  (3) according to works by nemat-nasser and hori [26], the fourth-order elastic stiffness tensor can be expressed as ( ) 3 ( ) 2 ( )c d k d j d k= + (4) where ( )k d is the bulk modulus of damaged materials and ( )d is shear modulus of damaged materials. the other two symmetric four-order tensors j and k are 1 3 j  =  and k i j= − (5) where  is the two-order unit tensor, i is the symmetric four-order unit tensors. the thermal forces related to the damage variable is expressed as [9] ( ) ( ) ( , )( )1 : : 2 p pp p d dc d y d d d       = − = − − − −    (6) according to the non-negativity of the internal energy dissipation, the following expression can be obtained [9] : 0 p dy d  +  (7) where  is the stress tensor of coal-rock, p is the derivation of p  to time t and d is the derivation of d to time t . then, the derivative form of the constitutive equation of coal-rock can be obtained as [9] ( ) ( ) : : ( ) ( ) : ( ) : ( ) e e p p c d c d d d c d c d d d         = +   = − + −  (8) where is the derivation of to time t . y.d. shou et alii, frattura ed integrità strutturale, 53 (2020) 434-445; doi: 10.3221/igf-esis.53.34 440 comparison of elastoplastic damage coupled model of coal and rock with experimental results determination of damage evolution characteristics of coal and rock he elastoplastic coupling model is established in section 3.2. according to eqn. (4), the elastic stiffness matrix of isotropic damaged materials is expressed by shear modulus and bulk modulus. moreover, the elastic modulus and poisson's ratio vary with the damage variable d . based on eqn. (4), the effect of damage on elastic mechanical properties can be determined accurately. for the moderate damage condition, the degradation of elastic mechanical properties [26-28] can be expressed as ( ) ( )0 1k d k d= − ， ( ) ( )0 1d d  = − (9) where 0k and 0 are respectively the bulk modulus and shear modulus of undamaged materials,  and  are the two parameters of coal-rock to present the effect of damage on the elastic mechanical properties of coal-rock. according to the damage criterion, the thermal forces related to the damage variable dy can be linearized as 0 d dy y md= + (10) where 0 dy is the initial energy release threshold, m is a parameter to control the damage evolution rate. determination of expression of plastic properties of coal and rock the yield equation of coal and rock includes some main characteristics, such as pressure sensitivity, unconnected plastic flow, asymmetric response under pressure and tension loading, plastic hardening and so on. the three-dimensional nonlinear strength criterion proposed by zhou et al. [29] is introduced to determine yield surface of coal-rock, which is expressed as follows: 2 1 3 2 3( ) ( ) p c cf n m      = + + (11) where n and m are the strength parameters, c denotes uniaxial compressive strength of rocks, 1 2 3, ,   are the major, intermediate and minor principal stresses, respectively. when the damage variable is considered, the nonlinear strength criterion eqn. (11) is rewritten in another form ( ) ( ) 2 1 2 ( , , ) 2 3 cos 3 1 3 cos 3 2 sin 0 3 p p c c f d j trd i m n j m m n           =     − − + + − + − =        (12) where the stress angle is equal to 3 1 2 1 2 2 ( ) arctan 3( )         − + =   +  , 30 30 o o −   , 1i is the first invariant of stress, 2j is the second invariant of deviator stress, c is an uniaxial compressive strength of an intact rock material, m and n are strength parameters of rocks. the cumulative inverse strain can be determined as 2 : 3 p p p e e = (13) where 1 3 p p p e tr  = − t y.d. shou et alii, frattura ed integrità strutturale, 53 (2020) 434-445; doi: 10.3221/igf-esis.53.34 441 determination of thermodynamic potential of coal and rock in this paper, it is assumed that the plastic flow is in the state of strain hardening. under the assumption of moderate damage, the closed plastic potential of the damaged coal-rock can be simplified as 0 ( , ) (1 ) ( )p p p pd d   = −  (14) where 0 ( )p p is the plastic hardening rate without damage. we introduce parameters [0,1]  in the coupling of damage evolution and plastic flow. if 0 = , there is no coupling between damage evolution and plastic flow. if 1 = , the model is a total damage model. based on the experimental data of coal-rock, the expression of plastic hardening rate without damage are proposed as ( ) ( )0 2 0 0m m mp p p p p p p pb       = − − − − (15) the plastic hardening rate of damaged materials can be written as ( ) ( )( )0 01 2 2 1mp p p p p p p d            = = − + − −   (16) where 0 p is the initial plastic yield threshold, m p is the final value of the hardening equation and b is the model parameter controlling the plastic hardening rate. in geotechnical materials, there is a transition from plastic compression to plastic expansion based on loading path [30, 31]. the expression of plastic potential can be determined as ( ) ( ) ( ) 0 1 ln 0 p c g qh d p c i     − = + + − =    (17) where 0i define the intersection point of plastic potential surface and p axis. the boundary of compression and expansion regions is defined by conditions of ( ), 0g p q p  = . it is assumed that p and q are both linear. then, the expression of plastic potential can be simplified as ( ) ( ) ( )1 0cdf qh d p c  = − − − = (18) where  is the boundary diagonals between the compression and expansion regions. the parameters of the coupled elastoplastic damage model of coal-rock twelve parameters involved in the coupled elastoplastic damage model of coal-rock, including two elastic constants of undamaged materials 0k and 0 , two parameters of coal-rock to present the effect of damage on the elastic mechanical properties of coal-rock  and  , five parameters related to plastic characteristics 0 p , m p , c , b , , two parameters related to damage characteristics 0 dy and m , and one parameter related to plastic-damage coupling  . all these parameters can be obtained from a series of triaxial compression tests under different confining pressures. the values of parameters are listed in tab. 1. substituting the parameters in tab. 1 into eqns. (8)-(22), the theoretical results of deviatoric stress 1 3 − versus axial strain 1 and transverse strain 3 can be obtained. the curves of deviatoric stress 1 3 − versus axial strain 1 and transverse strain 3 under the different confining stresses obtained from the theoretical and experimental results are depicted in figs 8-11. in this figures, the black solid lines represent the experimental result, and the dotted lines represent the theoretical results. it is found from figs 8-11 that the theoretical results agree well with experimental data. the y.d. shou et alii, frattura ed integrità strutturale, 53 (2020) 434-445; doi: 10.3221/igf-esis.53.34 442 experiment results prove that the model established in this paper can be well applied to evaluate the constitutive relation of coal-rock. parameters values 0k / mpa 1139.28 0 / mpa 351.84  0.25  0.8325 0 p 0.00479 m p 0.0032 c / mpa 1.49 b 2.5×10-4  3.75 0 dy 0.683 m 0.85  1.0 table 1: the values of parameter involved in the proposed model figure 8: the theoretical and experimental results of deviatoric stress 1 3 − versus axial strain 1 curve when the confining pressure is 0 mpa. y.d. shou et alii, frattura ed integrità strutturale, 53 (2020) 434-445; doi: 10.3221/igf-esis.53.34 443 figure 9: the theoretical and experimental results of deviatoric stress 1 3 − versus axial strain 1 and transverse strain 3 curve when the confining pressure is 5 mpa. figure 10: the theoretical and experimental results of deviatoric stress 1 3 − versus axial strain 1 and transverse strain 3 curve when the confining pressure is 10 mpa. figure 11: the theoretical and experimental results of deviatoric stress 1 3 − versus axial strain 1 and transverse strain 3 when the confining pressure is 15 mpa. y.d. shou et alii, frattura ed integrità strutturale, 53 (2020) 434-445; doi: 10.3221/igf-esis.53.34 444 conclusion novel coupled elastoplastic damage model for coal-rock is proposed to predict the deformation and potential disaster in coal mining. the conditions of small deformation and thermodynamic potential are considered, as well as the coupling of damage evolution process with the plastic deformation and the plastic hardening of coal-rock. based on the theory of damage mechanics, the formulas of damage evolution, plastic yield and plastic potential of coal-rock are deduced theoretically. in addition, triaxial compression tests of coal-rock under four confining stresses of 0mpa, 5 mpa, 10 mpa and 15 mpa are conducted to reveal the law of deviatoric stress and strain. based on the experimental data, the control parameters of the coupled elastoplastic damage model of coal-rock are determined. the theoretical results obtained from the coupled elastoplastic damage model for coal-rock agree well with those from the experiment. the proposed model is reasonable to predict the deformation of coal-rock. acknowledgments he work is supported by the national natural science foundation of china (nos. 41807251, 51809198 and 51839009), and the fundamental research funds for the central universities (grant no. 2042019kf0037). references [1] zhou, x.p., zhang, j.z. and wong, l.n.y. (2018). experimental study on the growth, coalescence and wrapping behaviors of 3d cross-embedded flaws under uniaxial compression, rock mech. rock eng., 51(5), pp. 1379-1400. doi: 10.1007/s00603-018-1406-4. [2] zhou, x.p., zhang, j.z., qian, q.h and niu, y. (2019). experimental investigation of progressive cracking processes in granite under uniaxial loading using digital imaging and ae techniques, j. struct. geol., 126, pp. 129-145. doi: 10.1016/j.jsg.2019.06.003. [3] liu, x.s., tan, y.l., ning, j.g., lu, y.w. and gu, q.h. (2018). mechanical properties and damage constitutive model of coal in coal-rock combined body, int. j. rock mech. min. sci., 110, pp. 140-150. doi: 10.1016/j.ijrmms.2018.07.020. [4] poulsen, b.a., shen, b., williams, d.j., huddlestone-holmes, c., erarslan, n. and qin, j. (2014). strength reduction on saturation of coal and coal measures rocks with implications for coal pillar strength, int. j. rock mech. min. sci., 71, pp. 41-52. doi: 10.1016/j.ijrmms.2014.06.012. [5] bertuzzi, r., douglas, k. and mostyn, g. (2016). an approach to model the strength of coal pillars, int. j. rock mech. min. sci. 89, pp. 165-175. doi: 10.1016/j.ijrmms.2016.09.003. [6] yang, x.b. xia, y.j. and wang, x.j. (2012). investigation into the nonlinear damage model of coal containing gas, safety sci., 50, pp. 927-930. doi: 10.1016/j.ssci.2011.08.001. [7] li, y.w., long, m., zuo, l.h., li, w. and zhao, w.c. (2019). brittleness evaluation of coal based on statistical damage and energy evolution theory, j. petrol. sci. eng., 172, pp. 753-763. doi: 10.1016/j.petrol.2018.08.069. [8] wu, c., dou, l.m., ju, y., cao, w.z., yuan, s.s. and si, g.y. (2018). a plastic strain-based damage model for heterogeneous coal using cohesion and dilation angle, int. j. rock mech. min. sci., 110, pp. 151-160. doi: 10.1016/j.ijrmms.2018.08.001. [9] shao, j.f., jia, y., kondo, d. and chiarelli, a.s. (2006). a coupled elastoplastic damage model for semi-brittle materials and extension to unsaturated conditions, mech. mater., 38, pp. 218-232. doi: 10.1016/j.mechmat.2005.07.002. [10] zhou, x.p. (2004). analysis of the localization of deformation and the complete stress–strain relation for mesoscopic heterogeneous brittle rock under dynamic uniaxial tensile loading, int. j. solids struct., 41(5-6), pp. 1725-1738. doi: 10.1016/j.ijsolstr.2003.07.007. [11] zhou, x.p., ha, q.l., zhang, y.x. and zhu, k.s. (2004). analysis of deformation localization and the complete stress– strain relation for brittle rock subjected to dynamic compressive loads, int. j. rock mech. min. sci., 41(2), pp. 311-319. doi: 10.1016/s1365-1609(03)00094-7. [12] shao, j.f., lu, y.f. and lydzba, d. (2004). damage modeling of saturated rocks in drained and undrained conditions, j. eng. mech., 130(6), pp. 733-740. doi: 10.1061/(asce)0733-9399(2004)130:6(733). a t y.d. shou et alii, frattura ed integrità strutturale, 53 (2020) 434-445; doi: 10.3221/igf-esis.53.34 445 [13] zhou, x.p. cheng, h. and feng, y.f. (2014). an experimental study of crack coalescence behaviour in rock-like materials containing multiple flaws under uniaxial compression, rock mech. rock eng., 47 (6), pp. 1961-1986. doi: 10.1007/s00603-013-0511-7. [14] chow, c.l. and june, w. (1987). an anisotropic theory of elasticity for continuum damage mechanics, int. j. fracture, 33, pp. 3-16. doi: 10.1007/bf00034895. [15] zhou, x.p. and yang, h.q. (2007). micromechanical modeling of dynamic compressive responses of mesoscopic heterogenous brittle rock, theo. appl. fract. mech., 48(1), pp. 1-20. doi: 10.1016/j.tafmec.2007.04.008. [16] zhou, x.p. (2005). triaxial compressive behavior of rock with mesoscopic heterogenous behavior: strain energy density factor approach, theo. appl. fract. mech., 45(1), pp. 46-63. doi: 10.1016/j.tafmec.2005.11.002. [17] zhou, x.p. (2005). localization of deformation and stress-strain relation for mesoscopic heterogeneous brittle rock materials under unloading, theo. appl. fract. mech., 44(1), pp. 27-43. doi: 10.1016/j.tafmec.2005.05.003. [18] zhang, j.x. wong, t.f. and davis, d.m. (1990). micromechanics of pressured-induced grain crushing in porous rocks, j. geophy. res., 95, pp. 341-351. doi: 10.1029/jb095ib01p00341. [19] budiansky, b. and o’connell, r.j. (1976). elastic moduli of a cracked solid, int. j. solids struct., 12, pp. 81-97. doi: 10.1016/0020-7683(76)90044-5. [20] zhou, x.p. zhang, y.x., ha, q.l. and zhu, k.s. (2008). micromechanical modelling of the complete stress-strain relationship for crack weakened rock subjected to compressive loading. rock mech. rock eng., 41(5), pp. 747-769. doi: 10.1007/s00603-007-0130-2. [21] horii, h. and nemat-nasser, s. (1983). overall moduli of solids with microcracks: load-induced anisotropy, j. mech. phys. solids, 31, pp. 155-171. doi: 10.1016/0022-5096(83)90048-0. [22] zhou, x.p. and wang, j.h. (2005). study on the coalescence mechanism of splitting failure of crack-weakened rock subjected to compressive loads, mech. res. commun., 32(2), pp. 161-171. doi: 10.1016/j.mechrescom.2004.06.003. [23] hashin, z. (1988). the differential scheme and its application to cracked materials, j. mech. phys. solids, 36, pp. 719734. doi: 10.1016/0022-5096(88)90005-1. [24] aboudi, j. and benveniste, y. (1987). the effective moduli of cracked bodies in plane deformations, eng. fract. mech., 26(2), pp. 171-184. doi: 10.1016/0013-7944(87)90195-0. [25] zhang, s.x. and xiao, h.y. (2000). study of the pore and micro fracture of the coal reservoirs in the sem. j. chin. electron. microsc. soc., 19(4), pp. 531-532. doi: 10.3969/j.issn.1000-6281.2000.04.070. [26] nemat-nasser, s. and hori, m. (1993). micromechanics: overall properties of heterogeneous materials, north-holland, amsterdam. doi: 10.1115/1.2788912. [27] krajcinovic, d. (1996). damage mechanics, north-holland, amsterdam, the netherlands. doi: 10.1016/s01675931(06)x8062-2. [28] pensee, v., kondo, d. and dormieux, l. (2002). micromechanical analysis of anisotropic damage in brittle materials, j. eng. mech., 128(8), pp. 889-897. doi: 10.1061/(asce)0733-9399(2002)128:8(889). [29] zhou, x.p. shou, y.d., qian, q.h. and yu, m.h. (2014). three-dimensional nonlinear strength criterion for rock-like materials based on the micromechanical method, int. j. rock mech. min. sci., 72, pp. 54-60. doi: 10.1016/j.ijrmms.2014.08.013. [30] chiarelli, a.s. (2000). experimental investigation and constitutive modelling of coupled elastoplastic damage in hard argillites, doctoral thesis, university of lille. [31] pietruszczak, s., jiang, j. and mirza, f.a. (1988). an elastoplastic constitutive model for concrete, int. j. solids struct., 24(7), pp. 705-722. doi: 10.1016/0020-7683(88)90018-2. shot peening processes to obtain nanocrystalline surfaces in metal alloys: s. zhao et alii, frattura ed integrità strutturale, 41 (2017) 412-423; doi: 10.3221/igf-esis.41.52 412 an experimental study on mechanical properties of fiber-reinforced concrete of energy piles songying zhao, lei chen college of municipal and environmental engineering, jilin jianzhu university, china coffeezsy@163.com, 7796549@qq.com yan fu the first construction engineering limited company of china construction third engineering bureau, china moonfuyan@foxmail.com abstract. the technology of energy piles for heat storage involves turning the concrete piles buried beneath the ground into a part of the ground-source heat pump system and burying the heat-transfer tubes in the foundation piles, which are regarded as heat transfer wells. the heat transfer tubes are embedded in the concrete foundation piles, destroying the mechanical bearing capacity of the piles and damaging the safety of the buildings. thus, considering the structural stability and the degree of heat transfer of concrete piles, as well as the selection of material for the foundation piles, the mixing ratio of the material of the energy piles is experimentally studied by the orthogonal method. the optimum mixing ratio of the energy pile is thus obtained. a concrete test block is used to conduct a static load test and splitting test to verify the mixing ratio of the concrete of the energy pile. the results show that steel fiber can be used to enhance the bearing capacity of the storage pile as a reinforcement material. under a reasonable ratio, the reinforced pile can absolutely meet the original design requirements. ordinary portland cement or composite portland cement can be used as cementitious materials for energy piles. through an experiment, it is proved that the composite portland cement can better meet the requirements of the concrete foundation piles than the cementitious material. as thermal conductivity materials, the addition of industrial graphite and scrap copper slag can improve the thermal conductivity of the pile, but it can also reduce the mechanical properties of the pile. it is necessary to control it in a certain range and not to add a large amount of graphite just to improve the thermal conductivity. keywords. energy pile; mixing ratio; fiber-reinforced material. citation: zhao, s., chen, l., fu, y., an experimental study on mechanical properties of fiber-reinforced concrete of energy piles, frattura ed integrità strutturale, 41 (2017) 412-423. received: 14.03.2017 accepted: 23.05.2017 published: 01.07.2017 copyright: © 2017 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. mailto:7796549@qq.com mailto:moonfuyan@foxmail.com s. zhao et alii, frattura ed integrità strutturale, 41 (2017) 412-423; doi: 10.3221/igf-esis.41.53 413 research on fiber-reinforced concrete of energy piles principles of material selection ig. 1 shows the load-strain curve of the non-tube pile and fig. 2 shows the load-strain curve of the buried pipes in the pile. it can be seen from the figures that if a heat transfer tube is buried in the pile, the concrete pile in the vicinity of the heat transfer tube is damaged more seriously, and the distribution of cracks is also very uneven, which indicates that after the heat transfer tube is buried, the compressive bearing capacity of the concrete pile foundation decreases greatly. after the heat transfer tube is buried in the pile foundation, the distribution of the strain curve of the pile is greatly changed, and the strain variation of the steel and the concrete is increased, which is more likely to cause the concrete pile to break [1-6]. figure 1: load-strain curve of the non-tube pile. figure 2: load-strain curve of the buried tubes in the pile. in addition, since the heat transfer tubes embedded in the concrete piles are to conduct the heat storage, a large amount of heat is stored in the energy piles, causing heat accumulation, which in turn causes the temperature of the center of the concrete piles to rise. when the concrete temperature rises to 100 ℃, the internal free water begins to evaporate, and the chemical composition and physical structure of the concrete will change to about 500 ℃ [7-10]. due to the decomposition of ca (oh) 2 leading to the concrete cracking, the concrete pile needs to remain at a high temperature to have favorable mechanical stability. meanwhile, the expansion coefficient of the concrete materials is required to be as close to the expansion coefficient of the material of the heat transfer tube, so that it can effectively reduce the presence of an air film to avoid the unfavorable thermal conductivity of the pile. based on the analysis above, it is required that the selection of the concrete material of energy piles should meet the following conditions: firstly, the pile foundation of the building can still have stable mechanical properties at high temperature; secondly, the material of the pile foundation should have good thermal conductivity, so that the heat exchange can be conducted completely between the energy pile and soil; thirdly, the thermal expansion coefficient values of the heat transfer tubes and the concrete should be the same if possible to ensure that the heat transfer tubes and the concrete are tightly integrated without an air film, which would affect the thermal effect [11-15]. choosing raw material the main materials referred to in connection with the energy piles contain cement binders, aggregate, fiber, admixtures, and so on. kind of cement: composite portland cement. type of coarse aggregate: basalt gravel with a density of 2.6×103kg/m3. type of fine aggregate: natural sand; its modular and density are 2.6 and 2.55×103kg/m3 respectively, its moisture content is 5%. type of fiber: the fiber-reinforced material mentioned here refers to steel fiber, whose length is 30-40 mm and whose tensile strength is 4500 mpa. type of material for storing heat: graphite and copper slag have a better thermal conductivity and the density of the graphite and copper slag in this experiment is 1.8×103kg/m3 and 3.3×103kg/m3 respectively. f s. zhao et alii, frattura ed integrità strutturale, 41 (2017) 412-423; doi: 10.3221/igf-esis.41.52 414 experimental study on mechanical properties of test piece of fiber-reinforced concrete in this study, the compressive strength and anti-splitting strength of the test blocks are investigated by using the mixing ratio of the material in the concrete of the energy pile. the contents of fiber, graphite, copper slag, and fine aggregate are taken as the main factors, of which each factor is divided into three levels. this can be seen in tab. 1. factor level a carbon (steel) fibers (v%) b graphite(kg/m3) c copper slag (v%) d fine aggregate (v%) 1 2 3 0.0 (0.0) 0.25 (0.5) 0.5 (1.0) 0.0 1.0 2.0 0.0 2.0 4.0 0.0 2.0 4.0 table 1: factors and levels. according to the factors and the levels, an l9 (34) orthogonal table is used, and the corresponding quality of each factor is determined to obtain orthogonal tests seen in tab. 2. columns no. test no. a carbon (steel) fibers(g) b graphite(g) c ordinary (composite) copper slag (g) d ordinary (composite) fine aggregate (g) 1 0(0) 0 0(0) 5.64(5.34) 2 3 0(0) 0(0) 0.84 16.8 138.3(131.2) 276.5(262.4) 5.53(5.20) 5.42(5.07) 4 37.8(372.6) 0 138.3(131.2) 5.53(5.20) 5 37.8(372.6) 0.84 276.5(262.4) 5.42(5.07) 6 37.8(372.6) 16.8 0(0) 5.64(5.34) 7 75.6(655.2) 0 276.5(262.4) 5.42(5.07) 8 75.6(655.2) 0.84 0(0) 5.64(5.34) 9 75.6(655.2) 16.8 138.3(131.2) 5.53(5.20) table 2: orthogonal test table. in the table, ordinary refers to ordinary portland cement and composite means composite portland cement. in this test, 2.97 kg of the ordinary portland cement are used together with 1.78 kg of water. moreover, 3.86 kg of composite portland cement are mixed with 1.78 kg of water. experiment on mechanical properties of the concrete and results analysis in accordance with the mixing ratio of the material in tab. 2, 36 groups of test blocks of different mixing ratios are made. each group with the same mixing ratio includes 6 blocks, which means 216 blocks are made in this experiment, which are to be used for the compressive strength and the anti-splitting experiments. the test results of the compressive strength are recorded in tab. 3. figs. 3 and 4 show the relationship between the factors, the levels, and the k values in the compressive strength test when the ordinary portland cement is used as the cementitious material and the carbon fiber and the steel fiber are selected as the fiber material. according to the conventional analysis of the orthogonal test, it can be seen that a is the carbon (steel) fiber, b is the graphite, and c is the scrap copper slag. in the course of the test, with the amount of these three materials increasing, the corresponding curves of the pile strength of k1, k2, and k3 can be seen in the figures. in fig. 3, in the case of a, for example, when the amount of fiber is increasing, the pile strength k1 to k3 are is gradually reduced, and it can be concluded that when the content of this fiber increases, the compressive strength of the concrete is negatively impacted, and tends to decrease; the amount of b has little effect on the strength of the test blocks, and the strength slightly increases at level 3. in fig. 4, it can be intuitive to seen that when the ordinary portland cement is selected as the cementitious material, combined with the steel fiber in the reinforced experimental group, the strength does not significantly decrease when the steel fiber content increases, but slightly improves. according to the data, we can s. zhao et alii, frattura ed integrità strutturale, 41 (2017) 412-423; doi: 10.3221/igf-esis.41.53 415 see that the content of graphite in this experiment is the biggest factor affecting the strength, followed by scrap copper slag. numbering carbon fiber compressive strength test results (mpa) steel fiber compressive strength test results(mpa) ordinary portland cement composite portland cement ordinary portland cement composite portland cement 1 19.77 22.52 19.77 22.52 2 20.23 21.73 20.23 21.73 3 21.59 21.88 21.59 21.88 4 18.49 22.93 23.31 27.14 5 17.33 20.28 15.31 28.67 6 16.31 19.70 20.85 26.04 7 13.25 16.11 19.91 26.99 8 13.82 20.66 15.97 27.48 9 16.32 16.82 23.08 25.36 table 3: test results of the compressive strength. figure 3: relationship between the factors, the levels, and the k values (carbon fiber). figure 4: relationship between the factors, the levels, and the k values (steel fiber). fig. 5 and fig. 6 show the relationship between the factors, the levels, and the k values in the compressive strength test when the composite portland cement is selected as the cementitious material, and carbon fiber and steel fiber are selected as the fiber materials. it can be intuitively seen from fig. 5 that when the composite portland cement is selected as the cementitious material, combined with the carbon fiber in the reinforced experimental group, the strength decreases slightly when the content of the carbon fiber increases., meanwhile, the content of the carbon fiber impacts has a large impact on the concrete's strength largely, followed by the scrap copper slag, and the graphite has the smallest impact. fig. 6 can be analyzed illustrates that when the content of the steel fiber is increased, the strength of the test block increases significantly. the amount of the steel fiber greatly affects the concrete strength largely, followed by the graphite, and the scrap copper slag has the smallest impact. tab. 4 shows the measured values of the anti-splitting strength of different material mixing ratios. s. zhao et alii, frattura ed integrità strutturale, 41 (2017) 412-423; doi: 10.3221/igf-esis.41.52 416 figure 5: relationship between the factors, the levels, and the k values (carbon fiber). figure 6: relationship between the factors, the levels, and the k values (steel fiber). numbering carbon fiber compressive strength test results (mpa) steel fiber compressive strength test results(mpa) ordinary portland cement composite portland cement ordinary portland cement composite portland cement 1 41.54 50.16 41.54 50.16 2 42.72 47.91 42.72 47.91 3 43.45 46.70 43.45 46.70 4 50.81 43.64 56.42 45.10 5 40.30 38.34 37.84 56.72 6 40.25 37.26 34.26 53.42 7 43.57 40.56 40.70 47.40 8 40.73 48.24 34.75 56.14 9 43.10 46.60 36.89 54.42 table 4: anti-splitting test results. figure 7: relationship between factors, levels, and k values (carbon fiber). figure 8: relationship between factors, levels, and k values (steel fiber). s. zhao et alii, frattura ed integrità strutturale, 41 (2017) 412-423; doi: 10.3221/igf-esis.41.53 417 fig. 7 and fig. 8 show the relationship between the factors, the levels, and the k values of the anti-splitting test when the ordinary portland cement is selected as the cementitious material and the carbon fiber and the steel fiber are selected as the fiber materials. it can be seen from fig. 7 that the splitting strength clearly increases obviously when the content of the carbon fiber increases, and it declines when the content of the carbon exceeds a certain amount. meanwhile, the content of the carbon fiber greatly affects the splitting strength of the concrete largely, followed by the graphite, and the scrap copper slag has the smallest impact. as can be analyzed concluded from fig. 8, when the ordinary portland cement is selected as the cementitious material, mixed with steel fiber in the splitting test group, with the amount of steel fiber increasing, the anti-splitting strength of the test block is basically even. according to the data in the figures, the content of graphite in this experiment is the biggest factor affecting the strength, followed by scrap copper slag. fig. 9 and fig. 10 show the relationship between the factors, levels, and k values in the anti-splitting test when the composite portland cement is selected as the cementitious material, and the carbon fiber and the steel fiber are selected as the fiber materials. it can be seen from fig. 9 that the strength of the test block decreases slightly when the content of the carbon fiber increases, but it increases when the content of carbon exceeds a certain amount. it can be seen from fig. 10 that the strength of the anti-splitting increases significantly when the content of the steel fiber increases, and the amount of the steel fiber greatly affects the concrete's strength largely. figure 9: relationship between factors, levels, and k values (carbon fiber). figure 10: relationship between factors, levels, and k values (steel fiber). when comparing the compression process of the test blocks, it can be found that the pressure value of the concrete piece with carbon fiber under the pressure of the pressure testing machine of the concrete suddenly decreases, but the integrity of the test block is good. under the pressure of the concrete pressure testing machine, the changes of in the compressive strength of the test block with steel fiber reflect are more uniform. however, after the test piece is damaged due to the pressure, the surface of the test block is more seriously damaged, as is shown in fig. 11. (a) ordinary concrete (b) concrete with carbon fiber (c) concrete with steel fiber figure 11: damage situation of the two different test blocks after the pressure test as can be seen from fig. 11, (a) the compressive process of the ordinary concrete is clearer, and the pressure value decreases uniformly before the destruction, in line with the general law of the damage of the ordinary concrete; (b) the s. zhao et alii, frattura ed integrità strutturale, 41 (2017) 412-423; doi: 10.3221/igf-esis.41.52 418 concrete test block with the addition of carbon fiber cannot have better dispersion of the fiber in the mixing process, and the strength of the test block compared with the test block of ordinary concrete test block decreases significantly, the pressure value gets shows a rapid decline after reaching a certain point during the compressive process, but the test block body does not get suffer obviously damaged, retaining the its original shape well; (c) compared with the ordinary concrete, the strength of the steel fiber concrete is obviously improved, but the damage is more thorough and the damage interface is clearer from the macro observation. from the analysis of the test data, it can be seen that the compressive strength and anti-splitting strength of the test blocks in the fifth group of materials are the largest in the orthogonal tests. that is, the composite portland cement is used as the cementitious material, and the steel fiber is used as the reinforcement material. the ratio of the composition in each 20 kg of concrete can be seen in tab. 5. no. combination steel fiber(g) graphite (g) copper slag(g) fine aggregate(kg) coarse aggregate(kg) cementations materials(kg) water (kg) 5 a2b2c3d1 372.6 8.4 262.4 5.07 9.02 3.86 1.78 table 5: proportion optimization table experimental research on mechanical properties of the energy piles hrough the experimental ratio obtained by orthogonal experiments as well as the actual mixing process of each group, the composite portland cement with steel fiber is selected to carry out the experiment with buried pipes in the piles, so as to further obtain the actual property indexes of the fiberreinforced concrete of the energy piles. test plan the test of mechanical properties of the energy piles is to involves testing the compressive strength of the pile body mainly through the static loading test of a pile. the heat-transfer tubes are supposed to be embedded in the energy piles, greatly weakening the vertical load of the foundation piles. this test is to verify the strength of the material of the energy piles so as to verify the correctness of the optimal ratio by conducting the pile loading without lateral force towards the energy piles through the compressive strength data and the damage mode of the piles. figure 12: hydraulic pressure testing machine. figure 13: preparation before the pile pile's static pressure. in this test, three groups of concrete test piles are made and three identical concrete piles are made in for each set group. so, there are nnine concrete piles are shared total in the test. as the standard pieces, the first group of the three concrete piles is the reinforced concrete piles with a normal ratio of material without reinforced fibers or embedded heat-transfer tubes. the second group of the three concrete piles is the reinforced concrete piles with a normal ratio of material with a group of single u-type heat-transfer tubes embedded in the piles, whose material is fits the ppr profile. the third group of the three piles is the energy piles whose material ratio is a2b2c3d1, with a group of single u-type heat-transfer tubes embedded in the piles, whose material is fits the ppr profile. the sizes of the test piles are that they have a diameter of t s. zhao et alii, frattura ed integrità strutturale, 41 (2017) 412-423; doi: 10.3221/igf-esis.41.53 419 piles dn=200mm, and the length of the piles is 600 mm. the test piles adopt the concrete c30, the six main bars adopt the first-class steel bar whose diameter is φ8, the stirrup is made of wire no.8@200mm, the thickness of the protective layer of the concrete is 50 mm, the diameter of the heat-transfer tubes pre-embedded in the piles is dn=30mm , and the single u-shaped plastic pipes. the material ratio of the concrete piles in each group is shown in tab. 6, fig. 12 refers to the hydraulic pressure testing machine, and fig. 13 shows the preparation before the pile's static pressure. no. combination steel fiber(g) graphite (g) copper slag(g) fine aggregate (kg) coarse aggregate (kg) cementitious materials(kg) water (kg) 1 first group 0 0 0 16.02 27.06 11.58 5.34 2 second group 0 0 0 16.02 27.06 11.58 5.34 3 third group 1117.8 25.2 787.2 15.21 27.06 11.58 5.34 table 6: material ratios of the test piles. test results and the analysis the ultimate strength in of the three groups should be recorded respectively separately as collected in tab. 7 when the foundation pile load is put on the upper part of the pile until the pile body is damaged, and fig. 14 shows the damage situation of the foundation pile. category no. group 1 group 2 group 3 strength of the test pieces(kn) 1 375 311 382 2 361 300 396 3 345 285 373 table 7: ultimate strength of the test piles (kn). (a) (b) (c) (d) figure 14: damage situation of the pile body: (a) the end face of the pile with non-steelfiber embedded pipes; (b) non-steelfiber pile without embedded pipes; (c) end face of the reinforced pile with steel fiber embedded pipes; (d) reinforced pile body with steel fiber embedded pipes. fig. 14 shows the situation when the load is put on the upper part of the piles until the piles are damaged. the pile in diagram a is a pile for burying the heat transfer tubes in the reinforced concrete piles. as can be seen from the damage, there are irregular cracks on the surrounding heat transfer tubes which are to be embedded, indicating that when the vertical load is carried out on the pile, the bearing capacity of the pile is affected due to by the irregular damage caused by reasons for the addition of the heat transfer tubes. the pile in diagram b is the reinforced concrete pile under normal perfusion. the pile body is damaged due to the vertical load on it. under the action of after the hydraulic pressure testing machine has been applied, cracks appear on the upper part of the concrete pile, and the concrete in the middle part of the pile breaks off, indicating that under the action of the vertical load force, the degree of the damage of to the pile is also serious. the piles in diagrams c and diagram d are the steel fiberreinforced concrete piles with single u-shaped heat transfer tubes. it can be seen from diagram c that although there are cracks on the top face of the pile, yet less but not as s. zhao et alii, frattura ed integrità strutturale, 41 (2017) 412-423; doi: 10.3221/igf-esis.41.52 420 many. moreover, no obvious cracks can be found in the vicinity of the heat transfer tubes. after the application of the vertical load, the pile also cracks, but the concrete on it does not break off as what occurs in opposed to what occurred in diagram b. fig. 15 shows the comparison between the test strength of the pile with buried pipes and the its theoretical strength. it can be seen from the figure that the theoretical strength of the second and third groups of test piles is supposed to be 97.5% of the theoretical strength of the first group. however, the test results show that the experimental strength of the second group of test piles with heat transfer tubes embedded in the concrete piles is only 47.8% of the theoretical strength. this result is far less than the result that the test strength is 58.8% of the theoretical strength in the first group of piles. the test group has a strength of 61.7% of the theoretical strength in the third group of teats piles with embedded heat transfer tubes with steel fiber. it can be verified by the experiment that the heat transfer tubes in the pile foundation can greatly reduce the compressive strength of the pile foundation, but the energy piles with the mixing ratio of a2b2c3d1 can improve the compressive strength of the pile foundation. the strength of the piles with the mixing ratio of a2b2c3d1 of the steel fiber, the heat storage material, and the thermal conductivity material will not be reduced, but improved to some extent. figure 15: comparison between the test of the pile with buried pipes and the its theoretical strength the measurement of the thermal conductivity the fourth group and the fifth group of the materials with the best compressive strength and the first group of the ordinary concrete materials are made as the test blocks to measure the thermal conductivity. the test blocks are made to be cuboid, the size of which is 0.03m × 0.1m × 0.1m. three blocks are included in each test block, with a total of nine in this test. the evaporation of water of the test block is processed in the drying oven after its steel mold is taken out. the test block is taken out of the drying oven and the thermal conductivity is measured when the quality is kept constant. the main instruments for measuring the thermal conductivity are shown in fig. 16, and the test results of the thermal conductivity are shown in tab. 8. as can be seen from tab. 8, the thermal conductivity of the test blocks in the fourth and fifth group is improved greatly. the thermal conductivity of the block in group 5 is over twice than that in group 1, and the thermal conductivity of the block in group 4 improves 1.5 times than that in group 1. the comparison of the heat storage capacity the degree of the capacity of heat storage of the material is represented as the heat storage coefficient: t c s πλρ2 = (1) in the equation, λ — the thermal conductivity of the material (w/m∙• k); ρ — density of the dry matter of the material (kg/m3); s. zhao et alii, frattura ed integrità strutturale, 41 (2017) 412-423; doi: 10.3221/igf-esis.41.53 421 c — the specific heat of the material j / (kg • k); t — time, 24 hours is set here. (a) drying oven (b) thermal conductivity tester figure 16: main instruments for measuring the thermal conductivity group thermal conductivity(w/m.k) group 1 1.85 group 4 2.81 group 5 4.41 table 8: test results of thermal conductivity the specific heat capacity of the concrete is: ∑ ∑= i ii p w cw c (2) in the equation, cp — the specific heat capacity of the concrete j / (kg • k) wi — mass fraction of different parts ci — specific heat capacity of different parts the specific heat capacity of different kinds of raw materials is: the specific heat capacity of the water is 4.186 ×103 j / (kg • k); the specific heat capacity of the cement is 900 j / (kg • k); the specific heat capacity of the fine aggregate is 920 j / (kg • k); the specific heat capacity of the coarse aggregate is 850 j / (kg • k); the specific heat capacity of the steel is 450 j / (kg • k); the specific heat capacity of the graphite is 710 j / (kg • k); the specific heat capacity of the copper slag is 1060 j / (kg • k). it can be seen through calculation that the specific heat capacity of the first group of ordinary concretes is 1.175 ×103 j / (kg • k), the specific heat capacity of the fourth group of the mixing material is 1.182 ×103 j / (kg • k), the specific heat capacity of the fifth group of the mixing material a2b2c3d1 is 1.172 ×103 j / (kg • k). with formula 1 added, it can be seen that the heat storage coefficient of the first group of materials is 19.3 w / (m2 • k), the thermal storage coefficient of the fourth group of materials is 24.47 w / (m2 • k), and the heat storage coefficient of the fifth group of materials is 30.6 w / (m2 • k). that is to say, the thermal storage capacity of the energy pile using a mixing ratio of a2b2c3d1 is 1.6 times than that of the ordinary reinforced concrete pile, whose effect of heat storage is relatively better. conclusion . based on the mixing ratio of the material of the energy piles through the orthogonal test, the test piles made of the composite portland cement with steel fiber are made, and the tests of the mechanical properties of the pile foundation are conducted to get the following conclusions: 1 s. zhao et alii, frattura ed integrità strutturale, 41 (2017) 412-423; doi: 10.3221/igf-esis.41.52 422 2. the concrete test blocks with the addition of carbon fiber cannot have a good dispersion of the fiber in the mixing process, and the strength of the test blocks compared with that of the test blocks with containing ordinary concrete decreases significantly. the pressure value gets a decline rapidly decline after reaching a certain point during the compressive process, but the test blocks do not reflect obvious damage, and retaining their original shape. compared with the strength of the ordinary concrete, the strength of the steel fiberreinforced concrete increases significantly. but from a macroscopic observation, the destruction of the steel fiber concrete is more thorough, and the damage interface is relatively clear. 3. as the thermal conductivity materials, the addition of the industrial graphite and the scrap copper slag can improve the thermal conductivity of the pile, but it can also reduce the mechanical properties of the pile. it is necessary to control the amount within a certain range. it is infeasible not feasible to add too much graphite just to improve the thermal conductivity of the pile. 4. from an analysis of the experimental data analysis, the bestexperimental program performing test group can be determined, which is the no. 5 test group with composite portland cement selected as the cementitious material, and steel fiber as the reinforcement material, that is to say, the material. the material mixing ratio of the energy pile after optimization isa2b2c3d1. 5. the a static loading test is carried out towards on the three test piles. the results show that the effect of the heat transfer tubes on the compressive strength of the pile is far greater than the its theoretical influence. from according to the theoretical calculations data, the strength of the second group of test piles shall should be 97.5% of that of the first group of test piles. while meanwhile in the static loading test, the strength of the second group of test piles is 80.7% of that of the first group of test piles. for the third group of piles with steel fiber, the result shows that the test strength of the piles in the third group is not only decreased, but also slightly improved, so as to which verifies the correctness of the material mixing ratio a2b2c3d1. 6. the thermal conductivity of the test blocks in the fourth and fifth group is improved greatly. the thermal conductivity of the block in group 5 is over twice than that in group 1; the heat storage coefficient of the first group of materials is 19.3 w / (m2 • k), the heat storage coefficient of the fifth group of materials is 30.6 w / (m2 • k). that is to say, the thermal storage capacity of the energy pile using a mixing ratio of a2b2c3d1 is 1.6 times than that of the ordinary reinforced concrete pile, whose effect of heat storage is relatively better. acknowledgments his work was supported by the national natural science foundation of china (grant no.51606084); ji lin sheng jiao yu ting science and technology research [2016] (grant no. 149); ji lin sheng ke ji ting qingnian science and technology research [2016] (grant no. 20160520028jh); zhu jian bu science and technology research [2016] (grant no. 2016-k1-30). references [1] denis, m., philippe, p., the effect of borehole inclination on fluid and ground temperature for glhe systems, geothermic, 38(4) (2009) 392-398. [2] zhan, n.y., xu, p.w., influence of building envelop on natural convection and heat transfer when con sidering indoor heat transfer and radiation coupled in natural convection, acta energiyae solaris sinica, 32(4) (2011) 501-507. [3] novoselac, a., burley, b.j., srebric, j., development of new and validation of existing convection correlations for rooms with displacement ventilation systems, energy and buildings, 38(3) (2006) 163-173. [4] franco, a., moffat, r., toledo, m., herrera, p., numerical sensitivity analysis of thermal response tests (trt) in energy piles, renewable energy, 86 (2016) 985-992. [5] caulk, r., ghazanfari, e., mccartney, j.s., parameterization of a calibrated geothermal energy pile model, geomechanics for energy and the environment, 5 (2016) 1-15. [6] brahim, t., jemni, a., a two-dimensional steady state roll heat pipe analyses for heat exchanger applications, international journal of heat and technology, 30(2) (2012) 115-119. [7] peng, x., natural ventilation and energy efficiency in building, industrial construction, 37(3) (2013) 5-9. [8] singh, s.n., flow and heat transfer studies in a double-pass counter flow solar air heater, international journal of heat and technology, 31(2) (2013) 37-42. t s. zhao et alii, frattura ed integrità strutturale, 41 (2017) 412-423; doi: 10.3221/igf-esis.41.53 423 [9] zhao, s.y., chen, c., zhan, n.y., research on the influences of insulation technology by plastic greenhouses on working temperature in aeration tanks in cold areas in winter, international journal of heat and technology, 32(1) (2015) 183-188. [10] bensenouci, a., benchatti, a., a bounif a., medjelledi, a., study of the energy efficiency in building house using the doe-2e and ee4 softwares simulation, international journal of heat and technology, 27(2) (2009) 57-63. [11] brandl, h., energy foundations and other thermo-active ground structures, geotechnique, 56(2) (2006) 81-122. [12] go, g.h., lee, s.r., yoon, s., kang, h.b., design of spiral coil phc energy pile considering effective borehole hermal resistance and groundwater advection effects, applied energy, 125(2) (2014) 165-178. [13] zhao, s.y., su, x.s., chen, c., chen, l., an application study on the simulative optimization of the ventilation of the existing buildings based on cfd, revista de la facultad de ingenieria, 31 (2016) 103-112. [14] pinel, p., cruickshank, c.a., beausoleil–morrison, i., wills. a., a review of available methods for seasonal storage of solar thermal energy in residential applications, renew sustain energy rev, 15(7) (2011) 3341-3359. [15] sekine, k., okar, r., hwang, s., eng, m., development of a ground-source heat pump system with ground heat exchanger utilizing the cast-in-place concrete pile foundations of buildings, ashrae transactions, 113 (2007) 558– 566. microsoft word numero_26_art_3 a. namdar et alii, frattura ed integrità strutturale, 26 (2013) 22-30; doi: 10.3221/igf-esis.26.03 22 an experimental study on flexural strength enhancement of concrete by means of small steel fibers abdoullah namdar, ideris bin zakaria, azimah bt hazeli, sayed javid azimi, abdul syukor bin abd. razak department of civil engineering & earth resources, universiti of malaysia pahang, malaysia ab_namdar@yahoo.com g. s. gopalakrishna department of earth science, university of mysore, india abstract. cost effective improvement of the mechanical performances of structural materials is an important goal in construction industry. to improve the flexural strength of plain concrete so as to reduce construction costs, the addition of fibers to the concrete mixture can be adopted. the addition of small steel fibers with different lengths and proportion have experimentally been analyzed in terms of concrete flexural strength enhancement. the main objectives of the present study are related to the evaluation of the influence of steel fibers design on the increase of concrete flexural characteristics and on the mode of failure. two types of beams have been investigated. the force level, deflection and time to failure of beams have been measured. the shear crack, flexural crack and intermediate shear-flexural crack have been studied. the steel fiber content controlled crack morphology. flexural strength and time to failure of fiber reinforce concrete could be further enhanced if, instead of smooth steel fibers, corrugated fibers were used. keywords. steel fiber; flexural strength; corrugated steel fiber; flexibility of beam; shear crack; flexural crack. introduction he fiber reinforcement concrete mix design helps to construct high quality of concrete structure. to improve concrete strength, effect of fiber distribution on flexural strength of ultra-high strength concrete has been investigated. the ultimate flexural strength and time to first crack have been affected [1]. the placing methods control fiber distribution and mechanical performance of short-fiber reinforced concrete [2, 3]. the flexural behavior include cracking, failure pattern, deflection, ductility, and flexural strength have been studied. a prediction model for the flexural strength and deflection of ultra-high strength concrete beams under bending conditions has been proposed [4]. there is an analytical solution for calculation of flexural strength of strengthened composite beams. and experimental results from literature have been employed to validate results of both the analytical and finite element method [5]. a design method has been reported on ultimate strength criteria for small steel fiber reinforced concrete (sfrc) slabs. the slabs under flexure, with longer fibers and higher fiber content provide higher energy absorption [6-7]. the splitting tensile and flexural strengths have largely been improved with increase fiber volume [8]. the ductility of concrete with synthetic fibers has been investigated for analysis flexural stress-deflection [9]. the objectives of this research work are, to investigate effect of small steel fibers on flexural strength of small beam. the length and proportion of steel fibers have been investigated. the deflection, time of stability and crack morphology of the concrete beams have been discussed. t http://dx.medra.org/10.3221/igf-esis.26.03&auth=true http://www.gruppofrattura.it a. namdar et alii, frattura ed integrità strutturale, 26 (2013) 22-30; doi: 10.3221/igf-esis.26.03 23 experimental set-up he small steel fiber has been mixed with plain concrete. the beam b1 made with100 mm × 100 mm ×500 mm dimensions. length of small steel fiber 10 mm, 20 mm, 30 mm, 40 mm and 50 mm has been varied. the quantity of small steel fiber 0.5% and 1% weight of concrete has been selected (fig. 1-2). figure 1: beam b1, steel fiber shown in surface of beam. figure 2: steel fiber. preparation procedure of specimens rdinary portland cement (opc), sand, coarse aggregate and water have been used for casting plain concrete. small smooth steel fiber of 0.5% & 1.0% has been mixed with plain concrete (fig. 2-3 and tab. 1). after curing the flexural strength and crack morphology of concrete beams have been investigated. the plain concrete cube with dimensions of 100 (mm) × 100 (mm) × 100 (mm) has been made and tested, the results show 28.51 (n/mm2) stress and strain of 0.01488 %, this is as predicted during the design stage (fig. 4-5). the plain concrete has been designed for sustain stress of 40 (n/mm2) on 28 days. the compressive strength of specimen reached to 70% of design on 14 days. the result is acceptable according to aci standard. figure 3: basic materials of concrete. t o http://dx.medra.org/10.3221/igf-esis.26.03&auth=true http://www.gruppofrattura.it a. namdar et alii, frattura ed integrità strutturale, 26 (2013) 22-30; doi: 10.3221/igf-esis.26.03 24 ingredients amount (kg/m³) grade 40 w/c ratio 0.47 mix water 92.73 cement (portland) 198 fine aggregate (sand) 320.76 coarse aggregate (max: 20mm) 593.9 table 1: proportion of materials for concrete grade 40. figure 4: stress-strain curve of plain concrete on 14 days. figure 5: deflection testing equipment for testing beam b1 (part a) and same equipment used to measured compressive strength of plain concrete cube (part b). method of concrete mixing he plain concrete has been produced by using conventional method. in order to make good plain concrete, first the water has been dropped in mixer and subsequently cement has been added to the water and mixture has been continued until the cement paste has been made, then all aggregates have uniformly been mixed, and mixer has been stopped. the fiber has been added at final step. the linearly distribution of fiber is critical part of this method. the steel fiber in surface of beam is shown in fig. 1. concrete-steel fiber mixture needs to be done carefully to ensure the steel t http://dx.medra.org/10.3221/igf-esis.26.03&auth=true http://www.gruppofrattura.it a. namdar et alii, frattura ed integrità strutturale, 26 (2013) 22-30; doi: 10.3221/igf-esis.26.03 25 fiber has uniformly been distributed. the fiber reinforced concrete has been poured into mould. for vibration of specimens, the vibration tab. has been used. the specimens have been covered by using wet sack about 24 hours. after 24 hours the concrete beams have been demoulded. the concrete beams have been kept at water 30 ± 5 ̊c for 14 days. experimental procedure he supporting loading rollers, specimen and bearing surfaces have been cleaned. the specimens have been weighed and marked then placed in the machine in right angle to the rollers. in beam b1 and b2 the strain gauges have been installed on one third of end at each side of beam. the maximum applied force, stroke and time to failure of beams have been recorded by using strain gauges. the load has been applied to beam steadily without shock. the rate of loading has been maintained in constant level until failure of beam. the types of failure mode and crack have been recorded. results and discussion he results indicate that the flexure strength of beam b1 (made up with non-fiber reinforcement concrete) is 3.932 n/mm2. tab. 2 and fig. 6 illustrate flexure strength of beam b1 (made up with fiber reinforcement concrete). the results show, for this type of fiber reinforcement concrete beam the best length of steel fiber is 50 mm. the economical proportion of steel fiber is 0.5%. increase steel fiber length maybe result in better product. figure 6: steel length (mm) vs 14 days stress (n/mm2). sl no length of fiber 14 days stress (mpa) used 0.5% steel fiber 14 days stress (mpa) used 1% steel fiber 1 10 4.033 3.831 2 20 4.099 4.685 3 30 4.370 4.940 4 40 4.768 4.979 5 50 5.218 5.218 table 2: flexure strength of reinforced concrete beam mode of failure and steel fiber mixture design ffect of steel fiber on flexural strength, time of stability, failure mode, force applicability, and crack morphology of a concrete beam needs to investigate. in this research work, effect of shape and surface roughness of steel fiber on concrete beam has not been investigated. the second types of beam namely b2 with dimensions of 150 (mm) t t e http://dx.medra.org/10.3221/igf-esis.26.03&auth=true http://www.gruppofrattura.it a. namdar et alii, frattura ed integrità strutturale, 26 (2013) 22-30; doi: 10.3221/igf-esis.26.03 26 × 150 (mm) × 1000 (mm) has been designed. the proportion of steel fiber for beam b1 0.5% and 1%, and for beam b2 1% of weight of concrete beam have been proposed (tab. 3). sl. no l.f (mm) w.f %.f w.f %.f w.f %.f beam b1 content 0.5% fiber beam b1 content 1% fiber beam b2 content 1% fiber 1 10 4.08 6.67 8.15 6.67 20 3.64 2 20 8.15 13.33 16.30 13.33 30 5.45 3 30 12.23 20.00 24.45 20.00 100 18.18 4 40 16.30 26.66 32.60 26.67 150 27.27 5 50 20.38 33.33 40.75 33.33 250 45.45 table 3: steel fiber mixture design for beam b2. the fig. 7 shows strain gauges installed on concrete beam. strain gauges have been measured applied force on concrete beam, stroke and time of stability of concrete beam. the cracking pattern at failure shows in fig. 8-9 for beams b1. the beams failed in the flexural-tension mode. if proportion of steel fiber increases to 1% the type of mode failure depends on harmony distribution of steel fiber. increases length of steel fiber modifies type of cracking pattern. the type and morphology of cracks have direct relationship with proportion of fiber. increases quantity of fiber, results in higher stroke before failure and improves time of stability. in beam b1 contents 0.5% fiber, failure occurs after 83 sec during applied force is 17.24 (kn) with stroke of 0.67 mm. in beam b1 contents 0.1% fiber, failure occurs after 196 sec during applied force reaches to 27.67 (kn) with stroke of 1.61 mm. (fig. 10-13). the experimental results have been revealed, using 1% steel fiber better improves flexibility and time of stability of beam b1. the types of graph of force versus stroke and force versus time are depending on steel fiber content. addition of steel fiber to beam b1 and b2 increases time to crack of beams. the load and deflection curve diagram have been affected by the addition of fibers. the appropriate quantity of steel fiber reduces beam deformation and increases flexural strength of beam. in beam b2 made up from plain concrete, failure occurs after 38 sec during applied force is 27.53(kn) with stroke of 0.3 mm. in beam b2 content 1% small steel fiber, failure occurs after 200 sec during force is 30.59 (kn) with stroke of 1.64 mm. (fig. 14-19). the fig. 8, 9, 14 and 15 show small steel fibre controls the crack behaviour. the fig. 14 depicts shear crack on beam b2, (builds up from plain concrete). the fig. 15 shows flexural crack on beam b2, (builds up from fiber reinforced concrete, content 1% steel fibre). content 1% steel fibre convert shear crack to the flexural crack. the fig. 8 shows morphology of crack appears between shear crack and flexural crack. this is intermediate shear-flexural crack propagation. this method has good agreement for mitigate of beam shear failure. figure 7: strain gauges installed on concrete beam. http://dx.medra.org/10.3221/igf-esis.26.03&auth=true http://www.gruppofrattura.it a. namdar et alii, frattura ed integrità strutturale, 26 (2013) 22-30; doi: 10.3221/igf-esis.26.03 27 figure 8: failure mode for beam b1, content 0.5% steel fibers. figure 9: failure mode for beam b1, content 1.0% steel fibers. figure 10: force vs stroke in beam b1, content 0.5% steel fibers. figure 11: force vs stroke in beam b1, content 1% steel fibers. http://dx.medra.org/10.3221/igf-esis.26.03&auth=true http://www.gruppofrattura.it a. namdar et alii, frattura ed integrità strutturale, 26 (2013) 22-30; doi: 10.3221/igf-esis.26.03 28 figure 12: force vs time in beam b1, content 0.5% steel fibers. figure 13: force vs time in beam b1, content 1% steel fibers. figure 14: failure mode for beam b2, non-fiber reinforced concrete. figure 15: failure mode for beam b2, content 1.0% steel fibers. figure 16: force vs stroke in beam b2, non-fiber reinforced concrete. figure 17: force vs stroke in beam b2, content 1.0% steel fibers. http://dx.medra.org/10.3221/igf-esis.26.03&auth=true http://www.gruppofrattura.it a. namdar et alii, frattura ed integrità strutturale, 26 (2013) 22-30; doi: 10.3221/igf-esis.26.03 29 figure 18: force vs time in beam b2, non-fiber reinforced concrete. figure 19: force vs time in beam b2, content 1.0% steel fibers. figure 20: crack on drainage networks facility, made up from thin plain concrete cross section. the accumulating sediment inside concrete drainage channel due to erosion, increases surcharge, decreases load acceptability and causes crack on channel (fig. 20). this problem can be controlled by enhancement of flexural strength of concrete. the reinforced steel cannot use in this thin cross section. by using small steel fiber in concrete mix design, appropriate flexural strength of concrete expects. this method mitigates collapse of concrete channel. the fiber reinforced concrete controls graph of force versus time stability, force versus deflection, morphology of cracks and time of starting cracks. enhancement of type of steel fiber improves stability of beam. the research program continues on how to improve the flexural strength of concrete beam by using different types and proportion of steel fiber. the shape and length of steel fiber plays important role in this investigation. graph of force versus time indicates flexibility of beam improves when beam content 1% steel fiber. according to this research plan the appropriate small steel fiber improves flexural strength of beam and minimizes crack on beam. conclusions he research outcomes indicate that this method is one of the easiest, cost effective technique and less time consumer for enhancement of flexural strength of concrete beam. in steel-concrete mixture design, different proportion and length of steel fibers have been used. two types of beams have been investigated. it has been understood that the type of mode failure for concrete beam depends on small steel fiber proportion and distribution. the strain gauges have been installed on beam, to measure level of applied force, deflection and time to failure of beams. the morphology of crack has been studied. shear crack, flexural crack and intermediate shear-flexural crack have been observed. the steel fiber has been controlled shear crack morphology. increase quantity of fiber, improves flexural strength of beam. to improve flexural strength of thin cross section concrete the proposed method is well suitable. in this t http://dx.medra.org/10.3221/igf-esis.26.03&auth=true http://www.gruppofrattura.it a. namdar et alii, frattura ed integrità strutturale, 26 (2013) 22-30; doi: 10.3221/igf-esis.26.03 30 research work smooth steel fiber has been used. it is well known that deformed steel fiber and rough surface steel fiber exhibit better performance. references [1] kang, s.t., lee, b.y., kim, j.k., kim, y.y., the effect of fibre distribution characteristics on the flexural strength of steel fibre-reinforced ultra high strength concrete, construction and building materials, 25 (2011) 2450-2457. [2] stähli, v., sutter, m., van mier, jgm., improving the mechanical properties of hfc by adjusting the filling method, in: proceeding of rilem fifth international workshop on high performance fibre reinforced cement composites (hpfrcc5), mainz, germany, (2007) 23-30. [3] toutanji, h., bayasi, z., effect of manufacturing techniques on the flexural behaviour of steel fiber-reinforced concrete, cem concr res, 28 (1998) 115-24. [4] yang, i.h., joh, c., kim, b.s., flexural strength of ultra high strength concrete beams reinforced with steel fibers, procedia engineering, 14 (2011) 793-796. [5] deng, j., lee, m.m.k., li, s., flexural strength of steel–concrete composite beams reinforced with a prestressed cfrp plate, construction and building materials, 25 (2011) 379-384. [6] khaloo, a.r., afshari, m., flexural behaviour of small steel fibre reinforced concrete slabs, cement & concrete composites, 27 (2005) 141-149. [7] ghalib, m.a., moment capacity of steel fibre reinforced small concrete slabs, aci journal, (1980) 247-57 [8] bernal, s., gutierrez, r.d., delvasto, s., rodriguez, e., performance of an alkali-activated slag concrete reinforced with steel fibers, construction and building materials, 24 (2010) 208-214. [9] soutsos, m.n., le, t.t., lampropoulos, a.p., flexural performance of fibre reinforced concrete made with steel and synthetic fibres, construction and building materials, 36 (2012) 704-710. nomenclature l.f = length of fiber (mm) w.f = weight of fiber in a beam (g) %.f = % of fiber in a beam b1 = beam with dimension of 100 (mm) × 100 (mm) × 500 (mm) b2 = beam with dimension of 150 (mm) × 150 (mm) × 1000 (mm) http://dx.medra.org/10.3221/igf-esis.26.03&auth=true http://www.gruppofrattura.it microsoft word numero_42_art_33.docx g. testa et alii, frattura ed integrità strutturale, 42 (2017) 315-327; doi: 10.3221/igf-esis.42.33 315 strain capacity assessment of api x65 steel using damage mechanics gabriel testa, nicola bonora, domenico gentile, andrew ruggiero, gianluca iannitti university of cassino and southern lazio, italy gabriel.testa@unicas.it, http://orcid.org/0000-0001-2345-6789 antonio carlucci saipem sa, italy antonio.carlucci@saipem.com yazid madi epf-ecole d'ingénieurs / mines paristech, france yazid.madi@epf.fr abstract. strain-based design for offshore pipeline requires a considerable experimental work aimed to determine the material fracture toughness and the effective strain capacity of pipe and welds. continuum damage mechanics can be used to limit the experimental effort and to perform most of the assessment analysis and evaluation in a simulation environment. in this work, the possibility to predict accurately fracture resistance of x65 steel using a cdm model proposed by the authors, is shown. the procedure for material and damage model parameters identification is presented. damage model predictive capability was demonstrated predicting ductile crack growth in senb and sent fracture specimens. keywords. damage mechanics; fracture toughness; strain capacity; strainbased design. citation: testa, g., bonora, n., gentile, d., ruggiero, a., iannitti, g., carlucci, a., madi, y., strain capacity assessment of api x65 steel using damage mechanics, frattura ed integrità strutturale, 42 (2017) 315-327. received: 25.07.2017 accepted: 22.08.2017 published: 01.10.2017 copyright: © 2017 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. introduction ipelines for transporting hydrocarbons are required to operate safely in extreme environments that include low temperature, sour surroundings, high stress and large deformation. in remote areas, such as arctic regions, these systems are exposed to unique environmental conditions not normally present in other regions of the world, which includes ice scours, permafrost thaw and/or frost heave. for buried pipelines, the key design issue is the potential for large bending strain resulting from frost heave and thaw settlement, ice gouging in the shallow waters and severe seismic events [1]. p g. testa et alii, frattura ed integrità strutturale, 42 (2017) 315-327; doi: 10.3221/igf-esis.42.33 316 under these varying operating conditions, a safe pipeline requires a combination of design and operational measures. it is recognized that design and operational measures are not mutually exclusive, and the interacting combinations must be appropriately considered. conventional pipeline design uses the allowable stress design (asd) approach, which limits pipeline stress to a prescribed fraction of its specified minimum yield strength, such as 72% of the yield strength in hoop direction and 90% of the yield strength for combined hoop and longitudinal stresses. this criterion, while appropriate for buried pipelines, is difficult to satisfy for pipelines that must withstand ground movements or buckling due to operating conditions. moreover, the asd approach makes no distinction between load-controlled and displacement-controlled conditions, between stable and unstable failure modes, or between the loss of serviceability and loss of pressure containment. thus, the safe-design process requires developing an understanding of the strains imposed on the pipe (strain demand) and the safe strain limits that the pipe can withstand without failure (strain capacity). recognizing these limitations, an increasing number of industry standards allow application of strain-based design for loading conditions outside those typically considered for more conventional pipelines. strain-based design is a specific application of a limit-state design approach: here, the capacity of the pipeline to withstand longitudinal strain without failure is quantified and compared to the strain expected in service under displacement-controlled conditions [2]. quantification of the strain demand side of the design condition requires a comprehensive understanding of the pipeline route, which includes soil characteristics and geothermal analysis, wall-thickness differences, and mechanical properties of adjacent pipe joints [3]. tensile strain capacity is generally governed by the strain capacity of the girth weld region and it is determined through a combination of tests and finite element analysis or semi-empirical models. these models are typically based on attempts to modify fracture assessment criteria in the form of failure assessment diagrams [4]. they often lead to highly conservative criteria with large uncertainties. these diagrams imply the presence of a plastic collapse load and, if the pipeline stress-strain response is relatively flat in the plastic region, are not representative of strain capacities. in strain-based design, fracture resistance is usually assessed by ctod fracture toughness. as for other fracture mechanics concepts, the ctod fracture criterion is valid only when some conditions are satisfied. ctod controlled crack growth under plain strain condition is ensured when:  0 , crb b a w a       (1) where = 50 and = 0.1 for bend and compact tension specimens, b is the specimen ligament, b is the thickness and w the specimen width [5]. gordon et al. [6] showed that the limits for the ctod controlled crack growth are material dependent. based on experimental measures on different material grades, it was postulated that the crack growth limit for ctod controlled crack growth in r-curves is 15% of the initial uncracked ligament, although this condition alone would not be sufficient to ensure size/geometry independent results. today, in astm 1820 the  limit is reduced to 35 [7]. in high toughness material grades operating over the mid-to-upper end of the ductile-to-brittle (dtb) transition region, these limits may not be fulfilled and, therefore, material resistance can be even strongly affected by the loss of constraint occurring at the crack tip. in these cases, fracture resistance and r-curve shows a significant geometry dependence that may hinder the transferability from laboratory samples to full-scale components [8]. when dealing with large plastic deformation, damage modelling is a valid alternative to investigate and predict material failure. recently, the use of finite element analysis simulating crack growth by means of damage modelling has been introduced in dnv design recommendations for submarine pipeline systems [9]. in the literature, several examples using porosity models (gurson-tvergaard-needleman (gtn), and rousselier) are available. fehringer et al. [10] investigated the stress triaxiality effect on the strain capacity of 20mnmoni5-5 grade steel calibrating rousselier model parameters on round notched bar tensile test results and validating predicting crack growth in ct-0.5t samples. acharyya and dhar [11] calibrated the gtn model parameters based on compact tension (ct) specimen fracture data and then used the model to predict crack growth in circumferentially cracked pipes. xu et al. [12] performed a systematic numerical investigation predicting circumferential crack growth in pipes with different sizes and properties using the complete gtn model finding a good transferability to single edge notch in tension (sent) specimen. geometry transferability is a major requirement for any micromechanical model. the gtn suffers the transferability of model parameters to different stress triaxiality [13]. for this reason, crack data of laboratory samples with constraint similar to that expected in full-scale components are necessary for model parameters calibration. furthermore, numerical solutions obtained with porosity models show mesh dependency because of softening in the flow curve caused by damage. because of this, a reference element length is often introduced as an additional material parameter. g. testa et alii, frattura ed integrità strutturale, 42 (2017) 315-327; doi: 10.3221/igf-esis.42.33 317 alternatively, continuum damage mechanics (cdm) provides a framework for constitutive modelling of damaged material in which some of the aforementioned issues can be avoided. in cdm, the damage variable accounts for the detrimental effects on the reference material properties caused by a generic damage state. differently from the concept of porosity, the damage in cdm is not strictly defined for a specific micromechanism of failure, making it suitable for describing progressive deterioration caused by the development of inelastic deformation at different length scales. bonora [14] proposed a damage model formulation for describing ductile damage evolution in different classes of metals and alloys. the model was successfully used to predict ductile rupture under different loading conditions and material microstructural states [15, 16]. one of the key feature of this model formulation is the capability to account for stress triaxiality effects on material ductility [17]. recently, carlucci et al. [18] used the bonora damage model (bdm) to predict fracture resistance of flaw in girth weld pipes showing the possibility to use cdm in support of strain-based design procedure [19]. a major limitation to the use of advanced material modelling for structural assessment route of engineering components relies on the difficulties of the determination of material model parameters. in porosity-based micromechanical models, material model parameters, in most of the cases, do not have a physical meaning and are determined numerically by inverse calibration of selected laboratory-scale test results. this approach relies on the experience and sensitivity of the operator, which becomes a major cause of uncertainty in model parameters identification. in cdm, in general, fewer material model parameters are required. in the bdm, these parameters are four but can be reduced to two for quasi-static loading. in this work, the bdm was used to predict the strain limit capacity of x65 steel grade used for pipeline application. the procedure for the identification of damage model parameters is presented. once determined, damage model parameters allow building the limit strain diagram (lsd) to predict strain capacity as a function of stress triaxiality. the solution is validated comparing the predicted limit strain with onset crack propagation data in sent specimen. damage model formulation he bonora damage model (bdm) is formulated in framework of continuum damage mechanics. the basic concept in cdm is that the constitutive response of the damaged material is described by the same set of equations of the undamaged material simply replacing the stress with the “effective” stress concept [20]: 1 d      (2) here, d is the damage variable that, under the assumption of isotropic damage, is a scalar. the definition of the “effective” stress together with the principle of strain equivalence [21] leads to the following definition of damage as, 0 1 e d e    (3) where e and 0e are the effective and the reference young modulus of the material, respectively. assuming that the mechanical and thermal dissipations are uncoupled, the second principle of thermodynamics requires the mechanical dissipation to be positive: : 0 p ij k kij yd a v      (4) kv indicates the rate of internal variables, ak designates the associated variables, and -y is the damage (elastic) strain energy release rate given by,   2 2 2 1 eq y r e d      (5) where, t g. testa et alii, frattura ed integrità strutturale, 42 (2017) 315-327; doi: 10.3221/igf-esis.42.33 318 2 2 (1 ) 3(1 2 ) 3 m eq r                 (6) r accounts for stress triaxiality, defined as the ratio of the mean and equivalent von mises stress, and  is the poisson ratio. because plastic flow can occur without damage and, similarly, damage can occur without noticeable macroscopic plastic flow, it can be assumed that the dissipation potential for plastic deformation and damage are independent,    , ; ; ,p ij k df f a t f y t d  (7) where t is the temperature. from the generalized normality rule, the following expression for damage evolution law is obtained, dffd y y         (8) the bdm differentiates from similar cdm formulations for the following additional assumptions. a) the damage rate depends on the “active plastic strain” rate defined as: pˆ m eq eq p      (9) here, peq is the rate of the equivalent plastic strain, 〈…〉 is the heaviside function that is equal to 1 when the stress triaxiality is positive and 0 otherwise. under compressive state of stress, damage cannot accumulate and its effects are temporarily restored ( 0 & 0d d  ). b) the damage dissipation potential depends on the total accumulated active plastic strain. the following expression was proposed,     1 2 0 0 1 2 1 ˆ cr d d dsy f s d p                     (10) where, s0 is a material constant,  is the damage exponent, = (2+n)/n and n is the hardening exponent. this assumption implies that the damage dissipation depends on the deformation history, which leads to a nonlinear evolution of damage with the active plastic strain for constant stress triaxiality load paths. c) in the experiments, it is impossible to separate plasticity (hardening) and damage (softening) effects. if performed correctly, damage measurement shown that the critical damage at rupture is very small and no larger than 0.1 for pure metals and alloys. consequently, it is convenient to assume that damage effect on the material plastic flow are already accounted for in the mathematical expression of the material flow curve identified in uniaxial tensile tests [22],   0p eq yf p    (11) this assumption, which is also justified by the fact that damage process are highly localized in the material microstructure and therefore their detrimental effects are overcome by hardening at macroscopic scale, eliminates softening in the expression of the flow curve with the advantage to avoid mesh dependence effect in finite element applications. g. testa et alii, frattura ed integrità strutturale, 42 (2017) 315-327; doi: 10.3221/igf-esis.42.33 319 from eq. (8) and eq. (10) together with the definition of y, and assuming a power law expression for the material flow curve, the following expression for the kinetic law of damage evolution can be obtained,   1 ˆ ˆcr p d a r d d p          (12) where   1/ ln cr f th d a     (13) a detailed derivation of eq. (12) can be found elsewhere [23]. under the assumption of proportional loading, eq. (12) can be integrated analytically,     ˆln / 1 1 ln / th cr f th p p d d r                  (14) at failure, for d=dcr, assuming that the strain threshold for damage initiation is pressure independent which is reasonable at relatively low stress triaxiality while it is not true in general [16, 24, 25] the following expression can be obtained, 1 ˆ rf f th th p           (15) this expression provides the relationship between the equivalent “active” plastic strain at failure and stress triaxiality and can be used to build the lsd. damage model parameters identification the model requires four material parameters to be determined: the uniaxial threshold strain at which the damage initiates ɛth; the failure strain for stress triaxiality equal to 1/3, ɛf, the damage at failure dcr and the damage exponent α. under quasistatic loading condition, the damage exponent does not affect the failure condition. it does have an effect on the damage rate that becomes relevant in time dependent deformation processes. the critical damage defines the maximum reduction of the elastic modulus and the released damage strain energy. for several classes of metals and alloys this value is usually less than 0.1, [26]. the remaining damage parameters can be identified by means of experiments and finite element simulation. firstly, uniaxial tensile tests on round notched bar samples (rnb) with at least three different notch radii are performed. the notch radius is selected to ensure that rupture will occurs at the specimen center (cup-cone type rupture). at least three samples for each notch radius shall be tested in order to have indication on the experimental scatter. from these tests, the diameter at fracture is measured and used to determine the average plastic strain at rupture according to the bridgman expression, 0ˆ 2 lnf r p          (16) successively, finite element simulation of each notched geometry is performed and the stress triaxiality versus plastic strain at the specimen center is obtained. the stress triaxiality does not remain constant during the traction; therefore, the average stress triaxiality for the selected sample is defined as follow,     ˆ1 ˆ ˆ f m thf th eq p t dp p                 (17) g. testa et alii, frattura ed integrità strutturale, 42 (2017) 315-327; doi: 10.3221/igf-esis.42.33 320 finally, the data points ( t , ˆ fp ) are plotted and fitted using eq. (15) to determine th and f . since, the average stress triaxiality requires the knowledge of both the threshold and failure strain, an iterative procedure is required. firstly th and f are assumed equal to 0 and ˆ fp respectively, and used in eq. (17). after fitting, the new th and f values are obtained and used until convergence is reached. alternatively, th and f can be determined by means of optimization of the calculated applied load vs diameter reduction (or axial elongation) response of notched samples. it was found that best results are obtained if the failure point on the traction-displacement curve is selected as the point at which the load starts to drop down. with this approach, no fitting is necessary, and the optimization will return the best estimate for th and f that minimize the error in terms of predicted failure for all available data. experimental data obtained from uniaxial smooth bar samples, used for the determination of material flow curve, shall not be considered in the fitting because the stress triaxiality in the sample varies considerably because of necking. these data can eventually be used for a preliminary assessment of the quality of damage parameters and prediction. material and experimental testing he material under investigation is api x65, customer grade, seamless pipe steel in as-received and welded conditions, hereafter indicated as “base metal” (bm) and “welded metal” (wm), respectively. the nominal composition is given in tab. 1. grade c si mn p s cr ni mo al api x65 0.094 0.195 1.420 0.011 0.004 0.19 <0.0025 0.003 0.34 table 1: nominal composition of x65 steel. the bm was characterized along pipe axial (l) and circumferential (t) directions. tensile tests were performed at different temperatures (rt, 0°, -20° and -40°c), with a nominal strain rate of 10-4/s, using a smooth axisymmetric sample geometry (sb). the specimen geometry used is shown in fig. 1. figure 1: uniaxial tensile specimens: smoothed round bar (sb) and round notched bars (nts). dimensions in mm. axial deformation was measured by means of extensometer with a reference base length of 9.625 mm. uniaxial tensile test results showed limited differences in the response along the two directions. in tab. 2, the summary of average tensile tests results at different temperature along t and l direction, are shown. here, rp0.2 is the engineering yield stress at 0.2% strain, rm is the engineering ultimate stress and εr is the strain at rupture calculated according to bridgman expression given in eq. (16). stress triaxiality effect on material ductility was investigated performing tractions on round notched bar samples with three different round notch radii: 1.2, 2.4 and 4.0 mm respectively. these geometries have the same minimum diameter of the sb t g. testa et alii, frattura ed integrità strutturale, 42 (2017) 315-327; doi: 10.3221/igf-esis.42.33 321 (= 6.0 mm) and are identified hereafter by the ratio between the notch radius and the minimum diameter: nt2, nt4 and nt6 respectively. specimen dimensions are given in fig. 1. during the tests, axial deformation and the minimum diameter reduction as a function of the applied load were measured and used for comparison with finite element simulation results. temperature direction rp0.2 [mpa] rm [mpa] r [mm/mm] rp0.2/rm rt l 445.40 548.35 0.135 81.23 t 446.50 552.25 0.140 80.85 -20°c l 467.50 594.30 0.110 78.67 t 462.60 582.30 0.160 79.27 -40°c l 488.50 610.60 0.160 80.00 t 468.10 13.00 0.130 75.64 table 2: average tensile properties of x65 custom grade steel at different temperatures. finite element analysis ll finite element simulations were performed using the commercial code msc marc v2016. round samples have been simulated using four node axisymmetric elements with bilinear shape functions. elastic-plastic analyses were performed using large displacement, finite strain and lagrangian updating formulation. the bdm is ready available in msc marc and was used for the purpose of the work. base and weld metal flow curve the identification of the material plastic flow curve was performed as follow. among all available uniaxial traction tests, those in which necking occurred in the gauge length, were selected. test results, in term of applied load vs extensometer displacement p vs l, were selected as objective function and used in an optimization procedure based on the minimization of the error between experimental data and fem calculated response. for the optimization procedure, the mathematical expression of the flow curve needs to be assumed. among all candidate functions, a voce type law allows to account for the fact that stress has to saturate asymptotically at large strain. for bm, two terms voce-type expression was found to be appropriate. however, because the material under investigation shows a considerable lüders plateau, the following description was used,   1 0 0 0 ; 1 /y i p i i max a r exp b                 (18) wherey0 is the reference yield stress at 0.2% of strain. the hardening in the weld metal was found similar to that of the bm. therefore, it was decided to assume for the wm the same expression as in eq. (18) scaling only the reference yield stress by the overmatching ratio. the material parameters are summarized in tab. 3. material y0 a0 r0 r1 b0 b1 bm 450 370.65 146.6 345.94 0.0233 0.384 wm 560 370.65 146.6 345.94 0.0233 0.384 table 3: flow curve parameters for bm and wm. damage model parameters assuming a trial set for the damage parameters, the identification was carried out by optimization, minimizing the error between the estimated displacement ( axial elongation for sb and minimum diameter reduction for nts), at which the load drop occurs, and the experimental values for different specimens. the critical damage and the damage exponent were a g. testa et alii, frattura ed integrità strutturale, 42 (2017) 315-327; doi: 10.3221/igf-esis.42.33 322 assumed the same for bm and wm since these values do not affect the determination of rupture condition. the damage parameters identified with this procedure are summarized in tab. 4. it is worth to be noted that the identification of damage parameters, based on the use of round notched bar samples only, suffers the fact that all the experimental points lays on a limited stress triaxiality range. this may lead to overestimate the ductility expected in the low stress triaxiality range (<1/3). to avoid this issue, failure data under pure torsion should be also used. this information would provide better insight about the possible change in rupture mechanism and the influence of other parameters such as the lode angle. however, this type of test is very difficult to be performed correctly for very ductile materials for which also the definition of the effective strain become an issue as discussed extensively in [27]. material th f dcr  bm 0.23 3.5 0.1 0.3 wm 0.10 6.2 0.1 0.3 table 4: damage model parameters for bm and wm. model verification and validation irstly, model verification was performed comparing the predicted response of nts specimens, given as applied load vs axial elongation, with experimental data. this comparison provides a first assessment of the transferability of material flow curve and damage model parameters, at least for the stress triaxiality range typical of these sample geometries. in fig. 2, the calculated applied load vs displacement curve for all three notched bar specimen geometry and for both bm and wm is shown. numerical simulation results are compared with experimental data from different tests. in all cases, the comparison seems to be adequately good. in fig. 3, the predicted failure locus for x65 bm is shown. here, the stress triaxiality vs plastic strain load path at the critical location for all three notched bar samples is also plotted. experimental data are also compared with data reported by oh et al. [28] for a commercial x65 grade which are consistent with present results. similar results are plotted for x65 wb in fig. 4. successively, the model transferability was verified predicting crack propagation in sent and senb specimens with shallow crack (a/w=0.25). fracture mechanics tests were carried out to determine the critical ctod at the onset crack propagation as prescribed in eca design route. the numerical simulation of these specimen geometries requires the use of 3d fem models. numerical simulation of 3d crack is prone to mesh sensitivity. in fact, the size of the elements in the near tip region along the entire crack front, has an effect on the computed plastic deformation field and consequently on the calculated damage. because of the steep plastic strain gradient, finite element calculation of cracked geometries showed that damage extension is usually limited to the first element along the crack ligament [29]. in general, reducing the element size increases the accuracy of the calculated stress field but leads to overestimating the plastic strain gradient at tip. from the damage calculation point of view, this results in a faster crack growth rate. in order to limit this mesh effect, the size of the elements to be used in the 3d simulation of cracked geometries was established a priori performing a mesh sensitivity study on nt2 specimen geometry. this geometry was selected because the stress triaxiality, under fully developed plastic deformation, is similar to that in sent. a parametric finite element analysis was performed, varying the element length along the radial direction and the element aspect ratio, measuring the variation of the relative error in the estimate of specimen axial displacement at failure. the largest element size and aspect ratio for which error convergence is obtained was selected for 3d simulation of cracked geometries (0.2 mm (ligament direction) x 0.05 mm x 0.05 mm in this present case). crack propagation was simulated by means of element removal technique: when damage becomes critical at the element gauss points, the element is removed and stresses are released. this feature, available in msc marc, does not suffer of convergence issues if the load step is relatively small to limit the overall number of elements that are removed at the same time. in fig. 5 and fig. 6, the comparison of the calculated response applied load vs displacement for sent and senb with experimental data is shown. for sent a parametric investigation on the effect of the ligament size on the calculated applied load vs displacement response was performed. this analysis was motivated by the difference initially found using the nominal specimen dimensions in the simulation. it was found that an uncertainty of 5% (0.5 mm in this case) in the f g. testa et alii, frattura ed integrità strutturale, 42 (2017) 315-327; doi: 10.3221/igf-esis.42.33 323 ligament size has a significant effect on the predicted specimen response. a posteriori measurements confirmed such uncertainty in the effective crack ligament of machined samples. a) d) b) e) c) f) figure 2: comparison of predicted applied load vs diameter reduction and rupture in nts samples for bm and wm. g. testa et alii, frattura ed integrità strutturale, 42 (2017) 315-327; doi: 10.3221/igf-esis.42.33 324 figure 3: failure locus for x65 bm showing the stress triaxiality vs plastic strain load path at the critical location in different notched bar samples. figure 4: failure locus for x65 wm. figure 5: comparison of calculated specimen response with experimental data for senb sample. multiple partial unloadings for rcurve determination are shown. g. testa et alii, frattura ed integrità strutturale, 42 (2017) 315-327; doi: 10.3221/igf-esis.42.33 325 figure 6: comparison of calculated specimen response with experimental data for sent sample. results of fem sensitivity analysis are given for different crack depths. figure 7: comparison of calculated crack resistance curve for x65 bm with senb a/w=0.25. finally, in fig. 7 the comparison of predicted crack resistance with experimental data obtained using unloading compliance method, given in astm e-1820, is shown. in the simulation, the j-integral was calculated using the domain integral method [30]. here, the comparison is very good all over the crack growth range of interest. at the intercept with the exclusion line, the error in the j-integral estimate is approximately 10%. at 0.2mm offset, the jic is correctly predicted with an error of 1.7%. conclusions n this work, the possibility to use cdm modelling to predict material strain capacity was demonstrated. the proposed modelling has the major advantage to capture correctly the effect of stress triaxiality on material ductility, which is critical for predicting the occurrence of rupture in ductile materials. this is of particular importance for high toughness materials, such as carbon steels operating in the right end side of ductile-to-brittle transition region, for which fracture mechanics validity limits are hard to be satisfied. i g. testa et alii, frattura ed integrità strutturale, 42 (2017) 315-327; doi: 10.3221/igf-esis.42.33 326 in its simplest implementation, the proposed damage model requires the identification of only two material parameters that can be determined performing simple tensile tests on round notched bar samples. the identification procedure, as discussed in this work, is suitable to be performed at industrial level and do not requires particular abilities. the geometry transferability of material model parameters has been demonstrated predicting the crack growth in geometry samples with different crack tip constraints. in particular, it was shown that numerical simulation with cdm could be used to carry on “virtual experiments” for the determination of the material fracture toughness with high degree of accuracy. consequently, the proposed cdm modelling could also be used to predict by simulation the resistance of components under different load/geometry configuration, reducing full-scale test effort for component qualification. references [1] mørk, k. the challenges facing arctic pipelines, design principles for extreme conditions. offshore oil and gas magazine, (2007) 67. [2] kan, w. c., weir, m., zhang, m. m., lillig, d. b., barbas, s. t., macia, m. l., biery, n. e. strain-based pipelines: design consideration overview. the eighteenth international offshore and polar engineering conference,. international society of offshore and polar engineers (2008). [3] degeer, d., nessim, m. arctic pipeline design considerations. asme 2008 27th international conference on offshore mechanics and arctic engineering, american society of mechanical engineers, (2008) 583-590. [4] bs7910:2013 guide on methods for assessing the acceptability of flaws in metallic structures. bsi -british standard institute (2013). [5] schwalbe, k. h., neale, b. k., ingham, t., draft egf recommendations for determining the fracture resistance of ductile materials: egf procedure egf p1–87d, fatigue & fracture of engineering materials & structures, 11 (1988) 409-420. [6] gordon, j., jones, r., challenger, n., an experimental study to determine the limits of ctod controlled crack growth. constraint effects in fracture. astm international, (1993). [7] standard, a. standard test method for measurement of fracture toughness. astm, e1820-01, (2016) 1-46. [8] moattari, m., sattari-far, i., bonora, n. the effect of subcritical ductile crack growth on cleavage fracture probability in the transition regime using continuum damage mechanics simulation, theoretical and applied fracture mechanics, 82 (2016) 125-135. [9] det norske veritas offshore standard dnv‐os‐f101. submarine pipeline systems, (2012). [10] fehringer, f., seidenfuß, m., schuler, x., experimental and numerical investigations on limit strains in ductile fracture. procedia structural integrity, 2 (2016) 3345-3352. [11] acharyya, s., dhar, s. a complete gtn model for prediction of ductile failure of pipe, journal of materials science, 43 (2008) 1897. [12] xu, j., zhang, z., østby, e., nyhus, b., sun, d., constraint effect on the ductile crack growth resistance of circumferentially cracked pipes, engineering fracture mechanics, 77 (2010) 671-684. [13] faleskog, j., gao, x., shih, c. f., cell model for nonlinear fracture analysis–i. micromechanics calibration. international journal of fracture, 89 (1998) 355-373. [14] bonora, n., cod of off-centred cracks in pipes under bending load: a geometrical solution. international journal of fracture, 75 (1996) 1-18. [15] bonora, n., ruggiero, a., esposito, l., iannitti, g. damage development in high purity copper under varying dynamic conditions and microstructural states using continuum damage mechanics, aip conference proceedings, (2009) 107110. [16] bonora, n., ruggiero, a., iannitti, g., testa, g. ductile damage evolution in high purity copper taylor impact test. aip conference proceedings, (2012) 1053-1056. [17] chiantoni, g., bonora, n., ruggiero, a., experimental study of the effect of triaxiality ratio on the formability limit diagram and ductile damage evolution in steel and high purity copper. international journal of material forming, 3 (2010) 171-174. [18] carlucci, a., bonora, n., ruggiero, a., iannitti, g., gentile, d., crack initiation and growth in bimetallic girth welds. proceedings of the international conference on offshore mechanics and arctic engineering omae, (2014). [19] bonora, n., carlucci, a., ruggiero, a., iannitti, g., simplified approach for fracture integrity assessment of bimetallic girth weld joint. proceedings of the international conference on offshore mechanics and arctic engineering omae, (2013). g. testa et alii, frattura ed integrità strutturale, 42 (2017) 315-327; doi: 10.3221/igf-esis.42.33 327 [20] kachanov, l. m., on creep rupture time. izv. acad.nauk. sssr, otd.techn. nauk, (1958) 8. [21] lemaitre, j., micro-mechanics of crack initiation. international journal of fracture, (1990) 42, pp. 87-99. [22] pirondi, a., bonora, n., modeling ductile damage under fully reversed cycling. computational materials science, 26 (2003) 129-141. [23] bonora, n., a nonlinear cdm model for ductile failure. engineering fracture mechanics, 58 (1997) 11–28. [24] iannitti, g., bonora, n., bourne, n., ruggiero, a., testa, g., damage development in rod-on-rod impact test on 1100 pure aluminum. aip conference proceedings, (2017). [25] iannitti, g., bonora, n., ruggiero, a., testa, g., ductile damage in taylor-anvil and rod-on-rod impact experiment. journal of physics: conference series, (2014) 500. [26] bonora, n., ruggiero, a., gentile, d., de meo, s., practical applicability and limitations of the elastic modulus degradation technique for damage measurements in ductile metals. strain, 47 (2011) 241-254. [27] gambirasio, l., chiantoni, g., rizzi, e., on the consequences of the adoption of the zaremba–jaumann objective stress rate in fem codes. archives of computational methods in engineering, 23 (2016) 39-67. [28] oh, c.-k., kim, y.-j., baek, j.-h., kim, y.-p., kim, w.-s., ductile failure analysis of api x65 pipes with notch-type defects using a local fracture criterion. international journal of pressure vessels and piping, 84 (2007) 512-525. [29] bonora, n., ruggiero, a., esposito, l., gentile, d., cdm modeling of ductile failure in ferritic steels: assessment of the geometry transferability of model parameters, international journal of plasticity, 22 (2006) 2015-2047. [30] shih, c., moran, b., nakamura, t., energy release rate along a three-dimensional crack front in a thermally stressed body. international journal of fracture, 30 (1986) 79-102. << /ascii85encodepages false /allowtransparency false /autopositionepsfiles true /autorotatepages /none /binding /left /calgrayprofile (dot gain 20%) /calrgbprofile (srgb iec61966-2.1) /calcmykprofile (u.s. web coated \050swop\051 v2) /srgbprofile (srgb iec61966-2.1) /cannotembedfontpolicy /error /compatibilitylevel 1.4 /compressobjects /tags /compresspages true /convertimagestoindexed true /passthroughjpegimages true /createjobticket false /defaultrenderingintent /default /detectblends true /detectcurves 0.0000 /colorconversionstrategy /cmyk /dothumbnails false /embedallfonts true /embedopentype false /parseiccprofilesincomments true /embedjoboptions true /dscreportinglevel 0 /emitdscwarnings false /endpage -1 /imagememory 1048576 /lockdistillerparams false /maxsubsetpct 100 /optimize true /opm 1 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can be opened with acrobat and adobe reader 5.0 and later.) >> /namespace [ (adobe) (common) (1.0) ] /othernamespaces [ << /asreaderspreads false /cropimagestoframes true /errorcontrol /warnandcontinue /flattenerignorespreadoverrides false /includeguidesgrids false /includenonprinting false /includeslug false /namespace [ (adobe) (indesign) (4.0) ] /omitplacedbitmaps false /omitplacedeps false /omitplacedpdf false /simulateoverprint /legacy >> << /addbleedmarks false /addcolorbars false /addcropmarks false /addpageinfo false /addregmarks false /convertcolors /converttocmyk /destinationprofilename () /destinationprofileselector /documentcmyk /downsample16bitimages true /flattenerpreset << /presetselector /mediumresolution >> /formelements false /generatestructure false /includebookmarks false /includehyperlinks false /includeinteractive false /includelayers false /includeprofiles false /multimediahandling /useobjectsettings /namespace [ (adobe) (creativesuite) (2.0) ] /pdfxoutputintentprofileselector /documentcmyk /preserveediting true /untaggedcmykhandling /leaveuntagged /untaggedrgbhandling /usedocumentprofile /usedocumentbleed false >> ] >> setdistillerparams << /hwresolution [2400 2400] /pagesize [612.000 792.000] >> setpagedevice microsoft word numero_55_art_13_2957 a.v. chernov et alii, frattura ed integrità strutturale, 55 (2021) 174-186; doi: 10.3221/igf-esis.55.13 174 influence of stress ratio on residual stress evolution near coldexpanded hole due to low-cycle fatigue by crack compliance data a.v. chernov, s. i. eleonsky, v.s. pisarev central aero-hydrodynamics institute named after prof. n.e. zhukovsky (tsagi). 1 zhukovsky street, zhukovsky 140180 moscow region, russia. andcherr@rambler.ru, https://orcid.org/0000-0003-4020-1643 juzzepka@mail.ru, https://orcid.org/0000-0003-4345-067x vsp5335@mail.ru, https://orcid.org/0000-0002-5378-609x abstract. modified version of the crack compliance method is used for determination of stress intensity factor (sif) related to narrow notches emanating from cold-expanded holes. these notches are inserted at different stages of low-cycle fatigue under constant external load. it is shown how residual sif values, generated by residual stress field influence, can be separated from total experimental sif values. residual sif values, obtained at different stage of low-cycle fatigue with the same stress range δσ = 350 mpa but different stress r = –0.4 and r = –1.0, provide quantitative description of residual stress evolution near cold-expanded hole. it shown that maximal residual stress relaxation of order 20 per cent occurs at 95 lifetime per cent for both loading programs. keywords. metal-composite joints; cold hole expansion; residual stress intensity factor; residual stress. citation: chernov, a.v., eleonsky, s. i., pisarev, v.s., influence of stress ratio on residual stress evolution near cold-expanded hole due to low-cycle fatigue by crack compliance data, frattura ed integrità strutturale, 55 (2021) 174-186. received: 25.11.2020 accepted: 02.12.2020 published: 01.01.2021 copyright: © 2021 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. introduction t has earlier been shown how localized displacement measurements, based on electronic speckle-pattern interferometry, can be implemented to obtain notch mouth opening displacement (nmod), stress intensity factor (sif) and t-stress values for narrow notches of different length emanating from cold-expanded holes [1]. a sequence of these notches, inserted under the constant external load, serves for crack modelling at different stages of low-cycle fatigue. the approach developed has been effectively implemented for quantitative description of low-cycle damage accumulation at the vicinity of through hole in plane rectangular specimens [2]. obtained experimental information might be very useful for verification of various numerical and theoretical methods of fatigue damage quantifying [3–4]. another application of created methodology, that is the subject of present paper, resides in investigation of residual stress evolution near cold-expanded hole caused by cyclic loading. advanced aircraft structures include various metal-composite bolted joints [5]. cold-expanded holes are the essential component of such structural elements. cold expansion, widely used in aircraft industry, eventually leads to enhance the fatigue life of structures with fastener holes [6]. the cold working introduces a zone of compressive residual stresses around i https://youtu.be/ueyo1loxfms a.v. chernov et alii, frattura ed integrità strutturale, 55 (2021) 174-186; doi: 10.3221/igf-esis.55.13 175 the hole. fatigue life improvement is mainly related to the circumferential residual stress influence that, firstly, delays the initial crack appearance increasing the damage tolerance life. secondly, residual stress influence leads to reducing the effective range of sif thus decreasing fatigue crack growth [7]. residual stresses have a beneficial effect on lifetime of pin/rivet joints with cold-expanded holes. thus, information related to initial residual stress level as well as residual stress evolution is of decisive importance for reliable lifetime estimation. a set of both numerical and experimental methods has been developed and realized to consider the first from above problems [8–17]. but only few experimental works concern an evolution of deformation parameters and residual stresses [18–20]. one of them employs non-contact full-field strain measurements using both digital image correlation (dic) and thermoelastic stress analysis (tsa) [18]. derived data serve to compare the strains during crack growth around holes that had and had not been cold-expanded by 4%. the objects of investigation were rectangular coupons made from 2024-t3 aluminum alloy, half had simple open, unexpanded holes and half had cold-expanded open holes. a dic system was used to monitor the mandrel entry face of the coupon while a tsa system was used to monitor the mandrel exit face of the coupon during cyclic tensile loading by three programs (2024-t3, yield limit  y = 310 mpa; stress ratio r = 0.1; stress range  = 184.8, 192.5 and 217.8 mpa). these two systems provide the measurements of simultaneous mandrel entry and exit surface strains surrounding a crack initiating from a plain and cold-expanded hole. cracks originating from the unexpanded hole exhibit a strain field around the crack tip which is characteristic of a mode i fatigue crack while those emanating from the coldexpanded holes show a significantly lower distribution of strains around the crack tip. crack opening displacements evaluated from the strain data obtained from dic, are substantially reduced by the residual compressive stresses from cold expansion, while the overall fatigue data show the life improvement achieved at various applied stress levels. the most important outcome consists of dependencies between crack opening displacements and fatigue crack length constructed for crack lengths of 1, 2 and 3.7 mm for coupons with plain and cold-expanded holes. but these data are of difficult use to predict residual stress evolution. experimental approach aimed to describing residual stress evolution due to cyclic loading by the crack compliance (slitting) method is presented in work [19]. residual stress measurements were made in aluminum 7075-t651 plates with coldexpanded holes. the yield limit  y and ultimate tensile strengths of 7075-t651 aluminum alloy were 541 and 568 mpa, respectively. the loading cycles parameters are: r=0.1;  = 182.1, 204.1 and 225.5 mpa. residual stresses were represented by symmetric legendre polynomials on opposite sides of the hole and compliance functions found by finite element analysis. measured residual stresses were smaller than predicted by finite element analysis. residual stress relaxation caused by cyclic loading was not observed even though two short cracks were formed between 45,000 and 50,000 cycles in the specimen cycled at  = 205 mpa for r = 0.1. the main drawback resides in the fact that that the initial point of a cut sequence, which is used for residual stress evaluation, is located at the external edge of the specimen, but not at the hole edge. the technique, which employs the secondary hole drilling and further measurements of hole diameter increments in principal stress directions by electronic speckle-pattern interferometry (espi), has been implemented to quantify residual strain evolution caused by low-cycle fatigue [20]. the cycles parameters are: r= –0.4;  = 350 mpa. it was shown that residual strain evolution cannot be characterized as monotonic relaxation. present paper has common features with all three above-mentioned works. the first of them resides in implementing fullfield measurement techniques as in works [18, 20]. the crack compliance method is the base of this paper and work [19]. the first distinctive point of the approach involved in present paper consists of combining the crack combining method and espi displacement measurement along narrow notch border. notch emanation from the hole edge is the second trait. the third feature resides in consideration of two low-cycle fatigue programs with negative stress ratio. deriving new information, which is related to residual stress redistribution near cold-expanded holes in plane rectangular specimens under low-cycle fatigue with different cycle parameters, is the main goal of this paper. further investigations will be directed toward a study of residual stress evolution in composite fragments of metal-composite joints. experimental procedure specimens and loading program luminium coupons of dimensions 180×30×5 mm, each of which includes centred open hole of nominal diameter 2 0r = 4.0 mm (fig. 1) are the objects of present study. whole set of specimens consists of 16 units. all coupons are manufactured from a single material bar by the same technology. absence of residual stresses in all specimens a a.v. chernov et alii, frattura ed integrità strutturale, 55 (2021) 174-186; doi: 10.3221/igf-esis.55.13 176 follows from data of probe hole drilling and further optical interferometric measurements of deformation response to local material removing [21]. mechanical properties (elasticity modulus e = 74,000 mpa, yield stress  y = 330 mpa and poisson’s ratio µ = 0.33) are obtained proceeding from standard tensile tests. a b c figure 1: drawing of specimens of т5h type. (a) scheme, (b) 3d view, (c) cyclic loading of cold-expanded hole. all specimens have been tested after cold hole expansion. the technology of the involved procedure is described in work [1]. the expansion level is 5% of nominal interference, defined as the ratio of the interference value to the hole radius. the results of research [11], obtained by finite element simulation, evidence that the degree of interference from 4% to 6% leads to the arising circumferential residual stress  rs = – (250÷300) mpa near expanded hole boundary. the exact value of  rs depends on the yield stress of aluminium alloy. optical interferometric measurements of the local deformation response to notch length increment are performed in the mandrel entrance (inlet) surface of all specimens. specimens are divided by two groups. the first of them, denoted as t5-h1, includes 8 specimens. required sif values are obtained at different stages of low-cycle fatigue with stress range δσ = 350 mpa and stress ratio r = –0.4. maximum remote tensile stress for this loading program is equal to  max = 250 mpa that corresponds to 0.76 of yield stress  y = 330 mpa. eight specimens from the second group (t5-h2) are tested at different stages of fatigue loading program with the parameters δσ = 350 mpa, r = –1.0. the cycle parameters expressed in the terms of maximum tensile and minimum compressive stress are equal to  max = − min = 175 mpa. the value of  max = 175 mpa corresponds to 0.53 of yield stress  y = 330 mpa. static strength of coupons with cold-expanded holes was not estimated because of limited number of specimens. a sequence of narrow notches is used for crack modelling at different stages of fatigue loading. step-by-step procedure of crack length increasing is performed by narrow jewellery saw of width δb = 0.2 mm. the original points of each symmetrical notch are located at the intersection of the hole boundary and the short symmetry axis of the specimen. details of experimental procedure are described in works [1, 22]. the first specimen, which is common for both groups, is tested before fatigue loading. other specimens are subjected to fatigue loading according to the above-mentioned programs. an electro-mechanical testing machine walter + bai ag, type lfm-z 200, with load range 0 – 200 kn is used for fatigue loading. the number of loading cycles for each investigated specimen is listed in tab. 1 and tab. 2 for specimens of t5-h1 and t5h2 group, respectively. two specimens serve for lifetime estimation. fracture of specimens is occurred after 1fn = 6300 a.v. chernov et alii, frattura ed integrità strutturale, 55 (2021) 174-186; doi: 10.3221/igf-esis.55.13 177 cycles for specimen t5_h1 and 2fn = 15800 cycles for specimen t5-h2. each specific cycle number from tab. 1 and 2 indicates the stage of fatigue loading, at which sif values are derived for cracks of different lengths from initial experimental data. three consecutive notches after fatigue loading of specimens are inserted under the constant external load that corresponds to remote stress σ = 80 mpa. an electro-mechanical testing machine walter + bai ag, type lfm-l 25, with loading range 0–25 kn serves for applying remote tensile stress during the measurement procedure. specimen t5_20h t5_13h t5_16h t5_12h t5_18h t5_19h t5_17h t5_h1 number of cycles, n 0 1000 2000 3000 4000 5000 6000 6300 lifetime, % 0 16 32 48 63 79 95 100 table 1: nomenclature of t5-h1 specimens and fatigue loading program. specimen t5_20 h t5_21 h t5_22 h t5_23 h t5_24 h t5_25 h t5_26 h t5_27 h t5_h2 number of cycles, n 0 1000 2000 3000 6000 9000 12000 15000 15800 lifetime, % 0 6 13 19 38 57 76 95 100 table 2: nomenclature of t5-h2 specimens and fatigue loading program. initial experimental information initial experimental information has the form of interference fringe patterns, which describe the distributions of both inplane displacement components near the crack tip. these interferograms correspond to increasing the length of the central symmetrical crack of mode i in thin rectangular plate under constant tensile load. the total crack length consists of three prolongation increments. interference fringe patterns obtained for different notch length increments in specimen t5-20h and t5-16h are shown in fig. 2 and 3, respectively. demonstrated high quality of interferograms in fig. 2 and 3 is inherent in all fringe patterns obtained at all investigated stages of low-cycle fatigue (see tab. 1 and 2). symmetrical configuration of fringe patterns in fig. 2 and 3 with respect to the crack line clearly demonstrates the validity of mode i conditions. the same takes place for all crack length increments considered for all specimens. this means that sif values can be reliably derived from the relationships developed for modified version of the crack compliance method [22]. these formulae are based on principals of linear fracture mechanics. but there is one important problem to be considered. it resides in a question how material plastic deformation inherent in the nearest vicinity of cold-expanded hole influences on a crack modelling by narrow notches. cold expansion induces a zone of residual compressive stress around and through a hole, typically extending at least one radius around hole in the radial direction. the problem of implementing linear fracture mechanics formulae to sif determination near cold-expanded holes is a question of further discussion. a b c figure 2: interference fringe patterns obtained in terms of in-plane displacement component v for specimen t5_20h. a.v. chernov et alii, frattura ed integrità strutturale, 55 (2021) 174-186; doi: 10.3221/igf-esis.55.13 178 a – initial crack length 0a = 0 with the increment  1a = 2.28 mm (left) and  1a = 2.31 mm (right); b – initial crack length  1a = 2.28 mm with the increment  2a = 1.96 mm (left) and initial crack length  1a = 2.31 mm with the increment  2a = 2.17 mm (right); c – initial crack length 2a = 2.28 mm with the increment  3a = 1.79 mm (left) and initial crack length  2a = 4.24 mm with the increment  3a = 2.08 mm (right). a b figure 3: interference fringe patterns obtained in terms of in-plane displacement component v for specimen t5_16h.a – initial crack length 0a = 0 with the increment  1a = 2.17 mm (left) and  1a = 2.10 mm (right); b – initial crack length  1a = 2.17 mm with the increment  2a = 1.89 mm (left) and initial crack length  1a = 2.10 mm with the increment  2a = 1.82 mm (right). parameters extraction esidual stress evolution analysis, presented in this paper, is based on redistribution of stress intensity factors, which are obtained at different stages of low-cycle fatigue. these sif values are related to a sequence of narrow notches, initial point of which is located at the edge of cold-expanded hole. that is why an accuracy of sif determination for notches emanating from hole of diameter 2 0r = 4 mm should be carefully established. comprehensive uncertainties analysis inherent in fracture mechanics parameters determination by a modified version of the crack compliance method is presented in work [22]. but this analysis concerns quantitative sif characterization for notches emanating from small hole of 0.5 mm diameter. uncertainty estimation to reach above-declared goal two specially designed tests have been performed. the first of them is connected with asserting the measurement errors evaluation for rectangular specimen, denoted as t5_08, with plain hole, geometrical parameters of which are shown in fig. 1. the essence of the methodology involved resides in comparison of real interference fringe patterns and analogous artificial images. this approach is a powerful instrument for fine verification of measurement results when initial experimental information is presented in the form of interference fringe patterns [20, 21, 23, 24]. interference fringe pattern obtained for specimen t5_08 with symmetrical crack for tensile load value p = 7.96 kn are shown in fig. 4a. special attention was paid to make symmetrical crack with left and right branch of equal length. simulation of reference fringe patterns involves a high-quality transition model that connects the object geometry in conjunction with an external load and the required in-plane displacement fields related to the object surface. in our case this model follows from the relationships of the elasticity theory. visualization of reference fringe patterns is founded upon the r a.v. chernov et alii, frattura ed integrità strutturale, 55 (2021) 174-186; doi: 10.3221/igf-esis.55.13 179 basic relations of speckle interferometry [25]. numerical solution, which corresponds to the difference between stress state of cracked specimen after notch formation and initial stress state of the specimen with an open plain hole only, is able of constructing a set of required reference fringe patterns. to reach this goal, a value of external load and width of real cut, which correspond to measurement conditions, have to be given. numerical determination of displacement component fields has to be based on a high-precision finite element solution of two stress concentration problems. in the case involved the first of them resides in uniaxial tension of rectangular plate of dimensions 180×30×5 mm with central through hole of diameter 2 0r = 4.00 mm. the second problem to be considered is uniaxial tension of the same plate with narrow notch of width δb = 0.20 mm and of average length 1a = 2.64 mm. the original point of each symmetrical notch is located at the intersection of hole boundary and transverse symmetry axis of the specimen as it shown in fig. 1. numerical data, describing the local displacement fields, are obtained by means of corresponding segments of the msc.nastran software. the finite element mesh consists of 101 000 plane shell elements of cquad4 type. then the reference fringe patterns can be constructed by using the difference of corresponding in-plane displacement components for two above-mentioned elasticity problems. a b figure 4: real (a) and reference (b) interference fringe patterns obtained in terms of in-plane displacement component v for specimen t5_08; initial crack length 0a = 0 with the increment  1a = 2.66 mm (left) and  1a = 2.62 mm (right). stage number, n 1 2 3     / 2n n na a a , mm 2.64 4.20 6.18  1nv , μm experiment 12.16 13.40 14.43 fem 13.68  0.5nv , μm experiment 9.60 10.64 11.78 fem 10.07 sif value, mpa m experiment,  nik 6.76 8.95 10.77 fem, femik 6.70 theory, tik 6.73 7.46 8.45 table 3: deformation and force fracture mechanics parameters for specimen t5_08. a.v. chernov et alii, frattura ed integrità strutturale, 55 (2021) 174-186; doi: 10.3221/igf-esis.55.13 180 artificial interference image related to the first crack length increment is denoted by letters b in fig. 4. a good coincidence in a configuration of real interferogram and analogous reference fringe pattern is quite evident. averaged notch mouth opening displacement (nmod  1nv ), notch opening displacement related to half of the crack length (nod  0.5nv ) and sif (  nik ) values are used to compare experimentally and numerically obtained fracture mechanics parameters in the case of symmetrically centred cracks as it is reflected in tab. 3. this is specially done, because ensuring equal crack length increments for both tips of symmetrical crack is quite a serious technical problem. but this difficulty is technically avoided for the first crack length increment    1 1a a . values of nmod and nod obtained experimentally and numerically differ by 11% and 4.7%, respectively. the sif values, calculated by using the real and artificial interference fringe patterns for the first crack length 1a as a source of initial information, are equal one to another. this very good result follows from data of tab. 3. it should be taken into account that the reference fringe pattern is obtained as the solution of stress concentration problem in terms of in-plane displacement component u and v. only the final step employs linear fracture mechanics relationships in the form of williams’ infinite series for each in-plane displacement component. the formula, used for sif values determination, has the following form [22]:         0.5 1 2 2 2 8 n i n n n e k v v a , (1) where e is the elasticity modulus of the material;  na is the crack length increment. the sif values are obtained by substituting nmod and nod values from tab. 3 into formula (1). the source of the initial information is the real and reference interference fringe pattern for experimental and numerical sif values, respectively. note that sif determination through the use of in-plane displacement component is very powerful numerical procedure in the course of finite element simulation of cracks in plane specimens [26]. moreover, data thus obtained might be very useful for refining numerical models, which serves for quantifying the crack tip surface displacements in the zone where the corner point of the crack front intersects a free surface [27, 28]. further accuracy analysis of the experimentally obtained sif values is based on comparison with the analytical results presented in the famous handbook of murakami [29]. one of the rows in tab. 3 includes theoretical sif values. these data correspond to the solution for the through symmetrical crack starting from the hole boundary in the infinite plane (section 5.1 of handbook [29]). theoretical and experimental sif values for the first crack length 1ik are in a good coincidence. the values of  2ik and  3 ik obtained experimentally and theoretically differ by 16% and 21%, respectively, with experimental sif values exceed analogous theoretical data. this fact reflects the influence of the specimen edges that is not taken into account by the theoretical solution when through hole is located in an infinite plate. the same trend takes place when the experimental sif values for mode i crack are compared with the theoretical data obtained for a crack in an infinite plane and a crack in a plane specimen of limited width under uniaxial tension [22]. comparison of the experimental, numerical and theoretical data presented above clearly demonstrates that the developed approach ensures the appropriate accuracy of sif determination in the considered case. determination of residual stress intensity factor the essence of modified version of the crack compliance method resides in the following. initial experimental information, derived in terms of crack opening displacements, is used for deriving the first four coefficients of williams’ asymptotic series and further calculations of sif values. this means that formula (1) is based on principal of linear fracture mechanics. thus, an influence of high-level plastic strains, which occur at the hole vicinity due to cold expansion, on formula (1) validity should be carefully considered. there is a hope to receive positive answer on this question because narrow notch, used for crack modelling, is inserted after complete redistribution of plastic strains in work-hardening aluminium alloy. determination of sif values for notches emanating from cold-expanded hole, which are related to different remote stress levels, is the essential step in this way. to do this, special experiments, connected with a determination of nmod and sif values for three remote stress levels, have been performed. interference fringe patterns obtained for the first notch of 1a = 2.3 mm length under remote stress σ = 60, 80 and 100 mpa are shown in fig. 5a, 5b and 5c, respectively. dependencies of nmod and sif values from remote stress level, obtained as the result of three specimens testing, are shown in fig. 6a and 6b, respectively. plot in fig. 6b has practically linear character. this fact means that formula (1), based a.v. chernov et alii, frattura ed integrità strutturale, 55 (2021) 174-186; doi: 10.3221/igf-esis.55.13 181 in principals of linear fracture mechanics, can be reliably implemented for sif determination when narrow notch is inserted in material volume that has been undergone to preliminary plastic deformation. a b c figure 5: interference fringe patterns obtained in terms of in-plane displacement component v for three different specimens; initial crack length 0a = 0 mm with increment  1a = 2.30 mm (left) and  1a = 2.30 mm (right). a – specimen t5_29h (σ = 60 mpa); b – specimen t5_20h (σ = 80 mpa); c – specimen t5_28h (σ= 100 mpa). a b figure 6: average values of nmod . 0v (a) and sif (b) as a function of remote stress level σ. complete set of data, required for residual stress evolution study near cold-expanded holes due to low-cycle fatigue, has previously been reported in work [1]. the whole set of interference fringe patterns is the source of initial experimental data, which represent in-plane displacement components measured by electronic speckle-pattern interferometry in the vicinity of the notch tip. this information gives distributions of nmod, sif and t-stress values along total crack length in specimens of both groups, obtained for different loading cycles. these distributions can be reconstructed to receive dependencies of fracture mechanics parameters for notches of fixed length against of loading cycle number. present analysis is founded upon redistribution of sif values obtained for notches of different length at different stages of low-cycle fatigue. dependencies of sif values from number of loading cycle are shown in fig. 7a and 7b for specimens of t5-h1 and t5-h2 group, respectively. considering these results, we should keep in mind that they are referred to the mandrel entrance (inlet) surface specimens. it has previously been shown that residual stresses arising at the inlet surface are always lower than those related to the outlet surface [7–17]. this means that fatigue crack always initiation point is always located at the hole edge corresponding to the inlet face where the lower compression residual stresses arise due to cold expansion. that is why optical interferometric measurements of the local deformation response to small notch length increment are performed in the mandrel entrance (inlet) surface of specimens. thus, the thickness effect is not taken into account. to reach this aim, a.v. chernov et alii, frattura ed integrità strutturale, 55 (2021) 174-186; doi: 10.3221/igf-esis.55.13 182 simultaneous measurements of deformation response, caused by local material removing, on both specimen faces have to be involved. a set of required experiments is currently under consideration. the results obtained will be reported later. a b figure 7: residual sif  nik values as a function of loading cycle number n for t5-h1 (a) and t5-h2 (b) specimens for notches of length na (n =1, 2, 3). data, presented in fig.6b, provide a way to derive sif values, connected with residual stress only, by means of technique proposed in work [11]. the essence of this approach resides in implementing the linear superposition principal in order to evaluate sif values  n rsik , which are related to pure residual stress field. in other words,  n rs ik can be presented as the difference in experimental sif value  nik and theoretical (numerical) sif value nt ik , which are obtained for specimens of equal geometry with the same crack length under the same remote stress:     n rs n nti i ik k k (2) where n =1, 2, 3. theoretical sif values 1tik are listed in tab. 4. this table also includes  1 rs ik values obtained by relationship (2) for notch of 1a length proceeding from experimental data shown in fig. 6b. σ, mpa 1a , mm  n ik , mpa m 1t ik , mpa m  1 rs ik , mpa m 60 2.52 −5.1 7.4 −12.50 80 2.30 −2.6 9.66 −12.26 100 2.43 0 12.2 −12.20 table 4: sif values for different remote stress levels. data of tab. 4 demonstrate that residual sif values, calculated for different remote stress levels, coincide within 2.4 percent. this fact provides reason enough to implement linear fracture mechanics relations in the course of experimental sif determination when a crack length met to the condition 1a 2 mm. thus, formula (1) can be reliably used for residual sif  n rs ik determination for all three notches of different length, emanating from cold-expanded holes at different stages of low-cycle fatigue. dependencies of residual sif values from number of loading cycle are shown in fig. 8a and 8b for specimens of t5-h1 and t5-h2 group, respectively. a.v. chernov et alii, frattura ed integrità strutturale, 55 (2021) 174-186; doi: 10.3221/igf-esis.55.13 183 a b figure 8: residual sif   1 rs ik values as a function of loading cycle number n for t5-h1 (a) and t5-h2 (b) specimens for notches of length na (n =1, 2, 3). plots, presented in fig. 8, indicate initial level of residual sif  n rsik values at different distances from cold-expanded hole edge and their evolution due to low-cycle fatigue. note that this evolution for most of presented curves cannot be characterises as monotonic relaxation. dependencies of residual stress sif values  n rsik from current crack length na in specimens of both groups, constructed at different stages of low-cycle fatigue, are shown in fig. 9. curves in fig. 8 and 9 evidence that an influence of negative residual stress takes place at distance 2a 4.10 mm from the hole edge for t5-h1 group and at distance 2a 4.50 mm for t5-h2 group. this influence is practically absence for  0 3r a radius for both cases. a b figure 9: residual sif   n rs ik values as a function of notches length na (n =1, 2, 3) for t5-h1 (a) and t5-h2 (b) specimens for different cycle number. averaged values of notch length, which are used for plots in fig. 7 and fig. 8, are listed in tab. 5. normalizes dependencies of residual sif values from loading cycle number, which follows from dependencies, shown in fig. 8, could be used for quantitative estimation of degree of residual stress relaxation in the hole vicinity. corresponding curves are presented in fig. 10. maximal relaxation reaches 23% for specimens of t5-h1 group (n = 6000 cycles) and 20% for specimens of t5-h2 group (n = 15000 cycles). this fact means that for low-cycle fatigue with stress range a.v. chernov et alii, frattura ed integrità strutturale, 55 (2021) 174-186; doi: 10.3221/igf-esis.55.13 184 δσ = 350 mpa the change of stress ratio from r = –0.4 to r = –1.0 does not influence on residual stress evolution. both extreme values of relaxation parameter are reached for 95 per cent of lifetime. specimen’s group 1a , mm 2a , mm 3a , mm t5-h1 2.20 4.10 5.90 t5-h2 2.60 4.50 6.40 table 5: averaged notch length. figure 10: normalized residual sif values as a function of loading cycle number for notches of 1a length. it is of interest to obtain quantitative parameters of residual stress field under study. rough but quite reliable estimation follows from the first term of westergaard’s decomposition [30]:      1 2 2 rs rs ik r (3) where  2 rs denotes circumferential residual stress components, related to the first notch increment of 1a length; r is a distance from the notch tip along x-axis. graphical representation of function (3) is shown in fig. 11. quantitative estimation that follows from formula (3) for r = 0.005 mm is  2 rs = –220 mpa. this result is in a good agreement with numerical data presented in work [11]. figure 11: values of circumferential residual stress component  2 rs at different distances from the tip of notch of 1a length. a.v. chernov et alii, frattura ed integrità strutturale, 55 (2021) 174-186; doi: 10.3221/igf-esis.55.13 185 conclusion nconventional method for a quantitative characterization of residual stress evolution near cold-expanded hole due to low-cycle fatigue is proposed and realized. the approach developed is based on modified version of the crack compliance method that is capable of sif determination for narrow notches emanating from cold-expanded holes. these notches are inserted at different stages of low-cycle fatigue under constant external load. the first distinctive point of the technique involved consists of the fact that in-plane displacement components are measured by espi along narrow notch border immediately. notch emanation from the hole edge is the second important trait, which considerably increases a sensitivity with respect to residual stress determination. the third feature resides in consideration of two low-cycle fatigue programs with negative stress ratio. validity of implementation of linear fracture mechanics relationships for transition from experimentally determined displacement components to required sif values in the cold-expanded hole vicinity is substantiated by comparing data, which are obtained for different external load values. above assertion follows from linear character of dependencies of nmod and sif values, obtained in residual stress field, from remote stress level. this fact opens a way to implement the linear superposition principal for evaluation of residual sif values. it is shown that residual sif values, which correspond to different remote stress levels, lie within 2.4 per cent interval. two loading programs are performed for stress range δσ = 350 mpa. it is established that maximal residual stress relaxation is equal to 23% and 20% for stress ratio r = –0.4 to r = –1.0, respectively. the results obtained demonstrate that negative circumferential residual stress remains its positive influence on fatigue crack resistance during 95% of low-cycle lifetime of specimen with coldexpanded hole for both low-cycle fatigue programs. acknowledgements he research was carried out within the frames of subsidy agreement 14.628.21.0009, project identification number rfmefi62818x0009 (ministry of science and high education of the russian federation). references [1] matvienko, y.g., pisarev, v.s., eleonsky, s.i. (2019). the effect of low-cycle fatigue on evolution of fracture mechanics parameters in residual stress field caused by cold hole expansion, fratt. ed int. str., 13(47), pp. 303-320. doi: 10.3221/igf-esis.47.23. [2] matvienko, y.g., pisarev, v.s., eleonsky, s.i. (2019). the effect of low-cycle fatigue parameters on damage accumulation near a hole, eng. fail. an., 106, doi: 10.1016/j.engfailanal.2019.104175. [3] wang, z.-q., huang, x.-g., zhang, d.-h. (2020). low cycle fatigue damage model and sensitivity analysis of fatigue crack initiation by finite element approach, fratt. ed int. str., 14(53), pp. 81-91. doi: 10.3221/igf-esis.53.07. [4] tumanov, a.v., shlyannikov, v.n., zakharov, a.p. (2020). crack growth rate prediction based on damage accumulation functions for creep-fatigue interaction, fratt. ed int. str., 14(52), pp. 299-309. doi: 10.3221/igf-esis.52.23. [5] feistauer, e. e., dos santos, j. f., amancio-filho, s. t. (2018). a review on direct assembly of through-the-thickness reinforced metal–polymer composite hybrid structures, polymer engineering & science, 59(4), pp. 661-674. doi: 10.1002/pen.25022. [6] reid, l. (2014). hole cold expansion – the fatigue mitigation game changer of the past 50 years, advanced materials research, 891–892, pp. 679-684. doi: 10.4028/www.scientific.net/amr.891-892.679. [7] stefanescu, d. (2004). measurement and prediction of fatigue crack growth from cold expanded holes, part 1: the effect of fatigue crack growth on cold expansion residual stresses, j. of str. analysis, 39(1), pp. 25-39. doi: 10.1177/030932470403900103. [8] ball, d.l. (1995). elastic-plastic stress analysis of cold expanded fastener holes, fatigue and fract.of eng. mat. and struct., 18(1), pp. 47-63. [9] zhang, y., fitzpatrick, m.e., edwards, l. (2005). analysis of the residual stress around a cold-expanded fastener hole in a finite plate, strain, 41(2), pp. 59-70. doi:10.1111/j.1475-1305.2005.00181.x. u t a.v. chernov et alii, frattura ed integrità strutturale, 55 (2021) 174-186; doi: 10.3221/igf-esis.55.13 186 [10] pavier, m.j., poussard, c.g.c., smith d.j. (1999). effect of residual stress around cold worked holes on fracture under superimposed mechanical load, eng. fract. mechanics, 63(6), pp.751-773. doi: 10.1016/s0013-7944(99)00050-8. [11] moreira, p.m.g.p., de matos, p.f.p., pinho, s.t., pastrama, s.d., camanho, p.p., de castro, p.m.s.t. (2004). the residual stress intensity factors for cold-worked cracked holes: a technical note, fatig. & fract. of eng. mat. & struct., (27), pp. 879-886. doi:10.1111/j.1460-2695.2004.00768.x. [12] yongshou, l., xiaojun, s., jun, l., yue zhufeng. (2010). finite element method and experimental investigation on the residual stress fields and fatigue performance of cold expansion hole, materials and design, 31(3), pp. 1208-1215. doi: 10.1016/j.matdes.2009.09.031. [13] mahendra babu, n., jagadish, t., ramachandra, k., sridhara, s. (2008). a simplified 3-d finite element simulation of cold expansion of a circular hole to capture through thickness variation of residual stresses. eng. fail. an., 15 (4), pp. 339-348. doi: 10.1016/j.engfailanal.2007.02.003. [14] garcia-granada, a.a., pavier, m.j., smith, d.j. (2001). a new procedure based on sachs’ boring for measuring nonaxisymmetric residual stresses, int. j. of mech. sciences, 42(6), pp. 1027-1047. doi: 10.1016/s0020-7403(99)00039-9. [15] garcia-granada, a.a., pavier, m.j., smith, d.j. (2001). a new procedure based on sachs’ boring for measuring nonaxisymmetric residual stresses: experimental application, int. j. of mech. sciences, 43(12), pp. 2753-2768. doi: 10.1016/s0020-7403(01)00071-6. [16] özdemir, a.t., edwards, l. (2004). through-thickness residual stress distribution after the cold expansion of fastener holes and its effects on fracturing, j. eng. mater. technol., 126, pp. 129-135. doi: 10.1115/1.1634278. [17] zuccarello, b., di franco, g. (2013). numerical-experimental method for the analysis of residual stresses in coldexpanded holes, exp. mechanics; 53(4), pp. 673-686. doi:10.1007/s11340-012-9669-2 [18] backman, d., cowal, c., patterson, e.a. (2010). analysis of the effects of cold expansion of holes using thermoelasticity and image correlation, fat. & fract. of eng. mat. & struct., 33(12), pp. 859–870. doi: 10.1111/j.1460-2695.2010.01472.x [19] keith, w.j., ralph, w.b. (2017). investigation of residual stress relaxation in cold expanded holes by the slitting method, eng. fract. mech., 179, pp. 213-224. doi: 10.1016/j.engfracmech.2017.05.004 [20] matvienko, y.g., pisarev, v.s., eleonsky, s.i. (2019). residual stress/strain evolution due to low-cycle fatigue by removing local material volume and optical interferometric data, fat. & fract. of eng. mat. & struct., 42, pp. 2061– 2078. doi:10.1111/ffe.13083 [21] pisarev, v.s., odintsev, i.n., eleonsky, s.i., apalkov, a.a. (2018). residual stress determination by optical interferometric measurements of hole diameter increments, optics and lasers in engineering, 110, pp. 437–456, doi: 10.1016/j.optlaseng.2018.06.022 [22] pisarev, v.s., matvienko, y.g., eleonsky, s.i., odintsev, i.n. (2017). combining the crack compliance method and speckle interferometry data for determination of stress intensity factors and t-stresses, eng. fract. mech., 179, pp. 348374. doi: 10.1016/j.engfracmech.2017.04.029 [23] pisarev, v.s., dzuba, a.s., grigoriev, v.d., chumak, s.v. (2001). reference fringe patterns as effective tool for local strain analysis based on holographic interferometry data. 4th international workshop on automatic processing of fringe patterns, bremen, september 17-19. [24] pisarev, v.s., balalov, v.v. (2004). a role of fringe pattern catalogue in the course of interferometrically based determination of residual stresses by the hole-drilling method, opt. & l. in eng., 41(2), pp. 411-462. doi: 10.1016/s0143-8166(02)00203-8 [25] rastogi, p. (2001). digital speckle pattern interferometry and related techniques, wiley, west sussex. [26] jogdand, p.v., murthy, k.s.r.k. (2010). a finite element based interior collocation method for the computation of stress intensity factors and t-stresses, eng. fr. mech., 77(7), pp. 1116-1127. doi: 10.1016/j.engfracmech.2010.03.002. [27] pook, l. p., campagnolo, a., berto, f. (2016). coupled fracture modes of discs and plates under anti-plane loading and a disc under in-plane shear loading, fat. & fract. of eng. mat. & struct., 39(8), pp. 924–938. doi: 10.1111/ffe.12389. [28] pook, l. p., berto, f., campagnolo, a.(2016). coupled fracture modes under anti-plane loading, fratt. ed int. str., 10(37), pp. 108-113. doi: 10.3221/igf-esis.37.15. [29] murakami, y. (1987). stress intensity factors handbook, oxford: pergamon. [30] westergaard, h.m. (1939). bearing pressures and cracks, j. of app. mech., 61, pp. a49-a59. microsoft word numero_38_art_32 m. lutovinov et alii, frattura ed integrità strutturale, 38 (2016) 237-243; doi: 10.3221/igf-esis.38.32 237 focussed on multiaxial fatigue and fracture a comparison of methods for calculating notch tip strains and stresses under multiaxial loading m. lutovinov, j. černý, j. papuga fme ctu in prague, technická 4, 166 07 prague 6, czech republic maxim.lutovinov@fs.cvut.cz jiri.cerny2@fs.cvut.cz jan.papuga@fs.cvut.cz, http://orcid.org/0000-0001-9569-4997 abstract. selected methods for calculating notch tip strains and stresses in elastic–plastic isotropic bodies subjected to multiaxial monotonic loading were compared. the methods use sets of equations where hypothetical notch tip elastic strains and stresses obtained from fem calculations serve as an input. the comparison was performed within two separate groups of methods: the first group consists of the methods intended for cases of multiaxial proportional loading and the second group deals with multiaxial non-proportional loading. originally, the precision of the methods was validated by comparison with results obtained from elastic–plastic fem analyses. since computer performance at the time was lower than nowadays, verification of the proposed methods on fem models with a finer mesh was needed. such verification was carried out and is presented in this paper. the effect of various formulations of material stress–strain curve was also evaluated. keywords. notch stresses; multiaxial loading; fem; neuber’s rule; esed rule. citation: lutovinov, m., černý, j., papuga, j., a comparison of methods for calculating notch tip strains and stresses under multiaxial loading, frattura ed integrità strutturale, 38 (2016) 237-243. received: 28.04.2016 accepted: 05.06.2016 published: 01.10.2016 copyright: © 2016 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. introduction here are several ways to obtain notch tip stresses and strains: numerical simulation, experiment, and estimation methods. since the first two approaches are time consuming, it is desirable to use estimation methods that provide results based on elastic fe simulation only. such methods have been developed since the last century and can work with different types of loading, including cyclic loading [1], [2]. the essence of those methods is in using results from elastic fe analyses and converting these results into elastic–plastic estimates using suitable sets of equations. in this paper, two sets of methods were selected for comparisons. the first set consisted of the methods intended for multiaxial proportional monotonic loading. the selected methods were moftakhar’s method [3], reinhardt’s method [4], and hoffmann–seeger’s method [5]. the second set consisted of the methods intended for multiaxial non-proportional monotonic loading. the selected methods were singh’s method [6] and buczynski’s method [7]. t m. lutovinov et alii, frattura ed integrità strutturale, 38 (2016) 237-243; doi: 10.3221/igf-esis.38.32 238 selected methods ue to the plane stress state at the notch tip, one component of principal stresses has a zero value and therefore, in case of principal components, there are five unknowns, for which five equations are needed. these unknowns are maximum principal strain ε1, middle principal strain ε2, minimum principal strain ε3, and two of principal stresses σ1, σ2, σ3 depending on the type of loading. all of the selected methods, with the exception of hoffmann–seeger’s method, were defined in two different variants. the first estimate is obtained when neuber’s rule is used for compiling the set of equations. the second estimate is obtained when the esed rule [3], [6] is used instead. hoffmann–seeger’s method uses only neuber’s rule. both neuber’s rule and the esed rule state that strain energy density at the notch tip of a body with elastic–plastic behaviour is equal to strain energy density at the notch tip of a body with ideal elastic behaviour. the difference between these rules is that neuber’s rule also takes in account complementary strain energy density [3]. as the first equation for prediction according to moftakhar’s method, the extensions either of neuber’s rule or the esed rule are used. these extensions were developed for multiaxial loading and are represented by a sum of products of the individual stress and strain components. the next three equations for moftakhar’s method are provided by hencky’s equations that relate strains, stresses, and a material model represented by the cyclic stress–strain curve. the last equation is provided by the energy distribution assumption which states that fractional contribution of the largest principal notch tip stresses and strains to the total notch tip strain energy density [3] is equal for a body with elastic–plastic behaviour and a for a body with elastic behaviour. besides the five unknown parameters mentioned above, there is another unknown which is a part of hencky’s equations. this parameter is the plastic component of equivalent deformation. moftakhar in [3] calculates it from bilinear approximation of cyclic stress–strain curve. another way to calculate this parameter is by using the ramberg–osgood expression. reinhardt’s method [4] represents a modification of moftakhar’s method. the motivation for the modification was the fact that, since the original method forms a set of nonlinear algebraic equations, several solutions for that set exist in general [4]. therefore, reinhardt et al. presented a new algorithm for calculating notch tip stresses and strains based on the equations derived from the original moftakhar’s set. in hoffmann–seeger’s method [5], another generalized form of neuber’s rule is used for calculating actual equivalent stress. the method also uses hencky’s expression, expression for von mises stress, and an assumption about the ratio of surface strains to calculate the unknown components of stress and strain tensors. the selected methods designed for non-proportional loading work with general components of stresses and strains, and therefore there are seven unknowns (ε11, ε22, ε23, ε33, σ22, σ23, σ33), for which seven equations are needed. since the ratio of deviatoric stresses in case of non-proportional loading is unlikely to be a constant value, the final stress–strain state is dependent on the applied loading path [6]. therefore, the equations used for predictions should be in an incremental form. the set of equations for singh’s method [6] consists of a) either generalized neuber’s rule or the esed rule, b) the prandtl– reuss relations, which reflect elastic–plastic material behaviour and provide four equations, and c) two equations provided by energy ration assumptions. the first three equations for buczynski’s method [7] are obtained from either generalized neuber’s or the esed rule, expressed as an equality of symmetric strain energy density tensors. the remaining four equations are provided by the prandtl–reuss relation. verification process he verification process was as follows: at first the selected methods were implemented in two programs written in matlab, one for the case of proportional loading, the other one for non-proportional loading. in the next step, in order to verify whether individual methods are implemented correctly, the data from elastic simulations referred originally by the authors, were derived from the articles. after obtaining the original inputs, they were imported into the matlab programs. at the beginning of the estimation process, input vectors were divided by preselected increments. in case of methods designed for non-proportional loading, the end of the first increment was the yielding state. the yielding state was found by linear interpolation using von mises stress (eq. 1) for comparison with yield strength d t m. lutovinov et alii, frattura ed integrità strutturale, 38 (2016) 237-243; doi: 10.3221/igf-esis.38.32 239 2 2 2 1 1 2 2       eq (1) where eq is equivalent stress. in all cases, estimations started from the yielding point. in case of proportional loading it was only natural since the modification of inputs was performed so that the first non-zero input values corresponded to the yielding state. in nonproportional load cases, it was checked whether the value of equivalent stress was higher than yield strength. if that condition was not met, the solutions for the current step were equal to the elastic solution. the solutions to the sets of equations provided by each method were obtained using matlab function fsolve. the results of estimations were compared with the elastic–plastic fe solutions presented in the original articles. the only exception was reinhardt’s method, the results of which were compared with moftakhar’s method. in case of non-proportional loading, besides the multilinear approximation of cyclic stress–strain curve, the material model described by the ramberg–osgood expression was used to compare the quality of estimates. after the verification of the implementation of the methods, the finite element analyses were carried out. the aim of those analyses was to provide inputs that were obtained on fe models with a mesh denser than used to be common, when the evaluated methods were first presented. to get a model with a representative fine mesh, sensitivity analyses were carried out on fe models with an elastic material model and different mesh densities. the appropriate model was then the model for which changes in values of equivalent stress were insignificant (less than 1% for cases of proportional loading, and less than 4% for cases of non-proportional loading). for proportional loading, simulations on two types of specimens were performed. the first one was a solid bar with a circumferential groove loaded simultaneously with tension and torsion. another specimen was a hollow tube with a circumferential groove loaded by internal pressure and tension. both types of specimens and loads corresponded to those presented in [3]. for non-proportional loading, a round bar with a circumferential groove loaded by torsion in the first step and by increasing tension and constant torsion in the second step, was used. this type of model is presented in [6]. after results from fe simulations were obtained, they were used as inputs for estimations in order to assess and compare prediction quality of selected methods. results of verification of methods implementation he same results as presented in [3] were obtained for moftakhar’s method using 4 increments in elastic–plastic region and bilinear approximation as the material model. same settings were used for reinhardt’s method and it led to the same results as in case of moftakhar’s method. the implementation of hoffmann–seeger’s method was verified using the results from [5]. the same results as in [6] were obtained for singh’s method using 28 increments per loading step and 6 linear approximation of the cyclic stress–strain curve. the attempt to get the same results as in [7] for buczynski’s method was not successful. the fsolve function failed to solve the set of equations defined by the method. numerical instability was observed for both definitions of the material model, with the ramberg–osgood expression or with the linear approximation. it was also observed that changing the settings of tolfun parameter, which defines termination tolerance on the fsolve function value [8], affects this behaviour. the smallest instability is observed in the case of 6 piecewise linear material model when estimations start from plasticized state with settings of tolfun to 1e-5. comparison with use of modern fe models proportional loading n fig. 1, the estimates of stress and strain components are presented. the stress estimates are very similar to those presented in [3]. there is a slight difference in minimum principal stress component for the bar specimen at the end of load sequence, where the prediction is most accurate as the elastic– plastic result is bounded by two moftakhar’s or two reinhardt’s estimates. there is also a slight difference in case of the hollow tube, where the estimate according to moftakhar’s method with the esed rule is closer to the elastic–plastic results from the fe simulation. t i m. lutovinov et alii, frattura ed integrità strutturale, 38 (2016) 237-243; doi: 10.3221/igf-esis.38.32 240 figure 1: results of estimations carried out on the round specimen (a, b) and the hollow tube (c, d) [3]. red is equivalent nominal net stress and sy is yield strength. for maximum principal stresses, hoffmann–seeger’s method seemed to be a better upper bound limit than moftakhar’s method with neuber’s rule. as in case of stresses obtained on the hollow tube, elastic–plastic strains from the fem simulation and from the prediction by moftakhar’s method with the esed rule are closer than presented in [3]. maximum principal strain could be well predicted with using hoffman–seeger’s method as the upper limit and moftakhar’s method with the esed rule as the lower limit. minimum and middle principal strains could be obtained by using hoffman–seeger’s method. all methods however are slightly non-conservative in case of minimum strain at round bar. non-proportional loading estimates of stress components 22 and 33 according to singh’s method are more precise than estimates presented originally in [6]. in case of shear stress component, once the yield stress is exceeded, all four estimations provide non-conservative results. estimates according to buczynski’s and singh’s methods are identical in this region. in the end of the load sequence, buczynski’s method with the esed rule provides the most accurate estimate. shear strain component calculated in the elastic–plastic fem model with the fine mesh result in substantially higher values than those referred to in [6]. it is possible to use singh’s methods as the upper and the lower limit. the use of average values of those two methods would lead to a slightly non-conservative solution for the component. other components are predicted quite well. m. lutovinov et alii, frattura ed integrità strutturale, 38 (2016) 237-243; doi: 10.3221/igf-esis.38.32 241 figure 2: results of estimations carried out on the bar specimen loaded non-proportionally with subsequent tension and torsion [6]. estimations were performed with the use of 6-linear approximation of cyclic stress–strain curve. using the ramberg–osgood material model the predictions using the ramberg–osgood material model led to worse estimation quality in general. in case of stresses, all estimates are shifted to the conservative region, while strains are shifted to the non-conservative region. the estimate of the shear stress component by buczynski’s method with the esed rule changed more than all other predictions and led to a distinctly non-conservative result. conclusions  quality of estimates of all methods is substantially dependent on used inputs. therefore, further investigation is needed in order to determine the extent of this dependence. for the same reason, it is also desirable to apply the methods to other types of specimens and to experimental data. proportional loading  for calculating maximum principal stresses and strains, hoffmann–seeger’s method should be used as the upper limit. as the lower limit, moftakhar’s method with the esed rule is the best option from those considered.  for calculating middle and minimum principal stress and strain components, both moftakhar’s estimations can be successfully used as the lower and the upper limit. non-proportional loading  due to the high dependence of the estimates according to buczynski’s method on settings of the solver function and based on the observation that predictions according to the buczynski’s method and singh’s method are very similar, it is proposed to use singh’s method. m. lutovinov et alii, frattura ed integrità strutturale, 38 (2016) 237-243; doi: 10.3221/igf-esis.38.32 242  the use of the multilinear approximation of the cyclic stress–strain curve for estimations led to better results than the use of the ramberg–osgood description of the cyclic stress–strain curve. figure 3: results of estimations carried out on bar specimen loaded non-proportionally with subsequent tension and torsion [6]. estimations were performed with the use of cyclic stress–strain curve described by the ramberg–osgood expression. acknowledgements he authors thank for the support of the research and of this contribution by the grant no. ga15-18274s of the czech science foundation and by the sgs14/181/ohk2/3t/12 ctu grant. references [1] ince, a., glinka, g., buczynski, a., computational modeling of multiaxial elasto-plastic stress–strain response for notched components under non-proportional loading, international journal of fatigue, 62 (2013) 42-52. doi:10.1016/j.ijfatigue.2013.10.008. [2] singh, m. n. k., notch tip stress strain analysis in bodies subjected to non-proportional cyclic loads, phd thesis, university of waterloo, canada, (1998). [3] moftakhar, a. buczynski, a., glinka, g., calculation of elasto-plastic strains and stresses in notches under multiaxial loading, international journal of fracture, 70 (1995) 357-373. doi: 10.1007/bf00032453. [4] reinhardt, w., moftakhar, a., glinka, g., an efficient method for calculating multiaxial elasto-plastic notch tip strains and stresses under proportional loading, fatigue and fracture mechanics, 27 (1997) 613-629. doi: 10.1520/stp16258s. t m. lutovinov et alii, frattura ed integrità strutturale, 38 (2016) 237-243; doi: 10.3221/igf-esis.38.32 243 [5] hoffmann, m., seeger, t., estimating multiaxial elastic-plastic notch stresses and strains in combined loading, mechanical engineering publications, (1989) 3-24. [6] singh, m.n.k., g. glinka, dubey, r.n., elastic-plastic stress-strain calculation in notched bodies subjected to nonproportional loading, international journal of fracture, 76 (1996) 39-60. doi: 10.1007/bf00034029. [7] buczynski, a., glinka, g., elastic-plastic stress-strain analysis of notches under non-proportional loading, 5th international conference on biaxial/ multiaxial fatigue and fracture, (1997) 461-479. 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/hrv (za stvaranje adobe pdf dokumenata najpogodnijih za visokokvalitetni ispis prije tiskanja koristite ove postavke. stvoreni pdf dokumenti mogu se otvoriti acrobat i adobe reader 5.0 i kasnijim verzijama.) /hun 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can be opened with acrobat and adobe reader 5.0 and later.) >> /namespace [ (adobe) (common) (1.0) ] /othernamespaces [ << /asreaderspreads false /cropimagestoframes true /errorcontrol /warnandcontinue /flattenerignorespreadoverrides false /includeguidesgrids false /includenonprinting false /includeslug false /namespace [ (adobe) (indesign) (4.0) ] /omitplacedbitmaps false /omitplacedeps false /omitplacedpdf false /simulateoverprint /legacy >> << /addbleedmarks false /addcolorbars false /addcropmarks false /addpageinfo false /addregmarks false /convertcolors /converttocmyk /destinationprofilename () /destinationprofileselector /documentcmyk /downsample16bitimages true /flattenerpreset << /presetselector /mediumresolution >> /formelements false /generatestructure false /includebookmarks false /includehyperlinks false /includeinteractive false /includelayers false /includeprofiles false /multimediahandling /useobjectsettings /namespace [ (adobe) (creativesuite) (2.0) ] /pdfxoutputintentprofileselector /documentcmyk /preserveediting true /untaggedcmykhandling /leaveuntagged /untaggedrgbhandling /usedocumentprofile /usedocumentbleed false >> ] >> setdistillerparams << /hwresolution [2400 2400] /pagesize [612.000 792.000] >> setpagedevice microsoft word numero_37_art_36 p. velev et alii, frattura ed integrità strutturale, 37 (2016) 272-279; doi: 10.3221/igf-esis.37.36 272 focused on fracture mechanics in central and east europe novel magnetic composites based on water soluble unsaturated polyester resin and iron oxide nanoparticles petar velev, rayna bryaskova university of chemical technology and metallurgy, bulgaria p_velev@uctm.edu, rbryaskova@uctm.edu abstract. magnetic nanocomposites on the basis of water soluble unsaturated polyester resin filled with different amount of iron oxide nanoparticles have been successfully prepared. the mechanical properties of thus prepared composites as tensile, impact and flexural strength were determined. the specific volume and surface resistance of the magnetic nanocomposites were also determined. keywords. magnetic nanoparticles; unsaturated polyester resin; copolymerization; mechanical properties; surface resistance. introduction ecently, great scientific and technological interest has been paid to the magnetic nanoparticles because of their unique properties and various applications [1-6]. they can be synthesized using different methods such as microemulsion [7], sol-gel synthesis [8], sonochemical reactions [9], hydrolysis [10] and thermolysis [11]. these methods are used for preparation of particles with homogeneous composition. the synthesis of magnetic nanoparticles is a complex process because of their colloidal nature. the first challenge consists in the determination of the experimental conditions leading to formation of uniform magnetic nanoparticles with appropriate size [12]. the second critical point is the choice of reproductive process, which can be industrialized without any additional purification procedures such as ultracentrufugation [13] or magnetic filtration [14-16]. the most used methods for the synthesis of magnetic nanoparticles is precipitation of iron salts. the production of magnetic nanoparticles in aqueous solutions is very perspective, environmental friendly process and possesses numerous advantages. it is well known that unsaturated polyester resins are a solution of unsaturated oligomers in monomer (usually styrene) which are able to copolymerize. this combination possesses a good complex of properties as relatively low viscosity, and easy and complete copolymerization after addition of initiator which makes them very suitable for different processing methods. it is established that the resin easily forms emulsion with water after alkalifying of the medium with ammonia in the range from 1.8% to 5.2% under simple stirring. the obtained emulsion is stable enough with the time in order to undergo various technological processes. it is known the preparation of suspension copolymerization of unsaturated resins with styrene and acrylonytrile using a redox system consisting of metylketohydroperoxide and cobalt naphtenate [17]. the aim of this investigation is the preparation of magnetic nanocomposites on the basis of water soluble unsaturated polyester resin and aqueous solution of magnetic nanoparticles without using of any surfactant. there are not data in the literature concerning the preparation of such water soluble unsaturated polyester resins filled with magnetic nanoparticles. the mechanical properties of the prepared magnetic nanocomposites will be investigated as well. r p. velev et alii, frattura ed integrità strutturale, 37 (2016) 272-279; doi: 10.3221/igf-esis.37.36 273 experimental part materials and methods. materials: nsaturated polyester resins viapal vup 4627 bemt/56 (cytec, germany), containing 44% styrene, which is previously accelerated. cyclohexanoneperoxide (peroximon k 41) ammonia-25% solution, fecl2 (acrosorganics) and fecl3 (acrosorganics) have been used without purification as received. methods: the average hydrodynamic diameter of the magnetic nanoparticles is determined using dynamic light scattering (dls) malvern cgs-3 equipped with не-ne laser with wave number 623,8 nm at temperature 25ос and angle 90о. the concentration of the iron in the hydrosol of γfe2o3 of 9600 µg/ml is determined by atomic absorption analysis (aaa) using perkin – elmer spectrophotometer. the composite materials are investigated with the aid of the following methods: tensile strength en iso 527 – 1,2 : 1996; impact strength en iso 179 : 1993; flexural strength en iso 178 : 1996; determination of specific volume and surface resistance [18]; relatively density and degree of swelling (weight and volume) in acetone synthesis synthesis of hydrosol of γfe2o 3. magnetic nanoparticles are prepared according to reference [19]. briefly, 0.85 ml of 12,1 м hcl and 25 ml degassed water are mixed with 5.2 g fecl3 and 2 g fecl2. the molar ration of fe2+ and fe3+ was fe2+/ fe3+=0.5 at рн=1112. thus prepared mixture is added dropwise into 250 ml 1.5 m naoh solution under vigorous stirring. the last stage consists in the formation of black precipitate. the precipitate is collected in magnetic fields and added to degassed water followed by centrifugation (three times for 1 min) at 4000 rpm. after this purification, 500 ml 0.01m hcl is added to the precipitate in order to neutralized the anionic charge of the particles. the cationic colloidal nanoparticles are separated again by centrifuging and they are peptized with addition of water. the result is a clear, transparent colloid (hydrosol). the oxidation of fe3o4 to γfe2o3 is based in the change in the ph of the hydrosol of fe3o4 to рн=3,5. the transparent hydrosol is stirred for 30 min at 100 ос under air. the color of the solution is changed from red to brown red. this solution is cooled to room temperature and the upper layer is collected after centrifugation for 30 min at 4000 rpm. the obtained transparent brown-red layer is a hydrosol of γfe2o 3 nanoparticles. copolymerization of unsaturated polyester resin the method of preparation is described in references [17, 20]. the unsaturated polyester resin is placed in a reactor where is tempered at appropriate initial temperature. then the initiator is added and the time of copolymerization is accounted as the reaction mixture is stirred during 30 sec. to determine the time and the maximum reached copolymerization temperature of unsaturated polyester resin at different initiator concentrations is used equipment shown in fig. 1. 1 2 3 4 5 figure 1: scheme of the reactor used to study the copolymerization process: 1-lid; 2-thermocouple; 3 – orifice for the tempered fluid; 4vessel for the investigated resin; 5 – circulating fluid. u p. velev et alii, frattura ed integrità strutturale, 37 (2016) 272-279; doi: 10.3221/igf-esis.37.36 274 preparation of magnetic nanocomposites. the polymer composites are prepared manually by mixing of the diluted with water unsaturated resin and hydrosol of γfe2o3 nanoparticles applying different concentrations. the sum of the added water and nanoparticles solution is equal and corresponds to degree of filling 0.5%. results and discussion t is well known that maleic, respectively fumaric bonds in the unsaturated polyester resins are not able to homopolymerize. in the presence of another unsaturated monomer, copolymerization takes place and the molecules of the unsaturated polyester resins have been cross-linked (bonded molecularly by the second monomer). styrene and, more seldom other vinyl monomers are used most often for this purpose [21]. in this investigation, unsaturated polyester resin containing 44% styrene was used. initially, the copolymerization of the unsaturated polyester resin containing 44% styrene was performed using different amount of initiator in order to determine the time for reaching the optimal copolymerization temperature during the process (fig. 2). it was established that during the copolymerization reaction, the increased amount of initiator lead to higher reaction temperatures reached at shorter times. the same dependence was established for the change of adiabatic temperatures with the time (fig. 3). on the base of these results, the initiator concentration of 2 wt.% (or 0,4 g for 20 g resin) was chosen as an optimal concentration for the copolymerization process. 0 20 40 60 80 100 120 140 160 180 1 2 3 4 5 6 7 8 9 10 11 12 13 t, min t , °c 0.3 g 0.4 g 0.5 g 0.6 g 0.7 g figure 2: dependence on the reaction temperature with the time for the copolymerization of unsaturated polyester resin with different amount of initiator. the examination on the extracted substances and swelling in resin solvent showed that regardless of the way in which it is heated and cooled, the reaction does not complete. the copolymerization processes proceeded slowly. therefore after reaching of maxexpt , the sample is transferred to the thermostat at temperature equal to the temperature max expt . after heating for 1 hour, the sample is placed in the reactor and the rate with which the temperature decreased is measured (fig. 3). it was established that after one hour of keeping the maximum temperature, the copolymerization process is completed. the extracted substances are decreased until the minimum values – under 4%, and the swelling in ethyl acetate decreased below 2.3%. to prepare magnetic nanocomposites on the basis of unsaturated polyester resin fe2o3 nanoparticeles are synthesized according to eq. 1: fecl2 (1mol) + fecl3 (2mol)→fe3o4 → oxidation γfe2o 3 the synthesized fe2o3 nanoparticles used as filler to prepare magnetic nanocomposites possess an average hydrodynamic diameter (dh) of 60±0.7 nm at particles size distribution (pdi) of 0.38 as measured by dls (fig. 4). i p. velev et alii, frattura ed integrità strutturale, 37 (2016) 272-279; doi: 10.3221/igf-esis.37.36 275 0 50 100 150 200 250 0 3 6 9 12 15 t, min t а d , o c 0.3 g 0.4 g 0.5 g 0.6 g 0.7 g figure 3: changes of adiabatic temperatures with the time depending on the initiator concentration. figure 4: average hydrodynamic diameter and particles size distribution of aqueous solution of γfe2o3 nanoparticles. the observed broader polydispersity of the nanoparticles could be due to some nanoparticles aggregation. further, different amounts of filler are added to the water alkaline solution of the resin thus obtaining following composites which are tested for their mechanical properties such as tensile, impact and flexural strength (tab. 1). № uper. g hydrosol of nanoparticles. ml water. ml content of magnetic nanoparticles. % 1 50 0 26 0 2 50 5.25 20.75 0.1 3 50 15.75 10.25 0.3 4 50 26 0 0.5 table 1: content of the used magnetic composites the tensile strength (fig. 5) decreases slightly with increasing the amount of magnetic nanoparticles in the resin as the obtained data are not significantly changed depending on the magnetic nanoparticles content. p. velev et alii, frattura ed integrità strutturale, 37 (2016) 272-279; doi: 10.3221/igf-esis.37.36 276 26.2 25.3 24.0 23.9 0.0 5.0 10.0 15.0 20.0 25.0 30.0 0.0 0.1 0.3 0.5 magnetic nanoparticles, % t en si le s tr en gt h , m p a figure 5: tensile strength of magnetic composites with different content of magnetic nanoparticles. the results for impact strength of the magnetic nanocomposites depending on the magnetic nanoparticles contents are presented in fig. 6. 6.1 6.0 4.9 4.8 0.0 1.0 2.0 3.0 4.0 5.0 6.0 7.0 0.0 0.1 0.3 0.5 magnetic nanoparticles, % im p ac t st re n gt h , k j /m 2 figure 6: impact strength of magnetic composites with different content of magnetic nanoparticles. the increased content of magnetic nanoparticles in the composites leads to decreasing of the values for the impact strength. the lowest value (4.8 kj/m2) is obtained for the composites containing higher amount of magnetic nanoparticles 0.5% . the results of magnetic composites for flexural strength are presented in fig. 7. the results for flexural strength showed insignificant change in dependence on the magnetic nanoparticles content. the best results are obtained for the samples containing 0.1% nanoparticles (0.33mpa) and the lowest (0.23mpa) for the samples containing 0.5%. tab. 2 presents the results for the specific volume ρv [ω.m] and surface ρs [ω] resistance. the increased amount of the magnetic nanoparticles in the composites leads to some decreasing of the specific volume and surface resistance. this trend allows the preparation and design of magnetic composites with desired conductivity. p. velev et alii, frattura ed integrità strutturale, 37 (2016) 272-279; doi: 10.3221/igf-esis.37.36 277 0.24 0.33 0.25 0.23 0.00 0.10 0.20 0.30 0.40 0.0 0.1 0.3 0.5 magnetic nanoparticles , % f le x u ra l st re n g th , m p a figure 7. flexural strength of magnetic composites in dependence on the filler content in %. magnetic nanoparticles content % ρv, [ ω.m] ρs, [ ω] 0 1.0.10 12 4.5.10 14 0.1 0.82. 10 11 2.0.10 13 0.3 0.42.10 11 1.5.10 13 0.5 0.35.10 11 1.0.10 13 table 2: variation of ρv and ρs in dependence on the magnetic nanoparticles content the obtained values for the density of the magnetic composites are presented in tab. 3. magnetic nanoparticle content, % density, g/cm3 0 1.21 0.1 1.14 0.3 0.82 0.5 0.98 table 3: density of magnetic composite in dependence on the amount of the filler as seen the density of the polymer composites decreases with increasing the amount of the magnetic nanoparticles content. the decreased density showed that probably there are some gas formations in the resins. the observed lower values of the some physicomechanical properties in the magnetic composites in comparison to the pure resin is probably due to the detected decreased density in the composites with increasing the amount of magnetic nanoparticles content. the higher mechanical strength possesses the pure resin and the composite containing 0.1% magnetic nanoparticles. the ph nanoparticles solution is 3.5. since the hydrolysis of uper has to be conducted at ph 8, the amount of nh4oh which has to be added to the mixture has to be increased in order to reach the desired alkalinity of the solution with the increasing concentration of magnetic nanoparticles. the neutralization process probably provokes the gas formations in the composites. this state is confirmed from the results for the degree of weight (fig. 8) and volume (fig. 9) swelling of the polymer composites. p. velev et alii, frattura ed integrità strutturale, 37 (2016) 272-279; doi: 10.3221/igf-esis.37.36 278 0 5 10 15 20 25 30 35 40 0 0.1 0.3 0.5 magnetic nanoparticles, % d eg re e o f sw el li n g, % 2 h 4 h 24 h figure 8: changes of degree of swelling (weight) in dependence on the amount of magnetic nanoparticles. the degree of weight swelling is increased with increasing the amount of magnetic nanoparticles in the magnetic composites. this increasing of the degree of swelling proves the presence of pores in the samples. 0 5 10 15 20 25 30 35 40 0 0.1 0.3 0.5 magnetic nanoparticles , % d eg re e o f sw el li n g , % 2 h 4 h 24 h figure 9:changes of degree of swelling (volume) in dependence on the amount of magnetic nanoparticles. as seen from the figure, degree of volume swelling decreases irregularly with the introduction of magnetic nanoparticles. the degree of swelling is higher at the samples without magnetic nanoparticles. the weight of the samples containing higher amount of magnetic nanoparticles increases and the volume of the samples decreases when staying in a solvent (acetone) for 24h. it can be concluded that the higher amount of the magnetic nanoparticles in the composites does not disturb the crosslinking process of the resin but the prepared magnetic composites posses higher amount of open and closed pores in which enters higher amount of solution. therefore, the density of the polymer composites decreased with increasing the amount of the magnetic nanoparticles (tab. 3). p. velev et alii, frattura ed integrità strutturale, 37 (2016) 272-279; doi: 10.3221/igf-esis.37.36 279 conclusions he nanocomposites on the basis of diluted with water unsaturated polyester resin containing magnetic nanoparticles with concentration ranging from 0.1% to 0.5% were successful prepared. it was established that the increased concentration of the magnetic nanoparticles leads to decreased mechanical properties of the composites due to the formation of micropore structure. as expected the specific volume and surface resistance of the composites is changed with increasing the amount of magnetic nanoparticles in the composites. references [1] sun, s., murray, c.b., weller, d., folk, l., moser, a., monodisperse fept nanoparticles and ferromagnetic fept nanocrystal superlattices, science, 287 (2000) 1989-92. [2] miller, m.m., prinz, g.a., cheng, s.f., bounnak, s., detection of a micron-sized magnetic sphere using a ring-shaped anisotropic magetoresistance-baced biosensors, appl. phys. lett., 81 (2002) 22112213. [3] jain, t.k., morales, m.a., sahoo, s.k., leslie-pelecky ,d.l., labhasetwar, v., iron oxide nanoparticles for sustained delivery of anticancer agents, mol. pharm., 2 (2005)194-205. [4] chourpa, i., douziech-eyrolles, l., ngaboni-okassa, l., fouquenet, j.f., cohen-jonathan, s., souce, m., marchais, h., dubois, p., molecular composition of iron oxide nanoparticles, precursors for magnetic drug targeting, as characterized by confocal raman microspectroscopy, analyst, 130 (2005) 1395-403 [5] bulte, j. w., intracellular endosomal magnetic labeling of cells, methods mol. med., 124 (2006) 419 -39. [6] modo, m., bulte, j.w., cellular mr imaging, mol. imaging, 4 (2005)143-64. [7] burtea, c., laurent, s., roch, a., vander, elst, l., muller, r.n., c-malisa (cellular magnetic-linked immunosorbent assay), a new application of cellular elisa for mri., j. inorg. biochem. 99 (2005) 1135-44. [8] boutry, s., laurent, s., vander, elst, l., muller, r.n., specific e-selection targeting with a superparamagnetic mri contrast agent., contrast med.mol. imaging, 1 (2006) 15-22. [9] babes, l., denizot, b., tanguy, g., le jeune, j.j., jallet, p.j., synthesis of iron oxide nanoparticles used as mri contrast agents: a parametric study, colloid interface sci., 212 (1999) 474-482. [10] sonvico, f., dubernet, c., colombo, p., couvreur, p., metallic colloid nanotechnology, applications in diagnosis and therapeutics, curr. pharm.des., 11 (2005) 2091 -2105. [11] corot, c., robert, p., idee, j.m., port m., recent advances in iron oxide nanocrystal technology for medical imaging, adv. drug delivery rev., 58 (2006) 1471-504. [12] modo, m. m. j., bulte, j. w. m., molecular and cellular mr imaging; crc press: boca raton, fl (2007). [13] charles, s.w., popplewell, j.; properties and applications of magnetic liquids, endeavour 6 (1982) 153 -61. [14] gupta, a.k., gupta, m., synthesis and surface engineering of iron oxide nanoparticles for biomedical applications, biomaterials 26 (2005) 3995-4021. [15] chastellain, m., petri, a., gupta, a., rao, k.v., hofmann, h., super magnetic silica-iron oxide nanocomposites for applications in hyperthermia, adv. eng. mater. 6 (2004) 235-241. [16] willard, m. a., kurihara, l.k., carpenter, e. e., calvin, s., harris, v.g., encyclopedia of nanoscience and nanotechnology; nalwa, h. s., ed.; american scientific publishers: valencia, ca, 1, (2004) 815. [17] natov, m., velev, p., suspension copolymerization of unsaturated resins with styrene and acrylonitrile, macromolecular chemistry and physics, 201 (2000) 1244-49. [18] al-hartomy, o. a., al-ghamdi, a., dishovsky, n., slavcheva, d., iliev, v., el-tantawy, farid, dielectric and microwave properties of natural rubber based composites containing fullerene black, international review of chemical engineering, 3(2011), 386-391. [19] kang, y. s., risbud, s., rabolt, j. f., stroeve, p., synthesis and characterization of nanometer-size fe3o4 and γ – fe2o3 particles, chem mater., 8 (1996) 2209-2211. [20] rojas, a.j., borrajo l.and williams r.j.; the curing of unsaturated polyester resins in adiabatic reactors and heated molds, polym. eng. sci., 17 (1981) 1122 -27. [21] fradet, a., arlaud, p., comprehensive polymer science, ed. eastmond, g. c.; ledwith, a.; russo, s.; sigwalt, p., pergamon press, oxford, 5 (1989) 331344. t << /ascii85encodepages false /allowtransparency false /autopositionepsfiles true /autorotatepages /none /binding /left /calgrayprofile (dot gain 20%) /calrgbprofile (srgb iec61966-2.1) /calcmykprofile (u.s. web coated \050swop\051 v2) /srgbprofile (srgb iec61966-2.1) /cannotembedfontpolicy /error /compatibilitylevel 1.4 /compressobjects /tags /compresspages true /convertimagestoindexed true /passthroughjpegimages true /createjobticket false /defaultrenderingintent /default /detectblends true /detectcurves 0.0000 /colorconversionstrategy /cmyk /dothumbnails false /embedallfonts true /embedopentype false /parseiccprofilesincomments true /embedjoboptions true /dscreportinglevel 0 /emitdscwarnings false /endpage -1 /imagememory 1048576 /lockdistillerparams false /maxsubsetpct 100 /optimize true /opm 1 /parsedsccomments true 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can be opened with acrobat and adobe reader 5.0 and later.) >> /namespace [ (adobe) (common) (1.0) ] /othernamespaces [ << /asreaderspreads false /cropimagestoframes true /errorcontrol /warnandcontinue /flattenerignorespreadoverrides false /includeguidesgrids false /includenonprinting false /includeslug false /namespace [ (adobe) (indesign) (4.0) ] /omitplacedbitmaps false /omitplacedeps false /omitplacedpdf false /simulateoverprint /legacy >> << /addbleedmarks false /addcolorbars false /addcropmarks false /addpageinfo false /addregmarks false /convertcolors /converttocmyk /destinationprofilename () /destinationprofileselector /documentcmyk /downsample16bitimages true /flattenerpreset << /presetselector /mediumresolution >> /formelements false /generatestructure false /includebookmarks false /includehyperlinks false /includeinteractive false /includelayers false /includeprofiles false /multimediahandling /useobjectsettings /namespace [ (adobe) (creativesuite) (2.0) ] /pdfxoutputintentprofileselector /documentcmyk /preserveediting true /untaggedcmykhandling /leaveuntagged /untaggedrgbhandling /usedocumentprofile /usedocumentbleed false >> ] >> setdistillerparams << /hwresolution [2400 2400] /pagesize [612.000 792.000] >> setpagedevice microsoft word numero_50_art_46_2623 ch. apostolopoulos et alii, frattura ed integrità strutturale, 50 (2019) 548-559; doi: 10.3221/igf-esis.50.46 548 focused on the research activities of the greek society of experimental mechanics of materials comparison of the mechanical response of b400c and b450c dual phase steel bar categories, in long terms charis apostolopoulos, argyro drakakaki university of patras, greece charrisa@upatras.gr, https://orcid.org/0000-0001-7414-8444 drakakaki@upatras.gr, https://orcid.org/0000-0002-0448-2719 alkiviadis apostolopoulos university of ioannina, greece prothesis.apostolopoulos@gmail.com konstantinos koulouris university of patras, greece kkoulouris@upnet.gr, https://orcid.org/0000-0003-2449-2751 abstract. in this work, the effects of chloride-induced corrosion on tempcore b400c and b450c steel grades are evaluated, in terms of corrosion resistance and mechanical characteristics, after the performance of tensile and low cycle fatigue tests. both steel categories, characterized by high strength and high ductility, have been used in existing structures, indicating that they demonstrate different performance against the ascribed corrosion environments. b450c steel grade seems to preserve higher energy reserves, ensuring higher expectancy to the corresponding reinforced concrete structures. additionally, due to buckling and buckling reversal, both steel grades demonstrate limited ductility at 4%. finally, when cyclically stresses occur, crack nucleation is taking place, at the areas where sulphides, fes and mns can be found, leading to sub-surface crack propagation, interacting with external pits. keywords. corrosion; dual phase steel bars; b400c; b450c; mechanical behaviour; degradation of mechanical performance. citation: apostolopoulos, ch., drakakaki, arg., apostolopoulos, alk., koulouris, k., comparison of the mechanical response of b400c and b450c dual phase steel bar categories, in long terms, frattura ed integrità strutturale, 50 (2019) 548-559. received: 28.01.2019 accepted: 29.05.2019 published: 01.10.2019 copyright: © 2019 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. introduction einforced concrete has been the most popular material for more than a century. during these years, in an effort to upgrade the reliability of the structures, various steel grades, characterized by high strength and ductility, have been used as reinforcement. however, there is a plethora of degradation factors that may affect the performance r http://www.gruppofrattura.it/va/50/2623.mp4 ch. apostolopoulos et alii, frattura ed integrità strutturale, 50 (2019) 548-559; doi: 10.3221/igf-esis.50.46 549 and the reliability, not only of the material, but also of the whole structure [1]. corrosion of steel reinforcement constitutes a major problem for reinforced concrete structures, as far as their durability is concerned, as it has also been mentioned by almusallam [2]. corrosion degradation is responsible for several issues, such as deterioration of both durability and service life of structures, resulting in premature failure. ιn recent years, the problem of the actual residual strength degradation of ageing reinforced concrete structures has attracted considerable attention, however it is far from being fully understood and even less resolved. according to apostolopoulos et al. [3], papadakis [4], capazucca[5], diamond [6] and alvarez et al. [7], this scenario becomes even worse when coastal environment, which is rich in chlorides, is combined with seismic phenomena. cyclic loading, which is due to seismic activity, in conjunction with the pre-existing downgrade, which results from corrosion effect, leads to prompt deterioration of useful lifespan of structures, that face durability issues. furthermore, cyclic loading, leads to a nonlinear response of the structures that face durability issues. therefore, to predict the time dependent damage of corroded reinforced concrete structures under seismic loading it is necessary to consider the effects of material degradation, due to corrosion [8]. in the present work, the effects of chloride-induced corrosion on two different steel bar categories, b400c and b450c are evaluated, in terms of corrosion resistance and mechanical characteristics, before and after the corrosion process. the method that was used for the accelerated corrosion tests, was salt spray chamber and the mechanical tests performed for both steel bar categories were tensile tests and low cycle fatigue tests. the goal of the study was to highlight the differences among the two steel categories, as far as their mechanical performance and their resistance to corrosion is concerned. given that both steel grades have been used in existing civil engineering structures, it is important to gain knowledge of their mechanical behavior and their vulnerability to corrosion factor, so as to be able to estimate their life expectancy. materials and methods or the goals of the present study, material of two different steel reinforcement categories b400c and b450c was used. the material, for both categories, was received from european factories and were produced by the same steel manufacturer using the “tempcore” method. the chemical composition, which is approximately the same for the two different steel bar categories. specifically, both steel categories contain 0.22% c, 0.05% p, 0.05% s, 0.8% cu and 0.012% n, while b450c has an additional 0.5% ceq. two series of specimens, 500mm and 250mm long, of 16mm nominal diameter, were organized for each steel grade. for comparison reasons, one more set of specimens of nominal diameter 12mm and 500mm long was prepared for b450c. given that the goal of the present study is to evaluate the mechanical performance of both steel categories, before and after corrosion, salt spray chamber method was used for the performance of the corrosion tests. exposure periods equal to 0 days, 45 days and 90 days were scheduled for each set of specimens. consequently, each set was separated into three smaller groups, the first of which was only mechanically tested (reference specimens) while for the rest two groups corrosion took place prior to the mechanical tests. before the corrosion process, specimens were properly prepared. they were primarily cleaned in order to remove all the unwanted impurities from their surface. the configuration of equal surface areas, that would be exposed to the corrosive media, was necessary for comparison reasons. the exposed length for each specimen was equal to 20mm, while the rest part of the metal was covered with wax, to prevent corrosion (fig.1). the samples were exposed to the corrosion process and they were mechanically tested in tensile and low cycle fatigue (lcf) tests. artificial corrosion tests were executed with the use of salt spray fog chamber – according to astm b117 [9]. figure 1: preparation of the “short” specimens. f ch. apostolopoulos et alii, frattura ed integrità strutturale, 50 (2019) 548-559; doi: 10.3221/igf-esis.50.46 550 corrosion tests salt spray chamber or the corrosion process all the specimens were placed in a salt spray chamber (fig.2). the corrosion tests were organized in accordance to astm b117-94 specification (directly exposed to the corrosive medium). the astm b117 [9] specification covers every aspect of the apparatus configuration, procedure and conditions required to create and maintain a salt spray (fog) testing environment. the selection of such a procedure for corroding the specimens, relies on the fact that the salt spray environment lies qualitatively closer to the natural coastal (rich in chlorides) conditions than any other accelerate laboratory corrosion test. in principle, the testing apparatus consists of a closed chamber in which a salted solution atomized by means of a nozzle, produces a corrosive environment of dense saline fog. in this particular study a special apparatus, model sf 450 (mode by cand w. specialist equipment ltd) was used. the salt solution was prepared by dissolving 5 parts by mass of sodium chloride (nacl) into 95 parts of distilled water (ph range 6.5-7.2). the temperature inside the salt spray chamber was maintained at 35°c (+1.1-1.7°c). figure 2: salt spray fog chamber. additionally, in the present study, a severe exposure environment of wetting/drying (chloride ponding) was organized in order to achieve a better approach to the environmental conditions and to simulate the chloride exposures of marine structures under splash and tidal zones. hence, it is widely known that that in reality, structures are subjected to wet and dry periods, rather than a constant relative humidity [10]. chloride ponding application is in agreement with the simulating corrosion methods used in existing studies as well [11-13] and ensures conditions which are qualitatively closer to the natural. this is because during wetting, chloride solution penetrates a layer of the material; during the drying stage the evaporation front moves inwards and takes some of the chloride with it [10]. it is deducted in theory that atmospheric corrosion rate of metals can be accelerated by increasing the frequency of wet-dry cycling [12]. consequently, the ponding cycles organized consisted of alternating 1.5 hour of exposure to wet conditions and 1.5 hour of dry conditions. eight ponding cycles of wet/dry conditions were scheduled per day. by the end of each exposure time, specimens were removed from the corrosive environment, washed with clean running water, to remove ant salt deposits from their surfaces and air dried. the corrosion products were removed from the surface of the specimen by means of a brittle brush, according to astm g1 specification [14]. the specimens were then weighted and the mass loss due to corrosion exposure was calculated as: c p m m x % m   0 0 100 (1) where m0 is the mass of uncorroded specimens and mc the reduced mass of the corroded specimens. mechanical tests fter the completion of the corrosion process the mechanical tests were organized. in table 1 is given in detail the number of the specimens used in each case. according to table 1, a total of 18 tensile tests and 134 low cycle fatigue tests was conducted for the goals of the present study. the differentiated number of the lcf tests, per strain, per steel category is owed to the fact that there were some additional tests that were invalid, the results of which are not included in the present paper. f a ch. apostolopoulos et alii, frattura ed integrità strutturale, 50 (2019) 548-559; doi: 10.3221/igf-esis.50.46 551 steel category nominal diameter number of specimens total length (mm) length exposed to corrosion (mm) type of mechanical test b400c φ16 9 500 20 tensile tests b400c φ16 20 250 20 ±2.5% strain-controlled low cycle fatigue tests b400c φ16 21 250 20 ±4% strain-controlled low cycle fatigue tests b450c φ16 9 500 20 tensile tests b450c φ16 20 250 20 ±2.5% strain-controlled low cycle fatigue tests b450c φ16 22 250 20 ±4% strain-controlled low cycle fatigue tests b450c φ12 25 250 20 ±2.5% strain-controlled low cycle fatigue tests b450c φ12 26 250 20 ±4% strain-controlled low cycle fatigue tests table 1: the specimens used for the goals of the current study. the tensile tests were performed according to the iso/fdis 15630-1 [15] specification, using a servo-hydraulic mts 250kn machine with a constant elongation rate of 2 mm/min. the mechanical properties, yield strength rp, ultimate strength rm, and uniform elongation agt, were determined. it should be noted that agt was measured according to the manual method described in the relevant standard (on a gauge length of 100 mm, at a distance of 50 mm away from the fracture). table 2 shows the minimum standards for medium and high ductility steel set by the ec2. class rp (mpa) agt (%) rp/rm b400c 400 ≥7.5 ≥1.15 ˂1.35 b450c 450 ≥7.5 ≥1.15 ˂1.35 table 2: steel classes. on the other hand, it is worth mentioning that lcf tests procedure for the cyclic mechanical behavior of steel bar is not included in the european production standards for reinforcements (en 10080:2005). only spanish and portuguese standards prescribe the execution of symmetrical tension/compression cycles for the production control of steel reinforcements, while the draft of new european standard for reinforcements (pren 10080:2012) gives only some indications for the execution of lcf tests by caprilli et al. [16-17]. in the present study, the lcf tests were performed using the abovementioned servohydraulic mts 250 kn machine. two free lengths, equal to 6d and 8d respectively, were tested for each steel category. the frequency used was equal to 2.5hz and strain imposed was equal to ±2.5% and ±4%, in reference to their free length (either 6d or 8d). results and discussion lthough both b400c and b450c steel bar categories have been used in existing structures, several worth mentioning differences can be reported, as far as their mechanical performance and their corrosion resistance are concerned, in long term. in tables 3 and 4 are presented the results concerning both the mass loss percentages and the mechanical properties of the long specimens (500mm), of 16mm nominal diameter. taking into consideration the data of tables 3 and 4, it is evident that both steel grades demonstrate similar vulnerability to the corrosion factor. as far as the mechanical characteristics are concerned, b400c recorded 6.5% drop of yield strength against 5.7% of b450c, after the 90 days of a ch. apostolopoulos et alii, frattura ed integrità strutturale, 50 (2019) 548-559; doi: 10.3221/igf-esis.50.46 552 exposure to the corrosive environment. on the contrary, for the same exposure period, elongation of b450c steel was diminished about 77.12% against 69.87% of b400c category. however, it is remarkable, that plastic deformation recorded for both steel categories, after the completion of the first 45 days, was lower than the value that eurocode 2 requires, which is equal to 7.5%. the corresponding results of lcf tests are presented in figs.3 and 4. steel grade tcorr (days) mass loss (%) rp (mpa) rm (mpa) agt (%) b400c 0 0 437 549 15.6 b400c 0 0 435 548 16.0 b400c 0 0 433 550 15.3 average 0 435 549 15.6 b400c 45 5.9 435 518 6.3 b400c 45 5.5 431 520 5.7 b400c 45 4.8 429 520 6.3 average 5.4 432 519 6.1 b400c 90 8.5 400 497 5.2 b400c 90 9.7 414 494 4.1 b400c 90 9.6 408 488 4.7 average 9.3 407 493 4.7 table 3: mass loss results and mechanical characteristics of b400c steel bar samples, of 16mm nominal diameter before and after their exposure to corrosive conditions steel grade tcorr (days) mass loss (%) rp (mpa) rm (mpa) agt(%) b450c 0 0 541 651 11.4 b450c 0 0 532 644 12.3 b450c 0 0 536 649 11.7 average 0 536.4 648 11.8 b450c 45 6.0 528 614 4.6 b450c 45 6.2 534 613 4.1 b450c 45 6.1 533 617 4.3 average 6.1 532 615 4.3 b450c 90 11.2 512 566 2.4 b450c 90 11.3 509 581 2.7 b450c 90 10.1 496 575 3.0 average 9.3 506 574 2.7 table 4: mass loss results and mechanical characteristics of b450c steel bar samples, of 16mm nominal diameter, before and after their exposure to corrosive conditions. examining the performance of both steel categories, in ±2.5% deformation (where buckling effects are relatively mild), reference b450c steel achieves 22.4% higher life cycle (67cycles) than the reference b400c steel (52 cycles). however, after 45 and 90 days of exposure to the corrosive conditions, life cycles of both steel categories are approximately equal. according to the results presented in figs.3 and 4, it seems that although corrosion factor is responsible for similar mass loss percentages in both steel categories, however they demonstrate different performance under the cyclic testing. this fact is owed to the different thickness of the martensite layer of the two steel grades [18]. precisely, b400c steel bar category recorded a great drop, of more than 60%, on the number of cycles up to failure until the first 45 days of exposure to the ch. apostolopoulos et alii, frattura ed integrità strutturale, 50 (2019) 548-559; doi: 10.3221/igf-esis.50.46 553 aggressive conditions, for both deformations imposed (δε= ±2.5% and δε= ±4%) and for both free lengths defined (6d and 8d). whereas, consistency was recorded for the next 45 days, up to the completion of the exposure period of 90 days. on the other hand, b450c steel grade, recorded an initial drop on its cyclic life, the mean value of which was higher than 50% for both deformations (δε= ±2.5% and δε= ±4%) and for both free lengths defined (6d and 8d) and an extra dron higher than 12.5% up to the 90 days, for δε= ±2.5% (for both free lengths 6d and 8d). 0 2 4 6 8 10 12 0 50 100 150 200 250 300 350 400 0 2 4 6 8 10 12 0 100 200 300 400 500 600 n cy cl es mass loss (%) e n er gy ( m p a) energy stock-mass loss-6d ncycles-mass loss-6d energy stock-mass loss-8d ncycles-mass loss-8d figure 3: a graphical depiction of energy stocks and number of cycles of the b400c (φ16) specimens tested in lcf, in reference to their corresponding mass loss, before and after their exposure to corrosive conditions. 0 10 20 30 40 50 60 70 0 50 100 150 200 250 300 350 400 450 500 0 2 4 6 8 10 12 0 100 200 300 400 500 600 700 800 n cy cl es mass loss (%) e n er gy ( m p a) energy stock-mass loss-6d ncycles-mass loss-6d energy stock-mass loss-8d ncycles-mass loss-8d figure 4: a graphical depiction of energy stocks and number of cycles of the b450c (φ16) specimens tested in lcf, in reference to their corresponding mass loss, before and after their exposure to corrosive conditions. ch. apostolopoulos et alii, frattura ed integrità strutturale, 50 (2019) 548-559; doi: 10.3221/igf-esis.50.46 554 additionally, due to buckling and buckling reversal, the material's ductility especially at 4% is particularly limited. explicitly, the free length of the specimen strongly influences the results of the experimental tests, since buckling phenomena due to compression axial loads can lead to premature unexpected failures of the rebars (fig.5); in order to avoid this problem, actual standards for reinforced concrete constructions (en 1998-1:2005, d.m. 14/01/2008) prescribe the adoption of opportune limits for the free length of reinforcements between stirrups, that shall be lower than 6 or 8 times the diameter for buildings respectively designed in high, medium or low ductility class. for comparison reasons, a few more lcf tests were performed on reference b450c steel bar specimens, of 12mm nominal diameter. the corresponding results are presented in fig.6. figure 5: buckling effect on a tested rebar. 0 50 100 150 200 250 300 350 400 450 500 0 20 40 60 80 0 100 200 300 400 500 600 700 800 0 2 4 6 8 10 12 n cy cl es e n er gy ( m p a) mass loss (%) energy stock-mass loss-6d ncycles-mass loss-6d energy stock-mass loss-8d ncycles-mass loss-8d figure 6: a graphical depiction of energy stocks and number of cycles of the b450c (φ12) specimens tested in lcf, in reference to their corresponding mass loss, before and after their exposure to corrosive conditions comparing the results of fig.4, with the corresponding results of fig.6, where the same steel categorybut with different nominal diameterwas used, it seems that specimens with 12mm diameter record lower mass loss percentages. this is owed to the fact that corrosion process, that is conducted in the salt spray chamber, is a method that mainly affects the external surface of the material. in the case of 16mm nominal diameter, the spread of the exposed surface is greater than in the case of 12mm, and it is a fact that results in a greater surface attack. this remark, in combination with the existing knowledge, related to the differential aeration corrosion phenomenon, can sufficiently explain that the rate of the electrons flowand therefore the corrosion ratedepend on the volume of the exposed material as well as the volume of the protected (not exposed to the aggressive conditions) part of the steel reinforcement. ch. apostolopoulos et alii, frattura ed integrità strutturale, 50 (2019) 548-559; doi: 10.3221/igf-esis.50.46 555 additionally, specimens of 12mm nominal diameter record higher performance under lcf testing, than the corresponding specimens of 16mm nominal diameter. this annotation is closely associated with the lower corrosion damage (e.g. mass loss rate or/ and pitting severity) recorded. combining the results of the tensile and the lcf tests, a correlation with real structures can take place. analytically, it is a fact, that during strong earthquakes, yielding structures are subjected to increased number of cycles into the inelastic range and the accumulated damage may significantly affect their overall performance. however, little attention has been devoted by the research community on the combined effect of corrosion and lcf on steel reinforcement, since each one of these factors affects the rebar durability and performance and shortens the life expectancy of structures [19-24]. it is known though, that besides external overt damage, more internal and subcutaneous phenomena are realized. at those areas, plethora of mns and fes compounds (potential sites of corrosion initiation or for the formation of corrosion paths) can be detected. synergy of both internal and external corrosion factor, may result in premature and unexpected failure of the material [25]. in an effort to further investigate the degradation phenomena, which are related to the internal downgrading of the material, several sem and edx analyses took place. prior to tensile testing, the cross sections of reference rebars were examined under scanning electron microscope, after having been polished to surface roughness of ra < 0.8 μm. figs.7 and 8 illustrate the sem and edx analyses in reference b400c, φ16 steel, without tension. the area depicted is about 1300μm from the outer surface within the martensitic zone. figure 7: sem analysis in reference b400c, φ16 steel, without tension. 0 1 2 3 4 5 6 7 8 kev 0.0 0.5 1.0 1.5 2.0 2.5 cps/ev fe fe mn mn s 1.00 * acquisition 8980 figure 8: edx analysis in reference b400c, φ16 steel, without tension. ch. apostolopoulos et alii, frattura ed integrità strutturale, 50 (2019) 548-559; doi: 10.3221/igf-esis.50.46 556 figs.9 and 10 illustrate the sem and edx analyses in a corroded b400c, φ16 sample, after tensile test. moreover, through x rays’ diffusion, the appearance of pores was obvious at the external martensitic surface and at the same area high sulfide concentration was noticed. this fact increased the requirements for damage expansion at the inner area of the external surface (skin). fig.11, which has been taken from study [26], that processes on the same rebar group, presents a sem analysis of a longitudinal cut in the fracture region in a non corroded b450c specimen after tensile test. figure 9: sem analysis in a corroded b400c, φ16 sample, after tensile test. 0 1 2 3 4 5 6 7 8 kev 0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0 2.2 cps/ev fe fe mn mn si s 1.00 * acquisition 8964 1.00 * acquisition 8963 figure 10: edx analysis in a corroded b400c, φ16 sample, after tensile test. figure 11: fracture surface (longitudinal cross section) of a non corroded specimen b450c [26]. ch. apostolopoulos et alii, frattura ed integrità strutturale, 50 (2019) 548-559; doi: 10.3221/igf-esis.50.46 557 figs.12 and 13 present a sem and an edx analysis of a longitudinal cut in the fracture region in a noncorroded specimen after tensile test (b450c). according to these findings, the area depicted is rich in mns and fes compounds, phenomenon which gradually leads to a local decomposition, and inevitably to the failure of the material. figure 12: sem analysis of the fracture region in a noncorroded specimen after tensile test (b450c). 2 4 6 8 10 12 14 kev 0.0 0.2 0.4 0.6 0.8 1.0 cps/ev fe-kamn-kas-ka fe fe mn mn s 1.00 * scan figure 13: edx analysis of the fracture region in a reference specimen after tensile test (b450c). it is very likely that the adsorption of clions in and around the strained regions of a mns–fe interface triggers the anodic dissolution of fe2+ ions. it is important to reemphasize here that clions are not involved in redox reactions but catalyze the anodic processes by adsorbing on the surfaces around the mns inclusions and by chasing away the conduction electrons of the strained matrix, which results in the anodic dissolution of iron from these regions as depicted in fig.14 [27]. figure 14: corrosion mechanisms surrounding a mns inclusion: refer to avci et al.[27] for details. ch. apostolopoulos et alii, frattura ed integrità strutturale, 50 (2019) 548-559; doi: 10.3221/igf-esis.50.46 558 from a structural point of view, dissolved mns sites and porosity represent high stress raisers, which upon loading can lead to the development of microcracks. these phenomena within the martensitic zone, near the location of surface pitting, result in local disruption of the material and a possible conjunction of extended imperfections with the surface pits. in these locations, the local disruption of the material is a crucial factor of its mechanical behavior since during the axial load an intense stress concentration is developed and the subsequent crack propagation is inevitable and rapid [8]. rapid depletion of the ductility or even failure may occur in high strength and ductility dual phase steel bars, due to the combination of interior and exterior damage phenomena under strong stresses. consequently, an additional purpose of this study is to highlight the significance of the corrosion factor on the mechanical performance of the dual phase steel bars and to estimate the degradation of its mechanical properties, which is the result of the cooperation of the internal and the external damage, under those hazardous circumstances [25]. the results of the mechanical tests confirmed that corrosion, due to chloride ions, is one of the main degradation factors of steel reinforcement. conclusions he conclusions of the present study can be summarized as follows: • steel bar category b450c recorded slightly higher mass loss percentages than b400c steel class, a fact that demonstrates that the first category is more vulnerable to corrosion. • in both steel categories, a slight mechanical degradation was recorded, in terms of yield and maximum strength, while ductility and dissipated energy were dramatically diminished. • due to buckling and buckling reversal, materials demonstrate limited ductility especially at 4%. • when cyclically stresses occur, sulphides, fes and mns sites will host crack nucleation leading to sub-surface crack propagation, which interact with external pits. the case becomes very complex in terms of analysis, especially under fully reverse loading and high plastic strain levels leading to buckling • among two specimens of the same steel class, the one with smaller nominal diameter records higher performance against lcf tests. • the areas with mns compounds present a significant development under the presence of (cl−) ions, which combined with the occurrence of other impurities, as well as pits at the surface of steel, may inevitably induce mechanical stress concentration during the tensile loading • therefore, the mechanical degradation of precorroded steels that were examined can result from the synergy of mass loss effect, external pitting, and a variety of inevitable side effects from regions with mns compounds within the martensitic zone. • examining the performance of both steel categories under lcf tests, it seems that reference b450c steel has grater life cycle and higher energy stocks than the reference b400c steel. however, when both categories record 5%-10% mass loss, under corrosion conditions, life cycles of both steel categories are approximately equal. acknowledgements he present work has been implemented within the framework of the european research project rusteel (effect of corrosion on low-cycle (seismic) fatigue behaviour of high strength steel reinforcing bars) (2008-2012), project funded by rfcs contract no. rfsr-ct-2009-00023 references [1] apostolopoulos, c.a., papadakis, v.g., (2008). consequences of steel corrosion on the ductility properties on reinforcement bar, construction and building materials, 22, pp. 2316-2324 [2] almusallam, a., (2001). effect of degree of corrosion on the properties of reinforcing steel bars, construction and building materials, 15(8), pp. 361-368 [3] apostolopoulos, ch., (2007). mechanical behavior of corroded reinforcing steel bars s500s tempcore under low cycle fatigue, construction and building materials, 21, pp.1447-1456 [4] papadakis, v.g., (1999). supplementary cementing materials in concrete-activity, durability and planning, danish technological institute concrete center t t ch. apostolopoulos et alii, frattura ed integrità strutturale, 50 (2019) 548-559; doi: 10.3221/igf-esis.50.46 559 [5] capazucca, r., (1995). damage to reinforcement concrete due to reinforcement corrosion, constr. build. mater., 9, pp. 295-303. [6] diamond, s.e, (1986). chloride concentration in concrete pore solutions resulting from calcium and sodium chloride admixtures, com concr. aggr., 8, pp. 97-102. [7] alvarez, m.g., galvele, j.r. (1984). the mechanisms of pitting of high purity iron in nacl solutions, corros. sci., 24, pp.27-48. [8] afsar, e. and kashani, m.m., (2017), exploring the impact of chloride-induced corrosion on seismic damage limit states and residual capacity of rc structures, structure and infrastructure engineering, 14 (6), pp.714-729. [9] astm b 117-94. (1995) standard practice for operating salt (fog) testing apparatus. in: annual book of astm standards, section 3, metal test methods and analytical procedures. philadelphia, usa: west conshohocken, astm. [10] quanmin, ma., sreejith, v., nanukuttan p.a, basheer, m., bai, y. and yang, ch. (2016). chloride transport and the resulting corrosion of steel bars in alkali activated slag concretes, materials and structures, 49, pp. 3663-3677. [11] angst, u.m. and elsener, b. (2017). the size effect in corrosion greatly influences the predicted life span of concrete infrastructures, applied sciences and engineering,.3. [12] vera cruz, r.p., nishikata, a. and tsuru, t. (1998). pitting corrosion mechanism of stainless steels under wet-dry exposure in chloride-containing environments, corrosion science, 40, pp. 125-139. [13] obla, k.h., lobo, c.l and kim, h. (2016). tests and criteria for concrete resistant to chloride ion penetration, aci materials journal, pp. 621-631. [14] astm g1-90 (1995). standard practice for preparing, cleaning and evaluating corrosion test specimens. in: annual book of astm standards, section 3, metal test methods and analytical procedures. philadelphia, usa: west conshohocken. [15] uni en iso 15630-1:2010, steel for the reinforcement and pre-stressing of concrete. test methods. part 1: reinforced bars, wire rod and wire. eur. com stand [16] caprili, s. and salvatore, w., (2015). cyclic behaviour of uncorroded and corroded steel reinforcing bars. construction and building materials, 76, pp.168-186. [17] apostolopoulos, alk. and matikas, t., (2018). the impact of corrosion and inelastic buckling on low cycle fatigue life of steel bars, procedia structural integrity, 10, pp. 49-58. [18] salvatore, w., caprili, s., braconi, a., finetto, m., bianco, l., ascanio, c., moersch, j., apostolopoulos, c., ferreira pimenta, g., (2014). effects of corrosion on low-cycle fatigue (seismic) behavior of high-strength steel reinforcing bars (rusteel), grant agreement rfsr-ct-2009-00023, directorate-general for research and innovation. [19] ma, s.y.m., bertero, v.v. and popov, e.p., (1976). experimental and analytical studies on the hysteretic behaviour of reinforced concrete rectangular and t-beams. earthquake eng. research report 76 (no.2), berkeley: univ. of california [20] yoshaki, t., (1983). proceedings of academical lectures of jas. tokyo, 606. [21] shigeru, h., (1995). research report, retrofitting of reinforced concrete moment resisting frames, supervised: park, r., tanaka, h., issn0110-3326 [22] clementa, g.g., (2002). testing of selected metallic reinforcing bars of extending the service life of future concrete bridges, fin. report, virginia transport, charlot, va, research council, vtrc 03-a7. [23] krawinkler, h., (1987). performance assessment of steel components. earthquake spectra 3, 27. [24] kasiraj, i. and yao, j.t.p., (1969). fatigue damage in seismic structures. journal of the structural division (asce) 95, 1673. [25] apostolopoulos, ch., drakakaki, arg., apostolopoulos, alk., matikas, t., rudskoi, a.i. and kodzhaspirov, g., (2017). characteristic defects-corrosion damage and mechanical behavior of dual phase rebar, materials physics and mechanics, 30, pp.1-19. [26] apostolopoulos, c.a, diamantogiannis, g and apostolopoulos, a.c, (2015). assessment of the mechanical behavior in dual phase steel b400c, b450c and b500b in marine environment, journal of materials in civil engineering, 28(2), 10.1061/ (asce)mt.1943-5533.0001271, 04015097. [27] avci, r., davis, b.h., wolfenden, m.l., beech, i.b., lucas, k. and paul, d. 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/hrv (za stvaranje adobe pdf dokumenata najpogodnijih za visokokvalitetni ispis prije tiskanja koristite ove postavke. stvoreni pdf dokumenti mogu se otvoriti acrobat i adobe reader 5.0 i kasnijim verzijama.) /hun 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can be opened with acrobat and adobe reader 5.0 and later.) >> /namespace [ (adobe) (common) (1.0) ] /othernamespaces [ << /asreaderspreads false /cropimagestoframes true /errorcontrol /warnandcontinue /flattenerignorespreadoverrides false /includeguidesgrids false /includenonprinting false /includeslug false /namespace [ (adobe) (indesign) (4.0) ] /omitplacedbitmaps false /omitplacedeps false /omitplacedpdf false /simulateoverprint /legacy >> << /addbleedmarks false /addcolorbars false /addcropmarks false /addpageinfo false /addregmarks false /convertcolors /converttocmyk /destinationprofilename () /destinationprofileselector /documentcmyk /downsample16bitimages true /flattenerpreset << /presetselector /mediumresolution >> /formelements false /generatestructure false /includebookmarks false /includehyperlinks false /includeinteractive false /includelayers false /includeprofiles false /multimediahandling /useobjectsettings /namespace [ (adobe) (creativesuite) (2.0) ] /pdfxoutputintentprofileselector /documentcmyk /preserveediting true /untaggedcmykhandling /leaveuntagged /untaggedrgbhandling /usedocumentprofile /usedocumentbleed false >> ] >> setdistillerparams << /hwresolution [2400 2400] /pagesize [612.000 792.000] >> setpagedevice microsoft word numero_29_art_2 l. cabras et alii, frattura ed integrità strutturale, 29 (2014) 9-18; doi: 10.3221/igf-esis.29.02 9 focussed on: computational mechanics and mechanics of materials in italy effective properties of a new auxetic triangular lattice: an analytical approach l. cabras università degli studi di cagliari, dipartimento di ingegneria civile, ambientale e architettura luigi.cabras@unica.it m. brun università degli studi di cagliari, dipartimento di ingegneria meccanica, chimica e dei materiali; university of liverpool, department of mathematical sciences mbrun @unica.it abstract. in this article we propose a new auxetic periodic lattice with negative poisson's ratio which tends to the limit ν=-1 under particular conditions. we have studied its generation and kinematic, and we give a full description of the mechanical properties of this innovative model. calibrating the geometrical configuration of the lattice and the mechanical properties of the constituent material we are able to have a poisson's ratio which is arbitrarily close to -1. keywords. auxetic lattice; negative poisson’s ratio; mechanical properties. introduction oisson's ratio, usually represented by ν, is defined as the ratio of transverse contraction strain to longitudinal extension strain with respect to the direction of stretching force applied. since tensile deformation is considered positive and compressive deformation is considered negative in the definition of poisson's ratio is introduced a minus sign, so that common materials have a positive ratio. however, there are particular materials that expand laterally when stretched longitudinally with a negative poisson's ratio, they were named for the first time auxetic materials by ken evans in an article in nature (1991). for isotropic materials it may be shown that poisson's ratio is between -1≤ν≤ ½ in 3d and -1≤ν≤1 in 2d, for anisotropic materials ν is not restricted by the above limits. the value of the poisson's ratio has also important consequences for other aspects of the behavior of materials, in fact the most materials resist a change in volume as determined by the bulk modulus k more than they resist a change in shape, as determined by the shear modulus μ, the values of k are typically larger than the values of μ. by changing the microstructure of a material in such a way that the poisson's ratio ν is lower, the values of k and μ can be altered. decreasing the value of ν to negative value, it would result into a material with a higher shear modulus μ than the bulk modulus k. different geometrical structures and models are created trying to reproduce some observed feature in auxetic materials, ranging from the macroscopic to microscopic and to the molecular levels. a simple classification can be based on mechanical considerations. almost all of these models are based on a simple mechanism that is treated as a unit cell leading to a global stiffening effect. one of the earliest models used to describe these special materials was that with re-entrant structure, firstly suggested in [1]. over the years, many more sophisticated models have been proposed. another model is based on chiral structure, the researchers in this area use the adjective "chiral" to mean a physical property of spinning. in this type of structures, basic chiral units p l. cabras et alii, frattura ed integrità strutturale, 29 (2014) 9-18; doi: 10.3221/igf-esis.29.02 10 are firstly formed by connecting straight ligaments to central nodes which may be circles or rectangles or other geometrical forms. the auxetic effects are achieved through wrapping or unwrapping of the ligaments around the nodes in response to an applied force, as shown in [2], the poisson's ratio ν of a chiral structure for in-plane deformations, with flexible ribs and rigid node, can be tailored to be around -1. later ruzzene and spadoni, in [3], have considered the behavior of structures by introducing the flexibility of the nodes. other models, as in [4], derive the auxetic behavior by the rotation of rigid or semi-rigid shapes (triangle, squares, rectangles and tetrahedron) when loaded, this type of structures has been developed to reproduce the behavior of foams and hypothetical nanostructure networked polymers. a different approach is followed by bathurst and rothenburg in [5], they formulate the incremental response of an assembly of elastic spheres, considering an isotropic distribution of contacts around a particle. since the negative poisson's ratio is a scale independent property the auxetic behavior can be achieved at a macroscopic or microstructural level, or even at the mesoscopic and molecular levels, many models were developed to simulate polymeric structure or anisotropic fibrous composites. the first auxetic microporous polymeric material was investigated in [6]. it was an expanded foam of ptfe which has a highly anisotropic negative ν =-12. several cases of negative poisson's ratios have been discovered in the analysis of anisotropic fibrous composites. in these composites there is a high degree of anisotropy and the negative poisson's ratio only occurs in some directions; in some cases only over a narrow range of orientation angle between the applied load and the fibers. in a recent advance, laminate structures have been presented which give rise to intentional negative poisson's ratios combined with mechanical isotropy in two dimensions or in three dimensions. these laminates have structure on several levels of scale; they are hierarchical. by appropriate choice of constituent properties one can achieve poisson's ratios approaching the lower limit of -1. auxetic systems perform better than classical material in a number of applications, due to their superior properties. they have been shown to provide better indentation resistance [7, 8 and 9] for their property of “densification” in the vicinity of an impact. the auxetic materials form dome shaped structures [10, 11] when they are subjected to out of plane bending moments instead the saddle shape adopted by the common materials. also, they can be useful when we need better acoustic and vibration properties than the conventional materials [12, 13 and 14]. model of periodic lattice with auxetic macroscopic behavior e consider radially foldable structure formed by two angulated elements abc and dbe, shown in fig. 1, connected together through a hinge in b. figure 1: pair of linkages movable with a single degree of freedom. the two rigid linkages abc and ebd are shown in grey and black, respectively. they are constraint at the “coupler” point b to have the same displacement components. points a and d and e and c can only move along straight lines. the coupled angulated elements abc and dbe can roto-translate with a single degree of freedom and the end point a, c, d and e can only translate along to ox-axis and the axis inclined by the angle α with respect to the ox-axis, respectively. w l. cabras et alii, frattura ed integrità strutturale, 29 (2014) 9-18; doi: 10.3221/igf-esis.29.02 11 in analyzing the trajectory of the central point b, we also follow the more general formulation given in [15]. in fig. 1, p is the length of the arms, θ the internal angle between them and α is the angle between the two straight lines along which the points a, d and c, e are constrained to move. b is the “coupler” point of the linkage. the equation for the oneparameter trajectory followed by the point b is obtained fixing the values of the geometric variables p, θ, α; then, the position of b is determined by the angle γ. when we couple the movement of the linkage abc with the linkage ebd, we obtain a relation between angles θ and α. the common point b follow the radial line ob: x cosθ1 sinθ y   (1) the two linkages are assembled in order to create a radially foldable structure, as depicted in fig. 2 and to avoid crossover with other pairs in a polar arrangement of the fully radially foldable structure the angle γ has to satisfy the bound ηπγηα  , (2) where edbcab   . different configurations are shown in fig. 2b; the point b for each pair of linkages moves radially and the corresponding poisson's ratios is equal to -1. we consider the triangular geometries with α=2π/3. (a) (b) (c) figure 2: (a) radially foldable structure with geometric parameters. (b) configurations of the single degree of freedom lattices at different values of the geometrical parameter. (c) the radial distance ob as a function of γ is also given for p=1. construction of periodic lattice the kinematically compatible periodic structures shown in fig. 3 is obtained by a periodic distribution of the single cell elements shown in fig. 2 as in [16]. figure 3: periodic microstructure. three different configurations, for different values of α are shown. the grey dashed region is the unit cell of the bravais lattice where t1 and t2 are the primitive vectors. the microstructure is composed of shaped elements with 12 arms of the same length. a system of cross couple is built where two elements are disposed in two different planes. each cross couple is mutually constrained to have the same displacement at the central point where a hinge is introduced. different couples of crosses are then constrained each other by internal hinges at the external end of each arm. the periodic structures have a bravais periodic lattice [17] consisting of points: r = n1t1+n2t2 (3) l. cabras et alii, frattura ed integrità strutturale, 29 (2014) 9-18; doi: 10.3221/igf-esis.29.02 12 where n1,2 are integers and t1,2 the primitive vectors spanning the lattice. effective properties of the periodic auxetic lattice acroscopic properties are derived analytically for our lattice. the triangular lattice have three-fold symmetries and basic considerations on the symmetry group of the material lead to the conclusion that its constitutive behavior is isotropic (in the plane of deformation). therefore, it will be necessary to compute two effective elastic constants. stability constraints the in-plane poisson's ratio to range between -1 and 1. effective properties are denoted as k*(bulk modulus), e*(young's modulus), μ*(shear modulus) and ν*(poisson's ratio) and macroscopic stress and strain as σ and ε , respectively. the structure is composed of slender crosses and classical structural theories can be conveniently applied to analyze the response of the elastic system. in particular, each arm of a single cross is modeled as an euler beam undergoing flexural and extensional deformations. each beam have young's modulus e, cross-sectional area a and second moment of inertia j. additional springs have longitudinal stiffness equal to kl or rotational stiffness equal to kr (see fig. 4). we also introduce the non-dimensional stiffness ratio parameters α1=klp/(ea), α2=klp3/(ej), α3=kr/(pea) and α4=krp/(ej). macroscopic stresses are computed averaging the resultant forces on the boundary of the unit cell. periodic boundary condition have been applied on the boundary of the unit cell so that displacements are periodic and forces are antiperiodic. additional constrains are introduced to prevent rigid body motions. to solve the structure we apply the principle of virtual work (pvw). it states that, if a structure is in equilibrium, then, for any arbitrary small virtual displacement satisfying kinematic boundary conditions, the work done by the external forces must equal the work done by the internal forces. in the following, we apply the pvw in two steps: in the first we find the internal actions (bending moments m, axial forces p and spring forces sl or moments mr) of the structure searching for the kinematic admissible configuration in the set of statically admissible ones (flexibility method) and in the second step we compute the macroscopic displacements. (a) (b) figure 4: lattice reinforced with elastic springs. (a) longitudinal springs of stiffness kl. (b) rotational spring of stiffness kr. the dashed contour indicates a typical unit cell of the periodic elastic system. this procedure has the advantage to maintain the analytical treatment sufficiently simple. we point out that all the results have been also verified numerically implementing a finite element code in comsol multiphysics®. we consider the elastic structure as in fig. 5a, subjected to normal and tangential external forces supposed to be known and corresponding to a macroscopic stress having components 11 and 22 different from zero. we define an equivalent statically determined system disconnecting two springs and introducing the dual static parameter as unknown x, equal for the two springs, as shown in fig. 5b. then, the general field of tension ξ (ξ=m, n, sl or mr) in equilibrium with the external loads is: ξ= ξ0 + xξ1 (7) where ξ0 is the solution of the static scheme in equilibrium with the external loads and x=0; while the field ξ1 is the solution of the static scheme in equilibrium with zero external loads and x=1. the deformed configurations of the isostatic equivalent structure violate the internal constraint in the two springs suppressed in the structure made isostatic. m l. cabras et alii, frattura ed integrità strutturale, 29 (2014) 9-18; doi: 10.3221/igf-esis.29.02 13 (a) (b) (c) (d) figure 5: application of the principle of virtual displacements. lattice reinforced with longitudinal springs. (a) simplified structured analyzed for the computation of the effective properties. the applied forces fn, fv, ft1 and ft2 correspond to macroscopic stresses components. (b) disconnected statically determined structure introduced for the determination of the internal actions (m,n,sl). (c-d) statically determined structure adopted for the computation of the displacement of the points a and b. such kinematic constraints must be restored imposing the kinematic compatibility equation that determines the values of the unknown x and uniquely defines the elastic solution of the problem, as follows:   cotγ 3+1α γ 2 3cos+2α γ 2 sin 1)+1(αvf+2)+2α γ 2 sin+11)α-γ 2 (3cosnf beam p 0 spring /2lk l 1sl 1s)dξ ea 1n 1n ej 1m 1(m beam p 0 spring /2lk l 1sl 0s)dξ ea 1n 0n ej 1m 0(m x                 (8) we note that for sufficiently slender beam structures, the contribution due to the shear deformation is negligible compared to that due to flexural and axial deformations and, therefore, it has been neglected. we reconstruct the distribution of internal actions by a linear combination of partial diagrams of n and m and of the spring forces sl, as functions of external forces fn, ft=(ft1+ft2)/2 and fv: n = n + x n0 1 m = m + x m0 1 l l ls = s + x s 0 1      (9) applying a second time the pvw we calculate the displacement of the point a and b (center of the spring) as shown in fig. 5c-5d. to do this we consider as kinematically admissible structure the real structure and as statically admissible structure, an isostatic structure subjected to horizontal and vertical forces of magnitude equal 1/4, respectively, so that the virtual external works coincide exactly with the horizontal and vertical displacement of the point b (u1 and u2 in fig. 5c), and we calculate the displacement of the point a (u3 in fig. 5d ) considering a vertical forces of unitary magnitude, so that the virtual external works coincide exactly with the vertical displacement of the point a. in particular the pvw equations have the form: l. cabras et alii, frattura ed integrità strutturale, 29 (2014) 9-18; doi: 10.3221/igf-esis.29.02 14    beam p 0 spring /2lk ls*l is)dξea n* inej m* i(miu , (i=1, 2 and 3), (10) where mi*, ni* and sil* (with i=1, 2 and 3) are the internal actions of the statically admissible structures subjected to forces applied in the point b in horizontal and vertical direction, and the internal actions of the statically admissible structure subjected to a vertical forces applied in the point a in vertical direction. the corresponding displacement are: u1 = a1 fn + b1 ft+c1 fv u2 = a2 fn + b2 ft+c2 fv u3 = a3 fn + b3 ft+c3 fv (11) where a1-3, b1-3, c1-3 are coefficients arising from the integrations. previous equations are explicit linear relations between the forces fn, ft and fv associated to macroscopic stresses 3f fn tσ11 psin γ 4f 2 3f 2fv ntσ22 2 3psinγ      (12) and the displacements of the points a and b associated to macroscopic strains: a f b f f2u 1 n 1 1 v1 tε 211 3psin γ 3psin γ a f b f fu 3 n 3 3 v3 tε 222 psin γ psin γ c c         (13) solving previous relations (13) in term of fn, ft, and fv and substituting the result into eqn. (12) leads to the macroscopic constitutive relation between the macroscopic stress σ and macroscopic strain ε . clearly, appropriate choices of the forces fn, ft, and fv can be considered in order to set to zero some components of the stress. the in-plane mechanical properties of the lattice with extensional springs are:  poisson's ratio )2α7d-1α6d-2α1α10d 2 2α43d 2 1α9d 2 2α1α23d 2α 2 1α8d 3 1α1d2α7d 1α6d 2α1α5d 2 2α4d 2 1α3d 2 2α1α2d 2α 2 13α3 1α1d 22 ε 22 σ 11 ε 11 σ 22 ε 11 σ 11 ε 22 σ lν       (14) where: d1=-9cos4γ d2=sin4γ d3=9(cos6γ -4 cos4γ +2cos2γ-1) d4=sin4 γ cos2γ d5=3(6cos4γ-7cos2γ-2cos6γ+1) (15) d6=-9cos2γ d7=-3cos2γ d8=3(4sin2γcos2γ+1) d9=9(3cos6γ-4cos4γ+2cos2γ+1) d10=3(10cos4γ-6cos6γ-5cos2γ+3)  bulk modulus )1α γ 2(cos 2 lk γ 2sin 3 22 ε 11 ε 22 σ 11 σ 2 1 lk      (16)  young's modulus l. cabras et alii, frattura ed integrità strutturale, 29 (2014) 9-18; doi: 10.3221/igf-esis.29.02 15 2 2σ σ 11 22e 2k (1 ν)l lσ ε σ ε 11 11 22 22 4 2 4 2 2 2 22 3 (9cos γ α sin γ α 3(2cos γ sin γ 1)α α 9α 3α )sin γ k1 2 1 2 1 2 l 3 2 2 2 2d α d α α 3d α α d α 3d α d α α d α d α1 1 8 1 2 2 1 2 9 1 4 2 10 1 2 6 1 7 2                  (17) where the constants d1, d2, d4, d6-10 are given in eq. (15).  shear modulus σ σ1 1 ν11 22μ kl lε ε2 1 ν11 22 4 2 4 2 2 2 23 (9cos γ α sin γ α 3(2cos γ sin γ 1)α α 9α 3α )sin γ k1 2 1 2 1 2 l 2 2 2 2 2 2 2 2 212cos γα α 4sin γα α 9sin 2γ 6(2 sin 2 )α α sin 2γ1 2 1 2 1 1 2 2                      (18) when rotational springs are considered the effective constants are as follows:  poisson's ratio 2 2e α e α e α α e α e α1 3 2 4 3 3 4 4 3 45ν r 2 2e α e α e α α e α e α6 3 7 4 8 3 4 4 3 45         (19) where: e1=9 (2cos4γ-3cos2 γ+1) e2=(2cos4γ-cos2γ) e3=3(4cos2γ sin2γ-1) e4=27cos2γ (20) e5 =9cos2γ e6=9(2cos4γ-cos2γ-1) e7=2cos4γ-3cos2γ e8=12cos2γ sin2γ-9  bulk modulus 23 3 (k / p )rk r 2 2 22 (3sin γ α cos γ α 9cos γ)3 4    (20)  young's modulus 26 3 (3α α )(k / p )3 4 rer 2 2 e α e α e α α e α e α6 3 7 4 8 3 3 4 3 35     (21)  shear modulus 23 3 (3α α )(k / p )3 4 rμr 2 2 2 2 2 9sin 2γ sin 2γ 6(2 sin 2 )3 4 3 4           (22) analysis of effective properties e analyze now the effective properties of the microstuctured media. we consider the case of vanishing stiffness of the springs kl, kr →0. we have that: w l. cabras et alii, frattura ed integrità strutturale, 29 (2014) 9-18; doi: 10.3221/igf-esis.29.02 16 * 2ν* 1 ν k o(k )1 l,r l,r * 2k* 0 k k o(k )1 l,r l,r * 2e* 0 e k o(k )1 l,r l,r * * 2μ* μ μ k o(k )1 l,r l,r0              ; (23) where the coefficient ν1*, k1*, e1*, μ0*>0 are shown in tab. 1. longitudinal spring rotational spring γ 2 tan 1 eaejη 3 η 2 η 3 4p* 1ν  γ 2 tan γ 2 cos 1 eaejη 3 η 2 η 9 4* 1ν  γ 2 tan 2 3* 1k  γ 2 cos 2 6p 3* 1k  γ 2 tan3 * 1e 2 γ 2 cos 2 3p 3* 1e 2  3 η 2 η 1 eaejη 4p 33* 0μ  3 η 2 η 1 eaejη 4p 33* 0μ  table 1: explicit expression of the coefficients in the asymptotic formulae in eqn. (23). in the table η1=3ej+p2ea, η2=3ejsin2γ+p2eacos2γ, η3=3ejcos2γ +p2easin2γ. it is shown in (23) that also for deformable structures the poisson's ratio remains -1 when the stiffness of the springs is zero, while the effect of the springs is to increase the value of ν*. in such a limit, the bulk and the young's moduli vanish while the shear modulus remains finite. the limiting behavior described in (23) can also be understood in term of relative stiffness between the spring elements and the elements of the lattice as described by the coefficients α1…..4. in this respect, when α1…..4→0, the same outcomes of eqns. (23) are obtained. the dependence of the poisson's ratio on the stiffnesses kl and (kr/p2) is shown in fig. 6. results confirm that the poisson's ratio approaches -1 when the spring constants are zero. it is worthwhile to mention the maximum theoretical values that can be reached by the poisson's ratios at the limit kl, kr/p2 →∞; the limiting expressions are: 22 21 1 sin γ cos γ s 4ν* o(( ) 23 psin γ 2 21 2 cos γ (s / p) 4ν* 1 o(( ) 2 23 2 cos γ 3 2 cos γ s / p) s / p)                         (24) where we have considered, for simplicity, rectangular cross-sections of the arms, so that a=ts and j=ts3/12, where s and t are the in-plane and out-of-plane thicknesses, respectively. in the following fig. 6 we compare the effective poisson’s ratio ν* of the triangular lattice in function of the stiffness of the longitudinal springs kl, see fig. 6a, and in function of the slenderness λ=p/s of the arms, see fig. 6b. in each figure we consider three different materials with young's modulus e=3000 mpa for thermoplastic polymer (abs), e=60000 mpa for granite and e=200000 mpa for steel, the geometric configuration considered is given by the angle γ=4π/9. all the computations are performed considering a thickness t of the lattice out of plane of 1 mm. in fig. 6a we have considered arms with length p=50 mm and in-plane thickness s=10 mm. in fig. 6b the values of the poisson’ ratio are significant when λ=p/s≥5, in the range of validity of the beam theory which has been used for the computation of the effective behavior, anyway we show with dotted line the values of the poisson’ ratio even for λ <5. the value of the stiffness of the springs has been set equal to kl=1 n/mm. as it is possible to see in fig. 6, when the contribution of the spring is less relevant the poisson’s ratio approaches -1, as confirmed by l. cabras et alii, frattura ed integrità strutturale, 29 (2014) 9-18; doi: 10.3221/igf-esis.29.02 17 analytical formulae, both when the stiffness of the spring kl→0, and when the slenderness of the arms λ→0. on the contrary when the stiffness of the springs is big the poisson’ s ratio approaches 1/3, as in the case of the classical triangular lattice used in several physical models and engineering. (a) (b) figure 6: effective poisson’s ratio ν* for three different materials in the case of longitudinal springs. (a) poisson’s ratio as a function of the stiffness kl. (b) poisson’s ratio as a function of the slenderness λ=p/s. in the fig. 7 we show the same results in the case of the lattice with rotational springs, for which the same considerations of the previous case are still valid. (a) (b) figure 7: effective poisson’s ratio ν* for three different materials in the case of rotational springs. (a) poisson’s ratio as a function of the stiffness kr/p2. (b) poisson’s ratio as a function of the slenderness λ=p/s. conclusions he constitutive properties of a new auxetic material are obtain analytically by using classical beam theory in the analysis of the microstructure of the lattice. result show that the effective poisson’ ratio of the lattice is arbitrarily close to -1. acknowledgments .b. acknowledges the financial support of the european community's seven framework programme under contract number pief-ga-2011-302357-dynameta and of regione autonoma della sardegna (lr7 2010, grant `m4' crp-27585). t m l. cabras et alii, frattura ed integrità strutturale, 29 (2014) 9-18; doi: 10.3221/igf-esis.29.02 18 references [1] gibson, l.j., ashby, m.f., schajer, g.s., robertson, c.i., the mechanics of two dimensional cellular solids, in: proc. r. soc. lond. a, 382 (1982) 25-42. [2] prall, d., lakes, r.s., properties of a chiral honeycomb with a poisson's ratio of ν=-1, int. j. mech. sci., 39 (1997) 305-307, 309-314. [3] spadoni, a., ruzzene, m., elasto-static micropolar behavior of a chiral auxectic lattice, j. mech. phys. solids, 60 (2011) 156-171. [4] wojciechowski, k.w., two-dimensional isotropic system with a negative poisson ratio elasto-static micropolar behavior of a chiral auxectic lattice, physics letters a, 137 (1989) 60-64. [5] bathrust, r.j., rothenburg, l., note on a random isotropic granular material with negative poisson's ratio, int. j. eng. sci., 26 (1988) 373-383. [6] caddock, b.d., evans, k.e., microporous materials with negative poisson's ratios, i. microstructure and mechanical properties, j. phys. d: appl. phys., 22 (1989) 1877-1882. [7] webber, r. s., alderson, k. l., evans, k.e., a novel fabrication route for auxetic polyethylene part 2: mechanical properties, polym. eng. sci., 48-7 (2008) 1351-1358. [8] lakes, r.s., elms, k.e., indentability of conventional and negative poisson’s ratio foams, j. compos. mater., 27-12 (1993) 1193-1202. [9] chan, n., evans, k. e., indentation resilience of conventional and auxetic foams, j. cell. plast., 34 (1998) 231-260. [10] lakes, r.s., foam structure with a negative poisson's ratio, science, 235 (1987) 1038-1040. [11] burke, m., a stretch of the imagination, new scientist, 154-2085 (1997) 36-39. [12] chen, c. p., lakes, r. s., dynamic wave dispersion and loss properties of conventional and negative poisson’s ratio polymeric cellular materials, cell. polym., 8-5 (1989) 343-369. [13] scarpa, f., dallocchio, f., ruzzene, m., identification of acoustic properties of auxetic foams, smart struct. mater.: damping isol., 5052 (2003) 468-474. [14] ruzzene, m., vibration and sound radiation of sandwich beams with honeycomb truss core, j. sound vib., 277-4-5 (2004) 741-763. [15] patel, j., ananthasuresh, g.k., a kinematic theory for radially foldable planar linkages, int. j. solids struct., 44 (2007) 6279-6298. [16] cabras, l., brun, m., auxetic two-dimensional lattice with poisson's ratio arbitrarily close to -1, submitted. [17] kittel, c., introduction to solid state physics, seventh ed., john wiley & sons, new york, (1996). microsoft word numero 16 articolo 1 l. susmel, frattura ed integrità strutturale, 16 (2011) 5-17; doi: 10.3221/igf-esis.16.01 5 on the overall accuracy of the modified wöhler curve method in estimating high-cycle multiaxial fatigue strength luca susmel department of engineering, university of ferrara, via saragat, 1 – 44100 italy department of mechanical engineering, trinity college, dublin 2, ireland department of civil and structural engineering, university of sheffield, mappin street, sheffield, s1 3jd, uk ssl@unife.it abstract. the aim of the present paper is to systematically investigate the accuracy of the so-called modified wöhler curve method (mwcm) in estimating high-cycle fatigue strength of plain and notched engineering materials damaged by in-service multiaxial load histories. in more detail, the mwcm, which is a bi-parametrical critical plane approach, postulates that initiation and stage i propagation of fatigue cracks occur on those material planes experiencing the maximum shear stress amplitude (this being assumed to be always true independently from the degree of multiaxiality of the applied loading path). further, the fatigue damage extent is hypothesised to depend also on the maximum stress perpendicular to the critical plane, the mean normal stress being corrected through the so-called mean stress sensitivity index (i.e., a material constant capable of quantifying the sensitivity of the assessed material to the presence of superimposed static stresses). in the present investigation, the overall accuracy of the mwcm in estimating high-cycle fatigue strength was checked through 704 endurance limits taken from the literature and generated, under multiaxial fatigue loading, by testing both plain and notched samples made of 71 different materials. such a massive validation exercise allowed us to prove that the mwcm is highly accurate, resulting in 95% of the estimates falling within an error interval equal to ±15%. keywords. multiaxial fatigue; critical plane approach; high-cycle fatigue strength; notch. introduction ince the pioneering work done by gough [1], over the last 60 years several researchers have made a big effort in order to devise sound criteria allowing high-cycle fatigue damage under multiaxial fatigue loading to be estimated accurately. as to the work that has been done so far, examination of the state of the art shows that the most important high-cycle fatigue criteria can be subdivided into the following three different groups: methods making use of the so-called microscopic approach [2, 3], fatigue assessment techniques based on the use of the stress invariants [4-6], and, finally, criteria taking full advantage of the classical critical plane concept [7-9]. amongst the above different strategies, it is the author’s opinion that the most promising approaches are those based on the assumption that fatigue damage reaches its maximum value on that material plane (i.e., the so-called critical plane) experiencing the maximum shear stress amplitude [10]. according to the above firm belief, over the last decade we have made a big effort in order to systematically investigate the peculiarities of a bi-parametrical critical plane approach which is known as the modified s http://dx.medra.org/10.3221/igf-esis.16.01&auth=true http://www.gruppofrattura.it l. susmel, frattura ed integrità strutturale, 16 (2011) 5-17; doi: 10.3221/igf-esis.16.01 6 wöhler curve method (mwcm) [11]. in more detail, initially we checked the accuracy and reliability of such a criterion in estimating both high-cycle fatigue damage [12, 13] and lifetime [14, 15] of plain engineering materials subjected to multiaxial fatigue loading. subsequently, attention has been focused on the problem of estimating multiaxial fatigue damage in the presence of stress concentration phenomena [16-19], by also investigating the related problem of designing welded connections against multiaxial fatigue [20-24]. recently, basing his investigation on several experimental results taken from the literature, jan papuga [25] has performed a systematic comparison amongst different criteria in order to select the most accurate one in estimating high-cycle fatigue damage in plain engineering materials subjected to multiaxial loading paths. according to his calculations, he has come to the conclusion that the use of the mwcm results in poor estimates, especially when superimposed static stresses are involved. in our opinion, such an erroneous conclusion has to be ascribed to the fact that dr. papuga has applied our approach in a wrong way, by systematically miscalculating the stress quantities relative to the critical planes. accordingly, in the present paper the main features of the mwcm are initially reviewed by focusing attention mainly on the problem of determining the so-called mean stress sensitivity index. subsequently, it is proven, through 704 experimental endurance limits generated by testing both plain and notched samples made of 71 different materials, that, when the mwcm is used correctly, it is capable of estimates falling mainly within an error interval of ±10%. fundamentals of the mwcm he mwcm is a critical plane approach which estimates multiaxial fatigue damage through the maximum shear stress amplitude, a, as well as through the mean value, n,m, and the amplitude, n,a, of the stress perpendicular to the critical plane. according to the fatigue damage model the mwcm is based on [11], the critical plane is defined as that material plane experiencing the maximum shear stress amplitude, a. from a practical point of view, the combined effect of both a, n,m and n,a are taken into account simultaneously through the following stress index [13]: a anmn eff m    ,,   (1) in the above identity, mean stress sensitivity index m [13] is a material property to be determined experimentally whose main features will be investigated in the next section in great detail. as to ratio eff instead, thanks the way it is defined, such a stress index is seen to be sensitive not only to the presence of superimposed static stresses, but also to the degree of non-proportionality of the applied loading path [11]. turning back to the mwcm, the way it estimates fatigue damage under multiaxial fatigue loading is schematically shown by the modified wöhler diagram reported in fig. 1a. the above log-log diagram plots the shear stress amplitude relative to the critical plane, a, against the number of cycles to failure, nf. by performing a systematic reanalysis based on numerous experimental data [12, 14, 15], it was proven that, as index eff varies, different fatigue curves are obtained (fig. 1a). in particular, it was observed that fatigue damage tends to increase as eff increases: this results in the fact that the corresponding fatigue curve tends to shift downward in the above diagram with increasing of eff (fig. 1a). according to the classical log-log schematisation used to summarise fatigue data, the position and the negative inverse slope of any modified wöhler curve can unambiguously be defined through the following linear relationships [11, 12, 15]:    k (2)   baf  re (3) in the above definitions, k(eff) is the negative inverse slope, while ref(eff) is the reference shear stress amplitude extrapolated at na cycles to failure (see fig. 1a). further, , , a and b are material constants to be determined experimentally. in particular, by remembering that eff is equal to unity under fully-reversed loading and to zero under torsional loading [11], constants a and b in eq. (3) can be calculated directly as follows:   aeffaaefff           2 re , (4) t http://dx.medra.org/10.3221/igf-esis.16.01&auth=true http://www.gruppofrattura.it l. susmel, frattura ed integrità strutturale, 16 (2011) 5-17; doi: 10.3221/igf-esis.16.01 7 where a and a are the endurance limits extrapolated at na cycles to failure under fully-reversed uniaxial and torsional fatigue loading, respectively. when our criterion is specifically used to estimate high-cycle fatigue damage, according to the mwcm’s philosophy, a material is at the endurance limit condition when the amplitude of the shear stress relative to the critical plane, a, equals the reference shear stress estimated, through eq. (3), for the pertinent value of ratio eff, that is [11]:        aeffa a efffa    2 )(re aeffa a aeqa           2 , (6) if the above equation is plotted in a a vs. eff diagram (fig. 1b), it is straightforward to see that, given the value of eff, fatigue breakage should not occur up to a number of cycles to failure equal to na as long as the shear stress amplitude relative to the critical plane is below the limit curve determined according to the criterion itself. (a) (b) figure 1: modified wöhler diagram (a) and adopted correction for the a,ref vs. eff relationship (b). to conclude, it is worth observing that, as shown by the above chart, the reference shear stress to be used to estimate multiaxial fatigue damage is assumed to be constant and equal to ref(lim) for eff larger than limit value lim [11, 13]. this correction, which plays a fundamental role in the overall accuracy of the mwcm, was introduced in light of the fact that, under large values of ratio eff, the predictions made by the mwcm were seen to become too conservative [26]. according to the experimental results due to kaufman and topper [27], such a high degree of conservatism was ascribed to the fact that, when micro/meso cracks are fully open, an increase of the normal mean stress does not result in a further increase of fatigue damage. therefore, by taking full advantage of the intrinsic mathematical limit of eq. (6), which becomes evident when our criterion is directly expressed in terms of a and n,max=n,a+n,m [11, 13], lim takes on the following value: aa a      2 lim (7) determining the mean stress sensitivity index n order to address the problem of estimating mean stress sensitivity index m, initially, it is useful to define the load ratio relative to the critical plane, rcp, as follows [13]: max, min, n n cpr    (8) i http://dx.medra.org/10.3221/igf-esis.16.01&auth=true http://www.gruppofrattura.it l. susmel, frattura ed integrità strutturale, 16 (2011) 5-17; doi: 10.3221/igf-esis.16.01 8 where n,min and n,max denote the minimum and the maximum value of the stress perpendicular to the plane of maximum shear stress amplitude, respectively. in order to estimate mean stress sensitivity index m, assume now that endurance limits a and a are known from the experiments, so that, the only unknown material property in eq. (6) is m itself. by observing now that both a and a are material fatigue properties generated under fully-reversed loading (i.e., rcp=-1), it is logical to argue that material constant m has to be estimated from a third endurance limit determined under a value of rcp larger than -1. accordingly, if * a , * ,mn and * ,an are the critical plane stress components referred to the above endurance limit condition, by rearranging eq. (6), it is trivial to derive the following identity [11, 19]:             * * , * * , * 2 2 a an aa aa mn am       (9) which allows m to be calculated directly. as to the expected values for m, it can be said that, since m quantifies the portion of the mean normal stress relative to the critical plane which effectively opens the micro/meso cracks by favouring their propagation [11], such a material fatigue property is expected to vary in the range 0-1: when m is equal to unity, the material being assessed is assumed to be fully sensitive to the mean stress perpendicular to the critical plane; on the contrary, an m value equal to zero implies that the investigated material is not sensitive at all to the presence of superimposed static tensile stresses. with regard to the estimation of the mean stress sensitivity index, it is not superfluous to notice here that, in situations of practical interest, the above material constant can easily be determined by directly using a uniaxial endurance limit generated under a load ratio, r=x,min/x,max (fig. 2), larger than -1. in more detail, under axial or bending fatigue loading with superimposed static stress, it is straightforward to see that the relevant stress quantities relative to the critical plane take on the following values [11]: 2 , , ax ana    ; 2 , , mx mn    (10) where x,a and x,m are the amplitude and the mean value of the applied stress, respectively. figure 2: cylindrical specimen and adopted frame of reference. from a physical point of view, the meaning of mean stress sensitivity index m can be explained by taking full advantage of the outcomes summarised by kaufman and topper in ref. [27]. in more detail, by performing an accurate experimental investigation they have observed that, when the mean stress perpendicular to the stage i planes is larger than a certain material threshold value, an increase of the mean stress itself does not result in any further increase of fatigue damage. this experimental evidence was ascribed by kaufman and topper themselves to the fact that, in the presence of large values of the mean stress perpendicular to the growth direction, micro/meso shear cracks are already fully open, so that, the shearing forces are directly transmitted to the crack tips by favouring the mode ii growth. on the contrary, when the mean stress normal to the stage i planes is lower than the above material threshold value, the effect of the shearing forces pushing the crack tips is reduced due to the interactions amongst the asperities characterising the two faces of the cracks themselves. since the microstructure morphology varies from material to material by resulting in a different roughness of x y z o http://dx.medra.org/10.3221/igf-esis.16.01&auth=true http://www.gruppofrattura.it l. susmel, frattura ed integrità strutturale, 16 (2011) 5-17; doi: 10.3221/igf-esis.16.01 9 the crack faces, it is logical to presume that the value of the mean stress sensitivity index changes as the microstructural features of the material being assessed vary. to conclude, it is worth observing that not only to estimate m correctly but also to apply the mwccm properly, a multiparameter optimisation process has to be run to unambiguously determine the orientation of the critical plane [28]. as to such a tricky aspect of the multiaxial fatigue issue, it has to be said that this laborious modus operandi is a direct consequence of the classical fatigue damage model on which the mwcm is based [11, 29]. in fact, independently from the complexity of the time-variable stress state damaging the material point at which the stress analysis is performed, there always exist two or more material planes experiencing the maximum shear stress amplitude, so that, amongst all the potential critical planes, the one which has to be used to calculate mean stress sensitivity index m as well as to perform the fatigue assessment is the plane experiencing the largest value of the maximum normal stress. validation by experimental results n order to show the accuracy of the mwcm in estimating high-cycle fatigue strength under multiaxial fatigue loading, a systematic bibliographical investigation was carried out to select an appropriate set of fatigue results. in more detail, initially attention was focused on multiaxial endurance limits generated by testing un-notched samples. in the most general case, the applied loading paths included in-phase and out-of-phase situations (combined axial loading, bending, torsion and internal/external pressure) with and without superimposed static stresses, the applied stress components being defined as follows (see fig. 2 for the adopted frame of reference):  xxyxyaxymxyxy xyyaymyy xaxmxx tt tt tt ,,, ,,, ,, sin)( )sin()( )sin()(       (11) in the above sinusoidal stress signals, subscript m and a denote the mean value and the amplitude of any stress components, respectively, x, y and xy are the angular velocities, whereas y,x and xy,x are the out-of-phase angles, both measured with respect to signal x(t). further, also a number of results generated under the complex loading paths sketched in fig. 3 were considered in the validation exercise discussed in the present section. tab. 1 summarises the static and fatigue properties of the materials of which the unnotched samples tested under multiaxial fatigue loading were made. tab. 2 instead lists the experimental values of mean stress sensitivity index m for those materials having m lower than unity. figure 3: investigated complex loading paths. i http://dx.medra.org/10.3221/igf-esis.16.01&auth=true http://www.gruppofrattura.it l. susmel, frattura ed integrità strutturale, 16 (2011) 5-17; doi: 10.3221/igf-esis.16.01 10 material reference a a uts loding path [mpa] [mpa] [mpa] 0.1% c steel (normalised) [1] 268.6 151.3 430.7 b-t 0.4% c steel (normalised) [1] 331.9 206.9 648.4 b-t 0.4% c steel (spheroidized) [1] 274.8 155.9 477.0 b-t 0.9% c steel (pearlitic) [1] 352.0 240.8 847.5 b-t 3% ni steel [1] 342.7 205.3 526.4 b-t 3/3.5% ni steel [1] 444.7 267.1 722.5 b-t cr-va steel [1] 429.1 257.8 751.8 b-t 3.5% nicr steel (n. impact) [1] 540.3 352.0 895.3 b-t 3.5% nicr steel (l. impact) [1] 509.4 324.2 896.9 b-t nicrmo steel (60-70 tons) [1] 602.1 337.7 1000.3 b-t nicrmo steel (75-80 tons) [1] 660.7 342.7 1242.7 b-t nicr steel [1] 772.3 452.3 1667.2 b-t silal cast iron [1] 240.8 219.2 240.9 b-t nicrosilal cast iron [1] 253.2 211.5 256.8 b-t s65a steel [30] 583.5 370.5 1000.8 b-t cast alloy steel [30] 366.8 247.5 721.2 b-t cucr cast iron [31] 251.0 198.6 445.4 b-t inoculated cast iron [31] 177.9 157.2 321.3 b-t nicr cast iron [31] 146.2 122.7 259.2 b-t crmo steel (solid samples) [32] 713.2 425.3 946.5 b-t crmo steel (hollow samples) [32] 688.9 412.8 946.5 b-t crmo steel [32] 509.0 306.9 954.0 b-t crmo steel [32] 589.6 367.6 944.8 b-t crmo steel [32] 593.3 350.7 944.8 b-t crmo steel [32] 628.3 366.6 954.0 b-t nicrmo steel s81 [32] 589.7 331.9 1103.8 b-t nicrmova steel [32] 660.7 342.7 1242.7 b-t crmova steel dtd551 [32] 667.8 398.3 1397.1 b-t crmova steel dtd551 [32] 659.9 386.5 1397.1 b-t crmova steel dtd551 [32] 706.1 412.5 1368.7 b-t crmova steel dtd551 [32] 737.7 447.4 1368.7 b-t nicr steel (solid samples) [32] 666.7 369.7 1389.4 b-t nicr steel (hollow samples) [32] 653.2 339.6 1389.4 b-t nicr steel [32] 771.9 452.3 1667.2 b-t sae 4340 [33] 462.0 286.0 b-t brass [7] 83.4 73.6 319.8 b-t high-strength steel [7] 461.1 274.7 809.3 b-t nodular cast iron [7] 196.2 186.4 476.8 b-t rolled steel (block d) [7] 215.8 137.3 b-t 0.34% c steel [34] 378.0 218.0 b-t carbon steel [35] 261.0 160.0 b-t table 1: (caption on the next page). http://dx.medra.org/10.3221/igf-esis.16.01&auth=true http://www.gruppofrattura.it l. susmel, frattura ed integrità strutturale, 16 (2011) 5-17; doi: 10.3221/igf-esis.16.01 11 material reference a a uts loding path [mpa] [mpa] [mpa] 30ncd16 (batch 1) [36] 586.0 405.0 1160.0 b-t 30ncd16 (batch 2) [37] 660.0 410.0 1160.0 b-t cast iron [38] 151.0 92.0 ip-t 0.35% c steel [39] 216.0 142.0 559.0 iep-ax mild steel [40] 235.4 137.3 375.0 b-t hard steel [40] 313.9 196.2 680.0 b-t 3% c cast iron [40] 96.1 91.2 180.9 b-t duraluminium [40] 156.0 100.0 433.0 b-t 34cr4 [41] 410.0 256.0 795.0 b-t 42crmo4 [42] 398.0 267.0 1025.0 b-t st35 [43] 206.0 123.0 395.0 ip-ax-t st35 [44] 230.0 130.0 ip-ax en24t [45] 405.0 270.0 850.0 ip-ax xc18 [46] 332.0 186.0 520.0 b-t 34cr4 [41] 343.0 204.0 710.0 ip-b-t 25crmo4 [47] 340.0 228.0 780.0 b-t fe-cu [48] 319.0 220.0 b-t 25crmo4 [49] 361.0 228.0 780.0 ip-b-t grey cast iron [50] 164.0 124.7 278.8 b-t ck45 [51] 423.0 287.0 b-t fgs 800-2 [52] 294.0 220.0 815.0 b-t fee 460 [53] 272.0 174.0 670.0 ax-t fgs 700/2 [54] 294.0 218.0 750.0 b-t ti-6al-4v [55] 652.0 411.0 1090.0 b-t high strength steel [56] 630.0 364.0 b-t high strength steel [56] 298.0* 172.0 b-t high strength steel [56] 320.0 184.7* b-t r7t (axial) [57] 514.4* 297.0 820-940 ax-t r7t (circum.) [57] 537.0* 310.0 820-940 ax-t 42crmo4 [58] 525.7 336.3 996.0 ax-t 39nicrmo3 [59] 367.5 265.0 856 ax-t sae 52100 [60] 866.0 540.0 2467.0 ax-t 30ncd16 [61] 690.0 428.0 1200.0 b-t ggg60 [62] 275.0 249.0 815.0 b-t st60 [63] 294.0 176.0 765.0 ip-ax 76s-t61 [64] 217.9 143.4 419.3 b-t 76s-t61 [64] 188.3 119.3 419.3 b-t 76s-t61 [64] 170.3 109.7 419.3 b-t 25crmo4 [65] 340.0 228.0 801.0 ip-ax-t c35n [66] 250.0 150.0 550.0 ax-t c35n [67] 189.0 150.0 533.0 ax-t table 1: mechanical properties of the unnotched materials, where: *estimated according to von mises, ax=axial loading, b=bending, t=torsion, i(e)p=internal (external) pressure. http://dx.medra.org/10.3221/igf-esis.16.01&auth=true http://www.gruppofrattura.it l. susmel, frattura ed integrità strutturale, 16 (2011) 5-17; doi: 10.3221/igf-esis.16.01 12 material reference m s65a steel [30] 0.41 42crmo4 [42] 0.35 34cr4 [41] 0.36 30ncd16 (batch 2) [37] 0.16 ck45 [51] 0.31 st35 [44] 0.29 30ncd16 [61] 0.64 st60 [63] 0.38 25crmo4 [65] 0.89 en3b [19] 0.22 table 2: values of the mean stress sensitivity index for those materials having m lower than unity. the experimental fully-reversed torsional endurance limit, a, vs. equivalent shear stress, a,eq, diagram reported in fig. 4 summarises the accuracy of the mwcm in estimating the multiaxial endurance limits experimentally determined by testing unnotched samples made of 65 different metallic materials, the error being calculated as follows [68]: 100[%] ,    a aeqa error   (12) the above diagram makes it evident that the mwcm is highly accurate in estimating high-cycle fatigue strength of plain engineering materials subjected to multiaxial fatigue loading, resulting in 95% of the estimates falling within an error interval equal to ±15%. figure 4: mwcm’s accuracy in estimating high cycle fatigue strength of plain metallic materials subjected to multiaxial loading paths, where iph=in-phase, ooph=out-of-phase, zms=zero mean stress, n-zms=non-zero mean stress, df=different frequences, clp=complex loading paths (see fig. 3). in order to further investigate the accuracy of our multiaxial fatigue criterion, the mwcm was subsequently used, in terms of nominal stresses, to estimate high-cycle fatigue strength of notched samples subjected to in-phase and out-of-phase biaxial loading, by also considering situations involving non-zero mean stresses. tab. 2 summarises the fully-reversed nominal uniaxial, an, and torsional, an, endurance limits of the considered notched samples, together with a brief description of the investigated geometrical features (see also tab. 3 for the values of mean stress sensitivity index m). as to the notch endurance limits summarised in tab. 2, it is worth observing that, since the uniaxial and torsional ones were not available for the notched samples of en3b [19], they have been estimated from the corresponding fatigue strength reduction factor, kf, calculated according to peterson’s rule [73, 74]. 10 100 1000 10 100 1000 a,eq [mpa] a [mpa] iph, zms iph, n-zms ooph, zms ooph, n-zms df clp conservative non-conservative error =-15% error =+15% 65 different materials 526 experimental results http://dx.medra.org/10.3221/igf-esis.16.01&auth=true http://www.gruppofrattura.it l. susmel, frattura ed integrità strutturale, 16 (2011) 5-17; doi: 10.3221/igf-esis.16.01 13 the accuracy of the mwcm when applied in terms of nominal stresses in estimating high-cycle fatigue strength of notched components is summarised in the an vs. a,eq diagram reported in fig. 5: the above chart makes it evident that the systematic use of our criterion resulted in 92% of the predictions falling within an error interval equal to ±15%. material ref. an an type of notched specimen [mpa] [mpa] 0.4% c steel (normalized) [1] 179.1 176.0 v-notched cylindrical bar 3% ni steel [1] 209.9 151.3 v-notched cylindrical bar 3/3.5% ni steel [1] 302.6 183.7 v-notched cylindrical bar cr-va steel [1] 216.1 160.6 v-notched cylindrical bar 3.5% nicr steel (n. impact) [1] 268.6 236.2 v-notched cylindrical bar 3.5% nicr steel (l. impact) [1] 247.0 182.2 v-notched cylindrical bar nicrmo steel (75-80 tons) [1] 271.7 240.8 v-notched cylindrical bar crmo steel [32] 450.9 295.5 cylindrical hollow sample with oil hole crmo steel [32] 223.4 162.1 cylindrical hollow sample with oil hole crmo steel [32] 424.7 305.5 cylindrical hollow sample with oil hole crmo steel [32] 423.4 300.3 cylindrical hollow sample with oil hole crmo steel [32] 423.4 288.4 cylindrical hollow sample with oil hole nicrmova steel [32] 271.7 240.8 v-notched cylindrical bar nicrmova steel [32] 288.7 211.5 cylindrical hollow sample with oil hole crmova steel dtd551 [32] 300.7 235.4 cylindrical hollow sample with oil hole crmova steel dtd551 [32] 297.8 220.9 cylindrical hollow sample with oil hole crmova steel dtd551 [32] 471.3 354.6 cylindrical hollow sample with oil hole crmova steel dtd551 [32] 448.1 354.9 cylindrical hollow sample with oil hole nicr steel [32] 312.5 225.5 cylindrical hollow sample with oil hole s65a steel [30] 259.3 180.6 cylindrical hollow sample with oil hole s65a steel [30] 347.3 270.1 cylindrical shaft with fillet s65a steel [30] 563.5 185.2 hollow specimens with 6 deep splines 16mnr [69] 96.1 120.7 v-notched cylindrical bar 16mnr [69] 174.3 155.3 v-notched cylindrical bar sae 1045 [70] 188.6 156.6 cylindrical shaft with fillet c40 [71] 117.8 152.8 v-notched cylindrical bar ck45 [51] 311.8 220.4 cylindrical shaft with fillet low carbon steel [72] 66.9 122.7 v-notched cylindrical bar low carbon steel [72] 95.3 156.4 v-notched cylindrical bar en3b* [19] 142.3 157.8 v-notched cylindrical bar en3b* [19] 204.7 211.3 v-notched cylindrical bar en3b* [19] 268.1 243.9 v-notched cylindrical bar sae 52100 [60] 631.0 539.0 v-notched cylindrical bar sae 52100 [60] 373.0 334.0 v-notched cylindrical bar *fully-reversed uniaxial and torsional endurance limits estimated according to peterson. table 3: fully-reversed uniaxial and torsional endurance limits for the investigated notched samples. http://dx.medra.org/10.3221/igf-esis.16.01&auth=true http://www.gruppofrattura.it l. susmel, frattura ed integrità strutturale, 16 (2011) 5-17; doi: 10.3221/igf-esis.16.01 14 finally, the diagram of fig. 6 shows the error distribution measured in terms of probability density function, which is nothing but the normal distribution calculated from the mean value and the standard deviation of any of the two considered data sets (i.e., plain and notched samples). in more detail, according to fig. 6, the error distribution obtained when estimating multiaxial endurance limits of plain materials was characterised by a mean value equal to 0.3% and by a standard deviation of 7.3. similarly, in the presence of stress concentration phenomena, the error distribution had mean value equal to -1.1% and standard deviation equal to 8.3. to conclude, it is possible to say that, as suggested by the probability density function diagram of fig. 6, the systematic use of the mwcm is seen to result in 85% of the estimates falling within an error interval of ±10%. figure 5: accuracy of the mwcm, applied in terms of nominal stresses, in estimating high-cycle fatigue strength of notched metallic materials subjected to multiaxial loading paths, where iph=in-phase, ooph=out-of-phase, zms=zero mean stress, n-zms=non-zero mean stress. figure 6: error distribution in terms of probability density function. conclusions 1) the mwcm is capable of correctly taking into account the mean stress effect in multiaxial fatigue; 2) the mwcm is seen to be highly accurate in accounting for the degree of multiaxiality and non-proportionality of the applied loading path; 10 100 1000 10 100 1000 a,e q [mpa] an [mpa] iph, zms iph, n-zms ooph, zms ooph, n-zms conservative non-conservative error =-15% error =+15% 19 different materials 178 experimental results 0 0.01 0.02 0.03 0.04 0.05 0.06 -30 -20 -10 0 10 20 30 error [%] p ro b a b il it y d en si ty f u n ct io n plain samples notched samples non-conservative conservative http://dx.medra.org/10.3221/igf-esis.16.01&auth=true http://www.gruppofrattura.it l. susmel, frattura ed integrità strutturale, 16 (2011) 5-17; doi: 10.3221/igf-esis.16.01 15 3) contrary to what stated by dr. papuga in ref. [25], the systematic use of the mwcm is seen to result in about 95% of the estimates falling within an error interval equal to ±15%: this fully proves that the mwcm is a powerful engineering tool suitable for designing engineering materials against multiaxial fatigue. references [1] h. j. gough, in: proceedings of the institution of mechanical engineers, 160 (1949) 417. [2] k. dang van, b. griveau, o. messagge, in: biaxial and multiaxial fatigue, egf 3, edited by m. w. brown and k. j. miller, mechanical engineering publications, london, (1989) 479. [3] i. v. papadopoulos, fatigue polycyclique des métaux: une novelle approche. thèse de doctorat, ecole nationale des ponts et chaussées, paris, france (1987). [4] g. sines, in: metal fatigue, edited by g. sines and j. l. waisman, mcgraw-hill, new york, (1959) 145. [5] b. crossland, in: proceedings of the international conference on fatigue of metals, institution of mechanical engineers, london, (1956) 138. [6] e. n. mamiya, j. a. araújo, f.c. castro, int. j. fatigue, 31 (2009) 1144. [7] t. matake, bulletin of the jsme 20 141 (1977) 257. [8] d. l. mcdiarmid, fatigue & fracture of engineering materials & structures, 14 (1991) 429. [9] a. carpinteri, r. brighenti, a. spagnoli, fatigue & fracture of engineering materials and structures, 23 (2000) 355. [10] k. kanazawa, k. j. miller, m. w. brown, transactions of the asme, journal of engineering materials and technology, july (1977) 222. [11] l. susmel, multiaxial notch fatigue: from nominal to local stress-strain quantities. woodhead & crc, cambridge, uk, isbn: 1 84569 582 8, (2009). [12] l. susmel, p. lazzarin, fatigue & fracture of engineering materials & structures, 25 (2002) 63. [13] l. susmel, fatigue & fracture of engineering materials & structures, 31 (2008) 295. [14] l. susmel, n. petrone, in: biaxial and multiaxial fatigue and fracture, edited by a. carpinteri, m. de freitas and a. spagnoli, elsevier and esis, (2003) 83. [15] p. lazzarin, l. susmel, fatigue & fracture of engineering materials and structures, 26 (2003) 1171. [16] l. susmel, d. taylor, fatigue & fracture of engineering materials & structures, 26 (2003) 821. [17] l. susmel, fatigue & fracture of engineering materials & structures, 27 (2004) 391. [18] l. susmel, d. taylor, international journal of fatigue, 28 (2006) 417. [19] l. susmel, d. taylor, fatigue & fracture of engineering materials & structures, 31(12) (2008) 1047. [20] l. susmel, r. tovo, fatigue & fracture of engineering materials & structures, 27 (2004) 1005. [21] l. susmel, r. tovo, international journal of fatigue, 28 (2006) 564. [22] l. susmel, international journal of fatigue, 30 (2008) 888. [23] l. susmel, international journal of fatigue, 31 (2009) 197. [24] l. susmel, international journal of fatigue, 32 (2010) 1057. [25] j. papuga, international journal of fatigue, 33 (2011) 153. [26] l. susmel, r. tovo, p. lazzarin, international journal of fatigue 27 (2005) 928. [27] r. p. kaufman, t. topper, in: biaxial and multiaxial fatigue and fracture, edited by a. carpinteri, m. de freitas and a. spagnoli, elsevier and esis, (2003) 123. [28] l. susmel, international journal of fatigue, 32 (2010) 1875. [29] d. f. socie, transactions of the asme, journal of engineering materials and technology, 109 (1987) 293. [30] h. j. gough, h. v.pollard, w. j. clenshaw, some experiments on the resistance of metals to fatigue under combined stresses. aeronautical research council, r and m 2522. hmso, london (1951). [31] h. j. gough, h. v. pollard, in: proceedings of institute of mechanical engineering, 131 (1935) 1. [32] p. h. frith, in: proceedings of the institution of mechanical engineers, (1956) 462. [33] w. n. findley, j. j. coleman, b. c. hanley, in: proceedings of international conference on fatigue of metals, institution of mechanical engineers, london, (1956) 150. [34] t. nishihara, m. kawamoto, memoirs of the college of engineering, kyoto imperial university 10, (1941) 177. [35] s. kitaioka, j. chen, m. seika, bulletin of the japan society of mechanical engineers, 29 (1986) 214. [36] c. froustey, fatigue multiaxiale en endurance de l’acier 30ncd16, phd thesis, ecole nationale supérieure d’arts et métiers, bordeaux, france(1987). [37] c. froustey, s. lasserre, international journal of fatigue, 11 (1989) 169. http://dx.medra.org/10.3221/igf-esis.16.01&auth=true http://www.gruppofrattura.it l. susmel, frattura ed integrità strutturale, 16 (2011) 5-17; doi: 10.3221/igf-esis.16.01 16 [38] m. ros, die bruchegefahr fester koper. empa bericht 173, zurich, germany (1950). [39] f. rotvel, international journal of mechanical science, 12 (1970) 597. [40] t. nishihara, m. kawamoto, memoirs of the college of engineering, kyoto imperial university, 11 (1945) 85. [41] h. zenner, r. heidenreich, i. richter, dauerschwingfestigkeit bei nichtsynchroner mehrachsiger beanspruchung. z. werkstofftechnik, 16 (1985) 101. [42] w. lempp, festigkeitsverhalten von stählen bei mehrachsiger dauerscwingbeanspruchung durch normalspannungen mit überlagerten phasengleichen und phasenverschobenen schubspannungen. dissertation, university of stuttgart, germany (1977). [43] l. issler, festigkeitsverhalten metallischer wekstoffe bei mehrachsiger phasenverschobener schwingbeanspruchung. dissertation, universität stuttgard, germany (1973). [44] j. liu beitrag zur verbesserung der dauerfestigkeitsberechnung bei mehrachsiger beanspruchung. dissertation, tu clausthal; germany (1991). [45] d. l. mcdiarmid, in: multiaxial fatigue, edited by k. j. miller and m. w. brown, astm stp 853, (1985) 606. [46] c. froustey, s. lasserre, l. dubar, in: proceedings of met-tech 92, grenoble, france (1992). [47] c. kaniut, zur betriebsfestigkeit metallischer werstoffe bei mehrashsiger beanspruchunng. diss rwth, aachen, germany (1983). [48] m. fougé, j. bahuaud, in : proceedings of comptes rendus 7ème congrès français de mecanique, bordeaux, france, (1985) 30. [49] s. mielke, festigkeitsverhalten metallischer werkstoffe unter zweiachsiger schwingender beanspruchung mit verschiedenen spannungszeitverlaeufen. phd thesis, rwth aachen (1980). [50] h. achtelik, i. j akubowska, e. macha, studia geotechnica et mechanica, v 2 (1983) 9. [51] a. simbürger, festigkeitverhalten zähler werkstoffe bei einer mehrachsigen, phasenverscobenen schwingbeanspruchung mit köroperfesten hauptspannungsrichtungen. lbf bericht nr. fb-121, darmstad, germany (1975). [52] t. palin-luc, s. lasserre, european journal of mechanics a/solids, 17 (1998) 237. [53] c. m. sonsino, international journal of fatigue, 17 (1995) 55. [54] r. akrache, j. lu, fatigue and fracture of engineering materials & structures, 22 (1999) 527. [55] t. delahay, t.palin-luc, international journal of fatigue, 28 (2006) 474. [56] h. altenbach, a. zolochevsky, fatigue and fracture of engineering materials & structures, 19 (1996) 1207. [57] a. bernasconi, m. filippini, s. foletti, d. vaudo, international journal of fatigue, 28 (2006) 663. [58] j. froeschl, g. gerstmayr, w. eichlseder, h. leitner, in: proceedings of 8th international conference on multiaxial fatigue and fracture, edited by u. s. fernando, sheffield, uk, (2007) s3-1. [59] bernasconi, m. foletti, i. v. papadopoulos, international journal of fatigue, 30 (2008) 1430. [60] h. bomas, s. kunow, g. loewisch, r. kienzler, r. schroeder, m. bacher-hoechst, f. muehleder, in: proceedings of fatigue 2006 conference. ed: johnson, w. s. oxford, elsevier ltd, (2006). [61] l. dubar, fatigue multiaxiale des aciers. passage de l'endurance a l'endurance limite. prise en compte des accidents geometriques. phd thesis, talence, ensam (1992). [62] r. heidenreich, h. zenner, schubspannungsintensitaetshypothese erweiterung und experimentelle abschaetzung einer neuen festigkeitshypothese fuer schwingende beanspruchung. technical report forschungshefte fkm, heft 77, frankfurt am main – niederrad (1979). [63] e. el magd, s. mielke, konstruktion, 29(7) (1977) 253. [64] w. n. findley, combined-stress fatigue strength of 76s-t61 aluminum alloy with superimposed mean stresses and corrections for yielding. technical report naca tn-2924, washington, usa (1953). [65] a. troost, o. akin, f. klubberg, konstruktion, 39 (1987) 479. [66] f. nolte, dauerfestigkeitsuntersuchungen an stahlwellen bei umlaufender beigeund überlagerter statischer verdrehbeanspruchung. phd thesis, tu berlin, germany (1973). [67] b. paysan, untersuchungen des einflusses einiger kerbformen auf die tragfähigkeit von wellen bei umlaufender biegung und überlagerter überlagerter statischer torsion. phd thesis, tu berlin, germany (1970). [68] v. papadopoulos, fatigue & fracture of engineering materials & structures, 18 (1995) 79. [69] z. gao, b. qiu, x. wang, y. jiang, international journal of fatigue, 32 (2010) 1960. [70] p. kurath, s. d. downing, d. r. galliart, in: multiaxial fatigue analysis and experiments. edited by g.e. leese and d. f. socie, sae ae-14 (1989) 13. [71] b. atzori, f. berto, p. lazzarin, m. quaresimin, international journal of fatigue, 28 (2006) 485. http://dx.medra.org/10.3221/igf-esis.16.01&auth=true http://www.gruppofrattura.it l. susmel, frattura ed integrità strutturale, 16 (2011) 5-17; doi: 10.3221/igf-esis.16.01 17 [72] g. quilafku, n. kadi, j. dobranski, z. azari, m. gjonaj, g. pluvinage, international journal of fatigue, 23 (2001) 689. [73] r. e. peterson, in: metal fatigue, edited by g. sines and j. l. waisman, mcgraw hill, new york, (1959) 293. [74] y.-l. lee, j. pan, r. b. hathaway, m. e. barkey fatigue testing and analysis. elsevier butterworth–heinemann. isbn 0-7506-7719-8 (2005). http://dx.medra.org/10.3221/igf-esis.16.01&auth=true http://www.gruppofrattura.it microsoft word numero_30_art_6 j. toribio et alii, frattura ed integrità strutturale, 30 (2014) 40-47; doi: 10.3221/igf-esis.30.06 40 focussed on: fracture and structural integrity related issues numerical analysis of hydrogen-assisted rolling-contact fatigue of wind turbine bearings j. toribio, m. lorenzo, d. vergara, v. kharin fracture of materials and structural integrity research group, university of salamanca, spain toribio@usal.es, mlorenzo@usal.es, dvergara@usal.es, gatogris@usal.es abstract. offshore wind parks at locations further from the shore often involve serious difficulties, e.g. the maintenance. the bearings of offshore wind turbines are prone to suffer hydrogen-assisted rolling-contact fatigue (ha-rcf). three important aspects linked with bearing failures are being extensively researched: (i) rolling contact fatigue (rcf), (ii) influence of carbide particles on fatigue life, and (iii) local microplastic strain accumulation via ratcheting. however, there is no reference related to bearing failure in harsh environment. this way, this paper helps to gain a better understanding of the influence of hydrogen on the service life of offshore wind turbine bearings through a numerical study. so, the widely used rcf ball-on-rod test was simulated by finite element method in order to obtain the stress-strain state inside the bearings during life in service and, from this, to elucidate the potential places where the hydrogen could be more harmful and, therefore, where the bearing material should be improved. keywords. hydrogen-assisted rolling-contact fatigue; wind turbines; bearings; numerical analysis. introduction ffshore wind farms reach higher levels of energy production than onshore installations. there are several reasons to this fact: (i) the wind turbine size does not have the usual onshore limitations related to road transportation or noise regulations, (ii) offshore wind speeds are considerably higher than onshore [1]. however, offshore wind parks present maintenance problems. the bearings of offshore wind turbines can suffer hydrogen-assisted rolling-contact fatigue (ha-rcf) due to: (i) the use of long-life lubricants with certain additives to extend the turbine maintenance intervals, what contributes to lubricant decomposition and hydrogen generation; (ii) the increased likelihood of moisture entering the bearing; (iii) the salty environment increases the corrosion of materials and hence the probability of hydrogen penetration. three important aspects linked with bearing failures are being extensively researched: (i) rolling contact fatigue (rcf) [25], (ii) influence of carbide particles on fatigue life [6,7], and (iii) local microplastic strain accumulation via ratcheting [810]. however, there is no literature related with bearing failures in harsh environment. this way, this paper helps to gain a better understanding of the influence of hydrogen on the life in service of offshore wind turbine bearings through a numerical study. so, the widely used rcf ball-on-rod test [10-13] was simulated by finite element method to obtain the stress-strain state of bearings during life in service and, from this, to elucidate the potential places where the hydrogen could be more harmful causing final catastrophic failure by hydrogen embrittlement (he) related phenomena. o j. toribio et alii, frattura ed integrità strutturale, 30 (2014) 40-47; doi: 10.3221/igf-esis.30.06 41 numerical modeling he study was divided into two uncoupled analysis. on one hand, the numerical simulation by means of a commercial finite element (fe) code was used for obtaining the stress and strain states after six revolutions of the bar. from the results of such an analysis, a simple estimation of the hydrogen accumulation for long time of exposure to hydrogenating environment was carried out allowing the estimation of the potential hydrogen damage places. the geometry analysed consist of a steel bar of length l= 6 mm and diameter d = 9.53 mm rotating in contact with three equidistant steel balls of diameter d = 12.70 mm and applying a point load of f = 300 n over the bar surface, as depicted in the scheme of fig. 1a. the complete 3d geometry can be simplified to a half just considering the symmetry plane r- shown in fig. 1b and applying the corresponding boundary conditions as restricted displacement on the bar axial direction for all the nodes placed inside the symmetry plane. thus, an important save of computing time is achieved optimizing the available resources. in addition, the geometry of the contacting balls can be also simplified considering the symmetry plane r-z of such components. taking this into account, only a quarter of the whole geometry is modelled, as seen in fig. 1b. (a) (b) figure 1: (a) scheme of the analysed geometry for a ball-on-rod test and (b) 3d geometry. the numerical modelling of the ball-on-rod test (six revolutions) was carried out by considering the material constitutive law to be elastic perfectly plastic corresponding to a steel with the following material properties for both rod and balls: young modulus, e = 206 gpa, poisson coefficient,= 0.3 and material yield stress y = 2065 mpa. the analysis was carried out with isotropic strain hardening of the material and updated lagrange procedure. according to the hertz theory considering only the elastic response of the components [14], a very localized effect can be expected in the contact zone between the rod and the balls. according to this, a ball pressuring a cylinder must undergo a contact pressure of 5.5 gpa with a elliptic contacting zone whose axis length are 160 m and 231 m respectively. from results of the mechanical simulation, a simple estimation of the behavior against he of the bar can be carried out considering that hydrogen diffusion proceeds from the bar surface to inner points as a function of the gradients of both hydrostatic stress () and hydrogen solubility (ks) [15-17]: sε ph p sε p ( ) ( ) ( ) kv d c c rt k                     j (1) r being the universal gases constant, vh the partial volume of hydrogen, t the absolute temperature and ks the hydrogen solubility that is itself a one-to-one monotonic increasing function of equivalent plastic strain, as explained in detail t j. toribio et alii, frattura ed integrità strutturale, 30 (2014) 40-47; doi: 10.3221/igf-esis.30.06 42 elsewhere [15-17]. in particular, a linear relationship between plastic strain and solubility in the form ksp was considered to be adequate, cf. [15-17]. after using the matter conservation law and applying the gauss-ostrogradsky, the following second-order partial differential equation of hydrogen diffusion is obtained:                  )( )( psε psεh k k rt v dccd t c (2) the equilibrium concentration of hydrogen for infinite time of exposure to harsh environment is the steady-state solution of the differential equation. it takes the form of a maxwell-boltzman distribution as follows:      rt v kcc hpsε0eq exp)( (3) where c0 is the equilibrium hydrogen concentration for the material free of stress and strain. according to previous equations, hydrogen diffusion is driven by: (i) the negative gradient of hydrogen concentration (in the classical fick´s sense); (ii) the positive gradient of hydrostatic stress; (iii) the positive gradient of hydrogen solubility, the latter is one-toone related to the gradient of equivalent plastic strain so that the plastic strain gradient (a continuum mechanics variable that appears as an output after the fe computation) can be analysed instead of the hydrogen solubility gradient. mechanical analysis: stress and strain umerical simulation allows the determination of the stress and strain state under cycling loading during the ballon-rod test. fig. 2a shows the global view of the distribution of von mises stress in the steel rod and the contacting balls at the end of the sixth cycle (after passing three contacting balls) and fig. 2b shows a detail view of the von mises distribution at the contact of one of the balls. (a) (b) figure 2: distribution of von mises stress after the sixth loading cycle: (a) 2d view of the contacting plane and (b) 3d detail view at the contact of one of the balls. results shown in fig. 2, reveal a heavy stress concentration localized at the contacting zones of each ball with the rolling rod. this effect progressively vanishes as the distance from the contact zone increases. outside of the locally affected zone, the von mises stress is homogenously distributed with a heavy stress concentration ring located at the vicinity of the rod surface. within the stress concentration zone, the values of the von mises stress reach the material yield stress what implies the appearance of plastic strains near the rod skin as will be discussed lately. for a more detailed analysis, the radial distribution for different values of the circunferential coordinate  are represented in fig. 3 considering the following sections: (i) = 45º, (ii) = 20º, (iii) = 10º, two planes placed close to the contacting ball (iv) = 5º, (v) = 2º and finaly (vi) = 0º representing the contact plane between one of the balls and the rod. n j. toribio et alii, frattura ed integrità strutturale, 30 (2014) 40-47; doi: 10.3221/igf-esis.30.06 43 the radial stress distribution reveals the localized effect at the contact zone with the balls which is spread through a depth from the rod surface of about 1.5 mm reaching null values at the rod centre. at the contact radius (= 0º) the maximum stress is placed out of the rod surface for an approximate depth of 165 m (reaching there the material yield stress) and, therefore, generating plastic strains at the surroundings of this place. the distribution for the other radius in contact with the other balls  120º and = 240º) is equivalent to that shown in fig. 3. as a consequence of the values of the von mises stress at the rod surface vicinity, plastic strains are distributed through such a zone. fig. 4 shows the 3d view of the field of equivalent (cumulative) plastic strain after the six cycle of the test was completed and the radial distribution of such a variable is plotted in fig. 5. in the same way, fig. 6 shows the 3d view of the field of hydrostatic stress after the sixth cycle of the test was completed and fig. 7 shows the radial distribution of such a variable for diverse values of . 0 500 1000 1500 2000 0 1 2 3 4 =45º =20º =10º =5º =2º =0º  vm (m p a) r (mm) 0 500 1000 1500 2000 3.15 3.5 3.85 4.2 4.55 =45º =20º =10º =5º =2º =0º  vm (m p a) r (mm) (a) (b) figure 3: radial distribution of von misses stress for diverse circumferential coordinate : (a) general plot and (b) detail plot near the rod surface (zone with strong gradients). (a) (b) figure 4: field of equivalent (cumulative) plastic strain on the cylinder after six cycles of the ball-on-rod test. (a) 2d view of the contacting plane and (b) 3d detail view at the contact of one of the balls. the first driving force for hydrogen diffusion, the gradient of equivalent plastic strain, is negative and only affects the plastic strain ring near the rod surface (fig. 5). with regard to the second driving force for hydrogen diffusion, the gradient of hydrostatic stress, at the contact plane (= 0º) a compressive nature distribution in radial direction of such a variable is obtained, progressively decreasing with depth up to becoming null for a depth from the rod surface of about 1 mm (fig. 7). j. toribio et alii, frattura ed integrità strutturale, 30 (2014) 40-47; doi: 10.3221/igf-esis.30.06 44 0 0.005 0.01 0.015 0.02 0 1 2 3 4 =45º =20º =10º =5º =2º =0º p r (mm) 0 0.005 0.01 0.015 0.02 4.4 4.45 4.5 4.55 4.6 4.65 4.7 4.75 =45º =20º =10º =5º =2º =0º p r (mm) (a) (b) figure 5: radial distribution of equivalent plastic strain for diverse circumferential coordinate : (a) general plot and (b) detail plot near the rod surface (zone with strong gradients). (a) (b) figure 6: distribution of the hydrostatic stress after the sixth loading cycle: (a) 2d view of the contacting plane and (b) 3d view. -3000 -2500 -2000 -1500 -1000 -500 0 500 0 1 2 3 4 =45º =20º =10º =5º =2º =0º  (m p a) r (mm) -3000 -2500 -2000 -1500 -1000 -500 0 500 3.6 3.8 4 4.2 4.4 4.6 =45º =20º =10º =5º =2º =0º  (m p a) r (mm) (a) (b) figure 7: radial distribution of the hydrostatic stress for diverse circumferential coordinate : (a) general plot and (b) detail plot near the rod surface (zone with strong gradients). j. toribio et alii, frattura ed integrità strutturale, 30 (2014) 40-47; doi: 10.3221/igf-esis.30.06 45 finally, fig. 8 shows the axial distribution of both hydrostatic stress and equivalent plastic strain for diverse values of depth from the rod surface (x). -3000 -2500 -2000 -1500 -1000 -500 0 500 0 2 4 6 8 10 x=0 m x=43 m x=86 m x=130 m x=210 m x=432 m x=600 m  (m p a) z (mm) 0 0.01 0.02 0.03 0.04 0.05 0 2 4 6 8 10 x=0 m x=43 m x=86 m x=130 m x=210 m x=430 m x=600 m  p z (mm) (a) (b) figure 8: axial distribution of the hydrostatic stress for diverse depths (x): (a) general plot and (b) detail plot near the rod surface (zone with strong gradients). in the axial direction, a very located distribution of both hydrostatic stress and plastic strains near the contact plane is obtained. with regard to the hydrostatic stress distribution, the high compressive stress at the contact plane is progressively decreased as the distance from the contact plane (z) is increased, obtaining a null distribution of such a variable for z > 1.5 mm. as the depth from the rod surface increases, the hydrostatic stress at the contacting plane (z = 0) progressively decreases and, consequently, the inwards gradient of hydrostatic stress in the axial direction is reduced as the depth from the rod surface is increased. thus, hydrogen placed close to the contact between ball and bar is also pumped in the axial direction due to the positive inwards gradient of hydrostatic stress. this effect is progressively reduced with the depth x becoming almost negligible for depths x > 600 m. finally, the axial distribution of plastic strains appears through a narrow zone becoming null for axial distances z > 500 m. as in the case of the hydrostatic stress distribution, the distribution of plastic strain at the contact plane (z = 0) decreases with depth from the rod surface (x), and consequently the inwards gradient is progressively reduced as the variable x is increased, becoming null for depths x > 600 m. however, the inwards gradient of equivalent plastic strains is negative, and so the hydrogen diffusion is not enhanced. this opposition is progressively nullified as the depth from rod surface is increased. so, two competitive factors are involved in the diffusion of hydrogen placed near to the contact between ball and bar. on one hand, the inwards gradient of hydrostatic stress enhances the diffusion of hydrogen out of the contact plane whereas, on the other hand, the inwards gradient of equivalent plastic strain is opposite, thereby impeding the aforesaid diffusion. this effect is very localized near the contact zone and, therefore, the diffusion of hydrogen placed at deeper points (x > 600 m) can be considered null in the axial direction. chemical analysis: hydrogen transport by diffusion or assessing the he of the rolling rod, it is interesting to analyse the long-time behaviour of the component under hydrogen exposure. to this end, the steady state distribution of hydrogen concentration through the rod radius was obtained (fig. 9) using eq. (3) and taking into account both hydrostatic stress and equivalent plastic strain. plot is associated with infinite time (steady state solution from the mathematical point of view) or with thermodynamical equilibrium of the hydrogen-metal system (from the physical view point). according to these results, for long time of exposure to the hydrogenating environment, the hydrogen amount at the rod surface vicinity (within the stress and strain affected zone of the rod, i.e., for depths from the rod surface lower than 1 mm) is progressively increased with the circumferential distance to the contacting ball. therefore, for the plane where the ball is contacting the rod, a huge reduction of the hydrogen amount is observed due to the high compressive stresses produced by the contact pressure that promote hydrogen movement out of the contact affected zone due to the negative f j. toribio et alii, frattura ed integrità strutturale, 30 (2014) 40-47; doi: 10.3221/igf-esis.30.06 46 gradient of both driving forces for hydrogen diffusion: the inwards gradient of plastic strain and the inwards gradient of hydrostatic stress. 0 0.2 0.4 0.6 0.8 1 1.2 0 1 2 3 4 =45º =20º =10º =5º =2º =0º c eq /c 0 r (mm) 0 0.2 0.4 0.6 0.8 1 1.2 3 3.2 3.4 3.6 3.8 4 4.2 4.4 4.6 =45º =20º =10º =5º =2º =0º c eq /c 0 r (mm) (a) (b) figure 9: radial distribution of the hydrogen concentration for diverse circumferential coordinate : (a) general plot and (b) detail plot near the rod surface. conclusion n a ball-on-rod test, non-uniform plastic strains are generated on the contact plane where the ball applies a huge pressure to the rod, thus overcoming material yield strength. this state is located near the rod surface with a plastic zone spreading over a maximum depth of 300 m. a huge compressive stress appears in the vicinity of the rod surface; it is progressively reduced as the distance from the surface increases in radial direction. as a result, hydrogen is accumulated out of the contact plane where a huge reduction of the hydrogen amount is achieved for long times of exposure to the environment due to the high compressive hydrostatic stress in the radial direction, thereby pumping hydrogen towards points outside the contact plane. the maximum hydrogen amount appears for a depth from the surface about 250 m. acknowledgements he authors acknowledge the financial support provided by the eu project multihy (http://multihy.eu): multiscale modelling of hydrogen embrittlement of crystalline materials (eu-fp7-nmp project no. 263335). references [1] europe's onshore and offshore wind energy potential: an assessment of environmental and economic constraints. european environment agency, copenhagen, (2009). [2] kumar, a., hahn, g., rubin, d., a study of subsurface crack initiation produced by rolling contact fatigue, metall. trans. a, 24 (1993) 351–359. [3] bhargava, v., hahn, g. t., rubin, c. a., rolling contact deformation and microstructural changes in high strength bearing steel, wear, 133 (1989) 65–71. [4] gupta, v., bastias, p., hahn, g. t., rubin, c. a., elasto-plastic finite-element analysis of 2-d rolling-plus-sliding contact with temperature-dependent bearing steel material properties, wear, 169 (1993) 251–256. [5] jiang, y., su, b., sehitoglu, h., three-dimensional elastic-plastic stress analysis of rolling contact, j. tribol., 124 (2002) 699–708. i t j. toribio et alii, frattura ed integrità strutturale, 30 (2014) 40-47; doi: 10.3221/igf-esis.30.06 47 [6] kabo, e., ekberg, a., fatigue initiation in railway wheels—a numerical study of the influence of defects, wear, 253 (2002) 26–34. [7] kabo, e., ekberg, a., material defects in rolling contact fatigue of railway wheels—the influence of defect size, wear, 258 (2005) 1194–1200. [8] rider, r. j., harvey, s. j., chandler, h. d., fatigue and ratcheting interactions, inter. j. fatigue, 17 (1995) 507–511. [9] lim, c.b., kim, k. s., seong, j. b., ratcheting and fatigue behavior of a copper alloy under uniaxial cyclic loading with mean stress, inter. j. fatigue, 31 (2009) 501–507. [10] pandkar, a. s., arakere, n., subhash, g., microstructure-sensitive accumulation of plastic strain due to ratcheting in bearing steels subject to rolling fatigue, inter. j. fatigue, 63 (2014) 191–202. [11] glover, d. a ball-rod rolling contact fatigue tester, in: rolling contact fatigue testing of bearing steels. astm stp 771, american society for testing and materials, baltimore, md, (1982) 107–124. [12] bhattacharyya, a., subhash, g., arakere, n., evolution of subsurface plastic zone due to rolling contact fatigue of m-50 nil case hardened bearing steel, inter. j. fatigue, 59 (2014) 102–113. [13] arakere, n. k., subhash, g., work hardening response of m50-nil case hardened bearing steel during shakedown in rolling contact fatigue, mater. sci. tech., 28 (2012) 34–38. [14] pilkey, w. d., formulas for stress, strain, and structural matrices, second ed., john wiley & sons, inc., hoboken, nj, usa, (2008). [15] toribio, j., lorenzo, m., vergara, d., kharin, v., hydrogen degradation of cold-drawn wires: a numerical analysis of drawing-induced residual stresses and strains, corros., 67 (2011) 075001–075008. [16] toribio, j., kharin, v., lorenzo, m., vergara, d., role of drawing-induced residual stresses and strains in the hydrogen embrittlement susceptibility of prestressing steels, corros. sci., 53 (2011) 3346–3355. [17] toribio, j., kharin, v., vergara, d., lorenzo, m., two-dimensional numerical modelling of hydrogen diffusion in metals assisted by both stress and strain, adv. mater. res., 138 (2010) 117–126. microsoft word numero_38_art_6 m. leitner et alii, frattura ed integrità strutturale, 38 (2016) 47-53; doi: 10.3221/igf-esis.38.06 47 focussed on multiaxial fatigue and fracture multiaxial fatigue assessment of crankshafts by local stress and critical plane approach m. leitner, f. grün montanuniversität leoben, chair of mechanical engineering, austria martin.leitner@unileoben.ac.at florian.gruen@unileoben.ac.at z. tuncali, r. steiner ge jenbacher gmbh & co og, austria zafer.tuncali@ge.com reinhard.steiner@ge.com w. chen ge water & distributed power, texas/usa wei5.chen@ge.com abstract. for multiaxially-loaded parts several stress-based fatigue assessment concepts are applicable mostly taking uniaxial test results as basis. these approaches work well in case of proportional loading states, but on contrary, for non-proportional stress conditions, implying a change of the principal stress direction, deviations in the fatigue life estimation may occur. the aim of this study is to evaluate the cyclic multiaxial material behavior experimentally and to proof the applicability of stress-based methods to assess the fatigue strength. the investigated base materials incorporate the commonly applied crankshaft steels 50crmo4 and 34crnimo6 without surface-layer post-treatments. extensive fatigue tests with small-scale specimens are performed to evaluate the material behavior under cyclic loading. the experiments include basic uniaxial characterizations, such as notch stress sensitivity and effect of loading type, including tests under tension, rotating bending, and torsion loading. additionally, combined loading tests with proportional and non-proportional situations are presented to reveal the fatigue resistance for multiaxial stress states. significant loading conditions, such as proportional stress under rotating bending and torsion, and further on, non-proportional effects like phase shifts and varying frequency ratios are presented. the local fatigue strength assessment is performed on the basis of the critical plane approach, whereat the normal and shear stresses are transformed in numerous cutting planes. equivalent stress hypotheses are applied and compared with the citation: leitner, m., grün, f., tuncali, z., steiner, r., chen, w., multiaxial fatigue assessment of crankshafts by local stress and critical plane approach, frattura ed integrità strutturale, 38 (2016) 47-53. received: 12.05.2016 accepted: 20.06.2016 published: 01.10.2016 copyright: © 2016 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. m. leitner et alii, frattura ed integrità strutturale, 38 (2016) 47-53; doi: 10.3221/igf-esis.38.06 48 experiments showing that the huber-mises-hencky criterion fits well to the test results in case of proportional rotating bending and torsion loading. keywords. multiaxial fatigue assessment; local stress concept; critical plane approach; crankshaft. introduction his paper presents a multiaxial fatigue strength assessment of crankshafts based on different local stress approaches. focus of the application is laid on stationary gas engines exhibiting a high level of electrical and thermal efficiency. by the permanent increasing demand to optimize specific power output, a reliable and accurate numerical fatigue analysis is of utmost importance. the investigations are separated in a uniaxial and multiaxial section, mainly focusing on the commonly applied steel 50crmo4. the results are partially supplemented and compared to a previous work [1] incorporating extensive tests with the steel types 34crnimo6 and 42crmo4. uniaxial fatigue strength characterization n this chapter a basic characterization of the base material focussing on 50crmo4 is provided. emphasis is laid on the major fatigue-related influences for a notch stress-based fatigue assessment, in particular  notch stress sensitivity, and  type of loading. notch sensitivity the effect of various notched specimens on the fatigue strength of the crankshaft base material 50crmo4 is presented in fig. 1. the results reveal a significant decrease by about 50 % of the high-cycle fatigue limit at five million load-cycles in case of the most sharply notched (notch radius r=0.8 mm) compared to the unnotched specimen under tension/compression (t/c) loading. all tests are performed at a stress ratio of r=-1. figure 1. influence of notch and loading type (tension/compression and rotating bending) on uniaxial fatigue strength (50crmo4). t i m. leitner et alii, frattura ed integrità strutturale, 38 (2016) 47-53; doi: 10.3221/igf-esis.38.06 49 for commonly applied steel materials, the reduction in fatigue strength due to notches is less than the elastic theory by terms of the stress concentration factor kt would estimate. notch influences are generally specified by the fatigue notch factor kf representing the ratio of the unnotched to the notched fatigue resistance. a study in [2] provides an overview and verification of several models evaluating kf for different base materials. engineering feasible concepts are mostly based on the relative stress gradient ' due to an efficient automated evaluation of finite element results. one method among them is presented by [3] calculating the fatigue support effect n=kt/kf as follows: kd b r t c r n d , / , ' 1 1 2 /                   (1) thereby, b,r equals the fatigue strength under bending and t/c,r the fatigue strength under tension/compression loading, d is the diameter of the specimens by which b,r is evaluated, and kd is a material-dependent parameter. the application of the model in order to assess the local notch fatigue strength is depicted in fig. 2 showing a good accordance to the fatigue test results. figure 2. assessment of local fatigue strength (50crmo4). figure 3. comparison of t/cand torsion loading (50crmo4) in addition to the to the local endurance limit, a method to estimate the slope k and the transition knee point nd of the local s/n-curve is presented in [3]. thereby, the determination is performed on the basis of the evaluated support effect and an exponential interpolation among a minimum and maximum value kmin and kmax, and ndmin and ndmax. these values are statistically evaluated by numerous fatigue tests, whereby kmin and ndmin represent a technically highest-notched case, and kmax and ndmax the unnotched condition. normal vs. shear stress loading as the crankshafts local loading scenario is not only affected by normal stresses, additionally the fatigue strength under shear stress (torsion) loading is investigated. the results in fig. 3 highlight a distinctive difference, whereas the shear stress high-cycle fatigue strength t,r features only 51 % compared to the behaviour under normal stress. multiaxial fatigue strength characterization proportional loading n overview of different concepts to assess the fatigue strength under proportional loading is given in [4]. one common approach is introduced by gough and pollard [5] taking the normal and shear stress by an elliptical correlation into account, see eq. (2). a m. leitner et alii, frattura ed integrità strutturale, 38 (2016) 47-53; doi: 10.3221/igf-esis.38.06 50 r r 2 2 1                  (2) multiaxial fatigue tests under proportional rotating bending and torsion loading are carried out in order to assess the fatigue behavior under multiaxial loading for the investigated steel 50crmo4. the tests are performed in the unnotched specimen condition at a loading stress ratio of r=-1 and a shear to normal stress ratio of t/=0.5. fig. 4 summarizes the uniaxial results under pure normal and pure shear stress, and the combined proportional loading mode. the application of the model according to gough and pollard illustrates a good accordance to the test results. moreover, the method demonstrates its applicability for numerous test results incorporating steel, cast iron and aluminium specimens in [6]. figure 4. multiaxial fatigue behaviour under proportional loading (50crmo4). critical plane approach mong stress, strain and energy based multiaxial fatigue criteria, the critical plane approach is one widespread method due to its effectiveness and broad application range. the general procedure of the approach is a reduction of the multiaxial stress condition to an equivalent uniaxial stress, firstly introduced by [7]. definition of the cutting plane angle  and calculation of the associated normal and shear stress is shown in fig. 5. figure 5. evaluation of normal and shear stress in critical plane. a review of critical plane orientations in multiaxial fatigue failure criteria for metallic materials is provided in [8]. one basic equivalent stress concept is introduced by huber-mises-hencky assuming a ratio of normal to shear stress fatigue strength of √3, see eq. 3 in case of plain stress condition. another approach by lamé takes only the portion of the (maximum) normal stress into account, see eq. 4. v n n 2 2 1 3     (3) a m. leitner et alii, frattura ed integrità strutturale, 38 (2016) 47-53; doi: 10.3221/igf-esis.38.06 51 v n2  (4) fig. 6 presents the stress-time distribution for the three tested load-cases and the corresponding characteristic of the equivalent stress amplitude by huber-mises-hencky depending on the actual load time t and cutting plane angle . the values are normalized to the experimentally evaluated bending fatigue strength b,r in accordance to fig. 4. figure 6: normalized equivalent stress v1 for (a.) t/b=0 (bending only), (b.) t/b=0.5 (bending and torsion) and (c.) t/b=∞ (torsion only). on the basis of the two presented equivalent stress criteria, the maximum allowable normal (bending b=xx) and shear (torsion t=xy) stress amplitudes are determined as summarized in tab. 1. in case of only bending loading (t/b=0), v1 reveals an almost comparable bending fatigue strength b as the experiments indicate, whereas the calculated value is slightly conservative. an application of the maximum normal stress criteria v2 also agrees well to the test results. for the combined loading state (t/b=0.5) both concepts lead to a slightly overestimation of the corresponding fatigue strength values. torsion loading without bending (t/b=∞) again overrates the experimental values, but however, in case of v1 by just 7 % compared to 49 % on the basis of v2. the accordant critical plane angles  also differ significantly, whereas for v1 the values match acceptably well to the failure modes of the tested specimens. m. leitner et alii, frattura ed integrità strutturale, 38 (2016) 47-53; doi: 10.3221/igf-esis.38.06 52 normalized stress v1 v2 t/b=0 b=0.94 & t=0.00 (=30°/150°) b=1.00 & t=0.00 (=0°/180°) t/b=0.5 b=0.74 & t=0.37 (=55°/170°) b=0.84 & t=0.42 (=25°) t/b=∞ b=0.00 & t=0.58 (=0°/90°) b=0.00 & t=1.00 (=45°/135°) table 1. multiaxial fatigue assessment for 50crmo4 fatigue assessment of crankshafts load-analysis of gas engine y the aid of a multi-body simulation the developing time-dependent loading situation of a crankshaft for a 16cylinder gas engine is evaluated. a subsequent numerical analysis of one selected notch illustrates the complex non-proportional stress condition considering the local normal and shear stress at the surface, see fig. 7. figure 7. normal and shear stress distribution over one firing sequence (rotation of crankshaft by 720°) at one selected notch of a 16cylinder gas engine. effect of phase shift and frequency ratio as the local stress distribution over one firing sequence shows a distinctive non-proportional load-case, the effect of phase shift and frequency ratio for normal and shear stress loading is experimentally investigated in [1] for the base material 34crnimo6. the results reveal that a phase shift of 45° (π/4) leads to an increase of 3 % and a phase shift of 90° (π/2) of 6 % compared to the fatigue strength of proportional normal and shear stress loading. furthermore, a frequency ratio of f/f=2 indicates just a minor decrease by 1 %, but a ratio of f/f=3 shows a more relevant reduction by 6 %. in addition to the analysis of the material behaviour, the resultant timeand cutting plane-dependent equivalent stress is of utmost importance to assess the local fatigue strength properly. hence, further investigations incorporating equivalent stress analysis with various basic non-proportional load-scenarios and the presented load distribution for a 16cylinder gas engine is scheduled. additional multiaxial stress criteria, such as integral-based methods [9], are applied in order to proof their accuracy. summary niaxial fatigue tests are performed to characterize basic influences, such as notch stress sensitivity and loading type, of the base material 50crmo4. the results show, firstly, that the stress gradient model introduced by [3] is well applicable, and secondly, that a significant difference between normal and shear stress loading is evaluated b u m. leitner et alii, frattura ed integrità strutturale, 38 (2016) 47-53; doi: 10.3221/igf-esis.38.06 53 exhibiting a ratio r/r of 1.96. proportional multiaxial fatigue tests illustrate that the elliptical model by gough and pollard [5] matches well to the results. an application of the huber-mises-hencky equivalent stress criterion shows, in comparison to the maximum normal stress concept, good accordance to the experiments. the effect of non-proportional loading on the fatigue strength of 34crnimo6 specimens is presented based on experimental investigations in [1]. further extensive analyses incorporating the huber-mises-hencky and additional multiaxial criteria, e.g. integral-based approaches [9], are scheduled. references [1] fröschl, j., fatigue behaviour of forged components: technological effects and multiaxial fatigue, phd thesis, montanuniversität leoben, austria, (2006). [2] buch, a., notch-size effect in fatigue of steel specimens verification of some calculation methods, z. werkstofftech., 15 (1984) 338-348. [3] eichlseder, w., fatigue analysis by local stress concept based on finite element results comp. & struct., 80 (2002) 2109–2113. [4] kurek, m., lagoda, t., comparison of the fatigue characteristics for some selected structural materials under bending and torsion, mat. sc., 47 (2011) 334-344. [5] gough, h. j., pollard, h. v., clenshaw, w. j., some experiments on the resistance of metals under combined stress, aeronautical research council, 2522, his majesty’s stationary office, london, (1951). [6] liu, j., zenner, h., berechnung der dauerschwingfestigkeit bei mehrachsiger beanspruchung teil 1, mat.-wiss. u. werkstofftech., 24 (1993) 240-249. [7] stanfield, g., discussion of the strength of metals under combined alternating stresses, proc. of the inst. of mech. eng., 131 (1935) 93. [8] karolczuk, a., macha, e., a review of critical plane orientations in multiaxial fatigue failure criteria of metallic materials, int. j. of fract., 134 (2005) 267-304. [9] zenner, h., simbürger, a., liu, j., on the fatigue limit of ductile metals under complex multiaxial loading, int. j. of fatigue, 22 (2000) 137-145. << /ascii85encodepages false /allowtransparency false /autopositionepsfiles true /autorotatepages /none /binding /left /calgrayprofile (dot gain 20%) /calrgbprofile (srgb iec61966-2.1) /calcmykprofile (u.s. web coated \050swop\051 v2) /srgbprofile (srgb iec61966-2.1) /cannotembedfontpolicy /error /compatibilitylevel 1.4 /compressobjects /tags /compresspages true /convertimagestoindexed true /passthroughjpegimages true /createjobticket false /defaultrenderingintent /default /detectblends true /detectcurves 0.0000 /colorconversionstrategy /cmyk /dothumbnails false /embedallfonts true /embedopentype false /parseiccprofilesincomments true /embedjoboptions true /dscreportinglevel 0 /emitdscwarnings false /endpage -1 /imagememory 1048576 /lockdistillerparams false /maxsubsetpct 100 /optimize true /opm 1 /parsedsccomments true 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can be opened with acrobat and adobe reader 5.0 and later.) >> /namespace [ (adobe) (common) (1.0) ] /othernamespaces [ << /asreaderspreads false /cropimagestoframes true /errorcontrol /warnandcontinue /flattenerignorespreadoverrides false /includeguidesgrids false /includenonprinting false /includeslug false /namespace [ (adobe) (indesign) (4.0) ] /omitplacedbitmaps false /omitplacedeps false /omitplacedpdf false /simulateoverprint /legacy >> << /addbleedmarks false /addcolorbars false /addcropmarks false /addpageinfo false /addregmarks false /convertcolors /converttocmyk /destinationprofilename () /destinationprofileselector /documentcmyk /downsample16bitimages true /flattenerpreset << /presetselector /mediumresolution >> /formelements false /generatestructure false /includebookmarks false /includehyperlinks false /includeinteractive false /includelayers false /includeprofiles false /multimediahandling /useobjectsettings /namespace [ (adobe) (creativesuite) (2.0) ] /pdfxoutputintentprofileselector /documentcmyk /preserveediting true /untaggedcmykhandling /leaveuntagged /untaggedrgbhandling /usedocumentprofile /usedocumentbleed false >> ] >> setdistillerparams << /hwresolution [2400 2400] /pagesize [612.000 792.000] >> setpagedevice microsoft word numero_38_art_14 j. papuga et al., frattura ed integrità strutturale, 38 (2016) 106-113; doi: 10.3221/igf-esis.38.14 106 focussed on multiaxial fatigue and fracture systematic validation of experimental data usable for verifying the multiaxial fatigue prediction methods j. papuga ú12105 fme ctu in prague, technická 4, 166 07 prague 6, czech republic papuga@pragtic.com, http://orcid.org/0000-0001-9569-4997 evektor, spol. s r.o., letecká 1008, 686 04 kunovice, czech republic jpapuga@evektor.cz s. parma evektor, spol. s r.o., letecká 1008, 686 04 kunovice, czech republic origon@seznam.cz m. růžička ú12105 fme ctu in prague, technická 4, 166 07 prague 6, czech republic milan.ruzicka@fs.cvut.cz abstract. the paper discusses some of the issues, the researchers interested in verifying various multiaxial fatigue limit estimation solutions are facing to. even recently, newly proposed criteria have been or are tested on dozens of experimental inputs. papuga in [1] pointed out, that applicability of the most often used test batch is limited and only half of these data items is worth using for such purposes. this paper extends that analysis by describing the weak points of various data sets used in this domain for validating new proposals on multiaxial fatigue limit estimates. the conclusion from the extensive analysis is that the researchers should adopt other test sets only if they very well know their background. keywords. multiaxial fatigue; multiaxial fatigue limit; fatigue prediction; fatigue prediction validation; multiaxial fatigue limit experiment. citation: papuga, j. parma, s., růžička, m., systematic validation of experimental data usable for verifying the multiaxial fatigue prediction methods, frattura ed integrità strutturale, 38 (2016) 106-113. received: 27.04.2016 accepted: 20.06.2016 published: 01.10.2016 copyright: © 2016 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. introduction hen papuga wrote the paper [1] on various multiaxial fatigue limit estimation methods and their validation, he referred to a set of 407 experimental items on various materials and obtained from different papers. at that moment, he cared little about the quality of the data obtained in that way. the reason for including a data item w j. papuga et al., frattura ed integrità strutturale, 38 (2016) 106-113; doi: 10.3221/igf-esis.38.14 107 into the validation set was a simple stating of the experimenter or of any other researcher, that the data items are usable for such a validation. already during preparation of that data set, some bad practice or misleading data interpretation was uncovered and discussed in [1]. anyhow, only a proper analysis [4] of the most often cited and reused data set defined by papadopoulos et al. [2] and of other often used data items from the paper by nishihara and kawamoto [3] made a start point for an extensive research on evaluating the data quality. method of evaluation his paper further extends the analyses provided in [4] by updating them and enlarging the scope of the data check. due to the multitude of papers available for validation, it can be in no way complete, and some other such papers can be found. on the other hand, it is covering now all data sources found, which were used by the cited authors in their effort to validate new or older multiaxial fatigue limit estimation methods, and which were used for such a purpose by at least one researcher not related to the team of experimenters. some newer sets from fresh experiment campaigns were reported meantime, but the scope of a conference paper cannot give a thorough overview. data presented here are quickly touched and only their weak points are commented. the experiments are very valuable, their realization took a lot of time, a lot of work and a lot of funds. anyhow, only short evaluation can get here. thus the sets are criticized when necessary, so that the other researchers were aware of potential problems if accepting them, while the detailed description or appraisal cannot be provided here. the measure of acceptability of experimental results for validation purposes has been already discussed in [4]. astm [5] e.g. recommends between 6 and 12 specimens to be used for an s-n curve applicable for an exploratory research. papuga in [4] proposed a system of weights, where 8 and more finished experiments per the s-n curve result in a full weight (1.0) of the item, while the weight decreases linearly to 0.2 for the case of 4 specimens per the s-n curve, and experiments with fewer test points are simply discarded. in this paper, we do not evaluate the appropriateness to the validation in another way than by the check if the s-n curve is described with minimum 4 specimens. the question of the data dispersion, applicability of experiments tested on one load level only, of the importance of the basic material curves in fully reversed push-pull and fully reversed torsion, the comparison between the statistical representativeness of the fatigue limit derived from an s-n curve and from the staircase analyses are only a few of the questions that should be further raised, but cannot be discussed in such a short paper. the basic reference for the next evaluation is tab. 1, where the individual papers describing validation of some multiaxial fatigue limit estimation method(s) are referred to, and the data sets used for this purpose are marked by “x“ symbol. the papers often just reuse data from a second-hand source, so the fact that some paper uses nishihara‘s and kawamoto’s data [3] need not mean that there are not error in interpreting it or in the transcription. the table also does not describe, if the authors referring to a particular data set used in a complete form or if they selected only its parts. the individual test sets described in tab. 1 are evaluated in the next section including also the test set marks extensively used in fatlim and finliv databases [6-7]. due to the limited space available for tab. 1, these marks could not be preserved there as well, but they can be deduced from the context. data sets nishihara and kawamoto (nkc, nkd, nkh, nkm [3]) he fact that the data items of this data set on fatigue limits obtained for hard steel, mild steel, cast iron and duralumin are the 1st, 5th, 8th and 9th as regards the frequency of their use shows its importance in validating of the multiaxial fatigue limit estimation methods. the careful analysis of the set in [4] anyhow uncovers that only two s-n curves obtained for the hard steel material can be seen as applicable, if accepting the low coefficient of determination r2 < 0.75 obtained during the regression analysis of data by the basquin formula. for the other materials, either the material curves (mild steel, cast iron) or the multiaxial experiments (duralumin) dispose of too few specimens, in some cases limited even to only one finished and one unfinished experiment. though the set is so broadly used for validation practice, the analysis of the original paper shows that applicability of so poorly documented s-n curves is inadequate. t t j. papuga et al., frattura ed integrità strutturale, 38 (2016) 106-113; doi: 10.3221/igf-esis.38.14 108 paper by m cd ia rm id p ap ad o p o ul o s st ef an o v p ap ad o p o ul o s et a l. c ar p in te ri , s p ag n o li m am iy a, a ra új o b an vi lle t et a l. c ru z, z o ua in g o n ca lv es e t al . g o n ca lv es e t al . l iu , m ah ad ev an n in ic n in ic , s ta rk b ra cc es i e ta l p ap ug a, r ůž ič ka sh ar iy at l i, r ei s, f re it as v u et a l. z h an g, y ao c ar p in te ri e t al . p ap ug a k en m eu gn e et a l. a ug us ti n s c ar p in te ri e t al . m at su b ar a, n is h io a ra új o e t al . g o lo s, d eb sk i e t al . b ru un , h är ke gå rd n um b er o f o cc ur re n ce s year 19 87 19 94 19 95 19 97 20 01 20 02 20 03 20 03 20 04 20 05 20 05 20 06 20 07 20 08 20 09 20 09 20 09 20 10 20 10 20 11 20 11 20 12 20 13 20 13 20 13 20 14 20 14 20 15 material ref [9 ] [2 ] [1 0] [2 ] [4 0] [4 1] [4 2] [4 3] [4 4] [4 5] [4 6] [4 7] [4 8] [4 9] [5 0] [5 1] [5 2] [2 0] [5 3] [5 4] [1 ] [5 5] [5 6] [3 1] [5 7] [2 1] [5 8] [2 6] cast iron [3] x x x x x x x x 8 duralumin [3] x x x x x 5 hard steel [3] x x x x x x x x x x x x x x x x x x x x x x x x 24 mild steel [3] x x x x x x x x x x x x x 13 ggg-40 [8] x 1 gts-45 [8] x x 2 30ncd16 [11,12] x x x x x x x x x x x x x x x x x x x x x 21 34cr4 [14] x x x x x x x x x x x x x x x x x x 18 42crmo4v [15] x x x x x x x x x x x x x x 14 25crmo4 [17] x x x x x x x x x x 10 fgs700/2 [22] x x x x 4 30ncd16 [11,12] x x x x x x x x x 9 xc18 [23] x x x x 4 6082-t6 [38] x x 2 76s-t6 [25] x x x x x 5 steels and cast irons [27,28] x x x 3 0.35%c steel [30] x x x 3 s65a [29] x x x x 4 42crmo4v [32] x x 2 st35 [32] x x 2 st35 [33] x x x x x 5 25crmo4 [19] x x 2 34crmo4 [34] x x 2 ck 35 [34] x x 2 st60 [35] x x 2 34cr4 [14] x x x 3 34cr4 [14] x x 2 xc48 [39] x x x 3 25crmo4 [18] x x x 3 cast iron [36] x 1 en24t [37] x 1 gg30 [34] x 1 table 1: list of papers referring to individual test sets. j. papuga et al., frattura ed integrità strutturale, 38 (2016) 106-113; doi: 10.3221/igf-esis.38.14 109 neugebauer (nba, nbb [8]) the research report of neugebauer on ggg-40 and gts-45 was extracted by mcdiarmid [9] and later by stefanov [10] to support their findings. the data are reported in graphs of the s-n curves only (mostly two load levels up to 6-13 data points in total) and have to be derived by an image analysis. the weak point of the test set is hidden in the text [8], where neugebauer notes that all pure torsion experiments were run with deformation control. the set thus mixes outputs of these deformation-controlled experiments with the common load-controlled experiments for all other load variants. froustey and lasserre (fla, flb – [11], [12]) the test sets have been already discussed in [4], and only the major conclusions are provided here. froustey and lasserre ran the tests on three different lots of 30ncd16, while only one of these lots (used for flb test set here) is complete as regards the uniaxial experiments, while the fla test set lacks such material data. this is probably the reason, why dubar [13] later attempted to prepare a unified test set on 30ncd16 by weighting the results of individual batches in an undefined way, while thus confusing other researchers by seeming wholly new set. heidenreich, zenner et al. (heg, hei, hrz, hz – [14], [15]) the authors repeatedly published results of their ongoing experimental campaign mainly on three different lots of 34cr4 steel. they also reported tests on ggg-60 cast iron (heg), but these are not anyhow present in tab. 1. the test set has been already commented in [4] as being acceptable for validation purposes, and only some individual curves should be sorted out (the authors used lower numbers of specimens for the staircase method). the only unacceptable exception is the hz test set, where no reversed torsion experiments were run, and the test set is not thus applicable to testing for most of the fatigue limit estimation criteria. lempp (lem – [16]) lempp’s tests on 42crmo4v steel are commonly reused for validation purposes thanks to papadopoulos’ test set [2], and thus they have been already evaluated in [4]. the originally reported fatigue limit estimates are mostly based on extrapolations to cycle counts far exceeding the last finished experiment. even if the number of cycles is decreased to define another section point for fatigue strength determination, other issues become obvious: • lempp describes pronounced anisotropy of the material (83% of fatigue strength of specimens oriented in the transverse direction compared to longitudinal ones). • the alternate torsion fatigue curve is defined by 7 data points, but the scatter of data is so high, that it leads to the coefficient of determination r2 = 0.624. • the test case of repeated axial loading is not covered at all. the prediction methods including also the fatigue limit in repeated axial loading cannot be validated by this test set. mielke (mie – [17]), troost, akin and klubberg (tak – [18]), kaniut (kan – [19]) mielke’s set of fatigue limits on hardened 25crmo4 steel tested by the staircase method is also often reproduced in various validation campaigns. its weak point can be found in the intrinsic unequal size effect involved in various load combinations. the push-pull tests were realized on tiny bars of 1.9 mm diameter, while the torsion test sets on hollow specimens with outer diameter 20 mm and 2 mm wall thickness and the multiaxial tests on hollow specimens with 34 mm outer diameter and 1 mm wall thickness. from further analysis of reports, it can be found that troost, akin and klubberg [18] continued on tests on the same batch of material, thus forming the tak set. they tested both specimen size configurations and nicely confirmed the size effect. thanks to that, they results can be combined with mielke’s multiaxial data, so that mielke’s set could be used for validation purposes. kaniut studied at the same university, and he reported experiments realized on the same material with identical material parameters. it can be deduced so that he also worked on the same lot of 25crmo4. his main focus was nevertheless set to determining the fatigue limit values for two-channel loading with unequal frequencies applied in each load channel. because he used the staircase method for obtaining the fatigue limits, there are no material curves available for fatigue damage accumulation, while the unequal frequencies on individual load channels are likely to form more than one load cycle per a complete period of the total load cycle. papuga highlighted this point in [1], and decided not to include similar load conditions into the validation test set, but other researchers [20-21] do not find such reasoning important and work with this test set as well. j. papuga et al., frattura ed integrità strutturale, 38 (2016) 106-113; doi: 10.3221/igf-esis.38.14 110 bennebach (ben – [22]), palin-luc (pal – [23]) as usually in the case of tests realized at ensam in bordeaux, staircase philosophy was adopted for fatigue limit determination for these both cases. because the first international publication of the test set was found in the paper by morel and palin-luc [24], test sets were originally marked mpc and mpb in [1]. bennebach’s phd thesis [22] allows the reader to define just two fatigue limits. such a low number differs from the mpc set, where four items are available. one more fatigue limit can be traced back to palin-luc [23], where unfortunately no information is present, whether the same lot of material was used. the origin of the last item in mpc test set has not been found yet. findley (fin – [25]) papuga reported in [1] this test set three times, because he defined three different s-n curve section cuts at 106, 107 and 108 cycles in order to increase the number of experiments realized on aluminum alloys. though the same strategy was accepted e.g. in [26], this simple multiplication of the same data set is not consequent, because it was not adopted while processing the other data sets. gough and pollard (gpx – [27-28]), gough (ggh – [29]) gough and pollard published in the 30th of the 20th century several papers (see e.g. [27-28]) describing results of their multiaxial tests on bar specimens manufactured from various steels and cast irons. the combination of plane bending and torsion without any phase shift and without any mean stress can be found in all data sets. apparently, the focus of their effort was mostly devoted to covering of various materials extensively, than to determining the fatigue limits precisely. therefore, many of these experiments do not conform to the lowest standards defined here before, and big scatter of data in some curves can be found in many cases. as a result of such practice, one half of the defined multiaxial fatigue limit items could be included into the validation data set at maximum. after the wwii, gough published further papers (e.g. [29]), mostly devoted to more complex testing on s65a steel. nevertheless, no information on the way the reported fatigue limits were set can be found in any of his papers from that period, and only his personal classification describing the reliability of the outputs is available. rotvel (rot – [30]) rotvel’s data were used for a validation study even recently [31], though papuga wrote in [1], that the experiments miss the case of pure torsion loading. this value has to be estimated, if the test set should be admitted for validation purposes, and this is apparently the method of determination used in [31]. bhongbhibhat (bho, bha – [32]) these tests realized on specimens on large hollow specimens manufactured from 42crmo4 (bho) and st35 (bha) are affected by substantially different cross-sections of specimens used for uniaxial and multiaxial fatigue tests. additionally, the lifetime regions of individual curves in these data groups differ so substantially, that only small intersections can be found. issler (iss – [33]) issler’s data set suffer from the doubtful way the fatigue limits were determined. no clue is provided by the author, but based on an analysis of his results, it seems that he either used the section cut at 2 000 000 cycles or the stress level of the last finished experiment with the longest lifetime. section cuts at lower number of cycles are recommended to avoid potential extrapolations. the s-n curves for multiaxial load combinations are described by graphs with data points only. unfortunately, the uniaxial fatigue curves are not present at all, and the fatigue limits derived by the author are provided solely. because of the way the fatigue limits were determined in other cases, it cannot be anticipated how precise these values are. baier (bab, bai, bag – [34]) the data on both steels (bab – ck35, bai – 34crmo4) are very interesting for validation purposes. the tests were realized as s-n curve tests on sufficient numbers of hollow specimens in most cases. anyhow, the tests on gg30 cast iron (bag test set), for which any fully reversed torsion tests are missing, should not be used. j. papuga et al., frattura ed integrità strutturale, 38 (2016) 106-113; doi: 10.3221/igf-esis.38.14 111 el-magd and mielke (emm – [35]) the authors did not run any reversed torsion fatigue tests, and the later transcription of this set seems to be accompanied by some kind of an estimate of this missing value. any more information about this test set, or other papers referring to these experiments would be welcomed. roš and eichinger (re – [36]) though the data set of these two authors is very huge, and relates to many various materials, there is no single note on the way the fatigue limits were derived. the number of specimens used to determine them can only be guessed. no fully reversed torsion sets are reported. mcdiarmid (mcd – [37]) the data do not refer to any fatigue experiments realized in pure torsion mode. conclusion f comparing the content of tab. 1 with the previous subsections, it can be concluded, that only a few from the commonly used data sets can be used for validation purposes without any hesitation. mostly, two major reasons can be found for rejecting a particular test set from the validation: 1. there are not enough experiments in order to adequately define the fatigue limits, or the statistical parameters of the regression outputs are not representative enough. 2. the torsion load case is not covered at all. the authors of the present paper understand such deficiency as too substantial, because they define the fatigue limit in fully reversed torsion as a standard input parameter. another potential mode of validation could be to define the weight parameters of individual stress parameters from the least square error analysis realized on the complete test set. according to the authors, such solution is not adequate, because it uses the weight coefficients derived from the best fit analysis. such strategy can be rarely used in engineering practice, because only minimum information is often available in these cases. it is thus reasonable to persuade the engineering audience about validity of tested prediction methods, while using standardized inputs of material parameters, and to convince it to ensure availability of the fully reversed fatigue limits in axial and torsion loadings at least. the authors of new criteria should be aware of various problematic issues of the described test sets. they should carefully analyze the reasons to include the particular data sets into their validation sets. acknowledgements he authors thank to the czech science foundation and to the technology agency of the czech republic for the support of their work in preparing this paper by the grant projects no. ga15-18274s and ta01011274 respectively. references [1] papuga, j., a survey on evaluating the fatigue limit under multiaxial loading, int. jnl. of fatigue, 33 (2011) 153-165. [2] papadopoulos, i.v., davoli, p., gorla, c., filippini, m. bernasconi, a., a comparative study of multiaxial high-cycle fatigue criteria for metals, int. jnl. of fatigue, 19 (1997) 219-235. [3] nishihara, t., kawamoto, m., the strength of metals under combined alternating bending and torsion with phase difference, mem. college engng., kyoto imperial university, 11 (1945) 85-112. [4] papuga, j., quest for fatigue limit prediction under multiaxial loading, procedia engineering, 66 (2013) 587-597. [5] anon.. standard practice for statistical analysis of linear or linearized stress-life (s-n) and strain-life (e-n) fatigue data, [e 739 – 91, reapproved 2004], astm international, west conshohocken, (2004). [6] papuga, j., new technologies for sharing research data and costs, procedia engineering, 2 (2010) 855-864. i t j. papuga et al., frattura ed integrità strutturale, 38 (2016) 106-113; doi: 10.3221/igf-esis.38.14 112 [7] papuga, j., parma, s., lutovinov, m., růžička, m., building a foundation for benchmarks for fatigue prediction methods – the finliv database. procedia engineering, 101 (2015) 372-379. [8] neugebauer, j., zum schwingfestigkeitsverhalten von gusswerkstoffen unter mehrachsiger, frequenzverschiedener beanspruchung, [technical report report fb-175], lbf, darmstadt, (1986). [9] mcdiarmid, d.l., fatigue under out-of-phase bending and torsion, fatigue fract. engng. mater. struct., 9 (1987) 457-475. [10] stefanov, s. h., the curvilinear integral method: computer realization and testing 1 (under non-proportional reversed axial force and torque), int. jnl. of fatigue, 17 (1995) 567-575. [11] froustey, c., fatigue multiaxiale en endurance de l'acier 30ncd16, [phd thesis], e.n.s.a.m. cer de bordeaux, bordeaux, (1987). [12] froustey, c., lasserre, s., fatigue des aciers sous sollicitations combinees. application a l'acier 30ncd16. [technical report rapport dret-lamef-ensam. contrat 87/115], ensam, talence, (1988). [13] dubar, l. fatigue multiaxiale des aciers. passage de l'endurance a l'endurance limite. prise en compte des accidents geometriques, [phd thesis], e.n.s.a.m. cer de bordeaux, bordeaux, (1992). [14] heidenreich, r., schubspannungsintensitätshypothese dauerschwingfestigkeit bei mehrachsiger beanspruchung [forschungshefte fkm, heft 105]. fkm, frankfurt am main – niederrad, (1983). [15] heidenreich, r., richter, i., zenner, h., schubspannungsintensitätshypothese weitere experimentelle und theoretische untersuchungen konstruktion, 36 (1984) 99-104. [16] lempp, w., festigkeitsverhalten von stählen bei mehrachsiger dauerschwingbeanspruchung durch normalspannungen mit überlagerten phasengleichen und phasenverschobenen schubspannungen, [phd thesis], technische universität stuttgart, stuttgart, (1977). [17] mielke, s., festigkeitsverhalten metallischer werkstoffe unter zweiachsiger schwingender beanspruchung mit verschiedenen spannungszeitverläufen, [phd thesis], rwth aachen, aachen, (1980). [18] troost, a., akin, o., klubberg, f., versuchsund rechendaten zur dauerschwingfestigkeit von metallischen werkstoffen unter mehrachsiger beanspruchung, materialwissenschaft und werkstofftechnik 23 (1992) 1-12. [19] kaniut, c., zur betriebsfestigkeit metallischer werkstoffe bei mehrachsiger beanspruchung, [phd thesis], rwth aachen, aachen, (1983). [20] vu, q., halm, d., nadot, y., multiaxial fatigue criterion for complex loading based on stress invariants, int. jnl. of fatigue, 32 (2010) 1004-1014. [21] araújo, j.a., carpinteri, a., ronchei, c., spagnoli, a., vantadori, s., an alternative definition of the shear stress amplitude based on the maximum rectangular hull method and application to the c-s (carpinteri-spagnoli) criterion, fatigue fract. engng. mater. struct., 36 (2014) 764-771. [22] bennebach, m., fatigue d'une fonte gs. influence de l'entaille et d'un traitement de surface, [phd thesis], ensam cer de bordeaux, bordeaux, (1993). [23] palin-luc, t., fatigue multiaxiale d’une fonte gs sous sollicitations combinées d’amplitude variable, [phd thesis], ensam cer de bordeaux, bordeaux, (1996). [24] morel, f., palin-luc, t., a non-local theory applied to high cycle multiaxial fatigue, fatigue fract. engng. mater. struct., 25 (2002) 649-665. [25] findley, w.n., combined-stress fatigue strength of 76s-t61 aluminum alloy with superimposed mean stresses and corrections for yielding, [technical report naca tn-2924], naca, washington, (1953). [26] bruun, ø.a., härkegård, g., a comparative study of design code criteria for prediction of the fatigue limit under inphase and out-of-phase tension–torsion cycles, int. jnl. of fatigue, 73 (2015) 1-16. [27] gough, h.j., pollard, h.v., the strength of metals under combined alternating stresses, in: proc. of institute of mechanical engineering, the institution of automobile engineers, london, 131 (1935) 1-103. [28] gough, h.j., pollard, h.v., properties of some materials for cast crankshafts, with special reference to combined stresses, in: proc. of the institution of automobile engineers, the institution of automobile engineers, london, (1937) 821-893. [29] gough, h.j., engineering steels under combined cyclic and static stresses, journal of applied mechanics, (1950) 113125. [30] rotvel, f., biaxial fatigue tests with zero mean stresses using tubular specimens, int jnl. of mech. sci., 12 (1970) 597613. [31] carpinteri, a., spagnoli, a., vantadori, s., bagni, c., structural integrity assessment of metallic components under multiaxial fatigue: the c–s criterion and its evolution, fatigue fract. engng. mater. struct., 36 (2013) 870-883. j. papuga et al., frattura ed integrità strutturale, 38 (2016) 106-113; doi: 10.3221/igf-esis.38.14 113 [32] bhongbhibhat, t., festigkeitsverhalten von stählen unter mehrachsiger phasenverschobener schwingbeanspruchung mit unterschiedlichen schwingungsformen und frequenzen, [phd thesis], universität stuttgart, stuttgart, (1986). [33] issler, l., festigkeitsverhalten metallischer werkstoffe bei mehrachsiger phasenverschobener schwingbeanspruchung, [phd thesis], universität stuttgart, stuttgart, (1973). [34] baier, f., zeitund dauerfestigkeit bei überlagerter statischer und schwingender zug-druckund torsionbeanspruchung, phd thesis, universität stuttgart, stuttgart, (1970). [35] el magd, e., mielke, s., dauerfestigkeit bei überlagerter zweiachsiger statischer beanspruchung, konstruktion, 29 (1977) 253-257. [36] roš, m., eichinger, m., die bruchgefahr fester körper bei wiederholter beanspruchung – ermüdung, [technical report bericht nr. 173 ]. eidgenössische materialprüfungsund versuchsanstalt für industrie, bauwesen und gewerbe, zürich, (1950). [37] mcdiarmid, d.l., mean stress effects in biaxial fatigue where the stresses are out-of-phase and at different frequencies, in: k.f. kussmaul, d.l. mcdiarmid, d.f. socie (eds.), fatigue under biaxial and multiaxial loading, mechanical engineering publication, london, (1991) 321-335. [38] susmel, l. petrone, n., in: a. carpinteri, m. de freitas, a. spagnoli (eds.), proc. of 6th international conference on biaxial/multiaxial fatigue and fracture, esis publication, london, (2001) 83-104. [39] simbürger, a., festigkeitsverhalten zäher werkstoffe bei einer mehrachsigen phaseverschobenen schwingbeanspruchung mit körperfesten und veränderlichen hauptspannungsrichtungen, [phd thesis], th darmstadt, darmstadt, (1975). [40] carpinteri, a., spagnoli, a., multiaxial high-cycle fatigue criterion for hard metals, int. jnl. of fatigue, 23 (2001) 135145. [41] mamiya, e.n., araújo, j.a., fatigue limit under multiaxial loadings: on the definition of the equivalent shear stress, mechanics research communications, 29 (2002) 141-151. [42] banvillet, a., palin-luc, t., lasserre, s., a volumetric energy based high cycle multiaxial fatigue criterion, int. jnl. of fatigue, 25 (2003) 755-769. [43] cruz, i., zouain, n., a shakedown model for high-cycle fatigue, fatigue fract. engng. mater. struct., 26 (2003) 123135. [44] gonçalves, c.a., araújo, j.a., mamiya, e.n., a simple multiaxial fatigue criterion for metals, comptes rendus mécanique, 332 (2004) 963-968. [45] gonçalves, c.a., araújo, j.a., mamiya, e.n., multiaxial fatigue: a stress based criterion for hard metals, int. jnl. of fatigue, 27(2005) 177-187. [46] liu, y., mahadevan, s., multiaxial high-cycle fatigue criterion and life prediction for metals, int. jnl. of fatigue, 27 (2005) 790-800. [47] ninic, d., a stress-based multiaxial high-cycle fatigue damage criterion, int. jnl. of fatigue, 28 (2006) 103-113. [48] ninic, d., stark, h.l., a multiaxial fatigue damage function, int. jnl. of fatigue, 29 (2007) 533-548. [49] braccesi, c., cianetti, f., lori, g., pioli, d. (2008). int. jnl. of fatigue 30, 1479-1497. [50] papuga, j., růžička, m., two new multiaxial criteria for high cycle fatigue computation, int. jnl. of fatigue, 30 (2008) 58-66. [51] shariyat, m., three energy-based multiaxial hcf criteria for fatigue life determination in components under random non-proportional stress fields, fatigue fract. engng. mater. struct., 32 (2009) 785-808. [52] li, b., reis, l., de freitas, m., comparative study of multiaxial fatigue damage models for ductile structural steels and brittle materials, int. jnl. of fatigue, 31 (2009) 1895-1906. [53] zhang, c.-c., yao, w.-x., an improved multiaxial high-cycle fatigue criterion based on critical plane approach, fatigue fract. engng. mater. struct., 34 (2011) 337-344. [54] carpinteri, a., spagnoli, a., vantadori, s., multiaxial fatigue assessment using a simplified critical plane-based criterion, int. jnl. of fatigue, 33 (2011) 969-976. [55] kenmeugne, b., soh fotsing, b.d., anago, g.f., fogue, m., robert, j.-l., kenne, j.-p., on the evolution and comparison of multiaxial fatigue criteria, international journal of engineering and technology, 4 (2012) 37-46. [56] augustins, l., an empirical multiaxial high cycle fatigue criterion for automotive cylinder head design, engineering failure analysis, 28 (2013) 264-274. [57] matsubara, g., nishio, k., multiaxial high-cycle fatigue criterion considering crack initiation and non-propagation, int. jnl. of fatigue, 47 (2013) 222-231. [58] golos, k.m., debski, d.k., debski, m.a., a stress-based fatigue criterion to assess high-cycle fatigue under in-phase multiaxial loading conditions, theoretical and applied fracture mechanics, 73 (2014) 3-8. << /ascii85encodepages false /allowtransparency false /autopositionepsfiles true /autorotatepages /none /binding /left /calgrayprofile (dot gain 20%) /calrgbprofile (srgb iec61966-2.1) /calcmykprofile (u.s. web coated \050swop\051 v2) /srgbprofile (srgb iec61966-2.1) /cannotembedfontpolicy /error /compatibilitylevel 1.4 /compressobjects /tags /compresspages true /convertimagestoindexed true /passthroughjpegimages true /createjobticket false /defaultrenderingintent /default /detectblends true /detectcurves 0.0000 /colorconversionstrategy /cmyk /dothumbnails false /embedallfonts true /embedopentype false /parseiccprofilesincomments true /embedjoboptions true /dscreportinglevel 0 /emitdscwarnings false /endpage -1 /imagememory 1048576 /lockdistillerparams false /maxsubsetpct 100 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can be opened with acrobat and adobe reader 5.0 and later.) >> /namespace [ (adobe) (common) (1.0) ] /othernamespaces [ << /asreaderspreads false /cropimagestoframes true /errorcontrol /warnandcontinue /flattenerignorespreadoverrides false /includeguidesgrids false /includenonprinting false /includeslug false /namespace [ (adobe) (indesign) (4.0) ] /omitplacedbitmaps false /omitplacedeps false /omitplacedpdf false /simulateoverprint /legacy >> << /addbleedmarks false /addcolorbars false /addcropmarks false /addpageinfo false /addregmarks false /convertcolors /converttocmyk /destinationprofilename () /destinationprofileselector /documentcmyk /downsample16bitimages true /flattenerpreset << /presetselector /mediumresolution >> /formelements false /generatestructure false /includebookmarks false /includehyperlinks false /includeinteractive false /includelayers false /includeprofiles false /multimediahandling /useobjectsettings /namespace [ (adobe) (creativesuite) (2.0) ] /pdfxoutputintentprofileselector /documentcmyk /preserveediting true /untaggedcmykhandling /leaveuntagged /untaggedrgbhandling /usedocumentprofile /usedocumentbleed false >> ] >> setdistillerparams << /hwresolution [2400 2400] /pagesize [612.000 792.000] >> setpagedevice microsoft word numero 1 art 2.doc r..l. colombo et al., frattura ed integrità strutturale, 1 (2007) 19-24 19 1 introduzione che l'uomo primitivo avesse nozione dell'esistenza dei gas è altamente dubbio. al contrario, egli certamente conosceva la differenza fra liquidi e solidi. per lui, i liquidi non offrivano praticamente nessuna resistenza alla deformazione, mentre i solidi la offrivano. la ragione di questa differenza di comportamento per molto tempo eluse la sua capacità di riflessione. nell'antica grecia, democrito (460-370 a.c.) ed epicuro (341-270 a.c.) tentarono di risolvere il problema. poichè la maggior parte dei loro lavori è andata perduta, noi sapremmo ben poco di quel che scrissero se non fosse stato per lucrezio (94-50 a.c.), un grande poeta latino mancante tuttavia di qualsiasi originalità scientifica, che riferì il pensiero di epicuro nel suo "de rerum natura": i solidi sono così resistenti perchè gli atomi che li costituiscono sono legati da uncini o "ami" [1]. ciò può sembrare piuttosto ingenuo all'uomo moderno, ma fino a questo secolo ben poco progresso venne fatto in questo campo: nei fatti, la teoria della coesione nei solidi, così come la conosciamo oggi, è parte della fisica dei solidi e necessita di concetti di meccanica quantistica. 2 leonardo tutti sanno che la fisica sperimentale, almeno ai suoi inizi, è una conquista del rinascimento italiano. crediamo che il primo uomo ad occuparsi della resistenza dei solidi agli sforzi sia stato leonardo da vinci (1453-1519), che certamente trasse profitto da molte visite agli arsenali italiani, tra i quali quello di venezia ebbe la più alta reputazione che gli meritò una citazione da parte di dante nella sua commedia. nel folio 325 del "codex atlanticus" [2] si legge: sperienza della forza che può fare un filo di ferro di varie lunghezze ricordo come tu debbi fare sperienzia del reggere, o vero quanto peso po sostenere uno filo di ferro; alla quale sperienzia terrai questo modo: appicca uno filo di ferro di lunghezza di 2 braccia, o circa, in loco che stia forte; di poi li appicca uno cavagno, o sporta, o quello che a te pare, nel quale, per uno picciolo buso, verserai una tramoggia di minuta rena; e quando esso filo di ferro non potrà più sostenere, si rompa, adatta una molletta che subito el buso della tramoggia si riserri, acciò che più rena non caggi in esso cavagno, il quale caderà in piè, perchè ½ dito caderà da alto; e nota quanto peso fu quello che esso filo spezzò, e nota in che parte di sè detto filo si rompe, e fa più volte questa pruova, per confermare se sempre ‘n un medesimo loco si rompe. di poi fa esso filo più corto la metà di prima, e nota quanto peso sostiene di più; e poi lo fa 1/4 della prima lunghezza, e così di mano in mano farai in diverse lunghezze, notansulla storia degli studi di frattura in italia roberto l. colombo consulente, pino torinese (to) donato firrao politecnico di torino, dipartimento di scienza dei materiali ed ingegneria chimica, corso duca degli abruzzi 24, 10129 torino riassunto: la storia degli studi sulla frattura è inestricabilmente connessa con il progresso della tecnologia. all'inizio pochissimo fu scritto. dobbiamo riconoscere a leonardo e galileo il merito di essere stati fra i primi a scrivere su questo problema e sui modi di misurare e prevedere carichi di rottura. più tardi, scienziati italiani si distinsero nel tentativo di stabilire leggi sulla resistenza dei materiali e sui criteri di rottura sotto sforzi multipli. in questa memoria si descrivono i lavori degli scienziati italiani dei secoli scorsi e si confrontano con i lavori di altri scienziati europei del passato. abstract. history of studies of fracture is inherently intermingled with the history of technology developments. in the beginning very little was written about. we must credit leonardo and galileo as the first ones that wrote about the problem and on how to measure and foresee rupture loads. later, nineteenth century italian scientists distinguished themselves in attempting to establish material laws and multiple stresses rupture criteria. a review of the works of past centuries italian scientists is presented, along with a critical comparison with the work of other past european scientists. parole chiave: leonardo, galileo, cavalli, curioni, beltrami, storia degli studi di frattura, criteri di frattura. r. l. colombo et al., frattura ed integrità strutturale, 1 (2007) 19-24 20 do il peso che ciascuno rompe e ‘l loco dove si rompe... ci vorranno secoli prima che un esperimento così accurato con una apparecchiatura così sofisticata venga fatto o almeno progettato (non sappiamo se leonardo lo eseguì mai davvero). in ogni modo è sorprendente che tanta attenzione venga dedicata alla lunghezza del filo, che noi sappiano irrilevante, piuttosto che al suo diametro. possiamo offrire solamente due spiegazioni: una è che ai tempi di leonardo la misura del diametro di un filo sottile di una data lunghezza fosse molto difficoltosa, l'altra che i fili fossero sovente difettosi per insufficienze tecnologiche e che la probabilità di avere difetti di dimensioni rilevanti fosse più alta in una certa lunghezza di filo e più bassa in fili di lunghezza inferiore, i quali quindi raggiungerebbero carichi di rottura più elevati. se questa seconda interpretazione fosse quella valida, potremmo considerare leonardo un diretto precursore delle teorie probabilistiche di frattura. in un' altra parte del codex leonardo si dilunga sulle resistenze relative di colonne di forma differente e sulla posizione delle rotture. leggendo leonardo bisogna por mente al fatto che egli non è a rigore nè uno scienziato, nè un filosofo, ma bensì un uomo dotato di una straordinaria curiosità per i fatti della natura, che egli riferisce in una serie di aforismi piuttosto che in trattati accademici, come avrebbe fatto galileo, e che molto spesso non si preoccupò di giustificare teoricamente [3]. secondo paolo rossi [4] la sua indagine, sempre oscillante fra l’esperimento e l’annotazione, non ha alcun interesse a lavorare ad un corpus sistematico di conoscenze; per tale ragione le sue intuizioni spesso incredibili ai nostri occhi sono qualche volta accompagnate da ciò che noi giudichiamo errori. 3 galileo galileo galilei (1564-1642) è universalmente considerato il fondatore della fisica sperimentale, che egli perseguì attivamente, quasi devotamente, in contrasto con l'aristotelismo imperante ai suoi tempi. il problema della rottura fu uno di quelli che attrassero la sua attenzione. egli ne trattò nel suo "discorsi e dimostrazioni matematiche intorno a due nuove scienze" [5], libro scritto nel medesimo stile del più famoso "dialogo sopra i due massimi sistemi del mondo" [6]: cioè una conversazione immaginaria tra tre persone, salviati, sagredo e simplicio, le prime due scienziati-filosofi morti giovani poco prima l'apparire dei due trattati, l'ultimo avente il nome, ovviamente significativo, di un filosofo aristotelico del vi secolo d.c., si ignora se attribuito realmente a qualche contemporaneo o semplicemente fantastico. la conversazione va avanti per tre giorni, dei quali quello che ci interessa è il secondo. simplicio incomincia pretendendo che la resistenza di una fune o di una trave dipenda dalla sua lunghezza, un' affermazione condivisa a quei tempi da molte persone intelligenti, tra cui, come abbiamo visto, leonardo. salvati non ha difficoltà a mostrarne l'infondatezza. in seguito egli si dimostra sorpreso dal fatto che, se si sospende la trave in qualche posto con un peso all'estremità (fig. 1), essa si romperà con un carico molto superiore a quello che causerà la rottura nel caso in cui fosse stata incastrata orizzontalmente in un muro di mattoni (fig. 2). figura 1. prova di trazione di una colonna (galilei [5], p.7). figura 2. prova di flessione di una trave (galilei [5], p. 128) queste sono evidentemente le condizioni che oggi chiamiamo di trazione e di flessione. sembra ovvio che galileo non avesse una chiara comprensione delle sollecitazioni che si manifestano sotto differenti condizioni di r. l. colombo et al., frattura ed integrità strutturale, 1 (2007) 19-24 21 carico. in ogni modo, usando brillanti analogie, egli viene alla conclusione che il carico (non la tensione) di rottura è inversamente proporzionale alla lunghezza l della trave e direttamente proporzionale al cubo del raggio della sua sezione (se cilindrica, altrimenti egli sarebbe bene in grado di distinguere fra il ruolo dell'altezza e quello della larghezza). ora, consideriamo un campione cilindrico di raggio r ed un prisma parallepipedo avente una sezione di altezza h e larghezza b. sappiamo dalla teoria dell'elasticità che al limite elastico, σ0, il carico è p = (r3/2l) σ0 (cilindro) (1) e p = (bh2/6l) σ0 (prisma) (2) così che noi siamo subito colpiti dalla somiglianza di queste espressioni (che, non dimentichiamolo, sono valide solo in campo elastico, certamente non fino allo snervamento e men che meno alla rottura torneremo su questi concetti in seguito) con le proporzionalità di galileo. ma galileo non si preoccupava nè del carico al limite elastico, nè dello snervamento. prima di tutto, egli non sapeva nulla dell'elasticità, che è la proprietà per cui se un carico agisce su di un corpo, il corpo da parte sua agisce sul carico. in più, come abbiamo visto, non aveva alcuna chiara visione delle tensioni. si deve ricordare, come abbiamo detto, che ciò che lo preoccupava era il calcolo del carico di rottura ed in questo proposito egli fallì completamente, seppure scusabilmente. gordon [7] spiega che gli scienziati del passato erano confusi dall'analogia col comportamento degli animali (inclusi gli uomini). se uno sostiene un peso di qualche sorta, generalmente non si vedono deformazioni nel suo corpo (per quanto naturalmente qualche deformazione avrà luogo nel suo scheletro). ma uno allora reagisce al peso mettendo i suoi muscoli in tensione, e questo lo stanca e produce un certo lavoro, sicchè alla fine deve smettere e deporre il peso. d'altro canto dobbiamo far credito a galileo della prima osservazione scritta (primo giorno) del fatto che sotto trazione travi più grandi sostengono carichi più elevati e col primo disegno di una prova di trazione su di un corpo di grande sezione (fig. 1). tuttavia egli non riuscì a trasferire questo concetto alla flessione, perchè oltre tutto gli mancava il concetto di asse neutro. certamente ci ha dato anche le prime immagini di quanto può essere considerata una prova di flessione su tre punti (fig. 3). una notazione curiosa ci viene dall’esame del volume originale di galileo. i suoi editori in leyda, dove il suo manoscritto arrivò in maniera probabilmente avventurosa e ufficialmente a sua insaputa [4] (probabilmente solo ufficialmente; non possiamo essere in contrasto con quanto in maniera provocatoria illustra brecht nella “vita di galileo”1), sono gli elfevirii, i quali ancora oggi continuano 1brecht, nella scena quattordicesima, riporta il dialogo fra galileo ed il suo discepolo, andrea sarti, figlio della serva, il quale si prepara a partire per a pubblicare di frattura sotto la traslitterazione moderna di elsevier. fra l’altro sono gli editori degli atti dei congressi quadriennali sulla frattura. figura 3. modi di rottura sotto flessione (galilei [5], p. 133). 4 hooke, newton e young non possiamo passare a prendere in considerazione scienziati italiani in secoli posteriori senza riferire di altri grandi scienziati che diedero inizio al lavoro che condusse alla scoperta dell'elasticità. l'elasticità non è altro che un aspetto del principio di azione e reazione di isacco newton (1642-1727), per quanto questi apparentemente non se ne accorgesse: il carico agisce su un solido deformandolo ed il solido reagisce opponendovisi. l'uomo che se ne accorse fu robert hooke (1635-1702), che per questo è considerato il padre della teoria dell'elasticità. nel 1660, riflettendo sull'opera di un amico che era un famoso orologiaio, egli annunciò i suoi risultati nel seguente anagramma: ceiiinosssttvv fortunatamente, nel 1676 (!) in un trattato intitolato "de potentia restitutiva" egli risolse così l'anagramma: vt tensio sic vis certamente e. mariotte (1620-1684) disse qualcosa sull'elasticità lineare entro il 1676, ma non prima del 1660, inoltre non tentò di risolvere l'anagramma dello hooke. per questo noi consideriamo costui, e non il mariotte, padre (forse sarebbe meglio dire nonno) della teoria dell'elasticità. tuttavia lo hooke con la parola "tensio" non intese quello che oggi intendiamo noi, ma piuttosto "estensione", cioè, in parole povere, "allungamento". nei fatti, egli comprese l'elasticità, ma non quello che noi intendiamo per tensione. questo perchè egli si disinteressò della forma e delle dimensioni del solido di cui andava occupandosi. inoltre egli non si accorse che la sua legge era valida solamente nel campo che noi chiamiamo elastico. ci ritorneremo su. l’olanda con il manoscritto dei “discorsi” sotto il mantello. andrea sarti non sembra essere una figura storica, ma introdotta perché nel populismo brechtiano il messaggero doveva essere, appunto, “figlio della serva”. r. l. colombo et al., frattura ed integrità strutturale, 1 (2007) 19-24 22 thomas young (1773-1829) ebbe senza alcun dubbio una chiara comprensione delle tensioni. nel 1807 era stato appena licenziato dalla royal society perchè il suo lavoro non era considerato abbastanza pratico (per fortuna fu presto assunto dal bureau des longitudes). in quell'anno egli annunziò la legge che porta il suo nome, cioè: σ / ε = e (3) dove σ e and ε sono ciò che noi chiamiamo tensione e deformazione. il coefficiente di proporzionalità e prende il nome di modulo di young o di elasticità. l'invenzione del modulo di young fu un fatto rivoluzionario ed il primo anello di una catena che in una ventina d'anni consentì di sviluppare la scienza dell'elasticità su basi rigidamente matematiche. come abbiamo suggerito, la legge di hooke è valida soltanto nel campo elastico, cioè fino al cosiddetto limite elastico o di proporzionalità. in seguito la deformazione cresce più rapidamente, cioè il materiale si snerva. alla fine si raggiunge un massimo nella tensione ingegneristica ed il solido incomincia a rompersi. 5 cavalli mentre gli scienziati si occupavano di sviluppare la matematica della teoria dell'elasticità usando l'analisi differenziale, introdotta dal newton e da gottfried wilhelm leibniz (1646-1716), l'interesse per lo snervamento e la rottura andava scemando. chi tentò di affrontare il problema, sebbene in maniera un po' rozza, fu giovanni cavalli (1807-1879). quando era capitano di artiglieria nell'esercito del re di sardegna, egli inventò un cannone a retrocarica e soprattutto il cannone a canna rigata, ed oggi è ricordato solo per questo, il che è francamente ingiusto. sebbene egli si occupò soprattutto di problemi di carattere militare (in seguito raggiunse il grado di generale nell'esercito italiano, divenne direttore della scuola di artiglieria, fu deputato al parlamento ed infine senatore del regno), condusse importanti studi di ingegneria e di meccanica fondamentale: per esempio, con federigo menabrea e carlo mosca fu membro del comitato di consulenza per la geologia creato dal ministro dei lavori pubblici pietro paleocapa per il traforo del frejus. in tre memorie [8, 9, 10] egli esprime il dubbio che la legge di proporzionalità dello hooke possa non esser mai interamente valida, specialmente per certi materiali, tra i quali egli cita la ghisa ed il ferro, ed in ogni modo sicuramente non oltre una certa tensione, cioè il limite elastico, al di là della quale hanno luogo deformazioni permanenti. nell'insieme egli esprime diverse leggi: 1 la proporzionalità fra carico e deformazione non esiste in maniera assoluta per la ghisa ed il ferro dolce, se non al massimo per tensioni fra 0 e la metà del carico di rottura. 2 un allungamento permanente ha luogo già sotto i carichi più bassi; il punto in cui la deformazione cresce molto più rapidamente che secondo la legge di hooke è altamente variabile anche in ferri della stessa provenienza. in conseguenza, il limite elastico, se esiste, perde qualsiasi rilevanza pratica. 3 omissis 4 omissis 5 ferro e ghisa non sottoposti ad urti e vibrazioni sopportano indefinitamente tensioni vicine alla tensione di rottura istantanea. 6 le formule di resistenza in uso devono essere emendate. nel 1846 il cavalli costruì una macchina di flessione, che sotto molti aspetti sembrava una macchina di rilassamento tipo denyson, eccetto che il carico veniva applicato deponendo gentilmente dei pesi crescenti, e munita di un sistema di registrazione. nei suoi esperimenti egli credette di poter distinguere due parti della deformazione, una elastica e reversibile, l'altra irreversibile dalla partenza e poi fino alla rottura: entrambe seguono leggi differenti, ma uniformemente regolari. tra i pesi deposti, egli ne scopre uno, che la provetta non può sopportare stabilmente perchè al di sopra di esso incomincia un rilassamento, che poi accelera man mano che si avvicina la rottura, e questo anche se la durata della prova è breve. come oggi sappiamo, questo rilassamento è una conseguenza dello snervamento, ma il cavalli, cui va anche il merito di aver posto attenzione a un fenomeno come l'incrudimento, credette di aver scoperto una legge di natura. egli propose che al carico intermedio che abbiamo appena descritto venisse dato il nome di limite di stabilità e che esso venisse usato nei calcoli di ingegneria al posto del limite elastico. 6 curioni molti tentarono di estendere la formula che fornisce il limite elastico alla tensione di rottura σr , scrivendo: σr = αpl/(bh2) (4) dove α è una costante numerica. galileo la pose uguale a 2, baumgarten a 2,5, hodkinson & fairbain a 2,63, leibniz a 3 ed infine navier a 6, cioè quest’ultimo trascurò completamente l'influenza della plasticizzazione. a molti sembrava possibile eliminare le incongruenze ammettendo semplicemente che al di sopra del limite elastico l'asse neutro non fosse più baricentrico, cioè che le caratteristiche meccaniche in trazione e compressione non fossero più uguali. presto si scoprì negli stati uniti che α non era per nulla una costante, il che significava che o la teoria era sbagliata o gli esperimenti in difetto. giovanni curioni (1831-1887) incominciò la sua carriera come allievo del mosca, che abbiamo già incontrato come membro del comitato di consulenza per il traforo del frejus e che progettò il ponte in muratura sulla dora r. l. colombo et al., frattura ed integrità strutturale, 1 (2007) 19-24 23 riparia a torino: a quel tempo, era considerata un'impresa rischiosa, così il mosca rimase sotto il ponte durante le prove di carico, per mostrare la sua fiducia nei suoi calcoli. a tempo debito, il curioni divenne professore della scuola di applicazione per gli ingegneri e del politecnico di torino e poi direttore di quest’ultimo e scrisse un libro col titolo: "resistenza dei materiali e stabilità delle costruzioni" [11]. marchis e jarre [12] ricordano che costruì un buon numero di macchine di prova differenti fino al 1880. il curioni definisce accuratamente le tensioni di snervamento e di rottura: "lo snervamento ha luogo nei corpi soggetti a forze esterne quando queste, crescendo al di sopra di un certo limite, hanno prodotto un tale spostamento molecolare che non è più possibile che le molecole spostate, mentre restano sotto l'azione delle dette forze, si riaggreghino in un nuovo stato di equilibrio stabile, il che quindi col tempo produce una disaggregazione totale, cioè la rottura. la rottura può aver luogo pressocchè immediatamente all'applicazione delle forze esterne, se sono abbastanza grandi." il curioni fece anche delle osservazioni interessanti sull'influenza del tempo, dichiarando: a) una forza esterna, che non produce snervamento in un corpo in cui è applicata, può farlo se la sua azione si prolunga per un tempo abbastanza grande; b) una forza esterna, che non può rompere un corpo dopo aver agito su di esso per breve tempo, può romperlo dopo un tempo supplementare; c) forze esterne intermittenti ripetute abbastanza frequentemente possono produrre lo stesso effetto di un'azione continua. oggi chiamiamo questi effetti rilassamento meccanico, frattura ritardata e fatica. e' interessante notare che due degli studiosi che abbiamo già nominato a proposito della tensione di rottura, e cioè e.a. hodkinson [13] e w. fairbain [14], sono fra i pionieri nello studio di quella che diventerà la scienza della fatica. 7 beltrami quando un corpo sottoposto ad un certo sistema di forze si snerva o si rompe (nei fatti, quando inizia lo snervamento massiccio, la rottura finisce col seguirne)? l'idea più semplice apparve ritenere che ciò succede quando la tensione di trazione raggiunge un certo valore, che è il carico di snervamento. al di fuori della trazione pura, questo non è vero. così sono stati introdotti numerosi criteri [15]. fra questi il criterio di tresca (in verità inventato dal coulomb) suggerisce che lo snervamento ha luogo quando la tensione tangenziale risolta raggiunge un certo valore. nel caso della torsione pura, cioè quando delle sei componenti della tensione soltanto τxy è diversa da 0, si trova: σs = 2τs (5) cioè: τs = 0,5σs (6) di solito sperimentalmente si trova un valore più alto (0,58). tuttavia il criterio di tresca è ancora usato in ragione della sua semplicità. eugenio beltrami (1835-1900) fu professore di algebra complementare e geometria analitica nell'università di bologna, poi di geodesia a pisa, quindi di meccanica razionale ancora a bologna e poi a roma con l'incarico ulteriore di analisi superiore, di fisica matematica e meccanica superiore a pavia, infine di meccanica e fisica matematica di nuovo a roma. nel suo peregrinare scientifico oltre che accademico, partendo dalla geometria analitica, si avvicinò progressivamente alla teoria dell’elasticità sulla scia di lamé, de saint-venant e neumann [16]. sulla scorta dei suoi studi sulle funzioni potenziali, beltrami si occupò a fondo del potenziale d’elasticità in una serie serrata di studi [17, 18, 19, 20]. egli arrivò così ad ipotizzare che, allorchè l'energia potenziale di deformazione raggiunge un massimo, si perviene ad un equilibrio instabile che comporta uno snervamento generalizzato a cui segue la rottura. l'energia potenziale volumica ϕ è: ϕ = (1/2e)(σid2) = [(1+1/m)/e]τxy2 (7) dove m è il modulo di poisson, approssimativamente uguale a 10/3. di qui: τs = 0,62σs (8) questo fattore non è ancora soddisfacente, ma il criterio di beltrami (nel mondo anglo-sassone individuato come criterio di haig) è importante perchè è il primo basato sul concetto di energia piuttosto che su quello di tensione o deformazione. oggi esso è sostituito da quello dovuto a richard von mises, che notò come una pressione puramente idrostatica, per quanto elevata, non conduca allo snervamento, e quindi adottò un criterio analogo a quello di beltrami, ma prendendo in considerazione solo quella parte delle tensioni che producono distorsione e non dilatazione (o contrazione). il criterio di von mises fornisce il valore corretto per il rapporto τs/σs = 0,58. 8 dal 900 ad oggi da quei tempi ormai remoti, il lavoro sulla frattura ha fatto progressi in italia come in qualsiasi altro paese. poichè un corpo completo di cognizioni teoriche come quello sviluppato da g.r. irwin sulla meccanica della frattura statica doveva attendere i tardi anni '50, molto dello sforzo compiuto nella prima metà di questo secolo fu de r. l. colombo et al., frattura ed integrità strutturale, 1 (2007) 19-24 24 dicato alla fatica, che venne presto riconosciuta come la causa della rottura della maggior parte dei pezzi meccanici. la rapida crescita della fiat auto spinse la ricerca in questo campo nei suoi laboratori centrali sotto la guida di l. locati, scomparso pochi anni fa. più tardi, un certo lavoro sulla meccanica della frattura iniziò da qualche luogo senza tuttavia essere inserito in uno sforzo coordinato. per esempio, s. venzi & a.h. priest [21] scoprirono che nei primi stadi delle prove di resilienza l'influenza dell' inerzia è tanto importante quanto la reazione delle incudini, di modo che la significatività dei risultati per solidi molto fragili finisce per scemare grandemente. la ricerca post-irwin iniziò al centro sperimentale metallurgico a roma ad opera di un gruppo di giovani ricercatori, principalmente s. venzi, m. mirabile, g. buzzichelli e m. castagna, sotto la direzione di p. brozzo. nel 1982 gli autori della presente memoria con numerosi compagni e per impulso di g. caglioti, fondarono a torino il gruppo italiano frattura come foro per la circolazione di idee ed applicazioni e come punto di incontro per scienziati di tutte le nazioni, che sono affluiti numerosi ai suoi congressi e giornate di lavoro. 9 conclusioni il contributo degli scienziati italiani all'insieme della ricerca sulla frattura risale ai tempi di roma antica: parole come "duttile" e "fragile" si trovano già nella "naturalis historia" di plinio il vecchio (23-79 d.c.) e riflettono quell'abitudine all'osservazione che aprì la strada, dopo la rivoluzione culturale dell'umanesimo, ai grandi scienziati del rinascimento e del principio dell'età moderna. nel secolo scorso sono emersi contributi importanti da quella culla della scienza ingegneristica che fu a quei tempi l'accademia delle scienze di torino, dove gli scienziati poterono anche condurre esperimenti sfruttando i progressi tecnologici dell'arsenale locale. abbiamo cercato di illustrare questi successi storici del nostro paese, dedicando minore attenzione agli sviluppi più recenti. abbiamo pensato infatti che il nostro contributo di storici autodidatti potesse giovare ai giovani ricercatori per fornire un senso dello sviluppo storico che li ha portati alle moderne teorie della meccanica della frattura, iniziate con g.r. irwin a metà di questo secolo. 10 bibliografia [1] lucretius t. caro, “de rerum natura“ (57 a.c.). testo latino con trad. ital. di e. cetrangolo, sansoni, firenze, 1978. [2] l. da vinci, , “codex atlanticus” (1483-1518) biblioteca ambrosiana milano. pinnati, milano, 1894-1904. [3] j. recupero, , “selezione di scritti di leonardo da vinci”, editrice italiana di cultura, roma (1966). [4] p. rossi “la nascita della scienza moderna in europa”, laterza, bari (1997). [5] g. galilei, , “discorsi e dimostrazioni sopra due nuove scienze attenenti alla mecanica & i movimenti locali”, elsevirii, leida (1638). [6] g. galilei, “dialogo sui due massimi sistemi del mondo”, 1632, einaudi, torino (1990). [7] j.e. gordon, “the new science of strong materials”, penguin book, harmondsworth (1971). [8] g. cavalli, , “memoria su vari perfezionamenti militari”. mem. acc. sci. torino, xvii, serie ii (1858) 1. [9] g. cavalli, “memoria sul delineamento equilibrato degli archi in muratura ed in armatura”, mem. acc. sci. torino, xix, serie ii (1859) 143. [10] g. cavalli, “mémoire sur la théorie de la resistance statique e dinamique des solides (surtout aux impressions comme celle du tir des canons)”, mem. acc. sci. torino, xxii, serie ii (1863) 157. [11] g. curioni, “resistenza dei materiali e stabilità delle strutture”, augusto federico negro, torino (1874). [12] v. marchis, g. jarre, “accademici o tecnologi?”, in: società e scienza. 200 anni di storia dell'accademia delle scienze di torino, allemandi & c., p.92, torino (1988). [13] w. fairbairn, phil., trans. roy. soc., (1864) 311 [14] e.a. hodkinson, ponts et chaussées, (1851) 193. [15] c. brutti, “costruzioni di macchine”, parte i (resistenza dei materiali). dispense ciclostilate dalle lezioni universitarie, roma (1947). [16] e. beltrami, “sulle equazioni generali dell’elasticità”, ann. mat. pura appl., x, serie ii (188082) 188. [17] e. beltrami, , “sulla rappresentazione delle forze newtoniane per mezzo di forze elastiche”, rend. r. ist. lombardo, xvii, serie ii (1884) 581. [18] e. beltrami, “sull’uso delle coordinate curvilinee nelle teorie del potenziale e dell’elasticità”, mem. r. acc. sc. ist. bologna, vi, serie iv (1884) 401. [19] e. beltrami, “sulle condizioni di resistenza dei corpi elastici“, rend. r. ist. lombardo, xviii, serie ii (1885) 704. [20] e. beltrami, “sull’interpretazione meccanica delle formole di maxwell”, mem. r. acc. sc. ist. bologna, vii, serie iv (1886) 1. [21] s. venzi, a.h. priest, “influence of inertial load on instrumented impact test”, bisra rep. mg/c/61/68, (1968). microsoft word numero 9 art 2 finale p. lazzarin, frattura ed integrità strutturale, 9 (2009) 13-26; doi: 10.3221/igf-esis.09.02 13 comportamento a fatica dei giunti saldati in funzione della densità di energia di deformazione locale: influenza dei campi di tensione singolari e non singolari paolo lazzarin università di padova, dipartimento di tecnica e gestione dei sistemi industriali, stradella san nicola 3, 36100 vicenza, italia plazzarin@gest.unipd.it riassunto. il criterio della densità di energia di deformazione (sed) considera un preciso volume di controllo posizionato in corrispondenza del piede o della radice dei cordoni di saldatura, ossia delle zone di possibile innesco delle cricche di fatica. modellati i cordoni come intagli a v non raccordati e con diverso angolo di apertura, il volume è riconducibile a un settore circolare nei casi di tensione o deformazione piana, e il raggio vale circa 0.3 mm per i giunti saldati in acciaio strutturale. il valore medio della densità di energia di deformazione dipende essenzialmente dalle distribuzioni singolari nei giunti di medio ed elevato spessore, mentre importante diventa il contributo della t-stress nei giunti di spessore ridotto. entrambi gli effetti sono correttamente computati utilizzando modelli agli elementi finiti, anche utilizzando mesh con un numero ridotto di gradi di libertà. il fatto è di notevole interesse per una possibile applicazione del metodo a strutture saldate di geometria complessa. agli effetti descritti, tipicamente riconducibili a una modellazione piana, si possono accompagnare campi singolari non convenzionali, legati a effetti tridimensionali indotti dalla geometria. l’effetto out-of-plane è qui evidenziato in relazione ai giunti a semplice sovrapposizione. abstract. in the strain energy density (sed) approach for fatigue strength assessments of welded joints a well-defined control volume is considered. this volume surrounds the weld root or weld toe, both modelled like sharp (zero radius) v-notches with different opening angles. the volume becomes a circular sector under plane strain conditions, with the radius being about 0.3 mm for welded joints made of structural steel. the mean value of the sed mainly depends on the singular stress fields when the main plate thickness is large enough, whereas the influence of the t-stress component cannot be neglected in the case of thin-walled welded joints. both contributions are directly accounted for by using finite element models, also when the relevant meshes are quite coarse. this fact makes the application of the sed approach easier than any stress-based approach in the case of complex structures. due to three-dimensional effects, a non conventional out-of-plane singular mode can be present, in addition with respect to modes i and ii of the williams’ solution. this out-of-plane mode, analogous to the mode iii, is discussed here with reference to welded (seam) lap joints under tensile-shear loads. parole chiave. giunti saldati, resistenza a fatica, fattori di intensificazione delle tensioni, densità di energia di deformazione. introduzione e verifiche a fatica delle unioni saldate possono essere condotte con criteri diversi, basati sulle tensioni nominali, sulle tensioni strutturali o di ‘hot-spot’, sulla meccanica della frattura lineare elastica [1]. come criterio locale, le raccomandazioni dell’international welding institute e quelle dell’ente fkm prevedono l’utilizzo del criterio di l http://www.gruppofrattura.it/ http://dx.medra.org/10.3221/igf-esis.09.02&auth=true mailto: plazzarin@gest.unipd.it p. lazzarin, frattura ed integrità strutturale, 9 (2009) 13-26; doi: 10.3221/igf-esis.09.02 14 radaj [2] che vede la resistenza a fatica ad alto numero di cicli di giunti saldati di diversa geometria correlata alle ‘effective notch stresses’, calcolate in corrispondenza di un raggio di raccordo fittizio f = 1.0 mm al piede e alla radice dei cordoni di saldatura. il valore di tale raggio, valido per i comuni acciai da costruzione, è stato determinato da radaj utilizzando l’espressione di neuber *ρsρρ f  . stime basate su un raggio di raccordo reale =0 e su una lunghezza microstrutturale *=0.4 mm (per ‘cast iron’), in combinazione con un fattore di multiassialità costante s = 2.5, si sono dimostrate realistiche per giunti comuni saldati in acciaio strutturale [1,2]. valori sensibilmente inferiori di * sono stati suggeriti per giunti di spessore ridotto saldati a punti o al laser [1]. fra le medologie più recenti per la valutazione di resistenza a fatica delle unioni saldate [1,3] vi è il criterio basato sui fattori generalizzati di intensificazione delle tensioni (‘notch stress intensity factors’, o nsifs), così come formalizzato da lazzarin e tovo [4]. il cordone di saldatura viene modellato come un intaglio a v non raccordato (‘pointed v-notch’,  = 0) e le distribuzioni locali di tensione nelle sezioni piane traversali sono date in funzione dei fattori generalizzati di intensificazione delle tensioni di modo i e di modo ii, k1 and k2. l’assunzione del raggio di raccordo nullo al piede dei cordoni e il legame tra vita a fatica e distribuzione asintotica determinata direttamente dai modelli fem era già presente in due lavori di atzori pubblicati diversi anni prima [5,6]. i fattori k1 e k2 esprimono l’intensità delle distribuzioni di tensione asintotiche in accordo con la soluzione teorica ottenuta da williams, valida nell’ipotesi di tensione o deformazione piana [7]. nei casi in cui si possa assumere in corrispondenza del piede dei cordoni di saldatura un angolo di 135 gradi, che è certamente il valore più comune nei giunti a cordone d’angolo, solo il contributo di modo i è singolare mentre quello di modo ii non lo è (si ricorda infatti che il contributo di modo ii è singolare solo per angoli di apertura inferiori a 102.6°). in questi casi è quindi possibile operare una semplificazione e usare direttamente il range del fattore di modo i, k1, per sintetizzare la resistenza a fatica di giunti a cordone d’angolo aventi differenti geometrie [4,8]. una curva in termini di k1n è possibile non solo nella fatica ad alto numero di cicli (n2x106), ma anche nella vita a termine, e questo perché una larga percentuale della vita di propagazione della cricca di fatica è spesa in propagazione di una cricca corta nella zona governata dalla singolarità dell’intaglio a v non raccordato [8]. il problema del criterio basato sui fattori di intensificazione delle tensioni è che una variazione dell’angolo presente al piede dei cordoni di saldatura impedisce un confronto diretto in termini di nsif. ciò vale ovviamente anche per la radice del cordone di saldatura dove la zona di mancata penetrazione definisce una fessura con angolo di apertura nullo e il fattore k1 torna ad avere le dimensioni dei più convenzionali fattori di intensificazione delle tensioni (sif) della meccanica della frattura lineare elastica, ossia mmpa . un confronto fra geometrie con angoli di apertura diversi può essere ristabilito utilizzando l’energia di deformazione mediata su un volume di controllo centrato sull’apice dell’intaglio a v che modella il piede o la radice dei cordoni di saldatura [9-12]. nei casi piani il volume di controllo diventa un settore circolare di raggio r0, così come rappresentato in fig.1. ovviamente, la densità di energia di deformazione è esprimibile in forma chiusa sulla base dei fattori k1 e k2 che caratterizzano la geometria del giunto e il tipo di sollecitazione, almeno nei casi in cui le distribuzioni di tensione siano strettamente legate ai soli termini aventi il massimo grado di singolarità. a parità di geometria locale e globale, i fattori cambiano in un caso di flessione pura rispetto a un caso di trazione pura [13]. in relazione al valore del raggio di controllo r0, questo è stato determinato riesaminando statisticamente centinaia di dati sperimentali relativi a giunti ottenuti con i più comuni procedimenti di saldatura ad arco. per i giunti saldati in acciaio da costruzione si ha un raggio di controllo r0=0.28 mm, che scende a r0=0.12 mm nel caso di giunti in lega leggera [11,12]. l’utilizzo del valore medio della densità di energia di deformazione in combinazione con un’ipotesi di deformazione piana, giustifica appieno l’utilizzo di un criterio lineare elastico anche nella fatica a medio termine. e’ stato infatti dimostrato [10] come sia possibile estendere a un volume finito che abbraccia l’apice di un intaglio a v non raccordato il criterio di glinka e moski [14] inizialmente formulato come criterio di punto valido solo per l’apice di un intaglio raccordato: l’energia di deformazione nel volume di controllo non cambia in condizioni di snervamento localizzato (‘small scale yielding’) rispetto al caso idealmente lineare elastico. la condizione di snervamento localizzato viene abbandonata molto prima in presenza di sollecitazione di modo iii di quanto non avvenga in presenza di sollecitazione nel piano, e questo può giustificare le diverse pendenze suggerite dalla normative in vigore per i giunti solleciti a trazione e a torsione [15]. un riesame e un confronto tra il criterio di radaj (‘notch rounding approach’) e il criterio basato sulla densità di energia di deformazione, ‘sed approach’, sono attualmente in corso [16,17] e la collaborazione con il prof dieter radaj è estesa anche a questioni teoriche legate alla variabilità del parametro di multiassialità s [18]. nel criterio basato sulla densità di energia di deformazione gioca un ruolo fondamentale il valore del raggio del volume strutturale. il valore di r0 per gli acciai strutturali saldati è stato ottenuto nelle referenze [11,12] usando in combinazione due valori medi sperimentali relativi a 5106 cicli e un rapporto nominale di ciclo r=0; http://www.gruppofrattura.it/ http://dx.medra.org/10.3221/igf-esis.09.02&auth=true p. lazzarin, frattura ed integrità strutturale, 9 (2009) 13-26; doi: 10.3221/igf-esis.09.02 15 1 il valore k1 =211 0.326mpa(mm) per giunti a croce con angolo di apertura 2 = 135° al piede dei cordoni; il range in questione rappresenta un valore medio ottenuto da giunti sollecitati con un rapporto nominale di ciclo r=0; 2 un range di tensione nominalea=155 mpa (r=0, pf=50%) relativo a giunti saldati testa a testa con cordone rasato (vari acciai da costruzione). una sintesi estesa a oltre 900 dati sperimentali, principalmente tratti da giunti a croce con cordone d’angolo portante e non portante) e rotture finali innescate sia al piede sia alla radice dei cordoni è mostrata in fig. 3 [19]. la figura mostra anche la banda di dispersione, così come suggerita in [11] su una base iniziale di circa 300 dati sperimentali. in tutti i casi qui considerati, il piede dei cordoni è modellato come un intaglio a v non raccordato, = 0, che diventa semplicemente una cricca nel caso della radice dei cordoni. fanno eccezione solo alcune serie di giunti saldati testa a testa, per i quali le referenze originali documentavano un raggio di raccordo minimo al piede dei cordoni sensibilmente diverso da zero [20]. la fig. 3 evidenzia come l’indice di dispersione tw, relativo a due diverse probabilità di sopravvi-venza, ps=2.3% e ps=97.7 %, sia pari a 3.3. comunque, l’indice di dispersione diventa 1.50 se riconvertito in termini di range della tensione locale e alle probabilità di sopravvivenza ps=10% e ps=90%, in perfetto accordo con la banda s-n normalizzata di haibach [21]. nel caso invece di giunti in lega leggera, il raggio del volume di controllo diminuisce (r0=0.12 mm) mentre aumenta la pendenza inversa k della banda di dispersione (k=2.0 contro k=1.5 dei giunti saldati in acciaio). e’ interessante notare come, riaggiornando il raggio r0, il valore medio della densità di energia di deformazione resti praticamente invariato rispetto a quello dei giunti saldati in acciaio [12]. una valutazione accurata degli nsif richiede modelli agli elementi finiti con maglia molto fine in modo da poter seguire i forti gradienti di tensione presenti nelle zone prossime ai punti di singolarità; al contrario, il valore medio della densità di energia di deformazione sul volume di controllo può essere determinato accuratamente anche utilizzando modelli a maglia larga [15,22,23]. questo fatto può giocare un ruolo essenziale per l’applicabilità del metodo sed ai componenti di geometria complessa. nel presente contributo, dopo un breve inquadramento analitico del metodo basato sulla densità di energia di deformazione e la presentazione di alcuni esempi applicativi, saranno illustrati alcuni temi aperti, oggetto di analisi ancora in corso. in particolare saranno prese sinteticamente in esame: il problema delle singolarità ‘out-of-plane’ indotte da effetti tridimensionali; la possibile estensione del criterio sed ai giunti di spessore ridotto, a cordone continuo e punti; i legami presenti tra sed, j-integral e fattore teorico di concentrazione delle tensioni, quest’ultimo valutato mediante analisi fem che vedono la radice dei cordoni modellata con un keyhole avente raggio all’apice s=0.05 mm. inquadramento analitico del criterio sed ed esempi applicativi l grado di singolarità dei campi di tensione indotti da intagli a v a spigolo vivo fu analizzato per la prima volta da williams [7] con riferimento a casi piani in presenza di sollecitazioni di modo i e modo ii. quando il raggio di raccordo  è posto pari a zero, gli nsif quantificano l’intensità delle distribuzioni asintotiche presenti vicino all’apice dell’intaglio a v (punto di singolarità). usando un sistema di coordinate polari )( ,r avente l’origine centrata sull’apice dell’intaglio a v (come già evidenziato in fig. 1), i fattori generalizzati di intensificazione delle tensioni di modo i e modo ii possono essere definiti, in accordo con gross e mendelson [24], nella forma seguente: )0(lim2 θθ 1 0 1 1       ,rrk r )0(lim2 rθ 1 0 2 2       ,rrk r (1) lungo la bisettrice dell’intaglio (=0), le componenti di tensione e rr sono disaccoppiate dalla componente r le prime due dipendono dal campo di tensione di modo i, la terza da quello di modo ii. la fig. 2 mostra l’andamento delle tensioni lungo la bisettrice dell’intaglio laterale a v con angolo di apertura di 135 gradi. per una distanza dall’apice dell’intaglio superiore a un decimo dello spessore, le tensioni seguono una variazione lineare in un diagramma con scale doppie logaritmiche. le tensioni  e rr hanno un grado di singolarità che coincide esattamente con quello teorico previsto dalla soluzione di williams ( 326011 . ). la componente rè invece non singolare, e la pendenza, in accordo con la soluzione teorica, vale   302012 . . i http://www.gruppofrattura.it/ http://dx.medra.org/10.3221/igf-esis.09.02&auth=true p. lazzarin, frattura ed integrità strutturale, 9 (2009) 13-26; doi: 10.3221/igf-esis.09.02 16 determinati i fattori k1 e k2 utilizzando le relazioni (1), tutte le tensioni presenti in un generico punto appartenente alla zona governata dalla singolarità posso essere espresse in funzione di k1 e k2. in campo lineare elastico tensioni e deformazioni sono, come ben noto, legate fra loro dalle equazioni di lame’. e’ quindi possibile esprimere la densità di energia di deformazione in qualunque punto prossimo al vertice dell’intaglio e mediare poi la densità di energia nel volume di controllo posto al piede o alla radice dei cordoni di saldatura, come già evidenziato in fig. 1. l t 2a r0 r0  piede del cordone radice del cordone (a)    rr  r   bisettrice dell’intaglio r (b) figura 1: volume (area) di controllo posizionato al piede e alla radice dei cordoni di saldatura (a); sistema di coordinate polari e componenti di tensione (b). in sintesi, considerando condizioni di deformazione piana, la densità di energia di deformazione mediata nel settore circolare di raggio r0 vale [9]: (2) i parametri e1 ed e2 dipendono dall’angolo di apertura dell’intaglio 2 , dall’ipotesi di rottura e dal rapporto di poisson  del materiale [9,25]. per alcuni angoli, la tab. 1 riporta i valori dei parametri nella relazione (2). con =0.3, e1 vale 0.117 quando 2=135° e 0.133 quando 2=0. nel secondo caso, che tipicamente rappresenta quanto avviene alla radice dei cordoni di saldatura, anche la distribuzione di modo ii è singolare. il raggio di controllo mostrato in fig. 3 è stato valutato usando la seguente relazione [9,11,12]: (3) dove i parametri di resistenza a fatica a e k1a (pf=50%) validi a na=5106 cicli a rottura sono stati ricavati sulla base di un ampio numero di dati sperimentali riportati in letteratura. 1 2 2 2 1 1 2 2 1 1 0 0 δ δ δ λ λ e k e k w e r e ré ù é ù ê ú ê ú= + ê ú ê ú ë û ë û 1 1 1 1 1 0.674 1 0 1 a 211 2 2 0.117 0.28 mm σ 155 akr e l-æ ö æ öd ÷ç ÷ç÷= ´ = ´ ´ =ç ÷ç÷ ÷çç ÷ç è ødè ø http://www.gruppofrattura.it/ http://dx.medra.org/10.3221/igf-esis.09.02&auth=true p. lazzarin, frattura ed integrità strutturale, 9 (2009) 13-26; doi: 10.3221/igf-esis.09.02 17 distanza lungo la bisettrice, r [mm] 0.5 t 0.5 t 0.5 t r 0.01 0.1 1 0.0001 0.001 0.01 0.1 1 10 n rn rn c om p o ne n ti d i te ns io n e/ te n si o n e n om in al e 10 100 t=10 mm n figura 2: componenti di tensione di modo i e di modo ii lungo la bisettrice dell’intaglio [4]. tabella 1: valori dei parametri presenti nell’equazione (2); e1 ed e2 ottenuti in ipotesi di deformazione piana utilizzando l’ipotesi di beltrami (criterio della densità di energia di deformazione totale) e un rapporto di poisson 0.3. figura 3: resistenza a fatica di giunti saldati in acciaio in funzione del valore medio della densità di energia di deformazione [19]; banda di dispersione definita da valore medio  2 deviazioni standard [11]; piatti principali di spessore t variabile tra 6 e 100 mm; piatti trasversali di spessore variabile tra 3 e 220 mm; rotture innescate in corrispondenza del piede o della radice dei cordoni di saldatura; per le geometrie, i materiali e le tecnologie si vedano le referenze [12,20, 22, 25]. 2rad] 1 2 e1 e2 0 0.5000 0.5000 0.134 0.341 /2 0.5445 0.9085 0.146 0.168 2/3 0.6157 1.1489 0.130 0.129 3/4 0.6736 1.3021 0.117 0.112 http://www.gruppofrattura.it/ http://dx.medra.org/10.3221/igf-esis.09.02&auth=true p. lazzarin, frattura ed integrità strutturale, 9 (2009) 13-26; doi: 10.3221/igf-esis.09.02 18 0.01 0.1 1 10 104 10 5 106 10 7 cicli a rottura, n v al o re m ed io d el la d en si tà d i en er g ia d i d ef o rm az io n e  w [n m m /m m 3 ] petershagen (1992), r=0, r= 1 yakubovskii e valteris (1989), r0 hentschel et al. (1999), r 0.2 r0= 0.28 mm a n=2x106 cicli: w50% = 0.105 nmm/mm 3 tw = 3.3 slope k=1.5 figura 4: resistenza a fatica di giunti saldati testa a testa in funzione del valore medio della densità di energia di deformazione [20]; confronto con la banda di dispersione riportata in [11]. figura 5: resistenza a fatica di giunti saldati tridimensionali in funzione del valore medio della densità di energia di deformazione [22]; dati originali dovuti a fricke and doerk (2006). figura 6: resistenza a fatica di giunti saldati tridimensionali in funzione del valore medio della densità di energia di deformazione [22]; dati originali dovuti a (fricke and doerk, 2006) e a ferreira et al. (1995). 0.01 0.1 1 10 1.00e+04 1.00e+05 1.00e+06 1.00e+07 cycles to failure, n  w [ n m m / m m 3 ] fricke and doerk, 2006, failure from the weld root (as-welded) fricke and doerk, 2006, failure from the weld toe (stress-relieved) fricke and doerk, 2006, failure from the weld root (stress-relieved) r0=0.28 mm k=1.5 tw=3.3 atx cycles: w = 0.105 [nmm/mm3] r=0 0.01 0.1 1 10 1.00e+04 1.00e+05 1.00e+06 1.00e+07 cycles to failure, n  w [ n m m / m m 3 ] fricke and doerk, 2006; r=0, 0.5, failure from the weld root (as-welded) fricke and doerk, 2006; r=0, 0.5, failure from the weld toe (as-welded) fricke and doerk, 2006; r=0, failure from the weld root (stress-relieved) ferreira et al., 1995, r=0.05 (as-welded) r0=0.28 mm k=1.5 tw=3.3 atx cycles: w = 0.105 [nmm/mm3] http://www.gruppofrattura.it/ http://dx.medra.org/10.3221/igf-esis.09.02&auth=true p. lazzarin, frattura ed integrità strutturale, 9 (2009) 13-26; doi: 10.3221/igf-esis.09.02 19 figura 7: resistenza a fatica di giunti saldati con irrigidimento longitudinale in funzione del valore medio della densità di energia di deformazione [22]; dati originali dovuti a maddox (1982). 0.01 0.1 1 10 104 10 10 6 107 cicli a rottura, n pendenza k=2.0 a 2x106 cicli: v al o re m ed io d el la d en si tà d i en er g ia d i d ef o rm az io n e c w  w [ n m m /m m 3 ] cw w1, 50% = 0.103 [nmm/mm 3] rapporto nominale di ciclo: r=0 e r= 1 180 dati tw = 3.2 r0=0.12 mm giunti saldati testa a testa giunti con cordoni d’angolo figura 8: resistenza a fatica di giunti saldati testa a testa e di giunti con cordone d’angolo in lega leggera in funzione del valore medio della densità di energia di deformazione [12,20]; banda di dispersione tratta dalla referenza [12]. singolarità ‘out-of-plane’ indotte da effetti tridimensionali l problema delle singolarità di tipo ‘out-of-plane’ per effetti tridimensionali legati al rapporto di poisson è stato sollevato recentemente da kotousov [27,28]. tali singolarità potrebbero avere pratiche conseguenze sulle proprietà di resistenza a fatica di alcune geometrie di giunti saldati [29]. si ritiene utile qui inquadrare analiticamente il problema, chiarendo le conseguenze sulle distribu-zioni di tensione relative ad alcune geometrie di interesse applicativo. adottata l’ipotesi di kane e mindlin di deformazione piana generalizzata e presa in esame una piastra di spessore 2h, gli spostamenti risultano espressi nella forma [30]: )( y,xuu xx  , )( y,xuu yy  , )( y,xw h z uz  . (4) introdotta una funzione di tensione  , le condizioni di equilibrio e quelle di compatibilità per le deformazioni comportano: 0.01 0.1 1 10 1.00e+04 1.00e+05 1.00e+06 1.00e+07 cycles to failure, n  w [ n m m / m m 3 ] maddox, 1982; -1<r<0.67 (as-welded) maddox, 1982; zero-compression (as-welded) r0=0.28 k=1.5 tw=3.3 atx cycles: w = 0.105 [nmm/mm3] i http://www.gruppofrattura.it/ http://dx.medra.org/10.3221/igf-esis.09.02&auth=true p. lazzarin, frattura ed integrità strutturale, 9 (2009) 13-26; doi: 10.3221/igf-esis.09.02 20      2 22 2 )1(3)1(6 eh w h w  , w e 2 2 4 1 2      , (5a-b) il sistema disaccoppiato dà luogo a due distinte equazioni scritte in termini di  e di w : 0224  ww , 0426  (dove )(h   1 6 2 2 ) (6a-b) adottando poi una funzione armonica per gli spostamenti  , gli spostamenti nel piano e quelli out-of-plane possono essere scritti in coordinate polari nel seguente modo [27]  d d 1 1 d d 1 2 r       r r u eh r r r u eh d d 1 1 d d1 1 2 2 φ                  d d d d 12 22 r r )(ew (7a-c) nel caso di piastre molto sottili o molto spesse, le relazioni (7a-b) si riducono a quelle valide per i casi notevoli di tensione piana o deformazione piana. nel caso di intaglio laterale a v mostrato in fig. 9, le condizioni al contorno sono rappresentate dall’annullamento delle tensioni e r sui fianchi dell’intaglio. assunto un comportamento asintotico in forma generale, con   r~,rw )( ,    r~,r )( e 2)(   r~,r , che comporta 1 r~ , e adottato il metodo proposto da williams per i problemi piani, l’equazione caratteristica in λ ha la seguente forma [28]   0)(cos2sin2sin   . (8) figura 9: rappresentazione schematica dell’effetto ‘out-of-plane’; sistema di coordinate utilizzato nella trattazione analitica (simbologia in accordo con le referenze [27-29]). l’espressione alla sinistra rappresenta l’equazione di williams relative al caso piano di un intaglio a v soggetto a modo ii. l’espressione di destra dà invece il modo ‘out-of-plane’. si noto come tale espressione coincida perfettamente con l’espressione che esprime gli autovalori di modo iii [29]. per illustrare la formulazione analitica, si consideri il giunto a sovrapposizione di fig. 10 e, in particolare, il suo modello tridimensionale rappresentato in fig. 10b. i campi di tensione sono stati determinati utilizzando modelli tridimensionali con raggio nullo alla radice dei cordoni (fig. 10c). i modelli piani con keyhole, anch’essi mostrati in fig. 10c, sono stati utilizzati solo per i giunti di spessore ridotto che saranno discussi nella sezione 4 del presente contributo. http://www.gruppofrattura.it/ http://dx.medra.org/10.3221/igf-esis.09.02&auth=true p. lazzarin, frattura ed integrità strutturale, 9 (2009) 13-26; doi: 10.3221/igf-esis.09.02 21 figura 10: giunto a sovrapposizione. modello bidimensionale avente l’origine del piano x-y posizionato in corrispondenza della radice (a); modello tridimensionale con coordinata z=0 nel piano medio del giunto (b); volumi di controllo per i modelli con =0 e modello con keyhole (c). tensione nominale sempre riferita alla componente membranale, nom=f/t. consideriamo dapprima le distribuzioni di tensione nel piano medio del giunto, z=0. le componenti yx e yy sono diagrammate in fig. 11 in funzione della distanza dalla linea di singolarità. la figura mostra anche la t-stress, che è pari doppio della tensione nominale e la componente zz. tutte le distribuzioni fanno qui riferimento, come detto, a una tensione nominale membranale di 100 mpa, e alla condizione d=2t, con spessore t=20 mm. nel piano medio solo i campi di tensione legati alla soluzione di williams sono singolari, mentre la componente out-of-plane yz è nulla per ragioni di simmetria. utilizzando le espressioni (1) e i valori numerici delle componenti di tensione yx and yy, è possibile determinare i fattori generalizzati di modo i e ii. i due fattori risultano per questa geometria quasi coincidenti: kii= 452 mpa(mm)0.5 e ki= 450 mpa(mm)0.5). la pendenza delle distribuzioni legate a yx e yy coincide perfettamente con quella teorica, 0.5. la stessa pendenza caratterizza la componente zz. in parallello il fattore di contrazione risulta avere una variabilità limitata, da circa 1.0 per x tendente a zero a circa 0.85 per x=1.0 mm. la fig. 12 mostra i campi di tensione relative sia alla superficie laterale (z=50 mm), sia a una superficie parallela a questa (z=49.2 mm). le componenti di tensione yx e yy continuano a essere singolari, ma i campi di modo ii hanno ora un’intensità nettamente superiore a quella di modo i. per z=49.2 mm, infatti, kii risulta leggermente aumentato rispetto al valore presente nel piano medio (467 contro 452 mpa(mm)0.5) mentre ki appare nettamente ridotto (da 450 to 63 mpa(mm)0.5). assieme ai campi singolari di williams (inplane modes), si ha la comparsa di un modo singolare di tipo out-of-plane, così come mostrato dalla distribuzione della componente yz, non prevista nella soluzione di williams. il fattore di intensificazione associato k0 risulta pari a 0.50kii. l’estensione del modo out-of-plane in direzione x è maggiore di quella di modo i, minore di quella di modo ii. la ‘t-stress’ rimane costante e pari a circa 200 mpa, ossia pari alla metà di una tensione ‘strutturale’ di riferimento che computi con la teoria della trave la tensione membranale e la tensione dovuta alla flessione secondaria (st=400 mpa). alle distribuzioni di tensione si accompagna una forte variazione del fattore di contrazione cz, non documentata in figura, che scende da 0.85 a circa 0 [29]. per z=50 mm, superficie laterale del giunto, la componente di tensione di modo ii yx raggiunge il suo valore massimo. il corrispondente nsif vale kii= 741 mpa(mm)0.5, con un incremento di oltre il 60% rispetto al piano medio. contemporaneamente il campo di modo i raggiunge l’intensità minima, con una tensione yy così bassa da comportare una tensione xx quasi coincidente con la t-stress. la forte variabilità del fattore kii risulta in accordo con i risultati ottenuti in passato da nakumura e parks [31] da analisi tridimensionali di una piastra criccata soggetta a modo ii. le fig. 11 e 12 hanno evidenziato uno stato di tensione assai complesso, con larghe variazioni dei fattori di intensificazione delle tensioni di modo i e ii, e la comparsa della singolarità out-of-plane. una possibile sintesi della criticità http://www.gruppofrattura.it/ http://dx.medra.org/10.3221/igf-esis.09.02&auth=true p. lazzarin, frattura ed integrità strutturale, 9 (2009) 13-26; doi: 10.3221/igf-esis.09.02 22 del campo di tensione lungo la linea x=0 può essere fatta, a parere dello scrivente, utilizzando il valore medio della densità di energia di deformazione. il volume di controllo è un cilindro di raggio rc0.3 mm e altezza ancora pari a rc. usando quel volume, i diagrammi risultano essere quelli di fig. 13, tutti riferiti a un rapporto di poisson =0.3. per uno spessore di 20 mm, il valore massimo della sed è in corrispondenza della superficie laterale, aumentato di circa il 20% rispetto al piano medio. la posizione varia in funzione del rapporto tra larghezza e spessore del giunto, dell’angolo di apertura e del rapporto di poisson v. figura 11: campi di tensione nel piano medio in funzione della distanza x (modello trimensionale; nom=f/t=100 mpa; w=100 mm; t=20 mm; d/t=2) (da harding et al. [29]). figura 12: componenti di tensione in due diversi piani in funzione della distanza x dal punto di singolarità: tensioni sulla superficie laterale del giunto (z=50 mm) e su una superficie immediatamente adiacente (z=49.2 mm). stessa geometria di figura precedente (da harding et al. [29]). 100 1000 10000 0.001 0.010 0.100 1.000 0.7 0.75 0.8 0.85 0.9 0.95 1 mid-plane distance x from the slit tip [mm] s tr es s co m p o n en ts [ m p a] yz=0 t-stress = xx yy yy (mode i) yx (mode ii) constraint factor cz zz xx http://www.gruppofrattura.it/ http://dx.medra.org/10.3221/igf-esis.09.02&auth=true p. lazzarin, frattura ed integrità strutturale, 9 (2009) 13-26; doi: 10.3221/igf-esis.09.02 23 figura 13: andamenti della densità di energia di deformazione locale (sed) per differenti spessori del piatto principale. modelli tridimensionali con d=2t; sed calcolata su un volume cilindrico di raggio e altezza r0=0.28 mm (da harding et al. [29]). analisi dei giunti a sovrapposizione di ridotto spessore o scrivente ritiene che il criterio basato sulla densità di energia di deformazione locale possa essere applicato anche ai giunti di ridotto spessore, in alternativa a altri criteri proposti in letteratura. fra questi citiamo il criterio basato sul ‘substitute notch radius’ che prevede l’introduzione di un keyhole con raggio di 0.05 mm all’apice [32,33] e il criterio basato su j-integral. quest’ultimo è stato recentemente rivisitato da lazzarin et al. [26] che hanno anche operato un confronto diretto tra i tre diversi metodi. il convenzionale j-integral di rice [34] per 'self-similar crack propagation’ dipende da ki e kii ma non dalla t-stress:              π π 2 ii 2 i π π 1 d x u dcosdd 'e k 'e k θrtθθrr,θws x u tyr,θwjj (9) una seconda componente di j-integral, che è differente da zero per ‘kinking crack propagation’ è stata formalizzata da knowles and stenberg [35]. tale componente è così definita:             π π π π 2 ddsindd θr y u tθθrr,θws y u txr,θwj  (10) nelle equazioni (9) e (10) u  e t  rappresentano, come noto, il vettore degli spostamenti e il vettore delle trazioni. poichè la densità di energia di deformazione w(r, ) dipende da ki, kii e dalla t-stress, la seconda componente di j-integral risulta: r e' tk e' kk jjj ,, π 822 iiiii t2k22  (11) il primo termine alla destra della eq. (11) è ben noto [36], mentre il secondo termine è stato determinato nella referenza [26] per la prima volta. si osservi come la t-stress renda j2 dipendente dal percorso di integrazione tramite il raggio r. l http://www.gruppofrattura.it/ http://dx.medra.org/10.3221/igf-esis.09.02&auth=true p. lazzarin, frattura ed integrità strutturale, 9 (2009) 13-26; doi: 10.3221/igf-esis.09.02 24 mettendo in conto la prima e la seconda componente, è possibile esprimere un j-integral totale e legarlo algebricamente a un fattore di intensificazione delle tensioni equivalente keq [26]: 'e k rtkkkkkkk 'e jjj 2 eq 2 iiiii 4 ii 2 ii 2 i 4 i 2 2 2 1 π 8 222 1          (12) la tab. 2 presenta i valori del sed da ‘full circles’ con raggio r0=0.28 mm assieme ai parametri j1, j2,k, j2,t, j e j/2πr0. l’ultimo parametro normalizza j rispetto al perimetro del volume di controllo 2r0, come suggerito da berto et al. [37,38]. il contributo di j2 è sempre maggiore del contributo di j1 quando t = 1 mm (mentre i due contributi sono invece vicini tra loro per t = 5 mm, [26]). per d/t ≥ 2.0, la massima differenza tra j e sed è minore dell’8%, il che significa 0π2 r/jw  in questi casi. le differenze crescono per d/t = 1.0 e 0.5, ma restano comunque piuttosto contenute. r0=0.28 mm j1 (103) j2,k (103) j2,t (103) j (103) j/(2r0) (103)  t=1 mm (n/mm) (nmm/mm3) (nmm/mm3) (%) d/t=0.5 0.671 0.175 1.815 2.100 1.194 1.412 -15.4 1 0.550 0.395 1.496 1.969 1.120 1.208 -7.3 2 0.726 0.710 1.336 2.172 1.235 1.183 4.4 3 0.765 0.757 1.307 2.201 1.252 1.181 6.0 8 0.764 0.756 1.307 2.200 1.251 1.180 6.0 tabella 2: giunti a cordone continuo saldati a sovrapposizione, f/(t1)=10 mpa (da lazzarin, berto e radaj, 2009 [26]). valori di basati sulla prima componente (j1) e la seconda componente (j2=j2,k+j2,t) di j-integral; confronto tra i parametri j/(2r0) e sed entrambi riferiti a un volume di controllo circolare di raggio r0=0.28 mm. si ritiene utile riportare un confronto tra previsioni espresse in termini di sed (tutte relative a modelli con =0) e previsioni basate sul fattore teorico di concentrazione delle tensioni, così come determinato da modelli con ‘keyhole’ (vedi fig. 4c). in questi casi l’apice della fessura presenta un raggio di raccordo s = 0.05 mm, così come suggerito da sonsino et al. in [32,33]. la tab. 3, tratta dalla referenza [26], mette a controllo valori di kt e di w , tutti normalizzati rispetto alla geometria di riferimento avente d/t=3.0. la corrispondenza è molto buona con variazioni percentuali inferiori al 4% per i modelli a cerchio pieno. kt/kt* =0.05 mm r0=0.28mm r0=0.28mm circle semicircle t=1mm, d/t=0.5 1.137 1.093 1.064 1 1.000 1.011 1.021 2 0.998 1.001 1.006 3 1.000 1.000 1.000 tabella 3: sed e fattori teorici di concentrazione delle tensioni normalizzati rispetto al caso d/t=3.0 (da lazzarin, berto e radaj, 2009, [26]). una sintesi finale in termini di sed è presentata in fig. 14 per giunti a sovrapposizione saldati a punti. lo spessore varia tra 0.65 mm e 1.75 mm, il rapporto nominale di ciclo r tra 0.05 e 0.3. i dati sperimentali sono stati tratti dalla letteratura recente, dal 2003 in poi. al momento il volume di controllo fa ancora riferimento al raggio r0=0.28 mm (valido a rigore per i giunti di medio ed elevato spessore), senza avere quindi ancora operato alcun processo di ottimizzazione per i giunti di spessore ridotto. la dispersione rimane in linea con quella caratteristica della banda di haibach, mentre la pendenza *w/w *w/w w 1 2j j j= + http://www.gruppofrattura.it/ p. lazzarin, frattura ed integrità strutturale, 9 (2009) 13-26; doi: 10.3221/igf-esis.09.02 25 risulta superiore a quella dei giunti di medio ed elevato spessore saldati ad arco, k=2.13, che diventa ovviamente k=4.26 in termini di range di tensione locale equivalente. figura14: banda di dispersione relativa a giunti a sovrapposizione saldati a punti soggetti a sollecitazioni di trazione/taglio (piatti e travi a c). valori di w determinati da modelli tridimensionali. conclusioni l lavoro ha presentato le linee guida del criterio basato sul valore medio della densità di energia di deformazione w valutata in un ben preciso volume di controllo posizionato al piede e alla radice dei cordoni di saldatura. nei giunti di medio ed elevato spessore la densità di energia di deformazione dipende quasi esclusivamente dai fattori di intensificazione di modo i al piede dei cordoni, dai fattori di modo i e ii alla radice nel caso di giunti a cordone portante. anche per queste geometrie il contributo di modo i resta prevalente. circa 900 dati sperimentali di resistenza a fatica relativi a giunti saldati aventi geometrie molto diverse fra loro sono stati presentati in termini di wn chiarendo la posizione e la pendenza della banda di dispersione associata. al ridursi delle dimensioni assolute dei giunti la zone controllate dalle singolarità di ordine prevalente si riducono e il calcolo della densità di energia non può più limitarsi ai termini singolari del primo ordine. il problema è stato evidenziato per il giunti a semplice sovrapposizione di spessore ridotto (t=1 mm) laddove l’effetto della t-stress parallela alle superficie affacciate gioca un ruolo rilevante sul stato di tensione e deformazione presente nella zona di innesco delle cricche di fatica. anche per i giunti di spessore ridotto il criterio basato sul valore medio della densità di energia di deformazione appare promettente e alternativo ad altri criteri basati su j-integral o su modelli che vedono la radice dei cordoni modellata mediante keyhole con raggio di raccordo all’apice molto ridotto (s=0.05 mm). il lavoro ha anche discusso la possibile esistenza di modi singolari out-of-plane, che nascono nei giunti saldati per effetto poisson, in combinazione con stati tensionali di modo ii (singolari e non singolari). questi singolarità non convenzionali, non contemplate dalla trattazione di williams, concorrono a giustificare lo spostamento del punto di innesco delle cricche di fatica dal piano medio dei giunti alle superficie laterali. comunque sia, il criterio basato della densità di energia di deformazione si mostra in grado di computare correttamente anche gli effetti out-of-plane se utilizzato in combinazione con modelli tridimensionali dei giunti. come evidenziato in alcuni contributi recenti riportati in bibliografia, uno dei maggiori vantaggi del criterio basato sulla densità di energia di deformazione è legato al possibile utilizzo di mesh a maglia larga attorno al volume di controllo posizionato nelle zone di possibile innesco delle cricche di fatica, superando il problema dei metodi basati sulla valutazione diretta dei campi di tensione locali che richiedono invece mesh con elevato grado di infittimento. i http://www.gruppofrattura.it/ http://dx.medra.org/10.3221/igf-esis.09.02&auth=true p. lazzarin, frattura ed integrità strutturale, 9 (2009) 13-26; doi: 10.3221/igf-esis.09.02 26 bibliografia [1] d. radaj, c. m. sonsino, w.fricke, fatigue assessment of welded joints by local approaches, woodhead publishing, cambridge, 2nd edn. (2006). [2] d. radaj design and analysis of fatigue resistant welded structures, abington publishing, cambridge (1990). [3] d.radaj, c. m. sonsino, w.fricke, int. j. fatigue, 31 (2009) 2. [4] p. lazzarin, r. tovo, fatigue fract. engng. mater. struct., 21 (1998)1089. [5] b. atzori, proc. xiii conference of the italian society for strain analysis, bergamo, italia (1985) 294. [6] b. atzori, proc. of the italian conference on fatigue strength of welded structures, genova, italia (1985). [7] m. l. williams, j. appl. mech., 19 (1952) 526. [8] p. lazzarin, p.livieri, int. j. fatigue, 23 (2001) 225. [9] p. lazzarin, r. zambardi, int. j. fract., 112 (2001) 275. [10] p. lazzarin, r. zambardi, fatigue fract. engng. mater. struct., 25 (2002) 917. [11] p. lazzarin, t. lassen, p. livieri, fatigue fract. engng. mater. struct., 26 (2003) 49. [12] p. livieri, p. lazzarin, int. j. fract., 133 (2005) 247. [13] p.lazzarin, welding int., 14 (2000) 115. traduzione da: riv. ital. saldatura, 51(1999) 137. [14] g. glinka, k.molski, mater. sci. engng., 50 (1981) 93. [15] p. lazzarin, f. berto, fatigue fract. engn. mater. struct., 31 (2008) 95. [16] d. radaj, f. berto, p. lazzarin local fatigue strength parameters for welded joints based on strain energy density with inclusion of small-size notches. engng. fract. mech., (2009) in press, available on line. [17] d. radaj, p. lazzarin, f. berto fatigue assessment of welded joints under slit-parallel loading based on strain energy density or notch rounding. submitted to int j fatigue (2009). [18] f. berto, p. lazzarin, d. radaj, fictitious notch rounding concept applied to sharp v-notches: evaluation of the microstructural support factor for different failure hypotheses. part i: basic stress equations. engng. fracture mech., 75 (2008) 3060. part ii: microstructural support analysis. engng. fracture mech., (2009) in press, available online. [19] f.berto, p. lazzarin, proc. mesomechanics conference, oxford (2009). [20] p. lazzarin, f. berto, d. radaj, proc. 9th int fatigue congress, ifc9, atlanta, usa (2006). [21] e. haibach, service fatigue strength – methods and data for structural analysis, springer verlag, berlino (2002). [22] p. lazzarin, f. berto, f.j. gomez, m. zappalorto, int j fatigue, 30 (2008) 1345. [23] p. lazzarin, f. berto, d. radaj, key engineering materials, advances in fracture and damage mechanics vi, 348349 (2007) 449. [24] r. gross, a. mendelson, int. j. fract. mech., 8 (1972)267. [25] p. lazzarin, p. livieri, f. berto, m. zappalorto, engng. fract. mech., 75 (2008)1875. [26] p. lazzarin, f. berto, d. radaj, fatigue-relevant stress field parameters of welded lap joints: pointed slit tip versus keyhole notch. fatigue fract. engng. mater. struct., (2008) under revision. [27] a. kotousov, t. l. lew, int. j.solids struct., 43 (2006) 5100. [28] a. kotousov, int. j. solids struct., 44 (2007) 8259. [29] s. harding, a. kotousov, p.lazzarin, f.berto transverse singular effects in v-shaped notches stressed in mode ii, (2009) submitted. [30] t. r. kane, r. d. mindlin, j. appl. mech. 23 (1956) 277. [31] t. nakamura, d. m. parks, int. j. solids struct., 25 (1989)1411. [32] m.eibl, c.m. sonsino, h. kaufmann, g. zhang, int. j. fatigue, 25 (2003) 719. [33] ö. karakas, c. morghenstern, c. m. sonsino, int. j. fatigue, 30 (2008) 2210. [34] j. r. rice, j. appl. mech., 35 (1968) 379. [35] j. k. knowles, e. stenberg, archives for rational mechanics and analysis, 44 (1972) 187. [36] e. e. gdoutos, fracture mechanics criteria and applications. kluwer academic publishers, dordrecht (1990). [37] f.berto, p. lazzarin, int. j. solids struct., 44 (2007) 4621. [38] f. berto, p. lazzarin, f. j. gómez, m. elices, int. j. fract., 148 (2007) 145. http://www.gruppofrattura.it/ http://dx.medra.org/10.3221/igf-esis.09.02&auth=true microsoft word numero_41_art_42.docx m. vormwald et alii, frattura ed integrità strutturale, 41 (2017) 314-322; doi: 10.3221/igf-esis.41.42 314 focused on crack tip fields variable mode-mixity during fatigue cycles – crack tip parameters determined from displacement fields measured by digital image correlation michael vormwald, yigiter hos technische universität darmstadt, materials mechanics group, franziska-braun-str. 3, d-64287 darmstadt, germany vormwald@wm.tu-darmstadt.de, hos@wm.tu-darmstadt.de josé l.f. freire, giancarlo l.g. gonzáles, jorge g. díaz pontifícia universidade católica do rio de janeiro, puc-rio, rua marquês de são vicente, 225, gávea rio de janeiro, brasil jlfreire@puc-rio.br, gonzalesglg@aaa.puc-rio.br, jorgegdiaz@aluno.puc-rio.br abstract. this paper focusses on discussing equivalent stress intensity factors and kink angles after a change of mode-mixity from one cycle to the next and when the mode-mixity changes continuously during the fatigue cycles. thin-walled tubes with through-wall cracks have been loaded by proportional and non-proportional tension and torsion. in the experimental investigation, the region of fatigue crack growth was observed by applying the digital image correlation technique. data on the variations of the displacement and strain fields during the cycles were acquired and used to determine mixed-mode variations of stress intensity factors associated with opening modes i, ii and iii. for each specific specimen the crack path was observed in order to relate its curvature – both kinks and continuously developing warped cracks – with the variations of the displacement field and associated stress intensity factors. keywords. mixed-mode; fatigue crack growth; digital image correlation; crack kinking. citation: vormwald, m., hos, y., freire, j. l. f., gonzáles, g.l.g., díaz j. g., variable mode-mixity during fatigue cycles – crack tip parameters determined from displacement fields measured by digital image correlation, frattura ed integrità strutturale, 41 (2017) 314-322. received: 28.02.2017 accepted: 03.05.2017 published: 01.07.2017 copyright: © 2017 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. introduction horough reviews on crack-path evolution rules and on fatigue crack-growth under non-proportional mixed-mode loading were presented by mróz et al. [1] and zerres et al. [2]. schöllmann et al. [3], richard and co-workers [4-6] and yang et al. [7] presented, discussed criteria for the prediction of crack growth, and summarized findings for 2d and 3d components subjected to multiaxial loading. analysis of the literature review revealed that it is still an open question the determination of equivalent stress intensity factors, sif, as well as crack growth rules and the prediction of crack path tangent for complex opening-mode problems, mainly if opening mode iii is present. the influence of several variables such as: structural component geometry and material, load mode-mixity, presence of all three opening modes, nominal load range ratio r, local crack tip effects including plasticity and 3d corner effects [8], crack flank roughness, crack closure and crack blunting, make the understanding of the fatigue crack growth an extraordinary problem. a t m. vormwald et alii, frattura ed integrità strutturale, 41 (2017) 314-322; doi: 10.3221/igf-esis.41.42 315 generally accepted and validated formulation of a crack force parameter still needs to be identified [2]. moreover, experimental investigations for the 3d mixed mode load to validate existing predicting assumptions need to be further developed [4]. the present paper discusses 2d and 3d formulations for equivalent sifs for complex mode problems, presented by erdogan and sih [9], by schöllmann et al. [3] and by richard et al. [4-6], under the light of experiments carried out by vormwald and his co-workers [10, 11]. these experiments used digital image correlation, dic, to measure full-field displacement and derived data for 3d tested specimens. the acquired data made possible the determination of relative crack flank opening displacements, cod, and their associated mode i, ii and iii sifs, as well as the calculation of equivalent sifs and tangents to crack paths for cases of mixed-mode variations (inside one cycle and from cycle to cycle) using the above mentioned formulations. experimental methods onstant amplitude fatigue tests have been performed using thin-walled tubes under alternated tensioncompression (force f ranging from 45kn to -45kn) and torsion (moment m ranging from 532 nm to -532 nm). data was acquired from five different loading sequences applied to individual specimens [2-3]: pure alternated tension-compression loading (specimen r-028), pure alternated torsion loading (specimen r-029), proportional alternated tension and torsion loading (specimen r-030), and out-of-phase loading with phase angles of 45° (specimen r-033) and 90° (specimen r-031). the load ratio was rf = rm = -1. the specimen geometry is shown in fig. 1. the specimens were machined from longitudinally welded tubes. the individual specimens were saw-cut and the slits or notches were milled. two holes, with a diameter of 4 mm, were drilled with a distance of 10 mm from the centers of the holes (length of an arc measured at the outer surface). the notch was positioned opposite to the longitudinal weld. the material was constructional steel s235 with the following mechanical properties: young’s modulus, e = 214gpa, yield strength (0.2% plastic offset), sy = 310mpa, ultimate tensile strength su = 435mpa, and the parameters of the cyclic ramberg-osgood stress-strain curve, k’ and n’, respectively equal to 1170mpa and 0.239. figure 1: specimen geometry (mm) the experiments have been conducted under load and moment control, respectively, using a servo-hydraulic, four-pillar tension-torsion testing machine with frequencies between 0.1 hz (when necessary, during 3 cycles for dic data acquisition) and 2 hz. the cracks were assumed to be through-wall cracks with a straight crack front. the crack length is defined as the arc length with the arc measured starting at the crack initiation location. depending on the loading type, two, or four cracks were observed [10, 11]. determination of stress intensity factors from crack-flank opening displacements he determination of sifs, ki (i = i, ii, iii) was based on their relationship with relative crack flank opening displacements, codi, [12] as given by eqs. (1). generally, points a and b are symmetrically located over the crack faces (~+π) and near the crack tip (small local crack path curvature and coordinate r << crack length a), as illustrated in fig. 2. in eq. (1) u’, v’ are in plane displacements respectively in the parallel and orthogonal crack directions and w’ is the out of plane displacement. polar coordinates are referred to the tangent and orthogonal axes relative to the crack line. c t m. vormwald et alii, frattura ed integrità strutturale, 41 (2017) 314-322; doi: 10.3221/igf-esis.41.42 316                                                                  1 2 2 1 2 2 2 2 sin( ). cos ( ) sin( ). cos ( ) 2(1 ) 2 2 1 2 2 2 1 2 2 2 sin( ). cos ( ) sin( ). cos ( ) 2(1 ) 2 2 1 2 2 2 1 2 4(1 ) i a a a b b b i ii a a a b b b ii iii a iii e cod r r k e cod r r k e cod r k                  1 ' ' ' ' ' ' sin( ) sin( ) 2 2 2 2 a b b i a b ii a b iii a b r cod v v cod u u cod w w (1) figure 2: displacements at points a, b located on the crack-flank and near to the crack tip. one advantage of using the sif related cod formulation is the possibility of determining elastic equivalent sifs when crack plasticity and blunting affect near field displacement or strain measurements occurring at points very close to and in front of the crack-tip. cods are lesser influenced by particular point measurements, once they correspond to integrated displacement values of points located over the crack flanks between the measuring point (a or b) and the crack tip. the total cod measurement in such cases corresponds to an elastic component code plus a plastic component codp resulting in a total sif* or k*, [13]. the k* value therefore results from an elastic sife or ke plus a plastic equivalent sifp or kp. of course, any relation between the total k* value with near crack tip stress or strain values must be understood as an equivalent linear crack tip elastic stress or strain value. calculation of equivalent sifs using dic or a number of 2d or 3d cracked body problems, the prediction of monotonic static fracture or the prediction of crack growth by the equivalent or comparison static stress intensity factor, kv, or by the equivalent fatigue crack growth sif range, kv, can be made by a number of different formulations, as for example those proposed by references [1-6, 9]. the present paper addresses kv calculations using kv equations initially developed by erdogan and sih [9] for opening modes i and ii and by schöllmann et al. [3] for opening modes i, ii and iii and the richard et al. [4-6] concept that sif ranges ki can be used in place of ki to determine equivalent ranges kv in fatigue crack growth evaluations, as given by eqs. (2) and (3).           20 0 0 3 cos cos sin 2 2 2 ves i iik k k (2)                         2 2 2 20 0 0 3 0 0 1 3 3 cos cos sin cos sin 4 2 2 2 2 2 2 vs d i ii i ii iiik k k k k k (3) the use of eqs. (2) and (3) is valid if the mixed-mode ratios do not change inside a specific loading cycle. when sif ratios change inside one cycle, the  0 angle also changes during the cycle. therefore, it is needed to find a maximum range value f m. vormwald et alii, frattura ed integrità strutturale, 41 (2017) 314-322; doi: 10.3221/igf-esis.41.42 317 kvmax that would occur during one cycle by searching which angle  0, function of the instantaneous ki occurring during the cycle, would lead to the maximum kv= kvmax. first, eqs. (1) for mode i, ii and iii sifs were calculated for each pair of frames (captured images) of three data acquisition cycles (300 pairs of frames). the interval between blocks of the three cycle acquired data lasted a number of cycles (500 or 1000). for example, sifs i, ii and iii calculated for specimen r-031 (subjected to non-proportional (90o) out-of-phase alternated axial-torsional load) are presented in fig. 3. the plot shows that sif are out-of-phase. if sifs were in phase, eqs. (2) and (3) could be applied straightforward using the kimax ranges occurring in the cycle. for the out-of-phase plot of fig. 3, the calculation of the equivalent range for the cycle using, for example, the schöllmann et al. eq. (3), kvs3d, follows the herein outlined procedure. terms pj and qj are defined in eq. (4) to simplify the representation of eq. (3). the subscript j denotes each data acquisition instant inside one cycle, for example j = 1,2, …, 100 (corresponding to one full cycle) designating each triple of sifs i, ii and iii to be determined along the cycle using eqs. (1). in eq. (4), the angle  k takes values from -60o to +60o in2o steps in order to find the maximum kvs3dj. for the pair (pj, qj), depicted in the plot of fig. 4, the square root of eq. (4) is given by the vector pqj, while for the pair (pj+n, qj+n) is given by the vector pqj+n. subtraction of these vectors gives the vector range pq and its algebraic addition to (pj – pj+n) results in the equivalent range kvs3dj,j+n depicted in eq. (5). the representative equivalent range for the cycle will result for the maximum value of kvs3dj,j+n found, after all values of  k had been investigated. after this search, not only the maximum range value is found, kvs3d , but also the crack-path tangent direction  k =  0 where it happens. figure 3: all mode sif variations, ranges and applied loads as calculated from the cod method after 30,000 load cycles for a crack sizing 9.28 mm for specimen r-031 under (90o) out-of-phase alternated axial-torsional load                2 2 3 2 3(cos ) cos sin 2 2 2 2 (cos ) 2 vs dj j j j k k ij iij k j k j iiij k p p q k k p q k (4)                2 2 3 ,vs dj j n j j n j j n j j nk p p p p q q (5) figure 4: calculation of the range of the square root term of eqs. (3) and (4). m. vormwald et alii, frattura ed integrità strutturale, 41 (2017) 314-322; doi: 10.3221/igf-esis.41.42 318 results and discussion igs. (5) to (8) present results for four of the five specimens tested. the first plot (top-left) shows the evolution of the each sif mode and the equivalent sif ranges with crack size. the mode i and equivalent range values are identical for specimen r-028 (single axial load), mode ii and iii ranges being very small. for specimens r-031 (phase angle of 90°) and r-033 (phase angle of 45°), the ratios between cycle maximum values of kii and ki change (and grow) considerably. the influence of kiii turns out to be very important, making the equivalent 2d and 3d sif calculated ranges differ reasonably. the second plot (bottom-left) shows the variation of the maximum i and ii mode ranges with crack size. experimentally determined crack-path tangent angle (orthogonal direction to the specimen axis) showed in the plot do not seem to be explained by the ratios between the maximum cycle values of the ii and i mode sif ranges. the third plot (top-right) shows experimentally measured ( o) and calculated (erdogan-sih  o es and schöllmann et al.  o s3d) crack-path tangent angles for each crack length. the way the angles were calculated would impose coincidence among experimentally measured and calculated path-directions. that is seen for most cases for the determined schöllmann et al. angles, but not seen for the erdogan-sih angles. the explanation comes from the fact that the 3d analyses take into consideration the large kiii values. the forth plot (bottom-right) shows the variation of mixedmode ratios during one cycle and from cycle to cycle. while for specimens r-028 (single axial load) and r-030 (axial and torsional proportional load) the variations are shown to be small due to reasonably proportional mixed-mode i and ii ratios, the same does not happen for both out-of-phase specimens, where mode-mixity variation occurs inside each cycle and gets accentuated when the crack grows with the number of cycles. figure 5: crack tip parameters measured and calculated for specimen r-028, single alternated tension 45kn max. force. numerical investigations he first simulation is done with the specimen r-028 (single axial load). the procedure and its results have been published in ref. [14]. summarizing, the finite-element based node-release scheme provide acceptable estimates for the effective ranges and crack growth rates could be successfully correlated with the effective cyclic jeff-integral. 0 10 20 30 40 50 60 70 2 3 4 5 6 7 8 [mpa√m] a*[mm] δk vs a*. r-028 δki δkii δkiii δk s3d δk es -30 -20 -10 0 10 20 30 2 3 4 5 6 7 8 θo [deg] a*[mm] θo vs a*. r-028 θo θo s3d θo es -45 -35 -25 -15 -5 5 15 25 35 45 0,0 0,2 0,4 0,6 0,8 1,0 2 3 4 5 6 7 8 θo[deg]δki/δki a*[mm] δki/δki vs a* r-028 δkii/δki δkiii/δki θo -15 5 25 45 65 -15 5 25 45 65 kii ki ki vs kii [mpa√m]. r-028 9970 10720 11220 12220 13220 14720 15720 16720 17220 f t m. vormwald et alii, frattura ed integrità strutturale, 41 (2017) 314-322; doi: 10.3221/igf-esis.41.42 319 figure 6: crack tip parameters measured and calculated for specimen r-030, proportional tension and torsion loads. figure 7: crack tip parameters measured and calculated for specimen r-031, phase shift 90° between tension 33kn and torsion 382nm loads. 0 20 40 60 80 100 2 4 6 8 10 [mpa√m] a*[mm] δk vs a*. r-030 δki δkii δkiii δk s3d δk es -50 -40 -30 -20 -10 0 3 4 5 6 7 8 9 10 θo [deg] a*[mm] θo vs a*. r-030 θo θo s3d θo es -90 -80 -70 -60 -50 -40 -30 -20 -10 0 0,0 0,5 1,0 1,5 2,0 2 3 4 5 6 7 8 9 10 θo[deg]δki/δki a*[mm] δki/δki vs a* r-030 δkii/δki δkiii/δki θo -25 -15 -5 5 15 25 35 45 55 65 -25 -15 -5 5 15 25 35 45 55 65 kii ki ki vs kii [mpa√m]. r-030 7500 9200 9600 10800 12000 13500 14000 14250 0 20 40 60 80 100 120 2 4 6 8 10 12 14 16 18 20 [mpa√m] a*[mm] δk vs a*. r-031 δki δkii δkiii δk s3d -70 -50 -30 -10 10 30 50 70 2 4 6 8 10 12 14 16 18 20 θo [deg] a*[mm] θo vs a*. r-031 θo θo s3d θo es -90 -75 -60 -45 -30 -15 0 15 30 45 0,0 0,5 1,0 1,5 2,0 2 4 6 8 10 12 14 16 18 20 θo[deg] δki/δki a*[mm] δki/δki vs a* r-031 δkii/δki δkiii/δki θo -60 -40 -20 0 20 40 -60 -40 -20 0 20 40 kii ki ki vs kii [mpa√m]. r-031 32400 32000 31500 30500 30000 28000 23500 m. vormwald et alii, frattura ed integrità strutturale, 41 (2017) 314-322; doi: 10.3221/igf-esis.41.42 320 figure 8: crack tip parameters measured and calculated for specimen r-033, phase shift 45° between tension 33kn and torsion 382nm loads. the second simulation was done with the r-031 specimen (axial and torsional non-proportional mixed load). the crack path was modeled by defining a surface where two parts of the geometry-model are connected. the surfaces (future crack faces) were initially connected with normal surface-to-surface contact, whose properties were changed when a contact surface was being opened. no penetration was allowed in the normal direction and friction was neglected between the crack surfaces. the growth of the crack was achieved by switching these tie constraints along the crack surface to normal contact properties. due to the complicated geometry of the 3d crack surfaces, linear tetrahedral elements were used to mesh the model. in the simulation, crack growth steps of 1 mm were applied. this step size is not actually recommended. however, achieving convergence was a bigger challenge in this simulation and this large step size was mandatory to achieve any result at all. after several iterations, convergence was achieved up to a crack size of 5 mm. it was not possible to attain convergence after this point, due to the many sources of nonlinearity such as the contact conditions and the complex plasticity model, see [14] for details. note that, this simulation includes plasticity induced crack closure. the crack closure from the simulation and the experiment for a crack length of 4 mm is given in fig. 9. in the experiments, the criterion for crack closure was whether the cod was negative or positive. in the simulations, the contact at one of the nodes on the crack surface was considered to be enough for the crack to be closed. the observed crack opening and closing times differ slightly between the simulation and the experiments. therefore, it can be concluded that the crack closure ranges from simulations can be seen as an acceptable source of information regarding crack closure ranges. more simulations have to be done in the future with other phase angles, or other types of non-proportional loadings to derive an overall conclusion. however, this comparison can be seen as promising and is expected to be a good foundation for future studies. a second result from the simulations was the crack tip parameters calculated from these simulations. as indicated before, the effective cyclic jeff-integral was used as a crack tip parameter. for the crack lengths of 3mm and 4mm and the given loading pattern nearly identical values of jeff 5 n/mm were obtained. transformed to an equivalent, plasticity-corrected stress intensity factor gives kj,eff 32 mpam. this value can be compared to the corresponding values derived from the dic-investigation and by applying eq. (5), fig. 7. although the dic-based values are in the order of magnitude, they appear to be larger, possibly due to the capturing of the mode iii contribution. comparing fatigue crack growth rates for pure mode i (r-028) and non-proportional mixed mode (r-031) it can be concluded that a valid mixed mode hypothesis 0 25 50 75 100 125 150 175 200 225 1 2 3 4 5 6 7 8 9 10 [mpa√m] a*[mm] δk vs a*. r-033 δki δkii δkiii δk s3d δk es -50 -40 -30 -20 -10 0 1 2 3 4 5 6 7 8 9 10 θo [deg] a*[mm]θo vs a*. r-033 θo θo s3d θo es -90 -80 -70 -60 -50 -40 -30 -20 -10 0 0,0 0,5 1,0 1,5 2,0 2,5 1 2 3 4 5 6 7 8 9 10 θo[deg]δki/δki a*[mm] δki/δki vs a* r-033 δkii/δki δkiii/δki θo -20 0 20 40 60 -20 0 20 40 60 kii ki ki vs kii [mpa√m]. r-033 15000 14500 14000 13000 12000 11000 10000 m. vormwald et alii, frattura ed integrità strutturale, 41 (2017) 314-322; doi: 10.3221/igf-esis.41.42 321 should provide a keqv,eff 45 mpam for the case under consideration. it seems that the cod-based hypothesis, eq. (5), currently is better able to uniquely describe fatigue crack growth under non-proportional mixed mode. moreover, it provides a growth direction which the energy release rate based approach is currently still lacking. figure 9: force-moment diagram from the simulation (left) and from experiment (right) of r-031 (axial and torsional nonproportional mixed load), a=4 mm. conclusion his paper presented a consistent way to determine opening mode sifs i, ii and ii from relative crack flank displacements that were measured using the 3d dic technique. use of a 3d technique is important because the 2d dic technique is only applicable to plane problems where out-of-plane displacements are negligible in order not to jeopardize the in-plane measurements. moreover, the use of 3d dic allows the measurement of out-of-plane and consequently determinations of mode iii crack openings and associated kiii values. calculations of mode iii sif values were useful to show that, in some cases, as for example in the present paper, they may be higher than the mode i and ii sifs and therefore influence the calculation of equivalent static sifs and cyclic sif ranges. this paper also presented a way to calculate equivalent sif ranges for non-proportional loading problems using formulations already presented in literature for proportional loading. in addition, crack tangent directions were calculated from the angles where the maximum equivalent sif range was found. finally, it was shown that mix-mode i, ii and iii were present in four of the tested specimens, and that the ratio between sifs ii and i varied considerably during one cycle and from cycle to cycle for the non-proportional loaded specimens. acknowledgement he german research foundation (deutsche forschungsgemeinschaft) is greatly acknowledged by the authors for financial support under grant vo729/13-1. references [1] mróz, k.p., mróz, z., on crack evolution rules, engineering fracture mechanics, 77 (2010) 1781-1807. [2] zerres, p., vormwald, m., review of fatigue crack growth under non-proportional mixed-mode loading, international journal of fatigue, 58 (2014) 75–83. doi: 10.1016/j.engfracmech.2010.02.008. [3] schöllmann, m., richard, h.a., kullmer, g., fulland, m., a new criterion for the prediction of crack development in multiaxially loaded structures, international journal of fracture, 117 (2002) 129-141. doi: 10.1023/a:1020980311611. t t m. vormwald et alii, frattura ed integrità strutturale, 41 (2017) 314-322; doi: 10.3221/igf-esis.41.42 322 [4] richard, h.a., schramm, b., schirmeisen, n.-h., cracks on mixed mode loading – theories, experiments, simulations, international journal of fatigue, 62 (2014) 93-103. doi: 10.1016/j.ijfatigue.2013.06.019. [5] richard, h.a., fulland, m., sander, m., theoretical crack path prediction, fatigue fract engng mater struct, 28 (2005) 3-12. doi: 0.1016/j.ijfatigue.2013.06.019. [6] richard, h.a., eberlein, a. material characteristics at 3d-mixed-mode-loadings, procedia structural integrity, 2 (2016) 1821-1828. doi: 10.1016/j.prostr.2016.06.229. [7] y. yang, m. vormwald, three-dimensional fatigue crack growth path simulation under non-proportional mixed-mode loading, 13th international conference on fracture, june 16-21, 2013, beijing, china. [8] z. he, a. kotousov, on the evaluation of stress intensity factor from in-plane and transvers surface displacements, experimental mechanics, 56 (2016) 1385-1393. doi: 10.1007/s11340-016-0176-8. [9] erdogan, f., sih, c.g., on the crack extension in plates under plane loading and transvers shear , j. basic eng., 1963, 8, 519-525. doi: 10.1115/1.3656897. [10] y. hos, m. vormwald, j.l.f. freire, measurement and simulation of strain fields around crack tips under mixed-mode fatigue loading, frattura ed integrità strutturale, 33 (2015) 42-55. doi: 10.3221/igf-esis.33.06. [11] y. hos, j.l.f. freire, m. vormwald, measurements of strain fields around crack tips under proportional and nonproportional mixed-mode fatigue loading, international journal of fatigue, 89 (2016) 87-98. doi: 10.1016/j.ijfatigue.2016.01.018. [12] gonzáles, g. l. g., diaz, j. g., gonzález, j. a. o., castro, j. t. p., & freire, j. l. f., determining sifs using dic considering crack closure and blunting. in experimental and applied mechanics, 4 (2017) 25-36. springer international publishing. doi: 10.1007/978-3-319-42028-8_4. [13] nowell, d., kartal, m.e., de matos, p.f.p., digital image correlation measurements of near-tip fatigue crack displacement fields: constant amplitude loading and load history effects, fatigue and fracture of engineering materials and structures, 36 (2012) 3-13. doi: 10.1016/j.ijfatigue.2008.12.003. [14] hos, y., vormwald, m., experimental study of crack growth under non-proportional loading along with first modeling attempts, international journal of fatigue, 92 (2016) 426-433. doi: 10.1016/j.ijfatigue.2016.03.036. << /ascii85encodepages false /allowtransparency false /autopositionepsfiles true /autorotatepages /none /binding /left /calgrayprofile (dot gain 20%) /calrgbprofile (srgb iec61966-2.1) /calcmykprofile (u.s. web coated \050swop\051 v2) /srgbprofile (srgb iec61966-2.1) /cannotembedfontpolicy /error /compatibilitylevel 1.4 /compressobjects /tags /compresspages true /convertimagestoindexed true /passthroughjpegimages true /createjobticket false /defaultrenderingintent /default /detectblends true /detectcurves 0.0000 /colorconversionstrategy /cmyk /dothumbnails false /embedallfonts true /embedopentype false /parseiccprofilesincomments true /embedjoboptions true /dscreportinglevel 0 /emitdscwarnings false /endpage -1 /imagememory 1048576 /lockdistillerparams false 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can be opened with acrobat and adobe reader 5.0 and later.) >> /namespace [ (adobe) (common) (1.0) ] /othernamespaces [ << /asreaderspreads false /cropimagestoframes true /errorcontrol /warnandcontinue /flattenerignorespreadoverrides false /includeguidesgrids false /includenonprinting false /includeslug false /namespace [ (adobe) (indesign) (4.0) ] /omitplacedbitmaps false /omitplacedeps false /omitplacedpdf false /simulateoverprint /legacy >> << /addbleedmarks false /addcolorbars false /addcropmarks false /addpageinfo false /addregmarks false /convertcolors /converttocmyk /destinationprofilename () /destinationprofileselector /documentcmyk /downsample16bitimages true /flattenerpreset << /presetselector /mediumresolution >> /formelements false /generatestructure false /includebookmarks false /includehyperlinks false /includeinteractive false /includelayers false /includeprofiles false /multimediahandling /useobjectsettings /namespace [ (adobe) (creativesuite) (2.0) ] /pdfxoutputintentprofileselector /documentcmyk /preserveediting true /untaggedcmykhandling /leaveuntagged /untaggedrgbhandling /usedocumentprofile /usedocumentbleed false >> ] >> setdistillerparams << /hwresolution [2400 2400] /pagesize [612.000 792.000] >> setpagedevice microsoft word numero_55_art_27_2926 n. hammadi et alii, frattura ed integrità strutturale, 55 (2021) 345-359; doi: 10.3221/igf-esis.55.27 345 using xfem to predict the damage with temperature of the steel pipe elbows under bending and pressure loading n. hammadi, m. mokhtari laboratoire la rtfm, ecole nationale polytechnique maurice audin, oran, algeria hammadi.nourddine@grtg.dz mokhtarimohamed44@yahoo.fr, https://orcid.org/0000-0002-2014-1172 h. benzaama laboratoire labab, ecole nationale polytechnique maurice audin, oran, algeria habenza@yahoo.fr, https://orcid.org/0000-0002-7145-3758 k. madani laboratoire mécanique physique des matériaux (lmpm), sidi bel abbes, algeria koumad10@yahoo.fr, https://orcid.org/0000-0003-3277-1187 a. brakna laboratoire la rtfm, ecole nationale polytechnique maurice audin, oran, algeria aek.kaki829@gmail.com e. abdelouahed laboratoire labab, ecole nationale polytechnique maurice audin, oran, algeria heabamine@gmail.com, https://orcid.org/0000-0002-6923-5305 abstract. the pipes, during their service, are subjected to accumulated loads such as internal pressure and that of the soil. the latter considerably accelerate their damage. in this work, the bending moment stress of api 5l x70 category steel elbows under thermo-mechanical behavior and in the presence of pressure were studied. we used fem (finite element method) through the numerical calculation code abaqus and the xfem technique for structural damage while using solid elements as a structure. our objective is to evaluate the response and resistance capacity of the steel elbow by its location in the tube – elbow-tube system under a mixed loading of pressure and moment for all scenarios. it is based on a single standardized dimensioning of the elbow (diameter and thickness). the effect of several parameters has been studied such as the type of loading and the pressure levels, which are clearly conditioned by the level of damage. numerical citation: hammadi, n., mokhtari, m., benzaama, h., madani, k., brakna, k., abdelouahed, e., using xfem to predict the damage with temperature of the steel pipe elbows under bending and pressure loading, frattura ed integrità strutturale, 55 (2021) 345359. received: 20.09.2020 accepted: 27.12.2020 published: 01.01.2021 copyright: © 2021 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. https://youtu.be/rjallofsvb4 n. hammadi et alii, frattura ed integrità strutturale, 55 (2021) 345-359; doi: 10.3221/igf-esis.55.27 346 damage results are presented by moment-rotation curves. they illustrate the variation in damage as a function of these effects, which act simultaneously. keywords. fem (finite element method); xfem (extended finite element modeling); damage. introduction he elbow, in its geometric configuration, will cause a variation in stress along its lower surface and upper surface and by several possible loading conditions, giving rise to several types of damage. several researches have been focused on the understanding of the mechanical behavior of these elbows; these researches were started by the analytical work of von karman [1] where he used a formulation between the longitudinal deformation due to bending and that due to ovalization. rodabaugh and george [2], improved this solution by introducing internal pressure. other researchers such as karamanos and shalaby [3], concluded that under heavy loading the elbow ovalization due to stresses and strains is greater in the circumference than in the longitudinal. they also concluded that the response under closing bending moments is different from that of opening. due to the different signs of ovalization, a series of tests in summer carried out by sobel and newman [4] and dhalla [5] on the flexion response of the elbows under closing moments. their results were compared with numerical results using shell elements. others add pressure in tests such as gresnigt et al [6] where they have developed with van foeken [7] an analytical model for the transverse deformation of elbows by introducing a correction factor to take into account the influence of elbow parameters on its ovalization. the defect and the temperature by their presence strongly destabilize the elbows in their resistance and localize the damage as well as they condition the response of the structures to loading until their failure [8]. they appear in tubular structures as microcracks and or cavities or others. the location of these defects categorizes the mode of damage. most of the time, they result in the degradation of their mechanical characteristics [9-10]. this is the reason why all these phenomena are the subject of numerous research studies applied to industry. the study of these tubular structures is the subject of several researchers such as the work of abdelouahed et al. [10] where they digitally analyzed the structure under pressure and damage moment by thermal effect and in the presence of defects. shao [11] evaluated thermal stresses as well as kandil et al. [12] by the digital model. several researchers such as greenstreet [13], hilsenkopf, suzuki and nasu [14] experimentally tested elbows with different dimensions under different loading modes and compared their results by numerical methods. others like tan et al. [15] recently studied the bending and opening flexion of an elbow and compared it with finite element analysis results. shalaby and younan [16] analyzed 90 degrees steel elbows for a wide range of diameter / thickness ratios under in-plane bending moment in opening and closing with internal pressure. karamanos et al. [17] studied the damage of non-pressurized buckling elbows numerically, a good comparison was found between the numerical results and the experimental tests. greenstreet [13] and hilsenkopf et al. [18] have also shown that 90 degrees elbows in out of plane loading undergo inelastic deformations before damage and that their capacity is affected by the presence of internal pressure. the first part of their work deals with its mechanical behavior with the presence of internal pressure, by analyzing the stresses in the structure requested under various loading conditions. the second part examines the effect of pressure and elbow angle on structural damage. curves show the response of structures to loading until they fail. xfem technique and input parameter he structure is studied by the xfem technique (extend finite element). this technique introduces an enrichment in the elements by an increase in the quality of approximation of the functions. these functions then make it possible to easily initiate and predict the propagation path of the crack and it is implemented in the standard abaqus computation code [19]. the following analysis using this technique xfem uses the elastic properties presented in table 1. the maximum principal stress is the value of the nominal strength, which is measured as 673.14 mpa. the damage evaluation criterion is maximum traction displacement (maximum crack opening of steel x70 measured as 4.2 mm). the damage is continuous throughout the structure by crack propagation resulting in a separation in the structure regardless of the t t n. hammadi et alii, frattura ed integrità strutturale, 55 (2021) 345-359; doi: 10.3221/igf-esis.55.27 347 architectural mesh. this crack propagation in the structure subsequently gives a degradation of the rigidity, which explains the drop in the response of structure under loading, presented in this study by the load-displacement curves. in the xfem technique, damage takes the following forms: *enrichment, name=crack-1, type=propagation crack, activate= on reliable numerical calculations are obtained by the choice of solid elements in three dimensions. there is no presence of cracks or defects in the structure. crack initiation and propagation occur when the structure detects pre-loading failure parameters. the parameters of numerical computation were in good agreement with the convergence of computation and with an optimal time. this allowed us to deepen the different effects on the resistance of our studied structure. these effects are hardly supported by numerical calculations using other criteria. the crack initiation criterion used in this analysis named maxs “the maximum nominal stress criterion” is integrated into the abaqus standard calculation code:         0 0 0 ,  ,   n s t n s t t t t f max t t t (1) nt , st , tt represent respectively the nominal stresses normal and tangential to the two directions (x) and (y). 0 nt , 0 st , 0 tt respectively represent the maximum normal and tangential stresses to the two directions (x) and (y). the initiation of the damage is done without taking into account the purely compressive stresses, and it is in the case where the maximum nominal stress ratio f = 1. the damage evolution law describes the rate at which the material stiffness is degraded once the corresponding initiation criterion is reached. a scalar damage variable, d, represents the overall damage in the material and captures the combined effects of all the active mechanisms. it initially has a value of zero. if damage evolution is modeled, d monotonically evolves from zero to one upon further loading after the initiation of damage. the stress components are affected by the damage according to: nt    { 1 ,                0  0,            n n nd t t t no damage to compressive stiffness (3)   1  s st d t (4)   1t tt d t (5) where   nt ,   nt and   tt are the stress components predicted by the elastic traction-separation behavior for the current strains without damage. the procedure below includes data entries of damage evolution available in the property module. we use displacement as type of damage evolution, it defines damage as a function of the total plastic for bulk elastic-plastic materials, displacement after damage initiation. this type corresponds to the displacement at failure field in the data table introduced in the calculation code.       2 2 2m n s t (2) represents the mixed displacement at failure. δn,, δs and δs represent respectively the normal and tangential displacement at failure. these damage models exhibit softening and stiffness degradation behavior, which often lead to convergence difficulties. the viscous regularization of the constitutive equations defining the behavior in an enriched element is used to overcome the difficulties of convergence. the damping of viscous regularization causes that the tangent stiffness matrix is positive definite for sufficiently small increments of time. a convergence stabilization coefficient was used when 0.00001 with an adequate time increment of 0.0001s was introduced to avoid the damage moment underestimation. the parameters introduced in the abaqus calculation code are: n. hammadi et alii, frattura ed integrità strutturale, 55 (2021) 345-359; doi: 10.3221/igf-esis.55.27 348 *damage initiation, criterion=maxs *damage evolution, type=displacement *damage stabilization 1e-5 description of model geometry and material properties he geometries of the analyzed structure are normalized [20] and illustrated in figures (1) and (2). the characteristics in elastic-plastic behavior and that of resistance are reported in figure (4) and in table (1). the elbow element is connected to two straight pipes of length 960 mm. the length is sufficient to ensure that there is no stress interference in the elbow region from loads applied to the ends of the linear parts. it is assumed that no failure occurs at the elbow; the straight pipe only acts as a means of uniformly transferring the bending moments to the elbow bends. numerically the bending moment load on the elbow was obtained by imposing a rotation around the elbow axis. figure 1: overview of the studied geometry. tubular structures having the following dimensions: the diameter equal to 160 mm and the thickness equal to 6.4 mm. for the three angles of the bend analyzed 30°, 60° and 90°, they have the same radius of curvature which is equal to 480 mm. in order to compare them, these elbows are uniformly subjected to an imposed rotational displacement of 60°. in order to cause only damage, each bend is subjected in the structure by the three modes of bending in addition to three levels of pressure. figure 2: schematic representation of ovalization in (a) in-plane closing moments, (b) out-of-plane opening moments reverse ovalization, and (c) out-of-plane bending for all the situations studied, the elbows are under pressure with the presence of existent temperature in the tubular structure. for all the structures analyzed, they are subject to the same conditions. that is to say a fixation at the edge of the linear part in three displacements according to x, y and z. in the other linear part at the edge of the tube, a rotation is applied depending on the case studied in the direction of opening or closing of the cross section of the tube and around the radius of curvature of the elbow. this rotational displacement leads to damage to the structure. t n. hammadi et alii, frattura ed integrità strutturale, 55 (2021) 345-359; doi: 10.3221/igf-esis.55.27 349 figure 3: state of stress chowing in the elbow geometry and in each finite element. figure 4: experimental stress–strain curves for the elbow material. the properties of api 5l x70 steel are chosen from the experimental work of bouledroua [21]. this allowed us to use these parameters of stiffness, plasticity and strength. the properties are taken from the curve presented in figure (4); the maximum principal stress is the value of the nominal resistance, which takes a level of 673.14 mpa. the criterion for evaluating damage is the maximum tensile displacement (maximum crack opening of the steel at a level of 1 mm). young's modulus e 222 gpa poisson ration 0.3 yield stress 483.03 mpa maximum stress 673.14 mpa elongation % 40.55 % table 1: material mechanical properties of api 5l x70 steel the mechanical properties of the experimental test performed by o. bouledroua (2015), those of the elastic-plastic behavior and of the damage are for a straight tube. in our analysis, we opted for the same material for the whole structure, that of the elbow and the two linear parts. the effects studied on the structure damage were limited only on the three modes of loading choice: moment in closing and in opening and that of the moment out of plans while evaluating at the same time the pressure applied for each different case (elbow angle). n. hammadi et alii, frattura ed integrità strutturale, 55 (2021) 345-359; doi: 10.3221/igf-esis.55.27 350 figure 5: mesh details of region in elbows. according to the geometrical model of this analysis, the mesh structure is carried out by geometrically simple and identical elements in the two linear parts as well as in the elbow. however, in the elbow, the ovalization and the concentration of the stresses responsible for the damage in these zones, require us a refinement of the mesh. this allows better capture and in a precise way the maximum stresses and the initiation of the crack. the linear behavior of x70 steel was modeled using c3d8r three-dimensional brick elements to allow us to assess the effect of the studied parameters. since the structure does not have the same geometries, the number of elements used is according to the angle of the elbow, with a number of elements of 8484 for a structure with a 30 ° elbow and 8200 elements for a 60° elbow as well as 7800 elements for the 90° elbow. figure (5) shows a detail of the mesh used for the calculations. stress analysis he numerous stresses subjected to steel elbows as well as their typical geometry in tubular systems; make them an important and widely studied area of research. hence the idea of studying their behavior under different bending moments and under the presence of both internal pressure and temperature. the geometric shape of the elbow causes an interdependence of effect with the mode of flexion. indeed, depending on the case, these interdependent effects are locally concentrated in the geometry. a preliminary analysis of a stress state in this part of the study is opted in order to better identify the damage to these structures under various parametric or geometric effects. these stress states grouped together in the following curves are stopped just before the damage and with the same level of moment to apply. this numerical computation modality with the xfem technique gave us the advantage with reliability of analyzing these geometric and complex loading situations without there being a problem of convergence. a preliminary analysis of the stress was carried out in order to select our choice on a tangential stress. this remains at a higher level, i.e. 1/3 more than the other components; radial and axial. note that this stress is largely responsible for the damage to the structure. this is mentioned in the work of spyros [20]. pressure effect on the stress pressure is constantly present in the tubular structures. the type of loading applied in an elbow causes radial, axial and circumferential stresses. tubular structures including the elbow, are largely subjected to circumferential stresses hence their representation in the figures, following the elbow circumference at 45°, the pressure effect is evaluated with the presence of temperature and bending moment in opening, closing and out of planes until the damage shown in the following figure. this figure explains that the stress distribution is present at a certain fixed level of the bending moment where the damage to these different structures has not yet taken place. the purpose of this is to see the modality of damage caused by the level and nature of stress distribution in structures. these figures show the bending mode effect of pressurized elbows at different levels on the tangential stresses taken around the circumference of the cross section of the elbow in the most stressed area and which is 15 ° from the curvature of the elbow. it is noted that in all cases of bending moments that the elbow is stressed in compression and in tension along its circumference. we note a symmetrical distribution by contribution to both sides, that of the upper surface and lower surface, by pressure effect. in the open bending mode, the compressive stresses are localized in the upper surface and lower surface of the elbow while the tensile stresses are located in these sides. t n. hammadi et alii, frattura ed integrità strutturale, 55 (2021) 345-359; doi: 10.3221/igf-esis.55.27 351 figure 6: tangential stress just before damage with effect of pressure in the case of angular elbows 90° and temperature of 40°c under opening, closing and out-off-plan flexion moment. n. hammadi et alii, frattura ed integrità strutturale, 55 (2021) 345-359; doi: 10.3221/igf-esis.55.27 352 figure 7: tangential stresses in the elbows of angular 90° for different imposed bending moments. the tangential stresses in their nature are inversely distributed in the case of the bending moment in closure. on the other hand for the case of bending out of planes, the symmetry of distribution is the same between the two parts the upper surface and the lower surface except that the most stressed areas are oriented along a 45 ° plane between the side of the elbow and its extrados. the pressure level effect appears clearly in the compression zones for the open and out-of-plane flexion mode and in the tension zones for the closed flexion mode. note that the greater the pressure inside the structure, the greater the bending moment reactions and the more the thickness of the tubular structure is stressed at the elbow and in these sensitive areas those of the upper surface and the intrados as well as its sides. effect of the angular elbows and loading condition on the stress in piping designs, the bend in tubular structures is presented by multiple angles, pressure and bending moment. each angle is subjected to stress according to the geometry of the elbow, according to the circumference of the elbow at 45 °, elbow at 90 ° and at 30°. for the 60° and 15° elbow and for the 30° elbow, the elbow angle effect is evaluated with the presence of temperature and bending moment in opening, closing and out of planes up to l damage shown in the following figure. it is always noted that the circumferential stresses play a large part in the stresses applied to the elbows. figure (8) explains the most stressed area in the elbow and subsequently the damage initiation area. it also explains the additive effect of temperature and more particularly that of pressure which directly influences the stress distribution under bending moment. the distribution of tangential stresses was selected in this analysis because it has higher levels than other stresses, radial and axial. it is clearly noticed that the stresses are more important for the most closed elbow except for the out-of-plane bending. the stresses change their nature from compression to tension along the circumference of the elbow for all three modes of flexion except that their areas of compression and tension change from one flex mode to another. it should be noted that in the case of bending in opening, the areas, which are closest to the sides of the elbow, are subjected to significant tensile stresses, and at the same level are the compressive stresses in the upper surface and the lower surface. this stress state is inversely distributed in these zones for the case of bending in closure, and for the case of bending out of planes. the most stressed areas are angularly offset and are oriented along a 45° plane between the side of the elbow and its extrados. damage analysis y virtue of these numerous advantages, elbows are frequently present in tubular structures, by their geometry and by the permanent presence of pressure and also under the various modes of stress. however, they are much more exposed to their damage than straight tubular structures. under thermo-mechanical behavior, the damage of these structures quickly becomes more favorable; hence, our problem of identifying their resistance capacity under the effect of various parameters, those of the mode of applied moment, of applied pressure and of dimension of the elbows. it is noted that according to the modes of bending, the resistance of systems is the resistance of the elbow itself in the system straight tube-elbow-straight tube. effect of the angular elbows and loading condition on the failure of structure the geometric configuration of the elbow in the straight tube-elbow-straight tube system conditions the structural response to loading as well as their resistance levels. in all cases, the presence of pressure and temperature act as an accelerator to b n. hammadi et alii, frattura ed integrità strutturale, 55 (2021) 345-359; doi: 10.3221/igf-esis.55.27 353 damage the structure. the angle of the elbow changes the shape not only of the elbow itself but also of the overall structure which is stressed in these different modes of flexion that of opening, closing and out of planes. under a pressure of 30bar and at the same temperature of 40 ° c, the angle effect of the elbow is well presented in the structural response up to their damage and under different bending modes. figure 8: tangential stress just before damage with effect of angular elbows in the case of temperature 40°c and pressure of 30 bar under opening, closing and hors plans flexion moment. n. hammadi et alii, frattura ed integrità strutturale, 55 (2021) 345-359; doi: 10.3221/igf-esis.55.27 354 figure 9: tangential stresses in the elbows of angular 90° 60° and 30° in the case of closing bending moments. figure (10) shows that the response of the elbow to the bending moment is nonlinear up to the maximum moment with different levels, widely different by the effect of the angle of the elbow. we notice that at a certain moment, this level is maximum. this explains the resilience of the system. the rotational displacement of the system becomes independent of the applied bending moment, in particular for the case of out-of-plane bending. it is also noted that the same nature of response of the structure to the bending moment is marked for the different angles of the elbow as for the different modes of bending, the more the angle of the elbow is open, the more the moment is important to damage the structure. in all these different cases, the damage occurs after the transverse ovalization of the elbow. depending on the bending mode, this ovalization takes several planes in the bend, the most dangerous is that which presents itself with the lowest damage moments and which are, in the case of closing moments. n. hammadi et alii, frattura ed integrità strutturale, 55 (2021) 345-359; doi: 10.3221/igf-esis.55.27 355 figure 10: damage moment–rotation curve with effect of angular elbows in the case of pressure 30bar and temperature of 40°c under opening, closing and out-off plan flexion moment figure 11: damage of the elbows of angular 90° 60° and 30° in the case of closing bending moments. in this figure (11), the damage zones caused by both the pressure effect and the closing bending moment effect have been presented, for the various cases for the angle of the elbow: 30°, 60° and 90°. this presentation has shown that these zones are the same, which are presented in the structure by the stress concentrations just before the damage. their mode, as shown in figure (11), differs depending on the angle of the elbow. for the 90 ° elbow, we notice wrinkles in the upper surface due to high tension in this area, while for the 60 ° elbow, damage is found only in the sides of the elbow, while the 30 ° elbow ° presents with several areas of damage. the tubular cross section of the elbow is subjected to internal pressure as a reaction to tensile forces. these are finely localized according to the angle of the elbow and the bending moment. once a crack appears in an area, the structure becomes destabilized in its resistance, resulting in the appearance of several areas of damage, especially for the 30 ° elbow. effect of the pressure with different loading condition on the failure of structure in this part of the study, we used dimensional conditions of the 90 ° elbow because it has low resistance compared to others such as the 30 ° and 60 °. the temperature is at a level of 40 ° c and is the same in all the different cases and this to have a response of the structures until their damage with a thermo-mechanical behavior. however, depending on the conditions in which they occur, the temperature and the pressure weaken the structure by accumulating charges. the mode of flexion and the angle of the elbow take place as comparative parameters to which the resistance capacity is related. the response and evolution of the system to thermo-mechanical damage under the evaluative parameters are presented below by the torque curves. rid n. hammadi et alii, frattura ed integrità strutturale, 55 (2021) 345-359; doi: 10.3221/igf-esis.55.27 356 figure 12: damage moment–rotation curve with effect of pressure values in the case of angular elbows 90° and temperature of 40°c under opening, closing and hors plans flexion moment we see in figure (12) the same responses up to the critical moment with slightly different levels of damage, which corresponds to clearly significant angular displacements, especially for the case of the bending moment in opening and closing. the structure with the greatest pressure does not allow a large deformation capacity. the lower the pressure, the n. hammadi et alii, frattura ed integrità strutturale, 55 (2021) 345-359; doi: 10.3221/igf-esis.55.27 357 more it allows the deformation of the structure and the more damage is delayed. one notes the opposite for the structure under the mode of bending except plans. a localized ovalization of the pipe of the elbow in the middle is perpendicular to the bending planes for the case of moment in closing and is parallel to the planes of bending for the case of moment in opening, and it is inclined for the case of bending out of planes. this oval deformation describes the response of the structure, which leads to rapid damage by the additive effect of temperature and pressure. the failure therefore occurs when the elbow is stressed by its thickness to high tensions at the level of the lower surface of the elbow in the case of the opening and at the level of the upper surface as well as on the sides of the elbow for the case closing. on the other hand, in the case of out of planes, it occurs throughout the part of the elbow. the areas of damage caused under the effect of different bending modes, with a pressure of 30 bar and a bend angle of 30°, are shown in figure (13). these zones always remain dependent on the bending mode. in all cases, the areas of stress concentration are the areas of initiation of damage. their modes, as shown in figure (13), differ depending on the bending moments. at the time of opening and during high tensions, the damage is localized in the sides of the elbow. also for the moment out of plans but which shifted from the middle of the elbow. on the other hand, for the moment of closure, we notice that there are several damage initiation zones. internal pressures stress the elbow thickness as a reaction to the tensile forces; these forces are localized according to the bending moment. figure 13: damage in the pressure of 30bar and elbows of angular 30° in the different case of bending moments. conclusion espite the numerical complications of this work of the model studied, such as: geometric and complex loading conditions (combined bending with internal pressure) and in fabric and geometrically tubular composite structures, the damage criterion clearly presented its effectiveness. the results obtained allowed us to gain an understanding of the interaction of defects and to compare the different parameters influencing the damage of our studied structures.  for our numerical result under application of a moment in the form of angular displacement of 60 º as well as a reinforcement of thickness up to 6.4mm, we found according to the studied case, a critical moment between 65 knm and 85 knm for a pressure between 20bar and 40bar. it is a difference of 11kn from the work of karamanos where he used thickness of 3mm and diameter of 270 mm.  the x-fem technique has proven its effectiveness as well as damage criterion, given that our structure is made with solid finite elements in three dimensions and that this technique is no longer limited in its use in interfaces such as vcct and czm and it is independent of the architecture of the mesh. in our case, it does not require the presence of a pre-crack.  purely pressurized tubular structures are circumferentially stressed in tension more than by other stresses, these stresses are more important than others are, and they can change the nature of the tension at compression depending on the loading and geometry conditions as in our elbow case.  the transverse oval plane of the elbow is according to the flexion mode in which it is subjected.  the open bend allows greater angular displacements with higher critical bending moments. d n. hammadi et alii, frattura ed integrità strutturale, 55 (2021) 345-359; doi: 10.3221/igf-esis.55.27 358  the less pressurized the system is, the more the structure supports angular displacements and significant bending moments.  plasticization of the metal occurs at the levels of the ovality, which explains the response of the structure in angular rotation under the bending moment.  by the presence of pressure and the bending moment, ovalization takes place in the middle of the elbow and the area of the damage.  the temperature weakens and accelerates the damage to the structure by accumulation of mechanical loads. in light of the above arguments, this work provided a suitable modeling for more problems, on the predictions of the damage in elastic-plastic behavior of different geometries in x70 steel and it may be of interest for further research. references [1] von karman, t., (1911). uber die formuanderung dunnwandiger rohre, zeit. des verienes. deutcher ingenieur,55, pp. 1889–1895. [2] rodabaugh, e. c., and george, h. h., (1957). effect of internal pressure on the flexibility and stress intensification factors of curved pipe or welding elbows, trans. asme, 79, pp. 939–948. [3] karamanos, s. a., tsouvalas, d., and gresnigt, a. m., (2006). ultimate bending capacity and buckling of pressurized 90 deg steel elbows, journal of pressure vessel technology, 128(3), pp. 348–356. doi: 10.1115/1.2217967. [4] sobel, l. h., and newman, s. z., (1980). comparison of experimental and simplified analytical results for the inplane plastic bending and buckling of an elbow, journal of pressure vessel technology, 102(4), pp. 400–409. doi: 10.1115/1.3263351. [5] dhalla, a. k., (1987). collapse characteristics of a thin-walled elbow,” journal of pressure vessel technology, 109(4), pp. 394–401, doi: 10.1115/1.3264922. [6] gresnigt, a. m., (1985). preofresultaten van proeven op gladde bochten en vergelijking daarvan met de in opl 85333 gegeven rekenregels, institute for construction materials and structures, tno-ibbc, report no. opl 85-334, delft, the netherlands. [7] auwal, m., ercan, ş., (2014). experimental and numerical study of energy absorption behavior of glass and carbon epoxy composite tubes under static compressive loading, iosr journal of applied physics, 6(4), pp. 30-37, doi: 10.9790/4861-06433037. [8] lemaître, j., chaboche, j.l., (1988). mécanique des matériaux solides, edition dunod, 2ème édition,france. [9] lachaud, f., michel, l. (1997). etude de l’endommagement de matériaux composites carbones à matrice thermodurcissable et thermoplastique, mécanique industrielle et matériaux, 50(2). [10] abdelouahed, e., mokhtari, m., benzaama, h. (2019). finite element analysis of the thermo-mechanical behavior of composite pipe elbows under bending and pressure loading, frattura ed integrita strutturale, 49, pp. 698-713, doi: 10.3221/igf-esis.49.63 [11] shao, z. s., (2005). mechanical and thermal stresses of a functionally graded circular hollow cylinder with finite length, international journal pressure vessels piping, 82(3), pp. 155–163. doi: 10.1016/j.ijpvp.2004.09.00. [12] kandil, a., el-kady, a. a., and el-kafrawy, a. (1995). transient thermal stress analysis of thickwalled cylinders, int. j. mech. sci., 37(7), pp. 721–732. doi: 10.1016/0020-7403(94)00105-s. [13] greenstreet, w. l., (1978). experimental study of plastic responses of pipe elbows”, ornl/nureg-24 categoty nrc5. [14] suzuki, n, and nasu, m., (1989). non-linear analysis of welded elbows subjected to in-plane bending”, comput. struct, 32(3/4), 871–881. doi: 10.1016/0045-7949(89)90371-4 [15] tan, y, matzen, v. c., and yu, l. x., (2002). correlation of test and fea results for the nonlinear behavior of straight pipes and elbows”, journal of pressure vessel technology, 124(4), pp. 465–475. doi: 10.1115/1.1493806. [16] shalaby, m. a., and younan, m. y. a., (1999). effect of internal pressure on elastic–plastic behavior of pipe elbows under in-plane opening bending moments, journal of pressure vessel technology, 121(4), pp. 400–405. [17] karamanos, s. a., giakoumatos, e., and gresnigt, a. m., (2003). nonlinear response and failure of steel elbows under in-plane bending and pressure, journal of pressure vessel technology, 125(4), pp. 393–402. [18] hilsenkopf, p., boneh, b., and sollogoub, p. (1988). experimental study of behavior and functional capability of ferritic steel elbows and austenitic stainless steel thin-walled elbows, int. j. pressure vessels piping, 33(2), pp. 111– 128. doi: 10.1016/0308-0161(88)90065-8. [19] abaqus, abaqus version (2009). 6.9documentation. providence, ri: dassault systems simulia corporation. n. hammadi et alii, frattura ed integrità strutturale, 55 (2021) 345-359; doi: 10.3221/igf-esis.55.27 359 [20] karamanos, s.a. (2016). finite element analysis of the mechanical behavior of mitered steel pipe elbows under bending and pressure, journal of pressure vessel technology. doi: 10.1061/9780784479957.117. [21] bouledroua, o., ouled mbereick, m., azari, z., hadj meliani, m. (2015). qualification d’un acier api 5l x70: etude expérimentale et validation numérique, journal of nature &amp; technologie, 13, pp. 34-39. microsoft word numero_39_art_21 s. k. kudari et alii, frattura ed integrità strutturale, 39 (2017) 216-225; doi: 10.3221/igf-esis.39.21 216 3d stress intensity factor and t-stresses (t11 and t33) formulations for a compact tension specimen s. k. kudari department of mechanical engineering, cvr college of engineering, hyderabad, india s.kudari@rediffmail.com k. g. kodancha research centre, department of mechanical engineering, bvb college of engineering & technology, hubli, india krishnaraja@bvb.edu abstract. the paper describes test specimen thickness effect on stress intensity factor (ki), and t-stresses stresses (t11 and t33) for a compact tension specimen. formulations to estimate 3d ki, t11 and t33 stresses are proposed based on extensive 3d finite element analyses. these formulations help to estimate magnitudes of 3d ki and t11 and t33 which are helpful to quantify in-plane and out-ofplane constraint effect of the crack tip. the proposed formulations are validated with the similar results available in literature and found to be within acceptable error. keywords. constraint effects; 3d finite element analysis; stress intensity factor; t-stress; ct specimen. citation: kudari, s. k., kodancha, k. g., 3d stress intensity factor and t-stresses (t11 and t33) formulations for a compact tension specimen, frattura ed integrità strutturale, 39 (2017) 216-225. received: 25.09.2016 accepted: 31.10.2016 published: 01.01.2017 copyright: © 2017 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. introduction tress tri-axiality at the crack-tip can alter crack-tip constraint and fracture toughness values of a material. this is the reason transferability of fracture toughness data estimated using laboratory test specimens to a full-scale cracked structure is an important issue in structural integrity assessment of engineering materials. in lefm non-zero nonsingular terms in the series expansion of three-dimensional stress field [1] referred as t-stresses (t11 and t33) can alter the crack-tip stress tri-axiality and are considered as constraint parameters [2]. t11 (the second term of william’s extension acting parallel to the crack plane) plays an important role on the in-plane constraint effect. the thickness at the crack tip contributes to the out-of-plane constraint, t33 (the second term of william’s extension acting along the thickness). to transfer fracture toughness data under different constraints, both in-plane and out-of-plane constraint effect should be considered for the specimens. s http://www.gruppofrattura.it/pdf/rivista/numero39/audio/21.mp3 s. k. kudari et alii, frattura ed integrità strutturale, 39 (2017) 216-225; doi: 10.3221/igf-esis.39.21 217 several researchers [3-13] have shown that the specimen thickness has major effect on the magnitude of stress intensity factor and t stresses. kwon and sun [7] have presented 3d fe analyses, to investigate the stress fields near the crack-tip and suggested a simple technique to determine 3d ki at the mid-plane by knowing 2d ki and poisson’s ratio () of the material using the eq. (1): d d k k 3 2 2 1 1    (1) for quantifications of in-plane and out-ofplane constraint issues, magnitudes of t11 and t33 stresses are to be computed. but simple formulations such as eq. (1) to estimate 3d ki, are not available to compute constraint parameters, t11 and t33 stresses. usually they are obtained by complex 3d numerical methods. the aim of this investigation is to study the variation of ki, t11 and t33 along the crack-front considering a ct specimen geometry having varied thickness, b, crack length to width ratio (a/w) and applied stress, , using 3d elastic fe analysis. based on the present finite element results an effort is made to formulate approximate analytical equations to estimate the magnitudes of maximum 3d ki, t11 and t33 for a ct specimen. the proposed analytical formulations can be used to estimate the maximum 3d ki, t11 and t33 for the ct specimen, which are helpful in quantifying in-plane and out-ofplane constraint issues in fracture. by means of numerical analyses, it is shown that specimen thickness and crack length play an important role on the constraint effects. figure 1: the geometry of the ct specimen used in the analysis (w=20 mm). finite element analysis ommercial fe software abaqus 6.5 [14] is used for the 3d fea. the dimensions of ct specimen have been chosen according to astm standard e1820 [15] and the specimen geometry is shown in the fig.1. one-half of the specimen geometry is modeled due to specimen symmetry. twenty noded quadratic brick elements available in the abaqus are used to discretize the analysis domain. this kind of elements was used in the earlier works [8, 9] available in the literature. initially, three-dimensional fe analyses on ct specimens were made by varying number of layers in thickness direction (each layer is of element thickness). it is observed that the variation in results of ki is insignificant for 8-14 layers. consequently, in the present analyses 11 layers along the thickness direction were chosen as it gives ten numbers of elements along the thickness direction to extract the ki and t-stress. due to half symmetry, the symmetrical boundary conditions have been imposed (ux2=0) along the ligament of the model. load is applied on approximately 1/3rd portion nodes of the loading-hole circle perpendicular to the ligament. to keep the loading in perfectly mode-i condition corresponding nodes are arrested except x2-direction. a typical mesh used in the analyses along with boundary conditions is shown in fig.2. the magnitudes of ki and t-stresses have been extracted by using abaqus post processor. the details of extraction of stress 3d stress intensity factor (ki) and t-stresses are discussed elsewhere [11,12,16,17]. the variation of ki and t-stresses along the crack-front has been studied for different specimen thickness (b/w=0.1-1.0) and crack length to width ratio (a/w=0.45-0.70). in this work the magnitude of applied stress, , for the ct specimen is computed using the relation [18]: c s. k. kudari et alii, frattura ed integrità strutturale, 39 (2017) 216-225; doi: 10.3221/igf-esis.39.21 218 p w a b w 2 2 ( 2 ) ( )    (2) where, p is applied load, w is width of the specimen, a is crack length. in these finite element calculations, the material behaviour has been considered to be linear elastic pertaining to an interstitial free (if) steel possessing yield stress y=155mpa, elastic modulus of 197 gpa, poisson’s ratio=0.30. figure 2: 3d ct specimen mesh along with boundary conditions for a/w=0.50: a) b/w=0.1; b) b/w=1. figure 3: effect of a/w on normalized stress intensity factor, ki /(a)1/2 along crack-front (x3) for b=10mm. results and discussion stress intensity factor (ki) typical variation of normalized stress intensity factor (ki/(a)1/2) and the distance along the crack front (specimen thickness direction, x3) for specimens having various a/w is shown in fig.3. the nature of variation of normalized stress intensity factor shown in fig.3 is in good agreement with the similar results [7,19]. the a s. k. kudari et alii, frattura ed integrità strutturale, 39 (2017) 216-225; doi: 10.3221/igf-esis.39.21 219 magnitudes of 3d maximum stress intensity factors (at the center of the specimen) are compared with the analytical 2d value computed by eq. (3). ik y a  (3) typically, such comparison for a specimen with a/w=0.65 is shown in fig.3. it is estimated that magnitude of 2d ki is about 10% lower than 3d ki. it is well known that variation of stress intensity factor against  a 1/2  for various specimen thickness (b) is linear, slopes of ki-max vs.  a 1/2  obtained for various a/w are plotted in fig 4. as the relation between ki-max/  a 1/2  and a/w (fig.4) is nonlinear, the data is fit with a suitable polynomial. in such exercise, it is found that a polynomial equation of third order fits the 3d fea results with least error (regression co-efficient=0.998). this polynomial fit (eq. (4)) is superimposed on the 3d fea results plotted in fig.4 and shows an excellent agreement. from this third order polynomial fit, the relation between ki-max, a/w and  can be expressed as: i k a a a w w wa 2 3 max 4.48287 14.99985 20.44016 3.85185                        (4) let, a a a c w w w 2 3 1 4.48287 14.99985 20.44016 3.85185                     (5) figure 4: variation of slopes, ki-max/  a 1/2  vs. a/w. the eq. (4) reduces to: ik c amax 1   (6) eq. (6) is similar to eq. (3) and the constant c1 shown in eq. (5) is similar to the geometric factor, y as used in eq. (3). hence, c1 in this work is referred as 3d geometric factor. eq. (6) can be used to estimate magnitudes of ki-max for the ct specimen. to validate the proposed formulation given in eq. (6), the computed values of ki-max using eq.(6) for various a/w are compared with the present 3d fea results and the results computed by eq.(1) proposed by kwon and sun [7] in fig.4. the figure shows that the results computed by eq. (6) are in good agreement with the results obtained by s. k. kudari et alii, frattura ed integrità strutturale, 39 (2017) 216-225; doi: 10.3221/igf-esis.39.21 220 present 3d fea for a/w 0.45 to 0.70 (entire range of study). the values of ki-max estimated from the eq.(1) [7] are found to in good agreement with the present results for specimens with a/w 0.45 to 0.65, but for a specimen having a/w>0.65 the eq.(1) [7] is showing higher error. the error analysis between the results obtained by present 3d fea and the eq.(6) is conducted. the maximum percentage of error estimated in use of eq.(6) for b=2 to 20mm and a/w=0.45 to 0.70 is < 2.95 %. figure 5: a typical variation of t11/ along the crack-front for various b and a/w=0.50. t11-stress the magnitudes of t11 are extracted from 3d fe analysis for varied , b and a/w. a typical variation of t11 along the crack-front for various b, a/w=0.50 and  =86.8 mpa is shown in fig.5. this figure shows that the variation of t11 along the crack-front (x3) depends on the specimen thickness. it is observed that the magnitude of t11 is maximum at the centre of the specimen than on the surface. however, for the specimen thickness, b<6mm the maximum value of t11 is found to be just below the surface. it is seen from fig.5 that for specimen with higher thickness, the magnitude of t11 decreases for a short distance from the specimen surface and again increases at the centre of the specimen thickness. similar kind of variation was observed in the work of pavel et al. [20]. to study the effect of a/w, a typical variation of t11/ for various a/w, b=10mm and  =86.8 mpa is plotted in fig.6. the figure illustrates that t11 depends on the specimen a/w, and it is observed to be maximum for higher a/w. the results in fig.5-6 indicate that the in-plane constraint parameter, t11, is not a unique value (as obtained in 2d analysis) for a specimen thickness, but it varies along the thickness and it is maximum at the centre. the variation of t11 at the center (t11-max) vs. normalized ki (ki-max/(πb)1/2) for various specimen thicknesses is studied. a typical plot of t11-max against ki-max/(πb)1/2 for various a/w and b=10 mm is shown in fig.7. it is seen from the fig.7 that the variation of t11-max vs. ki-max/(πb)1/2 is linear and is independent of a/w. the slopes of t11-max vs. ki-max/(πb)1/2 are computed for various a/w by fitting a straight-line equation to all the results shown in fig.7. the estimated slopes t11max/(ki-max/(πb)1/2) are plotted against normalized thickness (b/w) for various a/w in fig. 8. this plot indicates that, the nature of variation of slopes t11max/ (ki-max/(πb)1/2) against b/w is nonlinear and is almost independent of a/w. the result plotted in fig.8 is used to obtain a relationship between t11-max and ki-max. as there is a small difference is observed in the results presented in fig.8 for various a/w, the average slope of all a/w for particular b/w is used. the average results are fit by a polynomial equation of third order (regression co-efficient=0.994), which give a best fit to all the data. from this third order polynomial fit, the relation between t11-max and ki-max is obtained and can be expressed as: i t b b b k w w w b 2 3 11 max max 0.1477 0.93746 0.87183 0.35186                              (7) s. k. kudari et alii, frattura ed integrità strutturale, 39 (2017) 216-225; doi: 10.3221/igf-esis.39.21 221 figure 6: a typical variation of t11/ along the crack-front for various a/w and b=10mm. figure 7: variation of t11-max against ki-max/πb1/2 for various a/w and b=10 mm. figure 8: variation of slopes t11-max/(ki-max/(πb)1/2 against b/w for various a/w. let, b b b c w w w 2 3 2 0.1477 0.93746 0.87183 0.35186                     (8) the eq. (7) reduces to: ikt c b max 11max 2        (9) substituting for ki-max from eq.(6) s. k. kudari et alii, frattura ed integrità strutturale, 39 (2017) 216-225; doi: 10.3221/igf-esis.39.21 222 a t c c b 11 max 1 2. .            (10) a t c c b 11max 1 2. . (11) where, constant c1 and c2 are referred in this work as 3d geometric factors. the values of c1 for various a/w and c2 for various b/w for the ct specimen are tabulated in tab.1 and tab.2 respectively. a/w 0.45 0.50 0.55 0.60 0.65 0.70 c1 1.5211 1.6115 1.7753 2.0094 2.3111 2.6775 table 1: values of c1 computed from eq.(5). b/w 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 c2 0.2331 0.3031 0.3600 0.4057 0.4425 0.4723 0.4974 0.5199 0.5417 0.5652 table 2: values of c2 computed from eq.(8). the above eq.(11) can be used to estimate t11-max for the ct specimen for a given specimen dimensions and applied load, . a typical plot of t11-max computed from eq.(11) is superimposed (red curve) on 3d fea results shown in fig. 8. this plot shows a good agreement with the results estimated by eq.(11) and 3d fea. an error analysis is carried out between the estimated values from eq.(11) and the present 3d fea results. the maximum percentage of error in use of eq.(11) for various b, a/w and  used in this study is found to be < 5.1%. the proposed analytical eq.(11) is a simple method to compute t11-max for the ct specimen geometry. figure 9: variation of t33/ against b/w for various a/w. t33-stress the magnitudes of t33 are estimated using eq.(12) by substituting the extracted 33 (strain) from abaqus post processor and t11 for varied , b and a/w. t e t33 33 11   (12) s. k. kudari et alii, frattura ed integrità strutturale, 39 (2017) 216-225; doi: 10.3221/igf-esis.39.21 223 the variation of t33-max/ against b/w for various a/w is shown in fig.9. this figure indicates that, t33 strongly depend on b/w. it is observed that the magnitude of t33 is negative for all cases that were considered in this analysis, and approached to zero as b/w increased to 1. for b/w=0.5, astm requirement for kic test specimen [15], it is seen that t33 / is negative indicating loss of out-of-plane constraint. t33 also showed dependence on a/w, for b/w<0.7, t33 is found to be maximum for thinner specimens (b/w=0.1) with higher a/w =0.7. as t33 strongly depends on the specimen thickness, it is not possible to get a simple relation between t33 and specimen geometry as obtained in case of ki and t11. to obtain expressions between t33, specimen geometry and the applied load, the results in fig.9 are given a polynomial fit to suit the 3d fea results. in this exercise, it is found that the 5th order polynomial fits the data with least error. a typical equation for estimation of t33–max is given by eq. (13). the equations for the 3d geometric factors (c3) to compute t33-max for various a/w obtained by fitting 5th order polynomial are tabulated in tab.3. t c33max 3 (13) the computed values of c3 for various a/w are given in tab.4. the maximum percentage of error in the use of equations given in tab.3 for various b, a/w and  is found to be < 7.8%. table 3: polynomial equations for t33. a/w b/w 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 0.45 -1.7789 -1.1638 -0.8782 -0.7333 -0.6288 -0.5279 -0.4316 -0.3537 -0.2952 -0.2187 0.50 -1.9659 -1.2962 -0.9818 -0.8167 -0.6934 -0.5739 -0.4618 -0.3735 -0.3097 -0.2271 0.55 -2.3066 -1.5136 -1.1231 -0.9112 -0.7573 -0.6148 -0.4825 -0.3758 -0.2971 -0.2078 0.60 -2.6057 -1.6969 -1.2512 -1.0063 -0.8239 -0.6545 -0.5012 -0.3831 -0.3003 -0.1970 0.65 -3.2337 -2.0548 -1.4816 -1.1664 -0.9288 -0.7066 -0.5075 -0.3600 -0.2647 -0.1457 0.70 -3.7325 -2.3393 -1.6366 -1.2367 -0.9384 -0.6721 -0.4449 -0.2855 -0.1895 -0.0644 table 4: values of c3 computed from formulations given in tab.3. a/w polynomial equations 0.45 t b b b b b w w w w w 2 3 4 5 33 max 3.02667 16.98748 53.07517 86.44814 68.70629 21.15385                                      0.50 t b b b b b w w w w w 2 3 4 5 33 max 3.32333 18.49597 58.0134 95.41084 76.51515 23.71795                                      0.55 t b b b b b w w w w w 2 3 4 5 33 max 3.858 20.88005 62.97348 100.77273 79.1317 24.10256                                      0.60 t b b b b b w w w w w 2 3 4 5 33 max 4.40067 24.26372 74.31294 121.11772 96.8648 30                                      0.65 t b b b b b w w w w w 2 3 4 5 33 max 5.582 31.84602 98.58275 162.16142 130.62937 40.64103                                      0.70 t b b b b b w w w w w 2 3 4 5 33 max 6.44533 36.53654 110.79021 181.22902 146.36364 45.76923                                      s. k. kudari et alii, frattura ed integrità strutturale, 39 (2017) 216-225; doi: 10.3221/igf-esis.39.21 224 to evaluate the worthiness of the analytical expressions to estimate ki-max, t11-max and t33-max proposed in this analysis, the estimated magnitudes ki-max, t11-max and t33-max obtained by eq.(6), eq.(11) and tab.3 are compared with the similar results on the ct specimen presented by toshiyuki and tomohiro [12]. the authors [12] have given the variation of t11max and t33-max for the toughness value of the material (0.55% carbon steel) ki-max= 66 mpam1/2. fig. 10 shows a typical variation of estimated ki-max, t11-max and t33-max at the specimen thickness center against b/w (0.1 -1.0) obtained by proposed analytical expressions (eq.(6), (11) and tab.3) for ki-max= 66 mpam1/2 and results of toshiyuki and tomohiro [12]. the authors [12] have computed various parameters for b/w=0.25, 0.4 and 0.5 only. according to fig. 10, the magnitudes of ki-max were not affected by b/w as expected and are in excellent agreement with toshiyuki and tomohiro [12]. t11 showed visible dependence on b/w, though the variation was less than 20% and it is in good agreement with the earlier reported results [12]. in summary, the in-plane parameters at the specimen thickness center showed small dependence on b, and are in excellent agreement with the earlier results [12] providing validation for the proposed eq.(6) and (11). on the other hand, out-of-plane constraint factor, t33 showed strong dependence on b/w. t33 was found negative and approached zero as b/w increased from 0.1 to 1. fig. 10 shows that the nature of variation of present results of t33 (obtained by tab.3 expressions) is in similar manner to the one presented by toshiyuki and tomohiro [12]. however, some difference in the magnitude of t33 between both the results for b/w=0.25-0.5 is observed. this difference is attributed to the effect of side grooves in the ct specimen used in the work of toshiyuki and tomohiro [12]. the side grooves in the specimen affects the strain distribution in the out-of-plane direction and restricts the value of t33 (ref. eq.(12)). to study this effect, we have conducted 3d fea on ct specimen used by toshiyuki and tomohiro [12] without side groove and for the same material properties. these computed results are superimposed in fig.10 by red colored lines for comparison. this plot show that the results (ki-max, t11-max and t33-max) for the specimen without side groove match with the one computed by the analytical expressions (eq.(6), (11) and tab.3) proposed in this work. this exercise infers that the use of side grooves in a specimen controls 33 and improves the out-of-plane constraint (ref.fig.10: for a/w=0.5, t33 is improved from -150 mpa to -84 mpa (44%) by using 10% side groove [12]). the fig. 10 provides validation to the proposed analytical formulations to estimate ki-max, t11-max and t33-max. figure 10: a typical variation of ki-max, t11-max and t33-max against b/w obtained by proposed analytical expressions and results of toshiyuki and tomohiro [12]. summary n this study, stress intensity factor and t-stress (t11 and t33) solutions for ct specimens for wide range of specimen thickness and crack lengths were computed using 3d elastic fea. it is observed that magnitude of t33 (ref: fig.(9)) is highly negative for b/w=0.1 (thin specimens), and almost zero for b/w=1 (thick specimens), indicating that the thick specimens have higher out-of-plane constraint. for b/w=0.5, astm requirement for kic test [15], it is observed i s. k. kudari et alii, frattura ed integrità strutturale, 39 (2017) 216-225; doi: 10.3221/igf-esis.39.21 225 that t33 / is negative indicating some loss of out-of-plane constraint. for the specimens with similar a/w and b/w the loss of out-of-plane constraint (t33) is much significant than the in plane constraint (t11) (ref. fig.10). this infers that the major constraint loss in a ct specimen is due to the out-of-plane effects. the out-of-plane constraint loss can be corrected to some extent by providing side grooves to a ct specimen. using the present 3d fea results, approximate analytical formulations are proposed to evaluate the ki-max, t11-max and t33-max by knowing only applied stress and specimen dimensions. these formulations can be helpful in the analysis of in-plane and out-of-plane constraint issues. references [1] nakamura, t., parks, d. m., determination of elastic t-stress along three-dimensional crack fronts using an interaction integral, int. j. solids struct., 29 (1992) 1597–1611. [2] betegon, c., hancock, j. w., two-parameter characterization of elastic–plastic crack tip fields, j appl mech., 58 (1991) 104–110. [3] kudari, s. k., kodancha, k. g., a new formulation for estimating maximum stress intensity factor at the mid plane of a senb specimen: study based on 3d fea, frattura ed integrità strutturale, 29 (2014) 419-425. [4] nakamura, t., parks, d. m., three-dimensional crack front fields in a thin ductile plate, j. mech. phys. solids., 38 (1990) 787–812. [5] nevalainen, m., dodds, r. h., numerical investigation of 3-d constraint effects on brittle fracture in se(b) and c(t) specimens, int. j. fract., 74 (1995) 131–161. [6] leung, a. y. t., su, r.k.l., a numerical study of singular stress field of 3d cracks, finite elem. anal. design., 18 (1995) 389–401. [7] kwon, s. w., sun, c.t., characteristics of three-dimensional stress fields in plates with a through -the-thickness crack, int. j. fract., 104 (2000) 291-315. [8] jie, q., xin, w., solutions of t-stresses for quarter-elliptical corner cracks in finite thickness plates subject to tension and bending, int. j. pres. ves. pip., 83 (2006) 593–606. [9] moreira, p. m. g. p., pastrama, s. d., castro, p. m.. s. t., three-dimensional stress intensity factor calibration for a stiffened cracked plate, engng. fract. mech., 76 (2009) 298–2308. [10] kodancha, k. g., kudari, s. k., variation of stress intensity factor and elastic t-stress along the crack-front in finite thickness plates. frattura ed integrità strutturale, 8 (2009) 45-51. [11] toshiyuki, m., tomohiro, t., kai, l., t-stress solutions for a semi-elliptical axial surface crack in a cylinder subjected to mode-i non-uniform stress distributions, engng. fract. mech., 77 (2010) 2467-2478. [12] toshiyuki, m., tomohiro, t., experimental t33-stress formulation of test specimen thickness effect on fracture toughness in the transition temperature region, engng. fract. mech., 77 (2010) 867-877. [13] kai, l., toshiyuki, m., three-dimensional t-stresses for three-point-bend specimens with large thickness variation, engng. fract. mech., 116 (2014) 197-203 [14] abaqus v 6.5-1. (2004) hibbitt, karlsson & sorensen, inc. [15] american society for testing and materials., standard test method for measurement of fracture toughness, (2015) astm e1820-15a. [16] moran, b., shih, c. f., crack tip and associated domain integrals from momentum and energy balance. engng. fract. mech., 27 (1987) 615-642. [17] gosz, m., dolbow, j., moran, b., domain integral formulation for stress intensity factor computation along curved three-dimensional interface cracks. int. j solids struct., 35 (1998) 1763-1783. [18] priest, a. h., experimental methods for fracture toughness measurement, j. strain analysis, 10 (1975) 225-232. 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can be opened with acrobat and adobe reader 5.0 and later.) >> /namespace [ (adobe) (common) (1.0) ] /othernamespaces [ << /asreaderspreads false /cropimagestoframes true /errorcontrol /warnandcontinue /flattenerignorespreadoverrides false /includeguidesgrids false /includenonprinting false /includeslug false /namespace [ (adobe) (indesign) (4.0) ] /omitplacedbitmaps false /omitplacedeps false /omitplacedpdf false /simulateoverprint /legacy >> << /addbleedmarks false /addcolorbars false /addcropmarks false /addpageinfo false /addregmarks false /convertcolors /converttocmyk /destinationprofilename () /destinationprofileselector /documentcmyk /downsample16bitimages true /flattenerpreset << /presetselector /mediumresolution >> /formelements false /generatestructure false /includebookmarks false /includehyperlinks false /includeinteractive false /includelayers false /includeprofiles false /multimediahandling /useobjectsettings /namespace [ (adobe) (creativesuite) (2.0) ] /pdfxoutputintentprofileselector /documentcmyk /preserveediting true /untaggedcmykhandling /leaveuntagged /untaggedrgbhandling /usedocumentprofile /usedocumentbleed false >> ] >> setdistillerparams << /hwresolution [2400 2400] /pagesize [612.000 792.000] >> setpagedevice microsoft word numero_38_art_21 m. springer et alii, frattura ed integrità strutturale, 38 (2016) 155-161; doi: 10.3221/igf-esis.38.21 155 focussed on multiaxial fatigue and fracture combined simulation of fatigue crack nucleation and propagation based on a damage indicator m. springer vienna university of technology, institute for lightweight design and structural biomechanics, austria springer@ilsb.tuwien.ac.at m. nelhiebel kai – kompetenzzentrum automobilu. industrieelektronik gmbh, austria infineon technologies austria ag, austria michael.nelhiebel@infineon.com h. e. pettermann vienna university of technology, institute for lightweight design and structural biomechanics, austria pettermann@ilsb.tuwien.ac.at abstract. fatigue considerations often distinguish between fatigue crack nucleation and fatigue crack propagation. the current work presents a modeling approach utilizing one fatigue damage indicator to treat both in a unified way. the approach is implemented within the framework of the finite element method. multiaxial critical plane models with an extended damage accumulation are employed as fatigue indicators. locations of fatigue crack emergence are predicted by these indicators and material degradation is utilized to model local material failure. the cyclic loading is continued on the now degraded structure and the next location prone to material failure is identified and degradation modeled. this way, fatigue crack propagation is represented by an evolving spatial zone of material failure. this propagating damage zone leads to a changing structural response of the pristine structure. by recourse to the fatigue damage indicator a correlation between the number of applied load cycles and the changing structural behavior is established. finally, the proposed approach is exemplified by cyclic bending experiments in the low cycle fatigue regime. keywords. fatigue crack nucleation; fatigue crack propagation; damage indicator; finite element method. citation: springer, m., nelhiebel, m., pettermann, h. e., combined simulation of fatigue crack nucleation and propagation based on a damage indicator, frattura ed integrità strutturale, 38 (2016) 155-161. received: 27.04.2016 accepted: 05.06.2016 published: 01.10.2016 copyright: © 2016 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. m. springer et alii, frattura ed integrità strutturale, 38 (2016) 155-161; doi: 10.3221/igf-esis.38.21 156 introduction atigue failure and the mechanism leading to fatigue crack nucleation and propagation are of great concern in today’s design of engineering components. there are two groups of modeling concepts towards fatigue failure in materials and structures. first the classical fatigue laws of basquin [1] and coffin-manson [2,3] to predict crack nucleation, i.e. the number of cycles till some detectable crack emerges. to account for multiaxial loading conditions more complex models like critical plane approaches are utilized, e.g. fatigue indicator parameters (fip) [4]. second, methods treating the spatial advance of a failed region like fracture mechanics concepts as the paris law [5,6] for crack propagation or continuum damage mechanics based models for material degradation under cyclic loading. various approaches have been proposed to merge these two considerations in one unified or generalized concept. one way to do so is the generalization of crack propagation laws. different fatigue laws [7-12] have been proposed to find a relation between the paris law and the fatigue laws of basqin and coffin-manson. another approach is the combination of fatigue considerations with continuum damage mechanics [13,14] or crack propagation modeling [15]. such attempts are often suited in the field of numerical simulations especially in the framework of the finite element method (fem). fatigue indicators predict crack nucleation followed by the modeling of crack propagation realized, by crack modeling or material degradation. this way, a continuous simulation of the entire fatigue failure process is obtained. the present paper studies the estimation of the structural response due to the degradation of ductile materials. the focus is set on reversed cyclic plasticity, which is characterized by steady plastic strains from cycle to cycle with no net accumulation of directional plastic strains. this is the typical case for the low cycle fatigue (lcf) regime. a two level approach is implemented within the framework of the finite element method. cyclic loading on the structural level induces time varying multiaxial stress and strain states at the material level which, of course, are location dependent. fem simulations are utilized to compute the local constitutive response of the material points. a critical plane method is employed at all considered material points to identify the location most prone for material failure. there, crack emergence in the structure is modeled by material degradation in the region of the critical material points. crack propagation is obtained by repetitive application of the approach which results in an evolving spatial zone of material failure. consequently, a changing structural behavior is modeled by this propagating damage zone. methodology computational methodology is set up in which a fatigue indicator parameter (fip) is utilized to predict crack nucleation. the same indicator is also employed to model “crack propagation” in the sense of a spatial evolving region of material failure. depending on the fatigue damage behavior of the considered material different indicators can be appropriate [17, 18]. fatigue crack nucleation he fatemi-socie [19] fatigue indicator is employed in the present work which is typically used for ductile materials. this shear strain based critical plane method predicts fatigue crack nucleation and is given by, nfs y p k ,max 1 2            (1) the parameters governing crack nucleation are the shear strain amplitude, 2 , occurring on a particular plane and the maximum normal stress in a cycle, ,maxn , acting on that plane. y is the yield stress and k is a factor defining the influence of n ,max . the critical plane is identified as the plane experiencing the maximum value of the fatigue indicator. in case of non-proportional loading the determination of the shear strain amplitude usually requires numerical search f a t m. springer et alii, frattura ed integrità strutturale, 38 (2016) 155-161; doi: 10.3221/igf-esis.38.21 157 algorithm, which makes the identification of the fip computational expensive. for lifetime estimations in the lcf regime the maximum fip can be expressed as,  cp nfs,max f f2 (2) with the number of cycles to crack emergence, nf , and the material parameters f and c. the parameters in eqs 1 and 2 are taken for a stabilized cycle. the latter is identified by assessing the relative change of the dissipated strain energy density, i ii i i w w w w 1 , 1 1         (3) between two consecutive cycles i( 1) and i( ) . iw represents the dissipated strain energy in cycle i( ) and iw 1 for cycle i( 1) , respectively. a stabilized cycle is accepted when a defined tolerance value in a considered region is satisfied. fatigue crack emergence rom eq. 2 the number of cycles to crack emergence, nf , is estimated. at the location with the lowest nf material degradation is introduced in a small, flat region aligned with the critical plane. in this region the elastic stiffness is immediately decreased by several orders of magnitude. this way, material failure is modeled, representing an initial “crack” inside the structure. fatigue crack propagation he cyclic loading is continued on the now degraded structure. this leads to a change of the multiaxial stress and strain states in undamaged material points. consequently, the fips are changing, too, and their new contribution to crack nucleation has to be evaluated in the next stabilized cycle. therefore, an accumulation of the fip for all previously identified stabilized cycles has to be done, of course for all material points, at each plane. the palmgren-miner [20, 21] linear damage accumulation rule, i ii n n 1 (4) is employed, where in , is the number of cycles contributing to crack nucleation. in is the number of cycles to crack emergence, summed over i corresponding fip magnitudes. material points with the lowest remaining number of cycles to material degradation, in , are identified and selected to fail in the same way as crack emergence is modeled. the changing stress and strain states due to the changing structural behavior lead to increasing fatigue indicators in the vicinity of failed material and, consequently, to a higher contribution to the crack nucleation process. hence, further material is predicted to fail ahead the damaged area and “fatigue crack growth” is represented by an evolving spatial zone of material failure. additionally, the number of applied load cycles is correlated to the changing structural behavior caused by the evolving damage zone. implementation he described procedure is implemented within the framework of the finite element method (fem) to simulate the nonlinear structural fatigue behavior. python scripts have been developed in [16] and are utilized for the fip computations. the repetitive nature of the approach leads to an alternating utilization of fem simulations and f t t m. springer et alii, frattura ed integrità strutturale, 38 (2016) 155-161; doi: 10.3221/igf-esis.38.21 158 fip computations. cyclic loading is applied in the fem model and the simulation is halted after a stabilized cycle is found. regions for material degradation modeling are assumed to have a finite size of a disc like shape. this discs are aligned with the critical plane of the critical material point determined by the fip. elements intercepting this plane around the critical material point by a diameter of a2 are selected to fail. due to this element based selection method averaged element values of the stress and strain states are utilized for the fip computation. the cyclic loading is continued and the next stabilized cycle is searched. this alternating computations are continued until structural degradation has advanced to a specified stopping criterion. application he approach is exemplified by simulation of micrometer sized cyclic bending experiments in the lcf regime, see [22]. a 3d-fem model of the copper cantilever beam is shown in fig. 1. the bending sample has a cross-section of 23x23m2 and a length of 260m. linear interpolated, fully integrated, eight noded, continuum elements are used for discretization. displacement boundary conditions are used for fixation and cyclic loading. harmonic loading with an amplitude of 19.5 m is enforced at the neutral axis of the beam. an elastic–plastic j2 constitutive model with kinematic hardening is used to model the material behavior of copper. the elastic and plastic material data is summarized in tab. 1. the fatigue model is calibrated by recourse to the experimental data from [22], to identify material parameters as needed in eq. 2 for lifetime estimation. according to this data and neglecting the cyclic hardening behavior, a first significant change in the structural response is detectable at nf 1000 load cycles. the unified approach is calibrated in such a way that crack emergence will occur at this number of load cycles. figure 1: 3d fem-model of cyclic bending experiment of micrometer sized copper cantilever beam material young’s modulus (gpa) poisson’s ratio yield stress (mpa) tangent modulus (mpa) cu 102 0.35 104.4 3900 table 1: elastic and plastic properties of cu [16] therefore, the first stabilized cycle is identified by the fem simulation and a maximum fip, pfs,max 0.025573 , computed. due to the few existing experimental data only this single data point is available for the lifetime estimation. therefore, the material parameter c 0.7  is assumed and finally f 5.2300118  is obtained from eq. 2. the fatigue indicator parameter (fip) as discussed above are computed for a stabilized cycle. the latter is accepted when the relative change of the dissipated strain energy density, eq. 3, satisfies the criterion: i iw , 1 0.0001   . the dissipated t m. springer et alii, frattura ed integrità strutturale, 38 (2016) 155-161; doi: 10.3221/igf-esis.38.21 159 strain energy density in a cycle is computed for the region of plastic deformation in the cantilever beam. therefore, individual material points may not completely reach the defined criterion. this is accepted to reduce the number of load cycles in the fem simulation. the disc shape regions for material degradation modeling are defined to have a diameter, a2 , of four times the average element length in the refined region. figure 2: fatigue damage accumulation resulting in material degradation is indicated by contour plots on the lateral surface and the symmetry plane of the beam. left, the fip after the first stabilized cycle is indicating crack emergence. rightwards, the spatial evolution of material failure is visualized for an increasing number of load cycles. results ig. 2 presents the fatigue damage process. the fatigue indicator, eq. 1, is depicted by contour plots, in the top row for the lateral surface and in the lower row for the symmetry plane of the beam. the fatigue damage accumulation is depicted after three different numbers of load cycles. dark regions indicate an advanced damage accumulation. left, for 1000n  load cycles the fip in the first stabilized cycle is displayed. this image represents the undamaged structure indicating locations prone for crack emergence. the elements most prone to fail are located at the symmetry plane at the end of the shoulder. here, material failure is first introduced into the structure. the spatial evolution of this material degradation is depicted after 1131n  load cycles. the structural change due to the evolving damage zone is indicated by the decreasing reaction force f in relation to the initial one inif in the first stabilized cycle. the simulation is continued until the reaction force decreased under ten percent of the initial one. this criterion is fulfilled after 1276n  load cycles are reached. figure 3: structural degradation indicated by the decreasing reaction force compared to the number of applied load cycles – simulation vs. experiment [22]. f m. springer et alii, frattura ed integrità strutturale, 38 (2016) 155-161; doi: 10.3221/igf-esis.38.21 160 the corresponding spatial material failure is depicted in the right images. the damage zone is evolving from the location of crack emergence towards the neutral axis and is decreasing from the midplane to the outside of the beam. the decreasing reaction force versus the number of load cycles is displayed in fig. 3. the experimental results [22] are compared to the numerical simulation. after one thousand load cycles material failure modeling starts and a degrading structural behavior is obtained. compared to the experimental observation the degradation in the simulation is progressing more quickly than the degradation of the test specimen. conclusion fatigue damage modeling approach capable of predicting fatigue crack nucleation and propagation in one combined numerical simulation has been presented. a multiaxial critical plane concept combined with damage accumulation is utilized as fatigue damage indicator to identify locations of crack emergence. local material degradation is modeled in the pristine structure and the cyclic loading is continued until the next occurrence of material failure is detected. applying this procedure in a repetitive way, an evolving spatial zone of material failure is simulated, representing fatigue crack propagation. this way, a changing structural response of the initial perfect structure with respect to the number of applied load cycles is obtained. the combination of fatigue crack nucleation and crack propagation has been successfully exemplified in a numerical fem analysis of a cyclic loaded cantilever beam. acknowledgement he authors would like to thank balamurugan karunamurthy from kompetenzzentrum automobilund industrieelektronik gmbh for providing valuable input for this work. this work was jointly funded by the austrian research promotion agency (ffg, project no. 846579) and the carinthian economic promotion fund (kwf, contract kwf-1521 | 26876 | 38867). references [1] basquin, o. h., the exponential law of endurance tests, proc. astm., 10(2) (1910). [2] coffin, lf jr., a study of the effects of cyclic thermal stresses in ductile metals, asme, 76 (1954). [3] manson, s. s., behaviour of materials under cyclic stress, naca, tn 2933 (1953). [4] suresh, s., fatigue of materials, cambridge university press (1998). [5] paris, p. c., gomez m. p., william, e. a., a rational analytic theory of fatigue, trend. engng., 13 (1961) 9-14. [6] paris, p. c., erdogan, f., a critical analysis of crack propagation laws, j. basic engng, 85 (1963) 528-533. [7] newman, j. c., the merging of fatigue and fracture mechanics concepts: a historical perspective, progress in aerospace sciences, 34 (1998) 347-390. doi: 10.1016/s0376-0421(98)00006-2 [8] barenblatt, g. i., botvina, l. r., incomplete self-similarity of fatigue in the linear range of crack growth, fatigue fract. eng. mater. struct., 3 (1980) 193-202. doi: 10.1111/j.1460-2695.1980.tb01359.x [9] pugno, n., ciavarella, m., cornetti, p., carpinteri, a., a generalized paris’ law for fatigue crack growth, j. mech. phys. solids, 54 (2006) 1333-1349. doi: 10.1016/j.jmps.2006.01.007 [10] pugno, n, cornetti p., carpinteri a., new unified laws in fatigue: from the wöhler’s to the paris’ regime, eng, fract. mech., 74 (2007) 595-601. doi: 10.1016/j.engfracmech.2006.07.009 [11] ciavarella, m., dibello, s., demelio g., conductance of rough random profiles, int. j. solids struct., 45 (2008) 879893. doi: 10.1016/j.ijsolstr.2007.09.009 [12] carpinteri, a., paggi m., a unified interpretation of the power laws in fatigue and the analytical correlations between cyclic properties of engineering materials, int. j. fatigue, 31 (2009) 1524-1531. doi: 10.1016/j.ijfatigue.2009.04.014. [13] darveaux, r., effect of simulation methodology on solder joint crack growth correlation and fatigue life prediction, j. electronic packaging, 124 (2002) 147-154. doi: 10.1115/1.1413764. [14] lau, j. h., pan s. h., chang, c., a new thermal-fatigue life prediction model for wafer level chip scale package (wlcsp) solder joints, j. electronic packaging, 124 (2002) 212-220. doi: 10.1115/1.1462625. a t m. springer et alii, frattura ed integrità strutturale, 38 (2016) 155-161; doi: 10.3221/igf-esis.38.21 161 [15] proudhon, h. li, j., wang, f., roos, a., 3d simulation of short fatigue crack propagation by finite element crystal plasticity and remeshing, int. j. fatigue, 82 (2016) 238-246. doi: 10.1016/j.ijfatigue.2015.05.022. [16] kravchenko, g., karunamurthy b., nelhiebel, m., pettermann h.e., finite element analysis of fatigue cracks formation in power metallisation of a semiconductor device subjected to active cycling, eurosime, (2013). doi: 10.1109/eurosime.2013.6529951. [17] li, b., l. reis, de freitas, m., comparative study of multiaxial fatigue damage models for ductile structural steels and brittle materials, int. j. fatigue, 31 (2009) 1895-1906. doi: 10.1016/j.ijfatigue.2009.01.006. [18] ince, a., glinka g., a modification of morrow and smith–watson–topper mean stress correction models, fatigue fract. eng. mater. struct. 34 (2011) 854-867. doi: 10.1111/j.1460-2695.2011.01577.x. [19] fatemi, a., socie, d.f., a critical plane approach to multiaxial fatigue damage including out‐of‐phase loading, fatigue fract. eng. mater. struct., 11 (1988) 149-165. doi: 10.1111/j.1460-2695.1988.tb01169.x. [20] palmgren, a., die lebensdauer von kugellagern, z. deutsch. ing. 68 (1924) 339-341. [21] miner, m. a., cumulative damage in fatigue, j. appl. mech., 12 (1945) 159-164. [22] wimmer, a., heinz, w., detzel, t., robl, w., nellessen, m., kirchlechner, c., dehm, g., cyclic bending experiments on free-standing cu micron lines observed by electron backscatter diffraction, acta materialia, 83 (2015) 460-469. doi: 10.1016/j.actamat.2014.10.012. << /ascii85encodepages false /allowtransparency false /autopositionepsfiles true /autorotatepages /none /binding /left /calgrayprofile (dot gain 20%) /calrgbprofile (srgb iec61966-2.1) /calcmykprofile (u.s. web coated \050swop\051 v2) /srgbprofile (srgb iec61966-2.1) /cannotembedfontpolicy /error /compatibilitylevel 1.4 /compressobjects /tags /compresspages true /convertimagestoindexed true /passthroughjpegimages true /createjobticket false /defaultrenderingintent /default /detectblends true /detectcurves 0.0000 /colorconversionstrategy /cmyk /dothumbnails false /embedallfonts true /embedopentype false /parseiccprofilesincomments true /embedjoboptions true /dscreportinglevel 0 /emitdscwarnings false /endpage -1 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can be opened with acrobat and adobe reader 5.0 and later.) >> /namespace [ (adobe) (common) (1.0) ] /othernamespaces [ << /asreaderspreads false /cropimagestoframes true /errorcontrol /warnandcontinue /flattenerignorespreadoverrides false /includeguidesgrids false /includenonprinting false /includeslug false /namespace [ (adobe) (indesign) (4.0) ] /omitplacedbitmaps false /omitplacedeps false /omitplacedpdf false /simulateoverprint /legacy >> << /addbleedmarks false /addcolorbars false /addcropmarks false /addpageinfo false /addregmarks false /convertcolors /converttocmyk /destinationprofilename () /destinationprofileselector /documentcmyk /downsample16bitimages true /flattenerpreset << /presetselector /mediumresolution >> /formelements false /generatestructure false /includebookmarks false /includehyperlinks false /includeinteractive false /includelayers false /includeprofiles false /multimediahandling /useobjectsettings /namespace [ (adobe) (creativesuite) (2.0) ] /pdfxoutputintentprofileselector /documentcmyk /preserveediting true /untaggedcmykhandling /leaveuntagged /untaggedrgbhandling /usedocumentprofile /usedocumentbleed false >> ] >> setdistillerparams << /hwresolution [2400 2400] /pagesize [612.000 792.000] >> setpagedevice microsoft word numero_53_art_29_2833 i. monetto et alii, frattura ed integrità strutturale, 53 (2020) 372-393; doi: 10.3221/igf-esis.53.29 372 an analytical beam model for the evaluation of crack tip root rotations and displacements in orthotropic specimens ilaria monetto, roberta massabò department of civil, chemical and environmental engineering, university of genova, italy ilaria.monetto@unige.it, http://orcid.org/0000-0002-5682-9315 abstract. explicit and simple expressions for root compliance coefficients, which can be used to define root rotations and root displacements at the crack tip cross section of orthotropic cracked beams, are derived under general self-equilibrated loading conditions at the crack tip. the effects of both shear deformations and transverse elasticity are taken into account in order to accurately define displacement fields and energy release rate. the derivation builds on and extends one-dimensional formulations in the literature. the employment of the novel analytical expressions requires the determination of one a priori unknown parameter which describes the effects of the transverse elasticity and is determined through matching of well established 2d results in the literature. the one-dimensional model accurately reproduces crack tip effects in symmetric isotropic and orthotropic specimens; shear deformations are included in the formulation for an accurate derivation of the root displacement coefficients; the accuracy reduces in asymmetric specimens where the matching parameter becomes load dependent. keywords. root rotations; root displacements; collinear delamination; fracture specimens; orthotropy. citation: monetto, i, massabò, r., an analytical beam model for the evaluation of crack tip root rotations and displacements in orthotropic specimens, frattura ed integrità strutturale, 53 (2020) 372-393. received: 08.05.2020 accepted: 25.05.2020 published: 01.07.2020 copyright: © 2020 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. introduction n many problems of fracture in beam-type structures the effects of the transverse elasticity of the intact portion of the specimen ahead of the crack tip are not negligible and must be taken into account when calculating displacements and fracture parameters. such effects are usually associated with relative rotations and displacements at the crack tip section between the two arms of the cracked portion of the specimen. they are known in the literature as root rotations and displacements and have been the object of many studies. a great deal of attention has been focused on modeling the root rotations, which have been shown to enter into some important fracture mechanics calculations, such as those of the j-integral and the energy release rate [1-3]. among the others, e.g. [1-2,4-7], reference is made here to the results presented in [3] for orthotropic cracked beams subjected to i https://youtu.be/8yfzvbnxz3u i. monetto et alii, frattura ed integrità strutturale, 53 (2020) 372-393; doi: 10.3221/igf-esis.53.29 373 arbitrary end loadings. they determined the compliance coefficients describing root rotations due to elementary, selfequilibrated crack tip loading systems for a wide range of thickness-wise positions of the crack and orthotropy ratios. the results obtained through rigorous 2d finite element analyses were validated by comparison with results obtained using other methods for different geometries in both isotropic [2] and orthotropic [8-9] materials. recently, the accuracy of the numerical compliance coefficients has been demonstrated in [10] and by the analytical solutions in [11], for symmetric orthotropic strips, and in [12-13] for thin layers on half-planes. root rotation coefficients can also be obtained from expressions of the energy release rate in terms of crack tip forces using the methodology proposed in [3], which has been recently applied in [10] to double cantilever beam (dcb) specimens and in [14] to sandwich specimens under general end loadings. the methodology does not allow to derive root displacements. little attention has been placed on deriving the root displacements, which do not directly enter into the energy release rate and mode mixity and have been shown to play a role only in special problems. as examples, they need to be included in compliance-based analyses of the strain energy release rate, in the analysis of displacement controlled fracture tests, such as the wedge test, and in the analysis of problems where contact occurs along the crack surfaces, as in the inverted four point bending test. they are also important in modeling buckling and post-buckling of the detached layers using structural theories [5-6,15]. kanninen [16] was among the firsts to include the effects of the transverse elasticity of the intact portion ahead the crack tip in the study of crack propagation and arrest in a symmetrical dcb specimen. because of the symmetry, half of the specimen was treated as a finite length beam which is partly free and partly supported by a winkler foundation with stiffness modulus dependent on the beam elastic and geometrical parameters. this model was firstly based on the eulerbernoulli beam theory to be used for the analysis of stationary cracks. subsequently, the model was extended using the timoshenko beam theory and a generalized elastic foundation depending on two parameters [17-18]. recently thouless [10] proposed an approach which links to the original kanninen's [16] formulation and uses the solution of an elastic and isotropic euler-bernoulli beam on an elastic foundation in order to find the relationships between the compliance coefficients describing root rotations and root displacements for a symmetric dcb specimen subjected to transverse point forces. these relationships were furthermore used to derive the root displacements also for orthotropic specimens. in this paper, a structural model for the closed form derivation of the crack tip compliance coefficients in orthotropic specimens under general end loadings, as shown in fig. 1a, is presented. the main goal of the work is to formulate a simple but sufficiently accurate model for practical applications, which is able to provide the root displacement coefficients. the model is based on shear deformable beam theory and builds on the kanninen's original formulation, which is here extended in order to consider new end-loading conditions. in particular, the problem of the equilibrium of a two-layered system with elastic interlayer uplift is analysed, as shown in fig. 1b. the solution procedure previously followed by the authors to solve the problem of multi-layered systems with imperfect interfaces [19-24] is employed and leads to explicit expressions for the root rotation and displacement compliance coefficients under different crack tip loading conditions. figure 1: (a) edge cracked specimen subjected to end loadings. (b) elastically connected semi-infinite beams: model geometry and selfequilibrated elementary end loading conditions. the paper is organized as follows. in the next section the equilibrium, compatibility and constitutive equations governing the model formulation are detailed and rearranged into two coupled linear differential equations for the shear and normal interfacial tractions. details on the solution procedure leading to exact expressions for the interfacial tractions and all other static and kinematic variables are provided. in the third section explicit expressions for the relative rotation and displacement compliance coefficients under three elementary end loading conditions are derived analytically and presented for timoshenko and euler-bernoulli layers. the simplified formulation based on euler-bernoulli beam theory is detailed in appendix a. the novel expressions are employed on varying elastic moduli and geometrical parameters and the related numerical results are shown and discussed in the fourth section after validation through comparison with results in the literature. all numerical results shown are listed in table form in appendix b, where the matching procedure is described. i. monetto et alii, frattura ed integrità strutturale, 53 (2020) 372-393; doi: 10.3221/igf-esis.53.29 374 a practical application of the solutions to the analysis of an exemplary fracture specimen is shown in the fifth section, where the two formulations developed in the paper are compared to show the limits of the simplified model based on euler-bernoulli beam theory. the sixth section concludes the paper with a final discussion on the differences between the proposed model and others in the literature and on the limit of applicability of the present formulation. model formulation he two-layered system under consideration is shown in fig. 1b and consists of two semi-infinite beams (x≥0) which have constant rectangular cross sections, unit width and height hi (i=1,2). the beams are made of the same linearly elastic and orthotropic material with principal material directions x,y,z and longitudinal young's modulus ex, transverse young's modulus ez, in plane shear modulus gxz and poisson ratios xz and zx. the beams are connected by a continuous bond which is assumed to be perfect in the longitudinal x-direction, while it ensures a partial composite action in the transverse z-direction. as a consequence, interlayer uplifts can occur at the interface, but no slips between the layers at their interface are possible. such a connection is modeled by continuously distributed tangential and normal reactions; the latter are related to the relative deflection between the two beams according to a linearly elastic relationship with k the proportionality constant. for our convenience, this connection modulus is expressed in terms of the average transverse stiffness of the beams as 1 2 2 z wk e k h h   , (1) where an arbitrary correction factor, say kw, is introduced to take into account that the beam model is only an approximation. in kanninen's original formulation, where ez=ex and h1=h2, the correction factor was assumed as kw=1. recently, with reference to the same kanninen's symmetrical dcb specimen, thouless [10] proposed alternative values for kw to obtain a reasonably good approximation for the energy release rate under 2d linear elastic fracture mechanics (lefm) conditions. as detailed in the third section and appendix b, kw is here determined so that the results found according to the proposed model match well-established root rotation compliance coefficients in the literature. finally, the system is subject to the self-equilibrated loading condition shown in fig. 1b: each beam is loaded at the end x=0 by point forces acting in the axial direction, n0, and in the direction normal to the beam axis, v0, and by a bending moment, m0, in addition to a compensating moment, n0(h1+h2)/2, applied at the same end of the lower beam. these loading conditions are part of the elementary crack tip loadings which are used in the literature to fully describe the local crack tip fields and the energy release rate in beam-type structures subjected to arbitrary end loadings [2, 25]. under the assumption of small strains, displacements and rotations and assuming timoshenko beams to approximately account for the effects of the shear deformations, the problem of the equilibrium of the two-layered system under consideration is governed by three differential equations for each beam arm, with a total of eight unknowns: pt and pn, respectively the shear and normal tractions between the two layers at their common interface, and i, wi and ui, respectively the rotation, the deflection along the z-direction and the axial displacement along the x-direction for the i-th beam (i=1,2). the differential equations are     '' 1 '' ' 1 3 '' ' ( 1) 0 ( 1) 0 1 0 12 2 i x i i t i s xz i i i n i x i i s xz i i i t e h g h e h u p w p h g h w p                        (2) where, hereinafter, primes denote differentiation with respect to x and s=5/6 is the shear correction factor. in the reference systems of fig. 1b, the rotations are positive if counter-clockwise, whereas the deflections are positive if downward and the axial displacements are positive if rightward. furthermore, the continuously distributed normal tractions pn are defined as t i. monetto et alii, frattura ed integrità strutturale, 53 (2020) 372-393; doi: 10.3221/igf-esis.53.29 375  2 1np k w w  (3) whereas the continuously distributed shear tractions pt are consistent with the assumption of perfect connection in the longitudinal x-direction imposing that 1 2 2 1 1 2 0 2 2 h h u u      (4) it is worthwhile noting that the interface condition expressed by eqn. (4) makes the axial and bending problems of the two elastically connected semi-infinite beams coupled and it needs to be imposed in order to analyze the elementary end loading condition with n0≠0 and related compensating moment, which would otherwise generate unrealistic sliding displacements at the interface in asymmetric specimens. in order to solve the problem, it is convenient to rearrange the basic equations described above. such a rearrangement, based on differentiating eqn. (3) four times and eqn. (4) three times with respect to x, leads to the following two coupled linear differential equations with constant coefficients for the unknowns pn and pt: " ' ' 1 ˆˆ ˆ 0 ˆ ˆ 0 iv n n n t t n p p p a bp cp gp k c         (5) having defined, according to eqn. (1), 1 2 2 1 2 1 2 ˆ w x s xz s xz k eh h a k g h h gh       , 23 3 1 2 3 3 4 1 2 1 24 ( 1)12( )ˆ w x kh h b k e h h h       (6a) 2 2 2 1 2 2 3 1 2 1 12 (1 ) ˆ 6 w x kh h c k e h h h           and 1 2 1 2 1 4( ) 4(1 ) ˆ x x h h g e h h e h     (6b) where 1 2 h h   , z x e e   and / ( 2 )x z xz xz zxe e g    (6c) define relative thickness and orthotropy ratios in the layers and 2( // )x xz xze g     . it is worthwhile noting that all the coefficients in eqn. (6) are positive, except for the coefficient ĉ which is positive only for h2>h1 and vanishes in the case of symmetrical specimen with a mid-thickness interface (h1=h2). furthermore, under the assumption of infinite shear stiffness of the layers ˆ 0a  and eqn. (5) so simplified is proved to govern the problem of the two elastically connected semi-infinite beams according to euler-bernoulli beam theory, for which the effects of the shear deformations are neglected. appendix a presents this simplified formulation and a comparison with the model first proposed in [16] and recently reconsidered in [10] with reference to a dcb specimen. the solution of the coupled differential problem (5) requires further rearrangement of the equations: firstly, the second of eqn. (5) is solved for the first derivative of the interfacial shear tractions; secondly, this result is substituted in the first of eqn. (5) leading to the following fourth-order linear differential equation with constant coefficients for the interfacial normal tractions "ˆ ˆ 0ivn n np pa ep   (7) with 23 1 1 2 1 2 3 3 4 1 2 1 6 (1 )( )ˆˆ ˆ ˆ 3 w x kh h e b g k c k e h h h         (8) i. monetto et alii, frattura ed integrità strutturale, 53 (2020) 372-393; doi: 10.3221/igf-esis.53.29 376 the general solution of the differential equation can be written in three different forms: 1 1 2 2 3 1 4 2 1 2 3 4 1 3 4 2 3 4 3 3 4 4 3 4 ˆexp( ) exp( ) exp( ) exp( ) for 0 ˆ( ) exp( ) ( ) exp( ) for 0 exp( ) cos( ) exp( )sin( ) ˆfor 0 exp( ) cos( ) exp( )sin( ) n c x c c x c x d p c c x x c c x x d c x x c x x d c x x c x x x                                          (9) where 2ˆ ˆ ˆ4d a e  , ˆ 2 a   (10a) 1 ˆˆ 2 a d    , 2 ˆˆ 2 a d    , 3 1 ˆ ˆ2 2 e a   and 4 1 ˆ ˆ2 2 e a   (10b) with â and ê given by eqns. (6) and (8). when the normal tractions along the interface between the beams have been obtained, closed form expressions for the shear tractions and for the internal forces and displacements for each beam arm can be derived, as detailed in what follows. firstly, integration of the second of eqn. (5) gives the shear tractions along the interface between the two beams: 1 1 5ˆ ˆ dt np pg k c x c     (11) where for brevity, hereinafter, d x indicates integration of · once with respect to x; whereas c5 is an additional arbitrary constant. secondly, integration of eqn. (2) gives, respectively, the axial forces ' 5( 1) d i i x i i t in e h u p x c     (12a) the shear forces  ' 7( 1) dii s xz i i i n it g h w p x c       (12b) and the bending moments in the beams (i=1, 2) 3 ' 9 1 d 12 2 i i x i i i t ie h h m t p x c          (12c) which contain six more arbitrary constants c5+i, c7+i and c9+i (i=1,2). thirdly, integration of the internal forces gives the rotations 113 12 di i i x i m x c e h    (13a) the axial displacements i. monetto et alii, frattura ed integrità strutturale, 53 (2020) 372-393; doi: 10.3221/igf-esis.53.29 377 13 1 di i i x i u n x c e h   (13b) and the deflections of the beams (i=1,2) 15d i i i i s xz ig h t w x c              (13c) with six more arbitrary constants c11+i, c13+i and c15+i (i=1,2). from eqn. (13a) the relative rotation between the two beam arms is given by 2 1     (14a) whereas the relative deflection between the two beam arms follows directly from eqn. (3) 2 1 /nw p kw w    (14b) the general solution derived above contains 17 arbitrary constants, which are evaluated using suitable boundary conditions. seven conditions are obtained by imposing that the expressions given by eqn. (13) for displacements and rotations satisfy the bond conditions eqn. (4) of perfect connection in the longitudinal x-direction and eqn. (3) of elastic connection in the transverse z-direction for all points of the interface. the prescription of free end boundary at infinity (x→∞) gives five further conditions. these twelve conditions result in the following relations: 1 2 5 6 7 8 9 10 11 0c c c c c c c c c         , 13 12c c (15a) 17 16c c and  15 14 12 1 22 ( ) / 2c c c h h   (15b) then, imposing that the static quantities equate the applied forces at the end x=0 yields c3 and c4, which enter the expressions given by eqn. (14) for the relative rotation and deflection between the two beam arms. the remaining arbitrary constants c12, c14 and c16 remain indeterminate but are not of interest here because they describe a rigid motion of the whole self-equilibrated two-layered system. finally, substituting such results into the expressions given by eqn. (14), evaluated at x=0, gives the end relative deflection and rotation, say w0 and 0 respectively, between the two beams in terms of the end forces (v0, m0 and n0). the compliance coefficients describing the rotations and displacements follow directly from these relationships, as detailed below. root rotation and displacement compliance coefficients he three elementary schematics of the bi-layered system shown in fig. 2 are considered. the self-equilibrated end loading conditions shown in fig. 1b are reproduced by the superposition of these schematics. the relative rotation at x=0 given in eqn. (14) defines the root rotation and is related to the end forces by 0 0 00 0 0 0 1 1 1 v m n x m d v d d n e h h          (16) and the relative deflection at x=0 defines the root displacement and is given by 0 0 00 0 0 0 1 1 v m n x w m c v c c n e h          (17) t i. monetto et alii, frattura ed integrità strutturale, 53 (2020) 372-393; doi: 10.3221/igf-esis.53.29 378 where dk and ck (k=v0,m0,n0) are compliance coefficients, which depend on the relative thickness-wise position  of the delamination, on the orthotropy ratios  and , and on the correction factor kw, as detailed in what follows. figure 2: schematics of the elementary loading conditions considered for the analytical derivation of the compliance coefficients. (1) symmetrical transverse forces the first schematic, shown in fig. 2(s1), corresponds to the end loading with v0≠0, m0=0 and n0=0. in this case, we have 0 23(1 ) 2 v w d k     (18) and 0 1 (1 )v x s w xz c e f k g      (19) with 1 1 1 1 ˆfor 1 or 0 2 ˆ1 for 1 or 0 ˆfor 1 or 0 1 2 h h h d f h d h d h                    (20) where 22 26 (1 ) xzs w x h g k e           (21) noting that 2( // )x xz xze g     . (2) symmetrical bending the second schematic, shown in fig. 2(s2), corresponds to the end loading with m0≠0 and v0=n0=0. in this case, we obtain 0 0m vc d defined by eqn. (18), according to betti's theorem, and 0 2 6 (1 )m x s xz d e f g     (22) i. monetto et alii, frattura ed integrità strutturale, 53 (2020) 372-393; doi: 10.3221/igf-esis.53.29 379 together with eqns. (20) and (21). (3) pair of longitudinal forces with compensating moment the third schematic, shown in fig. 2(s3), corresponds to the end loading with n0≠0, v0=0 and m0=0. in this case, equilibrium is guaranteed by a compensating counter-clockwise moment equal to n0(h1+h2)/2 applied to the lower beam. in this case, the compliance coefficients are 0 23(1 ) 2 2 n w c k     (23) and 0 2 3 (1 ) 2 n x s xz d e f g     (24) where f is defined in eqn. (20) together with eqn. (21). the beam model proposed in this paper leads to the simple explicit expressions given by eqns. (18) to (24) for the compliance coefficients describing both root rotations and root displacements as functions of the model parameters. the model parameters characterize the specimen material and geometry (namely, the orthotropy ratios and the relative thickness of the two layers), in addition to the correction factor kw introduced in eqn. (1), which is the only a priori unknown model parameter. analogous root rotation and displacement compliance coefficients have been derived under the assumption of eulerbernoulli beam theory, as detailed in appendix a. they are listed below: 0 1/4 3/2 1/4 3/4 (1 )3 2 ( ) v eb eb w c k     , 0 0 2(1 )3 2 m v eb eb eb w c d k      , 0 2(1 )3 2 2 n eb eb w c k     (25a) 0 1/4 3/4 5/2 1/4 (1 )2 3 ( ) m eb eb w d k     , 0 3/4 5/2 3/4 1/4 (1 )3 2 ( ) n eb eb w d k     (25b) where the upper/sub-script eb has been used to differentiate with respect to the previous results. these coefficients could be obtained from eqns. (18)-(24) by imposing infinite shear stiffness, which implies ˆ 0a  and then ˆ 0d  . suitable values for kw or eb wk are here chosen by reproducing well-established values for the compliance coefficients in the literature. in particular, the root rotation coefficients determined in [3] using accurate 2d finite element analyses, shown in table 10 in appendix b, are considered. details about the matching procedure are given in appendix b. tabs. 1-9 show the values of kw or eb wk obtained by matching the three coefficients in isotropic and orthotropic specimens. the tables also define the values of the root rotation and displacement coefficients obtained a posteriori using the matched kw or eb wk in eqns. (18)-(24) and (25). in the next two sections some numerical results are shown and discussed, and an application of these results is presented with reference to an exemplary fracture problem. numerical results and discussion n this section, some sets of numerical results obtained by employing the analytical expressions for the root rotations and displacements derived in this paper and listed in tabs. 1-9 are presented. this has three aims. the first is to validate the model through comparison with the results of other methods in the literature. the second is to highlight the effects of the choice of the matching compliance coefficient. the third is to discuss the effects of the geometrical and material properties of the specimen on the compliance coefficients. i i. monetto et alii, frattura ed integrità strutturale, 53 (2020) 372-393; doi: 10.3221/igf-esis.53.29 380 figure 3: correction factors of the average transverse stiffness for isotropic materials (==1) with varying poisson ratio =0,0.3. results for matching on 0nd are in tabs. 3 and 9. figure 4: relative rotation compliance coefficients under symmetrical transverse forces for isotropic materials (==1) with varying poisson ratio =0,0.3. in figs. 3 to 8 the results based on timoshenko beam theory (continuous lines in all figures) are shown as functions of the relative thickness-wise position  of the delamination. results obtained using the simplified model based on eulerbernoulli beam theory are presented in figs. 3 and 9 to 11 (dashed lines). fig. 3 shows the correction factors kw and eb wk evaluated for isotropic materials (==1 and xz=zx=) on varying the poisson ratio  =0,0.3. figs. 4-11 show the root rotation and root displacement compliance coefficients obtained using timoshenko and euler-bernoulli beam theory and the previously matched correction factors in isotropic and degenerate orthotropic specimens with =1 and =0.5. the matching coefficient is shown in the diagrams using triangle marks for 0vd , circle marks for 0md and square marks for 0nd ; the compliance coefficients derived using 2d elasticity in [3] and used for the matching are shown by dashed-dot lines and presented in table 10. the diagrams, along with the equations in the previous section, highlight the features of the approach, its strengths and weaknesses. i. monetto et alii, frattura ed integrità strutturale, 53 (2020) 372-393; doi: 10.3221/igf-esis.53.29 381 figure 5: relative rotation compliance coefficients under symmetrical bending for degenerate orthotropic materials (=1) with varying =0.5,1. the three upper curves refer to =0.5, the lower to =1 (isotropy). figure 6: relative rotation compliance coefficients under a pair of longitudinal forces for degenerate orthotropic materials (=1) with varying =0.5,1. the three upper curves refer to =0.5, the lower to =1 (isotropy). in isotropic and orthotropic symmetric specimens, where =1, all matching procedures lead to the same value of kw, as shown in fig. 3 for isotropy. the same is true for ebwk , which differs from kw also because it does not depend on the poisson ratios. this implies that matching a single root rotation coefficient against the 2d solutions using timoshenko or euler-bernoulli beam theory yields accurate predictions of all other root rotation coefficients, through eqns. (18), (22), (24) and (25), as shown in figs. 4-6 and 9. as further validation of these results, tabs. 7 and 8 of appendix b show that for isotropic layers 0.812ebwk  , 0 5.436 v ebd  and 0 3.659 v ebc  . these values perfectly match the results derived in [10] for a symmetrical dcb specimen. in isotropic and orthotropic asymmetric specimens, with ≠1, using different root rotation coefficients in the matching procedure yields different predictions of kw or eb wk and the difference increases on decreasing , as shown in fig. 3 for an isotropic layer. fig. 3 shows that the percentage difference between the kws calculated using 0 vd and 0md as matching coefficient and the timoshenko model is about 6%,7% for =0.8 and =0,0.3 and 23%,29% for =0.6 and =0,0.3. the i. monetto et alii, frattura ed integrità strutturale, 53 (2020) 372-393; doi: 10.3221/igf-esis.53.29 382 discrepancies are observed also in results obtained using euler-bernoulli beam theory and imply that the other root rotation compliance coefficients calculated a posteriori using eqns. (18), (22), (24) and (25) differ from those of 2d elasticity in table 10. this is shown in figs. 4-8 and 9, which also highlight that the values of 0vd and 0md are quite well reproduced when one of the two compliance coefficients is chosen for matching, while quite significant differences are found on the derived coefficients when matching is performed on 0nd . figure 7: relative deflection compliance coefficients under symmetrical transverse forces for isotropic materials (==1) with varying poisson ratio =0,0.3. figure 8: relative deflection compliance coefficients under a pair of longitudinal forces for degenerate orthotropic materials (=1) with xz=0.3 and varying =0.5,1. the discrepancies between the sets of results for each compliance coefficient find an explanation in the different description of the mechanical behavior according to the beam theory and 2d plane stress conditions. this represents a limit of applicability for the structural model proposed in the paper to specimens having a relative position of the delamination lower than 0.6. i. monetto et alii, frattura ed integrità strutturale, 53 (2020) 372-393; doi: 10.3221/igf-esis.53.29 383 figure 9: relative rotation compliance coefficients under symmetrical transverse forces according to the simplified model and for degenerate orthotropic materials (=1) with varying =0.5,1. figure 10: relative deflection compliance coefficients under symmetrical transverse forces according to the simplified model and for degenerate orthotropic materials (=1) with varying =0.5,1. similar considerations can be made from the results shown in figs. 7, 8 and 10, 11 which depict the root displacement compliance coefficients 0vc , 0nc and 0vebc , 0n ebc under symmetrical transverse forces and a pair of longitudinal forces, respectively. 0 0m vc d and 0 0m veb ebc d are shown in figs. 4 and 9. it is worthwhile noting that the relative rotation compliance coefficients under symmetrical bending and a pair of longitudinal forces calculated using the euler-bernoulli model coincide with those pertinent to the timoshenko beam based model, shown in figs. 5 and 6: 0 0m mebd d and 0 0 n n ebd d , even if the correction factors differ. this is a consequence of the well known equivalence between the 2d elasticity and beam theory descriptions of the problem under such loading conditions, e.g. [8]. on the other hand, the relative rotation compliance coefficient under symmetrical transverse forces 0vebd , shown in fig. 9, differs from 0vd , shown in fig. 4, according to the following relationship i. monetto et alii, frattura ed integrità strutturale, 53 (2020) 372-393; doi: 10.3221/igf-esis.53.29 384 0 0 1(1 )v veb s xzd d               (26) which is a generalization of eqn. (b.4) introduced for matching. the difference is made clear by referring to how the effects of shear deformations are accounted for in the two formulations. within the timoshenko beam theory, the effects of the shear deformations are taken into account through the beam compatibility and constitutive equations leading to eqn. (2) which governs the problem and, as a consequence, they enter directly in the expressions of rotations and displacements. on the other hand, in the simplified formulation based on the euler-bernoulli beam theory the effects of shear deformations are included only in the matching procedure for the evaluation of the correction factor ebwk , as discussed in appendix b. this point is discussed again in the next section with reference to a practical application of the two formulations to the analysis of an exemplary fracture specimen, since it has important effects on the determination of the root displacement compliance coefficients. figure 11: relative deflection compliance coefficients under a pair of longitudinal forces according to the simplified model and for degenerate orthotropic materials (=1) with varying =0.5,1. the final comment regards the solutions for orthotropic specimens. the correction factors obtained using the eulerbernoulli model ebwk are independent of the orthotropy ratio  in all cases. this sets simple rescaling rules for the compliance coefficients in eqn. (25) and values for ≠1 can be easily obtained by rescaling the values for =1 by 1/4 for 0m ebd and 0n ebd , by  1/2 for 0 0v meb ebd c and 0 n ebc and by  3/4 0vebc . on the other hand, the correction factors obtained using the timoshenko model depend on all the elastic constants and the rescaling rules on the compliance coefficients in eqns. (18)-(24) are more complicated, but for 0md and 0nd which are independent of the poisson ratios and rescale as 1/4. to conclude, all compliance coefficients depend also on the second orthotropy ratio , however the effect of  is only quantitative and does not modify the conclusions drawn above. application of the results his section presents an application of the two formulations developed in the paper to the analysis of an exemplary fracture specimen. this allows to clarify how the described results can be effectively used in practice and the differences between the two formulations. the exemplary case of the symmetric dcb specimen shown in fig. 12a is considered. the material is linearly elastic and orthotropic with principal material directions x, y, z and longitudinal young's modulus ex, transverse young's modulus t i. monetto et alii, frattura ed integrità strutturale, 53 (2020) 372-393; doi: 10.3221/igf-esis.53.29 385 ez, in plane shear modulus gxz and poisson ratios xz and zx. the specimen is subjected to a pair of transverse forces f at a distance a from the crack tip. the interest is here focused on the derivation of the displacement field in the specimen and the calculation of the relative transverse load point displacement w, in particular. in order to do this, within classical beam theories, the upper and lower arms behind the crack tip are treated as cantilever beams, built-in at the crack tip cross section (x=a), and with the same length a and constant rectangular cross sections with unit width and height h. the effective compliance of the intact portion ahead of the crack tip is accounted for through suitable root rotations and displacements. figure 12: symmetric dcb specimen: a) geometry and loading configuration; b) loads at the crack tip. assuming timoshenko beams and using the concepts of root rotations and displacements, the maximum relative deflection w occuring between the two arms can be written as follows 3 0 03 11 8 2 s xzx w w fa fa a g he h         (27) where the first term on the right hand side is the result of the bending moment induced by the applied loads; the second term accounts for the effects of the shear deformations along the arms; the last two terms are the corrections related to the relative rotation 0 and deflection w0 at the crack tip cross section. alternatively, assuming euler-bernoulli beams, the maximum relative deflection web at the loaded point can be written as follows 3 0 03 1 8eb eb eb x w w fa a e h      , (28) which differs from eqn. (27) for the absence of the term accounting for the effects of the shear deformations along the arms. on the basis of eqns. (16) and (17), setting the crack tip loads n0=0, v0=f and m0=fa, as shown in fig. 12b, and noting that 2( // )x xz xze g     yield 0 0 0 0 3 2 3 2 11 1 8 4m v m v xz x s xx x w fa fa fa f d d c c e h ee h e h                     (29) and  0 0 0 0 3 2 3 2 11 1 8 m v m veb eb eb eb eb x xx x w fa fa fa f d d c c e h ee h e h       . (30) firstly, the equations above explain why some of the root displacement coefficients, those that do not multiply by the crack length, do not enter the expression of the energy release rate, which can be obtained using the compliance method. secondly, taking into account eqn. (26) and noting that 0 0m mebd d , 0 0m vc d , 0 0m veb ebc d show that all terms of the two relations assume the same values but for the last term, which describes the effect of the root displacement due to the i. monetto et alii, frattura ed integrità strutturale, 53 (2020) 372-393; doi: 10.3221/igf-esis.53.29 386 crack tip shear force. as an example, without loss of generality, in an isotropic specimen with =0.3 from tabs. 1 and 7 of appendix b we have 0 1.559vc  and 0 03.659 2.347v vebc c  . in order to clarify this relevant difference and understand which model leads to the most accurate estimate for the root displacement due to crack tip shear, the finite element method has been used and a numerical analysis has been carried out through the commercial finite element code ansys 2019r1. a mesh consisting of plane stress four-node quadrilateral elements has been used and convergence checked by varying the mesh in size and number of elements. the corresponding root rotation and displacement compliance coefficients have been determined following the method described in [3]. the root rotation compliance coefficients due to bending moment and transverse force listed in table 10 of appendix b have been successfully reproduced. furthermore, the root displacement compliance coefficient due to shear has been calculated, that is 0 1.537vc  . this result shows straightforwardly that the timoshenko beam based model leads to more accurate estimates for the root displacement compliance coefficients than the euler-bernoulli beam based model which yields a 138% error on the prediction. in order to account for the effects of shear deformations in fracture specimens approximated as euler-bernoulli beams, the simplified model requires that the particular matching procedure based on eqn. (b.4) is used, which has the effect of decreasing the correction factor of the transverse elasticity to include the effects of the shear deformations. however, this leads to accurate estimates for the root rotations but to eccessive overestimates for the root displacements. on the other hand, it is worthwhile noting that the terms on the right hand side of eqn. (29) have different relevance in the evaluation of the maximum relative deflection in the dcb specimen under consideration. in particular, the fourth term related to root displacements under shear is in general little to not relevant compared to the others for many geometries and orthotropy ratios. to better understand this point, the contributions due to bending moment, shear deformations and root rotations and displacements are conveniently evaluated as percentage of the total maximum relative deflection for degenerate orthotropic specimens (=1) with =1,0.5,0.05,0.025. in the case of medium/long delaminations (a/h≥6) the term 0vc has no relevance and is smaller than 1% of the total even for very low =0.025. for medium/short length delaminations (e.g. a/h=3), the first term related to bending moment induced by the applied loads is the most relevant for high =1,0.5 but decreases from about 55% of the total for =1 to 26% for =0.025; the contribution of root rotations becomes the most relevant for low =0.05,0.025 and increases from 40% for =1 to 58% for =0.025; the shear deformations term increases from 5% for =1 to 12% for =0.025; once again, the contribution of 0vc has very little relevance and is smaller than 1% for =1,0.5 and equals to 3% for =0.05 and 4% for =0.025. conclusions his paper deals with the analytical derivation of root compliance coefficients which can be used to define root rotations and root displacements at the crack tip cross section of orthotropic cracked beams. the work is limited to homogeneous and orthotropic materials with the axes of material symmetry parallel to the reference axes. explicit and simple expressions have been derived for use in practical applications under general loading conditions at the crack tip. accounting for root effects is important to accurately define energy release rate, mode mixity and displacements fields in the specimens. the derivation builds on and extends one-dimensional formulations in the literature and describes the intact part of the specimen as two beams joined by an elastic winkler type bond. the effects of both shear deformations and transverse elasticity are taken into account; in addition, the continuity condition imposed on the relative sliding displacements of the two beams at their interface to describe the continuity of the intact portion ahead of the crack tip makes the axial and bending problems coupled. this allows to extend thouless' [10] treatment to problems where the geometry is not symmetrical and where root displacements may be relevant, and to loading by axial forces. the novel analytical expressions for the root coefficients depend on the elastic constants and the geometrical parameters and one a priori unknown parameter, kw, which defines the connection modulus and describes the effects of the transverse elasticity. the parameter is obtained through matching of well established results in the literature for the root rotation compliance coefficients. for fixed geometry and material properties, obtaining an unique value for the parameter kw derived by matching the root rotations due to the different elementary loadings would imply an accuracy of the one-dimensional model in predicting the displacement field comparable to that of 2d elasticity. the results show that this is true in isotropic and orthotropic t i. monetto et alii, frattura ed integrità strutturale, 53 (2020) 372-393; doi: 10.3221/igf-esis.53.29 387 systems with mid-thickness cracks (=1) and in systems where the crack is only slightly misaligned, down to =0.8. in highly asymmetric systems, the connection modulus matching the elasticity solutions appears not to be unique and depends on the elementary loading conditions. the differences are due to the limitations of the structural model, which neglects mutual coupling effects due to the deformations of adjacent points along the longitudinal axis (winkler type support). in these problems, the matching coefficient to determine the a priori unknown model parameter should be chosen based on the role played by each compliance coefficient in the problem of interest. as an example, in a fracture mechanics problem devoted to the evaluation of the energy release rate, the fact that the contribution of the root rotations due to crack tip moments always prevails on that of the shear forces, since it varies as a higher power of the crack length, could suggest to choose the root rotation under symmetrical bending as matching coefficient. results also show that the model of two timoshenko beams connected by a winkler type bond accurately defines the root displacement coefficients of symmetric fracture specimens under general loading conditions and overcome the limitations of models based on euler-bernoulli beam theory, which largely overestimate predictions of these coefficients. on the other hand, the simplicity of the closed form solutions of the euler-bernoulli model, where the correction factor is independent of the material orthotropy and simple rescaling formulas can be used to define root coefficients, suggests the use of these solutions for all problems where the effects of the root displacements are negligible compared to the other root deformations. acknowledgements he authors acknowledge support by the italian department for university and scientific and technological research (murst) in the framework of the research miur prin15 project number 2015lyyxa8 "multi-scale mechanical models for the design and optimization of micro-structured smart materials and metamaterials", coordinated by professor a. corigliano. rm acknowledges support by the u.s. navy, office of naval research, grant n00014-17-1-2914. references [1] wang, j., qiao, p. (2004). interface crack between two shear deformable elastic layers, j. mech. phys. solids, 52, pp. 891-905. [2] li, s., wang, j., thouless, m.d. (2004). the effects of shear on delamination in layered materials, j. mech. phys. solids, 52(1), pp. 193-214. [3] andrews, m.g., massabò, r. (2007). the effects of shear and near tip deformations on energy release rate and mode mixity of edge-cracked orthotropic layers, eng. fracture mech., 74, pp. 2700-2720. [4] pandey, r.k., sun, c.t. (1996). calculating strain energy release rate in cracked orthotropic beams, j. thermoplast. compos. mater., 9(4), pp. 381-395. [5] yu, h.-h., hutchinson, j.w. (2002). influence of substrate compliance on buckling delamination of thin films, int. j. fracture, 113, pp. 39-55. [6] salganik, r.l., ustinov, k.b. (2012). deformation problem for an elastically fixed plate modeling a coating partially delaminated from the substrate (plane strain), mech. solids, 47, pp. 415–425. [7] ustinov, k.b. (2015). on influence of substrate compliance on delamination and buckling of coatings, eng. failure analysis, 47 (pb), pp. 338-344. [8] suo, z. (1990). delamination specimens for orthotropic materials, j. appl. mech., 57, pp. 627-634. [9] brandinelli, l., massabò, r. (2006). mode ii weight functions for isotropic and orthotropic double cantilever beams, int. j. fracture, 139(1), pp. 1-25. doi: 10.1007/s10704-006-6358-0. [10] thouless, m.d. (2018). shear forces, root rotations, phase angles and delamination of layered materials, eng. fracture mech., 191, pp. 153-167. [11] ustinov, k., massabò, r., lisovenko, d. (2020). orthotropic strip with central semi-infininite crack under arbitrary loads applied far apart from the crack tip. analytical solution, eng. failure analysis, 110, 104410. doi: 10.1016/j.engfailanal.2020.104410. [12] ustinov, k.b. (2019). on semi-infinite interface crack in bi-material elastic layer, european j. mech./a solids, 75, pp. 56-69. t i. monetto et alii, frattura ed integrità strutturale, 53 (2020) 372-393; doi: 10.3221/igf-esis.53.29 388 [13] massabò, r., ustinov, k., barbieri, l., berggreen, c. (2019). fracture mechanics solutions for interfacial cracks between compressible thin layers and substrates, coatings, 9 (3), art. no. 152. doi: 10.3390/coatings9030152. [14] barbieri, l., massabò, r., berggreen, c. (2018). the effects of shear and near tip deformations on interface fracture of symmetric sandwich beams, eng. fracture mech., 201, pp. 298-321. doi: 10.1016/j.engfracmech.2018.06.039. [15] cotterell, b., chen, z. (2000). buckling and cracking of thin films on compliant substrates under compression, int. j. fract., 104, pp. 169-79. doi: 10.1023/a:1007628800620. [16] kanninen, m.f. (1973). an augmented double cantilever beam model for studying crack propagation and arrest, int. j. fracture, 9, pp. 83-92. [17] kanninen, m.f. (1974). a dynamic analysis of unstable crack propagation and arrest in the dcb test specimen, int. j. fracture, 10, pp. 415-430. [18] williams, j.g. (1989). end corrections for orthotropic dcb specimens, j. compos. sci. technol., 35, pp. 367-376. [19] andrews, m.g., massabò, r. (2008). delamination in flat sheet geometries in the presence of material imperfections and thickness variations, composites part b, 39, pp. 139-150. doi: 10.1016/j.compositesb.2007.02.017. [20] massabò, r., cavicchi, a. (2012). interaction effects of multiple damage mechanisms in composite sandwich beams subjected to time dependent loading, int. j. solids struct., 49, pp. 720-738. doi: 10.1016/j.ijsolstr.2011.11.012. [21] campi, f., monetto, i. (2013). analytical solutions of two-layer beams with interlayer slip and bi-linear interface law, int. j. solids struct., 50, pp. 687-698. [22] monetto, i. (2015). analytical solutions of three-layer beams with interlayer slip and step-wise linear interface law, compos. struct., 120, pp. 543-551. [23] monetto, i., campi, f. (2017). numerical analysis of two-layer beams with interlayer slip and step-wise linear interface law, eng. struct., 144, pp. 201-209. [24] monetto, i. (2019). the effects of an interlayer debond on the flexural behavior of three-layer beams, coatings, 9, art. no. 258. [25] hutchinson, j.w., suo, z. (1991). mixed mode cracking in layered materials, adv. appl. mech., 29, pp. 63–191. appendix a. simplified formulation according to euler-bernoulli beam theory his appendix presents a simplified formulation based on modeling the two semi-infinite beams shown in fig. 1b as linearly elastic and orthotropic euler-bernoulli beams. according to euler-bernoulli beam theory, the shear strains within the two layers are neglected. this implies that, firstly, the rotations are related to the deflections of the beams (i=1,2) as ' i iw   (a.1) secondly, infinite shear stiffnesses are assumed so that ˆ 0a  and then ˆ ˆ4 0d e   . in this case, the general solution of eqn. (7) modifies as    1 2 3 4exp( ) cos( ) sin( ) exp( ) cos( ) sin( )np x c x c x x c x c x          (a.2) where 4 ˆ / 2e  (a.3) with ê given by eqn. (8). in analogy to the procedure described in the second section, the shear tractions follow from eqn. (11), the internal forces are given by eqn. (12), and the rotations and axial displacements are derived by eqns. (13a-b); whereas eqn. (13c) for the deflections is substituted by the following 15di i iw x c    (a.4) the remaining eqn. (14) for the relative rotation and deflection and eqn. (15) for the arbitrary constants are still valid. following the procedure described in the second section yields explicit expressions of the compliance coefficients t i. monetto et alii, frattura ed integrità strutturale, 53 (2020) 372-393; doi: 10.3221/igf-esis.53.29 389 pertinent to this simplified model based on euler-bernoulli beam theory. they are given by eqn. (25). once again, an a priori unknown parameter ebwk enters into these expressions. its identification requires a matching procedure similar to that presented in the third section and detailed in appendix b also for the timoshenko beam model. to conclude, it is worthwhile noting that for the special case of symmetric geometry (=1) and loadings (n0=0) the expressions for the compliance coefficients 0mebd , 0 0v m eb ebd c and 0 v ebc given by eqn. (25) coincide with those reported in [10] in both isotropy and orthotropy. appendix b. matching procedure and summary results tables n this appendix the numerical results shown and discussed in the fourth section are listed in table form for different geometries (=1,0.8,0.6,0.4). the results obtained using the model according to timoshenko beam theory are presented in tabs. 1 to 3 for isotropic specimens (==1) with varying poisson ratios xz=zx==0,0.3,0.5 and in tabs. 4 to 6 for orthotropic specimens with =1, =0.5 and varying poisson ratios xz=0,0.3,0.5. similar results through the simplified model according to euler-bernoulli beam theory are reported in tabs. 7 to 9 for =1 and =1.   kw 0vd 0md 0nd 0vc 0nc 0 2.603 3.036 2.044 1.518 1 0.3 4.472 2.316 16.154 8.077 1.559 1.158 0.5 7.116 1.836 1.236 0.918 0 2.458 2.830 2.137 1.415 0.8 0.3 4.134 2.182 13.214 6.607 1.648 1.091 0.5 6.427 1.750 1.322 0.875 0 1.988 2.871 2.535 1.436 0.6 0.3 3.111 2.295 10.851 5.426 2.027 1.148 0.5 4.486 1.911 1.688 0.956 0 1.309 3.318 3.656 1.659 0.4 0.3 1.820 2.814 9.071 4.536 3.101 1.407 0.5 2.347 2.478 2.730 1.239 table 1: numerical results according to the timoshenko beam based model and 0md based matching for isotropic materials (==1). matching the compliance coefficients using the timoskenko beam based model in order to define the correction factor kw, a matching has been performed on the root rotations due to moment, shear and normal force presented in [3]. the numerical values used in the present paper are the difference between the root rotation compliance coefficients for the upper, say 1 ka , and lower, say 2 ka , layers given in table 1 of [3] (the upper-script k=m0,v0,n0 denotes the end loading moment, shear or normal force). matching is then based on equating 1 2 k k kd a a  . for completeness, the numerical values 1 2 k ka a are reported in table 10. as an example, with reference to the model according to the timoshenko beam theory, for matching based on the root rotation compliance coefficient 0vd , under symmetrical transverse force, the use of eqn. (18) leads to the following expression   0 0 0 4 2 1 2 3(1 ) 2 v w v va a k      (b.1) where 0 0 0 1 2 v v va ad   has been enforced. substituting eqn. (b.1) into eqns. (19) to (24) gives the remaining compliance coefficients. these results are reported in table 2 for isotropic specimens and in table 5 for degenerate orthotropic specimens with =0.5 (=1). it is worthwhile noting that 0md and 0nd for a generic  could be obtained on rescaling of 1/4 those pertinent to =1; rescaling of the other coefficients is through more complicated expressions of the elastic i i. monetto et alii, frattura ed integrità strutturale, 53 (2020) 372-393; doi: 10.3221/igf-esis.53.29 390 constants. similar considerations are valid for matching based on the other root rotation compliance coefficients 0md and 0nd , under moment and normal force, but explicit expressions for 0mwk and 0n wk cannot be derived from eqns. (22) and (24) together with eqns. (20) and (21). the pertinent numerical results are listed in tabs. 1 and 3 for isotropic specimens and in tabs. 4 and 6 for degenerate orthotropic specimens with =0.5 (=1).   kw 0vd 0md 0nd 0vc 0nc 0 2.604 3.036 2.043 1.518 1 0.3 4.474 2.316 16.153 8.077 1.559 1.158 0.5 7.120 1.836 1.236 0.918 0 2.601 2.751 2.061 1.376 0.8 0.3 4.451 2.103 13.109 6.554 1.576 1.052 0.5 7.049 1.671 1.252 0.836 0 2.590 2.515 2.137 1.258 0.6 0.3 4.358 1.939 10.440 5.220 1.647 0.970 0.5 6.776 1.555 1.321 0.778 0 2.598 2.355 2.332 1.178 0.4 0.3 4.205 1.851 8.151 4.075 1.833 0.926 0.5 6.277 1.515 1.500 0.758 table 2: numerical results according to the timoshenko beam based model and 0vd based matching for isotropic materials (==1).   kw 0vd 0md 0nd 0vc 0nc 0 2.638 3.016 2.026 1.508 1 0.3 4.551 2.296 16.124 8.062 1.543 1.148 0.5 7.275 1.816 1.220 0.908 0 3.864 2.257 1.604 1.128 0.8 0.3 7.604 1.609 12.432 6.216 1.143 0.804 0.5 14.212 1.177 0.836 0.588 0 6.345 1.607 1.217 0.803 0.6 0.3 15.418 1.031 9.310 4.655 0.781 0.515 0.5 39.156 0.647 0.490 0.323 0 11.966 1.097 0.901 0.549 0.4 0.3 40.932 0.593 6.762 3.381 0.487 0.297 0.5 217.687 0.257 0.211 0.129 table 3: numerical results according to the timoshenko beam based model and 0nd based matching for isotropic materials (==1).   kw 0vd 0md 0nd 0vc 0nc 0 2.603 4.294 3.437 2.147 1 0.3 3.757 3.574 19.210 9.605 2.861 1.787 0.5 5.013 3.094 2.477 1.547 0 2.458 4.002 3.595 2.001 0.8 0.3 3.499 3.354 15.714 7.857 3.013 1.677 0.5 4.610 2.922 2.625 1.461 0 1.988 4.060 4.264 2.030 0.6 0.3 2.699 3.484 12.904 6.452 3.659 1.742 0.5 3.409 3.100 3.256 1.550 0 1.309 4.692 6.148 2.346 0.4 0.3 1.643 4.188 10.787 5.394 5.488 2.094 0.5 1.942 3.852 5.048 1.926 table 4: numerical results according to the timoshenko beam based model and 0md based matching for orthotropic materials with =1 and =0.5. i. monetto et alii, frattura ed integrità strutturale, 53 (2020) 372-393; doi: 10.3221/igf-esis.53.29 391   kw 0vd 0md 0nd 0vc 0nc 0 2.604 4.294 3.437 2.147 1 0.3 3.759 3.574 19.210 9.605 2.860 1.787 0.5 5.016 3.094 2.476 1.547 0 2.601 3.891 3.467 1.945 0.8 0.3 3.744 3.243 15.589 7.795 2.889 1.621 0.5 4.984 2.811 2.504 1.405 0 2.590 3.557 3.594 1.778 0.6 0.3 3.688 2.981 12.415 6.208 3.012 1.490 0.5 4.859 2.597 2.624 1.298 0 2.598 3.331 3.921 1.665 0.4 0.3 3.606 2.826 9.693 4.846 3.328 1.413 0.5 4.465 2.490 2.932 1.245 table 5: numerical results according to the timoshenko beam based model and 0vd based matching for orthotropic materials with =1 and =0.5.   kw 0vd 0md 0nd 0vc 0nc 0 2.638 4.266 3.408 2.133 1 0.3 3.818 3.546 19.175 9.587 2.833 1.773 0.5 5.107 3.066 2.449 1.533 0 3.864 3.192 2.697 1.596 0.8 0.3 6.084 2.544 14.784 7.392 2.149 1.272 0.5 8.828 2.112 1.784 1.056 0 6.345 2.272 2.047 1.136 0.6 0.3 11.386 1.696 11.072 5.536 1.528 0.848 0.5 19.023 1.312 1.183 0.656 0 11.966 1.552 1.516 0.776 0.4 0.3 26.246 1.048 8.041 4.021 1.023 0.524 0.5 56.875 0.712 0.695 0.356 table 6: numerical results according to the timoshenko beam based model and 0nd based matching for orthotropic materials with =1 and =0.5. matching the compliance coefficients using the euler-bernoulli beam based model with reference to the simplified model according to the euler-bernoulli beam theory, for matching based on the root rotation compliance coefficient 0mebd under moment, the use of the first of eqn. (25b) leads to the following expression   0 0 0 10 4 1 2 (1 )54m eb w m ma a k      (b.2) where 0 0 0 1 2 m m m ebd a a  has been enforced. substituting eqn. (b.2) into eqns. (25a) and (25b) gives the remaining compliance coefficients. similarly, for matching based on the root rotation compliance coefficient 0nebd under normal force, from the second of eqn. (25b) we derive   0 0 0 10 4 1 2 (1 )27 8 n eb w n na a k      (b.3) i. monetto et alii, frattura ed integrità strutturale, 53 (2020) 372-393; doi: 10.3221/igf-esis.53.29 392  ebwk 0v ebd 0m ebd 0n ebd 0v ebc 0n ebc 1 0.812 5.436 16.154 8.077 3.659 2.718 0.8 0.790 4.990 13.214 6.607 3.769 2.495 0.6 0.714 4.791 10.851 5.426 4.231 2.396 0.4 0.577 4.998 9.071 4.536 5.507 2.499 table 7: numerical results according to the euler-bernoulli beam based model and 0mebd based matching for orthotropic materials with ==1.  ebwk 0v ebd 0m ebd 0n ebd 0v ebc 0n ebc 1 0.812 5.436 16.153 8.077 3.659 2.718 0.8 0.816 4.911 13.109 6.555 3.680 2.456 0.6 0.833 4.435 10.440 5.220 3.768 2.218 0.4 0.885 4.035 8.151 4.075 3.995 2.018 table 8: numerical results according to the euler-bernoulli beam based model and 0vebd based matching for orthotropic materials with ==1. the third case of matching based on the root rotation compliance coefficient 0vebd under transverse force deserves more attention. neglecting the effects of shear deformations in fracture specimens approximated as euler-bernoulli beams leads to unacceptable underestimates of the energy release rate. in order to overcome this limit, as suggested in [10], it appears more suitable to base the matching of 0vebd on a modified root rotation coefficient obtained by modifying the exact 2d results 0 0 1 2 v va a to account for the effects of the shear deformations so that they are correctly modelled in the energy release rate. this is done by equating  0 0 0 0 0 1 1 2 1 2 (1 )v v eb v eb v veb s xzd a a a a                 (b.4) where the second term on the right hand side of eqn. (b.4) comes directly from the expression of the energy release rate defined in eqn. (6) in [3] in terms of modified crack tip stress resultants. for symmetric specimens this is equivalent to perform matching on the energy release rate. combining eqn. (b.4) and the second of eqn. (25a) gives   0 0 0 4 2 1 2 (1 )3 2 v eb w v eb v eba a k      . (b.5) this modification implies that, in the case for =1, the correction factors obtained by matching any of the three root compliance coefficients coincide. the rescaling laws presented in [3] for the root compliance coefficients 1 2 k k kd a a  show that the correction factors obtained using eqns. (b.3-5) are independent of . the root compliance coefficients in eqn. (25) for ≠1 can then be easily obtained by rescaling the values corresponding to =1 by 1/4 for 0mebd and 0 n ebd , by  1/2 for 0 0v meb ebd c and 0 n ebc and by 3/4 for 0vebc . tabs. 7 to 9 report results for =1 and =1.  ebwk 0 v ebd 0m ebd 0 n ebd 0v ebc 0 n ebc 1 0.818 5.416 16.124 8.062 3.639 2.708 0.8 1.009 4.417 12.432 6.216 3.138 2.208 0.6 1.317 3.527 9.310 4.655 2.672 1.763 0.4 1.868 2.777 6.762 3.381 2.281 1.389 table 9: numerical results according to the euler-bernoulli beam based model and 0nebd based matching for orthotropic materials with ==1. i. monetto et alii, frattura ed integrità strutturale, 53 (2020) 372-393; doi: 10.3221/igf-esis.53.29 393   0 0 1 2 m ma a 0 0 1 2 n na a 0 0 1 2 v va a 0 0 1 2 v eb v eba a xz = 0 0.3 0.5 1 16.154 8.062 3.036 2.316 1.836 5.436 1 0.8 13.214 6.216 2.751 2.103 1.671 4.911 0.6 10.851 4.655 2.515 1.939 1.555 4.435 0.4 9.071 3.381 2.355 1.851 1.515 4.035 1 19.210 9.587 4.294 3.574 3.094 7.688 0.5 0.8 15.714 7.392 3.891 3.243 2.811 6.945 0.6 12.904 5.536 3.557 2.981 2.597 6.272 0.4 10.787 4.021 3.330 2.826 2.490 5.706 table 10: numerical values of the root rotations calculated from [3] and used for matching for orthotropic materials with =1 and =0.5,1. << /ascii85encodepages false /allowtransparency false /autopositionepsfiles true /autorotatepages /none /binding /left /calgrayprofile (dot gain 20%) /calrgbprofile (srgb iec61966-2.1) /calcmykprofile (u.s. web coated \050swop\051 v2) /srgbprofile (srgb iec61966-2.1) /cannotembedfontpolicy /error /compatibilitylevel 1.4 /compressobjects /tags /compresspages true /convertimagestoindexed true /passthroughjpegimages true /createjobticket false /defaultrenderingintent /default /detectblends true /detectcurves 0.0000 /colorconversionstrategy /cmyk /dothumbnails false /embedallfonts true /embedopentype false /parseiccprofilesincomments true /embedjoboptions true /dscreportinglevel 0 /emitdscwarnings false /endpage -1 /imagememory 1048576 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can be opened with acrobat and adobe reader 5.0 and later.) >> /namespace [ (adobe) (common) (1.0) ] /othernamespaces [ << /asreaderspreads false /cropimagestoframes true /errorcontrol /warnandcontinue /flattenerignorespreadoverrides false /includeguidesgrids false /includenonprinting false /includeslug false /namespace [ (adobe) (indesign) (4.0) ] /omitplacedbitmaps false /omitplacedeps false /omitplacedpdf false /simulateoverprint /legacy >> << /addbleedmarks false /addcolorbars false /addcropmarks false /addpageinfo false /addregmarks false /convertcolors /converttocmyk /destinationprofilename () /destinationprofileselector /documentcmyk /downsample16bitimages true /flattenerpreset << /presetselector /mediumresolution >> /formelements false /generatestructure false /includebookmarks false /includehyperlinks false /includeinteractive false /includelayers false /includeprofiles false /multimediahandling /useobjectsettings /namespace [ (adobe) (creativesuite) (2.0) ] /pdfxoutputintentprofileselector /documentcmyk /preserveediting true /untaggedcmykhandling /leaveuntagged /untaggedrgbhandling /usedocumentprofile /usedocumentbleed false >> ] >> setdistillerparams << /hwresolution [2400 2400] /pagesize [612.000 792.000] >> setpagedevice microsoft word numero_39_art_7 a. lokaj et alii, frattura ed integrità strutturale, 39 (2017) 56-61; doi: 10.3221/igf-esis.39.07 56 focussed on modelling in mechanics comparison of behaviour of laterally loaded round and squared timber bolted joints antonín lokaj, kristýna klajmonová všb – technical university of ostrava, faculty of civil engineering, department of structures, l. podeště 1875, 708 33 ostrava-poruba, czech republic antonin.lokaj@vsb.cz, http://orcid.org/000-0003-2248-1848 kristyna.klajmonova@vsb.cz abstract. in the current european standards for design of timber structures, the issue of timber-to-timber joint type is addressed only to squared timber, which makes the pinpointing of the round timber bolted joints load carrying capacity near-unfeasible due to the insufficient support in the current standards. there have been made series of tests of round timber joints in different inclinations of the loading force and also the reference tests of squared timber joints to compare the behaviour of this type of joints. mechanical behaviour of the round and the squared timber bolted joints was tested in the laboratory of the faculty of civil engineering in ostrava. this paper presents results of static tests in tension at an angle of 0°, 90° and 60° to the grain of squared and round timber bolted joints. load carrying capacity was determined according to the applicable standards and theories of fracture mechanics. the test results of laboratory tests were then compared with the results of theoretical calculations. keywords. round timber; bolt; joint; load carrying capacity. citation: labudkova, j., cajka, r., numerical analyses of interaction of steel-fibre reinforced concrete slab model with subsoil, frattura ed integrità strutturale, 39 (2017) 5661. received: 11.07.2016 accepted: 14.09.2016 published: 01.01.2017 copyright: © 2017 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. introduction he strength of wood varies depending on the force direction relative to the orientation of the grains. the highest value reaches the tensile strength parallel to the grains, the average value indicates 120 nmm-2. this high strength is mainly due to the shape of cells and fibrous cell wall structure. tensile strength perpendicular to the grain is, on the other hand, the smallest strength of wood at all. the average tensile strength perpendicular to the grain is in the range between 2 nmm-2 and 5 nmm-2. this corresponds to 1/20 of the tensile strength of the wood parallel to the grain [1]. low value of tensile strength perpendicular to the grain is caused by orientation of the binding forces. hydrogen bonds and van der waals forces connect grains in the transverse direction. the tensile stress of timber perpendicular to the grain is desirable in use in the support structure. this paper focuses on the behaviour of round timber bolted joints. in the current european standards for the design of timber structures [2], the issue of timber-to-timber joint type is addressed only to squared timber, which makes the t http://www.gruppofrattura.it/pdf/rivista/numero39/audio/7.mp3 a. lokaj et alii, frattura ed integrità strutturale, 39 (2017) 56-61; doi: 10.3221/igf-esis.39.07 57 pinpointing of the round timber bolted joints load carrying capacity near-unfeasible due to the insufficient support in the current standards. to compare the behaviour of this type of connections, a series of laboratory static tests in different inclinations of the loading force to the grain has been made. the reference tests of squared timber joints were also carried out [3]. mechanical behaviour of the round and the squared timber bolted joints were tested in the laboratory of the faculty of civil engineering in ostrava. samples type value tension orientation at an angle to the grain 0° 60° 90° ̅ sd cv ̅ sd cv ̅ sd cv round timber number of samples 12 12 12 density (kgm-3) 412.6 42.1 10.2 405.9 26.4 6.5 414.9 46.2 11.1 moisture (%) 11.6 1.1 9.4 11.3 1.0 8,9 11.4 1.1 9.6 squared timber number of samples 9 10 12 density (kgm-3) 426.8 13.77 3.2 443.6 14.6 3.3 454.4 50.1 11.0 moisture (%) 11.2 0.6 5.3 12.2 0.5 4.1 11.6 0.5 4.3 table 1: characteristics of tested wood ( x is the arithmetical average; sd is the standard deviation; cv is the coefficient of variation). the special steel element for testing was prepared (fig. 1). in order for the load direction to be perpendicular (or at an angle 60°) to the grain, the samples were subjected to a simple tensile test with the loading force being increased gradually. the test parameters were invariable for all samples. each round timber sample subjected to a simple tension test had the same test parameters. the tension force on samples loaded parallel to the grain was increased gradually. the selected rate of displacement of the press jaws was optimal. each specimen failure occurred in time boundary of 300 ± 120 sec. it corresponds to the current european standard. figure 1: steel product for testing in tension perpendicular to the grain and sample in press machine. material and test method s spruce wood is the most common type of timber, it was used as samples for testing. a few non-destructive tests were carried out before the onset of the static tests in the press, [4, 5]. dimensions of the test samples were adjusted to the equipment possibilities of the laboratory at the faculty of civil engineering. thus, the specimen a a. lokaj et alii, frattura ed integrità strutturale, 39 (2017) 56-61; doi: 10.3221/igf-esis.39.07 58 length was 450 mm (for tests in tension at an angle of 0°) and 560 mm (for tests in tension at an angle of 60°and 90°), respectively, and the specimen diameter was 120 mm. the bolts of high strength steel (category 8.8) were used. the diameter of the bolts was 20 mm. the connection plates were made of steel s235 with thickness of 8 mm, length of 290 mm and width of 80 mm. the diameter of holes in steel plates was 22 mm and diameter in timber elements was 20 mm. the distance between holes and the free end in timber was 140 mm, in steel 50 mm [6]. the squared timber was used with the cross section of 60120 mm, the other geometry of joint was the same as in the case of round specimens. calculation of the load carrying capacity of joint or comparison with applicable european standards [2] there was carried out a numerical calculation of the joint resistance. the investigated joint is of the double-shear dowel type with an embedded steel sheet, which forms the central element of the joint. failure mechanisms for the investigated type of joint are shown in fig. 2. figure 2: failure mechanisms of double-shear dowel type steel to timber joint. according to johansen's theory [7] that underlies eurocode 5, the characteristic load carrying capacity of one coupling element in one cut at the steel-to-timber connection, where the steel plate is the middle joint element, is determined by expression: h k y rk v rk h k h k y rk h k f t d m f min f t d f d t m f d , 1 , , , 1 2 , 1 , , 4 2 1 2, 3                           (1) where: fv,rk is the characteristic load-carrying capacity per shear plane per fastener (n) without rope effect, fh,k is the characteristic embedment strength of timber member (nmm-2), t1 is the timber or board thickness or penetration depth (mm), d is the fastener diameter (mm), my,rk is the characteristic fastener yield moment (nmm). relationships mentioned above are based on the theory of johansen [7], which the calculation of dowel type joints in eurocode 5 is based. this theory is underscored by a series of laboratory measurements [8]. johansen's theory is based on the assumption that the load carrying capacity of the fastener is limited by the load capacity in bearing walls of the bolt hole in at least one of the constituent elements, or simultaneous occurrence of the embedment strength and plastic hinge in the dowel. f a. lokaj et alii, frattura ed integrità strutturale, 39 (2017) 56-61; doi: 10.3221/igf-esis.39.07 59 the mechanism of failure depends on the geometry of the connection and the properties of the construction materials, particularly on a plastic torque of dowel and tensile deformation of the wall of dowel hole in the case of timber or woodbased material [9, 10]. from equations for determining the load carrying capacity of the connecting means it is evident that calculation for determining the load carrying capacity of connections depends on characteristics of wood density and thickness of the timber embedding the bolt. the decisive parameter is the diameter of the bolt and the material embedment strength [11]. results he test results of bolt connections of the squared and round timber with embedded steel plates laterally loaded at different angles to the grain give similar values of resistance, which are higher than the load capacity determined according to the eurocode 5. it means that the equations for determining the resistance of joints eurocode 5, which were derived for squared timber, can be applied to the joints of round timber. figure 3: comparison of the test records of squared timber samples loaded in tension at different angles. figure 4: comparison of the test records of round timber samples loaded in tension at different angles. t a. lokaj et alii, frattura ed integrità strutturale, 39 (2017) 56-61; doi: 10.3221/igf-esis.39.07 60 from the course of deformation of the round timber joints and squared timber joints it is evident that resistance and stiffness at different angles reaches comparable values. only squared timber joints samples exposed to force parallel to the grain exhibit less deformation than the corresponding round timber joints. connections with squared timber also have significant plastic deformations prior to the collapse of the joints, in contrast to round timber joints. different behaviours during testing at different angles of the loading force to the grain are shown in fig. 3 and 4. summary of the test results of round timber and squared timber samples subjected loading force at different angles to the grain are shown in tab.2. samples type value loading force orientation at an angle to the grain 0° 60° 90° ̅ sd cv ̅ sd cv ̅ sd cv round timber density (kgm-3) 412.6 42.1 10.2 405.9 26.4 6.5 414.9 46.2 11.1 capacity from test (kn) 64.9 6.3 9.7 41.7 4.8 11.5 40.6 5.0 12.5 ec5 (kn) 38.7 30.8 28.5 squared timber density (kgm-3) 426.8 13.77 3.2 443.6 14.6 3.3 454.4 50.1 11.0 capacity from test (kn) 57.7 5.1 8.8 49.7 2.9 5.8 32.5 3.6 11.1 ec5 (kn) 39.3 32.8 31.4 table 2: summary of the carrying capacity test results and the calculated values of load carrying capacity according to ec5 ( x is the arithmetical average; sd is the standard deviation; cv is the coefficient of variation). figure 5: damaged round timber samples loaded in tension at different angles. figure 6: damaged squared timber samples loaded in tension at different angles. a. lokaj et alii, frattura ed integrità strutturale, 39 (2017) 56-61; doi: 10.3221/igf-esis.39.07 61 conclusions he test results of bolt connections of squared and round timber with embedded steel plates loaded at different angles to the grain give similar values of resistance, which is higher than the load capacity determined according to the eurocode 5. it means that the equations for determining the resistance of joints according to eurocode 5, which were derived for squared timber, can be applied to the joints of round timber. fracture destruction is principal especially for wood joints with higher density. that fact was confirmed in the static tests. acknowledgement his outcome has been achieved with funds of conceptual development of science, research and innovation assigned to všb technical university of ostrava by ministry of education youth and sports of the czech republic in 2016 (no. ip2216611). references [1] gandelová, l., horáček, p., šlezingerová, j., wood science (in czech), brno, (2009). [2] eurocode 52004: design of timber structures part 1-1: general – common rules and rules for buildings. [3] klajmonová, k., lokaj, a., round timber bolted joints with mechanical reinforcement. advanced material research. 838-841 (2014 )629-633, doi: 10.4028/www.scientific.net/amr.838-841.629. [4] lokaj, a., klajmonová, k., round timber bolted joints exposed to static and dynamic loading, wood research, 59 (2014) 439-448. doi: 10.4028//www.scientific.net/amr.838-841.629. [5] lokaj, a., vavrušová, k., contribution to the probabilistic approach of the impact strength of wood. engineering mechanics (2011) 363 366. [6] lokaj, a., klajmonová, k., carrying capacity of round timber bolted joints with steel plates under static loading. transactions of the všb – technical university of ostrava, civil engineering series. 12 (2012) 100–105. doi: 10.2478/v10160-012-0023-5. [7] johansen, k. w., theory of timber connections. international association of bridge and structural engineering, (9) (1949) 249-262. [8] šmak, m., straka, b., development of new types of timber structures based on theoretical analysis and their real behaviour, wood research, 59 (2014) 459-470. [9] malo, k.a., et al., fatigue tests of dowel joints in timber structures, part ii: fatigue strength of dowel joints in timber structures. in: nordic timber bridge project, nordic timber council ab, stockholm, sweden (2002). [10] blass, h. j., schädle, p., ductility aspects of reinforced and non-reinforced joints, engineering structures, 33 (2011) 3018-3026. [11] smith, i., et al., fracture and fatigue in wood. john wiley  sons, england, (2013). t t << /ascii85encodepages false /allowtransparency false /autopositionepsfiles true /autorotatepages /none /binding /left /calgrayprofile (dot gain 20%) /calrgbprofile (srgb iec61966-2.1) /calcmykprofile (u.s. web coated \050swop\051 v2) /srgbprofile (srgb iec61966-2.1) /cannotembedfontpolicy /error /compatibilitylevel 1.4 /compressobjects /tags /compresspages true /convertimagestoindexed true /passthroughjpegimages true /createjobticket false /defaultrenderingintent /default /detectblends true /detectcurves 0.0000 /colorconversionstrategy /cmyk /dothumbnails false /embedallfonts true /embedopentype false /parseiccprofilesincomments true /embedjoboptions true /dscreportinglevel 0 /emitdscwarnings false /endpage -1 /imagememory 1048576 /lockdistillerparams false /maxsubsetpct 100 /optimize true /opm 1 /parsedsccomments true /parsedsccommentsfordocinfo true /preservecopypage true 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can be opened with acrobat and adobe reader 5.0 and later.) >> /namespace [ (adobe) (common) (1.0) ] /othernamespaces [ << /asreaderspreads false /cropimagestoframes true /errorcontrol /warnandcontinue /flattenerignorespreadoverrides false /includeguidesgrids false /includenonprinting false /includeslug false /namespace [ (adobe) (indesign) (4.0) ] /omitplacedbitmaps false /omitplacedeps false /omitplacedpdf false /simulateoverprint /legacy >> << /addbleedmarks false /addcolorbars false /addcropmarks false /addpageinfo false /addregmarks false /convertcolors /converttocmyk /destinationprofilename () /destinationprofileselector /documentcmyk /downsample16bitimages true /flattenerpreset << /presetselector /mediumresolution >> /formelements false /generatestructure false /includebookmarks false /includehyperlinks false /includeinteractive false /includelayers false /includeprofiles false /multimediahandling /useobjectsettings /namespace [ (adobe) (creativesuite) (2.0) ] /pdfxoutputintentprofileselector /documentcmyk /preserveediting true /untaggedcmykhandling /leaveuntagged /untaggedrgbhandling /usedocumentprofile /usedocumentbleed false >> ] >> setdistillerparams << /hwresolution [2400 2400] /pagesize [612.000 792.000] >> setpagedevice microsoft word numero 18 articolo 5.docx v. di cocco et alii, frattura ed integrità strutturale, 18 (2011) 45-53; doi: 10.3221/igf-esis.18.05 45 structural transitions in a niti alloy: a multistage loading-unload cycle v. di cocco university of cassino, dimsat, via g. di biasio 43, 03043, cassino (fr), italy. v.dicocco@unicas.it c. maletta university of calabria, dip. of mechanical engineering, 87036 rende (cs), italy. carmine.maletta@unical.it s. natali university of rome “sapienza”, d.i.c.m.a., via eudossiana 18, 00185 roma, italy. stefano.natali@uniroma1.it abstract. niti shape memory alloys (smas) are increasingly used in many engineering and medical applications, because they combine special functional properties, such as shape memory effect and pseudoelasticity, with good mechanical strength and biocompatibility. however, the microstructural changes associated with these functional properties are not yet completely known. in this work a niti pseudo-elastic alloy was investigated by means of x-ray diffraction in order to assess micro-structural transformations under mechanical uniaxial deformation. the structure after complete shape recovery have been compared with initial state. sommario. le leghe a memoria di forma costituite da nickel e da titanio sono sempre più utilizzate in molti settori dell’ingegneria e della medicina, in quanto combinano speciali proprietà funzionali, quali la memoria di forma e la pseudo-elasticità, con buone caratteristiche meccaniche e di biocompatibilità. tuttavia, le trasformazioni mico-strutturali che conferiscono tali proprietà funzionali non sono ancora completamente note. in questo lavoro è stata analizzata una lega niti pseudo-elastica, mediante indagini diffrattometriche ai raggi x, al fine di mettere in evidenza le modificazioni strutturali che intervengono sotto l’effetto di deformazioni imposte. la microstruttura ottenuta dal completo recupero della forma è stata confrontata con quella iniziale. keywords. shape memory alloys; stress-induced martensitic transformation; x-ray analyses. introduction hape memory alloys (smas) are an important class of metallic alloy which exhibit unique features with respect to common engineering alloys, such as the shape memory effect (sme) and pseudo-elastic effect (pe). in particular, due to these properties smas are able to recover their original shape after high values of mechanical deformations, by heating up to a characteristic temperature (sme) or simply by removing the mechanical load (pe). different kinds of shape memory alloys have been exploited in the last decades, such as the copper-zinc-aluminum (zncual), copperaluminum-nickel (cualni), nickel-manganese-gallium (nimnga), nickel-titanium (niti), and other smas created by s http://dx.medra.org/10.3221/igf-esis.18.05&auth=true http://www.gruppofrattura.it v. di cocco et alii, frattura ed integrità strutturale, 18 (2011) 45-53; doi: 10.3221/igf-esis.18.05 46 alloying zinc, copper, gold, iron, etc. within this class of materials the near equiatomic niti binary system shows the most exploitable characteristics and it is currently used in an increasing number of applications in many fields of engineering [1], for the realization of smart sensors and actuators, joining devices, hydraulic and pneumatic valves, release/separation systems, consumer applications and commercial gadgets. however, due to their good biocompatibility the most important applications of niti alloys are in the field of medicine, where the pseudo-elasticity is mainly exploited for the realization of several components such as cardiovascular stent, embolic protection filters, orthopedic components, orthodontic wires, micro surgical and endoscopic devices. from the microstructural point of view shape memory and pseudo-elastic effects are due to a reversible solid state microstructural transitions from austenite to martensite, which can be activated by mechanical and/or thermal loads [2]. the phase transition of near equiatomic niti systems is illustrated in the phase diagram of fig. 1, where at t<900°c complete temperature transformations are not well specified. in the last years a triple transitions has been accepted, from an austenitic b2 phase for slowly cooling a b19 orthorhomic phase transformation occurs, but for long time at 500°c (about 120 hours) an monoclinic b19’ phase is obtained. but not all the transformation are possible when changing the ni content; in particular when increasing the ni content last transformation (b19’) can take place only under environmental temperature or under the zero absolute [3-11]. figure 1: niti alloy phase diagram. the near equiatomic niti system is capable of two successive martensitic phase transformations during cooling from its high temperature austenitic phase. in ti rich niti smas, the first phase transformation during cooling is observed just above room temperature and results in the r-phase, the second one occurs around room temperature and results in mphase (monoclinic structure), often with a fine lath morphology. these transformations give rise to thermo-elasticity and twin deformations in niti alloy facilitating shape memory effect (sme) [12-14]. elastic strain energy provides the reversible nonchemical contribution to the overall free energy of the system. the method of elastic strain energy generation depends upon whether or not external stress is applied. in the absence of external stress, the martensite transformations in niti produce a self-accommodating arrangement of martensite correspondent variant pairs (cvps) that minimizes elastic strain energy. as the volume fraction of self-accommodating groups (sags) of martensite cvps grows, the concomitant increases in interfacial energy and elastic strain raise the stored elastic strain energy of the system. the evolution of microstructure and the formation of microcracks during cyclic loading has been observed and crack propagation under cyclic loading conditions has been monitored in many works, but behavior of cracks under static loading conditions in martensitic, pseudo-plastic and austenitic pseudo-elastic niti microstructures is not yet clear [8, 15-19]. in this work the mechanical properties of a commercial niti shape memory alloy have been investigated by tensile tests of miniaturized dog bone shaped specimens carried out by using a mini testing machine. in addition, in situ xrd analyses were performed during mechanical tests, in order to understand the influence of microstructure and crystallographic parameter on the pseudo-elastic effect of the alloy, as well as on the related hysteresis in the stress-strain response. 600 700 800 900 1000 1100 1200 1300 1400 1500 1600 1700 1800 0 10 20 30 40 50 60 70 80 90 100 te m p e ra tu re  [ °c ] ni [at%] ti 2 n i ti n i 3 tini (ti) (ti) 1670°c 1310°c 1380°c 1455°c (ni) 1118°c 1304°c 942°c 675°c 882°c 984°c 630°c http://dx.medra.org/10.3221/igf-esis.18.05&auth=true http://www.gruppofrattura.it v. di cocco et alii, frattura ed integrità strutturale, 18 (2011) 45-53; doi: 10.3221/igf-esis.18.05 47 material and methods n this work a commercial pseudo-elastic niti alloy (type s, memory metalle, germany), with nominal chemical composition of 50.8at.% ni 49.2 at.% ti, was used to investigate the evolution of microstructure during loadingunloading cycle. in fig. 2 light micrographs of the initial austenitic microstructure of the alloy is illustrated at different magnification, which shows the presence of inclusions and subgrains. this is an expected results as the inclusions play a significant role in the stress-induced phase transformation mechanisms and, consequently, in the macroscopic pseudo-elastic response of the alloy.     a) b) figure 2: initial austenitic microstructure of the investigated niti alloy: a) at low magnification showing the presence of inclusions, b) high magnification with presence of subgrains. the engineering stress-strain curve of the material is illustrated in fig 3, which were obtained from isothermal tensile tests, carried out at room temperature (t=298 k) by using a servo hydraulic universal testing machine, equipped with an electrical extensometer with a gauge length of 10 mm to measure the engineering deformations of standard dog-bone shaped specimen. in particular, fig. 3.a shows the stress-strain curve obtained from a monotonic tensile test to fracture, while fig. 3.b illustrates the marked hysteretic behavior of the material obtained from a loading-unloading cycle up to a maximum deformation of about 6.1 %. furthermore, fig. 3.b also illustrates the values of the main thermomechanical parameters of the alloys, i.e. the young’s moduli of austenite (ea) and martensite (em), the transformation stresses from austenite to martensite (sam and fam), the stresses for reverse transformation from martensite to austenite (sma and fma), the uniaxial transformation strain (l) and the clausis-clapeyron constant of the material (c=d/dt). the evolution of the microstructure during uniaxial deformation was analyzed by a miniature testing machine which allows in-situ scanning electron microscopic (sem) observations as well as x-ray micro-diffraction analyses. in particular, the testing machine is equipped with a simple and removable loading frame, which allows sem and x-ray analyses at fixed values of applied load and/or deformations. the machine is powered by a stepping motor, which applies the mechanical deformation to the specimen through a calibrated screw, with pitch of 0.8mm, and a control electronic allows simultaneous measurement and/or control of applied load and stroke of the specimen head. the stroke is measured by a linear variable differential transformer (lvdt) while the load is measured by two miniaturized load cells with maximum capacity of 10 kn. miniature dog bone shaped specimens with dimension showed in fig. 4 were machined from niti sheets, by wire electro discharge machining, due to the poor workability of this class of materials by conventional machining processes as well as to reduce the formation of thermo-mechanical affected zone. step by step isothermal tensile tests were carried out, at room temperature, at increasing values of the specimen elongation. in particular, three levels of elongation have been applied, =0.8, 1.6 and 2.4 mm, which can be expressed as gross engineering strain (g) with respect to the gauge length l0=16 mm, i.e. g=5, 10 and 15%. in particular, for each loading step the loading frame containing the specimen was removed from the testing machine, at fixed values of deformation, and analyzed by means of a philips diffractometer in order to evaluate xrd spectra. xrd measurements were made with a philips x-pert diffractometer equipped with a vertical bragg–brentano powder goniometer. a step–scan mode was used in the 2θ range from 30° to 90° with a step width of 0.02° and a counting time of 2 s per step. the employed radiation was monochromated cukα (40 kv – 40 ma). the calculation of theoretical diffractograms and the generation of structure models were performed using the powdercell software [20]. i http://dx.medra.org/10.3221/igf-esis.18.05&auth=true http://www.gruppofrattura.it v. di cocco et alii, frattura ed integrità strutturale, 18 (2011) 45-53; doi: 10.3221/igf-esis.18.05 48 furthermore, the gross engineering strain has been correlated to the effective engineering strain by a finite element simulation as reported in the following section. a) b) figure 3: isothermal stress-strain curve of the investigated alloy carried out at room temperature (t=298k): a) monotonic loading to fracture and b) loading-unloading cycle. figure 4: uniaxial miniaturized specimens. results and discussion inite element analyses (fea) were carried out in order to correlate the gross engineering strain (g) to the effective engineering strain (e), i.e. to the experimentally measured engineering stress-strain curve of fig. 3. to this aim a 2d fe model was made, by using a commercial software, to simulate the testing conditions of the miniature specimen, and a standard non-linear solutions were adopted to model the complex stress strain behavior of the material illustrated in fig 3. in particular, a quarter of the miniature specimen was modeled, due to symmetric geometry and boundary conditions, together with a part of the loading frame, and contact conditions were defined between them in order to reproduce the testing conditions as close as possible to reality. fig. 5.a illustrates the fe mesh which consists of about 800 4-noded plane stress quadrilateral elements while fig. 5.b shows the equivalent stress fringes corresponding to the maximum elongation of the specimen during cyclic tests (=2.4 mm and g=15%). f http://dx.medra.org/10.3221/igf-esis.18.05&auth=true http://www.gruppofrattura.it v. di cocco et alii, frattura ed integrità strutturale, 18 (2011) 45-53; doi: 10.3221/igf-esis.18.05 49     a) b) figure 5: fe analysis of the testing condition: a) fe model and b) equivalent stress fringes at the maximum elongation. in fig. 6a a comparison between the experimentally measured engineering stress-strain curve of fig. 3 and the numerically simulated one is illustrated, and a good agreement is observed. fig. 7 shows a comparison between the numerically simulated stress-strain curve relative to net and gross engineering strain. this latter was calculated from the displacement of the specimen head, according to the experimental conditions. as expected, gross strain is significantly greater than net strain and the difference increases when increasing the applied stress. furthermore, this effect is also evident in the early stage of loading, i.e. in the range of elastic deformation of austenite, resulting in an apparent smaller value of the young’s modulus. this effect can be attributed to two different mechanisms: the compliance of the miniaturized testing machine and the deformation on the specimen heads. note that a linear correction of the gross strain cannot be used here as the material non-linearity causes a marked non-linear relation between gross and net strain. for a better understanding of the results reported in the following section, fig. 7 illustrates the relation between gross strain and net strain within the range of deformation of the experiments. figure 6: comparison between experimentally measured stress-strain curve and numerically simulated one. prior to investigate stress strain behavior and in order to investigate microstructural transitions it is necessary to evaluate the initial xrd spectrum. the first diffraction obtained on the calibrated length of the miniature specimen in stress free conditions, shows two picks at 42.39 and 77.54°, corresponding to [011] and [022] crystallographic plains, typical of the http://dx.medra.org/10.3221/igf-esis.18.05&auth=true http://www.gruppofrattura.it v. di cocco et alii, frattura ed integrità strutturale, 18 (2011) 45-53; doi: 10.3221/igf-esis.18.05 50 austenitic phases as illustrated in fig. 2 at different magnifications. using bragg’s low, the cell parameter evaluated for the two picks is about 3.012 å. figure 7: relation between gross and net engineering strain obtained from fe simulations. figure 8: x-ray spectra of the investigated niti alloy in stress free condition. the evolution of the microstructure during mechanical loading and subsequent unloading was analyzed by xrd investigations carried out at fixed values of applied deformations. in particular, when loading up to the gross engineering strain g=5%, corresponding to the effective engineering strain e=4.5% and to a stress =400 mpa (fig. 7), a different spectra was obtained with respect to the stress-free condition, as illustrated in fig. 9; in fact three new pecks at different angles (42.99, 78.17 and 80.29°) are observed and, as expected, these new pecks reveal the presence of another phase which is obtained on stress plateau of the  curve. in addition, the simultaneous presence of two phases indicate an incomplete transformation, i.e. a partial transformation from austenite to a martensite, characterized by different cell parameter and different lattice. evidence of phase transition is confirmed when increasing the gross deformation to g=10%, corresponding to the effective engineering strain e=7.9% and to a stress of about =800 mpa (fig. 7); this loading condition corresponds to the fully transformed martensitic structure as illustrated in fig. 7. in this case the new phase is completely developed and his spectra is illustrated in fig. 10, where five picks are observed corresponding to a monoclinic phase characterized by three cell parameters of about a=b=3.800 å, c=2.600 å and α=80°. the miller indexes of the three peaks are: 35 45 55 65 75 85 95 c o u n ts  [ u .  a .] 2·θ [°] a  ‐ [0 1 1 ] a  ‐ [0 2 2 ] http://dx.medra.org/10.3221/igf-esis.18.05&auth=true http://www.gruppofrattura.it v. di cocco et alii, frattura ed integrità strutturale, 18 (2011) 45-53; doi: 10.3221/igf-esis.18.05 51  [120] for 43.55°;  [112] for 54.39°;  [030] for 59.90°;  [003] for 78.72°;  [113] for 80.80°. figure 9: x-ray spectra obtained from monotonic loading up to g=5%. figure 10: x-ray spectra obtained from monotonic loading up to g=10%. when unloading from g=10% to g=5% martensite peaks [112] and [030] are not clearly evident, while [011] and [022] austenitic peaks grows which demonstrates the presence of both phases with a greater quantity of martensite as shown in fig. 11. it is worth noting that the x-ray spectra obtained during the monotonic loading stage under the same value of applied deformation is completely different, as shown in fig. 9, where the main phase was the austenite. this is a direct consequence of the marked hysteretic behavior of the material, as shown in fig. 3.b. the final step of the mechanical cycle consists in complete unloading, i.e. the applied load is removed and a final diffraction test was carried out; the corresponding spectra was compared with the initial one, as illustrated in fig. 12, in order to observe possible irreversible effects during loading unloading cycles. the figure shows good agreement between 35 45 55 65 75 85 95 c o u n ts  [ u .  a .] 2·θ [°] a ‐ [0 1 1 ] a ‐ [0 2 2 ] 35 45 55 65 75 85 95 c o u n ts  [ u .  a .] 2·θ [°] m ‐ [1 2 0 ] m ‐ [1 1 2 ] m ‐ [0 3 0 ] m ‐ [0 0 3 ] m ‐ [1 1 3 ] http://dx.medra.org/10.3221/igf-esis.18.05&auth=true http://www.gruppofrattura.it v. di cocco et alii, frattura ed integrità strutturale, 18 (2011) 45-53; doi: 10.3221/igf-esis.18.05 52 the two spectra, which indicates a complete recovery of initial structure. in particular, no residual martensitic structure has been observed confirming a good pseudo-elastic behavior of the alloy. however, a coexistence of the two phases (austenite and martensite) is expected if further increasing the applied deformation, as a consequence of the formation of stabilized martensite, and this mechanisms will be analyzed in future investigations. figure 11: x-ray spectra of obtained from unloading from g=10% to g=5%. figure 12: comparison of the x-ray spectra between initial condition and final stress free condition after unloading. conclusions n this work a pseudo-elastic niti shape memory alloy has been investigated by using a miniaturize testing machine, which allows to analyze the microstructure evolution of the alloy at fixed values of applied load or deformations, by in-situ x-ray analysis. in particular, miniaturized uniaxial specimens were used and the micro-structure evolution at increasing values of applied deformations was analyzed. the results can be summarized as follows:  an initial cubic structure, with cell parameter of about 3.012 å, characterizes the investigated alloy in stress free conditions; 35 45 55 65 75 85 95 c o u n ts  [ u .  a .] 2·θ [°] m ‐ [1 2 0 ] m ‐ [1 1 2 ] m ‐ [0 3 0 ] m ‐ [0 0 3 ] m ‐ [1 1 3 ] a ‐ [0 1 1 ] a ‐ [0 2 2 ] 35 45 55 65 75 85 95 c o u n ts  [ u .  a .] 2·θ [°] a  ‐ [0 1 1 ] a  ‐ [0 2 2 ] initial spectra after unloading i http://dx.medra.org/10.3221/igf-esis.18.05&auth=true http://www.gruppofrattura.it v. di cocco et alii, frattura ed integrità strutturale, 18 (2011) 45-53; doi: 10.3221/igf-esis.18.05 53  when loading up to an applied deformation g=5%, corresponding to about =400 mpa in the stress plateau of the  curve, a new phase, the martensitic one, is observed; as well known the stress plateau is attributed to the transition from initial cubic structure to the new structure;  when increasing the deformation up to g=10%, corresponding to about =800 mpa in the fully martensitic region of the  curve, the new structure is completely developed and the initial structure is not observed. the new structure is characterized by monoclinic cells with three cell parameters of about a=b=3.800 å, c=2.600 å and α=80°;  when unloading from g=10% to g=5% a different microstructure is observed with respect to the loading stage under the same value of applied deformation; this is a direct consequence of the marked hysteretic behavior of the material;  after complete unloading the specimen recovers his initial shape and it shows the same diffraction spectra of the alloy in its initial condition; this indicate that the initial micro-structure is completely recovered without the formation of stabilized martensite. references [1] k. otsuka, x. ren, progress in materials science, (2005) 511. [2] y. liu, g. s. tan, intermetallics, (2000) 8. [3] v. abbasi-chianeh, j. khalil-allafi, materials science and engineering a, 528, (2011), 5060-5065. [4] x yan, j van humbeeck, journal of alloys and compounds, 509, (2011), 1001-1006. [5] c.urbina, s. de la flor, f.ferrando, materials science and engineering a, 501, (2009), 197-206. [6] y. liu, d. favier, acta mater, (2000) 48. [7] k. c. russel, phase transformation, ohio, asm, (1969) 1219. [8] s. miyazaki, m. kimura, h. horikawa, in: advance materials, k. otsuka, y. fukai, editors. 93, v/b, elsevier (1994) 1097. [9] m. pattabi, k. ramakrishna, k.k. mahesh, materials science and engineering a, 448 (2007) 33. [10] a. sato, e. chishima, k. soma, t. mori, acta metall, 30 (1982) 1177. [11] k. otsuka, k. shimizu. scripta metall, 11 (1977) 757. [12] g.v. kurdjumov, l. g.khandros, dokl nauk, sssr, 66 (1949) 211. [13] j. w., christian, the theory of transformations in metals and alloys, oxford: pergamon press, (1965) 815. [14] k. bhattacharya, s. conti, g. zanzotto, j. zimmer. nature, 428 (2004) 55. [15] j. a. krumhansl, g. r. barsch, proceedings of the international conference on martensitic transformations '92, ed. c. m. wayman and j. perkins (monterey institute of advanced studies, carmel, 1993). [16] a. nagasawa, y. morii, mater trans jim, 34 (1993) 855. [17] a. planes, ll. mañosa, solid state phys, 55 (2001) 159. [18] k. otsuka, x. ren, intermetallics, 7 (1999) 511. [19] k. otsuka, x. ren, mater sci eng a, 89 (1999) 273. [20] powdercell 2.3—pulverdiffraktogramme aus einkristalldaten und anpassung experimenteller beugungsaufnahmen. available at http://www.bam.de/de/service/publikationen/powder_cell.htm. http://dx.medra.org/10.3221/igf-esis.18.05&auth=true http://www.gruppofrattura.it microsoft word numero 14 articolo 8 li im ab my ab_ ab is t ter res hav exp wit it i pre ke fo in qua log cha eve all stre th [fig inv stru me i t iquefac mprovem bdoullah n ysore university _namdar@ya bstract. th the largest a rritory, the s search. the d ve been coll periments ca th high level is applicable eviously con eywords. oundation. ntroductio n recent ye liquefactio effective f alities, includ gical and rat aracters as en en after decad experimental ength increm he bandar ab g.1]. this reg vestigation co ucture founda ethodolo he expe geotech stability i t ction ma ment str namdar, a ty, india ahoo.com; sina_ he stability o and most im soil mechani data relating lected and, a an be used f l of structura e for improv nstructed bui standard c on ears, a numbe on due to ear foundations, i ing bad soil tional evalua ncountering an des of hard w l or experien ment of soft so bbas city is p gion should b ome in picture ation in this t ogy and ex eriments wer hnical engine based on su athemat ructures zam khod _a_n@yahoo. of any struct mportant po ical properti g to the desig accordingly, for evaluatio al stability. u ving geotech ildings. code; 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s seismic hazard t with in eng anks, or other atment, are w and essentia inforcement, presently em for supporti nd treated wit an economic, other natural s. authors ma method directl iments, sever of safe beari turale, 14 (2010) h propriately d d occurring been selecte of structure een evaluated f urban area ation of liqu o for reanaly soil mechan d for the iran gineering prac r appropriate widely applied al work both is not very m mployed to as ing soft soil, th prefabricat , this city pla l disaster, for ade an attemp ly in the ba ral data were a ing capacity 0) 75-80; doi: 10 designed. th strong eart d as the sub at different d. the resul a for develo uefaction for ysis of struc nical prope nian region ha ctice all over e methods to d to resist the h for assessm mature and sat sess liquefact it is reporte ed vertical dr aced in horm this purpose pt to achievin andar abbas analyzed to im of any specim 0.3221/igf-esis. he bandar ab thquakes in bject of curr layer of sub ts of laborat opment a reg rce is sugges ture stability rties; struct as appeared [1 the world [3 improve gro e possible fail ment of gro tisfied up to n tion potential ed that the sh rains [9-16]. mozgan prov geotechnical ng best design city of iran mprove struc mens were m .14.08 75 bbas this rent bsoil tory gion sted. y of ture 1-2]. 3-4]. ound lure. ound now l are hear vince l site n of for cture made http://www.gruppofrattura.it http://dx.medra.org/10.3221/igf-esis.14.08&auth=true mailto: ab_namdar@yahoo.com mailto: sina_a_n@yahoo.com a. 76 usi of for als φ, cha liqu re the sho th pro thr me not th she loo but ind sur wit t namdar et alii, ng the terzag 1.5m and wid rmulas for ca 1fq  nfq q sq     so nq, nc and (was used aracteristics, c uefaction forc esults and he band 27° 12' 0 with an e north, and m oor, which is he water table operties, whic rough the ge ethod. the an t excess of 11 he local shear ear failure ma ose. tab.1 ind t based on u dicated that th rface. this w th structure st t frattura ed integ ghi calculatio dth of 2.5m*2 alculation of s .3 ccn d fq d nfq d f     d n are the g from sugge collected data ce to improve d discussio dar abbas is c 0” n with 15 average altitu mt. pooladi, rooted from figure 1: b e was found v ch controllin otechnical si ngle of frictio 1 (kn/m2) an failure gener ay be assume dicated that b unit weight it here is place work draw att tability. egrità strutturale, n method, an 2.5m for foun safe bearing c 0.4 qdn  general bearin stion by the a were interp ement of stru n capital city of 5 meters eleva ude of 9 m (3 16 km (10 m mt. geno an bandar abbas m very high and ng structure s ite investigati on in differen nd the soil uni rally occurs in ed, for φ>36 ased on soil a t could predi of developing tention to the , 14 (2010) 75nd cohesion, a ndation were capacity, sugg bn ng capacity fa e terzaghi c preted and ma ucture stability f hormozgan ation above s 30 ft) above s mi) to the no nd pours into map of iran pl d it was show stability. the ion and the t depth and p it weight (γ) i n loose sand 6°, the genera angle of fricti ict that local g liquefaction e importance -80; doi: 10.3221 angle of fricti assumed for gested by terz actors which calculation m athematical c y at the time n province an ea level in the sea level. the rthwest of th the persian g laced in horm wn to have a e soil angle o safe bearing place in the s s vary from 1 while general al shear failur ion that there l shear failure n in some are e of designing 1/igf-esis.14.08 ion and unit w calculation o zaghi, are pre depend on 1 method) [17] concept of wa of earthquake nd it is located e persian gul e nearest elev he city. the c gulf, 10 km ( ozgan provinc high effect o of friction, co g capacity cal subsoil are be 15.5 to 18.3 (k l shear failure re may be as e is may local e will occur. ea of city with g foundation 8 weight were c f safe bearing esented below 1) depth of fo ], and accor ave theory us e in the band d in longitud lf (fig. 1). th vated areas are closest river t (6 mi) east of ce in close to p on the subsoi ohesion, unit lculated by a etween 29-33 kn/m3) (figs e occurs in de ssumed, in th shear failure the cohesio h presence o n and improv calculated. in g capacity. w: ooting, 2) sha rdingly for a sed for accur dar abbas of i de: 56° 15' 0” his city situate e mt. geno, to bandar ab f the city. persian gulf. il stability and t weight hav adopting terz degree, and s. 2-3 and tab ense sand, wh his investigati or general sh on less subso f undergroun vement metho all models de (1) (2) (3) ape of footing assessing sub ate estimation iran. ” e and latitu ed on flat gro 17 km (11 mi bbas is the r d soil mechan ve been obtai zaghi calcula soil cohesion b. 1). hen φ<28° l on the subso hear failure oc oil of case st nd water near od, it is affec epth g, 3) bsoil n of ude: ound i) to river nical ined ation n (c) local oil is ccur tudy r the ctive http://www.gruppofrattura.it http://dx.medra.org/10.3221/igf-esis.14.08&auth=true specimen no 1 2 3 4 5 6 7 8 table fig f specimen no 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 1: experimen a. namdar et gure 2: angle o figure 3: unit w depth of investigation [m] 2 4 6 10 2 8 2 4 8 12 2 10 7 5 1 1 ts results of so t alii, frattura ed of friction [deg weight [kn/m n φ [°] [kn 31 30 28 30 30 29 1 30 31 31 1 32 32 33 29 30 29 30 oil mechanical p d integrità strutt gree] vs model m3] vs model n c n/m2] γ [kn/ 0 15 0 15 8 16 7 16 0 15 11 16 0 15 0 16 10 15 0 16 0 16 0 16 3 18 6 18 0 17 0 17 properties in b turale, 14 (2010) no. no. γ /m3] s. b. [kn/m .5 338.5 .7 295.4 .5 368.3 .8 428.9 .5 291.6 .9 455.9 .8 297.3 6 349.4 .5 516.4 6 397.8 6 397.8 .2 451.8 8 354.2 .3 441.0 7 291.8 7 319.8 bandar abbas o 0) 75-80; doi: 10 c m2] m.s.l [kn] 55 2115.9 42 1846.3 32 2301.9 96 2681.0 66 1822.8 96 2849.74 30 1858.1 47 2184.1 43 3227.6 87 2486.6 87 2486.6 85 2824.0 27 2214.2 07 2756.6 89 1824.3 88 1999.2 of iran. 0.3221/igf-esis. l 1 9 8 0 6 4 5 7 8 7 7 3 1 6 1 7 .14.08 77 http://www.gruppofrattura.it http://dx.medra.org/10.3221/igf-esis.14.08&auth=true a. 78 it c dep red stru cau on ear ma a c th afte cod res int act des mo sui goo and abb dat bet th ear geo cod to sho th wh f ρ d cd cm to vel pre wh p(f μ ( th namdar et alii, can be expla pth) could cr duction of th ucture, but in used mistake soil mechan rthquake shou apping macro ase-by-case b he structure s er the seismi de for this pa earch projec ternational ci tivity give bet sign. it should ost of structu table code fo od representa d developing bas can be co ta to develop tween soil mi here is no geo rthquake, seis ology and str de, in this reg geological ch ould be emplo here is a meth 0.f  here = force = dens = diam = drag m = inert better under locity and th esented for ob  p f  here f) = force f) = extre here is present velocity frattura ed integ ained that the reated of mo he bearing ca n practical dur in structure s nical propertie uld did not c seismic for ac basis. hall be desig ic events. for articular territ ct conducted ivil engineeri tter and upda d be noted th ures in this r or protecting ation of accel g site stress s onsidered in conventiona neralogy and otechnical ch smic waves w ructures posit gard different haracteristics oyee for analy od of calculat .5 ddc u u e sity of fluid meter of pile g coefficient tia coefficient rstanding of s e second is btaining that     0 f f df     e maxima eme force rat ted wave spec y spectrum s egrità strutturale, e amplificatio ore affect on apacity. ther ring site geot seismic design es through th ause any sign ccurate struct gned to withs r the damage tory not one d by local u ing society as ate knowledg hat, for new c region are un life and mitig lerations, vel train guide m high consequ al (empirical) propagate se haracteristic si with several ch tion, it is imp t theories cou of subsoil d ysis of liquefa ting wave for 0.25u d t seismic force acceleration, [19-21]. f te density ctrum, in term   4us f  , 14 (2010) 75on of the ear n structure s re is strong e technical anal n. it may be he shaking ta nificant dama ture design fo stand without e limitation it code for the niversity and s well as the g ge to civil eng ode compreh nprepared fo gation of dam ocities and d map instant o uence events. attenuation s eismic force a imilarity in th haracteristics portant to ac uld be accepti during the ea action force in rces on piles [ 2 m du d c dt on structure and also th ms of velocity 22 2 cosh kf sinh -80; doi: 10.3221 rthquake mot stability and earthquake co lysis, poisson suggested th able for simu ages to buildin or earthquake t collapse and t is required whole of the d local civil government a gineering com hensive inform or earthquake mage from an displacements of only produ . this territor seismic mode and its affect o he whole of could be dev ccurate analys ing for develo arthquake, liq n presence of [18], foundation t e force maxi y, acceleration    2 d k z d s h k   1/igf-esis.14.08 tion through appearing of ode [iran 28 ratio and mo at obtain of p ulation seismi ngs and struc e resistance, a d maintain ac to provide s e country, the engineering authority at m mmunity and mation on soi es and also th earthquake e for sites to ucing of eart ry has not ca ls in data coll on the structu the country, veloped and it sis of site ge oping seismic quefaction occ f seismic forc the force requ ima p(f) is m n and force fo  f 8 h soft subsoil f differential 800 code] fo odulus elastic poisson ratio ic force may ctures in the and it should cceptable soi structure and e local code m society and ministerial leve lead to enha il dynamic pr here is impo event. a new better assessi thquake risk aptured suffic lection it is al ure stability. and it could t is affected t ological char c wave. it is im cur and in th ce. uired to be in more difficul or analysis of l in bandarab settlement a or seismic res city have been o and modulu be applied o region. there determine fo il foundation geotechnical may be result d it should b el, it is clear th ancement of roperties is es ortant to con w code has to ing geomorp map. earthq cient near-fiel lso needed to be conclude to the structu racteristics be mportant to m his investigat nvestigated in lt to calculat f wave charact bbas (up to 1 and consider sistant design n assumed, th us elasticity ba on structure. e is no appro r each projec bearing capa l suitable seis of the long t be approved hat such resea structure seis sential step. nsider develop develop for v hology of reg quakes in ban ld strong mo o find correla ed that during ures based on efore establish mention that tion wave the (4) n two parts on te but a form (5) teristics [22]. (6) 12m rably n of his is ased the oved ct on acity smic term d by arch smic ping very gion ndar otion ation g an n site hing due eory ne is mula http://www.gruppofrattura.it http://dx.medra.org/10.3221/igf-esis.14.08&auth=true wh f k z d s dk uq ik all at t of for the on pro con co      re [1] [2] [3] [4] [5] [6] [7] [8] accelle force s here = sectio = num = half = dept  f = wave d = 0.5 ρ u = horiz i =      l formula are the time of an wave force c rce in liquefie e region. base the length, operties lique nsidering wav onclusion the result improveme for analysi dynamic pro the local co engineering in foundati with earthq the site geo liquefied su eferences a. shafiee, a g. g. amir j. p. bardet, a. king ste r. o. davis d. sam liya john m. fer felix y. yok ration spectr spectrum fs onal force on mber of wave length of wav th of liquid e spectrum d cd zontal velocit 2 4 m d c     presented ab n earthquake created by liq d subsoil cou ed on data pre depth, numb efaction magn ve characteris n revealed that nt of structur s of soil me operties. ode may be d g society and i on seismic d uake force. ological struc ubsoil. s a. azadi, jou ri, r. motame , m. kapuska ephanie, s. ki s, j. b. berrill, anapathirana, rritto, journa kel, r. dobry rum  as f    28 df k  n pile ve ty bove could be . in structure quid soil and uld be calcula esented in ta ber and spec nitude fluctua tics in liquefi t there is nee re have been chanical stab developed thr it should be a design it is req cture will affe urnal of asian ed, r. hashem ar, journal of iremidjian an , geotechniqu , h.g. poulos al of the tech y, david j. po a. namdar et 4 41 6 co f  2 2 u uq s f  e applied for u e stability not applied on ted using eqs ab. 1 and usin ctrum of wav ate. this inve ied subsoil. ed of establi constructed p bility need of rough the lon approved by i quire analysis ect on the len n earth scien mi, h. r. nou geotechnica nne, h. law k ue, 48(2) (199 s, soil dynam hnical council owell, richard t alii, frattura ed    2 2 d osh k z d sinh k   2 i ak s f understanding t only earthqu structure fou s 4-8. tab.1 a ng eqs. 4-8, c ve in the liq estigation can ishing better previously wi f accurate ma ng term resea international s of wave for ngth, depth, n ces, 29 (2007 uri, in: ice, g al engineering kincho, in: c 98) 289. mics and earth ls of asce: p d s. ladd, mi d integrità strutt    d s f g liquefaction uake force sh undation. the and figs. 2-3 could finalize quefied subso n be leads to geotechnical ithout conside athematical m arch project c civil engine rces created b number, spec )105. geotechnical g, 119(3) (199 conference on hquake engin proceedings o icrostructural turale, 14 (2010) n force is subj ould be calcu e force maxim indicated the that the site g oil, and due o develop a h l code as wel ering geotech modeling for conducted by ering society by liquid soil trum, velocit engineering, 93) 543. n natural dis neering, 24(1 of the asce, science, 2 (1 0) 75-80; doi: 10 jected to stru ulated it is ess ma, velocity, e soil mechan geological str to changing hypothesis fo ll as seismic hnical site inv better unde y local univer . l based on w ty and acceler , 159 (2006) 2 saster reducti 1) (2004) 867 103(1) (1977 980) 571. 0.3221/igf-esis. (7) (8) ucture founda sential to ana acceleration nical propertie ructure will af g soil mechan or mathematic map zoning vestigation. rstanding of rsity or local wave theory al ration of wav 275. ion, (1996) 12 7. 7) 65. .14.08 79 ation alysis and es of ffect nical cally g for soil civil long ve in 23. http://www.gruppofrattura.it http://dx.medra.org/10.3221/igf-esis.14.08&auth=true a. 80 [9] [10 [11 [12 [13 [14 [15 [16 [17 [18 [19 [20 [21 [22 no φ c [ om s.b γ [k μ es f m.s f ρ d cd cm p(f μ ( f k z d s dk uq ik namdar et alii, r. peck, b. 0] g. w. clou ithaca new ] o.u. chang 2] p. t. brown 3] h.-w. ying 4] r.-l. wei, c 5] j.-l. yu, x6] y. guanbao 7] b. c. punm 8] j. r. moriso 9] c. c. tung, 0] v. j. cardon ] r. g. ticke 2] l. e. borgm omenclatu [°] [kn/m2] mc % b.c [kn/m2] kn/m3] s.l m f) f)  f d u i frattura ed integ deep, in: 7th ugh, t. d. o’ w york, (1990) g-yu, lai chan n, computers g, x.-y. xie, k chinese journ -n. gong, ch o, g. yongfa, mia, soil mech on et al., petro j. eng. mech ne et al., j. pe ll, the struct man, in: offsh ure = f = s = o = s = u = p = m = s = m = f = d = d = d = i = f = e = s = n = h = d = w = 0 = h =  egrità strutturale, icsmkfe. rourke, in: d ) 439. ng-her, can. s and geotech k.-h. xie, jou nal of geotec hina civil eng , ejge, 15a hanics and fo ol. trans, aim h. div., asce etrol. tech., 2 tural enginee hore tech. c friction angle soil cohesion optimum mo safe bearing c unit weight poisson ratio modulus elas soil safety fa max safe loa force density of flu diameter of p drag coefficie inertia coeffic force maxima extreme force sectional forc number of w half length of depth of liqu wave spectru 0.5 ρ d cd horizontal ve 2 4 m d c         , 14 (2010) 75state-of-the-a design and p geotech. j., 3 h, 1(3) (1995) urnal of build chnical engin gineering jou (2010). undations, m me, 189 (195 e, 100 (1974) 28 (1976) 385 r, 55 (1977) 2 conf., housto e n oisture conten capacity sticity [kn/m ctor ad [kn] uid pile ent cient a e rate density ce on pile wave f wave uid m elocity m -80; doi: 10.3221 art-volume, performance o 31 (1994) 204 ) 8. ding structure neering, 19(6) rnal, 35(4) (2 madras (1988). 50) 149. ) 873. . 209. n, (1969) 721 nt % m2] y 1/igf-esis.14.08 mexico city, of earth reta 4. es, 20(4) (199 (1997) 88. 002) 86. . 1. 8 , (1969) 225. aining structu 99) 59. ure. asce sp pecial confere ence http://www.gruppofrattura.it http://dx.medra.org/10.3221/igf-esis.14.08&auth=true << /ascii85encodepages false /allowtransparency false /autopositionepsfiles true /autorotatepages /none /binding /left /calgrayprofile (dot gain 20%) /calrgbprofile (srgb iec61966-2.1) /calcmykprofile (u.s. web coated \050swop\051 v2) /srgbprofile (srgb iec61966-2.1) /cannotembedfontpolicy /error /compatibilitylevel 1.4 /compressobjects /tags /compresspages true /convertimagestoindexed true /passthroughjpegimages true /createjobticket false /defaultrenderingintent /default /detectblends true /detectcurves 0.0000 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/hrv (za stvaranje adobe pdf dokumenata najpogodnijih za visokokvalitetni ispis prije tiskanja koristite ove postavke. stvoreni pdf dokumenti mogu se otvoriti acrobat i adobe reader 5.0 i kasnijim verzijama.) /hun 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/pdfxoutputintentprofileselector /documentcmyk /preserveediting true /untaggedcmykhandling /leaveuntagged /untaggedrgbhandling /usedocumentprofile /usedocumentbleed false >> ] >> setdistillerparams << /hwresolution [2400 2400] /pagesize [612.000 792.000] >> setpagedevice microsoft word numero_41_art_12.docx f. berto et alii, frattura ed integrità strutturale, 41 (2017) 79-89; doi: 10.3221/igf-esis.41.12 79 focused on multiaxial fatigue multiaxial fatigue strength of titanium alloys filippo berto university of padova, department of management and engineering, vicenza, italy ntnu, department of mechanical and industrial engineering, trondheim, norway berto@gest.unipd.it alberto campagnolo university of padova, department of industrial engineering, padova, italy alberto.campagnolo@unipd.it torgeir welo ntnu, department of mechanical and industrial engineering, trondheim, norway torgeir.welo@ntnu.no sabrina vantadori, andrea carpinteri university of parma, dept. of civil-environmental engineering and architecture, parma, italy abstract. the present paper investigates the multiaxial fatigue strength of sharp v-notched components made of titanium grade 5 alloy (ti-6al-4v). axisymmetric notched specimens have been tested under combined tension and torsion fatigue loadings, both proportional and non-proportional, taking into account different nominal load ratios (r = -1 and 0). all tested samples have a notch root radius about equal to 0.1 mm, a notch depth of 6 mm and an opening angle of 90 degrees. the fatigue results obtained by applying multiaxial loadings are discussed together with those related to pure tension and pure torsion experimental fatigue tests, carried out on both smooth and notched specimens at load ratios r ranging between -3 and 0.5. altogether, more than 250 fatigue results (19 s-n curves) are examined, first on the basis of nominal stress amplitudes referred to the net area and secondly by means of the strain energy density averaged over a control volume embracing the v-notch tip. the effect of the loading mode on the control volume size has been analysed, highlighting a wide difference in the notch sensitivity of the considered material under tension and torsion loadings. accordingly, the control radius of the considered titanium alloy (ti-6al-4v) is found to be strongly affected by the loading mode. keywords. ti-6al-4v; multiaxial fatigue; v-notch; control volume; strain energy density. citation: berto, f., campagnolo, a., welo, t., vantadori, s., carpinteri, a., multiaxial fatigue strength of titanium alloys, frattura ed integrità strutturale, 41 (2017) 79-89. received: 28.02.2017 accepted: 15.04.2017 published: 01.07.2017 copyright: © 2017 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. f. berto et alii, frattura ed integrità strutturale, 41 (2017) 79-89; doi: 10.3221/igf-esis.41.12 80 introduction or a wide comparison between different approaches adopted to the multiaxial fatigue strength assessment of metallic materials, the reader is referred to a recent review [1] and a report [2], which are based on a large bulk of experimental data obtained from notched specimens. a fundamental role is occupied by critical plane approaches [3,4] and by some important variants [5-7]. in this context, approaches based on energy calculations find significant applications [8]. a multiaxial fatigue approach based on a frequency-domain formulation of a stress invariant, the so-called “projection by projection” (pbp) criterion has been reported in the recent literature [9]. the critical plane-based carpinteri-spagnoli approach has recently been extended to a frequency-domain formulation [10]. an energy-based parameter has been adopted to assess the fatigue strength under uniaxial fatigue loadings first by jasper [11] in 1923. then, ellyin suggested a criterion based on the combination of plastic and elastic strain energy [12-13], to deal with multiaxial fatigue loadings. a wide review of energybased criteria for multiaxial fatigue strength assessment has been reported in [14]. moreover, the problems relevant to multiaxial fatigue have been investigated both theoretically and experimentally by several researchers [15-22]. this contribution is aimed to analyse the fatigue strength of severely notched titanium grade 5 alloy under multiaxial loadings. the considered titanium alloy (ti-6al-4v) is widely employed in advanced military, civil aerospace and naval applications. the in-service conditions of titanium structural components are usually characterized by a complex stress state coupled with an aggressive environment. the titanium grade 5 alloy has high static and fatigue properties, a very good strength-to-mass ratio and an excellent wear resistance. the uniaxial fatigue strength of un-notched and notched titanium components has been extensively analysed in the literature. however, a complete set of experimental data relevant to sharp v-notched specimens made of ti-6al-4v and subjected to torsion and combined tension and torsion loadings, both proportional and non-proportional, is not available in the literature. to fill this lack, a complete set of experimental data from sharp v-notched components made of titanium grade 5 alloy (ti-6al-4v) under multiaxial fatigue loading is provided here. experimental fatigue tests under combined tension and torsion loadings have been carried out on circumferentially vnotched specimens, with two nominal load ratios, namely r = -1 and r = 0. the fatigue results obtained by applying multiaxial loadings are compared with those related to pure tension and pure torsion experimental fatigue tests, carried out on both smooth and notched specimens at load ratios r ranging between -3 and 0.5. all in all, more than 250 fatigue data (19 wöhler curves) are examined in terms of nominal stress amplitudes referred to the net area. then, the experimental fatigue strength data have been reanalysed in terms of the strain energy density (sed) averaged over a control volume embracing the notch tip [23-31]. the effect of the loading mode on the control volume size has been analysed, highlighting the need to use a different control radius under tension and torsion loading, due to a wide difference in the notch sensitivity of the considered material under tension and torsion loadings. the expressions for calculating the control radii, thought of as material properties, have been derived by imposing the constancy of the averaged sed relevant to un-notched and notched specimens, which depend on the critical notch stress intensity factors (nsifs) and the control radius, in correspondence of 2·106 cycles. the unifying capacity of the averaged sed criterion is highlighted, indeed the synthesis on the basis of the local sed enables to obtain a quite narrow scatter-band, which is characterised by an equivalent stress-based scatter index t equal to 1.58, taking into account all fatigue strength data relevant to notched and un-notched components subjected to pure tension, pure torsion and multiaxial loadings, independently of the nominal load ratio and the phase angle. some of the results reported in the present manuscript have been previously presented and extensively discussed in [31]. material and geometry of the specimens he material taken into consideration in the present contribution is a titanium grade 5 alloy, also known as ti-6al4v. the geometries of smooth and sharply notched specimens are reported in fig. 1, along with some details of the v-notch tip. the hourglass smooth specimens, shown in fig. 1a, are characterized by a 12-mm-diameter of the net transverse area and by a wide connecting radius between the net and gross sections,  = 100 mm, so that any stress concentration is avoided. the cylindrically v-notched samples, shown in fig. 1b, are characterized, instead, by a notch depth d equal to 6 mm and a notch angle of 90 degrees, while the notch tip radius, , is about equal to 0.1 mm. in particular, the notch root radius has been experimentally measured through an optical microscope and the dedicated software las (leica application suite) f t f. berto et alii, frattura ed integrità strutturale, 41 (2017) 79-89; doi: 10.3221/igf-esis.41.12 81 and a mean value of 0.09 mm with a very reduced scatter has been obtained. the precision ensured by the adopted method is about ± 5% of the measured quantity. the typical v-notch profile characterised by two rectilinear flanks tangent to the notch tip radius is reported in fig. 1b, for an example of the tested samples. to remove any scratches or processing marks on the surface, all specimens were polished before the fatigue test. (a) (b) figure 1: (a) geometries of smooth and sharply notched specimens and (b) examples of tested specimens. experimental results from fatigue tests he experimental fatigue tests have been carried out by means of a mts 809 servo-hydraulic bi-axial testing device (± 100 kn, ± 1100 nm, ± 75mm/± 55°) under load control conditions. in particular, a mts load cell with ± 0.5 % error at full scale has been employed to evaluate the nominally applied loads. a test frequency between 10 and 15 hz has been adopted as a function of the applied load level. all in all, 19 different fatigue test series are performed, according to the parameters reported below:  four series of fatigue tests on smooth and sharply notched samples subjected to pure tension and pure torsion fatigue loadings, with a nominal load ratio r = -1;  four series of fatigue tests on smooth and sharply notched samples subjected to pure torsion fatigue loading, with nominal load ratios r = 0 and 0.5;  three series of fatigue tests on smooth samples subjected to pure torsion fatigue loading, with nominal load ratios r = 0.25, -2 and -3;  four series of fatigue tests on sharply notched samples subjected to combined tension and torsion loadings, at a constant biaxiality ratio λ = 0.6. two load ratios, r = 0 and r = -1 (referred separately to the normal and shear stress components), and two phase angles, ф = 0° (proportional loadings) and ф = 90° (non-proportional loadings), are employed;  four series of fatigue tests on sharply notched samples subjected to combined tension and torsion loading, at a constant biaxiality ratio λ = 2.0. also in this case, two load ratios, r = 0 and r = -1, and two phase angles, ф = 0° (proportional loadings) and ф = 90° (non-proportional loadings), are adopted.  d = 6 mm = 0.1 mm 24 90° = 100 mm 24 150 mm t f. berto et alii, frattura ed integrità strutturale, 41 (2017) 79-89; doi: 10.3221/igf-esis.41.12 82 the statistical re-analyses of the fatigue strength data were carried out by assuming a log-normal distribution. all experimental data relevant to specimens with a fatigue life in the range 104 ÷ 2·106 cycles have been considered, while the run-outs have been excluded. in particular, tab. 1 reports the nominal stress amplitudes for a probability of survival ps = 50% and a number of cycles na = 2·106, the inverse slope k of the wöhler curves and the scatter-index t, which gives a measure of the width of the scatter band, between the curves with 10% and 90% probabilities of survival (with a confidence level equal to 95%). under multiaxial loading, the fatigue life results to be reduce if compared to the uniaxial loading case, with reference to the same normal stress amplitude, however the reduction is quite limited for the biaxiality ratios considered herein ( = 0.6 and 2.0). stronger is the multiaxial fatigue strength reduction tied to the effect of the load ratio r. on the other hand, the phase angle effect is weak for r = -1, being the mean values of the normal stress amplitudes about the same at 2·106 cycles. while, it is higher for r = 0, being the out-of-phase loading slightly beneficial with respect to in-phase loading at high-cycle fatigue regime, whereas the fatigue strength is almost the same at low-cycle regime. the sensitivity of the considered titanium alloy to the phase angle effect results to be quite limited, being lower than +15 percent for the r = 0 case and negligible for the r = -1 case. the fracture surfaces relevant to the specimens subjected to multiaxial loadings were examined. the phase angle seems to affect the fracture surface morphology. indeed, some signs of micro abrasions could be seen on all fracture surfaces and the extent to which the rubbing occurred depends on phase angle. in general, a limited but distinguishable quantity of debris and powder has been emanated from the notch tip, when a visible fatigue crack started to propagate. synthesis based on the averaged strain energy density ith regard to un-notched specimens, all fatigue results have been summarised here in terms of the averaged sed, which can be expressed, under linear elastic conditions, by means of beltrami’s expression. accordingly, in the case of pure tension loading, the local strain energy density is given by:    2 2 nomw e (1) while in the case of pure torsion loading it is given by:         2 1 nomw e (2) in previous expressions, nom and nom are the nominal stress ranges tied to tension and torsion loadings, respectively. for the considered titanium alloy, the young’s modulus e results to be 110 gpa, while the poisson’s ratio ν is 0.3. then, also the fatigue strength results relevant to notched samples have been reanalysed here in terms of the averaged sed, however, in this case the strain energy calculation is based on the local stress and strain state in a control volume embracing the v-notch tip. since the notch root radius is reduced ( less than 0.1 mm), the mode i and mode iii nsifs, k1 and k3, can be adopted to summarised the experimental data relevant to notched samples in terms of the local strain energy density. these parameters, which describe the local stress fields, have been evaluated from linear elastic fe analyses taking into consideration a sharp v-notch with tip radius equal to 0 (see fig. 2). let us consider a cylindrical coordinate system (r, θ, z) with origin at the notch tip, where r is the radial coordinate,  is the angle between a generic point and the notch bisector line, while z is the longitudinal axis of the specimen. in particular, with reference to this coordinate system (see fig. 2), the mode 1 and mode 3 nsifs can be defined by means of the following expressions:        1 11 0 2 lim ( , 0) r k r r (3)        1 33 0 2 lim ( , 0)zr k r r (4) w f. berto et alii, frattura ed integrità strutturale, 41 (2017) 79-89; doi: 10.3221/igf-esis.41.12 83 table 1: experimental results from fatigue tests. mean values, ps = 50%. stresses referred to the net area. series type of load number of specimens k tσ tτ σa or τa 2 · 106 1 tension r = -1 12 σ 9.25 1.120 475.74 2 torsion r = -1 16 τ 22.13 1.205 388.25 3 torsion r = 0 9 τ 15.03 1.322 287.22 4 tension r = -1, v-notch 2α = 90° 15 σ 6.26 1.133 100.89 5 torsion r = -1, v-notch 2α = 90° 9 τ 14.59 1.229 289.31 6 torsion r = 0, v-notch 2α = 90° 11 τ 13.82 1.159 247.16 7 torsion r = 0.5, v-notch 2α = 90° 7 τ 19.91 1.080 169.89 8 multiaxial r = -1, ф = 0°, λ= 0.6, v-notch 2α = 90° 13 σ 6.82 1.197 93.89 τ 56.39 9 multiaxial r = -1, ф = 90°, λ = 0.6, v-notch 2α = 90° 10 σ 7.84 1.124 96.11 τ 57.67 10 multiaxial r = 0, ф = 0°, λ = 0.6, v-notch 2α = 90° 12 σ 8.09 1.159 67.74 τ 40.64 11 multiaxial r = 0, ф = 90°, λ = 0.6, v-notch 2α = 90° 12 σ 10.43 1.158 79.65 τ 47.79 12 torsion r = 0.5 12 τ 21.19 1.134 180.73 13 torsion r = 0.25 8 τ 25.67 1.078 268.12 14 torsion r = -3 7 τ 16.25 1.178 357.55 15 torsion r = -2 8 τ 21.32 1.042 409.01 16 multiaxial r = -1, ф = 0°, λ = 2, v-notch 2α = 90° 26 σ τ 7.61 1.118 75.94 37.97 17 multiaxial r = -1, ф = 90°, λ = 2, v-notch 2α = 90° 22 σ τ 7.59 1.114 84.70 42.35 18 multiaxial r = 0, ф = 0°, λ = 2, v-notch 2α = 90° 21 σ τ 8.01 1.125 59.75 29.88 19 multiaxial r = 0, ф = 90°, λ = 2, v-notch 2α = 90° 21 σ τ 9.40 1.089 65.97 32.99 f. berto et alii, frattura ed integrità strutturale, 41 (2017) 79-89; doi: 10.3221/igf-esis.41.12 84 figure 2: polar coordinate system for v-shaped notches, with z normal to the plane; mode i nsif linked to the stress component  evaluated along the notch bisector line (=0); under mode iii the shear stress component z is oriented as . considering an opening angle of 90 degrees, the eigenvalues 1 and 3 result to be 0.545 and 0.667, respectively. moreover, under linear elastic conditions, the nsifs can be linked to the nominal stress components as follow:    1 11 1 nomk k d (5a)    1 33 3 nomk k d (5b) in previous expressions, d represents the notch depth (d = 6.0 mm), while k1 and k3 are the non-dimensional factors obtained by means of proper fe analyses. they represent the shape factors, similarly to the expressions of stress intensity factors in linear elastic fracture mechanics. the quadrilateral eight-node harmonic element plane 83 of the ansys element library has been adopted in the fe analyses. taking advantage of the symmetry conditions, only one quarter of the sample geometry has been modelled. according to the fe analyses carried out, k1 is equal to 1.000, while k3 equals 1.154. the trend of the mode iii stress field, normalized with respect to the nominally applied shear stress and evaluated on the notch bisector line, is reported in fig. 3 as a function of the distance from the notch tip. it can be observed that the stress field is controlled by the first singular term (nsif) up to a distance from the notch tip about equal to 1.0 mm. taking into account the notch depth of the tested samples, namely d = 6 mm, in previous eqs (5a) and (5b), the following simple expressions can be obtained:   1 2.260 nomk (in mpa ·mm0.445) (6a)   3 2.096 nomk (in mpa ·mm0.333) (6b) by substituting into eqs. (6a) and (6b) the ranges of the nominal stresses at na = 2·106 cycles relevant to notched samples subjected to pure tension and pure torsion loadings at a nominal load ratio r = -1 (see tab. 1), one can obtain:      0.4451 2.260 200 452ak mpa mm (7a)      0.3333 2.096 580 1216ak mpa mm (7b) dealing with a sharp v-notched component subjected to combined tension and torsion loadings under linear elastic conditions, the strain energy density averaged over a control volume surrounding the notch tip can be evaluated from the f. berto et alii, frattura ed integrità strutturale, 41 (2017) 79-89; doi: 10.3221/igf-esis.41.12 85 following closed-form expression:                  22 31 1 32 1 2 11 3 1 3 1 kk w e e e r r (8) figure 3: local shear stress field along the notch bisector line (mode iii loading). in previous expression, k1 and k3 are the mode i and mode iii nsif ranges, respectively, r1 and r3 represent the control volume sizes related to mode i and mode iii loadings, respectively, while e1 and e3 are known coefficients which take into account the local notch geometry. these parameters are tied to the integrals over the control volume of the angular stress functions and they can be evaluated a-priori by means of closed-form expressions, as a function of the notch opening angle. being the tested samples characterized by an opening angle 2 of 90 degrees, e1 and e3 result to be 0.146 and 0.310, respectively, with reference to a poisson’s ratio  = 0.3. very refined fe meshes must be adopted in the close vicinity of the singularity point to evaluate the nsifs on the basis of definitions (3) and (4). on the other hand, the local sed results to be insensitive to the mesh refinement. indeed, it can be accurately calculated also from fe analyses with coarse meshes, since it directly depends on nodal displacements. the most important and useful advantages tied to the use of the averaged strain energy density parameter are analysed and discussed in detail in ref. [30]. the expressions for calculating the control radii, thought of as material properties, have been derived by imposing the constancy of the averaged sed relevant to un-notched and notched specimens, which depend on the critical notch stress intensity factors (nsifs) and the control radius, in correspondence of 2·106 cycles. by taking into consideration, instead, cracked samples, the critical nsifs should be substituted by the threshold values of the stress intensity factors. by considering the mode i and mode iii loading conditions as independent, the control radii r1 and r3 (as shown in fig. 4) can be estimated. in particular, they result to be dependent on the high-cycle fatigue strengths of un-notched specimens, 1a = 950 mpa and3a = 776 mpa, and on the mean values of the nsifs, k1a andk3a, with reference to a given number of cycles, na = 2·106:          1 1 11 1 1 1 2 a a k r e (9a)            1 1 33 3 3 31 a a e k r (9b) 0,1 1 10 100 0,001 0,010 0,100 1,000   z/  n om distance from the notch tip, [mm] f. berto et alii, frattura ed integrità strutturale, 41 (2017) 79-89; doi: 10.3221/igf-esis.41.12 86 r1 2  r3 figure 4: control volumes for v-shaped notches under tension and torsion loadings. on the basis of eqs. (9a) and (9b), the control radii result to be r1 = 0.051 mm and r3 = 0.837 mm, respectively. accordingly, the control radius r1 has been adopted to compute the averaged strain energy contribution tied to tension loading, whereas the control radius r3 has been employed to evaluate the averaged sed contribution due to torsion loading. it should be noted that the control radius r3 is highly affected by the presence of larger plasticity under torsion loading as compared to tension loading, and by friction and rubbing between the crack surfaces, as previously discussed also for different materials [23,30]. under these conditions, the averaged sed is called also ‘apparent linear elastic sed’ to highlight that the strain energy density calculation over two different control volumes (under tension and torsion, respectively, as determined from experimental data) allows us to overcome the problem tied to shielding mechanisms, keeping a linear elastic criterion. to summarise in the same scatter band experimental results obtained by adopting different nominal load ratios r, a coefficient cw, defined on the basis of simple algebraic considerations (reported in detail in ref. [24, 31]), must be introduced. the coefficient cw results to be dependent on the nominal load ratio r according to the following expression:                     2 2 2 2 1 0 1 1 0 1 0 1 1 w r for r r c for r r for r r (10) the parameter cw equals 1.0 in the case r = 0, while it results equal to 0.5 for r = -1. by adopting the coefficient cw, the closed-form expressions to evaluate the averaged sed, related to smooth samples (eqs. (1, 2)) and to components weakened by sharp notches (eq. (8)), become as follow:                                     2 2 22 31 1 32 1 2 11 3 1 3 2 1 nom w nom w w c un notched specimens pure tension e sed c un notched specimens pure torsion e c kk e e v notched specimens multiaxial loading e r r (11) f. berto et alii, frattura ed integrità strutturale, 41 (2017) 79-89; doi: 10.3221/igf-esis.41.12 87 fig. 5 reports the synthesis of all experimental fatigue results analysed in the present contribution by means of the averaged sed. the control radius r1 = 0.051 mm has been adopted to evaluate the sed contribution due to tension loading, while the control radius r3 = 0.837 mm has been employed for the sed contribution due to torsion loading. all fatigue strength results relevant to smooth and notched samples under pure tension, pure torsion and multiaxial loading conditions are included in the obtained scatter band, independently of the nominal load ratio and of the phase angle. the design scatter band is characterized by an inverse slope k of 5.90, by an energy-based scatter index tw = 2.50 and by a sed value at na = 2·106 cycles equal to 3.08 mj/m3. however, the equivalent stress-based scatter index, that is t = (tw)0.5, equals 1.58, which is very similar to that of the haibach scatter band (t= 1.50). figure 5: local sed-based synthesis of experimental fatigue results relevant to smooth and sharply notched specimens. almost 250 fatigue data are summarised in the scatter band. conclusions large bulk of experimental fatigue results relevant to axisymmetric notched samples subjected to multiaxial loadings, both proportional and non-proportional, have been re-analysed and compared with the fatigue strength data relevant to smooth and notched samples subjected to pure tension and pure torsion loadings. all specimens were made of titanium grade 5 alloy (ti-6al-4v). altogether, more than 250 fatigue results, corresponding to 19 s-n curves, have been analysed in this contribution. first, the experimental results obtained from uniaxial and multiaxial fatigue tests have been examined on the basis of nominal stress amplitudes. then, they have been re-analysed by means of the linear elastic strain energy density (sed) averaged over a control volume surrounding the notch root. the effect of the loading mode on the control volume size has been analysed in detail, showing that different control radii must be adopted under tension and torsion loading conditions, dealing with notched components made of ti-6al-4v titanium alloy. the averaged sed-based synthesis enables to obtain a quite narrow scatter band, characterized by an energy-based scatter index of 2.50. in particular, the fatigue design scatter band was derived by taking into account all experimental results 0.2 2 20 1.0e+04 1.0e+05 1.0e+06 1.0e+07 s tr ai n e n er g y de n si ty r an g e,  w , [m j/ m 3 ] number of cycles to failure, n tension, r=-1 tension, r=-1 torsion, -3 ≤ r ≤ 0.5 torsion, -1 ≤ r ≤ 0.5 multiaxial, r=-1, in-phase multiaxial, r=-1, in-phase multiaxial, r=0, in-phase multiaxial, r=-1, out-of-phase multiaxial, r=-1, out-of-phase multiaxial, r=0, in-phase multiaxial, r=0, out-of-phase multiaxial, r=0, out-of-phase un-notched specimens k=5.90 sed range (2x106, p.s. 50%)= 3.08 mj/m3 tw=2.5 ti6al4v 251 data r1 = 0.051 mm r3 = 0.837 mm v-notched specimens v-notched specimens  = 0.6  = 2.0 a f. berto et alii, frattura ed integrità strutturale, 41 (2017) 79-89; doi: 10.3221/igf-esis.41.12 88 relevant to smooth and notched samples under pure tension, pure torsion and multiaxial loading conditions, regardless the nominal load ratio and the phase angle. references [1] fatemi, a., shamsaei, n., multiaxial fatigue: an overview and some approximation models for life estimation, int. j. fatigue, 33 (2011) 948-958. [2] nieslony, a., sonsino, c.m., comparison of some selected multiaxial fatigue assessment criteria, l.b.f. report, no. fb-234 (2008). [3] fatemi, a., socie, d.f., a critical plane approach to multiaxial fatigue damage including out-of-phase loading, fatigue fract. eng. mater. struct., 11 (1988) 149-165. [4] fatemi, a., kurath, p. p., multiaxial fatigue life prediction under the influence of mean stresses, asme j. eng. mater. techn., 110 (1988) 380-388. [5] łagoda, t., macha, e., bedkowski, w., a critical plane approach based on energy concepts: application to biaxial random tension-compression high-cycle fatigue regime, int. j. fatigue, 21 (1999) 431-443. [6] carpinteri, a., spagnoli, a., multiaxial high-cycle fatigue criterion for hard metals, int. j. fatigue, 23 (2001) 135-145. [7] carpinteri, a., spagnoli, a., vantadori, s., bagni, c., structural integrity assessment of metallic components under multiaxial fatigue: the c-s criterion and its evolution, fatigue fract. eng. mater., 36 (2013) 870-883. [8] ye, d., hertel, o., vormwald, m., a unified expression of elastic–plastic notch stress–strain calculation in bodies subjected to multiaxial cyclic loading, int. j. solids struct., 45 (2008) 6177-6189. [9] cristofori, a., benasciutti, d., tovo, r., a stress invariant based spectral method to estimate fatigue life under multiaxial random loading, int. j. fatigue, 33 (2011) 887–899. [10] carpinteri, a., spagnoli, a., vantadori, s., reformulation in the frequency domain of a critical plane-based multiaxial fatigue criterion, int. j. fatigue, 67 (2014) 55-61. [11] jasper, t.m., the value of the energy relation in the testing of ferrous metals at varying ranges and at intermediate and high temperature, philos. mag., 46 (1923) 609–627. [12] ellyin, f., cyclic strain energy density as a criterion for multiaxial fatigue failure, brown, miller, editors. biaxial and multiaxial fatigue, london: egf publication, (1989) 571–83. [13] ellyin, f., fatigue damage, crack growth and life prediction, edmonton: chapman and hall (1997). [14] macha, e., sonsino, c. m., energy criteria of multiaxial fatigue failure, fatigue fract. engng. mater. struct., 22 (1999) 1053–1070. [15] pook, l.p., sharples, j.k., the mode iii fatigue crack growth threshold for mild steel, int. j. fract., 15 (1979) r223r226. [16] pook, l.p., the fatigue crack direction and threshold behaviour of mild steel under mixed mode i and iii loading, int. j. fatigue, 7 (1985) 21-30. [17] tong, j., yates, j.r., brown, m.w., some aspects of fatigue thresholds under mode iii and mixed mode and i loadings, int. j. fatigue, 18 (1986) 279-285. [18] yu, h.c., tanaka, k., akiniwa, y., estimation of torsional fatigue strength of medium carbon steel bars with circumferential crack by the cyclic resistance-curve method, fatigue fract. eng. mater., 21 (1998) 1067-1076. [19] tanaka, k., akiniwa, y., yu, h., the propagation of a circumferential fatigue crack in medium-carbon steel bars under combined torsional and axial loadings, in: mixed-mode crack behaviour, astm 1359 (eds miller, k.j., mcdowell, d.l.), west conshohocked, pa, (1999) 295-311. [20] pippan, r., zelger, c., gach, e., bichler, c., weinhandl, h., on the mechanism of fatigue crack propagation in ductile metallic materials, fatigue fract. engng. mat. struct., 34 (2011) 1-16. [21] christopher, c.j., james, m.n., patterson, e.a., tee, k.f., towards a new model of crack tip stress fields, int. j. fracture, 148 (2007) 361–371. [22] christopher, c.j., james, m.n., patterson, e.a., tee, k.f., a quantitative evaluation of fatigue crack shielding forces using photoelasticity, eng. fract. mech., 75 (2008) 4190-4199. [23] berto, f., lazzarin, p., yates, j., multiaxial fatigue of v-notched steel specimens: a non-conventional application of the local energy method, fatigue fract. engng. mater. struct., 34 (2011) 921–943. [24] lazzarin, p., sonsino, c.m., zambardi, r., a notch stress intensity approach to assess the multiaxial fatigue strength of welded tube-to-flange joints subjected to combined loadings, fatigue fract. engng. mater. struct., 27 (2004) 127140. f. berto et alii, frattura ed integrità strutturale, 41 (2017) 79-89; doi: 10.3221/igf-esis.41.12 89 [25] berto, f., lazzarin, p., fatigue strength of structural components under multi-axial loading in terms of local energy density averaged on a control volume, int. j. fatigue, 33 (2011) 1055-1065. [26] berto, f. , lazzarin, p., marangon, c., fatigue strength of notched specimens made of 40crmov13.9 under multiaxial loading, mater. des., 54 (2014) 57-66. [27] berto, f., lazzarin, p., tovo, r., multiaxial fatigue strength of severely notched cast iron specimens, int. j. fatigue, 67 (2014) 15-27. [28] berto, f., campagnolo, a., chebat, f., cincera, m., santini, m., fatigue strength of steel rollers with failure occurring at the weld root based on the local strain energy values: modelling and fatigue assessment, int. j. fatigue. 82 (2016) 643–657. doi:10.1016/j.ijfatigue.2015.09.023. [29] campagnolo, a., berto, f., leguillon, d., fracture assessment of sharp v-notched components under mode ii loading: a comparison among some recent criteria, theor. appl. fract. mech. (2016) in press. doi: 10.1016/j.tafmec.2016.02.001. [30] berto, f., lazzarin, p., recent developments in brittle and quasi-brittle failure assessment of engineering materials by means of local approaches, mater. sci. eng. r, 75 (2014) 1-48. [31] berto, f., campagnolo, a., lazzarin, p., fatigue strength of severely notched specimens made of ti-6al-4v under multiaxial loading, fatigue fract. eng. mater. struct., 38 (2015) 503-517. << /ascii85encodepages false /allowtransparency false /autopositionepsfiles true /autorotatepages /none /binding /left /calgrayprofile (dot gain 20%) /calrgbprofile (srgb iec61966-2.1) /calcmykprofile (u.s. web coated \050swop\051 v2) /srgbprofile (srgb iec61966-2.1) /cannotembedfontpolicy /error /compatibilitylevel 1.4 /compressobjects /tags /compresspages true /convertimagestoindexed true /passthroughjpegimages true /createjobticket false /defaultrenderingintent /default /detectblends true /detectcurves 0.0000 /colorconversionstrategy /cmyk /dothumbnails false /embedallfonts true /embedopentype false /parseiccprofilesincomments true /embedjoboptions true /dscreportinglevel 0 /emitdscwarnings false /endpage -1 /imagememory 1048576 /lockdistillerparams false /maxsubsetpct 100 /optimize true /opm 1 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/hrv (za stvaranje adobe pdf dokumenata najpogodnijih za visokokvalitetni ispis prije tiskanja koristite ove postavke. stvoreni pdf dokumenti mogu se otvoriti acrobat i adobe reader 5.0 i kasnijim verzijama.) /hun 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can be opened with acrobat and adobe reader 5.0 and later.) >> /namespace [ (adobe) (common) (1.0) ] /othernamespaces [ << /asreaderspreads false /cropimagestoframes true /errorcontrol /warnandcontinue /flattenerignorespreadoverrides false /includeguidesgrids false /includenonprinting false /includeslug false /namespace [ (adobe) (indesign) (4.0) ] /omitplacedbitmaps false /omitplacedeps false /omitplacedpdf false /simulateoverprint /legacy >> << /addbleedmarks false /addcolorbars false /addcropmarks false /addpageinfo false /addregmarks false /convertcolors /converttocmyk /destinationprofilename () /destinationprofileselector /documentcmyk /downsample16bitimages true /flattenerpreset << /presetselector /mediumresolution >> /formelements false /generatestructure false /includebookmarks false /includehyperlinks false /includeinteractive false /includelayers false /includeprofiles false /multimediahandling /useobjectsettings /namespace [ (adobe) (creativesuite) (2.0) ] /pdfxoutputintentprofileselector /documentcmyk /preserveediting true /untaggedcmykhandling /leaveuntagged /untaggedrgbhandling /usedocumentprofile /usedocumentbleed false >> ] >> setdistillerparams << /hwresolution [2400 2400] /pagesize [612.000 792.000] >> setpagedevice microsoft word numero 24 articolo 14 p.v. makarov et alii, frattura ed integrità strutturale, 24 (2013) 127-137; doi: 10.3221/igf-esis.24.14 127 special issue: russian fracture mechanics school the numerical simulation of ceramic composites failure at axial compression p.v. makarov, m.o. eremin institute of strength physics and material science siberian branch of russian academy of science, national researching tomsk state university bacardi@sibmail.com abstract. on the basis of the developed model of quasibrittle medium the brittle and quasibrittle failure of composite ceramic materials with zirconium dioxide matrix and various percentage of hardening particles of corundum are studied numerically. the theory of the damaged media is applied in the calculations. it is shown that failure process educes in 2 stages a relatively slow quasistationary phase of accumulation of inelastic deformations and damages in all hierarchy of scales and superfast catastrophic phase a blow-up regime when the failure process reaches the macro-scale and there is a macro-crack formation. the failure process in the proposed model assumes to be completed when the damage function reaches its maximum value and the strength of the composite evolve to zero. keywords. brittle and quasi-brittle failure; quasistationary phase; blow-up regime. introduction onstructional ceramic composites have received a wide practical application in the industry because of their high unit strength, the raised toughness, hardness, crack stability, high resistivity to fatigue breakdown etc. constructional ceramics on the basis of strong oxides of various metals (zirconium, aluminum, etc.) are capable to resist the intensive mechanical loads effectively. however the brittle properties of ceramic composites, their rather low stability to shock loads strongly confine the ranges of their application. studying the mechanisms and features of brittle and quasibrittle failure of ceramic materials is one of the most urgent problems of modern fracture mechanics. according to the approach of physical mesomechanics [1] and ideas of paper [2] the loaded solid is the nonlinear dynamic system which evolution in fields of operating forces completely corresponds to the fundamental features of evolution of nonlinear dynamic systems. in the present paper the basic attention is given to the character of failure of quasibrittle solids and media – the presence of two stages of failure: rather slow quasistationary and superfast catastrophic stage – the blow-up regime according to the s.p. kurdyumov terminology [3] as it is the fundamental feature of evolution of the nonlinear dynamic systems possessing the self-organized criticality [4]. one of the central problems of solid mechanics is a problem of the formulation of the fracture criteria or conditions when the crack formation starts. many papers are dedicated to the problems of crack-growing in non-homogeneous media, such as rocks [19], polycrystalline materials or ceramics and ceramic composites [18]. for example, in paper [21] the equation of state is built on the basis of crack interaction and crack density accounting and strain rate dependency and used for simulation of macroscopic stress-strain curves. such approach gives good qualitative and quantitative results in calculation of the degradation stage in stress-strain curves, strain rate dependency and defects density evolution. however c http://dx.medra.org/10.3221/igf-esis.24.14&auth=true http://www.gruppofrattura.it p.v. makarov et alii, frattura ed integrità strutturale, 24 (2013) 127-137; doi: 10.3221/igf-esis.24.14 128 in the present paper the main accent is made on studying the transition from the quasistationary phase of media evolution to the blow-up regime which is assumed as local failure at crack formation which applies to be the new vision of the failure process. in the present paper these problem also dares on the basis of ideas of the mathematical theory of evolution of loaded solids and media [2]. according to traditional ideas of fracture mechanics a local fracture in solids occurs when a maximum load is reached. all experience of application of this approach to the problem of limiting design has shown its comprehensible working capacity and correctness for many practical problems. however we can tell nothing about the failure process especially about its forecast. if a certain constant or changing load is enclosed to solid it is only possible to calculate the conforming stress-strain state and to answer a question whether a maximum load is reached or not somewhere. such answers appear useful and sufficient in a number of important engineer cases but to tell something about the mechanisms and scenarios of failure locus formation is impossible. the fundamental law of fracture of any materials has been investigated in the 70s of the xx century: the final failure (not only fatigue but any) precedes more or less significant preparatory stage. for example for the silicate glasses which failure was considered as instant the speed of crack propagation in the beginning of failure has appeared in thousands times less than at the final stage [5] and this is with the fact that the whole failure process takes some ms. rapid development of ideas and methods of nonlinear dynamics at the same years and the next decades have allowed the group of s.p. kurdyumov to formulate the new concept of superfast catastrophic stages of evolution of nonlinear systems – the blow-up regimes [3] and both analytically and numerically to study the kinds and features of these regimes. these ideas and the qualitative results obtained on their basis are the key-ideas for understanding the failure process. in the considered case of brittle or quasibrittle failure (and also the failure of any materials and constructions, plastic metals, brittle concrete, rocks, geomedia etc.) the preparatory process of accumulation of inelastic deformations and damages in brittle media is localized in certain areas. this preparatory quasistationary stage because of the self-organized criticality of solid as nonlinear dynamic system passes sooner or later in the superfast catastrophic stage – blow-up regime by s.p. kurdyumov [2, 4, 7]. it is clear that any failure forecast basically is not possible without studying the features of development of these stages and conditions of transferring of one stage of sustainable development of failure to unstable superfast regime. mathematical statement of a problem. model of quasi-brittle medium ccording to the evolutionary concept of the description of inelastic deforming and the subsequent failure processes [2, 4, 6-9] the full set of equations includes: 1. fundamental conservation laws:  mass     0 d div dt (1)  impulse        iji ij d f dt x (2)  energy     1 ij ij dde dt dt (3) where  is the material density, i is the i-component of the speed vector, if is the i-component of the massive force, is energy, t is time. 2. the evolutionary equations of the first group which have been written down in the relaxation form in which increments of stresses    ij t are proportional to increments of total deformations  t ij and relax proportionally to the development of inelastic deformation pij . the procedure of stresses reduction to the instant limiting surface means the instant stress relaxation on each time layer to some dynamic equilibrium state defined both by relaxation and the rate of strength and elastic parameters of medium degradation. at       0p tij ij ij , there is a relaxation, at       0 p t ij ij ij and stresses steepen:                  2t p t pij ij ij ij (4) a http://dx.medra.org/10.3221/igf-esis.24.14&auth=true http://www.gruppofrattura.it p.v. makarov et alii, frattura ed integrità strutturale, 24 (2013) 127-137; doi: 10.3221/igf-esis.24.14 129     ij ij ijp s (5)     vp k v (6)          12 3 ij ij ij ds dt (7)      ij ij ik jk jk ik ds s s s dt (8)             1 2 jt i ij j ix x (9)             1 2 ji ij j ix x (10)  is the rate of volumetric strain,  , are the lame constants, k is the bulk modulus, p is pressure, ij are the components of deviator stress tensor, d dt is the co-rotation derivative of yauman considering the rotation of the medium elements at deforming, ij are the components of the rotation strain rate tensor. 3. the problem of the evolutionary equations of the second group is the definitions of rates of inelastic deformations in the eq. (4). generally it is the kinetic equations setting the rates of inelastic deformations and providing the relaxation of elastic stresses in (4). in the present paper the components of rates of inelastic deformations tensor are identified according to the theory of plasticity and instant stress relaxation on each time layer. the limiting surface of stresses is written down in the form of mises-schleicher that allows to satisfy the requirement of generalization of plasticity and brittle failure conditions: the form of a limiting surface and its properties are completely defined by three parameters of a stressed state octahedral normal stress octahedral shear stress oct and a kind of the stressed state  (parameter of lode-nadai)     1 21 2( ) ( ) 3 ij ijf j j y (11) where f is the yield surface and 1 2,j j are the first, the second invariants of the stress tensor and y current strength. eq. (11) is a generalization of plasticity criterion of coulomb-more. the model of drucker-prager-nikolaevskiy with nonassociated flow law is taken as basis allowing describing the dilatation and internal friction processes independently. in the case of non-associated flow law the plastic potential   ijg does not coincide with a function of plasticity and for a limiting surface (11) is written as follows [10]:            2 1 12 3 3 ijg j j y j const (12) components of rates of inelastic deformations tensor will be defined as follows:                1 2 ( ( ) ) 3 3 p ij ij ij ij g s y i (13) where  is the plasticity multiplier in the theory of plasticity.    1 2 1 22 ( ) p pi i (14) that allows to establish the connection between volumetric 1 pi and shear 2 pi components of inelastic strain (14) [7] where  is a speed of dilatation. however the model is not bound yet to the kind of stressed state. that dependence will be defined within the function of damages accumulation. http://dx.medra.org/10.3221/igf-esis.24.14&auth=true http://www.gruppofrattura.it p.v. makarov et alii, frattura ed integrità strutturale, 24 (2013) 127-137; doi: 10.3221/igf-esis.24.14 130 4. failure in the educed approach is considered as a process of avalanche degradation of material strength to zero at macro-cracking during the superfast catastrophic stage of stress-strain state evolution which is the closing stage of prefailure. however the medium remains consolidated macroscopically hence all the equations of inelastic deforming (1) ÷ (14) are fair. there is no need to introduce the strength parameters defining the “limiting” state of material into model. according to the ideas of the present paper the “limiting” condition should be formed in the loaded medium during the process of inelastic deformations and damages accumulation. it is necessary to set the initial strength of the material . according to the classic ideas of the failure kinetic concept (n.s. zhurkov, a.v. stepanov, r. bekker, ja.i. frenkel and others) [11-15] to lead an ideal crystal to a state of local shear it is necessary to make a work proportional to the difference of free energies f of an ideal crystal and a crystal in current state      0 2 2 ( )~ 2 a v (v volume, σ0 – the value of theoretical strength,  is the current stress). orowan modified this idea and put the critical increment of energy depending only on the size of plastic (inelastic) deformation [16]    2 p2( )~h v 2 f , where h is the strain hardening parameter, p is the accumulated inelastic strain. we use this idea and put the function of medium degradation   ( , , )pd d t in the form of dependence on inelastic deformation accumulated by medium     0p cur and the kind of stressed state:                  0 2 cur 0 2 0 0 ( ) dt (1 ) , y=y (1-d), d 1 t t n d t (15)      2 3 1 3 2 1 s s s s (16) cur is the current mean of total deformation intensity, 0 is the initial deformation when the damage accumulation begins. 0 is different for areas of compression and tension and makes 0.2 0.5 from the elasticity limit depending on a solved problem. such approach allows accumulating the damages at macroscopically elastic stage of deforming. rates of damage accumulation for local tension-shift areas where μσ<0 are essentially bigger than in compression-shift areas where μσ>0. this process is controlled by the parameter   * * ( ) in (15). thus the medium response (its current strength) is formed during loading. hence the strength and elastic parameters will degrade essentially faster in those areas (particles) of medium where the lode-nadai parameter μσ <0 that corresponds to tension-shift areas. this response depends also on the loading history. changing the deforming regime from tension-shear to compression-shear might mean the transition to another scenario of evolution and regeneration of the medium properties. ε0* is the model parameter, t* makes sense of the characteristic time of the process, 1 2 3, ,s s s – are the main deviatric stresses. calculations were made in 2d under the condition of a plane deformation and 3d with the scheme of the second order of accuracy described in detail in paper [17]. the numerical simulation results of brittle and quasi-brittle failure of composite ceramic materials he model specimens of ceramic composites with zirconium dioxide 2zro matrix and various content of hardening particles (15% (a) and 40% (b)) of corundum 2 3al o are represented on fig. 1. the content of the second phase was chosen as 15% and 40% to study the qualitative changes in the mechanical behavior of the composites. the presented structural models were developed on the basis of the well-known typical quasi-homogeneous distribution of the hardening particles within the matrix. in paper [22] the experimental study of uniaxial compression of porous ceramic on the base of zirconium dioxide was carried out and it’s structure and phase content were also studied. using the observations of structure from several papers of the author of paper [22] we developed the model of ceramic t http://dx.medra.org/10.3221/igf-esis.24.14&auth=true http://www.gruppofrattura.it p.v. makarov et alii, frattura ed integrità strutturale, 24 (2013) 127-137; doi: 10.3221/igf-esis.24.14 131 composites presented on the fig. 1. the uniaxial compression of specimens was carried out in the calculations. the dimensions of the specimens are 100 140 m . in paper [18] it has been shown that in loaded ceramic composites there are local areas of tension stresses on the interphase borders. formation of mesocracks occurs in these areas of tension stresses. we will show that failure of composites in the majority of cases occurs in tension areas. it is caused by two reasons: 1) the presence of structural heterogeneities always leads to the formation of local tension areas in composite; 2) strength of quasibrittle materials at tension is essentially low than at compression. rates of damages accumulation in tension areas are also essentially bigger. in tab. 1 the physical-mechanical properties of the materials compounding the composite are presented. (a) (b) (c) figure 1: the model specimens of composites with 15% (a) and 40% (b) content of the hardening particles and the principle loading scheme (c). . parameter material density, kg/m3 bulk modulus, mpa shear modulus, mpa strength, mpa  speed of dilatation  , internal friction coefficient 2zro 5700 1.433 510 0.6615 510 2100 0.22 0.62 2 3al o 3984 3.46  510 1.6  510 3740 0.12 0.6 table 1: the physical-mechanical properties of the materials compounding the composite. the macroscopic behavior the   diagrams for composite specimens are shown under various loading conditions on fig. 2 ideal sliding (fig. 2a) and friction (fig. 2b) on the loading border. (a) (b) figure 2: the   diagrams in case of: ideal sliding (a), friction (b) on the loading border. http://dx.medra.org/10.3221/igf-esis.24.14&auth=true http://www.gruppofrattura.it p.v. makarov et alii, frattura ed integrità strutturale, 24 (2013) 127-137; doi: 10.3221/igf-esis.24.14 132 the general for two variants of loading is the strength evolution of composites in the blow-up regime at final stage of deforming. steady slow accumulation of inelastic deformations and damages at lower structural levels than considered macrolevel is replaced by the stage of unstable avalanche accumulation of damages (the blow-up regime) which occupies the tenth lobes of macrodeformation. it means that there is a localization of failure process in time. during the blow-up regime the global loss of stability, strength and elastic moduli of composites degradation to zero occur very quickly. in the case of ideal sliding on the loading border (fig. 2a) the brittle failure of specimens occurs that is the sharp break on the   diagram and the system evolution is observed in the blow-up regime. the stage of the linear stress growth is followed by the blow-up regime with the global strength degradation. the feature of the deformation response in the case of friction on the loading border (fig. 2b) is the presence of the stage of inelastic deforming of specimens because of the compression-shear areas formation near the friction border that sharply reduces the rate of damages accumulation. this process detains the phase of the blow-up regime and the global degradation of physical-mechanical properties of medium. thus the stage of inelastic deformation occupies some % of macrodeformation. other scenario educes in the case of a lateral pressure (fig. 3). constraint of the deformation leads to tightening of the catastrophic phase of evolution of the system. the strength resource is spent gradually in this case, the sequence of relaxations and growths of stresses is observed. the similar situation is observed in geomedia at so-called “slow” earthquakes when the features of constraint of deformation lead to the tightening of the local failure process. figure 3: the   diagram in the case of the lateral pressure. the behavior on the meso-scale the part of specimen area reflecting the kind of the stressed state in a composite defined by the lode-nadai parameter is represented on fig. 4. first of all the formation of a strip of the localized failure occurs in a narrow regions of normal tension stresses   1 . figure 4: the part of specimen area reflecting the kind of the stressed state in the composite defined by the lode-nadai parameter  . besides in the generated mesocrack in the noted area the stressed state was replaced with compression-shears that means transferring to the compaction mode at the steepening of the deformation constraint due to the presence of the hardening  http://dx.medra.org/10.3221/igf-esis.24.14&auth=true http://www.gruppofrattura.it p.v. makarov et alii, frattura ed integrità strutturale, 24 (2013) 127-137; doi: 10.3221/igf-esis.24.14 133 particles. at the same time in the generated mesocrack areas neighboring with the compaction zone are in dilatation regime. this process of failure delay in matrix shows one more positive role of the hardening particles. on fig. 5 8 the calculated patterns of inelastic deformations in composites for three consecutive times (     1 2 34000 , 6000 , 8000t s t s t s ), the stressed state (by the lode-nadai parameter), damage function are presented at 2 variants of boundary conditions. in all presented cases the incipient states of specimens deforming accompanied with a vertical crack growing that also show the experiments [20]. comparison of failure patterns of composites with various percentage of hardening particles shows the distinction in mechanisms of their destruction. in the composite with 40 % content of corundum the great number of hardening particles simultaneously creates the possibility for formation of the of local tension stresses areas on the phase border where the degradation of physical-mechanical properties of medium descends much faster. but also interferes with the macrocrack growing. on the pre-failure stage of the composite with 40% content of corundum the significant number of mesocrack is generated and this is more power-intensive process than formation of the small number of long cracks within the composite with 15% content of hardening particles (fig. 5, 7). figure 5. simulation patterns: inelastic deformations (for three consecutive times), the stressed state (  ), damage function (d) in the composite specimen with 15% content of hardening particles in the case of ideal sliding on the loading border. figure 6: simulation patterns: inelastic deformations (for three consecutive times), the stressed state (  ), damage function (d) in the composite specimen with 40% content of hardening particles in the case of ideal sliding on the loading border. figure 7: simulation patterns: inelastic deformations (for three consecutive times), the stressed state (  ), damage function (d) in the composite specimen with 15% content of hardening particles in the case of friction on the loading border. d3t2t1t 1t d3t2t 1t d3t2t http://dx.medra.org/10.3221/igf-esis.24.14&auth=true http://www.gruppofrattura.it p.v. makarov et alii, frattura ed integrità strutturale, 24 (2013) 127-137; doi: 10.3221/igf-esis.24.14 134 figure 8: simulation patterns: inelastic deformations (for three consecutive times), the stressed state (  ), damage function (d) in the composite specimen with 40% content of hardening particles in the case of friction on the loading border. dynamics of crack growth in such composites (fig. 6, 8) for three consecutive times shows that during the pre-failure stage there is a steady accumulation of inelastic deformations and damages in the whole considered volume of composites. the catastrophic superfast phase of system evolution – the blow-up regime occurs when the process of inelastic deformations and damages accumulation reaches the macrolevel. it is anticipated by the quasistationary preparation phase which is expressed in the formation of percolation net of mesocracks. at final stage of deforming there is a confluence of the generated mesocracks in main macrocrack. other situation is observed in the composite with 15 % content of hardening particles. propagation of the crack fastigium generated on the interphase border is stopped by the smaller quantity of hardening particles that is the growing crack approximately three times rarely encounters the resistance of hardening particles. thus the average length of an individual mesocrack for the composite with 15% content of corundum exceeds the similar length of an individual mesocrack for the composite with 40% content of corundum in 1.5 2 times. such distinction at mesolevel leads to the distinction at macrolevel in characters of destruction of two composites. in the composite with 15% content of the hardening particles the macrocrack also has mainly vertical character. the mesocracks growing from the opposite edges of the specimen getting to a region of a dynamic influence and start to render the interference against each other that leads to their confluence at a final stage of deforming. the particles flow characters in the composites are shown in the shift-fields. for example on the fig. 9, 10 the shift-fields in composites related to the noted grain are presented for three consecutive times. 1t 2t 3t figure 9: simulation shift-fields for the composite with 40% content of the hardening particles in the case of ideal sliding on the loading border. shift-fields possess a strongly pronounced heterogeneity. the evolution of the shift-fields in time shows that the stressstrain state in the area of the fixed grain changes during the loading from compression on the incipient state of deforming then shears and formation of the curls and tension during the composite fragmentation. at main crack formation shiftfield shows the correlated locomotion of composite fragments in the normal direction to main crack. d3t2t1t http://dx.medra.org/10.3221/igf-esis.24.14&auth=true http://www.gruppofrattura.it p.v. makarov et alii, frattura ed integrità strutturale, 24 (2013) 127-137; doi: 10.3221/igf-esis.24.14 135 1t 2t 3t figure 10: simulation shift-fields for the composite with 15% content of the hardening particles in the case of friction on the loading border. figure 11: damage function monitoring for several particles of the specimen which are in the region of a prospective dynamic influence in the composite with 15% content of hardening particles (a – in the case of friction on the loading border, b in the case of ideal sliding on the loading border). the pattern of damage function monitoring for several particles in the specimen volume located in the region of the prospective mutual dynamic influence (fig. 11) shows the presence of slow quasistationary phase of damage growth and superfast phase of evolution – the blow-up regime with the damage growth in the particle of the composite to it’s maximum value. from fig. 11 also it is visible that damage in the particles consistently reaches the maximum value consecutively. the similar behavior can testify the migration of deformation activity. after the finish of the blow-up regime in one of the particles it begins in another (or the quasistationary phase in the next particle proceeds) and next the superfast phase of evolution occurs and there is a migration of deformation activity to the next particle. a generalization of the quasi-brittle medium on the case of 3d simulation the developed model of quasibrittle medium was applied for the 3d numerical simulation of the brittle failure of ceramic composites. the 3d stochastic structure of the composite with 15% content of the hardening particles with quasihomogeneous distribution was generated and presented on the fig. 12. the same parameters as for the 2d simulation presented in tab. 1 were applied in 3d simulation. the results of uniaxial compression at different boundary conditions are presented on the fig. 13. from the simulation patterns presented on the fig. 13 we can see that the generalization of the developed model on the case of 3d simulation qualitatively gives the same results. particularly we have the formation of the meso-cracks on the incipient stages of deforming mainly co-directed with the loading force. at later stages of deforming we can see that the formation of bridges between meso-cracks leads to the macro-crack formation which can be either co-directed with the loading force or disoriented to some angle with the loading force. in several cases the growing meso-crack change it’s direction on the angle of 90 when it gets into the region of the high compression near the hardening particle; such behavior at crack growing was observed in the experiments [23]. http://dx.medra.org/10.3221/igf-esis.24.14&auth=true http://www.gruppofrattura.it p.v. makarov et alii, frattura ed integrità strutturale, 24 (2013) 127-137; doi: 10.3221/igf-esis.24.14 136 (a) (b) figure 12: the 3d generated structural model of the ceramic composite with 15% contain of the hardening particles: the whole specimen (a) and a middle clip (b). (a) (b) figure 13: simulation patterns: cracking of the ceramic composite with 15% content of hardening particles (2 views from opposite sides) at ideal sliding (a) and fixing (b) on the loading border. http://dx.medra.org/10.3221/igf-esis.24.14&auth=true http://www.gruppofrattura.it p.v. makarov et alii, frattura ed integrità strutturale, 24 (2013) 127-137; doi: 10.3221/igf-esis.24.14 137 conclusions n the considered model of medium the limiting condition in the loaded material is formed during loading and depends on the stressed state kind. studying the laws of brittle and quasibrittle failure of composite ceramic materials with the usage of the developed model of quasibrittle medium it was shown that failure process always educes in two stages slow steady accumulation of inelastic deformations and damages in all hierarchy of structurally-scale levels as the quasistationary phase is replaced by the blow-up regime – the superfast catastrophic phase of evolution of system when the failure process reaches the macrolevel. at ideal sliding on the loading border failure has a brittle character when the linear steepening of stresses is followed by the global loss of stability and degradation of elastic and strength properties of composites to zero. at friction on the loading border the stage of pre-failure inelastic deforming of the composites with formation of the local areas of the strength loss which occupies some percent of macrodeformation is observed. thus the stage of evolution of system in the blow-up regime is tightened. in the case of constrained deformation the other scenario of the composite evolution is observed. the resource of elastic and strength properties of medium is spent gradually. during the general evolution of the system in the blow-up regime the sequence of steepens and relaxations of stresses on the   diagram is observed. it is shown that brittle and quasibrittle failure of materials descends mainly in the tension stresses areas where the rate of elastic and strength properties degradation of medium is bigger on several orders. at pre-failure stage the confluence of the mesocracks in percolation net evolves in the macrocracking at the final stage of deforming. references [1] v.e. panin, a.d. korotaev, p.v. makarov, v.m. kuznetsov, izvestiya of the high schools. physics, 9 (1998) 8. [2] p.v. makarov, phys. mesomech, 11 (3) (2008) 19. [3] s.p. kurdyumov, blow-up regimes. idea evolution, ed. g.g. malinetsky, 2nd ed., fizmatlit, (2006) 312. [4] p.v. makarov, phys. mesomech, 13(5) (2010) 97. [5] v.z. parton, е. м. morozov, mechanics of elasto-plastic failure, science, (1974) 416. [6] p.v. makarov, geology and geophysics, 48(7) (2007) 724. [7] p. v. makarov, i. yu. smolin, yu. p. stefanov, nonlinear mechanics of geomaterials and geomedia, novosibirsk, sb ras geo, (2007) 235 . [8] p.v. makarov, phys. mesomech, 8 (6) (2005) 39. [9] e. p. evtushenko, m. o. eremin, yu. a. kostandov, p.v. makarov et alii, phys. mesomech, 15(3) (2012) 35. [10] i. a. garagash, v. n. nikolaevskiy, successes of mechanics, 12(1) (1989) 131. [11] s. n. zhurkov, b. n. narzulaev, zhtf, xxiii(10) (1953) 1677. [12] a.v. stepanov, basics of the practical crystal strength, science (1974) 131. [13] v. r. regel, a. i. slutzker, e. e. tomashevskiy, science, (1974) 560. [14] i.i. frenkel, introduction to the metals theory, fizmatlit, (1958) 424. [15] r. becker, physikalische zeitschrift, 25(7) (1925) 919. [16] e. j. orowan, the creep of metals, west scot. iron and steel inst., 54 (1947) 45. [17] m. l. wilkins, computer simulation of dynamic phenomena, heidelberg, springer, (1999) 265. [18] g. i. barenblatt, g.p. cherepanov, izv. of ussr as, mechanics and mechanical engineering, 3 (1960). [19] yu. p. stefanov, phys. mesomech, 8(3) (2005) 129. [20] yu. a. kostandov, p. v. makarov, m. o. eremin, i. yu. smolin, i. e. shipovskii, international applied mechanics, 49 (1) (2013) 95. [21] b. paliwal, k. t. ramesh, j. of the mechanics and physics of solids, 56 (2008) 896. [22] s. v. panin, p. s. lyubutin, s. p.buyakova, s. n. kulkov, phys. mesomech, 11(6) (2008) 77. [23] j. d. kuntz, g. d. zhan, a. k. mukherjee, mrs bull., 29 (2004) 22. i http://dx.medra.org/10.3221/igf-esis.24.14&auth=true http://www.gruppofrattura.it microsoft word numero_51_art_35_2641 k. bahram et alii, frattura ed integrità strutturale, 51 (2020) 467-476; doi: 10.3221/igf-esis.51.35 467 simulation of the retardation effect after applying a simple overload on alloys of aluminum 2024t351 using the willemborg model kaddour bahram university centre of ain témouchent-belhadj bouchaib, department of mechanical engineering, po box 284,46000, algeria laboratory of materials and reactive systems lmsr, department of mechanical engineering, university djilali liabes, bp 89, cité ben m’hidi, sidi bel abbes, 22000, algeria kadero_7@hotmail.com, https://orcid.org/0000-0002-8963-4936 mohamed chaib smart structures laboratory (ssl) university centre of ain témouchent-belhadj bouchaib, po box 284,46000, algeria. pro19moh@hotmail.com,https://orcid.org/0000-0002-0493-1764 abdelkader slimane, benattou bouchouicha laboratory of materials and reactive systems lmsr, department of mechanical engineering, university djilali liabes, bp 89, cité ben m’hidi, sidi bel abbes, 22000, algeria slimane.aek@hotmail.com, https://orcid.org/0000-0001-5183-7420 benattou_b@yahoo.fr,https://orcid.org/0000-0002-6051-5108 abstract. the structures in service are subjected to loads whose amplitude varies most often over time. these differences in loading cycle levels will have a direct impact on the propagation of cracks that can lead to accelerations or slowdowns in the propagation speed of these cracks. indeed, the delay of the propagation of a crack produced by the application of a simple overload depends on several parameters, such as the material, the loading, the geometry of the specimen and the environment. in this paper, study the influence of the loading parameters such as the load ratio, and the overload rate, on both crack propagation, propagation speed, number of delay cycle, is investigated by using the afgrow code and the willenbourg model, which describes the delay after applying overloads. keywords. aluminum alloys; 2024t351; fatigue; plastic zone; simple overload; willenbourg model. citation: bahram, k., chaib, m., slimane, a., bouchouicha, b., simulation of the retardation effect after applying a simple overload on alloys of aluminum 2024t351 using the willemborg model, frattura ed integrità strutturale, 51 (2020) 467-476. received: 28.09.2019 accepted: 11.12.2019 published: 01.01.2020 copyright: © 2020 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. introduction he prevention of breaks in service is an ongoing objective of designers, builders and users, in both energy sector (thermal power stations, alternators), oil sector (gas pipelines, pipelines),aeronautical sector ( cells), rail and road transport, public works (bridges, dams, piers), consumer goods (automobiles) [1-3]. t http://www.gruppofrattura.it/va/51/2641.mp4 k. bahram et alii, frattura ed integrità strutturale, 51 (2020) 467-476; doi: 10.3221/igf-esis.51.35 468 structures subjected to cyclic loadings can undergo large variations in their behaviour ranging from the phase of plastic deformation to breaking through damage depending on the nature of the stresses. the constant nature of these stresses at constant amplitude implies the use of laws and models which are mastered by the current computation codes, currently, the paris law is the expression most used in fatigue research work with constant amplitude, it should be noted that this relation is applicable only in the field of slow crack propagation (domain ii) and it does not take into account what happens in domain i and iii [4-6] . nevertheless, the constant amplitude propagation laws make it possible to describe the propagation of long cracks under constant amplitude loading. indeed, it is implicitly assumed that a given cycle causes a loss assimilated to an advance regardless of the history of previous loading. however, actually, the structures are only very rarely subjected to loads of constant amplitude. on the other hand, the load spectrum measurements indicate a variation of the stress amplitude over time. in addition, experience shows that the damage induced by a given cycle may depend on the previous history of loading [7-9]. it has now been found that the application of an overload cycle during a fatigue crack propagation leads to a slowing of the crack propagation speed, in some cases to a stop of this crack [10-12], this phenomenon of delay due to the application of an overload, several authors [13-15], proposed different models to explain the causes due to the slowing of the crack propagation speed. these different approaches can be grouped into three categories of models, based on: i) the interaction effects of the plastic areas at the tip of the crack. these models are inspired by that of wheeler [14]. ii) the phenomenon of closing the crack due to the residual stresses induced by the plastification near the crack tip. these models are based on that of elber [13]. iii) iii) micromechanisms that act at the tip of the crack. these models are inspired by [16-18], in the case of an elastoplastic material. the strongly deformed area near the crack. is governed by an oligocyclic fatigue mechanism. in the following, we will use the afgrow calculation code and the model describing the delay of willembourg to study the influence of the application of simple overload on different parameters such as, crack spread, crack rate and overload rate. willenborg model he willenborg model is a slightly different approach since it proposes to determine a slowing factor [15], but an actual value of the ratio of load at crack point effr . the formulation of the generalized willenborg model implemented in the afgrow code is shown below: min max eff eff eff k r k  (1) with min eff min rk k k  (2) max eff max rk k k  (3) the value of the residual stress intensity factor rk is defined for a crack length ia , necessary to create a plasticized zone of size eqr , tangent the plasticized zone created by the overload rpic . min max min max   max   0    0 ,                 0    0 ,    0 ,  0                                              eff eff eff eff eff eff max eff eff eff if k and k k k if k and k k k if k k                 (4) the residual stress intensity factor is given by the following equation: t k. bahram et alii, frattura ed integrità strutturale, 51 (2020) 467-476; doi: 10.3221/igf-esis.51.35 469 01 ir pic max pic a a k k k r            (5) where  eqr is expressed by the following equation: 2 1max r eq y k k r               (6)  is state of stress in the direction of propagation of the crack (plane stress or plane strain) , and  define the level of residual stress induced by application of overload, it is given by the following equation: 1 sor    1 thok k      (7) where 0   thk represents the threshold stress intensity factor for a load ratio r = 0. sor: shut-off ratio ratio of overload maximum stress to the subsequent maximum stress required to arrest crack growth the value of kpic is updated whenever the maximum load exceeds the previous maximum value, or when the current plasticized area extends beyond the area created by the overload. the exact value of the sor is varied to adjust the life prediction to match test results. ideally, the sor should be a material parameter that is insensitive to spectrum or stress level. however, this does not always work out. the following is a list of common sor values for some materials: as an indication, 2sor  for the steels, 2.7 sor  for the titanium alloys and 3 sor  for the aluminum alloys. it is therefore assumed that the delay disappears as soon as the current plasticized zone enters a zone of marerial not affected by the overload. figure 1: willenborg retardation model k. bahram et alii, frattura ed integrità strutturale, 51 (2020) 467-476; doi: 10.3221/igf-esis.51.35 470 fatigue crack growth model he nasgro model used in the prediction of the fatigue crack growth rate was developed by forman [19] to take into account the entire propagation curve. the nasgro equation is shown below: 1 1   1 1 p tho n q max crit k fda k c k dn r k k                    (8) where: k is the stress intensity range. maxk is the maximum stress intensity range 0thk is the threshold stress intensity range at the stress ratio r under consideration. critk critical stress intensity factor f is the newman crack closure function [20]. the parameters c, n, p, are determined experimentally, where: c : is a constant for the case where stress ratio r=0 n : is the slope on a log-log scale p and q are empirical coefficients that determine the curvature of the growth rate curve in the tail regions. their values are selected to fit the growth rate curve to experimental data. the coefficient p controls the curve in the low growth rate (threshold) region, and q controls the curve in the high growth rate region. case study his study was conducted on aluminum alloys 2024 t351, whose mechanical properties are increased by a heat treatment to adulterate its micro-structure. this material is widely used in aeronautics and automobile industry. the mechanical properties as well as the nasgrow parameters used in the simulation are given in tab. 1 and 2 . e (mpa) σe (mpa) σmax (mpa) ε rupture (%) 74000 365 415 12.8 table 1: mechanical properties of the aluminum alloy 2024 t351 (afgrow database). aluminum alloy ∆ktho mpa√m kic mpa√m kc mpa√m n p q c 2024t351 2.857 37.36 74.72 3 0.5 1 1.707*10-10 table 2: propagation model parameters useful by the nasgro model (afgrow database). for the simulations, we used a ct 50 specimen (fig. 2); the specimen is subjected to a mode i loading. we chose to study the propagation of cracks under mode i because it is considered the most dangerous due to the opening by traction, which favors the initiation and the propagation of the cracks. t t k. bahram et alii, frattura ed integrità strutturale, 51 (2020) 467-476; doi: 10.3221/igf-esis.51.35 471 figure 2: detail of the ct50 specimen. influence of the overload on the crack propagation or the rest of the simulations, and in order to observe the influence of the overloads on the crack propagation ,we proceed to the application of the overloads (tab. 3) for the different load ratios 0.1, 0.5, and 0.7. load ratio pmax (kn) pmin (kn) number of loading cycles 0.1 4 0.4 40 000 10 0.4 1 4 0.4 200000 0.5 4 2 150 000 10 2 1 4 2 500 000 0.7 4 2.8 500 000 10 2.8 1 4 2.8 1 600 000 table 3: loading parameters. fig. 3 shows that for different load ratios 0.1, 0.5 and 0.7, after the application of the overload, the delay phenome is observed. we also observe for the three load ratios , only after the application of the overload the slope of the crack propagation curve decreased during a number of delay cycles ( dn ), this change of slope is affected by the creation of a plastic zone around the crack and once the crack passes through this area, it recovers its initial slope. it is also noted that the number of delay cycles is different from one load ratio to another, this is certainly due to the difference of the overload rate between 0.1, 0.5 and 0.7. f k. bahram et alii, frattura ed integrità strutturale, 51 (2020) 467-476; doi: 10.3221/igf-esis.51.35 472 figure 3: crack propagation evolution before and after application of the overload for the different load ratios. influence of overloads on the cracking rate ig. 4 illustrates the evolution of the cracking rate as a function of the number of loading cycles. by analysing this figure, several observations can be made between them. figure 4: evolution of the cracking rate as a function of the number of loading cycles. (i) it is noted that for different load ratios, after application of the overload the cracking rate is affected by the application of the overload. (ii) the cracking speed after applying the overload goes mainly through four steps: 1first stage: an increase in the cracking rate with a slight slope is observed. 2second stage: by applying the overload, the cracking rate increases very rapidly for recorded in pic. 3third stage: a rapid drop in the cracking rate may be observed to reach a minimum value noted ( / minda dn ). this area strongly disturbed by the overload corresponds to a crack length mina . 4fourth stage: the cracking rate begins to increase gradually in the plasticized zone created by the application of the overload, until it returns to almost its initial value ( /da dn ) before application of the overload. f k. bahram et alii, frattura ed integrità strutturale, 51 (2020) 467-476; doi: 10.3221/igf-esis.51.35 473 we also notice, for the three load ratios the maximum cracking rate ( / maxda dn ) recorded after the application of the overload is different from one load rate to another, this difference certainly has a major impact on the size of the plastic zone created by the application of the overload and consequently on the number of delay cycles. influence of the overload rate n order to better understand the influence of the overload rate on the various parameters, only one load ratio (r = 0.5) is considered in le following (tab. 4). overload rate pmax (kn) pmin (kn) number of loading cycles 2.5 4 2 150 000 10 2 1 4 2 500 000 2 4 2 150 000 8 2 1 4 2 500 000 table 4: loading parameters. figure 5: evolution of the cracking rate and crack propagation as a function of the number of cycles for an overload rate (τ = 2). by observing both figs. 5 and 6, we can deduce and advance several conclusions: 1the overload rate has a direct influence on several parameters such as the cracking speed, the propagation of the crack as well as / maxda dn and / minda dn after applying the overload. 2it can also be concluded that an increase in the overload ratio systematically increases the two peak cracking rate either / maxda dn and / minda dn , which also increases the number of delay cycle. 3we notice a decrease in the slope of the crack propagation curve, this regression is due to the formation of the plastic zone in the vicinity of the crack, the crack will not leave this zone until after a certain number of delay cycles . this regression is due to the formation of the plastic zone in the vicinity of the crack, the crack will not leave this i k. bahram et alii, frattura ed integrità strutturale, 51 (2020) 467-476; doi: 10.3221/igf-esis.51.35 474 zone until after a certain number of delay cycles., that is equal to 5438 cycles for the overload rate equal to 2 and 20,727 cycles for an overload rate of 2.5. 4the difference in the numbers of cycles delay is due to the size of the plastic zone, the one created by the overload rate equal to 2.5 is greater than that created by the overload rate equal to 2, which explains why the crack takes more cycles to get out of this zone to reach the same cracking rate before the application of the overload. figure 6: evolution of the cracking rate and crack propagation as a function of the number of cycles for an overload rate (τ = 2.5). conclusion and perspectives ollowing this study, which was conducted to predict the fatigue behavior of aluminium 2024t351 used in aircraft construction, and in light of the results presented, it can be concluded that: the application of a simple overload affects several parameters, such as the cracking rate, crack propagation and the number of delay cycles. whatever the load ratio 0.1.0.5 or 0.7, after applying the overload. the cracking rate increases until it reaches a maximum value / maxda dn , then it decreases until it reaches a minimum value / minda dn , then it begins to increase gradually until it reaches its initial value before application of the overload. the overload rate has a major impact on the number of delay cycles, increasing the overload rate increases the number of delay cycles. the overload rate is also the parameter responsible for the size of the plastic zone, increasing this parameter increases the size of the plastic zone which greatly increases the number of delay cycles this modest work has allowed us to better understand the influence of overloads on the propagation of fatigue cracks, for future work may be considered such as: study the influence of the application of blocks of overloads, or underloads or both handsets together. proceeded to a comparative study between different models which describe the delay. study repair structures by patch under a variable load references [1] ricardo, l. c. h and miranda, c. a. j, (2016). crack simulation models in variable amplitude loading-a review, frattura ed integrita strutturale, 10(35), pp. 456-471, doi: 10.3221/igf-esis.35.52. f k. bahram et alii, frattura ed integrità strutturale, 51 (2020) 467-476; doi: 10.3221/igf-esis.51.35 475 [2] benachour, m., benguediab, m., and benachour, n. (2013). notch fatigue crack initiation and propagation life under constant amplitude loading through residual stress field, in advanced materials research,682(2013) , pp. 17-24. doi: 10.4028/www.scientific.net/amr.682.17. [3] mahmoud, s. and lease, k. (2004). two-dimensional and three-dimensional finite element analysis of critical crack-tipopening angle in 2024-t351 aluminum alloy at four thicknesses, engineering fracture mechanics, 71(9), pp. 1379-1391. doi: 10.1016/s0013-7944(03)00167-x. [4] papasidero, j., doquet, v., and mohr, d. (2015). ductile fracture of aluminum 2024-t351 under proportional and nonproportional multi-axial loading: bao–wierzbicki results revisited, international journal of solids and structures, 69 (70), pp. 459-474, doi: 10.1016/j.ijsolstr.2015.05.006. [5] fitzka, m. and mayer, h. (2016). constant and variable amplitude fatigue testing of aluminum alloy 2024-t351 with ultrasonic and servo-hydraulic equipment, international journal of fatigue, 91(2), pp. 363-372, doi: 10.1016/j.ijfatigue.2015.08.017. [6] henkel, s., liebelt, e., biermann, h. and ackermann, s., (2015). crack growth behavior of aluminum alloy 6061 t651 under uniaxial and biaxial planar testing condition, frattura ed integrità strutturale, 9(34), doi: 10.3221/igf-esis.34.52. [7] moreno, b., martin, a., lopez-crespo, p., zapatero, j., and dominguez, j., (2016). estimations of fatigue life and variability under random loading in aluminum al-2024t351 using strip yield models from nasgro, international journal of fatigue, 91(2), pp. 414-422, doi: 10.1016/j.ijfatigue.2015.09.031. [8] wang, d.q., zhu, m.l. and xuan, f.z. (2017). crack tip strain evolution and crack closure during overload of a growing fatigue crack, frattura ed integrità strutturale,11(41), pp. 143-148, doi: 10.3221/igf-esis.41.20. [9] gates, n.r., fatemi, a., iyyer, n. and phan, n. (2016). fatigue crack growth behavior under multiaxial variable amplitude loading, frattura ed integrità strutturale, 10(37), pp. 166-172, doi: 10.3221/igf-esis.37.23. [10] rodopoulos, c.a. and kermanidis, a.t. (2007). understanding the effect of block overloading on the fatigue behaviour of 2024-t351 aluminium alloy using the fatigue damage map, international journal of fatigue,29(2), pp. 276-288, doi: 10.1016/j.ijfatigue.2006.03.008. [11] maligno, a.r, citarella, r., and silberschmidt, v.v. (2017). retardation effects due to overloads in aluminium-alloy aeronautical components, fatigue & fracture of engineering materials & structures, 40(9), pp. 1484-1500, doi: 10.1111/ffe.12591. [12] zhang, l., gao, q., ma, s. and tong, d. (2018). analysis of crack growth retardation after single overload based on fem simulation and corpus model prediction, in iop conference series: materials science and engineering . 28– 29 december 2017, shanghai, china. [13] elber, w. (1971). the significance of fatigue crack closure, in damage tolerance in aircraft structures, ed: astm international, pp230-242. doi: 10.1520/stp26680s. [14] wheeler, o.e. (1972). spectrum loading and crack growth, journal of basic engineering, 94(1), pp. 181-186, doi: 10.1115/1.3425362. [15] willenborg, j., engle, r. and wood, h. (1971). a crack growth retardation model using an effective stress concept, air force flight dynamics lab wright-patterson. doi: 10.0000/apps.dtic.mil/ada956517. [16] hutchinson, j. (1968) singular behaviour at the end of a tensile crack in a hardening material, journal of the mechanics and physics of solids,16(1), pp. 13-31, doi: 10.1016/0022-5096(68)90014-8. [17] rice, j., (1967) mechanics of crack tip deformation and extension by fatigue, in fatigue crack propagation, ed: astm international, pp.247-311, doi: 10.1520/stp47234s. [18] rice, j. and rosengren, g.f., (1968) plane strain deformation near a crack tip in a power-law hardening material, journal of the mechanics and physics of solids, 16(1), pp. 1-12, doi: 10.1016/0022-5096(68)90013-6. [19] forman, r.g. and mettu, s.r. (1990). behavior of surface and corner cracks subjected to tensile and bending loads in ti-6al-4v alloy, nasa technical memorandum id:19910009960. [20] newman, j.j. (1984) a crack opening stress equation for fatigue crack growth, international journal of fracture, 24(4), pp. 131-135, doi: 10.1007/bf00020751. nomenclature r : stress ratio.  effr : effective load ratio. k. bahram et alii, frattura ed integrità strutturale, 51 (2020) 467-476; doi: 10.3221/igf-esis.51.35 476 min effk : effective minimum stress intensity factor.  mink : minimal values of the stress intensity factor during a cycle.  maxk : maximum values of the stress intensity factor during a cycle. 0a : crack length. 0a : initial crack length. ia : crack length. , c n : material constants of fatigue crack growth. /da dn : fatigue crack growth rate. / maxda dn : maximum speed /da dn after applying the overload. / minda dn : minimum speed /da dn after applying the overload.  : describes the state of constraint.  pick : maximum value of stress intensity factor at the application of overload. critk : critical stress intensity factor. picr : maximum value of load ratio at the application 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/pdfxoutputintentprofileselector /documentcmyk /preserveediting true /untaggedcmykhandling /leaveuntagged /untaggedrgbhandling /usedocumentprofile /usedocumentbleed false >> ] >> setdistillerparams << /hwresolution [2400 2400] /pagesize [612.000 792.000] >> setpagedevice microsoft word numero 9 art 11 finale z.h. qian et alii, frattura ed integrità strutturale, 9 (2009) 105 112; doi: 10.3221/igf-esis.09.11 105 fatigue failure of welded connections at orthotropic bridges z.h. qian, d. abruzzese university of rome “tor vergata”, department of civil engineering, rome (italy) riassunto. le piastre ortotrope sono state applicate ai ponti di grande luce a partire dal periodo immediatamente successivo alla seconda guerra mondiale a causa dei numerosi vantaggi che esse presentano, come il peso contenuto, l'elevata resistenza, il ridotto numero di connessioni con l'impalcato, la durabilità, la rapidità costruttiva e l’economia dovuta alla manutenzione durante il ciclo di vita. lo studio della fatica nelle piastre ortotrope è iniziato circa venti anni fa, da quando sono state diagnosticate le prime rotture per fatica. da allora sono stati condotti un vasto numero di studi e indagini, ottenendo risultati interessanti. si è scoperto che la maggior parte delle rotture per fatica si verificano in corrispondenza delle connessioni saldate, ovvero le giunzioni rib-to-deck, rib-to-diaphragm, e rib-to-diaphragm-to-deck (plate) (rddp). questa tipologia di connessioni è sensibile alla nascita di fratture per fatica dovute agli accumuli di tensione ed alle tensioni residue nelle connessioni saldate. in questo articolo viene presentato e analizzato un caso studio di rottura a fatica nelle connessioni saldate, dove è più probabile una frattura, attraverso una modellazione numerica di una piastra ortotropa con un software ad elementi finiti (fe). inoltre viene affrontato il tema del miglioramento delle tecnologie adottate per limitare i problemi di fatica. i risultati di queste analisi possono rappresentare un proficuo contributo per la progettazione a fatica delle piastre ortotrope. abstract. orthotropic decks were applied to the long span bridges after world war ii due to several advantages, such as light weight, high strength, few deck joints, durability, rapid construction, life-cycle economy. the fatigue problem of orthotropic decks was realized twenty years ago since fatigue failure was found. in the past two decades large amount of studies and investigations were carried out and fruitful achievements were obtained. it was found that most of the fatigue cracks were occurred at the welded connection details, such as rib-to-deck plate, rib-to-diaphragm, and rib-to-diaphragm-to-deck plate (rddp). these connections are sensitive to fatigue cracking due to high concentrated stress and residual stress at welded connections. in this paper practical fatigue failure cases at the welded connections, ease to occur fatigue cracking, are presented, and analyzed through a numerical modeling of orthotropic deck via fe (finite element) software. furthermore, the improvement technologies of fatigue are also discussed. the results of the analysis can be contributed to the evaluation of the fatigue design for the orthotropic deck. keywords. fatigue failure; welded connection; orthotropic deck; numerical modeling; rib-to-deck plate connection. introduction atigue cracking is a common problem in steel structures for a long time due to the existing of welded connections. according to the practical cases, most of fatigue failures occurred at welded components since high residual stress and inherent defects existed [1]. since from 1960 a number of bridge structures in america and europe have experienced fatigue cracking which sometimes results brittle fractures, fatigue problem in steel bridges has been started to be investigated for many years and produced fruitful achievements. f http://www.gruppofrattura.it/ http://dx.medra.org/10.3221/igf-esis.09.11&auth=true z.h. qian et alii, frattura ed integrità strutturale, 9 (2009) 105 112; doi: 10.3221/igf-esis.09.11 106 from the british standard bs5400 is one of the most important specifications in the last century [2], and recently, some new specifications or standards were accomplished, such as eurocode3 (2004) [3] and aashto (2005) [4]. these specifications provide a mass of information to design steel bridges. among of these, eurocode 3 and aashto already have some specific guidelines to orthotropic deck bridges. s-n curves in eurocode 3, for fatigue design, are shown in fig. 1. figure 1: fatigue strength curves for direct stress ranges (eurocode3, 2004). the orthotropic deck is consisted by a deck plate supported in two mutually perpendicular directions by transverse diaphragms (or crossbeam) and longitudinal stiffeners (or ribs). it is effectively an orthogonal anisotropic (orthotropic) deck. orthotropic deck is widely utilized for long span bridges in recent decades with the development of computing methodologies and fabricating technologies. it was first used in germany after the second world war in order to reduce the construction material, since steel being in short. nowadays, orthotropic deck bridges are very popular in europe, particular in germany. meanwhile, more and more orthotropic bridges are being built in china, japan, u.s.a., and other countries. orthotropic deck has many advantages, main of one is the light weight, high strength, few deck joints, durability, rapid construction and life-cycle economy. however, fatigue problem is unavoidable at orthotropic deck bridges due to the complex structure and the large number of welded connections. fig. 2 shows a summary of welded connection details at orthotropic deck bridges [5]. it is obvious that most of these are potentially liable to cause fatigue cracking taking account into concentrated stress and residual stress in welded connections. in the past years various technologies were studied to improve the fatigue performance of welded joints. the fatigue life can be increased through surface treatment, reducing residual stress as well as optimizing design of structure. among of these, peening, as a cold treatment technology, is one of the most widely utilized in engineering, bringing better surface properties and producing beneficial compressive stress [6]. both of them can improve the fatigue strength of welded connections. this last technology is still highly improving. figure 2: main welded connections in a typical orthotropic bridge deck (gurney, 2006) http://www.gruppofrattura.it/ http://dx.medra.org/10.3221/igf-esis.09.11&auth=true z.h. qian et alii, frattura ed integrità strutturale, 9 (2009) 105 112; doi: 10.3221/igf-esis.09.11 107 in this paper, the fatigue failures at orthotropic deck bridges are discussed based on the previous investigations. the sensitive connection details to fatigue cracking, rib-to-deck plate, rib-to-diaphragm and rib-to-diaphragm-deck plate, are emphasized through practical cases and numerical analysis. furthermore, the three improvement techniques, shot peening, fluid bed peening (fbp) and ultrasonic impact treatment (uit) are detailed presented. this study aims to contribute to the design and reinforcement of orthotropic deck bridges. rib-to-deck plate connection ib-to-deck plate connections are submitted to local transverse bending moments and are therefore susceptible to fatigue cracking. the connections have been studied for a long time, particular in recent years. fig. 3 shows fatigue cracking at rib-to-deck plate connection [7]. the fatigue tests to rib-to-deck plate connection were carried out by janss in 1980 in belgium [8]. thirty-three small test specimens were manufactured and tested at a frequency of 4hz. figure 3: fatigue cracks at rib-to-deck plate connection (xiao, 2008). through the investigation, it was concluded that the stress range at two million cycles of the transverse stresses at the weld toe in the rib is equal to 80 n/mm2 when trapezoidal ribs with a thickness of 6mm are welded to deck plates with a thickness of 12mm and the gap between the rib and the deck plate does not exceed 0.5mm. the stress range (80 n/mm2), mentioned above, is certainly a lower limit due to the poor quality of the welds of the test pieces. based on the investigations of janss and the others, ecsc research carried out on the optimization of the welding procedure (automatic welding) and the influence of a gap, 0 or 2mm, between the rib and the deck plate [9]. the specimens used in the ecsc experiments were welded with automatic submerged arc welding in an industrial situation. it was found that full penetration welds with a lack of penetration less than 1mm can nearly be achieved without edge preparation. meanwhile, the fatigue strength significantly increases when using submerged arc welding, which allows larger penetration and larger throat of the weld. with the development of the compute technology, more and more numerical studies are put into practice. finite element analysis (fea) provides more results to details compared to the traditional method, such as p-e method. stress distributions of three different loadcases at the deck plate were shown in fig. 4 [10]. from the figure, two obvious differences can be concluded. the first one is that the range of high stress is much different, and loadcase1 is larger than the other two. the second one is that both maximal and minimal stresses of loadcase2 and loadcase3 are much higher than loadcase1. the stresses far from the vehicle appear like waves due to the restriction of longitudinal ribs, and are almost zero. another important point should be noted is that the peak stresses of all these there different loadcases produced near or exactly at the rib-to-deck plate connections. for loadcase1, symmetrical loading, both maximal and minimal stress are exactly at the connections, while for loadcase2 and loadcase3, asymmetrical loading, the maximal stresses are produced at the middle of the rib and maximal negative stresses occur at the rib-to-deck plate connections. this can explain why plenty of fatigue cracks occur at this position in laboratory tests and actual projects. submodel based on the global fe model is necessary to obtain the accurate results to the fatigue design. welded joints are not considered in global numerical model, therefore, a submodel is needed to describe the weld geometry influence to orthotropic deck. in comparison, few researches are carried out on the submodel analysis of the rib-to-deck plate connection [7, 11]. high compressive stresses are resulted in the weld toe and root regions, which is due to the large local load used and the abrupt geometry transition modeled in the linear elastic fea. this analysis may be useful for practical r http://www.gruppofrattura.it/ http://dx.medra.org/10.3221/igf-esis.09.11&auth=true z.h. qian et alii, frattura ed integrità strutturale, 9 (2009) 105 112; doi: 10.3221/igf-esis.09.11 108 design when choosing the detail geometry, the structural material and the welding technique and requirements. fig. 5 shows a submodel of rib-to-deck plate connection with a crack [11]. figure 4: stresses at the center deck plate of the middle span (abruzzese et al., 2008) rib-to-diaphragm connection ib-to-diaphragm connection is one of the most complex joint in the orthotropic deck. cutout has a significant influence to the stress performance at the diaphragm, especially the area near the cutout. the previous investigations have demonstrated that peak stresses occur at the rib-to-diaphragm connections easily due to concentrated influence. numerical as well as experimental work at ecsc research showed a reduction of the stress concentration at the edges of cutout by increasing the notch radius of cutout [12]. after investigating different continuous types of rib-to-diaphragm connection of railway bridges in the laboratory, haibach et al. proposed a new shape of cutout for rib passing through diaphragm [13], and it is applied in eurocode3 (2004). fatigue tests were carried out at delft university of technology by kolstein et al [14]. the results demonstrated that fatigue life of the continuous rib-to-diaphragm connection without cutout resulted in a longer fatigue life than the connection with cutout. furthermore, the fatigue life of the rib-to-diaphragm connection with additional cutouts is strongly affected by high shear stresses in the diaphragm. it was presented as well that besides quality aspects the durability of the rib-to-diaphragm connection is mainly restricted, due to shortcomings in design with respect to the underestimation of high shear forces (out-of-plane stress). atlss research center of lehigh university has investigated the fatigue performance at cutout more than 10 years, particularly at rib-to-diaphragm connection [15, 16]. both field measurements and laboratory tests were carried out to williamsburg bridge and bronx-whitestone bridge in new york city under supervision of fisher. from the long term remote monitoring of the williamsburg bridge orthotropic deck diaphragm, it is found that a number of stress cycles exceed the constant-amplitude fatigue limit for category c, which was found to be applicable to the rib-to-diaphragm welded joint at the cutouts. meanwhile, both in-plane and out-of-plane stresses were studied in atlss researches. it is inplane stress, not out-of-plane stress, dominant the stress range at diaphragm. however, out-of-plane bending can influence the fatigue behavior of rib-to-diaphragm connection significantly. fe method was used to analyze the influence of cutout geometry (with bulkhead) to welded rib-to-diaphragm connections by connor [17]. parameters considered included overall cutout shape, cutout depth, diaphragm plate thickness, and deck plate thickness. results of this study indicate that larger cutout geometries offer less resistance to out-of-plane displacements induced by longitudinal ribs rotations. however, cutouts that are excessively deep will increase in-plane stresses at the welded rib-to-diaphragm r http://www.gruppofrattura.it/ http://dx.medra.org/10.3221/igf-esis.09.11&auth=true z.h. qian et alii, frattura ed integrità strutturale, 9 (2009) 105 112; doi: 10.3221/igf-esis.09.11 109 connection. fig. 6 shows cracks in weld options at/near rib-to-diaphragm connections of the williamsburg bridge and the bronx-whitestone bridge [18]. based these investigations, the stresses at rib-to-diaphragm connections (without bulkhead) under different loadcases to diverse shapes of cutout were studied [19]. the numerical analysis clearly demonstrated that different load locations influence the stress status of diaphragm greatly, and peak stresses occur at the rib-to-diaphragm connections or rib-todiaphragm-deck plate (rddp) connections, see fig. 7. figure 5: fe model of submodel analysis (kiss, 2002). figure 6: cracks in weld options at near rib-to-diaphragm connection (tsakopoulos, 2005). figure 7: stress distribution at diaphragm (abruzzese et al., 2008). rib-to-diaphragm-to-deck plate (rddp) connection n recent, rib-to-diaphragm-to-deck plate connection is found to be another sensitive place to produce fatigue cracking [10, 20]. based on the numerical analysis, it is found that peak stresses are produced at rddp connections, and as well the out-of-plane stress should be considered to the fatigue design. i http://www.gruppofrattura.it/ http://dx.medra.org/10.3221/igf-esis.09.11&auth=true z.h. qian et alii, frattura ed integrità strutturale, 9 (2009) 105 112; doi: 10.3221/igf-esis.09.11 110 fig. 8 shows that the cracks developed at the rddp detail are not typical root crack opening mechanisms. the practice has been to use normal stress, at the bottom of the deck plate, facing the root, assuming a category d (in aashto). this detail may, in cases of simple beam, be cycled in compression, the question of the rate of propagation of this detail calls for answers, as does the case for a cantilevered deck. fatigue improvement techniques igh tensile residual stress and initial defect exist in as-welded joints in the welded region as a result of the welding process. advanced technology can reduce defects in weld, while a great benefit can be realized if compressive residual stresses are introduced. in general, fatigue improvement methodologies can be categorized as follows: (1) introduce beneficial compressive stress; (2) reduce stress concentration; (3) remove defects in components; (4) increase the rigidity in the connection. a summary of the various improvement techniques are presented in fig. 9. figure 8: fatigue cracks at rddp connection (camo, 2008). traditional peening peening is conventional and economy treatment method to improve the fatigue strength to welded connection. it includes various peening, such as shot peening, hammer peening, needle peening, fluid bed peening, ultrasonic peening, laser peening. among of these, shot peening is most widely studied and applied. the effectiveness of shot peening is affected by many variables, the control of which are cumbersome and impractical, therefore only two parameters are used to specify the process, almen intensity and coverage [21]. the major advantage of shot peening is that it covers area at low cost, however, care must be taken to ensure that the shot size is small enough to reach the bottom of all undercuts and weld inter-pass notches. it was reported by maddox that an increase of 33% in the fatigue strength at two-million cycles of joints with longitudinal attachments and fabricated from 260 and 390 mpa yield strength while the improvement was 70% for higher strength qt steels. fluid bed peening (fbp) fbp technique is relatively novel treatment to coat metal substrates, change the surface properties, and induce microstructural changes. specimens in fluid bed machine are kept in a fixed position on the inner bed, are subjected to strikes from abrasive grains driven by the fluid onto their surfaces. the investigations by barletta et al. [22, 23] showed a progressive change in both the surface topography of the metal (roundness, roughness and aesthetic aspect) and in superficial properties (surface hardness, residual stress, density of the dislocations) can be induced. furthermore, progressive smoothing of specimen surface associated with remarkable material removal can be expected, even at low temperature (fig. 10). after fbp treatment the delay of crack initiation and crack propagation can be expected. the investigations showed as well peening time and alternating stresses were the only two important experimental factors. therefore, fbp technique is more ease to control because less operational parameters are demanded. h http://www.gruppofrattura.it/ http://dx.medra.org/10.3221/igf-esis.09.11&auth=true z.h. qian et alii, frattura ed integrità strutturale, 9 (2009) 105 112; doi: 10.3221/igf-esis.09.11 111 figure 9: fatigue improvement techniques. figure 10: surface properties after fbm treatment at different temperature (barletta, 2007). novel techniques ultrasonic impact treatment (uit) and laser shock peening are two new techniques to improve the fatigue life for steel structure. it is revealed by lehigh university that the peak compressive residual stress induced uit exceeded the yield stress of the base material near the sample surface [24]. the depth of compressive stress layer in base metal was 1.5-1.7 mm for uit. the induced compressive residual stresses benefit to increase the threshold value of stress intensity factor range, thk , for fatigue crack initiation and early propagation. laser peening is an emerging surface treatment technology that is an extension of shot peening. compared to shot peening, laser peening indicates a significant increase in fatigue life based on the laboratory tests to the native welded specimens [25]. conclusions his paper reviewed the fatigue failures at welded connections of orthotropic deck, and presented several improvement techniques. stress performance of orthotropic deck is complex due to high concentrated stress, residual stress and out-of-plane stress. the fatigue behaviors of some welded connections are still in the dark, and t http://www.gruppofrattura.it/ http://dx.medra.org/10.3221/igf-esis.09.11&auth=true z.h. qian et alii, frattura ed integrità strutturale, 9 (2009) 105 112; doi: 10.3221/igf-esis.09.11 112 are necessary to carry out further researches. furthermore, more applicable technologies are needful for the fatigue design and the repairing of orthotropic deck. references [1] j.w. fisher. fatigue and fracture in steel bridges. john wiley&sons, (1984). [2] bs5400, steel, concrete and composite bridge–part 10: code of practice for fatigue, (1980). [3] eurocode 3: design of steel structures, part 1.9: fatigue, (2004). [4] aashto lrfd bridge design specifications, (2005). [5] t. gurney. cumulative damage of welded joints. crc press, (2006). [6] l. bertini, v. fontanari, g. straffelini, int. j. of fatigue, 20(10) (1998) 749. [7] z. xiao, k. yamada, s. ya, x. zhao, int. j. of fatigue, 30(8) (2008) 1387. [8] j.janss., j. of constructional steel research, 9 (1988) 147. [9] m.h. kolstein, j. wardenier, j.r. cuninghame, c. beales, a. bruls, e. poleur, s. caramelli, p. croce, j. carracilli, b. jacob, j.s. leendertz, a. bignonnet, le pautremat, h.p. lehrke, welding in the world, 38 (1996) 175. [10] d. abruzzese, z.h. qian. fatigue problems for orthotropic deck bridges. handling exceptions in structural engineering: robustezza strutturale, scenari accidentali, complessità di progetto”;university of rome “la sapienza”, italy: doi: 10.3267/he2008, (2008). [11] k. kiss, l. dunai, computers and structures, 8 (2002) 2321. [12] h. lehrke, iabse: remaining fatigue life of steel structures, ethhonggerberg, zurich, 59 (1990) 133. [13] s.j. maddox. the fatigue behavior of trapezoidal stiffener to deck plate welds in orthotropic bridge decks. trrl report sr96uc, transport research laboratory, crowthorne, (1974). [14] m.h. kolstein, j.s. leendertz, j. wardeenier, nordic steel construction conference, sweden, (1995). [15] w. j. bocchieri, j.w. fisher. williamsburg bridge replacement orthotropic deck as-built fatigue test. atlss report no. 98-04, (1998). [16] r.j., connor, j.w., fisher. results of field measurements on the prototype orthotropic deck on the bronx-whitestone bridge. atlss report no. 04-03, (2004). [17] r.j. connor, j. of the transportation research board, 1892 (2004) 78. [18] p.a. tsakopoulos, j.w. fisher, steel structure, 5 (2005) 211. [19] d. abruzzese, a. grimaldi, z.h. qian, international orthotropic bridge conference, u.s.a. (2008) 256. [20] s. camo, q. ye, r.c. prior, v. pandya, international orthotropic bridge conference, u.s.a., (2008) 573. [21] k.j. kirkhope, r. bell, l. caron, r.i. basu, k.-t. ma. marine structures, 12 (1999) 447. [22] m. barletta, v. tagliaferri. int. j. of machine tools & manufacture, 46 (2006) 271. [23] m. barletta, g. bolelli, s. guarino, l. lusvarghi, progress in organic coatings, 59 (2007) 53. [24] x. cheng, j. w. fisher, h. j. prask, t. gna¨upel-herold, b. t. yen, s. roy. int. j. of fatigue, 25 (2003)1259. [25] o. hatamleh, j. lyons, r. forman, fatigue fract. engng.mater. struct., 30 (2007) 115. http://www.gruppofrattura.it/ http://dx.medra.org/10.3221/igf-esis.09.11&auth=true microsoft word numero_30_art_39 d. tumino et alii, frattura ed integrità strutturale, 30 (2014) 317-326; doi: 10.3221/igf-esis.30.39 317 focussed on: fracture and structural integrity related issues mechanical behavior of a sandwich with corrugated grp core: numerical modeling and experimental validation d. tumino facoltà di ingegneria e architettura, università degli studi di enna kore, cittadella universitaria, 94100 enna (italy) davide.tumino@unikore.it t. ingrassia, v. nigrelli, g. pitarresi, v. urso miano dipartimento di ingegneria chimica, gestionale, informatica, meccanica, università degli studi di palermo, viale delle scienze, 90128 palermo (italy) abstract. in this work the mechanical behaviour of a core reinforced composite sandwich structure is studied. the sandwich employs a glass reinforced polymer (grp) orthotropic material for both the two external skins and the inner core web. in particular, the core is designed in order to cooperate with the grp skins in membrane and flexural properties by means of the addition of a corrugated laminate into the foam core. an analytical model has been developed to replace a unit cell of this structure with an orthotropic equivalent thick plate that reproduces the in plane and out of plane behaviour of the original geometry. different validation procedures have been implemented to verify the quality of the proposed method. at first a comparison has been performed between the analytical model and the original unit cell modelled with a finite element mesh. elementary loading conditions are reproduced and results are compared. once the reliability of the analytical model was assessed, this homogenised model was implemented within the formulation of a shell finite element. the goal of this step is to simplify the fe analysis of complex structures made of corrugated core sandwiches; in fact, by using the homogenised element, the global response of a real structure can be investigated only with the discretization of its mid-surface. advantages are mainly in terms of time to solution saving and cad modelling simplification. last step is then the comparison between this fe model and experiments made on sandwich beams and panels whose skins and corrugated cores are made of orthotropic cross-ply grp laminates. good agreement between experimental and numerical results confirms the validity of the proposed model. keywords. sandwich structures; corrugated core; homogenisation; finite element. introduction omposite sandwiches are a structural solution trying to integrate the advantages of the sandwich concept, high specific flexural rigidity, with those of fibre reinforced polymer (frp) composites, such as lightweight, complex shaping and flexible material assembling [1]. an optimised composite sandwich solution is a potential replacement of thick and heavy monolithic bidimensional structures, and hence an effective lightweight design strategy [2]. therefore c d. tumino et alii, frattura ed integrità strutturale, 30 (2014) 317-326; doi: 10.3221/igf-esis.30.39 318 consideration for composite sandwich panels, both as primary and secondary structures, has been growing in particular in the transport sector [3,4]. this is for instance witnessed by the many recent eu funded projects that have somewhat involved the development of sandwich solutions, some of which comprise: alcas, apoliss, celpact, de-light, enlight, hycoprod, litebus, mid-mod, sandwich, sandcore, [3, 5]. a limitation to this high demand of sandwich solutions, and their more widespread adoption, is the lack of an adequate mechanical characterisation and specific design tools [3]. furthermore, a composite sandwich is subjected to typical damaging of monolythic composites like delamination and debonding of laminated costituents [6-9]. the present study has considered a “structured core” sandwich concept, in which the traditional foam or honeycomb core is replaced or assisted by a corrugated laminate, in general made of the same material of the skin faces (see fig. 1). corrugated-core sandwich concepts with various geometries (the most recurring being the trapezoidal and the sinusoidal shapes) have been proposed since the beginning of the last century [10]. applications have been for many years limited to whole metallic or cardboard structures, and the extension to fully frp solutions dates around the end of last century [1113]. one reason for the special appeal of this class of sandwiches is the improved in-plane crashworthiness and out of plane impact resistance, mainly obtained by the more difficult skin-core debonding due to the generally stronger joining between the corrugated core and the skin faces [14-16]. the behaviour of corrugated sandwiches under transverse concentrated loading, typically poor for traditional foam cored sandwiches, is also significantly improved in many aspects: local indentation, local skin buckling, out-of-plane shear resistance [17,18]. finally, the overall in plane stiffness and strength performances, especially in the corrugation direction, are also significantly improved. these advantages usually come at the expenses of a weight penalty (densities of corrugated cores are generally higher than foam cores), and a more complex manufacturing assembly. another difficulty intrinsic to the adoption of corrugated core sandwiches has been the lack of analytical/numerical tools for the effective prediction of their mechanical response at large scales, essential for designing complex structures (e.g. ships, aircrafts, heavy mass transport structures, etc..). in these cases, a detailed 3d fem representation of the material is obviously far too computationally onerous and time consuming. by considering the periodic nature of the corrugation pattern, a number of works have tackled the problem by trying to homogenise the sandwich material into an equivalent two-dimensional orthotropic continuum material [10]. a structural sub-element of material is first identified as the repeating unit. the mechanical response of this elementary cell, subject to some kinematic conditions, is then reproduced by finding the elastic constants of a continuum plate element able to determine an equivalent response in terms of forces or energies. in general a simplified kirchoff-love plate behaviour is assumed (classical sandwich laminate theory), modified to allow for transverse shear deformation (reisner-midlin plate model). in fact the intrinsic out-of-plane low shear rigidity in sandwiches requires this further modelling effort [19,20]. one of the first homogenisation models, for a corrugated trapezoidal core shape, was proposed by libove et al [21,22]. in these seminal works, some simplifying assumptions are made on the strain behaviour of the corrugated sandwich, such as infinite out-of-plane rigidity (no local indentation and skin face buckling can then be modelled), and transverse sections remaining straight in the deformed configuration, although allowed to rotate with respect to the middle plane (accounting for first order transverse shear deformation). it is noticed that the method outlined in [21,22] considers isotropic material constituents, although the final homogenised element is orthotropic due to the unidirectional orientation of the corrugation (structural ortotropy). following the above-described general approach, several other more or less refined homogeneisation methods have been proposed [10]. a number of works have extended the libove’s approach to different corrugations, obtaining some closedform analytical solutions for specific geometries [23-28]. some other works have proposed a characterisation of the homogenised element by fem simulation of the behaviour of the corrugated sandwich elementary cell [29,30]. a number of works have proposed a plate formulation based on the classical lamination theory [27,31,32], in some cases considering the corrugation as a separate layer from the faces [33]. a few authors have dedicated special effort to improve the modelling of the transverse shear deformation behaviour [34-36]. another more sophisticated analytical approach, still based on the possibility to identify an elementary repeating element of material, is also the “asymptotic expansion homogenisation”, successfully extended to corrugated sandwiches by a number of authors [10,37]. in the present work the classic approach presented by libove et al [21,22] is revised in order to extend it to the use of orthotropic constituent materials. this in order to obtain an homogenisation model for a fully composite corrugated sandwich, where both skin faces and corrugated sheets are made of an orthotropic glass reinforce polymer (grp) material. the core laminate is in particular corrugated along one direction, and presents a trapezoidal shape type geometry with wide crests and troughs that provide the sites for the attachment to the skin faces, realised by a chemical bonding d. tumino et alii, frattura ed integrità strutturale, 30 (2014) 317-326; doi: 10.3221/igf-esis.30.39 319 continuity of the matrix resin. the space between the corrugate and skin laminates is filled by pvc foam, whose main contribution is to strengthen the core grp webs against buckling. the work provides an analytical formulation of the equivalent elastic constants of the homogenised model, which are also compared with those derived by a 3d fem simulation of the elementary sandwich cell. the homogenised model has then been implemented in a typical shell element in ansys. experimental tests have been performed on both beams and panels manufactured in-house by hand lay-up lamination. the beams have been tested in three point bending, along and perpendicular to the corrugation, in order to uncouple the relative bending stiffness. specific loading conditions for the panels have also been implemented in order to reproduce pure torsional and coupled torsional-bending conditions. results from all the experimental evaluations have matched very well the numerical predictions based on the homogenised model. analytical model of homogenisation n fig. 1 left, the geometry of the sandwich considered for the homogenisation is sketched. it can be noted that the core has a trapezoidal shape in the transversal section of the corrugated laminate, symmetric with respect to midplane of the sandwich and constant along x. because of its geometry, the corrugated laminate has an intrinsic orthotropy, in fact in-plane and out-of-plane behaviour changes between x and y direction. homogenisation can be obtained once the unit cell is defined: in fig. 1 middle its transversal section is depicted. it represents the repeated element of the periodic structure of the corrugated core, under the assumption of indefinite length in x. in fig. 1 right the equivalent homogenised cell is depicted: we can consider it as a portion of a thin plate subjected to small deformation which elastic constant must be equal to those of the unit cell with the corrugated core. these constants are: in-plane stiffness (ex, ey, gxy), flexural stiffness (dx and dy) and torsional stiffness (dxy) and shear transversal stiffness (dqx and dqy). the procedure exposed so far is the same as the one in [22] where some basic assumption were made: small deflections, elastic modulus of the equivalent plate in z is infinite, linear segments normal to the mid-plane remain linear but not necessarily normal to the mid-plane because of the shear effect, thickness of the skins small compared to the core, under these assumptions, in [22] expressions of the elastic properties of the equivalent cell were derived from the geometric parameters of the unit cell of the corrugated sandwich, for isotropic materials and symmetric transversal section of the core. in the present work, the limitation of an isotropic material has been removed for both skin and core. two assumptions were added to the ones previously cited and are: skins and core have the same layup, the layup is symmetric. procedure followed to obtain the expressions of the in-plane and out-of-plane stiffness is similar to the one in [22] but with the difference that, due to orthotropy of the laminate, the elastic constants of the material must be defined for the two directions x and y, in particular: ex, ey, xy and gxy. for purposes of the present work, only the out of plane equivalent properties are of interest. in-plane elastic stiffness were obtained too and are reported in appendix for completeness but they don’t play any role in the simulation and tests of the following paragraphs. flexural elastic stiffness are: 2 1 2 x x s x cd e t h e i  (1)     2 2 2 2 2 2 1 2 2 2 2 s c x y s y x s c xy yx s xy yx c xy y s t h i e e t h d e t h i t h i e t h           (2) where ic is the moment of inertia, per unit width, of the corrugation cross section with respect to its mid-plane, and ij are flexural poisson coefficients of the laminate. and for the torsional stiffness: 2xy mxy sd g t h (3) i d. tumino et alii, frattura ed integrità strutturale, 30 (2014) 317-326; doi: 10.3221/igf-esis.30.39 320 at this stage, an analytical homogenized formulation of the transversal shear stiffness has not been obtained yet. for this reason, case studies here analyzed will concern applications where the shear deformation can be neglected (for example because of the presence of a pvc filler in the corrugation). figure 1: axonometric view of the sandwich (left), definition of geometric parameters of the transversal section (middle), homogenised unit cell (right). numerical analyses validation of the analytical model he analytical model of homogenization has been validated with 3d finite element analyses on the unit cell subjected to simple load systems. in fig. 2 loads and boundary constrains used to evaluate entities in eq (1-3) are shown. in particular, in each case a displacement field has been applied to the free section of the unit cell in order to reproduce the deformation occurring by applying a rotation in x or in y or in xy. then, the total reaction force was calculated in correspondence of the constrained section and the stiffness obtained dividing the reaction by the imposed rotation. figure 2: load and constraint schemes to evaluate out of plane stiffness of the sandwich. the model used for simulations is depicted in fig. 3: a mapped mesh is obtained with solid hexaedral elements in apdl ansys [39]. the material model used is linear orthotropic and elastic constants of the material used are summarized in tab. 1, together with main dimensions of the unit cell. figure 3: fem model used to validate the analytical formulation. t d. tumino et alii, frattura ed integrità strutturale, 30 (2014) 317-326; doi: 10.3221/igf-esis.30.39 321 ex [gpa] ey [gpa] gxy [gpa] xy p [mm] f [mm] h [mm] ts [mm] tc [mm] 10 17 1.85 0.1 80 14 24.2 1.11 0.96 table 1: elastic properties of the laminate and geometric parameters of the sandwich. results obtained from the three load and boundary configuration in fig. 2 are given in terms of total reaction to an applied rotation (flexural or torsional). each component of stiffness can be calculated by the ratio between the reaction calculated and the rotation. in tab. 2, analytical results given by the proposed formulation in eq. (1,2,3) are compared with numerical results obtained with fem with this procedure. dx [nmm] dy [nmm] dxy [nmm] analytical eq. (1,2,3) 4.26e6 5.61e6 1.20e6 numerical fem 4.39e6 5.88e6 1.15e6 table 2: comparison between the analytical model and fem method numerical implementation of the analytical model the behavior of a sandwich structure with a corrugate core can be effectively numerically simulated by using suitable finite shell elements that implement the homogenized analytical model. in this way, an equivalent model of the real structure is obtained where only the mid-surface of the sandwich is considered. advantages of this technique with respect to a full 3d model mainly consist in remarkable time saving in modeling and numerical computation. in the present work, the shell99 element of the ansys library has been used [39]. this element has eight nodes with six degrees of freedom each (three displacements and three rotations) and can be customized via the direct definition of its stiffness matrix d that relates the vector of moments m with the vector of curvatures k. this relation is expressed with the following expression: 11 12 13 12 22 23 13 23 33 0 1 1 0 1 1 0 0 2 yx xx xy yx xy yx x x x yx x y y y y xy yx xy yx xy xy xy xy dd m d d d k k d d m d d d k k m d d d k k d                                                              (4) where coupling terms between flexural and torsional behaviour (d13 and d23) are null in a cross-ply layup [38] and where ij are poisson flexural coefficients of the whole sandwich, coming from poisson coefficients of the laminate skins via these expressions [21]: xy xy  and    y yx xy x d d   (5) submatrices a and b of the complete formulation of the stiffness matrix of a laminate are not considered in this work because only out-of-plane behaviour are simulated and symmetrical layups are assumed. experimental tests preparation of samples orrugated core sandwich panels have been prepared using unidirectional glass fiber fabric (with 220 g/m2 unit weight) and polyester resin. from a pvc panel (klegecell® r45 by diab) several prismatic bars with trapezoidal section have been cut off. the presence of the pvc was due both for the manufacturing process and to reduce the possibility of local indentation of the sandwich. sandwich has been assembled following this procedure (see also fig. 4 left for a detailed view): stacking of glass fiber fabrics by hand layup to obtain the bottom skin, positioning of the pvc c d. tumino et alii, frattura ed integrità strutturale, 30 (2014) 317-326; doi: 10.3221/igf-esis.30.39 322 bars to create the open mould for the corrugate, hand lay up of the corrugate onto the mould, positioning of the remaining pvc bars to create the planar surface for the final skin, hand lay up of the upper skin. layup and assembling of the whole sandwich have been finalized within pot-life time of the resin; in this way, all components of the sandwich have been bonded with co-cured joints. it must be remarked that the presence of the pvc filler in the corrugate does not affect the validity of the homogenized analytical model, because its contribution to the flexural and torsional stiffness is negligible. transversal shear stiffness of the sandwich is strongly influenced by the foam but, for the cases studied in the next sections where no shear is present, formulas (1,2,3) and the shell finite element described in sec. 2.2. can be applied. both for skins and for the core the layup used is [90/0/90] where the 0° direction is coincident to the longitudinal direction of the corrugate, defined as x. elastic properties of laminates have been calculated by means of standard characterization tests on unidirectional samples of the type [0n] and [90n]. resulting constants are summarized in tab. 1. from the sandwich panels, beams have been cut off with axes parallel to the x and to the y direction (named as x-type and y-type in the following). in particular, the width of the x-type beams is equal to the width of the unit cell of the corrugated core, see fig. 4 right. both beams and panels have been tested in quasi-static conditions with universal testing machines. figure 4: a sketch of the manufacturing process of the sandwich (left), a picture of a sandwich beam (right). 3.2. experimental validation of the analytical-numerical model at first, basic loading configurations have been chosen in order to maintain uncoupled flexural and torsional terms of the analytical model. in this way, it is easy to measure each component of stiffness of the sandwich and compare it with results previously obtained. for the flexural stiffness dx and dy, three point bending (tpb) tests have been performed on the x-type and y-type beams. to correct the measured data from any spurious contribution of shear deformation, a variable span strategy [1,40] was followed where all the loading data collected are plotted for different span length. the interpolation line of these data can be expressed as: 2 , , 1 1 48 4x y qx y w y mx q l pl d d      (6) where w is the displacement at mid-span (measured at the surface opposite to the loading pin to avoid errors due to indentation [12]), p is the applied load per unit width, l is the span between the supports and dq is the shear stiffness. fig. 5 shows results obtained in the tests for the x-type and the y-type beam at different span length, and fig. 6 shows the test setup. apparent flexural stiffness, ' ,x yd , is given in tab. 3: this entity is calculated from eq. (6) neglecting the term related to shear. it can be noticed that, in this way, the apparent flexural stiffness of the beam varies with the span length and is underestimated with respect to the one obtained analytically and numerically in tab. 2. the interpolation of data in fig. 5 fixes this issue and the stiffness obtained from the slope of the lines ( , 1/ 48x yd m ) are very similar to the ones in tab. 2. concerning torsional stiffness, it must be admitted that it is very difficult to setup such a test for a large sandwich. for this reason, the test we performed in laboratory (called scheme 1) is able to guarantee a torsional-dominant state, especially in the inner part of the sample, but some spurious effects still exist in proximity of supports. the panel is supported by the two opposite ends of one diagonal and is loaded by the two ends of the other diagonal. loading scheme and test setup are shown in fig. 7. from the test, a linear load vs. displacement curve was obtained and its slope was compared with the one obtained with the fem model, using the homogenized shell element, shown in fig. 7 right. results are: 43 n/mm from experiments and 45 n/mm from numerical analysis, confirming the validity of the proposed method. d. tumino et alii, frattura ed integrità strutturale, 30 (2014) 317-326; doi: 10.3221/igf-esis.30.39 323 figure 5: experimental results of the variable span tpb tests on xand y-type sandwich beams. figure 6: experimental setup for the tpb tests. x-type beam span [mm] 620 570 520 470 xd [nmm] qxd [n/mm] ' xd [nmm] 3.9e6 3.8e6 3.7e5 3.57e3 4.43e6 9.96e2 y-type beam span [mm] 721 671 621 571 yd [nmm] qyd [n/mm] ' yd [nmm] 5e6 4.9e6 4.7e5 4.66e3 5.76e6 8.42e2 table 3: results of tpb tests on xand y-type sandwich beams: apparent and corrected values of stiffness. application to coupled mode cases in the cases studied so far, only uncoupled load configurations were analysed. aim of this work is to give a versatile numerical tool able to simulate a complex case where coupling between flexural deformation in x and y direction and torsional deformation can occur. for this reason two cases have been simulated for which no closed form solution exist. both loading schemes depicted in fig. 8 are characterized by the presence of multiple terms in the matrix d. y = 4.70e-09x + 2.51e-04 0.0012 0.0013 0.0014 0.0015 0.0016 0.0017 0.0018 0.0019 0.002 0.0021 200000 250000 300000 350000 400000 w /p l [ m m /n ] l2 [mm2] x-type beam y = 3.61e-09x + 2.97e-04 0.0012 0.0014 0.0016 0.0018 0.002 0.0022 0.0024 300000 350000 400000 450000 500000 550000 w /p l [ m m /n ] l2 [mm2] y-type beam d. tumino et alii, frattura ed integrità strutturale, 30 (2014) 317-326; doi: 10.3221/igf-esis.30.39 324 figure 7: determination of the torsional stiffness: loading scheme 1 (left), experimental setup (middle) and fem model (right). figure 8: loading scheme 2 to couple flexural stiffness in x and y (left) and loading scheme 3 to couple flexural and torsional stiffness (right). in particular, scheme 2 on the left of fig. 8 couples terms dx and dy of the total stiffness matrix. the scheme 3 on the right, loaded in the centre and supported on two opposite vertex, couples flexural and torsional stiffness. this scheme can be considered as the superposition of scheme 1 (torsion dominated) and scheme 2 (x plus y flexion dominated), when the total load applied in scheme 1 is a half of the one applied to scheme 2. panels have been tested and slopes of the load vs. displacement curves evaluated. same loading schemes were applied to the fem model in fig. 7 right and the slope of loading curves calculated. results for loading scheme 2 are: 380 n/mm from experiments and 400 n/mm from numerical analysis. for loading scheme 3 are: 108 n/mm from experiments and 107.5 n/mm from numerical analysis. in tpb tests on xand ytype beams, it was noted how transversal shear can play important role, especially when dealing with not particularly slender samples, as panels tested in this work. in numerical analyses performed to obtained results in sec. 3.2. and 3.3, to take into account of transversal shear deformation, a complete formulation of the shell element was used where terms dqx and dqy were added. this entities were calculated from tpb tests on the beams and reported in tab. 3. conclusions he present work develops an analytical homogenisation model of the behaviour of a fully composite sandwich panel with a corrugated, trapezoidal shaped, core. the model is based on the reduction of the sandwich elementary cell unit, representative of the sandwich corrugation pattern, to a thick plate subject to small deformations, according to the approach proposed by libove et al. [21,22]. an extension of the treatment in [21,22] is in particular proposed, able to consider the intrinsic ortotropy of the sandwich constituent elements, i.e. skin faces and corrugated laminate, when these are made of symmetric frp laminates of equal thickness and lay-up. the present analysis has considered only the analytical evaluation of the flexural and torsional rigidities of the homogenised element, and the implementation of this formulation into a shell element of the ansys library. the compliance of the analytical homogenised model has been directly compared to the response obtained by a purely numerical three-dimensional model of the elementary sandwich cell. the values of the elastic constants obtained by the numerical simulation have resulted in good agreement with the analytical predictions. a number of experimental coupled and decoupled flexural and torsional tests have been performed on beam and panel sandwich elements, specifically designed in order to determine the experimental out-of-plane compliance response of the sandwich. all tests have indicated a significant influence of the transverse shear deformation component, indicating that the out-of-plane shear rigidity cannot be neglected. in the present work an experimental evaluation of the shear rigidity t d. tumino et alii, frattura ed integrità strutturale, 30 (2014) 317-326; doi: 10.3221/igf-esis.30.39 325 was obtained from the flexural tests of the beam samples, performed at various span values. adding the transverse shear rigidity in the formulation of the shell element has allowed the homogenised model to well predict all the experimental results. a number of future developments are then identified in order to complete the potentialities and effectiveness of the presented homogenised model. these developments comprise: the analytical formulation of the transverse shear rigidity; the experimental validation of the membrane behaviour of the homogenised model; the extension of the model to cases where the skin and core laminates have different lay-ups. appendix in-plane elastic stiffness of the sandwich can be stated as follows:  * 2x x s ce e t a  (a.1)     * * * *2 2 2 2 2 2 mx my s s c y x s x c x xy yx s c my s xy e e t t a e e t e a e t a e t          (a.2) where ac is the area, per unit width, of the corrugation cross section, * ij are in-plane poisson coefficients of the laminate. references [1] zenkert, d., an introduction to sandwich construction, london, chameleon press, (1995). [2] davies, j.m., lightweight sandwich construction, wiley-blackwell, (2001). [3] mangino, e., carruthers, j., pitarresi, g., the future use of structural composite materials in the automotive industry, int j veh des, 44(3-4) (2007) 211-32. [4] ingrassia, t., alaimo, g., cappello, f., mancuso, a., nigrelli, v., a new design approach to the use of composite materials for heavy transport vehicles, international journal of vehicle design, 44 (3-4) (2007) 311-325. [5] http://www.transport-research.info/web/, (2014). [6] tumino, d., cappello, f., simulation of fatigue delamination growth in composites with different mode mixtures, journal of composite materials, 41(20) (2007) 2415-2441. [7] tumino, d., zuccarello, b., fatigue delamination experiments on gfrp and cfrp specimens under single and mixed fracture modes, procedia engineering, 10 (2011) 1791-1796. [8] pitarresi, g., alessi, s., tumino, d., nowicki, a., spadaro, g., interlaminar fracture toughness behavior of electronbeam cured carbon-fiber reinforced epoxy-resin composites, polymer composites 35(8) (2014) 1529-1542. [9] spadaro, g., alessi, s., dispenza, c., sabatino, m.a., pitarresi, g., tumino, d., przbytniak, g., radiation curing of carbon fibre composites, radiation physics and chemistry, 94(1) (2014) 14-17. [10] ye z, berdichevsky vl, yu w. an equivalent classical plate model of corrugated structures, int j solids structures, 51(11-12) (2014) 2073-2083. [11] richardson, m.o.w., robinson, a.m., eichler, k. and c. moura branco, c., mechanical behaviour of a new stress dissipating composite sandwich structure, cellular polymers, 13 (1994) 305-317. [12] found, m.s., robinson, a.m., carruthers, j.j., the influence of frp inserts on the energy absorption of a foamcored sandwich panel, composite structures, 38(1-4) (1997) 373-381. [13] http://cordis.europa.eu/result/rcn/25868_en.html, (2014). [14] torre, l., kenny, j.m., impact testing and simulation of composite sandwich structures for civil transportation, composite structures, 50(3) (2000) 257-267. [15] pitarresi, g., carruthers, j.j., robinson, a.m., torre, g., kenny, j.m., ingleton, s., velecela, o., found, m.s., a comparative evaluation of crashworthy composite sandwich structures, composite structures, 78(1) (2007) 34-44. [16] jin, f., chen, h., zhao, l., fan, h., cai, c., kuang, n., failure mechanisms of sandwich composites with orthotropic integrated woven corrugated cores: experiments, composite structures, 98 (2013) 53-58. [17] pitarresi, g., amorim, j., indentation of rigidly supported sandwich beams with foam cores exhibiting non-linear compressive behaviour, journal of sandwich structures and materials, 13(5) (2011) 605-636. d. tumino et alii, frattura ed integrità strutturale, 30 (2014) 317-326; doi: 10.3221/igf-esis.30.39 326 [18] rejab, m.r.m., cantwell, w.j., the mechanical behaviour of corrugated-core sandwich panels. composites part b: engineering, 47 (2013) 267-277. [19] carlsson, l.a., kardomateas, g.a., structural and failure mechanics of sandwich composites, springer, 2011. [20] noor, a.k., burton, w.s., bert, c.w., computational models for sandwich panels and shells, appl mech rev., 49(3) (1996) 155-199. [21] libove, c. and batdorf, s.b., a general small-deflection theory for flat sandwich plates, naca tn 1526, 1948. [22] libove, c. and hubka, r.e., elastic constants for corrugated-core sandwich plates, naca tn 2289, 1951. [23] briassoulis, d., equivalent orthotropic properties of corrugated sheets, computers and structures, 23(2) (1986) 129138. [24] fung, t.c. and tan, k.h., shear stiffness for z-core sandwich panels, journal of structural engineering, 124(7) (1998) 809-816. [25] lok, t.s. and cheng, q.h., elastic stiffness properties and behavior of truss-core sandwich panel, j struct eng, 126(5) (2000) 552–559. [26] chang, w.s., ventsel, e., krauthammer, t. and john, j., bending behavior of corrugated-core sandwich plates, composites structure, 70 (2005) 81-89. [27] zangani, d., robinson, m., gibson, a.g., torre, l., holmberg, j.a., numerical simulation of bending and failure behaviour of z-core sandwich panels, plastics, rubber and composites, 36(9) (2007) 389-395. [28] xia, y., friswell, m., flores, e.s., equivalent models of corrugated panels, int j solids struct, 49(13) (2012) 1453– 1462. [29] samanta, a., mukhopadhyay, m., finite element static and dynamic analyses of folded plates, eng struct, 21(3) (1999) 277–287. [30] biancolini, m.e., evaluation of equivalent stiffness properties of corrugated board, composite structures, 69(3) (2005) 322-328. [31] aboura, z., talbi, n., allaoui, s., benzeggagh, m.l., elastic behavior of corrugated cardboard: experiments and modeling, composite structures, 63(1) (2004) 53-62. [32] talbi, n., batti, a., ayad, r., guo, y.q., an analytical homogenization model for finite element modelling of corrugated cardboard, composite structures, 88(2) (2009) 280-289. [33] bartolozzi, g., baldanzini, n., pierini, m., equivalent properties for corrugated cores of sandwich structures: a general analytical method, composite structures, 108(1) (2014) 736-746. [34] nordstrand, t., carlsson, l.a., allen, h.g., transverse shear stiffness of structural core sandwich, composite structures, 27(3) (1994) 317-329. [35] isaksson, p., krusper, a., gradin, p.a., shear correction factors for corrugated core structures, composite structures, 80(1) (2007) 123-130. [36] bartolozzi, g., pierini, m., orrenius, u., baldanzini, n., an equivalent material formulation for sinusoidal corrugated cores of structural sandwich panels, compos struct, 100 (2013) 173–185. [37] buannic, n., cartraud, p., quesnel, t., homogenization of corrugated core sandwich panels, composite structures, 59 (2003) 299-312. [38] agarwal, b.d., broutman, l.j., analysis and performance of fiber composites, john wiley, 1980. [39] ansys documentation, release 10.0. [40] astm c393, standard test method for flexural properties of sandwich construction, american society for testing material, (1994). microsoft word numero_26_art_4 s. agnetti, frattura ed integrità strutturale, 26 (2013) 31-40; doi: 10.3221/igf-esis.26.04 31 strength on cut edge and ground edge glass beams with the failure analysis method stefano agnetti department of engineering, university of perugia, italy stefano.agnetti@gmail.com abstract. the aim of this work is the study of the effect of the finishing of the edge of glass when it has a structural function. experimental investigations carried out for glass specimens are presented. various series of annealed glass beam were tested, with cut edge and with ground edge. the glass specimens are tested in four-point bending performing flaw detection on the tested specimens after failure, in order to determine glass strength. as a result, bending strength values are obtained for each specimen. determining some physical parameter as the depth of the flaw and the mirror radius of the fracture, after the failure of a glass element, it could be possible to calculate the failure strength of that. the experimental results were analyzed with the lefm theory and the glass strength was analyzed with a statistical study using two-parameter weibull distribution fitting quite well the failure stress data. the results obtained constitute a validation of the theoretical models and show the influence of the edge processing on the failure strength of the glass. furthermore, series with different sizes were tested in order to evaluate the size effect. sommario. il lavoro presentato ha lo scopo di valutare la resistenza di elementi in vetro. il vetro, materiale elasto-fragile per la sua struttura chimica amorfa, raggiunge la rottura in modo improvviso per valori di resistenza piuttosto dispersi a causa della presenza dei difetti sui bordi del vetro. sono stati eseguiti test a flessione su quattro punti su elementi in vetro float con differenti finiture superficiali, per valutare l’influenza della lavorazione dei bordi sulla resistenza. sono state testate alcune serie di elementi con bordi tagliati e altre con bordi molati. solitamente la rottura di un elemento in vetro avviene a partire del difetto di maggiore grandezza, nella zona maggiormente sollecitata. grazie alla lavorazione dei bordi si riesce a ridurre l’ampiezza dei difetti, che, sebbene di minore grandezza, sono ugualmente presenti nel vetro. la resistenza del vetro è stata determinata attraverso la teoria della meccanica della frattura lineare e mediante l’analisi post-rottura della superficie da cui si genere la frattura. l’analisi sperimentale ha permesso di valutare l’efficacia della finitura dei bordi in termini d’incremento della resistenza del vetro e la validazione dei modelli per la determinazione della resistenza. keywords. edge strength; fracture mechanic; glass flaw; grinding; size effect. introduction or hundreds of years, glass has been used as windows in buildings, while research on structural applications of glass has only just begun. in recent years, the knowledge on glass properties has expanded, bringing to light new ways of using glass, such as full transparent construction. due to transparent nature of glass, it is used in multiple ways by f http://dx.medra.org/10.3221/igf-esis.26.04&auth=true http://www.gruppofrattura.it s. agnetti, frattura ed integrità strutturale, 26 (2013) 31-40; doi: 10.3221/igf-esis.26.04 32 engineers and architects and today the research is further advancing at the field of studying glass properties both in structural aspects and in relation to building technology, energy and light. but glass is a challenging material due to its brittle feature. in order to use glass safely in structural applications, knowledge about its strength is required. the presence of the flaw in glass causes the failure [1]. the fracture mechanics shows how the failure depends on the depth of the flaw, on the number of them and also on the stress corrosion (called static fatigue in literature) [2]. the stress corrosion causes subcritical crack growth in glass. the crack propagation phenomenon occurs in glass when it is exposed to tensile stress and humidity. the particular flaw that produces the fracture is generally called the critical flaw. the processing of the edge of structural glass is studied; the edge has an important role to determine the failure. indeed the finishing of the edge could remove in part the flaws or in other case it could produce other micro-cracks, without nobenefit for the strength of the glass [3]. the most important type of edge processings object of study [4] are grinding and polishing the strength of the glass can be evaluated through the fracture surface analysis: determining some physical parameter as the depth of the flaw and the mirror radius of the fracture after the failure of a glass element, it could be possible to calculate the failure strength of that [5]. for this evaluation, it was tested a group of glass element, in bending. it results that the edge processing has an influence on the failure strength of the glass. fracture mechanics theory lass is an elastic material with a brittle behaviour at failure. therefore linear elastic fracture mechanics (lefm) is an ideal theory to model its behaviour. in fact, glass was the material used for the development of the basis of lefm. in lefm, mechanical material behaviour is modeled by looking at cracks. if we think at glass, as a material without flaws and defects, its resistance would be very high. but it doesn’t occur in practice because of the presence of the flaws. this phenomenon is explained by lefm theory. according to the stress analysis conducted of an elliptical cavity in a uniformly stressed plate, the local stresses about a sharp notch or corner could raise to a level several times higher than the applied stress. it thus became apparent that even submicroscopic flaws might be potential sources of weakness in solids. introducing the concept of the stress intensity factor (sif), expressed to evaluate the failure, glass element fails when this value reaches the critical value kic. the general relationship between the stress intensity factor ki, the nominal tensile stress normal to the crack’s plane σn, a correction factor y, and some representative geometric parameter a, in general the crack depth or half of the crack length, is given by: k y a i n   (1) the fracture toughness kic, also known as the critical stress intensity factor, is the sif that leads to instantaneous failure. kic is a constant value and is also called fracture toughness. values kic are available in literature, for soda-lime glass it is 0.75 mpa m1/2. from lefm is possible obtaining the failure stress form the measure of the depth of the flaw, as shown in [6] and [7]. stress corrosion glass is noted for its chemical inertness and general resistance to corrosion; therefore, it is used in the chemical industry and in the laboratory when chemical inertness is required. despite this well-known property, glass is extremely susceptible to stress corrosion cracking caused by water in the environment. this phenomenon is known in the glass literature as static fatigue or delayed failure. the susceptibility of glass to stress corrosion cracking was observed noting a time delay to failure and a loading rate dependence of strength. this effect is an activated process caused by water in the environment. static fatigue of glass results from the growth of small cracks in the surface of glass under the combined influence of water vapor and applied load. actually, glass is time dependent if it is in presence of humidity (only in vacuum it is time-independent). stress corrosion causes flaws to grow slowly when they are exposed to a positive crack opening stress. a glass element stressed below its momentary strength (e.g. the static load) will still fail after the time necessary for the most critical flaw to grow to its critical size at a particular stress level. g http://dx.medra.org/10.3221/igf-esis.26.04&auth=true http://www.gruppofrattura.it s. agnetti, frattura ed integrità strutturale, 26 (2013) 31-40; doi: 10.3221/igf-esis.26.04 33 a kinematic relationship between crack velocity v and stress intensity factor ki exists and it is commonly used for glass lifetime prediction. for values of ki close to the critical value of kic (that represents the glass toughness), v is independent of the environment and the crack propagates very rapidly (for soda lime silica glass is about 1500 m/s). in the v-ki logarithmic-curve, v0 represents the position and n is its slope. below certain threshold stress intensity kth no crack growth occurs. the value of v0 and n parameters are discussed by haldimann [1], for laboratory condition, v0 can be assumed equal to 0.01 mm/s, instead it is 6 mm/s in environmental condition. the parameter n is assumed 16. according to the theory of fracture mechanics, glass failure stress was defined using stress intensity factor ki. this equation is only valid in testing conditions where stress corrosion could be eliminated. if the subcritical crack growth is considered, the crack propagates as a function of loading time. this approach is presented by haldimann [1], in which the crack velocity parameter v0 has the dimension of a velocity, instead n is dimensionless.   2 2 0 0 2 ( ) ( ) n n ntn nn i ic n a t a v k y d n               (2) the same relation can be expressed in terms of the value σ with a static loading time. it is possible to obtain the failure stress σf, knowing the tf (s), i.e. the failure loading time and assuming aci (m) corresponding to the initial crack flaw depth.   1 2 2 0 2 2 ( ) ( ) / n f f n n f ic ci t t n v y k a                (3) until a certain loading time, the inert strength is considered to determine the failure. but with the increase of the loading time, in presence of the stress corrosion, the relation (3) is used to determine the failure strength. the theoretical transition time loading between inert condition and time-depending condition, tref, that could be considered a reference value is obtained by eq. (1) and (3). 0 2 2( ) ref a t n v   (4) it t>tref the strength decreases following (3), instead if t<tref the failure is assumed to follow the inert strength level. fracture surface analysis fractography can bring quantitative information about loading condition at failure. the fracture surface is a source of information to determine the failure condition. fractography of brittle materials is used to determine the origin of failure during strength testing, as in [8] and [9]. in general, this origin can be traced to material inhomogeneities, such as pores and micro-cracks, which occur due to machining (surface defects). fracture features, such as mirror, mist and hackle zones, and crack branching, are formed upon failure. the fracture surface is a mirror zone that forms around the critical flaw, at the cross-section of the failed specimen. under a failure stress, once the critical flaw starts to propagate, mirror boundary hackle lines are created after radiating crack reaches terminal velocity. the failure stress σf, i.e. the maximum principal tensile stress at the fracture origin, was approximately proportional to the reciprocal of the square root of the mirror radius (radius of the mirror/ mist boundary) rm: 1 2/f mr b  (5) where b is a constant value (mpa m1/2), that depends on the material properties. however, limited informations are available about the time-dependency of glass strength in relation to the mirror radius. the relation (5) related to brittle materials, is valid for inert strength values. the time-dependency in glass strength is not taken in consideration in the measurement of the mirror radius. the analysis and interpretation of fracture mirror sizes in brittle materials are given in [5]. fracture mirrors are revealing fractographic markings that surround a fracture origin in brittle materials. the fracture mirror size may be used with known fracture mirror constants to estimate the stress in a fractured component. alternatively, the fracture mirror size may be used in conjunction with known stresses in test specimens to calculate fracture mirror constants. http://dx.medra.org/10.3221/igf-esis.26.04&auth=true http://www.gruppofrattura.it s. agnetti, frattura ed integrità strutturale, 26 (2013) 31-40; doi: 10.3221/igf-esis.26.04 34 the relationship (6), called the crack branching equation, is generally accepted but its application is not always easy because reading the fracture pattern becomes quite complex for high stresses values that produce the failure. the crack branching equation is useful to evaluate the failure stress from the measure both of the mirror radius rm, both of the hackle radius rh, both of the half branching length rb (the subscripts m, h, b, represent respectively the mirror, the hackle and the branch): 1 2/f ar mr     (6) where σar is interpreted as being an apparent residual compressive surface stress and α is a constant value. finally, all three branching constants αm, αh and αb as well as the corresponding apparent residual stresses σar were determined in recent studies, [10], and presented in [2] and summarized in tab. 1. α [mpa m1/2] σar [mpa] mirror 1.98 9.6 hackle 2.11 9.1 branch 2.18 10.7 table 1: parameters of the crack branching equation for annealed glass. size effect the size of the loading area has an influence on the failure stress [11]. this effect can be explained with the weibull theory referring to the fact that a larger panel is more likely to have a large flaw in a high stress region, than small panel [12]. the relation that explains the size effect is: 1 21 2 1 . . eff eff v v           (7) where σ1 and σ2 are tensile stress value for two elements of different sizes, of effective volumes veff.1 and veff.2. the β parameter can be calculated according to weibull fit in en 12603 [13]. in a recent study [14], it was tested the influence of the size effect testing a large number of samples. it is notice that larger elements tend to have a greater probability of larger flaws. the results demonstrate some differences between experimental and theoretical rates of the characteristic strength values, so, it means that the size effect has to be investigated more thoroughly. numerical results ive sets of elements were tested in four points bending test. in tab. 2 the geometrical dimensions, the edge finishing and the number of the samples are shown. sets a and b present the same geometry, but different edge finishing. sets c and d have another size, in which the length is bigger than that of the former series. finally, the size of the samples of set e is the biggest. sets a, c and e present ground edges; instead sets b and d consist of glass beam with only cut edge. the ratio between height, h, and length l, of the elements of the various series is almost constant. the ratio between the load span, sl, and the support span, ss, are almost constant too. b [mm] h [mm] l [mm] edge finishing n° of samples ss [mm] ls [mm] h/l ls/ss set a 8 50 400 ground 25 360 120 49.56 0.33 set b 8 50 400 cut 25 360 120 35.01 0.33 set c 8 50 550 ground 19 500 160 47.41 0.32 set d 8 50 550 cut 18 500 160 109.7 0.32 set e 8 100 1100 ground 20 1000 300 56.94 0.30 table 2: geometrical dimensions, edge finishing and number of the samples for the various sets of glass elements. f http://dx.medra.org/10.3221/igf-esis.26.04&auth=true http://www.gruppofrattura.it s. agnetti, frattura ed integrità strutturale, 26 (2013) 31-40; doi: 10.3221/igf-esis.26.04 35 the specimens were subjected to in-plane four-point bending tests in a universal uts testing machine (fig. 1-a). the specimens were loaded at a stress rate of 0.75 mpa/s ± 0.15 mpa/s. for each sample the failure load pf, the time at failure tf and the maximum displacement in the midspan wf [mm] was collected. the test ends when the beams collapse. the failure stress values or tensile strength value f, were calculated with the following equation: 2 2 32 6 f f p d p d f h bh b        (8) where d [mm] is the distance between the load and the support; b [mm] is the width of the specimen and h [mm] is the height of the specimen. the failure initiated at the loaded area linked to the tensile stresses at the edge, creating a crack opening. the test set-up used is illustrated in fig. 1-b). a) b) figure 1: test set-up used for in-plane four point bending tests (for each sample). the mean results for each set are shown in tab. 3. as first result of the bending tests, it is possible to observe that the mean failure load for series a, having ground edges is higher than the one of series b. instead comparing series c and d, the mean failure load for the set of beams with cut edge is slightly higher than the one with ground edge. the failure happened always in the zone inside the load span: cracks propagate from the tensile zone, at the bottom edge, to the compressive zone, in which the cracks branch out into several branches. the moment at failure was determined by the failure load. pf [n] tf [s] mf [nmm] f [mpa] wf [mm] set a 2290.14 75.54 148859.10 44.24 2.52 set b 1864.60 66.56 121199.26 36.43 2.22 set c 1624.27 50.10 138063.26 40.81 2.09 set d 1925.89 52.77 163700.74 45.65 2.76 set e 3446.28 59.88 603098.64 40.82 2.79 table 3: mean values at failure for each series. observing the various failures, it was possible to identify some particular crack patterns that are frequently presented (fig. 2). the crack pattern depends on the strength of the beams and directly it depends on the flaw measure. beams having bigger strength (the flaws are small) presents more glass fragments, instead beams that collapse in a few number of pieces presents big flaws. the failure happened always in the zone inside the load span: cracks propagate from the tensile zone, at the bottom edge, to the compressive zone, in which the cracks branch out into several branches. http://dx.medra.org/10.3221/igf-esis.26.04&auth=true http://www.gruppofrattura.it s. agnetti, frattura ed integrità strutturale, 26 (2013) 31-40; doi: 10.3221/igf-esis.26.04 36 figure 2: crack patterns of glass beams. as regard the test performed, the experimental results were analyzed with the lefm theory and the glass strength was analyzed with a statistical study using two-parameter weibull distribution fitting quite well the failure stress data. lefm analysis glass specimens were examined using an optical microscope with polarized light after the failure. important information on the flaw sizes, the fracture origin and the fracture mirror sizes were collected. in the following fig. 3-b some examples of fracture surface are presented. it is easy to identify the flaw and the mirror zone (shown in fig. 3-a). a) b) figure 3: illustration of the depth flaw and of the mirror radius. the results of the post-fracture analysis are summarized in tab. 4, where the mean values of the mirror radius and of the flaw depth are presented for each series. it is possible to observe that the ratio between the mirror radius, rm, and the flaw depth, a, is almost constant and it is about 9÷10. the strength σf(tf) is obtained by eq. (3) knowing the measure of the flaw depth, a, the time at failure, tf and the critical value of kic. the value of v0 and n parameters are discussed in [1]; for laboratory condition, v0 can be assumed equal to 0.01 mm/s; the parameter n is assumed 16. the geometry factor, y, is defined as a constant value for various edge crack http://dx.medra.org/10.3221/igf-esis.26.04&auth=true http://www.gruppofrattura.it s. agnetti, frattura ed integrità strutturale, 26 (2013) 31-40; doi: 10.3221/igf-esis.26.04 37 configurations; it is chosen by literature, [1], observing each crack pattern. in tab. 4 the mean values of the strength, σf(tf), the time reference, tref, and the inert strength, σf(tref), are shown, too. rm[mm] a[μm] rm/a σf(tf) [mpa] tref [s] σf(tref) [mpa] set a 2.50 292.4 9.0 52.91 4.18 54.03 set b 3.89 456.1 8.4 45.43 6.52 46.50 set c 2.28 352.5 10.1 50.74 5.04 50.53 set d 2.31 247.1 9.4 50.14 3.53 50.21 set e 2.56 271.5 10.0 55.01 3.88 54.91 table 4: mean values of the failure parameters, failure strength, time reference and inert strength for each series. glass strength was analyzed with a statistical study using two-parameter weibull distribution fitting the failure stress data as presented in [15]. the two parameter weibull function is expressed as: 1( ) exp x g x              (9) where: g(x) means a distribution function of x percentage of failure; θ is a scale parameter in weibull two-parameter distribution; β is respectively a shape parameter. weibull two-parameter probability distribution permits a correct analysis of glass strength. in tab. 5 the two parameter of the weibull distribution are presented. θ β set a 4.161 59.555 set b 9.241 48.014 set c 4.694 55.128 set d 6.639 54.182 set e 3.166 63.726 table 5: parameter θ and β of the weibull two-parameter distribution. the diagram in fig. 4 shows the fitting of the weibull distribution for the series a, under the hypothesis that the specimens contain a random flaw population. the same diagrams were obtained for the other set of beams. the stress values vary largely in the range of 16.24 mpa to 97.35 mpa. the mean stress values vary in a range of 45.43 mpa to 55.01 mpa. the variation was noticed to exist between edge finishing; values of standard deviation vary from 5.5 to 16.4 for the five series of specimens. in order to compare the lefm theory with the failure surface analysis, the parameters for the crack branching equation, α and σar, were determined by a linear regression in the diagram of the failure stresses and the mirror length. the mirror length was measured together with the flaw depth, in the post failure microscopic analysis. the measured length of the mirror was used to evaluate the crack branching eq. and to establish a value for the branching constant. the objective is to compare the constants obtained from this analysis, using a trend line, with the ones proposed by the previous studies (fig. 5). http://dx.medra.org/10.3221/igf-esis.26.04&auth=true http://www.gruppofrattura.it s. agnetti, frattura ed integrità strutturale, 26 (2013) 31-40; doi: 10.3221/igf-esis.26.04 38 figure 4: weibull two-parameter probability distribution for sets a and b. figure 5: diagram of the measure of the mirror length rm (m-1/2) vs. the failure strength σf(tf) for sets a and b. the mean values of the parameters α and σar, calculated using the crack branching eq., are 2.00 and 11.06. these are slightly higher than the ones proposed in tab. 1 for the evaluation of the failure stress from the measure of the mirror radius rm, but they are in accordance with the ones proposed by literature. however, in general the inert strength is higher than the strength at failure time, when stress corrosion is considered. values of the strength at failure time, σf(tf), and values of the inert strength, σf(tref), are obtained and compared in the previous tab. 4. as explained by the theory, inert strength is higher than the strength measured at failure, σf(tf) (tab. 4). stress corrosion law was obtained by the mean values for each series of beams and it was plotted together with the mean strength for each lot of samples in the following fig. 6. figure 6: stress corrosion law for each series of samples. size effect was studied considering sets a and c, having ground edges. larger bodies generate lower mechanical strength values taking into account the higher probability of finding natural heterogeneities (flaws or cracks). in weibull weakest link theory, the ratio between the mean mechanical strength values and the ratio of the effective volumes of the specimens leads to a strength dependency on body size as explained in the relation (7). for the analysis on the size effect for the http://dx.medra.org/10.3221/igf-esis.26.04&auth=true http://www.gruppofrattura.it s. agnetti, frattura ed integrità strutturale, 26 (2013) 31-40; doi: 10.3221/igf-esis.26.04 39 ground edge samples, the results in terms of failure strength show that set e present the greater values, that is higher than the failure strength of sets a and c; for this reason set e was excluded from the analysis. instead the value of σf(tf) for the set a is higher than the one of the set c. in the latter case shorter samples present higher stresses that are what we expect by the theory: only sets a and b were compared. the analysis permits to obtain the same value 1.05 form the ratio of the strength σa/ σc that is equal to the corresponding (veff,c/ veff,a)1/β. conclusions law characterization on glass beams was studied. the experiments performed, confirm the applicability of the failure prediction theories commonly applied to explain the failure strength of glass. each specimen was assumed to fail in mode i (in lefm theory, mode i is a normal-opening, while modes ii and iii are shear sliding modes); the failures initiated inside the loaded area. the analysis and the measurements executed confirm the relation existing between flaw size and strength: the larger the critical flaw initiating the failure, the lower the strength. an equivalent relation is valid for the mirror radius: the larger the mirror radius, the lower the strength. the edge finishing produces advantage in terms of strength. the strength of ground edge glass is higher than the one of simply cut edge glass. the edge processing produces a reduction of the maximum depth of the flaw and an increase of the strength. furthermore it was observed that the failure strength had no linear relation to flaw depth. in analogy, the fracture surface analysis shows that the failure strength had no linear relation to the mirror radius. in the lefm the values of the geometric parameter y, were estimated by observing the fracture surface, in order to obtain the failure strength for each sample. in the fracture surface analysis, constant values α and σar, were confirmed using a linear regression law, fitting the measured data. the observations on the size effect show that the bigger is the length of the beam, the bigger is the probability to find flaws. in general, beams with edge processing, as grinding or polishing is recommended. references [1] haldimann, m., fracture strength of structural glass elements – analytical and numerical modeling, testing and design, phd these n. 3671, epfl, lausanne, switzerland (2006). [2] haldimann, m., luibe, a., overend, m., structural use of glass, structural engineering documents, iabse aipc – ivbh 10 (2010). [3] lindqvist, m., vandebroek, m., louter, c., belis, j., influence of edge flaws on failure strength of glass, in: proceedings of gpd 2011, tampere, finland, (2011) 126-129. [4] vandebroek, m., belis, j., louter, c., van tendeloo, g., experimental validation of edge strength model for glass with polished and cut edge finishing, engineering fracture mechanics, 96 (2012) 480-489. [5] astm c1678-10, standard practice for fractographic analysis of fracture mirror sizes in ceramics and glasses, america society for testing materials (2010). [6] carpinteri, a., meccanica dei materiali e della frattura, pitagora editrice, bologna, (1992). [7] lawn, b.r., fracture of brittle solids. 2nd ed. cambridge: cambridge university press, (1993). [8] dielhof, m. h., dortmans, l. j. m. g. , de with, g., fractography of borosilicate tested in threeand four-point bending glass, journal of the european ceramic society, 12 (1993): 215 220 [9] conoway, j. c., mecholsky, j. j., use of crack branching data for measuring near-surface residual stresses in tempered glass, journal of the american ceramic society, 72 (9) (1989) 1584–1587. [10] zaccaria, m., overend, m., validation of a simple relationship between the fracture pattern and the fracture stress of glass, in: engineered transparency. international conference at glasstec, düsseldorf, germany, (2012). [11] fischer, h., rentzsch, w., marx, r., a modified size effect model for brittle non-metallic materials. engineering fracture mechanics, 69 (2002) 781-791. [12] quinn, g. d., weibull effective volumes and surfaces for cylindrical rods loaded in flexure, journal of the american ceramic society, 86 (3) (2003) 475–479. [13] en 12603:2002, glass in building – procedures for goodness of fit and confidence intervals for weibull distributed glass stength data, cen (2002). f http://dx.medra.org/10.3221/igf-esis.26.04&auth=true http://www.gruppofrattura.it s. agnetti, frattura ed integrità strutturale, 26 (2013) 31-40; doi: 10.3221/igf-esis.26.04 40 [14] vandebroek, m., lindqvist, m., louter, c., belis, j., edge strength of cut and polished glass beams, in: proceedings of gpd 2011, tampere, finland, (2011) 476-479. [15] weibull, w., a statistical theory of the strength of materials, royal swedish institute for engineering research, 151 (1939). http://dx.medra.org/10.3221/igf-esis.26.04&auth=true http://www.gruppofrattura.it microsoft word numero_42_art_8.docx o. krepl et alii, frattura ed integrità strutturale, 42 (2017) 66-73; doi: 10.3221/igf-esis.42.08 66 focused on mechanical fatigue of metals crack onset assessment near the sharp material inclusion tip by means of modified maximum tangential stress criterion ondřej krepl, jan klusák ceitec ipm, institute of physics of materials as cr, žižkova 22, brno 616 62, czech republic krepl@ipm.cz abstract. in the case of particle reinforced composites, where the particles are in a form of sharp material inclusions, singular stress concentration exists on each tip of each inclusion. this is due to the geometric and material discontinuities between matrix and particle. these points of stress concentration are susceptible of crack initiation and thus often responsible for failure of the whole structure. the modified maximum tangential stress criterion is employed in order to predict crack onset conditions. keywords. sharp material inclusion; singular and non-singular stress terms; generalized fracture mechanics. citation: krepl, o., klusák, j., crack onset assessment near the sharp material inclusion tip by means of modified maximum tangential stress criterion, frattura ed integrità strutturale, 42 (2017) 66-73. received: 31.05.2017 accepted: 08.06.2017 published: 01.10.2017 copyright: © 2017 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. introduction omposites find application in a variety of engineering structures. overall excellent properties, which can only be achieved by combination of two or more homogenous materials, bring solution for high demands given by contemporary advanced technologies. however, the very nature of composites also causes a difficulty in their assessment in terms of fracture mechanics. common composite types, i.e. fibre reinforced composites or particle reinforced composites give rise to points of singular stress concentration. these points are found in loci where fibre ends are embedded in matrix or at each tip of each sharp particle and are referred as general singular stress concentrators (gsscs). this paper deals with the case of particle embedded in matrix which is in a form of sharp material inclusion (smi). the strength of singularity in this case is different and lower than in the case of a crack. however, the gsscs are points often susceptible for crack initiation and thus they can be responsible for failure of the whole structure. a thorough understanding of crack initiation conditions in gssc leads to improved estimation of the critical failure load. stress, energy or coupled criteria are commonly used in fracture mechanics analyses of many gssc types such as sharp notches. these criteria can be employed in order to predict crack onset conditions to the case of smi. the gssc characterized by weak singularity often require consideration of higher order non-singular terms of the asymptotic stress series to describe the stress state and thus to receive consistent critical load predictions. suggestion of modified maximum tangential stress stability criterion for the smi with consideration of non-singular terms is the main objective of this paper. c o. krepl et alii, frattura ed integrità strutturale, 42 (2017) 66-73; doi: 10.3221/igf-esis.42.08 67 fracture mechanics of sharp material inclusion he smi is modelled in 2d as a special case of multi-material junction, the bi-material junction [1, 2] as shown in fig. 1. both material regions are considered to consist of linear elastic material and fully described by young’s moduli e1 and e2 and poisson’s ratios ν1 and ν2. the geometry is characterized by the opening angle α. perfect bonding (traction and displacement continuity) is assumed at both interfaces γ0 and γ1. the problem is considered either in a state of plane stress or plane strain. the stress field in the vicinity of bi-material junction tip, i.e. when r  0, is described by following asymptotic series:      1 2 3 11 1 31 21 2 3 2 2 2 ij ij m ij m ij m hh h r f r f r f             (1) where hk is the kth generalized stress intensity factor (gsif) which corresponds to the kth eigenvalue k, that forms the stress singularity exponent (1 – k ). the terms of the series can be either singular, when 0 < (k) < 1 or non-singular when 1 < (k). as r  0 the singular terms become unbounded, while the non-singular terms vanish. fijkm(θ) is the dimensionless angular eigenfunction constructed for ijth component of the stress tensor, kth eigenvalue and mth material as in [2, 10]. note that the series above is in sake of simplicity written for real eigenvalues and real gsifs. such form of the series provides satisfactory description for most of the cases. figure 1: sharp material inclusion model. in majority of the fracture mechanics analyses of gsscs only the singular terms are used for description of stress field [3, 4] and following determination of crack onset conditions. in [5, 6] the effect of first non-singular stress term on stress distribution in case of sharp v-notch is studied. the effect of the first non-singular term in case of bi-material notches is studied in [7, 8]. in [9] klusák et al. have shown the significance of consideration of the first non-singular term in the case of sharp bi-material orthotropic plate. a study which has shown the effect of non-singular terms in the cases of smi has been conducted in [10]. in order to identify singular and non-singular terms for given configuration the dependence of the eigenvalues 1, 2 and 3 of chosen geometric smi cases on young’s moduli ratio e1/e2 is presented in fig. 2. here, material region 1 and young’s modulus e1 belongs to inclusion and the region 2 with modulus e2 corresponds to the matrix. in the case of rectangular smi characterized by  = 90° two singular and one non-singular terms for all e1/e2 ratios are found. in the case of sharper smi with  = 60° there are two singular terms together with one non-singular terms for cases where inclusion is more compliant than matrix, i.e. e1/e2< 1 and one singular term together with two non-singular terms for cases of inclusion stiffer than matrix, i.e. e1/e2>1. the smi with a blunt opening angle of  = 120° shows reverse trend, as the cases of more compliant inclusion have one singular term together with two non-singular terms and cases with stiffer inclusion have two singular together with one non-singular term. t o. krepl et alii, frattura ed integrità strutturale, 42 (2017) 66-73; doi: 10.3221/igf-esis.42.08 68 figure 2: dependence of 1, 2 and 3 on e1/e2 shown for 3 smi geometries  = 60°, 90°, 120°. to predict crack initiation conditions, a modified maximum tangential stress criterion is used. the tangential stress depends on radial distance from the singular concentrator tip. to mitigate the radial distance dependence the mean value can be calculated as:     0 1 , d d m r r d       (2) the parameter d is related to the fracture mechanism, e.g. in case of cleavage fracture it can be set as d = 2 5 × grain size of the material [13]. the criterion states that the crack will initiate in the direction θ0,m of maximum value of mean tangential stress. the extreme value is found as: 0 , 0 , 2 2 0; 0 m m                     (3) let’s consider the first 3 terms (singular and non-singular) of the stress series (1). by averaging it over specific distance d as in (2) and substituting it into eq. (3) we obtain: 31 2 1 2 3 1 2 3 1 2 3 0m m m f f fd d d h h h                     (4) the first gsif h1 is factored out and the consequent ratios are denoted as k1 = hk/h1. equation has now the only unknown, the crack initiation direction θ0,m. 31 2 1 2 3 11 21 31 1 2 3 0m m m f f fd d d                       (5) o. krepl et alii, frattura ed integrità strutturale, 42 (2017) 66-73; doi: 10.3221/igf-esis.42.08 69 in general, global and local extremes can be found in bi-material problem. the crack will be initiated in the direction of maximum of and corresponding minimum value of generalized fracture toughness [14]. note that the crack initiation direction does not depend on the absolute values of gsifs but rather on their ratios k1. the general form of the equation for n terms of the stress series is: 1 1 0 k km k n k k fd          (6) the crack initiation conditions of the smi are described by means of critical stress quantity. in this way, knésl in [13] assesses a stability of v-notch. he proposes comparison of such critical quantity of the crack and the v-notch. since in both cases (crack tip and the v-notch tip) the stress is singular, he supposes that crack initiation mechanism in v-notch will be the same as the crack propagation mechanism. then crack initiation conditions in case of gsscs can be assessed by means of critical average stress ascertained for a crack. for a crack in homogeneous material and loaded in normal mode i, the critical mean tangential stress value is:   icc 0 0 2 2 k d     (7) whereas for the gsif with consideration of first three singular and non-singular terms of the series (1), it is: 31 2 11 1 1c, c, 11 1 21 2 31 3 1 2 32 m m m m m dh f f f dd                      (8) by comparison of the two relations above the generalized fracture toughness h1c,m is: 1 2 3 ic, 1c, 1 1 1 2 2 2 11 1 210, 0, 02 31 3 1 2 , 3 ( ) ( ) ( ) 2 m m m m mm mm k h d f f d f d                    (9) which in general form for n terms of the stress series is written: (10) the generalized fracture toughness h1c,m depends on fracture toughness kic,m of the material m. it is obvious that in case of smi two materials m = 1 and 2 should be considered and possibility of crack initiation into the matrix and into the inclusion should be evaluated. if the value h1c,1 is lower than h1c,2 crack initiation is expected into the inclusion, otherwise it occurs into matrix. in sake of completeness, the case of crack initiation into the interface should be also evaluated. in that case, the value of h1c,interface has to be calculated based on fracture toughness of the interface kic,interface. note that for all the critical values h1c,1, h1c,2, and h1c,interface the shape functions f,m should contain corresponding angle of potential crack initiation 0,m (m = 1, 2, interface). the crack initiation occurs if the following stability criterion is violated (11): (11) crack is not initiated in smi tip if the value of gsif h1 is lower than its critical value. finally, the critical applied load σcrit can be calculated as: ic, 1c, 1 2 1 1 0, 2 ( ) k m m n k k km k m k h d f          1 1c,1 1c,2 1c, interface, ,minh h h h o. krepl et alii, frattura ed integrità strutturale, 42 (2017) 66-73; doi: 10.3221/igf-esis.42.08 70          1c,1 0,1 1c,2 0 ,2 1c, interface 0 1,2 crit appl 1 appl min , , )h h h h          (12) numerical example he smi is modelled by fem in 2d. the model geometry and boundary conditions are shown in fig. 3. the rectangular inclusion with α = 90° in a plane strain conditions is studied. the modelled specimen size is 25 × 25 mm. the model is loaded with unit tension of σappl = 1 mpa. in this numerical example the inclusion more compliant than matrix is considered, which represents sandstone inclusion in cement paste of various stiffness. the modelled bimaterial configurations are listed in tab. 1. the poisson’s ratios are identical for both materials, ν1 = ν2 = 0.2. the eigenvalues λk are determined as a solution of an eigenvalue problem [2, 10]. the gsifs hk are calculated semi-analytically by means of overdeterministic method [2, 10], with resulting values as shown in tab. 1. the diameter which provides inputs (nodal displacements) for gsifs calculation is chosen as r1 = 1 mm. the characteristic length d which corresponds to the fracture mechanism is for the case of cement paste composites chosen as d = 1 mm. fig. 4 shows the tangential stress distribution for the case e1/e2 = 0.5, nevertheless distribution of this kind is characteristic to the cases of inclusion more compliant than matrix in general. the distribution disposes of two extremes, global which is found in the matrix θ0,2 = 180° and local found in the inclusion θ0,1 = 0°. the values of crack initiation angles θ0,m are given by the symmetry of the problem. for the same reason the odd term, the skew related gsif h2 = 0 mpa·m1-λ2. it is necessary to asses potential crack initiation in all possible ways, i.e. in the direction of the global maximum, local maximum and the interface. the crack initiation angle in the latter case is θ0,interface = 45°. in tab. 1 the generalized fracture toughness is calculated for global function extremes, the local one and the interface. the fracture toughness value of matrix, inclusion and the interface is chosen equally, kic,m = 1 mpa·m1/2 for m = {1, 2, interface}. generalized fracture toughness for unit kic,m can be understood as normalized value and in tab. 1 is denoted as *1c,mh . e1 [gpa] e2 [gpa] e1/e2 h1 [mpa·m1-λ1] h3 [mpa·m1-λ3] kic [mpa·m1/2] h*1c,2 [mpa· m1-λ1] h*1c,1 [mpa· m1-λ1] h*1c,interface [mpa· m1-λ1] 20 80 0.25 1.857 -0.014 1 0.618 0.822 1.078 20 60 0.33 1.592 -0.020 1 0.657 0.784 1.149 20 40 0.50 1.310 -0.022 1 0.715 0.765 1.238 20 26.6 0.75 1.114 -0.020 1 0.774 0.782 1.455 table 1: bi-material configurations with resulting gsifs and values of generalized fracture toughness. figure 3: the numerical model. t o. krepl et alii, frattura ed integrità strutturale, 42 (2017) 66-73; doi: 10.3221/igf-esis.42.08 71 it is evident that the stress description (fig. 4) by means of the first and the third stress terms ( 1 3,  ) is more precise than the description by the first stress term only ( 1 ). it can be seen especially in directions θ = 90° and 270° corresponding to regions of lower tangential stresses. the stability criterion employing critical value h1c following from all three stress terms (9), (10) is used. fig. 5 shows results of the values h1 and the critical values h*1c corresponding to crack initiation into matrix, into the inclusion and into the interface. the values h1 follow from fem numerical solution of model with unit loading 1 mpa. the critical values h*1c,m are ascertained for unit fracture toughness kic,m = 1 mpa·m1/2 for m = {1, 2, interface}. particular values h1c,m for given fracture toughness of the matrix, the inclusion and the interface are: * 1c1c, ic,,mm mh kh (13) figure 4: tangential stress distribution for the case e1/e2 = 0.5. yellow and magenta curve stay for the analytical tangential stress solution on r = 1 mm obtained by one term h1 and by two terms h1 and h3 respectively. the cyan curve is the mean tangential stress obtained by two terms h1 and h3. black dots represent the fem solution on r = 1 mm. the yellow vertical lines denote the interfaces and black vertical lines the function local and global extreme. the results show that crack initiation conditions depend on the ratio of materials young's moduli, and on the fracture toughness of material components (matrix, inclusion) and the interface. in the numerical example e1 corresponds to young's modulus of the inclusion. the inclusion here is considered to be a sandstone aggregate with e1 = 20 gpa. corresponding fracture toughness of sandstone is between 0.28 and 0.52 mpa·m1/2. on the other hand, e2 corresponds to young's modulus of matrix. in the numerical example it varies from 26.6 to 80 gpa. the fracture toughness of common hardened cement paste is between 0.1 and 0.8 mpa·m1/2, where higher values of e2 usually match to higher values of kic,2. the fracture toughness of interface can widely vary. in case of silicate based composites it is dependent on the manufacturing process and development of interfacial transition zone. the values h1c,interface are higher than h1c,1 and h1c,2 thus it seems that the crack kink to the interface is not probable, but mind that usually kic,interface is lower than kic,matrix and kic,inclusion. when considering particular values of kic,m for particular ratios e1/e2, the curves of the critical values h1c,m for matrix, the inclusion and the interface will change by multiplying as indicated in (13). thus every particular case will show if crack initiation occurs to matrix, to the inclusion or the interface, i.e. min{h1c,1 , h1c,2 , h1c,interface}. let us note that studied material model is universal. although it supposes sharp concave inclusion embedded in matrix, at the same time it can describe convex corner of stiffer inclusion filled with matrix. in this case e1 would match to matrix and e2 to the inclusion. principally, the approaches will be the same and the results very similar. o. krepl et alii, frattura ed integrità strutturale, 42 (2017) 66-73; doi: 10.3221/igf-esis.42.08 72 figure 5: gsif h1 for unit applied load and the critical values h1c needed for crack initiation to matrix and to the inclusion. conclusions he article deals with generalized fracture mechanics of a crack initiation in a tip of polygonal material inclusion embedded in matrix. stability criterion for determination of crack initiation conditions is proposed by means of average value of tangential stress. the stability criterion is written for stress described by singular and non-singular (higher order) terms. the criterion employing higher order terms is necessary for the assessment of sharp material inclusion, because singular stress terms only do not describe stress state satisfactorily in some material and geometrical configurations. the proposed criterion allows indicating whether crack initiation occurs into matrix, into the inclusion or into the interface. its general form allows such assessment for particular known fracture toughness of the matrix, inclusion or the interface. description of stability of stress concentrators of this kind contribute to better understanding of toughening mechanisms in particle composites. this kind of understanding leads to composite design optimisation or composite structure failure prevention. acknowledgements his research has been financially supported by the ministry of education, youth and sports of the czech republic under the project ceitec 2020 (lq1601). the authors would like to thank the czech science foundation for financial support through the grant 16/18702s. references [1] paggi, m., carpinteri, a., on the stress singularities at multimaterial interfaces and related analogies with fluid dynamics and diffusion, applied mechanics reviews, 61 (2008) 1-22. [2] krepl, o., klusák, j., reconstruction of a 2d stress field around the tip of a sharp material inclusion, procedia structural integrity, 2 (2016) 1920-1927. t t o. krepl et alii, frattura ed integrità strutturale, 42 (2017) 66-73; doi: 10.3221/igf-esis.42.08 73 [3] williams, m.l., stress singularities resulting from various boundary conditions in angular corners of plates in extension. j appl mech,19 (1952) 526–8. [4] seweryn, a., molski, k., elastic stress singularities and corresponding generalized stress intensity factors for angular corners under various boundary conditions, engineering fracture mechanics, 55(4) (1996) 529-556. [5] kim, j.k., cho, s.b., effect of second non-singular term of mode i near the tip of a v-notched crack, fatigue and fracture of engineering materials and structures, 32 (2009) 346-356. [6] ayatollahi, m.r., dehghany, m., nejati, m., fracture analysis of v-notched components – effects of first non-singular stress term, international journal of solids and structures, 48 (2011) 1579-1589. [7] ayatollahi, m.r., mirsayar, m.m., nejati, m., evaluation of first non-singular stress term in bi-material notches, computational materials science, 50 (2010) 752-760. [8] mirsayar, m.m., aliha, m.r.m., samaei, a.t., on fracture initiation angle near bi-material notches – effects of first non-singular stress term, engineering fracture mechanics, 119 (2014) 124–131. [9] klusák, j., hrstka, m., profant, t., krepl, o., ševeček, o., kotoul m., the influence of the first non-singular stress terms on crack initiation direction in an orthotropic bi-material plate, theoretical and applied fracture mechanics, 71 (2014) 67–75. [10] krepl, o., klusák, j., the influence of non-singular terms on the precision of stress description near a sharp material inclusion tip, theoretical and applied fracture mechanics, in press. doi: 10.1016/j.tafmec.2017.03.007. [11] sih, g.c., a special theory of crack propagation, in: g.c. sih (ed.), mechanics of fracture – methods of analysis and solutions of crack problems, noordhoff international publishing, leyden, the netherlands, (1973) xxi-xlv. [12] sih, g.c., mechanics of fracture initiation and propagation, kluwer academic publishing, boston, (1991). [13] knésl, z., a criterion of v-notch stability, int j of fracture, 48 (1991) 79-83. [14] klusák, j. profant, t., knésl, z, kotoul m., the influence of discontinuity and orthotropy of fracture toughness on conditions of fracture initiation in singular stress concentrators, engineering fracture mechanics, 110 (2013) 438–447 << /ascii85encodepages false /allowtransparency false /autopositionepsfiles true /autorotatepages /none /binding /left /calgrayprofile (dot gain 20%) /calrgbprofile (srgb iec61966-2.1) /calcmykprofile (u.s. web coated \050swop\051 v2) /srgbprofile (srgb iec61966-2.1) /cannotembedfontpolicy /error /compatibilitylevel 1.4 /compressobjects /tags /compresspages true /convertimagestoindexed true /passthroughjpegimages true /createjobticket false /defaultrenderingintent /default /detectblends true /detectcurves 0.0000 /colorconversionstrategy /cmyk /dothumbnails false /embedallfonts true /embedopentype false /parseiccprofilesincomments true /embedjoboptions true /dscreportinglevel 0 /emitdscwarnings false /endpage -1 /imagememory 1048576 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/hrv (za stvaranje adobe pdf dokumenata najpogodnijih za visokokvalitetni ispis prije tiskanja koristite ove postavke. stvoreni pdf dokumenti mogu se otvoriti acrobat i adobe reader 5.0 i kasnijim verzijama.) /hun 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/pdfxoutputintentprofileselector /documentcmyk /preserveediting true /untaggedcmykhandling /leaveuntagged /untaggedrgbhandling /usedocumentprofile /usedocumentbleed false >> ] >> setdistillerparams << /hwresolution [2400 2400] /pagesize [612.000 792.000] >> setpagedevice microsoft word numero_30_art_7 f. felli et alii, frattura ed integrità strutturale, 30 (2014) 48-54; doi: 10.3221/igf-esis.30.07 48 focussed on: fracture and structural integrity related issues use of fbg sensors for monitoring cracks of the equestrian statue of bartolomeo colleoni in venice f. felli, a. brotzu, d. pilone, c. vendittozzi dip. icma, sapienza università di roma, via eudossiana 18, 00184 roma, italy ferdinando.felli@uniroma1.it m.caponero enea via e. fermi 45, 00044 frascati, roma abstract. the bartolomeo colleoni monument suffered for years damage from the local climate. the process of restoring the colleoni equestrian statue, started in 2003, allowed to understand how the bronze statue was originally cast and manufactured and the techniques used in its construction. during this process a relevant crack on the right foreleg was investigated in correspondence of the cast-on joining the right foreleg to the front portion of the horse body. the crack was investigated experimentally by fiber bragg grating (fbg) sensors, avoiding any modelling because of the very complex structure of the statue. an array of fbg sensors connected in series was glued on the crack with the aim of capturing live information about the effect of applying stress on the crack opening. the monitoring system was successfully tested during repositioning of the rider on the horse and is available for long term inspection of the crack opening evolution. keywords. fbg sensors; health monitoring; crack monitoring; restoration; colleoni equestrian statue. introduction he bartolomeo colleoni equestrian statue, located beside the scuola grande di san marco in the campo ss giovanni e paolo, was erected in fulfillment of a request made by the mercenary captain before his death in 1475. after switching allegiances several times, in 1457 he was endowed with supreme command of the venetian army by the doge of venice. shortly before his death, colleoni bequeathed a sizable portion of his estate to the republic of venice, with the stipulation that a bronze equestrian monument should be erected in the piazza san marco to perpetuate his memory. the venetian senate honored his request but placed the statue near the scuola grande di san marco rather than in piazza san marco. andrea del verrocchio won the commission for the colleoni statue in a competition. contests for public art commissions were frequent in fifteenth-century italy. in fact, sponsors hoped to obtain not only the best, but also the most efficient designs. the bartolomeo colleoni monument is among the best-known works of verrocchio, that was a teacher of leonardo da vinci. verrocchio died in 1488, before finishing the work, and the statue was finished by alessandro leopardi in 1495. t f. felli et alii, frattura ed integrità strutturale, 30 (2014) 48-54; doi: 10.3221/igf-esis.30.07 49 the bartolomeo colleoni monument suffered from years of neglect and damage from the local climate. in 2003 the world monument fund began the cleaning and restoring of the equestrian statue that was subjected to the last major conservation work in 1919 [1]. the process of restoring the colleoni monument allowed to understand how the bronze statue was originally cast and manufactured and the techniques used in its construction. these studies give a historical insight into the practice of skilled foundrymen and the technologies used for manufacturing big statues. considering the impressive size of the statue, verrocchio decided to use the lost-wax casting method for manufacturing different parts of the monument that would be subsequently joined by means of the cast-on method [2] used by the fifteenth century foundrymen to join two different castings. therefore the equestrian monument of bartolomeo colleoni, that weighs about 6000 kg, is composed of 14 different castings (8 for the horse and 6 for the rider). as far as the horse is concerned the single cast parts were: 1) right foreleg, 2) left foreleg; 3) right hind leg, 4) left hind leg, 5) front portion of the body; 6) rear portion of the body, 7) head, 8)tail. the cast-on method has to join the different parts in such a way that they fit closely and that joints are strong enough to support the monument weight. in fact the huge weight of the statue stands on a pedestal where three horse’s hoofs are placed at the vertexes of a slender triangle. during the restoration work of the colleoni equestrian statue a system of fbg sensors has been applied for long-term structural health monitoring of a crack in the right foreleg [3-5]. the system allowed to verify the structural stress during sensor calibration performed by applying a mechanical stress on the riderless horse and during the rider repositioning [6,7]. fbgs are basically optical strain gages but offer several advantages over the conventional ones. the most interesting characteristics for the applications under concern are the possibility to multiplex dozens of them within the same fiber and the long term stability. one of the processes commonly used for the production of fbg is that one of using coherent uv light illuminating transversally the fiber. the interference pattern can be produced with a phase mask positioned just above the optical fiber. the result of the irradiation is the production of a periodic fluctuation of the index of refraction (called bragg grating) in the longitudinal direction of the fiber core. the property of the fbg is to reflect a specific wavelength called bragg wavelength λb if some broad-band light propagates along the optical fiber. since the value of λb is affected by strain according to a predictable relationships, measuring λb allows measuring the strain of a structure to which the fbg has been attached with adequate structural contact [8,9]. crack monitoring by means of fbg sensors n the right foreleg in correspondence of the welding seam an extended crack affects almost the whole section of the thigh (fig. 1). in some places the crack branches into two or more paths. this crack was probably formed already during the welding seam cooling, in fact it is possible to find in it shrinkage cavities. the reinforcement of the right foreleg with an internal iron bar (fig. 2) suggests that leopardi had already identified this crack. figure 1: macrograph showing the crack in the right foreleg of the horse. figure 2: detail of the internal part of the horse right foreleg showing the iron bar used as a reinforcement. o f. felli et alii, frattura ed integrità strutturale, 30 (2014) 48-54; doi: 10.3221/igf-esis.30.07 50 the monument repair by means of welding was not recommended considering that welding could have a negative impact on the monument with unforeseeable consequences. for that reason the crack has been monitored by means of fbg sensors that should allow to evaluate the crack criticality and to check the crack propagation over the years. obviously this methodology can be used only if sensors are left on the statue and appropriately hidden. the measurements were performed using four fbg sensors, in particular three were used for structural monitoring and one was used for compensating the effect of temperature. the measurement method set up has been done in several stages. in a first stage needed to evaluate the method reliability, three sensors were glued in correspondence to the crack. one of them was used for compensating the effect of temperature. the sensor system has been tested and calibrated via measurement campaigns carried out by applying controlled thermal and mechanical stresses. in a second stage four fbg sensors arranged in series were glued in correspondence to the crack on the right foreleg by means of m-bond ae10. the array of sensors has been realised and positioned as shown in fig. 3. figure 3: fbg sensor system. fig. 4 shows the sensor array and highlights that the sensor with a wavelength centered at 1533 nm is about 20 cm away from the crack. two sensors were glued in correspondence of the same areas selected for the previous ones. the sensors’ system has been realized as shown in fig. 3 and glued on the horse right side as highlighted in fig. 4. figure 4: fbg sensor positions. measurements made by applying forces measured by a dynamometer n order to carry out tests, load was applied by a dynamometer. fig. 5 shows the points where the load was applied and measured by a dynamometer. on the right side of the horse, the load was applied in correspondence of points a, b, c, d and l while on the left side it was applied in correspondence of points h, g, f, e and i that are arranged symmetrically with respect to the previous ones. the last measurements were made while repositioning the rider on the horse (fig. 6). i f. felli et alii, frattura ed integrità strutturale, 30 (2014) 48-54; doi: 10.3221/igf-esis.30.07 51 results and discussion raphs of the tests performed with the dynamometer are reported below. fig. 7 shows the graphs, in arbitrary units, of the deformations detected by the sensors as a function of the time of application of a load of about 500 n (green line). these graphs were obtained in preliminary tests performed by using the first array of sensors and by applying loads only in the points a, b and d. graphs show concavities which arise as load is first applied and then removed: when load is applied, the signal either increases if the crack opens (positive deformation) or decreases if the crack closes (negative deformation); when the load is removed, the crack goes back to its initial configuration (no deformation) and the signal goes back to zero. tests highlighted the good response of the sensors showing that when load is applied on the points a and b the crack closes (compression) while the application of a load on the point d produces an area subjected to compression and an area subjected to tension. fig. 8 shows the graphs of the second array of sensors, always in arbitrary units. they highlight again the deformations detected by the sensors but in this case, as indicated in the figures, the load trend is represented by the blue curve. figure 5: points of load application. figure 6: repositioning of the rider on the horse. figure 7: deformation detected by sensor 1541 (white line) and by sensor 1545 (red line) when load (green line) is applied in correspondence of points a, b and d. g f. felli et alii, frattura ed integrità strutturale, 30 (2014) 48-54; doi: 10.3221/igf-esis.30.07 52 figure 8: deformation detected by sensor 1541 (white line), sensor 1549 (red line) and sensor 1557 (green line) when load is applied in correspondence of points a, b, c, d, e, f, g, h, i and l. the load trend, measured by a 500 n dynamometer, is described by the light blue line. it should be immediately pointed out that the most stressed crack area was on the front of the horse where the sensor 1557 is located. by moving towards the rear of the foreleg deformations are significantly reduced (sensor 1541). a further important information can be gathered considering the points of load application and distinguishing those on the right (l, a, b, c, d) from those on the left (i, h, g, f, e) of the horse. the points are taken from the front to the rear of the horse. when loads are applied on the right side the crack always closes. the only exception is the position d, at the extreme rear of the horse, where the load application determines the crack front opening. when loads are applied on the left side of the horse the crack opens predominantly on the front (sensor 1557). even in this case by applying the loads in the posterior areas of the horse (f and e) the rear part of the crack behaves differently and closes (sensor 1541). in conclusion measurements have shown good sensitivity and good reproducibility as revealed by the good comparability between measurements performed with the first and the second array of sensors. the sensors for the temperature measurements followed the daily temperature. the temperature range was not wide because the measurements were performed during the restoration when the horse was inside a special encasement built around it. for that reason the horse was not exposed to direct sunlight or to the night rigour. in any case, during the tests the temperature was almost constant. the plot in fig. 9 shows the trend of the crack deformation during the repositioning of the rider. it highlights an important opening of the crack always in the front area where the sensor 1557 is located. the crack does not deform in his central area (sensor 1549), while it closes in the posterior part of the foreleg (sensor 1541). in 2006 the monument restoration was completed but the crack monitoring over time was not possible because of logistical and bureaucratic problems. for this reason the results of this research have been published after several years. in any case a photographic reconnaissance carried out after 4 years in the area in which the sensors were positioned showed that the sensors detached from the metallic surface (fig. 10). this suggests that more efforts must be devoted to the study of sensors’ bonding and coating in order to ensure long lasting bond [8, 9]. f. felli et alii, frattura ed integrità strutturale, 30 (2014) 48-54; doi: 10.3221/igf-esis.30.07 53 figure 9: data acquired during the rider repositioning by means of sensor 1541 (white line), sensor 1549 (red line) and sensor 1557 (green line). figure 10: macrograph showing the sensor detached from the metallic surface. conclusions n important crack was present in the weld area of the right foreleg of the horse of the equestrian statue of bartolomeo colleoni in venice. this crack was monitored during the monument restoration with an innovative technique based on fbg sensors. this technique has proved to be reliable and repetitive and showed very well crack opening or closure according to the stresses applied in different areas of the horse. it was possible to measure in real time the crack deformation while repositioning the rider on the horse. the obtained data highlighted that the crack was not critical. as far as the continuous monument monitoring is concerned some bureaucratic, technical and logistical difficulties arose. especially the sensors’ gluing and coating durability over time is a considerable problem. in future research efforts should be made to increase their durability with the aim of making the proposed technique reliable over time. acknowledgments he authors would like to thank dr. morigi for his contribution to this research. references [1] http://www.wmf.org/project/bartolomeo-colleoni-monument a t f. felli et alii, frattura ed integrità strutturale, 30 (2014) 48-54; doi: 10.3221/igf-esis.30.07 54 [2] morigi, l., ridolfi, s., study of the quaternary alloysin the cast of the equestrian statue of bartolomeo colleoni by andrea del verrocchio (venice 1480) availing of edxrf systems, in: 9th int. conference on ndt of art, jerusalem, israel, (2008) 1-9. [3] felli, f., paolozzi, a., saviano, g., caponero, m.a., pastorelli, l., non destructive monitoring of cultural heritage using fiber optic sensor, in: c. parisi, g. buzzanca, a. paradisi (eds). in: 8th int. conf. on "non-destructive investigation and microanalysis for the diagnostics and conservation of the cultural and environmental heritage", brescia, (2005) 1-11. [4] paolozzi, a., camerlingo, p.c., felli, f., some application of fbg sensors from aeronautics to cultural heritage, in: the 14th materials and processing conference (m&p2006), tokyo, the japan society of mechanical engineers, 06-56 (2006) 297-298. [5] vendittozzi, c., felli, f., brotzu, a., saviano, g., caponero, m.a., impiego dei sensori fbg per il monitoraggio strutturale di beni di interesse storico artistico. in: igf xxi, cassino, (2011) 101-119. [6] brotzu, a., felli, f., paolozzi, a., caputo, l., passeggio, f., gaeta, s., use of fiber optic sensors for monitoring crack growth in fatigue and coorsion-fatigue tests, in: v. agarwala, f. bellucci, m. montuori, j. ippolito, corrosion in the military ii, trans tech publications ltd, zurich, 38 (2008) 155-160. [7] felli, f., brotzu, a., impiego di sensori in fibra ottica per il monitoraggio di fratture statiche e dinamiche. in: problematiche di frattura nei materiali per l'ingegneria, aspetti teorici e risvolti applicativi, gruppo italiano frattura, forni di sopra udine, (2010) 193-205. [8] brotzu, a., felli, f., fiori, l., caponero, m.a., characterization of both adhesion and interfacial interaction between optical fiber coating and structural adhesives, smart structure and systems, 4 (2008) 439-448. [9] brotzu, a., caponero, m.a., felli, f., polimadei, a., vendittozzi, c., saviano, g., valutazione della resistenza di incollaggi per sensori fbg per il monitoraggio strutturale. in: igf xxi, cassino, (2011) 191-200. vibration control in buildings under seismic excitation using optimized tuned mass dampers youtube aboutpresscopyrightcontact uscreatorsadvertisedeveloperstermsprivacypolicy & safetyhow youtube workstest new features© 2022 google llc microsoft word numero_41_art_53.docx s.m.j. razavi et alii, frattura ed integrità strutturale, 41 (2017) 424-431; doi: 10.3221/igf-esis.41.53 424 notched graphite under multiaxial loading s.m.j. razavi, m. peron, j. torgersen, f. berto department of mechanical and industrial engineering, norwegian university of science and technology (ntnu), norway javad.razavi@ntnu.no, mirco.peron@ntnu.no, jan.torgersen@ntnu.no, filippo.berto@ntnu.no abstract. cylindrical specimens made of polycrystalline graphite and weakened by circumferential v-notches under mixed mode i/iii loading were studied in this research. different geometries of v-notches varying the notch opening angle and the notch tip radius were tested. appling various ratios of tensile and torsion loads, the multiaxial static tests have been conducted. averaged strain energy density (ased) criterion previously presented by the same authors is employed here for the case of tension and torsion loadings applied in combination. the fracture behavior of the tested joints under multiaxial loading has been successfully predicted using the ased criterion. keywords. isostatic polycrystalline graphite; mixed mode i/iii; v-notch; strain energy density. citation: razavi, s.m.j., peron, m., torgersen, j., berto, f., notched graphite under multiaxial loading, frattura ed integrità strutturale, 41 (2017) 424-431. received: 15.05.2017 accepted: 23.05.2017 published: 01.07.2017 copyright: © 2017 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. introduction ue to its good compromise between thermal and mechanical properties, isostatic graphite is widely used in various industrial applications. a bulk number of the components made of graphite is subjected to loads transferred by the other parts of the structure. according to this fact, numerous researches have been devoted to the fracture assessment of graphite. considering the brittle behavior of this material, brittle fracture is a typical failure mechanism which usually happens after the initiation of micro-cracks in the most stressed parts of the structure, combined in some cases with a negligible amount of plasticity [1-4]. the majority of the studies focused on structural integrity of graphite components have been devoted to the investigation of cracked components by quantifying the fracture toughness under prevalent mode i loading [5-7]. innovative techniques have been proposed in the literature for fracture assessment of isotropic graphite under mode i loading [8-10]. although the brittle fracture of graphite components has been studied continuously for several years, only few predictive models are available for the fracture behavior of cracked components. reviewing the published papers in the field of fracture behavior of graphite components reveals that only a limited number of researches are focused on the notch sensitivity of graphite components including the researches conducted by bazaj and cox [8] and kawakami [9]. the fracture behavior of blunt notches has been studied in the past years by researchers, who have investigated the case of pure mode i loading and in-plane mixed mode loading [11-18]. due to the lack of information about the multiaxial behavior of graphite components in the literature, the authors aimed to investigate the static behavior of isostatic graphite subjected to multiaxial loadings which can be applied as a d s.m.j. razavi et alii, frattura ed integrità strutturale, 41 (2017) 424-431; doi: 10.3221/igf-esis.41.53 425 combination of tension and torsion with different values of the mode mixity ratios (i.e. the ratio between the tensile stress and the applied stress due to torsion loading): 0.4, 0.5 and 1.0. considering a large variety of geometrical configurations obtained by varying the notch opening angle, notch radius and notch depth, a complete set of experimental data on cylindrical specimens subjected to combined tension and torsion loads was provided by the authors in previous paper [23]. the notch opening angle has been varied from 30° to 120° and the notch radius from 0.3 to 2 mm. the ased criterion which is based on the strain energy density averaged over a control volume [19-25] is used for fracture assessment of notched samples subjected to the multiaxial static loading. the ased criterion allows a sound fracture assessment of the critical load for the specific material under investigation and it can be potentially extended to other types of graphite and brittle materials subjected to different combinations of mode i and mode iii loading conditions. in the current paper, first the experimental procedure for testing the notched graphite samples is presented. afterward, the formulation and application of the ased criterion is presented on the experimental data. fracture experiments he details of the graphite material, the test specimens and the fracture experiments are presented in this section. the fracture tests were conducted on a grade of isostatic polycrystalline graphite with commercial name of eg022a. the basic material properties of the tested graphite are as follows: the mean grain size is of 300 μm, the porosity of 15%, the bulk density of 1830 kg/m3, the mean tensile strength of 30 mpa, the young’s modulus of 8.00 gpa and the shear modulus of 3.30 gpa. nonlinear deformation sometimes is observed during fracture tests of graphites, which makes the determination of young’s modulus rather complicated. however, for simplicity the young’s modulus was obtained in this research from load-displacement graphs recorded by a universal tension-compression machine. the deviation observed from linear behaviour was less than 0.01% at failure for the specimen used in the test. young’s modulus has been measured at a load where the deviation from linear behaviour was less than 0.005%. the mean grain size was given in the material certify and measured by using the sem technique while the density of the material was determined from the buoyancy method, submerging the tested graphite in a liquid of known density. the values have been checked and confirmed by the authors independently. all tests were performed under displacement control on a servo-controlled mts bi-axial testing device (100 kn/ 1100 nm,  75 mm/ 55°). the load was measured by a mts cell with ± 0.5 % error at full scale. a mts strain gauge axial extensometer (mts 632.85f-14), with a gage length equal to 25 mm was used for measuring the tensile elastic properties on plain specimens while a multi-axis extensometer mts 632.80f-04 (with a gage length equal to 25 mm) was used for measuring the torsional elastic properties on unnotched specimens. some load-displacement curves were recorded to obtain the young’s modulus (e) of the graphite using an axial extensometer. the tensile strength (σt) was measured by means of axis-symmetric specimens with a net diameter equal to 12.5 mm and a diameter of 20 mm on the gross section (see fig. 1a). due to the presence of a root radius equal to 40 mm, the theoretical stress concentration factor is less than 1.03. the torque-angle graphs recorded by the mts device were employed together with the bi-axis extensometer to obtain the shear modulus (g) and to measure the torsion strength (τt) of the tested graphite. the ultimate shear strength τt was found to be equal to 37 mpa. 60 6080 p    2  40  plain specimens v-notched specimens (a) (b) figure 1: geometry of plain (a) and notched (b) specimens used in the experimental tests. t s.m.j. razavi et alii, frattura ed integrità strutturale, 41 (2017) 424-431; doi: 10.3221/igf-esis.41.53 426 as shown in fig. 1, different round bar specimens were used for multiaxial (tension and torsion) static tests: unnotched specimens (fig. 1a) and cylindrical specimens with v-notches (fig. 1b). this allows us to explore the influence of a large variety of notch shapes in the experiments. in more detail:  for v-notched graphite specimens with a notch opening angle 2α = 120° (fig. 1b), notches with four different notch root radii were tested; ρ = 0.3, 0.5, 1 and 2.0 mm. the effect of net section area was studied by changing the notch depth p. two values were used, p = 3 and 5 mm, while keeping the gross diameter constant (20 mm).  for v-notched graphite specimens with a notch opening angle 2α = 60° (fig. 1b), four different notch root radii were considered in the experiments: ρ = 0.3, 0.5, 1.0 and 2.0 mm. with a constant gross diameter (20 mm), also the net section area was kept constant, such that p = 5 mm.  for v-notched graphite specimens with a notch opening angle 2α = 30° (fig. 1b), three different notch root radii were considered in the experiments: ρ= 0.5, 1.0 and 2.0 mm keeping constant the notch depth p = 5 mm. at least three samples were prepared for each of the 15 specimen geometries described above, with a total number of 45 specimens. in order to prepare the specimens, first several thick plates were cut from a graphite block. then, the specimens were precisely manufactured by using a 2-d cnc cutting machine. before conducting the experiments, the cut surfaces of the graphite specimens were polished by using a fine abrasive paper to remove any possible local stress concentrations due to surface roughness. the tests were conducted under three different combinations of tensile and torsional stresses, with the nominal mode mixity ratios σnom/τnom = 0.4, 0.5 and 1. different nominal mode mixity ratios have been achieved by properly setting the torsional loading rate with respect to the tensile loading rate. in particular the tensile loading rate was varied keeping constant the rotation control conditions with a loading rate of 1°/min. the load-angle curves recorded during the tests always exhibited an approximately linear trend up to the final failure, which occurred suddenly. therefore, the use of a fracture criterion based on a linear elastic hypothesis for the material law is realistic. the same trend has been observed for the tensile curves plotting the load as a function of the axial displacement. all loads to failure (tensile load and torque) are reported in tabs. 1-3 for each notch configuration and loading conditions. in particular tab. 1 reports the data for σnom/τnom = 1 while tabs. 2 and 3 summarize the data for the two ratios 0.4 and 0.5, respectively. specimen code notch opening angle 2α (°) notch radius ρ (mm) tensile load (n) torque (n mm) σnom (mpa) τnom (mpa) σnom/τnom 1-01 120° 0.3 1193 2659 15.19 13.54 1.12 1-02 1025 2280 13.05 11.61 1.12 1-03 1114 2500 14.18 12.73 1.11 2-01 0.5 1190 2690 15.15 13.69 1.10 2-02 1234 2631 15.71 13.40 1.17 2-03 1200 2694 15.28 13.72 1.11 3-01 1 1302 2873 16.58 14.63 1.13 3-02 1251 2673 15.93 13.61 1.17 3-03 1283 2845 16.34 14.49 1.13 4-01 2 1497 3798 19.06 19.35 0.98 4-02 1451 3634 18.47 18.51 1.00 4-03 1532 3710 19.51 18.89 1.03 5-01 60° 0.3 1073 2632 13.66 13.40 1.02 5-02 1037 2867 13.20 14.60 0.90 5-03 1125 2883 14.32 14.68 0.98 6-01 30° 0.5 1097 2852 13.97 14.53 0.96 6-02 1157 2704 14.73 13.75 1.07 6-03 1213 2917 15.44 14.86 1.04 7-01 1 1178 3038 15.00 15.47 0.97 7-02 1112 2972 14.16 15.14 0.94 7-03 1214 3248 15.46 16.54 0.93 8-01 2 1302 3102 16.55 15.80 1.05 8-02 1319 3386 16.79 17.24 0.97 8-03 1486 3489 18.92 17.77 1.06 table 1: experimental results in the case of σnom/τnom = 1.0; notch depth p = 5 mm. s.m.j. razavi et alii, frattura ed integrità strutturale, 41 (2017) 424-431; doi: 10.3221/igf-esis.41.53 427 specimen code notch opening angle 2α (°) notch radius ρ (mm) tensile load (n) torque (n mm) σnom (mpa) τnom (mpa) σnom/τnom 9-01 60 0.5 636 3923 8.10 19.98 0.41 9-02 600 4010 7.64 20.42 0.38 9-03 630 4009 8.02 20.42 0.39 10-01 1 645 4449 8.21 22.66 0.36 10-02 660 4634 8.40 23.60 0.36 10-03 631 4326 8.03 22.03 0.36 11-01 2 895 5164 11.40 26.30 0.43 11-02 811 5259 10.33 26.78 0.39 11-03 750 4700 9.55 23.94 0.40 table 2: experimental results in the case of σnom/τnom = 0.4; notch depth p = 5 mm. specimen code notch opening angle 2α (°) notch radius ρ (mm) tensile load (n) torque (n mm) σnom (mpa) τnom (mpa) σnom/τnom 12-01 120 0.3 1482 11606 9.63 21.54 0.45 12-02 1324 9657 8.60 17.92 0.48 12-03 1768 12129 11.49 22.51 0.51 13-01 0.5 1701 11768 11.05 21.84 0.51 13-02 1619 11196 10.52 20.78 0.51 13-03 1657 12005 10.76 22.28 0.48 14-01 1 1739 12150 11.30 22.55 0.50 14-02 1788 12756 11.62 23.68 0.49 14-03 1816 12611 11.80 23.41 0.50 15-01 2 2034 13891 13.21 25.78 0.51 15-02 1756 12500 11.41 23.20 0.49 15-03 1931 13452 12.54 24.97 0.50 table 3: experimental results in the case of σnom/τnom = 0.5; notch depth p = 3 mm. as visible from the tables the imposed mode mixity ratio is almost fulfilled with a variation of approximately ±10% with respect to the nominal value. the variability of the loads to failure as a function of the notch opening angle is weak although not negligible. for a constant notch radius, the fracture load slightly increases for larger notch opening angles, although this effect is very low. strain energy density averaged over a control volume: the fracture criterion ith the aim to assess the fracture load in notched graphite components, an appropriate fracture criterion is required which has to be based on the mechanical behaviour of material around the notch tip. in this section, a criterion proposed by lazzarin and co-authors [19] based on the strain energy density (sed) is briefly described. the averaged strain energy density criterion (sed) states that brittle failure occurs when the mean value of the strain energy density over a given control volume is equal to a critical value wc. this critical value varies from material to material but it does not depend on the notch geometry and sharpness. the control volume is considered to be dependent on the ultimate tensile strength σt and the fracture toughness kic in the case of brittle or quasi-brittle materials subjected to static tensile loads. the method based on the averaged sed was formalised and applied first to sharp (zero radius) v-notches under mode i and mixed mode i+ii loading [19] and later extended to blunt uand v-notches [20]. when dealing with cracks, the control volume is a circle of radius rc centred at the crack tip (fig. 2a). under plane strain conditions, the radius rc can be evaluated according to the following expression [26]: 2 (1 )(5 8 ) 4 ic ic t k r             (1) w s.m.j. razavi et alii, frattura ed integrità strutturale, 41 (2017) 424-431; doi: 10.3221/igf-esis.41.53 428 where kic is the mode i fracture toughness,ν the poisson’s ratio and σt the ultimate tensile stress of a plain specimen. for a sharp v-notch, the critical volume becomes a circular sector of radius rc centred at the notch tip (fig. 2b). when only failure data from open v-notches are available, rc can be determined on the basis of some relationships where kic is substituted by the critical value of the notch stress intensity factors (nsifs) as determined at failure from sharp vnotches. dealing here with sharp notches under torsion loading, the control radius r3c can be estimated by means of the following equation: 1 1 33 3 3 1 c c t e k r           (2) where k3c is the mode iii critical notch stress intensity factor and τt is the ultimate torsion strength of the unnotched material. moreover, e3 is the parameter that quantifies the influence of all stresses and strains over the control volume and (1-λ3) is the degree of singularity of the linear elastic stress fields [27], which depends on the notch opening angle. values of e3 and λ3 are 0.4138 and 0.5 for the crack case (2α= 0°). for a blunt v-notch under mode i or mode iii loading, the volume is assumed to be of a crescent shape (as shown in fig. 2c), where rc is the depth measured along the notch bisector line. the outer radius of the crescent shape is equal to rc+r0, being r0 the distance between the notch tip and the origin of the local coordinate system (fig. 2c). such a distance depends on the v-notch opening angle 2α, according to the expression: 0 ( 2 ) ( 2 2 ) r         (3) for the sake of simplicity, complex theoretical derivations have deliberately been avoided in the present work and the sed values have been determined directly from the fe models. rc rc 2 r2=rc+r0  rc r0 (a) (b) (c) 22=0   figure 2: control volume for (a) crack, (b) sharp v-notch and (c) blunt v-notch, under mixed mode i+iii loading. sed approach in fracture analysis of the tested graphite specimens he fracture criterion described in the previous section is employed here to estimate the fracture loads obtained from the experiments conducted on the graphite specimens. in order to determine the sed values, first a finite element model of each graphite specimen was generated. as originally thought for pure modes of loading the averaged strain energy density criterion (sed) states that failure occurs when the mean value of the strain energy density over a control volume, w , reaches a critical value wc, which depends on the material but not on the notch geometry. under tension loads, this critical value can be determined from the ultimate tensile strength σt according to beltrami’s expression for the unnotched material: 2 2 t icw e   (4) t s.m.j. razavi et alii, frattura ed integrità strutturale, 41 (2017) 424-431; doi: 10.3221/igf-esis.41.53 429 by using the values of σt = 30 mpa and e = 8000 mpa, the critical sed for the tested graphite is w1c = 0.05625 mj/m3. under torsion loads, this critical value can be determined from the ultimate shear strength τt according to beltrami’s expression for the unnotched material: 2 3 2 t cw g   (5) by using the values of τt = 37 mpa and g = 3300 mpa, the critical sed for the tested graphite is w3c = 0.2074 mj/m3. in parallel, the control volume definition via the control radius rc needs the knowledge of the mode i and mode iii critical notch stress intensity factor k1c and k3c and the poisson’s ratio ν, see eqs (1) and (2). for the considered material k1c and k3c have been obtained from specimens weakened by sharp v-notches with an opening angle 2α = 10° and a notch radius less than 0.1 mm. a pre-crack was also generated with a razor blade at the notch tip. the resulting values are k1c = 1.06 mpa m0.5 and k3c = 1.26 mpa m0.5 which provide the control radii r1c = 0.405 mm and r3c = 0.409 mm, under pure tension and pure torsion, respectively. for the sake of simplicity, a single value of the control radius was kept for the synthesis in terms of sed setting rc = r1c = r3c. as discussed in previous papers [20,21], the control radii under tension and torsion can be very different and this is particularly true when the material behaviour differs from a brittle one: the difference is higher for materials obeying a ductile behaviour. for this specific case, the values are so close to each other that a single value can be employed for the final synthesis. the sed criterion has been applied here for the first time to mixed mode i+iii loading conditions. the proposed formulation is a reminiscent of the work by gough and pollard [28] who proposed a stress-based expression able to summarize together the results obtained from bending and torsion. the criterion was extended in terms of the local sed to v-notches under fatigue loading in the presence of combined tension and torsion loadings [29]. in agreement with lazzarin et al. [29, 30] and by extending the method to the static case, the following elliptic expression: 31 1 3 1 c c ww w w   (6) is obtained. in eq. (6) w1c and w3c are the critical values of sed under pure tension and pure torsion. for the considered graphite, w1c = 0.05625 mj/m3 and w3c = 0. 2074 mj/m3. the values of 1w and 3w have, instead, to be calculated as a function of the notch geometry and of the applied mode mixity ratio. each specimen reaches its critical energy when the sum of the weighted contributions of mode i and mode iii is equal to 1, which represents the complete damage of the specimen. figure 3: synthesis of the results from combined tension and torsion tests based on the averaged sed. s.m.j. razavi et alii, frattura ed integrità strutturale, 41 (2017) 424-431; doi: 10.3221/igf-esis.41.53 430 a synthesis in terms of the square root value of the considered parameter, that is the sum of the weighted energy contributions related to mode i and mode iii loading, is shown in fig. 3 as a function of the notch root radius ρ. the obtained trend is very promising. many of the results are inside a scatter band ranging from 0.9 to 1.1 with only few exceptions. the fracture model proposed in this paper can be used for predicting the onset of brittle fracture in notched graphite components which are subjected to a combination of tension and torsion loadings. such criterion would be very useful for designers and engineers who should explore the safe performance of graphite components particularly under complex loading conditions. conclusions rittle fracture in v-notched polycrystalline graphite specimens was investigated both experimentally and theoretically under combined tension and torsion loading. fracture tests were conducted on notched round bar graphite specimens. different notch depths, notch radii and opening angles were considered in the test specimens as well as different combinations of the mode mixity ratio σnom/τnom. the new set of data provided in the paper is unique because no previous papers have been devoted to similar topics dealing with graphite components. the sed criterion was used for the first time in order to estimate the fracture load of notched graphite components under mixed mode i+iii static loading. a new formulation of the sed criterion was proposed showing the capabilities of the suggested method to assess the fracture behaviour of polycrystalline graphite under the considered loading conditions. the results estimated by the sed approach were found to be in good agreement with the experimental results. the criterion based on the elliptic expression described above seems to be very advantageous because it requires, as experimental parameters, only the critical energies from unnotched graphite specimens under pure tension and pure torsion. references [1] sakai, m., urashima, k., inagaki, m., energy principle of elastic-plastic fracture and its application to the fracture mechanics of a polycrystalline graphite, j. am. ceram. soc., 66 (1983) 868–874. doi: 10.1111/j.1151-2916.1983.tb11003.x. [2] ayatollahi, m.r., razavi, s.m.j., rashidi moghaddam, m., berto, f., mode i fracture analysis of polymethylmetacrylate using modified energy—based models, phys. mesomech., 18(5) (2015) 53-62. doi: 10.1134/s1029959915040050. [3] ayatollahi, m.r., rashidi moghaddam, m., razavi, s.m.j., berto, f., geometry effects on fracture trajectory of pmma samples under pure mode-i loading, eng. fract. mech., 163 (2016) 449–461. doi: 10.1016/j.engfracmech.2016.05.014. [4] rashidi moghaddam, m., ayatollahi, m.r., razavi, s.m.j., berto, f., mode ii brittle fracture assessment using an energy based criterion, phys. mesomech. (in press). [5] hess, p., graphene as a model system for 2d fracture behavior of perfect and defective solids, frattura ed integrita strutturale, 9(34) (2015) 341-346. doi: 10.3221/igf-esis.34.37. [6] vo, t.t.g., martinuzzi, p., tran, v.x., mclachlan, n., steer, a., modelling 3d crack propagation in ageing graphite bricks of advanced gas-cooled reactor power plant, frattura ed integrita strutturale, 9(34) (2015) 237-245. doi: 10.3221/igf-esis.34.25. [7] doddamani, s., kaleemulla, m., experimental investigation on fracture toughness of al6061–graphite by using circumferential notched tensile specimens, frattura ed integrita strutturale, 11(39) (2017) 274-281. doi: 10.3221/igf-esis.39.25. [8] bazaj, d.k., cox, e.e., stress-concentration factors and notch-sensitivity of graphite, carbon, 7 (1969) 689–697. doi: 10.1016/0008-6223(69)90524-7. [9] kawakami, h., notch sensitivity of graphite materials for vhtr, trans. atomic energy soc. jpn., 27 (1985) 357–364. doi: 10.3327/jaesj.27.357. [10] sato, s., awaji, h., akuzawa, h., fracture toughness of reactor graphite at high temperature, carbon, 16 (1978) 95– 102. doi: 10.1016/0008-6223(78)90004-0. [11] ayatollahi, m.r., berto, f., lazzarin, p., mixed mode brittle fracture of sharp and blunt v-notches in polycrystalline graphite, carbon, 49 (2011) 2465–2474. doi: 10.1016/j.carbon.2011.02.015. b s.m.j. razavi et alii, frattura ed integrità strutturale, 41 (2017) 424-431; doi: 10.3221/igf-esis.41.53 431 [12] berto, f., lazzarin, p., ayatollahi, m.r., brittle fracture of sharp and blunt v-notches in isostatic graphite under torsion loading, carbon, 50 (2012) 1942–1952. doi: 10.1016/j.carbon.2011.12.045. [13] lazzarin, p., berto, f., ayatollahi, m.r., brittle failure of inclined key-hole notches in isostatic graphite under in-plane mixed mode loading, fatigue fract. eng. mater. struct., 36 (2013) 942–955. doi: 10.1111/ffe.12057. [14] berto, f., lazzarin, p., ayatollahi, m.r., brittle fracture of sharp and blunt v-notches in isostatic graphite under pure compression loading, carbon, 63 (2013) 101–116. doi: 10.1016/j.carbon.2013.06.045. [15] berto, f., lazzarin, p., marangon, c., brittle fracture of u-notched graphite plates under mixed mode loading, mater. des., 41 (2012) 421–432. doi: 10.1016/j.matdes.2012.05.022. [16] radaj, d., berto, f., lazzarin, p., local fatigue strength parameters for welded joints based on strain energy density with inclusion of small-size notches, eng. fract. mech., 76(8) (2009) 1109-1130. doi: 10.1016/j.engfracmech.2009.01.009. [17] lazzarin, p., campagnolo, a., berto, f., a comparison among some recent energyand stress-based criteria for the fracture assessment of sharp v-notched components under mode i loading, theor. appl. fract. mech., 71 (2014) 2130. doi: 10.1016/j.tafmec.2014.03.001. [18] radaj, d., lazzarin, p., berto, f., generalised neuber concept of fictitious notch rounding, int. j. fatigue, 51 (2013) 105-115. doi: 10.1016/j.ijfatigue.2013.01.005. [19] lazzarin, p., zambardi, r., a finite-volume-energy based approach to predict the static and fatigue behaviour of components with sharp v-shaped notches, int. j. fract., 112 (2001) 275-298. doi: 10.1023/a:1013595930617. [20] lazzarin, p., berto, f., some expressions for the strain energy in a finite volume surrounding the root of blunt vnotches, int. j. fract., 135 (2005) 161–185. doi: 10.1007/s10704-005-3943-6. [21] berto, f., lazzarin, p., a review of the volume-based strain energy density approach applied to v-notches and welded structures, theor. appl. fract. mech., 52 (2009) 183–194. doi: 10.1016/j.tafmec.2009.10.001. [22] berto, f., lazzarin, p., recent developments in brittle and quasi-brittle failure assessment of engineering materials by means of local approaches, mater. sci. eng. r reports, 75 (2014) 1–48. doi: 10.1016/j.mser.2013.11.001. [23] berto, f., campagnolo, a., ayatollahi, m.r., brittle fracture of rounded v-notches in isostatic graphite under static multiaxial loading, phys. mesomech., 18 (2015) 283–297. doi: 10.1134/s1029959915040025. [24] berto, f., ayatollahi, m., campagnolo, a., fracture tests under mixed mode i + iii loading: an assessment based on the local energy, int. j. damage mech., (in press). doi: 10.1177/1056789516628318. [25] campagnolo, a., berto, f., leguillon, d., fracture assessment of sharp v-notched components under mode ii loading: a comparison among some recent criteria, theor. appl. fract. mech., 85 (2016) 217-226. doi:10.1016/j.tafmec.2016.02.001. [26] yosibash, z., bussiba, a., gilad, i., failure criteria for brittle elastic materials, int. j. fract., 125 (2004) 307–333. doi: 10.1023/b:frac.0000022244.31825.3b. [27] qian, j., hasebe, n., property of eigenvalues and eigenfunctions for an interface v-notch in antiplane elasticity, eng. fract. mech., 56 (1997) 729–734. doi: 10.1016/s0013-7944(97)00004-0. [28] gough, h.j., pollard, h. v., properties of some materials for cast crankshafts, with special reference to combined stresses, arch. proc. inst. automob. eng., 31 (1936) 821–893. doi: 10.1243/piae_proc_1936_031_040_02. [29] lazzarin, p., sonsino, c.m., zambardi, r., a notch stress intensity approach to assess the multiaxial fatigue strength of welded tube-to-flange joints subjected to combined loadings, fatigue fract. eng. mater. struct., 27 (2004) 127–140. doi: 10.1111/j.1460-2695.2004.00733.x. [30] gallo, p., berto, f., glinka, g generalized approach to estimation of strains and stresses at blunt v-notches under non-localized creep, fatigue fract. eng. mater. struct., 39 (2016) 292-306. << /ascii85encodepages false /allowtransparency false /autopositionepsfiles true /autorotatepages /none /binding /left /calgrayprofile (dot gain 20%) /calrgbprofile (srgb iec61966-2.1) /calcmykprofile (u.s. web coated \050swop\051 v2) /srgbprofile (srgb iec61966-2.1) /cannotembedfontpolicy /error /compatibilitylevel 1.4 /compressobjects /tags /compresspages true /convertimagestoindexed true /passthroughjpegimages true /createjobticket false /defaultrenderingintent /default /detectblends true /detectcurves 0.0000 /colorconversionstrategy /cmyk /dothumbnails false /embedallfonts true /embedopentype false /parseiccprofilesincomments true /embedjoboptions true /dscreportinglevel 0 /emitdscwarnings false /endpage -1 /imagememory 1048576 /lockdistillerparams false /maxsubsetpct 100 /optimize true 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/pdfxoutputintentprofileselector /documentcmyk /preserveediting true /untaggedcmykhandling /leaveuntagged /untaggedrgbhandling /usedocumentprofile /usedocumentbleed false >> ] >> setdistillerparams << /hwresolution [2400 2400] /pagesize [612.000 792.000] >> setpagedevice microsoft word numero 9 art 3 finale b. atzori et alii, frattura ed integrità strutturale, 9 (2009) 27 32; doi: 10.3221/igf-esis.09.03 27 effetto delle dimensioni del cordone di saldatura sulla resistenza a fatica dei giunti a croce b. atzori, b. rossi università di padova, dipartimento di ingegneria meccanica, bruno.atzori@unipd.it g. demelio politecnico di bari, dipartimento di ingegneria meccanica e gestionale, demelio@poliba.it riassunto. la scelta della dimensione da assegnare al cordone di saldatura nel caso di giunzioni saldate a croce può presentarsi problematica, specie quando gli spessori delle lamiere che formano il giunto sono differenti tra loro. le normative di tipo tecnologico suggeriscono in genere di prevedere uno spessore del cordone di saldatura inferiore al minimo spessore della lamiera da collegare, mentre le normative di tipo strutturale non prevedono una dipendenza della resistenza del giunto, sia statica che a fatica, dalle dimensioni del cordone di saldatura, a meno che queste non siano tanto ridotte da portare a rotture che si inneschino e si propaghino non più nella lamiera base ma nel cordone di saldatura. scopo del presente lavoro è la verifica, teorica e sperimentale, della variazione della resistenza a fatica al variare del rapporto tra lo spessore del cordone di saldatura e quello minimo delle lamiere da saldare. abstract. the choice of the proper weld size for cruciform joints can be a critical topic especially in case of different thickness of the welded plates. according to technological recommendations the size of the weld bead should not exceed the thickness of the smallest plate. on the other hand, design standards do not suppose the joint static and fatigue resistance to be dependent on the weld size provided that it is thick enough to avoid the failure of the weld itself instead of the failure of the welded plate. the aim of this work is to study, both from a theoretical and an experimental point of view, the effect of different weld sizes on the fatigue resistance of cruciform joints. parole chiave. fatica; giunti saldati a croce; dimensioni del cordone; fattore di intensificazione delle tensioni introduzione ’ ben noto che, nel caso di giunti a croce portanti saldati con filetti d’angolo, dovrebbe essere sufficiente uno spessore del cordone di saldatura pari alla metà dello spessore della lamiera a cui è applicato il carico per ristabilire la resistenza della lamiera stessa. nella pratica applicativa non è però infrequente il caso di cordoni di saldatura di dimensioni maggiori, sia perchè espressamente previsti, per evitare il rischio di rotture per fatica che si inneschino alla radice del cordone di saldatura e si propaghino attraverso il cordone di saldatura stesso (molto più insidiose di quelle che si innescano al piede del cordone di saldatura e si propagano nel materiale base), sia anche non previsti, ma conseguenza delle modalità di saldatura adottate. le normative per la progettazione delle strutture in acciaio (in particolare la cnr-uni 10011 [1], la din 15018 [2], nonché le raccomandazioni dell’international institute of welding [3]) non fanno dipendere la previsione della vita a fatica di un giunto saldato dalle dimensioni del cordone di saldatura, tranne nel caso in cui questo non sia tanto ridotto da portare ad una maggiore criticità della radice del cordone di saldatura rispetto a quella del piede, con conseguente possibile cedimento del cordone e non della lamiera base. e http://www.gruppofrattura.it/ http://dx.medra.org/10.3221/igf-esis.09.03&auth=true mailto: bruno.atzori@unipd.it mailto: demelio@poliba.it b. atzori et alii, frattura ed integrità strutturale, 9 (2009) 27 32; doi: 10.3221/igf-esis.09.03 28 scopo del presente lavoro è l’analisi, sia teorica che sperimentale, dell’influenza dello spessore del cordone di saldatura sulla resistenza a fatica dei giunti saldati a croce, onde chiarire se il non tenerne conto, da parte delle normative di progettazione, sia giustificato o rappresenti invece un errore da correggere. analisi teorica e normali tecnologie di saldatura portano alla formazione di un cordone di saldatura che si raccorda con la lamiera base in maniera brusca, con raggi di raccordo di entità molto limitata (dell’ordine dei decimi di millimetro) ai quali corrisponde un effetto di intaglio molto elevato, al contrario di quanto avviene con tecnologie o procedimenti particolari, atti ad aumentare questo raggio di raccordo, rendendolo più dolce (dell’ordine di alcuni millimetri) e riducendo così l’effetto di intaglio, con conseguente aumento della resistenza a fatica. e’ stato evidenziato da tempo come, solo nel caso delle tecnologie di saldatura normali, la resistenza a fatica sia determinata dal campo di tensione che si ha in prossimità del piede del cordone di saldatura (poco dipendente dal valore del raggio di raccordo, purché piccolo), e non dal picco valutato in campo lineare elastico, molto dipendente invece dal raggio di raccordo [4, 5]. tale campo di tensione presenta un andamento esponenziale, analogo a quello che si ha in prossimità di una cricca nel caso della meccanica della frattura, ma con un esponente diverso, non più pari a 0.5 ma dipendente dall’ampiezza dell’angolo formato dal cordone di saldatura con la lamiera base. nel caso di un cordone simmetrico rispetto alle due lamiere disposte ortogonali, con un’inclinazione di 45° rispetto a ciascuna lamiera e quindi con angoli di apertura pari a 135°, l’esponente risulta pari a 0.326, in analogia a quanto trovato da williams [6] per gli intagli acuti con uguale angolo di apertura. l’approccio che studia le capacità di resistenza a fatica delle strutture saldate basandosi su questi concetti, denominato nsif (notch stress intensity factor), è stato sviluppato e formalizzato da diversi autori [7-19]. in particolare, lazzarin e tovo [12] lo hanno applicato all’analisi teorica dei giunti saldati a croce, giungendo ad esplicitare l’intensità del campo di tensione locale in funzione della forma del giunto, cioè, con riferimento alla fig. 1, ai rapporti t/t tra gli spessori delle lamiere e b/t tra il piede del cordone di saldatura e lo spessore t della lamiera soggetta al carico. senza entrare in questa sede in maggiori dettagli sulla trattazione effettuata da lazzarin e tovo, che esulerebbe dagli obiettivi della presente analisi, i risultati da loro raggiunti possono essere applicati al caso in esame, evidenziando la variazione relativa del campo di tensione (e quindi della resistenza a fatica ad un determinato numero di cicli) al variare dei rapporti dimensionali sopra ricordati. inoltre, poiché al variare della criticità del giunto saldato, la curva di woehler varia semplicemente traslando parallelamente a se stessa in un diagramma doppio logaritmico [5], la variazione della resistenza a fatica è la stessa indipendentemente dalla vita prevista, purché nel campo delle vite a termine. e’ pertanto possibile costruire il diagramma di fig. 2 che, nell’ipotesi di cordone portante a piena penetrazione con innesco al piede del cordone di saldatura e propagazione nella lamiera base e pendenza del cordone stesso pari a 45°, riporta, per un rapporto t/t pari a 3, la variazione della prevedibile resistenza a fatica al variare di b/t. la resistenza a fatica è espressa in termini di range di sollecitazione σ, pari alla differenza tra la σ massima e la σ minima del ciclo di sollecitazione, supposto costante nel tempo, ed è riferita al valore σ1 assunto nel caso di b = t. l’analisi teorica, che è in corso di approfondimento per estenderla al caso di saldatura a parziale penetrazione e a valori più elevati del rapporto b/t, sembra indicare un leggero miglioramento della resistenza a fatica al crescere dello spessore del cordone di saldatura. figura 1: tipologia di giunto saldato analizzato. l http://www.gruppofrattura.it/ http://dx.medra.org/10.3221/igf-esis.09.03&auth=true b. atzori et alii, frattura ed integrità strutturale, 9 (2009) 27 32; doi: 10.3221/igf-esis.09.03 29 figura 2: variazione prevedibile della resistenza a fatica σ a parità di numero di cicli n al variare dello spessore b del cordone di saldatura, per t/t = 3. valore di riferimento σ1 relativo al caso b/t = 1. saldatura a completa penetrazione. prove sperimentali e prove sperimentali sono state effettuate su giunti saldati a croce in acciaio da carpenteria fe 510. i giunti sono stati ottenuti saldando con cordoni d’angolo due lamiere principali, di spessore pari a 3 mm, su una lamiera trasversale, di spessore pari a 10 mm. sono state realizzate due tipologie di cordoni, variandone lo spessore. il piede del cordone di saldatura, indicato in fig. 3 ed utilizzato per quantificare la dimensione del cordone stesso, ha una dimensione media di 4 mm nella prima serie e di 7 mm nella seconda serie, mentre l’inclinazione dei cordoni non si discosta molto dai 45° per entrambe le serie. la larghezza nominale del giunto è pari a 50 mm ed i raggi di raccordo al piede del cordone di saldatura sono di entità molto ridotta, come evidente anche dalla fig. 3, non essendo stato effettuato alcun trattamento per renderli più ampi. prima di effettuare le prove di fatica, tre provini sono stati sottoposti a trazione statica ed hanno manifestato un comportamento regolare, con rottura della lamiera principale da 3 mm, a cui è stato applicato il carico, e non dalla saldatura. i risultati delle prove statiche sono riportati nella fig. 4. figura 3: geometria dei provini – sezione trasversale. le prove di fatica sono state effettuate utilizzando una macchina servo-idraulica instron 1342 controllata da elettronica mts. tutte le prove sono state condotte in controllo di carico, con frequenze variabili tra 8 e 18 hz e con rapporto di sollecitazione r = σmin/σmax = 0.1. in tab. 1 sono riportati i valori dell’ampiezza di sollecitazione e del numero di cicli che hanno portato a rottura i singoli provini. i risultati sono stati riportati in fig. 5 e a ciascuna serie è stata applicata la curva di woehler standard al 50% di probabilità di sopravvivenza determinata recentemente da atzori e meneghetti [20]. risulta evidente una certa differenza tra le due l http://www.gruppofrattura.it/ http://dx.medra.org/10.3221/igf-esis.09.03&auth=true b. atzori et alii, frattura ed integrità strutturale, 9 (2009) 27 32; doi: 10.3221/igf-esis.09.03 30 serie di risultati, che conferma le indicazioni fornite dall’analisi teorica: la resistenza a fatica migliora al crescere dello spessore del cordone di saldatura. figura 4: risultati delle prove di trazione statica. serie 1 (b = 4 mm) serie 2 (b = 7 mm) provino σ [mpa] n provino σ [mpa] n 1 270 40700 1 297 36590 2 270 45700 2 297 85000 3 225 70900 3 297 45000 4 225 37800 4 297 43945 5 180 149900 5 225 72000 6 225 131000 7 180 163000 tabella 1: risultati delle prove di fatica. figura 5: risultati delle prove di fatica. http://www.gruppofrattura.it/ http://dx.medra.org/10.3221/igf-esis.09.03&auth=true b. atzori et alii, frattura ed integrità strutturale, 9 (2009) 27 32; doi: 10.3221/igf-esis.09.03 31 poiché però la differenza di comportamento è modesta ed il numero di dati sperimentali per ora disponibili è limitato, i risultati delle due serie sono stati considerati come appartenenti ad un’unica popolazione e ad essi è stata applicata la banda di dispersione statistica recentemente determinata da atzori e meneghetti [20] e riportata in fig. 6. in fig. 7 è mostrato il risultato ottenuto. figura 6: banda di dispersione unificata per giunti in acciaio con cordoni d’angolo [20]. figura 7: banda di dispersione unificata applicata ai risultati sperimentali. figura 8: confronto tra normative e risultati sperimentali. http://www.gruppofrattura.it/ http://dx.medra.org/10.3221/igf-esis.09.03&auth=true b. atzori et alii, frattura ed integrità strutturale, 9 (2009) 27 32; doi: 10.3221/igf-esis.09.03 32 poiché la banda di dispersione ha un limite inferiore relativo ad una probabilità di sopravvivenza (p.s.) del 90%, la curva di resistenza a fatica ricavata dai risultati sperimentali e relativa a tale probabilità di sopravvivenza è stata confrontata con le curve di progetto fornite, per giunti della stessa tipologia, da alcune normative. in particolare si riportano in fig. 8 i valori relativi a p.s. = 90% moltiplicati per 3/4 secondo l’approccio di determinazione dei valori di resistenza della din 15018, quelli relativi a p.s. = 95% secondo l’approccio iiw e quelli relativi a p.s. = 97.7% secondo l’approccio cnr-uni 10011. conclusioni ia le analisi teoriche che i risultati sperimentali ottenuti mostrano che all’aumentare dello spessore del cordone di saldatura la resistenza a fatica del giunto saldato non diminuisce ma anzi migliora. poiché il miglioramento, almeno per ora, sembra essere modesto, appare giustificato ed ammissibile che le normative non tengano conto delle dimensioni del cordone di saldatura nel fissare la resistenza a fatica dei giunti saldati con cordoni d’angolo. i risultati sperimentali ottenuti evidenziano caratteristiche di resistenza congruenti ed entro i limiti di resistenza indicati, per la stessa tipologia di giunto, dalle normative di progettazione e verifica considerate. l’analisi svolta evidenzia una non banale differenza della resistenza di progetto a fatica fornita dalle tre fonti prese in esame. tali differenze non sembrano giustificabili con le modeste differenze delle probabilità di sopravvivenza a cui fanno riferimento le tre normative e, a parere degli autori di questo lavoro, merita un maggiore approfondimento che estenda il confronto anche ad altre normative, visto il rischio da un lato, di avere un inutile appesantimento delle strutture (con conseguente maggior costo e minore competitività sul mercato), dall’altro, di avere rotture catastrofiche dopo periodi anche lunghi di utilizzo delle strutture. bibliografia [1] cnr uni 10011 costruzioni di acciaio. istruzioni per il calcolo, l'esecuzione, il collaudo e la manutenzione (1988). [2] din 15018 steel structures verification and analyses. part 1 (1984). [3] a. hobbacher fatigue design of welded joints and components. recommendations of iiw joint working group xiiixv (1996). [4] b. atzori, g. crivellato, g. meneghetti, atti del xxvi convegno nazionale aias, calabria (1997). [5] b. atzori, rivista italiana della saldatura lii, 1 (2000) 27. [6] ml. williams, j. appl. mech. 19 (1952) 526. [7] e. haibach, die schwingfestigkeit von schweissverbindungen aus der sicht einer örtlichen beanspruchungsmessung. lbf report no. fb-77, darmstadt (1968). [8] s. usami, h. kimoto, s. kusumoto, trans jpn weld soc., 9(2) (1978). [9] b. atzori, g. blasi, c. pappalettere, exp. mech., 25(2) (1985) 129. [10] l.s. nui, c. chehimi, g. pluvinage, engng fracture mech., 49 (1994) 325. [11] y. verreman, b. nie, fatigue fract. engng mater. struct., 19 (1996) 669. [12] p. lazzarin, r. tovo, fatigue fract. engng. mater. struct. 21 (1998) 1089. [13] b. atzori, p. lazzarin, g. meneghetti, fatigue fract. eng. mater. struct., 22 (1999) 369. [14] r. tovo, p. lazzarin, int. j. fatigue, 21 (1999) 1063-78. [15] p. lazzarin, p. livieri, int. j. fatigue, 23(3) (2001) 225–32. [16] g. meneghetti, r. tovo, in: blom af, editor. proceedings of the 8th international fatigue congress. stockholm, sweden. (2002)1873. [17] d. taylor, n. barrett, g. lucano, int. j. fatigue, 24 (2002) 509-18. [18] y. verreman, n. limodin, eng. fract. mech., (2007) doi:10.1016/j.engfractmech.2007.07.005. [19] b. atzori, p. lazzarin, g. meneghetti, eng fract mech., (2007) doi:10.1016/j.engfracmech.2007.03.029. [20] b. atzori, g. meneghetti, int. j. fatigue, 23 (2001) 713-21. s http://www.gruppofrattura.it/ http://dx.medra.org/10.3221/igf-esis.09.03&auth=true microsoft word numero_40_art_4 e. d. pasiou et alii, frattura ed integrità strutturale, 40 (2017) 41-51; doi: 10.3221/igf-esis.40.04 41 focussed on recent advances in “experimental mechanics of materials” in greece correlation between the electric and acoustic signals emitted during compression of brittle materials ermioni d. pasiou national technical university of athens, department of mechanics, laboratory for testing and materials, 5 heroes of polytechnion avenue, theocaris building, 157 73, athens, greece epasiou@teemail.gr dimos triantis technological educational institution of athens, department of electronics, laboratory of electronic devices and materials, ag. spiridonos street, 122 10, athens, greece triantis@teiath.gr abstract. an experimental protocol is described including a series of uniaxial compression tests of three brittle materials (marble, mortar and glass). the acoustic emission (ae) technique and the pressure stimulated currents (psc) one are used since the recordings of both techniques are strongly related to the formation of cracking in brittle materials. in the present paper, the correlation of these techniques is investigated, which is finally proven to be very satisfactory. keywords. pressure stimulated currents (psc); acoustic emission (ae); compression; brittle materials. citation: pasiou, e.d., triantis, d., correlation between the electric and acoustic signals emitted during compression of brittle materials, frattura ed integrità strutturale, 40 (2017) 41-51. received: 23.12.2016 accepted: 07.02.2017 published: 01.04.2017 copyright: © 2017 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. introduction onitoring the mechanical response of various brittle materials under compressive loading is of great interest in a range of application fields. especially, monitoring their damage evolution is crucial since actions can be taken in time in order to preserve the integrity of structures. in this context, a series of diagnostic methods have been developed in order to assess damage and also to detect impending failure of the materials. acoustic emission (ae) technique is among the as above techniques [1]. when a material is loaded, transient elastic waves are generated within the material (which are mainly depended on the material’s irreversible deformations) and travel along the specimen. these waves are called acoustic emissions and they are recorded by sensors which are attached on the specimen. the first studies of acoustic emissions in geomaterials were carried out in 1938. monitoring a specimen/ structure during its whole loading history is one of the advantages of this technique since in general the increase of acoustic activity, which is observed as the specimen approaches failure, is strongly correlated to the decay of the m e. d. pasiou et alii, frattura ed integrità strutturale, 40 (2017) 41-51; doi: 10.3221/igf-esis.40.04 42 mechanical properties of the material. the improved b-value (ib-value) is one of the acoustic characteristics which is related to the impending failure [1-2] since its value changes during the failure process. ib-value, firstly introduced by shiotani et al. [3], is defined as:            21 21 nnib loglog (1) where μ is the mean amplitude, σ the standard deviation and α1, α2 constants (which are usually equal to 1 [1]). damage process is also well detected by the pressure stimulated currents (psc) technique [4] and more specific by the weak electric signals emitted during the generation of micro-cracks in brittle materials when they are subjected to mechanical loading [5-6]. more than ten years ago, electric signals were recorded by stavrakas et al. [6] during mechanical loading of marble. a few years later, electric signals were also recorded when specimens of rock materials and cement based materials were tested [7-10]. the signal was captured by a pair of gold plated electrodes and it was recorded using a sensitive electrometer. in all cases, when the applied stress was above 80% of the maximum stress, psc increased rapidly reaching a maximum value just before the specimen’s fracture [4, 10]. psc technique is also used by other researchers [1114] while similar techniques are used [15-16] to detect cracking of rocks and concrete specimens. some of the advantages of the psc technique are the low cost of the sensors and the easiness of sensors’ production as well as the fact that electrodes don’t affect the specimens’ structure or the stress and strain fields. the qualitative correlation of the aforementioned techniques has already been mentioned in previous studies during trivial tests [17-18] as well as in more complex specimens (i.e. made of more than one material [19]). in the present experimental protocol, specimens of three brittle materials (marble, mortar and glass) are subjected to uniaxial compression tests in order to confirm and quantify the correlation of psc and ae techniques. materials and experimental set up materials ionysos marble is the stone exclusively used for the restoration of the monuments of the athenian acropolis. its chemical composition is 98% of calcite, 0.5% of muscovite, 0.3% of sericite, 0.2% of quartz and 0.1% of chlorite. its grain size varies from 100 μm to 400 μm and its specific and apparent densities are equal to 2730 kg/m3 and 2717 kg/m3, respectively. the absorption coefficient by weight of dionysos marble is about 0.11% and its thermal expansion coefficient is 9x10-6 /oc between 15 oc and 100 oc. its very low porosity varies between 0.3% (virgin state) to 0.7% (superficial porosity) [20]. the mechanical properties of dionysos marble vary between broad limits [21]. the specific marble is of rather orthotropic nature, i.e. it is characterized by three different anisotropy directions. however, it can be approximately considered as a transversely isotropic material described adequately with the aid of five elastic constants as it was definitely concluded by detailed experimental protocols including direct tension and compression tests as well as three-point bending and brazilian disc tests [22-29]. the as above experimental protocols revealed also that dionysos marble is slightly non-linear (both in the tension and in the compression regime) and slightly bimodular, i.e. the elastic modulus in compression is about 15% higher than the respective one in tension [24, 25]. three marble specimens were used in the present study of prismatic shape with dimensions 40 mm x 40 mm x 100 mm. the load was applied normal to the material layers, i.e. along the strong direction of dionysos marble’s anisotropy. the second material tested was a mortar which consisted of three parts of fine sand, one part of ordinary portland cement and half part of water. the grain size of the sand varied between 3 mm to 6 mm and its fineness modulus was equal to 2.8. in addition, its specific gravity was found equal to 2.6, its density was 2200 kg/m3 and its porosity was evaluated at approximately 8% [10]. the constituents of the mortar were mixed at a low speed to enable better moisturizing of the cement grains while at the end of the production process the mixture was agitated very fast for 1 min. mortar was formed in three prismatic blocks using metallic moulds of dimensions 50 mm x 50 mm x 70 mm the inner surfaces of which were oiled. the moulds were mounted on a desktop vibrator in order to enable compaction. the mortar prismatic blocks were demoulded after 24 h and they were cured in a room with constant ambient temperature of 22 °c and 75-80% humidity. the specimens were stored for 100 days to reach 90-95% of their strength [30]. the third material studied in the present experimental protocol was one of the most common types of glass produced, i.e. the soda-lime-silica one (or simply soda glass). one of its most important advantages is that it is nearly chemically inert, d e. d. pasiou et alii, frattura ed integrità strutturale, 40 (2017) 41-51; doi: 10.3221/igf-esis.40.04 43 therefore it doesn’t react with other chemicals when they come into contact with it. soda glass in usually used to make windows, bottles, jars, vials and other laboratory equipment. the chemical composition of this type of glass is presented in tab. 1. in the present experimental protocol three prismatic blocks (30 mm x 30 mm x 80 mm) were used. components sio2 al2o3 na2o k2o cao mgo fe2o3 tio2 p2o5 zro2 % 72.4 1.26 13.4 0.24 8.53 3.95 0.16 0.063 0.018 0.05 table 1: chemical composition of soda-lime-silica glass [31]. experimental set up before testing, one kyowa strain gauge (of 5 mm gauge length and of 120 ω gauge resistance) was glued on the front surface of the specimen (at the middle of its height and of its width as it is seen in fig.1a) in order to measure the axial strain during the tests. in addition, one acoustic sensor r15α (denoted by number 3 in fig.1b) was coupled on the opposite surface of the specimen by means of silicone and one preamplifier with 40 db gain was also used (the equipment and the software used were by mistras group, inc.). finally, a pair of electrodes was attached on the two side opposite surfaces of each specimen (orange ellipses in fig.1a and numbers 1,2 in fig.1b) in such a way so as the imaginary line connecting them to be perpendicular to the loading axis. a sensitive programmable electrometer (keithley, 6517a), capable of resolving currents as low as 0.1 fa and as high as 20 ma in 11 ranges, was used to record the electric signals. it should be underlined that thin teflon plates were placed between the specimen and the loading platens for the specimen’s electrical isolation. all specimens were subjected to compressive loading under load control conditions (dσ/dt=0.3 mpa/s) simulating quasi-static loading. figure 1: (a) a sketch of the experimental set up, (b) a typical marble specimen. the pair of electrodes (1, 2) and the acoustic sensor (3) are also presented. results and discussion mechanical behaviour ypical stress-strain curves of each material are presented in fig.2. the commonly observed “bedding error” during compressive tests is obvious in all three materials. ignoring this initial part, the curves of both marble and cement mortar are mainly characterized by linearity up to about 80% of their maximum stress (points a and b in fig.2a,b). the mean value of the fracture stress is ~95 mpa for marble and ~50 mpa for cement mortar. the modulus of elasticity obtained was equal to ~70 gpa and ~20 gpa for marble and mortar, respectively, which are very close to the respective ones from literature [10, 22]. afterwards both curves deviate from linearity. on the other hand, the stress-strain curve of soda glass is linear almost up to 90% of the maximum stress of the specimens (point c in fig.2c). its modulus of elasticity was calculated equal to ~70 gpa as it is also mentioned in [31, 32] and its maximum stress was found to be equal to ~20 mpa. it is also to be noted that ductility of soda glass specimens is one order of magnitude lower than the respective ones of both marble and mortar. the mechanical characteristics obtained from all specimens are recapitulated in tab. 2. t teflon plates pair of electrodes strain gauge (a) (b) e. d. pasiou et alii, frattura ed integrità strutturale, 40 (2017) 41-51; doi: 10.3221/igf-esis.40.04 44 figure 2: typical stress-axial strain curves for (a) marble, (b) mortar and (c) glass specimens. (d) the three aforementioned curves together for comparison reasons. material specimen modulus of elasticity [gpa] fracture stress [mpa] peak axial strain [-] dionysos marble m1 68.8 98.7 1.7·10-3 m2 71.2 92.5 1.9·10-3 m3 70.7 94.7 2.2·10-3 mean value ± standard deviation 70.2 ± 0.2 95.3 ± 0.5 1.9·10-3 ± 0.3 cement mortar c1 19.8 50.1 3.5·10-3 c2 18.1 46.4 2.4·10-3 c3 23.3 51.7 3.1·10-3 mean value ± standard deviation 20.4 ± 0.8 49.4 ± 0.5 3.0·10-3 ± 0.5 soda glass g1 68.7 18.8 2.7·10-4 g2 70.5 20.5 3.3·10-4 g3 70.0 19.4 3.1·10-4 mean value ± standard deviation 69.7 ± 0.2 19.6 3.0·10-4 ± 0.3 table 2: the mechanical characteristics of all specimens. electric signals the electric signal produced during a typical compressive test of a marble specimen and the axial strain obtained (normalized over its maximum value) versus the normalized stress are presented in fig.3. a weak current (from 0.5 pa increases slightly to 2 pa) is initially observed until point a1 in fig.3(a1) where the stress level equals ~75% of the maximum stress and strain is ~55% of the fracture strain. this point almost corresponds to point a where the stress-strain curve y = 70653x 15.2 0 25 50 75 100 0.0e+0 8.0e-4 1.6e-3 2.4e-3 s tr es s [m p a] axial strain 0 25 50 75 100 0e+00 8e-04 2e-03 2e-03 3e-03 4e-03 s tr es s [m p a] axial strain marble mortar glass y = 70458x 1.6 0 6 12 18 24 0e+0 1e-4 2e-4 3e-4 4e-4 s tr es s [m p a] axial strain y = 19790x 9 0 14 28 42 56 0e+0 1e-3 2e-3 3e-3 4e-3 s tr es s [m p a] axial strain a b c (a) (b) (c) (d) e. d. pasiou et alii, frattura ed integrità strutturale, 40 (2017) 41-51; doi: 10.3221/igf-esis.40.04 45 deviates from linearity. afterwards, the electric current starts increasing with higher rate, indicating the onset of microcracking. when stress equals about 97% of the maximum applied stress (point a΄1 in fig.3(a2) where the stress-strain curve tends to become horizontal) and strain equals about 80% of the maximum strain the increase of psc is remarkable, severe cracking takes place (not yet visible with naked eyes) and the specimen is just before collapse. in case of mortar specimens, the first noticeable change of the psc values is observed when strain equals ~55% of the maximum strain and stress is ~60% of the maximum stress, point b1 in fig.3b) although the material is still below its proportional limit. the increase of the electric signal starts becoming significantly larger (point b΄1 in fig.3b) when the respective stress-strain curve deviates from linearity (~75% of the maximum stress and ~70% of the fracture strain, point b in fig.2b). psc gets its maximum value slightly before the final fracture (~90% of the maximum strain and ~95% of the maximum stress) indicating the impending failure. concerning soda glass, the variation of psc could be clearly divided in three stages. in the beginning of the test, a weak electric signal is detected until point c1 in fig.3c where strain is equal to ~60% of the maximum strain and stress is ~60% of the maximum stress. during the second stage (between points c1 and c΄1 in fig.3c), the increase of psc is considerable while the increase rate becomes even higher during the last stage where the applied stress is ~85% of the maximum stress and strain equals ~80% of the maximum strain. the maximum value of psc is attained ~96% of both the maximum stress and the maximum strain. figure 3: the electric current and the normalized axial strain versus the normalized stress for a typical specimen of (a) marble, (b) mortar and (c) glass. pcs values in comparison with ib-values in all cases, groups of 70 hits were used for the calculation of the ib-value. the first group included the first 70 hits while each successive group contained 35 hits of the previous one and the next 35 hits. each ib-value corresponds to the instant which was calculated as the mean time of the respective hits. the variation of ib-value in conjunction with the electric current is shown versus the normalized stress in fig.4(a1) for a typical marble specimen. in the beginning of the test, until ~30% of the maximum strain and ~35% of the maximum 0.00 0.25 0.50 0.75 1.00 0 250 500 750 1000 0.00 0.25 0.50 0.75 1.00 n o rm alized strain p s c [ p a ] normalized stress 0.00 0.25 0.50 0.75 1.00 0 8 16 24 32 0.00 0.25 0.50 0.75 1.00 n o rm alized strain p s c [ p a ] normalized stress 0.00 0.25 0.50 0.75 1.00 0 25 50 75 100 0.00 0.25 0.50 0.75 1.00 n o rm alized strain p s c [ p a ] normalized stress 0.60 0.80 1.00 0 50 100 0.90 0.95 1.00 n o rm alized strain p s c [ p a ] normalized stress (a1) (a2) (b) (c) a1 a΄1 c1 b1 b΄1 c΄1 normalized strain psc normalized strain psc normalized strain psc e. d. pasiou et alii, frattura ed integrità strutturale, 40 (2017) 41-51; doi: 10.3221/igf-esis.40.04 46 stress, ib has high values decreasing from ~2.4 to 1.7. this can be related to the closure of pre-existing micro-cracks of the specimen or/and to rubbing/friction [1]. afterwards, ib-value is almost constant with variance around ~2.0 indicating the slow generation of new micro-cracks (until point a2 in fig.4(a1) which corresponds to stress level ~80% of the maximum stress and strain ~60% of the maximum strain). this point coincides with the deviation of the stress-strain curve from linearity. slightly earlier, the first noticeable increase of the electric current was observed. finally, ib decreases systematically attaining at the end of the test values close to 1.0 (point a΄2 in fig.4(a2)). this happens at ~95% of the maximum applied stress and ~75% of the maximum strain and it is related to a large number of cracks. during the decrease of ib-value, psc increases further. at the final stage (after point a΄2), ib slightly decreases further due to the coalescence of cracks which leads the specimen to the final fracture while the electric current increases dramatically reaching its highest value. figure 4: the electric current and the ib-value against the normalized stress for a typical specimen of (a) marble, (b) mortar and (c) glass. in case of mortar, ib-value (fig.4b) is relatively high from the beginning of the test until ~35% of both the maximum strain and the maximum stress while a period with almost constant ib-value (~1.8) follows (until point b2, ~60% of the maximum strain and ~70% of the maximum applied stress). afterwards, ib-value decreases (while the increase of psc becomes significant) reaching the value of 1.0 (point b΄2) when the respective stress-strain curve ceases to be linear (~70% of the maximum strain and ~75% of the maximum stress). subsequently, the values of ib become slightly lower than 1.0 remaining almost constant until the fracture of the specimen. during this stage, the electric current attains its peak value indicating the impending failure. the variation of the ib-values for a typical soda glass specimen is presented in fig.4c. ib-value continuously decreases until point c2 (~80% of both the maximum strain and the maximum stress), i.e. almost during the first two stages of the psc variation. the rate of ib-value decrease is higher between ~40% and ~80% of both the maximum strain and the maximum stress. afterwards, ib-value remains almost constant until ~90% of the maximum stress. from this point on and up to the end of the test, ib-value decreases further. it is worth noticing that in case of soda glass, ib-value attains the 0.00 0.70 1.40 2.10 2.80 0 25 50 75 100 0.00 0.25 0.50 0.75 1.00 ib v alu e p s c [ p a ] normalized stress 0.60 0.80 1.00 1.20 1.40 0 25 50 75 100 0.90 0.95 1.00 ib v alu e p s c [ p a ] normalized stress 0.00 0.40 0.80 1.20 1.60 0 8 16 24 32 0.00 0.25 0.50 0.75 1.00 ib v alu e p s c [ p a ] normalized stress 0.00 0.60 1.20 1.80 2.40 0 250 500 750 1000 0.00 0.25 0.50 0.75 1.00 ib v alu e p s c [ p a ] normalized stress a2 a΄2 c2 b2 b΄2 (a1) (a2) (b) (c) psc ib-value psc ib-value psc ib-value e. d. pasiou et alii, frattura ed integrità strutturale, 40 (2017) 41-51; doi: 10.3221/igf-esis.40.04 47 value of 1.0 when strain is ~65% of the maximum strain and stress is ~65% of the maximum stress, i.e. relatively lower compared to the other two materials. it should be mentioned at this point that b-value is related, among others, to the heterogeneity of the material. as the degree of nonuniformity of the material increases, b-value also increases [33]. this is consistent with the results of the present study. the material layers of marble and the existence of sand in mortar make these structures quite heterogeneous compared to glass specimens and as a result the ib-values obtained for marble and mortar are larger than the respective values of glass. in addition, the heterogeneity of both marble and mortar results to the generation of low acoustic activity during the initial load levels leading to an almost constant ib-value in these first stages of loading. the absence of this constant segment in case of glass makes the variation of the respective ib-value to be monotonic in contrast to the respective variations of both marble and mortar. approach based on energies despite the fact that the correlation of psc and ae techniques became clear in the previous section, an alternative approach based on the released energy was decided to be used in order to quantitatively verify the correlation of the two experimental techniques. the absolute energy (measured in aj) produced and recorded by the acoustic sensors characterizes each acoustic hit and it is calculated by the software as the integral of the signal voltage at a power of two over the reference resistance (10 kω). in the present study, the sum of the energy released during each second of the tests, eae, was calculated since it is a measure of the size distribution of micro-cracks in such materials [34]. in case of psc technique, the energy released was calculated by the familiar expression: epsc=    tt t i i dttpsc 2 (2) where δt=1 s and ti= 0, 1, …, n-1 (n is the duration of the experiment). since psc is measured in pa, the units of epsc are (pa)2·s. finally, the strain energy density, sed, was calculated as the area below the stress-strain curves of the tests. all three quantities were normalized over the respective maximum value and the results are presented in logarithmic scale in fig.5. for all three materials of the present experimental protocol both curves are formed by two almost straight segments with different slope and a knee point is clearly seen corresponding probably to the formation of more severe cracks. in case of marble (fig.5a), it is quite interesting that psc technique seems to detect the internal damage of the specimen earlier than ae technique. in case of marble, the pscknee point and the aeknee point correspond to about 70% and 80% of the maximum stress, respectively (i.e. about 50% and 60% of the maximum strain, respectively). the same is true for mortar specimens (fig.5b). the knee point from psc technique is observed when stress equals about 60% of the maximum stress (~55% of the maximum strain) while aeknee point corresponds to ~65% of the maximum stress and ~60% of the maximum strain. in case of glass specimens (fig.5c), the knee points formed by the two techniques are observed almost simultaneously (~60% of both the maximum stress and strain). figure 5: the energy calculated by both psc and ae techniques versus the strain energy density for a typical specimen of (a) marble. 1e-6 1e-4 1e-2 1e+0 1e-3 1e-2 1e-1 1e+0 e n er gy strain energy density kneepsc kneeae (a) e. d. pasiou et alii, frattura ed integrità strutturale, 40 (2017) 41-51; doi: 10.3221/igf-esis.40.04 48 figure 5 (con’t): the energy calculated by both psc and ae techniques versus the strain energy density for a typical specimen of (b) mortar and (c) glass. as a next step, an effort was made to investigate any correlation which might exist between the quantities epsc and eae calculated by the two experimental techniques. in figs.6(a-c) both energies are presented in logarithmic scale for a typical specimen for each material studied here. the solid dark blue circles represents the period where the electric current produced is very weak without noticeable changes while the empty symbols corresponds to the increase of the psc until it reaches its maximum value. it is clear that the correlation is much better when the energy emitted increases considerably (empty dark blue circles). therefore, ignoring the period where psc is almost constant or increases very smoothly, it was found that the correlation of the energies calculated based on both experimental techniques obeys a power law, i.e.  mpscae ee  , where m~0.8 for both marble and glass specimens while m~0.7 for mortar specimens (figs.6(a-c)). conclusions he correlation of both experimental techniques used in the present experimental protocol is highlighted. more specific, it was found that when the ib-value decreases, the electric signal detected by the psc technique starts increasing considerably indicating the formation of cracks. all three materials (marble, mortar and glass) enter a critical state (i.e. ib-value tends to 1.0) when strain is equal to about 65-75% of the maximum strain (stress level equals to about 95% for marble, about 75% for mortar and about 65% for glass). the same stress level, at which the damage state of dionysos marble becomes critical, is also obtained by other researchers based on the variation of the b-value [35]. the alternative approach which was based on the energy released during loading of the specimens, although it makes very t 1e-4 1e-3 1e-2 1e-1 1e+0 1e-3 1e-2 1e-1 1e+0 e n er gy strain energy density 1e-7 1e-6 1e-5 1e-4 1e-3 1e-2 1e-1 1e+0 1e-5 1e-4 1e-3 1e-2 1e-1 1e+0 e n er gy strain energy density kneepsc kneeae kneepsc kneeae (b) (c) e. d. pasiou et alii, frattura ed integrità strutturale, 40 (2017) 41-51; doi: 10.3221/igf-esis.40.04 49 figure 6: the correlation of the energy calculated by both psc and ae techniques for a typical specimen of (a) marble, (b) mortar and (c) glass. y = 930.15x0.79 r² = 0.97 1.0e+00 1.0e+01 1.0e+02 1.0e+03 1.0e+04 1.0e+05 1.0e+06 1.0e+07 1.0e-01 1.0e+00 1.0e+01 1.0e+02 1.0e+03 1.0e+04 e a e epsc y = 60.73x0.72 r² = 0.98 1.0e+00 1.0e+01 1.0e+02 1.0e+03 1.0e+04 1.0e+05 1.0e+06 1.0e+07 1.0e+00 1.0e+02 1.0e+04 1.0e+06 e a e espc y = 20422.30x0.83 r² = 0.98 1.0e+00 1.0e+01 1.0e+02 1.0e+03 1.0e+04 1.0e+05 1.0e+06 1.0e+07 1.0e+00 1.0e+01 1.0e+02 1.0e+03 e a e epsc (b) (a) (c) e. d. pasiou et alii, frattura ed integrità strutturale, 40 (2017) 41-51; doi: 10.3221/igf-esis.40.04 50 clear the point where cracking becomes more severe, it seems to be more conservative. the knee points are observed when strain equals about 50-60% of the fracture strain for all three materials studied here (while the stress level equals about 70-80% for marble specimens and about 55-65% for mortar and soda glass specimens). ae technique has already been mentioned as a valuable tool for detecting the impending failure paying attention either to the general acoustic activity or to specific acoustic characteristics in accordance mainly to the stress induced on the specimens [18-19, 35-36]. psc technique is more recently developed compared to the ae technique and it is not yet fully standardized. it should be mentioned that the specific technique cannot be applied in heavily distorted electromagnetic environments since very low electrical currents (in the order of pa) are measured and the external electrical noise acts as additive electrical noise on the actual signal. in order to minimize such effects special care must be given to the shielding of the experimental apparatus, electrical ground and low noise cabling. despite the aforementioned limitations, the electric current recorded using the psc technique has already been related to the mechanical behaviour of the tested material [4, 7]. concluding, taking into account that strains are much easier to be measured, compared to the stress field developed, the fact that the critical state is detected by both techniques and it is determined at almost the same strain level for all three materials is an interesting finding which could be very useful for monitoring and assessing the integrity of structures. in addition, in the direction of quantifying the correlation of the ae and the psc techniques, a successful attempt is made for the very first time in the present paper. indeed a very good correlation exists between the energies measured by both techniques, which obeys a power law with exponent equal to 0.7-0.8 for the materials studied here. references [1] rao, m.v.m.s., lakschmi, p.k.j., analysis of b-value and improved b-value of acoustic emissions accompanying rock fracture, current science, 89 (2005) 1577-1582. [2] colombo, s., main, i.g., forde, m.c., assessing damage of reinforced concrete beam using ‘‘b-value’’ analysis of acoustic emission signals, journal of materials in civil engineering (asce), 15 (2003) 280-286. [3] shiotani, t., yuyama s., li, z.w., ohtsu, m., application of the ae improved b-value to qualitative evaluation of fracture process in concrete materials, journal of acoustic emission, 19 (2001) 118-132. [4] stavrakas, i., triantis, d., agioutantis, z., maurigiannakis, s., saltas, v., vallianatos, f., pressure stimulated currents in rocks and their correlations with mechanical properties, natural hazards and earth system sciences, 4 (2004) 563-567. [5] enomoto, j., hashimoto, h., emission of charged particles from indentation fracture of rocks, nature, 346 (1990) 641-643. [6] vallianatos, f., triantis, d., tzanis, a., anastasiadis, c., stavrakas, i., electric earthquake precursors: from laboratory results to field observations, physics and chemistry of the earth, 29 (2004) 339-351. [7] triantis, d., anastasiadis, c., vallianatos, f., kyriazis, p., nover, g., electric signal emissions during repeated abrupt uniaxial compressional stress steps in amphibolite from ktb drilling, natural hazards and earth system sciences, 7 (2007) 149-154. [8] vallianatos, f., triantis, d., scaling in pressure stimulated currents related with rock fracture, physica a, 387 (2008) 4940-4946. [9] triantis, d., anastasiadis, c., stavrakas, i., the correlation of electrical charge with strain on stressed rock samples, natural hazards and earth system sciences, 8 (2008) 1243-1248. [10] kyriazopoulos, a., anastasiadis, c., triantis, d., brown, c.j., non-destructive evaluation of cement-based materials from pressure-stimulated electrical emission preliminary results, construction and building materials, 25 (2011) 1980-1990. [11] aydin, a., prance, r.j., prance, h., harland, c.j., observation of pressure stimulated voltages in rocks using an electric potential sensor, applied physics letters, 95 (2009) art no. 124102. [12] freund, f., pre-earthquake signals: underlying physical processes, journal of asian earth sciences, 41 (2011) 383-400. [13] cartwright-taylor, a., vallianatos, f., sammonds, p., superstatistical view of stress-induced electric current fluctuations in rocks, physica a: statistical mechanics and its applications, 414 (2014) 368-377. [14] li, z., wang, e., he, m., laboratory studies of electric current generated during fracture of coal and rock in rock burst coal mine, journal of mining, 2015 (2015) article id 235636. [15] archer, j.w., dobbs, m.r., aydin, a., reeves, h.j., prance, r.j., measurement and correlation of acoustic emissions and pressure stimulated voltages in rock using an electric potential sensor, international journal of rock mechanics and mining sciences, 89 (2016) 26-33. e. d. pasiou et alii, frattura ed integrità strutturale, 40 (2017) 41-51; doi: 10.3221/igf-esis.40.04 51 [16] dann, d., demikhova, a., fursa, t., kuimova, m., research of electrical response communication parameters on the pulse mechanical impact with the stress–strain state of concrete under uniaxial compression, iop conference series: materials science and engineering, 66(1) (2014) 012036, doi:10.1088/1757-899x/66/1/012036 [17] stergiopoulos, c., stavrakas, i., hloupis, g., triantis, d., vallianatos, f., electrical and acoustic emissions in cement mortar beams subjected to mechanical loading up to fracture, engineering failure analysis, 35 (2013) 454–461. [18] stavrakas, i., pasiou, e.d., hloupis, g., malliaros, g.-t., triantis, d., kourkoulis, s.k., exploring the size effect of marble by combined use of pressure stimulated currents and acoustic emission, in: beskos d.e., stavroulakis g.e. (eds.), 10th hstam international congress on mechanics, chania, hellas, (2013) 185-186. [19] triantis, d., stavrakas, i., pasiou, e.d., hloupis, g., kourkoulis, s.k., innovative experimental techniques in the service of restoration of stone monuments part ii: marble epistyles under shear, procedia engineering, 109c (2015) 276-284. [20] tassogiannopoulos, a.g., a contribution to the study of the properties of structural natural stones of greece (in greek), ph.d. dissertation, national technical university of athens, greece (1986). [21] theocaris, p.s., coroneos, e., experimental study of the stability of parthenon, publications of the academy of athens, 44 (1979) 1-80. [22] kourkoulis, s.k., exadaktylos, g.e., vardoulakis i., u-notched dionysos-pentelicon marble in three point bending: the effect of nonlinearity, anisotropy and microstructure, international journal of fracture, 98(3-4) (1999) 369-392. [23] kourkoulis, s.k., ganniari-papageorgiou, e., mentzini, m., dionysos marble under bending: α contribution towards understanding the fracture of the parthenon architraves, engineering geology, 115 (3-4) (2010) 246-256. [24] exadaktylos, g.e., vardoulakis, i., kourkoulis, s.k., influence of nonlinearity and double elasticity on flexure of rock beams i. technical theory, international journal of solids and structures, 38 (22-23) (2001) 4091-4117. [25] exadaktylos, g.e., vardoulakis, i., kourkoulis, s.k., influence of nonlinearity and double elasticity on flexure of rock beams ii. characterization of dionysos marble, international journal of solids and structures, 38 (22-23), (2001) 41194145. [26] exadaktylos, g.e., kaklis, k.n., applications of an explicit solution of the transversely isotropic circular disc compressed diametrically, international journal of rock mechanics and mining sciences, 38(2) (2001) 227-243. [27] markides, ch.f., pazis, d.n., kourkoulis, s.k, influence of friction on the stress field of the brazilian tensile test, rock mechanics and rock engineering, 44(1) (2011) 113-119. [28] markides, ch.f., kourkoulis, s.k., the stress field in a standardized brazilian disc: the influence of the loading type acting on the actual contact length, rock mechanics and rock engineering, 45(2) (2012) 145-158. [29] kourkoulis, s.k., prassianakis, i., agioutantis, z., exadaktylos, g.e., reliability assessment of the ndt results for the internal damage of marble specimens, international journal of material and product technology, 26(1/2) (2006) 35-56. [30] kosmatka, s.h., kerkhoff, b., panarese, w.c., design and control of concrete mixtures (14th ed.), portland cement association (2002). [31] chorfa, a., madjoubi, m.a., hamidouche, m., bouras, n., rubio, j., rubio, f., glass hardness and elastic modulus determination by nanoindentation using displacement and energy methods, ceramics silikáty, 54(3) (2010) 225-234. [32] sehgal, j., ito, s., brittleness of glass, journal of non-crystalline solids, 253 (1999) 126-132. [33] mogi, k., earthquakes and fractures, tectonophysics, 5(1) (1967) 35-55. [34] rao, m.v.m.s., lakshmi k.j.p., rao, g.m.n., vijayakumar, k., udayakumar, s., precursory microcracking and brittle failure of latur basalt and migmatite gneiss under compressive loading, current science, 101(8) (2011) 1053-1059. [35] nomikos, p.p., sakkas, k.m., sofianos, a.i., acoustic emission of dionysos marble specimens in uniaxial compression, harmonising rock engineering and the environment, qian and zhou (eds.), taylor & francis group, london, isbn 978-0-415-80444-8. [36] agioutantis, z., kaklis, k., mavriagiannakis, s., verigakis, m., vallianatos, f., saltas, v., potential of acoustic emissions from three point bending tests as rock failure precursors, international journal of mining science and technology, 26 (2016) 155-160. << /ascii85encodepages false /allowtransparency false /autopositionepsfiles true /autorotatepages /none /binding /left /calgrayprofile (dot gain 20%) /calrgbprofile (srgb iec61966-2.1) /calcmykprofile (u.s. web coated \050swop\051 v2) /srgbprofile (srgb iec61966-2.1) /cannotembedfontpolicy /error /compatibilitylevel 1.4 /compressobjects /tags /compresspages true /convertimagestoindexed true /passthroughjpegimages true /createjobticket false /defaultrenderingintent /default /detectblends true /detectcurves 0.0000 /colorconversionstrategy /cmyk /dothumbnails false /embedallfonts true /embedopentype false /parseiccprofilesincomments true /embedjoboptions true /dscreportinglevel 0 /emitdscwarnings false /endpage -1 /imagememory 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/hrv (za stvaranje adobe pdf dokumenata najpogodnijih za visokokvalitetni ispis prije tiskanja koristite ove postavke. stvoreni pdf dokumenti mogu se otvoriti acrobat i adobe reader 5.0 i kasnijim verzijama.) /hun 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can be opened with acrobat and adobe reader 5.0 and later.) >> /namespace [ (adobe) (common) (1.0) ] /othernamespaces [ << /asreaderspreads false /cropimagestoframes true /errorcontrol /warnandcontinue /flattenerignorespreadoverrides false /includeguidesgrids false /includenonprinting false /includeslug false /namespace [ (adobe) (indesign) (4.0) ] /omitplacedbitmaps false /omitplacedeps false /omitplacedpdf false /simulateoverprint /legacy >> << /addbleedmarks false /addcolorbars false /addcropmarks false /addpageinfo false /addregmarks false /convertcolors /converttocmyk /destinationprofilename () /destinationprofileselector /documentcmyk /downsample16bitimages true /flattenerpreset << /presetselector /mediumresolution >> /formelements false /generatestructure false /includebookmarks false /includehyperlinks false /includeinteractive false /includelayers false /includeprofiles false /multimediahandling /useobjectsettings /namespace [ (adobe) (creativesuite) (2.0) ] /pdfxoutputintentprofileselector /documentcmyk /preserveediting true /untaggedcmykhandling /leaveuntagged /untaggedrgbhandling /usedocumentprofile /usedocumentbleed false >> ] >> setdistillerparams << /hwresolution [2400 2400] /pagesize [612.000 792.000] >> setpagedevice microsoft word numero_29_art_14 g. gianbanco et alii, frattura ed integrità strutturale, 29 (2014) 150-165; doi: 10.3221/igf-esis.29.14 150 focussed on: computational mechanics and mechanics of materials in italy ch of masonry materials via meshless meso-modeling giuseppe giambanco, emma la malfa ribolla, antonino spada department of civil, environmental, aerospace and materials engineering (dicam) university of palermo giuseppe.giambanco@unipa.it, emmalamalfa@hotmail.it, antonino.spada@unipa.it abstract. in the present study a multi-scale computational strategy for the analysis of masonry structures is presented. the structural macroscopic behaviour is obtained making use of the computational homogenization (ch) technique based on the solution of the boundary value problem (bvp) of a detailed unit cell (uc) chosen at the meso-scale and representative of the heterogeneous material. the smallest uc is composed by a brick and half of its surrounding joints, the former assumed to behave elastically while the latter considered with an elastoplastic softening response. the governing equations at the macroscopic level are formulated in the framework of finite element method while the meshless method (mm) is adopted to solve the bvp at the mesoscopic level. the work focuses on the bvp solution. the consistent tangent stiffness matrix at a macroscopic quadrature point is evaluated on the base of bvp results for the uc together with a localisation procedure. validation of the mm procedure at the meso-scale level is demonstrated by numerical examples that show the results of the bvp for the simple cases of normal and shear loading of the uc. keywords. multiscale; mesomodeling; meshless; masonry. introduction odeling of structures constituted by heterogeneous materials, as masonry and composite laminates, is still one of the most complex and challenging matters of the modern structural engineering. anisotropy, asymmetry, geometrical and material non-linearities are the main features of the mechanical behavior to be considered in the formulation of the structural model. in masonry structures the most relevant kinematical and mechanical phenomena take place at a scale which is small if compared to the dimensions of the structure. on the other side, the structure is governed, in its peculiar overall response, by its global geometrical and morphological configuration. in literature, two different scales of interest are distinguished, directly linked to as many theoretical approaches: the mesoscopic approach and the macroscopic approach. the mesoscopic approach considers units and their interfaces individually. most of the efforts in this research area are concentrated on the formulation of advanced interface constitutive laws capable to describe the damage evolution and the onset of irreversible strains and related coupled effects for different mechanical problems. in giambanco et al. [1] the masonry material is considered as an assembly of units in contact by means of elastoplastic zero-thickness interfaces, focusing on the cohesive-frictional joint transition. lourenço and rotz [2] proposed a joint failure criterion which adopts a cap model to take into account the mortar compaction due to high compressive stresses. alfano and sacco [3] introduced a damage-plasticity interface model that discriminated a linear elastic undamaged zone from a damaged zone with an unilateral coulomb friction law. more recently, spada et al. [4] and sacco and lebon [5] concentrated in the formulation of interface laws which include the non-linear effects of stiffness m g. gianbanco et alii, frattura ed integrità strutturale, 29 (2014) 150-166; doi: 10.3221/igf-esis.29.14 151 degradation, loss of adhesion and unilateral contact with related frictional phenomena. the contribution of internal stresses and strains at the interface level has been finally inserted by giambanco et al. [6] to enrich the interface model. the mesoscopic approach is a rigorous method of analysis but many difficulties arise in the mesh creation and a fine discretization of the structure has to be used, which lead to prohibitive computational costs for large structures. the macroscopic approach considers the structure as constituted by a fictitious homogeneous and continuous material. in this approach simplified constitutive models are formulated in a phenomenological manner, intentionally neglecting the actual material composition but smearing the effects of the heterogeneities presence by appropriate mechanical assumptions [7]. the multiscale techniques belong to the second approach and couple different scales of interest by means of specific transition laws capable to exchange information between different consecutive scales [8-10]. according to [11] three homogenization techniques exist: the analytical homogenization, the numerical homogenization, and the computational homogenization (ch). in particular the ch consists in the following steps. a macroscopic strain or stress is used to apply kinematic or static boundary conditions to the uc (macro-meso scale transition). the equilibrium of the uc is obtained by solving a bvp at the mesoscale. lastly, the macro-strains or macro-stresses are assumed to be the average on the uc of the corresponding meso-strains or meso-stresses (meso-macro scale transition). in a strain driven process, the aforementioned boundary conditions are of dirichlet type and are chosen linear or periodic. the latter imply the repetition of inelastic phenomena for adjacent ucs. despite it is known in literature that periodic conditions offer a better estimate of stiffness matrix with respect to linear conditions, in this paper linear conditions are used, with the aim to verify the difference in future works. two different ch methods are distinguished. in the first order ch method cauchy models are used at all scales. this method is based on the satisfaction of the principle of separation of scales, which asserts that the characteristic size of the uc is much smaller then the size of the structure [12]. massart [13] proposed an enhanced multiscale model for masonry structures using nonlocal implicit gradient isotropic damage models for both constituents of the uc. a second ch method employs cosserat or higher order continua to consider those cases in which strong strain or stress gradients arise at the macroscopic level or the mesoscopic dimensions of the uc constituents are comparable with the ones at the macro-level. addessi and sacco [14] analyzed masonry panels in the framework of transformation field analysis by using a two-dimensional cosserat continuum for macro-scale and a non-linear damage contact-friction model for the mortar joints at the meso-scale. many authors have also faced the problem of localization of deformations. for ductile materials with an elastic-plastic behavior sufficiently deformed into the plastic range, the abrupt changes in the deformation field occur across narrow zones (shear bands). this phenomenon is called localization of plastic deformation. rice [17] and ottosen and runesson [18] studied the problem and found the conditions under which the localization occurs. massart et al [16] inserted the localization procedure into a multi-scale problem, considering a gradient damage model at the mesoscale. in this paper a multiscale computational strategy for the analysis of masonry structures is presented. the applied technique belongs to the first order ch methods. the uc chosen at the meso-scale is composed by a brick and half of its surrounding joints. brick is assumed elastic while mortar joints are modeled by means of zero-thickness elasto-plastic interface elements. the bvp is solved applying the meshless method (mm) and the uc is subjected to linear boundary displacements. unlike fem, in mm the shape functions are only approximants and not interpolants. these are obtained by defining the influence of nodes on a fixed point by means of weight functions, which have a compact support. the support size is dependent by the so-called dilatation parameter or smoothing length. the smoothing length is critical for the solution accuracy and stability, it plays the role of the element size in the finite element method. the mm is employed to overcome the problem of computational cost associated with the use of a classical fem analysis at the meso-scale. this method is also able to easily treat the problem of crack formation and propagation. it will therefore be applied to describe crack formation and propagation in the brick, that is one of the future developments of the present work. another advantage is related to the possibility to use higher-order continuous weight functions. the macro-scale consistent tangent stiffness matrix and localization of deformation are derived. numerical examples show the behavior of the uc and results of localization for two different cases, i.e. when boundary displacements enslave the uc to normal and shear strains. the computational homogenization (ch) scheme et us consider, in the euclidean space 3 referred to the orthonormal frame 1 2 3( , , , )o i i i , a structure  constituted by an heterogeneous material, at the mesoscale (fig. 1). l g. gianbanco et alii, frattura ed integrità strutturale, 29 (2014) 150-165; doi: 10.3221/igf-esis.29.14 152 figure 1: mechanical scheme of a structure constituted by an heterogeneous material. our aim is to derive the structure-properties, or the properties at the macroscopic level (m), based on the kinematical and mechanical phenomena occurring at the mesoscale level (m) of the heterogeneous material. the boundary of the structure is divided in two parts u and t where kinematic and loading conditions are specified, respectively. the external actions are the body force f for unit volume and the surface tractions t . the structural response at the macroscopic level is given by the displacement mu , strains mε and stress mσ fields. the equilibrium of the structure can be assessed in a weak form making use of the principle of virtual displacement (pvd), thus t t t t m m m md d d            f u t u σ ε , (1) where mε are the virtual strains satisfying the following kinematical compatibility conditions expressed under the small displacement hypothesis: m m in  ε c u (2) with c the kinematical compatibility matrix. the above reported variational formulation of the structure equilibrium can be solved in an approximated way making use of the finite element method. the continuous structure is discretized in a finite number of subdomains or elements e (fig. 2). the equilibrium of the discretized structure requires the equilibrium of all the elements. it can be expressed in a weak form as follows: e te e t t t m m m md d d            f u t u σ ε . (3) the displacement at any point within the element is approximated making use of appropriate interpolation functions: m m u n u , (4) being n the matrix of interpolation functions and m u the virtual displacements vector of the element nodes. in the ch methods, the macroscopic response is evaluated as the average of the response of the uc. the scale transition is based on the hill-mandel principle [20, 21] which establishes that the virtual work density at the macro-scale must be equal the volume average of the virtual work at the meso-scale: 1 uc t t m m m m uc d      σ ε σ ε . (5) from eq. (3) and (5) it comes out that the equilibrium of the discretized structure constituted by the heterogeneous material can be solved if the equilibrium of the uc is assessed under specific boundary conditions. the downscaling operation, also known as macro-meso transition, consists in the evaluation of the boundary conditions to be applied to the uc. in the first-order computational homogenization the macro-meso transition is usually ”deformation driven” because this procedure can be directly fit into a displacement-based finite element framework. therefore, the macroscopic g. gianbanco et alii, frattura ed integrità strutturale, 29 (2014) 150-166; doi: 10.3221/igf-esis.29.14 153 deformation tensor is calculated at the material point of the finite element and it is next used to formulate the kinematical boundary conditions to be imposed on the uc associated to this point. figure 2: mechanical scheme of the ch strategy. in literature the periodic boundary conditions are suggested for periodic materials. in the present work, considering that the uc mechanical response in the non linear stage is strongly affected by the decohesion process occurring at the material interfaces, firstly the linear boundary conditions are imposed to the uc, thus onm m m uc u d ε (6) where, for 2d applications: 0 2 0 2 m yx xy          d is a matrix that depends on the x-y coordinates of the nodal point once a reference system is fixed. mu are the prescribed values of the displacements for the point of position x located on the boundary uc of the uc. this choice could be easily modified on the basis of the obtained numerical results. since the body forces can be neglected and the whole boundary is constrained, the variational form of the uc equilibrium can be expressed as follows: 0 uc t m m d    σ ε (7) and it has to hold in presence of the kinematical constraint onm m uc u u (8) the kinematical constraint (8) can be incorporated in the variational equality (7) making use of the lagrange multiplier method, thus   uc uc uc t t t m m m m md d d             σ ε r u u r u (9) where r is the vector of lagrangian multipliers and mε the virtual strain tensor of the uc related to the virtual displacements through the following compatibility condition: g. gianbanco et alii, frattura ed integrità strutturale, 29 (2014) 150-165; doi: 10.3221/igf-esis.29.14 154 inm m uc  ε c u (10) imposing the hill-mandel principle and substituting (6) in (9), after some algebra the following equation is obtained:  1 1 uc uc t t m m m m m m uc uc d d                 σ d r ε r d ε u (11) since the previous equation has to hold for any value of  r and mε , it provides the following conditions: m m mu d ε (12) 1 uc t m m uc d     σ d r (13) eq. (12) is the macro-meso transition condition here adopted for the multiscale problem. eq. (13) represents the equilibrium condition of the uc but also relates the macroscopic stress to the mesoscopic mechanical response in terms of reaction forces arising along the boundary of the cell and, in this sense, it can be considered as the meso-macro transition or upscaling equation. unit cell boundary value problem or the case of running bond masonry, according to [22] and [13], the smallest uc is constituted by a single block surrounded by half of the head and bed mortar joints and the periodicity is defined by the two directions 1i and 2i since the heterogeneous material can be constructed by repeating the uc along these directions (fig. 3). in the present work the material of the blocks is considered indefinitely elastic and the interfaces constitutive laws, expressed in terms of contact tractions iσ and displacement discontinuities at the interface  iu , are developed in the framework of elastoplasticity for non standard materials. figure 3: unit cell extracted from running bond masonry. the following general assumptions are adopted to describe the mechanical behavior of the interfaces:  the traction components are continuous at the interface  mi σ 0 (14)  the strain components along the thickness h of the interface are uniform and evaluated on the basis of the values assumed by the displacement discontinuity components  m mi h  u ε (15)  the total strain and the total displacement discontinuities are decomposed in the elastic (e) and inelastic (p) parts      , e pe pmi mi mi m m m   ε ε ε u u u . (16) f g. gianbanco et alii, frattura ed integrità strutturale, 29 (2014) 150-166; doi: 10.3221/igf-esis.29.14 155 with reference to the assumed hypotheses, the material of the block is considered elastic and inelastic displacement discontinuities arise at the zero-thickness interfaces, thus mb b mbσ e ε (17)     pmi i m m σ e u u (18) where be and ie are the elastic matrices of the block material and of the interfaces, respectively. irreversible discontinuous displacements occur when the interface stress state reaches a limit condition. the elastic domain is defined by two convex limit surfaces intersecting in a non-smooth fashion: the coulomb bilinear limit surface and a tension cut-off (fig. 4). the limit functions, reported in the stress space take the following form:    1 0, tan 1p p pmi mi mi c        τ (19)    2 0, 1p p pmi mi        (20) where miτ and mi are the tangential stress vector and the normal stress component of the contact stresses,  is the friction angle, 0c and 0 the cohesion and tensile strength of the virgin interfaces. p is a static variable which is associated to the internal variable p which regulates the isotropic hardening-softening interface behavior: p p ph  (21) with ph the hardening-softening parameter. figure 4: bilinear plastic limit condition represented in the plane stress space. the inelastic displacement discontinuities develop according to a non-associative flow rule:   2 1 2 1 2 1 2, p p p p p p p p p p m p p mi mi g                     u σ σ      (22) where 1p and 2p are the plastic multipliers which satisfy the complementarity conditions 1 2 1 2 1 1 2 20, 0, 0, 0, 0p p p p p p p p                . (23) the plastic potential related to the limit condition (19) is expressed by the following function:    , 1 tan 0p p pmi mi mig r        τ , (24) with  0,  dilatancy angle and r an arbitrary material constant selected in such a way to satisfy eq. (24) for any stress state. g. gianbanco et alii, frattura ed integrità strutturale, 29 (2014) 150-165; doi: 10.3221/igf-esis.29.14 156 the weak form of uc equilibrium (9) leads to the following conditions: div mb bon σ 0 (25) 1, , 4mb k mi bkon k  σ n σ  (26) 1, , 4mi ikon k  σ r  (27) 1, , 4m m ikon k  u u  (28) meshless solution of the bvp generally the solution of the uc boundary value problem is approached in an approximated way making use of the finite element method and, since two finite element meshes are used at the macroscopic and mesoscopic levels, the method is known as fe2. the present study approaches the numerical solution of the mesoscopic model by means of a meshless strategy which is described in the following for plane stress conditions. in two-dimensional models of masonry structures the plane stress or plain strain assumption is adopted depending on the geometry of the structural element. a specific study on the range of validity of the two different assumptions has been developed by anthoine [23]. the principal conclusion is that in the linear range both provide satisfactory results while in the non linear range the plane stress assumption may lead to inaccurate results. in this case the plane stress assumption is adopted because the implementation is finalized to the study of masonry walls where the thickness is quite small if compared to the other dimensions. the plane stress condition is also used to develop numerical simulations on masonry specimens under the assumption that the non linearities are concentrated at the joint level and the block material is indefinitely elastic. in view of this last assumption inaccurate results related to the plane stress condition can be considered of the same order of the numerical approximations. figure 5: unit cell meshless model. with reference to fig. 5 the uc is divided in five integration domains: the first ( b ) corresponds to the volume occupied by the block. the others integration domains are the interfaces ( 1, , 4 )k k   . totally seventeen nodes are used to discretize the uc but different choices are possible in order to refine the numerical solution. the displacement field inside each sub-domain is obtained from the nodal displacement values mu by the moving least square approximation (mls). the approximated value of a displacement component is expressed as a polynomial function:      tmu x p x a x (29) with  p x a monomial basis function and  a x a vector of coefficients which are functions of the spatial coordinates x . in the present case the basis function adopted is linear,    1 21t x xp x , and the coefficients are obtained by performing the minimization of the following functional: g. gianbanco et alii, frattura ed integrità strutturale, 29 (2014) 150-166; doi: 10.3221/igf-esis.29.14 157       2 1 n j m j mj j j w u u     x x x (30) where n is the number of nodes and    j j jw w x x x is the weight function depending on the distance between the sampling point and the node j. minimizing functional (30) the result is a system of linear equations      1 m  a x a x b x u (31) where         1 n t j j w   a x x p x p x (32)              1 1 2 2, , , n nw w w   b x x p x x p x x p x (33)  1 2 t m m m mnu u uu  (34) substituting the result (31) into (29) the mls approximation function is finally obtained as    tm mu x x u (35) where the shape function  t x is given by        1t t x p x a x b x (36) the weight function plays an important role in the performance of the mls approximation. the quartic spline function   2 3 41 6 8 3 for 0 1 0 for 1 j j j j j j r r r r w r          x (37) is adopted in this work, where /j jr d x x , being d the radius of the domain of definition of the point x (smoothing length). making use of the mls approximations for the two components of the displacement field, the kinematical compatibility conditions for the block and for the interfaces are    ,mb b b m m i i b b m  ε c φ s u u φ s φ s u (38) where bφ and iφ are the approximation functions, bs and is are the selectivity matrices, evaluated for the block and for the interface domains, respectively. c is the classical compatibility matrix for the plane stress case. in addition, the reaction forces on the boundaries k are approximated in terms of nodal values r as  r ψ x r (39) where  ψ x are the approximation functions for the reaction forces. considering the kinematical eq. (38), the approximation (39) and the elastic constitutive laws for the block (17) and for the mortar joints (18), the weak form of the uc equilibrium can be particularized in the following expression           4 1 4 4 1 1 4 1 0 b k k k k tt t t t m b b b b b i i b b i i i b b m k pt t t i i b b i m i i i i k k t t i i i i m m k d d d d d                                        u s φ c e cφ s φ s φ s k φ s φ s u φ s φ s k u s φ ψ s r r s ψ φ s u u (40) g. gianbanco et alii, frattura ed integrità strutturale, 29 (2014) 150-165; doi: 10.3221/igf-esis.29.14 158 where ik is the stiffness matrix for interfaces, defined as /i i hk e . making the following positions     4 1 b k tt t t b b b b b i i b b i i i b b k d d         k s φ c e cφ s φ s φ s k φ s φ s (41) 4 1 k t t i i i i k d    g s φ ψ s (42)     4 1 k pt p i i b b i m k d     f φ s φ s k u (43) 4 4 1 1 k k t t t t t m i i m i i m m m k k d d          u s ψ u s ψ d ε q ε (44) the (40) becomes     0t t tm m m m    u k u g r r g u u (45) since eq. (45) has to hold for any arbitrary m u and  r , the governing equations of the uc are obtained, in the following matrix form: m p t m                k g u f g 0 r u (46) in order to evaluate the integrals (41)-(44), the gauss quadrature rule is adopted with nine sample points in the block domain and three sample points for each interface. furthermore, it is assumed i iψ φ . in order to be introduced in a step-by-step algorithm, the governing eq. (46) need to be rewritten in a discrete formulation. a newton-raphson procedure is employed at the mesoscale to find the solution of the bvp for a single load step. each iteration of the load step is divided in an elastic trial predictor stage and a plastic corrector stage. consistent tangent stiffness matrix evaluation in the time step , 1n nt t    the increment of boundary displacements mu is assigned. the inverse form of equation system (46) reads 11 12 21 22 m p m                    u b b f r b b u separable in the two expressions 11 12m p m    u b f b u (47) 21 22p m    r b f b u (48) it is clear how nodal displacements and reactions are dependent on two contributes that can be assumed equal to an elastic part (function of mu ) and a plastic part (function of pf ). recalling (13), (39), (44) and (48) it is simply obtained that 22 21 1 1t m m p uc uc                  σ q b q ε q b f (49) the macroscopic tangent stiffness matrix is defined as: g. gianbanco et alii, frattura ed integrità strutturale, 29 (2014) 150-166; doi: 10.3221/igf-esis.29.14 159 22 21 1 1 pct tm m uc uc m                  fσ e q b q q b ε ε (50) in the previous equation the second term has to be explicitly evaluated. after mathematical manipulation it is possible to write that    p p m m m m m m           f f u u α ε u ε ε (51) where         4 3 1 1 ppj ppj p t m gpj i i b b i i i b b k j m w              x x u α φ s φ s k φ s φ s u (52) from eq. (47) 11 12 p tm m m      fu b b q ε ε (53) which, substituted in (51), furnishes:   111 12 p t m     f α i b α b q ε (54) the consistent macroscopic tangent stiffness matrix is therefore written as the sum of an elastic and a plastic part: ct ct ct e p e e e (55) with 22 1ct t e uc   e q b q (56)   121 11 12 1ct t p uc     e q b α i b α b q (57) localization of deformation at a single macroscopic quadrature point let us consider, at a macroscopic quadrature point, a discontinuity band characterized by an incipient loss of strain continuity (fig. 6). figure 6: body split by a potential discontinuity band. g. gianbanco et alii, frattura ed integrità strutturale, 29 (2014) 150-165; doi: 10.3221/igf-esis.29.14 160 the band splits the volume in the two subdomains v  and v  and is identified by the unit vector n oriented towards v  . the traction continuity condition imposes that t t n n n n      σ σ c σ c σ    (58) where σ and σ denote the rates of stress vectors on the negative and positive sides of the discontinuity band, respectively. nc is the kinematical compatibility matrix particularized for the surface having unit normal vector n . a kinematical condition has also to be imposed, concerning displacement continuity. this condition leads to the equation n   ε ε c c m   (59) in (59) ε and ε are the rates of strain vectors on the negative and positive sides. the following position has also been used: c c m (60) with c representing the jump magnitude, while m is a unit vector called polarization vector. the angle between m and n unit vectors characterizes the failure mode: when m is aligned with n a splitting mode i process is present; when m is perpendicular to n a shear mode ii is present. in general, v  and v  can be constituted by different materials and the following constitutive relations can be written: ct  σ e ε  (61) ct  σ e ε  (62) with ct e and ct e the tangent stiffness matrices in v  and v  . substituting the expressions (61) and (62) on (58), the following equation is obtained: t ct t ct n n    c e ε c e ε  (63) if eq. (59) is also introduced we finally derive:  t ct ct t ctn n n    c e e ε c e c m c  (64) in the case of continuous bifurcation (when the tangent stiffness matrices in v  and v  are the same: ct ct ct  e e e ), the condition of incipient macroscopic localization occurs if it happens that t ct n n  c e c m l m 0 (65) in the last condition t ct n nl c e c (66) is called localization matrix (or acoustic matrix). since m is a unit vector, the condition of incipient localization can be written as det 0l (67) besides, localization occurs when the stiffness matrix loses its positive definiteness. this means that the set of orientations n for which localization may appear is determined by the inequality [16]: det 0l (68) in a localization procedure n is not known in advance. therefore, scanning for all possible unit vectors n , the discontinuous band is chosen looking for all n directions that comply with (68) and whose minimum eigenvalue of l matrix is the absolute minimum one. the corresponding eigenvector finally identifies the polarization vector. g. gianbanco et alii, frattura ed integrità strutturale, 29 (2014) 150-166; doi: 10.3221/igf-esis.29.14 161 numerical examples o show the effectiveness of the meshless procedure for bvp solution and of the localization technique, the response of a uc under the two displacement conditions showed in fig. 7 is analyzed. figure 7: boundary conditions imposed to the uc in the three examples analyzed. the uc is composed by a brick having length equal to 204 mm and height equal to 50 mm, surrounded by a mortar layer of thickness equal to 5 mm. the mechanical parameters adopted for the two materials are reported in tab. 1, while interfaces’ parameters are reported in tab. 2. the uc is constrained for its entire boundary surface. the tests are run under displacement control. the elastic tangent stiffness matrix is: 3 10.2 0.31 0 0.31 3.39 0 10 mpa 0 0 1.55 ct e          e  mpae  block 16700 0.15 mortar 820 0.14 table 1: components mechanical properties.  0 mpac  0 mpa ph       0.35 0.25 5 37 2 3 table 2: interface parameters. example 1. horizontal strain applied in this case the external boundary nodes on 2 and 4 interfaces are forced to move along the 1x direction. as a consequence, the inner block is stretched and results in a biaxial tensile stress condition. the uc average stress versus average strain diagram is reported in fig. 8. different stages can be distinguished. at the beginning the response is elastic. the slope of the curve changes when plasticity starts to appear on vertical interfaces, at around 0.8 mpa of stress level. at the end of this first nonlinear branch the plasticity level at each gauss point of the interfaces is showed by histograms of fig. 9a. an histogram ranges from 0 (absence of plasticity, white colour) to 1 (complete loss of cohesion-adhesion, dark colour). increasing the strain, plasticity develops on horizontal interfaces also until the maximum stress is reached. a softening branch follows this stage until all gauss points, unless those on the symmetry axis, have their maximum plasticity level (fig. 9c,d). t g. gianbanco et alii, frattura ed integrità strutturale, 29 (2014) 150-165; doi: 10.3221/igf-esis.29.14 162 a residual stress is finally observed due to the uc confinement. the results of localization procedure is also showed at four stages of fig. 9. the localization matrix has a positive determinant until the maximum stress is obtained and no localization can be identified before. once the maximum load is reached det 0l for 0 60 65      but the minimum eigenvalue is obtained for 0   (fig. 10), that is the direction of n vector. eigenvector analysis of l matrix furnishes an m vector aligned with n , that confirms the mode i failure of the uc. figure 8: example 1: mx mx  diagram. (a) (b) (c) (d) figure 9: example 1: plasticity evolution at interface gauss points and results of localization at four stages indicated in fig. 8. (a) (b) figure 10: example 1: determinant of localization matrix (a) and minimum eigenvalue (b) for different configurations of n vector. colours of line refer to the stages indicated in fig. 8. example 2. shear strain applied in this second example the uc is subjected to a monotonically increasing shear strain. in this case plasticity appears at two opposite corners of the uc due to shear stresses at each interface gauss point. the average stress-strain curve is nonlinear and evolves from an elastic stage towards a residual line governed by mohr-coulomb limit condition and dilatancy angle (fig. 11). it is important to highlight that after the localization procedure the n direction is close to the diagonal of the uc, while m evolves during the test and, if at the beginning it seems to be closer to n , at the end the two vectors are g. gianbanco et alii, frattura ed integrità strutturale, 29 (2014) 150-166; doi: 10.3221/igf-esis.29.14 163 almost perpendicular. in this case the failure mode is of mixed type with a tendency to became of mode ii (fig. 12a-d). the angles of n and m vectors with respect to the 1x axis at the final configuration are of 15.9° and 86.4° respectively. in fig. 13 the determinant of localization matrix and minimum eigenvalue curves versus orientation  of n vector are reported. figure 11: example 2: m m  diagram. (a) (b) (c) (d) figure 12: example 2: plasticity evolution at interface gauss points and results of localization at four stages indicated in fig. 11. (a) (b) figure 13: example 2: determinant of localization matrix (a) and minimum eigenvalue (b) for different configurations of n vector. colours of line refer to the stages indicated in fig. 11. conclusions his paper focuses on a first order ch method based on a fe-meshless multiscale procedure to be employed to simulate running bond masonry materials in plane stress regime. the uc is chosen equal to a brick surrounded by half mortar joint layer and the boundary value problem is solved by means of a meshless approach, which is the principal novelty of the paper. linear displacements are applied on the uc boundary. the results will be compared with those obtained using periodic boundary conditions in a future work. a simple system represents the solving equations of t g. gianbanco et alii, frattura ed integrità strutturale, 29 (2014) 150-165; doi: 10.3221/igf-esis.29.14 164 the bvp. also, the consistent macroscopic tangent stiffness matrix is evaluated and a localization procedure to find discontinuity bands at the macroscale is taken into account. two numerical examples focusing on the uc response only are reported. the results of the bvp are analyzed to confirm the goodness of the meshless method to be employed to solve the problem at the mesoscale. the localization procedure for the two examples correctly identifies the failure mode type. future developments regards the extension of this strategy to other heterogeneous periodic or non-periodic materials also for 3d analyses and the introduction of a non linear behavior for bricks. particular attention will be paid on meshdependency for the response at the macroscale level. acknowledgements he authors acknowledge the financial support given by the italian ministry of education, university and research (miur) under the prin09 project 2009xwlfkw_005, “a multiscale approach for the analysis of decohesion processes and fracture propagation”. references [1] giambanco, g., rizzo, s., spallino, r., numerical analysis of masonry structures via interface models, comput. methods appl. mech. eng., 190 (49) (2001) 6493-6511. [2] lourenço, p.b., rots, j.g., multisurface interface model for analysis of masonry structures, j. eng. mech. (asce), 123 (7) (1997) 660-668. [3] alfano, g., sacco, e., combining interface damage and friction in a cohesive zone model, int. j. numer. methods engrg., 68 (2006) 542–582. [4] spada, a., giambanco, g., rizzo, p., damage and plasticity at the interfaces in composite materials and structures., comput. methods appl. mech. eng., 198 (49) (2009), 3884-3901. [5] sacco, e., lebon, f., a damage-friction interface model derived from micromechanical approach., int. j. solids and struct., 49 (26) (2012) 3666-3680. [6] giambanco, g., fileccia scimemi, g., spada, a., the interphase finite element, comput. mech., 50 (2012), 353-366. [7] fuschi, p., giambanco, g., rizzo, s., nonlinear finite element analysis of no-tension masonry structures, meccanica, 30 (3) (1995) 233-249. [8] kouznetsova, v., geers, m.g., brekelmans, w.m., multi-scale constitutive modelling of heterogeneous materials with a gradient-enhanced computational homogenization scheme, int. j. numer. meth. eng., 54 (2002) 1235-1260. [9] miehe, c., koch, a., computational micro-to-macro transitions of discretized microsctructures undergoing small strains, applied mech., 72 (2002) 300-317. [10] feyel, f., chaboche, j.l., fe2 multiscale approach for modelling the elasto-viscoplastic behavior of long fibre sic/ti composite materials, comput. methods appl. mech. eng., 183 (3) (2000) 309-330. [11] nguyen, v.p., stroeven, m., sluys, l.j., multiscale continuous and discontinuous modeling of heterogeneous materials: a review on recent developments, j. multiscale model., 3 (04) (2011) 229-270. [12] geers, m.g.d., kouznetsova, v.g., brekelmans, w.a.m., multiscale computational homogenization: trends and challenges, j. comput. appl. math., 234 (7) (2010) 2175-2182. [13] massart, t.j., multi-scale modeling of damage in masonry structures, ph. d. thesis, university of technology, eindhoven, (2003). [14] addessi, d., sacco, e., a multi-scale enriched model for the analysis of masonry panels, int. j. solids and struct., 49 (6) (2012) 865-880. [15] jirásek, m., mathemathical analysis of strain localization, regc – damage and fracture in geomaterials, 11 (2007) 977-991. [16] massart, t.j., peerlings, r.h.j., geers, m.g.d., an enhanced multi-scale approach for masonry wall computations with localization of damage, int. j. numer. meth. engrg, 69 (2007) 1022-1059. [17] rice, j.r., the localization of plastic deformation, theoretical and applied mech., proc. 14th iutam congr., delft, the netherlands, 30 aug-4 sept (1976) 207-220. [18] ottosen, n.s., runesson, k., properties of discontinuous bifurcation solutions in elasto-plasticity, int. j. solids and struct., 4 (1991) 401-421. t g. gianbanco et alii, frattura ed integrità strutturale, 29 (2014) 150-166; doi: 10.3221/igf-esis.29.14 165 [19] atluri, s.n., shen, s., the meshless method, tech. sci. press, forsyth, (2002). [20] hill, r., a self-consistent mechanics of composite materials, j. mech. and phys. solids, 13 (4) (1965), 213-222. [21] mandel, j., plasticit classique et viscoplasticit, springer-verlag, udine italy, (1971). [22] anthoine, a., derivation of the in-plane elastic characteristics of masonry through homogenization theory, int. j. solids struct., 32 (2) (1995) 137-163. [23] anthoine, a., homogenization of periodic masonry: plane stress, generalized plane strain or 3d modeling, com. num. meth. eng., 13 (1997) 319-326. microsoft word numero_29_art_33 w. guodong, frattura ed integrità strutturale, 29 (2014) 376-384; doi: 10.3221/igf-esis.29.33 376 the research for mechanics stimulation method of nonlinear random vibration based on statistical linear theory wang guodong chongqing water resources and electric engineering college chongqing, 402160, china 673843103@qq.com abstract. earthquake disasters have brought great harm to people's life safety and economic property. its effect on fabric mainly focus on random effects currently, the general pseudo excitation method could solve the inefficiency calculation problem of linear random earthquake. however it could not take the nonlinear problem factors into account for calculation. in this paper, we suggest that a nonlinear structural incentive method should be improved based on statistical linearity to calculate and solve absolute displacement value. through the analysis and research for cases, we calculate the displacement, speed, random vibration spectrum of bridge’s accelerated speed, as well as the influencing situation of axial force. the results indicate that such perfect incentive method could not only perform nonlinear structure analysis, but also to be very accurate and high effective. such method could reasonably avoid the displacement decomposition and solution of the pseudostatic model，thus it will be widely applied in common software. keywords. structure; incentive method; nonlinear random vibration; axial force. introduction n recent years, earthquake disasters occurred frequently in our country, it has brought more and more loss to people. the prevention and control efforts that we have taken for earthquake disasters have been enlarged in china. however the seismic theory has been gradually advanced, and transformed from static force into dynamic force, and transferred from established pattern into random one. now we should explore the transforming mechanism from linearity to nonlinearity. the effect of earthquake on structure mainly focuses on the random effects of seismic oscillation currently. the earthquake input process is generally assumed to be stationary stochastic process. when the actual earthquake occurs, its effect is small in early times, while it would be magnified in following period, afterwards it will be of attenuation gradually. thus the earthquake input process should be considered as non-stationary random process .accordingly, the effect of earthquake on structure could make construction be in linear elastic stage originally. as earthquake effect increases, the structure will enters into nonlinear phase gradually, and begins to have plastic accumulation. when plasticity accumulation reaches certain stage, the structure will be destroyed for it could not resist seismic action. in the seismic process, how architectural structure operates under the load of earthquake is the standard of measuring anti-seismic effect. in the original seismic experience, applying proper method into designing building structure is an approach suitable to actual circumstance. nowadays, the widely applied method in china includes response spectrum method, response spectrum method and vibration method. but these methods are relatively fixed, and could not be flexibly applied into the seismic construction of actual building, thus a set of more scientific and reasonable method was born. as it could adopt to the approach of earthquake’s random excitation, it is called random vibration method. it takes i w. guodong, frattura ed integrità strutturale, 29 (2014) 376-384; doi: 10.3221/igf-esis.29.33 377 power density as the core, and sufficiently considers the probability problem of earthquake occurring. it is very suitable for the building such as bridges, roads etc which have many structural support points with large span, and it could assist the more advanced analysis and be used as design tools. random vibration method is taken as the design and calculation tool of structural seismic resistance by european structural seismic design code (eurocode 8) in 1995.the highway bridge seismic design code in china also incorporates random vibration method into the calculating method of aseismic design currently. in recent years, jia-hao lin [1] has proposed simple, convenient and accurate pseudo excitation method starting from computational mechanics; jiwei zhang etc[2]have proposed the simple calculation method of response value in structure peak under the non-stationary seismic excitation based on traditional incentive method; yang jiang etc [3]have proposed the pseudo-excitation algorithm with high precision which could only be obtained by a small amount of vibration mode, which is the modified absolute displacement method. so far, calculating working amount with pseudo excitation method could solve the response problem of structural linear stochastic earthquake. there is still no in-depth research for analyzing nonlinear seismic buildings. as architectural design has such response requirement to nonlinear systematic random earthquake, such research method is urgently needed. through referring to the solution of fap numberical value by computer, this paper is to suggest simple and efficient approach of structural nonlinear pseudo excitation method, which could be applied into analyzing displacement, speed, random vibration spectrum of accelerated velocity as well as the influencing situation of axial force, thus we could realize the high accuracy and efficiency in mechanics stimulation method of nonlinear random vibration on the basis of statistical linear theory. statistical linear theory tatistical linear theory originated from the 1960s, r. isaacs etc in america and l.s. pontryagin etc in former soviet union had performed the initial study to this [4]. the numerical method applied in nonlinear differential game began taking shape in the 1980s, and it has developed into the method which could deal with random response problems in nonlinear dynamics system so far. for non-linear mechanics with n degree of freedom, it could be expressed with differential mode [5-7]: [ ]{y} [ {y},{y}] {f(t )}m g   (1) where [m] is the matrix of structural mass with n order; [ ({y},{y})]g  is the equivalent matrix of nonlinear restoring force and damping force. the equivalent linear equation of nonlinear system could be established according to this method: e[ ]{ } [ ]{y} [ ]{y} {f(t )}em y c k    (2) where e e[ ][ ]c k are the equivalent viscous drag coefficient matrix and stiffness matrix respectively, the following could be obtained through direct subtract between (1) type and (2) type: e e[ ] [ ({y},{y})] [ ]{y}-[k ]{y}g c     (3) where ij ij{y} {y(c , k , t )} the steady-state solution of type (2) is, ij ijc , k is the respective element in e e[ ][ ]c k matrix, statistical linear theory is to reasonably select the ij ijc , k in error matrix [ ] : [[ ] [ ]] minte    (4) where e is the mathematical expectation, the solution of type (4) could be obtained through calculation, and the equivalent linear stiffness and viscous damp of nonlinear system is derived. the solution of pseudo-excitation method or stimulation method, we generally establish the equation of motion through the variable generated on the basis of particle’s relative displacement. the equation of motion is established according to d’alembert principle, the inertia force is added on particle as load to avoid the matrix containing support quality in motion process. for the pseudo-excitation algorithm of multiple-support excitation, we could see from above solving idea that the dynamic s f w. guodong, frattura ed integrità strutturale, 29 (2014) 376-384; doi: 10.3221/igf-esis.29.33 378 relative displacement should be taken as the power balance equation of basic variable, then the dynamic relative displacement is derived, as well as the pseudo-static displacement of internal node caused by support movement will be solved, the sum of the two is the absolute displacement, and the solution procedure also avoids the participating computing of support quality matrix. but actually seismic action process is the quality mass vibration of support node generated by seismic excitation, the vibration of internal node is generated by the vibration of support node, earthquake force is directly added on support node, the quality of support node is not easy to determine, thus we usually solve the equation through applying this approach. type (2) could be written into partitioned matrix model: s s s sb s s sb s b bs b bs bb b b b 0 y y y 0 0 y y y m c c k k m c c k k f                                              (5) where by denotes the force displacement on ground of n supports, sy denotes the displacement of all unsupported node in construction system, bf denotes the force of ground effect on n supports, m, c, k denote mass matrix, damping matrix and stiffness matrix respectively, the small sign s, k correspond to the freedom degree of the internal structure node and support node respectively. we assume the damping force is in direct proportion to relative velocity in type (5), du , {0} is used to replace the freedom degree of internal nodes and support nodes in type(5), by which to derive the equation: s d s d s d s bu u u ym c k m a      (6) virtual acceleration excitation is constructed on eq. (6): * i t j j jx e   (7) where superscript“*”represents taking complex conjugate, ,  denote the complex characteristics pair of power spectrum matrix of input ground motion. the product of virtual acceleration excitation and bm in eq. (7) is taken as bf , then it will be substituted into eq. (5): s s s sb s s sb s * i t b j jb bs b bs bb b b 00 y y y e0 y y y m c c k k mm c c k k                                                  (8) type (8) could be expanded as: * i t b b bse s be b bse s bse b b j jy t y y y y em c c k k m         (9) both sides of type (9)is multiplied by 1bm  : 1 * i t b b bse s be b bse s bse b j jy t y y y y em c c k k         (10) when bm mass is big, bm   ; when 1 b bse s be b bse s bse b( y y y y )m c c k k      is 0, type (10) could obtain virtual acceleration excitation of support: * i t b j jy (t ) e   (11) in conclusion, as long as giving a larger mass on support and exerting stimulation, we could realize the load of virtual acceleration excitation. and support’s virtual velocity and virtual displacement incentives are: * i t b j j 1 y (t ) e     , * i tb j j2 1 y (t ) e      (12) type (8) is expanded to be: w. guodong, frattura ed integrità strutturale, 29 (2014) 376-384; doi: 10.3221/igf-esis.29.33 379 s s sc s bse b se s bse by y y y y 0m c c k k       (13) through substituting (12) into (13), virtual absolute displacement sy is obtained. according to pseudo excitation method, the power spectrum matrix of absolute displacement is: s s m * y y s s j 1 ( ) y yts      (14) the analysis and research for cases the exposition of main information about cases e take a prestressed concrete cable-stayed bridge with two span, single tower and double cable planes as an example whose length is 130 m, span arrangement is 75 + 55 m. its tower pier beam is semi-consolidated structural system. the girder section is the section of double solid girder cantilever, the center height of girder is 1.9 m, roof width is 38 m, cantilever length is 4.5 m, lateral solid beam of girder is 3 m, the width of lateral solid beam across back is 4 m, the thickness of roof between solid beam is 0.28 m. the girder section across back is added with baseplate as construction due to needing balance weight, thus box cross-section forms. the girder adopts two-way prestressed system, the king-tower is reinforced concrete leaning tower, the included angle between the center line of the tower and horizon is 75°, the vertical height above bridge is 50.7 m, the king-tower adopts the filled rectangle of variable cross-section, cross section height along the bridge changes from 3 m (tower top) into 8 m (the root of tower above bridge): the width across bridge is 2.5 m. the model is constructed through general finite element software ansys, main girder and main tower adopt c50 concrete, stayed-cable adopts high tensile steel wire psem7 241, cross section type of girder is simulated with finite element modeling, as it is shown in fig. 1, calculation model performs dispersing to tower with space beam element -beam 4, the girder is simplified as fishbone shape through applying spatial beamelement beam 4 with rigid arm, stayedcable adopts link 10 units, the left end of bridge is given vertical translational constraint of freedom degree, the right end of bridge is given transverse translational constraint of freedom degree, the bottom of cable support tower is completely constrained, cable element and beam element apply hinge constraint, as it is shown in fig. 2. figure 1: the girder’s sectional view of cable-stayed bridge (unit: m). figure 2 the diagrammatic figure of concrete deck cable stayed bridge. w w. guodong, frattura ed integrità strutturale, 29 (2014) 376-384; doi: 10.3221/igf-esis.29.33 380 computational analysis in order to verify the validity of pseudo excitation method directly solved with absolute displacement，this paper is to linearize system through applying statistical linearization method, then analyze it through applying the random vibration module and harmonious response module in finite element software. linearization procedure and its solution could refer to literature [8], which has well solved the response problem of nonlinear system with multi-degree of freedom under random excitation through taking full advantage of computer characteristics and combining fap numerical method. fap is the numerical method of statistical linearization method, and could compile corresponding computer program code with various algorithmic languages conveniently. this paper has compiled the procedure of fap algorithm through applying fortran 90, thus to realize the linearization of structure. for the pseudo excitation method directly solved with absolute displacement in this paper, the full method in harmonic response analysis could be applied. vibration isolation bearing is constructed through applying combin40 (it is the combination of mutually paralleled spring slider and damper, and cascaded with a clearance controller), its rigidity is k = 6×106n/, the former 150 order mode of vibration is taken during modal analysis, modal participation quality is as high as 97%, by which to guarantee the sufficient accuracy of algorithm. when applying pseudo excitation method directly solved with absolute displacement, mass 21 -big mass unit is added on 4 support nodes of model base, big mass unit is in rigid connection with support node, the mass takes 106 times of main bridges mass, then the constraint of freedom degree along x, y direction is released. according to the method proposed by above theory, every mass block is exerted with fictitious force, then harmonic response analysis is performed, the pseudo-excitation response after taking into account nonlinearity is obtained, and then the power spectral density matrix of absolute displacement is obtained according to type (14). the power spectrum inputted in calculation applies the practical seismic spectrum [10] obtained through gb50011 -2001 modifying response spectrum’s model iteration proposed by literature [3]. the consistent ground motion parameters: fortification of 7 degree, ⅲ site, the first group designs earthquake grouping, the wave velocity takes 100m/s, coherence function adopts l－w model, the overall structure adopts rayleigh damping, four nodes in base are taken out for performing consistent stimulus in three direction (the four nodes in base are: the constraint nodes at left end of bridge, the constraint nodes at right end of bridge as well as the constraint nodes on both sides of the centerline at the base of cable support tower along transverse direction of bridge). contrastive analysis through applying the traditional principle of random vibration solution，we perform solution through random vibration method, time-history method, spectra analysis respectively. its projects are the respective effect of displacement, velocity and acceleration on power spectral density, by which to compare absolute displacement method. the comparison between absolute displacement method and random vibration method the charts in fig. 3 are to respectively represent that the main span of cable-stayed bridge, the power spectral density of back span are influenced by several factors in the case, where the linear points denote random vibration method, the dashed points denote absolute displacement method. we could see from calculation results that after system linearization, the calculation result of two algorithms is basically consistent, and we find that there is also similar rule between the response power spectral density of other girders and main tower nodes through research, which demonstrates the validity of absolute displacement method. furthermore, through observation and contrast, we find that the value of displacement, velocity and the density value of acceleration response power spectral obtained through calculating with absolute displacement method are smaller than the value obtained through calculating with random vibration method. we analyze from the area surrounded by curve and the abscissa that the mean square value of seismic random vibration wave obtained through calculation with absolute displacement method is on the smaller side, namely the energy acting on cablestayed bridge is too small, and it demonstrates that random vibration method is a kind of seismic analysis method, which is conservative in relative speaking. as the frequency range of inputted acceleration power spectrum density is 0.48-15.9 hz, the figure does not represents the curved section whose frequency range is 0-0.48 hz .essentially, the inputted stimuli will make response power spectral density of structure have a sharp increase near the zero frequency. the average power spectral density model would reasonably reduce dynamic low frequency component of earthquake, when f =0, the power spectral density is generally 0 [9]. for displacement and velocity response power spectrum, the value is very small behind f ≥hz, thus it is not represented in the figure. for acceleration response spectrum, its value represents a certain range of volatility after f ≥hz, the changing curve is shown as fig. 3 (c), (f). w. guodong, frattura ed integrità strutturale, 29 (2014) 376-384; doi: 10.3221/igf-esis.29.33 381 (a) the density of displacement response power spectral in main span. (b) the density of displacement response power spectral in main span. (c) the density of displacement response power spectral in main span. (d) the density of displacement response power spectral in bridge’s back span. (e) the density of displacement response power spectral in bridge’s back span. (f) the density of displacement response power spectral in bridge’s back span. figure 3 the response power spectral density of main span, mid-span across back in cable-stayed bridge. when comparing the pseudo excitation method directly obtained with absolute displacement and traditional random vibration method, the relative error of its calculation results is shown as tab. 1. we could derive the following conclusion from the data in table that: (i) the calculation results of two algorithm are basically the same, it demonstrates that after linearization, the pseudo excitation method directly obtained with absolute displacement could replace traditional random vibration method in studying the seismic performance of structure. the excellence of this method has following points: the absolute displacement does not needs to be decomposed into quasi static displacement and dynamic relative displacement during calculating; quasi static modal matrix a does not needs calculation when constructing virtual stimuli for harmonic response analysis, thus it is simple and feasible; its essence does not changes the basic principle of traditional pseudo excitation method, its calculation efficiency is equivalent to traditional pseudo excitation method. w. guodong, frattura ed integrità strutturale, 29 (2014) 376-384; doi: 10.3221/igf-esis.29.33 382 (ii) when comparing absolute displacement method with random vibration method, the error of acceleration response power spectral density is the smallest, the biggest error of main span is only 1.15%, the biggest error of back span is only 1.37%. the main reasons resulting into such phenomenon is that the inputted stimulus is the acceleration power spectrum density during the early analysis stage of model, thus after a series of calculation, its corresponding acceleration response power spectral density is closest to actual situation, while displacement and velocity response power spectral density have experienced more calculation steps than acceleration response power spectral density, then results into error accumulation, thus the maximum error of displacement power spectral density in main span reaches 11.1%, the maximum error of displacement power spectral density in back span reaches 9.14 %. displacement power spectral density (main span ) velocity power spectral density (main span ) acceleration power spectral density (main span ) displacement power spectral density (back span ) velocity power spectral density (back span ) acceleration power spectral density (back span ) the minimum error/% 6.14 2.58 0.50 3.11 5.50 0.43 the maximum error/% 9.99 7.50 1.04 8.23 8.77 1.23 table 1: the error comparison for two methods. the comparison for absolute displacement method, time history method and spectra analysis in current vibration resistance analysis, in addition to above mentioned random vibration method and harmony response analysis, spectrum analysis and time history method are also very important research method, the essence of dynamic time history analysis method is transient analysis full method, various nonlinear factors could be considered, thus for the algorithm cases studied in this paper, the linearization process could be skipped to perform dynamic time history analysis directly. vibration isolation bearing is considered during calculation, the structure is non-orthogonal damping system, the inputted artificial wave is generated according to the above adopted condition, and seismic action adopts both horizontal and consistent earthquake excitation. according to seismic code, earthquake acceleration at the second-rate direction is multiplied by the coefficient of 0.85. in order to compare above analyzed nonlinear and linear results, the method in last section is equally applied. as it is shown in fig. 4, the straight line in (a) and (b) represents spectra analysis, point and line interval represents time history method, dotted line represents absolute displacement method; (c),(d) square lines represent spectra analysis, dot line represents time history method, triangle line represents absolute displacement method. through comparing the displacement time history diagram of nodes across main span and back span in fig. 4(a) and (b), we could find out following rules: (i) as spectral analysis is to study the displacement response of cable-stayed bridge within linear elastic range, thus all the displacement response value of absolute displacement method are too small when compared with dynamic time history method and the absolute displacement method after linear processing, and the maximum deviation reaches more than 50% when compared with dynamic time history method which has the largest displacement response, it demonstrates that when studying the anti-seismic property of structure, the structural nonlinearity must be considered, otherwise more error will occur and the calculation results will be made deviate from true value. (ii)the calculation results of absolute displacement method and dynamic time history after taking account nonlinearity are very close, the maximum displacement error at main span x direction is only 7.8%, for back span y direction ,its maximum error is 7.3%.and through research ,we find that there is similar regularity among the displacement response of main girder, main tower and stay-cables node, it demonstrates that the absolute displacement method could sufficiently consider structural nonlinearity after linearization, thus it could be taken as an effective method for aseismic design. through observing axial force response mean contrast figure at z direction of typical unit under the action of consistent earthquake for three calculation method in figure 3.4, we could see that the unit axial force response value obtained through absolute displacement method after linearization is the biggest, and it is basically the same with unit axial force value obtained through calculating with dynamic time history method, its maximum error is only 0.23% (the units near the middle section of main span), for spectral analysis, all its axial force response values at z direction are too small, when compared with dynamic time history method, the maximum error reaches 8%, thus it demonstrates that nonlinearity has certain effect on structural anti-seismic property, which should be considered in anti-earthquake analysis of bridge structure. w. guodong, frattura ed integrità strutturale, 29 (2014) 376-384; doi: 10.3221/igf-esis.29.33 383 (a) the displacement course of main span at x direction. (b) the axial force response of back span unit at z direction. (c) the axial force response of main span unit at z direction. (d) the axial force response of main span unit at z direction. figure 4: the comparison diagram of axial force response conclusions ompared with traditional pseudo excitation method, the new pseudo excitation method directly obtained through the absolute displacement based on statistical linearization could sufficiently consider structural nonlinearity and make its seismic analysis results be more close to actual situation; secondly, absolute displacement needs not to be discomposed into quasi static displacement and dynamic relative displacement during calculation, and quasi static modal matrix needs not to be calculated when constructing virtual stimuli for harmonic response analysis, it could be directly applied in general finite element analysis software and convenient for the application of pseudo excitation method in actual engineering. after system linearization, the node response power spectral density obtained through calculating with absolute displacement method and random vibration method is basically the same, and it demonstrates the correctness of the absolute displacement method, and the accuracy of response power spectral density outputted in calculation depends on the type of input excitation. compared with dynamic time history method and the absolute displacement after linearization method, spectrum analysis does not take into account the nonlinear structure, the value of node displacement response and the unit axial force response are too small, it demonstrates that nonlinearity has great influence on seismic performance of structure, and seismic analysis of bridge structure must be taken into account. the response value of node displacement and the unit axial force calculated through the absolute displacement method and dynamic time history method after linearization are basically the same. it demonstrates that the pseudo-excitation method directly solved through absolute displacement based on statistical linearization is equivalent to the dynamic time history method, as they can effectively analyze and study the seismic behavior of the nonlinear system. one point needs to distinguish is that performing harmonic response analysis with absolute displacement method is the required stimuli when taking frequency as interval input, while the dynamic time history method is the seismic wave data established by taking time as interval, but their essence is the same. c w. guodong, frattura ed integrità strutturale, 29 (2014) 376-384; doi: 10.3221/igf-esis.29.33 384 references [1] lin, j., zhang, y., pseudo-excitation method of random vibration. beijing: science press, (2004). [2] zhang, j., consider large-span spatial structure seismic analysis and design method of seismic spatial effect. tianjin: tianjin university, (2008). [3] jiang, y., the multi-point input earthquake response calculation of large-span structure and seismic design method research. beijing: tsinghua university, (2010). [4] bardi, m., raghavan, t. e. s., parthasarathy, t., stochastic and differential games: theory and numerical methods. berlin: birkhauser, (1999) 69−177. [5] huang, j. h., li, x,. wang, g. c., near-optimal control problems for linear forward-backward stochastic systems, automatica, 46(2) (2010) 397−404. [6] cheng. d. z., hu, x. m., shen, t. l., analysis and design of nonlinear control systems. beijing: science press, (2010) 1−20. [7] huber, m. f., adaptive gaussian mixture filter based on statistical linearization, in: proceedings of the 14th international conference on information fusion (fusion), chicago, il: ieee, (2011) 1−8. [8] chemyshov, k. r., statistical linearization based on the maximal correlation, in: siberian conference on control and communications (sibcon). moscow, russia: ieee, (2007) 29−36, [9] ernesto, h. z., vanmarcke, e. h., seismic random-vibration analysis of multisupport-structural systems, journal of engineering mechanics, 120(5) (1994) 1107 －1128. [10] shi, y., jiang, y., wang, y., the application and improvement of direct solving method in earthquake response calculation for structural multi-point input, engineering mechanics, 28(1) (2011) 75－81. microsoft word numero_38_art_34 a. gryguc et al, frattura ed integrità strutturale, 38 (2016) 251-258; doi: 10.3221/igf-esis.38.34 251 focussed on multiaxial fatigue and fracture tensile and fatigue behaviour of as-forged az31b extrusion a. gryguc, s.k. shaha, h. jahed university of waterloo (department of mechanical & mechatronics engineering, 200 university ave w, waterloo, on n2l 3g1, canada) agryguc@uwaterloo.ca, skumarshaha@uwaterloo.ca, hjahed@uwaterloo.ca https://uwaterloo.ca/fatigue-stress-analysis-lab/ m. wells university of waterloo (department of mechanical & mechatronics engineering, 200 university ave w, waterloo, on n2l 3g1, canada) mawells@uwaterloo.ca https://uwaterloo.ca/mechanical-mechatronics-engineering/people-profiles/mary-wells b. williams, j. mckinley canmetmaterials (natural resources canada, 183 longwood road south, hamilton, on l8p 0a1, canada) bruce.williams@nrcan-rncan.gc.ca, jonathan.mckinley@nrcan-rncan.gc.ca http://www.nrcan.gc.ca/mining-materials/materials-technology/8234 abstract. tensile and stress controlled fatigue tests were performed to investigate the influence of forging at a temperature of 400°c at different rates, on the performance of extruded az31b magnesium alloy. the obtained microstructural analysis showed that the extruded az31b magnesium alloy possesses a bimodal grain structure with strong basal texture. in contrast, the forged samples showed refined grains and a weaker texture. during tensile testing, a maximum yield and ultimate tensile strength of about 163 mpa and 268 mpa were obtained for the forged samples showing an increase of 102% and 7%, respectively from the as-extruded material. at the same time, a significant improvement of fatigue life was also observed for the sample forged at the rate of 100 mm/min. the fractographic analysis of the fracture surfaces showed that ductile type fractures occurred in both as-extruded and forged samples. however, more dimples and plastic deformation were identified in the fracture surfaces of the forged specimens. it is believed that forging improved the fatigue life by a combination of grain refinement and texture modification resulting in improved yield and ductility. keywords. az31b; forging; fatigue characterization; fracture; texture. citation: gryguc, a., shaha, s.k., jahed, h., wells, m., williams, b., mckinley, j., tensile and fatigue behaviour of as-forged az31b extrusion, frattura ed integrità strutturale, 38 (2016) 251-258. received: 13.05.2016 accepted: 23.06.2016 published: 01.10.2016 copyright: © 2016 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. a. gryguc et al, frattura ed integrità strutturale, 38 (2016) 251-258; doi: 10.3221/igf-esis.38.34 252 introduction here has been a significant amount of technology development in the past quarter century which has focused on developing lightweight vehicles to address the need for both better fuel economy and decreased emissions in the transportation industry [1]. as the lightest structural metallic material, magnesium and its alloys have shown to be promising candidates for use in vehicle components which are susceptible to fatigue fracture, such as suspension control arms [2]. however, the strong crystallographic texture that can form during processing and anisotropic mechanical properties leads to low ductility at room temperature which limits the uses of wrought magnesium alloys. numerous studies [3, 4] have been performed with the aim of weakening the crystallographic texture which reduces the anisotropy in mechanical properties. the most commonly reported mechanism for texture weakening of magnesium alloy is introducing rare earth materials. the addition of y, nb, gd, ce, ng etc. in magnesium alloys randomizes the texture during hot deformation processes like extrusion, forging and rolling, which causes a reduction of crystallographic texture intensity and activates the basal slip system [4]. however, the cost associated with rare earth elements significantly limits their application. recently, sarker et al. [3] proposes multidirectional compression as a method for randomizing the texture and improving the tension-compression asymmetry in magnesium. though the use of rare earth alloying elements have been shown to weaken texture, it has not been established whether modified texture improves fatigue performance of mg alloys. a goal of the current work is to better understand the mechanisms affecting fatigue performance of non-rare earth mg alloys, including both the grain structure and texture. although studies utilizing stress controlled fatigue methods provide important information into the design of engineering components [5], most of the published researches were focused on the tension-compression properties and fatigue behavior of cast, extruded, rolled or forged wrought magnesium alloys. for instance, somekawa et al. [6] studied the fully reversed stress controlled cyclic and compression testing and observed twinning behavior in extruded magnesium alloy. yin et al. [7] found that under strain controlled cyclic testing the stable crack propagation zone is characterized by a lamellar structure resulting from twinning, whereas the fracture zone has a dimpled morphology resulting from slip. other studies [8] [9] [10] also investigated the effect of sample direction on fatigue crack growth and propagation in magnesium alloys. more detailed studies [11-18] regarding multiaxial cyclic response, failure mechanism and fatigue life modeling also indicate analogous effects of mechanical processing on the texture evolution, monotonic and cyclic responses. the study of the stress controlled fatigue resistance of extruded then forged magnesium alloy is very limited in the literature, especially in those alloys suitable for automotive structural applications. specifically, it is not clear how changes in the microstructure and texture of extruded, then forged az31b magnesium alloy affect the fatigue performance. therefore, the aim of this study was to discuss the sensitivity of forging on both tensile and fatigue properties of az31b extruded magnesium alloy. another objective is to discuss the influence of forging on the microstructure and texture evolution. material and experiments he material used in this investigation was commercially available mg-al-zn magnesium alloy az31b. the chemical composition of this alloy in mass percentage is shown below in tab. 1. the material was received in the form of an extruded billet of diameter 88.9mm in the as-fabricated condition. al zn mn al 2.5-3.5 2.5-3.5 2.5-3.5 2.5-3.5 table 1: table of az31b alloy chemistry in wt. % forging trials were conducted at canmetmaterials using az31b extruded feedstock of the aforementioned diameter which was cut into 88.9 mm lengths. all tests were carried out on a 500 ton hydraulic press with an upper and lower platen (die) which were both flat. the billet and tooling were heated separately to a temperature of 400°c. the orientation of the billet to the press was such that the extrusion direction was along the direction of the press stroke (i.e. direction of forging was coincident to extrusion direction of the billet). forging was carried out at two different rates (10 and 100 mm/min with engineering strain rates of about 0.002 and 0.02 s1 subsequently referred to as sample s1 and s2, respectively). the as-extruded material was forged to a height of 13 mm corresponding to 85% compressive engineering t t a. gryguc et al, frattura ed integrità strutturale, 38 (2016) 251-258; doi: 10.3221/igf-esis.38.34 253 strain and then air cooled. graphite lubricant was used during the process on all test samples. although the die temperature remained almost constant throughout the test, heat loss to the surrounding air during forging was expected, particularly for the slower forging rate condition. fig. 1a and fig. 1b shows the orientation for which the metallographic, tensile and fatigue tested specimens were extracted from both the extruded and forged billets. for tensile and fatigue tests, different geometry of flat bar and round bar samples were used as shown in fig. 1c and fig. 1d. all specimens were taken with their axis coincident with the radial direction of the as-extruded and forged billets. figure 1: schematic diagram for sample preparation and extraction. (a) as-extruded billet (b) forged billet (c) tensile specimen (d) fatigue specimen. all dimensions in mm, light optical microscopy (lom) specimens taken from a position of 0.5r. the metallographic samples were prepared following standard metallographic techniques [19]. the microstructure was observed using a light optical microscope and a scanning electron microscope (sem), coupled with energy-dispersive xray spectroscopy (eds). the texture measurements of the alloy before and after forging tests were performed using a bruker d8 discover equipped with advanced 2d-detector of x-ray diffractometer on polished samples. tensile test samples with a gauge length of 26 mm were extracted from the as-extruded billet and pancake shape forged samples as shown in fig. 1 a,b. the quasi-static tensile tests were performed using an 8874 bi-axial instron servohydraulic test machine operating in displacement control mode. the displacement rate of the crosshead was 10-3 m/min for all tests, which corresponds to an approximate strain rate of 1.4e-3 sec-1. strain measurement was accomplished using a gom aramis 3d 5mp dic system. the fatigue tests were performed in an ambient environment using an instron r.r. moore four point rotating bending fatigue test machine at a frequency of 100 hz. the tests were conducted at a zero mean load (i.e., a load ratio of rl=-1, completely reversed load cycle) and stress amplitudes between 90 mpa and 125 mpa. the fracture surfaces after tensile and fatigue tests were examined using both stereo-microscopy and sem techniques. results microstructure and texture ig. 2a illustrates typical sem image with eds analysis of both the matrix and prominent intermetallic present in az31b extruded magnesium alloy, also optical microscopy images of as-extruded and forged samples. it is seen in fig. 2a that the az31b alloy contains al-mg-rich intermetallics. it is also evident that the as-extruded sample (fig. 2b) possesses severely elongated grains whose major axis is oriented along the extrusion direction, and surrounded by bands of smaller grains. the calculated average grain size for the as-extruded material is 10 μm with a significant bi-modal f a. gryguc et al, frattura ed integrità strutturale, 38 (2016) 251-258; doi: 10.3221/igf-esis.38.34 254 size distribution. the forged specimens both exhibited a refinement in grain size, with little obvious effect of forging speed. in contrast, the forged samples exhibited an average grain size of 6.8 μm and 6.9 μm for the forging conditions of 10 mm/min (fig. 2c) and 100 mm/min (fig. 2d), respectively. the grain morphology in the forged conditions appears to be much more “pancake” like in nature. figure 2: microstructures of az31b alloy in different conditions, (a) typical sem image with eds analysis on matrix and prominent intermetallic and om image of (b) as-extruded, and extruded followed by forging at 400°c temperature for the rate of (c) 10 mm/min (s1) and (d) 100 mm/min (s2). fig. 3 depicts the calculated pole figures for the basal (0001) and prismatic  10 10 planes obtained via xrd. there is a strong texture in the as-extruded condition (fig. 3a) with the c-axis of the crystal orientated along the radial direction of the billet. the forged material however, exhibited a somewhat weaker texture, particularly in the prismatic plane, with its c-axis being reoriented to be coincident with the extrusion axis (forging direction). figure 3: calculated pole figure of az31bextruded magnesium alloy in (a) as-extruded and (b) extruded followed by forging at a strain rates of 100 mm/min. (a) (b) (c) radial direction (rd) f o rg in g d ir ec ti on ( e d ) (d) radial direction (rd) radial direction (rd) f o rg in g d ir ec ti o n ( e d ) e x tr u si o n d ir ec ti on ( e d ) a. gryguc et al, frattura ed integrità strutturale, 38 (2016) 251-258; doi: 10.3221/igf-esis.38.34 255 this effect of forging on the basal texture is a 90° rotation of the c-axis from the radial direction in the as-extruded condition to the direction of loading (extrusion axis) in all forgings. the rotation of the c-axis during compression of the extruded magnesium alloy was reported by several researchers in the literature [20, 3, 12]. sarker and chen [3] reported that after undergoing severe plastic deformation, the c-axes of am30 extruded magnesium alloy were always rotated to be coincident with the loading direction. furthermore, they also concluded that texture weakening occurred due to multidirectional loading. tensile properties fig. 4a shows the engineering stress-strain response for the as-extruded (base material) and forged (s1, s2) materials in the radial direction. it can be seen that once forged, the yield strength and elongation to failure significantly increase. a similar increase in yield stress in compression samples of az31b after forging was observed by gryguc et al. [21]. this increase is attributed to the grain refinement and texture modification via the reorientation of the c-axis to the direction of forging. in addition, there is also a moderate increase in the ultimate tensile stress. both the yield and ultimate strengths exhibit a positive correlation with increasing strain rate, whereas failure elongation decreases with higher strain rates. fig. 4b illustrates the hardening behaviour for the investigated conditions. it can be observed that the base material is characterized by 3 distinct hardening response stages as described in [19] for am30. for the base material, an initial rapid decrease in strain hardening rate up until a true stress of ~130 mpa was observed which was followed by stage 2 hardening where the rate stabilizes between~130 mpa and 200 mpa. the final stage is a more moderate decrease in strain hardening rate until failure. in contrast, both forged samples (s1 and s2) exhibit only two distinct hardening response stages which are similar to stages 1 and 3 of the base material, however no rate stabilization similar to stage 2 was observed in the forged conditions. the presence of the hardening stabilization in stage 2 is an indicator of the occurrence of twinning deformation whereas the absence of the stabilization zone is indicative of slip deformation. the third stage shows almost identical hardening responses in all three conditions. wang et al. [22] observed a similar hardening behaviour in compression for az31b normal to the extrusion direction with no stabilization in stage 2 except in the samples parallel to the extrusion direction. figure 4: a comparison between base and forged conditions, (a) stress strain curves (b) and k-m plot of the base (as-extruded) and forged az31b magnesium alloy during tensile loading. as discussed in an earlier section, the mechanical properties of magnesium alloy are significantly influenced by the texture, especially the orientation of the crystallographic c-axis relative to the loading direction of the material. at room temperature when the applied load is perpendicular to the c-axis, {10 2} extension twins are formed via a rotation of ~ 86.3° towards the loading direction, this results in a reduction of yield stress. the rotation of the c-axis and its inferred effect on the stress-strain response was explored by gryguc et al. [21] where the compressive hardening response supports both the texture results and tensile hardening responses presented in this study. their findings illustrated that in the extrusion direction, under monotonic compression, a shift from strong sigmoidal hardening behaviour in the as-extruded material to conventional monotonic hardening occurred once forged. wang et al. [22] had found that following significant plastic strain, most c-axis orientations which are favourable for twinning will re-orient them to the compression direction. (a) (b) a. gryguc et al, frattura ed integrità strutturale, 38 (2016) 251-258; doi: 10.3221/igf-esis.38.34 256 fatigue properties fig. 5 shows the s-n curve obtained from both the as-extruded and forged specimens up to ~107 cycles. as seen in fig. 5, the forged samples obtained significantly longer fatigue life for the fixed stress amplitude. in the mid to high cycle regime (>105 cycles) the forged samples exhibited a significant improvement in s-n response, with an increase of ~35% in fatigue strength for both forged conditions. at 120 mpa stress amplitude, the as-extruded alloy showed a fatigue life of ~104 cycles while the sample forged at the rate of 100 mm/min (s2) exhibited a fatigue life of over 107 cycles. this is attributed to the forged material having a much larger elastic regime as compared to the as-extruded sample as discussed above. the fracture surface morphology, discussed below, also supports this observation. figure 5: fatigue life of forged az31b extruded magnesium alloy in comparison with the az31 extruded base alloy, obtained at total stress amplitudes of 90-125 mpa. points with arrow show run-out tests. stereoscopic microscope images showing the macroscopic features of the fracture surface of the fatigue specimens are shown in fig. 6. all samples exhibited fatigue crack initiation (fci) at the surface of the specimen. the as-extruded material (fig. 6a) exhibits a fracture surface with a very serrated and faceted morphology with a comparatively rough propagation zone relative to the forged samples (fig. 6b) and (fig. 6c). both forged samples exhibited very similar characteristics in terms of their fatigue fracture surface, with a distinct fci with radially branching fatigue striations and a large propagation zone which is much smoother than the as-extruded condition. the final fracture zone is opposite to the fci location indicating a stable crack propagation perpendicular to the initial fatigue crack. figure 6: stereoscopic microscope images showing an overall view of fatigue fracture surfaces of the samples tested at a total stress amplitude of 90 mpa (a) for the as-extruded sample, 120 mpa (b) and 125 mpa (c) for the forged sample. the red arrows indicate the crack initiation site. the fatigue cracks were initiated near the sample surfaces. fci-fatigue crack initiation. the propagation zone fracture surface morphology is shown in fig. 7 (a, b). it can be seen that for the as-extruded material (fig. 7a) the general direction of fatigue striations (fs) is in the transverse direction on the image (which is perpendicular to the crack propagation direction). all forged conditions (fig. 7b) exhibit fatigue striations which, in general, spread in radial directions from the crack origin (longitudinally in the image). the final fracture zone surface morphology is shown in fig. 7 (c, d). all conditions exhibit similar morphology to that of their monotonic tensile fracture (a) (a) a. gryguc et al, frattura ed integrità strutturale, 38 (2016) 251-258; doi: 10.3221/igf-esis.38.34 257 surface with the forged samples showing more evidence of ductile behaviour. the as-extruded material (fig. 7c) shows characteristic terrace like structure with distinct facet-like features indicating locations of grain boundaries. in contrast, the forged samples (fig. 7d) exhibit a very strong dimpled type morphology indicative of a ductile fracture surface supporting the longer fatigue life which was observed. figure 7: sem images showing a comparison of crack propagation zone (a, b) and final fracture (c, d) between the as-extruded (a, c) and forged (b, d) of fatigue fracture surfaces tested at the total stress amplitude of (a) 90 mpa for the base sample, and (b) 120 mpa for the forged sample. conclusions he tensile and fatigue behavior in the radial direction of as-extruded and forged az31b magnesium alloy were investigated. on the basis of the microstructure, stress-strain response characteristics and fatigue behavior, the following conclusions can be drawn: 1.microstructural analysis shows that az31b alloy in the as-extruded condition exhibited a significant bi-modal grain structure with average grain size of 10 μm while the forged sample shows smaller, equi-axed grains with average grain size of about 6.8 μm. at the same time, the plastic deformation imparted to the sample via forging resulted in both a weaker texture and a rotation of the crystal to align with the loading direction during forging. 2. the tensile tests showed that the az31b alloy in the forged condition had significantly higher yield strength and ductility in comparison with the az31b extruded alloy. it was observed that az31b alloy had a yield strength and failure elongation of about 81 mpa and 21% in as-extruded state while in the forged condition these properties improved to 168 mpa and 28% respectively. 3. the cyclic behaviour also showed a similar improvement in performance, i.e. longer fatigue life with an increase of 30 mpa in fatigue strength at 107 cycles being typical of the forged vs. as-extruded material. the improved fatigue performance in the forged samples was attributed to higher yield strength and increased ductility resulting from grain refinement and a modified texture. 4. the fracture surfaces of all samples were characterized by a terrace-like faceted morphology in the as-extruded condition, whereas the forged conditions exhibited a much more dimple-like fracture surface indicative of more plasticity. acknowledgement he financial support of nserc under automotive partnership canada is gratefully acknowledged. all forging experiments were performed at canmetmaterials. both multimatic technical centre and ford motor company are gratefully acknowledged for their contributions. references [1] skszek, t., zaluzec, m., conklin, j., wagner, d., mmlv: project overview, sae international, (2015). [2] chen, x., conklin, j. l., carpenter, r. m., wallace, j., flanigan, c., wagner, d. a., kiridena, v., betrancourt, s., logsdon, j., mmlv: chassis design and component testing, sae international, (2015). [3] sarker, d., friedman, j., chen, d. l., influence of pre-strain on de-twinning activity in an extruded am30 magnesium alloy, materials science and engineering: a, 605 (2014) 73-79. t t a. gryguc et al, frattura ed integrità strutturale, 38 (2016) 251-258; doi: 10.3221/igf-esis.38.34 258 [4] pan, h., ren, y., fu, h., zhao, h., wang, l., meng, x., qin, g., recent developments in rare-earth free wrought magnesium alloys having high strength: a review, journal of alloys and compounds, 663 (2016) 321–331. [5] fan, k. l., he, g. q., liu, x. s., liu, b., she, m., yuan, y. l., yang, y., lu, q., tensile and fatigue properties of gravity casting aluminum alloys for engine cylinder heads, materials science and engineering: a, 78-85 (2013) 586. [6] somekawa, h., maruyama, n., hiromoto, s., fatigue behaviors and microstructures in an extruded mg-al-zn alloy, materials transactions, 49 (2008) 681-684. [7] yin, s. m., yang, f., yang, x. m., wu, s. d., li, s. x., li, g. y., the role of twinning–detwinning on fatigue fracture morphology of mg–3%al–1%zn alloy, materials science and engineering a, 494 (2008) 397-400. [8] xu, d. k., liu, l., xu, y. b., han, e. h., the crack initiation mechanism of the forged mg–zn–y–zr, scripta materialia, 56 (2007) 1-4. [9] kalateh, e., mahmoudi-asl, h., jahed, h., an asymmetric elastic–plastic analysis of the load-controlled rotating bending test and its application in the fatigue life estimation of wrought magnesium az31b, international journal of fatigue, 64 2014) 33-41. [10] marzban, b., toyserkani, e., jahed, h., applications of fbg sensors to strain measurements of az31b extrusion in rotating bending test, in 25th cancam, london, ontario, canada, (2015). [11] albinmousa, j., jahed, h., lambert, s., cyclic behaviour of wrought magnesium alloy under multiaxial loading, international journal of fatigue, 33 (2011) 1403-1416. [12] albinmousa, j., jahed, h., multiaxial effects on lcf behavior and fatigue failure of az31b magnesium extrusion, international journal of fatigue, 64 (2014) 103-116. [13] albinmousa, j., jahed, h., lambert, s., estimation of fatigue crack orientation using critical plane parameters: an experimental investigation," in icmff10, kyoto, japan, (2013). [14] albinmousa, j., jahed, h., lambert, s., an energy-based fatigue model for wrought magnesium alloy under multiaxial load," in 9th international conference on multiaxial fatigue and fracture, parma, italy, (2010). [15] jahed, h., albinmousa, j., multiaxial behaviour of wrought magnesium alloys–a review and suitability of energybased fatigue life model, theoretical and applied fracture mechanics, 73 (2014) 97-108. [16] tokaji, k., kamakura, m., ishiizumi, y., hasegawa, n., fatigue behaviour and fracture mechanism of a rolled az31, international journal of fatigue, 26 (2004) 1217-1224. [17] morita, n. o. s., fatigue properties of rolled az31b magnesium alloy plate, trans. nonferrous met. soc. china, (2010) s523-s526. [18] albinmousa, j., jahed, h., lambert, s., cyclic axial and cyclic torsional behaviour of extruded az31b magnesium alloy, international journal of fatigue, 33(8) (2011) 1127-1139. [19] sarker, d., chen, d. l., detwinning and strain hardening of an extruded magnesium, scripta materialia, 67 (2012) 165-168. [20] sarker, d., chen, d. l., texture transformation in an extruded magnesium alloy under pressure, materials science and engineering: a, 582 (2013) 63-67. [21] gryguc, a., jahed, h., williams b., mckinley, j., magforge – mechanical behaviour of forged az31b extruded, materials science forum, 828-829 (2015) 291-297. [22] wang, b., xin, r., huang, g., liu, q., effect of crystal orientation on the mechanical properties and strain hardening, materials science and engineering a, 534 (2011) 588-593. << /ascii85encodepages false /allowtransparency false /autopositionepsfiles true /autorotatepages /none /binding /left /calgrayprofile (dot gain 20%) /calrgbprofile (srgb iec61966-2.1) /calcmykprofile (u.s. web coated \050swop\051 v2) /srgbprofile (srgb iec61966-2.1) /cannotembedfontpolicy /error /compatibilitylevel 1.4 /compressobjects /tags /compresspages true /convertimagestoindexed true /passthroughjpegimages true /createjobticket false /defaultrenderingintent /default /detectblends true /detectcurves 0.0000 /colorconversionstrategy /cmyk /dothumbnails false /embedallfonts true /embedopentype false /parseiccprofilesincomments true /embedjoboptions true /dscreportinglevel 0 /emitdscwarnings false /endpage -1 /imagememory 1048576 /lockdistillerparams false /maxsubsetpct 100 /optimize true /opm 1 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/hrv (za stvaranje adobe pdf dokumenata najpogodnijih za visokokvalitetni ispis prije tiskanja koristite ove postavke. stvoreni pdf dokumenti mogu se otvoriti acrobat i adobe reader 5.0 i kasnijim verzijama.) /hun 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can be opened with acrobat and adobe reader 5.0 and later.) >> /namespace [ (adobe) (common) (1.0) ] /othernamespaces [ << /asreaderspreads false /cropimagestoframes true /errorcontrol /warnandcontinue /flattenerignorespreadoverrides false /includeguidesgrids false /includenonprinting false /includeslug false /namespace [ (adobe) (indesign) (4.0) ] /omitplacedbitmaps false /omitplacedeps false /omitplacedpdf false /simulateoverprint /legacy >> << /addbleedmarks false /addcolorbars false /addcropmarks false /addpageinfo false /addregmarks false /convertcolors /converttocmyk /destinationprofilename () /destinationprofileselector /documentcmyk /downsample16bitimages true /flattenerpreset << /presetselector /mediumresolution >> /formelements false /generatestructure false /includebookmarks false /includehyperlinks false /includeinteractive false /includelayers false /includeprofiles false /multimediahandling /useobjectsettings /namespace [ (adobe) (creativesuite) (2.0) ] /pdfxoutputintentprofileselector /documentcmyk /preserveediting true /untaggedcmykhandling /leaveuntagged /untaggedrgbhandling /usedocumentprofile /usedocumentbleed false >> ] >> setdistillerparams << /hwresolution [2400 2400] /pagesize [612.000 792.000] >> setpagedevice microsoft word numero 16 articolo 2 g. pesquet et alii, frattura ed integrità strutturale, 16 (2011) 18-27; doi: 10.3221/igf-esis.16.02 18 the use of thermally expandable microcapsules for increasing the toughness and heal structural adhesives guillaume pesquet ensieta, 2 rue françois verny, 29806 brest, france lucas f. m. da silva departamento de engenharia mecânica, faculdade de engenharia da universidade do porto, rua dr. roberto frias, 4200-465 porto, portugal; lucas@fe.up.pt chiaki sato precision and intelligence laboratory, tokyo institute of technology, 4259 nagatsuta, midori-ku, yokohama 226-8503, japan abstract. in this research, the effect of thermally expandable microcapsules (tems) on mode i fracture toughness of structural adhesives were investigated. the single-edge-notch bending (senb) test was used. firstly, a standard toughness test was performed on adhesives with microcapsules. secondly, since tems start their expansion at approximately 60ºc, the next specimens were fatigue tested expecting a local heating in the notch leading to the desired expansion before being statically loaded for fracture toughness determination. thirdly, a manual local heating at 90ºc was applied in the notch before the fracture static test. the experimental results were successfully cross-checked through a numerical analysis using the virtual crack closure technique (vcct) based on linear elastic fracture mechanics (lefm). the major conclusion is that fracture toughness of the modified adhesives increased as the mass fraction of the tems increased. keywords. epoxy/epoxides; fracture mechanics; finite element stress analysis; thermal analysis; thermally expandable microcapsules (tems). introduction hermally expandable microcapsules, thermally expansive particles, thermo-expandable microsphere (tems), or a combination of these words, are all particles made up of a thermoplastic shell filled with liquid hydrocarbon. on the action of heat, the shell softens and the liquid hydrocarbon boils. the hydrocarbon gas works as a blowing agent because the shell expands as the inner pressure increases. the growth in volume can be from 50 to 100 times. this capability brings new and quite unique possibilities for engineers. because of its high sensitivity to temperature, storage at over 40ºc is not advised [1]. the use of tems in adhesives has allowed industry to have easily dismantlable joints. the simple heating of the joint over 100ºc leads to an easy separation of the bonded materials. the adhesive expansion may be up to 400% according to the study of nishiyama and sato [2]. this technique is promising because it does not need much time to make this kind of joint and greatly facilitates the dismantling. tems are mixed with the resin before the manufacture of the joint. since they t http://dx.medra.org/10.3221/igf-esis.16.02&auth=true http://www.gruppofrattura.it g. pesquet et alii, frattura ed integrità strutturale, 16 (2011) 18-27; doi: 10.3221/igf-esis.16.02 19 expand throughout the joint on the action of heat, they may dismantle the joint. a low fraction of tems does not allow the dismantling of the joint and a too high fraction reduces the bond strength. thus, 5 to 15 % [3] of tems in terms of weight fraction is generally considered for this use. it was even shown that the shear strength of a common lap joint increased thanks to microcapsules [1]. obviously, resin and particles must match to permit the dismantling. theoretically, matching means here that the resin must be in its rubbery plateau when particles expand to allow its expansion. the microcapsules cannot transmit more than 1 or 2 mpa to the resin [2]. this means that the temperature of expansion of the particles must be slightly higher than the glass transition temperature (tg) of the resin. thus, the joint can dismantle by itself or with a low force. if it is not the case, i.e. the tg of the resin is higher than the temperature of expansion of the tems, the joint cannot be dismantled. however, one can distinguish at least two cases. in the first, the tg of the resin is much higher than the temperature of expansion of the tems and the strength of the adhesive does not permit the expansion of the particles. in the second case, the tg of the resin is slightly higher than the temperature of expansion of the tems. in this last case, the stress increase due to the expansion of the microcapsules throughout the resin might create a kind of hydrostatic pressure and will affect its properties and its mechanical behaviour. an increase of hydrostatic stress leads to an increase of elastic limit and failure load [4]. the expansion of the particle would also possibly cause a crack barrier which would increase the fracture toughness of the adhesive. the propagation of cracks brings energy dissipation, hence local heating, especially in dynamic conditions such as in a fatigue test. this local heating may lead to the expansion of the tems and thus to a local healing by creation of hydrostatic pressure of crack barrier. in other words, a self-healing or self-toughening of the modified adhesive would occur. the obvious capacity of living beings to heal themselves was transposed recently to polymers [5] and polymer composites [6, 7]. it means that a secondary function of healing is embedded into the adhesive and the reaction of healing is triggered by the damage of the material. so it permits counteracting the service degradation whilst still achieving the primary structural requirement. the healing must lead to a local restoration of mechanical properties. the concept of a self-healing material already exists using numerous ways such as bleeding capsules [5] or hollow fibres [8]. it relies on the microencapsulation of a monomer spreading into cracks when ruptured. the polymerisation starts with the contact of the monomer with a dispersed particulate catalyst dispersed in the resin. thus, repair self occurs when a crack initiates. this concept of self-healing might also occur in the case of tems. note that if heat must be provided to enhance the mechanical properties of the composite tems-resin, then an artificial healing is taking place and not a self-healing. these ideas need to be confirmed or invalidated by experiments, which was the aim of the present investigation. assuming that tems may modify the fracture toughness by increasing the resistance to crack propagation, one has to choose a proper test to quantify this change. microcapsules expansion is wanted, and it would be even better if the test itself could lead to the expansion of the microcapsules. an idea is to use mechanical work in the material in order that it generates heat by itself, as fatigue does. therefore, self-heating by fatigue was considered. nevertheless, this local generated heat has to be well contained and not transfer to the full specimen. an adhesive joint between metallic adherends such as the double cantilever beam (dcb) test defined in standard astm d3433 was not considered because of the high conductivity of metals. composite adherends, which are less conductive, could have been used but to avoid interaction of adherends in a first analysis, a single-edge-notch bending (senb) test (astm d5045) using a bulk specimen was selected. the test might not bring enough heat to expand the particles. therefore, a solution to heat the joint must be defined and validated. moreover, the concentration of tems in the resin affects directly the results. several concentrations and different heating methods were tested. to exhibit differences brought by microcapsules, three types of tests were carried out. experimental details materials he diameter of these microcapsules ranges mainly from 10 to 20 m with an average of 15 m and the shell thickness from 3 to 4 m at room temperature. data from the manufacturer (matsumoto yushi-seiyaku co., japan) is given in tab. 1. these particles start to expand at 60ºc. epoxy resins are the most common structural adhesives. the following points were taken into account in the selection of the epoxy resins. the cure temperature must be lower than the temperature expansion of particles. the tg of the adhesive should be around the temperature of expansion of particles to maximise the effect of tems on adhesive. in light of these facts, the adhesives presented in tab. 2 were selected. the tensile stress-strain curves for the three used adhesives are presented fig. 1. these curves were determined on bulk dogbone samples. these curves show that adhesive av138m is t http://dx.medra.org/10.3221/igf-esis.16.02&auth=true http://www.gruppofrattura.it g. pesquet et alii, frattura ed integrità strutturale, 16 (2011) 18-27; doi: 10.3221/igf-esis.16.02 20 brittle, adhesive 2015 is ductile and adhesive aw106 is very ductile. the several mass fractions that were used are summarized in tab. 3.up to 25% of tems were added to the adhesives. particle size 10-20 µm shell thickness 3-4 µm density 1.13 g/cm3 chemical composition of shell vinylidene-chloride-copolymer chemical composition of core isobutane table 1: characteristic of the tems (f-30d) used in the present study. adhesive w/ hardener glass transition temperature (°c) araldite av138m/hv998 80 araldite 2015 67 araldite aw106/hv953u 45 table 2: adhesives selected with indication of tg. figure 1: tensile stress-strain curves of the epoxy adhesives without particles. av138m/hv998 0 wt% 10 wt% 20 wt% araldite 2015 0 wt% 10 wt% 20 wt% aw106/hv953u 0 wt% 25 wt% table 3: mass fractions studied for the three adhesives. specimens manufacture a critical point in this study is the mixing of tems in the adhesive. for that purpose, a mixer relying on centrifugal force was used (dac 150.1 fvz speedmixer, hauschild, germany). this allows an efficient and homogeneous dispersion, creating visibly bubble-free mixing. the mixture was checked through a scanning electron microscope (sem) analysis. small samples were immersed in liquid nitrogen before being fractured. at this temperature, the materials were very brittle and the fracture surfaces were very neat. the particles were always well dispersed. the mixture was poured in a mould consisting in a silicone rubber and a metallic frame [9]. a pressure of 2 mpa was applied in a hot press to the mould. all specimens were cured at 40ºc at varying times (16h for av138m, 4h for 2015 and 6h for aw106) to ensure complete cure. the specimens were machined afterwards from the bulk plates. http://dx.medra.org/10.3221/igf-esis.16.02&auth=true http://www.gruppofrattura.it g. pesquet et alii, frattura ed integrità strutturale, 16 (2011) 18-27; doi: 10.3221/igf-esis.16.02 21 expansion test the expansion with temperature of the neat and modified adhesives (tab. 3) was measured to check the behaviour with temperature of the adhesives. small samples (15 × 10 × 10 mm3) were heated from room temperature to 105ºc by step of 5ºc during 30 mins using an oven. after each temperature step, the specimens were cooled by natural convection. the upper surfaces of the dices were captured with a charge coupled device (ccd) camera through a stereo microscope. pictures were analysed and the area of the dice calculated for each temperature. then, 2d expansion of the upper surface was calculated. bending test bulk single-edge-notch bending (senb) specimens (fig. 2) in accordance with astm d5045 were tested in three point bending. all specimens were in accordance with eq. (1) to have comparable results. 55.045.0  wa (1) three specimens were tested for each case (tab. 3) corresponding to the following conditions: 1. the first specimen was manually saw up to meet the desired testing range relation for a. the thickness of the blade was 0.5 mm. in the bottom of the notch, a plastic impression was made by manually pushing in a fresh razor blade. then, specimens were tested. a natural crack is recommended by standard astm d5045 but the creation of a natural crack is very difficult for brittle adhesives such as adhesive av138m. 2. the second specimen was pre-fatigued to open a natural crack before testing it statically to fracture. the fatigue crack was propagated under displacement control conditions up to meet the desired testing range relation with a high frequency to self heat the sample (20 hz). the specimens were painted in matt black and an increase in macroscopic temperature was monitored with a thermographic camera (fluke ti25) with an accuracy of ±2ºc and a thermal sensitivity lower than 0.1ºc. 3. the third specimen was saw and received a plastic impression as the first specimen. next, a blade at 90ºc was inserted into the notch for 5 minutes, applying a controlled local heating with a copper sheet of 0.1 mm thickness that was carefully applied in the bottom of the notch. the temperature was controlled using a thermocouple and a thermographic camera. fig. 3 shows the local heating using thermal imaging. one hour later, when fully cooled by natural convection, the specimen was tested statically to failure. results are wholly comparable with the first specimen, the only difference being the heating step. figure 2: single edge notch three point bending test specimen (dimensions in mm). figure 3: thermal image of a heated notch with a copper sheet at 90ºc (temperature scale in ºc). the tests were carried out in a mts servo-hydraulic machine with a load-cell of 5 kn load in laboratory ambient conditions (25ºc and relative humidity of 50%) and a cross-head rate of 10 mm/min. the crack length was measured with a stereo microscope having a micrometer screw, being able to measure the crack on the two sides of the specimen. after failure, a ccd camera through a stereo microscope was used to observe all fracture surfaces. http://dx.medra.org/10.3221/igf-esis.16.02&auth=true http://www.gruppofrattura.it g. pesquet et alii, frattura ed integrità strutturale, 16 (2011) 18-27; doi: 10.3221/igf-esis.16.02 22 typical load-displacement curves are shown in fig. 4 for adhesive 2015. the load-displacement curves were almost linear up to fracture despite the non-linear behaviour exhibited in the tension specimens. even very ductile adhesives provide linear curves through the senb test. similar bending tests were conducted successfully by chen et al. [10] with a carboxyl-terminated butadiene nitrile rubber (ctbn) adhesive that exhibits a large strain to failure (max = 14%). the fracture toughness was calculated using the following relationship (astm e399-81)  waf bw ps k 2/3  (2) where p is the failure load, s is the span of the beam specimen, b is the thickness of the specimen, w is the width of the specimen, a is the crack length and the function f is as   2/92/72/52/32/1 7.386.378.216.49.2 xxxxxf  , where x = a/w. all the specimens broke in a brittle manner and the fracture surfaces were flat without shear lips. in order to calculate plane-strain fracture toughness kic, the conditions presented eq. (3) should be met, where max is the tensile strength of the adhesive.   2 max 5.2,,         k lawab (3) the criteria described in eq. (3) were not always met. however, all specimens having the same size, the results remain fully comparable. figure 4: experimental load-displacement curves for adhesive 2015 (type 1 specimen). tensile test tensile tests on dogbone bulk specimens 2 mm thick and 10 mm wide were carried to be able to check the plane-strain conditions (eq. (3)) and assess the effect of the tems on the stress-strain characteristics. tensile tests were only conducted on adhesive 2015 because it might deviate from plane-strain conditions due to its high ductility and low tensile strength. the tests were carried out in a mts servo-hydraulic machine with a load-cell of 5 kn load in laboratory ambient conditions (25ºc and relative humidity of 50%) and a cross-head rate of 10 mm/min. results expansion test ig. 5 shows the expansion of used adhesives with respect to temperature. this expansion was calculated from the area of the upper surface of a dice. this 2d expansion is defined by the area after the heating step divided by the initial area and is then called relative 2d size. f http://dx.medra.org/10.3221/igf-esis.16.02&auth=true http://www.gruppofrattura.it g. pesquet et alii, frattura ed integrità strutturale, 16 (2011) 18-27; doi: 10.3221/igf-esis.16.02 23 figure 5: expansion of neat and modified adhesives as a function of temperature. the three non-modified adhesives exhibited no expansion. when adhesives without tems are heated, they should merely expand according to their volumetric thermal expansion ratio coefficient and then contract to the original shape when naturally cooling. because all the measurements were done at the same room temperature, all adhesives without tems should exhibit no expansion. the three non-modified adhesives even showed a slight decrease in volume. because they were cured at 40ºc, when they went over 40ºc, they might have cured further. as it is known, adhesive may exhibit some shrinkage after curing. even if the non-modified adhesives exhibited some slight shrinkage, all the measurements of the three non-modified adhesives remained within a range of 1%. therefore, the accuracy of the measurements was under a satisfying 1%. fig. 5 shows that expansion starts at approximately 70ºc which is in accordance with the tems data sheet and the tg of the adhesives. there is less expansion for adhesive av138 because its tg is 80ºc and gives more resistance to expansion than the other adhesives. from 85ºc, all the modified adhesives exhibited more than 1% of expansion. therefore, the heating step at 90ºc for the bending test guarantees that there is expansion of the particles. bending test a typical fracture surface of specimens sawed and with a natural (pre fatigue tested) is shown in fig. 6. the fatigue precrack is clearly seen in fig. 6(b). also, ductile and brittle fracture areas can be identified. the values of stress intensity factor k for each kind of adhesive are plotted as a function of the tems mass fraction in fig. 7, fig. 8 and fig. 9. three curves are plotted for each adhesive corresponding to the three types of specimens (see section experimental details: bending test). (a) (b) figure 6: typical fracture surfaces (adhesive 2015 with 10wt%) for of a specimen with a sawed crack (a) and with a fatigue pre-crack (b). these figures show that the toughness of the modified adhesives is improved by microcapsules. it is confirmed by every result but the extreme case of aw106 adhesive with 25wt%. the toughness of specimens having received a plastic impression was always higher than the crack opened with fatigue. that makes totally sense (the required load to break the specimen with a notch is higher than with a natural crack because the stress concentration in a notch is lower than in a http://dx.medra.org/10.3221/igf-esis.16.02&auth=true http://www.gruppofrattura.it g. pesquet et alii, frattura ed integrità strutturale, 16 (2011) 18-27; doi: 10.3221/igf-esis.16.02 24 crack.) if we assume there was no healing effect brought by fatigue. the macroscopic temperature increase obtained by the thermographic camera was always under 2ºc, which is not enough to expand the particles. figure 7: fracture toughness as a function of tems mass fraction for adhesive 2015. figure 8: fracture toughness as a function of tems mass fraction for adhesive av138. figure 9: fracture toughness as a function of tems mass fraction for adhesive aw106. the local heating with the copper sheet expected to heal modified adhesives was unexpectedly highly salutary to nonmodified adhesives aw106 and av138m. however, the local heating at 90ºc did not heal the modified adhesives since no increase in toughness was noticed. modified adhesives were examined by sem. small samples were immersed in liquid nitrogen before being fractured. at this temperature, the materials were very brittle and the fracture surfaces were very neat. typical fractures surfaces are shown in fig. 10 for adhesive aw106 with 10%. it can be seen that the fracture surface is increased by the particles. it is as if the tems behave as obstacles for crack propagation. there is a consistent tail phenomenon where all tails go in the same direction. figure 10: fracture surface obtained by scanning electron microscopy for adhesive aw106 with 10wt%. http://dx.medra.org/10.3221/igf-esis.16.02&auth=true http://www.gruppofrattura.it g. pesquet et alii, frattura ed integrità strutturale, 16 (2011) 18-27; doi: 10.3221/igf-esis.16.02 25 the tems expanded did not increase the fracture toughness of modified adhesives but the simple presence of tems did. tems are filled with liquid hydrocarbon and are, therefore, probably poorly compressible as rubber particles are. in addition, their size and the mass fractions used are comparable to those of rubber particles. therefore, the dominant toughening mechanism might be similar to the one that occurs with adhesives modified with rubber particles. the tems as a second phase may trigger inelastic processes at a lower macroscopic stress than the stress required to trigger inelastic processes in single-phase adhesives [11]. therefore, the adhesive is able to absorb the energy of deformation through plastic shear deformation between the particles [12-13]. tensile test fig. 11 presents stress-strain curves for neat and modified araldite 2015 adhesive. the tems decrease the tensile strength and increase the failure strain. the energy under the tensile curve was computed (toughness modulus) and is presented in tab. 4 along with other values taken from the tensile curves such as the young’s modulus, the tensile strength and the failure strain. the tensile curves also show that the tems increase the toughness and confirm the results obtained with the bending tests. the response of the modified adhesives shows a drop in stress after the proportional limit after which the stress starts to increase again. the same effect was obtained with rubber particles by imanaka et al [14]. figure 11: tensile stress-strain curves for adhesive 2015. araldite 2015 0 wt% 10 wt% 20 wt% e (mpa) 1658 1565 1677 modulus of toughness (mj/mm3) 0.81 1.14 1.27 σmax (mpa) 26.9 21.8 19.8 εmax 5.4 % 7.7 % 9.1 % table 4: results from the tensile tests on adhesive 2015. finite element analysis finite element (fe) analysis of the bending test was carried out. the experimental values of the toughness were the input in the fe analysis and the corresponding numerical load-displacement curves were compared to the experimental ones. details of the numerical simulation the geometry represented in fig. 2 was considered. the simulation was conducted assuming linear elastic fracture mechanics (lefm) and the strain energy release rate was computed using the virtual crack closure technique (vcct). the crack was propagated when the strain energy release rate at the crack tip was above the critical strain energy release a http://dx.medra.org/10.3221/igf-esis.16.02&auth=true http://www.gruppofrattura.it g. pesquet et alii, frattura ed integrità strutturale, 16 (2011) 18-27; doi: 10.3221/igf-esis.16.02 26 rate of the material in mode i (gic). vcct does not need special elements or remeshing but needs two surfaces that are initially partially bonded. the experimental results showed that the maximum deflection is low compared to the size of the specimen, therefore geometric linearity can be assumed. the maximum deflection (obtained with 2015 20wt%) of the senb specimens was always under 3 mm. however, geometric nonlinearity option was used to help the convergence of the vcct analysis. plane strain condition was assumed. because first-order elements generally work best for crack propagation analysis [15], plain-strain, four-node, linear cpe4 [15] element were selected. 100 elements were used along the height and 100 elements were used along the length of each part with a geometric decrease in size next to the bonded surface. 20 000 elements were used in total. the width of elements next to the bonding area was 2.4×10 mm. vcct does not exhibit a strong mesh dependency. two computations were done with the same geometry and material properties but with 360 and 20,000 elements, respectively. the coarse mesh is slightly stiffer but the displacement needed to disbond the first nodes was rather accurately found with the coarse mesh. results of the numerical simulation three cases are presented here for illustration purposes: araldite 2015 0wt%, araldite aw106 25wt%, araldite av138m 20wt%. similar conclusions were obtained for the other cases. the three experimental load-displacement curves come from senb specimens with a crack opened under fatigue. for each case, both experimental and numerical curves are plotted for comparison purposes. the first case presented is for the ductile 2015 adhesive in fig. 12(a). as vcct use lefm approximation, there is no plasticity. that explains that the peak of the experimental curve is smoother than the numerical one. however, the prediction is overall correct. the same conclusion can be drawn from the case of adhesive aw106 with 25wt% of tems (fig. 12(b)). the third case is for adhesive av138m with 20wt% tems in fig. 12(c). in this case, the experimental failure of the specimen was instantaneous. the starting of disbonding was accurately determined by vcct. however, there is a softening of the specimen in the numerical simulation that was not captured experimentally. the numerical results show that modified adhesives can be properly simulated with a homogenous model knowing the critical strain energy release rate. the macroscopic deformation of the experimental specimens was ruled by linear elasticity and the assumption of lefm was correct for simulating these senb specimens. (a) (b) (c) figure 12: numerical and experimental load-displacement curves for (a) adhesive 2015 non modified; (b) adhesive aw106 with 25wt% tems; (c) adhesive av138 with 20wt% tems. http://dx.medra.org/10.3221/igf-esis.16.02&auth=true http://www.gruppofrattura.it g. pesquet et alii, frattura ed integrità strutturale, 16 (2011) 18-27; doi: 10.3221/igf-esis.16.02 27 conclusions he effect of thermally expandable microcapsules (tems) on structural adhesives was investigated in terms of mode i fracture toughness. the single-edge-notch-bending (senb) test was used. three adhesives were selected (aw106 that is very ductile, 2015 that is ductile and av138m that is brittle) and different mass fraction of tems were studied. firstly, a standard fracture test was conducted. secondly, since tems expands start their expansion at about 60ºc, specimens fatigue testing was performed expecting a local heating of the notch. then, the specimen was statically tested. thirdly, the specimen was heated locally in its notch at 90ºc to lead to a local expansion of the particles. then, the specimen was loaded for fracture toughness determination. the following conclusions can be drawn. 1. the fracture toughness increased as the mass fraction of tems increased. however, the very ductile adhesive aw106 did not show clearly this increase in terms of toughness. 2. the two local heatings tested did not heal tems-modified adhesives. 3. a parallel could be drawn between tems and rubber incorporation since the sizes of the particles are comparable and both are barely compressible. indeed, stress-strain curves for tems-modified and rubber-modified exhibit similarities. 4. as rubber particles, tems-induced shear yielding of the epoxy matrix is believed to be the dominant toughening mechanism. however, since tems are a shell filled with liquid, they may not exhibit the crack-bridging mechanism. 5. the specimens were successfully simulated using linear elastic fracture mechanics (lefm) approximation. the bending test was simulated with the virtual crack closure technique (vcct) using the experimental strain energy release rate. 6. tems have been developed for recycling purpose by allowing joints to be dismantled. however, tems also increase the fracture toughness of adhesives therefore, tems-modified adhesives could be used on a larger scale. references [1] y. nishiyama, n. uto, c. sato, h. sakurai, int j adhesion and adhesives, 23 (2003) 377. [2] y. nishiyama, c. sato, in: adhesion current research and applications, w. possart (editor), wiley, weinheim, (2005) 555. [3] h. ishikawa, k. seto, s. shimotuma, n. kishi, c. sato, int j adhesion and adhesives, 25 (2005) 193. [4] j.-y. cognard, r. créachcadec, j. maurice, p. davies, m. peleau, l.f.m. da silva, j adhesion science and technology, 24 (2010) 1977. [5] s.r. white, n.r. sottos, p.h. geubelle, j.s. moore, m.r. kessler, s.r. sriram, e.n. brown, s. viswanathan, nature, 409 (2001) 794. [6] r.s. trask, h.r. williams, i.p. bond, bioinspir. biomim., 2 (2007) 1. [7] m.r. kessler, n.r. sottos, s.r. white, composites part a, 34 (2003) 743. [8] i.p. bond, j.w.c. pang, compos part a, 36 (2005) 183. [9] l.f.m. da silva, r.d. adams, j. adhesion science and technology, 19 (2005) 109. [10] z. chen, r.d. adams, l.f.m. da silva, int j fracture, 167 (2011) 221. [11] j. du, m.d. thouless, a.f. yee, int j fract, 92 (1998) 271. [12] a.f. yee, r.a. pearson, j mater sci, 21 (1986) 2462. [13] y. huang, a.j. kinloch, j.mater sci, 27 (1992) 2753. [14] m. imanaka, d. yamashita, y. suzuki, a. fujinami, polymer & polymer composites, 13 (2005) 765. [15] abaqus analysis user’s manual. abaqus 6.9 (2009). t http://dx.medra.org/10.3221/igf-esis.16.02&auth=true http://www.gruppofrattura.it microsoft word numero_37_art_39 e. mihailov et alii, frattura ed integrità strutturale, 37 (2016) 297-304; doi: 10.3221/igf-esis.37.39 297 focused on fracture mechanics in central and east europe an effect of heat insulation parameters on thermal losses of water-cooled roofs for secondary steelmaking electric arc furnaces e. mihailov, p. popgeorgiev, m. ivanova university of chemical technology and metallurgy, sofia, bulgaria emil@uctm.edu abstract. the aim of this work is research in the insulation parameters effect on the thermal losses of watercooled roofs for secondary steelmaking electric arc furnaces. an analytical method has been used for the investigation in heat transfer conditions in the working area. the results of the research can be used to choose optimal cooling parameters and select a suitable kind of insulation for water-cooled surfaces. keywords. electric arc furnaces; heat transfer; mathematical modeling; water-cooled roofs. introduction n order to extend the run time between repairs of electric arc-heated furnaces and to reduce consumption of refractories, in recent years modular water-cooled components are used more frequently in their design. application of such components, however, involves increased thermal losses, and their faultless operation imposes additional design and operation requirements. it is well-known that, in the presence of water-cooled components, one of the possible ways to reduce thermal losses is application of low-emissivity coatings. another option is creation of additional heat resistance using refractory insulation. the effect of applying such insulations and coatings depends on the thermophysical characteristics of the materials. besides, one should expect that, depending on the particular construction, the influence of the thermophysical and radiation insulation characteristics on thermal losses is not simple. that provoked a more detailed study of the water-cooled elements thermal performance under various options of additional measures (application of additional insulation) which would help to establish the influence of various parameters. mathematical model of heat exchange he normal work and efficient usage of water cooling elements requires restrictions to be made and a number of special features to be taken in consideration when defining the constructive parameters:  heat load under the influence of the arcs and metal;  cooling water movement regime;  outlet cooling water temperature;  possibilities for heat losses decrease through protective cooling covering with a definite emissivity and thickness. i t e. mihailov et alii, frattura ed integrità strutturale, 37 (2016) 297-304; doi: 10.3221/igf-esis.37.39 298 from the published models[1-3] for the analysis of heat transfer process in the work area of the electric arc steelmaking furnaces(easf) using the water cooling elements two ways are used: 1. outer heat transfer at stationary heat conduction of the wall, roof and metal at which the electric arc can be taken as a point energy source. 2. outer and inner heat transfer on the basis of immediately heat balance of the whole system. the heat balance of the working area of easf can be given with the equation [2]: elwgelcma qqqqqp  . , (1) in the heat exchange description, the chamber space of the secondary steelmaking electric arc furnaces (fig. 1) was reduced to two surfaces (fsum =fm+fw-f and fc.el) forming a closed space. h d ar fm fw-f fc.el h d ar fm fw-f fc.el fsum fc l .el fsum fc l .el figure 1: ladle furnace scheme and heat transfer areas. scheme of the heat balance and different heat flows in water-cooled element is presented on fig. 2. w welc elc ins insr elcr tqt            1 . . . f mv out wt in wt  inwoutwww elc ttc q m    .  inwoutwwwelc ttmcq  . elc. pd elc. ins        elc elc ins insr elcr wc r qtt . . .     welc elc ins ins wrr elc tt q     1 . . .    ins insr elcr cins r qtt   .  elc. ins ins ins     2outwinww ttt  l elcq .   l elcelcrefl qq ..1  elcownabs r elc qqqq ..  4 .... 100 ..        relc l elcelcelc t qq   4. 100. relcown tq  0,14 s w0,330,8 p w w pr0,027re d            pipe of cooled elements insulation w welc elc ins insr elcr tqt            1 . . . f mv out wt in wt  inwoutwww elc ttc q m    .  inwoutwwwelc ttmcq  . elc. pd elc. ins        elc elc ins insr elcr wc r qtt . . .     welc elc ins ins wrr elc tt q     1 . . .    ins insr elcr cins r qtt   .  elc. ins ins ins     2outwinww ttt  l elcq .   l elcelcrefl qq ..1  elcownabs r elc qqqq ..  4 .... 100 ..        relc l elcelcelc t qq   4. 100. relcown tq  0,14 s w0,330,8 p w w pr0,027re d            pipe of cooled elements insulation figure 2: scheme of the heat balance and different heat flows in water-cooled. e. mihailov et alii, frattura ed integrità strutturale, 37 (2016) 297-304; doi: 10.3221/igf-esis.37.39 299 in the mathematical model is accepted, that the heat removed by cooling water (qc.el) and resultant heat flux are equal: r elcelc qq ..  (2) for the heat losses by the roof can be taken very well know equation: elc w wrr elc f r tt q .. 1     (3) the heat float falling through the flat cooling element can be determined by the following equation [2]:      elcrradga sum elc efelcrrs l f tt ckp f f kkkq elc . 44 . . 100100 111 .                             (4) determining of the heat lose according eq. (3) tr and w are unknown. the coefficient w can be defined from the equation [4]: 0,14 s w0,330,8 w pw pr0,027re d nu            for the purposes of the study, a mathematical model of the external heat exchange, under steady state thermal condition of walls and metal where the electric arc is viewed as energy point-source, was made. for computer implementation of the mathematical model an algorithm (illustrated by a simplified block diagram on fig. 3) was developed. the object of the study was the construction of real 100t secondary steelmaking electric arc installation. an effect of heat insulation parameters on thermal losses of water-cooled roofs hermal losses through cooling water have been calculated for various insulation thicknesses and types of materials. the thermophysical characteristics of silica, magnesite, chromitee, shamote, magnesite-chromite and chromitemagnesite refractory of various thicknesses and their own emissivity have been used as input data for the study. for faultless operation of the water-cooled roof panel, water temperature at the outlet shall not exceed 60ос. it was assumed that water temperature at the panel outlet was 30ос, and water temperature difference between the panel inlet and outlet was t=10 °c. as a result of the calculations, the thermal losses, the average heat transfer coefficient to the water, and the required water flow rate ensuring compliance with the restrictions imposed on outlet water temperature were obtained. the resulting heat losses and temperature changes on the insulation surface depending on its thickness for silica, magnesite, chromitee, shamote, magnesite-chromite and chromite-magnesite are presented in fig. 4 to 9. the thermophysical characteristics of these materials are presented on tab. 1. from fig. 4 it can be seen that, in the case of silica insulation depending on the insulation thickness 1mm to 20 mm, the thermal losses decrease with 50% from 1.83mw to 0.92 mw, or 8.3 % from the heat generated from the electric arcs. at the same time surface thermal resistance increases up to 0.01 m2k/w and temperature to 950°c. similar values can be seen in the case of cromite insulation (fig. 5) where the surface temperature increases up to 820 oc and temperature resistanceup to 0.013 m2k/w. the magnesite insulation (fig. 6) ensures heat losses in the range of 13% to 12.8% from the heat generated from the electric arcs, i.e. thermal losses decrease with very low values of 0.2%. this is in consequence of the high thermal conductivity with values of thermal resistance 0.003 m2k/w. the surface temperature increases up to 300 °c. t e. mihailov et alii, frattura ed integrità strutturale, 37 (2016) 297-304; doi: 10.3221/igf-esis.37.39 300 the shamote insulation (fig. 7) has a high level of thermal resistance, which at thickness of 0.012m is 0.012 m2k/w, the surface temperature increases up to 1040°c and heat losses decrease from 1.76mw to 0.73mw by 60%. kind of insulation emissivity ε coefficient of conductivity , w/m.k silica 0.70 1.58+0.00038.t magnesite 0.38 6.28-0.00270.t shamote 0.60 0.88+0.00023.t chromite 0.85 1.28+0.00410.t magnesite-chromite 0.82 4.10-0.00160.t chromite-magnesite 0.93 2.80-0.00087.t table 1: thermophysical characteristics of insulating material.[5] elc l r qq . elc fwmsum ff ffff .2 1    mw l elc w l rr tfrqt .. 1         elc elc ins insr . .           elcrradg a sum elc efelcrrelcs l elc f tt ck p f f kkkq . 44 . ... 100100 1 11                              a sla s l l k                          sum elc efr f f c .1 1 1 1 167,5  wm wwmm rad ff tftf t    0,14 s w0,330,8w w pr0,027re d             inwoutwww elc ttc q m    . 4 ... 100 .67,5.        relc l elcelc t qq  f mv  d re .v      2/ 2/ , , wins r cins r c ir cins r ins r ins ir ttt ttt     11,,   ins ir ins ir tt 11,,   c ir c ir tt aslelcinsefelcfw mfwr in w out wsla ldf ftttttp ,,,,,,, ,,,,,,, ..   trmre,prq welc ,,v,,,.  wsw pr  ,,,, inselc  ,. wwc , yes yes no no elc l r qq . elc fwmsum ff ffff .2 1    mw l elc w l rr tfrqt .. 1         elc elc ins insr . .           elcrradg a sum elc efelcrrelcs l elc f tt ck p f f kkkq . 44 . ... 100100 1 11                              a sla s l l k                          sum elc efr f f c .1 1 1 1 167,5  wm wwmm rad ff tftf t    0,14 s w0,330,8w w pr0,027re d             inwoutwww elc ttc q m    . 4 ... 100 .67,5.        relc l elcelc t qq  f mv  d re .v      2/ 2/ , , wins r cins r c ir cins r ins r ins ir ttt ttt     11,,   ins ir ins ir tt 11,,   c ir c ir tt aslelcinsefelcfw mfwr in w out wsla ldf ftttttp ,,,,,,, ,,,,,,, ..   trmre,prq welc ,,v,,,.  wsw pr  ,,,, inselc  ,. wwc , yes yes no no figure 3: simplified block diagram of the numerical algorithm. e. mihailov et alii, frattura ed integrità strutturale, 37 (2016) 297-304; doi: 10.3221/igf-esis.37.39 301 0 5 10 15 20 8.0x10 5 1.0x10 6 1.2x10 6 1.4x10 6 1.6x10 6 1.8x10 6 2.0x10 6 0 200 400 600 800 1000 1200 1400 0.000 0.002 0.004 0.006 0.008 0.010 0.012 0.014 t p , o c r , (m 2 .k )/ w q q , w /m 2 d, mm tp r 0 5 10 15 20 8.0x10 5 1.0x10 6 1.2x10 6 1.4x10 6 1.6x10 6 1.8x10 6 2.0x10 6 0 200 400 600 800 1000 1200 1400 0.000 0.002 0.004 0.006 0.008 0.010 0.012 0.014 t p , o c r , (m 2 . k )/ w q q , w /m 2 d, mm t r figure 4: heat losses, surfaces temperature and thermal resistance of insulation as a function of silica insulation thickness figure 5: heat losses, surfaces temperature and thermal resistance of insulation as a function of chromite insulation thickness. 0 5 10 15 20 8.0x10 5 1.0x10 6 1.2x10 6 1.4x10 6 1.6x10 6 1.8x10 6 2.0x10 6 0 200 400 600 800 1000 1200 1400 0.000 0.002 0.004 0.006 0.008 0.010 0.012 0.014 t p , o c r , (m 2 . k )/ w q q , w /m 2 d, mm t r 0 5 10 15 20 8.0x10 5 1.0x10 6 1.2x10 6 1.4x10 6 1.6x10 6 1.8x10 6 2.0x10 6 0 200 400 600 800 1000 1200 1400 0.000 0.002 0.004 0.006 0.008 0.010 0.012 0.014 t p , o c r , (m 2 .k )/ w q q , w /m 2 d, mm t r figure 6: heat losses, surfaces temperature and thermal resistance of insulation as a function of magnesite insulation thickness figure 7: heat losses, surfaces temperature and thermal resistance of insulation as a function of shamote insulation thickness in the case of chrome-magnesite (fig. 8) insulation the heat losses decrease to 14 % and the surface temperature is 580°c for 0.020m thickness of insulation. for magnesite-chromite insulation (fig. 9) these values are 15%, thermal resistance r=0.005 and surface temperature tr= 420°c fig.10 shows that, in the case of shamote insulation, thermal losses are smaller, which can be explained by the lower heat conductivity of this type refractory. at the same time, with such insulation, surface temperatures are higher than those of the rest insulations. it can be seen that all insulations have a higher level of initial values of heat losses than magnesite and with increasing of insulation thickness their heat losses decrease. it can be explained with the lower value of emissivity (=0.38) of magnesite material than the emissivity of the other materials. with the increase of magnesite insulation thickness to 0.008 m, the surface temperature increases up to 136°c and the heat losses are the same as in the case of shamote, but the surface temperature of shamote insulation increases up to 730oc. at about 0.015m thickness of the magnesite insulation, the heat losses are similar to the heat losses of magnesitechromite and crome-magnesite, but the surface temperatures of the cooling element for the last two materials are respectively 319°c and 436°c. a graphical summarizing of investigated materials behavior is presented on fig. 10. e. mihailov et alii, frattura ed integrità strutturale, 37 (2016) 297-304; doi: 10.3221/igf-esis.37.39 302 0 5 10 15 20 8.0x10 5 1.0x10 6 1.2x10 6 1.4x10 6 1.6x10 6 1.8x10 6 2.0x10 6 0 200 400 600 800 1000 1200 1400 0.000 0.002 0.004 0.006 0.008 0.010 0.012 0.014 t p , o c r , (m 2 .k )/ w q q , w /m 2 d, mm t r 0 5 10 15 20 8.0x10 5 1.0x10 6 1.2x10 6 1.4x10 6 1.6x10 6 1.8x10 6 2.0x10 6 0 200 400 600 800 1000 1200 1400 0.000 0.002 0.004 0.006 0.008 0.010 0.012 0.014 t p , o c r , (m 2 .k )/ w q q , w /m 2 d, mm t r figure 8: heat losses, surfaces temperature and thermal resistance of insulation as a function of chrome-magnesite insulation thickness figure 9: heat losses, surfaces temperature and thermal resistance of insulation as a function of magnesite-chromite insulation thickness 0 5 10 15 20 6,0x10 5 8,0x10 5 1,0x10 6 1,2x10 6 1,4x10 6 1,6x10 6 1,8x10 6 2,0x10 6 0 200 400 600 800 1000 1200 1400 qsh qd qmg qcr q , w d, mm t , o c td tsh tmg tcr figure 10: heat losses and surfaces temperature of insulations as a function of insulation thickness. as seen from the obtained results and the thermal balance of the water-cooled element (fig. 2), with the same insulation thickness and lower thermal conductivity coefficient, the surface temperature is higher compared to that in the case of higher thermal conduction, whereupon the own radiation heat flux (qown) of the roof cooling element is higher. in the case of lower insulation thickness, the surface temperatures are lower, and under such conditions and lower emissivity (<0,5), the reflected heat flux from the surface (qrefl) has a higher value than the absorbed flux (qabs) and the own radiation of the surface is lower. for larger thickness and lower values of thermal conductivity, the surface temperature becomes higher than 500°c, and the own radiation of roof cooling element has a higher effect on the surface's thermal balance. under such conditions, the cooling element participates in the heat transfer with significant quantities of the radiation heat flux from own radiation, depending, to the highest extent, on the surface temperature and surface emissivity and has the behaviour of a refractory-brick roof with all their shortcomings. for the same insulation thickness and higher thermal conductivity coefficient, the surface temperature is lower compared to that in the case of low thermal conductivity, consequently the own radiation (qown) of the water-cooling element is lower and under such conditions and lower emissivity (<0.5), the reflected heat flux from the surface (qrefl) has a higher values than the absorbed flux (qabs). obviously, the use of such heat insulating materials for heat losses reduction is restricted by insulation thickness, levels of thermal conductivity coefficient and emissivity. the high level of the surface temperature has to be avoided, because the higher surface temperatures are sources of thermal gradients and thermal stresses and can lead to destruction of insulations. e. mihailov et alii, frattura ed integrità strutturale, 37 (2016) 297-304; doi: 10.3221/igf-esis.37.39 303 therefore, the application of insulation materials on water-cooled roofs should be limited in their safety working conditions, i.e. in the range of surfaces temperatures with low values of thermal gradients and thermal stresses across insulation thickness. as can be seen from fig.10, magnesite can be recommended as an appropriate material with its own low values of emissivity, surface temperature of insulation and thermal gradient across insulation thickness. 4.conclusions detailed investigation of the water-cooled elements thermal performance under various options of application of additional insulation has been carried out. an analytical study was made to find the possible ways of reducing the thermal losses in the water-cooled roof of a 100t secondary steelmaking electric arc furnace. as a result of the study it was found that, magnesite can be recommended as an appropriate material with its own low values of emissivity, thermal losses and surface temperature of insulation during the work. references [1] velchev, a., mihailov, e., petkov,v., investigation of the parameters influence over the heat work of the watercooling roofs for small electric arc furnace, international conference “the efficient use of energy in metallurgy”, varna, bulgaria, 94 (1999) 100-105. [2] lingorsky, n., heat transfer in electric arc furnaces equipped with water cooled panels, iron and steel engineer, 10 41(1988). [3] toulouevski, y., zinurov, il., innovation in electric arc furnaces: scientific basis for selection, springer-verlag gmbh, (2013) 215-237 [4] kreit, f., black, w, basic heat transfer, harper and row, publishers, new york, (1980). [5] mastrukov, b., theory, constructions and calculations of metallurgical furnaces, moscow, metallurgy, (1986) (in russian). appendix list of symbols: c coefficient of heat transfer through radiation w/m2k4; cw specific heat capacity of water, kj/m3k; dp – diameter of cooling panel pipe, m; l c.elf , r c.elf , fm, fw-f -heat absorbing area of insulation, cooling element, metal and wall, m2; i – consecutive number of iteration; kg coefficient /0,1/; kr coefficient, marked the direct absorbing of the cooling element surface from the arc; ks arc screening coefficient; la length of arc, m; m volumetric flow of cooling water, m3/s; pa heat generated by arcs, w; pr , re prandtl and reynolds numbers; qw-f , qc.el, heat removed by walls and cooling water, w; l c.elq , r c.elq radiant heat flux fall on the roof and resultant heat flux, w; qown , qrefl, qabs – own, reflected and absorbed radiant heat flux by roof, w; qm heat observe by metal,w; qc.el heat removed by cooling water,w; qg-heat outlet by gases,w; qw heat removed by walls,w; a e. mihailov et alii, frattura ed integrità strutturale, 37 (2016) 297-304; doi: 10.3221/igf-esis.37.39 304 qel heat removed by electrodes, w. r heat resistance, m2k/w; tr surface temperature of the roof, k; c r ins r t ,t average temperature of insulation and wall of cooling panel, k; c-ins rt temperature between insulation and cooling panel , k; w-c rt temperature between cooling panel and water , k; trad radiation temperature of the total surface fsum=fw-f+fm, k; tm, tw temperature of the metal and wall, k; in wt , out wt inlet and outlet temperature of the water, k; tw – average temperature of the cooling water, k; v – cooling water velocities, m/s; w heat transfer coefficient by the water, w/m2k; c.el, ins, s thickness of cooling elements, insulation and slag layer, m; c.el, inscoefficient of thermal conductivity of cooling elements and insulation, w/mk; c.el , ef emissivity of heat roof absorbing surface and effective emissivity of fsum; s dynamic viscosity of the water at the temperature of the surface, n.s/m2; w dynamic viscosity at average temperature of the water, ns/m2; w density of the water, kg/m3;  kinematic viscosity at average temperature of the water, m2/s. << /ascii85encodepages false /allowtransparency false /autopositionepsfiles true /autorotatepages /none /binding /left /calgrayprofile (dot gain 20%) /calrgbprofile (srgb iec61966-2.1) /calcmykprofile (u.s. web coated \050swop\051 v2) /srgbprofile (srgb iec61966-2.1) /cannotembedfontpolicy /error /compatibilitylevel 1.4 /compressobjects /tags /compresspages true /convertimagestoindexed true /passthroughjpegimages true /createjobticket false /defaultrenderingintent /default /detectblends true /detectcurves 0.0000 /colorconversionstrategy /cmyk /dothumbnails false /embedallfonts true /embedopentype false /parseiccprofilesincomments true /embedjoboptions true /dscreportinglevel 0 /emitdscwarnings false /endpage -1 /imagememory 1048576 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/hrv (za stvaranje adobe pdf dokumenata najpogodnijih za visokokvalitetni ispis prije tiskanja koristite ove postavke. stvoreni pdf dokumenti mogu se otvoriti acrobat i adobe reader 5.0 i kasnijim verzijama.) /hun 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can be opened with acrobat and adobe reader 5.0 and later.) >> /namespace [ (adobe) (common) (1.0) ] /othernamespaces [ << /asreaderspreads false /cropimagestoframes true /errorcontrol /warnandcontinue /flattenerignorespreadoverrides false /includeguidesgrids false /includenonprinting false /includeslug false /namespace [ (adobe) (indesign) (4.0) ] /omitplacedbitmaps false /omitplacedeps false /omitplacedpdf false /simulateoverprint /legacy >> << /addbleedmarks false /addcolorbars false /addcropmarks false /addpageinfo false /addregmarks false /convertcolors /converttocmyk /destinationprofilename () /destinationprofileselector /documentcmyk /downsample16bitimages true /flattenerpreset << /presetselector /mediumresolution >> /formelements false /generatestructure false /includebookmarks false /includehyperlinks false /includeinteractive false /includelayers false /includeprofiles false /multimediahandling /useobjectsettings /namespace [ (adobe) (creativesuite) (2.0) ] /pdfxoutputintentprofileselector /documentcmyk /preserveediting true /untaggedcmykhandling /leaveuntagged /untaggedrgbhandling /usedocumentprofile /usedocumentbleed false >> ] >> setdistillerparams << /hwresolution [2400 2400] /pagesize [612.000 792.000] >> setpagedevice microsoft word numero_38_art_16 m. de freitas et alii, frattura ed integrità strutturale, 38 (2016) 121-127; doi: 10.3221/igf-esis.38.16 121 focussed on multiaxial fatigue and fracture comparison between ssf and critical-plane models to predict fatigue lives under multiaxial proportional load histories manuel de freitas, luis reis idmec, instituto superior técnico, av. rovisco pais, 1049-001 lisboa, portugal mfreitas@dem.ist.utl.pt, luis.g.reis@ist.utl.pt marco antonio meggiolaro, jaime tupiassú pinho de castro pontifical catholic university of rio de janeiro, puc-rio, r. marquês de são vicente 225, rio de janeiro, 22451-900, brazil meggi@puc-rio.br, jtcastro@puc-rio.br abstract. materials can be classified as shear or tensile sensitive, depending on the main fatigue microcrack initiation process under multiaxial loadings. the nature of the initiating microcrack can be evaluated from a stress scale factor (ssf), which usually multiplies the hydrostatic or the normal stress term from the adopted multiaxial fatigue damage parameter. low ssf values are associated with a shear-sensitive material, while a large ssf indicates that a tensile-based multiaxial fatigue damage model should be used instead. for tension-torsion histories, a recent published approach combines the shear and normal stress amplitudes using a ssf polynomial function that depends on the stress amplitude ratio (sar) between the shear and the normal components. alternatively, critical-plane models calculate damage on the plane where damage is maximized, adopting a ssf value that is assumed constant for a given material, sometimes varying with the fatigue life (in cycles), but not with the sar, the stress amplitude level, or the loading path shape. in this work, in-phase proportional tension-torsion tests in 42crmo4 steel specimens for several values of the sar are presented. the ssf approach is then compared with critical-plane models, based on their predicted fatigue lives and the observed values for these tension-torsion histories. keywords. multiaxial fatigue life prediction; critical-plane approach; polynomial stress scale factor approach. citation: de freitas, m., reis, l., meggiolaro, m. a., de castro, j.t.p., comparison between ssf and critical-plane models to predict fatigue lives under multiaxial proportional load histories, frattura ed integrità strutturale, 38 (2016) 121-127. received: 11.05.2016 accepted: 10.06.2016 published: 01.10.2016 copyright: © 2016 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. introduction nitiating microcracks under multiaxial fatigue loadings can be sub-divided into shear or tensile types [1]. the dominant fatigue mechanism in so-called shear-sensitive materials is mode ii microcrack nucleation in shear, so the cracks initiate in directions that maximize the ranges of the shear components, with the normal components only i m. de freitas et alii, frattura ed integrità strutturale, 38 (2016) 121-127; doi: 10.3221/igf-esis.38.16 122 playing a secondary role. however, other materials may initiate fatigue cracks on planes of maximum tensile strain or stress ranges, e.g. 304 stainless steel under certain load histories and cast irons [2]. in this case, even if the microcrack nucleates in shear, its so-called initiation life (which always includes some microcrack propagation) is controlled by its growth in a direction perpendicular to the maximum principal stress or strain. moreover, a material can be shear-sensitive for short, but tensile-sensitive for long fatigue lives, a behavior that can depend as well on the loading type. the shear or tensile nature of the initiating microcrack can be evaluated from a stress scale factor (ssf), which usually multiplies the hydrostatic or the normal stress term from the adopted multiaxial fatigue damage parameter. low values of the ssf indicate a shear-sensitive material, which should be described by shear-based multiaxial fatigue damage models such as findley’s [3] or fatemi-socie’s [4]. on the other hand, large ssf values indicate that a tensile-based model like smith-watson-topper’s [5] should be used instead to describe the crack initiation process. the approach proposed by anes et al. [6] for tension-torsion histories combines the shear and normal stress amplitudes applied on the specimen cross section, using a ssf polynomial function that depends on the stress amplitude ratio (sar) between the shear and normal components. alternatively, models based on the critical-plane approach calculate multiaxial fatigue damage on the plane where it is maximized (not on the plane where the load is applied), while adopting a ssf value that is assumed constant for a given material, sometimes varying with the fatigue life (in cycles), but not with the sar, stress amplitude level, or loading path shape. in this work, in-phase proportional tension-torsion tests are conducted in 42crmo4 steel specimens for several values of the sar. the ssf and two critical-plane approaches are then compared, based on their predicted fatigue lives and the experimentally measured ones. ssf equivalent shear stress approach he ssf equivalent shear stress approach proposed in [6] considers that both the sar and the stress loading level significantly influence the material fatigue strength in tension-torsion tests. such effects are accounted for through a polynomial ssf function, which is assumed to transform an axial damage into a shear one. with this equivalent stress, it is also possible to estimate fatigue lives nf, using the uniaxial shear stress sn curve represented as    bf block ssf a nmax     (1)  a a a assf a b c d f g h i2 3 2 3 4 5,                       (2) where σa and τa are respectively the amplitude of the axial and of the shear components of the tension-torsion loading, and λ  tan1(τa/σa) is the sar. the constants a to i from the polynomial (2) should be fitted to a suitable data set, therefore the ssf function is assumed to be a material fatigue property that must be determined experimentally. critical plane approach he critical-plane approach assumes that fatigue lives can be calculated from the damage accumulated at the critical plane of the critical point according to some multiaxial fatigue damage model, which is supposed to properly account for the effect of the driving forces that initiate the fatigue crack in the given material. it also assumes that the damage accumulated on all other planes do not influence the initiation of the microcrack, based on the idea that although many intrusions and extrusions may be formed, usually only one fatigue crack usually initiates and grows from the critical point. the main calculation challenge when applying models based on this approach is to compute the accumulated damage in many candidate planes at the critical point, to find the direction of the critical one where it is maximized (and thus where the crack is expected to initiate). this search is very much simplified for in-phase proportional constant amplitude load histories, such as the ones studied in this work. two pressure-insensitive stress-based critical damage models are briefly reviewed following, one in principle applicable to materials that are shear-sensitive (for which the main cyclic driving force for fatigue damage is ) and the other to tensile sensitive materials. findley's shear model findley explicitly introduced the critical plane idea in 1959 [3], proposing a stress-based multiaxial fatigue damage model that can be applied to proportional or non-proportional loads (recall that the principal stress directions remain invariant t t m. de freitas et alii, frattura ed integrità strutturale, 38 (2016) 121-127; doi: 10.3221/igf-esis.38.16 123 under proportional but vary under non-proportional loads). findley's pioneer model, like all subsequent critical-damage models, assumes that fatigue cracks initiate on the critical plane of the component’s critical point, where a suitable damage parameter is maximized. this is a physically sensible idea, which considers in a very reasonable way how the fatigue cracking process works in directional-damage materials, which tend to develop a single dominant fatigue crack, like most metallic alloys. critical plane models assume that fatigue damage can be properly evaluated based only on the normal and shear stress and/or strain histories acting on the critical plane, and neglects fatigue damage eventually induced on other planes, assuming they do not interact and so do not affect the microcrack initiation process on the critical plane. findley assumed fatigue damage is caused by a parameter [/2 fmax], which combines the shear stress range /2 acting on the critical plane with the peak of the normal stress perpendicular () to that plane max, during the considered load event. in this way, fatigue cracking is assumed to take place at the critical point in directions where this (reasonable) damage parameter is maximized. for a case a candidate plane, which is perpendicular to the free surface and makes an angle θ with the in-plane x axis, findley’s infinite-life criterion (for multiaxial fatigue under any type of loading) is given by the maximization problem  a f fmaxmax ( ) 2 ( )          (3) where findley’s coefficient f and shear fatigue limit βf must be calibrated from measurements in at least two types of fatigue tests, e.g. under rotatory bending and cyclic torsion, or else under push-pull pulsating tests with r min/max  0 and fully reversed push-pull tests under r 1. findley’s infinite-life model from eq. 3 can be extended to finite-life calculations using a shear version of wöhler’s curve, equating findley’s fatigue limit βf with the torsional fatigue limit l, resulting in ba f f c l nmax ( ) max ( ) ( 2 ) 2                   (4) where τc and bτ are the torsional strength coefficient and exponent, respectively, calibrated under pure torsion. for the studied in-phase tension-torsion histories, findley’s predicted fatigue life nf (in cycles) becomes after some algebraic manipulation bf f a a a c f f l f n2 2 2 2 2 4 ( 2 ) 1 1                 (5) therefore, nf can be obtained as a function of σa and τa. smith-watson-topper's tensile model findley’s shear model is not appropriate to account for fatigue damage in tensile-sensitive materials, in which case a tensile instead of shear cracks are likely to initiate. in these materials, the fatigue initiation life n of such cracks must be correlated with a damage parameter based on a normal stress or strain range  (not on a shear range ), combined with the peak stress max parallel to  to account for mean/maximum stress effects. the multiaxial version of smith-watson-topper’s (swt) model [5] is particularly useful for calculating fatigue damage on such materials, especially if the propagation phase of the microcracks (still within the so-called crack initiation stage), which is more sensitive to the normal stresses, is dominant over its shear-controlled initiation. the multiaxial version of swt’s equation for case a tensile cracks can be written as b b cc c cn n e 2 2 max ( )max ( ) ( 2 ) ( 2 ) 2             (6) where σc, εc, b, and c are coffin-manson’s material-dependent parameters. in high-cycle or long-life fatigue calculations, a simplified elastic version eswt of the swt model can be adopted to decrease the computational burden. indeed, under linear-elastic uniaxial conditions, the plastic term b cc c n( 2 )   in eq. 6 can be neglected, while hooke’s law gives ()/2 e()/2, resulting in m. de freitas et alii, frattura ed integrità strutturale, 38 (2016) 121-127; doi: 10.3221/igf-esis.38.16 124 b ceswt n 2 2 max ( )max ( ) ( 2 ) 2            (7) this equation can be simplified in the studied proportional history (which has zero mean stresses), because in this fullyalternate case the peak normal stress max() perpendicular to a case a plane along θ is equal to the normal amplitude ()/2. therefore, the eswt equation becomes wöhler’s curve using basquin’s formulation: b b c cn n 2 2 2 max ( ) ( ) ( )max ( ) max ( 2 ) max ( 2 ) 2 2 2                                         (8) thus, the damage parameter to be maximized in the eswt model simply becomes a a 2( ) / 2 | cos sin 2 |         for a fully-alternate cyclic loading. deriving this expression and equating it to zero, the critical-plane angle θeswt with respect to the x-axis, represented in the first quadrant 0º ≤ θ ≤ 90º, is obtained from a a a eswt p a 2 2 cos sin 2 cos 2 0 tan 2 tan 2 2 tan                   (9) where λ is the sar from the ssf model [6], and θp is the principal direction from the first quadrant. not surprisingly, θeswt is one of the fixed principal directions θp of such proportional tension-torsion loadings. on this principal plane, the damage parameter is maximized, resulting in the principal stress equation for the normal and shear amplitudes σa and τa: a a aeswt eswt a a eswt 2 24( ) 1 cos 2 sin 2 2 2 2               (10) from the definition λ  tan1(τa/σa), it follows that τa  σatan(λ); thus this maximized damage parameter on the θeswt plane can be expressed as a function of σa and λ: a a aeswt a 2 2 2 24 tan( ) 0.5 0.25 tan 2 2                  (11) assuming eswt’s model is able to predict crack initiation, the above expression would explain why the ssf can be represented as a function of σa and λ, however requiring a fifth-order polynomial function to approximately reproduce such a non-linear expression. finally, from the eswt equation it follows that the predicted fatigue life neswt (in cycles) is   b b b a a aeswt a eswt c c c n 1/ 1/ 1/2 2 2 4( ) 0.5 0.5 0.5 0.5 0.25 tan 2 2                                    (12) results and discussions material and loading paths he reasoning derived in the previous sections is applied to the experimental results published by anes et al. [6] for proportional tension-torsion multiaxial fatigue tests carried out in low-alloy steel 42crmo4, heat-treated by austenitizing, quenching, and tempering to improve its mechanical properties. the chemical composition and the monotonic and cyclic properties of 42crmo4 are available in [6, 7]. fatigue tests are carried out through a servo-hydraulic tension-torsion machine under stress control at room temperature, applying proportional loading paths. in order to perform the ssf mapping, five different proportional loading paths are t m. de freitas et alii, frattura ed integrità strutturale, 38 (2016) 121-127; doi: 10.3221/igf-esis.38.16 125 selected with different sar λ. although the sar is an important fatigue variable, the stress level also has a high influence on the fatigue damage mechanisms. these two variables will be used in the ssf mapping. fatigue life predictions the tested 42crmo4 steel has young’s modulus, coffin-manson’s fatigue strength coefficient and exponent, and coffinmanson’s fatigue ductility coefficient and exponent presented in freitas et al [6]. however, the eswt model adopts an elastic version of coffin-manson’s equation, which neglects its plastic term. therefore, the resulting purely-elastic calibration requires a better fit of the experimental data to also account for longer fatigue lives. from the normal and shear fittings, it is possible to write: b a c n n 0.0934( 2 ) 1654 ( 2 )      and ba c n n 0.0623( 2 ) 911 ( 2 )      (13) then, from findley’s calibration for case a fatigue cracks, its constants can be determined using eq. (3): αf  0.668 and βf  420.9mpa. figs. 1-3 present a comparison between the observed fatigue lives nobsv and the nssf, neswt and nf predicted by the ssf, eswt and findley’s models, respectively, for sar λ = 0º (uniaxial), 30º, 45º, 60º and 90º (pure torsion). as observed in fig. 1, the ssf polynomial fitting performs satisfactorily, allowing a reasonable match between nobsv and nssf for all cases. however, since all load histories are proportional, this performance should not be generalized for other cases. figure 1: comparison between the observed fatigue lives nobsv and the fitted nssf. as shown in fig. 2, the eswt’s critical-plane method results as well in reasonable, albeit a bit more disperse, fatigue life predictions, except for the pure torsion (λ  90º) case. this exception is not a surprise, since the pure torsion history involves significant shear damage, whereas the eswt’s model only accounts for tensile damage. findley’s critical-plane method also results in reasonable fatigue life predictions, except for the λ  30º and λ  45º cases, as shown in fig. 3. these exceptions suggest that such multiaxial load histories probably involve significant tensile damage, whereas findley’s model only accounts for shear damage. indeed, the maximum normal stress max influences findley’s shear damage parameter, however no measure of the normal range  perpendicular to the critical plane is considered. nevertheless, findley’s predictions for the uniaxial case are surprisingly good, indicating that at least in this in-phase zeromean proportional case the max term was able to properly capture the damaging  effects. m. de freitas et alii, frattura ed integrità strutturale, 38 (2016) 121-127; doi: 10.3221/igf-esis.38.16 126 fig. 4 shows critical-plane predictions based on eswt’s tensile model applied to the predominantly tensile cases λ  0º (uniaxial), 30º, and 45º; and on findley’s shear model to the shear-dominated cases λ  60º and 90º (pure torsion). notice that the prediction scatter is similar to the one from the ssf method. however, it must be noted that such critical-plane method calculations have a greater prediction potential, because they are only based on curve fittings of the uniaxial and pure-torsion experiments, while the polynomial fitting from the ssf method requires data calibration from all five tension-torsion tests. figure 2: comparison between the observed fatigue lives nobsv and the predicted neswt. figure 3: comparison between the observed fatigue lives nobsv and the predicted nf. m. de freitas et alii, frattura ed integrità strutturale, 38 (2016) 121-127; doi: 10.3221/igf-esis.38.16 127 figure 4: comparison between the observed lives nobsv and the lives neswt or nf predicted by critical-plane methods, according to the dominance of normal or shear applied loads. conclusions n this work, it was shown that both critical-plane and ssf approaches have the potential to predict multiaxial fatigue lives, at least for in-phase proportional loadings. findley’s model neglects tensile damage, while the eswt model neglects shear damage, which explains why their performance was not very good for all considered load histories. in its current form, the ssf method does not include mean/maximum stress effects, therefore experiments with zero mean loads were chosen to evaluate its performance. the ssf method resulted in a better fit of the experimental data, however it requires more calibration tests (to fit its 5th-degree polynomial) than the critical plane approach. references [1] castro, j.t.p., meggiolaro, m.a., fatigue design techniques (in 3 volumes), createspace, scotts valley, ca, usa (2016). [2] socie, d., marquis g., multiaxial fatigue, sae international, warrendale, pa, usa (2000). [3] findley, w.n., a theory for the effect of mean stress on fatigue of metals under combined torsion and axial load or bending, j. eng. industry, 81 (1959) 301-306. [4] fatemi, a., socie, d., a critical plane approach to multiaxial damage including out-of-phase loading, fatigue fract. eng. mater. struct., 11 (1988) 149-166. [5] smith, r.n. watson, p., topper, t.h., a stress-strain parameter for the fatigue of metals, j. mater., 5 (1970) 767-778. [6] anes,v., reis, l. li, b., fonte, m., de freitas, m., new approach for analysis of complex multiaxial loading paths, int. j. fatigue, 62 (2014) 21-33. 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can be opened with acrobat and adobe reader 5.0 and later.) >> /namespace [ (adobe) (common) (1.0) ] /othernamespaces [ << /asreaderspreads false /cropimagestoframes true /errorcontrol /warnandcontinue /flattenerignorespreadoverrides false /includeguidesgrids false /includenonprinting false /includeslug false /namespace [ (adobe) (indesign) (4.0) ] /omitplacedbitmaps false /omitplacedeps false /omitplacedpdf false /simulateoverprint /legacy >> << /addbleedmarks false /addcolorbars false /addcropmarks false /addpageinfo false /addregmarks false /convertcolors /converttocmyk /destinationprofilename () /destinationprofileselector /documentcmyk /downsample16bitimages true /flattenerpreset << /presetselector /mediumresolution >> /formelements false /generatestructure false /includebookmarks false /includehyperlinks false /includeinteractive false /includelayers false /includeprofiles false /multimediahandling /useobjectsettings /namespace [ (adobe) (creativesuite) (2.0) ] /pdfxoutputintentprofileselector /documentcmyk /preserveediting true /untaggedcmykhandling /leaveuntagged /untaggedrgbhandling /usedocumentprofile /usedocumentbleed false >> ] >> setdistillerparams << /hwresolution [2400 2400] /pagesize [612.000 792.000] >> setpagedevice microsoft word numero_53_art_22_2804 a. namdar, frattura ed integrità strutturale, 53 (2020) 285-294; doi: 10.3221/igf-esis.23.22 285 forecasting the bearing capacity of the mixed soil using artificial neural network abdoullah namdar faculty of architecture and civil engineering, huaiyin institute of technology, huai’an, china department for management of science and technology development, ton duc thang university, ho chi minh city, vietnam faculty of environment and labour safety, ton duc thang university, ho chi minh city, vietnam abdoullah.namdar@tdtu.edu.vn abstract. the bearing capacity of soil changes owing to the mechanical properties of the soil and it influences the structural stability. in most of the geotechnical engineering projects, there are several soil mechanic experiments, that need interpretation before application. the mechanical properties of soil interaction make the prediction of soil bearing capacity complex. however, the enhancement of construction project safety needs the interpretation of soil experiments and design results for proper application in a geotechnical engineering project. in this study, artificial neural network is proposed for the evaluation of the mixed soil characteristics to forecast the safe bearing capacity of soil due to the mechanical properties of the soil interaction phenomenon. the results for prediction of the safe bearing capacity reveal that the r2 and rmse for all mechanical properties effects on safe bearing capacity are 0.98 and 0.02, these values can provide a suitable accuracy for the prediction of the safe bearing capacity of the mixed soil. the higher inaccuracy is obtained when only the influence of single mechanical property on the mixed soil is considered in the prediction of the safe bearing capacity. this study supports the enhancement of geotechnical engineering design quality through the prediction of safe bearing capacity from characterized mechanical properties of the soil. keywords. bearing capacity; mechanical properties; artificial neural network; mixed soil. citation: namdar, a., forecasting the bearing capacity of the mixed soil using artificial neural network, frattura ed integrità strutturale, xx (2020) 285-294. received: 26.04.2020 accepted: 09.05.2020 published: 01.07.2020 copyright: © 2020 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. introduction aboratory experimental activity was performed for the characterization of red soil in soil mixture process and the assessment of soil mixture mechanical properties was performed for developing acceptable safe bearing capacity [1]. the bearing capacity of mixed soil foundation was investigated by changing the concrete footing dimensions and the soil mechanical properties systematically [2-3]. to study the bearing capacity of subsoil in the coastal region, the tsunami behavior was numerically simulated and mangrove for enhancement of subsoil was proposed [4]. the bearing capacity of soil foundation also was related to the seismic displacement of the soil foundation [5]. the bearing capacity of the embankment soil foundation was enhanced by developing dense zones in the subsoil [6]. the bearing capacity of the l https://youtu.be/tgebluzplhg a. namdar, frattura ed integrità strutturale, 53 (2020) 285-294; doi: 10.3221/igf-esis.23.22 286 clay and composite ground were investigated [7-8], and soil mixture such as silty clay, soft bangkok clay, fly and bottom ash mixtures, sand-clay mixtures using kenaf fiber reinforcement, chemical etc, were used to improve soil strength and stiffness [9-13]. with attention to the influence of the mineralogy on the soil and other construction materials [14-16], the bearing capacity of the soil is significantly controlled by the soil mineral. there are several types of research on the analytical, experimental and numerical analysis of the soil foundation, and the soil dynamic and static response evaluated with experimental, analytical and numerical results are reported in the literature [1-6, 14-15]. on the other hand, different prediction techniques were applied on mild steel pressure vessel, crack propagation, compressive failure surface of cement concrete, natural stone and concrete footing design [17-22]. to identify and apply the best results in the geotechnical engineering design the advanced technique for decision making is needed. however, the mechanical properties of soil interaction make the prediction of soil bearing capacity difficult. the goal of this study is to forecast the influence of mechanical properties of soil on bearing capacity of the mixed soil, and to predict each element of soil mechanical properties separately. to combine all the mechanical properties on the safe bearing capacity of the soil foundation, the artificial neural network (ann) is applied. methodology he maximum dynamic load and the statics load individually or combined that can be applied on the soil foundation without the unallowable settlement, deformation and shear failure are called the safe bearing capacity of the soil foundation. the safe bearing capacity of the soil foundation is a margin safety in geotechnical engineering design. the mechanical properties of the soil play an important role in the soil foundation and they support structural stability in transferring load from the structure to the subsoil. the appropriate interpretation of soil experiments results significantly enhance quality of geotechnical engineering design. on the other hand, the mechanical properties of soil interaction make complex the prediction of the foundation soil bearing capacity. the mechanical properties of the mixed soil and the calculated safe bearing capacity are shown in tab. 1. fig. 1 shows a flowchart to explain the steps in this investigation. the entire study contains five steps which are review analysis, problem identification, data selection, statistical analysis and interpretation of results for drawing conclusions. the procedure of the present work includes the behavior assessment of optimum moisture content, density, angle of friction and cohesive of the mixed soil, and the evaluation of the safe bearing capacity through the artificial neural network. in this study, for the interpretation of soil experimental results, each mechanical property of soil versus safe bearing capacity is graphically proposed and compared. it is aimed at analyzing the effect of the optimum moisture content (omc) (%), the density (kn/m3), the angle of friction (deg) and the cohesive of soil (kn/m2) on the safe bearing capacity of the soil separately. fig. 2 shows the distribution of the optimum moisture content, the density, the angle of friction and the cohesive of the mixed soil. the following are the steps of the research methodology. step 1, review analysis: the safe construction of a structure depends on the safe bearing capacity of soil foundation. the geotechnical engineering design of a soil foundation needs to decide if the soil behaves differently from place to place owing to the variation of the mineralogy and morphology of the natural soil. these combination parameters create a difficult situation to choose a safe bearing capacity in civil engineering project by the geotechnical designer. step 2, problem identification: the mechanical properties of soil interaction make the prediction of soil bearing capacity complex. it is needed to find an effect of each mechanical properties on mixed soil safe bearing capacity and to present guidelines to find the best decision. the soil mixture is a technique based on the soil mineralogy and morphology to control soil strength and stiffness, but because of probability function in soil mixture design and development of unexpected results during soil mixture process, feasible techniques are to be applied on soil mixture in geotechnical engineering design and soil foundation strengthening. however improper soil mixture design or use of unsuitable mixed soil hurt the strength of the soil foundation and they lead to a collapse of the structural elements and the whole structure, consequently. step 3, data selection: the several soil mechanic experiments need interpretation before application. the mechanical properties of the mixed soil and the calculated safe bearing capacity are shown in tab. 1, that is reported in the literature. the distribution of the optimum moisture content, density, angle of friction and cohesive of the mixed soil analyzed and their influence on the safe bearing capacity at each mixture design are studied. this process is repeated for 31 soil mixture models and significant factors impacting on the safe bearing capacity are identified and explained. it is well known that with the increasing number of collected data from the geotechnical site investigation or the laboratory experimental soil simulation the accuracy of the statistical analysis is more accurate in prediction and assessment. t a. namdar, frattura ed integrità strutturale, 53 (2020) 285-294; doi: 10.3221/igf-esis.23.22 287 step 4, statistical analysis: each element of soil mechanical properties behaves differently in a group of selected data from those reported in the literature [1], and the interaction between these elements requires a suitable technique for selecting the range of safe bearing capacity in the soil mixture design. to establish a histogram for safe bearing capacity of soil, the class interval of 500 was selected and the frequency of safe bearing capacity computed. to find intensity of repeating safe bearing at each 500 interval, relative frequency is divided into classes. after drawing rectangle for each class in construct histogram, the probability of safe bearing capacity was draw for the prediction. the central limit theorem was used for probability analysis. in application of the central limit theorem, a large enough sample is needed. it was suggested sample size of 30 or more is sufficient for application of central limit theorem [23]. in this study, 31 sample were selected from an experimental investigation, so the central limit theorem is applicable for probability analysis and prediction of safe bearing capacity. for this work, the following equations are used: 1  n x x x n   = sample mean (1) 1 n ns x x  = sample observation (2) 2 ~  ,    x n n         approximately (3)  2~  ,  ns n n n  approximately (4) where x1, x2, ………., xn constitute the random sample from population, µ is the mean and σ2 is the variance [23]. ann is applied to predict soil foundation behavior considering the mechanical properties of the mixed soil. ann contents three layers, which are the input, the hidden and the output layers. these three layers integrate assessment and prediction of safe bearing capacity mechanism of the soil foundation. in this study, one hidden layer has been used in the ann analysis. the minimum hidden layer in the ann is one and maximum hidden layers depend on the problem complexity. the safe bearing capacity prediction by the effect of optimum moisture content (%), density (kn/m3), angle of friction (deg) and cohesive of soil (kn/m2) was performed using ann. for the cover effect of each element of the mechanical properties in the prediction of the safe bearing capacity, r2 and rmse of optimum moisture content (%), density (kn/m3), angle of friction (deg) and cohesive of soil (kn/m2) on the safe bearing capacity of the soil are separately analyzed in the first stage. in the second stage, r2 and rmse of the safe bearing capacity are analyzed considering all mechanical properties together. figure 1: flowchart for explaining stepwise in this investigation. a. namdar, frattura ed integrità strutturale, 53 (2020) 285-294; doi: 10.3221/igf-esis.23.22 288 step 5, interpretation results for drawing conclusion: the morphology of mixed soil from the internal angle of friction, the mineralogy of mixed soil from soil cohesive, the moisture content and the density of the mixed soil have been interpreted to identify the best occurrence of safe bearing capacity. the method performed in the present work can be a guideline to be applied to soil mixed design in geotechnical engineering to improve subsoil strength and stiffness at acceptable quality. mixture number optimum moisture content (%) density (kn/m3) angle of friction (deg) cohesive (kn/m2) safe bearing capacity (kn/m2) 1 11.2 21.94 38 21 2036.22 2 10.61 21.83 39 12 1926.51 3 10.72 23.46 39 46 3334.44 4 12.15 23.82 36 28 1833.97 5 9.58 23.02 40 8 2060.95 6 22.39 20.09 32 20 888.70 7 18.86 20.95 32 26 1026.83 8 14.56 23.35 18 44 427.74 9 14.23 20.96 30 28 718.00 10 16.83 21.61 36 22 1567.43 11 18.27 21.56 15 47 349.69 12 16.76 21.07 22 49 608.36 13 20.21 21.83 21 33 431.67 14 18.68 21.179 27 38 786.91 15 19.34 20.96 29 8.5 487.99 16 16.55 20.31 31 22 834.95 17 21.14 21.18 20 27 341.94 18 20.79 21.18 20 23 311.26 19 16.31 20.96 33.5 12 879.86 20 20.88 20.96 24 23 439.56 21 23.00 21.5 23 10 287.22 22 20.06 22.05 23 32 503.18 23 20.11 21.07 23 22 398.52 24 20.75 20.41 19 22 280.01 25 22.69 20.748 22 16 310.33 26 18.87 21.72 21 28 389.32 27 20.31 21.94 24 26 479.81 28 19.51 21.72 17.5 28 298.58 29 20.52 22.59 17 9 170.00 30 18.99 22.47 18 24 286.20 31 14.56 21.61 28 26 700.05 table 1: soils mechanical properties and safe bearing capacity [1]. a. namdar, frattura ed integrità strutturale, 53 (2020) 285-294; doi: 10.3221/igf-esis.23.22 289 0 5 10 15 20 25 30 35 8 10 12 14 16 18 20 22 24 optimum moisture content (%) o p ti m u m m o is tu re c o n te n t (% ) mixture number 0 5 10 15 20 25 30 35 20.0 20.5 21.0 21.5 22.0 22.5 23.0 23.5 24.0 density (kn/m3) d e n si ty ( kn /m 3 ) mixture number 0 5 10 15 20 25 30 35 15 20 25 30 35 40 angle of friction (deg) a n g le o f f ri ct io n ( d e g ) mixture number 0 5 10 15 20 25 30 35 0 10 20 30 40 50 cohesive (kn/m2) c o h e si ve ( kn /m 2 ) mixture number 0 5 10 15 20 25 30 35 0 500 1000 1500 2000 2500 3000 3500 safe bearing capacity(kn/m2) s a fe b e a ri n g c a p a ci ty (k n /m 2 ) mixture number figure 2: the distribution of the mechanical properties of the mixed soil. a. namdar, frattura ed integrità strutturale, 53 (2020) 285-294; doi: 10.3221/igf-esis.23.22 290 results and discussion he safe bearing capacity of the soil is a critical factor in the geotechnical engineering design and plays the main role in structural stability. the enhancement of the safe bearing capacity of the soil foundation is considered important in geotechnical design basis. the soil mixture significantly changes the safe bearing capacity of the soil foundation. the soil mixture process develops safe bearing capacity in the high tolerance, it occurs because of the soil mechanical properties interaction. after the performance of the soil mixture, there is a complex result that requires to be investigated for enhancing structural stability. fig. 2 shows the distribution of the optimum moisture content, density, angle of friction, cohesive and safe bearing capacity of the mixed soil are following different mechanisms. fig. 3 shows the distribution of the safe bearing capacity associated to characterized optimum moisture content, density, angle of friction and cohesive of the mixed soil. safe bearing capacity exhibits different mechanisms because of the mechanical properties of the soil interaction, and the safe bearing capacity develops differently at each soil mixture model. fig. 3 is based on calculation done to show the direct relationship between different soil mechanical properties and the direct relationship between the safe bearing capacity and each individual soil mechanical property, in order to analyze the influence of each single mechanical property of the mixed soil on safe bearing capacity. however, to find influence all mechanical properties on safe bearing capacity, ann, that is a soft computing technique, is necessary. artificial neural network. the ann gathering all mechanical properties affects the safe bearing capacity. o m c ( % ) o m c (% ) 20.4 21.6 22.8 24.0 11 22 33 0 14 28 42 56 0 1100 2200 3300 9.2 13.8 18.4 23.0 20.4 21.6 22.8 24.0 d en si ty ( k n /m 3 ) d ensity (kn /m 3 ) 20.4 21.6 22.8 24.0 17.0 25.5 34.0 42.5 a n g le o f f ri ct io n ( d eg ) a ngle of friction (deg) 17.0 25.5 34.0 42.5 0 14 28 42 56 c o h es iv e (k n /m 2 ) cohesive (kn /m 2 ) 0 14 28 42 56 9.2 13.8 18.4 23.0 0 1100 2200 3300 s .b .c ( k n /m 2 ) omc (%) 20.4 21.6 22.8 24.0 density (kn/m3) 11 22 33 angle of friction (deg) 0 14 28 42 56 cohesive (kn/m2) s.b.c (kn/m 2) s.b.c (kn /m 2 ) figure 3: the prediction of safe bearing capacity (s.b.c) according to the mechanical properties. fig. 4 shows the safe bearing capacity frequency. the histogram presented in fig. 4 is based on a soft computing technique (sct) for the evaluation of the frequency of repeated safe bearing capacity, and it supports soil mixture design. the histogram is depicted for safe bearing capacity prediction analysis and it shows the distribution of values for the probability t a. namdar, frattura ed integrità strutturale, 53 (2020) 285-294; doi: 10.3221/igf-esis.23.22 291 of safe bearing capacity in soil mixture design. the shape of the histogram is skewed right. there is a large number of cases with low value of safe bearing capacity and few for high value. 0 500 1000 1500 2000 2500 3000 3500 0 2 4 6 8 10 12 14 16 18 f re q u en cy safe bearing capacity(kn/m2) safe bearing capacity(kn/m2) figure 4: the safe bearing capacity according to the number of occurrences. the internal angle of friction of soil has more influence on safe bearing capacity prediction. the increasing density, cohesive and internal angle of friction of mixed soil results in increasing the safe bearing capacity of the soil foundation, while the soil with higher moisture hurts the safe bearing capacity. the increase of optimum moisture content of the soil causes the reduction of density, cohesive and internal angle of friction of mixed soil and it results in the reduction of soil safe bearing capacity. the input, hidden and output layers of the ann are constructed for assessing the effect of modification of soil mechanical properties in the prediction of the safe bearing capacity mechanism of the soil foundation. tab. 2 shows the statistical analysis for examining the influence of each mechanical properties on safe bearing capacity. for the cover effect of each element of the mechanical properties in the prediction of the safe bearing capacity, r2 and rmse showed that the combination of all mechanical properties together enhances the accuracy of the safe bearing capacity prediction results. the mechanical properties interaction increases the safe bearing capacity of the mixed soil. according to tab. 2, the value of the r2 and rmse for all mechanical properties effects on safe bearing capacity are 0.98 and 0.02, these values can provide a suitable accuracy for the prediction of safe bearing capacity of the mixed soil. the higher inaccuracy obtained when only the influence of the cohesive of the mixed soil is considered in the prediction of the safe bearing capacity. mechanical properties r2 rmse optimum moisture content 0.731 0.683 density 0.597 0.293 angle of friction 0.861 0.230 cohesive of soil 6.04e-4 10.97 all mechanical properties 0.98 0.02 table 2: statistical analysis for realizing the influence of each mechanical properties on safe bearing capacity. discussion he mineralogy and the morphology of the soil interaction in the soil mixture process cause the distribution of the mechanical properties of the mixed soil and they lead to the development of the different levels of safe bearing capacity for each mixed soil. the moisture content of a mixed soil significantly affects the mineralogy and the morphology of the soil interaction. the optimum moisture content (%), density (kn/m3), angle of friction (deg) and cohesive of soil (kn/m2) never behave linearly in a group of mixed soils because of mechanical properties interaction. the t a. namdar, frattura ed integrità strutturale, 53 (2020) 285-294; doi: 10.3221/igf-esis.23.22 292 mineralogy, the morphology and the moisture content are changed with soil mixture and result in developing a new safe bearing capacity. for the design of the mixed soil, the attention to the soil mineralogy supports the geotechnical engineering design. analyzing the soil mechanical properties influence on the safe bearing capacity of the soil guides the geotechnical engineer to use proper soil which impacts on mineralogy and morphology of the mixed soil for achieving the best safe bearing capacity. for example, selecting the suitable percentage of a soil may increase soil strength because of the soil mineralogy or morphology. on the other hand, a combination of soil mineralogy and morphology controls moisture content of the soil. however, adjusting the moisture content of the mixed soil governs the strength of the soil. the results of this study reveal the importance of mineralogy science for civil engineering. it is an indirect relationship between mechanical properties of the mixed soil and the load transfer from the structure to the subsoil. considering the effect of optimum moisture content (%), density (kn/m3), angle of friction (deg) and cohesive of soil (kn/m2) on the safe bearing capacity of the soil separately could not provide a suitable prediction, while combining the effect of all mechanical properties on predicting safe bearing capacity provides suitable results in safe bearing capacity prediction. it has been reported in [24] that the mechanical properties of the soil foundation significantly control the lateral and vertical displacements of the subsoil and the failure pattern of the subsoil. in this study, an experimental report was used for the prediction and the probability analysis of the soil safe bearing capacity using advance sc techniques. there are several excellent research works available in the literature which apply different methods of statistical analysis, for example many research works can be referred to investigation on materials damage assessment [25-28], fatigue strength [29-31], crack analysis [32-33], strain analysis [34-35], and nonlinear displacement mechanism [24]. the application of statistical analysis on these researches enrich literature for industrial and educational sections. conclusion n most of the mixed soil used in a construction site, the safe bearing capacity behaves differently and results in various structures stability. the mineralogy and the morphology of mixed soil are considered in the safe bearing capacity of soil through the application of the artificial neural network (ann) for the prediction of soil foundation behavior considering mechanical properties of the mixed soil. this feasible technique supports the application of soil mixture in geotechnical engineering design. the following goal has been reached in the present study.  the internal angle of friction of soil has more influence on the safe bearing capacity prediction.  increasing density, cohesive and internal angle of friction of mixed soil results in increasing safe bearing capacity of the soil foundation, while increasing moisture has a negative influence on the safe bearing capacity of the soil. however, the combination of soil mineralogy and morphology controls moisture content of the soil and adjusting the moisture content of the mixed soil governs the strength of the soil mixture. increasing optimum moisture content of the soil causes the reduction of density, cohesive and internal angle of friction of mixed soil, resulting in a reduction of soil safe bearing capacity.  most of the safe bearing capacity occurs below 1000 (kn/m2). it is important for achieving high bearing capacity with proper interaction of mechanical properties of the mixed soil.  for prediction of the safe bearing capacity, the r2 and rmse for all mechanical properties effects on safe bearing capacity are 0.98 and 0.02, these values can provide a suitable accuracy for prediction safe bearing capacity of the mixed soil. the higher inaccuracy is obtained when only the influence of the cohesive of the mixed soil is considered in prediction of the safe bearing capacity. it can be concluded that the mechanical properties interaction increases the safe bearing capacity. the method presented in the present work can be a guideline to apply soil mixed design in geotechnical engineering to improve the subsoil quality.  plasticity is the main factor involved in the soil safe bearing capacity [1], it has not been evaluated in the present work and it could be a future research work. in the study of the plasticity, the level of moisture content and the mineralogy are two variables that could be analyzed using a suitable statistical technique to find their relationship with soil foundation safe bearing capacity. references [1] namdar, a. and pelko, m. k. (2009). bearing capacity of mixed soil model, fract. struct. int., 3 (7), pp. 73-79. doi: 10.3221/igf-esis.07.06. i a. namdar, frattura ed integrità strutturale, 53 (2020) 285-294; doi: 10.3221/igf-esis.23.22 293 [2] namdar, a. and feng, x. (2014). evaluation of safe bearing capacity of soil foundation by using numerical analysis method, fract. struct. int., 8 (30), pp. 138-144. doi: 10.3221/igf-esis.30.18. [3] namdar, a. and pelko, m. k. (2009). numerical analysis of soil bearing capacity by changing soil characteristics, fract. struct. int., 3 (10), pp. 38-42. doi: 10.3221/igf-esis.10.05. [4] namdar, a. and nusrath, a. (2010). tsunami numerical modeling and mitigation, fract. struct. int., 4 (12), pp. 57-62. doi: 10.3221/igf-esis.12.06. [5] namdar, a. (2016). a numerical investigation on soil-concrete foundation interaction, proc. struct. integ., 2, pp. 2803-2809. doi: 10.1016/j.prostr.2016.06.351. [6] namdar, a. and gopalakrishna, g. s. (2008). seismic mitigation of embankment by using dense zone in subsoil, emir. j. eng. res., 3(13), pp. 55–61. [7] skempton, a.w. (1951). the bearing capacity of clays, build. res. congr. 1, pp. 180–189. [8] pengpeng, n., yaolin, y. and songyu, l. (2019). bearing capacity of composite ground with soil-cement columns under earth fills: physical and numerical modelling, soils found., 59, pp. 2206–2219. doi: 10.1016/j.sandf.2019.12.004. [9] horpibulsuk, s., phetchuay, c., chinkulkijniwat, a. and cholaphatsorn, a. (2013). strength development in silty clay stabilized with calcium carbide residue and fly ash, soils found., 53(4), pp. 477–486. doi: 10.1016/j.sandf.2013.06.001. [10] vichan, s. and rachan, r. (2013). chemical stabilization of soft bangkok clay using the blend of calcium carbide residue and biomass ash, soils found., 53 (2), pp. 272–281. doi: 10.1016/j.sandf.2013.02.007. [11] kim, b., prezzi, m. and salgado, r. (2005). geotechnical properties of fly and bottom ash mixtures for use in highway embankments, j. geotech. geoenviron. eng., 131(7), pp. 914–924. [12] esmaeilpour shirvani, n., taghavi ghalesari, n., khaleghnejad tabari, m. and janalizadeh choobbasti, a. (2019). improvement of the engineering behavior of sandclay mixtures using kenaf fiber reinforcement, transp. geotech., 19, pp. 1–8. doi: 10.1016/j.trgeo.2019.01.004. [13] estabragh, a.r., rafatjo, h. and javadi, a.a. (2014). treatment of an expansive soil by mechanical and chemical techniques, geosynth. int., 21, pp. 233–243. doi: 10.1680/gein.14.00011. [14] namdar, a. (2010). mineralogy in geotechnical engineering, j. eng. sci. tech. rev., 3 (1), pp. 108-110. [15] namdar, a. (2012). natural minerals mixture for enhancing concrete compressive strength, fract. struct. int., 6 (22), pp. 2630. doi: 10.3221/igf-esis.22.04. [16] muhammad, n., zakaria, i. and namdar, a. (2013). modification of kaolin mineralogy and morphology by heat treatment and possibility of use in geotechnical engineering, int. j. geomater., 5(2), pp. 685-689. doi:10.21660/2013.10.3217. [17] huffman, p. j., ferreira, j., correia, j., de jesus, a., lesiuk, g., berto, f., fernandez-canteli, a. and glinka, g. (2017). fatigue crack propagation prediction of a pressure vessel mild steel based on a strain energy density model, fract. struct. int., 11(42), pp. 74-84. doi: 10.3221/igf-esis.42.09 . [18] funari, m. f., greco, f., lonetti, p. and spadea, s. (2018). a numerical model based on ale formulation to predict crack propagation in sandwich structures, fract. struct. int., 13(47), pp. 277-293. doi: 10.3221/igf-esis.47.21. [19] tzamtzis, a. and kermanidis, a. t. (2015). fatigue crack growth prediction in 2xxx aa with friction stir weld haz properties, fract. struct. int., 10(35), pp. 396-404. doi: 10.3221/igf-esis.35.45 [20] caporale, a. and luciano, r. (2014). a micromechanical four-phase model to predict the compressive failure surface of cement concrete, fract. struct. int., 8(29), pp. 19-27. doi: 10.3221/igf-esis.29.03. [21] contrafatto, l. and cosenza, r. (2014). prediction of the pull-out strength of chemical anchors in natural stone, fract. struct. int., 8(29), pp. 196-208. doi: 10.3221/igf-esis.29.17. [22] namdar, a. (2020). the application of soil mixture in concrete footing design using the linear regression model, mat design process comm., e179. doi: 10.1002/mdp2.179 [23] navidi, w., statistics for engineers and scientists, 3rd ed, (2011). published by mcgraw-hill. [24] namdar, a. and dong, y. (2020). the embankment-subsoil displacement mechanism, mat. des. process comm., e155. doi: 10.1002/mdp2.155. [25] fernandino, do., tenaglia, n., di cocco, v., boeri, re. and iacoviello, f. (2020). relation between microstructural heterogeneities and damage mechanisms of a ferritic spheroidal graphite cast iron during tensile loading, fat. fract. eng. mater. struct., 6(43), pp. 1262-1273. doi: 10.1111/ffe.13221. [26] d'angela, d., ercolino, m., bellini, c., di cocco, v. and iacoviello, f. (2020). characterisation of the damaging micromechanisms in a pearlitic ductile cast iron and damage assessment by acoustic emission testing, fat. fract. eng. mater. struct., 5(43), pp. 1038-1050. doi: 10.1111/ffe.13214. [27] d'angela, d., ercolino, m., bellini, c., di cocco, v. and iacoviello, f. (2020). analysis of acoustic emission entropy for damage assessment of pearlitic ductile cast irons, mat. des. process comm., pp. 1-5. doi: 10.1002/mdp2.158. [28] fernandino, d. o., di cocco, v., tenaglia, n., bellini, c., iacoviello, f. and boeri, r. e. (2019). microstructural damage evaluation of ferritic-ausferritic spheroidal graphite cast iron, fract. struct. int., 14(51), pp. 477-485. doi: 10.3221/igf-esis.51.36. a. namdar, frattura ed integrità strutturale, 53 (2020) 285-294; doi: 10.3221/igf-esis.23.22 294 [29] berto, f., campagnolo, a., welo, t., vantadori, s. and carpinteri, a. (2017). multiaxial fatigue strength of titanium alloys, fract. struct. int., 11(41), pp. 79-89. doi: 10.3221/igf-esis.41.12. [30] marsavina, l., iacoviello, f., pirvulescu, ld., di cocco, v. and rusu, l. (2019). engineering prediction of fatigue strength for am50 magnesium alloys, int. j. fat., 127, pp. 10-15. doi: 10.1016/j.ijfatigue.2019.05.028. [31] bellini, c., di cocco, v., favaro, g., iacoviello, f. and sorrentino, l. (2019). ductile cast irons: microstructure influence on the fatigue initiation mechanisms, fat. fract. eng. mater. struct., 9(42), pp. 2172-2182. doi: 10.1111/ffe.13100. [32] iacoviello, f., di cocco, v. and bellini, c. (2019). fatigue crack propagation and damaging micromechanisms in ductile cast irons, int. j. fat., 124, pp. 48-54. doi:10.1016/j.ijfatigue.2019.02.030. [33] iacoviello, f., di cocco, v. and bellini, c. (2019). overload effects on fatigue cracks in a ferritized ductile cast iron, int. j. fat., 127, pp. 376-381. doi: 10.1016/j.ijfatigue.2019.06.028. [34] berto, f., campagnolo, a., meneghetti, g. and tanaka, k. (2016). averaged strain energy density-based synthesis of crack initiation life in notched steel bars under torsional fatigue, fract. struct. int., 10(38), pp. 215-223. doi: 10.3221/igf-esis.38.29. [35] susmel, l., berto, f. and hu, z. (2018). the strain energy density to estimate lifetime of notched components subjected to variable amplitude fatigue loading, fract. struct. int., 13(47), pp. 383-393. doi: 10.3221/igf-esis.47.28. << /ascii85encodepages false /allowtransparency false /autopositionepsfiles true /autorotatepages /none /binding /left /calgrayprofile (dot gain 20%) /calrgbprofile (srgb iec61966-2.1) /calcmykprofile (u.s. web coated \050swop\051 v2) /srgbprofile (srgb iec61966-2.1) /cannotembedfontpolicy /error /compatibilitylevel 1.4 /compressobjects /tags /compresspages true /convertimagestoindexed true /passthroughjpegimages true /createjobticket false /defaultrenderingintent /default /detectblends true /detectcurves 0.0000 /colorconversionstrategy /cmyk /dothumbnails false /embedallfonts true /embedopentype false /parseiccprofilesincomments true /embedjoboptions true /dscreportinglevel 0 /emitdscwarnings false /endpage -1 /imagememory 1048576 /lockdistillerparams false /maxsubsetpct 100 /optimize true 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/hrv (za stvaranje adobe pdf dokumenata najpogodnijih za visokokvalitetni ispis prije tiskanja koristite ove postavke. stvoreni pdf dokumenti mogu se otvoriti acrobat i adobe reader 5.0 i kasnijim verzijama.) /hun 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can be opened with acrobat and adobe reader 5.0 and later.) >> /namespace [ (adobe) (common) (1.0) ] /othernamespaces [ << /asreaderspreads false /cropimagestoframes true /errorcontrol /warnandcontinue /flattenerignorespreadoverrides false /includeguidesgrids false /includenonprinting false /includeslug false /namespace [ (adobe) (indesign) (4.0) ] /omitplacedbitmaps false /omitplacedeps false /omitplacedpdf false /simulateoverprint /legacy >> << /addbleedmarks false /addcolorbars false /addcropmarks false /addpageinfo false /addregmarks false /convertcolors /converttocmyk /destinationprofilename () /destinationprofileselector /documentcmyk /downsample16bitimages true /flattenerpreset << /presetselector /mediumresolution >> /formelements false /generatestructure false /includebookmarks false /includehyperlinks false /includeinteractive false /includelayers false /includeprofiles false /multimediahandling /useobjectsettings /namespace [ (adobe) (creativesuite) (2.0) ] /pdfxoutputintentprofileselector /documentcmyk /preserveediting true /untaggedcmykhandling /leaveuntagged /untaggedrgbhandling /usedocumentprofile /usedocumentbleed false >> ] >> setdistillerparams << /hwresolution [2400 2400] /pagesize [612.000 792.000] >> setpagedevice microsoft word numero_42_art_36.docx a. strafella et alii, frattura ed integrità strutturale, 42 (2017) 352-365; doi: 10.3221/igf-esis.42.36 352 15-15ti(si) austenitic steel: creep behaviour in hostile environment alessandra strafella, antonino coglitore, paride fabbri, elena salernitano eneaitalian national agency for new technologies, energy and sustainable economic development-laboratory of materials technologies faenza, via ravegnana, 186 48018 faenza, italy alessandra.strafella@enea.it, antonino.coglitore@enea.it, paride.fabbri@enea.it, elena.salernitano@enea.it abstract. this work aims at studying the creep behaviour of 15-15ti(si) austenitic steel, under uniaxial stress (range of 300-560 mpa), and its interaction with liquid lead. the steel was tested to verify its sensitivity to liquid metal embrittlement (lme) and to simulate its behaviour in operating thermal and mechanical stress conditions of the iv generation lead-cooled fast reactor. the experimental results permitted to plot the time-strain creep curve and the characteristic norton-based curve, simulating the creep behaviour at all stress values. the comparison between the creep curves in air and in lead showed that the lme produces a decrease of creep-rupture time, a reduction of creep strain and then the loss of steel ductility. moreover, the raw material and fracture surfaces were analyzed by optical microscope and scanning electron microscope (sem). sem micrographs highlighted that lead changes both the mode and the type of specimen fracture. in addition, it was analyzed the lead action time, as the time after which the corrosion appears with macroscopic effects. although some tests are still ongoing, it can be assumed that at high stresses, lme takes place after a long time of steel/lead contact while at low stresses, lme tends to prevail on creep effect. keywords. 15-15ti(si); austenitic stainless steel creep; creep curves; steady strain creep rate; liquid metal embrittlement (lme); creep tests in lead. citation: strafella, a., coglitore, a., fabbri, p., salernitano, e., frattura ed integrità strutturale, 42 (2017) 352-365. received: 08.08.2017 accepted: 12.09.2017 published: 01.10.2017 copyright: © 2017 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. and source are credited. introduction ince several years, austenitic stainless steels are object of a great interest for their properties and then their applications in nuclear field. creep strength and resistance to irradiation-induced void swelling are the main requirements for high temperature components of fast reactors. for these reasons, type 15-15ti(si) material which is a ti-stabilized austenitic stainless-steel alloy, is one of most suitable for nuclear industry [1-3]. 15-15ti(si) was designed around the standard aisi 316 stainless steel with a specifically tailored composition, especially regarding the carbon and titanium content, in order to limit irradiation induced void swelling [1]. the french work on irradiation of rapsodie–fortissimo demonstration reactor demonstrated that addition of titanium led to improved void swelling resistance of austenitic steel. accordingly, the 15 ni-15 cr-ti (named aim1 or 15-15 ti steel) s http://www.gruppofrattura.it/pdf/rivista/numero42/audioslides/strafella/strafella.html a. strafella et alii, frattura ed integrità strutturale, 42 (2017) 352-365; doi: 10.3221/igf-esis.42.36 353 was developed and utilized in the phénix reactor where it exceeded the target burnup of 100 dpa. addition of silicon to 15-15ti further improved the swelling resistance. with silicon-modified 15-15ti, the maximum fuel pin deformation was reduced by a factor of 2.4 as compared to the silicon-free 15-15ti grade [3]. the addition of ti also improves the high temperature mechanical properties due to the precipitation of carbide particles, either m23c6, or tic in relation to the contents of ni and cr and to the matrix structure, grain size and dislocation density. it has been noticed for a long time that the high dislocation density found in cold-worked steels reduces the swelling. for this reason, ti-modified austenitic stainless steels are often cold-worked to increase their mechanical properties. dislocations trap vacancies and decrease their supersaturation. nevertheless, a recovering of the dislocation network is observed at high temperature (t > 540 °c) and reactivates the swelling. titanium has been added in the alloys to avoid this phenomenon. it induces the precipitation of nanosized titanium carbides which pin the dislocation network and stabilize it at high temperature. indeed, the cold-working promotes the precipitation of carbides which are liable to precipitate on slip planes produced by pre-strain and creep strain. therefore, the cold-worked steels have higher crack growth resistance at high stress intensity levels compared to solution-annealed stainless steel [4-7]. for its properties, 15-15ti(si) is one of the best candidates for high temperature components of nuclear reactor of iv generation lead-cooled fast reactor (lfr) [2-3] which is one of the systems to be deployed in the future. the main problem in lfr reactor development is the compatibility of the structural materials (steels) with the coolant as well as the corrosion of structural components and fuel. when steel comes in contact with liquid metal, the loss of ductility in normally ductile steel could occur; this phenomenon is named liquid metal embrittlement (lme) and takes place when steel is stressed in temperature under contact with liquid metal. although there is a great interest on these steel properties, only few data on its characterization can be found in the literature. so, the aim of this work is the study of the 15-15ti(si) stainless steels creep properties both in air and in lead. for this purpose, the creep behaviour was investigated at 550° c, under a wide range of applied stresses, in hostile condition or in air , following by a morphological analysis of fracture surfaces. experimental procedure materials ests were carried out on creep specimens prepared from 15-15ti(si) steel, an austenitic steel provided by ocas. the steel was manufactured in the form of plates (15mm x 750mm x 250mm), 20% cold-worked (cw): it was subjected to a homogenization annealing treatment in a furnace at 1230°c for 15h, hot-rolled at 1250°c for 1.52h, annealed at 1080°c (followed by a water-quench treatment) and 20% cw. the steel was cold-worked because this process promotes the precipitation of carbides, which generally increases the mechanical properties of materials. compared to solution-annealed stainless steel, the cold-worked steels have higher crack growth resistance at high stress intensity levels. the composition of 15-15ti(si) is given in tab. 1. table 1: chemical composition of 15-15ti(si) steel as anticipated in the previous paragraph, it must be underlined that the ti presence in the steel is important for the purposes of this work because induces the precipitation of carbide particles, m23c6 or tic, then improves the high temperature mechanical properties. moreover, ti addition decreases the irradiation swelling; that is important for nuclear applications. the used lead is provided by sigma-aldrich in particles with a purity ≥ 99.9%, size ≤ 2 mm and melting point 327.4°c. specimens creep specimens were machined from the plate in the rolling direction to obtain 6 mm in diameter and 70 mm of gauge length, as shown in fig. 1. t all elements c mn si p ti cr ni b mo % 0.090 1.502 0.791 0.041 0.404 14.392 15.607 0.007 1.509 a. strafella et alii, frattura ed integrità strutturale, 42 (2017) 352-365; doi: 10.3221/igf-esis.42.36 354 figure 1: creep specimen dimensions. creep tests the creep tests were carried out in air and in stagnant lead, at 550°c that is typical working temperature of lfr. the loads were applied in uniaxial tensile mode; stress values were in the range of 300-560 mpa, which is lower than yield stress value (theoretical 620 mpa ≤ rp0.002 ≤ 840 mpa, after 20% cw). all tests were performed by mayes machine with a maximum loading capacity of 20kn and maximum temperature of 1000°c. because of the measurement uncertainty in the determination of the specimen cross section, the initial tensile stress was measured with an accuracy of ±3%. the specimen elongation during the tests was measured by monitoring in continuous the grip movement; super linear variable capacitor (slvc) transducers were used for measuring and recording elongations smaller than 0.5 μm. the acquired data were plotted as conventional strain versus time curves. the matrix of main tests is shown in tab. 2. table 2: matrix of the main tests. where “” represents the creep test performed in air and “” that in lead. a particular cell, showed in fig. 2, was specifically designed and manufactured for tests in lead. for the tests in lead, the creep machine is equipped with a specifically designed and manufactured cell, for the containment of the molten liquid metal, as shown in fig. 2 and 3. the cell consists of a lead container to fully immerse the specimen during test, low and upper grips where the specimen is mounted to be subjected to tensile stress and rod grips for the slvc to measure the sample elongation during the test. the whole testing cell apparatus is then put into the furnace. the cell is mounted on a mayes machine; specimen was fixed to the grips of cell, filled with solid lead, heated up to the lead melting temperature and then the test temperature and load were applied. data points were acquired every 1 h. morphological and microstructural characterization the steel, both raw and after rupture, was analyzed by optical microscope and scanning electron microscope (sem). the specimen surfaces were observed both before and after boiling glyceregia etching (30 ml hci, 20 ml glycerol, 10 ml hno3). a reichert-jung mef 3 optical microscope was used to observe the microstructure, while a sem leo 438 vp to characterize in high vacuum the morphology and microstructure of the specimens surfaces. material temp. [°c] stress [mpa] 15-15ti(si) 550°c 300 400 500 560 575   ,  ,   a. strafella et alii, frattura ed integrità strutturale, 42 (2017) 352-365; doi: 10.3221/igf-esis.42.36 355 figure 2: overall sketch of testing cell with both the longitudinal and cross sections. figure 3: cell assembly, designed and manufactured for tests in lead, on a mayes machine during the specimen fixing and with its furnace. results and discussion creep curves in air he specimens were tested at 550°c under constant loads, corresponding to the initial tensile stresses in the range of 300-560 mpa, and the experimental data allowed to obtain the typical creep curves of 15-15ti(si). the most relevant curves were depicted in fig. 4, where the evolution of the creep strain with time at various stress levels is plotted. if we consider the same time value in the graph, it can be observed that the creep strain increased with the applied stress; moreover it can also noticed that at 560mpa, the rupture was reached at 1165h, while the tests at 300, 400 and 500mpa are still in progress. the shape of creep curve is consistent with the expectations: after long time (more than 1000h), at 300 and 400 mpa, the strain curves didn’t reach the tertiary creep stage, still remaining in the secondary creep phase; at 500 mpa, although is still ongoing, the creep curve clearly shows a defined primary and secondary stages. at stress values near the yield strength of t specim lead container a. strafella et alii, frattura ed integrità strutturale, 42 (2017) 352-365; doi: 10.3221/igf-esis.42.36 356 15-15ti, as 560mpa (theoretical 620mpa ≤ rp0.002 ≤ 840mpa, after 20%cw), all the three phases of creep can be recognized. these curves are plotted in fig. 5 (until 1000h, current time value of test at 500mpa), providing important results on the creep behaviour because the secondary creep stage was reached and the duration was greater than of 1000h. figure 4: comparison of 15-15ti(si) creep curves in air at 300, 400, 500 and 560 [mpa]. figure 5: comparison between creep curves in air at 300, 400 and 500 mpa, until 1000h. all tests enabled to calculate the creep rate of secondary stage, also defined steady strain creep rate (sscr) being the minimum and constant creep rate. the sscr values are obtained and compared with two methods, as illustrated in fig. 6: using the first derivative on curve strain-time to determinate the minimum; plotting fit linear of strain-time curve in secondary creep stage. 0 200 400 600 800 1000 1200 1400 1600 0,0 0,5 1,0 1,5 2,0 2,5 t= 550°c air c re e p s tr a in [ % ] time [h] creep strain % [560mpa] creep strain % [300 mpa] creep strain % [400mpa] creep strain % [500 mpa] 0 200 400 600 800 1000 0,00 0,02 0,04 0,06 0,08 0,10 0,12 0,14 0,16 0,18 0,20 t= 550°c air c re e p s tr a in [ % ] time [h] creep strain % [300 mpa] creep strain % [400mpa] creep strain % [500 mpa] a. strafella et alii, frattura ed integrità strutturale, 42 (2017) 352-365; doi: 10.3221/igf-esis.42.36 357 a) 0 200 400 600 800 1000 1200 1400 -0,005 0,000 0,005 0,010 0,015 0,020 0,025 ss cr -d e ri va tiv e c re e p s tr a in [ % /h ] time[h] derivative creep strain [560 mpa] derivative-creep strain % [400mpa] derivative y1-creep strain % [300 mpa] derivative-creep strain % [500 mpa] b) 0 200 400 600 800 1000 1200 1400 1600 0,0 0,5 1,0 1,5 2,0 2,5 t= 550°c air c re e p s tr a in [ % ] time [h] creep strain medio % [560mpa] creep strain % [300 mpa] creep strain % [400mpa] creep strain % [500 mpa] linear fit figure 6: sscr calculus: minimum of first derivative (a) and fit linear of secondary creep stage (b). the steady strain creep rates were plotted in a log–log graph. fig. 7 shows the variation of sscr with the applied stress. the variation of sscr with applied stress obeys a power law relationship in the form of norton-type: nsscr a (1) where σ is the applied stress, n is the stress exponent, and a is an empirical constant. for 15-15ti(si) steel, the found a and n values are shown in tab. 3. a. strafella et alii, frattura ed integrità strutturale, 42 (2017) 352-365; doi: 10.3221/igf-esis.42.36 358 figure 7: log–log plot of sscr-stress points. table 3: values of norton-power law parameters. the value of stress exponent n is indicative of the rate controlling deformation mechanism. for austenitic stainless steels stress exponents are generally in the range of 3–12 and are associated with dislocation creep [10]. this is due to the nature of austenitic stainless steels which are solid solution alloys where the precipitation takes place during creep; for this reason, they show a particular behaviour which is intermediate between those of solid solution alloys and precipitation hardened/dispersion strengthened materials. the literature data report a value of n=3–5 for pure metals and simple solid solution alloys where the main creep deformation mechanism is the dislocation creep; other major creep deformation mechanisms such as diffusion creep are characterized by n= 1, and grain boundary sliding controlled creep are identified with a value of n=2. instead, as also reported by literature, complex alloys and precipitation hardened/dispersion strengthened materials showed much higher values of n (≈40). it means that in austenitic stainless steels, the value of n is intermediate between those of solid solution alloys and precipitation hardened/dispersion strengthened materials and it is in a range of 3–12 [7]. the experimental analysis highlighted that the 15-15ti(si) austenitic steel value for the stress exponent is n=4.13; this result is consistent with the expectations and confirms that the steel deforms through the dislocation creep mechanism. based on the norton power law, on experimental data and on calculated values of n and a, the characteristic creep curve sscr-stress (log–log plot) was plotted, enabling to simulate the creep behaviour in air at all stress values (fig. 8). these analyses could provide some important information for the use of this material in nuclear field because only few data can be found in the literature on 15-15ti(si) characterization. creep curves in lead for its particular application on nuclear field, 15-15ti(si) was tested in lead in order to conduct a preliminary study on its lead corrosion sensitivity. a test at 575mpa and 550°c was performed to ascertain the correct working of new cell designed and manufactured for tests in liquid metal. the three stages are clearly recognized, as showed in fig. 9. the most important tests in lead were performed using the following parameters, deriving from tests in air: t= 550°c σ = 500 and 560 mpa   250 300 350 400 450 500 550 600 1e-5 1e-4 1e-3 n= 4.13 a= 5.90*10 -16 sscr-experimental points air s s c r [% /h stress a n 5.90*10-16 4.13 a. strafella et alii, frattura ed integrità strutturale, 42 (2017) 352-365; doi: 10.3221/igf-esis.42.36 359 to date, the test at 500mpa is still in progress: the strain is 0.46% and the test duration is 885h. the comparison among all lead curves up to 600h is depicted in fig. 10, where primary and secondary phases of creep are shown: it can be clearly recognized them and the calculation of sscr was possible. figure 8: characteristic creep curve sscr-stress. figure 9: creep curve in lead. to highlight the lead effect, creep curve obtained from the test on specimen in air was compared with that obtained in lead. the comparison between creep curve in air and in lead at 560mpa is depicted in fig. 11. as expected, an increase in creep strain was observed, but it isn’t really relevant, until the value of 800h: creep curves in lead and in air showed the same shape with a difference of creep strain percentage around 0.04% and it concerned only the primary creep; moreover, the strain rate is the same.   250 300 350 400 450 500 550 600 1e-5 1e-4 1e-3 n= 4.13 a= 5.90*10 -16 sscr-curve sscr-experimental points air s s c r [% /h stress 0 200 400 600 800 1000 1200 0,0 0,2 0,4 0,6 0,8 1,0 1,2 cr e e p s tr a in % creep strain % [575mpa]pb time [h] t= 550°c in pb a. strafella et alii, frattura ed integrità strutturale, 42 (2017) 352-365; doi: 10.3221/igf-esis.42.36 360 figure 10: creep curves of specimens tested in lead. 0 200 400 600 800 1000 1200 0,0 0,2 0,4 0,6 0,8 1,0 1,2 1,4 1,6 1,8 2,0 2,2 2,4 15-15 ti (si) t= 550°c c re e p s tr a in [ % ] time [h] creep strain % [575mpa]pb creep strain % [560 mpa]pb creep strain [560 mpa] figure 11: comparison of 15-15ti(si) creep curves in air at 560mpa and in lead at 560 and 575mpa. therefore, up to 800h, the behaviour of 15-15ti(si) in lead and in air at 560 mpa is almost similar. for these reasons the test in lead was stopped. an increase of steel deformation in lead took place, but it isn’t relevant and it can be said that creep mechanisms seem to be predominant than lead corrosion. it could be ascribable to the stress value near yield stress1 and it can be hypothesized that lead corrosion appears after a long time of steel/lead contact. to better understand the effect of lead corrosion, it is necessary to discuss the test in lead at higher stress level, 575mpa, and its comparison with curves at 560mpa because it can provide important information on creep corrosion. 1 theoretical 620 mpa ≤ rp0.002 ≤ 840 mpa, after 20% cw   0 100 200 300 400 500 600 0,0 0,1 0,2 0,3 0,4 0,5 t= 550°c in pb cr e e p s tr a in % creep strain % [575mpa]pb creep strain % [560 mpa]pb creep strain % [500 mpa]pb time [h] a. strafella et alii, frattura ed integrità strutturale, 42 (2017) 352-365; doi: 10.3221/igf-esis.42.36 361 although they weren’t obtained at the same stress level, creep curve at 575mpa in lead are plotted in fig.11. it can be noticed that rupture time of specimen tested at 575mpa in lead is lower than that tested in air at 560mpa, as expected. up to 850h, creep strain of specimen in lead is higher than creep strain in air and this supports the hypothesis that lead corrosion appears after a long time of steel/lead contact. for time greater than 850h, it can be observed a trend inversion. it is due to lme, which produces a loss of ductility and competes with creep strain at higher stress and long time. indeed, it can be noticed that the specimen tested at 575mpa in lead shows a lower percentage of final creep strain than specimen tested at 560mpa in air, although subjected to higher stress level, but it shows a lower time of rupture too; this means that it is less ductile than specimen tested in air and it is in accordance with lme effect. it is important to underline that these tests in stagnant liquid lead were performed to verify the steel sensitivity to lme. the handbook on lead-bismuth eutectic alloy and lead properties, materials compatibility, thermalhydraulics and technologies [8] proposes the following definition of lme: lme is the loss of ductility of a normally ductile metal or metallic alloy when stressed in contact with a liquid metal that can result in brittle fracture. typically the phenomenon is accompanied with a change from ductile to brittle fracture modes, intergranular or transgranular cleavage-like fracture modes. according to this definition, the lme justifies the decrease of rupture time, the reduction of creep strain and then the loss of specimen ductility tested in lead. the effect of lead is more evident at the lower stress (500mpa, fig. 12). the comparison between curves in lead and air at 500 mpa can better explain this phenomenon: a relevant increment of deformation growths with the time in the whole curve, unlike tests at 560mpa. it means that lead influences the sscr, then the shape of creep curves. in addition, the lead presence anticipates the tertiary stage which occurs at about 700h, unlike test in air that remains in the secondary stage. all these effects are ascribable to lme. figure 12: comparison between creep curves 500mpa in air and in lead. then, the analysis on tests in lead can be summarized as follows: for high stresses (near yield stress) the presence of liquid lead does not significantly affect the deformation of the specimens and its deformation rate sscr. this means that the creep effect dominates the deformation in primary and secondary stages. the effect of pb becomes prevalent only in the tertiary stage and it occurs with a reduction of the final time and final deformation percentage and then with a change in the rupture mode. for low stresses (significantly below the yield), the effect of pb is more evident. it was noticed that lead influences sscr and increases the deformation, with the time. then, lme tends to prevail on creep effect: the shape of curve changes, the sscr is higher than the test in air and the tertiary stage occurs at lower time.   0 200 400 600 800 1000 1200 0,00 0,05 0,10 0,15 0,20 0,25 0,30 0,35 0,40 0,45 0,50 0,55 c re e p s tr a in % creep strain % [500 mpa] creep strain % [500 mpa]pb time [h] a. strafella et alii, frattura ed integrità strutturale, 42 (2017) 352-365; doi: 10.3221/igf-esis.42.36 362 morphological and microstructural characterization steel specimens were observed by optical and scanning electron microscopy to characterize the raw materials and highlight the microstructure induced by 20% cold-working. before the analysis, the steel samples were glyceregia etched for the examination of grains structure [9]. glyceregia is indeed recommended for revealing the austenitic microstructure, as grain structure, and outlines carbides [10]. slip produced by cold-working is shown in fig. 13. a) b) figure 13: glyceregia etched as received steel: a) optical and b) sem micrograph. moreover, the specimens were examined after rupture by scanning electron microscopy. secondary electrons are used to obtain the fracture surface morphology. typical sem images of fracture surfaces obtained from the creep specimens tested in air are shown in fig. 14. fig. 14-a concerns a low magnification and also includes an insert macroscopically displaying the specimen immediately after rupture. both the specimen necking, identifying the ductile fracture, and the typical changes of fracture direction, characterizing the transgranular fracture, are pointed out. the fracture surface has a wrinkled appearance of mixed or ductile fracture. the micrographs of figs. 14-b,c,d showed a combination of a cup-cone and transgranular fracture modes. the first one is characterized by its typical dimples, while the second one by the river pattern. the typical equiaxed dimples, characteristic of ductile fracture in tension, and then dominant cup-cone mode, are characteristic of surfaces close to central area of specimen (fig. 14-b). instead a transgranular fracture mode is dominant in the central part of specimen, where local facets of quasi-cleavage are noticed (fig. 14-c). the other regions of the fracture surface are a combination of shear rupture (transgranular rupture) and cup-cone fracture (coalescence by shear of voids caused by plastic deformation). the transgranular rupture is incomplete, showing a mixed rupture mode, as in the case of external surface corresponding to the specimen necking. the deformation bands with the elongated dimples on the fracture surface are clearly displayed in fig. 14-d. these considerations move to the conclusion that the specimen rupture mode is mixed, transgranular and cup-cone mode. these observations are consistent with the expectations: the addition of ti induces the precipitation of carbide particles and consequently the improvement of the high temperature mechanical properties, as creep strength, as reported by zahra and schroeder (1982) [11]. they studied creep properties of an austenitic steel with a chemical compositions similar to that of 15-15ti(si), finding that the fine tic precipitates in ti-stabilized austenitic stainless-steel cold-worked alloy form preferentially on the intergranular dislocations and they are more stable [11]. this justifies transgranular or ductile fracture. even for specimen tested in lead, morphological features of fracture surface was analyzed by scanning electron microscopy (fig. 15), but a chemical polishing was necessary to differentiate steel surface fracture from eventual lead residues and to reveal the fracture mode. the fig. 15-a also includes an insert macroscopically displaying the specimen immediately after rupture. the loss of steel ductility and the typical brittle fracture are evident from the brilliant and polished fracture surface, along 45°, with negligible plastic deformation. it can be observed that the fracture is brittle, as showing by the typical intergranular fracture, where the decohesion occurring along a weakened grain boundary is evident (fig. 15-b). grains are clearly observed in their three-dimensional structure, within a polished fracture surface with no wrinkled appearance, unlike ductile materials (fig. 14). a. strafella et alii, frattura ed integrità strutturale, 42 (2017) 352-365; doi: 10.3221/igf-esis.42.36 363 a) b) c) d) figure 14: sem micrographs: a) fracture surface at low magnification; b) portion of surface showing a dominant ductile fracture mode; c) portion of surface showing both transgranular and ductile fraction; d) deformation bands: elongated dimples on fracture surface. a) b) figure 15: sem micrographs after pb creep: fracture surface a) before and b) after chemical polishing. the comparison between the specimen tested in air and in lead revealed a different fracture mode: mixed cupcone/transgranular for creep test in air, while intergranular for creep test in lead. this difference is ascribable to the effect of lead embrittlement: the transition from mixed fracture mode, ductile/transgranular, which takes place in air, to fully brittle/intergranular mode, in lead, is consistent with the definition of lme (stated in paragraph 3.2) and with the creep phenomena in liquid metal, as described in other scientific works. according to hough and rolls (1971)[12], phenomena associated with creep rupture in liquid metal can include: a. strafella et alii, frattura ed integrità strutturale, 42 (2017) 352-365; doi: 10.3221/igf-esis.42.36 364 cracking induced by the adsorption of liquid metal atoms accelerated failure due to the penetration of the liquid metal along the grain boundary of the solid stress aided dissolution of metal from a crack tip these considerations can justify the intergranular fracture mode: intergranular fracture usually occurs when the phase in the grain boundary is weak and brittle and this is probably due to the penetration of the liquid metal along the grain boundary of the steel which caused the embrittlement of phases and then the accelerated failure. it means that lead changes both mode and type of fracture: from mixed ductile/brittle to total brittle and, referring to brittle mode, from transgranular to intergranular type. that is the effect of liquid metal embrittlement [13]. conclusions he creep and corrosive behavior of the 15-15ti(si), for the nuclear systems using heavy liquid metals, has been addressed. for this purpose, the steel has been studied in a stress range of 300-575mpa at 550°c, in air and in hostile environment. from tests performed in air, the characteristic creep curve strain-time was obtained. the norton’s law parameters n and a were calculated and it was found that the dislocation creep mechanism is the main mechanism for the 15-15ti(si) creep deformation. the creep curve sscr-stress (log–log plot) was plotted based on norton's law, on experimental data and on the calculated values n and a. this curves is an important results because simulates the creep behaviour of 15-15ti(si) in air at all stress values. sem micrographs showed that the specimen fracture mode in air was mixed, transgranular and cup-cone. tests in lead were also performed and the main results can be summarized as follows: for high stresses, the creep effect dominates the deformation in primary and secondary stages, while the effect of pb becomes prevalent in the tertiary stage for low stresses, the effect of pb is more evident and lme tends to prevail on creep effect. the specimen rupture mode in lead is brittle, as confirmed by sem micrographs that highlights the typical intergranular fracture. moreover, the differences between mixed fracture mode, ductile-brittle/transgranular, occurring in air and fully brittle/intergranular mode, in lead were shown. it means that liquid metal embrittlement occurs: lead changes both the mode and type of fracture, from mixed ductile/brittle to total brittle and, referring to brittle mode, from transgranular to intergranular type. since only few data on 15-15ti(si) characterization can be found in the literature, the obtained results provide useful information for this austenitic steel applications in extreme conditions, such as nuclear field. acknowledgement the authors are grateful to dr. selene grilli for her careful revision of the manuscript. we also acknowledge the c.r. enea brasimone for financial support and providing the samples to be tested. references [1] latha, s., mathewa, m.d., parameswaran, p., bhanu sankara rao, k., mannan, s.l., thermal creep properties of alloy d9 stainless steel and 316 stainless steel fuel clad tubes, international journal of pressure vessels and piping, 85 (2008), 866–870 elsevier [2] gilbon, d., séran, t.l., maillard, a., touron rivera, h.c., lorant, h., permet, j., rabouille, o. swelling microstructure of neutron irradiated ti-stabilized austenitic steels, international conference on materials for nuclear reactor core applications, bristol (uk), (1987) 27-29. [3] iaea, international atomic energy agency. nuclear energy series technical reports structural materials for liquid metal cooled fast reactor fuel assemblies — operational behaviour no. nf.t.4.3 guidesprinted by the iaea in austria (2012). [4] vaidya gkss, w.v., radiation-induced recrystallization, its cause and consequences in heavy-ion irradiated 20% colddrawn steels of type 1.4970, journal of nuclear materials 113, north.holland publishing company, (1983) 149-162. t a. strafella et alii, frattura ed integrità strutturale, 42 (2017) 352-365; doi: 10.3221/igf-esis.42.36 365 [5] wilson, f. g., pickering, f. b., a study of zone formation in an austenitic steel containing 4% titanium. acta metallurgica, 16 (1968) 115-131 [6] daenner, w., a comparison of aisi type 316 and german type din 1.4970 stainless steel with regard to the firstwall lifetime. journal of nuclear material. north. holland publishing company, 103 & 104 (1981) 121-126 [7] caro, m., woloshun, k., rubio, f. and maloy, s., materials selection for the lead-bismuth corrosion and erosion tests in delta loop los alamos national laboratory, (2013). [8] nea expert group on heavy liquid metal technologies. handbook on lead-bismuth eutectic alloy and lead properties, materials compatibility, thermalhydraulics and technologiesnuclear energy agency organisation for economic co-operation and development, (2015) 487-570. [9] nelson, d. e., baeslack, w. a., characterization of the weld structure in a duplex stainless steel using color metallography metallography, 18 (1985) 215-225 . [10] radzikowska, j.m., metallography and microstructures of cast iron, metallography and microstructures, asm handbook, asm international, 9 (2004) 565–587. [11] abou zahra, d-a., schroeder, h. the dependence of the creep properties of din 1.4970 austenitic stainless steel at 973 k on different thermomechanical pre-treatments, journal of nuclear materials, north.holland publishing company, 107 (1982) 97-103. [12] hough, r.r., rolls, r., creep fracture phenomena in iron embrittled by liquid copper, journal of material science, 6 (1971) 1493-1498. [13] strafella, a., coglitore, a., salernitano, e., creep behaviour of 15-15ti(si) austenitic steel in air and in liquid lead at 550°c, procedia structural integrity, 3 (2017) 484-497. << /ascii85encodepages false /allowtransparency false /autopositionepsfiles true /autorotatepages /none /binding /left /calgrayprofile (dot gain 20%) /calrgbprofile (srgb iec61966-2.1) /calcmykprofile (u.s. web coated \050swop\051 v2) /srgbprofile (srgb iec61966-2.1) /cannotembedfontpolicy /error /compatibilitylevel 1.4 /compressobjects /tags /compresspages true /convertimagestoindexed true /passthroughjpegimages true /createjobticket false /defaultrenderingintent /default /detectblends true /detectcurves 0.0000 /colorconversionstrategy /cmyk /dothumbnails false /embedallfonts true /embedopentype false /parseiccprofilesincomments true /embedjoboptions true /dscreportinglevel 0 /emitdscwarnings false /endpage -1 /imagememory 1048576 /lockdistillerparams false /maxsubsetpct 100 /optimize true /opm 1 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can be opened with acrobat and adobe reader 5.0 and later.) >> /namespace [ (adobe) (common) (1.0) ] /othernamespaces [ << /asreaderspreads false /cropimagestoframes true /errorcontrol /warnandcontinue /flattenerignorespreadoverrides false /includeguidesgrids false /includenonprinting false /includeslug false /namespace [ (adobe) (indesign) (4.0) ] /omitplacedbitmaps false /omitplacedeps false /omitplacedpdf false /simulateoverprint /legacy >> << /addbleedmarks false /addcolorbars false /addcropmarks false /addpageinfo false /addregmarks false /convertcolors /converttocmyk /destinationprofilename () /destinationprofileselector /documentcmyk /downsample16bitimages true /flattenerpreset << /presetselector /mediumresolution >> /formelements false /generatestructure false /includebookmarks false /includehyperlinks false /includeinteractive false /includelayers false /includeprofiles false /multimediahandling /useobjectsettings /namespace [ (adobe) (creativesuite) (2.0) ] /pdfxoutputintentprofileselector /documentcmyk /preserveediting true /untaggedcmykhandling /leaveuntagged /untaggedrgbhandling /usedocumentprofile /usedocumentbleed false >> ] >> setdistillerparams << /hwresolution [2400 2400] /pagesize [612.000 792.000] >> setpagedevice microsoft word numero_55_art_01_2853 f. a. elshazly et al, frattura ed integrità strutturale, 55 (2021) 1-19; doi: 10.3221/igf-esis.55.01 1 analysis of strengthened short deficient rubberized concrete-filled steel tubular columns fady a. elshazly, suzan a. a. mustafa*, hesham m. fawzy zagazig university, egypt fadiame@zu.edu.eg, https://orcid.org/0000-0002-4247-0874 samustafa@eng.zu.edu.eg, http://orcid.org/0000-0001-9647-2456 hesham_fawzy2000@yahoo.com https://orcid.org/0000-0003-3847-7384 abstract. concrete-filled steel tubular (cfst) columns are broadly used in many structural systems for their well-known merits. this paper presents a finite element investigation on the structural behaviour of short circular deficient steel tubes filled with rubberized concrete (ruc), under axial compressive load. to accomplish this study, a validation of the proposed three-dimensional nonlinear finite element model; using ansys software; was carried out showing good accurateness. the analysis involved two different concrete mixes with 5% and 15% replacement of fine aggregate volume with crumb rubber particles. columns strength reduction due to horizontal or vertical deficiencies was handled by increasing the thickness of the steel tube or wrapping the columns with two different types of frp sheets. five strengthening arrangements were studied using gfrp sheets and cfrp sheets. the results indicated that the ultimate bearing capacity of the rucfst columns was increased with increasing the steel tube thickness. application of frp sheets for strengthening the deficient rucfst columns efficiently managed to retrieve the strength-lost due to either horizontal or vertical deficiency. moreover, an enhancement in the columns’ ductility was observed especially when using gfrp sheets. keywords. rubberized concrete; axial compression; deficiencies; rucfst; frp. citation: elshazly, f. a., mustafa, s. a. a., fawzy, h. m., analysis of strengthened short deficient rubberized concrete-filled steel tubular columns, frattura ed integrità strutturale, 55 (2021) 1-19. received: 09.06.2020 accepted: 20.09.2020 published: 01.01.2021 copyright: © 2021 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. introduction tructural engineering witness high rate of progress accompanied with high ambition to get the most benefit of all members consisting the structure. members with high ultimate strength and small cross sections are needed to achieve structural and architectural requirements. one of the most important structural members is the column, that must attain the loads of the structure safely. increasing loads in tall buildings need effective and economic design of columns. composite columns can attain high loads with small cross section in comparison with concrete columns. one of composite s https://youtu.be/qakemfsrd8e f. a. elshazly et al, frattura ed integrità strutturale, 55 (2021) 1-19; doi: 10.3221/igf-esis.55.01 2 columns types is concrete filled steel tube (cfst) columns. in order to increase the capacity of this type to meet the requirements of loads increase or to rehabilitate deficient members, fiber reinforced polymers (frp) sheets can be used. frp sheets can provide high confinement for the columns that leads to an increase in ultimate bearing capacity. earthquakes are great concern that must be taken in structures design. elements in seismic areas need high ductility. ductility of cfst columns can be increased by using rubberized concrete (ruc) in which rubber is added to the concrete mix as a partial replacement of fine or coarse aggregate. advantages of cfst and ruc can be gathered in rubberized concrete filled steel tube (rucfst) column. this column can attain high loads with high ductile behavior. concrete core in this column type has a great rule in controlling the local inward buckling occurrence of the steel tube. schneider [1] studied experimentally and analytically the behavior of short steel tubular columns filled with concrete under concentric compressive loads. he showed that columns with circular section had better behavior than square and rectangular sections. circular sections provided substantial post-yield strength, ductility, and stiffness more than the other two sections. he proposed that effective confinement was achieved at 92% of yield strength. he elucidated that after reaching the yield load, square and rectangular sections did not provide sufficient confinement. frp can be used to wrap cfst column to provide effective confinement that leads to an increase in ultimate bearing capacity and local outward buckling delaying. despite of frp materials’ high cost, they have several advantages that make their usage beneficial such as easy and rapid application and high provided confinement/thickness ratio in comparison with steel sections. frp materials can be used in design of cfst column or cfst rehabilitation. sundarraja and prabhu [2] studied experimentally the behavior of steel tubes filled with concrete and partially wrapped with carbon fiber reinforced polymers (cfrp) under axial compressive loads. they showed that cfrp provided effective confinement, delayed local buckling occurrence, and increased ultimate bearing capacity in agreement with the results of lu et al. [3] and the experimental and numerical results of shen et al. [4]. they concluded that unwrapped areas exhibited strains increase that led to local buckling occurrence at these areas. prabhu and sundarraja [5] studied experimentally and analytically the effect of strengthening cfst using cfrp strips under compressive load. they strengthened the specimens using transversal cfrp strips. they outlined that cfrp strips using in external wrapping of cfst specimens was effective in delaying the local buckling of the cfst specimens. increasing cfrp layers number increased the ultimate load of the columns depending of the cfrp strips spacing. prabhu et al. [6] agreed with the previous results of prabhu and and sundarraja [5]. they [6] figured out that confinement was enhanced with the increase in cfrp layers. they proposed that using cfrp strips in strengthening of cfst columns at spacing of 20 mm or 30 mm would be so effective. they preferred using spacing of 30 mm according to economical view. alam et al. [7] studied cfst specimens with and without frp strengthening under drop hammer impact. they observed that lateral displacement of cfst members could be reduced up to 18.2% by using frp sheets. they outlined that cfrp sheets, in case of wrapping in longitudinal direction, were weak under impact load. they proposed that using cfrp or gfrp sheets combination in both longitudinal and transversal directions could help in minimizing frp damage under lateral impact load. deng et al. [8] studied experimentally axial compressive capacity of cfst specimens confined with cfrp and basalt fiber reinforced polymers (bfrp). they elucidated that using cfrp and bfrp enhanced the axial compressive capacity up to 61.4% and 17.7%, respectively. liu et al. [9] studied experimentally and theoretically the axial static behavior of circular stub composite tubed concrete columns confined using cfrp. they observed high confinement of cfrp that caused an increase in ultimate load even after steel tube yielding. they proposed that specimens strengthened using cfrp exhibited better ductile behaviour compared to bare specimens. na et al. [10] investigated the effect of slenderness ratio on the behaviour of cfst columns strengthened using cfrp. they showed that transversal wrapping using cfrp enhanced the columns behaviour effectively. this enhancement decreased with the increase in slenderness ratio. reddy and sivasankar [11] studied the effect of gfrp sheets strengthening on the behaviour of corroded cfst columns. they showed that gfrp sheets were effective in delaying local buckling and increasing compressive strength. the failure mode was mainly by gfrp sheets rupture. they outlined an increase in ultimate compressive load of columns wrapped with one, two and three gfrp layers up to 5.32%m 8.41% and 10.19%, respectively, compared to bare specimens. cao et al. [12] studied experimentally the behaviour of ultra-high performance fiberreinforced concrete (uhpfrc) in cfst confined with frp under axial compressive load. they outlined enhancement in ultimate bearing capacity of the specimens due to confinement provided by frp. the enhancement level was higher in case of circular cross-sections compared to rectangular cross-sections. the main failure mode was mainly frp rupture at corners in case of rectangular cross-sections and at the mid-height in case of circular cross-sections. increasing gfrp or cfrp layers increased the confinement effectiveness. tang et al. [13] studied concrete-filled stainless steel tube (cfsst) stub columns confined using frp under axial load. they showed that the main failure mode was by cfrp rupture at mid-height. they proposed an enhancement in ultimate load capacity up to 71.35% depending on cfrp layers. they observed an improvement in energy absorption due to cfrp provided confinement. f. a. elshazly et al, frattura ed integrità strutturale, 55 (2021) 1-19; doi: 10.3221/igf-esis.55.01 3 several ways are available to upgrade columns and enhance their capacity. one of the most effective ways is using frp sheets to strengthen columns. several studies were performed to analyze this case by adding deficiencies to columns and strengthening them using frp sheets. ghaemdoust et al. [14] studied experimentally and numerically deficient short steel tubular columns wrapped with cfrp sheets. the specimens had initial horizontal or vertical deficiencies. karimian et al. [15] studied deficient hollow circular steel tubes with initial deficiencies in transversal or longitudinal directions and strengthened with cfrp under axial compressive loads. they [14, 15] showed that there was a loss in ultimate bearing capacity because of deficiencies occurrence. they [14, 15] proposed that using cfrp sheets compensated effectively this loss. number of cfrp layers had significant effect on confinement effectiveness, gain in ultimate bearing capacity, delaying local buckling occurrence and decreasing stress concentration at the deficiency location. concrete mixes’ properties depend on the materials composing the mix. several materials can enhance the properties of concrete mixes. adding rubber to concrete mixes that scientifically named rubberized concrete (ruc) can enhance the mix ductility, fawzy et al. [16]. several researchers studied the behavior of ruc. jiang et al. [17] studied experimentally specimens of steel tubes filled with rubberized concrete and normal concrete to analyze the differences in the behaviour of the two types. a number of 36 specimens were tested experimentally. all specimens were tested under cyclic and monotonic lateral loads with normalized axial loads at several levels. the results showed that the concrete core provided efficient restraining of steel tubes against occurrence of local buckling. thus, preventing premature failure that might occur due to local buckling. it was observed that the concrete damage controlled the ductility of the specimens. the cross-section slenderness had a great effect on the occurrence of the concrete damage which in turn influenced the ductility of the specimen. duarte et al. [18] studied short steel tubular columns filled with rubberized concrete. they showed that specimens with rubberized concrete exhibited lower strength under compression and tension and higher ductile behaviour in comparison with normal concrete specimens. they proposed that in case of specimens with circular section, confinement effectiveness decreased with the increase in rubber content. this effect was a result of concrete core crushing after the tube initiated to buckle, and as a result of lower dilation angle of rubberized concrete in comparison with normal concrete. abendeh et al. [19] studied the behavior of steel tubes filled with rubberized concrete. they showed that increasing rubber content led to a decrease in compressive strength. they elucidated that the bond in case of circular cross sections was higher than square cross sections. elchalakani et al. [20] studied experimentally short columns composed of circular steel tubes with double skin and filled with rubberized concrete with different contents of rubber in the concrete mix. the results showed that the ultimate compressive strength in case of rubberized concrete with 15% and 30% rubber content was lower than that of normal concrete mix by 50% and 79%, respectively. the results showed that adding of rubber to the concrete increased the ductility of the concrete filled steel tube up to 250 %. dong et al. [21] studied rubberized cfst (rucfst) to investigate the effect of confinement provided by the steel tube to the ruc core on specimens’ ductility and strength. they proposed that rubber existence in concrete caused strength decrease and ductility increase of the concrete mix. they showed that this strength reduction was effectively overcome by the steel tube confinement. rucfst specimens had better ductile behavior compared to normal cfst specimens. they outlined that high ductility of ruc led to well bond between the concrete core and the steel tube. the ruc core deformed and filled the buckles. rucfst specimens had higher energy absorption compared to normal cfst specimens. the main aim of this paper is to present a three-dimensional nonlinear finite element model using ansys [23] software to simulate the rucfst short columns under axial compressive load. the model simulated the behaviour of the rucfst columns and its accuracy was proven using twenty experimentally tested specimens from literature. the overall behaviour of the rucfst deficient columns was studied, in addition to studying the effect of increasing the steel tube thickness and strengthening the columns with frp sheets to retain the lost strength. finite element modeling general three-dimensional nonlinear finite element model was proposed to investigate the behavior of deficient short rucfst columns under axial compressive load. some of these columns were strengthened using frp sheets. all the components of the specimens such as steel, concrete core and frp sheets had to be modeled properly. in addition, the interface between steel tube and the concrete core had to be modelled carefully, to accurately simulate the real behaviour of the studied columns. ansys [22] software was utilized to perform the nonlinear finite element analysis (fea) of the specimens. choosing the appropriate element type and mesh size controls the accuracy and the computational time needed for accurate results. the proposed finite element model was verified by using seventeen specimens tested by the authors in addition to other research data available from literature. a f. a. elshazly et al, frattura ed integrità strutturale, 55 (2021) 1-19; doi: 10.3221/igf-esis.55.01 4 finite element type and mesh ansys [22] library provides several types of elements to simulate various structural elements with high accuracy. each element has its own properties. mesh sizes have to be determined accurately to obtain precise solution with acceptable solution time. the desired mesh size ratio; 1:3; was considered for accurate results. a three-dimensional 8-node solid element solid65 was used to simulate concrete elements. this element is used in 3-d modeling of solids in cases of using or not using reinforcing bars. it has the capability of cracking in tension and crushing in compressive stresses. each node of its eight nodes has three transitional degrees of freedom in x, y and z directions. to model the steel tube and the steel loading plates, a three-dimensional 8-nodes solid element solid185 was used. each node of its eight nodes has three transitional degrees of freedom in x, y and z directions. this element has the capability of stress stiffening, large deflections, large strain and creep. the different types of frp sheet were modelled using a 4-node shell181 element. it has six degrees of freedoms at each node; three transitional degrees of freedom in x, y and z directions and three rotational degrees of freedom about x, y and z axes. it is well-suited for layered materials analysis. the interface between the different components of the cfst columns was modelled as frictional contact, which affirmed friction provided that the two surfaces remain in contact. moreover, it inhibits physical penetration between the contacted components during the different loading steps. material modeling for the sake of accuracy of the proposed model, the material properties of each component were considered as existed in the experimental work. one of the most important aspects is the stress-strain relation of concrete. the concrete compressive strengths in the finite element analysis were obtained from the experimental data from elshazly et. al [23] and duarte et al. [18] for the different simulated specimens. a typical shape of the concrete stress-strain relation is shown in fig. 1 (a). the ascending branch of the stress-strain relationship followed eqn. (1) and eqn. (2) proposed by liang and fragomeni [24] and liang [25] & [26]. in all studied specimens, the d/t ratio of the used steel tubes ranged from 32 to 50. these values provide remarkable confining for the concrete core. the model ignored the descending branch of the relationship to avoid the convergence problems in the finite element analysis solution. the confined compressive strength in circular concrete filled steel tubes of each concrete mix and ultimate confined strain were calculated using eqn. (3) and eqn. (4) proposed by mander et al. [27], with the strength reduction factor γc proposed by liang [26].          cc c cc λ c cc ƒ  λ   ε /  ε'    λ 1    ε /  ε' c (1)       c c cc cc e e    ƒ /  ε'   (2)   cc 1 rpƒ ƒ  ƒc k (3)          rp 2 c c ƒ ' ' 1 γ  ƒ’ cc c k (4)    ruc nc concrete rubber rubberv v (5) where ƒ’cc refers to the confined compressive strength of the concrete, ε’cc refers to the strain at ƒ’cc, ƒrp refers to the lateral confining pressure on the concrete core presented by eqn. (3), ƒ’c refers to the unconfined compressive strength based on the experimental results, ε’c refers to the strain at ƒ’c as illustrated by tang et al. [28] and hu et al. [29]. k1 and k2 were taken as 4.1 and 20.5, respectively based on the results proposed by richart et al. [30]. the poisson’s ratio of the rubberized concrete mixes was calculated using eqn. (5) provided by duarte et al. [31], in which ruc is the poisson’s ratio of rubberized concrete. vconcrete and vrubber are the volumetric fraction of the concrete mix and the rubber particles, respectively. nc is the poisson’s ratio of normal concrete mix and was taken as 0.2, and rubber is the poisson’s ratio of the rubber particles that was taken as 0.5. using the aforementioned equations, confined compressive strength of concrete f. a. elshazly et al, frattura ed integrità strutturale, 55 (2021) 1-19; doi: 10.3221/igf-esis.55.01 5 mixes were calculated. confined compressive strengths for nc, ru5 and ru15 were 59.6 mpa, 56 mpa and 51.5 mpa, respectively. confined ultimate strain of nc, ru5 and ru15 was 0.00753, 0.00780 and 0.008268, respectively. open shear transfer coefficient was taken as 0.4 and closed shear transfer coefficient was taken as 0.8. uniaxial cracking stress was taken as 5.96 mpa, 5.6 mpa and 5.15 mpa for nc, ru5 and ru15, respectively. the steel properties were considered as the recorded experimental data in tab. 1 which lists the yield stress; ultimate stress; yield strain; ultimate strain and the elastic modulus. steel poisson’s ratio was assumed as 0.3 while the elastic modulus was 200 gpa. fig. 1(b) shows a typical shape of the utilized steel stress-strain relationship. some specimens tested by elshazly et al. [23] were strengthened using different types of frp sheets. the frp material was defined using linear elastic behavior with poisson’s ratio of 0.35. cfrp sheet had a thickness of 0.129 mm with ultimate tensile strength of 3500 mpa, ultimate strain of 1.56% and modulus of elasticity of 225 gpa. gfrp sheet had a thickness of 0.168 mm with ultimate tensile strength of 1500 mpa, ultimate strain of 2.14% and modulus of elasticity of 70 gpa as existed in the experimental work. (a) (b) figure 1: typical stress-strain relation; (a) concrete, (b) steel. fy (mpa) fu (mpa) y (%) u (%) elshazly et. al [23] 280 387 0.14 40.67 duarte et al. [18] 310 400 0.14778 24 table 1: material properties of steel tubes. boundary conditions and load application the test procedure performed by elshazly et. al [23] and duarte et al. [18] was imitated in the finite element analysis. two loading plates were positioned at the top and the bottom of the specimens to insure a uniform distribution of the load. the load was applied at the centroid of the upper plate in y direction. the top surface of the loading plate was restrained against any horizontal translation. the contact between the loading plates and cfst column components was fully bonded. the contact between the steel tube and concrete core was frictional contact with factor of friction 0.4, while the contact between the steel tube and the frp sheets was fully bonded contact. the bottom surface of the specimen was restrained against any translation or rotation in all directions. contact surfaces and load application of the proposed models are shown in fig. 2. the load was applied as static axial load with small increments identical to the experimental investigations. non-linear controls were by setting newton-raphson to program controlled option with force convergence criteria. the convergence tolerance limit was taken as 0.5% to achieve convergence of the solutions. 0 10 20 30 40 50 60 70 0 0,002 0,004 0,006 0,008 0,01 c o m p re ss iv e  s tr e ss  ( m p a ) compressive strain nc ru5 ru15 0 50 100 150 200 250 300 350 400 450 0 10 20 30 40 50 s tr e ss  ( n /m m 2 ) strain f. a. elshazly et al, frattura ed integrità strutturale, 55 (2021) 1-19; doi: 10.3221/igf-esis.55.01 6 (a) (b) (c) figure 2: loading and contact surfaces of the proposed model; (a) contact between loading plates and cfst column components, (b) contact between steel tube and concrete core, (c) load application. finite element model validation eventeen cfst columns tested by the authors in addition to three columns tested by duarte et. al. [18], were simulated to verify the proposed finite element model. specimen dimensions, material properties, boundary conditions and loading schemes were considered carefully from the experimental tests for the sake of accuracy, as detailed above. the comparison depended mainly on the ultimate load, load-axial shortening behaviour, deformed shapes and modes of failure. specimens tested by elshazly et al. [23] a wide range of parameters were considered in the seventeen specimens tested by elshazly et al. [23], as detailed in tab. 2. they examined non-deficient and deficient short rucfst columns under axial compressive load. they used three concrete mixes; normal concrete (nc) with zero rubber content; rubberized concrete mix with 5% fine aggregate replacement with rubber particles by volume (ru5); and rubberized concrete mix with 15% fine aggregate replacement with rubber particles by volume (ru15). all specimens were 500 mm in length. the steel tube outer diameter was 125 mm and the thickness was 2.5 mm. the total length to external diameter ratio (l/d) was 4 for all specimen. the external diameter to thickness ratio (d/t) of the steel tubes was 50. deficiencies were manufactured in some specimens in either longitudinal or transversal directions. longitudinal deficiency had 300 mm length and 20 mm width. transversal deficiency had a length of 100 mm and a width of 20 mm. deficient specimens were strengthened using cfrp or gfrp sheets with different number and orientation of layers. s f. a. elshazly et al, frattura ed integrità strutturale, 55 (2021) 1-19; doi: 10.3221/igf-esis.55.01 7 specimen l mm d mm t mm concrete deficiency strengthening ref. rubber % fcu mpa orientation length (mm) width (mm) type nt nl nc 500 125 2.5 0% 41.7 ------------ e ls ha zl y et a l [ 23 ] ru5 500 125 2.5 5% 38 ------------ ru5-hl 500 125 2.5 5% 38 t 100 20 ------ ru15 500 125 2.5 15% 33.3 ------------ ru15-hl 500 125 2.5 15% 33.3 t 100 20 ------ ru5hl-c1t 500 125 2.5 5% 38 t 100 20 cfrp 1 -- ru5hl-g1t 500 125 2.5 5% 38 t 100 20 gfrp 1 -- ru5hl-g1t1l 500 125 2.5 5% 38 t 100 20 gfrp 1 1 ru5vl-c1t 500 125 2.5 5% 38 l 300 20 cfrp 1 -- ru5vl-g1t 500 125 2.5 5% 38 l 300 20 gfrp 1 -- ru5vl-g2t 500 125 2.5 5% 38 l 300 20 gfrp 2 -- ru5vl-g1t1l 500 125 2.5 5% 38 l 300 20 gfrp 1 1 ru15hl-c1t 500 125 2.5 15% 33.3 t 100 20 cfrp 1 -- ru15hl-g1t 500 125 2.5 15% 33.3 t 100 20 gfrp 1 -- ru15hl-g2t 500 125 2.5 15% 33.3 t 100 20 gfrp 2 -- ru15vl-g2t 500 125 2.5 15% 33.3 l 300 20 gfrp 2 -- ru15vl-g1t1l 500 125 2.5 15% 33.3 l 300 20 gfrp 1 1 c114*3-235-0 300 114 2.7 0% 49.5 ------------ d ua rt e et al [1 8] c114*3-235-5 300 114 2.7 5% 39.3 ------------ c114*3-235-15 300 114 2.7 15% 25.2 ------------ t: transversal; nt: no. of layers in transversal direction; l: longitudinal; nl: no. of layers in longitudinal direction table 2: details of verified specimens. to validate the proposed finite element model, the obtained results were compared to the experimental results. axial loadaxial shortening relations of the finite element results were plotted against experimental results in fig. 3. good agreement was noticed in the compared relations, not only in the initial stiffness but also in the ultimate strength. the mean value of the ratio between the ultimate experimental load and the corresponding finite element (fe) ultimate load, as detailed in tab. 3, was about 0.988, with a corresponding coefficient of variation of about 0.026. however, the mean value of the ratio between the recorded axial shortening in the experimental results and their fe counterparts was about 0.89. the difference was due to the low deformation recorded in some experimentally tested specimens while the other specimens showed similar behaviour. modes of failure in both cases were compared as well. some examples of the compared specimens at failure are shown in fig. 4. in case of bare deficient specimens, failure occurred at the deficiency location. this location exhibited high stresses and strains concentration. with increasing the load, warning notices appeared telling that the concrete core initiated to crush specially at deficiency location. when the specimen reached its ultimate bearing capacity, the deficiency location witnessed concrete crushing accompanied with high deformation in the steel tube. in specimens with transversal deficiency, the width of the deficiency initiated to decrease with increasing the load, as shown in fig. 4. while in case of longitudinal deficiency, the width initiated to increase with increasing the load. in both cases, the edges of the deficiency started to buckle outward accompanied with concrete crushing at the deficiency location. in strengthened deficient specimens, the existence of frp sheets postponed the local outward buckling in both cases of deficiencies. when the frp sheets reached their ultimate strain, failure notice of the frp sheet appeared. this failure was at the deficiency location followed by different other locations. some of these failure modes from the finite element models which agrees with the modes of failure noticed in the experimental tests are shown in fig. 4. the figure shows the finite element specimens’ deformed shape attached with stress or strain values to clarify the most stressed and strained locations of the specimens. these values showed good accuracy in identifying the predicted failure position with good agreement with experimental results. strain values were in mm/mm, while stress values were in mpa, as shown in fig.4. specimens tested duarte et al. [18] three concrete filled steel tubular columns with circular cross section under axial compressive load were modeled using the same presented technique. all the specimens had a length of 300 mm. the steel tube had a circular cross section with 114 mm outer diameter and 2.7 mm thick. the total length to external diameter ratio (l/d) was 2.63 for all specimen. the external diameter to thickness ratio (d/t) of the steel tubes was 42.2. the three specimens had three different concrete mix properties, as detailed in tab. 2. the first concrete mix was normal concrete (nc) without any rubber content ( specimen f. a. elshazly et al, frattura ed integrità strutturale, 55 (2021) 1-19; doi: 10.3221/igf-esis.55.01 8 c114*3-235-0), the second concrete mix was rubberized concrete with 5% replacement of the total aggregate content with rubber (ru5) (specimen c114*3-235-5) and the third mix was rubberized concrete with 15% replacement of the total aggregate content with rubber (ru15) (specimen c114*3-235-15). (a) (b) (c) (d) (e) figure 3: load-axial shortening curves of proposed finite element model and experimental results; (a) reference bare specimens, (b) specimens with 5% rubber content and hl deficiency, (c) specimens with 5% rubber content and vl deficiency (d) specimens with 15% rubber content and hl deficiency (e) specimens with 15% rubber content and vl deficiency. a comparison between the results of the fe and the experimental results was carried out. very good agreement in the results was noticed between the results. the proposed finite element model predicted both the ultimate load and the loadaxial deformation relation efficaciously, as shown in fig. 5 and tab. 3. the mean value of the ultimate load ratio (pu(exp)/pu(fe)) was about 0.97 while the cov of these results was about 0.015. the corresponding axial deformation ratio (u(exp)/u(fe)) showed good results as well. the mean value was about 0.99 while the cov was about 0.053. these values indicate good accuracy of the proposed finite element model. perfect match was noticed between the finite element analysis and the experimental counterpart until a load of about 400kn, shown in fig. 5 (a, b, c). the axial shortening increased until the occurrence of local buckling in steel tube at mid-height of the columns, as shown in fig. 5(d). high strain in the steel tube at the location of local buckling was observed which agreed with the deformed shape of the experimental specimen. the ultimate loads from the experimental and the finite element results of the twenty simulated columns were plotted in fig. 6. the figure shows the accuracy and the reliability of the proposed finite element model to study the effect of some parameter to enhance the rucfst columns behaviour. f. a. elshazly et al, frattura ed integrità strutturale, 55 (2021) 1-19; doi: 10.3221/igf-esis.55.01 9 figure 4: failure shapes, stress and strain values of finite element models specimen  u expp  u fep     u exp u fe p p  u exp  u fe     u exp u fe   ref. nc 960 958 1.002 4.57 4.55 1.004 e ls ha zl y et a l [ 23 ] ru5 884 887 0.996 9.21 7.1 1.29 ru5-hl 874 870 1.005 7.7 7 1.1 ru15 833 824 1.01 6.8 7.5 0.906 ru15-hl 812 816 0.995 5.72 6.5 0.88 ru5hl-c1t 1094 1113.9 0.982 4.9 6.95 0.705 ru5hl-g1t 952 983.8 0.968 7.17 7.5 0.956 ru5hl-g1t1l 1073 1066.2 1.006 7.1 11.1 0.639 ru5vl-c1t 1007 1093.7 0.921 4.45 5.35 0.83 ru5vl-g1t 923 971 0.95 8 9.8 0.816 r 1045 1066.6 0.98 7.85 9.5 0.826 ru5vl-g1t1l 972 988 0.984 5.73 7.1 0.807 ru15hl-c1t 1020 1026.4 0.994 6 6.35 0.945 ru15hl-g1t 942 927 1.016 7.66 8.7 0.88 ru15hl-g2t 1066 1055.3 1.01 8.5 11.4 0.745 ru15vl-g2t 1042 1017 1.02 8.85 9.5 0.932 ru15vl-g1t1l 911 937.8 0.971 5.6 7.1 0.788 c114*3-235-0 723.5 732.8 0.987 5.48 5.75 0.953 d ua rt e et al [1 8] c114*3-235-5 595 617.5 0.964 8.8 8.95 0.983 c114*3-235-15 482 501.5 0.961 10.3 9.75 1.056 table 3: comparison between test results and fe model results. f. a. elshazly et al, frattura ed integrità strutturale, 55 (2021) 1-19; doi: 10.3221/igf-esis.55.01 10 (a) (b) (c) (d) figure 5: comparison between proposed model and experimental results of duarte et al. [18]; (a), (b), (c) load-axial shorteing curves (d) deformed shape at failure. figure 6: experimental and finite element ultimate load of the twenty simulated cfst columns. 0 100 200 300 400 500 600 700 800 0 2 4 6 8 10 a xi a l  lo a d  ( k n ) axial shortening (mm) (c114*3‐235‐0)‐exp (c114*3‐235‐0)‐fe 0 100 200 300 400 500 600 700 0 5 10 15 20 a xi a l  lo a d  ( k n ) axial shortening (mm) (c114*3‐235‐5)‐exp (c114*3‐235‐5)‐fe 0 100 200 300 400 500 600 0 5 10 15 20 a xi a l  lo a d  ( k n ) axial shortening (mm) (c114*3‐235‐15)‐exp (c114*3‐235‐15)‐fe f. a. elshazly et al, frattura ed integrità strutturale, 55 (2021) 1-19; doi: 10.3221/igf-esis.55.01 11 parametric study and discussion ixty-four columns were analyzed using ansys program to investigate the influence of some parameters on the structural behaviour of the rucfst columns. the studied parameters involved the rubber percentage included in the concrete mix design, the thickness of the steel tube, direction of manufactured deficiency, the type of the frp sheets used in strengthening the deficient specimens in addition to the number and the direction of the used frp sheets. the column dimensions, material properties and the sizes of the vertical and horizontal deficiencies were considered as tested by elshazly et al. [23] which were listed in tab. 1 and tab. 2. the studied parameters are detailed in tab. 4. the label of each column indicates the analyzed parameters. as an example (ru5-hl-c1t1l-t2.5): “ru” stands for rubberized concrete, “5” stands for rubber content of 5% as replacement of fine aggregate content, “hl” stands for horizontal (or transverse) deficiency, “c” stands for cfrp sheets, “1t” refers to one layer of frp sheet in transversal direction, “1l” refers to one layer of frp sheet in longitudinal direction and (t2.5) refers to the thickness of the steel tube. all the studied specimens had d/t ratios were chosen to be less than 125/ (fy/250); according to bradford et al. [32] to prevent local buckling. diameter to thickness ratio diameter to thickness d/t ratio may be either due to increasing the tube diameter or due to decreasing the tube’s thickness. in this study, the analysis was carried out by keeping the diameter of the tubes constant and the thickness was varied. twenty-four circular cfst columns were employed herein to explore the effect of this parameter on the column behaviour. the used steel tube thicknesses were 2.5, 3, 3.5 and 4 mm. this caused the d/t ratio to vary from 32 to 50 as illustrated in tab. 4. these twenty-four columns were analyzed in six groups, each group contained four specimens with the four different studied tube thicknesses. the first group contained columns with rubberized concrete with 5% rubber content. the second group contained columns with rubberized concrete with 15% rubber content. the third and fourth groups had specimens with horizontal deficiency, while the fifth and sixth groups had specimens with vertical deficiency, with the afore-mentioned two concrete mixes. it is worth pointing out that the four columns of each group had typical load-axial shortening behaviour until a load between 550 kn to 600 kn, as shown in fig. 7. beyond this limit, enhancement in the bearing capacity of the specimens was noticed with increasing the steel tube thickness. in the non-deficient column with 5% rubberized concrete, increasing the steel tube thickness increased the ultimate bearing capacity of the column up to 20.57%. while in the similar specimens with 15% rubber content, the ultimate bearing capacity was increased up to 23.9%, compared to the reference specimens. in these two groups, no noticeable effect on the columns’ ductility was noticed due to changing the tube thickness. however, it was observed that for the same steel tube thickness, the columns with ru15 concrete mix exhibited higher ductility and lower ultimate compressive strength than columns with ru5 concrete mix, as shown in fig. 8. in case of transversally (horizontal) deficiency in specimens with 5% rubber content (ruc 5%), increasing the steel tube thickness caused approximately uniform increase in ultimate load, as shown in fig. 7 (c). in comparison with the steel tube with 2.5 mm thickness, the steel tube with 3 mm thickness exhibited higher ultimate compressive load by 4.3%, the steel tube with 3.5 mm thickness exhibited higher ultimate compressive load by 8.65% and the steel tube with 4 mm thickness exhibited higher ultimate compressive load by 14.48%. the equivalent specimens with 15% rubber content (ruc 15%), had increased percentages in the ultimate loads about 5.07%, 9.68% and 16.29% for columns with steel tube thicknesses of 3 mm, 3.5 mm and 4 mm, respectively. with the existence of longitudinal (vertical) deficiency in specimens with 5% rubber content, the increase in the steel tube thickness caused higher increase in the ultimate load of the studied columns. the increase corresponding to thickness variation were 6.2%, 12.2% and 18.5% with respect to the column with steel tube thickness of 2.5 mm. very close increase values in the column capacities were noticed when 15% rubber content were used; 6.7%, 13.25% and 19.4%, as shown in fig. 7 (f). the results demonstrated that the ultimate axial load bearing capacity of the analyzed columns decreased with increasing the d/t ratio, as illustrated in fig. 9. increasing the diameter to thickness ratio decreases the difference in the section capacities between the non-deficient and the deficient columns, regardless the concrete mix type, as shown in fig. 9. to evaluate the change in ductility with different steel tube thickness, ductility index (di) was calculated as the ratio between the axial shortening at ultimate load to the axial shortening at yield. in general, the columns with concrete mix with 15% rubber content exhibited higher ductility compared to that with 5% rubber content. the value of the ductility index in specimens with vertical (longitudinal) deficiency were higher than that of specimens with horizontal (transversal) deficiency, as shown in fig. 8. this might be due to the noticeable increase in the axial deformation accompanied with increasing the load until the ultimate load of the former columns. s f. a. elshazly et al, frattura ed integrità strutturale, 55 (2021) 1-19; doi: 10.3221/igf-esis.55.01 12 specimen t [mm] d/t rubber % deficiency strengthening 𝑃 (kn)  di type nt nl ru5-t2.5 2.5 50 5% ----887 7.1 5 ru5-hl-t2.5 2.5 50 5% t ---870 7 7.1 ru5-vl-t2.5 2.5 50 5% l ---875 6.95 7.73 ru5-t3 3 42 5% ----942 7.1 5 ru5-hl-t3 3 42 5% t ---907.5 6.35 6.68 ru5-vl-t3 3 42 5% l ---930 7.15 8.36 ru5-t3.5 3.5 36 5% ----998.5 7.1 5 ru5-hl-t3.5 3.5 36 5% t ---945.3 6.15 6.47 ru5-vl-t3.5 3.5 36 5% l ---982 7.15 7.94 ru5-t4 4 32 5% ----1069.5 7.1 5 ru5-hl-t4 4 32 5% t ---996 6.45 6.52 ru5-vl-t4 4 32 5% l ---1037 7.35 8.36 ru5-hl-g1t 2.5 50 5% t gfrp 1 -983.8 7.5 10.7 ru5-hl-g1t1l 2.5 50 5% t gfrp 1 1 1066.2 11.1 15.85 ru5-hl-g2t 2.5 50 5% t gfrp 2 -1118.7 11.1 16 ru5-hl-g2t1l 2.5 50 5% t gfrp 2 1 1163.3 11.1 15.85 ru5-hl-g3t 2.5 50 5% t gfrp 3 -1192 10.3 14.71 ru5-hl-c1t 2.5 50 5% t cfrp 1 -1113.9 6.95 9.92 ru5-hl-c1t1l 2.5 50 5% t cfrp 1 1 1183 7.5 10.71 ru5-hl-c2t 2.5 50 5% t cfrp 2 -1281 6.7 9.57 ru5-hl-c2t1l 2.5 50 5% t cfrp 2 1 1363.2 7.1 10.14 ru5-hl-c3t 2.5 50 5% t cfrp 3 -1449 6.7 9 ru5-vl-g1t 2.5 50 5% l gfrp 1 -971 9.8 10.09 ru5-vl-g1t1l 2.5 50 5% l gfrp 1 1 988 7.1 10.44 ru5-vl-g2t 2.5 50 5% l gfrp 2 -1066.6 9.5 13.57 ru5-vl-g2t1l 2.5 50 5% l gfrp 2 1 1084.8 8.7 12.43 ru5-vl-g3t 2.5 50 5% l gfrp 3 -1113.9 8.3 11.5 ru5-vl-c1t 2.5 50 5% l cfrp 1 -1093.7 5.35 9 ru5-vl-c1t1l 2.5 50 5% l cfrp 1 1 1168.1 7.75 10.33 ru5-vl-c2t 2.5 50 5% l cfrp 2 -1112.1 3.95 5.26 ru5-vl-c2t1l 2.5 50 5% l cfrp 2 1 1225.3 5.35 7.13 ru5-vl-c3t 2.5 50 5% l cfrp 3 -1197.3 3.95 5.26 ru15-t2.5 2.5 50 15% ----824 7.5 6.8 ru15-hl-t2.5 2.5 50 15% t ---816 6.5 7.2 ru15-vl-t2.5 2.5 50 15% l ---827.8 7.15 7.78 ru15-t3 3 42 15% ----895.3 7.5 6.8 ru15-hl-t3 3 42 15% t ---857.4 6.35 6.77 ru15-vl-t3 3 42 15% l ---883.2 7.3 8.47 ru15-t3.5 3.5 36 15% ----948.2 7.1 6.8 ru15-hl-t3.5 3.5 36 15% t ---895 6.15 6.58 ru15-vl-t3.5 3.5 36 15% l ---937.5 7.55 8.18 ru15-t4 4 32 15% ----1021.5 7.1 6.8 ru15-hl-t4 4 32 15% t ---949 6.45 6.64 ru15-vl-t4 4 32 15% l ---988.4 7.65 8.47 ru15-hl-g1t 2.5 50 15% t gfrp 1 -927 8.7 12.43 ru15-hl-g1t1l 2.5 50 15% t gfrp 1 1 995 11 15.95 ru15-hl-g2t 2.5 50 15% t gfrp 2 -1055.3 11.4 16.43 ru15-hl-g2t1l 2.5 50 15% t gfrp 2 1 1092.1 11.4 15.95 ru15-hl-g3t 2.5 50 15% t gfrp 3 -1113.1 10 14.87 ru15-hl-c1t 2.5 50 15% t cfrp 1 -1026.4 6.35 10.2 ru15-hl-c1t1l 2.5 50 15% t cfrp 1 1 1125.9 7.9 11.3 ru15-hl-c2t 2.5 50 15% t cfrp 2 -1211.2 6.7 9.9 ru15-hl-c2t1l 2.5 50 15% t cfrp 2 1 1343 7.9 10.9 ru15-hl-c3t 2.5 50 15% t cfrp 3 -1448 6.7 9.6 ru15-vl-g1t 2.5 50 15% l gfrp 1 -900.2 6.15 8.2 ru15-vl-g1t1l 2.5 50 15% l gfrp 1 1 937.8 7.1 10.7 ru15-vl-g2t 2.5 50 15% l gfrp 2 -1017 9.5 13.8 ru15-vl-g2t1l 2.5 50 15% l gfrp 2 1 1035 8.7 12.8 ru15-vl-g3t 2.5 50 15% l gfrp 3 -1064 8.3 12 ru15-vl-c1t 2.5 50 15% l cfrp 1 -1009 5.55 8.25 ru15-vl-c1t1l 2.5 50 15% l cfrp 1 1 1117.5 7.75 11 ru15-vl-c2t 2.5 50 15% l cfrp 2 -1057.4 3.55 5.4 ru15-vl-c2t1l 2.5 50 15% l cfrp 2 1 1155.1 5.1 7.24 ru15-vl-c3t 2.5 50 15% l cfrp 3 -1061.5 2.95 4.22 t: transversal; nt: no. of layers in transverse direction; l: longitudinal; nl: no. of layers in longitudinal direction table 4: specimens details and results for the parametric study. f. a. elshazly et al, frattura ed integrità strutturale, 55 (2021) 1-19; doi: 10.3221/igf-esis.55.01 13 strengthening using frp sheets forty rucfst columns were externally bonded by frp sheets. two different fiber types were used in this study, carbon frp sheets and glass frp sheets. the sheets were utilized to strengthen deficient rucfst columns, with either horizontal (transversal) or vertical (longitudinal) deficiencies. five strengthening schemes were used for each deficiency type and each frp sheet. the layouts included layer(s) being wrapped around the rucfst column perpendicular to the load direction (transversely), and layer bonded parallel to the axial load (longitudinally). the five schemes were: one transversal layer denoted by (1t); one transversal layer and one longitudinal layer (1t1l); two transversal layers (2t); two transversal layers and one longitudinal layer (2t1l) and three transversal layers; as detailed in tab. 4. the aforementioned dimensions of the steel tubes with d/t ratio of 50 were used in this investigation. the proposed strengthening schemes were applied on specimens with transverse and longitudinal deficiencies with both types of rubberized concrete (with 5% and 15% crumb rubber content). figure 7: axial loadaxial shortening for specimens with various steel tube thickness. glass fiber reinforced polymer (gfrp) sheets composite columns filled with rubberized concrete with rubber replacements percentages of 5% and 15% were strengthened using the techniques mentioned above. for lateral strengthening schemes, increasing the number of gfrp layers increased the ultimate compressive load with increasing the number of layers. using two and three transversal gfrp layers increased the ultimate compressive strength by 13.7% and 21.16%, respectively, compared to that with one gfrp layer. it was observed that the orientation of the layers had its effect on that increase in the ultimate compressive load. in comparison with the column strengthened with one transversal gfrp layer, using one transversal layer in addition to one longitudinal gfrp layer increased the ultimate compressive strength by 8.4%. using two transversal layers in addition to 0 200 400 600 800 1000 1200 0 5 10 15 20 25 a xi a l  lo a d  ( k n ) axial shortening (mm) ru5‐t2.5 ru5‐t3 ru5‐t3.5 ru5‐t4 0 200 400 600 800 1000 1200 0 5 10 15 20 25 a xi a l  lo a d  ( k n ) axial shortening (mm) ru15‐t2.5 ru15‐t3 ru15‐t3.5 ru15‐t4 0 200 400 600 800 1000 0 2 4 6 8 a xi a l  lo a d  ( k n ) axial shortening (mm) ru15‐hl‐t2.5 ru15‐hl‐t3 ru15‐hl‐t3.5 ru15‐hl‐t4 0 200 400 600 800 1000 1200 0 4 8 12 a xi a l  lo a d  ( k n ) ru5‐vl‐t2.5 ru5‐vl‐t3 ru5‐vl‐t3.5 ru5‐vl‐t4 0 200 400 600 800 1000 1200 0 4 8 12 a xi a l  lo a d  ( k n ) ru15‐vl‐t2.5 ru15‐vl‐t3 ru15‐vl‐t3.5 ru15‐vl‐t4 0 200 400 600 800 1000 1200 0 2 4 6 8 a xi a l  lo a d  ( k n ) axial shortening (mm) ru5‐hl‐t2.5 ru5‐hl‐t3 ru5‐hl‐t3.5 ru5‐hl‐t4 f. a. elshazly et al, frattura ed integrità strutturale, 55 (2021) 1-19; doi: 10.3221/igf-esis.55.01 14 one longitudinal gfrp layer increased the ultimate compressive strength by 18.2%. these results indicated that using transversal layers in strengthening was more effective in increasing ultimate bearing capacity than using a combination of transversal and longitudinal layers with the same number of layers, as shown in fig. 10 (a). similar trend was observed in columns with 15% rubber content, as shown in fig. 10 (b). in comparison with the column strengthened with one transversal gfrp layer, using one transversal layer in addition to one longitudinal gfrp layer increased the ultimate compressive strength by 7.3% while using two transversal gfrp layers increased the ultimate compressive strength by 13.8%. using two transversal layers in addition to one longitudinal gfrp layer increased the ultimate compressive strength by 17.8% while using three transversal gfrp layers increased the ultimate compressive strength by 20% that led to the result that existence of transversal layers in strengthening was more effective than using a combination of transversal and longitudinal layers with the same number of layers. however, adding one longitudinal layer to transversal layers increased the ductility index of the specimen, as shown in fig. 11. using more than two gfrp layers led to a decrease in ductility index. figure 8: ductility index of the specimens with various steel tube thickness. (a) (b) figure 9: ultimate bearing capacity of the specimens with various steel tube thickness; (a) ru5 cfst, (b) ru15 cfst. strengthening specimens with longitudinal deficiency increased the ultimate bearing capacity, as shown in fig. 10 (c). it was observed that the orientation of the layers was impressive in enhancing the deficient columns behaviour. using two gfrp layers in transversal direction increased the ultimate compressive strength by 9.8%, while using one transversal layer and one longitudinal gfrp layer increased the ultimate compressive strength by only 1.7%, in comparison with the column strengthened with one transversal gfrp layer. three transversal gfrp layers increased the ultimate compressive strength by 14.7%, while using two transversal layers in addition to one longitudinal gfrp layer increased the ultimate compressive strength by only 11.7%. these results indicate that with existence of vertical deficiency, transversal gfrp layers in strengthening was more effective than using a combination of transversal and longitudinal layers with the same number of layers. the equivalent columns with 15% rubber particles replacement showed better performance. in comparison with the column strengthened with one transversal gfrp layer, using two transversal gfrp layers increased the ultimate compressive strength by 12.9%. however, using one transversal layer in addition to one longitudinal gfrp layer increased the ultimate compressive strength by only 4.17%. three transversal gfrp layers increased the ultimate compressive strength by 18.2%, whereas two transversal layers in addition to one longitudinal gfrp layer increased the ultimate compressive strength by 14.9%. f. a. elshazly et al, frattura ed integrità strutturale, 55 (2021) 1-19; doi: 10.3221/igf-esis.55.01 15 (a) (b) (c) (d) figure 10: axial load-axial shortening curves of specimens strengthened with various number and orientation of gfrp sheets; (a) ru5hl-g cfst, (b) ru15-hl-g cfst, (c) ru5-vl-g cfst and (d) ru15-vl-g cfst. the increase in the ultimate capacity of the columns was accompanied with contra verse effect on the column ductility, as shown in fig. 11. adding one longitudinal layer to the transversal layer increased the ductility index by 30.5% while using two transversal layers increased the ductility index by 68.3%. using two transversal layers in addition to one longitudinal layer increased the ductility index by 56.1% and using three transversal layers increased the ductility index by 46.3% in comparison with using only one transversal layer as shown in fig. 11. using of two transversal layers was the most effective in enhancing the ductile behavior. the ductility index decreased with the increase in number of strengthening layers more than two transversal layers. similar behaviour with slightly different enhancement percentages were noticed in specimens with 15% ruc, as illustrated in fig. 11. (a) (b) figure 11: ductility index for specimens strengthened with various number and orientation of frp sheets; (a) ruc 5%, (b) ruc 15%. carbon fiber reinforced polymer (cfrp) sheets cfrp sheets had a higher impact on the load carrying capacity of rucfst columns than gfrp sheets. the increase in the ultimate compressive strength of the studied columns with 5% rubber replacement and horizontal deficiency was about 15% and 30% when using two and three transversal cfrp layers, respectively, in comparison with the column strengthened with one transversal cfrp layer. the orientation of the layers was effective in enhancing the ductility of the columns. however, the increase in the load carrying capacity was not as high as when using the same number of cfrp layers in the transverse direction. using one transversal layer in addition to one longitudinal cfrp layer increased the ultimate f. a. elshazly et al, frattura ed integrità strutturale, 55 (2021) 1-19; doi: 10.3221/igf-esis.55.01 16 compressive strength by only 6.2%. while using two transversal layers in addition to one longitudinal cfrp layer increased the ultimate compressive strength by 22.4%. the same attitude was noticed in columns with 15% rubber replacement, as shown in fig. 12. the increase in ultimate compressive strength in columns wrapped with two and three layers of cfrp sheets reached 18% and 41%, respectively. using one longitudinal layer in addition to one and two transversal layers increased the ultimate compressive strength by 9.7% and 30.8%, respectively. (a) (b) (c) (d) figure 12: axial load-axial shortening curves of specimens strengthened with various number and orientation of cfrp sheets; (a) ru5hl-c cfst, (b) ru15-hl-c cfst, (c) ru5-vl-c cfst and (d) ru15-vl-c cfst. rucfst columns with vertical deficiency were strengthened with the aforementioned five patterns as well. using three transversal cfrp layers increased the ultimate compressive strength by 9.4% and 5.2%, respectively in columns with 5% and 15% rubber content. however, using the same number of cfrp layer with different orientations; two transverse layers and one longitudinal layer; resulted in increase the strength enhancement by 12% and 14.5%, respectively, as shown in fig. 12. this shows that existence of longitudinal layer in addition to transversal layers in strengthening was more effective than using only transversal layers with the same number of layers in specimens with vertical deficiency. this might be because of the effectiveness of longitudinal layer in resisting the local outward buckling at the deficiency location. moreover, it was observed that the existence of longitudinal layer led to an increase in ductility index which decreased with the increase in number of transversal layers added to one longitudinal layer. using two and three transversal layers led to a decrease in the ductility index in comparison with using only one transversal layer as shown in fig. 11. this decrease might be because of high confinement provided by the cfrp sheets. the highest ductility was achieved in specimen with one transversal layer in addition to one longitudinal cfrp layer. conclusion three-dimensional nonlinear finite element model of non-deficient and transversally/longitudinally deficient short rubberized concrete filled steel tubular (rucfst) columns was proposed in this paper. the model was verified against some available experimental results. to restore the loss in the column bearing capacity, the columns were strengthened with two types of frp sheets under axial compressive load. five different strengthening schemes were a f. a. elshazly et al, frattura ed integrità strutturale, 55 (2021) 1-19; doi: 10.3221/igf-esis.55.01 17 analyzed. increasing the steel tube’s thickness was considered as well. based on the results of the study, the following conclusions can be drawn:  increasing rubber content in the deficient rucfst columns led to an increase in the ductile behavior and a decrease in ultimate bearing capacity.  in bare rucfst columns, local buckling at the deficiency corners caused noticeable decrease in the column strength and premature failure. this was controlled by the bonded layers of the frp sheets wrapped around the columns.  the axial capacity of the rucfst columns increased by decreasing the diameter/thickness ratio of the steel tube. however, no significant enhancement was noticed in the ductile behavior of the columns due to this change in the d/t ratio.  increasing gfrp layers had its effect on columns behaviour. in case of horizontally and vertically deficient specimens, ultimate load increased with the increase of gfrp layers. using three transversal gfrp layers increased the ultimate load up to 21.16% and 18.2%, respectively, compared to using one transversal layer. for horizontally and vertically deficient rucfst columns, using two transversal layers achieved the highest ductile behaviour with increase up to 49.5% and 68.3%, respectively, compared to using one transversal layer.  significant higher increase in the ultimate load capacity was recorded in case of cfrp strengthening. horizontally deficient rucfst columns showed enhancement up to 41%. strengthening vertical deficiency showed lower enhancement reached 14.5%.  using two transversal gfrp layers achieved the highest ductility index with good increase in ultimate bearing capacity in case of transversally and longitudinally deficient specimens. using one transversal layer in addition to one longitudinal cfrp was the best strengthening pattern using cfrp and achieved the highest ductile behaviour with good enhancement in ultimate load.  strengthening deficient rucfst columns using gfrp sheets showed better ductility but lower bearing capacity compared to those strengthened using cfrp sheets. for all strengthened rucfst columns under axial load, it was remarkably observed that strengthening the whole deficient columns with frp sheets enhanced the ductility of the columns compared with the non-strengthened columns. references [1] schneider, s.p., 1998. axially loaded concrete-filled steel tubes, j. of structural engineering, 124(10), pp. 1125-1138. doi: 10.1061/(asce)0733-9445(1998)124:10(1125). [2] sundarraja, m. c. and prabhu, g. g. (2012). experimental study on cfst members strengthened by cfrp composites under compression, j. constructional steel research, 72, pp. 75-83. doi: 10.1016/j.jcsr.2011.10.014. [3] lu, y., li, n. and li, s. (2014). behavior of frp-confined concrete-filled steel tube columns, polymers, 6(5), pp. 13331349. doi: 10.3390/polym6051333. [4] shen, q., wang, j., wang, j. and ding, z. (2019). axial compressive performance of circular cfst columns partially wrapped by carbon frp, j. constructional steel research, 155, pp. 90-106. doi: 10.1016/j.jcsr.2018.12.017. [5] prabhu, g.g. and sundarraja, m.c., 2013. behaviour of concrete filled steel tubular (cfst) short columns externally reinforced using cfrp strips composite. construction and building materials, 47, pp.1362-1371. doi: 10.1016/j.conbuildmat.2013.06.038 [6] prabhu, g.g., sundarraja, m.c. and kim, y.y., 2015. compressive behavior of circular cfst columns externally reinforced using cfrp composites. thin-walled structures, 87, pp.139-148. doi: 10.1016/j.tws.2014.11.005. [7] alam, m.i., fawzia, s., zhao, x.l., remennikov, a.m., bambach, m.r. and elchalakani, m., 2017. performance and dynamic behaviour of frp strengthened cfst members subjected to lateral impact. engineering structures, 147, pp.160-176. doi: 10.1016/j.engstruct.2017.05.052. [8] deng, j., zheng, y., wang, y., liu, t. and li, h., 2017. study on axial compressive capacity of frp-confined concretefilled steel tubes and its comparisons with other composite structural systems. international journal of polymer science, 2017. doi: 10.1155/2017/6272754. [9] liu, j.p., xu, t.x., wang, y.h. and guo, y., 2018. axial behaviour of circular steel tubed concrete stub columns confined by cfrp materials. construction and building materials, 168, pp.221-231. doi: 10.1016/j.conbuildmat.2018.02.131. [10] na, l., yiyan, l., shan, l. and lan, l., 2018. slenderness effects on concrete-filled steel tube columns confined with cfrp. journal of constructional steel research, 143, pp.110-118. doi: 10.1016/j.jcsr.2017.12.014. f. a. elshazly et al, frattura ed integrità strutturale, 55 (2021) 1-19; doi: 10.3221/igf-esis.55.01 18 [11] reddy, s.v.b. and sivasankar, s., 2020. axial behaviour of corroded cfst columns wrapped with gfrp sheets— an experimental investigation. in advances in structural engineering (pp. 15-28). springer, singapore. doi: 10.1007/978-981-15-4079-0_2. [12] cao, s., wu, c. and wang, w., 2020. behavior of frp confined uhpfrc-filled steel tube columns under axial compressive loading. journal of building engineering, p.101511. doi: 10.1016/j.jobe.2020.101511 [13] tang, h., chen, j., fan, l., sun, x. and peng, c., 2020. experimental investigation of frp-confined concrete-filled stainless steel tube stub columns under axial compression. thin-walled structures, 146, p.106483. doi: 10.1016/j.tws.2019.106483 [14] ghaemdoust, m. r., narmashiri, k. and yousefi, o. (2016). structural behaviors of deficient steel shs short columns strengthened using cfrp, j. construction and building materials, 126, pp. 1002-1011. doi: 10.1016/j.conbuildmat.2016.09.099. [15] karimian, m., narmashiri, k., shahraki, m. and yousefi, o. (2017). structural behaviors of deficient steel chs short columns strengthened using cfrp, j. constructional steel research, 138, pp. 555-564. doi: 10.1016/j.jcsr.2017.07.021. [16] fawzy, h. m., mustafa, s. a. a. and elshazly, f.a. (2020). rubberized concrete properties and its structural engineering applications – an overview, j. eijest, vol. 30, 2020. [17] jiang, y., silva, a., castro, j.m. and monteiro, r., 2015. experimental assessment of the behaviour of rubberized concrete filled steel tube members. international conference on behavior of steel structures in seismic areas, shanghai, china. https://www.researchgate.net/profile/antonio_silva51/publication/303372060_experimental_assessment_of_the_ behaviour_of_rubberized_concrete_filled_steel_tube_members/links/573ee30f08ae9f741b320c17/experimentalassessment-of-the-behaviour-of-rubberized-concrete-filled-steel-tube-members.pdf [18] duarte, a. p. c., silva, b. a., silvestre, n., de brito, j., júlio, e. and castro, j. m. (2016). tests and design of short steel tubes filled with rubberised concrete, j. engineering structures, 112, pp. 274-286. doi: 10.1016/j.engstruct.2016.01.018. [19] abendeh, r., ahmad, h. s. and hunaiti, y. m. (2016). experimental studies on the behavior of concrete-filled steel tubes incorporating crumb rubber, j. constructional steel research, 122, pp. 251-260. doi: 10.1016/j.jcsr.2016.03.022. [20] elchalakani, m., hassanein, m.f., karrech, a., fawzia, s., yang, b. and patel, v.i., (2018). experimental tests and design of rubberised concrete-filled double skin circular tubular short columns. in structures, 15, pp. 196-210. doi: 10.1016/j.istruc.2018.07.004. [21] dong, m., elchalakani, m., karrech, a., hassanein, m.f., xie, t. and yang, b., 2019. behaviour and design of rubberised concrete filled steel tubes under combined loading conditions. thin-walled structures, 139, pp.24-38. doi: 10.1016/j.tws.2019.02.031. [22] ansys release 19.2 finite element analysis system, ansys inc. [23] elshazly, f. a, (2020). retrofitting of cfst columns using frp composites, msc thesis, structural engineering department, faculty of engineering, zagazig university. [24] liang, q.q. and fragomeni, s. (2009). nonlinear analysis of circular concrete-filled steel tubular short columns under axial loading, j. constructional steel research, 65 (12), pp. 2186–2196. doi: 10.1016/j.jcsr.2009.06.015. [25] liang, q.q. (2018). analysis and design of steel and composite structures, crc press. doi: 10.1201/9781315274843. [26] liang, q.q. (2011). high strength circular concrete-filled steel tubular slender beam-columns, part i: numerical analysis, j. constructional steel research, 67 (2), pp. 164–171. doi: 10.1016/j.jcsr.2010.08.006. [27] mander, j.b., priestley, m.j.n. and park, r. (1988). theoretical stress–strain model for confined concrete, j. structural engineering, 114 (8), pp. 1804–1826. doi: 10.1061/(asce)0733-9445(1988)114:8(1804). [28] tang, j., hino, s., kuroda, i. and ohta, t. (1996). modeling of stress–strain relationships for steel and concrete in concrete filled circular steel tubular columns, j. steel construction engineering, 3 (11), pp. 35–46. doi: 10.11273/jssc1994.3.11_35. [29] hu, h.t., huang, c.s., wu, m.h. and wu, y.m. (2003). nonlinear analysis of axially loaded concrete-filled tube columns with confinement effect, j. structural engineering, 129 (10), pp. 1322–1329. doi: 10.1061/(asce)0733-9445(2003)129:10(1322). [30] richart, f.e., brandtzaeg, a. and brown, r.l. (1928). a study of the failure of concrete under combined compressive stresses, bulletin 185, champaign, il: university of illinois, j. engineering experimental station. http://hdl.handle.net/2142/4277. [31] duarte, a. p. c., silva, b. a., silvestre, n., de brito, j., júlio, e. and castro, j. m. (2016). finite element modelling of short steel tubes filled with rubberized concrete. j. composite structures, 150, pp. 28-40. f. a. elshazly et al, frattura ed integrità strutturale, 55 (2021) 1-19; doi: 10.3221/igf-esis.55.01 19 doi: 10.1016/j.compstruct.2016.04.048. [32] bradford, m.a., loh, h.y. and uy, b., (2002). slenderness limits for filled circular steel tubes. j. constructional steel research, 58(2), pp. 243-252. doi: 10.1016/s0143-974x(01)00043-8. microsoft word numero 19 articolo 1.doc k. pham et alii, frattura ed integrità strutturale, 19 (2012) 5-19; doi: 10.3221/igf-esis.19.01 5 damage localization and rupture with gradient damage models k. pham université pierre et marie curie, institut jean le rond d'alembert, f75005 paris pham@lmm.jussieu.fr j.-j. marigo ecole polytechnique, laboratoire de mécanique des solides, f91128 palaiseau cedex marigo@lms.polytechnique.fr abstract. we propose a method of construction of non homogeneous solutions to the problem of traction of a bar made of an elastic-damaging material whose softening behavior is regularized by a gradient damage model. we show that, for sufficiently long bars, localization arises on sets whose length is proportional to the material internal length and with a profile which is also characteristic of the material. the rupture of the bar occurs at the center of the localization zone when the damage reaches there the critical value corresponding to the loss of rigidity of the material. the dissipated energy during all the damage process up to rupture is a quantity cg which can be expressed in terms of the material parameters. accordingly, cg can be considered as the usual surface energy density appearing in the griffith theory of brittle fracture. all these theoretical considerations are illustrated by numerical examples. keywords. damage mechanics; gradient damage models; variational methods; crack initiation. introduction t is possible to give an account of rupture of materials with damage models by the means of the localization of the damage on zones of small thickness where the strains are large and the stresses small. however the choice of the type of damage model is essential to obtain valuable results. thus, local models of damage are suited for hardening behavior but cease to give meaningful responses for softening behavior. indeed, in this latter case the boundary-value problem is mathematically ill-posed (benallal et al. [1], lasry and belytschko, [5]) in the sense that it admits an infinite number of linearly independent solutions. in particular damage can concentrate on arbitrarily small zones and thus failure arises in the material without dissipation energy. furthermore, numerical simulation with local models via finite element method are strongly mesh sensitive. two main regularization techniques exist to avoid these pathological localizations, namely the integral (pijaudier-cabot and bažant [13]) or the gradient (pham and marigo[10, 11]) damage approaches, see also [6] for an overview. both consist in introducing non local terms in the model and hence a characteristic length. we will use gradient models and derive the damage evolution problem from a variational approach based on an energetic formulation. the energetic formulations, first introduced by nguyen [9] and then justified by marigo [7, 8] by thermodynamical arguments for a large class of rate independent behavior, constitute a very promising way to treat in a unified framework the questions of bifurcation and stability of solutions to quasi-static evolution problems. francfort and marigo [4] and bourdin, francfort and marigo [3] have extended this approach to damage and fracture mechanics. considering the one-dimensional problem of a bar under traction with a particular gradient damage model, benallal and marigo [2] apply the variational formulation and emphasize the scale effects in the bifurcation and stability analysis: the instability of the homogeneous response and the localization of damage strongly depend on the ratio between the size of i http://www.gruppofrattura.it http://dx.medra.org/10.3221/igf-esis.19.01&auth=true k. pham et alii, frattura ed integrità strutturale, 19 (2012) 5-19; doi: 10.3221/igf-esis.19.01 6 the body and the internal length of the material. the goal of the present paper is to extend a part of the results (the questions of stability will no be investigated) of [2] for a large class of elastic-softening material. specifically, we propose a general method to construct localized solutions of the damage evolution problem and we study the influence of the constitutive parameters on the response. several scenarii depending on the bar length and on the material parameters enlighten the size effects induced by the non local term. the paper is structured as follows. section setting of the gamage problem is devoted to the statement of the damage evolution problem. in section non homogeneous solutions of the damage problem we describe, perform and illustrate the method of construction of localized solutions and conclude by the different scenarii of responses. the following notation are used: the prime denotes either the spatial derivative or the derivative with respect to the damage parameter, the dot the time derivative, e.g. = /  u u x , ( ) = ( ) /  e de d , = /   t . setting of the damage problem the gradient damage model e consider a one-dimensional gradient damage model in which the damage variable  is a real number growing from 0 to 1, = 0 is the undamaged state and = 1 is the full damaged state. the behavior of the material is characterized by the state function w which gives the energy density at each point x . it depends on the local strain ( )u x (u denotes the displacement and the prime stands for the spatial derivative), the local damage value ( ) x and the local gradient ( ) x of the damage field at x . specifically, we assume that w takes the following form 2 2 20 1 1 ( , , ) = ( ) ( ) 2 2          w u e u w e (1) where 0e represents the young modulus of the undamaged material, ( )e the young modulus of the material in the damage state  and ( )w can be interpreted as the density of the energy dissipated by the material during a homogeneous damage process (i.e. a process such that ( ) x = 0) where the damage variable of the material point grows from 0 to  . the last term in the right hand side of (1) is the ``non local" part of the energy which plays, as we will see later, a regularizing role by limiting the possibilities of localization of the damage field. for obvious reasons of physical dimension, it involves a material characteristic length  that will fix the size of the damage localization zone. the local model associated with the gradient model consists in setting = 0 and hence in replacing w by 0w : 2 0 1 ( , ) := ( ) ( ) 2     w u e u w (2) the qualitative properties of the (gradient or local) model, in particular its softening or hardening character, strongly depend on some properties of the stiffness function ( )  e , the dissipation function ( )  w , the compliance function ( ) = 1 / ( )   s e and their derivatives. from now on we will adopt the following hypothesis, the importance of which will appear later: hypothesis 1 (constitutive assumptions) ( )  e and ( )  w are non negative and continuously differentiable with (1) = 0e , (0) = 0w , ( ) < 0e and ( ) > 0w for all [0,1)  . moreover ( ) / ( )  w e is increasing to  while ( ) / ( )  w s is decreasing to 0 when  grows from 0 to 1. let us comment this hypothesis before to give an example 1. the interval of definition of  can always be taken as [0,1] after a change of the damage variable; 2. the condition < 0e denotes the decrease of the material stiffness when the damage grows; 3. the condition (1) = 0e ensures the total loss of stiffness when = 1 ; 4. the positivity and the monotonicity of w is natural since ( )w represents the energy dissipated during a damage process where the damage grows homogeneously in space from 0 to  ; 5. the boundedness of w is characteristic of strongly brittle materials with softening; this condition disappears in the case of weakly brittle materials with softening or in the case of brittle material with hardening; w http://www.gruppofrattura.it http://dx.medra.org/10.3221/igf-esis.19.01&auth=true k. pham et alii, frattura ed integrità strutturale, 19 (2012) 5-19; doi: 10.3221/igf-esis.19.01 7 6. the condition of monotonicity of / w e is introduced by sake of simplicity; it is unessential and denotes that the strain does not decrease when the damage grows; 7. the condition of monotonicity of / w s is essential; it denotes the softening property, i.e. the decreasing of the stress when the damage grows. 8. the condition 1 ( ) / ( ) = 0lim    w s ensures that the material cannot sustain any stress when its damage state is 1. example 1 a family of models which satisfy the assumptions above is the following one, when > > 0q p : 2 0 0 ( ) = (1 ) , ( ) = (1 (1 ) ) 2       q pc q e e w pe (3) it contains five material parameters: the sound young modulus 0 > 0e , the dimensionless parameters p and q , the critical stress > 0c and the internal length > 0 whose physical interpretation will be given in section the homogeneous solution and the issue of uniqueness. the condition > 0q is necessary and sufficient in order that ( )  e be decreasing from 0e to 0 while the condition > 0p is necessary and sufficient in order that ( )  w be increasing from 0 to a finite value. if > 0p and > 0q , then the condition >q p is necessary and sufficient in order that ( ) / ( )    w e be increasing to  while ( ) / ( )    w s is automatically decreasing to 0 . example 2 another interesting family of models which satisfy the assumptions above is the following one 2 0 0 0 (1 ) ( ) = , ( ) = ( ) (1 ) 2         q p e e w p q e (4) where 1p and 1q are two constants playing the role of constitutive parameters and 0 represents the critical stress of the material. the damage problem of a bar under traction let us consider a homogeneous bar whose natural reference configuration is the interval (0, )l and whose cross-sectional area is s . the bar is made of the nonlocal damaging material characterized by the state function w given by (1). the end = 0x of the bar is fixed, while the displacement of the end =x l is prescribed to a non negative value tu (0) = 0, ( ) = 0, 0 t t tu u l u t (5) where, in this quasi-static setting, t denotes the loading parameter or shortly the ``time", tu is the displacement field of the bar at time t . the evolution of the displacement and of the damage in the bar is obtained via a variational formulation, the main ingredients of which are recalled hereafter, see [2] for details. let ut  and  be respectively the kinematically admissible displacement fields at time t and the convex cone of admissible damage fields:      0= : (0) = 0, ( ) = , = : (0) = 0, ( ) = 0 , = : ( ) 0,   u tt v v v l u v v v l x x   (6) where 0 is the linear space associated with ut  . the precise regularity of these fields is not specified here, we will simply assume that there are at least continuous and differentiable everywhere. then with any admissible pair ( , )u at time t , we associate the total energy of the bar 2 2 2 00 0 1 1 ( , ) := ( ( ), ( ), ( )) = ( ( )) ( ) ( ( )) ( ) 2 2                 l l u w u x x x sdx e x su x w x s e s x dx (7) for a given initial damage field 0 , the damage evolution problem reads as: for each > 0t find ( , )t tu in ut  such that for all ( ) ( , ) , '( , )( , ) 0        t t t tu tv u v u   (8) http://www.gruppofrattura.it http://dx.medra.org/10.3221/igf-esis.19.01&auth=true k. pham et alii, frattura ed integrità strutturale, 19 (2012) 5-19; doi: 10.3221/igf-esis.19.01 8 with the initial condition 00 ( ) = ( ) x x . in (8), '( , )( , ) u v denotes the derivative of  at ( , )u in the direction ( , )v and is given by 2 200 1 '( , )( , ) = ( ) ( ) ( ) 2                           l u v e suv e su w s e s dx the set of admissible displacement rates u can be identified with ( )u t , while the set of admissible damage rates  can be identified with  because the damage can only increase for irreversibility reasons. inserting in (8) = t and = tv u w with 0w  , we obtain the variational formulation of the equilibrium of the bar, 00 ( ( )) ( ) ( ) = 0,     l t te x u x w x dx w  (9) from (9), we deduce that the stress along the bar is homogeneous and is only a function of time = 0, = ( ( )) ( ), (0, )     t t t te x u x x l (10) dividing (10) by ( )te , integrating over (0, )l and using boundary conditions (5), we find 0 ( ( )) =  l t t ts x dx u (11) the damage problem is obtained after inserting (9)-(11) into (8). that leads to the variational inequality governing the evolution of the damage 2 200 0 0 ( ) 2 ( ) 2 0                l l l t t t ts dx w dx e dx (12) where the inequality must hold for all   and becomes an equality when = t . after an integration by parts and using classical tools of the calculus of variations, we find the strong formulation for the damage evolution problem: for (almost) all 0t , irreversibility condition: 0 t (13) damage criterion: 2 20( ) 2 ( ) 2 0        t t t ts w e (14) loading/unloading condition: 2 20( ( ) 2 ( ) 2 ) = 0         t t t t ts w e (15) remark 1 we can deduce also from the variational approach natural boundary conditions and regularity properties for the damage field. in particular, we obtain that  t must be continuous everywhere. as boundary conditions at = 0x and =x l we will simply take (0) = ( ) = 0  t t l although the more general ones induced by the variational principle correspond to a combination of inequalities and equalities like (14)-(15). these regularity properties of the damage field (and consequently the boundary conditions) hold only for the gradient model ( 0 ) and disappear for the local model ( = 0 ). as long as the regularity in time is concerned, we will only consider evolution such that  tt is at least continuous. in terms of energy, we have the following property property 1 (balance of energy) let us assume that the bar is undamaged and unstretched at time 0, i.e. 0 = 0 and 0 = 0u . by definition, the work done by the external loads up to time t is given by 0 ( ) =   t e s st u ds (16) the total dissipated energy in the bar during the damage process up to time t is given by 2 20 0 0 1 ( ) = ( ) ( ( )) 2     l l d t tt e x dx w x dx (17) while the elastic energy which remains stored in the bar at time t is equal to http://www.gruppofrattura.it http://dx.medra.org/10.3221/igf-esis.19.01&auth=true k. pham et alii, frattura ed integrità strutturale, 19 (2012) 5-19; doi: 10.3221/igf-esis.19.01 9 2 0 ( ) = ( ( )) . 2   l t e tt s x dx (18) by virtue of the conditions (13)--(15) that the fields have to satisfy, the following balance of energy holds true at each time: ( ) = ( ) ( )e e dt t t   proof. by virtue of the equilibrium condition and the definition of the elastic energy, the work done by the external load can read as  0 0 0( ) = ( ( )) ( ( )) ( )         t l l e s s s s s st s x dx s x x dx ds 2 0 0 0 = ( ) ( ( )) ( ) 2       t t l s e s ss ds s x x dxds using the initial condition and the consistency condition in the bulk, one gets 2 00 0 0 0 ( ) = ( ) ( )          t l t l e e s s s st t w dxds e dxds  2 20 00 0 0 0 = ( ) ( ) ' ( ( ) ( ) (0) (0))                  l t l t e t s s s s s st w dx e dxds e l l ds using once more the initial condition and the consistency condition at the boundary, we obtain the desired equality. the homogeneous solution and the issue of uniqueness if we assume that the bar is undamaged at = 0t , i.e. if 0 ( ) = 0 x for all x , then it is easy to check that the damage evolution problem admits the so-called homogeneous solution where t depends on t but not on x . let us construct this particular solution in the case where the prescribed displacement is monotonically increasing, i.e. when =tu tl . from (11), we get = ( ) t te t . inserting this relation into (14) and (15) leads to 2 2( ) ( ) , = 0 2 ( ) 2 ( )               t t t t t w wt t e e (19) since 0 = 0 , t remains equal to 0 as long as 0 = 2 (0) / (0)   t w e . that corresponds to the elastic phase. for 0> t , since / w e is increasing by virtue of hypothesis 1, the first relation of (19) must be an equality. therefore t is given by 1 2 = 2             t w t e and grows from 0 to 1 when t grows from 0 to  . during this damaging phase, the stress  t is given by 2 ( ) = ( )      t t t w s since / w s is decreasing to 0 by virtue of hypothesis 1,  t decreases to 0 when t grows from 0 to  . this last property corresponds to the softening character of the damage model. note that  t tends only asymptotically to 0, what means that an infinite displacement is necessary to break the bar in the case of a homogeneous response. in terms of energy, the dissipated energy during the damage process is given by ( ) = ( )d tt w l hence, it is proportional to the length of the bar. the total energy spent to obtain a full damaged state is equal to (1)w l and hence is finite by virtue of hypothesis 1. http://www.gruppofrattura.it http://dx.medra.org/10.3221/igf-esis.19.01&auth=true k. pham et alii, frattura ed integrità strutturale, 19 (2012) 5-19; doi: 10.3221/igf-esis.19.01 10 the non local term has no influence on the homogeneous solution which is solution both for the gradient and the local damage models. let us now examine the issue of the uniqueness of the response. in the case of the local damage model, it is well known that the evolution problem admits an infinite number of solution. does the gradient term force the uniqueness? the answer to this fundamental question essentially depends on the ratio / l of the internal length with the bar length, as it is proved in [1] in the case = 2p , = 0q of example 2. specifically it was shown that the homogeneous solution is the unique solution of the evolution problem when 0 0  l e , i.e. when the bar is small enough, while there exists an infinite number of solutions otherwise. however, when the bar is long enough, although the number of solutions is infinite, the fundamental difference between the local and the gradient models is that the length of the damaged zone is bounded from below for the gradient model while it can be chosen arbitrarily small for the local model. the main goal of the next section is to extend these results for a large class of gradient models and to study the properties of non homogeneous solutions. let us remark that any solution of the evolution problem contains the same elastic phase, i.e. = 0t as long as 0t . therefore, localizations can appear only when 0> t . example 3 for the family of models of example 1, the homogeneous response is given by 0 0 0 2 < = 0 < = = = 1                                               c c c c p q p q p q c c c c c e if if e e and if if since > > 0q p , the stress is a decreasing function of the strain in the damaging phase what corresponds to a property of softening. for a given > 0p , the exponent of the power law goes from  to 1 when q goes from p to  . the area under the curve, i.e. the energy dissipated during the full process of homogeneous damage, is finite what corresponds to a strongly brittle behavior, see [12]. in the limit case where =p q , the damage evolves while the strain remains constant and equal to c . that corresponds to a perfectly brittle behavior, see fig. 1. in the limit case where = 0p or = q , the stress-strain curve is an arc of hyperbola in its softening part. the area under the curve, i.e. the energy dissipated during the full process of homogeneous damage, is infinite. this change of the boundedness of the dissipated energy marks the transition between a strongly brittle and a weakly brittle behavior, see [12]. figure 1: left: the stress-strain response (black curve) associated with the homogeneous evolution in the case of the models of example 1 with > > 0q p . the limit cases of perfectly brittle material ( =p q ) and weakly brittle material ( = 0p ) are in gray. right: graphical interpretation of the dissipated energy at the end of a homogeneous damage process. non homogeneous solutions of the damage problem the method of construction of non homogeneous solutions et us consider one solution of the evolution problem. setting l http://www.gruppofrattura.it http://dx.medra.org/10.3221/igf-esis.19.01&auth=true k. pham et alii, frattura ed integrità strutturale, 19 (2012) 5-19; doi: 10.3221/igf-esis.19.01 11 0 0 2 (0) := = (0) (0)     w e s (20) we deduce from (14), that 00   t . indeed, 0 t by virtue of (5) and (11). then, integrating (14) over (0, )l and using the boundary conditions (0) = ( ) = 0  t t l , we obtain 2 0 0 ( ( )) 2 ( ( ))     l l t t ts x dx w x dx (21) but, since / w s is a decreasing function of  by virtue of hypothesis 1 and since 0 t by virtue of the irreversibility condition, we have 202 ( ( )) ( ( )), (0, )     t tw x s x x l integrating over (0, )l and inserting the result into (21) gives 2 20 t . therefore 0 is the maximal stress that the material can sustain. the point of departure in the construction of localized damage solutions is to seek for solutions for which the equality in (14) holds only in some parts of the bar. for a given 0> t , the localized damage field will be characterized by its set =  it ti  of localization zones it where it is an open interval of [0, ]l of the form ( , ) i t i tx d x d (the independence of its length on i will be proved). in [0, ] \ tl  , the material is supposed to be sound and therefore these parts will correspond to elastic zones where = 0t . by sake of simplicity, we will not consider localization zones centered at the boundary of (0, )l , i.e. with = 0ix or =ix l . therefore, we force the damage to vanish at = 0x and =x l . the successive steps of the construction are as follows: 1. for a given t , assuming that  t is known, we determine the profile of the damage field in a localization zone; 2. for a given t , we obtain the relation between  t and tu ; 3. we check the irreversibility condition. damage profile in a localization zone since t is fixed, we omit the index t in all quantities which are time-dependent. let 0(0, )  be the supposed known stress and = ( , ) i i ix d x d be a putative localization zone. the damage field  must satisfy 2 20( ) 2 ( ) 2 = 0 .         is w e in  (22) since we assume by construction that the localization zone is matched to an elastic zone and since  and  must be continuous, see remark 1, the damage field has also to satisfy the boundary conditions ( ) = ( ) = 0.  i ix d x d (23) multiplying (22) by  and integrating with respect to x , we obtain the first integral 2 2 2 0( ) 2 ( ) =       is w e c in  (24) where c is a constant. using (23) and hypothesis 1, we get 2 0= /c e and (24) can read as 2 2( ) = ( , ( ))   ix h x in  (25) with 20 0 1 ( , ) := 2 ( ) ( ) [0,1)              e h w s for e (26) since 20 ( , ) = 2 ( ) ( )         h e w s and since, by virtue of hypothesis 1, ( ) > 0w and 2 ( ) 1 2 ( )       s w decreases from 2 201 / > 0  to  when  grows from 0 to 1, h is first increasing from 0, then decreasing to  . hence, there exists a unique positive value of  , say ( )  , where h vanishes: http://www.gruppofrattura.it http://dx.medra.org/10.3221/igf-esis.19.01&auth=true k. pham et alii, frattura ed integrità strutturale, 19 (2012) 5-19; doi: 10.3221/igf-esis.19.01 12 ( , ( )) = 0, 0 < ( ) < 1    h (27) ( )  corresponds to the maximal value of the damage (at the given time), taken at the center of the localization zone. therefore, we have obtained the property 2 (profile of a localized damage field) for a given stress (0, )  c , the damage field in an inner localized damage zone ( ( ), ( ))  i ix d x d is given by (31) while the half-length ( )d of the localized damage zone is finite, proportional to the internal length  and given by (28). the damage profile is symmetric with respect to the center ix of the localized damage zone, maximal at the center, the maximal value ( )  being given by (27). the damage profile is a continuously differentiable function of x , decreasing from ( )  at the center to 0 at the boundary of the localized damage zone. the matching with the undamaged part of the bar is smooth, the damage and the gradient of damage vanishing at the boundary of the localized damage zone, see fig. 2. figure 2: a typical damage profile in an inner localization zone and in a boundary localization zone when 0 < < c concerning the dependence of ( )  on  , we have: property 3 (the dependence on the stress of the maximal value of the damage in the localization zone.) when  decreases from 0 to 0, ( )  increases from 0 to 1. proof. indeed, let 1 2 00 < <   . since 1 1 2 2 1 20 = ( , ( )) = ( , ( )) < ( , ( ))        h h h , and, since 1( , ) < 0 h when 1( ) < < 1   , we have 1 2( ) > ( )    . hence ( )   is decreasing. since 0/ ( , ) < 0   h for > 0 , we have 0( ) = 0  . let us prove that 0 ( ) = 1lim   . let 0= ( )lim  m (the limit exists and is positive since ( )  is decreasing). if < 1m , passing to the limit in (27) when  goes to 0 gives 0 = (0, ) = 2 ( ) m mh w , a contradiction. hence = 1m . the size of the localization zone is deduced from (25) by integration. it depends also on  and is given by ( ) 0 ( ) = ( , )        d d h (28) ( )d is proportional to the internal length and is finite because the integral is convergent. (indeed, ( , ) h behaves like ( , 0)     h near = 0 and like ( , ( ))( ( ))          h near = ( )   . since ( , 0) > 0    h and ( , ( )) < 0      h , the integral is convergent.) provided that 2 ( )l d , it is really possible to insert a localization zone of size 2 ( )d inside the bar. concerning the dependence of ( )d on  , we obtain the following fundamental property the proof of which is not given here (it is based on a careful study of the behavior of the integral giving ( )d ): property 4 (dependence on the stress of the size of the localization zone.) the size ( )d of the localization zone varies continuously with  , 0( )d and 00 = ( )lim d d are finite and given by 1 0 0 0 02 0 0 2 ( ) = , = (0) 2 (0) 2 ( )         e e d d d s w w (29) http://www.gruppofrattura.it http://dx.medra.org/10.3221/igf-esis.19.01&auth=true k. pham et alii, frattura ed integrità strutturale, 19 (2012) 5-19; doi: 10.3221/igf-esis.19.01 13 the size function ( )  d is not necessarily decreasing. in particular 0( ) < 0 dd d if and only if the following inequality holds 2 20 0(0)( (0) 2 (0)) > (0)( (0) 2 (0))       s s w s s w (30) the position ix of the center can be chosen arbitrarily in the interval [ ( ), ( )] d l d . we finally deduce from (25) that, in the localization zone, the damage field is given by the following implicit relation between x and  : ( ) | |= ( , )        i d x x h (31) it is easy to see that the damage field is symmetric with respect to the center of the localization zone, decreasing continuously from ( )  at the center to 0 at the boundary. remark 2 the size of the localization zone and the profile of the damage field inside depends only on  . since  is a global quantity, all the localization zones have the same size and the same profile at a given time. the maximal number of localization zones that can exist at a given time depends on the length of the bar: the longer the bar, the greater the maximal number of localization zones. example 4 in the case of the family of models introduced in example 2 with 1q and 1p the size of the localization zone at 0=  or 0 are given by 0 0 2 00 2 2 ( ) = , = ( )         d d p qp q q p the necessary condition (30) of growing of the localization zone when the stress decreases reads as 2 2( ) > ( ) ( 2)   q p q p q p . it is in particular satisfied for = 2q and 4p , but it is never satisfied when 1q and 1 2 p . figure 3: left: the damage profile for a given  and its evolution for different  in the case of the model of example 2 with = 2q and = 4p (the lower  , the higher  ). right: we check numerically that ( )  d is decreasing. rupture of the bar when = 0 our previous construction of the damage profile is no more valid. indeed, the differential system (22)-(23) becomes 20> 0 ( ) = 0 , = = 0        i iand w e in on  integrating the differential equation over i and using the boundary conditions leads to ( ) = 0 i w dx  what is impossible by hypothesis 1. as this is suggested by the fact that the maximal value of the damage tends to 1 when  goes to 0, one has to search a profile such that the damage field takes the value 1 at the center of the zone. since some http://www.gruppofrattura.it http://dx.medra.org/10.3221/igf-esis.19.01&auth=true k. pham et alii, frattura ed integrità strutturale, 19 (2012) 5-19; doi: 10.3221/igf-esis.19.01 14 quantities like the compliance function ( )  s and its derivatives become infinite when  goes to 1, the regularity of the damage field is lost and ( ) x is no more defined at = ix x but undergoes a jump discontinuity. so the differential system reads now as 20> 0 ( ) = 0 \ , ( ) = 1, = = 0         i i i iand w e in x x on  multiplying by  the differential equation valid on each half-zone and taking into account the boundary conditions at the ends, one still obtains a first integral 2 20 ( ) = 2 ( ( )) e x w x in \i ix . since > 0 in i , denoting by 0d the halflength of the localization zone, one necessarily has 0 0 0 0 2 ( ) ( , ) = 2 ( ) ( , )          i i i i s w in x d x s w in x x d since ( ) = 1 ix , the jump of  at ix is equal to 02 2 (1) / s w . by integration we obtain the damage profile and the half-length of the localization zone 1 1 0 0 0 0 | |= , = 2 ( ) 2 ( )        i d d x x d s w s w (32) one can remark that this solution can be obtained formally by taking = 0 and (0) = 1 in (28)-(31). we have proved the following property 5 (rupture of the bar at the center of a localization zone) at the end of the damage process, when the stress has decreased to 0, the damage takes the critical value 1 at the center of the localized damage zone. the damage profile and the half length 0d of the damage zone are then given by (32). the profile is still symmetric and continuously decreasing to 0 from the center to the boundary, but its slope is discontinuous at the center. example 5 in the cases of the family of models of example 1, the half-length of the damage zone and the amplitude of the damage profile when the bar breaks are given by 1 1 0 0 0 | |= , = 1 1            i p p c c p dv p dv x x d q qv v for = 1p , the profile is made of two symmetric arcs of parabola: 2 0 0 | | 2 ( ) = 1 , =        i c x x x d d q for = 2p , the profile is made of two symmetric arcs of sinusoid: 0 0 | | ( ) = 1 sin , = 2 2       i c x x x d d q the greater p , the greater the size of the damage zone and the damage field, see fig. 4. dissipated energy in a localization zone by virtue of property 1 and (17) the energy dissipated in an inner localization zone when the stress is  is given by ( ) 2 2 0( ) 1 ( ) = ( ) ( ( )) 2               x di d x di e x w x dx by symmetry, it is twice the dissipated energy in a half-zone. using the change of variable x and (25), we obtain 2 ( ) 0 0 2 0 0 0 4 ( ) ( ( ) ) ( ) = 2 ( ) ( ( ) )               d w s s d s w s s s  (33) http://www.gruppofrattura.it http://dx.medra.org/10.3221/igf-esis.19.01&auth=true k. pham et alii, frattura ed integrità strutturale, 19 (2012) 5-19; doi: 10.3221/igf-esis.19.01 15 figure 4: damage profile in the localization zone when the bar breaks, for = 4q and different values of the parameter p ( = 1 / 2,1, 2, 4p ) in the family of brittle materials of example 1. figure 5: the damage profile for a given t and its evolution with t by assuming that  tt is decreasing in the case of the model of example 1 with = 2p and = 4q . the rupture occurs when = 0 t and ( ) = 1  t . we check numerically that ( )  d is decreasing. it is easy to check that ( )  d is decreasing with ( ) = 0d c while (0)d represents the dissipated energy in a localization zone during to the process of damage up to the rupture. let us call fracture energy and denote by cg this energy by reference to the griffith surface energy density in griffith theory of fracture. since (0) = 1 , we have property 6 (fracture energy) the dissipated energy in an inner localization zone during the damage process up to the rupture is a material constant cg which is given by 1 00 = 8 ( ) cg e w d (34) because of the lack of constraint on the damage at the boundary, the dissipated energy in a boundary localization zone up to the rupture is / 2cg . example 6 in the case of the family of strongly materials of example 1 the fracture energy is given by 1 0 = 2 , = 1  pc p c p q g j j v dv p (35) thus cg is proportional to the product of the critical stress by the internal length, the coefficient of proportionality depending on the exponents p and q . the force-displacement relation the time is fixed and we still omit the index t . let u be the prescribed displacement, = / u l the average strain and  the stress in the bar which contains 1n localization zones. using (11), recalling that = 0 outside the localization zones and that all localization zones have the same size 2 ( )d and the same profile, we get http://www.gruppofrattura.it http://dx.medra.org/10.3221/igf-esis.19.01&auth=true k. pham et alii, frattura ed integrità strutturale, 19 (2012) 5-19; doi: 10.3221/igf-esis.19.01 16 0 1 0 2 ( ) = ( ( )) = ( ( ))              l l nd u s x dx n s x dx e the integral 1 ( ( )) s x dx can be transformed into an integral over the range of  by using (25). indeed, by symmetry it can reads as 1 ( )1 2 ( ( ))    x x d s x dx . making the change of variables x , since = ( , )  d h dx , we obtain ( ) 01 ( ) ( ( )) = 2 ( , )          s d s x dx h recalling (28), we finally obtain the overall stress-strain relation 1= ( ) ( )     e dn l (36) with ( ) 1 0 0 0 1 ( ) = , ( ) = 2 ( ) ( , )                  e d d s e e h (37) remark 3 for a given n , (36) gives the average strain in term of the stress. that corresponds to a curve in the   plane, parametrized by  varying from 0 to 0 . the curve = 0n is the segment corresponding to the elastic phase. thus  can be decomposed into two terms, one associated with the elastic part of bar, the other with the localization zones. note that 1 ( )   d depends neither on the length of the bar nor on the internal length of the material. the properties of monotonicity of the function 1 ( )   d play an important role on the presence of snap-backs in the overall response of the bar, see the next subsection. since 1 0( ) = 0  d and since 1 ( ) > 0  d for 0<  , 1 ( )   d is necessarily decreasing in the neighborhood of 0 . we have in particular property 7 (behaviour of 1 ( )   d near 0 ). 1 0( ) = 0  d and 5/ 2 2 2 1/ 2 0 01 0 2 3/ 2 0 2 (0) ( ) = ( (0) 2 (0))          d s ed d s w (38) on the other hand, the behavior of 1 ( )  d when 0/  is small is very sensitive to the constitutive parameters as it is shown in the following example and on fig. 6. figure 6: graph of the function 1 ( )   d giving the contribution of a localized zone on the overall strain in the case of the model of example 2 with = 4p and different values of q (dashed: = 1q , thick: = 2q , thin: = 3q ). example 7 in the case of the family of models of example 2, we have http://www.gruppofrattura.it http://dx.medra.org/10.3221/igf-esis.19.01&auth=true k. pham et alii, frattura ed integrità strutturale, 19 (2012) 5-19; doi: 10.3221/igf-esis.19.01 17 5/ 2 2 / 21 0 0 12 3/ 2 0 0 < 2 2 ( ) ( ) = , ( ) = 2 = 2lim (( ) ) > 2                     d d p if q d p q if q d p q q p if q (39) consequently, when 2q , the overall strain remains finite when the stress goes to 0, contrary to the homogeneous response where the strain becomes infinite. checking of the irreversibility it remains to check that the localized damage fields that we have constructed at different values of  leads to an evolution in time which satisfies the irreversibility condition 0  . let us reintroduce the time and the index t in the notation. since the center of the localization zone is fixed, the condition of irreversibility is satisfied only if ( ) = ( )t t it x   is not decreasing. since ( )   is decreasing, it is possible only if tt  is not increasing. since ( , ( )) = 0t i i tx x d  and since ( ) > 0t x for | |< ( )i tx x d  by construction, the condition of irreversibility is satisfied only if ( )tt d  is not decreasing. that requires that ( )d  is not increasing, condition which is not automatically satisfied by the damage model, see example 4. when this condition is not satisfied, our construction of the localized solution is no more valid. we must consider an evolution of the damage where a part of the localization zone is unloaded and reenters in a non damaging phase, the size of the still damaging part decreasing with time. to avoid such a situation we make the following hypothesis hypothesis 2 we assume that ( )e  and ( )w  are such that ( )d  is decreasing. note that this hypothesis is satisfied in the class of models of example 2 when = 2q and 4p  . under this condition, it is possible to obtain the following property property 8 under hypothesis 2, in order that tt  given by (31) in a localization zone (and equal to 0 otherwise) is not decreasing it is necessary and sufficient that tt  is not increasing. proof. we know that it is necessary, it remains to prove that it is sufficient. let us assume that tt  is not increasing. then ( )tt   and ( )tt d  are not decreasing. let 1 2<t t and x be such that 1| | ( )i tx x d   . it is sufficient to prove that 2 12 1 := ( ) ( ) =:t tx x    . owing to (31), since h is a decreasing function of  and since 2 1t t  , we have 2 1 2 2 1 0 0 1 2 1 1 0 ( ) ( ) = ( , ) ( , ) ( , ) t t t t t d d d d d h h h                         hence 2 1  . by virtue of this last property, our construction of a non homogeneous solution is valid provided that the bar is sufficiently long so that a localization zone can appear and grow without reaching the boundary. since the size of the localization zone increases with t , that leads to the inequality 02l nd . owing to (29), that gives the following lower bound for l : 1 0 00 2 := > 2 ( ) ( ) m e l n d nl nd w      (40) remark 4 under hypotheses 1 and 2, we have really obtained a damage evolution tt  which satisfies the evolution problem (13)--(15) if the bar is long enough and if we can control the loading in such a manner that the stress is continuously decreasing. but the continuity of tt  is not automatically ensured as we show in the next subsection. size effects and the different scenarii let us consider a loading process where =tu tl , i.e. such that the displacement of the end =x l is monotonically increasing. consequently t corresponds to the average strain of the bar, = t , and (36) reads now 1 0 = ( )dt tt n e l     http://www.gruppofrattura.it http://dx.medra.org/10.3221/igf-esis.19.01&auth=true k. pham et alii, frattura ed integrità strutturale, 19 (2012) 5-19; doi: 10.3221/igf-esis.19.01 18 it remains to study under which condition this relation between t and  is invertible. in other words, we have to find when the overall curve  -- does not contain snap-backs. specifically, in order that there is no snap-back, we must have / ( ) 0,d d     . by virtue of (36), that gives an upper bound for l : 10 (0, ]0 ( ) :=inf d m d l n e nl d             (41) of course, this condition is never satisfied when 1 ( ) d   is not decreasing. (for example, in the case of the family of models of example 2, it is never satisfied if < 2q , cf example 7.) depending on the properties of the model, the length of the bar and the number of localization zones, we can obtain different scenarii. let us consider only the situation with one localization zone ( = 1n ), to simplify the presentation. we can distinguish two cases: 1. case 0> 2 ( )m ml d l  . in such a case we have three situations (a) for very short bars, i.e. 02 ( )l d  , no solution with localization is possible. the homogeneous solution is the unique solution; (b) for short bars, i.e. 02 ( ) < md l l  , a solution with localization is possible just after the elastic phase, but the localization zone will progressively cover all the bar and a snap-back is possible; (c) for long bars, i.e. > ml l , a solution with localization is possible, but it is necessarily discontinuous in time because of the presence of a snap-back in the overall stress-strain response. 2. case <m ml l . we have then four possibilities, the first two (a) and (b) are the same as before (a) for intermediate bars, i.e. <m ml l l , a continuous solution with localization is possible, the damaged zone does not reach the boundary, there is no snap-back; (b) for long bars, i.e. > ml l , a solution with localization is possible, but it is necessarily discontinuous in time because of the presence of a snap-back. example 8 in the case of the family of models of example 2, if < 2q , then < 0ml . it is not possible to find a non homogeneous solution without snap-back. if = 2q and = 4p , then 0 0 4 72 = < = 6 17 17 m ml l      . therefore, for bars with an intermediate length we can find a continuous in time localized solution, cf fig. 7 (left), while for long bars a localized solution is necessarily discontinuous in time just after the elastic phase, cf fig. 7 (right). figure 7: overall stress-strain relations for a law of example 2 with = 4p and = 2q (thin curve=homogeneous response; thick curve=localized response). left: for a bar of intermediate length; right: for a long bar. conclusion and perspectives e have proposed a method of construction of non homogeneous solutions for the one-dimensional damage evolution problem of a bar under traction. we have shown that the properties of such a localized solution is very sensitive to the parameters of the model. this strong dependence could be very interesting from an w http://www.gruppofrattura.it http://dx.medra.org/10.3221/igf-esis.19.01&auth=true k. pham et alii, frattura ed integrità strutturale, 19 (2012) 5-19; doi: 10.3221/igf-esis.19.01 19 experimental viewpoint to identify the right law. from a theoretical viewpoint, the presence of the gradient of damage in the model has a regularizing role as expected and limits the possibility of localization of the damage since the size of a localization zone is necessarily greater than a value fixed by the internal length of the material and the others parameters of the model. moreover, this non local term induces size effects in the response of the bar with in particular a necessarily discontinuous response and even a brutal onset of the damage after the elastic phase for long bars. when the bar is sufficiently long, our construction gives several solutions for the evolution problem, the number of localizations zones being only restricted by the length of the bar. we could probably construct many other solutions as it was made in [2]. this drastic lack of uniqueness that the introduction of a non local term has not removed needs to add a selection criterion. a good candidate is of course the stability criterion introduced in [2] and used to study the stability of homogeneous responses in [12]. the next challenge is to find which solutions among all those we have constructed satisfy the stability criterion. references [1] benallal, r. billardon, g. geymonat, in: c.s.i.m lecture notes on bifurcation and stability of dissipative systems, q.s. nguyen, editor, springer-verlag, (1993). [2] benallal, j.-j. marigo, modelling simul. mater. sci. eng., 15 (2007) 283. [3] bourdin, g.a. francfort, j.-j. marigo, j. elasticity, 91 (2008) 5. [4] g.a. francfort, j.-j. marigo, eur. j. mech. a/solids, 12 (1993) 149. [5] lasry, belytschko, int. j. solids structures, 24 (1988) 581. [6] lorentz, s. andrieux, int. j. solids struct., 40 (2003) 2905. [7] j.-j. marigo, nuclear engineering and design, 114 (1989) 249. [8] j.-j. marigo, in: continuum thermodynamics: the art and science of modelling material behaviour, volume 76 of solids mechanics and its applications: paul germain's anniversary, g. a. maugin, r. drouot, and f. sidoroff, editors, kluwer acad. publ., (2000). [9] q. s. nguyen, stability and nonlinear solid mechanics, wiley & son, london, (2000). [10] k. pham, j.-j. marigo, comptes rendus mécanique, 338(4) (2010) 191. [11] k. pham, j.-j. marigo, comptes rendus mécanique, 338(4) (2010) 199. [12] k. pham, j.-j. marigo, c. maurini, j. mech. phys. solids, 59(6) (2011) 1163. [13] g. pijaudier-cabot, z. p. bažant, j. eng. mech., 113 (1987) 1512. http://www.gruppofrattura.it http://dx.medra.org/10.3221/igf-esis.19.01&auth=true shot peening processes to obtain nanocrystalline surfaces in metal alloys: abdoullah namdar et alii, frattura ed integrità strutturale, 7 (2009) 73-79; doi: 10.3221/igf-esis.07.06 73 bearing capacity of mixed soil model abdoullah namdar dos in geology, manasa gangotri, mysore university, mysore, india, 570006; sina_a_n@yahoo.com mehdi khodashenas pelkoo amirkabir university, dept of mining engineering, tehran, iran abstract. the main objective of this research is the improvement of red soil by the addition of construction materials. this method could provide a scientific way to create a soil foundation with sufficient stability against geo-technical problems or instabilities. laboratory tests have been conducted to characterize the behavior of red soil when amended with different types of gravels, soils and sand under compacted conditions with optimum moisture content (omc). safe bearing capacity of all models have been calculated to identify the best and worst soil mixed model. keywords. red soil; shear stress; soil improvement; bearing capacity introduction oil mixing to stabilize soft or loose soils is considered a fairly new technology in the united states. this technique has been applied to improve and stabilize cohesive and cohesion-less soils under static loads. successful applications include liquefaction mitigation, steel reinforced retaining walls, groundwater cutoff walls, and stabilization of contaminated soils. applications of this technology have recently expanded to settlement control of soils, slope stabilization and the formation of composite gravity structures. design for these applications requires the unconfined compressive strength, elastic modulus and shear strength of the soil and soil-cement columns must be determined or estimated. on a recent project in honolulu, hawaii, loose soils were sufficiently stabilized with a 23% treatment ratio, and at a site in lakeland, florida, a very soft and compressible clay layer was sufficiently stabilized with only a 12% treatment ratio. in slope stability applications, soil mixing improves the overall shear strength of the soil to adequately increase the factor of safety, and also the soil-cement columns can force the potential failure surface deeper. lastly, soil mixing has been applied to construct in-situ gravity structures where its composite action design assumption was confirmed with an instrumented test wall, and used in two recent commercial applications [1]. another soil-cement mixing method uses jet grouting as a technique to improve the bearing capacity of sub-base foundation. this method reduces total settlement and increases shear strength of the soil foundation [2]. soil amendment is one of the economic techniques to improve soil bearing capacity and it guarantees achievement of safe soil bearing capacity in any situation with minimum time consumption. wide ranges of soils have shown improved soil characteristics based on application of the technique of soil mixing. in this regard, laboratory testing plays a critical role in assessing soil properties. this investigation is invaluable in terms of providing recommendations concerning site improvement. several laboratory experiments are required for developing the soil-mixing model necessary for reliable field application (a rational assessment selecting soil property for improvement of soil bearing capacity should include a logical investigation in laboratory testing method for accurate interpretation of results providing feasible data in field application). the research presented is the state of-the-practice for soil foundation bearing capacity over a wide range of soil foundation improvements. s http://dx.medra.org/10.3221/igf-esis.07.06&auth=true http://www.gruppofrattura.it abdoullah namdar et alii, frattura ed integrità strutturale, 7 (2009) 73-79; doi: 10.3221/igf-esis.07.06 74 methodology and experiment he experiments are conducted by the direct shear test method, in the geo-technical engineering laboratory of s. j. college of engineeringmysore, to evaluate mixed soil characteristics. using the current experiments, several models have been developed to improve red soil (plastic soil) by mixing with sand, gravels and non-plastic soils. in this investigation liquid limit, plastic limit, wet sieve analysis, standard compaction test and direct shear test have been employed to characterize accurate behavior of models in the laboratory. calculation of the safe bearing capacity of any mixed soil is done using the terzaghi calculation method. the necessary factors to characterize soil foundation include, c, φ, moisture and unit weight of the soil, which are used to find the best safe bearing capacity of soil. materials have been used for creation of the model illustrated in table. 1. all models have an assumed depth of 1.5 m and widths of 2.5 x 2.5 ft2, that are used in calculation of safe bearing capacity. sl. no % of red soil % of sand % of gravel 4.75 mm % of gravel 2 mm % of black soil % of green soil % of dark brown soil % of yellow soil % of light brown soil 1 100 0 0 0 0 0 0 0 0 2 55 45 0 0 0 0 0 0 0 3 55 0 45 0 0 0 0 0 0 4 55 0 0 45 0 0 0 0 0 5 55 15 15 15 0 0 0 0 0 6 55 0 0 0 45 0 0 0 0 7 55 0 0 0 0 45 0 0 0 8 55 0 0 0 0 0 45 0 0 9 55 0 0 0 0 0 0 45 0 10 90 0 0 0 2 2 2 2 2 11 80 0 0 0 4 4 4 4 4 12 70 0 0 0 6 6 6 6 6 13 60 0 0 0 8 8 8 8 8 14 50 0 0 0 10 10 10 10 10 15 70 0 0 0 10 10 10 0 0 16 70 0 0 0 10 10 0 10 0 17 70 0 0 0 10 10 0 0 10 18 70 0 0 0 10 0 10 10 0 19 70 0 0 0 10 0 10 0 10 20 70 0 0 0 10 0 0 10 10 21 70 0 0 0 15 15 0 0 0 22 70 0 0 0 15 0 15 0 0 23 70 0 0 0 0 0 0 15 15 24 70 0 0 0 15 0 0 15 0 25 70 0 0 0 15 0 0 0 15 26 70 0 0 0 0 15 15 0 0 27 70 0 0 0 0 15 0 15 0 28 70 0 0 0 0 15 0 0 15 29 70 0 0 0 0 0 15 15 0 30 70 0 0 0 0 0 15 0 15 31 55 0 0 0 0 0 0 0 45 table 1: mixed soil models. for all models, real soil characteristics were considered in order to assess soil foundation improvement. it has been done by performing laboratory tests thorough the interpreting of the test results. formulas for calculation of safe bearing capacity, are the following: t http://dx.medra.org/10.3221/igf-esis.07.06&auth=true http://www.gruppofrattura.it abdoullah namdar et alii, frattura ed integrità strutturale, 7 (2009) 73-79; doi: 10.3221/igf-esis.07.06 75 qf = 1.3c nc + γd nq + 0.4 γb nγ (1) qnf = qf qnf = qf γd (2) qs =(qnf / f)+ γd (3) also nq, nc and nγ are the general bearing capacity factors and depending upon 1) depth of footing; 2) shape of footing; 3) φ, friction angle. these parameters have been used from suggestion by the terzaghi calculation method [3]. result and discussion n order to determine soil morphological characteristics, wet sieve analysis has been employed. morphology of seven soils have been used in developing models, as shown in tab. 2 and fig. 1. among all soils, red and black soils have the most linear distribution of particles. tests of liquid limit and plastic limit, indicated that black green, yellow, dark brown and light brown soils are not plastic soils, and only red soil is a plastic one. results of liquid limit and plastic limit are mentioned in tab. 3, 4 and fig. 2. red soil has liquid limit of 32.7% and plastic limit of 17.785%. red soil has been selected for evaluation of its characteristics because of its plasticity. this will allow the eventual improvement of red soil as a construction and sub soil material. table 2: result of sieve analysis of soils (cof=community passing finer). figure 1: result of soils sieve analysis. i sl. no diameter of sieve cof red soil cof sand cof dark brown soil cof yellow soil cof green soil cof light brown soil cof black soil 1 4.75 100 100 99.59 100 100 100 96.94 2 2 99.58 96 89.10 99.6 99.6 92.6 91.83 3 1 94.16 79.8 50.15 99 99.4 73 83.66 4 0.6 88.12 63.2 36.23 98.6 99 63.2 80.59 5 0.425 86.24 50.6 33.40 98.2 98.8 59.6 78.55 6 0.3 71.24 7.6 22.10 93.8 98.2 48.2 67.52 7 0.212 61.86 2.8 16.45 86.8 97.6 40.4 60.77 8 0.150 58.94 1.8 14.84 75.2 97 34.6 56.88 9 0.075 55.40 1.2 11.61 68 95.2 31.6 52.19 10 received 0 0 0 0 0 0 0 http://dx.medra.org/10.3221/igf-esis.07.06&auth=true http://www.gruppofrattura.it abdoullah namdar et alii, frattura ed integrità strutturale, 7 (2009) 73-79; doi: 10.3221/igf-esis.07.06 76 optimum moisture content (omc) in all models ranges from 9.58 to 22.69. the maximum safe bearing capacity occurs when omc is 10.72. it is shown that an increase of omc is followed a decrease in safe bearing capacity. model 3 has the best safe bearing capacity (3334.44 kn/m2). it is made up of 55% red soil and 45% gravel with a diameter of 4.75mm. model 29 has been developed from 70% red soil, 15% yellow and 15% dark brown soils and has a minimum safe bearing capacity (sbc) of 170 kn/m2. sand and gravels have the positive effect of increasing the angel of friction (φ) in all models. any model consisting of gravel has shown better unit weight (tab. 5). the proper selection and evaluation of a soil improvement technique for a particular site is neither a simple nor a single out come proposition. local conditions and judgment are integral parts in the decision making process [4]. ground improvement by soil mixing has highly variable results, and this has a nonlinear impact on reliability analyses for soil foundation supported structures [5]. it is possible to study the influence of several factors affecting the mixing process simultaneously [6]. deep soil mixing is an extremely valuable and competitive ground engineering technology if applied correctly, designed properly, and constructed efficiently [7]. the method has more engineering possibilities than many the competitive methods resulting in a great possibility for optimization of the ground improvement measure in the actual project [8]. soil mixing provides an economical, reliable way of satisfying a difficult set of technical parameters [9]. the technique has also resulted in a shorter construction time schedule [10]. in model 3 the maximum sbc is due to the combination of red soil and gravel 4.75 mm. the model shows good binding and cohesion of particles which lead to increasing the angle of friction, cohesion, unit weight and shear strength. these characteristics eventually decrease settlement, deformation and landslide of the soil foundation. binding of particles in the model is dependent on particles shape as well as level of model compatibility, omc and plasticity. plasticity in the soil implies an increase of safe bearing capacity. if a model can achieve a high level of omc, this could have less bearing capacity due to significant decreasing angle of friction in the model. red soil’s plasticity demonstrates good safe bearing capacity, while increased sbc has been shown from the addition of angular gravel. figure 2: result of liquid limit of red soil. sl. no reading number cup number weight of wet sample weight of dry sample weight of cup weight of dry soil weight of water % of water 1 16 75 39.7 35.43 23.24 12.19 4.27 35.02 2 22 41 37.6 34.11 23.89 10.22 3.49 34.14 3 28 103 34.92 32 23.4 8.6 2.92 33.85 4 33 61 37.7 33.83 22.42 11.41 3.87 33.91 5 39 1 51.14 48.24 39.11 9.13 2.9 33.76 table 3: result of liquid limit of red soil http://dx.medra.org/10.3221/igf-esis.07.06&auth=true http://www.gruppofrattura.it abdoullah namdar et alii, frattura ed integrità strutturale, 7 (2009) 73-79; doi: 10.3221/igf-esis.07.06 77 sl. no cup number weight of wet sample weight of dry sample weight of cup weight of water weight of dry soil % of water average % of water 1 86 25.75 25.2 22.68 0.46 2.61 17.62 17.785 2 7 39.55 39.11 36.66 0.44 2.45 17.95 table 4: result of liquid plastic of red soil (plastic limit of red soil is 17.785%). sl. no model no 1 optimum moisture content γ [kn/m3] φ [°] c [kn/m2] s. b. c [kn/m2] 2036.22 1926.51 3334.44 1833.97 2060.95 888.70 1026.83 427.74 718.00 1567.43 349.69 608.36 431.67 786.91 487.99 834.95 341.94 311.26 879.86 439.56 287.22 503.18 398.52 280.01 310.33 389.32 479.81 298.58 170.00 286.20 700.05 table 5: experiments results. conclusion ed soil mixed angular gravel, 4.75mm, has a positive effect on increasing cohesion, angle of friction and unit weight of soil. these characteristics could increase soil foundation stability. plasticity, morphology, compatibility and optimum moisture content are the main factors involved in the soil safe bearing capacity. proper morphology, plasticity, optimum moisture content in any soil mixed model could support stability of the soil foundation and disable forces applied to the soil mixed model. r http://dx.medra.org/10.3221/igf-esis.07.06&auth=true http://www.gruppofrattura.it abdoullah namdar et alii, frattura ed integrità strutturale, 7 (2009) 73-79; doi: 10.3221/igf-esis.07.06 78 figure 3: model no vs safe bearing capacity references [1] b. kenneth et al, “stabilization of soft soils by soil mixing”, asce (2000) 194-205. [2] saravut jaritngam, “design concept of the soil improvement for road construction on soft clay”, proceedings of the eastern asia society for transportation studies, 4 (2003) 311-322. [3] b. c. punmia, soil mechanics and foundations, madras (1988) [4] salah sadek, gabriel khoury, int. j. engng ed, 16-6 (2000) 499-508. [5] george m. filz, “load transfer, settlement, and stability of embankments founded on columns installed by deep mixing methods”, national technical university of athens school of civil engineering geotechnical department – foundation engineering laboratory, (2007). [6] s. larsson, m. dahlstrom, b. nilsson, ground improvement 9-1 (2005) 1–15. [7] donald a. bruce, an introduction to the deep soil mixing methods as used in geo-technical applications, us department transportation, federal highway administration, office of infrastructure research and development 3300 georgetown pike mclean, (2000) va 22101-2296. [8] hakan bredenberg, goran holm and bengt baltzar broms, “dry mix methods for deep soil stabilization”, taylor & francis (1999). [9] christopher r. ryan, brian h. jasperse, deep soil mixing at the jackson lake dam, asce geotechnical and construction divisions, special conference june 25-29 (1989). [10] e. w. bahner member, asce, a.m. naguib, design and construction of a deep soil mix retaining wall for the lake parkway freeway extension, http://www.geocon.net/pdf/paper39.pdf nomenclature φ [°] = friction angle c [kn/m2] = soil cohesivity omc % = optimum moisture content % sbc [kn/m2] = safe bearing capacity γ [kn/m3] = unit weight qf [kn/m2] = ultimate bearing capacity qnf [kn/m2] = net ultimate bearing capacity qs [kn/m2] = safe bearing capacity nc = general bearing capacity factor nq = general bearing capacity factor http://www.geocon.net/pdf/paper39.pdf� http://dx.medra.org/10.3221/igf-esis.07.06&auth=true http://www.gruppofrattura.it abdoullah namdar et alii, frattura ed integrità strutturale, 7 (2009) 73-79; doi: 10.3221/igf-esis.07.06 79 nγ = general bearing capacity factor b [m] = foundation width d [m] = foundation depth f = safety factor = 3 http://dx.medra.org/10.3221/igf-esis.07.06&auth=true http://www.gruppofrattura.it abstract. the main objective of this research is the improvement of red soil by the addition of construction materials. this method could provide a scientific way to create a soil foundation with sufficient stability against geo-technical problems or ... microsoft word numero_41_art_43.docx s. seitl et alii, frattura ed integrità strutturale, 41 (2017) 323-331; doi: 10.3221/igf-esis.41.43 323 focused on crack tip fields williams expansion-based approximation of the stress field in an al 2024 body with a crack from optical measurements s. seitl, l. malíková brno university of technology, faculty of civil engineering, institute of structural mechanics, veveří 331/95, 602 00 brno, czech republic and academy of sciences of the czech republic, institute of physics of materials, v. v. i., žižkova 22, 616 62 brno, czech republic seitl@ipm.cz, http://orcid.org/0000-0002-4953-4324 malikova.l@fce.vutbr.cz, http://orcid.org/0000-0001-5868-5717 j. sobek, p. frantík brno university of technology, faculty of civil engineering, institute of structural mechanics, veveří 331/95, 602 00 brno, czech republic sobek.j@fce.vutbr.cz, http://orcid.org/0000-0003-4215-1029 frantik.p@fce.vutbr.cz, p. lopez-crespo department of civil and materials engineering, university of malaga, c/dr ortiz ramos s/n, 29071 malaga, spain plopezcrespo@uma.es abstract. a study on the approximation of the stress field in the vicinity of crack tip in a compact tension specimen made from al 2024-t351 is presented. crack tip stress tensor components are expressed using the linear elastic fracture mechanics (lefm) theory in this work, more precisely via its multi-parameter formulation, i.e. by williams power series (wps). determination of coefficients of terms of this series is performed using a least squares-based regression technique known as over deterministic method (odm) for which displacements data obtained experimentally via optical measurements are taken as inputs. the stress fields reconstructed based on the displacement data obtained experimentally by means of optical measurements are verified by means of the stress field approximations derived for the normalized ct specimen via hybrid elements. keywords. crack tip fields; optical measurements; dic; williams power series; higher-order terms; stress field reconstruction; multi-parameter approximation. citation: seitl, s., malíková, l., sobek, j., frantík, p., lopez-crespo p., williams expansion-based approximation of the stress field in a al2024 body with a crack from optical measurements, frattura ed integrità strutturale, 41 (2017) 323-331. received: 28.02.2017 accepted: 03.05.2017 published: 01.07.2017 copyright: © 2017 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. s. seitl et alii, frattura ed integrità strutturale, 41 (2017) 323-331; doi: 10.3221/igf-esis.41.43 324 introduction haracterization of crack tip stresses has been an area of active research for many decades; see short state-of-art in [1, 2] presenting an over-deterministic least squares technique to evaluate the mixed-mode multi-parameter stress field by photoelasticity underlining the fact that the use of a multi-parametric representation is not just for academic curiosity but a necessity in some cases of engineering interest. this fact is also underlined by ayatollahi et al. in [3] who used displacement fields obtained from finite element analysis and provided a specific algorithm for fast determination of the unknown parameters. in [4] the digital image correlation technique (dic) was applied to study the fracture properties of a commercial niti pseudoelastic alloy. the near crack tip displacement field of a single edge specimen was measured and the stress intensity factor (sif) was estimated by using a proper fitting procedure based on the williams series expansion. the effects of higher-order terms in the williams expansion (t-stress) were analysed for different sizes of the crack tip fitting region and the results were compared with analytical predictions. the aim of the contribution is to verify the stress fields near the crack tip reconstructed based on the displacement data obtained experimentally via comparison with the stress field approximations derived for the normalized compact tension specimen from hybrid elements [5]. the displacement field in the vicinity of crack tip, which is necessary for the subsequent analysis, is measured in a compact tension (ct) specimen made from al 2024-t351. crack tip stress tensor components are expressed using the linear elastic fracture mechanics (lefm) theory in this work, more precisely via its multi-parameter formulation, i.e. by williams power series (wps). determination of coefficients of terms of this series is performed using a least squares-based regression technique known as over deterministic method (odm) for which displacements data obtained experimentally via optical measurements are taken as inputs. note that this work is only a part of the extensive ongoing research of the authors on the application of this multi-parameter approach in more advanced fracture mechanics tasks. experimental study material al 2024 and method of measurement xperiments were conducted on a ct specimens which was extracted and machined in t-l direction (crack propagation along rolling direction) from a al 2024-t351 according to astm e-647 [6]. fig. 1 illustrates the specimen geometry and dimensions. the mechanical properties of the material are summarized in tab. 1. cyclic loading was applied then with a 100 kn instron servo hydraulic testing machine. the specimen was pre-cracked under mode i load for 120,000 cycles at a frequency of 10 hz, a load ratio r = 0.1. small scale yielding conditions were met in all tests. figure 1: geometry of the compact tension (ct) specimen in accordance with astm standard [6]. w=48 mm, b=24 mm. young’s modulus yield stress uts elongation at break 73 gpa 325 mpa 470 mpa 20 % table 1: mechanical properties of al 2024-t351 aluminium alloy. c e s. seitl et alii, frattura ed integrità strutturale, 41 (2017) 323-331; doi: 10.3221/igf-esis.41.43 325 method of measurement: digital image correlation (dic) dic was used to investigate the crack tip behaviour of the ct specimen for two different crack lengths and three load levels (see tab. 2). dic provides full-field displacement information by comparing images taken before and after straining the body. each image is divided into smaller regions or interrogation windows. the cross-correlation product [7] is used to measure the similarity between interrogation windows before and after straining the body in study:      2 2 2 2 , , , , n n x y a bn n x y c u v i x y i x u y v         (1) where c is the cross-correlation product which is a function of u and v, the displacement vectors joining the centres of the two regions of interest along directions x and y respectively, ia and ib are the intensity distribution of the two digital images before and after straining the sample, respectively, and n is the number of interrogation windows into which the digital images were divided. the maximum value of the cross-correlation product (eq. 1) is the probable displacement vector for the centre of the each interrogation window in ia. the camera was placed horizontally so that the positive x coordinate matched the crack growing direction and the y coordinate matched the crack opening direction [8]. this improves and makes the post-processing of the results easier under conditions leading to non-horizontal cracks [9]. dic requires the surface to have a random pattern so that each interrogation window is unique in each image and can be located easily in the same image after it has undergone some deformation or rigid body movement. in this work, this pattern with random grey intensity distribution was obtained by scratching the sample surface with abrasive sic sand papers grades 240, 380 and 800 [10], [11] for better imaging of the crack tip [12]. an 8-bit 2452x2052 pixels ccd camera with the maximum frame rate of 12 was used for taking images and recommendations from previous analyses were followed [13]. the experimental setup was similar to the one used previously [14]. dic generated a pair of matrices, u and v, with displacement values that were combined with an analytical model to infer fracture mechanics parameters (see next section). multi-parameter fracture mechanics crack tip fields for mode i fracture problem illiams [15] derived that the crack tip stress and displacement distribution can be expressed by means of a power series. assuming a plane crack with traction-free faces in a homogeneous linear-elastic isotropic material subjected to arbitrary remote mode i loading, the stress/displacement field around the crack tip obtained by the williams eigenfunction expansion can be expressed as:       1 2 2 1 cos 1 1 cos 3 2 2 2 2 2 1 cos 1 1 cos 3 2 2 2 2 2 1 sin 1 1 sin 3 2 2 2 2 n nx n y n xy n n n n n n n n n n r a n n n n                                                                                                                  1n            (2) similarly, the displacement vector can be written as:                                                          /2 1 1 cos cos 2 2 2 2 2 2 1 sin sin 2 2 2 2 2 n n n nn n n n n u r a v n n n n (3) in eq. 2 and 3, r and θ are polar coordinates centred at the crack tip (considering the crack faces coincident with the negative x-axis),  is shear modulus defined as  = e/2(1+), where e and  are young’s modulus and poisson’s ratio; n represents the index of the term of the power expansion and  is kolosov’s constant depending on plane stress or plane strain w s. seitl et alii, frattura ed integrità strutturale, 41 (2017) 323-331; doi: 10.3221/igf-esis.41.43 326 conditions. coefficients an are functions of relative crack length  = a/w and need to be calculated numerically in most cases. the origin of the coordinates was positioned at the crack tip [16] and no crack front curvature was considered [17]. it is worth mentioning that no bulk effects were taken into account in this study [18]. the truncated form of the williams power series considering n terms of the expansion is commonly used for the stress/displacement field approximation. when the crack is subjected to mixed-mode loads [19], eq. 2 and 3 also include a shear mode component that allows the shear mode sif to be estimated [20], [21]. over-deterministic method (odm) several methods have been derived and suggested for estimation of the coefficients of the higher-order terms of the williams expansion. most of those methods (such as hybrid crack element (hce) method [22], [23], boundary collocation method (bcm) [24] or others) require advanced mathematical procedures and extensive knowledge of special crack elements or fe code. therefore, the so-called over-deterministic method (odm) has been chosen for calculation of the coefficients of the higher-order terms in this paper. this method is based on knowledge of the displacement field data (u, v) in a set of k nodes around the crack tip. these values can be obtained either numerically from finite element simulations on the cracked specimen or experimentally via optical measurements (which is the case of this paper). the (u, v) data can be then together with the nodes coordinates (r, θ) put into eq. 2. thus, a system of 2k equations arises (in 2d) and the only variables are the coefficients an. the procedure for determination of the coefficients of the higher-order terms was programmed in a commercial mathematical package wolfram mathematica [25]. the odm is thoroughly described and tested previously [3], [26], [27]. in this study, the displacements of nodes closest to the crack tip (obtained experimentally) were considered for application of the odm; the total number of nodes in the radius of 1 mm around the crack tip was approximately 60 for each configuration. crack tip fields reconstruction when the coefficients of the higher-order terms of the williams expansion are known, the crack tip stress and/or displacement field can be reconstructed by means of eq. 2 and 3, respectively. in this paper, the approximation of the principal stress 1 and von mises stress hmh is presented because these stresses are often used in fracture mechanics criteria and thus, they are important for description of the crack behaviour. following relations were used for calculation of the stress components:                2 2 1 2 2 x y x y xy (4)         2 2 2hmh 3x x y y xy (5) in order to verify the experimental data, the comparison of the crack tip stress distribution is introduced. the coefficients of the williams expansion determined via the hybrid crack elements for a normalized ct specimen were taken from the literature [5], for mixed mode see [28]. results and discussion n the first step of the verification process, the stress intensity factor (sif) values were compared. the values obtained directly from the fracture tests are compared to values calculated from the displacements measured via dic and to values obtained by bednář and knésl by means of the hybrid crack elements [5]. data from measurements on three cracked specimens are introduced. a good agreement can be observed in the results shown in tab. 2. thus, further analysis taking into account also the higherorder term (the second one) of the williams expansion can be performed. in fig. 2 to 5 the stress distribution around the crack tip is presented. particularly, the stress levels with the values of 100, 150, 200 and 250 mpa are plotted for two stress components σ1 and σhmh. the values are calculated by means of the williams expansion taking into account its one or two initial terms and the comparison between the results based on the theoretical values of the coefficients calculated by means of the hybrid elements [5] and the results based on the experimentally i s. seitl et alii, frattura ed integrità strutturale, 41 (2017) 323-331; doi: 10.3221/igf-esis.41.43 327 measured values of displacements in the specimen. the set of data for two selected specimen configurations are presented, particularly for the specimen yx9 a6_im16 and yx9 a19_im30, see for instance tab. 2 for more details. specimen fracture test optical measurements (dic) knésl & bednář [5] yx9 a6_im16: p = 3.706 kn, a = 22 mm 6.02 6.06 6.01 yx9 a19_im16: p = 3.650 kn, a = 28.62 mm 9.34 9.10 9.45 yx9 a19_im30: p = 7.060 kn, a = 28.62 mm 18.07 18.60 18.28 table 2: values of the stress intensity factors (sifs) in mpa√m for three cracked specimens obtained: from fracture tests, via odm from displacements measured optically by means of dic, by using hybrid element analysis performed by knésl and bednář. it is clearly seen from the results introduced in fig. 2 to 5, that the stress levels near the crack tip in the specimen yx9 a19_im30 (with longer crack and larger loading force) are much higher than in the specimen yx9 a6_im16 (with shorter crack and smaller loading force) as it is expected. another very important conclusion is that the one-parameter fracture mechanics concept as well as the two-parameter fracture mechanics concept can describe rather precisely the stress state near the crack tip. the comparison between the purely theoretical results [5] and results based on the experimental measurement works very well. n = 1 n = 2 a) knésl & bednář [5] b) experiment + odm figure 2: σ1 crack tip stress approximation considering one and two initial terms of the williams expansion on specimen denoted as yx9 a6_im16 (p = 3.706 kn, a = 22 mm): a) stress values calculated from the coefficients determined theoretically [5]; b) stress values calculated from the coefficients obtained by means of the odm from the experimental measurements. s. seitl et alii, frattura ed integrità strutturale, 41 (2017) 323-331; doi: 10.3221/igf-esis.41.43 328 n = 1 n = 2 a) knésl & bednář [5] b) experiment + odm figure 3: σhmh crack tip stress approximation considering one and two initial terms of the williams expansion on specimen denoted as yx9 a6_im16 (p = 3.706 kn, a = 22 mm): a) stress values calculated from the coefficients determined theoretically [5]; b) stress values calculated from the coefficients obtained by means of the odm from the experimental measurements. n = 1 n = 2 a) knésl & bednář [5] b) experiment + odm figure 4: σ1 crack tip stress approximation considering one and two initial terms of the williams expansion on specimen denoted as yx9 a19_im30 (p = 7.060 kn, a = 28.62 mm): a) stress values calculated from the coefficients determined theoretically [5]; b) stress values calculated from the coefficients obtained by means of the odm from the experimental measurements. s. seitl et alii, frattura ed integrità strutturale, 41 (2017) 323-331; doi: 10.3221/igf-esis.41.43 329 n = 1 n = 2 a) knésl & bednář [5] b) experiment + odm figure 5: σhmh crack tip stress approximation considering one and two initial terms of the williams expansion on specimen denoted as yx9 a19_im30 (p = 7.060 kn, a = 28.62 mm): a) stress values calculated from the coefficients determined theoretically [5]; b) stress values calculated from the coefficients obtained by means of the odm from the experimental measurements. conclusions n the paper, the crack tip stress distribution is investigated in an al 2024-t351 body. the standardised ct test was carried out and the displacements data measured optically by means of dic. these data were used for calculation of the coefficients of the williams expansion and the stress distribution was reconstructed. the results were compared to the theoretical values of the stress distribution determined from the williams expansion with the coefficients obtained numerically by means of the hybrid elements. a very good agreement between the both kinds of results was found out. thus, it can be concluded that the experimental measurement by means of dic enables precise results to be obtained. these can be used for further fracture mechanics analysis on other types of specimens. acknowledgements inancial support from the czech science foundation (projects no. 15-19865y and 15-07210s), from junta de andalucía through proyectos de excelencia grant reference tep-3244 and from the university of malaga through lineas emergentes of campus de excelencia international del mar (ceimar) is gratefully acknowledged. this work is dedicated to the memory of our wonderful colleague, dr. vaclav veselý, who recently passed away. references [1] stepanova, l., roslyakov, p. multi-parameter description of the crack-tip stress field: analytic determination of coefficients of crack-tip stress expansions in the vicinity of the crack tips of two finite cracks in an infinite plane medium, int. j. solids struct., 100 (2016) 11–28. [2] ramesh, k., gupta, s., kelkar, a. a., evaluation of stress field parameters in fracture mechanics by photoelasticity— i f s. seitl et alii, frattura ed integrità strutturale, 41 (2017) 323-331; doi: 10.3221/igf-esis.41.43 330 revisited, eng. fract. mech., 56(1) (1997) 25–45. [3] ayatollahi, m. r., nejati, m., an over-deterministic method for calculation of coefficients of crack tip asymptotic field from finite element analysis, fatigue fract. eng. mater. struct., 34(3) (2011) 159–176. [4] sgambitterra, e., lesci, s., maletta, c., effects of higher order terms in fracture mechanics of shape memory alloys bydigital image correlation, procedia eng., 109 (2015) 457–464. [5] knésl, z., bednář, k., two-parameter fracture mechanics: determination of parameters and their values (in czech), ipm as cr, v. v. i. brno, 1998. [6] astm e647 standard test method for measurement of fatigue crack growth rates, (2005). [7] clocksin, w. f., da fonseca, j. q., withers, p. j., torr, p. h. s., image processing issues in digital strain mapping,” in proceedings of spie, application of digital image processing xxv, 4790 (2002) 384–395. [8] mokhtarishirazabad, m., lopez-crespo, p., moreno, b., lopez-moreno, a., zanganeh, m. optical and analytical investigation of overloads in biaxial fatigue cracks, int. j. fatigue, publ. online, (2017). doi: 10.1016/j.ijfatigue.2016.12.035. [9] lopez-crespo, p., moreno, b., lopez-moreno, a., zapatero, j., study of crack orientation and fatigue life prediction in biaxial fatigue with critical plane models, eng. fract. mech., 136 (2015) 115–130. [10] lopez-crespo, p., burguete, r. l., patterson, e. a., shterenlikht, a., withers, p. j., yates, j. r., study of a crack at a fastener hole by digital image correlation, exp. mech., 49 (2009) 551–559. [11] lopez-crespo, p., shterenlikht, a., yates, j. r., patterson, e. a., withers, p. j., some experimental observations on crack closure and crack-tip plasticity, fatigue fract. eng. mater. struct., 32 (2009) 418–429. [12] lopez-crespo, p., moreno, b., lopez-moreno, a., zapatero, j., characterisation of crack-tip fields in biaxial fatigue based on high-magnification image correlation and electro-spray technique, int. j. fatigue, 71 (2015) 17–25. [13] mokhtarishirazabad, m., lopez-crespo, p., moreno, b., lopez-moreno, a., zanganeh, m., evaluation of crack-tip fields from dic data: a parametric study, int. j. fatigue, 89 (2016) 11–19. [14] lopez-crespo, p., garcia-gonzalez, a., moreno, b., lopez-moreno, a., zapatero, j., some observations on short fatigue cracks under biaxial fatigue, theor. appl. fract. mech., 80 (2015) 96–103. [15] williams, m. l., on the stress distribution at the base of a stationary crack, j. appl. mech., 24(1) (1957) 109–114. [16] zanganeh, m., lopez-crespo, p., tai, y. h., yates, j. r., locating the crack tip using displacement field data: a comparative study, strain, 49 (2013) 102–115. [17] camas, d., lopez-crespo, p., gonzalez-herrera, a., moreno, b., numerical and experimental study of the plastic zone in cracked specimens, eng. fract. mech. accept. publ., (2017). doi: 10.1016/j.engfracmech.2017.02.016 [18] lopez-crespo, p., mostafavi, m., steuwer, a., kelleher, j. f., buslaps, t., withers, p. j., characterisation of overloads in fatigue by 2d strain mapping at the surface and in the bulk, fatigue fract. eng. mater. struct., 39(8) (2016) 1040– 1048. [19] lopez-crespo, p., pommier, s., numerical analysis of crack tip plasticity and history effects under mixed mode conditions, j. solid mech. mater. eng., 2(12) (2008) 1567–1576. [20] yoneyama, s., ogawa, t., kobayashi, y., evaluating mixed-mode stress intensity factors from full-field displacement fields obtained by optical methods, eng. fract. mech., 74 (2007) 1399–1412. [21] lopez-crespo, p., shterenlikht, a., patterson, e. a., withers, p. j., yates, j. r., the stress intensity of mixed mode cracks determined by digital image correlation, j. strain anal. eng. des., 43 (2008) 769–780. [22] tong, p., pian, t.h.h., lasry, s. j., a hybrid-element approach to crack problems in plane elasticity, int. j. numer. methods eng., 7(3) (1973) 297–308. [23] karihaloo, b. l., xiao, q. z., accurate determination of the coefficients of elastic crack tip asymptotic field by a hybrid crack element with p-adaptivity, eng. fract. mech., 68(15) (2001) 1609–1630. [24] xiao, q. z., karihaloo, b. l., liu, x. y., direct determination of sif and higher order terms of mixed mode cracks by a hybrid crack element, int. j. fract., 125(3) (2004) 207–225. [25] wolfram research, inc., ed., wolfram mathematica documentation center. (2007). [26] šestáková, l., how to enhance efficiency and accuracy of the over-deterministic method used for determination of the coefficients of the higher-order terms in williams expansion, appl. mech. mater., 245 (2013) 120–125, 2013. doi: 10.4028/www.scientific.net/amm.245.120. [27] šestáková, l., veselý, v., convergence study on application of the over-deterministic method for determination of near-tip fields in a cracked plate loaded in mixed-mode, appl. mech. mater., 249–250 (2013)76–81. doi: 10.4028/www.scientific.net/amm.249-250.76: s. seitl et alii, frattura ed integrità strutturale, 41 (2017) 323-331; doi: 10.3221/igf-esis.41.43 331 [28] ševčík, m., hutař, p. náhlík, l., seitl, s., the effect of constraint on a crack path, engineering failure analysis, 29 (2013) 83–92, doi: 10.1016/j.engfailanal.2012.11.011. << /ascii85encodepages false /allowtransparency false /autopositionepsfiles true /autorotatepages /none /binding /left /calgrayprofile (dot gain 20%) /calrgbprofile (srgb iec61966-2.1) /calcmykprofile (u.s. web coated \050swop\051 v2) /srgbprofile (srgb iec61966-2.1) /cannotembedfontpolicy /error /compatibilitylevel 1.4 /compressobjects /tags /compresspages true /convertimagestoindexed true /passthroughjpegimages true /createjobticket false 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/hrv (za stvaranje adobe pdf dokumenata najpogodnijih za visokokvalitetni ispis prije tiskanja koristite ove postavke. stvoreni pdf dokumenti mogu se otvoriti acrobat i adobe reader 5.0 i kasnijim verzijama.) /hun 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/pdfxoutputintentprofileselector /documentcmyk /preserveediting true /untaggedcmykhandling /leaveuntagged /untaggedrgbhandling /usedocumentprofile /usedocumentbleed false >> ] >> setdistillerparams << /hwresolution [2400 2400] /pagesize [612.000 792.000] >> setpagedevice microsoft word numero_58_art_02_3086 r.n. da cunha et alii, frattura ed integrità strutturale, 58 (2021) 21-32; doi: 10.3221/igf-esis.58.02 21 lumped damage mechanics as a diagnosis tool of reinforced concrete structures in service: case studies of a former bridge arch and a balcony slab rafael nunes da cunha federal university of alagoas, maceió, brazil rafael.cunha@ctec.ufal.br, http://orcid.org/0000-0003-2503-6758 camila de sousa vieira laboratory of mathematical modelling in civil engineering, federal university of sergipe, são cristóvão, brazil milavieira@gmail.com, http://orcid.org/0000-0002-5371-191x david leonardo nascimento de figueiredo amorim laboratory of mathematical modelling in civil engineering, federal university of sergipe, são cristóvão, brazil federal university of alagoas, maceió, brazil davidnf@academico.ufs.br, http://orcid.org/0000-0002-9233-3114 abstract. reinforced concrete structures may need repair in order to ensure the designed durability. the assessment of the structural condition usually is made in loco, but sometimes numerical analyses are required as a low cost and effective preliminary diagnosis. lumped damage mechanics (ldm) may be used as an alternative diagnosis procedure. in ldm approaches for reinforced concrete structures, the concrete cracking in modelled by a damage variable and the reinforcement yielding is represented by plastic deformations. therefore, this paper presents ldm as a diagnosis tool to analyse actual structures. then, the procedure is applied in two case studies. the first one is a former bridge arch tested in laboratory. such bridge was deactivated after almost three decades in service and some damage were observable. the second case study deals with a reinforced concrete balcony that collapsed after fifteen years of service. in the moment of collapse, only the dead load was acting in the balcony. the results show that ldm numerical response of those structures are quite close to laboratory observations, for the former bridge arch, and to in loco measurements, for the balcony. in this sense, according to the analysed structures, ldm may be used as a diagnosis tool. keywords. lumped damage mechanics; reinforced concrete; diagnosis; bridge arch; balcony. citation: cunha, r. n., vieira, c. s., amorim, d. l. n. f., lumped damage mechanics as a diagnosis tool of reinforced concrete structures in service: case studies of a former bridge arch and a balcony slab, frattura ed integrità strutturale, 58 (2021) 21-32. received: 29.04.2021 accepted: 03.07.2021 published: 01.10.2021 copyright: © 2021 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. https://youtu.be/c0vkiqebuyg r.n. da cunha et alii, frattura ed integrità strutturale, 58 (2021) 21-32; doi: 10.3221/igf-esis.58.02 22 introduction einforced concrete (rc) structures require periodical inspection, maintenance and repairs to ensure the designed durability. inspections can identify damages that, if were not corrected, can lead to partial or total collapse of the structure. when a structure shows signs of damage it is necessary to investigate its causes, which results in a diagnosis that serves as the basis for adopting intervention measures. the assessment of structural damage may occur in loco using non-destructive methods such as visual inspection [1], acoustic emission [2] and ground penetrating radar [3], or destructive methods as explosions [4]. this analysis can also take place in laboratory, using samples of an original structure [5] or with the combination of experimental and numerical analysis, aiming to reproduce the experimental behaviour, as the stress/strain and fatigue [6] or the damage and dynamic properties [7]. other diagnosis techniques are based only on numerical analysis of the structures such as nonlinear dynamic analysis [8] or on artificial neural networks [9]. one of the most used computational method for modelling the occurrence of damage and monitoring the cracking process in reinforced concrete structures is the finite element method (fem) [10-17]. however, a disadvantage of these procedures using fem is the significant computational cost. an efficient alternative to such procedures in order to assess damage in reinforced concrete structures is the lumped damage mechanics (ldm). this theory combines the concepts of the classic damage and fracture mechanics in plastic hinges, which defines the concrete cracking as the damage variable. ldm was firstly proposed to analyse rc structures submitted to seismic loads [18-22]. later, ldm was expanded for several other conditions, as impact loads [23-25] and tunnel linings [26-28]. one of the great advantages of using ldm to evaluate damage of reinforced concrete structures is the use of parameters easily obtained by civil engineers in practice, such as cracking moment and the load conditions. in order to ensure that ldm may be applied in actual engineering problems, flórez-lópez et al. [29] defined structure integrity according to the damage level of the structural elements. for reinforced concrete elements, a damage value around 0.3 or 0.4 represents the beginning of the reinforcement yield, and a damage of approximately 0.6 means the bearing capacity of the element [29]. in the light of the foregoing, the objective of this paper is the application of ldm as a diagnosis tool of rc structures, using a former bridge arch and a balcony that suffered collapse as case studies. the first case is an arch that was removed from an actual bridge in china [13] and tested in laboratory and the second one is a collapsed balcony of an actual building in brazil [30]. then, the damage variable is used as a diagnosis tool, presenting satisfactory results for both analysed structures. figure 1: relations among variables in a structural problem. review on lumped damage mechanics for frames and arches [26-29] he variables of a structural problem can be categorised in three sets: kinematic, static and internal ones (fig 1). such variables are related by three sets of equations, which can be called as kinematic equations, equilibrium relations and constitutive law (fig 1). classic finite element analysis usually relates directly the matrix of generalised displacements {u} and matrix of generalised external forces {p}. note that the approach presented in this paper presents more matrices, defined in this section. then, considering a structure composed by frame and arch elements in a xz cartesian reference [26], such quantities are described by: r t r.n. da cunha et alii, frattura ed integrità strutturale, 58 (2021) 21-32; doi: 10.3221/igf-esis.58.02 23        1 1 1 ... ... ... t i i i j j j n n nu w u w u w u wu (1)        1 1 1 ... ... ... t u w ui wi i uj wj j un wn np p p p p p p p p p p pp (2) where u1 is the node 1 displacement parallel to the x-axis, w1 is the node 1 displacement parallel to the z-axis and θ1 is the node 1 rotation on the xz plane. analogously, pun is the applied force on node n parallel to the x-axis, pwn is the applied force on node n parallel to the z-axis and pθn is the applied moment on node n on the xz plane. the structural equilibrium is given by:          1 m t b b b p b m (3) being [b]b the transformation matrix and {m}b the generalised stresses of a finite element b, both given as follows:     ti j ib m m nm (4)                                   frame element: sin cos sin cos 0 0 0 ... 1 ... 0 ... 0 0 0 sin cos sin cos 0 0 0 ... 0 ... 1 ... 0 0 0 0 0 0 ... cos sin 0 ... cos sin 0 ... 0 0 0 1 b b b b b b b b b b b b b b b b b b b b b l l l l l l l l node node i node j node n b (5)                                                                                       arch element: 1 sin cos 0 0 0 ... 1 ... sin sin sin cos 0 0 0 ... 0 ... sin sin cos 1 sin cos 1 cos 0 0 0 ... cos sin 0 ... sin sin cos cos sin ... sin b b b b b b b b b b b b b b b b b b b b b b b b b b b b b node node i r r r r r r b                                                                                                   sin cos cos 0 ... 0 0 0 sin cos cos sin sin cos cos ... 1 ... 0 0 0 sin sin cos 1 sin cos 1 cos ... cos sin 0 ... 0 0 0 sin sin b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b r r r r r r node j node n (6) r.n. da cunha et alii, frattura ed integrità strutturale, 58 (2021) 21-32; doi: 10.3221/igf-esis.58.02 24 where mi and mj are bending moments on the nodes i and j of the element, respectively, ni is the axial force on the node i of the element, αb is the orientation of the frame element and lb its length; βb, χb and rb geometrically define the circular arch element (fig 2). note that the second member of (3) is the sum of the internal forces of each finite element. figure 2: generalised stresses and geometric definition of (a) arch and (b) frame finite elements. the kinematic relations for a finite element are given by:          bbφ b u u (7) being [b(u)]b the same transformation matrix previously presented in (5-6) considering large displacements and {φ} the matrix of generalised deformations, which is conjugated to {m} and written as:       ti j ibφ (8) where φi and φj are flexural rotations due to the bending moments mi and mj, respectively, and δi is the axial deformation related to ni. if small displacements and small deformations are assumed, (7) can be rewritten as follows:       0b bφ b u (9) being [b0] the transformation matrix for the initial condition. the elastic relations of the element are obtained by assuming the deformation equivalence hypothesis, by applying the castigliano’s theorem [26-27, 29] and considering the inelastic phenomena are concentrated at hinges located at the edges of the element (fig 3):          p bbbφ φ f d m (10) where {φp}b is the matrix of generalised plastic deformations, that accounts for reinforcement yielding, and [f(d)]b is the damaged flexibility matrix, both written as:      0 tp p pi jbφ (11)                      0 0 0 11 12 13 0 0 0 12 22 23 0 0 0 13 23 33 1 1 1 1 i b j f f f d f f f d f f f f d (12) r.n. da cunha et alii, frattura ed integrità strutturale, 58 (2021) 21-32; doi: 10.3221/igf-esis.58.02 25 being di and dj the damage variables at hinges i and j, respectively, which account for concrete cracking. the terms fij0 are described in the appendix for frame and arch elements. figure 3: lumped damage modelling for reinforced concrete members [26-29]. in order to complete the constitutive law, the evolution laws of internal variables (damage and plastic rotation) must be considered. thus, consider the complementary energy of the finite element:     1 2 t p b b w m φ φ (13) the evolution law of the damage variables are obtained throughout the griffith criterion i.e.                                       2 0 11 2 2 0 22 2 0 0 2 1 0 0 2 1 i i i i i ii i i i j j j j j jj j j j d g y d m fw g dg y d d d d g y d m fw g dg y d d d (14) where gi and gj are the damage driving moments for the hinges i and j, respectively, and y(di) and y(dj) are the cracking resistance functions [28]. the cracking resistance function for reinforced concrete elements [29] is given by:       0 ln 1 1 i i i d y d y q d (15) being y0 and q model parameters. the plastic evolution laws for each hinge of the element are given by:                                 0 0 0 0 0 10 0 0 0 0 10 0 p i i pi i ip ii i p j j j p j jp jj j f m f c k df f m f c k df (16) r.n. da cunha et alii, frattura ed integrità strutturale, 58 (2021) 21-32; doi: 10.3221/igf-esis.58.02 26 being fi and fj the yield functions for the hinges i and j, respectively, and c and k0 model parameters. note that the model parameters y0, q, c and k0 can be directly related to the classic theory of reinforced concrete structures, as presented by [20, 27-29]. case studies bridge concrete arch [13] he first case study is the failure analysis of two reinforced concrete arch ribs that were part of a 28 years old bridge in china. the geometry of the arches is described in tab. 1. the failure experiments were made in laboratory where the arches were submitted to static loads [13]. fig. 4 presents the location of the applied loads (p). span (l) height (h) radius inclined angle at arch foot cross section width (t) cross section height (h) 19.72 m 3.08 m 17.89 m 35.5° 20 cm 28 cm table 1: arch geometric parameters [13]. figure 4: lumped damage modelling for the arch tested by [13]. the loads were applied at middle (point e), at the left quarter plus 27 cm (point c) and at the right quarter of the arch (point g), which were applied in eighteen load steps. the two end sections of the arches were fixed. the reinforcement is located near the upper and lower sides of the arch cross section. three bars with 16 mm of diameter composed each layer. tab. 2 presents the elastic constants of the materials. material concrete steel elastic modulus e (gpa) 9.8 210 poisson’s ratio ν 0.17 0.27 table 2: material elastic constants [13]. due the long usage time and problems related to the removal and transportation of the arches, both of them suffered damages at the two ends (nodes a and i). moreover, at 1/8 distance of the left and right supports (nodes b and h) the arches were also damaged, when they were being dismantling in the field, resulting in two notches. it was obtained that the collapse load (pmax) was equal to 68 kn and 65 kn for the tested arches. tab. 3 presents the experimental data of the vertical displacements at the measured location, for different load ratios. t r.n. da cunha et alii, frattura ed integrità strutturale, 58 (2021) 21-32; doi: 10.3221/igf-esis.58.02 27 load p/pmax (%) vertical displacement (mm) node e 0 0 6.76 8.46 10.15 4.43 11.84 5.02 13.53 5.77 16.91 7.24 27.99 12.63 39.06 17.39 47.91 22.35 52.35 24.96 54.57 26.53 59.41 30.07 68.97 36.4 73.09 39.49 77.5 43.45 90.88 56.43 table 3: experimental data of vertical displacements for pmax = 68kn [13]. figure 5: inclined balcony slab [30]. collapse of a reinforced concrete balcony slab [30] a balcony of a fifteen years old building suddenly collapsed. the balcony structure severely cracked at the clamped end of the cantilevered slab, rotating approximately 17 degrees, but remained connected to the rest of the structure of the building, as is shown in fig. 5. the balcony floor structure is a reinforced concrete slab with 12 cm of thickness, 9.32 m long and 2.03 m wide (fig. 6). the cantilevered slab is clamped in the outer edge of the living room slab, whose thickness is 15 cm, and both are simply supported on the facade beam. the bottom of the two slabs are on the same level, so the difference in thickness between them results in a 3 cm step at the top of the cantilevered slab, located next to the beam (fig. 7). r.n. da cunha et alii, frattura ed integrità strutturale, 58 (2021) 21-32; doi: 10.3221/igf-esis.58.02 28 the visual inspection of the fractured slab showed steel bars with 9.5 mm of diameter spaced 150 mm. analysis of samples of concrete and steel bars resulted in characteristic compressive strength (fck) equal to 30 mpa and yield stress of 500 mpa, respectively. the permanent vertical loads on the slab are concrete dead load (3.0 kn/m2), weight of the bottom coating (0.4 kn/m2), weight of the laying mortar (1.0 kn/m2) and weight of the marble floor (0.56 kn/m2). these loads generate a bending moment in the clamped section equal to -10.55 knm/m. the flexural design considering only the permanent vertical loads and concrete with fck of 14 mpa, value adopted in the building design, results in a steel area equal to 3.4 cm2/m. this value is lower than the steel area actually utilized on the balcony slab, which is 4.72 cm2/m. figure 6: dimensions of the living room and the balcony in cm. figure 7: cross-section a-a of the slabs (dimensions in cm). thus, it was concluded that the accident was caused by the abrupt rectification of the steel bars of the negative reinforcement that were installed with double curvature in the form of a step, due to the rupture of the surface layer of concrete by the action of the straightened bars (fig. 8). figure 8: detail of the steel bars before the accident [30]. results bridge concrete arch [13] he arch was divided in eight finite elements, as shown in fig. 4. although a complete nonlinear analysis is possible [14-29], since the goal of this paper is to present a diagnosis of the analysed structure, a single measurement of the tested arch [13] is taken into account. then, the procedure was carried out for the step of 10.15% of the collapse t r.n. da cunha et alii, frattura ed integrità strutturale, 58 (2021) 21-32; doi: 10.3221/igf-esis.58.02 29 load i.e., experimental value of 6.902 kn, since the collapse load is 68 kn. the vertical displacement at the mid-span of the tested arch is equal to 4.43 mm. the ldm analysis reached applied load of 6.802kn (about 10% of the collapse load) and vertical displacement of 4.334mm for the initial damage values in nodes a, b, h and i equal to 0.25, 0.23, 0.22 and 0.12, respectively. compared to the experimental values, the absolute and relative displacement errors were equal to 0.096 mm and 2.16%. for the estimated initial damage values in the arch, it is possible to suggest minor repairs at nodes a, b, h and i, considering what is indicated by flórez-lópez et al. [29] (tab. 4), if the arch was not tested up to collapse and then returned to service. performance level maximum expected damage in beams maximum expected damage in columns description 1 0.30 0.10 the elements do not require any intervention after the event 2 0.40 0.30 some minor repairs may be needed 3 0.50 0.40 the element requires reparation at reasonably costs 4 0.60 0.50 the structure requires a major rehabilitation process 5 > 0.70 > 0.60 inacceptable structural behaviour table 4: performance level for damage [29]. collapse of a reinforced concrete balcony slab [30] since the acting permanent load is 4.96kn/m² during the accident, it was verified that the damage evolution law (eqn. 14) that g < y(d), i.e. the loads did not cause the damage in the clamped section. this is corroborated by comparing the cracking moment (15.73knm/m) with the acting bending moment in the clamped section (10.22knm/m). to achieve the cracking moment (15.73knm/m) and the ultimate moment (23.69 knm/m), the load in the balcony should be 7.63kn/m² and 11.5kn/m², respectively. based on that and in the conditions observed in loco, the accident occurred due to the action of the straightened bars. in the ultimate condition of the slab section, was observed that the residual thickness was approximately 2 cm, as shown in fig. 9. the simulation, considering large displacements, reached a damage value of 0.9995 and the horizontal and vertical displacement in the edge of the slab are equal to 13.57cm and 58.99cm, respectively. these values lead to an angle approximately equal to 17.30°, which confirms the in loco observations. note that the damage obtained in the analysis characterises an inacceptable structural behaviour [29] (tab. 4), denoting that almost there is no cross section at the clamped end. assuming that the damage penalises directly the inertia moment [27], the remaining thickness at the clamped end is estimated as 0.95cm, quite close to the field observations. figure 9: geometry and typical reinforcement after the accident [25-26]. r.n. da cunha et alii, frattura ed integrità strutturale, 58 (2021) 21-32; doi: 10.3221/igf-esis.58.02 30 conclusion his paper presents lumped damage mechanics (ldm) as a diagnosis tool to evaluate damage levels (concrete cracking) in reinforced concrete (rc) structures. differently from all previous studies, where ldm was used in nonlinear analyses, this paper showed that the ldm formulation can be easily applied in practical engineering problems. therewith, ldm was applied as a diagnosis tool in two different structures: a former bridge arch in china that was tested in laboratory and a rc balcony slab in brazil that collapsed after 15 years of service. for the former bridge arch, ldm response was quite close to the experimental one and then initial damage values in four different points were estimate around 0.20, concluding that minor repairs might be needed if the arch was returned to service. on the other hand, the rc slab balcony collapsed with only permanent loads where, the reinforcement straightened up due to an incorrect design. by applying ldm, it was noticed that the analysis reached large displacements as the actual balcony, with a rotation near 17º, quite close to in loco observations. the calculated damage was 0.9995, characterising collapse. also, the residual thickness is estimated near to 1.0 cm, quite close to in loco measure (2.0 cm). finally, regarding the analysed engineering problems in this paper, it is possible to observe that the ldm may be adequately a diagnosis tool to evaluate the levels of damage in structures, being able to determine the distribution of initial/current damage values and to verify its acceptability and safety for use. moreover, it is feasible tool for technical analysis of actual structural accidents, such as the case of the rc balcony slab in brazil. acknowledgements he first author acknowledges capes for the financial support of his d.sc. studies. the second author acknowledges pnpd/capes for the financial support of her postdoc studies. appendix ust for convenience, the flexibility matrix of a damaged member (12) is reproduced here:                      0 0 0 11 12 13 0 0 0 12 22 23 0 0 0 13 23 33 1 1 1 1 i b j f f f d f f f d f f f f d (a.1) for frame members such matrix is denoted as:                        1 0 1 3 6 1 0 6 1 3 0 0 b b i b b b j b l l d ei ei l l ei d ei l ae f d (a.2) for arch elements the terms of the flexibility matrix are given by: t t j r.n. da cunha et alii, frattura ed integrità strutturale, 58 (2021) 21-32; doi: 10.3221/igf-esis.58.02 31                                                         2 0 11 2 2 0 12 2 2 2 2 0 13 2 4 sin 3 2 cos 3sin cos sin cos1 1 2 2sin sin 2 sin sin cos sin cos1 1 2 2sin sin 5sin 5 cos cos 3 2 cos1 2 sin 1 2 b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b r f ei r ae r f ei r ae r f ei                                                         2 0 22 2 2 2 0 23 2 2 3 2 0 33 sin sin cos cos sin sin cos sin cos1 1 2 2sin sin sin cos sin cos1 2 sin sin sin cos cos1 2 sin 3sin cos b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b ae r f ei r ae r f ei ae r f                          2 2 cos 2 3sin cos sin sin sin cos cos sin b b b b b b b b b b b b b b ei r ae (a.3) references [1] rehman, s.k.u., ibrahim, z., memom, s.a. and jameel, m. (2016). nondestructive test methods for concrete bridges: a review, constr. build. mater., 107, pp. 58-86. doi: 10.1016/j.conbuildmat.2015.12.011. [2] noorsuhada, m.n. (2016). an overview on fatigue damage assessment of reinforced concrete structures with the aid of acoustic emission technique, constr. build. mater., 112, pp. 424-439. doi: 10.1016/j.conbuildmat.2016.02.206. [3] solla, m., lorenzo, h., novo, a. and caamaño, j. (2012). structural analysis of the roman bibei bridge (spain) based on gpr data and numerical modelling, automat. constr., 22, pp. 334–339. doi: 10.1016/j.autcon.2011.09.010. [4] ruggiero, a., bonora, n., curiale, g., de muro, s., iannitti, g., marfia, s., sacco, e., scafati, s. and testa, g. (2019). full scale experimental tests and numerical model validation of reinforced concrete slab subjected to direct contact explosion, int. j. impact eng., 132, pp. 103309. doi: 10.1016/j.ijimpeng.2019.05.023. [5] jesus, a.m.p. de., silva, a.l.l. da., figueiredo, m. v., correia, j.a.f.o., ribeiro, a.s. and fernandes, a.a. (2011). strain-life and crack propagation fatigue data from several portuguese old metallic riveted bridges, eng. fail. anal., 18(1), pp. 148–163. doi: 10.1016/j.engfailanal.2010.08.016. [6] liu, z., correia, j., carvalho, h., mourão, a., jesus, a., calçada, r. and berto, f. (2019). global‐local fatigue assessment of an ancient riveted metallic bridge based on submodelling of the critical detail, fatigue fract. eng. mater. struct., 42(2), pp. 546–560. doi: 10.1111/ffe.12930. [7] masciotta, m.g., pellegrini, d., brigante, d., barontini, a., lourenço, p.b., girardi, m., padovani, c. and fabbrocino, g. (2019). dynamic characterization of progressively damaged segmental masonry arches with one settled support: experimental and numerical analyses, frat. ed integrità strutt., 14(51), pp. 423–441. doi: 10.3221/igf-esis.51.31. [8] vásques, j.a., junemann, r., de la llera, j.c., m.eeri, hube, m.a., m.eeri, and chacón, m.f. (2020). three-dimensional nonlinear response history analyses for earthquake damage assessment: a reinforced concrete wall building case study. earthq. spectra, 37(1), pp. 235-261. doi: 10.1177/8755293020944180. [9] ukrainczyk, n., ukrainczyk, v. (2008). a neural network method for analysing concrete durability, mag. concr. res., 60(7), pp. 475–486, doi: 10.1680/macr.2007.00016. r.n. da cunha et alii, frattura ed integrità strutturale, 58 (2021) 21-32; doi: 10.3221/igf-esis.58.02 32 [10] wu, j., zhou, y.m., zhang, r., liu, c.b. and zhang, z.c. (2020). numerical simulation of reinforced concrete slab subjected to blast loading and the structural damage assessment, eng. fail. anal., 118, pp. 104926. doi: 10.1016/j.engfailanal.2020.104926. [11] abedeni, m. and zhang, c.w. (2021). dynamic vulnerability assessment and damage prediction of rc columns subjected to severe impulsive loading, struct. eng. mech., 77(4), pp. 441-461. doi: 10.12989/sem.2021.77.4.441. [12] tenorio-monteiro, e. and juárez-luna, g. (2021). beam-column finite element with embedded discontinuities for modelling damage in reinforced concrete prismatic elements, structures, 29, pp. 1934-1953. doi: 10.1016/j.istruc.2020.12.055. [13] tang, x.s., zhang, j.r., li, c.x., xu, f.h. and pan, j. (2005). damage analysis and numerical simulation for failure process of a reinforced concrete arch structure, comput. struct., 83, pp. 2609–2631. doi: 10.1016/j.compstruc.2005.03.017. [14] ooi, e.t., yang, z.j. (2011). modelling crack propagation in reinforced concrete using a hybrid finite element–scaled boundary finite element method, eng. fract. mech., 78(2), pp. 252–73, doi: 10.1016/j.engfracmech.2010.08.002. [15] bakir, p.g., erdogan, y.s. (2013). damage identification in reinforced concrete beams by finite element model updating using parallel and hybrid genetic algorithms, int. j. comput. methods, 10(03), pp. 1350010, doi: 10.1142/s0219876213500102. [16] shardakov, i.n., shestakov, a.p., glot, i.o., bykov, a.a. (2016). process of cracking in reinforced concrete beams (simulation and experiment), frat. ed integrità strutt., 10(38), pp. 339–50, doi: 10.3221/igf-esis.38.44. [17] alañón, a., cerro-prada, e., vázquez-gallo, m.j., santos, a.p. (2018). mesh size effect on finite-element modeling of blast-loaded reinforced concrete slab, eng. comput., 34(4), pp. 649–58, doi: 10.1007/s00366-017-0564-4. [18] flórez-lópez j. (1993) modelos de daño concentrado para la simulación del colapso de pórticos planos, rev. int. mét. num. cálc. dis. ing., 9(2), pp. 123–139. [19] cipollina, a., lópez-inojosa, a. and flórez-lópez, j. (1995). a simplified damage mechanics approach to nonlinear analysis of frames, comput. struct., 54(6), pp. 1113–26. doi: 10.1016/0045-7949(94)00394-i. [20] perdomo, m.e., ramírez, a. and flórez-lópez, j. (1999). simulation of damage in rc frames with variable axial forces, earthq. eng. struct. dyn., 28(3), pp. 311–28. doi: 10.1002/(sici)1096-9845(199903)28:3<311::aid-eqe819>3.0.co;2-d. [21] rajasankar, j., iyer, n.r. and prasad, a.p. (2009). modelling inelastic hinges using cdm for nonlinear analysis of reinforced concrete frame structures. comput. concr.,6(4), pp. 319–41. doi: 10.12989/cac.2009.6.4.319. [22] teles, d.v.c., cunha, r.n., amorim, d.l.n.f, picón, r. and lópez, j.f. (2021). parametric study of dynamic behaviour of rc dual system design with the brazilian standard code using the lumped damage model, j. brazilian soc. mech. sci. eng., 43(5), pp. 246. doi: 10.1007/s40430-021-02977-8. [23] yang, t. -s. and wang, j. -l. (2010). damage analysis of three-dimensional frame structure suffering from impact, j. vib. shock, 29(12), pp. 177–180. [24] teles, d.v.c., oliveira, m.c. and amorim, d.l.n.f. (2020). a simplified lumped damage model for reinforced concrete beams under impact loads, eng. struct., 205. doi: 10.1016/j.engstruct.2019.110070. [25] oliveira, m.c., teles, d.v.c. and amorim, d.l.n.f. (2020). shear behaviour of reinforced concrete beams under impact loads by the lumped damage framework, frat. ed integrita strutt., 53, pp. 13-25. doi: 10.3221/igf-esis.53.02. [26] amorim, d.l.n.f., proença, s.p.b. and flórez-lópez, j. (2013). a model of fracture in reinforced concrete arches based on lumped damage mechanics, int. j. solids struct., 50(24), pp. 4070–4079. doi: 10.1016/j.ijsolstr.2013.08.012. [27] amorim, d.l.n.f., proença, s.p.b. and flórez-lópez, j. (2014). simplified modeling of cracking in concrete: application in tunnel linings, eng. struct., 70, pp. 23–35. doi: 10.1016/j.engstruct.2014.03.031. [28] brito, t.i.j., santos, d.m., santos, f.a.s., cunha, r.n. and amorim, d.l.n.f. (2020). on the lumped damage modelling of reinforced concrete beams and arches, frat. ed integrita strutt., 54, pp. 1-20. doi: 10.3221/igf-esis.54.01. [29] flórez-lópez, j., marante, m.e., picón, r. (2015). fracture and damage mechanics for structural engineering of frames: state-of-the-art industrial applications, engineering science reference. isbn: 978-1466663794. [30] lima, n.a. (1996). empuxo no vazio provoca o colapso da estrutura de uma varanda, in: acidentes estruturais na construção civil, são paulo, pini, 1, pp. 149-154. isbn: 978-8572660617. microsoft word numero_38_art_38 t. morishita et alii, frattura ed integrità strutturale, 38 (2016) 281-288; doi: 10.3221/igf-esis.38.38 281 focussed on multiaxial fatigue and fracture creep-fatigue life evaluation of high chromium ferritic steel under non-proportional loading t. morishita, y. murakami graduate school of science and engineering, ritsumeikan university, japan gr0202xp@ed.ritsumei.ac.jp, rm0038kk@ed.ritsumei.ac.jp t. itoh college of science and engineering, ritsumeikan university, japan itohtaka@fc.ritsumei.ac.jp h. tanigawa national institutes for quantum and radiological science and technology, japan tanigawa.hiroyasu@qst.go.jp abstract. t multiaxial creep-fatigue tests under non-proportional loading conditions with various strain rates were carried out using a hollow cylinder specimen of a high chromium ferritic steel at 823k in air to discuss the influence of non-proportional loading on failure life. strain paths employed were a push-pull loading and a circle loading. the push-pull loading test is proportional strain path test. the circle loading test is non-proportional strain path test in which sinusoidal waveforms of axial and shear strains have 90 degree phase difference. the failure life is affected largely by the strain rate and the non-proportional loading. this paper presents a modified strain range for life evaluation considering the strain rate based on a non-proportional strain parameter proposed by authors. the strain range is a suitable parameter for life evaluation of tested material under non-proportional loading at high temperature. keywords. life evaluation; creep-fatigue; multiaxial strain; nonproportional loading; high chromium ferritic steel. citation: morishita, t., murakami, y., itoh, t., tanigawa, h., creep-fatigue life evaluation of high chromium ferritic steel under nonproportional loading, frattura ed integrità strutturale, 38 (2016) 281-288. received: 30.07.2016 accepted: 31.08.2016 published: 01.10.2016 copyright: © 2016 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. introduction n the blanket structure of a demonstration fusion reactor, the material receives severe cyclic loading conditions such as combined thermal and mechanical cyclic deformations. by the combination of thermal and mechanical loading, the non-proportional loading in which the principal stress and strain directions rotate in a cycle occurs. it has been i t. morishita et alii, frattura ed integrità strutturale, 38 (2016) 281-288; doi: 10.3221/igf-esis.38.38 282 reported that failure lives are reduced accompanying with an additional hardening due to non-proportional loading depending on both the strain path and the material [1-5]. the failure life under non-proportional loading at high temperature has been discussed in the previous study for the high chromium ferritic steel [6]. however, open questions of discussing creep-fatigue property still exist. therefore, creep-fatigue test results and damage evaluation under multiaxial loading are required for reliable and safety design of strength for materials and components. in this study, creep-fatigue tests under a push-pull loading and a circle loading conditions with changing the strain rate were performed at 823k in air. the evaluation of failure life is also discussed from the obtained test results. experimental procedure ultiaxial creep-fatigue tests under non-proportional loading with various waveforms were carried out at 823k in air. a hollow cylinder specimen which has a 9mm inner-diameter, a 12mm outer-diameter and a 12mm in a gauge length as shown in fig. 1 was employed. the testing machine used was an electrical servo hydraulic tension and torsion fatigue testing machine. strain paths and strain waveforms are shown in fig. 2. they are the push-pull loading (pp) and the circle loading (ci). the pp test is the proportional strain loading test. the ci test is the nonproportional strain loading test in which axial strain and shear strain have 90 degree sinusoidal out-of-phase. total axial strain and total shear strain ranges were the same ranges based on von mises basis (=/3). in these strain paths, three strain rates were employed. they are 0.2%/s, 0.01%/s and 0.002%/s based on von mises basis which are indicated by ‘ff’, ‘ss’ and ‘ss*’, respectively. strain holdings are also employed, they are the tensile and the compressive holdings which are indicated by ‘th’ and ‘ch’. the holding times used were 180s (3min.) and 600s (10min.). number of cycles to failure (failure life) nf is defined as the cycles at which the axial or shear stress was reduced to 3/4 of the sudden decrease point. figure 1: shape and dimensions of test specimen (mm). a x ia l st ra in ε time t a x ia l st ra in time t strain rate 0.01 or 0.002%/s strain rate 0.2%/s a x ia l st ra in ε time t holding time 3 or 10min a x ia l st ra in ε time t holding time 3 or 10min pp-ff pp-ss, pp-ss* pp-th pp-ch t a x ia l st ra in ε s h ea r st ra in t a x ia l st ra in ε s h ea r st ra in t a x ia l st ra in ε s h ea r st ra in holding time 3 or 10min ci-ff ci-ss, ci-ss* ci-th push-pull (pp) circle (ci)  3 strain rate 0.01 or 0.002%/s strain rate 0.2%/s (a) strain path (b) strain waveform figure 2: strain path and strain waveform. m t. morishita et alii, frattura ed integrità strutturale, 38 (2016) 281-288; doi: 10.3221/igf-esis.38.38 283 experimental results and discussion failure life ab. 1 and fig. 3 show the test results and the failure life. the failure life is affected largely by not only strain path (strain non-proportionality) but also strain waveform (creep damage). in the pp test, the failure life is reduced with the decrease in the strain rate under the same strain range, which may be resulting from larger creep damage caused by the lower strain rate. on the other hand, in the ci test, the failure life is increased when the strain rate is reduced from 0.2%/s to 0.01%/s, but the failure life is decreased by the further reduction in the strain rate from 0.01%/s to 0.002%/s. the former may be resulting from the reduction in the intensity of strain non-proportionality caused by stress relaxation due to creep and the latter can by the increase of creep damage. strain path waveform strain rate (%/s) holding time (s) δεeq (%) nf (cycles) push-pull pp-ff 0.2 0 0.5 2,757 1.0 680 pp-ss 0.01 0.5 1,980 1.0 501 pp-ss* 0.002 0.5 1,780 0.7 945 1.0 323 pp-th 0.2 180 0.5 2,389 1.0 543 600 0.5 2,442 1.0 523 pp-ch 180 0.5 1,718 1.0 598 600 0.5 1,267 1.0 486 circle ci-ff 0.2 0 0.5 870 1.0 240 ci-ss 0.01 0.5 1,452 1.0 378 ci-ss* 0.002 0.5 682 0.7 325 1.0 164 ci-th 0.2 180 0.5 1,680 1.0 268 600 0.5 1,190 1.0 302 table 1: test conditions and results. fig. 4 shows a correlation of the failure life by von mises’ equivalent strain range eq. in the figure, a bold solid line is drawn based on the data in the pp-ff test which is the life curve for life evaluation and two thin lines show a factor of 2 band. the bold solid line is given by 6.0 f 12.0 feqδε   bnan (1) where the coefficients a and b are defined as 3.5b/e and f0.6 according to the definition of the universal slope method [7]. in this study, b is put as the curve to be fit with the data in the pp-ff test. this figure shows clearly a large reduction in the failure life in the ci test compared with the pp test according to the non-proportional loading effect. t t. morishita et alii, frattura ed integrità strutturale, 38 (2016) 281-288; doi: 10.3221/igf-esis.38.38 284 0.5 1.0 0.5 1.0 f ai lu re l if e n f, c y cl es strain range δεeq ff ss ss* push-pull circle 104 103 101 102 figure 3: comparison of creep-fatigue failure lives. 102 103 104 factor of 2 pp-ff pp-ss pp-ss* pp-th-3 pp-th-10 pp-ch-3 pp-ch-10 1.0 2.0 m is es ' e q u iv al en t st ra in r an g e   e q , % failure life nf, cycles ci-ff ci-ss ci-ss* ci-th-3 ci-th-100.4 0.2 figure 4: correlation of nf by mises’ equivalent strain range. in multiaxial low cycle fatigue tests, it has been reported that the large reduction in the failure life has a close relation with strain path and material. itoh et al. [8-13] proposed a non-proportional strain range np for life evaluation under nonproportional loading defined by   inpnp δεα1δε 　　f (2) where i is a maximum principal strain range under non-proportional loading which can be calculated by  and .  and fnp are a material constant and a non-proportional factor, respectively. the former is the parameter related to the additional hardening due to non-proportional loading and the latter is the parameter expressing the intensity of nonproportional loading. the value of  is the ratio to fit the failure life in the ci test to that in the pp test at the same i. fnp is defined by [12] t. morishita et alii, frattura ed integrità strutturale, 38 (2016) 281-288; doi: 10.3221/igf-esis.38.38 285     cpathc ir pathmaxi np d,d)(| 2 1 slsts ls f ee| (3) where si(t) is the maximum absolute value of principal strains at time t, simax is the maximum value of si(t). e1 and er are unit vectors of simax and si(t), ds the infinitesimal trajectory of the loading path. lpath is the whole loading path length during a cycle and “” denotes vector product. integrating the product of amplitude and principal direction change of stress and strain by path length in eq. (3) is a suitable parameter for evaluation of the additional damage due to nonproportional loading. detail descriptions of fnp and the life evaluations have been mentioned in reference [12] and are omitted here. fnp in the pp test (proportional loading) takes 0 and that in the ci (non-proportional loading) takes 1. fig. 5 shows a correlation of the failure life by np. this figure shows that dark symbols for pp-ff and ci-ff tests are plotted beside the bold line and np can evaluate non-proportional loading tests at the high strain rate. because of creep damage, the failure lives in lower strain rates are scattered even though almost of all data are correlated within the factor of 2 band. therefore, np may need some modification which considers the effect of strain rate. 102 103 104 factor of 2 pp-ff pp-ss pp-ss* pp-th-3 pp-th-10 pp-ch-3 pp-ch-10 1.0 2.0 s tr ai n ra n g e   n p , % failure life nf, cycles ci-ff ci-ss ci-ss* ci-th-3 ci-th-100.4 0.2 figure 5: correlation of nf by non-proportional strain range. creep fatigue damage under proportional loading condition the evaluation method proposed by coffin [14], which takes into account the strain rate under proportional loading, is employed for life evaluation. the equation is given by   cnvk  βf1pδε (4) where p and v are plastic strain and cyclic frequency. c,  and k are material constants. from the experimental results in pp-ff and pp-ss tests, the material constants and a correlation of strain ranges in pp-ff and pp-ss tests can be calculated by eq. (5).  β1 0 sspp p ffpp pδε          k v v (5) t. morishita et alii, frattura ed integrità strutturale, 38 (2016) 281-288; doi: 10.3221/igf-esis.38.38 286 in this material at the tested temperature, k and β take 0.6 and 0.9, respectively. δεppp-ff and δεppp-ss are plastic strain ranges when nf in pp-ff test takes the same value as that of pp-ss test. according to that correlation in this figure, a modified strain range np’ can be defined as,    β1 0 vivnpnp ,δεα1δε'         k v v kkf (6) where v0 is the frequency at the strain rate of the fatigue test in which creep effect can be ignored. in this study, the strain rate in the pp-ff test is set as v0. v is an arbitrary frequency in the tests with the lower strain rate of which creep effect is included. pp-th, pp-ch and ci-th tests which have strain holding are assumed to be transformed proximately into the test of triangular or sinusoidal waveform with low strain rate. fig. 6 shows how to transform the strain waveform in the holding test into an equivalent strain waveform to obtain the strain rate v’. the strain rate is calculated from the equivalent strain waveform. fig. 7 shows a correlation of the failure life by npδε' . the data in pp test under various strain rates including strain holding is correlated within the factor of 2 band even though data in high strain ranged tests are plotted conservatively. on the other hand, the data in ci test under low strain rates is underestimated. figure 6: assuming waveform of hold loading equivalent to triangular loading. creep fatigue damage under non-proportional loading condition the low strain rate reduces the failure life by creep damage. on the other hand, the intensity of strain non-proportionality decreases due to the stress relaxation caused by creep. for the life evaluation in low strain rates under non-proportional loading, a modified non-proportional strain range is proposed by eq. (6) by adding a new parameter ks which shows the reduction of intensity of non-proportionality. the modified strain range is given by   ivnps*np δεα1δε kfk           1 s 0χ 　 v v k (7) where the value of ks is calculated from test results in ci test, that is, a correlation of ks with strain rate is obtained by data fitting.  is a material constant, in case of this material =2.7. t. morishita et alii, frattura ed integrità strutturale, 38 (2016) 281-288; doi: 10.3221/igf-esis.38.38 287 102 103 104 factor of 2 pp-ff pp-ss pp-ss* pp-th-3 pp-th-10 pp-ch-3 pp-ch-10 1.0 2.0 s tr ai n ra ng e  ' n p , % failure life nf, cycles ci-ff ci-ss ci-ss* ci-th-3 ci-th-100.4 0.2 figure 7: correlation of nf by modified non-proportional strain range. fig. 8 shows a correlation of failure life by the modified non-proportional strain range. in the figure, all of the date can be plotted within the factor of 2 band. it suggests that np becomes a suitable parameter for evaluation of the creep-fatigue failure life under non-proportional loading. further creep-fatigue tests using other materials will be obtained for the discussion of this modified non-proportional strain range considering the strain rate. 102 103 104 factor of 2 pp-ff pp-ss pp-ss* pp-th-3 pp-th-10 pp-ch-3 pp-ch-10 1.0 2.0 s tr ai n r an g e  * n p , % failure life nf, cycles ci-ff ci-ss ci-ss* ci-th-3 ci-th-100.4 0.2 figure 8: correlation of nf by modified non-proportional strain range. conclusions (1) in the push-pull loading test (proportional loading test), failure life is decreased with decreasing in the strain rate resulting in creep damage. t. morishita et alii, frattura ed integrità strutturale, 38 (2016) 281-288; doi: 10.3221/igf-esis.38.38 288 (2) in the circle loading test (non-proportional loading test), failure life depends on the strain rate. the increase in the failure life can be explained by the reduction in the intensity of strain non-proportionality caused by stress relaxation due to creep. conversely, the decrease in the failure life can be explained by the increase of creep damage. (3) the modified non-proportional strain range considering the strain rate can correlate the failure life very well. acknowledgement his work was supported by the japan atomic energy agency under the joint work contract #27k400, as a part of the work assigned to the japanese implementing agency under the procurement number iferc-t3pa4-ja-rp1b within the "broader approach agreement" between the government of japan and the european atomic energy community. refereces [1] doong, s.h., socie, d.f., robertson, i.m., dislocation substructures and nonproportional hardening, journal of engineering materials and technology, 112 (1990) 456-464. [2] wang, c.h., brown, m.w., a path-independent parameter for fatigue under proportional and non-proportional loading, fatigue & fracture of engineering materials & structures, 16 (1993) 1285-1297. [3] itoh, t., nakata, t., sakane, m., ohnami, m., nonproportional low cycle fatigue of 6061 aluminum alloy under 14 strain paths, european structural integrity society, 25 (1999) 41-54. [4] socie, d.f., marquis, g.b., multiaxial fatigue, society of automotive engineers international, (2000). [5] sakane, m., itoh, t., kida, s., ohnami, m., socie, d.f., dislocation structure and non-proportional hardening of type 304 stainless steel, european structural integrity society, 25 (1999) 130-144. [6] itoh, t., fukumoto, k., hagi, h., itoh, a., saitoh, d., low cycle fatigue damage of mod.9cr-1mo steel under nonproportional multiaxial loading, procedia engineering, 55 (2013) 457-462. [7] manson, s.s., a complex subject: some simple approximations, experimental mechanics, 5 (1965) 193-226. [8] itoh, t., sakane, m., ohnami, m., socie, d.f., nonproportional low cycle fatigue criterion for type 304 stainless steel, journal of engineering materials and technology, 117 (1995) 285-292. [9] itoh, t., a model for evaluation of low cycle fatigue lives under nonproportional straining, journal of the society of materials science, 50 (2001) 1317-1322. [10] itoh, t., sakane, m., hata, t., hamada, n., a design procedure for assessing low cycle fatigue life under proportional and non-proportional loading, international journal of fatigue, 28 (2006) 459-466. [11] itoh, t., sakane, m., shimizu, y., definition of stress and strain ranges for multiaxial fatigue life evaluation under non-proportional loading, journal of the society of materials science, 62 (2013) 117-124. [12] itoh, t., sakane, m., ohsuga, k., multiaxial low cycle fatigue life under non-proportional loading, international journal of pressure vessels and piping, 110 (2013) 50-56. [13] itoh, t., sakane, m., morishita, t., evaluation and visualization of multiaxial stress and strain states under nonproportional loading, frattura ed integrita strutturale, 33 (2015) 289-301. [14] coffin, l.f., mechanical behavior of materials, 2 (1972) 516. t << /ascii85encodepages false /allowtransparency false /autopositionepsfiles true /autorotatepages /none /binding /left /calgrayprofile (dot gain 20%) /calrgbprofile (srgb iec61966-2.1) /calcmykprofile (u.s. web coated \050swop\051 v2) /srgbprofile (srgb iec61966-2.1) /cannotembedfontpolicy /error /compatibilitylevel 1.4 /compressobjects /tags /compresspages true /convertimagestoindexed true /passthroughjpegimages true /createjobticket false /defaultrenderingintent /default /detectblends true /detectcurves 0.0000 /colorconversionstrategy /cmyk /dothumbnails false /embedallfonts true /embedopentype false /parseiccprofilesincomments true /embedjoboptions true /dscreportinglevel 0 /emitdscwarnings false /endpage -1 /imagememory 1048576 /lockdistillerparams false /maxsubsetpct 100 /optimize true /opm 1 /parsedsccomments true /parsedsccommentsfordocinfo true /preservecopypage true /preservedicmykvalues true /preserveepsinfo 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/hrv (za stvaranje adobe pdf dokumenata najpogodnijih za visokokvalitetni ispis prije tiskanja koristite ove postavke. stvoreni pdf dokumenti mogu se otvoriti acrobat i adobe reader 5.0 i kasnijim verzijama.) /hun 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can be opened with acrobat and adobe reader 5.0 and later.) >> /namespace [ (adobe) (common) (1.0) ] /othernamespaces [ << /asreaderspreads false /cropimagestoframes true /errorcontrol /warnandcontinue /flattenerignorespreadoverrides false /includeguidesgrids false /includenonprinting false /includeslug false /namespace [ (adobe) (indesign) (4.0) ] /omitplacedbitmaps false /omitplacedeps false /omitplacedpdf false /simulateoverprint /legacy >> << /addbleedmarks false /addcolorbars false /addcropmarks false /addpageinfo false /addregmarks false /convertcolors /converttocmyk /destinationprofilename () /destinationprofileselector /documentcmyk /downsample16bitimages true /flattenerpreset << /presetselector /mediumresolution >> /formelements false /generatestructure false /includebookmarks false /includehyperlinks false /includeinteractive false /includelayers false /includeprofiles false /multimediahandling /useobjectsettings /namespace [ (adobe) (creativesuite) (2.0) ] /pdfxoutputintentprofileselector /documentcmyk /preserveediting true /untaggedcmykhandling /leaveuntagged /untaggedrgbhandling /usedocumentprofile /usedocumentbleed false >> ] >> setdistillerparams << /hwresolution [2400 2400] /pagesize [612.000 792.000] >> setpagedevice microsoft word numero_55_art_14_2933 s.s. ali et alii, frattura ed integrità strutturale, 55 (2021) 187-197; doi: 10.3221/igf-esis.55.14 187 mechanical performance of intelligent asphalt mixture utilizing rejuvenator encapsulated method sari sharif ali, mahyar arabani dept. of civil engineering, university of guilan, rasht, iran sarisharif@yahoo.com, m_arbani@yahoo.com hassan latifi department of civil engineering, science and research branch, islamic azad university, tehran, iran hassan.latifi@srbiau.ac.ir abstract. in this study, in order to evaluate the effects of heavy vacuum slops (h.v.s) as rejuvenator and nano-zycosil as an anti-stripping agent on used encapsulation method and mechanical performance of asphalt mixture samples, scanning electron microscopy (sem), computerized tomography (ct) scan and thermal gravimetric (tg) analyses and also, indirect tensile strength (its) and indirect tensile fatigue (itf) tests were performed. first, an encapsulation procedure to prepare different specimens including modified and unmodified samples with nano-zycosil was done. in the following, morphology of the nano-zycosil-modified capsules and aggregates were particularly evaluated. considering the morphology evaluation and tg analysis diagrams, it was found that most of the capsules resisted the mixing procedure of the asphalt mixture. so, the encapsulation procedure used in this study was a successful technique. in addition, modification with nano-zycosil as an anti-stripping agent significantly improved the adhesion strength in the matrix of capsules-aggregates-asphalt binder by converting the adhesion type from silanolian to siloxane. overall, modification of capsules and main aggregates together with nano-zycosil significantly improved moisture resistance and mechanical performance of asphalt mixture samples. keywords. rejuvenator capsule; nano-zycosil; indirect tensile; encapsulation procedure; moisture resistance. citation: ali, s.s., arabani, m., latifi, h., mechanical performance of intelligent asphalt mixture utilizing rejuvenator encapsulated method, frattura ed integrità strutturale, 55 (2021) 187-197. received: 06.10.2020 accepted: 08.12.2020 published: 01.01.2021 copyright: © 2021 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. introduction sphalt mixture is a porous material consists of asphalt binder, aggregates and air voids formed at high temperatures (~180 °c) during mixing process [1]. in long term aging during service life, the stiffness of asphalt mixture increases which results in an increase of asphalt binder’s brittleness due to oxidation and consequently a https://youtu.be/61yph16rtzq s.s. ali et alii, frattura ed integrità strutturale, 55 (2021) 187-197; doi: 10.3221/igf-esis.55.14 188 development of micro-cracks between aggregates and asphalt binder [2,3]. in addition, this procedure also occurs due to being exposd to heat, oxygen and ultraviolet (uv) light during storage, mixing, transport and laying down of asphalt mixture [4,5,6]. asphalt binder has usually two major components namely: asphaltenes and maltenes which are solid and liquid, respectively. the components of maltenes are polar aromatics (pas) and naphthalene aromatics (nas) [7]. liu et al. [8] found that asphalt binder produced asphaltenes and pas during aging process. in other words, pas and nas transformed into asphaltenes and pas, respectively. afterwards, the produced pas transformed into asphaltenes too. finally, the asphaltenes component increased. on the other hand, pas and nas decreased. in other words, the solid and liquid components increased and decreased, respectively. as a result, the brittleness of asphalt mixture increased [9]. one of the popular methods in order to restore the asphalt binder’s properties is using of rejuvenators. rejuvinating agents consist of maltnes of lubricating oils, have a important goal of restoring asphaltenes/maltenes ratio [10]. on the other hand, successful mixing of rejuvinating agents with asphalt binder and aggregates is very important due to the problem of penetration of them to pavement surface during paving operation. shen et al in [10] reports the same difficulties by using rejuvinators as they did not penetrate into asphalt binder more than 2 cm. also, reduction in surface friction of the pavement and the environmental contaminations were the other concers. on these matters, some researches let to encapsulate rejuvenators in order to use in asphalt mixtures [11]. in order to make capsules of rejuvenators, porous sand and epoxy resin-cement were chosen to cover the rejuvenators like a wall. one of the advantages of these capsules is their high resistance at high temperatures during mixing process. in addition, they could remain unbroken until the rejuvenators are necessary in resoring asphalt binder properties. on the other hand, reduction in mechanical resistance of the asphalt mixture is one of disadvantages of the encapsulation method. moreover, during the mixing process, a little amount of capsules would break which results in releasing the rejuvenators into asphalt binder and soften it. considering, capsule surface is smoother than the aggregate, so, the adhesive resistance between the asphalt binder and capsules is less than the adhesive resistance between the asphalt binder and aggregates and also, modification of asphalt binder with the capsules was by mass replacement of aggregates. so, indirect tensile and indirect tensile fatigue strengths of the asphalt mixture samples decreased [12,13]. in this study, in order to evaluate the effects of used rejuvenator encapsulated method and nano-zycosil as an anti-stripping agent on mechanical performance of asphalt mixture samples, scanning electron microscopy (sem), computerized tomography (ct) scan and thermal gravimetric (tg) analyses and also, indirect tensile strength (its) and indirect tensile fatigue (itf) tests were performed. all the analyses and tests were conducted in erbil asphalt laboratory in iraqi kurdistan. finally, a chart of the subjects of this study is shown in fig. 1. figure 1: chart of subjects of this study. experimental procedure materials ain materials used in the encapsulation included scoria porous sand. the particles sizes were between 3 and 4 mm. this type of sand has thousands of micro pores and simply absorbs liquids. this size of porous sand was selected by mass replacement of aggregates in asphalt mixtures. the used rejuvenator is heavy vacuum slops m s.s. ali et alii, frattura ed integrità strutturale, 55 (2021) 187-197; doi: 10.3221/igf-esis.55.14 189 (h.v.s) which is very dense and aromatic, obtained from baiji oil refinery in iraq. the heavy vacuum slops (h.v.s) is purchased from erbil asphalt laboratory in iraqi kurdistan. the wall of capsules is formed of cement type 1 bonded with a liquid epoxy resin (bisphenol a). properties of the materials forming the capsules are illustrated in tab. 1. properties density specific weight porosity unit g/cm3 g/cm3 rejuvenator 0.926 9.4 porous sand 2.58 1.54 49.08 cement 3.1 63.9 epoxy 1.13 1.14 table 1: properties of the materials forming the capsules. in the common asphalt mixture samples, crushed aggregates alongside sand and type 1 cement as filler were used according to iraqi standard specifications for road and bridge (issrb) and it is displayed in tab. 2. also, as it is shown in tab. 3, the used asphalt binder was 40/50-penetration grade from baiji oil refinery. sieve (mm) 19 12.5 9.5 4.75 2.36 0.36 0.075 specification limits 100 90-100 76-90 44-74 28-58 5-21 4–10 passing (%) 100 94.4 76.6 49.8 33.4 21 8.2 table 2: grading of the aggregates used in this study. tests tests method results specifications astm min max penetration of bituminous @ 25°c (100g ,5 sec) d5 [14] 48 40 50 softening point of bitumen (ring and ball) d36 [15] 54 50 60 ductility @ 25°c d113 [16] 135 >100 penetration of bituminous after heating d5 [14] 35 ductility @ 25°c after heating d113 [16] 107 >60 table 3: results of asphalt binder tests. encapsulation procedure the encapsulation procedure has been described in the following steps and briefly illustrated in the fig. 2.  in order to build the core of capsules the scoria porous sand was put in a tall container. then, heavy vacuum slops (h.v.s), the rejuvenator was pourd until the height of rejuvenator-sand blend were twice as the original sand. next, all of them were heated for 1 hour at 105 °c in order to decrease the viscosity of oil.  the blend of the rejuvenator-sand in order to eliminate the air and force the oil was put into a vacuum chamber during at least 30 min. heating and the vacuum process have been repeated twice to remove as much air as possible. after, the excess rejuvenator was eliminated; the blend was manually shaken in order to have a homogeneous blend.  in order to build the shell, the blend of epoxy-sand-rejuvenators was manually mixed in a weight ratio 1:2.5 until the epoxy covered entire soil grains. in another round, epoxy in a weight ratio 1:20 (1 gram of epoxy for each 20 gram of rejuvenator-sand blend) was added. next, cement was added fourfold as weight of the sand to the blend of epoxysand-rejuvenators. if the amount of cement were more than fourfold as weight of the sand, it would absorb all the epoxy and the oil inside the porous sand. s.s. ali et alii, frattura ed integrità strutturale, 55 (2021) 187-197; doi: 10.3221/igf-esis.55.14 190  the obtained capsules were added to a container of eight steel balls with a diameter of 2 cm in a volumetric ratio of 1:54 to the total volume of the container. then, the container was energetically moved in circles for about 15 s.  after forming the capsules’ shape like ball, they were left to cure for 8 hour at 35 °c.  in order to modify the wall of capsules, one part of nano-zycosil was mixed with 100 parts of pure water. capsules are immersed in the mixture for 2 to 5 s. next, the capsules were stored at room temperature for 24 hours. in order to evaluate the resistance of capsules during mixing process, they were incorporated into the asphalt mixtures as secondary aggregates. the mixture was blended during 15 min at 285 rpm at 160 °c in a 10 lit mixer and compacted using a superpave gyratory compactor (sgc) to simulate a real porous asphalt pavement. then, the sample was sawn in half and the cross section was examined. a) b) c) d) e) figure 2: encapsulation procedure step by step; a) dry and cleaned porous sands (particle size about 2.3 to 2.8 mm), b) porous sands with rejuvenator inside the grains, c) container with a diameter of 2 cm steel balls, d) energetically circles movement for 15 s, e) the sieved capsules between 3 and 4 mm. scanning electron microscopy (sem) and computerized tomography (ct) scan analyses scanning electron microscopy (sem) and computerized tomography (ct) scan analysis have been performed to analyse the capsule morphology. the sem photos are taken at a voltage of 20.8 kv by a sem microscope from erbil asphalt laboratory in iraqi kurdistan. thermal analysis in order to evaluate the resistance of capsules during the mixing process of the asphalt mixtures, thermal gravimetric (tg) analysis was conducted. thermo-microbalance of tg anlysis was performed using nitrogen atmosphere and heating rate of 10 °c/min. the compositions of capsules must resist temperatures between 160 °c and 180 °c. moreover, these s.s. ali et alii, frattura ed integrità strutturale, 55 (2021) 187-197; doi: 10.3221/igf-esis.55.14 191 temperatures can produce molecular scissions or intermediate compounds in the rejuvenator such as ketenes or alcohol [17], as well as mass loss due to the evaporation of these compounds. indirect tensile strength (its) test its test was conducted according to aashto-t283 [18] using the pneumatic load system in order to evaluate resistance of the asphalt mixtures samples against fracture and to determine their tensile strength. marshal machine has been used to apply a compression load on asphalt concrete specimens at a rate of loading 51 mm/min, along a diametrical plane through two opposite loadings which curved strip heads of 12.5 mm width. indirect tensile fatigue (itf) test itf test was done on three specimens for each studied asphalt mixture sample by applying a 0.2 s haversine repeated load followed by a rest period of 0.3 s at a frequency of 8 hz. the maximum load applied at each cycle was 0.138 mpa. the equipment used was universal testing machine (utm) according to astm-d4123 standard [19]. a) a section of the capsule b) a section of the capsule c) water repellent of the shell d) water repellent of the outer wall figure 3: sem images of capsule. results sem and ct-scan analyses results em images of the capsules are displayed in fig. 3. as it is illustrated in fig. 3 a, micro pores in the capsule are clear. also, shell part of the capsule with high density can be seen close to the porous sand. the shell part prevents the rejuvenator leakage from the capsule. fig. 3 b, shows a section of the capsule including two distinct area namely: the s shell hole shell hole 1 nm water drops 20.8 kv spot: 7.5 magn: x 34.0 10 µm 20.8 kv spot: 6.6 magn: x 164.0 20.8 kv spot: 6.3 magn: x 244.0 100 µm 100 µm 20.8 kv spot: 7.6 magn: x 241.0 s.s. ali et alii, frattura ed integrità strutturale, 55 (2021) 187-197; doi: 10.3221/igf-esis.55.14 192 core and the shell. considering fig. 3 b, it can be clearly seen that the shell has two different layers with variable density which are distinctly colored by adobe photoshop. in other words, the shell is completely made of a mixture of epoxy and cement, while the density significantly changes from inside toward outside of the capsule. in addition, during encapsulation procedure, the rejuvenator with low viscosity penetrated the wall of the capsule and changed the density of the shell from inside to the outside. fig. 3 c, presents the water repellent of the shell due to modification of the capsule by nano-zycosil. as it could be seen, water cannot penetrate the shell of capsule. finally, as shown in fig. 3 d, the outer wall of the capsule is well-repellent. in general, the shell well formed on the outer side. so, as an overall result, the shell of cement-epoxy prevents the leaving of rejuvenator to the outside of the capsule. ct-scan images of the six capsules are shown in fig. 4. in this figure the bond between the porous stone and the shell looks very strong. it can be seen that externally they look like main aggregates because of their very uniform surface. core and shell of the capsules are clearly seen in these figures. in general, the thickness of shell is directly related to the viscosity of rejuvenator. in other words, increase in viscosity resulted in increase in the thickness of wall and vice versa. figure 4: ct-scan images of different capsules by shell thickness from 0.7 to 1.2 mm. in order to ensure the integrity of the capsule’s wall and preventing the rejuvenator leakage, some of them randomly were bisected before mixing to asphalt binder-aggregates. as shown in fig. 5, the rejuvenator inside the capsule indicates the integrity of the wall. figure 5: a bisected capsule between 3 and 4 mm diameter. s.s. ali et alii, frattura ed integrità strutturale, 55 (2021) 187-197; doi: 10.3221/igf-esis.55.14 193 in order to evaluate the resistance of capsules during mixing process, they were incorporated into the asphalt mixtures as secondary aggregates. then, as it is displayed in fig. 6 a, the samples were sawn in half and examined with by naked eyes. according to fig. 6 a, the capsules had high resistance during mixing process and still had lots of oil in them. in this figure the capsules are integrated in the matrix of asphalt binder-aggregates-capsules as secondary aggregates. on the other hand, considering fig. 6 b, the capsule broke under the stress caused by condensation. figure 6: capsules with thickness from 3 to 4 mm embedded in asphalt mixture. a) capsule resisted the mixing process; b) capsule broke under the stress by condensation. b) a) d) c) figure 7: a) hydrophobicity of the aggregates modified with nano-zycosil; b) hydrophilic in the unmodified aggregates; c) amount of stripping in the modified aggregates (with grading according to tab. 2); d) amount of stripping in the unmodified aggregates (with grading according to tab. 2). in fig. 7 a, the aggregate is shown after modification with nano-zycosil. as shown in fig. 7 a, nano-zycosil modification led to creating a hydrophobic surface on the aggregates as the drop retained its shape and did not penetrate the aggregates. on the other hand, considering fig. 7 b in the normal state the surface of aggregates is hydrophilic and although holes in aggregate capsule aggregate capsule water bubble water bubble s.s. ali et alii, frattura ed integrità strutturale, 55 (2021) 187-197; doi: 10.3221/igf-esis.55.14 194 the aggregates are smaller than water molecules, but when the water molecules collide with the surface, atoms would break and water penetrate to the holes. moreover, one of the reasons is the presence of silica in the surface of the aggregate which make their surfaces hydrophilic. by modifying the surface of aggregates with nano-zycosil, this material due to their nano-meter size, penetrated into the pores of the aggregate and provided the hydrophobic properties. when the water collided the surface of the modified aggregates, it remained on the surface of them. figs. 7 c and d, are taken after water boiling test and indicate the amount of stripping for modified and unmodified aggregates with 1% nano-zycosil, respectively. the amount of stripping in the unmodified ones is significantly much more than the modified aggregates [20]. thermal analysis results fig. 8 shows tga diagrams for the capsule components. as it is illustrated in fig. 8, the mass loss of rejuvenator, nanozycosil and epoxy resin starts to fall down at 230°c, 190°c and 260 °c, respectively. as mentioned before, the asphalt mixture mixing temperatures was between 160 and 180 °c. this means the capsule can resist the asphalt mixture mixing temperature range. in addition, fig. 8 also shows, the most affected material by temperature is the scoria porous sand which lost a lot of mass between 30 and 160°c. that is because of the presence of water in its pores. so, to avoid such mass loss it is required before encapsulation, the porous sand should be heated in order to evaporate the moisture in its pores. figure 8: tga diagrams of encapsulated ingredients. its and itf tests results in figs. 9 a and b, results of its and itf tests are shown, respectively. in figs. 9 the prefix “treated” means the material is modified with nano-zycosil. as it is displayed in fig. 9, different types of samples including asphalt mixture without capsules, with capsules, with modified capsules, modified aggregate and with modification of both capsules and aggregates by nano-zycosil were experimented. according to fig. 9 a, it can be seen that the capsules reduce the stiffness of asphalt mixture and have some effect on the mechanical characteristics of the asphalt mixture. this could happen because some of the capsules broke during the mixing. another reason could be the diffrences in the adhesion between them and the asphalt binder compare to the adhesion between the main aggregates and the asphalt binder. in addition, during the mixing process, some of the capsules would break which results in releasing the rejuvenators. so, the released rejuvenators would soften the asphalt binder. moisture susceptibility of asphalt mixtures could be predicted by tensile strength ratio (tsr), wet/dry (conditioning/ unconditioned) ratio of its values [18]. in general, the higher the tsr, the more resistance mixture against moisture induced distresses such as stripping. as shown in fig. 9 a, the mixtures modified with nano-zycosil had lower susceptibility against wet condition due to having higher tsr values. treated capsule & aggregate-mixtures had the highest moisture resistance while +capsule-mixtures performed the worst among the others. as a result, modified capsules and aggregates with nano-zycosil improved the moisture resistance of asphalt mixture significantly regarding tsr values. s.s. ali et alii, frattura ed integrità strutturale, 55 (2021) 187-197; doi: 10.3221/igf-esis.55.14 195 also, the results showed that by modification of the capsule and aggregates, the indirect tensile and fatigue strength of specimens increased. that is because, without modification with nano-zycosil, the adhesion between the asphalt binder and the surface of the capsules very weak. by modifying the capsules and aggregates with nano-zycosil, the adhesion between the capsules and aggregates with asphalt binder converted from silanolian to siloxane types. in general, the seloxane bonding is much stronger than silanolian one. so, due to this conversion the percent of asphalt binder components which would contribute to the matrix of capsules-aggregates-asphalt binder increased from 40-45 % to 85-95 %. after modification of the aggregates, aggregates and capsule with nano-zycosil, the samples were examined in a twophase evaluation. the results showed that the modification of aggregates with nanozycosil in the samples including unmodified capsules significantly increased tensile strength and fatigue resistance compare to samples without modified aggregates. it indicated that modification of aggregates with nano-zycosil had great impact on indirect tensile strength and fatigue resistance of asphalt mixture samples. a) b) figure 9: the results of its and itf tests. a) the indirect tensile strength of specimens; b) number of cycles required to to break specimens. another part of the results of its and itf tests are illustrated in fig. 10. same as for figs. 9, in figs. 10 the prefix “treated” means the material is modified with nano-zycosil. in fig. 10 a, the displacement of specimens under the loading at un-conditioning state before and after the fracture is illustrated. as it was found, displacement of samples with capsules are more than the samples without capsules. that is because of the adhesion resistance between the capsules and asphalt binder is less than the adhesion resistance between the main aggregates and the asphalt binder. this caused a significant increase in the displacement of the samples including the capsules compare to the ones without the capsules. in addition, the samples modified with nano-zycosil had less displacement than the ones which did not modify with nanozycosil. fig. 10 b, presents the values of deformations under the fatigue loading until the fracture was indicated. as it is displayed in fig. 10 b, the effect of the modified capsules, modified aggregate and both together are so different. modification of the capsules by nano-zycosil reduced the deformation compare to the unmodified capsule samples. moreover, modified aggregate and modified capsules together samples had the least amount of deformation and the most amount of number of cycle of failure. conclusions he following conclusions can be deduced from the obtained results:  considering the morphology evaluation and the tga diagrams, it was found that most of the capsules resisted the mixing procedure of the asphalt mixture. so, the encapsulation procedure used in this study was a t s.s. ali et alii, frattura ed integrità strutturale, 55 (2021) 187-197; doi: 10.3221/igf-esis.55.14 196 successful technique to build rejuvenator capsules. on the other hand, some of them broke under indirect tensile tests and reduced the stiffness of the asphalt mixtures.  by adding the capsules to the asphalt mixture samples, fatigue resistance and deformation decreased and increased, respectively, because of less interlock between the capsules and asphalt binder compare to aggregates. on the other hand, modification with nano-zycosil as an anti-stripping agent significantly improved the adhesion strength in the matrix of capsules-aggregatesasphalt binder by converting the adhesion type from silanolian to siloxane. a) b) figure 10: the results of its and itf tests. a) displacement of specimens under indirect tensile load; b) maximum deformation of specimen during the loading until the samples broke.  obtained results demonstrated the increase of tsr by implementation of modified capsules and aggregates with nano-zycosil. for instance, tsr significantly increased about 14% for treated capsule & aggregate-mixtures compared with the conventional asphalt mixtures. on the other hand, the mixtures with modified capsules by nano-zycosil had 5% more tsr than the ones with unmodified capsules.  it was found that the capsules alongside main aggregates both modified with nano-zycosil improved resistance of studied mixture against moisture damage by improving the adhesion in the matrix of capsules-aggregatesasphalt binder.  overall, modification of capsules and main aggregates together with nano-zycosil significantly improved mechanical performance of the asphalt mixture samples. s.s. ali et alii, frattura ed integrità strutturale, 55 (2021) 187-197; doi: 10.3221/igf-esis.55.14 197 acknowledgments any thanks to all the staff and manager of erbil asphalt laboratory in iraqi kurdistan. also, special thanks to dr. masoud faramarzi for all his supports. references [1] arabani, m., faramarzi, m. (2015). characterization of cnts-modified hma’s mechanical propertis, construction and building materials., 83, pp. 207–215. doi: 10.1016/j.conbuildmat.2015.03.035. [2] branthaver, j.f., petersen, j.c., robertson, r.e., duvall, j.j., kim, s.s., harnsberger, p.m., mill, t., ensley, e.k., barbour, f.a., schabron, j.f. (1993). binder characterization and evaluation, 2: chemistry, shrp-a-368, national research council, washington, dc. [3] kumar das, p., balieu, r., kringos, n., birgisson, b. (2015). on the oxidative ageing mechanism and its effect on asphalt mixtures morphology, materials and structures., 48, pp. 3113–3127. doi: 10.1617/s11527-014-0385-5. [4] per g, redelius. (2011). the structure of asphaltenes in bitumen, road materials and pavement design., pp. 143-162. doi: 10.1080/14680629.2006.9690062. [5] yu, j.y., feng, p.c., zhang, h.l., wu, s.p. (2009). effect of organo-montmorillonite on aging properties of asphalt, construction and building materials., 23, pp. 2636–2640. doi: 10.1016/j.conbuildmat.2009.01.007. [6] masson, j.f., gagne, m. (2008). polyphosphoric acid (ppa)-modified bitumen: disruption of the asphaltenes network based on the reaction of nonbasic nitrogen with ppa, energy fuel., 22(5), pp. 3402–3406. doi: 10.1021/ef8002944. [7] corbett, l.w. (1969). composition of asphalt based on generic fractionation, using solvent deasphaltening, elutionadsorption chromatography, and densimetric characterization, anal. chem., 41(4), pp. 576–579. doi: 10.1021/ac60273a004. [8] lu, x., isacsson, u., (2002). effect of ageing on bitumen chemistry and rheology, construction and building materials., 16, pp. 15–22. doi: 10.1016/s0950-0618(01)00033-2. [9] karlsson, r., isacsson, u. (2003). investigations on bitumen rejuvenator diffusion and structural stability, journal of asphalt paving technologists., http://urn.kb.se/resolve?urn=urn%3anbn%3ase%3akth%3adiva-88391. [10] shen, j., amirkhanian, s., miller, j.a. (2007). effects of rejuvenating agents on superpave mixtures containing reclaimed asphalt pavement, journal of materials in civil engineering., 19(5), pp. 376–384. doi: 10.1061/(asce)0899-1561(2007)19:5(376). [11] garcia, a., schlangen, e., van de ven, m., s.b, guadalupe. (2010). preparation of capsules containing rejuvenators for their use in asphalt concrete, journal of hazardous materials, doi 10.1016/j.jhazmat.2010.08.078. [12] garcia, a., schlangen, e., van de ven, m. (2011). properties of capsules containing rejuvenators for their use in asphalt concrete, fuel., 90(2), pp. 583-591. doi: 10.1016/j.fuel.2010.09.033. [13] latifi, h., amini, n. (2020). effect of aggregate type on moisture susceptibility of modified cold recycled mix asphalt: evaluation by mechanical tests and surface free energy method, frattura ed integrità strutturale., 52, pp. 211-229. doi: 10.3221/igf-esis.52.17. [14] astm standard d5/d5m. (2013). standard test method for penetration of bituminous materials, astm international, west conshohocken. [15] astm standard d36/d36m. (2009). standard test method for softening point of asphalt (ring-and-ball apparatus). astm international, west conshohocken. [16] astm d-113 -99 (2002). standard test method for ductility test, astm international, west conshohockentest, pa, usa. [17] lins, vfc., araújo, mfas., yoshida, mi., ferraz, vp., andrada, dm., lameiras, fs. (2008). photodegradation of hotmix asphalt, fuel., 87, pp. 3254–3261. doi: 10.1016/j.fuel.2008.04.039. [18] aashto t283. (2003). standard method of test for resistance of compacted asphalt mixtures to moisture induced damage. [19] astm d4123. (2000). annual book of astm standards. road and paving materials. [20] erikson, k.l. (2007). thermal decomposition mechanism common to polyurethane, epoxy, poly (diallyl phthalate), polycarbonate and poly (phenylene sulfide), journal of thermal analysis and calorimetry., 89(2), pp. 427–440. doi: 10.1007/s10973-006-8218-6. m microsoft word numero_38_art_22 a. bolchoun et alii, frattura ed integrità strutturale, 38 (2016) 162-169; doi: 10.3221/igf-esis.18.22 162 focussed on multiaxial fatigue and fracture fatigue life assessment of thin-walled welded joints under non-proportional load-time histories by the shear stress rate integral approach a. bolchoun tu darmstadt, research group of system reliability and machine acoustics szm, magdalenenstr. 4, 64289 darmstadt, germany fraunhofer institute for structural durability and system reliability lbf, bartningstr. 47, 64289 darmstadt, germany alexandre.bolchoun@lbf.fraunhofer.de c. m. sonsino, h. kaufmann fraunhofer institute for structural durability and system reliability lbf, bartningstr. 47, 64289 darmstadt, germany t. melz tu darmstadt, research group of system reliability and machine acoustics szm, magdalenenstr. 4, 64289 darmstadt, germany fraunhofer institute for structural durability and system reliability lbf, bartningstr. 47, 64289 darmstadt, germany abstract. fatigue life tests under constant and variable amplitude loadings were performed on the tube-tube thin-walled welded specimens made of magnesium (az31 and az61) alloys. the tests included pure axial, pure torsional and combined in-phase and out-of-phase loadings with the load ratio  r r" ", " " 1  . for the tests with variable amplitude loads a gaußdistributed loading spectrum with sl 45 10  cycles was used. since magnesium welds show a fatigue life reduction under out-of-phase loads, a stress-based method, which takes this behavior into account, is proposed. the out-of-phase loading results in rotating shear stress vectors in the section planes, which are not orthogonal to the surface. this fact is used in order to provide an out-of-phase measure of the load. this measure is computed as an area covered by the shear stress vectors in all planes over a certain time interval, its computation involves the shear stress and the shear stress rate vectors in the individual planes. fatigue life evaluation for the variable amplitudes loadings is performed using the palmgren-miner linear damage accumulation, whereas the total damage of every cycle is split up into two components: the amplitude component and the out-of-phase component. in order to compute the two components a modification of the rainflow counting method, which keeps track of the time intervals, where the cycles occur, must be used. the proposed method also takes into account different slopes of the pure axial and the pure torsional wöhler-line by means of a wöhler-line citation: bolchoun, a., sonsino, c. m., kaufmann, h., melz, t., fatigue life assessment of thin-walled welded joints under non-proportional load-time histories by the shear stress rate integral approach, frattura ed integrità strutturale, 38 (2016) 162-169. received: 12.05.2016 accepted: 15.06.2016 published: 01.10.2016 copyright: © 2016 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. a. bolchoun et alii, frattura ed integrità strutturale, 38 (2016) 162-169; doi: 10.3221/igf-esis.18.22 163 interpolation for combined loadings. keywords. magnesium welds; multiaxial fatigue; variable amplitude loading; out-of-phase loading; rainflow; fatigue life assessment. introduction atigue life assessment of materials and components under multiaxial cyclic loading is a complex task, which requires to take a number of phenomena into account, e.g.:  depending on the material state out-of-phase loadings can lead to a reduced or to an increased fatigue life compared to in-phase loadings [1];  different slopes und knee points of the wöhler-lines under pure axial and pure torsional loadings [2,3];  influence of mean stresses [4]. magnesium thin-walled welds exhibit a fatigue life reduction under non-proportional loadings as well as different slopes of the wöhler-lines for pure axial and pure torsional loads. the influence of mean stresses is not considered in this paper. fatigue life evaluation is often performed using stress-based methods because of their simplicity and convenience. conventional stress-based methods, such as described in [5-7] were developed in order to calculate the so-called [8] fatigue limit. they usually lack the capability to assess the fatigue life reduction under out-of-phase loadings correctly. there is a number of more advanced methods, which take the out-of-phase behavior of the load into account explicitly, usually using an out-of-phase factor of some sort [9-13]. with these out-of-phase factors the stresses are scaled so, that the correct fatigue life is computed for an out-of-phase loading. another approach is employed by the idd-method [14]: no equivalent stress value is computed, however the damage of a load-time history or its part is computed according to the formula: total in phase out of phased d d 2 2 2     (1) where in phased  and out of phased   are the idd-specific damages resulting from the amplitude values and from the out-ofphase behavior of the loading. in fact in [14] there are two types of the out-of-phase damage: the one which is associated with the rotating principal stress axes and the one associated with out-of-phase principal stress values and no rotation of the principal axes. a very similar approach is used in the current paper, however out-of-phase loadings with and without rotating principal stresses are characterized mathematically in a uniform way using a stress rate integral. the proposed method requires to consider a general (three-dimensional) stress state. many methods are capable to take different slopes of the pure axial and pure torsional wöhler-lines into account, usually they contain a parameter, which, if dependency of the number of cycles n is introduced, allows to “pull” the axial and torsion wöhler-lines together. in this case iterative methods are required in order to compute the equivalent stress and hence the fatigue life. a method to avoid the iterative computation is to use a wöhler-line interpolation, as presented e.g. in [3]. in order to perform wöhler-line interpolation a numerical value, which characterizes, if the load is pure axial, pure torsional or a combined one, is required. fatigue life evaluation under variable amplitude loadings requires a procedure, which identifies damaging events (“cycles”). in [3, 15] it is proposed to find the plane with the highest shear stress aplitude using the maximum variance method (mvm) and perform the rainflow cycle counting. the 4-point rainflow cycle counting procedure [16, 17] was extended in order to keep track of the time intervals, in which each counting cycle occurred. the method discussed in this paper requires calculation of the local stress components, these are obtained using the femodeling according to the fictitious radius approach for thin-walled welds with refr  = 0.05 mm [2]. a short overview of the specimens and experimental results aserbeam-welded tube-tube specimens (specimen geometry is shown in fig. 1) were tested in a servohydraulic testing rig with two actuators, so cyclic axial and torsional loadings can be induced independently from each other. the welds were made of two self-hardening magnesium alloys az31 and az61. the testing program included f l a. bolchoun et alii, frattura ed integrità strutturale, 38 (2016) 162-169; doi: 10.3221/igf-esis.18.22 164 wöhler-tests under pure axial, pure torsional and combined in-phase and out-of-phase loadings and gaßnertests using a gauß-distributed amplitude spectrum with sl 45 10  cycles. the load ratio r 1  for wöhler-tests or r 1  for gaßner-tests was applied. linear-elastic fe-models of the specimens were created in order to obtain the local stress components. the weld was modelled according to the fictitious notch approach with refr 0, 05 mm [2]. for both materials a fatigue strength reduction under out-of-phase loading was observed. the results of wöhlerand gaßner-tests for az31 are presented in fig. 1. the wöhler-lines were obtained in [18]. for gaßner-tests real damage sums reald lie between 0.2 and 0.8 for pure axial, pure torsional and combined out-ofphase loadings and for combined in-phase loadings between 1.0 and 1.7 [19]. figure 1: wöhler (a) and gaßner (b)-lines for the welded joints made of az31 alloy. the specimen geometry is shown as well. shear stress rate integral as a measure of non-proportionality on-proportionality of the loading is observed if the proportion between single load components changes over time. non-proportionality can result from different configurations of the loading and can be accompanied by certain phenomena, like rotating principal directions of the stress tensor and/or presence of the mean stresses.    t t0 σ σ σ (2) where σ is the mean value of the tensor  tσ over the time interval  t0,  and    t t0  σ σ σ , that is 0 0σ . in the absence of the mean stresses, i.e. if 0σ , the non-proportionality can be observed, if the components of    t t0σ σ are out-of-phase. thereby the non-proportionality can be accompanied by rotating principal stress directions, if the normal and the shear stress components are out-of-phase (or, speaking more generally, are uncorrelated), as well as by fixed principal directions, if the normal stress components are out-of-phase and the shear stress components are all zero. however both out-of-phase cases result in rotating shear stress vectors in the cross-section planes. the idea is to use this rotation of the shear stress vectors in order to characterize the out-of-phase behaviour of the loading. in a single plane given by the normal unit vector n the area dan , which is covered by the movement of the time-dependent shear stress vector  tnτ in the infinitesimal time interval  t t dt,   computes to    da t t dt 1      2   n n nτ τ (fig.2), where the shear stress rate vector nτ is the time-derivative of nτ . now the out-of-phase behaviour in the infinitesimal  t t dt,   interval can be characterized as the “sum” of the areas dan in all the cross section planes associated with the different normal unit vectors n : n a. bolchoun et alii, frattura ed integrità strutturale, 38 (2016) 162-169; doi: 10.3221/igf-esis.18.22 165    opdf da d t t d dt 1     . 2         n n n n n n τ τ n figure 2: trajectory of the shear stress vector in a given plane and the area dan . for a finite time interval  t t1 2,  the overall out-of-phase measure computes to:     t op t f t t d dt 2 1 1  . 2   n n n τ τ n (3) formula (3) allows to express the out-of-phase behaviour of the loading in an arbitrary time interval, however it is dependent on the shear stress amplitudes and can attain any value between 0 and  . therefore, it is different from many out-of-phase measures, which can be found in the literature and attain values in the interval  0, 1 , e.g. [9-12]. maximum normal and shear stress amplitudes and wöhler-line interpolation s described in [3, 15] the maximum variance method (mvm) can be used in order to determine the plane, the direction and the value of the maximum shear stress amplitude a max, , it can also be applied in the same manner in order to determine the value of the maximum normal stress amplitude a max, as well as the plane, where it occurs. these two values can be computed for an arbitrary time interval and an arbitrary time-dependent stress history defined over this interval. for a pure torsional loading it follows a max a max, ,  and for a pure axial loading a max a max, , 1 2   . condition a max, 0  corresponds to a hydrostatic cyclic loading. whether there exists a cyclic loading with a max a max, ,  , is not known to the authors. if such loading exists, it should be a non-proportional one. the ratio a max i a max f , ,    can be used to interpolate a wöhler-line for a cyclic loading in the region between the pure axial loading and pure torsion, that is if 1   1 2   , as follows:  ax i tors ix x f x f 1 2    1   . 2            (4) where x is a wöhler-line parameter kk n,  or kl , furthermore ax torsk k k,  ,  represent the slopes of the respective wöhler-lines, k k ax k torsn n n, , ,  ,  represent the number of cycles and k k ax k torsl l l,  , ,  ,  the load amplitudes at the knee point. the values k k ax k torsl l l,  , ,  ,  must refer to the same damage parameter, for instance v. mises equivalent stress a a. bolchoun et alii, frattura ed integrità strutturale, 38 (2016) 162-169; doi: 10.3221/igf-esis.18.22 166 amplitude, the maximum normal stress amplitude, the maximum shear stress amplitude or any other equivalent stress amplitude. for the values if 1 2  the axial wöhler-line is assumed, for if 1 (if it can really occur) the torsional wöhlerline. if an experimental wöhler-line outside of the region between pure axial loading and pure torsion is available, the interpolation can be easily adapted to take it into account. modified rainflow counting method atigue life under variable amplitude loadings requires an identification of damaging events (loading cycles, hysteresis loops, etc. depending on the particular setting), which is usually followed by a suitable damage accumulation procedure. one or another version of the rainflow cycling counting method, e.g. [16, 17, 20], is a commonly used procedure. figure 3: schematic representation of the 4-point rainflow counting algorithm, that keeps time intervals in which cycles occur. parts of the time-history of the same colour and dashing belong to a single cycle. damage accumulation is often performed using the palmgren-miner approach. in the multiaxial fatigue problems it is hard to define a cycle or a value, which is going to be counted. some examples of application of the cycles counting procedures for multiaxial cyclic loadings can be found in [21-23]. these methods identify the cycles, but the information on the stress-time history is lost and hence the methods described in the previous two sections, especially eq. 3, cannot be applied. the following approach is employed in this paper: analogous to the mwc-method [3] the plane and direction of the maximum shear stress amplitude is identified using mvm. the 4-point rainflow counting with subsequent residuum evaluation is performed. for each identified cycle the intervals in the stress-time history, over which it is distributed, are identified as well. so a cycle is given by a set of time intervals  ni i i1 2,  , , in which it occurs. the number n of the intervals can vary between 1 and  depending on the load-time history. this approach is schematically shown in fig. 3. putting it all together he aim of the presented method is to evaluate fatigue life under cyclic variable amplitude in-phase and out-ofphase loadings (“arbitrary loadings”). the evaluation can be split in four steps. the required input data consist of: wöhler-lines for a pure axial loading and pure torsion as well as a wöhler-line for an out-of-phase loading. the wöhler-lines must be provided in terms of some local equivalent stress amplitude. all three wöhler-lines can be directly obtained from experiments or taken from the literature or some experience-based assumptions can be made. furthermore, a damage accumulation method as well as the damage sum must be defined. the first step is to define the equivalent stress amplitude. based on the position of the pure axial relative to the combined in-phase wöhler-line (fig. 1), the integral of the normal stress amplitudes over all plane is chosen. it is defined as follows:   a eq var d, 2  .  n n n f t a. bolchoun et alii, frattura ed integrità strutturale, 38 (2016) 162-169; doi: 10.3221/igf-esis.18.22 167 the second step is to compute the damage resulting from the out-of-phase loading. for the out-of-phase loading represented by the input out-of-phase wöhler-line the values i opf ,  and opf (eq. 3) are computed, whereas the value  op eq af , depends on the equivalent stress amplitude. the value i opf , allows to compute the interpolated wöhler-line, which has the slope i opk , . in the case of magnesium welds it lies above the experimental out-of-phase wöhler-line due to fatigue life reduction under out-of-phase loading. now for each amplitude the total damage  total a eqd , can be computed using the experimental wöhler-line and the in-phase damage  if a eqd , using the interpolated wöhler-line. the additional damage due to out-of-phase behaviour is then given by:       of op eq a total eq a if eq ad f d d2 2, , ,  .    (5) the value (5) depends on the equivalent stress amplitude eq a, and since there is a one-to-one correspondence between a eq, and off , ofd is a function of off and can be represented in the double logarithmic of off d diagram, which is somewhat similar to the wöhler-diagram. the third step is the rainflow counting and identification of cycles and intervals in which these cycles occur. in the fourth step for each cycle c the equivalent stress amplitude a eq c, , , the value i cf , , the interpolated wöhler-line with the slope i ck , and the out-of-phase stress rate integral of cf , are computed. now the damages  if c a eq cd ,  , ,   and  of c of cd f,  , can be calculated. the total damage of the cycle computes to ki c ki op total c if c if cd d d 2 , 2 , ,  , ,  .            the total damage of the loading sequence is then computed using palmgren-miner linear damage accumulation with modification according to haibach with k k2  2   [24]: total total c c d d ,  and finally correcting the theoretical damage sum thd 1.0 by the allowable one ald 1.0 based on the experimental observation [25] the fatigue life computes to s al total l n d d   . fatigue life evaluation results and conclusions stress-based fatigue life evaluation method, which is capable to process arbitrary multiaxial cyclic loadings, is proposed. it is capable to take into account effects like fatigue life reduction as well as fatigue life increase under out-of-phase loading. the method was applied in order to evaluate fatigue life of magnesium welds under multiaxial variable amplitude fatigue loadings. the results are shown in fig. 4. the method can be extended in order to handle the mean stresses. in each plane the mean normal stress as well as the mean shear stress can be defined. a suitable way to take these values into account is yet to be defined. for magnesium welds the integral of the normal stresses is chosen to be the equivalent stress in order to take into account the fact that combined in-phase wöhler-line lies very close to the pure axial wöhler-line. if necessary other effects can be taken into account, if other values of equivalent stress are chosen. for instance the maximum shear stress or the maximum normal stress amplitude will predict a fatigue life reduction under in-phase combined loading compared to the pure axial loading. a a. bolchoun et alii, frattura ed integrità strutturale, 38 (2016) 162-169; doi: 10.3221/igf-esis.18.22 168 figure 4: computational and experimental gaßner-lines for the welded joints made of az31 (a) and az61 (b) alloys, ald 0.5. acknowledgements he authors would like to thank the german research foundation (dfg) for the financial support of the multiaxial magnesium projects (dfg projects so 184/12-1 and so 184/12-2). references [1] sonsino, c. m., influence of material’s ductility and local deformation mode on multiaxial fatigue response, int. j. fatigue, 33 (2011) 930-47. [2] radaj, d., sonsino, c.m., fricke, w., fatigue assessment of welded joints by local approaches, 2nd ed., woodhead publishing, cambridge (2006). [3] susmel, l., multiaxil notch fatigue, woodhead publishing, cambridge, (2009). [4] papuga, j., a survey on evaluating the fatigue limit under multiaxial loading, int j. fatigue, 33 (2011) 153-65. [5] findley, w. n., modified theories of fatigue failure under combined stress, proc. sesa, 14 (1956) 1, 35-46. [6] simbürger, a., festigkeitsverhalten zäher werkstoffe bei einer mehrachsigen, phasenverschobenen schwingbeanspruchung mit körperfesten und veränderlichen hauptspannungsrichtungen, fraunhofer lbf, darmstadt, (1975). [7] zenner, h., richter, i., eine festigkeitshypothese für die dauerfestigkeit bei beliebigen beanspruchungskombinationen, konstruktion, 29 (1977) 11-18. [8] sonsino, c. m., "dauerfestigkeit" eine fiktion, konstruktion, 57 (2005) 87-92. [9] bishop, j. e., characterizing the nonproportional and out-of-phase extent of tensor paths, fatigue fract. egngn mater struct, 23 (2000) 1019-1032. [10] bolchoun, a., wiebesiek, j., kaufmann, h., sonsino, c. m., theor. appl. fracture mech., 73 (2014) 9-16. [11] gaier, c., lukacs, k., hofwimmer, k., investigations on a statistical measure of the non-proportionality of stresses int. j. fatigue, 26 (2004) 331-337 [12] sonsino, c. m., multiaxial fatigue of welded joints under in-phase and out-of-phase local strains and stresses, int. j. fatigue, 17 (1995) 55-70. [13] wiebesiek, j., störzel, k., bruder, t., kaufmann, h., multiaxial fatigue behaviour of laserbeam-welded thin steel and aluminium sheets under proportional and non-proportional combined loading, int. j. fatigue, 33 (2011) 992-1005. [14] stefanov, s. h., the curvilinear integral method: computer realization and testing 1 (under non-proportional reversed axial force and torque), int. j. fatigue, 17 (1995) 567-575. [15] susmel, l., a simple and efficient numerical algorithm to determine the orientation of the critical plane in multiaxial fatigue problems, int j. fatigue, 32 (2010) 1875-1883. t a. bolchoun et alii, frattura ed integrità strutturale, 38 (2016) 162-169; doi: 10.3221/igf-esis.18.22 169 [16] clormann, u. h., seeger, t., rainflow hcm. ein zählverfahren für betriebsfestigkeitsnachweise auf werkstoffmechanischer grundlage, stahlbau, 55 (1986) 65-67. [17] brokate, m., dreßler, k., krejci, p., rainflow counting and energy dissipation for hysteresis models in elastoplasticity, eur j. mech a/solids, 15 (1996) 705-737. [18] exel, n., schwingfestigkeit laserstrahlgeschweißter magnesiumlegierungen unter mehrachsigen proportionalen und nichtproportionalen beanspruchungen, shaker-verlag, aachen, (2013). [19] bolchoun, a., sonsino, c. m., kaufmann, h., melz, t., multiaxial random fatigue of magnesium laserbeam-welded joints experimental results and numerical fatigue life evaluation, proc. engng., 101 (2015) 61-68 [20] astm standard practices for cycle counting in fatigue analysis, (1985) e 1049 – 1085. [21] dong, p., wei, z., hong, j. k., a path-dependent cycle counting method for variable-amplitude multi-axial loading, int. j. fatigue, 32 (2010) 720-734. [22] langlais, t. e., vogel, j. h., chase, t. r., multiaxial cycle counting for critical plane methods, int. j. fatigue, 25 (2003) 641-647. [23] wang, c. h., brown, m. w., life prediction techniques for variable amplitude multiaxial fatigue—part 1: theories, j. eng. mater. technol., 118 (1996) 367-374. [24] haibach, e., betriebsfestigkeit – verfahren und daten zur bauteilberechnung, 3. auflage, springer-verlag, berlin, heidelberg, (2006). 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can be opened with acrobat and adobe reader 5.0 and later.) >> /namespace [ (adobe) (common) (1.0) ] /othernamespaces [ << /asreaderspreads false /cropimagestoframes true /errorcontrol /warnandcontinue /flattenerignorespreadoverrides false /includeguidesgrids false /includenonprinting false /includeslug false /namespace [ (adobe) (indesign) (4.0) ] /omitplacedbitmaps false /omitplacedeps false /omitplacedpdf false /simulateoverprint /legacy >> << /addbleedmarks false /addcolorbars false /addcropmarks false /addpageinfo false /addregmarks false /convertcolors /converttocmyk /destinationprofilename () /destinationprofileselector /documentcmyk /downsample16bitimages true /flattenerpreset << /presetselector /mediumresolution >> /formelements false /generatestructure false /includebookmarks false /includehyperlinks false /includeinteractive false /includelayers false /includeprofiles false /multimediahandling /useobjectsettings /namespace [ (adobe) (creativesuite) (2.0) ] /pdfxoutputintentprofileselector /documentcmyk /preserveediting true /untaggedcmykhandling /leaveuntagged /untaggedrgbhandling /usedocumentprofile /usedocumentbleed false >> ] >> setdistillerparams << /hwresolution [2400 2400] /pagesize [612.000 792.000] >> setpagedevice microsoft word numero 24 articolo 10 m.p. tretiakov et alii, frattura ed integrità strutturale, 24 (2013) 96-101; doi: 10.3221/igf-esis.24.10 96 special issue: russian fracture mechanics school tests in tension-torsion conditions with descending sections of strain curve construction m.p. tretiakov, v.e. vildeman center of experimental mechanics, perm national research polytechnic university, komsomolskiy pr. 29, 614990, perm, russia cem_tretyakov@mail.ru abstract. the paper is devoted to theoretical and experimental investigation of materials behavior on postcritical deformation stage (strain softening). tests results, which confirm theoretical justification of specimen configuration impact on the possibility of creating descending sections of strain curve, are given. it is shown that, with sufficient stiffness of loading system, equilibrium postcritical deformation of materials is possible. it is confirmed in uniaxial tension tests with unloading on postcritical deformation stage. test results on tension with torsion of thin-walled tubular specimens in strain softening conditions are adduced. keywords. experimental mechanics; postcritical deformation; proportional tension with torsion. introduction issipative processes of inelastic deformation, including the processes of structural failure and fracturing, reflect on the deformation curve as nonlinearity. at the final stage this leads to softening of materials and the appearance of a descending section on strain curve. completeness of implementation of the load-carrying capacity of strength constructions is determined by the degree of postcritical deformation. when postcritical deformation stage is taken into account in adjusted computation, it allows a reserve of constructions load-carrying ability to be revealed. it makes possible to forecast the destruction moment more accurately [1, 2]. questions of theoretical, experimental and numerical study of postcritical deformation mechanisms of materials attract attention of researches in connection with the questions of use of materials deformation reserves, the rise of load-carrying ability and survivability of materials, and the analysis of possibilities of failure processes management [1-9]. on the postcritical deformation stage the formation of macro-destruction conditions takes place. these conditions, unlike the traditional view that defines the use of force or deformation criteria are not definitely related to the stress-strain state at the point of deformed body. during the transition from the equilibrium stage of damage accumulation to nonequilibrium stage of destruction, interaction of the deformed body with the loading system plays the key role. as a result, based on loading conditions, each point on the descending section of stress-strain curve can correspond to the time of the loss of load-carrying ability as a result of transitioning from stable to non-equilibrium stage of the damage accumulation process. thus, the rigid loading system may contribute to the "adaptation" of the object in the process of destruction due to local dissipation of elastic energy [1, 2]. however the force or deformation criteria can be considered with a view to transition of material to postcritical strain stage (similarly the condition of transition to plastic state). it is necessary to experimentation verify of criteria, particularly by test results in plane stress state under combined tension-torsion loading [1113]. d http://dx.medra.org/10.3221/igf-esis.24.10&auth=true http://www.gruppofrattura.it m.p. tretiakov et alii, frattura ed integrità strutturale, 24 (2013) 96-101; doi: 10.3221/igf-esis.24.10 97 it is known that it is necessary to use high-stiffness test systems for obtaining equilibrium curves of materials postcritical deformation. however, even with high-stiffness test machine, in some cases obtaining descending sections of strain curve is not possible. it may be associated with specimen geometry. in work [10] a deformable body ω is considered with boundary σ and contact type boundary conditions:       0| ( ) sij j ij j i n r u r s    r r r where ijr are coefficients of loading system stiffness, ( )jn r are direction cosines of normal vector to the surface of body ω in the point with coordinate r . defining relationship is written in the following form: ' ( ,  )ij ijmn mnd с d    where χ is indicator reflecting the nature of the process (active loading ( 1  )or unloading). the condition of postcritical deformation stability in weakness zone ω0 is written as follows: 0 0 ' ij j i ijmn mn ij ijmn mn ijr u u d c d d d                where ' ( ,  1)ijmn ijmnd c     are components of softening modulus tensor. the sign of postcritical deformation is formulated in the following form: 0ij ijd d   in a particular case of uniaxial deformation of a solid cylindrical specimen with length l and cross section square f and with weakness zone length l’ and cross section square f’<f, the main volume of the specimen is part of the loading system with respect to the weakness zone. it has been shown that the necessary condition of reaching postcritical deformation stage in the weakness zone is: 0 c mq q q  where 1m mq r  is compliance of test machine ( mr is stiffness of test machine), '( ) / ( )cq l l ef  is compliance of bar (main volume), ' '0 / ( )q l df is compliance of the softening region ( /d d d   is the current meaning of tangent softening modulus). similarly for a thin-walled tubular specimen with length l and moment of inertia jp, with weakness region with length l’ and moment of inertia  ' 'p p pj j j , it can be seen that the condition necessary for postcritical stage realization in the weakness region under torsion can be written in the following form: 0 c ml l l  where 1m ml n  is the compliance of test machine on torsion ( mn is stiffness of test machine on torsion), '( ) / ( )c pl l l gj  is the compliance of the bar on torsion (main volume), ' ' 0 / ( )g pl l d j is the compliance of the softening region on torsion ( /gd d d   is the current meaning of tangent softening modulus on torsion). the aim of the work is experimental examination of the impact of loading system stiffness (particularly geometrical parameters of specimens) on the construction of strain curve with descending sections, and construction of strain curves with postcritical deformation stages in uniaxial tension and proportional tension-torsion tests. tests and results test equipment ests were carried out on instron 8850 biaxial servohydraulic test system (maximum load 100 kn, maximum torque 1000 nm, cyclic tests with frequency up to 30 hz). strain in the test part of specimen in uniaxial tension tests was registered by instron 2620-601 extensometer, and in proportional tension-torsion tests it was registered by epsilon 3550-010м biaxial extensometer. t http://dx.medra.org/10.3221/igf-esis.24.10&auth=true http://www.gruppofrattura.it m.p. tretiakov et alii, frattura ed integrità strutturale, 24 (2013) 96-101; doi: 10.3221/igf-esis.24.10 98 tests with various loading system stiffness experimental investigation of the effect of stiffness of the loading system on the construction of strain curves with descending sections was performed in two test groups. in the first test group, solid cylindrical specimens with test part length of 10 mm, diameter of 6 mm with additional deformation parts of different lengths (length of 30 mm, 60 mm, diameter of 8 mm) were used. in this case the additional test parts increased the compliance of the loading system with respect to the weakened central part. in the second test group specimens with different diameters (5 mm, 10 mm, 13.5 mm) with the same ratio of test part length to diameter (l0/d=1) were used. in this case, the change of the specimen’s diameter changes the specimen’s stiffness and consequently changes the ratio of specimen stiffness to test machine stiffness. in fig. 1 the results of two test groups of steel 20 (gost 1050-88) are shown. the influence of the loading system stiffness is reflected by the presence of different points on the descending section of strain curve, which correspond to the loss of stability moment of the deformation process. stress is calculated as ratio of load to initial cross-section square of the specimen, the strain is ln(1 )ln   , where ε is the ratio of extension by extensometer to initial gauge length. (a) (b) figure 1: strain curve of steel 20 and destruction moments: (a) is test results of specimens with additional elements (1 is specimen without additional elements, 2 and 3 are specimens with additional elements, with total lengths of 30 mm and 60 mm), (b) is test results of specimens with different stiffness (1, 2 and 3 are specimens with diameters 5.0 mm, 10.0 mm and 13.5 mm. the possibility of equilibrium material deformation on softening stage is also confirmed by unloadings and repeat loadings. in fig. 2 the strain curve of steel 20 at uniaxial tension with unloading on different stages of elastoplastic and postcritical deformation (a) and final section of softening with unloadings (b) are shown. strain rate at tension and unloading was 0.02 min-1. (a) (b) figure 2: strain curve of steel 20 at uniaxial tension: with unloading on different deformation stage (a), final section of strain curve (b). thus, to obtain equilibrium descending sections of the strain curve and complete curves (equilibrium drop of load to zero value), it is necessary to provide conditions of sufficient loading system stiffness with respect to test part of the specimen (high stiffness of the test machine, geometrical parameters of the specimen). with the above conditions, it is possible to http://dx.medra.org/10.3221/igf-esis.24.10&auth=true http://www.gruppofrattura.it m.p. tretiakov et alii, frattura ed integrità strutturale, 24 (2013) 96-101; doi: 10.3221/igf-esis.24.10 99 obtain strain curves with sections of softening both under uniaxial tension and under tension combined with torsion. from the perspective of creation and improvement of postcritical deformation mechanics models the important question is the behavior of materials at a softening stage in combined tension-torsion conditions. strain softening in tension-torsion tests proportional tension-torsion tests were implemented on thin-walled tubular specimens of steel 40x (gost 4543-71) and 15х2гмф (tu 14-159-227-93 (rf technical requirements)) with reduced test part length. shape and dimensions of specimens are shown in fig. 3. (a) (b) figure 3: shape and dimensions of thin-walled tubular specimens of steel 15х2гмф (a) and steel 40х (b). strain trajectories in deformation space correspond to straight lines. for steel 40x the ratio of axial strain to shear angle is 1.60 and 0.80, for steel 15х2гмф it is 0.57 and 0.30. the biaxial extensometer is intended for a small measurement range and it was used for correction of strain curves (by the linear section of the diagrams) which were obtained from the data of test system internal transducers. in fig. 4 and fig. 5 test results of steel 20 and 15х2гмф at proportional tension with torsion are shown. (a) (b) figure 4: test results of steel 40x at proportional tension-torsion with ratio ε/γ=1.60 (i) and ε/γ=0.80 (ii) in coordinates “axial stress – axial strain” (a) and “shear stress – shear angle” (b). http://dx.medra.org/10.3221/igf-esis.24.10&auth=true http://www.gruppofrattura.it m.p. tretiakov et alii, frattura ed integrità strutturale, 24 (2013) 96-101; doi: 10.3221/igf-esis.24.10 100 stress is calculated as ratio of load to initial cross-section square of the specimen, the strain is 0/l l  , shear stress is 2/ ( 2 )m r h  , shear angle is 0/r l  . in fig. 4 the strain curves are presented which were constructed at tests of two specimens for each strain trajectories. for steel 15х2гмф stress curves for the two specimens for each strain trajectories were obtained, in fig. 5 results for one specimen are shown. (a) (b) figure 5: test results of steel 15х2гмф at proportional tension-torsion with ratio ε/γ=0.57 (i) and ε/γ=0.30 (ii) in coordinates “axial stress – axial strain” (a) and “shear stress – shear angle” (b). the important question is which deformation moment corresponds to the start of the softening stage, i.e. the reduction of loads at constant increase of strains. in fig. 4 and fig. 5 curves are marked with points and numbered for the convenience of comparison of strain curves in coordinates “axial stress – axial strain” and “shear stress – shear angle”. in the analysis of experimental data diagram sections corresponding to the hardening of material at tension axis and shear axis can be highlighted. this corresponds to sections 2-3 and 7-8 in fig. 4 and sections from limits of elasticity to points 1 and 4 in fig. 5. there is also the strain range in which the softening of material at tension axis and shear axis occurs (the sections 4-5 and 9-10 in fig. 4 and the sections from points 2 and 6 to specimen destruction in fig. 5). it is necessary to draw special attention to areas of strain curves corresponding the hardening of material in coordinates “axial stress – axial strain” with synchronic softening in coordinates “shear stress – shear angle”. the above is shown in sections of strain curves 3-4 and 8-9 in fig. 4 and sections 1-2 and 4-6 in fig. 5. conclusions n a result of this work, there is experimental confirmation of the influence of loading system stiffness with respect to test part of the specimen (geometrical parameters of the specimen) on realization of strain curve descending section at uniaxial tension. this is reflected in the presence of different points on the descending section which corresponds with the loss of deformation processes stability. the possibility of obtaining postcritical strain curves with sufficient stiffness of the loading system is confirmed by unloadings and repeated loadings at the softening stage under uniaxial tension. the stress-strain curves of materials with softening sections at proportional tension with torsion of thin-walled tubular specimens are obtained at different trajectories of strain. it confirms the possibility of postcritical strain realization at different types of stress-strain state and allows us to obtain new data for creating models of softening medium mechanics. i http://dx.medra.org/10.3221/igf-esis.24.10&auth=true http://www.gruppofrattura.it m.p. tretiakov et alii, frattura ed integrità strutturale, 24 (2013) 96-101; doi: 10.3221/igf-esis.24.10 101 references [1] v.e. vildeman, yu.v. sokolkin, а.а. tashkinov, mechanics of inelastic deformation and fracture of composite materials, (1997) 288. [2] v.e. vildeman, int. j. for computational civil and structural engineering, 4(2) (2008) 43. [3] v.e. vildeman, yu.v. sokolkin, a.a. tashkinov, mechanics of composite materials, 28(3) (1992) 214. [4] yu.v. sokolkin, v.e. vildeman, mechanics of composite materials, 29(2) (1993) 120. [5] v.v. struganov, vestnik sstu, physics-mathematics science, 30 (2004) 5. [6] v.v. struganov, physical mesomechanics, 7(s1-1) (2004) 169. [7] yu.v. sokolkin, v.e. vildeman, a.v. zaitsev, i.n. rochev, mechanics of composite materials, 34(2) (1998) 171. [8] a.v. ilinykh, m.v. radionova, v.e. vildeman, composites: mechanics, computations, applications, 2(2) (2011) 95. [9] v.e. wildemann, a.v. ilyinykh, physical mesomechanics, 10(4) (2007) 23. [10] v.e. wildemann, j. appl. maths mechs, 62(2) (1998) 281. [11] s. nohut, a. usbeck, h. özcoban, d. krause, g.a. schneider, journal of the european ceramic society, 30 (2010) 3339. [12] a.a. lebedev, b.i. kovalchuk, f.f. gignyak, v.p. lamashevskii, mechanical properties of structural materials under complex stress state, (2003) 540. [13] n.m. zarroug, r. padmanabhan, b.j. macdonald, p. young, m.s.j. hashmi, j. of materials processing technology, 143–144 (2003) 807. nomenclature ω deformable body ω0 weak zone of deformable body σ boundary of deformable body σs boundary part with force conditions σij stress tensor components εij strain tensor components uj displacement vector components rij loading system stiffness tensor components si0 force vector components χ indicator of the process nature ' ijmnc components of tangent material modulus tensor ijmnd components of softening modulus tensor d softening modulus under tension gd softening modulus under shear rm coefficient of test machine stiffness under tension mn coefficient of test machine stiffness under torsion r radius-vector σ axial stress ε axial strain εln logarithmic axial strain τ shear stress γ shear angle e young modulus g shear modulus 0q compliance of the softening region 0l compliance of the softening region on torsion cq compliance of bar (main volume) cl compliance of bar (main volume) on torsion mq compliance of test machine ml compliance of test machine on torsion l current test part length 'l length of specimen weak zone l0 initial test part length m torque f cross section square of specimen main zone 'f cross section square of specimen weak zone pj polar moment of inertia of main zone of thinwalled tubular specimen ' pj polar moment of inertia of weak zone of thinwalled tubular specimen h wall thickness of thin-walled tubular specimen φ torsion angle r middle radius of test part of thin-walled tubular specimen d test part diameter of solid cylindrical specimen http://dx.medra.org/10.3221/igf-esis.24.10&auth=true http://www.gruppofrattura.it microsoft word numero_39_art_11 s. seitl et alii, frattura ed integrità strutturale, 39 (2017) 100-109; doi: 10.3221/igf-esis.39.11 100 focussed on modelling in mechanics numerical study and pilot evaluation of experimental data measured on specimen loaded by bending and wedge splitting forces s. seitl academy of sciences of the czech republic, v. v. i., institute of physics of materials, brno, czech republic brno university of technology, faculty of civil engineering, institute of structural mechanics, brno, czech republic seitl@ipm.cz, http://orcid.org/0000-0002-4953-4324 r. diego liedo academy of sciences of the czech republic, v. v. i., institute of physics of materials, brno, czech republic university of oviedo, department of construction and manufacturing engineering, campus de viesques, gijón, spain uo212533@uniovi.es abstract. the fracture mechanical properties of silicate based materials are determined from various fracture mechanicals tests, e.g. threeor fourpoint bending test, wedge splitting test, modified compact tension test etc. for evaluation of the parameters, knowledge about the calibration and compliance functions is required. therefore, in this paper, the compliance and calibration curves for a novel test geometry based on combination of the wedge splitting test and three-point bending test are introduced. these selected variants exhibit significantly various stress state conditions at the crack tip, or, more generally, in the whole specimen ligament. the calibration and compliance curves are compared and used for evaluation of the data from pilot experimental measurement. keywords. numerical simulation; stress intensity factor; t-stress; concrete; finite element method; wedge splitting test; three–point bending test. citation: seitl, s., liedo, r. d., numerical study and pilot evaluation of experimental data measured on specimen loaded by bending and wedge splitting forces, frattura ed integrità strutturale, 39 (2017) 100-109. received: 25.07.2016 accepted: 22.09.2016 published: 01.01.2017 copyright: © 2017 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. introduction or evaluation of fracture mechanical properties of materials like concrete, standardized methodology is not published yet. there is only recommendation for measurement of properties by rilem [18]. in the literature, researchers used various specimen geometries for experimental measurement of fracture properties of concrete, f http://www.gruppofrattura.it/pdf/rivista/numero39/audio/11.mp3 s. seitl et alii, frattura ed integrità strutturale, 39 (2017) 100-109; doi: 10.3221/igf-esis.39.11 101 see e.g. wedge splitting test (wst) [4, 5, 7, 14, 15, 21, 23, 24, 31], three–point bend [10, 17], comparison between data from wst and three–point bend (3pb) tests are introduced in [12], modified compact tension (mct) test [6] and another configurations can be found in handbooks e.g. [11, 27]. note that from various geometry, the different values of fracture parameters can be obtained for the same material. therefore the combined wst/3pbt geometry has been investigated, the variants are proposed in [29] fig. 1 (variant i represents the classical wst [7, 24] and is included in the study as a reference case), see in [29]. in all these cases the crack propagates from a notch provided on the top side of the specimen (in the groove for inserting of the wst loading fixtures. finally, the variant iiib differs from the variant iii by the central notch provided also from the bottom surface.), provides a wide range of various stress distributions in the specimen ligament – from bending to tension – which is expected to result in the desired variety e.g. in the fracture process zone size and shape, fracture energy or fracture toughness, etc. in the paper, the numerical support (calibration and compliance curves) for evaluation of the experimentally obtain data is shown/introduced. the pilot numerical study of the selected shape of specimens by using williams expansion was introduced in [22, 25, 28, 30]. the values of stress intensity factor (sif), t-stress and crack opening displacement (cod, see fig. 2) at the load line for load psp = 1000 n = 1 kn are introduced. the changes of properties are compared and discussed. these changes could be obtained modifying the specimen length to width and the span to length ratios (and/or simultaneously the wedge angle). at the end of the contribution, examples of the evaluation of experimental data measured by using the studied combination [29] have been presented. variant i variant iii variant ii variant iiib figure 1: considered variants for the combined bending/splitting configurations, taken from [29]. s. seitl et alii, frattura ed integrità strutturale, 39 (2017) 100-109; doi: 10.3221/igf-esis.39.11 102 dimensions of specimens for all four geometry variants are summarized in tab. 1 (dimensions common to all variants) and in tab. 2, there are unique dimension of all studied variants (i, ii, iii and iiib) with angles. width breadth height load position groove depth w [mm] b [mm] h [mm] h [mm] dn [mm] 150 150 130 8 20 effective width groove width load position eccentricity weff [mm] f [mm] i [mm] e [mm] 142 40 10 20 table 1: nominal variant dimensions and test geometry parameters, taken from [29]. geometry variant wedge angle length span depth of top notch depth of bottom notch initial crack length relative crack length specimen set 2αw [º] l [mm] s [mm] c [mm] c1 [mm] a [mm] α = a/weff [-] i, α1 30 150 0 13 25 0.18 i, α2 30 150 0 30 42 0.30 ii, α1 15 300 270 15 27 0.19 ii, α2 15 300 270 31 43 0.30 ii, α3 15 300 270 54 66 0.46 iii, α1 15, 30 600 540 13 25 0.18 iii, α2 15, 30 600 540 35 47 0.33 iii, α3 15, 30 600 540 54 66 0.46 iiib, α1 15, 30 600 540 8 53 53 0.37 iiib, α2 15, 30 600 540 9 81 81 0.57 table 2: nominal variant dimensions and test geometry parameters, taken from [29]. theoretical background ccording to the two-parameter fracture mechanics approach which uses t-stress as a constraint parameter [1, 11, 13, 24, 34], the stress field around the crack tip of a two-dimensional crack embedded in an isotropic linear elastic body subjected to normal mode i loading conditions is given by the following expressions [33]:                                                                      2 3 cos 2 sin 2 cos 2 2 3 sin 2 sin1 2 cos 2 2 3 sin 2 sin1 2 cos 2 i xy i yy i xx          r k r k t r k (1) a s. seitl et alii, frattura ed integrità strutturale, 39 (2017) 100-109; doi: 10.3221/igf-esis.39.11 103 where r and θ are the polar coordinates and x and y are the cartesian coordinates, both with their origins at the crack tip. ki is the stress intensity factor for mode i and t is the t-stress. thus, in two-parameter based fracture mechanics, the stress field is expressed by means of the two parameters, the stress intensity factor ki and the t-stress (see e.g. [1, 11, 24]). the values of crack opening displacement at load line is measured in the axes of roller bearings through which the load of specimens is applied (see e.g. in [4, 14] and sketch of forces in fig. 2). the applied load ratio between forces is following, [4, 14, 19, 24]: kpp vs 2 1  (2) where    wcw wc ctg k      1tan tan1 , (3) where αw is the angle of the slope of the wedge and µc refers to friction in the roller bearings. figure 2: detail of boundary conditions, see the half of specimen and the load application (psp and pv/2) with crack opening displacement (cod), position at load line. modeling in ansys he finite element software ansys [2] is used for numerical calculation of mentioned fracture parameters (k, tstress and cod). plots of variants of the test geometry selected for the experimental study are shown in fig. 1. note that geometries are symmetric for all considered specimen shapes (including boundary conditions); therefore, only one half of the problem was modelled like in [21, 22, 26]. the size of the smallest element in the crack tip is 5 × 10-5 mm. the specimen geometry iiib could leads to crack closure, therefore the whole body of the specimen was modeled and the example of numerical model with applied boundary conditions is shown in fig. 3. the crack length to depth ratio a/weff varies from 0.1 to 0.9. the thickness b is taken as unity in the computations, conditions of plane strain was applied. t psp cod pv/2 2 s. seitl et alii, frattura ed integrità strutturale, 39 (2017) 100-109; doi: 10.3221/igf-esis.39.11 104 figure 3: example of numerical model, where boundary conditions are shown, with detail in the vicinity of the crack tip. the material input data for the concrete used in the numerical simulations were as follows: ec = 33 000 mpa and νc = 0.2; and for the steel: es = 210 000 mpa and νs = 0.3. for good comparison of numerically obtain results for all cases, the load was applied as splitting force psp = 1 000 n = 1 kn. numerical results he numerically calculated values of ki and t-stress are given in figs. 4 and 5, respectively. in the present paper, four cases of the specimens’ shapes/arrangements on the calibration curves were investigated, see fig. 1 (i, ii, iii and iiib) for wedge angle: 15, 20 25, 30. on the left side of fig. 4, the wedge splitting test configuration for αw =15º is compared with bending/splitting combination as ii and iii and iiib. all four studied cases show similar trend of the sif results, when the configuration is changed the sif value for the same load decrease. on the right side of fig. 4, the iiib configuration with various wedge angles 15º, 20º, 25º and 30º are shown. up to a/weff = 0.6 the values have a smooth character, however for the a/weff reaches 0.6 till 0.9 the values change unpredictably, there is a dominant effect of the 3pb loading. figure 4: stress intensity factor (ki) as a function of the relative crack length, α/weff, for the combined bending/splitting variants defined in fig. 1, loaded by psp = 1000 n, on the left side for wedge angle =15° and on the right side for variant iiib for various wedge angles. on the left side of the fig. 5, the values of the t-stress for the wst configuration are compared with combination of wst and 3pb as variants ii, iii and iiib for angles 15º. as we suppose according to the reference [23] the function for wst vary from negative values for very short cracks to positive values for relative crack larger than 0.2. when the t s. seitl et alii, frattura ed integrità strutturale, 39 (2017) 100-109; doi: 10.3221/igf-esis.39.11 105 distance from the support is larger the values of the t-stress are always positive for ii and iii variants. for variants iiib the values of t-stress are always negative. on the right side of the fig. 5, the t-stress values for combinations of iiib with various wedge angles 15º, 20º, 25º and 30º are shown. figure 5: t-stress as function of the relative crack length, , for the combined bending/splitting variants defined in fig. 1, loaded by psp = 1000 n, on the left side for wedge angle =15° and on the right side for variant iiib for various wedge angles. figure 6: cod as a function of the relative crack length, α, for wst and combined bending/splitting variants defined in fig. 1 (as ii, iii and iiib), loaded by psp = 1000 n, on the left side for wedge angle =15° and on the right side for variant iiib for various wedge angle. the displacement, cod, in the line of the load is shown in fig. 6. on the left side of the fig. 6, the values of wst are compared with variants ii and iii for wedge angle 15°, where the splitting loading is dominant. it can be seen that for longer specimens the value of cod decreases. on the right side of the fig. 6, it can be seen the cod for configuration iiib and various wedge angles 15°, 20°, 25°, 30° when the 3pb load is dominant and the crack start from bottom side. s. seitl et alii, frattura ed integrità strutturale, 39 (2017) 100-109; doi: 10.3221/igf-esis.39.11 106 evaluation of experimental data and discussion t should be mentioned that quasi-brittle fracture of concrete is akin to elastic-plastic fracture of metals. the astm standard on fracture toughness kic [3] has clearly specified the conditions to avoid elastic-plastic or in study case quasi-brittle fracture, i.e. crack 10 times of characteristic crack etc. the simple methodology presented in this example is consistent with the astm standard for linear-elastic fracture, but can also cover the first part of the quasibrittle diagram. the material and experimental procedure are described in [29]. for evaluation of data in our paper, knowledge about selected input data are needed, therefore the relative initial notch length a/weff and the maximal value of splitting force pspmax are shown in tab. 3. note that for i variants the values of sif were evaluated according to [14] for wedge angle 30° and for all others the new calibration curves were used, see fig. 4. using the classical linear elastic fracture mechanics, the fracture toughness kic can be worked out on the basis of the initial relative notch length. the following expressions are used: ni nsp sp ic k bp p k 1000, 1000, max,  (4) using the results (calibration curves for 1000n) presented in fig. 4, relation between the maximum splitting force eq. (4) for relative notch length a/weff, we obtain results of fracture toughness of concrete, the results are shown in tab. 4. it can be seen, that the values of fracture toughness are within the interval 0.2÷1.4 mpam1/2, see in [1, 9]. the values of fracture toughness have decreasing tendency when the relative notch length grow, this is in accordance with the results in [34], where for this effect explanation the changes of t-stress values is used. variant, wedge angle a/weff [-] pspmax [kn] i, 30° 0.18 7.60 i, 30° 0.38 5.74 ii, 15° 0.18 9.80 ii, 15° 0.30 7.47 ii, 15° 0.46 4.17 iii, 15° 0.18 13.68 iii, 15° 0.33 9.33 iii, 15° 0.46 4.56 table 3: variants of evaluated experiments and corresponding wedge angle, and the relative notch length with maximal value of splitting force (both values are mean values from 3 up to 6 measurements, see detail in [29]. variant, wedge angle a/weff [-] kic [mpa m1/2] i, 30° 0.18 0.60 i, 30° 0.38 0.62 ii, 15° 0.18 0.68 ii, 15° 0.30 0.68 ii, 15° 0.46 0.59 iii, 15° 0.18 0.67 iii, 15° 0.33 0.65 iii, 15° 0.46 0.47 table 4: variants of evaluated experiments and relative notch length with corresponding value of fracture toughness. i s. seitl et alii, frattura ed integrità strutturale, 39 (2017) 100-109; doi: 10.3221/igf-esis.39.11 107 conclusions n this paper, the combinations of wedge splitting and three-point bending load applied on beam-shaped notched specimens are numerically analyzed. the numerically obtain data could be used for evaluation of experimentally obtain data as is shown in example. based on the numerical results presented here, the following conclusions can be drawn:  the values of the stress intensity factor (ki) have the same trend in the whole range of the relative crack length  for specimen variants i, ii and iii, see fig. 1.  the values of the t-stress increase with the distance of the two supports on the bottom side of the specimen, varies from negative to positive values with increasing relative crack length (a/weff), for specimen variants i, ii and iii.  the values of cod increase in the whole range of the relative crack length (a/weff) for all variants of the boundary conditions for specimen variants i, ii and iii.  the variant iiib has a crack from the bottom part of the specimens, the crack growth is influenced by combination of the wedge splitting force which in turn leads to crack closure during the load of specimen, see in fig. 6. the obtain calibration and compliance functions could be especially usefull for the published advanced model e.g. [8, 16, 20, 32]. acknowledgments he authors acknowledge the support of czech sciences foundation project no. 15-07210s and brno university of technology project no. fast-s-16-3475. the research was conducted in the frame of ipminfra supported through project no. lm2015069 of meys. references [1] anderson, t.l., fracture mechanics fundamentals and applications, crc press, (1991). [2] ansys: příručka ansys workbench 2012, česká technika – nakladatelství čvut, (2012). [3] astm e399-90. standard test method for plane-strain fracture toughness testing of high strength metallic materials. philadelphia: amer soc for testing and mater; (1990). [4] brühwiller, e., wittmann, f.h., the wedge splitting test, a new method of performing stable fracture mechanics test, engineering fracture mechanics, 35 (1990) 117–125. [5] cifuentes, h., karihaloo, d.l. determination of size-independent specific fracture energy of normal and highstrength self-compacting concrete from wedge splitting tests, construction and building materials, 48 (2013) 548– 553. doi: 10.1016/j.conbuildmat.2013.07.062. [6] cifuentes, h., lozano, m., holusova, t., medina, f., seitl, s., canteli, a., applicability of a modified compact tension specimen for measuring the fracture energy of concrete, anales de mecánica de la fractura, 32 (2015) 208– 213. [7] guinea, g.v., elices, m., planas, j., stress intensity factors for wedge–splitting geometry, int j fracture, 81 (1996) 113–124, doi: 10.1007/bf00033177. [8] havlíková, i., majtánová, r.v., šimonová, h., láník, j., keršner, z., evaluation of three-point bending fracture tests of concrete specimens with polypropylene fibres via double-k model, key engineering materials, 592-593 (2014) 185–188, doi: 10.4028/www.scientific.net/kem.592-593.185. [9] karihaloo, l.b., fracture mechanics and structural concrete, longman, (1995). [10] katzer, j., domski, j., optimization of fibre reinforcement for waste aggregate cement composite, construction and building materials 38 (2013) 790–795. doi: 10.1016/j.conbuildmat.2012.09.057. [11] knésl, z., bednár, k., two–parameter fracture mechanics: calculation of parameters and their values, institute of physics of materials academy of science of the czech republic, (1998). i t s. seitl et alii, frattura ed integrità strutturale, 39 (2017) 100-109; doi: 10.3221/igf-esis.39.11 108 [12] korte, s., boel, v., de corte, w., de schutter, g., static and fatigue fracture mechanics properties of self– compacting concrete using three–point bending tests and wedge–splitting tests. construction and building materials, 57 (2014) 1–8. doi: 10.1016/j.conbuildmat.2014.01.090. [13] leevers, p.s., radon, j.c., inherent stress biaxiality in various fracture specimen geometries, int j fracture, 19 (1983) 311–325. doi: 10.1007/bf00012486. [14] linsbauer, h.n., tschegg, e.k., fracture energy determination of concrete with cube shaped specimens, zement und beton, 31 (1986) 38–40. [15] merta, i., tschegg, e.k., fracture energy of natural fibre reinforced concrete, construction and buildings materials 40 (2013) 991–997. doi: 10.1016/j.conbuildmat.2012.11.060. [16] pazdera, l., topolar, l., simonova, h., fojtu, p., smutny, j., havlikova, i., kersner, z., rodriguezova, v., determine parameters for double-k model at three-point bending by application of acoustic emission method, applied mechanics and materials, 486 (2014) 151–156. doi: 10.4028/www.scientific.net/amm.486.151. [17] planas, j., elices, m., guinea, g.v., measurement of the fracture energy using three–point–bend tests: 2 influence of bulk energy dissipation. materials and structures, 25 (1992) 305–312. [18] rilem 106, determination of the fracture energy of mortar and concrete by means of three-point bend tests on notched beams, (1985) 285–290. [19] rilem report 5 fracture mechanics, test methods for concrete, (1991). [20] ruiz, g., ortega, j.j., yu, r.c., xu, s., wu, y., loading rate effect on the double –k fracture parameters of concrete, 9th international conference on fracture mechanics of concrete and concrete structures, (2016) 1–10. doi: 10.21012/fc9.038 [21] seitl, s., bermejo, c., sobek, j., veselý, v., two parametr description of crack tip stress fields for wedge splitting test specimen: influence of wedge angle, advanced materials research, 969 (2014) 345–350. doi: 10.4028/www.scientific.net/amr.969.345. [22] seitl, s., korte, s., de corte, w., boel, v., sobek, j., veselý, v., selecting a suitable specimen shape with low constraint for determination of fracture parameters of cementitious composites, key engineering materials, 577–578 (2014) 481–484. doi: 10.4028/www.scientific.net/kem.577-578.481. [23] seitl, s., nieto garcía, b., merta, i., wedge splitting test method: quantification of influence of glued marble plates by two-parameter fracture mechanics, frattura ed integrità strutturale, 30 (2014) 174-181. doi: 10.3221/igfesis.30.23. [24] seitl, s., veselý, v., routil, l., two–parameter fracture mechanical analysis of a near-crack-tip stress field in wedge splitting test specimens, computers & structures, 89 (2011) 1852–1858. [25] sobek, j., veselý, v., seitl, s., combination of wedge splitting and bending fracture testcrack tip stress field and nonlinear zone extent analysis, advanced materials research, 969 (2014) 67–72. doi: 10.4028/www.scientific.net/amr.969.67. [26] sobek, j., veselý, v., shape and compliance functions of splitting/bending test specimens for determination fracture parameters of quasi-brittle materials, 33rd spanish conference on fracture and structural integrity – 33er encuentro del grupo español de fractura gef in: m.r. elizalde gonzález, a. martín meizoso, j.m. martínez esnaola, i. ocaña arizcorreta (eds.) (anales de mécanica de la fractura volumen 33), donostia‐san sebastián, spain, (2016). [27] tada, h., paris, p.c., irwin, g.r., the stress analysis of crack handbook, third ed., the american society of mechanical engineers three park avenue, new york, (2000). [28] veselý, v., frantík, p., sobek, j., malíková, l., seitl, s., multi-parameter crack tip stress state description for evaluation of nonlinear zone width in silicate composite specimens in component splitting/bending test geometry, fatigue and fracture of engineering materials and structures, 38(2) (2015) 200–214. doi: 10.1111/ffe.12170. [29] veselý, v., merta, i., šimonová, h., schneemayer, a., seitl, s., keršner, z., component wedge-splitting/bending test of notched specimens with various crack-tip constraint conditions: experiments and simulations, 9th international conference on fracture mechanics of concrete structures framcos-9, (2016) 1–12. doi: 10.21012/fc9.086. [30] veselý, v., sobek, j., frantík, p., štafa, m., šestáková, l., seitl, s. estimation of the zone of failure extent in quasibrittle specimens with different crack-tip constraint conditions from stress field, key engineering materials, 592-593 (2014) 262–265. doi: 10.4028/www.scientific.net/kem.592-593.262. [31] veselý, v., sobek, j., šestáková, l., frantík, p., seitl, s., multi-parameter crack tip stress description for estimation of fracture proces zone extent in silicate composite wst specimens, frattura ed integrita strutturale, 7(25) (2013) 69– 78. doi: 10.3221/igf-esis.25.11. [32] wang, y., hu, x., liang, l., zhu, w., determination of tensile strength and fracture toughness of concrete using notched 3-p-b specimens, engineering fracture mechanics 160 (2016) 67–77. s. seitl et alii, frattura ed integrità strutturale, 39 (2017) 100-109; doi: 10.3221/igf-esis.39.11 109 doi: 10.1016/j.engfracmech.2016.03.036 [33] williams, m.l., on the stress distribution at the base of stationary crack, asme journal of applied mechanics, 24 (1957) 109–114. [34] zhao, y., xu, b., effect of t-stress on the mode-i fracture toughness of concrete, c. r. mecanique, 342 (2014) 490– 500. doi: 10.1016/j.crme.2014.03.001. << /ascii85encodepages false /allowtransparency false /autopositionepsfiles true /autorotatepages /none /binding /left /calgrayprofile (dot gain 20%) /calrgbprofile (srgb iec61966-2.1) /calcmykprofile (u.s. web coated \050swop\051 v2) /srgbprofile (srgb iec61966-2.1) /cannotembedfontpolicy /error /compatibilitylevel 1.4 /compressobjects /tags /compresspages true /convertimagestoindexed true /passthroughjpegimages true /createjobticket false /defaultrenderingintent /default /detectblends true /detectcurves 0.0000 /colorconversionstrategy /cmyk /dothumbnails false /embedallfonts true /embedopentype false /parseiccprofilesincomments true /embedjoboptions true /dscreportinglevel 0 /emitdscwarnings false /endpage -1 /imagememory 1048576 /lockdistillerparams false /maxsubsetpct 100 /optimize true /opm 1 /parsedsccomments true 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can be opened with acrobat and adobe reader 5.0 and later.) >> /namespace [ (adobe) (common) (1.0) ] /othernamespaces [ << /asreaderspreads false /cropimagestoframes true /errorcontrol /warnandcontinue /flattenerignorespreadoverrides false /includeguidesgrids false /includenonprinting false /includeslug false /namespace [ (adobe) (indesign) (4.0) ] /omitplacedbitmaps false /omitplacedeps false /omitplacedpdf false /simulateoverprint /legacy >> << /addbleedmarks false /addcolorbars false /addcropmarks false /addpageinfo false /addregmarks false /convertcolors /converttocmyk /destinationprofilename () /destinationprofileselector /documentcmyk /downsample16bitimages true /flattenerpreset << /presetselector /mediumresolution >> /formelements false /generatestructure false /includebookmarks false /includehyperlinks false /includeinteractive false /includelayers false /includeprofiles false /multimediahandling /useobjectsettings /namespace [ (adobe) (creativesuite) (2.0) ] /pdfxoutputintentprofileselector /documentcmyk /preserveediting true /untaggedcmykhandling /leaveuntagged /untaggedrgbhandling /usedocumentprofile /usedocumentbleed false >> ] >> setdistillerparams << /hwresolution [2400 2400] /pagesize [612.000 792.000] >> setpagedevice microsoft word numero_58_art_17_3107.docx a. i. fezazi. et alii, frattura ed integrità strutturale, 58 (2021) 231-241; doi: 10.3221/igf-esis.58.17 231 numerical prediction of the ductile damage for axial cracks in pipe under internal pressure fezazi amina ismahène, mechab belaïd, salem mokadem, serier boualem university of djillali liabes, lpmm laboratory, sidibel abbes, algeria fezaziismahane223@gmail.com, bmechab@yahoo.fr, moka_salem@yahoo.fr, boualems@yahoo.fr abstract. this study presents a numerical prediction of the ductile damage for axial cracks in pipe subjected to internal pressure. the three dimensional finite element methods used to evaluate the j-integral. the effect of the external radius (rext), thickness of the pipe (t), length crack (a), applied loads (p) and crack position has studied. the monte carlo method was used to determine the probabilistic characteristics of the j-integral. it’s also used later to predict the failure probability based on initiation of the crack growth. we note that the crack size and the geometries of the pipe are an important factor influencing on the durability of the pipe. keywords. failure; pipe; fracture mechanics; monte carlo method. citation: fezazi, a. i., mechab, b., salem, m., serier, b., numerical prediction of the ductile damage for axial cracks in pipe under internal pressure, frattura ed integrità strutturale, 58 (2021) 231-241. received: 19.05.2021 accepted: 26.07.2021 published: 01.10.2021 copyright: © 2021 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. introduction ipelines have been built to transport many other fluids (liquids and gases). for instance, liquid fertilizers are often transported long distances via pipelines. the mixture of oil and natural gas coming out of a well must be transported as two-phase flow by pipelines to processing facilities before the oil can be separated from the gas. the fracture prediction and the reliability of such piping systems in various practical applications are primordial given their impact on the economic plan and security [1-4]. several authors have been studied pipe fracture problems by means of numerical simulation in order to assess the mechanical integrity, taking into account different crack shapes [5-7]. the ductile fracture mechanics parameters for the cracked pipes subjected to internal pressure is important in structural integrity assessment of defective components [8-10]. the safety assessment of these structures and the comprehension of failure mechanisms are essential to study the reliability of pipelines for the liquid or gas transport [11-14]. probabilistic fracture mechanics is a means of quantifying the failure probability resulting from uncertainties in the values of the parameters used to perform a failure assessment of cracked structures through probabilistic analysis techniques [1517]. rahman [18] analyzed small cracks in tubes under internal pressure and bending loads, where one of the observations was that for through-wall-thickness cracks the effect of internal pressure was significant for highp a. i. fezazi et alii, frattura ed integrità strutturale, 58 (2021) 231-241; doi: 10.3221/igf-esis.58.17 232 hardening pipe materials, and insignificant otherwise. this study provides engineering j estimation for the ductile fracture mechanics of cracked pipe subjected to internal pressure. the effect of the of the external radius (rext), thickness of the pipe (t), length crack (a), applied loads (p) and crack position has been studied by the three dimensional finite element method for evaluating the j-integral. the monte carlo method is used to predict the distribution function of the mechanical response of the structure. geometrical models his study presents a three-dimensional finite element analysis of the code abaqus [19] for the cracked pipes under internal pressure load. the crack length (a)ranged from 10mm to 100 mm, and the external radius (rext)varied from 250mm to 800mm, the thickness of the pipe’s (t) varied from 10mm to 30mm and the internal pressure (p) varied from 10bar to 120bar (see fig.1). figure 1: (a)definition of the longitudinal crack, (b) schematic illustration for cracked pipes under internal pressure material model e analyses were performed to calculate elastic–plastic fracture mechanics parameters. the material in the fe analyses is assumed to follow the ramberg-osgood (r-o) relation:               0 n y y (1) tab. 1 give the mechanical properties of the material used in this study. e (gpa) y (mpa) u (mpa) υ α n 203 302 450 0.3 18.826 3.887 table 1: summary of tensile properties of sa333 gr. 6 carbon steel [20]. t f a. i. fezazi. et alii, frattura ed integrità strutturale, 58 (2021) 231-241; doi: 10.3221/igf-esis.58.17 233 finite element mesh ig. 2 gives a typical fe mesh of the cracked pipe. an 8-node doubly curved thick shell, reduced integration (sd8r in abaqus) was used to analyses a model of the pipe. the j integral values were extracted using a domain integral method within abaqus. this method provides high accuracy with rather coarse models in threedimensions. the j integral values were extracted using a domain integral method within abaqus. this method provides high accuracy with rather coarse models in three-dimensions. the resulting finite element model as shown in fig. 2. the crack tip was modelled with focused elements composed with 5 contours. the number of nodes and elements in the models studied are presented in tab. 2 and 3. figure 2: meshing model of the cylinder. models crack size (a) number of elements number of nodes 1 2 3 4 5 6 7 8 9 10 10mm 20mm 30mm 40mm 50mm 60mm 70mm 80mm 90mm 100mm 2508 3016 3604 4273 5022 5852 6762 7752 8823 9974 30816 34217 39017 45212 52803 61789 72171 83949 97122 111690 table 2: the number of nodes and elements in the models studied for (rext =500mm, t=20mm=30mm) models external radius (rext) number of elements number of nodes 1 2 3 4 5 6 7 8 9 10 11 250mm 300mm 350mm 400mm 450mm 500mm 550mm 600mm 650mm 700mm 750mm 5168 6109 7060 8021 8992 9974 10965 11967 12979 14001 15033 15847 27351 42687 61855 84856 111690 142354 176852 215182 257344 303339 table 3: the number of nodes and elements in the models studied for (a =100mm, t=20mm=30mm) the boundary conditions of the models studied in the two positions are: ux=uy=uz=urx=ury=urz=0 f a. i. fezazi et alii, frattura ed integrità strutturale, 58 (2021) 231-241; doi: 10.3221/igf-esis.58.17 234 figure 3: boundary condition of the cylinder results and discussion analysis of crack behavior o numerically simulate the fracture behaviour of pipes under high pressure using the finite element method, a crack of size "a" is initiated longitudinally in a pipeline of well-defined size by its radius "r" and thickness "t". the cracked pipe is subjected to a pressure of 100 bar. two approaches, elastic and elastic-plastic, were used in thisstudy.the results of this modelling are shown in figs. 4 and 5. the analysis of these figures clearly shows that the jintegral increases as the cracking defect advances. this increase is even more pronounced when the crack is initiated in a thin pipe (fig. 4 a, b). it should be noted, however, that compared to the elastic-plastic approach, the elastic model results in larger j-integral values (fig. 4b). this difference is much more pronounced for long cracks. the elastic-plastic approach is more realistic as the material used for pipelines has a ductile behaviour, characterised by a very high resistance to cracking (toughness). it is clearly shown in fig. 6a, b, that cracks initiated in a thick pipe are more stable than those initiated in a thin tubular structure. this behaviour is explained by the low values of the integral, regardless of the elastic or elastic-plastic approach used. this explicitly shows that thin pipes have a higher risk of bursting than thick pipes. this risk is strongly increased when the crack is initiated in a large diameter pipe (fig.5a, b). this figure shows that, irrespective of the elastic or elasticplastic approach used, cracks initiated in large pipes under high pressures are more unstable. this instability is much more pronounced for long cracking faults initiated in pipes exhibiting elastic-plastic behaviour. the relatively high values of the j-integral are characteristic of this instability. it is clearly established that the economic and efficient transport of hydrocarbons through pipelines requires an increase in pressure. this behaviour shows that the damage of pipes under high pressure is closely related to their geometric characteristics: thickness-diameter. these two quantities are fundamental parameters for improving the efficiency and performance of hydrocarbon transport by pipeline. to this end, it would be relevant to analyse in more detail the effect of these geometric parameters on the cost-effectiveness of these tubular structures, subjected to high pressures. this analysis is carried out in terms of the variation of the elastic and elastic-plastic j-integral. effect of geometric characteristics the profitability and performance of hydrocarbon transport by pipeline require increasingly high pressures. in order to meet this requirement, it is strictly necessary to play on both the geometric parameters of the tubular structure and especially on its diameter and thickness for a given type of pipe. to this end, it is relevant to analyze, numerically in three dimensions, the effect of these two geometric quantities on the mechanical behavior of pipes subjected to high pressures. two approaches, elastic and elastic-plastic, were chosen for this study.the results are shown in figs. 6 and 7. these two figures show the variation of the elastic and elastic-plastic j integral as a function of pipe thickness and radius respectively. it is explicitly shown in fig. 6 that cracks initiated longitudinally in thick pipes, subjected to high pressures, are more stable regardless of the approach used. t a. i. fezazi. et alii, frattura ed integrità strutturale, 58 (2021) 231-241; doi: 10.3221/igf-esis.58.17 235 figure 4: variation of the j-integral according to the crack length for two different values of thickness (t) of the pipe’s elastic analyses, (b) elastic-plastic analyses. figure 5: variation of the j-integral according to the crack length for two different values of the external radius (rext) of the pipe’s a) elastic analyses, b) elastic-plastic analyses the results are shown in figs. 6 and 7. these two figures show the variation of the elastic and elastic-plastic j-integral as a function of pipe thickness and radius respectively. it is explicitly shown in fig. 6 that cracks initiated longitudinally in thick pipes, subjected to high pressures, are more stable regardless of the approach used. this stability is defined by low values of the j-integral. conversely, these same cracks are very unstable when initiated in thin pipes. the high values of this failure parameter are characteristic of the risk of propagation of such cracking defects. this cracking behavior clearly shows that thick pipes have a good resistance to bursting and ensure a good efficiency of this type of transport. it should be noted, however, that this geometric parameter is a key determinant of the rigidity of the tubular structure. these thick structures are more rigid and resistant to higher and higher pressures and present a more efficient means of transport. to make this type of transport even more efficient and to withstand high pressures, it is strongly recommended to use large diameter pipelines. these allow for increased flow rates and good resistance to high media pressures. the effect of this geometric parameter on the behavior of longitudinal cracks initiated in pipes is illustrated in fig. 8. it should be noted, however, that large diameter pipes increase the risk of instability of these cracks by increasing the j-integral, regardless of the approach used. to reduce this risk, it is necessary to use large diameter pipes, as shown in fig. 6. the latter clearly illustrates that cracks initiated in large diameter pipes are stable and pose no risk of propagation. these tubular structures have a high resistance to bursting as shown in fig. 9a. analysis of this figure indicates that the propagation of long longitudinal cracks, initiated in thicker diameter pipelines, is stable (fig. 9b). a. i. fezazi et alii, frattura ed integrità strutturale, 58 (2021) 231-241; doi: 10.3221/igf-esis.58.17 236 figure 6: variation of the j-integral according to the thickness (t) for the elastic and elastic-plastic analyses of the pipes. figure 7: variation of the j-integral according to the external radius (rext) for the elastic and elastic-plastic analyses of the pipes. figure 8: variation of the j-integral according to the external radius (rext) for the two different values of thickness (t) for elastic-plastic analyses of the pipes. the results obtained in this work show that, in order to withstand the increasingly high pressures required to improve the performance of pipeline transport, these tubular structures must be large in diameter and thick. thicknesses significantly reduce the risk of bursting of large diameter pipes (fig. 10). the negative effect of the large pipe size (diameter) is compensated for by the increased thickness. a. i. fezazi. et alii, frattura ed integrità strutturale, 58 (2021) 231-241; doi: 10.3221/igf-esis.58.17 237 figure 9: variation of the j-integral according to the internal pressure (p) for the two different values of: (a) external radius (rext) and (b) thickness (t) for elastic-plastic analyses of the pipes. figure 10: variation of the j-integral according to the external radius (rext) for(a) the elastic and (b) elastic-plastic analyses of the pipes. effect of location in order to highlight the location of the preferential site of initiation of the cracking defect, a comparative study of the behavior of a longitudinal and circumferential crack of size "a", initiated in a pipe under high pressure was carried out (fig.11).the analysis of this figure shows that, regardless of the elastic or elastic-plastic approach and the size of the crack, the risk of bursting is more likely in the longitudinal direction than in the circumferential direction. compared to the elastic approach (fig. 11 a), the elastic-plastic model results in a high probability of crack propagation. this risk of pipe damage is more pronounced for relatively long cracks (fig.11b). the values of the " j-integral " growth criterion help to explain this crack instability. this behavior shows that the ultimate pressures stress the pipes more strongly according to their length than according to their circumference. the results shown in this figure explicitly demonstrate that threedimensional numerical modelling, using the finite element method, can predict not only the damage of pipes under high pressure but also its preferential direction. in other words, long cracks, under the same loading conditions, propagate more easily along the pipes. in the case of short cracks "a<50mm", the effect of the nature of the crack (longitudinal and circumferential) is very small, the very small difference between the j-integrals for these two types of cracks is characteristic of this behavior. beyond this size and whatever the elastic or elastic-plastic approach, this deviation a. i. fezazi et alii, frattura ed integrità strutturale, 58 (2021) 231-241; doi: 10.3221/igf-esis.58.17 238 increases with the progress of the crack. in the elastic approach and whatever the advance of the cracking defect, these two types of cracks are more stable, the low values of the j integral compared to that resulting from the elastic-plastic behavior allow to explain this stability. figure 11: variation of the j-integral as a function of crack size for longitudinal and circumferential cracks initiated in a pipeline in (a) elastic and (b)elastic plastic analyses. probabilistic elastic-plastic fracture mechanic analysis random parameters and fracture response he probabilistic approach involves the probability assessment of the damage of structure. this approach allows analyzing the chain of events and equipment failures and estimating the total probability of this problem. main disadvantage of this approach is related to the lack of statistics on equipment failure [21-23]. probabilistic calculations for ductile materials have mainly been contributed in the past decade by mechab et al [24].in this part a probabilistic fracture mechanics model established from three-dimensional fem analyses of axial cracked pipes subjected to internal pressure. the fem results were used to develop statistical parameters that were used with the deterministic model in a monte carlo analysis. the density function is evaluated by using monte carlo method. the basic idea is to draw random samples for the input parameters, then to compute the mechanical response for eachsample. we have realised this work by the fortran program, response by using monte carlo method. to achieve a highaccuracy of the results, we have carried out 105 simulations. the random components are: material tensile parameters, e, υ, α, n and applied stress σap, geometric parameters. the crack length (a)ranged from 10mm to 100 mm, and the external radius (rext) varied from 250mm to 750mm and the thickness (t). all or some of these variables can be modelled as random variables. hence, any relevant fracture response, such as the j integral, should be evaluated by the probability. the safety margin (j) (xi) is the probabilistic design rule, which defines the plate safety by the condition (j) (xi) >0 and the plate failure by (j) (xi) ≤ 0. in the fig. 12 the probability density function is obtained by fitting the histogram with theoretical models are investigated: the gaussian law offers an acceptable approximation of the j probability density function, with good estimation of the average. fig. 13 and 14 shows the cumulative probability of j integral for different values of the crack size and of the external radius (rext). we noted that when the crack size and the external radius (rext) is length the value of the cumulative probability of j is large. it can be seen that the margin increases significantly with the uncertainties related to the crack size and of the mean pipe’s radius to its thickness (rm/t), leading to larger failure probability. the uncertainty in the crack size (a) and the external radius (rext), have a significant effect on increasing the probability of failure of piping. finally, the failure probabilities depend on the crack size and geometries of piping. t a. i. fezazi. et alii, frattura ed integrità strutturale, 58 (2021) 231-241; doi: 10.3221/igf-esis.58.17 239 variable mean coefficient of variation (cov) young modulus (e) ramberg-osgood exponent (n) ramberg-osgood coefficient (α) crack length (a) thickness (t) external radius(rext) internal pressure (p) 203 mpa 3.887 18.826 10mm 30mm 500mm 100 bar 1% 1% 1% 2% 1% 2% 1% table 4: random variables and corresponding parameters. figure 12: histogram and probability density function of j integral. figure 13: the cumulative of j integral for different values of crack seize (a). figure 14: the cumulative of j integral for different values of the external radius (rext). a. i. fezazi et alii, frattura ed integrità strutturale, 58 (2021) 231-241; doi: 10.3221/igf-esis.58.17 240 conclusion he piping system is an important element in power plants, and thus application of fracture mechanicsanalysis to such pressurised piping is important in structural integrity assessment of plant components. the fracture mechanics is to describe the correlation between standard specimen fracture and macroscopic fracture of the cracked structure, through the use of various crack-tip governing parameters. the objective of this study was to evaluate of the ductile damage of the cracked pipe for j-estimation models used in probabilistic elastic plastic fracture mechanics subjected to internal pressure load. it is based on the engineering j estimation for the ductile fracture mechanics analyses using the three-dimensional finite element calculations of the j-integral. the effect of the external radius (rext), thickness of the pipe (t), length crack (a), applied loads (p) and crack position has studied. the fem results were used to develop statistical parameters that were used with the deterministic model in a monte carlo analysis. we note that the crack size and the external radius (rext) of the pipes are an important factor influencing on the durability of piping. references [1] budhe, s., banea, m.d. de barros, s. (2020). prediction of the burst pressure for defective pipelines using different semi-empirical models, frattura ed integrità strutturale, 52, pp. 137-147; doi: 10.3221/igf-esis.52.12. [2] nikhil, r., krishnan, s.a., sasikala, g., moitra, a., shaju, k., albert., bhaduri study, a.k.,(2021). on fracture transferability from compact type specimen to pipe for 316ln stainless steel”, int. j. pres. ves. pip. 192, 104437. doi: 10.1016/j.ijpvp.2021.104437 [3] barsouma, i., yurindatama, d t. (2020). collapse analysis of a large plastic pipe using cohesive zone modelling technique, int. j. pres. ves. pip. 187, 104155. doi: 10.1016/j.ijpvp.2020.104155. [4] zheng, q., abdelmoety, a k., li, y., kainat, m., nader ,y g., adeeb, s.,(2021). reliability analysis of intact and defected pipes for internal pressure related limit states specified in csa z622:19”, int. j. pres. ves. pip. 192, 104411. doi: https ://doi.org/10.1016/j.ijpvp.2021.104411 [5] chattopadhyay, j., dutta, b.k., vaze, k.k.,(2014). development of new correlations for improved integrity assessment of pipes and pipe bends”, nucl .eng. des, 269, pp. 108–115. doi: 10.1016/j.nucengdes.2013.08.015 [6] r6 (2001). assessment of the integrity of structures containing defects, revision 4. british energy generation ltd, gloucester. [7] weltevreden, m., hadley,i. , coules, h.,(2021). probabilistic treatment of pipe girth weld residual stress in fracture assessment, int. j. pres. ves. pip. 192, 104397. doi: 10.1016/j.ijpvp.2021.104397 [8] muthanna, b.g.n., bouledroua, o., benziane m.m., setvati, m r , djukic, m b., (2020). assessment of corroded [9] api 5l x52 pipe elbow using a modified failure assessment diagram, int. j. pres. ves. pip. 190, 104291. doi: 10.1016/j.ijpvp.2020.104291 [10] salem, b., mechab, b., berrahou, m., bachirbouiadjra, b., serier, b. (2019). failure analyses of propagation of cracks in repaired pipe under internal pressure, journal of failure analysis and prevention. 19(1), pp. 212–218. doi:10.1007/s11668-019-00592-3 [11] mechab, b., serier, b., bachir bouiadjra, b., kaddouri, k., feaugas, x. (2011). linear and non-linear analyses for semi-elliptical surface cracks in pipes under bending, int. j. pres. ves. pip. 88, pp. 57–63. doi: 10.1016/j.ijpvp.2010.11.001 [12] mechab, b., medjahdi, m., salem, m., serier, b. (2020). probabilistic elastic-plastic fracture mechanics analysis of propagation of cracks in pipes under internal pressure, frattura ed integrità strutturale, 54, pp. 202-210. doi: 110.3221/igf-esis.54.15. [13] jeong, s-h., won, m-g., huh, n-s., choi, j-b., kim, w-g., lee, h-y. (2021). on elastic-plastic and creep fracture mechanics parameters estimates of non-idealized axial through-wall crack in pressurized pipe, int. j. pres. ves. pip. 189, 104292. doi: 10.1016/j.ijpvp.2020.104292. [14] bassindale, c., wang, x., tyson., william, r., xu, s., (2020). fast ductile fracture: effect of inertia on propagation resistance and ctoa in pipe steels, int. j. pres. ves. pip. 187, 104163. doi: 10.1016/j.ijpvp.2020.104163. [15] bianchetti, c.,pino muñoz, d., leblé, b., bouchard, p-o. (2021). ductile failure prediction of pipe-ring notched aisi316l using uncoupled ductile failure criteria, int. j. pres.ves.pip.191, 104333. doi: 10.1016/.ijpvp.2021.104333 [16] qian, g., niffenegger, m.,karanki, d.r., li, s. (2013). probabilistic leak before-break analysis with correlated input parameters, nucl. eng. des. 254, pp. 266–271 doi: 10.1016/s0308-0161(96)00034-8. t a. i. fezazi. et alii, frattura ed integrità strutturale, 58 (2021) 231-241; doi: 10.3221/igf-esis.58.17 241 [17] tee, k.f., khan, l.r., chen, h.p. (2013). probabilistic failure analysis of underground flexible pipes, struct. eng. mech. 47(2), pp. 167–183. doi: 10.12989/sem.2013.47.2.167. [18] rahman, s. (1995). a stochastic model for elastic-plastic fracture analysis of circumferential through-wall-cracked pipes subject to bending, eng. fract. mech. 52, pp. 265–288. doi: 10.1016/0013-7944(95)00018-q. [19] rahman, s. (2000). probabilistic elastic-plastic fracture analysis of circumferentially cracked pipes with finite-length surface flaws, nucl. eng. des. 195, pp. 239–260. doi: 10.1016/s0029-5493(99)00214-9. [20] abaqus (1998), abaqus standard/user’s manual, version 5.8-1. hibbitkarlsson& sorensen, inc., pawtucket, ri, usa. [21] saxena, s., ramachandra murthy, d s. (2004). elastic-plastic fracture mechanics based prediction of crack initiation load in through-wall cracked pipes, engineering structures 26, pp. 1165–1172. doi: 10.1016/j.engstruct.2004.02.002 [22] rahman, s. (1997). probabilistic fracture analysis of pipes with circumferential flaws, int. j. pres. ves. pip. 70, pp. 223–236. doi: 10.1016/s0308-0161(96)00034-8. [23] rahman, s., brust, f.w. (1997). approximate methods for predicting j-integral of a circumferentially surface-cracked pipe subject to bending, int. j. fract. 85, pp. 11–130. doi: 10.1023/a:1007322018722 [24] yusa, n., song, h., iwata, d.,uchimoto, t., takagi, t., moroic, m., (2021). probabilistic evaluation of emar signals to evaluate pipe wall thickness and its application to pipe wall thinning management”, ndt & e international 122, 10247. doi: 10.1016/j.ndteint.2021.102475 [25] mechab, b., chioukh, n., mechab boubaker, b., serier, b. (2018). probabilistic fracture mechanics for analysis of longitudinal cracks in pipes under internal pressure, journal of failure analysis and prevention. 18(6), pp. 16431651. doi: 10.1007/s11668-018-0564-8. microsoft word numero_26_art_5 s. bulatovic et alii, frattura ed integrità strutturale, 26 (2013) 41-48; doi: 10.3221/igf-esis.26.05 41 failure of steam line causes determined by ndt testing in power and heating plants srdjan bulatovic yugoslav river shipping, belgrade, serbia srdjan.bulatovic@yahoo.com vujadin aleksic institute for testing materials-ims institute, bulevar voijvode mišića 43, belgrade, serbia ljubica milovic faculty of technology and metallurgy, belgrade, serbia abstract. this paper examines leakage and damages of steam and provides an overview of ndt testing in order to determine the cause of steam lines failure in power plants and heating plants. this approach may be applied to similar structures and its application in preventive maintenance would help extend the life of steam pipes. keywords. steam line; failure; ndt testing. introduction team lines and high pressure pipelines are vital parts of the thermal power plant system. in fact, they are the connection between the boiler and turbines in power plants or boilers in power stations and customers in heating plants. they are critical components in power plants and heating plants and have a significant impact on the reliability and availability of power plants and heating plants. continuous exploitation in very hard working conditions can lead to relatively frequent system steamline failure. damages on steam line elements may appear well before it is expected, and not just as a result of internal pressure and temperature, but also as a consequence of the loads that occur due to poor design and inadequate maintenance. also, damage of steam line elements may appear because of numerous on-off switching of the boiler as well as misuse of start diagram. failures of steam lines, other than direct material damage, could jeopardize the safety of personnel and equipment. among the causes of these failures inadequate operation and maintenance takes a high rank. leaking of steam lines caused by material creep is expected if number of hours spent in operation is higher than design number of hours. fig. 1 shows part of steam line of heated vapor in block 1 on tpp "kolubara a" veliki crljeni (near belgrade). the ra, rb and rc line thermal units 1 to 5 span lenghts of 200-300 m and capacities of 300-500 t/h. during its operation there were relatively frequent delays caused by defects of supporting structure [1, 2], and in extreme case even failure or steam line leakage, which is usually explained by gaps in technology development and mishandling. s s. bulatovic et alii, frattura ed integrità strutturale, 26 (2013) 41-48; doi: 10.3221/igf-esis.26.05 42 figure 1: part of the steam line during ndt. technical diagnostics uring the operation period, fatigue of steam line components may occur. degradation of material properties and deformation of elements can be accelerated due to the exploitation and repair errors, that's why periodic or continuous diagnostic measurements, conducting periodic tests and data collection programs defined by [1, 2] are needed. in this way, processes that could lead to the creation of system damage are under systematic control, what is also the legal obligation imposed by the regulations, directives and harmonized standards [3 5]. properly conducted technical diagnostics protects parts of the steam line from accident, and also ensures safer conditions for employees as well as rational techno-economic exploitation and maintenance. technical diagnostic of steam lines must be based on three basic principles:  volume of tests and measurements shall be in accordance with the program of research [1] and an expert knowledge of steam line structure and working conditions;  tests and measurements must be performed in accordance with special procedures, using appropriate equipment and qualified personnel;  test results should be presented in such way that the conclusions include steam line operating conditions, the availability of the test team and staff with appropriate experience and knowledge in the field of design, construction, installation, operation, maintenance, reliability, fracture mechanics and others. ndt to determine cause of steam line failure or purpose of determining the causes of failure it is necessary to make steam line 100% visual inspection, magnetic, penetrant, ultrasonic, hardness and method of replica testing. if necessary, other tests that would give us a reliable and useful results to determine causes of steam line failure could be done. fig. 2 shows the possibility of evaluating some damage using ndt methods in the life of the steam line. visually optical control (vt) vt is used to detect defects that are visible on the surface of the steam line from the outside or inside of the tube. it applies regardless the method to be applied after it, because it is possible to detect errors, such as in our case, and avoid the use of other, more costly methods of ndt. it is often used for the selection of critical areas of the facility for the application of other ndt testing methods. at the same objects it may be performed multiple times (eg, before and after cleaning, or before and after the execution of corrosion protection, etc.). control of the inside of the tube (endoscopy) allows optical access to the interior of steam lines. it is performed using an endoscope, and as a result we get control of video or photograph controlled inner surface, fig. 3.     d f s. bulatovic et alii, frattura ed integrità strutturale, 26 (2013) 41-48; doi: 10.3221/igf-esis.26.05 43     figure 2: application of ndt methods in detecting defects in the life of the steam line [6]. figure 3: photo of interior surfaces steamline. magnetic particle testing (mt) the method is based on emphasizing the stray magnetic flux caused by the presence of surface or subsurface defects like cracks, notches, inclusions and other types of sharp or planar defects. advantage of the method is that it requires a moderate cost, and if done correctly, you get a very good sensitivity for the detection of surface defects. the disadvantages of this method is that it could only be appllied to ferromagnetic materials as well as the potential need for degaussing after completing the testing. the method is commonly used for the detection of cracks and other defects in weld joints, castings and forgings. ultrasonic testing (ut) the method is based on detecting changes in acoustic resistance due to the presence of cracks, voids, inclusions, and general physical separation in the material. the advantage of the method is that is also applicable to the thicker material, it is excellent for detecting and locating cracks and other defects, and it is suitable for automation. the biggest disadvantages are the need for a medium on the surface to be tested (or complete immersion of testing item in contact medium), as well as the request that surface on which the probe is moving is relatively smooth (ie cleaning needs, grinding the metallic shine). the most common application is to detect and precisely determine the position of defects in plate, welded joints (and butt and fillet) steel castings and forgings (if their geometric configuration allows). application of this method for testing materials with high attenuation of ultrasound energy (for example, high alloyed austenitic steels, cast bronze ...) is difficult and can be done only under special circumstances. hardness testing (ht) for evaluation of properly applied heat treatment after welding, hardness testing of the base metal, haz and weld materials are performed. at the same time, hardness and hardness differences must be within the limits of applied materials. in tab. 1. the recommended values of hardness [7] of materials that are commonly used to produce steam line are shown. s. bulatovic et alii, frattura ed integrità strutturale, 26 (2013) 41-48; doi: 10.3221/igf-esis.26.05 44 materials hardness [hv] base materials2 weld joint heat affected zone (haz) 1.5415 15 mo3 140-190 260 320 1.7335 13crmo44 135-185 270 320 1.7380 10crmo910 140-190 280 320 1.7715 14mov63 145-190 280 320 1.7745 15crmov510 140-215 280 320 1.4922 x20crmov12-1 215-265 300 3501 1 hardness value of 350 hv must not be exceeded in the haz 2 for cold-rolled sections such as tube bends in the base material greater hardness for hv 60 are allowed. hb  0.95hv; m  1/3hb table 1 method of replica testing (rep) metallographic examination, fig. 4, the surface layer of material of pipe bends, weld joints and pipes on the old steam pipe ra 10 block a1, is conducted by the method of nondestructive testing of materials, using metallographic replica, according to [8]. figure 4: overview of possible damage to the established method of replica [9]. in order to detect the microstructure of materials, adequate preparation is made of tested surfaces, and that included cleaning and a range of fine sanding operations. after the final polishing and cleaning, the test surfaces were eroded with appropriate reagent, ie. 4% nital. determining damages tructures of the steam line is exposed to the low cycle fatigue loads. this load caused a fatigue damage of pipes and leakage of steam lines on observed object, fig. 5, which was confirmed by visual inspection. after that, ndt methods are used for testing the steam pipeline section and supporting structure before and after damage. fig. 6 and 7 show the measurement of control and testing methods, ndt, and in tab. 2 and 3 the results of measurements of diameter and wall thickness of the damaged part of the steam line are listed. s s. bulatovic et alii, frattura ed integrità strutturale, 26 (2013) 41-48; doi: 10.3221/igf-esis.26.05 45 figure 5: determination of damage by visual inspection. figure 6: scheme of measurement tests (dimensional inspection of the damaged steam line part). figure 7: scheme of measuring and making replicas of the damaged steam line part ra-10. s. bulatovic et alii, frattura ed integrità strutturale, 26 (2013) 41-48; doi: 10.3221/igf-esis.26.05 46 part of the tube diameters (mm) plane measurements a b c d e axis measurements 0º-180º 288.9 276.8 285.0 285.9 283.1 axis measurements 90º-270º 282.4 284.0 285.1 284.3 283.4 table 2 part of the tube wall thickness (mm) plane measurements a b c d e remark d es ig na tio n of m ea su ri ng p oi nt 0º 21.2 20.1 (r3) 22.4 22.4 22.9 23.2 (a-r1) 90º 24.3 24.7 25.6 25.8 25.5 24.7 (a-r2) 180º 27.0 27.3 27.0 27.9 27.1 / 270º 24.2 23.3 23.1 23.9 23.7 / r place where replicas are taken table 3 assessment of the microstructure of the materials that are used for tube bends and welded joints and creep damage level are made according to the recommendations for the assessment of the microstructure [10]. the degree of quality degradation of the microstructure of the old pipe was determined according to the recommendations of the european commission for assess the remaining life of the microstructure [11]. fig. 8 and 9 show the typical microstructure of the surface layer of the old pipe taken from a replica in accordance with the drawing in fig. 7. figure 8: replica ra10-r1. assessment of the microstructure [11]: level b / level c: initial spheroidization and carbide precipitation per grain boundary in places with the presence of globular pearlite. 4% nital. figure 9: replica ra10-r3. macro cracks. assessment of the microstructure [10]: 5; assessment of the microstructure [11]: level b / level c: initial spheroidization and carbide precipitation per grain boundary in places with the presence of globular pearlite. 4% nital. in microstructure of tested replica taken from the surface of the material of the old pipe, a certain degree of quality degradation was observed wich is caused by initial spheroidization and carbide precipitation per grain boundary in places with the presence of globular pearlitethe level of quality degradation of microstructure b / c, according to [11]. products of corrosion and corrosion damage in spots are present in the microstructure of tested replica. s. bulatovic et alii, frattura ed integrità strutturale, 26 (2013) 41-48; doi: 10.3221/igf-esis.26.05 47 analysis of damage he damaged parts of steam line were analyzed, to determine the cause of the problem, which is a process that requires a systematic approach. test results of ndt methods contribute to the knowledge of damage formation and allow us to determine the cause of steam line failure. based on the research of failure and causes of failure of certain components of steam line using method fmea and reliability parameters obtained from the analysis of the data collected in real operating conditions, a system of continuous diagnosis could be established. stress analysis [12,13,14], damage and fractures [15,16] of welded joints of steam line elements provide important directives for the development of design methods and construction elements of the steam line to improve the properties of existing materials and their processing technologies. also, by analyzing fractures, the development of new technical solutions and methods of testing is enabled [17] in the prototype stage. it is necessary to take into account the risk analysis and structural integrity [18,19], as a new approach to the assessment of structural integrity. the database information oad data, the characteristics of the base material and its welded joints, technology development, technical and physical characteristics reported fractures data and preventive measures provided for damage and destruction are obtained from the databases. database of implemented testing [2] and research [20] on the appropriate structures allows us to analyze the behavior of supporting elements of steam line in order to determine changes in mechanical properties of materials. load data, as well as the characteristics of the base material and its welded joints, technology development, technical and physical characteristics of the recorded fracture and destruction are inserted into the appropriate database. reliable assessment of the integrity of the observed elements, could be made only after creation of adequate database and the basis for the development of computer programs [21]. supporting software packages would allow more efficient use of the database, the analysis of some influencing factors, and the search of alternative solutions in all phases of design and development of construction. conclusion nly by examining the construction of steam line operating conditions it is possible to assess their condition completely. during examination period the necessary data are obtained to determine the quality and structural integrity assessment and evaluation of the impact of the elements on the capacity and is given the necessary data to establish the joint work of devices and structure of steam line. the results presented in this paper and conducted research projects allow us to analyze the behavior of supporting elements of steam line in order to determine changes in mechanical properties of materials. acknowledgements he paper was done within the project tr 35011, "the integrity of the pressure equipment with the simultaneous action of fatigue load and temperature," founded by the ministry of education, science and technological development of the republic of serbia. references [1] klba-m9-013: the test program of the technological metal machine part, tek a, jun, 2001. [2] reports on ndt testing methods of steam line at the kolubara a, institute ims, 2000-2012. [3] regulation on the technical requirements for the design, development and conformity assessment of pressure equipment (sluzbeni glasnik rs no. 87/2011). [4] regulation on pressure equipment inspections during the operation (sluzbeni glasnik rs no. 87/2011). [5] pressure equipment directive (ped 97/23/ec). t l o t s. bulatovic et alii, frattura ed integrità strutturale, 26 (2013) 41-48; doi: 10.3221/igf-esis.26.05 48 [6] sposito, g., et al.: a review of non-destructive techniques for the detection of creep damage in power plant steels, ndt&e international, 43 (2010) 555. [7] vgb-r 508 l : richtlinie für die herstellung und bauüberwachung von rohrleitungsanlagen in wärmekraftwerken. [8] srps iso 3057/2011: non-destructive testing -metallographic replica techniques of surface examination (identical with iso 3057/1998). [9] sprint sp 492. [10] vgb tw 507 e: guideline for the assessment of microstructure and damage development of creep exposed materials for pipes and boiler components (1992). [11] eccc recommendations volume 6: residual life assessment and microstructure, 1. [12] jakovljević, a., numerical stress analysis of high pressure steam lines in power plants, structural integrity and life, udk 620.169.1:621.643.023-988, 7 (1) (2007) 13-20. [13] petronić, s., comparative analysis of the design stress according to different regulations on pressure equipment, structural integrity and life, udk 66-988(083.133), 12(2) (2012) 143-148. [14] petronić, s., grujić, b., balać, m., test pressures and stresses for pressure vessels according to new regulation 87/11, structural integrity and life, , udk 620.1:66-988, 12(3) (2012) 209-213. [15] milović, l., significance of cracks in the heat-affected-zone of steels for elevated temperature application, structural integrity and life, udk 621.791.051:669.14, 8(1) (2008) 55-64. [16] milović, l., vuherer, t., radaković, z., petrovski, b., janković, m., zrilić, m., daničić, d., determination of fatigue crack growth parameters in welded joint of hsla steel, structural integrity and life, udk 620.172.24: 669.15, 620.172.24:66-988-112.81, 621.791.05:539.4.013, 11 (3) (2011) 183-187. [17] gubeljak, n., application of stereometric measurement on structural, structural integrity and life, udk 620.169.1, 6(1-2) (2006) 65-74. [18] đorđević, p., kirin, s., sedmak, a., džindo, e., risk analysis in structural integrity, structural integrity and life, udk 65.012.32, 11(2) (2011) 135-138. [19] kirin, s., jovanović, a., stanojević, p., sedmak, a., džindo, e., risk analysis in structural integrity – application to a large company, structural integrity and life, udk 65.012.32, 11(3) (2011) 209-212. [20] sedmak, s., radaković, z., milović, l., svetel, i., significance and applicability of structural integrity assessment, structural integrity and life, udk 620.172.24, 620.169.1, 539.42, 12(1) (2012) 3-30. [21] popović, a., marković, m., panić, b., nikolić, m., data acquisition and processing, structural integrity and life, udk 620.17.05:004, 6 (1-2) (2006) 53-64. microsoft word numero_27_art_4 a. kostina et alii, frattura ed integrità strutturale, 27 (2014) 28-37; doi: 10.3221/igf-esis.27.04 28 focussed on: infrared thermographic analysis of materials energy dissipation and storage in iron under plastic deformation (experimental study and numerical simulation) a. kostina, a. iziumova, o. plekhov institute of continuous media mechanics of the ural branch of the russian academy of sciences, 614013, ac. koroleva street, 1, perm, russia poa@icmm.ru abstract. the work is devoted to the experimental and numerical investigation of thermodynamic aspects of the plastic deformation in armco iron. dissipation and stored energies was calculated from processed experimental data of the surface temperature obtained by infrared thermography. an original mathematical model describing the process of mesoscopic defects accumulation was used for numerical simulation of the quasistatic loading of iron samples and for calculation of theoretical value of the stored energy. experimental and modeled values of the stored energy are in a good agreement. keywords. stored energy; infrared thermography; mesodefect evolution; numerical simulation. introduction he experimental and theoretical study of energy balance in metals under plastic deformation has a long history. the importance of this issue for understanding of nature of irreversible deformation of metals and its transition to fracture was originally shown by j. h. lambert in 1779 in his statement concerning the energy similarity of mechanical and thermal failure processes of solids. the review of experimental works devoted to the methods of stored energy study in the material under plastic deformation and the peculiarities of this process for different material structures and load conditions is available in [1]. to analyze the thermodynamic characteristics of deformation processes in solids, it is necessary to take into account the fact that the plastic deformation work is converted into two parts: heat energy caused by the movement and annihilation of defects at various structural levels, and hidden (stored) energy of plastic deformation accumulated in the elastic fields of defects. the first part of energy can be detected by different experimental techniques and gives us information about current state of structure evolution. during the last decades the enhanced ability to detect temperature evolution during mechanical testing leads to a great interest in the application of infrared (ir) thermography to study heat dissipation process caused by defect evolution under plastic deformation in metals. the theoretical and experimental study of this problem can be useful for explanation of many phenomena of mechanics of solids such as cold work evolution, study of damage to fracture transition and crack propagation process, investigation of crack tip closure effect, validation of linear failure mechanics formula to the investigation of fatigue cracks propagation in metals under different loading conditions and so on. the aforementioned experimental results indicate the importance of further development of methods for investigation of the thermodynamics of the deformation process and develop adequate theoretical models of plastic deformation describing the energy balance in metals under plastic deformation. this work is devoted to investigation of energy dissipation in armco iron under quasistatic tension. it was shown experimentally [2] that from macroscopic point of view the deformation process of armco iron can be divided into homogeneous and heterogeneous parts. as a first step of t http://www.gruppofrattura.it http://dx.medra.org/10.3221/igf-esis.27.04&auth=true a. kostina et alii, frattura ed integrità strutturale, 27 (2014) 28-37; doi: 10.3221/igf-esis.27.04 29 theoretical consideration of the phenomena we tried to simulate the energy storage process in armco iron under homogeneous plastic deformation. the simulation was based on the original statistical model of defect evolution and includes the separation of plastic deformation into dissipative and thermodynamic (structural) parts. the nonlinear constitutive equation for structural sensitive parameters allows us to obtain the qualitative agreement between experimental and theoretical results. material and experimental conditions xperimental study was carried out on the armco iron specimens. chemical composition of the examined material is presented in tab. 1. fig 1. shows geometry of the specimens. с mn si s p ni сr mo 0.004 0.04 0.05 0.005 0.005 0.06 0.038 0.01 table 1: armco iron chemical composition (wt%). figure 1: geometry of specimens. all sizes are in millimeters. after tooling, specimens were annealed in non-oxygen atmosphere with 1073 k temperature during 8 hours. non-oxygen atmosphere was created by co-annealing of metal and copper samples with developed surface for a better oxidation. mechanical test was carried out on servo hydraulic machine instron 8500. before starting of experiments the surface of the specimens was mechanically polished (at the last stage of the polishing the diamond suspension with a characteristic grit size of 3 microns was used). after polishing the surface was covered of matt black paint. it was done to obtain emissivity of the specimen’s surface close to 1 for better conditions of infrared monitoring. specimens were loaded in uniaxial stretching mode with strain rate 2·10-3 sec-1. infrared camera cedip jade iii was used to record the temperature evolution on the surface during mechanical test. the maximum frame size is 320×256 pixels; the spatial resolution is 10-4 meters. the temperature sensitivity is from 25 mk to 300 k. energy calculation based on the processed experimental data nfrared monitoring of the surface of examined specimen during quasistatic tension takes possibility to observe changes in temperature field in loading process. the fig. 2 presents the stress strain relation and temperature evolution of the gage part of the specimen for investigated materials. we can divide the deformation process into three parts. at the beginning if the process the plastic deformation has a heterogeneous nature. we can observe the propagation of luders bands (plastic deformation waves) on the specimen surface. this process is accompanied by the temperature wave propagation. the detail study of this part of plastic deformation in armco iron can be found in [3]. e i http://www.gruppofrattura.it http://dx.medra.org/10.3221/igf-esis.27.04&auth=true a. kostina et alii, frattura ed integrità strutturale, 27 (2014) 28-37; doi: 10.3221/igf-esis.27.04 30 0 0.1 0.2 0.3 0.4 0.5 0 50 100 150 200 250 300   , m p a () 0 0.1 0.2 0.3 0.4 0.5 299 300 301 302 303 304 305 306 307 308 t e m p e ra tu re , k t() figure 2: stress – strain evolution of armco iron specimen (solid line) and local temperature evolution (dash line); strain rate 2·10-3 s-1. the plastic wave propagation is finished by the transition to hardening process accompanied by an approximately homogeneous plastic deformation of the sample (the second part of plastic deformation). the last part of the deformation process is characterized by necking heterogeneous temperature distribution of the specimen surface. the second part of the process can be considered as a homogeneous at macroscopic level. the energy balance in specimen at this part of deformation will be simulated in the next part of this paper. all other parts of the process requests the consideration the nonlocal effects in defect ensemble and leads to the more complex model. heat sources calculation the heat sources evolution can be calculated based on the following equation [4] 2 2 2 2 ( , , ) t t t t s x y t c k t x y                  (1) where t is the temperature, ρ is the density (7870 kg/m3), c is the heat capacity (444 j/(kg·k)), k is the heat conductivity (76.2 w/(m·k)), s is the unknown specific power of heat source (w/m3) and τ is the constant describing the heat exchange process with the surroundings (160 sec) [5]. the definition of heat sources evolution requests the calculation of the space and time derivation of noisy temperature field. it leads to the situation when recorded experimental data of the temperature is not enough suitable to calculate the heat dissipation rate. in this work we use time and space filter for experimental data. to implement filtration procedure it was applied discrete fourier transform with gaussian kernel. the peculiarities of filtering procedure are described in [6]. this procedure allows us to smooth spatial and time heterogeneity. fig. 3 presents field of temperature range before and after processing. a) b) figure 3: temperature range on the surface of specimen before data processing (a) and obtained field of temperature range with zone of interest (b). http://www.gruppofrattura.it http://dx.medra.org/10.3221/igf-esis.27.04&auth=true a. kostina et alii, frattura ed integrità strutturale, 27 (2014) 28-37; doi: 10.3221/igf-esis.27.04 31 stored energy calculation fig. 4 presents field of heat dissipation rate on the small area of specimen surface limited by black rectangle shown in fig 3b. the small area for calculation was selected due to sample shape changing during deformation process. the field of heat sources is a little bit heterogeneous even during the second part of plastic deformation. figure 4: experimental data of the heat dissipation rate (w/m3) at the beginning and end of interest time range. the integral heat dissipation in zone of interest can be calculated as 22 1 1 ( ) ( , , ) yx x y q t s x y t dxdy   (2) where 1 2 1 2, , ,x x y y are the rectangular coordinates of the interest zone (fig. 3b). we suppose that some of the irreversible plastic work contributes to heat generation, while the rest is stored as the energy of crystal defects accompanying plastic deformation, traditionally known as the stored energy of cold work [7,8]. the goal of this work is to calculate value of the stored energy rate. plastic work spend on deformation of the specimen has to be known for calculation of the energy stored in metals during deformation. we obtained plastic work presented in expression (3) as a function of strain rate v and loading force f(t). ( ) ( )pw t f t v (3) we calculate stored energy of cold work as difference between plastic work spent on deformation and integral heat dissipation (wp (t)– q(t)) [9]. time dependence of these values is shown in fig. 5. ratio ( ) ( )p q t w t is usually used for determination of the parameter β characterized extent of material damage [10]. the stored energy ratio can be calculated as follow ( ) ( ) 1 ( ) p p w t q t w t     (4) in fig. 6 value of 1–β depending on strain is presented. value of stored energy decreases in the end of deformation process that means most of plastic work converted into heat and materials prepared to the failure. red line indicates part from 131.8 sec to 208.9 sec (surface of heat dissipation rate in the beginning and end of this range is presented in fig.4) described the second part of plastic deformation. this part was chosen for numerical modeling of the plastic deformation process in armco iron. http://www.gruppofrattura.it http://dx.medra.org/10.3221/igf-esis.27.04&auth=true a. kostina et alii, frattura ed integrità strutturale, 27 (2014) 28-37; doi: 10.3221/igf-esis.27.04 32 0 50 100 150 200 250 300 350 400 -0.5 0 0.5 1 1.5 2 2.5 3 3.5 time, sec w p , q a n d w p -q , j heat dissipation plastic work stored energy 0 0.1 0.2 0.3 0.4 0.5 0 0.2 0.4 0.6 0.8 1  1  figure 5: time dependence of plastic work, heat dissipation energy and stored energy. figure 6: strain dependences of stored energy ratio (1-β). mathematical model of energy balance in metals under homogeneous plastic deformation t is now well known that real metals have complex structure, which is a hierarchy of different levels. under deformation process the structural evolution observed at all scale levels and leads to irreversible deformation and destruction. to develop a model of defect evolution under plastic deformation we have to choose the basic physical level of description of the material microstructure and to describe the geometry of the elementary defects. one of the possible descriptions of defect kinetics is the statistical model of defect ensample. this model has to take into account the stochastically properties of defect initiation, their nonlinear integration and link between microplasticity and damage accumulation properties. problem statement typical mesoscopic defects (mesoshifts) are described as the symmetrical tensor s , which has the following form [11,12]: 1 ( ) 2 s s nl ln  where l is a unit normal to the shear plane, b is a unit vector in the shear direction, s is a shift intensity. defect density tensor that coincides with the strain caused by defects is defined as: p n s    where n is a defect density. the distribution function of defects can be represented in the following form: 1 exp( / )w z e   where e is the energy of the defect, z is the normalizing factor, θ is the effective temperature factor responsible for the system susceptibility. averaging procedure lets us to obtain the self-consistency equation between micro and macro parameters in the following form: ( )p n sw s ds     (5) the solution of the eq. (5) was proposed in [12]. based on these results we can introduce a phenomenological model of the quasistatic process. full strain rate can be represented as the sum of three components: elastic strain rate e , plastic strain rate p and strain rate caused by defects p : i http://www.gruppofrattura.it http://dx.medra.org/10.3221/igf-esis.27.04&auth=true a. kostina et alii, frattura ed integrità strutturale, 27 (2014) 28-37; doi: 10.3221/igf-esis.27.04 33 e p p           (6) elastic strains are defined by linear hooke’s law: 0 0 ek   (7) 2 ed dg    (8) where k isotropic elastic modulus, g elastic shear modulus, 0 spherical part of the stress tensor, d deviator part of the stress, 0 e spherical part of the elastic strain tensor, ed deviator part of the elastic strain. dissipation function for a medium with defects can be represented in the following form [13]: : ( ) : 0p t p q p t                 (9) where  is a free energy,  density, q heat flux vector, t temperature. dividing the thermal and mechanical problems and basing on the onsager principle, we can obtain from (9) constitutive equations for calculating kinetics of plastic and structural strains: ( )p p p                 (10) ( )p pp p               (11) the kinetic coefficients  , p and p have the following form: 1 1 1 1 c s exp a             2 1 1 ( , , , , ) 1 p p c c yh p p s exp a               1 p p     where  , p , p characteristic relaxation times,  stress intensity tensor, cs 1a , 2a material constants, ys yield stress, p intensity of p , ,c cp  scaling factors, ( , , , ) 2 ( 1)c c c ch p p f p p p p          material function ( it can be considered as “degree of system nonequilibrium”). it is supposed that thermodynamic force p        can be written as: 1 1 2 c c c c c p pp p f p g p p p p                                (12) where ( )f p denotes a power function for modeling of nonlinear hardening process: a c c p p f k p p             (13) k is a scaling factor, a is the exponent. eqs. (6)-(8) and (10)-(13) represent a closed system for a plastically deformed solid with nonlinear hardening. from the first thermodynamic law, we can obtain the expression for calculation the  parameter in the following form: http://www.gruppofrattura.it http://dx.medra.org/10.3221/igf-esis.27.04&auth=true a. kostina et alii, frattura ed integrità strutturale, 27 (2014) 28-37; doi: 10.3221/igf-esis.27.04 34 2 : 1 : ( ) p p p t p p t pq w p                        where pq inelastic contribution to the heat, pw plastic work. under isoentropy conditions it has the form: : 1 : ( ) p p p p pq w p                results of modeling fig. 7 presents the experimental results for tension of armco iron samples. to simulate the homogeneous part of plastic deformation, we propose the existence of two process steps. the first step is corresponding to the loading of the sample up to yield stress, luders bunds propagation and unloading. the second step corresponds to the loading of preloaded specimen. during the second step the specimen exhibits the homogeneous plastic deformation, parabolic hardening and decreasing of stored energy ratio. this process can be simulated by definition of nonzero initial deformation. the schematic of the process is presented in fig. 7. figure 7: experimental stress-strain curve for armco iron. numerical simulation of the considered process was carried out in the finite element package simulia abaqus 6.13. fig. 8 shows the finite-element mesh of the specimen. eight-node linear brick elements were used for the simulation. the above explained model was applied for the material behavior description using the subroutine umat. arrays of material constants, strain, strain increments and the time step passed as input data to the procedure. increments of the stress tensor components and increments of the defect density tensor components are determined from the system of constitutive equations. values of these components at the next time step are defined as the sum of the values on the previous step and the appropriate increment. fig. 9 presents the stress-strain curves obtained from experimental data (dash dot line) and results of numerical simulation (solid line). results calculated by the model are in a good agreement with experiment. figure 8: finite-element mesh of the specimen. http://www.gruppofrattura.it http://dx.medra.org/10.3221/igf-esis.27.04&auth=true a. kostina et alii, frattura ed integrità strutturale, 27 (2014) 28-37; doi: 10.3221/igf-esis.27.04 35 0.0625 0.1094 0.1562 0.2331 0.25 0 50 100 150 200 250   , m p a numerical results experimental results figure 9: numerical and experimental stress-strain curves for armco iron. fig. 10 demonstrates the simulation results of the 1–β value. the modeling results coincide to the experimental on the homogeneous stage of the plastic deformation. dash line corresponds to the red line in fig. 6. the numerical results exhibit increasing branch of stored energy ratio and coincide to the experimental results after some deformation value. this fact can be explained by the initial conditions for structural sensitive parameters of the model defined in the simulation process. the initial condition corresponds to the annealed materials with zero defect induced deformation. at the beginning of deformation process this material exhibits increasing rate of stored energy ratio corresponding to the increasing of defect density [1]. in contrast to this, the experimental result corresponds to initially deformed material which has created effective defect structure for the dissipation of deformation energy. the extension of the area of applicability of the model requests the simulation of nonlocal process of plastic deformation. 0.0625 0.1094 0.1562 0.2331 0.25 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8  1  numerical results experimental results figure 10: value of 1-β depending on strain. simulation results. conclusion he infrared technique has been applied to investigate the effect of heat dissipation under quasistatic loading of armco iron. a technique for experimental data treatment has been developed for determination of the stored energy rate. the heat dissipation field and average stored energy ration were calculated for whole deformation process including homogeneous and heterogeneous pats. the experimental results stimulate us to develop a phenomenological model describing the energy balance in metals under plastic deformation. extending the previous results of the research group in perm, we propose a statistical description of the mesodefect ensemble and introduce the thermodynamic potential of solid with defect. the key point of the model is definition of defect induced strain which can be considered as a thermodynamic variable. it allowed us to propose a three dimensional thermodynamic internal variable model of heat dissipation in metals and describe the energy storage in armco iron under homogeneous plastic deformation. t http://www.gruppofrattura.it http://dx.medra.org/10.3221/igf-esis.27.04&auth=true a. kostina et alii, frattura ed integrità strutturale, 27 (2014) 28-37; doi: 10.3221/igf-esis.27.04 36 the calculated value of stored energy rate was compared with experimentally determined value. a good agreement between experimental and numerical results in the range of homogeneous plastic deformation was found. acknowledgements he experimental investigation of iron specimen was carried out at the laboratory lamefip ensam (bordeaux, france). the authors thank the professors t. palin-luc and n. saintier for fruitful discussions and support of this experimental work. this work was supported by grant of president of the russian federation for support of young russian scientists and leading scientific schools (md-2684.2012.1) and scientific project for young researches and phd students (grant № 13-1np-349). nomenclature b unit vector in the shear direction c heat capacity e defect energy f loading force g elastic shear modulus ir infrared k heat conductivity k isotropic elastic modulus l unit normal vector to the shear plane n defect density p mesoscopic defect density tensor p intensity of p q heat flux vector q specific energy dissipation rate integrated over the coordinates pq inelastic contribution to the heat s microscopic defect tensor s specific energy dissipation rate s shift intensity ys yield stress t temperature v strain rate w distribution function of defects wp plastic work z normalizing factor β variable characterized extent of material damage e elastic strain tensor 0 e spherical part of the elastic strain tensor e d deviator part of the elastic strain p plastic strain tensor ρ density  cauchy stress tensor  stress intensity tensor 0 spherical part of the stress tensor t http://www.gruppofrattura.it http://dx.medra.org/10.3221/igf-esis.27.04&auth=true a. kostina et alii, frattura ed integrità strutturale, 27 (2014) 28-37; doi: 10.3221/igf-esis.27.04 37 d deviator part of the stress tensor i , , ,i p p  characteristic relaxation times τ the constant describing the heat exchange process with the surroundings  free energy references [1] bever, m.b., holt, d.l., tichener, a.l., the stored energy of cold work, progress in materials science, 17 (1973) 5– 173. [2] fedorova, a.yu., bannikov, m.v., plekhov, o.a., a study of the stored energy in titanium under deformation and failure using infrared data, fracture and structural integrity, 24 (2013) 81-88. [3] plekhov, o.a., naimark, o.b., saintier, n., palin-luc, t., elastic-plastic transition in iron: structural and thermodynamic features, technical physics, 54(8) (2009) 1141-1146. [4] chrysochoos, a., louche, h., an infrared image processing to analyse the calorific effects accompanying strain localization, international journal of engineering science, 38 (2000) 1759–1788. [5] chrysochoos, a., balandraud, x., wattrisse, b., identification procedure using full-field measurements applications in mechanics and structures, processing of cnrs summer school, 2013 may 21-25; montpellier, france. [6] fedorova, a.yu., bannikov, m.v., plekhov, o.a., infrared thermography study of the fatigue crack propagation, fracture and structural integrity, 21 (2012) 46-53. [7] hodowany, j., ravichandran, g., rosakis, a.j., rosakis, p., partition of plastic work into heat and stored energy in metals, exp. mech., 40(2) (2000) 113–123. [8] plekhov, o., uvarov, s., naimark, o., theoretical and experimental investigation of dissipated and stored energy ratio in iron under quasi-static and cyclic loading, strength of materials, 1(391) (2008) 101–105. [9] taylor, g.i., quinney, h., the latent energy remaining in a metal after cold working, proc. r. soc. a, 143 (1934) 307– 326. [10] rittel, d., wang, z.g., merzer, m., adiabatic shear failure and dynamic stored energy of cold work, physical review letters, 96 (2006) 075502(1–4). [11] naimark, o.b., structural-scaling transitions in mesodefect ensembles as mechanisms of relaxation and failure in shocked and dynamically loaded materials (experimental and theoretical study), j. phys. iv. france, 134 (2008) 3–9. [12] naimark, o.b., bayandin, yu.v., leontiev, v.a., panteleev, i.a., plekhov, o.a., structural-scaling transitions and thermodynamic and kinetic effects in submicro-(nano)crystalline bulk materials, phys. mesomech., 12(5-6) (2009) 239–248. http://www.gruppofrattura.it http://dx.medra.org/10.3221/igf-esis.27.04&auth=true microsoft word numero_41_art_13.docx m.v.c sá et alii, frattura ed integrità strutturale, 41 (2017) 90-97; doi: 10.3221/igf-esis.41.13 90 focused on multiaxial fatigue notched multiaxial fatigue of al7050-t7451: on the need for an equivalent process zone size m.v.c sá department of mechanical engineering, faculty of technology, university of brasília, brazil federal institute of brasília, brasília, brazil marcuscsa@gmail.com j.l.a ferreira, c.r.m da silva 2federal institute of brasília, brasília, brazil jorge@unb.br cosmeroberto@unb.br j.a. araújo department of mechanical engineering, faculty of technology, university of brasília, brazil jaaunb@gmail.com, alex07@unb.br abstract. the aim of this work is to investigate stress gradient effects on the fatigue life estimation of notched al 7050-t7451 specimens under combined torsion and push-pull loading conditions. initially, simple push-pull and torsion fatigue tests in plain and notched specimens were independently conducted not only to obtain the material properties necessary to calibrate a standard multiaxial critical plane based model, but also to raise the critical distance versus life curves in tension (l – nf) and in torsion (l – nf). this latter step also required a finite element elastic stress analysis of the notched specimens tested in the medium high-cycle fatigue regime. then, proportional multiaxial fatigue tests were carried out using this same notched geometry. the combination of a multiaxial model with the theory of critical distance (tcd) was applied to estimate fatigue lives. for this aluminium alloy, neither the use of the l – nf nor l – nf combined with the predictive multiaxial model was able to estimate lives in an accurate way. keywords. multiaxial fatigue; notched fatigue; stress gradient; process zone; critical distance; al 7050-t7451. citation: sá, m.v.c., ferreira, j.l.a., silva, c.r.m., araujo, j.a., notched multiaxial fatigue of al7050-t7451: on the need for an equivalent process zone size, frattura ed integrità strutturale, 41 (2017) 90-97. received: 28.02.2017 accepted: 15.04.2017 published: 01.07.2017 copyright: © 2017 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. m.v.c sá et alii, frattura ed integrità strutturale, 41 (2017) 90-97; doi: 10.3221/igf-esis.41.13 91 introduction luminium alloys have been used mainly in the aeronautical industry for more than eighty years due to its low density and good mechanical resistance. the al 7050-t7451 alloy was developed in the 1970´s and has been used not only in the fuselage but also to build structural parts of the wings and landing gears of aircrafts. despite its technical and economical relevance for such industry, there are few works available in the literature on fatigue of this alloy. further, most of the research carried out has been concentrated on the effects of shot peening or surface treatments on the fatigue resistance of the material under simple push-pull loadings. for instance, carvalho and voorwald [1] investigated the effect of shotpeening and hard chromium coating on the fatigue resistance of the al 7050-t7451. they found out that the deleterious effect of such a coating on the fatigue behavior of the alloy was caused by the presence of high tractive residual stresses and micro-cracks, both generated by the electrodeposition process. they also found that this deleterious effect could be mitigated by the use of shot peening. in 2011, gao [2] tested al 7050-t7451 specimens subjected to laser peening and conventional shot peening. the obtained results showed that laser peening was more effective to enhance the fatigue resistance than shot peening provoking an increase of 42% in strength when compared to specimens, which were not surface peened. this improvement was of 35% due to shot peening. under multiaxial fatigue conditions, as far as the authors are aware, only one article by chen et al. [3] reported experimental data on al 7050-t7451. these authors carried out seven different types of tests under axial-torsional variable strain amplitude. they sought to evaluate the accuracy in estimating life of four multiaxial fatigue parameters that did not include any weight factors in their formulation. they concluded that the use of such models provided good fatigue life estimates for this alloy. however, tests were in low cycle fatigue regime and no stress gradient was present. for components operating in the medium or high cycle fatigue regime (mhcf or hcf) the presence of geometric discontinuities is usual. there is a number of multiaxial fatigue criteria available in the literature to estimate fatigue life under more complex stress states [4-7]. the introduction of stress gradient effects caused by notches (or contact mechanics, etc) into such models is still a matter of strong debate among fatigue scientists. an interesting approach to do so is to consider the existence of a critical distance [8-10]. more recently, it has been suggested [11] that a combination of a critical plane based multiaxial model with a simple linear relation between critical distance and life extracted from pushpull data could provide good estimates of life for notched components under multiaxial loading in the mhcf or hcf regime. the purpose of this work is to further investigate this problem. in order to do so, the critical distance against life relation will be raised not only for fully reversed push-pull tests but also for alternated torsion. both curves will be combined with a critical plane multiaxial fatigue criterion to estimate life. the aim here is to assess the role of combined shear and normal stress gradients in the life methodology. to validate the analysis multiaxial fatigue tests were conducted on notched al 7050-t7451 specimens. multiaxial model and life dependent critical distance his work will require que use of a multiaxial fatigue criterion and a method to incorporate the stress gradient effects in the life estimation approach. the multiaxial model considered here is the modified wöhler curve method (mwcm) [6]. it is based on a diagram where a is plotted against the number of cycles to failure, nf. this diagram contains different fatigue curves characterized by different values of  ratio.  is the ratio between the shear stress amplitude, a, and the maximum normal stress, n,max, acting on the material plane experiencing the maximum shear stress amplitude (i.e., the so-called critical plane). each modified wöhler curve is defined by its negative inverse slope, , and by a reference shear stress amplitude, a,ref, extrapolated at an appropriate number of cycles to failure, na. for a given material, the corresponding modified wöhler diagram can directly be built provided that the  vs.  and a,ref vs.  relationships are calibrated by running at least two sets of basic experiments such as fully reversed push-pull (=1) and torsion (=0) as a function of life. after determining the appropriate material constants (see [6,11] for more details) any intermediate modified wöhler curve can be obtained. from the specific modified wöhler curve for the  ratio that characterizes the local stress history being assessed, the number of cycles to failure can then be estimated as [11]:                  ,a ref f a a n n (1) a t m.v.c sá et alii, frattura ed integrità strutturale, 41 (2017) 90-97; doi: 10.3221/igf-esis.41.13 92 the value of a is here computed by the maximum rectangular hull (mrh) method. it is based on the combination of shear stress amplitudes associated to mutually orthogonal directions on a material plane, and therefore it is capable to distinguish between the damage caused by proportional and non-proportional shear stress paths. the mrh method is well described elsewhere [7,12,13] and space only preclude us to provide a more detailed explanation about the method. more interested readers are invited to visit such references. the stress gradient effect is accounted by the theory of critical distances (tcd) [8-11] due to its simplicity. the central idea in the tcd is the definition of an effective stress, based on an averaging procedure over a volume surrounding the stress raiser. fatigue failure is expected to occur if this effective stress exceeds a reference material fatigue strength. simplified methods can also be formulated by considering averages over an area or a line (area and line methods, respectively) or the stress at a point located at a critical distance, l, from the stress raiser (point method). the point method is used in this work. at the medium-cycle fatigue regime, l, depends on the number of cycles to failure, nf. a power law relationship is used to relate l and nf , i.e.,    bf fl n an (2) where a and b are material constants. the fitting procedures to obtain these constants require two fatigue curves generated by testing plain and sharply notched specimens. although such curve has been usually determined for fully reversed push-pull tests (l – nf), here we would like to investigate the effect of the torsion mode on the analysis, hence a similar relationship (l – nf) will be raised from torsion tests of plain and notched specimens too. material and methods he methodology developed for the aim of this work involves experimental and numerical procedures. in the experimental field, fatigue tests were performed in order to obtain the σ-n and τ-n curves for the plain and the notched specimens, whose geometry and dimensions are shown in fig. 1 (a) and (b), respectively. all specimens were made of an aluminum alloy 7050 t-7451. tab. 1 reports the main mechanical properties of the material applied in this research. tensile yield strength ultimate tensile strength modulus of elasticity poisson´s ratio 453 [mpa] 513 [mpa] 73 [gpa] 0.33 table 1: mechanical properties of al 7050-t7451. (a) (b) figure 1: (a) plain and (b) notched fatigue specimens. the plain specimens were designed according to astm e 606 standard while the notched ones were designed seeking to achieve the sharpest notch that could be accurately machined and that could satisfy the relation proposed by [14]. this relation requires that the ratio between the radius of the notch root and the net diameter of the notched specimen be smaller than 0.01. in conjunction with the point method, this relation allows predictions of kth with an acceptable 20% error band. the uniaxial fatigue curves were generated according to astm e 739 standard. in this way, for each t m.v.c sá et alii, frattura ed integrità strutturale, 41 (2017) 90-97; doi: 10.3221/igf-esis.41.13 93 fatigue curve at least four stress amplitude levels were tested covering life ranges from 104 up to 2x107 cycles. these tests were then controlled by prescribed loads. l nf curves to obtain the l – nf and l – nf curves (and respective equations) it is necessary to compute the stress field around the notch root. to this aim, a finite element analysis (fea) was considered. a three dimensional structural element with eight nodes was adopted. each node had three degrees of freedom. the material behaviour was assumed to be linear elastic. a prescribed stress was applied in the normal direction to simulate the push-pull tests and later a prescribed torsion was applied to model the torsion tests. for a specific failure life, nf,i, it is possible to obtain from the experimental curves the respective values of stress amplitude that the unnotched and the notched specimens can withstand, un(nf,i) and n(nf,i), respectively. then, from the fea, the distance where un(nf,i) occurs for the notched specimen loaded by a nominal stress n(nf,i) can be found. therefore, conducting successive increments in the life cycles, nf,i+1, the l – nf is raised. fig. 2 shows an scheme of this procedure. the l – nf curve is obtained following these same steps, but using as a reference the τ-n curve. figure 2: schematic view of the procedure to obtain the l – nf curve. aplication of pm (tdc) and mwcm for life estimation in multiaxial fatigue the calibration of the modified wholer curve model (mwcm) can be achieved using the σ-n and τ-n curves for unnotched specimens. once calibrated, the amplitude of shear stress at the critical plane, a , at an initial distance from the notch root, i , is the input information for the mwcm and the respective life, n(i), is the output. if l(i)=i, then nf=n(i).if not, the next increment at the distancei should be sought until convergence is reached. fig. 3 shows the application of this methodology. this procedure can be repeated but using l – nf in conjunction with the mwcm to estimate the life. to assess the accuracy of the methodology presented above to estimate life of components containing geometrical discontinuities and subjected to complex loadings a set of 15 proportional multiaxial fatigue tests were carried on the notched specimens of al7050-t7451 shown in fig. 1. these tests were conducted in a mts 809 servohydraulic test rig and involved a combination of push-pull and torsion, hence normal load amplitude and torsion amplitude were prescribed to control the tests. the input signals were sinusoidal, synchronous and in phase, without superimposed mean components. results tests n figs. 4(a) and (b) are presented the results of the fatigue uniaxial tests performed under fully reversed push-pull and alternated torsion. these graphs contain then the σ-n and τ-n curves for the plain and for the notched specimens. in the case of the notched specimens these nominal stresses were computed in terms of the gross sectional area of the specimen. i m.v.c sá et alii, frattura ed integrità strutturale, 41 (2017) 90-97; doi: 10.3221/igf-esis.41.13 94 figure 3: scheme of the life estimation methodology used in the multiaxial fatigue tests. (a) (b) figure 4: σ-n and τ-n curves of plain and notched specimens performed under fully reversed (a) push-pull and (b) torsion conditions. the trend line and the scatter bands sketched in these diagrams are characterized by a significance level equal to 95% (it was assumed, by hypothesis, that a log-normal distribution represents the number of cycles to failure). the synthesis of the generated results, carried out according to the above statistical procedure, is summarized in tab. 2. the endurance limits reported in such a table were raised based on the parallel projection method (considering a number of cycles for g ro ss a m p lit ud e st re ss , a [m p a ] 103 104 105 106 107 108 number of cycles to failure, nf 10 100 20 30 40 50 60 70 80 90 200 300 400 500 sample observations unnotch sample observations notch trend line unnotch trend line notch 95% prediction intervals m.v.c sá et alii, frattura ed integrità strutturale, 41 (2017) 90-97; doi: 10.3221/igf-esis.41.13 95 failure equal to 5 x 108) and the respective fatigue notch factor, kf, was evaluated considering the relationship between the endurance limits estimated for the specific specimen type. specimen type loading conditions number of data parameters of the s-n curve a b endurance limit [mpa] fatiguenotch factor plain push-pull torsional 9 17 775.80 1298.36 -0.131 -0.187 56 31 1 1 v-notched push-pull torsional 7 9 194.66 259.72 -0.133 -0.155 14 12 4.1 2.7 table 2: synthesis of the experimental results generated under push-pull and torsion for plain and v-notched specimens table 3: loading conditions and test results for the multiaxial fatigue data generated from the v-notched specimens eqs. 3 and 4 below provide the l – nf and l – nf relations and were extracted using the methodology schematically shown in fig. 2. tab. 3 reports the loading conditions and experimental results generated for the multiaxial fatigue tests with the notched specimens. the experimental program considered two ratios between the normal and shear nominal stress amplitudes (column c, in tab. 3), i.e, 0.5 and 0.8. eight tests were conducted using the first ratio and seven for the latter one. the actual lives are reported in column d of tab. 3. the estimated lives either considering eq. (3), l – nf curve, or eq. (4), l – nf relation, in association with the multiaxial model (eq. (1)) are presented in columns e and f, respectively. graphically, the quality of the results of such estimates can be assessed by plotting the actual lives against the predicted ones, as shown in fig. 5. in such graph, the continuous lines parallel to the one passing through the origin and the dashed lines represent bandwiths by factors of 2 and 4, respectively. one can see in fig. 5 that when the l – nf curve was used the estimated lives were excessively conservative. note that 11 out of the 15 points plotted for this case were out of the factor of 4 bandwith, while the other 4 points fell between the factor of 2 and 4 lines. although an improvement in the predictions was clearly obtained when the l – nf relation was used, still 4 of the 15 points provided non-conservative life estimates by factors between 2 and 4.    0.003140.2041f fl n n (3)    0.063590.1784f fl n n (4) gross [mpa] gross [mpa] (a)/(b) number of cycles to failure experimental (l-nf) (lnf) (a) (b) (c) (d) (e) (f) 11.0 22.0 0.5 5.84e+06 3.66e+05 4.28e+06 11.0 22.0 3.34e+06 3.66e+05 4.28e+06 13.0 26.0 3.28e+05 1.37e+05 1.27e+06 13.0 26.0 7.24e+05 1.37e+05 1.27e+06 16.0 32.0 2.32e+05 4.06e+04 2.82e+05 16.0 32.0 2.42e+05 4.06e+04 2.82e+05 19.0 38.0 3.19e+04 1.47e+04 7.90e+04 19.0 38.0 1.04e+05 1.47e+04 7.90e+04 16.0 20.0 0.8 5.74e+06 1.51e+05 1.74e+06 16.0 20.0 3.45e+06 1.51e+05 1.74e+06 16.0 20.0 4.39e+06 3.60e+05 5.22e+06 18.4 23.0 2.11e+06 3.60e+05 5.22e+06 18.4 23.0 1.76e+06 3.60e+05 5.22e+06 25.6 32.0 1.13e+05 1.90e+04 1.34e+05 25.6 32.0 9.91e+04 1.90e+04 1.34e+05 m.v.c sá et alii, frattura ed integrità strutturale, 41 (2017) 90-97; doi: 10.3221/igf-esis.41.13 96 figure 5: observed versus estimated lives based on the use of the l – nf and l – nf. conclusions n this work a set of experimental fatigue data was produced for plain and notched specimens of al7050-t7451 under uniaxial and multiaxial proportional loading conditions. a methodology available in the literature, which combines a multiaxial critical plane criterion with a critical distance approach was used to estimate the life for the multiaxial tests. two curves of critical distance against life obtained under uniaxial and torsional loading were considered in order to determine the material point positon from the notch root where the multiaxial model should be computed. the results showed that neither the distance given by the l – nf diagram nor the one given by l – nf curve combined with the mwcm model was capable to estimate lives within a reasonable degree of accuracy. while the methodology provided significant conservative life estimates for all data analysed when the distance from the notch root was taken from the l – nf curve, non-conservative predictions up to a factor of four were obtained when such a distance was taken from the l – nf diagram. the authors believe that a and equivalent critical distance that could take into account the sensitiveness of the stress gradient produced by the shear and by the normal stress modes could enhance the life estimates. other multiaxial fatigue criteria should also be investigated and more data, preferably under non-proportional loading, should be used to corroborate the analysis. future work by the authors will tackle these issues. acknowledgements he authors would like to acknowledge the financial support of ate ii, ate iii, taesa, tbe, eate, brasnorte, aete, tme, finatec, and cnpq (309748/2013-5). references [1] gao, y. k., improvement of fatigue property in 7050–t7451 aluminum alloy by laser peening and shot peening. materials science and engineering: a, 528(10) (2011) 3823-3828. 104 105 106 107 observed fatigue life, nf (cycles) 104 105 106 107 e st im at ed f at ig ue l if e, n f (c yc le s) predictions based on l x n and mwcm predictions based on l x n and mwcm perfect correlation interval limits two bandwidths interval limits four bandwidths i t m.v.c sá et alii, frattura ed integrità strutturale, 41 (2017) 90-97; doi: 10.3221/igf-esis.41.13 97 [2] carvalho, a. l. m., voorwald, h. j. c., influence of shot peening and hard chromium electroplating on the fatigue strength of 7050-t7451 aluminum alloy. international journal of fatigue, 29(7) (2007) 1282-1291. [3] chen, h., shang, d. g., tian, y. j., liu, j. z., comparison of multiaxial fatigue damage models under variable amplitude loading. journal of mechanical science and technology, 26(11) (2012) 3439-3446. [4] socie, d.f., marquis, g.b., multiaxial fatigue. sae international, (2000). [5] carpinteri, a., spagnoli, a., vantadori, s., bagni, c. structural integrity assessment of metallic components under multiaxial fatigue: the c-s criterion and its evolution. fatigue fract engng mater struct, 36 (2013) 870–83. [6] lazzarin p, susmel l, a stress-based method to predict lifetime under multiaxial fatigue loadings. fatigue fract eng mater struct, 26 (2003) 1171–187. [7] mamiya en, castro fc, araújo ja. recent developments on multiaxial fatigue: the contribution of the university of brasília. theor appl fract mech, 73 (2014) 48–59. [8] taylor, d., geometrical effects in fatigue: a unifying theoretical model. int j fatigue, 21 (1999) 413–20. [9] susmel, l., a unifying approach to estimate the high-cycle fatigue strength of notched components subjected to both uniaxial and multiaxial cyclic loadings. fatigue fract engng mater struct, 27 (2004) 391–411. [10] carpinteri, a., spagnoli, a., vantadori, s., viappiani, d., a multiaxial criterion for notch high-cycle fatigue using a critical-point method. eng fract mech, 75 (2008) 1864–74. [11] susmel, l., taylor, d., a critical distance/plane method to estimate finite life of notched components under variable amplitude uniaxial/multiaxial fatigue loading. int j fatigue, 38 (2012) 7–24. [12] araújo, j.a., dantas, a.p., castro, f.c., mamiya, e.n., ferreira, j.l.a. on the characterization of the critical plane with a simple and fast alternative measure of the shear stress amplitude in multiaxial fatigue. int j fatigue, 33 (2011) 1092–100. [13] araújo, j.a., carpinteri, a., ronchei, c., spagnoli, a., vantadori, s., an alternative definition of the shear stress amplitude based on the maximum rectangular hull method and application to the c-s (carpinteri-spagnoli) criterion. fatigue fract engng mater struct, 37 (2014) 764–71. [14] da silva, b.l., ferreira, j.l.a., araújo, j.a., influence of notch geometry on the estimation of the stress intensity factor threshold by considering the theory of critical distances, international journal of fatigue, 42 (2012) 258-270. << /ascii85encodepages false /allowtransparency false /autopositionepsfiles true /autorotatepages /none /binding /left /calgrayprofile (dot gain 20%) /calrgbprofile (srgb iec61966-2.1) /calcmykprofile (u.s. web coated \050swop\051 v2) /srgbprofile (srgb iec61966-2.1) /cannotembedfontpolicy /error /compatibilitylevel 1.4 /compressobjects /tags /compresspages true /convertimagestoindexed true /passthroughjpegimages true /createjobticket false /defaultrenderingintent /default /detectblends true /detectcurves 0.0000 /colorconversionstrategy /cmyk /dothumbnails false /embedallfonts true /embedopentype false /parseiccprofilesincomments true /embedjoboptions true /dscreportinglevel 0 /emitdscwarnings false /endpage -1 /imagememory 1048576 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/hrv (za stvaranje adobe pdf dokumenata najpogodnijih za visokokvalitetni ispis prije tiskanja koristite ove postavke. stvoreni pdf dokumenti mogu se otvoriti acrobat i adobe reader 5.0 i kasnijim verzijama.) /hun 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can be opened with acrobat and adobe reader 5.0 and later.) >> /namespace [ (adobe) (common) (1.0) ] /othernamespaces [ << /asreaderspreads false /cropimagestoframes true /errorcontrol /warnandcontinue /flattenerignorespreadoverrides false /includeguidesgrids false /includenonprinting false /includeslug false /namespace [ (adobe) (indesign) (4.0) ] /omitplacedbitmaps false /omitplacedeps false /omitplacedpdf false /simulateoverprint /legacy >> << /addbleedmarks false /addcolorbars false /addcropmarks false /addpageinfo false /addregmarks false /convertcolors /converttocmyk /destinationprofilename () /destinationprofileselector /documentcmyk /downsample16bitimages true /flattenerpreset << /presetselector /mediumresolution >> /formelements false /generatestructure false /includebookmarks false /includehyperlinks false /includeinteractive false /includelayers false /includeprofiles false /multimediahandling /useobjectsettings /namespace [ (adobe) (creativesuite) (2.0) ] /pdfxoutputintentprofileselector /documentcmyk /preserveediting true /untaggedcmykhandling /leaveuntagged /untaggedrgbhandling /usedocumentprofile /usedocumentbleed false >> ] >> setdistillerparams << /hwresolution [2400 2400] /pagesize [612.000 792.000] >> setpagedevice microsoft word numero_50_art_48_2625 i. stavrakas et alii, frattura ed integrità strutturale, 50 (2019) 573-583; doi: 10.3221/igf-esis.50.48 573 focused on the research activities of the greek society of experimental mechanics of materials damage evolution in marble under uniaxial compression monitored by pressure stimulated currents and acoustic emissions ilias stavrakas electronic devices and materials laboratory, university of west attica, greece ilias@uniwa.gr, http://orcid.org/0000-0001-8484-8751 stavros k. kourkoulis national technical university of athens, department of mechanics, athens, greece stakkour@central.ntua.gr, https://orcid.org/0000-0003-3246-9308 dimos triantis electronic devices and materials laboratory, university of west attica, greece triantis@uniwa.gr, http://orcid.org/0000-0003-4219-8687 abstract. the spatiotemporal evolution of damage in marble specimens under uniaxial compression is monitored using pressure stimulated currents (pscs) and acoustic emissions (aes). the novelty of the study is the use of an integrated grid of sensors (instead of a single pair of electrodes) to detect the weak electrical signals, emitted during loading. the use of such a grid of sensors does indeed enhance the capabilities of the psc technique providing valuable information about the initiation and propagation of micro-fracturing at the interior of the specimens. the experimental results indicate that both the improved b-value of the ae hits and the energy of the pscs offer information about the proximity of the applied stress to that causing fracture. it is thus concluded that both quantities could be considered as pre-failure indicators. keywords. pressure stimulated currents; acoustic emissions; improved bvalue; damage evolution; uniaxial compression; marble. citation: stavrakas, i., kourkoulis, s.k., triantis, d., damage evolution in marble under uniaxial compression monitored by pressure stimulated currents and acoustic emissions, frattura ed integrità strutturale, 50 (2019) 573-583. received: 16.01.2019 accepted: 15.05.2019 published: 01.10.2019 copyright: © 2019 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. introduction nlightening the spatiotemporal evolution of damage at the interior of structural elements under mechanical load is an interesting, though demanding, task of mechanics of materials and engineering. its importance becomes evident by taking into account that, in case damage evolution is properly monitored, the respective data could be used, among others, as tools for assessing the element’s remaining life or, equivalently, as valuable pre-failure indicators. e http://www.gruppofrattura.it/va/50/2625.mp4 i. stavrakas et alii, frattura ed integrità strutturale, 50 (2019) 573-583; doi: 10.3221/igf-esis.50.48 574 the quest for pre-failure indicators attracts long ago the interest of engineers and researchers from quite a few scientific fields, ranging from civil engineering to the management of natural hazards and natural disasters. the key concept in studies dealing with pre-failure indicators is to understand the mechanisms leading to damage evolution within the volume of loaded structural elements. it is obvious that traditional strain/displacement sensing techniques used in mechanics of materials (like, for example, electric strain gauges, caustics, photoelasticity, moiré fringes, interferometry etc.) are not suitable for such applications. indeed, such techniques can only provide data from the external surface of the loaded members while it is definitely known that, well before any kind of damage is detected at the member’s outer surface, internal damage mechanisms have been already activated at the member’s interior, guiding in fact the phenomena observed on the member’s surface. the same is true for some modern (and flexible for many other purposes) sensing techniques like, for example, digital image correlation [1] and direct strain imaging [2]. in this context, description of the mechanical response of materials is usually achieved with the aid of analytic and numerical models, based on experimental data concerning the macroscopic mechanical properties of the material (or of its constituent materials in case of composite structures). in the direction of overcoming the above difficulties, various experimental techniques have been developed during the last decades, aiming to the quantitative description of the structural changes, which take place at the interior of mechanically loaded structures (both before and during the initiation and propagation of micro-fracturing processes). among them, the acoustic emission (ae) technique (i.e., the detection and analysis of the characteristics of transient elastic waves caused by the rapid release of strain energy during mechanical loading when micro-fracture phenomena take place) is, perhaps, the most mature and widely used one. it is based on firm and well understood physical principles [3-7]. recently, another promising experimental technique, permitting insight at the interior of loaded materials, has been introduced [8, 9], based on the detection of weak electrical current emissions, usually called pressure stimulated currents (pscs). these currents (the magnitude of which is of the order of pa), produced during mechanical loading, are detected using extremely sensitive electrometers. this technique, known as psc technique, has been successfully used for both natural building stones [10, 11] and artificial materials, like cement-based ones [12, 13]. it is already adopted by many researchers [14-16] worldwide while other researchers employ techniques [17, 18] based on the same natural principles. the two sensing techniques mentioned above (ae, psc) are here employed in a combined manner in order to monitor damage evolution within dionysos marble specimens subjected to uniaxial compression until fracture. the novelty of the study (besides the combined use of the two techniques and the comparative analysis of the respective data) is that the psc technique is applied, for the first time, using a grid of sensors rather than a single pair of electrodes. the specific system permits gathering data from multiple electrical current channels. valuable information is, thus, gained, concerning the spatial and the temporal distribution of micro-cracking processes, which precede final catastrophic crack propagation. the combined analysis of the experimental results indicates that the specific arrangement of electrical sensors provides a clear overview of the spatiotemporal evolution of damage at the interior of the loaded specimen. moreover, it is indicated that the time evolution of the improved b-value (ib-value) [15, 19] of the ae hits and the energy of the pscs provide reliable indicators of of upcoming catastrophic failure. experimental protocol the material and the specimens he specimens of the present experimental protocol are made of dionysos marble, an extremely fine-graded white marble quarried from mount dionysos in attica region. it is extensively used, among others, by the scientific personnel of the restoration project of the athenian acropolis monuments for the construction of copies of lost or destroyed members. dionysos marble is composed by about 98% of calcite, 0.5% of muscovite, 0.3% of sericite, 0.2% of quartz and 0.1% of chlorite [20]. it is emphasized here, that the extremely low quartz content is crucial for the present protocol, since it ensures that the electrical currents recorded are by no means related to the familiar piezoelectric effect. the specific and apparent densities of dionysos marble are equal to about 2730 kg/m3 and 2717 kg/m3, respectively. the thermal expansion coefficient between 15 oc and 100 oc is 9x10-6 oc-1. the coefficient of absorption by weight is about 0.11%. its porosity is extremely low, ranging between 0.3% (virgin state) and 0.7% (superficial porosity) [20]. its low porosity is another crucial aspect for the present study, since it blocks any electrokinetic effects (due to the existence of natural moisture) that would affect the behaviour of the electrical currents detected and recorded during the experiments. from the mechanics of materials point of view, dionysos marble is of orthotropic nature. data for its mechanical properties, reported in literature, vary between very broad limits [21-24]. based on a long series of experiments vardoulakis et al. [21, 24] drew the conclusion that the mechanical properties along two of the anisotropy directions are close to each other and therefore the material is usually considered as transversely isotropic, described with the aid of only five elastic constants. t i. stavrakas et alii, frattura ed integrità strutturale, 50 (2019) 573-583; doi: 10.3221/igf-esis.50.48 575 in addition, these experiments indicated that dionysos marble is slightly non-linear (both under tension and compression) and, also, slightly bimodular (the elastic modulus under compression exceeds that under tension by about 15%). the specimens prepared were prismatic of square cross section 40x40 mm2. their length was equal to l=100 mm. special attention was paid during the preparation of the specimens for their longitudinal axis to be normal to the material layers, in an attempt to avoid scattering of the experimental results due to the anisotropy of dionysos marble. the experimental set-up the main experimental protocol consists of a series of uniaxial compression tests with a specially designed loading scheme. the specific loading model was chosen due to its increased practical importance for quasi-brittle rock and rock-like materials. an additional factor taken into account, in order to choose compression tests, is the fact that the orientation of the fracture planes (along which increased acoustic activity is expected after a load threshold) is more or less clearly predefined. the force was applied normally to the material layers. the experiments were carried out using an instron-dx 300 loading frame of capacity equal to 300 kn under quasi-static loading conditions. preliminary tests indicated that the compressive strength, σf, of the specific block of dionysos was equal to about σf=63.8 mpa. concerning the psc technique, the sensing system consisted of an ultra-sensitive programmable electrometer (keithley, 6517a) resolving currents ranging from 0.1 fa to 20 ma in 11 ranges. the system was further supported by an electrical current 10-channel scanner card (keithley 6521). the data of the electrometer were stored in a computer using a gpib interface. the sensing system consisted of five pairs of electrodes, installed along the loading axis, enabling the collection of electric emissions as close as possible to any potential source of electric current (or, equivalently, to any point where damage occurs). the distance of the uppermost and the lowest pairs of electrodes from the upper and lower bases of the specimens, respectively, was 10 mm and the distance between two successive pairs of electrodes was 20 mm (fig.1). for the detection of acoustic emissions the 2-channel pci-2 ae detection system was used (physical acoustics corp). two r15α acoustic emission sensors (150 khz resonant frequency) were placed at the positions shown in fig.1a. the ae sensors were properly attached on the specimens by means of vacuum grease. preamplifiers with 40 db gain were used. the threshold of the ae amplitudes was set at 40 db. in addition to the electrodes and the ae sensors, an electric strain gauge was glued at the center of one of the free lateral surfaces at the mid-height of the specimens, in order to measure the axial strain developed. kyowa strain gauges were used, together with the microlink 770 resistor bridge. both the force exerted and the strain developed were digitized and stored to a computer using the kusb-3100 (manufactured by keithley) a/d data acquisition module. special attention was paid in all tests for the minimization of friction. the specific factor is of crucial importance, as it was pointed out by labuz and bridell [25]. in addition, drescher and vardoulakis [26] and read and hegemier [27] have definitely indicated that little can be inferred from non-lubricated tests. in this direction, two sheets of polytetrafluoroethylene (ptfe) were interposed between each loading platen and the respective base of the specimen. in addition, steatic acid was spread between both the specimen's surface and the ‘external’ ptfe sheet and also between the two ptfe sheets. a similar (a) (b) figure 1: (a) sketch of the experimental set-up (1: specimen, 2,3: lower and upper acoustic sensors, 4: strain gauge, 5(+) to 9(+): positive edge of the five successive channels (chan0-chan4) of the electrometer, 5(-) to 9(-): negative edge of the five successive channels, 10: load cell, 11: loading platens). (b) photo of a typical specimen and the position of the sensors of the psc technique. i. stavrakas et alii, frattura ed integrità strutturale, 50 (2019) 573-583; doi: 10.3221/igf-esis.50.48 576 lubrication technique was used by van vliet & van mier [28] with excellent results. it is mentioned here that the ptfe sheets provided also electrical insulation, a crucial parameter for the application of the psc technique. the main experimental protocol and the loading scheme the specimens were subjected to sequential, load-control, loading-unloading-reloading loops, up to stress levels very closely approaching the compressive fracture strength of dionysos marble. in fact, the stress level attained was equal to about 98% to 99% of the compressive strength, as it was determined during the preliminary tests. after the specific stress level (equal to about 62.7 mpa) was attained for the first time the externally applied compressive force was kept constant for a relatively long time interval equal to about tl=150 s. this step is considered necessary in order for the psc to return to its initial background level and also for the activity recorded by the ae sensors to be eliminated. after this time interval the mechanical load was removed and the specimen remained unloaded for a time interval equal to about tu=50 s. this procedure was repeated until the fracture of the specimen, which usually occurred during the second or the third loop. a typical loading protocol is shown in fig.2, in which the axial stress is plotted versus time in juxtaposition to the respective axial strain. the specific specimen collapsed suddenly during the second loading loop in its constant force branch. figure 2: the time variation of the applied stress and the corresponding axial strain during the whole experimental procedure. the respective axial stress axial strain pairs, for the as above experiment, are plotted in fig.3a. an almost perfectly linear region characterizes the first loading branch up to a stress level exceeding 50 mpa. the elastic modulus calculated from this branch is equal to about e1=76.2 gpa, in very good agreement with results of similar previous experimental projects [21, 24]. the non-reversible strain recorded after the load removal, equal to about 2x10-4, is, also, in good agreement with the respective results from previously published works with dionysos marble [29, 30]. as it is expected, during the loading branch of the second loading loop, the linear region of the stress-strain curve extends at higher stress levels (approaching 85% of the maximum compressive stress attained). in addition, the corresponding value of the elastic modulus becomes lower, equal to about e2=61.8 gpa, again in good accordance with previously published data by kourkoulis et al. [30], who have described the damage evolution in dionysos marble in terms of the decrease of its elastic modulus versus the non-reversible portion of the strain, as recorded after successive loading-unloading-reloading loops. taking advantage of their data, fig.3b is plotted. in this figure the modulus of elasticity is plotted against the non-reversible part of the total strain, εperm. on the same figure, the pair of εperm and e2 values obtained from fig.3a (i.e., εperm=2x10-4 and e2=61.8 gpa) are indicated (see the red arrowed lines) clearly concluded that the damage level imposed during the first loading branch of the two-loops loading procedure approached very closely the terminal damage level that can be sustained by dionysos marble. this close approach justifies the sudden collapse of the specific specimen during the second loading loop, even at its constant force branch. concerning the fracture mode, it is interesting to note that all specimens failed by almost axial splitting rather than along inclined planes, as it is suggested by the classical mohr-coulomb theory. in other words, in the specific series of tests the familiar mohr’s cones were almost totally suppressed. although such behaviour is not common in standardized laboratory tests, it can be attributed to the excellent lubrication conditions achieved. the specific behaviour was long ago observed experimentally by vardoulakis et al. [31] (fig.3c). to explain this observation the so-called “post-peak stress diffusion” theory was introduced, that is capable of describing fracture of brittle materials by axial splitting rather than along inclined (with respect to the load axis) planes [31]. the theory is based on an alternative normalization approach: instead of normalizing the axial stress over the area of the specimen’s cross-section (which according to van vliet and van mier [32] is inadequate for c o m p re s s iv e s tr e s s ( m p a ) a x ia l s tr a in 0.0000 0.0005 0.0010 0.0015 0.0020 0 25 50 7575 50 25 0 a xi al s tr es s [m p a] 0.20 0.15 0.10 0.05 0.00 0 100 200 300 400 500 t [s] a xi al s tr ai n [m st ra in ] stress strain i. stavrakas et alii, frattura ed integrità strutturale, 50 (2019) 573-583; doi: 10.3221/igf-esis.50.48 577 (a) (b) (c) figure 3: (a) the applied stress versus the corresponding axial strain during the two loading branches. (b) the degradation of the elastic modulus of dionysos marble in terms of the non-reversible strain, εperm [30]. (c) a specimen made of dionysos marble loaded up to fracture under monotonic axial compression. the lubrication system used (combination of ptfe sheets and steatic acid) was suggested by vardoulakis et al. [31]. it is clear that mohr’s cones are almost completely suppressed. the description of the compression test beyond the peak stress), the axial stress is normalized over its peak value, and it is plotted versus the post-peak axial displacement. describing the experimental results in this way provided very good correlations [32]. the main advantage of the “post-peak stress” diffusion theory is that it is totally independent of the strain concept, which is meaningless in the post-peak regime. in addition, it is quite advantageous that this theory permits description of the experimental results with a minimum number of parameters. experimental results and discussion spatiotemporal variation of the psc n previously published studies, in which the psc technique was employed, a single pair of electrodes was used as sensing tool. in spite of this limitation, it was definitely concluded that, when marble specimens are subjected to compression, the electric activity within the volume of the specimens starts almost simultaneously with the damage processes. it is then gradually intensified with increasing stress level and reaches its maximum value when final fracture is impending [33]. after this maximization, a steep decrease of the psc is systematically observed, designating exhaustion of the specimen’s load carrying capacity, even though the specimen is not yet macroscopically fragmented. in the present study the five pairs of electrodes attached on the specimens (fig.1) permitted, in addition, a (more or less) accurate matching of the electrical signals detected to the locus at which they were generated. the main reason for using five pairs instead of a single one is based on the simple argument that an electrical signal that is generated within the mass of the specimen will reach an electrode of the electrometer attenuated, in accordance with the path that it followed, i.e., to the distance from the electrode. assuming that the specimen is, more or less, homogeneous (and therefore it has the same electric resistance all over its volume) it can be concluded that when a damage event occurs in the vicinity of an electrode, the specific electrode will record higher electrical signal level while the electrodes at longer distances will also receive the signal but they will record it with lower amplitude. in this direction, all the channels of the electrometer are levelled and calibrated with a common reference in order to record electrical signals of the same source amplitude as equal. the time variation of the axial stress and strain as well as the electrical signals received from each one of the five channels is shown in fig.4, for a typical specimen that failed during the second loading loop (the specimen for which the loading scheme is shown in fig.2). the experimental results indicated that during both loading branches (i.e., with increasing stress level) a systematic psc increase is recorded from all the electrometer channels. when the applied stress reaches its maximum value, and it is then kept practically constant, the psc emission follows a restoration process back to a background level, in agreement with previously published works [34, 35]. the fact that during the loading branch of the first loading loop the psc emission is initially recorded stronger by channels 1, 2 and 3 (i.e., the ones located closer to the area around the mid-height of the specimen) indicates that for the specific specimen mechanical damage starts in the vicinity of its central cross section and it is gradually developed towards its bases. during the second loading loop, and while the mechanical stress was kept constant for about 100 s (i.e., at the time i i. stavrakas et alii, frattura ed integrità strutturale, 50 (2019) 573-583; doi: 10.3221/igf-esis.50.48 578 figure 4: time variation of the axial stress and the axial strain (a, g) and the corresponding behaviour of the electrical current emissions, as recorded by the psc channels 0-4 (b-f, h-l), for the first (left column) and the second (right column) loading loops. psc channel 0 x-loca�on: 10mm (b) 75 50 25 0 p sc [p a ] 0 50 100 150 200 t [s] psc channel 0 x-location: 10 mm (b) psc channel 1 x-loca�on: 30mm (c) 75 50 25 0 p sc [p a ] 0 50 100 150 200 t [s] psc channel 1 x-location: 30 mm (c) psc channel 2 x-loca�on: 50mm (d) 75 50 25 0 p sc [p a ] 0 50 100 150 200 t [s] psc channel 2 x-location: 50 mm (d) psc channel 3 x-loca�on: 70mm (e) 75 50 25 0 p sc [p a ] 0 50 100 150 200 t [s] psc channel 3 x-location: 70 mm (e) psc channel 0 x-loca�on: 10mm (h) 75 50 25 0 0 40 80 120 160 t [s] (h) psc channel 0 x-location: 10 mm p sc [p a ] psc channel 1 x-loca�on: 30mm(i) 75 50 25 0 0 40 80 120 160 t [s] (i) psc channel 1 x-location: 30 mm p sc [p a ] psc channel 2 x-loca�on: 50mm(j) 75 50 25 0 0 40 80 120 160 t [s] (j) psc channel 2 x-location: 50 mm p sc [p a ] psc channel 3 x-loca�on: 70mm (k) 75 50 25 0 0 40 80 120 160 t [s] (k) psc channel 3 x-location: 70 mm p sc [p a ] psc channel 4 x-loca�on: 90mm (f) 75 50 25 0 p sc [p a ] 0 50 100 150 200 t [s] psc channel 4 x-location: 90 mm (f) psc channel 4 x-loca�on: 90mm(l) 75 50 25 0 0 40 80 120 160 t [s] (l) psc channel 4 x-location: 90 mm p sc [p a ] (a) 0 50 100 150 200 t [s] 1.6 0.8 0.0 1st loading (g) 80 40 0 st re ss [m p a] st ra in [m st ra in ](a) 75 50 25 0s tr es s [m p a] 2.0 1.0 0.0 st ra in [m st ra in ] 0 40 80 120 160 t [s] 2nd loading (g) stress strain stress strain i. stavrakas et alii, frattura ed integrità strutturale, 50 (2019) 573-583; doi: 10.3221/igf-esis.50.48 579 instant with t=140 s in fig.4) a gradual increase of the psc was detected from all electrodes, designating the upcoming collapse of the specimen, which occurred about 30 s later, under constant external load. it is worth noting that, contrary to what happened during the loading branch of the first loop, the psc increase was now stronger at the edge electrodes (i.e., channel-0 and channel-4). it is thus indicated, that catastrophic cracking started at points closer to the bases rather than at the mid-height area of the specimen (although at the initial loading steps damage was more intense around the specimen’s mid-height). the time variation of the ae data the time variation of (i) the amplitudes of the ae hits recorded from both the ae sensors used (fig.1a), and of (ii) the rate (per second) of the ae hits is shown in figs.5(a,b), respectively, for the first loading loop, for the as above mentioned specimen. the corresponding plots for the second loading loop are shown in figs.5(c,d). comparing the behaviour of the amplitudes of the aes recorded during the two loading loops, it is clearly seen that the loading branch of the second loop is accompanied by aes of significantly lower amplitudes. this observation clearly supports the dominance of the kaiser effect [36]. in addition, it becomes clear that, during the first loading loop and after the maximum stress level is attained, the aes recorded are of lower amplitude. on the other hand, during the second loading cycle, and after reaching the maximum stress level, the number of ae hits increases and it is kept almost constant for about 100 s (fig. 5d). from this point on, the number of ae hits rate starts increasing and their amplitudes become gradually higher until the final fracture of the specific specimen, which occurred at a time instant around t=170 s. recapitulating, the ae activity is much weaker during the loading branch of the second loading loop, as it is well established in literature [37-39]. figure 5: time variation of (a, c) the axial stress and the corresponding amplitudes of the ae hits, and, (b, d) the corresponding behaviour of the rate of the ae hits (s-1), for the first (left column) and the second (right column) loading loop. similar conclusions can be drawn for the time variation of the rate of the ae hits during the two loading loops, which is plotted in figs.5(b,d). indeed, during the loading branch of the first loop the rate of the ae hits is significantly higher than the respective rate during the second loop, reaching a maximum value of about 600 ae hits/s. the corresponding value for the loading branch of the second loop is limited to only 200 ae hits/s, demonstrating again the existence of the kaiser effect. it is interesting to notice the sudden increase of the ae hits rate only a short while after the maximum stress value is attained during the second loading loop (although the stress level is kept constant). this is a clear sign that some kind of dynamic process is activated, which will soon lead to the final fracture of the specimen. the sudden increase of the rate of the ae hits, a little before the final fracture, is another pre-failure indicator that is worth to be highlighted. correlation between psc and ae data the correlation between the data regarding electric and acoustic emissions is here attempted in terms of the psc energy and the corresponding time variation of the ae ib-value. more specifically, the psc energy is calculated according to eq.(1), after applying proper de-noise and background elimination filters on the signals recorded: i. stavrakas et alii, frattura ed integrità strutturale, 50 (2019) 573-583; doi: 10.3221/igf-esis.50.48 580     δ 2 t t t e t psc t dt    (1) in order to compare the psc energy for each one of the electrode pairs and estimate the source location of the electrical emissions, as well as their time variation, matlab scripts were prepared. the results of this procedure are presented (in juxtaposition to the respective time variation of the axial stress and axial strain, which are plotted again in figs.6(a,d) for convenience) for both loading loops in figs.6(b,e). the colour variation in these figures corresponds to the level of the psc energy (according to the scale shown in the figure embedded between figs.6b and 6e) while the y-axis represents the x-location on the specimen. from fig.6b it is clearly seen that during the loading branch of the first loading loop and for stress values which do not exceed about 50% of the respective maximum value attained, electrical signals of relatively low energy are recorded. these signals may be well attributed to the pore closing process. increasing further the stress level, high energy psc emissions are recorded approximately at the mid-height of the specimen spreading gradually towards its bases. while the axial stress is then kept constant at its maximum level, the psc energy is relaxed back to a background level although the strain recorded does not exhibit significant variations. during the second loading loop the maximum values of the psc energy were lower compared to the corresponding ones of the first loop (fig.6e), as it could be perhaps expected according to the kaiser effect [36]. it is to be noticed here that during this second loading loop, and while the stress is kept constant at its maximum level, the corresponding strain keeps increasing though at a relatively low rate. however, what is astonishingly interesting in fig.6e is that, well before the final fracture of the figure 6: time variation of the axial stress and the axial strain (a, d), the spatial distribution of the psc energy (b, e), and the ib-value (c, f), for the first (left column) and the second (right column) loading loop. (a) 0 50 100 150 200 t [s] 1.6 0.8 0.0 1st loading (g) 80 40 0 st re ss [m p a] st ra in [m st ra in ] (a) 75 50 25 0s tr es s [m p a] 2.0 1.0 0.0 st ra in [m st ra in ] 0 40 80 120 160 t [s] 2nd loading (d) 0 50 100 150 200 t [s] 10 50 90 x [m m ] 5000 4000 3000 2000 1000 0 p sc e n er gy [a 2 ] (b) 10 50 90 x [m m ] 0 40 80 120 160 t [s] (e) 0 50 100 150 200 t [s] 3.0 2.0 1.0 0.0 im p ro ve d b -v al ue (c) 0 40 80 120 160 t [s] 3.0 2.0 1.0 0.0 im p ro ve d b -v al ue (f) stress strainstress strain [a 2 ꞏs ] i. stavrakas et alii, frattura ed integrità strutturale, 50 (2019) 573-583; doi: 10.3221/igf-esis.50.48 581 specimen (almost 10 s earlier), the electrodes closer to the specimen’s upper and lower bases start suddenly recording psc signals of high energy. this observation is in accordance with what was concluded from figs.4(h-l). during this last time interval only minor emissions are recorded from the area around the specimen’s mid-height. this sudden electric activity, which starts almost 10 s before the specimen’s collapse could be considered as an interesting pre-failure indicator, especially due to the time distance from the specimen’s collapse. concerning the amplitudes of the ae events, they were processed in the direction of conducting b-value analysis for both loading loops. in this context, the improved b-value (ib) was calculated for each one of the two loading loops according to well-known formalisms [5, 19, 40, 41]. the time variation of the ib-value calculated in this way during the two loading loops is plotted in figs.6(c,f). concerning the first loading loop, the ib-value (after a slight increase) decreases with increasing axial stress. this decrease is abruptly terminated when the stress attains its maximum value and an abrupt increase is observed. from this point on, the ib-value remains practically constant at a relatively high level (equal to about 2.0), implying that no strong ae events are recorded. during the second loading loop, the ib-values exhibit a similar behaviour. the most important observation during the second loading loop is that about 70 s after the stress has reached its maximum value (and is kept constant) the ib-value starts decreasing gradually implying that new ae events of higher amplitudes occur. then a characteristic drop of the ib-value at levels approaching ib=1 is observed, slightly before the specimen’s collapse, in excellent accordance with the respective behaviour of the psc energy. concluding remarks he pressure stimulated currents (psc) and the acoustic emission (ae) experimental techniques were employed according to a combined manner, in order to study the mechanical response of marble specimens subjected to successive compressive loading-unloading-reloading loops at stress levels very closely approaching the compressive strength of the specific marble variety. the two techniques were here combined for the first time (to the authors’ best knowledge) in order to assess the spatiotemporal damage evolution and at the same time to explore the applicability of their data as estimators of proximity to fracture. in this direction, the psc technique was here developed further by using a grid of electrode pairs, aiming to the collection of psc emissions from multiple sensors. it was clearly shown that the updated psc technique provides valuable information regarding the location of the psc source and the spatiotemporal evolution of damage within the specimens. the correlation of the two techniques was here implemented in terms of the psc energy and the improved b-value (ib) of the ae events. the comparison indicated very good qualitative and quantitative agreement between the results obtained by the two techniques. moreover, it was proven that both the as above mentioned quantities (psc energy and ib-value) provide clear indicators of the proximity to fracture: the psc energy starts increasing abruptly well before the specimens’ collapse while at the same time the ib-value exhibits a characteristic steep drop towards the ib=1 critical limit. references [1] chu, t.c., ranson, w.f. and sutton, m.a. (1985). applications of digital-image-correlation techniques to experimental mechanics, exp. mech., 25(3), pp. 232–244. [2] iliopoulos, a. and michopoulos, j.g. (2012). direct strain imaging for full field measurements, asme 2012 international design engineering technical conferences & computers and information in engineering conference idetc/ cie, august 13-15, 2012, chicago, il, usa. [3] lavrov, a. (2005). fracture-induced physical phenomena and memory effects in rocks: a review, strain, 41, pp. 135– 149. [4] lockner, d. (1993). the role of acoustic emission in the study of rock fracture, int. j. rock mech. min. sci. geomech. abstr., 3, pp. 883–899. [5] rao, m.v.m.s. and lakschmi, p.k.j. (2005). analysis of b-value and improved b-value of acoustic emissions accompanying rock fracture, curr. sci. india, 89, pp. 1577–1582. [6] stanchits, s., dresen, g. and vinciguerra, s. (2006). ultrasonic velocities, acoustic emission characteristics and crack damage of basalt and granite, pure appl. geophys, 163(5–6), pp. 975–994. [7] yamada, i., masuda, k. and mizutani, h. (1989). electromagnetic and acoustic emission associated with rock fracture, phys. earth. planet. in., 57, pp. 157–168. t i. stavrakas et alii, frattura ed integrità strutturale, 50 (2019) 573-583; doi: 10.3221/igf-esis.50.48 582 [8] stavrakas, i., triantis, d., agioutantis, z., maurigiannakis, s., saltas, v., vallianatos, f. and clarke, m. (2004). pressure stimulated currents in rocks and their correlation with mechanical properties, nat. hazards earth sys., 4, pp. 563–567. [9] vallianatos, f., triantis, d., tzanis, a., anastasiadis, c. and stavrakas, i. (2004). electric earthquake precursors: from laboratory results to field observations, phys. chem. earth, 29, pp. 339–351. [10] stavrakas, i., anastasiadis, c., triantis, d. and vallianatos, f. (2003). piezo stimulated currents in marble samples: precursory and concurrent with failure signals, nat. hazards earth sys., 3, pp. 243–247. [11] triantis, d., anastasiadis, c., vallianatos, f., kyriazis, p. and nover, g. (2007) electric signal emissions during repeated abrupt uniaxial compressional stress steps in amphibolite from ktb drilling, nat. hazards earth sys., 7, pp. 149–154. [12] kyriazopoulos, a., anastasiadis, c., triantis, d. and brown, j.c. (2011). non-destructive evaluation of cement-based materials from pressure stimulated electrical emission: preliminary results, const. build. mater., 25, pp. 1980–1990. [13] stergiopoulos, c., stavrakas, i., triantis, d., vallianatos, f. and stonham, j. (2015). predicting fracture of mortar beams under three-point bending using non-extensive statistical modelling of electric emissions, physica a, 419, pp. 603–611. [14] cartwright-taylor, a., vallianatos, f. and sammonds, p. (2014). superstatistical view of stress-induced electric current fluctuations in rocks, physica a, 414, pp. 368–377. [15] zhonghui, l., wang, e. and he, m. (2015). laboratory studies of electric current generated during fracture of coal and rock in rock burst coal mine, j. mining, 2015: 235636. [16] sun, m., liu, q., li, z. and wang, e. (2002). electrical emission in mortar under low compressive loading, cement concrete res., 32, pp. 47–50. [17] archer, j.w., dobbs, m.r., aydin, a., reeves, h.j. and prance, r.j. (2016). measurement and correlation of acoustic emissions and pressure stimulated voltages in rock using an electric potential sensor, int. j. rock mech. & mining sci., 89, pp. 26–33. [18] dann, d., demikhova, p., fursa, t. and kuimova, m. (2014). research of electrical response communication parameters on the pulse mechanical impact with the stress-strain state of concrete under uniaxial compression, iop conf. series: materials science and engineering, 66: 012036. [19] shiotani, t., fujii, k., aoki, t. and amou, k. (1994). evaluation of progressive failure using ae sources and improved b-value on slope model tests, prog. acoust. emission, vii, pp. 529–534. [20] tassogiannopoulos, a.g. (1986). a contribution to the study of the properties of structural natural stones of greece (in greek), national technical university of athens, doctoral dissertation, athens, greece. [21] exadaktylos, g.e., vardoulakis, i. and kourkoulis, s.k. (2001) influence of nonlinearity and double elasticity on flexure of rock beams ii. characterization of dionysos marble, int. j. solids struct., 38, pp. 4119–4145. [22] theocaris, p.s. and coroneos, e. (1979). experimental study of the stability of parthenon (in greek). publications of the academy of athens, 44, pp. 1–80. [23] zambas, c. (2004). mechanical properties of pentelik marble [in greek], ministry of culture, committee for the preservation of parthenon publications, athens, greece. [24] vardoulakis, i. and kourkoulis, s.k. (1997). mechanical properties of dionysos marble, final report of the european union environment project ev5v-ct93-0300 “monuments under seismic action”, nat. tech. univ. athens, athens. [25] labuz, j.f., bridell j.m. (1993). reducing frictional constraint in compression testing through lubrication, int. j. rock mech. min. sci. & geomech. abstr., 30, pp. 45l–455. [26] drescher, a. and vardoulakis, i. (1982). geometric softening in triaxial test on granular materials, geotechnique, 32, pp. 291–303. [27] read, h.e. and hegemier, g.a. (1984). strain softening of rock, soil and concrete a review article, mech. mater., 3(4), pp. 271–294. [28] van vliet, m.r.a. and van mier, j.g.m. (1995). concrete under uniaxial compression, report 25.5-95-9, tu delft, faculty of civil engineering, the netherlands. [29] kourkoulis, s.k. (2012). critical aspects of the mechanical behaviour and failure of dionysos marble under direct tension, j. serbian soc. comp. mech., 6(1), pp. 199–215. [30] kourkoulis, s.k., exadaktylos, g. and vardoulakis, i. (2000). the degradation of the mechanical properties of natural building stones: an “elastic-damage” model. in: structural integrity in the 21st century. the lifetime of plant, structures and components: evaluation, design, extension and management, j.h. edwards et al. (eds.), emas publishing, solihull, uk, pp.171–179. [31] vardoulakis, i., labuz, j., papamichos, e. and tronvoll, j. (1998). continuum fracture mechanics of uniaxial compression on brittle materials, int. j. solids struct., 35, pp. 4313–4335. [32] van vliet, m.r.a. and van mier, j.g.m. (1996). experimental investigation of concrete fracture under uniaxial compression, mech. cohes-frict. mat., 1(1), pp. 115–127. i. stavrakas et alii, frattura ed integrità strutturale, 50 (2019) 573-583; doi: 10.3221/igf-esis.50.48 583 [33] triantis, d., anastasiadis, c. and stavrakas, i. (2008). the correlation of electrical charge with strain on stressed rock samples, nat. hazards earth sys., 8, pp. 1243–1248. [34] alexandridis, a., triantis, d., stavrakas, i. and stergiopoulos, c. (2012). a neural network approach for compressive strength prediction in cement-based materials through the study of pressure-stimulated electrical signals, const. build. mater., 30, pp. 294–300. [35] triantis, d., vallianatos, f., stavrakas, i. and hloupis, g. (2012). relaxation phenomena of electrical signal emissions from rock following application of abrupt mechanical stress, ann geophys-italy, 55(1), pp. 207–212. [36] lavrov, a. (2003.) the kaiser effect in rocks: principles and stress estimation techniques, int. j. rock mech. min. sci., 40(2), pp. 151–171. [37] li, c. and nordlund, e. (1993). assessment of damage in rock using the kaiser effect of acoustic emission, int. j. rock mech. min. sci. & geomech. abstr., 30(7), pp. 943–946. [38] tsimogiannis, a., georgali, b. and anastassopoulos, a. (2000). acoustic emission/acousto-ultrasonic data fusion for damage evaluation in concrete, j. acoustic emissions, 18, pp. 21–28. [39] weber, z., svadbik, p., korenska, m. and pazdera, l. (2000). concrete crossbeam diagnosis by acoustic emission method, j. acoustic emissions, 18, pp. 29–32. [40] colombo, s., main, i.g. and forde, m.c. (2003). assessing damage of reinforced concrete beam using ‘‘b-value’’ analysis of acoustic emission signals, j. mat. civil eng., 15, pp. 280–286. [41] rao, m.v.m.s. 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/hrv (za stvaranje adobe pdf dokumenata najpogodnijih za visokokvalitetni ispis prije tiskanja koristite ove postavke. stvoreni pdf dokumenti mogu se otvoriti acrobat i adobe reader 5.0 i kasnijim verzijama.) /hun 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/pdfxoutputintentprofileselector /documentcmyk /preserveediting true /untaggedcmykhandling /leaveuntagged /untaggedrgbhandling /usedocumentprofile /usedocumentbleed false >> ] >> setdistillerparams << /hwresolution [2400 2400] /pagesize [612.000 792.000] >> setpagedevice microsoft word numero_58_art_14_3138.docx s. doddamaniet alii, frattura ed integrità strutturale, 58 (2021) 191-201; doi: 10.3221/igf-esis.58.14 191 fracture analysis of aa6061-graphite composite for the application of helicopter rotor blade saleemsab doddamani department of mechanical engineering, jain institute of technology, davangere, india. saleemsabdoddamani@gmail.com, https://orcid.org/0000-0002-8498-1488 chao wang department of mechanical engineering, the university of texas, dallas, usa, wcwangchao83@gmail.com, https://orcid.org/0000-0002-6668-704x m.jinnahsheik mohamed department of mechanical engineering, shinas college of technoogy, muscat, oman jinnah.mohamed@shct.edu.om, https://orcid.org/0000-0002-8499-501 md. arefinkowser department of mechanical engineering, dhaka university of engineering and technology, gazipur, bangladesh arefin@duet.ac.bd abstract. the main objective of the work is to study the fracture behavior of aa6061-graphite material using both experimental technique and finite element simulation by considering helicopter rotor blade as a case study. from the case study, it has been observed that the helicopter rotor blade, made of aa6061, has been failed at the threaded portion of the hole. experimental fracture toughness is carried out using the compact tension specimens as per astm standard testing procedure. modeling of compact tension specimens and the threaded portion of the bolt hole was utilized to analyze the fracture toughness using a simulation tool. from the results and the comparison, it is recommended to use aa6061-9wt% graphite material as a replacement of aa6061 in the application of main rotor blades of the helicopter. keywords. metal matrix composite; al-graphite composite; simulations; fracture toughness; rotor blade. citation:doddamani, s., wang, c., jinnah, m.s.m., arefinkowser, md., fracture analysis of aa6061-graphite composite for the application of helicopter rotor blade,frattura ed integritàstrutturale, 58 (2021) 191-201. received: 26.05.2021 accepted: 26.07.2021 published: 01.10.2021 copyright: © 2021 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. https://youtu.be/efnqx2d6ngk s. doddamanietalii, frattura ed integrità strutturale, 58 (2021) 191-201; doi: 10.3221/igf-esis.58.14 192 introduction he property of material through which it is capable of resisting the propagation of crack [1] is known as fracture toughness. many experimental measurement methods and standardized fracture toughness testing techniques were utilized to cherecterize the material, performance evalutionand also quality assurance of various engineering structures. thus the fracture toughness determination and testing plays the vital role in the development of fracture mechanics and their applications. the american society for testing and materials (astm) provides the standard method for fracture toughness testing and evaluation and also its terminology. one of those methods were astm e1823 [2]. the first fracture toughness testing for metallic materials was astm e399 [2] which is developed to determine the plain strain fracture toughness kic. the astm e399 can also be applied to the disconitusly reinforced or particulate reinforced metal matrix composites (mmcs). these composites nearly exhibits the isotropic properties [3] whereas the fiber aligned mmcs are highly anisotropic. some of the particulate reinforcements used were ceramic particles such as silicon carbide, alumina, graphite, boron carbide, titanium carbide etc. many experimentation techniques have been conducted [4] on the fracture toughness of the al6061-graphite particulate composites. also the comparison of the fracture toughness values of al-sic and al-graphite composites has been carried out. from the results it is observed that the al-graphite particulate composites exhibits the better fracture toughness, light weight, wear resistant, higher coefficient of friction and ductility than the other metal matrix composites. thus the algraphite composites can be utilized for the many automobile and aerospace composites. the al6061 t6 is used in the many applications like bycycle frames and components, wings and fuselages of aircrafts, helicopter rotor blade, etc. many authours [5-9] ware studied the failure of helicopter. literature shows that failure of helicopter occurred is at the threaded hole region of rotor blade. many helicopter rotor blades are failed due to the fatigue loading, corrosion of threaded holes [5-6]. litreatures also shows that many helicopter failures occurred in air i.ein the operational conditions [5-7]. crack developed and propagated, in the rotor blade fittings i.e bolt hole [6,8], edge spar [7] without giving any prior indication. many researchers reported that main rotor blades are made of aluminum 6061-t6 alloy [5-9]. mikael amura et al [5] investigated rescue military helicopter crash in italy in the oprating conditions. their investigation revealed that the crash was caused by the fatigue failure of the spar of a main rotor blade. among five rotor blades, four blades are found in the crash site whereas fifth blade found at a distance of about 900m from the crash site. from the investigation it was found that failure of blade happened while helicopter is in the air. main rotor blade was made of 6061t6 aluminum alloy. dr arjen romeyn [6] also reported that failure of one of the rotor blades of robinson r22 helicopter. failure of the blade occurred at the section of root fitting. material of the rotor blade is aluminum alloy. surise helicopters inc [7] investigated the failure of main rotor blade of bell 206l helicopter, canada. material used in the rotor blade is aluminum alloy. the blade fracture was intiated at on the inner surface of the spar, at the location of the void in the adhesive used to bond the lead weight to the spar at station. rolf kieselbach et al [8] studied the failure of a helicopter rotor. experiments have been conducted to find the material properties. from the result, it is suggested a proposal to detect the cracks before they reach to a critical size. sylwesterkłysz et al [9] also reported the faulire of main rotor blade of the mi-8 helicopter. blades of the mi-8 helicopter are made of 6061-t6 aluminum alloy. also conducted the strength and fatigue tests of the material of the helicopter blades. experiments have been carried out to find the strength and fracture characteristics of the material from the main rotor blades of mi-8 helicopter. specimens used are disk-shaped compact specimen (dct) per astm standards fatigue crack growth experiments have been carried out and found that threshold fracture toughness kicas 1.34 to 2.81 mpam. yasmin et al [10], s doddamani et al [11] worked on aluminum matrix reinforced with graphite particles has been studied for the mechanical and fracture characteristics of the composite respectively. astm has prescribed compact tension specimen for the fracture toughness testing [12]. s doddamani et al [13] uses compact tension specimen to study the fracture toughness of al6061-graphite mmc at varied weight fractions. k.k. alaneme et al [14] studied the fracture toughness of al6063-sic particulate mmc. it is observed from the results of the fracture toughness testing of al6061graphite [15] and al6063-sic [16] that al6061-graphite composite has more fracture toughness values. different authors [15-21] studied the different methods of the finite element techniques to determine the mechanical/fracture behavior of the materials. experimental techniques on prototype provide information concerning the structure in the pattern of the experiment only. whereas predicting the dynamic behavior of the structure, under different boundary conditions & loading, can be done by finite element models, but the reliability of the finite element model (fem) is often not guaranteed. to verification and optimization of these fem analysis results can be accomplished by the experimental data. the outcome of a model updating examination is a fem technique that is more reliable for further prediction. fem software, like t s. doddamaniet alii, frattura ed integrità strutturale, 58 (2021) 191-201; doi: 10.3221/igf-esis.58.14 193 ansys, solves the issues related to structural and mechanical. structural and mechanical issues incorporate static/dynamic, heat transfer & fluid problems, linear & nonlinear structural analysis, and additionally electromagnetic and acoustic issues. many two dimensional, three dimensional tutorials ware also available to evaluate the fracture toughness [22-24] using finite element methods, most of them ware used ansys tool for the same. while simulating the fracture related issues, it requires the use of plane182, which will fit the crack tip section. plane182, as shown in fig 1, is a higher order form of the 2-d, eight-node component. it gives more exact outcomes to blended (quadrilateral-triangular) automatic meshes and can hold up under sporadic shapes without as much loss of accuracy. the 8-node components have ideal displacement shapes and are appropriate to model curved boundaries. figure 1:plane182 geometry. the 8node component is characterized by eight nodes having two degrees of freedom at every node: interpretations in the nodal x and y directions. the component might be utilized as a plane component or as an axis-symmetric component. the component has stress stiffening, large deflection, plasticity, creep, swelling, and extensive strain abilities. the stress intensity factors at a crack for a linear elastic fracture mechanics analysis may be computed. the analysis uses a fit of the nodal displacements in the vicinity of the crack. from the literature it is identified the helicopter rotor blade, made of aa6061, was failed at the threaded portion of the rotor blade. the main objective of the work is to study the fracture behavior of aa6061-graphite material using both experimentation and finite element simulation method by considering helicopter rotor blade as a case study. the finite element model is built for the aa6061 and aa6061-graphite composite. through this work an attempt has been made to compare the existing use of material with the composite material to prepare the helicopter rotor blade so as to enhance its fatigue crack resistance property. materials luminum alloy (aa) 6061 and its main alloying elements are silicon (0.70%) and magnesium (0.81%). physical properties [25] of aa6061 were hardness 95 bhn, elastic modulus 68.9 gpa, ultimate tensile strength 315 mpa, yield strength 275 mpa, extension 17%. graphite is available in the shape of fibers and particles which has been identified as high strength material. physical properties of graphite [26] are elastic modulus 15 gpa, yield strength 119 mpa, thermal expansion coefficient is 8.2x10-6°c. out of many factors which influence the fracture properties, the particle size of graphite is most important microstructural variable. aa6061 and graphite particulate metal matrix composites produced by solidification techniques presents better mechanical properties which can be potential materials for aerospace and automobile applications [27-30].the mechanical properties of the aa6061-graphite composites used for this study are listed in the tab. 1. sl.no specimens yield strength (mpa) ultimate tensile strength (mpa) percentage elongation elastic modulus (gpa) 1 aa6061 85.6 102.4 16.8 68.9 2 aa6061-6wt%sic 93.3 114.1 14.1 65.6 3 aa6061-9wt%sic 99.1 117.3 14.3 64.2 4 aa6061-12wt%sic 98.9 115.8 13.7 64.4 table 1:mechanical properties of aa6061-graphite composites a s. doddamanietalii, frattura ed integrità strutturale, 58 (2021) 191-201; doi: 10.3221/igf-esis.58.14 194 methods experimentation he compact tension (ct) specimen is used to test the fracture toughness as per the astm e399 standard testing procedures. the geometry of the specimen is as shown in the fig 2(a). the crack length to width (a/w) ratio considered is 0.45, width of the specimen considered is 40mm and thickness of the specimen is 12mm which confirms the conditions [12-13, 28] of plane strain fracture toughness. the experimentation has been carried out using servo hydraulic testing machine by maintaining the frequency of 5 hz and displacement rate 1mm/min. figure 2(a): geometry of the ct specimens. figure 2(b): finite element model (a)full crack model (b) nodes around the crack tip figure 3: crack tip region. model generation using ansys, the geometric model was created. a finite element model was constructed utilizing plane182 and solid185 components shown in fig 2(b). the nodes around the crack tip appear in fig 3. von neumann's method is used, which is the most widely used approach, to study the stability of numerical schemes. it is not necessary to refine the mesh of the entire model. from the saint-venant’s principle, the model can be refined at the regions of interest. thus the coarse element sizes are refined at the crack tip to the fine mesh. the mesh refinement at the crack tip leads to reduction 1 11 x y z elements /expanded 1 11 elements /expanded t s. doddamaniet alii, frattura ed integrità strutturale, 58 (2021) 191-201; doi: 10.3221/igf-esis.58.14 195 of errors significantly. from the mesh refinement, the convergence of solutions can be increased without an increment in the problem size it can be solved. the singularity, in fracture mechanics, is essential. at the crack tip, there is the small localized plastic zone will be formed due to the higher stresses at that region. crack tip is the sharp corner which causes the worst conceivable geometrical singularity. in the singularity region the stresses become infinite. it is difficult to compute the stress field in finite element simulations because of the singularity. however it is not necessary to investigate the details of crack tip. there are direct approaches to determine the fracture toughness of the material. since these approaches determine the global quantities far from crack, the singularity can be ignored. the finite element model was built using plane182 element [31], for the crack analysis of the aluminum-graphite alloy. the crack analysis was carried out and the resulting analysis is shown in tab. 1. failure of a helicopter main rotor blade rescue military helicopter crashed in the middle of a ferry flight towards an air terminal where an activity was planned. all team individuals endured fatal injuries [5-7]. the rescue military helicopter suddenly changed direction, and lost control due to the detachment of one of the rotor blades. the increase of fatigue crack growth reduces the strength of the blade to an extent that allowed the fracture to occur under normal flight loads. in view of the direction of failure of the helicopter, the safety investigation board found part of the failed blade separated around 900 m before the disaster area. the failure analysis of the fractured blade was conducted and it was determined that part of the blade detached in the air due to which helicopter become uncontrollable. the main rotor blade is about 9 m long. the structural part of the blade is made of 6061-t6 aluminum alloy [5-8] and were 4.5 mm thick on average. the observations demonstrated various initiation points along an cut on the external and internal surface. blade fracture happened because of the initiation of a fatigue crack in the bolt hole in the blade spar to root fitting joint. fig 4 shows the root fitting of the blade, an aluminum alloy that accommodates the blade spindle and bearings, had fractured at the innermost bolt hole of the root fitting to blade spar joint. figure 4(a) recovered main rotor head assembly [6] figure 4 (b) fractured main rotor blade [6] figure 5(a) fitting side, or inboard side, of the fracture [6] figure 5(b) the blade side, or outboard side, of the fracture [6] a s. doddamanietalii, frattura ed integrità strutturale, 58 (2021) 191-201; doi: 10.3221/igf-esis.58.14 196 figure 6: sites of fatigue crack initiation (arrowed) [6]. figure 7(a) fea model figure 7(b) fea nodes around the crack tip from the fig 5(a), (b) it is observed from the fracture surface features that fracture take place as a result of the progressive crack growth from the inboard bolt hole. the fatigue crack growth mechanism was used, i.e., crack initiation and crack propagation in response to the development of repeated alternating stresses throughout the operation. due to the failure of the adhesive bond (disbonding) at the bolt hole, failure of the main rotor blade occurs. the disbonding take place at spar end, and the root fitting of upper and lower blade skins as shown in fig 5. from fig 6, it is clear that moisture reacted with the crack surfaces. followed by localized corrosion occurred in the counterbore (fig 6 (b,c)). the nature of crack propagation marks signifies that fatigue crack initiation occurred at (a) the lower side of the bolt hole, (b) the thread on the upper side of the bolt hole and (c) the counterbore on the upper side of the bolt hole. from fig 6 it is evident that the failure of the rotor blade occurred at the bolt hole and threaded portion of the bolt hole. s. doddamaniet alii, frattura ed integrità strutturale, 58 (2021) 191-201; doi: 10.3221/igf-esis.58.14 197 the fem model to find the fracture toughness is created using ansys. a structural model was created using an 8-node plane182 element with no real constants values. for the element plane182, the area has been created with a concentrated key point at the crack tip. the model was meshed, gave symmetric boundary conditions and loads applied before solving the problem. the finite element model is built using plane182 elements, crack tip and nodes around the crack tip are shown in fig 7. ansys, there is no possibility of voids, clustering of reinforcements, particle and matrix interfaces; material will not have any other crack in its structure. since the fracture toughness depends on the material properties (tab. 1), crack length and the load at fracture (pf), nearly better results will be obtained as compared to experimental results. results and discussions he fracture toughness of the aa6061 and aa6061-graphite composites has been carried out, both experimental and 3d simulations, using ct specimens and threaded portion of the aa6061 and aa6061-graphite composites using finite element simulations. the result of the analysis has been given in the tab. 2. sl no composite fracture toughness (kic) mpa m experimental simulation of ct specimen simulation of threaded portion 1 aa6061 15.45 15.34 15.94 2 aa6061-6%graphite 16.22 16.42 17.21 3 aa6061-9% graphite 16.74 18.73 18.28 4 aa6061-12% graphite 15.70 17.64 17.98 table 2: fracture toughness results of aa6061 & aa6061-graphite composites. the experimental fracture toughness of the aa6061-graphite composites has been carried out for the different weight fractions of the graphite. for each composition, three ct specimens were prepared and tested. the mean value of the fracture toughness has been listed in the tab.2. the fracture toughness with increment in the graphite percentage has been plotted as shown in the fig 8. specimens of unreinforced al6061 exhibits the lesser deviations for the samples tested. however, the samples aa6061-6wt% and 9wt%graphite shows the similar deviation whereas the aa606112wt%graphite have the increased deviation than others. this larger deviation is may be due to the difference in the fracture toughness values among the specimens tested. also as the graphite composition increases the fracture toughness increases up to 9wt% of graphite and later decreases at 12wt% of graphite. this decrement is due the increase of reinforcement decreases the ductility, thus decreases the fracture toughness of the said composite. figure 8: fracture toughness of the aa6061-graphite composites. t s. doddamanietalii, frattura ed integrità strutturale, 58 (2021) 191-201; doi: 10.3221/igf-esis.58.14 198 from the tab. 2 it is observed that the fracture toughness values are almost near to each other. however the fe simulation results are higher than the experimental results. this is due to the fact that only one crack has been introduced in the simulation model whereas in the experimental specimen there may be many voids, dislocations and micro-cracks were available leads to the reduction in the fracture toughness. figure9:stress concentration factor k1 of aa6061-9%graphite for rotor blade. (a) unreinforced al6061 alloy (b) al6061-6wt% of sic (c) al6061-9wt% of sic (d) al6061-12wt% of sic figure 10. sem fractographic images cracks cracks cracks small voids large voids s. doddamaniet alii, frattura ed integrità strutturale, 58 (2021) 191-201; doi: 10.3221/igf-esis.58.14 199 fig 9 shows the fracture toughness value of the aa6061 with 9wt% graphite particles and also shows the shape of the plastic zone. the shape of the plastic zone obtained indicates the plane strain fracture toughness [1]. the fracture toughness of the aa6061 with 9wt% graphite composite exhibits the higher values. thus it is considered to be the better composition of the composite among tested. from the above results it is recommended that aa6061-9%graphite material can be considered as a potential rotor blade material as a replacement of aa6061 in the application of main rotor blades of the helicopter. fig10 shows the fractographic images of the al6061-graphite composites obtained through the sem. fractographic images shows the formation of cracks at the unreinforced aluminum alloy and at 6wt% of graphite whereas at the 9wt% of graphite have the smaller voids which transforms into the cracks on loading. thus the increased fracture toughness has been observed. the decrement in the fracture toughness after the 9wt%graphite, is due to increased hardness and increased crack initiation sites and reduced ductility.from the fig. 9 it is also observed that, all the al-graphite composites exhibits the dull and fibrus surface. which means that the said composites have the ductile fracture. thus the increased fracture toughness of the al-graphite composite is the addition of graphite reinforcement. however the increment in other reinforcements such as sic [14] in the aluminum composites exhibits the lesser ductility and fracture toughness values. conclusions he failure of the helicopter rotor blade occurred at the threaded portion of the bolt hole. the finite element model of the bolt hole and the compact tension specimen was successfully modeled using the ansys. the fracture toughness values obtained from the fe simulation are in close agreement with data obtained from standard kic testing. from the comparison of experimental and the fe simulation results, it is recommended that aa6061-9%graphite material can be considered as a potential rotor blade material as a replacement of aa6061 in the application of main rotor blades of the helicopter. funding his research received no specific grant from any funding agency in the public, commercial, or not-for-profit sectors. conflict of interest he authors declare that they have no conflict of interest. references [1] anderson, t .l., (2013). fracture mechanics-fundamentals and applications. 3rd edition, taylor & francis group, new york. [2] zhu, x.k., joyce, j. a., (2012) review of fracture toughness (g, k, j, ctod, ctoa) testing and standardization, engineering fracture mechanics, elsevier, 85, pp.1–46. https://doi.org/10.1016/j.engfracmech.2012.02.001 [3] asm handbook. (2001) composites, 21, asm international. [4] doddamani, s. and kaleemulla, m. (2019). comparisons of experimental fracture toughness testing methods of al6061-graphite particulate composites, journal of failure analysis and prevention, springer, 19(3), pp.730-737. doi: 10.1007/s11668-019-00652-8. [5] amura, m., aiello, l., colavita, m., paolis, f.d., bernabei, m. (2014). failure of a helicopter main rotor blade, 20th european conference on fracture (ecf20), procedia materials science, 3, pp.726 – 731. t t t s. doddamanietalii, frattura ed integrità strutturale, 58 (2021) 191-201; doi: 10.3221/igf-esis.58.14 200 [6] romeyn, a., (2005). main rotor blade failure analysis report, engineered system failure analysis report. [7] sunrise helicopter inc, (2011). in-flight separation of main rotor blade and collision with terrain, aviation investigation report, a11o0205. [8] kieselbach, r., soyka, g., (2000). failure of a helicopter rotor, technology, law and insurance, t and f online, 5,(34), pp.141-146. [9] klysz, s., lisiecki, j., kurdelski, m. (2010). material testing of the helicopter main rotor blades, 37th solid mechanics conference, september. [10] yasmin, b., doddamani, s. (2015). mechanical properties of aluminium–graphite particulate composites, ncerame-2015, international journal of engineering research & technology (ijert), pp.121-124. [11] doddamani, s. and kaleemulla, m. (2016). indentation fracture toughness of alumnum6061-graphite composites, international journal of fracture and damage mechanics, 1(1), pp. 40-46. [12] astm standards, (2017). standard test method for plane-strain fracture toughness of metallic materials, astm international, e 399-17. [13] doddamani, s., kaleemulla, m. (2017). fracture toughness investigations of al6061-graphite particulate composite using compact specimens, frattura ed integritàstrutturale, 41, pp.490-497. doi: 10.3221/igf-esis.41.60 [14] alaneme, k.k., aluko, a.o. (2012). fracture toughness (k1c) and tensile properties of as-cast and age-hardened aluminium (6063)–silicon carbide particulate composites, scientia iranica a, 19 (4), pp 992–996. [15] allegrucci f .l., paolis a.d. coletta m. bernabei, (2013). crack of a helicopter main rotor actuator attachment: failure analysis and lessons learned, frattura ed integritàstrutturale, 26, pp.104-122; doi: 10.3221/igf-esis.26.11 [16] henkel, s., wolf, c. h., biermann, h., burgold, a. and kuna, m., (2019). cruciform specimens used for determination of the influence of t-stress on fatigue crack growth with overloads on aluminum alloy al 6061 t651, frattura ed integritàstrutturale, 13(48), pp.135-143. doi: 10.3221/igf-esis.48.16. [17] chen, g., huang, x. (2016). simulation of deformation and fracture characteristics of a 45 steel taylor impact specimen, engineering transactions, 64(2), pp.225–240 [18] talemi, r.h. (2016). numerical simulation of dynamic brittle fracture of pipeline steel subjected to dwtt using xfem-based cohesive segment technique, attura ed integrità strutturale, 36, pp.151-159; doi: 10.3221/igf-esis.36.15 [19] shlyannikov, v., yarullin, r., ishtyryakov, i. (2017). effect of different environmental conditions on surface crack growth in aluminum alloys, frattura ed integrità strutturale, 41, pp.31-39. [20] bharath, k.n., manjunatha, g. b. (2018). investigating the contribution of geometrical parameters and immersion time on fracture toughness of jute fabric composites using statistical techniques, frattura ed integrità strutturale, 12(46), pp. 14-24. doi: 10.3221/igf-esis.46.02. [21] dhummansure, v., kalyanrao, a.a., doddamani, s. (2020). optimization of process parameters for fracture toughness of al6061-graphite composites, structural integrity and life, 20(1), pp 51–55. [22] taha, b. b., benattou, b. and ghazi, a., (2018). simulation of the behavior of aluminum alloys welded in friction stir welding fsw: (case of aa5083 and aa 6082), frattura ed integrità strutturale, 12(46), pp. 1-13. doi: 10.3221/igf-esis.46.01. [23] seitl, s., viszlay, v., (2017). modified compact tension specimen for experiments on cement based materials: comparison of calibration curves from 2d and 3d numerical solutions, frattura ed integrità strutturale, 39, pp. 118128. doi:10.3221/igf-esis.39.13 [24] kikuchi, m., wada, y., li, y. (2015). crack growth simulation in heterogeneous material by s-fem and comparison with experiments, frattura ed integritàstrutturale, 34, pp. 318-325; doi: 10.3221/igf-esis.34.34 [25] hareesha g., chikkanna n., doddamani, s. (2021). finite element simulation of fracture toughness of al6061reinforced with silicon carbide, iop conference series: materials science and engineering, 1065, 012036, pp.1-6. doi: 10.1088/1757-899x/1065/1/012036. [26] doddamani, s. and kaleemulla, m. (2018). effect of graphite addition on the fracture and fatigue crack growth behavior of al6061-graphite, structural integrity and life, 18(3), pp.185–192. [27] doddamani, s. and kaleemulla, m. (2019). effect of aging on fracture toughness of al6061-graphite particulate composites, mechanics of advanced composite structures, 6(2), pp.139-146. doi: 10.22075/macs.2019.16436.1177. [28] doddamani, s., kaleemulla, m. (2017). experimental investigation on fracture toughness of al6061–graphite by using circumferential notched tensile specimens, frattura ed integrità strutturale, 39, pp.274-281. [29] doddamani, s. and kaleemulla, m. (2019). effect of thickness on fracture toughness of al6061-graphite, journal of solid mechanics, 11(3), pp. 635-643. doi: 10.22034/jsm.2019.666695. s. doddamaniet alii, frattura ed integrità strutturale, 58 (2021) 191-201; doi: 10.3221/igf-esis.58.14 201 [30] doddamani, s., kaleemulla, m., kiran j .o., bakkappa, b. (2019). fracture toughness testing of 6061al-graphite composites using senb specimens, journal of the institute of engineers (india)-series d, springer, 100(2), pp.195201. doi: 10.1007/s40033-019-00188-z. [31] yasmin b., bharath k .n., doddamani, s., rajesh a.m., mohamed kaleemulla k. (2020). optimization of process parameters of fracture toughness using simulation technique considering aluminum-graphite composites, transactions of the indian institute of metals, springer, 73(12), pp. 3095 – 3103. doi: 10.1007/s12666-020-02113-5. microsoft word numero 1 art 1.doc l. p. pook, frattura ed integrità strutturale, 1 (2007) 12-18 12 1 introduzione it is well-known that engineering structures and components, as well as consumer items, contain cracks or flaws and, therefore, crack growth must be considered both in design and in the analysis of failures. the path taken by a crack in a critical component or structure can determine whether fatigue failure is catastrophic or not. knowledge of potential crack paths is also needed for the selection of appropriate non-destructive testing procedures. much current work is concerned with crack growth viewed on macroscopic scale. the forthcoming esis international conference on crack paths (cp 2006) will be devoted to consideration of crack paths at various scales. from a theoretical viewpoint the complete solution of a crack growth problem includes determination of the crack path. figure 1: cracks in undercarriage bay bracket. it is often assumed that the crack path is known, either from theoretical considerations, or from the results of laboratory tests. at the present state of the art, the factors controlling the path taken by a crack are not completely understood [1]. eight brief case studies involving crack paths are presented. these are taken from the author’s professional and personal experience over many years. they have been chosen to illustrate various aspects of crack paths. one example is in a component from a major structure, three examples are in laboratory specimens, and four are in nuisance failures. such nuisance failures cause, in total, a great deal of inconvenience and expensive, but do not normally receive much publicity. 2 aircraft undercarriage bay bracket the relationship between mode of fatigue loading and paths taken by fatigue cracks has been of interest for a long time [2, 3]. this information can be useful in failure analysis and figure 1 shows an example from 1961. it is a bracket from an aircraft undercarriage bay which showed unexpected cracking at rivet holes. the bracket was a formed 18 swg (1.2 mm thick) aluminium alloy angle, 10 in × 0.8 in × 0.8 in (254 mm × 20.3 mm × 20. 3 mm). the figure shows a general view of typical cracks observed after the bracket was removed from the bay. examination of the fracture surfaces of the cracks showed that fatigue cracks had originated at both surfaces of the bracket at the rivet hole corner and then propagated inwards on elliptical crack fronts, with the two cracks intersecting at or near the centre line of the sheet. figure 2 shows the fracture surface of a typical crack. this indicates that failure was caused by out of plane alternating some practical crack path examples ( da esis newsletter 2006) les p. pook department of mechanical engineering, university college london, torrington place, london wc1e 7je, uk abstract. it is well known that many engineering structures and components, as well as consumer items, contain cracks or crack-like flaws. it is widely recognised that crack growth must be considered both in design and in the analysis of failures. the complete solution of a crack growth problem includes determination of the crack path. macroscopic aspects of crack paths have been of industrial interest for a very long time. at the present state of the art the factors controlling the path taken by a crack are not completely understood. eight brief case studies are presented. these are taken from the author’s professional and personal experience of macroscopic crack paths over many years. they have been chosen to illustrate various aspects of crack paths. one example is in a component from a major structure, three examples are in laboratory specimens, and four are in nuisance failures. such nuisance failures cause, in total, a great deal of inconvenience and expensive, but do not normally receive much publicity. keywords: crack growth, crack path l. p. pook, frattura ed integrità strutturale, 1 (2007) 12-18 13 bending fatigue loads, which were not anticipated by the designer. examination of the fracture surfaces at high magnification showed the presence of striations and hence confirmed that cracking was due to fatigue. this is an example of the useful crack path information which can be obtained from simple examination of a failed component with the naked eye. figure 2. surface of crack in an undercarriage bay bracket. 3 angle notch fracture toughness and fatigue specimens by 1965 plane strain fracture toughness testing using mode i specimens, in which crack growth is perpendicular to the applied load, was well established [4] but little was known about fracture toughness behaviour under mixed mode loading, where loads are applied at an angle to the crack.. some tests were therefore carried out in 1966 [5, 6] to investigate the mixed mode fracture toughness of dtd 5050, a 5½% zn aluminium alloy with kic = 28.8 mpa√m [5]. a 19 mm thick angle notch specimen was used, with the initial notch inclined at an angle β of 75°, 60° and 45°, as in figure 3. specimens were precracked in fatigue. figure 4 shows the fracture surface of one of the specimens with the initial notch inclined at β = 45°. the fatigue precrack (bright area at the notch root) is of nearly constant depth, and at the end of the precrack β ≈ 48°. a feature of the test is that under the static loading to determine the fracture toughness the specimen failed very abruptly, but the macroscopic crack path features followed on from the fatigue precrack. at the time the fracture surface appearance was puzzling, but is easily interpreted from a modern viewpoint [1], in that that there is a tendency to mode i crack growth on two scales. on a scale of 1 mm initially crack growth was mixed mode. as the crack grew the crack front rotated until it was perpendicular to the specimen surfaces, and crack growth was in mode i, with the exception of shear lips at specimen surfaces. on this scale the crack follows a curved path which tends towards a plane of symmetry. this is in accordance with the well known observation [1] that the tendency to mode i crack growth means that cracks tend to grow perpendicular to the maximum principal tensile stress. on a smaller scale of 0.1 mm the tendency to mode i fatigue crack growth results in the production of what is known as a twist crack [1] containing individual mode i facets connected by cliffs. the mode i facets gradually merge as, viewed on the 1 mm scale, the crack growth surface becomes perpendicular to the specimen surfaces. merging of mode i facets shows up more clearly under fatigue loading. some fatigue tests were carried out in 1989 on 20 mm thick medium strength structural steel angle notch specimens [7] with initial β values of 75°, 60° and 45°. figure 5 shows the fracture surface of one of the specimens, initial β = 60°. the light area at the top is where the specimen was broken open in liquid nitrogen. these examples illustrate the strong tendency to mode i crack growth in isotropic materials under essentially elastic conditions. figure 3. angle notch charpy specimen, crack initiation along notch tip. figure 4. fracture surface of dtd 5050 5½ zn aluminium angle notch fracture toughness test specimen, initial β = 45°. l.p.pook., frattura ed integrità strutturale, 1 (2007) 12-18 14 figure 5. fracture surface of medium strength structural steel angle notch fatigue test specimen, initial β = 60°. figure 6. crack path in a waspaloy sheet under biaxial fatigue load. the grid is 2.54 mm. 4 crack path stability under biaxial loading the question of the stability of a crack path had been of interest for some time [8] but in general it wasn’t possible to predict crack paths under biaxial fatigue loading. therefore, in 1974 some tests [9], were carried out at room temperature on waspaloy, a nickel based gas turbine material, in order to determine the conditions under which a fatigue crack path became unstable under biaxial loading. the specimens were 254 mm square and 2.6 mm thick. the material had been cross rolled during production to ensure that its properties were reasonably isotropic. tests were carried out using sinusoidal constant amplitude loading at a stress ratio (ratio of minimum to maximum load in fatigue cycle), r, of 0.1. in each test the fatigue load perpendicular to the crack was kept constant. cracks were first grown from each end of an initial slit under uniaxial loading an in phase load was then applied parallel to the crack, and crack path behaviour observed. figure 6 shows the crack path for a load parallel to the crack of twice the load perpendicular to the crack. the crack path became unstable and deviated from its initial path as soon as the load parallel to the crack was applied. at the time the tests were carried out it wasn’t possible to do more than describe the results. however, reanalysis of these and other results in 1997 [1, 10] showed it was possible to correlate crack path stability in terms of a parameter called the t-stress ratio. 5 plastic domestic tap in 1991 a plastic domestic tap in the author’s utility room was observed to be leaking where it was screwed into a fitting on the supply pipe. the tap had a fitting for a hose pipe, and appeared to be a replacement for the original brass tap. when an attempt was made to unscrew the tap it failed completely. the two parts of the broken tap are shown in figure 7 and a close up of the fracture surface in figure 8. the dark area is fatigue and the light area the final static failure. the age of the tap at the time of failure is unknown, but as one fatigue cycle is applied each time a tap is turned on and off it is likely that thousands of cycles had been applied. safety critical pressure containing components are often designed to leak-before-break [11] in order to avoid catastrophic failure. it is fortunate that the tap did so otherwise the utility room would probably have been flooded. the failed tap was replaced with a brass tap, and it was observed that the detail design in the vicinity of the threads was exactly the same. the replacement tap is still in use. the episode is an example of the danger of using a different material for a component without making appropriate changes to detail design. figure 7. plastic domestic tap. l. p. pook, frattura ed integrità strutturale, 1 (2007) 12-18 15 figure 8. crack surface of plastic domestic tap. figure 9. wall clock by john davidson, coatbridge. figure 10. failed wall clock mainspring. 6 wall clock mainspring before the days of quartz clocks, spring driven wall clocks were widely used in public buildings. the example shown in figure 9 was originally used in a school, but since 1968 it has been in use in the author’s kitchen. in 1994 the mainspring failed while the clock was being wound. examination showed that this was the final failure following fatigue crack growth. a general view of the failed mainspring is shown in figure 10. fatigue has been a problem in clock mainsprings for centuries, and traditionally they are designed using rules of thumb based on experience [12], rather than by detailed analysis. the total fatigue life is not known, but the clock is wound weekly so it must be thousands of cycles. a clock mainspring is loaded in bending, with loading and unloading moving along the spring as it is wound and unwinds. when a mainspring breaks in fatigue the crack is usually straight across the spring, with crack growth predominantly through the thickness. however, in this particular mainspring crack path behaviour is unusually complicated, and details are shown in figure 11. a fatigue crack initiated at a corner at one edge of the 27 mm wide mainspring. initially, crack growth was across the spring (downwards in the picture) but after about 9 mm of growth the crack turned sharply towards the outer end of the spring (right in the picture), and then grew in a spiral fashion towards the other edge of the spring until the final failure took place. during this crack growth two secondary cracks initiated, and then joined so that a small triangular piece of spring became detached. the joined secondary crack then grew in a spiral fashion towards the centre of the spring, but did not contribute to the final failure. this is an example of a nuisance fatigue failure which did not have serious consequences. such failures are not normally investigated at all. the offending component is simply replaced. in this particular case the replacement mainspring is still intact after 12 years. figure 11. centre portion of failed wall clock mainspring. l.p.pook., frattura ed integrità strutturale, 1 (2007) 12-18 16 7 angle notch charpy specimens some preliminary tests [13] were carried out in 1971 on angle notch charpy specimens, but crack paths were not investigated in detail. specimen design was based on the standard charpy v-notch specimen with β values (figure 3) of 90° (standard specimen), 75°, 60°, and 45°. the true notch tip radius was reduced so that the notch tip radius measured in a plane parallel to the specimen sides was the same as in the standard charpy specimen (0.25 mm). figure 12 shows the appearance of specimens tested at 10 c. more detailed tests were carried out in 1997 using en6a mild steel (0.36% c) specimens [14]. all specimens were tested in the normalised condition (tensile strength 550 mpa, yield stress 280 mpa). tests were carried out in a 300 j charpy machine equipped with a 2 mm radius striker. they are an example of the complexity often observed in crack path behaviour under dynamic loading. the fracture surface appearance of the standard charpy specimens (β = 90°) is typical of mild steel. in the lower shelf region, that is at below about -15°c, fracture surfaces are crystalline, and in the upper shelf region, above about 30°c, they are ductile. in the transition region fracture surfaces are initially ductile, and the amount of crystalline crack growth decreases with increasing temperature. shear lips appear at above about -15°c, and increase in size with increasing temperature. the fracture appearance transition temperature (50 per cent crystalline) is about 25°c. in the upper shelf region fracture surfaces are ductile. figure 12. fracture appearance of mild steel charpy specimens tested at 10 c. top, standard specimen, β = 90°. bottom, angle notch specimen, β = 45°. the fracture surface appearance of the angle notch specimens is controlled by a tendency towards square (mode i) crack growth, but modified by plasticity and by crack path constraint due to the initial notch. the value of β has little effect on either the 50 per cent crystalline transition temperature, or on the temperature below which fractures are crystalline. shear lips for β = 75° and 60° are similar to those on standard charpy specimens, but could not be distinguished for β = 45°. in the transition region fracture surfaces are initially ductile. the amount of initial ductile crack growth increases with increasing temperature. crack initiation is along the notch tip, and in the notch plane, so the initial crack growth is mixed mode. for β = 75° and 60° a crack twists as it grows, becoming mode i as it approaches the striker position (figure 3). for β = 45° there is an abrupt transition to mode i crack growth (figure 13). figure 13. angle notch charpy specimen, abrupt transition to crystalline crack growth. this mode i growth is at least initially crystalline. at below about -15°c fracture surfaces of the angle notch specimens are fully crystalline. crack origins are mode i. for β = 75° and 60° there are a number of individual mode i crack origins along a notch tip, linked by vertical cliffs (apparently mode iii). the initial mode i cracks link up as a crack grows, and overall a crack twists as it approaches the striker position. for β = 45° the tendency to mode i crack growth is so marked that the crack path is not constrained by the notch. at intermediate absorbed energy levels there is one crack origin at the centre of a notch, and crack growth is mode i throughout (figure l. p. pook, frattura ed integrità strutturale, 1 (2007) 12-18 17 14). at high absorbed energy levels there are crack origins at both notch corners. the cracks follow curved, apparently mode i paths, as shown schematically for a single crack in figure 15. the two paths merge as they approach the striker position. figure 14. angle notch charpy specimen, crack origin at centre of notch. figure 15. angle notch charpy specimen, crack origin at notch corner. 8 central heating boiler burner during routine maintenance in 2002 one of the two burners in the gas fired domestic central heating boiler installed in the author’s house was found to be cracked due to thermal fatigue. a general view of the burner is shown in figure 16, and the crack is shown in figure 17. the boiler was about 12 years old so, assuming it fired about 10 times per day, about 44,000 thermal fatigue cycles had been applied. the burner consists of a steel box with a series of small and large holes on top to distribute the gas to the flame above the box. the larger holes have reinforced perimeters. an internal wire mesh, just visible in figure 17, helps to distribute the gas evenly. cracking appears to have initiated at three places on the perimeter of a smaller hole, grown into two larger holes with a small triangular piece becoming detached, and then two cracks grew across most of the width of the box, resulting in improper combustion. the designer did not appear to have appreciated the point that stress concentration factors are largely independent of hole size. the reinforcement had prevented crack initiation at the large holes but its absence had allowed cracking at a small hole. this is another example of a nuisance fatigue failure. annual inspection was recommended by the boiler manufacturer. this ensured that the cracking was detected before it became dangerous, and the burner was replaced. figure 16. burner from domestic central heating boiler. figure 17. crack in burner from domestic central heating boiler. l.p.pook., frattura ed integrità strutturale, 1 (2007) 12-18 18 9 walking shoe in 2005 the author found that the plastic soles of pair of walking shoes had become badly cracked and one no longer fitted properly. this more severely damaged shoe is shown in figure 18. the sole of a shoe is subjected to repeated bending. going uphill a sole is also subjected to repeated tension as the rearward force applied by the wearer’s heel is transferred to the ground. this particular pair of shoes had covered several hundred kilometres, which is equivalent to around 3 × 105 cycles. in the shoe shown two separate cracks had initiated in grooves near the toe, grown past each other and then curved together, in a well known crack path behaviour [15], so that a piece of sole became detached. the heel had also cracked and, in what appears to have been the final event that reduced the stiffness of the shoe so much that it became unusable, the sole separated from the upper at the end of this crack. the use of a plastic, instead of rubber, for the soles has reduced the rate of wear but led to fatigue failure. this is another example where a change of material has resulted in fatigue cracking. figure 18. cracks in sole of walking shoe. 10 concluding remarks paths taken by cracks have been of interest for a very long time. a large amount of empirical knowledge has been accumulated, but at the present state of the art the factors controlling the path taken by a crack are not completely understood. the numerous possible crack configurations [7] mean that a systematic approach to the determination of crack paths isn't feasible, so particular practical problems need to be tackled on an ad hoc basis. the examples given have been chosen from the author’s experience to illustrate the variety of crack paths which occur in practice. 11 references [1] l. p. pook, crack paths, wit press, southampton (2002). [2] r. cazaud, fatigue of metals, chapman & hall ltd, london (1953). [3] j. longson, a photographic study of the origin and development of fatigue fractures in aircraft structures. rae report no. struct 267. royal aircraft establishment, farnborough (1961). [4] j. e srawley, w. f. brown, fracture toughness testing methods. in fracture toughness testing and its applications. astm stp 381. american society for testing and materials, philadelphia, pa, (1965) 133. [5] l. p. pook, brittle fracture of structural materials having a high strength weight ratio. phd thesis, university of strathclyde, glasgow (1968). [6] l. p. pook, eng. fract. mech., 3 (1971) 205. [7] l. p. pook, d. g. crawford, the fatigue crack direction and threshold behaviour of a medium strength structural steel under mixed mode i and iii loading. in: kussmaul, k., mcdiarmid, d. l. and socie, d. f. (ed). fatigue under biaxial and multiaxial loading. esis 10. (1991) 199. mechanical engineering publications, london. [8] b. cotterell, int. j. fract. mech., 2 (1966) 526. [9] l. p. pook, r.holmes, in: proc. fatigue testing and design conf., society of environmental engineers fatigue group, buntingford, herts, 2 (1976) 36.1 [10] l. p. pook, an alternative crack path stability parameter. in: brown, m. w., de los rios, e. r. and miller, k. j. (eds). fracture from defects. ecf 12. emas publishing, cradley heath, west midlands. i (1998) 187. [11] l. p. pook linear elastic fracture mechanics for engineers. theory and applications. wit press, southampton (2000). [12] f. j. britten, the watch & clock makers' handbook, dictionary and guide. 16th edition. revised by good, r. arco publishing company inc, new york (1978) [13] l. p. pook, eng. fract. mech., (1972) 483. [14] l. p. pook, m. j. podbury, int. j. fract., 90, (1998) l3-l8. [15] s.melin, int. j. fract., 23(1) (1983) 37. [16] l.p. pook, keyword scheme for a computer based bibliography of stress intensity factor solutions. nel report 704. national engineering laboratory, east kilbride, glasgow (1986). microsoft word numero_30_art_40 a. fernàndez-canteli et alii, frattura ed integrità strutturale, 30 (2014) 327-339; doi: 10.3221/igf-esis.30.40 327 focussed on: fracture and structural integrity related issues a probabilistic interpretation of the miner number for fatigue life prediction a. fernández-canteli, s. blasón university of oviedo afc@uniovi.es , sergioblasonglez@gmail.com j.a.f.o. correia, a.m.p. de jesus university of trás-os-montes e alto douro, vila real, portugal ucve-idmec-laeta/school of sciences and technology jcorreia@utad.pt, ajesus@utad.pt abstract. the miner number m, used as a tool for lifetime prediction of mechanical and structural components in most of the standards related to fatigue design, is generally accepted as representing a damage stage resulting from a linear progression of damage accumulation. nonetheless, the fatigue and damage approach proposed by castillo and fernández-canteli, permits us to reject this conventional cliché by relating m to the normalized variable v, which represents percentile curves in the s-n field unequivocally associated to probability of failure. this approach, allowing a probabilistic interpretation of the miner rule, can be applied to fatigue design of mechanical and structural components subjected to variable amplitude loading. the results of an extensive test program on concrete specimens under compressive constant and load spectra, carried out elsewhere, are used. a parallel calculation of the normalized variable v and the miner number m is performed throughout the damage progression due to loading allowing probabilities of failure to be assigned to any value of the current miner number. it is found that significant probabilities of failure, say p=0.05, are attained for even low values of m, thus evidencing the necessity of a new definition of the safety coefficient of structural or machine components when the miner rule is considered. the experimental and analytical probability distributions of the resulting miner numbers are compared and discussed, the latter still providing a nonconservative prediction in spite of the enhancement. a possible correction is analyzed. keywords. cumulative damage; miner number; statistical interpretation. introduction he cumulative concept proposed by palmgren and miner maintains that the damage level can be expressed in terms of the number of cycles applied at a given stress range divided by the number of cycles needed to produce failure for the same stress range. failure occurs when the summation of these damage increments at several stress t a. fernàndez-canteli et alii, frattura ed integrità strutturale, 30 (2014) 327-339; doi: 10.3221/igf-esis.30.40 328 ranges becomes unity. after this formulation, this rule is repeatedly tested for different materials under multi-step and variable amplitude loading programs. though its applicability has been often questioned, it has been practically adopted by all standards related to structural and mechanical fatigue design. while birnbaum and saunders [1] tried to find a relation of the probabilistic distribution of the miner number to the crack growth, van leeuwen and siemes [2, 3] conducted series of tests on plain concrete and interpreted directly the scatter of the miner number m by obtaining theoretical expressions for the mean and standard deviation values of m from the wöhler curve. these formulae, initially derived for the simple case of constant amplitude cycling were then extended to the case of general loading. they showed that the miner number m at failure is a stochastic variable with an approximate log-normal distribution and emphasized the importance of the study of the scatter of the wöhler curve for constant amplitude cycling. based on holmen’s investigation on concrete [4], fernández-canteli [5] justified a generalization of the van leeuwen and siemes work by considering a probabilistic s-n field providing a statistical distribution of the miner number although based on a log-normal distribution. some theoretical advances were performed in [6] and [7]. from this, it follows that the miner number can be used to ascertain the probability of failure, as a more suitable design criterion, rather than as a measure of a problematic and abstract “degree of damage”. it can then be taken as a basis for a consistent life prediction in fatigue design, in accordance with the consideration of fatigue failure as limit state. results from holmen n this section, the fatigue results for concrete specimens under compression provided in the study of holmen [4] are introduced and eventually adapted in order to proceed to the probabilistic interpretation of the miner number. figure 1: s-n field fitted with the mc call model [7] for the normalized fatigue results for concrete under compression from holmen [4]. s-n fatigue results for constant stress level fig. 1, shows the s-n field resulting from the fatigue data obtained in holmen’s fatigue experimental program, according to tab. 1, using the procedure proposed by mc call [8]. the tests were carried out for constant stress range s=smaxsmin=(max-min)/r and constant minimum stress level (smin=minr=0.05), where max and min are, respectively, the maximum and minimum stress applied during the test and r is the fracture stress of the concrete this model, based on fitting a regression hyperbola linking the respective percentiles values resulting from the cumulative distribution functions i a. fernàndez-canteli et alii, frattura ed integrità strutturale, 30 (2014) 327-339; doi: 10.3221/igf-esis.30.40 329 (cdf) at any of the intervening stress ranges seems to be applicable only when a large number of results are at disposal, as this is the case, with an extensive amount of data. nevertheless, it does not fulfil “a priori” the requested physical and statistical requirements for a model to be valid, in particular, the compatibility between the cumulative distribution functions of the number of cycles given stress range f[n;δσ] and of the stress range given number of cycles e[δσ;n]. as an alternative, the s-n resulting under consideration of the weibull (or gumbel) probabilistic model proposed by castillo and fernández-canteli is shown in fig. 2. the parameters estimated using the latter model allows us to define the normalized variable v=(log n-b)(log -c) as a weibull (or gumbel) distribution for minima, thus facilitating the relation of the v values to the probability of failure. figure 2: s-n field fitted with the weibull model of castillo-canteli [6] for the normalized fatigue results for concrete under compression from holmen [4]. s number of cycles to failure 0.95 257; 74; 105; 120; 206; 83; 123; 109; 37; 76; 143; 85; 203; 72; 217 0.90 356; 201; 295; 252; 680; 509; 540; 311; 257; 457; 216; 226; 451; 1129; 342 0.825 1246; 2590; 5560; 4820; 2410; 2400; 4110; 3590; 3330; 1460; 1258; 5598; 3847; 1492; 2903 0.75 16190; 27940; 67340; 1860; 12600; 6710; 26260; 50090; 15570; 9930; 20300; 48420; 24900; 36350; 17280 0.675 3294820; 1459140; 1329780; 1241760; 339830; 896330; 280320; 102950; 658960; 1399830; run-out; 485620; 366900; 1250200; 11784100 (run-out); run-out table 1: results of the fatigue tests under constant stress range loading for smin=0.05. from holmen [4]. load collective and basic loading block used when a continuous load collective is used for fatigue design or fatigue testing as a practical representation of the real random or pseudo-random load history, it may be discretized as a histogram and handled as a multi-step load sequence. in the variable amplitude tests of holmen’s investigation [4], the histogram called loading model 3, represented in fig. 3a, a. fernàndez-canteli et alii, frattura ed integrità strutturale, 30 (2014) 327-339; doi: 10.3221/igf-esis.30.40 330 was derived from a loading collective, consisting in 30 steps of the maximum normalized stress smax= max/ r . after truncation at level 18 and omission of stress ranges below level 9, which implies to discard the lower stress levels, presumably without causing damage, the definitive stress collective in fig. 3b, considered as representative of the effective stress being supported by the concrete in the real off-shore structure, was applied to the specimens in a pseudo-random sequence. a) b) figure 3: holmen’s load collectives from [4]: a) original load histogram consisting in 30 stress steps and b) loading model 3 with truncation of higher stress amplitudes and omission of lower stress amplitudes applied in the fatigue variable testing. in order to reduce as much as possible the influence of the sequence, a proportional fraction of the number of cycles represented in the histogram, the so called “basic loading block”, will repeatedly applied until failure. the smaller the length of the basic loading block, the closer the random nature of real load applied, and the better the agreement between the total number of cycles applied during the test and its correspondence to the different stress ranges intervening in the load collective for the purpose of the miner number calculation. an improvement of the real sequence could be achieved a. fernàndez-canteli et alii, frattura ed integrità strutturale, 30 (2014) 327-339; doi: 10.3221/igf-esis.30.40 331 by arranging the stress range sequence intervening in the basic stress block in a random manner. after direct conversion of the load to stress for the cylindrical specimens used in the test, the stress ranges corresponding to the 18 levels considered in the load collective, the number of cycles in the original block and those in the basic stress block are exposed in tab. 2. the number of total cycles to failure for the tests performed under variable loading according to holmen and the corresponding number of replications of the basic stress blocks necessary to achieve failure are displayed in tab. 3. stress range level normalized stress range number of cycles corresponding to the original histogram number of cycles corresponding to the basic loading block accumulated number of cycles applied in the original histogram accumulated number of cycles applied in the basic loading block 18 0.7750 18869 25 18869 25 17 0.7324 10915 14 29784 39 16 0.6897 16967 22 46751 61 15 0.6471 22927 30 69678 91 14 0.6044 33314 44 102992 135 13 0.5618 41992 55 144984 190 12 0.5191 56802 75 201786 265 11 0.4765 66522 88 268308 353 10 0.4338 83321 111 351629 464 9 0.3912 90008 120 441637 584 8 0.3485 103360 137 544997 721 7 0.3059 103360 137 648357 858 6 0.2632 101594 135 749951 993 5 0.2206 104832 139 854783 1132 4 0.1779 90695 120 945478 1252 3 0.1353 79438 105 1024916 1357 2 0.0926 54029 72 1078945 1429 1 0.0500 30788 41 1109733 1470 table 2: stress ranges corresponding to the 18 levels considered in the load collective and number of cycles in the original block and basic stress block a. fernàndez-canteli et alii, frattura ed integrità strutturale, 30 (2014) 327-339; doi: 10.3221/igf-esis.30.40 332 test ref. smax nf miner number of basic load blocks 1 0.775 294670 0.6 201 2 0.775 291911 0.58 199 3 0.775 687112 1.38 468 4 0.775 76328 0.15 52 5 0.775 143992 0.29 98 6 0.775 548075 1.12 373 7 0.775 809727 1.64 551 8 0.8 49698 0.22 34 9 0.8 64508 0.3 44 10 0.825 25537 0.25 18 11 0.825 55710 0.53 38 12 0.825 92798 0.93 64 13 0.825 102330 1.04 70 14 0.836 31890 0.5 22 15 0.836 31971 0.51 22 16 0.836 20388 0.22 14 17 0.836 83638 1.11 57 18 0.775 41038 0.18 71 19 0.775 189486 0.86 325 20 0.775 213384 0.83 366 21 0.775 161450 0.58 277 22 0.775 28714 0.13 50 23 0.775 43345 0.19 75 24 0.775 72929 0.34 125 25 0.775 32715 0.14 57 26 0.8 28717 0.3 50 27 0.8 39697 0.41 68 28 0.825 33856 0.75 58 29 0.825 9615 0.2 17 test ref. smax nf miner number of basic load blocks 30 0.825 4416 0.08 8 31 0.825 30583 0.68 53 32 0.836 8724 0.25 15 33 0.836 34492 1.04 60 34 0.836 20299 0.61 35 35 0.836 47683 1.47 82 36 0.836 27093 0.78 47 37 0.836 12300 0.41 22 38 0.743 34490 0.07 60 39 0.743 178077 0.35 305 40 0.743 79856 0.16 137 41 0.743 153162 0.3 263 42 0.743 75187 0.15 129 43 0.743 85593 0.17 147 44 0.743 96517 0.19 166 45 0.743 192318 0.38 330 46 0.756 120790 0.41 207 47 0.756 22476 0.08 39 48 0.779 49445 0.4 85 49 0.779 15298 0.14 27 50 0.779 66704 0.55 115 51 0.779 38960 0.31 67 52 0.79 55944 0.64 96 53 0.79 106438 1.29 183 54 0.79 58068 0.69 100 55 0.79 40810 0.48 70 56 0.79 51615 0.6 89 57 0.79 21427 0.25 37 table 3: number of total cycles nf applied until failure, experimental miner numbers resulting from the holmen’s variable loading tests and corresponding number of replications of the basic stress blocks necessary to achieve failure. a. fernàndez-canteli et alii, frattura ed integrità strutturale, 30 (2014) 327-339; doi: 10.3221/igf-esis.30.40 333 experimental miner number miner number (basic stress block based) 0.08 0.118 0.07 0.074 0.08 0.083 0.14 0.137 0.13 0.143 0.15 0.149 0.14 0.164 0.20 0.250 0.22 0.280 0.25 0.264 0.25 0.301 0.15 0.159 0.22 0.232 0.16 0.168 0.18 0.204 0.17 0.181 0.19 0.215 0.25 0.252 0.19 0.204 0.08 0.118 experimental miner number miner number (basic stress block based) 0.30 0.300 0.29 0.281 0.30 0.341 0.50 0.441 0.51 0.441 0.41 0.441 0.31 0.341 0.30 0.323 0.34 0.359 0.35 0.375 0.41 0.464 0.40 0.433 0.53 0.558 0.38 0.406 0.48 0.477 0.41 0.438 0.61 0.701 0.58 0.571 0.60 0.607 0.30 0.300 experimental miner number miner number (basic stress block based) 0.60 0.577 0.55 0.586 0.64 0.655 0.68 0.779 0.69 0.682 0.75 0.852 0.78 0.942 0.93 0.940 0.58 0.795 1.04 1.028 1.11 1.142 0.86 0.932 1.04 1.202 0.83 1.050 1.12 1.070 1.29 1.248 1.38 1.342 1.47 1.643 1.64 1.581 0.60 0.577 table 4: comparison between the miner numbers estimated using the basic stress block approach proposed in this work and those directly overtaken from holmen (shown in increasing order). the probabilistic s-n field or the damage assessment of the variable loading test results when the miner approach is applied, the fatigue weibull regression model proposed by castillo and fernández-canteli the derivation of which is extensively justified in [6]. the consideration of the compatibility condition between the lifetime and stress range distributions, see fig. 4, besides other physical and statistical considerations, leads to a functional equation, the solution of which provides the following s-n field:         ,loglog;loglogexp1;                       cbn cbn nf (1) where b and c are, respectively, a limit or threshold number of cycles and fatigue limit for n→ ∞ and β, λ and δ are, respectively, the weibull shape, location and scale parameters. the percentile curves are hyperbolas sharing the asymptotes log n =b and log =c (see fig. 4), with the zero percentile curve representing the minimum possible required number of cycles to achieve failure for different values of log . the model parameters can be determined with the free software program profatigue [9] in a two-step procedure: first b and c, then the weibull parameters β, λ and δ using well-established methods described in the literature. as soon as the five parameters are estimated, the whole s-n field is analytically defined enabling a probabilistic prediction of the fatigue failure under constant amplitude loading to be achieved, see fig. 5. from eq. (1) it is apparent that the probability of failure for an element subject to a stress range  during n cycles depends only on the product v=( log n−b )(log  −c). this illustrates that, as soon as b and c are known, v becomes a f a. fernàndez-canteli et alii, frattura ed integrità strutturale, 30 (2014) 327-339; doi: 10.3221/igf-esis.30.40 334 normalizing variable of the data results permitting the whole experimental data set to be pooled in a single weibull distribution with the same shape parameter β as they would pertain to a single sample. this statistical normalization proves to be a suitable and powerful procedure increasing the reliability of the parameter estimation, allowing the whole sn field to be described by a unique weibull distribution function. figure 4: s-n field according to [6] illustrating the compatibility condition. this means that any v value is associated to a percentile curves but also to a damage stage that may be unequivocally related to a probability of failure. in this way, an extension of lifetime prediction under varying load is achieved by identifying damage with the v value, and the v value with the probability of failure represented by its cumulative distribution function. now, the approach proposed consists in deriving the cdf for the miner number, as resulting from the s-n field found and the stress history applied. with this aim, simultaneous calculation of the normalized variable v and the corresponding miner number m at any stage of the loading history makes it possible to relate any miner number along the damage process to a probability of failure, i.e. mapping of the miner number into a cumulative distribution function [7]. 10 0 10 2 10 4 10 6 10 8 10 10 0.55 0.6 0.65 0.7 0.75 0.8 0.85 0.9 0.95 threshold lifetime endurance limit p f = 0% p f = 5% p f = 50% p f = 95% failure data run-outs transformed run-outs estimated parameters b c β δ λ 0 -0.59 3.86 1.39 1.56 figure 5: weibull s-n field with estimated parameters derived from holmen’s constant stress range concrete tests using the probabilistic fatigue model from [6]. a. fernàndez-canteli et alii, frattura ed integrità strutturale, 30 (2014) 327-339; doi: 10.3221/igf-esis.30.40 335 calculation of the miner number and its probabilistic analysis according to the approach proposed n this section, the miner numbers obtained in the experimental program of holmen [4] are estimated for the concrete specimens subject to pseudo-random load using the load collective described in the precedent section as being representative of the real load to which the concrete specimen is subjected during each test. in fact, three different test series, see tab. 4, were performed with small differences among the stress collectives applied, the influence of which is disregarded. thereafter, these miner number results are related to the normalized variable v and, subsequently, to probability of failure. finally, this theoretical miner number distribution will be compared with that obtained directly from the experimental results. since the total number of cycles, but not the real pseudo-random loading sequence, applied during holmen’s varying loading tests [4] is provided, only an estimation of the real loading history can be achieved as the number of replications of the basic stress block necessary to accomplish the total number of cycles. as a result, the value of the miner number obtained for the different tests using the substitutive basic stress block appraisal differs from that given by holmen, see tab. 4, which displays the miner numbers as directly overtaken from holmen and those estimated by equating the total number of cycles resulting for repeated application of the basic stress block. a median error of about 10% is observed, which seems to be acceptable for this study as the calculated miner numbers represents an underestimation of the real ones. a practical coincidence between both miner number families may be enforced by adequately determination of the number of replications, with a possible fraction of the last replication, irrespective of the total number of cycles considered, i.e. alternative to the values contained in tab. 3. once the miner number resulting for any of the real experimental tests is found as a result of the application of the prescribed number of replications of the basic stress blocks, we proceed to establish the probability of failure associated with them. first, the s-n field is evaluated from the constant stress range tests using the profatigue code, see fig. 5. this provides the model parameters and accordingly, the cdf of the normalizing variable v=(log n-b) (log -c) thus relating v values to probability of failure, see fig. 6. 1.5 2 2.5 3 3.5 4 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 v = (ln n b)  (ln  c) p f [ ] %smax [-] 0.68 0.75 0.82 0.9 0.95 data without run-outs run-outs figure 6: experimental weibull cumulative distribution functions for the normalized variable v obtained from the fatigue results under constant stress range tests of holmen [4] using the probabilistic fatigue model of castillo and fernández-canteli [6]. for each test, an experimental miner number mi has been obtained from the particular stress history “i” applied during the test consisting in a number of replications of the basic stress block according to tab. 3. the same stress history provides the corresponding value of the normalized variable vi for such a test, the probability of failure related to which is given by the cdf of the normalized variable v. in this way, the same probability of failure obtained for the vi value is assigned to the corresponding value of the experimental miner number mi. thus, an unequivocally correspondence i a. fernàndez-canteli et alii, frattura ed integrità strutturale, 30 (2014) 327-339; doi: 10.3221/igf-esis.30.40 336 between the experimental v values and those of the miner number m is established, allowing the cdf predicted for the experimental miner results to be established by simple mapping of the miner numbers obtained for the experimental test failures into probabilities of failure, see fig. 7. accordingly, an approach for probabilistic lifetime prediction is established by means of the normalized variable v that improves the reliability provided by the conventional miner rule. 00.20.40.60.81 0 0.2 0.4 0.6 0.8 1 probability of failure p ro b a b il it y o f fa il u re 2.2 2.4 2.6 2.8 3 3.2 3.4 0 0.2 0.4 0.6 0.8 1 v [normalized variable] p ro b a b il it y o f fa il u re 2.2 2.4 2.6 2.8 3 3.2 3.4 0 0.5 1 1.5 v [normalized variable] m in er n u m b er 00.20.40.60.81 0 0.5 1 1.5 probability of failure m in er n u m b er figure 7: from the experimental weibull cumulative distribution function for the normalized variable v (upper-right) and the established relation between v and m (down-right), the experimental cdf of the miner number (down-left) is found for the fatigue of holmen [5]. now, the cumulative distribution function for the miner number sample obtained from the results of the experimental program with varying stress range tests of holmen is determined by applying any plotting point position rule. the miner number values are ranged in increasing order and the corresponding probabilities of failure calculated. the resulting cdf is compared with that predicted from the normalized variable v distribution, as shown in fig. 8. 0 0.5 1 1.5 2 2.5 3 3.5 4 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 miner number p ro b ab il ty o f fa il u re fitting acording to weibull: p=0.5 & scale factor=1 experimental data p=0.5 0 0.5 1 1.5 2 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 miner number p ro b ab il ty o f fa il u re fitting acording to weibull: p=0.5 & scale factor=2.364 experimental data p=0.5 (a) (b) a. fernàndez-canteli et alii, frattura ed integrità strutturale, 30 (2014) 327-339; doi: 10.3221/igf-esis.30.40 337 figure 8: a) cumulative distribution functions for the miner number fitted, respectively, from the experimental results and from the approach proposed based on the normalized variable v assuming a weibull distribution and b) correspondence among those distributions when a scale correction is applied to the experimental results. the precedent procedure is summarized as follows: a) from holmen’s results, the experimental probabilistic s-n field is evaluated, in this case, using the profatigue program based on the weibull model proposed by castillo and fernández-canteli [6]. b) the load collective is defined from standards or other regulations related to the particular type of the structure considered. c) a histogram is derived from the stress collective in a sufficient number of stress steps to guarantee accurateness in the calculations. in this case, the results provided by holmen [4] are considered. possible truncation and omission of some levels of the histogram are undertaken in order to approximate the histogram to the practical load distribution. d) since the real load sequence applied to the specimens is unknown, though the peak distribution applied during the test is defined, an approximation is assumed by considering a proportional reduction of the original load collective. in this case, a basic loading block is defined as 1/750 times of the original load histogram. e) the miner number obtained for any of the real tests is calculated. herewith, the factual pseudo-random load history applied by holmen’s tests is not exactly known but can be approximated by means of the basic stress block derived from the load collective. a comparison is made between the miner number calculated using repetitions of until the total number of cycles corresponds to that given by holmen and the miner number provided by holmen. differences aro und 10% are found these being considered acceptable. f) for any test, the necessary repetitions of the basic stress block are evaluated as those giving the same total number of cycles to failure found by holmen. g) for any test, the normalized variable v= (log n-b) (log -c) is calculated for the test stress history up to failure owning to the particular miner number obtained for that test by replications of the basic stress block. h) since the cdf for v is defined according to the probabilistic fatigue model, and the correspondence between v and the miner number m is established, it is possible to derive the cdf for the miner number values, that is, it is possible to relate any value of the miner number to the corresponding probability of failure. the immediate relation of the miner number and probability is established. i) the cdf of the experimental miner number is calculated and compared with the theoretical one. a simple correction of the scale parameter lead to good agreement for fatigue lifetime prediction. discussion of the results ig. 6 displays the cumulative distribution function corresponding to the experimental miner numbers obtained from the test program of holmen and the predicted cdf of the miner number derived from the normalized variable v, which on its turn is calculated from the initial s-n field for constant stress range tests of holmen. since v belongs to a three parameter weibull distribution family according to the probabilistic model of castillo and fernándezcanteli it is expected that the miner number also belongs also to a three parameter weibull family, as stated in [9], the location parameter of the m distribution λ(m), i.e. the threshold m value below which the probability of failure is zero, is defined as that value of m associated with the location parameter for v, λ(v). account given of the small value of λ(m), nullity of λ(m)=0 can be accepted, which implies the miner number being described by a two-parameter weibull distribution. under this assumption, the parameter estimates of both m distributions, i.e. the experimental and the theoretical ones, are, respectively, β=1.436, δ=0.568 for the experimental miner number and β=1.515, δ=1.341 for the predicted one, i.e., for the theoretical one, confirming a reasonable coincidence between the shape parameters in both distributions but also with the shape parameter found for the s-n field. this allows us to assume “a priori” the value of the location parameter as known in the parameter estimation for the miner number. on the contrary, a significant difference arises between both miner scale parameters that, unfortunately stays on the unsafe side pointing out the necessity of introducing a correction if a safe lifetime prediction is intended. a scale parameter ratio δmod / δorig =2.364 is found, which can be used supposed an arbitrary correction for the moment being, see fig. 7. in such a case, a practical coincidence is achieved between both probability distributions, experimental and analytical. it follows that the consequence of applying the miner rule, which evidently cannot be accepted as a scientific law to reproduce faithfully the damage process, may be corrected by assuming a size effect that requires extrapolation of the theoretical distribution, as f a. fernàndez-canteli et alii, frattura ed integrità strutturale, 30 (2014) 327-339; doi: 10.3221/igf-esis.30.40 338 derived from the normalized variable, to a longer scale. the value of this correction must be checked for different materials and different load spectra so that further investigation is needed. anyway, the modification of the scale parameter, being simple though not yet fully understood, opens a new way for predicting lifetime under pseudo-random varying loading. assuming a gumbel instead a weibull distribution does not affect very much the calculations but obviates the question of the lower threshold value due to the existence of the gumbel function practically from the first cycle. other advantages, as reduction of the number of parameters and avoiding to accept nil probability of failure in legal cases, are also explained in [10]. miner as alleged linear cumulative damage hypothesis he miner number is generally accepted as representing a stage of damage resulting from a “linear” progression of damage accumulation. nonetheless, the probabilistic conception of the s-n field permits us to reject this conventional cliché as being a gratuitous and wrong assertion. in fact, we have shown above how m can be related to probability of failure, as a measure of damage progression, by means of the normalized variable v considered in the fatigue approach proposed by castillo and fernández-canteli [6] and the same can be achieved using as an alternative, in principle in better consonance to the real logarithmic scale characterizing lifetime problems, to the conventional the so called logarithmic miner, denoted lm defined as: lm= ∑ log ni / log ni (2) which according to a parallel interpretation as that applied in the case of the conventional miner number would be labelled as “logarithmic cumulative damage hypothesis” and, expectantly, lead to a fully different lifetime prediction. after applying the same load spectra as in the miner number case, totally different lm values are observed to those for conventional m, as expected. notwithstanding, the same probabilities of failure are found for the reciprocal m and lm values in both cases. this proves that the probability of failure, as a measure of damage, happens to be independent of the model adopted (conventional or logarithmic miner rule) if an adequate mapping of the measure of cumulative damage is adopted into the probability of failure is established, thus proving by extension, the inconsistency of the conventional belief, which denotes “linear” the damage progression for the conventional miner number. conclusions he main conclusions derived from the present work are: a probabilistic definition of the s-n field is necessary for the adequate probabilistic evaluation of the miner number. a statistical interpretation of the miner is possible, without practically maintaining the simplicity of its calculation in the conventional approach allowing an increase of reliability in the lifetime prediction of structural and mechanical components. the miner number statistical distribution happens to be weibull, as stated in former literature of the authors, whereas the prediction for the miner number in a probabilistic way needs to be modified by introducing a scale correction. the statement that the miner rule responds to a “linear cumulative damage hypothesis” is gratuitous and wrong. other fatigue programs under variable loading with other materials should be considered in order to confirm the properties of the miner distribution as exposed here. references [1] birnbaum, z.w., saunders, s.c., a probabilistic interpretation of miner’s rule, siam j. of applied mathematics, 16 (3) (1968) 637-652. [2] van leeuwen j., siemes, a.j.m.., miner’s rule with respect to plain concrete, heron, delft, 24(1) (1979). [3] van leeuwen j., siemes, a.j.m.., fatigue of concrete, report no b 76-443/04.2.6013, tables, tno-ibbc, delft, (1977). t t a. fernàndez-canteli et alii, frattura ed integrità strutturale, 30 (2014) 327-339; doi: 10.3221/igf-esis.30.40 339 [4] holmen, j.o., fatigue of concrete by constant and variable amplitude loading, institutt for betongkonstruksjoner, norges tekniske høgskole, universitet i trondheim (1979). [5] fernández-canteli, a., statistical interpretation of the miner-number using an index of probability of total damage, fatigue of steel and concrete structures, iabse, zürich, (1982). [6] castillo , e., fernández-canteli, a., a unified statistical methodology for modeling fatigue damage, springer, (2009). [7] castillo, e., fernández-canteli, a., statistical models for damage accumulation, encyclopedia of statistical sciences, john wiley & sons, balakrishnan (editor), chapter 5, (2011) 1-30. [8] mc call, j.t., probability of failure of plain concrete, aci journal, 55 (1958) 233-244. [9] profatigue. software program for assessment of fatigue results, university of oviedo. 2013. (free download at dcif.uniovi.es/profatigue/profatigue_pkg.exe. user’s guide: dcif.uniovi.es/profatigue/profatigue-userguide2013.pdf). [10] fernández canteli, a., castillo, e., a unified probabilistic approach for fatigue life and damage prediction, xiv portuguese conference on fracture, invited lecture, regua (2014) 31-42. microsoft word numero_56_art_16_3009 a. moulgada et alii, frattura ed integrità strutturale, 56 (2021) 195-202; doi: 10.3221/igf-esis.56.16 195 study of mechanical behavior by fatigue of a cracked plate repaired by different composite patches moulgada abdelmadjid lri, department of mechanical engineering, university of ibn khaldoun tiaret, city zaaroura bp 78 14000 tiaret, algeria amoulgada@hotmail.fr ait kaci djafar, sahli abderrahmane department of mechanical engineering, university of djillali liabes sidi bel abbes, algeria aitkaci07@yahoo.fr, sahliabderahmen@yahoo.fr zagane mohammed el sallah department of mechanical engineering, university of ibn khaldoun tiaret, city zaaroura bp 78 14000 tiaret, algeria salah_cao@yahoo.fr zahi rachid department of mechanical engineering, university of ahmed zabana relizane 48000, algeria zahirachid72@yahoo.fr abstract. this research is based on the study of the fatigue behavior of an aluminum alloy plate with a central crack. the plate is subjected to a tensile loading on its lower and upper parts. several parameters were highlighted, such as the loading effect with a load ratio r = 0. the effects of the load ratio on both the repaired and not repaired plates, by two composite patches, which are boron/epoxy and graphite/epoxy, were investigated, as well as the effect of the plate material on plate life, comparing different materials. keywords. fatigue; crack; composite patch; load ratio. citation : moulgada, a, ait kaci, d., sahli., a, zagane, m.e, zahi, r., study of mechanical behavior by fatigue of a cracked plate repaired by different composite patches. frattura ed integrità strutturale, 56 (2021) 195-202. received: 08.02.2021 accepted: 15.03.2021 published: 01.04.2021 copyright: © 2021 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. https://youtu.be/kgcxk5vhfnk a. moulgada et alii, frattura ed integrità strutturale, 56 (2021) 195-202; doi: 10.3221/igf-esis.56.16 196 introduction he study of the propagation of fatigue cracks in structures depends on the nature of the applied loads (constant amplitude loading). these loadings are characterized by several parameters, whose influences on the fatigue life and the cracking rate are very significant from the point of view of the mechanical integrity of the structures. constant amplitude loading is characterized by the stress amplitude and the load ratio. several parameters/factors of a cracked thin aluminum plate with bonded composite patch were considered. these were strain distribution, out-of-plane deformation, and residual strength, including the investigation of fatigue crack; growth behavior for thin plates repaired with composite patches, the characterization of crack retardation in thin plates after the repair, and the examination of debondinge growth [1]. in addition, the investigation of [2] focused on the response of cracked steel specimens repaired by polymer composite patches on single sides of the specimens subjected to tensile and bending loadings and hardness test. the un-cracked and patched specimens were tested in the above loading conditions and the test results were evaluated by analyzing the effect of patch thickness and patch materials. a fatigue experimental study to characterize the effect of carbon fiber reinforced polymer (cfrp) strengthening patches on the fatigue strength of aluminum alloy plates with fastener holes was carried out in [3]. three cfrp strengthening schemes were reported and the corresponding typical failure modes and fractographic patterns were discussed in detail. the investigation from the experimental, numerical, and analytical points of view for crack growth of cfrp-strengthened steel plates single edge notched tension (sent) specimens, reinforced on a single side by using cfrp strips, was considered. other reinforcing configurations are worth investigation, such as the crack emanating from the lateral side of the tension flange of a steel beam under cyclic bending loading [4]. a numerical simulation on a laterally cracked plate, repaired by two composite patches, namely boron/epoxy and carbon/epoxy, was proposed in [5]. the fatigue life and fatigue crack growth rates of 10 mm thick aluminum panels repaired with two-sided bonded patches were evaluated in [6]; also, the stress intensity factor (sif) values of the patched plates and the fatigue life prediction of two-sided repaired plates were investigated by using the 3-d finite element method (fem). the study of static analysis for different patch shapes like circle, rectangle, square, ellipse, and octagon was considered. performance comparison of bonded repair was done by analyzing sif reduction at the crack tip for double-sides patch model in [7]. naboulsi et al. [8] introduced the three-layer technique into the finite element analysis to model a cracked metallic plate repaired with a bonded composite patch. in [9], the fatigue lives of four drilling hole procedures were compared and the role of the residual compressive stresses introduced by each drilling process on the fatigue behavior of 2024 –t3 aluminum alloy was shown. in [10] a new geometry used for stop-hole was proposed, in which instead of a single hole, two symmetric and interconnected holes were drilled at the crack tip. the main concept of double stop-hole method is to diminish the stress singularity at the crack tip and to reduce the stress concentration at the edge of stop-holes in the cracked structural elements. a numerical study of fatigue cracks behavior damaged aeronautical structures repaired by composite was presented. various parameters were highlighted, such as the effect of the dimensions, the orientation of the fibers, and the mechanical properties of the patch, as well as the effect of the dimensions and the mechanical properties of the adhesive [11]. the sif for patched crack exhibits an asymptotic behavior as the crack length increases. this is due to the stress transfer toward the composite patch throughout the adhesive layer [12-13]. in addition, in [14] many desirable characteristics and the enforcement of the sq4c element were verified and proved through various numerical examples in static, frequency, and buckling analyses of laminated composite plates and shell structures. this study is focused on an aluminum alloy plate, presenting a central crack, subjected to tension on its upper and internal parts by cyclic loadings, to investigate the fatigue behavior of this plate. loads of different amplitudes were considered, thus varying the load ratio between the minimum and maximum stress, and, in the end, the analyzed material was varied to see, among the proposed materials, the one that was the most resistant for these stresses. this plate was stressed either without repair and with repair with two different composite patches, namely boron/epoxy and graphite/epoxy. forman / mettu (nasgro) model the nasgro model, used in the prediction of the fatigue cracking propagation rate and implemented in several fatigue calculation codes, was developed and modified by maierhofer et al. [14]. the nasgro model predicts the cracking rate for the 3d domains, and it is in the form:   1 1 1 1 p n q kch fda k c k dn k kmax kcrit                   (1) t a. moulgada et alii, frattura ed integrità strutturale, 56 (2021) 195-202; doi: 10.3221/igf-esis.56.16 197 load ratio r= min max   (2) the coefficients c, n, p, q are empirical parameters, while kmax and kcrit are respectively the maximum stress intensity factor and the critical stress intensity factor. the parameters required for the nasgro equation are in tab. 1. materials c(10-3) p n q δk e(gpa) ν 2024-t3 2024-t62 2024-t861 6.827 7.454 5.4 2.8 2.657 2.92 0.5 0.5 0.2 1 1 1 2.967 3.956 2.417 73.08 0.33 73.08 0.33 73.08 0.33 table 1: different parameters of nasgro equation for different materials. presentation of the model as visible in fig. 1, the aluminum alloy plate has the following dimensions: length l =200 mm, width w = 102 mm, and thickness e =2.3 mm, while the length of the crack is a=2mm. the materials chosen for this simulation are aluminum alloys, such as 204-t3, 2024-t62 and 2024-t861. figure 1: presentation of the model properties of the patch the composites used for the repair are graphite-epoxy and boron-epoxy, and the relevant mechanical properties are reported in tab. 2. the laminate consists of 12 plies of a unidirectional composite material, the thickness of each ply is 0.132 mm, and the stacking sequence is as follows: [-45°,0°,0°, 90°,0°,+45°]s composite el(gpa) et(mpa) glt(mpa) boron/epoxy graphite/epoxy 6.827 7.454 2.8 2.657 0.5 0.5 table 2: properties of composite patch. a. moulgada et alii, frattura ed integrità strutturale, 56 (2021) 195-202; doi: 10.3221/igf-esis.56.16 198 the fm-73 adhesive is used, with a shear modulus glt = 413.368 mpa, and a thickness of 0.1524 mm. for the studied case, the applied constraint is σmax = 100mpa. results and discussions effect of variation of loading material: al 2024 t3 ig. 2 shows the variation of the crack length as a function of the service life for the plates repaired by the two different composites and the not repaired plate, for different loading levels and a zero load ratio (r = 0). it is noted that the effect of the repair is very distinct, and the life of the repaired plate is enhanced for every load level. as an effect of the loading level on the plate with a load ratio r = 0, the four graphs indicate that the life of the plate is inversely proportional to the load, that is to say as the load is increased, the service life automatically decreases, and vice versa. in all the loading cases, the graphite/epoxy composite has a better performance with respect to the fatigue life for the repair, either for the absorption of the stresses at the head of the crack, and the prolongation of its life. however, the repair by the bore/epoxy composite; also gives long life to the plate. figure 2: variation of the crack propagation as a function of the number of cycles for the not repaired plate and repaired by boron/ epoxy and graphite/epoxy: (a) p=100mpa, (b) p=80mpa, (c) p=60mpa and (d) p=40mpa. effect of the load ratio fig. 3 shows the crack propagation trend as a function of the number of cycles of the unrepaired and repaired plates for the different load ratios (r = 0.2, 0.4 and 0.6), considering a single load level (80 mpa). it is noted that as the load ratio f (a) (b) a. moulgada et alii, frattura ed integrità strutturale, 56 (2021) 195-202; doi: 10.3221/igf-esis.56.16 199 increases, the service life of the plate cracked and repaired by the two composite patches also increases, so the load ratio is strictly proportional to the life of the plate. also, the effect of composite repair on the life extension of the cracked plates can be distinguished. figure 3: variation of crack propagation according to the number of cycles for the unrepaired and repaired plate by boron/epoxy and graphite/epoxy for: (a) r=0.2, (b) r=0.4 and (c) r=0.6. figure 4: effect of load ratio on fatigue life for unrepaired plate. (a) (b) (c) a. moulgada et alii, frattura ed integrità strutturale, 56 (2021) 195-202; doi: 10.3221/igf-esis.56.16 200 fig. 4 shows the evolution of the crack length "a" as a function of the number of cycles "n" under the effect of the load ratio "r". the increased load ratio increases the service life; this is in fact due to the decrease in the loading amplitude "δσ": at r = 0, the loading amplitude is 100 mpa, on the other hand at r = 0.2 the loading amplitude is 80 mpa. it is noted at r = 0, the fatigue life is 105 cycles. at r = 0.2; the service life is 125,000 cycles, for r = 0.4 the loading amplitude is 60 mpa, while the fatigue life is 235,000 cycles and for r = 0.6, the loading amplitude is 40 mpa. it is concluded that the increase in the life of a material is strictly proportional to the increase in the load ratio, i.e. with the increase in minimum stress. to study the effect of the load ratio on the fatigue life of the plate, repaired by the boron/epoxy patch, fig. 5 shows the variation of the crack length as a function of the service life for different load ratios. it is noted that the effect of the repair is very distinct and the life of the repaired plate is simultaneously progressed for every load; it is of the order of 35ꞏ105 cycles for r = 0.6, about 11.6ꞏ105 cycles for r = 0.4; 1.7ꞏ105 cycles for r = 0.2 and 4.8ꞏ105 cycles for r = 0. figure 5: effect of load ratio on fatigue life for the plate repaired by the boron/epoxy patch. figure 6: effect of al 2024-t62 material on the variation of the service life for the unrepaired and repaired plate by boron/epoxy and graphite/epoxy. effect of material aluminum alloy 2024-t62 (for p = 80 mpa and r=0) for the effect of 2024-t62 aluminum alloy, the variation of the crack propagation life for the unrepaired and repaired plates by boron/epoxy and graphite/epoxy, for the load ratio r = 0, is shown in fig. 6. it is very distinct in view of the best properties of composite patches for repairing and absorbing stresses. these patches improve and increase the life of these plates, which can reach approximately 4.6ꞏ105 cycles for boron/epoxy and 4.8ꞏ105 cycles for graphite/epoxy. a. moulgada et alii, frattura ed integrità strutturale, 56 (2021) 195-202; doi: 10.3221/igf-esis.56.16 201 aluminum alloy 2024-t861 for the effect of the al 2024-t861 material, the variation of the crack propagation life for the unrepaired and repaired plate by boron/epoxy and graphite/epoxy is shown in fig. 7. for the unrepaired plate, the number of cycles is 0.4ꞏ105 cycles, for the boron/epoxy patch it is approximately 2ꞏ105 cycles and finally for the graphite/epoxy it is approximately 2.25ꞏ105 cycles. therefore, the repair by the two composite patches is very significant, and the life of the plate is relative to the mechanical properties of each material. figure 7: effect of al 2024-t861 material on the propagation of crack for the unrepaired and repaired plate by boron/epoxy and graphite/epoxy. aluminum alloy 2024-t3 regarding the effect of the al 2024-t3; material on the variation of the service life, for the plate not repaired and repaired by boron/epoxy and graphite/epoxy, also in this case the graphite/epoxy is a better repair solution, given the increase in the life of the cracked and repaired plate, which reached 5ꞏ105 cycles, while the boron/epoxy repair achieved a number of cycles of approximately 4.8ꞏ105 cycles. figure 8: effect of al 2024-t3 material on the variation of the service life for the plate not repaired and repaired by boron/epoxy and graphite/epoxy. conclusion he use of the composite patch for repair absorbs the stresses induced from the damaged area through the adhesive, also reduces stress at the crack tip and improves the mechanical properties of the structure. it can be said that the patch considerably increases the strength of the plate as well as its rigidity to ensure a long fatigue life of the structure and it retards the progression of cracks for long use. t a. moulgada et alii, frattura ed integrità strutturale, 56 (2021) 195-202; doi: 10.3221/igf-esis.56.16 202 for the effect of loading on the plate with a load ratio r = 0, the life of the plate is inversely proportional to the loading level, that is to say; as the load is increased, the service life automatically decreases. for the variation of the crack propagation as a function of the number of cycles; for the plates unrepaired and repaired by boron/epoxy and graphite/epoxy, for the different load ratios (r = 0.2; 0.4 and 0.6), the life of the plate is strictly proportional to the load ratio, and also the effect of composite repair on the prolongation of the cracked plate life can be distinguished. for the different materials of the cracked plate, the graphite/epoxy composite presents a better repair solution, increasing the life of this plate, given its more efficient mechanical properties compared to the boron/epoxy composite. references [1] sabelkin, v., hansen, s., vandawaker, r.m. (2007). investigation into cracked aluminum plate repaired with bonded composite patch. composite structures 79, pp. 55-66. [2] pradhan, s.s., mishra, u., biswal, s.k. (2020). experimental study on mechanical performance of cracked aluminium alloy repaired with composite patch. materials today: proceedings. elsevier 26, pp. 2676-2680. [3] wanga, z.y., zhanga, t. l., xiaolei, w., huang, q.y. and shen, w. m. (2018) characterization of the effect of cfrp reinforcement on the fatigue strength of aluminium alloy plates with fastener holes. engineering structures: elsevier 177, pp. 739-752. [4] colombi, p., fava, g. and sonzogni, l. (2015). fatigue crack growth in cfrp-strengthened steel plates. composites part b: engineering, 72, pp. 87–96. [5] moulgada, a., zagane, e. m., sahli, a., ait kaci, d. and zahi, r. (2020). comparative study of the repair of cracked plates with two different composite patches. frattura ed integrità strutturale, 14, pp. 187-201. [6] jian-bin, h., xu-dong, l., zhi-tao, m. (2015). fatigue behavior of thick center cracked aluminum plates repaired by two-sided composite patching.” materials & design 88, pp. 331–335. [7] ramji, m., srilakshmi. r. and prakash, b.m. (2016). towards optimization of patch shape on the performance of bonded composite, repair using fem. composites part b: engineering, 45, pp. 710–720. [8] naboulsi, s., & mall, s. (1996). modeling of a cracked metallic structure with bonded composite patch using the three-layer technique. composite structures, 35, pp. 295–308. [9] elajrami, m., benguediab, m., guillen, r. (2008). effect of various drilling procedures on the fatigue life of rivet hole. sciences and technologie. [10] ayatollahi, m. r., razavi, s. m. j., sommitsch, c. and moser, c. (2016). fatigue life extension by crack repair using double stop-hole technique. materials science forum 879, pp. 3–8. [11] achache, h., aıt kacı, d., moulgada, a. (2018). numerical analysis of the behavior of structures damaged by fatigue and repaired by composite patch. the eurasia proceedings of science technology engineering and mathematics, pp. 35-42. [12] fekirini, h., bachir bouiadjra, b., belhouari, m., boutabout, b., serier, b. (2008). numerical analysis of the performances of bonded composite repair with two adhesive bands in aircraft structures. composite structures 82, pp. 84-89. [13] bachir bouiadjra, b.b., fekirini, h., serier, b., belhouari, m., and benguediab, m. (2008). energy release rate for repaired inclined cracks with bonded composite patch having two adhesive bands in aircraft structures. journal of reinforced plastic and composites 28, pp. 1135-1146. [14] ton-that, h. l., nguyen-van, h. (2021). a combined strain element in static, frequency and buckling analyses of laminated composite plates and shells. periodica polytechnica civil engineering, 65, pp. 56–71. [15] maierhofera, b., pippanb, r., gänser, h.p. (2014). modified nasgro equation for physically short cracks, international journal of fatigue 59, pp. 200-207. microsoft word numero_41_art_54.docx s.m.j. razavi et alii, frattura ed integrità strutturale, 41 (2017) 432-439; doi: 10.3221/igf-esis.41.54 432 effect of hot dip galvanization on the fatigue strength of steel bolted connections s.m.j. razavi, m. peron, j. torgersen, f. berto, f. mutignani department of mechanical and industrial engineering, norwegian university of science and technology (ntnu), norway javad.razavi@ntnu.no, mirco.peron@ntnu.no, jan.torgersen@ntnu.no, filippo.berto@ntnu.no abstract. hot dip galvanized steel bolted joints has been tested under fatigue loading to evaluate the effect of galvanizing coating on the fatigue strength of s355 structural steel. the experimental results showed that the decrease of the fatigue life of coated specimens in comparison with that of uncoated joints is very limited and the results are in good agreement with eurocode detail category, without substantial reductions. the procedure for coating and preparation of the bolted joints is described in detail in this paper providing a useful tool for engineers involved in similar practical applications. the experimental results are compared with the previously published data on central hole notched galvanized and not treated specimens characterized by the same geometry. keywords. high cycle fatigue; galvanized steel; notch effect; bolted joints. citation: razavi, s.m.j., peron, m., torgersen, j., berto, f., mutignani, f., effect of hot dip galvanization on the fatigue strength of steel bolted connections, frattura ed integrità strutturale, 41 (2017) 432-439. received: 15.05.2017 accepted: 24.05.2017 published: 01.07.2017 copyright: © 2017 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. introduction ajority of mechanical structures are made of various components which are connected using various kinds of joining methods such as welding, bolting, riveting and bonding. however, according to specific geometry of these joints, they are mostly considered as the critical components in structures. [1-6]. due to their versatility and reliability, bolted connections are one of the most widely used methods for joining structural steel members. among the numerous advantages of bolting as a joining method compared to the other methods of joining the following can be summarised: affordable process with less required time and cost, ease of assembly and inspection, reliability of service and good performance under variable applied loads [7]. the durability of structural components is significantly influenced by the environmental factors such as degree of corrosion encountered in service operative conditions [8-11]. deterioration due to corrosion usually leads to the seizure of fasteners and premature failures, in the form of corrosion fatigue. therefore, proper protections of the bolted joints from corrosion should be considered as the key parameter in design of the components. as a surface treatment, hot dip galvanizing protect the core material from corrosion and environmental aggressive agents and can be used in a wide range of materials and applications [12-17]. as the surface condition may directly effects the fatigue initiation of the materials, some authors correlated the fatigue strength to the coating thickness of the zinc layer [18]. on the other hand, other authors did not support any specific m s.m.j. razavi et alii, frattura ed integrità strutturale, 41 (2017) 432-439; doi: 10.3221/igf-esis.41.54 433 correlation of loss in the fatigue properties due to the coating thickness [19,20]. by employing the kitagawa–takahashi diagram, vogt et al. [21] specified a threshold value of the coating thickness that could not affect the fatigue behaviour of unnotched components made of structural steels. valtinat and huhn [22] published a preliminary study on hot dip galvanized bolted connections. due to the available gap between the recent and past literature and also limited available data on this topic, the present technical note is aimed to partially fill this gap by presenting a clear explanation for the preparation and final assembly methods of the specimens. in the current paper, the geometry and the procedure for fabrication and assembly of the specimens is described in details. additionally, the fatigue data are summarized and compared with those taken from the standard in force for the same detail category followed by a comparison between the present data and some recent data by the same authors berto et al. [23] from notched galvanized specimens weakened by a central hole. material and geometry of the specimens he test specimens, made of s355 structural steel, for the bolted connection are shown in fig. 1. preloaded m12 bolts of class 10.9, system hr, were used in drilled holes. hot dip galvanized coatings of fasteners according to uni en iso 10684. the dimensions of the test samples were designed primarily to produce a net section fatigue failure of the middle main plate, and not in the bolts or cover plates (en 1993-1-8). all the samples were hot-dip galvanized for an immersion time of 14 minutes which is typical in the application. the result was a zinc layer of about 400 µm. this layer is commonly employed in practise in large structures. subsequently, the joint surfaces were treated according to a light sandblasting process (sweep blasting). in the absence of precise information by the national and european regulations it is proposed a specific procedure which relates to indications in the literature (iso 8503). in fact, the hot-dip galvanized surface of structural steels requires special handling. the aim was to remove the outer layer consisting of pure zinc notoriously soft and malleable thereby making the surface rough. moreover, this type of blasting does not severely damage the existing coating obtained by hot dip galvanizing. a specified torque was applied to the nut in two steps using a calibrated wrench capable of an accuracy of ± 4 % according to iso 6789. most of these connections are used in steel structures frequently submitted to cyclic loading such as splice joints used in steel and composite bridges. figure 1: geometry of the test specimen employed in the research program. detailed procedure for specimen fabrication fter the hot dip galvanization process of steel plates, an adequate surface preparation was performed. the features of the sweep blasting procedure utilized are shown in tab. 1. all above mentioned data were certified by the sand blaster firm inspection procedure. the results were a roughness equal to 32 µm and a reduction of the zinc layer measured in 12 µm (max. value). the surface preparation grade corresponded to sa1 (light blast cleaning). fig. 2 t a s.m.j. razavi et alii, frattura ed integrità strutturale, 41 (2017) 432-439; doi: 10.3221/igf-esis.41.54 434 illustrates hot-dip galvanized bolted connection before the test. a comparison before and after sweep blasting procedure has been shown in fig. 3. according to prescriptions of uni en 1090-2 the assembly of the joints were carried out: the high strength bolts, class 10.9, system hr (uni en 14399-3) were tightened by the torque control method in two steps. the final torque applied to the fasteners (equal to 1.1 mr.2) corresponded to 91 nm as defined and declared by the fastener manufacturer in the box label. before the fatigue tests all the joint bolt torques were checked. adopted values suggested values (*) abrasive garnet garnet or ilmenite mesh 80 80-100 venturi nozzle orifice diameter (mm) 10 10÷13 distance from the surface (mm) 400 350÷400 angle to the surface 45° ≤45° blast pressure(kpa) 200 ≤275 table 1: sweep blasting procedure. (*) with reference to well established international specifications relating to surface treatment for paintings (iso 8503). figure 2: hot-dip galvanized bolted connection before the test. figure 3: comparison between specimens before and after sweep blasting. s.m.j. razavi et alii, frattura ed integrità strutturale, 41 (2017) 432-439; doi: 10.3221/igf-esis.41.54 435 results from fatigue tests he fatigue tests were performed by using a servo-hydraulic mts810 test system with a load cell capacity of 250 kn. all tensile stress-controlled fatigue tests were carried out over a range frequency varying from 5 to 10 hz depending on the level of the applied load. a constant value of the load ratio, r=0, was employed in all tests. after the tests the specimens were examined and the fracture surfaces were analysed to get information about the crack initiation and propagation. failure always happened, as expected, in correspondence of the first bolt of the connection, as visible in fig. 4. in particular fig. 4a shows a lateral view and fig. 4b an upper view of the specimen. fig. 5 shows two broken parts of a specimen. in particular fig. 5a shows the holed plate and fig. 5b the fracture surface in proximity of the bolted connection. the representative failures shown in the figure always started from the net section in correspondence of the hole. from there the crack propagated through the material until the net section was so much weakened that finally a static crack caused the final failure. multiple initiation points are well visible with a regular propagation until the final failure. this is in agreement with [22] which shows that in members with drilled holes a surface crack at the wall of hole was found always predominant. according to the fracture surfaces it can be observed that the crack has not a constant configuration in thickness. thus, it is verified that the preloading applied to bolts influence crack initiation phase. fig. 6 shows an example of the zinc layer from a sem image. fig. 7 summarizes the results from fatigue tests of hot-dip galvanized bolted connections subjected to a nominal load ratio r=0. the stress range over load cycles n is plotted in a log-log diagram. the unbroken specimens (run-out samples), over three million cycles, were not considered in the statistical analysis. they are marked with an arrow in fig. 7. the mean curve corresponding to a probability of survival, ps, equal to 50% is reported in the figure as well as the scatter band defined by lines with ps 10%-90%. the dashed line refers, instead to a ps of 97.7% for a direct comparison with the eurocode detail (en 1993-1-9). the typical expression for the s-n curve in ec3 is reported below: 62 10k kr r cn     (1) the inverse slope k value of the s–n curve and the scatter index t referred to ps 10%-90% are also shown. the complete list of data related to hot-dip galvanized bolted connections is summarised in tab. 2 properly marking the run-out specimens. the results from the statistical re-analysis is provided in tab. 3. from the re-analyses of the data it is clear that considering a ps of 97.7% at two million cycles δσ is equal to 100 mpa which is slightly lower than the corresponding classified category δσc=112 mpa derived from ec3 for the considered uncoated bearing-type connection. in contrast to [22], the inverse slope of the curve, k, is very close to that suggested by ec3. the data from hot dip galvanized specimens are plotted together with data from uncoated specimens characterized by the same geometry and tested in this research program. it is possible to observe that all data fall inside a narrow scatterband and that the reference value at two million of cycles and corresponding to a ps of 97.7% remains almost the same (101 mpa) with almost no significant differences between galvanized and not-galvanized specimens (see fig. 8). this result is in agreement with that reported in [22] where it was shown that the use of preloaded high strength bolts gave a remarkable positive influence on the achieved fatigue life and that the detrimental effect of hot dip galvanizing can be easily neutralized. the advantage of this method is the easiness of handling with the maximum of efficiency of the bolted connection under fatigue loading. in this optic the accurate procedure described in section 3 for specimens preparation and assembly is surely necessary to guarantee a good repeatability of the connections in the different specimens. this procedure permits to allow beneficial compressive stresses in the neighbouring of the holes which are advantageous for the fatigue behaviour. in fact, as described in [23], the difference between galvanized and non-galvanized simple plates weakened by a central hole is much higher than that reported in the present paper for bolted connections. in the research conducted by berto et al. [23] a non-negligible deviation approximately equal to 30% has been found between coated and uncoated specimens with an insignificant reduction of the fatigue life due to influence of galvanization process. in that case two well different scatter bands were given without the possibility of providing a unified band for coated and uncoated specimens which is instead possible in the present investigation dealing with bolted connections. some creep analyses are also planned [24]. t s.m.j. razavi et alii, frattura ed integrità strutturale, 41 (2017) 432-439; doi: 10.3221/igf-esis.41.54 436 a b figure 4: typical failure from the hole corresponding to the first bolt of the connection. (a) lateral view and (b) upper view. a b figure 5: typical fracture surface after cyclic loading. (a) plate and (b) bolted part. figure 6: layer thickness from a sem image. s.m.j. razavi et alii, frattura ed integrità strutturale, 41 (2017) 432-439; doi: 10.3221/igf-esis.41.54 437 figure 7: s-n-curves of hot dip galvanized connections. 10 100 1000 1.00e+04 1.00e+05 1.00e+06 1.00e+07 s tr es s ra n g e   [m p a] number of cycles to failure hot dip galvanized specimens uncoated specimens 101 mpa k=3.48 ps = 97.7 % ps = 2.3 % 89 mpa scatter index tσ = 1.409 σ50% = 120 mpa (n = 2 ∙ 106) figure 8: unified scatterband considering uncoated and hot dip galvanized connections. conclusions his short technical note reports some new data from hot dip galvanized steel bolted connections under fatigue loading. in particular the effect of a galvanizing coating on the fatigue strength of s355 structural steel has been accurately investigated showing that the reduction in the fatigue life is very limited if compared with that of uncoated joints. a detailed procedure for the accurate preparation of the specimens has been also systematically provided, showing a good repeatability in the assembly of the specimens and then in the final fatigue behavior. t s.m.j. razavi et alii, frattura ed integrità strutturale, 41 (2017) 432-439; doi: 10.3221/igf-esis.41.54 438 δσ [mpa] n notes 220 176000 120 3000000 run-out 160 736700 160 597000 280 85000 100 3000000 run-out 280 95000 140 3000000 run-out 140 3200000 run-out 160 3000000 run-out 220 253000 220 167000 220 187000 200 251000 180 432807 180 393000 180 395000 140 1324000 table 2: summary of all fatigue data from hot-dip galvanized bolted joints. ps ∆σ n 10% 529 10000 10% 130 2000000 50% 489 10000 50% 120 2000000 90% 452 10000 90% 111 2000000 97.70% 100 2000000 table 3: summary of the statistical re-analysis for the hot-dip galvanized series. references [1] khoramishad, h., razavi, s.m.j., metallic fiber-reinforced adhesively bonded joints, int. j. adhes. adhes. 55 (2014) 114-122. [2] ayatollahi, m.r., nemati giv, a., razavi, s.m.j., khoramishad, h., mechanical properties of adhesively single lap bonded joints reinforced with multi-walled carbon nanotubes and silica nanoparticles, j. adhes., (in press). doi: 10.1080/00218464.2016.1187069. [3] ayatollahi, m.r., samari, m., razavi, s.m.j., da silva, l.f.m., fatigue performance of adhesively bonded single lap joints with non-flat sinusoidal interfaces, fatigue fract. eng. mater. struct., (in press). doi: 10.1111/ffe.12575. s.m.j. razavi et alii, frattura ed integrità strutturale, 41 (2017) 432-439; doi: 10.3221/igf-esis.41.54 439 [4] ayatollahi, m.r., nemati giv, a., razavi, s.m.j., khoramishad, h., the effect of orientations of metal macrofiber reinforcements on the mechanical properties of adhesively bonded single lap joints, j. adhes., (in press). doi: 10.1080/00218464.2017.1305270. [5] razavi, s.m.j., esmaeili, e., samari, m., razavi, s.m.r., stress analysis on a non-flat interface bonded joint, j. adhes., (in press). doi: 10.1080/00218464.2016.1257942. [6] esmaeili, e., razavi, s.m.j., bayat, m., berto, f., flexural behavior of metallic fiber-reinforced adhesively bonded single lap joints, j. adhes., (in press). doi: 10.1080/00218464.2017.1285235. [7] lokaj, a., klajmonova, k., comparison of behaviour of laterally loaded round and squared timber bolted joints, frattura ed integrita strutturale, 11(39) (2017) 56-61. [8] espallargas, n., aune, r.e., torres, c., papageorgiou, n., munoz, a.i., bulk metallic glasses (bmg) for biomedical applications—a tribocorrosion investigation of zr55cu30ni5al10 in simulated body fluid, wear, 301(1-2) (2013) 271-279. [9] espallargas, n., johnsen, r., torres, c., munoz, a.i., a new experimental technique for quantifying the galvanic coupling effects on stainless steel during tribocorrosion under equilibrium conditions, wear, 307(1-2) (2013) 190-197. [10] espallargas, n., torres, c., munoz, a.i., a metal ion release study of cocrmo exposed to corrosion and tribocorrosion conditions in simulated body fluids, wear, 332-333 (2015) 669-678. [11] haugan, e.b., næss, m., torres rodriguez, c., johnsen, r., iannuzzi, m., effect of tungsten on the pitting and crevice corrosion resistance of type 25cr super duplex stainless steels, corrosion, 73(1) (2017) 53-67. [12] jiang, j.h., ma, a.b., weng, w.f., fu, g.h., zhang, y.f., liu, g.g., lu, f.m., corrosion fatigue performance of presplit steel wires for high strength bridge cables, fatigue fract. eng. mater. struct., 32 (2009) 769–779. [13] yang, w.j., yang, p., li, x.m., feng, w.l., influence of tensile stress on corrosion behaviour of high strength galvanized steel bridge wires in simulated acid rain, mater. corros., 63 (2012) 401–407. [14] berchem, k., hocking, m.g., the influence of pre-straining on the corrosion fatigue performance of two hot-dip galvanised steels, corros. sci., 48 (2006) 4094–4112. [15] berchem, k., hocking, m.g., the influence of pre-straining on the high-cycle fatigue performance of two hot-dip galvanised car body steels, mater. charact., 58 (2006) 593–602. [16] james, m.n., designing against lmac in galvanised steel structures, eng. fail. anal., 16 (2009) 1051–1061. [17] di cocco, v., sn and ti influences on intermetallic phases damage in hot dip galvanizing, frattura ed integrità strutturale, 22 (2012) 31-38. [18] bergengren, y., melander, a., an experimental and theoretical study of the fatigue properties of hot dip-galvanized high strength sheet steel, int. j. fatigue, 14 (1992) 154–162. [19] nilsson, t., engberg, g., trogen, h., fatigue properties of hot-dip galvanized steels. scand. j. metall., 18 (1989) 166– 175. [20] browne, r.s., gregory, e.n., harper, s., the effects of galvanizing on the fatigue strengths of steels and welded joints, in: proc. seminar on galvanizing of silicon containing steels, ilzro publishers, liege, (1975) 246–264. [21] vogt, j.b., boussac, o., foct, j., prediction of fatigue resistance of a hot-dip galvanized steel, fatigue fract. eng. mater. struct., 23 (2000) 33–39. [22] valtinat, g., huhn, h., bolted connections with hot dip galvanized steel members with punched holes. connections in steel structures v, amsterdam, (2004) 297-309. [23] berto, f., mutignani, f., tisalvi, m., laurenti, a., effect of hot-dip galvanization on the fatigue behavior of notched and welded structural steel, ingegneria ferroviaria, 2 (2016) 105-118. [24] gallo, p., berto, f., glinka, g generalized approach to estimation of strains and stresses at blunt v-notches under non-localized creep, fatigue fract. eng. mater. struct., 39 (2016) 292-306. << /ascii85encodepages false /allowtransparency false /autopositionepsfiles true /autorotatepages /none /binding /left /calgrayprofile (dot gain 20%) /calrgbprofile (srgb iec61966-2.1) /calcmykprofile (u.s. web coated \050swop\051 v2) /srgbprofile (srgb iec61966-2.1) /cannotembedfontpolicy /error /compatibilitylevel 1.4 /compressobjects /tags /compresspages true /convertimagestoindexed true /passthroughjpegimages true /createjobticket false /defaultrenderingintent /default /detectblends true /detectcurves 0.0000 /colorconversionstrategy /cmyk /dothumbnails false /embedallfonts true /embedopentype false /parseiccprofilesincomments true /embedjoboptions true /dscreportinglevel 0 /emitdscwarnings false /endpage -1 /imagememory 1048576 /lockdistillerparams false /maxsubsetpct 100 /optimize true 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/pdfxoutputintentprofileselector /documentcmyk /preserveediting true /untaggedcmykhandling /leaveuntagged /untaggedrgbhandling /usedocumentprofile /usedocumentbleed false >> ] >> setdistillerparams << /hwresolution [2400 2400] /pagesize [612.000 792.000] >> setpagedevice microsoft word numero 15 articolo 2 f. b 14 e el o ci fil un ber ab po and mi larg the de in mo ri lett acc re in ape fin l’ef berto et alii, fra esistenza llittici so on the m ircular a lippo berto niversità di pa rto@gest.unipd bstract. it oisson’s effec d numerical ght play a ro ge opening e mutual inci ealing with c the literatur ode o. on th an out-of-p previously d also for fini out-of-plan intensity of the strain dependent the plate t dimensiona assunto. i teratura dim coppiata al c ecenti analisi piastre intag ertura dell’in no ad ora eff ffetto di un r attura ed integrità a del m oggette mode o and ellip o, christia adova, diparti d.it t is known f ct leads to th analyses hav ole in failure angle. since idence of th circular and e. the main he basis of a plane mode demonstrate ite values of ne mode re f this stress c energy den is a paramet thickness. i ality is not ne il problema mostrando ch carico estern i teoriche e n gliate a spigo ntaglio magg fettuate hann raggio di rac à strutturale, 15 modo o i a modo o existen ptical ho an marango imento di tecni for long tim he generatio ve shown th e initiation p e the degree he two mode elliptic hole n aim of this a large bulk o e is present ed for plates f the notch ra esults in a s component s nsity average ter suitable t is surely egligible, or a di una pia he l’effetto no applicato numeriche h olo vivo. il n giori di 102. no riguardat ccordo diver 5 (2011) 14-20; in piast o ii nce in t oles und on ica e gestione d me that in a on of a coup hat this effec phenomena i of singulari es depends o s, the presen work is to d of numerica in plates w s weakened b adius. shear stress strongly dep ed on a giv for the natu a powerfu is not know astra criccat del coefficie e non conte hanno eviden nuovo modo .6° e cioè qu to piastre in rso da zero a doi: 10.3221/ig tre tridim three-di der mod dei sistemi indu cracked pla pled out-of-p ct is present in plates und ity character on the comp nce or not o demonstrate al results the eakened by by cracks an distribution pends on the ven control ural of captu ul tool in p wn in detail. ta tridimens ente di pois emplata dalla nziato come o (denomina uando il mo ndebolite da all’apice dell’ gf-esis.15.02 mension imensio de ii loa ustriali, strade ate subjected plane singula also in plate der mode ii rising the mo ponent size. of the out-of e the existen following co u-notches nd pointed v n symmetric e poisson’s r volume wh ure all three practical cas ionale sogg sson provoc a soluzione p e questo effe ato modo o odo ii risulta cricche o in ’intaglio. nali con onal plat ading della s.nicola 3 d to anti-sym ar mode (m es weakened loading par ode o is gre f-plane mod nce of a three onclusions c and subject v-notches; it c with respe atio . it inc hich should dimensiona ses where t etta a modo ca l’insorger piana di will etto tridimen o) rimane sin a essere non ntagli a spigo n fori ci tes wea 3, 36100 vi mmetric plan mode o). rec d by pointed rticularly in t eater than th de has never e-dimension can be drawn ted to mode ts intensity i ect to the m creases as  i d, in princip al effects occ the role pla o ii è stato e di una nu liams. nsionale sia ngolare anch n singolare. olo vivo non ircolari e akened b icenza (italy) ne loading, cent theoret v-notches a the presence hat of mode been discus nal effect tied n: e ii loading is not neglig mid-plane. t increases. ple, be mate curring thro ayed by th o affrontato uova singola presente anc he per angol tutte le ana n consideran ed by the tical and e of e ii, ssed d to g, as gible the erial ough reeo in arità che li di alisi ndo http://www.gruppofrattura.it mailto: berto@gest.unipd.it http://dx.medra.org/10.3221/igf-esis.15.02&auth=true l’o trid cir ke in tras ne sot spe tu ipo per l’ut spo trid num ten fun coe un trid i p con spe ben libe qu [13 in doc pia spe in ko coe sch not del la giu per effe pro ed i obiettivo de dimensionali colari ed elli eywords. t ntroduzion l problema risulta poc semplici. n scurano a pri elle applicazio ttile, lo stato essore non tra uttavia, non v otesi. r considerare tilizzo dell’ip ostamento uz dimensionali, meriche su p nsione reale lu nzione dello s efficiente di p na revisione c dimensionali i primi ricercat nsiderarono i essore del pia nthem (1977) era del comp uesto effetto, 3], yu et al.[14 relazione a p cumentarono ana di william essore finito forma chiusa otousov ha d efficiente di hematicament tare come il m lla piastra. presenza del unti saldati a s r quanto rigu fetti tridimens oprio quello d ellittici sogg i el presente i indebolite ittici variand three-dimen ne a della determ o agevole e l nella pratica s ori gli effetti oni lo stato d di tensione ascurabile risp vi è alcun crit e l’effetto trid otesi di defo z lungo lo sp come ampia piastre tridime ungo lo spess spessore è sta poisson per p completa dei p in piastre inta tori che si in i casi di trazio atto in funzion ) notò per pri ponente [10]. documentato 4]), è stato rec piastre cricca o per la prim ms. recentem [17-20]. in pa a l’equazione dimostrato in poisson ed te come il m modo o sia s l nuovo mod sovrapposizio arda invece i sionali di vol di colmare qu gette a modo contributo da intagli ra do sia la geom nsional effect minazione dei le soluzioni a si ricorre a te tridimensiona di tensione è l è generalme petto alle altr terio che per dimensionale ormazione pi pessore della amente dimos ensionali inta ore del comp ata ampiamen iastre indebo principali risu agliate e cricc nteressarono one e flession ne della dime rimo che la sin in questo pi o anche in al centemente an ate soggette a ma volta la pr mente, l’insorg articolare, ko agli autovalo noltre che l’in in particola odo o si gen simile al mod o singolare è one dove il m componenti lume legati a uesta lacuna a o ii, l’esisten f. berto et è quello d accordati e s metria dell’in ts; out-of-p i campi di ten analitiche in f eorie piane ch ali presenti ne legato allo sp ente consider re dimensioni rmetta di dist legato alla f iana generaliz piastra, prod strato nelle r agliate soggett ponente [4, 5] nte discussa n lite da fori ell ultati analitici ate è stata rec degli effetti ne. le equaz ensione del di ngolarità nel iano nasceva ltri contributi nalizzato con a modo ii, le esenza in pia gere del nuo otousov, utiliz ori per il mod ntensità dei c are aumentav neri in una p do iii ma a di è stato docum odo ii risulta tridimension al modo o n analizzando p nza del modo t alii, frattura ed di dimostrar soggette a m ntaglio sia il plane mode; m nsione in com forma chiusa he utilizzano l el componen pessore del co rato di tensio i del compon tinguere quale finitezza dello zzata [1]. qu duce buone eferenze [2, 3 te a prevalen . la variazion elle referenze littici e sogge , numerici e s centemente c tridimension ioni ottenute fetto e dello s piano scomp a invece una i ( tra gli altr n riferimento a e prime anali astre sottili d ovo modo sin zzando la teo do “out of plan campi di ten va all’aumen piastra tridime ifferenza di q mentato anche ava predomin nali indeboliti non sono ma per geometrie o o e di va d integrità struttu re che il m modo ii. si s valore del co mode ii; mo mponenti trid riguardano s le ipotesi di t nte. omponente tr one piana, se nente si consid e sia lo spess o spessore d uesta ipotesi, approssimazi 3]. negli ulti te modo i co ne del fattore e [5-7], nelle q tte a modo i. sperimentali o ondotta da k nali su piastre e descrivevan spessore stess pariva quando nuova singol ri da bazant e a problemi di isi furono co di un modo s ngolare è stat oria della defo ne” che è stat nsione legati ntare di ques ensionale cric quest’ultimo e e in piastre in nante rispetto da intagli rac ai stati analiz semplici, qu alutarne l’inte turale, 15 (2011) modo o è p sono quindi oefficiente d ode o. dimensionali solo casi cara tensione pian ramite una se invece la pi dera valida l’i sore limite pe della piastra è che conside ioni dello sta mi anni sono on lo scopo d teorico di co quali è stata a ottenuti fino kotousov et al e criccate fur o la variazion so. o il fronte di c larità tridimen ed estenssoro i resistenza a ondotte da n singolare non to evidenziato ormazione pia to chiamato al nuovo m st’ultimo [19 ccata soggetta esso sia simm ndebolite da i al modo i [2 ccordati e sog zzati. lo scop ali piastre trid ensità consid ) 14-20; doi: 10 presente an analizzate p di poisson. indeboliti da atterizzati da a o deformaz emplice regol iastra è carat ipotesi di defo er cui utilizza è molto diffu era lineare l’a ato tensionale o state condo di ottenere la oncentrazione analizzata anch ad ora e rigu l.[8]. rono hartran ne delle tensi cricca intersec nsionale all’ap o [11], pook fatica [15]. nakamura e p n contemplato o anche in p ana generaliz dallo stesso a modo risultava 9-20]. in fig a a taglio. da metrico rispett intagli a v a 1]. ggetti a preval po del prese dimensionali derando anch 0.3221/igf-esis. nche in pias piastre con f a cricche e in geometrie m zione piana e la. se la piast tterizzata da ormazione pi are l’una o l’a uso in lettera andamento d e in compon otte molte an a distribuzion e delle tension he l’influenza uardanti gli ef nft e sih [9] ioni attravers cava la super pice dell’intag [12], she e g parks [16] i q o dalla soluzi piastre criccat zata, ha otten autore “modo a influenzata g. 1 è most alla figura si o al piano me spigolo vivo lente modo i nte contribu con fori circo he l’influenza 15.02 15 stre fori tagli molto che tra è uno iana. altra atura dello nenti nalisi ne di ni in a del ffetti che o lo rficie glio. guo quali ione te di nuto o”. a dal trato può edio e in ii gli to è olari a del http://www.gruppofrattura.it http://dx.medra.org/10.3221/igf-esis.15.02&auth=true f. b 16 coe lav ge ne l berto et alii, fra efficiente di p voro in corso eometrie a e geome di piastr rag spessore de larghezza d coefficiente el caso di pias rapporto tr spessore de larghezza d coefficiente l attura ed integrità poisson. il mo di revisione [ analizzate etrie analizzat ra soggetta a f ggio del foro a el piatto 2t = del piatto w= e di poisson stra soggetta a ra i semiassi d el piatto 2t = del piatto w= e di poisson (b)cond (b) cons à strutturale, 15 odo o, in cas [22]. figura 1: rap schem e e modali te nel present foro circolare a=b=1, 5, 10, 40 mm; = 200 mm;  = 0 , 0.1, 0 a foro ellittico dell’ellisse a/b 40 mm; = 200 mm;  = 0 , 0.1, 0 (a) figura 2: ( dizioni al conto (a) three-di traint conditio 5 (2011) 14-20; so di intagli ad ppresentazione matic represent ità di appl te contributo e sono stati co , 20 mm; 0.3 e 0.5. o, invece, son b=5, 10, 20 ( 0.3 e 0.5. (a) piastra tridi orno applicate imensional plat ns applied to t doi: 10.3221/ig d u e a v ipe e schematica d tation of the “o licazione d e i principali onsiderati i se no stati consid (con b=1 mm imensionale co al modello sfr te weakened b the model takin gf-esis.15.02 rbolici e para dell’effetto “out out of plane” e dei carich parametri geo eguenti param derati i seguen m) on fori circolari uttando i piani y circular and ng advantage o abolici, è stato t of plane”. effect. i ometrici sono metri geometri nti parametri: (b) i ed ellittici; i di simmetria elliptic holes; of the double s o ampiamente o mostrati in ici e di materi esistenti. symmetry. e analizzato in fig. 2. nel ca iale: n un aso http://www.gruppofrattura.it http://dx.medra.org/10.3221/igf-esis.15.02&auth=true la la pos (x,y imp dir inf per app ne un nod ri le val ten p piastra è stat geometria d ssibile analizz y,z) è situata poste sui pia ezione x e z ( fine sulla supe r imporre un partenenti alle u 0x  ell’eq.(1) g ra n esempio del di “solid 95” sultati de er i fori c lo spesso alla supe figura 4: fig. 5a e 5b r lore massimo nsione yz, gen p ta sollecitata o del componen zare solament sul piano m ani di simme (ux=0 e uz=0) erficie laterale na sollecitazio e aree abde g u 00y    appresenta il lla mesh utiliz ed il codice d figura 3: d elle anali circolari ed el ore del mode erficie libera d distribuzione yz stress distri riportano inv della tension nerata dal mo opportuname nte analizzato te un quarto medio del mod etria del mod ). sul piano m e gfhi sono one nominale e e degf. l’ 2 w modulo di ela zzata per le an di calcolo ans iscretizzazione mesh used in si numeric llittici, le fig. llo. il picco d del componen della tensione ibution, tied to vece l’andame ne principale odo o, raggiu f. berto et ente mediante o è riportata della piastra dello, come m dello. sull’are medio invece o stati bloccat di modo ii ’intensità deg asticità tangen nalisi numeric sys 12.0®. e utilizzata nell the numerical che 4a e 4b ripor di tensione si nte. tale com (a) e yz, legata al m o mode o, in p ento, attravers . tale tensi unge il suo v t alii, frattura ed e degli sposta a in fig. 2a. di partenza ( mostrato in a trasversale sono stati vin ti gli spostame pari a 0=10 gli spostament nziale, g = e che è mostrat le analisi nume analyses: (a) c rtano la distri posiziona all mponente di te ) modo o, per p plates weakene so lo spessore ione risulta m valore massim d integrità struttu amenti che ga sfruttando le (fig. 2b). l’or fig. 2a. opp oabc sono ncolati solam enti uy. 00 mpa, sono ti applicati è d e/2(1+). ta nelle fig. 3 eriche: (a) foro circular hole; (b ibuzione delle l’apice dell’int ensione non è iastre indebolit ed by circular h e del modello massima al di mo lungo la bi turale, 15 (2011) arantissero un e simmetrie rigine del sist portune cond o stati vincol mente gli spost o stati applica data dalla segu 3a e b. sono s circolare; (b) f b) elliptic hole e tensioni yz taglio lungo l è contemplata te da fori circo holes (a) and ell o, delle tensio fuori della bi isettrice dell’i ) 14-20; doi: 10 n carico nomi presenti nel tema di riferim dizioni al con lati gli spost tamenti lungo ati degli spos uente espress stati utilizzati foro ellittico. e. (legate al mo la sua bisettri a dai modelli (b) olari (a) e fori e liptic holes (b) oni yz, norma isettrice dell’i intaglio. entr 0.3221/igf-esis. inale di modo modello è s mento cartesi torno sono s amenti nodal o la coordina stamenti sui n sione: (1) gli elementi odo o) attrav ce ed è pross piani. ) ellittici (b). . alizzate rispett intaglio mentr rambe le tens 15.02 17 o ii. stato iano state li in ta z. nodi a 20 erso simo to al re la sioni http://www.gruppofrattura.it http://dx.medra.org/10.3221/igf-esis.15.02&auth=true f. b 18 risu geo in for cas par val le risp del la spe libe /  berto et alii, fra ultano massim ometrici del m fig. 5a, relati ro le tensioni so riguardant rticolare dal r lore massimo figura 6: te e d princip fig. 6a e 6b petto al valo ll’intaglio lung fig. 6a mos essore. per r= era mentre, p 0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0  y z / σ 1 , m ax foro circ 2t=40 mm =0.3 path all'ap 0.8 0.9 1 0     m ax r=1 r= 5 r=1 r= 2 foro circola 2t = 40 mm =0.3 attura ed integrità me attraverso modello. le fi iva alla piastr aumentino d te il foro elli rapporto dei rimane semp figura 5: and v th ensione princip entrambi gli an ell’intaglio, lun pal stress, 1, an are plotted thr b mostrano l ore massimo go la linea in stra come, al =1 mm e 2t= per raggi più a 0.1 0 colare m pice dell'intaglio (x=0) 0.1 0.2 mm 5 mm 0 mm 20 mm are 11, max à strutturale, 15 o lo spessore igure fanno ri ra con foro c di intensità e ittico (fig. 5 semiassi dell pre in prossim (a) damento, attrav valore massimo hrough-the-thi of the pr (a) pale 1 e tensio ndamenti sono ngo la linea in c nd mode o str rough the thick l’andamento della tensio cui 1 assum variare del d =40 mm, il m ampi, il punto 0.2 0.3 z/2t r = r = 1 r = 5 mm 0.3 z/2t yz1,max caso r=1 5 (2011) 14-20; e ad una dis iferimento ad circolare, è po il punto di p 5b), l’intensità ’ellisse stessa mità della supe verso lo spesso o della tensione ckness stress d rincipal stress; oni yz di modo o plottati attrav cui 1 raggiung ress,yz, norma kness and out o delle tension ne principale e il suo valore diametro del massimo della o di picco tras 0.4 1 mm 10 mm r = 20 mm 0.4 0.5 1 mm doi: 10.3221/ig tanza dalla s d un coefficien ossibile notar picco si sposti à delle tensio a. il punto in erficie libera d ore, delle tensi e principale; fo distribution no circular holes o o normalizz verso lo spesso ge il suo valore alized by the m of the bisector ni fuori dal p e. entrambe e massimo. foro, il punt tensione 1 r sla attraverso 0.5 0 0.1 0.2 0.3 0.4  y z   m ax 5 0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.1  y z / 1 , m ax 0.6 0.7 0.8 0.9 1     m ax gf-esis.15.02 superficie libe nte di poisso re come al dim i sempre più oni risulta in cui la tensio del compone ioni fuori dal p ori circolari (a) rmalised by th (a) and elliptic zate rispetto al ore del material e di massimo; f maximum valu r along the line piano, yz, e le tensioni to di picco d risulta essere lo spessore, 0 0.1 a/b = 5 a/b = 10 a/b = 20 foro ellittico 2t = 40 mm w = 200 mm =0.3 path all'apice dell'in 0 0.1 a/b=5 a/b=20 a/b=10 foro ellittico 2t = 40 mm w = 200 mm =0.3 era variabile n =0.3. minuire della verso la supe nfluenzata da ne yz, legata ente. piano normalizz e fori ellittici (b he maximum va holes (b). (b) valore massim le ma al di fuor fori circolari (a) ue of the princi e of maximum della tension sono plottat della tensione in una zona m fino a situars 0.2 z ntaglio (x=0) 0.2 z/2t a/b=10 1/ e che dipend a dimensione erficie libera alle dimensio a al modo o, (b) zate rispetto al (b). alue mo della tension ri dalla bisettric a), fori ellittici ( ipal stress. the principal stres ne principale te al di fuor e principale v molto prossim i sul piano m 0.3 z/2t 0.3 0.4 yz/1,max 1,max de dai param del diametro del modello. ni del foro raggiunge il l ne principale. ce (b). e stresses s. 1 normaliz ri dalla bisett vari attravers ma alla super medio del mod 0.4 0 4 0.5 0 0.1 0.2 0.3 0.4 a/b=5 a/b=20 y z 1 , m ax metri o del nel e in suo zzate trice o lo ficie dello 0.5  y z / 1 , m ax http://www.gruppofrattura.it http://dx.medra.org/10.3221/igf-esis.15.02&auth=true nel bis ne dim situ cas sem rap l’a rife ma inf dif la s [m p ] l caso del rag ettrice può ri el caso di pia mensioni del d uato nell’imm si considerati miassi dell’elli pporto a/b=2 andamento de erita al caso r assima intensi figur coefficie tabella 1: fa fine, in tab. fferenti tipolo seguente espr 0 10 20 30 40 50 60 70 80 90 100 0  y z [m p a] foro circ 2t=40 mm w=200 m r = 5 mm path all'ap =0 =0.1 =0.3 =0.4 ggio di racco itenersi invece astre indeboli difetto solo l mediato sottop un valore di lisse. quest’u 20 essa raggiu ella compone r=5 mm men ità per valori e 7: andament nte di poisson of the attore teorico d theoretic 1 viene doc ogie di intaglio ressione: 0.1 0. colare m mm m pice dell'intaglio (x=0) 3 49 ordo più amp e trascurabile lite da un fo lontano dalla pelle, vicino a i massimo in ultima non ri unge un valore ente yz è mo ntre la fig. 7b elevati di  m (a) to della tension n del materiale. plate as a func foro circo r (mm 1 5 10 20 foro ellit (b=1 m a/b 5 10 20 di concentrazio cal stress conce cumentata la o analizzate, s 2 0.3 z/2t f. berto et pio (r=20 m e, essendo il v ro ellittico (f zona in cui e alla superficie prossimità d isulta trascur e pari al 20% ostrato in fig b è riferita al mentre l’effett ne yz (legata al foro circolare ction of the po olare m) k 4. 4. 4. 3. ttico mm) k 7. 12 21 one delle tensi entration facto variazione d sia nel caso b 0.4 t alii, frattura ed mm e 2t=40 valore del rapp fig. 6b), l’an essa raggiung libera della p della superfici abile al di fu della tension . 7a e 7b per caso a/b=5. to scompaia c l modo o) attr e (a) e foro ellit oisson’s ratio. c kt,2d =0 .001 4.0 .005 4.0 .002 4.0 .998 4.0 kt,2d =0 .221 7.2 2.063 12.3 1.689 22.5 ioni calcolato p or for two-dime del fattore teo bidimensional 0.5 0 50 100 150 200 250 300 350 400  y z /   m ax d integrità struttu mm). la com porto yz/1 ndamento del ge il valore m piastra. la com ie libera, la cu uori della bis ne principale m r diversi valor in entrambi completament raverso lo spes ttico (b). stress circular hole (a kt,3d 0.1 =0. 13 4.159 24 4.175 25 4.179 15 4.215 kt,3d 0.1 =0. 49 7.715 312 13.40 586 25.40 per modelli bid ensional and th orico di conc le che nel cas 0 0 0 0 0 0 0 0 0 0 0.1 foro ellittico 2t = 40 mm w = 200 mm a / b = 5 path all'apice dell' =0 =0.1 =0.3 =0.49 turale, 15 (2011) mponente di inferiore al 5 lla tensione  assimo, ment mponente di ui intensità d settrice dell’in massima. ri del coeffici i casi si nota te per =0. (b) ssore del comp s distribution  a) and elliptic h d 3 =0.5 9 4.407 5 4.424 9 4.425 5 4.509 d 3 =0.5 5 8.653 06 15.507 03 35.219 dimensionali e hree-dimension centrazione d so tridimensio 0.2 z intaglio (x=0) ) 14-20; doi: 10 tensione yz 5% in tutto il 1 risente de tre il punto d tensione yz p dipende dal ra ntaglio. infat iente di poiss come il mod ponente, al vari yz through the hole (b). per modelli tri nal models delle tensioni onale. kt è sta 0.3 z/2t 0.3221/igf-esis. al di fuori d campo di ana ell’influenza d di picco è sem presenta in tu apporto a/b tti per valori son. la fig. do o raggiung iare del e thickness idimensionali. i (kt) per le ato calcolato 0.4 0 15.02 19 della alisi. delle mpre utti i fra i i del 7a è ga la due con 0.5 http://www.gruppofrattura.it http://dx.medra.org/10.3221/igf-esis.15.02&auth=true f. b 20 si trid co le bi [1] [2] [3] [4] [5] [6] [7] [8] [9] [10 [11 [12 [13 [14 [15 [16 [17 [18 [19 [20 [21 [22 l berto et alii, fra tk   può notare dimensionali c onclusion ’obiettiv tridimen indeboli principali con la pres modo i la com compon particol la ten posizio posizio l’inten dei sem il fattor maggio bliografia t.r. kane, a. kotouso f. berto, p. z. li, w. g z. yang, c. p. yu, w. g c. she, w. g a. kotouso r. j. hartra 0] j. p. benthe 1] z. p. bazan 2] l. p. pook, 3] c. she, w. g 4] p. yu, c. sh 5] p. hutar, l. 6] t. nakamu 7] z. h. jin, r 8] c. s. huang 9] a. kotouso 0] a. kotouso 1] s. harding, 2] f. berto, p. l attura ed integrità nom max,1   come anch che non risul ni vo del presen nsionali intagl ite da fori circ nclusioni alle senza del mod ii, applicata n mponente di nente. l’inten lare essa cresc sione princip nato in pros ne varia attra sità delle tens miassi a/b). re teorico di re del valore a r. d. mindlin ov, c. h. wan lazzarin, c. guo, z. kuang .b. kim, c. c guo, c. she, j guo, int. j. f ov, p. lazzarin anft, g. c. sih em, int. j. sol nt, l. f. esten engng. frac guo, int. j. s he, w. guo, i . náhlík, z. k ura, d. m. par r. c. batra, en g, computers ov, t. l. lew, ov, int. j. soli a. kotousov lazzarin, a. à strutturale, 15 he il fattore ltano affatto t nte contribu liati in presen colari ed ellitt quali si è giu do o è stata nominalmente tensione yz nsità è risulta ce al crescere pale risulta i simità della s averso lo spes sioni di modo concentrazio ottenuto da u n, j. appl. m ng, int. j. soli h. wang, in g., int. j. solid cho, h.g. beo j. zhao, int. j fatigue, 29 (20 n, f. berto, s h, int. j. eng. lids struct., 13 nssoro, int. j. t. mech., 48 ( solids struct., int. j. solids s knésl, int. j. f rks, int. j. sol ngng. fract. m s and structur , int. j. solids ds struct., 44 v, p. lazzarin kotousov, l 5 (2011) 14-20; teorico di trascurabili ne to è quello nza di raggi d tici. unti, grazie all rilevata nei m e al modello t legata al m ata essere for e di quest’ultim invece massi superficie libe ssore in funzio o o è influenz one delle tens un’analisi pian mech., 23 (195 ids struct., 39 nt. j. fract., 12 ds struct., 37 om, int. j. so j. fatigue, 30 007) 330. s. harding, en sci., 8 (1970) 3 (1977) 479. solids struct (1998) 367. 44 (2007) 30 struct., 47 (20 fatigue, 32 (2 lids struct., 2 mech., 57 (19 res, 82 (2004) s struct., 43 (2 4 (2007) 8259. n, f. berto, in l.p. pook, fa doi: 10.3221/ig concentrazio ei casi analizz di dimostrar di raccordo n e analisi num modelli analizz tramite oppor modo o è ris rtemente influ mo. ma al di fu era nel caso one delle dim zata anche da sioni risente d na. 6) 277. 9 (2002) 4311 27 (2004) 265 (2000) 7617. olids struct., 4 (2008) 165. ngng. fract. m )711. t., 15 (1979) 4 021. 010) 2123. 2010) 1265. 25 (1989) 141 97) 343. ) 1657. 2006) 5100. . nt. j. fract., 16 tigue fract. e gf-esis.15.02 one delle ten zati. re l’esistenza on nulli. son meriche effettu zati ed è risul rtune condizi sultata essere uenzata dal c ori della bis di fori ellittic mensioni del fo ai parametri g degli effetti t . 5. . 45 (2008) 713 mech., 77 (20 405. 1. 64 (2010) 1. engng. mater nsioni risenta a del modo no state consi uate, sono le s ltata essere ac ioni al contor e simmetrica oefficiente di settrice dell’in ci, mentre ne foro stesso. geometrici (i.e tridimensiona 3. 010) 1665. . struct., in co a pesanteme o nel caso iderate piastre seguenti: ccoppiata alla rno. rispetto al p i poisson  d ntaglio. il pu el caso di for e. raggio del f ali del modell orso di revisione (2) ente degli ef di compone e tridimensio a sollecitazion piano medio del materiale unto di picc ri circolari la foro r e rapp lo e risulta es e. ffetti enti nali ne di del e in co è sua orto ssere http://www.gruppofrattura.it http://dx.medra.org/10.3221/igf-esis.15.02&auth=true << /ascii85encodepages false /allowtransparency false /autopositionepsfiles true /autorotatepages /none /binding /left /calgrayprofile (dot gain 20%) /calrgbprofile (srgb iec61966-2.1) /calcmykprofile (u.s. web coated \050swop\051 v2) /srgbprofile (srgb iec61966-2.1) /cannotembedfontpolicy /error 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/hrv (za stvaranje adobe pdf dokumenata najpogodnijih za visokokvalitetni ispis prije tiskanja koristite ove postavke. stvoreni pdf dokumenti mogu se otvoriti acrobat i adobe reader 5.0 i kasnijim verzijama.) /hun 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can be opened with acrobat and adobe reader 5.0 and later.) >> /namespace [ (adobe) (common) (1.0) ] /othernamespaces [ << /asreaderspreads false /cropimagestoframes true /errorcontrol /warnandcontinue /flattenerignorespreadoverrides false /includeguidesgrids false /includenonprinting false /includeslug false /namespace [ (adobe) (indesign) (4.0) ] /omitplacedbitmaps false /omitplacedeps false /omitplacedpdf false /simulateoverprint /legacy >> << /addbleedmarks false /addcolorbars false /addcropmarks false /addpageinfo false /addregmarks false /convertcolors /converttocmyk /destinationprofilename () /destinationprofileselector /documentcmyk /downsample16bitimages true /flattenerpreset << /presetselector /mediumresolution >> /formelements false /generatestructure false /includebookmarks false /includehyperlinks false /includeinteractive false /includelayers false /includeprofiles false /multimediahandling /useobjectsettings /namespace [ (adobe) (creativesuite) (2.0) ] /pdfxoutputintentprofileselector /documentcmyk /preserveediting true /untaggedcmykhandling /leaveuntagged /untaggedrgbhandling /usedocumentprofile /usedocumentbleed false >> ] >> setdistillerparams << /hwresolution [2400 2400] /pagesize [612.000 792.000] >> setpagedevice microsoft word numero_54_art_08_2837 j. akbari et alii, frattura ed integrità strutturale, 54 (2020) 116-127; doi: 10.3221/igf-esis.54.08 116 focussed on structural integrity and safety: experimental and numerical perspectives experimental evaluation of effects of steel and glass fibers on engineering properties of concrete jalal akbari*, amirhossein abed bu-ali sina university, hamedan, iran j.akbari@basu.ac.ir, https://orcid.org/0000-0001-9713-8652 abedi.amirhosein@gmail.com abstract. this paper experimentally investigates the effect of steel and glass fibers on the engineering properties of concrete. to achieve this, 0.3%, 0.6%, and 0.9% by volume fraction of steel and glass fibers are added in concrete mixtures with water-to-cement (w/c) ratios 0.35 and 0.45. for each ratio of water to cement, 21 cubic samples for compressive strength tests, 14 cylindrical samples for tension strength tests, and also 14 prismatic samples for three-point flexural strength tests were prepared. the experimental results show that adding 0.3% to 0.9% % steel fibers for concrete increases simultaneously the compressive, tension, and also flexural strengths in comparison with plain concrete. adding glass fibers only between 0.3% to 0.6% increases the compressive strength. the results reveal that the best range for reinforcing concrete with steel fiber is 0.3% to 0.9 %, and glass fiber is 0.3% to 0.6 % by volume fraction of fiber to improve the engineering strengths concrete. as a rule of thumb, the tension and flexural strengths of concrete could be explained as 8% and 13% of the compressive strength, respectively. keywords. steel fibers; glass fibers; compressive strength; tension strength; flexural strength; mechanical properties; engineering properties. citation: akbari, j., abed, a., experimental evaluation of effects of steel and glass fibers on engineering properties of concrete, frattura ed integrità strutturale, 54 (2020) 116-127. received: 28.05.2020 accepted: 31.07.2020 published: 01.10.2020 copyright: © 2020 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. introduction enerally, concrete is a weak material in tension in which cracks develop during hardening and shrinkage stages due to drying and cracking. most of the problem occurs when cracking is observed on the concrete surface and, generally causes an unpleasant surface on the concrete. these cracks are usually the pores for infiltration of salt and water into the concrete that increases the probability of rebar’s corrosion. if this weakness is remedied, the maintenance costs of the concrete structures would be reduced, and the useful lifetime of concrete structures will be extended. nowadays, fibers are competitive options to improve the mechanical properties of concrete. the resistance of the concrete increases due to the plastic shrinkage’s formation in concrete when the fibers are uniformly spread in concrete in all directions. on g https://youtu.be/k529c0dgblq j. akbari et alii, frattura ed integrità strutturale, 54 (2020) 116-127; doi: 10.3221/igf-esis.54.08 117 the other hand, the uniform spreading of the fibers does not allow the initiation of the small cracks and prevents forming large cracks. as well, fibers in the cementitious matrix decrease cracking width, increase flexural, tensile strengths, and increase the fracture toughness of concrete. steel fibers reinforced concrete (sfrc) is an advanced composite material that combines plain concrete with steel fibers with various lengths and diameters [[1],[2]]. sfrc is one of the most important materials that enhance the performance of concrete mainly after cracking under stresses [[3],[4],[5]]. in recent years, the researches on the effects of steel fibers are mainly focused on tension, shear, and flexural strengths. liu et al. [[6]] studied tensile properties of glass fiber; gansenan et al. [[7]] examined the influence of steel fibers on tension stiffening of concrete. ashour et al. [[8]] and kwak et al. [[9]] studied the shear behavior of high-strength fiber reinforced concrete beams. besides, many investigations are accomplished on the enhancement of the flexural behavior of concrete with fibers. soutsos and lampropoulos [[10]] and aldossari et al. [[11]] studied the effect of steel fiber on the flexural performance of normal and high strength concrete. wile and parramontesions [[12]], meng & khayat [[13]] studied the effect of fibers on the flexural behavior of ultrahigh-performance concrete. kushartomo and ivan [[14]] examined the effect of glass fiber on flexural, compressive, and splitting strengths of reactive powder concrete. many investigations were conducted on the effects of fibers on combined stresses. chalioris [[15]] proposed an analytical approach for the minimum fiber factor required for steel fibrous concrete beams under combined shear and flexural strengths. yoo et al. [[16]] studied the effect of fiber length and placement method on flexural behavior, tensionsoftening curve, and fiber distribution characteristics of ultrahigh-performance concrete. as well, many types of research have been carried out on improvement of mechanical properties using various fibers in concrete e.g.; sivakumar and santhanam [[17]]; xu and shi [[18]]; chandramouli et al. [[19]]; nili and afroughsabet [[20]]; bhikshma and manipal [[21]]; etchevery and barbosa [[22]]; kamal et al. [[23]]; ashik and sharma [[24]]; saba et al. [[25]]; ibrahim [[26]] and ahmadi et.al [[27]]. the surveys mentioned above did not comprehensively describe how much fibers should be added into concrete to improve the tensile, compressive, and flexural strengths simultaneously. to the knowledge of the authors, comprehensive studies have not yet been conducted to provide a practical guideline of the best ranges for adding various fibers to concrete and presenting applicable relation between different strengths. in this paper, the effects of steel and glass fibers on the mechanical properties of concrete are experimentally investigated. for this purpose, normal concrete with water to cement ratio of 0.45 and high strength concrete with water to cement ratio equal to 0.35 were considered. to perform the experimental tests of each water-cement ratio, for compressive strength, 21 cubic specimens, for tensile strength test 14 cylindrical specimens, and finally, for flexural strength test, 14 prismatic specimens are designed. procedures of research o prepare normal and high strength concretes, the water-to-cement ratios were selected to 0.45 and 0.35. for each water-to-cement ratio, seven concrete mixtures, including concrete without fiber, concrete containing 0.3%, 0.6% and 0.9% by volume fraction of steel and also glass fibers, were prepared. in all mixtures, only the effects of waterto-cement ratios, percentage of fibers, and the type of fibers were investigated. based on the experiences of the authors, the volume of the fibers is selected less than 1%. the reason is that the inhomogeneous spreading of fibers in concrete will occur when the percentage of fibers exceeds more than 1%. therefore, the volume fractions of the fibers were restricted to a maximum of 1% by volume fraction of fibers. to perform experimental tests for each water-cement ratio, for compressive strength 21 cubic specimens with dimensions of 100×100×100 mm, for tensile strength 14 cylindrical specimens with dimensions of 150×300 mm and flexural strength 14 prismatic specimens 100×100×500 mm are prepared in the laboratory environment. in this research, only the carboxylate superplasticizer was added in the concrete mixtures, and two types of fibers are used. for compressive strength astm c-39 [[28]], for tensile strength astm c-496 [[29]] and for flexural strength test, astm c-293-08 [[30]] standards are selected. materials and fibers properties he cement of the specimens is provided from the hekmatan cement factory in hamedan city. the water used in the mixtures was used from the hamedan drinking water distribution system with a ph equal to 6.5 and with a chloride ion concentration 0.013%. the superconductor polycarboxylate is added to mixtures for increasing the performance of the concrete. the range of polycarboxylate was between 0.20 to 1.50% by weight of the cement. sand is used with density and water absorption equal to 2.56 g/cm3 and 3.52%, respectively, according to the astm c-128 standard t t j. akbari et alii, frattura ed integrità strutturale, 54 (2020) 116-127; doi: 10.3221/igf-esis.54.08 118 [[31]]. fine aggregate (sand) with a 3.4 fineness modulus and coarse aggregate (gravel) with a maximum particle size of 19 mm were used in the specimens. according to the astm c-127 standard [[32]], density and water absorption of coarse aggregate equal to 2.684 g/cm3 and 1.01%, respectively. the mechanical properties of the steel and glass fibers are summarized in tab. 1. also, fig. 1 shows the shape and size of applied glass and steel fibers in this study. standard fiber shape diameter )3g/cm( diameter (mm) length (mm) l/d astm-a820 steel hooked-end 7.85 0.80 50 62.5 astm d790 glass straight 2.60 0.019 12 631.6 table 1: specifications of the steel fibers and glass figure 1: shape and geometry of steel fibers (left) and glass fibers (right). concrete mixing procedure ordinary portland cement (astm type 2), produced by the hekmatan cement factory, was used. additionally, coarse aggregate with the maximum particle size equal to 19 mm and also fine aggregate with a 3.4 fineness modulus was used in this research. the specific gravity and water absorption of the coarse and fine aggregates were 2.65 and 0.56%, and 2.61 and 1.92%, respectively. polycarboxylate with a commercial brand called lg is used in mixtures for increasing the workability of the concrete. hooked-end steel fibers with a length of 50 mm and a diameter of 0.80 mm were employed in this study. preparing of specimens & molding the trial and error approach was used for the mixing procedure, and it was chosen as follows: the binder and fine aggregates were mixed 70 seconds, and nearly half of the water and the superplasticizer were mixed for 150 seconds. the rest of the required water and coarse aggregate was added and then mixed for about 6 min. finally, selected fibers were added to the mixtures and then mixed for 6 min again to better mixing with concrete. the mixing procedure was designed to facilitate the spreading of the fibers in the mixtures. each type of fresh concrete was cast into cubic (100×100×100 mm), cylindrical (150×300 mm) and prismatic (100×100×500 mm) respectively. before de-molding, all specimens were stored at 023 c and 100% relative humidity for 24 2 hours. the concrete specimens were cured in lime-saturated water until testing. to convenient labeling to specimens, the name of each design is coded as follows: c refers to concrete; n is normal or plain concrete; s is steel fiber, and f is glass fiber. tab. 2 presents the labeling of the specimens in this research. there are seven different specimens in this research for each watertocement ratio. to perform the experimental tests for each watercement ratio, 21 cubic specimens for compressive strength, 14 cylindrical specimens for tensile strength test, and finally, 14 prismatic specimens for flexural strength test are designed. therefore, to conduct this research, 96 specimens are prepared. the proportion of required materials for w/c equal to 0.35 and 0.45. e.g., water, cement, sand, gravel, and also superplasticizer in the concrete mixtures are summarized in tab. 3. j. akbari et alii, frattura ed integrità strutturale, 54 (2020) 116-127; doi: 10.3221/igf-esis.54.08 119 code description cn normal concrete ( no fibers) csf0.3 concrete + 0.3% steel fiber csf0.6 concrete + 0.6% steel fiber csf0.9 concrete + 0.9% steel fiber cgf0.3 concrete + 0.3% glass fiber cgf0.6 concrete + 0.6% glass fiber cgf0.9 concrete +0.3% glass fiber table 2: labeling of the prepared specimens in this research. w/c cn csf0.3 csf0.6 csf0.9 cgf0.3 cgf0.6 cgf0.9 water (kg) 0.35 140 140 140 140 140 140 140 0.45 157.5 157.5 157.5 157.5 157.5 157.5 157.5 cement (kg) 0.35 400 400 400 400 400 400 400 0.45 350 350 350 350 350 350 350 sand (kg) 0.35 980 980 980 980 980 980 980 0.45 975 975 975 975 975 975 975 fine gravel 0.35 362 362 362 362 362 362 362 0.45 360 360 360 360 360 360 360 coarse gravel 0.35 561 561 561 561 561 561 561 0.45 559 559 559 559 559 559 559 fibers 0.35 23.5 23.5 23.5 23.5 23.5 23.5 0.45 23.5 47.1 70.6 8.4 16.8 25.2 superplastizer 0.35 0.40 0.80 1.40 2.00 1.20 1.60 2.20 0.45 0.35 0.53 1.05 1.05 0.70 0.88 1.23 table 3: concrete mixtures components (kg/m3) for w/c ratios equal to 0.35 and 0.45. compressive strength test the compressive strengths of the specimens were determined at the ages of 7 and 28 days, according to the mentioned standard. for this purpose, at each age, three cubic 100 × 100× 100 mm samples were used to report their mean compressive strength values. the specimens were cured in a water pond at a temperature of about 023 c until the age of testing. the adr 2000 hydraulic press machine with a capacity of 2000 kn with loading speed equal to 3 kn per second was used under the astmc39 standard [[28]] to determine the compressive strength. tensile strength test according to the astm-c496 standard [[29]], this experiment was performed at 28 days for cylindrical specimens with a diameter of 150 mm and a height of 300 mm. it should be noted that the adr hydraulic press machine with a capacity of 2000 kn and loading speed equal to 0.94 kn per second was used for this test (fig. 2). the splitting tensile strength is calculated from eq.(1). j. akbari et alii, frattura ed integrità strutturale, 54 (2020) 116-127; doi: 10.3221/igf-esis.54.08 120 2p t= πdl (1) where t is the splitting tensile strength (mpa), p is the maximum applied load (n), l is the distance between the supports (mm), and d is the sample diameter ( mm). figure 2: tensile strength test by the splitting method (left) and failure geometry of specimens (right). flexural strength test after currying of concrete containing glass and steel fibers at the age of 28-days, the flexural test of 100 × 100× 500 mm samples was carried out according to astm c-293-08 standard [[30]]. it should be noted that the gotech testing machine gt-tcs-2000 model is used for this text. the distance between the two supports was 300 mm for failing the specimen, and the rate of loading was 1 mm per minute. fig. 3 presents the flexural test and failure of the sample. figure 3: flexural three-point test (left) and failure of the sample (right) according to the astm c-293-08 standard [[30]], the flexural strength of specimens is obtained with eq.(2). j. akbari et alii, frattura ed integrità strutturale, 54 (2020) 116-127; doi: 10.3221/igf-esis.54.08 121 r 2 3pl f = 2bd (2) where rf refers to the failure strength (mpa), p is the maximum applied load by hydraulic jack (n), l is the distance between the supports (mm). parameters b and d are the average width and the effective depth of the sample at the moment of failure (mm), respectively. table 4: mechanical properties of designs for w/c equal to 0.35 and 0.45 at the ages of 7 and 28 days results n this section, according to tab. 4, the results of compressive, tensile, and flexural tests for steel and glass fibers in water to cement ratios equal to 0.35 and 0.45 are summarized. as well, the last four columns of tab. 4 refer to ratios of tensile to compressive and tensile to flexural strengths, respectively. hereafter, the results for all seven designs, according to tab. 2, are presented graphically for the age of 28 days only. the results for the age of 7 days could be followed in tab. 4. compressive strength fig. 4 demonstrates the results of the compressive tests for water to cement ratio equal to 0.35 and 0.45 at the ages of 28 days fig. 4 shows that at this age, for both water-to-cement ratios, increasing compressive strength for steel fiber is more than glass fiber. as well, adding steel fibers say up to 0.9% by volume fraction, increases the compressive strength, but adding glass fiber more than 0.6 % to 0.9% the strengths decrease. the reason for decreasing strength for glass fiber is the nonuniform dispersion of the fibers during mixing. besides, the figure reveals that steel fibers have a significant effect than glass fibers to increase the compressive strengths of all specimens. tensile strength fig. 5 depicts the tensile strength for the specimens at the age of 28 days for the water to cement ratios equal to 0.35 and 0.45. as can be seen from this figure, by adding steel and glass fibers in the range of 0.3% to 0.9% by volume of concrete, i cf (mpa) tf (mpa) rf (mpa) t c(f / f ) 100  t r(f / f ) 100 s am p le w /c 7-day 28day 7-day 28 days 7-day 28 days 7-day 28 days 7-day 28 days cn 0.35 22.84 37.12 1.88 3.03 3.05 4.91 8.2 8.2 62 62 0.45 21.61 30.88 1.67 2.49 2.51 3.96 7.7 8.0 50 63 csf0.3 0.35 32.20 45.36 2.26 3.41 3.75 5.31 7.0 7.5 60 64 0.45 26.17 37.93 1.74 2.76 2.81 4.30 6.7 7.3 62 64 csf0.6 0.35 34.81 50.44 2.62 3.91 4.74 7.38 7.5 7.8 55 53 0.45 29.73 41.29 2.14 3.06 4.15 5.85 7.2 7.4 52 52 csf0.9 0.35 38.32 53.81 3.12 4.46 5.94 8.48 8.1 8.3 53 53 0.45 32.31 45.51 2.66 3.52 4.88 6.78 8.2 7.7 55 52 cgf0.3 0.35 28.89 41.87 2.24 3.18 3.61 5.13 7.8 7.6 62 62 0.45 23.73 32.96 1.88 2.55 3.00 4.19 7.9 7.7 63 61 cgf0.6 0.35 30.66 42.59 2.76 3.75 4.61 6.26 9.0 8.8 60 60 0.45 22.92 32.22 2.13 2.89 3.66 5.07 9.3 9.0 58 57 cgf0.9 0.35 25.20 36.52 2.81 4.13 5.00 7.13 11.2 11.3 56 58 0.45 20.05 28.24 2.65 3.31 4.22 5.88 13.2 11.7 63 56 j. akbari et alii, frattura ed integrità strutturale, 54 (2020) 116-127; doi: 10.3221/igf-esis.54.08 122 the tensile strengths of all samples were gradually increased in both w/c ratios. the reason for increased tensile strength is that normal concrete is brittle, and adding fibers reduces the brittle behavior of concrete and also prevents crack propagation in the concrete. this figure illustrates that the effect of steel fiber is nearly similar to the effect of glass fiber to enhance the tensile strength in all specimens. for both fibers, adding steel and glass fibers up to 0.9% steadily increased the tensile strengths. figure 4: compressive strengths of specimens at the age of 28 days for w/c equal to 0.35 and 0.45. figure 5: comparison of tensile strength at the age of 28 days figure 6: ratios of the tensile strength of fiber-reinforced concrete to normal concrete j. akbari et alii, frattura ed integrità strutturale, 54 (2020) 116-127; doi: 10.3221/igf-esis.54.08 123 as well, fig. 6 illustrates the ratios of the tensile strength of concrete with fibers to plain concrete (without fiber) in both water to cement ratios at the age of 28 days. the figure shows that adding 0.9% steel fiber and glass fiber increase nearly 47% and 36% of tensile strength, respectively. as well, adding 0.3% and 0.9% fibers has the minimum and maximum effect on tensile strength in both w/c ratios, respectively. the graph reveals that adding fibers has a similar impact on strength increasing for both water-to cement-ratios. flexural strength fig. 7 displays the flexural strength of the designs in 28-day aging for water to cement ratios 0.35 and 0.45. as it is observed from fig. 8, by adding both steel and glass fibers in the range of 0.3% to 0.9% by volume fraction of concrete, the flexural strengths of the samples were steadily increased for both w/c ratios. additionally, the results show that the performance of steel fiber is better than glass fiber. figure 7: comparison of flexural strength of specimens at 28 days of aging as well, fig. 8 exhibits the ratios of flexural strengths of fiber-concrete to plain concrete (without fiber) in both water-tocement ratios. the figure shows that adding 0.9% steel fiber and glass fiber increase nearly 73% and 49% of flexural strength, respectively. as well, adding 0.3% and 0.9% fibers has the minimum and maximum effect on flexural strength in both w/c ratios, respectively. the graph reveals the effect of water-to cement-ratio has no significant impact on the increase of flexural strengths in specific concrete containing fiber with respect to plain concrete. for example, consider ratios 1.73 with 1.71 in csf0.9 specimen. the graph reveals that steel fibers have more influence than glass fiber in increasing the flexural strength. for instance, compare the numbers 1.73 and 1.71 for csf0.9 with 1.45 and 1.49 for cgf0.9. figure 8: ratios of flexural strengths of fiber-reinforced concrete to plain concrete the effect of the reduction of water to cement ratio for increasing flexural strength is investigated in fig. 9. according to the flexural test results, as shown in fig. 8, the effect of fibers in comparison with water to cement ratio is more important j. akbari et alii, frattura ed integrità strutturale, 54 (2020) 116-127; doi: 10.3221/igf-esis.54.08 124 in the enhancement of flexural strengths. as shown in fig. 9, the flexural strength ratio of fiber concrete with water to cement ratio of 0.35 to 0.45 was investigated. as seen from this figure, usually by reduction of water-to-cement from 0.45 to 0.35 in all designs, more than 24% increasing in flexural strengths are observed. on the other hand, with a reduction of 0.10 in water-to cement ration, an average increasing 24 % ( mean ratios in fig. 9) in flexural strength is observed. figure 9: effect of ratios of w/c=0.35 and w/c =0.45 in increasing flexural strengths relation of tensile strength with compressive strength the tensile strength of concrete is expressed as a percentage of the compressive strength. this percentage is usually reported in the range of 8% to 15%. in this study, the ratio of tensile strength to compressive strength at the age of 28-day plain and fiber concrete is presented in fig. 10. figure 10: ratios of tensile strength to compressive strength at the age of 28-day. as can be seen from fig.10, the mean ratio of tensile strength to compressive strength is about 8.5% for w/c equal to 0.35 and 8.3% for w/c equal to 0.45. however, in glass fiber concrete with 0.9% fiber (cgf0.9), this ratio has been reached 11%. therefore, in practical application, the lower bond value 8% is preferable than the upper bond value of 15%. as a result, as a practical application, confidently equation t cf 0.08f  is recommended. in which tf is tensile strength and cf  is the compressive strength of plain and reinforced concrete for the age of 28 days. as well, the ratios of tensile strengths to flexural strengths for seven designs at the age of 28 days in water to cement ratios equal to 0.35 and 0.45 illustrated in fig. 11. as can be seen from fig.11, the mean ratio of tensile strength to flexural strength is about 60% for both w/c equal to 0.35 and 0.45. however, in steel fiber concrete with 0.6% and 0.9% fibers (csf0.6, csf0.9), this ratio has been reached the j. akbari et alii, frattura ed integrità strutturale, 54 (2020) 116-127; doi: 10.3221/igf-esis.54.08 125 lowest value equal to 52%. for both fibers, in 0.3%, the ratios of tensile strength to flexural strength are in the highest value of about 62%. as an approximate estimation, we can say r tf 1.60f and r cf 0.13f  .   figure 11: ratios of tensile strength to flexural strength at the age of 28 days     conclusions n the present paper, the behavior of plain and fiber-reinforced concretes is experimentally studied. the effects of waterto-cement and steel and glass fibers on compressive, tensile, and flexural strengths were investigated. according to the results of this study, the following conclusions could be drawn;  the presence of steel fibers in concrete with 0.3% to 0.9% fraction volume of concrete increases the compressive, tensile, and flexural strengths for both watertocement ratios. glass fibers only increase compressive strength in the range of 0.3% to 0.6% and using more than this value decreases compressive strength. by increasing glass fibers up to 0.9%, tensile and flexural strengths are also increased.  the steel fibers have better performance in comparison with glass fibers in all cases. therefore, based on the results of this study, the authors suggest that adding steel fiber is preferable than adding glass fiber. if, for any reason, the fibers are not available, the reduction of water-to-cementratio is recommended instead of adding fibers to improve the mechanical properties of concrete.  using concrete containing steel fibers is preferable than glass fibers due to the lack of water absorption and the proper spreading of steel fibers.  the tensile strength and flexural strength of concrete could be approximately explained as 8% and 13% of compressive strength, respectively. in practical applications, for designers t cf 0.08 * f  and r cf 0.13 * f  is recommended conflicts of interest here is no conflict of interest to declare. references [1] aci committee 544 (1996), state-of-the-art report on fiber-reinforced concrete, report 544.1r-96 american concrete institute, detroit. i t j. akbari et alii, frattura ed integrità strutturale, 54 (2020) 116-127; doi: 10.3221/igf-esis.54.08 126 [2] patil, t. r., & burile, a. n. (2013). comparative study of steel and glass fiber reinforced concrete composites. international journal of science and research, 5(5), pp. 690-694. [3] kaikea, a., achoura, d., duplan, f., & rizzuti, l. (2014). effect of mineral admixtures and steel fiber volume contents on the behavior of high-performance fiber reinforced concrete. materials & design, 63, pp. 493-499. [4] wille, k., tue, n. v., & parra-montesinos, g. j. (2014). fiber distribution and orientation in uhp-frc beams and their effect on backward analysis. materials and structures, 47(11), pp. 1825-1838. [5] nili, m., azarioon, a., danesh, a., & deihimi, a. (2018). experimental study and modeling of fiber volume effects on frost resistance of fiber reinforced concrete. international journal of civil engineering, 16(3), pp. 263-272. [6] liu, h. d., yu, x. z., & li, g. w. (2005). experimental study on tensile mechanical properties of glass fiber reinforced plastic rebar. chinese journal of rock mechanics and engineering, 20. [7] ganesan, n., indira, p. v., & santhakumar, a. (2014). influence of steel fibers on tension stiffening and cracking of reinforced geopolymer concrete. magazine of concrete research, 66(6), pp. 268-276. [8] ashour, s. a., hasanain, g. s., & wafa, f. f. (1992). shear behavior of high-strength fiber reinforced concrete beams. structural journal, 89(2), pp. 176-184. [9] kwak, y. k., eberhard, m. o., kim, w. s., & kim, j. (2002). shear strength of steel fiber-reinforced concrete beams without stirrups. aci structural journal, 99(4), pp. 530-538. [10] soutsos, m. n., le, t. t., & lampropoulos, a. p. (2012). flexural performance of fiber-reinforced concrete made with steel and synthetic fibers. construction and building materials, 36, pp. 704-710. [11] aldossari, k. m., elsaigh, w. a., & shannag, m. j. (2014). effect of steel fibers on flexural behavior of normal and high strength concrete. international journal of civil and environmental engineering, 8(1), pp. 22-26. [12] wille, k., & parra-montesinos, g. j. (2012). effect of beam size, casting method, and support conditions on flexural behavior of ultra-high-performance fiber-reinforced concrete. aci materials journal, 109(3), 379. [13] meng, w., & khayat, k. h. (2016). experimental and numerical studies on the flexural behavior of ultrahighperformance concrete panels reinforced with embedded glass fiber-reinforced polymer grids. transportation research record, 2592(1), pp. 38-44. [14] kushartomo, w., & ivan, r. (2017). effect of glass fiber on compressive, flexural and splitting strength of reactive powder concrete. in matec web of conferences, 138, p. 03010. [15] chalioris, c. e. (2013). the analytical approach for the evaluation of minimum fiber factor required for steel fibrous concrete beams under combined shear and flexure. construction and building materials, 43, pp. 317-336. [16] yoo, d. y., kang, s. t., & yoon, y. s. (2014). effect of fiber length and placement method on flexural behavior, tension-softening curve, and fiber distribution characteristics of uhpfrc. construction and building materials, 64, pp. 67-81. [17] sivakumar, a., & santhanam, m. (2007). mechanical properties of high strength concrete reinforced with metallic and non-metallic fibers. cement and concrete composites, 29(8), 603-608. [18] xu, b. w., & shi, h. s. (2009). correlations among mechanical properties of steel fiber reinforced concrete. construction and building materials, 23(12), pp. 3468-3474. [19] chandramouli, k., srinivasa, r. p., pannirselvam, n., seshadri, s. t., & sravana, p. (2010). strength properties of glass fiber concrete. arpn journal of engineering and applied sciences, 5(4), pp. 1-6. [20] nili, m., & afroughsabet, v. (2010). the effects of silica fume and polypropylene fibers on the impact resistance and mechanical properties of concrete. construction and building materials, 24(6), pp. 927-933. [21] bhikshma, v., & manipal, k. (2012). study on mechanical properties of recycled aggregate concrete containing steel fibers. [22] etcheverry, m., & barbosa, s. e. (2012). glass fiber reinforced polypropylene mechanical properties enhancement by adhesion improvement. materials, 5(6), pp. 1084-1113. [23] kamal, m. m., safan, m. a., etman, z. a., & kasem, b. m. (2014). mechanical properties of self-compacted fiber concrete mixes. hbrc journal, 10(1), pp. 25-34. [24] ashik, k. p., & sharma, r. s. (2015). a review of the mechanical properties of natural fiber reinforced hybrid polymer composites. journal of minerals and materials characterization and engineering, 3(05), 420. [25] saba, n., paridah, m. t., & jawaid, m. (2015). mechanical properties of kenaf fiber reinforced polymer composite: a review. construction and building materials, 76, pp. 87-96. [26] ibrahim, k. i. m. (2016). mechanical properties of glass fiber reinforced concrete (gfrc). journal of mechanical and civil engineering, 13(4). [27] ahmadi, m., farzin, s., hassani, a., & motamedi, m. (2017). mechanical properties of the concrete containing recycled fibers and aggregates. construction and building materials, 144, pp. 392-398. j. akbari et alii, frattura ed integrità strutturale, 54 (2020) 116-127; doi: 10.3221/igf-esis.54.08 127 [28] astm international. astm c39. (2010). standard test method for compressive strength of cylindrical concrete specimens. [29] astm international. astm c496. (2011). test method for splitting tensile strength of cylindrical concrete specimens. [30] astm international. astm c293-08 (2008). standard test method for flexural strength of concrete (using simple beam white center-point loading). [31] astm international. (2012). astm c128: standard test method for density, relative density (specific gravity), and absorption of fine aggregate. [32] astm international. 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/hrv (za stvaranje adobe pdf dokumenata najpogodnijih za visokokvalitetni ispis prije tiskanja koristite ove postavke. stvoreni pdf dokumenti mogu se otvoriti acrobat i adobe reader 5.0 i kasnijim verzijama.) /hun 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can be opened with acrobat and adobe reader 5.0 and later.) >> /namespace [ (adobe) (common) (1.0) ] /othernamespaces [ << /asreaderspreads false /cropimagestoframes true /errorcontrol /warnandcontinue /flattenerignorespreadoverrides false /includeguidesgrids false /includenonprinting false /includeslug false /namespace [ (adobe) (indesign) (4.0) ] /omitplacedbitmaps false /omitplacedeps false /omitplacedpdf false /simulateoverprint /legacy >> << /addbleedmarks false /addcolorbars false /addcropmarks false /addpageinfo false /addregmarks false /convertcolors /converttocmyk /destinationprofilename () /destinationprofileselector /documentcmyk /downsample16bitimages true /flattenerpreset << /presetselector /mediumresolution >> /formelements false /generatestructure false /includebookmarks false /includehyperlinks false /includeinteractive false /includelayers false /includeprofiles false /multimediahandling /useobjectsettings /namespace [ (adobe) (creativesuite) (2.0) ] /pdfxoutputintentprofileselector /documentcmyk /preserveediting true /untaggedcmykhandling /leaveuntagged /untaggedrgbhandling /usedocumentprofile /usedocumentbleed false >> ] >> setdistillerparams << /hwresolution [2400 2400] /pagesize [612.000 792.000] >> setpagedevice microsoft word numero_40_art_5 a. kyriazopoulos, frattura ed integrità strutturale, 40 (2017) 52-60; doi: 10.3221/igf-esis.40.05 52 focussed on recent advances in “experimental mechanics of materials” in greece acoustic emissions and electric signal recordings, when cement mortar beams are subjected to three-point bending under various loading protocols a. kyriazopoulos laboratory of electronic devices and materials, technological educational institute of athens, 12210, athens, greece. akyriazo@teiath.gr abstract. two experimental techniques are used study the response of cement mortar beams subjected to three-point bending under various loading protocols. the techniques used are the detection of weak electric current emissions known as pressure stimulated currents and the acoustic emissions (in particular, the cumulative ae energy and the b-value analysis). patterns are detected that can be used to predict upcoming fracture, regardless of the adopted loading protocol in each experiment. the experimental results of the ae and psc techniques lead to the conclusion that when the calculated ib values decrease, the psc starts increasing strongly. keywords. pressure stimulated currents; acoustic emissions; cement mortar; three point bending; b-value. citation: kyriazopoulos, a., acoustic emissions and electric signal recordings, when cement mortar beams are subjected to three point bending under various loading protocols, frattura ed integrità strutturale, 40 (2017) 52-60. received: 05.01.2017 accepted: 26.02.2017 published: 01.04.2017 copyright: © 2017 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. introduction he mechanical behavior and the evolution of damage in heterogeneous materials under compressive loading are of great interest in a wide range of application fields. particularly, the service life of cement-based structures deteriorates due to heavy loads, fatigue, aging and natural disasters. accordingly, diagnostic methods for damage assessment have been developed and implemented, aiming to assess the impending failure. to this end, the acoustic emissions (ae) technique was developed and is being improved continuously in order to provide a useful tool for monitoring and understanding the mechanisms of dynamic processes, but also for warning of upcoming failure [1]. acoustic emission events occur due to sudden release of mechanical energy in the form of short mechanical vibrations due to the fact that a material is under mechanical loading. this mechanical vibration travels in the form of spherical waveforms through the material’s bulk. the ae event analysis is used to estimate the damage degree when brittle materials such as concrete and rocks are subjected to mechanical loading [2-5]. acoustic emission (ae) due to crack growth in brittle materials is usually observed in the high frequency range, typically between 50 khz and 800 khz. ae are recorded even from the early stages of the damage process. during the fracture process in quasi-brittle materials, the micro cracks formation and growth are manifested by a number of ae events released at different amplitudes. it has been shown that as a specimen under mechanical loading approaches failure, there is t a. kyriazopoulos, frattura ed integrità strutturale, 40 (2017) 52-60; doi: 10.3221/igf-esis.40.05 53 an increase in the ae activity rate, as a result of the deterioration of the mechanical properties. particularly in cement based materials and concrete structures the ae testing is one of the most widely used methods for monitoring crack growth [1]. another phenomenon related to the micro-crack growth in quasi-brittle nonmetallic materials is the production of electric charges that shape electric dipoles forming a rather complicated charge system [6-8]. such electric dipoles produce an electric potential across a crack resulting in the appearance of an electric current [9]. such currents have been measured in both laboratory [7, 10] and at a geodynamic scale [11] and their detection may be useful as a precursor of a fracture. these electrical signals (weak electrical current emissions) are detected using a novel experimental technique, called pressure-stimulated currents technique, and the recorded electrical currents are described by the term pressure stimulated currents (psc) [12]. the psc’s are weak electric currents detected with sensitive electrometers when a pair of electrodes is attached at proper locations on the specimen that is subjected to mechanical stress. initially, the psc technique was applied when rock specimens like marble [6, 13] and amphibolite [14] were subjected to compressive axial stress increasing up to failure. consequently, it was successfully applied to cement-based materials [15, 16]. the psc technique was also tested during laboratory experiments of three-point bending (3pb) tests on marble [17] and cementbased specimens [5]. the psc technique has been adopted by several researchers [9, 18], while others use similar techniques [19-21]. both ae and psc signals provide important information about the damage processes occurring in specimens under compression or under bending tests. in particular, the pscs show a considerable increase when the applied load reaches the vicinity of failure and attain their peak value shortly before failure [12, 13, 15, 16]. in acoustic emissions one of the statistical parameters, which is often used to estimate a critical situation, is the b-value [1, 22, 23], which exhibits systematic variations during the different stages of fracture processes. the ae based b-value analysis and the variation of the b-value, have attracted researchers working in the engineering field [23, 24]. other ae statistical parameters that have been used include the event and energy release rates, the cumulative energy and the ring down counts. in this paper attention is focused on the parallel presentation of ae and psc detected during 3pb of cement mortar specimens. the main difference between the three experiments is the loading mode. specifically, one test was conducted under a constant loading rate (i.e. linear load increase) up to fracture while at the other two experiments the load was increasing according to a non-linear mode. experimental details he specimens used for the experiments were prismatic cement mortar beams with dimensions 250x50x50 mm3. their bending strength (lf) varied from 3.5kn to 4.0kn. details regarding the specimens, the preparation process and the experimental apparatus can be found in a previous work [25]. contrary to previous publications [25], the electrodes that were used to capture the psc emissions were placed as shown in fig. 1, i.e. on the lower side of the beam (tension zone) and at the left and right sides, symmetrically with respect to the specimen’s central cross section where the load is applied. this topology was decided after several experiments conducted in order to estimate the best installation process that ensures the recording of strong pscs and limits the influence of electric noise. the best electrode distance ( ) was also investigated and it was empirically found that for the specific type of experiments it should be  / 5 , where  is the distance between the two rigid metallic cylindrical rods used to support the cement beam. the psc was captured by the electrodes and measured using a high sensitivity electrometer (keithley, model 6517). the data were recorded in real time and stored on a hard disk through a gpib interface. the mechanical load applied was recorded with the use of an analog-to-digital (a/d daq) data acquisition device (keithley model kusb-3108). the whole setup was placed in a faraday shield in order to avoid interference from external electrical noise. the system that was used to detect and record the ae is the 2-channel pci-2 ae acquisition system (physical acoustics corp). the r15a sensor (manufactured by pac, resonant at 75 khz) was placed in the middle of the beam (see fig. 1) in order to focus on the region of the crack development processes that take place due to the externally applied bending load. the sensor was coupled to the test specimen using vacuum grease. preamplifier was used along with the sensor with gain set at 40db. the signals were band-pass filtered between 20-400 khz using the software control of the data acquisition system. to set the threshold value for recording and to ensure that sensors were correctly performing, pencil lead breaks (5mm, hb leads) were carried out near the crack tip and the recorded signals were observed. the value of 40db was selected since it was found to prevent the recording of lower amplitude reflected signals from the pencil lead break tests. for the detected ae data processing the physical acoustics corp. noesis software was used. t a. kyriazopoulos, frattura ed integrità strutturale, 40 (2017) 52-60; doi: 10.3221/igf-esis.40.05 54 figure 1: the experimental installation and the location of the ae and psc sensors. results and discussion ab. 1 includes all the details regarding the loading protocol of each specimen for the three experiments implemented, i.e. load (l) vs. time (t), considering that the function is best described as:      21 2l t c t c t (1) where 1c and 2c are constants. during the first experiment (i.e. specimen cb01) a linear increase of the load was conducted at a rate of 100n/s while the two following experiments were conducted following a non-linear increase of the mechanical load (see tab. 1). specimen      21 2l t c t c t lf (kn) pscpeak (pa) qt (pc) αε hits cum. energy ae cb01 =0, =+100n/s 3.6 28.8 294 1062 5.17x107 aj cb02 =-7.3n/s2, =+333n/s 3.8 27.2 298 543 4.50x107 aj cb03 =+0.7n/s2, =35.4n/s 3.5 29.9 291 893 4.98x107 aj table 1. the characteristics of the loading protocol followed during each of the three experiments conducted and the main quantities studied regarding the psc and ae recordings. fig. 2 shows the temporal variation of the emitted psc from the three experiments, as well as the corresponding behavior of the mechanical load. shortly before failure of the specimens the emitted psc tends to show a peak. the recorded peak value (pscpeak) is similar in all three experimental loading protocols (see tab. 1). the fact that the psc is maximized before the failure of the cement mortar beam has been systematically observed during compressive stress tests on both cement based [15] and rock [26, 27] materials. this behavior is best demonstrated by the specimen cb02. this is attributed to the fact that the specimen approaches failure at the lowest load rate (see blue lines in fig. 2). the level of the bending load, for which the psc signal begins to show an intense and continuous increase, irrespectively of the loading mode, is estimated to be at approximately 60% of the ultimate 3pb strength (lf) (see fig. 3), in all three experiments. as a next step, it is interesting to consider the total electric charge ( tq ), released during the three experiments up to failure. the tq was calculated using the relation ( ft is the failure time). t a. kyriazopoulos, frattura ed integrità strutturale, 40 (2017) 52-60; doi: 10.3221/igf-esis.40.05 55    0 t f tq psc t dt (2) it is worth mentioning that the total electric charge for the three different loading modes reaches almost the same value (see tab. 1). in a previous work [13], during compressive stress application on marble specimens it was theoretically supported and experimentally proven [28] that the total electric charge value does not depend on the applied mechanical stress rate. this behavior is verified experimentally herein when cement mortar specimens are subjected to 3pb loading. figure 2: the time variation of the applied 3pb load and the corresponding time variation of the psc, during all three experiments conducted. figure 3: psc versus normalized load (l/lf) for all three experiments conducted. regarding the ae recordings, during the three experiments, a different number of ae hits was recorded (see tab. 1). the micro-cracks generated during loading are of different sizes and therefore different ae amplitudes are recorded. a common way of obtaining quantitative information from the above statements is by computing the b-value of ae using the methods adopted in seismology [29, 30]. the b-value is defined as the log-linear slope of the frequency–magnitude distribution of ae [31]. in the present study, the b-values were calculated by applying a method that is known as improved b-value (ib) analysis after shiotani et al. [32]. the ib-value is defined as:                      1 2 1 2 log log b n n i (3) 0 1 2 3 4 0 10 20 30 40 50time (s) lo a d  ( k n ) 0 5 10 15 20 25 30 p s c  ( p a ) cb01 cb02 cb03 0 5 10 15 20 25 30 0 0.2 0.4 0.6 0.8 1 l / lf p s c  ( p a ) cb01 cb02 cb03 a. kyriazopoulos, frattura ed integrità strutturale, 40 (2017) 52-60; doi: 10.3221/igf-esis.40.05 56 where,  is the standard deviation of the magnitude distribution in one group of events,  is the mean value of the magnitude distribution in the same group of events, and 1 as well as 2 are constants, for which usually a value equal to 1 is adopted [1]. in order to highlight the variability of the bi -value, during the three experiments, the b-value analysis of αε is, in general, applied to a certain number of events, as follows: from event 1 to n, then from event 2 to n+1, and so on. the determination of the value of n has been considered by shiotani et al. [32] and colombo et al. [22], since it constitutes a parameter that can influence the results. a value exceeding n=50 is assumed to be a satisfactory one. in the present study, n=70 has been selected. each value of bi was calculated from a group of the events 1 to 70, consequently from 2 to 71, and so on. each calculated bi value is associated to the time of the 70th event of each group and to that of the corresponding value of normalized (l/lf) load. the variability of the bi -value during the three experiments with respect to the normalized (l/lf) load is shown in fig. 4. in the same figure the corresponding variation of psc signals is also presented. figure 4: variation of bi -values and psc signals vs. normalized load (l/lf) for the three conducted experiments. cb01 0 10 20 30 0 0.2 0.4 0.6 0.8 1 l/lf p s c  ( p a ) 0.0 0.5 1.0 1.5 2.0 2.5 3.0 ib ‐v a lu e cb02 0 10 20 30 0 0.2 0.4 0.6 0.8 1 l/lf p s c  ( p a ) 0.0 0.5 1.0 1.5 2.0 2.5 ib  ‐  v a lu e cb03 0 10 20 30 0 0.2 0.4 0.6 0.8 1 l/lf p s c  ( p a ) 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 ib  ‐  v a lu e a. kyriazopoulos, frattura ed integrità strutturale, 40 (2017) 52-60; doi: 10.3221/igf-esis.40.05 57 it is obvious that during the early stages (l<0.6lf approximately), the -values show an almost constant increase indicating the prevalence of micro-cracking [33]. in these stages the psc signal is low, showing a slight increase (see fig. 4). then, at the following stages (l>0.6lf) -values show an intense reduction combined with a sharp increase of the psc. this behavioral change in the variability of the -value is observed at a critical normalized load value [l/lf]c ≈ 0.6, for all three experiments. as it is marked in fig. 4 (dotted arrows), the exact value [l/lf]c is 0.55, 0.62 and 0.70 for specimens cb01, cb02 and cb03, respectively. it seems that increasing the rate of the applied bending load the increase of the psc signal and the corresponding reduction of -values are recorded earlier. it should be pointed out that the value fluctuation, which is observed in all three experiments at the early stage, is related to the fact that the micro-cracks begin to form randomly. moreover, in all three experiments, attains values around 1 during the last seconds before the failure of the specimens, which is indicative of the final formation of a localized macro-crack. figure 5: the cumulative ring down count of αε hits vs. normalized load (l/lf) for the three conducted experiments. the ring down count (rdc) data was also used, since it is a measure of the number of ae waveform oscillations through a preset voltage threshold [1]. in order to highlight the identification and assessment of important stages of micro-crack damage in a cement mortar material, a common practice has been followed to examine the cumulative ring down count σ(rdc) and energy (σe). these results are illustrated in figs. 5 and 6 with respect to the normalized load (l/lf). in all three experiments an almost constant increase in σ(rdc) was initially observed, related to the initiation of new microcracks. for l/lf > [l/lf]c the σ(rdc) increases at a rate indicating the development of severe damage in the specimen. concurrently, an abrupt increase of the psc signal is observed. figure 6: (a) the cumulative ae energy vs. normalized load (l/lf) for the three experiments and (b) a detailed view close to the fracture load. 0.e+00 2.e+03 4.e+03 6.e+03 8.e+03 1.e+04 0 0.2 0.4 0.6 0.8 1 l/lf σ  ( rd c) cb02 cb01 cb03 a. kyriazopoulos, frattura ed integrità strutturale, 40 (2017) 52-60; doi: 10.3221/igf-esis.40.05 58 finally, the cumulative energy of the ae hits up to the fracture of the specimens for all three experiments versus the normalized load level (l/lf) is plotted in fig. 6a. a significant step-up increase of the cumulative ae energy is observed slightly before the failure of the specimens (see the detailed view in fig. 6b). the corresponding values of the cumulative energy practically start to converge (see tab. 1). concluding remarks he application of 3pb loading under various protocols regarding the bending load rate on cement mortar beams causes the emission of electric currents (psc) that show a clearly deterministic behavior. the total electric charge recorded during each experimental procedure is practically of similar value for all three experiments. it may be concluded that the corresponding behavior of the studied ae parameters is also similar. micro-cracks generate a sufficient number of weak acoustic emissions leading to a relatively high b-value. when increasing load levels, the fracture process moves from microto macro-cracking and the ib-value decreases. a distinct correlation between the psc and the calculated ib values is observed. specifically, when ib-values are relatively high and tend to increase, the psc signals also exhibit a smooth increase. when ib-values progressively decrease, the psc signals show intense increase, indicating that psc emissions are mainly attributed to crack formation and propagation. the peak of the psc signals is another clear indication of the upcoming failure. finally, the damage initiation is also verified by the study of the cumulative ring down count. the qualitative similarity of the results of the present protocol with recently published ones for natural stones and especially for dionysos marble [17], which is the material extensively used for the restoration of marble monuments in greece [34-38], supports further the potential use of the psc technique for in-situ monitoring the response of restored structural elements of masterpieces of cultural heritage. references [1] rao, m.v.m.s., lakschmi, p.k.j. analysis of b-value and improved b-value of acoustic emissions accompanying rock fracture. current science, 89 (2005) 1577-1582. [2] aggelis d.g., mpalaskas a.c., matikas t.e., investigation of different fracture modes in cement-based materials by acoustic emission, cement and concrete research, 48 (2013) 1–8 [3] stanchits, s., dresen, g., vinciguerra, s., ultrasonic velocities, acoustic emission characteristics and crack damage of basalt and granite, pure applied geophys,163 (2006) 5–6, 975–994 [4] lockner, d., the role of acoustic emission in the study of rock fracture. int. j. rock mech. min. sci. geomech. abstr., 30 (1993) 883–899. [5] stergiopoulos, c., stavrakas, i., hloupis, g., hloupis, d., triantis, vallianatos, f., electrical and acoustic emissions in cement mortar beams subjected to mechanical loading up to fracture, engineering failure analysis, 35 (2013) 454461. [6] stavrakas, ι., anastasiadis, c., triantis, d., vallianatos, f., piezo stimulated currents in marble samples: precursory and concurrent – with – failure signals, natural hazards and earth system sciences, 3 (2003) 243-247. [7] vallianatos, f., triantis, d., tzanis, a., anastasiadis, c., stavrakas, i., electric earthquake precursors: from laboratory results to field observations, physics and chemistry of the earth, 29 (2004) 339-351. [8] varotsos, p.a., sarlis, n.v., skordas, e.s., long-range correlations in the electric signals that precede rupture, phys. rev. e, 66 (2002) 011902. [9] cartwright-taylor, a., vallianatos, f., sammonds, p., superstatistical view of stress-induced electric current fluctuations in rocks, physica a: statistical mechanics and its applications, 414 (2014) 368–377. [10] frid, v., goldbaum, j., rabinovitch, a., bahat, d., electric polarization induced by mechanical loading of solnhofen limestone, phil. mag. lett., 89 (7) (2009) 453–463 [11] varotsos, p.a., the physics of seismic electric signals, terrapub (2005) [12] stavrakas, ι., triantis, d., agioutantis, z., maurigiannakis, s., saltas, v., vallianatos, f., pressure stimulated currents in rocks and their correlations with mechanical properties, natural hazards and earth system sciences, 4 (2004) 563567. [13] triantis, d., stavrakas, i., anastasiadis, c., kyriazopoulos, a., vallianatos, f., an analysis of pressure stimulated currents (psc), in marble samples under mechanical stress, physics and chemistry of the earth, 31 (2006) 234-239. t a. kyriazopoulos, frattura ed integrità strutturale, 40 (2017) 52-60; doi: 10.3221/igf-esis.40.05 59 [14] triantis, d., anastasiadis, c., vallianatos, f., kyriazis, p., nover, g., electric signal emissions during repeated abrupt uniaxial compressional stress steps in amphibolite from ktb drilling, natural hazards & earth system sciences, 7 (2007) 149-154. [15] kyriazopoulos, a., anastasiadis, c., triantis, d., brown, j. c, non-destructive evaluation of cement-based materials from pressure-stimulated electrical emission preliminary results, construction and building materials, 25 (2011) 1980-1990. [16] triantis, d., stavrakas, i., kyriazopoulos, a., hloupis, g., agioutantis, z., pressure stimulated electrical emissions from cement mortar used as failure predictors, international journal of fracture, 175 (2012) 53-61. [17] stavrakas, i., pasiou, e.d., hloupis, g., malliaros, g.-t., triantis, d., kourkoulis, s.k., exploring the size effect of marble by combined use of pressure stimulated currents and acoustic emission, in: beskos d.e., stavroulakis g.e. (eds.), 10th hstam international congress on mechanics, chania, hellas, (2013) 185-186. [18] li, z., enyuan, w., miao, h., laboratory studies of electric current generated during fracture of coal and rock in rock burst coal mine, journal of mining, 2015 (2015) id 235636. [19] sun, m., liu, q., li, z., wang, e. electrical emission in mortar under low compressive loading. cement and concrete research, 32 (2002) 47–50. [20] archer, j. w., dobbs, m. r., aydin, a., reeves, h. j., & prance, r. j., measurement and correlation of acoustic emissions and pressure stimulated voltages in rock using an electric potential sensor. international journal of rock mechanics and mining sciences, 89 (2016) 26-33. [21] dann, d., demikhova, a., fursa, t., kuimova, m., research of electrical response communication parameters on the pulse mechanical impact with the stress–strain state of concrete under uniaxial compression, iop conf. series: materials science and engineering, 66 (2014) 012036. doi:10.1088/1757-899x/66/1/012036 [22] colombo, s., main, i., g., forde, m. c., assessing damage of reinforced concrete beam using ‘‘b-value’’ analysis of acoustic emission signals. j. mat. civil eng. (asce), 15 (2003) 280-286. [23] vidya sagar, r., prasad, rv., raghu prasad, b.k., rao, m.v.m.s., microcracking and fracture process in cement mortar and concrete: a comparative study using acoustic emission technique. experimental mechanics, 53 (2013) 1161–1175. [24] vidya sagar, r., raghu prasad, b.k., shantha kumar, s., an experimental study on cracking evolution in concrete and cement mortar by the b-value analysis of acoustic emission technique, cement and concrete research, 42 (2012) 10941104. [25] stergiopoulos, c., stavrakas, i., hloupis, g., triantis, d., vallianatos, f., electrical and acoustic emissions in cement mortar beams subjected to mechanical loading up to fracture, engineering failure analysis, 35 (2013) 454–461. [26] anastasiadis, c., stavrakas, i., triantis, d., vallianatos, f., correlation of pressure stimulated currents in rocks with the damage variable, annals of geophysics, 50 (2007) 1-6. [27] vallianatos, f., triantis, d., scaling in pressure stimulated currents related with rock fracture, physica a, 387 (2008) 4940-4946. [28] triantis, d., anastasiadis, c., stavrakas, i., the correlation of electric charge with strain on stressed rock samples, natural hazards and earth system sciences, 8 (2006) 1243-1248. [29] scholz, c. h., the frequency–magnitude relation of microcracking in rock and its relation to earthquakes. bull. seis. soc. am., 58 (1968) 399–415. [30] aki, k., maximum likelihood estimates of b in the formula logn = a – bm and its confidence limits. bull. earthquake res. inst., tokyo univ., 43 (1965) 237–239. [31] main, i. g., meredith, p. g. and jones, c., a reinterpretation of the precursory seismic b-value anomaly from fracture mechanics. geophys. j., 96 (1989) 131–138. [32] shiotani, t., yuyama s., li, z. w., ohtsu, m. application of the ae improved b-value to qualitative evaluation of fracture process in concrete materials, j. acoust. emission, 19 (2001) 118–132. [33] rouchier, s., foray, g., godin, n., woloszyn, m., roux, j.-j. damage monitoring in fibre reinforced mortar by combined digital image correlation and acoustic emission, construction and building materials, 38 (2012) 371-380. [34] kourkoulis, s.k., ganniari-papageorgiou, e., mentzini, m., dionysos marble under bending: α contribution towards understanding the fracture of the parthenon architraves, engineering geology, 115 (3-4) (2010) 246-256. [35] kourkoulis, s.k., prassianakis, i., agioutantis, z., exadaktylos, g.e., reliability assessment of the ndt results for the internal damage of marble specimens, international journal of material and product technology, 26(1/2) (2006) 3556. [36] kourkoulis, s.k., exadaktylos, g.e., vardoulakis i., u-notched dionysos-pentelicon marble in three point bending: the effect of nonlinearity, anisotropy and microstructure, international journal of fracture, 98(3-4) (1999) 369-392. a. kyriazopoulos, frattura ed integrità strutturale, 40 (2017) 52-60; doi: 10.3221/igf-esis.40.05 60 [37] exadaktylos, g.e., vardoulakis, i., kourkoulis s.k., influence of nonlinearity and double elasticity on flexure of rock beams – ii. characterization of dionysos marble, international journal of solids and structures, 38(22-23) (2001) 41194145. 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can be opened with acrobat and adobe reader 5.0 and later.) >> /namespace [ (adobe) (common) (1.0) ] /othernamespaces [ << /asreaderspreads false /cropimagestoframes true /errorcontrol /warnandcontinue /flattenerignorespreadoverrides false /includeguidesgrids false /includenonprinting false /includeslug false /namespace [ (adobe) (indesign) (4.0) ] /omitplacedbitmaps false /omitplacedeps false /omitplacedpdf false /simulateoverprint /legacy >> << /addbleedmarks false /addcolorbars false /addcropmarks false /addpageinfo false /addregmarks false /convertcolors /converttocmyk /destinationprofilename () /destinationprofileselector /documentcmyk /downsample16bitimages true /flattenerpreset << /presetselector /mediumresolution >> /formelements false /generatestructure false /includebookmarks false /includehyperlinks false /includeinteractive false /includelayers false /includeprofiles false /multimediahandling /useobjectsettings /namespace [ (adobe) (creativesuite) (2.0) ] /pdfxoutputintentprofileselector /documentcmyk /preserveediting true /untaggedcmykhandling /leaveuntagged /untaggedrgbhandling /usedocumentprofile /usedocumentbleed false >> ] >> setdistillerparams << /hwresolution [2400 2400] /pagesize [612.000 792.000] >> setpagedevice microsoft word numero 9 art 12 finale a. risitano et alii, frattura ed integrità strutturale, 9 (2009) 113 124; doi: 10.3221/igf-esis.09.12 113 l’importanza del “parametro energetico” temperatura per la caratterizzazione dinamica dei materiali a. risitano università degli studi di catania, facoltà di ingegneria, dipartimento di ingegneria industriale e meccanica, via andrea doria, 6 –95125 catania, arisitan@diim.unict.it g. risitano università telematica guglielmo marconi, via plinio, 44 – 00153 roma. riassunto. le esperienze maturate nel campo dell’analisi termica di materiali utilizzati nelle costruzioni meccaniche [1,2,3] hanno permesso di evidenziare come il rilievo della temperatura (terzo parametro) in prove statiche e dinamiche costituisca un indicatore molto importante ai fini della caratterizzazione dinamica del materiale. essendo il rilascio termico funzione dell’energia applicata per portare a rottura il materiale, il rilievo di parametri ad esso legati, induce a nuovi ipotesi e definizioni di limiti di fatica e resistenza a tempo. mediante l’analisi termica è possibile valutare anche parametri correlabili con il valore limite di energia a rottura el del materiale. in [4] era stato già messo in evidenza da a. risitano e altri che, in prove statiche di trazione, l’inizio della zona di prima plasticizzazione del materiale, in termine di tensione, era osservabile dalla curva di variazione di temperatura δt con il procedere della prova. nello stesso lavoro si evidenziava come la velocità di prova avesse poca influenza sui valori della variazione di temperatura specialmente durante la fase elastica. operando con sensori sempre più precisi e per obbiettivi rivolti alla ricerca dell’energia limite a rottura è stato osservato dagli autori che il seguire la variazione della temperatura sulla superficie del provino, in prove statiche di trazione, permette di legare i classici valori di resistenza all’oscillazione σ0 con una “temperatura limite” t0 corrispondente all’inizio di andamenti non lineari della stessa. in questa sede si evidenzia un modello di comportamento fisico del materiale durante le prova di trazione che giustifica, in modo semplice, la capacità di risalire, attraverso la conoscenza sperimentale del limite di comportamento termo-elastico, ai classici parametri di resistenza a fatica. viene riportato, a titolo di esempio, il risultato relativo a provini piatti forati in acciaio facenti parte di una serie utilizzati per altri scopi (formeranno oggetto di altra pubblicazione) con i quali anche mediante prova statica si è determinata la loro resistenza all’oscillazione. abstract. following their research, the authors remarked on the importance of the knowledge of the temperature for stressed material (mechanical component). they show as a temperature (third parameter) is an important parameter to characterise dynamically the material. being that the thermal release is a function of the applied energy that leads to the failure, the knowledge of parameters linked to energy leads to new hypothesis and definitions of fatigue limit and lifespan. a thermal analysis permits one to evaluate parameters related to the amount of energy to failure of tested material. in [4] a. risitano and others, had remarked that during a static traction test, the beginning of plastic behaviour (linked to applied stress) was definable by analysing of the correspondent temperature curve. in the same work, they remarked about the low influence of the test velocity. http://www.gruppofrattura.it/ http://dx.medra.org/10.3221/igf-esis.09.12&auth=true mailto: arisitan@diim.unict.it a. risitano et alii, frattura ed integrità strutturale, 9 (2009) 113 124; doi: 10.3221/igf-esis.09.12 114 still working with high level temperature sensors, the authors observed that during static tests, the temperature variation of the surface specimen, permits to associated the lower dynamic fatigue limit σ0 to a “temperature limit” t0 coincident to the end of thermo-elastic phase. in this case a qualitative physical model, able to give and justify the possibility to evaluate the classic fatigue limit by experimental knowledge of thermo-elastic behaviour is discussed. as an example, the results of traction tests performed on two rectangular section specimens notched with one hole each, where the change of linearity was evident, are reported. the corresponding value of stress was coincident with the fatigue limit σ0 for r= 1, found by traditional method. keywords. energia, termografia, temperatura in prova di trazione, fatica introduzione er la caratterizzazione dei materiali o di componenti meccanici ci si è affidati da sempre a prove (statiche o dinamiche) nelle quali difficilmente si teneva conto di parametri energetici. nella prova di resilienza il parametro di riferimento come è noto è l’energia. le attuali tecnologie di misure, combinati con adeguati sistemi di analisi di immagini, permettono di tener conto di un parametro che è legato all’energia in gioco del sistema, ovvero, le variazioni di temperatura del materiale sottoposto a carichi. con i sistemi di rilievo a distanza e a tutto campo attuali è possibile rilevare la temperatura sulla superficie del provino durante tutta la prova ed analizzare successivamente l’andamento della stessa nei vari punti. l’analisi termica permette di evidenziare, già all’inizio delle prove (statiche o dinamiche), il punto della superficie del provino a temperatura più elevata che individua la zona dove la rottura successivamente si realizzerà. ciò diventa importante per la previsione di rotture anche in componenti meccanici in esercizio per cui sia possibile il rilievo a distanza della temperatura superficiale. negli ultimi 20 anni, sulla scia di quanto indicato già da foppel, ed altri ricercatori dello stesso periodo, con lo sviluppo di sensori per il rilevo della temperatura a distanza e a tutto campo sempre più precisi, tanti ricercatori hanno utilizzato la conoscenza della temperatura sulla superficie del provino durante le prove, in particolare dinamiche, per proporre metodologie e procedure per determinare sperimentalmente il limite di fatica del materiale in modo rapido [1,2,3,15,20]. tanti altri hanno proposto modelli analitici e numerici basati sull’energia necessaria a portare a rottura il materiale verificando i risultati con lo stato termico rilevabile sulla superficie esterna del provino o componente analizzato [12,22,27,28,31,32,33,35,38,41]. la vasta letteratura degli ultimi anni sull’argomento evidenzia il grande interesse dei ricercatori sull’aspetto energetico del processo di danno o cedimento del materiale ed evidenzia la necessità di strumenti di indagine sempre più evoluti. la temperatura nel caso di prove di fatica l prendere in considerazione la variazione di temperatura δt (terzo parametro oltre i due classici tensione σ e numero di cicli n) durante l’esecuzione di prove di fatica ha portato il gruppo di ricerca di a. risitano [1,2,3,4,5,18] a verificare, mediante sensori a tutto campo che, per una data frequenza di prova e per un dato rapporto di sollecitazione r, la variazione della temperatura sulla superficie del provino, con il numero di cicli era funzione della sollecitazione massima applicata. seguendo il punto più caldo (areola attorno), preso come riferimento sin dall’inizio della prova si notava che la temperatura (temperatura media) dopo un primo veloce incremento (ns qualche migliaio di cicli) si stabilizzava fino al cedimento del materiale con un veloce ultimo incremento finale (nf ancora qualche migliaio di cicli) prima della completa rottura (fig. 1). su tale osservazione si sono basati diversi metodi per la determinazione del limite di fatica del materiale [1,2,3,6,16,17,21,26] che permettono di ridurre in modo drastico i tempi di prova. in pratica, si è passati da un sistema a due parametri (tensioni, numero di cicli) ad un sistema a tre parametri (tensioni, numero di cicli, temperatura) e la durata del componente o del materiale può essere vista in termini energetici come una funzione dell’energia limite el necessaria per raggiungimento della rottura del provino (di un componente meccanico). p i http://www.gruppofrattura.it/ http://dx.medra.org/10.3221/igf-esis.09.12&auth=true a. risitano et alii, frattura ed integrità strutturale, 9 (2009) 113 124; doi: 10.3221/igf-esis.09.12 115 applicando il primo principio della termodinamica al sistema considerato chiuso, si può affermare che l’energia interna è data dalla differenza tra il lavoro fornito al sistema e il calore ceduto all’ambiente circostante. nel nostro caso il lavoro w fornito al sistema è lavoro meccanico dato dalla somma di una componente elastica we e di una componente plastica wp. figura 1: andamento qualitativo della temperatura in un punto della superficie del provino durante una prova di fatica. le due componenti però contribuiscono termicamente a livelli differenti. solitamente infatti le zone affette da plasticità vengono definite zone calde, e viceversa quelle soggette alla sola deformazione plastica sono definite fredde. in particolare il contributo della componente elastica è regolato dalla legge termoelastica che è inferiore a quello plastico. l’equilibrio globale tra l’energia meccanica fornita in termini elastici e plastici e il calore dissipato è dato dall’eq. (1) di bilancio del calore: (1) dove k è la conduttività termica,  la densità, ce il calore specifico, t la temperatura  è la frazione di potenza termica rilasciata sulla potenza meccanica trascurando la componente termoplastica,  e  sono le costanti di lamè,  il coefficiente di dilatazione termica. la componente plastica del lavoro meccanico wp coincide con l’area del ciclo, e può essere calcolata con la relazione (2): (2) pw è quindi pari al prodotto della componente deviatorica dello sforzo per l’incremento di deformazione plastica valutato su un ciclo. per i materiali comunemente adottati in campo meccanico, (acciaio e ghisa,)  (circa 0,9) si può considerare costante rispetto alle sollecitazioni ed alle deformazioni. per le normali frequenze di prova, il sistema può essere considerato adiabatico, la componente termoelastica può essere trascurata; vale dunque la relazione (3): (3) la temperatura raggiunta superficialmente, è dunque, sotto le condizioni suddette, direttamente correlabile all’energia meccanica di deformazione. nel caso di prove di fatica, quindi, l’energia liberata come calore che si va a mettere in relazione con gli altri due parametri (tensioni e tempo) diventa praticamente quella che si genera per effetto di micro-plasticizzazioni, ovvero, quella che si sviluppa allorché inizia il processo di cedimento del materiale essendo, in confronto a questa, molto piccola quella che si produce per effetto del classico fenomeno dello smorzamento interno (elastico) specialmente alle normali (minore di 50 hz) frequenze di prova. sperimentalmente si osserva che operando con sollecitazione oscillante, l’incremento di temperatura sulla superficie esterna del provino, rilevabile con sensori all’infrarosso termico, si manifesta allorquando la sollecitazione applicata al materiale supera in un punto il limite di fatica ovvero allorquando, in quel punto, la tensione è tale da produrre le prime micro-plasticizzazioni (interne o superficiali) che con il progredire del tempo (numero di cicli), raggiunto il valore di energia necessario alla rottura el per quel dato componente, conducono al cedimento fisico dello stesso. si evince che quando la sollecitazione applicata è tale da produrre in un punto del materiale plasticizzazione locale, inizia il fenomeno di progressivo cedimento del materiale che nel tempo porterà alla rottura. il valore di energia el “energia limite” costituisce il limite energetico per quanto riguarda la resistenza a sollecitazioni di fatica. il raggiungimento di tale 2 0( 3 2 ) p e ij ij ek t t c tbs e l m a e r+  + + =   0 t p pw ds e=ò ew c tb r=  http://www.gruppofrattura.it/ http://dx.medra.org/10.3221/igf-esis.09.12&auth=true a. risitano et alii, frattura ed integrità strutturale, 9 (2009) 113 124; doi: 10.3221/igf-esis.09.12 116 limite, conduce al cedimento del materiale che si può ottenere in infiniti modi diversi (storie di carico diverse), vedi figura 2. come prima detto, la “energia limite” è proporzionale alla quantità di calore ceduto all’esterno e quindi correlabile con la temperatura della superficie del provino. tali ipotesi sono stati verificati sperimentalmente da risitano e dal suo gruppo di ricerca[4,42] e sulla base delle stesse il metodo risitano permette di determinare l’intera curva di fatica (la classica curva di wohler) in tempi estremamente brevi. in particolare, in coerenza con quanto prima detto, è stato verificato sperimentalmente, che nel caso di prove di fatica, operando nelle stesse condizioni di prova (stessa frequenza, stesso rapporto di carico), il parametro energetico φ , integrale nel tempo della variazione di temperatura δt rilevata nel punto (areola) più caldo (preso come riferimento) della superficie del provino per valori diversi di sollecitazione, risulta anch’esso costante (fig. 2) e proporzionale al calore dissipato q e quindi alla energia limite el [4,42]. essendo el una costante caratteristica del materiale [10, 26], è possibile risalire alla classica curva “tensione vs numero di cicli” (-n ) dalla conoscenza del terzo parametro δt (incremento di temperatura in un punto della superficie del provino durante la prova di fatica).    c=ixfi=cost    figura 2: parametro energetico φ costante come el per storie di carico (σi) diverse. e’ noto poi che la rottura per fatica inizia nel punto in cui si raggiungono tensioni locali tali da produrre deformazioni (locali) plastiche. se nel materiale esistono difetti strutturali o se sulle superfici esterne si hanno dei micro-difetti di lavorazione, in tali punti, si possono avere intensificazioni delle sollecitazioni rispetto a quelle medie definite dal rapporto fra il carico applicato e l’area della sezione del provino. si raggiungono, quindi, condizioni di cedimento locale che costituiscono l’innesco del fenomeno della rottura per fatica. tali situazioni, ovviamente, non comportano alcun cambiamento visibile ed apprezzabile dal punto di vista statico non incidendo praticamente sulla sezione resistente del provino (la classica tensione media rimane la stessa). si potrebbe definire, pertanto, limite di fatica del materiale quel valore di tensione (rilevabile in modo macroscopico) che produce nel materiale (sulla superficie o all’interno) condizioni di plasticizzazione locale (puntuale) non rilevabili con le classiche strumentazioni o sulla base dei parametri tradizionali ma osservabile dal rilievo della situazione termica del provino (del componente) su cui si sta operando. da tutto quanto detto prima si deduce che per lo studio della rottura a fatica dei materiali bisognerebbe, più verosimilmente, fare riferimento ad una “energia limite” (el) intesa come quella energia caratterizzante la resistenza del provino, costante per ciascun materiale (provino). il raggiungimento di tale valore limite può essere attuato in infiniti modi (carichi elevati-tempi bassi, carichi bassi-tempi elevati) ovvero con diverse storie di carico (fig. 2). la temperatura nel caso di prove statica di trazione acendo riferimento al comportamento sotto carico (ad esempio di trazione) di un provino metallico, possiamo dividere il campo delle tensioni della classica prova statica (σ, ε) in differenti zone [7] (fig.3). zona i, la tensione media è così bassa che tutti i cristalli risultano stressati entro il loro campo elastico . zona ii, la tensione media è tale che nella maggior parte dei cristalli la deformazione è di tipo elastico, tuttavia in alcuni cristalli si presentano deformazioni plastiche accoppiate a quelle elastiche in modo che allo scarico il provino riprende ancora la forma iniziale. considerato in modo macroscopico il provino si comporta ancora come perfettamente elastico. f http://www.gruppofrattura.it/ http://dx.medra.org/10.3221/igf-esis.09.12&auth=true a. risitano et alii, frattura ed integrità strutturale, 9 (2009) 113 124; doi: 10.3221/igf-esis.09.12 117 zona iii, la tensione media è tale che in alcuni cristalli esistono deformazioni elastiche accompagnate da deformazioni plastiche preponderanti su quelle elastiche e tali che alla cessazione del carico i cristalli deformati elasticamente non hanno energia per riportare il provino nelle condizioni iniziali. in tali condizioni è rilevabile un cambiamento nella forma del provino (comparsa di deformazioni permanenti). zona iv, la tensione media ha raggiunto valori per cui la deformazione plastica è tale che la maggior parte dei cristalli risulta deformata plasticamente. i cristalli ancora deformati elasticamente risultano sempre di meno col progredire del carico e alla cessazione del carico le deformazioni diventano sempre più vistose.   figura 3: curva ingegneristica con l’individuazione qualitativa delle quattro zone caratteristiche. il valore della tensione di snervamento può essere assunto come quello di transizione fra la fase ii e la fase iii. nei metalli, anche in quelli apparentemente perfetti, spesso la prima zona è molto limitata. le tensioni interne fra le regioni deformate elasticamente e plasticamente danno origine nei metalli policristalli ad un effetto “dopo elastico”. a tale effetto risulta collegato il fenomeno della isteresi elastica. se il carico è variabile (ad esempio oscillante) e siamo in presenza di fatica ad alto numero di cicli, si può avere un cambiamento della struttura interna anche se la tensione applicata appartiene al campo ii. e’ infatti possibile che il cedimento incominci in un punto per scorrimento e proceda con successiva rottura di un cristallo. in tali condizioni, alla giunzione di certi legami atomici si verificheranno stati di tensione severi e con il progredire del numero di oscillazioni il processo continua con il superamento delle forze di coesione delle giunzioni. l’effetto cumulativo della rottura di giunzioni atomiche si incrementa dopo il primo apparire di discontinuità nella struttura passando dallo stato di microcricca, alla rottura per fatica (visibile). per quanto detto prima, se fossimo in presenza di un difetto localizzato, in una prova di trazione classica, avremmo lo stesso risultato globale (la stessa caratteristica macroscopica sforzi-deformazioni). se però riducessimo via via le dimensioni del provino evidenziando il difetto rispetto alla area utile del provino stesso, fino ad arrivare, al limite, ad un provino che contiene un solo cristallo “difettato”, troveremmo un andamento qualitativamente dello stesso tipo, ma con valori del limite elastico (nel senso della classica definizione) diverso. in altre parole, il processo di plasticizzazione nel punto avverrebbe per un valore di limite elastico (locale) diverso del limite elastico macroscopio (globale) inteso, quest’ultimo, come tensione nominale media dovuta al carico totale esterno capace di produrre deformazioni permanenti dello 0.2%. il valore della tensione media (nominale) per cui a livello locale si manifesta la prima plasticizzazione (microplasticizzazione) è quello che poi in sollecitazioni dinamiche porta alla rottura del pezzo. quindi si può definire come limite di fatica ad alto numero di cicli quella tensione limite σm=σ0. (della zona ii) per cui in nessun punto del materiale si manifestano microplasticizzazioni locali. è verosimile pensare che il limite di fatica definito come prima si riferisca alla resistenza all’oscillazione σ0 (rapporto di carico r = –1) . http://www.gruppofrattura.it/ http://dx.medra.org/10.3221/igf-esis.09.12&auth=true a. risitano et alii, frattura ed integrità strutturale, 9 (2009) 113 124; doi: 10.3221/igf-esis.09.12 118 dal punto di vista del comportamento termico di un materiale omogeneo sottoposto a trazione, possiamo distinguere due fasi: una prima fase in cui il materiale in tutti i punti si deforma elasticamente (zona i del diagramma di fig. 3) in tale fase vale una relazione lineare fra tensioni e deformazioni; una seconda fase in cui non tutti i punti sono deformati elasticamente ma in qualche punto del materiale iniziano deformazioni plastiche permanenti (zona ii del diagramma di fig. 3). la prima fase dal punto di vista del comportamento termico è regolata dalla teoria della termoelasticità. la teoria della termoelastica per materiali solido isotropi sviluppata da lord kelvin già nel 1851, come è noto, parte dal primo principio della termodinamica e posta una legge costitutiva (4) (in forma vettoriale) del tipo: {σ } = [c] ({ ε }-{ α }δt) (4) nell’ipotesi di fenomeno adiabatico, conduce all’equazione generale (5): ρcε δt/t=[({ ε }-{ α }δt) δ[c]/ δt – ({ α }+}-δt δ{ α }/δt) [c]] δ{ ε} (5) in cui cε rappresenta il calore specifico a volume costante. nel caso di materiale isotropo l’equazione si semplifica e diventa la (6): δt = -kmt δi (6) in cui δi è la variazione della somma delle tensioni principali e km è la costante termoelastica del materiale (per acciai 3,3x10-12 [pa-1]). nel caso di prova di trazione (tensione monoassiale) δi coincide con il valore della tensione media σm applicata e quindi più semplicemente la (7): δt = -kmt σm (7) nelle ipotesi precedenti, durante la prima fase della prova, esiste una perfetta proporzionalità fra tensioni applicate ed incrementi di temperatura rispetto alla temperatura iniziale (ambiente). il rilievo della temperatura sulla superficie del provino mostrerebbe, in questa fase, in tutti i punti, un andamento perfettamente lineare con il progredire dei carichi applicati. se la tensione σp applicata dall’esterno, magari una frazione della tensione di snervamento (σ 0,2), è tale che per effetto di qualsiasi difetto interno od esterno si raggiungono condizioni di tensioni locali tali da creare plasticizzazazione in un volume elementare dvp , il fenomeno per tale volume (in quel punto) non è più regolato dalla (6) (la legge costitutiva non è più la (4)) e per effetto delle deformazioni plastiche dissipative si producono sviluppi di calore dqp che modificano l’andamento lineare della variazione di temperatura con il carico. in tal caso il fenomeno non è più reversibile e l’entropia è funzione del “modo” in cui si raggiunge lo stato finale (la rottura). in tali condizioni, c’è, quindi, una parte del volume (vdvp) che segue la legge termo-elastica e la parte plasticizzata che produce una quantità di calore che, nell’ipotesi di plasticizzazione ideale, per unità di volume, è pari a dqp= σp d εp. man mano che aumenta la sollecitazione, aumentano le deformazione plastiche nel volumetto dvp ma, nello stesso tempo, si raggiungono condizioni locali in altri punti che producono l’inizio di altra plasticizzazione e l’apporto di ulteriori quantità di calore. le quantità di calore in gioco in questa fase sono, quindi, funzione non solo della sollecitazione ma anche delle coordinate del punto, della modalità di deformazione locale con il tempo di cedimento (inizio della plasticizzazione–rottura) di ciascun cristallo e del volume di materiale. in letteratura esistono modelli analitici [9,11,27,28,29,31,33,35,38,41] che legano il danno con le variazioni di temperatura, specialmente per casi di sollecitazioni cicliche, tuttavia, il passaggio dalla formulazione matematica al risultato applicabile impone scelte di funzioni idonee a descrivere il progredire del danno con le coordinate spaziali e con il tempo. il problema, dal punto di vista del modello del calcolo, si complica e per una soluzione analitica occorrerebbe fare: ipotesi di danno sul volume totale (ad esempio progressione del danno con il progredire di micro vuoti); ipotesi sul modello di plasticizzazione locale; ipotesi sulle modalità di trasmissione del calore all’interno e verso l’esterno. ipotesi tutte che, comunque, possono fornire indicazioni solo di carattere generale. in una prova di trazione, nella prima fase, fino a quando non intervengono fenomeni di plasticizzazione locali, vale la teoria termo-elastica e il legame fra tensioni e temperatura, come precedentemente detto, è regolato dalla legge di kelvin (7). http://www.gruppofrattura.it/ http://dx.medra.org/10.3221/igf-esis.09.12&auth=true a. risitano et alii, frattura ed integrità strutturale, 9 (2009) 113 124; doi: 10.3221/igf-esis.09.12 119 qualitativamente si può osservare che man mano che il carico aumenta e il numero di cristalli plasticizzati aumenta, l’andamento della temperatura del materiale si discosta dall’andamento lineare per due motivi: diminuisce il volume di materiale interessato dall’effetto termoelastico (che si raffredda) ed aumenta il volume di materiale plasticizzato che si riscalda. se ciascun cristallo avesse un comportamento perfettamente plastico, raggiunta il valore di tensione σp, la quantità di calore dqp fornito, sarebbe, come prima detto, proporzionale a (σp d εp). se si fosse in grado di valutare il primo insorgere del calore dqp per effetto del carico medio esterno sul provino si individuerebbe la tensione di prima microplasticizzazione e, di conseguenza, quello che convenzionalmente è definito limite di fatica del materiale per r=-1. infatti, sollecitando il provino con carichi oscillanti e corrispondenti tensioni superiori a tale valore, dopo un certo tempo, si raggiungerebbe la rottura. se invece il provino fosse sollecitato con valori inferiori a tale limite non si avrebbe alcuna rottura ed il materiale avrebbe durata infinita. l’osservazione precedente mostra che il limite di fatica si può individuare se si riesce a legare il valore di tensione media con la comparsa della prima plasticizzazione che, come detto prima, comporta cedimento di calore al materiale e di conseguenza variazione della temperatura sulla superficie esterna del provino. dalle osservazioni precedenti, si deduce che se si opera con una prova statica e si segue la variazione di temperatura sulla superficie esterna della superficie del provino, è possibile valutare l’intorno in cui finisce di valere la linearità fra tensioni e temperature e corrispondentemente, quindi, l’intorno della tensione media σ0 per la quale è iniziata la fase di prima plasticizzazione (zona ii). al valore della “temperatura limite” t0, coincidente con la fine della fase termoelastica, corrisponde quel valore σ0 che è stato la causa di inizio di microplasticizzazioni. ed ancora, in un diagramma “tensioni vs variazioni di temperatura”, tale valore di tensione media σ0 è, quindi, quello che ha prodotto una microplasticizzazione per la quale si è generata una quantità di calore che, in controtendenza, ha fatto variare la pendenza nella curva “sforzi vs variazioni di temperatura” ( σm δt). man mano che il carico cresce, le microplasticizzazioni aumentano (zona iii del diagramma di fig. 3) e la pendenza della curva varia con continuità fino a quando si raggiunge il valore del carico di snervamento. superata la fase di snervamento, con il progredire della plasticizzazione, le quantità di calore in gioco sono tali da mascherare completamente l’effetto termoelastico dei cristalli ancora non plasticamente deformati e nell’ultima fase, per gli acciai, al contrario di quanto avviene nella zona i, si ha il riscaldamento di tutto il materiale con valori di temperatura superficiale positiva (zona iv della fig. 3). nel diagramma qualitativo di fig. 3 viene mostrato quello di cui si è precedentemente detto per un materiale impiegato in costruzioni meccaniche (ad esempio acciaio) sollecitato a trazione. assieme al classico andamento “tensioni vs deformazione”, nello stesso diagramma, viene riportato il terzo parametro, ovvero, la variazione di temperatura media δt di una parte molto limitata della superficie del provino, quella più prossima alle prime variazioni di temperatura rispetto al valore iniziale ta (temperatura ambiente). in definitiva, per tensioni medie fino al valore σ0, il legame tensioni temperature è di tipo lineare in coerenza con il comportamento termoelastico del materiale. per valori superiori a σ0 ci si discosta dalla linearità e l’andamento della temperatura della zona di riferimento cambia pendenza in quanto non vale per tutti i punti del provino la legge di kelvin. tale fenomeno si esaspera man mano che il carico cresce fino a raggiungere, nell’ultima fase della prova, valori della temperatura superficiale positivi (ultima parte della curva). si può definire “temperatura limite” t0 quel valore di temperatura corrispondente alla fine della fase termoelastica, ovvero con riferimento alla fig. 3, quella temperatura t0 corrispondente al cambiamento di pendenza. a tale valore di “temperatura limite” corrisponde, come più volte detto, un valore di tensione media (macroscopico) coincidente con il valore della classica resistenza all’oscillazione σ0 del materiale. le variazioni di temperatura durante l’esecuzione di prove statiche su acciai, secondo gli andamenti prima descritti sono state riscontrate e riportate da a. risitano ed altri in [5]. gli autori operando con gli giusti accorgimenti (ambienti controllati sia dal punto di vista termico che luminoso), con sensori ad alta precisione (sensibilità di almeno 0,05 c° per limitare le strumentali oscillazioni di temperatura durante il rilievo) nonché a velocità di prova (controllo di carico) adeguate (fra i 60 e i 30 n/s) hanno, per differenti materiali, potuto verificare che il valore di tensione σ0 corrispondente a t0 coincideva con valori del limite di fatica rilevati con prove tradizionali (wohler) o con metodo termografico [2]. hanno anche osservato che dalla misura della temperatura superficiale in prossimità ad intagli e in zone di stabilità di tensione (a distanza dagli intagli) è possibile risalire ai valori di effetto di intaglio caratteristici di quel dato provino. rimandando ad altra sede i risultati prima accennati, in questo caso ci si limita a riportare, a titolo di esempio, qualche dato relativo ad una applicazione su provini forati per cui il limite di fatica era stato ottenuto con altri metodi e per cui l’obbiettivo era quello di analizzare l’influenza della lavorazione con cui veniva ottenuto il foro. http://www.gruppofrattura.it/ http://dx.medra.org/10.3221/igf-esis.09.12&auth=true a. risitano et alii, frattura ed integrità strutturale, 9 (2009) 113 124; doi: 10.3221/igf-esis.09.12 120 i test meccanici sono stati eseguiti con l’ausilio di una macchina di prova oleodinamica prodotta dalla instron (modello 8501, 100 kn servo hydraulic machine) dotata di cella di carico da ±100 kn. le immagini radiometriche sono state acquisite con uno scanner termografico prodotto dalla flir system modello sc3000. nella fig. 5 è riportata le curve “carico vs spostamento” di un provino di acciaio fe36 piatto forato sottoposto a prova di trazione. le dimensioni sono riportate nella tab. 1 e nella fig. 4. l lo b t  figura 4: disegno del provino con relative quote. l [mm] l0 [mm] b [mm] t [mm] ø [mm] 310.00 90 36 5.70 13.00 tabella 1: dimensioni geometriche provino. la velocità con cui variava il carico era di 22n/s. durante l’esecuzione della prova statica, è stato rilevato con lo scanner termografico il profilo della temperatura di tutta la superficie esterna del provino (fig. 6). figura 5: curva carico-spostamento provino a2-os2. figura 6: alcune immagini della sequenza termografica acquisita a2-os2. prova di trazione provino a2-os2 -7 0 7 14 21 28 35 42 49 56 63 0 1 2 3 4 5 6 7 8 9 spostamento [mm] c a ri c o [ kn ] http://www.gruppofrattura.it/ http://dx.medra.org/10.3221/igf-esis.09.12&auth=true a. risitano et alii, frattura ed integrità strutturale, 9 (2009) 113 124; doi: 10.3221/igf-esis.09.12 121 in fig. 7 è stato riportato il profilo termico di un punto della superficie del provino molto prossimo al bordo del foro. l’andamento del profilo evidenzia un primo tratto decrescente, tipico del comportamento termo-elastico del materiale. si evidenzia in tale zona, un “punto” in cui la pendenza della prima parte della curva subisce una variazione; variazione dipendente dalle caratteristiche termoelastiche del materiale e correlata ai primi fenomeni di micro-plasticizzazione del materiale. tale punto, come evidenziato da successive prove dinamiche, coincide, in termini di tensione, con il valore del limite di fatica oscillante (r=-1). nel caso in esame, il valore del carico corrispondente al cambio di pendenza del profilo termico è di 7 kn. ai valori di temperatura rilevati nella zona di comportamento totalmente elastico (carico minore di 7 kn) del diagramma, corrispondono valori di tensioni (locali) maggiori del valore della tensione media (carico/area netta della sezione). figura 7: profilo termico di un punto prossimo al foro del provino a2-os2. nella fig. 8, per un provino dello stesso acciaio e di dimensioni uguali a quello precedente ma con velocità di carico doppia 44 n/s, è riportato il profilo termico ottenuto in modo analogo a quanto detto prima (acquisizione di immagini e analisi in un punto prossimo al bordo del foro – fig. 9). la lavorazione con cui era stato ottenuto il foro era di tipo differente da quello precedente. come evidenziato da successive prove dinamiche, anche in questo caso, il valore del carico per cui avviene il cambio di pendenza nella curva di temperatura coincide con il valore del limite di fatica a carico oscillante (r = -1) figura 8: prova di trazione e profilo termico di un punto prossimo al foro del provino a2-pl1. rilascio termico provino a2-os2 22 22,1 22,2 22,3 22,4 22,5 22,6 22,7 22,8 22,9 23 0.00.00 0.07.12 0.14.24 0.21.36 0.28.48 0.36.00 0.43.12 tempo [h.mm.ss] t e m p e ra tu ra [ °c ] -7 0 7 14 21 28 35 42 49 56 63 c a ri c o [ k n ] temperatura carico media mobile su 15 per. (temperatura) prova statica a2-pl1 21,7 21,9 22,1 22,3 22,5 22,7 22,9 0.00.00 0.02.53 0.05.46 0.08.38 0.11.31 0.14.24 0.17.17 0.20.10 0.23.02 tempo t e m p e ra tu ra [ °c ] -70 -50 -30 -10 10 30 50 70 c a ri c o [ k n ] temperatura carico limite di fatica oscillante 11kn http://www.gruppofrattura.it/ http://dx.medra.org/10.3221/igf-esis.09.12&auth=true a. risitano et alii, frattura ed integrità strutturale, 9 (2009) 113 124; doi: 10.3221/igf-esis.09.12 122 figura 9: alcune immagine della sequenza termografica acquisita a2-pl1. conclusioni opo avere evidenziato l’importanza della conoscenza della variazione di temperatura (terzo parametro) in prove di caratterizzazione dei materiali o di componenti meccanici, viene, sulla base di anni di esperienza, per la prima volta, indicato un modo di procedere per l’individuazione mediante prova statica del parametro t0 “temperatura limite”, caratterizzante però il comportamento a fatica del materiale. sulla base di considerazioni energetiche viene evidenziato come la rottura per fatica sia regolata dal raggiungimento di una “energia limite” proporzionale a parametri valutabili mediante il rilievo della temperatura sulla superficie esterna del provino (o componente meccanico). viene, di conseguenza, fornita una definizione più generale di limite di fatica. viene evidenziato come la conoscenza del campo di comportamento elastico di tutto il materiale (di tutti i cristalli) durante una prova statica di trazione diventi importante per individuare parametri caratterizzanti il fenomeno di rottura per fatica. viene definita la “temperatura limite” t0 mediante prova statica e la corrispondente tensione σ0 che costituisce il valore limite di sollecitazione al di sopra del quale si manifestano fenomeni di microplasticizzazione che per carichi variabili nel tempo conducono alla rottura per fatica. viene osservato come dalla conoscenza della temperatura sul provino possa essere possibile risalire a fattori di forma o a fattori di effetti di intaglio. solo a titolo di esempio, infine, viene riportato, il risultato di prove effettuate su provini (utilizzati per altra ricerca) per i quali, la fine della fase termoelastica è particolarmente chiara, per cui, con la sola prova statica (di trazione), è stato possibile risalire al valore della resistenza all’oscillazione confermato anche da prove di fatica tradizionali. bibliografia [1] g. curti, g. la rosa, m. orlando, a. risitano, 14th aias italian national conference, catania italia, (1986) 211. [2] g. curti, a. geraci, a. risitano, ata ingegneria automotoristica, 10 (1989) 634. [3] g. la rosa, a. risitano, int. j. fatigue, 22 (2000) 65. [4] g. fargione, a. geraci, g. la rosa, a. risitano, int. j. fatigue, 24 (2002) 11. [5] a. geraci, g. la rosa and a. risitano, 7th international conference on mechanical behaviour of material, the hague (1995). [6] j. kaleta, r. blotny and h. harig, j. test. eval., 19 (1990) 326. [7] c.e. feltner, j.d. morrow, trans. asme, ser. d: j. basic eng, 83 (1961) 15. [8] r. houwink, w.g.burgers, elasticity, plasticity and structure of matter, cambridge at the university press, seconda edizione (1954). [9] k. middelford, h. harig, proceedings of international powder metallurgy conference and exhibition, verlag schmid gmbh, freiburg, (1986) 499. [10] d. dengel, h. harig, fatigue fract .eng. mater. struct., 3 (1980) 113. [11] h. harig, m. weber, proceedings of the 2nd international symposium, martinus nijhoff publ, the hague (1983) 161. d http://www.gruppofrattura.it/ http://dx.medra.org/10.3221/igf-esis.09.12&auth=true a. risitano et alii, frattura ed integrità strutturale, 9 (2009) 113 124; doi: 10.3221/igf-esis.09.12 123 [12] o.a. plenkev, n. saintier, t. palinluc, s.v. uranov, naimark, material science and engineering, 462 (1-2) (2007) 367. [13] g. la rosa, g. mirone, a. risitano, j. of engineering fracture mechanics, 68 (2001) 417. [14] g. la rosa, g. mirone, a. risitano, met. mat. trans. a, 34 (3) (2003) 615. [15] g. la rosa, g. mirone, g. risitano, aias xxxvi convegno nazionale, napoli, (2007). [16] m.p. luong, mech. mater., 28 (1988) 155. [17] a. blarasin, r. fracchia, m. pozzati, ata – ingegneria automotoristica, 51 (5) (1988) 255. [18] t. catalbiano, a. geraci, m. orlando, il progettista industriale, (1984) 2. [19] k.l. reifsnider, r.s. williams, exp. mech., 14 (1974) 479. [20] t. boulanger, a. chrysochoos, c. mabru, a. galtier, int. j. fatigue, 26 (2004) 221. [21] f. curà, g. curti, r. sesana, int. j. fatigue, 27 (2005) 453. [22] p. cugy, a. galtier, fatigue 2002. in: blom af, editors. proceedings of the 8th international fatigue congress, emas, i (2002) 549. [23] k. j.miller, in: piascik rs, newman jc, dowling ne, editors. astm stp 1296, (1997) 267. [24] y. akiniwa, k. tanaka, h. akimura, fatigue fract. eng. mater. struct., 24 (2001) 817. [25] y. murakami, metal fatigue: effects of defects and non metallic inclusions, elsevier (2002). [26] m.p. luong, nucl. eng. des., 158 (1995) 363. [27] g.r. halford, j. mater., 1 (1966) 3. [28] r. blotny, j. kaleta, int. j. fatigue, 1 (1986) 29. [29] c.e. feltner, j.d. morrow, trans. asme, ser. d: j. basic eng., 83 (1961) 15. [30] e. charkaluk, a. bignonnet, a. costantinescu, k. dang van, fatigue fract. eng. mater. struct., 25 (2002) 1199. [31] n.w. klingbeil, int. j. fatigue, 25 (2003) 117. [32] e.k. gamstedt, o. redon, p. brønsted, key eng mater, 221–222 (2002) 35. [33] b. atzori, e. gasparini, g. meneghetti, proceedings of 30th aias national conference; (2001) 367. [34] b. yang, p.k. liaw, h. wang, l. jang, j.y. huang, r.c. kuo, j.g. huang, mater. sci. eng. a, 314 (2001) 131. [35] b. atzori, g. meneghetti, proceedings of the 5th international conference on low cycle fatigue (p.d. portella, h. sehitoglu and k. hatanaka, editors) dvm, berlin (2003) 147. [36] n. ranc d. wagner, p.c. paris, acta materialia, 56(15) (2008) 4012. [37] p. starke, f. walther, d. eifler, 5th int. conference structural integrity of welded structures (iscs2007), timisora, romania, (2007). [38] g. meneghetti, int. j. of fatigue, 29(1) (2007) 81. [39] b. berthel , b. wattrisse, a. chrysochoos, a. galtier, strain, 43 (3) (2007)273. [40] m. selek, ö. s. şahin, ş. kahramanlı, eurocon 2007 the international conference on “computer as a tool” warsaw, (2007). [41] t. oulanger, a. chrisichoos, c. mabru, a. galtier, int. j. of fatigue, 26 (2004). [42] v.crupi, int. j. of fatigue, 30 (7) (2008)1150. nomenclatura el energia limite necessaria per raggiungere la rottura. σ0 resistenza all’oscillazione (tensione corrispondente alla fine della fase totalmente elastica) σi tensione minima σs tensione massima σm tensione media σp tensione plastica σ 0,2 limite elastico del materiale f frequenza di prova εp deformazione unitaria relativa alla fase plastica r fattore di carico n numero di cicli ε deformazione unitaria ε0 deformazione unitaria corrispondente alla fase totalmente elastica σ tensione α coefficiente di dilatazione termica lineare http://www.gruppofrattura.it/ http://dx.medra.org/10.3221/igf-esis.09.12&auth=true a. risitano et alii, frattura ed integrità strutturale, 9 (2009) 113 124; doi: 10.3221/igf-esis.09.12 124 t temperatura superficiale del provino durante la prova ta temperatura iniziale del provino (temperatura ambiente) t0 “temperatura limite” di un punto del provino corrispondente alla fine del comportamento termoelastico δt incrementi della temperatura superficiale del provino rispetto alla temperatura iniziale e modulo elastico del materiale v modulo di poisson del materiale ρ densità del materiale  ,  costanti di lamè cε calore specifico a deformazione costante cσ calore specifico a tensione costante kc coefficiente di convenzione termica km costante termoelastica del materiale we componente elastica del lavoro meccanico wp componente plastica del lavoro meccanico dqp energia liberata per deformazione plastica dqe energia liberata per deformazione elastica v volume di riferimento del provino vp volume plasticizzato http://www.gruppofrattura.it/ http://dx.medra.org/10.3221/igf-esis.09.12&auth=true microsoft word numero_29_art_15 j. toti et alii, frattura ed integrità strutturale, 29 (2014) 166-177; doi: 10.3221/igf-esis.29.15 166 focussed on: computational mechanics and mechanics of materials in italy damage propagation in a masonry arch subjected to slow cyclic and dynamic loadings j. toti, v. gattulli department of civil, construction-architectural and environmental engineering, university of l'aquila, italy jessica.toti@unicas.it, vincenzo.gattulli@univaq.it e. sacco department of civil and mechanical engineering, university of cassino and southern lazio, italy sacco@unicas.it abstract. in the present work, the damage propagation of a masonry arch induced by slow cyclic and dynamic loadings is studied. a two-dimensional model of the arch is proposed. a nonlocal damage-plastic constitutive law is adopted to reproduce the hysteretic characteristics of the masonry material, subjected to cyclic static loadings or to harmonic dynamic excitations. in particular, the adopted cohesive model is able to take into account different softening laws in tension and in compression, plastic strains, stiffness recovery and loss due to crack closure and reopening. the latter effect is an unavoidable feature for realistically reproducing hysteretic cycles. in the studied case, an inverse procedure is used to calibrate the model parameters. then, nonlinear static and dynamic responses of the masonry arch are described together with damage propagation paths. keywords. cyclic and dynamic analysis; masonry arch; nonlocal damage; finite element method. introduction ecent seismic events have led to an increased demand for the development of effective methods able to discern on the safety of existing masonry structures under dynamic loadings; in this context, arches and vaults have confirmed to be vulnerable with respect to the earthquakes showing the occurrence of extensive damage [1]. in this respect, while the static analysis of arches is widely investigated, a better understanding of the response of masonry vaults and arches under dynamic loading conditions is necessary for the evaluation of the behavior of these structural elements when located in seismically active areas. the seismic capacity of masonry arches is usually studied considering the well-known heyman’s hypotheses [2], who assumed infinite compressive strength and no tensile resistance. this modeling approach is often adopted in the framework of limit analysis [3]. the method provides analytical solutions and can lead to approximated estimates of the seismic capacity of arches. the results of the limit analysis have also been used to validate numerical simulations performed using the distinct element method (dem), which describes the structure as an assemblage of rigid blocks and nonlinear interfaces [4]. although, the dem method allows an accurate description of the dynamic behavior of masonry arches composed by blocks, it could be however inadequate for studying three-dimensional structures made out of a large number of elements. r j. toti et alii, frattura ed integrità strutturale, 29 (2014) 166-177; doi: 10.3221/igf-esis.29.15 167 a further alternative is the use of the finite element method (fem), by adopting a micro-modeling approach [5, 6] or a macro-modeling approach [7, 8]. the computational analysis of these structures subjected to dynamic loadings requires realistic stress-strain material models to satisfactorily reproduce their physical behavior. research efforts on the static response of the masonry material under cyclic loadings aim at providing an efficient model capable of predicting the hysteretic characteristics of the entire element. common models used to reproduce the cyclic behavior of cohesive material are based on damage mechanics, plasticity theory and coupling of both. as widely known, if the stress-strain laws with softening are used within the standard continuum theory, the obtained numerical results suffer from pathological sensitivity to the spatial discretization, e.g. to the size of the finite elements. upon mesh refinement, the energy dissipated by the numerical model decreases and tends to extremely low values, sometimes even to zero. as remedy, regularized models, based on nonlocal continuum approaches, can be adopted [9-12]. recently, efforts have been made to develop dynamic tests which appear particularly promising for a deeper understanding of the response of masonry arches and vaults. within this activity structural damage identification has been pursued to extract information on the health of these structures. indeed, the presence of damage or of other inelastic phenomena modifies the overall structural dynamic response and the damage propagation potentially interacts dynamically with the element vibrations; in particular, changes in its behavior are associated to the decay of the mechanical properties of the system. based on these considerations, several studies have been devoted to use the variations in the dynamic behavior to detect structural damage. particular attention has been focused on the use of frequencies only, because of the simplicity of measuring them and, therefore, their experimental reliability. in this framework, dynamic analyses of damaged structures have been performed in [13] with the aim to detect the damage state of an arched masonry structure. in the present paper the damage propagation in a large-scale masonry arch induced by cyclic and dynamic loadings is analyzed. in particular, the masonry arch tested in [13] is considered as case study. a two-dimensional modeling of the masonry arch is proposed. the constitutive material model developed by toti et al. [12] and extended to the dynamic analyses in [14] is used to reproduce the main hysteretic characteristics of the masonry material under cyclic or dynamic loadings, such as damage, inelastic strains, unilateral phenomena. an inverse procedure is used in order to calibrate the model parameters. the performance of the developed computational tool, in reproducing the experimental response of the arch and the damaging evolution, are investigated in the case of a static cyclic test. the damage propagation and the variations of the dynamic behavior (displacement, frequency contents) with respect to the undamaged condition are examined, when the studied mechanical system is excited by imposed base synchronous harmonic motions. the masonry arch case study he masonry arch studied during the experimental campaign presented in [13] is considered as case study. the masonry structure is built with standard clay bricks with size 100×50×25 mm3. the geometrical data of the tested circular arch, schematically reported in fig. 1, are the following:  internal radius r = 0.77 m;  width w = 0.45 m;  thickness t = 0.05 m;  height h = 0.59 m;  span l = 1.50 m. fig. 1 shows even the coordinate reference system adopted for the computations. static tests to induce damage and dynamic identification tests are performed during the experimental campaign [13]. during the static test, the damage of the arch is caused by the application of a point load located with a distance d from the abutment equal to 0.38 m (about a quarter span), where the lowest safety factor for arches is obtained. the point-wise load induces a damage evolution in the structure, which leads a four hinges collapse mechanism. dynamic tests for modal structural identifications have been conducted on the masonry arch through vibration measurements [13]. the frequencies and the modal shapes are estimated both for the undamaged arch and for damaged arch for different values of the increasing static force. as strains are measured at 11 points of the extrados and intrados of the arch, it was also possible to evaluate the centerline curvature mode shape. here, the novel two-dimensional model is calibrated in order to reproduce the measured quantities on the experimental apparatus presented in [13], in particular the values of modal frequencies obtained by vibration measurements are compared in tab. 1 with the same quantities obtained by the proposed numerical model. for sake of brevity, only the modal parameters related to first two in-plane modes of vibration of the arch computed in the undamaged condition are herein considered. t j. toti et alii, frattura ed integrità strutturale, 29 (2014) 166-177; doi: 10.3221/igf-esis.29.15 168 f r l t w x y h d s figure 1: geometry of the masonry arch. f1 [hz] f2 [hz] experimental 35.59 72.11 numerical 35.80 73.23 error [%] 0.5 2.5 table 1: comparisons between the first two experimental and numerical natural frequencies. fig. 2 shows the direct comparison between modal curvatures '' , experimentally measured and numerically evaluated, plotted along the ratio s/sa, in which s and sa being the curvilinear abscissa and the total length along the arch centerline, respectively. 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 -1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1  s/s a experimental mode 1 experimental mode 2 numerical mode 1 numerical mode 2 ‐‐‐ figure 2: curvature mode shapes. j. toti et alii, frattura ed integrità strutturale, 29 (2014) 166-177; doi: 10.3221/igf-esis.29.15 169 numerical model nonlocal damage-plastic model nonlocal damage-plastic model [12] is herein adopted to model the macroscopic cyclic behavior of the material point of the examined structure. the model is able to account for the tensile and compressive damage, the accumulation of irreversible strains and the unilateral phenomenon, i.e. the stiffness recovery and loss due to crack closure and reopening. the stress-strain constitutive relationship is given by the following expression:         1 11 1 1e et cd h j d h j      σ σ (1) with    σ c ε π ce (2) where σ and σ are the stress tensor and effective stress tensor, respectively; ε , π and e are the total strain, the plastic strain and elastic strain, respectively; c is the fourth-order constitutive tensor; td and cd are two damage variables which describe the stiffness degradation of the masonry in tension and compression, respectively; 1 ( ) ej tr e is the first invariant of the elastic strain;  h x denotes the heaviside function,   1h x  if 0x  , otherwise   0h x  . the evolution of the plastic strain is described by introducing a yield function representing a branch of a modified hyperbola and the loading-unloading conditions in the kuhn-tucker form:      2 21 2 1 2 0y y y y yf a b                   σ (3)    0, 0, 0y y y f f f         π σ σ σ    (4) where 1 and 2 are the principal values of the effective stress tensor σ ; the bracket symbol .  denotes the negative part of the number; y is the uniaxial compressive strength of the concrete related to the hyperbola asymptotes y through the expression  2 /y y ya    ; a and b are parameters governing the shape of the yield function; in the following analyses, it is always assumed 2 40.1 n mma  and 1b  ;  is the plastic multiplier. as a damage softening constitutive law is introduced, the localization of the strain and damage variables could occur. in order to overcome this pathological problem, to account for the correct size of the localization zone and, also, to avoid strong mesh sensitivity on the numerical results in finite element analyses, a nonlocal constitutive law is considered both for the compressive damage and the tensile damage. in particular, the evolution of the compressive damage cd is combined with the development of the plastic strain through the following cubic relationship:             3 2 3 2 2 3 max 0, min 1, withc c c history u u d d d (5) where u is the final accumulated plastic strain associated with the compressive damage 1cd  ;  is the nonlocal counterpart of the accumulated plastic strain given by the following expression:        1 , , c c d d           x x y y x y (6) being 0 t dt   π the local value of the accumulated plastic strain;   2 2, 1 /c cr    x y x y the compressive weight function which determines the influence of the point y on x ; the bracket symbol .  the positive part of the a j. toti et alii, frattura ed integrità strutturale, 29 (2014) 166-177; doi: 10.3221/igf-esis.29.15 170 number; the parameter 2 cr is the compressive characteristic length, which contributes to the definition of nonlocal accumulated plastic strain. the evolution of the tensile damage parameter td is governed through the following nonlocal exponential law:                 0 0exp max 0, min 1, with eq eq t t t history eq k d d d (7) where 0 is a material parameter indicating damage threshold strain; eq is the nonlocal equivalent strain defined as:        1 , , eq t eq t d d           x x y y x y (8) with 2 2 1 2eq e e    the equivalent elastic strain; 1e and 2e are the principal elastic strains;   2 2, 1 /t tr    x y x y defines the tensile weight function, with 2 tr the tensile characteristic length, which contributes to the definition of nonlocal equivalent strain. finally, the condition that the damage in compression must be lower than the one in tension is enforced t cd d . the constitutive law defined in eq. (1), for particular strain paths and damage conditions can be lead to discontinuities in the response of the material point. indeed, for an isotropic cohesive material subjected to 1j history and to a constant elastic shear strain xye , the shear stress is         1 12 1 1 1e exy xy t cg e d h j d h j        , with g the shear modulus. if t cd d the value of shear stress xy undergoes a sudden jump, when 1 ej changes from positive to negative value or vice-versa. while it can be considered realistic to have a stiffer shear response when the material point is subjected to volumetric contraction with respect to the case of volumetric expansion, because of the positive effect of the friction in compression, this strong discontinuity of response of the material point can be considered undesirable from both a physical and a mathematical point of view. for this reason, a regularized form of the heaviside function can adopted with the aim to avoid annoying jumps in the response; in particular, the following regularized form is considered for the heaviside function:   1 1 / 1 e e j h h j e   (9) where h is a small parameter governing the regularization effect (h=0.0001  0.001). finite element mesh a two-dimensional plane stress finite element model of the arch has been constructed. the opportune choice of the element size has been investigated demonstrating that a finite element model characterized by a total of 320 four node isoparametric quadrilateral elements (fig. 3a) is accurate. the chosen mesh assures a satisfactory numerical result, particularly with reference to the robustness in the frequency evaluation obtained by modal analysis (see the following section). indeed, considering refined meshes characterized by a higher number of finite elements, the first fundamental modal frequencies do not change significantly. concerning the constitutive laws, the above introduced cohesive continuum formulation is considered to model the macroscopic behavior of the masonry material. calibration n inverse procedure, based on the results of the dynamic and static tests carried out in [13], is herein developed in order to derive some material properties of the arch. the young’s modulus e , the poisson’s ratio  and the mass density  are set through a finite element updating procedure, using the modal structural properties estimated with the dynamic tests. in particular, the following objective function  to be minimized is considered: a j. toti et alii, frattura ed integrità strutturale, 29 (2014) 166-177; doi: 10.3221/igf-esis.29.15 171   22 2 , ,exp , , 2 1 , exp -1 , , with 2 n i n i i i i i e r r                  (10) where n denotes the number of the autofrequencies, ,ir is the residual, ,ni and ,expi are the values of the autofrequencies deriving by the numerical computation and experimental test, respectively. in particular, in the expression (10) of the objective function only the frequency of the first mode is taken into account. specifically, the solution is found using an optimization function in matlab and it is characterized by  4000 mpae , 0.2  and 325 kn/m  . fig. 3b-c show the modal shapes and the corresponding autofrequencies obtained by the developed updating technique. the comparison between the experimental modal parameters and the numerical one, provided in fig. 2 and in tab. 1, confirms a good accordance in term of curvature mode shapes and autofrequencies. f1=35.80 hz f2=73.23 hz a) b) c) figure 3: finite element model of the masonry arch: a) mesh; b) mode shape and frequency for mode 1; mode shape and frequency for mode 2. moreover, in tab. 2 the comparison between the considered mesh with 320 elements and two different meshes of 160 and 640 elements, respectively, shows that the chosen discretization assures the converge of the results. natural frequencies 1 2 elements 160 320 640 35.90 35.80 35.80 73.33 73.23 73.23 f f table 2: natural frequencies obtained with three different discretizations of the arch model. 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 f [k n ] v [mm] experimental data damage model 0=3.0e-005 damage model 0=3.5e-005 damage model 0=4.0e-005 figure 4: response of the masonry arch: comparison between the experimental result data and numerical results obtained for different values of the 0 . j. toti et alii, frattura ed integrità strutturale, 29 (2014) 166-177; doi: 10.3221/igf-esis.29.15 172 the model parameters characterizing the post peak behavior are set on the basis of the nonlinear response determined during the static test. several computations have been performed in order to study the influence of each parameter on the global behavior of the masonry arch; finally, the post peak parameters are set as the ones which ensure a satisfactory approximation of the global experimental behavior. in the numerical simulations, the action of the static force is reproduced by applying a monotonic displacement v along the y direction. sensitivity analyses of the solution demonstrate a strong influence of the post peak parameters characterizing the behavior in tension ( 0 and k ), while a quite reduced dependence of the parameters governing the behavior in compression ( y and u ). in particular, the sensitivity analyses of the response as function of 0 and k are depicted in fig. 4 and fig. 5, respectively, where the numerical response, plotted in term of nodal reaction versus the prescribed displacement, is compared with the experimental data. the set parameters governing the nonlinear behavior of the material are reported in tab. 3, with c tr r r  . it is also possible to observe from fig. 4 and fig. 5 that the elastic properties (i.e. e and  ) defined through the updating procedure provide a good estimation of the structural initial stiffness computed through the static analyses. 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 f [k n ] v [mm] experimental data damage model k=250 damage model k=500 damage model k=1000 figure 5: response of the masonry arch: comparison between the experimental result data and numerical results obtained for different values of the k .  [kn/m3] e [mpa]  0 k y [mpa] u r [mm] 25.0 4000 0.2 3.5e-005 500 -1 -0.07 30 table 3: material parameters adopted in the numerical model. damage propagation static-cyclic test he mechanical behavior of a masonry arch under cyclic loading is analyzed. the static-cyclic test performed in [13] is reproduced. the loading history reported in tab. 4 is applied to the displacement v in order to simulate the cycles of the experimental test. the comparison between the numerical result and experimental data of the global mechanical behavior is illustrated in fig. 6. observing this figure, it is possible to remark that the proposed modeling approach is able to catch with good approximation the actual behavior of the structural system occurred during the loading and unloading phases. fig. 7 shows the tensile damage map obtained by the simulation in correspondence of the two time steps indicated in fig. 6 with the letter a and b, respectively. from fig. 7, it appears evident that the collapse mechanism developed by the arch is characterized by the formation of four hinges, two on extrados and two on intrados. with reference to [13], the numerical model well reproduces the failure mechanism developed by the arch during the static test, indeed, the tensile damage assumes close to 1 in the zones where the fracture opening occurred. t j. toti et alii, frattura ed integrità strutturale, 29 (2014) 166-177; doi: 10.3221/igf-esis.29.15 173 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 f [k n ] v [mm] numerical data damage model a b 0 1 2 3 4 5 6 7 8 figure 6: cyclic test: comparison between numerical and experimental results. a) 0.00e+00 1.00e-01 2.00e-01 3.00e-01 4.00e-01 5.00e-01 6.00e-01 7.00e-01 8.00e-01 9.00e-01 1.00e+00 9.66e-01 0.00e+00 dt b) 0.00e+00 1.00e-01 2.00e-01 3.00e-01 4.00e-01 5.00e-01 6.00e-01 7.00e-01 8.00e-01 9.00e-01 1.00e+00 9.95e-01 0.00e+00 _________________ s t r e s s 4 dt figure 7: tensile damage map: a) time step a; b) time step b; loading history time step 0 1 2 3 4 5 6 7 8 [mm] 0 0.38 0.04 0.42 0.07 0.45 0.1 0.9 0.24v table 4: loading history for the displacement v dynamic test numerical analyses are conducted to investigate the damage propagation induced by a sinusoidal synchronous motion applied to all nodes of base    0 0sin 2gu t u f t , where 0u and 0f indicate the displacement amplitude and the frequency of the harmonic imposed displacement, respectively. the propagation of the damage in the arch is analyzed for frequency ratio 0 1f f  equal to 0.7 and 1.3. for each frequency ratio, two values of the displacement amplitude are considered: 0 0.10 mmu  and 0 0.11 mmu  . the equations of motion are integrated until the time 5 s is reached, with a time step equal to 0.001 s (approximately 1/14 of the second natural period of vibration) in order to correctly take into account the dynamics of the first two modes. the comparison between the damage model and the elastic model is provided in term of time histories of the displacement v evaluated at the extrados of the key-section of the arch. the effect of damage on the dynamic response is analyzed through the fourier spectral analyses. fig. 8 and fig. 9 show the displacement response and fourier spectra for all the considered forcing functions, adopting both elastic and the proposed damage model. observing these figures, it can be remarked that: the arch collapses before 5 s for 0.7  with 0 0.11 mmu  and for 1.3  with 0 0.10 mmu  or 0 0.11 mmu  ; the development of the damage in the nonlinear model leads, away from the failure mechanism, only to a decrease in time of the natural frequencies, while the frequency contents become richer for all cases close to the collapse condition; the reduction of the frequency contents became faster with increasing the forcing displacement amplitude. in particular, for 0.7  with 0 0.11 mmu  at the time equal to 1.5 s the first natural frequency of the damaged system is approaching the lower forcing one, the arch goes in resonance following its first modal shape and, as consequence, collapses. on the contrary, for the other case, characterized by lower forcing displacement amplitudes, the structural j. toti et alii, frattura ed integrità strutturale, 29 (2014) 166-177; doi: 10.3221/igf-esis.29.15 174 system does not reaches after 5 seconds the critical condition; the damage of the arch leads only to energy dissipation. in fact, the peak amplitudes associated to the frequency contents appear lower than the ones obtained with the elastic model, where the energy dissipation is always null. instead, the collapse of the arch for the case 1.3  is not due to the resonance phenomenon, but it occurs because the higher forcing frequency leads to a larger base acceleration and, as consequence, higher inertia forces. 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 -0.4 -0.2 0 0.2 0.4 v [m m ] t [s] 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 -0.4 -0.2 0 0.2 0.4 v [m m ] t [s] 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 -0.4 -0.2 0 0.2 0.4 v [m m ] t [s] 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 -0.4 -0.2 0 0.2 0.4 v [m m ] t [s] elastic model damage model a) b) c) d) figure 8: time history of the displacement: 0.7  a) 0 0.10 mmu  ; b) 0 0.11 mmu  ; 1.3  c) 0 0.10 mmu  ; d) 0 0.11 mmu  in fig. 10, the tensile damage maps close to the collapse condition for 0.7  , with 0 0.11 mmu  and 1.3  with 0 0.10 mmu  and 0 0.11 mmu  are illustrated. in particular, it can be remarked that for these three analysis cases, before 5 s, the arch tends to develop a four hinges collapse mechanism compatible with the first mode of vibration. indeed, the tensile damage variable assumes higher values exactly in the four zones where the maximum curvature values of first mode occur (fig. 2). the damage variable reaches first the unitary value at the two support areas because in these regions the bending curvatures are larger than the ones of other two zones (fig. 2). j. toti et alii, frattura ed integrità strutturale, 29 (2014) 166-177; doi: 10.3221/igf-esis.29.15 175 a) 0 50 100 150 200 0 0.05 0.1 0.15 0.2 a [m m ] f [hz] elastic model damage model b) 0 50 100 150 200 0 0.05 0.1 0.15 0.2 a [m m ] f [hz] elastic model damage model c) 0 50 100 150 200 0 0.05 0.1 0.15 0.2 a [m m ] f [hz] elastic model damage model d) 0 50 100 150 200 0 0.05 0.1 0.15 0.2 a [m m ] f [hz] elastic model damage model figure 9: fourier spectra of the displacement response: 0.7  a) 0 0.10 mmu  ; b) 0 0.11 mmu  ; 1.3  c) 0 0.10 mmu  ; d) 0 0.11 mmu  ; conclusions he present work focuses on the development of a computational strategy for studying the damage propagation in a masonry arch induced by slow cyclic and dynamic loadings. a nonlocal plastic damage model is adopted in order to reproduce the cyclic macroscopic behavior of the masonry material. an inverse procedure is used to define the material model parameters. in particular, the mass density and the elastic properties are set through an updating procedure, using the first two modal natural frequencies identified by dynamic tests. the found solution assures a good accordance of the modal parameters in term of curvature mode shapes and natural frequencies of the first two modes of vibrations between experimental and numerical quantities. the calibration of post peak parameters of the proposed formulation are set on the basis of the experimental nonlinear response determined during a static test. a numerical example concerning a slow cyclic test shows the effectiveness of the developed arch models in reproducing both the experimental response and the collapse mechanism. finally, the masonry arch is excited by sinusoidal imposed base motions to study the effect of both the amplitude and the frequency content of the base motion on damage propagation. the numerical computations conducted in the time and analyzed in the frequency content, show that the damage model is able to catch the dissipation of energy and the reduction of the natural frequencies. in particular, the base motions at forcing frequency higher than the first natural one is accompanied by large accelerations which induce the collapse of the structure. in the case of forcing frequency lower than the first natural one due to the stiffness degradation, even in the presence of small imposed acceleration, the collapse occurs due to an on-going resonance mechanism between the decreasing first natural frequency and the lower forcing frequency. t j. toti et alii, frattura ed integrità strutturale, 29 (2014) 166-177; doi: 10.3221/igf-esis.29.15 176 a) 0.00e+00 1.00e-01 2.00e-01 3.00e-01 4.00e-01 5.00e-01 6.00e-01 7.00e-01 8.00e-01 9.00e-01 1.00e+00 9.91e-01 0.00e+00 _________________ s t r e s s 4 time = 1.64e+00time = 1.64e+00 dt b) 0.00e+00 1.00e-01 2.00e-01 3.00e-01 4.00e-01 5.00e-01 6.00e-01 7.00e-01 8.00e-01 9.00e-01 1.00e+00 8.90e-01 0.00e+00 _________________ s t r e s s 4 time = 3.50e-01time = 3.50e-01 dt c) 0.00e+00 1.00e-01 2.00e-01 3.00e-01 4.00e-01 5.00e-01 6.00e-01 7.00e-01 8.00e-01 9.00e-01 1.00e+00 9.04e-01 0.00e+00 _________________ s t r e s s 4 time = 7.00e-01time = 7.00e-01 dt figure 10: damage maps: 0.7  , a) 0 0.11 mmu  ; 1.3  , b) 0 0.10 mmu  ; c) 0 0.11 mmu  . references [1] ceci, a. m., contento, a. fanale, l. galeota, d. gattulli, v., lepidi, m., potenza, f., structural performance of the historic and modern buildings of the university of l’aquila during the seismic events of april 2009, engineering structures, 32 (2010) 1899-1924. [2] heyman, j., the stone skeleton, international journal of solids and structures, 2(1966) 249-279. [3] de luca, a., giordano, a., mele, e, a simplified procedure for assessing the seismic capacity of masonry arches. engineering structures, 26 (2004) 1915-1929. [4] de lorenzis, l., dejong, m., ochsendorf, j., failure of masonry arches under impulse base motion, earthquake engineering and structural dynamics, 36(2007a) 2119-2136. [5] pelà, l., aprile, a., benedetti, a., seismic assessment of masonry arch bridges, engineering structures 31(2009), 1777-1788. [6] sacco, e., toti, j., interface elements for the analysis of masonry structures, international journal for computational methods in engineering science and mechanics, 11 (2010) 354–373. [7] resemini, s., lagormarsino, s., displacement-based methods for the seismic assessment of masonry arch bridges. fifth international conference on arch bridges arch’07, (2007) 441-450. [8] cancelliere, i., imbimbo, m., sacco, e., experimental tests and numerical modeling of reinforced masonry arches. engineering structures, 32 (2010) 776-792. j. toti et alii, frattura ed integrità strutturale, 29 (2014) 166-177; doi: 10.3221/igf-esis.29.15 177 [9] pijaudier-cabot, g., bažant, z., nonlocal damage theory, journal of engineering mechanics asce, 113 (1987) 1512–1533. [10] borino, g., failla, b., parrinello, f., a symmetric nonlocal damage theory, international journal of solids and structure, 40 (2003) 3621-3645. [11] marfia, s., sacco, e., toti, j., a coupled interface-body nonlocal damage model for frp strengthening detachment. computational mechanics, 50 (2012) 335-351. [12] toti, j., marfia, s., sacco, e., coupled body interface nonlocal damage model for frp detachment, computational method in applied mechanics, 260 (2013) 1-23. [13] ramos, l.f., de roeck, g., lourenço p.b., campos-costa, a., damage identification on arched masonry structures using ambient and random impact vibrations, engineering structures, 32 (2010) 146-162. [14] toti, j., gattulli, v., sacco e., nonlocal damage propagation in the dynamics of masonry elements. computers & structures, submitted 2014. [15] bažant, z.p., pijaudier-cabot, measurement of characteristic length of nonlocal continuum, journal of engineering mechanics asce, 115 (1989) 755–767. microsoft word numero_55_art_26_2961 b. đorđević et alii, frattura ed integrità strutturale, 55 (2021) 336-344; doi: 10.3221/igf-esis.55.26 336 failure analysis and numerical simulation of slab carrying clamps branislav đorđević, simon sedmak innovation center of faculty of mechanical engineering, university of belgrade, 11120 belgrade, serbia brdjordjevic@mas.bg.ac.rs, https://orcid.org/0000-0001-8595-6930 simon.sedmak@yahoo.com, https://orcid.org/0000-0002-2674-541x drakče tanasković, marko gajin hbis group serbia iron & steel ltd., 11300 smederevo, serbia drakcetanaskovic@gmail.com filip vučetić innovation center of faculty of mechanical engineering, university of belgrade, 11120 belgrade, serbia fvucetic@mas.bg.ac.rs abstract. the goal of this study was to determine the reasons for failure of slab carrying clamps which had occurred in one of the clamp support levers. detailed fractography analysis revealed that there was a welded joint at the location where failure occurred, which was not expected, since the second lever was not welded. once the presence of the welded joint was confirmed by hardness measuring and the analysis of chemical composition, attempts were made to determine which materials were used for the welding, in order to obtain a more detailed insight into the nature of the failure. the first step of this extensive analysis involved the development of a simple, approximated numerical model, with the goal of determining the location of stress concentration in the support lever, so that it could be compared to the real failure location. further investigations will involve more complex models, including the ones that will simulate crack growth, once its location is numerically verified. keywords. failure; fem analysis; simulation; welding influence; fractography. citation: đorđević, b., sedmak, s., tanasković, d., gajin, m., vučetić, f., failure analysis and numerical simulation of slab carrying clamps, frattura ed integrità strutturale, 55 (2021) 336-344. received: 04.12.2020 accepted: 25.12.2020 published: 01.01.2021 copyright: © 2021 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. introduction nalytical calculations used for remaining life assessment, strength and load of machine elements provide the basis for checking the reliability of structures and elements under their corresponding working conditions. scientific fields such as strength of materials and mechanics represent the basic disciplines which are used for this purpose, a https://youtu.be/vsb8tjxfcvu b. đorđević et alii, frattura ed integrità strutturale, 55 (2021) 336-344; doi: 10.3221/igf-esis.55.26 337 even today, often combined with real experience. relations resulting from these disciplines were included in standards and are typically used in basic calculations related to equipment used for various purposes, subjected to different types of load. this approach is often not sufficient when it comes to analyzing of failure causes, and requires the aid of other scientific discipline and approaches, such as fracture mechanics and finite element methods (fem). this combination of analytical and numerical calculation is widely used in solving of certain engineering problems, wherein the assumptions and approximations adopted for the analytical calculations are used as input data for the fem simulation. these simulations can be based on approximations resulting from strength of materials and statics principles [1-4], typically by their combined use. in addition, the combination of fracture mechanics and fem principles is used for determining of the remaining life of structures, utilising experimental fracture mechanics data as the basis for the numerical simulation, as can be seen in the works of milovanović et al [5] and jeremić et al [6], both of which refer to hydro power plant equipment integrity (turbine in the former and a penstock in the latter case). in both cases, analytical and numerical analyses provided a solid basis for structural integrity of pipelines and other equipment via finite element method application. this combination is widespread in other literature as well, especially in case studies involving the investigation of failure causes, damage effects and integrity assessment, for a wide variety of structures [7-10]. more often than not, even all of this is insufficient, and other methods may need to be included, such as risk analysis [11, 12]. each of the previously described approaches and analysis methods is often not sufficient, even with all assumptions and including of other disciplines, in terms of understanding of engineering problems, especially when it comes to structural failure analysis. the cause of this can sometimes lie in the simple facts, like not knowing the properties of the broken equipment, the ways in which it was manufactured, manufacturing process etc. all afore mentioned in previous sentence can be caused by age, or loss of certain technical documentation due to unexpected circumstances, human negligence, etc. such circumstances impose the need for some form of inspection of the fractured surface, or even a thorough analysis of the whole structure or equipment, along with the need to take account all aspects which could affect and lead to equipment failure. insufficient knowledge of the state of materials often requires a chemical and/or microstructural analysis of the fractured surface in order to gain better insight into the nature of the damage that had occurred [13-15]. if welding is included in this problem, along with its various technological, metallurgical and geometry, related problems become additionally complicated, especially when welding technology parameters are unknown (including the filler material characteristics, amperage, voltage etc.), or when it is not known if there was any welding to begin with. one such study, by dzindo et al [16], which required the use extended finite element method (xfem) for the purpose of simulating fatigue crack growth in a welded joint. it should be taken into account that insufficient amount of relevant information for the analysis can result in wrong conclusions taking the whole study in a wrong direction. (a) (b) figure 1: a) 3d model of the slab carrying clamps; b) one of the clamp levers where the failure occurred. b. đorđević et alii, frattura ed integrità strutturale, 55 (2021) 336-344; doi: 10.3221/igf-esis.55.26 338 this paper presents the analysis of slab carrying clamps failure, in the part of the clamp used for transporting slabs through the steel mill, wherein these slabs are used for further manufacturing of sheets in the hot-rolling facility. clamps are exposed to static loads during their work life. in order to determine the reasons behind this failure, analytical and numerical calculations (using fem) were performed, wherein numerical simulations were performed using abaqus software. additionally, visual inspection of the entire equipment was performed, along with the chemical analysis of the fractured surface, which will be presented here in detail. fig. 1a shows the 3d model of the clamps, whereas fig. 1b shows the appearance of the broken support lever, i.e. the location of the failure. an additional complication arose due to the fact that the visual testing revealed a welded joint in one of the support levers, which resulted in the need for additional analyses, including the determining of the chemical composition of the fracture surface and discovering the reason why fracture had occurred. based on the aforementioned figure, i.e. figure of lever fracture, it can be observed that the influence of welding was noticeable, but despite of that the following questions arose: why did failure occur and why was it not located in the central hole of the support lever? macro-fractography of broken lever surface s can be seen in the above figure, one pair of clamps, with a carrying capacity of 35t consists of two levers. fracture occurred in both of these levers, due to exploitation conditions, in service, which resulted in loads far exceeding the expected, i.e. calculated values. the second lever most likely failed after the first one broke, as it could not carry the full load on its own. on the fig. 2 are presented fracture surfaces of the levers after performed visual inspection. this inspection also revealed that one of the lever was actually welded. this was initially assumed based on the fracture surface appearance, due to the presence of fusion lines. figs. 2a and 2b show the fracture surface of the welded lever, whereas fig. 2c shows the fracture surface of non-welded lever. differences in these surfaces of the two levers can be easily observed. in order to verify the above assumption that one of the levers was welded, hardness testing was performed on both levers, in the fracture location. this measuring was performed using adequately calibrated equipment, and is given in hb units of hardness. fig. 3a shows the measuring points on the lever which was welded. it can be seen that the region in the vicinity of the fracture surface has higher hardness (236 hb), compared to the region further away (191 hb), which indicates that this was the heat affected zone of the weld. fig. 3b shows the measuring point in the lever which was not welded, also located in the vicinity of the fracture surface. no significant differences in hardness values were observed in this case, suggesting a much more homogeneous material, i.e. that there was no welded joint in this lever. magnetic flux method of the ndt examination revealed no other cracks in the vicinity of fracture surfaces of both broken levers. figure 2: a) appearance of fracture surfaces of the welded lever; c) fracture surface of the non-welded lever. a a) b) c) b. đorđević et alii, frattura ed integrità strutturale, 55 (2021) 336-344; doi: 10.3221/igf-esis.55.26 339 figure 3: a) hardness values and measuring locations on the welded lever; b) hardness values and measuring location on the non-welded lever. element [%] c si mn p s cr ni cu al mo ti fracture surface (weld) 0.234 1.540 3.451 0.023 0.010 19.28 8.685 0.143 0.033 0.3172 0.0582 base material 0.2473 0.252 0.641 0.003 0.0072 0.0939 0.1148 0.249 0.034 0.0186 0.002 element [%] as v nb sn w sb ta co n ca b pb fracture surface (weld) 0.0059 0.1197 0.0303 0.0174 0.0019 / / 0.0477 / 0 0 0 base material 0.009 0.003 0.001 0.011 0.0103 0.003 0.003 0.0184 0.01 0 0 0 table 1: chemical composition of welded lever and the base material. chemical composition analysis he fact that one of the slab carrying clamp support levers was welded unknown until the failure had occurred. it should be pointed out that this equipment was in exploitation for over 20 years, and that the original documentation had no information about one lever being welded. it was known that the base material for the levers was s355 j2 g3, which is a non-alloy structural steel, with a yield strength is 350 mpa, while its tensile strength is in rage of 490-630 mpa [17], which depends on sheet thickness. on the other hand, characteristics and mechanical properties of the electrode, i.e. filler material, used for welding were unknown, as well as the welding parameters. chemical analysis was performed in order to determine which type of filler material was used for welding of the lever, as well as to determine the state of the base material. this analysis was performed using optical emission spectrometry. chemical composition of the fracture surface of the welded joint and the base material is shown in tab. 1. based on the chemical composition, mainly the chrome, nickel and manganese content, it can be concluded that the filler material used was similar to the high-alloyed austenitic type of electrode from series inox 18/8, manufactured by jesenice [18]. these types of electrodes are obviously not the electrodes t a) b) b. đorđević et alii, frattura ed integrità strutturale, 55 (2021) 336-344; doi: 10.3221/igf-esis.55.26 340 that should be used for welding of low-alloyed structural steels, although their mechanical properties are similar and slightly better compared to the base metal. fem analysis analytical calculation he stresses as well as loading in the lever pair were determined by using analytical calculations based on relations from scientific disciplines such as strength of materials and statics [19-21]. the calculation given here only applies to a relatively uniform load, i.e. the load which is equally distributed between the two clamps. certain approximations were necessary for the sake of calculation, which included representing of the levers as simple beams and adopting of point a as the clamp support (fig. 4). fig. 4a represents the clamp lever loading scheme. force q is the maximum working load of the clamps and is equal to 35t (converted to 343.5 kn). force gx* represents the weight of the clamps and is equal to 10.5 t, whereas fk represents the sum of these two forces. lever dimensions are given in centimeters. figure 4: a) loading scheme of the levers, with their dimensions; b) lever cross section at the support o location and its dimensions. by decomposing the forces along the directions of the levers and their normal components, and by using the well-known statics relation given by (1), the moment for point o is obtained, i.e. for the circular opening approximated with it. this moment equals 72688 kncm. since this moment is transferred onto four levers, the moment for each levers is equal to 18172 kncm according to (2).  no p pm f l (1) 1 4 o o m m (2) fig. 4b shows the cross-section of one of the levers at the support, along with the dimensions. basic concepts of strength of materials were used to determine the cross-section centre mass, moment of inertia and the elastic section modulus in the “upper” and the “lower” zone (denoted as u and l), and the stresses in both these zones were obtained for a lever which was subjected to compression in the “upper” and tension in the “lower” zone, as shown by relations (3) and (4). values of stresses obtained by these calculations were as follows: -93 mpa for the upper zone (negative due to the fact these were compressive stresses), and 88.4 mpa in the lower zone of the cross section. these values were below the allowed stress for the lever, which was 230 mpa. this value was determined based on the yield stress of the base material and the safety factors which are adopted in these cases (and are usually around 1.5). t a) b) b. đorđević et alii, frattura ed integrità strutturale, 55 (2021) 336-344; doi: 10.3221/igf-esis.55.26 341    1 u u o x x m w (3)   1 l l o x x m w (4) in the case of extremely non-uniform load, to be accurate, when only one pair of clamps is subjected to the full load, maximum values for the “upper“ and “lower“ zones are obtained -186 mpa and 176.8 mpa, respectively. even though these values are, as expected, two times higher than the stresses obtained in the case of uniform load on both pair of clamps, and they are still below the allowed stress levels. these remarks and afore obtained load level leave the space for numerical simulation and fem analysis, because analytical calculation did not give the answer of reason for fracture occurrence. analytical calculations presented in this section provided the input data (in terms of loads) and the information necessary (allowed stresses and actual stresses in the levers) for numerical simulation, which was performed in abaqus dassault systèmes software package. numerical part of the analysis will be presented in the following section. simulation in abaqus numerical simulation in this research was focused on one of the levers, for the purpose of determining the stresses that would occur in it, and whether the critical location (where highest tensile stresses were observed) would correspond to the actual fracture location, without taking into account the material heterogeneity. this was done in order to see if the initial assumptions about the model were correct, and to determine the location of crack initiation in the future, improved models. for the reason of initial model simplicity, certain approximations were made to the model – only the fractured lever itself was modelled, and its connection with the upper lever which is supported in point a from the fig. 4 was replaced with the corresponding force fp. it should be noted that this force was decomposed into x and y axes components, instead along the lever axis, due to abaqus requirements. hence, the values of this load were -269034 (x axis) and 143048 n (y axis). to avoid confusion with the results, all forces were defined in newtons and dimensions were assumed to be in milimeters, so that the stress results would be obtained in n/mm2, i.e. in mpa. another load was defined at the bottom part of the lever, and it was equal to one quarter of the work load (since only one lever was modelled). hence it was equal to -85837.5 n. model geometry and loads can be seen in fig. 5a. boundary conditions were defined in the central opening, by constraining its inner surface. all displacements and rotations were prevented, with the exception of rotation about the z axis, in order to replicate the real boundary conditions as close as possible. there is also a possibility to further improve this boundary condition, but this will be done in the future, once new and more complex models are developed. the boundary condition can be seen in fig. 5b. (a) (b) figure 5: a) numerical model geometry and loads (defined in rp-1 and rp-2 points b) the boundary condition (only the rotation about the z-axis is allowed. b. đorđević et alii, frattura ed integrità strutturale, 55 (2021) 336-344; doi: 10.3221/igf-esis.55.26 342 finally, the finite element mesh is given in fig. 6. element size was approximately 13.5 mm, since it was determined that this size provides sufficient convergence of results, after a number of iterations. element type used for this analysis was c3d8r, and the total number of elements and nodes was 30285 and 38330, respectively. figure 6: finite element mesh of the model. figure 7: strain (top) and stress (bottom) distribution in the numerical model. b. đorđević et alii, frattura ed integrità strutturale, 55 (2021) 336-344; doi: 10.3221/igf-esis.55.26 343 the results, including stress and strain magnitudes and distribution, are shown in fig. 7 below. as can be seen, there are some very high stress values obtained in certain locations, which suggests that a more detailed approach is necessary in order to make a fully functional model. however, the goal of this initial version was to determine the location of the maximum tensile stresses, which is denoted by the red colour in the aforementioned figure. the areas with much higher stresses (grey) can be neglected in this case since they are:  in the support, which is a commonly encountered case in static numerical simulations, and can be ignored.  in the upper zone of the lever, where compressive stresses are dominant. since these stresses have no influence on crack initiation, they were also not relevant. strain distribution indicated that the most deformed part, outside of the support, was the region where highest tensile stresses, with a magnitude of 138.5 mpa, had occurred. if this is compared to the real situation, it can be seen that there is good agreement between the locations of highest tensile loads, i.e. the potential crack in the model would be initiated near the location where the actual support lever broke. the stress value in this case is still considerably below the allowed stress, although it is over 50% higher than the analytical, which also confirms that the model needs to be improved. conclusion ailure of the slab carrying clamp support lever had occurred in the heat affected zone of the welded joint. it can be concluded and repeated from the introduction that welding had its influence, more accurately, lever failure was likely caused by inadequate preheating (taking into account the 70 mm thickness of the welded joint), which contributed to the forming of cold cracks specific for ferritic base material. this lead to a significant decrease in the toughness of the welded joint, which made it more vulnerable to calculated exploitation conditions. performed and presented analytical calculation shows that highest stresses were indeed in the part of the lever where failure had occurred. the second lever failed in an identical manner, since it could not carry the load for both ones, it is simple remark that is not questionable. the following fact about structures like these is well-known: lever used as a load-bearing element should not have been welded and exposed to a high temperature. non-uniform chemical composition of lever has its influence and indicates that allowed stress in analytical calculation has a different, lower, value. exposing to high temperature may have had an influence on grain size of the lever microstructure as well, which can lead to a brittle and unpredictable fracture. numerical simulation of the behavior of the lever under the load also indicated that the highest tensile stresses, which are responsible for crack initiation, were at the location corresponding to the real failure location. however, this model was made with numerous approximations, and in order to obtain more accurate results in terms of stress distribution and magnitudes, it will need to be further developed. this includes the making of a more complex model, which would include more carrying clamp elements, and slightly different boundary conditions. once the comparison between these models is made, the relevant one will be adopted as the base for analyzing the behavior of this structure in the presence of a crack in the heat affected zone. acknowledgement he authors of this paper acknowledge the support from serbian ministry of education, science and technological development contract no. 451-03-68/2020-14/200135 and 451-03-68/2020-14/ 200213. references [1] đurđević, đ., anđelić, n., milošević-mitić, v., maneski, t., rakin, m., đurđević, a. (2019). influence of encastering on thin-walled cantilever beams with u and z profiles on the magnitude of equivalent stress and deformation, structural integritya and life, 19(3), eissn 1820-7863, pp. 251–254 . [2] akbari, j., salami, o., isari, m. (2020). numerical investigation of the seismicbehavior of unanchored steel tanks with an emphasis on the uplift phenomenon, frattura ed integrità strutturale, 53, pp. 92-105. doi: 10.3221/igf-esis.53.08. f t b. đorđević et alii, frattura ed integrità strutturale, 55 (2021) 336-344; doi: 10.3221/igf-esis.55.26 344 [3] sobrinho, b., gomes, g., v. silva, w., silva, r., bezerra, l, palechor, e (2020). differential evolution algorithm for identification of structural damage in steel beams, frattura ed integrità strutturale, 52, pp. 51-66. doi: 10.3221/igf-esis.52.05. [4] gašić v., arsić, a., flajs, ž. (2019). experimental study on the stresses at the i-beam end-plate moment connection, structural integritya and life, 19(1), pp. 53–57. [5] milovanović, n., sedmak, a., arsic, m., sedmak, s. a., & božić, ž. (2020). structural integrity and life assessment of rotating equipment, engineering failure analysis, 104561. doi: 10.1016/j.engfailanal.2020.104561. [6] jeremić, l., sedmak, a., petrovski, b., đorđević, b., sedmak, s. (2020). structural integrity assessment of welded pipeline designed with reduced safety, technical gazzete, 27(5), pp. 1461-1466. doi: 10.17559/tv-20200413142538. [7] medjo, b. arsić, m., mladenović, m., savić, z., grabulov, v., radosavljević, z., rakin, m. (2020). influence of defects on limit loads and integrity of the pipeline at hydropower plant ‘pirot’, structural integrity and life, 20(1), pp. 82– 86 [8] martić, i., sedmak, a., mitrović, n., sedmak, s., vučetić, i. (2019). effect of over-pressure on pipeline structural integrity, technical gazzete, 26(3), pp. 852-855. doi: 10.17559/tv-20180708213323 [9] tanasković, d., tatić, u., đorđević, b., sedmak, s., sedmak, a. (2017). the effect of cracks on stress state in crane wheel hard-surface under contact loading, technical gazzete, 24(supplement 1), pp. 169-175. doi: 10.17559/tv-20151227221434. [10] molaei, s., attarian, m., kermajani, m., jahromi, s. k. g., alemi, m. (2019). failure analysis of a damaged drilling stabilizer, engineering failure analysis 103, pp. 517-529. doi: 10.1016/j.engfailanal.2019.05.014. [11] kirin, s., jeremić, l., sedmak, a., martić, i., sedmak, s., vučetić, i., golubović, t. (2020). risk based analysis of rhpp penstock structural integrity, frattura ed integrità strutturale, 2020, 14(53), pp. 345-352. doi: 10.3221/igf-esis.53.27. [12] zaidi, r., sedmak, a., kirin, s., grbovic, a., li, w., lazic vulicevic, l., sarkocevic, z. (2020). risk assessment of oil drilling rig welded pipe based on structural integrity and life estimation, engineering failure analysis 112, 104508. doi: 10.1016/j.engfailanal.2020.104508. [13] milovanović, n., đorđević, b., tatić, u., sedmak, s.a., štrbački, s. (2017). low-temperature corrosion damage and repair of boiler bottom panel tubes, struuctural integrity and life, 17(2), pp. 125–131. [14] wang, k., tan, z., cheng, c., gao, b., gao, g., misra, r. . k., & bai, b. (2016). effect of microstructure on the spalling damage in a 20mn2sicrmo bainitic fail, engineering failure analysis, 70, pp. 343–350. doi: 10.1016/j.engfailanal.2016.09.011. [15] bieniaś, j., dębski, h., surowska, b., sadowski, t. (2012). analysis of microstructure damage in carbon/epoxy composites using fem, computational materials science, 64, pp. 168–172. doi: 10.1016/j.commatsci.2012.03.033. [16] džindo, e., sedmak, s.a., grbović, a., milovanović, n., đođrević, b. (2019). xfem simulation of fatigue crack growth in a welded joint of a pressure vessel with a reinforcement ring, archive of applied mechanics, 89(5), pp. 919-926, doi: 10.1007/s00419-018-1435-1. [17] total materia http://www.totalmateria.com [18] elektrode jesenice catalogue – additional materials for welding (https://sij.elektrode.si) [19] beer, f. p., johnston jr, e. r., dewolf, j. t., mazurek, d. f. (2012). mechanics of materials (6th edition), mcgraw hill, isbn 978-0-07-338028-5. [20] meriam, j. l., kraige, l g. (2012). engineering mechanics – statocs (7th edition), john wiley & sons, inc., isbn: 9780-470-61473-0. [21] golubović, z., simonović, m., mitrović, z. (2007). mehanika – statika, mašinski fakultet univerziteta u beogradu, beograd. microsoft word numero_29_art_36 l. zhao et alii, frattura ed integrità strutturale, 29 (2014) 410-418; doi: 10.3221/igf-esis.29.36 410 numerical investigation on stress corrosion cracking behavior of dissimilar weld joints in pressurized water reactor plants lingyan zhao school of science, xi’an university of science and technology, xi’an 710054, china zhlyan7878@163.com he xue school of mechanical engineering, xi’an university of science and technology, xi’an 710054, china xue_he@hotmail.com fuqiang yang school of science, xi’an university of science and technology, xi’an 710054, china yang_afreet@163.com yaohong suo school of science, xi’an university of science and technology, xi’an 710054, china yaohongsuo@126.com abstract. there have been incidents recently where stress corrosion cracking (scc) observed in the dissimilar metal weld (dmw) joints connecting the reactor pressure vessel (rpv) nozzle with the hot leg pipe. due to the complex microstructure and mechanical heterogeneity in the weld region, dissimilar metal weld joints are more susceptible to scc than the bulk steels in the simulated high temperature water environment of pressurized water reactor (pwr). tensile residual stress (rs), in addition to operating loads, has a great contribution to scc crack growth. limited experimental conditions, varied influence factors and diverging experimental data make it difficult to accurately predict the scc behavior of dmw joints with complex geometry, material configuration, operating loads and crack shape. based on the film slip/dissolution oxidation model and elastic-plastic finite element method (epfem), an approach is developed to quantitatively predict the scc growth rate of a rpv outlet nozzle dmw joint. moreover, this approach is expected to be a pre-analytical tool for scc experiment of dmw joints in pwr primary water environment. keywords. dissimilar metal weld; stress corrosion cracking; residual stress; crack growth rate. introduction issimilar metal weld (dmw) joints are widely used to connect the low alloy steel (las) nozzles to austenitic stainless steel (ss) pipes in primary water systems of pressurized water reactors (pwr). to form a dmw joint, nickel-based alloy is generally pre-deposited on the ferritic reactor pressure vessel (rpv) nozzle face firstly, then d l. zhao et alii, frattura ed integrità strutturale, 29 (2014) 410-418; doi: 10.3221/igf-esis.29.36 411 welding is carried out between the buttering layer and the pipe with nickel-based alloy. stress corrosion cracking (scc) of dmw joints has been paid more attention in the nuclear power industry [1]. failures show that nickel-based alloy and its associated weld metals are more susceptible to scc in the simulated high temperature water environments of pwr [2-4]. as a weld filler metal, the high-temperature yield strength of alloy 182 makes it more susceptible to scc and produce high welding residual stresses [5]. generally, residual stresses (rs) in dmw joints are up to or even over the material yield stresses at service temperature. tensile residual stress is one of dominant factors resulting in scc of dmw joints [6]. rs may have a great contribution to the total stress field when pipe surface scc in nuclear power plants is assessed. therefore, before evaluating scc growth at flaws in actual dmw joints of pwr plants, accurate rs distribution needs to be performed. the film slip/dissolution oxidation model is widely regarded as a reasonable description of scc growth estimation in the nickel-based alloys in high temperature oxygenated environment [7]. in this model, the strain rate at crack tip is usually used as a unique factor to describe the mechanical condition. because it is difficult to directly obtain the strain rate at the steadily growing crack tip, elastic-plastic finite element method (epfem) is adopted to simulate the local stress-strain field and calculate the strain rate at crack tip [8]. moreover, the scc growth rate could be quantitatively estimated [9]. in this paper, based on the film slip/dissolution oxidation model and epfem, an approach is developed to quantitatively predict the scc growth rate of a rpv outlet nozzle dmw, which services in complex operating loads and welding residual stress. moreover, the crack driving force and the scc behavior of the dmw joint were discussed in detail. calculation model geometry and material configuration he schematic of the configurations and weld geometry of a rpv outlet nozzle dmw joint is shown in fig. 1. the hot leg pipes are typically large diameter and thick wall pipes. the outside and inside diameters of the pipe are 1001.6mm and 834.6mm, respectively, and the thickness is 83.5mm. assume that the dmw joint consists of a low alloy steel rpv nozzle, alloy 182 buttering, alloy 182 weld metal and a stainless steel safe-end. figure 1: geometry and material configuration of a dmw joint. to study the cracking behavior and estimate the scc growth rate of a representative dmw joint used in pwr, three models with small size flaws are considered in our simulation, that is, three axial semi-elliptic cracks are of different crack length (2c) and crack depth (a) as shown in fig. 2 and fig. 3. for an axial semi-elliptic crack, the crack angle (θ) varies from 0º to 180º. an initial axial inner surface crack having an aspect ratio (2c/a) of 3 and a flaw depth (a) of 5mm, 7.5mm and 10mm for the axial crack case are assumed, respectively. t l. zhao et alii, frattura ed integrità strutturale, 29 (2014) 410-418; doi: 10.3221/igf-esis.29.36 412 figure 2: geometry of the dmw joint sub-model. figure 3: crack locations and depths in the sub-model. material mechanical property of the dmw joint the stress-strain relationship beyond yielding is represented as romberg-osgood equation at the loading stage, and the relationship is linearly elastic at the unloading stage in this simulation. romberg-osgood equation is written as: 0 0 0                n (1) where: σ0 is the yield strength of the material; ε0 is the yield strain of the material;  is the dimensionless material constant; n is the strain-hardening exponent of the material. the mechanical properties of materials are given in tab. 1. the strain-hardening exponent of these materials is obtained in the following equation [10]. 0 1 ln(1390 / )  n (2) where κ=0.163. the microstructure characterization of the fusion boundary region of an alloy 182-a533b las dissimilar weld joint has showed that there is a narrow high hardness zone (hhz) in the dilution zone of alloy 182. further, a sharp increase of the hardness was observed in the hhz of alloy 182 [11]. high yield stress is consistent with high hardness. therefore, alloy 182 buttering has higher yield stress than that of alloy 182 weld because of the existence of hhz. l. zhao et alii, frattura ed integrità strutturale, 29 (2014) 410-418; doi: 10.3221/igf-esis.29.36 413 material elastic modulus, e (mpa) poisson ratio,  yield stress, σ0 (mpa) hardening exponent, n constant,  a508 193000 0.288 440 5.333 1.0 alloy 182 buttering 193000 0.288 480 5.769 1.0 alloy 182 weld 193000 0.288 385 4.779 1.0 304ss 193000 0.288 254 4.402 1.0 table 1: material mechanical parameters for the fem simulation. residual stress and operating loads only the hoop stress is used in the current evaluation based on some assumptions because the pipe flaw is an axial crack. the distribution of residual stress [12] is shown in fig.4. note that only the hoop stress for an axial crack was applied in the weld region. 0 .0 0 .1 0 .2 0 .3 0 .4 0 .5 0 .6 0 .7 0 .8 0 .9 1 .0 -5 0 0 5 0 1 0 0 1 5 0 2 0 0 2 5 0 3 0 0 3 5 0 4 0 0 4 5 0 w el di ng r es id ua l s tr es s (m p a) n o rm a liz e d d is ta n c e fro m p ip e in s id e to o u ts id e h o o p s tre s s figure 4: welding residual stress profiles. normal operating loads for rpv nozzles are listed in tab. 2. in addition to that, both axial and hoop stresses varying through-thickness induced by internal fluid pressure are considered. the welding residual stress applied as field and remote bending moment are also taken into account. service temperature [13] (°c) inner pressure (mpa) axial pressure (mpa) bending moment (knm) welding residual stress (mpa) 345 15.59 44 2 492 shown in fig. 4 table 2: normal operating loads for rpv nozzles. fem model a commercial fem code, abaqus, was used in this simulation analysis. based on symmetry condition, half of the model was investigated. the pipe symmetry surface is symmetric restrained in x-y plane. appropriate extensions of the left and right ends in the model have been made to reduce the influence of edge effect on the analysis results. considering the nozzle and pressure vessel are rigidly connected, the fixed constraint on the left is set. the combined operating loads such as internal pressure, weight and moment loads are applied on the safe end dmw joint. sub-model technique was adopted to investigate the crack local stress-strain field in detail. with different sampling location, three models are calculated based on the sub-model technique. boundaries of the sub-model are driven by the stress-strain obtained from the global model analysis [14]. fig.5 gives the mesh of a dmw joint specimen (global model and sub-mode), where x-y datum is the crack surface and z-axis is the crack growth direction. mesh at the vicinity of crack front is observably refined in both global model and l. zhao et alii, frattura ed integrità strutturale, 29 (2014) 410-418; doi: 10.3221/igf-esis.29.36 414 sub-model. 90387 and 46110 8-node linear brick elements are adopted in the global model and sub-model, respectively. there are 28020 elements in the vicinity of 2 mm around the crack front in the sub-model, more than the half the element total number. the minimum size of the element is about 0.02mm in the sub-model. figure 5: mesh of the finite element model. results and discussions echanical factors, such as crack opening stress, plastic strain and j-integral ahead of crack front, are always important to discuss the scc crack growth behaviors. to quantitatively estimate scc growth rate of the flaws in dmw joints, the local opening stress, plastic strain and j-integral ahead of crack front are investigated in this section. distributions of the hoop stress and hoop strain the hoop stress and the hoop plastic strain are shown in fig. 6 and fig. 7, respectively. it is obvious that the effect of operating loads on the dmw joint containing defects is much smaller than that of residual stress. only operating loads (ol) applied, the hoop stress and strain is linear along pipe through-thickness. comparing fig. 4 with fig. 6, the hoop stress induced by rs and ol is not a simple summation of that induced by hoop rs and ol due to the high stress, which exceeds the yield stress of alloy 182 weld. under the combined effects of rs and operating loads, the distribution of hoop stress and hoop strain along pipe through-thickness is consistent with that of hoop residual stress in fig. 4. 0.0 0.2 0.4 0.6 0.8 1.0 0 100 200 300 400 500 rs+ol only ol h o op s tr es s,  h( m p a) normalized distance from pipe inside to outside 0.0 0.2 0.4 0.6 0.8 1.0 0.0000 0.0002 0.0004 0.0006 0.0008 0.0010 0.0012 rs+ol only ol h oo p pl as ti c st ra in , h normalized distance from pipe inside to outside figure 6: hoop stress along pipe through-thickness. figure 7: hoop strain along pipe through-thickness. m l. zhao et alii, frattura ed integrità strutturale, 29 (2014) 410-418; doi: 10.3221/igf-esis.29.36 415 distributions of stress and strain ahead of crack fronts crack tip strain εct is the main mechanical parameter affecting scc growth rate in ford’s model [15], which is widely used in analyzing scc behavior of key materials in pwr components. because it is difficult to directly obtain εct, plastic strain εp was used to replace εct at a characteristic distance r0 ahead of crack tip in fri model [16]. thus, the critical issue is to estimate r0 when scc growth rate is predicted. considering that the mechanical field near crack front is pertinent to scc growth, r0 is regarded to be smaller than the plastic zone size. strain and strain rate quickly decrease with the increasing r0. on the other hand, the error in numerical calculation is very big at the crack tip because of the stress-strain singularity near the crack tip. considering the above factors and comparing the crack tip plastic zones where the equivalent plastic strain is 0.2% with different crack depths, the reasonable distance from crack front is designated as 60μm in this paper. in fig. 8 and fig. 9, the opening stress and normal plastic strain at a characteristic distance (r0=60μm) ahead of crack front are observably small when the crack depth is 5mm. the difference between yield stresses of interface materials lead to the jump of opening stress along crack fronts in fig. 8 could be explained that for 7.5 and 10 mm cracks the crack passes alloy 182 buttering, where contains much higher yield stress. the opening stress and normal plastic strain for 7.5 and 10mm crack make little difference. these results suggest that the normal plastic strain ahead of deeper crack front has a smaller gradient. the stress and strain are symmetrically distributed ahead of crack front when the crack depth is 5mm. for the partial crack in alloy 182 buttering, the opening stress ahead of the crack front (a=7.5mm and θ=150º) increases sharply, whereas the strain decreases. as the crack grows, the opening stress ahead of the crack front (a=10mm and θ=120º) becomes larger. the effect of crack depth on the stress ahead of crack fronts is more dramatic than it on the strain. at the interfacial region between alloy 182 buttering and alloy 182 weld, the stresses ahead of crack fronts suddenly increase while the strains decrease due to different material yield stresses of the two sides. under the same loading condition, the equivalent stress intensity factor ahead of crack front increases with crack length. the increment of stress ahead of crack front, which increases with the applied loads, is connected with the yield stresses of interface materials. 0 30 60 90 120 150 180 300 400 500 600 700 800 a=5mm a=7.5mm a=10mm crack angle, (o) o pe ni ng s tr es s,  zz (m p a) 0 30 60 90 120 150 180 0.000 0.001 0.002 0.003 0.004 0.005 0.006 0.007 0.008 0.009 a=5mm a=7.5mm a=10mm crack angle, (o) n or m al p la st ic s tr ai n,  p figure 8: opening stress ahead of crack fronts (r0=60μm). figure 9: normal plastic strain ahead of crack fronts (r0=60μm). cracks are mainly located in the high residual stress region when the crack depth varies from 5mm to 10mm. thus, residual stress has a great influence on stress and strain ahead of crack front. the local stress-strain field of shallow surface crack is dominated by rs, not the welded mechanical heterogeneity. the effect of residual stress on crack local stress and strain will become smaller with deeper crack. normal plastic strain rates and j-integrals normal plastic strain rates and j-integrals ahead of the crack fronts can be seen in fig. 10 and fig. 11, respectively. located in the middle of a homogeneous material alloy 182 weld, the stress, plastic strain, plastic strain rate and j-integral ahead of crack front are minimal and of the same trend when the crack length is 5mm. the normal plastic strain rate is higher at the deepest point than each end of the crack front. correspondingly, the growth rate at the deepest point of the l. zhao et alii, frattura ed integrità strutturale, 29 (2014) 410-418; doi: 10.3221/igf-esis.29.36 416 crack front is the highest. the strain rate increments significantly decrease with the increasing crack depth, which indicates that the deep surface crack growing slow down. the j-integral is not increasing with crack length (from 7.5 mm to 10 mm) in fig. 11 because the hoop stress that causes the crack opening is decreasing (normalized distance from 0.09 to 0.125) in fig. 4 with crack length (from 7.5 mm to 10 mm). that is, the loading conditions (mainly the rs) are different when the crack length is 7.5 mm and 10 mm. the increase of j-integral should be offset by the decrease of crack driving force. the distributions of strain rate and j-integral ahead of deeper surface crack front are quite different in the interfacial region of alloy 182 buttering and alloy 182 weld. the strain rate decreases due to the constraint of material with high hardness while j-integral increases in the interfacial region. some researchers discovered that the mechanical properties of welded joints had many distinct characteristics compared with homogeneous materials, especially for the fracture properties. path dependence of j-integral exists because of the finite deformation in the vicinity of crack tip and the heterogeneous mechanical properties of welded joint. therefore, there are some doubts on the applications of j-integral in heterogeneous dmw joints [17]. the plastic strain rate should be a more reliable fracture parameter to evaluate the scc behavior of dmw joint than j-integral. 0 30 60 90 120 150 180 0.000 0.003 0.006 0.009 0.012 0.015 0.018 0.021 a=5mm a=7.5mm a=10mm crack angle, (o) n or m al p la st ic s tr ai n ra te , d  p /d a( 1/ m m ) 0 30 60 90 120 150 180 0 1 2 3 4 5 6 7 8 9 a=5mm a=7.5mm a=10mm crack angle, (o) jin te gr al , j (n /m m ) figure 10: normal plastic strain rate ahead of crack fronts (r0=60μm). figure 11: j-integral ahead of crack fronts. scc growth rate in order to predict the amount of time required before leakage occurs in normal pwr, a detailed prediction on stress corrosion cracking growth rate of dmw joints are performed by many researchers. generally, stress corrosion cracking growth law for alloy 82/182 weld metals in pwr primary water environment has been described as a function of applied stress intensity factor ki and thermal activation corrosion term: temperature, based upon the extensive scc material testing data [18]. these correlations provide the flaw evaluation guidelines for ni-based alloy materials in pwr environment. the stress intensity factor ki along the crack front in the elastic-plastic material is converted by the value of j-integral. however, there are some doubts on the applications of j-integral along interface crack front in heterogeneous dmw joints. combined with epfem, a pre-analytical method is used to predict scc growth rate of dmw joints in pwr environment. the stress corrosion cracking growth rate can be written as: 1( )     m p m a dda dt da (3) where the oxidation rate constant a is 7.478×10-7, the exponent of current decay curve m is 0.5 [19]. fig. 10 shows the normal plastic strain rate at a characteristic distance (r0=60μm) ahead of the crack fronts. based on the normal plastic strain rates and the formula, scc growth rate evaluations were performed for alloy182 weld metal conservatively at a service temperature of 345°c. the disposition curves of scc growth rate are shown in fig. 12. the units describe crack growth rate in terms of millimeter per second. note that for the axial crack case, because low alloy l. zhao et alii, frattura ed integrità strutturale, 29 (2014) 410-418; doi: 10.3221/igf-esis.29.36 417 steel and stainless steel have significantly lower scc susceptibilities and growth rates, the crack growth law was only applied to the partial model including alloy182 buttering and alloy182 weld. 0 30 60 90 120 150 180 10-9 10-8 10-7 10-6 a=5mm a=7.5mm a=10mm crack angle, (o) e a c c ra ck g ro w th r at e, d d /d t ( m m /s ) figure 12: crack growth rate of alloy 182 in the dmw joint. the shallow surface crack growth rate at both ends is much lower than that at the middle. however, the deep surface crack growth rate is relatively uniform and its increment slows down with the increasing crack depth. the gradients of plastic strain and plastic strain rates decrease as the crack advances. due to the constraint of strong material, cgr of the deep surface crack locates in alloy 182 buttering decreases sharply, and the crack growing in alloy 182 buttering is inhibited. however, the partial crack locates in alloy 182 weld comes to stable growth. the crack will no longer be ideal semi-elliptic with the continuous crack growing. the crack shape will change considerably. the welding residual stress referred here is a result of higher hoop stress in the dmw joint scc susceptible region, and dropping off in the safe-end and nozzle regions. finally, the crack shape development results in crack growth outside of the dmw region. conclusions onsidering the interactive effect of operating loads and welding residual stress, the stress-strain field ahead of inner surface axial crack fronts of a rpv outlet nozzle dmw joint is simulated by using epfem. the crack driving force, such as opening stress, plastic strain, plastic strain rate and j-integral are analyzed. focusing on rs and crack depth, the scc growth rate of a dmw joint was quantitatively predicted. main conclusions can be summarized as follows: (1) crack local stress-strain field, j-integral and crack growth rate of dmw joints are dominated by residual stress, not welded mechanical heterogeneity. the hoop stress and hoop strain varying through-thickness of the welded area is quite different with or without residual stress. the distributions of hoop stress and hoop strain are consistent with residual stress. (2) the strain rate ahead of deeper crack front decreases due to the constraint of high hardness material, whereas, jintegral increases in the interfacial region of alloy 182 buttering and alloy 182 weld. path dependence of j-integral exists because of welded mechanical heterogeneity. therefore, plastic strain rate should be a more reliable fracture parameter to evaluate the scc behavior of dmw joint than j-integral. (3) the shallow surface crack growth rate at both ends is much lower than that at the middle. however, the deep surface crack growth rate is relatively uniform. due to the constraint of strong material, located in alloy 182 buttering, the crack growing is inhibited. the crack locates in alloy 182 weld grows steady and the crack shape will change considerably. (4) based on the film slip/dissolution oxidation model and epfem, a valid approach is provided to quantitatively estimate scc growth rate of dmw joints in pwr environment. c l. zhao et alii, frattura ed integrità strutturale, 29 (2014) 410-418; doi: 10.3221/igf-esis.29.36 418 acknowledgements he supports from natural science foundation of china (grants nos. 11072191 and 1201277), scientific research program funded by shaanxi provincial education commission (program nos. 12jk0851 and 2013jk0611) and research fund for the doctoral program of higher education of china (grants nos. 20136121110001) are appreciated. references [1] bamford, w., hall, j., a review of alloy 600 cracking in operating nuclear plants including alloy 82 and 182 weld behavior, asme 12th international conference on nuclear engineering, (2004) 131–139. [2] bamford, w., newton, b., seeger, d., recent experience with weld overlay repair of indications in alloy 182 butt welds in two operating pwrs, asme 2006 pressure vessels and piping conference, (2006) 427–434. [3] li, g.f., congleton, j., stress corrosion cracking of a low alloy steel to stainless steel transition weld in pwr primary waters at 292 , corros. sci., 42(6) (2000) 1005–1021. [4] li, g.f., li, g.j., fang, k.w., stress corrosion cracking behavior of dissimilar metal weld a508/52m/316l in high temperature water environment, acta metallurgica sinica, 47(7) (2011) 797–803. [5] andresen, p.l., young, l.m., emigh, p.w., et al., stress corrosion crack growth rate behavior of ni alloys 182 and 600 in high temperature water, nace corrosion, (2002) 02510. [6] deng, d., kiyoshima, s., fem prediction of welding residual stresses in a sus304 girth-welded pipe with emphasis on stress distribution near weld start/end location, comp. mater. sci., 50(2) (2010) 612–621. [7] andresen, p.l., environmentally assisted growth rate response of nonsensitized aisi 316 grade stainless steels in high temperature water, corrosion, 44(7) (1988) 450–460. [8] xue, h., ogawa, k., shoji, t, effect of welded mechanical heterogeneity on local stress and strain in stationary and growing crack tips, nucl. eng. des., 236(5) (2009) 628–640. [9] xue, h., shoji, t., quantitative prediction of eac crack growth rate of sensitized type 304 stainless steel in boiling water reactor environments based on epfem, j. press. vess.-t. asme, 129(3) (2007) 460–467. [10] ueda, y., shi, y., sun, s., et al., effect of crack depth and strength mis-matching on the relation between j-integral and ctod for welded tensile specimens (mechanics, strength & structure design), trans. jwri, 26(1) (1997) 133– 140. [11] peng, q.j., xue, h., hou, j., et al., role of water chemistry and microstructure in stress corrosion cracking in the fusion boundary region of an alloy 182-a533b low alloy steel dissimilar weld joint in high temperature water, corros. sci., 53(12) (2011) 4309–4317. [12] hayashi, t., hankinson, s.f., saito, t., et al., flaw evaluation for pwr and bwr component weld joints using advanced fea modeling techniques, asme 2009 pressure vessels and piping conference, (2009) 1125–1139. [13] lu, z.p., shoji, t., xue, h., et al., deterministic formulation of the effect of stress intensity factor on pwscc of nibase alloys and weld metals, j. press. vess.-t. asme, 135(2) (2013) 021402. [14] abaqus v6.7, hibbitt, karlsson and sorensen inc, (2007). [15] ford, p., mechanisms of environmentally-assisted cracking, int. j. pres. ves. pip., 40(55) (1989) 343–362. [16] shoji, t., li, g., kwon, j., et al., quantification of yield strength effects on igscc of austenitic stainless steels in high temperature water, proceedings of the 11th conference of environmental degradation of materials in materials in nuclear systems, (2003) 834–844. [17] kang, j.d., wen, w.d., zhang, y.f., et al., path dependence of j-integral in welded joint with an overmatching weld, trans. of nuaa, 12(1) (1995) 1–8. [18] xue, h., sato, y., shoji, t., quantitative estimation of the growth of environmentally assisted cracks at flaws in light water reactor components, j. press. vess.-t. asme, 131(1) (2009) 011404. [19] peng, q.j., kwon, j., shoji, t., development of a fundamental crack tip strain rate equation and its application to quantitative prediction of stress corrosion cracking of stainless steels in high temperature oxygenated water, j. nucl. mater., 324(1) (2004) 52–61. t microsoft word numero_58_art_31_3090.docx t. v. tretyakova et alii, frattura ed integrità strutturale, 58 (2021) 434-441; doi: 10.3221/igf-esis.58.31 434 experimental study of the portevin-le chatelier effect under complex loading of al-mg alloy: procedure issues tatyana v. tretyakova center of experimental mechanics, perm national research polytechnic university, russia cem.tretyakova@gmail.com, http://orcid.org/ 0000-0001-9445-5185 mikhail p. tretyakov center of experimental mechanics, perm national research polytechnic university, russia cem_tretyakov@mail.ru, http://orcid.org/0000-0001-6146-6769 evgeniia a. chechulina ural research institute of composite materials, perm, russia zhenya-chechulina@yandex.ru, https://orcid.org/0000-0003-4834-7911 abstract. the aim of this work is to solve the methodological issues of the experimental study of the nucleation and propagation of deformation bands due to the portevin-le chatelier effect under conditions of complex loading. it is of interest to determine the boundaries of unstable plastic deformation of the amg6 alloy under complex loading conditions. a technique for controlling the loading process with a given rate of deformation intensity of materials has been worked out. short stops of the loading process and unloading have an impact on the manifestation of the jerky flow. stops and unloading reduce the strain level at which the diagram starts to manifest the effect portevin-le chatelier. the experimental results show the evolution of inhomogeneous strain fields and local strain rates under conditions of manifestation of jerky flow during tension with torsion tests of al-mg alloy samples. keywords. jerky flow; the portevin-le chatelier effect; strain field; plasticity; digital image correlation technique; aluminum-magnesium alloy. citation: tretyakova, t. v., tretyakov, m. p., chechulina, e.a, experimental study of the portevin-le chatelier effect under complex loading of al-mg alloy: procedure issues, frattura ed integrità strutturale, 58 (2021) 434-441. received: 09.05.2021 accepted: 25.09.2021 published: 01.10.2021 copyright: © 2021 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. introduction eal conditions of operation and complex external thermomechanical influences determine the operation of the loaded elements of critical structures in the conditions of a complex stress state. there is a need to create the scientific basis for predicting the deformation ability and the limiting state of metals and alloys, taking into account r https://youtu.be/kp_wy6wzpci t. v. tretyakova et alii, frattura ed integrità strutturale, 58 (2021) 434-441; doi: 10.3221/igf-esis.58.31 435 the phenomena of spatial heterogeneity and temporary instability of plastic deformation under given operating conditions. the effects of discontinuous fluidity lead to a significant decrease in strength and ductility, reduce the quality of the surface of the material, affect the technological process of processing [1-7 and etc.]. macroscopic localization of the plastic flow as a result of the formation of deformation bands leads to the difference in thickness of the material and, as a result, to the formation of defects and premature failure. aluminum-magnesium alloys exhibit a tendency to dynamic strain aging at relatively low homologous temperatures, which leads to the appearance of numerous stress discontinuities in the tensile curves. the manifestation of the jerky flow significantly reduces the strength and ductility of materials, and decreases the surface quality as well [8]. an urgent task of the experimental study of the plc effect is to determine the region of existence of instability in order to exclude it from the real modes of processing products. in addition, of particular interest is the experimental study of inelastic deformation of structural materials, taking into account their processing in real technological processes, characterized by non-monotonicity and complexity of deformation paths, loading modes (including the imposition of monotonous and oscillating vibrational influences), and the properties of the loading system [9-12]. the vast majority of known experimental studies of the plc effect were carried out under uniaxial (simple) loading. it is known that inelastic deformation processes are significantly affected by loading complexity. moreover, the behavior of metals and alloys is significantly affected by the energy of the stacking fault [13, 14], which determines the tendency of edge dislocations to split. in view of the foregoing, it seems possible to suggest that the energy of the stacking fault and complex load also affect the occurrence and characteristics of intermittent ductility. the influence of complicated loading on the plc effect [15-17], based on the physical analysis of dislocation deformation mechanisms, will manifest itself in the form of an increase in the intensity of the formation of barriers (for example, the lomer cottrell), which, by assumption, will lead to an increase in the amplitude of loading jumps in the stress strain diagram. the aim of this work is to solve the methodological issues of experimental study of the regularities of the nucleation and propagation of deformation bands of localized plastic flow, determination of the boundaries of unstable plastic deformation of the amg6 alloy under conditions of complex loading. the choice of the amg6 alloy was determined by the importance of the problem of stability of its deformation behavior in connection with its wide application in aviation engineering, shipbuilding, chemical industry and transport engineering. experimental procedure material and specimen geometry he structural aluminum-magnesium alloy in the form of a thick-walled pipe in the state of delivery (ø28 mm, wall thickness 5 mm) was selected as the material for the study. the chemical composition of the alloy in mass fractions according to gost 4784-97 is presented in tab. 1. al mg mn fe si zn ti cu be 92.55 6.12 0.84 0.27 0.17 0.005 0.039 0.001 0.005 table 1: the chemical composition of the used alloy (%wt). figure 1: sketch of a thin-walled tubular test specimen for tensile torsion tests. in mechanical tests, thin-walled tubular specimens were used, a sketch of which is shown in fig. 1. the specimens were manufactured on a numerically controlled chuck-center lathe in accordance with gost 25.505-85. the samples satisfy the thin-walled condition, that is, the ratio of the wall thickness of the working part to the diameter is less than 0.1. to achieve t t. v. tretyakova et alii, frattura ed integrità strutturale, 58 (2021) 434-441; doi: 10.3221/igf-esis.58.31 436 homogeneity of the microstructure and relieve residual stresses, samples of the al-mg alloy were annealed in a muffle furnace at 400 ° c for 3 hours and cooled in the furnace to room temperature. testing equipment and registration technique in this work, to assess the stress-strain state and the characteristics of the deformation process, the values of the intensity of deformations and the intensity of the rates of deformations were used. the calculation of the intensity of deformations is made according to the following formula [18]:        2 2 2 2 2 2i 11 22 22 33 33 11 12 23 312ε = ε ε + ε ε + ε ε + 6 × ε +ε +ε 3 , (1) where 11ε , 11ε и 11ε – normal strain components, 12ε , 23ε и 31ε – components of shear deformations. for the case when only a tensile load and a torque act on a thin-walled tubular specimen, the formula for calculating the intensity of deformations can be written in the following form: 2 2 i 11 12 2 9 3 ε = ε + γ 3 2 2 . (2) the strain rate intensity according to [11] is calculated using similar formulas, while strain rate components are used instead of strain components. the strain rate components for proportional loading are selected from the conditions that the strain rate intensity is constant and equal  -4iε = 5, 4 × 10 1/s, as well as a fixed ratio of the shear angle and axial strain rate components  12 11γ ε = 0,125 . as a result, the following velocities were obtained for the components of deformations:  -411ε = 5, 385 ×10 1/s and  -4 12γ = 0, 675 ×10 1/s. in tests for complex loading at successive tension with torsion, tension and torsion, the rates of the deformation components corresponded to the given rate of the deformation intensity and are given in tab. 2. components tension with torsion tension torsion 11ε 5.384·10-4 1/s 5.4·10-4 1/s 0 12γ 0.675·10-4 1/s 0 9.35·10-4 1/s iε 5.4·10-4 1/s 5.4·10-4 1/s 5.4·10-4 1/s table 2: values of velocities by deformation components for various types of tests. figure 2: the biaxial servo-hydraulic test system instron 8850 (left), the biaxial extensometer epsilon 3550-025m (right). t. v. tretyakova et alii, frattura ed integrità strutturale, 58 (2021) 434-441; doi: 10.3221/igf-esis.58.31 437 mechanical tests on tension, torsion and tension-torsion were carried out using the biaxial (tension/torsion) servo-hydraulic test system instron 8850 (fig. 2, а). the maximum loads are 100 kn in tension / compression and 1000 nm in torsion. the travel ranges are ± 75 mm in the tension / compression axis and ± 45° in the torsion axis. to fix the specimens in the testing system, hydraulic collet-type grippers were used. at the first stage of testing, registration of axial and shear deformations in the working part of the specimens was carried out by using a two-axis extensometer epsilon 3550-025m (fig. 2, b). registration of inhomogeneous displacement and strain fields was carried out by using the vic-3d digital image correlation measurement system (fig. 2). the shooting of specimens was realized with a set of high-resolution cameras (prosilica, 16 mp), the shooting speed was 3 frames per second. the systems were synchronized with an analog-to-digital converter (ni usb-6251). results methodology for tensile torsion test at discontinuous yield owever, the use of a hinged extensometer imposes some restrictions on the test methodology due to its limited range of strain measurement. in this regard, the original test procedure provided for stopping the loading process, unloading (or holding on load and torque) to reinstall the extensometer. the stop duration ranged from 30 s to 60 s. at the same time, it was found that after unloading (or suspension) of loading in the region of uniform deformation, further loading led to the manifestation of the effect of intermittent yield. fig. 3 shows the experimental diagrams in the coordinates load-elongation (left) and torque-twist angle (right), obtained under proportional tension with torsion of the sample up to an elongation of 3.5 mm (point 1), followed by unloading for reinstallation of the extensometer and further proportional loading. at point 2, the extensometer was reinstalled when the loading process was stopped without unloading. the data obtained demonstrate that with repeated proportional loading, the onset of non-uniform intermittent deformation is provoked. figure 3: deformation diagrams in the coordinates load-elongation (left) and torque-angle of twist (right), obtained under proportional tension with torsion of the sample up to an elongation of 3.5 mm (point 1), unloading and subsequent loading. point 2 is to reset the extensometer when stopped without unloading. in the next test, the stop for reinstallation of the extensometer was implemented at a lower value of the achieved elongation (extension of 2.5 mm), while no unloading was performed. however, even at this level of deformations after stopping with further proportional loading, a process of inhomogeneous intermittent deformation is provoked. fig. 4 shows the experimental diagrams in the coordinates load-elongation (left) and torque-twist angle (b), obtained with proportional tension with torsion of the sample up to an elongation of 2.5 mm (point 1) for reinstallation of the extensometer and further proportional loading. at point 2, the extensometer was also reset when the loading process was stopped without unloading. experimental data show that when the proportional loading process stops even at small values of plastic deformations, further loading leads to the occurrence of inhomogeneous intermittent plastic deformation processes. this is reflected in the recorded deformation diagrams in the form of the plc effect. in this regard, it was decided to adapt the test methodology and carry out proportional loading of the samples with control using the built-in sensors of the testing system. this makes it possible to realize quasi-static loading up to the required values of axial and shear deformations without h t. v. tretyakova et alii, frattura ed integrità strutturale, 58 (2021) 434-441; doi: 10.3221/igf-esis.58.31 438 interruptions in the process of plastic deformation. in order to achieve the strain rates, elongation rates and rotational angles shown in tab. 2, the built-in transducers of the test system were determined from previous tests in the elastic section. the obtained speeds of the specified elongation and rotation angle are shown in tab. 2. figure 4: deformation diagrams in coordinates load-elongation (left) and torque-twist angle (right), obtained under proportional tension with torsion of the sample up to an elongation of 2.5 mm (point 1) and subsequent loading. point 2 repositioning the extensometer when stopped without unloading. components tension with torsion tension torsion u [mm/s] 0.05332 0.05347 0  [grad/s] 0.31870 0 4.4146 table 3: values of elongation and rotation rates for various types of tests. a quasi-static proportional tension-torsion tests were carried out with the loading parameters indicated in tab. 3. the test was stopped at the loss of stability of the working part of the thin-walled tubular specimen. the test results in the form of diagrams in the coordinates load-elongation (left) and torque-twist angle (right) are shown in fig. 5. the figure also shows the section of the transition from the process of homogeneous plastic to discontinuous deformation. figure 5: diagrams of proportional quasi-static deformation of the specimen with control by the built-in sensors of the test system in the coordinates load-elongation (left) and torque-twist angle (right). the portevin-le chatelier effect during tension-torsion loading the registration of strain distribution fields during plastic deformation of the samples was carried out with a vic-3d correlated solutions non-contact three-dimensional optical system [19, 20]. the use of two cameras located at a certain t. v. tretyakova et alii, frattura ed integrità strutturale, 58 (2021) 434-441; doi: 10.3221/igf-esis.58.31 439 angle in the video system makes it possible to work not only with flat specimens, but also with cylindrical specimens, specimens of complex shape and structural elements. the use of this system makes it possible to obtain data on the distribution of normal and shear strain components on the surface of the working part of the specimen. of particular interest is the analysis of the distribution of deformations and rates of deformation in the process of inhomogeneous discontinuous plastic flow. distributions are plotted in the form of diagrams for different stages of the formation of bands of localized plastic deformation. fig. 6 shows a set of plots of longitudinal strain ( yy ), plotted at equal time intervals   1.5t s with along the length of the specimen (along the oy axis), the center of coordinates is located in the center of the working section. by analyzing the configuration of the longitudinal deformation profile [13], it is possible to track the moment of initiation of the process of macroscopic localization of plastic deformation due to the plc bands. figure 6: series of plots of longitudinal deformations plotted at equal time intervals along the length of a thin-walled cylindrical specimen. inelastic deformation proceeds in a macro-uniform manner until the beginning of the manifestation of the effect of discontinuous flow. this is confirmed by a uniform increase in the level of longitudinal deformation, recorded by the video system (fig. 6). it is of interest to consider in detail the process of the appearance of the first stress abrupt jump on the deformation diagram, which is accompanied by the initiation of the macrolocalization zone of the plastic flow. tensile torsion tests of thin-walled tubular samples of the amg6 alloy were carried out under kinematic loading with a constant strain rate with control of axial displacements and torsion angle. the analysis of the spatio-temporal inhomogeneity of inelastic deformation during loading was carried out on the basis of the use of video system data, which made it possible to estimate the configuration of the plc strips and the moment of the onset of the manifestation of the discontinuous yield effect. acknowledges his work was carried out by using the capabilities of a large unique scientific facility (unu) ‘a set of test and diagnostic equipment for studying the properties of structural and functional materials under complex thermomechanical influences’, which is part of the center of experimental mechanics, pnrpu (perm, russia). this work was supported by the russian science foundation (no. 20-79-10235). t -40 -30 -20 -10 0 10 20 30 y, mm εyy 0.16 0.14 0.12 0.10 0.08 0.06 0.04 0.02 0 t. v. tretyakova et alii, frattura ed integrità strutturale, 58 (2021) 434-441; doi: 10.3221/igf-esis.58.31 440 figure 7: section of the load-time diagram at the moment of initiation of the plc effect (left) and a series of corresponding longitudinal deformation diagrams (right). figure 8: evolution of inhomogeneous fields of local rates of longitudinal deformation on the surface of a thin-walled cylindrical specimen at the moment of initiation of the plc effect (fig. 7). references [1] cottrell, a.h. (1953). a note on the portevin-le chatelier effect, philosophical magazine series, 44 (355), pp. 829‒ 832. doi: 10.1080/14786440808520347 [2] estrin, y., kubin, l.p. (1991). plastic instabilities: phenomenology and theory, materials science and engineering. a, 137, pp. 125–134. doi: 10.1016/0921-5093(91)90326-i [3] estrin, y., ling, c.p., mccormick, p.g. (1991). localization of plastic flow: spatial vs temporal instabilities, acta metal, 39 (11), pp. 2943–2949. doi: 10.1016/0956-7151(91)90110-m 1 2 3 4 5 t. v. tretyakova et alii, frattura ed integrità strutturale, 58 (2021) 434-441; doi: 10.3221/igf-esis.58.31 441 [4] mccormick, p.g. (1988). theory of flow localization due to dynamic strain aging, acta metall, 36 (12), pp. 3061–3067. doi: 10.1016/0001-6160(88)90043-0 [5] wang, x.g., wang, l., huang, m.x. (2017). kinematic and thermal characteristics of lüders and portevin-le châtelier bands in a medium mn transformation-induced plasticity steel, acta materialia, 124, pp. 17-29. doi: 10.1016/j.actamat.2016.10.069 [6] krishtal, m.m. (2004). instability and mesoscopic inhomogeneity of plastic deformation (analytical review). part i. phenomenology of yield drop and jerky flow, phys. mesomech., 7 (5-6), pp. 5-26 [7] krishtal, m.m. (2004). instability and mesoscopic inhomogeneity of plastic deformation (analytical review). part ii. theoretical views on mechanisms of plastic deformation instability, phys. mesomech., 7 (5-6), pp. 27-39 [8] bell j.f. (1973). volume i: the experimental foundations of solid mechanics. springer, berlin. isbn 978-3-54013160-1. [9] dietrich l., socha g. (2012). accumulation of damage in a336 gr5 structural steel subject to complex stress loading. strain, 48, pp. 279-285. doi: 10.1111/j.1475-1305.2011.00821.x [10] feltner c.e., laird c. (1967а). cyclic stress-strain response of f.c.c. metals and alloys–i. phenomenological experiments. acta metallurgica, 15, pp.1621-1632. doi: 10.1016/0001-6160(67)90137-x [11] tretyakova, t.v., wildemann, v.e. (2017) influence the loading conditions and the stress concentrators on the spatialtime inhomogeneity due to the yield delay and the jerky flow: study by using the digital image correlation and the infrared analysis, frattura ed integrita strutturale 11 (42), pp. 303-314. doi: 10.3221/igf-esis.42.32 [12] tretyakova, t.v., wildemann, v.e., tretyakov, m.p. (2019) investigation of the portevin-le chatelier effect in metals under additional vibration impact by using the dic-technique and the ir-analysis, procedia structural integrity 18, pp. 837-842. doi 10.1016/j.prostr.2019.08.233 [13] koneva, n.a., trishkina, l., cherkasova, t.v. (2017) influence of stacking fault energy on the accumulation of dislocations during plastic deformation of polycrystalline copper-based alloys. letters on materials, 7 (3), pp. 282-286. [14] maksimkin, o.p. (2010) packing faults, their energy and influence on the properties of irradiated metals and alloys, almaty, p. 70. [15] benallal a., marquis d. (1988). effects of non-proportional loadings in cyclic elasto-viscoplasticity: experimental, theoretical and numerical aspects, engineering computations, 5(3), pp. 241-247. doi: 10.1108/eb023742 [16] benallal a., le gallo p., marquis d. (1989). an experimental investigation of cyclic hardening of 316 stainless steel and of 2024 aluminium alloy under multiaxial loadings. nuclear engineering and design, 114, pp. 345-353. doi: 10.1016/0029-5493(89)90112-x [17] borodii m. v., stryzhalo v. o., kucher m. k., danyl’chuk e. l., and adamchuk m. p. (2014). an experimental study of ratcheting effect under multiaxial proportional loading. strength of materials, 46(1), pp. 97-104. doi: 10.1007/s11223-014-9520-3 [18] ilyushin, a.a. (2004). plasticity. part 1: elastic-plastic deformations, moscow, logos. isbn 5-94010-377-4. [19] sutton, m.a., orteu, j.-j., schreier, h. (2009) image correlation for shape, motion and deformation measurements, university of south carolina, columbia, sc, usa, springer. doi: 10.1007/978-0-387-78747-3. [20] tretyakova, t.v., wildemann, v.e. (2018) plastic strain localization and its stage in al-mg alloys. physical mesomechanics 21 (4), pp. 314-319. doi: 10.1134/s1029959918040057 microsoft word numero_38_art_39 t. morishita et alii, frattura ed integrità strutturale, 38 (2016) 289-295; doi: 10.3221/igf-esis.38.39 289 focussed on multiaxial fatigue and fracture fatigue strength of ss400 steel under non-proportional loading t. morishita, t. takaoka graduate school of science and engineering, ritsumeikan university, japan gr0202xp@ed.ritsumei.ac.jp, rm0033px@ed.ritsumei.ac.jp t. itoh college of science and engineering, ritsumeikan university, japan itohtaka@fc.ritsumei.ac.jp abstract. this study discusses fatigue properties of low carbon steel, type ss400 steel, under non-proportional loading. multiaxial fatigue tests under proportional and non-proportional loading conditions with various stress amplitudes were carried out using a hollow cylinder specimen at room temperature. in the test, three types of stress paths were employed. they are a push-pull, a reversed torsion and a circle loading. the circle loading is a cyclic loading combined the push-pull and the reversed torsion loading in which axial and shear stress waveforms have 90 degrees phase differences. from the obtained test results, poor evaluations of failure life under non-proportional loading are indicated when the life is correlated by the equivalent strain range based on von mises δεeq and the non-proportional strain range δεnp. a modified strain parameter is presented which can evaluate the failure life in high and low strain levels under non-proportional loading. keywords. fatigue; multiaxial stress; non-proportional loading; life evaluation; carbon steel. citation: morishita, t., takaoka, t., itoh, t., fatigue strength of ss400 steel under nonproportional loading; frattura ed integrità strutturale; 38 (2016) 289-295. received: 30.07.2016 accepted: 31.08.2016 published: 01.10.2016 copyright: © 2016 this is an open access article under the terms of the cc-by 4.0; which permits unrestricted use; distribution; and reproduction in any medium; provided the original author and source are credited. introduction on-proportional loading of which directions of principal stress and principal strain are changed in a cycle occurs in various structures such as machinery for construction and transportation. in studies of multiaxial fatigue under non-proportional loading conditions; it has been reported that failure life is reduced accompanying with an additional hardening depending on both strain path and material [1-12]. itoh et al. have carried out series of multiaxial low cycle fatigue (lcf) tests under non-proportional loading conditions to examine properties of cyclic deformation and failure life [10-12]. they presented a strain parameter for life evaluation under non-proportional loading; a nonproportional strain range δεnp; which includes a non-proportional factor taking into account the effect of loading path n t. morishita et alii, frattura ed integrità strutturale, 38 (2016) 289-295; doi: 10.3221/igf-esis.38.39 290 and a material constant related to the additional hardening due to non-proportional loading [4;10-12]. however; there is few studies discussing failure life in high cycle region and fatigue strength under non-proportional loading [13;14]. in order to ensure reliability and safety of machinery; evaluating models for non-proportional loading including the high cycle region is required. in this study; multiaxial fatigue tests under proportional and non-proportional loading conditions were carried out in the low stress level to discuss fatigue strength. for evaluation of failure life in the high cycle region; an applicability of equivalent stress and strain ranges based on von mises and δεnp is discussed and δεnp is also modified to be suitable strain range for life evaluation. test material and experimental procedure aterial tested was rolled steel for general structure; type ss400 steel (a283 grade d for astm; st 44-2 for din). a hollow cylinder specimen with 12mm outer-diameter; 9mm inner-diameter in a gauge part is used. an electrical servo controlled hydraulic fatigue testing machine for push-pull and reversed torsion loadings of which maximum push-pull loading and torque are ±50 kn and ±500 n·m was employed as testing machine. load controlled fatigue tests were carried out at room temperature. stress paths were a push-pull; a reversed torsion (rev. torsion) and a circle loading. fig. 1 shows the stress paths and the stress waveforms. the push-pull and the rev. torsion loading tests are proportional loading tests in which principal directions of stress and strain are fixed. the circle loading test is non-proportional loading test in which axial stress and shear stress have 90 degrees sinusoidal out-of-phase difference. in the circle loading test; axial and shear stress ranges are the same value based on von mises; δσ= 3 δτ. number of cycles to failure (failure life) nf was determined as the cycle at which a crack occurred on the surface of test specimen. the crack size is big enough to be checked by looking and this test is controlled by loading. therefore; nf can be considered as the cycle at which test specimen ruptured. (a) stress path (b) stress waveform figure 1: stress path and stress waveform. experimental results and discussion evaluation of failure life with equivalent stress and strain ig. 2 shows a correlation of failure life with an equivalent stress amplitude based on von mises δσeq/2. failure life can be correlated by a unique line independent of loading path in the stress region over the fatigue strength σw. in the load controlled test; failure life in the circle loading test tends to be longer than those in the push-pull and rev. torsion loading tests. the strain range in the circle loading test becomes smaller in comparison with that in the push-pull loading test at the same stress range because of additional hardening caused by non-proportional loading. in addition; it is known that failure life in the circle loading test is smaller than that in the push-pull loading test at same strain range due to m f t. morishita et alii, frattura ed integrità strutturale, 38 (2016) 289-295; doi: 10.3221/igf-esis.38.39 291 non-proportional loading. in this stress level and the material of ss400; a relative good agreement of data correlations may be resulted from that the additional hardening is balanced with the reduction in failure life. fatigue strength in the circle loading test σwci (150mpa) is lower than that in others σwpp (175mpa). fig. 3 shows observations of specimen surface in the push-pull and the circle loading tests at stress amplitude level around the fatigue strengths; δσeq/2=200; 175 and 150mpa. the observed location was set at the sufficient distances from a main crack which contributes directly to nf. in the push-pull loading test; the roughness caused by local plastic deformation can be observed clearly on the specimen surface only at δσeq/2=200mpa. in the circle loading test; on the other hand; the remarkable roughness can be observed at δσeq/2=200 and 175mpa in comparison with those in the push-pull loading test at each equivalent stress amplitude; which may be resulted from the increase in the number of activated slip systems due to the rotation of principal direction of stress under non-proportional loading. the roughness leads to more chance of initiation of microcracks and the earlier crack initiation. consequently; the surface roughness causes reduction of the fatigue strength in the circle loading test. fig. 4 is the failure life correlated by an equivalent total strain range based on von mises δεeq. the strain ranges used are those at the cycle of 0.5nf in experiments. in this figure; the bold solid line is drawn by a universal slope curve [16] based on the experimental data in the push-pull loading test. the universal slope curve is given by 6.0 f 12.0  bnan -feq (1) where the coefficients a and b are equated as 3.5σb/e and εf0.6 according to the definition of the universal slope method. e; σb and εf are yong’s modulus; a tensile strength and an elongation; respectively. in this study; a is put as the mechanical properties obtained from the tensile test but b is defined to fit the universal slope curve to the data of the push-pull loading test. in lcf region; failure life in the rev. torsion loading test is underestimated and conversely that in the circle loading test is overestimated out of the factor of 2 band. the same tendency of failure life was shown in the previous study of strain controlled multiaxial lcf test [11]; therefore it suggests that the failure life and the nonproportionality are not affected by the difference in the test control of strain or stress for the tested material. in the high cycle fatigue region; with decrease in strain range; failure life in the circle loading test approaches to that in the push-pull loading test. this trend indicates that the effect of non-proportional loading on failure life is decreased in the lower strain level; which will be mentioned in next. 103 104 105 106 107 100 150 200 250 300 350 number of cycles to failure nf, cycles e q u iv al en t st re ss a m p li tu de , m p a   eq 2 mpa175σ ppw  mpa145σ ciw  push-pull rev.torsion circle figure 2: correlation of nf with equivalent stress amplitude based on von mises. t. morishita et alii, frattura ed integrità strutturale, 38 (2016) 289-295; doi: 10.3221/igf-esis.38.39 292 equivalent stress amplitude δσeq/2, mpa 200 175 150 p u sh -p u ll c ir cl e 20 μm 20 μm 20 μm 20 μm 20 μm 20 μm axial direction figure 3: observation of specimen surface after fatigue tests at δσeq/2=200mpa; 175mpa and 150mpa. factor of 2 method of universal slope curve 103 104 105 106 107 0.1 0.5 1 number of cycles to failure nf, cycles e qu iv al en t st ra in r an g e   e q , % 2.0 1.0 push-pull rev.torsion circle figure 4: correlation of nf with δεeq. applicability of non-proportional strain range for life evaluation itoh et al. have reported that the large reduction in failure life has a close relation with the strain path and the material [4;6;7;10;11] and they also proposed the non-proportional strain range δεnp for life evaluation defined as eqnp )1(  fnp (2) t. morishita et alii, frattura ed integrità strutturale, 38 (2016) 289-295; doi: 10.3221/igf-esis.38.39 293 where δεeq is the maximum principal strain range under non-proportional loading which can be calculated by ε and γ. α and fnp are the material constant and the non-proportional factor; respectively. the former is the parameter related to the additional hardening due to non-proportional loading and the latter is the parameter expressing the intensity of nonproportional loading. the value of α is the ratio to fit nf in the circle loading test to that in the push-pull loading test at the same δεeq. in this study; the value of α for ss400 is put α = 0.59. fnp is defined as st l f d)( 2 c ir1 pathaxim np     ee (3) where εi(t) is the maximum absolute value of principle strain at time t and εimax is the maximum value of εi(t) in a cycle. e1 and er are unit vectors for εimax and εi(t); ds the infinitesimal trajectory of the strain path. lpath is the whole strain path length during a cycle and “×” denotes vector product. the integral measures the rotation of the maximum principal strain direction and the integration of strain amplitude after the rotation. therefore; fnp totally evaluates the severity of nonproportional loading in a cycle. fig. 5 (a) shows failure life correlated by δεnp. a relative good correlation can be seen in the lcf region but the failure life in the high cycle fatigue region tends to be underestimated. fig. 5 (b) is a comparison of the failure life in evaluation nfeva and experiment nfexp; where nfeva is evaluated from the life curve in the push-pull loading test and the following equation np ff eq f bnan     1 6.012.0 (4) fig. 5 (b) also shows conservative estimation of failure life in the high cycle fatigue region. in the figure; data which did not reach to failure are omitted. the cause of the underestimation of nfeva in high cycle fatigue region is considered from that eq. (4) does not take into account the effect of non-proportional loading on life being weak under elastic deformation. actually; additional hardening becomes smaller in the lower stress and strain levels. in order to modify nonproportional strain range; the effect of non-proportionality depending on strain level is discussed in next section. factor of 2 method of universal slope curve 103 104 105 106 107 0.1 0.5 1 number of cycles to failure nf, cycles n o n p ro p or ti on al s tr ai n r an g e   n p , % 2.0 1.0 push-pull rev.torsion circle n o n -p ro p o rt io n al s tr ai n r an g e   n p , % 102 103 104 105 106 107 102 103 104 105 106 107 failure life in experiment nf exp , cycles f ai lu re l if e in e v al u at io n n fe v a , cy cl es push-pull rev.torsion circle exp f eva f nn  factor of 2 push-pull rev.torsion circle (a) correlation of nf with δεnp (b) comparison of nfeva and nfexp figure 5: evaluation of failure life by non-proportional strain range. modified non-proportional strain range fig. 6 shows correlations of nf with elastic and plastic strain ranges (δεeeq and δεpeq). δεeeq in the circle loading test is defined as δεeeq=anf0.12 based on elastic part of universal slope curve [16] and δεpeq is defined as δεpeq=δεeq  δεeeq; where δεeq is the strain range obtained by test results. in fig. 6; the bold lines show the relationships of δεeeqnf and t. morishita et alii, frattura ed integrità strutturale, 38 (2016) 289-295; doi: 10.3221/igf-esis.38.39 294 δεpeqnf; the thin line shows the relationship of δεpeqnf assuming δεpeq to be bnf 0.6/(1+α fnp). the relationships of δεpeqnf are drawn by separate lines in the proportional loading and the non-proportional loading. this results show that the elastic deformation behaviour may be independent on the non-proportional loading becomes of the smaller chance of interaction of slip systems due to non-proportional loading [2;3;6;12]. in order to estimate the effect of non-proportional loading in the lower stress/strain level; the modified equation is presented as np . 12.0 + 1 f bn an     f feq (5) fig. 7 shows comparison between nfeva* and nfexp. nfeva* is evaluated by the modified non-proportional strain range defined in eq. (5). in fig. 7; almost of the data are replotted within the factor of 2 band and the correlation becomes better in comparison with that in fig. 5 (b). therefore the modified non-proportional strain range becomes a suitable parameter for life evaluation in the high and the low strain levels under non-proportional loading. however; the definition of α still needs more discussion with additional experimental results in future studies. 102 103 104 105 106 107 0.01 0.05 0.1 0.5 1 number of cycles to failure nf, cycles s tr ai n r an g e  e eq ,  p eq , % push-pull (elastic strain) push-pull (plastic strain) rev. torsion (elastic strain) rev. torsion (plastic strain) circle (elastic strain) circle (plastic strain) 12.0 f e eq  an 6.0 f p eq  bn np 6.0 fp eq 1 f bn    2 figure 6: correlations of nf by δεeeq and δεpeq. 102 103 104 105 106 107 102 103 104 105 106 107 failure life in experiment nf exp , cycles f ai lu re l if e in e va lu at io n n fe va * , c y cl es exp f *eva f nn  factor of 2 push-pull rev.torsion circle figure 7: comparison of nfeva* and nfexp. t. morishita et alii, frattura ed integrità strutturale, 38 (2016) 289-295; doi: 10.3221/igf-esis.38.39 295 conclusions (1) the failure life in proportional and non-proportional loading tests can be correlated by a unique life curve in the stress region over the fatigue strength. (2) the fatigue strength in the circle loading test is lower than that in the push-pull and the rev. torsion loading tests. in the circle loading test; the remarkable roughness can be observed in comparison with those in the push-pull loading test at each equivalent stress range. the surface roughness leads to earlier crack initiations and reducing fatigue strength. (3) in the circle loading test; non-proportional strain range tends to overestimate failure life in the high cycle fatigue region because the effect of non-proportional loading becomes weak. (4) the modified non-proportional strain range is the suitable strain parameter for life evaluation independent on strain path and strain level. references [1] nitta, a., ogata, t., kuwabara, k., the effect of axial-torsional straining phase on elevated-temperature biaxial lowcycle fatigue life in sus304 stainless steel, journal of the society of materials science, 36 (1987) 376-382. [2] doong, s.h., socie, d.f., robertson, i.m., dislocation substructure and nonproportional hardening, journal of engineering materials and technology, 112 (1990) 456-464. [3] doong, s.h., socie, d.f., constitutive modeling of metals under nonproportional cyclic loading, journal of engineering materials and technology, 113 (1991) 23-30. [4] itoh, t., sakane, m., ohnami, m., ameyama, k., effect of stacking fault energy on cyclic constitutive relation under non-proportional loading, journal of the society of materials science, 41 (1992) 1361-1367. [5] wang, c.h., brown, m.w., a path-independent parameter for fatigue under proportional and non-proportional loading, fatigue & fracture of engineering materials & structures, 16 (1993) 1285-1298. [6] itoh, t., sakane, m., ohnami, m., socie, d.f., non-proportional low cycle fatigue criterion for type 304 stainless steel, journal of engineering materials and technology, 117 (1995) 285-292. [7] itoh, t., nakata, t., sakane, m., ohnami, m., nonproportional low cycle fatigue of 6061 aluminum alloy under 14 strain paths, european structural integrity society, 25 (1999) 41-54. [8] socie, d.f., marquis, g.b., multiaxial fatigue, society of automotive engineers international, (2000) 129-339. [9] itoh, t., sakane, m., hata, t., hamada, n., a design procedure for assessing low cycle fatigue life under proportional and non-proportional loading, international journal of fatigue, 28 (2006) 459-466. [10] itoh, t., sakane, m., ozaki, t., determination of strain and stress ranges under cyclic proportional and nonproportional loading, journal of the society of materials science, 60 (2011) 88-93. [11] itoh, t., yang, t., material dependence of multiaxial low cycle fatigue lives under non-proportional loading, international journal of fatigue, 33 (2011) 1025-1031. [12] itoh, t., fukumoto, h., hagi, h., itoh, a., saitoh, d., evaluation of multiaxial low cycle fatigue strength for mod.9cr-1mo steel under non-proportional loading, journal of the society of materials science, 62 (2013) 110-116. [13] chamat, a., azari, z., jodin, ph., gilgert, j., dominiak s., influence of the transformation of a non-proportional multiaxial loading to a proportional one on the high cycle fatigue life, international journal of fatigue, 30 (2008) 1189-1199. [14] pejkowski, l., skibicki, d., sempruch, j., high-cycle fatigue behavior of austenitic steel and pure copper under uniaxial, proportional and non-proportional loading, journal of mechanical engineering, 60 (2014) 549-560. [15] morishita, t., liu, s., itoh, t., sakane, m., kanayama, h., sakabe, m., takeda, n., fatigue failure life of ss400 steel under non-proportional loading in high cycle region, advanced materials research, 891-892 (2014) 1385-1390. [16] manson, s.s., halford, g.r., practical implementation of the double linear damage rule and damage curve approach for treating cumulative fatigue damage, international journal of fracture, 17 (1981) 169-172. << /ascii85encodepages false /allowtransparency false /autopositionepsfiles true /autorotatepages /none /binding /left /calgrayprofile (dot gain 20%) /calrgbprofile (srgb iec61966-2.1) /calcmykprofile (u.s. web coated \050swop\051 v2) /srgbprofile (srgb iec61966-2.1) /cannotembedfontpolicy /error /compatibilitylevel 1.4 /compressobjects /tags /compresspages true /convertimagestoindexed true /passthroughjpegimages true /createjobticket false /defaultrenderingintent /default /detectblends true /detectcurves 0.0000 /colorconversionstrategy /cmyk /dothumbnails false /embedallfonts true /embedopentype false /parseiccprofilesincomments true /embedjoboptions true /dscreportinglevel 0 /emitdscwarnings false /endpage -1 /imagememory 1048576 /lockdistillerparams false /maxsubsetpct 100 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can be opened with acrobat and adobe reader 5.0 and later.) >> /namespace [ (adobe) (common) (1.0) ] /othernamespaces [ << /asreaderspreads false /cropimagestoframes true /errorcontrol /warnandcontinue /flattenerignorespreadoverrides false /includeguidesgrids false /includenonprinting false /includeslug false /namespace [ (adobe) (indesign) (4.0) ] /omitplacedbitmaps false /omitplacedeps false /omitplacedpdf false /simulateoverprint /legacy >> << /addbleedmarks false /addcolorbars false /addcropmarks false /addpageinfo false /addregmarks false /convertcolors /converttocmyk /destinationprofilename () /destinationprofileselector /documentcmyk /downsample16bitimages true /flattenerpreset << /presetselector /mediumresolution >> /formelements false /generatestructure false /includebookmarks false /includehyperlinks false /includeinteractive false /includelayers false /includeprofiles false /multimediahandling /useobjectsettings /namespace [ (adobe) (creativesuite) (2.0) ] /pdfxoutputintentprofileselector /documentcmyk /preserveediting true /untaggedcmykhandling /leaveuntagged /untaggedrgbhandling /usedocumentprofile /usedocumentbleed false >> ] >> setdistillerparams << /hwresolution [2400 2400] /pagesize [612.000 792.000] >> setpagedevice 404 not found microsoft word numero_29_art_34 m. romano et alii, frattura ed integrità strutturale, 29 (2014) 385-398; doi: 10.3221/igf-esis.29.34 385 experimental investigation of fibre reinforced plastics with hybrid layups under high-velocity impact loads marco romano, carl j. j. hoinkes, ingo ehrlich ostbayerische technische hochschule regensburg, department of mechanical engineering, laboratory of composite technology, galgenbergstrasse 30, 93053 regensburg, germany johann höcherl university of the bundeswehr munich, department of mechanical engineering, laboratory of ballistics, arms and munitions, werner-heisenberg-weg 39, 85577 neubiberg, germany norbert gebbeken university of the bundeswehr munich, department of civil engineering and environmental sciences, institute of engineering mechanics and structural analysis, werner-heisenberg-weg 39, 85577 neubiberg, germany abstract. this paper deals with experimental investigations concerning energy dissipation capacity of different kinds of reinforcement fibres in monolithic and hybrid layups under high-velocity impact loads. the investigated kinds of fibres are carbon, glass and basalt fibres. therefore test panels, using the same thermoset resin, were built up and cured by autoclave processing. the fibre volume content of the test panels has been determined. furthermore the influence of a separating layer at selected positions in the hybrid stacked panels was investigated. the results show the influence and the energy dissipation capacity of each single kind of fibre and the enhanced properties for the hybrid layups by hybrid stacking sequences and the use of a separating core material. sommario. in questo lavoro le capacità di dissipazione dell’energia cinetica sotto carico trasversale ad alta velocità di materiali polimerici rinforzati con fibre sono state studiate mediante prove sperimentali. le costruzioni delle piastre sono monolitiche ed ibride con e senza strato separante. i materiali di fibra usati in dettaglio sono carbonio, vetro e basalto, ciascuno come tessuto spigato con una tessitura 2/2. i materiali sono stati impregnati con la stessa matrice termoindurente e curati con un’autoclave. i contenuti di fibra sono stati determinati sperimentalmente. in oltre l’effetto di uno strato separante ad una posizione selezionata nella costruzione delle piastre ibride è stato identificato. i risultati mostrano l’effetto e la capacità di dissipazione dell’energia cinetica a causa di penetrazione per ogni tipo di fibra rinforzante e le maggiori proprietà delle costruzione ibride con e senza strato separante. keywords. fibre reinforced plastic; high-velocity impact; energy dissipation; hybrid stacking. m. romano et alii, frattura ed integrità strutturale, 29 (2014) 385-398; doi: 10.3221/igf-esis.29.34 386 introduction ibre reinforced plastics are increasingly applied in the automotive sector as well as for personal impact protection issues. thereby especially the crash behavior and the failure mechanisms have to be researched properly in order to ensure safety for car passengers and facilitate recovery in the crash case. fibre reinforced plastics consisting of only one kind of reinforcement fibres under high-velocity impact loads mostly fail in a brittle failure mode causing sharpedged fracture surfaces and splitters. in order to use the outstanding properties of each single kind of fibre and to avoid the afore-mentioned brittle failure modes to an optimum, the idea of using hybrid stacking sequences is adequate. under these conditions fibre reinforced plastics with hybrid stacking sequences can be used as load-bearing structures and at the same time as safety structure for passengers in automotive or aerospace applications. moreover, with the hybrid stacked composites lightweight concepts can efficiently be realized regarding energy saving issues. research environment he research environment is the material behavior of fibre reinforced plastics under transversal loads in the highvelocity range. therefore a brief literature review is presented. this leads to several conclusions and to the pursued mechanical principle described thereafter. literature review energy dissipation mechanisms in fibre reinforced plastics are dominated by interand intralaminar failure modes as well as adhesive failure in the interface between fibre and matrix. whereas interlaminar failure means the delamination of sequent plies, intralaminar failure means fracture of fibre and matrix. only a small amount of energy is dissipated by friction effects between fibre and matrix and plastic deformation in the polymeric matrix system. different material parameters affect the failure modes. these are amongst others fibre orientation, fibre volume content, layup, geometry of the specimen and of the impactor as well. maier 1990 [7] investigated the crash-behavior of tubular specimens with different cross-sections by experiments and finite-element-analyses. the specimens were made of glass fibre reinforced vinyl ester, poly ester and epoxy matrix system. the specimens with the epoxy matrix systems exhibited the highest energy dissipation capacity. additionally the influence of the processing and the geometry on the energy dissipation capacity has been investigated. morita et al. 1997 [9] characterized the damage tolerance of fibre reinforced plastics under high-velocity impact loads with a varied degree of anisotropy. thereby the degree of anisotropy means the change of fibre orientation for sequent layers in the layup. the results showed an enhanced energy dissipation capacity with an increased degree of anisotropy for sequent layers in the layup. simultaneously the damage area in terms of interlaminar delaminations increased. holmquist and johnson 2002 and 2005 [5, 4] investigated the reaction of silicone carbide to transversal impact loads in the high-velocity range. the investigated material is a ceramic. the originally high energy dissipation capacity could even be enhanced by creating predefined residual stresses, suited to the specific material properties. muhi, najim and moura. 2009 [11] considered the effect of hybridization of glass fibre reinforced plastics with single layers of aramid fabrics under transversal high-velocity impact. therefore five kinds of different layups have been investigated experimentally. these are a monolithic layup consisting of only four layers of glass fabrics and in comparison four hybrid layups where at different positions in the layup one layer of glass fabric is substituted by one layer of aramid fabric (kevlar 29) at a time. additionally three different geometries of the impactor have been used. as a completion analytical approaches following morye et al. 2000 [10] have been carried out. the hybridization in terms of substituting one layer of glass fabric with one layer of aramid fabric yields enhanced penetration resistance as well as sensitivity to the position of the hybrid substitute layer in the construction of the layup. in detail the hybridized layup where the opposite impact side has been substituted exhibits the highest energy dissipation properties. fadhel 2011 [3] carried out finite-element-analyses for pure polycarbonate specimens under high-velocity impact-loads varying their thickness. additionally two different geometries of the impactor have been investigated. even though the work is focused on pure polymeric materials the essential conclusion of the simulations is that an enhanced elastic sag could be identified as the main reason for an increasing dissipated energy. melo and villena 2012 [8] investigated the influence of the fibre volume content on the energy dissipation capacity of fibre reinforced plastics. for glass fibre reinforced plastics with epoxy, polyester and vynilester matrix systems higher f t m. romano et alii, frattura ed integrità strutturale, 29 (2014) 385-398; doi: 10.3221/igf-esis.29.34 387 values of the fibre volume content in the specimens yield significant higher energy dissipation properties. additionally the materials with epoxy matrix system exhibited the highest energy dissipation capacity. rosenberg and dekel 2012 [21] basically describe the experimental setup and procedure as well as the evaluation of the experimentally determined results when transversal impact-tests in the high-velocity range are described. pursued mechanical principle the object in the carried out investigations is the identification of the energy dissipation capacity of fibre reinforced plastics under high-velocity impact loads. thereby besides monolithic layups selected hybrid layups with and without separating layer are investigated. the aim is to enhance the energy dissipation capacities by hybrid layups based on fabrics of different kinds of fibre reinforcements besides using the outstanding material properties of fibre reinforced plastics as load bearing structures. therefore two basic ideas are followed. hybrid stacking sequences as a first approach the use of hybrid stacked layups instead of monolithic layups is relatively simple. thereby the characteristic properties of carbon and glass fibres, completed by basalt fibres, respectively, can be used through the thickness in by reasonably defined hybrid stacking sequences. aramid fibres have not been considered, because of their distinct hygroscopicity and resulting in difficulties when being impregnated as described later on. separating layer as elastic support a second approach is the use of separating layers as a core material. here, especially relatively thin separating layers with relatively low stiffness are used. in the present application, however, it is not used with the aim of enhancing the moment of inertia as usually done. in contrast the used separating layers with the afore described properties provide an elastic support and a shear plane for the single layers in the layup. thereby transversal loads can increasingly be transferred to inplane loads. this effect is reached by additionally providing transversal deflection due to shear effects and therewith enhances the resulting in-plane loads in the material [6]. the reason for this pursued principle is, that fibre reinforced plastics show its outstanding properties under in-plane tensile loads in direction of the reinforcement fibres. the aim is to reduce the effect of simply stamping the material by the impactor but enable the afore described structural mechanic effects similarly to fadhel 2011 [3]. limit of the experimental investigations with the afore described basic ideas the initial situation for using the light-weight properties of fibre reinforced plastics as well as enhance their resistance to transversal impact loads in the high-velocity range can be created. these two basically different properties enable the application of fibre reinforced plastics as load-bearing structure and at the same time as protective structure. if thereby for load-bearing structures additional protective structures can be omitted, a holistic lightweight approach can be achieved. alternative approaches for enhancing the resistance of fibre reinforced plastics under transversal impacts in high-velocity range by the impact resistance of the matrix, i.e. by definably adding small amounts of thermoplastics in the thermoset matrix system is not the aim of the carried out investigations. they are merely focused on the material suited or fibre suited application of different kinds of reinforcement fibres in hybrid stacked layups, respectively. general experimental conditions knowing that different layer orientations have influence on the energy dissipation capacity [9] all test panels have been built up with a [(0/90)n] orientation. this was done as a first attempt for characterizing the general material behavior the fibre volume content is a significant parameter for the quality and reproducibility of fibre reinforced plastics [6], [24], [25]. moreover it has a massive influence on the energy dissipation capacity [8]. in order to experimentally investigate the specific capacities of monolithic and hybrid stacking sequences regarding energy dissipation high-velocity impact tests with an impact velocity of approx. 560 m/s have been carried out. thereby bearing balls have been used as an impactor. with a mass of approx. 1.12 g the initial kinetic energy before the impact lies in the range of 175 j. the reason therefore is that the spheric bearing balls are insensitive to variations in the angle of incidence. in contrast cylindrical blunt-ended or conical projectiles would cause distinct stress peaks in the specimen. this is due to variations of the angle of incidence caused by statistic deviations. analog observations have been made e. g. by muhi, najim and moura. 2009 [11]. it is additionally observed that the selected spheric geometry provides reasonable values for the energy dissipation properties [11]. m. romano et alii, frattura ed integrità strutturale, 29 (2014) 385-398; doi: 10.3221/igf-esis.29.34 388 evaluation of the experimentally obtained results for the velocities of the impactor before and after the penetration according to [21] provides information about the capacity for each single stacking sequence to dissipate kinematic energy. materials and test procedures n the following the used materials and the material processing is described. the used experimental equipment to determine the fibre volume content and the energy dissipation capacity are mentioned. the respective standards (din, en or iso) are indicated. materials and processing for the processing of the test panels three different kinds of fabrics and one core material have been used. tab. 1 contains the fabrics used for the production of test panels and the core material. the tested hexagonal core material is of the kind lantor soric xf [19] with a thickness of approx. 4 mm. it is used as a hexagonal separating layer. this separating layer aims at an enhanced sag of the test panels [6], which should dissipate more energy when penetrated [3]. three kinds of reinforcement fibres have been used. in each case a twill weave 2/2 has been used as a textile semifinished product for further processing and building-up the selected layups. in order to achieve a statistically secured amount of comparable specimens five test panels have been produced for each selected layup. therefore the single fabric reinforced layers have manually been pre-impregnated. this process enables the choice of the selected thermoset resin epikote resin 04572 [17] as a matrix system for all produced test panels. the curing was done in an autoclave process under a vacuum bag according to the process indicated in the data sheet of the matrix system epikote resin 04572 [17]. kind of fibre type of fabric spec. weight [g/m²] warp [1/cm] fill [1/cm] literature carbon twill 2/2 245 6 6 [13] glass twill 2/2 280 7 6.5 [18] basalt twill 2/2 345 12 9 [12] hexagonal core mat. 240 [19] table 1: types of fabrics and core material. with these parameters a panel thickness of approx. 4 mm and a fibre volume content of approx. 60 % have been achieved. in order to reach a constant thickness of the test panels the number of single layers in each layup has to be adopted due to the varying thicknesses of the fabrics. fig. 1 left shows the scheme of the used processing layup considering the vacuum bag in the autoclave curing process. fig. 1 right shows the corresponding autoclave curing cycle in terms of temperature t in °c, relative pressure p in bar, and relative vacuum in bar over the process time t in min. the geometric dimensions have been selected following din 65561 [14]. the german standard requires a final lateral geometry of the specimens of 150 mm x 100 mm. the panels have been built up with a dimension of 210 mm x 160 mm since the edges of the test panels become inhomogeneous and unsteady. the edges have then been cut off by water jet cutting. specimens for the experimental determination of the fibre volume content f have been cut of from the cut-off regions near the cutting edge. their dimensions are approx. 15 mm x 15 mm according to din en iso 1172 [15] and din en 2564 [16], respectively. fig. 2 shows schematic the layup and the cutting lines for test panels and the specimen for fibre volume content determination. tab. 2 lists the investigated types of test panels with their respective labeling, stacking sequence and number of single layers. thereby five test panels have been produced for every single type, so that 25 specimens have been investigated. there are three kinds of monolithic layups consisting of only carbon, glass and basalt fabric reinforced layers. additionally there are two kinds of hybrid layups consisting of carbon, glass and basalt. they distinguish from each other by an additionally added hexagonal separating layer lantor soric xf [19] as a core material after the first twelve fabrics or before the last four fabrics, respectively, considering the direction of the later impact. i m. romano et alii, frattura ed integrità strutturale, 29 (2014) 385-398; doi: 10.3221/igf-esis.29.34 389 -0.5 0 0.5 1 1.5 2 -50 0 50 100 150 200 0 60 120 180 240 300 360 420 480 540 600 a u to cl a v p re ss u re a n d v a cu u m i n b a r (r el a ti v ) t em p er a tu re i n ° c time in min temperature in °c temperature in °c autoclavpressure in bar vacuum in bar figure 1: left: scheme of the layup used in the processing: 1 sealant tape, 2 vacuum connector, 3 release film, 4 peel ply, 5 composite layup, 6 peel ply, 7 perforated foil, 8 bleeder, 9 vacuum bag. right: autoclave curing cycle for test panel processing in terms of temperature t in °c, relative pressure p in bar, and relative vacuum in bar over the process time t in min. approx. 210 150 10 0 ap p ro x . 1 60 determination of fiber volume content test panel specimen figure 2: schematic cutting lines for test panels and fibre volume content specimens (left) and exemplary specimens for basalt fibre reinforced material before and after the thermal treatment according to din en iso 1172 [15], [23] (right). type of test panel stacking sequence number of layers carbon  c180 / 90 18 glass  g180 / 90 18 basalt  b180 / 90 18 c+g+b      c g b 4 4 8 0 / 90 / 0 / 90 / 0 / 90   16 c+g+hex+b          c g b b 4 4 4 1 4 0 / 90 / 0 / 90 / 0 / 90 / hex / 0 / 90   16+1 table 2: labeling, stacking sequences and number of layers of the test panels. m. romano et alii, frattura ed integrità strutturale, 29 (2014) 385-398; doi: 10.3221/igf-esis.29.34 390 experimental determination of the fibre volume content basically there are two methods for experimentally investigating the fibre volume content. whereas for inorganic fibres like glass or basalt fibres it can be determined by thermal vaporization the polymeric matrix system according to din en iso 1172 [15], [23], for organic fibres like carbon fibres it can be determined by chemical extraction of the fibres according to din en 2564 [16]. for a statistically ensured determination five specimens of every test panel with geometric dimensions of approx. 15 x 15 mm have been investigated. in both cases knowing the mass of the initial specimen and the remaining fibres as well as the densities of the single components, namely fibre and matrix, it is possible to determine the fibre volume content f . in the following the two afore mentioned experimental methods are described. thermal vaporization of the polymeric matrix system according to din en iso 1172 for the panels that contain only glass or basalt fibres as inorganic reinforcement fibres the fibre volume content f can be determined experimentally using a muffle furnace and a precision balance following din en iso 1172 [15]. the furnace is of the type carbolite eml 11/6, required to reach the temperature of 620 °c. this temperature is necessary to evaporate the polymeric matrix without affecting the mass of the fibres [2], [22], [23], [24]. the precision balance is of the type mettler toledo 204-s being able to supply an accuracy of measurements in a range of 0.1 mg. with the precision balance it is possible to weigh the specimens before and the remaining fibres after the thermal treatment and so determining the fibre volume content f . chemical extraction of the fibres according to din en 2564 the afore described process is not suitable for carbon fibres. these kinds of reinforcement fibres show a distinct loss of weight under thermal loads [1], [24] as they are of organic structure. therefore the process of chemical extraction was used for test panels that only contain carbon fibres following din en 2564 [16]. the fibres are extracted from the matrix by placing the specimens in concentrated sulphuric acid and heating up to 160 °c. after the solution turns brown, hydrogen peroxide solution is added until the solution turns clear again. this effect is an indicator that the fibres have been completely extracted from the matrix. redrying wet fibres enables weighing them and thereby the calculation of the fibre volume content f . evaluation of the results and calculation of the fibre volume content as previously described, the specimens have been weighted before and the remaining fibres after the respective treatment. knowing these weights the fibre mass content can be calculated by f c m m   (1) where m indicates the mass and the subscripts f and c indicate the properties of the fibres and of the composite, respectively. knowing the fibre mass content  and the densities of the single components, namely reinforcement fibres and polymeric matrix system, out of the respective technical data sheets [12, 13, 17, 18] the fibre volume content can be calculated by f f m 1 1 1          (2) where  is the density,  is the fibre mass content and the subscripts f and m indicate the properties of the fibre and the matrix, respectively [6], [24]. analytical approximation of fibre volume content for test panels with hybrid stacking sequences when the hybrid stacked layups are considered none of the two afore described experimental methods for the determination of the fibre volume content are suitable because both organic and inorganic kinds of reinforcement fibres are used in the respective layups, as listed in tab. 3. neither the thermal vaporization method according to din en iso 1172 [15] nor the chemical extraction method according to din en 2564 [16] is applicable. therefore an approximation method has been developed in order to being able to analytically evaluate the fibre volume content of the hybrid stacked layups. the approximation is based on the specific weights of the dry fabrics and the weight of the prepared specimens. the mass of the fabrics in the specimen can be calculated by m. romano et alii, frattura ed integrità strutturale, 29 (2014) 385-398; doi: 10.3221/igf-esis.29.34 391 m f i i i 1 m a (q n )    (3) where m is the mass, a is the area of the test panel, q is the specific weight of the fabric, n is the number of the single layers of each fabric and the subscript f indicates the property of all fabrics in the layup. considering the summation i is the counter for the different kinds of reinforcement fibres used and m is the upper limit of the counter, i. e. the number of the different kinds of reinforcement fibres used in the hybrid stacked material. the mass of the composite cm is obtained by weighing the single specimens on a precision balance. the fibre mass content in the specimen  can then be calculated by evaluating eq. (1). for an analytical evaluation of the fibre volume content f the density of the fibres f is necessary. because more than one kind of reinforcement fibre is used in the hybrid stacked materials the fibre density is not a uniform value for the material. yet it is possible to analytically evaluate a mean value of the density of the fibre reinforcement in the composite material f . therefore the volume of each kind of dry fabrics is calculated by i iv a t n   (4) where a is the area of the specimen, n is the number of the single layers of each fabric, i is the counter for the different kinds of reinforcement fibres used and t is the thickness of each single fabric reinforced layers. thereby the values of the thickness of the single fabric reinforced layers have been taken from the respective technical data sheets [12], [13] and [18]. the mean value of the density of the fibre reinforcement in the composite material is analytically calculated by f , f , 1 f 3 f , 1 ( ) m i i i i i v v         (5) where v is the volume of each kind of dry fabrics,  is the nominal density of each kind of reinforcement fibre and the subscript f indicates the property of the fabric reinforcement. considering the summation i is the counter for the different kinds of reinforcement fibres used and m is the upper limit of the counter, i.e. the number of the different kinds of reinforcement fibres used in the hybrid stacked material. type of test panel mean value f (%) standard deviation f (%) carbon 63.60 0.46 glass 58.65 0.94 basalt 61.16 0.66 c+g+b 63.07 0.72 c+g+hex+b 57.15 1.36 table 3: fibre volume contents of the test panels. the calculation of the fibre volume content according to eq. (2) can be carried out by using the mean value of the density of the fibre reinforcement in the composite material f instead of the density of a single kind if reinforcement fibre  . though, it is sufficient to average the density of the used fibre reinforcement and carry out the evaluation according to eq. (5). m. romano et alii, frattura ed integrità strutturale, 29 (2014) 385-398; doi: 10.3221/igf-esis.29.34 392 resulting values for the fibre volume content f obtained by the different applied methods the results of the fibre volume content of the single layups are listed in tab. 3 with its mean values and corresponding standard deviations. the relatively high values of the fibre volume content show high mechanical quality of the material. the relatively low standard deviations represent a high degree of reproducibility of the process at the same time. experimental setup for high-velocity impact tests in order to carry out and properly evaluate high-velocity impact tests an adequate experimental setup of test equipment is necessary. the experimental setup is schematically shown in fig. 3 left. it consists of  an instrumented barrel for acceleration of the impactor on the target,  two photoelectric barriers for measuring the velocity of the impactor before the impact,  a test panel mounting where the specimens are inserted and clamped all around with eight bolts m8, each tightened with 5 nm,  a double exposure instrumentation with the respective high-speed photographic camera for measuring the velocity of the impactor after penetration of the target and  a bullet screen and a fire case for absorbing the impactor and fragments that have eventually been released. accelerator for sabbots and impactor photoelectric barrier double exposure cameratest panel mounting bullet screen fire casevision panel figure 3: schematical illustration of the experimental setup for high-velocity impact tests (left) and high-speed image of the debris after penetration under double exposure (right). the bearing balls are of the steel type 100cr6. with a diameter of 6.5 mm and the corresponding density of 7.61 g/cm³ the impactors have a mass of 1.12 0.0005 g. computer numerically controlled (cnc) manufactured plastic sabots were used to accelerate the bearing balls in a barrel. the case on which the plastic sabot is mounted is filled with a special propellant, which was weighted to 0.1 mg precision in order to properly accelerate the impactor in the barrel after ignition. the aforedescribed procedure provides reproducible velocities of the impactor after having left the barrel [21]. on the ballistic flight of the impactor the photoelectric barrier provides the velocity of the impactor before the impact 1v , the impactor hits the target and after penetration the double exposure with the high-speed camera provides the velocity of the impactor after the penetration 2v . fig. 3 right exemplarily shows an image of the high-speed camera after the impactor has penetrated the material. due to the double exposure the impactor is pictured twice. knowing the time between the two exposures measuring the distance between the two pictured impactors on the image allows the calculation of the velocity of the impactor after the penetration 2v . the design of the plastic sabots exhibits four defined slots in longitudinal direction. these slots guarantee the bulking of the plastic sabot after having left the barrel whereas the bearing ball continues its ballistic flight nearly straightly and at constant speed. with the specific design of the plastic sabots the impact of fragments of the plastic sabot in the area of the specimen can be excluded. fig. 4 left shows the manufactured plastic sabots made of the material pom [20] with the mounted case. fig. 4 right exemplarily shows a high-speed image of the bulking of the plastic sabot after having left the barrel. m. romano et alii, frattura ed integrità strutturale, 29 (2014) 385-398; doi: 10.3221/igf-esis.29.34 393 figure 4: cnc-manufactured plastic sabots with the mounted case containing precisely weighted propellant (left) and high-speed image of the bulking of the plastic sabot after having left the barrel whereas the bearing ball continues its undisturbed ballistic flight (right). results and discussion n the following the evaluation of the experimental results is described. the obtained results are discussed and lead back to acting effects. evaluation of experimental results for the evaluation of the experimental investigation each bearing ball is weighted to 0.1 mg precision. the mass of the impactors m lie in the range of 1.12 0.0005 g. knowing the velocity of the impactor before the impact provided by the photoelectric barrier 1v and the velocity of the impactor after penetration of the material provided by the double exposure and the high-speed camera 2v the kinetic energy for both states can be calculated by 2 kin, 1 2 n ne m v (6) where m is the mass, v is the velocity and n indicates the states, 1 before and 2 after the penetration of the material [21]. the mean value of the velocity of the impactor before the impact 1v lies in the range of m560.3 5.8 s and the respective kinetic energy before the impact kin ,1e lies in the range of 175.8 3.7 j . the difference between the kinetic energies before the impact kin ,1e and after the penetration of the material kin ,2e allows calculating the absolute value for the dissipated energy by penetrating the material by [21]  2 2diss kin kin,1 kin,2 1 21 2 e e e e m v v      (7) in order to properly evaluate each single test and achieve nondimensional comparable results for the carried out experimental investigations it is reasonable to introduce the relative dissipated kinetic energy [21]  2 2 2 2 21 2 kin 1 2 2 diss,rel 2 2 2kin ,1 1 1 1 1 2 1 1 2 m v v e v v v e e v vmv        (8) where the dissipated kinetic energy due to penetration of the material kine is related to the initial kinetic energy of the impactor kin,1e . the introduction of the relative dissipated kinetic energy diss,rele provides a specific value in percent. it i m. romano et alii, frattura ed integrità strutturale, 29 (2014) 385-398; doi: 10.3221/igf-esis.29.34 394 indicates the capacity of a material to dissipate kinetic energy applied by high-velocity impacts when the material gets penetrated. the experimentally determined fibre volume contents f vary in a range of 63 % to 57 %. the distinct variation exists even though the same manufacturing process described before as well as the same autoclave curing cycle illustrated in fig. 1 right has been used. that is the reason why the former described evaluation of the relative dissipated kinetic energy diss,rele has to be evaluated additionally. in order to standardize the further calculated values based on the nominal values a standardization of the relative dissipated kinetic energy diss,rele to a constantly presumed fibre volume content f,s is carried out by calculating   f,sdiss,rel, f,s diss,rel f,e e e     (9) where the subscripts s and e indicate the desired standardized value for the fibre volume content and the experimentally determined fibre volume content listed in tab. 3, respectively. as already mentioned before the autoclave curing cycle was modified in order to achieve a fibre volume content of approx. 60 %. therefore the presumed fibre volume content for the standardization is selected to f,s 60%  . results the results are illustrated in terms of the relative dissipated energy of the materials based on the nominal values of the fibre volume content ef, as well as standardized to the desired value of the fibre volume content %60sf,  . because five test panels of each selected layup have been investigated experimentally, the evaluation of the experimental results allows statistically assured results by calculating mean value and standard deviation for each material. as it can later be seen, the standard deviations are generally very low. this is an indicator for constant material quality for all the investigated test panels provided by the manufacturing process as well as for the high reproducibility of the experimental investigations of high-velocity impact loads. results based on the nominal values of the fibre volume content f,e fig. 5 illustrates the relative dissipated kinetic energy diss,rele for each selected type of layup calculated by eq. (8) for the three monolithic layups and for the hybrid stacking sequences with and without the hexagonal separating layer. the relative dissipated kinetic energy of the test panels consisting of monolithic layups containing only a single kind of reinforcement fibre, illustrated in fig. 5, range from 34 % to 44 %. the highest value of the relative dissipated kinetic energy of approx. 44 % is obtained for the test panels built up of only basalt fabrics. the test panels consisting of only glass fabrics dissipated approx. 37 % whereas the test panels containing only carbon fabrics dissipated approx. 34 % of the initial impact energy. the standard deviation is persistently low and lies in a range of 0.85 % to 2.2 %. thereby the carbon fibre reinforced test panels showed the lowest standard deviation in contrast to the basalt fibre reinforced specimens that showed the highest values of the standard deviation. 33,8% 37,1% 43,6% 34,9% 38,5% 0% 10% 20% 30% 40% 50% 0 1 2 3 4 5 6 r el a ti v e d is si p a te d k in . en er g y e d is s, re l layup configuration figure 5: relative dissipated kinetic energy diss,rele of the monolithic and hybrid materials based on the absolute values of the fibre volume content f,e . m. romano et alii, frattura ed integrità strutturale, 29 (2014) 385-398; doi: 10.3221/igf-esis.29.34 395 the relative dissipated kinetic energy of the test panels consisting of the hybrid layups with and without the hexagonal separating layer range from 35 % to 39 %. confronting the hybrid stacked layup without hexagonal separating layer and the hybrid stacked layup with hexagonal separating layer as a core material a distinct effect can be noticed. the hybrid stacked material with separating layer shows approx. 4 % higher values for the relative dissipated kinetic energy than the hybrid stacked layup without separating layer. in contrast to the monolithic materials the hybrid stacked materials showed the lowest standard deviation. standardizing the results to a fibre volume content f,s 60%  fig. 6 illustrates the relative dissipated kinetic energy  diss,rel, f,s 60%e   for each selected type of layup calculated by eq. (9) as standardized results for the monolithic and hybrid layups with and without the hexagonal separating layer. the relative dissipated kinetic energy diss,rele and the standardized relative dissipated kinetic energy  diss,rel, f,se  to desired value of the fibre volume content f,s 60%  vary only slightly when the monolithic materials are considered. the standardized relative dissipated kinetic energy  diss,rel, f,se  of the monolithic materials, illustrated in fig. 6, range from 32 % to 43 %. the highest value of the relative dissipated kinetic energy of approx. 43 % is still obtained for the test panels built up of only basalt fabrics. to the test panels consisting of only glass fabrics a value of approx. 38 % is assigned. for the monolithic carbon fibre reinforced layups the standardization yields a value of approx. 32 %. the standard deviations are standardized as well, so that the tendencies in the results based on the nominal values do not change. 31,9% 38,0% 42,7% 33,2% 34,8% 0% 10% 20% 30% 40% 50% 0 1 2 3 4 5 6 r el . d is si p at ed k in . en er g y e d is s, re l (φ f, s) st an d a rd iz ed t o φ f, s= 6 0% layup configuration figure 6: relative dissipated kinetic energy  diss,rel, f,se  of the monolithic and hybrid materials standardized to a fibre volume content f,s 60%  . the relative dissipated kinetic energy diss,rele and the standardized relative dissipated kinetic energy  diss,rel, f,se  to the desired value of the fibre volume content f,s 60%  vary only slightly, too, when the hybrid stacked materials are considered. they range from 33 % to 35 %. because the initial values of the fibre volume content f,e do not distinctly differ from the desired value of the fibre volume content f,s 60 %  the tendencies are similar to the results obtained for the nominal values. however, the effects caused by the separating layer used as a core material are a little less distinct, yet clearly observable. the hybrid stacked material with separating layer shows approx. 2 % higher values for the standardized relative dissipated kinetic energy than the hybrid stacked layup without separating layer. because the standard deviations are standardized as well, the tendencies in the results based on the nominal values do not change, as already mentioned before. description of failure modes – impact surface and outlet areas in the following the characteristic failure modes of the different kinds of layups are confronted with each other. therefore the fractured surfaces of the impact side as well as of the opposite side are described. fig. 7 exemplarily shows the m. romano et alii, frattura ed integrità strutturale, 29 (2014) 385-398; doi: 10.3221/igf-esis.29.34 396 characteristic fractured surfaces of the penetrated specimen. whereas the top row shows the fractured surfaces on the impact side the bottom row shows the fractured surfaces on the opposite side. the specimens that only contain carbon fibres show a distinct contour due to the penetration on the impact side. the distinct contour can be interpreted as a die-cutting effect because of the relatively high stiffness of the carbon fibre reinforced material. on the opposite side a splinted surface due to brittle fracture can be observed. due to the typical opaque property for carbon fibre reinforced plastics interlaminar delaminations are not visible yet exising. in contrast for the glass fibre reinforced specimens the interlaminar delaminations are cognizable due to the transparency of both the fibres and the matrix system. on the opposite side of the impact a clearly outlined delamination area can be identified between the last two single layers. comparing the delamination areas on the impact side to the area on the opposite side a conical spreading of the delamination areas through the thickness can be assumed. due to the [(0/90)n] layups with equilibrated twill fabrics and the rectangular form of the free part of the specimen in the test panel mounting the delamination has a slight rectangular shape, too. furthermore the lateral dimensions of the delamination on the opposite side of the impact are approx. 28 mm x 25 mm. because the visible delaminated area is considerably smaller than the free part of the specimen in the test panel mounting the assumption that the boundary conditions are negligible can be confirmed. for the basalt fibre reinforced material the interlaminar delaminations are not clearly identifiable due to the opaque optical properties of basalt fibres. confronted to the glass fibre reinforced material the interlaminar delaminations on the opposite side of the impact can slightly be discerned. because of the slightly unbalanced construction of the basalt fabric the delamination on the opposite side of the impact is distinctly rectangular with lateral dimensions of approx. 25 mm x 15 mm. the contour due to the penetration on the impact side of the hybrid layups without separating layer are similar to the contours of the specimens that only contain carbon fibre reinforcement. on the opposite side of the impact the basalt fabrics cause a fine extensive fractured surface. on the opposite side of the impact the interlaminar delamination between the last single layers of basalt fabrics can slightly be discerned. regarding the hybrid layups with separating layer the contour due to the penetration on the impact side is shaped like the ones of the hybrid layups without separating layer or the purely carbon fibre reinforced material. on the opposite side of the impact the hexagonal structure of the core material is slightly visible. the fractured area can be identified to be slightly smaller compared to the hybrid specimens without separating layer. 10 mm 10 mm 10 mm10 mm 10 mm 10 mm 10 mm 10 mm 10 mm 10 mm figure 7: characteristic failure modes of the different kinds of layups: from left to right: c (carbon), g (glass), b (basalt), c+g+b and c+g+hex+b (top row: impact side, bottom row: opposite impact side). m. romano et alii, frattura ed integrità strutturale, 29 (2014) 385-398; doi: 10.3221/igf-esis.29.34 397 conclusions or all evaluated results the standard deviations are generally very low. this is an indicator for constant material quality for all the investigated test panels provided by the manufacturing process as well as for the high reproducibility of the experimental investigations of high-velocity impact loads. the carried out high velocity impact tests showed the respective properties of each single kind of fibre when the monolithic layups have been considered. with a hybrid stacking it is possible to optimize the use of the outstanding material properties of each single kind of reinforcement fibres when energy dissipation issues under high-velocity impact loads are considered. even though aramid fibres have not been considered as for example described in muhi, najim and moura. 2009 [11] hybridization yields noticeable effects. the effect can directly be lead back to hybridization. the reasons therefore are the relatively high values of the fibre volume content f,s 60%  and at the same time the relatively low standard deviations. these two indicators regarding the composite material imply a high mechanical quality as well as a high degree of reproducibility of the process at the same time. however, aramid fibres should be taken into account in further investigations as even a more distinct enhancement of the energy dissipation capacity can be expected. the initially described idea to enhance transversal deflection due to shear effects and therewith enhance the resulting normal loads in the material can be identified in the evaluated results for the hybrid stacked materials with and without the hexagonal separating layers. the improved relative energy dissipation based on the nominal values as well as standardized to the desired fibre volume content distinctly proves the acting of the aimed structural mechanic effect. thus, the functional capability of the layer as well as of the hybrid stacked layups can be stated. in further investigations different hybrid layups should be considered additionally. thereby the focus should lie on the identification of the sensitivity of the energy dissipation properties to the sequential arrangement of the monolithic blocks in the construction of the hybrid stacked layups as basically carried out in muhi, najim and moura. 2009 [11]. acknowledgements he authors would like to thank mr marco vogelsberg and mr uwe riedel from the laboratory of ballistics, weaponry and munitions at the university of the bundeswehr munich as well as mr florian roidl from the laboratory of manufacturing engineering and machine tools (lfw) and mr bastian jungbauer, b.eng. from the laboratory of composite technology (lft), both at the ostbayerische technische hochschule regensburg. further mrs carmen löpelt and mr elmar lauterborn, both from the wehrwissenschaftliches institut für werkund betriebsstoffe (wiweb) erding are gratefully acknowledged for carrying out the determination of the fibre volume content by chemical extraction. the authors are grateful to the donation of the bearing balls from the company schaeffler technologies ag & co. kg that have exhibited excellent properties as spheric impactors. references [1] cherif, c., textile werkstoffe für den leichtbau, techniken-verfahren-materialien-eigenschaften. springerverlag, berlin/heidelberg/new york, (2011). [2] deak, t.; czigany, t., chemical composition and mechanical properties of basalt and glass fibers: a comparison, textile research journal, 79(7) (2009) 645-651. [3] fadhel, b. m., numerically study of ballistic impact of polycarbonate. international symposium on humanities, science and engineering research (shuser), kuala lumpur, (2011) 101-105. [4] holmquist, t., johnson, g., characterization and evaluation of silicon carbide for high-velocity impact, journal of applied physics, 97 (2005) 1-12. [5] holmquist, t., johnson, g., response of silicon carbide to high velocity impact, journal of applied physics, 91( 9) (2002) 5858-5866. [6] jones, r., mechanics of composite materials, 2nd edition, taylor & francis, philadelphia (pa.), (1999). f t m. romano et alii, frattura ed integrità strutturale, 29 (2014) 385-398; doi: 10.3221/igf-esis.29.34 398 [7] maier, m., experimentelle untersuchung und numerische simulation des crashverhaltens von faserverbundwerkstoffen. dissertation, universität kaiserslautern, ludwigshafen, (1990) [8] melo, j., villena, j., effect of fiber volume fraction on the energy absorption capacity of composite materials, journal of reinforced plastics and composites, 31(3) (2012) 153-161. [9] morita, h., adachi, t., tateishi, y., matsumot, h., characterization of impact damage resistance of cf/peek and cf/toughened epoxy laminates under low and high velocity impact tests, journal of reinforced plastics and composites, 16(2) (1997) 131-143. [10] morye, s. s., hine, p. j., duckett, r. a., carr, d. j., ward, i. m., modelling of the energy absorption by polymer composites upon ballistic impact, composites science and technology, 60(14) (2000) 2631-2642. [11] muhi, r. j., najim, f., de moura, m. f. s. f., the effect of hybridization on the gfrp behavior under high velocity impact, composites: part b, 40 (2009) 798-803. [12] basalt fabric bbk.2/2.345.100.12 twill weave 2/2. technical data sheet, incotelogy limited, pulheim, germany, (2013). [13] carbon fabric twill weave 2/2. technical data sheet, ecc engineered cramer composites, heek, germany, (2013). [14] din 65561 luftund raumfahrt; faserverstärkte kunststoffe, prüfung von multidirektionalen laminaten, bestimmung der druckfestigkeit nach schlagbeanspruchung. beuth verlag, berlin/heidelberg/new york, (1991). [15] [din en iso 1172 textilglasverstärkte kunststoffe; prepregs, formmassen und laminate; bestimmung des textilglasund mineralfüllstoffgehalts. beuth verlag, berlin, (1998). [16] din en 2564 luftund raumfahrt; kohlenstofffaser-laminate, bestimmung der faser-, harzund porenanteile. beuth verlag, berlin, (1998) [17] epikote resin 04572 anhydrid warm curing epoxy resin. technical data sheet, momentive, columbus oh, (2011). [18] glass fabric interglas type 92125 twill weave 2/2. technical data sheet, p-d interglas technologies gmbh, erlbach, germany, (2013). [19] lantor soric xf. technical data sheet, lantor bv, veenendaal, netherlands, (2013).. [20] polyoxymethylen (pom). technical data sheet, siegele, augsburg, germany, (2013). [21] rosenberg, z., dekel, e., terminal ballistics, springer-verlag, berlin/heidelberg/london/new york, (2012). [22] saravanan, d.: spinning the rocks – basalt fibres. ie(i) journal-tx, 86 (2006) 39-45. [23] schmid, v., jungbauer, b., romano, m., ehrlich, i., gebbeken, n., diminution of mass of different types of fibre reinforcements due to thermal load. in: proceedings of the applied research conference, nürnberg, (2012) 231-235, doi: 10.2370/9783844010930, in: mottok, j., ziemann, o. (eds.): applied research conference 2012 – arc 2012. shaker verlag, aachen/herzogenrath, (2012), doi: 10.2370/9783844010930. [24] schürmann, h., konstruieren mit faser-kunststoff-verbunden. springer-verlag, berlin/heidelberg, (2005). [25] witten, e., handbuch faserverbundkunststoffe, grundlagen verarbeitung anwendungen. gwv fachverlag, wiesbaden, (2010). microsoft word numero 3 art 1 m. zakeri et al., frattura ed integrità strutturale, 3 (2008) 2 10; doi: 10.3221/igf-esis.03.01 2 1 introduction many structural materials are subjected to crack forming and propagation during their service life. these cracks influence the stress distribution in the component and can result in significant decrease of its strength. because of the importance of safety and reliability, the crack problem has been of interest to a large number of researchers. elastic stress field around a crack tip is usually written as a set of infinite series expansions as [1]: ( ) i xx 1/2ii k θ θ 3θ = cos 1 sin sin 2 2 22πr k -θ θ 3θ + sin 2 + cos cos + t + o r 2 2 22πr σ ⎡ ⎤⎛ ⎞ ⎛ ⎞ ⎛ ⎞ ⎜ ⎟ ⎜ ⎟ ⎜ ⎟⎢ ⎥ ⎝ ⎠ ⎝ ⎠ ⎝ ⎠⎣ ⎦ ⎡ ⎤⎛ ⎞ ⎛ ⎞ ⎛ ⎞ ⎜ ⎟ ⎜ ⎟ ⎜ ⎟⎢ ⎥ ⎝ ⎠ ⎝ ⎠ ⎝ ⎠⎣ ⎦ ( ) i yy 1/2ii k θ θ 3θ = cos 1 + sin sin 2 2 22πr k θ θ 3θ + sin cos cos + o r 2 2 22πr σ ⎡ ⎤⎛ ⎞ ⎛ ⎞ ⎛ ⎞ ⎜ ⎟ ⎜ ⎟ ⎜ ⎟⎢ ⎥ ⎝ ⎠ ⎝ ⎠ ⎝ ⎠⎣ ⎦ ⎛ ⎞ ⎛ ⎞ ⎛ ⎞ ⎜ ⎟ ⎜ ⎟ ⎜ ⎟ ⎝ ⎠ ⎝ ⎠ ⎝ ⎠ (1) ( ) i xy 1/2ii k θ θ 3θ = cos sin sin 2 2 22πr k θ θ 3θ + cos 1 sin sin + o r 2 2 22πr σ ⎛ ⎞ ⎛ ⎞ ⎛ ⎞⎜ ⎟ ⎜ ⎟ ⎜ ⎟ ⎝ ⎠ ⎝ ⎠ ⎝ ⎠ ⎡ ⎤⎛ ⎞ ⎛ ⎞ ⎛ ⎞ ⎜ ⎟ ⎜ ⎟ ⎜ ⎟⎢ ⎥ ⎝ ⎠ ⎝ ⎠ ⎝ ⎠⎣ ⎦ on the influence of t-stress on photoelastic analysis under pure mode ii loading mahnaz zakeri mechanical eng. dep., iran university of science and technology, narmak, tehran 16844, iran e-mail: m_zakeri@iust.ac.ir chiara colombo politecnico di milano, dipartimento di meccanica, via la masa 34, 21058 milano e-mail: chiara.colombo@mecc.polimi.it riassunto: dalla definizione classica dello stato di sollecitazione elastica in prossimità dell’apice di una cricca, il termine t costante nello sviluppo in serie del fattore di intensificazione degli sforzi esiste solo in presenza del modo i di carico. tuttavia, recenti studi mostrano che il t-stress può esistere anche in condizione di modo ii, e modificare significativamente il campo di sforzi elastici presenti nell’intorno dell’apice della cricca. questi effetti possono essere visualizzati e testati sperimentalmente col metodo della fotoelasticità. in questo lavoro è proposto uno studio sull’influenza del t-stress in cricche sollecitate secondo il modo ii e i suoi effetti sul campo di frange visibili sperimentalmente. i provini utilizzati sono dischi, chiamati brazilian disks, al cui interno sono contenute cricche centrali da analizzare: i risultati sperimentali indicano che questi tipi di provini contengono valori negativi di t-stress. i valori ottenuti sperimentalmente sono poi confrontati con i risultati di simulazioni numeriche. per meglio interpretare le differenze tra valori sperimentali e numerici, sono inoltre state eseguite analisi fem 3d: i risultati mostrano l’influenza della reale geometria del fronte sui valori dei fattori di intensificazione degli sforzi. abstract. according to the classical definition for in-plane modes of crack deformation, the constant stress term t exists only in the presence of mode i. however, recent studies show that this term can exist in mode ii conditions as well, and significantly affect the elastic stress field around the crack tip. these effects can be visualized using the experimental method of photoelasticity. based on the analytical studies, presence of the t-stress in mode ii cracks transforms the isochromatic fringe patterns from symmetric closed loops to asymmetric and discontinuous shapes. in this paper, presence of the t-stress in mode ii cracks and its effects on the fringe patterns is experimentally investigated. the test specimens are brazilian disks containing very sharp central cracks: experimental results indicate that these specimens contain negative values of t-stress. experimental values are then compared to numerical results. to better understand the differences between experimental and numerical values, a thee dimensional analysis is performed with the finite element method: results show the influence of the real geometry of the crack front on the stress intensity factors. keywords: sharp crack generation, curved crack tip, brazilian disk specimen, t-stress, mode ii loading. http://dx.medra.org/10.3221/igf-esis.03.01&auth=true http://www.gruppofrattura.it http://www.gruppofrattura.it wher crack are t mode term, ent o this terms domi f base mode tions cond analy can a effec mode the c the c an im mate als or of tture leads is po this lahi a fect fractu affec that t crack ii sp aroun t af stress nifica in m study cons the c ordin xx =σ re r and θ a k tip (fig. 1) the singular e ii stress in , often called of the distanc expansion, r s which are inated zone. figure 1. crac d on the cl es [1], the t of mode i dition. howe ytical and nu also exist in ct can introdu e ii brittle fra constant stre rack tip. the mportant effe rials, whethe r elastic-plas -stress influe path. presen s the crack to ositive, the c effect is not and abbasi considerably ure path in m cts the mode t is the mos k tip constrai ecimens exh nd the crack ffects the siz ses inside th antly by a re mode ii can ying of mode sidering this rack tip in m nate system a iik -θ= sin 22πr ⎛ ⎜ ⎝ are the polar ). the two fi stresses, dep ntensity fact d the t-stres ce r from the represented e usually n ck tip coordina assical defin -stress exists and ii, and ever, some p umerical rese mode ii prob uce significa acture. ess term t ac e amounts of ect on the br er in predom stic cases. it ences the sta nce of the n o grow along crack deviate t restricted to [6] have sho y the angle mode ii as w ii fracture to st important int in constra hibiting smal tip, ayatolla ze and shap he plastic zo emote t-stres introduce c e ii brittle fra point, the el mode ii can b as: θ θ 2 + cos 2 2 ⎡⎞ ⎛ ⎟ ⎜⎢ ⎠ ⎝⎣ m. zakeri et r coordinate first terms in pending on tors ki and ss, is constan e crack tip. t by o(r1/2), a neglected in ates and stress nition of cra s only in mod it vanishes published re arches indica blems [2-4], ant inaccurac cts over a larg f this stress a rittle fracture minantly linea has been sho ability and d negative t-s g its plane, w es from its i o mode i con own that the between the ell. presence oughness. it parameter fo ained yieldin ll to moderat ahi et al. [8] pe of the pl one are also ss. thus, ign considerable acture. lastic stress c be expressed θ 3θ cos + 2 2 ⎤⎞ ⎛ ⎞ ⎟ ⎜ ⎟⎥ ⎠ ⎝ ⎠⎦ t al., frattura s centred at n each expan the mode i kii. the sec nt and indepe the next term are higher o the singula s components. ack deforma de i or comb in pure mod esults of sev ate that this t and ignorin cies in predic ge distance f and its sign h e of enginee ar elastic ma own that the direction of f stress in mo while when th initial plane nditions. aya t-stress can e crack line e of t-stress has been sh or describing ng [7]. for m te scale yield have shown lastic zone. influenced oring the t-t inaccuracie components in cartesian ( )1/2+ t + o r ed integrità s 3 t the nsion and cond endms of order arity . ation binade ii veral term g its cting from have ering aterisign fracde i he t [5]. atoln afand also own g the mode ding that the sigterm es in near n coyyσ xyσ the dete peri met calc spe bee from usi men gen thre ods whi vide fiel four frin num new squ nur ana alth high prob pur sug mod hav [13 con due spe the pres the usin foll is p peri ing ate buc use cen the num are (fe agre strutturale, 3 ii y k = sin 2πr iik= cos 2πr ⎛ ⎜ ⎝ e crack param ermined usin imental meth thod of phot culating the cimens [e.g. en suggested m photoelast ing the stress ntal optic equ neral, a nonee unknown have been ich, the over e a more ac d method th r or more nges. the re merically, an wton-raphso uares. anoth rse and pat alysis which i hough the fu h degree of blems, some e mode ii. o ggest that the de ii condit ve been obse ]. as describ nsistency bet e to neglectin cimens. e main obje sence of t i isochromati ng the exper lowing, a bri presented. th imental prog a mechanica sheets (thic ckling in the d to make b ntral cracks, l e observed f merical predi validated by em). althou eement with (2008) 2 10 θ θ n cos 2 2 ⎛ ⎞ ⎛ ⎜ ⎟ ⎜ ⎝ ⎠ ⎝ θ θ 1 sin 2 2 ⎡⎛ ⎞ ⎛ ⎟ ⎜⎢ ⎝ ⎠ ⎝⎣ meters kii an ng different hods. among toelasticity h e crack par 9,10]. more d and utilized tic fringe pat s series expa uations for a -linear equa parameters k suggested t rdetermini curate analy hat can use t arbitrary po esultant non nd the fittin on method her full-field tterson [12], is more comp full-field met accuracy for etimes the re on the other e fringe patte tions [11]. h rved in some bed by previ tween the th ng the effect ctive of thi in a mode ii ic fringe pat rimental met ief review on hen, differen gram are des al shock, in ckness of 10 following lo brazilian disk loaded in mo fringe pattern ictions. also y using result ugh the expe h fem, the 3θ cos + 2 ⎞ ⎛ ⎞ ⎟ ⎜ ⎟ ⎠ ⎝ ⎠ θ 3θ sin 2 2 ⎤⎞ ⎛ ⎞ ⎟ ⎜ ⎟⎥ ⎠ ⎝ ⎠⎦ nd t in these analytical, n g the experim has been fre rameters in eover, severa d to determi tterns. ansion (eq. an isochroma ation is obta ki, kii, and t to solve this stic techniqu ysis [11]. be the coordina oints on giv n-linear equa ng process i and the m d technique , based on plicated. thods genera r mode i and esults are no r hand, the t erns are alw however, as e of the prev ious research heory and ex t of t-stress s paper is t i specimen, tterns around thod of phot n the analyti nt steps of th cribed: crack sufficiently 0 mm) to av oading phas k specimens ode ii conditi ns are finall o, calculated ts from finite erimental re ere were so ( )1/2+ o r ( )1/2+ o r e equations c numerical, an mental techni equently use various cra al procedures ine ki, kii a 1) and the f atic fringe [1 ained in term t. different m s equation a ue is able to ecause it is a ates r and θ ven isochro ations are s nvolves bot method of is propose complex fo ate solutions d mixed mod ot satisfactor theoretical r ways symmet symmetric fr vious experim hes [2,13], th xperiments c in some mo to investigat and its effec d the crack t toelasticity. i ical relations he performe ks are create thick polyca void problem e. this proc s containing ions. ly compared crack param e element an sults had a ome minor e (2) can be nd exiques, ed for acked s have and t funda11], in ms of methamong o proa fullfrom omatic solved th the least ed by ourier s with de i/ii ry for results tric in ringes ments his inan be ode ii te the cts on tip by in the s [13] ed exd, usarbonms of cess is sharp d with meters nalysis good errors whic front also i crack singu apply node 2 m is base of an press m2τ wher the f and h shear nents m(2τ subs math aroun prese param s = ⎛⎜ ⎝ in wh h could be r t through the investigated k front is ass ular element ying the qua e elements. mathema sochrom d on the cla n isochroma sed as [11]: nf = h re τm is max fringe order h is the thic r stress τm is s with this eq 2 m xx) = (σ σ tituting stres hematical eq nd a mode i ented in ref. meters: 2 nf ht ⎛ ⎞ ⎟ ⎝ ⎠ , b = hich a is the related to th e specimen th by using a 3 sumed to be s around the arter point atical re matic frin assical conce atic fringe a imum in-pla and materia kness of spe s related to quation [11]: 2 2 yy xyσ ) + 4σ ss terms from quation for ii crack tip [13] and d ii t πa = k , r′ e crack lengt figure 3 m. zakeri et he curved sha hickness. th 3d finite elem e in a circula e crack tip a technique o elations nges epts of photo around the c ane shear str al fringe valu ecimen. also the cartesia m eqs. (2,3) a fringe l is written in defining thre = r/2a th for edge c 3. created sem t al., frattura ape of the c his latter effe ment model. ar arc form; are generated on quadratic of oelasticity, lo crack tip is ( ress. n and f ue, respectiv o, the maxim an stress com ( ) in eq. (4), oop develop n a simple f ee dimension ( cracks and se mi-natural cra ed integrità s 4 rack ect is the and d by 20ocus ex(3) f are vely, mum mpo(4) , the ping form nless (5) emicrac equ isoc as: r′ whe thi con whi mat clos 90° [11 2.b. r = figu tip: acks: a) front v strutturale, 3 ck length fo uation is obta chromatic fri 2bb +± =′ ere: ⎜ ⎝ ⎛ = sinb is equation p ntinuous alon ile, in the ca tic fringes is sed loops, sy , similar to , 14]. a typi . 2 iihk1= 2π nf ⎡ ⎤ ⎢ ⎥ ⎣ ⎦ ure 2. typical a) t≠0, b) t= view, b) throu (2008) 2 10 or central c ained. solvin inges in pres )1(2 34)(1( sb s − −−+ + 2 2 3 cosn θ θ predicts asym ng the crack ase of zero t s obtained as ymmetric ab the earlier a cal scheme o ( ) 2 24 3sin θ l isochromatic =0. gh the sheet th cracks, a qu ng this equa ence of t-str )sin3 2 θ ⎟ ⎠ ⎞ 2 sin2 θ mmetric fring k edges (see t-stress, the s eq.(7) that out direction analytical re of these loop ) c fringes arou hickness. uadratic alge ation, the loc ress is determ ges which ar fig. 2-a). m locus of iso t suggests a ns θ = 0° an sults present ps is shown in und a mode ii ebraic cus of mined (6) re not meanochroset of nd θ = ted in n fig. (7) i crack 3 e 3.1 for e elasti utiliz of th first jet te gen o come by ap crack with tal cr the s r=66 2), re in th ness, speci since all re ting p accor heati 145° ture in th check the d 3.2 as a fring [n/(m to he experime specimen pr experimental ic stress fie zed. the disk ickness t =1 an initial sm echnology. t of -196°c tem e completely pplying a me k obtained in sharp tips (f rack lengths sheet was cu 6.5mm (spec espectively. i his way are n and there is ially in the ca e the specim esidual stress process were rding to fig ng rate is c, which is for polycarb he furnace ked in the po disks are almo determinati an optical p ge value for mm·fringe)] eat treatmen ental pro reparation l investigatio ld, two bra ks were made 0mm. for cr mall notch w the notched s mperature fo y brittle, and echanical sho n this way is fig. 3-a). for were 2a=58 ut in the fo cimen n-1) it is notable not perfectly s a curvature ase of thick s mens should b ses induced d e removed b g. 4. it is se decreased in the minimu bonate [15]. for 59 hour olariscope m ost stress-fre ion of materi property of an intact p [11]. since t nt, a materia figure m. zakeri et ocedure on of t-stres azilian disk e from a poly reation of th was made by sheet was pu or 15 minute d then the cr ock on the no very close to r the perform 8.8mm and 2 orm of two and r=60mm that the crac y straight thr which may sheets (fig. 3 be stress-free during the cr by using a th een from the n temperatu um glass tran the specim rs and then machine. it w ee. ial fringe va photoelastic polycarbonate the specimen al calibratio e 4. applied th t al., frattura e ss effects on specimens w ycarbonate s he central cra using the w ut in liquid n es in order to rack was cre otched zone. o a natural c med tests, the 2a=60mm. t disks of ra m (specimen ck tips gener rough the th affect the res 3.b). e before load racking and hermal treatm e figure that ures higher nsition temp ens were pla n, stresses w was observed value c materials, e is about f ns were expo n test was hermal cycle t ed integrità s 5 n the were sheet acks, water nitroo beeated the rack e tothen adius n nrated hicksults ding, cutment t the than peraaced were that the f =7 osed perform ess. sam spe test tes unlo was isoc the cen 3.3 the fram plie forc p=3 sho [4], tion pos for o remove resi strutturale, 3 med to deter . for this pu me material w cimens. this t under diago st was condu oading, and s obtained as chromatic fri two fringes ntre of disk. figure 5. i photoelast e cracked b me as shown ed by using t ce amount. t 367.5n for s uld be ment , the angle α n (see fig. 6) ed to mode n-1 (a/r=0. idual stresses f (2008) 2 10 rmine the fri urpose, a disk was put in th s disk was th onal compre ucted in two considering s f =6.9 [n/(m inge patterns of order n= isochromatic f tic tests brazilian disk n in fig. 6. the loading s the loads w specimens n tioned that u between the ) was such s ii condition 44), and α=2 from test spec inge value af k of diamete e furnace alo hen employed essive load a o steps inclu g both cases, mm·fringe)] s in the calib =8 are joinin fringes in cali ks were site compressiv screw and th were selected n-1 and n-2 using the ea e crack line a elected that n. these ang 23.2° for n-2 cimens. fter thermal er 50mm from ong with the d for a calibr according to uding loading , the fringe . fig. 5 show bration disk ng together i ibration disk. ed in the lo ve loads wer he gage show d as p=525n 2, respective arlier fem r and loading d the crack wa gles were α= 2 (a/r=0.5). f procm the main ration [16]. g and value ws the when in the oading re apws the n and ely. it results direcas ex=24.5° fig. 7 show tips f 4 e as s aroun obser with tence term calcu this a using and t lect s ders. gram deter tant n fittin f ws the resulta for the two d experime shown in fi nd the crack rved discont the theoret e of the t-st can be quan ulating the c aim, the obta g a compute the image pr some data p these data m prepared fo rministic tech non-linear eq ng process in figure 6. load ant isochrom disks. ental re ig. 7, the ob k tips are asy tinuous loop ical predicti tress in mod ntified by usi crack tip par ained isochro er code prepa rocessing to points from f were utilize or a full field hnique [11]. quations are nvolves both ding frame em figure m. zakeri et matic fringes a sults btained pho ymmetric in ps are in go ions, and co de ii conditi ing the comm rameters, ki omatic fringe ared in mat oolbox was e fringe loops d in another d analysis ba in this tech numerically h the newto mployed to app e 7. isochroma t al., frattura around the c toelastic frin both cases. ood consiste onfirm the e ions. this st mon methods , kii, and t es were analy tlab softw employed to of different r matlab ased on the o nique, the re y solved, and on-raphson ply compressi atic fringes aro ed integrità s 6 rack nges the ency existress s for t.for yzed ware, colt orprooveresuld the method kno sent it s spe the tab disk exp the of t thes ive load on th ound the crack strutturale, 3 d and the m own paramet ted in tab. 1 hould be me ct to kii in b crack tips w specime n-1 n-2 n-1 n-2 ble 1. experi ks, compared w perimental fi investigated t-stress in pu se results, th e disks and de k tips of the d (2008) 2 10 method of le ters kii, and 1. entioned tha both cases. h was subjected en experim 4.34 4.82 -0.38 -0.26 imental result with fem res indings pres d brazilian d ure mode ii hey are com efinition of the disks: a) n-1, b east squares. d t were c at ki was ve hence it could d to mode ii c kii [mpa ment fem 4 4.7 2 5.13 t-stress [m 89 0.40 62 0.27 ts obtained f ults [4]. sented in ta disks contain condition. in mpared with e characteristi b) n-2. . finally, th calculated as ery small wi d be assume conditions. m m ] m error 1 7.9% 3 6.0% mpa] 0 2.7% 7 2.9% from the bra b. 1 indicate n negative v n order to va numerical r ic dimensions he uns preth red that azilian e that values alidate results . [4] o that t two m cially curve was n mode by de that i 5 in c in ex possi mens use o mens figu line) obtained from there is a go methods, tho y in the case ed crack fron not taken int els. hence, t eveloping a is explained nfluence crack fro xperimental ible to analy s considering of polycarbo s allows to i ure 9. finite e ). m fem anal ood agreeme ough there a e of kii. this nt through th to considerat the role of c three dimen in the next s e of the ont studies usin yze the stress g them as 2 onate sheet to nvestigate o element mode m. zakeri et lysis (see ta ent between are some mi s problem m he specimen tion in the 2d rack tip curv nsional finite ection. curvatu ng the phot s condition i 2d-models. i o prepare th nly the pres figure 8. m el with the ap t al., frattura ab. 1). it is s the results f inor errors e may be due to thickness w d finite elem vature is stu e element m ure of th toelasticity, inside the sp in this way, e cracked sp ence of mod meshing conf pplied loads an ed integrità s 7 seen from espeo the hich ments died model he it is peci, the pecides i and pola fact the as w outiii. crac thre elem the spe mm in c nes as s spo the figuration arou nd displacem strutturale, 3 d ii condition ariscope and tors values, stress condi well. in this -of-plane str with the ai ck front on th ee dimension ment softwar e model sch cimens used m and thickne corresponden s and has a shown in fi ndent to the curvature e und the curved ments (crack p (2008) 2 10 ns. however d utilized to are an integ ition along t way, the cra resses that le im to study he stress inte nal model is res patran hematizes a d in experim ess h=10 mm nce of a diam curved front ig. 8. even e real situatio effect though d crack tip. osition is ind r, the fringe calculate th gral of the lig the thickness ack tip can a ead to the p the influenc ensity factor developed b n/abaqus. brazilian di ental part, w m. the centr meter, cross t in the form if it is not c ons, the circ h the thickn dicated in surf es observed a he stress inte ght that desc s of the spec lso be impos presence of e of a curvi s determinat by using the . isk similar t with radius r ral crack is p es the disk t m of a circula completely c ular arc incr ness of the face with a th at the ensity cribes cimen sed to mode linear tion, a finite to the r=120 placed thickar arc, correreases crack hicker m. zakeri et al., frattura ed integrità strutturale, 3 (2008) 2 10 8 front and enable to get an indication about the stress intensity factors trend along a non-straight crack front. crack curvature radius through the thickness is 10 mm, and the maximum extension of the crack is 2a=96 mm, indicated with a black thicker line in fig. 9. the angle α between the direction of application of the compressive force (f=375n) and the crack line is 25.4°. this angle is chosen according to [4] in order to obtain pure mode ii on the crack, considering the problem in 2d plane stress state. displacements of the nodes in which the force is applied, are forced to be in line with the loading direction. since the results in terms of kii are equivalent considering both the crack tips, only for one of them the mesh has been refined in the circumferential direction. in this way, it is possible to reduce the analysis run time, without loosing accuracy in the final result. the material of the disk in numerical model is the polycarbonate, with elastic modulus of e=2480mpa and poisson’s ratio ν=0.38, according to [11]. solid elements used for the modeling have a shape function of the second order, with a midside node in each edge. this choice allows having more nodes despite a not excessively refined mesh. moreover, the use of quadratic element is necessary to use the quarter point technique [17, 18], that is to move the midside nodes next to the tip to ¼ of the edge length, which results in a better stress gradient in this area with singularity in the crack tip. since good results are achievable with these elements even if the singularity is not well modeled on lines other than elements edges [19, 20], no collapsed element is used. it should be mentioned that to get better results in jintegral evaluation and consequently on stress intensity factors assessment, mesh directions should always be perpendicular to the crack front [21], avoiding distorted elements. however, the circular shape of the crack front causes a particular pattern for the mesh through the specimen thickness. as shown in fig. 8, in the upper part form point a to b, the mesh is more regular and the elements of this region describe the radial directions perpendicular to the crack front. in the lower part, the arc geometry makes it impossible to draw a regular mesh, and the normal to the crack front is not coincident with the mesh direction. numerical results are obtained starting from node 1 corresponding to point a to node 33 that is point c in fig. 8. convergence of j-integral and stress intensity results is obtained at the third contour. the trend of stress intensity factors can be graphically observed in fig. 10 in function of the node distance from the surface. however, the stress intensity factor values obtained near to point c should not be taken into consideration, since elements present a high level of distortion producing low accuracy in the results. values of the first three nodes are moreover invalid in the discussion, since the third contour integral cannot be calculated and results are infected by the presence of the surface border. 6 discussion the semi-natural cracks created with a mechanical shock after making brittle the polycarbonate in the liquid nitrogen, have a nonlinear curved tip through the thickness. when the specimen containing such a crack is subjected to mode ii loading condition, the global deformation of the crack front is in-plane sliding in x-direction. however, considering local coordinate systems n-t moving along the crack tip curve (see fig. 11), the global displacement of the crack tip points will have two components. the normal component in n-direction leads to mode ii; and the tangential component in t-direction implies that there is also mode iii deformations in local view. in order to find the effect of specimen thickness on the numerical results, they can be compared with the previous results [4] obtained from 2d finite element modeling. for this aim, a new parameter kiieq is defined as: 2 2= +iieq ii iiik k k (8) figure 10. stress intensity factors along the crack front in function of the depth. (-●ki, -♦kii, -▲kiii, -xkiieq, __ kii-2dfem [10]). -3.5 -3.0 -2.5 -2.0 -1.5 -1.0 -0.5 0.0 0.5 1.0 0 2 4 6 8 10 distance from the surface [mm] k [m p a√ m m ] m. zakeri et al., frattura ed integrità strutturale, 3 (2008) 2 10 9 which presents the equivalent mode ii stress intensity factor in x-direction of the global coordinate system. it can be noticed from fig. 10 that ki is negligible with respect to kii and kiii for all the considered nodes. also, kiii is initially less than kii. increasing the curvature that is going toward points b and c, kiii values are increasing and finally becoming more than kii values. however, values of kiieq remain about constant, except from surface nodes which are not valid as described before. the observed difference between kiieq and the result of 2d model [4] shows that the thickness of specimen affects the ideal plane stress conditions and leads to some errors in the photoelastic experiment results. 7 conclusion in this research, presence of the t–stress and its effects on the elastic stress field around a mode ii crack tip were experimentally studied. very sharp cracks were created in polycarbonate sheets by using a new method with different steps. the cracks obtained in this way are completely sharp, but the crack tip has a curved shape through the thickness of the specimen. specimens were cut in the form of centrally cracked brazilian disk specimens. photoelastic experiments were conducted on these specimens subjected to mode ii loading conditions, to determine from the isochromatic fringe patterns the crack parameters ki, kii, and t by using computer codes developed with the matlab software. experimental results revealed that the specimens had negative t–stresses in mode ii condition. the experimental results were consistent very well with numerical bidimensional predictions in that the t-stress significantly affects the symmetric shape of the fringe loops, and causes the loops to become asymmetric and discontinuous along the crack edges. however, there were some minor errors which could be related to the curved shape of the crack front through the specimen thickness. the effect of crack tip curvature on the crack parameters was also investigated by developing a 3d finite element model. the crack front was assumed to be in a circular arc form and, even if it is not completely correspondent to the real situations, aim of this model is to get an indication about the stress intensity factors trend along a non-straight crack front. the numerical results show that though the global deformation of the crack is in-plane sliding (mode ii), in local coordinates there are two shear components which are parallel and perpendicular to the crack front. that is, the crack tip points are subjected to a combination of mode ii and mode iii deformations. this local mixed mode condition can lead to some errors in the experimental results, which can be a source of difference of experimental results compared to the values of the finite element model. 8 references [1] m.l. williams, “on the stress distribution at the base of a stationary”, journal of applied mechanics, (1957) 109-114. [2] m.r. ayatollahi, m. zakeri, m.m. hassani, “on the presence of t-stress in mode ii crack problems”, 11th international conference on fracture, turin, italy (2005). [3] m.r. ayatollahi, a. asadkarami a, m. zakeri, “finite element evaluation of punch-type crack specimens”, international journal of pressure vessels and piping, 82 (2005) 722–728. [4] m.r. ayatollahi, m.r.m. aliha, “wide range data for crack tip parameters in two disc-type specimens under mixed mode loading”, computational materials science, 38 (2007) 660-670. [5] b. cotterell, j.r. rice, “slightly curved or kinked cracks”, international journal of fracture, 16 (1980) 155-169. [6] m.r. ayatollahi, h. abbasi, “prediction of fracture using a strain based mechanism of crack growth”, building research journal, 49 (2001) 167-180. [7] c. betegon, j.w. hancock, “two-parameter characterization of elastic-plastic crack-tip fields”, journal of applied mechanics, 58 (1991) 104-110. [8] m.r. ayatollahi, m.j. pavier, d.j. smith, “crack-tip constraint in mode ii deformation”, international journal of fracture, 113 (2002) 153-173. figure 11. global (x-y) and local (n-t) coordinate systems. m. zakeri et al., frattura ed integrità strutturale, 3 (2008) 2 10 10 [9] k. ramesh, s. gupta, a.a. kelkar, “evaluation of the stress field parameters in fracture mechanics by photoelastic-revisited”, engineering fracture mechanics, 56 (1997) 25-45. [10] a. shimamoto, j.h. nam, t. himomura, e. umezaki, “determination of stress intensity factors in isotropic and anisotropic body by the photoelastic and caustic methods under various load ratios”, key engineering materials, 183-187 (2000) 115-120. [11] j.w. dally, w.f. riley, “experimental stress analysis”, 3rd edition, mcgraw hill, singapore (1991). [12] a.d. nurse, e.a. patterson, “determination of predominantly mode ii stress intensity factors from isochromatic data”, fatigue and fracture of engineering materials and structures, 16 (1993) 1339-1354. [13] m.r. ayatollahi, m. zakeri, “t-stress effects on isochromatic fringe patterns in mode ii”, international journal of fracture, 143 (2007) pp. 189–194. [14] l. banks-sills, m. arcan, “an edge-cracked mode ii fracture specimen”, experimental mechanics, 23 (1983) 257-261. [15] c. pappalettere, “annealing polycarbonate sheets”, strain, 20 (1984) 179-180. [16] a. mondina, “la fotoelasticità”, cusl (1958). [17] r.d. henshell, k.g. shaw, “crack tip finite elements are unnecessary”, int. journal for numerical methods in engineering, 9 (1957) 495-507 (1957). [18] r.s. baursom, “on the use of isoparametric finite elements in linear fracture mechanics, int. journal for numerical methods in engineering, 10 (1976) 25-37. [19] l. banks-sills, d. sherman, “on the computation of stress intensity factors for three-dimensional geometries by means of the stiffness derivative and j-integral methods”, international journal of fracture, 53 (1992) 1-20. [20] o.c. zienkiewicz, r.l. taylor, “the finite element method”, fifth edition, volume 1: the basis, chap. 9, butterworth-heinemann edition (2000). [21] c. colombo, m. guagliano, l. vergani, “determinazione numerica dei fattori di intensificazione degli sforzi di cricche caricate in modo misto”, atti del convegno nazionale igf19, milano, italy (2007). microsoft word numero_58_art_23_3240.docx t.-h. nguyen et alii, frattura ed integrità strutturale, 58 (2021) 308-318; doi: 10.3221/igf-esis.58.23 308 focussed on steels and composites for engineering structures evaluating structural safety of trusses using machine learning tran-hieu nguyen, anh-tuan vu hanoi university of civil engineering, vietnam hieunt2@nuce.edu.vn, https://orcid.org/0000-0002-1446-5859 tuanva@nuce.edu.vn abstract. in this paper, a machine learning-based framework is developed to quickly evaluate the structural safety of trusses. three numerical examples of a 10-bar truss, a 25-bar truss, and a 47-bar truss are used to illustrate the proposed framework. firstly, several truss cases with different cross-sectional areas are generated by employing the latin hypercube sampling method. stresses inside truss members as well as displacements of nodes are determined through finite element analyses and obtained values are compared with design constraints. according to the constraint verification, the safety state is assigned as safe or unsafe. members’ sectional areas and the safety state are stored as the inputs and outputs of the training dataset, respectively. three popular machine learning classifiers including support vector machine, deep neural network, and adaptive boosting are used for evaluating the safety of structures. the comparison is conducted based on two metrics: the accuracy and the area under the roc curve. for the two first examples, three classifiers get more than 90% of accuracy. for the 47-bar truss, the accuracies of the support vector machine model and the deep neural network model are lower than 70% but the adaptive boosting model still retains the high accuracy of approximately 98%. in terms of the area under the roc curve, the comparative results are similar. overall, the adaptive boosting model outperforms the remaining models. in addition, an investigation is carried out to show the influence of the parameters on the performance of the adaptive boosting model. keywords. machine learning; classification; adaptive boosting; structural safety; truss structure. citation: nguyen, t.-h., vu, a.-t., evaluating structural safety of trusses using machine learning, frattura ed integrità strutturale, 58 (2021) 308-318. received: 19.08.2021 accepted: 29.08.2021 published: 01.10.2021 copyright: © 2021 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. introduction ssessing the safety of an existing structure is a common problem in practice. for example, many constructions after a long period of use have been seriously degraded. safety assessment is a key factor in deciding whether to rehabilitate or demolish these constructions. a second example might be: a steel structure exposed to a corrosive environment needs to be regularly checked the structural safety due to the development of rust. for one more example, a structure subjected to an extreme impact, such as seismic loads, fire loads, or blast loads should be evaluated the safety state before continuing use. a https://youtu.be/z8jbaxobosa t.-h. nguyen et alii, frattura ed integrità strutturale, 58 (2021) 308-318; doi: 10.3221/igf-esis.58.23 309 the traditional safety assessment of structural elements is often investigated based on experimental tests and numerical simulations. for instance, the research work conducted by capuzucca and bonci [1] indicated that the state of damage of carbon fiber reinforced polymer (cfrp) laminate elements can be evaluated by measuring the reduction of vibration frequencies. subsequently, a hybrid approach that combines the proper orthogonal decomposition with radial basis function (pod-rbf) and the cuckoo search optimization algorithm to determine the position and dimensions of notches in cfrp beams was proposed in ref. [2]. the proposed approach was validated with experimental results in ref. [1]. in 2019, a technique coupling pod-rbf, the extended isogeometric analysis method, and the jaya algorithm was developed [3]. this technique allows to accurately identify the locations of cracks in a steel plate based on strain readings. in [4], the damages in the frp-strengthened reinforced concrete (rc) beams were investigated using finite element modeling. recently, a twostage approach for detecting damages was introduced, in which the modal strain energy change ratio is used to forecast the damages’ locations and the slime mould algorithm is then employed to quantify the damages [5]. this approach is verified with the experimental results of a 3d four stories frame. such methods can accurately evaluate the safety of structures but very time-consuming. in some cases, there is a need for a model that can rapidly predict the safety state of structures in order to promptly evacuate people from the whole structure if it is unsafe. after that, the structure still needs to be exactly re-checked by engineers. the rapid safety assessment model can be integrated with the structural health monitoring system, in which information obtained from sensors is fed into such model as inputs. the output of the model is a prediction of whether the structure is safe or unsafe. this is a kind of binary classification problem and it can be solved by machine learning (ml) algorithms. in the literature, there are many previous studies that have applied ml for structural health monitoring. in several works, artificial neural networks (anns) were used to forecast the damages in the plates instead of solving the inverse problem by optimization algorithms [6,7]. besides, it can be observed that the topic of deep learning has been received great attention from researchers. since alexnet, the winner of the imagenet challenge, was first introduced in 2012, the convolutional neural network (cnn) architecture has become extremely popular in the field of computer vision and it has been used in many domains. in the field of civil engineering, the cnn architecture and its variations such as unet have been applied to detect cracks on concrete [8-10] as well as welded joints [11], corrosions on steel surfaces [12], damages on buildings [13], etc. for handling time series data, the rnn architecture and its variation lstm are state-of-theart [14-16]. obviously, deep learning algorithms like cnn, rnn outperform conventional ml algorithms on unstructured data due to their automatic feature extraction capability. however, they don’t work well on tabular data. for such kinds of data, the conventional ml algorithms, for example, decision tree (dt), support vector machine (svm), are good choices. recently, ensemble methods have been particularly preferred, shown by their applications in kaggle data science competitions. the concept of ensemble methods is to create a strong classifier from several weak classifiers. some commonly used ensemble methods are random forest (rf), extreme gradient boosting (xgboost), gradient tree boosting (gtb). in the literature, zhang et al. [17] utilized dt and rf for evaluating the structural safety state of rc buildings after an earthquake. in [18], the gtb algorithm was used to evaluate the safety of trusses. in addition, a comparative study of ml algorithms for predicting the load-carrying capacity of steel frames was conducted [19]. the results showed that two ensemble methods, including rf and gtb, achieved better performance than the remaining ones. among ensemble methods, adaboost, short for adaptive boosting, was the first successful boosting algorithm developed for binary classification [20]. this algorithm has been applied to predict the failure modes and the load-bearing capacity of rc columns [21], and the compressive strength for concrete [22]. however, according to the literature review, there has not been a study related to the application of adaboost for classifying the safety of structures. this paper aims to investigate the capability of the ensemble method adaboost in evaluating the safety of truss structures. for this purpose, the performance of adaboost is compared with two popular classification algorithms, i.e., ann and svm, in terms of the accuracy and the area under the roc curve. the comparison is conducted on three well-known truss structures of 10 bars, 25 bars, and 47 bars. additionally, an investigation on the influence of the parameters on the performance of the adaboost model is also carried out. classification of the safety state of trusses using machine learning machine learning-based framework for safety classification of trusses he framework for structural safety classification of truss structures using ml is presented in fig. 1. the main characteristics of truss structures are truss members’ sectional areas and these values are used as inputs of the ml model. the output is the safety state of structures. the inputs of training data are generated using a sampling method, t t.-h. nguyen et alii, frattura ed integrità strutturale, 58 (2021) 308-318; doi: 10.3221/igf-esis.58.23 310 which is the latin hypercube sampling (lhs) method in this paper. the cross-sectional areas that have just been created are assigned to truss members and the structure is then analyzed using the finite element method (fem). based on the results obtained from the structural analysis such as stresses inside members and the deflection, design constraints are checked. if all constraints are satisfied, this structure is safe. otherwise, if any constraint is violated, this structure is considered unsafe. inputs and outputs are also saved into the database. once sufficient data has been collected, the training process begins. if the accuracy of the trained model when verifying on the testing dataset is acceptable, this ml model is ready to use. predictiontraining & testingdata generation generating n inputs containing areas of truss members xi = {ai,1, ai,2, …, ai,p}, i = 1, 2,…, n using lhs structural analysis using fem & constraint verification assigning output: yi = 1 if “safe” yi = -1 otherwise i = 1, 2,…, n dataset (xi, yi) i = 1, 2,…, n training dataset testing dataset training model testing model the ml classification model new input xnew predicted output ynew “safe” if ynew = 1 “unsafe” if ynew = -1 figure 1: overview of the ml-based framework for safety classification of trusses. the above procedure can be applied to all ml algorithms. in this study, three powerful classification algorithms are taken for comparison including svm, ann, and adaboost. the brief introductions of these algorithms are presented in the following sections. support vector machine svm was initially developed to solve binary classification problems. for separating data, the best hyperplane is found by maximizing the margin between it and the support vectors as shown in fig. 2. other kernel functions such as sigmoid kernel, polynomial kernel, or rbf kernel can be used to separate nonlinear data. margin support vectors figure 2: support vector machine. t.-h. nguyen et alii, frattura ed integrità strutturale, 58 (2021) 308-318; doi: 10.3221/igf-esis.58.23 311 artificial neural network the first ann model that was introduced in 1958 by rosenblatt contains only three layers: an input layer, a hidden layer, and an output layer. each layer has some neurons where the activation function is attached to mimic the nonlinear data. the state-of-the-art anns have more than one hidden layer that allows learning extremely complex data. fig. 3 presents a typical architecture of an ann model with multiple hidden layers. hidden layers output layerinput layer ... ... ... ...... ... output 1 output m input 1 input 2 input n figure 3: artificial neural network. adaptive boosting the base classifier used in the adaboost model is often a decision tree. however, a deep decision tree can be overfitted on a specific dataset. to overcome this problem, the adaboost model uses several shallow decision trees which are sequentially trained by the weighted data. each decision tree is assigned a weight based on its accuracy. the final prediction is determined by using the weighted majority voting method. the adaboost algorithm is illustrated in fig. 4.  original dataset d1 weak classifier 1 weight 1 weighted dataset d2 weak classifier 2 weight 2 weighted dataset d3 weak classifier 3 weight 3 weighted dataset dn weak classifier n weight n strong classifier figure 4: adaptive boosting. datasets hree well-known truss structures are used in this study. all these problems were initially expressed using the imperial system. in this study, the imperial units are kept without affecting the final results. the first structure is a planar 10-bar truss which is displayed in fig. 5. all members are made of the same material having the modulus of elasticity e=10,000 ksi and the density =0.1 lb/in3. the cross-sectional areas of truss members range from 6 to 35 in2. the allowable stress inside all members is 25 ksi, and the allowable displacement for all nodes is 2 in. the second structure is a spatial 25-bar truss as presented in fig. 6. this structure is fabricated from the same material as the 10-bar truss. there are eight groups of members with corresponding stress limits shown in tab. 1. members in the same t t.-h. nguyen et alii, frattura ed integrità strutturale, 58 (2021) 308-318; doi: 10.3221/igf-esis.58.23 312 group have the same cross-sectional area varying from 0.6 to 3.5 in2. the limitation of displacements along horizontal directions is 0.35 in. this structure subjects to two load cases independently. the first load case contains two point loads p1 = (0, 20, -5) and p2 = (0, -20, -5) acting on the node (1) and the node (2), respectively. the second load case consists of four point loads p1 = (1, 10, -5), p2 = (0, 10, -5), p3 = (0.5, 0, 0), and p6 = (0.6, 0, 0) acting on the node (1), (2), (3), and (6), respectively. p=100 kips p=100 kips (1)(3)(5) (2)(4)(6) 1 2 3 4 5 6 7 9 8 10 360 in 360 in 360 in y x figure 5: 10-bar truss structure. (1) (2) (3) (10) (8) (7) 3 2 4 5 8 9 67 13 14 10 12 (9) 11 17 18 15 19 20 21 16 22 23 24 25 100 in 100 in z x y (4) (5) (6) 1 figure 6: 25-bar truss structure. the final structure is a planar truss as schematized in fig. 7. this structure contains 47 members which are divided into 27 groups as shown in tab. 2. all members in a group are assigned a cross-sectional area range from 0.1 to 35 in2. the modulus of elasticity of the material used in this structure e=30,000 ksi and the material density =0.3 lb/in3. this tower is subjected to one of three independent load cases. the first load case (lc1) consists of two loads of 14 kips and 6 kips applying to the node (17). the second load case (lc2) has two loads of 14 kips and 6 kips acting on the node (22). the third load case (lc3) is the sum of the two above load cases (lc1) and (lc2). t.-h. nguyen et alii, frattura ed integrità strutturale, 58 (2021) 308-318; doi: 10.3221/igf-esis.58.23 313 group member maximum compressive stress maximum tensile stress 1 1 35.092 40.0 2 2, 3, 4, 5 11.590 40.0 3 6, 7, 8, 9 17.305 40.0 4 10, 11 35.092 40.0 5 12, 13 35.092 40.0 6 14, 15, 16, 17 6.759 40.0 7 18, 19, 20, 21 6.959 40.0 8 22, 23, 24, 25 11.082 40.0 table 1: limitation of stresses for eight groups of the 25-bar truss structure unit: ksi. (1) 1 60 in y x (2) (3) (4) (5) (6) (7) (8) (9) (10) (11) (12) (13) (14) (15) (17) (18) (19) (16) (20) (21) (22) 2 3 4 5 6 8 9 7 1011 17 23 25 21 19 13 27 15 16 12 18 2426 22 1914 29 30 31 32 28 33 34 35 36 37 39 40 41 42 38 43 44 45 46 47 60 in 60 in 60 in 60 in 60 in 60 in 60 in 60 in 120 in 120 in 120 in 60 in 60 in figure 7: 47-bar truss structure. t.-h. nguyen et alii, frattura ed integrità strutturale, 58 (2021) 308-318; doi: 10.3221/igf-esis.58.23 314 group members group members group members 1 1, 3 10 17, 18 19 33 2 2, 4 11 19, 20 20 34, 35 3 5, 6 12 21, 22 21 36, 37 4 7 13 23, 24 22 38 5 8, 9 14 25, 26 23 39, 40 6 10 15 27 24 41, 42 7 11, 12 16 28 25 43 8 13, 14 17 29, 30 26 44, 45 9 15, 16 18 31, 32 27 46, 47 table 2: group member of the 47-bar tower. stresses inside members must be smaller than limit values. the limited tensile and compressive stresses are 20 ksi and -15 ksi, respectively. the maximum buckling stress of the ith member can be calculated by the following equation:   i icr i kea l (1) where: k is the buckling constant that is fixed to 3.96 in this study; ai and li are the cross-sectional area and the length of ith member, respectively. for each structure, two separated datasets are independently generated, one for training and one for testing. each dataset contains 1000 data samples. the number of safe samples and unsafe samples in each dataset are shown in fig. 8.   figure 8: distribution of safe and unsafe samples in the training and the testing datasets. comparison setups  l models for evaluating the safety of truss structures are developed based on the open-source library scikit-learn [23]. there are three numerical examples and three classification algorithms used in this work, so a total of 9 models are developed. the hyperparameters tuning of ml models is conducted by combining the grid search m t.-h. nguyen et alii, frattura ed integrità strutturale, 58 (2021) 308-318; doi: 10.3221/igf-esis.58.23 315 method and k-fold cross-validation. the training datasets are divided into five parts (k=5), in which four parts are used to train and the remaining one is used to validate. the final parameters of each algorithm are summarized in tab. 3. after finding the hyperparameters, the full training datasets are fed into the ml models. when the training process is completed, these models are ready to predict the structural safety state of the testing datasets. algorithm hyperparameters  svm kernel=’rbf’; c=1000; gamma=0.1 ann architecture (100-100-100-2); activation=’relu’; solver=adam; batch_size=5; max_iter=1000 adaboost base_estimator=decisiontreeclassifier; max_depth=2; n_estimators=100; learning_rate=1 table 3: hyperparameters of ml models. metrics  two evaluation metrics are used in this study. the first metric is the accuracy which can be determined using the following equation:      tp tn accuracy tp tn fp fn (2) where: tp, tn are the numbers of positive and negative samples that are correctly classified; fp, fn are the numbers of positive and negative samples that are misclassified. additionally, the area under the roc curve (auc) is also used to compare three algorithms. the roc curve originally developed for operators of military radar receivers is the relationship between true positive rate and false positive rate.   true positive rate tp fn tp (3)   false positive rate fp tn fp (4) results  each problem is carried out 30 times. the average accuracies of three ml algorithms are summarized in tab. 4. it can be seen that for two problems of 10-bar truss and 25-bar truss, all three algorithms achieve high accuracy (over 90%). particularly for the 47-bar truss problem, the accuracies of the svm and the ann models are quite low (below 70%), while the adaboost models still retain the high accuracy (97.7%). problem number of features svm ann adaboost  10-bar truss 10 0.959 0.937 0.936 25-bar truss 8 0.974 0.967 0.974 47-bar truss 27 0.658 0.669 0.976 table 4: accuracy comparison of three ml models. furthermore, fig. 9 shows the typical roc curves of these ml algorithms for three examples. there is a good agreement when comparing three algorithms in terms of the accuracy and the auc metrics. in more detail, all svm, ann, and adaboost obtained the auc close to one for the first two problems. however, the svm and the ann models obtain the auc of 0.69 while the adaboost model achieves the auc=0.99 when classifying on the 47-bar truss testing dataset. t.-h. nguyen et alii, frattura ed integrità strutturale, 58 (2021) 308-318; doi: 10.3221/igf-esis.58.23 316 false positive rate t ru e p o si ti ve r at e false positive rate t ru e p o si ti ve r at e false positive rate t ru e p o si ti ve r at e (a) (b) (c) figure 9: roc curves of three ml algorithms for three datasets. (a) 10-bar truss – testing dataset. (b) 25-bar truss – testing dataset. (c) 47-bar truss – testing dataset. overall, it can be noted that for problems with a small number of features, all three algorithms give accurate results. but for problems having a large number of features, the adaboost algorithm outperforms the two remaining algorithms. model performance analysis ne of the most important parts when building an ml model is the training data. in this study, data is collected through conducting a parametric finite element analysis (fea). for large-scale structures, each fea consumes several hours or days. performing a large number of feas leads to time-consuming. therefore, in this section, the influence of the number of samples of the training dataset is investigated. besides, the performance of the adaboost model strongly depends on the number of base classifiers. thus, the influence of the number of base classifiers is also considered in this section. figure 10: the influence of the training dataset amount on the performance of the adaboost model. influence of the training dataset amount  to investigate the influence of the training dataset amount, seven training datasets of the 47-bar truss problem are generated. the numbers of samples of seven datasets are 100, 250, 500, 1000, 2500, 5000, and 10000, respectively. the amount of the testing dataset remains 1000 samples. the accuracies of seven adaboost models are shown in fig. 10. it can be observed that the accuracy of the classification model significantly improves when increasing the number of samples from 100 to 250 (0.669 for 100 samples and 0.876 for 250 samples). when augmenting the training dataset to 500 samples, the accuracy achieves 0.923. the accuracies for 1000, 2500, 5000, 10000 samples are 0.976, 0.986, 0.988, 0.991, respectively. generally, the number of 1000 samples is a good choice when balancing the accuracy and the quantity of the training data. influence of the number of base classifiers an important key factor of an ensemble model is the number of base classifiers used in this model. in this study, six adaboost models are compared where the numbers of base classifiers are 5, 10, 50, 100, 500, and 1000, respectively. these o t.-h. nguyen et alii, frattura ed integrità strutturale, 58 (2021) 308-318; doi: 10.3221/igf-esis.58.23 317 models are trained by the same 47-bar truss training dataset of 1000 samples. the prediction results on the 47-bar truss testing dataset are presented in fig. 11. it can be clearly seen that the accuracy of the adaboost model is greatly enhanced when extending the number of base classifiers from 5 to 50. however, when increasing the number of base classifiers from 50 to 1000, the model quality does not improve. figure 11: the influence of the number of base classifiers on the performance of the adaboost model. conclusions he rapid evaluation of the structural safety state is an important task for escaping people when a hazard occurs. in this study, three machine learning algorithms including support vector machine, artificial neural network, and adaptive boosting are used to identify the safety state of truss structures. the results of the present work demonstrate the potential application of machine learning for structural safety evaluation. the comparative study indicates that all three algorithms achieve high accuracy (over 90%) for small-scale structures with few input features. however, for large-scale structures having many input features, the adaboost algorithm exhibits a strong ability in comparison with other algorithms (over 95% for the adaboost, about 65% for both the svm and the ann). additionally, an investigation on the influence of the training dataset size and the number of base classifiers is implemented. the results of the investigation provide a good suggestion when developing machine learning models later. in the future, the study can be extended to other structures such as frames, dams, etc. acknowledgment he first author t.-h. nguyen was funded by vingroup joint stock company and supported by the domestic ph.d. scholarship programme of vingroup innovation foundation (vinif), vingroup big data institute (vinbigdata) code vinif.2020.ts.134. references [1] capozucca, r. and bonci, b. (2015). notched cfrp laminates under vibration. composite structures, 122, pp.367-375. doi: 10.1016/j.compstruct.2014.11.062. [2] samir, k., brahim, b., capozucca, r. and wahab, m.a. (2018). damage detection in cfrp composite beams based on vibration analysis using proper orthogonal decomposition method with radial basis functions and cuckoo search algorithm. composite structures, 187, pp.344-353. doi: 10.1016/j.compstruct.2017.12.058. [3] khatir, s. and wahab, m.a. (2019). fast simulations for solving fracture mechanics inverse problems using pod-rbf xiga and jaya algorithm. engineering fracture mechanics, 205, pp.285-300. doi: 10.1016/j.engfracmech.2018.09.032. [4] magagnini, e. and capozucca, r. (2020). detection of damage in rc beams strengthened with nsm cfrp rectangular rod by finite element modeling. in: fracture, fatigue and wear, singapore, springer, pp. 227-242. t t t.-h. nguyen et alii, frattura ed integrità strutturale, 58 (2021) 308-318; doi: 10.3221/igf-esis.58.23 318 doi: 10.1007/978-981-15-9893-7_16. [5] tiachacht, s., khatir, s., le thanh, c., rao, r.v., mirjalili, s. and wahab, m.a. (2021). inverse problem for dynamic structural health monitoring based on slime mould algorithm. engineering with computers, pp.1-24. doi: 10.1007/s00366-021-01378-8. [6] zenzen, r., khatir, s., belaidi, i., le thanh, c. and wahab, m.a. (2020). a modified transmissibility indicator and artificial neural network for damage identification and quantification in laminated composite structures. composite structures, 248, p.112497. doi: 10.1016/j.compstruct.2020.112497. [7] khatir, s., boutchicha, d., le thanh, c., tran-ngoc, h., nguyen, t.n. and abdel-wahab, m. (2020). improved ann technique combined with jaya algorithm for crack identification in plates using xiga and experimental analysis. theoretical and applied fracture mechanics, 107, p.102554. doi: 10.1016/j.tafmec.2020.102554. [8] cha, y.j., choi, w. and büyüköztürk, o. (2017). deep learning‐based crack damage detection using convolutional neural networks. computer‐aided civil and infrastructure engineering, 32(5), pp.361-378. doi: 10.1111/mice.12263. [9] dung, c.v. (2019). autonomous concrete crack detection using deep fully convolutional neural network. automation in construction, 99, pp.52-58. doi: 10.1016/j.autcon.2018.11.028. [10] liu, z., cao, y., wang, y. and wang, w. (2019). computer vision-based concrete crack detection using u-net fully convolutional networks. automation in construction, 104, pp.129-139. doi: 10.1016/j.autcon.2019.04.005. [11] dung, c.v., sekiya, h., hirano, s., okatani, t. and miki, c. (2019). a vision-based method for crack detection in gusset plate welded joints of steel bridges using deep convolutional neural networks. automation in construction, 102, pp.217229. doi: 10.1016/j.autcon.2019.02.013. [12] atha, d.j. and jahanshahi, m.r. (2018). evaluation of deep learning approaches based on convolutional neural networks for corrosion detection. structural health monitoring, 17(5), pp.1110-1128. doi: 10.1177/1475921717737051. [13] gao, y. and mosalam, k.m. (2018). deep transfer learning for image‐based structural damage recognition. computer‐ aided civil and infrastructure engineering, 33(9), pp.748-768. doi: 10.1111/mice.12363. [14] qu, x., yang, j. and chang, m. (2019). a deep learning model for concrete dam deformation prediction based on rslstm. journal of sensors, 2019. doi: 10.1155/2019/4581672. [15] guo, a., jiang, a., lin, j. and li, x. (2020). data mining algorithms for bridge health monitoring: kohonen clustering and lstm prediction approaches. the journal of supercomputing, 76(2), pp.932-947. doi: 10.1007/s11227-019-03045-8. [16] zhang, j., cao, x., xie, j. and kou, p. (2019). an improved long short-term memory model for dam displacement prediction. mathematical problems in engineering, 2019. doi: 10.1155/2019/6792189. [17] zhang, y., burton, h.v., sun, h. and shokrabadi, m. (2018). a machine learning framework for assessing postearthquake structural safety. structural safety, 72, pp.1-16. doi: 10.1016/j.strusafe.2017.12.001. [18] truong, v.h., vu, q.v., thai, h.t. and ha, m.h. (2020). a robust method for safety evaluation of steel trusses using gradient tree boosting algorithm. advances in engineering software, 147, p.102825. doi: 10.1016/j.advengsoft.2020.102825. [19] kim, s.e., vu, q.v., papazafeiropoulos, g., kong, z. and truong, v.h. (2020). comparison of machine learning algorithms for regression and classification of ultimate load-carrying capacity of steel frames. steel and composite structures, 37(2), pp.193-209. doi: 10.12989/scs.2020.37.2.193. [20] freund, y. and schapire, r.e. (1997). a decision-theoretic generalization of on-line learning and an application to boosting. journal of computer and system sciences, 55(1), pp.119-139. doi: 10.1006/jcss.1997.1504. [21] feng, d.c., liu, z.t., wang, x.d., jiang, z.m. and liang, s.x. (2020). failure mode classification and bearing capacity prediction for reinforced concrete columns based on ensemble machine learning algorithm. advanced engineering informatics, 45, p.101126. doi: 10.1016/j.aei.2020.101126. [22] feng, d.c., liu, z.t., wang, x.d., chen, y., chang, j.q., wei, d.f. and jiang, z.m. (2020). machine learning-based compressive strength prediction for concrete: an adaptive boosting approach. construction and building materials, 230, p.117000. doi: 10.1016/j.conbuildmat.2019.117000. [23] pedregosa, f., varoquaux, g., gramfort, a., michel, v., thirion, b., grisel, o., blondel, m., prettenhofer, p., weiss, r., dubourg, v. and vanderplas, j. (2011). scikit-learn: machine learning in python. the journal of machine learning research, 12, pp.2825-2830. microsoft word numero 18 articolo 1.doc g. del piero et alii, frattura ed integrità strutturale, 18 (2011) 5-13; doi: 10.3221/igf-esis.18.01 5 the variational theory of fracture: diffuse cohesive energy and elastic-plastic rupture gianpietro del piero dipartimento di ingegneria, università di ferrara, ferrara (italy) dlpgpt@unife.it giovanni lancioni dipartimento di architettura, costruzioni e strutture, università politecnica delle marche, ancona (italy) riccardo march istituto per le applicazioni del calcolo, cnr, roma (italy) abstract. this communication anticipates some results of a work in progress [1], addressed to explore the efficiency of the diffuse cohesive energy model for describing the phenomena of fracture and yielding. a first local model is partially successful, but fails to reproduce the strain softening regime. a more robust non-local model, obtained by adding an energy term depending on the deformation gradient, describes many typical features of the inelastic response observed in experiments, including strain localization and necking. fracture occurs as the result of extreme strain localization. the model predicts different fracture modes, brittle and ductile, depending on the analytical form of the cohesive energy function. sommario. nella presente comunicazione si anticipano alcuni risultati del lavoro [1], in preparazione, in cui si analizza l’efficienza del modello dell’energia coesiva diffusa nel descrivere i fenomeni di plasticizzazione e rottura. un primo modello locale dà risultati parzialmente soddisfacenti, ma si rivela incapace di descrivere il regime di strain softening. un più robusto modello non locale, ottenuto aggiungendo un termine energetico dipendente dal gradiente della deformazione, riesce a descrivere molte peculiarità della risposta anelastica osservate sperimentalmente, incluse la localizzazione della deformazione e il necking. la frattura avviene per estrema localizzazione. il modello prevede la possibilità di diversi modi di frattura, duttile o fragile, a seconda della forma analitica ipotizzata per l’energia coesiva. keywords. fracture mechanics; energy methods; elastic-plastic rupture; variational theory of fracture. introduction leading idea in fracture mechanics is that the growth of a fracture surface is decided by the competition between the strain energy lost in, and the amount of fracture energy required to, the creation of a new fracture surface [2]. however, it was soon clear that this idea is appropriate to the description of brittle fracture, typically exhibited in large-size bodies, but is unfit to describe the ductile fracture modes which prevail in small-size bodies. this size effect is captured by the cohesive energy models [3, 4]. a http://www.gruppofrattura.it http://dx.medra.org/10.3221/igf-esis.18.01&auth=true g. del piero et alii, frattura ed integrità strutturale, 18 (2011) 5-13; doi: 10.3221/igf-esis.18.01 6 other basic problems, such as the formation of a fracture in an initially unfractured body, were neglected for long time, and ony recently came to the attention of the scientific community. the use of variational techniques for energy minimization was introduced first for griffith’s fracture model [5], and extended later to cohesive energy models [6, 7]. from the engineering side, it became clear that an appropriate choice of the analytic form of the cohesive energy may lead to a unified description of the phenomena of yielding, damage, and fracture [8, 9]. a very recent research trend consists in questioning the surfacic character of the fracture energy, and in exploring the alternative possibility of an energy diffused over the volume. an example is the paper [10], in which, in the context of a damage model, a rather detailed description of the process zone preceding the final rupture is obtained. in this communication a diffuse cohesive energy is considered, and fracture is regarded as the extreme stage of the localization of inelastic deformation. in a one-dimensional context, we assume that at every point of the bar the energy density is the sum of an elastic and a cohesive part. an incremental energy minimization is performed, under the only assumption that the cohesive energy is totally dissipative. with this simple model, a rather accurate description of the inelastic response of the bar, from the onset of the inelastic regime up to rupture, is obtained. the strain-softening case is not adequately described, but this inconvenience is repaired with the introduction of a non-local energy term of the gradient type. the traditional elements of elastic-plastic response, such as the yield condition, the flow law, the hardening law, the elastic unloading, come out of the model as necessary conditions for an energy minimum. we also find that a convex shape of the cohesive energy favorizes a uniform distribution of inelastic strain and a work-hardening response, while a concave shape is responsible of the localization of the inelastic strain, which, in turn, produces the phenomena of strain softening and necking. rupture takes place when the localization becomes extreme. if the cohesive energy is approximated by a piecewise polynomial function, its expression becomes a function of a small number of material parameters. the first results of a series of numerical simulations show that an appropriate choice of these parameters provides a good approximation of the experimental response curves. this seems to confirm the efficiency and flexibility of the proposed model. the local model onsider a bar of length l , with constant cross section, free of external loads, and subject to the axial displacements u(0) = 0 , u(l) = l , (1) at the endpoints x  0 and x  l. the bar’s deformation is measured by the derivative uof the axial displacement u. we assume that, at every point x of the bar’s axis, the deformation u(x) can be split into the sum of an elastic part (x) and of an inelastic part (x): u(x) = (x) + (x) , (2) and that the total energy of the bar has the form   l dxxxwe 0 )))(())(((),(  (3) where w and  are the volume densities of the elastic strain energy and of the cohesive energy, respectively. we also assume that w can be recovered, while  is totally dissipated. the last assumption requires that the cohesive power ((x,t)) ),( tx be non-negative for all x and at all instants t, and if we assume that  is an increasing function of  we get the dissipation inequality 0),( tx (4) to be satisfied for all x and at all t. in the spirit of the calculus of variations, the equilibrium configurations of the bar are identified with the stationary points of the energy 0))())((')())(('(),,,( 0   dxxxxxwe l  (5) c http://www.gruppofrattura.it http://dx.medra.org/10.3221/igf-esis.18.01&auth=true g. del piero et alii, frattura ed integrità strutturale, 18 (2011) 5-13; doi: 10.3221/igf-esis.18.01 7 with the inequality due to the presence of the dissipation inequality (4), which requires the restriction  (x)  0 (6) on the perturbations . the analysis of the first variation leads to the following characterization of the equilibrium configurations [dlm] :  the elastic deformation (x) and the axial force   = w((x)) (7) are constant all over the bar,  the axial force cannot exceed a limit depending on the current inelastic deformation:   ((x)) . (8)  the equilibrium condition (8) is in fact a yield condition. it is remarkable that it has not been postulated, but deduced from the variational procedure. the energy minimization is insufficient to determine the evolution of the deformation under a loading process  = (t). to do this, it is necessary to formulate an incremental equilibrium problem, in which at any time t the deformations (t) and (x,t) are supposed to be known, and the unknowns are the deformation increments ),(),( txt   , produced by a given load increment )(t . one considers the expansion )())(),(())(),(())(),(())(),(( 22 2 1  ottettettette   (9) and minimizes for sufficiently small to legitimate the truncation at the second-order term. the term of order zero being known, a first-order approximation involves the minimization of the function  dxxttxttltte l ))())(),(('()()())(),(( 0     (10) in it, everything is known except )(x . then e is an affine function of  , and a proper use of the dissipation inequality leads to the kuhn-tucker conditions 0)( x , 0))(('  x , 0)()))(('(  xx   (11) as necessary conditions for a minimum. the first two conditions are (4) and (8), respectively. the third condition, the complementarity condition, states that when  is positive the force  must lie on the border of the yield surface, and that when  lies at the interior of the yield surface then  must be zero. again, it is remarkable that these distinctive aspects of plastic response have not been postulated, but deduced from incremental energy minimization. conditions (11) are still insufficient to determine the evolution of the deformation. this is done by minimizing the second-order term of (9) dxxtxtxttltte l ))()()()),((''()()())(),(( 0     (12) which is a quadratic function of  . the new minimization provides a second set of kuhn-tucker conditions 0)( x , 0)())((''   xx , 0)())())((''(  xxx   , x (13) to be satisfied at the portion  of the bar at which (8) is satisfied as an equality. indeed, we already know that  = 0 out of . in (13), the first condition is again the dissipation inequality (4). the second condition provides a relation between the increments of the force and of the inelastic deformation. by the complementarity condition (13)3 , inequality (13)2 is satisfied as an equality when  > 0. this equality provides the flow rule for the inelastic strain rate in the regime of inelastic deformation. condition (13)3 is the consistency condition, which says that the inelastic deformation cannot increase when a http://www.gruppofrattura.it http://dx.medra.org/10.3221/igf-esis.18.01&auth=true g. del piero et alii, frattura ed integrità strutturale, 18 (2011) 5-13; doi: 10.3221/igf-esis.18.01 8 point x tends to re-enter the elastic range (8). this condition determines the property of elastic unloading. again, these typical properties of plastic response are not assumed, but come as results of the second-order incremental minimization. together with the necessary condition  ((x))  0 (14) imposed by the non-negativeness of the second variation, conditions (11) and (13) determine the solution ( ,  ) of the incremental problem. here we summarize some properties of the continuations. for a more detailed analysis we refer to the main paper [1].  if at the time t = 0 we start with (0)=0 from the natural configuration (x) = (x) = 0, from the constitutive assumption (0) > 0 we have that, initially, inequality (8) is strict. then  is zero, and a purely elastic evolution occurs. this elastic regime ends when, with growing , the force  reaches the limit value  =(0), corresponding to the boundary of the elastic range. this event marks the onset of the inelastic regime.  the response in the inelastic regime strongly depends on the sign of (0). if (0) is positive, the deformation is homogeneous, that is, both  and  are constant all over the bar. if 0 , the inelastic deformation is given by the solution of the differential equation )( ))()((''))(('' ))()(('' )( t ttwt ttw t         (15) joined with an appropriate initial condition. the slope of the force-elongation response curve is given by )( ))()((''))(('' ))()((''))(('' )( t ttwt ttwt t         (16) the slope is positive, that is, the inelastic regime starts with a work-hardening response. if 0 , elastic unloading takes place.  if (0) is zero, the initial response is perfectly plastic. the force is constant in time, 0)( t , the total inelastic deformation rate is equal to the total elongation rate )(tl , while the punctual distribution of )(t remains undetermined.  finally, if (0) is negative the necessary condition for equilibrium (14) is violated. the deformation tends to concentrate on a very small portion of the bar, and the slope )(/)( tt   tends to . this is the model’s representation of the catastrophic failure of the bar. the work-hardening regime ends if, with growing inelastic deformation, ((t)) becomes equal to zero. of course, this may or may not be possible, according to the shape assumed for the function   figure 1: force-elongation response curves at the onset of the inelastic regime, for different signs of (0)  the main result of the local model is that the initial part of the inelastic response is determined by the sign of the second derivative  (0). that is, by the initial convexity or concavity of the cohesive energy. the predictions of the local model http://www.gruppofrattura.it http://dx.medra.org/10.3221/igf-esis.18.01&auth=true g. del piero et alii, frattura ed integrità strutturale, 18 (2011) 5-13; doi: 10.3221/igf-esis.18.01 9 at the onset of the inelastic regime are summarized in fig.1. the subsequent part of the response curve depends on the analytic expression of the cohesive energy away from the origin. anyway, the picture shows a major defect of the model, that is, the incapability of reproducing the regime of strain softening, in which the response curve exhibits a negative slope. indeed, catastrophic failure occurs as soon as  (0) takes a negative value.  the non-local model he reproduction of strain softening becomes possible in the non-local model obtained by adding to the energy (3) a term proportional to the square of the gradient of the inelastic deformation   l dxxxwe 0 )))(())(((),(  +  l dxx 0 2 2 1 )(' (17) where  is a small positive constant. the addition of the new term brings additional terms to the yield condition (8)    ((x)) (x) (18) and to the kuhn-tucker conditions (11) 0)( x , 0)(''))(('  xx  , 0)())(''))(('(  xxx   (19) and (13) 0)( x , 0)('')())((''  xxx   , 0)())('')())((''(  xxxx   , x (20) it also adds a positive term to the second variation. then the necessary condition (14) is relaxed, and this is the reason why a description of strain-softening becomes possible. at the onset of the inelastic regime, due to the additional boundary conditions required by the supplementary gradient term, the inelastic deformation is not anymore constant all over the bar. the choice of the additional boundary conditions is a delicate point. our choice of taking  (l ) = (0) = 0 (21) is discussed in detail in the paper [1]. with these conditions, for the inelastic strain rate we get the expression xk xl x sinh 2 tanh 2 tanh )0('' )(              , (22) with  =((0) /)1/2, if (0) > 0, and )( 2 )( xlxx       (23) if (0) = 0. in both cases, the added energy term has the effect of increasing the slope of the force-elongation response curve. in particular, for (0) = 0 a hardening response takes the place of the perfectly plastic response predicted by the local model. for (0) < 0, there are two types of solutions: the full-size solution xk lkxk x sin 2 tan 2 tan )0('' )(           , (24) with k =((0) /)1/2, if kl < 2, and the localized solution  ))(cos1( )0('' )( axkx     , (25) t http://www.gruppofrattura.it http://dx.medra.org/10.3221/igf-esis.18.01&auth=true g. del piero et alii, frattura ed integrità strutturale, 18 (2011) 5-13; doi: 10.3221/igf-esis.18.01 10 if kl > 2.the latter are concentrated on an interval (a, a + ly) of length ly = 2 /k < l. the initial slope of the inelastic response curve is positive for kl < , and negative for kl > . it is usual to consider the material constant li =  / k (26) as an internal length of the material. from the preceding analysis it follows that the inelastic regime starts with  a full-size solution and a work-hardening response if l < li ,  a full-size solution and a strain-softening response if li < l < 2 li ,  a localized solution and a strain-softening response if l > 2 li . catastrophic failure again occurs when the slope of the response curve becomes . this never happens for l < li . for li < l < 2 li , this happens when 0)('' 2/ 2/tan 1)0(''        cw kl kl  (27) where c is the elongation at the onset of the inelastic regime. for l > 2 li , this happens when 0)('')0(''  c y w l l  (28) the occurrence of catastrophic rupture at the onset is the response predicted by griffth’s theory of brittle fracture. for all remaining situations, the subsequent response depends on the behavior of  away from the origin. depending on the form assumed for as a function of , it may happen that an initially full-size solution localizes for some  > c , and in some cases it may also happen that a localized solution becomes full-size. catastrophic fracture may take place in both localized and full-size solutions. numerical simulations ith an appropriate choice of the expression of , the non-local model gives the possibility of describing many experimental situations in which rupture is preceded by more or less extended regimes of inelastic deformation, as well as many intermediate situations between the extreme cases of a totally brittle and a totally ductile response. however, the non-homogeneous character of the solutions in the non-local model makes hopeless any attempt of describing the evolution of the inelastic deformation by a simple differential equation, like eq. (15) in the case of the local model. for this reason, we made a series of numerical simulations. here we present the current status of our study, which is still in progress. the purpose of our simulations was to determine the shape of the function  giving the best reproducion of the response curves of two experimental tests, one on a steel bar and one on a concrete specimen. for  we chose a piecewise polynomial c2 representation. this was obtained by subdividing the domain {  0 } into n intervals, in each of which  was taken to be a third-order polynomial, and by imposing the continuity of the function and of its first and second derivatives at the nodal points of the subdivision. the number and position of the nodal points determine the accuracy of the approximation. the advantage of a better approximation obtained with large n is paid with the disadvantage of working with a larger number of material constants. for the steel bar we made two series of simulations, one with n = 3 and one with n = 6. the results of the first series are shown in fig. 2. in it, we see the response curves obtained numerically for a bar length l equal to 40, 80, 160 mm. they show that a short bar is more ductile than a long bar, since for short bars catastrophic failure takes place for larger . this is a manifestation of the size effect. in the same figure, the curve for l = 80 mm is compared with the experimental curve, represented by the dotted line, for a bar of the same length. we see a very good agreement, except for the initial horizontal plateau exhibited by the experimental curve and not reproduced in the simulation. the second series of simulations was done with the purpose of eliminating this discrepancy, by increasing the number n of parameters. the result is shown in fig. 3, where we see an almost perfect agreement between experiment and simulation. w http://www.gruppofrattura.it http://dx.medra.org/10.3221/igf-esis.18.01&auth=true g. del piero et alii, frattura ed integrità strutturale, 18 (2011) 5-13; doi: 10.3221/igf-esis.18.01 11  figure 2: response curves for a steel bar in numerical simulations with n = 3 and different values of l, and experimental response curve (the dotted line) for l = 80 mm.   figure 3: force-elongation response curve for a steel bar in a numerical simulation with n = 6 and l = 80 mm, compared with the experimental response curve (the dotted line) (a). detail of the plateau at the onset of the inelastic regime (b) for the concrete specimen, at present the simulations are still in progress. a first result is shown in fig. 4. while the general trend of the response is well reproduced, just after the onset of the inelastic deformation a sharp change of the slope occurs in the simulation but not in the experiment. a larger n is probably necessary to eliminate this discrepancy. the distribution of the inelastic deformation (x) along the bar’s axis is shown in fig. 5 for different values of . the resemblance with the measurements by miklowitz made many decades ago [11], is impressive. both diagrams show a progressive concentration of inelastic deformation at the central zone of the bar. if we imagine that, by a sort of poisson effect, axial elongation is accompanied by a proportional transversal contraction, we have that a concentration of axial deformation is accompanied by the necking of the cross section. therefore, the proposed model provides a good description of the phenomenon of necking observed in bars subjected to a tensile load. http://www.gruppofrattura.it http://dx.medra.org/10.3221/igf-esis.18.01&auth=true g. del piero et alii, frattura ed integrità strutturale, 18 (2011) 5-13; doi: 10.3221/igf-esis.18.01 12  figure 4: force-elongation response curve for a concrete specimen in a numerical simulation with n = 4 compared with the experimental curve (the dotted line)  figure 5: the inelastic deformation  as a function of x, for different values of the total elongation . the first diagram shows the results of the numerical simulations, and the second shows the experimental measurements reported in [11]. references [1] g. del piero, g. lancioni, r. march, a diffuse cohesive energy approach to fracture and plasticity: the onedimensional case. in preparation (2011). http://www.gruppofrattura.it http://dx.medra.org/10.3221/igf-esis.18.01&auth=true g. del piero et alii, frattura ed integrità strutturale, 18 (2011) 5-13; doi: 10.3221/igf-esis.18.01 13 [2] a.a. griffith, phil. trans. roy. soc. a221, 163-198 (1920). [3] d. dugdale, j. mech. phys. solids, 8 (1960)100. [4] g.i. barenblatt, adv. appl. mech. , 7 (1962) 55. [5] g.a. francfort, j.-j. marigo, j. mech phys. solids, 46 (1998) 1319. [6] j.-j. marigo, l. truskinovsky, cont. mech. thermodyn, 16 (2004) 391. [7] m. charlotte, j. laverne, j.-j. marigo, eur. j. mech., a/25 (2006) 649. [8] g. del piero, l. truskinovsky, cont. mech. thermodynamics, 21 (2009) 141. [9] l. freddi, g. royer-carfagni, j. mech. phys. solids, 58 (2010) 1154. [10] k. pham, h. amor, j.-j. marigo, c. maurini, int. j. damage mechanics, 20 (2011) 618. [11] j. miklowitz, in: proc. nat. meeting of the applied mechanics division, asme, ann harbor, mich, (1949) 159. http://www.gruppofrattura.it http://dx.medra.org/10.3221/igf-esis.18.01&auth=true microsoft word 2329 a. namdar et alii, frattura ed integrità strutturale, 47 (2019) 451-458; doi: 10.3221/igf-esis.47.35 451 timber beam seismic design – a numerical simulation abdoullah namdar, *yun dong, yuyi liu faculty of architecture and civil engineering, huaiyin institute of technology, china ab_namdar@yahoo.com, hadyun@163.com (*), liuyuyi88@163.com abstract. in order to design a seismic timber beam, the effect of near-fault ground motion on timber beam has numerically been investigated, with reference to small displacement theory. the simulated near-fault ground motion is applied on the fixed base of a timber frame model. the beam is placed in single span of a timber frame. the beam has two different length sizes of 1.8 and 3.3 meters. the seismic load-displacement, seismic load-strain and strain-displacement have been calculated for all models and shown in graphs. the beam is designed with nonlinear analysis method and some mechanical properties for all models have been used, in numerical analysis. the numerical analysis results indicate that, the inertial interaction, energy dissipation and nonlinear deformation of beams in timber frames have directly related with frame span. in beams with a smaller length, higher seismic loading caused lower displacement. the displacement is reduced by reducing the length of the beam. the inertial interaction, energy dissipation and nonlinear deformation are changed respect to the length of the beam. the innovation of this paper is to develop cycling graphs by using abaqus, to improve design of timber frame and give an adequate explanation of seismic behavior of timber beam. keywords. seismic load; timber beam; displacement; nonlinear deformation; cycling graphs. citation: namdar, a., dong, y., liu, y., timber beam seismic design – a numerical simulation, frattura ed integrità strutturale, 47 (2018) 451-458. received: 20.10.2018 accepted: 14.12.2018 published: 01.01.2019 copyright: © 2019 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. introduction owadays, the timber well adapted in the construction industry, including timber frame which is very popular. the strength of timber depends on the material and manufacturing process. however, the timber seismic behavior is different from concrete and steel. there are several historical timber structures around the world available that need maintenance and retrofits. the wentong pagoda timber tower with nine floors is one heritage and beautiful monument constructed in huai’an city, jiangsu province of china (fig. 1). there are several towers made from timber frames existing in china, some of them are, changzhou tianning, changzhou wenbi pagoda, jimingsu-sunset, lufeng temple, twin pagodas of shuixi and etc. n http://www.gruppofrattura.it/va/47/2329.mp4 a. namdar et alii, frattura ed integrità strutturale, 47 (2019) 451-458; doi: 10.3221/igf-esis.47.35 452 in the construction industry and related field, several characteristics of different structure, structural elements, substructure and construction materials are numerically, theoretically and experimentally reported in the literature [1-19], but little research has been done on timber structure design. a timber structure state of art has numerically been investigated, to understand seismic resistance by the evaluation of the load, displacement and stress have been applied on the timber structures [1]. an investigation has been made comparing the behavior of laterally loaded round and squared timber bolted joints [2]. a research work on damage of bamboo and wooden materials based on linear elastic fracture mechanics has been reported [3]. the collapse prediction and non-linear behavior of the t-joint have experimentally and numerically been investigated [4]. the measurement of the compression strength of wood was studied [5]. but seismic design of timber frame subjected to near-fault ground motions, developing cycling graph using abaqus, and an explanation of the seismic behavior of timber beams have never been reported in the literature. in this paper, the beam is placed in a single span of a timber frame, with two different length sizes of 1.8 and 3.3 meter. the timber frame is subjected to nearfault ground motions. the seismic load-displacement, seismic load-strain and strain-displacement curves have been investigated, to understand the inertial interaction, energy dissipation and nonlinear deformation of beams in timber frames, with reference to the small displacement theory. materials and modeling he failure mitigation of soil foundation and soil-footing interaction have been investigated, considering analytical and numerical analysis. 2d numerical analysis has been performed for soil-concrete foundation interaction by using abaqus software [20-21]. in the present study, 3d numerical analysis has been used to understand timber frame seismic response, during timber frame subjected to near-fault ground motion, also by using abaqus software. fig. 1, shows wentong pagoda timber tower with nine floors, the tower consists of small span timber frame. it is important to seismic analysis of timber frame, while many heritage and modern structure made up from timber. from other hand high flexibility of timber frame compare to steel and concrete frame, seismic resistance of timber frame shows more stability. figure 1: wentong pagoda timber tower with nine floors is one heritage and beautiful monuments constructed in huai’an city, jiangsu province of china two timber frame models have been developed and analyzed, at each model the timber frame built up with single span. the size of spans in the first and second models are respectively 1.8 and 3.3 meter. in all models, the foundations of frame have been installed with suitable boundary condition. for each individual node, at the base of foundation, the fixed boundary condition has been simulated. it is hope this kind of boundary condition improves quality of analysis. the timber structure has been modeled with deformable mesh and has been numerically analyzed by using abaqus software. on the timber t a. namdar et alii, frattura ed integrità strutturale, 47 (2019) 451-458; doi: 10.3221/igf-esis.47.35 453 frame model, the near-fault ground motion is applied, and the three processes of loading-unloading mechanism have been shown, using cycling graph under abaqus environment. the method of merge node for all model including boundary condition, has been adopted in analysis of timber frame, during execute of numerical analysis. both foundations of frame are characterized by the same geometry and material. tab. 1, indicates the mechanical properties used in numerical analysis. the figs. 2 and 3 show the timber frame and the type of meshes used in numerical analysis. both frame and foundation are built up from the timber. the maximum value of seismic acceleration (4.25 [m/s2]) is applied on the model (fig. 4). the beams are characterized by two different sizes (1.8 and 3.3 meter length), and both of beams have 0.3x0.3 meters cross section. the column size is 3 meter length, and 0.3x0.3 meters of cross section in both models. the timber frame is installed on a foundation of 0.3x0.3x0.3 meter and beneath the foundation a footing is designed with dimension of 0.9x0.9x0.4 meters. type of material modulus elasticity, e (mpa) poisson’s ratio, ν unit weight, γ (kn/m3) timber 147.5 0.3 6.2 table 1: soil and concrete mechanical properties [22]. figure 2: typical timber frame models figure 3: typical timber frame models, with mesh is used in numerical simulation a. namdar et alii, frattura ed integrità strutturale, 47 (2019) 451-458; doi: 10.3221/igf-esis.47.35 454 figure 4: acceleration history of earthquake used in numerical analysis [23]. theoretical concept timber beam of homogeneous, isotropic and linearly elastic material with modulus of elasticity e and poisson ratio ν, and constant cross section is installed in single span of timber frame, has been numerically investigated. the model has been considered under internal and external dynamic loading. considering a static problem, during the action of internal and external forces. the sum of all the virtual work is: 0w  (1) when all the external and internal forces are derived from a potential function u, which is a function of the coordinates of the system of particles, w u    (2) the virtual work leads to establish the principle of stationary potential energy 0u  (3) the above formulation may be extended to the dynamical problem of a system when it is subjected to time-dependent applied forces and geometrical constraints. the principal virtual work for the dynamical problem is given by: 2 2 1 1 0 t t t t tdt wdt    (4) where t is the kinetic energy of the system. the state of the strain at a point of the body is defined by six components of strain ( ,  ,  ,  ,  , x y z yz zx xy      ). in small displacement theory, the strain-displacement relationship are given as follows [24]:  x u x     (5)    y v y     (6) a a. namdar et alii, frattura ed integrità strutturale, 47 (2019) 451-458; doi: 10.3221/igf-esis.47.35 455    z w z     (7)    yz w v y z        (8)    zx u w z x        (9)    xy v u x y        (10) in the present study, the above theoretical concept has been applied in numerical analysis, and the strain-displacement cyclic behavior of timber beam has been graphically shown, in order to understand timber beam seismic response. numerical analysis and discussion he numerical analysis results show that the timber-frame resists well against seismic loading. in comparative analysis of two types of timber frames, the safety and the economy concepts are demonstrated. with higher span of timber frame, the bending moment on controls the beam seismic response, while in smaller span of timber frame the shear force is controlled seismic behavior of the beam. this phenomenon causes a nonlinear deformation of the beam. the same stiffness of timber cross section in both models, will induce larger displacements in beam with the longer length. seismic response of both models illustrated that, for finite elastic strains, the timber beam involves large displacements and strains. load-displacement in the cycling direction is obtained from numerical analysis, using abaqus software [figs. 5-6]. in comparison models 1 and 2, the loading, unloading and reloading cycles, show different shape for each model. this is also reflected to displacement of beam. it is observed that increasing the distribution level of seismic load in timber beam, model 1, shows a significantly effect on the change displacements mechanism. figure 5: load vs displacement on timber beam with 3.3 (m) length, model-1. figure 6: load vs displacement on timber beam with 1.8 (m) length, model-2. the magnitude of a nonlinear deformation of timber beam during an individual earthquake, occurs both on the basis of the beam length and in the maximum displacement. although there are significantly differences between developing cycling graphs of load-displacement in each models, which are produced on timber frame seismic load response. in t a. namdar et alii, frattura ed integrità strutturale, 47 (2019) 451-458; doi: 10.3221/igf-esis.47.35 456 consideration of models response, it has been observed that, the elastic displacement of timber beam with the same stiffness, but with nonlinear deformation, have been occurred. the inertia is developed in a timber frame during the seismic loading, producing shear, moment and torsional excitation. however, these loads cause hysteretic displacement variation in all timber frame components, with respect to flexibility level of timber frame. the seismic wave propagation into the timber frame, causes hysteretic displacement. the seismic energy dissipation significantly affects the overall timber frame seismic behavior. considering the structural inertia, the kinematic interaction, results in stiff beam elements, which cause timber frame motions to deviate from free-field motion. the structure and foundation inertia, consist of the relative foundation-free field displacements. the flexural, axial and shearing nonlinear deformations of timber frame elements that occur, due to seismic load mechanism, are applied on model. these deformations significantly change the model behavior, especially in terms of damping, inertial interaction and energy dissipation. the strain-displacement of timber frame is a representation of the nonlinear model behavior, and illustrates kinematic interaction of beam, which solve kinematic interaction problem beyond the ability of most commercial software. abaqus is able to show kinematic interaction, drawing cyclic graphs. the strain-displacement curve and nonlinear deformation of timber beam are dependent on the stiffness and geometry. the high strain-displacement have been observed in both models. the shape of strain-displacement curve are shown. the shear strain is developed with reduction of timber length [figs. 7-8]. figure 7: strain vs displacement on timber beam with 3.3 (m) length, model-1. figure 8: strain vs displacement on timber beam with 1.8 (m) length, model-2. the load-strain curve describes the stiffness and damping characteristics of timber frame and beam-column interaction as well. two different strain energies are developed in the models 1 and 2. the morphology of timber beams is correlated to different strain energy magnitude and shape for, each location and timber beams. from the seismic design point of view in a force-displacement diagram, the strain energy stored in the timber beam has been illustrated. the load-strain mechanism is part of the strain energy corresponding to the linear elastic response. for timber beam it is responding in the nonlinear range of loading, unloading and reloading. the energy dissipation causes nonlinear deformation and displacement. therefore, the hysteresis loop of load-strain, illustrates the strain energy dissipation process. a flexibility of timber beam of 3.3 (m) reached at failure displacement with lower elastic strain energy, is reduced in this model by the damping ratio. the structural damping ratio will depend on elemental damping ratio and on the stiffness of the models. the relationship between the work done by seismic force and the elastic strain energy in one cycle of loading, unloading and reloading are shown in the graphs. the percentage of the seismic load carried out by beam and columns is affected to flexibility of frame. this process leads to develop different load-strain curve for each model. the magnitude and the direction of load sharing between beam and columns in each model, have specific characteristics, depending on timber frame span [figs. 9-10]. in this numerical analysis, only one types of wood has been used in timber frame simulation. but it is indicated that [25], the strength of materials has significant effect on load sharing. the load sharing process effects to yielding of the lower strength and stiffness, resulting in change load transmission. a. namdar et alii, frattura ed integrità strutturale, 47 (2019) 451-458; doi: 10.3221/igf-esis.47.35 457 figure 9: load vs strain on timber beam with 3.3 (m) length, model-1. figure 10: load vs strain on timber beam with 1.8 (m) length, model-2. conclusion he timber beam seismic resistance correlated to displacement and nonlinear strain, has been investigated. the timber frame model performance is represented by seismic load-displacement, and by seismic load-strain. the load-displacement diagram relationship is subjected in considerable research in timber frame. the small displacement theory concept has been applied in numerical analysis, and the strain-displacement cyclic behavior of timber beam has been investigated, in order to understand the timber beam seismic response. in this work the follows goals have been achieved:  from the load-displacement diagram analysis it has been found that, for the same stiffness in timber cross section in both models, it will induce larger displacements in beams characterized by longer length.  the inertia is not negligible in a timber frame during subjected to seismic loading. it produces base shear, moment and torsional excitation which cause hysteretic displacement of timber beam.  the deformation of beam significantly influences the model behavior, especially with respect to damping, inertial interaction and energy dissipation.  the energy dissipation causes nonlinear deformation and the displacement. in load-strain mechanism, only the part of the strain energy, corresponding to the linear elastic response, is recovered.  a flexible 3.3 m timber beam reaches the failure displacement with lower elastic strain energy.  the percentage of the seismic load supported by beams and columns is affected by flexibility of frame. references [1] namdar, a., darvishi, e., feng, x. and ge, q. (2016). seismic resistance of timber structure a state of the art design. procedia structural integrity, 2, pp. 2750-2756. doi:10.1016/j.prostr.2016.06.343. [2] lokaj, a. and klajmonová, k. (2017). comparison of behaviour of laterally loaded round and squared timber bolted joints. frattura ed integrità strutturale, 11 (39), pp. 2750-2756. doi: 10.3221/igf-esis.39.07. [3] haiyan, t. (2016). damage of bamboo and wooden materials based on linear elastic fracture mechanics in garden design. frattura ed integrità strutturale, 10(35), pp. 472-480. doi: 10.3221/igf-esis.35.53. [4] santos, c.l. dos., morais, j.j.l and jesus, a.m.p. de. (2015). mechanical behaviour of wood t-joints. experimental and numerical investigation. frattura ed integrità strutturale, 9(31), pp. 23-37. doi: 10.3221/igf-esis.31.03. [5] jingran, g., jian, l., jian, q and menglin, g. (2014). degradation assessment of waterlogged wood at haimenkou site. frattura ed integrità strutturale, 8(30), pp. 495-501. doi: 10.3221/igf-esis.30.60. [6] drbe, of., el naggar, mh. (2014). axial monotonic and cyclic compression behaviour of hollow-bar micropiles. can geotech j, 52(4), pp. 426-41. doi: 10.1139/cgj-2014-0052. t a. namdar et alii, frattura ed integrità strutturale, 47 (2019) 451-458; doi: 10.3221/igf-esis.47.35 458 [7] namdar, a., darvishi, e., feng, x., zakaria, i. and yahaya, f.m. (2016). effect of flexural crack on plain concrete beam failure mechanism a numerical simulation. frattura ed integrità strutturale, 10 (36), pp. 168-181. doi: 10.3221/igf-esis.36.17. doi: 10.3221/igf-esis.36.17. [8] namdar, a., bin zakaria, i., bt hazeli, a., azimi, s. j., bin abd. razak, a.s. and gopalakrishna, g. s. (2013). an experimental study on flexural strength enhancement of concrete by means of small steel fibers. frattura ed integrità strutturale, 7 (26), pp. 22-30. doi: 10.3221/igf-esis.26.03. [9] namdar, a. (2012). natural minerals mixture for enhancing concrete compressive strength. frattura ed integrità strutturale, 6 (22), pp. 26-30. doi: 10.3221/igf-esis.22.04. [10] namdar, a., failure analysis of concrete frame a numerical analysis. (2016). procedia structural integrity 2, pp. 2796-2802. doi: 10.1016/j.prostr.2016.06.350. [11] santis, a de., bartolomeo, o di., iacoviello, d. and iacoviello, f. (2008). quantitative shape evaluation of graphite particles in ductile iron. journal of materials processing technology, 196 (1-3), pp. 292-302. [12] lazzarin, p., livieri, p., berto, f. and zappalorto, m. (2008). local strain energy density and fatigue strength of welded joints under uniaxial and multiaxial loading. engineering fracture mechanics, 75 (7), pp. 1875-1889. doi:10.1016/j.engfracmech.2006.10.019. [13] susmel, l. and taylor, d. (2008). the theory of critical distances to predict static strength of notched brittle components subjected to mixed-mode loading. engineering fracture mechanics, 75 (3-4), pp. 534-550. doi:10.1016/j.engfracmech.2007.03.035. [14] bonora, n., gentile, d., pirondi, a. and newaz, g. (2005). ductile damage evolution under triaxial state of stress: theory and experiments. international journal of plasticity, 21 (5), pp. 981-1007. doi: 10.1016/j.ijplas.2004.06.003. [15] rose, a., taylor, r. and el naggar, mh. (2013). numerical modelling of perimeter pile groups in clay. can geotech j, 50(3), pp. 250-8. doi: 10.1139/cgj-2012-0194. [16] iacoviello, f., cocco, v di., cavallini, m., marcu, t. and molinari, a. (2005). influence of sintered stainless steel microstructure on fatigue crack paths. fatigue & fracture of engineering materials & structures, 28 (1‐2), pp. 187193. doi: 10.1111/j.1460-2695.2005.00836.x. [17] salvini, p., vivio, f. and vullo, v. (2000). a spot weld finite element for structural modelling. international journal of fatigue, 22 (8), pp. 645-656. doi: 10.1016/s0142-1123(00)00044-x. [18] abd elaziz, ay. and el naggar, mh. (2014). geotechnical capacity of hollow-bar micropiles in cohesive soils. can geotech j, 51(10), pp. 1123-38. doi: 10.1139/cgj-2013-0408. [19] cavallini, m., bartolomeo, o di. and iacoviello, f. (2008). fatigue crack propagation damaging micromechanisms in ductile cast irons. engineering fracture mechanics, 75 (3-4), pp. 694-704. doi: 10.1016/j.engfracmech.2007.02.002. [20] namdar, a. and xiong, f. (2014). the understanding failure mitigation of soil foundation by using numerical analysis method. frattura ed integrità strutturale, 8(30), pp. 138-144. doi: 10.3221/igf-esis.30.18. [21] namdar, a. (2016). a numerical investigation on soil-concrete foundation interaction. procedia structural integrity 2, pp. 2803-2809. doi: 10.1016/j.prostr.2016.06.351. [22] dackermann, u., li, j., rijal, r. and crews, k. (2016). a dynamic-based method for the assessment of connection systems of timber composite structures. construction and building materials, 2(102), pp. 999-1008. doi: 10.1016/j.conbuildmat.2015.10.009. [23] https://strongmotioncenter.org/ [24] washizu k., variational methods in elasticity and plasticity, 2nd ed, (1975). published by pergamon press. [25] alnuaim, am., el naggar, mh. and el naggar, h. (2016). numerical investigation of the performance of micropiled rafts in sand. computers and geotechnics, 77, pp. 91-105. doi: 10.1016/j.compgeo.2016.04.002. << /ascii85encodepages false /allowtransparency false /autopositionepsfiles true /autorotatepages /none /binding /left /calgrayprofile (dot gain 20%) /calrgbprofile (srgb iec61966-2.1) /calcmykprofile (u.s. web coated \050swop\051 v2) /srgbprofile (srgb iec61966-2.1) /cannotembedfontpolicy /error /compatibilitylevel 1.4 /compressobjects /tags /compresspages true /convertimagestoindexed true /passthroughjpegimages true /createjobticket false /defaultrenderingintent /default /detectblends true /detectcurves 0.0000 /colorconversionstrategy /cmyk /dothumbnails false /embedallfonts true /embedopentype false /parseiccprofilesincomments true /embedjoboptions true /dscreportinglevel 0 /emitdscwarnings false /endpage -1 /imagememory 1048576 /lockdistillerparams false /maxsubsetpct 100 /optimize true /opm 1 /parsedsccomments true 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/hrv (za stvaranje adobe pdf dokumenata najpogodnijih za visokokvalitetni ispis prije tiskanja koristite ove postavke. stvoreni pdf dokumenti mogu se otvoriti acrobat i adobe reader 5.0 i kasnijim verzijama.) /hun 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can be opened with acrobat and adobe reader 5.0 and later.) >> /namespace [ (adobe) (common) (1.0) ] /othernamespaces [ << /asreaderspreads false /cropimagestoframes true /errorcontrol /warnandcontinue /flattenerignorespreadoverrides false /includeguidesgrids false /includenonprinting false /includeslug false /namespace [ (adobe) (indesign) (4.0) ] /omitplacedbitmaps false /omitplacedeps false /omitplacedpdf false /simulateoverprint /legacy >> << /addbleedmarks false /addcolorbars false /addcropmarks false /addpageinfo false /addregmarks false /convertcolors /converttocmyk /destinationprofilename () /destinationprofileselector /documentcmyk /downsample16bitimages true /flattenerpreset << /presetselector /mediumresolution >> /formelements false /generatestructure false /includebookmarks false /includehyperlinks false /includeinteractive false /includelayers false /includeprofiles false /multimediahandling /useobjectsettings /namespace [ (adobe) (creativesuite) (2.0) ] /pdfxoutputintentprofileselector /documentcmyk /preserveediting true /untaggedcmykhandling /leaveuntagged /untaggedrgbhandling /usedocumentprofile /usedocumentbleed false >> ] >> setdistillerparams << /hwresolution [2400 2400] /pagesize [612.000 792.000] >> setpagedevice microsoft word numero_46_art_2 g. b. manjunatha et alii, frattura ed integrità strutturale, 46 (2018) 14-24; doi: 10.3221/igf-esis.46.02 14 developments in the fracture and fatigue assessment of materials and structures investigating the contribution of geometrical parameters and immersion time on fracture toughness of jute fabric composites using statistical techniques g. b. manjunatha department of mechanical engineering, g m institute of technology, karnataka, india, manjugb4444@gmail.com, https://orcid.org/0000-0001-8942-8887 k. n. bharath department of mechanical engineering, g m institute of technology, karnataka, india, kn.bharath@gmail.com, https://orcid.org/0000-0003-1004-099x abstract. the aim of this work is to evaluate the failure analysis of jute fabric reinforced composite using statistical technique for marine applications. a fracture mechanics approach is proposed to determine the failure load and fracture toughness of the composite. jute fiber reinforced epoxy composites were fabricated by hand lay-up technique. the polymer composite is intended for marine applications as an alternative material, mainly in high moisture environments. thus an investigation was conducted to evaluate the fracture mechanic parameter by immersing composite specimens in sea water. the statistical method of taguchi was used for experimental design. edge notched tension (ent) and single edge notched bend (senb) test were conducted according to the astm e1922 and astm d5045 respectively. main effect graphs are obtained to study the effect of a/w (crack length to width ratio), thickness and immersion time of composite on fracture mechanics parameters. the approach of calculating the percentage of contribution of control factors was established using by analysis of variance (anova). the influence of fracture parameters of control factors can be analysed by using 3-d response surface graph (rsm). the validation of experimental results for fracture parameters agreed well with the predicted values. keywords. polymer composites; natural fiber; fracture toughness; taguchi; anova; rsm. citation: manjunatha, g. b., bharath, k. n., investigating the contribution of geometrical parameters and immersion time on fracture toughness of jute fabric composites using statistical techniques, frattura ed integrità strutturale, 46 (2018) 14-24. received: 07.03.2018 accepted: 07.04.2018 published: 01.10.2018 copyright: © 2018 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. http://www.gruppofrattura.it/va/46/2.mp4 g. b. manjunatha et alii, frattura ed integrità strutturale, 46 (2018) 14-24; doi: 10.3221/igf-esis.46.02 15 introduction merging environmental awareness and social concern, the unmanageable consumption of petroleum, and new system demands for ecofriendly materials with economic. fiber-reinforced composite materials have some advantages such as high stiffness, relatively good resistance to environmental actions, recyclable, fatigue and failure resistance, etc. [1]. the natural fibers are a large amount of moisture absorbed. the absorption of water in a polymeric matrix is a volumetric diffusion process which follows the fick’s law [2]. it’s an important issue nature life when composite materials are subjected to both mechanical loadings and exposed to severe environmental conditions [3]. in recent developments, the laminated polymer matrix composite materials are being extensively used in extreme environments. correspondingly needs to be characterizing the fracture toughness over environmental conditions. this behaviour has been interrelated to the effect of moisture on matrix ductility, an amount of matrix deformation and the size of the plastic zone around the crack tip that occurs during fracture [4]. for fiber-reinforced composite materials, the interlaminar and/or intralaminar interface will have a great effect on their fracture mechanisms. the interface is probably the weakest part of a fracture process. hence, the enhancement of interface behaviour is even more important [5]. the advance of fracture mechanics tests methods for the determination of delamination resistance or fracture toughness of fiber-reinforced polymer matrix composites is an active area of research [6]. many machine elements have failed in the form of holes, notches, or cracks that are very significant factors influencing stress distributions in the structures. in such cases, stress cannot be defined as a strength parameter. mechanical systems are designed by using the fracture mechanics' parameter as fracture toughness and can be used during the determination of the material strength against crack growth under external loads [7]. the increased use of polymer composites also requires the understanding of the fracture behaviour. evaluation of damage and prediction of residual strength and fracture toughness is critical because the deboned can grow in an unstable manner and finally leads to catastrophic failure [8]. fiber-reinforced composites used structural materials. since these structures are to be used under some environmental conditions. it’s necessary for understanding the environmental effects on the fracture toughness and deformation behaviour to prevent damage to the structure. among the many different kinds of environmental effect, the hydrothermal effect is one of the most important issues for polymeric composites [9]. taguchi methods are statistical methods developed by grenichi taguchi to improve high-quality products at a low-cost [10]. by using the taguchi techniques, industries are able to greatly reduce cycle time for both design and production. the objective of this technique is to optimize the settings of the process parameter values for improving performance characteristics. the design of parameters is the key step in the taguchi method [11]. design of experiment (doe) is one of the extensively used methods for experimental study. doe is a statistical approach in which a mathematical model is established through experimental results. the trial data were developed in a pattern of l9 orthogonal array (oa) so possible output can be predicted based on the input parameters of the experimentation. results can be analysed by using analysis techniques such as anova and linear regression [12]. experimental results are shown by plotting response surface methodology (rsm) graph. materials and experimental methods specimen preparation he specimens used in the present study were fabricated using a hand lay-up technique. main materials are jute fiber and epoxy polymer. the 40% of volume fraction as matrix material used is a medium viscosity epoxy resin (lapox l-12) and a room temperature curing hardener (k-6). it provides excellent resistance to alkalis and good adhesive properties [13]. jute fiber of 60% used as reinforcement by volume fraction in this composite material. the specimens were dipped in seawater about 7, 14, 21 days. fracture testing the experiment was conducted on a computerized universal testing machine (utm). for ent, loading fixtures are used on the specimen to maintain a tensile load on the crack tip is uniaxial. the load was applied eccentrically to the specimen. hence the fixture freely allows the material to rotate interns reduces the torsion effect. the crack will propagate across the laminate. for senb, specimen was placed in between the two jaws of the testing machine the dial gauge of extensometer and vernier scale which as placed on the vertical column of the machine must be set to zero. the precracked specimen was loaded at the center of the specimen with suitable loading device. there are five trails were conducted for each condition of the specimen. e t g. b. manjunatha et alii, frattura ed integrità strutturale, 46 (2018) 14-24; doi: 10.3221/igf-esis.46.02 16 edge notched tension test (ent) the ent test specimens were prepared according to astm e1922 standard [13]. the crack has to be introduced by sawing a fine razor blade. the standard dimensions of the specimen are as shown below the fig.1. figure 1: ent specimen as per astm standard [13]. single edge notched bend (senb) single edge notched bend specimen was prepared based upon the astm d5045 standard, and it involves the specimen has to be precracked [14]. the standard specimen configuration of the specimen as shown in fig.2 figure 2: senb specimen as per astm standard [14]. experimental design for ent and senb test trial a b c 1 1 1 1 2 1 2 2 3 1 3 3 4 2 1 3 5 2 2 1 6 2 3 2 7 3 1 2 8 3 2 3 9 3 3 1 table 1: experimental design using l9 oa [15] g. b. manjunatha et alii, frattura ed integrità strutturale, 46 (2018) 14-24; doi: 10.3221/igf-esis.46.02 17 code control factors level 1 level 2 level 3 a (a/w) ratio 0.3 0.4 0.5 b thickness(mm) 7 10 12 c immersion time (days) 7 14 21 table 2: factors and levels considered taguchi’s orthogonal array (oa) table was prepared by choosing three control factors that could affect the load and facture toughness. tab. 1 shows the parameters and the levels used in this experiment. the orthogonal array of l9 type was used and is represented in tab. 2. l is latin square and subscript 9 means the number of the experiment [15]. analysis of variance (anova) analysis of variance (anova) is done on the minitab software. it gives a clear picture about the extent to which a particular process parameter affects the response. the main objective of this analysis is to estimate the relative contribution of each control factor to the overall response. the contributions are expressed in terms of percentage [16]. main effect plots the main effect plots are the mean response of each level factor connected by the line. when the line is in horizontal, there is no main effect present. each factor for the level effects in the response same way the response means also same across the level. when the line is a small deflection from horizontal my significant effect on the response. different levels of the factors may affect the response differently. stepper the slope along the line shows the greater magnitude of the main effect [17]. results and discussion n the present work, the effect of varying a/w, thickness and immersion time with a fixed percentage of polymer epoxy on the load carrying capacity and fracture have been identified experimentally. the configurations of the specimen for ent and senb tests were controlled by the astm e1922 and astm d5045 standards, respectively. experimental results have been discussed throughout this section. main effect plot for edge notched tension (ent) test the main effect plot of ent test for load carrying capacity under sea water immersion is as presented in the fig.3 (a). failure with unstable crack growth is common problem accompanying with brittle polymer matrix composite [13]. load carrying capacity decreases with increasing the ratio. this is because of the crack length increases, then the critical stresses are decreased inters reduces the load withstanding capacity [18]. previously established in the literature the sea water formed in a closed cell of polymeric foams. the immersion time increases from 7 to 14 days, then the load carrying capacity decreases due to the significant moisture absorption, sea water degradation and plasticization of the matrix inter deboning of the fiber matrix interface. again the load carrying capacity increase, when immersion time from 14 to 21 days is mainly due to the secondary mechanism of sea water provides the foam permeability which increases the 4% of weight gain [18]. there is no much deflects in the line of immersion time; this indicates that the sea water treatment does not the abundant cause of composite material. main effect plot for fracture toughness on ent test under sea water immersion is as shown in fig.4. fracture toughness increases with increasing the a/w ratio because of the plastic zone size increases with increases crack length in the meantime energy required for growth of crack is high. as long as the material becomes thicker don’t allow for the generation of the larger plastic zone, hence the fracture toughness decreases with increase in thickness of the composite [20]. the immersion time the seawater increases the fracture toughness decreases initially and again increases. it is observed that sea water treatment yields a higher value of fracture toughness [13]. i g. b. manjunatha et alii, frattura ed integrità strutturale, 46 (2018) 14-24; doi: 10.3221/igf-esis.46.02 18 (a) (b) figure 3: main effect plot of (a) load carrying capacity (b) fracture toughness mpa m½. analysis of variance (anova) for ent test the percentage of contribution of each factor on load carrying capacity is clearly revealed in anova as shown in tab.3. the thickness is main factor influence on load carrying capacity is about 71.57%. the percentage of contribution of a/w ratio is 21.39% and immersion time is 4.8%. here the sea water immersion is not a major influence on load carrying capacity. the error of 2.17% is due to the fabrication defects. source df ss ms f p % of contribution a/w ratio 2 10688.9 5344.4 9.82 0.092 21.39 thickness (mm) 2 35755.6 17877.8 32.84 0.030 71.57 immersion time (days) 2 2422.2 1211.1 2.22 0.310 4.8 error 2 1088.9 544.4 2.17 total 49955.6 100 table 3: anova for load carrying capacity source df ss ms f p % of contribution a/w ratio 2 311.702 155.851 1.63 0.051 74.5 thickness (mm) 2 78.439 39.220 4.69 0.176 18.74 immersion time (days) 2 11.519 5.760 0.69 0.592 2.7 error 2 16.728 8.364 3.9 total 8 418.389 100 table 4: anova for fracture toughness mpa m½. anova for the fracture toughness of jfrp under sea water environment is as shown in tab. 4. the main influencing factor on the fracture toughness is the a/w ratio about 74.5%. the thickness of the composite contributes about 18.74% to decrease the fracture toughness. and immersion time of 2.7% contributes to fracture toughness. it shows toughness alters very least by immersing the composite in sea water. the error of 3.9 % is due to fabrication defects. g. b. manjunatha et alii, frattura ed integrità strutturale, 46 (2018) 14-24; doi: 10.3221/igf-esis.46.02 19 main effect plot for single edge notched bend (senb) test the main effect plot of load carrying capacity for senb test under sea water environment is as shown in fig.4 (a). the failure of the polymer composite by bending load causes the delamination. the delamination occurs over the edge region, predominantly due to the plane stress developed [19]. in the main effect, the plot shows that the load carrying capacity decreases with increase in a/w ratio. the load carrying capacity increases with an increase in thickness is due to the more surface area is exposed to the load. and also the load carrying capacity decreases initially and the increases small amount to an increase in immersion time. this is because of the structural degradation occurs within in laminates causes the rapture of blisters, and viscous acid is expelled with immersion [18]. composite under wet condition showed an initial decrease in the load carrying capacity and again increases due to the plasticization of jute samples caused by moisture absorption. [21] main effect plots of fracture toughness for senb test under sea water environment are as shown in fig.4 (b). fracture toughness increases with increase in a/w ratio. a large amount of energy is required for failure of the composite structure. as thickness increases the fracture toughness goes on decreases is due to the small quantity of water absorb over the voids and cracks, this damage the fiber exposed [22]. and immersions time also some little effect on fracture toughness which decreases initially and then increases. this is because of chemical degradation of fiber and matrix interface region [23]. (a) (b) figure 4: main effect plot of (a) load carrying capacity (b) fracture toughness mpa m½. analysis of variance (anova) for senb test anova for load carrying capacity of senb test under sea water environment is as shown in tab. 5. the major factor influencing on load carrying capacity is the thickness of 78.32%. this is because of the larger surface area is exposed to the load. the a/w ratio is also contributing to load carrying capacity is about 17.09%, but load carrying capacity decreases with increase in crack length. the immersion time is a very little contribution to just 2.19% of load carrying capacity. this shows that sea water treatment does not more effect on the reinforced composite. and the error of 2.4% is due to the fabrication defect. source df ss ms f p % of contribution a/w ratio 2 18822 9411 7.00 0.125 17.04 thickness (mm) 2 86489 43244 32.17 0.030 78.32 immersion time (days) 2 2422 1211 0.90 0.526 2.19 error 2 2689 1344 2.4 total 8 110422 100 table 5: anova for load carrying capacity. g. b. manjunatha et alii, frattura ed integrità strutturale, 46 (2018) 14-24; doi: 10.3221/igf-esis.46.02 20 source df ss ms f p % of contribution a/w ratio 2 761.58 380.79 14.7 0.063 57.34 thickness (mm) 2 471.69 235.84 9.16 0.098 35.1 immersion time (days) 2 43.26 21.63 0.84 0.544 3.25 error 2 51.51 25.76 3.87 total 8 1328.04 100 table 6: anova for fracture toughness mpa m½. the main influencing factor on the fracture toughness is the a/w ratio about 57.34% because of decrement in load withstanding capacity as shown in tab. 6. the thickness of the composite contributes about 35.1% to decrease the fracture toughness. this is due to the plastic zone size with increase in thickness [24]. and immersion time of 3.25% contributes to fracture toughness. it shows toughness alters very least by immersing the composite in sea water. the error of 3.87 % is due to fabrication defects. experimental validation by linear regressions o obtain the relationship between the load carrying capacity /fracture toughness and different parameter such as a/w ratio, width and thickness in general and a/w ratio, thickness and immersion time for seawater treatment, mathematical equations were developed. the regression coefficients in a mathematical model are estimated experimental responding. to investigation of these models, experiments are executed by taking an arbitrary combination of factor and matched with the predicted values. these mathematical equations with different control were obtained using statistical software minitab [25]. mathematical equations for ent test load carrying capacity: 246500 a+ 30.9 t+ 1.67 i (1) fracture toughness: 31.5 + 72.1 a – 1.12 t + 0.133i … .. (2) mathematical equations for senb test load carrying capacity: 395550 a + 47.2 t – 1.19 i .... (3) fracture toughness: 92.2 + 111 a – 3.25 t – 022 i …. (4) where, a= a/w ratio t= thickness (mm) i= immersion time (days) experimental validation of ent test he comparison of load carrying capacity/fracture toughness from the mathematical model developed in the present work with values obtained experimentally. the tab. 7 and tab. 8 show the percentage of error from the experimental t t g. b. manjunatha et alii, frattura ed integrità strutturale, 46 (2018) 14-24; doi: 10.3221/igf-esis.46.02 21 value corresponding predicted values for tests under sea water immersion. the difference in error for load carrying capacity is varies from 0.45 to 8.36%. and the fracture toughness varies from 1.46 to 7.49%. factor combination (a/w, thickness mm, immersion time) experimental load (n) predicted load (n) % error 0.3, 7mm, 7days 351.106 323.99 8.36 0.4, 10mm, 14days 376.66 378.38 0.45 0.5, 12mm, 21days 375.55 401 6.77 table 7: confirmation test table for load carrying capacity (n). factor combination (a/w, thickness mm, immersion time) experimental load (n) predicted load (n) % error 0.3, 7mm, 7days 49.59 46.22 7.29 0.4, 10mm, 14days 51.75 51.00 1.46 0.5, 12mm, 21days 52.98 59.90 7.39 table 8: confirmation test table for fracture toughness mpa m½. experimental validation of senb test imilarly, tab. 9 shows the senb test for load carrying capacity under sea water immersion that difference in error varies from 3.33 to 8.27%. and the fracture toughness varies from 0.6 to 1% is as shown in tab.10. factor combination (a/w, thickness mm, immersion time) experimental load (n) predicted load (n) % error 0.3, 7mm, 7days 597.77 552.07 8.27 0.4, 10mm, 14days 609.99 630.34 3.33 0.5, 12mm, 21days 635.55 661.41 4.06 table 9: confirmation test table for load carrying capacity (n). factor combination (a/w, thickness mm, immersion time) experimental load (n) predicted load (n) % error 0.3, 7mm, 7days 102.16 101.15 1 0.4, 10mm, 14days 100.18 100.91 0.8 0.5, 12mm, 21days 103.31 103.91 0.6 table 10: confirmation test table for fracture toughness mpa m½. s g. b. manjunatha et alii, frattura ed integrità strutturale, 46 (2018) 14-24; doi: 10.3221/igf-esis.46.02 22 response surface methodology he influence of fracture parameters on a/w, thickness and immersion time can be analysed by using a 3-d response graph. these response surface graphs are drawn from varying two parameters over the load and fracture toughness [26]. (a) (b) (c) (d) figure 5: rsm graphs of different control factors v/s load and fracture toughness of ent test (a) (b) (c) (d) figure 6: rsm graphs of different control factors v/s load and fracture toughness of senb test. t g. b. manjunatha et alii, frattura ed integrità strutturale, 46 (2018) 14-24; doi: 10.3221/igf-esis.46.02 23 surface plot of load carrying capacity/ facture toughness vs. a/w ratio, thickness and immersion time is shown in fig.5. & fig.6 for both ent and senb test. the figures clearly describe load carrying capacity increases on the thickness and decreases on a/w ratio. it also notices that the load initially decreased and then increases with immersion time in both ent and senb. the fracture toughness decreases in thickness, increases on a/w ratio and initially decreases and then increases with immersion time in both ent and senb. the behaviour of the materials, which were treated with sea water environment, is noticed that, as the duration of immersion increases, fracture toughness also increased for all other control factors. it is observed that specimens with sea water treatment yielded a higher value of fracture toughness. conclusions ailure analysis of jute fiber reinforced composites has been made experimentally; the parameters such as load carrying capacity and fracture toughness have been identified for different control factors like a/w ratio and thickness. the effect of seawater immersion on this composite has evaluated. taguchi method can be applied to experimental results using an l9 orthogonal array. based on the results following conclusions were derived.  the load carrying capacity increases with thickness and decreases with a/w ratio, but the facture toughness increases with a/w and decreases with a thickness in both ent and senb respectively.  the percentage of contribution of the thickness of 71.57% and an a/w ratio of 21.39% of load carrying capacity, a/w ratio of 74.5% and thickness of 35.1% on fracture toughness in ent specimen.  the composite specimen immersed in seawater has little influence on its (4.8 %, 2.19%) load carrying capacity and (2.7%, 3.87%) fracture toughness on both ent and senb respectively.  the experimental validation with the predicted result shows the error of less than 10% is acceptable.  rsm graph shows the variation of fracture mechanics parameters with control factors.  these results highlight that the jute fibres may be considered as a possible alternative material could be used in the manufacturing of a boat. references [1] khan, r. a. et al. (2011). comparative studies of mechanical and interfacial properties between jute fiber/pvc and e-glass fiber/pvc composites, polymer-plastics technology and engineering, 50(2), pp. 153–159. doi: 10.1080/03602559.2010.531422. [2] silva, r. v. et al. (2009) ‘curaua/glass hybrid composite: the effect of water aging on the mechanical properties’, journal of reinforced plastics and composites, 28(15), pp. 1857–1868. doi: 10.1177/0731684408090373. [3] akil, h. m. et al. (2009). water absorption study on pultruded jute fibre reinforced unsaturated polyester composites, composites science and technology 69(11–12), pp. 1942–1948. doi: 10.1016/j.compscitech.2009.04.014. [4] davidson, b. d., soffa, m. a. and kumar, m. (2008). temperature and moisture effects in a particulate interlayered composite: mode i data reduction and toughness, journal of reinforced plastics and composites, 28(17), pp. 2049– 2068. doi: 10.1177/0731684408090844. [5] ni, q.-q. (2005). a method to evaluate interfacial fracture energy on a fibre/ matrix interface, proceedings of the institution of mechanical engineers, part l: journal of materials: design and applications, 219(2), pp. 77–83. doi: 10.1243/146442005x10274. [6] brunner, a. j., blackman, b. r. k. and davies, p. (2008). a status report on delamination resistance testing of polymermatrix composites, engineering fracture mechanics, 75(9), pp. 2779–2794. doi: 10.1016/j.engfracmech.2007.03.012. [7] kaman, m. o. (2011). effect of fiber orientation on fracture toughness of laminated composite plates [0??/????]s, engineering fracture mechanics. elsevier ltd, 78(13), pp. 2521–2534. doi: 10.1016/j.engfracmech.2011.06.005. [8] grau, d. l. (2006). relation between interfacial fracture toughness and mode-mixity in honeycomb core sandwich composites, journal of sandwich structures and materials, 8(3), pp. 187–203. doi: 10.1177/1099636206061774. [9] society, m. p.. from the sage social science collections . all rights reserved , social science. [10] mikovic, j. and velickovic, s. (2014). application of taguchi methods in testing tensile strength of polyethylene, 8th f g. b. manjunatha et alii, frattura ed integrità strutturale, 46 (2018) 14-24; doi: 10.3221/igf-esis.46.02 24 international quality conference, pp. 575–582. [11] vidal, c. et al..application of taguchi method in the optimization of friction stir welding. [12] kondapalli, s. p., chalamalasetti, s. r. and damera, n. r. (2013). application of taguchi based design of experiments to fusion arc weld processes: a review, international journal of technology and management, 2(1), pp. 1–8. [13] arun, k. v., basavarajappa, s. and sherigara, b. s. (2010). damage characterisation of glass/textile fabric polymer hybrid composites in sea water environment, materials and design. elsevier ltd, 31(2), pp. 930–939. doi: 10.1016/j.matdes.2009.07.029. [14] m.s. sham prasad, c.s. venkatesha, t. j. (2011). experimental methods of determining fracture toughness of fiber reinforced polymer composites under various loading conditions, journal of minerals & materials characterization & engineering, 10(13), pp. 1263–1275. doi: 10.4236/jmmce.2011.1013099. [15] manjunath g. b, bharath k. n, vijaykumar, t. n. (2015). optimization of notch parameter on fracture toughness of natural fiber reinforced composites using taguchi method. journal of materials science & surface engineering, 3 (2), pp 244-248. [16] thirumavalavan, k., karunamoorthy, l. and padmanabhan, k. a. (2014). optimization of process parameters using taguchi technique in severe surface mechanical treatment of aa6061, 6(2), pp. 1026–1032. [17] jenarthanan, m. p. and jeyapaul, r. (2013). optimisation of machining parameters on milling of gfrp composites by desirability function analysis using taguchi method, international journal of engineering, science and technology, 5(4), pp. 23–36. [18] du, y., yan, n. and kortschot, m. t. (2014). the use of ramie fibers as reinforcements in composites, biofiber reinforcements in composite materials. doi: 10.1533/9781782421276.1.104 [19] directorate, m. and base, w.a.f. (1997) 58(1), pp. 87-96. [20] low, i. m. et al. (2007). mechanical and fracture properties of cellulose-fibre-reinforced epoxy laminates, composites part a: applied science and manufacturing, 38(3), pp. 963–974. doi: 10.1016/j.compositesa.2006.06.019. [21] deo, c. and acharya, s. k. (2010). effect of moisture absorption on mechanical properties of chopped natural fiber reinforced epoxy composite, journal of reinforced plastics and composites, 29(16), pp. 2513–2521. doi: 10.1177/0731684409353352 [22] gope, p. c. and rao, d. k. (2014). fracture behaviour of epoxy biocomposite reinforced with short coconut fibres (cocos nucifera) and walnut particles (juglans regia l.), journal of thermoplastic composite materials, pp. 1–20. doi: 10.1177/0892705714556835. [23] siriruk, a., penumadu, d. and jack weitsman, y. (2009). effect of sea environment on interfacial delamination behavior of polymeric sandwich structures, composites science and technology, 69(6), pp. 821–828. doi: 10.1016/j.compscitech.2008.02.033. [24] mata, f. and beamud, e. m. (2010). response surface methodology ( rsm ) analysis approach to model experimental data of machining of plastic composites, xviii congreso nacional de ingeniería mecánica. [25] manjunath, g. b. et al. (2017). anova and response surface methodology for the optimization of fracture toughness parameters on jute fabric-epoxy composites using senb specimens, materials today: proceedings. elsevier ltd, 4(10), pp. 11285–11291. doi: 10.1016/j.matpr.2017.09.052. [26] govindaraju, r. et al. 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can be opened with acrobat and adobe reader 5.0 and later.) >> /namespace [ (adobe) (common) (1.0) ] /othernamespaces [ << /asreaderspreads false /cropimagestoframes true /errorcontrol /warnandcontinue /flattenerignorespreadoverrides false /includeguidesgrids false /includenonprinting false /includeslug false /namespace [ (adobe) (indesign) (4.0) ] /omitplacedbitmaps false /omitplacedeps false /omitplacedpdf false /simulateoverprint /legacy >> << /addbleedmarks false /addcolorbars false /addcropmarks false /addpageinfo false /addregmarks false /convertcolors /converttocmyk /destinationprofilename () /destinationprofileselector /documentcmyk /downsample16bitimages true /flattenerpreset << /presetselector /mediumresolution >> /formelements false /generatestructure false /includebookmarks false /includehyperlinks false /includeinteractive false /includelayers false /includeprofiles false /multimediahandling /useobjectsettings /namespace [ (adobe) (creativesuite) (2.0) ] /pdfxoutputintentprofileselector /documentcmyk /preserveediting true /untaggedcmykhandling /leaveuntagged /untaggedrgbhandling /usedocumentprofile /usedocumentbleed false >> ] >> setdistillerparams << /hwresolution [2400 2400] /pagesize [612.000 792.000] >> setpagedevice microsoft word numero_55_art_17_2940 f. hamadouche et alii, frattura ed integrità strutturale, 55 (2021) 228-240; doi: 10.3221/igf-esis.55.17 228 influence of contact parameters in fretting-fatigue contact 3d problems fella hamadouche, habib benzaama, mohamed mokhtari laboratory of biomechanics and biomaterials,national polytechnic school of oran enpo, algeria fella.ham@hotmail.fr ,http://orcid.org/0000-0002-5306-0336 habib.benzaama@enp-oran, mokhtarimohamed44@yahoo.fr miloud abbes tahar laboratory of mechanical and energy, university of hassiba benbouali, chlef, algeria taharabbes@yahoo.fr abstract. a numerical study on the influence of contact parameters on fretting fatigue behavior is carried out by using a new method sfem (stretching finite element method) is presented in this article. several parameters are made to vary: geometric shapes of the mesh, materials and contact parameters. the three-dimensional parametric model is composed by specimen and a pad in full contact. a fortran code is used to generate the parametric mesh. the stress intensity factors are calculated by varying the above contact parameters and the stress intensity factor under modes 1, 2 and 3 are computed. keywords. fretting fatigue; finite element method; 3 dimensions; crack and the stress intensity factors. citation: hamadouche, f., benzaama, h., mokhtari, m., abbes tahar, m., influence of contact parameters in fretting-fatigue contact 3d problems, frattura ed integrità strutturale, 55 (2021) 228-240. received: 20.10.2020 accepted: 13.12.2020 published: 01.01.2021 copyright: © 2021 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. introduction retting occurs when two bodies are in contact, where a load presses these two bodies together [1]. a damage process is created between them. fatigue is a phenomenon that occurs when a metal component is subjected to variable loads over time and after a given number of loading, a crack can initiate and grow until the component reaches breaking point [2]. fatigue can occur when there are parts in contact, called fretting fatigue [2]. this phenomenon may occur in several mechanical connections such as the turbines, bearing; steel cables etc. fretting fatigue can reduce the lifetime of a component compared with plane fatigue [4]. many researchers use the fretting fatigue models to understand the details of fretting fatigue and to classify the importance of the design parameters involved in this phenomenon [5]. in recent years, a major effort has been made to study the phenomenon of fretting fatigue. nowell et al. [6] describes a series of fretting fatigue experiments carried out under closely controlled conditions of partial slip. ochi et al. [7] investigated the effect of contact pressure and slip amplitude on fretting fatigue behaviour of rail steel with fishplate: the results shows that the fretting fatigue strength decrease with increasing the contact pressure and the pad length. tesh et al. [8] investigated the titanium alloy ti-6al-4v behaviour in fretting fatigue using a sphere on flat contact, to study the influence of microstructure and f https://youtu.be/4mj21xdc0-0 f. hamadouche et alii, frattura ed integrità strutturale, 55 (2021) 228-240; doi: 10.3221/igf-esis.55.17 229 contact condition. kond et al. [9] proposed a local stress concept to evaluate the fretting fatigue limit for contact edge cracks. ciavarella et al. [10] solved the contact problem compared with plain of fatigue for a flat punch having rounded corners under condition of normal loading and a shearing force. heung et al. [11] proposed hybrid layer method to examine the effect of finite width of contact finite on fretting fatigue according to this method traction distribution obtained from the coarse finite element three-dimensional analyses was used in two-dimensional plane strain finite element model to increase computational efficiency. kataoka et al. [12] study the effect of contact conditions on growth of small crack in fretting fatigue. juoksukangas et al. [13] compared the effect of both round contact edge and the sharp contact edge on fretting fatigue behavior of a complete contact using the finely multi-axial criterion and the theory of criterion distance to calculate the cracking. in another work [14] they compared between the measured displacement from digital image correlation and the computed displacements of corresponding finite elements method, where the displacement field and its derivate were compared using the friction coefficient as a variable in the numerical model. eugenio et al. [23] use the finite element method (fem ), the extended finite element method (xfem) and a simple experimental to predicted crack propagation direction and path on fretting fatigue in complete contact condition. noraphaiphipaksa et al. [15] used the maximum shear stress range criterion, the maximum relative slip amplitude and the maximum tangential stress range criterion to predict the location of fretting fatigue crack nucleation and the fretting fatigue crack path with cylindrical-onflat contact. in addition, using the effective stress intensity factor range estimated the fretting fatigue lives. in the same year, tongyan et al. [16] explained the effects of roughness on fretting fatigue. they indicate that the higher roughness of surface reduces the life of fretting fatigue. rodrigo et al. [24] studied the behavior of two cables (1350-h19 aluminum) in contact; subjected to the phenomenon of fretting fatigue using a numerical method such as a 3d finite element model, they also used an experimental method on the mts3222.21 machine. kyvia et al. [25] published a very interesting article on aspects of fretting fatigue, based on the experiences, analyzes and research of researchers in this field. he was able to present an article to fully understand the parameters that relate to fretting fatigue such as cylindrical contact, crack nucleation, crack propagation, and fretting fatigue modeling. in this work, stress intensity factors are calculated by the abaqus code using the edi calculation [22]. fortran program allows to create a parametric mesh using the stretching finite element method sfem [18]. this mesh permits to change various model parameters, such as the applied load, mesh sizes, the shape and the dimensions of the crack as well as the contact parameters. the problem is solved by the abaqus computer code to determine the main crack parameter, the stress intensity factor k, and its influence on fretting fatigue behavior. fretting fatigue contact type s fig. 1 shows, the contact types can be classified depending on the geometry of the contacting bodies [17]. the first type is plan/plan contact (fig. 1a) or the complete contact witch a flat contact surface is used for fretting pad [17]. this type produces contact area that is independent of load. complete contact condition necessarily has singularities at its outside edges [18], where the stress is theoretically infinite, hence, plastic deformation is expected to occur at the pad edge. fig. 2 presents the model utilized in this investigation; it clarifies the surface contact formed between the specimen and pad, the crack position and loads applied in two bodies. the second type is incomplete contact (fig. 1b and 1c) where at least of the two bodies is cylinder or spherical, which produces a contact area whose size depends on the magnitude the normal force magnitude [18]. figure 1: different types of contacts according to the bodies geometry: (a) plan/plan contact, (b) sphere/plan contact, c) cylinder /plan contact the stress intensity factor is determined by considering the displacements and stress field near the crack front. it describes the stress state at crack tip. historically, stress intensity factors k have been obtained from elastic solutions by considering 3d problems, under plain stress/strain condition. in the case of finite dimensional structure, ik (i = 1, 2 and 3 for mode 1, 2 and3) can be expressed in the following general form: a (a) (b) (c) f. hamadouche et alii, frattura ed integrità strutturale, 55 (2021) 228-240; doi: 10.3221/igf-esis.55.17 230   a    i ifk (1) where  if is the stress correction factor or form factor, taking into account the geometry of the crack as well as the type of stress applied on the structure, σ is the applied stress, and a is the crack length or the crack depth [20]. figure 2: specimen and pad in complete contact equivalent domain integral (edi) he integral j is a measure of variation of potential energy, which in linear elasticity, can be directly related to the stress intensity factor sif [21]:      2 1 ( г) г  j ij u wdx t d x (2) w is the strain energy density, г is the contour around the end of the crack,  iu displacement vector at a point of the contour, it stress vector given by  it = ij jn . for an elastic material, this integral is identical to the rate of energy release g [19]         2 2 2 ' ' 2 i ii iii t i ii iii k k k j g g g g e e (3) where: e'=e in plane constraints (4) e'=  21 e in plane deformation (5) µ =  2 1 e is the shear modulus (6) the equivalent domain integral method use all the area a* showed in fig.3, it is well applied to solve problems of solid in 3d with crack [18]. t f. hamadouche et alii, frattura ed integrità strutturale, 55 (2021) 228-240; doi: 10.3221/igf-esis.55.17 231              1 ( )1 j ij iv u q s j s w dv f x x (7)      s s s f q s ds (8) q is a regularized virtual displacement of the points of a * in direction x1 between a maximum value in γ0 and a zero minimum value in γ1[2]. figure 3: definition of contours for the evaluation of the integral of equivalent domain (edi) stretching finite element method (sfem) he finite element method by stretching of the mesh sfem is a new method; bentahar et al. [3] have used it for a two dimensional crack propagation. using a fortran program to generate a parametric mesh, this non-remeshing method allows us to stretch the mesh elements with giving new node coordinates at each new mesh. [3]. a parametric mesh is created by using a fortran code that keeps the same number of the elements and nodes but their coordinates are changed at each new mesh parameters (mesh size, crack orientation, crack size and singularity zone size). as fig. 4 shows, this mesh is composed of the specimen and the pad, and they are exposed to two external forces σ and p, which means, the mesh is deformed during each new mesh parameters. figure 4: mesh analysis and details of the singularity zone l, loads p and σ, and limit condition for crack plane inclination α=0° in order to simulate the singularity that characterized the crack point, we use singular elements called 'quarter point' around the front of the crack, that is quadratic elements collapsed to obtain a triangular element. t f. hamadouche et alii, frattura ed integrità strutturale, 55 (2021) 228-240; doi: 10.3221/igf-esis.55.17 232 the modeling of contact with abaqus is based on the interaction of surfaces. the contact between the two bodies, specimen and pad is called an 'even contact' where a surface can interact on the other. a contact pair is defined by a slave surface (pad) which is the deformable surface, and the master surface (specimen) which is the most rigid surface, and the direction of contact is always perpendicular to this area. for each node of the slave surface, abaqus looks for the nearest point on the master surface. the interaction is then discretized between the points obtained on the master surface and the nodes of the slave surface [2]. a contact pair is defined by the commands: *contact pair, interaction=interaction-name surface-slave, surface-master [2]. numerical model parametric mesh is composed of two bodies, which are in complete contact: the specimen that contains the crack is subjected to a tensile load σ = 100 mpa, and the pad is subjected to both a small displacement oscillation and a pressure p=10 mpa.the mesh for different sizes w/t = 1.0 with t = 25 mm. tab. 1 shows different materials for the two bodies that are considered in the present study. material young modulus e (gpa) poisson coefficient ʋ brass 92 0.33 steel 220 0.29 aluminum 67.5 0.34 table 1: material properties for each case study, the friction coefficient parameters (f), the size of the mesh (h), the inclination of the plane (α), the size of the singularity zone (l) and the stress (σ) are varied according to tab. 2 above: case study no f {0.1 , 0.5, 1.0} h (mm) {8, 12, 16 } α(°) {15, 30, 45 } l (mm) {0.4, 0.5, 0.6} σ (mpa) {100, 400, 700} table 2: varied mesh parameters due to the symmetry, only half of the structure, specimen and pad, is modeled. a fortran code is used to create a parametric mesh, which allows changing the values of the shape and dimension parameters. abaqus 6.14 software is used to resolve the problem. the results of the stress intensity factor, for the three modes 1, 2 and 3, are obtained numerically from abaqus. results and discussion baqus calculates the stress intensity factor for 5 contours which are shown in fig. 5. each contour has 17 values from the integral j=1 to j=17 according to the angular division number n. we took the stress intensity factors sif values of the third contour avoiding the first contour because of the singularity where the stresses are infinite and the more we move away from the point of singularity, the more we lose in precision. only the second values and third values of the contour can give good results. a a f. hamadouche et alii, frattura ed integrità strutturale, 55 (2021) 228-240; doi: 10.3221/igf-esis.55.17 233 figure 5: the position of the 5 contours. for each contact parameter friction parameters f, mesh size h, plane inclination α, singularity zone size l, stress σ, materials steel, aluminum and brass), the results of the stress intensity factor for modes 1, 2 and 3, are represented as a function of angular division n = 17, see fig. 7, fig. 8, fig. 10, fig. 11, fig. 12. fig. 6 presents a case of analysis of the mesh of a steel material with a coefficient of friction f = 1.0, a mesh of size h = 8 mm and an inclination of the crack plane α = 45 °. the same study work is used to obtain the results of the stress intensity factors according to the values of the parameters presented in tabs. 1 and 2. figure 6: mesh analysis for f=1.0, h= 8 mm and (α=45°). coefficient of friction he effect of the coefficient of friction, ranging between 0.1 and 1.0 is investigated. fig. 7 presents three graphs for three different materials, graph a for steel, graph b for aluminum and graph c for brass. for each graph, the evolution of the intensity factors of stress ki / k0 (mode k1, k2 and k3) is presented as a function of the angular division n for different values of the friction coefficient. for the three different materials, the k1 mode has the greatest value; it is the most important mode in this study because it is considered as the most damaged mode because of the tensile force applied to the mesh. the more the coefficient of friction increase from 0.1 to 1.0, the more the value of k1 decreases. aluminum has the greatest value of k1 / k0 = 20.36 at n = 7, followed by brass with k1/ k0 = 20.28 at n = 7, and steel k1/ k0 = 19.99 at n = 6. regarding the second kii mode and for each material, its evolution as a function of the number of division n increases from n=1 to n=17, but the friction effect is weaker the same observation is made for third k3 mode. it is also observed that the value of the second mode k2 between the two points n = 1 and n = 2 is greater for aluminum and brass compared to steel. it is also noted that the first node of the zone of singularity, the value is not correct and that for the reason that this zone the constraint is infinite. t 1 2 4 5 j=1 j=17 3 crack surface f. hamadouche et alii, frattura ed integrità strutturale, 55 (2021) 228-240; doi: 10.3221/igf-esis.55.17 234 figure 7: factors ki / k0 as a function of the angular division n for different values of friction coefficient f for the three materials (a) steel, (b) aluminum, and (c) brass. effect of the mesh size n order to identify the effect of the dimensions of the mesh on the values of the stress intensity coefficients, we varied the size mesh h of the mesh for different values h = 8, 12 and 16 mm applied to the mesh as shown in the figures below. note that the other parameters f = 1.0, α = 15 °, l = 0.6 mm and σ = 100 mpa, remain unchanged. the results obtained from ki / k0 are shown in the following graphs: graph a for steel, graph b for aluminum, graph c for brass. figs. 8 presents the results of ki / k0 for a mesh height h as a function of the angular division number n for the three materials. always, k1 mode has the highest value compared to k2 and k3 mode. the evolution of the k1 mode decreases each time the size mesh h increases. while the evolution of k2 increases as a function of the angular division number n, it is proportional to the height of the cell h, but from n=11, the proportion becomes proportional. 0 2 4 6 8 10 12 14 16 18 -15 -10 -5 0 5 10 15 20 k i/ k 0 angular division n k1/k0 f=0.1 k1/k0 f=0.5 k1/k0 f=1.0 k2/k0 f=0.1 k2/k0 f=0.5 k2/k0 f=1.0 k3/k0 f=0.1 k3/k0 f=0.5 k3/k0 f=1.0 steel 0 2 4 6 8 10 12 14 16 18 -15 -10 -5 0 5 10 15 20 k i/ k 0 angular division n k1/k0 f=0.1 k1/k0 f=0.5 k1/k0 f=1.0 k2/k0 f=0.1 k2/k0 f=0.5 k2/k0 f=1.0 k3/k0 f=0.1 k3/k0 f=0.5 k3/k0 f=1.0 aluminum 0 2 4 6 8 10 12 14 16 18 -15 -10 -5 0 5 10 15 20 k i/ k 0 angular division n k1/k0 f=0.1 k1/k0 f=0.5 k1/k0 f=1.0 k2/k0 f=0.1 k2/k0 f=0.5 k2/k0 f=1.0 k3/k0 f=0.1 k3/k0 f=0.5 k3/k0 f=1.0 brass i a b c f. hamadouche et alii, frattura ed integrità strutturale, 55 (2021) 228-240; doi: 10.3221/igf-esis.55.17 235 for the evolution of the k3 mode, it is proportional to the size mesh h. for the three tests of materials, the curves show that the values of k3 increase slightly as a function of the number of angular division n between n = 2 and n = 16. aluminum has the highest value (k1=19.77, n = 7). figure 8: the factors ki/k0 as a function of the angular division n for different values of the mesh size (h), for the three materials (a) steel, (b) aluminium, and (c) brass. crack plane inclination he position of the crack plane has changed from the horizontal position to the tilt position of 15 °, 30 ° and 45 ° as presented in fig. 9. for each parameter and material, the parameters h = 8 mm, f = 1.0, l = 0.6 mm and σ = 100 mpa are kept constant during the analysis. the results obtained are presented in fig. 10. the evolution of the crack tilt parameter is presented above in figs. a, b and c for the steel, aluminum and brass. the behavior of the stress intensity factor (mode k1, k2and k3) is similar in the graphs. in the k1 mode curve, the values increase in the first points of the angular division thereafter remain constant. on the other hand, the values of k1are inversely proportional to the inclination of the crack plane from 15 ° to 45 °. 0 2 4 6 8 10 12 14 16 18 -15 -10 -5 0 5 10 15 20 k i/ k 0 angular division n k1/k0 h=8 k1/k0 h=12 k1/k0 h=16 k2/k0 h=8 k2/k0 h=12 k2/k0 h=16 k3/k0 h=8 k3/k0 h=12 k3/k0 h=16 steel 0 2 4 6 8 10 12 14 16 18 -15 -10 -5 0 5 10 15 20 k i/ k 0 angular division n k1/k0 h=8 k1/k0 h=12 k1/k0 h=16 k2/k0 h=8 k2/k0 h=12 k2/k0 h=16 k3/k0 h=8 k3/k0 h=12 k3/k0 h=16 aluminum 0 2 4 6 8 10 12 14 16 18 -15 -10 -5 0 5 10 15 20 k1/k0 h=8 k1/k0 h=12 k1/k0 h=16 k2/k0 h=8 k2/k0 h=12 k2/k0 h=16 k3/k0 h=8 k3/k0 h=12 k3/k0 h=16 k i/ k 0 angular division n brass t a b c f. hamadouche et alii, frattura ed integrità strutturale, 55 (2021) 228-240; doi: 10.3221/igf-esis.55.17 236 in the k2 mode curve, the values increase as a function of the number of angular division n, therefore we observe two parts, the first is before n = 4 or the values of k2 decrease each time the angle increases in contrast. the second part the evolution becomes proportional. the k3 mode has an inverse relationship as a function of the angle of inclination of the crack plane. note that between the three materials aluminum has the highest value of (k1/ k0 = 29.30; n=3). figure 9: mesh analysis for α=15°, α=30°and α=45°. figure 10: factors ki / k0 as a function of the angular division n for different values of crack plane inclination for the three materials (a) steel, (b) aluminum, and (c) brass. 0 2 4 6 8 10 12 14 16 18 -10 0 10 20 30 k i /k 0 angular division n k1/k0 α=15° k1/k0 α=30° k1/k0 α=45° k2/k0 α=15° k2/k0 α=30° k2/k0 α=45° k3/k0 α=15° k3/k0 α=30° k3/k0 α=45° steel 0 2 4 6 8 10 12 14 16 18 -10 0 10 20 30 k i/ k 0 angular division n k1/k0 α=15° k1/k0 α=30° k1/k0 α=45° k2/k0 α=15° k2/k0 α=30° k2/k0 α=45° k3/k0 α=15° k3/k0 α=30° k3/k0 α=45° aluminum 0 2 4 6 8 10 12 14 16 18 -10 0 10 20 30 k i/ k 0 angular division n k1/k0 α=15° k1/k0 α=30° k1/k0 α=45° k2/k0 α=15° k2/k0 α=30° k2/k0 α=45° k3/k0 α=15° k3/k0 α=30° k3/k0 α=45° brass α=15° α=30° α=45° α α α a b c f. hamadouche et alii, frattura ed integrità strutturale, 55 (2021) 228-240; doi: 10.3221/igf-esis.55.17 237 effect of the side of the singularity zone revious fig. 4 presents the singular zone dimension in the mesh; this zone is located at the front of the crack. it is represented by the dimension l considered as an important parameter to study its effect on the evolution of the stress intensity factor sif. the values of l (mm) vary as {0.4, 0.5 and 0.6} where the other parameters are fixed at h = 8 mm, f = 1.0, α = 15 ° and σ = 100 mpa. the results obtained are presented in fig. 11 for steel, aluminum and brass. figure 11: the factors ki / k0 as a function of the angular division n for different values of the side of the singularity zone l (mm) for the three materials (a) steel, (b) aluminum, and (c) brass. the results of ki / k0 concerning the effect of the singularity zone size l are presented in graphs a for steel, b for aluminum and c for brass. for each graph, the results are almost identical depending on the variation of l from 0.4 to 0.6. the evolution of k1 mode for the three materials increases for the first points as a function of the number of angular divisions in succession, it remains constant. it is observed that the mode curve k1 for the value of l = 0.6 mm is greater than l = 0.5 mm and l = 0.4 mm. that is to say the values of sif in the curve increase with the increase in the dimension of the singularity zone l. note that the greatest value is recorded for aluminum (k1/ k0 = 19.77 at n = 7 ). the values of stress intensity factor sif in the k2 mode curve for the three material tests increase with the angular division angle n. we also observe that the effect of the dimension of the zone of singularity l is not very visible, up to point n = 9 0 2 4 6 8 10 12 14 16 18 -15 -10 -5 0 5 10 15 20 k i/ k 0 angular division n k1/k0 l=0.4 k1/k0 l=0.5 k1/k0 l=0.6 k2/k0 l=0.4 k2/k0 l=0.5 k2/k0 l=0.6 k3/k0 l=0.4 k3/k0 l=0.5 k3/k0 l=0.6 steel 0 2 4 6 8 10 12 14 16 18 -15 -10 -5 0 5 10 15 20 k i/ k 0 angular division n k1/k0 l=0.4 k1/k0 l=0.5 k1/k0 l=0.6 k2/k0 l=0.4 k2/k0 l=0.5 k2/k0 l=0.6 k3/k0 l=0.4 k3/k0 l=0.5 k3/k0 l=0.6 aluminum 0 2 4 6 8 10 12 14 16 18 -15 -10 -5 0 5 10 15 20 k i/ k 0 angular division n k1/k0 l=0.4 k1/k0 l=0.5 k1/k0 l=0.6 k2/k0 l=0.4 k2/k0 l=0.5 k2/k0 l=0.6 k3/k0 l=0.4 k3/k0 l=0.5 k3/k0 l=0.6 brass p a b c f. hamadouche et alii, frattura ed integrità strutturale, 55 (2021) 228-240; doi: 10.3221/igf-esis.55.17 238 where its evolution increases each time l increases from 0.4 mm to 0.6 mm. for the third mode, the effect of the dimension of the singularity zone l on the evolution of k3 is very weak. effect of the load n this case, the effect of external forces on the evolution of the stress intensity factor sif was studied. we always note that σ is the tensile force, and p is the pressure force of the pad on the specimen and this is the force that is created by the fretting phenomenon. this force is very small compared to the tensile force, that is why we have fixed the relation between the two forces by the following relation σ = 10 p, 10 times greater. the other parameters remain constant during the three materials tests (f = 1.0, h = 8 mm, l = 0 .6 mm and α = 45 °). the results obtained are shown in fig. 12. figure 12: the factors ki / k0 as a function of the angular division n for different values of load for the three materials (a) steel, (b) aluminum, and (c) brass 0 2 4 6 8 10 12 14 16 18 -100 -50 0 50 100 150 k i/ k 0 angular division n k1/k0 σ =100 k1/k0 σ =400 k1/k0 σ =700 k2/k0 σ =100 k2/k0 σ =400 k2/k0 σ =700 k3/k0 σ =100 k3/k0 σ =400 k3/k0 σ =700 steel 0 2 4 6 8 10 12 14 16 18 -100 -50 0 50 100 150 k i/ k 0 angular division n k1/k0 σ =100 k1/k0 σ =400 k1/k0 σ =700 k2/k0 σ =100 k2/k0 σ =400 k2/k0 σ =700 k3/k0 σ =100 k3/k0 σ =400 k3/k0 σ =700 aluminum 0 2 4 6 8 10 12 14 16 18 -100 -50 0 50 100 150 k i/ k 0 angular division n k1/k0 σ=100 k1/k0 σ =400 k1/k0 σ=700 k2/k0 σ=100 k2/k0 σ=400 k2/k0 σ=700 k3/k0 σ=100 k3/k0 σ=400 k3/k0 σ=700 brass i a b c f. hamadouche et alii, frattura ed integrità strutturale, 55 (2021) 228-240; doi: 10.3221/igf-esis.55.17 239 in fig. 12 the effect of the tensile force σ on the evolution of the stress intensity factor sif in the three graphs appears clearly. these graphs show a proportional relationship between the change in mode k1 and the tensile force values σ for the three material tests the highest k1 mode value appears in the aluminum graph b (k1=138.47 at n=7). the evolution of the second mode of k2 as a function of the angular division number n is increasing. we observe two parts of the evolution on the three graphs. the first is before n = 6, where the evolution of mode k2 decreases each time the tensile force σ increase from 100 to 700 mpa. the second part is after n = 6 , where the relation becomes inverse. for mode k3 between n = 2 and n = 16, the evolution of the three curves increases as a function of the number of divisions n while the evolution as a function of the tensile force σ decreases each time the force σ increases by 100 at 700 mpa. conclusions numerical simulation of parametric mesh witch composed of two bodies in full contact is developed in this study. for that, a parametric mesh is analyzed with the abaqus 6.14 software to study the effect of the different contact parameters of fretting fatigue phenomenon. this model is subjected to two cyclic loads, the first is a tensile stress, it is applied to the specimen and the second is a perpendicular pressure on the pad. in this study, we calculated the stress intensity factor in three modes k1, k2 and k3. the results are presented on graphs, which show the evolution of the factors as a function of the angle of division n for the different parameters. from the results obtained, the parameters are divided into two groups. the first group (the size mesh h, the angle of inclination of the plane of crack α and the tensile force σ) all have a significant effect on the evolution of the stress intensity factor sif, and the second group (coefficient of friction and the dimension of the singularity zone l) have a weaker effect. through the results obtained, k1 mode shows the higher value for the three material tests and for all different parameters. it is noted that the following parameters: the size mesh h, the inclination of plane of the crack α and the coefficient of friction have an inverse effect on the evolution of mode k1. regarding the material effect, although the results obtained for the three material tests are close, aluminum is more influential on the evolution of k1 mode. we conclude that the parameters which have been applied externally (σ, h and, α) have an efficiency compared to the parameters which have been applied internally (f, l and the different materials). finally, with this sfem method we can study a large field (range) of parameters and compare several results at the same time which allows us to make a rather rich study. references [1] maslan, m.h., sheikh, m.a., arun, s. (2014). prediction of fatigue crack initiation in complete contact fretting fatigue applied mechanics and materials vol. 467. pp 431-437, trans tech publications, switzerland. doi: 10.4028/www.scientific.net/amm.467.431 [2] benzaama, h. (2008), study and modeling in 3-dimensional finite element and fretting fatigue application, phd thesis, university of scence and technologie of oran, m.b. algeria [3] bentahar, m., benzaama, h., bentoumi, m., mokhtari, m. (2017). a new automated stretching finite element method for crack propagation in two dimension journal of theoretical and applied mechanics, 55, 33. doi: 10.15632/jtam-pl.55.3.869. [4] hojjati talemi, r., abdel wahab, m., de baets, p. (2011), numerical modelling of fretting fatigue, journal of physics: conference series, 305(1), st anne's college, university of oxford, 9th international conference on damage assessment of structures (damas 2011). [5] lehtovaara, a., lönnqvist, c., & mäntylä, a. (2010). a numerical model for the calculation of fretting fatigue crack initiation for a smooth line contact. tribologia finnish journal of tribology, 29(1), 7-16. https://journal.fi/tribologia/article/view/69634. [6] nowell, d. (1988), an analysis of fretting fatigue, phd thesis, university of oxford. [7] ochi, y., hayshi, h., tateno, b., ishii, a. and kuroki, t. (1996), effects of contact pressure and slip amplitude on fretting fatigue properties of rail steel with fish plate, transactions on engineering sciences, 13, pp 6. doi: 10.2495/ld960761. a f. hamadouche et alii, frattura ed integrità strutturale, 55 (2021) 228-240; doi: 10.3221/igf-esis.55.17 240 [8] venkatesh, t.a., conner, b.p., suresh, s. et al. (2001). an experimental investigation of fretting fatigue in ti-6al-4v: the role of contact conditions and microstructure. metall and mat trans a 32, 1131–1146. doi: 10.1007/s11661-001-0124-8. [9] kondo, y., sakae, c., kubota, m., nagasue, t. ( 2004), fretting fatigue limit as a short crack problem at the edge of contact ,journal of fatigue and fracture of engineering materials and structures, 27(5), pp 361-368. doi: 10.1111/j.1460-2695.2004.00750.x. [10] ciavarella, m., demelio, g. and hills d.a. (2008), fretting fatigue problems associated with almost flat contacts. [11] heung soo, k., mall, s., ghoshal, a. ( 2010). two-dimensional and three-dimensional finite element analysis of finite contact width on fretting fatigue, materials transactions, 52(2), pp. 147-154. doi: 10.2320/matertrans.m2010268. [12] kataoka, s, ono, h, kubota, m & kondo, y. (2012). effect of contact conditions on growth of small crack in fretting fatigue, nihon kikai gakkai ronbunshu, a hen/transactions of the japan society of mechanical engineers, part a, 78(785), pp. 1-13. doi: https://doi.org/10.1299/kikaia.78.1. [13] juoksukangas, j., lehtovaara, a., mäntylä, a. (2013). the effect of contact edge geometry on fretting fatigue behavior in complete contacts, wear, 308(1–2), 206–212. doi: 10.1016/j.wear.2013.06.013. [14] juoksukangas, j., lehtovaara, a. and mäntylä, a. (2016). a comparison of relative displacement fields between numerical predictions and experimental results in fretting contact, proc. imeche, part j: j. engineering tribology, 230(10), 1273–1287. doi: 10.1177/1350650116633573 [15] noraphaiphipaksa, n., manonukul, a., kanchanomai, c. (2017). fretting fatigue with cylindrical-on-flat contact:crack nucleation, crack path and fatigue life, materials, 10, 155, doi:10.3390/ma10020155. [16] yue, t., abdel wahab, m. (2017), roughness effects on fretting fatigue, iop conf. series: journal of physics: conf. series 843 (2017) 012056, porto, portugal, 6th international conference on fracture fatigue and wear. [17] haidir maslan, m. (2015), development of predictive finite element models for complete contact fretting fatigue , phd thesis, the faculty of engineering and physical sciences, school of mechanical, aerospace and civil engineering, university of manchester. [18] benzaama, h., giner, e., elachachi, b. (2007). a 3d finite element modelling of semi-elliptical inclined cracks under fretting fatigue conditions, proceeding of the international conférence on modeling and simulation. algiers, algeria. [19] saidi, h. ouled ahmed, m. (2006), calculation of the stress intensity factor by abaqus for a central crack and an emerging crack, master thesis, university saad dahlab blida, algeria. [20] delvallee, i. (1999). harmfulness of a semi-elliptical defect of complex orientation in a closed cylindrical shell subjected to internal pressure, phd thesis, university of science and technology of lille 1, ufr of mathematics. https://ori-nuxeo.univ-lille1.fr/nuxeo/site/esupversions/d07db432-cc59-457d-ac18-20077598a6c2 [21] lalonde, s. (2008). modeling of crack propagation in gears by the boundary element method, master in mechanical engineering thesis, higher technology school, montérial https://espace.etsmtl.ca/id/eprint/108/4/lalonde_s%c3%a9bastien-web.pdf [22] shivakumar, k. n. and raju, i. s. (1992), an equivalent domain integral method for three-dimensional mixed-mode fracture problems, engineering fracture mechanics, 42(6), pp. 935-959. doi:10.1016/0013-7944(92)90134-z [23] giner, e., díaz-álvarez, j., marco, m., miguélez, m.h., (2015). orientation of propagating crack paths emanating from fretting-fatigue contact problems. frat. ed integrità strutt. 10, 285–294. doi: 10.3221/igf-esis.35.33. [24] pereira, r.l., díaz, j.i.m., ferreira, j.l.a., da silva, c.r.m., araújo, j.a. (2020). numerical and experimental analysis of fretting fatigue performance of the 1350-h19 aluminum alloy. j. braz. soc. mech. sci. eng. 42, 419. doi: 10.1007/s40430-020-02498-w [25] pereira, k., v. vanegas-useche, l., abdel wahab, m., 2020. aspects of fretting fatigue finite element modelling. comput. mater. contin. 64, 97–144. doi: 10.32604/cmc.2020.09862 microsoft word numero_50_art_1_2293 o. plekhov et alii, frattura ed integrità strutturale, 50 (2019) 1-8; doi: 10.3221/igf-esis.50.01 1 focused on new trends in fatigue and fracture the effect of fatigue crack rate on the heat dissipation in metals under mixed-mode loading oleg plekhov institute of continuous media mechanics of the ural branch of russian academy of science, perm, russia poa@icmm.ru aleksei vshivkov institute of continuous media mechanics of the ural branch of russian academy of science, perm, russia vshivkov.a@icmm.ru abstract. the study of energy balance at crack tip could give comprehensive information for estimation of durability and reliability cracked construction under cyclic loading. the first step for estimation energy balance is monitoring of dissipated part of energy (heat generation). one of the most effective techniques for investigation of temperature evolution on the surface of deformed body is infrared thermography. the work is devoted to the experimental study of energy dissipation in cracked samples made of titanium grade 2 under multiaxial cyclic loading. to explain the experimentally obtained correlation between fatigue crack rate and power of heat dissipation we developed a phenomenological model describing the evolution of plastic work at the crack tip under arbitrary loading. the theoretical and experimental data about heat dissipation exhibit a good quantitative agreement. keywords. energy dissipation; crack propagation; infrared thermography; mixed-mode loading. citation: plekhov, o., vshivkov, a., the effect of fatigue crack rate on the heat dissipation in metals under mix mode loading, frattura ed integrità strutturale, 50 (2019) 1-8. received: 26.12.2018 accepted: 08.07.2019 published: 01.10.2019 copyright: © 2019 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. introduction he most frequently used technique for estimation of lifetime of cracked samples is based on the correlation between stress intensity factor and fatigue crack rate (paris` law). paris law is results treatment of many experimental data in framework of elastic solution of crack propagation problem. as a consequence, this law doesn`t explain the physical nature of the process of crack propagation in metals and initiates a lot of scientific discussions and attempts to derive alternative description of crack propagation law. such alternative laws of crack propagation were proposed by many authors based on correlations of the fatigue crack growth rate and mechanical-structural parameters describing the failure process at crack tip. for instance, the intensity of plastic t http://www.gruppofrattura.it/va/50/2293.mp4 o. plekhov et alii, frattura ed integrità strutturale, 50 (2019) 1-8; doi: 10.3221/igf-esis.50.01 2 deformation, the rise integral, the sizes of plastic deformation zone at crack tip, the dissipated energy were used as the crack propagation control parameters [1-4]. to derive a crack propagation law valid for arbitrary loading conditions we have to consider an energy concept of crack propagation. the current state of development of experimental mechanics allows one to monitor the dissipated part of energy with very high precision using infrared thermography [5-7]. the main problem of application of thermography technique is caused by the uncertainty of the solution to the inverse thermal problem [8]. few years ago, we proposed an effective chip solution for the problem. we developed an additional system for direct monitoring of a heat flow [9]. to treat the experimental data we need a simple description of elasto-plastic deformation in process zone valid for arbitrary (multiaxial) loading conditions. following by idea [10], we proposed a model of energy dissipation at crack tip. the key point of this approach is a hypothesis of the link between the elastic and elasto-plastic solutions at the fatigue crack tip proposed by dixon [11]. in the framework of the model we divided the dissipated energy into two parts corresponding to reversible (cyclic) and monotonic plastic zones. analysis of this approximation has shown zero effect of fatigue crack advance on the energy dissipation into cyclic plastic zone. this dissipation is a function of spatial size of a cyclic plastic zone and characteristic size of the yield surface. under isotropic hardening, the change of the applied stress amplitude leads to the change of characteristic size of the yield surface and, as consequence, to the heat dissipation at constant crack rate. the dissipation in monotonic plastic zone is a function of both crack rate and characteristic size of the yield surface. this part of the model gives correlation between fatigue crack rate and power of heat dissipation [4,7]. the previous authors’ investigations were focused on crack growth problems under an opening or mode i mechanism [9] and a relationship was proposed for the growth rate of a fatigue crack based on an analysis of the energy balance at its tip. however, most structures are failed due to mixed mode loading. many uniaxial loaded materials, structures and components often contain randomly oriented defects and cracks which develop a mixed mode state by rotation of their orientation with respect to the loading axis. for example mixed mode i/ii cyclic deformation at the tip of a short kinked inclined crack with frictional surfaces as discussed in the following [12-15]. in this work, we verify the main hypothesis used for our phenomenological description of fatigue crack propagation law and verify the approach for fatigue cracks titanium grade 2 samples subject to the multiaxial cyclic loading. energy dissipation at the crack tip under cyclic loading n the previous work [9] we obtained the relation to calculate the energy of plastic deformation as a consequence, energy dissipation at fatigue crack tip:    2 21 2 ,totp dau w a w a dn    (1) where aτ– stress amplitude. terms in eqn. (1) correspond to reversible (cyclic) and monotonic plastic zones. analysis of this approximation has shown that energy dissipation in a cyclic plastic zone is independent of crack growth. this dissipation is fully determined by the spatial size of a cyclic plastic zone and the characteristic diameter of the yield surface. for isotropic hardening materials, the change of the applied stress amplitude leads to the change in the characteristic diameter of the yield surface and, as consequence, to the energy dissipation at a constant crack rate. dissipation in the monotonic plastic zone is a function of both crack rate and characteristic diameter of the yield surface. it was shown by short [1], that crack growth can be determined by heat generation: pda w dn j      (2) where wp hysteresis energy rate, φ heat generation rate, j fracture energy added to v per unit crack advance, γ fracture energy required per unit crack advance (original notation are used). we can write the equation for heat generation from (2): i o. plekhov et alii, frattura ed integrità strutturale, 50 (2019) 1-8; doi: 10.3221/igf-esis.50.01 3  p daw j dn      (3) in the general case, eqns. (1) and (3) are same. the calculation of analytical relations for w1, w2 can be carried out similarly to the monotonic loading. it allows us to predict the existence of peculiarities of energy dissipation at the crack tip reported in [17] for multiaxial loading. thus, we have an analytical equation for calculating heat generation, obtained in two different ways. the relation (1) obtained based on dixon’s hypothesis (eqn. (4)) [11] about relation between elastic and plastic deformation. 1 2 ij , ef el ij s e e          (4) where 𝐸– the young’s modulus, 𝐸 secant plasticity modulus. numerical simulation of strain field at the crack tip he check an applicability of dixon’s hypothesis (eqn. (1)) about relation between elastic and plastic deformation was carried out by numerical simulation of strain field at the crack tip. there was considered a two-dimensional model of biaxial loading. half of a sample with symmetry of inner boundary was studied. in calculation the plane strain assumption was adopted. a square grid with a concentration in the region near the crack tip was used. an element size at crack tip was up to 5e-6 m. to describe plastic deformation the isotropic hardening function was used which was obtained from the approximation of experimental data. the applied load corresponds to the experimental values. a crack path was taken from the digital image correlation data. the system of equations for modeling of a strain field near the crack tip has the following form:   σ 0 , (5)  : p σ с ε ε , (6) 1 2 t     ε u u , (7) p f    ε σ , (8) where σ – stress, ε – strain, u – displacement, λ – hardening parameter, f=σm-σys, σys=σys0+ σh(εpe), σh(εpe) hardening function. a numerical simulation of plastic deformation near the crack tip has been carried out. the estimation of the plastic strain field was carried out using the elastic solution and the eqn. (4) for the strain components ε11, ε12, ε22, maximum shear strain γ, effective plastic deformation εpe:         1/2 2 222 3 2 2 2 11 22 11 33 33 22 12 13 233 2 pe                        . (9) numerical and theoretical calculations were made for four biaxial coefficients (η = 0, 0.5, 0.7, 1). the characteristic distributions of normal to the crack path strain component and second strain invariant are shown in figs. 1, 2. to compare the theoretical and calculated results, point-by-point error was calculated for different strain levels corresponded to the applied load (fig. 3). the loading levels correspond to the crack growth rate 1e-8 1e-3m/cycle. t o. plekhov et alii, frattura ed integrità strutturale, 50 (2019) 1-8; doi: 10.3221/igf-esis.50.01 4 (a) (b) figure 1: plastic strain (η=0, component ε22): (a) numerical simulation; (b) analytic solution by eqn. (4). (a) (b) figure 2: plastic strain (η=1, component εi): (a) numerical simulation; (b) analytic solution by eqn. (4). the analysis of data presented in fig. 3 allows us to conclude that the maximum relative error of eqn. (1) is less than 20 percent. as a result, we can expect qualitative description of energy dissipation process at fatigue crack based on the simple hypothesis (4). experimental study of strain field at the crack tip series of samples made of grade 2 titanium alloy were tested using servo-hydraulic biaxial testing system biss bi00-502, located in kazan scientific center of russian academy of sciences. the photo of the experimental setup is presented in fig. 4. the geometry of the samples is shown in fig. 5. during tests the samples were subjected to cyclic loading of 10 hz with constant stress amplitude, different biaxial coefficient η=px/py (1, 0.7, 0.5, 0) and stress ratio r (0.1, 0.3, 0.5). the crack length was measured by an optic method. the strain field was measured by digital image correlation method based on strainmaster system and lavision software. surface of the sample near the crack tip was polished and covered with a black matte paint before the experiment. then, the white paint was sprayed over the black paint to obtain a high contrast image. a macro lens and an elevated led lamp were used for recording of material displacement at the crack tip. to restore the deformation field at the crack tip area, each frame was subjected to additional processing: calibration to level distortions caused by distortion of the lens, motion compensation, regulation of the illumination with digital filters. the spatial resolution of the strain field near the crack tip was 3e-6 m. fig. 6 shows the characteristic result of measurements for the case of uniaxial loading. the deformation field is asymmetric due to the influence of the relative direction of the crack. fig. 7 shows the shape of the plastic area boundary and characteristic sizes which have been used for the comparison of the experimental and numerical data. tab. 1 gives a quantitative comparison of the obtained data. a o. plekhov et alii, frattura ed integrità strutturale, 50 (2019) 1-8; doi: 10.3221/igf-esis.50.01 5 (a) (b) (c) (d) figure 3: a relative error in plastic strain prediction (a) η = 0; (b) η = 0.5; (c) η =0.7; (d) η = 1. figure 4: testing machine biss bi-00-502, biaxial testing system. figure 5: geometry of samples (all sizes in millimeters). 1 2 3 4 5 6 7 load, kn 5 10 15 20 25 30 e rr o r, % 11 12 22 pe 1 2 3 4 5 6 7 load, kn 5 10 15 20 25 e rr o r, % 11 12 22 pe 1 2 3 4 5 6 7 load, kn 6 8 10 12 14 16 18 20 22 e rr o r, % 11 12 22 pe 1 2 3 4 5 6 7 load, kn 5 10 15 20 25 e rr o r, % 11 12 22 pe o. plekhov et alii, frattura ed integrità strutturale, 50 (2019) 1-8; doi: 10.3221/igf-esis.50.01 6 figure 6: measured field of strain for uniaxial loading figure 7: boundary of plastic area. numerical, mm measure, mm ab 1,20e-01 9,13e-02 ac 1,35e-02 3,13e-02 ad 1,19e-01 6,98e-02 bd 2,18e-01 1,27e-01 table 1: character size of plastic zone. figure 8: heat dissipation histories obtained under constant stress amplitude (up to 2200-th second of the test) and constant stress intensity factor (remaining time) (solid line – approximation (1), the dotted line – experimental results). figure 9: crack growth versus energy dissipation at fatigue crack tip under biaxial loading details of heat measurement during the fatigue test can be find in [9]. the eqn. (1) gives a good qualitative description of peculiarities of heat dissipation in both regimes with the constant stress amplitude and constant stress intensity factor, fig. 8. experimental works [3, 16] have shown that the rate of the stored energy has a maximum value on the initial stage of the plastic deformation. from the analysis of the energy balance, it follows that the dissipated energy during the cycle of the deformation differs from the expended energy insignificantly. we used the assumption of the proportionality of dissipated energy and plastic work. this formally corresponds a approximation of small stored energy. for constant stress amplitude the plastic work and, as a consequence, energy dissipation at the crack tip is determined by the crack growth rate as is shown [17] but for constant crack rate we can observe the regimes with the decrease of the heat dissipation caused by the decrease 1.0 0.5 0.5 1.0 1.5 1.0 0.5 0.5 1.0 0 500 1000 1500 2000 2500 3000 3500 4000 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 h e a t flu x, w time, s sensor calculate 0.01 0.02 0.03 0.04 0.05 0.06 0.07 heat dissipation, w 10-6 10-5 10-4 c ra c k r a te , m /c yc le n=1; r=0.1 ;f=7kn n=1; r=0.1 ;f=12kn n=0.5; r=0.1 ;f=10kn n=0; r=0.1 ;f=10kn n=1; r=0.5 ;f=10kn c b a d o. plekhov et alii, frattura ed integrità strutturale, 50 (2019) 1-8; doi: 10.3221/igf-esis.50.01 7 of the applied stress amplitude. the same comparison of experimental results and approximation (1) can be obtained for biaxial test (fig. 9). conclusion series of experiments was carry out. for different biaxial coefficients, the strain field at the fatigue crack tip was measured. the results of the measurements have a good agreement with numerical simulation. the theoretical calculation of plastic deformation based on the elastic solution and the secant modulus of elasticity is carried out. according to the results of calculations, the error in determining the plastic deformation through the elastic solution does not exceed 30% for each component of the strain tensor, the maximum shear strain, and the intensity of plastic deformations. this allows us to conclude that it is possible to use eqn. (4) for the theoretical calculation of the deformation field at the fatigue crack tip and the subsequent calculation of energy dissipation. an approximation for the energy dissipation at fatigue crack tip was proposed. the proposed phenomenological equation gives a good qualitative description of peculiarities of the heat dissipation. for the constant stress amplitude the plastic work and, as a consequence, energy dissipation at the crack tip is a linear function of the crack rate but for the constant crack rate mode the scenarios with a drop in the heat dissipation takes place. this approximation was confirmed by the experimental heat measurement from the crack tip under two experimental tests (constant stress amplitude and constant stress intensity factor) and different coefficients of biaxiality. acknowledgments he work was supported by the russian science foundation (grant no. 19-77-30008). references [1] matvienko, yu.g., morozov, e m. (2004). calculation of the energy j-integral for bodies with notches and cracks, international journal of fracture, 125, pp. 249-261. [2] rosakis, p., rosakis, a.j., ravichandran, g., hodowany, j. a, (2000). thermodynamic internal variable model for the partitional of plastic work into heat and stored energy in metals, j. mech. phys. solids, 48, pp. 581-607. [3] oliferuk, w., maj, m., raniecki, b. (2004). experimental analysis of energy storage rate components during tensile deformation of polycrystals, materials science and engineering, 374, pp. 77-81. [4] izyumova, a., plekhov, o. (2014). calculation of the energy j-integral in plastic zone ahead of a crack tip by infrared scanning, ffems, 37, pp. 1330–1337. [5] meneghetti, g., ricotta, m. (2016). evaluating the heat energy dissipated in a small volume surrounding the tip of a fatigue crack, international journal of fatigue, 92(2), pp. 605-615. [6] risitano, a., risitano, g. (2013). cumulative damage evaluation in multiple cycle fatigue tests taking into account energy parameter, international journal of fatigue, 48, pp. 214-222. [7] ranganathan, n., chalon, f., meo, s. (2008). some aspects of the energy based approach to fatigue crack propagation original research article, international journal of fatigue, 30, pp. 1921-1929. [8] fedorova, a.yu., bannikov, m.v., terekhina, a.i., plekhov, o.a. heat dissipation energy under fatigue based on infrared data processing (2014). quantitative infrared thermography journal, 11(1), pp. 2-9 [9] vshivkov, а., iziumova, a., bär, u., plekhov, o. (2016). experimental study of heat dissipation at the crack tip during fatigue crack propagation, frattura ed integrità strutturale, 35, pp. 131-137. [10] raju, k.n. (1972). an energy balance criterion for crack growth under fatigue loading from considerations of energy of plastic deformation, international journal of fracture mechanics, 8(1), pp. 1-14. [11] dixon, j.r. (1965). stress and strain distributions around cracks in sheet materials having various work-hardening characteristics, ministry of technology, national engineering laboratory, materials group: east kilbride, glasgow, scotland, pp. 224-244. a t o. plekhov et alii, frattura ed integrità strutturale, 50 (2019) 1-8; doi: 10.3221/igf-esis.50.01 8 [12] hammouda m.m.i., fayed a.s., sallam h.e.m. (2004). stress intensity factors of a central slant crack with frictional surfaces in plates with biaxially loading, int. j.fract, 129, pp. 141-148. [13] hammouda m.m.i., fayed a.s., sallam h.e.m. (2003). simulation of mixed mode i/ii cyclic deformation at the tip of a short kinked inclined crack with frictional surfaces. j. of fatigue, 25(8), pp. 743-753. [14] hammouda m.m.i., fayed a.s., sallam h.e.m. (2003). stress intensity factors of a shortly kinked slant central crack with frictional surfaces in uniaxially loaded plates, j. of fatigue, 25(4), pp. 283-298. [15] hammouda m.m.i., fayed a.s., sallam h.e.m. (2002). mode ii stress intensity factors for central slant cracks with frictional surfaces in uniaxially compressed plates, j. of fatigue, 24(12), pp. 1213-1222. [16] bever m.b., holt d.l., titchener a.l. (1973). the stored energy of cold work, progress in materials science, 17, pp. 5177. [17] iziumova a., vshivkov a., plekhov o. 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/hrv (za stvaranje adobe pdf dokumenata najpogodnijih za visokokvalitetni ispis prije tiskanja koristite ove postavke. stvoreni pdf dokumenti mogu se otvoriti acrobat i adobe reader 5.0 i kasnijim verzijama.) /hun 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/pdfxoutputintentprofileselector /documentcmyk /preserveediting true /untaggedcmykhandling /leaveuntagged /untaggedrgbhandling /usedocumentprofile /usedocumentbleed false >> ] >> setdistillerparams << /hwresolution [2400 2400] /pagesize [612.000 792.000] >> setpagedevice microsoft word numero_59_art_23_3219.docx o. rahim et alii, frattura ed integrità strutturale, 59 (2022) 344-358; doi: 10.3221/igf-esis.59.23 344 experimental contribution to the study of the physic-mechanical behavior and durability of high-performance concretes based on ternary binder (cement, silica fume and granulated blast furnace slag) ouahab rahim, djamel achoura materials, geomaterials and environment laboratory, department of civil engineering, badji mokhtarannaba university, p. o. box 12, 23000 annaba, algeria ouahab.rahim@univ-annaba.org, achoudj@yahoo.fr mohammed benzerara materials, geomaterials and environment laboratory, department of civil engineering, badji mokhtarannaba university, p. o. box 12, 23000 annaba, algeria université bretagne-sud, umr cnrs 6027, irdl, f-56100 lorient, france mohammed.benzerara@univ-annaba.org, mohammed.benzerara@univ-ubs.fr céline bascoulès-perlot université de pau et des pays de l'adour/e2s uppa, laboratoire des sciences de l'ingénieur appliquées à la mécanique et au génie electrique siameipra, ea4581, 64600, anglet, france celine.bascoules@univ-pau.fr abstract. high performance concrete (hpc) is an innovative concrete used widely in modern construction. new techniques of formulating and designing hpc have made it possible to obtain remarkable mechanical performance and durability compared to the conventional concrete. the main advantages of hpc are related to its low porosity, very high mechanical resistance, and excellent durability. the ease of hpc application is obtained by the combined use of superplasticizer and mineral addition, which results in a significant increase in the compressive strength while improving workability and durability. the algerian steel industry in north africa generates very large quantities of slag which are currently little or not used for the formulation of hydraulic binders in the field of construction materials. in the current economic climate, research on high-performance concretes in algeria is mainly focused on their formulations with a view to producing cement-based concretes composed of better strengths and more durable. the objective of this work is to optimize a formulation of hpc based on a ternary binder integrating granulated algerian blast furnace slag as a cement substitute. this can partially solve an environmental problem by recycling citation: rahim, o., achoura, d., benzerara, m., bascoulès-perlot, c., experimental contribution to the study of the physicmechanical behavior and durability of highperformance concretes based on ternary binder (cement, silica fume and granulated blast furnace slag), frattura ed integrità strutturale, 59 (2022) 344-358. received: 09.08.2021 accepted: 10.11.2021 published: 01.01.2022 copyright: © 2022 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. https://youtu.be/-xu_idapyka o. rahim et alii, frattura ed integrità strutturale, 59 (2022) 344-358; doi: 10.3221/igf-esis.59.23 345 waste and by-products from the steel industry. the manufacture of a hpc with less cement could lead to both environmental benefits thanks to a reduction in co2 emissions and financial benefits through a lower construction cost and build more sustainable structures. keywords. high performance concrete; granulated blast furnace slag; ternary binders; mechanical behaviors; durability; environment. introduction oncrete is the most widely used construction material in the world [1–3], and many types of concrete have been developed in recent years [4–7]. high performance concrete (hpc) has also been widely used in recent years because of its superior mechanical properties and excellent durability performance. by the use of the new generation of superplasticizer and the addition of mineral, the new types of hpc have a denser microstructure with very low permeability. this improves workability, increases mechanical resistance (> 60 mpa), provides increased resistance to the physicochemical attacks, and therefore improves the performance under extreme stresses and the durability under harsh environmental conditions [8–11]. the general principle for the formulation of hpc involves the improvement of compactness. this is achieved primarily by lowering the w/c ratio by a superplasticizer and adjusting the granular extent by adding ultra-fine minerals. these fillers play a dual role in concrete by increasing the compactness by filling micro-pores, on the one hand, and on the other hand providing chemical reactions with the other materials, which participate in the formation of secondary hydrates and consequently improves the resistance and durability [12]. hpcs are characterized by a marked improvement in durability performance, resulting from extremely reduced porosity. indeed, the high compactness gives them a low permeability that opposes the transfer of aggressive agents in liquid or gas phase in their mass [13]. hpcs which, are simply known as low water/cement or water/lian ratios concretes, are also economical concretes from the point of view of the initial cost because it is possible to build an equivalent structure with less formwork, less concrete to be placed and less reinforcements [14,15]. although several research works have been carried out on hpc durability, this work is essentially focused on basic constituents (binder, aggregate, and superplasticizer), and in particular mineral additions. the use of a ternary binder (cement, silica fume, and granulated slag) is one of the recent areas of research, which aims to improve hpc durability and mechanical behavior, and minimize the negative environmental impacts. cementitious materials made of ternary binders can in fact exhibit superior performance to those based on binary binders in terms of heat release, mechanical resistance at early ages, and durability [16,17]. several research studies have reported that the incorporation of silica fume combined with other mineral additions (pozzolan, blast furnace slag, or fly ash) in the cement matrix improves the mechanical properties and the durability of hpc [18,19]. nowadays, reducing the environmental impacts of waste materials such as slag and fly ash is inevitable and must go through innovative constructive solutions. development of different concretes based on binary or ternary binders composed of waste materials other than clinker, such as blast furnace slag or fly ash, etc., not only ensures mechanical performance and proper durability in the short and long term but also provides ecological and economic benefits [20]. the incorporation of industrial by-products in the form of mineral additions in concrete makes it possible to reduce the consumption of cement and therefore reduce e co2 emissions, which presents a significant environmental advantage [21]. the granulated slag, as a fine-grained powder, possess several interesting properties such as chemical composition which is close to that of cement, regularity of composition for the same production source and latent reactivity activated in the presence of portland cement. granulated slag is an additive commonly used in the manufacturing of different types of cements [22–24]. the properties of ground granulated blast furnace slag, specifically its low water absorption rate by the smooth surfaces of the granulated slag grains, work together to improve the workability of hpc over ordinary portland cement concrete [22,25– 27]. c o. rahim et alii, frattura ed integrità strutturale, 59 (2022) 344-358; doi: 10.3221/igf-esis.59.23 346 silica fume and superplasticizer are the basic and necessary components in the formulation of an hpc. they significantly contribute to improving the mechanical strength and durability. their effects on the physical and chemical properties of concrete are due to the filling mechanism and chemical reactions in concrete. thus, the difference in particle size of the silica fume and cement contributes to the intensification of the paste through the physical effect of the filler type, which leads to more compaction and accumulation of the solid grains [15]. this research work falls within the framework of concern to take into account and protect the environment, natural resources and to fight against pollution leads to a new behavior. to this environmental concern is obviously linked an economic aspect of the use of waste and local by-products in the construction sector in north africa. algeria has a steel industry, which generates a significant amount of this waste and by-products. high performance concretes have very satisfactory intrinsic mechanical characteristics. however, several questions remain unanswered, particularly with regard to the use of a high dosage of cement without additions, the manufacture of which is associated with a high emission of co2. to overcome this environmental and economic problem, one of the solutions that can be considered is the use of granulated blast furnace slag as a partial replacement for portland cement. the objective of this work is to optimize a formulation of hpc based on a ternary binder integrating the granulated blast furnace slag from the steel complex of el-hadjar annaba (north-east of algeria), which presents a slow reactivity, as a substitute for cement in order to improve its durability and its long-term mechanical performance. the experimental work presents a study of the influence of the substitution of portland cement by granulated slag, for a fixed dosage in silica fume, on the physico-mechanical behavior and the durability of hpc. materials and methods materials he mechanical properties and durability of high performance concretes depend mainly on the quality of their constituents. the analysis of each constituent allows optimizing the amount of raw materials used in hpcs. the main constituents related to the formulation of hpcs are raw materials. cement the cement used in this study is an algerian cement (cpa-cem i / 42.5 n) (nf en197-1) from a single delivery from the cement plant (biskria ciment spa) in the town of biskra, algeria. the chemical and mineralogical compositions are given in tabs. 1 and 2 respectively. elements cao sio2 fe2o3 al2o3 k2o mgo so3 clp.a.f content (%) 57.45 18.25 3.02 4.79 0.51 2.00 3.88 0.006 table 1: chemical compositions of cement. normal consistency absolute density (g/cm3) blaine specific surface (cm2/g) 26 3.1 3900 table 2: physical characteristics of cement. ground granulated blast furnace slag the ground granulated blast furnace slag used is a by-product of the manufacturing of cast iron in steel complex of elhadjar annaba, algeria. it was obtained in the form of coarse-grained powder, and by grinding in the laboratory, with a granular extent of <80μm. (standard xp p 18-540). the chemical compositions and physical characteristics of the ground granulated blast furnace slag are shown in tabs. 3 and 4 respectively. elements cao sio2 fe2o3 al2o3 k2o na2o mgo so3 clp.a.f content (%) 41.63 38.81 3.31 8.39 0.740 0.14 4.14 0.38 0.00 table 3: chemical compositions of ground granulated blast furnace slag. t o. rahim et alii, frattura ed integrità strutturale, 59 (2022) 344-358; doi: 10.3221/igf-esis.59.23 347 absolute density (g/cm3) apparent volumetric mass (g/cm3) blaine specific surface (cm2/g) 2.89 1.19 4800 table 4: physical characteristics of ground granulated blast furnace slag. silica fume the silica fume used in this work was a very fine-grained powder of grey color supplied by the granitex company in algeria. the average grain diameter of the used silica fume was around 0.1μm. the chemical composition and physical characteristics of silica fume are shown in tabs. 5 and 6 respectively. elements cao sio2 fe2o3 al2o3 k2o na2o mgo so3 clp.a.f content (%) 0.02 96.15 0.05 0.04 1.05 0.09 0.5 0.05 0.01 table 5: chemical compositions of silica fume. absolute density (g/cm3) apparent volumetric mass (g/cm3) blaine specific surface (cm2/g) 2.24 0.5 5000 table 6: physical characteristics of silica fume. aggregates in this study, two types of crushed limestone aggregates of granular classes (3/8) and (8/15) are used from the region of guelma, algeria. two types of sand with different mineralogical nature, from the region of tebessa, algeria are used, the first is fine siliceous sand and the second quarried sand. the physical characteristics of the aggregates used are grouped in tab. 7. characteristics materials absolute density (g/cm3) fineness modulus (%) sand equivalent (%) los angeles (%) dune sand 2.61 1.60 81.30 quarry sand 2.55 3.93 78.92 gravel 8/15 2.62 19 gravel 3/8 2.62 21 table 7: physical characteristics of aggregates used. superplasticizer medaflow30 is the super plasticizer chosen in this research. it is a high-range water reducer sourced from granitex. it has a liquid form and a light brown color. it complies with standard nf en 934-2. its properties are shown in tab. 8. form color ph density chlorine content liquid light brown 6 6.5 1.07 ± 0.01 <1 g/l table 8: property of the granitex medaflow30. o. rahim et alii, frattura ed integrità strutturale, 59 (2022) 344-358; doi: 10.3221/igf-esis.59.23 348 mixing water the quality of water can also affect the mechanical properties of concrete and cementitious materials [28–32]. according to nfp 18-303, in this study tap (drinking) water was used for preparing the specimens and distilled water was used for the characterization and durability tests [31–35]. methods mix design of hpc two methods were used to optimize the formulation and mix design of hpc. the dreux-gorisse method was used to optimize the granular extent, and the hpc formulation approach from the university of sherbrook [8,36], was followed for the determination of the dosages of various constituents. the optimal composition of the five hpc mixtures is reported in tab. 9. concretes constituents unit control hpc hpc 10% slag hpc 20% slag hpc 30% slag hpc 50% slag cement kg 524 471.60 419.20 366.80 262 gravel (8/15) kg 856 856 856 856 856 gravel (3/8) kg 194 194 194 194 194 dune sand (0/2) kg 331 331 331 331 331 quarry sand (0/5) kg 272 272 272 272 272 silica fume kg 58 58 58 58 58 granulated slag kg 52.40 104.80 157.20 262 water kg 160 160 160 160 160 water/binder (%) 0.27 0.27 0.27 0.27 0.27 superplasticizer (2.2 %) kg 11.6 11.6 11.6 11.6 11.6 table 9: mix design and formulation of hpc concretes. experimental procedure he preparation of the specimens was carried out according to standard nf en 12390-1. the mixing was carried out using a concrete mixer with a capacity of 30 l. the mixing process took 5 minutes time, and the vibration was performed on a vibrating table with adjustable vibration amplitude. the abrams cone test nf en12350-2 was used to measure the workability of the mixtures. fig. 1 presents an example of workability test carried out by the abrams' cone. after 24 hours of storage in a humid chamber, the demoulded samples were stored in baths filled (saturating humidity) with distilled water (ph= 7, t = 20 ± ° c, rh = 100%). mechanical characterization was obtained by measuring the tensile strength bending 7×7×28 cm3 specimens (fig. 2), and compressive strength was performed on cubic specimens with the dimensions of 10×10×10 cm3 (fig. 3) according to standard nf en 12390-5 and nf en 12390 -3. concrete in the hardened state has a porosity, which is due to the presence of pores included in the actual texture of the hydrates and of capillaries, which develop in the structure of the grains. the durability of concrete depends primarily on the difficulty that aggressive agents have in penetrating the porous network of concrete. porosity is a determining parameter of the durability of concrete; the more the porosity decreases, the more the mechanical properties increase and the more the t o. rahim et alii, frattura ed integrità strutturale, 59 (2022) 344-358; doi: 10.3221/igf-esis.59.23 349 permeability decreases. this is why the tests for water absorption by capillarity, the porosity accessible to water and the gas permeability were carried out to evaluate the porosity of the hpcs studied. figure 1: abrams' cone test. figure 2: tensile machine, three point bending test. figure 3: machine for compression test the capillarity water absorption test was carried out according to the recommendations of afpc-afrem 1997on 360 days cured concrete specimens in the form of discs with 110 mm in diameter and 50 mm in height (fig. 4). capillary absorption measures the rate of water absorption by capillary suction of concrete specimens placed in contact with water without hydraulic pressure (fig. 5). this test consists of following by successive weighing the quantity of water absorbed by a sample previously dried at intervals of 0 min, 15 min, 30 min, 1h, 2h, 4h, 8h, and 24h. this allows indirect characterization of capillary porosity. the absorption coefficient was determined and defined by the following relationship:    mx m0 ca a (1) with: ca: absorption coefficient in kg/m2; mx: mass of the sample after absorption up to constant mass in kg; m0: mass of the sample after drying to a constant mass of 105 ± 5 ℃ in kg; a: area in m2. o. rahim et alii, frattura ed integrità strutturale, 59 (2022) 344-358; doi: 10.3221/igf-esis.59.23 350 figure 4: preparation of specimens for absorption test. figure 5: capillarity water absorption test. the accessible porosity test was carried out according to standard nf p 18-459 on 360 days cured specimens with 110 mm in diameter and 50 mm in height (fig. 6). the principle of this test is to measure the percentage of voids connected with the surface and inside the mass of the concrete. the device measures the porosity accessible to water penetration using a desiccator (fig. 7). the calculation of the porosity accessible to water is expressed as a volumetric percentage given by the following formula:        air dry air water m m m m p (2) with: mwater: hydrostatic weighing (mass in grams weighed under water; mair: weighing in the air of the water-saturated test tube; mdry: weighing in the air of the dry specimen (drying at t = 105 ° c to constant mass). figure 6: preparation of specimens for accessible porosity test. figure 7: accessible porosity test protocol. the gas permeability test was carried out using the cembureau constant charger with air as percolating neutral gas according to afpc-afrem protocol on 360 days cured specimens. the intrinsic permeability of concrete is an important indicator of durability. darcy's law describes the viscous laminar flow of a fluid in a porous medium according to a linear relationship between velocity and pressure gradient [25]. the determination of the intrinsic gas permeability consists of performing a linear regression for different points of apparent permeability measured for different applied pressures. the tools used and the experimental protocol for this test are represented in fig. 8. o. rahim et alii, frattura ed integrità strutturale, 59 (2022) 344-358; doi: 10.3221/igf-esis.59.23 351 figure 8: tools used and experimental protocol for the gas permeability test. the first step is to prepare cylindrical specimens with 110 mm in diameter and 50 mm in height. it is also necessary to check whether the gas cylinder (nitrogen) is open and the gas valve is closed. after that, place the sample with a rubber sleeve to ensure that it is sealed in a cylindrical permeable cell and contact with a grooved metal plate with the same diameter as the sample. the air chamber must be inflated to 8 bar to ensure the radial seal of the sample. to obtain the pressure value (for example: 1bar), wait for the value to stabilize, and then read the flow measurement value on the screen. repeat this application with pressures of 2 bar, 3 bar and 4 bar. use the formula of darcy's law to determine the apparent permeability for each pressure value:          atm 2 2 atm 2 q p l u a p p kgaz (3) with: q: measuring the flow of gas through the specimen; patm: the outlet atmospheric pressure; p: the applied inlet pressure; l: thickness of the test body; s: section of the test body; u: the dynamic viscosity of the gas. finally, we can draw the curve of apparent permeability versus back pressure (1/p). they intercept of the linear curve gives the value of intrinsic permeability. results and discussion the effect of the cement substitution rate by the ground granulated blast furnace slag on the sag test of high performance concretes (workability) he effect of the cement substitution rate by the ground granulated blast furnace slag in the ternary binder on the workability of hpc was studied by the abrams' cone test. the results are illustrated in fig. 9. fig. 9 shows that the workability was improved with the increase in the substitution rate of ground granulated blast furnace slag as compared to that of without granulated slag, which exhibits an improvement value of around 10.5 cm. this improvement in workability is very significant for the substitution rates of 20%, 30%, and 50%. these are confirmed by most research over the years [37–39]. this increase is mainly due to the morphological state of the ground granulated blast furnace slag which possesses grains with smooth surfaces. t o. rahim et alii, frattura ed integrità strutturale, 59 (2022) 344-358; doi: 10.3221/igf-esis.59.23 352 figure 9: workability of different hpcs mixes as a function of the substitution rate. density in the fresh state this measurement was carried out in accordance with nf en 12350-62012. a container of a known volume was filled entirely with vibrated concrete and then weighed. the effect of the cement substitution rates by the ground granulated blast furnace slag on the density is shown in fig. 10. figure 10: the density of fresh hpcs. according to fig. 10 which show the effect of the cement substitution rate with the ground granulated blast furnace slag on the density of the hpc in the fresh state, the density of the control hpc is slightly higher than that of the hpc with the addition of 10%, 20%, 30% and 50% of ground granulated blast furnace slag in partial substitution of cement. this is mainly attributed to the difference between the intrinsic densities of cement and ground granulated blast furnace slag, these confirmed by research work [38,40]. the effect of the cement substitution rate by the ground granulated blast furnace slag on the mechanical behavior of hpcs studied tensile strength by three-point bending (at 28 days) the influence of the rate of substitution of cement by the ground granulated blast furnace slag on the flexural strength was studied by performing the test on prismatic specimens with the dimensions of 7 × 7 × 28 cm3. the results are illustrated in fig. 11. the analysis of the values obtained for the tensile strength by bending shows the same findings as that of the compression, which is presented below. at short-term, the tensile strength by bending of the control hpc is slightly higher than that of the hpc with 10%, 20%, 30 %, and 50% substitution of cement with ground granulated blast furnace slag. this is due to 2,571 2,565 2,551 2,541 2,524 2 2,1 2,2 2,3 2,4 2,5 2,6 2,7 d e n si ty  ( k g /m 3 ) concretes hpc control hpc 10% slag hpc 20% slag hpc 30% slag hpc 50% slag 10,5 12 14 17 20 0 2 4 6 8 10 12 14 16 18 20 22 s a g g in g  ( cm ) concretes hpc control hpc 10% slag hpc 20% slag hpc 30% slag hpc 50% slag o. rahim et alii, frattura ed integrità strutturale, 59 (2022) 344-358; doi: 10.3221/igf-esis.59.23 353 granular slag is slow in the hydration process preventing the formation of hydration products within 28 days that fill the voids. the results obtained are considered suitable compared to the results obtained on high ultra-performance concretes [41] and high performance concretes [39]. figure 11: tensile strength by bending of hpcs at 28 days. compressive strength (at 2, 7, 14, 28, and 360 days) the mechanical resistance in the compression test is the main benchmark demonstrating the quality of concrete. the evolution of the compressive strength for different mix designs of hpcs is shown in fig. 12. figure 12: compressive strength of hpcs at 2, 7, 14, 28, and 360 days. in the short term and up to 28 days, the compressive strength decrease when the substitution rate increases. a nonsignificant decrease is relatively for hpcs with 10%, 20%, and 30% of ground granulated blast furnace slag and significant for hpc with 50% as a partial replacement for cement. this is mainly due to the nature of the ground granulated blast furnace slag from the steel plant of el-hadjar (annaba, algeria) which presents in the short term a relatively slow hydraulic reactivity but sufficient to ensure a compressive strength at 28 days greater than 60 mpa required for having an hpc conforming to the standard as it is observed by several researches [39–41]. in this phase, the blaine fineness of the slag which is higher than that of the cement fills the tiny voids and accentuates the densification. furthermore, a remarkable increase in compressive strengths is observed for hpc with the addition of slag in partial substitution of the cement after 360 days of curing, which is greater than those of hpc without the addition of ground granulated blast furnace slag. this is due to the chemical reactions between the portlandite and the silica of the slag with the formation of an additional calcium 10,64 10,237 9,335 8,456 8,121 0 2 4 6 8 10 12 a v e ra g e    te n si le  s tr e n g th  b y  b e n d in g (m p a ) concretes hpc control hpc 10% slag hpc 20% slag hpc 30% slag hpc 50% slag 0 10 20 30 40 50 60 70 80 90 100 2 7 14 28 360 a v e ra g e  c o m p re ss iv e  s tr e n g th  ( m p a ) time (days) hpc control hpc 10% slag hpc 20% slag hpc 30% slag hpc 50% slag o. rahim et alii, frattura ed integrità strutturale, 59 (2022) 344-358; doi: 10.3221/igf-esis.59.23 354 silicate hydrate (csh) gel and the consumption of lime, which leads to the densification of microstructure and consequently an improvement in the compressive strength [27,38–41]. durability porosity is the first fundamental factor that affects the durability of concrete and can lead to a loss of structural bearing capacity by influencing the compressive strength and other properties of concrete. the mechanical performance and durability of concrete depend on the porosity. in particular the durability which is associated with the open porosity and more particularly with the interconnected open porosity which allows the penetration of external aggressive agents into the concrete. this porosity promotes the transfer rate by diffusion or by permeability of aggressive chemicals as well as the penetration of gases. for this, the hpcs studied were subjected to tests of water absorption by capillarity, the porosity accessible to water and gas permeability. in this part, three concrete formulations were tested in the various durability tests: hpc control, hpc 20% slag and hpc 50% slag. the choice of 20% and 50% in comparison with a control is linked to a compromise between economic and environmental benefits and mechanical performance. a 20% substitution rate ensures very significant compressive strength at 28 days for a bhp with minimal economic and environmental benefits. on the other hand, the 50% replacement rate gives us maximum economic and environmental benefits with acceptable resistance. the porosity accessible to water (at 360 days) the results of the influence of the cement substitution rate by the ground granulated blast furnace slag on the porosity accessible to water as a function of the density are shown in fig. 13. figure 13: effect of the cement substitution rate by the ground granulated blast furnace slag on the porosity accessible to water of hpcs at 360 days. the results indicate that the incorporation of ground granulated blast furnace slag tends to decrease slightly with density and increases the porosity accessible to water for hpc by 50% cement substitution by the granulated slag compared to control hpc. on the other hand, the density increases slightly and the porosity accessible to water almost equals for hpc with 20% substitution of cement by the ground granulated blast furnace slag in comparison with control hpc. the pozzolanic activity of ground granulated blast furnace slag is latent over time. the result of the porosity accessible to water for hpc by 50% substitution of cement by the ground granulated blast furnace slag is better than expected compared to the range of porosity accessible to water in such a concrete context. the study carried out by tafraoui, [42] shows a porosity accessible to water equal to 6.1% on samples of ultra-high performance concrete with a water / cement ratio equal to 0.27. these results are close to those obtained on the samples of hpcs studied [27,38–41]. capillarity water absorption (at 360 days) the results of the influence of the cement substitution rate by the ground granulated blast furnace slag on the capillary absorption coefficient of hpc based on ternary binder over time are shown in fig. 14. it is clear that the addition of 20% ground granulated blast furnace slag as partial substitution for cement reduces the capillary absorption coefficient compared to hpc without substitution. this can be explained by the filling effect of slag, which increases the tortuosity of the pore network and therefore makes the transfer of water more difficult. however, the addition of 50% ground granulated blast furnace slag as a partial replacement for cement results in an increase in the capillary 0 1 2 3 4 5 6 7 8 9 10 2,42 2,43 2,44 2,45 p o ro si ty  a cc e ss ib le  t o  w a te r  (% ) density (kg/m3) hpc control hpc 20% slag hpc 50% slag o. rahim et alii, frattura ed integrità strutturale, 59 (2022) 344-358; doi: 10.3221/igf-esis.59.23 355 absorption coefficient. nevertheless, this value is considered to be good compared to some research for bhp without substitution of cement by the slag granules in the same region of the materials used as [38,40]. the hydraulic or pozzolanic activities of mineral admixtures promote slower hpc absorption velocity. in fact, the capillary voids surface is covered by csh produced during chemical reactions of mineral admixtures. the use of ground granulated blast furnace slag and silica fume mineral admixtures significantly reduces the absorption velocity by improving the porous structure which is appropriate for the results found in the literature [11,19,24,25]. figure 14: effect of the cement substitution rate by the ground granulated blast furnace slag on the capillarity water absorption of hpcs at 360 days. gas permeability (at 360 days) the results of the influence of the cement substitution rate by the ground granulated blast furnace slag on the gas permeability of hpbs based on ternary binder are shown in fig. 15. figure 15: gas permeability of hpc control, hpc 20% slag and hpc 50% slag at 360 days. the results of the medium-term (360 days) gas permeability of the control and ternary binder based hpc with cement substitution rates by the ground granulated blast furnace slag of the order of 20% and 50% are shown in fig. 15. at this time, the gas permeability recorded for the control hpc is the lowest with an average intrinsic value of the order of 6.83e18 m2. the hpc based on a ternary binder recorded at this time a slightly higher permeability than that of the control hpc (the values remain comparable). the mean intrinsic permeability values are of the order of 2.81e-17 m2 and 5.98e-17 m2 0 0,005 0,01 0,015 0,02 0,025 0,03 0 1 2 3 4 5 6 a b so rp ti o n  c o e ff ic ie n t  (k g /m 2 ) time square root √t (√hours) hpc control hpc 20% slag hpc 50% slag r² = 0,9879 r² = 0,9298 r² = 0,9873 1,00e‐18 1,10e‐17 2,10e‐17 3,10e‐17 4,10e‐17 5,10e‐17 6,10e‐17 7,10e‐17 8,10e‐17 9,10e‐17 1,01e‐16 1,5e‐06 2,5e‐06 3,5e‐06 4,5e‐06 5,5e‐06 6,5e‐06 7,5e‐06 g a s  p e rm e a b il it y  ( m 2 ) 1/pm (bar‐1) hpc control hpc 20% slag hpc 50% slag o. rahim et alii, frattura ed integrità strutturale, 59 (2022) 344-358; doi: 10.3221/igf-esis.59.23 356 respectively for 20% and 50% replacement of cement by ground granulated blast furnace slag. this difference in permeability can be explained by the low hydraulic reactivity of the algerian ground granulated blast furnace slag and therefore the period of 360 days of maturation was not sufficient for a good hydration of the studied slag and did not allow the densification of the microstructure necessary for improving permeability. however, for slags with good hydraulic reactivity, a better performance in permeability of concrete slag is reported at 28 and 90 days [15,16,24,38,40]. this proves both the low reactivity of the slag studied and the importance of wet curing for improving the durability of slag concretes. conclusions n this article, the physical and mechanical properties of hpcs based on ternary binders formulated with granulated slag in partial substitution for cement are presented. we were able to demonstrate the value of replacing cement with granulated slag in the development of high performance concretes. based on the results obtained, the following conclusions can be drawn: • increasing the ground granulated blast furnace slag by 20 to 50% increased the workability of hpcs. this may be due to the smooth surfaces of the crushed granulated blast furnace slag. • at early and middle ages (up to 28 days), the addition of ground granulated blast furnace slag causes a decrease in compressive strength. however, after 360 days of curing, blends containing up to 30% ground granulated blast furnace slag showed an improvement in compressive strength. this is due to the latent hydration reaction of the ground granulated blast furnace slag. • the experimental results presented in this article confirmed that the addition of granulated blast furnace slag crushed (up to 30%) as a substitute for portland cement can improve physical and mechanical properties of hpc based on ternary binder (cement, silica fume, and granulated blast furnace slag) with a compressive strength equal to 68.32 mpa at 28 days and 92.17 mpa at 360 days. as a result, the substitution up to 50% of cement is suitable for long-term mechanical properties (compressive strength equal to 80.412 mpa). • the use of ground granulated blast furnace slag with a low replacement rate (10 and 30) reduced the porosity of the water. however, the use of 50% granulated blast furnace slag as a replacement for cement slightly increased the porosity accessible to water. • the gas permeability coefficient increases with the increase in the replacement rate of crushed granulated slag from blast furnaces. the results obtained on the durability of high performance concrete are acceptable and stimulating compared to previous research of hpcs concrete [24,38,40,42]. • the results obtained show that it is possible to greatly limit the portland cement content thanks to a granulated slag substitution rate of up to 50% in the manufacture of a new range of hpcs. this helps to reduce the emission of co2 into the atmosphere by reducing the energy required for the production of the non-additive cement used in the manufacture of hpcs which is very beneficial for the environment. acknowledgments he authors would like to thank dr. céline bascoulès-perlot and the staff of laboratory siameipra, ea458 of uppa university (anglet, france) who provided facilities for conducting the various durability tests in their laboratory. references [1] toghroli, a., mehrabi, p., shariati, m., trung, n.t., jahandari, s., rasekh, h. (2020). evaluating the use of recycled concrete aggregate and pozzolanic additives in fiber-reinforced pervious concrete with industrial and recycled fibers, constr. build. mater., 252, pp. 118997, doi: 10.1016/j.conbuildmat.2020.118997. [2] afshar, a., jahandari, s., rasekh, h., shariati, m., afshar, a., shokrgozar, a. (2020). corrosion resistance evaluation of rebars with various primers and coatings in concrete modified with different additives, constr. build. mater., 262, pp. 120034, doi: 10.1016/j.conbuildmat.2020.120034. [3] jahandari, s., saberian, m., tao, z., mojtahedi, s.f., li, j., ghasemi, m., rezvani, s.s., li, w. (2019). effects of saturation i t o. rahim et alii, frattura ed integrità strutturale, 59 (2022) 344-358; doi: 10.3221/igf-esis.59.23 357 degrees, freezing-thawing, and curing on geotechnical properties of lime and lime-cement concretes, cold reg. sci. technol., 160, pp. 242–252, doi: 10.1016/j.coldregions.2019.02.011. [4] kazemi, m., li, j., lahouti harehdasht, s., yousefieh, n., jahandari, s., saberian, m. (2020). non-linear behaviour of concrete beams reinforced with gfrp and cfrp bars grouted in sleeves, structures, 23, pp. 87–102, doi: 10.1016/j.istruc.2019.10.013. [5] sadeghian, f., haddad, a., jahandari, s., rasekh, h., ozbakkaloglu, t. (2021). effects of electrokinetic phenomena on the load-bearing capacity of different steel and concrete piles: a small-scale experimental study, can. geotech. j., 58(5), pp. 741–746, doi: 10.1139/cgj-2019-0650. [6] kazemi, m., hajforoush, m., talebi, p.k., daneshfar, m., shokrgozar, a., jahandari, s., saberian, m., li, j. (2020). insitu strength estimation of polypropylene fibre reinforced recycled aggregate concrete using schmidt rebound hammer and point load test, j. sustain. cem. mater., 9(5), pp. 289–306, doi: 10.1080/21650373.2020.1734983. [7] rasekh, h., joshaghani, a., jahandari, s., aslani, f., ghodrat, m. (2020).rheology and workability of scc. selfcompacting concrete: materials, properties and applications, elsevier, pp. 31–63. [8] aïtcin, p.-c. (2001).bétons haute performance. eyrolles, paris, p. 683. [9] lakhal, r., achoura, d. (2009).elaboration des bétons à haute performances à base de laitier granulé. 1st international conference on sustainablebuiltenvironment infrastructures in developing countries enset oran, oran, algeria. [10] vejmelková, e., pavlíková, m., keršner, z., rovnaníková, p., ondráček, m., sedlmajer, m., černý, r. (2009). high performance concrete containing lower slag amount: a complex view of mechanical and durability properties, constr. build. mater., 23(6), pp. 2237–2245, doi: 10.1016/j.conbuildmat.2008.11.018. [11] biskri, y., achoura, d., chelghoum, n., jauberthie, r. (2016). effect of mineral admixtures and aggregate natures on the behavior of high performance concrete, j. mater. environ. sci., 7(7), pp. 2617–2628. [12] hadj sadok, a., foudhil, c.i., si-tayeb, s. (2014). méthode simplifiée de formulation d’un béton à haute performance avec et sans fibre métallique, matec web conf., 11, pp. 01044, doi: 10.1051/matecconf/20141101044. [13] shi, h. sheng., xu, b. wan., zhou, x. chen. (2009). influence of mineral admixtures on compressive strength, gas permeability and carbonation of high performance concrete, constr. build. mater., 23(5), pp. 1980–1985, doi: 10.1016/j.conbuildmat.2008.08.021. [14] adjoudj, m., ezziane, k., kadri, e.h., ngo, t.t., kaci, a. (2014). evaluation of rheological parameters of mortar containing various amounts of mineral addition with polycarboxylate superplasticizer, constr. build. mater., 70, pp. 549–559, doi: 10.1016/j.conbuildmat.2014.07.111. [15] benamara, d., mezghiche, b. (2010). vers un beton de haute performance elabore de materiaux locaux « bhp », courr. du savoir, 10, pp. 9–14. [16] menéndez, g., bonavetti, v., irassar, e.f. (2003). strength development of ternary blended cement with limestone filler and blast-furnace slag, cem. concr. compos., 25(1), pp. 61–67, doi: 10.1016/s0958-9465(01)00056-7. [17] khalifa, n.e.h., bouasker, m., mounanga, p., ben kahla, n. (2012). etude du comportement mécanique de liants binaires et ternaires à base de ciment portland, de laitier de haut fourneau et de filler calcaire, matec web conf., 2, pp. 01009, doi: 10.1051/matecconf/20120201009. [18] aoual-benslafa, f.k., semcha, a. (2011). influence des additions minérales sur la résistance mécanique des mortiers, afrique sci. rev. int. des sci. technol., 7(2), pp. 16–26. [19] kaïkea, a., achoura, d., duplan, f., rizzuti, l. (2014). effect of mineral admixtures and steel fiber volume contents on the behavior of high performance fiber reinforced concrete, mater. des., 63, pp. 493–499, doi: 10.1016/j.matdes.2014.06.066. [20] petitpain, m. (2017).bétons à faible impact environnemental pour l’industrie du béton : accélération du durcissement de bétons à base de liants ternaires. ph.d. final thesis, université lille 1, 2017. [21] ali-boucetta, t., behim, m., cassagnabere, f., mouret, m., ayat, a., laifa, w. (2021). durability of self-compacting concrete containing waste bottle glass and granulated slag, constr. build. mater., 270, pp. 121133, doi: 10.1016/j.conbuildmat.2020.121133. [22] alexandre, j., jean-louis, s. (1988). le laitier de haut fourneau : élaboration, traitements, propriétés, emplois, paris. [23] zeghichi, l., mezghiche, b., merzougui, a. (2007). l’influence de l’activation du laitier sur le comportement mecanique des betons, leban. sci. j., 8(2), pp. 105. [24] melais, f.z., melais, s., achoura, d., jauberthie, r. (2015). valorisation des sous-produits de hauts fourneaux dans la fabrication d’une nouvelle gamme de béton de sable, j. mater. environ. sci., 6(3), pp. 735–742. [25] biskri, y., achoura, d., chelghoum, n., mouret, m. (2017). mechanical and durability characteristics of high performance concrete containing steel slag and crystalized slag as aggregates, constr. build. mater., 150, pp. 167–178, doi: 10.1016/j.conbuildmat.2017.05.083. o. rahim et alii, frattura ed integrità strutturale, 59 (2022) 344-358; doi: 10.3221/igf-esis.59.23 358 [26] kourounis, s., tsivilis, s., tsakiridis, p.e., papadimitriou, g.d., tsibouki, z. (2007). properties and hydration of blended cements with steelmaking slag, cem. concr. res., 37(6), pp. 815–822, doi: 10.1016/j.cemconres.2007.03.008. [27] chaid, r., molez, l., sabria, m., talah, a. (2016). comportement des bhp de laitier soumis aux cycles immersionséchage behaviour of slag hpc submitted to immersion-drying cycles, j. mater. eng. struct., 3, pp. 23–33. [28] banfill, p.f.g. (2011). additivity effects in the rheology of fresh concrete containing water-reducing admixtures, constr. build. mater., 25(6), pp. 2955–2960, doi: 10.1016/j.conbuildmat.2010.12.001. [29] mani, m., bouali, m.f., kriker, a., hima, a. (2021). experimental characterization of a new sustainable sand concrete in an aggressive environment, frat. ed integrita strutt., 15(55), pp. 50–64, doi: 10.3221/igf-esis.55.04. [30] papachristoforou, m., mitsopoulos, v., stefanidou, m. (2019). use of by-products for partial replacement of 3d printed concrete constituents; rheology, strength and shrinkage performance, frat. ed integrita strutt., 13(50), pp. 526–36, doi: 10.3221/igf-esis.50.44. [31] benzerara, m., guihéneuf, s., belouettar, r., perrot, a. (2021). combined and synergic effect of algerian natural fibres and biopolymers on the reinforcement of extruded raw earth, constr. build. mater., 289, pp. 123211, doi: 10.1016/j.conbuildmat.2021.123211. [32] melais, f.z., achoura, d., ghorbel, e. (2021). durability of mortars containing blast furnace slags used as a partial substitute of portland cement exposed to external sulfate attacks, 12(6), pp. 837–852. [33] melais, s., bouali, m.f., melaikia, a., amirat, a. (2021). effects of coarse sand dosage on the physic-mechanical behavior of sand concrete, frat. ed integrita strutt., 15(56), pp. 151–159, doi: 10.3221/igf-esis.56.12. [34] benyahia, a., choucha, s., ghrici, m., omran, a. (2018). influence of limestone dust and natural pozzolan on engineering properties of self-compacting repair mortars, frat. ed integrita strutt., 12(45), pp. 135–146, doi: 10.3221/igf-esis.45.11. [35] jadidi, a., amiri, m., zeighami, e. (2017). experimental evaluation of steel fiber effect on mechanical properties of steel fiber-reinforced cement matrix, frat. ed integrita strutt., 11(42), pp. 249–262, doi: 10.3221/igf-esis.42.27. [36] boudina, t., benamara, d., zaitri, r. (2021). optimization of high-performance-concrete properties containing fine recycled aggregates using mixture design modeling, frat. ed integrita strutt., 15(57), pp. 50–62, doi: 10.3221/igf-esis.57.05. [37] manai, k. (1995).étude de l’effet d’ajouts chimiques et minéraux sur la maniabilité, la stabilité et les performances des bétons autonivelants. ph.d. final thesis, université de sherbrooke, canada. [38] kaïkea, a. (2015).elaboration des bétons à hautes performances fibrés avec addition du laitier granulé (comportement mécanique et durabilité. ph.d. final thesis, université badji mokhtar annaba, algeria. [39] abdelli, k. (2010).influence des laitiers sur la microstructure des bétons a l’état frais et durci. ph.d. final thesis, université des sciences et de la technologie houari boumediene usthb, algeria. [40] biskri, y. (2017).comportement physico-mécanique et durabilité des bétons à hautes performances à base de deux influence de la nature des granulats. ph.d. final thesis, université badji mokhtar annaba, algeria. [41] zenati, a. (2014).formulation des bétons à ultra hautes performances à base d’ajouts cimentaires. ph.d. final thesis, université des sciences et de la technologie houari boumediene usthb, algeria. [42] tafraoui, a. 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can be opened with acrobat and adobe reader 5.0 and later.) >> /namespace [ (adobe) (common) (1.0) ] /othernamespaces [ << /asreaderspreads false /cropimagestoframes true /errorcontrol /warnandcontinue /flattenerignorespreadoverrides false /includeguidesgrids false /includenonprinting false /includeslug false /namespace [ (adobe) (indesign) (4.0) ] /omitplacedbitmaps false /omitplacedeps false /omitplacedpdf false /simulateoverprint /legacy >> << /addbleedmarks false /addcolorbars false /addcropmarks false /addpageinfo false /addregmarks false /convertcolors /converttocmyk /destinationprofilename () /destinationprofileselector /documentcmyk /downsample16bitimages true /flattenerpreset << /presetselector /mediumresolution >> /formelements false /generatestructure false /includebookmarks false /includehyperlinks false /includeinteractive false /includelayers false /includeprofiles false /multimediahandling /useobjectsettings /namespace [ (adobe) (creativesuite) (2.0) ] /pdfxoutputintentprofileselector /documentcmyk /preserveediting true /untaggedcmykhandling /leaveuntagged /untaggedrgbhandling /usedocumentprofile /usedocumentbleed false >> ] >> setdistillerparams << /hwresolution [2400 2400] /pagesize [612.000 792.000] >> setpagedevice microsoft word 2346 c.a.c.p. coelho et alii, frattura ed integrità strutturale, 48 (2019) 411-418; doi: 10.3221/igf-esis.48.39 411 impact response of laminate cylindrical shells carlos a.c.p. coelho, fábio v.p. navalho esta, escola superior de tecnologia de abrantes, instituto politécnico de tomar, tomar, portugal cccampos@ipt.pt, fabionavalho@gmail.com p.n.b. reis c-mast, depart. of electromechanical engineering, university of beira interior, covilhã, portugal preis@ubi.pt, http://orcid.org/0000-0001-5203-3670 abstract. composite laminates subjected to low-velocity impact events on the through-thickness direction are conveniently studied and disseminated in the open literature. however, in terms of laminate cylindrical shells this subject is less common. therefore, the main goal of the present work is to study the impact response of laminate composite cylindrical shells composed by different type of fibres. for this purpose, laminates with different configurations (6c, 2c+2k+2c and 2c+2g+2c), where the “number” represents the number of layers used and c=carbon, k=kevlar and g=glass fibre layers, were analysed in terms of static and impact strength. it is possible to conclude that both static and impact performance are strongly influenced by the shells’ configuration. in terms of compressive static strength, the kevlar hybrid shells present values 53.2% higher than the 6c shells, while the glass hybrid shells present values 17.3% lower. the impact analyses shows, regardless the similarity of the maximum loads for all configurations, that kevlar hybrid shells achieved the highest elastic recuperation and the glass hybrid shells the maximum displacement. keywords. impact strength; composites; cylindrical shells; mechanical testing. citation: coelho, c.a.c.p., navalho, f.v.p., reis, p.n.b., impact response of laminate cylindrical shells, frattura ed integrità strutturale, 48 (2019) 411-418. received: 15.12.2018 accepted: 21.01.2019 published: 01.04.2019 copyright: © 2019 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. introduction omposite materials, day after day, are increasingly replacing the traditional metallic materials in several engineering applications, and this tendency will continue as consequence of their high stiffness and strength, low weight, adjustable properties, competitive cost, good static and dynamic properties, good resistance to corrosion and simplified fabrication. c http://www.gruppofrattura.it/va/48/2346.mp4 c.a.c.p. coelho et alii, frattura ed integrità strutturale, 48 (2019) 411-418; doi: 10.3221/igf-esis.48.39 412 however, the main disadvantages of those materials are related with their poor compression and transverse properties [1, 2]. in this context, literature reports a high sensitivity of these materials to low-velocity impact events that occur easily inservice or during the maintenance activities. these type of events are responsible by damages that are difficult to detect [3, 4] and, simultaneously, responsible by significant reductions of the residual mechanical properties [5–8]. studies about composite laminates subjected to low-velocity impact events on the through-thickness direction are abundant in the literature, especially in terms of damage characterization [9-12], compression-after-impact [13], multi-impacts [14], environmental effects [15-17] and numerical investigations [18, 19]. on the other hand, literature also presents strategies to improve their impact performance with resource to hybridisation [20-22] or using nano-enhanced resins [23–27]. however, the impact characterization in all these works was performed in composite plates. the analysis of laminate cylindrical shells, are less disseminated in the open literature, but this topic should be empathized due to the complexity and design of many advanced structures. gong et al. [28], for example, developed an analytic solution to predict the response of laminate shells subjected to impact loads. this solution included both contact deformation and transverse shear deformation and it was used to study the effects of different impact conditions and shell size, as well as the curvature´s effect, on the contact force and central deflection of the shell. results were compared with those reported in the literature and good agreement was found. an experimental study was developed by kistler [29] and he noticed that the geometry strongly influences the impact response. stiffer structures have higher impact strength, smaller centre deflections and shorter contact time. a threedimensional eight-node non-conforming element with taylor’s modification was used by zhao and cho [30] to analyse the interlaminar stress distribution, initial damage pattern and progressive failure on laminate composite shells subjected to impact loads. the stiffness effect was also studied by arachchige et al. [31, 32] and the results shown that the impact load increases with increasing stiffness while the contact time decreases. regarding the velocity of impact, it was verified a direct relationship with the contact load. kistler and waas [33] studied the impact behaviour of cylindrical graphite/epoxy panels with different thicknesses, curvatures and support conditions. they concluded that increasing the thickness leads to increased stiffness and, consequently, higher impact force as well as lower deflection and contact time. krishnamurthy et al. [34, 35] studied the damage and the impact response of cylindrical graphite/epoxy shells using the finite element method. according with the study developed, higher mass values of the impactor are responsible by the increasing of the contact time and the damage occurred under the impact point. a nonlinear finite element analysis of impact response and impact-induced damage in curved composite laminates subjected to transverse impact by a foreign object was developed by kumar [36]. it was possible to conclude that the impact response is significantly dependent on the shell curvature. therefore, this study intends to improve the knowledge related to the impact response of hybrid composite cylindrical shells. combining two or more fibre types, hybridisation is a promising strategy to toughen composite materials, and a better balance of the mechanical properties is obtained relatively to non-hybrid composites. for this purpose, laminates with the same number of layers, but composed by different type of fibres, were manufactured and conveniently characterized in terms of static and impact strength. both loading modes were tested with the same boundary conditions, where the curved edges of the test specimens were free while the straight edges were supported. experimental procedure aminate composite cylindrical shells were manufactured by hand lay-up and overall dimensions are shown in fig 1. a system of sr1500 epoxy resin and a sd2503 hardener standard, both supplied by sicomin (châteauneuf-lesmartigues, france), was used with six layers, all in the same direction, of bi-directional woven fabrics to produce the specimens. three different typologies were investigated with the following stacking sequence: 6c; 2c+2k+2c and 2c+2g+2c, where the “number” represents the number of layers used and c = carbon (taffeta with 196 g/cm2), k = kevlar (taffeta with 281 g/cm2) and g = glass (taffeta with 205 g/cm2) fibre layers. carbon bi-directional woven fabrics were supplied by cit (legnano, italy), while the kevlar woven fabrics were supplied by dupont (richmond, usa) and glass fibre woven fabrics by porcher industries germany (erbach, germany). the system was placed inside a vacuum bag for 24 hours and a maximum pressure of 0.5 mbar was applied for 9 hours in order to maintain a constant fibre volume fraction and an uniform laminate thickness, beyond to eliminate any air bubbles existing in the laminate. according the supplier’s datasheet, the post-cure was carried out in an oven at 60ºc for 16h. the tg of the resin is about 70ºc. low-velocity impact tests were performed using a drop weight-testing machine imatek-im10 (old knebworth, united kingdom). more details of the impact machine can be found in [37]. an impactor diameter of 10 mm with a mass of 2.826 kg was used. as shown in fig. 2, the impact will occur at the centre of the samples with free support of the curved edges while the straight edges are bi-supported. the impact energy used was 5 j, which corresponds to an impact velocity l c.a.c.p. coelho et alii, frattura ed integrità strutturale, 48 (2019) 411-418; doi: 10.3221/igf-esis.48.39 413 of 1.88 ms-1. this energy was previously selected in order to promote damage, but without perforation of the specimens. the impact tests were performed according to astm d7136 standard and, for each configuration, five specimens were tested at room temperature. flexural tests were also performed using a shimadzu ag-100 universal testing machine (kyoto, japan), with the same support and loading nose shown in fig. 2, equipped with a 100 kn load cell at a displacement rate of 3 mm/min. all tests were also carried out at room temperature, and five specimens were tested for each configuration. all results will be discussed in terms of average values. a) b) figure 1: a) view of the manufacturing process and mold; b) geometry and dimensions of the specimens (thickness 1.4±0.1 mm). figure 2: general views of the apparatus (support) used in the experimental tests. results and discussion n order to understand the impact performance of the different laminate composite semi-cylindrical shells, flexural tests were carried out for each configuration. fig. 3 shows typical load-displacement curves and tab. 1 presents the average results, with the respective standard deviation. stiffness was defined as the slope in the linear region of the load-displacement response and the displacement is the value obtained for the maximum load. i c.a.c.p. coelho et alii, frattura ed integrità strutturale, 48 (2019) 411-418; doi: 10.3221/igf-esis.48.39 414 figure 3: typical load-displacement curves for the different configurations. it is possible to observe a linear region in all curves shown in fig. 3, which is longer for the non-hybrid laminates. the stiffness presents the highest value for the non-hybrid composite semi-cylindrical shells, while the lowest value occurs for hybrid composite shells involving carbon and glass fibres. according with the literature [38], the zigzag aspect of the curves represents fractures of the fibres, in compression, and some delaminations around the broken fibres are also expected. the high compressive stress concentration at the loading nose contact region associated with the low compressive strength of the fibres promotes the failure damage described previously. laminates maximum load [n] displacement at max. load [mm] stiffness [n/mm] average std. average std. average std. 6c 873 121 4.4 1.0 354 41 2c+2k+2c 1337 203 11.3 3.1 252 62 2c+2g+2c 722 184 7.1 1.9 203 54 table 1: compressive strength of the different laminate composite semi-cylindrical shells. the maximum average load obtained in the hybrid carbon and kevlar fibres shells is 53.2% higher than the maximum load obtained in the non-hybrid shells, while this parameter for hybrid shells with carbon and glass fibres is 17.3% lower. in terms of stiffness, the highest average value occurs for shells with carbon fibres (354 n/mm) followed by the hybrid configurations that involve kevlar fibres and glass fibres with values, respectively, 28.8% and 42.7% lower. finally, the lowest maximum average displacement occurs for shells with carbon (about 4.4 mm) and this value increases 38% and 156.8%, respectively, for shells with carbon and glass fibres and shells with carbon and kevlar fibres. the intrinsic mechanical properties of the fibres and the damage mechanisms justify the tendency described previously. dong et al. [39] observed a flexural modulus decreasing with higher percentage of glass fibres and positive hybrid effects by substituting carbon fibres with glass fibres. according to giancaspro et al. [40], carbon fibre composites fail mainly on the compression side, while glass fibre composites fail on the tension side. therefore, adding carbon fibres on the tension side of glass fibre composites increase the flexural strength, but when they are added on the compressive side the failure mode changes from tensile to crushing. on the other hand, literature reports that there is an optimal content of glass fibre to achieve maximum flexural strength [40, 41]. according to dong et al. [41], for carbon/glass hybrid composites, this value is around 12.5% when all glass fibres are placed on the compressive side. impact tests were carried out and fig. 4 shows the force-time curves for each configuration. the curves that can be observed are similar with those find in literature [23-25]. the curves contain oscillations that, according schoeppner and abrate [42], result from the elastic wave and are created by the vibrations of the samples. it depends on the stiffness and on the mass of the specimen and impactor being excited by the rapid variation of the cinematic magnitudes at the time of collision [43]. 0,0 0,2 0,4 0,6 0,8 1,0 1,2 1,4 0 2 4 6 8 10 12 l o ad [ kn ] displacement (mm) 6c 2c+2k+2c 2c+2g+2c c.a.c.p. coelho et alii, frattura ed integrità strutturale, 48 (2019) 411-418; doi: 10.3221/igf-esis.48.39 415 figure 4: typical load-time curves for the different configurations. in detail, for the hybrid shells, it is possible to observe that the load increases up to a maximum value (pmax) followed by a drop after the peak load. on the other hand, for shells only with carbon fibres after pmax the load decreases and remains practically constant while the time increases. this untypical curve, compared with the other two, means that major damage occurs but with a non-perforating impact event. according with the literature [25], the value of pmax is very dependent of the impact energy and represents the peak load value that the composite laminate can tolerate, under a particular impact level, before undergoing major damage. fig. 5 shows the typical energy-time curves, where it is possible to observe that the impact energy was not high enough to infringe full penetration. figure 5: typical energy-time curves for the different configurations. in all tests, the impactor sticks the specimens and rebound (non-perforating impact). the beginning of the plateau coincides with the loss of contact between the striker and the specimen, so, this value is the energy absorbed by the specimen [11, 25]. in this context, as reported previously, the non-hybrid specimens present the highest absorbed energy, 0,0 0,2 0,4 0,6 0,8 1,0 0 2 4 6 8 10 12 14 16 18 l o ad [ n ] time [ms] 2c+2k+2c 2c+2g+2c 6c 0 1 2 3 4 5 6 0 2 4 6 8 10 12 14 16 18 20 e n er gy [ j] time [ms] 2c+2k+2c 2c+2g+2c 6c c.a.c.p. coelho et alii, frattura ed integrità strutturale, 48 (2019) 411-418; doi: 10.3221/igf-esis.48.39 416 consequently higher damages, and the hybrid specimens involving the carbon and kevlar fibres are the ones that present the lowest absorbed energy. tab. 2 presents the average values, and respective standard deviation, of the peak load, of the maximum displacement and the rebounded energy (elastic recuperation). the elastic recuperation is the difference between the absorbed energy and the energy at peak load [23]. laminates peak load [n] max displacement [mm] elastic recuperation [j] average std. average std. average std. 6c 0.924 0.12 7.8 1.9 1.71 0.91 2c+2k+2c 0.920 0.16 8.9 0.8 2.35 0.72 2c+2g+2c 0.916 0.21 9.5 3.1 2.14 0.98 table 2: average values of the peak load, maximum displacement and elastic recuperation. from tab. 2, it is possible to observe that the maximum load (pmax) is very close for all configurations with an average value of 0.920 n. with more detail, it is evident a light increasing of the average maximum load (from 0.916 to 0.924 n) with the stiffness of the laminate (from 203 to 354 n/mm), as reported in tab. 1. on the other hand, the average maximum displacement has higher amplitude of values. the lowest value observed occurs for the non-hybrid shells, while the highest is for the stacking sequence of 2c+2g+2c. this difference is around 21.8%, but when compared the 6c and 2c+2k+2c configurations the difference is only 14%. in fact, according with the literature, stiffer structures produce higher impact forces, smaller deflections, and shorter contact duration times [29, 33, 36, 44, 45]. the geometry of a laminate composite structure, boundary conditions and material properties strongly influences its impact response [29]. for example, the impact response is found to be significantly dependent on the shell curvature, where flatter panels respond to impact with larger peak forces than more curved panels, as well as smaller peak displacements and contact durations [33]. furthermore, changing the boundary conditions from clamped to simply supported decreases the peak impact force, and increases the peak displacement and contact duration [33]. finally, as consequence of higher damages, the elastic recuperation of the carbon shells is the lowest of all laminates (1.71 j), while the 2c+2k+2c configuration presents the highest elastic recuperation (37.4% higher). according to zhao and cho [30], the damage appears at the top ply first and then propagates into bottom layers, however, the maximum damage area occurs at the top surface. additional to that, as reported previously, the severity of the damage is higher because carbon fibres fail mainly on the compression side in composites exposed to bending mode [40]. in terms of the stacking sequence and number of interfaces, zhao and cho [30] observed that the dynamic response and impact-induced damage of composite shells are also very sensitive to these parameters. cross-ply laminate suffers less damage, but the effect of ply orientation change on the maximum contact force reveals to be small [34]. therefore, an optimization process in design is required, because the minimum damage zone is achieved for equal bending stiffness in both axial and circumferential directions [30]. finally, a comparative study carried out by zhao and cho [30] between a laminate composite shell against a similar plate with the same dimensions and impact conditions shows different damage propagations; while the damage propagates from the outer layer into the inner layers for the shell, the damage appears at the bottom layer and propagates from the bottom to middle layer for the plate. conclusions his study analysed the impact response of laminate composite semi-cylindrical shells composed by different type of fibres. it was possible to conclude that the static properties are strongly influenced by the shells’ configuration. shells only with carbon fibres present the highest stiffness and the lowest displacement at maximum load, but, when the glass fibre is incorporated, the lowest stiffness is obtained. on the other hand, the kevlar fibres are responsible by the highest maximum load and displacement. in terms of impact performance, the configuration that involves the kevlar fibres is responsible by the highest elastic recuperation, while the non-hybrid shells evidence the lowest rebounded energy. t c.a.c.p. coelho et alii, frattura ed integrità strutturale, 48 (2019) 411-418; doi: 10.3221/igf-esis.48.39 417 references [1] reis, p.n.b., ferreira, j.a.m., costa, j.d.m., richardson, m.o.w. (2009). fatigue life evaluation for carbon/epoxy laminate compositesunder constant and variable block loading, compos. sci. technol., 69, pp. 154–160. doi: 10.1016/j.compscitech.2008.09.043. [2] reis, p.n.b., neto, m.a., amaro a.m. (2018). effect of the extreme conditions on the tensile impact strength of gfrp composites, compos. struct., 188, pp. 48–54. doi: 10.1016/j.compstruct.2018.01.001. [3] adams, r.d., cawley, p.d.r.d. (1998) a review of defects types and non-destructive testing techniques for composites and bonded joints, ndt&e int., 21, pp. 208–222. doi: 10.1016/0308-9126(88)90333-1. [4] amaro, a.m., reis, p.n.b., de moura, m.f.s.f., santos, j.b. (2012). damage detection on laminated composite materials using several ndt techniques, insight, 54, pp. 14–20. doi: 10.1784/insi.2012.54.1.14. [5] de moura, m.f.s.f., marques, a.t. (2002). prediction of low velocity impact damage in carbon-epoxy laminates, compos. part a appl. s., 33, pp. 361–368. doi: 10.1016/s1359-835x(01)00119-1. [6] reis, p.n.b., ferreira, j.a.m., antunes, f.v., richardson, m.o.w. (2009). effect of interlayer dalamination on mechanical behavior of carbon/epoxy laminates, j. compos. mater., 43, 2609–2621. doi: 10.1177/0021998309344649. [7] amaro, a.m., de moura, m.f.s.f., reis, p.n.b. (2006). residual strength after low velocity impact in carbon-epoxy laminates, mater. sci. forum, 514–516, pp. 624–628. doi: 10.4028/www.scientific.net/msf.514-516.624. [8] amaro, a.m., reis, p.n.b., de moura, m.f.s.f. (2011). delamination effect on bending behaviour in carbon-epoxy composites, strain, 47, pp. 203–208. doi: 10.1111/j.1475-1305.2008.00520.x. [9] richardson, m.o.w., wisheart, m.j. (1996). review of low-velocity impact properties of composite materials, compos. part a-appl. s., 27, pp. 1123–1131. doi: 10.1016/1359-835x(96)00074-7. [10] río, t.g., zaera, r., barbero, e., navarro, c. (2005). damage in cfrps due to low velocity impact at low temperature, compos. part b-eng., 36, pp. 41–50. doi: 10.1016/j.compositesb.2004.04.003. [11] aktas, m., atas, c., icten, b.m., karakuzu, r. (2009) an experimental investigation of the impact response of composite laminates, compos. struct., 87, pp. 307–313. doi: 10.1016/j.compstruct.2008.02.003. [12] dhakal, h.n., zhang, z.y., bennett, n., reis, p.n.b. (2012). low-velocity impact response of nonwoven hemp fibre reinforced unsaturated polyester composites: influence of impactor geometry and impact velocity, compos. struct., 94, pp. 2756–2763. doi: 10.1016/j.compstruct.2012.04.004. [13] kulkarni, m.d., goel, r., naik, n.k. (2011). effect of back pressure on impact and compression after-impact characteristics of composites, compos. struct., 93, pp. 944–951. doi: 10.1016/j.compstruct.2010.06.027. [14] amaro, a.m., reis, p.n.b., de moura, m.f.s.f., neto, m.a. (2013). influence of multi-impacts on gfrp composites laminates, compos. part b-eng., 52, pp. 93–99. doi: 10.1016/j.compositesb.2013.03.041. [15] amaro, a.m., reis, p.n.b., neto, m.a., louro, c. (2013). effects of alkaline and acid solutions on glass/epoxy composites, polym. degrad. stabil., 98, pp. 853–862. doi: 10.1016/j.polymdegradstab.2012.12.029. [16] mortas, n., er, o., reis, p.n.b., ferreira, j.a.m. (2014). effect of corrosive solutions on composites laminates subjected to low velocity impact loading, compos. struct., 108, pp. 205–211. doi: 10.1016/j.compstruct.2013.09.032. [17] amaro, a.m., reis, p.n.b., neto, m.a. (2016). experimental study of temperature effects on composite laminates subjected to multi-impacts, compos. part b-eng., 98, pp. 23–29. doi: 10.1016/j.compositesb.2016.05.021. [18] aslan, z., karakuzu, r., okutan, b. (2003). the response of laminated composite plates under low-velocity impact loading, compos. struct., 59, pp. 119–127. doi: 10.1016/s0263-8223(02)00185-x. [19] karakuzu, r., erbil, e., aktas, m. (2010). impact characterization of glass/epoxy composite plates: an experimental and numerical study, compos. part b-eng., 41, pp. 388–395. doi: 10.1016/j.compositesb.2010.02.003. [20] hosur, m.v., adbullah, m., jeelani, s. (2005). studies on the low-velocity impact response of woven hybrid composites, compos. struct., 67, pp. 253–262. doi: 10.1016/j.compstruct.2004.07.024. [21] halvorsen, a., salehi-khojn, a., mahinfalah, m., nakhaei-jazar, r. (2006). temperature effects on the impact behavior of fiberglass and fiberglass/kevlar sandwich composites, appl. compos. mater., 13, pp. 369–383. doi: 10.1007/s10443-006-9023-x. [22] salehi-khojin, a., mahinfalaha, m., bashirzadeh, r., freeman, b. (2007). temperature effects on kevlar/hybrid and carbon fiber composite sandwiches under impact loading, compos. struct., 78, pp. 197–206. doi: 10.1016/j.compstruct.2005.09.005. [23] ávila, a.f., soares, m.i., neto, a.s. (2007). a study on nanostructured laminated plates behavior under low-velocity impact loadings, int. j. impact eng., 34, pp. 28–41. doi: 10.1016/j.ijimpeng.2006.06.009. c.a.c.p. coelho et alii, frattura ed integrità strutturale, 48 (2019) 411-418; doi: 10.3221/igf-esis.48.39 418 [24] iqbal, k., khan, s.-u., munir, a., kim, j.-k. (2009). impact damage resistance of cfrp with nanoclay-filled epoxy matrix, compos. sci. technol., 69, pp. 1949–1957. doi: 10.1016/j.compscitech.2009.04.016. [25] reis, p.n.b., ferreira, j.a.m., santos, p., richardson, m.o.w., santos, j.b. (2012). impact response of kevlar composites with filled epoxy matrix, compos. struct., 94, pp. 3520–3528. doi: 10.1016/j.compstruct.2012.05.025. [26] reis, p.n.b., ferreira, j.a.m., zhang, z.y., benameur, t., richardson, m.o.w. (2013). impact response of kevlar composites with nanoclay enhanced epoxy matrix, compos. part b-eng., 46, pp. 7–14. doi: 10.1016/j.compositesb.2012.10.028. [27] reis, p.n.b., ferreira, j.a.m., zhang, z.y., benameur, t., richardson, m.o.w. (2014). impact strength of composites with nano-enhanced resin after fire exposure, compos. part b-eng., 56, pp. 290–295. doi: https://doi.org/10.1016/j.compositesb.2013.08.048. [28] gong, s., toh, s., & shim, v. (1994). the elastic response of orthotropic laminated cylindrical shells to low-velocity impact, compos. eng., 4, pp. 247-266. doi: 10.1016/0961-9526(94)90030-2. [29] kistler, l. (1994). experimental investigation of the impact response of cylindrically curved laminated composite panels, aiaa paper, 94-1604-cp, pp. 2292-7. [30] zhao, g., cho, c. (2007). damage initiation and propagation in composite shells subjected to impact, compos. struct., 78, pp. 91-100. doi: 10.1016/j.compstruct.2005.08.013. [31] arachchige, b., ghasemnejad, h., augousti, a.t. (2016). theoretical approach to predict transverse impact response of variable-stiffness curved composite plates, compos. part b-eng., 89, pp. 34-43. doi: 10.1016/j.compositesb.2015.11.036. [32] arachchige, b., ghasemnejad, h. (2017). post impact analysis of damaged variable-stiffness curved composite plates, compos. struct., 166, pp. 12-21. doi: 10.1016/j.compstruct.2017.01.018. [33] kistler, l.s., waas, a.m. (1998). experiment and analysis on the response of curved laminated composite panels subjected to low velocity impact. int. j. impact eng., 21, pp. 711-736. doi: 10.1016/s0734-743x(98)00026-8. [34] krishnamurthy, k., mahajan, p., mittal, r. (2003). impact response and damage in laminated composite cylindrical shells, compos. structur., 59, pp. 15-36. doi: 10.1016/s0263-822 3(02)00238-6. [35] krishnamurthy, k., mahajan, p., & mittal, r. (2001). a parametric study of the impact response and damage of laminated cylindrical composite shells, compos. sci. technol., 61, pp. 1655–1669. doi: 10.1016/s0266-3538(01)00015-x. [36] kumar, s. (2008). analysis of impact response and damage in laminated composite shell involving large deformation and material degradation, j. mech. mater. struct., 3, pp. 1741-1756. doi: 10.2140/jomms.2008.3.1741. [37] amaro, a.m., reis, p.n.b., magalhães, a.g., de moura, m.f.s.f. (2011). the influence of the boundary conditions on low-velocity impact composite damage, strain, 47, pp. e220–226. doi: 10.1111/j.1475-1305.2008.00534.x. [38] reis, p.n.b., ferreira, j.a.m., antunes, f.v., costa, j.d.m. (2007). flexural behaviour of hybrid laminated composites, compos. part a appl. sci. manuf., 38, pp. 1612–1620. doi: 10.1016/j.compositesa.2006.11.010. [39] dong, c.s., duong, j., davies, i.j. (2012). flexural properties of s-2 glass and tr30s carbon fiber reinforced epoxy hybrid composites. polym. composite., 33, pp. 773-781. doi: 10.1002/pc.22206. [40] giancaspro, j.w., papakonstantinou, c.g., balaguru, p.n. (2010). flexural response of inorganic hybrid composites with e-glass and carbon fibers. j. eng. mater. technol., 132, pp. 021005-1-021005-8. doi: 10.1115/1.4000670. [41] dong, c., davies, i.j. (2012). optimal design for the flexural behaviour of glass and carbon fibre reinforced polymer hybrid composites. mater. des., 37, pp. 450-457. doi: 10.1016/j.matdes.2012.01.021. [42] schoeppner, g.a., abrate, s. (2000). delamination threshold loads for low velocity impact on composite laminates. compos. part a-appl. s., 31, pp. 903–915. doi: 10.1016/s1359-835x(00)00061-0. [43] belingardi, g., vadori, r. (2002). low velocity impact of laminate glass-fiber-epoxy matrix composite materials plates. int. j. impact. eng., 27, pp. 213–229. doi: 10.1016/s0734-743x(01)00040-9. [44] cho, c., zhao, g. (1999). dynamic response and damage of composite shell under impact, ksme int. j., 13, pp. 596608. [45] her, s.-c., liang, y.-c. (2004). the finite element analysis of composite laminates and shell structures subjected to low velocity impact, compos. struct., 66, pp. 277-285. doi: 10.1016/j.compstruct.2004.04.049. << /ascii85encodepages false /allowtransparency false /autopositionepsfiles true /autorotatepages /none /binding /left /calgrayprofile (dot gain 20%) /calrgbprofile (srgb iec61966-2.1) /calcmykprofile (u.s. web coated \050swop\051 v2) /srgbprofile (srgb iec61966-2.1) /cannotembedfontpolicy /error /compatibilitylevel 1.4 /compressobjects /tags /compresspages true /convertimagestoindexed true /passthroughjpegimages true /createjobticket false /defaultrenderingintent /default /detectblends true /detectcurves 0.0000 /colorconversionstrategy /cmyk /dothumbnails false /embedallfonts true /embedopentype false /parseiccprofilesincomments true /embedjoboptions true /dscreportinglevel 0 /emitdscwarnings false /endpage -1 /imagememory 1048576 /lockdistillerparams false /maxsubsetpct 100 /optimize true /opm 1 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/hrv (za stvaranje adobe pdf dokumenata najpogodnijih za visokokvalitetni ispis prije tiskanja koristite ove postavke. stvoreni pdf dokumenti mogu se otvoriti acrobat i adobe reader 5.0 i kasnijim verzijama.) /hun 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/pdfxoutputintentprofileselector /documentcmyk /preserveediting true /untaggedcmykhandling /leaveuntagged /untaggedrgbhandling /usedocumentprofile /usedocumentbleed false >> ] >> setdistillerparams << /hwresolution [2400 2400] /pagesize [612.000 792.000] >> setpagedevice microsoft word numero_58_art_15_3140.docx i. elmeguenni, frattura ed integrità strutturale, 58 (2021) 202-210; doi: 10.3221/igf-esis.58.15 202 asymptotic response of friction stir welded joint under cyclic loading imane elmeguenni mechanical research center crm, constantine, algeria imaneelmeguenni@gmail.com, https://orcid.org/0000-0001-7272-9843 abstract. fatigue takes a place more and more important in the design of structures, it remains a key point in the mechanical dimensioning of structures. the friction stir welding (fsw) process is regarded today as the most promising alternative to traditional joining methods. it ranks among the most recent assembly processes and is considered a new technique for the 21st century. indeed, if the fsw welding process has several advantages, it introduces very strong microstructure heterogeneities in the welded joints. this leads to heterogeneous mechanical behavior in each of the constituent zones. some important efforts have been deployed in industry as well as in research laboratories to understand the behavior of welded joints by the fsw process. there are many questions about the behavior of these areas. this study led to the characterization and understanding of the fatigue behavior of a 2024-t351 structure welded by the fsw process. it presents in a numerical work which aims to help determine the asymptotic response of each zone constituting the 2024-t351 joint welded by fsw subjected to a cyclic loading and to fully understand the behavior of these zones. to carry out an analysis and a simulation under cyclic loading, our choice fell on the use of the direct cyclic method. numerical simulation of crack propagation was performed using the extended finite element method (xfem). this research consists in the implementation of the xfem in fatigue in a multiscale model xfem / direct cyclic. the numerical results consist in highlighting the heterogeneities in the mechanical behavior of the welded joint and in evaluating the impact of the fsw process on the failure of these fsw zones. keywords. direct cyclic; fsw; xfem; fatigue; asymptotic response. citation: elmeguenni, i., asymptotic response of friction stir welded joint under cyclic loading, frattura ed integrità strutturale, 58 (2021) 202-210. received: 14.06.2021 accepted: 13.08.2021 published: 01.10.2021 copyright: © 2021 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. introduction riction stir welding (fsw) is a new solid-state welding, method developed by twi in the 1990s, offering several advantages over conventional welding methods [1, 2] fsw uses a rotating and traversing non consumable tool to generate frictional heat and cause mechanical deformation at the joint [4]. f https://youtu.be/bicfzngy1ns i. elmeguenni, frattura ed integrità strutturale, 58 (2021) 202-210; doi: 10.3221/igf-esis.58.15 203 friction stir welding uses the principle of convection of mechanical energy, produced by the pressure and rotation of the tool, into thermal energy by friction of the latter with the parts to be assembled. the heat generated generates localized transformations where the material changes from an elasto-viscoplastic behaviour with high mechanical resistance to a viscoplastic behavior with low resistance, favoring the formation of the junction [22]. the fsw process, shown schematically in fig..1, during the welding process, heat is generated due to the friction between the tool and the workpiece, as well as due to the severe plastic deformation of the material [5]. figure 1: geometry of fsw process, also indicating the tool transverse direction [6]. a welded joint is made only from the base metals of the assembled parts and does not require any filler metal [4]. the weld created by this process is not symmetrical about the parting line. the side where the two velocity vectors (translation and rotation) are in the same direction is called “advancing side” (as). the one where these two vectors are opposite is called a "retreating side" (rs) (fig. 1) [2]. during welding, a thermal and mechanical gradient is introduced, leading to a microstructure gradient within and around the weld [1]. the fsw community unanimously agrees on the number and naming of the macroscopic areas that make up the fsw welded joint. in general, the welded joint has four zones: the core, the thermomechanically affected zone (zatm), the thermally affected zone (zat) and the base metal (mb). so the fsw welding has a very heterogeneous microstructure along the joint, the shape of the bead, the grain size and the size of the areas constituting the joint (fig.2). figure 2: macrographic section of a weld bead from aa7020 showing four distinct areas: (a) base metal, (b) heat affected area, (c) thermo-mechanically affected area and (d) nugget. these heterogeneities introduced by fsw welding make it difficult to study the mechanical behavior of these joints this study constitutes an element of response and of the comprehension of the behavior of the joint 2024-t351 welded by fsw aiming at the numerical development of this joint and the implementation of the method of the extended finite elements (xfem) in cyclic loading. i. elmeguenni, frattura ed integrità strutturale, 58 (2021) 202-210; doi: 10.3221/igf-esis.58.15 204 for broadening and improve understanding the joints fsw, it is necessary to clarify the local fatigue behaviour of different areas of the fsw joints. the fatigue crack propagation of fsw is known to be concerned by the both microstructures around the welded zone [3]. numerical approach and developed model espite a good number of publications on the fsw process, the characterization and numerical analysis of the harmfulness of the defects in the different areas of these joints remains limited. this work is in addition to the various research studies that deal with the mechanical behavior of aluminum alloys welded by the fsw process and strongly contributes to numerically understanding the local fatigue behavior of the 2024t351 joint. the xfem method has been used in order to successfully simulate the phenomenon of crack propagation in friction stir welded joint, without forgetting to take into account the plasticity at the crack tip, and to perform analysis and simulation under cyclic loading, we chose to use the direct cyclic method. so therefore our work consists in the establishment of the xfem in fatigue in a multi-scale model xfem / direct cyclic. the model coupled will be the most powerful and efficient tool for solving various problems in the fatigue behavior. the xfem was introduced by moës and al. in 1999. the idea of xfem consists in enriching the basis of the classical finite element method by a step function along the crack line to take into consideration the discontinuity of the displacement field across the crack and by some non-smooth functions representing the asymptotic displacement around the crack tip. the latter enrichment is the so-called singular enrichment [7], it allows enables automatic mesh generation with each new step of the crack growth [8, 9]. till now xfem has been most widely applied in solving crack problems, including fatigue crack propagation, and threedimensional crack propagation, xfem has also been implemented to solve plasticity problems [10]. many works have been achieved in order to explore the capabilities of the xfem and improve its accuracy as in [7, 9, 10, 11, 16, 17, 18, 19, 20, 21]. figure 3: 2d finite element mesh of a cracked body [11]. presentation of the direct cyclic method he study and the numerical characterization of the mechanical behavior of a structure is based on the determination of the stabilized response of the structure subjected to cyclic loading. however, this asymptotic response remains difficult to determine by conventional simulation techniques, in particular because of the necessary computation times. it then makes it possible to construct the mechanical response of the studied structure, loading increment by loading increment, then cycle after cycle until a possible stabilized cycle. at each increment, the calculation codes generally use an iterative scheme of the newton-raphson type to construct the solution of the problem [15]. an iteration of the direct cyclic method includes 4 stages main: d t i. elmeguenni, frattura ed integrità strutturale, 58 (2021) 202-210; doi: 10.3221/igf-esis.58.15 205  the global step: which makes it possible to search the kinematically and statically admissible fields at all times of the cycle by supposing known the field of plastic strains and internal variables at all times of the cycle.  the local step: which allows, from the solutions of the global step, to search for fields that verify the law of behavior.  the periodicity of the solutions which is imposed by a reinitialization of the plastic strains and the internal variables at the beginning of the cycle from the values obtained at the end of the cycle.  the convergence condition which makes it possible to stop the iterative process checks the periodicity of the plastic strain fields and the internal variables at the end of the local step as well as the static admissibility of the stresses at the end of the local step. figure 4: general principle of the direct cyclic method [12]. application of the method to the calculations of joint fsw 2024-t351 our distinct materials are defined for the different zones ; base material (mb) heat affected zone (haz) -thermomechanically affected zone (tmaz) and nugget (n) within the developed model, so the constants are taken as follows: elastic party ; the mechanical properties of the welded joint 2024 t351 have been determined, the young's modulus and the poisson's ratio are the same for all the zones, the hardening modulus and the exponent (n) vary along the welding zones (tab. 1). elasto plastic ; stresses-strains have been described for all zones (tab. 2), and without forgetting we take into account the mixing temperature of 2024-t351 t = 550 ° c [23]. fsw regimes nz tmaz haz pz young’s modulus (gpa) 68 68 68 68 poisson’s ratio 0.33 0.33 0.33 0.33 yield stress (mpa) 350 272 448 370 hardening constant 800 719 770 hardening exponent 0.1266 0.05546 0.086 hardness (hv1) 142 118 167 132 residual stress (mpa) -41 95 -20 0 table 1: material properties of fsw zones [14]. f i. elmeguenni, frattura ed integrità strutturale, 58 (2021) 202-210; doi: 10.3221/igf-esis.58.15 206 pz ha z tma z nz strain stress strain stress strain stress strain stress 0.0003 20 0.0004 25 0.0007 50.34 0.00044 30.43 0.0006 40 0.0006 35 0.00123 75.86 0.0008 51.30 0.0009 45 0.0010 58 0.0016 106.9 0.0012 69.56 0.0014 90 0.00126 83 0.0020 131.03 0.0015 91.30 0.0021 125 0.0015 95 0.0031 186.21 0.0021 130.43 0.0034 220 0.0020 130 0.0045 268.96 0.0032 186.95 0.0050 300 0.0028 175 0.0057 331.03 0.0043 286.96 0.0058 320 0.00438 280 0.0055 331.91 0.0084 440 0.00558 330 0.0120 487 0.00898 480 0.01166 540 table 2: stress-strain data of fsw zones [14]. so, we formed numerically all the zones constituting the joint fsw 2024-t351 with the properties of each one ..., the model is already developed previously in our article [13] which treated a calculation xfem under monotonic loading to determine the parameters of cracking of the joint 2024-t351. in this work we wanted to highlight this approach on the same model in the cyclic regime, the same approach was adapted but with the cyclic numerical tests in order to achieve the asymptotic response of each zone in the welded joint 2024-t351. figure 5: the model developed a) geometry of the analyzed structure; b) mesh of joint 2024-t351 [13]. the model fsw welded joint 3d using the calculation code by fe abaqus, developed on a rectangular thin plate precracked (a0 = 3mm) dimensions 60x20x1mm, so we choose a structured mesh (hexahedron) with volume elements at 8 (c3d8r) nodes without forgetting to finely mesh the cracked zone, of course the results are much more precise if the mesh of the the cracked area is finer. elasto-plastic crack-tip behavior must be written in order to take into account plasticity-induced loading history effects. using the direct cyclic method, the stress-strain curves in each zone were determined. i. elmeguenni, frattura ed integrità strutturale, 58 (2021) 202-210; doi: 10.3221/igf-esis.58.15 207 fatigue tests in traction-traction were simulated in abaqus / standard under sinusoidal cyclic loading with imposed stress (fig. 4). the maximum load applied to the specimen is 1kn, the load ratio is r = fmin / fmax = 0.1 and the stress frequency is 20 hz. fig. 5 illustrates the periodic amplitude imposed on abaqus. figure 6: amplitude applied during the fatigue test. stabilization analysis and numerical illustrations (asymptotic behavior of the different zones) ig. 6 illustrates the strain stress cycles (σ22 as a function of ε22) at the nugget of the welded joint during a cyclic numerical test. the plot represents an element located very close to the crack point, which is why we see that the stress state changes from traction to compression during cycle depending on external loading. part (a) of the curve corresponds to the time required for the calculation code to reach the set point of the imposed loading. the calculation code requires one cycle (an average of 265 iterations) to perfectly reach the setpoint. it is important to specify that for the simulated tests, the size of the time steps, size increments are 9.434e-4 for each cycle (t = 0.05) and the average number of iterations is at least 5, therefore the calculation code repeats each iteration 53 times to complete the calculation and ensure satisfactory precision of the solution. over the course of iterations, the solution is corrected until convergence. it is noted that the cyclic mechanical behavior of the nugget of the welded joint in alloy 2024-t351 around the crack point has a ratchet effect (part b of the curve); strong variations of the variables of the model are observed, in particular with incipient plasticity. once the plastic field is well established the variations between the cycles are less important and the evolution of the internal variables tend towards a periodic state over a certain number of cycles, this is the accommodation. (part c of the curve) up to about 90% of total life. we note that the stabilization is very slow, the evolution of the stress-strain cycles during the iterations shows that we obtain a good approximation of the solution from 120 iterations with 50 fourier terms as indicated in fig. 7. the shape of the cycle is well represented, while the level of average deformations of the solution remains slightly estimated. figure 7 : evolution of the stress-strain cycle of the nugget every 5 iterations, element 137. f i. elmeguenni, frattura ed integrità strutturale, 58 (2021) 202-210; doi: 10.3221/igf-esis.58.15 208 figure 8: a) stress-strain cycle obtained by dcm after 120 iterations. b) deformation fields at the end of the cycle stabilized by dcm. figure 9: stress-strain loop in each zone of the welded joint. ‐200 ‐100 0 100 200 300 0,029 0,031 0,033 0,035 0,037 s tr es s (m p a) strain (%) hysteresis cycles, iteration 120 i. elmeguenni, frattura ed integrità strutturale, 58 (2021) 202-210; doi: 10.3221/igf-esis.58.15 209 fig. 8 illustrates the cyclic mechanical behaviour in each of the zones constituting the welded joint in alloy 2024-t351: zat (as-rs), nugget, zatm (as-rs). these hysteresis loops recorded at 106 cycles; the solution no longer evolves. convergence is reached and the solution is stable. the points chosen are located after the crack front, the different areas show a ratchet at the start of the test before elastic adaptation. the buckles remain a little closed throughout the test. this is the elastic adaptation phenomenon observed for each zone of the joint. finally, the difference observed between the asymptotic behaviours of each of the zones is presented in the levels of plastic deformation which appears during the test. it is noted that the maximum strain is well established in the nugget followed by the zatm (as, rs) then those are the zat (as and rs) which are the least deformed. this last phase represents the place of damage due to the levels of very important deformations. the elastic adaptation is recorded until the end of the test. thus, we note that the shape of the cycles is different in each finite element chosen in the structure, but we finally obtain the same adaptation response recorded at the end of the cycle. by this analysis, we notice that the less deformed zones stabilize more quickly compared to the other zones. these results showed that the slowest zones to stabilize correspond to the maximum deformation. conclusion he direct cyclic method allowed to determine the local mechanical responses of the different zones of the welded joint by the fsw process of the 2024-t351 aluminum alloy. we have shown that the zones constituting this welded joint exhibit very different behaviors the ones to the others. the numerical tests in traction-traction (r = 0.1) allowed to highlight the heterogeneities of cyclic mechanical behavior in each of the zones constituting the joint 2024-t351 welded by fsw. the curves of local behavior (σ22 ε22) in each of the zones made it possible to note that the various zones constituting the joint present very heterogeneous mechanical behaviors, of 0.025% of deformation in the haz and up to 0.038% of total deformation in the nugget, because of the strong microstructure gradient introduced by the welding process. for the welded joint in alloy 2024-t351, the deformation field is located in the nugget followed by the zatm and finally the zat. this study showed the interest of the xfem method for the simulation of fatigue crack propagation without remeshing or projection of the field. the coupling of the xfem with the direct cyclic technique, makes it possible to perform cyclic calculations and obtain the precise response of the studied structure. references [1] ericsson, m., sandstrom, r. (2002). influence of welding speed on the fatigue of friction stir welds, and comparison with mig and tig. international journal of fatigue 25, pp. 1379–1387. doi: 10.1016/s0142-1123(03)00059-8. [2] sangshik, k., chang, g., sung, j. (2007). fatigue crack propagation behavior of friction stir welded 5083-h32 and 6061t651 aluminum alloys, international journal of materials science and engineering a 478, pp. 56–64. doi: https://doi.org/10.1016/j.msea.2007.06.008. [3] demmouche, y. (2012). study of the fatigue behavior of fsw welded joints for aeronautical applications, ph.d. thesis, national school of arts and crafts. [4] tran, h., masakazu, o., kenji, s. (2012). fatigue crack propagation behavior in friction stir welding of aa6063-t5: roles of residual stress and microstructure, international journal of fatigue 43, pp. 23–29. doi: 10.1016/j.ijfatigue.2012.02.003. [5] dickerson, t.l., przydatek, j. (2002). fatigue of friction stir welds in aluminium alloys that contain root flaws, international journal of fatigue, 25, pp. 1399–1409. doi: 10.1016/s0142-1123(03)00060-4. [6] jesper, h., hattel, m. r. (2014). modelling residual stresses in friction stir welding of al alloys—a review of possibilities and future trends, int j adv manuf technol 76, pp1793–1805. doi: 10.1007/s00170-014-6394-2. [7] charitidis, c.a., dragatogiannis, e.p., koumoulos, i.a., kartsonakis (2012). residual stress and deformation mechanism of friction stir welded aluminum alloys by nanoindentation, international journal of materials science and engineering a 540, 226. doi: 10.1016/j.msea.2012.01.129. t i. elmeguenni, frattura ed integrità strutturale, 58 (2021) 202-210; doi: 10.3221/igf-esis.58.15 210 [8] chahine, e., laborde, p., renard, y. (2006). crack tip enrichment in the xfem method using a cut-off function, international journal for numerical methods in engineering, pp1–15. doi: 10.1002/nme.2265. [9] živojinović, d., đurđević, a., grbović, a., sedmak, a., rakin, m. (2014). numerical modelling of crack propagation in friction stir welded joint made of aluminium alloy, international journal of procedia materials science 3, pp. 1330 – 1335. doi: 10.1016/j.mspro.2014.06.215. [10] živojinović, d., sedmak, a., grbović, a. (2013). crack growth analysis in friction stir welded joint zones using extended finit element method, journal of structural integrity and life, 13, 03. [11] elruby, a. y., nakhla, s., and hussein, a. (2018). automating xfem modeling process for optimal failure predictions, international journal for mathematical problems in engineering, 2018, 1654751. doi: 10.1155/2018/1654751. [12] pommier, b. (2003), determination of the asymptotic response of an anelastic structure subjected to cyclic thermomechanical loading, ph.d. thesis, polytechnic school. doi: 10.1016/s1631-0721(02)01516-4. [13] trollé, b. (2014). multi-scale simulation of fatigue crack propagation in rails. ph.d. thesis, national institute of applied sciences of lyon. [14] elmeguenni, i., mazari, m. (2019) numericql investigation on stress intensity fatocr and j integral in friction stir welded joint throught xfem method, frattura ed integrita strutturale, 47 (2019) 54-64. doi: 10.3221/igf-esis.47.05. [15] andrijana, d., danijila, z., aleksandar, g., aleksandar, s., marko, r., horia, d., snezana, k., (2015). numerical simulation of crack propagation in friction stir welded joint made of al 2024-t351 alloy, int. j. of engineering failure analysis, 58, pp. 477-484. [16] herbland, t. (2009) an elastoplastic correction method for the fatigue calculation of the stress concentration zones under non-proportional multiaxial cyclic loading, ph.d. thesis, mines school of paris. [17] casey, l., richardson, j., hegemann, e., (2002). an xfem method for modelling geometrically elaborate crack propagation in brittle materials, international journal for numerical methods in engineering, doi: 10.1002/nme.321. [18] benhaddou, m., ghammouri, m., latrache, f., hammouch, z. study of cleavage in a rectangular plate by the xfem method and the integral contour j method, international journal of materials today: proceedings. doi: 10.1016/j.matpr.2020.03.256. [19] lok singh, k., keswani. k, vaggar. m, (2014). crack growth simulation of stiffened fuselage panels using xfem techniques, indian journal of engineering of materials sciences, 21, pp.418-428. [20] bjr zagane, m., el sallah benbarek, s., benouis. a. (2017). numerical simulation of the femur fracture with and without prosthesis under static loading using extended finite element method (x-fem), journal of mechanical engineering, 14(1), 97-112. [21] golestaneh, a. f., aidy a., shaw voon, w. (2008). simulation of fatigue crack growth in friction stir welded joints in 2024-t351 al alloy, suranaree j. sci. technol. 15(4). [22] liu, g., hu, y., li, q. and zuo, z. (2013). xfem for thermal crack of massive concrete, (2013), mathematical problems in engineering, 343842, doi: 10.1155/2013/343842. [23] cavaliere. p. (2013). friction stir welding of al alloys: analysis of processing parameters affecting mechanical behavior, 2nd international through-life engineering services conference, elsevier. [24] genevois, c. (2004). genesis of microstructures during friction stir welding of aluminium alloy of the series 2000 & 5000 and resulting mechanical behavior, ph.d. thesis, polytechnic national institute of grenoble. microsoft word numero_58_art_18_3181.docx a. mishra et alii, frattura ed integrità strutturale, 58 (2021) 242-253; doi: 10.3221/igf-esis.58.18 242 supervised machine learning classification algorithms for detection of fracture location in dissimilar friction stir welded joints akshansh mishra centre for artificial intelligent manufacturing systems, stir research technologies, india akshansh@stirresearchtech.in , https://orcid.org/0000-0003-4939-359x apoorv vats department of computer science and engineering, jaypee university of information technology, india apoorvvats181@gmail.com, https://orcid.org/0000-0003-4339-4110 abstract. machine learning focuses on the study of algorithms that are mathematical or statistical in nature in order to extract the required information pattern from the available data. supervised machine learning algorithms are further sub-divided into two types i.e. regression algorithms and classification algorithms. in the present study, four supervised machine learning-based classification models i.e. decision trees algorithm, knearest neighbors (knn) algorithm, support vector machines (svm) algorithm, and ada boost algorithm were subjected to the given dataset for the determination of fracture location in dissimilar friction stir welded aa6061t651 and aa7075-t651 alloy. in the given dataset, rotational speed (rpm), welding speed (mm/min), pin profile, and axial force (kn) were the input parameters while fracture location is the output parameter. the obtained results showed that the support vector machine (svm) algorithm classified the fracture location with a good accuracy score of 0.889 in comparison to the other algorithms. keywords. fracture location; machine learning; classification; friction stir welding; dissimilar joints; python programming citation: mishra, a., vats, a., supervised machine learning classification algorithms for detection of fracture location in dissimilar friction stir welded joints, frattura ed integrità strutturale, 58 (2021) 242-253. received: 09.07.2021 accepted: 23.08.2021 published: 01.10.2021 copyright: © 2021 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. introduction achine learning algorithms are vital tools or methods for understanding and handling the data. it should be noted that a statistic can be a graphical or numerical summary of a collection of the given data [1-3]. data is overwhelming in nature which involves summarization and reduction which makes the dataset comprehensible to a human observer. understanding the data is very important because sometimes the available data can be misleading. so, the implementation of machine learning algorithms provides statistical framework for assessing the quality of available data [4-5]. m https://youtu.be/ycrrozmsbos a. mishra et alii, frattura ed integrità strutturale, 58 (2021) 242-253; doi: 10.3221/igf-esis.58.18 243 data is further classified into two key types i.e. organic/processed data and "designed" data collection [6]. organic data is extracted by a computerized system or from audio and video recordings. this type of data is generated organically as a result of some process and is generated over time. these processes generate massive quantities of data which is called big data. in order to process this type of data, significant computational resources are required. on the other hand, "designed" data collection is used to specifically address a stated research objective for example a particular individual sampled from the population. machine learning algorithms have gained some popularity in the friction stir welding process [7–9]. machine learning classification-based approach was used for predicting the mechanical properties of friction stir welded copper joints [10]. the results showed that the artificial neural network model resulted in a good accuracy score of 0.94. balachandar et al. [11] monitored the friction stir welding tool condition by using the random forest algorithm which gave better results. there is limited number of research studies available on the application of supervised machine learning classification models in the friction stir welding process. du et al. [12] used machine learning based classification models for studying the conditions of void formation in friction stir welding process. the results showed that the implemented artificial neural network (ann) and decision tree (dt) algorithms resulted in the accuracy of 96.6 %. machine learning based classification algorithms were used for the determination of mechanical properties of friction stir welded copper joints [13]. the results showed that the artificial neural network (ann) resulted in the accuracy of 96.6 %. in the present work, the fracture position of dissimilar friction stir welded joints is determined by using four supervised machine learning classification algorithms which will be discussed in the next sections. rotational speed (rpm) welding speed (mm/min) pin profile axial force (kn) fracture position 800 90 1 12 0 800 100 1 12 1 800 110 1 12 1 800 90 2 12 1 800 100 2 12 1 800 110 2 12 1 800 90 3 12 0 800 100 3 12 0 800 110 3 12 0 900 90 1 12 1 900 100 1 12 1 900 110 1 12 1 900 90 2 12 1 900 100 2 12 1 900 110 2 12 1 900 90 3 12 1 900 100 3 12 1 900 110 3 12 1 1000 90 1 12 0 1000 100 1 12 0 1000 110 1 12 0 1000 90 2 12 1 1000 100 2 12 1 1000 110 2 12 1 1000 90 3 12 1 1000 100 3 12 1 1000 110 3 12 0 table 1: experimental dataset. a. mishra et alii, frattura ed integrità strutturale, 58 (2021) 242-253; doi: 10.3221/igf-esis.58.18 244 experimental procedure he material used for welding purpose belonged to 6xxx and 7xxx aluminium series. in order to prepare the plate specimens machining process was done to remove the uneven surfaces. the experimental dataset is prepared on 27 friction stir welded specimens [12]. for testing purpose the transverse tensile specimens were prepared according to astm e8m-04 standard shown in fig. 1. tensile testing was carried out at a room temperature according to astm d 557 m94 standards. in the present research work, python programming language was executed on jupyter lab notebook for subjecting the supervised machine learning algorithms on the given dataset [12]. jupyter is a web-based interactive development environment that supports multiple programming languages used in which commonly used language is python programming. tab. 1 shows the parameters involved in the experimental study. rotational speed (rpm), welding speed (mm/min), pin profile, and axial force (kn) are input parameters while fracture position is an output parameter. figure 1: tensile test specimen [12] pin profiles such as simple square is labelled as 1, taper cylindrical threaded is labelled as 2 and taper square threaded is labelled as 3 while the output column i.e. in fracture position column, the fracture occurring in stir zone (sz) is labelled as 0 and fracture occurring at heat affected zone (haz) of 6061 is labelled as 1. specimens after and before tensile testing are shown in fig. 2 a) and 2 b). (a) (b) figure 2: a) specimens before testing; b) specimens after testing. the required python libraries such as pandas, numpy, seaborn, and pyplot were imported. after importing the libraries, the dataset was loaded into the jupyter environment. pair plot function is used for establishing the relationship between t a. mishra et alii, frattura ed integrità strutturale, 58 (2021) 242-253; doi: 10.3221/igf-esis.58.18 245 the multiple pairwise bivariate distributions in a given dataset as shown in fig. 3. count function was subjected to the given dataset to obtain the number of 0s and 1s in the output column i.e. in the fracture position column as shown in fig. 4. figure 3: multiple pairwise bivariate distributions. a. mishra et alii, frattura ed integrità strutturale, 58 (2021) 242-253; doi: 10.3221/igf-esis.58.18 246 figure 4: counting numbers of 0s and 1s. as shown in fig. 5, exploratory data analysis is used to know about the data pattern and further summarize their main characteristics. figure 5: exploratory data analysis in order to find out the important input parameters affecting the output parameter, the feature importance method was used. from fig. 6 it is observed that the axial force (kn) parameter creates no effect on the output parameter. so due to this reason, this parameter is dropped from the input parameters which are subjected to machine learning algorithms. a. mishra et alii, frattura ed integrità strutturale, 58 (2021) 242-253; doi: 10.3221/igf-esis.58.18 247 figure 6: calculation of feature importance results and discussion decision tree algorithm decision tree is a supervised machine learning algorithm that can be both implemented for classification and regression analysis. a decision tree model consists of a terminal node, a decision node, and a root node as seen in fig. 7. figure 7: decision tree algorithm architecture. the main objective is to create many pure nodes with the help of the splitting process. the nodes can be further categorized as pure or homogenous nodes and impure or heterogeneous nodes. after the splitting operation, the pure node contains the data points which belong to the same class while the impure node contains the data points that belong to a different class. the three important parameters which are used to determine the level of impurity are gini index, entropy, and classification error. it should be noted that the information gain and entropy are related to each other as seen in eqn. 1 while entropy can be further calculated by eqn. 2. a a. mishra et alii, frattura ed integrità strutturale, 58 (2021) 242-253; doi: 10.3221/igf-esis.58.18 248    1information gain entropy (1)     2 2entropy p log p q log q (2) where probabilities of success and failure are represented by p and q respectively. fig. 8 shows the decision tree plot for the given parameters in the dataset. fig. 9 shows the confusion matrix which is used to describe the performance of the classification model. tab. 2 shows the classification report of the decision tree algorithm. figure 8: decision tree plot for the experimental study. figure 9: confusion matrix showing the performance of decision tree algorithm. a. mishra et alii, frattura ed integrità strutturale, 58 (2021) 242-253; doi: 10.3221/igf-esis.58.18 249 precision recall f1-score 0 0.00 0.00 0.00 1 0.88 0.88 0.88 accuracy 0.78 macro average 0.44 0.44 0.44 weighted average 0.78 0.78 0.78 table 2: classification report of decision tree algorithm. from the tab. 2 it is observed that the accuracy score obtained from the decision tree algorithm is 0.78. k-nearest neighbor algorithm -nearest neighbors (knn) are the most popularly used machine learning algorithm where learning is based on the availability of similar data points. knn represents the model which is nonparametric in nature and its classification mechanism depends on the simple majority votes obtained from the neighbors. the knn model can be successfully implemented on classification tasks where there is a complex relationship between the target class and attributes. fig. 10 a) shows the representation of two classes i.e. fracture position at stir zone represented by red dots and fracture position at heat affected zone of 6061 by green dots. fig. 10 b) shows the yellow new data point which has to be classified. the new data point can fall into the class of fracture location at stir zone or to the class of fracture location at heat affected zone of 6061. in order to perfectly classify to which class this new point belongs, the knn algorithm is used to make classification on the basis of majority votes from the neighborhood data points. to achieve this state, nearest neighbor points are selected on the basis of distance matrices which can be euclidean distance as shown in eqn. 3, manhattan distance as shown in eqn. 4, and minkowski distance as shown in eqn. 5.       2 22 1 2 1         eucledian distance between data points x x y y (3)    1 2 1 2 manhattan distance x x y y (4)          1 1     n p p i i i minkowski distance x y (5) a) b) figure 10: a) representation of two classes of fracture location b) evaluating the nearest neighbours for a new data point. k a. mishra et alii, frattura ed integrità strutturale, 58 (2021) 242-253; doi: 10.3221/igf-esis.58.18 250 tab. 3 shows the classification report of k-nearest neighbour algorithm and fig. 11 shows the confusion matrix obtained. precision recall f1-score 0 0.00 0.00 0.00 1 0.86 0.75 0.80 accuracy 0.67 macro average 0.43 0.38 0.40 weighted average 0.76 0.67 0.71 table 3: classification report of k-nearest algorithm. figure 11: confusion matrix showing the performance of k-nearest neighbor algorithm. from tab. 3 it is observed that the accuracy score of k-nearest neighbor is 0.67 which is less than the accuracy score of decision tree algorithm. support vector machine (svm) algorithm ecision boundaries generally classify the class based on which the data point falls on as shown in fig. 12 a) which represents a bad decision boundary as it is unable to properly separate the two classes. there is an infinite number of decision boundaries so the main goal is to choose the best decision boundary. in order to find the optimal line, the support vector machine (svm) algorithm is used that can perfectly separate the two classes i.e. fracture location at stir zone and fracture position at the heat-affected zone of 6061 as shown in fig. 12 b). the decision boundary line can be represented by eqn. 6. in order to calculate the distance from the decision boundary to any point eqn. 7 is used. the main goal is to maximize the value of r for the support vectors points to the required optimal decision boundary.      0tg x w x b (6) d a. mishra et alii, frattura ed integrità strutturale, 58 (2021) 242-253; doi: 10.3221/igf-esis.58.18 251    g x r w (7) tab. 4 shows the classification report of svm algorithm. from the results it is observed that it resulted in the accuracy score of 0.89. fig. 13 shows the confusion matrix obtained for the svm algorithm precision recall f1-score 0 0.00 0.00 0.00 1 0.89 1.00 0.94 accuracy 0.89 macro average 0.44 0.50 0.47 weighted average 0.79 0.89 0.84 table 4: classification report of svm algorithm. (a) (b) figure 12: a) decision boundary separating two classes of fracture location b) optimal decision boundary separating the two classes of fracture location. figure 13: confusion matrix showing the performance of svm algorithm. a. mishra et alii, frattura ed integrità strutturale, 58 (2021) 242-253; doi: 10.3221/igf-esis.58.18 252 ada boost algorithm daboost is also known as adaptive boosting falls into the classification category of ensemble boosting as shown in fig. 14. the multiple weak classifiers are combined to increase the accuracy of the classifiers. adaptive boosting works on an iterative ensemble method that allocates the weights of the classifiers and further data samples are trained in each iteration step. figure 14: working mechanism of adaptive boosting algorithm. tab. 5 shows the classification report of ada boost algorithm and fig. 15 shows its performance. it is observed that the ada boost algorithm resulted in lowest accuracy score of 0.56 in comparison to the other algorithms. precision recall f1-score 0 0.00 0.00 0.00 1 0.83 0.62 0.71 accuracy 0.56 macro average 0.42 0.31 0.36 weighted average 0.74 0.56 0.63 table 5: classification report of ada boost algorithm. figure 15: confusion matrix showing the performance of ada boost algorithm. a a. mishra et alii, frattura ed integrità strutturale, 58 (2021) 242-253; doi: 10.3221/igf-esis.58.18 253 conclusion he recent work successfully implemented the supervised machine learning based classification models for first time detecting the fracture location dissimilar friction stir welded joints.  the present study successfully implemented the four supervised machine learning classification-based algorithms for the determination of fracture location in dissimilar friction stir welded joints. support vector machine algorithm resulted in highest accuracy score of 0.89 in comparison to the other algorithms while ada boost algorithm resulted in the lowest accuracy score of 0.56.  it can be concluded that the support vector machine algorithm works really well with a clear margin of separation and is effective in cases where the number of dimensions is greater than the number of samples i.e. in high-dimensional spaces.  the main insight of the present work is that the machine learning based algorithms can reduce the experimental time and cost by resulting in greater accuracy for prediction purpose.  the future scope of this work is to implement genetic algorithms and to check whether they can classify the given task better than the machine learning algorithms. references [1] mitchell, t.m. (1999). machine learning and data mining. communications of the acm, 42(11), pp.30-36. [2] sajda, p., gerson, a., muller, k.r., blankertz, b. and parra, l. (2003). a data analysis competition to evaluate machine learning algorithms for use in brain-computer interfaces. ieee transactions on neural systems and rehabilitation engineering, 11(2), pp.184-185. [3] džeroski, s., grbović, j., walley, w.j. and kompare, b. (1997). using machine learning techniques in the construction of models. ii. data analysis with rule induction. ecological modelling, 95(1), pp. 95-111. [4] ratner, b. (2017). statistical and machine-learning data mining: techniques for better predictive modeling and analysis of big data. crc press. [5] gilardi, n. and bengio, s. (2000). local machine learning models for spatial data analysis. journal of geographic information and decision analysis, 4, pp.11-28. [6] xie, j., song, z., li, y., zhang, y., yu, h., zhan, j., ma, z., qiao, y., zhang, j. and guo, j. (2018). a survey on machine learning-based mobile big data analysis: challenges and applications. wireless communications and mobile computing. [7] eren, b., guvenc, m.a. and mistikoglu, s. (2021). artificial intelligence applications for friction stir welding: a review. metals and materials international, 27(2), pp.193-219. [8] mahadevan, r., jagan, a., pavithran, l., shrivastava, a. and selvaraj, s.k. (2021). intelligent welding by using machine learning techniques. materials today: proceedings. [9] hartl, r., bachmann, a., habedank, j.b., semm, t. and zaeh, m.f. (2021). process monitoring in friction stir welding using convolutional neural networks. metals, 11(4), p.535. [10] thapliyal, s. and mishra, a. (2021). machine learning classification-based approach for mechanical properties of friction stir welding of copper. manufacturing letters. [11] balachandar, k. and jegadeeshwaran, r. (2021). friction stir welding tool condition monitoring using vibration signals and random forest algorithm–a machine learning approach. materials today: proceedings. [12] ravikumar, s., seshagiri, r.v. (2014). effect of process parameters on mechanical properties of friction stir welded disiimilar materials between aa6061-t651 and aa7075-t651 alloy. int j adv mech eng 4, pp. 101–114. [13] du, y., mukherjee, t. and debroy, t. (2019). conditions for void formation in friction stir welding from machine learning. npj computational materials, 5(1), pp.1-8. [14] thapliyal, s. and mishra, a. (2021). machine learning classification-based approach for mechanical properties of friction stir welding of copper. manufacturing letters, 29, pp.52-55. t microsoft word numero_30_art_41 a. shanyavskiy et alii, frattura ed integrità strutturale, 30 (2014) 340-348; doi: 10.3221/igf-esis.30.41 340 focussed on: fracture and structural integrity related issues in-service fatigue cracking of the propeller shafts joined by a spline-pinned construction to the engines of an-24, an-26, and il-18 aircrafts a. shanyavskiy, a. toushentsov state centre for flights safety, sheremetievo-1 airport, po box 54, moscow region, khimki state, 141426, russia shananta@mailfrom.ru, 103otdel@mail.ru abstract. the paper delivers a critical review of the research data on the crack initiation and crack growth patterns characteristic of the components of the spline-bolted joints between the propeller shaft and reducer shaft at an-24, an-26, and il-18 aircrafts. cracks in the shafts nucleated because of reduced bolt-fastening force. actually, the bolt (bolts) failed first (also by fatigue) and then fatigue cracks nucleated and grew in the shafts, the spline surface fretting zones and/or sharp edges of the attachment (bolt-conducting) holes making the crack origin sites. the crack growth history shows itself through the regular macro-beach marks, each mark sequentially pointing to the next loading event of the propeller shaft, i.e., to each next flight. the cracks cease growing for some while in the airscrews and their shafts just replaced to another aircraft. for the airscrew shafts, the critically assessed data show the crack growth period np ranging as five to ten percent of a total running period nf . we recommend performing nondestructive inspection of the airscrew shafts on every 250hour running period to ensure the safety flights. keywords. propeller shaft; fatigue; spline-bolted joint; fractography; crack-growth period. introduction t the stresses reduced to the level typical of high-cycle fatigue (hcf) behavior, the structure components exhibit lowered ratios np/nf between their crack growth period np and total duration nf of cyclic loading [1]. so, near the stress levels low as the so-called fatigue limit, the (np/nf) magnitudes can range as 0.05 to 0.1 for a smoothsurface test body. the (np/nf) data scatter primarily in response to the stress concentration effects peculiar to the free surface of a structure component. an np/nf magnitude can increase, typical of the contacting components of structure joints that additionally suffer surface damage from wear, and, thus, exceed the magnitude peculiar to a stationary loading regime free of a surface damage. as regards the propeller shafts (ps) of ai-24 and ai24vt engines of an-24, an-26, and il-18 aircrafts, cracks nucleated and grew—at the hcf or ultra-high cycle fatigue (uhcf) regimes (for the durations of 108 – 109 loading cycles [2–4])—from spline fretted sites, from sharp edges, or from material defects in a shorter spline area. in some cases, crack propagation terminated at the complete separation of the ps from a still operating engine, fig. 1. though the aircraft did land successfully this time, an urgent problem arose to reveal why the cracks generation occurred and to program reasonably periodic in-service inspection of the ps items to prevent, thereby, the in-flight cases of broken away ps. a a. shanyavskiy et alii, frattura ed integrità strutturale, 30 (2014) 340-348; doi: 10.3221/igf-esis.30.41 341 a) b) c) figure 1: (a) the an-24 aircraft wing (general view) in the braking zone of the propeller shaft; (b) a fraction divided by braking from the propeller shaft; (c) the view of the propeller shaft with a fatigue crack (pointed to by arrow). we mentioned above that, in a ps case, one should relate estimations of the np/nf magnitude to the hcf-to-uhcf transition range and to np/nf varying as 5 to 10%. such an approach appears realistic as confirmed by the np/nf estimations done for the cracks that grew from the surface damage sites in gear wheels [5]. yet one still wants to ascertain which of the two cases -unsatisfactorily tightened bolts or locally overstressed (beyond a limiting state in above-mentioned zones) joint-structure componentsdominates as the cause of the spline joints failure. below we critically assess the data (of more than 40-year period research) on the patterns and various causes of the inservice propagation of fatigue cracks in the airscrew shafts of ai-24 and ai24-vt engines on il-18, an-24, and an-26 aircrafts [2–4]. information on the cracks and failures of propeller shafts hey use a spline-bolted joint to have a propeller hub fasten to the propeller shaft of an ai-24 engine (fig. 2). the splined flange portion of an ps experiences dynamically applied loads that cause fretting over the spline surface. cracks became visible in the ps of ai-24 engines almost as early as at the very beginning period of running the engine. the first two ps exhibited many a cracked spline on the first 500 and 300 hours of running. those cracks were of fatigue nature, started propagating from fretting-corrosion zones and grew as far as for 2/3 spline length at the smaller-modulus side. nevertheless, even having inspections repeatedly and frequently performed (see fig. 2), with the magnetic inspection t a. shanyavskiy et alii, frattura ed integrità strutturale, 30 (2014) 340-348; doi: 10.3221/igf-esis.30.41 342 included, one remained unable to guarantee against in-service crack growth likely to bring the ps about failure (see fig. 1a). a) b) figure 2: (a) the joint (schematic) of the (1) propeller hub and (2) propeller shaft; (3) to (6) internal parts with (4 and 5) the sealing caps; (b) the sequences and durations of running periods; one can also see, at the ordinate, the dates and periodicity of inspecting the ps torn out in flight (see in fig. 1a). cracking took place either because of having the nuts (fastening the propeller) tightened unequally or as caused by the dynamic loadings (born by excessive misbalance). effects of the said loadings revealed themselves in the propeller obliquely blown–up in flight. when insufficiently tightened, the ps flange experience tiny shifts and, consequently, local fretting-corrosion and cracking of splines occurs over their contacting areas. experimental investigations of the dynamic stress patterns in the elements of a splined joint of an av-72 airscrew shaft with an ai-24a engine shaft revealed the following. with the fastening nuts tightened uniformly, the level of the stresses (tensile component) applied dynamically to the fillet part of an ps remains insensitive to the momentum of tightening (in 9 to 18 kgm range) of the pin nuts pressing to one another the flanged portion and the body of an ps. having reduced the tightening momentum from 13 to 9 kgm does not reduce the stresses in the ps fillet portion. in-service inspections of ps-to-engine junctions confirmed stability of the tightening momentums of the nuts fastening the av-72 ps units to the ai-24 engine shafts. the cases of broken pins belonging to the splined joints ceased owing to the constructional improvements that brought about greater fatigue resistance of the pins, stronger tightening of ps to its hub, as well as greater total rigidity of the splined junction itself. zones of extensively fretted splines shifted from the miner-module area to the middle part— between the pinholes. nevertheless, statistically and regarding an equal running time, the ps units of an ai-24 (two series) engine, screened out on repairs in 2001 to 2003 years, showed that the above constructional improvements did not alter the cracking trends as compared with those of the ass unites screened out in 1977 (fig. 3). a. shanyavskiy et alii, frattura ed integrità strutturale, 30 (2014) 340-348; doi: 10.3221/igf-esis.30.41 343 a) b) figure 3: ps rejected out of the service in (a) 1977 and (b) 2001, 2002, and 2003 (statistical data). the greatest stress 175 mpa (average for various frights) achieved by dynamic loading and measured by experiment in the r = 8 mm fillet part approaches the bifurcation point-fatigue limit for a fatigue life of 107 loading cycles. this case is closely reproducing an in-service state of the most stressed ps when executing, landed, a nonstandard abrupt turn by 90o in a twoto three-seconds time. however, only two ps unites broke over the r = 8 mm fillet zone in service (see fig. 3) after the most extensive cracking after the 3000to 6000-h operation. despite the thorough screening out of the cracked ps conducted on repairs or in service, several cases of ps broken away in flight still took place. one of the incidents occurred with an an-26 no. 26582 ak aircraft, named irbis, which belonged to kazakhstan: on april 04, 2004, an ps broke out of the right engine and hit the plane cabin, which caused decompression and forced landing. on the strength of this in-service incident of a broken ps, they took up again regular magnetic inspections of these structure components. another breakdown incident with an ps (an-26rv ra-4628 aircraft) inspired, in february of the same year, inspection of 18 ps units (already inspected once earlier) of which six units exhibited cracks. next to the first inspection, the ps running time continued to 977 h … 1158 h and to 286 h … 811 h for the an-24 and an-26 aircrafts, respectively. the second inspection done 286 h past the previous one showed that this running time was long enough for the cracks in the ps to extend by another 12 mm. a) b) c) figure 4: (a) the running time and (b) percent of rejected out ps, respectively, for an an-26 aircraft; (c) a similar histogram for the rejected out ps, with the superimposed curves of their running times for different engines. a. shanyavskiy et alii, frattura ed integrità strutturale, 30 (2014) 340-348; doi: 10.3221/igf-esis.30.41 344 in the following years, inspection for cracking at the repairing plants brought about greater amounts of the sorted out ps articles (from 8.8% in 2001 to 41.8% in 2003). the most numerous of the sorted out were the articles run for 2000 to 4000 h on ai-24vt engines. no data are available regarding a peak percent of the shafts screened out of the engines ai24vt, series 2. one can expect such a peculiarity as long as the type ai-24vt engine differs from type ai-24, series 2, engine in the strength of a combined effect that the loading conditions have on an ps. if one replaces arbitrarily an ps between the two engine types, he alters in the opposite direction the running duration required to initiate fatigue cracking. so having moved an ps from an ai-24, series 2 to an ai-24vt engine brings about longer running time (4000…6000 h) to initiate fatigue cracks, whereas the opposite change of the running time (to 2000…4000 h) is the case for having the ps moved in the reversed direction—to an ai-24, series 2 engine. having analyzed the screening trends of ps on repairs revealed that the numbers of fatigue cracks increased in the ps from ai-24 engines. such an increase occurs owing to the more extensive employment of an-26 aircrafts that, though at the ordinary service regimes, bring the greatest damage in the splined joints. such a view follows from the statistical data acquired since1996 and compared with those acquired earlier between the 1991 and 1993 (fig. 4) on the screening intensity of ps for the sake of cracks. in the earlier period, the share of the ps screened out at repairs increased from 6.3 to 32.1% despite the prominently reduced total running period of the an-24 and an-26 aircrafts. by 1993, the share of the ps screened out at repairs exceeded 30%; nevertheless, in that year the first case of an airscrew shaft broken out in flight took place. that share also exceeded 30% in 2003 and, again, the airscrews torn out in flight showed themselves on (year 2003) an24rb ra-46828, (year 2004) an-26 ra-26552, and (year 2004) an-26 ra-26582 aircrafts. at last, late in 2004, a through crack showed itself in the fillet part (r = 8 mm) by oil leak and increased shaking of the plane in flight. they only had two flights to perform until the full separation of the shaft! characteristic patterns of initiating and growing cracks racking begins from a spline surface in the fretting-corrosion area or, otherwise, form a conjugation edge (corner) between the surfaces of a shorter spline and a pinhole. crack initiation in a fretting-corrosion site shows that the shaft material behavior is characteristic of a partially closed synergetic system (fig. 5). crack initiation at the corner is largely relevant to the behavior of an open synergetic system (fig. 6). a) b) c) figure 5: (a) a spline rim (general view) with the spline sites of the fretting damage; (b) the fractures (open cracks) initiated at the fretting sites (pointed to by arrows); (c) the main fatigue fracture surface with macro-beach-marks of the propeller shaft, with the crack origin site (shown by arrow) at a fretting spot. nevertheless, fractographically, the crack origin site at the corner showed the crack focus situated at some distance from the metal surface—under a sort of beading—a burr formed due to the pinhole machining. an important finding was that in some instances of breaking ps by growing fatigue cracks the latter grew concurrently from the damage (fretting) sites of spline surface and from the edge corners of the pinholes (fig. 7). from the origin sites of both kinds, the cracks grew leaving behind the patches of the macroscopic lines (macro-beachmarks) of fatigue fracture. on the fracture surface, each of the single macroscopic fatigue lines is representative of a single flight cycle (fc) [2]. at the early stage—not far from the fracture origin site—the cracks propagate slowly. they grow, cutting the pinhole surface as well as the spline surface until they hit the rounded zone of transition to the internal buttend surface of an ps. c a. shanyavskiy et alii, frattura ed integrità strutturale, 30 (2014) 340-348; doi: 10.3221/igf-esis.30.41 345 a) b) c) figure 6: (a) the fracture surface (general view) of the broken shaft with the crack origin site at the pinhole edge (pointed to by arrow); (b) the fracture morphology by the crack origin site; (c) the crack initiation zone at the pinhole edge under the work-hardened (by drilling) surface layer of the shaft material. the dashed line divides the work-hardened zone from all the other parts of the fracture area. a line spacing increases monotonically (see fig. 6) toward the place in which the crack front changes for a new propagation plane. the crack growth period can last to 200 flight cycles at this stage. quite often, such a crack can show its farther propagation behavior as drastically transformed as much the reinstallation of airscrew violated the stress state of the ps joint. the engines vary in the stress pattern of an airscrew; so, having reinstalled an airscrew from other engine, one can expect nonlinear transient effects of building up damage in the shaft material. consequently, crack propagation can slow down for some time (several tens flights) required for having formed a ledge, characteristic of the transition between different loading routines. next to such a transient period, crack propagation accelerates and can bring about a failure as soon as in several flights. at a rotation rate of 1247 rev/min, an ps experiences (2.25–5) x 108 loading cycles in its 3000 to 6000-h running period. so mostly, the actual operation conditions conform to the revealed level of stress applied to the fillet part of an ps. such a view proves realistic as conforming to the actual ps operating periods. the latter appear 50-times over the figure 107—the number of loading cycles designed for the shaft material under the fatigue-limit stress. the cases of ps with fatigue cracks formed at the above operation times have nothing in common with off-design loading regimes. fatigue cracks initiated in the range of uhcf is a normal effect, peculiar to the construction under a standard operating regime; the cracks form, once the material achieves its limiting state in the spline fretting zones and at the acute edges or at the material defects in the area of shorter splines. at a nominal applied stress, the mentioned ps zones experience stresses raised (concentrated) to a level that, at the mentioned above operating times, is creative of fatigue cracks. in the mentioned above range of running times and with the characteristic effects of fretting damage and high enough cyclically applied loads, the operating conditions of the splined joints appear creative of the cracks even if having removed acute edges (reduced local stress a. shanyavskiy et alii, frattura ed integrità strutturale, 30 (2014) 340-348; doi: 10.3221/igf-esis.30.41 346 concentrations) and excluded press forming defects. a cyclically loaded airscrew shaft can exchange energy with the environment through its free spline surface; thereby, at a standard stress level, the ps experiences a surface damage that is more extensive than is the damage creative—after a longer running time—of a crack without the energy exchange (most likely under the surface of the most severely loaded zone). the other stress raising areas—at the pinhole edges or splinematerial defects—are the sites of locally overstressed material, equally susceptible to cracking in their own locations zones. a) b) c) figure 6: (a) and (b) the crack origin zones (general view) of the fracture surfaces of two different ps; cracks nucleated at a pinhole edge (pointed to by arrows a and at the fretting zones of splines (pointed to by arrows b; (c) magnified view a portion of fracture surface showing the mesoscopic lines of fatigue fracture (pointed out by several arrows). owing to a torque effect, the crack growth direction turned upward (see at the bottom part the group of fatigue lines crossing the lines of the other group)—to the external surface of the ps. relation of the np/nf ratio to the inspection periodicity of operating ps e mentioned above, that, , using a ratio np/nf of 5 to 10% was the only way to calculate the crack growth duration in an ps as long as no data on the actual time to crack initiation were available. we applied such a ratio to the cases of cracks, initiated at various stress raisers—fretting zones, acute edges, and material defects—but never grown to their critical size. w a. shanyavskiy et alii, frattura ed integrità strutturale, 30 (2014) 340-348; doi: 10.3221/igf-esis.30.41 347 we also took into account the forced (for various reasons) disconnections of an airscrew and of its reinstallation at other aircraft, which had its effect on the crack-growth behavior. such a replacement of an airscrew can result in a long-term arrest or deceleration of the crack growth. therefore, those increments in the operating time of ps supplied us with correction figures to the calculated np/nf magnitudes. the carefully examined patters formed by the macroscopic lines (macro-beach-marks) of fatigue fracture made it possible to estimate the relative duration of fail-safety operation (durability) of the shafts. in case that, for various objective reasons, necessary information was lacking, we employed the ratio np/nf of 5 to 10% to have acquired the estimations of the relative durability by calculations. those estimations showed such a share of a crack growth period in the total running time of an ps as being reasonable and worth using. fractographically, early crack growth periods appeared to share 7.1 or 8.1 percent of the intermediate running time—up to the first violation of the crack growth pattern, caused by the first ps reinstallation, and the shaft no. 1456e exhibited (also by the first violation point of the crack growth pattern) a relative durability of 9.9%. our calculations show these ideas to agree completely with the operation history of the ps. at the intermediate (between the ps installation events) stages of running which do involve crack propagation, the relative durability of ps can vary as 22 to 100 per cent, depending on whether the crack retardation effects do (22%) or do not take place. at a single running stage (no. 1109e shaft), which showed both fatigue fracture and a crack retardation effect, the relative durability achieved 7.25%; subsequently, the crack continued growing to cut through. the growth rate of fatigue cracks in ps, calculated based on the spacing of fatigue mbm, was twice as high in the ps of ai-24vt engines as of ai-24, series 2 engines. this finding indicates that the ps are more extensively loaded on the aivt engines and confirms that the above transient effects of crack retardation do show themselves when having the ps reinstalled from an ai-24vt to ai-24, series 2 engine. therefore, the earlier recommended 500-h periodicity of inspection appears only efficient for the ai-24, series 2 engines. the ps of аi-24вт engines, however, can fail before its next standard inspection time, be a crack overlooked in a repair or in periodic inspection. statistical data on screening out ps (see figs. 3 and 4) indicate that, notwithstanding the three stress raiser phenomena present, one should regard the cracking effects in ps as being a consequence of imperfect designing. the actual operating regimes, materials quality, pinholes geometry, and the contact characteristics of the splined joint—all accepted by the designer—concurrently contribute to the imperfection manifesting insufficient fatigue resistance of the construction. compared with the acute edges, the fretting areas of the spline surface do not so efficiently shorten the initiation period of fatigue cracks. only if we completely prevent the energy exchange of the shaft surface and environment, and, thereby, shift the crack origin site to the subsurface regions in the most highly stressed part of the shaft, a significant lengthening of the lifetime can occur. practically, however, such a reconstruction of the joining, employed in its present design for transmitting a torque, appears hardly possible. for that reason and according to the above discussion, the safety operation of an ps – ai-24vn engine assembly, in its present design, is possible providing a nondestructive inspection occurs after every 250 hours of the operating period. thereby, a small crack, even if unnoticed by an inspector, will not achieve its critical length but become definitely detectable by the time of the next nondestructive inspection. conclusion 1. owing to the special characteristics of their present design, the spline-bolted joints between the propeller and reducer shafts of an ai-24 engine remain unsafe from the in-service initiation and propagation of fatigue cracks. 2. in the components of a spline-bolted joint, a crack nucleates owing to the (1) lost tension and to fatigue failure of the fastening bolts, (2) fretting corrosion of the spline surface, which makes a crack-origin site, and (3) the sharp edge of a pinhole. cracks can form concurrently at both the fretting spot and the acute edge. 3. the ratio np/nf for the periods of crack growth and propeller operation (durability) ranges as 5 to 10%; as regards the examined components of spline-bolted joint in that fatigue cracks nucleated in and propagated from various crack-origin sites; this ratio also holds in case that the crack ceases growing for a while on having the propeller assembly replaced to another engine. 4. having acquired the period of crack growth in the propeller shafts from the number of macro-beach-marks on the fracture surface made it approved to perform nondestructive in-service inspection of the shafts after each of the 250-h running periods. a. shanyavskiy et alii, frattura ed integrità strutturale, 30 (2014) 340-348; doi: 10.3221/igf-esis.30.41 348 references [1] ivanova, v.s., terentyev, v.f., the nature of metal fatigue, metallurgy, moscow, russia, (1975). [2] shanyavskiy, a.a., toushentsov, a.l., spline joints critical state of airscrew shafts of engines ai-24 and periodicy of their in-service non-destructive inspection, science papers of the society of aircraft accidents investigators, moscow, 16 (2004) 42-61. [3] shanyavskiy, a.a., tolerant fatigue cracking of in-service aircraft structures. synergetics in engineering applications, monograph, ufa, russia, (2003). [4] shanyavskiy a.a., modeling of metals fatigue cracking. synergetics in aviation, monograph, ufa, russia, (2007). microsoft word numero_49_art_58_2421 h. berrekia et alii, frattura ed integrità strutturale, 49 (2019) 643-654; doi: 10.3221/igf-esis.49.58 643 behavior and damage of a pipe in the presence of a corrosion defect depth of 10% of its thickness and highlighting the weaknesses of the asme / b31g method h. berrekia, d. benzerga university of sciences and technology of oran, mechanical department, b.p. 1505, 31000 oran, algeria habib.doctorat@hotmail.com, djeb_benz@yahoo.fr a. haddi university of artois, ea 4515, laboratoire de génie civil et géo-environnement, béthune f-62400, france abdelkader.haddi@univ-artois.fr abstract. the company drc (pipe repair department) located within the sonatrach company of oil and gas in algeria, which is responsible for the repair of pipelines for the transport of gas or crude petroleum, will rehabilitate old pipes that have operated on-line for approximately 30 years or come from remaining projects. on the assumption that rehabilitating a pipeline means making it workable under the same conditions as a new structure and reducing the overall cost of the project. the abandonment of these tubes will have an important environmental and financial impact. the rehabilitation, which consists of recovering the maximum of tube, already used, therefore reduces the cost of the project. inspection and evaluation of corrosion defects are carried out in accordance with asme/31g method that is applied to low alloyed carbon steels with corrosion defects having soft profiles with low stress concentration. our research will consist in developing a method using a behavior-damage coupling of the material to highlight the weaknesses of the asme / b31g method [1] and show for defects whose depth does not exceed 10%, these defects can survive hydrostatic testing but will develop during service when the pressure is variable. keywords. pipeline, corrosion, damage mechanics, damage, finite element method, elastoplastic. citation: berrekia, h., benzerga, d., haddi, a., behavior and damage of a pipe in the presence of a corrosion defect depth of 10% of its thickness and highlighting the weaknesses of the asme / b31g method, frattura ed integrità strutturale, 49 (2019) 643-654. received: 03.03.2019 accepted: 17.06.2019 published: 01.07.2019 copyright: © 2019 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. introduction n a pipeline project, steel represents more than 35% of the total cost; the rehabilitation, which consists of recovering the maximum of tube, already used, therefore reduces the cost of the project. on the assumption that rehabilitating a pipeline means making it workable under the same conditions as a new structure and reducing the overall cost of the i http://www.gruppofrattura.it/va/49/2421.mp4 h. berrekia et alii, frattura ed integrità strutturale, 49 (2019) 643-654; doi: 10.3221/igf-esis.49.58 644 project. by way of example, the rehabilitation of the gz1 hassi r'mel-arzew gas pipeline carried out by drc / sonatrach for the sc5-ta section, ie 108 km, was based on a comparative study between two variants: -installation of a new line of 108km with acquisition of new tubes. -reuse of recovered tubes that have already been used for some thirty years of service or from remaining projects and rehabilitated according to the conditions of the asme / b31g method [1] which confirms the reuse of the tubes at the maximum operating pressure of the gas pipeline at 70 bars. the example of the gas pipeline gz1: translates into an overall cost of around 24.892 da per linear meter for a rehabilitated tube (tube + coating + pose) while if a new section was put the cost would have been 35.065 da lm. in conclusion, drc / sonatrach opts for the first variant which consists in realizing a significant financial saving, ie the use of rehabilitated pipes. the asme / b31g method [1] used by drc / sonatrach for the determination of the new operating pressure of a corroded pipe assumes that a pipe with a depth of corrosion defect not exceeding 10% of its thickness can be reused at the operating pressure without any risk and this regardless of the extension and the width of the corrosion defect. many researchers have investigated the effect of corrosion and fatigue phenomena on the life-cycle of materials and structures. based on the visual, metallurgical, and fractographic analyses as well as calculations using established asme methodologies, caligiuri has studied the rupture of natural gas pipeline in san bruno, california [2]. he observed that the failure was caused by the combination of a missing interior weld, a ductile tear, and fatigue cracking. zampieri et al. have investigated the influence of the corrosive phenomenon on the fatigue strength of a friction type joint made of high strength preloaded bolts [3]. they observed that the accelerated corrosion process applied to the specimens caused a not negligible reduction of the fatigue strength of joints. these authors have studied the fatigue behaviour of a bolted connection with high strength bolts using finite element method in order to determine the fatigue life cycles of the studied joint. these results suggest that other factors may influence the decrease in fatigue resistance of the corroded connection, such as a variation in the slip coefficient between plates or a certain amount of loss of bolts pretension, which may resulted in a decrease in the friction resistance of the connection and consequently a bearing type behaviour of it [4]. based on continuum damage mechanics (cdm), gabriel testa et al. [5] have used the bonora damage model (bdm) to predict the strain limit capacity of x65 steel grade used for pipeline application. it was shown that numerical simulation with cdm could be used to carry on “virtual experiments” for the determination of the material fracture toughness with high degree of accuracy. using conventional mathematical methods, b31g, rstreng-1, shell-92, dnv, pcorr, and fitnet ffs, terán et al. [6] analyzed a combined corrosion defects, which joins together a general corrosion and a pitting corrosion defects to predict the failure pressure of corroded steel pipelines. it was found that the failure pressure predictions of general corrosion combined with a pit are affected by the length and depth of two corrosion defects. in our study, we develop constitutive equations taking into account behavior-damage coupling of material to highlight the weaknesses of the asme / b31g method [1] and show for defects whose depth does not exceed 10%, these defects can survive hydrostatic testing but will develop during service when the pressure is variable [2]. our research work will focus on developing a method to highlight the weaknesses of the asme / b31g method [1] and its subsequent modifications. asme / b31g code is one of the solutions for an assessment of the influence of corrosion defects on pipe integrity .since it is often regarded as too conservative. considering a behavior-damage coupling of the material, finite element numerical simulations were carried out on xc65 steel pipes with pitting in the axial direction. depending on the size of the corrosion defect (length and width) [3].for a depth equal to 10% of the pipe wall thickness, the critical or dangerous area where the equivalent von mises stress is maximal is determined by the finite element code ansys [7]. the calculation of the crack initiation conditions in the critical area is obtained from the history of strain components taken as the output of the finite element calculation. modeling o model the pipeline, we used the ansys workbench 15.0 [7] software with two cases, a model with a rectangular defect and a model with a parabolic defect. given the symmetry of the pipeline, we modeled a half cylinder. the dimensions of the structure are length, radius and thickness. thus, we have been able to model the corrosion of the x65 steel pipe taking into account the geometry of the defects, the boundary conditions and the mesh. t h. berrekia et alii, frattura ed integrità strutturale, 49 (2019) 643-654; doi: 10.3221/igf-esis.49.58 645 figure 1: pipe with elliptic defect. figure 2: pipe with rectangular defect. figure 3: model with mesh. using the programmable language ansys [7], a subroutine was developed and implemented in the main code for the determination of critical point (m*) in the zone of corrosion defect (see figure 4) where microcracks may grow [8]. next, the constitutive law of the critical point (m*) where the equivalents stress σ* is maximum, obtained using the ansys code [7], and is implanted in the postprocessor based on the newton iterative method [9]. the study was conducted on pipes of external diameter of 40 '' and a thickness of 12.7 mm in steel x65 whose mechanical properties are grouped in the table 1 [10]. h. berrekia et alii, frattura ed integrità strutturale, 49 (2019) 643-654; doi: 10.3221/igf-esis.49.58 646 figure 4: analysis of local coupling of crack initiation. young’s modulus poisson’s ratio yield strength tensile strength 210.7 (gpa) 0.3 464.5 (mpa) 563.8 (mpa) table 1: mechanical properties of x65 steel. to highlight the effect of the width of the defect, we selected the following corrosion defects with a constant depth d / t = 10%. the table 2 bellow groups the defects retained. defect of corrosion extension [l] mm with [c] mm depth [d] mm defect -5 5 5 1.27 defect -10 10 10 1.27 defect -15 15 15 1.27 defect -20 20 20 1.27 defect -25 25 25 1.27 defect -30 30 30 1.27 defect -35 35 35 1.27 defect -40 40 40 1.27 defect -45 45 45 1.27 defect -50 50 50 1.27 table 2: the defects retained. the graph (see figure 5) shows the variation of the maximum von mises equivalent stress as a function of the extension of the corrosion defect. we note the graphs of all the defects are superimposed this explains the almost negligible effect of the width on the behavior of the corroded pipe. this can be explained by the fact that the depth of the corrosion defect is the most affected area mef calculations critical point (m*) post-processor h. berrekia et alii, frattura ed integrità strutturale, 49 (2019) 643-654; doi: 10.3221/igf-esis.49.58 647 low. there is also a relaxation of the stress of von mises from an extension of the defect of 15 mm. from this value the defect of corrosion begins to lose its acuity, there is less stress concentration in the vicinity of the defect. 0 10 20 30 40 50 60 400 410 420 430 440 450 460 470 480 width variation e q u iv a le n t st re ss [ m p a] length variation 5 10 15 20 25 30 35 40 45 50 figure 5: equivalent stress variation of maximum von mises as a function of the length of the corrosion defect. for the hydrostatic test, the test pressure has been increased until 1.5 times the service pressure according to the standards. each pipe with its corresponding corrosion defect (extension, width and depth fixed at 10% of the pipe thickness of 1.27 mm (see table 3 below) was subjected to the pressure of the hydrostatic test with a lifetime. the objectif is to determine whether corroded pipes with a depth equal to 10% of the thickness of the pipe can survive the hydrostatic test and consequently the service pressure. extension [l] mm width[c] mm depth [d] mm defect -5 5 5 1.27 defect -10 10 10 1.27 defect -20 20 20 1.27 defect -25 25 25 1.27 defect -35 35 35 1.27 defect -45 45 45 1.27 defect -60 60 60 1.27 defect -65 65 65 1.27 defect -75 75 75 1.27 defect -95 95 95 1.27 table 3: corrosion defect of each pipe the figure 6 represents the maximum von mises stress as a function of the tangential deformation in the vicinity of the corrosion defect. it clearly shows the behavior of all the corroded pipes exhibiting no damage during the hydrostatic test, which confirms and supports the asme / b31g method which states that a pipe with a defect whose depth does not exceed 10% of its thickness, can be reused at the same service pressure without any risk of damage. h. berrekia et alii, frattura ed integrità strutturale, 49 (2019) 643-654; doi: 10.3221/igf-esis.49.58 648 0,0000 0,0002 0,0004 0,0006 0,0008 0,0010 0,0012 0,0014 0 50 100 150 200 250 300 350 400 450 500 550 600 650 e q u iv a le n t st re ss [ m p a] deformation déf-5 déf-10 déf-20 déf-25 déf-35 déf-45 déf-60 déf-65 déf-75 déf-95 figure 6: behavior of corroded pipes during hydrostatic test. the internal pressure of the gas fluctuates according to the gas demand (see figure 7), therefore undergoes variations which causes the phenomenon of fatigue. fatigue is an insidious phenomenon because of its hidden nature can cause breaks for stress levels well below the limit of elasticity. 0 5 10 15 20 0 1000 2000 3000 4000 5000 6000 7000 p re ss u re ( m p a ) number of days figure 7: variation in service pressure as a function of time [11]. note that during service the pipe can be damaged this is explained by the fact that the phenomenon of fatigue is insidious because of its hidden nature. the rupture can occur for stress values well below the yield point since the fatigue limit is always below the yield point. fatigue is a phenomenon characterized by a strong micro plasticity in the vicinity of micro defects (micro voids, inclusions, precipitates) that are potential sources of damage. behavior – damage coupling t present, it is well established that the damage affects the elastic characteristics of the material, because of the reduction of the effective section of the force-resistant volume element. in damage mechanics, the damage variable is defined by a surface density of microcracks [12]. a h. berrekia et alii, frattura ed integrità strutturale, 49 (2019) 643-654; doi: 10.3221/igf-esis.49.58 649 d s d s    (1) if the damage is isotropic, d is a scalar; this allows the introduction of the notion of the effective stress: 1 d      (2) by considering the principle of deformation equivalence [13], the coupling deformation damage is done at two levels:  at the level of the elastic potential  ( ee , d) which leads to the law of elasticity of the damaged material : = ee     or ij ije ij .1+ e = 1-d 1-d ij e e       (3) where e is young’s modulus, and  , poisson’s ration. the associated variable to d is defined by: d      ;   2 22 1 eq vr e d        (4) y is the strain energy density release rate [14] defining the power dissipated in the damaging process where:     3 2 3 1 3 1 2 2 d d eq ij ij h v eq d ij ij h ij r                                           with: 1 3 h kk   at plastic yield function: 1 eq sf d     (5) where: s is the threshold of plasticity (defined previously). the condition eq s  deviates any plastic deformation and ensures a pure elastic deformation the zone in the vicinity of the corrosion defect (whose plasticity threshold s ) undergoes a plastic deformation, therefore a damage, while the zones further from the corrosion defect (whose elastic limit is y ) undergo only one elastic deformation. the kinetic law of damage for ductile damage derives from the dissipation potential f [15]: h. berrekia et alii, frattura ed integrità strutturale, 49 (2019) 643-654; doi: 10.3221/igf-esis.49.58 650 3 2 d ijp ij eq        si: 0f f  1 1 1 ije kk ij ij d d               e p ij ij         2 0 2 1 f f h p p es d      (6) the normality rule provides the evolution laws of: with: 1 32 3 p ij ij         (8) the damage evolution law (7.b) can be written: d s    if 0p p (9) when replacing y by its value of (4) we obtain:       22 2 2 1 3 1 2 32 1 eq h eq d s d                      (10) in summary, the constitutive laws written for newton's numerical method [16]: with: 2 2 eq vd r s     if: 0p p (11) where: s: is a constant characterizing the damage, depends on the material and the temperature. h: heavyside function. 0p : is the accumulated plastic strain, when the damage is zero (the threshold of damage) with:  0 0h p p  if: eq s   0 0h p p  if: 0p p p fe      (7.a)  0. f d p h p p s          (7.b) where: λ: is the plastic multiplier, determined by the consistency condition 0f f  p: is the accumulated plastic strain ( 0p p if d = 0) h. berrekia et alii, frattura ed integrità strutturale, 49 (2019) 643-654; doi: 10.3221/igf-esis.49.58 651 using a stepwise method simultaneously with the method (scheme) implicit newton, which ensures good convergence [17]. the method developed above gives versus of the internal pressure of the pipe, the value of the damage, and the accumulated plastic strain and stress components at each instant until a macroscopic crack initiation at the defect corrosion. this allows determining the maximum lifetime that a corroded pipe could support in the case of a longitudinal corrosion defect. the maximum lifetime is the lifetime value corresponding to the critical value of the damage dc (corresponding to crack initiation). figure 8 shows the damage as a function of cycles number for retained corrosion defects. it is noted that the damage is initiated in the material for a number of cycles equal to n0 (microscopic crack initiation) and the microcrack propagates until a macroscopic crack is obtained for a number of cycles equal to nr. figure 8 also highlights the effect of the degree of corrosion (extension and width of the defect) on the pipe lifetime. 0 6000 12000 18000 24000 30000 36000 42000 48000 54000 0,000 0,025 0,050 0,075 0,100 0,125 0,150 0,175 0,200 0,225 0,250 0,275 0,300 déf-95 déf-75 déf-65 déf-60 déf-45 déf-30 déf-25 déf-20 déf-10 déf-5 d am a ge number of cycle figure 8: damage as a function of cycles number. based on figure 6, we can transform the numbers of cycles in lifetime, that is to say in number of days or years knowing that: 1 cycle = 10 days cycles number days number defect n0 nr n0 nr defect-95 44 7143 440 71430 defect-75 88 14286 880 142860 defect-65 132 21429 1320 214290 defect-60 154 25000 1540 250000 defect-45 176 28572 1760 285720 defect-30 198 32143 1980 321430 defect-25 220 35715 2200 357150 defect-20 242 39286 2420 392860 defect-10 264 42858 2640 428580 defect-5 286 46429 2860 464290 table 4: number of cycles according to corrosion defect. h. berrekia et alii, frattura ed integrità strutturale, 49 (2019) 643-654; doi: 10.3221/igf-esis.49.58 652 déf-5 déf-10 déf-20 déf-25 déf-30 déf-45 déf-60 déf-65 déf-75 déf-95 1 10 100 1000 10000 lo g 1 0 n number of defects number of cycles at crack initiation number of cycles at rupture crack fracture histogram: service life according to degree of corrosion (extension, width) the histogram groups the results of the lifetime obtained in number of cycles for each corrosion defect. the investigated pipeline has an initial cycle number n0 of which the damage has appeared (initiation of crack). on the other hand, the pipeline considered can go up to a number nr of cycle (the maximum lifetime) related to the damage causing a rupture. it can be seen that the lifetime n0 at crack initiation or nr at failure decrease when the extension and the width of the defect increase keeping a constant depth equal to 10% of the thickness of the pipe. it is also noted that the lifetimes increase in the case where the extension of the defect is important this can be explained by the increase in the loss of metal and the increase in the volume of the corrosion defect. this shows the effect of the extension of the corrosion defect on the lifetime of the pipe in the case where the depth remains low. the effect of the width of the defect remains negligible for a depth of the defect equal to 10% of the pipe thickness. figure 9 shows the cycle variation at initiation as a function of the length and width of the corrosion defect during pipe service. it is noted that the lifetime at the initiation of a crack in the vicinity of the corrosion defect decreases when the length and width of the defect increase. 0 20 40 60 80 100 50 100 150 200 250 0 20 40 60 80 100 lif e tim e n 0 a t in iti a tio n o f ct a ck width o f corro sion de fect in mm e xte n sio n o f co rro sio n d e fe ct figure 9: number of cycles at initiation. h. berrekia et alii, frattura ed integrità strutturale, 49 (2019) 643-654; doi: 10.3221/igf-esis.49.58 653 figure 10 shows the cycle variation at rupture as a function of the length and width of the corrosion defect during pipe service. it is noted that the lifetime at rupture in the vicinity of the corrosion defect decreases when the length and width of the defect increase. 0 20 40 60 80 100 10000 20000 30000 40000 50000 0 20 40 60 80 100 lif e ti m e n r a t ru p tu re width o f corro sion de fect in mm e xte n sio n o f co rro sio n d e fe ct figure 10: number of cycles at rupture. conclusion n this study, a method was developed to highlight the weaknesses of the asme / b31g method using the concept of damage mechanics. the prediction of damage initiation from an existing corrosion defect of steel pipes has been investigated using numerical approach. a constitutive coupled behaviour-damage based on the concept of effective stress and on finite element method to determine a critical value of stress at the vicinity of corrosion defect. a finite element simulation is based on the steel elastoplastic constitutive law and on the chosen mesh for a good relative convergence accuracy of the damage values. for the depth of defects does not exceed 10% of the pipe thickness, we have shown that defects can resist to the hydrostatic pressure test or a constant service pressure without damaging the pipe. however, these defects do not resist to pressure variations, which may generate a phenomenon of fatigue causing a failure of pipe. therefore, failures can occur for corrosion defects when the depth value reached 10% of the pipe thickness, while the asme / b31g method states that no rupture of pipe occur in this case. however, it has been shown that the concept of damage mechanics allows determining the optimum depth defect in order to predict the failure of pipe. references [1] asme b31g (2009): manual for determining the remaining strength of corroded pipelines [s]. american society of mechanical engineers, new york. [2] caligiuri, r. d. (2015). critical crack path assessments in failure investigations, frattura ed integrità strutturale, 34 125-132; doi: 10.3221/igf-esis.34.13 [3] zampieri, p. curtarello, a.pellegrino, c. maiorana, e. (2018). fatigue strength of corroded bolted connection frattura ed integrita strutturale, 12 (43), pp. 90-96. doi: 10.3221/igf-esis.43.06 i h. berrekia et alii, frattura ed integrità strutturale, 49 (2019) 643-654; doi: 10.3221/igf-esis.49.58 654 [4] zampieri, p. curtarello, a. maiorana, e .pellegrino, c. (2017).numerical analyses of corroded bolted connections. 2nd international conference on structural integrity, icsi 2017, 4-7 september 2017, funchal, madeira, portugal, procedia structural integrity 5, pp. 592-599. [5] testa, g., bnora, n., gentile, d., ruggiero, a, iannitti, g. (2017). strain capacity assessment of api x65 steel using damage mechanics. frattura ed integrità strutturale, 42, pp. 315-327; doi: 10.3221/igf-esis.42.33 [6] terán, g. capula-colindres, s. velázquez, j.c. fernández-cueto, m. j. angeles-herrera, d.héctor herrerahernández. (2017). failure pressure estimations for pipes with combined corrosion defects on the external surface: a comparative study. int. j. electrochem. sci., 12, pp. 10152 – 10176, doi: 10.20964/2017.11.86. [7] ansys: http://www.ansys.com/products/academic. [8] benzerga, d. (2015).burst pressure estimation of corroded pipeline using damage mechanics, mmssd, isbn 978-3319-14531-0. doi: 10. 1007/978-3-319-14532-7 springer. [9] saheya, b., guo-qing, c., yun-kang, s., cai-ying, w. (2016). a new newton-like method for solving nonlinear equations, springer plus 5, pp. 1269.doi 10.1186/s40064 016 2909 7. [10] antónio .a. f, abílio m. p., renato n.j. (2018). monotonic and ultra-low-cycle fatigue behaviour of pipeline steels experimental and numerical approaches, pp. 36-120.doi.org/10.1007/978-3-319-78096-2_2. [11] acpre: (1996). risk management program standard, for use in the pipeline risk management demonstration program produced by the joint risk management standard team, the office of pipeline safety, american petroleifin institute, interstate natural gas association of america, national association of pipeline safety representatives, gas research institute. [12] lemaitre, j. (1998). micro-mechanics of crack imitation, i.u.t.a.m symposium on recent advances in nonlinear fracture mechanics, pasadena california (u.s.a) march. [13] lemaitre, j., doghri, i. (1994). damage 90: a post processor for crack initiation, comput. methods appl. mech. eng.115, pp. 197-232. [14] lemaitre, j. (1993). mécanique des solides déformables et endommage ables, cours de d.e.a, cachan, edition october. [15] artioli, e., auricchio, f., beirão da veiga, l. (2007). second-order accurate integration algorithms for von-mises plasticity with a nonlinear kinematic hardening mechanism, comput. methods appl. mech. engrg. 196, pp. 1827– 1846. [16] benallal, a. billardon, r. doghri, i. (1988). an integration algorithm and the corresponding consistent tangent operator for fully coupled elastoplastic and damage equations, comm. appl. numer. methods 4, pp. 731-740. [17] courtney, r. 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can be opened with acrobat and adobe reader 5.0 and later.) >> /namespace [ (adobe) (common) (1.0) ] /othernamespaces [ << /asreaderspreads false /cropimagestoframes true /errorcontrol /warnandcontinue /flattenerignorespreadoverrides false /includeguidesgrids false /includenonprinting false /includeslug false /namespace [ (adobe) (indesign) (4.0) ] /omitplacedbitmaps false /omitplacedeps false /omitplacedpdf false /simulateoverprint /legacy >> << /addbleedmarks false /addcolorbars false /addcropmarks false /addpageinfo false /addregmarks false /convertcolors /converttocmyk /destinationprofilename () /destinationprofileselector /documentcmyk /downsample16bitimages true /flattenerpreset << /presetselector /mediumresolution >> /formelements false /generatestructure false /includebookmarks false /includehyperlinks false /includeinteractive false /includelayers false /includeprofiles false /multimediahandling /useobjectsettings /namespace [ (adobe) (creativesuite) (2.0) ] /pdfxoutputintentprofileselector /documentcmyk /preserveediting true /untaggedcmykhandling /leaveuntagged /untaggedrgbhandling /usedocumentprofile /usedocumentbleed false >> ] >> setdistillerparams << /hwresolution [2400 2400] /pagesize [612.000 792.000] >> setpagedevice microsoft word numero_39_art_22 m. romano et alii, frattura ed integrità strutturale, 39 (2016) 226-247; doi: 10.3221/igf-esis.39.22 226 parametric characterization of a mesomechanic kinematic caused by ondulation in fabric reinforced composites: analytical and numerical investigations marco romano, ingo ehrlich ostbayerische technische hochschule regensburg, department of mechanical engineering, laboratory of composite technology, galgenbergstrasse 30, 93053 regensburg, germany norbert gebbeken university of the bundeswehr munich, department of civil engineering and environmental sciences, institute of engineering mechanics and structural analysis, werner-heisenberg-weg 39, 85577 neubiberg, germany abstract. a parametric characterization of a mesomechanic kinematic caused by ondulation in fabric reinforced composites is investigated by analytical and numerical investigations. due to the definition of plain representative sequences of balanced plain-weave fabric reinforced single layers based on sines the variable geometric parameters are the amplitude and the length of the ondulation. the mesomechanic kinematic can be observed in both the analytic model and the fe-analyses. the analytic model yields hyperbolic correlations due to the strongly simplifying presumptions that neglect elasticity. in contrast the fe-analyses yield linear correlations in much smaller amounts due to the consideration of elastic parts, yet distinctly. keywords. fiber reinforced plastics; mesomechanic scale; fabric reinforced layer; ondulation. citation: romano, m., ehrlich, i., gebbeken, n., parametric characterization of a mesomechanic kinematic caused by ondulation in fabric reinforced composites: analytical and numerical investigations, frattura ed integrità strutturale, 39 (2017) 226-247. received: 29.09.2016 accepted: 02.12.2016 published: 01.01.2017 copyright: © 2017 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. introduction owadays the use of fiber reinforced plastics become indispensable in many areas in industry. the feature of high stiffness and strength which simultaneously combine low mass allows new design approaches for weight loss, which leads to energy savings, for example in the automotive and aircraft industry. simplified theoretical approaches for fiber reinforced plastics often presume a layup of only unidirectionally reinforced single layers. as a first approach in applied engineering the structural mechanic properties can analytically be determined by the use of so-called micromechanical homogenization theories. these are usually based on the single components’ properties, namely matrix and fiber. however, different kinds of fabrics are often applied as reinforcements in the layup of structural parts. in this case homogenization theories reach their limit. the reason therefore is that the mesomechanic n http://www.gruppofrattura.it/pdf/rivista/numero39/audio/22.mp3 m. romano et alii, frattura ed integrità strutturale, 39 (2016) 226-247; doi: 10.3221/igf-esis.39.22 227 geometry of fabric reinforced single layers cannot be considered sufficiently by relatively simple homogenization approaches. yet, mesomechanic correlations are distinctly different as they significantly influence the mechanical properties of a structure. research environment he research environment is the description of the structural mechanic behavior of fabric reinforced plastics. a chronological literature review is presented. the conclusions lead to the pursued mechanical principle. literature review naik and shembekar 1992 [1] present linear-elastic investigations of plain-weave fabric reinforced single layers. the ondulation influences the plane structural mechanical material properties. there is a significant discrepancy between the one-dimensional analytical and numerical investigations to them of the experiments. in contrast the two-dimensional analytical and numerical investigations correlate very well with the experiments. mital, murthy and chamis 1996 [2] investigate the micromechanics of plain weave composites. as a result the effects of the fabric reinforcement have been described analytically and basically verified numerically. the fiber-orientation in the mesoscopic dimension has been described by sinusoid parts in the ondulation region connected by straight parts above and under the ondulated yarn. for means of simplicity and in order to reduce computation time symmetry characteristics has been used in the model. guan 1997 [3] investigates the visco-elastic damping in fabric reinforced single layers by fe-calculations. a plain-weave fabric is modeled by representative volume elements. a sensitivity analysis regarding the length of the ondulation shows, that the model is relatively insensitive to a variation of this geometric parameter. a basic validation is carried out by the decay of vibrating flat beam-like specimens. byun 2000 [4] presents an analytical model of a so called unit cell in a mesomechanic scale in order to calculate the geometric characteristic and the three-dimensional structural material properties. in detail the ondulation is presumed continuously differentiable and investigated by coordinate transformation. a validation in one-dimensional tensile tests is carried out for seven different fabric constructions. huang 2000 [5] treats the structural mechanical properties of laminates of fabrics according to the introduced the socalled bridging model. it describes linear-elastic, plastic and strength aspects of balanced plain-weave fabrics under arbitrary loading. the presumed geometry causes three mechanically different regions, namely warp and fill yarn and surrounding matrix. several geometric parameters are considered for a verification of the model. an experimental validation yields a good correlation with the results of the analytic model. guan and gibson 2001 [6] suppose the acting of a mesomechanic mechanism for damping in fabric reinforced composites. therefore a pain-weave construction is investigated numerically and validated basically by the decay of vibrating flat beam-like specimens. tabiei and yi 2002 [7] confront different methods for the determination of structural mechanic material properties of fabric reinforced plastics, amongst representative volume elements, four-cell-method and three-dimensional fecalculations. in detail results of different numerical investigations with fe-calculations are confronted. besides precision the numerical efficiency and thereby the applicability is taken into account. le page et al. 2004 [8] carry out two-dimensional fe-calculations, presuming plane stress and considering mesomechanic geometric parameters. the aim is the prediction of damage propagation in fabric reinforced laminates as a function of the number of layers. thereby layups with different numbers of single layers of plane-weave fabrics are investigated under the presumption of the “in-phase” arrangement and “out-of-phase” arrangement. against this background parametrical fecalculations are carried out. wielage et al. 2005 [9] emphasize the relevance of a detailed mesomechanic description of laminates of fabric reinforced single layers. the carried out fe-calculations consider representative volume elements of three kinds of fabrics, namely plain-weave, twill 2/2 and satin 1/4. the independent structural mechanic material properties of the ondulated rovings are presumed as 0°-unidirectionally reinforced regions. the structural mechanic stiffnesses and the thermal expansion coefficients are calculated and validated experimentally. barbero et al. 2006 [10] describe a fe-model for the calculation of laminates of plain-weave fabrics. the basically different arrangements, namely “in-phase” (here called “iso-phase”) and “out-of-phase”, are considered. the difference between the global and local fiber volume content is discussed. the determination of the local fiber volume content in the t m. romano et alii, frattura ed integrità strutturale, 39 (2016) 226-247; doi: 10.3221/igf-esis.39.22 228 ondulated rovings is done by the weighted average of the experimentally determined global fiber volume content, based on the relative part of the areas of the different regions. ballhause 2007 [11] investigates the structural mechanics of dry fabrics on the mesomechanic scale under oneand twodimensional loading. a failure model is formulated based on the increase of contact forces and simultaneously the reduction of the curvatures at the crossings under increasing loads. matsuda et al. 2007 [12] besides the elastic behavior investigate the viscoplastic parts in plain weave fabrics. a homogenization theory is developed numerically considering the in-phase and out-of-phase arrangement. nakanishi et al. 2007 [13] investigate the damping properties of fabric reinforced composites. thereby glass fibers as a plain weave fabric in a polymeric matrix system are considered in numerical investigations. based on the determined mesomechanic properties flat beam-like specimens have been modeled by means of fe-analyses and investigated up to the third bending mode in vibration. badel, vidal-sallé and boisse 2007 [14] as well as hivet and boisse 2008 [15] identify a mesoscopic mechanical behavior for woven composites. therefore dry fabrics under biaxial tension are investigated numerically. a strong nonlinearity is reported especially at the beginning of the loading. el mahi et al. 2008 [16] present an analytical description of structural mechanic material damping mechanisms in fabrics. the carried out fe-calculations are validated. the strain energy under the presumption of plane stress is considered. the validation is carried out by the decay of vibrating flat beam-like specimens at the first three natural frequencies. the 0°unidirectionally reinforced specimens show smaller structural material damping as the fabric reinforced ones, whereat the plain-weave reinforced specimens showed distinctly higher damping values than the twill-fabric reinforced ones. the effect, however, is lead back to friction, what is rather improbable when the specimens originally are neither prestressed nor damaged. szablewski 2009 [17] treats representative sequences of plain-weave reinforced single layers under the simplifying presumption of sine-shaped ondulations of the rovings in the mesomechanic scale. the geometrically definitely defined model provides the determination of stress and strength aspects. finally, the possible adaption of the presented idealized geometry to other types of fabric constructions is mentioned. hivet and duong 2010 [18] carry out similar numerical investigations for dry fabric reinforcements under shear load conditions. thereby the load is applied by a picture-frame mechanism. nonlinearities are detected regarding the angle of deformation and the resulting orientation of the yarns in the fabric. ansar, xinwei and chouwei 2011 [19] give a review about modeling strategies. even if 3d woven composites are focused, a parametric consideration of the geometric dimensions is supposed. correlations between geometric and technical parameters are indicated. different approximations for modeling the cross-section, amongst others a lens-shaped crosssection, of the single tows are listed. kreikmeier et al. 2011 [20] introduce sine-shaped fiber-orientation in the in-plane direction as an imperfection due to a selected manufacturing process. the sine as an analytical function is processed analytically for a basic description of the phenomenon, yet without parametric variation of the geometric dimensions. valentino et al. 2013 [21] and valentino et al. 2014 [22] mechanically characterize basalt fiber reinforced plastics with different fabric reinforcements by experimental tensile tests and fe-calculations. in ranges of small deformations and at a comparable fiber volume content the fabric reinforced specimens exhibit slightly lower stiffnesses as the comparable 0°unidirectionally reinforced ones. pursued mechanical principle the aim of the carried out investigations is the identification and verification of a mesomechanic kinematic caused by ondulations in fabric reinforced composites. based on a sine as a purely analytic trigonometric function according to eq. (2) a so called plain representative sequence of a balanced plain weave fabric reinforced layer can be derived. the amplitude a and the length l are the characteristic geometric parameters. they define an entire cross-section of one complete ondulation. two reasonable basic geometries for further analytical processing and for the carried out feanalyses are shown in fig. 1 left. the simplified geometry of the ondulation for the carried out fe-analyses represents an idealized cross-section of the warp yarn of a fabric reinforced single layer cut along its theoretic center line perpendicular to the crossing fill yarns. three structural mechanically different regions can be identified. regarding their stiffnesses as the characteristic structural mechanical properties there are  the warp yarn with predominant direction following the longitudinal sine and so e1 following the sine and e2 perpendicular to it, m. romano et alii, frattura ed integrità strutturale, 39 (2016) 226-247; doi: 10.3221/igf-esis.39.22 229  the two fill yarns with predominant direction perpendicular to the cross-section and so e e2 3 in the investigated plain model and  the matrix region that is not reinforced at all with em. there are significant differences in the values of the stiffnesses of the different regions. thereby the stiffness e1 of the unidirectionally reinforced yarns is significantly higher in the direction of the reinforcement compared to the stiffness e2 in direction perpendicular to the reinforcement and the stiffness em of the matrix region. the relations can mathematically be related by e e e1 2 m  (1) common homogenization theories yield e e e1 2 m150 gpa 11.5 gpa 3.3 gpa     in case of a unidirectionally reinforced single layer with high tenacity (ht) carbon fibers with a presumed fiber volume content of f 60 %  as absolute values for the stiffnesses. two different effects in the model can be identified, when positive and negative longitudinal deformations are considered. in both cases the unidirectionally reinforced ondulated yarn is subjected to a purely elastic deformation. additionally at the same time in case of positive longitudinal deformations a smoothing or flattening, and in case of negative deformations an upsetting of the unidirectionally reinforced ondulated yarn is induced due to its ondulated shape. in both cases the variation of the amplitude is a superposition of transversal deformation due to poisson effects as a purely elastic response and a purely kinematic response due to geometric constraints in the mesomechanic scale. in contrast longitudinal deformations applied on a unidirectionally reinforced single layer in direction of the reinforcement leads to a lengthening and shortening in longitudinal direction and a transversal contraction directly coupled due to poisson effects only. the repeated acting of this mesomechanic kinematic due to geometric constraints is presumed to enhance the damping properties of fabric reinforced single layers compared to unidirectionally reinforced ones. for an evaluation the free decay behavior of flat beamlike specimens with fabric and unidirectionally reinforced single layers can be considered. thereby the fixed-free boundary condition has been identified as adequate. during the free decay the structure undergoes the kinematic in a number of cycles equal to the fundamental frequency. the basic concept and the identification of the acting mechanism has been validated basically in ottawa et al. 2012 [23] for one set of comparable specimens of basalt fiber reinforced epoxy (0° unidirectionally and 0° twill fabric 2/2 reinforced in warp direction) and more detailed in romano et al. 2014 [24, 25] and romano 2016 [26] for three sets of comparable specimens of carbon fiber reinforced epoxy (0° unidirectionally and 0° plain and twill fabric 2/2 reinforced in warp direction). thereby, the term comparable is defined by the property and the quality of the composite material of the respective set of specimens. one set of specimens is considered comparable when its single layers consist of the same kind of reinforcement fiber, 0° unidirectionally reinforced on the one hand and 0° fabric reinforced single layers (i. e. in warp direction) on the other hand, with the same polymeric matrix system and additionally at approximately same fiber volume contents f 60 %  and overall thicknesses of the laminate t. mesoscopic approach he phenomena of ondulation in fabric reinforced composites are examined on the mesoscopic scale. it is an effect in fabrics as textile semi-finished products. the warp yarns are perpendicularly crossed by the fill yarns alternating at its top and at its bottom. in the following investigations the relatively simple and at the same time easily describable geometry of a balanced plain weave fabric is considered further. the aim of the carried out investigations is the identification of the previously described acting mesomechanic kinematic correlations. in the carried out analytical and numerical investigations based on plain representative sequences the variable characteristic geometric parameters are the amplitude a and the length of the ondulation in the fabric lf and the length of the cross-section of a roving as a fill yarn lr, respectively. the parametric variation of the geometric dimensions in realistic steps provides the analysis of the sensitivity of the acting mesomechanic kinematic to the differently shaped ondulations. first a one-dimensional analytic approach is carried out. a kinematic is derived analytically and investigated parametrically. for a first approach strongly simplifying presumptions are necessary, so the elastic parts are neglected in this case. t m. romano et alii, frattura ed integrità strutturale, 39 (2016) 226-247; doi: 10.3221/igf-esis.39.22 230 parametric fe-calculations allow the consideration of elastic parts. the numerical investigations focus on plain representative sequences as a two-dimensional verification of the analytic model. degree of ondulation in order to definitely describe the differently shaped ondulations regarding the respective intensity of ondulation the specific value o ~ is introduced. the non-dimensional value is based on the afore mentioned characteristic and variable geometric parameters amplitude a and lengths lf and lr, respectively. the definition of the degree of ondulation is based on a purely analytical sine        l x ay 2sin (2) for modeling more sequences in a row it can be repeated in series as often as required, and still yields a continuously differentiable function over the whole domain of definition [27], [28]. for the introduction of the degree of ondulation o ~ the wave steepness s used in nautics, as exemplarily defined in büsching 2001 [29] l a l h s 2  (3) is modified. in eq. (3) the geometric parameters are the (absolute) wave height ah 2 and the wave length l. in contrast, following the outlook of ottawa et al. 2012 [23] and the ideas described in romano et al. 2014 [24, 25] and elaborated in romano 2016 [26], the degree of ondulation in fabric reinforced plastics is defined by rf ~ l a l a l a o   (4) where the geometric parameters are the amplitude a, the lengths of the ondulation in the fabric lf and the length of the cross-section of a roving as a fill yarn lr, respectively, and  is a characteristic factor characterizing the type of the fabric. it is for example 2 for a plain weave fabric and 4 for a twill weave 2/2 fabric and can be varied for different fabric constructions. in case of a plain weave fabric it is frrpl 2 llll   (5) comparison of the structural mechanical motivations the reason for the modification of the wave steepness s in eq. (3) to the degree of ondulation o ~ in eq. (4) is based on the different motivations, necessities and intentions of the respective subject area. in nautics it is important to characterize the absolute load a structure undergoes during its life-cycle, e. g. regarding fatigue strength issues. therefore, twice the amplitude a corresponding to the absolute wave height h is considered in the calculation of the specific value s [29]. in contrast, when fabric reinforced composites are considered, the characterization of the deviation from the ideally orientated unidirectionally reinforced single layer caused by the ondulation in the fabric is focused. the modification towards considering the single value of the amplitude a can also be interpreted as a degree of eccentricity compared to an unidirectionally reinforced single layer that exhibits an ideally orientated reinforcement without ondulations. the degree of ondulation o ~ defined in eq. (4) is a non-dimensional specific value. it corresponds to the rate of intensity of the continuously differentiable geometric direction change of the ondulation. the value enables the comparability of the representative sequences of the analytic model and the ones of the numeric investigations by fe-analyzes. this is at the same time the requirement for the later described verification. the geometric are chosen in selected and at the same time realistic steps. whereas the amplitude a is varied from 0.05 mm to 0.25 mm in five substeps of 0.05 mm (0.05 mm; 0.10 mm; 0.15 mm; 0.20 mm; 0.25 mm) the length of the crosssection of a roving as a fill yarn lr is varied from 2.5 mm to 7.5 mm in five substeps of 1.25 mm (2.5 mm; 3.75 mm; 5.0 mm; 6.25 mm; 7.5 mm). according to eq. (5) for a plain weave fabric this yields lengths of the ondulation in the fabric lf from 5.0 mm to 15.0 mm. m. romano et alii, frattura ed integrità strutturale, 39 (2016) 226-247; doi: 10.3221/igf-esis.39.22 231 the selected values can be considered realistic, as described in detail for the comparable sets of specimens in the experimental validations carried out in ottawa et al. 2012 [23], romano et al. 2014 [24, 25] and romano 2016 [26] or reported by ballhause 2007 [11], matsuda et al. 2007 [12] and kreikmeier et al. 2011 [20]. for a plain weave fabric according to eq. (5) with 2 and the afore listed geometric parameters yield values of the degree of ondulation o ~ according to eq. (4) lying in the range of 0.0033 and 0.0500. fig. 1 right illustrates the degree of ondulation o ~ over a plane spanned by the axes for amplitude a and length of the ondulation in a plain weave fabric lpl with isolines. 0,000 0,010 0,020 0,030 0,040 0,050 5,0 10,0 15,0 d eg re e o f o nd ul at io n õ = a /l p l h s l ,n = 4 a lr lpl=2 lr h r = 2 a a a 0 l/4 l/2 3l/4 l h s l ,a = 2 a . . . . . . . . . figure 1: representative sequences of one complete ondulation based on the characteristic geometric parameters amplitude a and length l of a sine in the analytic model (left top) and for the numerical investigations with fe-calculations (left bottom). graphical illustration of the degree of ondulation o ~ over a plane spanned by the axes of the geometric parameters amplitude a and length of the ondulation in a plain weave fabric lpl with isolines (right). analytical model and processing he investigations of the purely analytic model are described with its presumptions, processing and evaluation. mathematical model and presumptions the mathematical model for the analytical description of ondulations in fabric reinforced composites reduces the complexity down to a one-dimensional problem. therefore, only the centerline of an ondulated yarn is considered. the obtained mesoscopic geometry is thus an analytical sine. for a representative sequence of one complete ondulation according to eq. (2) the argument of the sine is presumed in the interval    xl2 0, 2  that leads to the domain of definition  x l0, . the advantages of a trigonometric function are steadiness, differentiability and integrability of its shape on the whole domain of definition [27, 28]. furthermore the representative domain of definition can be reduced to the wavelength of one complete ondulation, i. e.  d l0, because of symmetry properties. with arbitrary amplitude a and  x l0, the representative domain of the argument in the trigonometric function  d 0, 2 is obtained. in the analytical approach the ondulated yarn is assumed not to lengthen or shorten due to strain or compression, but remaining constant in length. mechanically the presumption of an ideally stiff and at the same time ideally flexible yarn can be stated in terms of an infinite high young’s modulus in longitudinal direction and a negligible flexural modulus transverse to it, e el 1   and e et 2 0  (6) t m. romano et alii, frattura ed integrità strutturale, 39 (2016) 226-247; doi: 10.3221/igf-esis.39.22 232 the sine shaped yarn further is presumed to be fixed at x 0 . the displacements are applied at the zero-crossing x l . a comparable value of deformation due to a displacement in x-direction is the sum of the original length l l0  and the applied displacement l l l l l1 0 1     referred to the original length by l l ll l u l l l l 1 1 rel 0 1        (7) that is positive for elongation and negative for shortening. the above stated and introduced relation of relative displacements urel according to eq. (7) is not a classic elongation or compression that leads to stresses as internal forces, but a geometric deformation due to displacements applied on an ideally stiff and at the same time ideally flexible yarn, indicated by the relations (6) that idealize the qualitative relation (1). -1,5 -1,0 -0,5 0,0 0,5 1,0 1,5 0,0 1,6 3,1 4,7 6,3 urel=0 urel=+0,2 urel=-0,2 %20rel u %1rel u %10rel u %1rel u %10rel u %20rel u    2,1mit2sin 00        la l x axy     0für 1 2sin rel rel 1         u ul x axy  0 π/2 π 3π/2 2π     0für 1 2sin rel rel 1           u ul x axy  . . . . . . . figure 2: obtained sines under the presumption of purely geometric deformation of an initial sine with a0=1 and l=2π: original graph as bold solid line; elongated graphs as dashed lines; shortened graphs as dash-dotted lines. the applied degrees of deformation urel (7) have been selected in relevant ranges for structural mechanics of fiber reinforced plastics [10, 30-33]. in detail two decades are considered. the large interval is relu 3 31 10 1 10      in steps of 41 10 and the small interval is relu 4 41 10 1 10      in steps of 51 10 . counting the zero 39 and 21 substeps result for urel. the previously stated presumptions lead to two different effects in the model. positive deformations lead to a smoothing or flattening. the amplitude decreases. in this case the maximum in elongation is reached when the yarn gets completely flattened. in contrast the amplitude increases for a negative deformation applied. in this case the maximum applicable value of the negative deformation is the limit of the domain of definition. fig. 2 shows the obtained sines under the presumption of purely geometric deformation of an initial sine with an initial amplitude a0 1 and domain of the argument  d 0, 2 . mathematical processing the arc length of a function is defined by [27, 28]   l s y dx 2 0 1   (8) as carried out in the following, in the case of the presumed sine the solution of eq. (8) can be achieved by converting it into an elliptic integral of the second kind m. romano et alii, frattura ed integrità strutturale, 39 (2016) 226-247; doi: 10.3221/igf-esis.39.22 233  e k k d2 2 0 , 1 sin      (9) for the description of real geometric dimensions the consideration of the arbitrary amplitude a and an arbitrary length l as two independent parameters is necessary. the arc length of a sine can then be achieved by considering the complete elliptic integral of the second kind. therefore the relation x x2 2sin cos 1  between the squared sine and cosine with the same arguments has to be applied. additionally, the lower integration limit is set to 0 and the upper integration limit to 2  , respectively. carrying out the substitution x x l2 one quarter of the arc length can be calculated by     a x s dx l l a x dx l l a a x dx l l l a a xl dx l la l 22 2 0 22 2 0 2 22 2 0 2 2 2 2 2 0 1 1 2 cos 2 4 1 2 1 sin 2 1 2 2 sin 2 2 1 2 1 sin 2 1 2                                                                                       (10) the application of the substitution x x l2 yields the differential  dx dx l 2  and leads to             a a lls x dx l a l a l la x dx a l a l la e a l l a a e l a 2 2 2 2 2 0 2 2 2 2 2 2 0 2 2 2 2 2 2 2 2 2 2 2 2 2 21 1 2 1 sin 4 21 2 2 1 sin 2 1 2 2 , 22 1 2 4 4 , 24 4                                                                    (11) where the factor l a2 2 2 2 4 4    can be interpreted as a diminution factor and the argument a l a 2 2 2 2 2 4 4   can be determined as the elliptic modulus k. the arc length of one complete ondulation s can be calculated by simply multiplying the repeating quarter-sequences with 4 yielding a x s dx l l 2 2 2 0 1 2 cos 2                m. romano et alii, frattura ed integrità strutturale, 39 (2016) 226-247; doi: 10.3221/igf-esis.39.22 234         a l la x dx a l a l la e a l 2 2 2 2 2 2 0 2 2 2 2 2 4 1 sin 2 1 2 2 4 , 22 1 2                                        (12) the previously stated presumptions and boundary conditions have to be fulfilled in order to derive a kinematic due to geometrical constraints only. therefore the arc length has to remain constant under the application of selected relative displacements urel. for selected degrees of deformations the governing equation is      rel relf a s u s u1 0 0    (13) that is solved numerically in order to determine the resulting root a1. for each pre-selected degree of deformation urel a respective shift in the amplitude δa can be calculated according to eq. (13) by    rel rela a u a u a a1 00      (14) that is the shift in amplitude as a function of the applied relative displacements urel. for further investigations it is reasonable to introduce the relative shift of the amplitude rel a a aa w a a a 1 0 1 0 0 0 1      (15) in order to receive another relative dimension, corresponding to the relative dimension urel (7). the relative shift of the amplitude wrel (15) is plotted against the relative displacements urel (7), and wrel-urel-diagrams result. the correlation reaches its limit at a degree of deformation   rel,max s a l u l 0 0 0   (16) for this value the algorithm to numerically determine the shift in amplitude reaches a singularity. in this case the singularity represents the state when the former sine gets completely flattened by positive deformation. this leads to an absolute decay of the amplitude a. in contrast shortening as negative deformation shows a less gradient of the shift of the amplitude a towards higher values. in case of applied negative deformations the model under the previously stated presumptions is able to theoretically describe the increase of the amplitude a up to a maximum value in the degree of deformation relu 1  . this state means a complete compression. for this value the algorithm to numerically determine the shift in amplitude exhibits its second singularity. numerical investigations by finite-element-analyses n order to verify the analytical model numerical investigations with the finite-element-analyses (fe-analyses) are carried out. as linear-elastic fe-calculations are carried out the elastic parts, formerly neglected in the analytical model, are considered. these are namely elasticity and transversal deformation due to poisson effects of the model under selected longitudinal deformations as strains in terms of relative displacements. in order to identify the originally acting mesomechanic kinematic correlations due to geometric constraints, non-linearities, failure mechanisms and friction effects are neglected. the modeling, setting and processing described in the following is based on the investigations of ottawa et al. 2012 [23]. therein different element formulations, number of elements (degree of discretization) and i m. romano et alii, frattura ed integrità strutturale, 39 (2016) 226-247; doi: 10.3221/igf-esis.39.22 235 convergence behavior is considered in sensitivity analyses. the numerical investigations are carried out with the fesoftware ansys workbench version 14.0.1 [34]. fe-model of plain representative sequences the kinematic is investigated parametrically by varying the characteristic geometric dimensions as well as the boundary conditions. in order to enable a proper meshing, avoid too small or acute triangle elements, reduce computing time and improve convergence two slight but essential modifications of the geometry are necessary. first, the lens-shaped fill yarns are cut by 2 % regarding the length lr in the region of each intersection. the resulting length of the cross-section of the fill yarn is l lr ,mod r0.96  . the length of the complete plain representative sequence lpl according to eq. (5) is thereby not affected. second, the upper and lower horizontal boundary of the surrounding matrix region is increased by 10 % of the amplitude a. the resulting thickness of the modified plain representative sequences is then t amod 4.2  . fig. 3 illustrates the modified parametric model for the numerical investigations by the fe-analyses confronting the extremes of its geometric dimensions. figure 3: modified parametric model for investigations by the fea based on analytic dimensions confronting its extremes. upper left: biggest length l=15 with lowest amplitude a=0.05 yielding o ~ =0.00333; upper right: shortest length l=5 with lowest amplitude a=0.05 yielding o ~ =0.01000; lower left: shortest length l=5 with highest amplitude a=0.25 yielding o ~ =0.05000, lower right: biggest length l=15 with highest amplitude a=0.25 yielding o ~ =0.01667. fe-settings: meshing, element types and contact definition as a first approximation a two dimensional fe-analyses is carried out. the representative sequence is discretized by elements with an average edge length of 3101  . as the fe-model represents a cross-section of a structure, a plain strain condition in the x-y-plane is presumed. plain four-node solid elements with linear shape functions are assigned to each region of the model. an orthotropic material model is chosen for properly applying the material properties to warp and fill yarn. in case of the region of the warp yarn elements of the formulation plane42 are assigned to by apdl (ansys parametric design language). in this case the enabled first keyoption by the command keyopt(1) for the element formulation plane42, makes the local x-y-element coordinate system follow the element i-j sides. as a mapped meshing has been applied to this region, the element coordinate systems follow the sine-shaped ondulation. as the material properties of orthotropic materials in ansys [34] are orientated along the element coordinate system, the modification is essential for a reality based fe-simulation. to the two other regions (fill yarns and matrix) the default elements of the formulation plane182 are retained. it does not provide the afore mentioned keyoption. it neither is necessary because the fill yarns are modeled in their plane of isotropy and the matrix is modeled isotropic. after sensitivity analyses and as a reasonable approach for the real conditions the contact between the single regions is defined by coincident nodes. fig. 4 illustrates the effect of the different element formulations on the orientation of the element coordinate systems in the region of the zero-crossing. m. romano et alii, frattura ed integrità strutturale, 39 (2016) 226-247; doi: 10.3221/igf-esis.39.22 236 figure 4: different element formulations in the region of the zero-crossing: plane42 with enabled first keyoption keyopt(1) in the region of the ondulated warp yarn causing the element coordinate systems to follow the sine-shaped ondulation and plane182 in the region of the fill yarns and the matrix with the element coordinate systems aligned to the global coordinate system. boundary conditions and application of selected deformations a clamped edge is defined on one vertical edge. on the opposite vertical edge a free edge is defined where the selected displacements are applied. both definitions on the boundaries allow a transversal deformation of the cross-section due to poisson effects, as the translational displacements in the vertical y-direction as well as the rotational degree of freedom to the z-direction perpendicular to the x-y-plane are defined free. on the nodes of the defined free vertical edge selected longitudinal deformations as strains x l u l l0 f     (17) are applied in two intervals. for verification and comparison issues they are the same as used in the analytical model for urel (7), i. e. the large one is x 3 31 10 1 10       in steps of 41 10 and the small one is x 4 41 10 1 10       in steps of 51 10 , resulting in 39 and 21 substeps. regarding the boundary conditions on the horizontal edges, i. e. on the top and bottom side of the model, two basically different conditions exist. fabric reinforced composites usually consist of more than one layer, mostly an even number of plies. thus the single layers can be considered as elastically supported on both sides, when located as an inner ply, and elastically supported on one side, when located as an outer ply. therefore, a case-by-case analysis is considered further. the calculation of the value of the elastic support kel is done by means of a weighted average of the plane stiffnesses based on the areas of the different regions. the similar calculation is carried out by barbero 2011 [35], 2006 [10] and 1995 [36] as well as by byun 2000 [4]. structural mechanic material properties of the single components the two exemplarily considered single components are ht-carbon fibers as reinforcement fibers and epoxy resin as a polymeric matrix system. because of its characteristic structural mechanic material properties this combination is commonly used in mechanically highly loaded structures. tab. 1 contains the structural mechanic material properties the two components, taken from [30-33]. the densities of the single components as a physical material property are indicated for the ht-carbon fibers 3ht carbon 1.74 g/cm   and for the epoxy resin as matrix system 3 m 1.20 g/cm  . in detail the structural mechanic material properties correspond to the values indicated in the data sheets of the three sets of comparable specimens of ht-carbon fiber reinforced epoxy, used in the experimental investigations described in romano et al. 2014 [24, 25] and romano 2016 [26]. m. romano et alii, frattura ed integrità strutturale, 39 (2016) 226-247; doi: 10.3221/igf-esis.39.22 237 reinforcement fibers ht-carbon polymeric matrix epoxy resin structural mechanic material property value structural mechanic material property value young’s modulus ef,1 230 gpa young’s modulus em 3.3 gpa young’s modulus ef,2 28 gpa shear modulus gm* 1.22 gpa* shear modulus gf,12 50 gpa poisson’s ratio νm 0.35 shear modulus gf,23* 11.4 gpa* poisson’s ratio νf,12 0.230 poisson’s ratio νf,21** 0.028** poisson’s ratio νf,23 0.225 * no independent structural mechanic material property, determined because of presumed (quasi-)isotropy ** no independent structural mechanic material property, determined by relation according to maxwell-betti table 1: structural mechanic material properties of the single components according to [30-33]: left: ht-carbon as reinforcement fibers. right: epoxy resin as polymeric thermoset matrix system. kind of fiber reinforcement: ht-carbon fiber reinforced epoxy region of plane rep. sequence longitudinally cut (warp yarn) micromechanic homogenization transversally cut (fill yarn) young’s modulus e1 150.7 gpa weighted average stiff 11.4 gpa young’s modulus e2 11.4 gpa chamis 1983/84 [37], [38] 11.4 gpa young’s modulus e3 11.4 gpa chamis 1983/84 [37], [38] 150.7 gpa shear modulus g12 5.7 gpa chamis 1983/84 [37], [38] 3.7 gpa* shear modulus g23 3,7 gpa* tsai 1980 [39] 5.7 gpa shear modulus g13 5.7 gpa chamis 1983/84 [37], [38] 5.7 gpa poisson’s ratio ν12 0.272 weighted average poisson 0.333 poisson’s ratio ν23 0.333 foye 1972 [40] 0.021* poisson’s ratio ν13 0.272 weighted average poisson 0.021* * no independent structural mechanic material property for transversally isotropic material behavior table 2: homogenized structural mechanic material properties of the 0°-unidirectionally reinforced single layer of ht-carbon fiber reinforced epoxy resin in the local 1-2-3-coordinate system of the respective region of the warp and fill yarn at the presumed fiber volume content of %65rf,  as the input values for the input mask of the fe-preprocessor of ansys [34] homogenized structural mechanic material properties of the 0°-unidirectionally reinforced single layer the fiber reinforced regions (warp and fill yarns) are considered as 0°-unidirectionally reinforced, having the same (local) fiber volume content. because of the transversally isotropic material behavior to the fiber direction, there are five independent structural mechanic material properties in the local 1-2-3-coordinate system. tab. 2 contains the homogenized structural mechanic material properties of the 0°-unidirectionally reinforced single layer of ht-carbon fiber reinforced epoxy resin in the local 1-2-3-coordinate system of the respective region of the warp and fill yarn. thereby, an achievable and technically reasonable local fiber volume content of f,r 65 %  is presumed. the applied rules of mixtures are referenced. the density of the composite material ρc is calculated as a weighted average of the densities of the single components based on the fiber volume content. the physical material property for ht-carbon fiber reinforced epoxy at f,r 65 %  is 3 c,ht carbon-ep 1.55 g/cm   . m. romano et alii, frattura ed integrità strutturale, 39 (2016) 226-247; doi: 10.3221/igf-esis.39.22 238 assignment of the structural mechanic material properties to the different region the assignment of the structural mechanic material properties to the different region follows according to the respective input mask of the fe-preprocessor of ansys [34]. for the ht-carbon fiber reinforced regions the input mask of an orthotropic material behavior is used. for a complete and consistent fe-simulation the input of 3d-properties are required, although 2d-properties are applied due to the carried out 2d-analyses. nine independent structural mechanic material properties are required. yet, the five independent values of the 0°-unidirectionally reinforced regions suffice, as pairwise equal inputs are made in the plane of isotropy for simulation of transversal isotropic material behavior. tab. 2 contains the input values of the structural mechanic material properties of the fiber reinforced regions. to the regions of pure matrix without fiber reinforcement are assigned the isotropic material properties em 3, 3 gpa and m 0.35  as indicated in tab. 1. according to the case-by-case analysis, considering the two basically different boundary conditions, the elastic support kel,ht carbon ep 9.5 gpa   acting in transversal y-direction of the fe-model is assigned to. the detailed calculation of the value of the elastic support, by the weighted average of the perpendicular stiffnesses e2 and em in the plane of the representative sequence, based on the relative part of the areas of the different regions, is carried out according to barbero 2006 [10], 2011 [35] and 1995 [36] as well as to byun 2000 [4]. results and discussion he obtained results of both the analytical model and the numerical investigations by the fe-analyses are evaluated and compared to each other. the acting mechanisms of the mesomechanic kinematic in fabrics due to the degree of ondulation and its sensitivity to geometric parameters and boundary conditions are described and discussed. aspects of the evaluation the variation of the two characteristic geometric dimensions of the ondulation in five substeps each provides 25 combinations of different degrees of ondulation o in total. for each of the models, the same selected deformations are applied in two decades of ten equidistant steps each. the relevant results are evaluated for every degree of ondulation o at every substep n 0, , 39  and plotted against the selected deformations. these are urel (7) in the analytical model and εx in the numerical investigations (17). positions of evaluation and separation of elastic and kinematic parts the relevant positions of evaluation of the analytical model correspond to the ones of the fe-model. in case of the plain representative sequence of a plain weave fabric they are the two extrema, namely maximum and minimum of the sine. in case of the numerical investigations these are located on the theoretical center-line of the longitudinally cut ondulated warp yarn. the evaluation of the results is carried out by the linearly presumed correlation between the applied displacements and the considered relevant values, analog to ottawa et al. 2012 [23]. in the fe-calculations the resulting elastic deformation basically consists of two parts. these consist of the purely kinematic parts due to geometric constraints and of the resulting elastic behavior of the linear-elastically modeled material. in order to identify the kinematic part only, the elastic part has to be separated from the total deformation. sensitivity to the mesomechanic kinematic in each case almost linear correlations can be identified, especially in the smaller interval. a direct and linear coupling between deformation and shape of the ondulation in fabric reinforced single layers can be stated, and the absolute value of the negative slope       y y x y x x x w m o u m o m o rel ,a rel , kin , kin d d d in case of the analytical model and   and in case of the numerical model d d d            (18) as a function of the degree of ondulation o represents the sensitivity to the mesomechanic kinematic. with the definition of the slopes m (18) another relative value is introduced. thereby, a higher slope m or a higher absolute value of it t m. romano et alii, frattura ed integrità strutturale, 39 (2016) 226-247; doi: 10.3221/igf-esis.39.22 239 m| | corresponds to a higher sensitivity to the mesomechanic kinematic, whereas a smaller value implies a smaller one. in the following the sign sensitive values of the slopes m are considered. results the results are presented in terms of the transversal kinematic part and in the difference of the applied and the evaluated longitudinal deformation. transversal kinematic part the displacements v in transversal direction as y-displacements v are evaluated by the difference of the values v1 and v2, where the indices indicate the opposite relevant positions. because the fe-calculations consider the elastic part, the relative shift of the amplitude is lead back to the total transversal deformation (y-strain y ). this value results as the ratio of the difference of the y-displacements δv to the originally perpendicular distance of the positions of evaluation to each other. it is twice the amplitude, i. e. 2a, for every mesomechanic geometry. the total transversal deformation for every substep n 1, , 39  is n n y n v vv a a 1, 2, , ,tot 2 2     (19) it is the sum of the purely kinematic part due to geometric constraints y ,kin and the transversal strain due to poisson effects y ,prs of the plain representative sequence. the results of eq. (19) have to be corrected by the transversal deformation due to poisson effects. solved for the kinematic part due to mesomechanic geometric constraints it is n n y n y n y n y n v v a 1, 2, , ,kin , ,tot , ,prs , ,prs 2          (20) where the transversal deformation due to poisson effects of the sequence is determined by y n x n u, ,prs prs,12 , prs,12       (21) it is defined as the negative relation of transversal deformation due to the longitudinal one (cf. eq. (17)). the value of the plain representative sequence prs,12 , used in eq. (21), is calculated by the weighted average of the poisson’s ratios of the three structural mechanic different regions based on its areas of the sequence a. for simplification, for the longitudinally cut warp yarn the value of a 0°-unidirectionally reinforced region ν12 is presumed, despite of its ondulation. for the perpendicularly cut transversal isotropic fill yarns the value is the one of the plane of isotropy, i. e. ν23, and the poisson’s ratio of the isotropic matrix is νm. thus, the poisson’s ratio of the plain representative sequence follows by a a a a a a w f m prs,12 12 23 m prs prs prs       (22) in case of the values of the ht-carbon fiber reinforced epoxy, namely 12 0.272  , 23 0.333  and m 0.35  , as indicated in tab. 1 and tab. 2, eq. (22) yields prs,12 0.306  as the value of the poisson’s ratio of the representative sequence. difference of the applied and the evaluated longitudinal deformation an additional indicator for the acting of the mesomechanic kinematic due to geometric constraints is the difference of the applied and the evaluated deformations in longitudinal direction (x-direction) x x,kin   . the difference of the applied m. romano et alii, frattura ed integrità strutturale, 39 (2016) 226-247; doi: 10.3221/igf-esis.39.22 240 deformations x n, (17) and the evaluated or calculated ones by fe-analyzes in longitudinal direction at the relevant positions x n, ,fe for every substep n 1, , 39  is x n, x n x n x n,, kin , , , fe       (23) it serves for the identification of the elastic deformation of the plain representative sequence and the longitudinally cut ondulated warp yarn in the fe-model. results of the analytical model tab. 3 lists the evaluated results according to eq. (18) in the wrel-urel-diagram as absolute values ym ,a over the selected degrees of ondulation o of the analytical model. the results are listed in ascending order regarding the corresponding degree of ondulation o . fig. 5 graphically illustrates the correlations of the selected degrees of ondulation and the corresponding sensitivity to the mesomechanic kinematic. the consideration of the absolute values of the slopes in the wrel-urel-diagram ym ,a allows a graphical illustration of the correlation between degree of ondulation o and the sensitivity to the mesomechanic kinematic in a linear equidistant scaled diagram and in a double logarithmic scaled diagram. in both cases the results are illustrated separately for the large and for the small interval, and the equations of a hyperbolic approximation of the correlation for the respective interval are indicated. additionally, the upper bound that can be identified for the exponent -1.5 is visualized by a bold dashed line. geometric parameters of the ondulation slope a, ~ ym in the wrel-urel-diagram amplitude a length of ondulation l degree of ondulation o ~ analytically for 3 rel 101  u in steps of 4101  analytically for 4 rel 101  u in steps of 5101  0.05 15.0 0.00333 -2448.20 -5040.10 0.05 12.5 0.00400 -1886.70 -3288.40 0.05 10.0 0.00500 -1369.90 -2047.40 0.10 15.0 0.00667 -914.03 -1143.40 0.05 7.5 0.00667 -914.59 -1141.30 0.10 12.5 0.00800 -729.59 -793.20 0.15 15.0 0.01000 -540.08 -507.26 0.10 10.0 0.01000 -540.13 -507.13 0.05 5.0 0.01000 -540.14 -505.79 0.15 12.5 0.01200 -369.62 -352.36 0.20 15.0 0.01333 -293.84 -285.42 0.10 7.5 0.01333 -293.67 -285.23 0.15 10.0 0.01500 -229.49 -225.43 0.20 12.5 0.01600 -200.78 -198.17 0.25 15.0 0.01667 -184.74 -182.66 0.25 12.5 0.02000 -127.63 -126.94 0.20 10.0 0.02000 -127.54 -126.90 0.15 7.5 0.02000 -127.64 -126.92 0.10 5.0 0.02000 -127.50 -126.90 0.25 10.0 0.02500 -81.45 -81.28 0.20 7.5 0.02667 -71.61 -71.49 0.15 5.0 0.03000 -56.60 -56.54 0.25 7.5 0.03333 -45.86 -45.83 0.20 5.0 0.04000 -31.92 -31.91 0.25 5.0 0.05000 -20.50 -20.50 table 3: slopes in the wrel-urel-diagram, i. e. a, ~ ym of the selected degrees of ondulation o ~ for the two considered intervals of urel. m. romano et alii, frattura ed integrità strutturale, 39 (2016) 226-247; doi: 10.3221/igf-esis.39.22 241 |my,a| = 0,1085·õ -1,806 |my,a| = 0,0481·õ -2,014 |my,a| = õ -1,5 1 10 100 1000 0,001 0,010 0,100 |m | im u re lw re ld ia gr am m grad der ondulation õ=a/l analytically for 44 rel 101...101  u 33 rel 101...101  u analytically for upper bound for exponent = -1,5 |my,a| = 0,1085·õ -1,806 |my,a| = 0,0481·õ -2,014 |my,a| = õ -1,5 0 500 1000 1500 2000 2500 3000 3500 4000 4500 5000 0,00 0,01 0,02 0,03 0,04 0,05 |m | im u re lw re ld ia gr am m grad der ondulation õ=a/l ~ . . . . . . . . . . .. .. .. . degree of ondulation õ=a/l degree of ondulation õ=a/l |m y, a| in t he u re lw re ld ia gr am ~ |m y, a| in t he u re lw re ld ia gr am ~ ~ ~ ~ ~ ~ ~ analytically for 44 rel 101...101  u 33 rel 101...101  u analytically for upper bound for exponent = -1,5 . . . figure 5: absolute values of the slopes, i. e. a, ~ ym , over the selected degrees of ondulation o ~ plotted against the selected degrees of ondulation o ~ in a linear equidistant scale (left) and in a double logarithmic scale (right). results of the fe-calculations in case of the two-sided elastic support the opposed positions of evaluation in the transversal direction (y-direction) behave symmetrically and contrary identical, because of the symmetry of the model and the boundary conditions. in contrast in case of the one-sided elastic support the free position behaves distinctly more sensitive as the supported position. the consideration of the longitudinal direction (x-direction) in both cases of the elastic support the evaluated results behave identically. thereby the evaluation of eq. (20) and eq. (23) yields causally determined comprehensible and significant correlations. the evaluated results over the degree of ondulation o for the applied deformations x of the numerical model are listed in tab. 4 for the kinematic parts y ,kin (20) in terms of the slopes ym , and in tab. 5 for the difference of the applied and evaluated longitudinal deformation x ,kin (23) in terms of the slopes xm . the results are graphically illustrated in fig. 6 and fig. 7, respectively. with an increasing degree of ondulation o the results show an increasing sensitivity in terms of the absolute values of the slopes m . in case of the kinematic parts y ,kin (20) it is possible to imply a sigmoidal correlation. the case of the one-sided elastic support shows a 1.8 times higher sensitivity to the mesomechanic kinematic as the case of the two-sided one. in case of the difference of the applied and evaluated longitudinal deformation x ,kin it is possible to imply a quadratic correlation, where the one-sided elastic support shows again a higher sensitivity as the twosided one. discussion due to its geometric similarity the results of the analytical model and of the numerical investigations of the plain weave fabric are comparable to each other, although they are partially identified by strongly simplifying presumptions. however both provide a description of the kinematic behavior by trend. the elastic parts of the ondulated roving due to the applied deformation are not negligible. additionally, it has a certain bending stiffness due to its extent in the direction of the thickness. both effects are considered by the numerical investigations with the fe-calculations. furthermore the difference of the structural mechanic behavior of fiber reinforced plastics under tensile and compression load, the quality of the interand intralaminar adhesion between the single components (interphase) or the single layers (interlaminar shear stiffness) or other damages as imperfections, influence the real material behavior. aspects considered in previously published contributions regarding mesomechanic kinematic correlations in fabric reinforced plastics are generally non-linear, especially when the kinematic correlations for dry fabrics without matrix system under uniaxial and biaxial loading as well as under shear loading are considered [11, 14, 15, 18]. thereby at high rates of positive deformations the smoothing or flattening of the loaded yarns causes an upsetting of the transversally m. romano et alii, frattura ed integrità strutturale, 39 (2016) 226-247; doi: 10.3221/igf-esis.39.22 242 orientated yarns. this mechanism results in an increase of the thickness of the fabric instead of a decrease of the thickness. geometric parameters of the ondulation slope ym ~ in the kin,y x -diagram amplitude a length of ondulation l degree of ondulation o~ cfrp one-sided elastically supported cfrp two-sided elastically supported 0.05 15.0 0.00333 -0.3180 -0.1588 0.05 12.5 0.00400 -0.4301 -0.2156 0.05 10.0 0.00500 -0.6451 -0.3260 0.10 15.0 0.00667 -0.5985 -0.2714 0.05 7.5 0.00667 -1.0954 -0.5525 0.10 12.5 0.00800 -0.8398 -0.3902 0.15 15.0 0.01000 -0.9322 -0.4124 0.10 10.0 0.01000 -1.2895 -0.6098 0.05 5.0 0.01000 -2.3964 -1.1946 0.15 12.5 0.01200 -1.3223 -0.6001 0.20 15.0 0.01333 -1.3044 -0.5711 0.10 7.5 0.01333 -2.2863 -1.1021 0.15 10.0 0.01500 -2.0499 -0.9564 0.20 12.5 0.01600 -1.8562 -0.8374 0.25 15.0 0.01667 -1.6981 -0.7333 0.25 12.5 0.02000 -2.4066 -1.1001 0.20 10.0 0.02000 -2.8025 -1.3188 0.15 7.5 0.02000 -3.4763 -1.7109 0.10 5.0 0.02000 -4.7204 -2.4144 0.25 10.0 0.02500 -3.4963 -1.6928 0.20 7.5 0.02667 -4.4191 -2.2506 0.15 5.0 0.03000 -6.0830 -3.3707 0.25 7.5 0.03333 -5.0427 -2.6973 0.20 5.0 0.04000 -6.4358 -3.8950 0.25 5.0 0.05000 -6.1304 -4.0234 table 4: slopes in the kin,y x -diagram ym ~ for the selected degrees of ondulation o ~ . -10 -8 -6 -4 -2 0 0,00 0,01 0,02 0,03 0,04 0,05 leinwand cfk einseitig elastisch gebettet -10 -8 -6 -4 -2 0 0,00 0,01 0,02 0,03 0,04 0,05 leinwand cfk beidseitig elastisch gebettet ~~ . .. .. . degree of ondulation õ=a/l . .. .. . degree of ondulation õ=a/l s lo p e m y in t he ε y, ki nε x -d ia g ra m ~ s lo p e m y in t he ε y, ki nε x -d ia g ra m ~ plain weave fabric ht-carbon fiber reinf. ep one-sided elastically supported plain weave fabric ht-carbon fiber reinf. ep one-sided elastically supported figure 6: slopes in the kin,y x -diagram ym ~ plotted over the selected degrees of ondulation o ~ . m. romano et alii, frattura ed integrità strutturale, 39 (2016) 226-247; doi: 10.3221/igf-esis.39.22 243 geometric parameters of the ondulation slope ym ~ in the kin,x x -diagram amplitude a length of ondulation l degree of ondulation o ~ cfrp one-sided elastically supported cfrp two-sided elastically supported 0.05 15.0 0.00333 0.0182 0.0172 0.10 15.0 0.00400 0.0170 0.0162 0.15 15.0 0.00500 0.0189 0.0177 0.20 15.0 0.00667 0.0184 0.0182 0.25 15.0 0.00667 0.0196 0.0186 0.05 12.5 0.00800 0.0189 0.0193 0.10 12.5 0.01000 0.0203 0.0207 0.15 12.5 0.01000 0.0211 0.0212 0.20 12.5 0.01000 0.0241 0.0224 0.25 12.5 0.01200 0.0232 0.0234 0.05 10.0 0.01333 0.0248 0.0248 0.10 10.0 0.01333 0.0286 0.0275 0.15 10.0 0.01500 0.0308 0.0300 0.20 10.0 0.01600 0.0321 0.0309 0.25 10.0 0.01667 0.0324 0.0326 0.05 7.5 0.02000 0.0464 0.0432 0.10 7.5 0.02000 0.0501 0.0463 0.15 7.5 0.02000 0.0559 0.0483 0.20 7.5 0.02000 0.0666 0.0554 0.25 7.5 0.02500 0.0797 0.0690 0.05 5.0 0.02667 0.1026 0.0865 0.10 5.0 0.03000 0.1560 0.1257 0.15 5.0 0.03333 0.1683 0.1392 0.20 5.0 0.04000 0.2746 0.2254 0.25 5.0 0.05000 0.3917 0.3333 table 5: slopes in the kin,x x -diagram xm ~ for the selected degrees of ondulation o ~ . 0,0 0,1 0,2 0,3 0,4 0,5 0,00 0,01 0,02 0,03 0,04 0,05 leinwand cfk einseitig elastisch gebettet 0,0 0,1 0,2 0,3 0,4 0,5 0,00 0,01 0,02 0,03 0,04 0,05 leinwand cfk beidseitig elastisch gebettet ~~ . .. .. . degree of ondulation õ=a/l s lo p e m x in t he ε x, ki nε x -d ia g ra m ~ . . . . . . ~ s lo p e m x in t he ε x, ki nε x -d ia g ra m ~ . . . . . . . .. .. . degree of ondulation õ=a/l plain weave fabric ht-carbon fiber reinf. ep one-sided elastically supported plain weave fabric ht-carbon fiber reinf. ep one-sided elastically supported figure 7: slopes in the kin,x x -diagram xm ~ plotted over the selected degrees of ondulation o ~ . m. romano et alii, frattura ed integrità strutturale, 39 (2016) 226-247; doi: 10.3221/igf-esis.39.22 244 0,0 0,5 1,0 1,5 2,0 2,5 0,00 0,01 0,02 0,03 0,04 0,05 leinwand cfk einseitig el. geb. vs. beidseitig el. geb. 0,0 0,5 1,0 1,5 2,0 2,5 0,00 0,01 0,02 0,03 0,04 0,05 leinwand cfk einseitig el. geb. vs. beidseitig el. geb. versus versus ~ ~ ~ ~ . .. .. . degree of ondulation õ=a/l . . . . . . m y, o /m y, t m es o m ec h. k in em at ic ε y, ki n ~ ~ m x, o/ m x, t el as ti c p ar t ε x ,k in ~ ~ . .. .. . degree of ondulation õ=a/l . . . . . . plain weave fabric ht-carbon fiber reinf. ep one-sided el. sup. versus two-sided el. sup. plain weave fabric ht-carbon fiber reinf. ep one-sided el. sup. versus two-sided el. sup. figure 8: relations of the sensitivity of the mesomechanic kinematic of the model with one-sided elastic support to the one of twosided elastic support for the kinematic part (left) and for the difference of the longitudinal deformation (right). the relations of the sensitivity of the values of the slopes ym over the degree of ondulation o for the applied deformations x for a balanced plain weave fabric construction of ht-carbon fiber reinforced epoxy are illustrated in fig. 8, left for the kinematic parts y ,kin (20) and right for the difference of the applied and evaluated longitudinal deformation x ,kin (23). in case of the kinematic parts y ,kin (20) the model with a one-sided elastic support shows a 1.8 times higher sensitivity as the model with a two-sided one. in case of the difference of the applied and evaluated longitudinal deformation x ,kin (23) the model with a one-sided elastic support only slightly differs from the model with a two-sided elastic one. correspondingly the relation of the sensitivities x, xm mo ,t/  plotted over the degrees of ondulation o is almost constant about approximately 1. conclusions he identified correlations in the analytical and numerical investigations definitely prove and verify the acting of a mesomechanic kinematic due to geometric constraints. within the limits of the validity of the analytical and numerical model a direct linear coupling between the applied longitudinal deformations and the mesomechanic kinematic exists. in case of the fe-calculations the transversal deformation due to poisson effects as an elastic reaction is separated and corrected, in order to obtain the purely mesomechanic kinematic. yet, the simplifying presumptions of the analytical model are suitable only to describe the tendency of the kinematic behavior, because the idealized stiffnesses only qualitatively represent the huge differences of the stiffnesses in the direction of the fibers and transverse to it. in order to obtain more precise results, more parameters, especially in the fe-calculations, can be varied in further investigations. considering plain representative sequences, amongst others, correlations regarding loading and displacements or deformations as well as detailed analyses of the resulting stress condition are relevant. a parameter identification of the mesomechanic kinematic regarding the resulting correlations of load and displacement provides the basis for the identification of the influence of the kind of reinforcement fiber (glass, aramid, basalt compared to carbon) and of the kind of fabric construction (twill weave, satin weave (balanced and unbalanced) compared to plain weave) on the structural mesomechanic material behavior of fabrics. detailed analyses of the stress conditions allow the description of damage mechanisms and the formulation of failure criteria. the consideration of a linear visco-elastic material model instead of a linear-elastic material model, and the consideration of the sensitivity of the material behavior on the kind of deformation (tension or compression) provide another expansion of the limits of the model conceptions. the expansion t m. romano et alii, frattura ed integrità strutturale, 39 (2016) 226-247; doi: 10.3221/igf-esis.39.22 245 of the model to the third direction as the width of the (laminated) load bearing structures, so that representative volume elements (rves) instead of plain representative sequences (prs) are considered, provides a further extension for the consideration of surface structures. references [1] naik, n. k., shembekar, p. s., elastic behavior of woven fabric composites: i-lamina analysis, journal of composite materials, 26/15 (1992) 2196-2225. doi:10.1177/002199839202601502 [2] mital, s. k., murthy, l. n., chamis, c. c., simplified micromechanics of plain weave composites, nasa technical memorandum 107165, (1996) 1-12. [3] guan, h., micromechanical analysis of viscoelastic damping in woven fabric-reinforced polymer matrix composites, wayne state university, detroit , aai9725829 (1997). http://digitalcommons.wayne.edu/dissertations/aai9725829. [4] byun, j.-h., the analytical characterization of 2-d braided textile composites, composites science and technology, 60(5) (2000) 705-716. [5] huang, z. m., the mechanical properties of composites reinforced with woven and braided fabrics, composites science and technology, 60(4) (2000) 479-498. [6] guan, h., gibson, r.f., micromechanic models for damping in woven fabric-reinforced polymer matrix composites, journal of composite materials, 35(16) (2001) 1417-1434. [7] tabiei, a., yi, w., comparative study of predictive methods for woven fabric composite elastic properties, composite structures, 58(1) (2002) 149-164. doi:10.1016/s0263-8223(02)00028-4 [8] le page, b. h., guild, f. j., ogin, s. l., smith, p. a., finite element simulation of woven fabric composites, composites part a, 35/7-8 (2004) 861-872. doi:10.1016/j.compositesa.2004.01.017 [9] wielage, b., müller, t., lampke, t., richter, u., kieselstein, e., leonhardt, g., simulation der elastischen eigenschaften gewebeverstärkter verbundwerkstoffe unter berücksichtigung der mikrostruktur, in: m. schlimmer (ed.), proceedings of the 15. symposium verbundwerkstoffe und werkstoffverbunde, kassel, wiley vch verlag, weinheim, (2005) 441-446. http://www.dgm.de/download/tg/706/706_77.pdf [10] barbero, e. j., trovillion, j., mayugo, j. a., sikkil, k. k., finite element modeling of plain weave fabrics from photomicrograph measurements, composite structures, 73(1) (2006) 41-52. [11] ballhause, d., diskrete modellierung des verformungsund versagensverhaltens von gewebemembranen, university of stuttgart, stuttgart, (2007). [12] matsuda, t., nimiya, y., ohno n., tokuda m., elastic-viscoplastic behavior of plain-woven gfrp laminates: homogenization using a reduced domain of anlysis, composite structures, 79 (2007) 493–500. [13] nakanishi, y., matsumoto, k., zako, m., yamada, y., finite element analysis of vibration damping for woven fabric composites, key engineering materials, 334-335 (2007) 213-216. [14] badel, p., vidal-sallé, e., boisse, p., computational determination of in-plane shear mechanic behaviour of textile composite reinforcements, computational material science, 40 (2007) 439-448. [15] hivet, g., boisse, p., consistent mesoscopic mechanical behavior model for woven composite reinforcements in biaxial tension, composites part b, 39 (2008) 345-361. [16] el mahi, a., assarar, m., sefrani, y., berthelot, j.-m., damping analysis of orthotropic composite materials and laminates, composites part b, 39 (2008) 1069-1076. [17] szablewski, p., sinusoidal model of fiber-reinforced plastic composite, journal of industrial textiles, 38(4) (2009) 277-288. doi: 10.1177/1528083708098914. [18] hivet, g., duong, a.v., a contribution to the analysis of the intrinsic shear behavior of fabrics, journal of composite materials, 45(6) (2010) 695–716. [19] ansar, m., xinwei, w., chouwei, z., modeling strategies of 3d woven composites, a review, composite structures, 93 (2011) 1947-1963. [20] kreikmeier, j., chrupalla, d., khattab, i. a., krause, d., experimentelle und numerische untersuchungen von cfk mit herstellungsbedingten fehlstellen, proceedings of the 10. magdeburger maschinenbau-tage, magdeburg, (2011). [21] valentino, p., romano, m., ehrlich, i., furgiuele, f., gebbeken, n., mechanical characterization of basalt fibre reinforced plastic with different fabric reinforcements, tensile tests and fe-calculations with representative volume elements (rves), in: f. iacovello, g. risitano, l. susmel (eds.), acta fracturae xxii convegno nazionale igf (italiano gruppo frattura), roma, (2013) 231-244. m. romano et alii, frattura ed integrità strutturale, 39 (2016) 226-247; doi: 10.3221/igf-esis.39.22 246 http://www.gruppofrattura.it/ocs/index.php/cigf/igf22/paper/view/10914/10241. [22] valentino, p., sgambitterra, e., furgiuele, f., romano, m., ehrlich, i., gebbeken, n., mechanical characterization of basalt woven fabric composites: numerical and experimental investigation, frattura ed integrità strutturale (fracture and structural integrity), 8(28) (2014) 1-11. doi:10.3221/igf-esis.28.01. [23] ottawa, p., romano, m., wagner, m., ehrlich, i., gebbeken, n., the influence of ondulation in fabric reinforced composites on dynamic properties in a mesoscopic scale in composites reinforced with fabrics on the damping behavior, in: dynamore gmbh (ed.), proceedings of the 11. lsdyna forum, ulm, (2012) 171-172. http://www.dynamore.de/de/download/papers/ls-dyna-forum-2012 [24] romano, m., micklitz, m., olbrich, f., bierl, r., ehrlich, i., gebbeken, n., experimental investigation of damping properties of unidirectionally and fabric reinforced plastics by the free decay method, journal of achievements in materials and manufacturing engineering (jamme), 63/2 (2014) 65-80. http://www.journalamme.org/vol63_2/6323.pdf [25] romano, m., micklitz, m., olbrich, f., bierl, r., ehrlich, i., gebbeken, n., experimental investigation of damping properties of unidirectionally and fabric reinforced plastics by the free decay method, in: meran, c. (ed.): proceedings of the 15th international materials symposium (imsp'2014). pamukkale university, denizli, (2014) 665-679. http://imsp.pau.edu.tr/imsp2014_proceedings_final_security.pdf [26] romano, m., charakterisierung von gewebeverstärkten einzellagen aus kohlenstofffaserverstärktem kunststoff (cfk) mit hilfe einer mesomechanischen kinematik sowie strukturdynamischen versuchen, university of the bundeswehr munich, department of civil engineering and environmental sciences, neubiberg, (2016). http://athene-forschung.unibw.de/doc/112760/112760.pdf [27] bronstein, i. n., semendajew, k. a., taschenbuch der mathematik, seventh edition, verlag harri deutsch, frankfurt am main, (2008). [28] papula, l., mathematische formelsammlung für ingenieure und naturwissenschaftler, ninth edition, vieweg+teubner, wiesbaden, (2006). [29] büsching, f., combined dispersion and reflection effects at sloping structures, proceedings of icpmrdt international conference on port and marine r&d and technology, singapore, i (2001) 410-418. [30] jones, r. m., mechanics of composite materials, second edition, taylor & francis, philadelphia, (1999). [31] moser, k., faser-kunststoff-verbund, entwurfsund berechnungsgrundlagen, vdi-verlag, düsseldorf, (1992). [32] schürmann, h., konstruieren mit faser-kunststoff-verbunden, springer-verlag, berlin/heidelberg/new york, (2005). [33] stellbrink, k., micromechanics of composites, hanser-verlag, münchen/wien, (1996). [34] n. n., ansys 14.0 help, helpsystem of ansys workbench version 14.0.1, sas ip inc., canonsburg, (2011). [35] barbero, e. j., introduction to composite materials design, second edition, crc press taylor & francis group, boca raton/london/new york, (2011). [36] barbero, e. j., luciano, r., micromechanics formulas for the relaxation tensor of linear viscoelastic composites with transversely isotropic fibers, international journal of solid structures, 32 (1995) 1859-1872. [37] chamis, c. c., simplified composite micromechanics equations for hygral, thermal and mechanical properties, nasa technical memorandum 83320 (1983) 1-10. [38] chamis, c. c., simplified composite micromechanics equations for hygral, thermal and mechanical properties, sampe quarterly, (1984) 14-23. [39] tsai, s. w., hahn, h. t., introduction to composite materials, technomic, (1980). [40] foye, r. l., the transverse poisson's ratio of composites, journal of composites materials, 6 (1972) 293-295. symbols and nomenclature the symbols and the nomenclature are indicated in alphanumerical order: 1, 2, 3 local principal directions 0, 1 states before and after deformation a analytical a amplitude, area c composite cfrp carbon fiber reinforced plastic d domain of definition m. romano et alii, frattura ed integrità strutturale, 39 (2016) 226-247; doi: 10.3221/igf-esis.39.22 247 e stiffness, young’s modulus  ke , elliptic integral of the second kind x longitudinal deformation as strain kin,x difference of the applied and evaluated deformations in longitudinal direction kin,y kinematic part due to mesomechanic geometric constraints in transversal direction f fabric, fill-yarn f fiber fe numerically determined by finite-element-analysis f fiber volume content g shear modulus h absolute height kel elastic support kin kinematic l length l longitudinal  factor 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/pdfxoutputintentprofileselector /documentcmyk /preserveediting true /untaggedcmykhandling /leaveuntagged /untaggedrgbhandling /usedocumentprofile /usedocumentbleed false >> ] >> setdistillerparams << /hwresolution [2400 2400] /pagesize [612.000 792.000] >> setpagedevice microsoft word numero_57_art_16_3057 k. benyahi et alii, frattura ed integrità strutturale, 57 (2021) 195-222; doi: 10.3221/igf-esis.57.16 195 reliability assessment of the behavior of reinforced and/or prestressed concrete beams sections in shear failure karim benyahi, mohand said kachi, youcef bouafia department of civil engineering, mouloud mammeri university, 15000 tizi ouzou, algeria. karim.benyahi@ummto.dz, https://orcid.org/0000-0003-2033-6217 kachi_ms@yahoo.fr, youcef.bouafia2012@yahoo.com salma barboura, jia li c.n.r.s. lspm – upr 3407 laboratory, paris 13 university, paris, france. salma.barboura@univ-paris13.fr, jia.li@univ-paris13.fr abstract. the object of this article is to be able to simulate the behavior of reinforced and/or prestressed concrete beam’s section in the shear loading through a model allowing the evaluation of nonlinear strains caused by shear, while taking into account the real behavior of the materials. in this approach, we are often confronted with problems of modeling uncertainties linked to some insufficiencies of the mechanical model allowing to describe the physical phenomena in a realistic way. for that, it is necessary to use a reliability model making it possible to evaluate their probability of failure, by establishing failure curves according to the different transition zones of the limit state curve of the nonlinear behavior in the shear loading up to at section failure of reinforced and/or prestressed concrete beams. in this work, we also propose a coupling of the reliability method by response surface to carry out the reliability optimization on complex mechanical models, where the mechanical and reliability models developed have been implemented on the fortran. this allows the estimation in an efficient way of the different reliability characteristics according to each transition zone from the limit state curve to the real behavior until failure in the shear loading. keywords: nonlinearity; reinforced concrete; shear; reliability; probability of failure. citation: benyahi, k., kachi, ms., bouafia, y., barboura, s., li, j., reliability assessment of the behavior of reinforced and/or prestressed concrete beams sections in shear failure, frattura ed integrità strutturale, 57 (2021) 195-222. received: 03.04.2021 accepted: 06.06.2021 published: 01.07.2021 copyright: © 2021 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. introduction n order to best estimate the shear loading behavior of elements of reinforced and prestressed concrete structures, several studies have been considered by the world, so knowledge of the real behavior of the constituent materials makes it possible to predict their behavior in a global manner. research that has been carried out to improve our understanding of the shear loading behavior is summarized below. collins [1] was the first to propose a theoretical i https://youtu.be/lx8trsk-jhk k. benyahi et alii, frattura ed integrità strutturale, 57 (2021) 195-222; doi: 10.3221/igf-esis.57.16 196 approach to the compression field, using stress-strain relationships for cracked concrete applied to members with shear reinforcement, where he made an assumption that after cracking, the concrete does not support a tensile force which leads to a diagonal compression field. vicchio and collins [2,3] proposed a model making it possible to predict the loadstrain response for reinforced concrete elements, subjected to a normal force and a shear force. several equilibrium and compatibility relationships have been developed as a function of the average stresses and strains. several observations have been made; cracked concrete subjected to high tensile forces in the direction normal to the compressive direction is lower in compression, and significant tensile forces have been observed in concrete between cracks. although many studies have been reviewed on the shear behavior of reinforced and / or prestressed concrete structures, the proposed models (bažant and kazemi [4]; bentz et al. [5]; carbone et al. [6]; hsu and zhang [7]; hsu, [8]; miguel et al. [9]; rahal [10,11] and vecchio [12,13]), have been regarded as major contributions in this area of research. this proposed approach admits that the cracking of a panel can occur by plasticization of the transverse and longitudinal reinforcements and cracking of the concrete before plasticization of the reinforcements. kachi et al. [14] continue the work of grelat [15] and nait-rabah [16], showed in their model that the stress in concrete in the transverse direction is a compressive stress; they studied each section subjected to the bending moment, the normal force and the shear force in nonlinear elasticity in the case of the reinforced and prestressed concrete beams. the developed program has been validated on several reinforced and prestressed concrete beams which have been the subject of experimental tests. jeong et al. [17] propose a method to improve the nonlinear stress-strain analysis process of a reinforced concrete panel subjected to pure shear. through this study, a comparison was made against the experimental data obtained by hsu et al. [7], where it was found that the shear history was accurately estimated in the result of the analysis. filho et al. [18] propose a softened truss model with variable angle (refined ra-stm) to model the behavior of reinforced concrete structural membranes under pure shear. they found that the general characteristics of the reinforced concrete (rc) panels under shear are well captured by the refined rastm, namely for the ultimate state, as well as the need to refine the model for low load conditions. the ra-stm has been refined in several works (bernardo et al. [19-21], bernardo et al. [22]), in order to improve the numerical efficiency as well as provide good stability of the calculation procedure of membrane elements in reinforced concrete (rc) and prestressed concrete (pc). the refined model equations are reformulated using an optimization algorithm and an appropriate stress-strain relationship for tensile concrete is implemented. on the other hand, in the works (bernardo et al. [23], silva [24]), the contribution of tensile stresses in concrete has been neglected in the efficient ra-stm procedure. through their comparison, it was shown only a good agreement for ultimate stage, namely for resistance, which is not the case for low loading stages. bernardo and sadieh [25] used the efficient ra-stm monotonic procedure in order to be able to predict the envelope curves t45◦ g45◦ of reinforced concrete (rc) panels under cyclic shear loading. from the results obtained, they found that the efficient ra-stm procedure is a reliable model for predicting some important characteristics of the response of reinforced concrete (rc) panels studied under cyclic shear. also, in order to take into account, the uncertainties related to the physical phenomena that can be created during the sizing of structures, it is necessary to resort to probabilistic methods allowing the sizing of these structures to be optimized. the resulting research which has greatly improved our understanding of estimating the impact of the various uncertainties that can be created during the design of a structure, making it possible to evaluate their responses to uncertain variables, are summarized below. freudenthal [26] first effectively investigated the possibility of using statistical techniques to quantify the safety of structural components which is based on the allowable stress method. then several basic works of cornell [27], hasofer and lind [28], found an ever increasing use in different fields of engineering. mohamed and lemaire [29] were interested in the coupling of mechanical analysis to reliability analysis to determine the probability of failure of marine platform structures. they opted for a materials model adopting linear sections, and an element’s model admitting unloading situations. they proposed a reliability-model based on the concept of safety margins. the validation of their model was tested on examples of flat tubes and space gantries. state of the art reliability methods are briefly discussed by rackwitz [30]. benyahi et al. [31] proposed an analytical model making it possible to take account the mechanical nonlinearity in the nonlinear elasticity calculation of spatial trusses structures. the proposed mechanical model has been validated on several elements of three-dimensional metal trusses structures. then, a reliability model was also used in order to estimate the reliability of this mechanical model, while proposing a method for estimating the distribution laws of the different random variables used in the mechanical model, by a response surface coupling technique between the two models. some applications of reliability analysis for reinforced concrete structures have been reported by (schlune et al. [32], allaix et al. [33], el ghoulbzouri et al. [34]; olmati et al. [35]; słowik et al. [36]), and prestressed concrete structures by (rakoczy and nowak [37], hadidi et al. [38]). the combination of nonlinear analysis k. benyahi et alii, frattura ed integrità strutturale, 57 (2021) 195-222; doi: 10.3221/igf-esis.57.16 197 with reliability methods for the assessment of the reliability index has been used (robuschi et al. [39], slobbe et al. [40], grubišić et al. [41]). this paper aims to develop numerical models making it possible to represent as faithfully as possible the physical phenomena studied, and that by the use of an efficient theoretical model for the analysis of the sections behavior in the shear loading in the case of the reinforced and/or prestressed concrete beams. this calculation procedure should allow the analysis of different section shapes, and take into account the real materials behavior. in fact, given the complexity of the mechanical model studied, errors can occur because of a lack of information on the various design parameters. it is for this reason, that an evaluation of the reliability characteristics will be made by a procedure (form/sorm) in order to evaluate the probabilities of failure for the various transition zones of the limit state of the mechanical model solving the section’s behavior in the shear loading in the case of the reinforced and/or prestressed concrete structural elements. (a). compression in principal compressive direction with sargin [42] (b). concrete in principal tensile direction with grelat [15] (b). concrete in principal tensile direction with grelat [15]. (d). prestressing cable with bpel99 [44] figure 1: constitutive relations used in analysis procedure. stress-strain relationships used in analysis procedure n nonlinear elasticity, the stresses are related to the strains by the following relation:     (1) i k. benyahi et alii, frattura ed integrità strutturale, 57 (2021) 195-222; doi: 10.3221/igf-esis.57.16 198 the compressive concrete stresses are described by sargin [42] law, the average tensile stress located between two cracks is described by the relation of grelat [15], the stress of the reinforcement is described by the perfect elastoplastic constitutive law recommended by the bael99 rules [43], and the behavior of prestressing reinforcements is represented by the law recommended by the bpel99 rules [44] (fig. 1). (a). cross section of concrete in trapezoidal tables (b). cross section of reinforced concrete (c). cross section of reinforced and/or prestressed concrete figure 2: discretization of a layered beam cross section. k. benyahi et alii, frattura ed integrità strutturale, 57 (2021) 195-222; doi: 10.3221/igf-esis.57.16 199 discretization of the reinforced and prestressed concrete beam sections o better approximate the contour of a concrete section of any shape, the concrete section is considered as a succession of trapezoidal tables. each table is defined by the width of its lower and upper base: jb , j+1b as well as their ordinates jy , j+1y , with relatively to a reference axis passing through the sections gravity center, (fig. 2.a). the integration process is numerical simpson's method according to the ref (atkinson [45]), the trapeze width expression related to its ordinate y, is:        j j+1 j j j+1 jb y =b + b -b . y-y / y -y (2) the section of each reinforcement is concentrated in its gravity center. the reinforcements are therefore defined as a succession of reinforcing beds, (fig. 2. b). each bed is defined by its ordinate aiy and by the total area of the reinforcement located at this level aia . the reinforcements prestressing are defined by their eccentricities pke and their area pka (fig. 2. c). on tensioning, the prestress practice on the concrete section an compressive force equal and opposite to the tensile force in the cable. this force is applied along the tangent to the mean line of the cable at the point where it crosses the section. the global strains in the concrete result from the external stresses and the actions of the prestressing reinforcement. from this state, it is considered that the prestressing cables become perfectly integral with the concrete, and they have a predeformation comparatively to the concrete section. calculation procedure for a cross section in reinforced and/or prestressed concrete he study of a cracked element subjected to the shear force consists on separately analyzing the materials constituting this element (concrete, steel). to solve the problem, it will be used the equilibrium equations, the compatibility equations and the constitutive laws of the different materials [14]. a) average stresses b) main stresses figure 3: average concrete stresses. the longitudinal strain x is a linear function of the y ordinate, responding to the cross-section navier-bernoulli hypothesis and expressed as follows: t t k. benyahi et alii, frattura ed integrità strutturale, 57 (2021) 195-222; doi: 10.3221/igf-esis.57.16 200   ( ) .x y u w y (3) on the assumption of an equivalent continuous medium for the concrete alone allowing to balance the shear stresses  x and  y . the equilibrium equations linked the concrete stresses are:      2 21 2bx b b b bsin cos (4)      2 21 2by b b b bcos sin (5)        1 2( )b b b b bsin cos (6) we make the assumption of the coincidence of the principal directions of the concrete stresses with that of the average strains:  b (7) we assume that the strains of the concrete in the principal directions 1b and 2b , which are related to the principal stresses  1b and  2b , are equal to the average principal strains of the equivalent medium: 1 1b  (8) 2 2b  (9) while considering that the main direction (1) is perpendicular to the cracks. and the main direction (2) where the compressed connecting rods are parallel to the cracks (fig. 3), and where we have a continuity of the concrete. the state of stress in concrete and steel is as follows, (see fig. 4). a) concrete b) steel figure 4: mohr’s circle for average stresses. the general relations between the concretes main strains are thus: k. benyahi et alii, frattura ed integrità strutturale, 57 (2021) 195-222; doi: 10.3221/igf-esis.57.16 201   2 21 2x sin cos   (10)   2 21 2y cos sin   (11)    12( )sin cos  (12) the local equilibrium of the concrete layers can be expressed as follows:     x x ax bx (13)       0y y ay by (14) the overall equilibrium of the sections is expressed by the equality of the external loads n, m, v and the resultants of the internal loads intn , intm , intv , it is expressed by the following relation:    xi axi i i bxia b hint i i n (15)    xi axi ai i i bxi ia y b h yint i i m (16) for the shear force, only the shear stresses in the concrete are involved:   i i bib hint i v (17) the principal stress  2b is a function of the two principal strains 1 and 2 :  2 2 2 1 2( , ).b be    (18) the stress-strain law of concrete in traction is linear before concrete cracking. beyond that, the tensile stress decreases with increasing mean tensile strain, which includes the effect of crack opening (fig. 5). figure 5: behavior of tensile concrete according to belarbi and hsu [46]. k. benyahi et alii, frattura ed integrità strutturale, 57 (2021) 195-222; doi: 10.3221/igf-esis.57.16 202 before concrete cracking:    1 ft b1 b0 1 : = e . (19) to describe the decreasing branch, after cracking, which reflects the influence of the concrete loaded between the cracks on the average strain, we adopt the relation proposed by belarbi and hsu [46]:           0,4 ft 1 t 1 fb (20) where:  0 t ft b f e  the behaviors of reinforcement and the prestressing reinforcement are characterized by the types of relations admitted by the rules bael99 [43] and bpel99 [44]: longitudinal reinforcement   ( ).ax a x xe   (21) transverse reinforcement   ( ).ay at y ye   (22) prestressing reinforcement   ( ).px ap x xe   (23) the shear stresses are then deduced from the equilibrium of the layers between the design section under the loading state (n, m, v) and the neighboring section subjected to the forces ( 1n , 1m , 1v ) which are expressed by:     1 1 1 . n n m m v d v v (24) the two sections are analyzed so as to satisfy in each of them the equilibrium equations. by applying the classical rdm method, we study the equilibrium of all the forces acting on a layer of order k shown in the figure (fig. 6): figure 6: forces acting on a concrete layer between two sections. k. benyahi et alii, frattura ed integrità strutturale, 57 (2021) 195-222; doi: 10.3221/igf-esis.57.16 203 the equilibrium of the section makes it possible to calculate the shear value kv , by writing that the moment of the forces is zero at point p:   k-1 k kk ( g g ) h v 2 d (25) the average value of the shear stress on the layer k is then given by:     k-1 kkk k k k ( g g )v b h 2 d b (26) the mean shear strain of the section  moy is calculated from the theorem of virtual work expressing the equality of the external forces work  ew and that of the internal forces  iw :    m i 1 wew from where:         m i i i i moy 1 b h v (27) for the resolution of the problem, we explain some quantities from the previous general equations. we take from eqn. 10:        21 2 2sin x tg (28) we also rewrite the eqn. 4, eqn. 5 and eqn. 6 between the concrete stresses in the following form (taking into account eqn. 7):      2 1bx b b by (29)         1 1/22 2 ' ( )b bx b by tg (30)      2 tg b by (31) the study of the equilibrium of a reinforced concrete layer, where x and  are known uses a system of equation. to solve it, we call on an iterative method. for a given distribution of the longitudinal strains, we assume known the main strain 2 and we look for the value of the angle  which makes it possible to satisfy the conditions of compatibility and equilibrium of the layer. the tangential stresses ( )y are calculated by the equilibrium of two neighboring sections (eqn. 26). the complete resolution at the section level is described by the flowchart in fig. 7. reliability calculation procedure he concept of safety based on the concept of allowable stress was recognized insufficient because of the uncertainty of the loading parameters and the uncertainty of the structures mechanical properties. however, in recent years, a so-called semi-probabilistic theory ensures safety by introducing various partial coefficients taking t k. benyahi et alii, frattura ed integrità strutturale, 57 (2021) 195-222; doi: 10.3221/igf-esis.57.16 204 into account the limit state considered. the use of reliability methods (form/sorm) consists in determining the reliability index  and obtaining an approximation of the probability of failure [22]. figure 7: general flowchart of the study of a section [14]. the first step is to find the most probable point of failure *p in the space of standard variables. then, the limit state function is approximated by its first order taylor expansion (form) or second order (sorm), around the point of conception. results of step n [ks]n increased loading p increased internal efforts n , m , v neighbor section n , m1 = m – d.v , v section studied n , m, v compound bending balance n , m without interaction of force v choose a value of the curvature w choose a value of the strain u calculate the longitudinal strain x by the eqn. 3 calculate the stresses bx and ax by the eqn. 18, 21 and 22, 24 calculate the internal normal force by eqn. 15 nint = n calculate the internal moment by the eqn.16 mint = m calculate the distribution (y) according to the relation which satisfies vint = v calculate the mean distortion of the section moy by the eqn. 27 [ks]n+1 of step n+1 calculate section stiffness n/δδu ….. δv/δγmoy u , w known so x(y) known, (y) known equilibrium of a layer yi with x and  known loop on layers compound flexural balance with interaction of force v calculate the stresses ax by the eqn. 22, eqn. 24, bx is known from the balance of the layers check the convergence of tangential stresses iteration on u and w to get nint = n (eqn. 15), and mint = m (or m1) (eqn. 16) recompute the tangential stresses with eqn. 26 which satisfies vint = v k. benyahi et alii, frattura ed integrità strutturale, 57 (2021) 195-222; doi: 10.3221/igf-esis.57.16 205 in the space of physical variables x , the limit state function is denoted  g x and in the standard space, we denote it  h u . the second-order taylor series expansion of the limit state function  h u around the point  kp is written as follows:                      2 = + + -k k kk u h u h u h u u u o u u (32) the search for the design point *u is a solution of the following optimization problem:          i jg x u 0 min t hl u u (33) under constraint    0h u the design point (or most probable point of failure) is the point on the limit state surface where the probability density of u is maximum, it is also defined as the point on the limit state surface closest to the origin. in this study the constrained minimization problem will be solved, using the hasofer-lind-rackwitz-fiessler algorithm which is an adaptation of a first order optimization algorithm to the design point search problem. figure 8: safe and unsafe regions approach for computing hasofer lind reliability index. the equation of the tangent hyper-plane to  h u at the point  k+1p is defined as follows:                      11 0k k kk k uh u h u h u u u (34) by dividing the equation by the norm     kuh u and by introducing the direction cosines of h at the point  kp we obtain:                     k 1 0 k k k k u h u u u h u (35) k. benyahi et alii, frattura ed integrità strutturale, 57 (2021) 195-222; doi: 10.3221/igf-esis.57.16 206 it results:                       k 1 k k k k k u h u u u h u (36) with              k k k u h u h u the vector of direction cosines (or the vector of the normalized gradient) of h at the point  kp . ultimately when  k ,    kd u and      u if the algorithm is convergent at iteration  k , let us set:                       1 1. .k k k kk ku u (37) solving the problem gives a value of  which corresponds to the reliability index known as of hasofer and lind. which leads to the iterative relation giving the reliability index:                    k k k kk u h u u h u (38) the reliability index search algorithm stops when the standard        1k ku u t . where t : the fixed tolerance. and   1ku , is deduced by replacing eqn. 38 in eqn. 37 by:                           k 1 k k k k k k u h u u u h u (39) in standardized space, the approximate form/sorm (first/second order reliability method) consists of substituting for the failure surface a hyperplane tangent to this surface at the design point. an estimate of the probability of failure is then obtained by:                   21 22 c f c u p exp du (40) in this present study the hasofer-lind index will be used because it allows to solve the problem caused by the noninvariance. to overcome this problem, hasofer and lind proposed not to place themselves in the space of physical variables, but to perform a change of variable, towards a new space of statistically independent gaussian variables with zero means and unit standard deviations: i ix u gaussian vector  0,1 ,       0, 1, 0, , i iu u ij i j (41) in the case of independent gaussian variables, the transformation of the physical space into the standard normal space is iso-probabilistic: k. benyahi et alii, frattura ed integrità strutturale, 57 (2021) 195-222; doi: 10.3221/igf-esis.57.16 207     i i t i x i i x x x u (42) for uncorrelated variables of any law, the principle of the transformation consists in writing the equality of the functions distribution:            -1x xu f x x u f x (43) the hasofer-lind-rackwitz-fiessler (hl-rf) algorithm is summarized by the following steps: figure 9: algorithm to compute hl . the flowchart of the mechano-reliability coupling by analytical response surface is described below: figure 10: flowchart of the mechano-reliability coupling by response surface. k. benyahi et alii, frattura ed integrità strutturale, 57 (2021) 195-222; doi: 10.3221/igf-esis.57.16 208 results and validation he mechanical shear-bending model of beam sections was used to simulate the behavior of several beams tested by various researchers at the university of toronto (vecchio and collins [2,3]). the beams have a solid or hollow rectangular cross section of reinforced and/or prestressed concrete. the geometric characteristics and the properties of the different materials are given in the tab. 1. referen ce beam dimensions concrete transverse reinforcement longitudin al reinforcem ent prestressing reinforcement s ext (mm) int (mm) fc (mpa) b0 10-3 barres  (m) st (mm) fe (mpa) nb.x  (mm) fe (mpa) ap (mm2) fpe (mpa) p 10-3 sa3 305x610 152x406 40.0 2.8 9.5 72 373 12x 29 4 x 22 345 462 _ _ _ sa4 305x610 152x406 40.0 2.8 9.5 72 373 12x 29 4 x 22 345 462 _ _ _ sk1 305x610 26.9 2.25 9.5 100 400 8 x 25 442 1540 1450 4.82 sk2 305x610 121x381 26.9 2.25 9.5 100 400 8 x 25 442 1540 1450 4.82 sk3 305x610 28.2 2.2 9.5 100 400 8 x 25 442 _ _ _ sk4 305x610 121x381 28.2 2.2 9.5 100 400 16x 25 442 _ _ _ sp0 305x610 152x406 25.0 2.3 9.5 150 373 16x 25 421 _ _ _ sp1 305x610 152x406 33.5 2.3 9.5 150 373 12x 22 421 510 1450 4.21 sp2 305x610 152x406 32.0 2.0 9.5 150 373 12x 22 421 1010 1450 4.11 sp3 305x610 152x406 32.2 2.0 9.5 150 373 12x 22 421 1520 1450 4.26 sm1 305x610 152x406 29.0 2.4 9.5 175 424 12x 22 452 _ _ _ cf1 305x610 152x406 38.6 3.0 9.5 150 367 6 x 9.5 367 930 1450 5.17 table 1: properties of different beams vecchio and collins [2, 3]. the figs. (11-15) from a comparative calculation results to the experiment results in the case of reinforced and prestressed concrete tested at toronto university. we can observe from the figs. (11-15) that the results obtained from the numerical model compared to the experimental results make it possible to approach the real behavior of all the reinforced and/or prestressed concrete beams studied, as well before and after cracking of the concrete. we notice an error made on the ultimate values of the load varying between (0.28% and 8.94%) for reinforced concrete; and (3.40% and 12.89%) for prestressed concrete beams. the distortion observed in the beams (sa3, sa4, sk2, sp0, sp1, sp3) shows an important value, especially when approaching the maximum load. however, there are no results measures other than the distortion  moy to analyze the cause of the observed differences in some cases between calculation and testing. we can also note, in the phase of the behavior before concrete cracking, that all the curves obtained display an elastic plateau approaching the experimental results, and that the numerical model fairly correctly predicts the evolution of the distortion  moy with the shear force v. on the other hand, in the behavior phase after cracking of the concrete and before plasticization of the steel, we notice a decrease in the shear rigidity of the reinforced and/or prestressed concrete beams studied, which increases the distortion until plasticization reinforcements. beyond that, the distortion tends to increase significantly until failure. t k. benyahi et alii, frattura ed integrità strutturale, 57 (2021) 195-222; doi: 10.3221/igf-esis.57.16 209 figure 11: analysis of shear beam (sa). figure 12: analysis of shear beam (sk). k. benyahi et alii, frattura ed integrità strutturale, 57 (2021) 195-222; doi: 10.3221/igf-esis.57.16 210 figure 13: analysis of shear beam (sp). figure 14: analysis of shear beam (sm). k. benyahi et alii, frattura ed integrità strutturale, 57 (2021) 195-222; doi: 10.3221/igf-esis.57.16 211 figure 15: analysis of shear beam (cf). figure 16: comparison of experimental and predicted results. fig. 16 and the tab. 2 show the evolution of the ultimate values of shear force calculated by this model and those observed experimentally. it can be seen that the numerical model approaches the real behavior both before and after the cracking of the concrete, as well as the ultimate value of the shear force of all the beams studied. however, in order to better appreciate the differences between the results obtained, it would be more judicious to proceed to further analysis by using a reliability method thus making it possible to better estimate the differences that may exist between the calculation and the experiment. k. benyahi et alii, frattura ed integrità strutturale, 57 (2021) 195-222; doi: 10.3221/igf-esis.57.16 212 beams experimental numerical beams experimental numerical sa3 716 745.0 sp0 436 475.0 sa4 534 532.5 sp1 463 478.75 sk1 672 750.0 sp2 547 498.75 sk2 530 575.0 sp3 574 500.0 sk3 725 733.75 sm1 427 436.25 sk4 601 608.75 cf1 467 502.5 table 2: experimental and numerical ultimate values of the shear force vu (kn). reliability assessment of the shear loading behavior he sensitivity of the mechanical model to the different characteristics of the materials is introduced by using the random variables and failure scenarios, through a reliability method applied in this study for the different sections of the beams tested. this thus allows us to efficiently estimate the various reliability characteristics, according to each transition zone of the performance curve (limit state) on the shear loading behavior until the failure of the sections in the case of reinforced and/or prestressed concrete beam. the random variables retained in this study are considered continuous, independent and they are represented by the vector x. first, it is necessary to evaluate the nonlinear limit state function (implicit function) by an equivalent failure function, and which can be expressed for each transition zone as follows: zone 01 : phase before concrete cracking   ( 0 )fiss  1v = .fiss fiss (44) zone 02 : post cracking phase and before plasticization of steels    ( )fiss plas      2v -v = . -plas fiss plas fiss (45) zone 03 : post plasticization phase of steels    ( )plas r      3v -v = . -r plas r plas (46) in this problem, we are looking for a performance function making it possible to characterize the three transition zones of the limit state curve, where can for example express the performance function of the beam section (sa3) in the form of a function of polynomial limit state which can be represented as follows:     3 21 2 1 2 2 2( , ) 0.0002 0.0034 0.0426 1.7298g x x x x x x (47) where:            1 2 2 . r r x v x t k. benyahi et alii, frattura ed integrità strutturale, 57 (2021) 195-222; doi: 10.3221/igf-esis.57.16 213 after having chosen the surface of polynomial responses, it will be used through several calls of the limit state function by the reliability calculation code, following an approach (form/sorm) making it possible to determine the position of the most probable point of failure and to estimate the reliability index for each transition zone of the performance function in a reduced centered space. figure 17: limit state in physical space g( , )v of the beam section (sa3). figure 18: performance function in physical space of the beam section (sa3). basic and output random variables in the limit state, their laws of random distributions are modeled as given in the tab. 3. and for the other parameters (remaining input variables), they are considered deterministic. we have performed a coupling between our reliability modeling and the implementation of the nonlinear calculation taking into account the loading shear behavior, and the limit state chosen as a performance function is a function which links the shear force and the shear strains corresponding to it, and taking as an example the limit state function of the (sa3) type beam section shown in the fig. 19 in the reduced centered space. k. benyahi et alii, frattura ed integrità strutturale, 57 (2021) 195-222; doi: 10.3221/igf-esis.57.16 214 beams vector x random variables type distribution law mean  n x coefficient of variation (cov) sa3 x1 v load normal 340.8798077 0.10 x2’ 𝛾 resistance normal 1.608293732 x 10-3 0.10 x3 e resistance normal 37620000 0.10 x4 ε resistance normal 0.0028 0.10 sa4 x1 v load normal 280.4348465 0.10 x2’ 𝛾 resistance normal 1.469326912 x 10-3 0.10 x3 e resistance normal 37620000 0.10 x4 ε resistance normal 0.0028 0.10 sk1 x1 v load normal 364.1120197 0.10 x2’ 𝛾 resistance normal 1.673839467 x 10-3 0.10 x3 e resistance normal 33000000 0.10 x4 ε resistance normal 0.00225 0.10 sk2 x1 v load normal 283.1132093 0.10 x2’ 𝛾 resistance normal 1.59049967 x 10-3 0.10 x3 e resistance normal 33000000 0.10 x4 ε resistance normal 0.00225 0.10 sk3 x1 v load normal 365.359418 0.10 x2’ 𝛾 resistance normal 1.560761406 x 10-3 0.10 x3 e resistance normal 33481000 0.10 x4 ε resistance normal 0.0022 0.10 sk4 x1 v load normal 312.336953 0.10 x2’ 𝛾 resistance normal 1.50661078 x 10-3 0.10 x3 e resistance normal 33000000 0.10 x4 ε resistance normal 0.0022 0.10 sp0 x1 v load normal 229.8279712 0.10 x2’ 𝛾 resistance normal 1.51393884 x 10-3 0.10 x3 e resistance normal 35460000 0.10 x4 ε resistance normal 0.0023 0.10 sp1 x1 v load normal 229.3812147 0.10 x2’ 𝛾 resistance normal 1.550932824 x 10-3 0.10 x3 e resistance normal 35000000 0.10 x4 ε resistance normal 0.0023 0.10 sp2 x1 v load normal 264.6198399 0.10 x2’ 𝛾 resistance normal 1.607561042 x 10-3 0.10 x3 e resistance normal 34000000 0.10 x4 ε resistance normal 0.002 0.10 sp3 x1 v load normal 259.5594739 0.10 x2’ 𝛾 resistance normal 1.630069451 x 10-3 0.10 x3 e resistance normal 33000000 0.10 x4 ε resistance normal 0.002 0.10 sm1 x1 v load normal 204.2503351 0.10 x2’ 𝛾 resistance normal 1.482089057 x 10-3 0.10 x3 e resistance normal 33000000 0.10 x4 ε resistance normal 0.0024 0.10 cf1 x1 v load normal 230.661821 0.10 x2’ 𝛾 resistance normal 1.667889239 x 10-3 0.10 x3 e resistance normal 37200000 0.10 x4 ε resistance normal 0.003 0.10 table 3: characteristic of random variables (base and output). taking into account the complexity of the mechanical model (taking account of mechanical nonlinearity), it is difficult to carry out the study by a direct coupling between the mechanical model and reliability. it is for this reason in order to assess the probability of failure, it is necessary to use the method of response surfaces (mrs) of the polynomial type. the determined response surfaces (fig. 20) will allow us to approach the explicit limit state function, which is an implicit k. benyahi et alii, frattura ed integrità strutturale, 57 (2021) 195-222; doi: 10.3221/igf-esis.57.16 215 nonlinear function (known numerically from our nonlinear calculation), whose failure of the system is observed when   1 2g x , x 0 . figure 19: limit state  1 2g x , x in 2d in the reduced centered space of the beam section (sa3). figure 20: limit state function  1 2g x , x in 3d of the beam section (sa3). the calculation is carried out for mean values of the various random parameters, and where several reliability iterations have been taken into consideration to converge towards the design point. the rackwitz-fiessler algorithm is used to perform the reliability study, and after analysis by mechanical reliability coupling by polynomial response surfaces (mrs), the hl-rf method allowed us to obtain the coordinates from the design point, the absolute values of the direction cosines of the random variables, as well as the reliability index and the probability of failure (tab. 4) for each transition zone of the different limit state curves of the beams sections tested. as shown in the tab. 4, there is a very good agreement of the results of the mechano-reliability coupling using a response surface method expressed as a limit state function. k. benyahi et alii, frattura ed integrità strutturale, 57 (2021) 195-222; doi: 10.3221/igf-esis.57.16 216 beams zones reliability index probability of failure director cosine (α1, α2) design point (u1, u2) design point (x1, x2) sa3 01 6.1981 2.824 x 10-10 (0.9486, -0.3162) (-5.8800, 1.9600) (95.5249, 1.5994) 02 3.3448 4.117 x 10-4 (-0.9119, -0.4103) (3.0501, 1.3725) (243.8263, 1.4338) 03 7.6029 1.422 x 10-14 (-0.9997, -0.0230) (7.6008, 0.1754) (159.9053, 0.6863) sa4 01 8.4909 1.0332 x 10-17 (0.9738, -0.2272) (-8.2688, 1.9293) (65.1281, 1.6065) 02 4.9439 3.83264 x 10-7 (-0.9635, -0.2676) (4.7635, 1.3232) (136.4759, 1.4348) 03 7.6029 1.42234 x10-14 (-0.9997, -0.0230) (7.6008, 0.1754) (159.9053, 0.6863) sk1 01 3.1235 8.9363 x10-4 (0.7808, -0.6246) (-2.4390, 1.9512) (204.4285, 1.5914) 02 3.8065 7.04345 x10-5 (-0.9138, -0.4061) (3.4784, 1.5459) (266.8430, 1.5078) 03 8.9349 2.13911 x10-19 (-0.9992, -0.0384) (8.9283, 0.3433) (66.8240, 1.0761) sk2 01 2.7059 3.40623 x 10-3 (0.7474, -0.6643) (-2.0224, 1.7977) (120.9005, 1.6204) 02 2.6664 3.83404 x 10-3 (-0.8849, -0.4657) (2.3595, 1.2418) (274.1525, 1.3566) 03 9.4728 1.4511 x10-21 (-0.9993, -0.0363) (9.4665, 0.3442) (28.9641, 0.6067) sk3 01 5.2240 8.80556 x 10-8 (0.9230, -0.3846) (-4.8221, 2.0092) (141.2907, 1.5900) 02 2.3491 9.42795 x 10-3 (-0.6536, -0.7568) (1.5354, 1.7778) (300.7293, 1.4331) 03 5.6622 7.49141 x 10-9 (-0.9728, -0.2316) (5.5082, 1.3114) (283.2090, 0.7687) sk4 01 5.7507 4.42197 x 10-9 (0.9388, -0.3442) (-5.3991, 1.9796) (101.4725, 1.5939) 02 3.0571 1.11773 x 10-3 (-0.8999, -0.4359) (2.7512, 1.3327) (222.9546, 1.4375) 03 9.6125 3.54862 x10-22 (-0.9998, -0.0190) (9.6107, 0.1830) (21.5302, 0.7287) sp0 01 5.0617 2.08389 x 10-7 (0.9284, -0.3713) (-4.6996, 1.8798) (81.5037, 1.6163) 02 2.2965 1.08215 x 10-2 (-0.8348, -0.5504) (1.9172, 1.2641) (246.1723, 1.1360) 03 9.0856 5.30577 x10-20 (-0.9995, -0.0285) (9.0819, 0.2594) (36.1524, 0.7342) sp1 01 2.8491 2.1923 x 10-3 (0.7348, -0.6782) (-2.0934, 1.9324) (109.2482, 1.5914) 02 4.0323 2.77117 x 10-5 (-0.9279, -0.3726) (3.7418, 1.5027) (177.8183, 1.3292) 03 9.0748 6.01284 x10-20 (-0.9988, -0.0475) (9.0644, 0.4316) (39.5503, 0.5601) sp2 01 3.1235 8.9223 x 10-4 (0.6401, -0.7682) (-1.9995, 2.3995) (144.3488, 1.5007) 02 3.2279 6.2352 x 10-4 (-0.9494, -0.3138) (3.0647, 1.0131) (232.5354, 1.4703) 03 7.3386 1.12074 x10-13 (-0.9934, -0.1146) (7.2902, 0.8411) (129.3096, 0.7071) sp3 01 3.4873 2.43984 x 10-4 (0.8320, -0.5547) (-2.9015, 1.9343) (167.6967, 1.5887) 02 4.2637 1.0082 x 10-5 (-0.9438, -0.3303) (4.0243, 1.4085) (208.8308, 1.3920) 03 7.5889 1.63048 x10-14 (-0.9970, -0.0766) (7.5665, 0.5820) (116.4464, 0.6541) sm1 01 5.1072 1.63712 x 10-7 (0.9284, -0.3713) (-4.7419, 1.8967) (74.2200, 1.6097) 02 4.6074 1.9523 x 10-6 (-0.9474, -0.3197) (4.3654, 1.4733) (115.3302, 1.4417) 03 8.6089 3.66322 x10-18 (-0.9993, -0.0363) (8.6032, 0.3128) (49.9285, 0.6267) cf1 01 3.1235 8.9363 x 10-4 (0.7808, -0.6246) (-2.4390, 1.9512) (118.4773, 1.5931) 02 5.4176 3.03553 x 10-8 (-0.9776, -0.2102) (5.2965, 1.1390) (134.5162, 1.5123) 03 7.1983 2.99974 x10-13 (-0.9987, -0.04993) (9.1022, 0.4551) (37.7926, 0.9045) table 4: results of the mechano-reliability analysis of the different sections of the beams tested. figure 21: reliability indices from numerical analysis. k. benyahi et alii, frattura ed integrità strutturale, 57 (2021) 195-222; doi: 10.3221/igf-esis.57.16 217 figure 22: absolute value of the direction cosines of the random variables  1 2x , x at the level of zone 02. beams zones numerical results experimental results deviations (%) reliability index probability of failure reliability index probability of failure sa3 01 6.1981 2.824 x 10-10 6.1888 3.051 x 10-10 0.1502 02 3.3448 4.117 x 10-4 3.2419 5.936 x 10-4 3.17 03 7.6029 1.422 x 10-14 7.8920 1.491 x 10-15 3.66 sa4 01 8.4909 1.0332 x 10-17 7.9632 8.82851 x 10-16 6.6267 02 4.9439 3.83264 x 10-7 4.6886 1.37962 x 10-6 5.4451 03 7.6029 1.42234 x10-14 8.0074 5.80751 x 10-16 5.0515 sk1 01 3.1235 8.9363 x10-4 3.1073 9.44094 x 10-4 0.5213 02 3.8065 7.04345 x10-5 3.9492 3.91536 x 10-5 3.6133 03 8.9349 2.13911 x10-19 8.5254 7.84242 x 10-18 4.8032 sk2 01 2.7059 3.40623 x 10-3 2.6901 3.57194 x 10-3 0.5873 02 2.6664 3.83404 x 10-3 2.7736 2.2604 x 10-3 3.8650 03 9.4728 1.4511 x10-21 9.2484 1.21946 x 10-20 2.4263 sk3 01 5.2240 8.80556 x 10-8 5.1280 1.4728 x 10-7 1.8720 02 2.3491 9.42795 x 10-3 2.3380 9.6942 x 10-3 0.4747 03 5.6622 7.49141 x 10-9 5.8133 3.28927 x 10-9 2.5992 sk4 01 5.7507 4.42197 x 10-9 5.7254 5.18532 x 10-9 0.4418 02 3.0571 1.11773 x 10-3 3.0121 1.29718 x 10-3 1.4939 03 9.6125 3.54862 x10-22 9.6801 1.927 x 10-22 0.6983 sp0 01 5.0617 2.08389 x 10-7 5.0298 2.46802 x 10-7 0.6342 02 2.2965 1.08215 x 10-2 2.3303 9.89517 x 10-3 1.4504 03 9.0856 5.30577 x10-20 9.5366 7.81774 x 10-22 4.7291 sp1 01 2.8491 2.1923 x 10-3 2.8352 2.29008 x 10-3 0.4902 02 4.0323 2.77117 x 10-5 4.2204 1.22388 x 10-5 4.4569 03 9.0748 6.01284 x10-20 9.4266 2.19861 x 10-21 3.7319 sp2 01 3.1235 8.9223 x 10-4 3.0904 9.99664 x 10-4 1.0710 02 3.2279 6.2352 x 10-4 3.3684 3.78024 x 10-4 4.1711 03 7.3386 1.12074 x10-13 7.5445 2.3724 x 10-14 2.7291 sp3 01 3.4873 2.43984 x 10-4 3.4649 2.65198 x 10-4 0.6464 02 4.2637 1.0082 x 10-5 4.4168 5.02669 x 10-6 3.4663 03 7.5889 1.63048 x10-14 7.9138 1.25506 x 10-15 4.1054 sm1 01 5.1072 1.63712 x 10-7 5.0981 1.71334 x 10-7 0.1784 02 4.6074 1.9523 x 10-6 4.6817 1.42903 x 10-6 1.5870 03 8.6089 3.66322 x10-18 8.9083 2.56737 x 10-19 3.4777 cf1 01 3.1235 8.9363 x 10-4 3.1287 8.77926 x 10-4 0.1662 02 5.4176 3.03553 x 10-8 5.0133 2.6845 x 10-7 8.0645 03 7.1983 2.99974 x10-13 7.6272 1.23246 x 10-14 5.6232 table 5: comparison of the deviations of the mechano-reliability analysis of the different sections of beams. k. benyahi et alii, frattura ed integrità strutturale, 57 (2021) 195-222; doi: 10.3221/igf-esis.57.16 218 the fig. 22 presents the respective values of the variables introduced to the modeling on the reliability of the numerical model at the level of zone 02. the direction cosine of the random variables of the beam’s sections tested allows us to measure the influence of each of the design variables, which gives us information on the sensitivity of the design point and the reliability index to each standardized random variable. the few differences observed are related to the fact that the load case differs depending on the type of beam tested, and where we can generally see that their increase in absolute value induces better reliability. the results of the comparison of the deviations resulting from the mechano-reliability analysis on the various tested beams are presented in the tab. 5 and the fig. 21, where it is possible to observe a very good consistency numerical results compared to those provided by the experiment at the level of the different transition zones. figure 23: difference in reliability indices between calculation and test. the reliability study shows the importance of taking into account the three transition zones of the performance curve in order to appreciate the deviations of the distortion evolution curve moy with the shear force v that may exist between calculation and testing. in fact, we can see generally from the tab. 5 that in the phase before concrete cracking the difference is practically negligible, on the other hand a small difference in the post cracking phase (before steel yielding) and the post yielding steel phase between the calculation and the testing is observed. it can be seen from the tab. 5 and from the fig. 23 that the design point of the limit state function (performance function) is given by the second transition zone, they which gives the lowest reliability index. these reliability results allow us to show us the most significant area of the performance curve in estimating the design point. conclusion he real constitutive laws of concrete, passive and active reinforcements were taken into account by the various models of behavior presented (grelat, sargin, bael99, bpel99) allowing to correctly reproduce their stressstrain envelope curves, and they have been implemented in order to deal with the shear loading behavior of reinforced and/or prestressed concrete beam sections, which makes it possible to best estimate their actual displacements. thus, the model used satisfactorily describes the behavior of reinforced and/or prestressed concrete beams whether in terms of resistance or of displacement, in the different phases of the behavior (before cracking of the concrete, post cracking and before steels yielding, post steels yielding). the limit state function (performance) obtained by the numerical model is not explicitly possible, we then proposed a technique for estimating the performance function, then we reduced ourselves to using a coupling technique by t k. benyahi et alii, frattura ed integrità strutturale, 57 (2021) 195-222; doi: 10.3221/igf-esis.57.16 219 polynomial response surface in order to be able to use the reliability methods (form/sorm). the reliability analysis approach having been carried out mainly because of the uncertainties of the various phenomena brought into play during the dimensioning of the structures, we carried out this approach by building the performance function (limit state) according to three transition zones resulting from the real behavior of the beams tested in the shear loading in order to take into account a possible feared event which could cause its failure. the method of coupling by response surface of the different transition zones proposed, allowed us to efficiently approximate the real limit state surface by a performance function, which evolves in three distinct phases resulting from the nonlinear behavior in the shear loading until the breakage of the reinforced and/or prestressed concrete beam sections. the results obtained from this study allowed us to determine the probability of failure and all the reliability characteristics (reliability indices, direction cosines, performance point coordinates) for each transition zone of the limit state function (performance) in order to perform a reliability analysis of the numerical model. acknowledgements he authors wish to thank the algerian ministry of higher education and scientific research for funding the university education research project (prfu – n° a01l02un150120180004) and tassili project (phc – 43940nj). declaration of interest statement n behalf of all authors, the corresponding author states that there is no conflict of interest. notation φ ε : defines the actual behavior of the materials, e : concrete modulus at the origin, ε : peak strain corresponding to f , f : concrete compressive strength at the age j, k : dimensionless parameters, sargin law, k : dimensionless parameters, sargin law, f : concrete tensile strength, ε : steel ultimate strain, ε : concrete fiber tensile strain, 𝜀 : tension deformation corresponding to 𝑓 , 𝜀 : deformation corresponding to the end of the plastic bearing, 𝜀 : deformation corresponding to the end of the firming, 𝜀 : breaking strain, 𝐸 ∶ steel longitudinal module, 𝜀 : deformation elastic limit of the steel, 𝜎 ∶ elastic yield stress of steel, 𝜀 : ultimate deformation of steel, 𝐸 ∶ is the young's modulus of steel at the origin, 𝜎 : is the conventional elastic limit at 2‰, 0,7. 𝜎 ∶ is constraint or stops the linear diagram, 𝜎 : is the stress in the prestressing steel, 𝜀 : is the deformation in the prestressing steel, t o k. benyahi et alii, frattura ed integrità strutturale, 57 (2021) 195-222; doi: 10.3221/igf-esis.57.16 220 𝐸 : is young's modulus at the origin, 𝑓 ∶ is the conventional elastic limit at 0.1%, 0,9 . 𝑓 : is constraint or stops the linear diagram, 1,06 . 𝑓 : is the breaking stress, ε : failure strain, 𝜀 : steel yield strain, 𝜎 ∶ steel yield stress, 𝜀 : steel ultimate strain, e ∶ steel modulus at the origin, ε ∶ gravity center strain, 𝑁 : number of concrete trapezes, 𝑁 : number of passive reinforcing beds, 𝐴 : passive steel bed area, 𝑦 : passive steel bed dimension relative to the oy reference axis, y : lower trapezoidal ordinate, y : upper trapezoid ordinate, b : the lower abscissa of trapezoid along the x axis, b : the upper abscissa of trapezoid along the x axis, fk and fk1 : the normal forces acting on layer k in both sections, gk-1 and gk : the resulting sliding forces on the lower and upper faces of the k layer, vk : the share of the shear force balanced by the layer k, m : the number of layers of concrete, 𝑋 : basic random vector, g : failure function or limit state function, φ : the normal law distribution function reduced centered (mean 0 and standard deviation 1), m : means strength, m : means loads, σ : standard deviations of the strength, σ : standard deviations of the loads, p∗ : point of the most probable failure, 𝑢∗ : design point, 𝛽∗: reliability index associated with the design point, 𝑔, 𝑔 : failure function in u space, α : vector cosine directors, 𝛽 : reliability index associated with 𝑃 , 𝑃 : probability of failure. references [1] collins, m.p. (1978). towards a rational theory for rc members in shear, j. struct. div., 104(4), pp. 649–666. [2] vecchio, f.j., collins, m.p. (1982). the response of reinforced concrete to in-plane shear and normal stresses. university of toronto, department of civil engineering, publication no.82–03. [3] vecchio, f.j., collins, m.p. (1986). the modified compression-field theory for reinforced concrete elements subjected to shear, aci struct. j., 83(2), pp. 219–231. [4] bažant, z.p., kazemi, m.t. (1991). size effect on diagonal shear failure of beams without stirrups, aci struct. j., 88(3), pp. 268–276. [5] bentz, e.c., vecchio, f.j., collins, m.p. (2006). simplified modified compression field theory for calculating shear strength of reinforced concrete elements, aci struct. j., 103(4), pp. 614–624. [6] carbone, v.i., giordano, l., mancini, g. (2001). design of rc membrane elements, struct. concr., 2(4), pp. 213–223. [7] hsu, ttc., zhang, l. (1997). nonlinear analysis of membrane elements by fixed-angle softened-truss model, aci struct. j., 94(5), pp. 483–491. k. benyahi et alii, frattura ed integrità strutturale, 57 (2021) 195-222; doi: 10.3221/igf-esis.57.16 221 [8] hsu, t.t.c. (1996). toward a unified nomenclature for reinforced concrete theory, j. struct. eng., 122(3), pp. 275– 283. doi: 10.1061/(asce)0733-9445(1996)122:3(275). [9] miguel, p.f., navarro-gregori, j., fernández-prada, m.a., bonet, j.l. (2013). a simplified method to predict the ultimate shear stress of reinforced concrete membrane elements, eng. struct., 49, pp. 329–344. doi: 10.1016/j.engstruct.2012.11.009. [10] rahal, k.n. (2010). shear-transfer strength of reinforced concrete, aci struct. j., 107(4), pp. 419–426. [11] rahal, k.n. (2008). simplified design and capacity calculation of shear strength in reinforced concrete membrane elements. eng. struct., 30(10), pp. 2782–2791. doi: 10.1016/j.engstruct.2008.03.002. [12] vecchio, f.j. (2000). disturbed stress field model for reinforced concrete: formulation, j. struct. eng., 126(9), pp. 1070–1077. doi: 10.1061/(asce)0733-9445(2000)126:9(1070). [13] vecchio, f.j. (2001). disturbed stress field model for reinforced concrete: implementation, j. struct. eng., 127(1), pp. 12–20. doi: 10.1061/(asce)0733-9445(2001)127:1(12). [14] kachi, m.s., fouré, b., bouafia, y., muller, p. (2006). l'effort trenchant dans la modélisation du comportement jusqu' à rupture des pouters en béton armé et précontraint. revue européenne de génie civil, 10(10), pp. 1235–1264. doi: 10.1080/17747120.2006.9692914. [15] grelat, a. (1978). nonlinear analysis of reinforced concrete hyperstatics frames. doctoral thesis engineer. university paris vi. [16] nait-rabah, o. (1990). numerical simulation of nonlinear behavior of frames space. doctoral thesis. central school of paris. [17] freudenthal, a.m. (1947). the safety of structures, transactions of asce, 112(1), pp.125–159. [18] cornell, c.a. (1969). a probability based structural code, journal of american concrete institute, 66(12), pp. 974– 985. [19] hasofer, a.m. (1974). reliability index and failure probability, j. struct. mech., 3(1), pp. 25–27. doi: 10.1080/03601217408907254. [20] mohamed, a.m., lemaire, m. (1995). linearized mechanical model to evaluate reliability of offshore structures, structural safety 17(3), pp. 167–193. doi: 10.1016/0167-4730(95)00009-s. [21] rackwitz, r. (2001). reliability analysis – a review and some perspectives, structural safety, 23(4), pp. 365–395. doi: 10.1016/s0167-4730(02)00009-7. [22] benyahi, k., bouafia, y., barboura, s., kachi, m.s. (2018). nonlinear analysis and reliability of metallic truss structures, front. struct. civ. eng., 12, pp. 577–593. doi: 10.1007/s11709-017-0458-y. [23] jeong, j.p., kang, d.h. (2019). investigation on shear strain of reinforced concrete membrane panels subjected to pure shear, advances in mechanical engineering, 11(8), pp. 1–12. doi: 10.1177/1687814019869488. [24] filho, b., bernardo, l., horowitz b. (2020). softened variable angle truss model (ra-stm): model description and refinement/optimization proposals, kne engineering, 5(5), pp. 36–48. doi: 10.18502/keg.v5i5.6909. [25] bernardo, l.f.a., filho, b.m.v.c., horowitz, b. (2020). predicting the behavior of prestressed concrete membrane elements by refined rotating-angle softened-truss model with efficient solution procedure, struct. concr. j. fib., 21(3), pp. 934–948. doi: 10.1002/suco.201900481. [26] bernardo, l.f.a., filho, b.m.vc., horowitz, b. (2020). refined efficient ra-stm procedure for rc membrane elements, eng. struct., 213. doi: 10.1016/j.engstruct.2020. 110552. [27] bernardo, l.f.a., filho, b.m.v.c., horowitz, b. (2021). predicting the behavior of frp-strengthened rc membrane elements with efficient rotating-angle softened-truss model procedure, mater. struct., 54. doi: 10.1617/s11527-021-01631-y. [28] bernardo, l.f.a., lyrio a.r.b., silva, j.r.b., horowitz, b. (2018). refined softened truss model with efficient solution procedure for prestressed concrete membranes, j. of struct. eng., 144(6). doi: 10.1061/(asce)st.1943-541x.0002044. [29] bernardo, l.f.a., cerquido, b.m.d., silva, j.r.b., horowitz, (2018). efficient refined rotating angle softened truss model procedure to analyze reinforced concrete membrane elements, struct. concr. j. fib., 19(6), pp.1971–1982. doi: 10.1002/suco.201800012. [30] silva, j.r.b. (2016). efficient procedure for the analysis of reinforced concrete sections using the softened truss model, master thesis, department of civil engineering, federal university of pernambuco, recife, brazil [in portuguese]. [31] bernardo, l., sadieh, s. (2021). a monotonic smeared truss model to predict the envelope shear stress–shear strain curve for reinforced concrete panel elements under cyclic shear, applied mechanics, 2(1), pp. 174-194. doi: 10.3390/applmech2010011. k. benyahi et alii, frattura ed integrità strutturale, 57 (2021) 195-222; doi: 10.3221/igf-esis.57.16 222 [32] schlune, h., plos, m., gylltoft, k. (2011). safety formats for nonlinear analysis tested on concrete beams subjected to shear forces and bending moments, eng. struct., 33(8), pp. 2350–2356. doi: 10.1016/j.engstruct.2011.04.008. [33] allaix, d.l., carbone, v.i., mancini, g. (2013). global safety format for non-linear analysis of reinforced concrete structures, struct. concr., 14(1), pp. 29–42. doi: 10.1002/suco.201200017. [34] el ghoulbzouri, a., kissi, b., khamlichi, a. (2015). reliability analysis of reinforced concrete buildings: comparison between form and ism, procedia eng., 114, pp. 650–657. doi: 10.1016/j.proeng.2015.08.006. [35] olmati, p., sagaseta, j., cormie, p., jones, a.e.k. (2017). simplified reliability analysis of punching in reinforced concrete flat slab buildings under accidental actions, eng. struct., 130(1), pp. 83–98. doi: 10.1016/j.engstruct.2016.09.061. [36] słowik, m., skrzypczak, i., kotyniac, r., kaszubskac, m. (2017). the application of a probabilistic method to the reliability analysis of longitudinally reinforced concrete beams, procedia eng., 193, pp. 273–280. doi: 10.1016/j.proeng.2017.06.214. [37] hadidi, a., azar, b.f, rafiee, a. (2017). efficient response surface method for high-dimensional structural reliability analysis, struct. saf., 68, pp. 15–27. doi: 10.1016/j. strusafe.2017.03.006. [38] rakoczy, a.m., nowak, a.s. (2013). reliability-based sensitivity analysis for prestressed concrete girder bridges, pci journal, 58(4), pp. 81–92. doi: 10.15554/pcij.09012013.81.92. [39] roy, a., robuschi, s., hendriks, m.a., belletti, b. (2016). safety assessment of existing reinforced concrete beams using probabilistic methods at different levels, key engineering materials, 711, pp. 958–965. doi: 10.4028/www.scientific.net/kem.711.958. [40] slobbe, a., rózsás, á., allaix, d.l., bigaj-van vliet a. (2020). on the value of a reliability-based nonlinear finite element analysis approach in the assessment of concrete structures, struct. concr., 21(1), pp. 32–47. doi: 10.1002/suco.201800344. [41] grubišić, m., ivošević, j., grubišić, a. (2019). reliability analysis of reinforced concrete frame by finite element method with implicit limit state functions, buildings, 9(5). doi: 10.3390/buildings9050119. [42] sargin, m. (1971). stress-strain relationship for concrete and the analysis of structural concrete sections. solid mechanics division, university of waterloo. [43] rules bael 91, revised 99 (1999). technical rules for the design of reinforced concrete structures according to the limit states method. publisher: association francaise de normalisation. [44] rules bpel91, revised 99 (1999). technical design rules and calculation of works and structures prestressed concrete according to the limit states method. publisher: association francaise de normalisation. [45] atkinson, k. (1989). an introduction to numerical analysis. john wiley & sons inc., 2nd edition, new york. [46] belarbie, a., hsu, t.t.c. (1995). constitutive low of softened concrete in biaxial tension-compression, aci struct. j., 92(5), pp. 562–573. microsoft word numero_50_art_49_2626 n. a. fountas et alii, frattura ed integrità strutturale, 50 (2019) 584-594; doi: 10.3221/igf-esis.50.49 584 focused on the research activities of the greek society of experimental mechanics of materials multi-response optimization of cuzn39pb3 brass alloy turning by implementing grey wolf algorithm nikolaos fountas school of pedagogical and technological education, department of mechanical engineering educators, laboratory of manufacturing processes and machine tools, aspete campus, gr 14121, n. heraklion, greece fountasnikolaos@hotmail.com angelos koutsomichalis hellenic air-force academy, faculty of aerospace studies, dekelia air force base, gr 19005, greece angelos.koutsomichalis@hafa.haf.gr john d. kechagias technological educational institute of thessaly, mechanical engineering department, tei campus, gr 41110, larissa, greece jkechag@teilar.gr nikolaos m. vaxevanidis school of pedagogical and technological education, department of mechanical engineering educators, laboratory of manufacturing processes and machine tools, aspete campus, gr 14121, n. heraklion, greece vaxev@aspete.gr abstract. machinability of engineering materials is crucial for industrial manufacturing processes since it affects all the essential aspects involved, e.g. workload, resources, surface integrity and part quality. two basic machinability parameters are the surface roughness, closely associated with the functional and tribological performance of components, and the cutting forces acting on the tool. knowledge of the cutting forces is needed for estimation of power requirements and for the design of machine tool elements, tool-holders and fixtures, adequately rigid and free from vibration. this work investigates the influence of cutting conditions on machinability indicators such as the main cutting force fc and surface roughness parameters ra and rt when longitudinally turning cuzn39pb3 brass alloy. full quadratic regression models were developed to correlate the machining conditions with the imparted machinability characteristics. further on, an advanced artificial grey wolf optimization algorithm was implemented to optimize the aforementioned responses with great success in finding the final optimal values of the turning parameters. keywords. turning; surface roughness; cutting forces; multi-parameter analysis; optimization; grey wolf algorithm. citation: fountas, n.a., koutsomichalis, a., kechagias, j.d., vaxevanidis, n.m., multi-response optimization of cuzn39pb3 brass alloy turning by implementing grey wolf algorithm, frattura ed integrità strutturale, 50 (2019) 584-594. received: 23.01.2019 accepted: 27.05.2019 published: 01.10.2019 copyright: © 2019 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. http://www.gruppofrattura.it/va/50/2626.mp4 n. a. fountas et alii, frattura ed integrità strutturale, 50 (2019) 584-594; doi: 10.3221/igf-esis.50.49 585 introduction ue to their physical and mechanical properties copper and zinc alloys (brass) possess excellent machinability; high electric as well as thermal conductivity, significant resistance to corrosion and noticeable antibacterial properties. consequently they are used in several industrial branches such as electronics, sanitary and automotive. lead (pb) is a key element added to brass alloys to facilitate chip breakage, extend tool life and allow for wider applicable ranges of machining parameters [1]. on the other hand, it must be noted that in recent years the use of lead in brass alloys is restricted more and more, due to the legislation on protecting health and environment, since lead is a hazardous heavy metal. alternatively, numerous studies revealed that adding bismuth, selenium, indium, as well as graphite as substitution for lead improves the machinability of lead-free brasses. however, the manufacturing process of these materials is very complex and cost-intensive. apart from that, low-leaded binary brass alloys, meeting the future requirements on maximum lead contents of 0.1%-0.25%, have been developed recently. in general,  machinability of low-leaded brasses is significantly worse compared to leaded free-brass whilst given their chemical composition and microstructure, different machinability problems arise [2]. for the silicon alloyed materials, i.e. cuzn21si3p (cw724r), tool wear is to be higher due to a siliconrich and hard κ-phase in the microstructure. for other low-leaded brasses, such as cuzn42 (cw510l) and cuzn38as (cw511l), the main problems exist due to the formation of long chips and higher thermal as well as mechanical tool load [3]. additionally, high adhesion tendency may result in chipping of the cutting edge and reduced work piece quality. kato et al. [4] enhanced the chip evacuation in micro-drilling of cuzn21si3p by optimizing tool geometry. klocke et al. [2] and nobel et al. [3] published approaches to enable high-performance cutting of low-leaded brass alloys. in ref. [5] nobel et al. investigates also the chip formation, the flow and its breakage in free orthogonal cutting.  metal cutting operations are widespread in manufacturing industry and the prediction and/or the control of the resulted machinability always is of great importance. one basic machinability parameter is the surface roughness, as it is closely associated with the quality, reliability and functional performance of components [6,7]. another one is the cutting force system developed; it is needed for the estimation of power requirements and for the design of machine tool elements, tool-holders and fixtures, adequately rigid and free from vibration. moreover, the cost of machining is strongly dependent on the rate of material removal, and this cost may be reduced by increasing the cutting speed and/or the feed rate; however, there are restrictions to the speed and feed values above which the life of the tool is shortened excessively. axis-symmetrical components are primarily manufactured using turning operations. due to the various factors influencing surface integrity in turning, non-competitive production times as well as poor surface finish may be experienced which in turn degrade functional behavior of turned components [8]. therefore, as it occurs in any other metal cutting process and any other engineering material, finding the optimal process parameters is of paramount importance [8,9]. arc-chain surface patterns are quite often in turning, yet; significant deviations may be observed owing to irregular chip formation phenomena such as discontinuous chip, built-up edge, low feeds, chattering and intense tool flank wear. such occurrences are experienced especially when it comes to productivity or material selection limitations [6]. manufacturing operations should be performed such that all aspects of design requirements for high performance, aesthetics and functionality are met. obviously such requirements are directly related to dimensioning and tolerancing as well as surface texture indicators for ensuring longer lifespan for manufactured components and tribological functioning [10]. despite the fact that arithmetic surface roughness average (ra) and the maximum height of the profile (rt) are not able to provide full information about the shape of profile they are two crucial indicators for judging surface finish. characteristics like inclination and curvature of the surface roughness asperities, “emptiness” or “fullness” of the profile, distribution of the profile material at various heights are registered in the profile shape. the essential tribological aspects (e.g. friction, wear, state of lubrication) are highly dependent on profile shape [7,11-13]. cutting forces occur when extreme conditions encountered at the tool-workpiece contact [7,14,15]. this interaction can be related to tool wear and failure. as a result tool wear and cutting forces are related to each other. surface roughness as well as cutting force monitoring is essential for evaluating the performance of machining processes, expand tool life and improve productivity. nowadays, due to the development of computer technology, finite element and soft computing/artificial intelligence techniques are being used extensively for modeling and optimization of machining processes. soft computing/ artificial intelligence methods include neural network (nn), fuzzy set theory, genetic algorithm (ga), simulated annealing (sa), ant colony optimization (aco) and particle swarm optimization (pso); see refs. [7,14]. the present study investigates the influence of cutting parameters on machinability indicators such as the main cutting force fc and surface roughness parameters ra and rt when longitudinally turning cuzn39pb3 brass alloy. full quadratic regression models were developed to express the correlation of the machining conditions with the imparted machinability characteristics. further on, an advanced artificial grey wolf optimazation algorithm [16] was implemented to optimize successfully the aforementioned responses. d n. a. fountas et alii, frattura ed integrità strutturale, 50 (2019) 584-594; doi: 10.3221/igf-esis.50.49 586 it should be noted that nowadays, due to the increasing trend towards unmanned manufacturing systems, machinability assessment procedures are crucial part in process planning for machining. these procedures are based on a number of either individual or combined machinability criteria such as the tool-life and wear, material removal rate, cutting monitoring of cutting forces and/or power consumption, surface finish and machining accuracy [17]. in particular, for continuous mode machining operations, such as turning, achieving efficient chip breaking is necessary and therefore the chip breakability rating under the selected cutting conditions can be considered as an essential machinability criterion [17-19]. experimental work he main cutting conditions, rotational speed n, feed rate f and depth were systematically studied by using an l18 mixed-level taguchi orthogonal array for building an experimental design. the scope of the experiment is the investigation of the effect of cutting conditions on surface roughness parameters; ra and rt, as well as main cutting force component; fc, when turning cuzn39pb3 (cw614n) alloy. the formulation of full quadratic prediction models are also of major concern. a randomized order of executions was followed to eliminate the experimental bias for the results. table 1 summarizes the turning parameters and their levels. parameter units level 1 level 2 level 3 spindle speed (n) rpm 800 1600 feed rate (f ) mm/rev 0.10 0.18 0.33 depth of cut (α) mm 0.5 1.0 1.5 table 1: investigated machining conditions and levels. turning experiments were performed on a colchester triumph® 2500 conventional lathe. cylindrical rods of 40 mm in diameter and 150 mm in length were used as the experimental specimens. regions of cut were determined as 20 mm wide to provide space for the measurements. a seco® coated tool insert, coded as tnmg 160404 – mf2 with tp 2000 coated grade, was selected as a cutting tool for the series of experiments performed. the tool had a triangular geometry with cutting edge angle, kr=55o. the kinematics of the longitudinal turning process is illustrated in fig.1a. a 3d cutting force system was considered according to standard theory of oblique cutting; see also fig.1b. note that the cutting force is of the most important yet least understood operation parameters of a machining operation. in general, this force is represented by three components, namely, the power component (fc), the radial component (fr) and the axial (or feed) component (ff) as shown in fig.1b. of these three components, the greatest, usually, is the power component, which is often called the main cutting force (fc) [7]. (a) (b) figure 1: (a) kinematics of the longitudinal turning process; (b) three-dimensional cutting force system. the material under investigation was a cuzn39pb3 (cw614n-brass 583) brass alloy of 130 hb hardness. studies concerning the microstructure and machinability of cuzn39pb3 alloy may be found in [13,20,21]. surface roughness was evaluated using a taylor-hobson® surtronic 3 profilometer with the talyprof® software. the cut-off length was selected at 0.8 mm whereas five measurements were taken on every pass at the longitudinal direction. the three-component cutting force t n. a. fountas et alii, frattura ed integrità strutturale, 50 (2019) 584-594; doi: 10.3221/igf-esis.50.49 587 dynamometer kistler® ch-8408 was used for measuring cutting forces. a typical filtered profile corresponding to a surface roughness measurement is depicted in fig.2 and an indicative cutting forces measurement graph is shown in fig.3. measured values for the objectives ra, rt and fc are tabulated in table 2 along with the corresponding cutting conditions. figure 2: typical filtered surface roughness profile of a turned brass alloy. figure 3: indicative graph of the cutting forces measurement from a turning experiment. results and discussion n the case of steels it was identified [9,22], that surface roughness decreases with increasing cutting speed and decreasing depth of cut and feed rate; such a behavior was not observed for the cuzn39pb3 brass alloy. during the present series of experiments it is observed that high values for rotational speed in relation to moderate feeds are necessary to minimize surface roughness, whilst combinations of low speeds and low-to-moderate feeds favor the minimization of main cutting force; see table 2. these observations are, in general, in agreement with previous reports; see refs. [2,14]. fc is reduced under low values for depth of cut and constant rotational speed n=800 rpm whilst it increases for f=0.1 mm/rev and f=0.33 mm/rev. however, a feed rate value f=0.18 mm/rev seems to reduce fc referring to all three levels for depth of cut (fig.4a). in addition ra reduces when applying moderate cutting depth levels; i.e., 1.0 mm under constant rotational speed, n=800 rpm. a feed rate equal to 0.18 mm/rev reduces ra under a cutting depth equal to 0.5 mm and 1.0 mm. when applying depth of cut a=1.0mm the increase of ra is less noticeable under the feed rate level of 0.33 mm/rev. the opposite observation is noticed for ra when applying a depth of cut equal to 1.5 mm. ra increases for depth of cut a=1.5 mm and feed rate f=0.1 mm/rev whilst it reaches its highest value for f=0.18 mm/rev (fig.5a). rt reduces when applying depth of cut 1.0 mm and 1.5 mm under a feed rate value f=0.18mm yet; a different behavior is noticed when applying a depth of cut equal to 0.5 mm. rt gradually increases when applying higher values for feed rate under a constant depth of cut equal to 0.5 mm (fig.6a). for n=1600 rpm main cutting force fc is reduced under the lowest depth of cut as it is expected. main cutting force seems to increase in general when using high feed rate values however when applying depth of cut equal to 1.0 mm both the second and the third feed rate levels maintain the result of fc. main cutting force fc, reaches its highest value when applying depth of cut equal to 1.5mm and feed rate equal to 0.33 mm/rev whereas it reaches its lowest value for depth of µm -40 -30 -20 -10 0 10 20 30 40 50 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 2.2 2.4 2.6 2.8 3 3.2 3.4 3.6 3.8 mm length = 4 mm pt = 49.7 µm scale = 100 µm i n. a. fountas et alii, frattura ed integrità strutturale, 50 (2019) 584-594; doi: 10.3221/igf-esis.50.49 588 cut equal to 0.5 mm and feed rate equal to 0.1 mm/rev (fig.4b). as opposed to the case of using n=800 rpm, depth of cut doesn’t seem to significantly affect ra when applying n=1600 rpm. however it seems to slightly increase under higher depth of cut and feed rate values (fig.5b). as far as rt is concerned, it takes its lowest value when using the second level of cutting depth which is equal to 1.0 mm and under f=0.1 mm/rev (fig.6b). nevertheless, switching from f=0.18 mm/rev to f=0.33mm/rev an exponential increase to the result of rt is noticed. by taking into account the levels for rotational speed, n=800 rpm and n=1600rpm similar effects are shown for depth of cut a=0.5 mm as well as a=1.0 mm as opposed to a=1.5 mm where different results in terms of the effects are observed, when it comes to rt. finally rt parameter takes its highest value when applying a=0.5 mm and f=0.33 mm/rev. experiment n (rpm) f (mm/rev) a (mm) ra (μm) rt (μm) fc (n) 1 800 0.10 1.5 7.34 37.7 200 2 800 0.10 1.0 4.33 25.6 160 3 800 0.10 0.5 6.02 36.5 090 4 800 0.18 1.5 4.62 25.2 130 5 800 0.18 1.0 4.23 21.1 120 6 800 0.18 0.5 5.52 34.5 080 7 800 0.33 1.5 7.14 33.8 165 8 800 0.33 1.0 8.51 42.7 160 9 800 0.33 0.5 8.02 37.5 100 10 1600 0.10 1.5 1.44 13.2 160 11 1600 0.10 1.0 1.78 11.5 130 12 1600 0.10 0.5 2.03 12.4 085 13 1600 0.18 1.5 4.24 22.2 170 14 1600 0.18 1.0 3.94 19.0 150 15 1600 0.18 0.5 4.00 21.7 100 16 1600 0.33 1.5 5.13 30.7 190 17 1600 0.33 1.0 5.26 26.8 150 18 1600 0.33 0.5 5.28 28.5 110 table 2: cutting conditions and measured values of surface roughness parameters and main cutting force. figure 4: feed rate effect on main cutting force, fc: (a) n=800 rpm; (b) n=1600 rpm. n. a. fountas et alii, frattura ed integrità strutturale, 50 (2019) 584-594; doi: 10.3221/igf-esis.50.49 589 figure 5: feed rate effect on mean surface roughness, ra: (a) n=800 rpm; (b) n=1600 rpm. figure 6: feed rate effect on maximum surface roughness, rt: (a) n=800 rpm; (b) n=1600 rpm. statistics and predictive modeling regression analysis was applied for developing the second order regression models for responses ra, rt and fc. in order to study the effect of turning parameters on the responses, first order, second order and interactions models among the different levels were considered. the general equation for regression model may be given as: 2 0 1 1 n n i i ii i ij i j i i i j y b bx b x b x x         (1) in eq.(1) y is the response; xi, xj represent the coded variables corresponding to the rotational speed n (rpm), feed rate f(mm/rev) and depth of cut a(mm) whilst bi, bii, and bij are the linear, the quadratic and the interaction terms respectively. the control factors in this relation may change from i=1 to n where n is the total number of control factors. by using experiential values of ra, rt and fc, the coefficients for second order regression models have been determined with the help of minitab® 17 software by using uncoded units (actual experimental values of process parameters and responses). final models for ra, rt and fc may be obtained by removing the insignificant terms. the insignificant terms can be removed either by using null hypothesis or by using backward elimination process using p-values of different terms. in this study insignificant terms from the models have been removed by considering p-values. here, we eliminate the variable (term) with the highest p-value for the test of significance of the variable, conditioned on the p-value being bigger than a predetermined level (0.05 or 95 % confidence level for this case). next, we fit this model after elimination, and further remove the variable with the highest p-value for the test of significance. the procedure ends when no more variables can be removed from the model. the final models obtained for predicting ra, rt and fc responses are as follows: n. a. fountas et alii, frattura ed integrità strutturale, 50 (2019) 584-594; doi: 10.3221/igf-esis.50.49 590 ra (μm) = 9.3 0.004n 3.1f 2.5a+29.1f 2 +1.56a2+0.005nf 0.00002na3.5fa (2) rt (μm) = 75.3 0.032n 103f 35.3a+210f 2+13.5a2+0.051nf + 0.006na 3.5fa (3) fc (n) = 69.7 0.022n – 612f +195a+1283f 2 53.4a2+0.135nf – 65fa (4) to test whether the data predicted by regression models are well-fitted or not, the coefficient of determination r2 has been calculated for each model. these values have been found to be equal to 97.29 %, 96.76 % and 99.44 % for ra, rt and fc respectively. in other words the correlation coefficients for ra, rt and fc are 0.97, 0.96 and 0.99 respectively. hence, the data predicted by the developed models for each quality characteristic (output) are well-fitted. in order to graphically examine the adequacy of the models, correlation plots were produced. from fig.7, it is evident that the models developed for fitting the experimental results corresponding to ra, rt and fc are both significant and adequate whilst, simultaneously, they are capable of providing outputs in very good agreement with experimental results. (a) (b) (c) figure 7: comparison of experimental and predicted results for: (a) ra, (b) rt and (c) fc . multi-response optimization using the grey wolf algorithm eta-heuristic optimization techniques have drawn the researchers’ interest over the last two decades. such techniques are genetic algorithms (gas) [23], ant colony optimization (aco) [24], and particle swarm optimization (pso) [25]. in addition to the huge number of theoretical works, such techniques have been applied in various engineering fields. the reason why such algorithms have become very popular in terms of their implementation to engineering problem-solving lies on four main reasons, simplicity; flexibility; derivation-free mechanism; and local optima avoidance. in general, meta-heuristic algorithms are quite simple in their application since they have been mostly inspired by simple concepts. the inspirations mimic physical phenomena like animals’ behavior, or evolutionary concepts. this simplicity allows for simulating several natural ideas, proposing novel meta-heuristics, hybridizing two or more meta-heuristics, or 1 81 61 41 21 08642 9 8 7 6 5 4 3 2 1 number of experiment su rfa ce ro ug hn es s, ra (μ m ) ra (μm) exp. ra (μm) model 1 81 61 41 21 08642 45 40 35 30 25 20 1 5 1 0 number of experiment su rfa ce ro ug hn es s, rt (μ m ) rt (μm) exp. rt (μm) model 1 81 61 41 21 08642 200 1 80 1 60 1 40 1 20 1 00 80 60 number of experiment m ain cu tt in g fo rc e, fc (n ) fc (n) exp. fc (n) model m n. a. fountas et alii, frattura ed integrità strutturale, 50 (2019) 584-594; doi: 10.3221/igf-esis.50.49 591 even enhancing current ones. in addition this simplicity contributes to the rapid understanding of metaheuristics for their application to problem-solving. flexibility deals with the metaheuristics’ applicability to the various problems without changing the basic algorithmic infrastructure. applications of metaheuristics to problems involve only the inputs and outputs of a system. therefore what needs to be known is how to successfully determine a specific problem to be handled by a metaheuristic. furthermore the majority of metaheuristics comprise derivation-free utilities. as opposed to gradient-based optimization techniques, metaheuristics optimize problems stochastically. optimization initializes randomly created candidate solutions, and there is no need to compute derivatives for search spaces to converge to optimal solutions. this makes metaheuristics highly suitable for real-world problems with expensive or unknown derivative information. finally, metaheuristics exhibit superior abilities to avoid local trapping compared to traditional optimization techniques. this occurs owing to the stochastic nature of metaheuristics allowing them to avoid stagnation in local regions and search the solution space thoroughly. when it comes to real-world problems, solution spaces are usually unknown and quite complex with a vast number of local optima, hence, metaheuristics are suitable modules for optimizing such challenging real-world problems. according to the no-free lunch theorem [26] there is no metaheuristic best suited for successfully solving all optimization problems. this implies that a particular metaheuristic may exhibit quite promising results on a set of problems, but the same one might achieve poor performance on a different set of other kinds of problems. obviously, no-free lunch theorem turns this research field to a highly active one where contributions in enhancing current algorithms and/or developing novel ones are published very often. fundamental features of the grey wolf algorithm and optimization problem setup to optimize cutting parameters during turning of cuzn39pb3 brass alloy, the multi-objective version of grey wolf optimazation algorithm was implemented [16]. according to the optimization problem’s nature the responses were set for being optimized as follows: 1. minimization of the arithmetic surface roughness average, ra ; 2. minimization of the maximum height of the profile, rt ; 3. minimization of the main cutting force, fc. the three-objective genetic algorithm optimization method used is a population-based non-dominated intelligent algorithm developed by mirjalili et al. [16]; following the behavior and social life of grey wolves. this algorithm simulates the haunting hierarchy of wolves towards capturing their prey. the algorithm establishes candidate solutions according to the hierarchy of grey wolves in nature, i.e.; alpha, beta, delta and omega. mirjalili et al. have properly developed the mathematical relations concerning the unique features of this algorithm based on the physical characteristics of grey wolves. the main stages that grey wolves follow to capture their prey are: 1. tracking, chasing, and approaching the prey; 2. pursuing, encircling, and harassing the prey until it stops moving and 3. attacking the prey. these stages mimic the different intelligent operators an artificial algorithm requires so as to be effective. hence, attacking a prey technically means the exploitation of the search space whilst searching for prey simulates the exploration of the search space. of particular interest and practical merit is the c-vector in the grey wolf optimization algorithm. c-vectors suggest random weights for prey so as to stochastically emphasize or partially ignore the effect in defining the euclidean distance. this contributes to the algorithm’s random behavior thus removing the inherent bias of elite solutions and facilitating exploration as well as local optima avoidance. in addition the c-vector can be assumed as the effect of obstacles towards approaching the prey. thus, depending on the position of a wolf it may randomly give the prey a weight for making it harder to be reached by wolves; or increasing its distance and vice versa. searching initializes by randomly creating a population of grey wolves (candidate solutions) in the algorithm. over the course of iterations, alpha, beta, and delta wolves estimate the probable position of the prey. each candidate solution updates its distance from the prey. the algorithm-specific parameters of the grey wolf algorithm are set accordingly in order to emphasize exploration and exploitation. finally, the algorithm is terminated once the optimization criteria have been satisfied or the number of generations has been reached.  optimization results the results obtained from the grey wolf algorithm for the responses of ra, rt and fc with respect to turning parameters n (rpm), f (mm/rev) and a (mm) are presented in fig.8 that depicts the non-dominated pareto optimal solutions obtained. by examining the spread of the non-dominated solutions appeared in the three-objective pareto front it can be concluded that the non-dominated solutions are concentrated such that all potential values for objectives are obtained. however, since all three optimization criteria are of minimization, it is expected to consider that the non-dominated solutions close to the pareto front’s origin are those of particular benefit. therefore the non-dominated solutions close to the axes representing the objectives ra, rt and fc are considered as the optimal points for achieving simultaneous optimization, characterized by their parameter values corresponding to the independent variables n (rpm), f (mm/rev) and a (mm). n. a. fountas et alii, frattura ed integrità strutturale, 50 (2019) 584-594; doi: 10.3221/igf-esis.50.49 592 figure 8: pareto front of the non-dominated optimal solutions obtained by the multi-objective grey wolf algorithm. nevertheless, it is reasonable to argue that the suitability of the different non-dominated solutions provided by the optimization process is to be decided by the process engineer with regard to particular requirements or constraints. this is beneficial to the increase of production rates by reducing machining time as well. for the purpose of optimizing turning parameters in order to minimize ra, rt and fc a population of 20 grey wolves and a maximum number of 250 iterations were selected. the multi-objective grey wolf algorithm was run several times independently to examine the variability in terms of the obtained results. it was deduced that the algorithm maintains repeatability in converging to the same optimal values despite its stochastic nature. the convergence diagram of the algorithmic evaluations is illustrated in fig.9. it is shown that the algorithm is capable of obtaining the optimal solution for the three objectives by determining smaller numbers for both candidate solutions and interactions. apparently the latter depends on the problem’s characteristics; optimization trade off (i.e. simultaneous minimization and maximization of several objectives) and settings for algorithm-specific parameters. the optimal solutions the algorithm obtains refer to alpha, beta and delta wolves holding the best positions in the pareto front. according to the outputs and the related archive with the resulting costs, the best point of alpha wolf is for ra = 3.025 μm; rt =16.804 μm and fc =83.209 n. the values for turning parameters corresponding to these results are 1600 rpm for n; 0.1184 mm/rev for f and 0.6182 mm for a. the best point of beta wolf is for ra=3.108 μm; rt=17.180 μm and fc=83.153 n. the values for turning parameters corresponding to these results are 1313 rpm for n; 0.1741 mm/rev for f and 0.5000 mm for a. the best point of delta wolf is for ra = 2.966 μm; rt =16.594 μm and fc=83.326 n. the values for figure 9: convergence speed during the algorithmic evaluations performed by the multi-objective grey wolf algorithm. 2502252001 751 501 251 007550251 1 40 1 30 1 20 1 1 0 1 00 90 80 objective evaluation number pa re to o bj ec tiv e va lu e n. a. fountas et alii, frattura ed integrità strutturale, 50 (2019) 584-594; doi: 10.3221/igf-esis.50.49 593 turning parameters corresponding to these results are 1479 rpm for n; 0.1709 mm/rev for f and 0.5000 mm for a. it is deduced that the results simultaneously satisfying all three objectives are not necessarily the values of upper or lower points of the problem’s intervals. these values for turning parameters occur according the interactions between them. it is also observed that the different solutions prioritize a different hierarchy among the objectives. the best result for ra comes from the multi-objective solution of the delta wolf which is equal to 2.966 μm whereas the worst value for ra comes from the multi-objective solution of the beta wolf which is equal to 3.108 μm. the best result for rt comes from the multiobjective solution of the delta wolf which is equal to 16.594 μm whereas the worst value for rt comes from the multiobjective solution of the beta wolf which is equal to 17.180 μm. finally the best best result for fc comes from the multiobjective solution of the beta wolf which is equal to 83.153 n whereas the worst value for fc comes from the multiobjective solution of the delta wolf which is equal to 83.326 n. whether the significance of these small differences among the results is of major or minor importance, it depends on manufacturing specifications and surface finish requirements. conclusions and future research n this work an experimental study on machinability parameters in turning of cuzn39pb3 brass alloy was performed. machinability was investigated with reference to arithmetic mean surface roughness ra (μm), maximum height of the profile rt (μm) and main cutting force fc (n) which were considered as dependent responses affected by the cutting conditions; rotational speed n (rpm); feed rate f (mm/rev) and depth of cut a (mm). an l18 mixed-level taguchi orthogonal design of experiments was set to build the design space according to the operational range of cutting conditions as well as their corresponding levels. the results obtained suggest that cutting conditions and their interactions differently affect the responses of ra, rt and fc. main cutting force is minimized by applying low speeds and moderate feeds whereas roughness parameters ra and rt are minimized by using high speeds combined to moderate feeds for a depth of cut equal to 1.0 mm. full quadratic predictive models were generated via regression analysis and good correlation was achieved between experimental and predicted results for all responses. the resulting models were then considered as the objective functions for solving a multi-response optimization problem for turning of cuzn39pb3 brass alloy. an advanced multiobjective intelligent algorithm following the behavior and social activity of grey wolves was applied to solve the problem. it was revealed that the algorithm is efficient in its heuristic search during all independent algorithmic runs with emphasis to the final recommended optimal parameters to solve the optimization problem. as a major future perspective the authors currently plan to further investigate soft computing methods and several intelligent algorithms for optimizing the turning of cuzn39pb3 brass alloy and apply the same methodology to optimize the machining operations such as turning or milling of other engineering materials. acknowledgements he authors are grateful to dr.-ing. g.a. pantazopoulos of elkeme hellenic research centre for metals s.a for the supply of cuzn39pb3 brass specimens. n.m. vaxevanidis wishes to thank the special account for research of aspete for supporting the presentation of a preliminary version of this work in the “1st international conference of the gsemm” through the funding program “strengthening research of aspete faculty members”. references [1] kuyucak, s., sahoo, m. (1996). a review of the machinability of copper-base alloys, can. metall. quart., 35(1), pp. 1-15. [2] klocke, f., nobel, c., veselovac, d. (2016). influence of tool coating, tool material, and cutting speed on the machinability of low-leaded brass alloys in turning, mater. manuf. process. 31(14), pp. 1895-1903. [3] nobel, c., klocke, f., lung, d., wolf, s. (2014). machinability enhancement of lead-free brass alloys, proc. cirp, 14, pp. 95-100. [4] kato, h., nakata, s., ikenaga, n., sugita, h. (2014). improvement of chip evacuation in drilling of lead-free brass using micro drill, int. j. autom. technol., 8 (6), pp. 874-879. [5] nobel, c., hofmann, u., klocke, f., veselovac, d. (2015). experimental investigation of chip formation, flow, and breakage in free orthogonal cutting of copper-zinc alloys, int. j. adv. manuf. technol., 84(5-8), 1127-1140. i t n. a. fountas et alii, frattura ed integrità strutturale, 50 (2019) 584-594; doi: 10.3221/igf-esis.50.49 594 [6] petropoulos, g.p., pandazaras, c.n., davim, j.p. (2010). surface texture characterization and evaluation related to machining, in: surface integrity in machining, ed. j.p. davim, springer, london, pp. 37-66. [7] vaxevanidis, n.m., kechagias, j.d., fountas, n.a., manolakos, d.e. (2014). evaluation of machinability in turning of engineering alloys by applying artificial neural networks, open construction & building technol. j., 8, pp. 389-399. [8] grzesik, w., kruszynski, b., ruszaj, a. (2010). surface integrity of machined surfaces, in: surface integrity in machining, davim, j.p. (ed.), springer, london, pp. 143-179. [9] vaxevanidis, n.m., galanis, n., petropoulos, g.p., karalis, n., vasilakakos, p., sideris, j. (2010). surface roughness analysis in high speed-dry turning of tool steel, proc. esda 2010: 10th biennial asme conference on engineering systems design and analysis, july 12-14, istanbul, turkey. [10] petropoulos, g.p., pandazaras, c.n., vaxevandis, n.m., antoniadis, a. (2006). multi-parameter identification and control of turned surface textures, int. j. adv. manuf. technol. 29, pp. 118-128. [11] petropoulos, g. pandazaras, c., vaxevanidis, n.m., ntziantzias, i., korlos, a. (2007). selecting subsets of mutually unrelated iso 13565-2: 1997 surface roughness parameters in turning operations, int. j. comput. mater. sci. surf. eng., 1(1), pp. 114-128. [12] petropoulos, g., vaxevanidis, n.m., pandazaras, c., koutsomichalis, a. (2009). postulated models for the fractal dimension of turned metal surfaces, j. balkan tribol. assoc., 15(1), pp. 1-9. [13] toulfatzis, a.i., pantazopoulos, g.a., paipetis, a.s. (2014). fracture behavior and characterization of lead-free brass alloys for machining applications, j. mater. eng. perform., 23, pp. 3193-3206. [14] gaitonde, v.n., karnik, s.r., davim, j.p. (2012). optimal mql and cutting conditions determination for desired surface roughness in turning of brass using genetic algorithms, mach. sci. technol., 16(2), pp. 304-320. [15] hanief, m., wani, m.f., charoo, m.s. (2017). modeling and prediction of cutting forces during the turning of red brass (c23000) using ann and regression analysis, eng. sci. technol., 20(3), pp. 1220-1226. [16] mirjalili, s., mirjalili, s.m., lewis, a. (2014). grey wolf optimizer. adv. en. soft., 69, pp. 46-61. [17] jawahir, i.s. (1988). the chip control factor in machinability assessments: recent trends, j. mech. work. techn., 17, pp. 213-224. [18] jawahir i.s., van luttervelt, c.a. (1993). recent developments in chip control research and applications, ann. cirp, 42(2), pp. 659-693. [19] toulfatzis, a.i., pantazopoulos, g.a., besseris, g.j., paipetis, a.s. (2016). machinability evaluation and screening of leaded and lead-free brasses using a non-linear robust multifactorial profiler, int. j, adv. manuf. techn., 86(9-12), pp. 3241-3254. [20] pantazopoulos, g. (2002). leaded brass rods c 38500 for automatic machining operations: a technical report, j. mater. eng. perform. 11(4), pp. 402-407. [21] pantazopoulos, g.a., toulfatzis, a.i. (2012). fracture modes and mechanical characteristics of machinable brass rods, metall., microstruct., anal., 1(2), pp. 106-114. [22] galanis, n.i., manolakos, d.e. (2010). surface roughness prediction in turning of femoral head, int. j. adv. manuf. technol., 51(1-4), pp. 79-86. [23] bonabeau, e., dorigo, m., theraulaz, g. (1999). swarm intelligence: from natural to artificial systems: oup usa. [23] dorigo, m., birattari, m., stutzle, t. (2006). ant colony optimization, comput. intell. magaz., ieee, 1, pp. 28–39. [25] kennedy, j., eberhart, r. (1995). particle swarm optimization in neural networks. in: proceedings, ieee international conference on neural networks icnn’95, pp. 1942–1948. [26] wolpert, d.h., macready, w.g. 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/hrv (za stvaranje adobe pdf dokumenata najpogodnijih za visokokvalitetni ispis prije tiskanja koristite ove postavke. stvoreni pdf dokumenti mogu se otvoriti acrobat i adobe reader 5.0 i kasnijim verzijama.) /hun 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/pdfxoutputintentprofileselector /documentcmyk /preserveediting true /untaggedcmykhandling /leaveuntagged /untaggedrgbhandling /usedocumentprofile /usedocumentbleed false >> ] >> setdistillerparams << /hwresolution [2400 2400] /pagesize [612.000 792.000] >> setpagedevice microsoft word numero_56_art_19_3022 a. mohamed ben ali et alii, frattura ed integrità strutturale, 56 (2021) 229-239; doi: 10.3221/igf-esis.56.19 229 computation of mode i strain energy release rate of symmetrical and asymmetrical sandwich structures using mixed finite element mohamed ben ali amina civil engineering department, university of august 20, 1955, skikda, algeria. benaliamina21@gmail.com bouziane salah, bouzerd hamoudi civil engineering department, university of august 20, 1955, skikda, algeria. laboratory of civil engineering and hydraulics, university of may 8, 1945, guelma, algeria. bouziane_21@yahoo.fr, http://orcid.org/0000-0002-0831-1167 bib_ham@yahoo.fr, http://orcid.org/0000-0002-8216-2980 abstract. the use of composite materials is on the rise in different engineering fields. the main advantage of these materials for the aerospace industry being their low weight for excellent mechanical qualities. the analysis of failure modes, such as delamination, of these materials has received great attention from researchers. this paper proposes a method to evaluate the mode i strain energy release rate (serr) of sandwich structures. this method associates a two-dimensional mixed finite element with virtual crack extension technique for the analysis of interfacial delamination of sandwich beams. the cases of a symmetrical double cantilever beam (dcb) and a asymmetrical double cantilever beam (udcb) have been analyzed in this study. the comparison of the results obtained by this method with those found in the literature shows efficiency and good precision for the calculation of strain energy release rate (serr). keywords. numerical modelling; cracking; mixed finite element; sandwich structures; strain energy release rate. citation: mohamed ben ali, a., bouziane, s., bouzerd, h., computation of mode i strain energy release rate of symmetric and asymmetrical sandwich structures using mixed finite element, frattura ed integrità strutturale, 56 (2021) 229-239. received: 16.02.2021 accepted: 22.03.2021 published: 01.04.2021 copyright: © 2021 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. introduction andwich structures offers a lot of advantages in many applications ranging from satellites, aircraft, ships, automobiles, rail cars, wind energy systems, and bridge construction to mention only a few. due to the need of developing new materials with high performance and low-weight their use continues to increase rapidly. sandwich structures have two stiff, strong skins separated by a low stiffness core. their concepts have an excellent construction technique which combines weight with rigidity and strength. s https://youtu.be/vgfeklry2eo a. mohamed ben ali et alii, frattura ed integrità strutturale, 56 (2021) 229-239; doi: 10.3221/igf-esis.56.19 230 however, overall bearing capacity of the sandwich component is often limited not by the strength of the face sheets, but by the strength of the core material and the bond between the two components [1]. therefore, strength and stiffness are usually considered as being fundamentally important criteria in the selection of a core material for sandwich application[2]. among the most important phenomena in the study of composite materials in general and sandwich structures in particular is cracking which can lead to a local or global collapse of the structure. cracks generated by low-speed impacts which are often accidental in nature, can propagate to a premature failure of the structure [3]. furthermore, the most common type of failure in the composite structures is relevant to delamination and debonding of composite assemblies, that’s why many previous studies have focused on the study of failure in sandwich beams. other studies, however, have been devoted to understanding and characterizing cracks properties and the interface fracture using different analytical, numerical and experimental methods. avilés and carlsson [4] analyzed the compliance and the energy release rate of the sandwich double cantilever beam (dcb) specimen using the beam theory, elastic foundation analysis (efa) and finite element analysis (fea). østergaard et al [5] presented an analytical evaluation of the j-integral for the purpose of calculating the energy release rate for interface cracking of a sandwich specimen with isotropic face sheets. nairn [6] calculated the energy release rate in heterogeneous laminates using residual stresses. wang and zhang [7] developed a new analytical solution for the calculation of the energy release rate where they have analyzed the typical delaminated sandwich and adhesively bonded joint specimens. they analyzed the stress field using an interface stress-based method. davidson et al [8] obtained experimentally the critical mode i and mode ii energy release rates in a sandwich composite panel using double cantilever beam by modifying the geometry of the sandwich structure, to obtain (udcb), and end notch flexure (enf) tests, respectively. shah and tarfaoui [9] compared the different approaches to calculate the strain energy release rates of mode i & ii in composite foam core sandwiches of the wind turbine industry. an experimental study used a single density of foam core for the most part of the turbine blade to determine the effect of scale on the calculation of serr with different thicknesses of the foam cores. shah and tarfaoui [10] studied the effect of adhesive thickness on the mode i and ii strain energy release rates, comparative study was carried out using different approaches for the calculation of mode i and ii serr. the main objective of this study is to propose a method for the calculation of the mode i strain energy release rate (serr) and to validate its results on cases, which were well established by some researches. this method combines a twodimensional mixed finite element with the virtual crack extension technique to calculate the strain energy release rate of crack interfaces in sandwich beams. a double cantilever beam (dcb) [11–13] and asymmetrical double cantilever beam (udcb) [14–16] tests have been studied in this paper. several numerical tests, for different values of the initial crack size and sandwich beam dimensions, were analyzed and the results obtained using the proposed method were compared with those found in the literature. mixed finite element he sandwich structure have been discretized using a special mixed finite element rmq-7 (reissner modified quadrilateral) as shown in fig. 1. the element is a quadrilateral mixed finite element with 7 nodes and 14 degrees of freedom[17]. the final configuration of the element, in a natural (ξ, η) plane, was obtained after the three following stages[18]: (i) construction of the parent element by adding a displacement node (node 5); (ii) delocalization of some variables inside the element and displacement of static nodal unknown of the corners towards the side itself; (iii) static condensation of the internal unknown variables to obtain the final form of the present mixed finite element. the obtained element has three of its sides compatible with linear traditional elements and presents a displacement node at each corner. on the fourth side, in addition to its two displacement nodes of corner (node 1 and node 2), there are three additional nodes: a median node (node 5) and two intermediate nodes in the medium on each half-side (nodes 6 and 7), introducing the components of the stress vector along the interface. the formulation and the validation of the element have been presented by bouziane et al. [18]. the element displacement component is approximated by:     u n q (1) where    t 1 1 2 2 3 3 4 4 5 51 2 1 2 1 2 1 2 1 2q u , u , u , u , u , u , u , u , u , u is the vector of nodal displacements and  n is the matrix of interpolation functions for displacements. the shape functions are: t a. mohamed ben ali et alii, frattura ed integrità strutturale, 56 (2021) 229-239; doi: 10.3221/igf-esis.56.19 231                        1 2 3 1 1 1 1 1     ,     1 1     ,      1 1 2 4 4 n n n (2)              24 51 11 1      ,       1 1 4 2 n n the stress field in any point is written as:       m (3) where  m is the matrix of interpolation functions for stresses and  τ is the vector of nodal stresses. figure 1: mixed finite element rmq-7. in the configuration of fig. 1, the shape functions used to approximate 11σ are given by:           8 911 11 1 1 m 1 2ξ 1 2η        ,           m 1 2ξ 1 2η 4 4 (4)           10 1111 11 1 1 m 1 2ξ 1 2η        ,           m 1 2ξ 1 2η 4 4 the shape functions used to calculate 12σ and 22σ are given as follows:           6 7i 2 i 2 1 1 m 1 2ξ 1 2η        ,           m 1 2ξ 1 2η 6 6 (5)            8 9i 2 i 2 1 1 m 1 2ξ 1 η          ,           m 1 2ξ 1 η     ,    i 1, 2 3 4 it should be noted that nodes 8, 9, 10 and 11 are inside the element, and which are eliminated by the static condensation technique [18]. the nodal approximation of the displacement and stress fields is expressed by:                                τσ m 0 qε 0 b (6) a. mohamed ben ali et alii, frattura ed integrità strutturale, 56 (2021) 229-239; doi: 10.3221/igf-esis.56.19 232 where  b is the strain-displacement transformation matrix. the element matrix  ek is given by:                     0 u e t u k k k k (7) here the sub-matrix  σσk is defined by:           e t e a k t m s m da (8) and the sub-matrix  σuk is given by:         e t e u a k t m b da (9) where: t is the thickness,  s is the compliance matrix, ea is the element area and  t indicate the matrix transpose. computation of strain energy release rate he virtual crack extension method associated with the mixed finite element rmq-7 is used to calculate the strain energy release rate g[17]. in this technique, the first calculation of the deformation energy∏1 is carried out in the initial configuration of the crack. the crack is then moved by an infinitesimal distance δa in the direction of its axis (fig. 2) and the deformation energy π2 is calculated. the energy release rate g will be evaluated thereafter starting from the following relation:         2 1 π π g a a (10) indeed the intermediate displacement node of the rmq-7 element is associated to crack tip, and consequently the length of crack "a" can be increased by a quantity δa while acting inside strict of the crack element by translation of the tip crack node without disturbing the remainder of the mesh. figure 2: mesh around tip crack after extension δa. t a. mohamed ben ali et alii, frattura ed integrità strutturale, 56 (2021) 229-239; doi: 10.3221/igf-esis.56.19 233 if we consider that the external loading does not vary during the increase in δa , the energy release rate is calculated as follows:            a a a g a (11) where  π a δa and  π a represent respectively the deformation energy of the cracked structure in the configuration a δa and "a". with the assumption of linear elastic behavior and small displacements, the solutions  u a and  u a δa are as close as the disturbance δa is small compared to the dimensions of the crack element. the energy release rate g becomes:                             1 1 2 ne t i i i i i g u a a k a a k a u a a a (12) with: ne : total number of elements in discretized structure,   i u : vertical vector containing the nodal values of element i,  ik : elementary matrix of element i, and the exponent "t" indicates the transposed vector. as only the crack element is disturbed, then g results more simply in the relation:                            1 2 t c c c c g u a a k a a k a u a a a (13) where the index "c" indicates that the matrix and vector used are those of the crack element. the expression of g can be written differently as follows:           1 2 t f c c k g u u a (14) after the resolution phase, the nodal values of the crack element are extracted, and a special module is used to evaluate the energy release rate according to the following formula:           1 2 t f c c k g u u a (15) results and discussions he present mixed finite element, associated with the virtual crack extension method, was used to carry out numerical tests on sandwich beams. for the examples treated in this study, the geometric and mechanical characteristics of the samples tested are the same found in the literature in order to compare the results found under the same conditions. symmetrical double cantilever beam (dcb) test the specimens used to model the pure mode i strain energy release rates of the symmetrical sandwich structure are of the type double cantilever beam(dcb), the core–skin interfaces of which are shown schematically in the fig. 3. the sandwich specimens are made up of a 45° biax type composite face plate joined to a pvc foam core of 80 kg/m3 density with different thicknesses 10, 20 and 30 mm. the face plates for all of the specimens are 2mm thick [9]. t a. mohamed ben ali et alii, frattura ed integrità strutturale, 56 (2021) 229-239; doi: 10.3221/igf-esis.56.19 234 figure 3: double cantilever beam (dcb) test coupon geometry [9]. the mechanical properties of the composite material in the fiber direction are given in tab. 1. fiber direction modulus e(gpa) poisson’s ratio avg resistance (mpa) 00 el 48.11±6 lt 0.28±0.3 x(mpa) 965.50±25 900 et 11.21±2 tl 0.096±0.010 y(mpa) 33.50±3 450 glt 4.42±0.5 savg(mpa) 48.69±3 table 1: mechanical properties of the composite material in the fiber direction [9]. the different specimens of symmetrical double cantilever beam were modeled using the proposed mixed finite element in order to calculate the mode i strain energy release rate at initiation gii by the method proposed in this study. different meshes were used to test the convergence and the precision of the results. the calculation of the mode i strain energy release rate (serr) is made by conducting double cantilever beam (dcb) test using the mixed finite element rmq7. then, it was compared with that of shah and tarfaoui [9], who used modified beam theory 1 and 2 (mbt1, mbt2), compliance calibration method (cc) and virtual crack closure technique (vcct) (see tab. 2). these analytical approaches are based on the classical beam theory and are formulated for the evaluation of g in mode i. they are listed in the following: modified beam theory 1 (mbt 1) the modified beam theory models the dcb specimen as a simple cantilever beam based on the timoshenko beam theory [9]: i 3pδ g 2ba with p is the load to give a δ displacement, 𝔞 is the crack length and b is the specimen width. modified beam theory 2 (mbt 2) in the modified beam theory 2 ,the rotation of the crack front as well as the partially cracked interface are considered to account for the fiber bridging [9]:     i 3pδ g 2b a with p is the applied load, δ is the displacement of the two beams, 𝔞 is the crack length, b is the specimen width and  is the crack front rotation correction factor. a. mohamed ben ali et alii, frattura ed integrità strutturale, 56 (2021) 229-239; doi: 10.3221/igf-esis.56.19 235 compliance calibration method (cc) with the compliance calibration method, the compliance was considered as a function of the crack length [9]. the formulation for gi is thus given by:   2 1 i np g 2 hra b where r is anti-natural log of the intersection of a plot between lη (c) and lη(a). virtual crack closure technique (vcct) the formulation of gi given by [9] is:    m 3 u li σ w w g 2 the nodes “u” and “l” are displaced through “wu” and “wl” in the vertical direction specimen 1. sandwich beam: skin 2mm, core 10mm method gii(kj/m2) present mixed finite element rmq-7 0.465 shah and tarfaoui [9] mbt1 0.452 mbt2 0.520 cc 0.563 vcct 0.488 specimen 2. sandwich beam: skin 2mm. core 20mm method gii(kj/m2) present mixed finite element rmq-7 0.459 shah and tarfaoui [9] mbt1 0.436 mbt2 0.446 cc 0.405 vcct 0.593 specimen 3. sandwich beam: skin 2mm. core 30mm method gii(kj/m2) present mixed finite element rmq-7 0.579 shah and tarfaoui [9] mbt1 0.533 mbt2 0.571 cc 0.813 vcct 0.662 table 2: energy release rates obtained from dcb tests. a. mohamed ben ali et alii, frattura ed integrità strutturale, 56 (2021) 229-239; doi: 10.3221/igf-esis.56.19 236 tab. 2 shows the comparison of the results obtained for different values of the core thickness. the results found using the proposed method are in good agreement with the values obtained by different analytical approaches [9]. the results show that with a monotonic increase in the core thickness from 10 to 30 mm, the value of gi grows non-monotonically. this effect has been observed experimentally [9] and it is mainly due to the resin penetration in the core-face interface, which modifies the stiffness of the core material and hence the behavior of the interface. numerically, due to the choice of the value of virtual extension of crack on the level of the interface, which will influence the rigidity of the elements at the interface face-core. consequently, it influences the value of the strain energy release rate (serr). asymmetrical double cantilever beam (udcb) test the specimens used to model the pure mode i strain energy release rates is that the asymmetrical double cantilever beam (udcb), in order to produce a dominant mode i loading. due to their large utilization a double cantilever beam specimens are typically used in this study with some modification which was developed by davidson et al.[8]. the asymmetrical udcb specimen (fig. 4) was used with simple modification of the geometry such that the intended plane of fracture coincides with the neutral axis [8]. figure 4:udcb specimen used for mode i fracture resistance test [8]. fig. 4 shows the geometry of the sample of the udcb specimen and specify interface and crack location, where the interfaces in question are between the foam core and face sheet of the sandwich panel and the crack between the top face sheet and the core. the dimensions of the sandwich beam are given in tab. 3. l(mm) b(mm) h1(mm) h2(mm) h3(mm) a0(mm) 120 25.4 4.83 3.5 2.76 53 table 3: dimensions of asymmetrical dcb [8]. the material properties of the bi-axial face sheet and core are given in tab. 4. modulus e(gpa) poisson’s ratio avg modulus of rigidity g(gpa) composite e11 11.5 12 0.3 g12 3.0 e22 8.0 21 0.25 core e11 3.0 12 0.3 g12 1.2 e22 3.0 12 0.3 table 4: nominal specimen material properties[8]. numerical simulations of the asymmetrical dcb test were made using the mixed finite element rmq-7 for the calculation of mode i strain energy release rate. several meshes were used in these simulations to ensure the convergence of the results. tab. 5 shows the comparison between the mixed finite element prediction and experimental value [8]. a. mohamed ben ali et alii, frattura ed integrità strutturale, 56 (2021) 229-239; doi: 10.3221/igf-esis.56.19 237 gi(kj/m2) present mixed finite element 2.29 davidson et al [8] 2.08 table 5: comparison of calculated and experimental data for udcb tests. the difference between the value of the mode i strain energy release rate, given by the present mixed finite element, and these empirical findings [8] is 10%. this difference is very acceptable because in calculations, the layers are considered as a direct assembly, but in reality, the adhesive between them has certain mechanical properties. for this reason, the findings show that the value of the mode i strain energy release rate, given by the proposed method, and that of found experimentally, are in a good agreement [8]. several specimens with different dimensions of the sandwich beam layers were used in these numerical simulations. the variation of the dimensions was made in the same way for the different layers. tab. 6 gives the results obtained of the mode i strain energy release rate for the different cases. gi(kj/m2) asymmetrical sandwich beam specimen 1: h1=4 .83 mm h2= 3.5 mm h3=2.76 mm 2.29 asymmetrical sandwich beam specimen 2: h1=6.83 mm h2=5.5 mm h3=4.76 mm 2.20 asymmetrical sandwich beam specimen 3: h1=8.83 mm h2=7.5 mm h3=6.76 mm 2.62 table 6: strain energy release rate for udcb of different sizes. noting a certain stability of the values obtained by keeping the same ratio between the dimensions of the different layers of the sandwich beam. the computation of mode i strain energy release rate (serr) of symmetrical and asymmetrical sandwich beams cracks is given in this paper. the results obtained using the present mixed finite element rmq-7 was compared with analytical and experimental results, for that the following conclusions can be made: the results of both symmetrical double cantilever beam (dcb) and asymmetrical double cantilever beam (udcb) tests show a very slight difference between the numerical simulation and the previous studies. this difference is very reasonable taking into account the possible defects during the process of the development of the sandwich beam. we should note that the adhesive between the skins and the core in the numerical study is considered as a direct assembly but in the experimental study it is a resin with significant mechanical characteristics. delamination of double cantilever beam (dcb) for the determination of the critical strain energy release rate of mode i, another example which treats the problem of delamination of a symmetrical dcb was studied. this experimental study was carried out by djemai [19] for which we have all the data necessary to calculate the critical strain energy release rate (fig. 5). figure 5: delamination of double cantilever beam [19]. a. mohamed ben ali et alii, frattura ed integrità strutturale, 56 (2021) 229-239; doi: 10.3221/igf-esis.56.19 238 the tab. 7 shows the geometrical dimensions of the dcb specimen used. length (mm) width (mm) skin thickness (mm) core thickness (mm) 180 20 3.5 15 table 7: dimensions of dcb. the sandwich is made up with glass-polyester as skin and cork agglomerate as core [19]. the mechanical properties of the composite material are given in tab. 8. modulus e(gpa) poisson’s ratio avg modulus of rigidity g(gpa) composite e11 4.995 12 0.3675 g12 1.827 e22 4.997 21 0.3675 core e11 21 12 0.05 g12 4.3 e22 5.5 12 0.05 table 8: nominal specimen material properties [19]. tab. 9 shows the comparison between the experimental values obtained by djemai [19] and those found by the proposed mixed finite element for various values of the critical load "p" and the size of crack "a". djemai [19] present mixed finite element a(mm) p(n) gic(kj/m2) gic(kj/m2) 30 23.03 0.0634 0.0638 40 18.32 0.0565 0.0542 50 14.53 0.0648 0.0639 60 13.12 0.0678 0.0657 70 12.64 0.0650 0.0647 gic 0.0635 0.0624 standard deviation 0.00379 0.00445 table 9: comparison of the strain energy release rate for mode i. the results obtained of the mode i strain energy release rate using the proposed method are in good agreement with experimental values given by djemai [19]. according to the results obtained, one notices that each time the length of the crack increases, the critical load decreases, the energy release rate remains almost constant with the variation of the size of the crack, which indicates that the resistance to the starting of delamination remains constant in spite of the variation of the initial size of the crack between the skin and the core in the sandwich. conclusion n this paper, a method for the calculation of the mode i strain energy release rate for cracked sandwich structures has been proposed. this method associated a two-dimensional mixed finite element with virtual crack extension technique for the analysis of interfacial delamination of sandwich beams. symmetrical double cantilever beam (dcb) and asymmetrical double cantilever beam (udcb) cases have been analyzed in this study. the use of the present mixed finite element makes it possible to introduce one mesh for the calculation of the strain energy release rate, which represents a considerable profit in computing times and setting in data compared to the traditional techniques which use two meshes. the results obtained using the proposed model were compared with those found experimentally or obtained by other techniques proposed in the literature. the analysis of the results shows the efficiency and the good performance of the i a. mohamed ben ali et alii, frattura ed integrità strutturale, 56 (2021) 229-239; doi: 10.3221/igf-esis.56.19 239 proposed method for the evaluation of the strain energy release rate for symmetrical and asymmetrical cracked sandwich beams. the difference between the values of the mode i strain energy release rate, given by the present mixed finite element, and that of found experimentally is attributed to the fact that in calculations, the layers are considered as a direct assembly, but in fact, the adhesive between them has some mechanical properties. in this case, neglecting this fact gives rise to an underestimation or an overestimation of the strain energy release rate values. references [1] el-sayed,s., sridharan, s. (2002). cohesive layer models for predicting delamination growth and crack kinking in sandwich structures, international journal of fracture.,117, pp. 63–84. [2] vinson, j.r. (2005). sandwich structures: past, present, and future, sandw. struct. 7 adv. with sandw. struct. mater., aalborg university, aalborg, denmark, pp. 3–12, doi: 10.1007/1-4020-3848-8_1. [3] peng, l. (2013). modélisation numérique d’assemblages collés: application à la réparation de structures en composites , thèse de doctorat. université de bourgogne. [4] aviliés, f., carlsson, l.a. (2008). analysis of the sandwich dcb specimen for debond characterization, engineering fracture mechanics., 75, pp. 153–68, doi: 10.1016/j.engfracmech.2007.03.045. [5] østergaard, r.c., sørensen, b.f. (2007). interface crack in sandwich specimen,int j fract., 143, pp. 301–316, doi: 10.1007/s10704-007-9059-4. [6] nairn, j.a. (2006). on the calculation of energy release rates for cracked laminates with residual stresses, int. j. fract., 139(2), pp. 267–93, doi: 10.1007/s10704-006-0044-0. [7] wang, j., zhang, c. (2009). energy release rate and phase angle of delamination in sandwich beams and symmetric adhesively bonded joints, int. j. solids struct.,46, pp. 4409–4418, doi: 10.1016/j.ijsolstr.2009.09.003. [8] davidson, p., waas, a.m., yerramalli, c.s. (2012). experimental determination of validated , critical interfacial modes i and ii energy release rates in a composite sandwich panel , compos. struct., 94(2), pp. 477–483, doi: 10.1016/j.compstruct.2011.08.007. [9] shah, o.r., tarfaoui, m. (2017). determination of mode i & ii strain energy release rates in composite foam core sandwiches. an experimental study of the composite foam core interfacial fracture resistance, compos. part b eng., 111, pp. 134–142, doi: 10.1016/j.compositesb.2016.11.044. [10] shah, o.r., tarfaoui, m. (2016). effect of adhesive thickness on the mode i and ii strain energy release rates. comparative study between different approaches for the calculation of mode i& ii serr’s, compos. part b eng., 96, pp. 354–363, doi: 10.1016/j.compositesb.2016.04.042. [11] ma, m., yao, w., chen, y. (2018). critical energy release rate for facesheet/core delamination of sandwich panels, eng. fract. mech., 204(september), pp. 361–368, doi: 10.1016/j.engfracmech.2018.10.029. [12] balaban, a.c., tee, k.f. (2019). strain energy release rate of sandwich composite beams for different densities and geometry parameters, theor. appl. fract. mech., 101(february), pp. 191–199, doi: 10.1016/j.tafmec.2019.03.001. [13] moroni, f., pirondi, a. (2019). comparison of tensile strength and fracture toughness under mode i and ii loading of co-cured and co-bonded cfrp joints, 47, pp. 294–302, doi: 10.3221/igf-esis.47.22. [14] sundararaman, v., davidson, b.d. (1997). an unsymmetric double cantilever beam test for interfacial fracture toughness determination, int j solids struct.,34(7), pp. 799–817. [15] ma, m., yao, w., li, p. (2020). critical energy release rate for interface delamination of asymmetrical specimen, compos. struct., 237(september 2019), pp. 111919, doi: 10.1016/j.compstruct.2020.111919. [16] zambelis, g., da silva botelho, t., klinkova, o., tawfiq, i., lanouette, c. (2018). evaluation of the energy release rate in mode i of asymmetrical bonded composite/metal assembly, eng. fract. mech., 190, pp. 175–185, doi: 10.1016/j.engfracmech.2017.12.007. [17] bouzerd, h. (1992). elément fini mixte pour interface cohérente ou fissurée, thèse de doctorat. université claude bernard , lyon, france. [18] bouziane, s., bouzerd, h., guenfoud, m. (2009). mixed finite element for modelling interfaces, eur. j. comput. mech., 18(2), pp. 155–75, doi: 10.3166/ejcm.18.155-175. [19] djemai, h. (2017). contribution à l’étude de l’endommagement dans les matériaux composites sandwiches, thèse de doctorat. université mohamed khider , biskra, algérie. microsoft word numero_54_art_06_2857 r. b. p. nonato, frattura ed integrità strutturale, 54 (2020) 88-103; doi: 10.3221/igf-esis.54.06 88 bi-level hybrid uncertainty quantification in fatigue analysis: s-n curve approach r. b. p. nonato mechanical engineering department, federal center for technological education, cefet/rj, nova iguaçu, brazil raphaelbasilio@gmail.com, https://orcid.org/0000-0002-4740-9888 abstract. due to its physical complexity, fatigue phenomenon inherently presents a significant number of uncertain parameters to be predicted. in uncertainty quantification (uq), research has demonstrated that even a small variation in uncertain input quantities (uiqs) may lead to a wide dispersion in the system response quantities (srqs). in this paper, a bi-level hybrid uq analysis of a fatigue problem is presented based on the s-n curve approach. the uncertain fatigue analysis presented is able to deal simultaneously with aleatoryand epistemic-type uncertainties in two levels (a srq in the first level is a uiq in the second level). to this end, the proposed scheme is tested for an aisi 4130 clamped beam subjected to a concentrated load, which material information comes from experiments reported in the literature. the uiqs are geometrical parameters, material properties, loading magnitude, and stress, while the srqs are the stress (which is also a uiq for fatigue life) and fatigue life. the results evidenced that the uncertain fatigue analysis, instead of providing a unique value for a srq, now produces a possible range of values. therefore, depending on the risk an engineer can take on a design, there will be a corresponding level of optimization achieved. keywords. fatigue analysis; uncertainty quantification; uncertain fatigue analysis; s-n curve; hybrid uncertainty quantification; bi-level hybrid uncertainty quantification. citation: nonato, r.b.p., bi-level hybrid uncertainty quantification in fatigue analysis: s-n curve approach, frattura ed integrità strutturale, 54 (2020) 88-103. received: 26.05.2020 accepted: 25.06.2020 published: 01.10.2020 copyright: © 2020 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. introduction nder the actual paradigm of industrial competition, the improvement of engineering design is an important issue in the usual quality-cost trade-off. in this context, uncertainty consideration in design intends to turn this process more realistic by measuring the impact of the quantities assumed as uncertain in the mechanical behavior of a structural system. under fluctuating stresses, it has been estimated that the fatigue phenomenon contributes to the majority of service failures due to mechanical causes [1]. in this sense, although it is of great importance, the modeling of a fatigue phenomenon itself is a complex issue mainly due to the scarce experimental data available, which may lead to inadequate u https://youtu.be/k7etkyfjjb4 r. b. p. nonato, frattura ed integrità strutturale, 54 (2020) 88-103; doi: 10.3221/igf-esis.54.06 89 design assumptions. therefore, inherently to the nature of this phenomenon, variability is present, for example, in the following parameters: geometry, material properties, loading, and environmental conditions [2-4]. consequently, the integration of fatigue analysis with uncertainty quantification (uq) intends to partially fulfill the gap of investigating the influence of each uncertain input quantity (uiq) in the required system response quantities (srqs) of a fatigue problem. from this perspective, the quantification mentioned may represent considerable knowledge for partially achieving the referred engineering design improvement, besides turning the analysis more complex [2,5]. one of the greatest challenges presented in a fatigue analysis is to have the availability of the minimum required data in order to perform the most adequate analyses [1,6]. the scarcity or even the inexistence of this data leads the engineer to make assumptions and simplifications that may significantly affect the model accuracy. however, in possession of the minimum adequate information, the challenge relies on the modeling phase, key contributor for the accuracy of the responses obtained. consequently, in the sense that uq may diminish the technical gap between the conceptual model and the reality, uq plays an important role in the accuracy of representation. therefore, aiming at qualifying a fatigue analysis to be more realistic, the integration with uq deserves attention as a relevant topic of research. in this particular, three main approaches coexist: (a) probabilistic; (b) bayesian inference; (c) probability bounds analysis (pba). a considerable amount of research works is based on the so-called probabilistic methods, for example, [7-16]. the probabilistic approach is an adequate representation of an uiq when there is sufficient random data to be representative of the distribution. in principle, the natural degree of data dispersion cannot be simply removed. however, this degree may be reduced by, e.g., improving the control of the generating process. another branch of research within uq in the context of fatigue analysis is the one related to bayesian inference, as seen on [15,18]. based on bayes’ theorem, more accurate inferences on srqs may be reached by the available knowledge as the prior trustworthiness on model parameters. finally, the probability bounds analysis (pba), which is applied in [3-4,19]. this type of analysis, on which this paper is structured, is fundamentally related to: (a) monte carlo sampling (mcs) or a variation of it; and (b) evidence theory [4]. pba includes a mathematical characterization of aleatory uncertainties as probability distributions, and a characterization of epistemic uncertainties as interval-valued functions. if the two types of uncertainties are dependent on each other (which is not the case of this paper), the dependence should be assumed as an epistemic-type uncertainty [4]. however, under the segregation of aleatoryand epistemic-type of uncertainty throughout all uq analysis, all assumed uiqs are mapped through the model and the srqs are illustrated as bounds of probability distributions, known as p-boxes (set of all possible cumulative distribution functions – cdfs – contained within design boundaries). thenceforth, a general bi-level uq analysis of a fatigue problem based on the s-n curve approach is introduced in this paper. the scheme presented here has the capability of treat aleatoryand epistemic-type uncertainties simultaneously in two levels (a srq in the first level is a uiq in the second level). the uiqs were assumed to be the following: (a) geometrical parameters; (b) material properties, and magnitude of variable loading under cycles of constant amplitude, whereas the stress (which is also a uiq for fatigue life in the second level) and fatigue life are the required srqs. in order to test the proposed method, a clamped rectangular cross-section beam made of aisi 4130 subjected to a concentrated load is the object of study of the propagated uncertainties. material properties were extracted from experimental data available in the literature. all the information was coded in matlab® in order to propagate the uncertainties (via mcs) throughout the mathematical model applied. the results are given in terms of the mean convergence studies of the srqs, their probability density functions (pdfs), cdfs, coefficients of variation, correlation coefficients, and p-boxes. the sensitivity analyses (sas) conducted evidenced that, under the conditions imposed herein, the greatest probabilistic contributor to the srq stress (first level) is the cross-section height of the beam. when the impact is verified on the srq fatigue life (second level), the height now turns to be the second most contributor, and the stress itself now is the most impacting factor in this fatigue design. additionally, in order to also check the impact of the epistemic-type, the p-boxes are presented, segregating the two types of uncertainty in the same representation, aiming at showing the design boundaries for the loading condition of the problem studied. therefore, under the consideration of uncertain parameters, a design point in the deterministic s-n curve turns to a lower and upper bounded set of design points, now obligating the designer to assume a certain risk when deciding to perform an analysis with fixed input parameters. deterministic fatigue analysis: s-n curve approach with constant amplitude loading his section presents the deterministic fatigue design methodology under constant amplitude loading, its corresponding governing equations, assumptions, and particularities. a brief description of the deterministic s-n curve equation is given, in addition to the concept of damage. t r. b. p. nonato, frattura ed integrità strutturale, 54 (2020) 88-103; doi: 10.3221/igf-esis.54.06 90 description of the s-n approach for each design philosophy, there is at least one corresponding design methodology. in the fatigue context, the design methodology that conforms to a safe and infinite life is the stress-life approach, which the principal testing data description is the well-known s-n (wöhler) curve. although the method is recognized to be relatively simple and easy to apply, besides being able to give some initial perspective of the analysis, it is restricted to situations where continuum (absence of cracks) assumptions can be made. in addition, its range of application is reduced to the elastic range or near this limit, also addressing constant amplitude loading conditions. a great number of researchers have devoted themselves to the process of s-n curve modeling, e.g., [1,6]. in order to build these curves, many tests in metallic materials in air at room temperature were performed, in which the independence between the number of cycles and the frequencies of the test could be verified. the fatigue life is also independent of the wave path that connects negative and positive stress peaks [6]. therefore, the next subsection exposes the s-n approach under the mentioned conditions. mathematical background of the s-n approach with constant amplitude loading as far as this research could reach, there are three basic types of fatigue stress-life mathematical expressions, which have been studied by [20]. they are the following: (a) three-parameter stress-life model [21]; (b) langer [22]; and (c) basquin [23]. presuming the existence of an infinite life, the latter model is the most common found in the literature and it is described by eqn. (1), which represents the finite life portion adopted in this work and its limits.   fr fr fr fr 0 , s s , s , s u m el u el s n c s s s         . (1) in eqn. (1), c and m are constants corresponding to the material tested, sfr is the fatigue limit in fully reversed loading condition, sel is the endurance limit (threshold between finite and infinite life), su is the ultimate stress (rupture limit) and n is the fatigue life (in number of cycles). if the actuating stress sfr is greater than the rupture limit, the component will fail; and if sfr is lower than the endurance limit of this component, it will present an infinite life. simply taking the logarithm on both sides of eqn. (1) correspondent to the finite life, a straight-line representation results in eqn. (2):      frlog log log sn c m  . (2) sfr is selected particularly in this formulation because fatigue data is mostly obtained in the fully reversed loading condition. the non-linear model adopted is the classical gerber expression [1] because it is the least conservative when compared to soderberg and goodman, for example. therefore, the fatigue limit in fully reversed loading condition can be written in accordance with eqn. (3): 2 1 a fr m u s s s s        , (3) where sa is the cyclic stress amplitude and sm is the mean stress. in the case of constant amplitude loading, sa and sm may be obtained in terms of the minimum and maximum stresses, smin and smax, respectively, by eqns. (4) and (5): 2 max min a s s s   ; (4) 2 max min m s s s   . (5) r. b. p. nonato, frattura ed integrità strutturale, 54 (2020) 88-103; doi: 10.3221/igf-esis.54.06 91 for the condition of fully reversed stress amplitude, eqns. (4) and (5) yield eqns. (6) and (7): a maxs s ; (6) 0ms  . (7) substituting eqns. (3), (6), and (7) into eqn. (1), an equation of fatigue life as a function of materials properties and maximum stress turns into eqn. (8):   max max max max 0 , s s , s , s u m el u el s n c s s s         . (8) to estimate when a component will fail, the fatigue process is based on the assumption of damage accumulation paradigm, which does not consider the effects of understressing and overstressing. the specimen with finite life resists until the life of the component is exhausted. under the stress range corresponding to infinite life, theoretically, the part never reaches the exhaustion. the cumulative damage during this process is frequently obtained by applying the palmgren-miner linear cumulative damage rule, which has several limitations referred to its applicability conditions, but it is simple and fast to implement. this rule states that the fatigue life of a component can be predicted by adding up the part of the life correspondent to each stress level. mathematically, the cumulative fatigue damage d is represented in eqn. (9): 1 j i i d d    , (9) where di is understood as the damage corresponding to the i-th stress level. in this particular, now representing smax as simply si , the fractional damage di is given by eqn. (10): i m i i i i , s 1 n s , s 0 , s u i el u el s d s s c s          , (10) where ni is the number of cycles performed at the i-th stress level si and ni is the fatigue life (in number of cycles) at si considering the fully reversed amplitude loading condition. therefore, when d = 1, theoretically, the component fails by fatigue [24]. uncertain fatigue analysis: s-n curve approach his section presents some generic sources and a basic classification of uncertainties. it also describes the methodology to treat aleatoryand epistemic-type uncertainties in a fatigue problem under the stress-life method of solution. mathematical models for the stress as a function of geometrical parameters and applied loads (first level) and for the number of cycles as a function of applied loads, geometrical parameters, and material properties (second level) are also presented. sources of uncertainty and classification some of the sources of uncertainty present in real engineering applications occur due to manufacturing, material variability, initial conditions, system wear or damaged condition and its surroundings. information on magnitude, type, behavior, and sources of uncertainty is crucial in the decision-making process for engineered systems. the main sources of uncertainty can be listed as: (a) model inputs (data from surroundings and model); (b) numerical approximation (when solving discrete t r. b. p. nonato, frattura ed integrità strutturale, 54 (2020) 88-103; doi: 10.3221/igf-esis.54.06 92 equations, instead of differential, for example); and (c) model form (assumptions, simplifications, mathematical formulations, etc.) [4]. in the field of model-based predictions, uncertainty originates from model inputs (boundary conditions, initial conditions, etc.), gap between real system and adopted model, computational costs (time to accomplish the run, analysis feasibility, and complexity), solution, and errors [25]. there are several classifications related to uncertainties, which mainly diverge in the nomenclature adopted but rarely related to the concept, for example, [4,26]. the selected terminology of the types of uncertain parameters employed here are described in [4]. according to this reference, they can be listed as: (a) aleatory: commonly represented by a pdf and/or cumulative density function (cdf). the modeled system has intrinsic variability, such that it is inherent to the phenomenology of the problem. this type of uncertainty cannot be eliminated, even if the available information is the most reliable, but can be better quantified in order to be reduced; (b) epistemic: represented by an interval variable, it occurs when there is a lack of complete information or knowledge. if more information is added into the analysis, it can be reduced; (c) mixed: it is simply a combination of the previous two, and, therefore, can be characterized by a pdf or a cdf with an interval. for example, if the sample size is small compared to the population, the pdf or cdf characterization related to the random variable is impaired in its accuracy. in this case, the uncertainty is defined as a combination of aleatoryand epistemic-type. aleatory-type uncertainty in the case of aleatory-type uncertainty, the information comes from a selected, candidate, or available probability distribution. let nk be the number of known parameters of the probability distribution function of the i-th probabilistic uiq xi. if the pdf of xi is denoted by fxi(xi, k,…, nk), then the realizations of xi are obtained by the inverse function of the pdf (eqn. (11)):  1 , , , ii x i k x f x k n  , (11) where xi is a possible outcome of a universal set χi of all possible outcomes and k is the k-th known parameter. a cumulative distribution function (cdf) fxi can be assigned to every element xi such that the following conditions are satisfied (eqns. (12) and (13)):     , , , 0 , 1 , ix i k i i f x k n x    ; (12)   , , , 1 ii i x i kx f x k n    . (13) epistemic-type uncertainty originated by the interval analysis [27], the epistemic model of uncertainty is implemented in a uq process in which there is no sufficient knowledge about the behavior of a variable. it is a non-probabilistic method to represent and propagate epistemic-type of uncertainties in engineering problems. any realization within the interval represents only a possibility without a probability associated. therefore, it can be simply described by the j-th uiq as an interval variable (eqn. (14)): ,lb ub ij j jy y y     , (14) in which ℝi is the set of all closed real interval numbers, yjlb and yjub are the lower and upper bounds of the j-th epistemic uiq, respectively. the governing theory characterizes an interval variable by two basic parameters: the mean or central value and the amplitude, respectively, given by eqs (15) and (16):  1 2 m lb ub j j jy y y  ; (15)  1 2 ub lb j j jy y y   . (16) r. b. p. nonato, frattura ed integrità strutturale, 54 (2020) 88-103; doi: 10.3221/igf-esis.54.06 93 bi-level hybrid uncertain s-n curve approach a uq process comprises the obtainment of uncertainties correspondent to model-based predictions [4], which can be based on the different types of uncertainty throughout calculation levels. the bi-level hybrid approach adopted in this paper can deal with aleatoryand epistemic-type uncertainties simultaneously, but in a segregated manner in two distinct levels. the srq obtained in the first level turns out to be the uiq in the second level of propagation, i.e. the srq calculated in the second level is influenced by the uiqs of the same level and by the srq of the previous level. values of the srqs are obtained as a result of the mapping of the uiqs throughout the uncertainty propagation process. in order to accomplish this task some propagation methods were proposed [28-33]. in view of these, monte carlo simulation (mcs) is the method through which the uncertainties are propagated in this work. although it requires a larger sample size, the example solved herein shows that the convergence is achieved without a reasonable computational effort, which partially justifies the application of the mcs. the ease of implementation also explains its selection. in a generic form, eqn. (17) is presented as the model structure responsible for mapping the required srqs in terms of the types of uncertainties:   ..., , ..., , , ..., , ..., , , , ..., , ..., , , 212121 kji nknjni zzzzyyyyxxxx  (17) in which ni is the number of column vectors of aleatory-type uiqs, nj is the number of column vectors of epistemic-type uiqs, and nk is the number of column vectors of srqs required in the uq analysis. under the conditions of the adopted mathematical model 𝕄, the mapping of the dependence of the output uncertain data on the input uncertain data is performed. the named process (propagation of uncertainties) is fundamentally dedicated to obtain the effect of the set of the ni vectors and the nj vectors on the nk vectors. therefore, the column vectors corresponding to each type of parameter are represented by the following structure (eqn. (18)):          11 2 , , ... , , ... , , r r t p n n i i i i i ix x x x x    x          11 2 , , ... , , ... , y , yr r t q n n j j j j j jy y y    y (18)          11 2z , z , ... , z , ... , z , zr r t n nr k k k k k k    z , where the superscript of each element of each vector refers to the realization number. since just one srq can be obtained from each mathematical expression (one level), the r-th realization of the k-th srq should be obtained by solving the corresponding equation with the p-th realization of all the needed aleatory-type uiqs in conjunction with the q-th realization of all the needed epistemic-type uiqs. this is true if, and only if, p = q = r , ∀ 1 ≤ p, q, r ≤ nr. performing these calculations for all the nk srqs, a number of nk x nr values (elements) are obtained to compose the responses of whole model. according to the deterministic s-n curve approach presented, i.e. assuming the condition of fully reversed constant amplitude loading, the general basquin mathematical model, represented by eqn. (1), was particularized into the eqn. (8). regarding only its finite domain, eqn. (19) states the second level as a function of the srq smax (from the first level) and the uiqs c and m (from the second level) (eqn. (19):        pel, , , s , | 1 p p max max u rf s s p p n      n s c m  . (19) for the purposes of the second level uq analysis, the independent variable column vectors, c, smax, and m, may constitute a set of one, two, or three uiqs, whereas the dependent variable column vector n is the srq. if a parameter is known exactly, then it can be assumed as deterministic in this process (not a uiq). among other factors, the quantity of nondeterministic parameters in an analysis is defined by the focus of the study and limitations of computational capacity. analogously to the model of eqn. (17), the column vector smax (now an srq in the first level) can be expressed as a function of ns vectors of applied loads and nt vectors of geometrical parameters involved, as can be seen in eqn. (20). fs is the column vector of the s-th applied force and gt is the column vector of the t-th geometrical parameter considered.        p1 2 1 2 el, , ..., , ..., , , , ..., ,..., , s , | 1 .s t p pmax s n t n max u rf s s p p n      s f f f f g g g g  (20) r. b. p. nonato, frattura ed integrità strutturale, 54 (2020) 88-103; doi: 10.3221/igf-esis.54.06 94 thenceforth, combining eqns. (17) and (20), the mathematical model wherewith the propagation of all uiqs is performed is given by eqn. (21), where mu is the vector of the u-th material property and nu is the number of vectors of material properties involved. since smax is implicit in eqn. (21), this expression corresponds to the bi-level hybrid uq model already mentioned.   s t1 2 n 1 2 n 1 2 , , ..., ,..., , , ,..., ,..., , , , ..., , ..., us t u n fn f f f f g g g g m m m m . (21) therefore, eqns. (20) and (21) are applied to the uncertain fatigue problem to be solved (uncertain s-n curve approach with all the assumptions made) and is calculated for each realization of each uiq, obtaining the correspondent value for the same realization of the required srq. numerical example: cantilever beam with concentrated load he numerical example treated herein consists of a clamped beam subjected to a concentrated load near its free end, in which its uiqs were identified and characterized. a bi-level hybrid uq analysis was conducted to investigate the behavior of the required srqs in the two levels followed by a sensitivity analysis (sa) to rank the uiqs, disposing them in decreasing order of impact on the variability of the srqs. basic description of the problem to illustrate the problem to be solved in the context of a uq analysis, fig. 1 is now introduced. the beam made of aisi 4130 is clamped at its left end, whereas its right end is free to displace. a concentrated variable load with constant amplitude has magnitude f and is pointed downward the y-axis near the free end, thus producing a downward deflection. however, because it is fully reversed, an upward deflection is produced when the load direction is upward. the prismatic beam is characterized geometrically by its length l (parallel to x-axis), cross-section base b (parallel to z-axis), cross-section height h (parallel to y-axis), and the longitudinal distance d (parallel to x-axis) between the structural support and the load application point (taken orthogonally to the upper clamped edge of the beam). its material properties are the parameters related to fatigue (c, m, and sel), and su. it is important to observe that the deflection magnitude is not a design restriction (serviceability requirement) in this work and that the body forces are neglected for simplification purposes. figure 1: cantilever beam subjected to a concentrated variable load with constant amplitude f near its free end with the nomenclature of geometrical parameters. the uiqs and srqs considered in this analysis are organized in tab. 1, which also contains the characterization of each input quantity, and the values of the parameters needed to calculate the behavior of the uiqs and srqs. the specific values of c and m were extracted from an interpolated equation based on experimental data points collected from [34], in which the material selected corresponds to unnotched specimens which ultimate stress is approximately 806.687 mpa. this interpolated equation (eqn. (22)) is valid only for the stress ratio r = -1 (eqn. (22)). thenceforth, rearranging for the srq n, eqn. (23) is obtained:        log 9.27 3.57 log 43.3 log log 43.3max maxn s c m s      , (22) t r. b. p. nonato, frattura ed integrità strutturale, 54 (2020) 88-103; doi: 10.3221/igf-esis.54.06 95  43.3 mmaxn c s    , (23) where smax is given in ksi and c is in (ksi)m. in order to work with units of système internationale (si), where smax is now given in mpa and c is in (mpa)m, the converted form of eqn. (23) yields eqn. (24):  6.895 298.543 mm maxn c s    , (24) where the maximum stress for this problem is obtained by eqn. (25): 2 6 max fd s bh  . (25) uiq srq deterministic value of uiq type of uncertainty mathematical representation parameters b smax, n bd = 33.60 mm aleatory gaussian μb = 33.60 mm ; σb = 0.084 mm h smax, n hd = 60.48 mm aleatory uniform μh = 60.48 mm ; hlb = 60.17 mm ; hub = 60.79 mm f smax, n fd = 6000 n aleatory weibull α = 6000 n ; β = 3 x 10-4 d smax, n dd = 2000 mm epistemic interval dm = 2000 mm ; dlb = 1990 mm ; dub = 2010 mm c n cd = 109.27 (mpa)m epistemic interval cm = 109.27 (mpa)m ; clb = 1.852777 x 109 (mpa)m ; cub = 1.871398 x 109 (mpa)m m n md = 3.570 epistemic interval mm = 3.57 ; mlb = 3.552 ; mub = 3.588 smax n smaxd = 585.8 mpa not applicable not applicable not applicable table 1: detailing of the uiqs and srqs of the cantilever beam example. in tab. 1, μ is the mean, σ is the standard deviation, α is the shape parameter, and β is the scale parameter. the superscripts m, lb, and ub stand for mean, lower bound, and upper bound of the indicated interval, respectively. the type of uncertainty, its mathematical representation, and its parameters are not applicable for smax as a uiq (condition of the second level) because smax is a consequence of the first level, thus not being a direct input for n. all the parameters contained in tab. 1 refer to the load condition of closest proximity to the maximum stress and minimum number of cycles of the finite part of the s-n curve modeled by eqn. (21). the study of the behavior of the structure at high stresses was made in order to show the variability of the fatigue life in the condition where it presents its lowest value. in this situation, a fixed coefficient of variation in fatigue life would be more representative. however, this makes sense especially when dealing with structural systems which loading is of low frequency. in other words, this loading condition corresponds to the maximum applied load f = 6000 n, which corresponds to the stress s = 585.8 mpa. it can also be noted from tab. 1 that the deterministic values are used as information for the uiqs: (a) for the aleatory-type of uncertainty, the deterministic value of each uiq is assumed as the mean of the adopted distribution; (b) in the case of epistemic-type, the deterministic value is attributed to the central value of the corresponding interval. it is important to observe that since body forces were neglected, the only condition that length l has to comply with is that l ≥ dub. therefore, l can be equal to 2020 mm (deterministic) for the purposes of this analysis. the particularization of the eqn. (17) for the problem just described is shown in eqn. (26), which consists of the bi-level model. consequently, ni = 3 (b, h, and f), nj = 3 (d, c, and m), and nk = 2 (smax and n).   nsmcdfhb , , , , , , max (26) analogously, eqns. (20) and (21) adapted to the proposed problem, yields eqns. (27) and (28), respectively.  , , ,max fs f b h d . (27) r. b. p. nonato, frattura ed integrità strutturale, 54 (2020) 88-103; doi: 10.3221/igf-esis.54.06 96  , , , , ,fn f b h d c m . (28) in accordance with eqns. (27) and (28), all the calculation and generation of graphical results were performed in matlab® 2016. the mcs coded in this software was implemented using a different seed random number for each sample generated (pseudo-random number generation). next section is dedicated to show the results of these simulations, besides some comments about them. results and comments the pdfs of the aleatory-type uiqs for the mentioned load case are pictured in fig. 2. cross-section basis b, cross-section height h (both in mm), and applied load f (in n) are represented by blue continuous lines according to 5000 realizations of their correspondent distributions (characterization of uncertainties in tab. 1). vertical continuous red lines correspond to their deterministic values, represented by the letter d. fig. 3 shows their cdfs and also the related deterministic values. the variation profile of the epistemic-type uncertainty is represented by an interval between the lower and upper bounds with the possible values between them (without a probability associated to each one), reason why their graphical representation will not be made here. figure 2: pdfs of the aleatory-type uiqs and their deterministic values. figure 3: cdfs of the aleatory-type uiqs and their corresponding deterministic values. fig. 4 and fig. 5 illustrate the pdfs and cdfs of the srqs of this problem, respectively. some statistical parameters of the uiqs and srqs shown in these figures are presented in tabs. 2 and 3. the estimated values indicated by the columns of these tables are those obtained from the simulations in the code developed. the relative errors between the deterministic values (tabs. 2 and 3) and the obtained means (tab. 2) are shown in the penultimate column of tab. 3. the good agreement between the deterministic and the means of the srqs is partially explained by the assumption of a considerable degree of symmetry verified in the distributions of the aleatory uiqs. particularly for epistemic-type, it is conceptually understood as symmetrically disposed. in the case of parameters which have intervals associated, the lower and upper bounds (tab. 2) were achieved with a good precision too (comparison of tabs. 1 and 2). the last column of tab. 3 presents the coefficient of variation, which can only be evaluated in what refers to aleatory-type uiqs and the srqs. between the uiqs, h is the r. b. p. nonato, frattura ed integrità strutturale, 54 (2020) 88-103; doi: 10.3221/igf-esis.54.06 97 variable that presents the greatest value, followed by b, and f (the minor contributor). in other words, the standard dispersion of data is the greatest for the cross-section height of the beam and the lowest for the applied load. when analogous comparison is made between the srqs, the fatigue life n is almost one order of magnitude greater than the stress, thus presenting the greatest dispersion. uiq/ srq deterministic value estimated lower bound estimated mean estimated upper bound b bd = 33.600 mm blb = 33.279 mm μb = 33.598 mm bub = 33.863 mm h hd = 60.480 mm hlb = 60.178 mm μh = 60.477 mm hub = 60.782 mm f fd = 6000.000 n flb = 5984.296 n μf = 5998.931 n fub = 6004.135 n d dd = 2000.000 mm dlb = 1990.001 mm μd = 1999.942 mm dub = 2009.989 mm c cd = 1.862087 x 109 (mpa)m clb = 1.852784 x 109 (mpa)m μc = 1.861998 x 109 (mpa)m cub = 1.871393 x 109 (mpa)m m md = 3.570 mlb = 3.552 μm = 3.569 mub = 3.588 smax smaxd = 585.800 mpa smaxlb = 572.932 mpa μs = 585.823 mpa smaxub = 597.900 mpa n nd = 3071 cycles nlb = 2421 cycles μn = 3080 cycles nub = 3781 cycles table 2: statistical parameters obtained from the simulations for both uiqs and srqs. uiq/ srq deterministic value estimated mean estimated standard deviation relative error (x 10-3 %) coefficient of variation (x 10-3) b bd = 33.600 mm μb = 33.598 mm σb = 0.0827 mm εb = 5.952 covb = 2.461 h hd = 60.480 mm μh = 60.477 mm σh = 0.174 mm εh = 4.960 covh = 2.877 f fd = 6000.000 n μf = 5998.931 n σf = 2.329 n εf = 17.82 covf = 0.388 d dd = 2000.000 mm μd = 1999.942 mm not applicable εd = 2.900 not applicable c cd = 1.862087 x 109 (mpa)m μc = 1.861998 x 109 (mpa)m not applicable εc = 4.780 not applicable m md = 3.570 μm = 3.569 not applicable εm = 2.801 not applicable smax smaxd = 585.800 mpa μs = 585.823 mpa σs = 4.0558 mpa εs = 0.5121 covs = 6.923 n nd = 3071 cycles μn = 3080 cycles σn = 197.9 cycles εn = 293.1 covn = 64.25 table 3: statistical parameters obtained from the simulations for both uiqs and srqs. figure 4: pdfs of srqs and their deterministic values. r. b. p. nonato, frattura ed integrità strutturale, 54 (2020) 88-103; doi: 10.3221/igf-esis.54.06 98 figure 5: cdfs of srqs and their deterministic values. the convergence of the means of the aleatory-type uiqs and srqs are shown in fig. 6 and fig. 7, respectively. the relative error of these variables are presented in tab. 4. for example, if a relative error criteria of 0.02% is adopted for these uiqs, the minimum required number of realizations will be nr = 4775 in order to have a relative error of 0.3% in the srqs. at nr = 5000, a relative error of 5.952 x 10-3 %, 4.960 x 10-3 %, and 17.82 x 10-3 % in the uiqs b, h, and f, respectively, produce relative errors of 0.5121 x 10-3 % and 293.1 x 10-3 % in the srqs s (first level) and n (second level), respectively. this leads to the partial conclusion that the fatigue life n is the more restrictive parameter when the objective is to minimize the number of realizations (computational effort). this is explained by the fact that the uncertainty is propagated through two levels to achieve the results for the number of cycles; in contrast, the obtainment of stress demands just one level. it is important to note that the low nr for the uiqs does not account for the stabilization of the mean throughout the process of generation of realizations. therefore, the number of realizations contained in this table accounts only for the strictly necessary to achieve the deterministic value within the error margin defined in tab. 4. to also ensure the stabilization of the mean values obtained for all variables involved, nr was chosen to be 5000. figure 6: convergence analysis of the means of the aleatory-type uiqs and their deterministic values. figure 7: convergence analysis of the means of the srqs and their deterministic values. r. b. p. nonato, frattura ed integrità strutturale, 54 (2020) 88-103; doi: 10.3221/igf-esis.54.06 99 uiq or srq deterministic value relative error (x 10-3 %) relative error criteria (%) stopping realization estimated mean b bd = 33.600 mm 5.952 0.02 nr = 51 μb = 33.598 mm h hd = 60.480 mm 4.960 0.02 nr = 49 μh = 60.477 mm f fd = 6000.000 n 17.82 0.02 nr = 19 μf = 5998.931 n smax smaxd = 585.800 mpa 0.5121 0.3 nr = 4 μs = 585.823 mpa n nd = 3071 cycles 293.1 0.3 nr = 4775 μn = 3080 cycles table 4: statistical parameters of the obtained srqs stress and fatigue life. the sensitivity analyses (sas) performed also help in the task of mapping the impact of non-deterministic parameters in terms of the required response for future actions aiming at reducing the dispersion and improving the accuracy of the srqs. the sas were performed via scatter plots of the srqs related to the aleatory-type uiqs involved and by the comparison of the correlation coefficients. fig. 9 pictures how the stress s depends on these three parameters and fig. 10 illustrates the dependence of fatigue life n on these parameters. the dashed black horizontal lines correspond to the deterministic values of the srqs and the continuous red vertical lines in these figures give the deterministic values of the uiqs. the correlation coefficients between the variables are found in tab. 5, where the most relevant aleatory-type uiq in these simulations is the cross-section height h of the beam for both s and n srqs. the least influencing uiq is the applied load f, presenting a low correlation factor. the intermediate parameter in terms of impact on the srqs is the cross-section basis b. independently of their magnitude of contribution to the srqs variability, the extent to which the uncertainty is propagated, all the uiqs lose influence when the analysis is first made related to s and, right after to n. for example, the correlation coefficient of b related to s is φbs = -0.3747 while the coefficient of b directly related to n is φbn = 0.3048, where the parameter b partially loses approximately 18.65% of its correlation capacity throughout the process of uncertainty propagation. height h and applied f load lose 21.76% and 13.29%, respectively. figure 8: sensitivity analysis of the aleatory-type uiqs related to the stress srq and their deterministic values. figure 9: sensitivity analysis of the aleatory-type uiqs related to the number of cycles srq and their deterministic values. r. b. p. nonato, frattura ed integrità strutturale, 54 (2020) 88-103; doi: 10.3221/igf-esis.54.06 100 fig. 10 shows the distribution realizations with respect to the mentioned load condition, which covers just a little portion of the s-n curve. the correlation factor is φsn = 0.7922, which demonstrates great influence of the uiq s on the srq n. figure 10: sensitivity analysis of srq stress related to the srq fatigue life and their deterministic values. uiq srq correlation coefficient b smax φbs = -0.3747 h smax φhs = -0.8347 f smax φfs = 0.0790 b n φbn = 0.3048 h n φhn = 0.6531 f n φfn = -0.0685 smax n φsn = -0.7922 table 5: correlation coefficients between uiqs and srqs. combining the information from tabs. 3, 4, and 5, the cross-section height h is the aleatory-type uiq with simultaneously the greatest dispersion and the greatest impact on the stress srq. in the second position, the parameter b; and the last in dispersion and correlation is the applied load. it is important to observe that not always the one with the highest correlation will have the greatest dispersion. figure 11: p-boxes of srqs stress and number of cycles, and their deterministic values. r. b. p. nonato, frattura ed integrità strutturale, 54 (2020) 88-103; doi: 10.3221/igf-esis.54.06 101 in order to assess the overall contribution of the uiqs on the srqs, but in a segregated mode, the p-boxes of both srqs are shown in fig. 11. the p-box indicates the set of all possible cdfs contained within design boundaries and it tries to allow the engineer to make the most adequate decisions in terms of uiqs, aiming at reducing the dispersion of the required srq. the first p-box illustrates the effect of the aleatory-type uncertainty from the uiqs b, h, and f, and the epistemictype due to uiq d on the srq stress. in the second p-box, besides the influence of the uiqs just described, the epistemic uiqs c and m are also taken into account when assessing the effect on srq fatigue life. the blue curves represented by circles are the lower probabilistic boundaries of the srqs shown on the horizontal axis. the black continuous curves are the probabilistic responses if the possibility of the deterministic values of the epistemic-type uiqs are realized. the pointed lines correspond to the upper probabilistic boundaries of the srqs, and the vertical dashed lines are the deterministic values of the srqs represented. consequently, any design point within these design boundaries is theoretically possible. to reduce the variability of these results more information should be added up to the design and/or process controls should be improved. conclusions his paper presents a bi-level hybrid uncertainty quantification scheme capable of dealing with both aleatoryand epistemic-type uncertainties in the context of a fatigue analysis. the bi-level hybrid methodology adds up the possibility of working with cases where there is no sufficient knowledge about the behavior of a variable in two distinct levels. from this perspective, the uncertain fatigue analysis is able to produce a range of possible solutions, working with limited information from the uiqs. with these capabilities attached, the proposed scheme was assessed by conducting an analysis of a clamped rectangular cross-section beam subjected to a concentrated load, which material information is extracted from experimental data available in the literature for the aisi 4130. as this type of analysis evidenced that there is a rank of most influencing fatigue design factors (uiqs), the most effective manner to improve the referred design is to implement changes directly on the most relevant uiqs, if possible. the comparison of the results obtained via this scheme with those achieved by the deterministic analysis evidences that the first tries to reproduce the discreteness intrinsic to uncertainties from manufacturing processes, design, and service conditions. besides that, the uncertain fatigue analysis, instead of providing a unique threshold value for the srqs, now yields a possible working range. depending on the risk that an engineer can take on a specific design, there will be a corresponding level of optimization achieved. another point to be highlighted is that the results obtained in terms of the required srqs directly depends on the choice of the mathematical model of each uiq. a different range of results would be obtained in the case of adding up information to the analysis performed. moreover, the method wherewith the uncertainties are propagated through the model is determinant to the definition of possible ranges of response variables. in a general manner, the referred findings emphasize that the behavior of the uncertain responses depends largely on the information provided as input uncertain data. thenceforth, there is a growing need to expand the knowledge related to these types of problems in order to produce not only a safe design, but also to propose the most effective design improvements. acknowledgements he author is very grateful to cerearerm for the support under project number 01262113. references [1] campbell, f. c. (2012). fatigue and fracture: understanding the basics, materials park, asm international. [2] echard, b., gayton, n., and bignonnet, a. (2014). a reliability analysis method for fatigue design, international journal of fatigue, 59, pp. 292-300. doi: 10.1016/j.ijfatigue.2013.08.004. [3] meng, g., feng, x., zhou, l., and li, f. (2016). hybrid reliability analysis of structural fatigue life: based on taylor expansion method, advances in mechanical engineering, 8(11), pp. 1-11. doi: 10.1177/1687814016677023. t t r. b. p. nonato, frattura ed integrità strutturale, 54 (2020) 88-103; doi: 10.3221/igf-esis.54.06 102 [4] oberkampf, w. l. and roy, c. j. (2010). verification and validation in scientific computing, cambridge, cambridge university press. [5] li, y., hu, m., and wang, f. (2016). fatigue life analysis based on six sigma robust optimization for pantograph collector head support, advances in mechanical engineering, 8(11), pp. 1-9. doi: 10.1177/1687814016679314. [6] pook, l. (2007). metal fatigue: why it is, why it matters, dordrecht, springer. [7] paolino, d. s., tridello, a., geng, h. s., chiandussi, g., rossetto, m. (2014). duplex s-n fatigue curves: statistical distribution of the transition fatigue life, frattura ed integrità strutturale, 30, pp. 417-423. doi: 10.3221/igf-esis.30.50. [8] shimizu, s. (2005). p-s-n/p-f-l curve approach using three-parameter weibull distribution for life and fatigue analysis of structural and rolling contact components, tribology transactions, 48, pp. 576-582. doi: 10.1080/05698190500313536. [9] paolino, d. s., chiandussi, g., and rossetto, m. (2012). a unified statistical model for s-n fatigue curves: probabilistic definition, fatigue and fracture of engineering materials and structures, 36, pp. 187-201. doi: 10.1111/j.1460-2695.2012.01711.x. [10] righiniotis, t. d., chryssanthopoulos. (2003). probabilistic fatigue analysis under constant amplitude loading, journal of constructional steel research, 59, pp. 867-886. doi: 10.1016/s0143-974x(03)00002-6. [11] kelma, s., schaumann, p. (2015). probabilistic fatigue analysis of jacket support structures for offshore wind turbines exemplified on tubular joints. 12th deep sea offshore wind r&d conference, trondheim, norway, 4-6 february. [12] su, c., yu, s., wang, z., and tayyab, z. (2018). a time-dependent probabilistic fatigue analysis method considering stochastic loadings and strength degradation, advances in mechanical engineering, 10(7), pp. 1-9. doi: 10.1177/1687814018785560. [13] chen, b., and zhi, p. (2019). fatigue strength analysis of bogie frame in consideration of parameter uncertainty, frattura ed integrità strutturale, 48, pp. 385-399. doi: 10.3221/igf-esis.48.37. [14] endeshaw, h. b., ekwaro-osire, s., alemayehu, f. m., and dias, j. p. (2017). evaluation of fatigue crack propagation of gears considering uncertainties in loading and material properties, sustainability, 9, pp. 1-15. doi: 10.3390/su9122200. [15] guida, m., and penta, f. (2010). a bayesian analysis of fatigue data, structural safety, 32, pp. 64-76. doi: 10.1016/j.strusafe.2009.08.001. [16] zhu, s.-p., huang, h. z., ontiveros, v., he, l.-p., and modarres, m. (2012). probabilistic low cycle fatigue life prediction using an energy-based damage parameter and accounting for model uncertainty, international journal of damage mechanics, 21, pp. 1128-1153. doi: 10.1177/1056789511429836. [17] wang, x., rabiei, m., hurtado, j., modarres, m., and hoffman, p. (2009). a probabilistic-based airframe integrity management model, reliability engineering & system safety, 94, pp. 932-941. doi: 10.1016/j.ress.2008.10.010. [18] li, m., and wang, l. (2011). feature fatigue analysis in product development using bayesian networks, expert systems with applications, 38, pp. 10631-10637. doi: 10.1016/j.eswa.2011.02.126. [19] sofi, a., muscolino, g., and giunta, f. (2019). fatigue analysis of structures with interval axial stiffness subjected to stationary stochastic excitations, meccanica, 54, pp. 1471-1487. doi: 10.1007/s11012-019-01022-2. [20] zou, l., yang, x., tan, j., and sun, y. (2017). s-n curve modeling method of aluminum alloy welded joints based on the fatigue characteristics domain, frattura ed integrità strutturale, 40, pp. 137-148. doi: 10.3221/igf-esis.40.12. [21] weibull, w. (1961). testing and analysis of results, oxford, pergamon press. [22] boiler, a., s., o., m., e., committee, p., v. (1995). asme boiler & pressure vessel code: an internationally recognized code, american society of mechanical engineers. [23] nishijima, s. (1980). statistical analysis of small sample fatigue data, transactions of the japan society of mechanical engineers a, 46, pp. 234-245. [24] miner, m. a. (1945). cumulative damage in fatigue, journal of applied mechanics, 12, pp. a159-a164. [25] ghanem, r., higdon, d., and owhadi, h. (2017). handbook of uncertainty quantification, cham, springer. [26] modarres, m., kaminskiy, m., and krivtsov, v. (1999). engineering and risk analysis – a practical guide, new york, marcel dekker. [27] wu, z. r., hu, x. t., li, z. x., xin, p. p., and song, y. d. (2017). probabilistic fatigue life prediction methodology for notched components based on simple smooth fatigue tests, journal of mechanical science and technology, 31(1), pp. 181-188. doi: 10.1007/s12206-016-1219-x. [28] morgan, m. g. and henrion, m. (1990). uncertainty: a guide to dealing with uncertainty in quantitative risk and policy analysis, cambridge, cambridge university press. r. b. p. nonato, frattura ed integrità strutturale, 54 (2020) 88-103; doi: 10.3221/igf-esis.54.06 103 [29] haldar, a. and mahadevan, s. (2000). probability, reliability, and statistical methods in engineering design, new york, john wiley. [30] ang, a. h.-s. and tang, w. h. (2007). probability concepts in engineering: emphasis on applications to civil and environmental engineering, new york, john wiley. [31] vose, d. (2008). risk analysis: a quantitative guide, new york, wiley. [32] xiao, z., han, x., jiang, c., and yang, g. (2015). an efficient uncertainty propagation method for parameterized probability boxes, acta mech, 227, pp.633-649. doi: 10.1007/s00707-015-1492-2. [33] rahman, s., karanki, d. r., epiney, a., wicaksono, d., zerkak, o., and dang, v. n. (2018). deterministic sampling for propagating epistemic and aleatory uncertainty in dynamic event tree analysis, reliability engineering and system safety, 175, pp. 62-78. doi: 10.1016/j.ress.2018.03.009. [34] federal aviation administration. 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can be opened with acrobat and adobe reader 5.0 and later.) >> /namespace [ (adobe) (common) (1.0) ] /othernamespaces [ << /asreaderspreads false /cropimagestoframes true /errorcontrol /warnandcontinue /flattenerignorespreadoverrides false /includeguidesgrids false /includenonprinting false /includeslug false /namespace [ (adobe) (indesign) (4.0) ] /omitplacedbitmaps false /omitplacedeps false /omitplacedpdf false /simulateoverprint /legacy >> << /addbleedmarks false /addcolorbars false /addcropmarks false /addpageinfo false /addregmarks false /convertcolors /converttocmyk /destinationprofilename () /destinationprofileselector /documentcmyk /downsample16bitimages true /flattenerpreset << /presetselector /mediumresolution >> /formelements false /generatestructure false /includebookmarks false /includehyperlinks false /includeinteractive false /includelayers false /includeprofiles false /multimediahandling /useobjectsettings /namespace [ (adobe) (creativesuite) (2.0) ] /pdfxoutputintentprofileselector /documentcmyk /preserveediting true /untaggedcmykhandling /leaveuntagged /untaggedrgbhandling /usedocumentprofile /usedocumentbleed false >> ] >> setdistillerparams << /hwresolution [2400 2400] /pagesize [612.000 792.000] >> setpagedevice microsoft word numero_29_art_25 s. de miranda et alii, frattura ed integrità strutturale, 29 (2014) 293-301; doi: 10.3221/igf-esis.29.25 293 focussed on: computational mechanics and mechanics of materials in italy a simple beam model to analyse the durability of adhesively bonded tile floorings in presence of shrinkage s. de miranda, a. palermo, f. ubertini university of bologna stefano.demiranda@unibo.it, antonio.palermo6@unibo.it, francesco.ubertini@unibo.it abstract. a simple beam model for the evaluation of tile debonding due to substrate shrinkage is presented. the tile-adhesive-substrate package is modeled as an euler-bernoulli beam laying on a two-layer elastic foundation. an effective discrete model for inter-tile grouting is introduced with the aim of modelling workmanship defects due to partial filled groutings. the model is validated using the results of a 2d fe model. different defect configurations and adhesive typologies are analysed, focusing the attention on the prediction of normal stresses in the adhesive layer under the assumption of mode i failure of the adhesive. keywords. tile flooring; tile debonding; adhesive joint; elastic foundation. introduction ile floorings are extensively used in residential and industrial buildings. a typical tiled floor consists of an upper layer of tiles separated by grouting interfaces and attached via an adhesive stratum to a lower cementitious substrate (fig. 1). although tile floorings guarantee high resistance and durability also in severe exposure conditions, they are prone to suffer from debonding failure, typically induced by differential elongation/shortening between tile layer and substrate. the differential deformation may be caused by substrate shrinkage, either due to thermal gradients or residual maturation of cementitious substrate. substrate shrinkage determines an eccentric compression in the tiles transferred by a shear mechanism through the adhesive layer. the inherent eccentricity of compression due to the geometric configuration of the tiled floor, eventually increased by the presence of grouting defects due to poor workmanship, may induce tile debonding due to mode i failure of the adhesive layer. nowadays several types of adhesives are available in the market with increasing performance in terms of strength and deformation capacities at the prize of increasing costs. therefore, for a cost-effective design of the tile flooring systems it is of fundamental importance an assessment of the stress state of the adhesive layer induced by the differential deformations. in recent years, the extensive use of adhesive layers and adhesive lap joints in different engineering applications has driven the attention of several researches. different studies have been carried out by modelling the adhesive layer as a fracturing interface. analytical models have been developed to describe the interface decohesion in laminated beams and simulate peeling tests [1]. finite element models have been widely used to simulate the debonding of adhesive lap joints (see e.g. [2,3]). mahaboonpachai et al. [4] investigated the debonding of tiles in external wall claddings by formulating a two dimensional cohesive interface element. lignola et al [5]. developed a refined finite element model to analyse the stress and strain distributions in a tile-adhesive-substrate subjected to substrate shrinkage. the same problem has been studied t s. de miranda et alii, frattura ed integrità strutturale, 29 (2014) 293-301; doi: 10.3221/igf-esis.29.25 294 by cocchetti et al. [6]. the authors modelled a tile bonded to a rigid substrate through an elastic adhesive as an eccentrically compressed beam on a pasternak foundation. the eccentricity of compression is induced by the presence of an out-of-plane workmanship defect leading to a mode i failure of the adhesive. this approach leads to closed-form estimation of the ultimate strength of tile-substrate adhesive joint. more recently the use of simplified beam model with elastic constraints has been successfully applied also for the estimation of crack opening area in longitudinally cracked pipes [7, 8]. in the present paper, a simple beam model is developed to evaluate the stress state of tiled floors subjected to debonding due to substrate shrinkage. then, an ad-hoc finite element is developed in order to solve the governing differential equations of the tile-adhesive-substrate system. the presence of inter-tile grouting is modelled through rotational/translational springs. the additional eccentricity induced by workmanship defects is taken into account by means of a partial/eccentric grouting modeled with the same rotational/translational springs collocated in eccentric position. numerical analyses are performed on different tiled flooring configurations. the robustness and reliability of the proposed model is verified by comparing the model results in terms of normal stresses within the adhesive layer with those obtained with a 2d fe model developed with the commercial software abaqus. figure 1: tile flooring. mechanical model s regards the tile-adhesive-substrate system, reference is made to the mechanical model shown in fig. 2. grouting modelling will be described in the next section. the tile, bonded to the flexible substrate by means of an elastic adhesive, is modelled as an euler-bernoulli beam on a pasternak foundation connected to a second layer of vertical springs by means of a shear deformable layer. the adoption of a two-layer system with an interposed shear deformable stratum is inspired by the model developed by kerr [9] in the contest of geotechnical engineering. figure 2: mechanical model. in the following, ( )u x and ( )v x denote the longitudinal (axial) and the transversal displacement of the tile respectively, and ( )sv x the transversal displacement of the substrate. moreover, the young modulus, the poisson ratio and the thickness of material i are denoted by ie ,   i ,    it , respectively. subscript i can become t , a , or s if the quantity refers to tile, adhesive or substrate, respectively. plane strain conditions are assumed and, thus, for a material i the plane strain modulus * ii 2 i  e e   1 ν   is used. indeed, this hypothesis does not consider some specific features related to the bidimensional periodicity of the problem, but allows to preserve the main essence of the bi-dimensional problem in its reduction to the one-dimensional beam model and is, in fact, commonly adopted in the literature dealing with the a s. de miranda et alii, frattura ed integrità strutturale, 29 (2014) 293-301; doi: 10.3221/igf-esis.29.25 295 debonding of tile flooring (see e.g. [6]). with this notation, the stiffness coefficients of the springs modelling the adhesive are expressed as * , a a t a e k t  and , a a l a g k t  for the transverse and the longitudinal springs respectively, while, as regards the substrate, it follows * s s s e k t  . no vertical loads are applied to the flooring, self-weight is neglected and constant substrate shrinkage 0 is imposed. the assumed axial deformed configuration of the flooring due to substrate shrinkage is shown in fig. 3. the imposed substrate shrinkage 0 induces a displacement 0u along the substrate height, which, in turn, induces a tile compression acting at the interface between adhesive and tile (i.e. eccentric with respect to tile axis). this compression is equal to  *, 0a lk u u , where *u denotes the longitudinal displacement at the bottom position of the tile. according to the classical euler-bernoulli hypothesis, *u can be expressed as follows: * ' 2 ttu u v  (1) where 'v denotes the derivative of v with respect to tile axis direction. of course, the above assumption leads to a coupled axial-flexural response of the tile. in this regard, it should be noted that a beam on a pasternak foundation has been already used by cocchetti et al. [6] to model tile debonding with a simple but effective mathematical formulation which does not account for the inherent eccentricity due to the geometrical configuration of the system. in the present work, by considering the eccentric position of the compression transferred by the adhesive to the tile, the coupled axial-flexural response of the tile is recovered. furthermore, the assumption of flexible substrate, modeled as a layer of vertical springs interconnected by a shear layer, allows to enrich the model still preserving its formulation relatively simple. figure 3: longitudinal interaction forces at tile-adhesive interface due to substrate shrinkage. the potential energy  π of the tile-adhesive-substrate system can be expressed as: t a sπ π π π     (2) where t a sπ , π , π are the functionals of the potential energy associated to the tile, the adhesive and the substrate, respectively: s. de miranda et alii, frattura ed integrità strutturale, 29 (2014) 293-301; doi: 10.3221/igf-esis.29.25 296 * ' 2 * '' 2 t 1 π 2 t t t l e a u e i v dx    (3) 2 2 ' a , , 0 1 π 2 2 t a t a l l t k v k u v u dx              (4)  2 ' 2s 1  π 2 s s s s s l k v v g a v dx      (5) in the above equations, ta , ti , sg and sa  are the tile cross section area, the tile moment of inertia, the substrate shear modulus and the substrate cross section area, respectively. as it can be noted, the potential energy t π  of the tile consists of the classical euler-bernoulli energy terms, the potential energy of the adhesive a π collects all the terms of the pasternak formulation and the coupling terms and the substrate potential energy sπ collects the elastic energy of the vertical springs and of the shear layer. finite element discretization tile-adhesive-substrate tandard shape functions are used to represent the axial and transversal displacement fields    , u x v x of the tile and the transversal displacement field  sv x of the substrate:                            su v s v s u x v x v x  n u n v n v (6) where un ,  vn and svn collect linear lagrangian, cubic hermitian and cubic lagrangian shape functions, respectively, and u , v , sv are vectors collecting nodal parameters. with these assumptions, following standard procedures, the discrete equilibrium equations are derived: ku p (7) with: t t 0          00 s s s s uu uv u uv vv vv v svv v v k k u p k k k k u v p p vk k                               (8) the expressions of the different submatrices of k and of the nodal load vectors up , vp are given in appendix. grouting-adhesive-substrate grouting is modeled by means of a discrete approach based on the use of elastic springs as shown in fig. 4. the grouting itself is modeled by an axial spring uk , a vertical transversal spring vk and a rotational spring k . the axial spring can be placed in an eccentric position with respect to tile axis in order to account for partial-eccentric grouting configurations. the attached portion of the adhesive layer is modeled with two vertical springs adk while the related portion of substrate is modeled with two vertical springs sdk and a transversal spring gk . the definition of each stiffness coefficient is reported in fig. 4. from the above discrete model, the definition of a grouting-adhesive-substrate stiffness matrix gk is straightforward. the rationale to adopt a discrete approach for modelling inter-tile grouting is twofold: on the one hand the discrete approach allows a simple definition and straightforward implementation of the grouting stiffness matrix   gk , on the other hand it allows to preserve all the fundamental stiffness properties of the grouting (axial, transverse and rotational s s. de miranda et alii, frattura ed integrità strutturale, 29 (2014) 293-301; doi: 10.3221/igf-esis.29.25 297 stiffness). in this regard, in the work by lignola et al. [6] the authors highlighted the influence of tile-joint details on the adhesive stress distribution and the need to account for these details. moreover, the use of the proposed discrete approach allows to account for the presence of partial/eccentric inter-tile groutings that are a common typology of workmanship defects in tiled floors. figure 4: grouting-adhesive-substrate discrete model. numerical results case study n this section some numerical examples are presented to show the capability of the proposed model to predict the response of a flooring system subjected to substrate shrinkage. the analysed flooring system is composed of 8 tiles with interposed groutings laying on an adhesive stratum attached to the substrate (fig. 5). the mechanical and geometrical properties of the flooring are listed in tab. 1. the presence of a localized defect is assumed by considering two different grouting configurations located at midspan of the flooring (fig. 5): partial grouting bottom (pgb): partial grouting in low eccentric position with respect to the tile axis; partial grouting top (pgt): partial grouting in high eccentric position with respect to the tile axis. in addition, the case with no defects (fg) has been considered. details of the partial grouting configurations are given in tab. 2. length [mm] thickness [mm] e [gpa] ν tile 600 8 49 0.18 adhesive 4848 3 6.5 0.22 substrate 4848 40 30.7 0.21 grouting 6 8 19 0.2 table 1: case study. geometrical and mechanical parameters. for the pgb configuration, two different grouting lengths (2 mm and 6 mm) have been considered. in all the analysed cases, uniform substrate shrinkage 40 5 10   mm/mm is imposed along the substrate longitudinal direction. the chosen value of substrate shrinkage is a typical value for concrete structures [10]. i s. de miranda et alii, frattura ed integrità strutturale, 29 (2014) 293-301; doi: 10.3221/igf-esis.29.25 298 as usual in a kerr-like foundation [11], for the substrate an effective shear area *sa is calibrated. for the proposed model, an effective shear area *   10 s s a a  has been numerical calibrated for the tile configurations described above and validated through the parametric study developed in the next section. the same flooring configurations (fg, pgb, pgt) have been modelled with 2d fe models, developed using the commercial software abaqus. the solutions provided by the 2d fe models are taken as a reference to validate the results of the proposed model. attention is focused on the distribution of normal stresses in the adhesive, in accordance with the fact that the most typical failure condition of the flooring is determined by a mode i failure mechanism of the adhesive layer. figure 5: the flooring system and the grouting configurations. length [mm] thickness [mm] eccentricity [mm] pgb 2-6 2 -3 pgt 2 2 3 table 2: grouting configurations: geometrical dimensions. fig. 6a, 6b and 6c compare the normal stresses in the adhesive layer close to the defect location as obtained from the proposed model and the 2d fe models for the three different grouting configurations pgb, pgt and fg, respectively. inspecting the graphs reveals the good capability of the model in predicting the adhesive normal stress distribution. in particular, the peak tensile stress that could induce the initiation of the debonding mechanism is accurately evaluated for both the pgt and pgb configurations (fig. 6a, fig. 6b). as far as the fg case is concerned (fig. 6c), it is worth noting that the proposed model is still able to accurately predict the normal stresses of the adhesive thanks to the assumed coupled axial-to-flexural response. a) b) c) figure 6: adhesive normal stress distribution at defect location. a) pgb configuration (grouting 2 mm length ), b) pgt configuration, c) fg configuration. s. de miranda et alii, frattura ed integrità strutturale, 29 (2014) 293-301; doi: 10.3221/igf-esis.29.25 299 parametric study the elastic properties (e and ν) and the thickness of the adhesive layer have been varied in order to assess the robustness of the proposed simplified model. ranges of variation are reported in tab. 3. a total of 40 different cases have been analysed and compared with the results of the 2d fe models. adhesive thickness [mm] e [gpa] ν 3-5 3.5 0.3 5 0.25 6.5 0.22 8.0 0.18 10 0.175 table 3: adhesive elastic parameters and thicknesses. tab. 4 lists the peak tensile stresses in the adhesive layer as obtained from the proposed model ( p ) and from the 2d fe models ( ,2p d ) for all the analysed cases. it can be observed that the proposed approach shows an adequate robustness and reliability in predicting the peak tensile stress in the adhesive layer, resulting in a mean error equal to the 10%. the accuracy of the proposed model is clearly higher for medium stiff adhesive (6.5 gpa) for which the effective shear area *sa has been calibrated and deteriorates only for very stiff or very flexible adhesive configurations, less common in actual flooring applications. moreover, it is worth noting that for the most common defect typology, the pgb configuration, the accuracy of the proposed model is high for all the analysed cases (mean error ~ 6%). conclusions simple beam model to analyse tile flooring debonding due to substrate shrinkage has been presented. in particular, a beam model on a two-layer foundation has been adopted to model the tile-adhesive-substrate system. inter-tile grouting has been modeled by means of a discrete approach based on elastic springs, able to model both full and partial/eccentric grouting configurations. the results of the proposed model have been compared with those of 2d fe models. the attention has been focused on the evaluation of the adhesive normal stress distribution, with the final aim of evaluating tile debonding due to mode i failure mechanism of the adhesive layer. numerical results have shown that the model allows an accurate evaluation of the stress state in the adhesive layer. further efforts could be devoted to extend the proposed model for the inelastic analyses of floorings and to consider the presence of adhesion defects at the tile to substrate interface. a s. de miranda et alii, frattura ed integrità strutturale, 29 (2014) 293-301; doi: 10.3221/igf-esis.29.25 300 case a e [gpa] at [mm] p [mpa] ,2p d [mpa] %e case a e [gpa] at [mm] p [mpa] ,2p d [mpa] %e fg 3.5 3 0.06 0.05 15 pgb(2mm) 3.5 3 1.00 0.94 6 fg 3.5 5 0.04 0.03 32 pgb(2mm) 3.5 5 0.87 0.84 4 fg 5.0 3 0.07 0.07 2 pgb(2mm) 5.0 3 1.08 1.00 7 fg 5.0 5 0.05 0.04 20 pgb(2mm) 5.0 5 0.95 0.90 5 fg 6.5 3 0.08 0.09 13 pgb(2mm) 6.5 3 1.12 1.05 7 fg 6.5 5 0.06 0,05 7 pgb(2mm) 6.5 5 1.00 0.95 4 fg 8.0 3 0.09 0.10 18 pgb(2mm) 8.0 3 1.17 1.07 9 fg 8.0 5 0.07 0.07 2 pgb(2mm) 8.0 5 1.06 0.98 7 fg 10.0 3 0.10 0.12 27 pgb(2mm) 10.0 3 1.22 1.11 9 fg 10.0 5 0.08 0.08 6 pgb(2mm) 10.0 5 1.11 1.02 8 pgb(6mm) 3.5 3 0.90 0.84 7 pgt 3.5 3 3.17 3.37 6 pgb(6mm) 3.5 5 0.79 0.74 6 pgt 3.5 5 2.69 3.14 7 pgb(6mm) 5.0 3 0.97 0.90 7 pgt 5.0 3 3.61 3.34 7 pgb(6mm) 5.0 5 0.85 0.80 6 pgt 5.0 5 3.06 3.23 6 pgb(6mm) 6.5 3 1.01 0.95 5 pgt 6.5 3 3.84 3.33 13 pgb(6mm) 6.5 5 0.89 0.85 5 pgt 6.5 5 3.24 3.31 2 pgb(6mm) 8.0 3 1.06 0.99 7 pgt 8.0 3 4.15 3.12 25 pgb(6mm) 8.0 5 0.95 0.88 7 pgt 8.0 5 3.49 3.20 8 pgb(6mm) 10.0 3 1.11 1.04 6 pgt 10.0 3 4.48 3.02 33 pgb(6mm) 10.0 5 1.00 0.93 7 pgt 10.0 5 3.77 3.20 15 fg mean relative error: 14% pgb (2mm) mean relative error: 6% pgb (6mm) mean relative error: 7% pgt mean relative error: 13% mean relative error: 10% table 4: peak tensile stresses ,2, p p d  and relative errors. appendix n the following the expressions of the submatrices uuk ,   uvk , vvk , svvk ,   svvk and the nodal load vectors up ,   vp are given: ' t * ' , duu u t t u u a l u l e a k x    tk n n n n (a. 1) t ' , d 2 t uv u a l v l t k x     k n n (a. 2) 2 ' t * ' ' t ' t , , d 4 t vv v t t v v a l v v a t v l t e i k k x         k n n n n n n (a. 3) t , ds svv v a t v l k x    k n n (a. 4) t t 't * , ' ds s s s s s sv v v s v a t v v s s v l k k g a x    k n n n n n nsv (a. 5) i s. de miranda et alii, frattura ed integrità strutturale, 29 (2014) 293-301; doi: 10.3221/igf-esis.29.25 301 ' t , 0 d  u u a l l k u x   p n (a. 6) ' t , 0' d 2 t v v a l l t k u x     p n (a. 7) the imposed displacement 0u is evaluated from 0 corrected by the factor * * *  (1 )t t t t s s e t e t e t   to take into account the substrate-tile axial deformability. references [1] williams, j., hadavinia, h., analytical solution for cohesive zone models, journal of the mechanics and physics of solids, 50 (2002) 809-825. [2] schmidt, p., edlund, u., analysis of adhesively bonded joints: a finite element method and a material model with damage, international journal for numerical methods in engineering, 66 (2006) 1271-1308. [3] goncalves, j. p. m,. de moura, m. f. s. f., de castro, p. m. s. t., a three-dimensional finite element model for stress analysis of adhesive joints, international journal of adhesion & adhesives, 22 (2002) 357–365. [4] mahaboonpachai, t., matsumoto, t., inaba, y., investigation of interfacial fracture toughness between concrete and adhesive mortar in an external wall tile structure, international journal of adhesion and adhesives, 30 (2010) 1-9. [5] lignola, g.p., collina, a., prota, a., manfredi, g., analysis of tile-substrate behavior subjected to shrinkage, 19 aimeta conference, september 2009, paper # 129. [6] cocchetti, g., comi, c., perego, u., strength assessment of adhesively bonded tile claddings, international journal of solids and structures, 48 (2011) 2048-2059. [7] de miranda, s., molari, l., scalet, g., ubertini, f., simple beam model to estimate leakage in longitudinally cracked pressurized pipes, asce journal of structural engineering, 138 (2012) 1065-1074. [8] de miranda, s., molari, l., scalet, g., ubertini, f., a physically-based analytical relationship for practical prediction of leakage in longitudinally cracked pressurized pipes, submitted to engineering structures. [9] kerr, a. d., a study of a new foundation model, acta mechanica, 1 (1965) 135-147. [10] aci committee 209, guide for modeling and calculating shrinkage and creep in hardened concrete, (2008) [11] avramidis, i. e., morfidis, k., bending of beams on three-parameter elastic foundation, international journal of solids and structures, 43 (2006) 357-375. microsoft word 001 plenary marciniak rozumek poland paper final z. marciniak et alii, frattura ed integrità strutturale, 34 (2015) 1-10; doi: 10.3221/igf-esis.34.01 1 focussed on crack paths models of initiation fatigue crack paths proposed by macha z. marciniak opole university of technology, poland z.marciniak@po.opole.pl d. rozumek opole university of technology, poland d.rozumek@po.opole.pl abstract. professor e. macha devoted his academic life to solving the problems connected with random multiaxial fatigue in components of machines and structures. in his studies he formulated stress, strain and energy criteria related to critical plane concept. he also proposed several methods to determine critical plane position. in particular, he formulated and verified weight functions applied in order to determine critical plane position. the variance method constituted another significant contribution to the development of methods for determining critical plane position. apart from these criteria, macha was exploring energy approach in fatigue of materials and the development of fatigue cracks. he has also observed that strain characteristics multiplied by stress amplitude determined at specimen half-life are applied to estimate fatigue life using energy criteria. however, for cyclically instable materials, stress amplitude value may differ a lot; therefore he proposed the method to determine energy fatigue characteristics directly from experimental research. keywords. multiaxial fatigue criteria; energy; crack growth; variance method; weight function. introduction redicting service life of different objects is a very important issue for modern engineering. wrong service life estimation may result in accidents and disasters. therefore, studies aimed to understand and control this phenomenon, started already in the 19th century, are continued today. the multitude of problems connected with it suggests that scientists still have plenty of work ahead. initially, the scope of studies was limited to uniaxial, constantamplitude issues only. with increasing knowledge on the phenomenon, the interest in multiaxial fatigue (most frequent in engineering practice) was growing. at the same time, many stress assessment criteria were proposed. another step in the development involved attempts to assess life for random loads. this problem was explored by professor macha as well [14]. he started his work from proposing mathematical models to assess fatigue life for materials in the conditions of random complex stress state, where besides stress criteria he demonstrated the method for determining critical plane position using weight functions. further studies were connected with strain and energy criteria, and methods used to p z. marciniak et alii, frattura ed integrità strutturale, 34 (2015) 1-10; doi: 10.3221/igf-esis.34.01 2 determine critical plane position. many scientists became interested in these studies, which resulted in numerous contacts and team work, e.g. with carpinteri [5, 6], sakane [7], sonsino [8], dragon [9], petit [9], and others. the purpose of this study is to present academic achievements of professor macha. mathematical models and their experimental verification ne of the first criteria proposed by e. macha for multiaxial random loads [1, 2] has the following form:  max ( ) ( )ns n t b t k t f   (1) where ( )ns t and ( )n t are: shear stress and normal stress in fracture plane, respectively; and b, k, f – constants for the selection of a given criterion version. initially, in this criterion fracture plane was regarded as the critical plane. however subsequent analyses make it possible to observe that this plane changes especially for elastic-plastic materials. detailed criterion guidelines are: (i) fatigue crack is generated (caused) by the activity of normal stresses σn(t) and shear stresses τns(t) in the direction s  in plane with normal n  , (ii) direction s  is concurrent with average direction of shear stresses. in the criteria related to critical plane it is very important to determine critical plane position. in order to determine its position, it was proposed to apply the weight function method. the weight function method involves finding averaged positions of main axes directions through properly selected weight functions wk. 1 1 1 1ˆ cos l k k k l w w     , 2 2 1 1 ˆ cos l k k k m w w     , 3 3 1 1 ˆ cos l k k k n w w     , (2) where: 1 l k k w w    sum of weights, l – number of averages, 1, β2, 3 – angles between main stresses and axes in the cartesian coordinates, (1, x), (2, y), (3, z), respectively then, critical plane position is being determined relative to these averaged directions. 6 weight functions are demonstrated in the study [1]: weight i – wk = 1 – it is assumed that each position of the main axes has the same effect on the critical plane position, weight ii – 1 1min 1max 1min k kw        for k = 1, 2,…,n – this weight reduces the impact of maximum main stress 1(t) value on the critical plane position, weight iii – 1 1 0 0 1 1 k af k k af for a w a for a              for k = 1, 2,…,n – according to this weight, only those positions of main axes are averaged, for which maximum stress value is 1(t)  a·f, where f is fatigue limit, weight iv – 1 1 0 1 k e k k e for r w for r             for k = 1, 2,…,n – only those positions of main axes are averaged, for which maximum stress value 1(t) is higher than product of poisson’s ratio and yield point, o z. marciniak et alii, frattura ed integrità strutturale, 34 (2015) 1-10; doi: 10.3221/igf-esis.34.01 3 weight v – 1 1 1 max 1min 10 k f k af k k k af a for a w for a                   – this weight was developed as a result of combining weights ii and iii, weight vi – 1 1 10 m k k af f k k af for a a w for a                    – in this proposal only those positions of main axes are taken for averaging, in which 1(t) is higher than fatigue limit fraction, while their share is in exponential function dependent on wöhler curve inclination. however, the selection of proper angles for averaging creates problems, and there are no physical guidelines, which angles should be averaged. the issue of averaging proper angles is discussed in the study [10], where direction cosines were made dependent on euler angles. matrix of direction cosines defined in this way is expressed in the following form cos cos cos sin sin cos cos sin sin cos cos sin sin cos cos cos sin sin cos sin cos cos sin sin sin cos sin sin cos                                          . (3) nevertheless, some transformations are required in order to obtain values of euler angles. the first step involves calculation of the quantity:  1 2 3 1 arccos 1 2 l m n     , 3 21 2sin m n u    , 1 32 2sin n l u    , 2 13 2 sin l m u    . (4) then, euler rodriguez parameters are used: 1 sin 2 u    , 2 sin 2 u    , 3 sin 2 u    , cos 2    (5) to determine values of angles arctg arctg                   , 3arcsin sin m          , arctg arctg                   . (6) euler angles calculated in this way are averaged using the following relations:     1 1 ˆ l k k w k w      ,     1 1ˆ l k k w k w      ,     1 1 ˆ l k k w k w      . (7) then, macha and będkowski [11] developed variance method to determine critical plane position. in this method, the critical plane is considered to be the plane, for which the variance of equivalent stress reduced by selected criterion reaches maximum. the study [12] contains comparison of lives of steel specimens using variance method with damage accumulation method for criterion of maximum shear stress in the critical plane. according to this criterion, the equivalent stress eq (t) takes the following form z. marciniak et alii, frattura ed integrità strutturale, 34 (2015) 1-10; doi: 10.3221/igf-esis.34.01 4 ( ) ( ) sin( 2 ) 2 ( ) cos( 2 )eq x xyt t t        , (8) where: x (t) normal stress along the specimen axis, xy (t) shear stress in the specimen cross section,  angle determining the critical plane position. from eq. (8) it appears that the equivalent stress eq (t) is linearly dependent on the stress state components x (t) and xy (t), so it can be expressed as 1 1 2 2 1 n eq j j j a x a x a x     , (9) where: a1 = sin (2), a2 = 2cos (2), x1 = x, x2 = xy. from theory of probability [13] it results that the variance of random variable being a linear function of some random variables is expressed by the following formula 1 2 1 2 2 2 2 1 2 1 2 1 2 2 n eq j xj j k xjk x x x x j j k a a a a a a a              , (10) where: eq variance of equivalent stress eq, x1 variance of normal stress x, x2 variance of shear stress xy, x1x2 covariance of normal x and shear stress xy stresses. under biaxial random stationary and ergodic stress state, the variances x1, x2 and the covariance x1x2 in eq. (10) are constant. in the method of variance for determination of the critical plane position the maximum function of eq. (10) is searched in relation of the angle  occurring in coefficients a1 and a2. after reduction, the variance of equivalent stress eq versus the angle  can be written as       1 2 1 2 2 2sin 2 4 cos 2 2sin 4eq x x x x         . (11) an exemplary assessment of the critical plane position for loading combination k01 [12] obtained using the variance and damage accumulation methods is shown in fig. 1. a) b) figure 1: dependence of the normalized value of: a) variance, b) damage accumulation on the angle  of critical plane position for loading combination k01 (λ = 0.189) [14]. z. marciniak et alii, frattura ed integrità strutturale, 34 (2015) 1-10; doi: 10.3221/igf-esis.34.01 5 fig. 2 compares calculated life values and experimental values for variance and damage accumulation [12]. a) b) figure 2: comparison of calculated and experimental fatigue lives with critical planes determined according to: a) variance and b) damage accumulation methods [14]. strain fatigue criterion [3] expressed as  max ( ) ( )ns n t b t k t q   (12) is another proposal to formulate multiaxial random fatigue in the field of strains, where εns(t) and εn(t) are shear and normal strain in critical plane, respectively; and a, b, k, q – constants for the selection of a given criterion version. in 1991, macha, grzelak and łagoda [14] attempted to apply spectral method to determine fatigue life. studies on these issues were continued further in cooperation with niesłony [15]. in these studies, assuming linear effort criteria, a generalised spectral method was formulated for determining fatigue life of materials put to multiaxial loading, using the function of power spectral density in the field of frequency. multiaxial state of stress is reduced to uniaxial state, and accumulation of damage is carried out using standard material characteristics. the study proves that the results for lives assessed using spectral method in the field of frequency and cycle counting method in the field of time are much the same. whereas, determination of expected critical plane position using variance method for time histories gives results equivalent to the function of power spectral density. then, professor macha focused his attention on stress distribution in notch root. like in neuber [16] and molski-glinka [17] criteria, łagoda-macha [18] proposed an energy equation for determining the state of stresses in notch bottom as 1 2 max max max 1 2 1 n lm n w e n k             , (13) where: nexponent of cyclic strain curve, k coefficient of cyclic strain curve. experimental verification proved that the values obtained through this relation are between the results obtained using neuber and molski-glinka relations. tab. 1 contains sample calculation results for the above three models [19]. z. marciniak et alii, frattura ed integrità strutturale, 34 (2015) 1-10; doi: 10.3221/igf-esis.34.01 6 kt model neuber max (mpa) molski-glinka max (mpa) macha-łagoda max (mpa) 9.61 421 386 405 4.30 329 302 316 3.23 294 270 282 1.85 233 215 224 table 1: the presentation max depending on kt and strain energy density models. professor macha was interested most in energy criteria of multiaxial random fatigue. in this field, in cooperation with łagoda he proposed a generalised criterion of energy density parameter for normal and shear strains in critical plane, shown as [18, 20]  max ( ) ( )ns n t w t w t q   or max ( )eq t w t q    (14) where , , q – constants for the selection of a given criterion version. guidelines of the proposed criterion are as follows [21]: “a) this portion of strain energy density is responsible for fatigue crack, which matches the work of normal stress n (t) in normal strain n(t), that is wn(t) and work of shear stress ns(t) in a shear strain ns(t) in the direction s in plane with normal n, that is wns(t), b) direction s in the critical plane matches average direction, in which density of shear strain energy is maximal, c) in boundary state, material effort is determined by the maximum value of linear combination of energy parameters wn(t) and wns(t).” for uniaxial stress state, strain energy density parameter is expressed as       sgn ( ) sgn ( ) ( ) 0.5 ( ) ( )sgn ( ), ( ) 0.5 ( ) ( ) 2 t t w t t t t t t t            . (15) for multiaxial stress state, the course of equivalent strain energy density parameter is calculated in the critical plane with normal n and shear direction s as     ( ) ( ) ( ) 0.5 ( ) ( )sgn ( ), ( ) 0.5 ( ) ( )sgn ( ), ( ) eq ns n n n n n ns ns ns ns w t w t w t t t t t t t t t               . (16) the proposed energy criterion in the critical plane is applicable for cyclic and random loads for small and large number of cycles. depending on the coefficients chosen, different criteria are obtained and thus, for:  = 0,  = 1 we have the criterion of maximum energy density for normal strain in the critical plane,  = 1,  = 0 we have the criterion of maximum energy density for shear strain in the critical plane,  = 1,  = 1 we have the criterion of maximum energy density for normal and shear strain in the critical plane. when applying energy fatigue criteria to assess life, energy characteristics are used, developed as a result of the coffinmanson-basquin characteristic multiplication [22-24] by stress amplitude determined for specimen half-life. however, this characteristic not fully illustrates the behaviour of cyclically unstable materials. being aware of these differences, professor macha and słowik proposed a new model to determine energy fatigue characteristics directly from experimental research. this model is described as [25]      0.5 pliw t t t     , (17) where ipl = (ti) for (ti) = 0 and i = 1, 2, 3,.... are successive numbers of the hysteresis loop (σ-ε). z. marciniak et alii, frattura ed integrità strutturale, 34 (2015) 1-10; doi: 10.3221/igf-esis.34.01 7 in eq. (17), w(t), σ(t), ε(t) are continuous functions of time t, and εipl and εi+1pl are constant values in time t in the hysteresis loop with the number i, while ipl is the plastic strain registered in the moment ti, when the stress (ti) is equal to zero, and remains constant to the moment ti+1 when the stress reaches zero again, i.e. (ti+1) = 0. then the new registered value of plastic strain i+1pl replaces the previous one ipl. this procedure is repeated for each cycle of loading. fig. 3 shows sample hysteresis loops and energy parameter course calculated on the basis of variable-amplitude history of stresses and strains. energy parameter course calculation procedure for variable-amplitude loads: step 1. in point 0, individual values of stresses, strains and energy parameter are: σ(t0) = 0, ε(t0) = 0, ε0pl= 0, w(t0) = 0. step 2. in point a, individual parameters have the following values: σ(ta) = σa, ε(ta) = εa, εapl= ε0pl =0, w(ta) = 0.5·σa׀εa ε0pl0.5 = ׀·σa·εa. step 3. then, going to point b we obtain: σ(tb) = σb=0, ε(tb) = εb = 0, εbpl= εbpl, w(tb) = 0.5·σb· ׀εbεbpl0 = ׀. step 4. point c: σ(tc) = σc, ε(tc) = εc, εcpl= εbpl, w(tc) = 0.5·σc· ׀εcεbpl׀ . step 5. point d: σ(td) = σd =0, ε(td) = εd =0, εdpl= εdpl, w(td) = 0.5·σd·׀εdεdpl0 = ׀. step 6. point e: σ(te) = σe, ε(te) = εe, εepl= εdpl, w(te) = 0.5·σe· ׀εeεd׀pl, etc. fig. 3d presents energy parameter course calculated based on above procedure. figure 3: sample hysteresis loops a), stress courses b), strain courses c), energy parameter courses d). fig. 4 shows energy fatigue characteristic for steel c45 according to the formula (17). the models and methods proposed above were used to assess fatigue life until crack initiation. whereas, as regards development of fatigue cracks, rozumek and macha proposed an energy criterion based on parameter j for three crack modes [26]. this criterion was verified for mode i and mode iii [27]. 2 2 2 1i ii iii ic iic iiic j j j j j j                       , (18) where jic, jiic, jiiic are critical values for modes i, ii and iii. the criterion (18) was successfully verified while tests of aluminium alloy and steels. different bending (cracking mode i) to torsion (cracking mode iii) ratio in steel 18g2a is shown in fig. 5 [28]. it provides grounds to observe shift of experimental points towards increasing the value of parameter ji, except of the z. marciniak et alii, frattura ed integrità strutturale, 34 (2015) 1-10; doi: 10.3221/igf-esis.34.01 8 angle  = 60, where decrease in these values was confirmed. considerable increase of parameter ji and jiii values was observed with rising fatigue crack growth rate (fig. 5, curves 1 to 2). diagrams 1 and 2 shown in fig. 5 concern fatigue crack growth rates: da/dn = 1.6810-8 m/cycle and da/dn = 4.2310-8 m/cycle, respectively. figure 4: energy fatigue characteristic for steel c45. figure 5: comparison of experimental results for different bending to torsion ratios with those calculated according to the eq. (18) for 18g2a steel [27]. different bending (cracking mode i) to torsion (cracking mode iii) ratio in alcumg1 alloy is shown in fig. 6. fig. 6 [28] provides grounds to observe shift of experimental points towards increasing the values of parameter ji these increment values were lower than for steel 18g2a. experimental results of interdependences between cracking mode i and iii, for constant da/dn ratio value were defined by eq. (18). diagrams 1 and 2 shown in fig. 6 concern fatigue crack growth rates: da/dn = 7.6410-8 m/cycle and da/dn = 1.4110-7 m/cycle, respectively. z. marciniak et alii, frattura ed integrità strutturale, 34 (2015) 1-10; doi: 10.3221/igf-esis.34.01 9 figure 6: comparison of experimental results for different bending to torsion ratios with those calculated according to the eq. (18) for alcumg1 alloy. summary his brief description of professor macha activity irrefutably proves his wide interests and great influence on progress regarding the issues of fatigue life assessment for components of machines and structures. during his academic career, macha with colleagues proposed many fatigue criteria concerning the parameters of stress, strain and strain energy density both in the field of time and frequency. macha’s interests covered initiation range and propagation of fatigue cracks. many times these criteria were verified in various load conditions for different materials, and were presented during various scientific conferences. references [1] macha, e., mathematical models of the life to fracture for materials subject to random complex stress systems, monographs no 13, wrocław university of technology, wrocław, (1979) (in polish). [2] macha, e., generalization of fatigue fracture criteria for multiaxial sinusoidal loadings in the range of random loadings. biaxial and multiaxial fatigue, egf 3, eds m.w. brown and k.j. miller, mechanical engineering publications, london, (1989) 425-436. [3] macha, e., generalization of strain criteria of multiaxial cyclic fatigue to random loadings, studies and monographs, no. 23, opole university of technology, opole, (1988) (in polish). [4] macha, e., simulations investigations of the position of fatigue plane in materials with biaxial loads, mat.-wiss. u. werkstofftech., 20 (1989) 132-136. [5] carpinteri, a., macha, e., brighenti, r., spagnoli, a., expected principal stress directions for multiaxial random loading part i, theoretical aspects of the weight function method, int. j. fatigue, 21 (1999) 83-88. [6] carpinteri, a, macha, e, brighenti, r, spagnoli, a., expected principal stress directions under multiaxial random loading. part ii: numerical simulation and experimentally assessment through the weight function method. int. j. of fatigue, 21 (1999) 89-96. t z. marciniak et alii, frattura ed integrità strutturale, 34 (2015) 1-10; doi: 10.3221/igf-esis.34.01 10 [7] będkowski, w., macha, e., ohnami m., sakane m., fracture plane of cruciform specimen in biaxial low cycle fatigue – estimate by variance method and experimental verification, journal of engineering materials and technology, 117 (1995) 183-190. [8] macha, e., sonsino, c.m., energy criteria of multiaxial fatigue failure, fatigue fract. engng. mater. struci., 22 (1999) 1053-1070. [9] lagoda, t, macha, e, dragon, a, petit, j., influence of correlations between stresses on calculated fatigue life of machine elements, int. j. fatigue, 18 (1996) 547–555. [10] carpinteri, a, karolczuk, a., macha, e., vantadori, s., expected position of the fatigue fracture plane by using the weighted mean principal euler angels, int. j. of fracture, 115 (2002) 87-99. [11] będkowski, w., macha, e., fatigue fracture plane under multiaxial random loadings – prediction by variance of equivalent stress based on the maximum shear and normal stresses, mat.-wiss. u. werkstofftech., 23 (1992) 82-94. [12] marciniak, z., rozumek, d., macha, e., verification of fatigue critical plane position according to variance and damage accumulation methods under multiaxial loading, int. j. of fatigue, 58 (2014) 84-93. [13] korn, ga, korn tm., mathematical handbook, sec. ed., mc graw-hill book company, new york, (1968). [14] grzelak, j., lagoda, t., macha, e., spectral-analysis of the criteria for multiaxial random fatigue, mat.-wiss. u. werkstofftech., 22 (1991) 85-98. [15] niesłony, a., macha, e., spectral method in multiaxial random fatigue, springer-verlag berlin heidelberg, (2007) 147. [16] neuber, h., theory of stress concentration for shear-strained prismatical bodies with arbitrary nonlinear stress-strain law, asme j. applied mech. 28 (1961) 544-550. [17] molski k., glinka g. a method of elastic-plastic stress and strain calculation at a notch root, mat. sci. and engng. 50 (1981) 93-100. [18] łagoda, t., macha, e., multiaxial random fatigue of machine elements and structures, cyclic energy based multiaxial fatigue criteria to random loading, part iii, studies and monographs 104, opole university of technology, opole, (1998) (in polish). [19] rozumek, d., marciniak, z., fatigue properties of notched specimens made of fep04 steel, materials science, 47 (2012) 462-469. [20] łagoda, t., macha, e., będkowski, w., a critical plane approach based on energy concepts: application to biaxial random tension–compression high-cycle fatigue regime, int. j. fatigue, 21 (1999) 431–443. [21] karolczuk, a., macha, e., critical planes in multiaxial fatigue of materials, monograph. fortschritt-berichte vdi, mechanik/bruchmechanik, reihe 18, nr. 298. düsseldorf: vdi verlag, (2005) 204. [22] manson, s.s., behaviour of materials under conditions of thermal stress, naca tn-2933, (1953). [23] coffin, l.f., a study of the effects of cyclic thermal stresses on a ductile metal, trans. asme 76 (1954) 931-950. [24] basquin, o.h., the experimental law of endaurance test, astm, 10 (1910) 625-630. [25] macha, e., słowik, j., pawliczek, r., energy based characterization of fatigue behavior of cyclically unstable materials, solid state phenomena, 147-149 (2009) 512-517. [26] rozumek, d., macha, e., a survey of failure criteria and parameters in mixed-mode fatigue crack growth, materials science, 45 (2009) 190-210. [27] rozumek, d., macha, e., j-integral in the description of fatigue crack growth rate induced by different ratios of torsion to bending loading in alcu4mg1, mat.-wiss. u. werkstofftech., 40 (2009) 743-749. [28] rozumek, d., mixed mode fatigue cracks of constructional materials, studies and monographs, no. 241, opole university of technology, opole, (2009) (in polish). microsoft word numero 9 art 13 finale l. susmel et alii, frattura ed integrità strutturale, 9 (2009) 125 134; doi: 10.3221/igf-esis.09.13 125 sulla stima della vita a fatica di giunti saldati soggetti a carichi multiassiali ad ampiezza variabile l. susmel dipartimento di ingegneria, università di ferrara, ferrara (italia); ssl@unife.it department of mechanical engineering, trinity college, dublin (ireland) r. tovo dipartimento di ingegneria, università di ferrara, ferrara (italia) d. benasciutti dipartimento di ingegneria elettrica gestionale meccanica, università di udine, udine, (italy) riassunto. nel presente articolo viene proposta una nuova metodologia di progettazione a fatica, basata sull’utilizzo del metodo delle curve di wöhler modificate, per la previsione della vita a fatica di giunzioni saldate, sia in acciaio che in alluminio, soggette a carichi multiassiali ad ampiezza variabile. in particolare, il criterio delle curve di wöhler modificate è stato applicato determinando l’orientazione del piano critico mediante il metodo della massima varianza, ovvero definendo il piano critico come quello contenente la direzione che sperimenta la massima varianza della tensione tangenziale risolta. l’accuratezza della metodologia di progettazione a fatica proposta nella presente memoria è stata valutata mediante due serie di dati sperimentali di letteratura ottenute sollecitando, sia ad ampiezza costante che variabile, giunti saldati tubo-piastra in acciaio e lega di alluminio con carichi di flesso/torsione in fase e sfasati di 90°. il criterio delle curve di wöhler modificate, applicato in concomitanza con il metodo della massima varianza, si è dimostrato capace di fornisce stime accurate della durata a fatica anche in presenza di sollecitazioni multiassiali ad ampiezza variabile, e questo sia quando applicato in termini di tensioni nominali che in termini di tensioni di “hot-spot”. abstract. this paper summarises an attempt of devising a new engineering approach, based on the so-called modified wöhler curve method, suitable for estimating fatigue lifetime of both steel and aluminium welded connections subjected to variable amplitude multiaxial fatigue loading. the maximum variance method is used to determine the orientation of the critical plane and the cycle counting is directly performed in terms of shear stress resolved along the maximum variance direction. the accuracy of the proposed methodology was checked by using two different datasets taken from the literature and generated by testing both steel and aluminium tube-to-plate welded connections under in-phase and 90° out-of-phase variable amplitude bending and torsion. the proposed fatigue life assessment technique was seen to be highly accurate, resulting in estimates falling within the scatter bands of the curves used to calibrate the modified wöhler curve method itself. this seems to strongly support the idea that the proposed approach can be considered as an effective engineering tool, capable of performing multiaxial fatigue assessment under variable amplitude loading by fully complying with recommendations of the available standard codes. keywords. multiaxial fatigue; variable amplitude; weldments. http://www.gruppofrattura.it/ http://dx.medra.org/10.3221/igf-esis.09.13&auth=true mailto: ssl@unife.it l. susmel et alii, frattura ed integrità strutturale, 9 (2009) 125 134; doi: 10.3221/igf-esis.09.13 126 introduzione e strutture saldate sono spesso soggette in esercizio a stati di sollecitazione e/o deformazione multiassiali, responsabili di un danneggiamento in prossimità del cordone di saldatura. fin dalla metà del secolo scorso un'intensa attività di ricerca si è specificatamente rivolta alla formulazione di criteri di calcolo, basati sull'utilizzo di tensioni nominali, strutturali o locali [1-3], applicabili a giunti saldati soggetti a sollecitazioni multiassiali ad ampiezza costante. tuttavia, esistono solo alcuni approcci specificatamente formalizzati per stimare la resistenza a fatica di giunzioni saldate soggette a sollecitazioni multiassiali ad ampiezza variabile [4-7]. riguardo a questo aspetto, è interessante notare che, per sollecitazioni ad ampiezza variabile, alcune normative propongono procedure di calcolo essenzialmente basate sulla combinazione di tensioni normali e tangenziali, e sull'applicazione dell'ipotesi di palmgren-miner, lasciando tuttavia aperta la necessità di una sistematica indagine e verifica sperimentale [8-10]. vista l'importanza di sviluppare metodologie di calcolo efficienti ed accurate utilizzabili nella pratica progettuale per valutare la resistenza a fatica di giunzioni saldate, questo lavoro intende proporre un approccio di piano critico basato sull'uso delle curve di wöhler modificate (cwm) [11-14] applicabile a sollecitazioni multiassiali ad ampiezza variabile. in particolare, l'approccio proposto utilizza congiuntamente il metodo delle cwm ed il metodo della massima varianza (mmv) [15, 16], per stimare la vita a fatica post-processando lo stato di sollecitazione agente sul piano critico, dove la tensione tangenziale viene risolta lungo la sua direzione di massima varianza. l’aspetto più interessante dell'approccio proposto è la possibilità di applicare i metodi di conteggio convenzionali alla tensione tangenziale risolta sulla direzione di massima varianza, estendendo di fatto l'applicabilità dei metodi di calcolo uniassiali a stati multiassiali di tensione. e' importante, infine, evidenziare come l'accuratezza del metodo discusso nel presente articolo è stata verificata considerando dati sperimentali relativi a giunti saldati tubo-piastra in acciaio e lega di alluminio, soggetti ad uno spettro di carico di flesso-torsione in fase ed in quadratura. metodo delle curve di wöhler modificate el metodo delle cwm si assume che la probabilità di nucleazione della cricca di fatica sia massima sul piano dove è massima la variazione della tensione tangenziale, δτ. la complessità dello stato di sollecitazione sul piano critico è poi quantificata combinando la variazione della tensione tangenziale, δτ, e normale, δσn, tramite il seguente indice [11, 12]:    nw , (1) che risulta essere unitario per sollecitazioni monoassiali con r=-1, mentre è uguale a zero per sollecitazioni di torsione alterna. il parametro ρw, inoltre, è correlato al livello di non-proporzionalità della sollecitazione applicata, mentre il suo valore non dipende dalla presenza di tensioni medie non nulle, e questo in accordo con quanto suggerito dalle procedure proposte nelle normative vigenti per giunti non trattati termicamente [8-10]. la stima della vita a fatica in accordo con il metodo delle cwm è illustrata nel diagramma di wöhler modificato di fig. 1a, che riporta le rette che forniscono il numero di cicli a rottura, nf, in funzione della variazione della tensione tangenziale, δτ, per differenti valori di ρw. in particolare, al diminuire di ρw, le rette traslano verso l'alto, indicando una diminuzione del danno a fatica. in altri termini, il metodo delle cwm assume che, per un dato materiale, il danneggiamento a fatica dipenda esclusivamente dai valori di δτ e w, indipendentemente dalla complessità del percorso di carico individuato sul piano critico. ogni curva di wöhler è poi caratterizzata dalla sua pendenza inversa, kτ, e dall'ampiezza di riferimento, a,ref, estrapolata a na cicli a rottura (in accordo con le vigenti normative [8-10], si assume na=2·106 cicli a rottura). il diagramma di wöhler modificato di fig. 1 permette il calcolo della vita a fatica una volta stimate su base sperimentale le correlazioni fra a,ref e ρw e quella fra kτ e ρw. in particolare, adottando una semplice dipendenza lineare è possibile calcolare le costanti sulla base delle curve a fatica a trazione (ρw=1) e a torsione (ρw=0) alterne [11, 12]:     0w0w kkkk  per lim,ww  l n http://www.gruppofrattura.it/ http://dx.medra.org/10.3221/igf-esis.09.13&auth=true l. susmel et alii, frattura ed integrità strutturale, 9 (2009) 125 134; doi: 10.3221/igf-esis.09.13 127     constkk lim,ww   per lim,ww    awaawfre,a 2          per lim,ww      constlim,wfre,awfre,a  per lim,ww  (a) (b) figura 1: (a) diagramma di wöhler modificato e (b) andamento di a,ref e kτ con ρw. il significato dei simboli e l'andamento qualitativo delle funzioni è mostrato in fig. 1b. il precedente diagramma schematico mostra anche l'esistenza di un valore soglia, ρw,lim, oltre il quale si assume che a,ref e kτ restino entrambi costanti. in particolare, numerosi risultati sperimentali confermano che per elevati valori di ρw gli approcci di piano critico tendono a fornire stime troppo conservative, e questo sembra essere dovuto al fatto che, in tali circostanze, il danneggiamento a fatica non è solo correlato alle tensioni tangenziali, ma anche, e in modo molto forte, a quelle normali al piano critico. questo implica che, per valori di ρw elevati, stime accurate possano essere ottenute solo valutando l'influenza delle tensioni normali al piano critico mediante differenti assunzioni. in particolare, si è osservato che in componenti non intagliati ρw,lim è correlato alle proprietà a fatica del materiale ad alto numero di cicli [14, 17], mentre in componenti intagliati (analizzati in termini di tensioni nominali) ρw,lim è più difficilmente quantificabile, dato che le tensioni sopraccitate hanno scarsa correlazione con i fenomeni fisici responsabili della fase di nucleazione della cricca di fatica. quando il metodo delle cwm viene utilizzato per stimare la vita a fatica in componenti saldati, si suggerisce sempre l’utilizzo di valori di ρw,lim compresi nell’intervallo 1.4÷1.5, e questo valutando lo stato tensionale sia in termini di quantità nominali, che in termini di grandezze strutturali. metodo della massima varianza n sollecitazioni random uniassiali, sia gaussiane che non-gaussiane, il danno a fatica è proporzionale alla varianza [1821]. il metodo della massima varianza (mmv) assume che il piano di massimo danneggiamento a fatica coincida con il piano contenente la direzione dove la tensione tangenziale risolta ha varianza massima [14-16]. con riferimento a fig. 2, è assegnato il piano δ di normale n , su cui sono individuati i versori a e b , caratterizzati, nel sistema di riferimento oxyz, dai seguenti coseni direttori:                          )cos( )sin()sin( )cos()sin( n n n n z y x ,                         0 )cos( )sin( a a a a z y x ,                          )sin( )sin()cos( )cos()cos( b b b b z y x (3) i (2) http://www.gruppofrattura.it/ http://dx.medra.org/10.3221/igf-esis.09.13&auth=true l. susmel et alii, frattura ed integrità strutturale, 9 (2009) 125 134; doi: 10.3221/igf-esis.09.13 128 l'orientazione di una generica retta m appartenente al piano δ è individuata dall'angolo ξ:                          )sin()sin( )sin()cos()sin()cos()cos( )cos()cos()sin()sin()cos( m m m m z y x (4) la tensione tangenziale τm(t) risolta lungo m può pertanto essere calcolata come:                          )sin()sin( )sin()cos()sin()cos()cos( )cos()cos()sin()sin()cos( m m m m z y x (5) definendo ora il vettore delle tensioni come:  )t()t()t()t()t()t()t(s yzxzxyzyx  (6) la tensione tangenziale risolta lungo m può essere direttamente calcolata a mezzo del seguente prodotto scalare: )t(sd)t(m  , (7) dove d è un vettore dei coseni direttori di facile determinazione (si omette l'espressione). figura 2: definizione delle grandezze utilizzate dal mmv. in termini generali, la varianza della tensione tangenziale risolta τm(t) può scriversi come:            i j jiji k kkm )t(s),t(scovdd)t(sdvar)t(var (8) dove per i=j si ottengono termini di varianza, cov[si(t),sj(t)]=var[si(t)], mentre per i≠j si hanno termini di covarianza. definendo, infine, la matrice di covarianza come:     ts,tscovc jiij  (9) è possibile riscrivere formalmente l'eq. (8) in modo compatto, ovvero: http://www.gruppofrattura.it/ http://dx.medra.org/10.3221/igf-esis.09.13&auth=true l. susmel et alii, frattura ed integrità strutturale, 9 (2009) 125 134; doi: 10.3221/igf-esis.09.13 129   d]c[d)t(var tm  (10) nell'ipotesi che il piano critico contenga la direzione dove τm(t) ha varianza massima, è immediato utilizzare la eq. (10) per individuare tale piano mediante i coseni direttori rappresentati dal vettore d , e calcolare così in modo diretto anche le grandezze ad esso correlate. analisi di sollecitazioni multiassiali ad ampiezza variabile oti i vettori n , m che definiscono il piano critico e la direzione di massima varianza, è possibile ricondurre una storia temporale del tensore delle tensioni alle storie di carico della tensione tangenziale risolta, τ(t), e della tensione normale al piano critico, σn(t). questa semplificazione permette, pertanto, di estendere i metodi di conteggio monoassiali (es. rainflow) al caso multiassiale. in particolare, per la semplice storia temporale in fig. 3a è immediato individuare per ogni ciclo i range della tensione tangenziale, δτ(t), e normale, δσn(t), e quindi calcolare l'indice w,i, w,j,..., con cui determinare, attraverso le relazioni (2), le corrispondenti curve di resistenza. per ogni valore di w, ed individuato lo spettro di carico, si può quindi calcolare prima il danno di ogni singolo ciclo contato, poi il danno totale nell'ipotesi di palmgren-miner, ovvero: ...dd...d..., )(n n d, )(n n d jitot j,wf j i,wf i      (11) dove i cicli a rottura nf(w,i), n=(w,j) si valutano sull'opportuna curva di wöhler modificata, individuata dal particolare valore di w considerato (vedere fig. 1). (a) (b) (c) figura 3: (a) esempio di conteggio per una storia di carico semplice; (b), (c) esempi di conteggio per storie di carico più complesse. l'esempio di fig. 3a, in quanto molto semplice, permette l'individuazione univoca dei cicli. per sollecitazioni più complesse, invece, il conteggio dei cicli può risultare non solo poco agevole ma anche ambiguo. in fig. 3b, per esempio, ad un singolo ciclo della tensione τ(t) sono associati più cicli di σn(t), così che la definizione di σn(t) non è evidentemente univoca. in modo simile, in fig. 3c un singolo ciclo di ampiezza δσn(t) caratterizza più cicli della tensione τ(t), rendendo difficile il calcolo del corrispondente w per ogni ciclo in τ(t) contato. questo suggerisce che ulteriori studi di tipo teorico/sperimentale debbano essere condotti onde formalizzare delle procedure che consentano di eseguire il conteggio dei cicli anche in presenza di storie di carico multiassiali estremamente complesse. confronto con i dati sperimentali prescindere dai problemi ancora aperti menzionati alla fine del precedente paragrafo, la precisione del metodo proposto è stata verificata utilizzando i dati sperimentali riportati in [5, 6] e ottenuti sollecitando, sia ad ampiezza costante che variabile, giunti saldati tubo-piastra in acciaio e lega di alluminio, con carichi di flesso-torsione in n a http://www.gruppofrattura.it/ http://dx.medra.org/10.3221/igf-esis.09.13&auth=true l. susmel et alii, frattura ed integrità strutturale, 9 (2009) 125 134; doi: 10.3221/igf-esis.09.13 130 fase e sfasati di 90° (dove il rapporto fra l'ampiezza della tensione tangenziale nominale rispetto alla tensione nominale flessionale era costante ed uguale a 0.58). in altre parole, da un punto di vista del conteggio dei cicli, il metodo proposto è stato valutato con storie di carico del tipo riportato in fig. 3a, ovvero in condizioni in cui il conteggio dei cicli in (t) e la determinazione del corrispondente valore di w è univoca. per sollecitazioni di sola flessione o torsione ad ampiezza costante, la fig. 4 mostra come le curve fornite dall’iiw [10], riferite alle tensioni nominali, forniscano, in genere, stime conservative, aspetto peraltro confermato dai valori riportati in tab. 1, dove le curve sperimentali (per un livello di confidenza del 95%), espresse come resistenza a na=2·106 cicli a rottura e pendenza inversa k, sono confrontate con i corrispondenti valori delle curve di normativa. i dati sperimentali ad ampiezza variabile qui utilizzati per validare il metodo proposto considerano uno spettro di carico gaussiano di 5·104 cicli complessivi (si veda [5, 6]). materiale risultati sperimentali tensioni nominali tensioni strutturali ('hot-spot') a,50% k a,50% k0 a a,50% k a a,50% k0 a a,50% k a a,50% k0 [mpa] [mpa] [mpa] [mpa] [mpa] [mpa] [mpa] [mpa] [mpa] [mpa] ste460 209.8 4.3 178.6 4.9 90 129.6 3 100 144.0 5 90 129.6 3 100 144.0 5 al 6082 86.8 6.8 77.0 6.1 32 46.0 3 36 51.8 5 36 51.8 3 36 51.8 5 tabella 1: curve a flessione e torsione utilizzate per calibrare il metodo delle cwm. il criterio delle cwm è stato inizialmente utilizzato per stimare la vita a fatica (in termini di tensioni nominali) dei giunti saldati in acciaio sollecitati ad ampiezza costante, calibrando il criterio stesso con i dati sperimentali uniassiali ed a torsione riportati in tab. 1. le costanti di calibrazione sono invece elencate in tab. 2. il confronto fra durata sperimentale, nf, e durata stimata, nf,e, mostrato in fig. 5a conferma che, assumendo un valore di w,lim pari a 1.4, le stime fornite dal metodo delle cwm per sollecitazioni biassiali ad ampiezza costante cadono all'interno delle banda di dispersione delle due curve (uniassiale e torsionale) utilizzate per calibrare il metodo stesso. figura 4: confronto fra le curve di normativa iiw [10] ed i risultati sperimentali di [5, 6]. per quanto concerne invece i risultati ottenuti con sollecitazioni ad ampiezza variabile con spettro gaussiano, il metodo delle cwm è stato applicato nell'ipotesi (come suggerito in [5]) di un valore pari a 0.35 per il danno critico nella somma di palmgren-miner. la fig. 5b mostra chiaramente che, per sollecitazioni biassiali ad ampiezza variabile, il metodo proposto, basato sulle cwm ed il mmv, fornisce stime di durata che cadono all'interno della banda di dispersione definita dalle due curve ad ampiezza costante usate per calibrare il metodo stesso. http://www.gruppofrattura.it/ http://dx.medra.org/10.3221/igf-esis.09.13&auth=true l. susmel et alii, frattura ed integrità strutturale, 9 (2009) 125 134; doi: 10.3221/igf-esis.09.13 131 1000 10000 100000 1000000 1 0000000 10 0000000 100 0 1 0000 1000 00 100000 0 1 0000000 1000000 00 n f, e [cyc les] nf [cyc les] uniaxial torsion in-ph as e 90° out-o f-ph as e p s=90% ps=10% non-c onservativ e conserv ative torsional s catter band uniaxial scatt er band r = -1 steel vari able ampli tu de d = 0 .35 materiale risultati sperimentali tensioni nominali tensioni strutturali ('hot-spot')  β a b  β a b  β a b w,lim [mpa] [mpa] [mpa] [mpa] [mpa] [mpa] ste460 -73.7 178.6 -0.6 4.9 -79.2 144.0 -2 5 -79.2 144.0 -2 5 1.4 al 6082 -33.6 77.0 0.7 6.1 -28.8 51.8 -2 5 -25.9 51.8 -2 5 1.4 tabella 2: costanti di calibrazione del metodo cwm in accordo a tre differenti approcci. (a) (b) figura 5: stime per sollecitazioni ad ampiezza costante (a) e variabile (b), dove il metodo cwm è calibrato sui dati sperimentali di tab.1 ed applicato in tensioni nominali. (a) (b) figura 6: time per sollecitazioni ad ampiezza costante (a) e variabile (b), dove il metodo cwm è calibrato sulle curve di normativa iiw ed applicato in tensioni nominali. per verificare, successivamente, se il metodo proposto fornisce stime di durata in accordo con le normative vigenti, il metodo stesso è stato applicato, ancora in termini di tensioni nominali, al set di dati sperimentali già considerato in precedenza, ma utilizzando le curve di resistenza uniassiale e torsione fornite, per le geometrie adottate, dall’iiw [10]. si noti che le costanti di calibrazione (, β, a, b) riportate in tab. 2 sono state ottenute ricalcolando le curve sperimentali di normativa per una probabilità di sopravvivenza, ps, pari al 50%. come confermato in fig. 6a, il metodo proposto fornisce stime generalmente accurate, in particolare per la zona ad alto numero di cicli, anche quando è calibrato con le curve di normativa. per quanto concerne infine i risultati per sollecitazioni biassiali con spettro gaussiano, la fig. 6b mostra che, assumendo un valore del danno critico unitario nella sommatoria di palmgren-miner, si ottengono stime in buon accordo con i risultati sperimentali.   1000 10000 100000 1000000 1 0000000 10 0000000 100 0 1000 0 100000 1 000000 100 00000 10000 0000 nf ,e [ cycles] nf [c ycles] un iaxial tors ion in-phase 90° out -of-phase ps=97.7% ps=2.3% non-c onservativ e conse rv ativ e tors io nal scatt er band uniaxial scatter band r = -1 steel constan t am pli tude 1000 10000 100000 1000000 1 0000000 10 0000000 1000 10000 1000 00 100 0000 10 000000 1000 00000 nf ,e [ cycles] nf [c ycle s] uniaxial torsion in-phas e 90° ou t-of-phas e ps=97.7% ps=2.3% non-conservative c onserv ativ e tors io nal scatt er band un iaxial scatt er band r = -1 steel vari abl e am pli tude d = 1   1000 10000 100000 1000000 1 0000000 10 0000000 10 00 10000 10 0000 1000000 10 000000 1000000 00 nf,e [c ycles] nf [cy cles] uniaxial torsion in-phas e 90° out-of-p has e ps=90% ps=10% non-conserv ativ e c onserv ativ e tors ional scat ter ban d uniaxial scat ter band r = -1 steel constan t am pli tude http://www.gruppofrattura.it/ http://dx.medra.org/10.3221/igf-esis.09.13&auth=true l. susmel et alii, frattura ed integrità strutturale, 9 (2009) 125 134; doi: 10.3221/igf-esis.09.13 132 i buoni risultati ottenuti considerando giunti saldati in acciaio, ci hanno incoraggiato a provare ad applicare la medesima metodologia anche per la stima della vita a fatica multiassiale di giunti saldati tubo-piastra in lega di alluminio, i cui risultati sperimentali sono peraltro caratterizzati da una maggiore dispersione statistica. a titolo di esempio, il diagramma di fig. 7a confronta i risultati sperimentali ad ampiezza variabile con spettro gaussiano con le stime fornite dal metodo cwm applicato in tensioni nominali, dove il metodo stesso è calibrato sui dati sperimentali uniassiali ed a torsione di tab. 1 (le costanti di calibrazione sono riportate in tab. 2), e dove si assume, come suggerito in 0, un valore di 0.6 per il danno critico nella sommatoria di palmgren-miner. per concludere, la fig. 7b mostra il confronto complessivo fra risultati sperimentali ad ampiezza variabile e le stime fornite dal metodo cwm applicato in termini di tensioni strutturali ('hot-spot'). i risultati sperimentali e le costanti di calibrazione sono riportate in tab. 1 e tab. 2, rispettivamente. come si può osservare, anche nel caso dell'approccio in tensioni strutturali il metodo proposto è in grado di fornire stime accurate, che comunque cadono all'interno delle bande di calibrazione, e questo sia per giunti saldati in acciaio che in lega di alluminio. (a) (b) figura 7: (a) stime per sollecitazioni ad ampiezza variabile su giunti in lega di alluminio, in cui il metodo cwm è calibrato sui dati sperimentali di tab. 1ed applicato in tensioni nominali. (b) stime per sollecitazioni ad ampiezza variabile, in termini di tensioni strutturali ('hot-spot'). conclusioni risultati illustrati nel presente lavoro permettono di trarre le seguenti conclusioni: 1) il metodo delle cwm fornisce stime accurate della durata a fatica di giunzioni saldate in acciaio e lega di alluminio soggette a sollecitazioni multiassiali ad ampiezza variabile; 2) le stime fornite dall'approccio proposto, sia in termini di tensioni nominali che strutturali ('hot-spot'), si sono rivelate in buon accordo con le normative vigenti; 3) è necessario approfondire lo studio del problema della definizione dei cicli in presenza di sollecitazioni multiassiali ad ampiezza variabile allo scopo di formalizzare metodi di conteggio che consentano di stimare il danneggiamento a fatica in modo rigoroso ed univoco. appendice a: formule esplicite per sollecitazioni biassiali er una sollecitazione biassiale σx(t), τxy(t), il piano critico è sempre perpendicolare al piano x-y in fig. 2 (  90 ,  0 ), mentre la tensione tangenziale risolta dipende solo da  : )t()2cos()t( 2 )2sin( )t( xyxm    (a.1) i p   100 0 1000 0 10000 0 100000 0 1000000 0 1 0000000 0 1 000 10000 10 0000 100000 0 100 00000 1 000000 00 nf,e [cy cles] nf [cy cles] uniaxial in-phas e out -of-phase p s=90% p s=10% n on-c onservativ e c onservativ e torsional scatter band uniaxial scatter band r = -1 alu mi ni um vari able ampl itu de d = 0 .6 100 0 1000 0 10000 0 100000 0 1 000000 0 10 000000 0 10 00 10 000 100000 1000 000 10 000000 10 0000000 nf,e [c ycle s] nf [c ycles] steel, in-ph as e steel, out-of-phas e alumin ium, in-ph as e alumin ium, out-of-phas e ps=97.7% ps=2.3% non-conserv ative c onservative tors ional scatt er band un iaxial scatt er ban d r = -1 variabl e ampl itu de d = 1 http://www.gruppofrattura.it/ http://dx.medra.org/10.3221/igf-esis.09.13&auth=true l. susmel et alii, frattura ed integrità strutturale, 9 (2009) 125 134; doi: 10.3221/igf-esis.09.13 133 analogamente, anche la varianza di τm(t) dipende solo da  :       , 2 2 m c)2cos()2sin(v)2cos(v 4 )2sin( )t(var (a.2) dove vσ=var[σx(t)], vτ=var[τxy(t)] e cσ,τ=cov[σx(t),τxy(t)]. uguagliando a zero la derivata prima di eq. (a.2), si ottengono le direzioni di massima varianza per τm(t), tab. 3. nel caso particolare di sollecitazioni biassiali sinusoidali sincrone sfasate (δ è lo sfasamento): )tsin()t( )tsin()t( a,xyxy a,xx   (a.3) con 2/v 2 a,x , 2/v 2 a,xy , 2/)cos(c a,xya,x,  , le direzioni di massima varianza sono ottenibili utilizzando i risultati di tab. 3, posto cσ,τ=δx,xy (δx,xy=π/2, δx,xy≠π/2) e:    a,xya,x 2v4v   ;           2 a,xy 2 a,x a,xya,x 0 4 cos4 arctan 4 1 (a.4) 0c ,  0c ,    04   vv 2 0   i 2  i   04   vv 28 3  i qualunque    04   vv 24 0   i       24  i dove           vv c 4 4 arctan 4 1 , 0 , ...,2,1,0i  tabella 3: angoli  per la direzione di massima varianza per sollecitazioni biassiali bibliografia [1] d. radaj, c. m. sonsino, w. fricke, fatigue assessment of welded joints by local approaches, woodhead publishing limited, cambridge, uk (2007). [2] m. bäckström, g. marquis, fatigue fract. engng. mater. struct., 24 (2001) 279. [3] m. kueppers, c. m. sonsino, fatigue fract. engng. mater. struct. 26 (2003) 507. [4] c. m. sonsino, r. pfohl, int. j. fatigue, 12 (1990) 425. [5] c. m. sonsino, m. kueppers, fatigue fract. engng. mater. struct., 24 (2001)309. [6] m. kueppers, c. m. sonsino, int. j. fatigue, 28 (2006) 540. [7] c. m. sonsino, int. j. fatigue 31 (2009) 173. [8] anon., design of steel structures. env 1993-1-1, eurocode 3, (1988). [9] anon., design of aluminium structures – part 2: structures susceptible to fatigue. env 1999, eurocode 9, (1999). [10] a. hobbacher, recommendations for fatigue design of welded joints and components. iiw document xiii-215107/xv-1254-07, (2007). [11] l. susmel, r. tovo, fatigue fract. engng. mater. struct., 27 (2004) 1005. [12] l. susmel, r. tovo, int. j. fatigue, 28 (2006) 564. [13] l. susmel, p. lazzarin, fatigue fract. engng. mater. struct., 25 (2002) 63. [14] p. lazzarin, l. susmel, fatigue fract. engng. mater. struct., 26 (2003)1171. [15] w. bedkowski, e. macha, m. ohnami, m. sakane, j. eng. materials and technology, 117 (1995) 183. [16] k. bel knani, d. benasciutti, a. signorini, r. tovo, int. j. materials product tech., 30 (2007) 172. http://www.gruppofrattura.it/ http://dx.medra.org/10.3221/igf-esis.09.13&auth=true l. susmel et alii, frattura ed integrità strutturale, 9 (2009) 125 134; doi: 10.3221/igf-esis.09.13 134 [17] l. susmel, r. tovo, p. lazzarin, int. j. fatigue, 27 (2005) 928. [18] s. sarkani, d. p. kihl, j. e. beach, prob. engng. mech., 9 (1994) 179. [19] d.p. kihl, s. sarkani, j.e. beach, int. j. fatigue, 17(5) (1995) 321. [20] d. benasciutti, r. tovo, int. j. fatigue, 27 (2005) 867. [21] d. benasciutti, r. tovo, prob. engng. mech., 20 (2005) 115. http://www.gruppofrattura.it/ http://dx.medra.org/10.3221/igf-esis.09.13&auth=true microsoft word numero_34_art_9 i. ivanova et alii, frattura ed integrità strutturale, 34 (2015) 90-98; doi: 10.3221/igf-esis.34.09 90 focussed on crack paths static and dynamic experimental study of strengthened reinforced short concrete corbel by using carbon fabrics, crack path in shear zone i. ivanova university of reims champagne-ardenne, reims, france ivelina_ivanova82@hotmail.com j. assih university of reims champagne-ardenne, reims, france jules.assih@yahoo.com abstract. the paper presents an experimental analysis of tracking the path of the cracks and crack growth in strengthened or repair reinforced concrete short corbels bonded by carbon fiber fabrics under static and dynamic loads. the reinforced short concrete corbel is a used precast element, for industrial buildings and structures. in fact, their functioning interestingly unconventional is compared to classical beam type elements. then the effects of bending and shearing are combined in this case. the horizontal reinforced steel is localized to resist to tensile strength induced in bending top and a transversal strength-absorbing contribution. the introduction of carbon fiber composite in the field of civil engineering allows to strengthen or repair reinforced concrete structures using adhesive. so the carbon fiber material has many advantages as its low weight, flexibility, easier handling and also interesting physicochemical properties. however maintenance of civil engineering works is to protect them by ensuring better sealing or limiting corrosion. then strengthening is to repair structures by using bonding technique to compensate their rigidity loss and limit the cracking. this allows to improve their performance and durability. bonding of composite material in tensile zone of corbel retrieves most tensile stress and allows the structure to extend their load-bearing capacity. the local behavior of the structure is measured by means of the extensometer technique based on electrical strain gauges. this technique allowed to measure strains of steel, carbon fiber fabrics and concrete. the results of this investigation showed that strengthened reinforced concrete corbel bonded by carbon fiber fabrics can improve the ultimate load to twice and stiffens less than a third. the ultimate load, strain and displacement of the specimen are compared to reference experimental model of monotonic and cyclic applied loads. the success of strengthening depends strongly on surface preparation conditions. the cracking mechanisms and collapse modes under static and dynamic loadings are presented. the strengthened reinforced concrete short corbel behavior can be presented in three areas: overall elastic area, crack propagation area and opening of diagonal crack area. keywords. strengthening; short corbel; composite materials; reinforced concrete; mechanism of crack; failure. i. ivanova et alii, frattura ed integrità strutturale, 34 (2015) 90-98; doi: 10.3221/igf-esis.34.09 91 introduction n the 20th century the people believed that concrete is eternal material. nonetheless today everyone knows that all concrete structures and elements have a certain service life. during their life the original quality and sustainability changed. in fact it's necessary to have a good deal of knowledge about the mechanical properties and mechanical behavior of reinforced concrete structures [1] under different environmental conditions. it allows to take timely measures for the protection and extend the life of reinforced concrete. the reinforced concrete short corbel is one important element as cast monolithic with the column element to wall element like demonstrated by ivanova and all [2-4]. corbels are used very often in industrial buildings and structures. for example: a participating corbel in reinforced concrete bridge construction lay on the structural elements of the bridge superstructure (beams and plates). then they are subjected to repeat varying load of traffic [10]. these stresses on a large scale can lead to reaching the ultimate limit state of fatigue. indeed the strengthening of concrete elements operating under static and dynamic loads is of special interest for the following reasons: cyclically variable dynamic load caused uniquely or dual significance stress and strain state. the intensity and diversity of dynamic load action create conditions for specific behavior of reinforced concrete elements [8]. then also the joint work between reinforced concrete and composite material allowed a resumption of fatigue stresses. the development of new technologies using composite materials leads to improve the load carrying capacity and the mechanical properties of reinforced elements. it is possible also to increase flexural and shear strength to reduce deformations and cracks expected [9, 11]. the carbon fiber fabrics as external reinforcement are bonded with epoxy resin which resumed tensile stress in the fiber direction. in award, carbon fiber materials are characterized by a low specific gravity, a high tensile strength, fatigue performance and anti-corrosion. this paper presents an experimental study of strengthened reinforced short concrete corbels under static and dynamic loads. the carbon fiber fabrics is applied on a tensile zone where it is located and available supporting tensile steel. so carbon fiber fabrics absorbed more tensile stresses and provided a high strength of element [5, 6 and 7]. based on the inventory of researches have concluded that reinforcement with carbon fiber fabrics reduced appearance and spread of cracks, provided greater durability and higher maximum load. experimental program our reinforced short concrete corbels are tested. among them two specimens without reinforcement and the other two specimens are strengthened by externally bonded carbon fiber fabrics in wrapping. the experimental study is investigated to study the crack path and crack growth in reinforced short concrete corbel. this study is compared with repaired reinforced short concrete corbel bonded with carbon fiber fabrics under static and dynamic loads. the objective of this study was to exhibit strengthened reinforced concrete corbel behavior under repeated load. then, this study is compared with strengthened reinforced concrete behavior under static loading. then this paper described also the ultimate load versus the cracking mechanisms and the failure modes. test specimens geometry he column supporting two short trapezoidal corbels cantilevering on either side was 150 mm by 300 mm in cross section and 1000 mm of length. corbels had cantilever projection length of 200 mm, with thicknesses of 150 mm at both faces of column and in the free end. all reinforced concrete corbel specimens have the same sizes and are strengthened reinforced concrete corbels in the same way detailed as in fig. 1. for all specimens are tested using a single load with a shear span to depth ratio a/d equal to 0.45. the control specimen without strengthening is denoted "c0", the first letter "c" means corbel and "0" zero indicates without strengthening. the name of strengthened reinforced concrete corbel "cb3u" is made up as follows: the first letter "c" is, as previously corbel and the second letter represents the type of strengthening (e.g.: b for bandage). then digit indicates the number of layers (e.g.: 3) and the small letter indicates finally the type of composite material (e.g. u for unidirectional). i f t i. ivanova et alii, frattura ed integrità strutturale, 34 (2015) 90-98; doi: 10.3221/igf-esis.34.09 92 figure 1: details of corbel geometry and steel frame. materials ormal strength concrete materials are rolled gravel, dried sand and ordinary portland cement. the cement:sand:gravel proportion in the concrete mix are 1:1.73:2.93 by weight and the water/cement ratio is 0.50. portland cement type cem ii is used and the maximum size of the aggregate is 12.5 mm. five concrete cylinders 160 mm x 320 mm are also cast and tested when each short corbel is tested to find the compressive strength of concrete at 28 days of age. the actual mean compressive strength was 33 mpa, young module of 30 gpa and poisson's ratio is equal to 0.25. steel bars, s500 are used for different diameters: 6, 10, 14 mm. the steel specimens were characterized by simple tensile test. the stress fu and the modulus of elasticity es are obtained to 610 mpa and 210 gpa. the poisson's ratio is equal to 0.29. the high strain in the user steel at the failure is 11.04%. in fact the experimental results of unidirectional carbon fiber fabrics are given by failure tensile stress of 2000 mpa, elastic modulus of 232 gpa, poisson ratio of 0.42 and the high strain of 9182.10-6. but, the glue used for carbon fiber fabrics and for bonding technics are generally into two parts: a resin and a hardener. then, they are mixed. the glue had an elastic modulus of 8.7 gpa and yield stress of 19 mpa. in according of experimental results yield strength corresponds to the tensile strength. finally, the carbon composite sheets have a linear elastic behavior up to failure. preparation of the bonded surface and testing procedure surface preparation and bonding of carbon fiber fabrics. he surface preparation was of primary importance and calls for care. however, preparation of the concrete surfaces must be carried out to remove any loose or weak material, oil, grease etc... in this case grit blasting was a good method, fig. 2a. the four corners of the corbel are rounded to reduce the decrease in strength and to prevent tearing of composite material. preparation of surface should be carried out just prior to the bonding operation to prevent any contamination. after, the contamination can be avoided by applying glue on concrete and carbon fiber fabrics is applied. the concrete surface already become roughened and then leveled before sticking on the wraps using epoxy adhesive. pressure must be applied to squeeze out excess glue and held the plate in place until the glue has hardened. the epoxy adhesive used was sikadure-330 composed of two components laminating compound on epoxy resin. resin components a and b were thoroughly mixed at a ratio 4:1 proportion. the resin and hardened glue is just mixed before the gluing operation, because, the pot life is not long. the greater the amount of material mixed, the shorter was the pot life. to achieve a longer pot life at high ambient temperatures, the mix may be divided into smaller units or the components cooled before mixing. so, epoxy is applied on concrete with a brush and then, fabric is placed on epoxy. second coat of epoxy is rolled into the fabric like fig. 2b. the fabric is wrapped completely around the corbel and the fabric is overlapped on the face of the corbel. pressure must be applied to squeeze out excess glue. n t i. ivanova et alii, frattura ed integrità strutturale, 34 (2015) 90-98; doi: 10.3221/igf-esis.34.09 93 then the second strip of fabric is applied and a third coat of epoxy is rolled into the second strip of fabric. the epoxy is allowed to cure well before testing. a) b) figure 2: details of bonding system of: a) sandblasting of corbels and b) application of carbon fiber on concrete surface by wrapping. testing procedure with "wishay measure" of 24 ways, all data of local strain of electric gauges are saved at different points of structure. all corbels are tested under three points blending load. so, at each test, strain of concrete, carbon fiber fabrics, steel bar and cracking system are noted. the measures of deformation are done at embedding section where strains are high. all tests are performed with a loading speed average of 0.2 kn/s. the data acquisition is recorded every 0.1 second. the maximum load capacity of bending test is 1000 kn. firstly, the reference specimen without strengthening is submitted to a vertical load under static loading to collapse. this test enabled to determine the three specific areas: elastic area, crack propagation area and open diagonal crack area showed in fig. 3. knowing the load-strain curve, an average value of load is defined. this value is corresponded to average load in between 20 % to 40 % of maximum tensile strength. the magnitude and number of fatigue of the repeated loads are fixed to one million cycles. figure 3: mechanical behavior of reinforced concrete corbel c0, strain of tensile steel bar. i. ivanova et alii, frattura ed integrità strutturale, 34 (2015) 90-98; doi: 10.3221/igf-esis.34.09 94 the results allowed to know when the first crack appeared. this crack is created before fatigue loading. the changed slope is proof that a crack is created. in fact, this study needs to follow crack propagation. initially, the unarmed concrete corbel is charged up to the initiation of the first crack. it is characterized by a change in slope and then a second time, is applied a triangular signal with a mean stress up to one million cycles. triangular signal is applied with a mean stress. next, reinforced concrete short corbel is subjected to cyclic loading up to one million cycles. after one million cycles, reinforced concrete corbel was static loading until failure. secondly, it was the same proceeding with strengthened reinforced concrete corbel "cb3u". tab. 1 shows values of ultimate load fu, minimal load fmin and maximal load fmax in between 20 % and 40 % of maximum load fu. in fact, with a cyclic load in this range, the development of crack can be followed. the previous experimental study identified the occurrence of cracks and their propagations. fu (kn) fmin(kn) 20% fmax(kn) 40% reference corbel: c0 357 71.4 142.8 strengthened corbel by wrapping: cb3u 651 130.2 260.4 table 1: conditions of fatigue load. experimental results and discussions he results showed for static test the ultimate tensile strengths are respectively 357 kn for reinforced concrete corbel without strengthening and 651 kn for strengthened reinforced concrete corbel bonded by wrapping carbon fiber fabrics. figure 4: effect of fatigue on reinforced concrete corbels under static tests. influence of static and dynamic loadings on reinforced concrete corbels behavior fig. 4 described the comparison of behavior between reinforced concrete corbels "c0" loaded in static and dynamic tests. there is a change in slope at 60 kn for unstrengthened corbel in static loading. in fact, after one million cycles of fatigue, t i. ivanova et alii, frattura ed integrità strutturale, 34 (2015) 90-98; doi: 10.3221/igf-esis.34.09 95 the reinforced concrete corbel is loaded in simple tensile test to failure. after dynamic loading the curves showed that the range elastic area was lost. the diagonal crack appears at 254 kn more lately than without fatigue at 235 kn as shown in fig. 4. the fatigue changed the stress distribution in the concrete corbel therefore cracking so, the structure is consolidated further. after one million cycles, the tensile ultimate load of reinforced concrete corbel was 381 kn. however, the test results showed an increase load of 6 % compared with reinforced concrete corbel static loading. of course, it would be a little impact on the ultimate failure load after one million cycles. the fatigue results of reinforced concrete corbels on fig. 5, showed that strains of steel tie are very small (less than 200.106) after one million cycles. the jack displacement was also smallest. one million cycles did not enough increasing to failure. in fact, the experimental tests will continue up to one million cycles. there would be little influence on the ultimate tensile strength of strengthened reinforced concrete corbel after one million cycles. figure 5: strains of steel bar in cross section and support load point of corbel ("c0" fatigue). figure 6: strains of steel and carbon fiber fabrics of strengthened corbels under fatigue test. i. ivanova et alii, frattura ed integrità strutturale, 34 (2015) 90-98; doi: 10.3221/igf-esis.34.09 96 influence of cyclic load on strengthened reinforced concrete corbels behavior two strengthened reinforced concrete corbels are tested in static and dynamic loads. the failure load of strengthened reinforced concrete corbel after one million cycles, was 584 kn with fatigue test and 651 kn with static test. that was 11 % less than reinforced concrete corbel under a simple bending test. the carbon fiber fabrics included the strain of structures about 400.10-6 while the steel bar is deformed less than 200.10-6 as shown in fig. 6. the appearance of bearing at 365 kn physically characterized by diagonal and deformations reached at 600.10-6. the carbon fibre fabrics have resumed strain of structure. the strain of steel tie at mounting section is relatively small in the range of 100.10-6 as shown in fig. 6. the strain at point g1 pulling close cross section where strains are highest. deformations are sufficient to cause the disorder in the structure. the investigating did not show failure of carbon fabrics. the strain of carbon fibres fabrics at point gc1, the same position like g1, at least 400.10-6 between in fig. 6 of 900.10-6 to 1300.10-6, is insufficient to generate cracks in strengthened reinforced concrete corbel. cracking and mode of failure fig. 7 shows two reinforced concrete corbels "c0" (fig. 7 a) and "c0 fatigue" (fig. 7 b). the first one is tested up to failure without fatigue and the second one is tested after one million cycles in bending load to collapse. the results showed a new crack is appeared after fatigue testing. many apparent cracks are showed on reinforced concrete corbel. the difference is depending on the type of loading. their propagations are different into static tests which proves the fatigue effect with the appearance of a diagonal crack in the concrete column, see fig. 7b. a) "c0" static test without fatigue b) "c0" static test after fatigue figure 7: cracking and failure of reinforced concrete corbel: a) c0 static loading to failure, b) c0 fatigue after one million cycles of unreinforced concrete corbel. the results show in fig. 8, the cracking and failure modes of strengthened reinforced concrete corbels. after static test, the specimen ruptured in shearing and splitting failures fig. 8a. strengthened corbel after one million cycles has no visible cracks, when the corbel is strengthened by wrapping, fig. 8b. in fact, the results show the same failure cracks as cb3u static test. conclusion his study focused on the strengthening of reinforced concrete short corbel bonded by composite carbon fiber fabrics. particularly, this paper investigates the effect of damaged fatigue test of strengthened structure. so, this influence of fatigue damage on mechanical behavior and durability of strengthened reinforced concrete corbel under three-point bending test are examined. the adhesion is assumed to be perfect for this type of loading, fatigue is t i. ivanova et alii, frattura ed integrità strutturale, 34 (2015) 90-98; doi: 10.3221/igf-esis.34.09 97 taken into account for the concrete in compression and tensile reinforcement through wöhler curves associated with the accumulation to deal with law. a) cb3u static test without fatigue b) cb3u after one million cycles figure 8: cracking and failure in strengthened concrete corbel. a) cb3u-static loading to failure, b) cb3u -after one million cycles. this paper interested of reinforced short concrete jacket having a defect such as an undersized tensile steel. carbon fiber fabrics have interesting properties and offer the user new opportunities in the civil engineering sector. the preparation of concrete surface described by ivanova and all [12], was very important in gluing success. the specimens are instrumented with sensors strain electric gauges which allowed to follow strains in several carefully selected points. in fact, the results show a significant improvement of the ultimate load capacity of up to twice the value obtained by an unstrengthened reinforced corbel. it is increased third of rigidity of strengthened reinforced concrete corbel by wrapping. the fatigue test had a definite influence on the cracking of reinforced concrete corbel and modified stresses in the specimen. but, the mechanical damage has little effect on ultimate load. of course, in this case of reinforced concrete corbel, after fatigue damage, the ultimate load is substantially the same as to undamaged reinforced concrete corbel. the results show also that, the effect of fatigue on reinforced concrete short brackets, in a substantially lower tensile strength to 10 % relative to reinforced concrete short corbel load under monotone static test. the experimental results of this study are interesting and must be completed by further tests to highlight the significant damage parameters in the numerical and analytical modeling of strengthened corbel. references [1] robinson, j.r., l’armature des consoles courtes. aus theorie und praxis des stahlbetonbaues, wilhelm ernst u. sohn, berlin/münchen (1969). [2] ivanova, i., comportement mécanique de consoles cortes en béton armé renforce ou réparée par collage de matériaux composites, thèse de doctorat, université de reins champagne-ardenne, france, (2013). [3] ivanova, i., assih, j., li, a., delmas, y., experimental investigation of strengthened short reinforced concrete corbels by bonding carbon fiber fabrics, journal of adhesion science and technology, 29 (20), 2176-2189, 2015. [4] ivanova, i., assih, j., li, a., dontchev, d., hadjov, k., delmas, y., effet du renforcement sur la performance de consoles courtes en béton armé, 32ème rencontres universitaires de génie civil, orléans, (2014). [5] quiertant, m., benzarti, k., matériaux composites pour le renforcement des structures de génie civil, revue des composites et des matériaux avancés, 22 (2) (2012). [6] ahmad, s., shah, a., nawaz, a., salimullah, k., shear strengthening of corbels with carbon fibre reinforced polymers (cfrp), materiales de construcción, 60(299) (2010) 79-97. [7] anis a. mohamad-ali, muhammad abed attiya, experimental behaviour of reinforced concrete corbels strengthened with carbon fibre reinforced polymer strips, basrah journal for engineering science, (2012 31-45. i. ivanova et alii, frattura ed integrità strutturale, 34 (2015) 90-98; doi: 10.3221/igf-esis.34.09 98 [8] ivanova, i., assih, j., li, a., delmas, y., experimental and analytical study of bandage strengthening of reinforced concrete short corbel by bonding carbon fiber fabric, international journal of fracture fatigue and wear: conference series proceedings, 2 (2014) 43-49. [9] chatelain, j., l’extensométrie par jauges à fil résistant, bulletin de liaison des laboratoires routiers, l.c.p.c, 39 (1969). [10] afgc, réparation et renforcement des structures en béton au moyen des matériaux composites – recommandations provisoires. bulletin scientifique et technique de l’afgc, (2011). [11] assih, j. t., contribution à l’étude du renforcement et de la réparation de poutre en béton armé par collage de plaques composites en fibres de carbone, thèse de doctorat, ufr sciences de reims, (1998). [12] ivanova, i., assih, j., experimental study of local behavior of strengthened concrete short corbel by bonding carbon fiber fabrics. international journal of structural and civil engineering research, 4(1) (2015) 148-158. microsoft word numero_49_art_60_2474 y. saadallah et alii, frattura ed integrità strutturale, 49 (2019) 666-675; doi: 10.3221/igf-esis.49.60 666 a viscoelastic-viscoplastic model for a thermoplastic and sensitivity of its rheological parameters to the strain-rate younès saadallah university of jijel, algeria sayounes@live.fr semcheddine derfouf, belhi guerira university of biskra, algeria chems.derfouf@gmail.com, guerirabelhi@gmail.com abstract. the behavior of thermoplastics depends on several factors, mainly time and temperature. the present work is focused on an analysis of the time sensitivity of the viscoelastic and viscoplastic parameters of a rheological model. the material considered in this study is a polyamide 6. the analogical model is represented by the kelvin-voigt viscoelastic mechanism mounted in series with a viscoplastic branch of bingham. after a mathematical formulation of the equations governing the model, tensile tests at different strain rates are conducted. the model parameters are then identified by inverse analysis. the technique of genetic algorithms has been favored. a nonlinear dependence of these parameters on the rate of strain has been observed. the dependence function has been established by a nonlinear regression technique. the comparison of the experimental results with those obtained by the model reveals a satisfactory agreement, hence the validation of the approach adopted. keywords. viscoelasticity; viscoplasticity; strain-rate; rheological parameters; thermoplastic; genetic algorithms. citation: saadallah, y., derfouf, s., guerira, b., a viscoelastic-viscoplastic model for a thermoplastic and sensitivity of its rheological parameters to the strain-rate, frattura ed integrità strutturale, 49 (2019) 666-675. received: 08.04.2019 accepted: 28.05.2019 published: 01.07.2019 copyright: © 2019 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. introduction hermoplastics are materials widely used in various industry applications. indeed, these polymeric materials have relevant mechanical and electrical properties that allow them to adapt and meet different requirements in a wide variety of fields including automotive, aeronautics and medicine [1, 2]. therefore, the understanding of their behavior under external loading and in the conditions of their commissioning requires, in recent years, a considerable interest. t http://www.gruppofrattura.it/va/49/2474.mp4 y. saadallah et alii, frattura ed integrità strutturale, 49 (2019) 666-675; doi: 10.3221/igf-esis.49.60 667 many models have been developed to represent the rheological behavior of thermoplastics [3-8]. phenomenological models inspired by analog mechanisms such as spring, damper and pad combinations are well placed to represent viscoelastic and viscoplastic responses. the simplest mechanisms are the maxwell and kelvin-voigt viscoelastic models and the bingham viscoplastic model. the combination of these mechanisms in series or in parallel makes it possible to represent a wide variety of mechanical behaviors capable of representing linear or non-linear viscoelastic and viscoplastic rheological behaviors. the mechanical behavior characterization of thermoplastic polymers is always a complicated task. this behavior depends on many external factors such as temperature and strain rate, but also other internal factors including entanglements, crosslinking and crystallinity degree [2, 6]. this dependence is physically explained by their structure in macromolecular chains whose mobility, entanglement, branching and crosslinking are the main factors at the origin of the viscous aspect [9]. taking into account these microscopic factors makes it possible to better understand the macroscopic response and contributes to the establishment of relevant behavior models [10]. on the other hand, it is very difficult to account the influence of all the physical mechanisms in the behavior laws, from which the application of the phenomenological models . demonstration of time behavior dependence is usually done by means of creep, relaxation or tensile tests at different strain rates. experimental data is used to identify the model parameters under consideration using different methods. two major classes of methods are distinguished: analytical-graphical methods and inverse identification methods. methods based on the formulation of inverse problems are the most used. they consist in the minimization of a function that establishes the gap between the experimental data and the results of the modeling. it is therefore a question of solving an optimization problem by setting up the appropriate calculation algorithm. in recent years, so-called metaheuristic optimization methods have been developed. as an example, genetic algorithms and ant colony algorithms are mentioned [refs]. genetic algorithms based on evolutionary ideas of natural selection and genetics [11, 12]. they serve as powerful tools for solving very complicated optimization problems when the derivative of the objective function is very difficult to obtain or does not exist [13, 14]. so, they saw their use for determining material parameters for models with a large number of parameters. the authors of the reference works [14-16] used them for the estimation of the viscoelastic parameters while those of the references [6, 17, 18] used them for the determination of the viscoplastic parameters. numerous studies relating to the sensitivity of polymer behavior to time and temperature are identified in the literature. the references [19-24] are cited for illustrative purposes. since mechanical behavior models are controlled by parameters, it is natural that these parameters also depend on time and temperature. several researchers have investigated the relationship of the sensitivity of elastic parameters, including young's modulus and elastic limit, to strain rate and temperature [20, 21, 25, 26]. it is found that increasing the rate of strain increases the elastic parameters while the increase in temperature decreases them. on the other hand, although there is also much published work on the sensitivity of viscoplastic parameters, few of them have established dependence functions. the present work is an analysis of the sensitivity to strain rate of the parameters of a viscoelastic-viscoplastic behavior model applied to thermoplastic materials. the proposed model is an assembly of the kelvin-voigt viscoelastic mechanism in series with the bingham generalized viscoplastic mechanism with nonlinear hardening. the material under study is a polyamide 6. tensile tests at different strain rates were conducted to serve as data necessary for the identification of model parameters. the latter are identified by means of an inverse analysis based on the technique of genetic algorithms. as testmodel results are confronted and good consistency is enforced, dependency functions are then derived from non-linear regression. rheological modeling viscoelastic-viscoplastic model he proposed rheological model is illustrated in fig. 1. it is a series assembly of two mechanisms, one representing the viscoelastic behavior and the other the viscoplastic behavior. the viscoelastic mechanism is represented by the instantaneous kelvin-voigt model, consisting of a spring representing instantaneous elasticity mounted in series with a parallel combination of another spring and another damper thus reproducing a viscoelasticity. this model is adopted to describe the viscoelastic behavior of polymers [27, 28]. the viscoplastic mechanism, which is activated only when the loading exceeds a critical value known by the plasticity threshold, is described by the generalized model of bingham defined by the parallel association of a pad indicating the threshold of plasticity, a non-linear spring representing the work hardening of the material and a damper simulating the viscoplastic strain. the bingham model is applied to t y. saadallah et alii, frattura ed integrità strutturale, 49 (2019) 666-675; doi: 10.3221/igf-esis.49.60 668 describe the viscoplastic behavior of wood [29, 30] and polymers [28, 31]. the proposed model, by its components, is extensible and therefore likely to simulate a wide variety of materials. figure 1: viscoelastic-viscoplastic rheological model mathematical formulation the viscoelastic response is represented by the rheological model composed of kelvin-voigt with instant elasticity. it follows that the total viscoelastic strain  is all of an instantaneous elastic part e and a deferred part ve .  e ve    . (1) the stress  generated in the viscoelastic mechanism is expressed by: e ve ve vee k        (2) where e, k and ve represent the viscoelastic parameters of the model (fig. 1). the speed of instantaneous elastic strain e being zero, replacing e by its value, we obtain:  ve e k e k        (3) where  . is the rate of total viscoelastic strain. the threshold of plasticity being reached, the response of the material takes a second component that is the viscoplastic strain vp . the latter is described by the generalized model of bingham with nonlinear hardening. e ve vp      (4) it follows that the equations governing the viscoplastic behavior of material are expressed by:  ne vp vp vph        (5) where h, n and vp represent the viscoplastic parameters of the model (fig. 1); e is the elastic limit. this allows us to write: kelvin-voigt bingham elastic viscoelastic viscoplastic 𝜇 𝐸 𝐾 𝜎 𝐻 𝜇 y. saadallah et alii, frattura ed integrità strutturale, 49 (2019) 666-675; doi: 10.3221/igf-esis.49.60 669    ne ve e vp ve eh                 (6) replacing the elastic strain, the viscoelastic strain and its velocity by their formulas, and considering that the rate of elastic strain is zero, we obtain: 1 exp exp n e vp ve ve ve kt kt h k e                                                        (7) since the above equation is non-linear, numerical methods must be used for its resolution. several methods are used to solve this kind of problem. here is favored the bisection method [32]. the implementation is done under matlab. material and experimentation material of study he material under study is a polyamide 6. it is a technical thermoplastic named tecamid 6 sold in sheets 7 mm thick. the conditions under which the tests are carried out are summarized in a temperature of 300 k and a humidity of 20%. the specimen’s geometry was established according to astm d638. they were cut by cnc milling. testing machine the test machine is a instron 5969 with a capacity of 50 kn. it is equipped with a contactless video extensometer. this one allows to correct some problems like those related to the sliding of the edges of knife and the inertia of moving parts. the data is processed using the bleuhill 3 control and acquisition system. perimental results tensile tests at different constant strain rates are conducted. the strain rates correspond to the speeds of the crosshead movement. they are of the order of (0.0000646, 0.000625, 0.00612, 0.0556) min-1. the curves obtained, as shown in fig. 2, clearly demonstrate the strain rate sensitivity of the tensile behavior. figure 2: stress-strain curves of a polyamide 6 at different strain rates. t y. saadallah et alii, frattura ed integrità strutturale, 49 (2019) 666-675; doi: 10.3221/igf-esis.49.60 670 the results obtained are described by the strain-strain curves of fig. 2. it clearly shows a time-dependent rheological behavior. the strain rate plays remarkably influence on the stress-strain relationship both in the viscoelastic domain and in the viscoplastic domain. in terms of quality, the shape of the curves is insensitive to the speed of strain. however, quantitatively, the difference between the curves as a function of the rate of strain is clearly distinguished. there is an increase in the resistance of the material with the increase in the rate of strain. identification of rheological parameters genetic algorithms t is generally accepted that genetic algorithms [11] are particularly suited to multidimensional global search problems where the search space potentially contains multiple local minima [14]. unlike other research methods, genetic algorithms do not require a thorough knowledge of the search space, such as the limits of probable solutions or the derivatives of functions. they begin with a set of potential solutions chosen at random; and evolve by iteratively applying a set of stochastic operators, known as selection, crossover, and mutation. no gradient information is needed. only the objective function and the constraints are necessary to determine the solution of the problem. thus, they have the possibility of facing problems with a complicated objective function, where its derivative is difficult to obtain, or even non-existent. as a result, these techniques are well placed to be applied in the present work. identification of parameters the identification of the three viscoelastic (e, k, ve ) and four viscoplastic ( e , h, n, vp ) parameters is done by setting up respectively objective functions veq and vpq minimizing the difference between the experimental measurements and the values of the model. so the optimization problems are formulated as follows:     2 1 ,   ,   , , ,   ,   , , n i i ve ve c ex ex c ve i q e k e k            (8)      2 1 , , ,   , , , , ,   , , n i i vp e vp c ex ex c e vp i q h n h n              (9) where n is the number of measurement points ; iexσ and i cσ respectively represent the experimental stress and simulated by the model. the genetic algorithm optimization technique was applied in the matlab environment to determine the viscoelastic and viscoplastic parameters of the model. the elastic limit corresponds to the stress at which the material begins to have a permanent strain. for metals, this limit is practically determined at the stress at which a 0.2% strain is attained. moreover, according to the references [8, 33], polymers have an elastic limit corresponding to a strain of 1%, where the stress-strain curve becomes clearly nonlinear. results and discussion he proposed viscoelastic-viscoplastic rheological model was applied to simulate the behavior of the polyamide 6 material. the following sections present the experimental and simulation results obtained from a tensile test at several strain rates. identified parameters tabs. 1 and 2 represent respectively the viscoelastic and viscoplastic identified parameters. it can be seen that the modulus e is constant and independent of the strain rate, whereas the viscoelastic parameters k and ve depend considerably on it. it should be noted that with the increase of the strain-rate, the parameter k increases while the ve parameter decrease. i t y. saadallah et alii, frattura ed integrità strutturale, 49 (2019) 666-675; doi: 10.3221/igf-esis.49.60 671 as for the viscoplastic parameters, the coefficient of work hardening is constant whatever the strain-rate, or the other viscoplastic parameters are a function of the strain-rate. the higher the strain-rate, the greater the elastic limit e and the modulus h, and the lower the viscoplasticity coefficient vp . strain-rate  1min .   e gpa .  k gpa    .ve gpa min 0.0000646 2.9765 7.3122 23.8816 000625 2.9765 12.2063 5.0066 0.00612 2.9765 18.6363 0.7380 0.0556 2.9765 32.3085 0.0640 table 1: viscoelastic parameters strain-rate  1min   e mpa .   h mpa n .    .vp mpa min . 0.0000646 22.0151 69.8468 0.3072 6962.33 0.000625 20202 94.9441 0.3072 3044.22 0.00612 24.8992 122.883 0.3072 210.346 0.0556 26 155.818 0.3072 23.11376 table 2: viscoplastic parameters figure 3: comparison test-model of the stress–strain curves of polyamide 6 at various strain-rates y. saadallah et alii, frattura ed integrità strutturale, 49 (2019) 666-675; doi: 10.3221/igf-esis.49.60 672 stress-strain curves to evaluate the relevance of the rheological model taken into account, the stress-strain curves of the experiment and those of the simulation, at four strain-rates, are compared. below the elastic limit, the stress is related to the strain by a linear function. the threshold of plasticity being reached, the curve takes another pace. indeed the spring of the viscoplastic mechanism connecting the stress to the strain with a nonlinear function is at the origin of the nonlinearity observed on the curve. the error between the test-model results is almost insignificant. sensitivity of the elastic limit to the strain-rate the stress corresponding to the elastic limit depends considerably on the strain-rate. indeed, the higher the strain-rate, the greater the stress corresponding to the elastic limit. fig. 4 illustrates the dependence of the elastic limit on the strain-rate. in the references [19, 20, 34-36], the authors extensively discussed the sensitivity of the elastic limit to the strain rate. different functions have been established. it should be mentioned that the elastic limit also depends on the temperature, an aspect that is not considered in this study because the tests were conducted at constant room temperature. in the present work, the dependence can be expressed by a power law as illustrated in fig. 4. in addition, fig. 5 shows the elastic limit versus the logarithm of the strain-rate. there is a linear increase in the elastic limit as a function of the strain-rate. this is in perfect agreement with other work on polymers with references [35-37]. in another plane, the strain corresponding to the elastic limit is insensitive to the strain-rate. figure 4: sensitivity of the elastic limit to the strain-rate. figure 5: linearity of elastic limit at the logarithm of the strainrate sensitivity of the parameters to the strain-rate in order to verify the dependence of the viscoelastic and viscoplastic parameters of the strain-rate, four different speeds were taken into account in the tensile tests. following the identification step, it turned out that the elastic modulus e is independent of the strain-rate while the other two viscoelastic parameters show non-linear dependency. referring to fig. 6, it is noted that the k module increases with the increase of the strain-rate while the viscosity parameter ve decreases. on the viscoplastic plane, the work hardening coefficient n is independent of the strain rate whereas the other two viscoplastic parameters depend on it and are connected to it with nonlinear functions. referring to fig. 7, an analogy can be observed qualitatively between the viscoplastic parameters h and vp on the one hand and the viscoelastic parameters k and ve respectively on the other hand. thus with the increase of the strain-rate, the module h increases while the parameter vp decreases. y. saadallah et alii, frattura ed integrità strutturale, 49 (2019) 666-675; doi: 10.3221/igf-esis.49.60 673 figure 6: dependence of viscoelastic parameters at the strain-rate figure 7: dependence of viscoplastic parameters at the strain-rate to define the functions that represent the mathematical relationship of the strain rate with the viscoelastic and viscoplastic parameters, a nonlinear regression technique is considered. as a result, a power law connects both the viscoelastic parameters and the viscoplastic parameters to the strain-rate. the curves that represent the sensitivity of the viscoelastic parameters to the strain-rate are illustrated in fig. 6. the sensitivity of the viscoplastic parameters is illustrated in fig. 7. with the exception of the elastic modulus e and the coefficient of hardening n which are independent of it, the functions obtained are shown in tab. 3. k ve e . h . vp 0,2158881 0,876, 6166  0,0228, 059 0,12222, 27 0,882, 3512  table 3: relationship of the parameters with the strain-rate 0 5000 10000 15000 20000 25000 30000 35000 0 0,02 0,04 0,06 k ( m p a) strain-rate (1/min) 0 5000 10000 15000 20000 25000 30000 35000 0 0,02 0,04 0,06 µ_ ve ( m p a. m in ) strain-rate (1/min) 0 20 40 60 80 100 120 140 160 180 0 0,02 0,04 0,06 h ( m p a) strain-rate (1/min) 0 2000 4000 6000 8000 10000 12000 0 0,02 0,04 0,06 µ_ vp ( m p a. m in ) strain-rate (1/min) y. saadallah et alii, frattura ed integrità strutturale, 49 (2019) 666-675; doi: 10.3221/igf-esis.49.60 674 conclusion n this work, we have mainly studied the sensitivity to the strain-rate of the viscoelastic and viscoplastic parameters of a rheological model applied to thermoplastics. the proposed behavior model takes into account several elementary responses including instant elasticity, viscoelasticity, viscoplasticity and hardening. the identification of the parameters was carried out on the basis of the experimental results obtained following a simple tensile test at different strain rates. the parameters were identified by means of inverse analysis by genetic algorithms. the comparison of the test-model results reveals a very good coherence. except the modulus of elasticity and the exponent of work hardening, the results obtained reveal a strong dependence of the other viscoelastic and viscoplastic parameters to the strain rate. a nonlinear regression technique has made it possible to establish dependence functions which show relations in power law. references [1] maurel-pantel, a., baquet, e., bikard, j., bouvard, j. l., and billon, n. (2015). a thermo-mechanical large deformation constitutive model for polymers based on material network description: application to a semi-crystalline polyamide 66, international journal of plasticity, 67, pp. 102-126. [2] colak, o. u. (2005). modeling deformation behavior of polymers with viscoplasticity theory based on overstress, international journal of plasticity, 21, pp. 145-160. [3] müller, s., kästner, m., brummund, j., and ulbricht, v. (2011). a nonlinear fractional viscoelastic material model for polymers, computational materials science, 50, pp. 2938-2949. [4] zhang, c., and moore, i. d. (1997). nonlinear mechanical response of high density polyethylene. part ii: uniaxial constitutive modeling, polymer engineering & science, 37, pp. 414-420. [5] miled, b., doghri, i., and delannay, l. (2011). coupled viscoelastic–viscoplastic modeling of homogeneous and isotropic polymers: numerical algorithm and analytical solutions, computer methods in applied mechanics and engineering, 200, pp. 3381-3394. [6] abdul-hameed, h., messager, t., zaïri, f., and naït-abdelaziz, m. (2014). large-strain viscoelastic–viscoplastic constitutive modeling of semi-crystalline polymers and model identification by deterministic/evolutionary approach, computational materials science, 90, pp. 241-252. [7] zaïri, f., naït-abdelaziz, m., woznica, k., and gloaguen, j.-m. (2007). elasto-viscoplastic constitutive equations for the description of glassy polymers behavior at constant strain rate, journal of engineering materials and technology, 129, pp. 29-35. [8] tscharnuter, d., jerabek, m., major, z., and pinter, g. (2012). uniaxial nonlinear viscoelastic viscoplastic modeling of polypropylene, mech time-depend mater, 16, pp. 275-286. [9] ferry, j. d. (1980) viscoelastic properties of polymers, john wiley & sons. [10] davoodi, b., muliana, a., tscharnuter, d., and pinter, g. (2015). analyses of viscoelastic solid polymers undergoing degradation, mech time-depend mater, 19, pp. 397-417. [11] golberg, d. e. (1989). genetic algorithms in search, optimization, and machine learning, addion wesley. [12] holland, j. h. (1975). adaptation in natural and artificial systems: an introductory analysis with applications to biology, control, and artificial intelligence, u michigan press. [13] mccall, j. (2005). genetic algorithms for modelling and optimisation, journal of computational and applied mathematics, pp. 184, 205-222. [14] kohandel, m., sivaloganathan, s., and tenti, g. (2008). estimation of the quasi-linear viscoelastic parameters using a genetic algorithm, mathematical and computer modelling, 47, pp. 266-270. [15] feng, x.-t., chen, b.-r., yang, c., zhou, h., and ding, x. (2006). identification of visco-elastic models for rocks using genetic programming coupled with the modified particle swarm optimization algorithm, international journal of rock mechanics and mining sciences, 43, pp. 789-801. [16] wang, g. y., and wang, m. (2011). multi-parameter identification of geomembrane viscoelastic-plastic creep constitutive model by genetic algorithm, in applied mechanics and materials, pp 182-188, trans tech publ. [17] dusunceli, n., colak, o. u., and filiz, c. (2010). determination of material parameters of a viscoplastic model by genetic algorithm, materials & design, 31, pp. 1250-1255. [18] zhang, w., cho, c., and xiao, y. (2014). an effective inverse procedure for identifying viscoplastic material properties of polymer nafion, computational materials science, 95, pp. 159-165. i y. saadallah et alii, frattura ed integrità strutturale, 49 (2019) 666-675; doi: 10.3221/igf-esis.49.60 675 [19] siviour, c. r., and jordan, j. l. (2016). high strain rate mechanics of polymers: a review, journal of dynamic behavior of materials, 2, pp. 15-32. [20] şerban, d. a., weber, g., marşavina, l., silberschmidt, v. v., and hufenbach, w. (2013). tensile properties of semicrystalline thermoplastic polymers: effects of temperature and strain rates, polymer testing, 32, pp. 413-425. [21] cao, k., wang, y., and wang, y. (2012). effects of strain rate and temperature on the tension behavior of polycarbonate, materials & design, 38, pp. 53-58. [22] nakai, k., and yokoyama, t. (2008). strain rate dependence of compressive stress-strain loops of several polymers, journal of solid mechanics and materials engineering, 2, pp. 557-566. [23] viana, j. (2005). structural interpretation of the strain-rate, temperature and morphology dependence of the yield stress of injection molded semicrystalline polymers, polymer, 46, pp. 11773-11785. [24] lubarda, v. a., benson, d. j., and meyers, m. a. (2003). strain-rate effects in rheological models of inelastic response, international journal of plasticity, 19, pp. 1097-1118. [25] manaia, j.p., pires, f.a., de jesus, a.m.p., wu, s. (2019). yield behaviour of high-density polyethylene: experimental and numerical characterization, engineering failure analysis, 97, pp. 331-353. [26] manaia, j.p., pires, f.a., de jesus, a.m.p. (2019). elastoplastic and fracture behaviour of semi-crystalline polymers under multiaxial stress states, frattura ed integrita strutturale, 13, pp. 82-103 [27] riande, e. (2000). polymer viscoelasticity: stress and strain in practice, 55, crc press. [28] ashrafi, h., and farid, m. (2009). a mathematical boundary integral equation analysis of standard viscoelastic solid polymers, computational mathematics and modeling, 20, pp. 397-415. [29] lemaitre, j., and chaboche, j. l. (1994). mechanics of solid materials, cambridge university press. [30] moutee, m., fortin, y., and fafard, m. (2007). a global rheological model of wood cantilever as applied to wood drying, wood science and technology, 41, pp. 209-234. [31] papanastasiou, t. c., and boudouvis, a. g. (1997). flows of viscoplastic materials: models and computations, computers & structures, 64, pp. 677-694. [32] otto, s., denier, j.p. (2005). an introduction to programming and numerical methods in matlab. springer science & business media, [33] schodek, d. l., ferreira, p., and ashby, m. f. (2009). nanomaterials, nanotechnologies and design: an introduction for engineers and architects, butterworth-heinemann. [34] morin, d., haugou, g., lauro, f., bennani, b., and bourel, b. (2015). elasto-viscoplasticity behaviour of a structural adhesive under compression loadings at low, moderate and high strain rates, journal of dynamic behavior of materials, 1, 124-135. [35] mulliken, a. d., and boyce, m. c. (2006). mechanics of the rate-dependent elastic–plastic deformation of glassy polymers from low to high strain rates, international journal of solids and structures, 43, pp. 1331-1356. [36] srivastava, v., chester, s. a., ames, n. m., and anand, l. (2010). a thermo-mechanically-coupled large-deformation theory for amorphous polymers in a temperature range which spans their glass transition, international journal of plasticity, 26, pp. 1138-1182. [37] bauwens-crowet, c., bauwens, j., and homes, g. 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can be opened with acrobat and adobe reader 5.0 and later.) >> /namespace [ (adobe) (common) (1.0) ] /othernamespaces [ << /asreaderspreads false /cropimagestoframes true /errorcontrol /warnandcontinue /flattenerignorespreadoverrides false /includeguidesgrids false /includenonprinting false /includeslug false /namespace [ (adobe) (indesign) (4.0) ] /omitplacedbitmaps false /omitplacedeps false /omitplacedpdf false /simulateoverprint /legacy >> << /addbleedmarks false /addcolorbars false /addcropmarks false /addpageinfo false /addregmarks false /convertcolors /converttocmyk /destinationprofilename () /destinationprofileselector /documentcmyk /downsample16bitimages true /flattenerpreset << /presetselector /mediumresolution >> /formelements false /generatestructure false /includebookmarks false /includehyperlinks false /includeinteractive false /includelayers false /includeprofiles false /multimediahandling /useobjectsettings /namespace [ (adobe) (creativesuite) (2.0) ] /pdfxoutputintentprofileselector /documentcmyk /preserveediting true /untaggedcmykhandling /leaveuntagged /untaggedrgbhandling /usedocumentprofile /usedocumentbleed false >> ] >> setdistillerparams << /hwresolution [2400 2400] /pagesize [612.000 792.000] >> setpagedevice microsoft word numero_29_art_19 n. cefis et alii, frattura ed integrità strutturale, 29 (2014) 222-229; doi: 10.3221/igf-esis.29.19 222 focussed on: computational mechanics and mechanics of materials in italy damage modelling in concrete subject to sulfate attack n. cefis, c. comi department of civil and environmental engineering, politecnico di milano, piazza leonardo da vinci 32, 20133 milano, italy. nicola.cefis@polimi.it, claudia.comi@polimi.it abstract. in this paper, we consider the mechanical effect of the sulfate attack on concrete. the durability analysis of concrete structures in contact to external sulfate solutions requires the definition of a proper diffusion-reaction model, for the computation of the varying sulfate concentration and of the consequent ettringite formation, coupled to a mechanical model for the prediction of swelling and material degradation. in this work, we make use of a two-ions formulation of the reactive-diffusion problem and we propose a bi-phase chemo-elastic damage model aimed to simulate the mechanical response of concrete and apt to be used in structural analyses. keywords. sulfate attack; concrete; damage; finite element method; porous media. introduction nder particular environmental conditions, some kinds of concrete may be subject to deleterious chemical reactions that cause swelling and micro-cracking, alter the mechanical properties and affect the durability of concrete structures. the chemistry behind different degradation processes in cement based material in aggressive environments has been the subject of a number of publications in the last twenty-five years; a comprehensive up-to-date review can be found e.g. in [1]. the present work focuses in particular on the sulfate attack and the consequent delayed ettringite formation. there are two kinds of sulfate attack: the internal sulfate attack (isa) and external sulfate attack (esa). in the first case, the sulfate ions are already present within the material because of the thermal depletion of primary ettringite due to curing at high temperature or to the excessive heat of hydration developed in massive structures, see e.g. [2, 3]. in the second case, the sulfate is present in the environment and diffuses within the material through the porous microstructure; this happens e.g. in foundations, galleries, stores of radioactive waste in contact with sulfate-rich soils, [4, 5]. in both cases, the reaction between the sulfate and hydrated products of the cement leads to the formation of gypsum and of secondary ettringite, [6-8]. the product formed in the hardened paste exerts an internal pressure resulting in the appearance of micro-cracks and material degradation. the kinetics of the reactions and, consequently, the severity of the damage depends on environmental factors (species and concentration of sulfate, ph of the solution, humidity, temperature) and intrinsic material properties (chemical composition of the cement paste, in particular aluminates content, pore distribution, diffusivity properties). the numerical description of these phenomena requires a proper diffusion-reaction model, for the computation of the amount of reaction expansive products and a mechanical model for the prediction of swelling and material damage. in this work we use the coupled model proposed in [7] and further developed in [9] which allows to compute the sulfate molar u n. cefis et alii, frattura ed integrità strutturale, 29 (2014) 222-229; doi: 10.3221/igf-esis.29.19 223 concentration and the amount of formed ettringite from a diffusive-reaction equation, taking into account the aluminate depletion due to the reaction. the ettringite formation implies a volume increase and, once the initial porosity is filled, it induces a volumetric deformation. several proposal exist in the literature to describe the mechanical consequences on concrete of this swelling. in [7] the volumetric expansion is treated as an eigenstrain and a simple uniaxial stress-strain law is used. in [10] basista and weglewski develop a micromechanical model based on the eshelby solution of the equivalent inclusion method to determine the eigenstrain of the ettringite crystals in cement paste. in [11] a poroelasticity approach is followed and the mazars’ damage model is used to describe concrete microcracking. idiart et al. in [9] present finite element simulations of the phenomenon at the meso-scale, considering concrete as a two phase composite, constituted by aggregates and cement matrix and describe degradation by cohesive-crack interface elements. in the present work we follow a weakly coupled approach, similar to that proposed in [12, 13] for concrete affected by alkali-silica reaction. in the context of the biot's theory of porous media, the concrete subject to sulfate attack is represented as a continuous medium consisting of two phases: the solid skeleton of concrete and the expansive products of the reaction. a phenomenological isotropic damage model, [14], describes the material degradation. the reactive-diffusion model and the mechanical model have been implemented in a finite element code and used to simulate the experimental tests concerning esa reported in [15, 16]. chemo-transport model he reactions that take place inside the concrete when in contact with sulfate solutions are briefly reviewed in this section. the usual cement notation will be used: c ≡ cao; a ≡ al2o3; s ≡ so3; h ≡ h2o. driven by a concentration gradient, the sulfates present in the environment penetrate into the material and, reacting with the calcium hydroxide (ch) and with the calcium silicate hydrates (c-s-h gel), form gypsum 2hsc . the gypsum thus produced reacts with the calcium aluminates which are present in the cement paste, forming ettringite 3236 hsac [6-7]. the set of chemical equations that describe the gypsum formation are 22 2 4 2242 )( 2 hscohsohsc naohhscohsonach    (1) the reactions between the gypsum and the aluminates ip ( 1p 124 hsac mono-sulphoaluminate, acp 32  unreacted tricalcium aluminate, 1343 ahcp  tetra-hydrated aluminate and afcp 44  alumino-ferrite) read respectively:   3323624 3236134 323623 32362124 ,2)(4123 1732 263 162 hfahsachαhscafc hsachschahc hsachhscac hsachhschsac     (2) as proposed in [9], the reactions (2) can be lumped in a single reaction 3236 hsacsqc eq  (3) where ceq is the equivalent grouping of calcium aluminates ii ieq pγc    4 1 ,    4 1i i i i c c  (4) ci is the molar concentration of the single species of calcium aluminate ip and 4321 4332 γγγγq  is the stoichiometric weighting coefficient of the sulfate phase. the molar concentration ),( ts x of sulfate s , varying in space x and time t, can be computed taking into account the diffusion process and the consumption of sulfates due to the ettringite formation, through the following reactive-diffusion equation, ds being the diffusion coefficient for the sulfate concentration and k the rate of take-up of sulfates: t n. cefis et alii, frattura ed integrità strutturale, 29 (2014) 222-229; doi: 10.3221/igf-esis.29.19 224 sksd t s s ))(graddiv(   (5) during the process of delayed ettringite formation also the calcium aluminates concentration ),( tcc eqeq x decreases and the phenomenon affects the diffusion process of the sulfates. a more accurate description can be obtained by considering a second order chemical reaction in a two-ions formulation and computing the evolution of both the concentration of sulfate and aluminates from the following system:             sc q k t c scksd t s eq eq eqs )) (graddiv( (6) note that no diffusion term is present in the second equation since aluminates can not move in the cement paste. to integrate the system of differential eq. (6), one should specify proper boundary conditions fixing the sulfate concentration s or its normal gradient and initial conditions for both sulfate and aluminate concentrations. the simplified single-ions formulation (5) is obtained for eqckk  , with eqc constant. the two-ions formulation (6) predicts a faster penetration of the sulfate with respect to the one-ion formulation (5), since the depletion of aluminates reduces the sulfate consumption due to the reactive term sck eq in (6a) and thus results in a higher diffusion. in the present work the two-ions formulation has been implemented. assuming that ettringite is the only reaction product governing the expansion of the concrete, the volumetric strain of chemical nature chemvε is obtained from the amount of reacted calcium aluminates eqeq reac ccc  0 (i.e the difference between the initial aluminates molar concentration and the current one) and the volume change associated with the reaction. for any of the individual reactions described above, eq. (2), the volume change for unit volume associated to the formation of one mole of ettringite can be calculated as in [7]: 1 δ    gypsumii ettringite i i mam m v v (7) where ettringitei mm , and gypsumm are the molar volumes (m3/mol) of the aluminate phase, of the ettringite and of the gypsum, respectively, and ai is the stoichiometric coefficient involved in the reaction. to obtain the overall volume change per unit volume one has to multiply the change related to one mole by the number of reacted moles )( 0 iii reac ii ccmcm  and then take the sum of the contributions coming for the different aluminates. using the lumped formulation (3) one finally obtains 0 0 φ)( fccε eqeq chem v  α with    4 1 δ i ii i i γm v v α (8) in the above equation  denotes the positive part of  and 0φf is a fraction of the initial porosity 0φ , introduced to take into account the fact that the reaction products partially fill the initial porosity, without producing any macroscopic expansion. mechanical behavior of concrete he mechanical response of the material to the chemical expansion expressed by eq. (8) is computed in this work by a poroelastic-damage model. within the framework of the biot’s theory [17], the concrete is described as a twophase material: the homogenized skeleton phase, including cement paste and aggregates, and the expansive phase of the products of the reaction. the total stress σ is the sum of the effective stress acting on the solid skeleton σ and of the stress on the reaction products phase, p being the pressure at the microscale, b the biot’s coefficient related to the concrete porosity and 1 the unit second-order tensor: t n. cefis et alii, frattura ed integrità strutturale, 29 (2014) 222-229; doi: 10.3221/igf-esis.29.19 225 1σσ bp (9) the effective stress on the concrete skeleton is related to the total strain ε by an elastic law with isotropic damage d, d is tensor of the elastic properties of the homogenized skeleton: εdσ :)1( d (10) the pressure of the expansive phase depends on the volumetric deformation vε and on the volumetric expansion ζ due to ettringite formation, m being the biot’s modulus   ζmεbmdp v  1 (11) the expansion term ζ can be related to chemvε for the unconstrained material by the skempton coefficient )/( 2mbkmb  : chem vε mb mbk ζ 2  (12) only tensile damage is considered in this work and its evolution is governed by the loading-unloading conditions proposed in [14], expressed in term of the inelastic effective stress 1σσ pβ , with β ( )bβ  a material parameter which tunes the level of material degradation: 0 ;0 ;0  dfdf dd  (13) the activation function fd depends on the first invariant of inelastic effective stress tensor i1 and on the second invariant of deviatoric stress tensor j2: 0)()()( 2312 2 112  dhadhiaiajf d σ (14) where a1, a2, a3 are non-negative parameters to be identified through experimental tests. the function h(d) governs the hardening and softening behavior of the material and its expression is                                                  0 75.0 0 0 0 2 00 for 1 1 for 111 )( 4 dd d dd dd d d σ σ dh a e (15) in the above equation eσ is the elastic limit stress, 0σ is the peak stress, d0 is the damage corresponding to the peak stress. the parameter a4 governs the slope of the softening branch of the stress-strain curve. in the finite-element implementation, the exponent a4 is used to scale the fracture energy density of the material in such a way that each finite element can dissipate the correct amount of energy, independently of its size. this so called ‘‘fracture energy regularization” prevents the occurrence of spurious mesh dependency in the structural global response. results he numerical solution of the diffusion-reaction problem and of the subsequent chemo-damage problem are obtained by an ad-hoc developed finite element code. fracture energy pseudo-regularization is adopted. the finite element internal length for the constant strain tetrahedral elements is assumed to be the cubic root of the volume. to validate the approach proposed in this paper we simulate the external sulfate attack experiments on mortar prism reported in [15] and also simulated in [16]. the experimental campaign was carried out on 25×25×285 mm3 mortar prisms immersed in a solution with 3mol/m2.35 of na2so4. simulations of the reaction-diffusion process were performed in 3d considering three symmetry planes and solving the two ions formulation (6). the reaction and diffusion parameters used t n. cefis et alii, frattura ed integrità strutturale, 29 (2014) 222-229; doi: 10.3221/igf-esis.29.19 226 in the simulation are: day/mm07.0 2sd and day/molm108 35k . a constant sodium sulfate concentration is imposed at the outer surfaces and no flux is allowed through the symmetry planes. the initial concentration of equivalent aluminates, reported in [16], is 100 mol/m3. figure 1: external sulfate attack on a mortar specimen: a) sulfate concentration, b) ettringite concentration and c) damage for three different exposure times (200, 400, 600 days). fig. 1a depicts the results of the evolution of the molar concentration of the sulfate at three different exposure times t = 200 days, 400 days and 600 days. fig. 1b depicts the corresponding ettringite concentration: because of the penetration of sulfate, the ettringite front advances towards the center of the specimen. fig. 2 shows the profiles of ettringite concentration at different times as a function of the distance from the center in the mean section of the specimen. (a) (b) (c) n. cefis et alii, frattura ed integrità strutturale, 29 (2014) 222-229; doi: 10.3221/igf-esis.29.19 227 distance [mm] figure 2: profiles of ettringite concentration in the central section of the specimen. the subsequent mechanical analysis allows computing the strains and damage in the specimen. a non-uniform initial porosity has been considered, leading, through eq. 8, to a non-uniform chemical expansion in the specimen. assuming a normal distribution with men value 0.08 and standard deviation 0.02, the porosity of the different finite elements have been extracted by the marsaglia’s algorithm, also called “ziggurat” algorithm; fig. 3 displays the obtained pseudo-random distribution. figure 3: pseudo-random distribution of porosities within the specimen. fig. 4 shows the comparison between the longitudinal expansion obtained in the simulations and the experimental measurements. after the first 150 days, a good agreement is observed. the discrepancy in the early response is due to the fact that full saturation is assumed in the numerical simulation, therefore the initial expansion due to imbibition is not reproduced. figure 4: evolution of longitudinal expansion with time of exposure to a na2so4 solution: experimental points from [15] and numerical results. n. cefis et alii, frattura ed integrità strutturale, 29 (2014) 222-229; doi: 10.3221/igf-esis.29.19 228 fig. 1c depicts the evolution of the corresponding damage pattern. since the chemical swelling reaction starts from the outer skin of the specimen, the central part of the specimen is subject to tensile stresses and undergoes damage. the pattern and the evolution of damage can be better appreciated in fig. 5 that illustrates the results obtained with a finer mesh on a different geometry, representative of the central portion of the specimen. in the continuum approach here followed, the damage distribution simulates the presence of the cracking pattern experimentally observed, see e.g. [18]. figure 5: external sulfate attack on a mortar specimen: a) ettringite concentration and b) damage for three different exposure times (200, 400, 600 days) conclusions he model developed and implemented in this work allows for the computation of the mechanical response of concrete subject to sulfate attack. the weakly coupled approach followed makes the formulation simple enough to be used to effectively compute the response at the structural level. the predictive capabilities of the model have been shown on a preliminary simple example concerning esa. a fully coupled formulation in which the effect of damage on the diffusion-reaction problem is taken into account is currently under development. references [1] rilem tc 211 – pae state-of-the-art report, performance of cement-based materials in aggressive aqueous environments, m. alexander a. bertron n. de belie editors, springer 2013. [2] al shamaa, m. , lavaud, s., divet, l., nahas, g., torrenti, j.m., coupling between mechanical and transfer properties and expansion due to def in a concrete of a nuclear plant, nuclear engineering and design, 266 (2014) 70-77. [3] batic, o.r., milanesi, c.a., maiza, p.j., marfil, s.a., secondary ettringite formation in concrete subjected to different curing conditions, cement and concrete research, 30 (2000) 1407-1412. [4] lei, m., peng, l., shi, c., wang, s., experimental study on the damage mechanism of tunnel structure suffering from sulfate attack, tunnelling and underground space technology, 36 (2013) 5-13. [5] el-hachem, r., rozière, e., grondin, f., loukili, a., multi-criteria analysis of the mechanism of degradation of portland cement based mortars exposed to external sulphate attack, cement and concrete research, 42 (2012) 1327– 1335. [6] skalny, j., marchand, j., odler, i., sulfate attack on concrete, first ed., spon press, london, (2002). t (a) (b) n. cefis et alii, frattura ed integrità strutturale, 29 (2014) 222-229; doi: 10.3221/igf-esis.29.19 229 [7] tixier, r., mobasher, b., modeling of damage in cement-based materials subjected to external sulfate attack, i: formulation. ii: comparison with experiments, asce j. mater. civ. eng, 15 (2003) 305-322. [8] collepardi, m., a state-of-the-art review on delayed ettringite attack on concrete, cement & concrete composites, 25 (2003) 401–407. [9] idiart, a. e., lópez, c. m., carol, i., chemo-mechanical analysis of concrete cracking and degradation due to external sulfate attack: a meso-scale model, cement & concrete composites 33 (2011) 411–423. [10] basista, m., weglewski, w., chemically assisted damage of concrete: a model of expansion under external sulfate attack, international journal of damage mechanics, 18 (2009) 155-175. [11] bary, b., simplified coupled chemo-mechanical modeling of cement pastes behavior subjected to combined leaching and external sulfate attack, int j numer anal meth geomech, 32 (2008) 1791–816. [12] comi, c., fedele, r., perego, u., a chemo-thermo-damage model for the analysis of concrete dams affected by alkalisilica reaction, mechanics of materials, 41 (2009) 210-230. [13] comi, c., kirchmayr, b., pignatelli, r., two-phase damage modeling of concrete affected by alkali–silica reaction under variable temperature and humidity conditions, international journal of solids and structures, 49 (2012) 3367– 3380. [14] comi, c., perego, u., fracture energy based bi-dissipative damage model for concrete, international journal of solids and structures, 38 (2001) 6427–6454. [15] akpinar, p., casanova, i., a combined study of expansive and tensile strength evolution of mortars under sulfate attack: implications on durability assessment, materiales de construcción, 60-297 (2010) 59-68. [16] idiart, a. e., coupled analysis of degradation processes in concrete specimens at the meso-level, doctoral thesis, universitat politècnica de catalunya, (2009). [17] coussy o., poromechanics, john wiley & sons, (2004). [18] al-amoudi o.s.b., attack on plain and blended cements exposed to aggressive sulfate environments, cement & concrete composites 24 (2002) 305–316. microsoft word numero 12 art 2 s. marfia et alii, frattura ed integrità strutturale, 12 (2010) 13-20; doi: 10.3221/igf-esis.12.02 13 an approach for the modeling of interface-body coupled nonlocal damage s. marfia, e. sacco, j. toti university of cassino, dimsat, italy; sacco@unicas.it riassunto. i materiali composite fibrorinforzati (frp) possono essere utilizzati con successo per il rinforzo di costruzioni in conglomerato cementizio ed in muratura. uno dei maggiori problemi nell’uso degli frp, che spesso ne limita l’impiego, è la possibile decoesione della lamina in frp dalla struttura esistente realizzata in materiale coesivo (calcestruzzo o muratura). il presente lavoro affronta la problematica della modellazione della decoesione di lamine o tessuti frp dal supporto, tenendo conto del possibile accoppiamento tra il degrado del materiale di supporto (calcestruzzo o muratura) ed il danneggiamento dell’interfaccia frp-supporto in materiale coesivo. in particolare, per il materiale coesivo di supporto è proposto un modello di danno non locale di tipo integrale, governato dalla media pesata nello spazio di una deformazione equivalente, capace di evitare i problemi di localizzazione della deformazione e del danno e la forte dipendenza dalla discretizzazione nello schema agli elementi finiti. relativamente all’interfaccia frp-supporto, si utilizza un modello di danno locale governato dal valore dello spostamento relativo, tenendo conto della decoesione per modo i, modo ii e modo misto. il modello tiene in conto dell’accoppiamento tra il danno del supporto ed il danno di interfaccia. alcune applicazioni numeriche sono presentate. abstract. fiber reinforced plastic (frp) can be used for strengthening concrete or masonry constructions. one of the main problem in the use of frp is the possible detachment of the reinforcement from the support material. this paper deals with the modeling of the frp-concrete or masonry damage interface, accounting for the coupling occurring between the degradation of the cohesive material and the frp detachment. to this end, a damage model is considered for the quasi-brittle material. in order to prevent strain localization and strong mesh sensitivity of the solution, an integral-type of nonlocal model based on the weighted spatial averaging of a strain-like quantity is developed. regarding the interface, the damage is governed by the relative displacement occurring at bond. a suitable interface model which accounts for the mode i, mode ii and mixed mode of damage is developed. the coupling between the body damage and the interface damage is performed computing the body damage on the bond surface. numerical examples are presented. keywords. interface damage; body damage; coupled model; frp strengthening. introduction he use of fiber reinforced plastic (frp) materials for the strengthening of existing concrete and masonry elements is growing and, actually, many structures have been yet reinforced adopting frp; moreover several experimental and modeling scientific works have been published in the last decade [1-8]. the use of frp materials applied on the external surface of concrete or masonry structures has aroused new modeling problems. one of the main problem in the use of frp is the so-called delamination phenomenon, which consists in the sudden decohesion of the frp reinforcement from the concrete or masonry element, see for instance ref. [9]. in order to model the delamination t http://www.gruppofrattura.it http://dx.medra.org/10.3221/igf-esis.12.02&auth=true s. marfia et alii, frattura ed integrità strutturale, 12 (2010) 13-20; doi: 10.3221/igf-esis.12.02 14 phenomenon and to predict the possible decohesion of the frp from the support material, special interface models are often adopted. the response of these special elements is mainly based on the damage and/or on plasticity models. on the other hand, the concrete as well as the masonry are quasi-brittle materials, whose mechanical response is characterized by damage with softening, which is due to the development of micro-cracks. thus, two damage effects could be present in the quasi-brittle reinforced structural elements: the body damage, which develops inside the domain of the continuous body, and the interface damage, which occurs at the frp – concrete or masonry interface. it has to be remarked that experimental evidences demonstrate that the detachment of the frp from the support material occurs with the peeling of a thin layer from the external surface of the quasi-brittle material; this collapse behavior is due to the fact that the strength of the glue used to fix the frp to the support is greater than the strength of the concrete or masonry support. from this observation, it can be deduced that the body damage and the interface damage cannot evolve independently one from the other, in other words, they are coupled. in particular, the interface damage has to depend on the distribution of the body damage. in the knowledge of the authors, the first paper in which a coupled body-interface damage model has been developed is due to freddi and frémond [1]. in the present paper a damage model is proposed for the quasi-brittle material. the damage evolution is governed by an equivalent strain variable. in order to prevent strain localization and strong mesh sensitivity of the solution, typical of cohesive heterogeneous materials subjected to damage and softening, an integral-type of nonlocal model based on the weighted spatial averaging of a strain-like quantity is developed. regarding the interface, the damage is governed by the relative displacement occurring at bond. a suitable interface model which accounts for the mode i, mode ii and mixed mode of damage is developed. the coupling between the body damage and the interface damage is performed ensuring that the interface damage is not lower than the body damage evaluated on the bond surface. an initial simple application is performed in order to assess the performances of the proposed model in reproducing the mechanical behavior of quasi-brittle material strengthened with external frp materials. position of the problem mechanical system made of two bodies 1 and 2 , schematically illustrated in fig. 1, is considered. the two bodies, subjected to body forces, surface forces and prescribed displacements, are connected by an adhesive interface 1 2    , which is assumed to have zero thickness. the problem is developed in the framework of small strain and displacement theory. the displacement fields of the two joined bodies are denoted as 1u and 2u , while the relative displacement at the typical point x on the interface  is      1 2   s x u x u x . a local coordinate system on the interface  ,t nx x is introduced. figure 1: mechanical system of two bodies in adhesion. it is assumed that the body 1 and the interface  can develop damage, while the body 2 is assumed to behave as a linear elastic material. thus, two damage variables are introduced, d and d , associated to the degradation state of the body 1 and of the interface  , respectively. in many physical problems, the interface failure is not due to the damage of the adhesive material joining the two bodies 1 and 2 , but it occurs because of the properties degradation of a thin layer of the body 1 ; in fact, the decohesion is a http://www.gruppofrattura.it http://dx.medra.org/10.3221/igf-esis.12.02&auth=true s. marfia et alii, frattura ed integrità strutturale, 12 (2010) 13-20; doi: 10.3221/igf-esis.12.02 15 often characterized by the peeling of a thin layer from the external surface of the body 1 . this observation leads to the consequence that the interface damage depends on the degradation state of the material constituting 1 . thus, a coupling between the interface and body damage variables, d and d , respectively, arises. on the other hand, the independent evolution of the two damage variables can lead to physically unacceptable results. the mechanical system illustrated in fig. 2, representing the scheme of a possible decohesion test, is considered. a damage evolutive model is adopted for the material constituting the body 1 ; regarding the interface, a mode ii damage model is assumed. in particular, limiting the analysis to the tangential effect, i.e. neglecting the normal stress, the interface constitutive relationship is written in the form: (1) the damage parameter is function of the history of relative displacement as follows: (2) where the parameter d  is expressed by the relationship : (3) with 0 0 /t t ts k the first cracking relative displacement and 02 /ft ct ts g  the full damage relative displacement, being 0t the peak stress on the first cracking relative displacement and ctg the specific fracture energy in mode ii. the properties of the materials constituting the considered scheme are the following: 1 1 2 2 3 0 3 16000 mpa 0.2 230000 mpa 0.0 1500 n/mm 3 mpa 0.3 n/mmt t ct e e k g           (4) figure 2: scheme for decohesion test. finite element analyses are performed in order to evaluate the maximum value of the carried force maxf before the decohesion of the body 2 from the body 1 , for different lengths of adhesion. computations are developed considering the damage state of the body 1 assigned and constant during the whole analysis, while the interface damage evolves during the loading history. thus, the body and interface damages are uncoupled. in fig. 3, the value of maxf is plotted versus the adhesion length. note that id denotes the initial value of the interface damage. it can be remarked that increasing the adhesion length, initially the value of maxf grows, till the optimal adhesion length e is reached, after which maxf remains constant. moreover, it can be emphasized that for higher values of the damage state of the body 1  1t t td k s     max min 1, history d d   0 0 f t tt f t t t s ss d s s s           http://www.gruppofrattura.it http://dx.medra.org/10.3221/igf-esis.12.02&auth=true s. marfia et alii, frattura ed integrità strutturale, 12 (2010) 13-20; doi: 10.3221/igf-esis.12.02 16 the optimal adhesion length increases and also the maximum value of maxf increases. while the first results is absolutely expected, the second one appears physically unacceptable, as it implies that more the support material is damaged greater values of the forces can be transmitted from 2 to 1 . this strange effect is due to the uncoupled damage evolution of the body and of the interface. figure 3: decohesion force maxf versus adhesion length, uncoupled damage model. the freddi-fremond model he freddi-fremond (ff) model is based on the assumption of the following forms for the free energy and the pseudo-potential of dissipation of the domain 1 : (5) (6) where ε is the strain tensor,  and  are the lamé parameters, w is the initial threshold energy, k is a parameter measuring the nonlocal effect, i and i are the indicator functions of the sets  0,1 and  0, , respectively, c is the viscosity parameter of damage, while the dot symbol  denotes the scalar product between two tensors, the superposed dot on the damage variable indicates the derivative with respect to the time. the free energy and the pseudo-potential of dissipation of the interface  are: (7) (8) where w is surface dupré energy, k is a parameter measuring the nonlocal effect, i is the indicator function of the set  , 0 ,  indicates the scalar product, n is the outward versor normal to the domain 1 in correspondence of the interface  , k̂ is the interface stiffness, ,k  is the surface-domain interaction parameter and c is the viscosity parameter of interface damage. moreover, a further nonlocal interface effect is also introduced in the ff model. 0 50 100 150 200 250 300 350 400 450 0 50 100 150 200 250 300 350 400 adhesion length [mm] f m ax [ n ] d  =0.00 di=0 d  =0.90 di=0 d  =0.95 di=0 d  =0.99 di=0 t        2 21 11 2 2 2 d tr w d k d i d               ε ε ε    21 2 c d i d                  2 2 1 2 2 2 1 , 1 2 1 1ˆ1 2 2 w d k d i d i d k k d d                           u u n u u    21 2 c d i d        http://www.gruppofrattura.it http://dx.medra.org/10.3221/igf-esis.12.02&auth=true s. marfia et alii, frattura ed integrità strutturale, 12 (2010) 13-20; doi: 10.3221/igf-esis.12.02 17 the derivatives of the free energies with respect to the observable and internal variables lead to the state equations. the derivative of the pseudo-potentials of dissipation with respect to the damage variable allows to derive the evolutionary law for the damage. balance equation are recovered in the ff model using the virtual power principle. the following remarks regarding the ff model can be reported: o both the continuum damage model and the interface damage model are nonlocal; in particular, the nonlocal effect is accounted for by the presence of the squares of the damages gradient appearing in the free energies  and  ; o damage and strain localizations are avoided by the nonlocal damage effect and by the presence of the viscosity in the damage evolution law; o the interface-body damage coupling is due to the presence of the term  2,k d d    in the definition of the free energy  ; o the interface damage and the body damage evaluated on the surface of adhesion are constrained, in the limit that ,k    , to assume the same value; o because of the damage coupling and of the nonlocal damage diffusion, if the body damage evolves, then the interface damage occurs; analogously, the growth of the interface damage induces the body damage evolution. the nonlocal interface-body damage model he mechanical system under investigation is composed by the body 2 , whose behavior is considered linear elastic, in adhesion with the body 1 , characterized by a quasi-brittle cohesive response, by means of a glue whose mechanical properties are much better that those of the support cohesive material. in such a case, the interface model describes the overall response of the glue material and of a thin layer on the surface of the support material. experimental evidences show that the body damage strongly influences the degradation state of the interface, reducing the mechanical properties of the thin layer on the surface of the support material. on the contrary, the damage and also the failure of the interface does not induces damage diffusion inside the body 1 . in other words, if the body 1 is damaged the degradation of the interface occurs; but it is possible to induce damage and even failure of the interface without damaging the body, i.e. the body 2 can be detached from the body 1 without inducing degradation of the mechanical properties of the body 1 , unless of the thin layer of material which, indeed, is modeled by the interface. for this reason, the idea is to develop a interface-body damage model whose coupling is governed by a unilateral effect: d d  . a very simple body damage model is considered, developed in the two-dimensional framework. as a softening constitutive law is introduced for the body 1 , localization of the strain and damage could occur. in order to overcome this pathological problem and, also, to avoid strong mesh sensitivity in finite element analyses, nonlocal constitutive law is considered. in particular, an integral nonlocal model is adopted; in fact, the nonlocal value of the strain tensor evaluated as: (9) where   x is a weight function. it is assumed that the degradation of the cohesive material is due to the positive principal strain [11, 12]; thus, the equivalent strain is introduced: (10) where 1 and 2 are the nonlocal principal strains and the symbol  denotes the positive part of a number. an exponential damage evolution law is considered: (11) t         1 1 1 d d           ε x x y ε y x y 2 2 1 2eq        0 0 max min 1, eqk eq history eq e d d d               http://www.gruppofrattura.it http://dx.medra.org/10.3221/igf-esis.12.02&auth=true s. marfia et alii, frattura ed integrità strutturale, 12 (2010) 13-20; doi: 10.3221/igf-esis.12.02 18 where the starting value of d is zero, 0 is the initial threshold damage strain and k is a material parameter associated to the damage energy. about the evolution of the interface damage parameter d , a model which accounts for the coupling of mode i of mode ii of fracture is considered [13, 14]. in fact, the two quantities n and t , defined as the ratios between the first cracking relative displacement 0ns and 0 ts and the full damage relative displacement f ns and f ts are introduced: (12) where 0n and 0 t are the peak stresses on the first cracking relative displacement and cng and ctg are the specific fracture energies in mode i and mode ii, respectively. then, the parameter  , which relates the two modes of fracture, is defined as follows: (13) then, the relative displacement ratios are introduced: (14) and the equivalent relative displacement ratio is considered: (15) finally, the damage parameter is assumed to be a function of the history of relative displacement as follows: (16) where the parameter d  can be expressed by the relationship : (17) note that the eq. (17) allows to obtain a linear stress relative displacement relationship when pure mode i or pure mode ii is activated. in fact, setting for instance 0ts  , formula (17) becomes: (18) thus, in the softening phase, the normal stress at the interface results: (19) which is a linear relation between the stress n and the relative displacement ns . analogously, setting 0ns  , the tangential stress is related to ts by the linear relationship: (20) indeed, as previously emphasized, the interface damage depends also on the state of deterioration of the support material, i.e. on the damage occurring in the body 1 . thus, the body damage d has to be evaluated on the surface corresponding to the interface  . once the interface damage  d  x and the body damage  d  x , are evaluated, the damage state of the interface  cd  x is set as the maximum between the two obtained values, i.e.: 0 0 0 0 0 0 , 2 2 n n n t t t n tf f n cn t ct s s s s s g s g        2 2 2 2 n t n t s s     s s 0 0 n t n t n t s s y y s s   2 2 n ty y y    max min 1, history d d     1 1 y d y          01 1 1 n n n n n n n y s s d y s             001 f nn n n n n nf n n k d k s s s s s s            001 f tt t t t t tf t t k d k s s s s s s        http://www.gruppofrattura.it http://dx.medra.org/10.3221/igf-esis.12.02&auth=true s. marfia et alii, frattura ed integrità strutturale, 12 (2010) 13-20; doi: 10.3221/igf-esis.12.02 19 (21) where the superscript c indicates that the evaluated damage accounts for the coupling between the interface and the body damages. the following remarks can be emphasized: o if the body 1 is damaged, implicitly the interface is even damaged; in other words, the damage state of the interface depends on the state of degradation of the body. o if the body 1 is not damaged, the interface damage is governed by the variable d , i.e. on the relative displacement occurring on the interface. in order to perform a first and simple assessment of the proposed model, the problem proposed in previous section, as a possible delamination test, is considered again, but accounting for the coupling damage given in eq. (21). the damage of the body indeed is equivalent to the reduction of the initial properties of the interface. figure 4: decohesion force maxf versus adhesion length, coupled damage model. in fig. 4, the value of maxf is plotted versus the adhesion length. when the coupling between the interface and body damage is accounted for, the following observations can be remarked: o as in the case of the uncoupled model, increasing the adhesion length  the value of maxf grows, until the optimal adhesion length e is reached, after which maxf remains constant; o as in the case of the uncoupled model, for higher values of the damage state of the body 1 the optimal adhesion length increases; o for higher values of the damage state of the body 1 the maximum value of maxf decreases. this last results appears much more reliable with respect to the one obtained adopting the uncoupled damage model. conclusions n conclusion, a coupled interface-body nonlocal damage model is proposed. the presented application consider a very simple structural scheme, subjected to elementary loading and damage histories. although the simplicity of the scheme and the damage evolution of the considered application, it is remarked the necessity of the use of the coupled damage model for the analysis of the reinforced concrete or masonry structural elements. the research will continue implementing the proposed model in a finite element code in order to develop an effective tool for the strengthening design and to investigate on mode complex structural applications. 0 50 100 150 200 250 300 350 400 450 0 50 100 150 200 250 300 adhesion length [mm] f m ax [ n ] d  =di=0.00 d  =di=0.90 d  =di=0.95 d  =di=0.99 i       max ,cd d d    x x x http://www.gruppofrattura.it http://dx.medra.org/10.3221/igf-esis.12.02&auth=true s. marfia et alii, frattura ed integrità strutturale, 12 (2010) 13-20; doi: 10.3221/igf-esis.12.02 20 references [1] t. c. triantafillou, m. n. fardis, materials and structures, 30 (1997) 486. [2] t. c. triantafillou, journal of composites for constructions asce, 2 (1998) 96. [3] m. r. valluzzi, m. valdemarca, c. modena, journal of composites for constructions asce, (2001) 163. [4] s. marfia, e. sacco, international journal of solids and structures, 38 (2001) 4177. [5] j. f. chen, advances in structural engineering, 5 (2002) 37. [6] p. foraboschi, journal of composites for constructions asce, (2004) 191. [7] s. marfia, m. ricamato, e. sacco, international journal for computational methods in engineering science and mechanics, 9 (2008) 77. [8] e. grande, g. milani, e. sacco, engineering structures, 30 (2008) 1842. [9] m. a. aiello, m. s. sciolti, international journal for restoration of buildings and monuments, 9(6) (2003) 639. [10] f. freddi, m. frémond, journal of mechanics of materials and structures, 1(7) (2006). [11] j. mazars, journal of engineering fracture mechanics, 25 (1986) 729. [12] j. mazars, g. pijaudier-cabot, asce journal of engineering mechanics, 115 (1989) 345. [13] e. sacco, j. toti, frattura ed integrità strutturale, 8 (2009) 3; doi: 10.3221/igf-esis.08.01. [14] g. alfano, e. sacco, international journal for numerical methods in engineering, 68 (2006) 542. http://www.gruppofrattura.it http://dx.medra.org/10.3221/igf-esis.12.02&auth=true microsoft word numero_34_art_22 p.o. judt et alii, frattura ed integrità strutturale, 34 (2015) 208-215; doi: 10.3221/igf-esis.34.22 208 focussed on crack paths crack path predictions and experiments in plane structures considering anisotropic properties and material interfaces p.o. judt, a. ricoeur university of kassel, institute of mechanics, 34125 kassel, germany judt@uni-kassel.de, ricoeur@uni-kassel.de abstract. in many engineering applications special requirements are directed to a material's fracture behavior and the prediction of crack paths. especially if the material exhibits anisotropic elastic properties or fracture toughnesses, e.g. in textured or composite materials, the simulation of crack paths is challenging. here, the application of path independent interaction integrals (i-integrals), j-, land m-integrals is beneficial for an accurate crack tip loading analysis. numerical tools for the calculation of loading quantities using these path-invariant integrals are implemented into the commercial finite element (fe)-code abaqus. global approaches of the integrals are convenient considering crack tips approaching other crack faces, internal boundaries or material interfaces. curved crack faces require special treatment with respect to integration contours. numerical crack paths are predicted based on fe calculations of the boundary value problem in connection with an intelligent adaptive re-meshing algorithm. considering fracture toughness anisotropy and accounting for inelastic effects due to small plastic zones in the crack tip region, the numerically predicted crack paths of different types of specimens with material interfaces and internal boundaries are compared to subcritically grown paths obtained from experiments. keywords. j-,m-,l-integral; interaction integral; fracture toughness anisotropy; material interfaces; crack paths; fracture process zone. introduction or the sake of an accurate prediction of crack paths, the loading analysis at cracks is one crucial part of the model. here, the application of path-independent integrals with remote integration contours is beneficial compared to local approaches, as no special requirements regarding the crack tip meshing have to be considered. integrating along large contours far from the crack tip essentially exploits numerically reliable data. the theory of forces at defects and singularities was established by eshelby [1] and applied to cracks and notches by cherepanov [2] and rice [3], introducing the path-independent j-integral. investigations by günther [4] and knowles and sternberg [5] provided balance equations including the j-, mand l-integrals, which were generalized to linear elastic fracture mechanics (lefm) by budiansky and rice [6]. later these balance laws founded the theory of the material or configurational forces [7]. in lefm, the jk-integral vector, representing the crack driving force, is related to the stress intensity factors (sif) [8] and the energy release rate (err). large integration contours at curved cracks require the integration along crack faces, f p.o. judt et alii, frattura ed integrità strutturale, 34 (2015) 208-215; doi: 10.3221/igf-esis.34.22 209 providing numerically inaccurate values approaching the crack tip, finally leading to large deviations in j2. improvements for an accurate calculation of j2 have been presented by eischen [9] and judt and ricoeur [10]. the interaction integral or i-integral is another conservation integral of the j-integral type [11]. here, the interaction of the physical and an auxiliary crack tip loading is used for the direct calculation of sif. in general, auxiliary fields are obtained from the asymptotic near tip solution for stresses and displacements. considering curved cracks, the jump of the auxiliary fields represents the straight auxiliary crack, introducing another strong discontinuity. calculating the global i-integral, path-independence is maintained considering the integration along both physical and auxiliary crack faces [12]. due to the fact that the auxiliary fields may be chosen arbitrarily, just satisfying balance, constitutive and kinematic laws, the i-integral can be applied to elegant analyzing multiple cracks systems [13]. the mand l-integrals are akin to the j-integral and, in terms of the concept of material forces, represent the scalar moment and vector moment induced by the crack driving force. especially if multiple defects are considered, these integrals provide a distinction between the crack driving force and other material forces [14]. in the paper this concept is adopted for a separation of the crack driving force and the forces acting in the plastic deformation. for an accurate calculation of crack paths, the anisotropic elastic and fracture mechanical properties must also be considered in the model. the elastic anisotropy is related to the crack tip loading analysis [15], whereas the fracture toughness anisotropy requires an extended theory for determining the crack deflection angle [16]. material interfaces and internal boundaries represent inhomogeneities in the material space, thus producing configurational forces along these boundaries. to obtain the crack driving force, the integration along these boundaries is necessary, providing path-independence. this paper presents a numerical model for the accurate loading analysis and crack path prediction considering anisotropic properties and material interfaces. calculated crack paths are presented and compared to those obtained from crack growth experiments. theory of path-independent integrals he lagrangian density of a system exhibiting a potential u is defined as t u  , with t being the kinetic density. the balance laws in the configurational space are derived from applying the gradient, divergence and curl operator to the lagrangian  and the lagrangian moment kx [17]. assuming quasi-static conditions, material isotropy and homogeneity, thus neglecting an explicit dependence of  on the location kx , the balance laws read   , ,,gard 0kj ij i k kj jju u q       (1)   , , div 1 0, 2 kj k ij i kj j k j m q x u q x            x (2) ,, curl( ) 0,mkn kj n kj n mkn kj j nj q x u q x     x   (3) with kjq being eshelby's energy-momentum tensor, kj kronecker's identity tensor, mkn the levi-civita symbol, ij the stress tensor, iu the displacements and m = 2 in two-dimensional and m = 3 in three-dimensional space. eqs. (1) (3) represent balance equations in a defect-free material. applying these laws to boundary value problems including a crack, the integrals of a domain v provide finite values and are denoted as jk-, mand lm-integrals. considering plane problems, i.e. m = 2, and 3l l in the following, the integrals are transformed with gauss' theorem into line integrals, surrounding the defect or the crack tip, see fig. 1(a), now reading 0 lim d ,k kj jj q n s       (4)   0 0 lim d lim d ,kj k j kj j k k km q x n s q n s x j x             (5) t p.o. judt et alii, frattura ed integrità strutturale, 34 (2015) 208-215; doi: 10.3221/igf-esis.34.22 210   0 0 ,lim d lim dkn kj n kj n j kn kj j n kn k nl q x u n s q n s x j x                 (6) if the contour  is shrunk to the crack tip. a reduced notation 3kn kn  is introduced for the levi-civita symbol. applying finite integration contours and considering curved cracks and mixed-mode loading, integration along the crack faces is required to provide path-independence. special treatment is necessary for the accurate calculation of j2 and l. here, numerical inaccuracies are adjusted, e.g. extrapolating the non-singular part of tangential stresses on the crack faces towards the crack tip [10]. (a) (b) figure 1: integration contours, for path-independent jk-, m-, l and ik-integrals, considering physical ( p ) and auxiliary ( a ) crack faces and a material interface ( i ). the mand l-integrals depend on the origin of the global coordinate system ke  . from eqs. (5) and (6) and from fig. 1(a) it becomes clear that if the global coordinate system coincides with the crack tip coordinate system ( )ike  , mand lintegrals vanish as 0kx   . otherwise, if the vector 0kx is pointing from the origin of the global frame to the crack tip and thus 0k k kx x x   , mand l-integrals are finite and represent the scalar and vector moments induced by the crack driving force jk. this feature can be applied to the separation of crack tip loadings in two-cracks systems by a global approach, i.e. by calculating the integrals along remote contours including both crack tips [14]. the ik-integral represents the interaction of two loading scenarios at a crack, i.e. the physical (a) and an auxiliary (b) loading [11]. ik is derived by substituting the superimposed stress and displacement fields ( a )+( b ) ( ) ( )a b i i iu u u  and ( a )+( b ) ( ) ( )a b ij ij ij    into eq. (4), yielding ( a )+( b ) ( a ) ( b ) k k k kj j j i   . with the interaction energy-momentum tensor ( a/b ) kjq the ik-integral reads    ( a ) ( ) ( b ) ( ) ( ) ( ) ( ) ( ) ( a/b ), , 0 0 1 lim d lim d . 2 b a a b b a k mn mn mn mn kj ij i k ij i k j kj ji u u n s q n s                        (7) applying finite integration contours, the integration along both the physical ( p ) and the auxiliary ( a ) crack faces is required to provide path-independence [12]. if material interfaces are considered, e.g. i between material a and b in fig. 1(b), integration along the interfaces is required in eqs. (4) (7) for the sake of path-independence. jkand ik-integrals accounting for crack face and interface integrals read 0 p i a b d d d ,k kj j kj j kj jj q n s q n s q n s                       (8) p.o. judt et alii, frattura ed integrità strutturale, 34 (2015) 208-215; doi: 10.3221/igf-esis.34.22 211 0 p a i a ( a/b ) ( a/b ) ( a/b ) ( a/b ) b d d d d ,k kj j kj j kj j kj ji q n s q n s q n s q n s                                    (9) and kjq     denotes the jump of the energy-momentum tensor across crack faces and interfaces. a local coordinate system *ke  is introduced, with *1e  pointing into the tangential direction of the interface. the stress vector it and the tangential derivatives of displacements ,1iu are continuous at the interface. the integrand related to the jk-integral reads      ab a a ( a ) ( b ) ( ) ( ) ( ab ) ( b ) ( ) ( a ) ( b ) 2 11 11 1,1 12 1,2 1,2 22 2,2 2,2 b ab1 , 2 j jq n u u u u u                   (10) with (ab) denoting values that are continuous across the material interfaces. the additional integrand related to the ikintegral reads         a a/b ( b, a ) ( b,b ) ( a , ab ) ( a , ab ) ( b, a ) ( b,b ) ( a , ab ) ( b, a ) ( b,b ) 2 11 11 1,1 12 1,2 1,2 22 2 ,2 2 ,2 b .j jq n u u u u u                 (11) bearing in mind that the auxiliary fields do not have to exhibit an interface, an appropriate choice is (b, a) = (b, b), providing   a a/b 2 b 0j jq n      . therefore, according to yu et al. [18], the integration along the interface should be superfluous. our investigations reveal, however, that the integral along the interface according to eq. (9) must not be neglected. path-independence is investigated at a model with a straight slant crack, hole and interface as presented by judt and ricoeur [19], where the values j2 were obtained without special treatment of the crack face integrals [10] thus being inaccurate. the jkand ik-integrals along small circular contours enclosing the crack tip (denoted as local) are compared to the values obtained by the approach as presented in this section according to eqs. (8) and (9) (denoted as global). furthermore, sif are calculated for a comparison of jkand ik-integrals. three different choices of the auxiliary fields are considered in the region b (see fig. 1(b)): a) the auxiliary fields are chosen according to the material constants in b, respectively; b) the auxiliary fields are chosen according to the material constants in a and the integration along the interface is neglected in eq. (9); c) the auxiliary fields are chosen according to the material constants in a and the ik-integral is calculated according to eq. (9). method j1 or i1 / (n/mm) j2 or i2 / (n/mm) ki / mpamm kii / mpamm jk local 0.05721 -0.03304 104.46 33.21 jk global 0.05731 -0.03301 104.58 33.15 ik local 0.0009954 -0.0003162 104.52 33.21 ik global 0.0009948 -0.0003168 104.46 33.27 ik global 0.0008242 -0.0004517 86.54 47.43 ik global 0.0009725 -0.0003119 102.12 32.75 table 1: numerical values of local and global jkand ik-integrals and sif, three different choices of the auxiliary fields a – c. from the results in tab. 1 it is obvious that path-independence is only retained considering interface integrals. nevertheless, values for the non-physical choice of the auxiliary fields differ slightly from those of the physically motivated choice with dissimilar elastic constants in a and b. anisotropy in elastic properties and fracture toughness he extrusion, drawing or rolling process applied to wrought metal products, in general yields a specified geometric orientation of the microstructure (texture) and thus of the material’s mechanical properties. the jk-integral according to eq. (8) may be applied straight forwardly to anisotropic elastic material [15]. as the near-tip stress t p.o. judt et alii, frattura ed integrità strutturale, 34 (2015) 208-215; doi: 10.3221/igf-esis.34.22 212 and displacement fields differ from the isotropic case, the relation between jk-integral and sif must be adapted. furthermore, due to the rolling process, anisotropic fracture toughness is observed. in plates of al-7075-t651, the crack resistance in the rolling direction (rd) is smaller than in the transverse direction (td), rd tdc cg g , thus depending on the global angle α. the crack resistance anisotropy is accounted for in the fracture criterion by introducing an elliptic interpolation function c ( )g  . the err is the projection of the jk-vector onto the crack growth direction and thus can be written as a function of α. finally, the maximum value of the ratio r ( ) / ( )cg g g  provides the crack deflection angle. in rolled plates of al-7075-t651, the anisotropy of the crack resistance is measured by standard ct tests providing rd 9.0cg  n/mm and td 11.4cg  n/mm. the ratio of fracture toughness anisotropy, i.e. td rd/ 1.12c cg g   for this material, is an important parameter of the model and must be considered for the correct prediction of crack paths [16]. crack path prediction he presented model is applied for the prediction of crack paths at specimens with material interfaces. the specimen is cut from a rolled plate of aluminum alloy al-7075-t651 (young’s modulus e = 72000mpa, poisson’s ratio ν = 0.3) and exhibits a circular hole. the incipient crack, exhibiting a length of a0 = 13.5mm, is aligned parallel to the td. a cylindrical steel core (steel 9s20k, young’s modulus e = 210000mpa, poisson’s ratio ν = 0.3) is grouted into the hole leading to an initial stress distribution at the interface region, see fig. 2(b). the hole’s diameter is d = 22mm and the diameter of the steel core is slightly larger. the clamping of the steel core leads to an initial stress distribution at the interface region. the calculation procedure involves an intelligent remeshing algorithm refining the mesh at the crack faces and tip, and a repeated incremental extension of the crack. the crack extension parameter is chosen 0.5a  mm. a numerical loading analysis is performed applying remote integration contours according to section 2, providing the jk-integral after each crack extension step. the crack deflection angle is calculated according to section 3. further details are presented in [16]. three configurations of the model with different boundary conditions at the hole are investigated in the simulation and compared with the experiment. in configuration 1 the phase b is just air, the hole representing a free boundary. the configuration 2 considers the material b to be a steel core which is perfectly bonded to the aluminum specimen. in the configuration 3 the material b also represents a steel core, which is grouted into the hole allowing for a separation of the materials a and b. to provide path independence of the jk-integral, the integration along the hole h is considered, see fig. 2(b). the calculated crack paths reveal that the impressed steel core, according to configuration 3, attracts the crack even stronger than solely a hole with free surfaces (configuration 1). in contrast to configuration 3 a perfectly bonded steel core induces the crack to veer away from the core. similar results as observed at configuration 2 have been reported by patton and santare [20], bouchard et al. [21] and nielsen et al. [22]. the crack path obtained from the experiment, where the boundary conditions of configuration 3 are met, is in very good agreement with the numerically predicted path. at the beginning, the crack veers away from the steel core and is then strongly attracted finally ending in the hole. (a) (b) figure 2: (a) comparison of experimental and numerically predicted crack paths for three different model configurations, (b) aluminum alloy specimen with hole and cylindrical steel core, incipient crack length a0 and loading p0 t p.o. judt et alii, frattura ed integrità strutturale, 34 (2015) 208-215; doi: 10.3221/igf-esis.34.22 213 application of mand l-integrals to crack tip plastic zones he concept of the configurational forces signifies their vanishing in a defect-free body. within the framework of the fe-method, however, it is observed that, depending on the applied mesh, configurational forces arise though no defects are existent [23]. this phenomenon may be used for the adaption of fe meshes in terms of vanishing configurational forces at internal nodes [23], and as an error indicator of the fe solution [24]. our investigations confirm that these configurational forces depend on the mesh and the loading. however, configurational forces in an homogeneous body are small compared to those resulting from defects. (a) (b) figure 3: (a) integration contour 0 and c enclosing the crack tip and the plastic zone, material forces ( )n kf and the crack driving force jk, (b) shapes of crack tip plastic zones in normalized depiction max p p( ) /r r from the von mises yield criterion. a new application of the configurational forces approach is the separation of the crack driving force and the forces acting at a plastic deformation ( )nkf , see fig. 3(a). evaluating the mand l-integrals at remote integration contours e.g. along the external boundaries of the model, as presented in section 2, the contribution of configurational forces in the crack tip plastic zone in general is implicitly included in the result. in contrast to a global approach of the jk-integral, always providing the sum of all configurational forces including jk and ( )n kf , the global approaches of mand l-integrals exclusively represent the contribution of the material forces in the plastic zone, if the origin of the global coordinate system is the crack tip. in that case the crack driving force jk has no contribution to m or l. the model of a double cantilever beam (dcb) specimen with different loading conditions is investigated, see fig. 4(a), including a single mode-i (f1 = f2 = f), a single mode-ii (f1 = −f2 = 0.5f) and a plane mixed-mode loading with mixed mode ratio β = kii/ki = −2/3 (f1 = f, f2 = 0). the material model is that of an idealized linear elastic-perfectly plastic behavior with tensile yield strength σy = 462mpa. a first approximation of the plastic zone p ( )r  is obtained by substituting the closed-form representation of the asymptotic crack tip field into the von mises yield criterion for the investigated mode cases, leading to the normalized shapes depicted in fig. 3(b). with this, the extension of the plastic zone rp along the ligament is calculated according to 2 2 i ii p 2 y 3 , 2 k k d    (12) being a simplified measure for the size of the crack tip plastic zone. the global mand l-integrals are calculated for an increasing load. the calculated values mpl and lpl must be corrected considering the initial configurational forces resulting from mesh and external loading. the correction terms are obtained from the global mand l-integrals at the linear-elastic regime, and thus pl elm m m  and pl ell l l  . in fig. 4(b) t p.o. judt et alii, frattura ed integrità strutturale, 34 (2015) 208-215; doi: 10.3221/igf-esis.34.22 214 corrected m and l -integrals are plotted vs. the simplified theoretical size of the plastic zone according to eq. (12). the values are normalized with respect to the maximum values max 288m  n and maxp 4.4r  mm of the mode-i loading case. in fig. 4(b) it is obvious that the m-integral increases as the region of the plastic deformation around the crack increases. the mixed-mode crack opening provides negligible values in l compared to m which even remain zero for the mode-i and mode-ii crack openings. nevertheless, the l-integral may serve as an additional condition describing the distribution of the material forces in the plastically deformed region. these first results seem promising with respect to a new application of the mand l-integrals, separating the crack driving force and the plastic deformation driving forces in a similar manner as the separation of the jk-integrals of two interacting cracks [14]. (a) (b) figure 4: (a) dcb specimen with applied loads f1 and f2 and crack length a = 40mm, (b) normalized global mand l-integrals with a linear elastic-perfectly plastic material model vs. the normalized plastic zone size maxp p/r r from eq. (12). closure ath-independent integrals are introduced applying remote integration contours along the external boundaries of the model. this global approach is beneficial compared to a local approach, where small integration contours around the crack tip are applied, as no special requirements regarding the crack tip meshing have to be considered and crack tips approaching interfaces can be appropriately handled. additional integrals along crack faces, material interfaces and internal boundaries are calculated providing path-independence. it is emphasized, that the integration along material interfaces is important for both, the jkand ik-integral for the accurate calculation of the crack tip loading. crack paths at material interfaces are predicted accurately and compared to experimental findings. next to the fracture toughness anisotropy, the boundary conditions at a material interface have a strong impact on crack paths. based on global mand l-integrals, a new approach for the separation of the crack driving force and forces inducing plastic deformation at the crack tip is motivated. acknowledgement he authors would like to acknowledge the financial support of the “landes-offensive zur entwicklung wissenschaftlich-ökonomischer exzellenz (loewe)” research funding program “safer materials”. references [1] eshelby, j.d., the force on an elastic singularity. phil. trans. a, 244 (1951) 87-112. p t p.o. judt et alii, frattura ed integrità strutturale, 34 (2015) 208-215; doi: 10.3221/igf-esis.34.22 215 [2] cherepanov, g.p., crack propagation in continuous media (translation from russian). j. appl. math. mech., 31 (1967) 503-512. [3] rice, j.r., a path independent integral and the approximate analysis of strain concentration by notches and cracks. j. appl. mech., 35 (1968) 379-386. [4] günther, w., über einige randintegrale der elastomechanik. abh. braunschweigischen wissen. gesell., 14 (1962) 5372. [5] knowles, j.k., sternberg, e., on a class of conservation laws in linearized and finite elastostatics. arch. rational mech. ana., 44 (1972) 187-211. [6] budiansky, b., rice, j.r., conservation laws and energy-release rates. j. appl. mech., 40 (1973) 201-203. [7] kienzler, r., herrmann, g., mechanics in material space with applications to defect and fracture mechanics. springer, berlin, 2000. [8] bergez, d., determination of stress intensity factors by use of path-independent integrals. mech. res. commun., 1 (1974) 179-180. [9] eischen, j.w., an improved method for computing the j2 integral. eng. fract. mech., 26 (1987) 691-700. [10] judt, p.o., ricoeur a., accurate loading analyses of curved cracks under mixed-mode conditions applying the jintegral. int. j. fract., 182 (2013) 53-66. [11] stern, m., becker, e.b., dunham, r.s., a contour integral computation of mixed-mode stress intensity factors. int. j. fract., 12 (1976) 359-368. [12] judt, p.o., ricoeur, a., consistent application of path-independent interaction integrals to arbitrary curved crack faces. arch. appl. mech., 85 (2015) 13-27. [13] judt, p.o., ricoeur, a., crack growth simulation of multiple cracks systems applying remote contour interaction integrals. theo. app. fract. mech., 75 (2015) 78-88. [14] judt, p.o., ricoeur, a., a new application of mand l-integrals for the numerical loading analysis of two interacting cracks. z. angew. math. mech., (2015). doi: 10.1002/zamm201500012. [15] sih, g.c., paris, p.c., irwin, g.r., on cracks in rectilinearly anisotropic bodies. int. j. fract. mech., 1 (1965) 189-203. [16] judt, p.o., ricoeur, a., linek, g., crack path prediction in rolled aluminum plates with orthotropic properties and experimental validation. engineering fracture mechanics, 138 (2015) 33-48. [17] eischen, j.w., herrmann g., energy release rates and related balance laws in linear elastic defect mechanics. j. appl. mech., 54 (1987) 388-392. [18] yu, h., wu, l., guo, l., du, s., he, q., investigation of mixed-mode stress intensity factors for nonhomogeneous materials using an interaction integral method. int. j. solids struct., 46 (2009) 3710-3724. [19] judt, p.o., ricoeur, a., crack growth in elastic materials with internal boundaries and interfaces. in proceedings in applied mathematics and mechanics 12 (2012) 159-160, gamm tagung, darmstadt, germany. [20] patton, e.m., santare, m.h., crack path prediction near an elliptical inclusion. engineering fracture mechanics, 44 (1993) 195-205. [21] bouchard, p.o., bay, f., chastel, y., numerical modelling of crack propagation: automatic remeshing and comparison of different criteria. comput. meth. appl. mech. eng., 192 (2003) 3887-3908. [22] nielsen, c.v., legarth, b.n., niordson c.f., extended fem modeling of crack paths near inclusions. int. j. numer. meth. eng., 89 (2012) 786-804. [23] braun, m., configurational forces induced by finite-element discretization. proc. estonian acad. sci. phys. math., 46 (1997) 24-31. [24] gross, d., mueller, r., kolling, s., configurational forces morphology evolution and finite elements. mech. res. commun., 29 (2002) 529-536. microsoft word numero_34_art_37 p. hess, frattura ed integrità strutturale, 34 (2015) 341-346; doi: 10.3221/igf-esis.34.37 341 focussed on crack paths graphene as a model system for 2d fracture behavior of perfect and defective solids p. hess institute of physical chemistry, university of heidelberg, d-69120 heidelberg, germany peter.hess@urz.uni-heidelberg.de abstract. a 2d bond-breaking model is presented that allows the extraction of the intrinsic line or edge energy, fracture toughness, and strain energy release rate of graphene from measured and calculated 2d young’s moduli and 2d pristine strengths. the ideal fracture stress of perfect graphene is compared with the critical fracture stresses of defective graphene sheets containing different types of imperfections. this includes (multiple) vacancies in the subnanometer range, grain boundaries, slits in the nanometer region, and artificial pre-cracks with sizes of 30 nm to 1 µm. independent of the type of defect, a common dependence of the critical fracture strength on the square root of half defect size is observed. furthermore, the results suggest the applicability of the griffith relation at length scales of several nanometers. this observation is not consistent with simulations pointing to the existence of a flaw tolerance for defects with nanometer size. according to simulations for quasi-static growth of pre-existing cracks, the atomic mechanism may also consist of an alternating sequence of bond-breaking and bond-rotation steps with a straight extension of the crack path. independent of the exact atomic failure mechanism brittle fracture of graphene is generally assumed at low temperatures. keywords. graphene; 2d bond-breaking model; 2d mechanical properties; fracture mechanism; fracture toughness; strain energy release rate. introduction haracterization of the elastic and fracture properties of covalent graphene monolayers is of fundamental scientific interest, because they define the upper limits of mechanical behavior [1]. since perfect samples with an area sufficient for nanoindentation experiments can be prepared, the intrinsic mechanical properties of the class of two-dimensional (2d) solids can be measured directly by nanoindentation with an atomic force microscope, as first realized for graphene [2]. it is important to note that this opens up the unique possibility of studying fracture mechanics of perfect crystals experimentally, a possibility not available for three-dimensional (3d) solids. furthermore, many theoretical approaches used in dynamic failure analysis are based on 2d models and thus can be applied directly to 2d solids without simplification. accordingly, the role played by dimensionality is an important issue in advanced fracture analysis. in addition, graphene sheets are of enormous practical importance owing to promising technological applications of larger samples, which, however, may be more or less defective. therefore, the influence of structural defects such as vacancies, dislocations, microcracks, grain boundaries, and pre-cracks on crack nucleation and propagation must be c p. hess, frattura ed integrità strutturale, 34 (2015) 341-346; doi: 10.3221/igf-esis.34.37 342 studied in engineering devices and compared with the behavior of the corresponding perfect solids to judge the mechanical quality and reliability of real materials. graphene is the paragon of the new class of 2d covalently bonded solids with unsurpassed intrinsic strength and strong in-plane but very weak out-of-plane stiffness. together with h-bn monolayers (boronitrene) the one-atom-thick sp2bonded hexagonal graphene structure is one of the thinnest known materials, however, without the partially ionic character of boronitrene, which makes the isolation of boronitrene monolayers more difficult. compared to these singleatom layer crystals, the presently actively studied transition-metal dichalcogenide (tmd) monolayers consist of several atomic layers, similar to the most widely studied mos2 sheets, which contain a central hexagonal plane of mo sandwiched between two hexagonal s planes. for these multilayer materials the exact layer thickness still is a controversial issue with differences in the assumed thickness of a factor of two and the failure behavior is considerably less understood than for the single-atom monolayers. graphene is an ideal model system for studying the limitations of continuum mechanics, where the 2d crystal can no longer be characterized by the usual macroscopic mechanical properties. this is of interest for the application of the griffith criterion, which is the most important basic relationship for investigating the role played by defects in engineering materials [3]. therefore, an estimate of the critical size, where the model breaks down at the nanoscale, is of paramount importance for practical applications. restrictions comparable to those for the griffith relation may not be expected in the case of the 2d bond-breaking model introduced below, which contains the same mechanical quantities, however, a different meaning of the length scale. presently, no contributions from experiments can be expected to solve this fundamental question concerning the range of validity of these basic models in applications to nanoobjects. molecular dynamics (md) simulations, which allow the treatment of fracture at the atomic scale, are strongly limited by the feature size. however, since a graphene monolayer is only one atom thick, larger sample areas may be investigated at reasonable computational cost, where size effects should be negligible. the md simulations give access to microscopic details of the fracture process in graphene such as the difference between uniaxial and biaxial tension, the role played by chirality, e.g., the difference of strength in the zigzag and the armchair directions, and the temperature dependence of failure. unfortunately, the uncertainties involved in these simulations are still large and in fact may be larger than the difference between the specific types of tension or the effect of chirality. for these reasons, it is useful to consider mean values of mechanical properties to extract the main characteristic behavior, such as the decrease of the critical fracture stress with the actual size of defects. to date contradictory results have been obtained by md simulations at the nanoscale, yielding, for example, on one hand flaw tolerance in the nanometer range and on the other hand the applicability of continuum models at the nanometer length scale. theory 2d fracture model of 2d mechanical properties of graphene he 2d bond-breaking model can be derived [4] from the corresponding 3d cleavage model [5] that combines the basic elastic and fracture properties with a subnanometer length. the analytical 2d bond-breaking model connects the relevant in-plane mechanical quantities of 2d solids belonging to continuum mechanics with a subnanometer length scale, describing the atomistic fracture behavior of chemical bonds by introducing a morse-type interaction function 2d = [(1de2d)/(4r0)]1/2 (1) here 2d is the 2d intrinsic strength or critical stress in (n/m), e2d the 2d young’s modulus in (n/m), 1d the breaking force in (n) or line (edge) energy or (j/m), and r0 the nanoscopic length scale representing the equilibrium bond length of the covalent monolayer. this parameter-free 2d fracture model provides a versatile tool to determine any missing intrinsic mechanical property if the other two and the length scale are known. the so-called 2d solids are not really 2d in the strict mathematical sense but possess a finite thickness and volume determined in the single-atom layers by the size of the constituent atoms. for this reason bulk mechanical properties can be assigned to this particular atomic volume, despite the subnanometer thickness of the monolayer. the thickness of the building blocks in the layered graphite material agrees well with a definition of the active nanoscopic volume in such a way that the average electron density of the isolated monolayer matches that in the parent bulk material [6]. as expected, this t p. hess, frattura ed integrità strutturale, 34 (2015) 341-346; doi: 10.3221/igf-esis.34.37 343 general definition provides layer thicknesses in very close agreement with those known for the building blocks in the layered structure of the corresponding bulk crystals, however, takes into consideration the real shape of the nanoobject. the 2d young’s modulus and 2d intrinsic strength of perfect graphene have been measured by nanoindentation under biaxial tension and have also been studied by density-functional theory (dft) calculations and md simulations, considering fracture by uniaxial tension. from this information the breaking force and line or edge energy can be obtained by using eq. (1). furthermore, the fracture toughness and critical strain energy release rate can be determined. owing to the large scatter of published experimental and theoretical data on graphene, which is larger than the differences due to chirality and the type of tension, the following mean 2d values were used in the present analysis: e2d = 333 n/m, 2d = 34.6 n/m, and 1d = 2.0 nj/m, using r0 = 0.142 nm as bond length in graphene [4]. in addition, the values of the fracture toughness and critical strain energy release rate were estimated from these quantities: 2 dick = 2d(8r0)1/2 = 1.210-3 n/m1/2 and 2 dicg = 21d = 4.0 nj/m. for comparison with literature data, bulk properties were calculated by dividing these properties by the thickness of the graphene monolayer of h = 0.334 nm, extracted from the interlayer thickness of the covalent layers in bulk graphite [7]. the layer thickness is generally employed to connect the 2d monolayer properties with the corresponding bulk properties of the 3d solid. these formal bulk properties are: e3d = 997 n/m2, 3d = 104 n/m2, 2d = 6.0 j/m2, kic = 3.5 mpa m1/2, and gic = 12 j/m2. atomic-scale mechanisms of fracture pathways in graphene elucidation of the elementary steps of graphene fracture by first-principles calculations and experimental investigations employing high-resolution imaging are largely lacking. for this reason, atomistic simulations have been performed to investigate the fracture pathways in graphene. for example, an analytical bond-order potential has been used to describe the interaction of the covalent cc bonds in graphene [8]. with this model two competing atomic failure processes have been identified, namely bond breaking at the crack-tip and cc bond rotation by 90°, leading to the formation of two pentagon/heptagon stone–wales (sw) defects. usually, brittle fracture via bond breaking is expected to prevail at low temperatures, whereas plastic deformation based on dislocations and the nucleation and motion of sw defects should dominate at high temperatures. simulations of the minimum energy paths indicate that bond rotation may be energetically and kinetically more favorable with a 12 ev lower energy barrier. however, the generation of the sw defect changes the local environment at the crack tip, leading to a crossover point, where symmetric and asymmetric bond breaking may dominate kinetically. crack extension is expected to remain straight according to the condition of quasi-static growth on the plane of maximum normal stress. consequently, the model suggests a mixed mechanism involving an alternating sequence of bond breaking and bond rotation under quasi-static loading conditions near the energetic limit of fracture [8]. the non-uniform bond deformation and rupture processes with highly localized stresses at the tip may create a variety of edge morphologies including reconstructed edges, which influence the electronic properties of graphene [8]. thus, alternatively to a simple bond-breaking process as the atomic-scale fracture pathway in the presence of pre-existing cracks in graphene, an alternating bond-breaking and bond-rotation mechanism may occur. besides the temperature, the fracture mechanism depends also on the loading rate. in the case of fast strong loading, crack kinking and branching will take place in graphene. atomistic md simulations on the dynamics of rapid fracture show that under pure opening load (mode i) the crack moves straight along the zigzag direction with atomically smooth edges at a speed of up to 8.2 km/s, which corresponds to 65% of the rayleigh wave phase velocity that is 12.56 km/s in graphene [9]. above this critical speed, kinking and instability with the formation of rough and irregular edges involving pentagons and heptagons is observed, owing to the strong energy input. results and discussion theoretical analysis of the influence of defects in graphene s mentioned before, structural defects such as vacancies may play an important role in deteriorating the structural integrity and mechanical performance, especially of large graphene layers. in the subnanometer length scale range the effects of (multiple) vacancies on the fracture strength have been studied by md simulations [10,11]. fig. 1 shows the critical fracture strength of n =1, 2, and 3 vacancy units with a crack length of l = na, where a is the lattice spacing a = 3 r0 = 0.246 nm, normalized to the mean intrinsic strength of 2d = 34.6 n/m [10] as a function of the a p. hess, frattura ed integrità strutturale, 34 (2015) 341-346; doi: 10.3221/igf-esis.34.37 344 square root of half defect length. these values are for tensile load at 300 k, where graphene is expected to fail by brittle fracture either by bond breaking or combined bond-rupture and bond-rotation processes. larger slits in the range of 0.74 nm have been studied by a quantum mechanical/molecular mechanical/continuum mechanical (qm/mm/cm) model and compared with the griffith formula [12]. quantum mechanics was used to describe a small region around the slit and the coupled continuum-atomistic model was applied elsewhere. the electronic structure calculations agree with continuum fracture mechanics within 10% for the longest crack investigated. the griffith relation, assuming linear behavior of the stress–strain relationship and neglecting lattice trapping, allows a reasonable description of graphene fracture initiated by crack-like defects as small as 1 nm in size. in fact, dft calculations of the energy release rate exceeded the lower bound value of gic = 22d by only 10%, indicating modest lattice trapping [12]. fig. 1 presents the normalized critical fracture strengths of the nanometer slits obtained by the qm/mm/cm calculations versus the square root of half defect lengths. the decrease of the critical strength values is nearly paralel to the main correlation, however, with higher fracture strengths. as stated by the authors, the shape of such slits bears little relationship to sharp cracks assumed in the griffith model. this could be a simple explanation for the higher strength values. molecular dynamics simulations indicate that tensile fracture in nanocrystalline graphene may become insensitive to a preexisting hole or notch below a characteristic critical length of 30 nm [13,14]. circular holes with 16 nm radius created in the center of a nanostrip of nanocrystalline graphene with 2 nm average grain size did not initiate crack nucleation by stress concentration at the flaw but nucleation of cracks started some distance away from the hole [14]. this increase of the characteristic length scale of flaw tolerance in nanocrystalline graphene was connected with a decrease in the elastic modulus, fracture strength, and the strain energy release rate to 8 j/m2 compared to about 12 j/m2 for single-crystalline graphene. as stated above, higher critical fracture strengths are expected for circular holes in comparison with atomically sharp tips due to reduced stress amplification. 0.1 1 10 50 (half defect length) 1/2 1/2 (nm) 10 50 s tr en g th ( n /m ) hess (2015) this work daly et al. (2015) wang et al. (2012) khare et al. (2007) yin et al. (2015) rasool et al. (2013) 1 zhang et al. (2014) figure 1: intrinsic stress of perfect [4] and critical engineering stress of defective graphene containing vacancies [10,20], slits [12], grain boundaries [15], and pre-cracks studied theoretically by dft and md calculations [17] and experimentally by nanoindentation [16]. the straight line is a guide to the eye. experimental analysis of graphene with defects measurements of the intrinsic strength of crystalline and polycrystalline graphene membranes have been performed with a custom-fabricated diamond tip of 115 nm radius, to ensure a uniform stress distribution [15]. the strongest single-crystal membrane failed at 31.5 n/m, which is slightly lower than our mean value of 34.6 n/m presented in fig. 1. for most large angle grain boundaries a strength of 80 gpa has been measured that corresponds to 26.8 n/m. normalization of this value to the mean intrinsic strength considered here yields 29.4 n/m. by high-resolution transmission electron microscopy the atomic-scale strain field has been mapped showing bond lengths of up to 0.185 nm in comparison to the p. hess, frattura ed integrità strutturale, 34 (2015) 341-346; doi: 10.3221/igf-esis.34.37 345 average bond length of 0.142 nm observed for the single-crystal material [15]. this maximum bond extension is used to display the reduction of the fracture strength by large angle grain boundaries in fig. 1. if defects are present, as is usually the case for large-area engineering graphene sheets, the concept of fracture toughness can be employed to characterize the real engineering strength of the material, using the griffith relationship. for example, the griffith relation has been employed for failure analysis in the case of artificial pre-cracks. the aim of this model is to explain the discrepancy between the theoretically predicted pristine strength and the actually observed real fracture strength. griffith’s brittle fracture model depends on the same mechanical properties as eq. (1) and deviates only by a numerical factor and the meaning of the length scale involved in the brittle cleavage process between the weakest crystallographic cleavage planes [3] cr = [(22de3d)/(a0)]1/2 (2) here cr is the actual critical fracture strength of real crystals governed by the stress amplification effect generated by defects or flaws, e3d the bulk young’ modulus, and 2d the surface energy. the length scale a0 is connected with half the length of an internal failure-inducing microcrack or the depth of a surface-breaking crack responsible for inducing crack nucleation. note that the intrinsic length scale occurs in eqs. (1) and (2) for dimensionality reasons. for example, in eq. (2) the young’s modulus has the dimension ‘energy per volume’ and the surface energy the dimension ‘energy per surface area’. experimental values reported recently for the effective fracture stresses and corresponding crack lengths, observed for various artificial central cracks introduced with a focused ion beam, show for the first time the applicability of the griffith relation to defective 2d crystals [16]. the extrapolation of the measured fracture strength values to the intrinsic value yields a surprisingly good agreement, as can be seen in fig. 1. thus, it is important to stress that the 2d bond-breaking model applied to the intrinsic fracture behavior of perfect graphene and the griffith analysis of defective graphene deliver consistent results covering four decades of flaw size from the subnanometer to the micrometer range, despite the relatively large scatter in the data. this conclusion is supported by recent md simulation indicating that the difference between the griffith criterion and md simulation is small for cracks propagating along the zigzag direction with the lowest critical fracture stress. for an energetically less favorable crack path, e.g., a kinked path approaching during propagation the zigzag direction from a different chirality, deviations of more than 15% may be observed for small crack sizes below 10 nm [17]. this conclusion has been obtained by comparing the apparent fracture resistance used as a fitting parameter in the relationship of the griffith stress to crack length and the evaluation of the fracture resistance by md calculations of the line or edge energy for different chiralities. such an overestimation of the fracture strength in the nanometer region by the griffith criterion is in agreement with the results observed in the previously discussed qm/mm calculations [12]. conclusions ith the two 2d fracture models discussed above a complete and consistent set of mechanical properties of graphene has been derived that is in good agreement with the extensive published data. the pristine strength is consistent with most modeled and the measured critical fracture strengths of graphene containing crack-like defects, stretching from vacancies with subnanometer size to artificial pre-cracks extending to micrometer size. the observed correlation of defect size behavior in the nanometer range is in disagreement with a general flaw tolerance in the nanoscale, where essentially theoretical strengths should be observed in the presence of cracks of nanometer size [13,14]. the present findings clearly support the alternative point of view discussed in more detail in [18]. a further argument against general flaw tolerance is that the pathway and direction of crack propagation in graphene can be controlled under tensile load by the presence of atomistic defects in the form of vacancies placed deliberately in the monolayer. this has been demonstrated by applying a first-principles-based reactive force field potential (reaxff) that features specific patterns of vacancies to simulate the fracture paths in graphene [19]. in fact, it was possible to cut graphene monolayers along these selected patterns simply according to the spatial arrangement of vacancies. the mechanical reliability and ability of defective covalent monolayers to resist failure is an important practical issue, because graphene and other 2d solids may play a crucial role in the post-silicon era. the critical strength–defect size dependence presented in fig. 1 provides essential information on the degree of degradation of the engineering strength with the square root of half defect length taking into consideration very different structural imperfections. furthermore, it confirms that the combination of the 2d bond-breaking model, describing the perfect monolayer, and the griffith model, w p. hess, frattura ed integrità strutturale, 34 (2015) 341-346; doi: 10.3221/igf-esis.34.37 346 taking into account the specific defect size dependence postulated by the griffith relation, grasps the main features of graphene fracture mechanics, however, neglecting detailed features such as the dependence of fracture on crystallographic direction and the nature of applied tension. references [1] cao, g., atomistic studies of mechanical properties of graphene, polymers, 6 (2014) 2404-2432. [2] lee, c., wei, x., kysar, j. w., hone, j., measurement of the elastic properties and intrinsic strength of monolayer graphene, science, 321 (2008) 385-388. [3] griffith, a. a., the phenomena of rupture and flow in solids, philos. trans. r. soc. london, a221 (1920) 163-198. [4] hess, p., 2d microscopic model of graphene fracture properties, mater. res. express, 2 (2015) 055601-1-6. [5] hess, p., strength of semiconductors, metals, and ceramics evaluated by a microscopic cleavage model with morsetype and lennard-jones-type interaction, j. appl. phys., 116 (2014) 053515-1-6. [6] wagner, p., ivanovskaya, v. v., rayson, m. j., briddon, p. r., ewels, c. p., mechanical properties of nanosheets and nanotubes using a new geometry independent volume definition, j. phys.: condens. matter, 25 (2013) 155302-1-22. [7] hod, o., graphite and hexagonal boron-nitride have the same interlayer distance. why?, j. chem. theory comput., 8 (2012) 1360-1369. [8] terdalkar, s. s., huang, s., yuan, h., rencis, j. j., zhu, t., zhang, s., nanoscale fracture in graphene, chem. phys. lett., 494 (2010) 218-222. [9] zhang. b., yang, g., xu, h., instability of supersonic crack in graphene, physica b, 434 (2014) 145-148. [10] wang, m. c., yan, c., ma, l., hu, n., chen, m. w., effect of defects on fracture strength of graphene sheets, comput. mater. sci., 54 (2012) 236-239. [11] sun, x., fu, z., xia, m., xu, y., effects of vacancy defect on the tensile behavior of graphene, theor. appl. mech. lett., 4 (2014) 051002-1-5. [12] khare, r., mielke, s. l., paci, j. t., zhang, s., ballarini, r., schatz, g. c., belytschko, t., coupled quantum mechanical/molecular mechanical modeling of the fracture of defective carbon nanotubes and graphene sheets, phys. rev. b, 75 (2007) 075412-1-12. [13] gao, h., ji, b., jäger, i. l., arzt, e., fratzl, p., materials become insensitive to flaws at nanoscale: lessons from nature, proc. natl. acad. sci. usa, 100 (2003) 5597-5600. [14] zhang, t., li, x., kadkhodaei, s., gao, h., flaw insensitive fracture in nanocrystalline graphene, nano lett., 12 (2012) 4605-4610. [15] rasool, h. i., ophus, c., klug, w. s., zetti, a., gimzewski, j. k., measurement of the intrinsic strength of crystalline and polycrystalline graphene, nat commun., 4 (2013) 2811-1-7. [16] zhang, p., ma, l., fan, f., zeng, z., peng, c., loya, p. e., liu, z., gong, y., zhang, j., zhang, x., ajayan, p. m., zhu, t., lou, j., fracture toughness of graphene, nat. commun., 5 (2014) 3782-1-7. [17] yin, h., qi, h. j., fan, f., zhu, t., wang, b., wei, y., griffith criterion of brittle fracture in graphene, nano lett., 15 (2015) 1918-1924. [18] ballarini, r., kayacan, r., ulm, f. j., belytschko, t., heuer, a. h., biological structures mitigate catastrophic fracture through various strategies, int. j. fract., 135 (2005) 187-197. [19] jack, r., sen, d., buehler, m. j., graphene nanocutting through nanopatterned vacancy defects, j. comput. theor. nanosci., 7 (2010) 1-6. [20] daly, m., reeve, m., singh, c. v., effects of topological point reconstructions on the fracture strength and deformation mechanisms of graphene, comp. mater. sci., 97 (2015) 172-180. microsoft word numero_50_art_8_2403 m. baghdadi et alii, frattura ed integrità strutturale, 50 (2019) 68-85; doi: 10.3221/igf-esis.50.08 68 modeling of a cracked and repaired al 2024t3 aircraft plate: effect of the composite patch shape on the repair performance baghdadi mohammed, serier boualem, salem mokadem, zaoui bouchra, kaddouri khacem university of djillali liabes, laboratory of mechanics physics of materials (lmpm laboratory), sidi bel abbes, algeria. mohbagh0@gmail.com, boualems@yahoo.fr, moka_salem@yahoo.fr, zaouibouchra55@yahoo.com, kaddourikacem@yahoo.fr abstract. in this work the finite element method was used to analyse the composite patch shape effect of the repair performance. unlike all the works done conducted so far in this domain, this work proposed here, takes into account the reducing both, the stress intensity factor in repairing crack heads and the maximum shear stresses in the adhesive layer. this is the originality of this work. in function of the surface and the volume of the rectangular patch, three cases were taken into consideration: with conservation of the patches surface and its volume, with a reduction of the patches surface and its volumes, and in the end, with a reduction of the patches surface and conservation of its volume. the obtained results show that in the first case, the patch shape have no effect on the sif, the sharp edges (obtuse, right and acute) of oblique shapes generate high shear stresses, in the second case, the reduced surfaces lead to significant mass gain with the same sif values. and to an increase in the maximum shear stresses, in the latter case the patches shapes lead to a reduction of the sif and the shear stresses. keywords. patch; composite; sif; stress; shape; adhesive; crack. citation: baghdadi, m., serier, b., salem, m., zaoui, b., kaddouri, k., modeling of a cracked and repaired al 2024t3 aircraft plate: effect of the composite patch shape on the repair performance, frattura ed integrità strutturale, 50 (2019) 68-85. received: 18.02.2019 accepted: 07.07.2019 published: 01.10.2019 copyright: © 2019 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. introduction he birth of cracks in a structure metal in any field, such as aeronautical and marine structures, is a major concern of maintenance operators. to extend the life of these structures, becker [1] has developed a repair technique which consists of bonded a composite patch with polymer matrices, usually epoxy, on the cracked area. this technique has shown its effectiveness in reducing of the stress intensity factor (sif) at the crack tip, and by improving the behaviour of the damage structures durability [2,3]. in addition to their high stiffness, these composites materials offer good corrosion resistance and low density. the quality of the repair depends on several parameters, geometrical and mechanical on the composite patch and the adhesive layer. thus, the composite patches shapes seem to be a determining element of the repair effectiveness. this is the objective of several research projects, bouchiba and al [4] have developed a static approach to optimise the composite patch shape, they conclude that the butterfly shape reduces the failure energy in t http://www.gruppofrattura.it/va/50/2403.mp4 m. baghdadi et alii, frattura ed integrità strutturale, 50 (2019) 68-85; doi: 10.3221/igf-esis.50.08 69 the crack tip and minimise the shear stresses in the adhesive layer. mhamdia and all [5], proceeding at conception of a new patch shape, named patch double arrow, show that, compared with the conventional rectangular shape, this shape, resulting in a more performing and more efficient repair in terms of the normal tension stresses relaxation, highly concentrated in the crack heads. chung k.h and al [6, 7], jeong gi-hyeon and all [8], by analysing the efficiency of patch geometry, from a point of view, fracture mechanics and disbonding of the patch, proceeded with the development of a composite patch geometry leading to the maximum reduction of the sif. ramji and srilakshmi [9], by analysing the repair of the structure solicited in mixed mode with composite patch, have shown that the sif in repairing crack is insensitive to the patch shapes. in another study, ramji and al [10], studying the effect of the circular, square, rectangular, elliptical and octagonal shapes of the patch on the crack repair efficiency in mixed mode, they concluded that, the rectangular and octagonal shapes are the performances, in terms of the sif reducing. kashfuddoja and all. [11] developed this analysis by adding the elliptical shape, they studied the effects of these shapes on the repair quality in terms of reducing of the stress concentration factor "scf" in the circular notch vicinity located in a plate centre, repaired with a composite patch unidirectional, by comparing the values of these parameter resulting from these different shapes, these authors have shown that the octagonal patch elongated perpendicular to the traction direction, is the most effective shape. fekih and al [12], analysed the patch shapes effect on the durability and reliability of the repair, in term of “j” integral reducing, shown that the patch shaped star is the most effective. mahadesh kumar and all. [13] analysed the values of the sif resulting from the repair using four principal regular patches geometries, square, rectangular, circular and elliptical. they show as well, from a point of view a reduction of this parameter, that the classic rectangular shape with important elongation in the direction parallel to the crack, is the most effective. based on these findings, these authors have developed a new patch shape, called "skewed patch", they concluded that, this last, leads to a mass gain around 28% in practically the same value of the sif. or it reduces this value of 10% for the same volume of the patch. mohamed ibrahim and all [14], analysed the effect of a rectangular patch on the repair performance of the two cracks interaction. this analysis is done in terms of reducing the stress intensity factor in mode i. this work fits into this context and aims to analyse the effect of the patch composite shapes on the efficiency and performance of the repair, in terms of reduction of the stress intensity factor in cracks heads and the shear stresses in all the adhesive layer. a finite element method was used for this analysis. for this purpose, a geometric model has been developed. figure 1: geometric model of the structure. geometric model he geometric model developed consists of a 2024-t3 aluminium alloy plate of an aircraft structure, this plate is characterized by its height h = 250 mm, its width w= 125 mm and its thickness ep = 2 mm. this plate is subjected to uniaxial tension stresses of varying amplitude, allowing the crack propagation in opening mode, the t m. baghdadi et alii, frattura ed integrità strutturale, 50 (2019) 68-85; doi: 10.3221/igf-esis.50.08 70 most dangerous mode. the composite patch, defined by its height hp, its width wp, and its thickness er = 2 mm, is supposed to be perfectly bonded to the plate by an fm-73 adhesive type of thickness ea = 0.2 mm (fig.1). the mechanical properties of the plate, the patch and the adhesive are shown in tab. 1. properties plate al (2024-t3) carbon /epoxy engineering constants fm-73 adhesive type e1 (mpa) 72 10³ 153 103 2.55 103 e2 (mpa) ---9.1 103 --- e3 (mpa) ---9.1 103 --- ν12 0.33 0.258 0.3 ν13 ---0.258 --- ν23 ---0.384 --- g12 (mpa) ---4.57 103 420 g13(mpa) g23(mpa --- ---4.57 103 3.15 103 --- --- table 1: mechanical properties of the materials. presentation of the calculation software used in this study he performance of abaqus software version 6.11 [15] is used for the analysis of cracked aircraft plates and after repaired with composite patches. abaqus software has many finite element analysis capabilities, ranging from a simple linear static study to another complex nonlinear static. the documentation of this software gives the procedures to be followed to make analyses of different fields of engineering. the ultimate objective of finite element analysis is to recreate mathematically the behaviour of a true engineering system. in other words, the analysis must be based on a precise mathematical model of a physical prototype. presentation of the model he three-dimensional numerical model developed for this study consists of a cracked al2024 t3 plate repaired by composite patch (carbon-epoxy) (fig. 1). finite element modelling requires the mesh of the structure to be analysed. the choice of the types and sizes of elements to be used, especially in the crack tip depends on the fundamental parameters, to control the strong gradients of stresses and deformations in the vicinity of the crack tip vicinity, the first step is to choose the type of element, the most adapted to the problem studied, then we divide the structure into a number of elements. in general, and according to the fracture mechanics and the finite element modelling of a cracked plate, the structure has been meshed globally using elements of the type c3d8. (an 8-node linear brick) (fig.2). to obtain a correct representation of the displacement field near the crack, the elements called singular are used, as suggested by the abaqus software documentation. the type of singularity 1/√r, for the stress fields are obtained by moving all the intermediate nodes of the elements around the crack tip to a quarter of a distance from the nodes belonging to the considered crack tip. the mesh of the crack tip was exclusively refined using this special type element (fig.2). the total number of elements for the repaired structure depends on the patch shape. for the rectangular patch, the total number of elements is shown in tab. 2. the different components of the analysed structure numbers of elements sizes of elements aluminium 2024-t3 11796 2mm cracking front 2500 0.078mm fm-73 adhesive type 3200 0.5mm composite patch 12800 0.5mm table 2. numbers and sizes of the mesh elements. t t m. baghdadi et alii, frattura ed integrità strutturale, 50 (2019) 68-85; doi: 10.3221/igf-esis.50.08 71 the side sizes of an element, far from the crack and in the crack vicinity, was represented in tab. 2. this sizes and types of mesh, remains the same for all the simulations in this work, to avoid any influence of the mesh on the results. figure 2: mesh of the structure. adhesive has been considered as a third material to introduce its actual mechanical properties. the interaction between adhesive and the cracked plate area, firstly, and between the composite patch and adhesive, secondly is considered perfectly welded (the two bodies can be considered welded during the simulations). the symmetry allows the modelling of the structure quarter, which leads to a reduction in calculation times, the boundary conditions imposed on the plate analysed are represented as follows (fig. 3): figure 3: boundary conditions imposed on the structure. validation of the model o validate the model developed in this work, fig. 4 shows a comparative analysis of the sif variation obtained from the numerical model, developed in this work, and that resulting from an analytical model. the sif is the only significant parameter, which allows to know the state of stress and deformation in any crack heads. for a central crack solicited in opening mode, the relation between the far applied stress on the plat (σ) and the stress intensity factor ki is as follows: ki= y σ √𝜋𝑎 (1) t m. baghdadi et alii, frattura ed integrità strutturale, 50 (2019) 68-85; doi: 10.3221/igf-esis.50.08 72 where y is a geometric factor, depends on the plate geometry and the crack shape. y = 1.12 (for a finished plate containing a central crack "2a"). the analysis of this result shows that the numerical and the analytic model lead practically the same results and whatever the applied stress intensities to the plate. this behaviour clearly illustrates that the model developed in this study and the boundary conditions imposed are reliable and allows a better mechanical behaviour analysis of the cracked structure and repaired with composite patch. -2 0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 k i (m p a .m 1 /2 ) a (m m ) n um erical , a pplied stress 50 m pa a nalytical , a pplied stress 50 m pa n um erical , a pplied stress 100 m pa a nalytical , a pplied stress 100 m pa n um erical , a pplied stress 150 m pa a nalytical , a pplied stress 150 m pa figure 4: variation of the sif in crack head as a function of the crack length, for different applied stress intensities these conditions will be retained along in this work and will allow a reliable analysis of the patch shape effect on the performance of the repair. results and discussion t has been reported previously that the composite patch shapes have a significant effect on the performance and reliability of the repair in terms of reduction of the stress intensity factor in crack heads and the shear stresses in the adhesive layer. the reduction of these two physical parameters is required for the stability and durability of cracked structures repaired with composite patches. effect of the patch geometric parameters (height hp and its width wp) he cracked plate is repaired using a rectangular carbon-epoxy patch, characterized by its height hp and its width wp (fig.1). the junction between these two structures is ensured by means of an fm73 adhesive type. the latter has been very often used in many works in the patch repair case. the objective of this study is to analyse the effect of these two geometrical parameters hp and wp on the repair quality in terms of sif reduction in opening mode. the results obtained are illustrated in fig. 5. the analysis of the (fig. 5, a), clearly shows that the sif decrease when the repair is done by a wider patch. whatever the applied stress intensities, the repair becomes more and more effective and efficient with the use of the wider patch. this behaviour was observed by dajmel ouinas [16] and al, mahadesh kumar and al. [13] and confirmed by ramji and al. [10] as well as by kashfuddoja and al. [11] that have demonstrated the effectiveness of designing an elongated patch in the direction perpendicular to the tensile loading. this efficiency is closely related to optimizing the height of this patch, noted hp, it is clearly shown that the composite patches with higher heights lead to a clear decrease in the sif in mode i (fig 5.b). for the more important height of the patch, this geometrical parameter does not appear to play an important role in improving the service life of the repair in terms of sif reduction (fig5. b). in fact, there is a threshold value beyond which this rapture parameter does not vary with increasing the height of the patch. as shown in (fig. 5, b). the results obtained in fig. 5, show more clearly the possibility of determining an optimal height of a rectangular patch, nevertheless, this last is closely related to its width. in our simulation conditions, for a repaired crack size of "a = 18mm" and whatever the applied stress intensities, for width values greater than or equal to "wp> 72mm", the optimum height hp is equal to 40mm. in this case, the repair is only effective if wp> hp, in other words, the repair is effective only if the i t m. baghdadi et alii, frattura ed integrità strutturale, 50 (2019) 68-85; doi: 10.3221/igf-esis.50.08 73 rectangular patch has a height (perpendicular to the crack) is less than its width (parallel to the crack). these results are in good agreement with those obtained by mahadesh kumar and al. [13]. 0,8 1,0 1,2 1,4 1,6 1,8 2,0 2,2 2,4 2,6 2,8 3,0 1,5 2,0 2,5 3,0 3,5 4,0 4,5 5,0 5,5 6,0 6,5 7,0 7,5 8,0 8,5 9,0 k i (m p a * m 1 /2 ) wp/2a applied stress = 50 mpa applied stress = 100 mpa applied stress = 150 mpa a) 0,4 0,6 0,8 1,0 1,2 1,4 1,6 1,8 2,0 2,2 2,4 1,5 2,0 2,5 3,0 3,5 4,0 4,5 5,0 5,5 6,0 6,5 7,0 7,5 8,0 8,5 k i ( m p a *m 1 /2 ) hp/2a applied stress = 50 mpa applied stress = 100 mpa applied stress = 150 mpa b) figure 5: variation of the sif for different applied stress intensities, repaired crack a =18mm. a) as a function the composite patch width, b) as a function of the composite patch height. (=18mm) these results explicitly show the interaction between the width (wp ) and the height (hp ) of a rectangular patch in the determination of the sif in crack heads and the shear stresses in the adhesive layer. which leads us to think that the optimization of the patch should go through by other shapes for which the height varies with the width. the interaction between these two geometric parameters (width and height) of the patch, shows the need to perform an optimization analysis to predict the best variation of these dimensions, allowing the reduction of the sif in crack heads as well as shear stresses in the adhesive layer. effect of the patch shape on the stress intensity factor on the crack heads he sizes of the patch shapes were deduced from the height hp and the width wp of the initial rectangular patch which were optimized according to the size of the repaired crack (a = 18mm), according to the results shown in (figs. 5). seven shapes of patches were selected for this analysis: rectangular, arrows-shaped, h-shaped, trapezoidal, elliptical, octagonal and butterfly-shaped. the effect of these shapes on the repair performance, in terms of reduction of the sif in crack heads and shear stresses in the adhesive layer, is made in three steps: with conservation of the patch surface and its thickness (fig.6), with a variation of the patch surface and conservation of its thickness ( fig.8), and in the end, with a variation of the patch surface and its thickness (fig.10). patch with conservation of the surface and its thickness firstly, the repair is done with patches having the same surface and the same thickness (fig 6). the compensation of the surface is done by playing on its hp height. these conditions allow the elimination of the other parameters effect, and lead to a more realistic analysis of the composite patch shape effect on the mechanical behaviour of cracked plate, in order to reduce the fluctuations of the results that may be due to the nature of the mesh elements. the same elements, the same sizes and the same simulation conditions have been retained. (tab. 2). the results obtained are shown in fig. 7, which show that the sif in crack heads repaired seems to be practically insensitive to the patch shape. this insensitivity, much more marked for short sizes cracks (less than 18mm), can be explained by the fact, that the overlapping surface is identical for all patch shapes analysed. this surface is a geometric parameter determining of the repair performance in terms of crack stability. the rupture criteria resulting from these patch shapes, converge to the same value. the repair of larger sizes cracks resulting in a negligible fluctuation of the sif. this leads to say that, contrary to the results obtained by [17,18], when the overlapping surface of the cracked zone remains invariable, the patch shape has no t m. baghdadi et alii, frattura ed integrità strutturale, 50 (2019) 68-85; doi: 10.3221/igf-esis.50.08 74 effect on the repair efficiency in terms of fracture energy reduction in mode i. in fact, the sharp edges (obtuse, right and acute) of these patch shapes, are positioned too far from the crack heads, which considerably reduces their effect of indefinitely storing normal stresses, strongly localised in this crack heads. these results explicitly show that it is the overlapping surface of the damaged part that controls the mechanical behaviour of the repair using patches of different shape. so, it will be wise to analyse the response of these repaired structures using these same patch shapes with variable overlap surface. figure 6: the different dimensions of the quarter of the patch shapes (constant surfaces ant thicknesses). 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 8,0 8,5 9,0 9,5 10,0 10,5 11,0 11,5 12,0 12,5 13,0 13,5 14,0 14,5 k i (m p a* m 1 /2 ) a (mm) rectangular patch elliptical patch patch shaped arrow octagonal patch trapezoidal patch patch shaped h patch shaped butterfly a) the repaired face 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 k i (m p a* m 1 /2 ) a (mm) rectangular patch elliptical patch patch shaped arrow octagonal patch trapezoidal patch patch shaped h patch shaped butterfly b) the unrepaired face figure 7: of the patch shape on the sif level, applied stress 150 mpa. a) repaired face, b) unrepaired face. patch with a variation of the surface and conservation of its thickness to develop this study, all the patches shapes, analysed previously are deduced from a rectangular patch (fig.8). the seven patches obtained have variable surface. the fig. 9, illustrates the shape effect of such patches on the variation of the sif in mode i, this results clearly shows that this rupture criterion does not vary much with the variation of this patch shape (fig.9a). the same behaviour is observed on the unrepaired face of the plate (fig.9b). for repairing cracks smaller than “a <18mm”, the patch shape has virtually no effect on the repair quality in terms of rupture parameter reducing (fig. 9). beyond this size, a slight variation of this parameter is observed. he noted, however, that such cracks (a >18mm) remain virtually theoretical for the repair performance prediction. the global analysis of the cracked structure shows that this performance is almost insensitive to the patch shape. remember that compared to the rectangular patch, all other shapes have a much smaller overlapping surface (fig 8). it is relevant to note that the patch shaped arrow has a surface that is doubly smaller than the surface of the rectangular patch. which is very interesting, from a point of view, mass gain, corresponding to a value of 50%. compared to the rectangular patch, all the other shapes lead to a significant mass gain and practically at the same values of the sif. this clearly shows that the composite patch shape control significantly the repaired cracks behaviour. m. baghdadi et alii, frattura ed integrità strutturale, 50 (2019) 68-85; doi: 10.3221/igf-esis.50.08 75 a surface twice as small, leads to the same values of the fracture energy in crack heads (fig 9, a). the values of the sif recorded on the unrepaired face of the plate are higher when the repair is done by using patches with an important overlapping surface (fig.9b). this shows that the risk of the plate bending is minimized when the repairs is done by patches with greatly reduced on the overlapping surface. such behaviour is only possible by modifying the composite patch geometry. this change results in sharp edges (obtuse, straight, acute) located very close of crack heads, thus promoting a large normal stress located in this crack head, transfer to the patch. to better understand this effect, an analysis of this modification with conservation of its volume is necessary. in other words, with modification of the patch surface and its thickness (fig.10). figure 8: the different dimensions of the quarter of the patch shapes (variation surfaces and constant of its thicknesses). 0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 6,0 6,5 7,0 7,5 8,0 8,5 9,0 9,5 10,0 10,5 11,0 11,5 12,0 12,5 13,0 13,5 14,0 14,5 15,0 k i ( m p a* m 1 /2 ) a (mm) rectangular patch elliptical patch patch shaped arrow octagonal patch trapezoidal patch patch shaped h patch shaped butterfly a) the repaired face 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 k i ( m p a* m 1 /2 ) a (mm) rectangular patch elliptical patch patch shaped arrow octagonal patch trapezoidal patch patch shaped h patch shaped butterfly b) the unrepaired face figure 9: effect of the patch shape on the sif level, applied stress 150 mpa. a) repaired face, b) unrepaired face. several works [4, 5, 13, 19-22] have focused on the analysis of the patch shapes effect on the quality of the repair in terms of stress intensity factor reduction. these shapes have been optimised to reduce two parameters, the mechanical energy, highly concentrated in crack head (energy gain) and the composite patch mass (mass gain). taking into account this last parameter, our results are in good agreement with this works. in contrast to these, our study exclusively considers the impact of patch shapes on repair performance from a point of view, level and distribution of the shear stresses in the adhesive layer. patch with variation of the surface and its thickness to complete this study, the same volume was used for all these shapes with variation of the surface. the variation of the patches thickness makes it possible to obtain constant volume (fig.10). the fig. 11, represents the sif variation of the repaired face and unrepaired face by such patches respectively. the analysis of this result clearly shows that the repair using patches with smaller overlapping surface lead to the lower values of this rupture parameter. in other words, the m. baghdadi et alii, frattura ed integrità strutturale, 50 (2019) 68-85; doi: 10.3221/igf-esis.50.08 76 repair is more efficient when done by thick patches and less extensive (small surfaces). this thickness is a fundamental parameter where the composite patch stiffness is stronger. so, in terms of fracture energy reducing in repairing cracks heads, the patch shaped arrow is more efficient. at equal volume and in the case of the long crack repair, it has, compared to the rectangular patch, an energy gain about 45% on the unrepaired face (fig. 11.b) and about 25% on the repaired face (fig. 11.a). this patch shape greatly reduces the instability of the crack on the unrepaired face and minimize the risk of plate bending. in conclusion, from a point of view, fracture energy reduction in crack heads of repaired face and unrepaired face, and in terms of minimizing the bending due to the stiffness of the repair material, the patch shaped arrow is the most effective. compared to all the other patch shapes, this shape leads to a significant mass gain, which is an economic issue, not negligible in aircraft structural repairs. at constant volume of the composite patch, and in terms of fracture energy relaxation of the repaired and unrepaired face, and reduction of the plate bending effect, this shape remains the most efficient. it would be wise to analyse the effect of these shapes and particularly of this shape on the level and distribution of the shear stresses in the adhesive layer. it is clear that the minimization of this parameter plays a determining role on the repair performance in terms of improving the aircraft service life. these stresses are usually responsible for the disbonding of the repair. figure 10: the different dimensions of the quarter of the patch shapes (constant volume). 0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 8 9 10 11 12 13 14 15 16 17 18 k i ( m p a* m 1 /2 ) a (mm) rectangular patch elliptical patch patch shaped arrow octagonal patch trapezoidal patch patch shaped h patch shaped butterfly a) the repaired face 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40 k i ( m p a* m 1 /2 ) a (mm) rectangular patch elliptical patch patch shaped arrow octagonal patch trapezoidal patch patch shaped h patch shaped butterfly b) the unrepaired face figure 11: effect of the patch shape on the sif level, applied stress 150 mpa. a) repaired face, b) unrepaired face. m. baghdadi et alii, frattura ed integrità strutturale, 50 (2019) 68-85; doi: 10.3221/igf-esis.50.08 77 effect of the patch shapes on the shear stresses level in the adhesive layer t is important to maintain the shear stresses in the adhesive layer at the lowest possible level. any design of the patch shape aims not only to relax as much possible the fracture energy in crack heads, but also to reduce the intensity of these stresses in order to prevent the adhesion failure. the performance of the composite patch repair depends essentially on the mechanical behaviour of the adhesive layer. this constitutes the weakest link of structure and practically the essential cause of the repair damage by the disbonding process. the comprehension of the mechanisms type degradation of the repair, is still only very superficial. the disbonding is a rather complex phenomenon whose physical mechanisms are still very poorly known, depends practically on the mechanical and geometrical parameters of the patch, and especially an induced the shear stresses in the adhesive layer, during the repair process. these stresses are generally responsible for the repair disbonding. thus, several works have been devoted to such a type of degradation, among them can be cited the use of the zone damaged theory to explain the disbonding mechanisms due to the adhesive ruin. this theory is based primarily on the formation and development of a damaged zone, then on the crack propagation initiated in this zone, having reached a critical size, under more intense loads [23]. crombr [24] and al, sheppard [25] and al, have developed a model for predicting damage of the adhesive layer. they show that the degradation of this layer occurs when the stress induced in the adhesive crosses a threshold stress. these authors conclude that this degradation is not the result of the repaired crack propagation, but rather the initiation and growth of new cracks in the adhesive layer. ban and al. [26] have made the correction taking into account, the damaged zone ratio, defined by the ratio of the estimated surfaces sum, where the deformation at fracture is reached, and the total adhesive layer surface. this model was used as a criterion for predicting damage to the adhesive. they conclude that the disbonding of an adhesive "type fm 73", occurs when this report tends towards an estimated limit value of 0.247. based on this model, ibrahim and al [27] analysed the degradation of the adhesive layer used for composite patch repair of cracked aircraft structures. again, based on the same model, papanikos and al [28] observed that the top edge of the patch is a source of disbonding initiation. they conclude that this disbonding, responsible for the partial decohesion of the assembled surfaces, leads to a considerable reduction in the effective surface of the junction. magalhaes and al. [29], by analysing the nature of the adhesive layer degradation, have shown that the ruin is manifested inside the adhesive near the adhesive-adherent interface. the existence of an adhesive film on the bonded surface illustrates that the disbonding is the result of a cohesive failure of the adhesive. the shear stresses induced in the adhesive layer are generally responsible for disbonding of structures repaired with composite patches. to complete the previous study, the effect of the patch shapes on the level and distribution of these stresses, is analysed. it is important to keep these stresses as low as possible. the shear stresses were determined in the xoy, xoz and yoz planes along the propagation path (fig. 12, 14 and 16), and the maximum shear stresses in the adhesive layer (fig. 13,15 and 17), this is the originality of this work, virtually no studies have focused on analysing of the repair performance in terms of reducing of all shear stresses in the adhesive layer. most numerical analytical works have analysed the effectiveness of repair from a point of view, a reduction of fracture energy [4, 5, 13, 19-22]. figure 12: path of shear stresses analysis in the adhesive layer. i m. baghdadi et alii, frattura ed integrità strutturale, 50 (2019) 68-85; doi: 10.3221/igf-esis.50.08 78 patch with conservation of the surface and its thickness in this analysis, the repair was done by different patch shapes having the same surface (fig. 6) and differing only in their geometry. their effect on the level and distribution of the shear stresses in the adhesive layer are shown in fig. 13 and 14. these results shows that in terms of relaxation of these stresses, the repair using an elliptical patch is the most effective and, whatever the plane of the structure (fig 13a, b and c). figure 13: the effect of the patch shape on the shear stresses level in the adhesive layer along the crack propagation path. repaired crack a =18mm, applied stress = 150 mpa. m. baghdadi et alii, frattura ed integrità strutturale, 50 (2019) 68-85; doi: 10.3221/igf-esis.50.08 79 the maximum shear stresses in the adhesive layer are reduced by using an elliptical patch shape (fig.14a, b and c). this results explicitly illustrates that the sharp or oblique edge effect, of other patches (rectangular, arrows-shaped, h-shaped, trapezoidal, octagonal and butterfly-shaped), located sufficiently far from the crack heads, to store a high proportion of mechanical energy in this crack heads, is almost non-existent. these edges are sources of localised shear stresses at the free edges of the adhesive. for that, the level of the shear stresses in a repair using such patch shapes are high level. the highest tangential stresses due to the crack opening, are relative to the plane yoz of the structure (fig 13c). these stresses can lead to the degradation of the adhesion by a disbonding mechanism, this risk is minimized when the repair is done by an elliptical patch. the results shown in fig. 14c, illustrate the maximum shear stresses induced in the adhesive layer located on the free edge of the repair. these stresses increase with the sizes of the repaired crack, can lead to the initiation and propagation of cracks at the adhesive layer-plate interface, thus also leading to the disbonding of this repair. these results are in good agreement with those obtained by [30,31]. so, it is interesting to analyse the effect of the surface reduction of these patch shapes, with conservation of its stiffness. in other words, with constant of its thickness, on the mechanical behaviour of the repair. 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 0,5 1,0 1,5 2,0 2,5 3,0 3,5 4,0 4,5 5,0 5,5 6,0 m ax s h ea r st re ss x y ( m p a) a (mm) rectangular patch elliptical patch patch shaped arrow octagonal patch trapezoidal patch patch shaped h patch shaped butterfly a) 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 0 2 4 6 8 10 12 14 16 18 20 22 24 m ax s h ea r st re ss x z ( m p a) a (mm) rectangular patch elliptical patch patch shaped arrow octagonal patch trapezoidal patch patch shaped h patch shaped butterfly b) 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 m ax s h ea r st re ss y z ( m p a) a (mm) rectangular patch elliptical patch patch shaped arrow octagonal patch trapezoidal patch patch shaped h patch shaped butterfly c) figure 14: effect of the patch shape on the maximum shear stresses level in the adhesive layer, applied stress = 150 mpa. patch with a variation of the surface and conservation of its thickness in this part, the patch shapes studied previously with in particular a regression of the surface (fig.8). the effect o0f these shapes on the level and distribution of the shear stresses, is shown in figs. 15 and 16. these results, show that in terms of minimizing of the shear stresses, relative to the two planes xoy and yoz ((fig 15, a and b), the orthogonal and elliptical patch is more efficient. outside of these two patches, the effect of the patch shapes on the level of these two stresses hardly appears. our results show that, compared to all the patch shapes analysed, the elliptical and orthogonal patch minimises considerable the shear stresses in the adhesive (fig.15a, b) and disadvantage the risk of the repair disbonding. the tangential stresses specific to the yoz plane are relatively high level, due to the crack opening. they can be responsible for the repair degradation (fig.15c) by initiation and propagation of cohesive or adhesive cracks in the adhesive layer. the level of these stresses is closely related to the patch surfaces. in fact, more this surface is important, m. baghdadi et alii, frattura ed integrità strutturale, 50 (2019) 68-85; doi: 10.3221/igf-esis.50.08 80 more the level of this stresses drops (fig.15c). thus, the repair with a rectangular patch, results the lowest shear stresses in this adhesive layer. -5 0 5 10 15 20 25 30 35 40 45 -6 -5 -4 -3 -2 -1 0 1 2 3 4 s h ea r st re ss x y ( m p a) the total distance along the path (mm) rectangular patch elliptical patch patch shaped arrow octagonal patch trapezoidal patch patch shaped h patch shaped butterfly a) 15 16 17 18 19 20 21 22 -4 -3 -2 -1 0 1 2 3 4 s h ea r st re ss x y ( m p a) path (mm) rectangular patch elliptical patch patch shaped arrow octagonal patch trapezoidal patch patch shaped h patch shaped butterfly a) 0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40 42 44 -4 -2 0 2 4 6 8 10 12 14 16 18 20 22 24 s h ea r st re ss x z ( m p a) the total distance along the path (mm) rectangular patch elliptical patch patch shaped arrow octagonal patch trapezoidal patch patch shaped h patch shaped butterfly b) 14,0 14,5 15,0 15,5 16,0 16,5 17,0 17,5 18,0 18,5 19,0 19,5 20,0 -4 -2 0 2 4 6 8 10 12 14 16 18 20 22 24 s h ea r st re ss x z ( m p a) path (mm) rectangular patch elliptical patch patch shaped arrow octagonal patch trapezoidal patch patch shaped h patch shaped butterfly b) -5 0 5 10 15 20 25 30 35 40 45 -90 -80 -70 -60 -50 -40 -30 -20 -10 0 10 s h ea r st re ss y z ( m p a) the total distance of the path (mm) rectangular patch elliptical patch patch shaped arrow octagonal patch trapezoidal patch patch shaped h patch shaped butterfly c) 0 2 4 6 8 10 12 14 16 -90 -80 -70 -60 -50 -40 -30 -20 -10 0 s h ea r st re ss y z ( m p a) path (mm) rectangular patch elliptical patch patch shaped arrow octagonal patch trapezoidal patch patch shaped h patch shaped butterfly c) figure 15: the effect of the patch shape on the shear stresses level in the adhesive layer along the crack propagation path, repaired crack a =18mm, applied stress = 150 mpa. taking as a criterion the reducing of the maximum stresses induced in the adhesive layer during the commissioning process, the most reliable repair results from an elliptical patch as shown in (figs. 16 a, b and c), these figures represent the variation of these stresses generated in the xoy, xoz and yoz planes respectively. the stresses on the free edge of the yoz plane explicitly indicate that these stresses are at the lowest level when the repair is done by an elliptical patch and whatever the sizes of the repaired cracks. this geometry does not present a singular end, or sharp edges can be the seat of stresses concentration, causing the increase of the shear stresses in the adhesive layer. nevertheless, in our m. baghdadi et alii, frattura ed integrità strutturale, 50 (2019) 68-85; doi: 10.3221/igf-esis.50.08 81 simulation conditions, these edges considerably relax the normal tension stresses highly concentrated in the repaired crack heads (fig 9). compared to the stresses generated in the xoy plane (fig. 16a). the maximum tangential stresses in the adhesive layer, relative to the xoz and yoz planes (fig. 16 b and c), are of a much higher level, and whatever the sizes of the crack and the patch shapes. the intensively stresses generated in the yoz plane, localised on the free edge of the adhesive, can be sources of initiation and propagation of new cracks in the adhesive, leading to the repair damage by the phenomenon of cracked plate-composite patch disbonding. in fact, the maximum stresses, measured in this adhesive zone, exceed its shear failure threshold. this risk is all the more likely when the crack is of important sizes and whatever the patch shape with which it is repaired (fig 16c). the important sizes of cracks in our simulations remain theoretical for a better analysis of repair efficiency in terms of reduction of the normal stresses in the crack head. these sizes are mainly responsible for the excessive values of the shear stresses found on this plane of the plate. this last, shows that, whatever the cracks sizes, the failure of the adhesive is most likely when the repair is done by a patch shape having sharp edges of angles acute, straight or obtuse. if such geometries have the advantage to store infinitely intense normal stresses located in the crack heads, they favour the intensification of the shear stresses in the adhesive layer and finally increases the risk of the repair disbonding. 0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 0,5 1,0 1,5 2,0 2,5 3,0 3,5 4,0 4,5 5,0 5,5 m ax s he ar s tr es s x y ( m p a) a (mm) rectangular patch elliptical patch patch shaped arrow octagonal patch trapezoidal patch patch shaped h patch shaped butterfly a) 0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 5 10 15 20 25 30 35 40 m ax s h ea r st re ss x z ( m p a) a (mm) rectangular patch elliptical patch patch shaped arrow octagonal patch trapezoidal patch patch shaped h patch shaped butterflly b) 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 m ax s h ea r st re ss y z ( m p a) a (mm) rectangular patch elliptical patch patch shaped arrow octagonal patch trapezoidal patch patch shaped h patch shaped butterfly c) figure 16: the effect of the patch shape on the maximum shear stresses level in the adhesive layer, applied stress = 150 mpa. patch with variation of the surface and its thickness the same volume of the patches initially deduced from the rectangular shape has been retained. to complete the previous study, the patches shape differs only in their geometry and their surface. the conservation of the patch volume is done by playing on its thickness (fig.10). remember that this thickness is a determining parameter for the repair material stiffness. the conservation of the patches volume with reduced of its surface, require high patch thicknesses which lead to high m. baghdadi et alii, frattura ed integrità strutturale, 50 (2019) 68-85; doi: 10.3221/igf-esis.50.08 82 stiffness. for this purpose, and in comparison, with the rectangular patch, a patch shaped arrow with a doubly smaller surface and doubly important stiffness (fig.10) leads practically to the lower values of the shear stresses relative to the yoz planes, in the adhesive layer, as shown in (fig. 17 c). these stresses are due to the crack lips opening (fig. 17c) in mode i. -5 0 5 10 15 20 25 30 35 40 45 -6 -5 -4 -3 -2 -1 0 1 2 3 4 s he ar s tr es s x y ( m p a) the total distance of the path (mm) rectangular patch elliptical patch patch shaped arrow octagonal patch trapezoidal patch patch shaped h patch shaped butterfly a) 15,0 15,5 16,0 16,5 17,0 17,5 18,0 18,5 19,0 19,5 20,0 20,5 21,0 -5 -4 -3 -2 -1 0 1 2 3 4 s h ea r st re ss x y ( m p a) path (mm) rectangular patch elliptical patch patch shaped arrow octagonal patch trapezoidal patch patch shaped h patch shaped butterfly a) -5 0 5 10 15 20 25 30 35 40 0 5 10 15 20 25 s h ea r st re ss x z ( m p a) the total distance of the path (mm) rectangular patch elliptical patch patch shaped arrow octagonal patch trapezoidal patch patch shaped h patch shaped butterfly b) 15,0 15,5 16,0 16,5 17,0 17,5 18,0 18,5 19,0 19,5 20,0 0 5 10 15 20 s he ar s tr es s x z ( m p a) path (mm) rectangular patch elliptical patch patch shaped arrow octagonal patch trapezoidal patch patch shaped h patch shaped butterfly b) -4 -2 0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40 42 44 -65 -60 -55 -50 -45 -40 -35 -30 -25 -20 -15 -10 -5 0 5 10 s h ea r st re ss y z ( m p a) the total distance of the path (mm) rectangular patch elliptical patch patch shaped arrow octagonal patch trapezoidal patch patch shaped h patch shaped butterfly c) -2 -1 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 -64 -62 -60 -58 -56 -54 -52 -50 -48 -46 -44 -42 -40 -38 -36 -34 -32 -30 s h ea r st re ss y z (m p a) path (mm) rectangular patch elliptical patch patch shaped arrow octagonal patch trapezoidal patch patch shaped h patch shaped butterfly c) figure 17: effect of the patch shapes on the shear stresses level in the adhesive layer along the crack propagation path. repaired crack a =18 mm, applied stress = 150 mpa. m. baghdadi et alii, frattura ed integrità strutturale, 50 (2019) 68-85; doi: 10.3221/igf-esis.50.08 83 the theoretical sizes of the repaired crack, and the magnitude of the applied stress too high, are responsible for their excessive level. these extreme simulation conditions have been voluntarily used to estimate the repair effectiveness in terms of fracture energy reductions in crack head and tangential stresses in the adhesive layer. it should be noted that the excessive displacement of the crack lips can lead to the disbonding initiation by the adhesive failure. this zone of the plate constitutes a privileged site of the repair damage. these stresses are partly responsible. the shear stresses generated in the xoy plane are not very intense and whatever the patch shapes used in the repair (fig.17a). the localised stresses on the xoz plane of the structure (fig.17b) are all the weaker when the repair is done by the patches with reduced surfaces, in other words, by using a thicker patch, therefore more stiffness. these stresses do not pose any risk of the adhesive damage. the maximum shear stresses generated in the xoy, xoz and yoz planes of the structure are shown in (fig. 18), these results show that the most important stresses are located at the free edge (yoz plane) of the adhesive (fig.18c). they are all important when the repair uses patches with edge angle obtuse, right or acute. these last, are the seat of the shear stresses concentration. for this purpose, the elliptical shape generates the least intense stresses. these stresses are largely responsible of the patch edges disbonding. so, these results are in good agreement with those obtained by [30,31]. 0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 0,5 1,0 1,5 2,0 2,5 3,0 3,5 4,0 4,5 5,0 m ax s tr es s x y ( m p a) a (mm) rectangular patch elliptical patch patch shaped arrow octagonal patch trapezoidal patch patch shaped h patch shaped butterfly a) 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40 m ax s tr es s x z ( m p a) a (mm) rectangular patch elliptical patch patch shaped arrow octagonal patch trapezoidal patch patch shaped h patch shaped butterfly b) 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 20 30 40 50 60 70 80 90 100 110 120 m ax s tr es s y z ( m p a) a (mm) rectangular patch elliptical patch patch shaped arrow octagonal patch trapezoidal patch patch shaped h patch shaped butterfly c) figure 18: effect of the patch shapes on the maximum shear stresses level in the adhesive layer, applied stress = 150 mpa. conclusion his study shows that the performance of the repair, in terms of stress intensity factor reduction, is almost independent of the composite patch shape with the same overlapping surface. many works [4,5, 13,18, 19,20,21,22,] have an interest in the patch shapes effect on the fracture energy level in crack head. the effect of these shapes on the intensity of the shear stresses, relative not only to all the adhesive planes, but also to its free edge, is lacking in these works. the study proposed here takes into account the patch shapes effect on these two physical parameters reduction (fracture energy and shear stresses). this is the originality of this work. unlike all the works done until now, this work highlights a site of the adhesive, located in the vicinity very close to the crack lips, where the risk of disbonding is the most privileged. t m. baghdadi et alii, frattura ed integrità strutturale, 50 (2019) 68-85; doi: 10.3221/igf-esis.50.08 84 this risk is even more likely when the overlapping surface of the crack lips is small using a less stiffness patch. for the same stiffness and for the same overlapping surface, the elliptical shape is the patch geometry, allowing the minimization of these two physical parameters (fracture energy and shear stresses). in this case, the (obtuse, straight, acute) of the patches, located far from the crack head, having no effect on localised tension stresses at the cracking front, these sharp edges are responsible for increasing the shear stresses in the adhesive layer. the obtaining of different patch shapes from the rectangular classic geometry, is only possible with a reduction of its surface. the seven shapes patch an analysed lead practically the same values of the sif. this behaviour is due to the modification of the patch morphology and not to the decrease of its surface. compared to a repair using a rectangular patch, that using a patch shaped arrow, with a doubly reduced overlapping surface, leads to the same level of this fracture energy. this corresponds to a mass gain too important. nevertheless, this patch shape results the most important shear stresses in the adhesive layer. they have privilege initiation sites of disbonding due to the low overlapping surface of the repaired crack lips. if the sharp edges of this shape have the advantage of storing the highest mechanical energies (normal tension stresses), they are the seat of intensification of shear stresses. the risk of disbonding is very likely when the repair uses this patch shape. this risk is very likely in the adhesive, in the vicinity of the crack lips opening, can be greatly reduced by increasing the stiffness of this patch. application of a stiffer adhesive to the free edge seems to reduce the maximum shear stresses localised on this portion of this adhesive like suggested by kaye and al [32] and wang and al [33]. references [1] baker, a.a. (1984). repair of cracked or defective metallic aircraft components with advanced fiber composites an overview of australian work. compos struct. pp. 2153 –2581. doi: 10.1016/0263-8223(84)90025-4. [2] baker, a.a. and jones, r. (1988). bonded repair of aircraft structures. martinus nijhoff: dordrecht. doi: 10.1017/s0001924000016560. [3] rose, l.r.f. (1982). a cracked plate repaired by bonded reinforcement. int j fract 18, pp. 135–144. doi: 10.1007/bf00019638. [4] bouchiba, s. and serier, b. (2016). new optimization method of patch shape to improve the effectiveness of cracked plates repair. structural engineering and mchanic. 58(2), pp. 301-326. doi: 10.12989/sem.2016.58.2.301. [5] mhamdia, r., serier, b., bachir bouiadjra, b. and belhouari, m. (2012). numerical analysis of the patch shape effects on the performances of bonded composite repair in aircraft structures. composites: part b, 43, pp. 391–397. doi: 10.1016/j.compositesb.2011.08.047. [6] chung, k.h. and yang, w.h. (2003). a study of the fatigue crack growth behavior of thick aluminum panels repaired with composite patch. composite structures.60. pp. 1-7. doi: 10.1016/s0263-8223(02)00095-8. [7] chung, k.h., yang, w.h. and cho, m.r. (2000). fracture mechanics analysis of cracked plate repaired by composite patch. key engineering material, 43-8, pp. 183-187. doi: 10.4028/www.scientific.net/kem.183-187.43. [8] jeong, g.h.y., won-ho, jo. and myeong, rae. (2000). fracture mechanics analysis of cracked plate repaired by patch (i). transaction of the korean society of material engineers 24 (8), pp. 2000-2006. doi: 10.22634/ksme-a.2000.24.8.2000. [9] ramji, m. and srilakshmi, r. (2012). design of composite patch reinforcement applied to mixed mode cracked panel using fea. j reinf plast comp 39(9), pp. 585-95. doi: 10.1177/0731684412440601. [10] ramji, m., srilakshmi, r. and bhanu prakash, m. (2013). towards optimization of patch shape on the performance of bonded composite repair using fem, compos. b. eng, 45, pp. 710–20. doi: 10.1016/j.compositesb.2012.07.049. [11] kashfuddoja, m. and ramji, m. (2014). design of optimum patch shape and size for bonded repair on damaged carbon fibre reinforced polymer panels. materials and design, 54, pp. 174–183. doi: 10.1016/j.matdes.2013.08.043. [12] fekih, s.m., albedah, a. f., benyahia benhouari, m., bachir bouadjra, b. and miloudi, a. (2012). optimization of the sizes of bonded composite repair in aircraft structures. matérials & design,41, pp. 171-176. doi: 10.1016/j.matdes.2012.04.025. [13] mahadesh, k. and hakim, s.a. (2000). optimum design of symmetric composite patch repair to centre cracked metallic sheet.compos.struct 49, pp. 285-292. doi: 10.1016/s0263-8223(00)00005-2. [14] ibrahim, n.c.m., serier, b. and mechab, b. (2018). analysis of the crack-crack interaction effect initiated in aeronautical structures and repaired by composite patch, frattura ed integrità strutturale, 46, pp. 140-149. doi: 10.3221/igf-esis.46.14. [15] simulia, dassault systems. abaqus software. version 6.11. (2011). m. baghdadi et alii, frattura ed integrità strutturale, 50 (2019) 68-85; doi: 10.3221/igf-esis.50.08 85 [16] ouinas, d., bachir bouadjra, b., achour, t. and benderdouche, n. (2007). the effect of disbands on the stress intensity factor of aluminum panels repaired using composite materials. compos struct 78, pp. 278-84. doi: 10.1016/j.compstruct.2005.10.012. [17] brighenti, b. (2007). patch repair design optimization for fracture and fatigue improvements of cracked plates. international journal of solids and structure, 44, pp. 1115-1131. doi: 10.1016/j.ijsolstr.2006.06.006. [18] brighenti, r. (2005). optimum patch repair shapes for cracked members, int. j.mech mater. 1(4), pp. 365-381. doi : 10.1007/s10999-005-0525-8. [19] ouinas, d., zenasni, r. and sahnoun, m. (2011). effet de la forme géométrique du patch sur la réduction du fic en mode i. journées d’etudes nationales de mécanique, ouargla, algérie., 07-08 mars. [20] bachir bouiadjra, b. fari bouanani, m. albedah, a. benyahia, f. and es-saheb, m. (2011). comparison between rectangular and trapezoidal bonded composite repairs in aircraft structures: a numerical analysis. materials and design. 32, pp. 3161–3166. doi: 10.1016/j.matdes.2011.02.053. [21] kaddouri, k., ouinas, d. and bachir bouiadjra, b. (2008). fe analysis of the behavior of octagonal bonded composite repair in aircraft structures. computational materials science, 43, pp. 1109–1111. doi: 10.1016/j.commatsci.2008.03.003. [22] ouinas, d., hebbar, a., bachir bouiadjra, b., belhouari, m. and serier, b. (2009). numerical analysis of the stress intensity factors for repaired cracks from a notch with bonded composite semicircular patch. composites part b engineering, 40, pp. 804-810. doi: 10.1016/j.compositesb.2009.06.002. [23] apalak, k. m., apalakgul, z. and gunes, r. (2004) thermal and gemetrically nonlinear stress analyses of an adhesively bonded composite, tee joints with double support. j thermoplast compos mater,17, pp. 10.3-36. doi: 10.1177/0892705704033337. [24] crombe, a., richardson, g.p. and smith, a. (2006). a unified approach for predicting the strength of cracked and non-cracked adhesive joints. int j adhes, 49, pp. 211-244. doi: 10.1080/00218469508014357 [25] sheppard, a., kelly, d. and tong, l. (1998). a damage zone model for the failure analysis of adhesively bonded joints. int j adhes, 18, pp. 385-400. doi: 10.1016/s0143-7496(98)00024-4. [26] chang-su, b., young-hwan, l., jin-ho, c. and jin-hwe, k. (2008), strength prediction of adhesive joints using the modified damage zone theory. compos struct; 86, pp. 96–100. doi: 10.1016/j.compstruct.2008.03.016. [27] nour, c.i., fari bouanani, m., bachir bouiadjra, b. and serier, b. (2016). analysis of the adhesive damage between composite and metallic adherends: application to the repair of aircraft structures: advances in materials research, 5 (1). pp. 11-20. doi: 10.12989/amr.2016.5.1.011. [28] papanikos, p., tserpes, k.i. and pantelakis, s. (2007). initiation and progression of composite patch debonding in adhesively repaired cracked metallic sheets. compos.struct.81, pp. 303-311. doi : 10.1016/j.compstruct.2006.08.022. [29] maglhaes, a.g., de moura, m.f.s.f. and gonçaves, jpm. (2005). evaluation of stress concentration effects in singlelap bonded joints of laminate composite materials. int j adhes; 25, pp. 313-9. doi: 10.1016/j.ijadhadh.2004.10.002. [30] da silva, l. f. m, and adams, r.d. (2007). techniques to reduce the peel stresses in adhesive joints with composite. international journal of adhesive & adhesives.27, pp. 227-235. doi: 10.1016/j.ijadhadh.2006.04.001. [31] underhil, p.r. and du quesnay, d.l. (2006). the dependence of the fatigue life of adhesive joints on surface preparation. international journal of adhesion and adhesives,26, pp. 62-66. doi: 10.1016/j.ijadhadh.2005.03.006. [32] kaye, r.h. and heller, m. (2002). through-thickness shape optimization of bonded repairs and lap-joints international journal of adhesion and adhesives,22, pp. 7-21. doi: 10.1016/s0143-7496(01)00029-x. [33] wang, a., rider, n., heller, m. and kaye, r. (2006). theoretical and experimental research into optimal edge taper of bonded repair patches subject to fatigue loadings. international journal of adhesion an adhesive,25, pp. 410-426. doi: 10.1016/j.ijadhadh.2004.11.007. << /ascii85encodepages false /allowtransparency false /autopositionepsfiles true /autorotatepages /none /binding /left /calgrayprofile (dot gain 20%) /calrgbprofile (srgb iec61966-2.1) /calcmykprofile (u.s. web coated \050swop\051 v2) /srgbprofile (srgb iec61966-2.1) /cannotembedfontpolicy /error /compatibilitylevel 1.4 /compressobjects /tags /compresspages true /convertimagestoindexed true /passthroughjpegimages true /createjobticket false /defaultrenderingintent /default /detectblends true /detectcurves 0.0000 /colorconversionstrategy /cmyk /dothumbnails false /embedallfonts true /embedopentype false /parseiccprofilesincomments true /embedjoboptions true /dscreportinglevel 0 /emitdscwarnings false /endpage -1 /imagememory 1048576 /lockdistillerparams false 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can be opened with acrobat and adobe reader 5.0 and later.) >> /namespace [ (adobe) (common) (1.0) ] /othernamespaces [ << /asreaderspreads false /cropimagestoframes true /errorcontrol /warnandcontinue /flattenerignorespreadoverrides false /includeguidesgrids false /includenonprinting false /includeslug false /namespace [ (adobe) (indesign) (4.0) ] /omitplacedbitmaps false /omitplacedeps false /omitplacedpdf false /simulateoverprint /legacy >> << /addbleedmarks false /addcolorbars false /addcropmarks false /addpageinfo false /addregmarks false /convertcolors /converttocmyk /destinationprofilename () /destinationprofileselector /documentcmyk /downsample16bitimages true /flattenerpreset << /presetselector /mediumresolution >> /formelements false /generatestructure false /includebookmarks false /includehyperlinks false /includeinteractive false /includelayers false /includeprofiles false /multimediahandling /useobjectsettings /namespace [ (adobe) (creativesuite) (2.0) ] /pdfxoutputintentprofileselector /documentcmyk /preserveediting true /untaggedcmykhandling /leaveuntagged /untaggedrgbhandling /usedocumentprofile /usedocumentbleed false >> ] >> setdistillerparams << /hwresolution [2400 2400] /pagesize [612.000 792.000] >> setpagedevice microsoft word numero_57_art_27_3109 a. basiri et alii, frattura ed integrità strutturale, 57 (2021) 373-397; doi: 10.3221/igf-esis.57.27 373 effect of nano-clay addition and heat treatment on tensile and stresscontrolled low-cycle fatigue behaviors of aluminum-silicon alloy a. basiri, a. dadashi, m. azadi faculty of mechanical engineering, semnan university, semnan, iran m_azadi@semnan.ac.ir, http://orcid.org/ 0000-0001-8686-8705 g. winter, b. seisenbacher, f. grün chair of mechanical engineering, montanuniversität leoben, leoben, austria abstract. the objective of the present paper is to investigate the stresscontrolled low-cycle fatigue behavior of piston aluminum-silicon (alsi) alloy reinforced with nano-clay particles and t6 heat treatment. the piston aluminum-silicon alloy strengthened by 1 wt.% nano-clay particles were prepared by the stir casting method and then subjected to the heat treatment. the optical microscopy analysis demonstrates that the heat treatment changed the size, morphology, and distribution of silicon phases through the microstructure of the aluminum matrix. in addition to tensile tests, stresscontrolled low-cycle fatigue experiments at different loading conditions including the variation of the mean stress, the stress rate, and the stress amplitude were conducted at room temperature. the obtained experimental results showed no clear improvement in either mechanical or fatigue properties of the material. moreover, the density measurements using the archimedes method reveal a higher content of the porosity in nanocomposite. it was observed that the reinforcement (nano-particles and the heat treatment) can change the cyclic behavior of the alsi alloy, significantly. the cyclic hardening feature of the alsi alloy changed to cyclic softening and also the fatigue lifetime and the ratcheting resistance decreased after the nanoparticles addition and the heat treatment. through the microstructural analysis, it was indicated that the neglecting of higher kinematics of age hardening in nano-composite was the major source of mechanical properties reduction. in the end, it was shown that the fatigue lifetime of samples can be described adequately utilizing a modified plastic strain energy technique considering the mean stress effect. keywords. aluminum-silicon alloys; stress-controlled cyclic behavior; fatigue lifetime; nano-clay-particles; heat treatment. citation: basiri, a., dadashi, a., azadi, m., gruen, f., winter, g., seisenbacher, b., effect of nano-clay addition and heat treatment on tensile and stress-controlled low-cycle fatigue behaviors of aluminum-silicon alloy, frattura ed integrità strutturale, 57 (2021) 373-397. received: 21.05.2021 accepted: 17.06.2021 published: 01.07.2021 copyright: © 2021 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. https://youtu.be/5mlhgzq1kmw a. basiri et alii, frattura ed integrità strutturale, 57 (2021) 373-397; doi: 10.3221/igf-esis.57.27 374 introduction istons in internal combustion engines are one of the critical and heavy-duty components, which are subjected to low-cycle fatigue (lcf) and wear damages during engine performance [1,2]. therefore, the utilized material should provide high resistance under cyclic loadings and also high strength to weight ratio for the fuel consumption and consequently reducing the gas emission. for this purpose, the aluminum-silicon alloys are a potential candidate because of their high strength to weight ratio, good castability, acceptable ductility, and corrosion resistance [3]. there are several concepts available that could achieve improvements in mechanical and fatigue properties through the piston design including the optimized geometries, novel materials, advanced manufacturing processes, and different strengthening methods [1]. one of the most common strengthening methods is the development of metal-matrix composites reinforced with ceramic particles, which have attracted great attention over the past decade [4]. several studies [5-7] had demonstrated the superior mechanical properties of aluminum-matrix nano-composites in comparison to similar micro-composites with the same volume fraction of particles. in the context of the cyclic behavior, lcf properties of particle-reinforced aluminum-matrix composites had been investigated in the literature extensively [812]. results indicate the inferior fatigue lifetime compared to their counterpart monolithic alloys. this was mainly due to the limited ductility of the metal matrix in the presence of the ceramic particles contrary to high-cycle fatigue (hcf), in which the fatigue lifetime was mostly strength-dependent. llorca [13] indicated that the particle cracking was the major source of the fatigue crack initiation and growth through the matrix in composites. on the other hand, wallin et al. [14] pointed out that the particle fracture probability could be decreased by the particle size reduction. therefore, it was desirable to investigate the lcf behavior of metallic materials reinforced by nano-sized ceramic particulates. senthilkumar et al. [15] conducted fully reversed lcf tests on two materials including aa2014 aluminum alloy containing microand nano-al2o3 particles and its counterpart micro-composite, which were both followed by hot extrusion and t6 heat treatment. they showed that the hybrid micro/nano-composite offered a higher fatigue lifetime and cyclic hardening at high strain amplitudes in comparison to almost stabilized response of the micro-composite. azadi et al. [16] conducted fully-reversed strain-controlled lcf experiments on piston aluminum alloys and their counterpart nano-clay reinforced and t6 heattreated nano-composites at different temperatures. they concluded that the fatigue behavior of the aluminum alloys was not influenced significantly by nano-particles and the heat treatment except a lifetime reduction at the temperature of 300 °c due to the over-aging phenomenon. ghasemi yazdabadi et al. [17] studied hcf and lcf responses of an aluminum alloy reinforced with nano-sic particulates prepared by the powder metallurgy route. they showed that the hcf resistance of nanocomposites improved followed by increasing the tensile strength while increasing the volume fraction. however, the lcf lifetime reduced as a result of the limited slip distance of dislocations caused by hard particles. jabbari et al. [18] conducted strain-controlled lcf experiments on extruded az31b magnesium alloy reinforced by nano-al2o3 particles at different temperatures. they indicated that although the mechanical properties of the material degraded at elevated temperatures, the fatigue lifetime increased as a result of ductility enhancement. besides, they showed that the jahed-varvani model was able to describe the fatigue lifetime of the material appropriately. the common feature of aforementioned lcf tests is that they have been conducted under strain-controlled conditions. however, it is difficult to realize the cyclic loading mode in the actual service condition of the components since strains and stresses are related to each other by some constitutive behaviors. therefore, knowing both the strain and stress fields and the relation between them in a component would allow both stressand strain-controlled tests to be used to identify the fatigue behavior of the materials [19,20]. an important field of this area is stress-controlled lcf accompanying mean stress, which usually results in ratcheting i.e., the progressive accumulation of the inelastic strain and consequently to premature fatigue failure. the investigation of symmetric and asymmetric stress-controlled lcf behavior of aluminum alloys had been performed during recent years in the literature [21-26] but not as extensively as steel and magnesium alloys. in the context of the stress-controlled lcf experiments on metal-matrix composites, the ratcheting deformation in 6061 aluminum alloy reinforced with sic particulates was systematically discussed by kang [27] and kang and liu [28]. the effects of the particulate volume fraction, the heat treatment, the multiaxiality, the temperature, and some other factors on the ratcheting were discussed. useful results along their purposes were that the ratcheting resistance of composite increased as the sic volume fraction enhanced. besides, the ratcheting behavior of composite had a great time-dependence even at low temperatures, which implied the presence of the creep component in the total ratcheting deformation. regarding the stresscontrolled lcf loading on nano-composites, goh et al. [29] investigated the effect of nano-sized y2o3 particulates addition into magnesium alloys in different volume fractions on the cyclic plastic response under stress-controlled lcf loading. they showed that the intensity of cyclic hardening in nano-composite increased with the volume fraction of reinforcements, which was a result of the forest dislocation’s pinning role of dispersed nanoparticles. p a. basiri et alii, frattura ed integrità strutturale, 57 (2021) 373-397; doi: 10.3221/igf-esis.57.27 375 through the above literature review, studies demonstrated the advantage of nano-particles addition [5-7,15-18] and the heat treatment [15,16] on mechanical and fatigue properties improvement of metallic materials. regardless of the little investigations that were carried out on the strain-controlled lcf behavior of nano-composites [15-18], there was only one investigation [29] focusing on stress-controlled lcf behavior of metal matrix nano-composites to the author’s best knowledge. the promising results of such loading conditions in micro-composites [27-28] and also fewer studies on stress controlled lcf behavior of aluminum alloys [21-26] in comparison to other metallic materials, motivated the present investigation to be made. therefore, the objective of this article was to evaluate the effect of the addition of nano-clay particles and the heat treatment on mechanical and stress-controlled lcf properties of piston alsi alloys. experimental procedure materials processing he matrix material, which was utilized in the present research, was a cast aluminum-silicon (alsi) alloy (enac48000). this alsi12cunimg alloy had been widely utilized in the manufacturing of engine pistons in automotive industries. in the primary ingots of this alsi alloy, the chemical composition is measured as si: 12.7 wt.%, ni: 0.8 wt.%, cu: 1.16 wt.%, fe: 0.56 wt.%, mg: 1.00 wt.%, zn: 0.16 wt.%, mn: 0.12 wt.% and the aluminum as balance. two groups of specimens were made in this research, including aluminum alloy specimens reinforced with nano-clay particles and the original un-reinforced alloys for comparison. the fabrication method of original aluminum alloys is a permanent mold gravity casting method described in the following paragraph: the aluminum ingots were first melted and the temperature was held at 700 °c for 2 hours in an electrical resistance furnace [30,31] before pouring them into a permanent steel mold. for the production of 1 wt.%, nano-clay particles reinforced specimens with the stir-casting process, clay (type: montmorillonite k10) as nano-particles with the chemical composition according to tab. 1 were used. in this research, nano-clay particles were first pre-heated to the temperature of 420 °c for 20 minutes [31,32] to achieve a better wettability of nano-clay particles in the aluminum melt. the nano-particles powder was wrapped in aluminum foil. then, they were added gradually to the aluminum melt. the clay amount is 2 g by 2 g in order to eliminate any gas accumulations in the aluminum melt. the density of the nano-clay particles (0.5 g/cm3) was lower than that of the molten aluminum. the density of the aluminum alloy was 2.7 g/cm3. this causes the floating of nanoparticles in the crucible surface. to get an appropriate distribution of reinforcements in a uniform condition in the molten aluminum alloy, a steel stirrer was used. this stirrer was redesigned in order to have a falling stream in the melt through the casting process. it should be noted that high stirring time and rotational speed can result in better dispersion of nanoparticles in the melt. on the other hand, it caused the degradation of mechanical properties because of the formation of some undesired chemical components and increasing the gas entrapment in the melt [6,30,33]. it should be noted that for the nano-composite, it took 20 minutes to put the molten aluminum in the steady-state condition after adding the nanoclay particles. then, the resulting composite slurry was poured into the cast-iron mold. oxides (%) material sio2 al2o3 tio2 fe2o3 mgo cao k2o na2o loi nano-clay 50.95 19.60 0.62 5.62 3.29 1.97 0.86 0.98 15.45 table 1: the chemical composition of nano-clay particles. after the casting process, all initial cylinders of aluminum alloys and nano-composites were cooled down in the air. then, the machining process was performed to fabricate the standard-sized samples from initial casted cylinders. for these specimens, the geometry, which is suited for both tensile and fatigue tests, is illustrated in fig. 1. in addition, mechanical polishing was done to have a mirror-like surface. after machining, the nano-composite specimens were subjected to t6 heat treatment to the following schedule: a solution treatment of the alloy at 500 °c for 1 hour, water quenching and then artificial aging at 300 °c for 2 hours (air-cooled) [16,34]. microstructural evaluation for investigating the material microstructure, aluminum alloy and nano-composite specimens were firstly mounted. this job was done with the struers citopress embedding device. then, they were subjected to a five-step grinding process at 300 t a. basiri et alii, frattura ed integrità strutturale, 57 (2021) 373-397; doi: 10.3221/igf-esis.57.27 376 rpm and under 4 n. moreover, the last stage for having smooth surfaces was four-step polishing in the water-based diamond lubricant and also was using the etchant of keller’s reagent solution. microstructural characterizations before testing were carried out using the optical microscopy (om) of keyence vhx5000. in addition, the icna energy dry cool 350 was utilized as the energy-dispersive x-ray spectroscopy (eds). for the image of the field emission scanning electron microscopy (fe-sem), the jeol-7200f equipment was also used. furthermore, the porosity content of the samples as a measure of void spaces in the materials was determined by comparing the measured density of the samples using the archimedes method with that of their theoretical density. the details of this method were referred to in the literature [35]. figure 1: the geometry for samples used in tensile and fatigue tests (dimensions in mm). tensile and fatigue testing uniaxial tensile and lcf experiments were carried out using an automated mechanical testing machine (instron servohydraulic testing machine), equipped with the 100 kn load cell. instron room temperature extensometer was used in order to measure the strain value through the test. tensile tests were done at a constant strain rate of 2.5×10-3 s-1 at room temperature, based on the astm e8m standard testing procedure [36]. the fatigue tests were carried out in a tension-compression engineering stress-controlled loading mode at room temperature according to the standard fatigue testing procedure of astm e466 [37]. the response of materials to varied the stress amplitude, the mean stress and the stress rate were examined and the detailed loading conditions for original aluminum alloys and nano-composites are presented in tabs. 2 and 3, respectively. it should be noted that σa was the stress amplitude, σm was the mean stress and σ˙ was the stress rate. since the cyclic loading condition was tensile-compressive, the stress distribution was uniform on the cross section of the sample. therefore, cracks would initiate either on the specimen surface (through the gauge length) or inside the sample. however, the fatigue lifetime of samples was defined as the cycle number, corresponding to the first abrupt reduction of the load carrying capacity in the strain amplitude diagram versus the number of cycles. it should be noted that “alsi” was used for the original aluminum alloy (without reinforcement) and “alsi_n_t6” referred to the heat-treated nano-composite through the rest of the paper. sample no. σa (mpa) σm (mpa) σ˙ (mpa/s) 3 200 0 100 6 200 10 100 4 200 20 100 9 210 0 10 11 210 0 100 10 210 0 1000 8 220 0 10 7 220 0 100 5 220 0 1000 table 2: loading conditions in stress-controlled fatigue tests on alsi. a. basiri et alii, frattura ed integrità strutturale, 57 (2021) 373-397; doi: 10.3221/igf-esis.57.27 377 sample no. σa (mpa) σm (mpa) σ˙ (mpa/s) 13 200 0 10 8 200 0 100 12 200 0 100 4 200 10 100 3 200 20 100 14 200 0 1000 10 210 0 10 9 210 0 100 5 210 0 1000 2 220 0 100 11 190 0 100 table 3: loading conditions in stress-controlled fatigue tests on alsi_n_t6. results and discussion microstructure characterization he optical micrographs of original aluminum alloys (alsi) and heat-treated nano-composites (alsi_n_t6) were depicted in fig. 2-5. as a first observation, the finer microstructure of alsi_n_t6 compared to alsi alloys could be observed. it was commonly confirmed that the addition of hard particles to the metal-matrix materials resulted in reduction of the grain size [5,30], which was generally related to the pinning role of particles at the grain boundaries during the solidification. such a phenomenon in the nano-composites can improve the mechanical strength of the matrix material through the hall-petch effect [38]. considering figs. 4 and 5, in the microstructure of alsi alloys, four different phases could be distinguished. the first phase was the aluminum (α-al) matrix with the white color. the second one is the alsi phase with the dendritic morphology that is homogeneously distributed in the matrix. the third one is the silicon (si) phase as a gray-colored area and finally, intermetallic phases as black-colored and light gray-colored script-like areas. similar phases could be found in alsi_n_t6, but a change in the shape and also the distribution of both si phases and intermetallic phases could be observed as a result of the nano-particles addition and the heat treatment. in the following paragraphs, a discussion on the size and morphology of both si and intermetallic phases, which can determine the mechanical and fatigue behavior of the material has been performed. as could be observed qualitatively in fig. 5, the content of the si phase was increased for alsi_n_t6 compared to alsi alloys. this could be a result of the presence of about 50% sio2 in the chemical composition of nano-clay particles according to tab. 1. as reported in the literature [39], the si phase in the piston aluminum alloys was usually detected to exist in two types including the flake shape and the coarse primary blocky shape, in which the primary si phase had a dominant role in the determination of mechanical properties [40-41]. based on reports in the previous research [16], the circularity of the si phase increased as a result of the heat treatment that implied a higher number of blocky shape si particles compared to the needle shape ones in alsi_n_t6. this result was consistent with the reports in the literature [42-44], which states that after the heat treatment, si particles tend to become spherical. such results can cause an improvement in the mechanical properties [40,44]. besides, the size of blocky si particles increased as a result of nano-particles and the heat treatment, which could be a source of reduction in fatigue lifetime and mechanical properties in the base metal [43]. the distribution of intermetallic phases was similar in both alsi alloy and also alsi_n_t6. however, it was demonstrated quantitatively in the previous research [16] that the content of these phases and their sizes in alsi-n_t6 were lower than the base alsi alloys. lower content and size of intermetallic phases were reported to cause better fatigue performance [4546]. t a. basiri et alii, frattura ed integrità strutturale, 57 (2021) 373-397; doi: 10.3221/igf-esis.57.27 378 figure 2: optical micrograph images of alsi samples with 200x magnification. figure 3: optical micrograph images of alsi_n_t6 samples with 200x magnification. figure 4: optical micrograph images of alsi samples with 1000x magnification. a. basiri et alii, frattura ed integrità strutturale, 57 (2021) 373-397; doi: 10.3221/igf-esis.57.27 379 figure 5: optical micrograph images of alsi_n_t6 samples with 1000x magnification. to study the material microstructures more accurately, the fe-sem images were depicted in fig. 6-7 for both alsi alloys and alsi_n_t6. the intermetallic phases could be distinguished easily from the rest of the microstructure. as it could be observed, the intermetallic phases in alsi_n_t6 have a nearly needle-shaped morphology, which could act as stressconcentration sites and eventually reduce mechanical properties [47]. for the determination of the dominant chemical element of intermetallic phases, the eds results for alsi_n_t6 were depicted in fig. 8. both si and intermetallic phases could be found through the aluminum matrix. the elements, which have percentages of more than 1% including al, si, cu, mg, and o according to tab. 1, were presented. as it could be observed, two main intermetallic phases including cu-rich and mg-rich could be distinguished. the presence of such intermetallic phases could result in the improvement of mechanical properties [48]. figure 6: fe-sem images of alsi with low magnifications. it is widely accepted that nano-particles have a high tendency to attract each other and create agglomerations as a result of their high surface to volume ratio. the agglomerations are a possible site for the crack nucleation and therefore, could be the reason for achieving undesirable mechanical properties compared to the original metal matrix. nevertheless, reaching completely distributed single nano-particles is quite impossible in most cases [7]. the dispersion of nano-particles in the metal matrix is highly dependent on the processing route. fig. 9-10 demonstrates the fe-sem images of the surface of a. basiri et alii, frattura ed integrità strutturale, 57 (2021) 373-397; doi: 10.3221/igf-esis.57.27 380 alsi_n_t6 sample at two typical sites. fig. 9 exhibits the nano-clay particle distribution in the aluminum matrix. a highly magnified fe-sem image for alsi_n_t6 at a clustered particle site is depicted in fig. 10 and its counterpart eds results in fig. 11. the elements, which had percentages more than 1% including al, si, cu, mg, and o according to tab. 1, were presented. from fig. 11, it was easy to recognize the nano-particles dispersed in the aluminum matrix by focusing on the two most abundant elements including si and o in the nano-clay chemical composition. observations indicated that the dispersion of nano-particles was proper but not perfect and so desirable and therefore, some small degrees of agglomerations were detected in the microstructure. figure 7: fe-sem images of alsi_n_t6 with low magnifications. figure 8: eds results for alsi_n_t6 with low magnifications [16]. a. basiri et alii, frattura ed integrità strutturale, 57 (2021) 373-397; doi: 10.3221/igf-esis.57.27 381 figure 9: fe-sem images of alsi_n_t6 sample at a region of dispersed particles. figure 10: fe-sem images of alsi_n_t6 sample at highly clustered particles region. density measurement it could be observed in fig. 7 that some black tiny areas were present in the microstructure of alsi_n_t6, which represents the micro-porosity areas. it has been indicated in several studies [7,49-50] that an enhancement in micro-porosity content would be achieved after nano-particles addition to the metal matrix, which results in mechanical properties degradation. such a phenomenon was mainly attributed to poor wettability features of ceramic particulates [7,49], which stimulated the pore nucleation at nano-particles sites or agglomeration sites. the results of the pore measurement of both alsi and alsi_n_t6 using the archimedes method are presented in tab. 4. as it could be seen in tab. 4, the porosity content of alsi_n_t6 has increased in comparison to its counterpart alsi alloy following the reports in the literature [7,49-50]. a. basiri et alii, frattura ed integrità strutturale, 57 (2021) 373-397; doi: 10.3221/igf-esis.57.27 382 figure 11: eds results with high magnifications for alsi-n_t6. measured density (g/cm3) theoretical density (g/cm3) porosity (%) alsi 2.6813 2.7000 0.67 alsi_n_t6 2.6571 2.5862 2.74 table 4: results of the pore measurement. tensile properties the tensile flow curves of alsi alloys and alsi_n_t6 are depicted in fig. 12. moreover, the measured mechanical properties corresponding to tensile curves were presented in tab. 5. based on the results, alsi_n_t6 showed different tensile properties compared to alsi alloys. the yield strength and also the ultimate tensile strength in the nano-composite reduced by 7% and 5% respectively. in addition, the elastic modulus decreased by 21%. however, the elongation percent increased by about 2.5 times with respect to alsi alloy. cyclic behaviors the results of cyclic deformation had been presented focusing on mean stress, stress amplitude, and stress rate effects, respectively. fig. 13-16 depicts the first and mid-life hysteresis cycle of both alsi and alsi_n_t6 under the stress amplitude of 200 mpa, stress rate of 100 mpa/s, and different mean stresses. besides, fig. 16 demonstrates the evolution of plastic strain amplitude of the mentioned experiments. it could be readily seen in figs. 13, 14, and 15 the softer response of alsi_n_t6 in comparison to alsi alloys. the plastic strain amplitude could be measured as the width of the hysteresis loop, where the horizontal axis is located at the mean stress axis. the softer response of alsi_n_t6 means a higher plastic strain amplitude and as a consequence a wider hysteresis loop. besides, the width of hysteresis loops of alsi alloys demonstrated a decreasing trend, which implies the cyclic hardening behavior, whereas the mentioned width has an increasing trend in alsi_n_t6, which indicates the cyclic softening behavior of the material. such an observation had been approved by the evolution of plastic strain amplitude of samples in fig. 16. it could be seen in fig. 16 that the alsi alloys experience a decreasing trend of plastic strain amplitude over cycles, which implies the cyclic hardening feature of piston aluminum alloys. however, the cyclic hardening feature of monolithic alloys had been changed to a cyclic softening feature after the nano a. basiri et alii, frattura ed integrità strutturale, 57 (2021) 373-397; doi: 10.3221/igf-esis.57.27 383 particles addition and the heat treatment. besides, as it was reported in the literature [22,23], a higher value of mean stress has resulted in higher responded plastic strain amplitude and also a higher rate of cyclic hardening in the case of alsi alloys and a higher rate of cyclic softening in the case of alsi_n_t6. figure 12: tensile flow curves of alsi and alsi_n_t6. alsi alsi_n_t6 elastic modulus (gpa) 85.55±6.26 70.53±7.60 yield stress (mpa) 105.93±10.03 99.12±6.96 ultimate stress (mpa) 236.67±16.21 224.40±10.20 elongation (%) 1.51±0.23 3.69±0.21 table 5: mechanical properties of alsi and alsi_n_t6. figure 13: first and mid-life hysteresis loops of alsi and alsi_n_t6 under the stress amplitude of 200 mpa, the stress rate of 100 mpa/s and the mean stress of 0 mpa. a. basiri et alii, frattura ed integrità strutturale, 57 (2021) 373-397; doi: 10.3221/igf-esis.57.27 384 figure 14: first and mid-life hysteresis loops of alsi and alsi_n_t6 under the stress amplitude of 200 mpa, the stress rate of 100 mpa/s and the mean stress of 10 mpa. figure 15: first and mid-life hysteresis loops of alsi and alsi_n_t6 under the stress amplitude of 200 mpa, the stress rate of 100 mpa/s and the mean stress of 20 mpa. in addition to the cyclic softening feature of nano-composites, from figs. 13, 14, and 15 it is easy to identify the movement of hysteresis loops in the strain axis direction for alsi_n_t6, which implies the ratcheting deformation. for a better interpretation, the evolutions of strain amplitude and mean strain of both alsi and alsi_n_t6 over cycles for the same test conditions in figs. 13-16 are presented in figs. 17-18. fig. 17 indicates another evidence of the cyclic hardening/softening feature of the samples. as it could be observed in fig. 18, alsi alloys demonstrated a nearly constant mean strain over cycles, which increased as the mean stress increased. however, after the nano-particles addition and the heat treatment, the mean strain demonstrated an ascending order over cycles, which implies the ratcheting deformation. the rate of ratcheting strain (mean strain), increased as the applied mean stress increased. it is shown in the introduction that cyclic stress loadings with non-zero mean stresses could result in the ratcheting response. nevertheless, the ratcheting strain for alsi alloys showed no significant trend counting for the ratcheting behavior even though the applied mean stress for two tests was positive. on the other hand, the applied mean stress in fig. 13 was zero but still, the ratcheting deformation could be observed in alsi_n_t6. a. basiri et alii, frattura ed integrità strutturale, 57 (2021) 373-397; doi: 10.3221/igf-esis.57.27 385 figure 16: evolution of plastic strain amplitude of alsi and alsi_n_t6 at different mean stresses. figure 17: evolutions of the strain amplitude during cycles under the stress amplitude of 200 mpa and the stress rate of 100 mpa/s. figs. 19-22 depict the test results regarding the stress amplitude effect. in the mentioned tests, the mean stress was equal to zero and the stress rate had been set to 100 mpa/s. as commonly noted in the literature [22,23], with increasing the stress amplitude, the strain amplitude also increased and exhibited a higher degree of hardening in the case of the alsi alloy and softening in the case of alsi_n_t6. from fig. 19, a great difference between the response of as-cast alsi alloys and alsi_n_t6 to stress amplitude variations could be observed. first of all, despite the zero applied mean stress on these tests, the mean strains were non-zero. this fact could be also confirmed from the curves of the mean strain versus cycles in fig. 22. generally, the asymmetrical behavior of the material under fully-reversed cyclic loadings was related to the different deformation mechanisms operating in tension and compression. the tests related to alsi alloys in fig. 22 illustrated the tensile mean strain, which implied the larger deformation resistance of the material under tension than compression. however, a nearly constant mean stress sustained most of the fatigue lifetime. this positive mean strain increased as the stress amplitude increased. that was in an agreement with the results in the literature [18,19]. the addition of nano-particles and the heat treatment changed the mean strain response of the material completely. the responded mean strain in alsi_n_t6 was non-zero under fully-reversed stress-controlled loading similar to alsi alloys, but with increasing the stress amplitude, the mean strain continuously decreased. it seems that the resistance of the material to the tensile deformation decreased with increasing the stress amplitude and as a consequence, the mean strain changed the polarity from tensile to a. basiri et alii, frattura ed integrità strutturale, 57 (2021) 373-397; doi: 10.3221/igf-esis.57.27 386 compression. it could be observed in figs. 19 and 22 that under the stress amplitude of 220 mpa, the mean strain was completely compressive. besides, the mean strain was not constant during cycles and despite zero applied mean stress, a ratcheting deformation in tests with stress amplitudes of 200 and 220 mpa had been observed. figure 18: evolutions of the mean strain during cycles under the stress amplitude of 200 mpa and the stress rate of 100 mpa/s. figure 19: test results regarding the stress amplitude effect under zero mean stress and the stress rate of 100 mpa/s for mid-life hysteresis loops for both alsi and alsi_n_t6. figs. 23-26 depict the test results regarding the stress rate effect. in the mentioned tests, the mean stress was equal to zero and stress amplitude had been set to 210 mpa. it should be noted that experimental data for 10 mpa/s of the stress rate on alsi_n_t6 were eliminated from these figures, due to have only two cycles of loading for the sample. from figs. 24 and 25, it could be claimed that both the alsi alloys and alsi_n_t6 nano-composites presented a ratedependent response. the viscosity effect or the time-dependent response normally occurred at high temperatures as a consequence of the creep phenomenon, but it was shown that some materials experienced the viscosity effect even at room temperature. in such materials, the variation in the stress rate influenced the cyclic response [27]. besides, the sensitivity of nano-composites to the stress rate variations was larger than their counterpart alsi alloys. increasing the stress rate, the strain amplitude of alsi alloys changed negligibly contrary to alsi_n_t6, which the change of the strain amplitude was significant. the common feature observed in the literature [24-25,51-53], was that with increasing the stress rate, the ratcheting strain decreases in rate-dependent alloys. considering figs. 23 and 26, with increasing the loading rate, mean a. basiri et alii, frattura ed integrità strutturale, 57 (2021) 373-397; doi: 10.3221/igf-esis.57.27 387 strain increases in the case of alsi alloys but after nano-particles and the heat treatment, the mean strain tends to move toward the compressive region as the loading rate increases. based on figs. 24-26 and the tensile test results in tab. 5, a verification of obtained experimental data could be reported. since the fatigue lifetime was only some cycles (less than 10 cycles) under high stress levels, near the ultimate strength of studied materials. however, one important note is to have different material behaviors under different stress rates. in other words, tensile testing was done at a different loading rate, compared to the loading rate in lcf testing. therefore, the results of tensile and fatigue testing could not exactly compare to each other. figure 20: test results regarding the stress amplitude effect under zero mean stress and the stress rate of 100 mpa/s for evolutions of the strain amplitude over cycles for both alsi and alsi_n_t6. figure 21: test results regarding the stress amplitude effect under zero mean stress and the stress rate of 100 mpa/s for evolutions of the plastic strain amplitude over cycles for both alsi and alsi_n_t6. a. basiri et alii, frattura ed integrità strutturale, 57 (2021) 373-397; doi: 10.3221/igf-esis.57.27 388 figure 22: test results regarding the stress amplitude effect under zero mean stress and the stress rate of 100 mpa/s for evolutions of the mean strain over cycles for both alsi and alsi_n_t6. figure 23: test results regarding the stress rate effect under zero mean stress and the stress amplitude of 210 mpa for mid-life hysteresis loops for both alsi and alsi_n_t6. fatigue lifetime prediction the fatigue life of the samples has been investigated through this sub-section. generally, in the lcf regime, the strainbased models have been utilized to predict the fatigue lifetime but in the special case of stress-controlled lcf loading, the validity of these models is questionable because of unusual changes in maximum and mean strains during stress-controlled fatigue tests. therefore, the stress-based models were utilized to predict the fatigue lifetime. such models [54-55] are presented originally for the high-cycle fatigue (hcf) regime, but some investigations [56-57] demonstrated the validity of these models for the lcf applications. the classical models like stressand strain-based models were limited by a constant condition during the fatigue loading, for example, the constant temperature or the constant loading rate. besides, they were restricted to uniaxial loading. the generalization of such models to multiaxial cases needs the consideration of equivalent forms of the stress and the strain or utilizing the critical plane theories [57]. noting such difficulties, the energy-based models overcome these problems and even though, they consider both the stress and strain parameters in their formulations. using such models facilitates the consideration of different loading conditions, the damage accumulation in samples and components with notches. a. basiri et alii, frattura ed integrità strutturale, 57 (2021) 373-397; doi: 10.3221/igf-esis.57.27 389 therefore, a hysteresis energy-based model would be selected in this article in order to describe the fatigue lifetime of both alsi and alsi_n_t6 samples. figure 24: test results regarding the stress rate effect under zero mean stress and the stress amplitude of 210 mpa for evolutions of the strain amplitude over cycles for both alsi and alsi_n_t6. figure 25: test results regarding the stress rate effect under zero mean stress and the stress amplitude of 210 mpa for evolutions of the plastic strain amplitude over cycles for both alsi and alsi_n_t6. the power-law formulation describing the relationship between the energy related damage parameter p and fatigue lifetime nf has been described as follows [57]:   bfn a p (1) where a and b are two material constants. the energy related damage parameter that has been utilized in this investigation is the plastic strain energy density to represent the fatigue damage inside the material. the plastic strain energy at each cycle had been reported to be a. basiri et alii, frattura ed integrità strutturale, 57 (2021) 373-397; doi: 10.3221/igf-esis.57.27 390 representative of the necessary energy for the crack propagation [58]. such a plastic strain energy is equal to the area of the stress-strain hysteresis loop, which could be written as follows [57]: δ𝑊𝑝 = ∮ 𝜎𝑑𝜀 ≈△𝜎δ𝜀𝑝 (2) figure 26: test results regarding the stress rate effect under zero mean stress and the stress amplitude of 210 mpa for evolutions of the mean strain over cycles for both alsi and alsi_n_t6. the literature [56] suggests that the plastic strain energy could be approximated as the product of the stress range, δσ, and the plastic strain range, δεp, determined at the mid-life hysteresis loop, instead of integrating the hysteresis area over cycles. it has been known primarily that the tensile mean stress has a detrimental effect on the fatigue lifetime [59-60], while the compressive mean stress has a beneficial effect. therefore, the influence of mean stress has been embedded in lifetime prediction models as an additional parameter. it had been indicated in the “cyclic behaviors” section that in some tests, the ratcheting phenomenon had been observed. generally, the effect of ratcheting on the fatigue lifetime had been considered as the effect of the mean stress on the lifetime [61-62]. therefore, in this investigation, the mean stress effect on the fatigue lifetime has been considered as an additional factor. the plastic strain energy damage parameter has been modified to the following formulation [57]:                   2 11 b m m f p a n a w m (3) where m1 and m2 are two material constants. the value of material constants is calibrated using experimental data by a regression approach. the values of these parameters for both alsi and alsi_n_t6 had been reported in tab. 6. figs. 27-28 depictes the regression analysis on fatigue data of both alsi and alsi_n_t6 in a logarithmic scale analyzed by the plastic strain energy (pse) model and its counterpart corrected version based on the mean stress effect. the coefficient of determination (cd) or the 𝑅 value has been considered for evaluating fitting capability of the lifetime model. the related formulation of the cd parameter has been presented in the literature [57]. as it could be observed, the coefficient of determination (cd) of alsi_n_t6 data was smaller in value than alsi data since the scatter in nano-composite data was larger. it is interesting to note that the mean stress correction factor in the energy model could enhance the accuracy of the model significantly, especially in the case of alsi_n_t6. this argument could be proved by noting the cd parameter as its value increases in the pse model with the addition of the mean stress effect. besides, it has been proven that the dissipated plastic strain energy has a reverse relationship with the fatigue lifetime, which implied a negative slope in the following diagrams. such a negative slope had not been seen for alsi_n_t6 based on the uncorrected model but after the embedding of the mean stress correction factor into the models, the mentioned condition has been satisfied. a. basiri et alii, frattura ed integrità strutturale, 57 (2021) 373-397; doi: 10.3221/igf-esis.57.27 391 material without correction with mean stress correction a b a b m1 m2 alsi 9.8444 -0.4678 12.6252 -0.5016 2.0000 3.1000 alsi_n_t6 2.4013 0.0522 3.6743 -0.2970 0.9900 -13.1000 table 6: the martial constants of un-corrected and corrected plastic strain energy based on mean stress effect for both alsi and alsi_n_t6. figure 27: the regression analysis of the energy model for both alsi alloys and alsi_n_t6 without the mean stress correction factor. figure 28: the regression analysis of the energy model for both alsi alloys and alsi_n_t6 with the mean stress correction factor. by the extrapolation of the fitted curve for alsi_n_t6, as a claim, it could be predicted that for lower stress/strain amplitudes, the fatigue lifetime for the heat-treated nano-composite specimens could be equal to or higher than that for non-heat-treatment samples. fig. 29 illustrates the scatter-band analysis for both alsi alloys and alsi_n_t6 with the consideration of uncorrected and corrected plastic strain energy models. it could be observed that the scatter-band for alsi_n_t6 data had significantly wider than the data corresponding to alsi alloys. such results explained the higher value of cd for alsi alloys in comparison to nano-composites. it was seen that the energy model with the correction factor presented a smaller scatter-band in both a. basiri et alii, frattura ed integrità strutturale, 57 (2021) 373-397; doi: 10.3221/igf-esis.57.27 392 cases of alsi and alsi_n_t6 samples in comparison to the un-corrected plastic strain energy model. it could be observed in fig. 29 that the scatter-band parameter for alsi alloys with the un-corrected model was about 2.5, while the corrected model presented the value of 1.6. furthermore, in the case of alsi_n_t6, the scatter-band in the uncorrected model was about 5000, while with the addition of the mean stress correction factor, the scatter-band parameter decreased considerably to about 3. figure 29: the scatter-band analysis of the fatigue data of both alsi alloys and alsi_n_t6. it could be claimed that the present energy approach had a satisfying accuracy in the stress-controlled lcf lifetime prediction. the addition of a mean stress correction factor could enhance the accuracy of the model and also provide good results for the fatigue lifetime prediction in ratcheting-fatigue interaction cases. the simplicity and the consideration of both stress and strain parameters were other advantages of the presented model. as it could be seen in figs. 27-28, the addition of the reinforcement by nano-clay particles and the heat treatment influenced the fatigue lifetime significantly. in many samples, the fatigue lifetime decreased more than 50%. such a result was in an agreement with the literature [9-11]. discussion the microstructure, tensile, and stress-controlled lcf behaviors of alsi alloys and alsi_n_t6 nano-composites have thoroughly described in previous sections. it had been shown that the piston aluminum alloy presented a weaker and softer behavior in both tensile and fatigue experiments after the nano-particles addition and the heat treatment. in the two following sections, the role of nano-particles and the heat treatment on such a behavior will be discussed. effect of nano-clay particles most of the studies [3-7,30-35,49-52] had proved that the nano-particles addition to the aluminum alloy results in an enhancement of mechanical properties. such an enhancement had been attributed to several strengthening mechanisms including hall-petch strengthening, enhanced dislocation density, orowan strengthening, and load transfer effect. as it had shown in tab. 5, the results of the present investigation were in contradiction with mentioned studies. it has been reported in the literature [7,30] that beyond a threshold nano-particles volume/weight fraction, the strength and elongation of aluminum matrix nano-composites (amncs) would be declined as a result of excessive presence of particle agglomerations and micro-porosities. also, very high casting temperature, stirring velocity, and time had been reported [30] to produce degraded mechanical properties in the stir-casting process. since the elongation of alsi_n_t6 in the present investigation has increased after the nano-particles addition and the heat treatment, the nano-particles cannot be considered as the major source of the poor performance of alsi_n_t6. particle agglomerations and micro-porosities would decrease the yield and ultimate tensile strengths as well as ductility of the material because of providing potential sites for crack initiation and accelerating the crack propagation. it has been indicated in figs. 9-10 that some degrees of agglomerations are present in alsi_n_t6. nevertheless, with a qualitative comparison with similar micrographs of ammncs [6,7,30,51] the dispersion of nano-particles demonstrated no a. basiri et alii, frattura ed integrità strutturale, 57 (2021) 373-397; doi: 10.3221/igf-esis.57.27 393 intensive heterogeneity and there were no large agglomerations (larger than 1 micrometer) exist in the microstructure of alsi_n_t6. the higher porosity content in alsi_n_t6 in comparison to the alsi alloy had been reported in tab. 4. it had been shown [63] that the aluminum alloy with 10 wt.% nano-clay particles corresponding to 3.60% porosity content still offered enhanced strength and decreased ductility in comparison to the monolithic alloy. particle agglomerations and micro-porosities were characteristic features of nano-composites. their formation was inevitable during the processing of such materials; however, it was reported that nano-composites processed by the compo-casting method [49], the ultrasonic cavitation [46], and the extrusion after casting [50] offered lower agglomerations and porosities content in comparison to the stir-casting method. it had been observed in figs. 23-26 that alsi_n_t6 produced a cyclic softening behavior with more plastic strain amplitudes regarding the alsi monolithic alloy. it had been proved in the literature [8-12,27,28] that the dislocation hindering role of ceramic particles results in a higher rate of cyclic hardening response and also the lower exhibited plastic strain. the response of nano-composites is the same but more effective in that way because of more particulate content in comparison to microparticles with the same volume fraction. the results of the present investigation also disagree with the mentioned phenomena. such a poor fatigue performance of alsi_n_t6 also follows the tensile properties. in general, it could be claimed that particle agglomerations and micro-porosities were not able to increase the ductility alongside the material strength reduction. the nano particles affected the response of alsi_n_t6 but it could be claimed that the major source of poor performance of alsi_n_t6 was the heat treatment. effect of heat treatment the studies on amncs have accounted for the t6 heat treatment as an improver of mechanical properties [7,51,63-66] and also the fatigue properties [51,67-69] but such a positive effect has not been observed in the results of the present investigation. it could be claimed that the poor performance of alsi_n_t6 was related to the excessive aging time and temperature of the t6 process. as it had been indicated in figs. 2-5, the size and the circularity of si particles within the microstructure of alsi alloys enhanced after the nano-particles addition and the heat treatment. the spheroidization and the size reduction of eutectic si particles have been reported to be the results of the solution treatment and artificial aging, respectively during t6 heat treatment [67]. besides, the nano-particles addition had some effects on the size reduction of the eutectic si as a result of enhanced si particles nucleation at the nano-particles site. such a change in the morphology could explain the significant strengthening and the increase in the ductility [51,66]; however, the reduction in the size of si particles had not been met in this research. this observation implied a t7 over-aged state of alsi_n_t6. it has been reported in several studies [51,68] that the presence of the nano-reinforcement could change the aging kinetics of the material. the segregation of elements like mg at the matrix-reinforcement interface and grain boundaries, which resulted in the prevention of forming mg2si or mgzn2 precipitates, had been reported to reduce the precipitation hardening and subsequently, the detrition of mechanical properties. regarding the above statements, it is necessary to use the lower aging time and temperature in comparison to those normally used in the literature for nano-composite materials [65] and inevitably optimize the heat treatment parameters with the objective of reaching the optimum strength and ductility combination in aluminum-based nano-composites. such a work could be reserved for the future work. the weaker and softer behavior of alsi_n_t6 during tensile tests could explain the cyclic softening behavior under stresscontrolled lcf loading. as it was reported in the literature [67], the excess aging time or temperature during t6 heat treatment could result in cyclic softening of the a356 alloy and subsequently producing severe plastic deformation in the material. therefore, the wrongly chosen aging time and temperatures for alsi_n_t6 appeared as the lower resistance of alsi_n_t6 against the applied cyclic stress. it was obvious in fig. 26 that the reduced ability of alsi_n_t6 to the tensile deformation noting on the compressive mean strain in alsi_n_t6 nano-composites even though the applied mean stress was zero. therefore, alsi_n_t6 accommodated the deformation mostly by the compressive deformation. such an anisotropy in tension and compression conditions could explain the ratcheting deformation in alsi_n_t6, as could be observed in fig. 18. conclusions n this research, tensile and stress-controlled lcf properties of piston alsi alloys, with and without heat treatment besides nano-clay particles was investigated. the obtained experimental data showed the following highlights and behaviors:  the heat treatment could increase the size and circularity of the silicon phases. i a. basiri et alii, frattura ed integrità strutturale, 57 (2021) 373-397; doi: 10.3221/igf-esis.57.27 394  some small degrees of agglomerated nano-particles are detected in the microstructure.  the porosity content of alsi alloy was enhanced after the nano-particles addition.  the mechanical properties of the alsi alloy decreased after the nano-particles addition and the hat-treatment.  the cyclic response of the alsi alloy after the nano-particles addition and the heat treatment changed from a cyclic hardening feature to a cyclic softening feature.  the resistance of the alsi alloy against the ratcheting deformation reduces after the nano-particles addition and the heat treatment. the ratcheting deformation was observed in some nano-composite samples, even at zero mean stress.  a tensile mean strain is observed in many tests at fully-reversed stress cycling. such a result implied the decreased resistance of the material against the tensile deformation, especially for nano-composite.  nano-composite presented a rate-dependent response even at room temperature, unlike its counterpart monolithic alloy.  the fatigue lifetime of nano-composite was mostly less than 50% in comparison to its counterpart monolithic alloy.  it was shown that the major source of mechanical and fatigue properties degradation of nano-composite was related to the excessive aging time as a result of neglecting the higher aging kinetics in nano-composite.  the fatigue lifetime prediction of samples was done using a plastic strain energy approach. it was shown that the addition of a mean stress correction factor to the model could enhance the accuracy of the model considerably. for the further investigation, the fracture surface analysis could be performed on the failed sample (after the tests), in order to find the failure mechanism and the fracture behavior of the material. moreover, this report could be considered to find the influence of the nano-clay addition and the heat treatment on the fracture behavior and the failure mechanism of studied materials, besides the effect of the mean stress, the stress amplitude and the stress rate. moreover, performing a higher number of lcf testing on nano-composite samples with a pre-designed plan for loading conditions could help the researcher to investigate the material behavior in a high accurate state. acknowledgement hrough the impulse program, this project was financed by the austrian agency for international cooperation in education and research (oead) and the ministry of science, research and technology of the islamic republic of iran and also kharazmi university. moreover, authors thank the mpn company in iran for providing the initial aluminum ingots. references [1] silva, f.s. (2006). fatigue on engine pistons a compendium of case studies, eng. fail. anal., 13(3), pp. 480–492, doi: 10.1016/j.engfailanal.2004.12.023. [2] azadi, m. (2013). effects of strain rate and mean strain on cyclic behavior of aluminum alloys under isothermal and thermo-mechanical fatigue loadings, int. j. fatigue, 47, pp. 148–153, doi: 10.1016/j.ijfatigue.2012.08.005. [3] prasad reddy, a., vamsi krishna, p., narasimha rao, r., murthy, n. v. (2017). silicon carbide reinforced aluminium metal matrix nano composites-a review. materials today: proceedings, 4(2), pp. 3959–3971, doi: 10.1016/j.matpr.2017.02.296. [4] bhoi, n.k., singh, h., pratap, s. (2020). developments in the aluminum metal matrix composites reinforced by micro/nano particles – a review, j. compos. mater., 54(6), pp. 813–833, doi: 10.1177/0021998319865307. [5] tahamtan, s., halvaee, a., emamy, m., zabihi, m.s. (2013). fabrication of al/a206-al2o3 nano/micro composite by combining ball milling and stir casting technology, mater. des., 49, pp. 347–359, doi: 10.1016/j.matdes.2013.01.032. [6] sajjadi, s.a., torabi parizi, m., ezatpour, h.r., sedghi, a. (2012). fabrication of a356 composite reinforced with micro and nano al 2o3 particles by a developed compocasting method and study of its properties, j. alloys compd., 511(1), pp. 226–231, doi: 10.1016/j.jallcom.2011.08.105. [7] karbalaei akbari, m., baharvandi, h.r., shirvanimoghaddam, k. (2015). tensile and fracture behavior of nano/micro tib2 particle reinforced casting a356 aluminum alloy composites, mater. des., 66, pp. 150–161, doi: 10.1016/j.matdes.2014.10.048. t a. basiri et alii, frattura ed integrità strutturale, 57 (2021) 373-397; doi: 10.3221/igf-esis.57.27 395 [8] luk, m.j., mirza, f.a., chen, d.l., ni, d.r., xiao, b.l., ma, z.y. (2015). low cycle fatigue of sicp reinforced aa2009 composites, mater. des., 66, pp. 274–283, doi: 10.1016/j.matdes.2014.10.070. [9] koh, s.k., oh, s.j., li, c., ellyin, f. (1999). low-cycle fatigue life of sic-particulate-reinforced al-si cast alloy composites with tensile mean strain effects, int. j. fatigue, 21(10), pp. 1019–1032, doi: 10.1016/s0142-1123(99)00099-7. [10] han, n.l., wang, z.g., lizhi sun, (1995). effect of reinforcement size on low cycle fatigue behavior of sic particle reinforced aluminum matrix composites, scr. metall. mater., 33(5), pp. 781–787, doi: 10.1016/0956-716x(95)00281-y. [11] srivatsan, t.s. (1995). cyclic strain resistance and fracture behaviour of al2o3-particulate-reinforced 2014 aluminium alloy metal-matrix composites, int. j. fatigue, 17(3), pp. 183–199, doi: 10.1016/0142-1123(95)98939-z. [12] gasem, z.m., ali, s.s. (2013). low-cycle fatigue behavior of powder metallurgy 6061 aluminum alloy reinforced with submicron-scale al2o3 particles, mater. sci. eng. a, 562, pp. 109–117, doi: 10.1016/j.msea.2012.10.097. [13] llorca, j. (2002). fatigue of particle-and whisker-reinforced metal-matrix composites, prog. mater. sci., 47(3), pp. 283– 353, doi: 10.1016/s0079-6425(00)00006-2. [14] wallin, k., saario, t., törrönen, k. (1986). fracture of brittle particles in a ductile matrix, int. j. fracture, 32, pp. 201209, doi: 10.1007/bf00018353. [15] senthilkumar, r., arunkumar, n., manzoor hussian, m. (2015). a comparative study on low cycle fatigue behaviour of nano and micro al2o3 reinforced aa2014 particulate hybrid composites, results phys., 5, pp. 273–280, doi: 10.1016/j.rinp.2015.09.004. [16] azadi, m., bahmanabadi, h., gruen, f., winter, g. (2020). evaluation of tensile and low-cycle fatigue properties at elevated temperatures in piston aluminum-silicon alloys with and without nano-clay-particles and heat treatment, mater. sci. eng. a, 788, 139497, doi: 10.1016/j.msea.2020.139497. [17] ghasemi yazdabadi, h., ekrami, a., kim, h.s., simchi, a. (2013). an investigation on the fatigue fracture of p/m alsic nanocomposites, metall. mater. trans. a phys. metall. mater. sci., 44, pp. 2662–2671, doi: 10.1007/s11661-013-1620-3. [18] jabbari, a.h., shafiee sabet, a., sedighi, m., jahed, h., sommitsch, c. (2020). low cycle fatigue behavior of magnesium matrix nanocomposite at ambient and elevated temperatures, mater. sci. eng. a, 793, pp. 139890, doi: 10.1016/j.msea.2020.139890. [19] zhang, b., wang, r., hu, d., jiang, k., mao, j., jing, f., hao, x. (2021). stress-controlled lcf experiments and ratcheting behaviour simulation of a nickel-based single crystal superalloy with [001] orientation, chinese j. aeronaut., 34(8), pp. 112–121, doi: 10.1016/j.cja.2020.05.030. [20] chang, l., zhou, b. bin., ma, t.h., li, j., he, x.h., zhou, c.y. (2019). comparisons of low cycle fatigue behavior of cp-ti under stress and strain-controlled modes in transverse direction, mater. sci. eng. a, 746, pp. 27–40, doi: 10.1016/j.msea.2018.12.125. [21] agius, d., wallbrink, c., kourousis, k.i. (2017). cyclic elastoplastic performance of aluminum 7075-t6 under strain and stress-controlled loading, j. mater. eng. perform., 26, pp. 5769–5780, doi: 10.1007/s11665-017-3047-2. [22] sreenivasan, s., mishra, s.k., dutta, k. (2017). ratcheting strain and its effect on low cycle fatigue behavior of al 7075t6 alloy, mater. sci. eng. a, 698, pp. 46–53, doi: 10.1016/j.msea.2017.05.048. [23] dutta, k., ray, k.k. (2012). ratcheting phenomenon and post-ratcheting tensile behaviour of an aluminum alloy, mater. sci. eng. a, 540, pp. 30–37, doi: 10.1016/j.msea.2012.01.024. [24] kreethi, r., verma, p., dutta, k. (2015). influence of heat treatment on ratcheting fatigue behavior and post ratcheting tensile properties of commercial aluminum, trans. indian inst. met., 68, pp. 229–237, doi: 10.1007/s12666-014-0449-9. [25] wang, y., yang, s., xie, c., liu, h., zhang, q. (2018). microstructure and ratcheting behavior of additive manufactured 4043 aluminum alloy, j. mater. eng. perform., 27, pp. 4582–4592, doi: 10.1007/s11665-018-3563-8. [26] mishra, s.k., roy, h., mondal, a.k., dutta, k. (2017). damage assessment of a356 al alloy under ratcheting-creep interaction, metall. mater. trans. a phys. metall. mater. sci., 48, pp. 2877–2885, doi: 10.1007/s11661-017-4077-y. [27] kang, g. (2006). uniaxial time-dependent ratchetting of sicp/6061al composites at room and high temperature, compos. sci. technol., 66(10), pp. 1418–1430, doi: 10.1016/j.compscitech.2005.09.002. [28] kang, g.z., liu, y.j. (2007). uniaxial and multiaxial cyclic deformation behaviors of sicp/6061al alloy composites, key eng. mater., 353-358, pp. 1247–1250, doi: 10.4028/www.scientific.net/kem.353-358.1247. [29] goh, c.s., gupta, m., wei, j., lee, l.c. (2008). the cyclic deformation behavior of mg-y2o3 nanocomposites, j. compos. mater., 42(19), pp. 2039–2050, doi: 10.1177/0021998308094544. a. basiri et alii, frattura ed integrità strutturale, 57 (2021) 373-397; doi: 10.3221/igf-esis.57.27 396 [30] dehghan hamedan, a., shahmiri, m. (2012). production of a356-1wt% sic nanocomposite by the modified stir casting method, mater. sci. eng. a, 556, pp. 921–926, doi: 10.1016/j.msea.2012.07.093. [31] juang, s.h., fan, l.j., yang, h.p.o. (2015). influence of preheating temperatures and adding rates on distributions of fly ash in aluminum matrix composites prepared by stir casting, int. j. precis. eng. manuf., 16, pp. 1321–1327, doi: 10.1007/s12541-015-0173-3. [32] azadi, m., zolfaghari, m., rezanezhad, s., azadi, m. (2018). effects of sio2 nano-particles on tribological and mechanical properties of aluminum matrix composites by different dispersion methods, appl. phys. a mater. sci. process., 124, pp. 1–13, doi: 10.1007/s00339-018-1797-9. [33] karbalaei akbari, m., mirzaee, o., baharvandi, h.r. (2013). fabrication and study on mechanical properties and fracture behavior of nanometric al2o3 particle-reinforced a356 composites focusing on the parameters of vortex method, mater. des., 46, pp. 199–205, doi: 10.1016/j.matdes.2012.10.008. [34] zeren, m. (2007). the effect of heat-treatment on aluminum-based piston alloys, mater. des., 28(9), pp. 2511–2517, doi: 10.1016/j.matdes.2006.09.010. [35] nassar, a.e., nassar, e.e. (2017). properties of aluminum matrix nano composites prepared by powder metallurgy processing, j. king saud univ. eng. sci., 29(3), pp. 295–299, doi: 10.1016/j.jksues.2015.11.001. [36] astm e8 / e8m-11, (2011). standard test methods for tension testing of metallic materials, astm int. west conshohocken, pa, , doi: 10.1520/e0008_e0008m-13a. [37] astm e466 15, (2015). standard practice for conducting force controlled constant amplitude axial fatigue tests of metallic materials. doi: 10.1520/e0466-15. [38] casati, r., vedani, m. (2014). metal matrix composites reinforced by nano-particles – a review, metals (basel)., 4(1), pp. 65–83, doi: 10.3390/met4010065. [39] zainon, f., rafezi ahmad, k., daud, r. (2015). effect of heat treatment on microstructure, hardness and wear of aluminum alloy 332, appl. mech. mater., 786, pp. 18–22, doi: 10.4028/www.scientific.net/amm.786.18. [40] shi, w., gao, b., tu, g., li, s., hao, y., yu, f. (2010). effect of neodymium on primary silicon and mechanical properties of hypereutectic al-15si alloy, j. rare earths, 28(suppl. 1), pp. 367–370, doi: 10.1016/s1002-0721(10)60363-8. [41] chen, c., liu, z. xia., ren, b., wang, m. xing., wang, y. gang., liu, z. yong. (2007). influences of complex modification of p and re on microstructure and mechanical properties of hypereutectic al-20si alloy, trans. nonferrous met. soc. china (english ed., 17(2), pp. 301–306, doi: 10.1016/s1003-6326(07)60089-2. [42] zhu, m., jian, z., yang, g., zhou, y. (2012). effects of t6 heat treatment on the microstructure, tensile properties, and fracture behavior of the modified a356 alloys, mater. des., 36, pp. 243–249, doi: 10.1016/j.matdes.2011.11.018. [43] pio, l.y. (2011). effect of t6 heat treatment on the mechanical properties of gravity die cast a356 aluminium alloy, j. appl. sci., 11(11), pp. 2048–2052, doi: 10.3923/jas.2011.2048.2052. [44] rezanezhad, s., azadi, m., azadi, m. (2021). influence of heat treatment on high-cycle fatigue and fracture behaviors of piston aluminum alloy under fully-reversed cyclic bending, met. mater. int., 27, pp. 860–870, doi: 10.1007/s12540-019-00498-7. [45] zolfaghari, m., azadi, m., azadi, m. (2021). characterization of high-cycle bending fatigue behaviors for piston aluminum matrix sio2 nano-composites in comparison with aluminum-silicon alloys, int. j. met., 15, pp. 152–168, doi: 10.1007/s40962-020-00437-y. [46] salehi, a., babakhani, a., zebarjad, s.m. (2015). microstructural and mechanical properties of al-sio2 nanocomposite foams produced by an ultrasonic technique, mater. sci. eng. a, 638, pp. 54–59, doi: 10.1016/j.msea.2015.04.024. [47] han, l., sui, y., wang, q., wang, k., jiang, y. (2017). effects of nd on microstructure and mechanical properties of cast al-si-cu-ni-mg piston alloys, j. alloys compd., 695, pp. 1566–1572, doi: 10.1016/j.jallcom.2016.10.300. [48] firouzdor, v., rajabi, m., nejati, e., khomamizadeh, f. (2007). effect of microstructural constituents on the thermal fatigue life of a319 aluminum alloy, mater. sci. eng. a, 454–455, pp. 528–535, doi: 10.1016/j.msea.2007.01.018. [49] sajjadi, s.a., ezatpour, h.r., torabi parizi, m. (2012). comparison of microstructure and mechanical properties of a356 aluminum alloy/al2o3 composites fabricated by stir and compo-casting processes, mater. des., 34, pp. 106–111, doi: 10.1016/j.matdes.2011.07.037. [50] ezatpour, h.r., sajjadi, s.a., sabzevar, m.h., huang, y. (2014). investigation of microstructure and mechanical properties of al6061-nanocomposite fabricated by stir casting, mater. des., 55, pp. 921–928, doi: 10.1016/j.matdes.2013.10.060. [51] ahmed, a., neely, a.j., shankar, k., nolan, p., moricca, s., eddowes, t. (2010). synthesis, tensile testing, and microstructural characterization of nanometric sic particulate-reinforced al 7075 matrix composites, metall. mater. trans. a phys. metall. mater. sci., 41, pp. 1582–1591, doi: 10.1007/s11661-010-0201-y. a. basiri et alii, frattura ed integrità strutturale, 57 (2021) 373-397; doi: 10.3221/igf-esis.57.27 397 [52] choi, h., jones, m., konishi, h., li, x. (2012). effect of combined addition of cu and aluminum oxide nanoparticles on mechanical properties and microstructure of al-7si-0.3mg alloy, metall. mater. trans. a phys. metall. mater. sci., 43, pp. 738–746, doi: 10.1007/s11661-011-0905-7. [53] akbari, m.k., baharvandi, h.r., mirzaee, o. (2013). nano-sized aluminum oxide reinforced commercial casting a356 alloy matrix: evaluation of hardness, wear resistance and compressive strength focusing on particle distribution in aluminum matrix, compos. part b eng., 52, pp. 262–268, doi: 10.1016/j.compositesb.2013.04.038. [54] kwofie, s., chandler, h.d. (2007). fatigue life prediction under conditions where cyclic creep-fatigue interaction occurs, int. j. fatigue, 29(12), pp. 2117–2124, doi: 10.1016/j.ijfatigue.2007.01.022. [55] basquin, o. h. (1910). the exponential law of endurance tests, am. soc. test. mater. proc., 10, pp. 625–30. [56] kwofie, s., chandler, h.d. (2001). low cycle fatigue under tensile mean stresses where cyclic life extension occurs, int. j. fatigue, 23(4), pp. 341–345, doi: 10.1016/s0142-1123(00)00098-0. [57] farrahi, g.h., azadi, m., winter, g., eichlseder, w. (2013). a new energy-based isothermal and thermo-mechanical fatigue lifetime prediction model for aluminium-silicon-magnesium alloy, fatigue fract. eng. mater. struct., 36(12), pp. 1323–1335, doi: 10.1111/ffe.12078. [58] skelton, r.p. (1991). energy criterion for high temperature low cycle fatigue failure, mater. sci. technol., 7(5), pp. 427– 440, doi: 10.1179/mst.1991.7.5.427. [59] ostergren, w. (1976). a damage function and associated failure equations for predicting hold time and frequency effects in elevated temperature, low cycle fatigue, j. test. eval., 4(5), 339, doi: 10.1520/jte10520j. [60] pawliczek, r., rozumek, d. (2020). cyclic tests of smooth and notched specimens subjected to bending and torsion taking into account the effect of mean stres, mater., 13(9), 2141, doi: 10.3390/ma13092141. [61] rozumek, d., faszynka, s., (2017). fatigue crack growth in 2017a-t4 alloy subjected to proportional bending with torsion, frattura ed integrità strutturale, 11(42), pp. 23–29, doi: 10.3221/igf-esis.42.03. [62] kreethi, r., sivateja, c., mondal, a.k., dutta, k. (2019). ratcheting life prediction of quenched-tempered 42crmo4 steel, j. mater. sci., 54, pp. 11703–11712, doi: 10.1007/s10853-019-03705-3. [63] pan, x.m., li, x., chang, l., zhang, g.d., xue, f., zhao, y.f., zhou, c.y. (2018). thermal-mechanical fatigue behavior and lifetime prediction of p92 steel with different phase angles, int. j. fatigue, 109, pp. 126–136, doi: 10.1016/j.ijfatigue.2017.12.021. [64] gholipour, v., shamanian, m., ashrafi, a., maleki, a. (2020). development of aluminium-nanoclay composite by using powder metallurgy and hot extrusion process, met. mater. int., , pp. 1–14, doi: 10.1007/s12540-020-00791-w. [65] knowles, a.j., jiang, x., galano, m., audebert, f. (2015). microstructure and mechanical properties of 6061 al alloy based composites with sic nanoparticles, j. alloys compd., 615(supplement 1), pp. s401–s405, doi: 10.1016/j.jallcom.2014.01.134. [66] el-mahallawi, i., abdelkader, h., yousef, l., amer, a., mayer, j., schwedt, a. (2012). influence of al2o3 nanodispersions on microstructure features and mechanical properties of cast and t6 heat-treated al si hypoeutectic alloys, mater. sci. eng. a, 556, pp. 76–87, doi: 10.1016/j.msea.2012.06.061. [67] azadi, m., shirazabad, m.m. (2013). heat treatment effect on thermo-mechanical fatigue and low cycle fatigue behaviors of a356.0 aluminum alloy, mater. des., 45, pp. 279–285, doi: 10.1016/j.matdes.2012.08.066. [68] shaha, s.k., czerwinski, f., kasprzak, w., friedman, j., chen, d.l. (2016). effect of mn and heat treatment on improvements in static strength and low-cycle fatigue life of an al-si-cu-mg alloy, mater. sci. eng. a, 657, pp. 441– 452, doi: 10.1016/j.msea.2016.01.015. [69] borrego, l.p., abreu, l.m., costa, j.m., ferreira, j.m. (2004). analysis of low cycle fatigue in almgsi aluminium alloys, eng. fail. anal., 11(5), pp. 715–725, doi: 10.1016/j.engfailanal.2003.09.003. microsoft word numero_58_art_09_2964.docx j. wang et alii, frattura ed integrità strutturale, 58 (2021) 114-127; doi: 10.3221/igf-esis.58.09 114 structural model updating based on metamodel using modal frequencies jutao wang, zhenzhong liu, lijun xue tianjin key laboratory for advanced mechatronic system design and intelligent control, school of mechanical engineering, tianjin university of technology, tianjin 300384, china national demonstration center for experimental mechanical and electrical engineering education (tianjin university of technology) tjwjt@163.com, liusdcn@gmail.com, meilideshijieali@163.com abstract. modal frequencies are often used in structural model updating, based on the finite element model, while the metamodel approach is often used in the respective optimization process. in this work, the kriging model is adopted as the metamodel. first, the influence of different correlation functions of kriging model is inspected, followed by the investigation of the approximate capability of kriging model by inspecting the approximate accuracy of nonlinear functions. next, a model updating procedure is proposed, based on the kriging model, constructed using samples generated via the method of optimal latin hypercube. finally, a typical frame structure is taken as a case study, demonstrating the feasibility and efficiency of the proposed approach. the results show that, the kriging model can match the target functions very well, while the finite element model can achieve accurate frequencies and can reliably predict the frequencies after model updating. keywords. model updating; metamodel; modal frequency; optimization. citation: wang, j., liu, z., xue, l., structural model updating based on metamodel using modal frequencies, frattura ed integrità strutturale, 58 (2021) 114-127. received: 08.12.2020 accepted: 30.05.2021 published: 01.07.2021 copyright: © 2021 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. introduction etamodel has been introduced, for some years now, to model updating procedure, due to its fast iteration advantage. specifically in the structural dynamic model updating case, the metamodel can achieve computational efficiency, when used in place of the finite element model (fem), during the iteration process of optimization. ling [1] combined an adaptive kriging metamodel with importance sampling strategies, to analyze the safety level of time– variant structures. based on metamodel, lin [2] proposed an intelligent sampling approach and employed this for the design of a bus body frame. hamdani [3] used the kriging model to efficiently solve the expensive mechatronic optimization problem in soldered joints. metamodel has not only been applied in the updating process, but also in structural optimization [4], uncertainty quantification [5] and damage detection [6], among others. the metamodel can be considered as the description of the input-output relation in the simulation of fem, where the relation appears obviously nonlinear in dynamic m https://youtu.be/oynrkryonmq j. wang et alii, frattura ed integrità strutturale, 58 (2021) 114-127; doi: 10.3221/igf-esis.58.09 115 simulation cases. the metamodel, offering a strong approximation capability to nonlinear function, is important in dynamic model updating, where fast iteration with accurate metamodeling is needed. in other words, the metamodels are supposed to describe more exact input-output relations in the simulations of fem. an adaptive kriging method was successfully applied to solve the multidisciplinary design optimization (mdo) problem of the geostationary (geo) satellite [7]. in another study, a multi-objective multidisciplinary design optimization problem of unmanned aerial vehicle wing was solved based on kriging model [8]. as one of the most common dynamic model updating approaches, modal parameter based model updating is applied on different finite element models for various structures. bautista-de castro [9] combined a polynomial chaos expansion metamodel and sobol’s indices for the sensitivity analysis, in the masonry arch bridge case. based on the modal parameter, the proposed method made particle swarm optimization (pso) possible to apply, for the model updating of a large-scale railway bridge [10]. in the analysis of vibration characteristics of track structures, gao [11] carried out 3 model updating schemes, based on the measured modal parameters. in the case of dynamic model updating, the dynamic analysis and objective function of the optimization problem have nonlinear characteristics, which the commonly used response surface method (rsm) [12] is incapable of approximating, therefore the kriging model is introduced to the dynamic model updating, as a more accurate metamodel. in this article, multidimensional functions are considered as objective functions, for inspecting the approximation capability of the kriging model. the required training samples, for constructing kriging model, are obtained by design of experiment (doe). the accuracy of the constructed kriging model, in respect to the objective functions, is estimated by root mean square error (rmse) and determination coefficient. accordingly, a procedure of model updating is proposed, while a model updating of modal frequencies in a typical frame structure is used as case study. characteristic of kriging model nlike the conventional rsm, the kriging model goes through all the training samples, providing a more accurate approximation than the conventional rsm [13, 14]. the kriging model is constructed based on the interpolation technique, which can provide evaluation of unknown points. these evaluated values are the unbiased estimation of the least estimated variance of the known points. the kriging model generally consists of two parts: linear regression and non-parametric sections. the model exhibits statistical characteristics, since the non-parametric section follows random distribution. thereby the kriging model can be formulated by polynomial section and random distribution, as follows:     ( ) ( , ) ( ) ( ) ( )ty x f x z x f x z x (1) where, is the regression coefficient, f(x) denotes the polynomial of variable x; and z(x) denotes the errors of random distribution. the construction process of the kriging model the kriging model derives from statistics, based on the theory that the closer the regions, the more similar they are. the function value at an unknown point can be evaluated via weighted summation of the information of known points, located nearby the unknown point. the weighted summation is obtained via minimized variance of the error among the known points. accordingly, the kriging model needs to satisfy two requirements: unbiased property and minimizing error estimation. the construction of the kriging model can then be achieved, as follows: (i) unbiased property based on eqn. (1), the unbiased property is the unbiased estimation which obtains y(x0) from ŷ(x0), that is, y(x0) and ŷ(x0) have the same expectation: e[ŷ(x0)]=e[y(x0)] (2) where, ŷ(x0)= w   1 ( ) n i i i y x eqn. (2) can also be written as follows: u j. wang et alii, frattura ed integrità strutturale, 58 (2021) 114-127; doi: 10.3221/igf-esis.58.09 116 e      0 1 1 [ ( )] [ ( )] [ ( )] n n i i i i i i e w y x w e y x y x (3) where, wi are the weight coefficients and therefore the unbiased condition followed is as follows:   1 1 n i i w (4) (ii) minimizing error estimation (optimal results) the estimated variance of the unknown point x0 can be obtained as                 2 2 2 0 0 0 1 0 0 0 1 1 1 ˆ[( ( ) ( )) ] [( ( ) ( )) ] ( ( ), ( )) 2 ( ( ), ( )) ( ( ), ( )) n e i i i n n n i j i j i i i j i e y x y x e w y x y x w w c y x y x w c y x y x c y x y x (5) where, c denotes the matrix of the covariance, while the correlation vector r(xi, xj), based on the unbiased results, can convert eqn. (5) into the following form:        2 0 0 0 1 1 1 2 ( , ) ( , ) ( , ) n n n e i i i j i j i i j w r x x w w r x x r x x ,   2( , ) ( , )i j i jr x x c x x (6) the minimization of estimated variance of eqn. (6), at the unbiased condition, is an extreme-value problem with constraints, while the solution can be obtained based on the lagrange multiplier method, which means:       2 1 ( , ) 2 ( 1) n i e i i l w w (7) where, φ is the vector of lagrange multiplier, the partial derivatives of wi and φ to l are set to 0, deriving:                  0 1 1 2 ( , ) 2 ( , ) 2 0 2( 1) 0 n j i j i ji n i i l w r x x r x x w l w (8) after adjustment, the form is:              0 1 1 ( , ) ( , ) 1 n j i j i j n i i w r x x r x x w (9) the weight coefficient wi and lagrange coefficient φ can be obtained via solving linear eqn. (9), while the evaluated value of ŷ(x0) at unknown point x0 can be derived, based on eqn. (2). eqn. (9) can be written as a matrix: j. wang et alii, frattura ed integrità strutturale, 58 (2021) 114-127; doi: 10.3221/igf-esis.58.09 117                                                       11 12 1 1 10 21 2 2 2 20 1 2 0 1 1 1 1 1 1 0 1 n n n n n nn n n r r r w r r r r w r r r r w r (10) where, rij=r(xi, xj). the values of wi and φ can be solved directly by reversing the matrix eqn. (10), where the matrix rij of correlation coefficient can be obtained independently, in advance. accordingly, the construction steps of kriging model can be summarized as follows: step 1: the distance and r(xi, xj) between every two known points are calculated successively. step 2: the correlation function is selected based on the value of dij and rij, as provided from step 1. step 3: ri0 of the unknown point x0 is calculated based on the selected correlation function. step 4: the optimal value of the weight coefficient wi is obtained based on eqn. (10). step 5: the weighted array of the known points, based on the wi, is used to evaluate the unknown point x0. the matrix of the correlation coefficient is fixed once the left side of eqn. (10) is evaluated. therefore, the column vector of the right side equation is the only calculation held separately, thus the values of the unknown points can be obtained. the parameter  is introduced into the function r(xi, xj) for more flexibility. the function y(x) follows normal distribution, since z(x) follows normal distribution in eqn. (1), while the  value is obtained by maximizing the likelihood estimation of y(x), which can assure that y(x) goes through the known points with maximum probability. the equation form, after logarithm to likelihood function of y(x), for reasons of facilitating calculation, can be given as:           1 2 2 1 ( ) ( ) ln[ ( )] ln( ) ln( ) 2 2 2 t t t sn y f r y flh r y r (11) after partial derivative and maximum likelihood estimation, the construction of kriging model focuses on the maximum solution of  value [16]. figure 1: the approximation result by kriging model using different correlation functions. the types of correlation function the correlation function rij describes the correlation between samples, being stronger among the closer together samples. the evaluation of the unknown point depends on the stronger correlations. the main types of correlation functions are: linear, spherical, gaussian, exponential and cubic. each of the functions shows its own advantages, in specific applications, e.g. exponential function is more suitable for biology, while the application of gaussian function is more j. wang et alii, frattura ed integrità strutturale, 58 (2021) 114-127; doi: 10.3221/igf-esis.58.09 118 extensive [17, 18]. a comparative graph is illustrated in fig. 1, to show the approximation ability to a one-dimension function (eqn. (12)). the “initial” line represents the one-dimension function (objective function), the other 3 lines represent the approximation of different correlation functions. fig. 1 shows that, the smoothest curve is constructed based on gaussian function, which is suitable for optimization algorithms.   2( ) (6 2) sin(12 4)f x x x (12) selection of training samples he training samples (known points) are usually obtained via the doe method and used to construct the kriging model. the matrix of design parameters is generated by the doe method (a planning method), in which the response of the design matrix can reflect the properties of the designed object, such as the sensitivities and interactions of design parameters. the design matrix consists of the descriptions of the samples distribution, in which the uniformity and orthogonality can affect the approximate accuracy of the derived kriging model. the commonly used sampling methods are: all factors, orthogonal array, central composite, latin hypercube and optimal latin hypercube (olh). each parameter can be involved and given average values by the latin hypercube method, making it possible for fewer samples to fill the design domain. based on latin hypercube method, olh method can minimize the “ununiformity” of distribution of the samples, via central l2 (cl2) criterion [19, 20]. the advantage of the cl2 criterion is illustrated in fig. 2 and its expression is given by eqn. (13). each dot in fig. 2 represents a sample, while the grid represents the design domain. obviously, in the same small number of samples, the distribution of samples in olh is more uniform. briefly stating that, in constructing kriging model, the olh method is more suitable in cases of fewer samples.                      22 2 1 1 2 1 1 1 13 2 1 1 ( ) ( ) (1 0.5 0.5 ) 12 2 2 1 1 1 1 (1 0.5 0.5 ) 2 2 2 mn ik ik i k mn n ik jk ik jk i j k cl x x x n x x x x n (13) where, n denotes the times of sampling, m denotes the number of design variables, xik denotes the ith sampling of design variable xk. figure 2: the comparison of latin hypercube to olh. test for kriging model etamodel is seen as an approximation to the target model (objective function) and the approximation accuracy must be determined, before replacing the target model. in this section, the approximation capability of kriging model is investigated, by interpolating standard test functions. the kriging model is constructed based on the training samples, derived from the test functions. next, the check points are re-sampled, providing different sets from the training samples. the check points are used to compare the corresponding output of the kriging model to the target model. the discrepancies (i.e. error) revealed by the comparison are estimated by rmse method or using the determination coefficient (r2), to describe the approximation capability. t m j. wang et alii, frattura ed integrità strutturale, 58 (2021) 114-127; doi: 10.3221/igf-esis.58.09 119 the deviations between target values and approximated values are estimated by rmse method, deriving an average value of the observed discrepancies, which the lower it is, the smaller the error. in engineering, the error is usually supposed to be less than 0.1 (rmse<0.1). the value of r2 is used to estimate the similarity between the target model and the metamodel, whereas the greater the value, the more similar the 2 models are. the range of r2 is between 0 and 1, while the value is supposed to be greater than 0.9 (r2>0.9). the expressions of rmse and r2 method are as follows:             2 2 2 1 21 1 ˆ( ) 1 ˆ( ) , 1 ( ) k i ik i i i k i i i y y rmse y y r ky y y (14) where, k denotes the number of test points, ȳ denotes the average value of target model response, yi denotes the response of the target model at the test points, ŷi denotes the response value of the kriging model at the test points. one of the commonly used functions, branin function is applied to inspect the approximation capability of kriging model. fig. 3 shows that, branin function is an asymmetric function of nonlinear function, with input variables ranges of [-5,10] and [0,15]. the expression is as follows:                2 21 1 2 1 1 22 5.1 5 1 ( ) ( 6) 10(1 ) cos( ) 10, ( 5 10, 0 15) 4 8 x x y x x x x x (15) the number of samples population are 10, 15 and 20 respectively, sampled by the olh method respectively. based on the samples, the contrasts between the constructed kriging model and branin function are illustrated in figs. 4(a), 4(b) and 4(c), respectively. the largest error appears in the range of (-5, 0), while it is apparently decreasing as the number of samples increases. there is a large edge error illustrated in fig. 4(a), but the kriging model also has a very similar shape to the one of the objective function. better consistencies appear in figs. 4(b) and 4(c), whereas the main errors at the boundaries are far from the samples. the values of rmse and r2, at the check points, are used to test the approximation accuracy of the kriging model. 5 samples are sampled, using latin hypercube method, as check points, while 3 errors at the check samples of each kriging model are compared to the target function (fig. 5). it is evident that, the error is decreasing when the number of training samples is growing. the values of rmse and r2, in the 3 different training samples, are listed in table 1, at the check samples. the results show that, the kriging models have a better approximation accuracy, when constructed by 15 samples and 20 samples. however, there is little improvement in accuracy, when using the 20 samples, which means that 15 training samples is an adequate number in this test function. sample number 10 15 20 rmse value 0.1366 0.0467 0.0433 r2 value 0.9350 0.9924 0.9935 table 1. the errors in different sample sets of kriging model in different estimations figure 3: the 3 dimensional plot of branin function. j. wang et alii, frattura ed integrità strutturale, 58 (2021) 114-127; doi: 10.3221/igf-esis.58.09 120 (a) (b) (c) figure 4: the kriging model for branin function for different number of samples: (a) 10 samples, (b)15 samples, (c) 20 samples. j. wang et alii, frattura ed integrità strutturale, 58 (2021) 114-127; doi: 10.3221/igf-esis.58.09 121 figure 5: the error at the check points. the dynamic model updating based on kriging model the construction of objective function odel updating aims to make the updated fem have the same behavior as the real experiment, as much as possible. model updating is a mechanical inverse problem, where the fem is calibrated, based on the known response of the experiment model. the objective function is formulated based on the response of fem and the experiment, while the model updating can then be converted to constrained optimization problem. the form of a commonly used objective function is formulated as follows:                   （ ） 2 1 1, 2, ..., min ( ) . . i i a i i h t i t d u j j j j n w r r f x r s t x x x (16) where, wi denotes the weight coefficient, ra denotes the response of the fem, rt denotes the response of the experiment model, xj denotes design parameters, xd denotes the lower bound of design parameter and xu denotes the upper bound. the process of dynamic model updating based on kriging model the structural features and response types are taken into account for the construction of a suitable fem, requiring rational simplification and parameterization and so on. the doe of the fem is carried out to generate the training samples for constructing the respective kriging model. the objective function is established based on the response deviation between the experiment and the fem, while then the optimal value of design parameters is obtained by solving the optimization problem. the optimized parameters are used to modify the fem and produce the updated fem. the process of dynamic model updating, based on kriging model, is plotted in fig. 6 and summarized below: step 1: constructing original fem based on the experiment. step 2: parameterizing the fem and selecting the design parameters to be optimized. step 3: doe is carried out, based on the fem, while the design matrix is obtained using the olh method for design parameters. the training samples are generated by calculating the response on each level of the doe. step 4: the relative parameters are determined based on the training sample, to construct the kriging model. step 5: the approximation accuracy of the constructed kriging model is estimated and when the accuracy satisfies the requirements the process goes to the next step, otherwise there is another iteration starting from step 3. step 6: the response between fem and experiment are used to establish the objective function, whose design variables are the parameters to be modified. step 7: the kriging model is iterated using a global optimization algorithm, to get the optimal value of design parameters, whereas the iteration will continue until the end condition is satisfied. m j. wang et alii, frattura ed integrità strutturale, 58 (2021) 114-127; doi: 10.3221/igf-esis.58.09 122 step 8: the optimal parameters are used to calibrate the fem, while the model updating is completed after checking the update effect. construction of objective function optimization solution fem updating by optimal parameters satisfy error? model updating results experiment data simulation of fem parameters selection doe construction of metamodel satisfy accuracy? yes no yes no figure 6: flow chart of the process of model updating. case study rame structure is one of the main bearing structures in engineering, such as in the vehicle chassis, or in some civil structure. the dynamic response of the frame structure is very important to the dynamic behavior of the overall structure. the modal control is one of the necessary considerations of dynamic design. the simulation model usually needs model updating, based on the modal frequencies. in this section, an experiment with a typical frame structure [21] is used, to demonstrate the efficiency of the proposed model updating process. (a) (b) figure 7: the frame structure: (a) the frame geometry for experiment, (b) the fem. f j. wang et alii, frattura ed integrità strutturale, 58 (2021) 114-127; doi: 10.3221/igf-esis.58.09 123 the construction of fem and kriging model the frame structure (fig. 7(a)) is assembled by aluminum alloy profile, of 25.4 mm square side length and 2.38 mm wall thickness. the modal experiment is performed by hammer testing, where the frame is suspended freely. the first 5 frequencies of the obtained results are listed in the second column of table 2. the frame is assembled by 5 beams, while its simplified fem is constructed by beam elements, similarly to the initial fem of 140 elements and 139 nodes (fig. 7(b)). the software patran has been employed. all elements have same material properties as the initial given values: e=71000mpa (elastic modulus), μ=0.3 (poisson ratio), ρ= 2700 kg/m3 (density). after free modal analysis of the initial fem, the first 5 frequencies of the modal results are listed in the third column of table 2. the initial errors between the fem and the experimental model are listed in the 4th column of table 2. obviously, all errors are too large to be accepted, except the case of the second frequency, whereas all the simulation values are higher than the experimental values. this means that, the initial fem has internal defects and needs to be calibrated through the process of model updating. regarding the parameters to be updated, the geometry dimensions are easily measured and should not be selected as parameters to be updated, whereas the material properties are usually coming from handbooks and may easily include errors, so these three properties are selected as parameters to be updated by the model updating process. order experiment(hz) fem(hz) initial error (%) 1 226.8 246.13 8.52 2 275.2 283.61 3.06 3 537.4 574.38 6.88 4 861.5 911.46 5.80 5 974.8 1062.70 9.02 table 2. initial value of modal frequencies of experiment and fem in order to demonstrate the efficiency of the model updating process, based on kriging model, the five frequencies of the modal experiment are divided into two groups, during model updating. the first three frequencies are selected as the updating objective and are named “updating group”. on the other hand, the last two frequencies, which will not be updated during model updating, are named “predictive group”. the deviations between the experiment and simulation of the first three frequencies are considered as the output response of the doe, while the expression is as follows:      1 1 2 2 3 3(3) t a t a t ar f f f f f f (17) where, i tf denotes the experiment frequencies, i af denotes the simulated frequencies of fem. the three material properties are selected as the updating parameters and are considered as the factors of the doe. the artificial range of each factor is from 90% to 110% of their initial values, while 20 training samples are generated by olh. next, the θ values are obtained as: θe=0.17174, θμ= 0.02724 and θρ= 0.17027. the kriging model in the (e, ρ) dimension is plotted in fig. 8, with the μ parameter fixed at its initial value. five check samples are re-sampled by latin hypercube method, to estimate the accuracy. the comparison of response values between the fem and kriging model, at each of the check samples, are plotted in fig. 9. evaluation produces the values of rsme=0.375 and r2=0.993, while it can be considered that the kriging model shows good accuracy for replacing the fem in the next process of optimization. model updating results and discussion minimizing the error between the fem value and experimental value of the first three frequencies is the optimization objective. the sum of the error at each frequency is considered as the objective function, whose weight coefficient is set to 1, since the frequencies have the same order of magnitude. the form of the objective function remains the same as in eqn. (17), while the input variables (updating parameters) have the same value ranges as in the doe. based on the constructed kriging model, the optimal values of each updating parameter are obtained by multi-island genetic algorithm as: e=67008.5mpa (elastic modulus), μ=0.3122 (poisson ratio), ρ=2885.6 kg/m3 (density). the fem is then calibrated according to the optimal parameters values, while the updated first 5 frequencies are listed in the 3rd column of table 3. the errors of the updating group and the predictive group evidently decrease, excluding the 2nd frequency case. j. wang et alii, frattura ed integrità strutturale, 58 (2021) 114-127; doi: 10.3221/igf-esis.58.09 124 figure 8: the kriging model in (e, ρ) dimension. figure 9: the error at check points. as illustrated in fig. 8, the minimum is close to the boundary of the design domain, while the global optimal results are possibly located outside the design domain. therefore, the design domain (value ranges of design parameters) is further expanded, to find out if there is a better optimal result. a new doe is then operated in a wider design domain, which means each factor ranges between 80% to 120% of its initial values, while then 20 training samples are generated by olh. next, the corresponding θ values are obtained as: θe=0.32992, θμ= 0.00010 and θρ=0.33473. consequently, a new kriging model in the (e, ρ) dimension is constructed and plotted (fig. 10), where the minimum location is promoted so that it is not very close to the boundary. the estimation of the accuracy of the new constructed kriging model is illustrated in fig. 11, while the corresponding values are the following: rmse=0.0584 and r2= 0.9894. the accuracy declines slightly after expanding the design domain, because the design domain is expanded but the number of samples remains the same. based on the kriging model in fig. 10, the optimal parameters values, upon completion of the solution process, are: e= 72384.4mpa, μ= 0.3486, ρ= 3068.2kg/m3. the corresponding result of model updating is listed in the 5th column of table 3, where it is evident that, the errors of the 1st, 2nd and 4th frequencies decline and the other errors slightly increase, while the errors still meet the relative engineering requirements. the results listed in the last two lines in table 3 are the predicted values, where the 4th and 5th frequencies are updated correctly, meaning that the two kriging models have a good predictive capability. moreover, for comparison reasons, the commonly used rsm with second-order polynomial is constructed, based on the 20 training samples, previously generated in the expanded design domain. the updated results are listed in the 7th column of table 3, where most of the error is larger than the other three groups of errors, except at the 2nd frequency. meanwhile, j. wang et alii, frattura ed integrità strutturale, 58 (2021) 114-127; doi: 10.3221/igf-esis.58.09 125 the optimization without metamodel is applied to the fem directly (the parameters are in the expanded design domain), and the updated result is listed in the penultimate column of table 3, the error is almost at the same level as the proposed method. this can lead to the conclusion that the kriging model shows advantages in the specific dynamic model updating. figure 10: the kriging model in (e, ρ) dimension figure 11: the error at checking points. orde r experime nt (hz) ±10% variation ±20% variation rsm directly after updated (hz) error (%) after updated(hz ) error (%) after updated(hz ) error (%) after updated(h z) erro r (%) 1 226.8 230.39 1.58 229.57 1.22 232.14 2.35 228.18 0.61 2 275.2 266.46 -3.18 268.50 -2.43 272.44 -1.00 267.79 -2.69 3 537.4 538.66 0.23 539.80 0.45 546.80 1.75 537.46 0.01 4 861.5 856.08 -0.63 861.81 0.036 874.20 1.47 859.26 -0.26 5 974.8 998.06 2.39 1004.48 3.04 1018.85 4.52 1001.43 2.73 table 3. comparison before and after model updating j. wang et alii, frattura ed integrità strutturale, 58 (2021) 114-127; doi: 10.3221/igf-esis.58.09 126 conclusion odel updating method based on metamodel is studied in this article, where the advantages of different correlation functions and different sampling methods are compared, so that gaussian function and olh are selected for the kriging model. first, the approximation accuracy of kriging model to the objective function (branin function) is inspected in different number of samplings. the errors between the objective function and kriging models are quantified by rsme and r2 criteria, based on the check points. after inspection, all the constructed kriging models can achieve rmse<5%, r2>0.99, which means kriging model exhibits a good capability to approximate the nonlinear function. according to the characteristic of dynamic model updating, kriging model is considered as the metamodel, to replace the fem in the iterations, during the optimization process. based on the proposed approach, a typical frame structure is used as the case study, where the fem is established by beam elements. the doe response and optimization objective are constructed based on the errors of modal frequencies between the fem and the experiment. after model updating, the modal errors of the fem are reduced, while the updated results are better than the results of rsm, while the updated fem shows considerable prediction ability. therefore, the efficiency of dynamic model updating, using the proposed method, is demonstrated and further lays a foundation for subsequent relative research. acknowledgement his work was supported in part by the national natural science foundation of china under grant 61873188, and in part by the tianjin science and technology plan projects under grant 18zxzngx00360. reference [1] ling, c., lu, z. (2020). adaptive kriging coupled with importance sampling strategies for time-variant hybrid reliability analysis, applied mathematical modelling, 77(2), pp. 1820-1841. doi: 10.1016/j.apm.2019.08.025. [2] lin, c., gao, f., bai, y. (2018). an intelligent sampling approach for metamodel-based multi-objective optimization with guidance of the adaptive weighted-sum method, structural & multidisciplinary optimization, 58, pp.1047-1060. doi: 10.1007/s00158-017-1793-2 [3] hamdani, h., radi, b., hami, a. e. (2019). metamodel assisted evolution strategies for global optimization of solder joints reliability in embedded mechatronic devices, microsystem technologies, 25, pp. 3801-3812. doi: 10.1007/s00542-019-04520-1 [4] shu, l., jiang, p., zhou, q., et al. (2018). an on-line variable fidelity metamodel assisted multi-objective genetic algorithm for engineering design optimization, applied soft computing, 66, pp. 438-448. doi: 10.106/j.asoc.2018.02.033. [5] rodriguez, s., ludkovski, m. (2020). probabilistic bisection with spatial metamodels, european journal of operational research, 286(2), pp. 588-603. doi: 10.1016/j.ejor.2020.03.049. [6] ghiasi, r., ghasemi, m. r., noori, m. (2018). comparative studies of metamodeling and ai-based techniques in damage detection of structures, advances in engineering software, 125, pp. 101-112. doi: 10.1016/j.advengsoft.2018.02.006. [7] shi, r., liu, l., long, t., et al. (2019). filter-based adaptive kriging method for black-box optimization problems with expensive objective and constraints, computer methods in applied mechanics & engineering, 347, pp. 782-805. doi: 10.1016/j.cma.2018.12.026. [8] zadeh, p. m., sayadi, m. (2019). an efficient metamodel-based multi-objective multidisciplinary design optimization framework, applied soft computing, 74, pp. 760-782. doi: 10.1016/j.asoc.2018.09.014. [9] bautista-de castro, a., javier sanchez-aparicio, l. (2019). carrasco-garcia p., et al. a multidisciplinary approach to calibrating advanced numerical simulations of masonry arch bridges, mechanical systems and signal processing, 129, pp. 337-365. doi: 10.1016/j.ymssp.2019.04.043. [10] tran-ngoc, h., he, l., reynders, e., et al. (2020). an efficient approach to model updating for a multispan railway bridge using orthogonal diagonalization combined with improved particle swarm optimization, journal of sound and vibration, 476. pp. 1-18. doi: 10.1016/j.jsv.2020.115315. [11] gao, l., an, b., xin, t., et al. (2020). measurement, analysis, and model updating based on the modal parameters of high-speed railway ballastless track, measurement, 161, pp. 1-14. doi: 10.1016/j.measurement.2020.107891. m t j. wang et alii, frattura ed integrità strutturale, 58 (2021) 114-127; doi: 10.3221/igf-esis.58.09 127 [12] gunst, r. f. (2008). response surface methodology: process and product optimization using designed experiments, technometrics, 38(3), pp. 284-286. doi: 10.1080/00401706.1996.10484509. [13] fang, j., gao, y., xu, c., et al. (2014). multi-body dynamic model revision techniques based on surrogate model, automotive engineering, 36(4), pp. 448-452. doi: 10.19562/j.chinasae.qcgc.2014.04.012. [14] simpson, t. w., maucry, t. m., korte, j. j., et al. (2001). kriging models for global approximation in simulation-based multidisciplinary design optimization, aiaa j, 39(12), pp. 2233-2241. doi: 10.2514/3.15017. [15] simpson, t., mistree, f., korte, j., et al. (1998). comparison of response surface and kriging models for multidisciplinary design optimization, in aiaa paper 7 thaiaa/usaf/nasa/issmo symposium on multidisciplinary analysis & optimization, 98, 4755. doi: 10.2514/6.1998-4755. [16] wang, j., wang, c., zhao, j. (2017). frequency response function-based model updating using kriging model, mechanical systems & signal processing, 87, pp. 218-228. doi: 10.1016/j.ymssp.2016.10.023. [17] martin, j. d., simpson, t. w. (2004). on the use of kriging models to approximate deterministic computer models, in asme 2004 international design engineering technical conferences and computers and information in engineering conference. american society of mechanical engineers. utah, usa. september 28october 2. [18] gano, s., renaud, j., martin, j., et al. (2005). update strategies for kriging models for use invariable fidelity optimization, struct. multidiscip. optim, 32(4), pp. 287-298. doi: 10.1007/s00158-006-0025-y. [19] jin, r., chen, w., sudjianto, a. (2004). an efficient algorithm for constructing optimal design of computer experiments, journal of statistical planning & inference, 134(1), pp. 268-287. doi: 10.1016/j.jspi.2004.02.014. [20] fang, k. t., ma, c. x., winker, p. (1999). centered l2-discrepancy of random sampling and latin hypercube design, and construction of uniform designs, mathematics of computation, 71 (237), pp. 275-296. doi: 10.1090/s0025-5718-00-01281-3. [21] ahmadian, h., mottershead, j. e., friswell, m. i. (1998). regularisation methods for finite element model updating, mechanical systems & signal processing, 12(1), pp. 47-64. doi: 10.1006/mssp.1996.0133. shot peening processes to obtain nanocrystalline surfaces in metal alloys: h. bai et alii, frattura ed integrità strutturale, 56 (2021) 16-45; doi: 10.3221/igf-esis.56.02 16 experimental investigation of cracking behaviors of ductile and brittle rock-like materials hao bai, wei du* sichuan expressway construction & development group co., ltd, chengdu, china secdcbh@126.com 582126107@qq.com yundong shou*, lichuan chen national breeding base of technology and innovation platform for automatic-monitoring of geologic hazards (chongqing engineering research center of automatic monitoring for geological hazards), chongqing, china wuhan university, china shouyundong@whu.edu.cn, https://orcid.org/0000-0001-7424-4006 chen_lichuan@163.com filippo berto norwegian university of science and technology, norway filippo.berto@ntnu.no abstract. the cracking characteristics of ductile rocks were studied by similar materials with sand, barite, epoxide resin, polyamide, silicone rubber and alcohol, while the cracking characteristics of brittle rocks were investigated by similar material with sand, barite, rosin and alcohol. in this paper, to enhance the application range of the rock-like materials in the field of geotechnical engineering model tests, the values of the elastic modulus and the compressive strength of the artificial rock-like materials are changed in a wide range by adjusting the amount of cementitious materials (epoxide resin, polyamide, rosin, etc). the elastic modulus, compressive strength and cracking characteristics were obtained from the complete axial stress–strain curves of the specimens made of similar materials, which were cast using the different mixture ratios. these experimental data can provide quantitative investigation on mixture ratios of similar materials of rocks to model the geotechnical engineering. furthermore, the effect of mixture ratios on mechanical properties and crack propagation pattern of specimens were also investigated by the specimens with pre-existing flaws under uniaxial compressive tests. keywords. rock-like materials; material composition; ductility; brittleness; crack evolution. citation: bai, h., du, w., berto, f., experimental investigation of cracking behaviors of ductile and brittle rock-like materials, frattura ed integrità strutturale, 56 (2021) 16-45. received: 02.01.2021 accepted: 17.01.2021 published: 01.04.2021 copyright: © 2021 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. https://youtu.be/pki-k_hsmbg h. bai et alii, frattura ed integrità strutturale, 56 (2021) 16-45; doi: 10.3221/igf-esis.56.02 17 introduction he similar simulation test in rocks on the basis of the similarity theory of modeling test is an explorative method to study the mechanical properties of geotechnical materials. the mechanical phenomena and the stress-strain variation characteristics of prototype are analyzed through the observation of stress and strain on similar models casted by using single or multiple materials, which provides a more reasonable scientific basis for the design of the geotechnical engineering and the selection of the construction scheme. in similar model experimental studies, the ratio of similar materials and the casting method of test models have a great influence on the physical and mechanical properties of the material, which plays a decisive role in the success of similar simulation tests. for a long period of time, the geotechnical similar simulation test has been an important means of solving complex engineering problems. it can not only study the normal stress state of engineering, but also acquire the ultimate load and failure modes of engineering. meanwhile, compared with the numerical calculation, the results given by similar simulation tests are more intuitive and can give people a deeper impression, and are widely used in geotechnical engineering research. the cracking mechanisms of rocks have been studied experimentally on rock-like materials or rock materials, and rock-like materials are widely used because the flaws are easy to be fabricated. the first experimental study on rock-like specimens that contained flaws under uniaxial compression condition was conducted by brace and bombolakis [1]. since then, many studies have examined the fracture processes of pre-cracked rock-like materials subjected to compression. experimental studies have been performed on many different types of rock-like materials, including glass [2,3], columbia resin [4], polymethyl methacrylate [5,6], cement mortar [7], sandstone-like composite material [8-11], and gypsum [12-18]. to investigate the initiation, propagation, and coalescence of cracks in real rock materials, some experiments and numerical simulation on rock such as granite [19-21], marble [17-18,22] and mudstone [23] have also been conducted. zhou et al. [24] and bi et al. [25] proposed general particle dynamics to simulate the crack initiation, growth and coalescence in rock or rock-like materials. wang et al. [26-27] developed the conjugated bond-based peridynamics to investigate the cracking behaviors in rock or rock-like materials. zhou et al. [28-29] established micromechanics-based model to study the damage mechanism of rocks. zhou et al.[30] investigated the initiation, growth and coalescence of 3d crack in rock-like rocks. the cracking behaviors in rock or rock-like materials. zhou et al. [30] and zhang et al. [31-34] studied progressive failure of brittle rocks with non-isometric flaws. such rock-like materials and real rock materials have not only common characteristics for crack evolution, but also differences caused by the material properties, loading methods, and specimen geometry [3536]. moreover, since rock is a very complex and anisotropic material whose mechanical properties vary widely, ranging from hard rock with very high mechanical properties to soft rock with very low mechanical properties [30-36]. however, there is scarce study on the cracking behaviors and mechanical properties of ductile and brittle rock-like materials. to simulate different kinds of rock with a wide range of intensity variation, a new type of rock-like material with wideranging and stable mechanical properties must be developed. in this paper, the certain raw materials were selected according to the mechanical properties of ductile and brittle rocks and the mechanical laws of ductile and brittle rock-like materials were obtained by experimental analysis of materials with different ratios, which provides a reference for the ratio of rocklike materials in experiments. in addition, two rock-like materials were applied to crack propagation experiment, and the influence rules of different ratios of rock-like materials on crack propagation modes and mechanical properties of the specimens were obtained. experimental studies specimen preparation he composition of the raw materials used to make similar models can be basically divided into three categories according to their use: the first one is filling material acted as the skeleton, the second one is cementing material that plays a role in bonding, and the third one is auxiliary admixture served as regulation of physical and mechanical properties. in similar simulation experiments, in order to make the similar model satisfy requirements of the volumetric weight similarity ratio, it is more common to use barite, gypsum, sand, iron powder as the filling material. there are also many cementitious materials commonly used as bonding materials like gypsum, white latex, epoxide resin, polyamide, cement, rosin, etc. at the same time, for the purpose of adjusting the physical and mechanical properties of rock-like materials to better simulate the actual rock, it is essential to add additional auxiliary agents, such as silicone rubber, lime, t t h. bai et alii, frattura ed integrità strutturale, 56 (2021) 16-45; doi: 10.3221/igf-esis.56.02 18 neoprene, glycerin (humectant), borax (retarder) mica powder, softwood chips, etc. furthermore, to make rock-like materials isotropic and homogeneous after hardening molding, it is also necessary to incorporate a certain amount of organic solvent, including frequently-used gasoline, engine oil, alcohol, etc. and its purpose is to dissolve organic substances such as silicone rubber, so that the components can be more uniformly mixed. in this paper, the experiment was designed to prepare rock-like materials which could simulate ductile and brittle rocks. initially some raw materials are selected as rock-like materials. after that tentative raw materials are added for trial matching. eventually, the preparative rock-like materials are tested in uniaxial compression in order to figure out whether the full stress-strain curve of the rock-like materials is similar to the corresponding curve of actual rocks. when simulating the raw material composition of ductile rock-like materials, it was finally decided to use sand and barite as filling materials. moreover, epoxide resin and polyamide were used as cementitious materials, silicone rubber and rosin were used as auxiliary adjusting agents, and alcohol was used as organic solvent. the force-displacement curve of whole process in uniaxial compression test for ductile rock-like material is shown in fig. 1. with regard to brittle rock-like materials, sand and barite were used as filling materials, rosin was used as cementitious material, silicone rubber, epoxide resin and polyamide were used as auxiliary adjusting agents, and alcohol was used as organic solvent. fig. 1 and fig. 2 are the force-displacement curve of whole process in uniaxial compression test for ductile and brittle rock-like materials, respectively. figure 1: force-displacement curve of the uniaxial compression ucs test for ductile rock-like materials. figure 2: force-displacement curve of ucs test for brittle rock-like materials. h. bai et alii, frattura ed integrità strutturale, 56 (2021) 16-45; doi: 10.3221/igf-esis.56.02 19 to obtain the experimental phenomena and make data reliable, two specimens for each ratio of materials were made and relevant test data was processed averagely. the ratio relationship of raw material is shown in tabs. 1 and 2. number raw materials weight ratio percentage of variable components a1 sand, barite, epoxy, polyamide and alcohol 500:300:4:4:40 59% (sand) a2 sand, barite, epoxy, polyamide and alcohol 600:300:4:4:40 63.3% (sand) a3 sand, barite, epoxy, polyamide and alcohol 700:300:4:4:40 66.8% (sand) a4 sand, barite, epoxy, polyamide and alcohol 800:300:4:4:40 69.7% (sand) b1 sand, barite, epoxy, polyamide and alcohol 500:300:4:4:40 35.4% (barite) b2 sand, barite, epoxy, polyamide and alcohol 500:350:4:4:40 39% (barite) b3 sand, barite, epoxy, polyamide and alcohol 500:400:4:4:40 42.7% (barite) b4 sand, barite, epoxy, polyamide and alcohol 500:450:4:4:40 45.1% (barite) c1 sand, barite, epoxy, polyamide and alcohol 500:300:4:4:40 0.9% (epoxy and polyamide) c2 sand, barite, epoxy, polyamide and alcohol 500:300:6:6:40 1.4% (epoxy and polyamide) c3 sand, barite, epoxy, polyamide and alcohol 500:300:8:8:40 1.9%(epoxy and polyamide) c4 sand, barite, epoxy, polyamide and alcohol 500:300:10:10:40 2.3%(epoxy and polyamide) d1 sand, barite, epoxy, polyamide and alcohol 500:300:4:4:40 0% (silicone rubber) d2 sand, barite, epoxy, polyamide, alcohol and silicone rubber 500:300:4:4:40:5 0.6% (silicone rubber) d3 sand, barite, epoxy, polyamide, alcohol and silicone rubber 500:300:4:4:40:10 1.2% (silicone rubber) d4 sand, barite, epoxy, polyamide, alcohol and silicone rubber 500:300:4:4:40:15 1.7% (silicone rubber) e1 sand, barite, epoxy, polyamide and alcohol 500:300:4:4:40 0% (rosin) e2 sand, barite, epoxy, polyamide, alcohol and rosin 500:300:4:4:40:2 0.2% (rosin) e3 sand, barite, epoxy, polyamide, alcohol and rosin 500:300:4:4:40:4 0.5% (rosin) e4 sand, barite, epoxy, polyamide, alcohol and rosin 500:300:4:4:40:6 0.7% (rosin) f1 sand, barite, epoxy, polyamide, alcohol and silicone rubber 500:300:4:4:40:5 0% (rosin) f2 sand, barite, epoxy, polyamide, alcohol silicone rubber and rosin 500:300:4:4:40:5:2 0.2% (rosin) f3 sand, barite, epoxy, polyamide, alcohol silicone rubber and rosin 500:300:4:4:40:5:4 0.5% (rosin) f4 sand, barite, epoxy, polyamide, alcohol silicone rubber and rosin 500:300:4:4:40:5:6 0.7% (rosin) table 1: the raw materials and ratio of ductile rock-like materials. in the process of fabricating specimens, the raw materials were first weighed according to the ratio of each rock-like materials. at the same time, the mold was cleaned and assembled, and the inner surface of the mold was coated with an appropriate amount of lubricating oil so that the mold could be removed later. subsequently the sand and barite powder were mixed evenly, and the rosin powder or the epoxide resin-polyamide was dissolved in alcohol to form an alcohol solution (which was thoroughly stirred and slightly heated with hot water to accelerate dissolution), then the alcohol solution was then added evenly to the already mixed mixture. since silicone rubber was not easily dissolved in alcohol, it could only be slowly dispersed in the agitated material during agitation. finally, the mixture was poured into the mold and tamped (the hammer was stopped when there was no obvious sinking during the hammering process). the specimens after pouring molding is shown in fig. 3. h. bai et alii, frattura ed integrità strutturale, 56 (2021) 16-45; doi: 10.3221/igf-esis.56.02 20 number raw materials weight ratio percentage of variable components a1' sand, barite, rosin and alcohol 200:200:5:15 47.6% (sand) a2' sand, barite, rosin and alcohol 250:200:5:15 53.2% (sand) a3' sand, barite, rosin and alcohol 300:200:5:15 57.7% (sand) a4' sand, barite, rosin and alcohol 350:200:5:15 61.4% (sand) b1' sand, barite, rosin and alcohol 200:200:5:15 47.6% (barite) b2' sand, barite, rosin and alcohol 200:250:5:15 53.2% (barite) b3' sand, barite, rosin and alcohol 200:300:5:15 57.7% (barite) b4' sand, barite, rosin and alcohol 200:350:5:15 61.4% (barite) c1' sand, barite, rosin and alcohol 200:200:5:15 1.2% (rosin) c2' sand, barite, rosin and alcohol 200:200:7:15 1.7% (rosin) c3' sand, barite, rosin and alcohol 200:200:9:15 2.1% (rosin) c4' sand, barite, rosin and alcohol 200:200:11:15 2.6% (rosin) d1' sand, barite, rosin and alcohol 200:200:5:15 0% (epoxy and polyamide) d2' sand, barite, rosin, alcohol, epoxy and polyamide 200:200:5:15:1:1 0.47% (epoxy and polyamide) d3' sand, barite, rosin, alcohol, epoxy and polyamide 200:200:5:15:2:2 0.94% (epoxy and polyamide) d4' sand, barite, rosin, alcohol, epoxy and polyamide 200:200:5:15:3:3 1.4% (epoxy and polyamide) e1' sand, barite, rosin and alcohol 200:200:5:15 0% (silicone rubber) e2' sand, barite, rosin, alcohol and silicone rubber 200:200:5:15:2 0.47% (silicone rubber) e3' sand, barite, rosin, alcohol and silicone rubber 200:200:5:15:4 0.94% (silicone rubber) e4' sand, barite, rosin, alcohol and silicone rubber 200:200:5:15:6 1.4% (silicone rubber) table 2: the raw materials and proportion of brittle rock-like material. figure 3: prepared specimens. h. bai et alii, frattura ed integrità strutturale, 56 (2021) 16-45; doi: 10.3221/igf-esis.56.02 21 testing system in this paper, an electronic universal testing machine was used to carry out the uniaxial compression test of specimens. the test machine has two loading modes (load control and displacement control) which can automatically collect data throughout the test. in order to prevent the damage of the test machine caused by the sudden destruction of specimen and to ensure integrity of the stress-strain curve obtained by experiments, the loading mode of displacement control was selected in the experiments. the device used for testing the fracture toughness of rock-like materials consists of a loading device (electronic universal testing machine) and a bracket device (for supporting cylindrical specimens to meet the three-point bending loading requirements). in the process of processing the specimen, 1 mm wide crack was first machined on the specimen, then the crack tip was ground with a diamond wire saw to a diameter of 0.5 mm. in the test, the crack length is 10 mm (generally, the ratio of the crack length to the specimen diameter is 0.15 to 0.5), and the crack tip angle is 30° (the crack tip angle is generally required to be small enough to produce a relatively strong i-type stress filed), the ratio of span to diameter is 1.5 (the ratio of span and diameter of the specimen is relatively small when the material strength is low, generally 1.5 to 4). after the specimen was processed, the specimen was placed in the exact position of the test holder and was tested under loading by the electronic universal testing machine. during the loading process, the crack propagation and failure modes of the specimen were observed and recorded, and finally the maximum load at the time of crack propagation was recorded. the crack geometry and loading diagram of the specimen are shown in fig. 4. figure 4: crack geometry and loading schematic. analysis of experiment results analysis of experimental results of ductile rock-like materials effect of raw materials on stress-strain curves and brittleness indexes of ductile rock-like materials enerally, the complete stress-strain curve of rocks can be used to qualitatively analyze the brittleness of rock. therefore, based on the brittleness index of the full stress-strain curve, another brittleness index, namely “brittle modulus”, is obtained. eqn. (1) is the calculation expression of the brittle modulus.     − = − 0 0 0 c c e (1) were 0e is the brittle modulus,  c is peak strength,    + = 10 2 c ,  0 is the strain corresponding to0 , c is the strain corresponding to c . fig. 5 and fig. 6 are respectively diagrams of the stress-strain curves and brittle modulus changes of ductile rock-like materials under different raw material ratios. combining the failure process of the specimen and analyzing the curve change in the figure, it can be seen that: g h. bai et alii, frattura ed integrità strutturale, 56 (2021) 16-45; doi: 10.3221/igf-esis.56.02 22 ① when the amount of sand increases, the difference in the damage of the specimen is little. the reason may be that a large amount of cementitious material and barite has a certain ductility when the sand content is low, and the shear failure of the sand also has a certain ductility when the sand content is high. ② when the barite content is relatively low, the specimen exhibits a certain ductility, and as the barite content increases, the ductility of the specimen is more pronounced. the reason is probably due to the fact that the cementitious materials, epoxide resin and polyamide, have a certain ductility, and the barite material itself also has good ductility when it is failed. when the barite content is relatively high, the specimen is mainly failed by the shear failure of sand and barite, and the barite itself has better ductility when it is failed. ③ when the content of epoxide resin and polyamide is relatively low, the specimen has a certain ductility, and as the content of epoxide resin and polyamide increases, the ductility of the specimen is more obvious. the reason should be that the cementitious materials, epoxide resin and polyamide, have good ductility when they are dried and hardened. ④ when the silicone rubber is not added, the specimen has a certain ductility, and the ductility of the specimen is more obvious as the amount of added silicone rubber increases. the reason is that the silicone rubber after coagulation hardening has a good ductility, which increases the ductility of the specimen. ⑤ in the absence of silicone rubber, when the amount of rosin is 0, the specimen exhibits certain ductile failure properties, and as the amount of added rosin increases, the specimen no longer has good ductility, but exhibits brittle failure properties. the reason should be that the hardened rosin exhibits a distinct brittle character when it is failed, and ultimately changes the ductile failure properties of rock-like material itself. ⑥under the condition of containing silicone rubber, when the amount of rosin is 0, the specimen also exhibits certain ductile failure properties, and as the amount of added rosin increases, the ductility of the specimen is not severely reduced. but only when the rosin is added in a large amount, the ductility of specimen is slightly reduced. the reason should be that rock-like materials added with silicone rubber without rosin have good ductility, and the addition of a small amount of rosin is not sufficient to change their ductility. it can also be seen from figures that: ① as the amount of sand decreases, the strain corresponding to the maximum stress tends to increase, which may be related to the strain of epoxide resin and polyamide after hardening. with the decrease of sand content, the residual strength of rock-like materials tends to increase, which may be due to the high residual strength of both epoxy and polyamide, as well as barite. ② as the barite content increases, there are some differences in the residual strength of rock-like materials. this is most likely due to the high residual strength of both epoxy and polyamide, as well as barite. ③ as the content of epoxide resin and polyamide increases, the strain corresponding to the maximum stress tends to increase slightly, because epoxide resin and polyamide will have a larger strain when broken. moreover, the residual strength of the specimen tends to increase when the content of epoxide resin and polyamide is high, because epoxide resin and polyamide also have high residual strength. ④ when the amount of added silicone rubber increases, the residual strength of the specimen slightly decreases, which is likely to be related to the high residual strength of the silicone rubber. ⑤ as the amount of rosin added increases, the strain corresponding to the maximum stress tends to decrease, which may be related to the less strain of the rosin. in the absence of silicone rubber, the residual strength of the specimen does not change substantially when the amount of added rosin changes. in the case of silicone rubber, the residual strength of the specimen slightly changes when the amount of rosin added increases, which may be related to the high residual strength of rock-like materials without rosin. effect of raw materials on stress-strain curves and brittleness indexes of ductile rock-like materials the elastic modulus can be obtained by the stress-strain curve of rock-like material. fig. 7 shows the relationship between the content of each raw material and the elastic modulus. it can be clearly seen from the fig. 7 that the elastic modulus of the ductile rock-like material can be increased by increasing the content of epoxide resin and polyamide, and adding an appropriate amount of rosin. the elastic modulus of rock-like materials increases when rosin is added, which may have a great relationship with the elastic modulus of rosin. in the experiment, when the amount of sand and barite powder in the raw material component cannot be changed, the purpose of lowering the elastic modulus of the material can be achieved by adding the auxiliary admixture silicone rubber. from the effect of the raw material on the stress-strain curve, it can be known that if the elastic modulus of the ductile rocklike material is to be enhanced and the ductile rock-like material has a certain brittleness, the epoxide resin and polyamide should not be added excessively, but an appropriate amount of the auxiliary regulator rosin should be added. h. bai et alii, frattura ed integrità strutturale, 56 (2021) 16-45; doi: 10.3221/igf-esis.56.02 23 0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 0.0 0.2 0.4 0.6 0.8 1.0 1.2 sand for 59% sand for 63.3% sand for 66.8% sand for 69.7% a x ia l st re ss ( m p a ) axial strain (%) 0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 0.0 0.2 0.4 0.6 0.8 1.0 1.2 barite powder for 35.4% barite powder for 39% barite powder for 42.7% barite powder for 45.1% a x ia l st re ss ( m p a ) axial strain (%) 0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0 2.2 0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 epoxy resin-polyamide for 0.9% epoxy resin-polyamide for 1.4% epoxy resin-polyamide for 1.9% epoxy resin-polyamide for 2.3% a x ia l st re ss ( m p a ) axial strain (%) 0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 0.0 0.2 0.4 0.6 0.8 1.0 1.2 silicone rubber for 0% silicone rubber for 0.6% silicone rubber for 1.2% silicone rubber for 1.7% a x ia l st re ss ( m p a ) axial strain (%) 0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 0.0 0.3 0.6 0.9 1.2 1.5 1.8 rosin for 0% rosin for 0.2% rosin for 0.5% rosin for 0.7% a x ia l st re ss ( m p a ) axial strain (%) 0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 rosin for 0% rosin for 0.2% rosin for 0.5% rosin for 0.7% a x ia l st re ss ( m p a ) axial strain (%) figure 5: stress-strain curve of ductile rock-like materials with different raw material ratios. h. bai et alii, frattura ed integrità strutturale, 56 (2021) 16-45; doi: 10.3221/igf-esis.56.02 24 60.0 62.5 65.0 67.5 70.0 72 80 88 96 b ri tt le m o d u lu s (m p a ) sand content (%) 35.0 37.5 40.0 42.5 45.0 40 48 56 64 72 b ri tt le m o d u lu s (m p a ) barite content (%) 1.0 1.5 2.0 2.5 50 55 60 65 70 75 b ri tt le m o d u lu s (m p a ) content of epoxide resin and polyamide (%) 0.0 0.5 1.0 1.5 2.0 20 40 60 80 b ri tt le m o d u lu s (m p a ) content of silicone rubber (%) 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 80 100 120 140 160 b ri tt le m o d u lu s (m p a ) rosin content (without silicone rubber) (%) 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 50 100 150 200 b ri tt le m o d u lu s (m p a ) rosin content (adding silicone rubber) (%) figure 6: brittle modulus of ductile rock-like materials with different raw material ratios. h. bai et alii, frattura ed integrità strutturale, 56 (2021) 16-45; doi: 10.3221/igf-esis.56.02 25 60.0 62.5 65.0 67.5 70.0 120 140 160 180 e la st ic m o d u lu s (m p a ) sand content (%) 35.0 37.5 40.0 42.5 45.0 100 120 140 160 180 e la st ic m o d u lu s (m p a ) barite content (%) 1.00 1.25 1.50 1.75 2.00 2.25 2.50 180 190 200 210 e la st ic m o d u lu s (m p a ) epoxide resin and polyamide content (%) 0.00 0.25 0.50 0.75 1.00 1.25 1.50 1.75 50 100 150 200 e la st ic m o d u lu s (m p a ) content of silicone rubber (%) 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 150 200 250 300 350 e la st ic m o d u lu s (m p a ) rosin content (without silicone rubber) (%) 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 120 140 160 180 200 220 e la st ic m o d u lu s (m p a ) rosin content (adding silicone rubber) (%) figure 7: relations between raw materials contents and elastic modulus of ductile rock-like materials. h. bai et alii, frattura ed integrità strutturale, 56 (2021) 16-45; doi: 10.3221/igf-esis.56.02 26 60.0 62.5 65.0 67.5 70.0 0.8 0.9 1.0 1.1 1.2 u n ia x ia l c o m p re ss iv e s tr e n g th ( m p a ) sand content (%) 35.0 37.5 40.0 42.5 45.0 0.85 0.90 0.95 1.00 1.05 1.10 1.15 u n ia x ia l c o m p re ss iv e s tr e n g th ( m p a ) barite content (%) 1.00 1.25 1.50 1.75 2.00 2.25 2.50 1.0 1.1 1.2 1.3 1.4 1.5 1.6 1.7 u n ia x ia l c o m p re ss iv e s tr e n g th ( m p a ) content of epoxide resin and polyamide (%) 0.00 0.25 0.50 0.75 1.00 1.25 1.50 1.75 0.7 0.8 0.9 1.0 1.1 u n ia x ia l c o m p re ss iv e s tr e n g th ( m p a ) content of silicone rubber (%) 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 u n ia x ia l c o m p re ss iv e s tr e n g th ( m p a ) rosin content (without silicone rubber) (%) 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.8 0.9 1.0 1.1 1.2 1.3 1.4 1.5 u n ia x ia l c o m p re ss iv e s tr e n g th ( m p a ) rosin content (adding silicone rubber) (%) figure 8: relationships between raw materials contents and uniaxial compressive strength of ductile rock-like materials. h. bai et alii, frattura ed integrità strutturale, 56 (2021) 16-45; doi: 10.3221/igf-esis.56.02 27 effect of raw materials on uniaxial compressive strength of ductile rock-like materials the uniaxial compressive strength of the rock-like materials, that is, the peak stress on the curve, can be obtained by the stress-strain curve. fig. 8 shows the relation between the content of each raw material and the uniaxial compressive strength. it can be clearly seen from fig. 8 that the uniaxial compressive strength of ductile rock-like materials can be enhanced by increasing the content of epoxide resin and polyamide and adding an appropriate amount of the auxiliary regulator rosin. to reduce the uniaxial compressive strength of ductile rock-like materials, it is possible to increase the content of sand and barite, and to add an appropriate amount of auxiliary regulator silicone rubber. in the experiment, when the content of sand and barite powder cannot be changed, the purpose of reducing the uniaxial compressive strength of the ductile rock-like material can be achieved by adding the auxiliary admixture silicone rubber. from the effect of the raw material on the stress-strain curve, it can be known that if the uniaxial compressive strength of the ductile rock-like material is to be enhanced and the ductile rock-like material has a certain brittleness, the epoxide resin and polyamide cannot be excessively added, but an appropriate amount of the auxiliary regulator rosin should be added. effect of raw materials on fracture toughness of ductile rock-like materials referring to the relevant literature [37], the formula for fracture toughness of rock-like materials is shown in eqns. 2 and 3. = − + − + − 2 3 4 2 [3.75 11.98 24.4( ) 25.69( ) 10.02( ) ] ( ) ic ps a a a a a k d d d dd d a (2) where p represents the maximum load at the time of loading, s is the span, d denotes the diameter, which is 0.05 m, and a is the crack length, which is 0.02 m. substituting a and d into eqn. 2 yields = 2675 ( a m )ick ps p (3) by substituting relevant experimental data into eqn. 3, the fracture toughness of ductile rock-like materials can be obtained. the relationship between the fracture toughness and the content of each raw material is shown in fig. 9. it can be clearly seen from fig. 9 that the fracture toughness of ductile rock-like materials can be enhanced by increasing the content of epoxide resin and polyamide and adding an appropriate amount of auxiliary regulator rosin. at the same time, it can be seen that for the purpose of improving the fracture toughness of rock-like materials, the addition of silicone rubber and rosin is not as good as the case of adding rosin alone. to reduce the fracture toughness of ductile rock-like materials, the content of sand and barite can be increased, and an appropriate amount of auxiliary regulator silicone rubber can be added. in the experiment, when the content of sand and barite powder cannot be changed, the purpose of reducing the fracture toughness of the ductile rock-like material can be achieved by adding the auxiliary admixture silicone rubber. from the effect of the raw material on the stress-strain curve, it is also known that if the fracture toughness of the ductile rock-like material is to be improved and the ductile rock-like material has a certain brittleness, the epoxide resin and polyamide should not be excessively added, but an appropriate amount of the auxiliary regulator rosin should be added. analysis of experimental results of brittle rock-like materials effect of raw materials on stress-strain curves and brittleness indexes of brittle rock-like materials the uniaxial compressive stress-strain curve and brittle modulus of brittle rock-like materials can be obtained by the same treatment method. fig. 10 and fig. 11 show respectively stress-strain curves and brittle modulus changes for brittle rocklike materials at different raw material ratios. it can be seen from the curves in the figures: ① when the sand content is relatively low, the specimen exhibits relatively brittle fracture properties, and the brittle fracture characteristics of the specimen are no longer obvious as the sand content increases. because when the sand content is low, the damage of the specimen is mainly the brittle failure of the rosin. when the sand content is relatively high, the specimen is mainly failed by the shear failure of the sand. in addition, it can be seen that as the sand content increases, the strain corresponding to the maximum stress tends to increase. h. bai et alii, frattura ed integrità strutturale, 56 (2021) 16-45; doi: 10.3221/igf-esis.56.02 28 60 65 70 0.024 0.026 0.028 0.030 0.032 f ra c tu re t o u g h n e ss ( m p a ·m 1 /2 ) sand content (%) 35 40 45 0.026 0.028 0.030 0.032 f ra c tu re t o u g h n e ss ( m p a ·m 1 /2 ) barite content (%) 1.0 1.5 2.0 2.5 0.030 0.035 0.040 0.045 f ra c tu re t o u g h n e ss ( m p a ·m 1 /2 ) content of epoxide resin and polyamide (%) 0.0 0.5 1.0 1.5 2.0 0.026 0.028 0.030 0.032 f ra c tu re t o u g h n e ss ( m p a ·m 1 /2 ) content of silicone rubber (%) 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.030 0.035 0.040 0.045 f ra c tu re t o u g h n e ss ( m p a ·m 1 /2 ) rosin content (without silicone rubber) (%) 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.028 0.030 0.032 0.034 0.036 0.038 f ra c tu re t o u g h n e ss ( m p a ·m 1 /2 ) rosin content (adding silicone rubber) (%) figure 9: relationships between raw materials contents and fracture toughness of ductile rock-like materials. h. bai et alii, frattura ed integrità strutturale, 56 (2021) 16-45; doi: 10.3221/igf-esis.56.02 29 0.0 0.5 1.0 1.5 2.0 0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 sand for 47.6% sand for 53.2% sand for 57.7% sand for 61.4% s tr e ss ( m p a ) strain (%) 0.0 0.5 1.0 1.5 2.0 0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 barite powder for 47.6% barite powder for 53.2% barite powder for 57.7% barite powder for 61.4% s tr e ss ( m p a ) strain (%) 0.0 0.3 0.6 0.9 1.2 1.5 0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 rosin for 1.2% rosin for 1.7% rosin for 2.1% rosin for 2.6% s tr e ss ( m p a ) strain (%) 0.0 0.4 0.8 1.2 1.6 2.0 0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 epoxy resin-polyamide for 0% epoxy resin-polyamide for 0.47% epoxy resin-polyamide for 0.94% epoxy resin-polyamide for 1.4% s tr e ss ( m p a ) strain (%) 0.0 0.4 0.8 1.2 1.6 2.0 0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 silicone rubber for 0% silicone rubber for 0.47% silicone rubber for 0.94% silicone rubber for 1.4% s tr e ss ( m p a ) strain (%) figure 10: stress-strain curve of brittle rock-like materials with different raw material ratios. h. bai et alii, frattura ed integrità strutturale, 56 (2021) 16-45; doi: 10.3221/igf-esis.56.02 30 45 50 55 60 65 60 80 100 120 140 160 b ri tt le m o d u lu s (m p a ) sand content (%) 45 50 55 60 40 60 80 100 120 140 160 b ri tt le m o d u lu s (m p a ) barite content (%) 1.0 1.5 2.0 2.5 150 200 250 300 350 b ri tt le m o d u lu s (m p a ) rosin content (%) 0.0 0.5 1.0 1.5 60 80 100 120 140 160 b ri tt le m o d u lu s (m p a ) epoxide resin-polyamide content (%) 0.0 0.5 1.0 1.5 60 80 100 120 140 160 b ri tt le m o d u lu s (m p a ) silicone rubber content (%) figure 11: brittle modulus of brittle rock-like materials with different raw material ratios. h. bai et alii, frattura ed integrità strutturale, 56 (2021) 16-45; doi: 10.3221/igf-esis.56.02 31 ② when the barite content is relatively low, the specimen exhibits relatively obvious brittle fracture properties. with the increase of barite content, the brittle fracture characteristics of the specimen are no longer obvious. this is because when the barite content is relatively low, the damage of the specimen is mainly the brittle failure of the rosin. when the barite content is relatively high, the damage of the specimen is mainly reflected by the shear failure of sand and barite, and the barite material itself has relatively good ductility. it can also be found that as the barite content increases, the strain corresponding to the maximum stress tends to increase. ③ when the content of rosin is relatively high, the specimen exhibits obvious brittle fracture properties, and the brittle fracture characteristics of the specimen are no longer obvious with the decrease of rosin content. this is also because when the rosin content is relatively high, the damage of the specimen is mainly the brittle failure of the rosin. when the content of rosin is relatively low, the damage of the specimen is mainly reflected by the shear failure of sand and barite, and the barite itself has better ductility. it can be seen that as the amount of added epoxide resin and polyamide increases, the strain corresponding to the maximum stress tends to increase, which may be related to the greater strain of epoxide resin and polyamide during failure. moreover, it can also be seen that as the content of epoxide resin and polyamide increases, the residual strength of the specimen increases, which may be related to the good ductility of epoxide resin and polyamide. ④ when rock-like materials do not contain the epoxide resin and polyamide, the specimen exhibits relatively obvious brittle fracture properties, and the brittle fracture characteristics of the specimen are no longer obvious as the amount of epoxide resin and polyamide added increases. the reason may be that epoxide resin and polyamide have good ductility during failure, thereby improving the brittle fracture property of the rosin itself. ⑤ when the silicone rubber is not added, the specimen exhibits relatively obvious brittle fracture properties. with the increase of the silicone rubber content, the brittle fracture characteristics of the specimen are no longer obvious. the reason may be that the silicone rubber has good ductility, thereby improving the brittle fracture properties of the rosin itself. it can also be seen that as the amount of added silicone rubber increases, the strain corresponding to the maximum stress tends to increase, which may be related to the greater strain of the silicone rubber during failure. in addition, it can be seen that there is no significant difference in the residual strength of the specimen when the amount of added silicone rubber is increased, which may be related to the ductility of the hardened silicone rubber. effect of raw materials on elastic modulus of brittle rock-like materials similarly, the relationship between the content of each raw material and the elastic modulus is shown in fig. 12. it can be seen that in order to increase the elastic modulus of brittle rock-like materials, it can only be achieved by increasing the content of the rosin in the raw materials. when the rosin content increases, the elastic modulus of rock-like materials increases significantly, which may have a great relationship with the elastic modulus of rosin itself. in the experiment, when the content of sand and barite powder cannot be changed, the purpose of lowering the elastic modulus of the material can be achieved by adding the auxiliary admixture epoxide resin, polyamide, or silicone rubber. it can also be seen from fig. 12 that silicone rubber has a better effect of lowering the elastic modulus of the material relative to the epoxide resin and the polyamide. effect of raw materials on uniaxial compressive strength of brittle rock-like materials the uniaxial compressive strength of brittle rock-like material was obtained by the stress-strain curve, and the relationship between the content of each raw material and the uniaxial compressive strength was as shown in fig. 13. it can be clearly seen from the figure that the uniaxial compressive strength of the brittle rock-like material can be enhanced by increasing the content of the rosin and adding an appropriate amount of the auxiliary regulator epoxide resin and polyamide. to reduce the uniaxial compressive strength of brittle rock-like materials, the content of sand and barite can be increased, and an appropriate amount of auxiliary regulator silicone rubber can be added. in the experiment, when the content of sand and barite powder cannot be changed, the purpose of reducing the uniaxial compressive strength of the brittle rock-like material can be achieved by adding the auxiliary admixture silicone rubber. from the effect of the raw material on the stress-strain curve, it can be known that if the uniaxial compressive strength of the brittle rock-like material is to be increased and the brittle rock-like material has a certain ductility, the rosin should not be added too much, but an appropriate amount of the auxiliary regulator epoxide resin and polyamide should be added. effect of raw materials on fracture toughness of brittle rock-like materials similarly, the fracture toughness of the brittle rock-like material can also be obtained by substituting the relevant test data into eqn. 3. the relationship between the fracture toughness and the content of each raw material is shown in fig. 14. it can be clearly seen that in order to improve the fracture toughness of brittle rock-like materials, it is possible to increase the h. bai et alii, frattura ed integrità strutturale, 56 (2021) 16-45; doi: 10.3221/igf-esis.56.02 32 content of rosin and add an appropriate amount of auxiliary regulator epoxide resin and polyamide. it has also been found that the addition of epoxide resin and polyamide to improve the fracture toughness of rock-like materials is better. to reduce the fracture toughness of brittle rock-like materials, the content of sand and barite in the raw materials should be increased, and an appropriate amount of auxiliary regulator silicone rubber can be added. 45 50 55 60 140 160 180 200 220 e la st ic m o d u lu s (m p a ) sand content (%) 45 50 55 60 140 160 180 200 220 e la st ic m o d u lu s (m p a ) barite content (%) 1.0 1.5 2.0 2.5 200 250 300 350 400 e la st ic m o d u lu s (m p a ) rosin content (%) 0.0 0.5 1.0 1.5 160 170 180 190 200 210 220 e la st ic m o d u lu s (m p a ) content of epoxide resin and polyamide (%) 0.0 0.5 1.0 1.5 130 140 150 160 170 180 190 200 210 e la st ic m o d u lu s (m p a ) silicone rubber content (%) figure 12: relationships between raw materials contents and elastic modulus of brittle rock-like materials. h. bai et alii, frattura ed integrità strutturale, 56 (2021) 16-45; doi: 10.3221/igf-esis.56.02 33 47.5 50.0 52.5 55.0 57.5 60.0 62.5 0.9 1.0 1.1 1.2 u n ia x ia l c o m p re ss iv e s tr e n g th ( m p a ) sand content (%) 45 50 55 60 0.9 1.0 1.1 1.2 u n ia x ia l c o m p re ss iv e s tr e n g th ( m p a ) barite content (%) 1.0 1.5 2.0 2.5 1.1 1.2 1.3 1.4 1.5 1.6 1.7 u n ia x ia l c o m p re ss iv e s tr e n g th ( m p a ) rosin content (%) 0.0 0.5 1.0 1.5 1.15 1.20 1.25 1.30 1.35 1.40 1.45 u n ia x ia l c o m p re ss iv e s tr e n g th ( m p a ) content of epoxide resin and polyamide (%) 0.0 0.5 1.0 1.5 0.9 1.0 1.1 1.2 u n ia x ia l c o m p re ss iv e s tr e n g th ( m p a ) silicone rubber content (%) figure 13: relationships between raw materials contents and uniaxial compressive strength of brittle rock-like materials. h. bai et alii, frattura ed integrità strutturale, 56 (2021) 16-45; doi: 10.3221/igf-esis.56.02 34 45 50 55 60 65 0.026 0.028 0.030 0.032 0.034 f ra c tu re t o u g h n e ss (m p a ·m 1 /2 ) sand content (%) 45 50 55 60 65 0.026 0.028 0.030 0.032 0.034 f ra c tu re t o u g h n e ss (m p a ·m 1 /2 ) barite content (%) 1.0 1.5 2.0 2.5 0.032 0.034 0.036 0.038 0.040 0.042 f ra c tu re t o u g h n e ss (m p a ·m 1 /2 ) rosin content (%) 0.0 0.5 1.0 1.5 0.032 0.034 0.036 0.038 f ra c tu re t o u g h n e ss (m p a ·m 1 /2 ) epoxide resin-polyamide content (%) 0.0 0.5 1.0 1.5 0.026 0.028 0.030 0.032 0.034 f ra c tu re t o u g h n e ss (m p a ·m 1 /2 ) content of silicone rubber (%) figure 14: relationships between raw materials contents and fracture toughness of brittle rock-like materials. h. bai et alii, frattura ed integrità strutturale, 56 (2021) 16-45; doi: 10.3221/igf-esis.56.02 35 in the experiment, when the content of sand and barite powder cannot be changed, the purpose of reducing the fracture toughness of the brittle rock-like material can be achieved by adding the auxiliary admixture silicone rubber. from the effect of the raw material on the stress-strain curve, it can be known that if the fracture toughness of the brittle rock-like material is to be increased and the brittle rock-like material has a certain ductility, the rosin should not be added too much, but an appropriate amount of the auxiliary regulator epoxide resin and polyamide should be added. application of rock-like materials in crack propagation experiments experimental design n this experiment, crack propagation studies were carried out on specimens with the same original crack arrangement. according to the previous test results, the raw material ratios of the crack propagation experiment was finally determined, which was divided into the ratio of ductility group and the ratio of brittleness group, as shown in tab. 3 and tab. 4. number raw materials ratio epoxide resin polyamide content (%) g1 sand, barite, epoxy, polyamide and alcohol 300:300:4:4:40 1.23 g2 sand, barite, epoxy, polyamide and alcohol 300:300:6:6:40 1.84 g3 sand, barite, epoxy, polyamide and alcohol 300:300:8:8:40 2.47 g4 sand, barite, epoxy, polyamide and alcohol 300:300:10:10:40 3.11 g5 sand, barite, epoxy, polyamide and alcohol 300:300:12:12:40 3.61 table 3: ductility group ratio. number raw materials ratio rosin content (%) h1 sand, barite, rosin and alcohol 200:200:5:15 1.19 h2 sand, barite, rosin and alcohol 200:200:7:15 1.66 h3 sand, barite, rosin and alcohol 200:200:9:15 2.12 h4 sand, barite, rosin and alcohol 200:200:11:15 2.58 h5 sand, barite, rosin and alcohol 200:200:13:15 3.04 table 4: brittleness group ratio. the initial crack layout of this experiment is shown in fig. 15 (2a shows the crack length, c shows the crack unconnected rate, s indicates the crack pitch, and α indicates the crack inclination angle), and the specimen has a pre-crack opening degree of 0.8 mm. the dimension of the specimen are 140mm high, 90mm wide and 40mm thick. in the experiment, the geotechnical experimental servo test machine from chongqing university was used as the experimental device, which can control the loading mode by using a computer program and collect test data synchronously. different ways of loading can be performed by setting a computer program, and the loading rate can also be adjusted. this experiment was to observe the whole process of cracking of cracked specimens, and the crack initiation, expansion and coalescence speed were relatively fast. therefore, in order to achieve the ideal image acquisition effect, the rdt/16 high-speed dynamic recording system was applied in the experiment. the loading mode of displacement control was selected where the loading rate was 1mm/min, and the shooting speed of the high-speed dynamic recording system during loading was 25 images per second. i h. bai et alii, frattura ed integrità strutturale, 56 (2021) 16-45; doi: 10.3221/igf-esis.56.02 36 figure 15: crack layout. characteristics of the crack propagation process comparative analysis of crack initiation modes tab. 5 is a comparison table of the crack initiation modes of the ductile group. the content of epoxide resin and polyamide is gradually reduced from left to right, that is, the brittleness of the material is gradually increased. by comparing and analyzing tab. 5, it can be seen that as the content of epoxide resin and polyamide decreases gradually, the new crack initiation mode gradually changes from the state where the initial wing crack and shear crack coexist to only the wing crack. through the observation of the experimental loading process and the analysis of the experimental data, it is found that there is no significant difference in the vertical compression displacement of each specimen when the new crack starts to sprout. g5 g4 g3 g2 g1 awing crack bshear crack cwing crack dshear crack ashear crack bwing crack cwing crack dshear crack ashear crack bshear crack cwing crack dwing crack awing crack bwing crack cwing crack dwing crack awing crack bwing crack cwing crack dwing crack table 5: crack initiation mode of the ductile group. g5 g5 g4 g4 g3 g3 g2 g2 g1 g1 20mm 20mm 20mm 20mm 20mm h. bai et alii, frattura ed integrità strutturale, 56 (2021) 16-45; doi: 10.3221/igf-esis.56.02 37 tab. 6 is a comparison table of the crack initiation modes of the brittle group. the rosin content increases from left to right, that is, the brittleness of the material increases gradually. by comparing and analyzing tab. 6, it can be seen that as the rosin content increases gradually, the new crack initiation mode is almost all wing crack. observing the experimental loading process and analyzing the experimental data, it is found that when the new crack begins to sprout, the vertical compression displacement of the specimen with more rosin content is smaller. h1 h2 h3 h4 h5 awing crack bwing crack cwing crack dwing crack awing crack bwing crack cwing crack dwing crack awing crack bwing crack cwing crack dwing crack awing crack bwing crack cwing crack dwing crack awing crack bwing crack cwing crack dwing crack table 6: crack initiation mode of the brittle group. according to the comprehensive analysis of the two tables, as the brittleness of the material increases gradually, the new crack initiation mode of the rock-like material gradually changes from shear crack to wing crack. at the same time, when the new crack starts to sprout, the vertical compression displacement of the specimen gradually decreases. comparative analysis of crack coalescence failure mode tab. 7 is a comparison table of the crack coalescence failure modes of the ductile group. the content of epoxide resin and polyamide gradually reduces from left to right, that is, the brittleness of the material gradually increases. by comparing and analyzing tab. 7, it can be seen that as the content of epoxide resin and polyamide reduces gradually, the crack coalescence failure mode gradually changes from the initial composite failure of tensile and shear to the tensile failure. observing the experimental loading process and analyzing the experimental data, it can be found that when the cracks coalesce, the vertical compression displacement of the specimen with lower content of epoxide resin and polyamide is smaller. tab. 8 is a comparison table of the crack coalescence failure modes of brittle group. the content of rosin is gradually increased from left to right, that is, the brittleness of the material is gradually increased. by comparing and analyzing tab. 8, it can be seen that as the content of rosin increases gradually, the crack coalescence failure mode is almost all tensile failure. observing the experimental loading process and analyzing the experimental data, it can be found that when the cracks coalesce, the vertical compression displacement of the specimen with more rosin content is smaller. according to the comprehensive analysis of the two tables, as the brittleness of the material increases gradually, the crack coalescence failure mode of the rock-like material gradually changes from the composite failure of tensile and shear to tensile h1 h1 h2 h2 h3 h3 h4 h4 h5 h5 20mm 20mm 20mm 20mm 20mm h. bai et alii, frattura ed integrità strutturale, 56 (2021) 16-45; doi: 10.3221/igf-esis.56.02 38 failure. at the same time, the vertical compression displacement of the specimen gradually decreases when the cracks coalesce. g5 g4 g3 g2 g1 composite failure of tensile-shear composite failure of tensile-shear composite failure of tensile-shear composite failure of tensile-shear tensile failure table 7: sketch of crack coalescence of ductile group. h1 h2 h3 h4 h5 tensile failure tensile failure tensile failure tensile failure tensile failure table 8: sketch of crack coalescence. analysis of mechanical properties of rock-like materials analysis of crack initiation stress ① crack initiation stress of ductile group crack initiation stress refers to the value of instantaneous stress when the initial crack of the specimen is expanded to form a new crack. under the action of uniaxial compression load, the two initial pre-cracks in the specimen do not necessarily produce new cracks at the same time, that is, the initial crack initiation stress of the two initial pre-cracks may be different. comparing the photos taken by the high-speed camera at different times with the stresses and strains recorded by the uniaxial compression servo system, then the time, strain and stress of cracking of each initial pre-crack can be determined. the crack initiation stress and its average value of the two initial pre-cracks are shown in tab. 9 and tab. 10. the relationship between the crack initiation stress and the ratio of different raw materials is shown in fig. 16. it is found that each specimen produces new cracks in the experiment. moreover, it can be found that changing the content of epoxide resin-polyamide or rosin, the crack initiation stress of the first crack in the specimen is not significantly different from the crack initiation stress of the second crack. the reason may be that the cracking of the first crack causes stress redistribution, which in turn causes rapid cracking of the other crack. by comparing and analyzing the crack initiation stress of the specimen with different content of epoxide resin-polyamide or rosin, it is found that the initial pre-crack in the specimen with less content of epoxide resin-polyamide or rosin is more susceptible to cracking. g5 g4 g3 g2 g1 h1 h2 h3 h4 h5 20mm 20mm 20mm 20mm 20mm 20mm 20mm 20mm 20mm 20mm h. bai et alii, frattura ed integrità strutturale, 56 (2021) 16-45; doi: 10.3221/igf-esis.56.02 39 number crack initiation stress of crack① crack initiation stress of crack② average value of crack initiation stress g1 0.61 0.71 0.66 g2 0.78 0.72 0.75 g3 0.82 0.94 0.88 g4 1.07 1.11 1.09 g5 1.38 1.34 1.36 table 9: crack initiation stress of ductile group (mpa). number crack initiation stress of crack① crack initiation stress of crack② average value of crack initiation stress h1 0.63 0.55 0.59 h2 0.86 0.76 0.81 h3 0.93 0.97 0.95 h4 1.11 1.13 1.12 h5 1.19 1.15 1.17 table 10: crack initiation stress of brittle group (mpa). 1.0 1.5 2.0 2.5 3.0 3.5 4.0 0.4 0.6 0.8 1.0 1.2 1.4 1.6 crack① crack② c ra c k i n it ia ti o n s tr e ss ( m p a ) content of epoxide resin and polyamide (%) 1.0 1.5 2.0 2.5 3.0 3.5 0.4 0.6 0.8 1.0 1.2 1.4 crack① crack② c ra c k i n it ia ti o n s tr e ss ( m p a ) rosin content (%) figure 16: the crack initiation stress of two cracks in specimens. analysis of peak strain ① peak strain of ductile group the peak strain of the specimen with different epoxide resin-polyamide content was obtained by processing the experiment data, as shown in tab. 11. the relationship between the peak strain of the specimen and the content of epoxide resinpolyamide is shown in fig. 17. it can be seen from the figure that the minimum peak strain of the specimen is 0.80% and the maximum peak strain is 1.55%. therefore, it can be considered that the change of the content of epoxide resin-polyamide has a relatively striking influence on the peak strain of the specimen. at the same time, with the increase of epoxide resin-polyamide content, the h. bai et alii, frattura ed integrità strutturale, 56 (2021) 16-45; doi: 10.3221/igf-esis.56.02 40 peak strain of the specimen shows an increasing trend. meanwhile the peak strain increases rapidly from the beginning, and then increases slowly. epoxide resin polyamide content (%) 1.23 1.84 2.47 3.11 3.61 peak strain (%) 0.80 1.04 1.23 1.47 1.55 table 11: peak strain of ductile group. 1.0 1.5 2.0 2.5 3.0 3.5 4.0 0.8 1.0 1.2 1.4 1.6 p e a k s tr a in ( % ) content of epoxide resin and polyamide (%) figure 17: the relationship between peak strain and epoxide resin-polyamide content. ② peak strain of brittle group the peak strain of the specimen with different rosin content was obtained by processing the experiment data, as shown in tab. 12. the relationship between the peak strain of the specimen and the rosin content is shown in fig. 18. it can be seen from the figure that the minimum peak strain of the specimen is 0.41% and the maximum peak strain is 0.70%. therefore, it can be considered that the change of the rosin content has modest influence on the peak strain of the specimen but is not very obvious. at the same time, with the rosin content increases, the peak strain of the specimen shows a decreasing trend, and the strain decreases rapidly from the start and then decreases slowly. rosin content (%) 1.19 1.65 2.13 2.56 3.05 peak strain (%) 0.70 0.64 0.51 0.44 0.41 table 12: peak strain of brittle group. 1.0 1.5 2.0 2.5 3.0 0.4 0.5 0.6 0.7 p e a k s tr a in ( % ) epoxide resin-polyamide content (%) figure 18: the relationship between peak strain and rosin content. h. bai et alii, frattura ed integrità strutturale, 56 (2021) 16-45; doi: 10.3221/igf-esis.56.02 41 by comparing the peak strains of the ductile group and the brittle group, it can be known that the content of the cementitious material has a certain influence on the peak strain of the material. moreover, with the brittleness of the material increases, the peak strain of the material gradually decreases. analysis of crack connection mode and connection stress tab. 13 is a table of crack connection modes of ductile group. the epoxide resin-polyamide content gradually reduces from left to right, that is, the brittleness of the material gradually increases. by analyzing tab. 13, it shows that as the epoxide resin-polyamide content decreases gradually, the crack connection mode has no obvious regularity, and the wing crack connection is the main connection mode. at the same time, it can be found that as the epoxide resin-polyamide content reduces, and correspondingly the crack connection stress gradually reduces. g5 g4 g3 g2 g1 initial crack ① is connected to wing crack “c”. wing crack “b” is connected to wing crack “c”. shear crack “b” is connected to wing crack “c”. wing crack “b” is connected to initial crack ②. wing crack “b” is connected to wing crack “c”. connection stress is 1.54 mpa connection stress is 1.30 mpa connection stress is 1.05 mpa connection stress is 0.89 mpa connection stress is 0.74 mpa table 13: crack connection mode of ductile group. tab. 14 is a table of crack connection modes of brittle group. the rosin content gradually increases from left to right, that is, the brittleness of the material gradually increases. through the analysis of tab. 14, it indicates that as the rosin content increases gradually, the crack connection mode has no obvious regularity, and the wing crack connection is the main connection mode. at the same time, it can be found that as the rosin content increases, the crack connection stress gradually increases accordingly. in order to compare the relative magnitude relationship between crack initiation stress, connection stress and peak intensity, a comparative analysis of the three is performed, as shown in fig. 19. it can be found that as the epoxide resin-polyamide content increases gradually, that is, the ductility of the material gradually increases, the crack connection stress gradually approaches the peak strength. at the same time, as the rosin content increases gradually, that is, the brittleness of the material increases gradually, the crack connection stress gradually approaches the initiation stress. future developments will be addressed to improve the mechanical strength in case of more complex geometrical discontinuities [38-39]. a specific focus on the cyclic behavior will be addressed to improve the total final fatigue life at room [40-42] and high temperature [43] as made for traditional materials. this will allow to improve locally the strength to counterbalance local geometrical effects that can occur in a real 3d component [44-49]. g5 g4 g3 g2 g1 g5 g4 g3 g2 g1 20mm 20mm 20mm 20mm 20mm h. bai et alii, frattura ed integrità strutturale, 56 (2021) 16-45; doi: 10.3221/igf-esis.56.02 42 h1 h2 h3 h4 h5 wing crack “b” is connected to wing crack “c”. wing crack “b” is connected to wing crack “c”. wing crack “b” is connected to initial crack ②. wing crack “b” is connected to wing crack “c”. wing crack “b” is connected to wing crack “c”. connection stress is 0.73 mpa connection stress is 0.90 mpa connection stress is 1.06 mpa connection stress is 1.17 mpa connection stress is 1.22 mpa table 14: crack connection mode of brittle group. 1.0 1.5 2.0 2.5 3.0 3.5 4.0 0.6 0.8 1.0 1.2 1.4 1.6 s tr e ss ( m p a ) epoxide resin-polyamide content (%) peak intensity crack connection stress crack initiation stress 1.0 1.5 2.0 2.5 3.0 0.6 0.8 1.0 1.2 1.4 s tr e ss ( m p a ) rosin content (%) peak intensity crack connection stress crack initiation stress figure 19: the relationship between peak intensity, connection stress and initiation stress. conclusions ased on the mechanical properties of ductile and brittle rocks, certain raw materials were selected and the mechanical laws of ductile and brittle rock-like materials were obtained. and two rock-like materials were applied to the experiment of crack propagation. the main conclusions can be summarized as follows: for the simulation of ductile rock-like materials, sand and barite powder as filler materials, epoxide resin and polyamide as cementitious materials, and alcohol as organic solvent can be chosen. when the content of the cementitious material increases, the uniaxial compressive strength and fracture toughness of the ductile rock-like material significantly improve, b h1 h2 h3 h4 h5 h1 h2 h3 h4 h5 20mm 20mm 20mm 20mm 20mm h. bai et alii, frattura ed integrità strutturale, 56 (2021) 16-45; doi: 10.3221/igf-esis.56.02 43 and the change of elastic modulus is not obvious. when the content of other raw materials cannot be changed, the addition of auxiliary material silicone rubber is mainly to reduce the elastic modulus and strength of this ductile rock-like material, and the addition of rosin is mainly to improve the elastic modulus and brittleness of ductile rock-like materials. similarly, using sand and barite powder as a filling material, rosin as a cementitious material, and alcohol as an organic solvent brittle rock-like materials can be better simulated. when the content of the cementitious material increases, the elastic modulus and the uniaxial compressive strength of brittle rock-like materials significantly improve, and the fracture toughness even improves more obviously. when the content of other raw materials cannot be changed, the auxiliary materials epoxide resin and polyamide are mainly added to make the brittle rock-like materials have certain ductility, and the addition of silicone rubber is mainly to reduce the elastic modulus and brittleness of brittle rock-like materials. through the crack propagation model experiment of rock-like materials, it is found that as the brittleness of the material increases, the new crack initiation mode of the rock-like material gradually changes from shear crack to wing crack, and the vertical compression displacement of the specimen will gradually decrease when the new crack starts to sprout. when the cracks coalesce, the wing crack connection is the main connection mode, and the vertical compression displacement of the specimen with low content of epoxide resin and polyamide in the ductile group or high content of rosin in the brittle group is smaller. it can be also known that the damage of the ductile group specimen is mainly based on the tensile-shear composite failure mode, while the damage of the brittle group specimen is mostly the tensile failure mode. moreover, for the specimens of ductile group, as the content of epoxide resin and polyamide increases gradually, the crack connection stress increases and gradually approaches the peak strength. for the specimens of brittle group, as the rosin content increases gradually, the crack connection stress increases but gradually approaches the initiation stress. acknowledgements he work is supported by the national natural science foundation of china (nos. 41807251, 52027814, 51809198, 51839009 and 51679017), fundamental research funds for the central universities (no. 2042018kf0008). references [1] brace, w.f. and bombolakis, e.g. (1963). a note on brittle crack growth in compression, j. geophys. res., 68(12), pp. 3709–3713. doi: 10.1029/jz068i012p03709. [2] hoek, e. and bieniawski, z.t. (1965). brittle fracture propagation in rock under compression, int. j. fract., 1(3), pp. 137–155. doi: 10.1007/bf00186851. [3] bieniawski, z.t. (1967). mechanism of brittle fracture of rock, part ii—experimental studies, int. j. rock mech. min. sci., 4(4), pp. 407–423. doi: 10.1016/0148-9062(67)90031-9. [4] horii, h. and nemat-nasser, s. (1985). compression-induced microcrack growth in brittle solids: axial splitting and shear failure, j. geophys. res., 90(b4), pp. 3105–3125. doi: 10.1029/jb090ib04p03105. [5] petit, j. and barquins, m. (1988). can natural faults propagate under mode ii conditions, tectonics, 7(6), pp. 1243– 1256. doi: 10.1029/tc007i006p01243. [6] chaker, c. and barquins, m. (2015). sliding effect on branch crack, phys. chem. earth, 21(4), pp. 319–323. doi: 10.1016/s0079-1946(97)00055-4. [7] cao, p., liu, t., pu, c. and lin, h. (2015). crack propagation and coalescence of brittle rock-like specimens with preexisting cracks in compression, eng. geol., 187, pp. 113–121. doi: 10.1016/j.enggeo.2014.12.010. [8] wong, r.h.c. and chau, k.t. (1998). crack coalescence in a rock-like material containing two cracks, int. j. rock mech. min. sci., 35(2), pp. 147–164. doi: 10.1016/s0148-9062(97)00303-3. [9] wong, r.h.c., chau, k.t., tang, c.a. and lin, p. (2001). analysis of crack coalescence in rock-like materials containing three flaws—part i: experimental approach, int. j. rock mech. min. sci., 38(7), pp. 909–924. doi: 10.1016/s1365-1609(01)00064-8. [10] zhou, x.p., cheng, h. and feng, y.f. (2014). an experimental study of crack coalescence behaviour in rock-like materials containing multiple flaws under uniaxial compression, rock mechanics rock engineering, 47, pp. 1961–1986. doi: 10.1007/s00603-013-0511-7. [11] cheng, h., zhou, x.p., zhu, j. and qian, q.h. (2016). the effects of crack openings on crack initiation, propagation and coalescence behavior in rock-like materials under uniaxial compression, rock mechanics rock engineering, 49, pp. 3481–3494. doi: 10.1007/s00603-016-0998-9. t h. bai et alii, frattura ed integrità strutturale, 56 (2021) 16-45; doi: 10.3221/igf-esis.56.02 44 [12] reyes, o. and einstein, h.h. (1991). failure mechanisms of fractured rock: a fracture coalescence model, proc. seventh int. congr. rock mech., 1, pp. 333–340. [13] shen, b., stephansson, o., einstein, h.h. and ghahreman, b. (1995). coalescence of fractures under shear stress experiments, j. geophys. res. 100(b4), pp. 5975–5990. doi: 10.1029/95jb00040. [14] bobet, a. and einstein, h.h. (1998). fracture coalescence in rock-type materials under uniaxial and biaxial compression, int. j. rock mech. min. sci., 35(7), pp. 863–888. doi: 10.1016/s0148-9062(98)00005-9. [15] sagong, m. and bobet, a. (2002). coalescence of multiple flaws in a rock-model material in uniaxial compression, int. j. rock mech. min. sci., 39(2), pp. 229–241. doi: 10.1016/s1365-1609(02)00027-8. [16] wong, l.n.y. and einstein, h.h. (2006). fracturing behavior of prismatic specimens containing single flaws, proceedings of the 41st us symposium on rock mechanics, june. colorado. usa. [17] wong, l.n.y. and einstein, h.h. (2009). crack coalescence in molded gypsum and carrara marble: part 1. macroscopic observations and interpretation, rock mech. rock eng., 42, pp. 475–511. doi: 10.1007/s00603-008-0003-3. [18] wong, l.n.y. and einstein, h.h. (2009). crack coalescence in molded gypsum and carrara marble: part 2. microscopic observations and interpretation, rock mech. rock eng., 42, pp. 513–545. doi: 10.1007/s00603-008-0002-4. [19] basu, a., mishra, d.a. and roychowdhury, k. (2013). rock failure modes under uniaxial compression, brazilian, and point load tests, bull. eng. geol. environ., 72, pp. 457–475. doi: 10.1007/s10064-013-0505-4. [20] liang, c.y. zhang, q.b., li, x. and xin, p. (2016). the effect of specimen shape and strain rate on uniaxial compressive behavior of rock material, bull. eng. geol. environ., 75, pp. 1669–1681. doi: 10.1007/s10064-015-0811-0. [21] zhao, f. and he, m.c. (2017). size effects on granite behavior under unloading rockburst test, bull. eng. geol. environ., 76, pp. 1183–1197. doi: 10.1007/s10064-016-0903-5. [22] zou, c. and wong, l.n.y. (2014). experimental studies on cracking processes and failure in marble under dynamic loading, eng. geol., 173, pp. 19–31. doi: 10.1016/j.enggeo.2014.02.003. [23] hu, m., liu, y.x., ren, j.b., wu, r. and zhang, y. (2019). laboratory test on crack development in mudstone under the action of dry-wet cycles, bull. eng. geol. environ., 78, pp. 543–556. doi: 10.1007/s10064-017-1080-x. [24] zhou, x.p., bi, j. and qian, q.h. (2015). numerical simulation of crack growth and coalescence in rock-like materials containing multiple pre-existing flaws, rock mechanics and rock engineering, 48(3), pp. 1097-1114. doi: 10.1007/s00603-014-0627-4. [25] bi, j., zhou, x.p. and qian, q.h. (2016). the 3d numerical simulation for the propagation process of multiple preexisting flaws in rock-like materials subjected to biaxial compressive loads, rock mechanics and rock engineering, 49(5), pp. 1611-1627. doi: 10.1007/s00603-015-0867-y. [26] wang, y.t., zhou, x.p., wang, y. and shou, y.d. (2018). a 3-d conjugated bond-pair-based peridynamic formulation for initiation and propagation of cracks in brittle solids, international journal of solids and structures, 134, pp. 89-115. doi: 10.1016/j.ijsolstr.2017.10.022. [27] wang, y.t., zhou, x.p. and shou, y.d. (2017). the modeling of crack propagation and coalescence in rocks under uniaxial compression using the novel conjugated bond-based peridynamics, international journal of mechanical sciences, 128, pp. 614-643. doi: 10.1016/j.ijmecsci.2017.05.019. [28] zhou, x.p. and yang, h.q. (2008). micromechanical modeling of dynamic compressive responses of mesoscopic heterogenous brittle rock, theoretical and applied fracture mechanics, 48(1), pp. 1-20. doi: 10.1016/j.tafmec.2007.04.008. [29] zhou, x.p., zhang, y.x., ha, q.l. and zhu, k.s. (2008). micromechanical modelling of the complete stress-strain relationship for crack weakened rock subjected to compressive loading, rock mechanics and rock engineering, 41(5), pp. 747-769. doi: 10.1007/s00603-007-0130-2. [30] zhou, x.p., zhang, j.z. and wong, l.n.y. (2018). experimental study on the growth, coalescence and wrapping behaviors of 3d cross-embedded flaws under uniaxial compression, rock mechanics and rock engineering, 51(5), pp. 1379-1400. doi:10.1007/s00603-018-1406-4. [31] zhou, x.p., zhang, j.z. qian, q.h. and niu, y. (2019). experimental investigation of progressive cracking processes in granite under uniaxial loading using digital imaging and ae techniques, journal of structural geology, 126, pp. 129145. doi: 10.1016/j.jsg.2019.06.003. [32] zhang, j.z., zhou, x.p., zhou, l.s. and berto, f. (2019). progressive failure of brittle rocks with non-isometric flaws: insights from acousto-optic-mechanical (aom) data, fatigue & fracture of engineering materials & structures, 42(8), pp. 1787-1802. doi: 10.1111/ffe.13019. [33] zhang, j.z. and zhou, x.p. (2020). forecasting catastrophic rupture in brittle rocks using precursory ae time series, journal of geophysical research-solid earth, 125(8), e2019jb019276. doi: 10.1029/2019jb019276. h. bai et alii, frattura ed integrità strutturale, 56 (2021) 16-45; doi: 10.3221/igf-esis.56.02 45 [34] zhang, j.z. and zhou. x.p. (2020). ae event rate characteristics of flawed granite: from damage stress to ultimate failure, geophysical journal international, 222(2), pp. 795-814. doi: 10.1093/gji/ggaa207. [35] zhou, x.p., wang, y.t., zhang, j.z. and liu. f.n. (2019). fracturing behavior study of three-flawed specimens by uniaxial compression and 3d digital image correlation: sensitivity to brittleness, rock mechanics and rock engineering, 52(3), pp. 691-718. doi: 10.1007/s00603-018-1600-4. [36] zhou, x.p., lian, y.j., wong, l.n.y. and berto, f. (2018). understanding the fracture behavior of brittle and ductile multi-flawed rocks by uniaxial loading by digital image correlation, engineering fracture mechanics, 199, pp. 438-460. doi: 10.1016/j.engfracmech.2018.06.007. [37] kjellman, w. (1936). report on an apparatus for con-summate investigation of the mechanical properties of soils, proceedings of the 1st icsmfe, pp. 16–20. [38] ayatollahi, m.r., rashidi moghaddam, m., razavi, s.m.j., berto, f. (2016). geometry effects on fracture trajectory of pmma samples under pure mode-i loading, engineering fracture mechanics, 163, pp. 449–461. doi: 10.1016/j.engfracmech.2016.05.014. [39] torabi, a.r., campagnolo, a., berto, f. (2015). local strain energy density to predict mode ii brittle fracture in brazilian disk specimens weakened by v-notches with end holes materials and design, 69, pp. 22–29. doi: 10.1016/j.matdes.2014.12.037. [40] zhu, s-p., yu, z-y, correia, j., de jesus, a., berto, f. (2018). evaluation and comparison of critical plane criteria for multiaxial fatigue analysis of ductile and brittle materials, international journal of fatigue, 112, pp. 279-288, doi: 10.1016/j.ijfatigue.2018.03.028. [41] correia, j., apetre, n., arcari, a., de jesus, a., muñiz-calvente, m., calçada, r., berto, f., fernández-canteli, a. (2017). generalized probabilistic model allowing for various fatigue damage variables, international journal of fatigue 100, pp. 187-194. doi: 10.1016/j.ijfatigue.2017.03.031. [42] ferro, p., lazzarin, p., berto, f. (2012). fatigue properties of ductile cast iron containing chunky graphite, materials science and engineering a, 554, pp. 122–128. doi: 10.1016/j.msea.2012.06.024. [43] berto, f., gallo, p., lazzarin, p. (2014). high temperature fatigue tests of un-notched and notched specimens made of 40crmov13.9 steel. materials and design, 63(1), pp. 609–619. doi: 10.1016/j.matdes.2014.06.048. [44] berto, f., lazzarin, p., wang, c.h. (2004). three-dimensional linear elastic distributions of stress and strain energy density ahead of v-shaped notches in plates of arbitrary thickness. int. j. fracture, 127(3), pp. 265–282. doi: 10.1023/b:frac.0000036846.23180.4d. [45] berto, f., lazzarin, p., kotousov, a. (2011). on higher order terms and out-of-plane singular mode. mechanics of materials, 43(6), pp. 332–341. doi: 10.1016/j.mechmat.2011.03.004. [46] berto, f., lazzarin, p. (2013). multiparametric full-field representations of the in-plane stress fields ahead of cracked components under mixed mode loading, international journal of fatigue, 46, pp. 16–26. doi: 10.1016/j.ijfatigue.2011.12.004. [47] wu, w., hu, w., qian, g., liao, h., xu, x., berto, f. (2019). mechanical design and multifunctional applications of chiral mechanical metamaterials: a review, materials and design, 180, 107950. doi: 10.1016/j.matdes.2019.107950 [48] f. berto, e. barati. fracture assessment of u-notches under three point bending by means of local energy density. materials & design 32 (2011), 822-830. doi: 10.1016/j.matdes.2010.07.017. [49] s.m.j. razavi, p. ferro, f. berto, j. torgersen. fatigue strength of blunt v-notched specimens produced by selective laser melting of ti-6al-4v. theoretical and applied fracture mechanics 97 (2018) 376-384. doi: 10.1016/j.tafmec.2017.06.021. microsoft word numero_33_art_40 m.a. meggiolaro et alii, frattura ed integrità strutturale, 33 (2015) 368-375; doi: 10.3221/igf-esis.33.40 368 focussed on multiaxial fatigue shortcuts in multiple dimensions: the multiaxial racetrack filter m.a. meggiolaro, j.t.p. castro pontifical catholic university of rio de janeiro meggi@puc-rio.br, jtcastro@puc-rio.br h. wu tongji university in shanghai wuhao@tongji.edu.cn abstract. filtering techniques have been proposed for multiaxial load histories, usually aiming to filter out non-reversals, i.e. sampling points that do not constitute a reversal in any of its stress or strain components. however, the path between two reversals is needed to evaluate the equivalent stress or strain associated with each event. filtering out too many points in such path would almost certainly result in lower equivalent stresses or strains than expected. to avoid such issues, it is important to consider how a measured multiaxial loading path deviates from its course using some metric, such as the von mises stress or strain. in this work, a multiaxial version of the racetrack filter is proposed, which is able to perform efficient filtering even for 6d nonproportional histories. in the multiaxial racetrack algorithm, the stress or strain history is represented in a 6d space, only requiring from the user a desired scalar filtering amplitude r. for uniaxial histories, the proposed algorithm exactly reproduces the classic racetrack filter. the efficiency of the proposed multiaxial racetrack filter is qualitatively verified from a tension-torsion history example, showing the reduction in the number of data points for larger filter amplitudes r. the procedure can efficiently filter out non-damaging events but preserving the overall multiaxial path shape and multiaxial reversion points, which usually do not coincide with the reversion points of individual stress or strain components. keywords. multiaxial fatigue; racetrack filter; non-proportional loading; variable amplitude loading. introduction he racetrack filter, originally proposed by fuchs et al. in 1973 [1] for uniaxial histories, aims to eliminate small amplitude load events that, although usually plenty, do not induce fatigue damage from a variable amplitude loading history. so, the resulting condensed histories can much accelerate both experiments and computations, focusing only on the few events that cause most or all of the damage. fig. 1 illustrates the uniaxial racetrack filter concept. the original history of fig. 1(a) is condensed into the history in fig. 1(d), eliminating amplitudes smaller than a userspecified value r. the idea of the filter is to draw a “racetrack” of width 2r, bounded by upper and lower “fences” that have the same profile as the original history, see fig. 1(b). if a “driver” racing in this racetrack needs to change its direction from upward to downward (or vice versa), then a reversal point is identified, as seen in fig. 1(c), where the racer needed to change twice its direction, near points b and e. in this example, points c and d are filtered out, because the driver didn’t have to change direction to avoid the fences associated with them. clearly, the track width 2r determines the number of counted reversals: wider tracks will filter out most of the original loading history, while narrow tracks will t http://www.gruppofrattura.it/pdf/rivista/numero33/audioslides/castro2/castro2.html m.a. meggiolaro et alii, frattura ed integrità strutturale, 33 (2015) 368-375; doi: 10.3221/igf-esis.33.40 369 almost keep all the original reversals. in other words, the racetrack filter condenses the original variable amplitude history into a smoother history, discarding the small amplitude changes that cause negligible fatigue damage [2]. moreover, the condensed history does not change the order of the significant load events, which is an essential feature to account for plasticity memory effects. figure 1: uniaxial racetrack filter example, showing: (a) the original history; (b) the racetrack defined between the upper and lower fences; (c) the driver path from a to f; and (d) the filtered history. the algorithm of the uniaxial racetrack filter is easier to implement through another physical analogy, a small round peg p that can oscillate inside a slotted plate whose center is the point o, see fig. 2. the range that the peg can oscillate inside the slot is 2r, the racetrack filter range. both peg and slot center are initially aligned with point a, as seen in fig. 2(a). during the path ab, the peg moves up until reaching the upper limit of the slotted plate, which then starts to move up, see fig. 2(b), where the dark dashed line represents the path of point o. as shown in fig. 2(c), the following path bcd moves the peg but does not involve any translation of the slotted plate, an indication that the points c and d can be filtered out: peg oscillations alone can be discarded. then, both paths de and ef involve slotted plate translations, see fig. 2(d) and (e), so they must be maintained in the filtered history. after the initial point a, only the peg locations p associated with the end of a translation of the slotted plate are stored in the filtered history. point b is the peg location at the end of the first slotted plate upward translation, so it is stored. similarly, points e and f are stored since they are the peg locations at the end of the next downward and upward slotted plate translations. the filtered history is then the path abef, as shown in fig. 2(f), always identical to the path obtained from the original racetrack filter. this amplitude filter is very efficient in practice, since besides small damageless load events it can remove the unavoidable noise e.g. from strain measurements, which can induce much more small reversions than the load itself in the measured signal. m.a. meggiolaro et alii, frattura ed integrità strutturale, 33 (2015) 368-375; doi: 10.3221/igf-esis.33.40 370 figure 2: physical analogy between the uniaxial racetrack filter and a peg oscillating inside a slotted plate with center o and slot range 2r. the peg p oscillates according to the original history, resulting in translations of o represented by the dark dashed line. issues with existing multiaxial load filters most important practical issue in multiaxial fatigue calculations, even more than in the uniaxial case, is how to filter out a load history to decrease their intrinsically high computational cost. so, like in the 1d case it may seem a good idea to first remove from the multiaxial loading all data points that are not peaks or valleys of any of their stress or strain components, since to properly measure a load signal it is necessary to oversample the digitalized data at a rate high enough to not distort the signal [3-4]. but this simple filtering practice is not recommended in np multiaxial histories, for two reasons: first, the path between two load reversals is needed to evaluate the path-equivalent stress or strain associated with each rainflow count, e.g. using a convex enclosure method [5] or even better the moment of inertia method [6]. filtering out too many points in such path almost certainly results in lowering the equivalent stresses or strains, so some points along the multiaxial path should not be filtered out, even if they do not constitute a load component reversal. moreover, reversal points obtained from a multiaxial rainflow algorithm may not occur at the reversal of one of the stress or strain components. for instance, the relative von mises strain, used in the wang-brown (wb) rainflow method and its variations [7], may reach a peak value at a point that is neither a maximum nor a minimum of any strain component. but this important point would have been filtered out by any non-reversal filtering algorithm, resulting in inadmissible non-conservative predictions. the second reason is because the reversal points obtained from a multiaxial rainflow algorithm might not occur at the reversal of one of the stress or strain components. for example, the relative mises strain, used in the wb rainflow count, may reach a peak value at a point that is neither a maximum nor a minimum of any strain component. but such most important points would be filtered out by a non-reversal filtering algorithm, resulting in non-conservative fatigue damage and life and predictions. the “peaks procedure” proposed in [8] e.g. filters out all events whose components are not peaks or valleys, potentially eliminating important load points that could have the highest mises stresses or strains of the load history, even though each individual component was not maximized. moreover, such procedure would store each and every event that constitutes a peak or valley from any single component, which for (unavoidably) noisy measurements could result in no events at all being filtered out, even if the noise had very low amplitudes. to avoid such issues, how a measured multiaxial loading path deviates from its course must be evaluated by some metric, such as the mises stress or strain. this is needed to avoid filtering out important counting points from multiaxial rainflow a m.a. meggiolaro et alii, frattura ed integrità strutturale, 33 (2015) 368-375; doi: 10.3221/igf-esis.33.40 371 algorithms or significant paths that can affect the calculation of an equivalent stress or strain, since all stress or strain components contribute altogether for the reversals that can be eliminated. note that an amplitude filter is a most desirable feature in practical applications, to not only eliminate redundant measurement noise and oversampled data, but also small amplitudes that do not cause fatigue damage. in fact, it may be practically impossible to analyze unfiltered multiaxial fatigue data. a multiaxial version of the racetrack filter must perform such tasks even for np histories. the multiaxial racetrack filter n the multiaxial racetrack algorithm proposed here, the stress or strain history is represented in a 6d space, and a suitable filtering amplitude r must be chosen like in the 1d case. a small peg p  is then allowed to move in this 6d space, but instead of being restricted within a 1d slot, it is kept inside a 6d hyper-sphere of center o  and radius r. when the peg reaches the hyper-sphere surface and tries to move out of it, both the peg and the hyper-sphere translate altogether, similarly to the 1d slotted plate example. fig. 3 shows a 2d tension-torsion example of a hyper-sphere translation caused by the peg movement from its current position ip  to the next 1ip   , where in  is the current normal vector that defines the surface translation direction (still to be determined), and bi, ai, and di are distances (measured in stress or strain units) used in the filtering algorithm. figure 3: hyper-sphere translation along in  , caused by a peg movement from ip  to 1ip   . for this 2d tension-torsion example, the hyper-sphere simply becomes a circle. the next peg location 1ip   is given by the input load history. when combined with the current location io  of the hypersphere center, and a known translation direction in  , the values of bi, ai, and di can be obtained from 2 1 1( ) ( ) t i i i i ib p o p o        , 1( ) t i i i ia p o n     , and 2 2 2i i id b a  (1) where bi must be greater than r to guarantee that 1ip   is outside the current hyper-sphere, otherwise there is no translation. while ai  0 and di  r, the next peg location 1ip   can still be located on the border of the hyper-sphere translated in the in  direction, where the center translation shown in fig. 3 can be calculated by 2 21 ( )i i i i io o a r d n         (2) the process is then repeated for the next peg location. fig. 4 shows two consecutive translations where the conditions ai  0 and di  r are satisfied, allowing the hyper-sphere translation direction to remain constant, i.e. 1i in n    . in this example, point ip  can be filtered out, since it does not alter the translation direction during the (multiaxial) load history path 1 1i i ip p p     . this filtering process that happens while the hyper-sphere is translated is called here dynamic filtering. i m.a. meggiolaro et alii, frattura ed integrità strutturale, 33 (2015) 368-375; doi: 10.3221/igf-esis.33.40 372 figure 4: hyper-sphere translations along 1i in n    , caused by the path 1 1i i ip p p     . dynamic filtering eliminates ip  because it does not alter the translation direction. the initial locations 1p  of the peg and 1o  of the hyper-sphere center must coincide with the first loading point from the load history in the 6d stress or strain space. as seen in fig. 5(a), no hyper-sphere translation happens while the peg moves inside it, therefore points 2p  through 1ip   are filtered out, in a process called static filtering (because it does not involve hyper-sphere translations). when the peg reaches for the first time the hyper-sphere border and tries to move outside it, the translation direction in  must be defined. a simple translation direction rule assumes here that in  is determined from the segment that joins the current hyper-sphere center io  and the next peg location 1ip   , i.e. 1( )i i i in p o b   , see fig. 5(a). other improved rules for the translation direction of the hyper-sphere center could be defined. figure 5: hyper-surface location (a) during its first translation and (b) during a load kinking. in summary, static filtering happens while the next peg location 1ip   is not outside the current hyper-sphere, i.e. bi  r in fig. 3, while dynamic filtering happens during hyper-sphere translations where bi > r, ai  0, and di  r. besides the initial 1p  , the only points that are not filtered out are the ones where some significant path kinking happens due to di > r, and the ones where a load “reversal” forces a change of more than 90o in the hyper-surface translation direction, i.e. 1 0i in n     and therefore ai < 0. in these kinking or reversal cases, the new hyper-surface translation direction could be determined by the simple rule 1( )i i i in p o b   . m.a. meggiolaro et alii, frattura ed integrità strutturale, 33 (2015) 368-375; doi: 10.3221/igf-esis.33.40 373 note that the kinking and reversal criteria could happen at the same time, as exemplified in fig. 5(b), where the path kinks at ip  because 1ip   has di > r and thus the translation direction needs to change, while ip  can also be interpreted as a load reversal point because 1 0i in n     and thus ai < 0. since the distance between io  and 1ip   is equal to bi, see fig. 3, the hyper-surface center translation during kinking and/or reversal, shown in fig. 5(b), can be calculated by 1 ( )i i i io o b r n        (3) the filtered history is then composed of the initial point and all kinking and reversal points. the reversal criterion ai < 0 keeps track of abrupt changes in loading direction that might characterize a “peak” condition, while the kinking criterion given by di > r guarantees that a significant curvature of the load history path between two points is accounted for without assuming it is a straight line. such path curvature is important in the calculation of path-equivalent stress and strain ranges, because the use of a straight path could lead to a non-conservative range calculation when compared to the actual np curved stress or strain path. fig. 6 summarizes the procedures involved in the multiaxial racetrack algorithm. note that it exactly reproduces the classical uniaxial racetrack algorithm if p  and o  are represented by scalars. figure 6: multiaxial racetrack algorithm, with static and dynamically-filtered history resulting from the p  output values, where n  is the hyper-sphere translation direction. tension-torsion example ig. 7(a) shows an example of a normal  effective shear stress path obtained under tension-torsion, used to exemplify the multiaxial racetrack algorithm. fig. 7(b) shows the filtered history for a given relatively large filter amplitude r, where only four out of the sixteen original data points were not filtered, significantly decreasing the computational cost of multiaxial fatigue life calculations for this load history. in this figure, the points that suffered static filtering are marked with an ×, while the dynamically-filtered ones are represented with triangular markers. note once again the immense practical importance of these amplitude filter procedures. since the calculation of multiaxial fatigue damage accumulation is an intrinsically intensive computational procedure, it is most important to eliminate from the calculation effort all points that are not essential for its result, i.e. all points that do not cause significant fatigue damage. f m.a. meggiolaro et alii, frattura ed integrità strutturale, 33 (2015) 368-375; doi: 10.3221/igf-esis.33.40 374 fig. 7(c) compares the (dashed) original history with the filtered one. the filtered data tends to the original one as the filter amplitude r decreases, at the cost of increasing the number of unfiltered points, see fig. 7(d) and (e). in practice, a relatively large r value can be initially chosen, and then decreased until the calculated damage converges. note that the adopted 6d space can be defined for example by the normal and by the effective shear components, 3 3 3 t y zx xy xz yz       or 3 3 3 t y zx xy xz yz        , respectively for stress or strain histories. figure 7: multiaxial racetrack filter applied to a tension-torsion history path with 16 points, showing (a) the translating hyper-spheres, (b) the static and dynamically-filtered points (respectively × and triangles), and the effect of decreasing the filter amplitude r, resulting in histories with (c) four, (d) seven, and (e) fourteen points. conclusions mplitude filters are most important in practical fatigue analyses to manage their computational cost when (as usual) the input history is oversampled, too long, and/or contains too many non-damaging low-amplitude cycles. the proposed multiaxial racetrack algorithm is very versatile, allowing the synchronous filtering of stress and strain histories acting at a given material point, based on a single scalar amplitude value. references [1] fuchs, h.o., nelson, d.v., burke, m.a., toomay, t.l., shortcuts in cumulative damage analysis, sae automobile engineering meeting paper 730565, (1973). [2] nelson, d.v., fuchs, h.o., predictions of cumulative fatigue damage using condensed load histories, in fatigue under complex loading, sae, (1977). a m.a. meggiolaro et alii, frattura ed integrità strutturale, 33 (2015) 368-375; doi: 10.3221/igf-esis.33.40 375 [3] bannantine, j.a., socie, d.f., a variable amplitude multiaxial fatigue life prediction method, fatigue under biaxial and multiaxial loading, esis publ. 10 (1991) 35-51. [4] langlais, t.e., vogel, j.h., chase, t.r., multiaxial cycle counting for critical plane methods, int. j. fatigue, 25 (2003) 641-647. [5] meggiolaro, m.a., castro, j.t.p., an improved multiaxial rainflow algorithm for non-proportional stress or strain histories part i: enclosing surface methods, int. j. fatigue, 42 (2012) 217-226. [6] meggiolaro, m.a., castro, j.t.p., prediction of non-proportionality factors of multiaxial histories using the moment of inertia method, int. j. fatigue, 61 (2014) 151-159. [7] meggiolaro, m.a., castro, j.t.p., an improved multiaxial rainflow algorithm for non-proportional stress or strain histories part ii: the modified wang-brown method, int. j. fatigue, 42 (2012) 194-206. [8] bannantine, j.a., a variable amplitude multiaxial fatigue life prediction method, fcp report n.151, university of illinois at urbana-champaign, (1989). microsoft word 2330 v. p. berardi et alii, frattura ed integrità strutturale, 48 (2019) 222-229; doi: 10.3221/igf-esis.48.23 222 cohesive fracture in composite systems: experimental setup and first results valentino paolo berardi department of civil engineering, university of salerno, via giovanni paolo ii 132, fisciano (sa), italy berardi@unisa.it michele perrella, gabriele cricrì department of industrial engineering, university of salerno, via giovanni paolo ii 132, fisciano (sa), italy mperrella@unisa.it, gcricri@unisa.it abstract. composite systems are widely used in many engineering applications for new structures and strengthening of existing ones. within the structural rehabilitation of civil constructions, the plating technique of beams with fiber reinforced polymer (frp) represents a quick and optimal intervention with respect to traditional ones. the failure of these composite systems usually occurs due to the frp debonding, which corresponds to a mode ii fracture of concrete specimens. in this paper, a new experimental setup for investigating the mode ii fracture behavior of frp-concrete composite structures is presented. the test equipment consists of both conventional equipment and a non-contact optical technique, digital image correlation (dic), and the test system was realized at the design machine laboratory of the university of salerno. a preliminary test was performed and the corresponding results are shown and discussed. keywords. composite systems; fiber reinforced polymer (frp); debonding; mechanical testing; digital image correlation (dic). citation: berardi, v. p., perrella, m., cricrì, g., cohesive fracture in composite systems: experimental setup and first results, frattura ed integrità strutturale, 48 (2019) 222-229. received: 11.12.2018 accepted: 09.01.2019 published: 01.04.2019 copyright: © 2019 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. introduction dhesive junctions have become widely adopted for structural applications in many engineering fields, typically for realizing industrial, automotive, naval and aerospace high-tech structural elements [1, 2], as well as for rehabilitating existing civil structures (reinforced concrete and masonry structures) with external fiber reinforced polymer (frp) reinforcements [3-12]. within the field of civil engineering, the design of strengthening by bonding composite plates and sheets requires the evaluation of brittle and ductile failure modes, in order to achieve a controlled overall ductile behavior of the structure. typical brittle failure modes are associated with debonding close to either frp cut-off cross sections (end debonding) or a http://www.gruppofrattura.it/va/48/2330.mp4 v. p. berardi et alii, frattura ed integrità strutturale, 48 (2019) 222-229; doi: 10.3221/igf-esis.48.23 223 flexural cracks (intermediate debonding). according to the capacity design criteria, failure due to brittle debonding phenomena shall not forego flexural or shear failure of the strengthened member. in common applications, the end debonding generally represents the design condition and a maximum value of composite stress (lower than composite strength) is associated with it. no specific standards are available to experimentally evaluate the frp maximum stress corresponding to end debonding. some technical recommendations are provided in the american aci 440.2r-08 [13], the european fib t.g. 9.3 [14] and the italian cnr-dt 200 r1/2013 [15] guidelines to predict such design frp stress by means of semi-empirical formulae. within this context, some specific aspects of this technique have yet to be studied in deeper detail. with reference to frp-concrete end debonding, it is well-known that the corresponding mechanical behavior can be modeled via a cohesive law, that allows also the prediction of the mode ii fracture mechanism experimentally observed in failure of strengthened systems [16-20]. several researchers are being studied this local failure mechanism by proposing different test setups, generally based on either linear variable displacement transducers (lvdts) or laser meter devices installed on composite plate and located at the beginning of bonded area, as well as on strain gauges, positioned along longitudinal direction [21-23]. some recent studies have introduced a non-contact optical technique, digital image correlation (dic), to obtain the frpconcrete slip on extended areas of tested specimen rather than only on the beginning of bonded area [24-32]. this promising method also allows for an estimation, with a good accuracy, of the strain field on frp and concrete core external surfaces. within this context, a new experimental setup for the identification of cohesive law at the adhesive interface of strengthened systems is presented. it is based on a mechanical anchorage system of specimen and dic outcomes, without requiring any strain gauges and lvdts/laser meter records. an optimized dic procedure is proposed, consisting of a data processing limited to selected regions of interest (roi), in order to drastically reduce the computational burden and point out experimental displacements in a more accurate way and overcoming the boundary effects of inhomogeneous zones. several experimental debonding tests on a concrete block externally plated with gfrp pultruded laminate have been performed for validation purposes at the design machine laboratory of the university of salerno. figure 1: anchoring device – lateral and top views (dimensions in mm). materials and methods he experimental setup was designed with the aim to achieve an effective anchoring of strengthened specimen and an optimal placement of camera. it consists of: t v. p. berardi et alii, frattura ed integrità strutturale, 48 (2019) 222-229; doi: 10.3221/igf-esis.48.23 224  a testing device to apply load;  a data acquisition system. a still anchoring device mounted on the laboratory modular basement was realized to fix the reinforced specimen (fig. 1). load is applied using a 20-kn servo-hydraulic actuator mounted on the laboratory modular basement (fig. 2). the data acquisition system includes:  actuator load cell and lvdt;  industrial 5 mpixel camera;  strain gauges bonded to external surface of the specimens;  database management system. the equipment can automatically record the data at fixed time steps. figure 2: testing device. a preliminary debonding test was performed on a concrete specimen reinforced with gfrp composite laminate. the tested prismatic concrete block (150x150x400 mm3) is one of a series of specimens manufactured using low strength concrete to best simulate the interface behavior of strengthened existing structures. composite reinforcement was made of a pultruded e glass/polyester fiber reinforced polymer with a thickness of 1.6 mm. the e-glass fiber volume fraction was equal to 35%. a two component epoxy resin was used for bonding. a controlled thickness of 1.6 mm was imposed to the adhesive layer. the specimens were cured at 30 °c for 72 hours. first, five cubic samples (150x150x150 mm3) made of the same concrete mixture of the prismatic specimens were prepared and tested, according to iso 1920-4 standard, in order to evaluate the mean compressive strengths, respectively cubic rcm and cylindrical fcm. second, tensile tests, according to astm d3039m standard, were performed to obtain the mean young’s modulus egfrp and ultimate tensile stress fgfrp along fiber direction of the pultruded gfrp composite. the experimental mechanical properties of concrete and gfrp laminate, together with the nominal young’s modulus er and tensile strength fr of resin, according to the manufacturer technical datasheet, are listed in tab. 1. rcm [mpa] fcm [mpa] egfrp [mpa] fgfrp [mpa] er [mpa] fr [mpa] 24.54 20.37 48000 800 11200 25-30 table 1: mechanical properties of specimens’ materials. v. p. berardi et alii, frattura ed integrità strutturale, 48 (2019) 222-229; doi: 10.3221/igf-esis.48.23 225 the glued zone (hatched zone) and the strain gauges configuration are depicted in figs. 3 and 4, respectively. the origin of loading x axis corresponds to the top edge of the bonded area. figure 3: details of the glued zone. figure 4: strain gauges configuration. the tests were performed under displacement control with a rate of 0.01 mm/s until failure occurrence. the following experimental data were recorded during test execution:  digital video for image processing with dic technique;  relative displacement between specimen edges by the test machine (lvdt);  load applied to composite laminate by the test machine load cell;  strains of composite and concrete, measured via strain gauges. the dic analysis was performed for the preliminary test (specimen #1) by considering 25 small (2 mm diameter) circular regions of interest (roi) as shown in fig. 5. figure 5: details of rois. the ncorr algorithm [33], enhanced via an in house made matlab routine, was used for dic analysis. such a routine allows to evaluate the resulting displacement vector for each roi center by getting the mean value of the computed data in a roi center neighborhood. thus improving the displacement measurement accuracy. x v. p. berardi et alii, frattura ed integrità strutturale, 48 (2019) 222-229; doi: 10.3221/igf-esis.48.23 226 results and discussion he load-displacement curve, acquired by the testing machine during the preliminary debonding experiment (specimen #1), is plotted in fig. 6, exhibiting a typical trend as in literature. the maximum value of the applied force of about 13 kn was recorded, whereas the maximum displacement ranged within 3 mm. a typical debonding failure mode was observed (fig. 7), corresponding to the optimal collapse mechanism of strengthened concrete due to the fact that the concrete shear strength is lower than for the adopted resin. figure 6: load-displacement curve. figure 7: debonding failure mode. figure 8: gfrp strain vs. time curves. figure 9: tangential slip vs. time curves obtained by dic technique. the tangential slips δi,i+1 evaluated by dic technique, are considered as the relative displacement of mid points between the cross-sections corresponding to i-th and (i+1)-th gfrp strain gauges. the gfrp strain εi versus time curves and the tangential slip δi,i+1 versus time curves are plotted in figs. 8 and 9 respectively. the proposed methodology is capable of 0 2 4 6 8 10 12 14 0 0.5 1 1.5 2 2.5 3 3.5 4 lo a d  [ k n ] displacement [mm] 0 0.001 0.002 0.003 0.004 0.005 0 50 100 150 200 250 300 350 s tr a in  [ ] time [s] strain gauge # 0 strain gauge # 1 strain gauge # 2 strain gauge # 3 strain gauge # 4 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0 50 100 150 200 250 300 350 ta n g e n ti a l  sl ip  [ m m ] time [s]   t v. p. berardi et alii, frattura ed integrità strutturale, 48 (2019) 222-229; doi: 10.3221/igf-esis.48.23 227 properly determining the slips over extended areas respect to punctual displacement evaluation provided by traditional lvdts. in such a way, it is possible to model a more accurate adhesive interface behavior and to track the debonding propagation. the strains provided by dic technique, obtained by the displacements of 16th-17th rois, resulted in good agreement with those measured by the strain gage #2, except for the final debonding stage, close to the failure occurrence (fig. 10). this is probably due to the formation of out of plane displacements that affect the accuracy and effectiveness of bidimensional dic technique. the mean shear stresses at the adhesive interface, τi,i+1, acting between the cross-sections corresponding to the i-th and (i+1)-th gfrp strain gauges, were evaluated by means of strains variation measured along the loading x axis, according to the method proposed in literature [13-14]: τi,i+1=egfrp·agfrp· εi+1-εi bgfrp· xi+1-xi (1) being:  agfrp=tgfrp·bgfrp the cross sectional area of the composite laminate;  gfrp gfrp gfrpt , b  and e the thickness, the width and the young’s modulus along the fiber direction of the composite laminate, respectively. the shear stress vs. tangential slip curves are depicted in fig. 11. these curves are representative of experimental evaluations of cohesive shear acting at the concrete-gfrp interface in a form coherent with a cohesive zone (czm) approach and with recent literature results [21-32]. figure 10: strains vs. time curve by dic. figure 11: shear stress vs. tangential slip curves. the value of the observed debonding force falls within the range of experimental outcomes obtained by the authors through a previous testing system on similar specimens made of the same gfrp lamina and epoxy resin [18]. moreover, further experimental tests were carried out in order to validate the proposed testing system. the outcomes, in terms of debonding force, are reported in tab. 2, thus assessing the reproducibility of the results. specimen # debonding force [kn] mean value [kn] standard deviation [kn] variance [kn2] 1 13.04 13.05 0.902 0.814 2 14.16 3 11.95 table 2: debonding force values. 0 0.001 0.002 0.003 0.004 0.005 0 50 100 150 200 250 300 350 s tr a in  [ ] time [s] dic strain strain gauge # 2 0 0.5 1 1.5 2 2.5 3 3.5 4 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 s h e a r  st re s  [m p a ] tangential slip [mm]   v. p. berardi et alii, frattura ed integrità strutturale, 48 (2019) 222-229; doi: 10.3221/igf-esis.48.23 228 conclusions new experimental setup for investigating the mode ii fracture behavior of frp-concrete composite structures was proposed in this paper. the presented approach allows to model the interface behavior between the adherends via few experimental data provided by testing machine load cell and dic technique applied to proper regions of interest. the experimental methodology was validated within experimental tests on debonding failure of concrete blocks reinforced with gfrp pultruded laminate, carried out at the design machine laboratory of the university of salerno. results of a preliminary test were presented and discussed in detail. the dic method allows to provide with the full field displacement measurement, overcoming the limits of the conventional acquiring by lvdt or laser measurement devices. this non-contact optical technique has also allowed to evaluate the strain field with a good accuracy. the proposed test methodology can be easily extended in a near future to the analysis of long-term behavior of adhesive interface, accounting its viscous nature [34-39], against a limited computational and time burden due to the optimized use of dic technique. references [1] citarella, r., cricrì, g., (2014). three-dimensional bem and fem submodelling in a cracked fml full scale aeronautic panel, applied composite materials, 21(3), pp. 557-577. [2] corato, v., affinito, l., anemona, a., besi vetrella, u., della corte, a., di zenobio, a., fiamozzi zignani, c., freda, r., messina, g., muzzi, l., perrella, m., reccia, l., tomassetti, g., turtù, s., (2015). detailed design of the large-bore 8t superconducting magnet for the nafassy test facility, superconductor science and technology, 28(3), article no 034005. [3] ascione, l., berardi, v.p., feo, l., mancusi, g., (2005). a numerical evaluation of the inter-laminar stress state in externally frp plated rc beams, composites part b: engineering, 36(1), pp. 83-90. [4] ascione, l., berardi, v.p., di nardo, e., feo, l., mancusi, g., (2005). an experimental and numerical investigation on the plating of reinforced concrete beams with frp laminates, lecture notes in applied and computational mechanics, 23, pp. 303-314. [5] marfia, s., sacco, e., toti, j., (2010). an approach for the modeling of interface-body coupled nonlocal damage, frattura ed integrità strutturale, 12, pp. 13-20. [6] marfia, s., sacco, e., toti, j., (2011). a coupled interface-body nonlocal damage model for the analysis of frp strengthening detachment from cohesive material, frattura ed integrità strutturale, 18, pp. 23-33. [7] ronagh, h.r., eslami, a., (2013). flexural retrofitting of rc buildings using gfrp/cfrp a comparative study, composites part b: engineering, 46, pp. 188-196. [8] bennati, s., dardano, n., valvo, p.s., (2012). a mechanical model for frp-strengthened beams in bending, frattura ed integrità strutturale, 22, pp. 39-55. [9] d’ambrisi, a., mezzi, m., feo, l., berardi, v.p., (2014). analysis of masonry structures strengthened with polymeric net reinforced cementitious matrix materials, composite structures, 113(1), pp. 264-271. [10] shardakov, i.n., shestakov, a.p., bykov, a.a., (2016). delamination of carbon-fiber strengthening layer from concrete beam during deformation (infrared thermography), frattura ed integrità strutturale, 38, pp. 331-338. [11] de piano, m., modano, m., benzoni, g., berardi, v.p., fraternali, f., (2017). a numerical approach to the mechanical modeling of masonry vaults under seismic loading, ingegneria sismica, 34(4), pp. 103-119. [12] berardi, v.p., de piano, m., teodosio, g., penna, r., feo, l., (2017), advanced numerical models for the analysis of unreinforced and strengthened masonry vaults, in compdyn 2017 proceedings of the 6th international conference on computational methods in structural dynamics and earthquake engineering, 2, pp. 5056-5069. [13] american concrete institute (aci), (2017). guide for the design and construction of externally bonded frp systems for strengthening concrete structures, aci440.2r-17, farmington hills, mi. [14] fédération internationale du béton (fib), (2001). technical report on the “design and use of externally bonded fibre reinforced polymer reinforcement (frp ebr) for reinforced concrete structures”, 1-138, isbn 2-88394-054-1. [15] national research council of italy, (2013). guide for the design and construction of externally bonded frp systems for strengthening existing structures cnr-dt 200r1-2013. advisory committee on technical regulations for constructions, rome. a v. p. berardi et alii, frattura ed integrità strutturale, 48 (2019) 222-229; doi: 10.3221/igf-esis.48.23 229 [16] lepore, m.a., perrella, m., (2017). from test data to fe code: a straightforward strategy for modelling the structural bonding interface, frattura ed integrità strutturale, 11(39), pp. 191-201. [17] perrella, m., berardi, v.p., cricri, g., (2017). mode ii fracture behaviour of adhesively bonded reinforcements, in aimeta 2017 proceedings of the 23rd conference of the italian association of theoretical and applied mechanics, 2, pp. 1824-1832. [18] perrella, m., berardi, v.p., cricrì, g., (2018). a novel methodology for shear cohesive law identification of bonded reinforcements, composites part b: engineering, 144, pp. 126-133. [19] orefice, a., mancusi, g., berardi, v.p., feo, l., zuccaro, g., (2018). residual stiffness of bonded joints for fibrereinforced polymer profiles, composites part b: engineering, 144, pp. 237-253. [20] cricrì, g., (2018). cohesive law identification of adhesive layers subject to shear load – an exact inverse solution, international journal of solids and structures, 12, pp. 492-498. [21] mazzotti, a., savoia, m., ferracuti, b., (2009). a new single-shear set-up for stable debonding of frp–concrete joints, construction and building materials, 23, pp. 1529–1537. [22] bencardino, f., condello, a., ashour, a.f., (2017), single-lap shear bond tests on steel reinforced geopolymeric matrix-concrete joints, composites part b: engineering, 110, pp. 62-71. [23] de santis, s., ceroni, f., de felice, g., fagone, m., ghiassi, b., kwiecień, a., lignola, g.p., morganti, m., santandrea, m., valluzzi, m.r., viskovic. a., (2017). round robin test on tensile and bond behaviour of steel reinforced grout systems, composites part b: engineering, 127, pp. 100-120. [24] ali-ahmad, m., subramaniam, k., ghosn, m., (2006). experimental investigation and fracture analysis of debonding between concrete and frp sheets, journal of engineering mechanics, 132(9), pp. 914-923. [25] carloni, c., subramaniam, k.v., (2010). direct determination of cohesive stress transfer during debonding of frp from concrete, composite structures, 93(1), pp. 184-192. [26] carozzi, f.g., colombi, p., poggi, c., (2015). calibration of end-debonding strength model for frp-reinforced masonry, composite structures, 120, pp. 366-377. [27] napoli, a., de felice, g., de santis, s., realfonzo, r., (2016). bond behaviour of steel reinforced polymer strengthening systems, composite structures, 152, pp. 499-515. [28] carloni, a., santandrea, m., imohamed, i.a.o., (2017). determination of the interfacial properties of srp strips bonded to concrete and comparison between single-lap and notched beam tests, engineering fracture mechanics, 186, pp. 80104. [29] pohoryles, d.a., melo, j., rossetto, t., fabian, m., mccague, c., stavrianaki, k., lishman, b., sargeant, b., (2017). use of dic and ae for monitoring effective strain and debonding in frp and frcm-retrofitted rc beams, journal of composites for construction, 21(1). [30] ghorbani, m., mostofinejad, d., hosseini, a., (2017). bond behavior of cfrp sheets attached to concrete through ebr and ebrog joints subject to mixed-mode i/ii loading, journal of composites for construction, 21(5). [31] bilotta, a., ceroni, f., lignola, g.p., prota, a., (2017). use of dic technique for investigating the behaviour of frcm materials for strengthening masonry elements, composites part b: engineering, 129, pp. 251-270. [32] tekieli, m., de santis, s., de felice, g., kwiecien´, a., roscini, f., (2017). application of digital image correlation to composite reinforcements testing, composite structures, 160, pp. 670-688. [33] babler, j., adair, b., antoniou, a., (2015). ncorr: open-source 2d digital image correlation matlab software, experimental mechanics, 55, pp. 1105-1122. [34] calì, c., cricrì, g., perrella, m., (2010). an advanced creep model for hardening and damage effects, strain, 46, pp. 347–357. [35] ascione, l., berardi, v.p., d’aponte, a., (2011). a viscoelastic constitutive law for frp materials, international journal of computational methods in engineering science and mechanics, 12(5), pp. 225-232. [36] ascione, l., berardi, v.p., d’aponte, a., (2012). creep phenomena in frp materials, mechanics research communications, 43, pp. 15-21. [37] mancusi, g., spadea, s., berardi, v.p., (2013). experimental analysis on the time-dependent bonding of frp laminates under sustained loads, composites part b: engineering, 46, pp. 116-122. [38] berardi, v.p., perrella, m., feo, l., cricrì, g., (2017). creep behavior of gfrp laminates and their phases: experimental investigation and analytical modelling, composites part b: engineering, 122, pp. 136-144. [39] berardi, v.p., feo, l., mancusi, g., de piano, m., (2018). influence of reinforcement viscous properties on reliability of existing structures strengthened with externally bonded composites, composite structures, 200, pp. 532-539. << /ascii85encodepages false /allowtransparency false /autopositionepsfiles true /autorotatepages /none /binding /left /calgrayprofile (dot gain 20%) /calrgbprofile (srgb iec61966-2.1) /calcmykprofile (u.s. web coated \050swop\051 v2) /srgbprofile (srgb iec61966-2.1) /cannotembedfontpolicy /error /compatibilitylevel 1.4 /compressobjects /tags /compresspages true /convertimagestoindexed true /passthroughjpegimages true /createjobticket false /defaultrenderingintent /default /detectblends true /detectcurves 0.0000 /colorconversionstrategy /cmyk /dothumbnails false /embedallfonts true /embedopentype false /parseiccprofilesincomments true /embedjoboptions true /dscreportinglevel 0 /emitdscwarnings false /endpage -1 /imagememory 1048576 /lockdistillerparams 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/hrv (za stvaranje adobe pdf dokumenata najpogodnijih za visokokvalitetni ispis prije tiskanja koristite ove postavke. stvoreni pdf dokumenti mogu se otvoriti acrobat i adobe reader 5.0 i kasnijim verzijama.) /hun 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can be opened with acrobat and adobe reader 5.0 and later.) >> /namespace [ (adobe) (common) (1.0) ] /othernamespaces [ << /asreaderspreads false /cropimagestoframes true /errorcontrol /warnandcontinue /flattenerignorespreadoverrides false /includeguidesgrids false /includenonprinting false /includeslug false /namespace [ (adobe) (indesign) (4.0) ] /omitplacedbitmaps false /omitplacedeps false /omitplacedpdf false /simulateoverprint /legacy >> << /addbleedmarks false /addcolorbars false /addcropmarks false /addpageinfo false /addregmarks false /convertcolors /converttocmyk /destinationprofilename () /destinationprofileselector /documentcmyk /downsample16bitimages true /flattenerpreset << /presetselector /mediumresolution >> /formelements false /generatestructure false /includebookmarks false /includehyperlinks false /includeinteractive false /includelayers false /includeprofiles false /multimediahandling /useobjectsettings /namespace [ (adobe) (creativesuite) (2.0) ] /pdfxoutputintentprofileselector /documentcmyk /preserveediting true /untaggedcmykhandling /leaveuntagged /untaggedrgbhandling /usedocumentprofile /usedocumentbleed false >> ] >> setdistillerparams << /hwresolution [2400 2400] /pagesize [612.000 792.000] >> setpagedevice microsoft word numero_50_art_50_2422 m.a. khiat et alii, frattura ed integrità strutturale, 50 (2019) 595-601; doi: 10.3221/igf-esis.50.50 595 focused on fracture mechanics versus environmen effect of environmental conditions on the resistance of damaged composite materials sidi mohammed amine khiat, ramdane zenasni, mawloud hamdi university of mostaganem, algeria aminek@netcourrier.com, zramdane@netcourrier.com, mawloud.hamdi@univ-mosta.dz abstract. the present paper proposes a strength model for unidirectional composites with lin/epoxy. the model assumes that, a central core of broken fibers flanked by unbroken fibers which are subject to stress concentrations from the broken fibers. the approach of the model consists of using a modified shear lag model to calculate the ineffective lengths and stress concentrations around fiber breaks. in this paper, we attempt to incorporate in the proposed model the unidirectional composite property variation with temperature and moisture in order to predict even composite strength degradation. strength degradation is often seen as a result of changes in ineffective lengths at fiber breaks. subsequently, damage to the material can be estimated at the micromechanical scale under the effect of temperature and humidity. keywords. unidirectional composite; broken fibers; micromechanics; composite lin/epoxy. citation: khiat, m.a., zenasni, r., hamdi, m., effect of environmental conditions on the resistance of damaged composite materials, frattura ed integrità strutturale, 50 (2019) 595-601. received: 04.03.2019 accepted: 26.07.2019 published: 01.10.2019 copyright: © 2019 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. introduction arbon fibers reinforced polymers are widely applied for mechanical and structural components because of their high specific strength and rigidity, and excellent durability. because such reinforcing fibers are generally brittle and have a large scatter in strength, mechanical properties of composites have often been discussed from the viewpoint of materials reliability engineering. predicting the strength of these materials from the properties of their constituents is a task which has not yet been solved for all classes of materials. from literature, oldest models have been used for predicting the strength of polymer matrix composites are introduced by zweben and rosen [1, 2]. both authors related the failure of the fiber bundles in the company of the matrix material. they used the ineffective length to estimate the tensile strength. this was based on shear lag analysis. however, this model did not consider the effects of stress concentrations in the fibers adjacent to the broken one. phoenix et al. [3] obtained statistical strength and rupture lifetimes of unidirectional model carbon fiber/epoxy matrix micro-composites. their model consists of seven parallel carbon fibers forming approximate hexagonal packing embedded in an epoxy matrix. landis et al. [4] addressed the question of how to choose effective dimensions of the matrix springs connecting c http://www.gruppofrattura.it/va/50/2422.mp4 m.a. khiat et alii, frattura ed integrità strutturale, 50 (2019) 595-601; doi: 10.3221/igf-esis.50.50 596 neighboring fibers by modeling the matrix by finite elements and the fibers by continuous one-dimensional springs. their model also considered direct interactions of broken fibers with the next to nearest neighbors. landis and mcmeeking [5] later extended the work of landis et al. [4] to account for the effects of interface sliding, axial matrix stiffness and uneven fiber positioning, on stress concentrations surrounding the broken fiber. nedele and wisnom [6, 7] also showed that the peak stress concentration on fibers close to the broken fiber occurred slightly out of the rupture plane. case et al. [8] proposed an entirely different analysis technique to study the stress field in a general unidirectional composite material containing fiber fractures. the model is based on approximating annular ring of fibers to represent the unbroken neighboring fibers. multiple fiber breaks were modeled by a fiber discount methodology. case and reifsnider [9] addressed the problem of a penny shaped crack in the center of multiple concentric cylinders. the problem was solved by applying standard elasticity assumptions, with appropriate choice of stress functions in each constituent. this solution was applied to the problem of a fiber fracture in a unidirectional composite material by making geometrical assumptions. foster [10] proposed a direct numerical simulations and analytic models to predict the strength of fiber reinforced composites under tensile and flexural loading. the main strength prediction model used in the present paper is the proposed by model gao and reifsnider [11]. in order to predict the unidirectional composite strength degradation, we incorporated in this model the mechanical characteristics changes. the strength degradation is a result of changes in ineffective lengths at fiber breaks and the corresponding stress concentrations in intact neighboring fibers. after the calculation of stress concentrations and ineffective lengths of composite lin/epoxy. figure 1: schematic representation of unidirectional composite with broken fibers and adjacent regions [11]. micromechanics of tensile strength model ao and reifsnider [11], according to the model proposed by, tensile properties of fiber-reinforced composites are dependent on fiber strength and modulus, strength and chemical stability of matrix and efficiency of fiber/matrix interfacial bond in transferring loads. by introducing the micromechanical characterization with changes in temperature and moisture concentration, this model enables the prediction of changes in ineffective lengths at g   fiber   matrix   broken composite bulk composite zone of matrix yielding crack u0 u1 u2x r0 r0+d r0-d rf m.a. khiat et alii, frattura ed integrità strutturale, 50 (2019) 595-601; doi: 10.3221/igf-esis.50.50 597 fiber breaks and the corresponding stress concentrations in intact neighboring fibers. ineffective length  is generally defined as the length along a fiber from the site of fiber break, necessary to regain the capability to carry full load. in the case of lin fibers reinforced polymers, the fiber strength and modulus are relatively insensitive to temperature and moisture concentration variation, but epoxy matrix is influenced by theses environmental conditions. consequently, the interface fiber/matrix is con cerned by changes in matrix properties. however, because interfacial properties are difficult to measure, the interfacial bonding strength is assumed to be directly related to the yield stress of the matrix at interface, τ0. interfacial failure is said to occur when the shear stress of the interface reaches τ0 [12]. as illustrated in figure 1, the model considers a central core of i broken fibers which are flanked by unbroken fibers which are subject to stress concentrations due to broken fibers. the unbroken fibers are, in turn, flanked by a homogenous effective material that is considered to be strained uniformly. although the fiber bundle is not arrayed neatly, hexagonal array of fibers is assumed. it is also assumed that the influence of broken fiber is limited to a critical length, and that the stress concentration occurs to only neighboring fibers according to the arrangement. it is further assumed that broken core can be approximated by a homogeneous material with circular cross-section whose young’s modulus may be obtained by the rule-of-mixtures:      22 0 0 2 0 f f m mi a e i a r r d e e r d           (1) a and e are the area and modulus of hexagonal arrangement of i broken fibers flanked by unbroken fibers, respectively. in the present model, we have included the local damage by introducing a region of debonding and local plasticity where the shear strength of the matrix τ0 is multiplied by a constant η. in the region 0 x a  , the equilibrium equations are given by: 2 0 0 02 2 0f f d u ia e r dx     (2) 2 1 0 2 1 0 02 2 ( 2 2 ) ( ) 2 0 2 m f f f gd u ia e r d r u u r ddx         (3) where β is given as a function of geometry and fiber and matrix modulus and a is the half length of the region of debonding and plasticity. u0, u1 and u2 are tensile displacements in the three regions (figure 1). the solutions of the differential eqns. (2) and (3) are given below: 20 0 0 0 1 ( )u x x c r e    (4)    1 1 10 01 1 2 2 2 2 0 1 2 1 ( ) c 1 ( ) x x x c c r u x e e e x er r e             (5) similarly, for the region a x   where no interfacial yielding occurs, the equilibrium equations are: 2 2 0 0 0 1 02 ( ) 2 ( ) 0 2 md u ge r d r u u ddx      (6) 2 1 0 2 1 0 1 02 2 ( 2 2 ) ( ) 2 ( ) 0 2 2 m i f f f gd u gm n a e r d r u u r u u d ddx         (7) m.a. khiat et alii, frattura ed integrità strutturale, 50 (2019) 595-601; doi: 10.3221/igf-esis.50.50 598 the solutions of both differential equations are given by: 1 2 0 2 3( ) x x cu x c e c e x ec       (8) 1 21 1 1 2 3( ) (1 ) (1 ) x x c c u x c e c e x a a e          (9) all applications are made on unidirectional graphite epoxy specimen with length l, width w and thickness t. mechanical and geometrical characteristics of the studied considered material are given in tabs. 1 and 2, these data are drawn from ef (gpa) em (gpa) 0 (mpa) 0(gpa)  vf  27.6 4.2 25.2 3.10 0.43 0.53 1.0 table 1: mechanical properties of lin/epoxy specimen. l (mm) w (mm) t (mm) rf (mm) ni 152.4 12.7 1.016 0.0035 43 table 2: geometrical characteristics of lin/epoxy specimen. figure 2: evolution of the ineffective length according to the number of broken fibers with progressive variation of moisture concentration for t=20° and = 0.50. ineffective lengths at fiber breaks he ineffective length is defined as the length along a fiber from the break location that it takes for the fiber to regain its ability to carry full load. therefore it must include the zone of matrix yielding a (  a), as in constitutive laws of unidirectional composites, we distinguish three regions: a plastic, transitory and elastic zone, where σf is the t m.a. khiat et alii, frattura ed integrità strutturale, 50 (2019) 595-601; doi: 10.3221/igf-esis.50.50 599 fiber stress, δ is the ineffective length and “a “is the zone of matrix yielding. in figs. 2 and 3, we plot the evolution of the ineffective length according to the number of broken fibers with progressive variation of moisture concentration from 0% to 100% for t=20°c, and 120°c, respectively. ton figure 2, we can clearly see a superposition of all curves representative the ineffective length. we can deduce that for low temperatures, the variation of the moisture concentration does not have any effect on the ineffective length. with the increase in the temperature to 120°c (figure 3), the sensitivity of the ineffective length to the variation of the moisture concentration becomes more and more significant. at t = 120°c, the ineffective length for 43 broken fibers which is 0.11 mm for c=0% become 0.10 mm for c=100%. figure 3: evolution of the ineffective length according to the number of broken fibers with progressive variation of moisture concentration for t=120° and = 0.50. evolution of stress concentrations nder hygrothermal loading of unidirectional composites, the influence of interfacial adhesion on the tensile strength is mandatory effects on stress concentration in the fibers adjacent to broken fibers, and critical length of broken fibers. since the matrix is very sensitive to the variation in temperature, the adherence at interface region between fibers and matrix becomes very weak; thus the phenomenon of debonding appears, leading to the break of fibers. when a fiber breaks in the composite, there is a region of influence generated around the end of the broken fiber where a stress concentration exists. on the other hand, the load can be transferred back into the broken fiber with a shear stress at the fiber/matrix interface. to illustrate the effect of environmental conditions on the degradation of interfacial region surrounding the broken fibers, we plot in (figs. 4 and 5) the evolution of the stress concentrations according to the number of the broken fibers with progressive variation of moisture concentration from 0% to 100% for t=20°c and 120°c, respectively. in both figures, the stress concentrations become more significant with the increase in the number of broken fibers. thereafter, this stress concentration becomes relatively stable if the number of fibers becomes very large. for low temperatures, the effect of the moisture concentration on the stress concentration is almost negligible (fig. 4). the effect of the moisture concentration becomes increasingly significant with the increase in the temperature to 120°c (fig. 5). at t=120°c, a clear distinction appears between all curves; for example, with 43 broken fibers, the stress concentration varies from 1.17 for c=0% to 1.20 for c=100%. u m.a. khiat et alii, frattura ed integrità strutturale, 50 (2019) 595-601; doi: 10.3221/igf-esis.50.50 600 figure 4: evolution of the stress concentrations according to the number of broken fibers with progressive variation of moisture concentration for t=20° and = 0.50. figure 5: evolution of the stress concentrations according to the number of broken fibers with progressive variation of moisture concentration for t=120° and = 0.50. conclusions he aim of this work is to develop a better understanding of how temperature and moisture may affect the stress concentration of unidirectional composite materials, in terms of the number of broken fibers. by introducing the micromechanical characterization with changes in temperature and moisture concentration, the proposed model enables the prediction of changes in stress concentrations in the neighboring fibers. consequently, the interface fiber/matrix is concerned by changes in the matrix properties because the stress is transferred to the neighboring fibers. if the surrounding matrix becomes less stiff, the ineffective length becomes larger and the fiber fractures regions will interact more easily and may connect together to cause complete failure. t m.a. khiat et alii, frattura ed integrità strutturale, 50 (2019) 595-601; doi: 10.3221/igf-esis.50.50 601 references [1] rosen, b.w., 1964. tensile failure of fibrous composites. aiaa j. 2, 1985–1991. doi: 10.2514/3.2699. [2] zweben, c., 1968. tensile failure of fiber composites. aiaa j. 6, 2325–2331. doi: 10.2514/3.4990. [3] phoenix, s. l., schwartz, p. (1988). statistics for the strength and lifetime in creep-rupture of model carbon/epoxy composites, compos sci technol, 32, pp. 81-120. doi: 10.1016/0266-3538(88)90001-2. [4] landis, c. m., mcglockton, m. a. (1999). an improved shear lag model for broken fibers in composite materials, j compos mater, 33(7), pp. 667-680. doi: 10.1177/002199839903300704. [5] landis, c. m., mcmeeking, r. m. (1999). stress concentrations in composites with interface sliding, matrix stiffness, and uneven fiber spacing using shear lag theory, int j solids struct, 36, pp. 4333-4361. doi: 10.1016/s0020-7683(98)00193-0. [6] nedele, m. r. (1994). three-dimensional finite element analysis of the stress concentration at a single fiber break, compos sci technol, 51, pp. 517-524. doi: 10.1016/0266-3538(94)90084-1. [7] nedele, m. r., wisnom, m. r. (1994). stress concentration factors around a broken fiber in a unidirectional carbon fiber-reinforced epoxy, composites, 27, pp. 549-557. doi: 10.1016/0010-4361(94)90183-x. [8] case, s. w., carman, g. p., lesko, j. j., fajardo, a. b., reifsnider, k. l., (1995). fiber fracture in unidirectional composites, j compos mater, 29(2), pp. 208-228. doi: 10.1177/002199839502900205. [9] case, s. w., reifsnider, k. l. (2006). micromechanical of fiber fracture in unidirectional composite materials, int j solids struct, 33(26), pp. 379-381. doi: 10.1016/0020-7683(95)00214-6 [10] foster, g. c. (2008). tensile and flexure strength of unidirectional fiber-reinforced composites: direct numerical simulations and analytic models, master of science in engineering mechanics, virginia polytechnic institute and state university. [11] gao, z., reifsnider, k. l. (1993). micromechanics of tensile strength in composite systems, composite materials: fatigue fract, fourth volume, astm stp 1156, pp. 453-470. doi: 10.1520/stp24745s. [12] curtin, w. a. and takeda, n. (1998). tensile strength of fiber-reinforced composites: ii. application to polymer matrix composites, j compos mater., 32, pp. 2060-2081. << /ascii85encodepages false /allowtransparency false /autopositionepsfiles true /autorotatepages /none /binding /left /calgrayprofile (dot gain 20%) /calrgbprofile (srgb iec61966-2.1) /calcmykprofile (u.s. web coated \050swop\051 v2) /srgbprofile (srgb iec61966-2.1) /cannotembedfontpolicy /error /compatibilitylevel 1.4 /compressobjects /tags /compresspages true /convertimagestoindexed true /passthroughjpegimages true /createjobticket false /defaultrenderingintent /default /detectblends true /detectcurves 0.0000 /colorconversionstrategy /cmyk /dothumbnails false /embedallfonts true /embedopentype false /parseiccprofilesincomments true /embedjoboptions true /dscreportinglevel 0 /emitdscwarnings false /endpage -1 /imagememory 1048576 /lockdistillerparams false /maxsubsetpct 100 /optimize true /opm 1 /parsedsccomments true /parsedsccommentsfordocinfo 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/hrv (za stvaranje adobe pdf dokumenata najpogodnijih za visokokvalitetni ispis prije tiskanja koristite ove postavke. stvoreni pdf dokumenti mogu se otvoriti acrobat i adobe reader 5.0 i kasnijim verzijama.) /hun 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/pdfxoutputintentprofileselector /documentcmyk /preserveediting true /untaggedcmykhandling /leaveuntagged /untaggedrgbhandling /usedocumentprofile /usedocumentbleed false >> ] >> setdistillerparams << /hwresolution [2400 2400] /pagesize [612.000 792.000] >> setpagedevice microsoft word 2294 o. plekhov et alii, frattura ed integrità strutturale, 48 (2019) 451-458; doi: 10.3221/igf-esis.48.43 451 focussed on “crack paths” a model of energy dissipation at fatigue crack tip in metals oleg plekhov, aleksei vshivkov, anastasia iziumova institute of continuous media mechanics russian academy of sciences ural branch poa@icmm.ru, vshivkov.a@icmm.ru, fedorova@icmm.ru balasubramaniam venkatraman indira gandhi centre for atomic research, tamil nadu, kaplakkam, india bvenkat@igcar.gov.in abstract. experimental and numerical studies investigating fatigue crack growth were conducted on flat samples made of stainless steel aise 304 and titanium alloy grade 2. the heat flux from the crack tip caused by plastic deformation localization was measured using the contact heat flux sensor previously developed by the authors. this provides a possibility to find a correlation between energy dissipation and crack propagation rate under fatigue uniaxial loading with constant stress intensity factor and under biaxial loading with constant stress amplitude. the experiments with constant stress intensity factor have shown a decrease in energy dissipation at constant crack rate and stress ratio r=σmin/σmax=-1 (r=0). a theoretical analysis of the stress field at the fatigue crack tip has been carried out to explain this phenomenon. based on the obtained results, the heat flux from the crack tip is represented as the sum of two functions describing energy dissipation in monotonic and reversible plastic zones separately. it has been shown that dissipation in a reversible plastic zone is a function of the applied stress amplitude only. this causes a decrease of energy dissipation at constant stress intensity factor. the proposed phenomenology was successfully verified by testing both materials under biaxial loading. keywords. fatigue crack; dissipated energy; plastic deformation zone. citation: plekhov, o., vshivkov, a., iziumova, a., venkatraman, b., a model of energy dissipation at fatigue crack tip in metals, frattura ed integrità strutturale, 48 (2019) 451-458. received: 28.11.2018 accepted: 04.02.2019 published: 01.04.2019 copyright: © 2019 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. introduction he kinetics of fatigue crack growth over a wide range of crack propagation rates can be described using a correlation with stress intensity factor (paris`s law). this correlation is the result of approximation of a large amount of experimental data and it does not explain the physical nature of this process. t http://www.gruppofrattura.it/va/48/2294.mp4 o. plekhov et alii, frattura ed integrità strutturale, 48 (2019) 451-458; doi: 10.3221/igf-esis.48.43 452 many authors proposed other correlations between the fatigue crack rate and different mechanical-structural parameters. for instance, the j-integral, the work of plastic deformation, the size of plastic deformation zone, the amount of dissipated energy were used as a parameter determining the crack propagation rate [1-4]. the propagating crack interacts with the material which can be considered as a complex hierarchical structure. mechanical behavior at different spatial levels can be described in terms of energy concepts. monitoring of energy dissipation during fatigue crack propagation can give significant information about the kinetics of deformation processes and the current crack propagation rate [5-8]. infrared thermography is an efficient method for estimating energy dissipation under mechanical testing. the main difficulty associated with application of this technique to the study of energy dissipation is related to the uncertainties in the solution of the inverse problem. the determination of energy dissipation under deformation can be obtained by the development of an additional system for direct monitoring of a heat flow. such a system based on the seebeck effect was developed at icmm ub ras [9]. in this work, we have derived an equation describing the evolution of plastic work at the crack tip. following the idea given in [10], we have divided the plastic work and, as a consequence, energy dissipation at crack tip into two parts corresponding to reversible (cyclic) and monotonic plastic zones. analysis of this approximation has shown the independence of energy dissipation in cyclic plastic zone from the crack growth. this dissipation is fully determined by the spatial size of a cyclic plastic zone and the characteristic diameter of the yield surface. for isotropic hardening materials, the change of the applied stress amplitude leads to the change of the characteristic diameter of the yield surface and, as consequence, to energy dissipation at a constant crack rate. dissipation in the monotonic plastic zone is a function of both crack rate and characteristic diameter of the yield surface. this gives a well know correlation between fatigue crack rate and dissipated energy [4,7]. to confirm the proposed approximation, we have compared it with the results of two fatigue crack propagation tests (uniaxial loading with constant stress intensity factor and biaxial loading with different biaxial coefficients). the experiments with constant stress intensity factor were reported in [11] for the first time. the main unexpected results of these experiments have shown that the energy dissipation measured by the contact heat flux sensor decreases during the crack propagation with the constant stress intensity factor. the proposed approximation demonstrates good qualitative agreement with the experimental data obtained during the uniaxial test. the developed approach gives us an opportunity to generalize it for complex loading conditions. analysis of the experimental data on crack propagation under biaxial loading has revealed similar qualitative features of energy dissipation [8]. we observed two stages of energy dissipation: constant value at the first stage and sharp increase at its final stage. the comparison of the phenomenological predictions and the obtained experimental results shows good qualitative agreement as well. experimental setup wo types of experiments were carried out to analyze energy dissipation under fatigue crack propagation in metals. we conducted uniaxial tests at constant stress intensity factor and tests on biaxial loading with a constant stress amplitude. fig. 1 shows the geometry of samples examined during the tests. samples for uniaxial testing were made of stainless steel aise 304. the experiments were carried out at bundeswehr university munich. the samples were subjected to cyclic loading of 20 hz at constant stress intensity factor and at loading ratio r = -1. the crack length was measured by the potential drop method. the electrical potential drop method has been chosen due to its ability to monitor fatigue crack propagation and to set the stress intensity factor controlling a feedback. in this case, the potential method provides sensitivity up to 0.02 mm for a d.c. (direct current) of 5 a. the experimental program includes four tests with constant stress intensity factor. the constant stress intensity factors are 15 mpa m1/2, 17.5 mpa m1/2, 20 mpa m1/2 and 22.5 mpa m1/2, and the crack rates are 2.0076e-08 m/cycle, 6.6391e-08 m/cycle, 1.0245e-07 m/cycle, and 1.7177e-07 m/cycle, respectively. the first part of each experiment was performed subject to loading with a constant stress amplitude to initiate a 1 mm long fatigue crack, and the second part – at constant stress intensity factor until a 8 mm long crack was obtained. a similar experimental program was realized at icmm ub ras. the detailed description of the mechanical properties, geometry of the samples and corresponding test conditions are given in [9]. the russian steel analogous to that used to prepare samples of different geometries was tested for the loading ratio r=0. the stress intensity factors were equal to 25 mpa m1/2 and 30 mpa m1/2 (for crack rates of 1.4e-07 m/cycle, 1.65e-07 m/cycle, respectively). the results of both experimental programs are similar. in the future analysis, we are going to use the results obtained for the aise 304 t o. plekhov et alii, frattura ed integrità strutturale, 48 (2019) 451-458; doi: 10.3221/igf-esis.48.43 453 samples through the recording of both crack propagation modes at constant stress amplitude and at constant stress intensity factor in each test. a) b) figure 1: geometries of samples: for uniaxial test (a), for biaxial test (b). samples for biaxial testing were made of titanium alloy grade 2 and were tested in the servo-hydraulic biaxial test system biss bi-00-502 at kazan scientific center of the russian academy of sciences. while testing, the samples were subjected to cyclic loading of 10 hz at constant stress amplitude and at different biaxial coefficients η=px/py (1, 0.7, 0.5) and various ratios r (0.1, 0.3, 0.5). the crack length in the course of the experiment was measured by applying the optic method. to analyze the dissipated energy at the crack tip, a contact heat flux sensor was used. the proposed sensor is based on the seebeck effect, which is the reverse of the peltier effect. the peltier effect is a thermoelectric phenomenon, in which the passage of electric current through a conducting medium leads to the generation or absorption of heat at the point of contact (junction) of two dissimilar conductors. the quantity of heat and its sign depend on the type of materials in contact and on the electric current direction and strength. a thermal contact between the sample and the sensor is provided by the introduction of a thermal paste. these sensors were calibrated using a device reproducing the sample during the test with a controlled heat flux. a) b) figure 2: stress intensity factor/applied load (a) and energy dissipation/crack length (b) histories during the uniaxial fatigue test. 0 500 1000 1500 2000 2500 3000 3500 4000 0 20 40 s tr e s s in te n s it y f a c to r, m p a time, s 0 500 1000 1500 2000 2500 3000 3500 4000 0 5000 10000 l o a d , n stress intensity factor load 0 500 1000 1500 2000 2500 3000 3500 4000 0 2 4 6 8 10 c ra c k le n g th , m m time, s 0 500 1000 1500 2000 2500 3000 3500 4000 0 0.1 0.2 0.3 0.4 0.5 h e a t fl u x , w crack length heat flux o. plekhov et alii, frattura ed integrità strutturale, 48 (2019) 451-458; doi: 10.3221/igf-esis.48.43 454 results of fatigue experiments he results of the uniaxial fatigue test are presented in fig. 2. the test includes part with a constant stress amplitude up to the 2200-th second. we can observe a stable accelerated crack in the 500-th to 2200-th second interval accompanied by energy dissipation increase. from the 2200-th second, the stress intensity factor was kept constant. it leads to the decrease of the stress amplitude (fig.2a) and energy dissipation and results in nearly uniform crack propagation (fig.2b). the results of the biaxial fatigue tests are presented in fig. 3. fig. 3a shows a plot of crack length versus time. fig. 3b presents evidence that the fatigue crack propagates in the paris regime. a) b) figure 3: crack length versus time under biaxial loading conditions (different lines indicate different values of biaxial coefficients) (a), paris curve (b) for biaxial test. theoretical analysis of heat dissipation ollowing the idea proposed in [10], we can start from a relationship between elastic and real deformation at the crack tip: 1 2 ij , ef el ij s g g          (1) where g – the shear modulus, gs – secant shear modulus. eqn. (1) was originally proposed in [12] as a result of photo elastic experiment data treatment. using the rambergosgood relationship as the first approximation of mechanical behaviour of material under consideration 0 , n a g             we can write the following estimation for octahedral stress and link it with an elastic solution 1 21 1 2(1 ) 1 3 , 1 n el oct octn b b              (2) 0 0.5 1 1.5 2 2.5 time, s 104 0 10 20 30 40 50 c ra ck le n g th , m m n=1; r=0.1 ;f=7kn n=1; r=0.1 ;f=12kn n=0.5; r=0.1 ;f=10kn n=0; r=0.1 ;f=10kn n=1; r=0.5 ;f=12kn n=1; r=0.5 ;f=10kn 10 20 30 40 50 60 70 sterss intensity factor, mpa 10-6 10-5 10-4 c ra ck r a te , m /c yc le n=1; r=0.1 ;f=7kn n=1; r=0.1 ;f=12kn n=0.5; r=0.1 ;f=10kn n=0; r=0.1 ;f=10kn n=1; r=0.5 ;f=12kn n=1; r=0.5 ;f=10kn approximation t f o. plekhov et alii, frattura ed integrità strutturale, 48 (2019) 451-458; doi: 10.3221/igf-esis.48.43 455 where 0, ,a n – material constants, 0 0 , , n e oct e e ga b               – elastic limit. the energy of plastic deformation in representative volume near the crack tip can be estimated as follows 1 0 3 3 . 2 2 1 n n e oct p oct oct e e an u d n                         (3) the energy increment caused by crack advance under monotonic loading can be written as 0 3 , 2 n ne p e d du an dl dl             (4) where l crack length. using definition 1 1 2 2 3 el p eoct e e e r fkf rr              (here k – stress intensity factor, rp – estimation for plastic zone size, r,  – polar coordinates, fe – function of polar coordinate , we can rewrite eqn. (4) as 0 3 . 2 n ne p e d d du an dl d dl               (5) where 1 sin cos . 2 p e e e p e r dfd f c f dl r dr f r               (6) to analyse plastic deformation at the crack tip under cyclic loading we need to divide energy dissipation in cyclic and monotonic plastic zones at the crack tip .tot cyc monp p pu u u  (7) the energy of representative volume at cyclic zone can be estimated as 3 2 cyc p ec pcu   , (8) where ec – characteristic size of the yield surface,  , 1 1 pc oct c ec sg g            – amplitude of plastic deformation under an assumption of the validity of ramberg-osgood relationship ship, ,oct c – stress change in the representative volume. the full energy of cyclic plastic zone can be calculated as a double integral over the region (s) bounded on the outside of the monotonic plastic deformation zone and inside of the fracture zone ,2 0 3 1 1 2 1 2 oct ccyc p ec s ecs u rdrd g g                  (9) the simple approximation of plastic zone boundary can be given by ,p c er r f , for cyclic-fracture zone boundary – o. plekhov et alii, frattura ed integrità strutturale, 48 (2019) 451-458; doi: 10.3221/igf-esis.48.43 456 , ec p c e fr r r f    . (10) the energy increment in cyclic plastic zone can be written as ,2 0 1 1 3 cyc el p oct c oct ec el s octs du d d rdrd dn g g dnd               . (11) the integration of eqn. (5) gives . 0 cyc pdu dn  .. it means that dissipation in cyclic plastic zone doesn’t depend on the crack advance but it is fully determined by the applied load. the energy dissipation in monotonic plastic zone can be estimated as 3 2 mon p e pu   . (12) energy increment per one cycle can be written as 1 0 1 1 3 mon el p oct oct e oct el s octs du d d dl rdrd dn g g dl dnd                 (13) solution of (13) for the case of 0 pdr da  gives linear relationship between energy increment and crack rate. finally, the eqns. (11) and (13) allow us to propose the following approximation for energy of plastic deformation at the fatigue crack tip    2 2 2 21 2 1 2, , tot p p p du dl dl w a r w a r a a a a dn dn dn        , (14) where a – applied stress amplitude which determines the diameter of yield surface. figure 4: energy dissipation histories during the biaxial test carried at constant stress amplitude (solid line – experimental results, dotted line –approximation (14)). o. plekhov et alii, frattura ed integrità strutturale, 48 (2019) 451-458; doi: 10.3221/igf-esis.48.43 457 figure 5: energy dissipation histories during the uniaxial test carried out at constant stress amplitude and at constant stress intensity factor (solid line – experimental results, dotted line –approximation (14)). the process of heat dissipation is determined by the plastic work. this relationship could be complex due to the peculiarities of energy storage in material structure but taking into account the simplicity of eqn. (13) we will use the linear dependence of heat dissipation versus energy of plastic deformation for the first approximation of experimental results. the eqns. (2)-(4) are used for the qualitative analysis of plastic deformation into one loading cycle. qusistatic loading and unloading of materials near crack tip are considered to approximate dissipation caused one cycle. the analysis allows us to divide the dissipations caused by monotonous and revers loadings and propose both explanation and approximation for energy dissipation process. the qualitative calculation of energy dissipation based on this model will request more precise analysis and determination and correct exponent in ramberg-osgood model. figs. 4, 5 present the comparison of approximation (14) and results of the contact heat flux sensor. the eqn. (14) gives a good qualitative description of peculiarities of heat dissipation in both regimes with the constant stress amplitude and constant stress intensity factor. in case of uniaxial loading for constant stress amplitude the plastic work and, as a consequence, energy dissipation at the crack tip is determined by crack rate as is shown in [7,8] but for constant crack rate we can observe the regimes with the decrease of the heat dissipation caused by the decrease of the applied stress amplitude. for biaxial loading there is good agreement between experimental and theoretical results. conclusions n this work, experimental and theoretical studies of energy dissipated at fatigue crack tip in aise 304 steel were carried out. two types of experiments were performed: uniaxial loading tests and biaxial loading tests with constant stress amplitude for different values of the biaxial coefficient. for samples under uniaxial loading, two regimes of crack propagation were realized: constant stress amplitude and constant stress intensity factor. the results of the experiments have shown that at constant stress amplitude there is an increase in energy dissipation correlated with the fatigue crack rate. crack propagation at constant stress intensity factor is accompanied by a decrease in energy dissipation. this effect was observed independently in two different experimental programs. to provide an adequate explanation for the observed results, a theoretical analysis was performed in order to study the plastic work at the fatigue crack tip taking into account the evolution of both monotonic and cyclic plastic zones. this analysis allowed us to propose a simple approximation for energy dissipation at the fatigue crack tip. the obtained theoretical results give a good qualitative description of the specific features of energy dissipation in both regimes: loading with constant stress amplitude and loading with constant stress intensity factor. for constant stress amplitude, plastic work and, as a consequence, energy dissipation at the crack tip were determined by the crack rate, but for constant crack rate regime the scenario with a drop in energy dissipation takes place. in the case of biaxial loading there were two stages of energy dissipation: a constant heat flux accompanied by crack initiation and a sharp increase in energy dissipation associated with the occurrence of a large crack. the theoretical approach proposed for calculating energy dissipation correlates well with the experimental results. i o. plekhov et alii, frattura ed integrità strutturale, 48 (2019) 451-458; doi: 10.3221/igf-esis.48.43 458 acknowledgements his work was supported by the russian foundation for basic research (grant no. 16-51-48003). references [1] matvienko, yu.g., morozov, e m. (2004). calculation of the energy j-integral for bodies with notches and cracks, international journal of fracture, 125, pp. 249-261. [2] rosakis, p., rosakis, a.j., ravichandran, g., hodowany, j. (2000). a thermodynamic internal variable model for the partitional of plastic work into heat and stored energy in metals, j. mech. phys. solids, 48, pp. 581-607. [3] oliferuk, w., maj, m., raniecki, b. (2004). experimental analysis of energy storage rate components during tensile deformation of polycrystals, materials science and engineering, 374, pp. 77-81. [4] izyumova, a., plekhov, o. (2014). calculation of the energy j-integral in plastic zone ahead of a crack tip by infrared scanning, ffems, 37, pp. 1330–1337. [5] meneghetti, g., ricotta, m. (2016). evaluating the heat energy dissipated in a small volume surrounding the tip of a fatigue crack, international journal of fatigue, 92(2), pp. 605-615. [6] risitano, a., risitano, g. (2013). cumulative damage evaluation in multiple cycle fatigue tests taking into account energy parameter, international journal of fatigue, 48, pp. 214-222. [7] ranganathan, n., chalon, f., meo, s. (2008). some aspects of the energy based approach to fatigue crack propagation, international journal of fatigue, 30(10–11), pp. 1921-1929. [8] bär, u., vshivkov, a., plekhov, o. (2015). combined lock-in thermography and heat flow measurements for analysing heat dissipation during fatigue crack propagation, fracture and structural integrity, 34, pp. 521-530. [9] vshivkov, а., iziumova, a., bär, u., plekhov, o. (2016). experimental study of heat dissipation at the crack tip during fatigue crack propagation, frattura ed integrità strutturale, 35, pp. 131-137. [10] raju, k. n. (1972). an energy balance criterion for crack growth under fatigue loading from considerations of energy of plastic deformation, international journal of fracture mechanics, 8(1), pp. 1-14. [11] bär, u. (2016). determination of dissipated energy in fatigue crack propagation experiments with lock-in thermography and heat flow measurement, procedia structural integrity, 2, pp. 2105-2112. [12] dixon, j.r. (1965). stress and strain distributions around cracks in sheet materials having various work-hardening characteristics, ministry of technology, national engineering laboratory, materials group: east kilbride, glasgow, scotland, pp. 224-244. t << /ascii85encodepages false /allowtransparency false /autopositionepsfiles true /autorotatepages /none /binding /left /calgrayprofile (dot gain 20%) /calrgbprofile (srgb iec61966-2.1) /calcmykprofile (u.s. web coated \050swop\051 v2) /srgbprofile (srgb iec61966-2.1) /cannotembedfontpolicy /error /compatibilitylevel 1.4 /compressobjects /tags /compresspages true /convertimagestoindexed true /passthroughjpegimages true /createjobticket false /defaultrenderingintent /default /detectblends true /detectcurves 0.0000 /colorconversionstrategy /cmyk /dothumbnails false /embedallfonts true /embedopentype false /parseiccprofilesincomments true /embedjoboptions true /dscreportinglevel 0 /emitdscwarnings false /endpage -1 /imagememory 1048576 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can be opened with acrobat and adobe reader 5.0 and later.) >> /namespace [ (adobe) (common) (1.0) ] /othernamespaces [ << /asreaderspreads false /cropimagestoframes true /errorcontrol /warnandcontinue /flattenerignorespreadoverrides false /includeguidesgrids false /includenonprinting false /includeslug false /namespace [ (adobe) (indesign) (4.0) ] /omitplacedbitmaps false /omitplacedeps false /omitplacedpdf false /simulateoverprint /legacy >> << /addbleedmarks false /addcolorbars false /addcropmarks false /addpageinfo false /addregmarks false /convertcolors /converttocmyk /destinationprofilename () /destinationprofileselector /documentcmyk /downsample16bitimages true /flattenerpreset << /presetselector /mediumresolution >> /formelements false /generatestructure false /includebookmarks false /includehyperlinks false /includeinteractive false /includelayers false /includeprofiles false /multimediahandling /useobjectsettings /namespace [ (adobe) (creativesuite) (2.0) ] /pdfxoutputintentprofileselector /documentcmyk /preserveediting true /untaggedcmykhandling /leaveuntagged /untaggedrgbhandling /usedocumentprofile /usedocumentbleed false >> ] >> setdistillerparams << /hwresolution [2400 2400] /pagesize [612.000 792.000] >> setpagedevice microsoft word numero_55_art_11_2905 d. benyarou et alii, frattura ed integrità strutturale, 55 (2021) 145-158; doi: 10.3221/igf-esis.55.11 145 parametric study of friction stir spot welding (fssw) for polymer materials case of high density polyethylene sheets: experimental and numerical study djilali benyerou, el bahri ould chikh, habib khellafi, hadj miloud meddah university of mascara, lste laboratory, 29000, mascara, algeria. djilali.benyerou@univ-mascara.dz, https://orcid.org/0000-0003-1457-4403 b.ouldchikh@univ-mascara.dz, https://orcid.org/0000-0002-7360-7677 khellafi29@univ-mascara.dz, hm.meddah@univ-mascara.dz ali benhamena university of mascara, lpq3m laboratory, 29000, mascara, algeria ali.benhamena@univ-mascara.dz kaddour hachelaf, abdellah lounis university of mascara, lste laboratory, 29000, mascara, algeria kaddour.hachellaf@univ-mascara.dz, lounis.abdallah@univ-mascara.dz abstract. friction stir spot welding (fssw) is a very important part of conventional friction stir welding (fsw) which can be a replacement for riveted assemblies and resistance spot welding. this technique provides high quality joints compared to conventional welding processes. the fssw is a new technology adopted to join various types of metals such as titanium, aluminum, magnesium. it is also used for welding polymer materials which are difficult to weld by the conventional welding process. in various industrial applications, high density polyethylene (hdpe) becomes the most used material. the parameters and mechanical properties of the welds are the major problems in the welding processes. in this paper, we have presented a contribution in finite element modeling of the fssw process using finite element method (fem). the objective of this paper is to study the hdpe plates resistance of stir spot welding joints (fssw) using tensile test in the experimental part. first, we show the experimental tests results of hdpe plates assembled by fssw. three-dimensional numerical modeling by the finite element method makes it possible to determine the best representation of the weld joint for a good prediction of its behavior. comparison of the results shows that there is a good agreement between the numerical modeling predictions and the experimental results. citation: benyarou, d., ould chikh, b., khellafi, h., meddah, h.m, benhamena, a., hachelaf, k., lounis, a., parametric study of friction stir spot welding (fssw) for polymer materials case of high density polyethylene sheets: experimental and numerical study, frattura ed integrità strutturale, 55 (2021) 145-158. received: 26.08.2020 accepted: 17.11.2020 published: 01.01.2021 copyright: © 2021 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. https://youtu.be/ktyjcs2-t6g d. benyarou et alii, frattura ed integrità strutturale, 55 (2021) 145-158; doi: 10.3221/igf-esis.55.11 146 keywords. polymers; tensile tests; high-density polyethylene; fssw; numerical analysis; fem. introduction olymer is a word of greek origin, and it means poly (many) and mere (repetition unit). by the origin of the word, it can be inferred that polymers are structures formed by the repetition of many mere. the mere are connected by covalent bonds and the raw material that gives rise to the polymer is the monomer, which is the basic unit of repetition of polymers. the polymer can have very different characteristics, according to the type of monomer that forms it, the average number of monomers per polymeric chain and the type of covalent bond that is present. the polymer pipes offer several advantages: they have good resistance to wear and corrosion, low density, low cost, easy of installation, they have durability and reasonable mechanical resistance, production of complex shape [1, 2]. these authors showed that the fracture behavior of high density poly-ethylene (hdpe) pipe is related to the loading condition, the shape and the position of crack in the wall of pipe. in other words, it is known, that during the process of forming solid materials, the plastic instability phenomena often control the appearance and performance of the finished product according to moulai ali et al. [3], khellafi habib [4], and abdel nour zaim [5,6]. these authors examined the effect of stress triaxiality on the mechanical behavior response of polyvinylchloride (pvc), polybutylene terephthalate (pbt) and the thermoplastic copolyetherester (tpc) under large plastic strain. they have concluded that the damage evolution of pvc and pbt in service has influenced by the level of stress triaxiality. in addition, polymer pipes have another major advantage is that they can be assembled by fusion techniques which efficient and easy to implement techniques in industry field. mostly, electrofusion welding and butt fusion welding are common methods for joining polyethylene pipes used for water and gas distribution in national and worldwide levels. pathak and pradhan [7] performed several experimental studies related to electrofusion and butt fusion welding of hdpe pipe in order to study the effect of some parameters such as: starting welding voltage, specific fusion time, and cooling time for electrofusion welding and for the butt fusion welding the heating plate temperature, drag pressure has been analyzed and its effects on the tensile strength of hdpe pipe. they concluded that the welding parameters of any welding process must be optimized. for this study, the optimized parameters for electro fusion welding of this hdpe pipes are welding voltage, specific fusion time, cooling time and optimized parameters for butt welding are heating plate temperature, drag pressure, welding pressure. on the other hand, it is known that the conventional welding techniques (fusion welding) are more prone to the formation of defects in the material during the solidification process after melting the material, which leads to a decrease in the mechanical properties of welded joints. in addition, the procedure for conducting fusion welds requires both greater training for the operator and the use of appropriate clothing to ensure his safety. the need for protective gas during the process, affects the environment. also, the use of the filler metal and the high energy levels required to perform fusion welds, increase the costs of the welding process. in this context, bouchouicha et al. [8] analyzed the evolution of the energy at the crack tip taking into account the different conditions such as the mechanical aspects, stress conditions, geometry of the specimen and the effects of closing. the use of solid state welding (friction stir welding: fsw) is an alternative to make joints in different types of materials: ferrous, non-ferrous, polymers, composites and different materials. fsw was developed in 1991 at the welding institute in england. the fsw technique, offers advantages in quality, as it avoids the melting of the material, which means a decrease in the tendency to form defects and better mechanical properties compared with conventional welding techniques [9]. the low heat input reduces distortions in the part especially in the weld region. the procedure for performing welds using the fsw technique is simple, does not require any filler metal and does not present any risks to the operator health compared to the fusion welding. in fsw process, several parameters are adjusted and must be checks to ensure the quality of the joints. according to thomas and nicholas [10] and mishra and ma [11], friction welding is part of a new generation of welding processes, which was recently developed with the ability to weld high-strength aluminum alloys, which are difficult to be welded by fusion welding process. lee et al. [12] presented an experimental analysis in order to study the weldability of hot rolled az31b-h24 magnesium alloy by fsw. they found that the welding parameters such as tool rotation speed and linear welding speed has a great effect on the tensile strength of welded joints, an insufficient heat input, which was generated in the case of higher linear speed and lower rotation speed leading to an inner void or lack of bonding in the stir zone. in the industry field of mazda [13], the engineers have introduced a new welding technology in the production of the rx-8 sports car. use of the technology enabled mazda to reduce electricity consumption by 99%. sundaram and murugan [14] investigated experimentally the effect of friction stir p d. benyarou et alii, frattura ed integrità strutturale, 55 (2021) 145-158; doi: 10.3221/igf-esis.55.11 147 welding parameters on the tensile strength of dissimilar welding joints of aluminium alloys welded by fsw. they indicated that the increase in tool rotational speed and welding speed leads to the increase in the tensile strength of the welded joints. in the same context, the effect of tool rotation speed on the microstructure and mechanical properties of butt welded dissimilar pure copper/brass alloy plates by friction stir welding have been carried out by barlas and uzun [15]. they have concluded that the grain size and the onion ring formation in the weld nugget zone and the mechanical properties of the joints were affected by tool rotation speed, these authors showed that the tensile strength of the joints was lower than that of the copper and brass base metals. a further examination of this subject can be found in [15-19]. welding techniques for plastics are nowadays consolidated processes in several industrial areas [20, 21]. strand et al. [22] carried out experimental work to investigate the relationships between several parameters of fsw process and its effect on the microstructural and flexural properties of a polymer welded joints. they showed that the pin diameter, feedrate, shoe temperature, and pressure time has a significant impact on mechanical properties of welded joint. arici and selale [23] investigate the effect of tool tilt angle on friction stir welding (fsw) of polyethylene (pe). they showed that the welding parameters had significant effects on tensile properties and fracture locations of the welds. the tensile strength decreased with increasing tool tilt angle. similar study was carried out by kiss and czigany [24] to investigate the effect of rotation and translation speed on the joint strength of welded polypropylene sheets by fsw process. aydin [25] investigate the weldability of uhmw-polyethylene via friction stir welding method. this author concluded that the preheating process increases the tensile strength of welded joint. several authors [26-28] have presented a very interesting and comprehensive review regarding the effect and optimization of friction stir welding process parameters on the tensile strength of polymeric materials welded by fsw. in 2001, a new derivative of friction stir welding (fsw) appeared, it is called the friction stir spot welding (fssw). it was developed in the automotive industry to replace resistance spot welding for aluminum sheets [29]. gerlich et al. [30] studied the feasibility of using the fssw process using dissimilar materials, in the case of aluminum and magnesium. these results reveal that the level of fracture loads is related to the energy input during fsw spot welding. also, they showed a partial pull-out of the stir zone occurred in high energy input fsw spot welds with fracture initiating from unbonded regions located on either side of the welded joint. arici and mert [31] noticed the influence of tool penetration depth and dwell time on joint strength of lap joints of polypropylene welded by fssw. it was concluded that the increases of dwell time improve the tensile shear and change the failure mode of welded joints. in the same subject, bilici and his co-authors [32-35], presented interesting experimental results on friction stir spot welding of thermoplastics. they found that the tool geometry, tool rotational speed, tool plunge depth and dwell time were determined to be important in the joint formation and its strength. the (fsw) and (fssw) welding provide significant advantages over traditional welding. they make it possible to weld materials which are difficult or impossible to weld with other welding techniques [13, 36]. fssw have been employed for a wider range of metals including titanium, magnesium, copper and even high strength steels, also it has been successfully applied to thermoplastic sheets since 2003 [22]. this type of materials are employed for replacing metals in a wide range of industrial fields as, aerospace, automotive industry, navy, armament… because of their advantages, such as reduced manufacturing cost, weight saving, high thermal insulation, the investment of less equipment, excellent mechanical properties, respecting the environment, weaker requirement of energy and aptitude for automation [28]. in fssw, frictional heat is generated by the interaction of the tool pin with the material that becomes pasty and extrudes vertically. the tool shoulder then exerts an upsetting action on the stirred material to form the weld nut. the operation of friction stir spot welding fssw consists in providing heat to basic material by friction between the tool and the plates to be welded and by plastic dissipation. the fssw process of thermoplastics consists of four phases; plunging, stirring, solidifying and retracting as shown in fig. 1. in fssw process, firstly the two plates to be welded are fixed to restrict the deformations caused by the welding process. the fssw process has four stages: plunging, stirring, solidifying and retracting according to fig. 1 [32-34]. tool rotates and plunged into the attached work pieces with force to a certain depth. in the stirring phase the tool doesn’t plunge. this operation generates a frictional heat. then, heated and softened material adjacent to the tool deforms plastically, and a solid state bond is made between the surfaces of the upper and lower sheets. the tool consists of two parts, the shoulder and the pin. the pin generates friction heat, deforms the material around it and stirs the heated material [30]. in fssw, several parameters such as the geometry of the tool, the rotation speed, the plunge depth, the dwell time and material type affect directly the friction stir spot welding nugget formation and the weld strength [32]. in this work, we focus on the weldability of a polymer (hdpe) by the friction stir spot welding technique (fssw). these polymers are used in water and gas transporting pipes (chiali group) [37-40]. this study is a contribution to a parametric analysis in order to optimize the welding parameters which are necessary to understand their effects in order to obtain a good weld quality. and to understand the behavior of the assembly by proposing a numerical d. benyarou et alii, frattura ed integrità strutturale, 55 (2021) 145-158; doi: 10.3221/igf-esis.55.11 148 model which predicts the global behavior of the weld using the finite element method to optimize the fssw welding parameters of hdpe sheets. we recall also, that the present study is an extension of previous studies [37, 38]. figure 1: friction stir spot welding process [32]. . experimental procedure materials and specimens e have used a standard polyethylene with high density hdpe, of molar mass that is about 500 kg/mol. the temperatures of vitreous transition and fusion are respectively of -125°c and 135°c, and the density is equal to 0.97g/cm3. it is about a semi-crystalline thermoplastic comprising a crystalline phase and an amorphous phase. this polymer is used generally in the manufacture of pipes reserved for the supply and distribution of water in accordance with na7700-2 standards manufactured by the chiali group [39]. physical and mechanical characteristics are given in tab. 1. characteristics units pe100 density kg/m3 956 961 melt flow index mfi (190 °c ; 5kg) g/10 mn 0.2 0.5 resistance at the yield point mpa ≥19 elongation at break % >600 elasticity modulus mpa 1000 fragility temperature °c <-100 linear expansion k-1 24.104 electrical resistance ω/cm ≥1012 table 1: physical and mechanical characteristics of hdpe [38, 39] the friction stir spot welding (fssw) welding process is new and has received great attention from the automotive, aeronautical and other industries. this welding technology involves a process similar to that of fsw linear friction-mixing welding [37, 38], except that the tool, instead of moving along a butt joint, only penetrates an overlapping joint (lap joint) formed by the plates (fig. 2). this process can be explained, basically, by three distinct stages: penetration, mixing and indentation. in this way, the process starts with the rotary tool slowly penetrating the weld point until the head touches the upper plate (penetration). then, the mixing stage begins, which allows the plates to join, and finally the recoil of tool. the recoil is done quickly, just after the tool reaches the final depth of penetration or after a dwell time (dwell), in which the tool only rotates at the maximum depth determined. during the process, heating due to friction softens the material, the rotation of the pin is responsible for the material flow in the radial and axial directions, and the pressure applied by the tool head allows the formation of solid weld around the pin. finally, after withdrawing the tool, a characteristic exit hole is left. a high-density polyethylene (hdpe) sheets with a thickness of 4 mm, a width of 60 mm, and a length of 150 mm were used to study the fssw welding under shear conditions loading. fig. 2 shows the specimen dimensions and the tool w d. benyarou et alii, frattura ed integrità strutturale, 55 (2021) 145-158; doi: 10.3221/igf-esis.55.11 149 position during the fssw welding process. the specimens were welded on a semi-automatic milling machine (fig. 3) using a steel tool gs 235 (steel e36) whose geometry is presented in fig. 4 [38]. this tool is suitable for friction welding fssw of hdpe plates. it is able to perform the three main welding functions: heat the parts by friction and by plastic deformation mix the materials to form the joint contain the flow of material under the shoulder and around the pin. figure 2: specimen geometry and tool position for the fssw process the shoulder is used to provide heat by friction and to knead the material under the effect of the rotational speed of tool. the milling machine has the necessary characteristics for welding by fssw. the hdpe plates are fixed to the machine table by flat metal shims which are held in place by fixing the plates one on the other in order to ensure a uniform distribution of the pressure on the specimen test [38]. figure 3: milling machine figure 4: fsw welding tool the experimental campaign was performed by means of a milling machine in order to weld by ffsw an hdpe lap shear joint. several tests were carried out by varying tool rotational speed and dwell time. a typical hdpe lap shear joint specimen used for testing is shown in fig. 2. to investigate the influence of tool rotational speed on the failure load and strength of bonded joints, three different values overlap length values were chosen: 750, 875 and 1100 rpm and by varying of dwell time. all the welding conditions for each performed test are tabulated in tab. 2. all in all, 36 different tension test series are performed. d. benyarou et alii, frattura ed integrità strutturale, 55 (2021) 145-158; doi: 10.3221/igf-esis.55.11 150 specimens id tool rotation speed (rpm) dwell time (s) mean value of maximum shearing force (n) pc _1 750 60 1366 pc _2 750 60 pc _3 750 60 pc _4 875 60 1832 pc _5 875 60 pc _6 875 60 pc _7 1100 60 686 pc _8 1100 60 pc _9 1100 60 pc _10 750 90 1450 pc _11 750 90 pc _12 750 90 pc _13 875 90 1111 pc _14 875 90 pc _15 875 90 pc _16 1100 90 1815 pc _17 1100 90 pc _18 1100 90 pc _19 750 120 1511 pc _20 750 120 pc _21 750 120 pc _22 875 120 1723 pc _23 875 120 pc _24 875 120 pc _25 1100 120 2155 pc _26 1100 120 pc _27 1100 120 pc _28 750 150 2032 pc _29 750 150 pc _30 750 150 pc _31 875 150 1151 pc _32 875 150 pc _33 875 150 pc _34 1100 150 733 pc _35 1100 150 pc _36 1100 150 table 2: welding parameters ranges. all the welding operations were done at the room temperature. at the beginning of each welding operation, the pin and the shoulder of the tool were cooled to the room temperature. the joint shape is presented in fig. 5 which shows the appearance of the test specimen after the friction stir spot welding. the tool shape is transferred onto the joint on the upper sheet and the metal that is pushed out by the tool forms a ring of excess metal around the weld. d. benyarou et alii, frattura ed integrità strutturale, 55 (2021) 145-158; doi: 10.3221/igf-esis.55.11 151 figure 5: friction stir spot weld joint. we can resume the different welded joint shapes obtained by different welded parameters (tool rotation speed and dwell time) in tab. 3. dwell time (s) 60 90 120 150 t o o l ro ta ti o n s p ee d ( rp m ) 75 0 87 5 11 00 table 3: joint production form on upper sheet after friction stir spot welding at different parameters tensile test tensile-shear tests were performed on universal testing machine instron/5887 at room temperature. the movement of the mobile traverse of the machine allows us to directly measure the automatic displacement of the specimen during the test using integrated software. the quasi-static tensile test was carried out under a crosshead speed of 5mm/s. the load and the displacement are registered simultaneously during the tests. the typical load–displacement curves of hdpe sheets (without welding) and lap shear joint of hdpe (fssw test) obtained by monotonic loading are shown in fig. 6. it can be seen from this figure that the influence of welding process on the monotonic load displacement curves of hdpe is very significant, where the tensile strength increases with the increase of the tool rotating speed. from the tensile test results, the following inferences can be derived tool rotational speed has a significant effect on tensile strength of the joints. tensile failure loads of the joints increase with the increase in tool rotational speed. this phenomenon can be explained by the fact of temperature level change and produces higher heat input in stir zone, which lead to change in stir zone strain and consequently, the initiation and crack growth is located within the contact zone (stir zone). the same conclusion has been found by other authors [40, 41]. effect of tool rotating speed and dwell time fig. 7 shows an overview of the tool rotational speed and dwell time effect on the weld joint behavior. we notice that tool rotation speed and dwell time and its interaction in contact zone have a significant effect on the peak of lap shear tensile load, the maximum value is obtained for rotation speed of 1100 rpm and dwell time t = 120 s. these values were d. benyarou et alii, frattura ed integrità strutturale, 55 (2021) 145-158; doi: 10.3221/igf-esis.55.11 152 considered the optimum parameters of fssw for this hdpe and must be used to obtain high quality welds and increase its strength. from the results, we deduce that the operating point of these parameters is established for 1100 rpm tool rotational speed and 120 s dwell time giving a maximum shearing force equal to 2155 n. these parameters represent the optimal welding values. the maximum load is for 1100 rpm and begins to decrease until it reaches a minimum value for 750 rpm. in order to investigate the tool rotating speed effect on failures mechanical behavior of hdpe lap-shear joint welded by fssw process, three values of tool rotating speed v (750, 875, 1100 rpm) were considered at room temperature. fig. 8 shows the typical load-displacement curves of the hdpe lap shear joint (fssw test) for a dwell time of 120s. the average failure loads for these rotational speed values of the tool welds in lap-shear specimens are changed from 1.5 kn for v = 750 rpm to 2.15 kn for v = 1100 rpm. tensile tests have shown that the sample with 1100 rpm and 120s has good welding quality. the locations of the load drops in the load-displacement curves of hdpe lap-shear joint is possible correspond to different stages of the crack initiation at the interface and propagation occurred in these joints specimens during the tests. further investigation should be conducted to fully investigate this phenomenon. the tensile/shear strength of the joint increased with increasing tool rotational speed according to fig. 9. figure 6: load versus displacement curves of specimens for dwell time =90s figure 7: comparison diagram of the tensile / shear strength for the different fssw welding parameters we have analyzed the effect of dwell time on the mechanical performance of hdpe lap-shear tensile load. the optimum parameters used in this study to obtain high quality welds are 1100 rpm tool rotational speed and 120 s dwell time as d. benyarou et alii, frattura ed integrità strutturale, 55 (2021) 145-158; doi: 10.3221/igf-esis.55.11 153 shown in fig. 7. fig. 10 illustrates the effect of dwell time on lap-shear tensile load of the friction stir spot welding joints for 1100 rpm tool rotation speed. figure 8: load-displacement curve, effect of rotational speed for dwell time =120s figure 9: tool rotation speed effect we can notice that there is an increase in weld tensile shear strength from 60s to 120s of dwell time, and the maximum tensile load was obtained with the 120 s dwell time as shown in fig. 10. beyond 120 s, the weld strength decreased with increasing dwell time fig. 10. during the welding process, there is an increase in frictional heat production as the dwell time increased and the change of shear strength values explained by the fact that there are the formation of four microstructures zones in welded joint, namely the: stir zone (sz), thermo mechanical affected zone (tmaz), heat affected zone (haz) and unaffected base material zone (bmz). the growth of grains in these zones and especially in sz and tmaz was influenced by the combination of mechanical deformation and heat input which also depends on the parameters of welded process (tool rotational speed and dwell time). on the other hand, an increasing of the dwell time lead to a more mechanical strain of the sz and tmaz and consequently influenced on the mechanical behavior of hdpe materials. finally, we observe that the fssw welded strength depends on the tool rotation speed and the dwell time. d. benyarou et alii, frattura ed integrità strutturale, 55 (2021) 145-158; doi: 10.3221/igf-esis.55.11 154 figure 10: dwell time effect numerical analysis and results he processes of friction-stir spot welding (fssw) have been widely and extensively used to join sheet metals in the automotive components. however, the stress field close to the contact region (stir zone: sz and thermo mechanical affected zone: tmaz) is very complex and far from being achieved. meanwhile, these structures are also subjected to multi-axial loads during service. although the relative displacement, stress and stain cannot be easily measured and its values are required, the analysis of stresses field at process zone (stir zone: sz and thermo mechanical affected zone: tmaz) under given loading condition is important to predict the fracture and the reliability of welded structure. moreover, the welded polymer modeling is not fully understood and represents a very active research field. this work focuses on numerical simulation using finite elements to predict the overall behavior of welded assembly. finite element analysis (fea) is an important tool to design practical mechanical joints, such as hdpe lap shear joints by fssw process. during fssw process, the tool undergoes a low strain so it is modeled as rigid material. its mechanicals properties are young modulus e = 200 mpa and poisson's ratio 0.3. an elastic-plastic response was considered for modeling the hdpe lap-shear joint welded by fssw. the mesh is designed to be highly refined in the interface and near the process zone (sz and tmaz zones) in order to obtain more accurate results (typical element dimension in these zones is 0.2 mm). in addition, a master-slave approach is used to simulate numerically the contact problems in the interfaces between all connected parts of lap-shear joint. the coulomb friction law in a partial sliding/sticking condition was employed, where the friction coefficient was set at 0.25. according to the structure dimensions, a three dimensional model was generated using the fem in order to determine and to perform the stress and strain field analyses in process zone (sz and tmaz zones). a general description of the geometric model and the mesh of the studied assembly are presented in fig. 11 and fig. 12. the different boundary conditions and loading are detailed by highlighting the consideration of all the contact surfaces related to the specificity of such an assembly. fig. 11 illustrate a lap-shear joint and the boundary conditions employed in the finite element models. a three-dimensional brick element (hexahedral) is used for the modeling, this element is defined by eight nodes and each having three degrees of freedom. the optimized model has 7782 nodes and 3315 elements for lap-shear joint welded by fssw. the theory of incremental plasticity is introduced to modeling the material nonlinearity. the iterative method of newton–raphson is used as an approach to solve nonlinear equations by finite elements. the variation of the various cylinders geometry is based on the variation of its thickness, its diameter and its shape. the reference thickness is 1.5 mm. the model has 8900 nodes and 6592 elements for this configuration of tool. whatever the geometry of the joint, the geometric modifications made: rigid surface at the contact of the two plates the lower plate and the upper plate, rigid surface formed of two cylinders introduced into the two plates, solid cylinder and a cylinder of hollow conical shape. fig. 13 show that the high equivalent stress is strongly concentrated at the interface between the plates. this phenomenon can be explained by the fact of strain incompatibility at the interface and the sliding effect. the optimal form will be tested later on a bilateral model to see how the result extends to multiple joints. t d. benyarou et alii, frattura ed integrità strutturale, 55 (2021) 145-158; doi: 10.3221/igf-esis.55.11 155 figure 11: geometrical model: half of a lap-shear joint, boundary condition and loading. figure 12: joint geometry and mesh (contact zone) figure 13: numerical result for a weld spot d. benyarou et alii, frattura ed integrità strutturale, 55 (2021) 145-158; doi: 10.3221/igf-esis.55.11 156 figure 14: mechanical behavior of lap shear joints by fssw fig. 14 illustrate the responses obtained from the mechanical behavior of the materials in terms of lap-shear tensile load versus displacement response during the tensile test and predicted by the numerical model taken for the optimum values, a speed of rotation of 1100 rpm and a dwell time of 120 s which gave a good welding quality. from this figure, the results obtained numerically compared with the experimental results are presented. from a qualitative point of view the evolutions present similar behavior. the explanation of this mechanical behavior is that the deformation response of an amorphous polymer (hdpe) strongly depends on the stress conditions but also on the environment and the effect of the welding parameters (dwell time and tool rotating speed). temperature is a very important parameter conditioning the response of polymers. it can be seen that the numerical results are in good agreement with the experimental results. this phenomenon can be explained by the fact, that the friction stir spot welding parameters has a significant effect on the material mixing and consequently on the static strength of welded joints. we recall also, that is difficult to make a complete characterization of welded joints behavior by fssw process. in other words, creation of complex phenomena in welded zone during the welding process which related to the level and the interaction between the welded parameters such as: tool geometry, tool rotational speed and dwell time from where a difficulty to make a precise and reliable numerical analysis. conclusions riction stir spot welding of polymer materials is a promising technique which provides high quality joints compared to conventional welding processes. this study was carried out in order to analysis the effect of some parameters on the mechanical behavior of hdpe single lap joint welded by friction-stir spot welding (fssw) under tensile loading. the obtained results allow us to deduce the following conclusions:  the developed a nonlinear finite element modeling approach to simulate the single-lap joints welded by (fssw) and subjected to static tensile loading.  good correlation was found between the fem simulations and the experimental results.  the level of tool rotating speed determines the mode failure of welded assemblies and on the mechanical behavior of hdpe material compared to hdpe sheets without welding.  we can obtained a high quality welds and high quality weld strength using the optimum welding parameters (tool rotation speed and dwell time).  the results found confirm that the tool rotation speed and dwell time play a predominant role in determining the tensile / shear strength.  the increase in dwell time increases the tensile shear strength in a limited range of fssw joints.  tensile failure loads of the joints increase with the increase in tool rotational speed f d. benyarou et alii, frattura ed integrità strutturale, 55 (2021) 145-158; doi: 10.3221/igf-esis.55.11 157 acknowledgments he authors warmly thank the scientific support of the three research teams, lste laboratory and lpq3m laboratory from mustapha stambouli university, mascara, algeria and lille mechanics unit (france). references [1] benhamena, a., bachir bouiadjra, b., amrouche, a., mesmacque, g., benseddiq, n., benguediab, m., (2010). three finite element analysis of semi-elliptical crack in high density poly-ethylene pipe subjected to internal pressure. materials and design. 31 (6), pp. 3038–3043. doi: 10.1016/j.matdes.2010.01.029 [2] benhamena, a., aminallah, l., bachir bouiadjra, b., benguediab, m., amrouche, a., benseddiq, n., (2011). j integral solution for semi-elliptical surface crack in high density poly-ethylene pipe under bending. materials and design. 32 (5), pp. 2561–2569. doi: 10.1016/j.matdes.2011.01.045 [3] moulai ali, b., ould chikh, b., meddah, h.m., bachir bouiadjra, b. (2019), plasticity effect on the mechanical behavior of an amorphous polymer, international journal of engineering research in africa, 43, pp 1-19. doi: 10.4028/www.scientific.net/jera.43.1 [4] khellafi, h., meddah, h.m., ould chikh, b., bouchouicha, b., benguediab, m., bendouba, m. (2015). experimental and numerical analysis of the polyvinyl chloride (pvc) mechanical behavior response, cmc, 49-50(1), pp.31-45. [5] abdel nour zaim, benattou bouchouicha, hadj miloud meddah, el bahri ould chikh, (2018). the stress triaxiality effect under large plastic deformation of a polybutylene terephthalate (pbt), international journal of engineering research in africa, 34, 13-28. [6] abdel nour, z., chikh el bahri, o., benattou, b. (2018). thermo-mechanical characterization of a thermoplastic copolyetherester (tpc): experimental investigation. fibers and polymers, 19(4), pp. 734-741. [7] pathak, s., pradhan, s.k. (2020). experimentation and optimization of hdpe pipe electro fusion and butt fusion welding processes. materials today: proceedings. 27(3), pp. 2925-2929. doi: 10.1016/j.matpr.2020.03.517. [8] bouchouicha, b., zemri, m., zaim, a., ould chikh, b. (2015). estimation of the energy of crack propagation in different zones of a welded joint by the local technique, int. j. fract., 192, pp.107–116. doi 10.1007/s10704-015-9989-1 [9] singh, v. p., patel, s. k., ranjan, a., kuriachen, b. (2020). recent research progress in solid state friction-stir welding of aluminium–magnesium alloys: a critical review. journal of materials research and technology, 9(3), pp. 6217-6256. doi: 10.1016/j.jmrt.2020.01.008 [10] thomas, w.m., nicholas, e.d. (1997). friction stir welding for the transportation industries. materials and design, 18(4/6), pp. 269–273. doi: 10.1016/s0261-3069(97)00062-9. [11] mishra, r.s., ma, z.y. (2005). friction stir welding and processing. materials science and engineering: r: reports, 50 (1–2/31), pp. 1-78. doi: 10.1016/j.mser.2005.07.001. [12] lee, w. b., yeon, y. m., jung, s. b. (2003). joint properties of friction stir welded az31b– h24 magnesium alloy. journal of materials science and technology, pp. 785-790. doi: 10.1179/026708303225001867. [13] hancock, r. (2004), friction welding of aluminum cuts energy costs by 99%. welding journal, 83 (2), pp. 40-43. https://wenku.baidu.com/view/dd05837d4028915f804dc2fb. [14] sundaram, n. s., murugan, n. (2010), tensile behavior of dissimilar friction stir welded joints of aluminium alloys. materials and design, 31(9), pp.4184–4193. doi: 10.1016/j.matdes.2010.04.035. [15] barlas, z, uzun, h. (2010), microstructure and mechanical properties of friction stir butt-welded dissimilar pure copper/brass alloy plates. int. j. mat., 101(6), pp. 801-807. doi: 10.3139/146.110340. [16] amirizad, m., kokabi, a.h., abbasi gharacheh, m., sarrafi, r., shalchi, b., azizieh, m. (2006), evaluation of microstructure and mechanical properties in friction stir welded a356+15%sic cast composite. mater. lett., 60, pp. 565–568. doi: 10.1016/j.matlet.2005.09.035, [17] bozkurt, y., duman, s. (2011), the effect of welding parameters on the mechanical and microstructural properties of friction stir welded dissimilar aa 3003-h24 and 2124/sic/25p-t4 alloy joints. int. j. phys. sci., 6(17), pp. 3702-3716. doi: 10.5897/sre11.616, [18] vijay, s.j., murugan, n. (2010). influence of tool pin profile on the metallurgical and mechanical properties of friction stir welded al–10 wt.% tib2 metal matrix composite. materials and design, 31, pp. 3585–3589. t d. benyarou et alii, frattura ed integrità strutturale, 55 (2021) 145-158; doi: 10.3221/igf-esis.55.11 158 doi: 10.1016/j.matdes.2010.01.018. [19] rajamanickam, n., balusamy, v., madhusudhann, reddy, g., natarajan, k. (2009). effect of process parameters on thermal history and mechanical properties of friction stir welds. materials and design 30 (7), pp. 2726–2731. doi: 10.1016/j.matdes.2008.09.035. [20] grewell, d.a., benatar, a., park, j.b. (2003). plastics and composites welding handbook. carl hanser verlag, munchen. [21] strand, s. (2003). joining plastics can friction stir welding compete. ieee, 0-941783-23. [22] strand, s., sorensen, c., nelson, t. (2003). effects of friction stir welding on polymer microstructure. antec 2003 proceedings, 2, pp.1078-1082. [23] arici, a., selale, s. (2007), effects of tool tilt angle on tensile strenght and fracture locations of friction stir welding of polyethylene, science and technology of welding and joining, 12, pp. 536-539. doi: 10.1179/174329307x173706. [24] kiss, z., czigany, t. (2007). applicability of friction stir welding in polymeric materials. periodicapolytechnica. 51(1): pp. 15-18. doi: 10.3311/pp.me.2007-1.02. [25] aydin, m. (2010), effects of welding parameters and pre-heating on the friction stir welding of uhmw-pe. polymerplastics technol. eng., 49(6), pp. 595-601. doi: 10.1080/03602551003664503. [26] bozkurt, y. (2011). the optimization of friction stir welding process parameters to achieve maximum tensile strength in polyethylene sheets, materials and design. doi:10.1016/j.mat des.2011.09.008. [27] payganeh, g.h., mostafa arab, n.b., dadgar asl, y., ghasemi, f.a., saeidi, b. m (2011). effects of friction stir welding process parameters on appearance and strength of polypropylene composite welds. int. j. phys. sci., 6(19), pp. 4595-4601. doi: 10.5897/ijps11.866. [28] mendes, n., neto, p., simão, m.a., loureiro, a., pires, j.n. (2016), a novel friction stir welding robotic platform, welding polymeric materials. the international journal of advanced manufacturing technology, 85, pp. 37-46. doi: 10.1007/s00170-014-6024-z. [29] aota, k., ikeuchi, k. (2009), development of friction stir spot welding using rotating tool without probe and its application to low carbon steel plates, welding international 23, pp. 572-580. doi: 10.1080/09507110802543054. [30] gerlich, a., su, p., north, t., bendzsak, g. (2005), friction stir spot welding of aluminum and magnesium alloys, materials forum, 29, pp. 290-294. doi: 10.4271/2005-01-1255. [31] arici, a., senol, m. (2008), friction stir spot welding of polypropylene, journal of reinforced plastics and composites, 27, pp. 2001-2004. doi: 10.1177/0731684408089134. [32] bilici, m.k. and yukler, a.i. (2012), effects of welding parameters on friction stir spot welding of high density polyethylene sheets, materials and design, 33, pp. 545-550. doi: 10.1016/j.matdes.2011.04.062. [33] bilici, m.k. and yukler, a.i. (2012), influence of tool geometry and process parameters on macrostructure and static strength in friction stir spot welded polyethylene sheets, materials and design, 33, pp. 145-152. doi: 10.1016/j.matdes.2011.06.059. [34] bilici, m.k. ahmet i. y., memduh k. (2016). pin profile and shoulder geometry effects in friction stir spot welded polymer sheets, the international journal of engineering and science, 5(6), pp. 29-36. http://www.theijes.com/. [35] kurtulmus, m. (2012), friction stir spot welding parameters for polypropylene sheets, scientific research and essays, 7(8), pp. 947-956. doi: 10.5897/sre11.1909. [36] awang, m., mucino, v., feng, z., david, s. (2006), thermo-mechanical modeling of friction stir spot welding (fssw). sae technical paper 2006-01-1392, doi: 10.4271/2006-01-1392. [37] hachellaf, k., meddah, h. m., ould chikh, b., lounis, a. (2019, mechanical behavior analysis of the welding cord by friction stir welding (fsw) for a polymer material, frattura ed integrità strutturale, 47, pp. 459-467. doi: 10.3221/igf-esis.47.36. [38] lounis, a., ould chikh, b., meddah, h. m., gueraiche, l., hachellaf, k. (2018), parametric study of the mechanical behavior of fssw welded polymer plates using a new form of welding tool, defect and diffusion forum, 389, pp 205-215. doi: 10.4028/www.scientific.net/ddf.389.205. [39] catalogues groupe chiali (sidi bel-abbes –algeria) http:/www.groupe-chiali.com, (2017). [40] zhang, z., yang, x., zhang, j., zhou, g., xu, x., zou, b. (2011). effect of welding parameters on microstructure and mechanical properties of friction stir spot welded 5052 aluminum alloy, materials and design 32. pp. 4461–4470. doi: 10.1016/j.matdes.2011.03.058. [41] khuder, a. w. h., muhammed, m. a., ibrahim, h. k. (2017). numerical and experimental study of temperature distribution in friction stir spot welding of aa2024-t3 aluminum alloy, international journal of innovative research in science, engineering and technology, 6 (5), doi: 10.15680/ijirset.2017.0605004. microsoft word numero_30_art_42 a. carofalo et alii, frattura ed integrità strutturale, 30 (2014) 349-359; doi: 10.3221/igf-esis.30.42 349 focussed on: fracture and structural integrity related issues modification of creep and low cycle fatigue behaviour induced by welding a. carofalo, v. dattoma, r. nobile, f.w. panella università del salento dipartimento di ingegneria dell’innovazione, via per arnesano, 73100 lecce, italy alessio.carofalo@unisalento.it; vito.dattoma@unisalento.it; riccardo.nobile@unisalento.it; francesco.panella@unisalento.it g. alfeo ge avio srl– ingegneria – ricerca e sviluppo tecnologico, via angelo titi 16, 72100 brindisi, italy giovanni.alfeo@avioaero.com a. scialpi ge avio srl – ingegneria – progettazione componenti motori, via arno 60 angelo titi 16, 72100 brindisi, italy agostino.scialpi@avioaero.com g.p. zanon ge avio srl – ingegneria – ricerca e sviluppo tecnologico, via i maggio 99, 10040 rivalta di torino (to), italy giovanni.zanon@avioaero.com abstract. in this work, the mechanical properties of waspaloy superalloy have been evaluated in case of welded repaired material and compared to base material. test program considered flat specimens on base and tig welded material subjected to static, low-cycle fatigue and creep test at different temperatures. results of uniaxial tensile tests showed that the presence of welded material in the gage length specimen does not have a relevant influence on yield strength and uts. however, elongation at failure of tig material was reduced with respect to the base material. moreover, low-cycle fatigue properties have been determined carrying out tests at different temperature (room temperature rt and 538°c) in both base and tig welded material. welded material showed an increase of the data scatter and lower fatigue strength, which was anyway not excessive in comparison with base material. during test, all the hysteresis cycles were recorded in order to evaluate the trend of elastic modulus and hysteresis area against the number of cycles. a clear correlation between hysteresis and fatigue life was found. finally, creep test carried out on a limited number of specimens allowed establishing some changes about the creep rate and time to failure of base and welded material. tig welded specimen showed a lower time to reach a fixed strain or failure when a low stress level is applied. in all cases, creep behaviour of welded material is characterized by the absence of the tertiary creep. keywords. low-cycle fatigue; welding; fatigue damage; nickel-base superalloys. a. carofalo et alii, frattura ed integrità strutturale, 30 (2014) 349-359; doi: 10.3221/igf-esis.30.42 350 introduction esign of gas turbine engine components is influenced by repeated request of higher performances in terms of high power, efficiency improvement, reduction of weight and costs. another important point is the reliability of the design model used, that determines the flight safety. these objectives are generally achieved following two approaches: firstly, the development of material that could increase the maximum working temperature and could have a direct impact on the performance of the gas turbine; secondly, the development of advanced modelling techniques that could lead to the reduction of the safety factors generally used in the design phase. thermomechanical damage is the main limiting factor of the life in a nickel-based superalloy mechanical component [1]. complex loads often lead to severe non-linear material behaviour, such as creep deformation and fatigue, while high temperature increases the probability of localized material plasticization under the service loads. therefore, design against fatigue failure utilizes fatigue behaviour obtained through strain control fatigue tests. creep and fatigue damages are generally studied using different models, even if some attempts to unify the material behaviour can be reached in literature [2, 3]. anyway, these models were developed and experimentally verified for high strain levels in case of fatigue and for high stress-temperature condition in case of creep. the extension of their prediction to moderate strain levels, where elastic behaviour is predominant, constitutes a serious limitation [4]. nucleation of fatigue crack represents the critical phenomenon that lead to failure of nickel-based components [5-7]. from a metallurgical point of view, nickel-based superalloys at high temperature are characterized by a change of ductility and the formation of an oxidation film on the surface. these two phenomena are antithetical with respect to the fatigue damage: the softening of the metallic matrix causes an increase of the probability of a fatigue crack initiation, while crack nucleation and propagation is interfered by oxide layer on the surface [8]. the combination of these factors determines the behaviour of the considered material. the interaction of creep and fatigue phenomena is a further complication and it is a phenomenon not well understood [9]. in this work, the mechanical properties of base material and tig welded waspaloy have been compared carrying out static, low-cycle fatigue and creep test on specimen obtained by a laminated sheet having a nominal thickness of 3.1 mm. in most cases, fatigue tests have been carried out with applied strain range δε ≤ 0.6%. this kind of low stress level is associated to limited damage process. in this condition, the damage models are generally inapplicable or lead to inconsistent prediction. on the other hand, material behaviour at this stress level is very useful for industrial application, since it is close to component working condition. therefore, simple and quick indicators of the different behaviour performance for static, fatigue and creep properties have been chosen and calculated, both for base and tig welded material. the reduction of performances originated by welding has been estimated by the percentage variation of these indicators. material and experimental procedure aspaloy is a conventional nickel-based superalloy that is subjected to hardening precipitating heat-treating. waspaloy is widely used in the aeronautical field due to its good strength to corrosion and to high temperature, in particular for the realization of turbine disk, blade and casing. mechanical strength is comparable to haynes r-41 and higher than inconel 718 at temperature higher than 650-705°c [8]. microstructure is characterized by a face centered cube matrix with dominant precipitates γ’. ductility of waspaloy has been studied in [10], showing a reduction starting from room temperature to about 300 °c, an irregular behaviour up to 600 °c and a quick reduction at higher temperature. waspaloy can be welded using conventional or advanced welding techniques. in presence of a localized damage in a large high-cost component, a possible maintenance strategy is to repair it removing the damage zone and substituting it with welded material. the residual life of the component would be increased with evident economic advantages, on condition that the reliability and the safety of the component are not reduced. weldability of waspaloy from a technological and metallurgical point of view has been studied in [11, 12]. generally speaking, the fusion and the following solidification determine at least grain growth and introduce defect like microcracks. from a macroscopic point of view, these phenomena produce a reduction in ductility, showed by lower elongation at failure and lower fatigue and creep strength [13-17]. starting from a laminated plate having a nominal thickness of 3.1 mm, base material specimens for static, fatigue and creep tests have been realized. at the same time, a similar plate has been butt-welded using an optimized tig process in d w a. carofalo et alii, frattura ed integrità strutturale, 30 (2014) 349-359; doi: 10.3221/igf-esis.30.42 351 order to avoid the introduction of microdefects in the weld cord both in the as-welded condition and after pwht heattreating. tig welded specimens are obtained taking care to guarantee the presence of a transversal welding cord in the specimen gage length. weld cord has been removed through flattening and the welded plate has been subjected to an optimized aging heat-treating. finally, specimens have been obtained by cutting and milling. however, thermal cycle of welding, aging heat-treating and final milling introduced specimen distortions, which was not compatible with the standard required for the execution of the mechanical tests, in particular low-cycle fatigue tests. therefore, specimens have been plastically deformed at room temperature to respect the straightness tolerance. flat specimens are not the usual choice to carry out high temperature mechanical test, due to the highest difficulty for a correct load application and a reliable strain measurement. however, a particular care has been used in order to achieve correct results from the mechanical test. since a three-zone split furnace was used for heating, load application to specimen was obtained through serrated face grip designed and realized in udimet720. this grip allows the application of a preload to the specimen in order to guarantee the backlash recover especially during low-cycle fatigue test. even if the dimension of the specimen were opportunely reduced to limit the maximum load, grip was subjected to severe creep and plastic deformation that requires its substitution to complete the experimental program. static test has been carried out following the indication of astm e8-04 and e21-09 standards, respectively for room temperature (rt) and high temperature 503°c, 704°c and 760°c. sub-size specimen has been used for test at 503°c, in order to limit the maximum load during test. all the tests are carried out in displacement control imposing a speed of 0.1 and 0.5 mm and repeated on 3 and 5 specimens, respectively for room and high temperature. test temperature is measured and controlled in three point using k thermocouples in contact in three different point of the specimen gage length. low-cycle fatigue tests are carried out following the indication of astm e606-04 standard, using a triangular waveform in strain control and a frequency of 0.5 hz. specimen geometry has been changed with respect to the standard indication increasing the fillet radius to a value of 15 mm, in order to avoid failure due to excessive stress concentration (fig. 1a). it was verified that this geometry was able to hold compressive strength close to yield strength without showing buckling and transversal deflection of the specimen. all the test are characterized by a strain ratio rε = εmin/εmax= 0. applied strain is in the range δε = 0.4-0.9 %, therefore plastic deformation is low or absent and the expected fatigue life is relatively high. run-out level was fixed at 105 cycles, after which test is continued in load control using the stabilized cycle stress range. experimental test plan considers tests at room temperature (rt), 538°c and 760°c, both for base and tig welded material. in this work only the results of rt and 538°c conditions are showed and discussed. static and low-cycle fatigue tests were carried out on a servohydraulic testing machine 100 kn mts810, while extensometers used for strain control test have a 10 mm gage length. creep test are carried out on a dead-weight creep machine nortest tc50 equipped with adapters for flat specimen, which geometry is reported in fig. 1b. two different stress levels and a temperature of 704°c have been considered. each test condition has been repeated on three specimens to guarantee the repeatability of the result. experimental results and discussion static test tatic behaviours of laminated waspaloy obtained in this work are resumed in tab. 1, which reports the mean values of the most representative static parameters. all the values have been normalized considering a reference value equal to maximum strength. yielding stress and tensile strength of the base material are coherent with the data reported in literature for waspaloy [10, 18]. at temperature above 700°c, hardening disappeared justifying the decay of the tensile strength at high temperature. finally, young modulus undergoes a reduction of about 50% at 760°c, which is higher than that reported in literature for waspaloy. a wide extension of the plastic zone is observed at temperature above 700°c (fig. 2a), which is in contrast with the marked reduction observed in [10]. assuming base material as a reference, the modification of the static behaviour induced by tig is clearly highlighted. if the variability of yielding stress and young modulus is excluded, which are data sensitive to error and numerical manipulation during elaboration, tensile strength is practically not affected by the presence of weld cord. as expected, a relevant change consists in a reduction of the plastic zone in all the condition. in particular, at the highest temperature, the presence of the weld cord restrained the extension of the plastic zone that was found for the base material (fig. 2b). s a. carofalo et alii, frattura ed integrità strutturale, 30 (2014) 349-359; doi: 10.3221/igf-esis.30.42 352 (a) (b) figure 1: specimen geometry for lcf test (a) and creep test (b). (a) (b) figure 2: static behaviour of base (a) and tig welded (b) material. yielding stress tensile strength elongation to failure young modulus σy [n/mm 2] σr [n/mm 2] a [%] e [n/mm2] base material tig var % base material tig var % base material tig var % base material tig var % rt 0.617 0.622 0.78 1 0.968 -3.24 0.65 0.43 -33.64 1 0.948 -5.22 503°c 0.519 0.484 -6.7 0.867 0.836 -3.58 0.47 0.34 -28.18 0.738 0.658 -10.83 704°c 0.516 0.607 0.93 0.571 760°c 0.444 0.446 0.53 0.497 0.514 3.39 1 0.25 -75.00 0.522 0.560 7.27 table 1: static behaviour of base and tig welded material. a. carofalo et alii, frattura ed integrità strutturale, 30 (2014) 349-359; doi: 10.3221/igf-esis.30.42 353 low-cycle fatigue test relevant data about the fatigue tests are resumed in tab. 2-5 for each test condition. all the data are normalized with respect to a reference value corresponding to the maximum one. failure is identified by a decay of 10 % of the maximum stress with respect to the stabilized cycle. specimens that reached the run-out level of 105 cycles are marked in bold to indicate that the test was completed in load control up to failure. in the same tables, several indicators are reported, referred to the stabilized cycle, which is generally identified as the half-life cycle. in particular, the stress range, stress ratio r, tangent elastic modulus et and the amount of the hysteresis area h have been calculated and showed. strain range cycles to failure normalized stress range stress ratio hysteresis area tangent modulus δε/δεmax nf/nmax δσ/δσmax r = σmin/σmax h [mj/mm 3] et [n/mm 2] mb-rt-1 0.984 0.0037 1.0000 -0.86 1.536 214109 mb-rt-2 0.879 0.0045 0.9798 -0.74 0.886 218793 mb-rt-3 0.771 0.0093 0.8824 -0.66 0.329 212641 mb-rt-4 0.686 0.0136 0.8408 -0.64 0.151 224218 mb-rt-5 0.581 0.0310 0.7667 -0.97 0.040 235026 mb-rt-6 0.795 0.0077 0.9620 -0.97 0.549 229147 mb-rt-8 0.790 0.0087 0.9492 -0.84 0.500 226862 mb-rt-9 0.562 0.0223 0.7410 -0.40 0.035 226357 mb-rt-10 0.564 0.1611 0.7563 -1.64 0.015 228901 mb-rt-11 0.602 0.0180 0.7832 -0.54 0.051 231935 mb-rt-13 0.461 0.0621 0.6062 -0.48 0.009 232259 mb-rt-14 0.460 0.0436 0.5952 -0.28 0.012 230506 mb-rt-15 0.459 0.0562 0.6050 -0.61 0.053 231954 mb-rt-16 0.460 0.0432 0.5511 -0.24 0.026 216363 table 2: base material – room temperature: fatigue test results. strain range cycles to failure normalized stress range stress ratio hysteresis area tangent modulus δε/δεmax nf/nmax δσ/δσmax r = σmin/σmax h [mj/mm 3] et [n/mm 2] mb-538-1 0.789 0.3191 0.5377 -0.36 0.051 118358 mb-538-3 0.697 0.4474 0.4091 -0.11 0.024 106123 mb-538-4 0.785 0.4518 0.4354 0.00 0.291 114078 mb-538-5 1.000 0.0040 0.6852 -0.52 0.392 123529 mb-538-6 0.880 0.0102 0.6565 0.56 0.065 129012 mb-538-8 0.890 0.0127 0.6001 -0.37 0.231 131086 mb-538-9 0.950 0.0030 0.7795 -0.80 0.378 154759 mb-538-10 0.786 0.0526 0.5511 -0.13 0.405 160511 mb-538-11 0.973 0.0396 0.6375 -0.40 0.179 100070 mb-538-12 0.895 0.1313 0.5450 -0.40 0.464 132828 mb-538-13 0.898 0.1002 0.5622 -0.37 0.190 101577 mb-538-14 0.786 0.3942 0.4440 -0.14 0.023 103100 mb-538-16 0.981 0.0034 0.6944 -0.31 0.153 115671 table 3: base material – 538°c: fatigue test results. the application of load cycle in strain control originates non-linear phenomenon within the material. the applied work can be divided in potential and dissipated energy and several predictive models based on macroscopic energy approaches have been developed to evaluate fatigue damage. the importance of considering energy parameters to describe fatigue a. carofalo et alii, frattura ed integrità strutturale, 30 (2014) 349-359; doi: 10.3221/igf-esis.30.42 354 damage is undoubtable, as testified by the generalized approach that has been proposed recently using experimental data of waspaloy [19]. anyway, the errors associated to measured strain and stress during test are so high that a notable scatter generally affects calculation of energy parameters. this observation is particularly true in large part of the test carried out in this work, where elastic behaviour is predominant and the loading and unloading curves are practically coincident. nevertheless, hysteresis area reported in the previous tables can be correlated to the resulting stress range and a clear correlation exists in all the test conditions (fig. 3a). on the other hand, it is not possible to use the values of hysteresis area as a damage indicator due to its low magnitude. from a practical point of view, the trends of hysteresis area against fatigue life that have an initial value higher than 0.5 mj/mm3 have been considered. hysteresis area is practically constant or show limited variation up to failure (fig. 3b). therefore, the use of energy indicator related to hysteresis area to describe damage phenomena has a limited importance for the stress-strain level that is usually present in the working condition of an industrial component. strain range cycles to failure normalized stress range stress ratio hysteresis area tangent modulus δε/δεmax nf/nmax δσ/δσmax r = σmin/σmax h [mj/mm 3] et [n/mm 2] tig-rt-1 0.767 0.0011 0.5352 -0.15 0.169 143012 tig-rt-2 0.581 0.0203 0.7324 -1.18 0.217 222952 tig-rt-3 0.795 0.0041 0.9081 -0.66 0.551 216812 tig-rt-4 0.472 0.0157 0.5677 -0.20 0.042 211581 tig-rt-5 0.473 0.0179 0.5664 -0.08 0.035 213285 tig-rt-6 0.571 0.0617 0.6718 -3.94 0.702 217488 tig-rt-7 0.472 0.0095 0.5389 -0.17 0.404 209687 tig-rt-8 0.690 0.0084 0.8389 -0.57 0.144 213285 tig-rt-9 0.795 0.0022 0.8065 -0.46 0.089 143342 tig-rt-10 0.476 0.0328 0.5462 -0.16 0.162 203959 tig-rt-11 0.584 0.0146 0.6691 -0.27 0.081 200947 tig-rt-12 0.584 0.0105 0.6883 -0.34 0.125 205143 tig-rt-13 0.804 0.0014 0.8598 -0.59 0.235 196114 tig-rt-14 0.476 0.0308 0.5407 -0.11 0.087 203601 table 4: tig welded material – room temperature: fatigue test results. strain range cycles to failure normalized stress range stress ratio hysteresis area tangent modulus δε/δεmax nf/nmax δσ/δσmax r = σmin/σmax h [mj/mm 3] et [n/mm 2] tig-538-3 0.686 0.0031 0.4097 -0.35 0.112 162957 tig-538-4 0.660 0.1699 0.4905 -0.21 0.032 133696 tig-538-5 0.675 0.0200 0.6552 -0.34 0.161 147811 tig-538-6 0.801 0.0027 0.6730 -0.53 0.169 149473 tig-538-8 0.516 0.0272 0.4562 -0.11 0.029 153746 tig-538-9 0.660 0.0804 0.4764 -0.21 0.031 129936 tig-538-11 0.794 0.0040 0.5328 -0.09 0.283 137832 tig-538-12 0.574 0.0049 0.4525 -0.06 0.027 135120 tig-538-13 0.551 1.0000 0.3246 0.16 0.092 131529 tig-538-14 0.676 0.0160 0.4133 0.02 0.144 124787 tig-538-16 0.780 0.0009 0.6105 -0.26 0.038 139634 tig-538-17 0.789 0.0095 0.6203 -0.45 0.040 141017 tig-538-18 0.684 0.0105 0.4146 0.07 0.046 103570 tig-538-19 0.589 0.0240 0.5909 -0.18 0.081 131791 table 5: tig welded material – 538°c: fatigue test results. a. carofalo et alii, frattura ed integrità strutturale, 30 (2014) 349-359; doi: 10.3221/igf-esis.30.42 355 (a) (b) figure 3: correlation between resulting stress range and hysteresis area (a) and hysteresis area trend against fatigue life (b). fig. 4 reports an example of an hysteresis cycle, while the change of peak stress for two tests carried out at a strain range δε/ δεmax = 0.44 is showed in fig. 5. material plastic behaviour is very limited and the stress range is practically constant for the whole life of the specimen, with the exclusion of the last cycles, when a fatigue crack initiation process is already started. similar trends are obtained for tig welded specimen and at high temperature also. change of tangent modulus et and hysteresis area h is generally considered an important indicator of the progress of the damage process in the material. crack initiation has the effect to reduce specimen stiffness and a measurable reduction of the tangent modulus is showed. hysteresis area represents the work associated to plastic deformation in each load cycle [20], which is partially stored in the material as a potential damage and partially dissipated as heating [21]. therefore, these two parameters have been calculated starting from the whole data cycle and correlated to number of cycles for each specimen. an example of tangent modulus et trend is reported in fig. 6. observing this last graph, it is possible to show that the decay of tangent modulus is always measurable only at the end of life, when a crack is already present. consequently, this parameter has a limited interest to follow the damage evolution in the material. moreover, the trends of hysteresis area h (fig. 3b) have no practical utility, due to its low values. from a quantitative point of view, fatigue behaviour of base and tig welded material is synthetically expressed by the fatigue curves in terms of applied strain range (fig. 7) or in terms of measured stress range (fig. 8). in all the conditions, tig welded material shows a lower fatigue curve than base material. the reduction of fatigue strength can be quantified interpolating the experimental data to calculate basquin’s law and finally the strain range δεa and the stress range δσa corresponding to a reference life nref (tab. 6). a careful analysis of these data reveals that the fatigue strength expressed in terms of strain range δεa is increased when temperature test changes from rt to 538°c. on the contrary, fatigue stress in terms of stress range δσa is reduced in the same condition. figure 4: example of stabilized hysteresis cycle. a. carofalo et alii, frattura ed integrità strutturale, 30 (2014) 349-359; doi: 10.3221/igf-esis.30.42 356 (a) (b) figure 5: peak stress trend of a base (a) and tig welded specimen (b). figure 6: example of tangent modulus et trend this behaviour is clearly confirmed by the experimental data both for base and tig welded material. however, not only this observation is not reported in any experimental work existing in literature, but also it is not verified for other experimental data obtained using standard circular specimen. it is very difficult to indicate a clear explanation, but some hypothesis can be formulated. a possibility is to invoke a complex interaction between fatigue and creep damage, which become relevant when applied strain is so low that the load cycle can be considered fully elastic and the test duration is over 24 hours. another possibility is to consider that the specimens have been obtained by a laminated plate rather than round bars, as usual: the different influence of the residual stress field existing in the laminated plate could shows its detrimental effect only at room temperature, while at higher temperature relaxation phenomena could mitigate the effects. however, no quantitative data or qualitative observations are available to support one hypothesis with respect to others and this constitutes an open problem. creep test. creep strength of base and tig welded material has been expressed in terms of time to reach a fixed inelastic strain or failure (tab. 7). also in this case data reported in tab. 3 are normalized with respect to the maximum measured life and represents the mean values over 3 specimens. it is interesting to observe that tig specimens show a lower time to reach a fixed strain or failure but only if the lower stress level is considered. at a stress level of 475 n/mm2, creep strength is a. carofalo et alii, frattura ed integrità strutturale, 30 (2014) 349-359; doi: 10.3221/igf-esis.30.42 357 increased, with the exception of failure. at this purpose, the failure of tig specimens happen roughly, without showing the increase of strain rate that usually characterizes the tertiary creep behaviour (fig. 9). (a) (b) figure 7: comparison of fatigue curves in terms of applied strain range at rt (a) and 538°c (b). (a) (b) figure 8: comparison of fatigue curves in terms of measured stress range at rt (a) and 538°c (b). δσa/δσmax δεa/δεmax [%] base material tig var % base material tig var % rt 0.673 0.601 -10.7 0.516 0.433 -8.6 538°c 0.565 0.464 -17.9 0.862 0.581 -26.5 table 6: fatigue strength at nref cycles of base material and tig. time [h/hmax] σ εc = 0.2% εc = 0.5% εc = 1% εc = 2% failure n/mm2 bm tig var % bm tig var % bm tig var % bm tig var % bm tig var % 427.5 0.0372 0.0057 -84 0.0976 0.0406 -58 0.1919 0.1431 -25 0.4047 0.3616 -10 1.0000 0.6107 -38 475 0.0006 0.0010 57 0.0023 0.0042 83 0.0167 0.0190 13 0.0336 0.0606 80 0.2743 0.1178 -57 table 7: creep behaviour of base material and tig. a. carofalo et alii, frattura ed integrità strutturale, 30 (2014) 349-359; doi: 10.3221/igf-esis.30.42 358 (a) (b) figure 9: creep deformation against normalized time at 427.5 mpa (a) and 475 mpa (b). conclusion ase and tig welded waspaloy has been mechanically tested and static, low-cycle fatigue and creep behaviour have been evaluated. the comparison of the experimental data between base and tig welded material allowed calculating the reduction of the material performance for each mechanical property. the low level of the applied strain in a large number of fatigue tests constituted a limitation in order to utilize damage models for fatigue life prediction. acknowledgments his work has been financially supported by apulia region in the field of “program agreement about research and competitivity” approved with regional council deliberation n° 2553 dated 22 december 2009. references [1] taira, s., fatigue at elevated temperatures, american society for testing and materials, philadelphia, (1973). [2] tong, j., vermeulen, b., the description of cyclic plasticity and viscoplasticity of waspaloy using unified constitutive equations, int. journal of fatigue, 25 (2003) 413-420. [3] kneifl, m., černý, i., bína, v., damage of low-alloy high temperature steels loaded by low-cycle fatigue and creep, int. j. press. vessel and piping ,78 (2001) 921-927. [4] yeom, j.t., williams, s.j., park, n.k., low-cycle fatigue life prediction for waspaloy, materials at high temperatures, 19(3) (2002) 153-161. [5] garimella, l., liaw, p., klarstrom, d., a study of fatigue crack growth behavior of haynes 242 alloy, jom, 49 (1997) 67-71. [6] cao, m., gabrielli, f., pelloux, r., effect of temperature, loading frequency and heat treatment on fatigue crack growth in a nickel base alloy, res mechanica, 17 (1986) 163-177. [7] bache, m.r., evans, w.j., hardy, m.c., the effects of environment and loading waveform on fatigue crack growth in inconel 718, int. journal of fatigue, 21 (1999) 69-77. [8] goto, m., yamomoto, t., kawagoishi, n., nisitani, h., growth behaviour of small surface cracks in inconel 718 superalloy, in: international conference on temperature-fatigue interaction, ninth international spring meeting, 29 (2002) 237-246. [9] tong, j., dalby, s., byrne, j., henderson, m.b., hardy, m.c., creep, fatigue and oxidation in crack growth in advanced nickel-base superalloys, int journal of fatigue, 23 (2001) 897-902. b t a. carofalo et alii, frattura ed integrità strutturale, 30 (2014) 349-359; doi: 10.3221/igf-esis.30.42 359 [10] roy, a.k., venkatesh, a., marthandam, v., ghosh, a., tensile deformation of a nickel-base alloy at elevated temperatures, journal of material engineering and performance, 17(4) (2008) 607-611. [11] li, z., gobbi, s.l., loreau, j.h., laser welding of waspaloy sheets for aero-engines, journal of mat processing tech, 65 (1997) 183-190. [12] chamanfar, a., jahazi, m., gholipour, j., wanjara, p., yue, s., mechanical property and microstructure of linear friction welded waspaloy, metallurgical and materials transactions a, 42 (2011) 729-744. [13] huang, z.w., li, h.y., preuss, m., karadge, m., bowen, p., bray, s., baxter, g., metall. mater. trans. a, 38a (2007) 1608–20. [14] adam, p., welding of high strength gas turbine alloys, applied science publisher ltd., london, (1978) 737–68. [15] vishwakarma, k.r., richards, n.l., chaturvedi, m.c., in: 6th int. symp. on superalloys 718, 625, 706 and derivatives, e.a. loria, ed, tms, pittsburgh, pa, 2005, 637–47. [16] sekhar, n.c., reed, r.c., power beam welding of thick section nickel base superalloys, sci. technol. weld. join., 7 (2002) 77–87. [17] ma, t.j., li, w.y., xue, q.z., zhang, y., li, j.l., yang, s.q., mater. sci. forum, 580–582 (2008) 405–408. [18] oja, m., ravi chandran, k.s., tryon, r.g., orientation imaging microscopy of fatigue crack formation in waspaloy: crystallographic conditions for crack nucleation, international journal of fatigue, 32 (2010) 551–556. [19] warren, j., wei, d.y., a microscopic stored energy approach to generalize fatigue life stress ratios, int. journal of fatigue, 32 (2010) 1853-1861. [20] morrow, j., cyclic plastic strain energy and fatigue of metals, internal friction, damping, and cyclic plasticity, astm stp 378, philadelphia pa, (1965) 45-84. [21] leis, b.n., an energy-based fatigue and creep-fatigue damage parameter, j press ves tech trans asme, 99 (1977) 524–533. microsoft word numero_34_art_53 k.l. yuan et alii, frattura ed integrità strutturale, 34 (2015) 476-486; doi: 10.3221/igf-esis.34.53 476 focussed on crack paths modelling of ultrasonic impact treatment (uit) of welded joints and its effect on fatigue strength k.l. yuan, y.sumi yokohama national university, japan sumi@ynu.ac.jp abstract. ultrasonic impact treatment (uit) is a remarkable post-weld technique applying mechanical impacts in combination with ultrasound into the welded joints. in the present work, a 3d simulation method including welding simulation, numerical modelling of uit-process and an evaluation of fatigue crack growth has been developed. in the fe model, the actual treatment conditions and local mechanical characteristics due to acoustic softening are set as input parameters. the plastic deformation and compressive stress layer are found to be more pronounced when acoustic softening takes place. the predicted internal residual stress distributions of welded joint before and after uit are compared with experimental results, showing a fairly good agreement with each other. finally, simulated results of fatigue crack growth in various residual stress fields are well compared with test results, so that the proposed model may provide an effective tool to simulate uit-process in engineering structures. keywords. uit; residual stress; fem; surface crack growth. introduction t is well known that the fatigue strength of steel plates increases in proportion to its static strength. on the other hand, the fatigue strength of the welded joints is little influenced by the static strength level because of the tensile welding residual stress and high stress concentration near the weld toe. ultrasonic impact treatment (uit) is a new method for increasing fatigue strength by improving the weld toe geometry, removing defects and introducing beneficial compressive residual stress [1-3]. recently, new iiw guidance on fatigue strength improvement using high frequency mechanical impact (hfmi) methods including uit has been prepared by marquis et al. [4-5]. in parallel to the development of iiw guideline, ship classification societies have also accepted or investigated the uit as post-weld treatments in ship and offshore structures [6-7]. in order to better understand the effects of uit on fatigue performance of welded joints, its mechanism has been experimentally investigated in several studies. cheng et al. [2] measured the residual stress induced by uit using both xray and neutron diffraction (nd) techniques for the first time. the compressive stress layer was found not less than 1mm in depth for welded specimen. a german research project [8, 9] has presented the experimental data that the compressive residual stress is generated down to a depth of 1.5 to 2 mm with maximum values at approximately 0.4 to 0.5 mm below the surface. after treatment the weld toe radius is averaged by 1.5 to 2 mm with its groove depth of 0.1 to 0.2 mm. the study at the university of waterloo, canada [10, 11] was carried out to investigate the fatigue performance of structural steel welds subjected to uit at under-, proper and over-treatment levels, respectively. a close relationship was found between the measured groove depth and local residual stress, indicating the groove depth as an important quality control i k.l. yuan et alii, frattura ed integrità strutturale, 34 (2015) 476-486; doi: 10.3221/igf-esis.34.53 477 parameter. ultrasonic impact treatment consists of ultrasonic waves and mechanical impacts. very limited studies [12-14] have demonstrated that the ultrasonic vibration superimposed by uit on metals has indeed an acoustic softening effect on material properties undergoing deformation. normally the experimental methods for residual stress measurements need considerable cost, time and skillful technique. it is practically impossible to obtain full field measurement of residual stress. for this reason, the residual stress induced by uit has been recently evaluated by some studies using finite element (fe) analysis. there are mainly two groups of simulation methods for uit process: quasi-static implicit and dynamic explicit methods. the former is modelled as pressing the pin at the weld toe to one prescribed depth by displacement or load control approaches, rather than peening [15-16]. in the latter [17-18], the modelled pin impacts to a symmetry-cell model that is widely used in shot peening simulation [19], however, the welding residual stress is not taken into account. it is found that the predicted in-depth residual stress and groove depth could not consist well with measurements together [15-16], because in the above mentioned simulations the acoustic softening effect has not been introduced, which plays an important role in the mechanism of uit. therefore in this study, one novel 3d prediction approach including thermal-mechanical welding simulation, dynamic elastic-plastic fe analysis of uit-process, and an evaluation of surface fatigue crack growth for cruciform weld joint has been proposed. the actual process parameters and ultrasonic induced material softening, which is appropriately adjusted to fit experimental results, are considered. the predicted residual stresses distributions, treated weld toe shape and fatigue strength are compared with published test data [3, 20]. the uit process s depicted in fig.1, the ultrasonic impact treatment method is based on conversion of harmonic oscillations of the ultrasonic transducer into impact pulses at the treated surface. in order to efficiently transfer the energy into the work piece, the installed cylindrical pins can freely move in a gap between the waveguide end and treated surface. this kind of high frequency impacts of the pin in the combination with the ultrasonic stress waves transmitted into the work piece through the pin contacting the treated surface is called as ultrasonic impact [12]. figure 1: mechanism of uit [12]. model of ultrasonic impact in order to consider ultrasonic impact phenomenon in numerical simulation, one simplified model based on the description by statnikov [12, 21] as illustrated in fig.2 is proposed. during one impact period tim, it comprises both the ultrasonic impact period t1 and pause between impacts t2. in this work, the t1 is assumed as 1 millisecond, in the case of impact frequency fim of 100hz and the relation t1/tim=0.1, which is in the range of ultrasonic impact time from hundreds of microseconds to units of milliseconds measured by statnikov [12]. the oscillations of pin at a frequency of 27 khz, which mainly cause the plastic deformation, will recur about 30 times during reboundless contact phase up to 1 millisecond. to construct uit fe model, the impact velocity of pin during reboundless period is essential. for the impact velocity, it can be assumed here that all the ultrasonic impact on the treated surface will occur at the same velocity and an average a k.l. yuan et alii, frattura ed integrità strutturale, 34 (2015) 476-486; doi: 10.3221/igf-esis.34.53 478 velocity is considered. this average velocity is taken to be the maximum initial velocity of the waveguide. considering that the sinusoidal harmonic signal delivered by the transducer is ( ) sin( 2 )x t a ft (1) the maximum initial velocity is max 2v fa (2) where a is the maximum displacement amplitude at the waveguide output end and f represents ultrasonic oscillation frequency of uit. a) b) figure 2: (a) oscilloscope picture of transducer excitation (top) and ultrasonic impact excitation (bottom) with uit [12] , (b) model of ultrasonic impact, t1-ultrasonic impact length (reboundless), t2-pause between ultrasonic impacts (rebounding off), fim-impact frequency, ful-ultrasonic oscillation frequency, and t1/tim=0.1~0.3 [12], fim=100~120hz, ful =27~44 khz [1]. a) b) figure 3: ultrasonic-assisted tension tests; (a) schematic diagram of test devices with different modes, (b) measured force-deformation data [12]. acoustic softening effect the effect of ultrasonic energy on metal deformation behavior for a wide range of metals has been well known since early 1950’s [22]. it was observed that the apparent yield strength of the material is immediately reduced upon the application of ultrasonic energy and restores as the removal of ultrasonic energy. as for uit, the relative motion between the specimen and pin complicates the acoustic softening process. statnikov [12] performed an ultrasonic-assisted tension test, in order to confirm the effect of ultrasonic impact via an intermediate pin on the deformation resistance reduction in comparison with a direct contact of the ultrasonic transducer and the specimen, as shown in fig.3. an obvious reduction about 24 k.l. yuan et alii, frattura ed integrità strutturale, 34 (2015) 476-486; doi: 10.3221/igf-esis.34.53 479 26% in ultimate tensile strength under ultrasonic impact was observed, which is just a little less than the 27-30% reduction in the case of direct ultrasonic action. nevertheless, the results suggested that the uit could effectively transfer ultrasound into the treated objects through the area of plastic deformation by means of ultrasonic impact. to the best knowledge of the authors, there is no model to directly quantify the acoustic softening effect related to uit. hence, in this work a yield stress reduction parameter η accounting for acoustic softening in eq.3 is employed. the value of η is iteratively adjusted by comparing the predicted indentation depth with experiment. as o (1 )    (3) where σas is the flow stress considering acoustic softening, σo is the flow stress without vibration and η ranges from 0 to 1 depending on the amount of acoustic softening. finite element modeling n the present study, a three dimensional simulation procedure is set up including the uncoupled thermo-mechanical welding simulation by sysweld [23], transfer of the results to the initial-stress state of a dynamic model of uit by explicit method in ls-dyna [24], as shown in fig.4. figure 4: flowchart of welding-uit process simulation. figure 5: geometry and dimensions of uit specimen. analysis model and process parameters a non-load-carrying cruciform joint used in the recent experimental work by suzuki et al [20] is selected as analysis object. fig.5 shows the dimensions of test specimen, which was welded using co2 fillet welding with jis-sm490a base metal plate. the welding parameters are given in tab. 1. i k.l. yuan et alii, frattura ed integrità strutturale, 34 (2015) 476-486; doi: 10.3221/igf-esis.34.53 480 the welded joints for as-weld and uit were fabricated by one pass welding with leg length of 7mm.the used uit equipment was esonixtm 27 uis. the operating frequency of ultrasonic generator was 27 khz, shifting speed of 10 mm/s and 3-mm-diameter hardened metal pins. welding material wire diameter[mm] speed [mm/min] current [a] voltage [v] arc efficiency sf-1 1.2 300 250 29 80% table 1: welding conditions. simulation of welding process for welding simulation, a half symmetrical 3d model of cruciform joint is created. this fe model has been constructed for small width of 4 mm, in order to be most effective considering the accuracy and computational effort (see fig.6). therefore both sides of this segment are restrained in z-direction, to simulate the specimen in plane strain state. the fe model mainly employs 8-node hexahedral solid elements except for few wedge elements in the weld bead region. near the weld toe, an extremely fine mesh (0.2×0.1×0.2mm) is required for the following uit process simulation. in the first step of thermal analysis, heat input (1160 j/mm) is given all at once to the weld metal and an initial temperature of 1400°c for activation of the weld bead material elements is assumed. accompanying with heat radiation and convection, the cooling-down period between the subsequent weld is set as 1 hour. for the second step of mechanical analysis, the material model is assumed to follow von mises yield criterion with bilinear kinematic hardening. the used temperature-dependent thermal and mechanical material properties are illustrated in fig.7. figure 6: finite element model for welding simulation. a) b) figure 7: temperature-dependent material properties referring to sysweld material database [23]. k.l. yuan et alii, frattura ed integrità strutturale, 34 (2015) 476-486; doi: 10.3221/igf-esis.34.53 481 simulation of uit process after welding simulation in sysweld, the results of cruciform joint including element information, as-weld residual stress distribution and plastic strain are imported into ls-dyna. the tips of 3-mm-diamter pins are modelled as elastic body with an elastic modulus of 206 gpa, poisson’s ratio of 0.3 and measured mass of 1.5 gram [16]. the pins are angled at 67.5° to the top and bottom surfaces of the specimen. according to eq. 2, the impact velocity vimp is estimated as 5m/s with corresponding equipment parameters (oscillation frequency of 27 khz and amplitude of 30 μm under loaded condition [1]). the pin is controlled to continuously impinge the weld toe at the same location for 30 times (equivalent to one ultrasonic impact as mentioned before) by using restart analysis option of ls-dyna. after each ultrasonic impact, the pin is moved 0.4 mm along weld line to achieve a smooth peened groove with reasonable calculation efforts. this leads to at least four overlapping indentations for the contact area of pin. the weld toe on the top surface is first peened, and that on the bottom surface is subsequently treated. a) b) figure 8: (a) finite element model of uit, (b) mechanical properties considering acoustic softening. the material of the weld joint is assumed to follow linear kinematic hardening behavior. to consider the acoustic softening effect in eq.3, the parameter η is selected as 40% by trial and error, so that predicted groove depth fits to the experimental results. the softening zones (sz) around the weld toe in fig.8 are assumed to be affected by acoustic softening during peening, of which each depth is determined as 8mm according to measured stress reduction in 16-mmthickness specimen [14], and the remain zones (nsz) are not affected by softening. it should be noted that the apparent yield stress dominantly affected by acoustic softening reveals reduction, although the strain-rate effect due to oscillatory stress has been implicitly included in the above mentioned ultrasonic-assisted test [12]. in order to prevent unnecessary long post-impact residual oscillations, which may lead to numerical instability, in this model the material proportional damping is employed as follow: 02   c m m (4) 0 2 e t     (5) where c is the damping matrix, m is the mass matrix, α is the mass proportional rayleigh damping, ω0 is the lowest natural frequency, ξ is the corresponding damping ratio, e is elastic modulus, ρ and t are density and thickness of the plate, respectively. according to [19], the adopted value of ξ=0.5 is adequate for the rapid stress convergence. moreover, the contact surfaces are set between the pin tip and the specimen with a coulomb friction coefficient μ=0.5. validation of welding-uit simulation determination of acoustic softening parameter he acoustic softening parameter η is firstly selected by trial and error so as to match the experimentally measured indentation depth d and weld toe radius r [20] on a cross-section with the predicted ones after one ultrasonic impact, as shown in fig.9. it can be seen that it is easier to form a smooth change of the shape at the weld toe t k.l. yuan et alii, frattura ed integrità strutturale, 34 (2015) 476-486; doi: 10.3221/igf-esis.34.53 482 when the resistance necessary for plastic deformation is decreased due to acoustic softening, and the parameter, η=40%, is used in the following uit simulation. this result is comparable to the measured yield strength reduction of 45% in stainless steel specimen under direct ultrasonic energy 600 watt [14], while the consumed power of 27 khz-type uit equipment is 600-1200 watt [1]. the internal residual stress profiles during 30 times of pin’s impinging (one ultrasonic impact without translation along weld line) are shown in fig.10. near the plate surface the compressive residual stress layer appears. the surface compressive residual stress gradually increases with the peening, but this increase is saturated after 30 times of continuous peening. having introduced the yield strength reduction due to acoustic softening, the compressive residual stress layer is deepened approximately by 2mm, while the maximum value decreases in comparison with that without acoustic softening (see fig.10b). a) b) c) figure 9: determination of acoustic softening by comparing the treated weld toe shape; (a) simulated with η=0%, (b) simulated with η=40%, (c) measured by suzuki et al. [20]. a) b) figure 10: evolution of in-depth transverse residual stress distributions during one ultrasonic impact; (a) simulated without acoustic softening, (b) simulated with η=40%. residual stress distribution in the depth direction of as-weld and uit joints in practice, the peening tool is travelling along the weld line, until the original shape of the weld toe disappears and the smooth groove is formed. the transverse residual stress σx acting perpendicular to the welding line is considered as the driving or resistance force for the surface crack at the weld toe. therefore, considering the movement of the pin, the transverse residual stress distribution and weld toe shape before and after uit are illustrated in fig.11. it has been confirmed that the tensile welding residual stress at the weld toe has been changed to significant compressive residual stress. the step-by-step movement of 0.4 mm provide sufficient overlapping of the impacts. in order to verify the accuracy of the finite element simulation, the residual stress distributions in the depth direction are compared with those measured by x-ray and neutron diffraction methods, respectively [20]. as show in fig.12, there exist good agreements between the experimental and numerical results. slight over-estimation of uit compressive residual stress on the surface k.l. yuan et alii, frattura ed integrità strutturale, 34 (2015) 476-486; doi: 10.3221/igf-esis.34.53 483 is seen, however, it has been found that the measured surface stress by x-ray method is very sensitive to the location of measurement spot [25]. a) b) figure 11: transverse residual stress distributions and plastic deformation at weld toe; (a) as-weld, (b) uit with η=40%. figure 12: distribution of transverse residual stress of as-weld and uit specimens in the depth direction, and comparison with experimental results [20]. fatigue life prediction or accurate fatigue life prediction of a weld joint, it is necessary to consider the stress concentration and residual stress near the weld toe. according to the measurements [20], the weld toe radius r of as-weld and uit specimen are assumed as 0.25 mm and 2 mm, respectively. the stress concentration factor, kt , of the weld toe is estimated by the following formula proposed by tsuji [26] 0.467t 1 [1.348 0.397 ln( )] s tk q f     (6) where ( / ) / [ 2.8( / ) 2]q l r w t  2[1 exp( 0.9 / 2 )] / [1 exp( 0.9 / 2 ( )]f w l w l          t is the main-plate thickness of 16mm, l is the leg length of 7mm, θ is the flank angle of 45°, and w=s=t+2l. under tension load, the stress distribution near the weld toe is calculated by 1/2 3/2t n 1 ( ) [( ) ( ) ] / 2 2 / 22 2 x k r r y y r y r       (7) f k.l. yuan et alii, frattura ed integrità strutturale, 34 (2015) 476-486; doi: 10.3221/igf-esis.34.53 484 proposed by glinka [27] in the vicinity of the weld toe taking kt so obtained by eq.6 into account, while that apart from the weld toe is calculated by elastic finite element analysis. the symbol used for eq. 7 and the combined stress distributions are shown in fig.13, where σn represents the nominal stress. a) b) figure 13: (a) symbol and coordinate used in eq.7, (b) assumed stress concentration near the weld toe. the stress intensity factors ki are calculated by 1/2i 0[ ( ) ( , ) ] [sec( )] a x c a k y m y a dy b t    (8) which is based on the weight function method in code api [28]. here, the uniform stress distributions in the specimen width direction are assumed, and m(y,a): the weight function which is standardized by the api, σx(y): the stress distributions, y: distance from surface, a: surface crack depth, c : half crack length, and b: width of specimen. the crack growth rate of the surface crack at the weld toe is given by eff eff th/ [( ) -( ) ] m mda dn c k k   (9) based on modified paris-elber law using the effective stress intensity range, keff, and its threshold value, ( keff)th. the total and effective stress intensity ranges, k and keff, are calculated by total total min res eff max min total total max res / (1.5 ) 0.5 for , with =, 0.5 k r r k k k k k k r k r k k             (10) where material constants c=1.45e-11, m=2.75, ( keff)th=2.45 mpa m according to wes2805[29], rtotal is the total stress ratio, kmax, kmin and kres are stress intensity factors for maximum, minimum applied stress and residual stress, respectively. a single initial semi-circular crack of depth 0.2 mm and final crack depth of 0.8t is assumed to propagate at the weld toe in the center of specimen width, referring to the wes recommendation. fig. 14 shows a comparison of the results of estimations, experiments [3, 20] and recommended fat-values [4]. these results demonstrate that the proposed fatigue life prediction method clearly distinguishes the difference of fatigue strengths of as-weld and uit weld joints, by taking the stress concentration and residual stress near the weld toe into account. it should be noted that since multi initial crack followed by crack coalescence are not considered in this work, the present simulation may lead to a slight over-estimation at high applied stress range. in addition, the predicted surface crack shapes are also compared in fig.14, in which we can clearly observe that the aspect ratio of the uit case is relatively higher than that of as-weld case because of the compressive residual stress combined with a lower stress concentration factor near the plate surface. k.l. yuan et alii, frattura ed integrità strutturale, 34 (2015) 476-486; doi: 10.3221/igf-esis.34.53 485 a) b) figure 14: (a) validation of the predicted fatigue life of the as-weld and uit joints, (b) predicted evolution of surface crack shapes. conclusions ased on the existing experimental observations, a model describing the ultrasonic impact phenomenon is proposed in this paper. employing commercial codes sysweld and ls-dyna, a three dimensional numerical simulation approaches for uit-improved welded joints is established, of which the effectiveness has been well validated by comparing with experimental results. from the numerical results, it has been verified that uit is an effective method to re-distribute the residual stress and reduce the stress concentration near the weld toe area. deformation and compressive residual stress layer are more pronounced when acoustic softening occurs, which is necessary to be considered in numerical simulation. acknowledgements he authors are grateful to professor y. kawamura, yokohama national university, dr. h. shimanuki and dr. t. okawa, nippon steel & sumitomo metal corporation, for their helpful discussions. references [1] galtier, a., statnikov, e., the influence of ultrasonic impact treatment on fatigue behavior of welded joints in highstrength steel, weld world, 48 (5-6) (2004) 61-66. [2] cheng, x.h., fisher, j.w., prask, h.j., gnäupel-herold, t., yen, b.t., roy, s., residual stress modification by postweld treatment and its beneficial effect on fatigue strength of welded structures, int j fatigue, 25(9) (2003)1259-1269. [3] okawa, t., shimanuki, h., funatsu, y., nose, t., sumi, y., effect of preload and stress ratio on fatigue strength of welded joints improved by ultrasonic impact treatment, weld world, 57(2) (2013) 235-241. [4] marquis, g.b., mikkola, e., yildirim, h. c., barsoum, z., fatigue strength improvement of steel structures by highfrequency mechanical impact: proposed fatigue assessment guidelines, weld world, 57(6) (2013) 803-822. [5] marquis, g.b., barsoum, z., fatigue strength improvement of steel structures by high-frequency mechanical impact: proposed procedures and quality assurance guidelines, weld world, 58(1) (2014) 19-28. [6] american bureau of shipping, commentary on the guide for the fatigue assessment of offshore structures (2014). [7] polezhayeva, h ., howarth, d., kumar, m., kang, j. k., ermolaeva, n., lee, j.y., effect of ultrasonic peening on fatigue strength of welded marine structures-lloyd’s register research programme., proc. 24th isope conference, (2014) 359-365. [8] weich, i., edge layer condition and fatigue strength of welds improved by mechanical post-weld treatment, weld world, 55(1-2) (2011) 3-12. b t k.l. yuan et alii, frattura ed integrità strutturale, 34 (2015) 476-486; doi: 10.3221/igf-esis.34.53 486 [9] fosta research association for steel applications, rerresh-extension of the fatigue life of existing and new welded steel structures (2011). [10] yekta, r.t., ghahremani, k., walbridge, s., effect of quality control parameter variations on the fatigue performance of ultrasonic impact treated welds, int j fatigue, 55 (2013) 245-256. [11] ghahremani, k ., safa, m., yeung, j., walbridge, s., haas, c., dubois, s., quality assurance for high-frequency mechanical impact (hfmi) treatment of welds using handheld 3d laser scanning technology, weld world, 59(3) (2014) 391-400. [12] statnikov, e., physics and mechanism of ultrasonic impact treatment, iiw document 13 (2004) 2004-04. [13] dutta, r.k., petrov, r.h., delhez, r., hermans, m., richardson, i. m., böttger, a. j., the effect of tensile deformation by in situ ultrasonic treatment on the microstructure of low-carbon steel, acta materialia, 61(5) (2013) 1592-1602. [14] gao, h., dutta, r.k., huizenga, r.m., amirthalingam, m., hermans, m., buslaps, t., richardson, i.m., stress relaxation due to ultrasonic impact treatment on multi-pass welds, sci technol weld joining, 19(6) (2014) 505-513. [15] roy, s., experimental and analytical evaluation of enhancement in fatigue resistance of welded details subjected to post-weld ultrasonic impact treatment, diss. lehigh university, (2006). [16] le quilliec, g., lieurade, h. p., bousseau, m., drissi-habti, m., inglebert, g., macquet, p., jubin, l., mechanics and modelling of high-frequency mechanical impact and its effect on fatigue, weld world, 57.1 (2013) 97-111. [17] yang, x., zhou, j., ling, x., study on plastic damage of aisi 304 stainless steel induced by ultrasonic impact treatment, mater des, 36 (2012) 477-481. [18] yang, x., ling, x., zhou, j., optimization of the fatigue resistance of aisi304 stainless steel by ultrasonic impact treatment, int j fatigue, 61 (2014) 28-38. [19] meguid, s. a., shagal, g., stranart, j. c., 3d fe analysis of peening of strain-rate sensitive materials using multiple impingement model, int j impact eng, 27(2) (2002) 119-134. [20] suzuki, t., okawa, t., shimanuki, h., nose, t., ohta, n., suzuki, h., moriai, a., effect of ultrasonic impact treatment (uit) on fatigue strength of welded joints, adv mat res, 996 (2014) 736-742. [21] statnikov, e., method for modifying or producing materials and joints with specific properties by generating and applying adaptive impulses a normalizing energy thereof and pauses there between, u.s. patent no. 7,301,123 (2007). [22] izumi, o., oyama, k., suzuki, y., effects of superimposed ultrasonic vibration on compressive deformation of metals, trans jpn inst met, 7(3) (1966) 162-167. [23] esi group, sysweld ver.2014 (2014). [24] livermore software technology corporation, ls-dyna keyword user’s manual ver. 971 (2007). [25] yildirim, h.c., marquis, g.b., a round robin study of high-frequency mechanical impact (hfmi)-treated welded joints subjected to variable amplitude loading, weld world, 57(3) (2013) 437-447. [26] tsuji, i., estimation of stress concentration factor at weld toe of non-load carrying fillet welded joint, j soc naval architects jpn, 80 (1990) 241-251, in japanese. [27] glinka, g., calculation of inelastic notch-tip strain-stress histories under cyclic loading. eng fract mech, 22(5) (1985) 839-854. [28] american petroleum institute, api 579-1 recommended practice for fitness-for-service (2007). [29] the japan welding engineering society, wes 2805 method of assessment for flaws in fusion welded joints with respect to brittle fracture and fatigue crack growth (1997). microsoft word numero_46_art_1 t. bounini et alii, frattura ed integrità strutturale, 46 (2018) 1-13; doi: 10.3221/igf-esis.46.01 1 developments in the fracture and fatigue assessment of materials and structures simulation of the behavior of aluminum alloys welded in friction stir welding fsw (case of aa5083 and aa 6082) bousekrine taha bounini, benattou bouchouicha university of sidi bel abbes, algeria tahabounini@yahoo.fr, benattou_b@yahoo.fr abdelkader ghazi university of mascara, algeria ghaziaek@yahoo.fr abstract. the friction stir welding fsw is a topical technique to date, either for experimental or numerical research topics. based on the fact that the majority of the heat generated, comes from the contact between the workpiece and the shoulder, and from the work of friction done by the pin. thus, it is crucial to approach the reality, by simulating the most of the conditions, related to the fsw process. the development of a numerical model allows us, not only to simulate the fsw welding process, but also to conduct a parametric study and vary the welding conditions as desired. therefore, a numerical study is conducted on the friction stir welding of aa 5083h111 work piece, in order to perceive the optimal settings. a three dimensional model designed by ansys apdl was used. before proceeding with this, a preliminary experimental study was carried out on fsw welded aa 6082 –t6 specimens and base material, using tensile and fatigue tests. the numerical results obtained, essentially longitudinal residual stresses, are compared to other studies, experimental and numerical. keywords. fsw; parametric study; aa5083h111; aa 6082-t6; fatigue test. citation: bounini, t., bouchouicha, b., ghazi, a., simulation of the behavior of aluminium alloys welded in fsw (case of aa5083, aa6082), frattura ed integrità strutturale, 46 (2018) 1-13. received: 28.03.2018 accepted: 17.07.2018 published: 01.10.2018 copyright: © 2018 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. introduction riction stir welding (fsw) is a solid-state welding technique that involves the joining of metals without filler materials. a cylindrical rotating tool plunges into a rigidly clamped workpiece and moves along the joint to be welded. as the tool moves along the joint, heat is generated by friction between the tool shoulder and the workpiece. additional heat is generated by plastic deformation of the workpiece material. the generated heat results in thermal softening of the workpiece material. the translation of the tool causes the softened workpiece material to flow from the f http://www.gruppofrattura.it/va/46/1.mp4 t. bounini et alii, frattura ed integrità strutturale, 46 (2018) 1-13; doi: 10.3221/igf-esis.46.01 2 front to the back of the tool where it consolidates. as cooling occurs, a solid continuous joint between the two plates is formed. no melting occurs during the process, and the resulting temperature remains below the solidus temperature of the metals being joined. fsw offers many advantages over conventional welding techniques, and has been successfully applied in the aerospace, automobile, and shipbuilding industries. thermal and mechanical behaviors are mutually dependent during the fsw process. because the temperature field affects stress distribution, this example uses a fully thermo-mechanically coupled model. the model consists of a coupled-field solid element with structural and thermal degrees of freedom. the model has two rectangular steel plates and a cylindrical tool. all necessary mechanical and thermal boundary conditions are applied on the model. the simulation occurs over three load steps, representing the plunge, dwell, and traverse phases of the process (fig. 1) [1]. figure 1: schematic drawing of fsw process [2]. numerical analysis of friction stir welding will allow many different welding processes to be simulated in order to understand the effects of changes in different system parameters before physical testing, which would be time-consuming or prohibitively expensive in practice [2]. this model assumes that two sheets of aa 5083 h111 are welded by a rotating tool. this model takes into account the actual interaction between the tool and the workpiece, and the deformation of the material around the tool. it should be noted that most of the finite element fe models, consider the two sheets as one, or simulate the heat flux without simulating the tool, or a part of the tool. the welding parameters, such as the variation of the welding speed, the rotation speed, and the material of the welded sheets, and their effects on the longitudinal stress, and on the distribution of the temperature flow. an experimental study was carried out, for the purpose of defining the impact of the change of welding parameters on the tenacity of welded joints. the friction stir welding is done using a milling machine. fatigue and tensile tests were carried out on test tubes of material alluminium alloy 6082-t6. experimental study on aa6082-t6 ur study focuses on the characterization of two materials 6082-t6 (base material and fsw welded material). the characterization tests are based on two essential tests, tensile test to identify the behavioral laws of the different materials and fatigue test to see the evolution of a crack in the different configurations. the chemical composition of the studied alloy is reported in the table below: table 1: the chemical composition of aa 6082-t6. tensile test for the different parts of the mechanical tests allowing the characterization of the materials, we carried out simple tensile tests on "dumbbell" specimens machined in aluminum sheets (longitudinal). the geometry of the specimens is described in fig. 2. o al alloy si mg fe cu mn cr zn ti al 6082-t6 1.3 1.2 0.5 0.1 1.0 0.25 0.2 0.1 98.3 t. bounini et alii, frattura ed integrità strutturale, 46 (2018) 1-13; doi: 10.3221/igf-esis.46.01 3 the following figure shows the true stress-true strain curves that characterize an elasto-plastic behavior of the studied materials. figure 2: details of the dumbbell specimen. figure 3: tensile behavior of 6082 t6 aluminum alloy with and without welding. the usual mechanical characteristics of the two materials are given in tab. 2 below: table 2: tensile mechanical characteristics. the conventional yield stress in the base material (314mpa) is well above the yield strength in fsw welded specimens (260mpa). fatigue test the cracking tests were carried out on ct50 test specimens of thickness 06 mm, in accordance with astm-e-647 norm, the dimensions of which are given in fig. 4. the cracking tests were carried out at the university of sidi belabbes, on an instron electrohydraulic machine of capacity 100 kn in static and 50 kn in dynamics. 0,00 0,02 0,04 0 100 200 300 400 500 600 700  v ( m p a ) v (%) 6082 6082 fsw material e (mpa) σe (mpa) σmax (mpa) εy (%) εfailure (%) k (mpa) n al 6082-t6 74000 314 487 0.0046 0.029 1351 0.21 al 6082-t6 fsw 69000 260 391 0.0038 0.019 848 0.19 t. bounini et alii, frattura ed integrità strutturale, 46 (2018) 1-13; doi: 10.3221/igf-esis.46.01 4 the crack length was measured using a magnifying optical binocular bezel and a stroboscope mounted on a device attached to the machine. figure 4: dimensions of the ct50 specimen used for cracking tests. propagation rates the fatigue crack propagation tests were carried out for both materials (fig. 5), in the range of speeds between 4.10-5 and 2.10-2 mm/cycle at ambient air and with a load ratio (r = 0.1). the values of k vary from: 10 to 47 in aluminum 6082-t6 10 to 45 in fsw welded aluminum 6082-t6. the results obtained for the different specimens are represented by fig. 5: figure 5: evolution of the cracking speed as a function of k for the two materials. in order to compare more clearly and more systematically the evolution of the cracking rate in the two grades, we chose to represent them by their respective linear regression lines obtained from the experimental points (seven point method) on the linear parts of the curves. indeed, we can notice that the curves present an almost rectilinear look on a large part of the domain explored, being able to be presented by paris’ law of the form:   mda c k dn   (2.1) the results of the cracking tests obtained in the two materials respectively recorded in the tab. (3). 10 100 1e-4 1e-3 0,01 0,1 1 6082 welded 6082 d a /d n ( m m /c yc le ) k (mpa m 1/2 ) t. bounini et alii, frattura ed integrità strutturale, 46 (2018) 1-13; doi: 10.3221/igf-esis.46.01 5  table 3: equations characterizing the paris’ law in the different zones studied. the cracking rate da/dn, for low values of (δk <10) is decreasing respectively in both cases (6082-t6 and 6082-t6 fsw), however, this gap decreases as increases, which means that: microstructure in the two shades possesses almost the same appearance and the same characteristics. in this area (typical of paris), the cracking rate is almost similar in the two materials.  material and numerical study on aa5083-h111 introduction he development of a numerical model allows us not only to simulate the fsw welding process, but also to make a parametric study and vary the welding conditions as desired. song and kovacevic have modeled the heat transfer in fsw using the finite difference method [4, 5]. few papers have dealt directly with the modeling of thermomechanical stresses in fsw. chao [6] proposed a model to predict the thermal history and the subsequent thermal stress and distortion of the workpiece without involving the the tool mechanical effect. dong [7] developed several models to deal separately with the subproblems of heat transfer, material flow, and plastic flow. from the point of physics for the fsw process, the tool mechanical effect needs to be included into the thermo-mechanical model. c.m. chen, r. kovacevic has considered the the tool mechanical effect (only the shoulder was included) [8]. the model used is based on the model developed by ansys, which took as a reference the the zhu and chao model. the approach presented in this article is more realistic, because it takes into consideration the whole tool: the shoulder and the pin, what it approaches us to reality. the main parameters affecting the mechanical behaviour are multiple: the rotational and advancing speed, the tool size and the tool penetration. however, the parameters taken under consideration are the rotation speed, the welding speed and material change. we observed the residual stress and the heat distribution. experimental reference study on aa 5083 h111 to be able to compare and validate the numerical study we chose the experimental study on the material aa 5083h111. the results obtained by ghazi [3], on another material aa 5083, by varying the welding parameters, rotational and welding speed, led to identify the optimal welding parameters. the alloy studied is al 5083h111, which is an al-mg (tab.4) in the h111 state (deformed by 25% by rolling). this strain hardening alloy will serve us to understand the different phenomena occurring during welding without involving precipitation. the alloy 5083h111 was chosen because it has magnesium and manganese levels fairly close to those of the alloy 2024 used in aeronautical structures for the fuselage. the chemical composition of aluminum al 5083h111 is given by the tab. 4. the mechanical properties of the aluminum alloy were determined along the longitudinal directions l. the following table shows the material properties: al si fe cu mn mg cr zn ti 0.15 0.40 0.40 0.10 0.10 4.90 0.25 0.25 0.15 e [mpa] ys[mpa] uts[mpa] a[%] hv k[j/cm2] 71008 155 236 16.5 88 45 table 4: plates material characteristics: aluminum alloy 5083h111. the welding parameters are shown in the tab. 6. alloy paris’ law k 6082-t6 da/dn=7.41e-8k3.02 10 to 47 mmpa 6082-t6 fsw da/dn= 3.32e-14k7.32 10 to 45 mmpa t t. bounini et alii, frattura ed integrità strutturale, 46 (2018) 1-13; doi: 10.3221/igf-esis.46.01 6 table 5: plates material other mechanical and thermal characteristics. table 6: welding parameter (speed of rotation welding speed). (a) (b) figure 6: a) variation of the elastic limit re as a function of the rotational speed. b) variation of the elastic limit re as a function of the welding speed. density (kg/m3) 2660 thermal conductivity( w/m.k) 110 -140 thermal expansion coefficient k-1 24.2 10-6 specific heat (j/kg°c) 900 speed of rotation ω [rpm] 710 1000 1400 2000 welding speed v [mm/min] 40 80 100 200 400 40 80 100 200 400 40 80 100 200 400 40 80 100 200 400 t. bounini et alii, frattura ed integrità strutturale, 46 (2018) 1-13; doi: 10.3221/igf-esis.46.01 7 the analysis of the tensile curves, clearly shows the variation of the elastic limit re as a function of the variation of the rotational speed and the welding speed (fig. 6). tensile tests have shown that these parameters give a good quality of welding: [710 rpm, 80 mm/min]. [1000 rpm, 100 mm/min]; [1000 rpm, 200 mm/min]. [1400 rpm, 100 mm/min]. [2000 rpm, 80 mm/min]; [2000 rpm, 100 mm/min] modeling and meshing for reducing the calculation time, dimensions are reduced. the reduced model is constituted by two rectangular shaped plates 1 x 0.7 x 0.1 mm. the tool shoulder diameter is 0.2 mm. the pin has a height of 0.3 mm. a direct coupled-field analysis is performed on a reduced-scale version of the zhu and chao model [6]. also, rather than using a moving heat source as in the reference model, a rotating and moving tool is used for a more realistic simulation. the simulation welds two alu alloy 5083 h111 plates (workpiece) with a cylindrical shape tool, as shown in the fig. 7. the fsw process was simulated taking into account a fully three-dimensional model, a thermo-mechanical analysis was developed with ansys software. both the workpiece and the tool are modeled using coupled-field element solid226. the contact pairs has (contact analysis) was identified by the two elements conta174 and targe170 for contact and target surfaces (fig. 8). figure 7: geometry of the workpiece and tool by ansys. figure 8: finite element mesh of fsw. mechanical boundary conditions the workpiece is fixed by clamping each plate [1]. the clamped portions of the plates are constrained in all directions. to simulate support at the bottom of the plates, all bottom nodes of the workpiece are constrained in the perpendicular direction (z direction). thermal boundary conditions the frictional and plastic heat generated during the fsw process propagates rapidly into remote regions of the plates. on the top and side surfaces of the workpiece, convection and radiation account for heat loss to the ambient. conduction losses also occur from the bottom surface of the workpiece to the backing plate. mechanical and physical properties accurate temperature calculation is critical to the fsw process because the stresses and strains developed in the weld are temperature-dependent. thermal properties of the alluminium alloy 5083 h111 plates such as thermal conductivity, specific heat, and density are temperature-dependent. mechanical properties of the plates such as young’s modulus and the coefficient of thermal expansion are considered to be constant due to the limitations of data available in the literature. it is assumed that the plastic deformation of the material uses the von mises yield criterion, as well as the associated flow rule and the work-hardening rule [6). therefore, a bilinear isotropic hardening model is selected [1]. t. bounini et alii, frattura ed integrità strutturale, 46 (2018) 1-13; doi: 10.3221/igf-esis.46.01 8 heat generation the friction between the shoulder and workpiece results in the biggest component of heating. from the heating aspect, the relative size of pin and shoulder is important, and the other design features are not critical. the shoulder also provides confinement for the heated volume of material. the tool plunges into the workpiece, then rotates to generate heat. the depth and rotating speeds are critical parameters for the weld temperatures. the tool travels from one end of the welding line to the other [9]. loading the fsw process consists of three primary phases:  plunge -the tool plunges slowly into the workpiece  dwell -friction between the rotating tool and workpiece generates heat at the initial tool position until the workpiece temperature reaches the value required for the welding.  traverse (or traveling) -the rotating tool moves along the weld line. during the traverse phase, the temperature at the weld line region rises, but the maximum temperature values do not surpass the melting temperature of the workpiece material. as the temperature drops, a solid continuous joint appears between the two plates. numerical results and discussion he mechanical properties studied are the longitudinal residual stress and temperature distribution. the analysis takes different translation speeds (40, 80, 100 and 200 mm/ min) and two rotational speed (710 rpm and 1400 rpm). (a) (b) (c) (d) figure 9: heat distribution on cross-section of the workpiece: a) welding speed of 40mm/min, b) welding speed of 80mm/min, c) welding speed of 100mm/min, d) welding speed of 200 mm/min. t t. bounini et alii, frattura ed integrità strutturale, 46 (2018) 1-13; doi: 10.3221/igf-esis.46.01 9 influence of welding speed on heat generation from the fig. 9, it is remarkable that decreasing the welding speed produces a hotter weld. heat generation during friction stir welding arises from two main sources: friction at the surface of the tool and the deformation of the material around the tool. increasing the welding speed produces less work of deformation and in result, less heat generated. the temperature distribution shows an asymmetric profile due to the stirring effect of the pin. influence of welding speed on longitudinal residual stress it should be observed that residual stresses in fsw processes are due both to thermal and mechanical causes. the former are due to the friction forces work and to the deformation work both decaying into heat. the latter are strictly connected to the strong gradients of strain and strain rates occurring due to the tool pin action on the material to be welded and which determine relevant microstructure changes in the parent material but low influence in the residual stresses [10]. (a) (b) figure 10: a) longitudinal stress profiles in a cross-section of the workpiece (rotational speed: 710 rpm). b) only 80, 100 and 200 mm/min welding speeds are represented. (a) (b) figure 11: a) longitudinal stress profiles in a cross-section of the work piece (rotational speed: 1400 rpm). b) only 40, 80 and 200 mm/min welding speeds are represented. -8,0e-04 -4,0e-04 0,0e+00 4,0e-04 8,0e-04 0,0 0,8 1,6 2,4 3,2 40 mm/min 80 mm/min 100 mm/min 200 mm/min l o n g it u d in a l r e s id u a l s tr e s s ( m p a ) distance from the weld center (mm) 8,0e-04 4,0e-04 0,0e+00 +4,0e-04 +8,0e-04 0,0 0,2 0,4 0,6 0,8 1,0 1,2 80 mm/min 100 mm/min 200 mm/min l o n g itu d in a l r e si d u a l s tr e s s (m p a ) distance from weld center (mm) -8,0e-04 -4,0e-04 0,0e+00 4,0e-04 8,0e-04 0 2 4 6 8 10 40mm/min 80mm/min 100mm/min 200mm/min l o n g itu d in a l r e si d u a l s tr e s s ( m p a ) distance from the weld center (mm) -8,0e-04 -4,0e-04 0,0e+00 4,0e-04 8,0e-04 0,0 0,2 0,4 0,6 0,8 1,0 1,2 40mm/min 80mm/min 200mm/min l o n g it u d in a l r e si d u a l s tr e s s ( m p a ) distance from welding center(mm) t. bounini et alii, frattura ed integrità strutturale, 46 (2018) 1-13; doi: 10.3221/igf-esis.46.01 10 the graphs show the influence of the welding speed, on the longitudinal residual stresses lrs. we noticed that the following parameters are optimal: (1400 rpm-100 mm/min), (1400 rpm-80 mm/min), (710 rpm-100 mm/min) (710 rpm -80 mm/min), which is consistent with the study of ghazi already quoted [3]. the studies show that residual stress has three regions. there are the nugget region, the thermo-mechanically affected zone tmaz and the heat affected zone haz. each region has qualitatively or quantitively distinct values of microstructure, hardness and residual stress [11]. influence of rotational speed on heat generation higher tool rotational speed resulted in a higher temperature and slower cooling rate in the friction stir processed fsp zone after welding. fig. 12 shows that the temperature is higher with the rotational speed 1400 rpm. in the retreating side, the temperature distribution is lower than the advancing side. the temperature is decreasing, when the distance from weld center is increasing. (a) (b) figure 12: heat distribution on cross-section of the workpiece : a) rotational speed of 1400 rpm, b) rotational speed of 710 rpm. influence of rotational speed on longitudinal residual stress rotational speed appears to be the most significant process variable since it also tends to influence the translational velocity. very high rotational speeds (>10,000 rpm) could raise strain rate, and there by influence the recrystallisation process; which in turn could influence the fsw process [12]. at a constant welding speed of 80 mm/min, residual stresses increased as rotational speed augmented from 710 to 1400 rpm. a higher rotational speed causes excessive release of stirred materials to the upper surface, which resultantly left voids in the fsp zone. lower heat input condition due to lower rotational speed resulted in lack of stirring [13]. figure 13: influence of rotational speed on longitudinal residual stress. figure 14: influence of material properties on residual longitudinal stress. -8,0e-04 -4,0e-04 0,0e+00 4,0e-04 8,0e-04 0,0 0,3 0,6 0,9 1,2 710 rpm 1400 rpm l o n g it u d in a l r e si d u a l s tr e ss ( m p a ) distance from the center (mm) -8,0e-04 -4,0e-04 0,0e+00 4,0e-04 8,0e-04 0 5 10 15 20 25 aa 5052 aa 5083 distance from weld center (mm) lo n g it u d in a l r e si d u a l s tr e s s ( m p a ) 0,0 0,2 0,4 0,6 0,8 1,0 1,2 lo n g itu d in a l r e s id u a l s tr e s s ( m p a ) t. bounini et alii, frattura ed integrità strutturale, 46 (2018) 1-13; doi: 10.3221/igf-esis.46.01 11 the heat input (generated by the friction between tool shoulder and base metal) increases with increase in tool rotational speed and decrease in welding speed. low heat input causes the intermittent metal flow and improper stirring action around the tool pin due to insufficient plasticization of the base metal under the tool shoulder. on the other side, high heat input causes turbulent metal flow around the tool pin due to excess plasticization of base metal under the tool shoulder. both these welding conditions produced defective welds. the base metal with low yield strength, low hardness and higher ductility can be plastically deformed very easily and the flow of plasticized metal around the non-consumable tool will also be uniform compared to the base metal with high strength, high hardness and low ductility. [14] influence of material properties in the longitudinal residual stress fig. 14 shows that the material aa 5052 has undergone higher stresses at the nugget, tmaz and less at taz, compared to aa 5083 alloy, which means higher deformation. (a) (b) figure 15: comparison between: a) influence of welding speed on lrs (710 rpm), b) influence of welding speed on micro-hardness [3]. (a) (b) figure 16: a) longitudinal residual stress with (1400 rpm, 100 mm/min), b) experimental and numerical longitudinal stress profiles in a cross-section of the weld piece [10]. validation of numerical results comparison with the validation study: stress – microhardness relationship the relationship between stress and strain (deformation) and microhardness is a factor to check the numerical model. strain or reduced deformation is a term that expresses the trend of the deformation change among the material field. strain is the 8,0e-04 4,0e-04 0,0e+00 +4,0e-04 +8,0e-04 0,0 0,2 0,4 0,6 0,8 1,0 1,2 80 mm/min 100 mm/min 200 mm/min l o n g it u d in a l r e si d u a l s tr e ss ( m p a ) distance from weld center (mm) -8,0e-04 -4,0e-04 0,0e+00 4,0e-04 8,0e-04 0 2 4 6 8 10 l o n g it u d in a l r e s id u a l s tr e s s (m p a ) distance from weld center(mm) t. bounini et alii, frattura ed integrità strutturale, 46 (2018) 1-13; doi: 10.3221/igf-esis.46.01 12 deformation per unit length [15]. applying a stress to material results in a strain. on the other side, hardness is a measure of the resistance to localized plastic deformation induced by either mechanical indentation or abrasion. from these definitions, it is deductible that the relationship between hardness and strain is an inverse relationship, to the opposite of the positive relationship between stress and strain. from this perspective, the longitudinal stress results in the numerical study shown in the figs. (10, 11, 12, 13), are comparable to the micro-hardness results, obtained by ghazi [3]. the inverse relationship is shown in fig. 16. by longitudinal stress profile in a cross-section of the weld piece: fig. (16-a) shows longitudinal stress profile, achieved with ansys apdl for a rotation speed equal to 1400 rpm, and a welding speed equal to 100 mm/min. fig. (16-b) shows the residual stress profiles used as a typical stress profile for comparaison. it can be seen that the residual stresses are compressive in the weld with external regions subjected to compressive stresses [10]. the comparison between figs. (16-a) and (16-b), shows a similarity. conclusions experimental the conventional yield stress in the base material aa 6082-t6 (314 mpa) is well above the yield strength in fsw welded specimens aa 6082 – t6 fsw (260 mpa). the cracking rate da/dn, for low values of (∆k < 10 ) is almost similar in the two materials. numerical decreasing the welding speed produces a hotter weld. the optimal parameters are these combinations (1400 rpm-100 mm/min), (1400 rpm – 80 mm/min), (710 rpm – 100 mm/min) and (710 rpm – 80 mm/min). higher temperature is generated with the rotational speed 1400 rpm, then with 710 rpm, for a constant welding speed 80 mm/min. residual stress increased as rotational speed augmented from 710 to 1400 rpm. comparing aa 5083 with aa 5052, the latter has undergone higher stresses. this is translated into deformation, which means less weldabilty. validation the longitudinal stress results in the numerical study shown in figs. (10, 11, 12 and 13) are comparable to the microhardness results obtained by ghazi [3]. the inverse relationship is shown in the fig. 17. the longitudinal residual stresses lrs profile resulted in the numerical study, shows similarity with the typical lrs profile [10]. references [1] ansys 14.5 help// technology demonstration guide // 30. friction stir welding (fsw) simulation. [2] he, x., gu, f. and ball, a. (2014). a review of numerical analysis of friction stir welding, progress in materials science 65, pp. 1-66. [3] ghazi, a. (2013). caractérisation mécanique des assemblages soudés par friction malaxage (etude numérique et expérimentale). [4] song, m. and kovacevic, r. (2002). numerical simulation and experimental analysis of heat transfer process in friction stir welding process, proceeding of institution of mechanical engineers, part b, journal of engineering manufacture 216 (12), pp. 73–85. [5] song, m. and kovacevic, r. (2003). thermal modeling of friction stir welding in a moving coordinate and its validation, international journal of machine tool and manufacturing 43 (6), pp. 605–615. [6] zhu, x. k. and chao, y. j. (2004). numerical simulation of transient temperature and residual stresses in friction stir welding of 304l stainless steel. journal of materials processing technology 146(2), pp. 263-272. [7] dong, p., lu, f., hong, j.k. and cao, z. (2001). coupled thermomechanical analysis of friction stir welding process using simplified models, science and technology of welding and joining 6(5), pp. 281-287. t. bounini et alii, frattura ed integrità strutturale, 46 (2018) 1-13; doi: 10.3221/igf-esis.46.01 13 [8] chen, c.m. and kovacevic, r. (2003). finite element modeling of friction stir welding—thermal and thermomechanical analysis. science direct, international journal of machine tools & manufacture 43, pp. 1319– 1326. [9] mishra, r.s. and ma, z.y. (2005). friction stir welding and processing, materials science and engineering r, 50(1-2), pp. 1-78. [10] buffa, g., fratini, l. and pasta, s. (2009). residual stresses in friction stir welding: numerical simulation and experimental verification, jcpds-international centre for diffraction data, pp. 444-453 [11] kambouz, y., benguediab, m. and bouchouicha, b. (2017). numerical study of the mechanical behavior and fatigue in a weld bead by friction stir for a 6082–t6 aluminum alloy. mechanics and mechanical engineering, 21(1), pp. 6783. [12] elangovan, k. and balasubramanian, v. (2007). influences of pin profile and rotational speed of the tool on the formation of friction stir processing zone in aa2219 aluminium alloy, material science and engineering: a, 459 (1-2), pp. 7-18. [13] elangovan, k., balasubramanian, v. and valliapan, m. (2008). effect of tool pin profile and tool rotational speed on mechanical properties of friction stir welded aa6061 aluminium alloy materials and manufacturing processes, 23(3), pp. 251-260. [14] fernandez, g.j., and murr, l.e. (2004). characterization of tool wear and weld optimization in the friction-stir welding of cast aluminum 359+20% sic metal-matrix composite. materials characteization 52(1), pp. 65-75. [15] beer, f. p., russell johnston jr., e., dewolf, j. t. and mazurek, d.f. 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/hrv (za stvaranje adobe pdf dokumenata najpogodnijih za visokokvalitetni ispis prije tiskanja koristite ove postavke. stvoreni pdf dokumenti mogu se otvoriti acrobat i adobe reader 5.0 i kasnijim verzijama.) /hun 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can be opened with acrobat and adobe reader 5.0 and later.) >> /namespace [ (adobe) (common) (1.0) ] /othernamespaces [ << /asreaderspreads false /cropimagestoframes true /errorcontrol /warnandcontinue /flattenerignorespreadoverrides false /includeguidesgrids false /includenonprinting false /includeslug false /namespace [ (adobe) (indesign) (4.0) ] /omitplacedbitmaps false /omitplacedeps false /omitplacedpdf false /simulateoverprint /legacy >> << /addbleedmarks false /addcolorbars false /addcropmarks false /addpageinfo false /addregmarks false /convertcolors /converttocmyk /destinationprofilename () /destinationprofileselector /documentcmyk /downsample16bitimages true /flattenerpreset << /presetselector /mediumresolution >> /formelements false /generatestructure false /includebookmarks false /includehyperlinks false /includeinteractive false /includelayers false /includeprofiles false /multimediahandling /useobjectsettings /namespace [ (adobe) (creativesuite) (2.0) ] /pdfxoutputintentprofileselector /documentcmyk /preserveediting true /untaggedcmykhandling /leaveuntagged /untaggedrgbhandling /usedocumentprofile /usedocumentbleed false >> ] >> setdistillerparams << /hwresolution [2400 2400] /pagesize [612.000 792.000] >> setpagedevice microsoft word numero_49_art_23_2487 v. matveenko et alii, frattura ed integrità strutturale, 49 (2019) 225-242; doi: 10.3221/igf-esis.49.23 225 focused on russian mechanics contributions for structural integrity construction of analytical eigensolutions for isotropic conical bodies and their application for estimation of stresses singularity v. matveenko, i. shardakov institute of continuous media mechanics of the ural branch of russian academy of sciences, russia mvp@icmm.ru shardakov@icmm.ru t. korepanova institute of continuous media mechanics of the ural branch of russian academy of sciences, russia perm military institute of the national guard troops of the russian federation, russia ton@icmm.ru abstract. a complete set of eigensolutions is constructed for different variants of circular conical bodies: homogeneous cone with one lateral surface (solid cone), homogeneous cone with two lateral surfaces (hollow cone) and composite cone for different boundary conditions on the lateral surface. it has been shown that the constructed eigensolutions can be readily applied for estimation of the character of stress singularity at the vertices of conical bodies. the character of stress singularity at the vertex of the solid and hollow cones for different boundary conditions on the lateral surfaces has been defined by direct numerical simulations. numerical results obtained for solid, hollow and compose cones under different boundary conditions on the lateral surfaces are discussed. keywords. stress singularity; conical bodies; eigensolutions. citation: matveenko, v., shardakov, i., korepanova, t., construction of analytical eigensolutions for isotropic conical bodies and their application for estimation of stresses singularity , frattura ed integrità strutturale, 49 (2019) 225-242. received: 17.04.2019 accepted: 24.05.2019 published: 01.07.2019 copyright: © 2019 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. introduction ne of the main findings of the classical elasticity theory is the possibility of existence of singular solutions due to the occurrence of infinite stresses at the points of surface non-smoothness, changes in the type of boundary conditions, contact of different materials and inside the body at the points of contact of dissimilar materials. an example of theoretical justification of this statement can be found in kondratiev (1967), where it was shown that the solutions to the equations of the linear theory of elasticity in the vicinity of angular points can be expressed as o http://www.gruppofrattura.it/va/49/2487.mp4 v. matveenko et alii, frattura ed integrità strutturale, 49 (2019) 225-242; doi: 10.3221/igf-esis.49.23 226 nα -1 1 2 nn n 1 τ r 0 < ...c < reα < reα < ... < reαf r~ , ,    (1) or can be written in a more complicated form involving logarithmic components in the case of multiple spectrum points n . here r is the distance to the angular point, nf is the function of an angular distribution of the stress field  in the vicinity of an angular point, which in 2d case depends on one polar angular variable  , 0c  , and in 3d case on two spherical coordinates , , 1 / 2с    . such a representation of the problem solution suggests that if there are n with re 1n  , the stresses tend to infinity at r tends to zero. one of the trends in the construction of the solutions of form (1) concerns the analysis of regions with specific configuration. in two-dimensional problems these are plane wedges. for almost half-a century history of studying these problems the researchers have investigated nearly all types of wedge-shaped bodies: homogeneous, composite, isotropic, anisotropic, etc. in [2-3] the authors give an extended review of the literature concerning the construction and analysis of singular solutions in two-dimensional problems of the theory of elasticity. in three-dimensional problems one can differentiate between two types of regions: an edge of a 3d wedge (an edge is not necessarily rectilinear, the wedge angle can vary along the edge) and a vertex of a polyhedral wedge or a cone. the results of some publications have disengaged further interest in the problems of the first class. in these articles (for example, in [4]) it has been shown that the solution of the plane and anti-plane problems for wedges obtained in the planes perpendicular to the edge of a 3d wedge defines the type of stress singularity at the edge points, through which the plane passes. in recent years, considerable attention has been focused on studying the stress singularity at the vertices of polyhedral wedges or cones. these problems are solved by different algorithms of the finite element method, the boundary elements method or by applying the mellin transformation to the two-dimensional boundary integral equations. out of numerous papers, which have used the concepts of these numerical methods, one should set aside papers [5-12]. as in the other branches of the elasticity theory, the analytical methods are of considerable importance both for numerical simulation and testing of numerical methods. in three-dimensional problems the analytical methods are generally applied to circular cones. one of the pioneering works in this field bazant and keer [13] is concerned with the stress singularity problem for a solid cone under axisymmetric deformation and torsion, for which the boundary conditions are specified in terms of displacement and stresses. a detailed theoretical analysis of the construction of axisymmetric solutions for elastic cone is given in [14]. the method of construction of singular and regular solutions to the laplace and navier-stokes equations written for the axisymmetric domain is described in [15]. the idea of the method is the expansion of the desired solution in the fourier series in the cyclic coordinate for axisymmetric coordinate systems, which is followed by the numerical solution of a sequence of two-dimensional problems for series coefficients. in the papers that followed the above cited studies, the analytical solutions were constructed for some particular problems. for example, in [16-17] the authors presented the results for a composite cone under axisymmetric deformation. in this case, a composite cone is a body composed of two embedded cones, which have a common contact surface. the solutions were obtained for the perfect bonding and frictionless slip conditions. the axisymmetric problem for a circular cone made of transversally isotropic material was considered in [18]. a rather complete list of papers dealing with the investigation of circular cones by the analytical methods can be found in review article [3]. the most comprehensive research on this topic was carried out in [19], in which the authors constructed the analytical solution for a solid circular cone and presented numerical data on the character of stress singularity at the vertex of a circular solid cone with the boundary conditions at the lateral surface specified in terms of the displacements and stresses. compared to the known results, the present work presents a full spectrum of analytical eigensolutions, which allow constructing the solutions not only for a homogeneous isotropic cone but also for other types of isotropic cone, as for example, for hollow and composite cones for different boundary conditions on the lateral surfaces. mathematical statement of the problem of constructing eigensolutions for semiinfinite circularconical bodies onsider a homogeneous circular cone (fig. 1a), the vertex of which coincides with the center of spherical coordinates , ,r   , and the base is perpendicular to the axis 0  . the volume occupied by the cone is defined as 1 00 , , 0 2r            , and its boundary is defined by the coordinate surfaces 1 0,     . c v. matveenko et alii, frattura ed integrità strutturale, 49 (2019) 225-242; doi: 10.3221/igf-esis.49.23 227 the case when 1 0  corresponds to a solid cone. figure 1: hollow cone (a); composite cone (b). we state the problem of constructing eigensolutions, which will satisfy the homogeneous equations of equilibrium (1 ) 0s grad div rot rot  u u (2) (here 1/1 2s n= , n is poisson's ratio, u is the displacement vector) and homogeneous boundary conditions at the surfaces 1 0,q q q q= = for displacements 0, 0, 0ru u u    (3) and stresses 0, 0, 0r       (4) or mixed boundary conditions, which in the context of solid mechanics correspond to a perfect slip boundary condition at the lateral surface 0, 0, 0ru      (5) for the examined body of revolution and boundary conditions (3)-(5), the eigensolutions can be represented as a fourier series [20] in the circumferential coordinate                          0 0 0 1 1 1 , , sin , , v v sin , , cos r w k k k k k k u r u r u r k u r r r k u r w r r k                                                (6) here the dependence on the radius is expressed according to (1), , ,ru u u  -are the components of the displacement vector along the , ,r   -axes, , ,r     are the components of the stress tensor,  is the characteristic index. v. matveenko et alii, frattura ed integrità strutturale, 49 (2019) 225-242; doi: 10.3221/igf-esis.49.23 228 if 1 0  , the region under consideration is bounded by only one coordinate surface 0  , and at 0  is assumed to meet the regularity conditions / 0, 0, 0ru u u     (7) in the framework of the proposed problem formulation we can consider a composite cone occupying a region (1) ( 2 )v v v  , where a subregion (1)v (subregion ( 2 )v ) is made of the material with the shear modulus ( 1) ( ( 2 ) ) and poisson’s ratio (1) ( ( 2 ) ) and its geometry is defined by the relations 0 r   , 0 2   , 2 0    ( 1 2    ) (fig. 1b). in particular cases 1 and 0 can be equal to 0 and  , respectively. for a composite cone eigensolutions (6) are constructed for each subregion. at the contact line 2  we can prescribe perfect bonding conditions ( 1) ( 2 ) ( 1) ( 2 ) ( 1) ( 2 ), , ;r ru u u u u u      ( 1) ( 2 ) ( 1) ( 2 ) ( 1) ( 2 ), ,r r             (8) or perfect slip conditions ( 1) ( 2 ) ( 1) ( 2 ) ( 1) ( 2 ) ( 1) ( 2 ); , 0r ru u                  (9) upon substituting eqns. (6) into the equilibrium eqn. (2) and going to a new independent variable (1 cos )/ 2x   [20] we obtain the following equations for each harmonic of the fourier series:                            22 1 2 2 2 4 1 1 1 2 4 1 1 v 1 v 0 2 21 1 k k k k k k xh x kd u x du x x x x u x dx x xdx x x h d x kw xh x x dxx x x x                         (10)                               22 2 1 1 12 1 1 3 4 1 1 1 2 4 1 1 1 2 1 1 0 2 4 1 k k k k k k xg x k gd v x dv x g x x g x v x dx x xdx k g g k xdw xd g x x u x w x dx dx x x                       (11) ( )( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) 22 1 2 1 13 4 1 1 1 1 2 4 1 1 1 2 1 0 2 4 12 1 k k k k k k xg x g kd w x dw x x x x w x dx x xdx g k dv x g k xkg u x v x dx x xx x 2 é ù+ +ê úë û+ + + é ù+ -ê ú + + + ⋅ =ê ú ê ú-ë û (12) here we introduce the following notation:        1 22 1 1 2 / 2 1 , 3 4 /( 2 1), h h                        1 2 32 1 / 1 2 , 1 , 2 4 4 / 1 2 .g g g               using (6) we can reduce boundary conditions (3)-(5) and regularity conditions (7) to condition for v. matveenko et alii, frattura ed integrità strutturale, 49 (2019) 225-242; doi: 10.3221/igf-esis.49.23 229 displacements ( ) ( ) ( )0 , 0 , 0 , k k ku x v x w x= = = (13) stresses        1 1 0k k du x x x v x dx                                  2 1 1 1 11 0 2 1 2 1 k k k k dv x s s u x s x x dx s k s x v x w x x x x x                         (14)               1 2 1 0 2 1 2 1 k k k dw x x k x x w x v x dx x x x x                    1 0 ; 0 ; 0.k k k du x x x v x w x dx     (15) construction of partial solution for zeroth harmonic of the fourier series solution for zeroth harmonic of the fourier series is considered separately, because it does not follow explicitly from the algorithm for construction of partial solutions to the system of differential eqns. (10)-(12) for any 0k  . at 0k  there are two problems: axisymmetric rotation and axisymmetric deformation. in the first problem, the component of the displacement vector 0w is defined by eqn. (12). in the problem of axisymmetric deformation the components of the displacement vector 0 0,u v are defined by eqns. (10), (11). the solutions for the function 0w are constructed in the form of the generalized power series    0 0 m m m w x r x         (16) where mr are the coefficients of the series,  is the characteristic index. the possibility of constructing a solution in the form of (16) was proved in [21]. for eqn. (12) the point 0x  is a regular singular point. in this case, one of the partial solutions is written as a power series (16), for which the range of convergence lies in the interval 0 1x  , because the value 1x  is the zero of the high-order derivative. function closest to the point 0x  . the coefficients of the series mr and the characteristic index  are found by substituting (16) into (12). setting to zero the expressions with like powers of x , yields a recurrence relation for mr :            1 2 2 2 1 2 2 1 4 1 2 2 1 1 4 2 1 0,( =0, if 0 ) m m m m m m r m m r m m r r m                                    (17) from the condition of existence of non-zero solution for 0r we obtain the characteristic equation: ( 2 1)( 2 1) 0    (18) for which 1 1/ 2  and 2 1/ 2   are the roots. a v. matveenko et alii, frattura ed integrità strutturale, 49 (2019) 225-242; doi: 10.3221/igf-esis.49.23 230 according to the theory of differential equations [21], there always exists a solution in the form of a generalized power series (16), that fits the largest root 1 . substituting the value of the root 1 into (17), we obtain a recurrence relation for ( 1) mr            2 2 (1) ( 1) (1) (1) 1 2 0 2 2 1 2 2 3 2 , 0, 1 1 4 1 m m m m m m m r r r m r m m m m                    (19) here in after, the superscript will denote the number of the partial solution. after completing these transformations we obtain the first partial solution for eqn. (12) represented as a generalized power series   1 (1) (1) 2 0 0 m m m w x r x                (20) a quantity that plays an important part in the construction of the second, linearly independent partial solution in the form of the generalized power series is the difference in the roots of the characteristic equation [21], i.e. the number 1 2 1     . if the number g is not a positive integer there exists a second, linearly independent solution in the form of the generalized power series (16). however, if  is a positive integer, the existence of the second partial solution in the general case in the form of a generalized power series (16) is not assured. this is exactly the case we have, because 1 2 1.     to eliminate this ambiguity, we use an approach, which is based on a subsequent reduction of the initial differential equation and retention of a certain number of series terms. the performance of this technique is illustrated by way of constructing the second particular solution  ( 2 )0w x to eqn. (12) at 0k  , which corresponds to axisymmetric deformation. eqn. (12) at 0k  takes the following form:                22 10 0 02 4 1 1 1 1 2 0 4 1 xg x g kd w x dw x x x x w x dx x xdx           (21) the construction of the second particular solution proceeds as follows. at the first stage using the obtained first particular solution  (1)0w x (20) we reduce the second order differential eqns. (21) to the first order equation replacing the desired solution in eqn. (21) by the relation [21]    (1)0 0 ( )w x w x f x dx  (22) where ( )f x is a new unknown function. upon this substitution we obtain the linear first-order differential equation for 1 0 ( ) ( ) ( ) ( ) 0 df x p x p x f x dx   (23) where (1) 1 0 (1) (1) 2 0 0 0 ( ) (1 ) ( ) ( ) ( ) (1 ) ( ) 2( ) . p x x x w x dw x p x x w x x x dx       (24) v. matveenko et alii, frattura ed integrità strutturale, 49 (2019) 225-242; doi: 10.3221/igf-esis.49.23 231 for this equation we can also construct a solution [21] for f(x) in the form of a generalized power series ( ) 0 ( ) mm m f x n x         (25) in the traditional approach, the coefficients mn and index  of this series are determined by substituting (25) into eqn. (23). by setting the expressions of the same power of x equal to zero we can obtain the recurrence relations for mn and from the condition of the existence of zero solution for 0n we get the characteristic equation, determining the index  . however, it should be noted that practical implementation of this procedure presents considerable difficulties, because the expressions in front of the function ( )f x and its derivatives in eqn. (23) will appear in the form of in finite series. moreover, the fact that that after construction of series (25) it will be necessary to proceed to the solution ( )0w x through the relation (22), implies that analytical transformations of infinite series will become increasingly complex. in this regard, we suggest using an algorithm, which allows us to circumvent the above difficulties in the construction of a particular solution. to illustrate our ides we will apply the proposed algorithm to eqn. (23). 1. at the first stage we define the form of the characteristic equation for the index . for this purpose, we retain in the series (25) only the first term with the coefficient 0n , and in the expressions (24) in front of the function ( )f x and its derivatives in eqn. (23) we retain only the lowest powers of the variable x , which, however are not less than the order of the highest derivative (in this case, for eqn. (23) this is the first order). after these manipulations the coefficients (24) take the following form: (1) 1/ 2 1 0 (1) 1/ 2 (1) 3/ 2 2 (1) 1/ 2 (1) 1/ 2 0 0 1 0 1 ( ) (1 ) ( ) (1 2 )( ) 2( )(1/ 2 3/ 2 ). p x x x r x p x x r x r x x x r x r x         (26) 2. upon substituting relations (25) and (26), in which we retain only the first term with the coefficient 0n , into eqn. (23) and setting to zero the expression with the lowest power of x , we obtain 0 ( 2) 0n    (27) from (27) it follows that the characteristic index 2   . with a knowledge of this index we can formally represent the structure of the solution for ( )f x : 2 1 0 0 1 2 3( ) ...f x n x n x n x n x       (28) using the obtained solution (28), we can find a formal representation of the second particular solution for  0w x based on the relation (22). in this case the number of the series terms retained in the series (28) and (20) should be no less than  (namely, no less than 2). substitution of these segments of the series into relation (22) yields   3 (1) ( 2 ) ( 2 ) (1/ 2 ) 0 0 ( ) ( ) ln( )m m m w x f x dx r x t x x        (29) thus, after generalization of this form of relation to the infinite number of terms we obtain the following form of the second particular solution:       1/ 2( 2 ) ( 2 ) ( 2 )0 0 lnm m m x r t x x         (30) in this expression the coefficients ( 2 )mr , ( 2 ) mt are still to be defined. v. matveenko et alii, frattura ed integrità strutturale, 49 (2019) 225-242; doi: 10.3221/igf-esis.49.23 232 3. substituting relation (30) into the initial differential eqn. (21) and equating to zero the expressions with the same powers of x , we obtain the recurrence relations for determination of the coefficients ( 2 )mr , ( 2 ) mt           2 ( 2 ) ( 2 ) ( 2 ) 1 2 1 2 3 2 3 2 2 5 2 1 4 1 m m m m m m m t t t m m m m                                          2 ( 2 ) 2 ( 2 ) ( 2 ) 1 1 ( 2 ) ( 2 ) 2 2 1 2 31 2 4 5 1 1 1 2 3 2 2 5 2 2 2 4 1 1 m m m m m m m mm m r t r t m m m m m m m m m r t m m m m                               (31)  ( 2 ) ( 2 ) ( 2 ) ( 2 )0 1 0 1( 1, 1, 1 , 1, 1)m t t r r        the proposed algorithm is valid for the linear ordinary differential equations of any order. hence, the proposed method allows us to define step by step the types of the generalized power series for all partial solutions of the initial differential equation and in all partial solutions to set apart the regular from irregular solutions (in our case for 0x  ). such a capability of the method is rather essential for constructing solutions to particular problems, for example, for hollow and composite cones. the form of the obtained solutions (1) ( 2 )0 0 , w w suggests that (1) 0w is a regular solution, and ( 2 ) 0w is irregular solution at 0x  . a general solution to differential eqn. (12) takes the following form:      (1) ( 2 )0 1 0 2 0w x c w x c w x    (32) where 1c , 2c are the constants defined by the prescribed combination of the boundary conditions (3) (5). to construct partial solutions to eqns. (10), (11), corresponding to the axisymmetric deformation, we need to solve this system for 0v                      3 22 0 0 0 0 3 22 1 1 4 2 2 1 1 2 x x s d u x d u x du x v x x x x s s dxdx dx                    (33) and with respect to the function 0u , which yields a differential equation of the fourth order ( ) ( ) ( )( ) ( ) ( )( )( )[ ] ( ) ( )( ) ( ) ( )( )( ) ( ) 4 3 2 22 0 0 0 4 3 2 20 0 1 1 4 8 2 2 3 2 1 2 2 2 1 1 2 0 d u x d u x d u x x x x x x x x dx dx dx du x x u x dx a a a a a a a a + + + + + + = (34) this equation is the differential equation with a regular singular point. therefore, the linearly independent partial solutions can be represented in the form of convergent generalized power series. using the above procedure for constructing such series, we obtain four partial solutions (1) ( 2 ) (3) ( 4 )0 0 0 0, , , u u u u written as                   1(1) (1) ( 2) ( 2 ) 0 0 0 0 1( 3) ( 3) ( 3) ( 4 ) ( 4 ) ( 4 ) 0 0 0 0 , , ln , ln , m m m m m m m m m m m m m m u x a x u x a x u x a b x x u x a b x x                                 (35) v. matveenko et alii, frattura ed integrità strutturale, 49 (2019) 225-242; doi: 10.3221/igf-esis.49.23 233 where the coefficients (1) ( 2 ) ( 3 ) ( 4 ) ( 3 ) ( 4 ) , , , , , m m m m m ma a a a b b are determined from the recurrence relations available on eresource (www. icmm.ru/compcoeff) and can be calculated using the suggested options. for this purposes, it is necessary to input the number of terms of a series m , poisson's ratio  , the number of harmonics k and the desired  , which can be either complex or real. substituting (35) into (33), we obtain partial solutions (1) ( 2 ) ( 3 ) ( 4 )0 0 0 0, , , v v v v for the function 0v ( ) ( ) ( )[ ]( ) ( ) ( ) ( )[ ]( ) ( ) ( ) ( )[ ]( ) ( ) ( )( ) ( ) ( ) ( )[ ]( ) ( )( ) ( ) (1) (1) 0 2 0 (2) (2) 0 2 0 (3) (3) (3) 0 2 0 (4) 1(4) (4) 0 2 0 1 , 1 2 1 , 1 2 1 1 ln , 1 2 1 ln 1 2 m m m m m m m m m m m m m m x x v x p x s x x v x p x s x x s v x p d x x xs x x v x p d x x s a a a a a a a a a a a a ¥ = ¥ = ¥ = ¥ = é ù= ê úë û+ é ù= ê úë û+ ì üï ï+ é ùï ï= + +í ýê úï ïë û+ ï ïî þ ìé ù= + ⋅ê úë û+ å å å å , üï ïï ïí ý ï ïï ïî þ (36) where the coefficients (1) (2) (3) (4) (3) (4) , , , , , m m m m m mp p p p d d are available on e-resource (www. icmm.ru/compcoeff) and can be calculated ibidem. a general solution for 0u and 0v can be written as                     (1) ( 2 ) ( 3) ( 4 ) 0 1 0 2 0 3 0 4 0 (1) ( 2 ) ( 3) ( 4 ) 0 1 0 2 0 3 0 4 0 ,u x c u x c u x c u x c u x v x c v x c v x c v x c v x                 (37) where 1 2 3 4, , ,c c c c are the constants defined by the prescribed combination of boundary conditions (3) (5). construction of partial solution for nonzeroth harmonics of the fourier series he construction of partial solutions to eqns. (10)-(12) involves some transformations [21], which yield a system of two differential equations with respect to , k kw v                                             4 3 2 4 3 2 1 04 3 2 2 3 2 2 0 3 2 1 02 3 2 0k k k k k k k k k k k d w x d w x d w x dw x f x f x f x f x f x w x dxdx dx dx d v x d w x d w x dw x x x v x x x x x w x dxdx dx dx                 (38) where 0 1 2 3 4 0 2 0 1 2 3, , , , , , , , , , f f f f f       are given by             2 220 1 1 1 1 2 3 2 1 1 1 1 2 16 f x x x x x k k k                            2 220 1 1 1 1 2 3 2 1 1 1 1 2 16 f x x x x x k k k                       2 21 1 11 2 1 4 3 1 2 2 f x x x x x x k            t v. matveenko et alii, frattura ed integrità strutturale, 49 (2019) 225-242; doi: 10.3221/igf-esis.49.23 234       22 2 22 1 1 4 18 1 13 2 f x x x x x k                    3 43 43 46 1 2 1 1f x x x x f x x x     (39)                                    22 2 0 2 2 0 2 2 1 2 3 2 3 2 3 1 1 1 1 ; 1 4 2 11 4 1 1 1 2 11 4 4 1 1 2 1 1 5 2 1 2 x x x k x x x x x x x x k k x x x x x k k x x x x x x x k k                                           moreover, the results of these transformations is a set of equations, which relate the function ku to the functions , k kw v and their derivatives ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) 2 2 2 1 4 1 4 2 1 2 1 2 2 k k k x x d w x dw x u x x x x x x x k s s dxdxa ìïï= + -í ï+ + ïî ( )( ) ( ) ( ) ( ) ( ) ( )( ) ( )24 1 1 1 1 2 1 2 1 2kk k dv x x x k s w x ksx x k x s v x dx a a üé ùïïé ù+ + + + + +ê úýê úë û ïê úë ûïþ (40) eqn. (38) is independent of (39) and represents a linear differential equation of the fourth order with respect to the function kw . eqn. (39) can be considered as a differential equation of the second order with respect to the function kv with right –hand side depending on kw . such a peculiarity of the differential eqns. (28) and the obtained relation (30) allows us to determine the sequence of constructing partial solutions for functions , , k k kw v u . the hang of this sequence can be outlines as follows. first, from the solution of eqn. (38) we obtain four partiсular solutions ( 1) ( 2 ) ( 3 ) ( 4 ), , , k k k kw w w w , written as               1 1 (1) (1) ( 2 ) ( 2 )2 2 0 0 1 1 ( 3 ) ( 3 ) ( 3) ( 4 ) ( 4 ) ( 4 )2 2 0 0 , , ln , ln k k m m k m k m m m k k m m k m m k m m m m w x a x w x a x w x a b x x w x a b x x                                                                       (41) where the coefficients (1) ( 2 ) ( 3) ( 4 ) ( 3) ( 4 ), , , , , m m m m m ma a a a b b can be determined and calculated e-resource (www. icmm.ru/compcoeff). then substituting the obtained particular solutions (1) ( 2 ) ( 3 ) ( 4 ), , , k k k kw w w w into the right-hand side of eqn. (28. b) and solving it as an inhomogeneous equation we arrive at four partial solutions (1) ( 2 ) ( 3 ) ( 4 ), , ,k k k kv v v v , which can be written as ( ) ( ) 1 1 (1) (2)(1) (2)2 2 0 0 , , k k m m m mk k m m v x p x v x p x æ ö æ ö+ -÷ ÷¥ ¥ç ç+ +÷ ÷ç ç÷ ÷÷ ÷ç çè ø è ø = = é ù é ù ê ú ê ú= =ê ú ê ú ê ú ê ú ë û ë û å å ( ) ( ) 1 (3) (3) (3) 2 0 ln , k m m mk m v x p d x x æ ö÷¥ ç ÷ç ÷÷çè ø = ì üï ïï ïï ïé ù= +í ýê úë ûï ïï ïï ïî þ å (42) v. matveenko et alii, frattura ed integrità strutturale, 49 (2019) 225-242; doi: 10.3221/igf-esis.49.23 235 ( ) ( ) 1 (4) (4) (4) 2 0 ln , k m m mk m v x p d x x æ ö+ ÷¥ ç ÷ç ÷÷çè ø = ì üï ïï ïï ïé ù= +í ýê úë ûï ïï ïï ïî þ å where the coefficients (1) ( 2 ) ( 3) ( 4 ) ( 3) ( 4 ), , , , , m m m m m mp p p p d d can be determined and calculated e-resource (www. icmm.ru/compcoeff). then, solving eqns. (39) as a homogeneous one, we find two more partial solutions ( 5 ) ( 6 ), k kv v . the form of this differential equation indicates that the point 0x  is a regular singular point. the construction of partial solutions in the form of the generalized power series is accomplished in the framework of the proposed approach. the obtained partial solutions are expressed as   1 ( 5 ) ( 5 ) 2 0 , k m k m m v x p x                     1 ( 6 ) ( 6 ) ( 6 ) 2 0 ln k m k m m m v x p d x x                 (43) where the coefficients ( 5) ( 6 ) ( 6 ), ,m m mp p d can be determined and calculated e-resource (www. icmm.ru/compcoeff). at the next stage, we use the partial solutions (1) ( 2 ) ( 3 ) ( 4 ), , , k k k kw w w w , (1) ( 2 ) ( 3 ) ( 4 ) ( 5 ) ( 6 ), , , , , k k k k k kv v v v v v and the obtained relation (40) to derive six partial solutions ( 1) ( 2 ) ( 3 ) ( 4 ) ( 5 ) ( 6 ), , , , , k k k k k ku u u u u u , which are expressed as        1 (1) (1) 2 0 2 1 1 2 2 k m k m m x x u e x kx x s                           1 ( 2 ) ( 2 ) 2 0 2 1 1 2 2 k m k m m x x u e x kx x s                              1 ( 3) ( 3) ( 3) 2 0 2 1 ln 1 2 2 k m k m m m x x u e g x x kx x s                     (44)           1 ( 4 ) ( 4 ) ( 4 ) 2 0 2 1 ln 1 2 2 k m k m m m x x u e g x x kx x s                            1 ( 5 ) ( 5 ) 2 0 1 1 2 2 k m k m m x x u e x kx x s                              1 ( 6 ) ( 6 ) ( 6 ) 2 0 1 ln 1 2 2 k m k m m m x x u e g x x kx x s                     where the coefficients (1) ( 2 ) ( 3) ( 4 ) ( 5 ) ( 6 ) ( 3) ( 4 ) ( 6), , , , , , , , m m m m m m m m me e e e e e g g g for any value of 0m  can be determined and calculated e-resource (www. icmm.ru/compcoeff). the general solutions for , , k k ku v w are given by                                             (1) ( 2 ) ( 3) ( 4 ) ( 5 ) ( 6 ) 1 2 3 4 5 6 (1) ( 2 ) ( 3) ( 4 ) ( 5 ) ( 6 ) 1 2 3 4 5 6 (1) ( 2 ) ( 3) ( 4 ) ( 5 ) ( 6 ) 1 2 3 4 5 6 (1 1 k k k k k k k k k k k k k k k k k k k k k k k u x c u x c u x c u x c u x c u x c u x v x c v x c v x c v x c v x c v x c v x v x c v x c v x c v x c v x c v x c v x w x c w                                              ) ( 2 ) ( 3) ( 4 )2 3 4k k kx c w x c w x c w x      (45) v. matveenko et alii, frattura ed integrità strutturale, 49 (2019) 225-242; doi: 10.3221/igf-esis.49.23 236 where 1 2 3 4 5 6, , , , ,c c c c c c are the constants defined by the prescribed combination of boundary conditions (3) –( 5). example of calculation of characteristic indices for conical bodies he general solutions obtained for 0k  and 1k  under the prescribed combination of the boundary conditions were used to construct a homogeneous system of algebraic equations with respect to constants ic for the examined conical body. the coefficients of this system of equations depend on the vertex angles of conical bodies, elastic characteristics of the materials and characteristic index  . the indices  , defining the character of stress singularity at the vertices of conical bodies are calculated from the condition of the existence of non-zero solution to the system of linear algebraic equations. solid cone let us consider a solid cone ( 00 , 0 , 0r          ). for this case, in general solutions (32), (37), (45) it is necessary to retain terms with particular solutions (15) at 0x  (or 0  ). subject to this condition the solutions take the following form: axisymmetric rotation ( 0k  )    (1) (1)0 0 0w x c w x  (46) axisymmetric deformation ( 0k  )             (1) (1) ( 2 ) ( 2 ) 0 0 0 0 0 (1) (1) ( 2 ) ( 2 ) 0 0 0 0 0 ,u x c u x c u x v x c v x c v x         (47) non-axisymmetric deformation ( 0k  )                       (1) (1) ( 2 ) ( 2 ) ( 5 ) ( 5 ) (1) (1) ( 2 ) ( 2 ) ( 5 ) ( 5 ) (1) (1) ( 2 ) ( 2 ) k k k k k k k k k k k k k k k k k k k u x c u x c u x c u x v x c v x c v x c v x w x c w x c w x                 (48) the substitution of these solutions in one of the boundary conditions (3)–(5) at 0q q= yields a system of linear homogeneous algebraic equations for the unknown quantities, (1) ( 2 ) (1) ( 2 ) ( 5 )0 0, , , ,k k kc c c c c , which have the following representation: axisymmetric rotation ( 0k  ) (1) (1,1) 0 0 0c   (49) axisymmetric deformation ( 0k  ) (1) (1,1) ( 2 ) (1,2 ) 0 0 0 0 (1) ( 2,1) ( 2 ) ( 2,2 ) 0 0 0 0 0, 0. c c c c         (50) non-axisymmetric deformation ( 0k  ) t v. matveenko et alii, frattura ed integrità strutturale, 49 (2019) 225-242; doi: 10.3221/igf-esis.49.23 237 (1) (1,1) ( 2 ) (1,2 ) ( 5 ) (1,5 ) (1) ( 2,1) ( 2 ) ( 2,2 ) ( 5 ) ( 2,5 ) (1) ( 5,1) ( 2 ) ( 5,2 ) ( 5 ) ( 5,5 ) 0, 0, 0. k k k k k k k k k k k k k k k k k k c c c c c c c c c                   (51) a particular form of the coefficients (1,1)0 , (1,1) 0 , (1,2 ) 0 , ( 2,1) 0 , ( 2,2 ) 0 , ( 1,1) k , … ( 5,5 ) k will be specified by the selected boundary conditions, but in any case these coefficients will depend on the finite series determining the form of particular solutions ( 1)0w , (1) (1) ( 2 ) ( 2 ) 0 0 0 0, , ,u u  , (1) (1) (1) ( 2 ) ( 2 ) ( 2 ) ( 5 ) ( 5 ), , , , , , ,k k k k k k k ku w u w u   the cone angle, the elastic characteristics of the material and the sought-for characteristic index  . the condition for the existence of nontrivial solutions to the systems of the algebraic eqns. (49) (51) are written as (1,1) 0 0  (52) (1,1) (1,2 ) 0 0 ( 2,1) ( 2,2 ) 0 0 det 0           (53) (1,1) (1,2 ) (1,5 ) 0 0 0 ( 2,1) ( 2,2 ) ( 2,5 ) 0 0 0 ( 5,1) ( 5,2 ) ( 5,5 ) 0 0 0 det 0                    (54) from these relations we obtain the values of the characteristic indices  for each of the examined cases (axisymmetric rotation, axisymmetric deformation and non-axisymmetric deformation). when implementing numerically the algorithm for evaluation of the characteristic indices one should bear in mind that the number of terms in the series of constructed particular solutions (20), (30), (35), (36), (41) – (44) is selected in such a way that a subsequent increase in their number do not change the values of the characteristic indices in the third decimal place. it should be noted that the most “unfavorable” cases required the retention of 300-400 series terms. fig. 2 presents the values of re 1n  , determining singular solutions for a solid cone under the boundary conditions expressed in terms of displacements and stresses. the values given on the graphs are identical to the data presented in [19]. figure 2: re 1n  as a function of the vertex angle of the solid cone with boundary conditions on the lateral surface for displacements (a) and stresses (b) (▲ 0k  ,●1k  ,■ 2k  ). it should be noted that the singular solutions for a solid cone under the boundary conditions in terms of stresses take place for the zeroth, first and second harmonics of the fourier series and under the boundary conditions in terms of displacementsfor the zeroth and first harmonics of the fourier series. v. matveenko et alii, frattura ed integrità strutturale, 49 (2019) 225-242; doi: 10.3221/igf-esis.49.23 238 all results in this paper were obtained for a material with poisson’s ratio 0.3  . fig. 3 displays new data on the character of stress singularity at the vertex of the solid cone for the perfect-slip boundary conditions at the lateral surface. here singular solutions occur at the zeroth first and second harmonics of the fourier series and at the angle 0 less than 180°. figure 3: re 1n  as a function of the vertex angle of the solid cone under the perfect slip boundary conditions on the lateral surface (▲ 0k  ,●1k  ,■ 2k  ). figure 4: variation re 1n  with the angle 0 at fixed values of the angle 1 of the hollow cone under zero-stress boundary conditions on the lateral surface (▲ 0k  ,●1k  ,■ 2k  ). the algorithm for evaluation of the characteristic indices described above was applied to a hollow cone with two conical boundary surfaces 0  and 1  subject to different homogeneous boundary conditions (13) (15). note that in search for a solution to this problem we had to use a full set of particular solutions ( ( 1) ( 2 )0 0, ,w w (1) (1) ( 2 ) ( 2 ) ( 3 ) ( 3 ) ( 4 ) ( 4 ) 0 0 0 0 0 0 0 0, , , , , , , ,u u u u    (1) (1) (1), , ,k k ku w (1) (1) (1) ( 2 ) ( 2 ) ( 2 ) ( 3 ) ( 3) ( 3), , , , , , , , ,k k k k k k k k ku w u w u w   ( 4 ) ( 4 ) ( 4 ), , ,k k ku w ( 5 ) ( 5 ) ( 6 ) ( 6 ), , ,k k k ku u  ) defined by relations (20), (30), (35), (36), (41) (44). since the number of particular solutions doubled, the order of determinants (52) (54) doubled, too. v. matveenko et alii, frattura ed integrità strutturale, 49 (2019) 225-242; doi: 10.3221/igf-esis.49.23 239 fig. 4 shows the dependence of the eigenvalues re 1n  on the cone angle formed by the external surface 0 at different values of the internal cone angle 1 . the conical surfaces meet zero boundary conditions for stresses. here the solid line corresponds to real eigenvalues and the dashed line to complex eigenvalues. in fig. 5, the dependence of eigenvalues re 1n  on 0 is plotted for two values of the internal cone angle for the case when the conical surfaces meet zero boundary conditions for displacements. figure 5: variation re 1n  with the angle 0 at fixed values of the angle 1 (▲ 0k  ,●1k  ) of the hollow cone under zerostress boundary conditions on the lateral surface. for a hollow cone different combinations of the boundary conditions can be realized at the internal and external conical surfaces. we have considered two variants. in the first case, the internal surface meets the zero-stress boundary conditions and the external surface – the condition of zero displacements. in the second case the condition of zero displacements is prescribed on the internal surface and on the internal surface – the condition of zero stresses. the variation of the stress singularity index re 1n  with the cone angle 0 formed by the external surface at different values of the internal cone angle is shown in fig. 6. the eigenvalues, at which singular stresses occur, are observed at the values of 0 higher than 80˚. figure 6: re 1n  as a function of 0 for different values of the cone angle 1 at zero stresses on the internal surface and zero displacements on the external lateral surfaces (▲ 0k  ,●1k  ,■ 2k  ). for the second variant of the boundary conditions the dependence of the values of re 1n  on 0 is shown in fig. 7. composite cone in the case of a composite cone the algorithm for computation of characteristic indices presented in subparagraph “solid cone” can be applied to different versions of a composite cone. first we consider a composite cone with a single boundary conical surface 0  and contact boundary 2  . a solution to this problem is found by using regular particular solutions for the internal sub-domain 1 2(0 , , 0 2 )r            and non-regular particular solutions defined by relations ((20), (30), (35), (36), (41) (44)) for the external sub-domain 2 0(0 , ,r        v. matveenko et alii, frattura ed integrità strutturale, 49 (2019) 225-242; doi: 10.3221/igf-esis.49.23 240 0 2 )   . as second case we consider a composite cone with two boundary conical surfaces, and contact boundary. in this case, it is necessary to use a full set of particular ( ( 1) ( 2 )0 0, ,w w (1) (1) ( 2 ) ( 2 ) ( 3 ) ( 3 ) ( 4 ) ( 4 ) 0 0 0 0 0 0 0 0, , , , , , , ,u u u u    (1) (1) (1), , ,k k ku w (1) (1) (1) ( 2 ) ( 2 ) ( 2 ) ( 3 ) ( 3) ( 3), , , , , , , , ,k k k k k k k k ku w u w u w   ( 4 ) ( 4 ) ( 4 ), , ,k k ku w ( 5 ) ( 5 ) ( 6 ) ( 6 ), , ,k k k ku u  ) defined by relations ((20), (30), (35), (36), (41)-(44)) both for the internal and external sub-domains. figure 7: re 1n  as a function of 0 for different values of the cone angle 1 of the hollow cone at zero displacements on the internal surface and zero stresses on the external lateral surfaces (▲ 0k  ,●1k  ,■ 2k  ). figure 8: re 1n  at different values of 1 2log( / )g g for 2 0 1 260 , 120 , 0.3         (a). re 1n  at different values of poison`s coefficient for 1 2,  for 2 060 , 120     (b). (▲ 0k  ,●1k  ,■ 2k  ). as an example, let us consider a composite cone with zero stress conditions on the external lateral boundary surface and perfect contact conditions on the boundary between different cone parts made of dissimilar materials. fig. 8a shows variation re 1n  of with the ratio between shear modules of different materials 1 2/g g . the dependence of eigenvalues on poisson's ratio for 1 2/ 1g g  is given in fig. 8b. solid lines denote eigenvalues for 1 0.3  as a function of 2 and dash and dot lines denote eigenvalues for 2 0.3  as a function of 1 . of particular interest is a composite cone with the internal singular point. in this case, two types of conditions can be prescribed at the boundary between two different materials 2  (perfect bonding condition (8) or frictionless slip conditions (9). the stress singularity indices shown in fig. 9 correspond to condition (8) for different shear modules ratios of different cone layers. it has been found that at the internal singular point the condition of stress singularity is realized at any ratio between shear modules of the inner and outer cones, except for the trivial case of 2 90   . v. matveenko et alii, frattura ed integrità strutturale, 49 (2019) 225-242; doi: 10.3221/igf-esis.49.23 241 figure 9: variation of re 1n  with 1 2log( / )g g in condition of perfect contact between two different materials at 2 1 260 , 0.3      . (▲ 0k  ,●1k  ,■ 2k  ). conclusion e have considered the analytical method of constructing eigensolutions for circular cones. it has been shown that the proposed analytical relations can be used to construct solutions and to evaluate the character of stress singularity for different conical bodies (solid, composite) and different types of boundary conditions on the lateral surfaces and contact surface of dissimilar materials. the numerical results presented in this paper provide information about the character of singular stresses at the vertex of a solid cone for displacement, stress and combined boundary conditions and at the vertex of a hollow cone for different boundary conditions on the internal and external lateral surfaces. the importance of the theoretical output of this research is that the obtained analytical solutions provide full information about singular solutions for different types of circular conical bodies made of isotropic elastic materials. all formulas and options for calculation, allowing readers to obtain independently numerical results for the problems considered in the paper, can be found on e-resource (www. icmm.ru/compcoeff). the results of this work may have considerable practical implications in various fields. recent advances in the development of computational methods extend the possibilities of the in-depth analysis of the stress state, so that present computations of real objects provide a great deal of information on the stresses in the vicinity of singular points, which are often the stress concentrator zones. a search for effective ways of reducing the level of stress concentration, for example, by changing the geometry in the vicinity of singular points leads to the conclusion that the variants close to optimal are related with the character of singular solutions [22]. such conclusions have found commercial applications, for example, for the development of techniques allowing engineers to increase the strength of adhesive or glue [23-25]. in this respect, the results presented in the paper can be used to find an appropriate variant of reducing the level of stress concentration in the vicinity of non-smooth points on the surface of three-dimensional elastic bodies. the obtained information has its own practical value since it allows us to estimate the character of stress behavior at the vertices of different conical natural objects and engineering structures. moreover, the available data on the indices of stress singularity open up new possibilities for construction of singular finite elements [22]. references [1] kondratiev, v.a. (1967). boundary value problems for elliptic equations in the regions with conical and angular points. transactions of the moscow mathematical society 16, pp. 209-292. [2] sinclair, g.b. (2004). stress singularities in classical elasticity i: removal, interpretation, and analysis. applied mechanics reviews 57(4), pp. 251-297. [3] sinclair, g.b. (2004). stress singularities in classical elasticity ii: asymptotic identification. applied mechanics reviews 57(5), pp. 385-439. w v. matveenko et alii, frattura ed integrità strutturale, 49 (2019) 225-242; doi: 10.3221/igf-esis.49.23 242 [4] mikhailov, s.e. (1979). stress singularity in the vicinity of a rib of inhomogeneous composite anisotropic body and some applications to composites. proceedings of the academy of sciences of the ussr. solid mechanics. 5, pp. 103110. [5] apel, t., mehrmann, v., watkins, d. (2002). structured eigenvalue methods for the computation of corner singularities in 3d anisotropic elastic structures. computer methods in applied mechanics and engineering 191, pp. 4459-4473. doi: 10.1016/s0045-7825(02)00390-0 [6] babeshko, v.a., glushkov, e.v., glushkova, n.v., lapina, o.n. (1991). stress singularity in the vicinity of the vertex of elastic trihedral. proceedings of the russian academy of sciences 318(5), pp. 1113-1116. [7] dimitrov, a., andra, h., schnack, e. (2002). singularities near three-dimensional corners in composite laminates. international journal of fracture 115, pp. 361-375. doi: 10.1002/nme.230 [8] matveenko, v.p., nakaryakova, t.o., sevodina, n.v., shardakov, i.n. (2006). investigation of singularity of stresses at the apex of a cone with an elliptic base. doklady physics 51(11), pp. 630-633. doi: 10.1134/s1028335806110140. [9] matveenko, v.p., nakaryakova, t.o., sevodina, n.v., shardakov, i.n. (2008). stress singularity at the vertex of homogeneous and composite cones for different boundary conditions. journal of applied mathematics and mechanics 72, pp. 331-337. doi: 10.1016/j.jappmathmech.2008.07.012. [10] korepanova, t.o., matveenko, v.p., sevodina, n.v. (2010). numerical analysis of stress singularity at the vertex of a cone with unsmooth lateral surface. computer mechanics of continuum mechanics 3(3), pp. 68-76. [11] korepanova, t.o., matveenko, v.p., sevodina, n.v. (2013). numerical analysis of stress singularity at singular points of three-dimensional elastic bodies. acta mechanica 224, pp. 2045-2063. doi 10.1007/s00707-013-0845-y. [12] savruk, m.p. and shkaraev, s.v. (2001). stress singularities for three-dimensional corners using the boundary integral equation method. theoretical applied mechanics 36, pp. 263-275. [13] bazant, z.p., keer, l.m. (1974). singularities of elastic stresses and of harmonic functions at conical notches or inclusions. international journal of solids and structures 10(9), pp. 957-965. [14] beagles, a.e. and sänding, a.m. (1991). singularities of rotationally symmetric solutions of boundary value problems for the lame equations. zamm. journal of applied mathematics and mechanics. 71(11), pp. 423-431. doi: 10.1002/zamm.19910711102. [15] bernardi, c., dauge, m., maday, y. (1999). spectral methods for axisymmetric domains. series in applied mathematics 3. [16] parihar, k.s., keer, l.m. (1978). elastic stress singularities at conical inclusions. international journal of solids and structures 14, pp. 261-263. doi: 10.1016/0020-7683(78)90036-7. [17] picu, c.r. (1996). stress singularities at vertices of conical inclusions with freely sliding interfaces, international journal of solids and structures 33(17), pp. 2453-2457. doi: 10.1016/0020-7683(95)00164-6. [18] somaranta, n., ting, t.c.t. (1986). three dimensional stress singularities at conical notches and inclusions in transversely isotropic materials, journal of applied mechanics 53, pp. 89-96. [19] kozlov, v.a., maz'ya, v.g., rossmann, j. (2001). spectral problems associated with corner singularities of solutions to elliptic equations. providence ri.n.j.: american mathematical society, ser. mathematical surveys and monographs 85. doi: http://dx.doi.org/10.1090/surv/085. [20] nowacki, w. (1970). theory of elasticity. pwn. warsaw. [21] kamke, e. (1959). differentialgleichungen: lösungsmethoden und lösungen. gewöhnliche differentialgleichungen, leipzig. [22] matveyenko, v.p. and borzenkov, s.m. (1996). semianalytical singular element and its application to stress calculation and optimization. international journal for numerical methods in engineering 39(10), pp. 1659-1680. doi: 10.1002/(sici)1097-0207(19960530)39 [23] he, d., sawa, t., karami, a. (2009). stress analysis and strength evaluation of scarf adhesive joints with dissimilar adherends subjected to static tensile loadings, international journal of adhesion and adhesives 3(8), pp. 1033-1044. [24] lang, t.p., mallick, p.k. (1998). effect of spew geometry on stresses in single lap adhesive joints. international journal of adhesion and adhesives 18, pp. 167-177. doi: 10.1016/s0143-7496(97)00056-0. [25] xu, l.r., kuai, h., sengupta, s. 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/pdfxoutputintentprofileselector /documentcmyk /preserveediting true /untaggedcmykhandling /leaveuntagged /untaggedrgbhandling /usedocumentprofile /usedocumentbleed false >> ] >> setdistillerparams << /hwresolution [2400 2400] /pagesize [612.000 792.000] >> setpagedevice microsoft word numero_58_art_22_3182.docx h. suiffi et alii, frattura ed integrità strutturale, 58 (2021) 296-307; doi: 10.3221/igf-esis.58.22 296 the effect of using polypropylene fibers on the durability and fire resistance of concrete hassan suiffi, anas el maliki control and mechanical characterization of materials and structure laboratory (lccmms); national higher school of electricity and mechanics, bp 8118 oasis, hassan ii, casablanca, morocco hassane.suiffi@ensem.ac.ma;a.elmaliki@ensem.ac.ma fatima majid laboratory of nuclear, atomic, molecular, mechanical and energetic physics, fsj, university chouaib doukkali, el jadida, morocco. majidfatima9@gmail.com omar cherkaoui laboratory on textile materials remtex, esith, higher school of textile and clothing industries casablanca, bp 7731, casablanca, morocco cherkaoui@esith.ac.ma abstract. in order to study the effect of polypropylene fibers on the durability of cementitious composites, several experimental tests have been carried out in the laboratory. the composite was tested with different volume fractions of polypropylene fibers (0.05%, 0.10%, 0.30% and 0.50%). all the results relating to the indicators (porosity accessible to water εb, to the oxygen permeability kapp.gas and diffusivity dns) indicate that the addition of polypropylene fibers in a cement matrix represents only a small effect on durability. this panel of general sustainability indicators can be supplemented by indicators more specific to each degradation process identified or envisaged depending on the environmental conditions of the structure. however, for fire resistance, concrete mixes are prepared using different volume fractions of polypropylene fibers (0.05%, 0.10%, 0.30% and 0.50%), samples are heated to 300 and 600 ° c, for exposures up to 6 hours, and tested for compressive strength. based on the results of the study, it is concluded that the relative compressive strengths of concretes containing pp fibers were higher than those of concretes without pp fibers. in addition, it can be concluded that concrete mixes which are prepared using 0.50% pp fibers, by volume, can significantly promote residual compressive strength during heating. keywords. polypropylene fibers; porosity; permeability; diffusivity; durability; fire resistance. citation: suiffi, h., el maliki, a., majid, f., cherkaoui, o., the effect of using polypropylene fiberson the durability and fire resistance of concrete, frattura ed integrità strutturale, 58 (2021) 296-307. received: 10.07.2021 accepted: 03.09.2021 published: 01.10.2021 copyright: © 2021 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. https://youtu.be/pafsbdum6em h. suiffi et alii, frattura ed integrità strutturale, 58 (2021) 296-307; doi: 10.3221/igf-esis.58.22 297 introduction owadays, the addition of fibers to a cement matrix is a technique to be explored in the field of polymer reinforced materials [1-4]. in the construction and civil engineering sector, these composites are distinguished from other composite materials intended for industry and transport, by the variety of types of matrices and fibers, as well as by the different types of additions (mineral particles, synthetic powders or chemical agents), making a wide range of combinations or mixtures possible. with the diversity of composite products in construction, it is becoming increasingly difficult to compare their properties and performance to construction or rehabilitation needs, which must meet several structural, thermal, economic and environmental criteria and requirements [5-8]. the inclusion of fibers in a concrete composite can be in the form of textile fabrics, or randomly dispersed in the matrix. nevertheless, the use of dispersed fibers has been more evident for economic reasons. among the different types of discrete fibers, steel fibers, but also polypropylene fibers have been widely used [9-11]. both are generally used as secondary reinforcement in concrete, controlling the opening and propagation of cracks. steel fibers can also be used as the main reinforcement. but they are sensitive to corrosion degradation and therefore influence the durability of the composite. polymer fibers are an alternative to the use of steel fibers due to their chemical resistance and higher durability in cementitious matrices [12]. nowadays, important work is devoted to the development of new approaches to the durability of concrete, in fact, by combining the measurement of the diffusion coefficient of chlorides and the gas permeability with others (such as in particular the determination of porosity, resistance to freeze-thaw cycles, etc.), it is thus possible to have various methods available to design concretes capable of protecting reinforced concrete structures against a given degradation (corrosion of reinforcements or alkaline reaction), for a lifetime and under given environmental conditions [13]. research studies on the fire resistance of fiber composites [14] reported that the relative compressive strengths of concretes containing polypropylene fibers were higher than those of concrete without pp fibers, for temperatures up to at 600°c. komonen and penttala [15] studied the effect of high temperature on residual properties a composite reinforced with polypropylene fibers with cement paste exposed to temperature up to 700 °c. it is concluded that polypropylene fibers decrease compressive strengths and improve fire resistance. over time, a cement matrix structure must resist various aggressions or stresses (physical, mechanical, chemical, etc.), it can be subjected to various actions such as wind, rain, cold, heat, ambient environment, while maintaining its aesthetics. it must meet the needs of users at a constant level during its lifetime. durability is directly linked to the immediate or future environment of the structures and is today the important parameter to consider in order to optimize the resistance of concrete to external influences: bad weather, soil aggressiveness, and chemically aggressive atmospheres [16]. it is one of the critical issues that can affect concrete structures, especially as the issue of durability becomes more and more important. permeability is considered to be the most important indicator for the long-term performance of a reinforced concrete structure [17,18]. micro structural properties such as the size, distribution and interconnection of micro cracks and pores are the main factors that affect the permeability of concrete [19]. even today, it is clear that few studies have been devoted to the durability of cementitious composites using the inclusion of polypropylene fiber. the study of the effect of adding these fibers on durability is certainly necessary and very useful to promote their uses in the building and civil engineering fields. the aim of this work is to study the influence of the addition of polypropylene fibers in a cement matrix on the durability and fire resistance of the composite. this article is organized into several sections. the first section presents the characteristics of the materials used (gravel, cement and fibers, etc.), and the preparation of the formulation of the composites according to the different percentages of fibers (0.05%, 0.10%, 0.30% and 0.50%). the experimental program with the necessary laboratory tools is described in the next section. a chapter deals with the description of the laboratory test equipment, with the procedure followed to perform the tests according to the standards for each indicator of durability and fire resistance. in the results section, laboratory tests were presented in the form of graphs and curves with analysis and comments. finally, the conclusion summarizes the main results related to the durability of the cementitious composite and the identification of the best fiber composition in the cement matrix in terms of fire resistance as well as its benefits and future prospects. n h. suiffi et alii, frattura ed integrità strutturale, 58 (2021) 296-307; doi: 10.3221/igf-esis.58.22 298 materials and method sand composition he sand used is normal sand. it comes from the quarries of the city of kenitra (morocco). the maximum size of gi lightweight aggregates is 16mm and the maximum size of normal gii aggregates is 20mm. cement composition the type of cement used is the product lamaalem35®, a portland cement composed of class cpj 35 as defined by standard nm 10.1.004. this cement is obtained by grinding clinker, gypsum and other constituents. it has an onset of setting at 20 °c measured on a pure paste, which only appears after 1 hour 30 minutes with a hot expansion of less than 10 mm and shrinkage after 28 days measured on a normal mortar of less than 800 μm/m. concrete formulation with polypropylene fibers the composition of the concrete used is a cement matrix made up of gravel gi and gii from the kenitra quarries, sand, cement, water and an appropriate nanoment hp 2038 admixture, for an overall density of 2417 kg/m3, see tab. 1. water cement sand coarse aggregates gi coarse aggregates gii admixture pp by volume of concrete pp by weight of concrete liters kg/m 3 kg/m3 kg/m3 kg/m3 kg/m3 % kg/m3 sample concrete 185 350 865 492 522 1.4 0 0 concrete with 0.05% pp 185 350 865 492 522 1.4 0.05 0.45 concrete with 0.10% pp 185 350 865 492 522 1.4 0.10 0.90 concrete with 0.30% pp 185 350 865 492 522 1.4 0.30 2.70 concrete with 0.50% pp 185 350 865 492 522 1.4 0.50 4.50 table 1: composition of concrete with polypropylene fibers in this experimental part, four concrete formulations with volume percentages of addition of polypropylene ranging from 0.05%, 0.10%, 0.30% and 0.50% were prepared for each fiber. a formulation of a control concrete without fiber is included for comparison. fiber used the fiber used is a polypropylene fiber (fig..1). it is manufactured by the sika company and fibrillated in pre-dosed pulp bags. figure 1: polypropylene fiber (pp). t h. suiffi et alii, frattura ed integrità strutturale, 58 (2021) 296-307; doi: 10.3221/igf-esis.58.22 299 the polypropylene fibers chosen for this study were selected from among the most widely used in the building and civil engineering markets. data from the data sheet for these fibers are shown in tab. 2. length (mm) 12 specific gravity 0.91 diameter 29 µm melt point 160°c ignition point 590°c tensile strength 400 mpa table 2: properties and technical data of the polypropylene fibers. the development of the final composition of the fiber-reinforced concrete requires knowledge of the properties of the fibers used. the authors' interest has been focused on the influence of the nature of fibers on the mechanical and physicochemical behavior of composites. in this sense, a series of formulations with volume fractions of polypropylene (pp) fibers ranging from 0.05% to 0.50% was adopted in this study. experimental program he experimental tests have been carried out at the level of the public testing and studies laboratory (lpee). the 150 mm x 300 mm cylindrical specimens were obtained by mixing gravel, cement and fiber, in accordance with standard nf p 18-470 [20]. the mixture is carried out in a standardized tilting drum mixer. at the start, 10% of the mixing water is added with the aggregates. then the remaining 90% of the mixing water is gradually added during the mixing process to the solid ingredients. the cement is added inside the mixer after about 10% of the aggregates have been loaded, while the polypropylene fibers are gradually added to the cement to have a more homogeneous mixture. first, a raw concrete mix was prepared to be considered as a reference, as shown in tab. 1. the same composition was retained for the concrete matrix in all mixtures with polypropylene fibers studied in the part of this research. for the preparation of the tests, cylindrical specimens of dimensions 16x32cm by 18x3 (3 for the raw concrete and 3 for each mixture of fiber-reinforced gravel) were carried out. the tests are carried out on samples cored on test pieces stored in humidity (rh = 50 ± 10%) at an ambient temperature of 20 ° c ± 2 ° c. test protocol durability indicators for fiber-reinforced concrete he objective of choosing sustainability indicators is to formalize a methodology for obtaining concrete capable of protecting structures against a given degradation, in particular within the contractual framework where it must meet a lifetime requirement. the approach is, based on the choice of a reduced number of durability indicators, key parameters in the quantification and prediction of the durability of concrete. these parameters are measured from laboratory tests on test tubes. the choice of these indicators (porosity, permeability and diffusivity) and the specification criteria (thresholds and classes) of acceptability of these parameters, depending on the type of environment considered constitute the main stages of the sustainability experimentation process. first, the porosity test consists in measuring the open porosity εb which characterizes the ratio of the total volume of the open pores of the sample to its apparent volume. specimens of the fiber composite having as diameter and height the following values (ø100 mm h 50 mm) (fig. 2 (a)) and are obtained by mechanical coring on the cylindrical specimens 150/300 mm. the procedure adopted is that recommended by standard nfp 18-459 [21]. the test consists of weighing the sample in air and then in a liquid of known density. the test pieces are placed in a standardized vacuum desiccator, then we fill it with water until the test pieces are completely submerged for 48 hours. t t h. suiffi et alii, frattura ed integrità strutturale, 58 (2021) 296-307; doi: 10.3221/igf-esis.58.22 300 next, we measure the mwater mass of the test tube in water using a submerged boat suspended from a balance according to the device shown in fig. 2 (b). after cleaning the sample, we carry out a second weighing to obtain the mass mair, we end the test by placing the test piece in a ventilated oven at 105c ° ± 5 until a mass mdry is obtained, and the process is stopped once the difference in measurement of two successive weighing at 24-hour intervals does not exceed 0.10%.        (a) (b) figure 2: porosity test (a) three samples of the fiber-reinforced concrete (ø100x 50 mm) prepared; (b) weighing the sample the porosity accessible to water, εb moy is therefore given by eqn. (1). this is a laboratory method, applicable to molded and cored specimens of structures     air dry b moy air water m m .100 m m (1)  second, the gas permeability test is carried out with a constant load permeameter as recommended by cembureau [22]. its purpose is to measure the oxygen permeability (in m²) of concrete test bodies, hardened, this is a laboratory method, applicable to molded and cored test pieces of structures, within the limits of the dimensional tolerances imposed by the measuring cells of the device. the test consists in subjecting a cylindrical specimen to a constant pressure gradient (fig. 3). the apparent permeability (kapp.gas) is determined, according to standard xp p18-463 [23]. from the measurement (fig. 3) of the flow in steady state with the assumption of a laminar flow at a given pressure using the law of hagen-poiseuille below (2):        atmapp.gas 2 2 o atm 2 q p l µ k a p p (2) where: q: volume flow in m3/s, patm: atmospheric pressure in pa, l: thickness of the sample in m, a: section of the test body in m², po: absolute inlet pressure in pa, µ: dynamic viscosity of oxygen at 20 °c in pa·s. the kapp.gas permeability of a concrete specimen depends on the porous structure of the material and also on the state of the water in the specimen. the permeability increases as the average water saturation rate of the test piece decreases. to determine the permeability of a concrete, it is therefore necessary, on the one hand, to at least partially dry the test specimen intended for the measurement so that the gas can pass through this test specimen, and on the other hand, to know the average saturation rate or even the distribution of the water content in the test piece, corresponding to the measured permeability. h. suiffi et alii, frattura ed integrità strutturale, 58 (2021) 296-307; doi: 10.3221/igf-esis.58.22 301 figure 3: inflation of the chamber to 8 bars and measurement of oxygen permeability for the diffusivity, the objective is to determine the diffusion coefficient of the chloride ionsdns, following a test in saturated conditions of migration under an electric field in non-stationary mode according to the standard xp p 18-462 [24]inspired by the danish standard " nord test method «standard ntb 492 [25]. for each fiber composition, three concrete samples are subjected to an accelerated diffusion test (see the experimental device in fig. 4) with chloride ions according to the following principle: one sample (test tube ø100mm h 50mm) within the meaning of standard nf en 206-1 [26] saturated one and a half months with water is placed between two upstream and downstream compartments. figure 4: device for chloride diffusion test. at the end of the test set-up, the sample is cut parallel to its axis. a section is covered with a solution of silver nitrate to determine the depth of penetration of chloride ions (see fig. 5). figure 5: depth of penetration of chloride ions in the sample. h. suiffi et alii, frattura ed integrità strutturale, 58 (2021) 296-307; doi: 10.3221/igf-esis.58.22 302 the diffusion coefficient in non-stationary regime dmoy is calculated according to formula (3):                          d moy d 0.0239 273 t l 273 t l x d x 0.0238 u 2 t u 2 (3) where: u: potential difference applied in volts, t: average temperature of the solution in °c, l: specimen thickness in mm, xd: average value of the penetration depth of chloride ions in mm, t: test duration in hours. fire resistance regarding this component, the objective is to study the effect of polypropylene fibers on the fire resistance of the concrete composite. concrete mixes are prepared using volume fractions 0.05%, 0.10%, 0.30% and 0.50% polypropylene fibers. in order to take into account, the accuracy of the test result, three specimens were prepared from each group of concrete mixes. after the sample curing period, each group was exposed to 300 and 600 ° c on a standard electric oven for 2 hours, 4 hours and 6 hours. after the step of cooling the samples inside the oven, the compressive strength of the specimens was measured by the "controls" uniaxial press model 82-0331/2 according to the en standard. n.12390-3 [27]. results and discussion he results of durability indicators (porosity, gas permeability and diffusivity) of laboratory samples in a cured state according to the different volume fractions of polypropylene fibers are presented in tab. 3. porosity εbmoy% volumic mass ρa in (g/cm3) gas permeability kapp.gas (10-18m2) diffusivity dmoy 10-12 m2/s sample concrete 13.20 2.47 97.30 5.90 concrete with 0.05% pp 13.30 2.38 97.80 6.00 concrete with 0.10% pp 13.50 2.30 98.60 6.20 concrete with 0.30% pp 13.70 2.19 98.40 6.20 concrete with 0.50% pp 13.80 2.19 98.90 6.40 table 3: concrete durability indicator test results with polypropylene effect of pp fibers on the porosity of the composite at the reference state (105° c), the porosity of the different cementitious matrices with different volume fractions of polypropylene fibers is almost equivalent and close to 13.2% (13.3% minimum for the composite with polypropylene fibers). with the increase in the dosage of polypropylene fibers, the porosity increases slightly by 4.55% (tab. .3) on average compared to non-fibrous concrete (see fig. 6). this is explained by the fact that the presence of these polypropylene fibers in a cementitious composite causes the interconnectivity of the pores of the composite with the concrete and consequently an increase in the pore volume. but this porosity remains low compared to other matrices with other types of fibers (metallic, synthetic, etc.); in the case of steel fibers [28], a study showed that the addition of these fibers with a length of 30 mm, did not affect the porosity when the volume fraction varied from 0.50 to 1% but, beyond 1%, there was a slight increase in porosity. t h. suiffi et alii, frattura ed integrità strutturale, 58 (2021) 296-307; doi: 10.3221/igf-esis.58.22 303 with increasing temperature, the porosity of concrete with polypropylene fibers increases faster than that of concrete without fibers. this increase in porosity is very probably related to the channels formed after the fusion of the fibers in accordance with previous studies [29, 30]. figure 6: evolution of porosity with addition of fibers effect of pp fibers on the gas permeability of the composite the gas permeability of the various non-fibrous and fibrous matrices is equivalent, close to 97.3e-18 m² (97.8e-18 m² minimum for the composite with polypropylene fibers). with a dosage of polypropylene fibers of 0.10%, the gas permeability increases by 1.34% on average compared to concrete without fibers (see fig. 7). all the concrete compositions have a relatively low intrinsic permeability of the order (98 e-18 m²). it can be seen that concrete without fibers (97.3e-18 m²) generally has permeability close to those containing polypropylene fibers (98.6 ± 1.10 e-18 m²). according to fig. 7, we notice a small increase in permeability as the volume factions of polypropylene fibers are increased; this increase is still very low and places the fiber-reinforced concrete in the same group as concrete without fiber. this slight increase in the permeability of the composite is justified by the fact that the flow network which conditions the passage of a gas through the fiber-reinforced concrete is clearly coarser than that represented by the capillary porosity of its hydrated cement paste [31], under the effect of extreme degradation, the concrete loses its strength and the presence of micro cracks facilitates the passage of a gas through the networks of capillary pores connected due to the presence of fibers in the concrete matrix. figure 7: evolution of permeability with addition of fibers h. suiffi et alii, frattura ed integrità strutturale, 58 (2021) 296-307; doi: 10.3221/igf-esis.58.22 304 effect of pp fibers on the diffusivity of the composite the chloride ion penetration tests in the sample of the various cement matrices containing polypropylene fibers show that there is little difference compared to the control concrete without fiber. the diffusivity values are close to 6.2·10-12 m2/s (as minimum value for the composite with 0.05% polypropylene fibers). similarly, to permeability, there is a slight increase in diffusivity with the dosage of 0.10% polypropylene fibers, approaching 7.25% on average compared to non-fiber concrete (see fig. 7). this is explained by the low absorption rate of polypropylene fibers. these results are in line with research done by antoni [32] who studied the effect of chloride penetration and found the effect to be insignificant for short polypropylene fibers identical to those used in this research. at the end of these results, the durability indicators examined remain within the same range of normal concrete, which gives the cement matrix with polypropylene fibers an almost identical durability to concrete without fibers, which favors its use in more specific cases in the building sector. effect of pp fibers on the fire resistance of the composite laboratory tests have been carried out on samples prepared for this purpose, the results of the compressive strength (hardened state) of the various samples exposed to temperatures of 300 and 600°c, and according to the volume fractions 0.05%, 0.10%, 0.30% and 0.50% polypropylene fibers are shown in tab. 4. fiber dosage compressive strength (mpa) reduction (compressive strength) in % at 300°c reduction (compressive strength) in % at 600°c at 23°c 2 hours 4 hours 6 hours 2 hours 4 hours 6 hours without fiber 30.25 17.60 26.50 33.54 19.45 28.05 36.58 0.05% pp 30.80 18 26.80 33.12 19.95 28.10 36.12 0.10% pp 31.40 19.60 27.30 32.00 20.45 28.30 34.00 0.30% pp 34.33 20.10 25.35 29.65 22.55 26.50 29.54 0.50% pp 34.50 16.45 17.90 21.50 19.00 19.60 24.25 table 4: compressive strength test results with pp fibers under different temperatures. the maximum compressive strength at 23 ° c was determined for the 0.50% polypropylene fiber composite and this increase was approximately 14% compared to the non-fiber control concrete samples, for the test pieces heated to 300 ° c we see that the compressive strength of concrete without fibers has undergone a reduction from 17.6% to 33.54% against 16.45 to 21.5% compared to concrete with 0.50% fibers, and from 19.45% to 36.58% against 19% at 24.25% for test pieces heated to 600 ° c, this is in line with studies [33, 34]made by researchers on the fire resistance of composites with polypropylene fibers. for temperatures of 300 and 600 ° c, the composite with 0.50% fibers exhibits the least loss in compressive strength, this loss is increased at 6 hours of exposure for the two temperature ranges, the fiber-reinforced concrete at 0.50% gains approximately 15.44% in 300 ° c and approximately 14.58% in 600 ° c. analysis of the curves in fig. 8 (a) and (b) shows that the compressive strength of the 0.50% polypropylene fiber composite remains close to 27 mpa compared to 20 mpa for non-fiber concrete. this is because when fiber less concrete is exposed to fire, heat penetrates the concrete, which results in moisture desorption in the outer layer. moisture vapors flow back to the cold interior and are reabsorbed in the voids. water and steam build up inside, increasing the steam pressure, quickly causing cracks and splinters in the concrete. in the case of concrete containing polypropylene fibers, the fibers melt at 160°c creating voids in the concrete. vapor pressure is released in the newly formed voids and explosive spalling is greatly reduced [35]. this observation is corroborated by the studies of certain researchers [36, 37], who announce that the inclusion of polypropylene fibers in concrete, manages to reduce or prevent the phenomenon of bursting which occurs in concrete, h. suiffi et alii, frattura ed integrità strutturale, 58 (2021) 296-307; doi: 10.3221/igf-esis.58.22 305 during the heating and under the effect of very high temperatures the fibers decompose without producing harmful gases, this helps to create spaces which act as escape routes, thus reducing the pressure in the pores. (a) (b) figure 8: evolution of compressive strength (a) at 300°c, (b) at 600°c. conclusion hen concrete degrades under the influence of external agents, the existence of cracks allows liquids and chemical particles to penetrate into the composites and accelerate the deterioration of structures. to improve the ductility and durability of the composite and prevent the formation of cracks in the concrete components, we considered reinforcing them with polypropylene fibers to reduce the entry of harmful particles into the concrete elements. the results obtained in this study show an insignificant increase in porosity, permeability and a small acceleration of the infiltration of chemical agents compared to concrete without fibers, this could be explained by the presence of connected pores created by the existence of polypropylene fibers inside the composite. with the incorporation of polypropylene fibers into the cement matrix, the composite remains durable and can be used in specific applications depending on the degradation process envisioned and depending on the environmental conditions of the structure. under conditions of very high temperatures, the use of polypropylene fibers in the cement matrix reduces the effect of spalling and bursting of the concrete and consequently improves its durability, the optimal percentage of polypropylene to be used in the concrete for improving fire resistance is about 0.50% by volume fraction. this study using durability indicators revealed that concrete containing polypropylene fibers is in the same family as ordinary concrete in terms of durability but acquires better resistance in terms of fire resistance and therefore has some potential. in the civil engineering market. nomenclature εb porosity l thickness of the sample k app.gas gas permeability a section of the test body drns diffusivity po absolute inlet pressure mair air density µ dynamic viscosity of oxygen mdry dry air density u potential difference applied mwater density in water t temperature of the solution q volume flow xd value of the chloride penetration patm atmospheric pressure t test duration in hours w h. suiffi et alii, frattura ed integrità strutturale, 58 (2021) 296-307; doi: 10.3221/igf-esis.58.22 306 acknowledgements he authors express their sincere thanks to the heads of the public testing and studies laboratory (lpee) of titmelil, casablanca, morocco and more particularly mr. ouali a. for carrying out the tests. references [1] regilan, m., silva, d, (2013). dominguez and all, characterization of lightweight cementitious composites reinforced with piassava fibers using mechanical tests and micro-tomography, international review of chemical engineering (i.re.ch.e), 5(6), pp. 2035-1755. [2] kaarthik, n. k. (2018). enhancement of properties of concrete using natural fibers, materials today proceedings, 5(11), 3, pp. 23816-23823. doi: 10.1016/j.matpr.2018.10.173. [3] formisano. a., galzerano. b., durante, m., ottavio, m., liguori, b.. (2018). mechanical response of short fiber reinforced fly ash based geopolymer composites, international review of mechanical engineering (ireme), 12(6), pp. 485-491. doi: org/10.15866/ireme.v12i6.14826 [4] bashar, b., ahamad, a. (2019). properties of fiber-reinforced structural and non-structural ultra lightweight aggregate concrete, international review of civil engineering (irece), 10(5), pp. 227-234. doi: 10.15866/irece.v10i5.16971. [5] chanvillard, g. (1993). experimental analysis and micromechanical modeling of the behavior of wiredrawn steel fibers, anchored in a cementitious matrix, etude et recherche du lpc. [6] martijn, l., m., stijn, n., cok, b., worrell, e., shen, l. (2017). life cycle assessment of sisal fibre – exploring how local practices can influence environmental performance, journal of cleaner production, 149(15), pp. 818-827. elsevier. doi: 10.1016/j.jclepro.2017.02.073 [7] muhammad, a., ghulam, m., hafsa, j. (2020). comparative experimental investigation of natural fibers reinforced light weight concrete as thermally efficient building materials, journal of building engineering, 31, pp. 101411. doi: 10.1016/j.jobe.2020.101411. [8] el mabchour, f. e., abouchadi, h., zeriab es-sadek, m., taha-janan, m. (2020). theoretical and numerical contribution for prediction of the mechanical properties of a randomly distributed reinforcement in the matrix, international review of mechanical engineering (ireme), 14(5), pp. 1970-8734. doi: 10.15866/ireme.v14i5.19150. [9] conforti, f., minelli, g.a., plizzari, g.(2018). comparing test methods for the mechanical characterization of fiber reinforced concrete, structural concrete, 19(1), pp. 656-669. doi: 10.1002/suco.201700057. [10] caggiano, a., gambarelli, s., martinelli, e., nisticò, n., pepe, m. (2016). experimental characterization of the postcracking response in hybrid steel/polypropylene fiber-reinforced concrete, construction and building. materials, 125, pp. 1035-1043. doi: 10.1016/j.conbuildmat.2016.08.068. [11] yermak n., pliya, p., beaucour, a.l., simon, a., noumowé, a. (2017). influence of steel and/or polypropylene fibers on the behavior of concrete at high temperature: spalling, transfer and mechanical properties, construction and building. materials, 132, pp. 240-250. doi: 10.1016/j.conbuildmat.2016.11.120. [12] de alencar, v. m., monteiro, l. r., lima, f. de andrade, s. (2018). on the mechanical behavior of polypropylene, steel and hybrid fiber reinforced self-consolidating concrete, construction and building. materials, 188(10), pp. 280291. doi: 10.1016/j.conbuildmat.2018.08.103. [13] al-katib, h., hayder, a. haider, a. (2018). behavior of polypropylene fibers reinforced concrete modified with high performance, cement, international journal of civil engineering and technology (ijciet), 9(5), pp. 1066– 1074. available online at http://www.iaeme.com/ijciet/issues.asp?jtype=ijciet&vtype=9&itype=5. [14] chen, b., liu, j. (2004). residual strength of hybrid-fiberreinforced high-strength concrete after exposure to high temperatures, cement and concrete research, 34(6), pp. 1065–1069. doi: 10.1016/j.cemconres.2003.11.010. [15] komonen, j., penttala, v. (2003). effects of high temperature on the pore structure and strength of plain and polypropylene fiber reinforced cement pastes, fire technology, 39(1), pp. 23–34. doi: 10.1023/a:1021723126005. [16] lagrini, k., ghafiri, a., ouali, a. (2016). morocco frost map contribution to the durability of concrete, construction review, lpee, n°134, available at: www.lpee.ma. t h. suiffi et alii, frattura ed integrità strutturale, 58 (2021) 296-307; doi: 10.3221/igf-esis.58.22 307 [17] shi, x., xie, n., fortune, k., gong, j. (2012). durability of steel reinforced concrete in chloride environments: an overview, construction and building. materials, 30, pp. 125–138. doi: 10.1016/j.conbuildmat.2011.12.038. [18] teng, s., divsholi, b. s., lim, t., gjørv, o.e. (2014). concrete with very high resistance to chloride ingress, concr. int, 36(5), pp.30–36. available at: http://www.concrete.org/publications/internationalconcreteabstractsportal.aspx?m=details&i=51686931 [19] zhang, m.h., li, h. (2011). pore structure and chloride permeability of concrete containing nano-particles for pavement, construction and building. materials, 25(2), pp. 608–616. doi: org/10.1016/j.conbuildmat.2010.07.032. [20] the standard nf p 18-470. (july 2013). concrete ultra high-performance fiber concrete specification, performance, production and conformity. [21] the standard nfp 18-459. (march 2010). test for hardened concrete porosity and density test, ics: 91.100.30. [22] kollek, j. j. (1989). the determination of the permeabilityof concrete to oxygen by the cembureau method, a recommendation, materials and structures, 22, pp. 225-230. doi: org/10.1007/bf02472192. [23] the standard xp p18-463, e. (2011). concrete testing gas permeability on hardened concrete, ics: 91.100.30. [24] the standard xp p 18-462. (june 2012). test on hardened concrete accelerated ion migration testchloride in nonstationary regime: determination of the apparent diffusion coefficient of chloride ions, ics: 91.100.30. [25] danish standard "nord test method” ntb standard 492. [26] standard nf en 206-1. (december 2012). concrete part 1: specification, performance, production and conformity national supplement. [27] nf, en, n, 12390-3. (2012). tests for hardened concrete – part3: compressive strength of the specimens, france. [28] miloud, b. (2005). permeability and porosity characteristics of steel fiber reinforced concrete. asian journal of civil engineering, 6(4), pp. 317-330. available at: corpus id: 137743977. [29] noumowe, a., lefèvre, a., duval, r. (2002). porosité supplémentaire consécutive à la fusion de fibres de polypropylène dans un béton à hautes performances. revue française de génie civil 6(2), pp. 301-313. doi: org/10.1080/12795119.2002.9692366. [30] komonen, j., penttala, v. (2003). effects of high temperature on the pore structure and strength of plain and polypropylene fiber reinforced cement pastes, fire technology 39(1), pp. 23-34. doi: 10.1023/a:1021723126005. [31] praton, d., aitcin, p., carles-gibergue, a. (1999). measurement of the gaseous permeability of concrete: part i validation of the carman and klinkenberg concepts in the case of a high-performance concrete (bhp), bulletin des laboratoires des ponts et chaussées, 221, ref, 4241, pp. 69-78. available at: https://trid.trb.org/view/959607 [32] honguchi, t., saeki, n. (2003). influence of stress on chloride penetration into fiber reinforced concrete, jci, 25, pp. 779-784. available at: corpus id: 55101444 [33] chang, y, f., chen, y., sheu, m., yao, g. (2006). residual stress-strain relationship for concrete after exposure to high temperatures, cements and concrete research, 36(10), pp. 1999-2005. doi: org/10.1016/j.cemconres.2006.05.029. [34] shihada, s. (2011). effect of polypropylene fibers on concrete fire resistance, journal of civil engineering and management, 17 (2), pp. 259-264. doi: 10.3846/13923730.2011.574454. [35] aulia, t, b. (2002). effects of polypropylene fibers on the properties of high-strength concretes, lacer, 7, pp. 4359. [36] kalifa, p. chéné, g. gallé, c. (2001). high temperature behavior of hpc with polypropylene fibers from spalling to microstructure, cement and concrete research, 31(10), pp. 1487-1499. doi: org/10.1016/s0008-8846(01)00596-8. [37] bayasi, z., al dhaheri, m. (2002). effect of exposure to elevated temperature on polypropylene fiber reinforced concrete, aci materials journal, 99(1), pp. 22-26. available at: https://www.concrete.org/publications/internationalconcreteabstractsportal.aspx?m=details&i=11312. microsoft word numero_59_art_07_3230.docx p. munafò et alii, frattura ed integrità strutturale, 59 (2022) 89-104; doi: 10.3221/igf-esis.59.07 89 focussed on steels and composites for engineering structures effect of nylon fabric reinforcement on the mechanical performance of adhesive joints made between glass and gfrp. p. munafò, f. marchione università politecnica delle marche, italy p.munafo@staff.univpm.it, f.marchione@pm.univpm.it g. chiappini università telematica e-campus, italy gianluca.chiappini@ecampus.it m. marchini università politecnica delle marche, italy ing.monicamarchini@gmail.com abstract. the use of reinforcements in adhesive joints makes the stress distribution more uniform, improving their mechanical performance and adhesion. the present paper aims to verify the effectiveness and efficiency of the insertion of nylon 6 fabric in the adhesive layer, to study their applicability and functionality in building components. the increase in stiffness achieved by applying nylon 6 fabric in the adhesive layer between glass and gfrp pultruded profiles and steel laminates applied to gfrp beams is investigated. three different epoxy adhesives and one epoxy resin are used and compared. three different types of tests are carried out in order to study the different properties of the reinforcement system: tensile tests on gfrp/gfrp singlelap adhesive joints, with and without nylon fabric reinforcement; tensile tests on double-lap adhesive joints between float glass and pultruded gfrp profiles reinforced with nylon fabric according to four configurations (in the middle plane of the adhesive layer, on the glass surfaces, on the gfrp surfaces, on both gfrp and glass configurations) to verify the influence of its position; three-point bending tests on long gfrp tubular profiles reinforced with steel plates and nylon fabric in different configurations, to study resistance to bending loads. the results from the experimental campaign show the effectiveness of the reinforcement system using nylon fabric 6. in general, both a reduction in ultimate strength and an increase in joint stiffness compared to unreinforced configurations are observed. keywords. nylon reinforcement; reinforced adhesive joint; adhesively bonded joints; shear tests; three points bending tests. citation: munafò, p., marchione, f., chiappini, g., marchini, m., effect of nylon fabric reinforcement on the mechanical performance of adhesive joints made between glass and gfrp, frattura ed integrità strutturale, 59 (2022) 89-104. received: 18.08.2021 accepted: 12.10.2021 published: 01.01.2022 copyright: © 2022 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. https://youtu.be/dpawpvwawre p. munafò et alii, frattura ed integrità strutturale, 59 (2022) 89-104; doi: 10.3221/igf-esis.59.07 90 introduction n recent years, gfrp (glass fiber reinforced polymer) pultruded profiles are increasingly used in different fields of application, thanks to various benefits such as reduced weight, ease of installation, low electrical and thermal conductivity, corrosion resistance and durability in critical exposure conditions [1–3]. these features configure gfrp profiles as a valid alternative to traditional materials in the field of civil engineering. many applications see the use of gfrp in the structural field or in new building components [3–5]. at the same time, several factors such as their mechanical orthotropic properties [6], brittleness in bolted connections [7] and their young modulus lower than other materials such as steel [3,8,9], make the application of gfrp profiles disadvantageous, especially when concentrated loads occur [10–12]. moreover, the extreme sensitivity of gfrp to fire is a relevant problem. therefore, notch sensitivity and low mechanical properties in shear of composites make traditional joints unsuitable, favoring the adhesive ones [13,14]. recently, an increase in the use of structural adhesives in the civil engineering field could be observed. the widespread use of adhesives is the consequence of their reduced weight, their capacity to distribute stresses in a more uniform and contained way and to allow more flexibility in the realization of connections and the possibility of bonding different materials. adhesive joints also avoid concentrated stresses, which are typical of traditional joining methods (e.g., bolted joints). the new capabilities of structural adhesives led to the development of hybrid structures made of glass and steel [15]. an extensive experimental campaign demonstrated the effectiveness of an adhesive joint between gfrp profiles [16] and between gfrp and steel adherends [17]. munafò et al. [18] demonstrated through experimental studies the compatibility of adhesive joint made between glass and gfrp adherends, even under different exposure and aging conditions, by observing that the best adhesion occurs with epoxy adhesives. in fact, the epoxy adhesive was the best in terms of bearing capacity and durability. to date, however, few studies are still available to evaluate the compatibility of hybrid glass-gfrp adhesive joints. this is partly due to the wide variation of the physical properties of the adhesives along with their nonlinear properties and unknown behavior during their service life. figure 1: curtain wall mullion scheme, axonometric view. one of the objectives of the present paper is the development of a curtain wall construction technology using gfrp mullions (fig. 1), illustrated in the patent n. 10202020000025636 (inventor prof. munafò). this solution for curtain walls i p. munafò et alii, frattura ed integrità strutturale, 59 (2022) 89-104; doi: 10.3221/igf-esis.59.07 91 involves bonding thin steel plates (2 mm) to the extrados of gfrp beams to stiffen the profile and allow the glazed panels to be fixed mechanically using bolted joints. these panels are made of gfrp profiles positioned inside the glazing unit and joined to the frame by means of structural adhesives. the aim of the invention is, on the one hand, to allow the use of large, glazed surfaces (e.g., 3.50 × 3.00 m2) and, on the other hand, to simplify the assembling technique of commercial mullions, thanks to the characteristic of the material which allows the elimination of the thermal bridge (as stated in the invisible window patent, ep.3071775b1. another aim is to assess the compatibility of the bonding system between gfrp and float glass by verifying the mechanical contribution of nylon reinforcement to the joint performance in terms of stiffness. the mechanical performance of adhesive joints in unreinforced configuration is investigated and compared to that of reinforced ones. the use of adhesive bonding enables structural cooperation between glazing panels and substrate elements [19], making it possible to reduce the crosssection of the load-bearing substrate element and to guarantee high mechanical performance. this objective seeks to meet market research, which is oriented towards the assembling of large, glazed panels supported by structural elements with reduced dimensions. numerous techniques, aimed at reducing stresses concentration and increasing cross-resistance [20], were developed in terms of material design and joint geometry. amiri et al. [19] investigated the effect of the geometrical parameters of the “button-shaped” edge reinforcement experimentally and numerically. different parameters such as the radius and the height of the button, the geometric and mechanical properties of the adhesive were considered. it was observed that by increasing the radius up to six times the thickness of the adhesive, it was possible to increase the resistance of the joints significantly (up to 300%). nosouhi et al. [20] studied experimentally the effects of the geometric parameters of wavy edges on the strength of adhesive joints. for the optimal configuration, the corrugated edge joint offered 32% more strength than the normal single-lap joint. davies et al. [21] investigated the use of metal particles to reinforce single-lap adhesive joints. this reinforcement highlighted its effectiveness by increasing the tensile strength. further studies [22] tested the effect of adhesive joints reinforcements experimentally, using steel wires positioned inside a brittle glass matrix, studying their mechanical behavior through mathematical models. kaji et al. [23] experimented with a reinforcement technology using steel wires inside the adhesive layer. a significant increase in joint strength was observed (up to 90%). morgado et al. [13] analyzed the mechanical performance of single-lap joints in cfrp with aluminum reinforcements. an increase in joint strength and absorbed energy was observed. zhu et al. [24] demonstrated the effectiveness of metallic solder balls reinforcement in the adhesive by improving the distribution of transversal stresses, associated with an increase in strength and absorbed energy. from state-of-the-art, three epoxy adhesives and one epoxy resin were selected, which were more suitable for bonding different materials such as glass, gfrp pultruded composite material, and steel [17]. in order to assess the mechanical compatibility between gfrp/float glass adherends in adhesive bonding and to study the variations in stiffness provided by nylon reinforcement, different types of specimens were assembled. in the first phase, single-lap joints were manufactured, characterized by pultruded adherends bonded with two-component epoxy by interposing – or not – the nylon 6 fabric in the adhesive joint, to verify its effectiveness. subsequently, double-lap joints between glass and gfrp adherends bonded with three different epoxy adhesives by applying nylon fabric 6 inside the adhesive layer according to four positions (in the adhesive midplane, on the glass surface, on the gfrp surface and on both surfaces), were assembled and tested to evaluate its effectiveness as the position of nylon fabric changes. finally, tubular squared long beams in gfrp pultruded profiles, characterized by the application of nylon on the lower web, steel plate and combined reinforcement made of nylon and steel plate both by resin and by epoxy adhesive were tested. for the first two types of samples, shear tests were carried out, while the beams were tested in three-points bending tests. the mechanical parameters analyzed are the stiffness and ultimate strength of the joint. in the particular field of application considered, the resistance to wind loads, standardized by uni en 12210 [25] defines the capacity of the window, subjected to strong pressures and depressions (up to 2000 pa), to undergo admissible deformations within which the element maintains its functionality materials and methods he present study aims to evaluate the effect of nylon 6 fiber reinforcement on the mechanical performance of gfrpglass adhesive joints and on the flexural performance of gfrp profiles reinforced with steel plates. experimental tests include:  shear tests on gfrp-gfrp single-lap adhesive joints assembled with epoxy resin (epxrn) and reinforced with nylon 6 fabric; t p. munafò et alii, frattura ed integrità strutturale, 59 (2022) 89-104; doi: 10.3221/igf-esis.59.07 92  shear tests on gfrp-float glass double-lap adhesive joints assembled with three different commercial epoxy adhesives (epx1, epx2, epx3); in detail:  unreinforced joint;  reinforced joint with nylon 6 fabric applied on the pultruded profile;  reinforced joint with nylon 6 fabric applied on the glass;  reinforced joint with nylon 6 fabric applied both on the glass and on the gfrp profile;  three-points bending tests on tubular long gfrp beams, in detail:  unreinforced gfrp beam;  gfrp beam reinforced with steel plate applied with epx1 adhesive;  gfrp beam reinforced with steel plate applied with epx1 adhesive and reinforced with nylon 6 fabric;  gfrp beam reinforced with steel plate applied with epxrn resin;  gfrp beam reinforced with steel plate applied with epxrn resin and reinforced with nylon 6 fabric. shear tests on single-lap and double-lap adhesive joint specimens, assembled with gfrp profiles adhesively bonded on float glass, are carried out according to astm d3528-16 [26]; the three-point bending tests on tubular pultruded beams are carried out according to uni en 13706-2. through these tests the effectiveness of the adhesion between adherends and adhesives is studied by comparing shear strength, shear stress at failure, ultimate displacement, and stiffness of the joints. material properties in this study four different materials were used: transparent float glass, manufactured by vetromarche (italy), gfrp pultruded profiles manufactured by fibrolux (germany), s275jr steel plates manufactured by termoforgia (italy), and nylon 6 fabrics manufactured by lazzati group (italy). the properties of the materials, as reported by the manufacturers in their technical sheets, are reported in tabs. 1 and 2. glass steel plates* gfrp profiles** et (gpa) σt (mpa) et (gpa) σys (mpa) σt (mpa) εt (%) et (gpa) σt (mpa) εt (%) 75 40 210 326.7 385.5 29.1 26 400 1.5 *according to en 10025-2:2004 **according to en 755-2 table 1: technical and mechanical parameters of the adherends, reported by manufacturers. nylon 6 type a dtex at brill (kg/bave) 0.840/96 wires 5600 mechanical stop 7.50 fabric armor tela weight (kg/m) 0.0335 thickness (mm) 0.24 table 2: mechanical parameters of the adherends, of the nylon 6 reinforcement as reported by manufacturer. four commercial two-component structural epoxy adhesives for the adhesive joints between glass and gfrp were used. three types of epoxy adhesives (epx), namely: 3m™ scotch-weld™ epoxy adhesive 7260 b/a [27] (epx1), gurit spabond 340 lv [28] (epx2), gurit spabond 345 [29] (epx3), and an epoxy resin, namely kimitech ep-tx [30] (epxrn) were selected. the relative technical and mechanical characteristics reported by the manufacturers are summarized in tab. 3. p. munafò et alii, frattura ed integrità strutturale, 59 (2022) 89-104; doi: 10.3221/igf-esis.59.07 93 adhesive epx 1 epx 2 epx 3 epxrn chemical base two-part epoxy two-part epoxy two-part epoxy two-part epoxy consistency controlled flow thixotropic paste thixotropic paste thixotropic paste wt (min) 90 ÷ 300 15 ÷ 45 at (°c) 15 ÷ 25 15 ÷ 25 15 ÷ 25 > 5 st (°c) -50 ÷ 120 < 80 < 80 10 ÷ 35 τ (mpa) 33.50* (24.9 ÷ 30.7) * (29 ÷ 36) * 6 σt (mpa) 6 et (mpa) 3000 1800 5000 εt **(%) 3 use structural semi-structural semi-structural semi-structural * on aluminium-steel adherents **at failure table 3: technical and mechanical parameters of the adhesives reported by the manufacturers. experiments single-lap shear tests hear tests are carried out to evaluate the effectiveness of the adhesive joint between gfrp adherends and to verify the mechanical contribution of the nylon reinforcement applied in the middle plane of the adhesive layer. for each configuration three specimens were assembled and tested. the geometry of the specimens was manufactured according to iso 4587 [24]. the adherends had a width of 25 mm and a length of 100 mm; the overlap length was 12.7 mm. the thickness of the adherends was 5 mm. the thickness of the adhesive layer varies from 2 to 4 mm for unreinforced and reinforced joints, respectively. the geometry of the specimens is depicted in figs. 2-3. the nylon fabric was first manually cleaned in order to remove any impurities (e.g. dust particles), dried and brought to environmental conditions at the time of the bonding phase. the surfaces of the gfrp adherends were treated in the bonding region by manual abrasion with sandblasting paper and degreased with acetone and isopropyl alcohol. 100 mm epoxy resin gfrp adherend gfrp adherend gfrp adherend gfrp adherend 2 5 m m 12,7 mm 1 2 m m 100 mm 2 m m 5 m m figure 2: unreinforced single-lap specimens’ geometry (mm), section view and plan view. s p. munafò et alii, frattura ed integrità strutturale, 59 (2022) 89-104; doi: 10.3221/igf-esis.59.07 94 figure 3: reinforced single-lap specimens’ geometry (mm), section view and plan view. all tests were carried out with a zweick/roell z050 testing machine of 50 kn capacity under displacement control. fig. 4(a-b) shows the setup of the tensile test, with the specimen subjected to shear test. the load was applied at the slow rate of 1.25 mm/min in laboratory conditions of 22 ± 1 °c/ 43 ± 3% rh measured using a datalogger. load, displacement, and strain were measured by transducers connected to the machine. figure 4: experimental setup: shear test on gfrp-gfrp single-lap joints (a), shear test on gfrp-glass double-lap joints (b), bending test on gfrp steel squared tubular beams (c). double-lap shear tests double-lap adhesive joints were manufactured according to astm d3528-16 [31]. three samples were assembled for each type of adhesive and nylon reinforcement position (on gfrp surfaces, on glass surfaces, middle position, on glass and gfrp surfaces). fig. 5 illustrates the geometry of the specimens with epx1, epx2, epx3 adhesives. gfrp adherends had section 25×5 mm2 and 100 mm in length; float glass panels were 200×100 mm2 and 5 mm thick. the area of the adhesive layer measured 25×12.70 mm2 and the thickness was 0.30 mm, as recommended by the manufacturer for unreinforced specimens [27–29]. in nylon-reinforced configurations, the thickness was increased to 2 mm to allow the reinforcement application. the assembly phase of the specimens took place under laboratory environmental conditions (20±1 °c/50±5% rh, measured using a datalogger). as recommended by the manufacturer, the surfaces of the gfrp adherends were treated near the adhesive joint by manual abrasion with sandblasting paper and degreased with acetone and isopropyl alcohol. the nylon fabric was first cleaned manually, dried and brought to laboratory environmental conditions before the bonding phase. all specimens were labeled according to the adhesive used and cured in laboratory conditions for 30 days before testing, as recommended by manufacturers [27–29]. p. munafò et alii, frattura ed integrità strutturale, 59 (2022) 89-104; doi: 10.3221/igf-esis.59.07 95 0.3÷ 2 mm 2 5 m m 100 mm 20 0 m m 100 mm 2 mm 5 m m gfrp adherend gfrp adherend float glass adherend gfrp adherend gfrp adherend float glass adherend (a) (b) (c) (d) (e) (f) figure 5: double-lap specimens’ geometry (mm), section view and plan view (a); detail of unreinforced joint (b), adhesive reinforced joint with nylon in middle position (c); adhesive reinforced joint with nylon on glass (d); adhesive reinforced joint with nylon on gfrp (e); adhesive reinforced joint with nylon both on glass and gfrp (f). three points bending tests three points bending tests – according to uni en iso 14125 [32] – were performed to simulate the wind load to which the structural parts of a facade or windows are subject. the experiments involved the combined use of steel plates and nylon 6 reinforcements to increase the stiffness of the gfrp element. the external beam section in gfrp was 50 × 80 mm2, 5 mm thick and 1000 mm long. the steel plate was made of s275jr steel with a 2 mm thickness (fig. 6). the reinforcements were applied for each type of configuration along the entire length of the beam. the adhesives used for the application of reinforcements are the epxrn resin with a thickness of 2 mm and the epx1 adhesive, applied with a thickness of 0.30 mm, as recommended by manufacturers. the specimens were prepared by sandblasting and then cleaning the bonding regions with denatured isopropyl alcohol. the nylon fabric was prepared according to the methods illustrated for the previous tests. fig. 4c illustrates the setup of the three-points bending test; the displacement was applied with a speed rate of 3 mm/min. the displacement was measured through dic technology. the digital image correlation is a three-dimensional measurement technique using two or more cameras. this method allows the analysis of deformations and three-dimensional displacements using non-flat objects. p. munafò et alii, frattura ed integrità strutturale, 59 (2022) 89-104; doi: 10.3221/igf-esis.59.07 96 the 3d dic method consists of three main phases: i) preliminary preparation of the test specimen and setup of the test setup; ii) acquisition of the images during the experimental test; iii) analysis of the images acquired by a correlation program aimed at measuring the displacement and deformation field. figure 6: gfrp-nylon-steel squared tubular specimens in three different configurations. results and discussion n this section, the mechanical performance and failure modes of the tested specimens (single-lap gfrp-gfrp joints, double-lap gfrp-glass joints, three points bending tests on gfrp squared tubular long profiles) are shown in both the unreinforced and the reinforced configurations. the results are subdivided according to the type of test. shear tests on single-lap joints fig. 7 shows the comparison between the load-displacement graphs for the single-lap gfrp-gfrp joints assembled using epxrn resin and the same joints reinforced with nylon 6, applied in the midplane of the adhesive layer. figure 7: representative load-displacement graphs of gfrp-gfrp unreinforced and reinforced adhesive joint made with epoxy resin epxrn. adhesive nylon reinforcement fmax (n) τmax (mpa) γmax (%) s* (mm) k1** (n/mm) k2** (n/mm) epxrn 1818±244.95 5.73±0.77 0.96±0.18 3.04±1.10 283.61±126.99 1067.01±100.49 epxrn middle 1665±584.32 5.24±1.84 0.78±0.05 1.99±0.20 332.01±300.26 1126.70±302.03 * at failure ** obtained by bilateral approximation. table 4: mechanical parameters of the adhesives reported by the manufacturers. 0 200 400 600 800 1.000 1.200 1.400 1.600 1.800 2.000 0,00 0,50 1,00 1,50 2,00 2,50 3,00 3,50 l o ad [ n ] displacement [mm] epxrn epxrn+nylon i p. munafò et alii, frattura ed integrità strutturale, 59 (2022) 89-104; doi: 10.3221/igf-esis.59.07 97 tab. 4 shows the average values of the ultimate load (n), the ultimate displacement (mm) and stiffness (n/mm) of singlelap specimens both unreinforced and reinforced, subjected to shear test. due to the non-linearity of the curves, the evaluation of the joint stiffness was carried out by means of a bilinear approximation of the experimental curves (fig. 8). the best stiffness (k) performance is observed in the reinforced configuration with the nylon 6 fabric applied in the midplane of the resin layer, although failure occurs at a lower load value than the unreinforced specimen. the insertion of the nylon reinforcement results in an increase in stiffness in both the segments of the curves. stiffness increases of +17% and +6% were recorded in the first and second segments, respectively. in addition, a slight decrease (-8.42%) in the ultimate load of the reinforced configuration, compared to the unreinforced one could be observed. therefore, the insertion of the nylon fabric inside the adhesive layer leads to an increase in the overall elastic modulus of the joint, making it stiffer, reducing the ultimate load. figure 8: bilinear approximation of load-displacement graphs and evaluation of the joint stiffness. according to astm d5573-99 [33] standard, at the end of the test, it was observed that the failure modes of all the specimens realized with epxrn resin, with and without nylon, are of the lftf type (light-fiber-tear-failure), i.e. there is a few glass fibers of gfrp transferred from the adherend to the interface of the adhesive (fig. 9). in fact, in the bonding region (dotted in red), the specimens show a different color of substrate material to the rest of the specimen. this is dictated by the specific failure mode (lftf) that involved the whole bonding surface of the adherend. figure 9: failure modes of gfrp-gfrp single-lap joints: light-fiber-tear lftf. shear tests on double-lap joints the test procedures and the parameters evaluated on the double-lap specimen shear tests are the same as for the single-lap ones. tab. 5 illustrates the average results obtained in terms of ultimate loads, displacements and of the corresponding stiffness (k) and ultimate strain and strength. 0 500 1000 1500 2000 2500 0,00 1,00 2,00 3,00 4,00 5,00 l o ad [ n ] displacement [mm] k1epxrn k1epxrn+nylon k2epxrn k2epxrn+nylon p. munafò et alii, frattura ed integrità strutturale, 59 (2022) 89-104; doi: 10.3221/igf-esis.59.07 98 * at failure table 5: mechanical properties of gfrp-glass double-lap joints bonded with epoxy adhesives in unreinforced and reinforced configuration. figure 10: average load displacement curves of double-lap joints bonded with three different epoxy adhesives in unreinforced and reinforced configurations. adhesive nylon reinforcement fmax (n) τmax (mpa) γmax (%) s* (mm) k (n/mm) epx1 11721 ± 2572 0.33 ± 0.07 14.00 ± 0.75 0.81 ± 0.14 43995 ± 4308 middle position 7867 ± 254 0.17 ± 0.03 12.19 ± 0.39 0.49 ± 0.03 55613 ± 350 on gfrp 8898 ± 225 0.21 ± 0.01 13.79 ± 0.35 0.66 ± 0.18 56406 ± 2506 on glass 8786 ± 697 0.21 ± 0.03 13.62 ± 1.08 0.63 ± 0.14 57678 ± 7563 on gfrp and glass 10558 ± 1808 0.25 ± 0.01 15.06 ± 2.80 0.51 ± 0.05 49990 ± 4719 epx2 4513 ± 501 0.20 ± 0.07 6.98 ± 0.79 0.09 ± 0.02 29692 ± 1972 middle position 5638 ± 1967 0.14 ± 0.05 6.58 ± 0.87 0.07 ± 0.03 35533 ± 9814 on gfrp 3851 ± 1283 0.11 ± 0.03 5.97 ± 1.99 0.06 ± 0.02 35458 ± 7085 on glass 4270 ± 1481 0.11 ± 0.03 6.62 ± 2.30 0.05 ± 0.02 36635 ± 4538 on gfrp and glass 3469 ± 600 0.08 ± 0.04 4.38 ± 1.41 0.05 ± 0.02 42631 ± 4780 epx3 5459 ±1651 0.24 ± 0.01 9.08 ± 1.49 0.12 ± 0.00 33665 ± 4780 middle position 4729 ± 820 0.14 ± 0.04 7.33 ± 1.27 0.07 ± 0.02 36090 ± 5029 on gfrp 5504 ± 357 0.17 ± 0.02 8.53 ± 0.55 0.09 ± 0.02 34124 ± 2624 on glass 4353 ± 1899 0.13 ± 0.09 6.75 ± 2.94 0.07 ± 0.05 43835 ± 1794 on gfrp and glass 4140 ± 2078 0.12 ± 0.06 6.42 ± 3.22 0.07 ± 0.03 37654 ± 3502 p. munafò et alii, frattura ed integrità strutturale, 59 (2022) 89-104; doi: 10.3221/igf-esis.59.07 99 the graphs shown in fig. 10 compare the load-displacement curves for the adhesives in the reinforced and unreinforced configurations. the curves represent the average graphs of load-displacement curves obtained in the different combinations. the application of the nylon fabric in the adhesive layer causes a decrease in the value of the ultimate strength in almost each application. a reduction in ultimate displacements accompanied by an increase in stiffness of the adhesive joint could be observed. the following is a comparison of the three types of adhesives based on the position of the nylon fabric. as could be observed, epx1 adhesive provides the best mechanical performance, in any nylon reinforcement configuration. the reduction in ultimate load for most reinforced joints is due to the interposition of nylon, which has a lower strength than the pure adhesive layer. the nylon-reinforced configuration in the middle position offers the worst mechanical performance, showing a lower ultimate load value of -32.88% compared to the unreinforced configuration. in general, all reinforced configurations exhibit a variable increase in stiffness depending on the position of the reinforcement. in particular, the joint configuration with reinforcement on the glass surface allows to obtain an overall stiffness increase of +31.10%. in the case of epx2 and epx3 adhesives, a general decay of the ultimate strength values (up to -24%) is observed, varying according to the combinations tested, except for the configuration with reinforcement in the middle position (epx2) and on the gfrp surfaces (epx3) respectively. fig. 11 illustrates the stiffness values of the joints as the position of nylon reinforcement changes. the nylon 6 fabric increases the stiffness of the adhesive joint, and the epx1 adhesive is the best performing in any configuration, especially when the nylon is applied on the glass surface. figure 11: stiffness distribution of gfrp-glass double-lap joints. figure 12: different types of specimens’ failure modes: mixed (a), light fiber tear (b), glass delamination (c) failures according to astm d5573-99 [34], during the test the following failure modes were observed. the most frequent mode is the mf “mixed failure” (fig. 12a). a combination of adhesive (af) and cohesive (cf) failure is observed, as shown in fig. 12a. part of the adhesive adhering to the gfrp profile and the remaining part adhering to the glass – characterised by the texture of the nylon fabric – could be observed. fig. 12b illustrates an example of “light-fibertear-failure” lftf failure: gfrp profile defibration at the adhesive interface could be observed. in this case, the adhesive is perfectly adhering to the glass surface. fig. 12c shows an example of a failure characterized by the delamination of the glass adherend. a slight defibration of the glass layer in the interface of the adhesive could be observed. in this case the 0 10 20 30 40 50 60 70 m id dl e p o si ti on o n g f r p o n g la ss o n g f r p & g la ss m id dl e p o si ti on o n g f r p o n g la ss o n g f r p & g la ss m id dl e p o si ti on o n g f r p o n g la ss o n g f r p & g la ss epx1 epx2 epx3 k [k n /m m ] p. munafò et alii, frattura ed integrità strutturale, 59 (2022) 89-104; doi: 10.3221/igf-esis.59.07 100 adhesive is perfectly adhering to the surface of the gfrp. the percentage of failure modes was assessed through a graphical process. adhesive nylon reinforcement failure modes epx 1 2 mf: (49% af+ 51% lftf) 1 mf: (67% af+ 33% lftf) middle position 2 mf: (50% af+ 50% lftf) 1 mf: (71% af+ 29% lftf) on gfrp 1 mf: (85% cf+ 15% af) 1 mf: (95% cf+ 5% lftf) 1 mf: (89% cf+ 11% lftf) on glass 1 mf: (93% cf+ 7% af) 2 mf: (95% cf+ 5% af) on gfrp and glass 1 mf: (92 cf+ 8% af) 2 mf: (93% cf+ 7% af) epx 2 3 af middle position 1 lftf 1 mf: (80% lftf+ 20% af) 1 mf: (60% lftf+ 40% af) on gfrp 1 mf: (30% cf+ 70% af) 2 lftf on glass 3 lftf on gfrp and glass 1 gd 1 lftf 1 mf: (50% lftf + 30% af + 20% cf) epx 3 2 cf 1 mf: (50% af + 50% lftf) middle position 1 gd 1 lftf 1 mf: (gd + cf) on gfrp 1 mf: (70% lftf + 30% af) 1 mf: (30% lftf + 70% af) 1 gd on glass 1 mf: (50% af + 40% cf + 10% lftf) 1 mf: (83% cf + 17% af) 1 mf: (52% af + 48% cf) on gfrp and glass 2 gd 1 mf: (80% af + 20% cf) table 6. summary of failure modes observed in double-lap adhesive joint. * at failure table 7. mechanical properties of gfrp squared specimens, with and without the steel and nylon reinforcement. tab. 6 summarizes the failure modes occurred according to the adhesive used. it could be observed that for the epx3 adhesive there is a mixed failure in 58% of cases, lftf in 8% and glass delamination for 30% of specimens. for the epx2 adhesive, there is a 33% mixed failure, 58% lftf type and the remaining 8% failure with glass delamination. all specimens made with epx1 adhesive shown mixed failure. adhesive configurations fmax (n) displacement* (mm) k (n/mm) epx1 steel plate 18545 ± 2592 9.72 ± 4.58 2725 ± 142.96 nylon and steel plate 17527 ± 900 7.63 ± 0.03 2506 ± 139.38 epxrn nylon 18997 ± 1288 12.88 ± 3.66 2210 ± 32.19 steel plate 16589 ± 2235 8.25 ± 0.26 2796 ± 111 nylon and steel plate 16509 ± 1461 7.67 ± 0.68 3140 ± 113.72 unreinforced 16118 ± 1580 8.82 ± 0.40 2183 ± 45.60 p. munafò et alii, frattura ed integrità strutturale, 59 (2022) 89-104; doi: 10.3221/igf-esis.59.07 101 three points bending tests tab. 7 shows the average values of the gfrp squared tubular profiles subjected to the three points bending tests relatively to the maximum load (n), to the maximum displacement in the middle (mm) and to the stiffness (n/mm) as the position of the reinforcement changes. figure 13: average load displacement curves of gfrp tubular profiles in unreinforced and reinforced configurations, bonded with epx1 adhesive. figure 14: average displacement curves of gfrp tubular profiles in unreinforced and reinforced configurations, bonded with epxrn adhesive. since the lower flange is the most stressed part of the profile, it was decided to test experimentally only the configurations with the reinforcement applied on the outer surface of the flange. the adhesives used are the epxrn resin and the epx1 structural adhesive, selected from the previous tests. the mechanical performance of unreinforced pultruded profiles was improved by reinforcements in all the configurations tested. experimental stiffness k was in any case superior to the stiffness of the pultruded gfrp samples without reinforcement (figs. 13-14), up to a maximum of 43% in the nylon and steel reinforcement configuration. bondings with the epxrn resin exhibited the best mechanical performance, while reinforcements applied with epx1 provided an increase in stiffness of up to 15% if compared to the unreinforced configuration. finally, it was observed that the beams reinforced with nylon 6 and those reinforced with steel plates observed an increase in stiffness of 29% and 26% respectively if compared to the unreinforced beams. failure modes fig. 15 illustrates the failure mode of the non-reinforced gfrp specimen. in the middle section of the beam, the concentrated applied load causes a localized failure on the corners of the section. a lower value of the deflection at failure on the specimens with both reinforcements was observed. figure 15: failure mode of gfrp specimen. p. munafò et alii, frattura ed integrità strutturale, 59 (2022) 89-104; doi: 10.3221/igf-esis.59.07 102 in the specimens reinforced by the epx1 adhesive, the materials applied as reinforcement showed no delamination (nd failure); failure was due to a localized failure on the corners of the section, as for unreinforced specimens. the beams reinforced with epxrn resin (fig. 16) showed failure at the interface between resin and steel plate, classifiable as “adhesive” failure (af) according to cnr dt 200/2004. the steel plates constituted the surface in which detachment was more easily obtained by delamination of the reinforcement of the beams due to their smooth surface. the adhesive failure mode (af) between the resin and the steel plate occurred earlier than the cohesive failure of the resin, therefore the internal cohesion of the nylon 6 fabric was higher than the adhesion to the steel reinforcement. figure 16: failure mode of gfrp specimen reinforced with epoxy resin epxrn and steel plate. conclusions n this study, an experimental campaign to analyze the effectiveness of the application of nylon 6 fabric in adhesive joints in building components is proposed. mechanical tests were performed on three types of specimen:  shear tests on gfrp-gfrp single-lap specimens, adhesive joint both unreinforced and reinforced with nylon 6 fabric were tested;  shear tests on gfrp-glass double-lap specimens, in which nylon was interposed using three types of epoxy adhesives and tested in shear with optical measurement;  gfrp squared tubular profiles in three-point bending tests, both in the unreinforced configuration and with two different epoxy adhesives according to different reinforcement configurations. the main outcomes are: i. shear tests shown that applying the nylon 6 fabric in the adhesive layer improves the mechanical performance in terms of stiffness, with different failure modes depending on the material used. ii. shear tests on single-lap specimens showed that nylon 6 fabric increased the stiffness of adhesive joints while the ultimate strength was reduced, and displacements were more contained. load-displacement curves were simplified into bilinear curves since the joint did not show linear behavior. iii. shear tests on double-lap joints showed that epx1 adhesive exhibited the best mechanical behaviour, especially when the nylon was applied on the glass surface, as it achieved better adhesion to the substrate. contained deformations, due to the presence of the nylon fabric, were observed. iv. bending tests performed on tubular squared gfrp beams showed an increase in stiffness with the application of the nylon fabric in the adhesive layer with the steel plate reinforcement, especially in the case of the epxrn resin. for this configuration, at failure, the detachment of the steel plate was observed. in this case an additional layer of resin could be applied to increase the ultimate strength, or a metal surface corrugation treatment could be made improving the adhesion between the steel plate and the adhesive. previous works [18,19,34], show the effectiveness of the adhesive bond. due to the proven structural cooperation between glass and substrate element, stiffness increases in the resulting structure are achieved [19], and hybrid structures with high ductility could be obtained [18,34]. the results listed in this paper show the effects of the nylon fabric reinforcement system on the mechanical behaviour of adhesive joints. in general, in the various applications tested, the effect of nylon fabric reinforcement results in a reduction of the ultimate load and an increase in the overall stiffness of the joint. a further advantage of this technology is the improved adhesion between gfrp and glass substrates. in fact, an increase in the percentages of lftf and cf failure modes is observed, in contrast to the higher percentages of adhesive (af) failure modes in the case of unreinforced joints. therefore, this type of reinforcement proves to be appropriate for the application on structural elements of gfrp curtain walls since with the i p. munafò et alii, frattura ed integrità strutturale, 59 (2022) 89-104; doi: 10.3221/igf-esis.59.07 103 same load an increase in stiffness is obtained which allows the reduction of the maximum deformations (e.g. resistance to wind loads for windows and doors, classification according to the uni en 12211 test method [25]). however, the reinforcement system studied implies a complication of the mass production process, with a possible increase in costs, for example in terms of time and types of production controls. once the mechanical effectiveness of the reinforcement for the uses considered has been verified, a scale test will follow on the possible production processes and on the economic character of the technology illustrated. references [1] godat, a., légeron, f., gagné, v., marmion, b. (2013). use of frp pultruded members for electricity transmission towers, compos. struct., 105, pp. 408–421, doi: 10.1016/j.compstruct.2013.05.025. [2] hollaway, l.c. (2010). a review of the present and future utilisation of frp composites in the civil infrastructure with reference to their important in-service properties, constr. build. mater., 24(12), pp. 2419–2445, doi: 10.1016/j.conbuildmat.2010.04.062. [3] wu, c., bai, y., zhao, x.-l. (2015). improved bearing capacities of pultruded glass fibre reinforced polymer square hollow sections strengthened by thin-walled steel or cfrp, thin-walled struct., 89, pp. 67–75, doi: 10.1016/j.tws.2014.12.006. [4] appelfeld, d., hansen, c.s., svendsen, s. (2010). development of a slim window frame made of glass fibre reinforced polyester, energy build., 42(10), pp. 1918–25, doi: 10.1016/j.enbuild.2010.05.028. [5] terlizzi, v., alderucci, t., munafò, p. (2017). an innovative window with an invisible frame: from the applied research to the industrial production, tema technol. eng. mater. archit., 3(2), pp. 61–71, doi: 10.17410/tema.v3i2.142. [6] turvey, g.j. (2013). testing of pultruded glass fibre-reinforced polymer (gfrp) composite materials and structures, adv. fibre-reinforced polym. compos. struct. appl., , pp. 440–508, doi: 10.1533/9780857098641.3.440. [7] de castro, j., keller, t., castro], j. [de., keller, t. (2008). ductile double-lap joints from brittle gfrp laminates and ductile adhesives, part ii: numerical investigation and joint strength prediction, compos. part b eng., 39(2), pp. 282– 291, doi: https://doi.org/10.1016/j.compositesb.2007.02.016. [8] kim, h.-y., lee, s.-y. (2012). a steel-reinforced hybrid gfrp deck panel for temporary bridges, constr. build. mater., 34, pp. 192–200, doi: 10.1016/j.conbuildmat.2012.02.029. [9] qureshi, j., mottram, j.t. (2013). behaviour of pultruded beam-to-column joints using steel web cleats, thin-walled struct., 73, pp. 48–56, doi: 10.1016/j.tws.2013.06.019. [10] wu, c., bai, y. (2014). web crippling behaviour of pultruded glass fibre reinforced polymer sections, compos. struct., 108, pp. 789–800, doi: 10.1016/j.compstruct.2013.10.020. [11] borowicz, d.t., bank, l.c., t., b.d., c., b.l. (2011). behavior of pultruded fiber-reinforced polymer beams subjected to concentrated loads in the plane of the web, j. compos. constr., 15(2), pp. 229–238, doi: 10.1061/(asce)cc.1943-5614.0000082. [12] marchione, f. (2020). investigation of vibration modes of double-lap adhesive joints: effect of slot, int. j. eng., 33(10), pp. 1917–1923, doi: 10.5829/ije.2020.33.10a.10. [13] morgado, m.a., carbas, r.j.c., marques, e.a.s., da silva, l.f.m. (2019). reinforcement of cfrp single lap joints using metal laminates, compos. struct., 230, pp. 111492, doi: 10.1016/j.compstruct.2019.111492. [14] marchione, f. (2021). stress distribution in double-lap adhesive joints: effect of adherend reinforcement layer, int. j. adhes. adhes., 105, doi: 10.1016/j.ijadhadh.2020.102780. [15] machalická, k., eliášová, m. (2017). adhesive joints in glass structures: effects of various materials in the connection, thickness of the adhesive layer, and ageing, int. j. adhes. adhes., 72(september 2016), pp. 10–22, doi: 10.1016/j.ijadhadh.2016.09.007. [16] stazi, f., giampaoli, m., rossi, m., munafò, p. (2015). environmental ageing on gfrp pultruded joints: comparison between different adhesives, compos. struct., 133, pp. 404–414, doi: 10.1016/j.compstruct.2015.07.067. [17] giampaoli, m., terlizzi, v., rossi, m., chiappini, g., munafò, p. (2017). mechanical performances of gfrp-steel specimens bonded with different epoxy adhesives, before and after the aging treatments, compos. struct., 171, pp. 145– 57, doi: 10.1016/j.compstruct.2017.03.020. [18] alderucci, t., rossi, m., chiappini, g., munafò, p. (2019). effect of different aging conditions on the shear performance of joints made between gfrp and glass with a uv absorbance coating, int. j. adhes. adhes., 94(may), pp. 76–83, doi: 10.1016/j.ijadhadh.2019.05.009. [19] alderucci, t., terlizzi, v., urso, s., borsellino, c., munafò, p. (2018). international journal of adhesion and adhesives p. munafò et alii, frattura ed integrità strutturale, 59 (2022) 89-104; doi: 10.3221/igf-esis.59.07 104 experimental study of the adhesive glass-steel joint behavior in a tensegrity fl oor, int. j. adhes. adhes., 85(april), pp. 293–302, doi: 10.1016/j.ijadhadh.2018.04.017. [20] shang, x., marques, e.a.s., machado, j.j.m., carbas, r.j.c., jiang, d., da silva, l.f.m. (2019). review on techniques to improve the strength of adhesive joints with composite adherends, compos. part b eng., 177(november 2018), pp. 107363, doi: 10.1016/j.compositesb.2019.107363. [21] kilik, r., davies, r. (1989). mechanical properties of adhesive filled with metal powders, int. j. adhes. adhes., 9(4), pp. 224–228, doi: 10.1016/0143-7496(89)90065-1. [22] ashby, m.f., blunt, f.j., bannister, m. (1989). flow characteristics of highly constrained metal wires, acta metall., 37(7), pp. 1847–1857, doi: 10.1016/0001-6160(89)90069-2. [23] kaji, m., farahani, m., ansari, m. (2017). a reinforcing technique for the adhesive bonded composite joints using metallic wires, j. adhes. sci. technol., 31(17), pp. 1963–1975, doi: 10.1080/01694243.2017.1290573. [24] zhu, x.b., yang, x., li, y.b., carlson, b.e. (2016). reinforcing cross-tension strength of adhesively bonded joints using metallic solder balls, int. j. adhes. adhes., 68, pp. 263–272, doi: 10.1016/j.ijadhadh.2016.04.009. [25] european committee for standardization. (2016). windows and doors resistance to wind load classification, . [26] astm d3528-96 (2016), standard test method for strength properties of double lap shear adhesive joints by tension loading, astm international, west conshohocken, pa, www.astm.org. [27] (2001). 3m scotch-weldtm 7260b/a series: technical data sheet. bracknell: 3m industrial tapes & adhesives department laboratory. [28] (2019). spabondtm 340lv ht high tg structural epoxy adhesive. [29] (2019). spabond 345 epoxy adhesive system. [30] (2012). kimitech ep-tx st10-0419 thixotropic two-component epoxy resin, ,. [31] astm d3528-16. standard test method for strength properties of double lap shear adhesive joints by tension loading. [32] norm, d.i.n. (2011). en iso 14125. [33] astm 5573-99. standard practice for classifying failure modes in fiber-reinforced-plastic (frp) joints, annu. b. astm stand., 15(03). [34] marchione, f., munafò, p. (2020). experimental strength evaluation of glass/aluminum double-lap adhesive joints, j. build. eng., 30, pp. 101284, doi: 10.1016/j.jobe.2020.101284. microsoft word numero_57_art_07_3058 a. sobhy et alii, frattura ed integrità strutturale, 57 (2021) 70-81; doi: 10.3221/igf-esis.57.07 70 behavior of structural concrete frames with hybrid reinforcement under cyclic loading asmaa sobhy, louay aboul nour, hilal hassan zagazig university, egypt asmaasobhyamer@eng.zu.edu.eg, http://orcid.org/0000-0002-3660-4725 louayabdelrazek@yahoo.com, http://orcid.org/0000-0003-1557-0244 hilalcivil@yahoo.com@yahoo.com, http://orcid.org/0000-0001-5486-5497 alaa el-sisi university of missouri, usa; on research leave from zagazig university, egypt elsisiae@missouri.edu, http://orcid.org/0000-0001-8190-6100 abstract. a substantial amount of work was carried out on the use of fiberreinforced polymer (frp) in reinforced concrete structural elements, which demonstrated considerable inelasticity or deformity through monotonic and cyclic loads. even so, the action of frp bars in reinforced concrete columns and frame structures has not yet been studied during reversed cyclic loading. in this research, reversed cyclic loading was applied on three beam-column joint models using the finite element method with ansys software. the first model was for a joint designed with steel rebar for both the longitudinal and transversal reinforcement. glass fiber reinforced polymer (gfrp) rebar was used in the second joint model for the longitudinal reinforcement with steel transversal reinforcement. the third joint model was designed with hybrid steel/gfrp reinforcement for the longitudinal reinforcement and steel transversal reinforcement. the performance of the three models under reversed cyclic loading, such as load vs. story drift and energy dissipation capacity, were compared. the gfrp-reinforced model displayed a predominantly elastic behavior up to failure. although its energy dissipation was lower, its performance in terms of total story drift demand was satisfactory. keywords. gfrp; hybrid reinforcement; cyclic loading; beam-column joint; frames. citation: sobhy, a., aboul nour, l., hassan, h., el-sisi, a., behavior of structural concrete frames with hybrid reinforcement under cyclic loading, frattura ed integrità strutturale, 57 (2021) 70-81. received: 05.04.2021 accepted: 12.05.2021 published: 01.07.2021 copyright: © 2021 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. https://youtu.be/oyysut2xnjo a. sobhy et alii, frattura ed integrità strutturale, 57 (2021) 70-81; doi: 10.3221/igf-esis.57.07 71 introduction he primary reason for the collapse of the reinforced concrete (rc) buildings is steel corrosion, which requires multimillion annual maintenance costs worldwide. furthermore, the use of modern equipment with magnetic interferometers, such as in medical radiology buildings, requires a non-magnetic structure without steel reinforcement. this led to growing interest in the use of the non-magnetic and corrosion-resistant fiber-reinforced polymer (frp) reinforcement [1,2]. in the last decade, substantial efforts were made to extend frp composite materials to the construction sector, and, finally, structural uses of composite materials have started to arise in civil structures. frp composite materials are being used as interior and exterior reinforcements in the field of structural engineering due to the high tensile strength to weight ratio, higher stiffness, lower density, chemical attack resistance, and other properties [3– 8]. significant research activities in recent years have demonstrated that frp materials can be used successfully to strengthen reinforced concrete structures [9–13]. high-tensile fiber stiffeners, such as carbon, glass, aramid, and basalt, are integrated into polymeric arrays and made in different shapes such as rods, grids, and tubes [3]. the characteristics of lightweight, high strength, acceptable fatigue resistance, and superior corrosion resistance also make frp composites a major source of use as construction material or reinforcement in civil engineering [14–16]. frp composite materials showed poorer elasticity and lowered bonding with concrete compared to traditional steel reinforcement. a bonding of frp with concrete is being strengthened with mechanical anchorages such as sanding and surface deformation; however, particularly in structures subjected to dynamic loading, its poor ductility persists as a major problem [1]. in recent decades, most research works were conducted on the concrete beam behavior and column structures with frp rebar reinforcement. still, little research was conducted on frp reinforced concrete frame structures, particularly subjected to seismic loading. nehdi and said studied the experimental behavior of rc frames reinforced with hybrid bars under cyclic loading [17]. the three beam-column joints were tested under cyclic loading and were reinforced with steel, glass fiber reinforced polymer (gfrp), and hybrid gfrp/steel. the cross-section of the beam of the hybrid joint had three steel bars and three gfrp bars as longitudinal bottom and top reinforcements, respectively. it was found that the gfrp joint significantly displayed lower plastic characteristics. this led to poorer dissipation of energy compared to hybrid and steel joints. the hybrid joint has shown lower stiffness than the steel joint and higher stiffness than the gfrp joint [17]. the cyclic behavior of beam-column joints of reinforced concrete with gfrp bars and stirrups was investigated [18]. the case study consisted of five full-scale rc beam-column joints with t-shape, which were experimented under cyclic load. the key parameters analyzed are the transversal and longitudinal reinforcement ratios and types. the study has indicated that the reinforced joints with gfrp could reach a 4.0% drift percentage without suffering noteworthy damage. in addition, it was concluded that increasing the beam reinforcement ratio can enhance the ability of the joint to dissipate the seismic energy through utilizing the inelastic behavior of concrete. ghomi and el-salakawy [19,20] investigated the seismic behavior of the rc beam-column joints with gfrp reinforcement. it was inferred that the axial load level of the columns greatly affects the earthquake's behavior of the rc beam-column joints with gfrp reinforcement. structural elements are sensitive to brittle collapse in this region and are unable to achieve extreme strength capability. in comparison, the rising axial load of columns in steel-rc samples did not show a substantial effect on the envelope of lateral load drift relation of the joints [19,20]. furthermore, m. hasaballa and e. el-salakawy [21] analyzed the external shear strength of the rc beam-column joint with gfrp reinforcement, and the results indicated that the overall joint shear stress must be reduced to avoid joint damage [21]. in recent decades, there has been increasing attention in comparison between frp-rc and steel-rc structures. however, research in this field was usually limited to some column and beam tests. most of the recently accepted design standards for reinforced concrete elements with frp are not completed, and detailed seismic provisions are not always included. a study is also required to investigate the frp-rc frame performance under cyclic reversed loading in order to create the foundation for future design code requirements for frp reinforced concrete for seismic areas. in this research, the beam-column joints reinforced with steel, gfrp, and hybrid steel/gfrp rebars were studied numerically by using ansys finite element code [22]. the joints were analyzed under cyclic reversed loading. comparison and discussion of their performance, including energy dissipation and load-story drift envelope, were performed. t a. sobhy et alii, frattura ed integrità strutturale, 57 (2021) 70-81; doi: 10.3221/igf-esis.57.07 72 numerical analysis and verification model he finite element method (fem) is a numerical method to solve integral or differential equations and also to obtain approximate solutions for a variety of engineering problems [23]. in this research, 3d finite element modeling was conducted using ansys 18.2 software. this section presents the analytical approach and assumptions used in the analysis and the elements and material models selected from the software library. element solid 65 is used for the simulation of concrete. solid 65 is an eight nodes element, where each node has three translation nodal degrees of freedom in the x, y, and z directions. the solid 65 element can estimate cracking in three principal directions, plastic deformation, creep, and crushing concrete. element link 180 was used for the simulation of steel and gfrp rebar. the element is a uniaxial compression-tension element with three degrees of freedom at each node; the translations in the nodal directions x, y, and z. element solid 185 is used for the simulation of loading and bearing plates. this element is characterized by eight nodes with three translations nodal degrees of freedom in the nodal cartesian directions x, y, and z [7, 24–28]. an experimentally tested beam-column joint was used from literature to validate numerical analysis via ansys software [29]. the dimension of the tested joint is shown in fig. 1. the flexural reinforcement of the beam was five longitudinal rebars with a diameter of 19.5 mm top and bottom and rectangular stirrups with a bar diameter of 11.3 mm every 100 mm. the reinforcement steel of the column was eight longitudinal rebars with a bar diameter of 15.9 mm and rectangular stirrups with 11.3 mm diameter every 90 mm. a) joint geometry b) joint reinforcement figure 1: details of tested beam-column joint (dimensions in mm and φ denotes the rebar diameter). the steel reinforcement yield strength (𝑓𝑦) was equal to 400 mpa, and the concrete compressive strength (𝑓𝑐) was equal to 32.4 mpa. the joint specimen was loaded under reversed cyclic load, where two phases exist in the loading process. a loadcontrolled mode was carried out in the first phase, while a displacement-controlled mode was employed in the second phase. the cyclic reversed load, as seen in fig. 2, has been applied to the beam end top surface, the column head has been subjected to an axial force with a constant magnitude of 670 kn and continued constant in all loading cycles. restraints against both vertical and horizontal displacements were applied to the two ends of the column; meanwhile, their rotations were permitted (hinged boundary conditions). the beam-column joint was modeled by using the ansys program, as shown in fig. 3. the hysteretic diagram of the model is shown in fig. 4a, and a comparison between the numerical and experimental results is shown in fig. 4b. it can be concluded that analysis using the ansys fe code obtained the same trend of the experimental work results with good accuracy as the percentage difference between results was 10%. t a. sobhy et alii, frattura ed integrità strutturale, 57 (2021) 70-81; doi: 10.3221/igf-esis.57.07 73 a) first phase load-controlled load. b) second phase displacement-controlled load. figure 2: load history for the reversed cyclic load [29]. figure 3: finite element model details of the studied joint. figure 4: fe model results; a) load-story drift relationship of fe model and b) fe vs experimental load-drift envelope. parametric study hree models of beam-column joint have analyzed under reversed cyclic loading by finite element method using ansys software. the numerical model has the same characteristics as the verification model, but there are some differences, such as the model dimension, reinforcement, and the load history for the reversed cyclic load. figs. 5a shows the overall reinforcement and dimensions of the three models where the column height was 3000 mm with a crosssection of 300×400 mm. the control beam sample was 2300 mm with a 300×400 mm cross-section. the first model (s1) was reinforced with steel stirrups and longitudinal rebar. the second model (g1) was reinforced with steel stirrups and gfrp longitudinal rebar. hybrid reinforcements and steel stirrups were used in the third model (h1). the reinforcement of the three models is shown in fig. 5b to 5d. time, min l o ad , k n 0 5 10 15 20 25 30 35 40 -80 -40 0 40 80 time, min d ri ft , % 0 5 10 15 20 25 -5 -2 1 4 t a. sobhy et alii, frattura ed integrità strutturale, 57 (2021) 70-81; doi: 10.3221/igf-esis.57.07 74 a) beam dimension and reinforcement. b) reinforcement of s1. c) reinforcement of h1. d) reinforcement of g1. figure 5: geometric and reinforcement details of beam-column joints; a) joint geometry and reinforcement, b) reinforcement of s1, c) reinforcement of h1; and d) reinforcement of g1. (dimensions in mm, s denotes steel rebar, and f denotes gfrp rebar). the material model used for concrete is associated with the element solid 65. the model is defined by the concrete compressive strength, tension strength, shear stiffness for opened and closed concrete crack, and the residual stiffness after failure. this model simulates the elastic damage of concrete, but it can also include the effect of the plasticity by adding multilinear isotopic hardening relation to the material definition. at each element integration point, if the compressive failure criteria are achieved, the element loses its stiffness contribution at this point. bilinear isotropic hardening plasticity model was used for the steel. these model characteristics are the elastic constants, the yield stress, and the plastic tangent modulus. the mechanical properties and plasticity parameters of the materials used in the beam-column joint models according to ecp (201), ecp (208), isis canada, and aci 440.r1.06 [30–33], are shown in the following tab. 1. modeling and meshing methodology the solid element solid 65 was used to model the concrete. before cracking or crushing, the material of concrete was modeled to behave initially isotropic. eight integration points exist at each element at which crushing and cracking checks are executed. crushing or cracking occurs once the principal stresses of any element exceed the compressive or tensile concrete strength. the damaged regions are shaped perpendicular to the direction of the related principal stress. local redistribution of the stresses then occurs. therefore, an iterative solution is needed to handle the element nonlinearity. a link 180 element was used to model the steel gfrp reinforcement. generally, steel is very uniform, unlike concrete and the specification of a single stress-strain relation is satisfactory to be defined numerically. the solid element solid 185 a. sobhy et alii, frattura ed integrità strutturale, 57 (2021) 70-81; doi: 10.3221/igf-esis.57.07 75 was used to model the loading and bearing plates. finite element analysis requires meshing of the model; hence the models are divided into many small elements. convergency analysis was performed in order to balance the results accuracy, the solution time, and storage file size. after several trials, it was found that meshing the model with an element size of 50 x 50 x 50 mm has obtained good results with 3d concrete elements solid 65 and hexagonal sweep mesh option. the finite element model of beam and column is shown in fig. 6. material property notation value concrete elastic modulus 𝐸𝑐 28125 𝑀p𝑎 poisson's ratio 𝑣 0.25 unconfined compressive strength 𝑓𝑐 30.00 𝑀p𝑎 tensile strength 𝑓𝑡 2.91 𝑀p𝑎 reinforcement steel elastic modulus 𝐸s 200 𝐺p𝑎 poisson's ratio 𝑣 0.2 yield strength 𝑓𝑦 longitudinal stirrup 400 𝑀p𝑎 280 𝑀p𝑎 gfrp elastic modulus 𝐸f 43 𝐺p𝑎 ultimate strength 𝑓fu 765 𝑀p𝑎 table 1: mechanical characteristics of concrete, steel reinforcement and gfrp reinforcing bars materials. figure 6: components of the fe model. the concrete was connected to the reinforcement steel or frp bars in ansys using bonded contact. the concrete was bound to the loading and bearing plates by merging the coincide nodes at the interface between them. to simulate hinged support condition at the lower column end and roller support condition at the upper ends of the column, restraints were applied, as shown in fig. 7a. a. sobhy et alii, frattura ed integrità strutturale, 57 (2021) 70-81; doi: 10.3221/igf-esis.57.07 76 a) boundary conditions b) the applied loads figure 7: boundary conditions and the applied loads of the fe model. beam-column joint models have been analyzed under reversed cyclic load. as seen in fig. 7b, the cyclic reversed load has applied to the upper end of the beam, while the column head has been subjected to a constant axial load with a magnitude of 140 kn, which was maintained constant in all loading cycles. the history of the reversed cyclic load was used similar to the experimental work performed by paknejadi, [34], as seen in fig. 8. figure 8: load history for the reversed cyclic load. results and discussion n this section, the results of the three cases under investigation will be discussed. results such as hysteretic relations will be presented. the deformed shapes of the models at failure are shown in fig. 9. steel-reinforced model (s1) the hysteretic diagram of the steel model s1 is shown in fig. 10. the diagram displays that model achieved a maximum drift ratio of 5.35 % with a maximum load of 51 kn in a positive direction. ultimate capacity was measured to drift ratios in both of the positive and negative directions of 5.53 % and 5 %, respectively. after completion of the 4.5 % drift cyclic load step, the model failure happened at a drift ratio of 5 % in a negative direction. the fe analysis was promptly terminated without having completed the 5% drift ratio loop. failure mode was the cracking of the concrete in the sections of the beam near the face of the column, as shown in fig. 9a. the elements in this zone were highly distorted due to the loss of stiffness caused by ye concrete cracking. a significant loss in the shear capacity of the beam was evaluated, which caused a large movement of the beam part near the joint. in addition, due to the plastic deformation of steel reinforcement, a shifting was observed in the cycles, as seen in fig. 10. i a. sobhy et alii, frattura ed integrità strutturale, 57 (2021) 70-81; doi: 10.3221/igf-esis.57.07 77 a) model s1 b) model g1 c) model h1 figure 9: total deformation of the fe models. figure 10: load-story drift relationship of steel model s1. gfrp-reinforced model (g1) the hysteretic diagram of the gfrp model g1 is shown in fig. 11. linear elastic performance was demonstrated in the model until failure. model g1 achieved a maximum drift ratio of 4.21% with a maximum load of 44.7 kn in a positive direction, as displayed in the hysteretic diagram. ultimate capacity was measured to drift ratios in both of the positive and negative directions of 4.21% and 3.19 %, respectively. after completion of the 3.5 % drift ratio-cyclic load step, the failure happened at 4% drift ratio in a negative direction. the fe analysis was promptly terminated without completing the 4% drift ratio loop. failure mode was the cracking of the concrete in the sections of the beam close to the face of the column, and diagonal shear cracks appeared in the joint area, as seen in fig. 9b. the concrete elements in this zone were subjected to excessive crushing and cracking, while the gfrp rebar remained in the elastic range. due to the low deformation of the gfrp rebar and the absence of the plastic deformation, no significant shear failure happened to like the case of s1. in addition, no shifting was observed in the cycles, as seen in fig. 11. hybrid -reinforced model (h1) the hysteretic diagram of the hybrid model h1 is shown in fig. 12. the diagram displays that model achieved a maximum drift ratio of 3.13 % with a maximum load of 41.14 kn in a positive direction. ultimate capacity was measured to drift ratios in both of the positive and negative directions of 3.13 % and 2.71 %, respectively. after completion of the 2.5 % drift ratiocyclic load step, the failure happened at 3 % drift ratio in a negative direction. the fe analysis was promptly stopped without having completed the 3% drift ratio loop. failure mode was the cracking of the concrete in the sections of the beam near the face of the column, as seen in fig. 9c. the concrete elements in this zone were subjected to excessive crushing and cracking. the gfrp rebar remained in the elastic range, while plastic deformation was found in the steel rebar. due to the plastic deformation of steel reinforcement, a shifting was observed in the cycles less than the case of s1, as seen in fig. 12. a. sobhy et alii, frattura ed integrità strutturale, 57 (2021) 70-81; doi: 10.3221/igf-esis.57.07 78 figure 11: load-story drift relationship of gfrp model g1. figure 12: load-story drift relationship of hybrid model h1. load vs. story drift envelopes comparison of load vs. story drift envelopes for all models is shown in fig. 13. envelopes began at similar stiffness; however, once cracking occurs, a distinguished variation between the performance for all models has been shown. comparison between the three envelopes displayed that the steel-reinforced model has a higher stiffness relative to other models. the total drift of the gfrp model g1 was about 20% lower than that of the solid model s1 and was 23% higher than that of the hybrid model h1 in terms of total drift. the steel model was capable of achieving a much more constant post-yield load capability compared with the other models. model g1 had an elastic envelope, model s1 had a conventional elastic-plastic envelope, and model h1 provided a compromise between the performance of the standard steel-reinforced structure and the gfrp-reinforced structure. these results were consistent with previous experimental literature [17,18]. it was concluded in the literature that the gfrp joint displayed very lower plasticity characteristics, and the steel joint showed higher stiffness than the hybrid joint with a higher stiffness than the gfrp joint [17]. in addition, it was concluded that the low modulus of elasticity of the gfrp reinforcement decreased the rigidity of the specimens tested, resulting in lower reactions resulting from the drifts action [18]. cumulative dissipated energy an earthquake resistance relies on the structure's capability to dissipate the ground movement-supplied energy. while the measurement of this energy input by way of the ground movement is complex, and appropriate design must ensure a structure has a higher energy dissipation capacity than demand. a. sobhy et alii, frattura ed integrità strutturale, 57 (2021) 70-81; doi: 10.3221/igf-esis.57.07 79 the cumulative energy dissipated was measured in successive load-displacement cycles by summing the dissipated energy during the reverse cyclic load analysis. the energy dissipated during the cycle is calculated as the area occupied by the hysteretic loop in the load-displacement graph. fig. 16 displays cumulative dissipated energy plots vs. story drift for the models analyzed. it can be found that the gfrp reinforced model, i.e., g1 has around 2.5% of the standard steel-reinforced model s1 capacity of energy dissipation before failure. figure 13: comparison between load vs. story drift envelopes of all models. figure 14: cumulative energy dissipated for the models. the hybrid-reinforced model h1 had about 7.07 % of the standard steel-reinforced model s1 energy's dissipation capacity before failure. the cumulative energy dissipation capacity of the hybrid model h1 was around three times greater at failure than the gfrp model g1. this is apparent in the form of the calculated model individual hysteretic loops, see figs. 10, 11, and 12, which are wider for the steel model. the ductility of the steel reinforcement caused the beam to produce greater plastic deformations, thereby increasing the area of each loop. the amount of damage suffered by the models during failure, as seen in figs. 9, indicates that while the significant crack in the hinge region of the beam allowed the model to achieve more energy dissipation for the steel model, the gfrp and the hybrid models suffered more although localized destruction. steel yield has become a significant technique for the dissipation of energy by rc structures, while plastic deformations and friction around concrete cracks typically have a minimizing the dissipation of total energy. these results were consistent with previous experimental literature [17,18]. it was a. sobhy et alii, frattura ed integrità strutturale, 57 (2021) 70-81; doi: 10.3221/igf-esis.57.07 80 concluded that specimens with gfrp had poorer energy dissipation compared to steel and hybrid specimens before failure. in addition, the steel-reinforced specimen has absorbed energy much greater than the gfrp and hybrid-reinforced specimens [17,18]. conclusions his research was conducted to investigate the performance of beam-column reinforced joints using hybrid steel/gfrp and gfrp reinforcement in longitudinal reinforcement bars and steel stirrups and compared them to conventional steel-reinforced joints under cyclic reversed load. based on finite element analysis using ansys software and analysis of the results, the following conclusions were drawn: ‐ gfrp bars may be used as longitudinal reinforcement in beam-column joints exposed to cyclic loading. gfrp bars without any performance degradation can withstand tension-compression cycles. ‐ the gfrpbeam-column joint demonstrated a declining stiffness compared with the standard beam-column joint enhanced by steel. ‐ the hybrid gfrp reinforced joint displayed the lowest rigidity compared with the traditional steel-reinforced joint; however, it displayed greater rigidity compared to the gfrp reinforced joint. ‐ the low elastic modulus of the gfrp reinforcement caused a drop in the total rigidity of this model in operation, resulting in the converging drift ratios being obtained, however at the same time receiving lower forces due to its acting cyclic loading. ‐ gfrp reinforced joints displayed primarily elastic properties with very poor plasticity characteristics while evaluated under cyclic reversed loading. this resulted in decreased dissipated energy compared with traditional steelreinforced joints. ‐ the hybrid reinforced model provided a compromise between the performance of the standard steel-reinforced structure and the frp-reinforced structure. ‐ a variety of performance requirements, including strength, ductility, durability, stiffness, etc., may be modified to provide a hybrid reinforced frame. the designer may alter the hybrid system's strengthening specification to improve the balance among the design specifications. references [1] said, a.m., nehdi, m.l. (2004). performance of structural concrete frames reinforced with gfrp grid, 13th world conf. earthq. eng. [2] amer, a., abdel kader, h., abdel-razek, l., el-sisi, a. (2021). numerical analysis of frp reinforced frames under cyclic loading, egypt. j. eng. sci. technol., doi: 10.21608/eijest.2021.60164.1045. [3] benaoum, f., khelil, f., benhamena, a. (2020). numerical analysis of reinforced concrete beams pre-cracked reinforced by composite materials, frat. ed integrita strutt., 14(54), pp. 282–96, doi: 10.3221/igf-esis.54.20. [4] abedini, m., akhlaghi, e., mehrmashhadi, j., mussa, m.h., ansari, m., momeni, t. (2017). evaluation of concrete structures reinforced with fiber reinforced polymers bars: a review, j. asian sci. res., 7(5), pp. 165–175, doi: 10.18488/journal.2.2017.75.165.175. [5] elshazly, f.a., mustafa, s.a.a., fawzy, h.m. (2021). analysis of strengthened short deficient rubberized concrete-filled steel tubular columns, frat. ed integrita strutt., 15(55), pp. 1–19, doi: 10.3221/igf-esis.55.01. [6] chiozzi, a., grillanda, n., milani, g., tralli, a. (2020). nurbs-based kinematic limit analysis of frp-reinforced masonry walls with out-of-plane loading, frat. ed integrita strutt., 14(51), pp. 9–23, doi: 10.3221/igf-esis.51.02. [7] el-emam, h., el-sisi, a., reda, r., seleem, m., bneni, m. (2020). effect of concrete cover thickness and main reinforcement ratio on flexural behavior of rc beams strengthened by nsm-gfrp bars, frat. ed integrita strutt., doi: 10.3221/igf-esis.52.16. [8] mogahed, s.m.m. (2019).seismic evaluation of framed structures reinforced with frp bars. zagazig university, 2019. [9] davalos, j.f., chen, y., ray, i. (2008). effect of frp bar degradation on interface bond with high strength concrete, cem. concr. compos., doi: 10.1016/j.cemconcomp.2008.05.006. [10] alam, m.i., fawzia, s., liu, x. (2015). effect of bond length on the behaviour of cfrp strengthened concrete-filled steel tubes under transverse impact, compos. struct., doi: 10.1016/j.compstruct.2015.06.065. t a. sobhy et alii, frattura ed integrità strutturale, 57 (2021) 70-81; doi: 10.3221/igf-esis.57.07 81 [11] zhang, h., xu, x. (2018).finite element analysis of seismic behavior of frp reinforced concrete frame structure. iop conference series: earth and environmental science. [12] shanour, a.s., mahmoud, a.a., adam, m.a., said, m. (2014). experimental investigation of concrete beams reinforced with gfrp bars, int. j. civ. eng. technol. [13] hasaballa, m., el-salakawy, e. (2018). anchorage performance of gfrp headed and bent bars in beam-column joints subjected to seismic loading, j. compos. constr., doi: 10.1061/(asce)cc.1943-5614.0000888. [14] li, s., guo, s., yao, y., jin, z., shi, c., zhu, d. (2021). the effects of aging in seawater and swssc and strain rate on the tensile performance of gfrp/bfrp composites: a critical review, constr. build. mater., 282, pp. 122534, doi: 10.1016/j.conbuildmat.2021.122534. [15] vantadori, s., carpinteri, a., głowacka, k., greco, f., osiecki, t., ronchei, c., zanichelli, a. (2021). fracture toughness characterisation of a glass fibre-reinforced plastic composite, fatigue fract. eng. mater. struct., 44(1), pp. 3–13, doi: 10.1111/ffe.13309. [16] serovaev, g.s., kosheleva, n.a. (2020). the study of internal structure of woven glass and carbon fiber reinforced composite materials with embedded fiber-optic sensors, frat. ed integrita strutt., 14(51), pp. 225–235, doi: 10.3221/igf-esis.51.18. [17] nehdi, m., said, a. (2005). performance of rc frames with hybrid reinforcement under reversed cyclic loading, mater. struct. constr., 38(280), pp. 627–37, doi: 10.1617/14221. [18] mady, m., el-ragaby, a., el-salakawy, e. (2011). seismic behavior of beam-column joints reinforced with gfrp bars and stirrups, j. compos. constr., doi: 10.1061/(asce)cc.1943-5614.0000220. [19] ghomi, s.k., el-salakawy, e. (2018). seismic behavior of exterior gfrp-rc beam–column connections: analytical study, j. compos. constr., 22(4), pp. 04018022, doi: 10.1061/(asce)cc.1943-5614.0000858. [20] ghomi, s.k., el-salakawy, e. (2016). seismic performance of gfrp-rc exterior beam–column joints with lateral beams, j. compos. constr., doi: 10.1061/(asce)cc.1943-5614.0000582. [21] hasaballa, m., el-salakawy, e. (2016). shear capacity of exterior beam-column joints reinforced with gfrp bars and stirrups, j. compos. constr., doi: 10.1061/(asce)cc.1943-5614.0000609. [22] ansys. (2018). ansys workbench 19.2 documentation. [23] abdulkadir, m.r., aziz, z.a., muhammad, j.h. (2017). nonlinear finite element analysis of reinforced concrete beams strengthened with externally bonded steel plate using ansys, sulaimania j. eng. sci., 4(4), pp. 41–50. [24] ansys. (2013). ansys mechanical apdl theory reference, ansys inc. [25] alsharari, f., el-zohairy, a., salim, h., el-din el-sisi, a. (2021). pre-damage effect on the residual behavior of externally post-tensioned fatigued steel-concrete composite beams, structures, doi: 10.1016/j.istruc.2021.02.064. [26] el-emam, h., el-sisi, a., bneni, m., ahmad, s.s.e., sallam, h.e.d.m. (2020). effects of tensile reinforcing steel ratio and near-surface-mounted bar development length on the structural behavior of strengthened rc beams, lat. am. j. solids struct., doi: 10.1590/1679-78255836. [27] el-sisi, a.e., saucier, a., salim, h.a., hoemann, j.m. (2019). experimental and numerical evaluation of reinforced concrete walls retrofit systems for blast mitigation, j. perform. constr. facil., 33(2), doi: 10.1061/(asce)cf.1943-5509.0001265. [28] el-sisi, a.e., saucier, a., salim, h.a., nawar, m. (2017).experimental and numerical analysis for non-load bearing sandwich wall panels for blast mitigation. structures congress 2017: blast, impact loading and response of structures selected papers from the structures congress 2017. [29] hasaballa, m. (2009). seismic behaviour of exterior gfrp-reinforced concrete beam-column joints, msc thesis, , pp. 197. [30] housing and building national search centre. ministry of housing, utilities and urban planning. (2018). egyptian code for design and constructions concrete structures, cairo. [31] housing, m.o.f., utilities, u., code, e., practice, o.f. (2005). arab republic of egypt ministry of housing , utilities and urban utilities egyptian code of practice the use of fiber reinforced polymer (frp). [32] aci committee 440.1r-06. (2006). guide for the design and construction of concrete reinforced with frp bars, am. concr. inst., pp. 44. [33] williams, b.k., banthia, n., bisby, l., cheng, r., fallis, g., hutchinson, r., mufti, a., neale, k.w., newhook, j., soudki, k., wegner, l. (2006). an introduction to frp-reinforced concrete. [34] paknejadi, a.h., behfarnia, k. (2020). performance of reinforced self-consolidating concrete beam-column joints with headed bars subjected to pseudo-static cyclic loading, ain shams eng. j., doi: 10.1016/j.asej.2019.12.008. microsoft word numero_49_art_14_2450 p. trusov et alii, frattura ed integrità strutturale, 49 (2019) 125-139; doi: 10.3221/igf-esis.49.14 125 focused on russian mechanics contributions for structural integrity multi-level model describing phase transformations of polycrystalline materials under thermo-mechanical impacts peter trusov, elena makarevich, nikita kondratev perm national research polytechnic university, russia tpv@matmod.pstu.ac.ru, http://orcid.org/0000-0001-8997-5493 makareviches@inbox.ru kondratevns@gmail.com, http://orcid.org/0000-0002-0261-3017 abstract. the problem of constructing the multilevel physical model of inelastic deformation in steels allowing to take into consideration diffusionless solid-state phase (martensitic) transitions is considered. the model structure includes three scale levels with the closed system of equations offered for them. explicit internal variables reflecting the evolution of the material structure (both the defect structure and the grain one) are introduced at the lower scale levels of the model. the distinctive feature of the developed model is consideration of the lower scale level in such a way that a homogeneous element of this level completely turns into a new phase at a high speed (relative to the kinematic quasi-static loading), that is close to the speed of sound in the crystal medium. based on the principles of classical thermodynamics the phase transformation criterion is written. according to this criterion, the choice of a transformational system under the martensitic transition is made. the algorithm of the model is developed and its realization features are described in connection with the high-rate restructuring of the face-centered cubic lattice to the body-centered tetragonal one. the result of this restructuring is a severe change in the physic-mechanical properties of the material. keywords. crystal plasticity; multiscale modeling; phase transformations; microstructure; defect structure; improved steels. citation: trusov, p., makarevich, e., kondratev, n., multi-level model describing phase transformations of polycrystalline materials under thermo-mechanical impacts, frattura ed integrità strutturale, 49 (2019) 125-139. received: 31.03.2019 accepted: 16.05.2019 published: 01.07.2019 copyright: © 2019 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. introduction dvanced high-strength steels have a wide range of applications in industry and technology, which is constantly increasing due to the excellent combination of their plastic and durability properties [1–2]. enhanced physics and mechanical properties of steels are achieved by the state of grain and defect structure formed as a result of previous thermo-mechanical processing, mechanisms of its formation and evolution [3]. numerous experimental studies indicate that phase transformations may be the main reason for the set of physical and mechanical properties in steels, ensuring their a http://www.gruppofrattura.it/va/49/2450.mp4 p. trusov et alii, frattura ed integrità strutturale, 49 (2019) 125-139; doi: 10.3221/igf-esis.49.14 126 wide usage [4–5]. all known phase transitions for solid state are observed in steels and their alloys, such as polymorphic transformations with a wide range of morphological and kinetic features, eutectoidal (pearlite) transformations, decay of solid interstitial and substitutional solutions, ordering with a change in the local and long-range order in austenite and martensite. the possibility of realization for certain phase transformations and kinetics of transformations depends on the steel composition and the parameters of thermo-mechanical impacts, such as temperature, heating or cooling conditions, holding time, mechanical loading parameters, etc. the important feature of such systems is that the diffusion mobility of metal atoms and carbon is sharply different. therefore, the crystal lattice restructuring during transformations can occur together with the diffusion redistribution of carbon and alloying elements. another feature of steels is that during phase transitions of supercooled austenite, the transformation of a face-centered cubic crystal lattice into a body-centered tetragonal lattice can occur simultaneously with the diffusion redistribution of carbon and alloying elements. the experimental study of this issue is quite resource-expensive. therefore, in solid mechanics, the problem of constructing the models describing the state and evolution of the structure for a material taking into consideration solid-state phase transformations becomes actual. it is widely known, that the physic-mechanical properties of polycrystalline materials and the functional characteristics of finished products are determined by the current state of the structure at various scale levels [6–7]. the latter significantly changes in thermo-mechanical processing of metals. the correct description of the internal structure for a material provides a fundamental opportunity to optimize existing and develop new methods for obtaining materials and products made of them with increased strength and performance characteristics. as a result, in recent decades, models based on explicit considering the mechanisms and the carriers of inelastic deformation (crystal plasticity based multilevel models of inelastic deformation) are of great interest in solid mechanics [8]. as a rule, in such models, the correct description of the existing mechanisms for inelastic deformation requires the introduction of several (two or more) scale levels. the multilevel approach from the point of view of physical description of the occurring processes is rather universal and can be applied to designing structures made of new, not yet existing materials and creating technologies for their manufacturing. the theoretical basis of this approach to the study of inelastic deformation is the methods of mathematical modeling with the introduction of internal variables, supplemented with the model identification and verification procedures. internal variables make it possible to explicitly include a description of the physical mechanisms, their carriers, and processes accompanying inelastic deformation at various scale levels of a material. also, the internal variables of a model reflect structural interactions and restructuring the mesoand microstructure of a material. the scale levels involved into consideration are determined by the objectives of the study and the most important mechanisms of inelastic deformation. at the lower scale levels there is a principal possibility for correct accounting the physical mechanisms of inelastic deformation. thermo-mechanical effects are transmitted from the macro level to the lower scales and cause changes in the internal structure. in turn, the latter determines the effective characteristics of the material at the macro level. in the framework of the multilevel approach to describe inelastic deformation of metals under thermo-mechanical processing a material point with a necessary set of homogeneous (averaged) characteristics is allocated at the macro-level. a set of homogeneous areas corresponds to this material point at one or several lower scale levels. the multilevel approach allows to describe the response of the material with the constitutive relations of a same type at various scale levels. in the framework of this work, hooke's law in the rate relaxation form, written in terms of asymmetric measures of strain rates, is used. at the lower scale level, crystallite (a homogeneous part of a polycrystalline material) is considered. each crystallite has a set of properties: anisotropic elastic modules, lattice orientation, a set of slip systems, transformation systems, the thermal conductivity coefficients. in the models of this type, an important aspect is the correct description of the internal variables evolution being responsible for the properties of both a crystallite and a polycrystal [6]. constitutive and kinematic equations describing the irreversible deformation at the meso-level due to the slip of dislocations, phase transitions, the evolution equations for critical shear stresses (by different mechanisms), description of rotation for the crystallites, the influence of the temperature changing and the attached stresses on the evolution of the defect structure are included into consideration. the problem of taking into account the geometric nonlinearity at the upper scale level and the connection for the similar characteristics of the scale levels remains important [9]. modeling the processes of inelastic deformation taking into consideration phase transformations t present, in scientific literature there are various models of different types to describe the behavior of steels taking into consideration martensite transformations. the reviews of the works devoted to this problem can be found in the articles [10–11]. two main approaches to constructing the models of polymorphic transformations can been distinguished. the first one is based on the models with explicit account of the phase boundaries taking into consideration a p. trusov et alii, frattura ed integrità strutturale, 49 (2019) 125-139; doi: 10.3221/igf-esis.49.14 127 the conditions at the phase boundary of the deformable material and the kinetics of a new phase evolution. the second one is based on the models with introduction of additional state parameters or model variables characterizing certain features of the material structure “on average” (for example, the concentration of a new phase), and the formulation of relations for them. in the models of the first type, with the explicit introduction of interphase boundaries into consideration [see 12–13], there is an opportunity to describe phase transformations from the point of solid mechanics using the ideas of the classical phase transitions theory by j. gibbs. phase boundaries appear in solids as a result of phase transitions. they can be considered as surfaces where deformations have a discontinuity whereas a field of displacement is continuous. the microstructure of a material changing in the process of the phase transition generates its own transformation deformations and modification in the elastic modules. so that, at the phase boundary some components of the strain tensor can break, and it leads to limitations on the constitutive relations. appearance of an equilibrium discontinuous deformation field in an elastic body requires some regions in the deformation space where the hadamard's inequality, being a necessary condition for stability with respect to infinitely small deformations, is failed. to maintain an equilibrium at the phase boundary, the following conditions must be satisfied: continuity keeping, force continuity, and a thermodynamic condition being an analogous of the chemical potentials' equality in the gibbs theory. the latter condition imposes restrictions on determining the shape of the phase boundary and the corresponding deformations at the boundary. since, even if the defining relations allow the existence of two-phased states, not all deformations can be realized at the phase boundary. this leads to the concept of a phase transitions' zone, which boundary determines the limit surface of transformation in the space of deformations. for the second type models, the phase field method is often applied, which is used to describe both diffusion transformations and diffusionless (martensite) ones at the meso-level (the simulated area consists of several grains) in many cases [see, for example, 14]. this approach assumes the presence of a “blurred” (“diffusion”) boundary between the phases in contrast to the classical methods using the concept of “sharp boundary”, when the multiphase structure is described by the position of the boundary and the set of differential equations is solved together with the flow equations and the constitutive equations at the boundary for each of the areas. in the “diffusion boundary” approach, the form and mutual arrangement of the regions occupied by individual phases are described by a set of parameters determining their fraction φi. the value of the parameter can vary from 0 to 1; φi=0 corresponds to the area where there is no phase i, φi=1 corresponds to the single-phase region. thus, the microstructure (with the exception of grain boundaries, defects, etc.) can be described by a set of single-phased regions separated by boundaries where more than one value φi is different from zero. in the “diffusion boundary” approach, the change in the shape of the regions (and hence, the position of the boundary) over time is implicitly determined by the change in the fractions of phases. the time change of the phase fractions is described by the kinetic equation obtained in terms of thermodynamics of irreversible processes, i.e. the linear relationship between the rate of change for the phase fractions and the derivative of the thermodynamic potential for this parameter is used. phase transformations occurring in isothermal conditions are most often investigated, and free energy is taken as a thermodynamic potential, but there are works studying non-isothermal processes where entropy is chosen as a thermodynamic potential [15]. in most studies devoted to description of thermo-mechanical processes, the so-called direct models of the first type are used [16] when a set of finite elements is matched to each grain and a model is used to describe the phase transitions for each of the elements. the usage of such models for modeling the real processes in three-dimensional formulation requires significant computational resources. therefore, the statistic type models [17] are actual, where the set of homogeneous elements of the lower scale level constitutes a representative volume with homogeneous properties at a higher scale. within this paper, a multilevel model of the hybrid type to describe the behavior of steels under thermo-mechanical loading, taking into consideration the phase transformations, is proposed by the authors. within the framework of this model at the macro level, a direct type model is used. to determine the response of each material point at this scale level, a statistic model is applied, comprising the elements from a lower scale. the structure of this model includes internal variables being divided into two groups: explicit ones and implicit ones. explicit internal variables are included into the constitutive relations at the considered scale level, and the implicit ones are the parameters of evolution equations. to connect the internal variables of two above mentioned groups, the closing equations are applied. when using the approach with explicit introduction of internal variables, the following hypothesis is accepted. the reaction of the material at any moment is determined by the current values of thermo-mechanical characteristics, internal variables and parameters of external influence. the considered hypothesis allows to give up rather complicated constitutive relations in the operator form. at the same time, the material memory about the prehistory of influences is preserved due to the evolving internal variables being the impact history carriers in this case. within this article, the structure of the proposed model is described, its scale levels are introduced, the constitutive relations and evolutionary equations are given, as well as the algorithm for the implementation of the model. p. trusov et alii, frattura ed integrità strutturale, 49 (2019) 125-139; doi: 10.3221/igf-esis.49.14 128 the structure of multi-scale model with phase transformations solid phase transformation in a polycrystalline material is understood as a polymorphic transformation leading to changing the physic-mechanical properties of some region in the material at a microand/or meso-level as a result of the crystal lattice transformation under external influences (loading, temperature, etc.). a phase is understood as some part of a grain being characterized by a specific type of crystal lattice, a chemical composition, a type of solid solutions, etc., at a fixed moment of a thermo-mechanical loading process. from the point of mathematical modeling and solid mechanics a phase is understood as a certain sub-region inside a material which behavior under deformation is described by the constitutive relations of the fixed type with a specified (determined from the solution of some auxiliary subtasks) set of properties being defined by the parameters and the current value of internal variables. with a goal of modeling the phase transformations of polycrystalline materials in thermo-mechanical processing the multilevel model of a hybrid type is developed. within this model three structure-scale levels are taken into consideration inside the material. they are macro-level, meso-level i and meso-level ii. internal variables are added into the structure of the model at each scale level being the carriers of impacts' history. the macro-level is supposed to be the material representative volume (consisting of some hundreds of grains). to analyze a behavior of this volume, the boundary value problem is offered to be formulated and solved (for the chosen computational domain) with determination of fields for stresses, strains and temperature in the considered material volume. the finite element method procedure is applied for the numerical solution of the problem at the macro-level. within the framework of the proposed multilevel model the problem of determining the reaction of a material to the applied thermo-mechanical impact is essentially nonlinear. a step-by-step procedure (in time) is used to solve it. decomposition of the whole problem according to the physical processes is realized. the subtasks of determining the stress-strain state, the temperature and the problem of determining the phase composition of a material are considered being connected (using a step-by-step procedure). the solution of this problem allows to determine the impacts (velocity gradient, temperature and temperature rate of change) at each point of the considered area (i.e. within each finite element), which are then given down to a deeper scale level within the multilevel model. thus, within the framework of the finite element scheme at the macro level, the finite elements themselves are precisely the elements of meso-i. as a basic constitutive relation at the meso-i, the generalized hooke's law in the rate relaxation form and the heat equation are used. the mentioned constitutive relations contain in their structure explicit internal variables. the values of those variables depend on the history of the impacts on the material, are changed in the process of deformation and are determined from the deeper scale levels as a response to the thermo-mechanical effects. for example, the tensor of elastic properties of a material, the inelastic strain rate tensor, the heat capacity coefficient, the thermal conductivity tensor, the power of internal heat sources can be such variables. herewith, an element of the meso-i is understood as a certain subdomain of a grain, the state of which at each moment of the thermo-mechanical loading process is assumed to be homogeneous in all parameters characterizing the state of the meso-i element, and within which the crystal lattice of the material can be considered as approximately perfect (a grain is supposed to consist of crystallites with a minor misorientation). in turn, a meso-i element is represented as an aggregate, consisting of n elements of meso-ii, such as subgrains, fragments, cells, phase components. wherein, to determine the response of the meso-i element, the modified statistical model (taking into account the relative position of the neighboring meso-ii elements) is used [17]. herewith, a size of a meso-ii element is assumed to be so small that its state can be considered as a homogeneous one according to all parameters at each time moment. the velocity gradient, temperature, and the rate of temperature changing are transmitted from meso-i to meso-ii as impact factors. a model based on crystal plasticity is applied for the meso-ii element. the voigt hypothesis is used when transmitting exposure from meso-i to meso-ii. at any fixed moment of a thermo-mechanical loading process each meso-ii element is supposed to be in some specific phase (i.e. it is always single phased), but the phase characterizing it can change as a result of external influence, which leads to a change in all its properties. belonging to a particular phase determines the basic properties of the meso-ii element, including the type of its crystal lattice. orientation of the axes of the moving coordinate system [18–19] is considered as known for each meso-ii element. this orientation changes during a deformation process (as a result of rotation for the meso-ii element or as a result of the transformation the element lattice after the realized phase transition). the moving coordinate system is associated with the lattice of the element (but, doesn't coincide with it in general case, as the lattice may have distortions in the deformation process). as a result of thermal and mechanical effects (transmitted from the upper scale level) in case of fulfillment the thermodynamic criterion a phase transition can occur in a meso-ii element. herewith, due to the homogeneity of the all parameters' values for the meso-ii element, it is assumed that its entire volume undergoes a phase transformation simultaneously. all processes in the meso-ii element are considered in its moving coordinate system being oriented definitely with respect to the laboratory coordinate system. wherein, the following modes are realized in the meso-ii element: inelastic deformation by a p. trusov et alii, frattura ed integrità strutturale, 49 (2019) 125-139; doi: 10.3221/igf-esis.49.14 129 shears on slip systems, the lattice rotation i.e. quasi-rigid motion with a spin tensor being determined by one or another rotation law (here, the taylor model is used), temperature deformation, deformations of an element caused by a phase transformation, elastic distortions of a crystal lattice in a crystallite, the changing the lattice type of the crystallite and all its properties (internal variables) as a result of phase transformation, the changing the orientation of the moving coordinate system for the element as a result of a phase transformation, the formation of internal heat sources as a result of inelastic deformation processes and phase transformations at meso-ii level. the acting stresses in the element, the inelastic strain rate tensor, the power of internal heat sources (due to latent heat of phase transformations and inelastic deformation), the orientation tensor of a meso-ii element, characterizing the current orientation of the moving coordinate system for the element with respect to the fixed laboratory coordinate system, and the information about phase composition are transmitted as a response from meso-ii to meso-i. the statistical averaging procedures are carried out at the meso-i level (among all meso-ii elements, taking into consideration the current orientations of the moving coordinate systems for the elements) to determine the values of the model internal variables at an integration point for a finite element (for simplexelements, this matches the data for an entire finite element). thus, the meso-i element constitutive relations are “formed” in the process of solving the problem depending on transformation of the material structure at a deeper scale level in the thermo-mechanical processing and may change during the process itself. the constitutive relations constructed by this way for the meso-i element are then used to solve the boundary value problem at the macro level at the next time step. the subject for discussion in this article is a description of the structure and the implementation features of the model at the meso-levels i and ii. about motion decomposition for the meso-ii element as in solving the boundary value problems connected with description of thermo-mechanical processing for polycrystalline materials, as a rule, it is necessary to take into consideration large displacement gradients, the problem under consideration, being essentially nonlinear, is posed and solved in a rate form. within the framework of the model, description of kinematics for the meso-ii element is based on introduction of the multiplicative decomposition for the deformation gradient by the following way: e=        e tr p tr pf f f f f f r f f f , (1) where ef , trf , f , pf are elastic, transformation, temperature and plastic components of the deformation gradient; ef is the component of the deformation gradient characterizing the elastic distortion of the lattice with respect to the rigid moving coordinate system connected with the lattice of the initial phase; r is the rotation tensor describing the material rotation together with the moving coordinate system (from the initial position of the moving coordinate system to its current position); pf is the plastic component of the deformation gradient that does not change the symmetry properties of the material. based on the accepted decomposition (1) the transposed velocity gradient is defined as follows:                                                      1 1 1 1 1 1 1 1 1 1 1 1 . e e e t e e tr tr t e e tr tr t e e tr p p tr t e l f f f f f r r f f r f f r f f r f f f f r f f r f f f f f f r f (2) when considering metallic polycrystals, the magnitude of the elastic distortions of the lattice can be assumed to be small, therefore ef i and the relation (2) is converted into the following form:                                          1 1 1 1 1 1 1 1 . e e t tr tr t tr tr t tr p p tr t l f f f f r r r f f r r f f f f r r f f f f f f r (3) then, the additive decomposition of the transposed velocity gradient in the actual configuration based on the multiplicative decomposition (1) can be represented as follows     e tr pl l ω l l l , (4) p. trusov et alii, frattura ed integrità strutturale, 49 (2019) 125-139; doi: 10.3221/igf-esis.49.14 130 where   tω r r is the spin determining the rate of rotation for the moving coordinate system connected with the material symmetry axes of a meso-ii element,   1e e el f f is the rate of elastic distortions of the lattice. the model constitutive relations for a meso-ii element as the model is intended to describe the processes of thermo-mechanical treatment being characterized by large displacement gradients, geometrically nonlinear kinematic and constitutive relations are used in its structure [18–19]. the rate statement of the problem is done in the current configuration and the following constitutive relations are used [20–21]:             о ρ; ; ;ρ̂ cr p tr cr t πk : l ω l l l k k k ω ω k k σ (5) where π is the tensor of elastic properties for the meso-ii element, defined by the constant components in the basis of the crystallographic coordinate system of the current phase in the initial configuration;  ̂l v is the transposed velocity gradient for the material particles of the meso-ii element in the current configuration, transmitted from the meso-i; pl is the plastic part of the relative velocity gradient connected with the shears on the slip systems inside the meso-ii element in the deformation process; l is the thermal part of the transposed relative velocity gradient; trl is the transposed velocity gradient of the transformation deformation, associated with the phase transformation in the material; , crk k are the weighted kirchhoff stress tensor and its corotational derivative; о ˆρ, ρ are the densities of the meso-ii element's material in the initial (unloaded) and current configurations (the density depends on the phase the element at the considered moment is in); σ is the cauchy stress tensor of the meso-ii element; ω is the spin tensor of the meso-ii element (to define it, any physically based model of rotation can be used, for example, it can be the teylor's model of turning in a fully constrained conditions [22] or the model of lattice rotation [18]). wherein, at each moment of the process, the rotation of the rigid moving coordinate system's axes of the meso-ii element, connected with the lattice of the element in its current phase, is considered. the plastic part of the velocity gradient pl is determined by shears on the slip systems in the meso-ii element:           1 ; k k k kp k l b n (6) where k is the number of the slip system. herewith, the shear rate on each slip system in the meso-ii element is considered as a function of the acting stresses   k , critical shear stresses   kс and temperature  :           , ,k k kсf ; (7) in general case, any physically valid model can be used to define it. in particular, a non-linear viscoplastic model [21, 23] can be used:                          1 0 . mk k k k сk с h (8) the thermal part of the transposed relative velocity gradient in the meso-ii element is defined using the following relation:   l α , (9) where α is the thermal expansion tensor for the material of the meso-ii element. herewith, a simplification can be accepted for cubic crystals, and the relation for the thermal component of the velocity gradient can be written in the following form: p. trusov et alii, frattura ed integrità strutturale, 49 (2019) 125-139; doi: 10.3221/igf-esis.49.14 131 α θ   l i , (10) where α is the coefficient of linear thermal elongation-compression for the material of the meso-ii element, i is the unit tensor. the power of internal heat sources in the meso-ii element is determined by two components connected with, firstly, the inelastic deformation on the slip systems in the element, and secondly, the phase transformation in the meso-ii element:           1 ρ̂ k k k meso k q g (11) where g is the specific latent heat of a phase transition,  is the new phase (martensite) formation rate. determining the transformational part of the deformation gradient at the meso-ii martensitic transformations occur at speeds comparable to the speed of sound in the crystal environment under consideration. in multilevel models, as a rule, the martensitic phase transitions are considered at a higher scale level [for example, 24], than the meso-ii one (according to the division of the scale levels adopted in this work). it allows to use the magnitude of the martensite volume fraction in the considered volume to describe phase transitions, “smoothing” and assuming it as a continuous value in the process of thermo-mechanical loading, i.e. the martensitic transformation process is “smeared” in time and space. within the framework of this model, the meso-ii element is assumed to be so small, that it turns into a new phase almost instantly. wherein, out of all possible variants of the transformational system, an energetically more favorable one is chosen. the hypothesis is accepted that the phase transition is fully realized in a time step (in the general algorithm of the inelastic deformation model). for the elements experiencing a phase transition at a given time step, a time step is divided into a fixed number of substeps. the number of substeps is determined in numerical experiments. for these elements experiencing a phase transition, the temperature changing per step is neglected; the velocity gradient is assumed to be fixed throughout the entire step. in this case, the additive decomposition of the transposed velocity gradient in the current configuration, based on the multiplicative decomposition (4), can be represented as:    e tr pl l ω l l , (12) within the framework of the proposed model, at this stage, the relations, allowing to determine the gradient of transformational deformation for the martensitic phase transformation obtained in [25–26] based on the application of crystallographic theory of martensitic transformations in steels [27–28], are used. the transformational deformation gradient of the meso-ii element during the transformation from the initial phase to the new one under the conditions of deformation with an invariant plane can be represented as follows:   ξtrf i sm , (13) where the vector m of a normal to the invariant habit plane (a unit vector) and the vector s of a shear set the transformational system (these vectors are not perpendicular in a general case). these vectors aren't determined by the crystallography entirely, like their analogues in the theory of plastic shear along slip planes. they are calculated taking into consideration the magnitude of changing the lattice parameters during the phase transition and the accommodation mechanisms accompanying it [25]. the volume fraction ξ after a martensitic phase transition within the element, is introduced into consideration. the dependence of the volume fraction ξ on the current time at the step is given by a smooth function, being satisfied by the following properties: 1) at the beginning of the first substep of the phase transition, it is equal to 0, at the end of the last substep it is equal to 1; 2) at the ends of the phase transition interval (time step), the ξ derivative is equal to 0 or 1. it is necessary to note that the latter requirement is optional. further, an internal step-by-step process of solving according to the initial scheme of the elastic-viscoplastic problem is organized for these elements. wherein, the three components of the deformation gradient are changed: the elastic one, the transformational one and the viscoplastic one. herewith, the critical shear stress is determined by averaging the critical austenite stress (with a weight (1– ξ)) and the critical martensite one (with a weight ξ). the transformational component of the relative velocity gradient trl is determined by the transformational deformation gradient, being depended on the phase transformation type occurring in the material, and has the following form: p. trusov et alii, frattura ed integrità strutturale, 49 (2019) 125-139; doi: 10.3221/igf-esis.49.14 132     1 ξ= det( ) tr tr tr tr l f f sm f . (14) choosing the phase transformation criterion for a meso-ii element n researches on phase transformation modeling different approaches for creating the relations to determine the volume fraction of a new phase in a material under consideration depends on the impact process parameters are used. the koistinen-marburger [29] type equations are the most widely used ones in material science practice in case of macrophenomenological description of heat treatment processing. the relations of such a type and their different modifications make it relatively easy to determine parameters in equations for phases' volume fractions from the macro-experiments. but these relations don't allow to take into consideration the physics peculiarities in the process of a new phase forming at the meso-scale and don't allow to include besides the temperature impact also the mechanical one into consideration. they also naturally don't allow to analyze the influence of a thermo-mechanical impact parameters on the process of transformation. in recent decades, the alternative thermodynamic approach to the constructing the kinetic equations for the description of the phase volume fractions evolution and the phase transformations criteria has been evolved. this approach allows to construct the models for continuum media and suggest the relations for thermodynamic driving forces of phase transformations based on the analyses of the nature of the effects on the material and the physic-mechanical processes occurring inside the structure of the material during these effects. the short review of the thermodynamic criteria of phase transformations nowadays, there is a significant amount of papers wherein exactly the thermodynamic approach is used to construct a phase transformation criterion. the short overview for the ways of introducing this criterion in some of them is given below. in the paper [30] the double phased system (austenite + martensite) is considered as a thermodynamic nonequilibrium system with dissipation. it is supposed that the principle of maximum dissipation can be used to describe its evolution. herewith, the dissipation power is determined as a difference between the power of external forces and the helmholtz free energy rate of change for the quasistatic isothermal case considered in the cited article. the specific helmholtz free energy (per unit volume) is supposed to be consisted of three parts: free chemical energy, surface energy and elastic strain energy. an increment of free chemical energy is expressed by the difference between the corresponding free chemical energies of martensite and austenite being multiplied by the volume fraction of martensite. it is assumed to be a linear function of temperature. elastic energy is defined as convolution of the stress and the difference between total and phase deformations. all the values are determined at the meso-scale. the change in free energy associated with the boundaries is introduced through the analyses of jumps in chemical and elastic energy and boundary motion speed. the term associated with discontinuities at the phase interface also appears in the power of external forces. in terms of the specified parameters, an expression for the dissipation power is obtained. the force criterion (analogically with plastic deformation) is used as a condition of phase transformation realization. the critical stresses of phase transformations are supposed to be linearly related to the accumulated shifts in austenite (moreover, the coupling coefficient is negative, i.e. the accumulated shifts in austenite make the critical phase transformation stresses lower) and the martensite volume fraction. in [31] the relation for dissipated energy with excretion the generalized thermodynamic force of phase transformation (being conjugate to the rate of change for the specific volume fraction of the martensite phase) explicitly is given. the specific relations for the thermodynamic forces under various conditions (for example, the absence of internal additional stresses in austenite from phase transformation) are considered. separately, the definition of the thermodynamic force associated with the inhomogeneous plastic deformations in the austenitic phase is considered. herewith, the inhomogeneous plastic deformations are assumed to be proportional to the average plastic deformations in austenite. in the paper [32] it is suggested to determine the generalized thermodynamic force using the difference of the helmholtz free energy in the initial and martensite phases and the meso-stresses' work averaged over two phases made on the difference between transformation and plastic deformations in the initial and final phases. in turn, the helmholtz free energy is represented as a sum of “chemical” energy (determined by the position of the atoms in the phases and dependent on temperature) and strain energy (dependent on elastic strains and temperature). the excess by the generalized thermodynamic force its critical value for a given material is used as a criterion of a possibility for the phase transformation. in the paper [33] the rate of change for the volume fraction of each variant in martensite phase is determined by the power low depending on the shear stress in the habit plane of the transformation and hydrostatic stress. to determine the critical i p. trusov et alii, frattura ed integrità strutturale, 49 (2019) 125-139; doi: 10.3221/igf-esis.49.14 133 resistant stress to the martensite transformation, the olson's and roitburd's solution, based on the assumption of the spherical shape of the original grain, is used. for the martensite plate the shape of a flattened ellipsoid is taken. into the proposed relation, there is chemical energy difference (the gibbs free energy), surface energy of an "austenite – martensite" boundary and transformation strain energy. in [34] to describe the martensite transformation, a set of internal variables is introduced (the martensite volume fractions for each of the possible variants). their associated thermodynamic forces are introduced being dimensioned as energy per unit volume. the dissipation rate due to the phase transition has been defined as the sum of multiplications of thermodynamic forces and the rate of change for the martensite fraction (in all variants). the thermodynamic forces are dependent on elastic energy, temperature, crystallography of the martensite transformation, the fraction of the transformed phase (according to different variants). the criterion for implementation of the phase transformation is also the excess of the critical value by the chosen thermodynamic force. in [35], following the model proposed by olson and cohen [36], temperature and hydrostatic stress (related to the stress intensity) are considered to be the driving forces of the transformation; plastic deformations of the austenitic phase are taken into account; it is believed that martensite nuclei are formed by the intersection of the shear bands. in [37–38] an expression for the thermodynamic potential is introduced. as a potential the gibbs free energy is used. constitutive relations (for strains and entropy) are obtained from the second law of thermodynamics. the expressions for the dissipation rate, the thermodynamic force conjugated with a fraction of the martensite phase, and the temperature for the onset of the martensite transformation (taking into account the effective stresses) are given. the formulations for the corresponding evolutionary equations are given. the paper [24] contains a thermodynamic description of the phase transformation process, based on onsager’s (linear) irreversible thermodynamics. in accordance with the onsager formalism, dissipation is represented as a sum of the products of affinity (essentially, thermodynamic forces) and flows. the hypothesis of additive decomposition for entropy into reversible (elastic) and irreversible (transformational) components is accepted. the latter is determined through the latent heat of a phase transformation. the expressions for thermodynamic forces are obtained from the 2nd law of thermodynamics in the form of dissipation inequality using different thermodynamic potentials such as internal energy, the helmholtz and the gibbs free energies. the achievement of the corresponding critical value by the thermodynamic force on the transformation system is taken as the criterion of phase transformation. the paper [39] contains thermodynamic analysis of phase transformation. in particular, the relations for the components of free energy (helmholtz) for the representative volume and energy dissipation are given. free energy has been defined as a sum of elastic strains energy, crystallographic energy (often called chemical energy) and energy of interphase boundaries (the latter can be neglected, as well as energy of the defects (point, dislocations, etc.)). elastic energy is decomposed into elastic energy of the average (for a representative volume) elastic strains and energy of interphase interactions. to determine the latter, analytical solution in terms of the green function and the eshelby tensor is applied. using the legendre transformation transition from the helmholtz free energy to the gibbs free energy is realized. the latter is completed with restriction on the total fraction of the phases and the non-negativity condition for the fraction of the phase for each variant using lagrange multipliers method and kuhn-tucker conditions. the expression for internal dissipation, determined by the difference between the power of external forces and the rate of change for free energy is obtained. from it, the relation for the driving (thermodynamic) force is derived to determine the phase boundary displacement. paper [40] provides relations for determination the “driving mechanical force of transformation” (in fact, the work of applied stresses on transformation strains), elastic stored energy of the environment, and dissipated plastic work of deformations. at the same time, for a specific implementation, the criterion of accumulation of a certain plastic strain level in the residual austenite is used as a condition for a phase transformation. in [41], additive decomposition of specific (per mass unit) entropy into elastic (reversible), plastic and transformation parts is introduced. the transformation part is determined by the weighted sum of the latent heat of phase transformations according to different variants divided by phase transition temperature. the rate of change for the plastic part, related only to austenite, is determined by the sum of multiplications of the entropy change measure due to the shifts in each slip system and the shift rate in the corresponding systems. following by the procedure proposed by coleman and noll, the dissipation function is introduced being represented by the sum of multiplications for thermodynamic forces and flows. a general form of the defining relation and expression for thermodynamic forces is obtained from the dissipation inequality. from the internal energy (included into the dissipation expression), the transition to the helmholtz free energy is made. the helmholtz free energy is proposed to be written as a sum of the following components: elastic, thermal (including the heat of phase transformations), surface and energy of defects (dislocations). specific expressions for each of the introduced components are proposed. a similar decomposition for the thermodynamic (driving) forces of phase transformations and plastic deformation is proposed. relations for determination all the components included into the specified decomposition p. trusov et alii, frattura ed integrità strutturale, 49 (2019) 125-139; doi: 10.3221/igf-esis.49.14 134 are introduced. the kinetic equations for the corresponding flows (fractions of martensite according to the variants and shear rates for slip systems) and the phase transformation criterion (in terms of the thermodynamic force) are formulated. in [42–43], the helmholtz free energy and the dissipative function are introduced for each of the phases. free energy is represented as a sum of chemical, elastic and “accumulated plastic” parts. a specific view for each of them is proposed. the dissipative function is determined by the difference between the mechanical work performed on the body and the helmholtz free energy. the expressions for the driving force and the criterion of phase transformation are also obtained from the dissipation inequality. in [44] there is a criterion of phase transformations (for direct and reverse ones) including the driving force of the phase transformation (consisting, in turn, of the mechanical (stress) and thermodynamic (determined through the "chemical" potential of components) and the critical value of the driving force. and besides, the latter is adopted to be the same for the forward transformation and the reverse one. at the same time, the critical force of formation for a martensite nucleus is assumed to be higher than its critical value for propagation of the transformation front. about the phase transformation criterion choosing within the framework of the proposed structure of the model, the formation of the new phase is assumed to occur at the meso-level ii. for a fixed time moment, a thermodynamic criterion of a phase transformation is checked out for each element, allowing to choose an active transformation system for a given element from energy considerations, as well as the elements (within a representative volume) being energetically beneficial to move into a new phase under these conditions. in this work, the meso-ii element is considered as a closed thermodynamic system which has undergone some influence (temperature and kinematic) at a fixed moment of process. the phase transformation criterion is formulated for the mesoii element and, due to homogeneity of all parameters' values for this element, the hypothesis, that its entire volume goes into a new phase completely if the phase transformation criterion is carried out for it at a fixed moment of process, is accepted. the construction of the phase transformation criterion for an element is based on the approach, used in the work [45], where based on the principles of classical thermodynamics of irreversible processes [46–47], a kinetic equation for a new phase fraction in a certain multiphase volume, has been obtained. the hypothesis about the "single-phased" meso-ii element at any arbitrary moment allows to simplify the expression being obtained in the above-cited paper for the thermodynamic driving force of phase transformation and write it in the following form:  0 0 * 1 2; , , , ..., ,p p eg g g g g g phase c c      q , (15) where 0g is the free energy (gibbs) function of the element in the initial phase; pg is the free energy (gibbs) function of the element into some phase p , whereto the element can (theoretically) go at the current values of the model internal variables under conditions of a given thermo-mechanical effect; 0 pg  is the phase transformation driving force; 1 2, , ...c c are the component concentrations; eq is an elastic strain measure;  is temperature. herewith, free energy of the system is considered to be a function of the current phase characteristics, the component composition, the elastic part of strain measure and temperature. according to the introduced criterion, the phase transition is realized for the meso-ii element if the change of the thermodynamic potential value for the system (in this case, it is the gibbs free energy) during the transformation from the initial phase (index 0) to some new phase (index p) exceeds some critical threshold. it should be noted that within the framework of the proposed model numerical implementation, the values of all internal variables and parameters characterizing the stress-strain state of the meso-ii element are changed at the end of a time step within the used computational scheme. wherein, the verification of the phase transition criterion for each meso-ii element is performed at the current step. for this, a special computational procedure with splitting the main numerical algorithm time step into substeps and the “virtual” transfer of the element into a new phase is implemented inside the step. if the phase transition criterion is fulfilled at the end of a step for an element, it is considered to have passed into a new phase and all its properties are redefined. the other elements (for which the criterion of phase transformation was not fulfilled) remain in the initial phase. details of the algorithm for checking the phase transition criterion fulfillment for the meso-ii element are described below in the corresponding section. the specific free energy of an element in the initial phase is assumed to consist of the specific elastic energy eg and the specific chemical energy chg :    0 1 2, , , , , ..., .e e chg g phase g phase c c  πq (16) p. trusov et alii, frattura ed integrità strutturale, 49 (2019) 125-139; doi: 10.3221/igf-esis.49.14 135 the contribution associated with the specific surface energy is not taken into consideration, as the phase boundaries are not explicitly considered within the statistical submodel of this level. herewith, within the accepted structure of the multilevel model, all properties of the meso-ii element (such as the tensor of elastic characteristics, the elastic part of the strain measure, etc.) are defined in its moving coordinate system associated with the lattice, and therefore, are also dependent on the phase the element is in, at the considered moment of the process. the elastic part of the specific free energy is a quadratic form of the elastic part of the strain measure and in the moving coordinate system of the element at the current time moment it can be determined as follows:   , , : :e e e eg phase π πq q q , (17) where elastic deformations in the meso-ii element are determined as a result of integration of the elastic part of the relative velocity gradient el at a current moment (i.e., they directly depend on the external action parameters, the type of the element crystalline lattice and the orientation of this lattice at the considered moment of the process), where el is defined from the decomposition (4) without the transformational part, but with allowance for plastic and temperature deformations in the element at the considered time moment. it is assumed that the specific free energy of some newly formed phase p can be represented in the following general form:    1 2_ , , , ..., _ , , ,p ch trg g new phase c c g new phase    σ  , (18) where trg is a transformational part of the specific free energy associated with implementation of the phase transformation in the system under consideration (the meso-ii element). in particular, in simulating a martensitic transformation, the rate of temperature changing is assumed to be so high, that no diffusion processes have time to go through the material; i.e., the component composition of the element remains unchanged. for further describing the diffusion phase transformations, it is necessary to take into consideration the cooling rate and to describe the diffusion processes occurring in the material at the meso-level. within this work, in describing the diffusionless (martensitic) transformation, the transformational part of the specific free energy is introduced in the following form:  _ , :trg new phase σ σ sm . (19) the chemical component of the meso-ii element specific free energy in a certain phase includes both free energy of a separate phase itself and contributions into the free energy due to mixing and chemical interaction of the components. by analogy with the works [48–50], it is determined using the following relation:         1 1 2 1 1 1 1 1 1 , , , ..., ln n n n n ch k kj k k k k j k k k j k r g phase c c c g c c c c r                    , (20) where kc is a k-component concentration in a phase under consideration, measured in mole fraction; kg is a specific free energy of a separate component k in the considered phase; a сn v z  is a mole volume (where an is an avogadro constant; cv and z are the unit cell volume of the material and the number of atoms per cell in the considered phase, respectively); kjr is a parameter, depending on temperature and describing interaction between the components k and j within the considered phase; b ar k n , where bk is a boltzmann constant. the free energy of each individual component kg is approximated by a functional dependence on temperature of the following type:    1 2 3 ln k k k kg          , (21) where 1 k , 2 k , 3 k are the constants determined for the constituent component of the material, depending on the phase it is in, using the thermodynamic databases [51]. p. trusov et alii, frattura ed integrità strutturale, 49 (2019) 125-139; doi: 10.3221/igf-esis.49.14 136 features of the model implementation algorithm at the meso-level escription of the algorithm general structure for implementing a two-level statistical model without taking into consideration phase transitions can be found, for example, in the paper [52]. the features of the algorithm taking into consideration the phase transformations in the material in the process of external thermo-mechanical impacts are described below. at the considered moment of the thermo-mechanical loading process, each element of meso-ii (within the framework of the modeled representative volume of meso-i) is exposed to the impact from the upper scale level. the velocity gradient ˆ l v , temperature  and the temperature changing rate are transmitted into it. the problem of determining the stressstrain state of a meso-ii element is solved in its own moving coordinate system (at each fixed moment of the process it is definitely oriented relative to the laboratory coordinate system). the calculation is carried out at the current (determined at the end of the previous time step) values of all parameters (including the internal variables). the shear rates for all slip systems within the element are calculated using relation (8), being allowed to determine the inelastic part of the relative velocity gradient pl from eqn. (6). the spin ω of an element moving coordinate system is determined using the taylor rotation model (full constraint). the thermal part of the transposed relative velocity gradient l is determined from relation (9). farther, the velocity of lattice elastic distortions for a material in the initial phase is calculated: e p    l l ω l l . (22) the last relation is integrated to determine the part of the deformation gradient ef , characterizing the elastic distortions of the lattice with respect to the current rigid moving coordinate system of the meso-ii element. the value of the kirchhoff weighted stress tensor corotational derivative crk is determined from relations (5), and as a result of its integration, the kirchhoff tensor k and the cauchy stress tensor σ are defined themselves. thus, as a result of integrating the found values at the end of the step, stresses and strains acting in the element are defined. the procedure of the stress-strain state determining is performed for all meso-ii elements within the framework of the mezo-i representative volume with the definition of the values for all model internal variables at the end of the time step. farther, a phase transformation at the meso-level ii is assumed being able to occur during the considered time step. the verification of the phase transition criterion (15) fulfillment is carried out for all meso-ii elements with examining all possible transformation options for each element. in particular, in simulating a martensitic transformation, the meso-ii element is assumed being able to experience 24 transformation variants (corresponding to 24 variants of martensite, obtained from the kurdjumov-sachs relationships [27–28]). the most energetically favorable transformation option, for which the value of the thermodynamic driving force 0 pg  is greater (at the end of the considered time step), is chosen of all the possible ones. to implement the phase transition in the meso-ii element within the framework of the adopted calculation scheme, the full time step is divided into a fixed number of substeps (their required number is determined in computational experiments). the element is assumed jumping completely into a new phase in a full time step. herewith, the smoothing the transition process is realized at the substeps inside the full step, with introducing the fraction of a new growing phase. the process of solving the problem within the time step (at substeps) is carried out without taking into account the changing the temperature component of the impact inside the step, the velocity gradient (full) is determined at the beginning of the full time step and is considered as fixed within the whole step. an internal step-by-step process for solving the elastic-viscoplastic problem (on substeps) is implemented at the time step for each element, taking into account the transformational component of the relative velocity gradient trl , defined from relation (14) (wherein, the accommodative mechanisms are realized due to plastic shears). in calculating inside the step the critical shear stress is defined as a result of averaging the critical stresses of the initial (with a weight (1– ξ)) and the new (with weight ξ) phase. the value of the element thermodynamic potential used in the energy criterion in a new phase is assumed to be determined at the end of the total time step, i.e., for the state the considered element has completely passed into a new phase. it should be noted, that in the process of thermo-mechanical loading, orientation of the axes of the element moving coordinate system may change both as a result of the element quasi-solid motion in the process of inelastic deformation (with the spin tensor) and as a result of the phase transformation in the material. during phase transformation (of a martensitic type), orientation of the element moving coordinate system axes is assumed to be changed almost instantly if the criterion of phase transformation is fulfilled. it means, that if the criterion of a phase transformation was fulfilled in the element at the end of the time step, then it comes to a new time step with a new orientation of the moving coordinate system axes corresponding to its new crystal lattice. in particular, in the martensitic transition the orthogonal tensor, defining d p. trusov et alii, frattura ed integrità strutturale, 49 (2019) 125-139; doi: 10.3221/igf-esis.49.14 137 the saltatory change in orientation of the element moving coordinate system axes as a result of the transformation, can be directly determined from orientation relationships (for example, the kurdjumov-sachs ones [27]). this lattice orthogonal transformation is also included into multiplicative decomposition of the transformational deformation gradient under the martensitic transition [25] and ensures existence of an invariant plane. thus, if the meso-ii element experienced a phase transition at the considered time step, the values of all model internal variables are recalculated for this element at the end of the step (taking into consideration the change of the properties and the element lattice type as a result of phase transformation). conclusions he multilevel crystal plasticity model for describing inelastic deformation of polycrystalline materials taking into account the evolving internal material structure is formulated within the paper. the model allows to take into consideration diffusionless solid-state phase transitions of martensitic type. this model, unlike the most existing macro-phenomenological models, provides the opportunity to study evolving material mesoand microstructure. this allows to describe the intense elastoplastic deformations and material’s properties after the end of thermo-mechanical processing in detail. within the presented structure of the model three scale levels are distinguished. they are the macrolevel, the mesolevel-i and the mesolevel-ii. the peculiarity of the model is its hybrid character, when the boundary value thermomechanical problem is solved at the macro-level by the finite element method, and lower scale levels are used to consider the material structure applying the statistical modeling methods. the hybrid character of the model determines its relatively low computational costs, allowing to set and solve problems for constructions, not only for material representative volume. another distinctive feature of the model is that the smallest structural element is so small that it instantly turns into a new martensitic phase. the choice of the martensitic transition variant is based on the thermodynamic criterion of the phase transformation. at the same time, it is not necessary to introduce a huge number of such elements into consideration, the statistical sample under consideration should be a representative volume in the statistical sense, i.e. addition of new elements to the existing ones does not change the current average material properties. in this case, one of the main characteristics determining the anisotropic mechanical and thermo-physical properties of the meso-ii element is orientation of the crystallographic coordinate system being abruptly changed as a result of phase transition. the mathematical formulation of the relations describing different modes of inelastic deformation (plastic deformations, lattice rotations, phase transformations), taking into consideration the influence of the external parameters (temperature, applied loading and their rates) and the material characteristics (chemical and phase composition, stacking fault energy, internal stresses due to the defective structure), is provided in the paper. the features of the model implementation algorithm associated with a high rate structure evolution in the phase transition process are given. acknowledgments he work was supported by the russian science foundation (grant no. 17-19-01292). references [1] dini, g., najafizadeh, a., ueji, r., & monir-vaghefi, s. m. (2010). improved tensile properties of partially recrystallized submicron grained twip steel, materials letters, 64(1), pp. 15-18. doi: 10.1016/j.matlet.2009.09.057 [2] latypov, m. i., shin, s., de cooman, b. c., & kim, h. s. (2016). micromechanical finite element analysis of strain partitioning in multiphase medium manganese twip+ trip steel, acta mater., 108, pp. 219-228. doi: 10.1016/j.actamat.2016.02.001. [3] ding, h., tang, z. y., li, w., wang, m., & song, d. (2006). microstructures and mechanical properties of fe-mn-(al, si) trip/twip steels, j. iron. steel res. int., 13(6), pp. 66-70. doi: 10.1016/s1006-706x(06)60113-1. [4] grässel, o., krüger, l., frommeyer, g., meyer, l. w. (2000). high strength fe–mn–(al, si) trip/twip steels development-properties-application, int. j. plast., 16(10-11), pp. 1391-1409. doi: 10.1016/s0749-6419(00)00015-2. [5] kulawinski, d., nagel, k., henkel, s., hübner, p., fischer, h., kuna, m., biermann, h. (2011). characterization of stress–strain behavior of a cast trip steel under different biaxial planar load ratios, eng. fract. mech., 78(8), pp. 16841695. doi: 10.1016/j.engfracmech.2011.02.021. t t p. trusov et alii, frattura ed integrità strutturale, 49 (2019) 125-139; doi: 10.3221/igf-esis.49.14 138 [6] roters, f., eisenlohr, p., hantcherli, l., tjahjanto, d. d., bieler, t. r., & raabe, d. (2010). overview of constitutive laws, kinematics, homogenization and multiscale methods in crystal plasticity finite-element modeling: theory, experiments, applications, acta mater., 58(4), pp.1152-1211. doi: 10.1016/j.actamat.2009.10.058. [7] trusov, p.v., shveykin, a.i., nechaeva, e.s., volegov, p.s. (2012). multilevel models of inelastic deformation of materials and their application for description of internal structure evolution, phys. mesomech., 15(3-4), pp. 155-175. doi: 10.1134/s1029959912020038. [8] mcdowell, d.l. (2010). a perspective on trends in multiscale plasticity, int. j. plast., 26(9), pp. 1280-1309. doi: 10.1016/j.ijplas.2010.02.008. [9] trusov, p.v., yanz, a.y. (2016) physical meaning of nonholonomic strain measure, phys. mesomech., 19 (2), pp. 215222. doi: 10.1134/s1029959916020156. [10] isupova, i.l., trusov, p.v. (2013) review of mathematical models on phase transformations in steels (in russian), pnrpu mech. bull., 3, pp. 157-191. [11] tasan, c. c., diehl, m., yan, d., bechtold, m., roters, f., schemmann, l., zheng, c., peranio, n., ponge, d., koyama, m., tsuzaki, k., raabe d. (2015). an overview of dual-phase steels: advances in microstructure-oriented processing and micromechanically guided design, annu. rev. mater. res., 45, pp. 391-431. doi: 10.1146/annurev-matsci-070214-021103. [12] freidin, a.b., viltchevskaya, e.n., sharipova, l. (2002). two-phase deformations within the framework of phase transition zones, theor. appl. mech. lett., 28-29, pp. 145-168. doi: 10.2298/tam0229145f. [13] grinfeld, m.a. (1990). methods of continuum mechanics in the theory of phase transformations (in russian), moscow, nauka. [14] yeddu, h. k., borgenstam, a., ågren, j. (2013) stress-assisted martensitic transformations in steels: a 3-d phase-field study, acta mater., 61(7), pp. 2595-2606. doi: 10.1016/j.actamat.2013.01.039. [15] loginova, i., amberg, g., agren, j. (2001). phase-field simulations of nonisothermaly binary alloy solidification., acta mater., 49, pp. 573-581. doi: 10.1016/s1359-6454(00)00360-8. [16] trusov, p.v., shveykin, a.i. (2013). multilevel crystal plasticity models of singleand polycrystals. direct models, phys. mesomech., 16(2), pp. 99-124. doi: 10.1134/s1029959913020021. [17] trusov p.v., shveykin a.i. (2013). multilevel crystal plasticity models of singleand polycrystals. statistical models, phys. mesomech., 16(1), pp. 17-28. doi: 10.1134/s1029959913010037. [18] trusov, p.v., shveykin, a.i., yanz, a.yu. (2017). motion decomposition, frame-indifferent derivatives, and constitutive relations at large displacement gradients from the viewpoint of multilevel modeling, phys. mesomech., 20(4), pp. 357– 376. doi:10.1134/s1029959917040014. [19] trusov, p.v., shveykin, a.i. (2017). on motion decomposition and constitutive relations in geometrically nonlinear elastoviscoplasticity of crystallites, phys. mesomech., 20(4), pp. 377–191. doi:10.1134/s1029959917040026. [20] shveykin, a.i., trusov, p.v. (2018) correlation between geometrically nonlinear elastoviscoplastic constitutive relations formulated in terms of the actual and unloaded configurations for crystallites, phys. mesomech., 21(3), pp. 193–202. doi: 10.1134/s1029959918030025. [21] trusov, p.v., shveykin, a.i., kondratev, n.s. (2017). multilevel metal models: formulation for large displacement gradients, int. j. nanomech. sci. tech., 8(2), pp. 133-166. doi: 10.1615/nanoscitechnolintj.v8.i2.40. [22] shveykin, a.i., ashikhmin, v.n., trusov, p.v. (2010) about models of lattice rotation by metal deformation (in russian), pnrpu mech. bull., 1, pp. 111-127. [23] asaro, r. j., needleman, a. (1985). overview no. 42 texture development and strain hardening in rate dependent polycrystals, acta metall., 33(6), pp. 923-953. doi: 10.1016/0001-6160(85)90188-9. [24] turteltaub, s., suiker, a.s.j. (2006). a multiscale thermomechanical model for cubic to tetragonal martensitic phase transformations, int. j. solids struct., 43(14-15), 4509-4545. doi: 10.1016/j.ijsolstr.2005.06.065. [25] nyashina, n.d., trusov, p.v. (2014). modelling of martensitic transformations in steels: kinematics of the meso-level (in russian), pnrpu mech. bull., 4, pp. 118-151. doi: 10.15593/perm.mech/2014.4.05. [26] nyashina, n.d. (2015) mathematical model of the steel deformation at martensitic transformation (in russian), pnrpu appl. math. cont. sci., 1, pp. 36-46. [27] bhadeshia, h., honeycombe, r. (2017) steels: microstructure and properties, amsterdam, elsevier. [28] kurdyumov, g.v., utevskij, l.m., entin, r.i. transformations in iron and steel (in russian), мoscow, nauka. [29] koıstinen, d. p., marbürger, r. e. (1959). a general equation prescribing extent of austenite-martensite transformation in pure fe-c alloy and plain carbon steels. acta metall., 7(1), pp. 59-60. doi: 10.1016/0001-6160(59)90170-1. p. trusov et alii, frattura ed integrità strutturale, 49 (2019) 125-139; doi: 10.3221/igf-esis.49.14 139 [30] cherkaoui, m., berveiller, m., sabar, h. (1998). micromechanical modeling of martensitic transformation induced plasticity (trip) in austenitic single crystals, int. j. plasticity., 14(7), pр.597–626. doi: 10.1016/s0749-6419(99)80000-x [31] cherkaoui, m., berveiller, m., lemoine, x. (2000). couplings between plasticity and martensitic phase transformation: overall behavior of polycrystalline trip steels, int. j. plasticity, 16 (10-11), pр.1215–1241. doi: 10.1016/s0749-6419(00)00008-5. [32] fischer, f.d., reisner, g., werner, e., tanaka, k., cailletaud, g., antretter, t. (2000). a new view on transformation induced plasticity (trip), int. j. plasticity, 16 (7-8), pp. 723–748. doi: 10.1016/s0749-6419(99)00078-9. [33] grujicic, m., zhang, y. (2000). crystal plasticity analysis of stress–assisted martensitic transformation in ti–10v–2fe– 3al(wt.%), j. mater. sci., 35(18), pp. 4635 – 4647. doi: 10.1023/a:1004826301287. [34] thamburaja, p., anand, l. (2001) polycrystalline shape-memory materials: effect of crystallographic texture, j. mech. physics solids., 49(4), pр.709-737. doi: 10.1016/s0022-5096(00)00061-2 [35] iwamoto, t. (2004). multiscale computational simulation of deformation behavior of trip steel with growth of martensitic particles in unit cell by asymptotic homogenization method, int. j. plasticity., 20(4-5), pp.841–869. doi: 10.1016/j.ijplas.2003.05.002. [36] olson, g.b., cohen, m. (1975). kinetics of strain-induced martensitic nucleation, metall. trans. a., 6(4), pр.791–795. doi: 10.1007/bf02672301 [37] lagoudas, d.c., entchev, p.b. (2004). modeling of transformation-induced plasticity and its effect on the behavior of porous shape memory alloys. part i: constitutive model for fully dense smas, mech. mater., 36(9), pp. 865–892. doi: 10.1016/j.mechmat.2003.08.006. [38] lagoudas, d.c., entchev, p.b., popov, p., patoor, e., brinson, l.c. gao, x. (2006). shape memory alloys. part ii: modeling of polycrystals, mech. mater., 2006, 38(5-6), pр. 430-462. doi: 10.1016/j.mechmat.2005.08.003. [39] patoor e., lagoudas d.c., entchev p.b., brinson l.c., gao x. (2006). shape memory alloys, part i: general properties and modeling of single crystals, mech. mater., 38 (5-6), pр.391–429. doi: 10.1016/j.mechmat.2005.05.027 [40] van rompaey, t., lani, f., jacques, p.j., blanpain, b., wollants, p., pardoen, t. (2006). three-dimensional computational-cell modeling of the micromechanics of the martensitic transformation in transformation-inducedplasticity–assisted multiphase steels, metall. mater. trans. a, vol. 37(1), pр.99–107. doi: 10.1007/s11661-006-0156-1 [41] tjahjanto, d.d., turteltaub, s., suiker, a.s.j. (2008). crystallographically based model for transformation-induced plasticity in multiphase carbon steels, continuum mech. thermodyn., 19(7), pp.399–422. doi: 10.1007/s00161-007-0061-x. [42] kouznetsova, v.g., balmachnov, a., geers, m.g.d. (2009). a multi-scale model for structure-property relations of materials exhibiting martensite transformation plasticity, int. j. mater. form., 2(1), pр.491–494. doi: 10.1007/s12289-009-0578-6. [43] kouznetsova, v.g., geers, m.g.d. (2008). a multi-scale model of martensitic transformation plasticity, mech. mater., 40(8), pp. 641–657. doi: 10.1016/j.mechmat.2008.02.004. [44] sengupta a., papadopoulos p., taylor·r.l. (2009). multiscale finite element modeling of superelasticityin nitinolpolycrystals, comput. mech., 43(5), pр.573–584. doi: 10.1007/s00466-008-0331-x. [45] isupova, i.l., trusov, p.v. (2013) mathematical modeling of phase transformations in steel under thermomechanical loading (in russian), pnrpu mech. bull., 3, pp. 127-157. [46] de groot, s.r. (1951). thermodynamics of irreversible processes, amsterdam, north-holland publishing company. [47] kondepudi, d., prigogine, i. (2015). modern thermodynamics. from heat engines to dissipative structures, chichester, wiley. [48] trusov, p.v., isupova, i.l. (2014) two-scale model of thermomechanically loaded steel with martensite transformations (in russian), phys. mesomech., 17(2), pp. 5-17. [49] miettinen, j. (1997). calculation of solidification-related thermophysical properties for steels, metall. mater. trans b., 28(2), pp. 281–297. doi: 10.1007/s11663-997-0095-2. [50] redlich, o., kister, a.t. (1948). algebraic representation of thermodynamic properties and the classification solutions, ind. eng. chem., 40(2), pp.345–348. doi: 10.1021/ie50458a036. [51] dinsdale, a.t. (1991). sgte data for pure elements, calphad., 15(4), pp.317-425. doi: 10.1016/0364-5916(91)90030-n. [52] nechaeva, e.s., trusov, p.v. (2011). constitutive model of semicrystalline polymer material. implementation algorithm for mezolevel model (in russian), comp. cont. mech., 4(1), pp. 74-89. microsoft word numero_57_art_01_3025 h. s. patil et alii, frattura ed integrità strutturale, 57 (2021) 1-13; doi: 10.3221/igf-esis.57.01 1 the effect of surface texturing in the sliding surface on tribological characteristics of alloy steel under wet condition h. s. patil, d. c. patel mechanical department, gidc degree engineering college, abrama, gujarat, india hspatil28@gmail.com, pateldcp@gmail.com abstract. surface texturing plays an increasingly important role as it can directly influence the tribological behaviors of contact surfaces in many ways. in texturing, tribological performance depends upon the types of design texture used and methods of fabricating texture on the surface. in this research work, friction and wear behaviors of surface textured en-31 alloy steel have been investigated under wet condition by using ducom linear reciprocating tribometer. the textured dimples are fabricated by micro-edm and micro-drilling cnc machining processes. initially un-textured surfaces of en-31 alloy steel with en-8 steel pin are experimented for friction and wear under iso-68 and iso-220 lubricant oil. under the different normal load conditions, it has been observed that the iso 68 oil gives better friction-wear characteristics with respect to iso-220 oil. then after textured surfaces were investigated by using optimized iso-68 lubricant. experimental results on micro-edm provide better friction and wear properties with respect to micro-drilling cnc. surface texturing may act as wear debris trapper, lubricant reservoirs, hydrodynamic lift, and retarding the lubricant molecules flow in a particular path where potential exists. in this work, it has observed that texturing by micro-edm enhanced mixed lubrication and minimum friction in mixed lubrication leads to decrement of wear loss. keywords. micro dimples; en-31 alloy steel; normal load; friction and wear. citation: patil, h. s., patel, d. c., the effect of surface texturing in the sliding surface on tribological characteristics of alloy steel under wet condition, frattura ed integrità strutturale 57 (2021) 1-13. received: 20.02.2021 accepted: 29.04.2021 published: 01.07.2021 copyright: © 2021 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. introduction n the recent era surface texturing has become an area of interest for modifying the surface topography of the materials. surface texturing is the process of modifying the surface to alter its surface features such as surface tension, wettability, and tribological characteristics i.e. friction and wear properties. in recent years, surface texturing which involves flat and smooth lands interrupted by local depressions has been well known in improving the tribological characteristics of the materials [1]. it has also been proved that textured surfaces exhibit good performance from i https://youtu.be/qsxu9qo_aiu h. s. patil et alii, frattura ed integrità strutturale, 57 (2021) 1-13; doi: 10.3221/igf-esis.57.01 2 boundary lubrication to fluid film lubrication. many studies have shown the outstanding performance of surface texturing technology in improving tribological properties. to create micro-texturing on the surface many fabrication methods like micro grinding, micro casting and chemical etching, micro-electrical discharge machining (micro-edm), micro-electro chemical machining, micro-cnc, abrasive jet machining, ultrasonic machining, laser beam machining method, vibromechanical texturing method are commonly adopted. a. greco et al. [2] used vibromechanical texturing (vmt) in which a controlled vibratory motion of the tool was used to cut micro-sized dimples into the surface of the work piece. j. choo et al. [3] utilizes nano imprint lithography (nil) in producing textures on the surface of ultra-high molecular weight polyethylene (uhmwpe) to efficiently improve the tribological properties of the polymer material. in cutting of complex profiles and drilling holes in wide range of work piece material laser beam machining becomes a powerful method and it has good beam quality, better efficiency, excellent reliability characteristics, and high average beam power [4]. chemical etching and abrasive machining method has been used to create undulated or modulated patterns that surface texture act as traps for wear debris of oxide [5]. vibro-rolling technique was prepared by schneider y. et al. [6] to produce shallow grooves by plastic deformation using a hard indenter on metallic channels. in the area of hydrodynamic lubrication of textured steel surfaces under reciprocating sliding conditions, costa et al. [7] investigated the effect of surface texturing on lubricant film thickness for the reciprocating sliding motion of patterned plane steel surfaces against cylindrical counter bodies under hydrodynamic action. a micro-dimple surface texture contributed significant role in improving tribological characteristics and lifespan of mechanical components. g. ryk et al. [8] experimented to evaluate the effect of laser surface texturing in the form of micro dimples in reciprocating automotive components. the effect of surface texturing under starved lubrication conditions was presented for the plane surfaces configuration. it was shown that dimples act as lubricant reservoirs, when lubricant film is broken down, back-up lubricants was supplied. laser surface texturing (lst) by dimpling enhanced the mixed, hydrodynamic, and hydrostatic lubrication of conformal sliding components under a point ball-on-flat contact configuration. in lst mechanical seals and thrust bearings there were improvements in high load-carrying capacity, high wear resistance, and low friction coefficients [9]. e. willis et al. [10] investigated the effect of honing morphologies on cylinder bores of internal combustion engines. these micro-grooves develop the lubrication regimes between the cylinder walls and the piston ring. the effect of elastomer surface texturing in soft elastohydrodynamic lubrication was modelled by a. shinkarenko et al., [11]. in the presence of viscous lubricant, the model of an elastomer with spherical micro-dimples slides at a constant velocity with respect to a rigid and smooth counterpart. in full and partial texturing of the elastomer surface, both problems are solved simultaneously i.e. hydrodynamic lubrication and elasticity. tomanik et al. [12] developed a one computer dimensional model to simulate surface texture effects on cylinder bore, top and oil control rings of engine. it has been observed that micro-dimples on the bore and rings were able to generate significant hydrodynamic effect to reduce friction and wear. a significant result was observed when the microdimples were on the oil control rings surfaces. f. meng et al. [13] studied effect of rectangle shape dimples with flat bottom on the friction of parallel surfaces at various sliding conditions based on lubrication equations. the elastic deformation of rough surfaces is evaluated using continuous convolution fast fourier transform. x. zhang et al. [14] used sandwich-like electrochemical micromachining to produce micro-dimples. the experimental results show that a porous metal cathode can remove gas bubbles and some nonconductive insoluble electrolytic products, leading to deep microdimples. ultrasonic vibration was applied by p. liew et al. [15] to dielectric fluid by a probe-type vibrator to assist microedm of deep micro-holes in ceramic materials. ultrasonic vibration influences two major effects one is stirring effect contributing in uniform distribution the carbon nano-fibers and other is the cloud cavitation bubbles which flush out the debris. ze wu et al. [16] investigated tribological properties of dimple-textured titanium alloys under high-speed dry sliding contact. the dimpledistance has a remarkable effect on both the average friction coefficients and the wear rates of titanium surfaces. yang fu, et al. [17] studied the influence of conductive grease (cg) on the tribological properties of carbon brushes and the collection effect of surface texture on carbon powder. studies have shown that a conductive lubricating film is formed on the surface of the carbon brush, and a large amount of carbon powder is detected in the surface texture holes of the carbon brush, indicating that surface texture can be used as a collector for carbon powder. jiang et al. [18] fabricated micro-grooves on gcr15 steel disc and filled by epoxy resin composites, formed hybrid laser surface texture and investigated tribological properties of textured disc sliding against ceramic ball. it was found that this hybrid laser surface texture could form a transfer layer on the contact surface, which contribute to the friction and wear reduction of tribo-pairs under dry friction condition. zhang h. et al. [19] studied the tribological performance of journal bearings by optimizing the coverage area of circular micro-textures in divergent region of the sleeve and proposed a numerical model is to calculate the friction coefficient and bearing load of textured journal bearings. ming et al. [20] studied the effect of nitriding/surface texturing combined treatment on vacuum tribological properties of titanium. it has been observed that nitriding/surface texturing combined treatment not only enhances the wear resistance but also has a lower friction coefficient than the nitriding treatment. the high hardness of nitrided layer and the function of micro-trap h. s. patil et alii, frattura ed integrità strutturale, 57 (2021) 1-13; doi: 10.3221/igf-esis.57.01 3 for wear debris of surface texture results in the excellent tribological properties. huang et al. [21] constructed the texture of the circular pits with different areal densities on the nickel surface by laser surface texturing. the coefficient of friction of the circular pit under the water-lubricated friction condition was kept at about 0.17, while the untreated metal nickel under the same conditions exceeds 0.65. the circular pit texture improves the frictional properties of the nickel surface. in the present study, surface texturing by micro dimple formation on en-31 alloys steel was performed using micro drillingcnc and micro-edm processes and textured samples were tested for wear analysis on ducom pin-on-reciprocating plate tribometer under wet condition. micro-edm method provides superior frictional characteristics and hence that can enhance mixed film hydrodynamic lubrication between plate and pin which leads to decrease in wear loss. materials and experimental methods n the present work, the tribological characteristic of en-31 alloy steel plate of size 40 × 40 × 6 mm3 under wet conditions was investigated. the normal loading was applied through an en-8 steel pin on en-31 alloy steel plate by using pin-on-plate reciprocating tribometer. the chemical compositions and mechanical properties of en-8 steel pin and en-31 alloy steel plate are shown in tab. 1 to tab. 4. table 1: chemical compositions of en-8 steel. ys [mpa] uts [mpa] hardness heat treatment 280 mpa 550 mpa 152-207 normalizing table 2 mechanical properties of en-8 steel. c% si% mn% cr% s% 0.95-1.10 0.10-0.35 0.40-0.70 1.20-1.60 0.05 table 3: chemical compositions of en-31 alloy steel. table 4: mechanical properties of en-31 alloy steel. initially pin on plate tribo-analysis was carried out for un-textured en-31 alloy steel plate by using two different lubricants iso-68 and iso-220 oil under the following operating conditions: normal loading = 20 to 100n; temperature = 40 0c; humidity = 37rh; stroke length = 10mm; frequency = 12hz. the property of lubricants used in experiments is shown in tab. 5. then after a surface texturing i.e. micro-dimples are generated by using two machining processes i.e. micro-edm and micro-drilling cnc. fig. 1(a) shows micro-dimples on the surface of the en-31 specimen which are uniformly arranged in a rectangular array. the surface texture density (td) is calculated by using the following equation; i c% si% mn% p% s% 0.36-0.44 0.10-0.40 0.60-1.00 0.05 0.05 bulk modulus elastic modulus shear modulus hardness, knoop poisson’s ratio 140 gpa 190-210 gpa 80 gpa 706-739 0.27-0.30 h. s. patil et alii, frattura ed integrità strutturale, 57 (2021) 1-13; doi: 10.3221/igf-esis.57.01 4 dt =                   area of the dimple area of the micro dimple unit   d t a a (%) if, d = diameter of the dimple; k and l = sides length of the micro-dimple unit or spacing between dimples, then, ad = d2/4; and at = k  l ;     dt =    2 4 d k l (%) the dimple parameters of the textured surface for friction-wear test analysis are shown in tabs. 6. table 5: properties of lubricant. table 6: dimple parameters of textured surface. the electro discharge machining (edm) process plays a significant role in research of micro machining especially in the machining of micro-dimple textures. the micro-dimples were performed on the elektra ems-5535 as shown in fig. 1(b). in edm process, copper electrode of diameter 1.4 mm was used for the fabrication of micro-dimple texture on en-31 alloy steel plate. edm is an electro-thermal non-traditional machining process, where electrical energy is used to produce electrical spark and removal of material mostly arises due to current dynamism of the spark. the process parameters used for the fabrication of micro-dimple through edm machine on en-31 alloy steel are as follows: working voltage (v) = 120 130v; maximum current (i) = 5amp; pulse on time (t) = 5μs; gap between the workpiece and the tool (δ) = 5 – 50μm; polarity = straight polarity tool (-ve); dielectric medium= edm oil; electrode material = copper; external flushing through spark gap. vertical machining, also known as milling, relies on rotary cutters to remove metal from a work piece. vertical machining occurs on a vertical machining centre (vmc), which employs a spindle with a vertical orientation. with a vertically oriented spindle, tools stick straight down from the tool holder, and often cut across the top of a work piece. fig. 2 shows the experimental setup to perform texturing experiments using ball end mill tool in cnc machine. detailed view of micro-dimple textures is shown by enlarging the part of experimental setup. the cutting parameters used to fabricate the texture through cnc machine are as follows: feed rate = 150mm/rev, spindle speed = 5500rpm and depth = 10μm. after preparation of micro-dimples on en-31 plate, these textured surfaces were tested for friction wear analysis on linear reciprocating tribometer setup as shown in fig. 3. the test parameter being used for friction-wear analysis are shown in tab. 7. lubricant viscosity at 40°c (cst) viscosity at 100°c (cst) density at 15.60c (kg/m3) viscosity index flash point (0c) pour point (0c) iso 68 68.0 10.2 0.88 × 10 3 135 204 -40 iso 220 220.0 30.4 0.86 × 103 180 233 -39 parameters → test ↓ dimples diameter (d) μm dimple depth (h) μm side length (k) μm side length (l ) μm texture density (td)% 1. 500 10 1800 2200 5 2. 700 10 1800 2200 10 h. s. patil et alii, frattura ed integrità strutturale, 57 (2021) 1-13; doi: 10.3221/igf-esis.57.01 5 figure 1: (a) micro-dimple array; (b) edm machineelektra ems-5535. figure 2: vmc machine jyoti px-20. h. s. patil et alii, frattura ed integrità strutturale, 57 (2021) 1-13; doi: 10.3221/igf-esis.57.01 6 normal load 60 to 120n temperature 400c stroke length 15mm frequency 10hz oil quantity 20ml test duration 20 minutes lubricant slide-way oil iso68 and iso220 texture density 5% and 10% table 7: test parameter for friction-wear analysis. figure 3: linear reciprocating tribometer. results and discussions effect of lubricant on friction and wear rom fig. 4 and fig. 5, it is observed that the average frictional force and co-efficient of friction experienced by pin on plate is lesser in case of iso-68 oil. the wear loss is more in iso-220 oil with respect to iso-68 oil as shown in fig. 6. these observations indicate that the oil film of iso-220 lubricant does not remain stable and it breaks during rubbing action which leads to poor friction characteristics as compared to iso-68. also during test operated under iso-220 oil, unpleasant noise was noticed that may be due to boundary lubrication between pin and plate. it is noticeable that the friction force and the cof have reduced for applied loading in iso-68 oil. therefore it can be predicted that the semi-finished surface of the specimen acts as a surface texture itself. it is clear from the above results that iso-68 proves itself to be better lubricant as compared to iso-220 for relative sliding motion of en-8 pin and en31 plate. based on the above results the friction-wear test is carried out on textured samples at varying load conditions under slide-way iso-68 oil. f h. s. patil et alii, frattura ed integrità strutturale, 57 (2021) 1-13; doi: 10.3221/igf-esis.57.01 7 figure 4: frictional force with normal load under different lubricant. figure 5: variation of coefficient of friction with normal load under different lubricant. figure 6: variation of wear with normal load under different lubricant. h. s. patil et alii, frattura ed integrità strutturale, 57 (2021) 1-13; doi: 10.3221/igf-esis.57.01 8 figure 7: variation in coefficient of friction with normal load in wet condition. figure 8: variation in wear with normal load in wet condition. fig. 7 represents the effect of normal load on coefficient of friction operated under wet condition. in this, the test was performed on un-textured plate at temperature of 400c by keeping constant frequency of 10hz and increasing normal load from 30 n to 120n. the test was carried out in slide-way oil iso-68 for 20minutes time duration. on increasing normal load, coefficient of friction decreases and its minimum value obtained during test is 0.085 and wear also decreases up to 38m on increasing normal load as shown in fig. 8. effect of surface texture density on friction and wear figs. 9-10 shows effect of texture densities on friction coefficients of the pin on plate with respect to normal load for both the methods of texturing respectively. during the friction-wear test on tribometer, normal loads of 30 n to 120n were applied for duration of 20 minutes each time. in initial phase of the experimentation operated under the normal load of 30n to 60n with 5% and 10% texture density, the friction coefficients of the test surfaces observed very high for both methods i.e. micro-edm as well as micro-drilling cnc. this is because, here the lubricating oil iso-68 exhibits the colloidal characteristics, which makes it difficult to form a uniform stable oil film on the surface contact of en-31 alloy steel, which results in a poor lubrication effect. h. s. patil et alii, frattura ed integrità strutturale, 57 (2021) 1-13; doi: 10.3221/igf-esis.57.01 9 figure 9: coefficient of friction with normal load for 5% texture density in wet condition. figure 10: coefficient of friction with normal load for 10% texture density in wet condition. it can be also seen that the friction coefficients of the micro-edm and micro-drilling cnc specimens are reduced by increasing the normal load ranging from 30n to 150n. in both cases of micro-dimple texturing the friction coefficient of all the specimens was very high under initial loading of 30-60n. from the friction-wear test it is observed that the textured plate with 5% density has low coefficient of friction in comparison with respect to plate with 10% density. this signifies that at low contact pressure, the roughness of the surface had a certain effect on the frictional properties of sliding surfaces, as higher texture density led to higher roughness value, and therefore a higher coefficient of friction was more easily found. later on, as the load on the surfaces increased, the coefficients of friction of the textured surfaces were sharply reduced. this is attributing to the large quantity of oil being constantly released from the micro-dimples into the sliding contact surface. thus, here the lubricant contributed to achieve a steady lubricating oil film due to the squeezing effect of the load. figs. 11-12 shows effect of texture densities on wear loss with respect to normal load for both the methods of texturing respectively. in both the texturing methods the loss of wear decreases with respect to increasing applied normal load. from these figures, it is observed that the textured plate with 5% density has low wear loss with respect to plate with 10% density for micro-edm texturing process. fig. 13 shows the optical micro-graph of textured surface with 5% and 10% density for friction-wear test. around the micro-dimple, it can be seen that the heat zone was formed due high energy. the bulges around dimple are little higher h. s. patil et alii, frattura ed integrità strutturale, 57 (2021) 1-13; doi: 10.3221/igf-esis.57.01 10 than plane surface which increases the surface roughness of textured specimens. average surface roughness measured for 5% textured and 10% textured plates are 0.21 µm, and 0.25 µm respectively. figure 11: wear loss with normal load for 5% texture density in wet condition. figure 12: wear loss with normal load for 10% texture density in wet condition. figure 13: optical micro-photograph of textured surface (a) 5% texture density (b) 10% texture density. wear debris analysis during reciprocating testing, the gathering of wear rubbles is obviously a major factor affecting the wear performance of the textured surfaces. scanning electron micrographs of the wear tracks helped the tribological analysis of the un-textured h. s. patil et alii, frattura ed integrità strutturale, 57 (2021) 1-13; doi: 10.3221/igf-esis.57.01 11 and textured surface at different load conditions of sliding motion. the sem of specimen was performed on magnifications of 50x and 100x. sem micrograph in fig. 14 shows the worn out surfaces of the un-textured surface i.e. plane surface. deep surface scratches and material loss could be clearly observed as an abrasive wear during the test. for un-textured surface, it is difficult to reserve debris and lubricant. the debris generated by friction can cause micro-cutting on the un-textured surface and that can lead to abrasive wear. figure 14: wear surface of un-textured samples:( a) low (b) high magnification showing fragmentation. figs. 15-16 show the sem micrographs of micro-edm surfaces having 5% texture and 10% texture respectively, which represents the presence of worn surface topography as an abrasive wear. that is similar to that of the un-textured surface but here wear area as well as the width and depth of scratches looks smaller than those on the un-textured surface. these results signify that micro-dimples have an influence on wear resistance. it is observed that in textured plate wear debris and lubricant present between pin and plate filled into circular dimple cavity due to which friction between pin and plate is reduced as compare to un-textured plate and as a result of these, only shallow shape scratches were observed on the wornout surface of textured plate and some original surface topography can still be observed on the plate (fig. 15). figure 15: wear surface of 5% surface textured samples. figure 16: wear surface of 10% surface textured density. h. s. patil et alii, frattura ed integrità strutturale, 57 (2021) 1-13; doi: 10.3221/igf-esis.57.01 12 conclusion he current research work investigated the effect of surface texturing in the sliding surface on tribological characteristics of en-31 alloy steel under lubricated condition. two texturing methods, edm and cnc machining were adopted to fabricate micro-dimples on the contact surface of the plate with different texture densities. the experimentations helped in understanding the tribological characteristics of textured surfaces in wet condition. based on the experimental results, the conclusions drawn are: a. the surface texturing leads to better tribological characteristics in terms of friction and wear. the cost of surface texturing can be justified by the increased life of materials. b. the friction and wear are influenced by the geometry and method of surface texturing. increase in texture densities leads to rise in friction and wear at a constant texture depth. c. experimentally observed that 5% surface texture exhibited the best friction – wear properties in all conditions as it could supply more lubricant and trap wear debris. d. surface texturing by micro-edm process provides better tribological characteristics with respect to micro-drilling cnc process under iso-68 oil lubricated condition. e. friction reduction by surface texturing may be attributed to the hydrodynamic action, which increases the sliding gap and reduces the possibility of material asperity contact. references [1] bruzzone, a. a. g., costa, h. l., lonardo, p. m. and lucca, d. a. (2008). advances in engineered surfaces for functional performance, cirp annals manufacturing technology, 57, pp. 750-769. [2] greco, a., raphaelson, s., ehmann, k., jane wang, q., lin, c. (2009), surface texturing of tribological interfaces using the vibromechanical texturing method, journal of manufacturing science and engineering transactions of the asme, 131, pp.1-8. [3] kustandi, t.s., choo. j.h., low, h.y. and sinha s.k. (2010), texturing of uhmwpe surface via nil for low friction and wear properties, journal of physics d:applied physics, 43, pp. 1-6. [4] dubey, a.k. and yadav, v. (2008), laser beam machining a review, international journal of machine tools and manufacture, 48(6), pp. 609-628. [5] suh, n.p., m. mosleh and p.s. howard (1994), control of friction, wear, 175, pp. 151158. [6] schneider, y.g. (1984) formation of surfaces with uniform micro-patterns on precision machine and instrument parts, precision engineering, 6, pp. 219-225. [7] h l costa, i m hutchings, (2007). hydrodynamic lubrication of textured steel surfaces under reciprocating sliding conditions, tribology international 40, pp. 1227-1238. [8] g. ryk, y. kligerman, i. etsion (2002) experimental investigation of laser surface texturing for reciprocating automotive components”, tribology transactions, 45, pp. 444-449. [9] kovalchenko, a., ajayi, o., erdemir, a. (2011), friction and wear behaviour of laser surface textured surface under lubricated initial point contact”, wear, 271, pp. 1719-1725. [10] willis, e. (1995). surface finish in relation to cylinder liners, wear, 109, pp. 351-366. [11] shinkarenko, a., kligerman, y., etsion, i. (2009). the effect of surface texturing in soft elasto hydrodynamic lubrication, tribology international, 42, pp. 284-292. [12] tomanik, e., profito, f.j., zachariadis, d.c. (2013), modelling the hydrodynamic support of cylinder bore and piston rings with laser textured surfaces, tribology international, 59, pp. 90-96. [13] fanming, m., rui, z., tiffany, d., cao, j., jana wang, q., diann, h. and liu, j. (2010), study on the effect of dimples on friction of parallel surfaces under different sliding conditions, applied surface science, 256, pp. 2863-2875. [14] zhang, x., ningsong, q., fang, x (2017). sandwich-like electrochemical micromachining of micro-dimples using a porous metal cathode. surface and coatings technology, 311, pp 357-364. [15] liew, p.j., yan, j., kuriyagawa, t. (2014). fabrication of deep micro-holes in reaction-bonded sic by ultrasonic cavitation assisted microedm. int j mach tools manuf. 76, pp. 13–20. [16] wu, z., xing, y., huang, p., liu, l. (2017), tribological properties of dimple-textured titanium alloys under dry sliding contact, surface and coatings technology, 309, pp. 21-28 t h. s. patil et alii, frattura ed integrità strutturale, 57 (2021) 1-13; doi: 10.3221/igf-esis.57.01 13 [17] fu, y., qin, h., xu, x., zhang, x., guo, z. (2021), the effect of surface texture and conductive grease filling on the tribological properties and electrical conductivity of carbon brushes, tribology international, 153, pp. 106637. [18] jiang, s., li, j., liu, s., zhou, n., yu, a., deng, y. (2019), tribological properties of hybrid surface textured gcr15 steel filled by epoxy resin-based material under dry friction, surface topography: metrology and properties, 7(2), pp. 25018. [19] zhang, h., hafezi, m., dong, g., and liu, y. (2018), a design of coverage area for textured surface of sliding journal bearing based on genetic algorithm. asme. journal of tribology, 140(6), pp. 61702. [20] wang, m.-z., kang, j.-j., yue, w., fu, z.-q., zhu, l.-n., she, d.-s., wang, c.-b. (2019), effects of combined treatment of plasma nitriding and laser surface texturing on vacuum tribological behaviour of titanium alloy, materials research express, 6(6), pp. 66511. [21] huang, j., zhang, l., wei, s., yang, y., yang, s., shen, z. (2019), fabrication of the laser textured nickel surface and its tribological property under the water lubrication, aip advances 9-11, pp.119901. microsoft word numero_33_art_13 j.t.p. castro et alii, frattura ed integrità strutturale, 33 (2015) 97-104; doi: 10.3221/igf-esis.33.13 97 focussed on characterization of crack tip fields can keff be assumed as the driving force for fatigue crack growth? j.t.p. castro, m.a. meggiolaro, j.a.o. gonzález pontifical catholic university of rio de janeiro jtcastro@puc-rio.br, meggi@puc-rio.br, jaog1608@hotmail.com abstract. this work raises some new questions about the validity of blindly assuming that elber’s effective stress intensity factor is the actual fatigue crack driving force, and that as so it can be used to explain all load sequence effects on fatigue crack growth (fcg). although plasticity-induced crack closure can be a quite reasonable heuristic explanation for many non-elementary fcg behaviors, it has some limitations that cannot be ignored. in fact, this never settled discussion is particularly important for the simulation of fcg lives under real service loads, a most important practical issue. after arguing that keff can spoil the use of the most important similitude principle in fcg problems, simple but convincing experimental data that cannot be explained by this classical idea is presented here. this data involves the shape of fatigue crack fronts and the fcg behavior under nominally plane stress and plane strain conditions. keywords. sequence effects on fcg; near and far field opening loads; crack front shapes. introduction atigue crack growth rates are very much susceptible to brusque changes in crack driving forces, which may cause important load sequence effects by significantly altering subsequent rates as compared to the rates induced by identical driving forces that have not been previously affected by sudden load changes. such effects include delays, arrest, or even acceleration of fcg rates after tensile overloads (ol) or abrupt decreases in the applied stress intensity factor (sif) range k and/or peak kmax; sudden fracture caused by very large ols; and reduction of ol-induced delays after compressive underloads (ul). the order of variable amplitude load (val) events can thus have a huge influence on fcg lives, particularly in cracked components that must tolerate rare but significant ols during their duties. in fact, fcg lives simply cannot be properly estimated in many if not most practical applications if such load history effects are neglected. such effects can be induced by several mechanisms that can be divided into three main classes [1]: (i) fatigue crack closure induced by plasticity, roughness, phase transformation, and/or oxidation, all mechanisms that act on the crack faces, thus before the crack tip; (ii) blunting, kinking, or bifurcation of the crack tip, mechanisms that act at the crack tip; and (iii) residual stresses and/or strains, mechanisms that act ahead of the crack tip. moreover, the importance of the various mechanisms that can induce load order effects on fcg may depend on many factors, like for example: the sizes of the crack and of the residual ligament rl; the transversal constraints around the crack tip; the residual stress state around the crack tip; the load and the overload (ol) ranges and maxima; the microstructure of the material; the number of ol cycles; and the environment. in many practical cases one of those mechanisms can be so dominant that the others may become negligible, but in other cases they may be not. such mechanisms can act competitively reducing the effects of the others (e.g. crack tip bifurcation after an ol can reduce its opening load and decrease the subsequent influence of crack closure), or else, they can act symbiotically (e.g. as martensite is less dense than ferrite, martensitic transformation induced by plasticity increases the material volume inside the plastic zones, thus tends to increase residual stresses ahead, as well as crack opening loads f http://www.gruppofrattura.it/pdf/rivista/numero33/audioslides/castro1/castro1.html j.t.p. castro et alii, frattura ed integrità strutturale, 33 (2015) 97-104; doi: 10.3221/igf-esis.33.13 98 behind the crack tip). since too many variables can affect the fcg behavior under val, it is no surprise to still find controversy in the vast literature about this important subject. many experts vigorously defend that elber’s crack closure is the single or at least the dominant cause for all load order effects, whereas others simply deny that plasticity-induced crack closure may have any importance on fcg. moreover, there are respectable arguments and even sound experimental data to justify such different points of view [2-6], sometimes sustained in a regrettably radical way. anyway, it is an undisputable fact that cracks do not grow by fatigue through virgin material. instead, they propagate by small growth steps that cut material previously deformed by the monotonic and reverse plastic zones pz and pzr that always follow their tips, leaving an envelope of residual strains around their faces. moreover, as their uncracked residual ligaments normally remain elastic during most of their lives, fatigue cracks usually grow accompanied by pzr < pz << rl. according to elber, plasticity-induced crack closure is caused by such elastic rl, which tend to compress the plastified envelopes that wrap fatigue cracks as they try to recover their previous shape when unloaded. so, when a crack closed by its rl is reloaded, it should first gradually relieve the compressive loads transmitted through its faces until it reaches its opening load kop > 0. this behavior can be macroscopically detected by compliance measurements [7-9], see fig. 1, although some modern 3d microtomography studies [10-11] question the existence of a clearly defined opening load. figure 1: macroscopic fatigue crack opening load measurement from compliance plots that display the load p versus the load point displacement  (or vs. a suitable strain , e.g. the back face strain, which is proportional to  in linear elastic components). note that [p(m)  m]m is the signal from the linearity subtractor, an interesting equipment described in [9], and that m is the crack mouth displacement, which is also proportional to p, the load point displacement. using a highly simplified 2d view of the fcg problem and arguing that fatigue crack tips cannot be reloaded before they are completely opened, so that they cannot grow when still closed under loads k < kop, elber defined an effective stress intensity factor (sif) range that would be responsible for fcg:  keff  kmax  max(kop, kmin) k  kmax  kmin (1) elber also assumed that keff (instead of k) controls fcg rates. if it really does so, then any load event that alters kop also affects subsequent fcg rates. in such cases, ol-induced fcg rate delays would be due to the larger reaction of elastic residual ligaments over the plastic zones hypertrophied by the overloads, pzol, when compared to the rl reaction over the smaller pz that accompanies crack tips under normal loads (not affected by their previous histories). so, using simplified macroscopic 2d arguments, kop should increase when the crack penetrates pzol, decreasing keff and delaying subsequent fcg rates. this plausible hypothesis can reasonably explain why fcg rates decrease after ols, at least in plane stress (pl-) cases. it can also explain the existence of fcg thresholds and why uls can decrease the beneficial effects induced by ols (they tend to reduce the tensile residual strains inside pzol, hence to decrease kop and to increase keff). elber’s model is popular because it seems reasonable to assume that kop should increase after the crack tip penetrates pzol, decreasing keff and delaying the crack. in this simplified 2d macroscopic point of view, the ol should first locally blunt the crack tip, decreasing kop and accelerating the crack before it penetrates pzol. the maximum retardation should occur after the crack grows for a while after the ol, a phenomenon called delayed retardation. moreover, as the residual strains inside pzol decrease from the ol application point up to its boundary, ol-induced delay effects should decrease while the crack gradually crosses pzol, and end after the plastic zone that follows the crack tip leaves it (assuming fcg under j.t.p. castro et alii, frattura ed integrità strutturale, 33 (2015) 97-104; doi: 10.3221/igf-esis.33.13 99 otherwise fixed load conditions). this idealized phenomenology was experimentally verified in thin plates, soon after the plasticity-induced crack closure concept was proposed, another reason for its quick acceptance [12]. the same idea can be applied to justify load order effects caused by abrupt decreases in k and/or kmax. many articles support such hypotheses [13-15], but most of them deal with delay effects measured on phase ii fcg under relatively high k and low r  kmin/kmax in dominant plane stress conditions, with pz sizes not much smaller than the specimen thickness. the r effect on kop has been studied e.g. by newman, schijve, and topper, see fig. 2 [16-18]. according to the predictions shown in this figure, high-r fcg should be closure-free especially under plane strain (pl-), as discussed in [1]. figure 2: keff/k versus r predictions by newman, schijve, and topper models ( is a parameter in schijve’s model). so, neither newman’s model predicts crack closure under pl-for r > ~0.5, nor does topper’s model for r > ~0.4, for this max level [1]. issues with keff as the fcg driving force f classical closure predictions like the ones mentioned above are true, and if keff indeed controls fcg rates, then the basic fracture mechanics’ similarity principle based on sifs could be questioned. indeed, whereas the sifs of cracked components can be listed, their crack opening loads kop cannot, because they are not unique for a loading/geometry pair. in fact, keff values depend on the applied stress levels and at least on the cracked piece thickness t as well. moreover, kop may depend on the residual ligament size too, and there is no general model that can account for all such factors in generic structures yet. so, if keff controls fcg, based on the analyses studied in the previous sections the fatigue lives of relatively thin pieces under pl- fcg (with a large pz/t ratio) should thus be larger than the lives of similar but thicker pieces that work under equally fixed loading conditions (k, r) in pl-. besides, even under such simple conditions, if the crack starts to grow under pl-, as they usually do when they are small, and gradually changes to a pl- dominated stress state as its size increases, then fcg rates should vary in the same piece between these two limit cases as the crack sizes increases. hence, not even da/dnkeff data would provide enough information on the fcg behavior of structural materials. so, without the k-similarity, it would be very difficult to reliably predict residual lives of cracked structures even in very simple practical applications. however, unlike in fracture predictions, thickness effects usually are not a major concern for fcg applications, and da/dnk (instead of da/dnkeff) curves keep on being reliably used for residual life predictions in most structural integrity analyses. fig. 3 shows some data that supports this practice: its points are much less scattered if plotted against k than keff [19]. due to the low r  0.05 value, crack closure was clearly identified during such tests, and the opening load kop needed to calculate the effective sif range keff in this figure was properly measured using strain gages bonded on the back face of dc(t) specimens and the linearity subtractor technique described in [9]. such data also supports astm e647 standard procedures, which suggest but do not impose thickness limits for the specimens it accepts to measure da/dnk curves, implicitly accepting that k (instead of keff) is the parameter that controls fcg under fixed r. i j.t.p. castro et alii, frattura ed integrità strutturale, 33 (2015) 97-104; doi: 10.3221/igf-esis.33.13 100 figure 3: fcg rates plotted as a function of k and of the measured effective range keff. although not a hard evidence against the idea that keff is the fcg driving force, another test clearly demonstrates that a partially closed fatigue crack can grow in the portion of its front that opens under tensile loads, while the portion that is under compression stands still [21]. in this way, it also shows that fcg driving force gradients along the crack fronts can induce different growth rates along them, so that they can distort the crack front shape as the crack grows. first, a mode i edge crack was grown for a while in se(t) plate-like specimens under pure tension loads at r  0.05, generating approximately straight fronts as usual. then the pre-cracked specimens were repositioned and reloaded under pulsating 4-point bending, working in this way as a beam with a side crack, see fig. 4. the main objective of such tests was to verify 3d modeling procedures needed to describe 2d fcg considering contact stresses along a portion of the crack face, an interesting non-trivial numerical modeling problem, see [21] for details. however, since there is no doubt that the bent cracks partially close their fronts due to the compressive stresses induced by the bending loads, they can verify as well how such cracks propagate under variable driving forces along their fronts. moreover, since the partial closure of their fronts is induced by the variable bending loads along it, it is independent of elber’s or of any other type of closure mechanism. thus, their behavior does not depend on any assumption about their actual driving forces, i.e., it does not matter if they are driven by {k, kmax} or by keff. figure 4: pre-cracked se(t) specimen loaded in pure bending to partially close its crack. anyway, the cracks tested under transverse bending severely distorted their initially (quasi) straight fronts as they grew after the load applied on the pre-cracked plates changed from pure tensile to pure bending, see fig. 5. note that the successive crack fronts depicted in this figure clearly show that although the pre-crack front started almost linear, it slowly assumed an increasingly pronounced l-shape after partially closed during its subsequent 2d fcg under pulsating bending loads. this is exactly the expected behavior of a crack front that advances by fatigue depending on the local value of the crack driving force along it. j.t.p. castro et alii, frattura ed integrità strutturale, 33 (2015) 97-104; doi: 10.3221/igf-esis.33.13 101 figure 5: successive crack fronts propagated in bending from an initially straight shape. in other words, such tests confirm the (reasonable) idea that fcg is a local phenomenon, i.e., that it is induced by the local value of the driving force along the crack front. consequently, the characteristic approximately parallel striations generated by the homologous propagation of crack fronts at every load cycle that so nicely illustrate the gradual nature of the fcg process in most fatigue textbooks would require an iso-driving force along them, see [22] for a sound mechanical evidence that supports this claim. consequently, if the fatigue cracks are subjected to driving force gradients along their fronts (like e.g. after tensile ols pin the pl- part of the crack front, as mcevily claims is the mechanism responsible for fcg delays in his nice experiments [23-24]), then the subsequent crack fronts should tunnel or bow with increasing curvature while the crack is delayed by the ol. if the crack fronts do not tunnel, then their driving force should be constant along their fronts, with no difference between pl- and pl- regions, caused by plasticity-induced closure or by any other mechanism. it is quite surprising that this powerful argument is not widely used in fractographic studies of fatigue surfaces, particularly those obtained under variable amplitude load tests. a third data set reinforces the idea that although elber’s plasticity-induced closure certainly is a plausible mechanism to explain many peculiarities of the fcg behavior, it has at least some limitations. in these simple but discriminating fatigue tests the cracks were grown under quasi-constant k and r loading conditions in thin and thick specimens of the same material, carefully measuring both the fcg rate da/dn and the crack opening load pop while the cracks grew. the test specimens thickness t was chosen to guarantee pl- conditions (making pz/t  1) in the thin specimens and pl- conditions in the thicker ones, assuming that classical astm e399 pl- requirements can be used in fatigue as well (making t > 2.5(kmax/sy)2). all the test specimens were cut from an as received 1020 steel 3” wrought round bar with yield and ultimate strengths sy  262mpa and su  457mpa. the applied load was maintained approximately constant by adjusting the load at small crack increments, following traditional standard astm procedures [20]. the crack length was redundantly measured by compliance and by optical methods, using a strain gage bonded on the back face of the specimens and a traveling microscope. the crack opening load pop was also redundantly measured by the procedures studied in [9], using the back face strain gage and a gage strip with several strain gages bonded ahead of the notch tip, see fig. 6. the pop values measured form the various gages showed no discrepancy, meaning the same value was obtained from the near and from the far-field strain signals. the crack face of one of the thick specimens with its homologous crack fronts is shown in fig. 7. figure 6: gage strips and back face strain gages bonded on a thin and on a thick dc(t) ts. standard 76mm diameter dc(t) specimens were cut perpendicularly to the round 1020 steel bar axis, but with two very different thicknesses. the thinner specimens were loaded under k  20mpam and r  0.1 and, to force the crack to grow under nominally pl- conditions, they had t  2mm < pzmax  (1/)(kmax/sy)2  (1/)[20/(0.9262)]2  2.29mm (using irwin’s estimate for the maximum plastic zone ahead of the crack tip, assuming that this traditional 2d view is appropriate j.t.p. castro et alii, frattura ed integrità strutturale, 33 (2015) 97-104; doi: 10.3221/igf-esis.33.13 102 to define a plane stress state in fcg). the thicker ones were loaded under k  20mpam and r  0.05, and to force the crack to grow under predominantly pl- conditions they had t  30mm > 2.5(kmax/sy)2  2.5[20/(0.95240)]2  16.14mm, using the astm e399 criterion to define a plane strain state in fcg, as mentioned before. figure 7: cracked surface of one thick specimen, showing its homologous successive crack fronts, an evidence that it grew under an iso-driving force across the ts thickness. four such dc(t) specimens were fatigue tested, two thin and two thick ones. it must be emphasized that the loading conditions were maintained essentially constant, and that no overloads or similar events that could possibly alter the crack propagation behavior were applied on the tested specimens. the da/dn fcg rates and the crack opening ratios kop/kmax measured along the crack propagation path are shown in fig. 8-9. note that in those figures the crack size is quantified by a/w, the ratio between the crack length a and the uncracked ligament size w, measured from the load line. those are the simplest tests that can possibly be made to verify the basic question “is keff the actual driving force for fcg?” indeed, the only fancier detail in such tests was the careful and continuous measurement of the opening loads while the cracks propagate, made with the help of a specially developed software written in labview to numerically implement the straight line fitting and the linearity subtractor techniques to the redundantly measured p near and far field signals [9]. the fcg experiments were performed in an instron 100kn servohydraulic testing machine and the data acquisition was made using national instruments ni 9215, ni 9235, and cdaq-9172 instruments. it must be emphasized as well that the opening loads macroscopically measured from compliance curves as originally proposed by elber were obtained using the best available techniques, as discussed elsewhere [7-9]. such measurements are the best way to identify if keff is indeed the fcg driving force in any given fatigue experiment, since it eliminates any doubt about the opening load, at least from the macroscopic point of view used to defend (or to deny) elber’s ideas [13]. moreover, since in relatively recent works some important groups are claiming that such closure measurements should be performed on p curves measured using the near field strains close to the crack tip instead of the far field strains measured e.g. in the back face of the test specimen [25], in the tests presented here both measurements were redundantly made. however, no difference was observed in the opening loads identified by both techniques. in fact, even if such signals lead to different kop values, the approximately homologous crack fronts would indicate that they propagated under macroscopically uniform driving forces. note in fig. 8-9 that the measured fcg rates in the four tested specimens can be clearly bounded by a single dispersion line, so it can be said they are were essentially equal independently of the ts thicknesses. this simple and reliable experimental result certainly confirms the traditional astm view that da/dnk rates measured under fixed r-ratios can properly characterize the fcg of structural materials, at least when applied to the tested steel. this result also confirms the more physically appropriate idea that {k, kmax} can be view as the fcg driving forces, so it reassures that k can be indeed used as a similitude parameter in fcg predictions. however, this data can be used as well to question the alternative view that fcg is driven by keff. since those tests follow straightforward procedures, and since they clearly show that the crack opening ratio kop/kmax steadily decreased in both the thin and in the thick specimens as the cracks increased in size, decreasing the (predominantly elastic) residual ligament that tends to close them, it can be concluded that keff  kmax  kop was not the fcg controlling driving force in this case. indeed, since the loading conditions {k, kmax} were maintained constant during those tests, there is no doubt that keff steadily increased as the crack grew, because the decrease in kop/kmax ratio is well beyond the (small) uncertainty of the measured data. moreover, despite their slight lower r-ratios, note that the opening loads were a little bit higher along j.t.p. castro et alii, frattura ed integrità strutturale, 33 (2015) 97-104; doi: 10.3221/igf-esis.33.13 103 the crack path in the thicker than in the thinner test specimens, or under plane strain instead of plane stress conditions, contrary to what could be expected beforehand. finally, it should be mentioned that other limitations of the hypothesis “keff is the actual fcg driving force” are explored in [1]. figure 8: fcg rates da/dn and crack opening ratios kop/kmax measured along the crack path in the thin dc(t) specimens (t  2mm), supposedly under pl- conditions. figure 9: fcg rates da/dn and crack opening ratios kop/kmax measured along the crack path in the thick dc(t) specimens (t  30mm), supposedly under pl- conditions. conclusions long standing discussion about the actual fatigue crack growth driving force, which for many is the {k, kmax} pair whereas for many others is keff, remains more relevant than ever because it is a necessary condition to decide which model is the most appropriate to make fcg predictions under variable amplitude loading in practical applications. this study certainly does not settle this point, but it does present some easily reproducible results that clearly cannot be explained by the keff hypothesis. references [1] castro, j.t.p., meggiolaro, m.a., miranda, a.c.o., singular and non-singular approaches for predicting fatigue crack growth behavior, int j fatigue, 27 (2005) 1366-1388. a j.t.p. castro et alii, frattura ed integrità strutturale, 33 (2015) 97-104; doi: 10.3221/igf-esis.33.13 104 [2] elber, w., the significance of fatigue crack closure, astm stp, 486 (1971) 230-242. [3] newman, j.c., an evaluation of the plasticity-induced crack-closure concept and measurement methods, nasa/tn1998-208430, langley research center, (1998). [4] mcevily, a.j., ishihara, s., on the development of crack closure at high r levels after an overload, fatigue fract eng mater struct, 25 (2002) 993-998. [5] vasudevan, a.k., sadananda, k., louat, n., reconsideration of fatigue crack closure, scripta metall mater, 27 (1992) 1663-1678. [6] kujawski, d., on assumptions associated with keff and their implications on fcg predictions, int j fatigue, 27 (2005) 1267-1276. [7] paris, p.c., hermann, l., twenty years of reflections on questions involving fatigue crack growth, part ii: some observations of fatigue crack closure, fatigue thresholds, emas, 1 (1982) 11-33. [8] castro, j.t.p., some critical remarks on the use of potential drop and compliance systems to measure crack growth in fatigue experiments, j braz soc mech sci eng, 7 (1985) 291-314. [9] castro, j.t.p., a circuit to measure crack closure, exp techniques, 17(2) (1993) 23-25. [10] toda, h., sinclair, i., buffière, j.y., maire, e., connolley, t., joyce, m., khor, k.h., gregson, p., assessment of the fatigue crack closure phenomenon in damage-tolerant aluminium alloy by in-situ high-resolution synchrotron x-ray microtomography, philos mag, 83 (2003) 2429-2448. [11] withers, p.j., preuss, m., fatigue and damage in structural materials studied by x-ray tomography, annu rev mater research, 42 (2012) 81-103. [12] von euw, e.f.g., hertzberg, r.w., roberts, r., delay effects in fatigue crack propagation, astm stp, 513 (1972) 230-259. [13] kemp, p.m.j., fatigue crack closure – a review, tr90046, royal aerospace establishment, (1990). [14] skorupa, m., load interaction effects during fatigue crack growth under variable amplitude loading a literature review part i: empirical trends, fatigue fract eng mater struct, 21 (1998) 987-1006. [15] skorupa, m., load interaction effects during fatigue crack growth under variable amplitude loading a literature review part ii: qualitative interpretation, fatigue fract eng mater struct, 22 (1999) 905-926. [16] newman, j.c., crews, j.h., bigelow, c.a., dawicke, d.s., variations of a global constraint factor in cracked bodies under tension and bending loads, astm stp, 1244 (1995) 21-42. [17] schijve, j., the stress ratio effect on fatigue crack growth in 2024-t3 alclad and the relation to crack closure, technische hogeschool delft, (1979). [18] duquesnay, d.l., topper, t.h., yu, m.t., pompetzki, m., the effective stress range as a mean stress parameter, int j fatigue, 14 (1992) 45-50. [19] durán, j.r., castro, j.t.p., variação de kefetivo na propagação de trincas por fadiga, proceedings vi coteq, (2002). [20] astm e647 standard test methods for measurement of fatigue crack growth rates, astm standards v, 03.01. [21] corbani, s., martha, l.f., castro, j.t.p., carter, b., ingraffea, a., crack front shapes and stress intensity factors in plates under a pure bending loading that induces partial closure of the crack faces, procedia mater sci, 3 (2014) 12791284. [22] góes, r.c.o., castro, j.t.p., martha, l.f., 3d effects around notch and crack tips, int j fatigue, 62 (2014) 159-170. [23] mcevily, a.j., current aspects of fatigue, metal sci, 11 (1977) 274-284. [24] ishihara, s., sugai, y., mcevily, a.j., on the distinction between plasticityand roughness-induced fatigue crack closure, metall mater trans a, 43 (2012) 3086-3096. [25] yamada, y., newman, j.c., crack closure under high load-ratio conditions for inconel-718 near threshold behavior, eng fract mech, 76 (2009) 209-220. microsoft word numero_58_art_12_3141.docx m. ravikumar et alii, frattura ed integrità strutturale, 58 (2021) 166-178; doi: 10.3221/igf-esis.58.12 166 study on micro nano sized al2o3 particles on mechanical, wear and fracture behavior of al7075 metal matrix composites m. ravikumar* department of mechanical engineering, r l jalappa institute of technology, bangalore (r), karnataka, india ravikumar.muk@gmail.com h. n. reddappa department of mechanical engineering, bangalore institute of technology, bangalore, karnataka, india reddyhn.phd@gmail.com r. suresh department of mechanical and manufacturing engineering, m.s. ramaiah university of applied sciences, bangalore-560058, karnataka, india sureshchiru09@gmail.com e. r. babu, c. r. nagaraja department of mechanical engineering, bangalore institute of technology, bangalore, karnataka, india rajjbabu@gmail.com, cnraaja@gmail.com abstract. having low density and being light weight with better mechanical properties, aluminum is the most significant material and is universally used in highly critical applications like navy, aerospace and particularly in automotive applications. this research work is aimed to investigate the effect of micro and nano al2o3 (alumina oxide) to aluminium (al) on the mechanical and wear properties of the al composites. the micro nano composites with 1, 2, 3 and 4 % of al2o3 particulates in al are fabricated using stircasting processes. it was found that an increase of al2o3 both as micro and nano particulates content resulted in improved hardness, enhanced tensile strength and high wear resistance. however, nano al2o3 reinforced mmcs have better hardness, improved tensile strength and higher wear resistance as compared with micro-sized al2o3 reinforced mmcs. grain refinement of composite and nano composite materials as compared with pure al were observed in the microscopic structures. analysis of wornout surface and tensile fracture surface was studied by sem analysis to examine the nature of wear and tensile fracture mode of composite samples. keywords. al7075; al2o3; micro; nano; hardness; tensile; wear loss. citation: ravikumar, m., reddappa, h.n., suresh, r., babu, e.r., nagaraja, c.r., study on micro nano sized al2o3 particles on mechanical, wear and fracture behavior of al7075 metal matrix composites, frattura ed integrità strutturale, 58 (2021) 166-178. received: 15.06.2021 accepted: 11.08.2021 published: 01.10.2021 copyright: © 2021 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. https://youtu.be/iyzxajv2qvi m. ravikumar et alii, frattura ed integrità strutturale, 58 (2021) 166-178; doi: 10.3221/igf-esis.58.12 167 introduction ue to the high strength, low density and better wear resistance, aluminum (al) composites are the most useful materials for several engineering applications. in particular, aluminum alloys are used in several components manufactures namely, engine blocks, pistons, brakes, engine blocks, impellers, and valve components. the main reasons for considering these al alloys used in above-mentioned applications possess excellent weldability, castability and good corrosion resistance. mechanical properties are significantly influenced by the chemical composition, microstructure and solidification process [1]. different types of particles are used as reinforcements such as al2o3, tic, sic, b4c, zro2, fly ash and etc., with al combination to obtain high wear resistance and strength. among these, ceramic particulates are broadly used as the support in the development of materials as they possess high strength and modulus. increase in the content of particulates in the al matrix leads to improvement in the rigidity of the produced composites. in aluminium composites, ceramic particles help in providing improved hardness, higher wear resistance and acts like a lubricating film on the contact surface and also provides to low thermal expansion. ceramic particles help in the development of mechanical properties and wear resistance of the material [2]. mainly, al alloy-based composites applicable in aerospace, automotive and also other engineering applications are relatively popular due to their better mechanical behavior. properties of alloy can be improved upon by adding micro and nano hard ceramic reinforcements. al composites have gained specific attention for automobile applications as possibly advanced essential materials in the last two-three decades due to their better properties and accessibility of the low cost production methods. the technique used to manufacture a composite depends on the chemical properties and mechanical characteristics of the reinforcements and matrix, the particulate size and the desired particle configuration [3 5]. the mmcs (metal matrix composites) of micro and nanocomposites can be produced by using three different processes like liquid state, solid state and solid-liquid mixed process. stir casting, spray casting and squeeze castings are liquid state techniques. friction stir casting and powder technology are solid state techniques used in matrix composite fabrication. the semi-solid forming and compo casting are considered as liquid-solid (semi solid) mixed methods used in the manufacture of mmcs. among the numerous composite fabrication methods, casting techniques and powder metallurgy are more common compared to other manufacturing techniques. although stir casting methods are cheaper, straightforward and more manageable, the inherent non-wettability of the hard ceramic in the al melt is difficult. some techniques are based on employing mechanical parameters in fabrication to improve the wettability, such as stir-casting [6]. the main drawbacks of stir casting process are agglomeration of reinforcing particulates due to the insufficient heat and unbalanced material flow throughout the stirring process [7, 8]. particulates agglomeration is not only owing to the high wt. % of reinforcing ceramic micro/nanoparticles, but also due to non-wettability of these particulates by the melt and the inherent tendency of these particulates to absorb each other. numerous studies have been conducted to overcome this challenge. the researches in the matrix of al composites reinforced by hard ceramic nano particulates, especially al2o3, have received much attention because of extensive use of these types of materials in the aerospace applications [6]. al2o3 is one of the regularly used reinforcing materials for al metal matrix composites. alaneme and bodunrin [9] studied the mechanical characterization of al alloy 6063 al2o3 composites fabricated by stir-casting method. mmcs having 6 18 wt. % of al2o3 were produced. it was found that mmcs had less porosity levels and good uniform distribution of the al2o3 particles with in the base matrix. the ultimate tensile strength (uts) and hardness enhanced with increasing in wt. % of al2o3 content while the fracture toughness decreased with increase in wt. % of alumina content. l singh et al. [5] produced the mmcs containing al with 3 to 9 wt. % of al2o3 particulates by stir-casting technique. it was found that the hardness of composites enhanced with increase in wt. % of al2o3 content, but decreased with increasing in particulates size. velavan et al. [10] in their investigation, used al 7075 powder of 60 μm (mesh size) and reinforcing particulates like sic (2, 4, 6 %) and al2o3 (2 %) of particle size ˂ 51 nm to produce hybrid composites. from the outcomes it was witnessed that the grain boundaries showed no pore cavities in the composites and also confirmed that the sintering was effective. the silicon carbide particulates had fine granular structure and also precipitated with the grain boundaries of the al matrix. the separation at interfaces showed outstanding sintering and therefore reduction in size of grains was observed due to the addition of nano-sized hard ceramic particles and also due to presence of secondary reinforcements (al2o3) within the parent material. this acted like a heterogeneous nucleation throughout process and it restricted the grain growth which showed the motion of dislocations. s. mula et al. [11] studied the structure of a nanocomposite of al with 2 % nano sized al2o3 particulates. nearly 57% increase in the tensile strength and 92% increase in the hardness were found from the results. these developments in the tensile strength and hardness were due to reinforcing by only 1.4 wt. % of nano-sized al2o3 particulates in the matrix. huda et al. [12] developed al7075 composite reinforced by 0 5 wt. % of al2o3 particulates by using stir-casting technique. from the outcomes it was observed that, the wear rate and mechanical strength of the produced mmcs considerably improved by d m. ravikumar et alii, frattura ed integrità strutturale, 58 (2021) 166-178; doi: 10.3221/igf-esis.58.12 168 addition of al2o3 nano particulates. these material properties were significantly enhanced as the wt. % of hard reinforcements increased from 1% 5%. the enhancement of 26.3% and 14.3% was observed for hardness and tensile strength of composites respectively. al-jafaari [13] studied the effect of al7075 reinforced with al2o3 nanocomposites produced by stir-casting process. it was witnessed that the tensile strength of mmcs significantly enhanced by 8% at 0.3 wt. % of al2o3 content. the higher tensile strength of nano composite could be attributed due to the reason that al2o3 particulates act like an obstacle to the movements of the dislocation. c. kannan and r. ramanujam [14] investigated the microstructural and mechanical characterization of al7075-based mono and hybrid nano composites manufactured through stir-casting techniques. the composites were produced with reinforcement of 2, 4 wt. % nano sized al2o3 particulates and 4 % sic particulates. in comparison with as-cast, hardness enhanced by 63.7% and 81.1% for mono and hybrid nano composite. sajjadi et al. [15] examined the aluminum composites reinforced with micro and nano al2o3 particulates. it was observed that the hardness of mmcs samples improved with increasing wt. % of al2o3 particles. some studies confirmed that, the smaller nano sized particulates provided better as compared to micro-sized particulates. recent studies found that, the reinforcing the nano particulates considerably increased mechanical properties of composites, whereas the ductility was retained [16]. the microstructural characterization and mechanical behavior of mmcs are highly influenced with respect to parameters like uniform distribution, particles size and wt. % of micro nano sized reinforcing particulates. among these parameters, uniform dispersal of reinforcements determines the micrographical structure and mechanical behavior of mmcs is influenced by the factors due to matrix material and fabrication technique. wettability and distribution of particulates are two major glitches to be avoided while reinforcing micro or nano sized particulates into the al matrix through stir casting method. whereas, these two factors can create unfavorable effects on mechanical behavior of both composites / nano composites if they have not been taken proper care of at processing stage. the wettability is very poor for nano sized reinforcement particulates. also, it is very difficult to achieve uniform dispersal of nano particulates in a base matrix by stircasting technique [17]. in the literature survey, there is mention of several studies which have examined the effect of micro or nanosized reinforcing particulates on the mechanical behavior of al composites at various wt. % of hard ceramic reinforcements. generally, it is very difficult to equate the mmcs with micro / nanosized particulates. due to this reason, the research studies have been done to examine the influence of micro nano particulates on the microstructures, mechanical and wear characteristics of albased composite/nanocomposite reinforced with varying wt. % of al2o3 particulates by using stircasting technique. in the present research, the two types of al2o3 particles like micro size (30-50 microns) and nano size (30-50 nm) were used in the reinforcing phase for the fabrication of al matrix composite and nano composite. the stir-casting method is selected in the present research work, since it is one of the best inexpensive methods of processing of al composites. the fabricated composite and nanocomposites were further studied for microstructure, mechanical and wear properties. experimentations materials n present research, al7075 has been used as the base matrix. two different types of alumina oxide (al2o3) particulates i.e., micro and nano-size were used as a reinforcements for the production of composite and nanocomposite. al7075 (rod) was purchased from perfect metal works, bangalore, karnataka. al2o3 particulates (micro and nano-size) were purchased from prince chemical bangalore, karnataka. the stircasting facility was provided by m/s aluminium fabrications, bengaluru. fabrication of composites/nanocomposites stir-casting method helps to enhance the wettability in mmcs by evading the development of oxide and gaseous layers on surface of melt and also prevents agglomerations of the particulates in the base matrix. in this method, the fluidity can be continued, like cleaning the molten melt from the oxides and decreasing the rate of heat transfer by the mold box. the mmcs were reinforced by 1, 2, 3 and 4 wt. % of al2o3 particles of micro size (30-50 microns) and nano size (30-50 nm). the casting facility was provided by m/s aluminium fabrications, bengaluru. the mmcs were produced by a stircasting technique. coke furnace was used to melt the al7075 alloy at 850ºc. the preheated reinforcement was added into the al melt. degasifier tablets were used to remove the gases from the molten melt. while adding hard reinforcements, the stirring process was done at 150±5 rpm for the duration of 3 min and the ready composite melt was poured into the metal die. then the composite samples of 20 mm diameter and 200 mm long were separated from the die. composites were machined by using cnc machining process to prepare test samples. the tensile test specimens were prepared as per the i m. ravikumar et alii, frattura ed integrità strutturale, 58 (2021) 166-178; doi: 10.3221/igf-esis.58.12 169 astm e8 standards of size (12.5 mm diameter and gauge length of 50 mm). the composite samples used for testing purposes are depicted in fig. 1. figure 1: (a) tensile test specimen (b) hardness test specimen (c) wear test specimen characterizations of composites/nanocomposites the composite and nanocomposites test samples were polished by using 500 grit size emery sheets. the test specimens were polished by velvet disk to achieve adequate finish on the specimen surface. the dispersal of hard particles with in the matrix was examined by optical microscope. tensile tests were carried out according to the astm e8 standards. the tests were conducted by using utm at a load of 400-410 kn. three tensile test samples of similar compositions were tested and the average values were considered and the variation of tensile strength values was less than 5 %. for each trials hardness of composite and nanocomposites were studied according to e92 standards by using vickers micro hardness testing apparatus. here, 12 mm diamond-shaped indenter was used under load of 1 kg for the duration of ½ minute on the test samples. hardness of the composite and nanocomposites was examined at 3 different places to obtain indentations on the test samples. the average value of micro hardness was determined. the pin-on-disc test equipment was used to examine the wear loss of composite and nanocomposites. the tests were carried out according to the astm g99 standards under the constant sliding speed of 2.1 m/s and load of 2.5 kg against the en-32 hard steel disc for time duration of 30 minutes. the three wear test samples of similar compositions were tested and the average values are considered and the variations were less than 5 %. initial weights of composite and nanocomposites samples were measured by digital weighing machine. the test samples were vertically fixed rigidly and made to be contact with rotating hardened steel disc. the test was conducted by bringing surfaces of the specimen in contact with the surface of flat hard steel disc. finally, the samples were removed and acetone (organic solvent) was used to clean the tested sample surface. the wear behavior of composite and nanocomposites was studied by determining the difference between initial and final weights. microstructural observations ig. 2 depicts the microscopic images of al7075, composite and nanocomposite samples. the fig. 2(a) shows the base matrix material microscopic image without any presence of reinforcements. the micrograph shows images free from casting defects or any voids. the presence of al and al2o3 particulates is observed in the micrograph image of micro-composite sample (fig. 2(b)) with 4 % of micro size al2o3. the matrix phase shows proper dispersal of reinforcements. here, the particles are free from agglomeration and clustering due to the stir casting method adopted to manufacture the composites. micrograph image of 4 % nano-sized al2o3 reinforced nano composite specimen (fig. 2(c)) reveals the presence of al in light (color) portion, whereas the dark portion depicts the agglomeration of nano al2o3. the dispersal of al2o3 nano particulates in al matrix is a vital requirement for increase of the mechanical strength and wear f m. ravikumar et alii, frattura ed integrità strutturale, 58 (2021) 166-178; doi: 10.3221/igf-esis.58.12 170 characteristics of the composites [18]. reinforcing micro and nano al2o3 particulates in the al matrix enhance the grain refinement. the microscopic study revealed that the grain around al2o3 is much finer compared to the grains around al2o3 free matrix alloy. therefore, al2o3 particulates can induce the recrystallization of al alloy by accelerating particulates nucleation among the reinforcement and matrix phase. the al2o3 micro/nano particulates can defer the crystal growth of grains during the casting process. the microscopic image reveals that nano al2o3 reinforced composite induces improved grain refinement when compared with the micro al2o3 reinforced composite [19, 20]. due to the nano size of particles, it is very difficult to distinguish with matrix material and also very difficult to observe the grain boundaries of the reinforced particles. (a) (b) (c) figure 2: microstructure images of: (a) base alloy (b) micro composite (c) nano composite hardness he outcomes of hardness for all the composites produced by stircasting are shown in fig. 3. from the fig it is seen that the composite/nanocomposites reinforced with hard ceramic particulates (al2o3) exhibit improved hardness values compared to al alloy. in addition, the composite reinforced by nano-sized al2o3 particulates exhibit improved hardness when compared to mmcs reinforced with macro sized al2o3 particulates. a comparatively better hardness values are revealed for 4% of al2o3 particles in both composite and nanocomposites. research by dash et al. [21] revealed enhanced hardness for al composite reinforced by nano-sized al2o3 particles when compared to al mmcs reinforced with equal wt. % of the micro sized al2o3 particulates. the hard nano particulates are more closely bound and uniformly distributed with in the matrix. so, higher stress is necessary for the movement of dislocations once t m. ravikumar et alii, frattura ed integrità strutturale, 58 (2021) 166-178; doi: 10.3221/igf-esis.58.12 171 they encounter these hard particulates. thus, the uniformly dispersed nano sized particulates may be attributed to better dispersion strengthening by the appropriate particulates dislocation interaction. therefore, the mmcs reinforced with nano sized particulates possess higher hardness. the improved hardness of nano-composites may also be attributed due to the presence of hard intermetallic phases and improved grain refinements [22 24]. in addition, as the wt. % of nano particulates increases, the agglomeration of nano particles also increases because of insufficient processing time of the molten melt. the hardness of nano composites at higher wt. % of nano particles is not affected due to this. figure 3: hardness of micro vs nano composite samples tensile strength he outcomes of tensile strength for composite nano composites are depicted in fig. 4. when compared to the al alloy, the composite and nano composites possess better tensile strength. the results exhibit that the uts is enhanced by increase in the wt. % of al2o3 particulates content. this improvement in tensile strength was found may be due to the existence of hard ceramic particles of al2o3 in the al matrix, which tends to enhance the tensile strength of al composite. the tensile strength enhanced with an increase in the wt. % of al2o3 content which is attributed to be low degree-of-porosity and uniform dispersal of al2o3 particulates. this remark conforms with the outcomes of most hard particulates reinforced in the mmcs. abhishek et al. [25] investigated the mechanical characteristics of composites reinforced by hard ceramic particles. the results revealed that, the solidification of composites increased based on the quantity of reinforcements in the base matrix. generally, this is because of the intricacy involved in adding hard ceramic particulates which creates obstacles to dislocation of movement over the matrix material. it is also found that the tensile strength of the nano-particles reinforced mmcs is higher than micro-sized particle reinforced composites due to better interfacial bonding strength among the particles and the base matrix. it is known that the addition of al2o3 nano particulates into the base material provides better heterogeneous nucleation at the time of solidification resulting in refined grains. therefore, the improvement of the tensile strength can be ascribed to the grain size [12]. other researchers suggested that the different strengthening mechanisms for the mmcs like load sharing, grain refinement, particulate strengthening and thermal mismatch strengthening were caused by nano-particulates. out of all these strengthening mechanisms, the effect of load sharing is very minimal and improvement in uts is mainly because of the grain refinements based on hall-petch theory concept and the restriction towards the movement of dislocation with in the base matrix due to nano-particulates rendering to “orowan” mechanism concept. improved strength of nano-sized particulates reinforced composites could also be ascribed to the difference in the cte (coefficients of thermal expansion) of matrix and nano-particles when it is cooled under the room temperature (27ºc). whereas these nano-composites were prepared by stir casting method, due to this reason grain refinement and reduction of porosity were attained. this may be the main reason for increase in tensile strength of stir cast nano-composites [26 29]. in addition, it was observed that the uts of nano sized particulates reinforced composites remain unaffected when the wt. % of nano-particulates was more t m. ravikumar et alii, frattura ed integrità strutturale, 58 (2021) 166-178; doi: 10.3221/igf-esis.58.12 172 than 3%. higher wt. % of nano-particles reinforcements led to higher agglomeration with in the composite due to high content of nano-particles [30 32]. figure 4: tensile strength of micro vs nano composite samples stress-strain graphs of the micro and nano composites are depicted in fig. 5 (a & b). the main features of these curves are that the tensile strength increases when the fracture strain is decreased with increasing particulate content. it is observed that the monolithic alloy has the highest plastic strain and also exhibits the least resistance to plastic deformation from its comparatively lower flow stress when compared with the composite and nano-composites. it is observed that all the mmcs provide better strength when compared to the base alloy. this is due to the grain refinements and the strengthening of particles. the improvement of strength in the mmcs is generally due to the mismatch strengthening and high load bearing caused by the nano-sized particulates. it is inferred that could be due to difference in the cte among the matrix and the reinforcements. due to the thermal-mismatch stress, there is a chance of increase in dislocation density within the base material at the time of cooling from the solidification temperature. dislocations might cause stress at interface of the particulates and the base matrix. the stress generally depends on the temperature from which the mmcs were cooled. high temperature led to increased stress at an interface generally, which made the plastic deformation harder and resulted in increased strength of the composites. when it is compared to the base matrix, the improvement in the strength revealed in the mmcs is due to the presence of the hard particulates as an obstacle that restrict the motion of dislocation with in the matrix. the increase in wt. % of micro particles might increase the dislocation density with in the base matrix of mmcs, which can be designated as a dislocation strengthening. the dislocations trapped by the hard ceramic nano sized particles led to increase the tensile strength of the nano-composites during tensile tests [26, 31, 33]. the sem analysis of the tensile fracture surfaces for a composite and nano composites is illustrated in the fig. 6 (a & b). the fractured surfaces of the test samples indicates distributed shallow portions and dimples with different sizes with in the mmcs and also confirms the high ductility witnessed in the tensile test studies. it is observed that there are more number of large sized dimples which are linked together along with the boundaries, presenting an increased amount of clustering along with the grain boundaries. of-course, in these mmcs, due to the utilization of the sufficient reinforcement with a better strength, the fracture particulates are not likely to occur. also, due to the better strength within the base metal, de-cohesion of the matrix and particulates interface is more likely than fracture of the base matrix during the tensile strength test. hence, nucleation of micro voids at the matrix and particulates interface and their development is the fracture mechanism. this is caused due to the merging the micro voids and the shear among them within a base matrix. deep and stretched dimples are formed due to the nucleation of micro voids, their resultant growth in the structure and lastly their coalescence, which is affected by shear-stress. the al2o3 particulates have a substantial effect on the fractured surfaces of the mmcs. the existence of hard particulates in the core of maximum dimples means that the matrix and particulates interface and particles agglomeration provided proper sites for development of cracks and as well as propagation. the crack propagation is produced due to decohesion at the base matrix and particulates interface as a weak place within the structure. comparison among the fractured surfaces of two different composites such as micro and nano-sized particulates shows that particle size is decreased and number of cavities has increased while their sizes are m. ravikumar et alii, frattura ed integrità strutturale, 58 (2021) 166-178; doi: 10.3221/igf-esis.58.12 173 decreased. generally, this phenomenon is affected by reducing the distance among particles and also increasing the matrix and particle interface as a suitable place for the nucleation of cracks or cavities. hence, interface debonding was the main cause for deprived ductility of the mmcs in the present research work. moreover, nano-sized al2o3 particle clusters are the foremost causes for the rapid failure and also it shows no effect on the mechanical strength of the mmcs at higher wt. % of reinforcements [31, 34, 35]. (a) (b) figure 5: stress strain curve of (a) micro composite (b) nano composite. 0 20 40 60 80 100 120 140 160 180 0% 2% 4% 6% 8% 10% 12% 14% 16% 18% s t r e s s ( m p a ) strain as casted 1% al₂o₃ (microns) 2% al₂o₃ (microns) 3% al₂o₃ (microns) 4% al₂o₃ (microns) 0 20 40 60 80 100 120 140 160 180 0% 2% 4% 6% 8% 10% 12% 14% 16% 18% s t r e s s ( m p a ) strain as casted 1% al₂o₃ (nano) 2% al₂o₃ (nano) 3% al₂o₃ (nano) 4% al₂o₃ (nano) m. ravikumar et alii, frattura ed integrità strutturale, 58 (2021) 166-178; doi: 10.3221/igf-esis.58.12 174 (a) (b) figure 6: fracture images of the tensile specimen (a) micro composite (b) nano composite wear behavior he adding of hard ceramic al2o3 particles in to the aluminium is thought to considerably enhance the high wear resistance of the mmcs. fig. 7 shows the wear behavior of al7075 reinforced micro / nano al2o3 particulates. the wear rate is completely correlated with the load for composite and nanocomposites containing up to a 4% of micro and nano al2o3 particulates. wear rate of the nano-sized particle reinforced composites shows improved wear resistance when compared to micro-sized particulate reinforced mmcs. figure 7: wear behavior of micro vs nano composite samples the enhancement of the high wear resistance of the nanocomposites when compared to composites is generally due to the grain refinement. however the wear loss of the as-cast is higher when compared to composite and nano composites. it is known that the wear behavior strongly depends on the reinforcements. however, the wear loss decreases upto a certain wt. % of reinforcement and then remains unaffected due to various factors such as wettability and agglomeration of nano reinforcement particles. this leads to reduction in the wear resistance of nano-composite at higher wt. % of reinforcement content. normally, the wear loss is inversely correlated to the material hardness. generally, the decrease in the hardness is due to the high porosity and also heterogeneous dispersal of the hard particles in the al matrix. therefore, the wear behavior of the micro and nano composites reinforced with 4% by weight remains unaffected. t m. ravikumar et alii, frattura ed integrità strutturale, 58 (2021) 166-178; doi: 10.3221/igf-esis.58.12 175 (a) (b) figure 8: sem analysis of wornout surface of (a) micro composite (b) nano composite to evaluate the wear mechanisms, the wornout surfaces of composites and nanocomposite specimens were inspected by sem investigation. sem images of composites and nanocomposite specimens wornout surfaces for 4% reinforcements are depicted in fig. 8 (a & b). the wornout surfaces were characterized by narrow grooves, micro-pits and heavy flow of materials. in the sem image, the dark layer shows the development of narrow grooves. the wornout surfaces of mmcs are concealed by micro pits, fine grooves, signifying that the wear mechanism is delaminating and ploughing. severe deformation & delamination is witnessed on the wornout surface of mmcs, signifying that the wear behavior is delamination. the load applied on the ceramic particulates, caused wrapping on the composite surface. generally, these hard ceramic particles acted like a wrapping material on the sliding surfaces which offered better wear resistance. figure 9: eds spectrum of nano composite specimen. m. ravikumar et alii, frattura ed integrità strutturale, 58 (2021) 166-178; doi: 10.3221/igf-esis.58.12 176 the ceramic particles are get deposited in the voids and it is observed that few particles have broken into pieces and some of the particulates are pulled away from the wornout face [18, 36]. it indicates the high rough wear mechanism which is due to the presence of hard ceramic particulates exposed on wornout surface. the microstructure shows that large numbers of narrow grooves were present on wornout surfaces of composite and nano composites. so, these parallel continuous grooves are the evidence for micro ploughing. wide ploughing can also be seen on the worn out surfaces of composite and nano composites which show prominent wear behavior in the mmcs. the sem analysis of the wornout surface of nanocomposites depicts the formation of narrow-grooves with dark layers. generally, this indicates that nano composite exhibits improved wear resistance when compared to the micro sized particulates reinforced al composites. the chance of debonding of nano particles due to the incessant sliding causes the particles to get slackened from the matrix material and get stuck among the sliding surfaces, whereas it might act like an abrader leading to a short period of wear. generally, this is the cause for enhanced wear rate [37, 38]. the energy dispersive spectroscopy study of nano particles reinforced composite is shown in fig. 9. the outcomes reveal that the presence of al, mg, c and o within in the interface layer. smaller volume of o (oxygen) was detected in eds study due to the formation of the oxide layer within the composites. from the outcomes, it is concluded that oxygen (o) noticed in eds study is due to the existence of alumina oxide (al2o3) content during composite preparation. the eds structures have been indexed to the combination of various elements and the other small peaks ascribed to the impurity [39 41]. conclusions n this research work, al7075 reinforced with al2o3 (micro / nano) were effectively fabricated by using stircasting method. the effects of micro nano sized al2o3 particulates on mechanical and wear behavior were been studied.  the optical microstructure images revealed that better grain refinement was found in composite and nano composite when compared to as-cast.  hardness and tensile strength values were enhanced with increasing reinforcement content with in the metal matrix. it is observed that nano composites exhibit better strength as compared to micro composites.  the fractured surfaces of the test samples indicated plenty of distributed shallow portions and dimples with different sizes with in the composites which also is in concurrence with the high ductility witnessed in the uts studies  the wear rate of composite and nano composite materials was enhanced as compared with as-cast and wear loss decreased up to a certain wt. % of reinforcement and then remained unaffected due to various factors such as wettability and agglomeration of nano reinforcement particles. this leads to reduction in the wear resistance of nanocomposite at higher wt. % of reinforcement content.  the wornout surfaces of mmcs are concealed by micro pits, narrow fine grooves, signifying that the wear mechanisms are delaminating and ploughing. severe deformation & delamination are witnessed on the wornout surface of mmcs which signifies that the wear behavior is delamination.  the eds study reveals the existence of al, mg, c and o within in the interface layer. smaller volume of o (oxygen) was noticed in eds study due to the progress of the oxide layer within the composites. from the outcomes, it is concluded that oxygen (o) noticed in eds study is due to the existence of alumina oxide (al2o3) content during composite preparation. references [1] avinash, l. t., ram prabhu, udayagiri, s. b., praveennath, g. k., manoj, g., munishamaiah, k. and srikanth, b. (2020). the effect of heat treatment on the mechanical and tribological properties of dual size sic reinforced a357 matrix composites. journal of material research and technology, 9(3), pp. 6434–6452. [2] madeva, n., deshapande., auradi., satish, b. b., samuel, d. and anilkumar, m. r.. (2021). mechanical and wear characterization of ceramic boron carbide-reinforced al2024 alloy metal composites. journal of bioand tribocorrosion, 7(19), pp. 1-12. [3] shanta, m., anil kumar, s. b., ashok kumar, m. and arunachalam, t. (2016). dry sliding wear and corrosion behaviour of al-based hybrid composites reinforced with micro-tip and micro/nano-al2o3p. trans indian inst met., 69(6), pp. 1155-1167. i m. ravikumar et alii, frattura ed integrità strutturale, 58 (2021) 166-178; doi: 10.3221/igf-esis.58.12 177 [4] gurmeet, s., jasgurpreet, s. c. and niraj, b. (2017). hardness and wear analysis of micro/nano sized sic reinforced aluminium composites. ijamr, 9(2), pp. 61-66. [5] lakhvir, s., baljinder, r. and amandeep, s. (2013). optimization of process parameter for stir casted aluminium metal matrix composite using taguchi method. ijret, 2(8), pp. 1-9. [6] sadegh, s., saeed, p. and omid, m. (2020). investigation of the effect of sr on the mechanical properties and microstructure of nano-alumina reinforced aluminum matrix composites by the vortical casting method. metals and materials international, doi: 10.1007/s12540-020-00715-8. [7] amar, m. and subrata, m. (2020). fabrication and microstructure of micro and nano silicon carbide reinforced copper metal matrix composites/nanocomposites. silicon, doi: 10.1007/s12633-020-00491-5. [8] kumaraswamy, j., vijay, k. and purushotham. (2021). effect of reinforcements on mechanical properties of nickel alloy hybrid metal matrix composites processed by sand mold technique. applied science and engineering progress, 14(1), pp. 44-51. [9] kenneth, k. a. and michael, b. (2013). mechanical behaviour of alumina reinforced aa 6063 metal matrix composites developed by two step stir casting process. acta technica corviniensis bulletin of engineering, 3, pp. 105-110. [10] velavan., mohan., anbuchezhiyan. and senthilkumar. (2021). implications of sic/al2o3 reinforced al-mg-zn alloy hybrid nano composites using vacuum sintering method. silicon, doi: 10.1007/s12633-020-00928-x. [11] mula., padhi., panigrahi., pabi and ghosh. (2009). on structure and mechanical properties of ultrasonically cast al2% al2o3 nanocomposite. materials research bulletin, 44, pp. 1154-1160. [12] huda., adil, a. m. and hussain, j. a. (2019). mechanical and wear behavior of aa7075 aluminum matrix composites reinforced by al2o3 nanoparticles. nanocomposites, doi: 10.1080/20550324.2019.1637576. [13] al-jafaari, m. (2017). cryogenic treatment effect on fatigue behavior of 2024 and 7075 aluminum alloys with nano alumina composite material [ph.d thesis]. university of technology, mechanical engineering department. [14] kannan. and ramanujam. (2017). comparative study on the mechanical and microstructural characterisation of aa 7075 nano and hybrid nanocomposites produced by stir and squeeze casting. journal of advanced research, 8, pp. 309-319. [15] sajjadi., ezatpour. and beygi. (2011). microstructure and mechanical properties of al-al2o3 micro and nano composites fabricated by stir casting. materials science and engineering, a 528, pp. 87658771. [16] omid, y., hamid, r. b., ali, r. a. and ermia, a. (2019). development of the properties of al/sic nano-composite fabricated by stir cast method by means of coating sic particles with al. silicon, 11, pp. 643-649. [17] tennur, g. u. and ege, a. d. (2018). properties of alsi9cu3 metal matrix micro and nano composites produced via stir casting. open chem., 16, pp. 726-731. [18] harichandran., selvakumar. and venkatachalam. (2016). high temperature wear behaviour of nano/micro b4c reinforced aluminium matrix composites fabricated by an ultrasonic cavitation-assisted solidification process. trans indian inst met, doi 10.1007/s12666-016-0856-1. [19] amar, mahato. and subrata, m. (2021). fabrication and microstructure of micro and nano silicon carbide reinforced copper metal matrix composites/nanocomposites. silicon, 13, pp. 1097-1105. [20] kumaraswamy, j., vijaya, k., purushotham. and suresh, r. (2021). thermal analysis of nickel alloy/al2o3/tio2 hybrid metal matrix composite in automotive engine exhaust valve using fea method. journal of thermal engineering, 7(3), pp. 415-428. [21] khushbu, d. k., debasis, c. and ray, b. c. (2013). synthesis and characterization of aluminium-alumina microand nano-composites by spark plasma sintering. materials research bulletin, 48(7), pp. 2535-2542. [22] zhang., tremblay. and dube. (2004), microstructure and mechanical properties of za104 (0.3-0.6ca) die-casting magnesium alloys. materials science and engineering, a 385, pp. 286-291. [23] razavi, t., yazdani, r. and sahebali, m. (2011). effect of volume fraction and particle size of alumina reinforcement on compaction and densification behavior of al-al2o3 nanocomposites, materials science and engineering, a 528(3), pp. 1105-1110. [24] kumaraswamy, j., vijaya, k. and purushotham, g. (2021). a review on mechanical and wear properties of astm a 494 m grade nickel-based alloy metal matrix composites. materials today: proceedings, 37, pp. 2027-2032. [25] abhishek, kumar., shyam, lal. and sudhir, k. (2013). fabrication and characterization of a359/al2o3 metal matrix composite using electromagnetic stir casting method. journal of material research and technology, 2(3), pp. 250254. m. ravikumar et alii, frattura ed integrità strutturale, 58 (2021) 166-178; doi: 10.3221/igf-esis.58.12 178 [26] sajjadi., ezatpour. and torabi, parizi. (2012). comparison of microstructure and mechanical properties of a356 aluminum alloy/al2o3 composites fabricated by stir and compo-casting processes. materials and design, 34, pp. 106111. [27] zhang. and chen. (2006). consideration of orowan strengthening effect in particulate-reinforced metal matrix nanocomposites: a model for predicting their yield strength. scripta materialia, 54, pp. 1321-1326. [28] hamid, r. e., seyed, a. s., mohsen, h. s. and yizhong, h. (2014). investigation of microstructure and mechanical properties of al6061-nanocomposite fabricated by stir casting. materials and design, 55, pp. 921-928. [29] shaik, m. q., suryanarayana, m. and pinninti, r. r. (2016). processing and mechanical properties of al2o3 and red mud particle reinforced aa6061 hybrid composites. journal of minerals and materials characterization and engineering, 4, pp. 135-142. [30] jufu, j., guanfei, x., changjie, c. and ying, w. (2018). microstructure, mechanical properties and wear behavior of the rheoformed 2024 aluminum matrix composite component reinforced by al2o3 nanoparticles. metals, 8 (460), doi: 10.3390/met8060460. [31] ali, m. and mohsen, o. (2011). investigation on mechanical properties of nano-al2o3-reinforced aluminum matrix composites. journal of composite materials, pp. 1-8. [32] kumaraswamy, j., vijaya, k. and purushotham, g. (2021). evaluation of the microstructure and thermal properties of (astm a 494 m grade) nickel alloy hybrid metal matrix composites processed by sand mold casting. international journal of ambient energy, pp. 1-11. doi: 10.1080/01430750.2021.1927836. [33] zhang. and chen. (2008). contribution of orowan strengthening effect in particulate-reinforced metal matrix nanocomposites. materials science and engineering, a 483-484, pp. 148-152. [34] razieh, y., esmaeil, e. and sadreddin, b. (2018). manufacturing of the aluminum metal-matrix composite reinforced with micro and nanoparticles of tio2 through accumulative roll bonding process (arb). rev. adv. mater. sci., 55, pp. 1-11. [35] ming-jie, s., tao, y., fu-yu, c. and jun-ming, h. (2016). effect of micro and nano-sic particulate reinforcements in magnesium-based metal matrix composites. jmepeg, 25, pp. 2222-2229. [36] rajesh, a. m., mohamed, k., saleemsab, d. and bharath, k. n. (2019). material characterization of sic and al2o3reinforced hybrid aluminum metal matrix composites on wear behavior. advanced composites letters, 28, pp. 1-10. [37] reddappa, h. n., niranjan, h. b., suresh, k. r. and satyanarayana, k. g. (2012). effect of quenching media and ageing time on al6061-beryl composites. applied mechanics and materials, 110 (116), pp. 1374-1379. [38] harichandran, r. and selvakumar, n. (2016). effect of nano/micro b4c particles on the mechanical properties of aluminium metal matrix composites fabricated by ultrasonic cavitation-assisted solidification process. archives of civil and mechanical engineering, 16, pp. 147-158. [39] ashokkumar, r. and devaraju, a. (2020). modeling of mechanical properties and high temperature wear behavior of al7075/sic/crs composite using rsm. silicon, doi: 10.1007/s12633-020-00801-x. [40] shorowordi, k. m., laoui, t., haseeb., celis, j. p. and froyen, l. (2003). microstructure and interface characteristics of b4c, sic and al2o3 reinforced al matrix composites: a comparative study. journal of materials processing technology, 142, pp. 738-743. [41] yogesh, k. s., rahul, c., hitesh, b. and anil, k. (2015). wear behavior of aluminum alloy 6061-based composites reinforced with sic, al2o3, and red mud: a comparative study. jom, 67 (9), pp. 2160-2169. microsoft word numero_29_art_26 a. infuso et alii, frattura ed integrità strutturale, 29 (2014) 302-312; doi: 10.3221/igf-esis.29.26 302 focussed on: computational mechanics and mechanics of materials in italy flaw-tolerance of nonlocal discrete systems and interpretation according to network theory a. infuso politecnico di torino, department of structural, geotechnical and building engineering, corso duca degli abruzzi 24, 10129 torino, italy andrea.infuso@polito.it m. paggi imt institute for advanced studies lucca, p.zza san francesco 19, 55100 lucca, italy marco.paggi@imtlucca.it abstract. discrete systems are modeled as a network of nodes (particles, molecules, or atoms) linked by nonlinear springs to simulate the action of van der waals forces. such systems are nonlocal if links connecting non-adjacent nodes are introduced. for their topological characterization, a nonlocality index (nli) inspired by network theory is proposed. the mechanical response of 1d and 2d nonlocal discrete systems is predicted according to finite element (fe) simulations based on a nonlinear spring element for large displacements implemented in the fe programme feap. uniaxial force-displacement responses of intact and defective systems (with links or nodes removed) are numerically simulated. strain localization phenomena, size-scale effects and the ability to tolerate defects are investigated by varying the degree of nonlocality. keywords. nonlocality; discrete systems; mdfem; large displacements; network theory. introduction onlocal continuum theories based on gradient models, integral formulations or fractional calculus have been widely explored in mechanics to describe long-range interactions (see e.g. [1-10], among others). at the same time, discrete systems composed of particles or molecules have been proposed in the physics community to analyze the behaviour of materials at the nano or micro scales. lattice beam models [11], albeit suffering from mesh dependency due to the local nature of the bonds/links, have been extensively used to simulate the meso-scale behavior of concrete. efforts accounting for nonlocal effects, such as the three-dimensional born model [12], have been proposed to study the distribution of broken bonds within a homogeneous discrete mechanical system. with the progress in computer technology, wide tridimensional discrete systems can nowadays be modelled by molecular dynamics (md), accounting for nonlinear interatomic potential laws and nonlocal interactions among the discrete molecules. attempts to couple md with fem have been explored in [13], with the intent to perform multi-scale analyses where discrete systems are connected to continuum finite elements. in the present study, the ability of nonlocal molecular systems to tolerate flaws is investigated. to this aim, a nonlinear spring element for large displacements whose constitutive relation is ruled by van der waals forces is implemented in the n a. infuso et alii, frattura ed integrità strutturale, 29 (2014) 302-312; doi: 10.3221/igf-esis.29.26 303 finite element analysis programme feap. the tensile and compressive responses of 1d and 2d discrete systems of molecules with or without flaws are numerically simulated, by varying the range of nonlocal interactions defined by a novel nonlocality index nli inspired by graph and network theories. for each system, the distribution of the internal forces at different load levels is analyzed in relation to the topological properties of the underlying network, in order to understand the force redistribution mechanisms in the presence of defects. finite element formulation onsidering a discrete system composed of atoms or molecules subjected by nonlinear interactions governed by generalized lennard-jones potentials, graph theory can be efficiently invoked for their characterization. atoms can be topologically represented by nodes and the nonlinear interactions between them can be modelled by a set of nonlinear springs. in this framework, each link can be implemented as a finite element defined by two nodes whose coordinates in the initial global undeformed reference system are: x  (x1, y1, x2 , y2 ) t (1) each i-th node (i=1,2) has two translational degrees of freedoms in case of 2d problems, ui and vi, collected in the element displacement vector u: u (u1, v1, u2 , v2 ) t (2) the nodal coordinates vector in the updated configuration is given by: x x u (3) a local reference system is now introduced, since the constitutive relation is usually defined in this frame. hence, the normal vector n pointing from node 1' to node 2' and the vector t perpendicular to the link are introduced, see fig. 1. the origin of the local reference system is in the node 1'. such a frame is rotated by an angle  with respect to the axis of the global reference system. the following rotation matrix r can be introduced: r  cos sin sin cos       (4) figure 1: reference coordinate systems for the large displacements analysis. the gap vector g collecting the relative opening and sliding displacements between the nodes 1' and 2' is given by the product between a matrix operator l and the position vector x containing the coordinates of the element nodes in the updated configuration: g lx (5) where the matrix l takes the form: l  1 0 1 0 0 1 0 1       (6) c a. infuso et alii, frattura ed integrità strutturale, 29 (2014) 302-312; doi: 10.3221/igf-esis.29.26 304 the gap vector between the nodes in the local reference system is obtained by the product between the rotation matrix r and the gap vector g: gloc  rg (7) the constitutive law used here stems from a generalization of the lennard-jones (l-j) potentials: plj  4 r0 gn       r0 gn             (8) where  is the depth of the potential well, r0 is the distance at which the potential between two neighbouring atoms is equal to zero, , are the parameters defining the shape of the l-j potential. keeping the exponents , as free parameters was suggested in [14-16] to bypass the rapid decay of the law after the equilibrium point and being able compute non-bonded interactions between nodes also at longer distances, or for coarse-grained representations. the corresponding displacement-force relation can be obtained by differentiating the l-j potential with respect to the normal opening displacement gn: flj (gn)  plj (gn)   d d(gn) plj (gn)  4  r0  gn 1      r0  gn 1           (9) in the proposed formula, whose graphical trend is depicted in fig. 2(a), the first term in brackets represents the repulsive force contribution between atoms (pauli repulsion), while the second one describe the long-range attractive force (van der waals force). different force-displacement curves are shown in fig. 2(b) by varying the parameters of the model. in the numerical simulations discussed in the next sections, the selected parameters are   13 and   2 . (a) (b) figure 2: (a) lennard-jones potential law: attractive and repulsive branches. (b) different force-displacement forces by varying and  : the red curve refers to l-j potential in fig. 2(a). the blue curve is the modified law used in this study. the force in eq. (9) directed along the normal vector n is collected in the local force vector, floc  (flj , 0) t . starting from the principle of virtual work where each element contribution is related to the scalar product between the force vector and the gap vector as for a classical interface element [17,18], its virtual variation and fully consistent linearization have to be performed in order to derive the residual vector p and the stiffness matrix k for the application of the newtonraphson iterative procedure. after a lengthy calculation, which is here omitted for the sake of brevity, we obtain:                             crl u r lulu u r crllu u r c u r luk crlrlk kkk flu u r rlp t tttt t tt geom tt mat geommat loc t (10) a. infuso et alii, frattura ed integrità strutturale, 29 (2014) 302-312; doi: 10.3221/igf-esis.29.26 305 where c is the tangent operator stemming from the consistent linearization of the local force vector floc with respect to the local gap vector gloc: c  flj gn 0 0 0           (11) whereas the term r / u related to the differentiation of the rotation matrix with respect to the displacements vector is a third order tensor. this mathematical formulation has been implemented in the finite element analysis program feap [19]. a flow chart of the operations is shown in tab. 1. table 1: sequence of element operations. numerical investigation: monodimensional model he first step of the study is the understanding of the nonlinear behaviour of a l-j nonlocal system of atoms for different degrees of nonlocality. let us consider a 1d system of nodes representing atoms equally spaced by a length l0 along a straight line. a local system would be represented by the case where only local interactions take place between each node and its nearest neighbours (fig. 4(a)). this is just a mechanical system of nonlinear springs in series, where the removal of a link (failure of one spring) leads to the failure of the entire chain (fig. 4(b)). (a) (b) figure 4: (a) system with only local links. (b) collapse of the system due to failure of just one link. long range interactions can be modelled by introducing additional links between a generic node and the nodes located at distances 2 l0 , 3l0 ,… and so forth. various systems with different degree of nonlocality can be generated by changing the cut-off distance for nonlocal interactions. for comparison purposes, it is useful to introduce a dimensionless number nli (nonlocality index) synthesizing the topological properties of the system: nli  max(li ) l0 (12) where li is the length of the i-th link between two connected nodes and l0 is the length of the local link between two adjacent nodes. therefore, nli=1 corresponds to a local system, whereas nli>1 refers to systems with long range interactions. as a first example, let us consider the uniaxial tension test for a system composed of 5 nodes and nli=2 (fig. 5(a)). four local links are present and three additional links due to long-range interactions are introduced. for a preliminary qualitative analysis of the system, a linearized version would consist in springs with different stiffnesses ki, depending on t loop until convergence of the newton-raphson scheme call to the element subroutine input: x initial nodal coordinates, u nodal displacements compute: updated coordinates x=x+u rotation matrix r and gap vector g (eq. 5) gap vector in the local frame gloc (eq. 7) local force vector floc and the tangent operator c (eq. 11) output: residual vector p and tangent stiffness matrix k (eq. 10) end loop a. infuso et alii, frattura ed integrità strutturale, 29 (2014) 302-312; doi: 10.3221/igf-esis.29.26 306 the distance between the connected nodes. due to the symmetry of the problem, only half model can be analyzed (fig. 5(b)). figure 5: (a) complete 5 nodes nli=2 system. (b) simplified configuration due to the symmetry. for a given set of stiffnesses, it is possible to compute analytically the relation between the displacement  of the whole system and the displacement i of each single spring, satisfying the equilibrium and the congruence: 1  k2  2 k4 k1  k2  2 k4  2  k1 k1  k2  2 k4  3            (13) the relations between the spring forces and the total imposed displacement  are: f1  k1 1  k1  k2  2 k4 k1  k2  2 k4  f2  k2 2  k2  k1 k1  k2  2 k4  f3  k3  f4  k4 2 2  k4  2 k1 k1  k2  2 k4             (14) these analytical results provide some qualitative information on the solution of the fully nonlinear system. in general, comparing 1 and 2 in eq.(13), we expect 1 > 2, which is a main difference with respect to a purely local system where all the local springs experience the same elongation. moreover, if a spring is removed, then the system has still an equilibrium configuration, whereas a purely local system would fail. the solution of the fully nonlinear problem is discussed in the next subsections. monodimensional model without defects: the effect of nonlocality and system size let us consider the discrete system in fig. 6 with nli=1, 2 or 3. in the local system characterized by springs in series, the forces and the elongations are the same for all the springs. each spring presents an increasing branch until the achievement of the maximum force and then a softening, according to the l-j constitutive equation (9). in case of nli=2, the situation is much more complex. due to the symmetry, it is sufficient to comment on the behaviour of the springs 1, 2, 5 and 6. the forces in such springs vs. the total imposed displacement  are shown in fig. 7(a). the positions of the nodes of each spring vs.  are illustrated in fig. 7(b). from these diagrams we note that springs (a) (b) a. infuso et alii, frattura ed integrità strutturale, 29 (2014) 302-312; doi: 10.3221/igf-esis.29.26 307 1 and 5 have elongations monotonically increasing during the simulation. the force level of the local spring 1 is much higher than that of the nonlocal spring 5. this is due to the fact the spring 5 is connecting nodes that are at an initial distance twice larger than that of the spring 1. springs 2 and 6, after an initial positive relative displacement between their connected nodes, then experience a progressive reduction of their elongations with a consequent elastic unloading. figure 6: sketch of the discrete system with 5 nodes by varying nli. (a) nli=1; (b) nli=2; (c) nli=3. (a) (b) figure 7: system with 5 nodes and nli=2. (a) spring forces vs. imposed displacement. (b) spring nodal positions vs. imposed displacement. a similar response takes place for the system with nli=3. springs 1, 5 and 6 have an elongation monotonically increasing with time, whereas springs 2 and 6 experience an elastic unloading after an initial increased separation. a comparison between the force-displacement curves of the various systems depending on nli is shown in fig. 8(a). the nonlocality increase the peak force observed in case of nli=1. moreover, a gain in the capacity of tolerating defects takes place, as we will quantify in the next subsection. the difference between the responses of the systems with nli=2 and nli=3 is quite small, in line with the observation that nonlocal interactions are rapidly decaying by increasing the nodal distance, see fig. 2(b). (b) (c) (a) a. infuso et alii, frattura ed integrità strutturale, 29 (2014) 302-312; doi: 10.3221/igf-esis.29.26 308 (a) (b) figure 8: global force vs. global displacement curves. (a) the effect of nli for a system with a size h 4 l0 . (b) the effect of the size h of the system with nli=2. for a given degree of nonlocality, e.g., nli=2, the effect of the size of the system can be explored by increasing the number of nodes at a distance l0 for each pair (see fig. 8(b)). as a trend, the peak force does not change, whereas the post-peak response becomes more and more brittle by increasing h. monodimensional model with defects let us consider a system with 5 nodes ( h 4 l0 ) and with a broken link (see fig. 9(a)). this can be the case in nanoscopic systems when there is an atomic vacancy or a weakened interatomic potential due to dislocations. the problem is solved numerically under displacement control and a very complex behaviour of the various springs is observed. to comment on that, it is useful to analyze the force-nodal distance curve of each spring, fig. 9(b). all the springs in series (1, 3, 4) are initially in the initial branch of the van der waals forces and all of them experience an elastic unloading (see the direction of the arrows in fig. 9(b)). springs 5, 6 and 7 used to model long-range interactions are all in the softening branch of the van der waals force diagram. the spring 7 experiences an increasing in the corresponding load level due to the shortening of springs 3 and 4. on the other hand, 5 and 6 increase their elongation monotonically in time. the global response, shown in fig. 10(a) presents softening due to the heavy damage induced by the removal of a local link. however, the defect can be tolerated due to the nonlocality and the load-carrying capacity of the system is an increasing function of nli, see fig. 10(a). by increasing the system size and removing only the second spring in all the cases, the force is an increasing function of h as shown in fig. 10(b), as the same was observed in case of a defect-free system. (a) (b) figure 9: (a) geometry of the 5 nodes system without the link no. 2. (b) force-displacement diagram of the springs. a. infuso et alii, frattura ed integrità strutturale, 29 (2014) 302-312; doi: 10.3221/igf-esis.29.26 309 (a) (b) figure 10: global force-displacement response. (a) the effect of nli ( h 4 l0 ). (b) the effect of the system size (nli=2). numerical investigation: bidimensional model computational complexity s is the monodimensional case, a bidimensional system can be modelled as a collection of nodes and links, thus forming a grid in the plane. an hexagonal disposition of nodes is adopted to simulate materials like graphene. also in this case the nli can be defined as the maximum cut-off radius for long range interactions and the length of the link for pure local connections. the numerical construction of the finite element meshes for numerical simulations requires the definition of the list of nodes and the element connectivity matrix. for the latter, a pre-processor written in matlab® has been developed where, centering in the i-th node of the grid, all the other nodes within the cut-off radius defined by the product nli l0 are identified and spring elements are inserted. clearly, by increasing nli and the size of the system, the computational complexity drastically increases. as an illustrative example, let us consider square grids with l0=3.5å and with lateral size 14x14 å, 31x31 å, and 70x70 å, respectively. for each grid, the nli can range from 1 up to a maximum value nlimax, given by the longest distance between two nodes belonging to the system. for the three system sizes considered, we have nlimax  6,12 and 29. the maximum number of links in case of nlimaxis equal to 600 for the smallest system, 4,851 for the intermediate system, and 126,756 for the largest one. in dimensionless form, fig. 11, the ratio between the number of links and the maximum value has a nonlinear dependency with the ratio between nli and nlimax. the deviation from linearity observed for all the cases when nli is approaching nlimaxis due to the finite size of the system. figure 11: number of links vs. nli in dimensionless form, for 3 systems with different sizes. a a. infuso et alii, frattura ed integrità strutturale, 29 (2014) 302-312; doi: 10.3221/igf-esis.29.26 310 as far as the numerical simulations are concerned, the increase of nli leads to a transition from a sparse connectivity matrix to a very dense one, see fig. 12 where systems with nli=1, 2 and 3 are compared. flaw-tolerance in this section, the behaviour of the bi-dimensional system subjected to uniaxial tension in the vertical direction is investigated. we compare the case where all the links are present with other three cases presenting defects: (1) removal of a single node in the centre of the specimen; (2) removal of 2 not adjacent nodes; (3) removal of 2 adjacent nodes. three different values of nli are considered for each system: nli=1 (local system), nli=2, nli=3. a sketch of the three configurations with defects are shown in fig. 13 for the case with nli=1. (a.1) nli=1 (a.2) nli=2 (a.3) nli=3 (b.1) nli=1 (b.2) nli=2 (b.3) nli=3 figure 12: (a) representation of the bidimensional hexagonal geometric network by varying nli. (b) connectivity matrices for the same nli. (a) case 1 (b) case 2 (c) case 3 figure 13: representation of the bidimensional hexagonal network with different types of flaws (nli=1). the global force vs. displacement curves for all the examined configurations are shown in fig. 14. for a given value of nli, we note that case 3 leads to the higher load and stiffness reduction. case 1 is the less critical one, whereas case 2 a. infuso et alii, frattura ed integrità strutturale, 29 (2014) 302-312; doi: 10.3221/igf-esis.29.26 311 provides an intermediate response. this trend is in line with the fact that the removal of two adjacent nodes is particularly critical and induces a significant number of removed links. the effect of nli is particularly important. the system with nli=1 is initially compressed, due to the fact that the nodes are initially at a distance slightly smaller than the equilibrium one given by the l-j potential. by increasing nli, further links in a tension state are introduced and reduce this initial compressive stress state. although the nodes removal has a higher impact on the systems characterized by higher nonlocality indices since a larger number of links is removed, the force is an increasing function of nli, thus showing that nonlocality has a very important role for flaw-tolerance. figure 14: comparison of the force-displacement curves varying nli, depending on the type of defect. conclusions aking into consideration nonbonded interactions between nodes according to the l-j generalized potential, the influence of nonlocality on the mechanical response of discrete systems has been investigated. in the monodimensional case, we have observed a complex behaviour of the links depending on the nonlocality index nli. in the case of a link absent or removed, a phenomenon analogous to strain localization observed in continuum systems has been evidenced. results on bi-dimensional systems have also shown the important role exerted by the nonlocality on the load carrying capacity of the system and its ability to tolerate defects or vacancies. the proposed approach and its further extension to 3d can be applied to predict strength and stiffness of discrete systems as, e.g., 2d graphene layers of carbon-carbon bonds, or nanotubes, represented by a 3d network of carbon atoms. moreover, a constitutive law based on l-j potential is definitely useful to study problems where interactions between two different materials are governed by nonbonded forces. this is for example the case of an interphase boundary interaction between collagen and graphene. future developments regarding the implementation of bonded interactions, including not only stretching energy, but also bending and torsion energy contributions to describe physical links between atoms or molecules, are envisaged. acknowledgements he financial support of the italian ministry of education, university and research to the project firb 2010 future in research “structural mechanics models for renewable energy applications” (rbfr107akg) is gratefully acknowledged. references [1] aifantis, e.c. ,on the gradient approach – relation to eringen’s nonlocal theory, int. j. eng. sci., 49 (2001) 1367t t a. infuso et alii, frattura ed integrità strutturale, 29 (2014) 302-312; doi: 10.3221/igf-esis.29.26 312 1377. [2] peerlings, r.h.j., de borst, r., brekelmans, w.a.m., de vree, j.h.p., gradient enhanced damage for quasi-brittle materials, int. j. numer. meth. eng. , 39 (1996) 3391-3403. [3] eringen, a.c., kim, b.s., relation between non-local elasticity and lattice dynamics, crystal lattice defects , 7 (1977) 51-57. [4] di paola, m., zingales, m., long-range cohesive interactions of non-local continuum faced by fractional calculus, int. j. solids struct., 45 (2008) 5642-5659.
 [5] carpinteri, a., cornetti, p., sapora, a., di paola, m., zingales, m., fractional calculus in solid mechanics: local vs non-local approach, physica scripta, t136 (2009) 014003-014010. [6] di paola, m., marino, f., zingales, m., a generalized model of elastic foundation based on long-range interactions: integral and fractional model, int. j. solids struct, 46 (2009) 3124-3117. [7] di paola, m. failla, g., zingales, m., physically based approach to the mechanics of strong non-local linear elasticity theory, j. elasticity, 97 (2009) 103-130. [8] bertoldi, k., bigoni d., drugan, w.j., structural interfaces in linear elasticity. part i: nonlocality and gradient approximations, j. mech. phys. solids, 55(1) (2007), 1-34. [9] marfia, s., sacco, e., toti, j., a coupled interface-body nonlocal damage model for frp strengthening detachment, comput. mech., 50(3) (2012), 335-351. [10] giambanco, g., fileccia scimeni, g., spada, a., the interphase finite element, comput. mech., 50(3) (2012), 353-366. [11] van mier, j.g.m., schlangen, e., vervuurt, a., lattice type fracture models for concrete, h.b. mühlhaus (ed.), continuum models for materials with microstructure, john wiley & sons (1995), 341-377. [12] parisi, a., caldarelli, g., pietronero, l., roughness of fracture surfaces, epl, 52 (3), (2000), 304-310. [13] nasdala, l., kempe, a., rolfes, r., the molecular dynamic finite element method (mdfem), cmc 19 (2010) 57-104. [14] tan, h., jiang, l.y., huang, y., liu, b., hwang, k.c., the effect of van der waals-based interface cohesive law on carbon nanotube-reinforced composite materials, compos. sci. technol. 67 (2007) 2941–2946. [15] jiang, l.y., huang, y., jiang, h., ravichandran, g., gao, h., hwang, k.c., liu, b., a cohesive law for carbon nanotube/polymer interfaces based on the van der waals force, j. mech. phys. solids 54 (2006) 2436-2452. [16] van mier, j.g.m., multi-scale interaction potentials (f-r) for describing fracture of brittle disordered materials like cement and concrete, int. j. fract., 143 (2007) 41-78. [17] paggi, m., wriggers, p., a nonlocal cohesive zone model for finite thickness interfaces – part i: mathematical formulation and validation with molecular dynamics, comp. mat. sci., 50 (2011) 1625-1633. [18] paggi, m., wriggers, p., a nonlocal cohesive zone model for finite thickness interfaces – part ii: fe implementation and application to polycrystalline materials, comp. mat. sci., 50 (2011) 1634-1643. [19] zienkiewicz, o.c., taylor, r.l., the finite element method, 6th edition, elsevier oxford, 1 2, (2005). shot peening processes to obtain nanocrystalline surfaces in metal alloys: z.-y. han et alii, frattura ed integrità strutturale, 50 (2019) 21-28; doi: 10.3221/igf-esis.50.03 20 stress corrosion behavior of x80 pipeline steel in the natural seawater with different dissolved oxygen contents zhong-ying han school of petroleum engineering, china university of petroleum (east china), qingdao, 266580, china. hanzhying@upc.edu.cn xiao-guang huang college of pipeline and civil engineering, china university of petroleum (east china), qingdao, 266580, china. huangxg@upc.edu.cn abstract. stress corrosion slow strain rate tensile tests of the x80 steel in the natural seawater are carried out to study the effect of dissolved oxygen (do) on the sensitivity of stress corrosion. scanning electron microscope (sem) combined with the electrochemical measurement is adopted to analyze the mechanism and affecting factor of the stress corrosion cracking (scc). the results show that the sensitivity of scc in the natural seawater increases and the stress corrosion cracking gradually transforms from ductile to quasibrittle fracture, with the increase of dissolved oxygen content. tafle polarization curves and electrochemical impedance spectroscopy of x80 steel show that the dissolved oxygen aggravates the electrochemical corrosion and reduces the corrosion resistance. the corrosion pits and micro cracks at the lateral and fracture surface trigger the stress concentration and promote the anodic dissolution under the applied stress, thereby accelerate the process of stress corrosion cracking of the x80 steel. keywords. stress corrosion; dissolved oxygen; sensitivity; stress concentration; anodic dissolution. citation: han, z. y., huang, x. g., stress corrosion behavior of x80 pipeline steel in natural seawater with different dissolved oxygen, frattura ed integrità strutturale, 50 (2019) 20-28. received: 11.04.2018 accepted: 07.07.2019 published: 01.10.2019 copyright: © 2019 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. introduction ubmarine pipeline is an indispensable part and the lifeline of offshore oil-gas exploitation. during the laying and service period, submarine pipelines are often subjected to various loadings, such as the internal pressure, temperature, bending, and wave and flow [1-2]. under the interaction of these external loadings, the inner and outer coatings of pipeline are easy to break or fall off. once the seawater penetrates, the corrosion of pipeline is inevitable. the coupling effect of corrosion and stress is easy to induce the stress corrosion failure even under very lower stress and this greatly shortens the service life of the pipeline [3-4]. rupture of the pipeline and the accompanying oil leakage often result in a s http://www.gruppofrattura.it/va/50/2478.mp4 z.-y. han et alii, frattura ed integrità strutturale, 50 (2019) 21-28; doi: 10.3221/igf-esis.50.03 21 serious environmental pollution and huge economic losses. therefore, stress corrosion failure has aroused a worthy concern for safe service of the submarine pipeline [5-6]. stress corrosion cracking (scc) is a low-stress brittle cracking phenomenon of pipeline steel under the coupling of stress and a specific corrosive environment. unlike corrosion fatigue, stress corrosion has an obvious dependence on material and environment. scc occurs in an environment that contains corrosive media such as co2, h2s, cl-, oh-, hco3-, and co32 [7]. according to the ph value of the service environment, scc of the pipelines steel can be divided into high, near neutral and low ph types. at present, the research on the scc of the pipeline steel mainly focuses on the near neutral and high-ph scc. the high-ph scc mainly occurs in the soil environment (ph 8~10.5) with high concentration of na2co3 and nahco3 and induces an intergranular cracking [8]. the mechanism of the high-ph scc is consistently recognized to be the film rupture and slip dissolution [9-10]. however, the transgranular scc often occurs in the near neutral (ph 6~8) environment. at present, the stress corrosion mechanism of pipeline steel in a near neutral environment has been widely accepted as the interaction of anodic dissolution and hydrogen embrittlement. however, in a marine environment, the situation may be more serious. for example, high concentration of claccelerates the pitting corrosion and greatly promote the crack nucleation of scc [11]. additionally, the subsea is a complex and changeable corrosive environment with various hydrostatic pressures, varying do contents and ph values at different depths [12]. a number of studies have been performed to investigate the corrosion behavior of pipeline steel in the natural marine environment [13-15]. however, research work on the stress corrosion behavior of x80 pipeline steel in the natural seawater is very limited. in this paper, the slow strain rate tensile (ssrt) tests of x80 steel were conducted to study the sensitivity of stress corrosion cracking in the natural seawater with different do contents. sem analyses of the lateral and fracture surface were complemented to investigate the mechanism of stress corrosion in different environments. electrochemical polarization and impedance spectroscopy of the stressed x80 samples in the seawater were measured to explain the effect of do on the corrosion and stress corrosion behavior. also, a model that stress concentration promotes the anodic dissolution and the scc fracture is adopted to explain this accelerating effect once the corrosion pits and microcracks are formed. figure 1: microstructure of x80 steel. experimental process samples he selected x80 pipeline steel for stress corrosion ssrt tests contains (w.t. %) 0.055 c, 1.392 mn, 0.328 mo, 0.202 si, 0.264 ni, 0.0017 p, 0.002 s, 0.032 cr, 0.017 al, and fe rem. the microstructure of x80 pipeline steel is shown in fig. 1. the microstructure is composed of acicular ferrite (af), polygonal ferrite (pf), bainite (b), and many small precipitates dispersed in the matrix. the tested yield strength σs and tensile strength σb of x80 steel are 680mpa and 710mpa, respectively, which indicated that the x80 steel has a better ability to resist deformation. the plate-shaped specimen shown in fig. 2 is machined from an x80 steel plate by wire-cutting and fine grinding to achieve the requirement of accuracy. according to the literature [11], the do content in seawater of china sea varies from 2.6 to 6.8mg/l, gradually decreasing from 6.8% at shallow sea to 2.6 % along with the depth of the seawater. to analyze the effect of do on the stress corrosion af b pf t z.-y. han et alii, frattura ed integrità strutturale, 50 (2019) 21-28; doi: 10.3221/igf-esis.50.03 22 behavior, the do content of the natural seawater (do: 6.8 mg/l) is regulated to 2.6, and 4.7 mg/l respectively by infilling with the high purity nitrogen (99.9%), and the amount of nitrogen for each do is obtained through the pre-test monitored by a jpb-607 dissolved oxygen meter. experimental preparation the ssrt tests were run on a hlfs−50 slow strain rate tensile test system at a strain rate of 1×10-6 s-1. during the ssrt tests, the system automatically recorded the stress-displacement curves, as well as the fractured lives of the samples. each test was reproduced at least three times to ensure the reliability of the experimental data. the scc sensitivity of the sample was evaluated by the elongation-loss rate ( i ) and the reduction-in-area loss rate ( i ). the definitions of these two parameters are: s 01 / 100%( )i  = −  (1） s 01 / 100%( )i  = −  (2） where s and s , 0 and 0 are the elongation and reduction-in-area in air and in the seawater, respectively. after the ssrt tests, the fracture surfaces of the specimens were cleaned by the distilled water and ethanol, respectively. a scanning electron microscope (sem) was used to analyze the stress corrosion mechanism of the x80 steel in the seawater with different do contents. figure 2: dimensions of the ssrt test specimen (unit: mm). experimental results results of ssrt he stress-strain curves of the x80 specimens measured in the seawater with different do contents are shown in fig. 3, and the stress-strain curve in air is also depicted for comparison. the tensile strength and elongation of x80 steel in seawater are obviously lower than that in air, and this decline increase with the increasing do, indicating that x80 steel has a strong susceptibility of scc to the do in the seawater. the time-to-fracture of x80 steel in different environments can be obtained by the ssrt tests, as shown in fig. 4. the stress corrosion lives decrease with the increase of do, i.e., the stress corrosion of x80 steel is more serious in the shallow sea. additionally, to investigate the sensitivity of scc in the seawaters, two sensitivity factors of x80 steel, i and i , in different environments are also shown in fig. 5. as the do increases, both i and i decrease at different extents, when compared with 42.1 % i and 31.4 % i measured in air. fracture morphologies of ssrt tests fig. 6 demonstrates the sem images of the fractured surfaces after the ssrt tests in the seawater with different do contents. the macro fracture morphology of x80 steel shows an apparent necking deformation when tested in air. while in the seawater, the necking deformation weakens with the increase of do. the fracture surface in air exhibits many ductile dimples, showing a good ductile fracture property. while in the seawater, the appearances are completely different. the 140.0 40.0 40.0 8.0r 1 6 .0 2 .0 6 .0 6.0 12.0 unit: mm t z.-y. han et alii, frattura ed integrità strutturale, 50 (2019) 21-28; doi: 10.3221/igf-esis.50.03 23 fracture region of x80 steel possesses some quasi-cleavage zones when testing in the 2.6% do seawater, and there are still some small ductile dimples next to most quasi-cleavage of the fracture surface, as shown in fig. 6(b). but the number of ductile dimples decreases and the size of ductile dimples also shrinks when do increases to 6.8%, and the fracture surface is primarily composed of quasi-cleavage which is seen as the main characteristic of transgranular fracture, as shown in fig. 6(d). it indicates that the fracture in the seawater gradually transforms from ductile fracture to brittle one with the increase of do content. at the same time, a large number of stripes in river patterns appear at the fracture surface, showing the increase of scc susceptibility with the increase of do content. figure 3: stress-strain curves of the x80 samples measured in the ssrt tests. figure 4: times to fracture of x80 samples in the seawater with different do contents. figure 5: scc sensitivities (elongation-loss rate iδ, and reduction-in-area loss rate iψ) of the x80 samples in the seawater with different do contents fig. 7 shows the morphology evolution at the lateral surface of the samples in the seawater with 6.8% and 2.6% do during the ssrt process. it can be seen that the microcracks gradually nucleates on the lateral surface of the sample with the testing time. in the 2.6% do environment, the visible corrosion pits and microcracks begin to emerge after 75 h, but at this moment, the lateral surface is covered with dense corrosion pits and microcracks in the 6.8% do environment. then micro cracks gradually merge and expand, eventually lead to the fracture of the samples. comparing these two sets of images, the microcrack distributions at the lateral surface in the 6.8% do seawater are more serious than that in 2.6 % do environment, indicating that the dissolved oxygen accelerates corrosion and induces the nucleation of micro crack. the observations are consistent with the results of the rrst tests, and the dissolved oxygen increases the sensitivity of stress corrosion and shortens the stress corrosion life of x80 steel in the natural seawater. 0 100 200 300 400 500 600 700 800 0 5 10 15 20 25 s tr e ss / m p a strain /% 图表标题 in air do 2.6% do 4.7% do 6.8% 0 30 60 90 120 150 180 t im e t o f ra c tu re / h do=2.6% do=4.7% do=6.8% 0 10 20 30 40 2 4 6 8 do / % s c c s e n si ti v it y / % i  i  z.-y. han et alii, frattura ed integrità strutturale, 50 (2019) 21-28; doi: 10.3221/igf-esis.50.03 24 figure 6: sem images of the fracture surfaces of x80 steels in (a) in air, (b) 2.6 % do, (c) 4.7 % do, (d) 6.8 % do figure 7: variation of the lateral morphology of the samples with testing time b 50 50 a quasi-cleavage zones c d 50 50 quasi-cleavage zones 25h 50h 100h75h 25h 50h 100h75h do=2.6% do=6.8% z.-y. han et alii, frattura ed integrità strutturale, 50 (2019) 21-28; doi: 10.3221/igf-esis.50.03 25 discussion effect of do on electrochemistry corrosion o investigate the mechanism that the do content accelerates the scc of x80 steel in the natural seawater, the method of electrochemistry measurement was adopted to study the corrosion behavior in the seawater with different do content. the potentiodynamic polarization measurements were performed in perkin-elmer m283 constant potential electrochemical testing system. polarization measurements were conducted starting from -250 mv (vs open circuit potential), and scanned toward more positive direction with scanning rate of 0.5 mv/s. electrochemical impedance spectroscopy (eis) measurements were carried out with a sinusoidal perturbation of 10 mv amplitude at measurement frequency ranging from100 khz-100 mhz, aided by m1025 frequency response instrument. fig. 8(a) depicts the results of tafle polarization and eis nyquist circuits of x80 steel in the seawater with different do, and the fitting results of tafle polarization curves are listed in tab. 1. it can be seen that (i) the cathodic depolarization reaction gradually transforms from the oxygen reduction reaction to the hydrogen evolution reaction; (ii) the cathodic reaction is suppressed, the cathodic tafel slope bc decreases and the anodic tafel slope ba increases; and (iii) the corrosion current density icorr decreases from 21.364×10−6 a/ cm2 to 4.678×10−6 a/cm2, with the decrease of do. fig. 8(b) shows the electrochemical impedance spectroscopy of x80 steel under different do contents. it can be seen that in the low do environment, the capacitive reactance arc of x80 steel is larger than that under high do environment, indicating that the decrease of do resulting in an increase of corrosion resistance. at the same time, the higher resistance of the reaction decreases the corrosion rate, which is consistent with the results obtained by the polarization curve. figure 8: results of electrochemical measurements: (a) tafle polarization curves; (b) nyquist plots. do(%) ecorr (v) icorr (μa.cm2) ba (v.dec-1) bc (v.dec-1) 2.6 -0.883 4.678 0.093 0.038 4.7 -0.866 9.332 0.087 0.097 6.8 -0.856 21.364 0.072 0.153 table 1: the instantaneous electrochemical parameters from polarization curve. stress concentration promotes scc fracture the stress corrosion mechanism of x80 steel in the seawater is widely recognized as the combined effect of corrosion pits or hydrogen-induced cracking [16-17]. therefore, the formation of corrosion pit during stress corrosion process is strongly influenced by the tensile stress [18-19]. from fig. 6, there are numerous corrosion pits and micro cracks at the lateral surface of the tested sample, and these defects, especially microcracks can cause a serious stress concentration, as shown in fig. 9. corresponding to the principle of thermodynamics and electrochemical theory, the anodic dissolution current density ip under an active dissolution condition, such as corrosion pit and microcrack, can be expressed as [16, 20] 0 1000 2000 3000 4000 5000 6000 0 2000 4000 6000 do-2.6% do-4.7% do-6.8% 2 re / cmz  2 m / c m z  b -1 -0.9 -0.8 -0.7 -0.6 -0.5 -0.4 -6 -5 -4 -3 -2 -1 0 1 do-2.6% do-4.7% do-6.8% 2 lg (a.cm )i − s c e ( v ) e a t z.-y. han et alii, frattura ed integrità strutturale, 50 (2019) 21-28; doi: 10.3221/igf-esis.50.03 26 1 1 p 0 0 p 0 ( ) exp( ) exp( ) (1 ) m m s m m mg i i i k i rt m p rt    + + + = = = + (3） where δg is the change of gibbs free energy, r is universal gas constant, t is absolute temperature value, i0 is anodic dissolution current density in the condition of no applied stress, m and ρ are the molar mass and the density of the electrode material, p and m are the material constants using the ramberg-osgood power model, σs is the yielding strength of the electrode material, and kp is the current concentration factor. figure 9: stress concentration at the corrosion pit and microcrack: (a) corrosion pit, (b) microcrack. from fig. 9, the stresses at the bottom of the corrosion pit and the tip of crack are far bigger than the applied tensile stress. according to eqn. (3), the anodic dissolution current density ip increases drastically, which significantly promote the anodic dissolution of the metal at the pits and microcracks, resulting in the accelerating loss in cross-sectional area and fracture process of the sample. fig. 10 depicts the variation of current concentration factor kp with the concentrated stress, and the measured current densities of x80 steel from ref. [19] are quoted and were depicted in fig. 10 for comparison. although the current concentration factors of the measured currents under different stresses have certain differences with the theoretical kp, the fact that high stress increases the anode dissolution current can be affirmative. from the above analysis, it can be seen that even under lower applied stress, the stress concentration can cause local high stress at the corrosion pit and crack tip. the interaction of high stress and electrochemical reaction promotes the anodic dissolution and the growth of corrosion pits and cracks, thereby accelerates the process of stress corrosion cracking of the x80 steel in the seawater. figure 10: the effect of applied stress on active anodic dissolution a b 0 1 2 3 4 5 6 7 0 200 400 600 800 k p stress /mpa test data [19] 0 1 2 3 4 5 6 7 0 200 400 600 800 k stress/mpa 2 exp 2     =     e m k e rt ( ) ( ) 1 1 exp 1    + + +  =  +   m m s p m m m k m p rt 3 56g/mol, =7.84g/cm 206gpa, =695mpa 4.37, 293k r=8.31j/mol.k = = = = m e p m t 0 1 2 3 4 5 6 7 0 200 400 600 800 k stress/mpa 2 exp 2     =     e m k e rt ( ) ( ) 1 1 exp 1    + + +  =  +   m m s p m m m k m p rt 3 56g/mol, =7.84g/cm 206gpa, =695mpa 4.37, 293k r=8.31j/mol.k = = = = m e p m t z.-y. han et alii, frattura ed integrità strutturale, 50 (2019) 21-28; doi: 10.3221/igf-esis.50.03 27 conclusion n the present study, the stress corrosion ssrt tests of x80 steel in the natural seawater with different do contents were conducted to analyze the stress corrosion sensitivity. sem and the electrochemical measurements are adopted to investigate the stress corrosion mechanism and the contribution of do on the scc behavior. the main results obtained can be concluded as follows: (1) x80 steel has a strong susceptibility of scc to the do content in the natural seawater. the stress corrosion lives decrease with the increase of do, i.e., the stress corrosion of x80 steel is more serious in the shallow sea. the decrease in elongation-loss rate and reduction-in-area loss rate indicate the susceptibility of scc increasing with the increase of do. (2) the distribution of the corrosion pits and micro cracks at the lateral and fracture surfaces aggravate with the increase of do, which is consistent with the time-to fracture results of ssrt tests. the fracture of x80 steel possesses some quasi-cleavage zones in low do, but the number of ductile dimples decreases and the size of ductile dimple also shrinks when do content increases to 6.8%, revealing that the fracture transforms gradually from ductile fracture to quasibrittle fracture. (3) the results of tafle polarization and electrochemical impedance spectroscopy show that the corrosion current increase and corrosion resistance decrease at higher do, indicating that the increase of do content results in a speeded-up of corrosion. at the same time, corrosion pits and micro cracks at the lateral surfaces cause the stress concentration and promote the anodic dissolution and growth of corrosion pits and cracks even under lower applied stress, thereby accelerates the process of stress corrosion cracking of x80 steel in the seawater. acknowledgments he research work is supported by the national natural science foundation of china (no.51404286), and the fundamental research funds for the central universities of china (no.17cx02065). the authors are also grateful for the financial support from china scholarship council (no. 201806455016). references [1] caleyo, f., gonzález, j.l., hallen, j.m. (2002). a study on the reliability assessment methodology for pipelines with active corrosion defects. international journal of pressure vessels and piping, 79(1), pp. 77-86. doi: 10.1016/s0308-0161(01)00124-7. [2] lai, z.s., chen, q.s., wang, c.f., zhou, x.l. (2019) modeling dynamic responses of heterogeneous seabed with embedded pipeline through multiresolution random field and coupled hydromechanical simulations. ocean engineering, 173, pp. 556-570. doi: 10.1016/j.oceaneng.2019.01.015. [3] eliassen, s. (2004). new concept for cathodic protection of offshore pipelines to reduce hydrogen induced stress cracking (hisc) in high strength 13%cr stainless steels. corrosion engineering, science and technology, 39(1), pp. 31-37. doi: 10.1179/147842204225016868. [4] chen, y.f., zhang, h., zhang, j., liu, x.b., li, x., zhou, j. (2015). failure assessment of x80 pipeline with interacting corrosion defects. engineering failure analysis, 47, pp. 67-76. doi: 10.1016/j.engfailanal.2014.09.013. [5] li, x.h., chen, g.m., chang, y.j., xu, c.h. (2019). risk-based operation safety analysis during maintenance activities of subsea pipelines. process safety and environmental protection, 122, pp. 247-262. doi:10.1016/j.psep.2018.12.006. [6] yang, y.s., khan, f., thodi, p., abbassi, r. (2017) corrosion induced failure analysis of subsea pipelines. reliability engineering & system safety, 159, pp. 214-222. doi: 10.1016/j.ress.2016.11.014. [7] arafin, m.a., szpunar, j.a. (2009). a new understanding of intergranular stress corrosion cracking resistance of pipeline steel through grain boundary character and crystallographic texture studies. corrosion science, 51(1), pp.19128. doi: 10.1016/j.corsci.2008.10.006. [8] charles, e.a., parkins, r.n. (2015). generation of stress corrosion cracking environments at pipeline surfaces. corrosion, 51(7), pp. 518-527. doi: 10.5006/1.3294372. i t https://www.sciencedirect.com/science/article/pii/s0308016101001247#! https://www.sciencedirect.com/science/article/pii/s0308016101001247#! https://www.sciencedirect.com/science/article/pii/s0308016101001247#! https://www.sciencedirect.com/science/journal/03080161 https://doi.org/10.1016/s0308-0161(01)00124-7 https://www.sciencedirect.com/science/article/pii/s0029801819300162#! https://www.sciencedirect.com/science/article/pii/s0029801819300162#! https://www.sciencedirect.com/science/article/pii/s0029801819300162#! https://www.sciencedirect.com/science/article/pii/s0029801819300162#! https://www.sciencedirect.com/science/journal/00298018 https://www.sciencedirect.com/science/journal/00298018 https://doi.org/10.1016/j.oceaneng.2019.01.015 https://doi.org/10.1179/147842204225016868 https://www.sciencedirect.com/science/article/pii/s135063071400288x#! https://www.sciencedirect.com/science/article/pii/s135063071400288x#! https://www.sciencedirect.com/science/article/pii/s135063071400288x#! https://www.sciencedirect.com/science/article/pii/s135063071400288x#! https://www.sciencedirect.com/science/journal/13506307 https://doi.org/10.1016/j.engfailanal.2014.09.013 https://www.sciencedirect.com/science/article/pii/s095758201830733x#! https://www.sciencedirect.com/science/journal/09575820 https://doi.org/10.1016/j.psep.2018.12.006 https://www.sciencedirect.com/science/article/pii/s0951832016308316#! https://www.sciencedirect.com/science/article/pii/s0951832016308316#! https://www.sciencedirect.com/science/article/pii/s0951832016308316#! https://www.sciencedirect.com/science/journal/09518320 https://www.sciencedirect.com/science/journal/09518320 https://doi.org/10.1016/j.ress.2016.11.014 https://doi.org/10.1016/j.corsci.2008.10.006 https://doi.org/10.5006/1.3294372 z.-y. han et alii, frattura ed integrità strutturale, 50 (2019) 21-28; doi: 10.3221/igf-esis.50.03 28 [9] arafin, m.a., szpunar, j.a. (2009). a new understanding of intergranular stress corrosion cracking resistance of pipeline steel through grain boundary character and crystallographic texture studies. corrosion science, 51(1), pp. 119-128. doi: 10.1016/j.corsci.2008.10.006. [10] liu, z.y., li, x.g., cheng, y.f. (2012). mechanistic aspect of near-neutral ph stress corrosion cracking of pipelines under cathodic polarization. corrosion science, 55, pp. 54-60. doi: 10.1016/j.corsci.2011.10.002. [11] sun, f.l., ren, s., li z., liu z.y., li x.g., du c.w. (2017).comparative study on the stress corrosion cracking of x70 pipeline steel in simulated shallow and deep sea environments. materials science & engineering a, 685, pp.145–153. doi: 10.1016/j.msea.2016.12.118. [12] liu, y., wang, j.w., liu, l., li, y., wang, f.h. (2013). study of the failure mechanism of an epoxy coating system under high hydrostatic pressure. corrosion science, 74, pp. 59–70. doi: 10.1016/j.corsci.2013.04.012. [13] melchers, r.e. (2015). effect of immersion depth on marine corrosion of mild steel. corrosion, 61, pp. 895–906. doi: 10.5006/1.3280659. [14] junghans, a., chellappa, r., wang, p., majewski, j., luciano, g., marcelli, r., proietti, e. (2015). neutron reflectometry studies of aluminum–saline water interface under hydrostatic pressure. corrosion science, 90, pp.101–106. doi: 10.1016/j.corsci.2014.10.001. [15] zhang, t., yang, y.g., shao, y.w., meng, g.z., wang, f.h. (2009). a stochastic analysis of the effect of hydrostatic pressure on the pit corrosion of fe–20cr alloy. electrochimica acta, 54, pp. 3915–3922. doi: 10.1016/j.electacta. 2009.02.010. [16] huang, y.h., xuan, f.z., tu, s.t. itoh, t. (2011). effects of hydrogen and surface dislocation on active dissolution of deformed 304 austenitic stainless steel in acid chloride solution. materials science and engineering a, 528, pp.1882– 1888. doi: 10.1016/j.msea.2010.10.055. [17] huang, y.h., tu, s.t., xuan, f.z. (2013). modeling and simulation of pit chemistry of 304 austenitic stainless steel under applied stress in sodium chloride solution. nuclear engineering and design, 257, pp.45–52. doi: 10.1016 /j.nucengdes. 2013.01.019. [18] mao, s.x., li, m. (1998) mechanics and thermodynamics on the stress and hydrogen interaction in crack tip stress corrosion: experiment and theory. journal of the mechanics and physics of solids, 46(6), pp. 1125-1137. doi: 10.1016 /s0022-5096(97)00054-9. [19] wang, y.x., zhao, w.m., ai, h., zhou, x.g., zhang, t.m. (2011). effects of strain on the corrosion behaviour of x80 steel. corrosion science, 53, pp.2761–2766. doi: 10.1016/j.corsci.2011.05.011. [20] ramberg, w., osgood, w.r. (1943). description of stress‐strain curves by three parameters. naca technical note no. 902. https://doi.org/10.1016/j.corsci.2008.10.006 https://doi.org/10.1016/j.corsci.2011.10.002 https://doi.org/10.1016/j.corsci.2013.04.012 https://doi.org/10.5006/1.3280659 https://doi.org/10.1016/j.corsci.2014.10.001 https://doi.org/10.1016/j.electacta.2009.02.010 https://doi.org/10.1016/j.msea.2010.10.055 https://scholar.google.com.hk/citations?user=m_otgq8aaaaj&hl=zh-cn&oi=sra https://www.sciencedirect.com/science/article/pii/s0022509697000549 https://www.sciencedirect.com/science/article/pii/s0022509697000549 https://doi.org/10.1016/s0022-5096(97)00054-9 https://doi.org/10.1016/j.corsci.2011.05.011 shot peening processes to obtain nanocrystalline surfaces in metal alloys: a. sadeghi et alii, frattura ed integrità strutturale, 57 (2021) 138-159; doi: 10.3221/igf-esis.57.12 138 reliability and reliability-based sensitivity analyses of steel moment-resisting frame structure subjected to extreme actions abbasali sadeghi department of civil engineering, mashhad branch, islamic azad university, mashhad, iran abbasali.sadeghi@mshdiau.ac.ir , http://orcid.org/0000-0002-3016-9080 hamid kazemi, mayasam samadi department of civil engineering, mashhad branch, islamic azad university, mashhad, iran kazemi0518@mshdiau.ac.ir , http://orcid.org/0000-0003-2590-1051 samadi4432@mshdiau.ac.ir , http://orcid.org/0000-0003-4485-4174 abstract. the ground external columns of buildings are vulnerable to the extreme actions such as a vehicle collision. this event is a common scenario of buildings' damages. in this study, a nonlinear model of 2-story steel moment-resisting frame (smrf) is made in opensees software. this paper aims investigating the reliability analysis of aforementioned structure under heavy vehicle impact loadings by monte carlo simulation (mcs) in matlab software. to reduce computational costs, meta-model techniques such as kriging, polynomial response surface methodology (prsm) and artificial neural network (ann) are applied and their efficiency is assessed. at first, the random variables are defined. then, the sensitivity analyses are performed using mcs and sobol's methods. finally, the failure probabilities and reliability indices of studied frame are presented under impact loadings with various collision velocities at different performance levels and thus, the behavior of selected smrf is compared by using fragility curves. the results showed that the random variables such as mass and velocity of vehicle and yield strength of used materials were the most effective parameters in the failure probability computation. among the meta-models, kriging can estimate the failure probability with the least error, sample number with minimum computer processing time, in comparison with mcs. keywords. reliability; meta-model; sensitivity; impact loading; steel moment-resisting frame. citation: sadeghi, a., kazemi, h., samadi, m., reliability and reliability-based sensitivity analyses of steel moment-resisting frame structure subjected to extreme actions, frattura ed integrità strutturale, 57 (2021) 138-159. received: 09.05.2021 accepted: 27.05.2021 published: 01.07.2021 copyright: © 2021 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. introduction n the last decade, due to the increasing terrorist threats in different parts of the world, special attention has been paid to the design and analysis of resistant structures to abnormal loadings. one of the most common accidental loading scenarios is the vehicle collision impact, which may typically happen at the ground level of a building. this scenario can lead considerable damages to the impacted column or even results to the local or global failure of a building. based on i mailto:abbasali.sadeghi@mshdiau.ac.ir https://youtu.be/7c7_fcvn8ms a. sadeghi et alii, frattura ed integrità strutturale, 57 (2021) 138-159; doi: 10.3221/igf-esis.57.12 139 the structural codes, buildings should be designed in such a way that the probable damage caused by an accidental event does not generate unsuitable effects [1]. traditionally, structural engineers have designed and analyzed buildings against normal lateral loadings such as an earthquake and wind, but in some cases, assessing the nonlinear performance of structures against abnormal loadings is vital, too. in this regard, it is necessary for structural engineers to understand the failure behavior of buildings under intentional and or accidental impact loadings as extreme actions and then, the performance levels of structures should be specified under this loading [2]. numerous studies are devoted to assess the influences of vehicle impact to performance of buildings and bridges. in the following, these researches are extracted from technical literatures related to this issue. el-tawil et al. (2003, 2005) evaluated the performance of bridge columns under the effect of heavy vehicles impact. the results showed that the present collision design codes could be conservative and the bridge columns were vulnerable to impact loadings, so the effect of them should be considered in design procedure [3, 4]. in following, probabilistic framework is proposed by sharma et al. (2014, 2015) for the assessment of dynamic shear force capacity and demand of reinforced concrete (rc) columns subjected to vehicle impact using fragility curves [5, 6]. also, the effects of different foundation connection details are investigated by kang and kim (2017) on performance of a steel column under vehicle impact. the results of mentioned paper indicated that the reinforcement plots were influential in reducing the damages and finally, the optimized reinforcement layout was proposed for the best reaction against this kind of loading [7]. then, with growing the study of the structures based probability, the probabilistic analyses are recently increased these days. these analyses includes reliability evaluation and fragility curves of 3-story steel moment-resisting frame (smrf) that are performed by javidan et al. (2018) in weak and strong axis directions, and compared the results between artificial neural network (ann) and finite element analysis. the results demonstrated that the precision of ann is considerable and acceptable [8]. recently, santos et al. (2020) presented the results of a numerical investigation about smrf structures subjected to vehicle impact loadings. the results of the mentioned study revealed that the vehicle impact analyses would lead to greater structural responses and critical damages especially for high collision velocities than column removal approach by using alternative-load path method (apm) [9]. oliveira et al. (2020) proposed a simplified lumped damage model to assess the performance of rc structures under impact loading with considering shear failure mode [10]. sadeghi et al. (2021) evaluated the collapse capacity and endurance duration of smrf structure including a corner damaged column due to light vehicle impact under seismic records. the mentioned study investigated the effects of impact and earthquake loadings on performance of smrf. in an aforementioned research, the damaged column scenarios are considered with 3 states. the first scenario without considering a damaged column and scenarios 2 and 3 are assumed to have a corner damaged column due to vehicle impact with velocities 60 and 120 km/h, respectively. the results showed that scenario 3 had a weaker seismic performance in comparison with other scenarios [11]. reliability theory is a branch of general probability theory that has gradually applied in engineering platform over the last four decades. today, computer simulations are a favorite gadget to analyze, design, and optimize structural systems against various loadings. therefore, in recent years, probabilistic analyses including application of the reliability-based simulation methods are growing for failure mechanism evaluation of structural systems. also, assessing performance of a structure under extreme loadings needs huge nonlinear dynamic analyses to specify failure probability. to get a solution for this issue, numerous mathematical techniques have been proposed called meta-models [12]. the research background of reliability field using meta-models is presented in the following. kim et al. (2011) studied the sensitivity analysis of design variables of 2d smrf and concentric braced frame (cbf) under progressive collapse. to this goal, monte carlo simulation (mcs), tornado diagram analysis (tda), and first-order second moment (fosm) methods are conducted with regarding to the different uncertainties. the new findings showed that the beam yield strength and column yield strength were the most important uncertainty in smrfs and cbfs, respectively [13]. also, the reliability analyses of seismic performance of rc and smrfs are studied by gholizadeh et al. (2014). for this aim, the above mentioned frames are designed optimally. then, mcs is utilized to estimate the total exceedance probability related to different performance levels. then, two surrogate models such as radial basis function (rbf) and back propagation (bp) are applied for predicting the structural responses. the results showed that the superiority of bp to rbf in prediction of structural responses related to structural performance levels [14]. in the following, a developed probabilistic framework based on kriging meta-model is presented by gidaris et al. (2015) for seismic risk assessment using stochastic ground motion models to describe the seismic hazard [15]. vazirizade et al. (2017) used ann to reduce the computational costs required for reliability analysis and damage detection of steel structures [16]. as well as, ann surrogate model is applied by hashemi et al. (2018) for predicting the quantity of used steel materials in smrf structures. the results demonstrated that the weights of structures could be approximated using ann with an admissible precision [17]. hadianfard et al. (2018) assessed the reliability theory and taking into account the different uncertainties related to blast loading and material properties. the results indicated that assessing the damage index of the columns against the blast was important with considering the random parameters [18]. in this regard, hedayat et al. (2019) showed that the proposed formula developed based on ann and bilin element of the opensees software to anticipate the a. sadeghi et alii, frattura ed integrità strutturale, 57 (2021) 138-159; doi: 10.3221/igf-esis.57.12 140 minimum strength requirement of smrfs at any performance levels. also, it was clear that ann was more precise than the other available surrogate models [19]. in the following, the reliability indices of structural systems are calculated by hoseini vaez et al. (2020) with an implicit limit state function (lsf). then, in order to decrease the computational costs of mcs, the reliability indices obtained by using meta-heuristic algorithms [20]. recently, rahgozar et al. (2021) evaluated the seismic reliability of controlled-rocking steel cores (crscs) with considering a set of uncertainty parameters. the findings of this study showed that the design process was reliable and the safety of crscs is considered; however, the probability failure for mid-rise crscs was more than low-rise prototypes [21]. apart from the above mentioned studies, very little attention has been paid to experimental researches for understanding the structural behavior of buildings against vehicles collision due to its setup and an expensive procedure [22, 23]. therefore, this is a major reason for developing the analytical models based on probabilistic approaches to perceive the performance of buildings under vehicle impact. in this study, a 2-story smrf structure with intermediate ductility is designed based on regulations, and nonlinear dynamic analyses are performed using opensees software [24]. then, sensitivity analyses using mcs and sobol's methods are conducted by matlab [25]. as a significance and novelty, a probabilistic versatile framework is proposed based on the reliability analyses under heavy vehicle impact loadings with different collision velocities using mcs, meta-models including kriging, polynomial response surface methodology (prsm) and artificial neural network (ann) are considered for reducing computational costs, while having high accuracy and least error rate. finally, it may provide a throughout framework based on probabilities under vehicle impact loadings, which has gained great interest in practical researches in this field. moreover, the comparison of different sensitivity tests results will show the important random variables and at last, the best meta-model will be specified by using reliability and fragility analyses which is useful and practical for future researchers in this aspect. structural reliability analysis he performance of structural systems is assessed mathematically in term of reliability analysis by failure criteria. these failure levels are usually specified by structural damage levels. in this regard, for both reliability and sensitivity analyses, mcs is applied by producing a large number of samples and assessing their structural responses due to statistical distributions. in spite of its easiness and power, this approach requires high computer processing time and much more cost. as a result, many methods such as meta-models have been proposed by researchers to solve this problem [26, 27]. therefore, the introduction of mcs and meta-models are briefly explained in the following. mcs and score function approach mcs is a reliability based simulation method that is widely used in structural reliability of different problems. based on statistical sampling theory, mcs solves structural reliability by statistical sampling of random variables mathematically [26, 28]. mcs can be applied for complex problems including material and geometric nonlinearity and high dimensional that cannot be solved analytically. in this route, considering x and ( ) g x as the uncertain quantities and the performance function of the structural systems, respectively. in the following, the failure probability ( )fp is estimated using eqn. 1 [26, 28]: ( ) ( ) ( ) ( ) ( ) ( ) ( )( ) = = =  0 00 x x fg x g xg x f x dx x f x dx xfp (1) according to eqn. (1), f is the expectation operator, xf is the probability density function (pdf) of random variables x , the function ( )  0 g x shows the failure set and ( )0 g x is an indicator function that is specified in eqn. 2. also, based on this equation the parameter i x is the i th random variable and when the indicator function ( )0g x is 0 and 1, it means that the samples are considered in safe and failure regions, respectively. ( ) ( ) ( ) ( )     =    0 0, 0 1, 0 i i x g x g g x x (2) t a. sadeghi et alii, frattura ed integrità strutturale, 57 (2021) 138-159; doi: 10.3221/igf-esis.57.12 141 the reliability index ( ) is computed using the first-order approximation with regarding to eqn. 3, where φ-1 is the inverse cumulative distribution function of the standard normal distribution [8]. ( )−= − 1 fpβ (3) in this regard, independent and identically distributed (iid) samples  =    : 1, , i x i n are generated according to pdf of ( )xf and evaluating ( ) ( )0 ( f g x x , mcs only provides an exact failure probability for any kind of structural systems [26]. also, the partial derivative of the failure probability related to a statistical specification of the i-th random variable i.e.  i can be determined with eqn. 4: ( ) ( ) ( )    =     ,f x i x f x dx f i p ξ ξ (4) then, lebesgue dominated convergence theory and importance sampling (is) are used and in the following, eqn. 4 would be rewritten as eqn. 5 [26, 28, 29]: ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( )                  = = =      = =  = =      , , , , , / , , log , , [ . , x x x f f i i x x i f x x x f x x f i i f x f x f x x dx x dx f x f x x f x dx f x f x x f x dx x x f i p ξ ξ (5) therefore, the so-called score function presented as eqn. 6: ( ) ( )   =  log , , x i f x i x ξ (6) also, it is recommended that researchers refer to the authentic papers [26, 29] for more information about mcs and score function. with regarding to high computational efforts of mcs, application of meta-model techniques in structural reliability problems has been developed and proposed [30, 31, 32]. meta-models in recent years, meta-models are widely used among researchers over the world to reduce the computational costs of the reliability analyses by predicting the structural responses [33]. meta-model techniques can provide an accurate representation of the pdf of the model response. some meta-models, such as kriging [34, 35], prsm [36], and ann [8] have been successfully applied for structural reliability problems that are briefly presented in the following sections. kriging kriging is a mathematical interpolation approach for constructing a surrogate model instead of the original prototype. kriging surrogate model is widely applied in reliability evaluation and failure probability computation of problems. this method aims to minimize the error rate and fit the mean of the prediction errors to zero [37]. also, considering support points and related response y as ( ) ( )=   1 , , t sy g x g x , kriging meta-model presents the definite response ( )g x as a realization of a random function [36]. the function ( )g x is presented as eqn. 7: ( ) ( ) ( )= +tg x f x z x (7) a. sadeghi et alii, frattura ed integrità strutturale, 57 (2021) 138-159; doi: 10.3221/igf-esis.57.12 142 as well as, in eqn. (7), ( ) ( ) ( )=   1 , , t mf x f x f x is a vector of m basis functions; and ( ) ( )  =   , , t x x indicates the vector of m regression coefficients. also, the parameter ( )z x specifies a stationary gaussian process with zero mean, the parameter  2 is the process variance, and the parameter ( ),i jr x x represents the correlation function between samples ix and jx . the following covariance function is presented according to eqn. 8: ( ) ( )( ) ( )= 2, ,i j i jcov z x z x r x x (8) the gaussian type, which is the widely used correlation function, defined as eqn. 9: ( ) ( )( ) = = − − 2 1 ,1 ,1 1 , exp n i j i x xi jr x x (9) in which ,1ix is the first component of vector ix ; and 1 is the first correlation parameter. these parameters can be evaluated and approximated by the maximum probability method [37]. polynomial response surface methodology (prsm) prsm is a proper surrogate model for the structural cases where the closed form expression is not specific for the performance function. this meta-model is first presented by box and wilson [36], and faravelli [38] in structural reliability problems and it is still popular topic for further studies among researchers [39–42]. the predicted structural responses by this method can be presented as eqn. 10:  = + yxy (10) where the parameters x, β and  y are input data vector, unknown coefficient vector and error vector, respectively. response surface can be mathematically defined for a typical quadratic polynomial basis as eqn. 11:    = = = = + + 0 1 1 1 k k k i i ij i j i i j x x xy (11) the least-squares method (lsm) is used for unknown polynomial coefficients. they can be approximated by minimizing the error rate based on eqn. 12: ( ) ( ) ( )     = = = = = − − = − −   2 0 1 1 1 1 ( ) n k k k t i i i ij i j i i i j y x x x y x y xe β (12) also, based on lsm, the parameter  is approximated and extracted according to eqn. 13:   −  =   1 t t x x x yβ (13) in this method, the initial input data (x and y) should be selected carefully to proportionate an accurate function [38]. artificial neural network (ann) today, neural network (nn) methods are widely used in engineering issues as meta-model. the basis of nn approach which named weight function, is very flexible and trainable for different kind of functions, so there is no limitation on the shape, size, importance, or type of function [8]. the goal of ann surrogate model is mapping from an input variable space to a response space using a number of simple mathematical models called artificial neurons. each neuron includes the input a. sadeghi et alii, frattura ed integrità strutturale, 57 (2021) 138-159; doi: 10.3221/igf-esis.57.12 143 channels receiving the input vector [xi], weight vector [wi], bias b, transfer function f, and one output channel y. this mathematical process is shown in fig. 1. figure 1: mathematical procedure of ann [8]. the input signals are multiplied by the weights and summed with the bias as a corrective term. to produce the output y, the summation is input to the transfer function which is usually one of the linear, tan-sigmoid, log-sigmoid, or step functions [43, 44]. this method with consideration of the tan-sigmoid function can be defined as eqns. 14 and 15: ( )= + .f w x by (14) ( ) − = −  2 2 1 1 x e f x (15) the given parameters such as input vector, the weight vectors and bias must be well-balanced in order to anticipate the structural responses exactly. the connecting neurons to each other and regulating them with a proper network architecture leads to a regular framework called anns [44]. modeling procedure n this study, a three-dimensional 2-story smrf with intermediate ductility is considered as the prototype structure for an analysis model. this structure is loaded based on asce07 [45] and design control criteria of the asce07 and aisc-360 [46] are checked and confirmed. seismic design category type d is assume. the story height, and the span length were 3.2 and 6 m, respectively. in the following, the both dead and live loads are assumed as gravity loadings. the applied values for distributed dead and live loads to all stories were taken 500 and 200 kg/m2, respectively. by checking the results of prototype design, it is observed that the dominant design criterion in building was drift control, therefore the values of demand to capacity ratio in all its structural elements were far less than one. critical rayleigh damping ratio is considered 0.05, for all vibration modes of the structure and the effect of non-structural elements was ignored. all seismic requirements are applied for the prototype structure. then, the two-dimensional frame of the side axis is extracted and modeled in opensees software for nonlinear dynamic analyses under impact loadings. the applied dead and live loads to this frame were 1500 and 600 kg/m, respectively. the materials used in the beams and columns were st37 with elasticity modulus, yield stress and ultimate stress of 200 gpa, 240 mpa and 370 mpa, respectively. the bilinear uniaxial steel materials with kinematic and isotropic stiffness are assumed based on steel01 model with a post-yielding stiffness of 3% [13]. for structural sections, nonlinear fiber elements are used for all members as a distributed plasticity model. therefore, in this paper, the performance of steel building is investigated under vehicle impact loading to the external corner column as a research scenario. to estimate the failure probability, uncertainties in materials and applied loadings have been noticed in the modeling and analyses and then, lsfs are considered according to the maximum permitted beam rotation of damaged bay for different performance levels. the behavior of the frame is evaluated under impact loadings caused by a heavy vehicle collision with considering the effect of p−. also, building plan view and determination the exterior frame enclosed in the red rectangle, elevation of 2d frame, and location of impacted column by vehicle collision are illustrated in figs. 2 to 4, respectively. tab. 1 shows the designed members’ cross sections of a 2-story smrf. also, the overall scheme of the developed probabilistic flowchart of the current study is presented in fig. 5. this developed flowchart summarizes the present research stages. it includes sampling generation, designing and nonlinear dynamic analyses, and then reliability, fragility, and sensitivity analyses. i a. sadeghi et alii, frattura ed integrità strutturale, 57 (2021) 138-159; doi: 10.3221/igf-esis.57.12 144 figure 2: building plan view and location of the studied frame. figure 3: elevation of a 2-story smrf. figure 4: location of vehicle impact to corner column. column sections beam sections story external internal external internal box200*20 box200*20 ipe220 ipe200 1 box200*18 box200*18 ipe200 ipe180 2 table 1: the designed cross sections of beam and column of 2-story smrf. in this probabilistic framework, the smrf model is first verified, and then the structural modeling procedure is performed in opensees software to generate the analysis numerical prototype parametrically. three meta-models such as kriging, prsm and ann are conducted in the matlab programming code which is trained by the samples from the studied frame that is extracted from finite element analysis by opensees software. accordingly, determination of uncertainty parameters, assigning them and number of samples for training procedure can be applied in the current introduced framework based on fig. 5. at the next stage, for comparison the aforementioned surrogate models in the same conditions, three meta-models are trained with the similar samples to conduct probabilistic analyses at a low computational costs. in the following, the applicability of the present framework for probabilistic analyses under vehicle impact loadings is investigated and compared when uncertainties in loading, geometry, and material properties are completely applied. then fragility curves are proposed by exact method and meta-model with the best performance for assessing the behavior of smrf model. finally, the suitable meta-model will be specified for vehicle impact scenario. verification of modeling in this study, to indicate the performance, precision, and effectiveness of the developed probabilistic framework, a smrf structure is separately verified under impact and seismic loadings. at first, kang and kim (2017) investigated the performance of a steel column of smrf standing on a rc footing when the impact loading induced by collision of truck with an eightton was exerted. the specifications of model are presented in reference paper [7]. according to fig. 6, the displacementtime curve of the analysis model is extracted and compared with the reference prototype. the results showed that they have a relatively good agreement with each other. vehicle impact a. sadeghi et alii, frattura ed integrità strutturale, 57 (2021) 138-159; doi: 10.3221/igf-esis.57.12 145 figure 5: representation the flowchart of the current study. fragility analysis based meta-model of the selected frame. designing a 2-story steel moment-resisting frame structure. modeling a 2d -frame of steel structure under vehicle impact. n o n li n e a r d y n a m ic a n a ly s e s determination of random variables and their statistical parameters. distributing samples for each variable and compute their pdf. s a m p li n g g e n e ra ti o n computing 𝐿𝑆𝐹𝑠 for each performance level of the studied frame. v e ri fi c a ti o n & d e s ig n in g p ro c e d u re computing sensitivity results using eqs. (21) to (24). reliability analysis by using meta-models. r e li a b il it y , f ra g il it y , a n d s e n s it iv it y a n a ly s e s assessment the accuracy of meta-models and selecting the best one. verification & designing a 2-story smrf structure. modeling a 2d smrf structure under vehicle impact. determination of random variables and their statistical parameters. distributing samples for each variable and compute their pdfs. computing 𝐿𝑆𝐹𝑠 for each performance level of the studied frame. computing sensitivity results using eqns. 19 to 22. reliability analysis by using meta-models. assessment the accuracy of meta-models and selecting the best one. a. sadeghi et alii, frattura ed integrità strutturale, 57 (2021) 138-159; doi: 10.3221/igf-esis.57.12 146 figure 6: comparison of displacement-time curve of analytical model versus reference model. impact loading scenario impact loading is applied to the structure dynamically with high intensity and short duration. types of impact loadings include the vehicles impact hitting to the columns of steel, concrete buildings and or bridge piers and the impact induced by a sudden start or stop of a crane or elevator. an example of impact time history loading applied to the various heights of the building is shown in fig. 7 [47]. figure 7: time history of impact loading due to vehicle collision [47]. the european standard for accidental actions is considered for vehicle impact loadings [1]. according to previous studies, a heavy vehicle with 8t mass is considered that collides at a height of 50 cm of the frame column. in this study, several vehicle velocities including 10, 20, 30, 40 and 50 km/h are assumed [1]. the impact force and impact duration in terms of vehicle velocity, stiffness, and mass are obtained from eqns. 16 and 17, with v, k and m signs, respectively [48, 49]: =v kmf (16)  = . m v f t (17) the limit state function (lsf) in this paper, mcs and meta-models are used to calculate the failure probability of studied frame. for this purpose, at first, the existing samples in the safe and failure regions are specified, and then by performing nonlinear dynamic analyses by finite element software, the lsfs of the reliability problems are evaluated. in each structural analysis, the random variables are defined based on the selected pdfs. a total of nine random variables are considered which are shown in tab. 2. they are used to propose versatile probabilistic framework. the uncertainty parameters are classified into four categories including gravity load, material, geometric characteristics, and impact load due to the collision of a heavy vehicle. these a. sadeghi et alii, frattura ed integrità strutturale, 57 (2021) 138-159; doi: 10.3221/igf-esis.57.12 147 variables include: yield strength and elasticity modulus of the used materials, beam length, column height, live load, dead load, and finally, the impact loading due to the heavy vehicle collision. on the one hand, the response parameters of the structure are assumed constant for achieving reasonable conclusion in order to compare the parameters of probabilistic properties. according to building regulations and technical literatures, these indicators are usually based on performance levels related to damage levels of structures. tab. 2 presents the category, symbol, unit and references of all random variables and then their statistical characteristics such as mean, coefficient of variation, standard deviation values, and pdf of the uncertainty parameters. * n: normal, ln: lognormal, g: gamma table 2: list of uncertainty parameters. in recent decades, the different damage modes of steel structures have been specified against extreme loadings, and damage levels commensurate with performance levels of structures can be established. their corresponding lsfs are defined according to the reference book "structural design for physical security – state of the practice" [53] as shown in tab. 3. these limit states and failure criteria such as lsf1, lsf2 and lsf3 are related to three damage levels of steel structures subjected to extreme loads which are associated with the light, moderate, and severe damage states, respectively. damage levels failure type element severe (rad) moderate (rad) light (rad) 0.25 0.12 0.05 bending beam table 3: failure criteria for steel structures under extreme loads [53]. the damage rate of studied frame is calculated based on the maximum permitted beam rotation of damaged bay as a structural response through nonlinear dynamic analyses at each failure level. therefore, the structural collapse has occurred, when the values of beam rotation become over 25%. (i.e. severe damage state). then, by calculating the structural responses by using opensees software, mcs is applied for reliability analyses and comparing the failure probability of studied model. moreover, to reduce the computational efforts, three meta-model techniques including kriging, prsm and ann are also used for reliability analyses. the estimated structural responses by these approaches are also compared with mcs and the accuracy rate of them is assessed and finally, the suitable meta-model will be chosen for predicting the structural responses in present scenario. category symbol description unit pdf mean c. o. v or σ references gravity load dl dead load kg/m n 1500 0.1 [8, 49] ll live load kg/m g 600 0.4 [8, 49] material yf yield strength mpa ln 240 0.07 [8, 50] e modulus of elasticity mpa ln 2*105 0.03 [51, 52] geometric l beam length m n 6 0.0304 [50, 51] h column height m n 3.2 0.0304 [50, 51] impact load k stiffness kn/m ln 300 60 (kn/m) [1, 50] m mass kg n 8000 4000 ( kg) [1, 50] v velocity km/h ln 40 8 (km/h) [1, 50] a. sadeghi et alii, frattura ed integrità strutturale, 57 (2021) 138-159; doi: 10.3221/igf-esis.57.12 148 results and discussion reliability analysis using meta-models n this study, constructing surrogate models, 3000 random samples are generated based on the specified statistical distribution for each random variable inserted in tab. 2 based on its statistical characteristics by augmenting standard deviations of random variables. for a sample size specified for each reliability method, a combination of generated samples is randomly set as input variables. the beam rotation of damaged bay of selected frame is calculated and then, 2000 random samples and the corresponding beam rotation of mentioned frame is opted to train the introduced metamodels randomly. then, 1000 samples are opted to test the surrogate models. the remaining samples are utilized to test the surrogate models for predicting beam rotation of frame i.e. estimation the lsf values. in this paper, the coefficient ( 2 r ), was applied in order to specify the performance of the meta-models. the details of the coefficient 2 r computation could be explained more in [54, 55, 56]. the coefficient r2 has been utilized as necessary quality criteria in different kinds of engineering applications. in this section, the performance of three meta-models such as kriging, prsm and ann is investigated in predicting the beam rotation. then, for 90 samples that are selected randomly, the values of predicted beam rotation versus the corresponding actual outputs are presented in figs. 8 to 10 for different lsfs, respectively. also, in each graph, the fitted linear lines are also plotted (black lines) to show the performance of the meta-models. the values of 2 r with respect to 90 samples were estimated at 0.96, 0.93, and 0.91, for three lsfs respectively, showing the best ability of kriging surrogate model in structural response prediction. in other words, in all lsfs, it is clear that a strong linear correlation between actual and predicted beam rotation values is related to the kriging surrogate model and it has the least error for predicting the structural responses. therefore, this method is recommended to be used in the vehicle collision impact scenarios. a) kriging b) prsm c) ann figure 8: regression graphs between predicted and actual values of beam rotation using the studied meta-models for lsf1. i a. sadeghi et alii, frattura ed integrità strutturale, 57 (2021) 138-159; doi: 10.3221/igf-esis.57.12 149 a) kriging b) prsm c) ann figure 9: regression graphs between predicted and actual values of beam rotation using the studied meta-models for lsf2. a) kriging b) prsm c) ann figure 10: regression graphs between predicted and actual values of beam rotation using the studied meta-models for lsf3. a. sadeghi et alii, frattura ed integrità strutturale, 57 (2021) 138-159; doi: 10.3221/igf-esis.57.12 150 fig. 11 (a) to (c) indicate the reliability index of aforementioned frame in terms of the mean of different velocity values in range 0 to 50 km/h for lsf1, lsf2 and lsf3, respectively. as it can be seen, by increasing the mean vehicle velocity from 0 to 50 km/h for lsf1, lsf2 and lsf3, the reliability index decreased by 13%, 20% and 18%, respectively. also, for example, in lsf3, the reliability index difference of smrf for kriging versus mcs in vehicle velocities 10, 20, 30, 40 and 50 km/h are 0.62, 0.95, 0.66, 0.34 and 0.58, respectively. based on fig. 11 (a) to (c), the obtained values of reliability index in metamodels and mcs are compared with each other, it is found that kriging surrogate model has the highest accuracy for all three lsfs with regarding to variation of the mean value of vehicle velocity. moreover, prsm and ann meta-models achieved the 2nd and 3rd ranking in estimating the reliability indices of aforementioned frame with regarding to the mean value of vehicle velocity variations. b) lsf2 a) lsf1 c) lsf3 figure 11: reliability index obtained due to mean value of vehicle velocity variation based on the studied lsfs. for different number of support points, the reliability problem is solved for three lsfs to investigate the sensitivity of applied meta-model techniques to the number of samples and employed doe strategy. fig. 12 (a) to (c) indicate that for 2000 support points, the accuracy of three meta-models are improved versus mcs. these figures illustrate that kriging surrogate model provided the best solution for the reliability problem. similar results are obtained for the other two lsfs. in this section, to perform reliability analyses of representative frame subjected to vehicle impact using meta-models, for some random input samples of each variable, the corresponding beam rotation with those variables are predicted by kriging surrogate model. for 3000 random samples, the frequency histogram of the predicted responses using kriging surrogate model is illustrated in fig. 13. therefore, the suitable distribution function that associated with the predicted structural responses is the weibull function. also, by increasing the beam rotation, pdf is decreased. the maximum values of beam rotation in the representative frame were obtained due to the vehicle collision with speeds of 10, 20, 30, 40 and 50 km/h by ann, prsm, kriging and mcs methods for three lsfs and then, these values are shown in fig. 14. for example, by increasing the vehicle velocity from 30 to 40 km/h and 40 to 50 km/h, the maximum values of beam rotation for mcs has increased by 41% and 24%, respectively. also, for kriging surrogate model, by increasing the velocity of vehicle from 30 to 40 km/h and 40 to 50 km/h, the maximum values of beam rotation have increased by 42% a. sadeghi et alii, frattura ed integrità strutturale, 57 (2021) 138-159; doi: 10.3221/igf-esis.57.12 151 and 25%, respectively . kriging surrogate model predicted the beam rotation values with the least difference in various vehicle velocities versus mcs. b) lsf2 a) lsf1 c) lsf3 figure 12: reliability results of four methods with different number of support points based on the studied lsfs. figure 13: frequency histograms of the predicted structural responses using kriging surrogate model. a. sadeghi et alii, frattura ed integrità strutturale, 57 (2021) 138-159; doi: 10.3221/igf-esis.57.12 152 figure 14: reliability results of four methods with different vehicle velocities. in the following, the reliability analysis results such as reliability index (β), failure probability (pf) and the number of calling lsf (#g call) are presented for impact velocity 50 km/h, for three lsfs that they are performed using mcs, ann, prsm and kriging methods based on tab. 4. simulation method mcs ann prsm kriging lsf1 β 2.373 2.425 2.341 2.359 fp 0.0088 0.0076 0.0096 0.0092 #g call 510 2000 2000 2000 lsf2 β 2.633 2.675 2.668 2.651 fp 0.0043 0.0034 0.0039 0.0040 #g call 510 2000 2000 2000 lsf3 β 2.853 2.798 2.901 2.821 fp 0.0021 0.0026 0.0018 0.0024 #g call 510 2000 2000 2000 table 4: reliability analysis results using mcs and meta-models. for indicating the accuracy and efficiency of kriging meta-model versus mcs, the beam rotation values are obtained for three lsfs. then, the comparison results of these methods are illustrated in fig. 15. it is concluded that the failure probability of aforementioned frame is reduced by increasing the maximum permitted beam rotation. also, by investigating this figure, it is clear that the calculated values of failure probability by kriging surrogate model are matched very well with mcs in different lsfs. therefore, kriging meta-model is introduced as the fast, suitable and optimized method for predicting the failure probability in this scenario. according to the extracted analyses results, it is concluded that the probabilistic developed framework is proper for performance evaluation of smrf structures under impact loadings without conducting numerous probabilistic analyses. however, more and special attention must be paid to training meta-models for problems with high dimensional responses. the results from the reliability analyses of the selected frame indicated that the structure was highly vulnerable to vehicle impact loadings on the corner column and kriging surrogate model is suitable approach for predicting the collapse performance of structures. a. sadeghi et alii, frattura ed integrità strutturale, 57 (2021) 138-159; doi: 10.3221/igf-esis.57.12 153 figure 15: comparison of the failure probability of frame for different lsfs. fragility analysis in current paper, fragility analysis is an available gadget for assessing the performance of structures under vehicle impact loading scenario. fragility curves can be performed using the developed framework in this study by two approaches including an exact method and kriging surrogate model. in these methods, the fragility analysis is conducted for evaluating the behavior of a prototype smrf through different damage levels. based on eqn. 18, the parameters such as the fragility function fd (x), damage measure (dm), and the intensity measure (im) are mentioned. fd (x) = p (dm ⩾ d|im = x) (18) therefore, the damage measure is defined by the maximum beam rotation in the damaged bay. in the following, fragility curves have been completely described as a function of gravity loads for progressive collapse assessment [57]. also, the intensity measure in the above mentioned equation is considered as the vehicle velocity. a) b) figure 16: fragility curves for vehicle impact scenario by two methods: a) exact method by opensees software; b) kriging meta-model. the fragility curves are plotted by two approaches such as an exact method by opensees software outputs and kriging metamodel under vehicle impact loadings. based on fig. 16 (a) and (b), it is seen that the smrf structure is more vulnerable to vehicle collision by two methods and its fragility curves showed that by increasing the vehicle velocity, the performance of the studied frame is changed critically. the median collapse velocities associated with the light, moderate, and severe damage a. sadeghi et alii, frattura ed integrità strutturale, 57 (2021) 138-159; doi: 10.3221/igf-esis.57.12 154 states are presented in tab. 5. finally, it should be noted that, fragility curve based kriging meta-model has the least error rate versus an exact method in three lsfs. median collapse velocity (km/h) method frame severe moderate light 37.6 26.5 23.7 exact 2-story 39.7 27.36 24.32 kriging 5.2% 3.1% 2.5% error rate table 5: median collapse velocities using exact method and kriging meta-model. sensitivity analysis based reliability sensitivity analysis based mcs sensitivity analysis based reliability aims studying the influence of the random parameters in the probabilistic model onto the failure probability computation. it is one of the key points in simplification and optimal design, especially in reliability problems with a large number of uncertainties. in mcs, sensitivity analysis is often performed by evaluating the rate of failure probability variation for each random variable [58]. by using this method, the rate of variation can be calculated as eqn. 19: ( ) ( ) ( )   =       0 x p i g x f x dx p fp p (19) in eqn. 19, the parameters such as: ( )fp the probability of failure, (p) a random variable, ( )( ) g x a limit state function, ( )xf a function of probability density of both variables, and (i) a counter vector are presented. here, sensitivity analysis is performed by calling (#g call:100,000 times) as lsf and evaluating the variation rate of failure probability related to the changes of each random variable and the results of sensitivity analysis are represented in tab. 6 and fig. 17. it can be found that the uncertainty parameters such as mass and velocity of vehicle and yield strength of the used materials had the maximum effect, respectively and the applied live load of the studied frame had the least effect on the failure probability calculation. table 6: sensitivity analysis results of the selected frame subjected to impact loading. no. failure probability variation for each variable 1 (∂pf)⁄(∂dl) 0.0095378 2 (∂pf)⁄(∂ll) 0.000078194 3 (∂pf)⁄(∂fy) -0.045519 4 (∂pf)⁄(∂e) 0.000087344 5 (∂pf)⁄(∂l) 0.00033172 6 (∂pf)⁄(∂h) 0.00078112 7 (∂pf)⁄(∂k) 0.022132 8 (∂pf)⁄(∂m) 0.61225 9 (∂pf)⁄(∂v) 0.49325 a. sadeghi et alii, frattura ed integrità strutturale, 57 (2021) 138-159; doi: 10.3221/igf-esis.57.12 155 figure 17: the contribution of different uncertainties on the total structural systems failure. sensitivity analysis based sobol's sobol’s sensitivity analysis is a variance based sensitivity test. this method attempts to specify numerically the effect of input variables with different statistical distributions on the output variance of a global structural system based on probabilistic analyses. the supplementary descriptions are given about this method in sobol' researches [59, 60]. also, a global sensitivity analysis is used by arwade et al. [61] for structural systems and assessing the effects of input distributions and possible approximation of the structural response function on final results. in this approach, the parameter y is introduced as the scalar output and function of ( 1 2, , , ). kx x x then, this function is the main contribution of the i th input variable alone versus to ( ) v y as the total output variance. this global sensitivity analysis method is named the first-order index, and this extracted index can be obtained by using the conditional variance as eqn. 20: ( )( ) ( ) = | iv e y x v y is (20) eqn. 20 shows that the variance is calculated while changing ix alone and for all possible variations of other input variables , ix the averaging of outputs is presented. also, for models, si is a sum of the first-order indices that is equivalent to one. the variables ix and jx are related to each other, therefore the interaction among them can be determined as eqn. 21: ( )( ) ( ) = − − | ,i j i j v e y x x s s v y ijs (21) the total influence as another approach for global sensitivity analysis is applied in the following, which can be specified by eqn. 22: ( )( ) ( ) = − ~| 1 iv e y x v y tis (22) in eqn. 22, the inner expectation is defined by the parameter ~ix which is conditional on all variables except ix . thus, all sources of variation except the i th variable are appertained to the term ( )~ ( | iv e y x , and the total influence of the mentioned variable can be computed by subtracting it from the total variance. the results of global sensitivity analysis are indicated in fig. 18. also, it shows the sensitivity indices and total influences of uncertainty parameters in current study. both global sensitivity analyses indicate the good agreement for specifying the effective random variables on failure probability computation. these results demonstrate the effect of each random variable on the output variance. however, according to the outcomes from global sensitivity analyses, it is specified that the main factors related to the vehicle features are important in the structural responses. secondly, material properties such as yield strength is more effective under impact a. sadeghi et alii, frattura ed integrità strutturale, 57 (2021) 138-159; doi: 10.3221/igf-esis.57.12 156 loadings. the total influences and the first-order sensitivity analyses are compared and indicated the interaction between variables and high-order sensitivity analyses. based on the obtained results, for instance, the total influences and the firstorder sensitivity indices for random variable vehicle velocity are obtained 0.58 and 0.49, respectively. the comparison of these methods show that the total influences approach has more accurate versus the first-order sensitivity method. a global sensitivity analysis shows the ability of quantifying the effect of each random variable exactly. therefore, considering uncertainties in loading, geometric and material properties is necessary for probabilistic assessment of smrf structures subjected to vehicle impact. at last, based on the extracted results of sensitivity analyses, it is obvious that the vehicle velocity should be controlled and this action is the best way for collapse prevention of structures under vehicle impact loadings. figure 18: the importance of random variables by first-order sensitivity indices and total influences. conclusion n this paper, the probabilistic evaluation and reliability analyses of a 2-story smrf were conducted under impact loadings. the verification of the modeling was confirmed in opensees software with regarding to the verification of authentic studies in the technical literatures. the uncertainties of model in terms of gravity loads, material, geometric and impact loading were taken into account. sensitivity analyses were performed to identify the major uncertainty parameters that affect the failure probability of model with two sensitivity tests such as mcs and sobol's methods. to reduce the computational costs in the reliability analyses, three meta-models including kriging, prsm, and ann were constructed. finally, fragility curves are applied by two approaches such as kriging and exact methods in order to determine the accuracy of meta-model and specifying the performance levels of aforementioned frame under vehicle impact. the findings are summarized as below: sensitivity analyses showed that vehicle parameters were the most influential factors in failure probability calculation. the mass and velocity of vehicle and the yield strength of structural members had the greatest effect and the live load of the studied frame had the least effect on the structural failure probability computation. by calculating the failure probability under different vehicle collision velocities for the three lsfs, it is determined that by increasing vehicle velocity, the probability of failure increases and the reliability index decreases up to 13%, 20% and 18% for three lsfs, respectively. the least error rate of kriging surrogate model in estimating responses of studied frame in comparison with mcs and other meta-models indicated that it is the best surrogate model for using in reliability analyses. the validity of kriging results was confirmed though comparing those given results with the mcs results, whereas it could significantly reduce the computational processing time in comparison with mcs. hence, kriging is a powerful surrogate model for reliability analyses of nonlinear problems. based on kriging surrogate model, the minimum failure probability variations are increased by 75%, 68% and 55%, with vehicle velocity augment from 20 to 40 km/h, for lsf1, lsf2 and lsf3, respectively. then, the maximum failure probability variations showed an increase of 56%, 25% and 20%, with increasing vehicle velocity from 40 to 50 km/h for aforementioned three lsfs, respectively. i a. sadeghi et alii, frattura ed integrità strutturale, 57 (2021) 138-159; doi: 10.3221/igf-esis.57.12 157 according to kriging surrogate model, by increasing the range of vehicle velocity from 10 to 20 km/h, 20 to 30 km/h, 30 to 40 km/h and 40 to 50 km/h, the maximum values of beam rotation has increased by 80%, 54%, 42% and 25%, respectively . the overall behavior of smrf structure is evaluated under impact loadings using fragility analysis based kriging, which showed that the probabilities of reaching the three different damage states are similar to the exact method that extracted from finite element results with the least computational processing time. the analysis results revealed that the computational efficiency is improved in terms of application the kriging surrogate model for probabilistic assessment of smrf structures under vehicle impact loadings. however the effective methods, the performance investigation of smrf structures under this scenario is still discussed as hot research topic using soft computing methods. references [1] eurocode 1. (2006). actions on structures – part 1-7: general actions – accidental actions. [2] cormie, d., mays, g. and smith, p. (2009). vehicle-borne threats and the principles of hostile vehicle mitigation, in blast effects on buildings (2nd edition.), thomas telford. [3] severino, e. and el-tawil, s. (2003). collision of vehicles with bridge piers, computational fluid and solid mechanics, pp. 637–640. doi: 10.1016/b978-008044046-0.50156-1. [4] el-tawil, s., severino, e. and fonseca, p. (2005). vehicle collision with bridge piers, journal of bridge engineering, 10(3), pp. 345–53. doi: 10.1061/(asce)1084-0702(2005)10:3(345). [5] sharma, h., gardoni, p. and hurlebaus, s. (2014). probabilistic demand model and performance based fragility estimates for rc column subject to vehicle collision, engineering structures, 74, pp. 86–95. doi: 10.1016/j.engstruct.2014.05.017. [6] sharma, h., gardoni, p. and hurlebaus, s. (2015). performance-based probabilistic capacity models and fragility estimates for rc columns subject to vehicle collision, computer-aided civil and infrastructure engineering, 30, pp. 555–69. doi: 10.1111/mice.12135. [7] kang, h. and kim, j. (2017). response of a steel column-footing connection subjected to vehicle impact, structural engineering and mechanics, 63, pp. 125–36. doi: 10.12989/sem.2017.63.1.125. [8] javidan, m.m., kang, h., isobe, d. and kim, j. (2018). computationally efficient framework for probabilistic collapse analysis of structures under extreme actions, engineering structures, 17, pp. 440–452. doi: 10.1016/j.engstruct.2018.06.022. [9] santos, a.f., santiago, a., latour, m. and rizzano, g. (2020). robustness analysis of steel frames subjected to vehicle collisions, structures, 25, pp. 930–942. doi: 10.1016/j.istruc.2020.03.043. [10] oliveira, m.c., teles, d.v.c. and amorim, d.l.n.f. (2020). shear behaviour of reinforced concrete beams under impact loads by the lumped damage framework, frattura ed integrità strutturale, 53, pp. 13-25. doi: 10.3221/igf-esis.53.02. [11] sadeghi, a., kazemi, h. and samadi, m. (2021). probabilistic seismic analysis of steel moment-resisting frame structure including a damaged column, structures, 33, pp. 187-200. doi: 10.1016/j.istruc.2021.03.065. [12] rashki, m., miri, m. and azhdary moghaddam, m. (2012). a new efficient simulation method to approximate the probability of failure and most probable point, structural safety, 39, pp. 22–29. doi: 10.1016/j.strusafe.2012.06.003. [13] kim, j., park, j. and lee, t. (2011). sensitivity analysis of steel buildings subjected to column loss, engineering structures, 33, pp. 421–432. doi: 10.1016/j.engstruct.2010.10.025. [14] bai, l. and zhang, y. (2012). collapse fragility assessment of steel roof framings with force limiting devices under transient wind loading, frontiers of structural and civil engineering, 6, pp. 199–209. doi: 10.1007/s11709-012-01684. [15] gidaris, i., taflanidis, a.a. and mavroeidis, g.p. (2015). kriging metamodeling in seismic risk assessment based on stochastic ground motion models. earthquake engineering and structural dynamics, 44, pp. 2377–2399. doi: 10.1002/eqe.2586. [16] vazirizade, s.m., nozhati, s. and allamehzadeh, m. (2017). seismic reliability assessment of structures using artificial neural network, journal of building engineering, 11, pp. 230– 235. doi: 10.1016/j.jobe.2017.04.001. [17] hashemi, s.s., sadeghi, k., fazeli, a. and zarei, m. (2019). predicting the weight of the steel moment-resisting frame structures using artificial neural networks, international journal of steel structures, 19, pp. 168–180. doi: 10.1007/s13296-018-0105-z. https://doi.org/10.1016/b978-008044046-0.50156-1 https://doi.org/10.1061/(asce)1084-0702(2005)10:3(345) http://dx.doi.org/10.1016/j.engstruct.2014.05.017 http://dx.doi.org/10.1016/j.engstruct.2014.05.017 http://dx.doi.org/10.1111/mice.12135 http://dx.doi.org/10.12989/sem.2017.63.1.125 https://doi.org/10.1016/j.engstruct.2018.06.022 https://doi.org/10.1016/j.engstruct.2018.06.022 https://doi.org/10.1016/j.istruc.2020.03.043 https://doi.org/10.3221/igf-esis.53.02 https://www.sciencedirect.com/science/article/abs/pii/s0167473012000410?via%3dihub#! https://www.sciencedirect.com/science/article/abs/pii/s0167473012000410?via%3dihub#! https://www.sciencedirect.com/science/article/abs/pii/s0167473012000410?via%3dihub#! https://www.sciencedirect.com/science/journal/01674730 https://doi.org/10.1016/j.engstruct.2010.10.025 https://doi.org/10.1002/eqe.2586 https://doi.org/10.1002/eqe.2586 https://doi.org/10.1016/j.jobe.2017.04.001 a. sadeghi et alii, frattura ed integrità strutturale, 57 (2021) 138-159; doi: 10.3221/igf-esis.57.12 158 [18] hadianfard, m.a., malekpour, s. and momeni, m. (2018). reliability analysis of h-section steel columns under blast loading, structural safety, 75, pp. 45–56. doi: 10.1016/j.strusafe.2018.06.001. [19] hedayat, a.a., ahmadi afzadi, e., kalantaripour, h., morshedi, e. and iranpour, a. (2019). a new predictive model for the minimum strength requirement of steel moment frames using artificial neural network, soil dynamics and earthquake engineering, 116, pp. 69–81. doi: 10.1016/j.soildyn.2018.09.046. [20] hoseini vaez, s.r., mehanpour, h. and fathali, m.a. (2020). reliability assessment of truss structures with natural frequency constraints using metaheuristic algorithms, journal of building engineering, 28. doi: 10.1016/j.jobe.2019.101065. [21] rahgozar, n., pouraminian, m. and rahgozar, n. (2021). reliability-based seismic assessment of controlled rocking steel cores, journal of building engineering, 44. doi: 10.1016/j.jobe.2021.102623. [22] fathi, p., oskouei, a.n., vahedi, k. and petrudi, a.m. (2020). numerical and experimental analysis of stacking sequences effects in composite mechanical joints under impact loadings, frattura ed integrità strutturale, 53, pp. 457-473. doi: 10.3221/igf-esis.53.36. [23] staroverov, o.a., strungar, e.m. and wildemann, v.e. (2021). evaluation of the survivability of cfrp honeycomb-cored panels in compression after impact tests, frattura ed integrità strutturale, 56, pp. 1-15. doi: 10.3221/igf-esis.56.01. [24] opensees. (2007). open system for earthquake engineering simulation manual, pacific earthquake engineering research center, university of california, berkeley, ca. http://opensees.berkeley.edu. [25] matlab. (2013). multi paradigm numerical computing environment and proprietary programming language developed by math works. https://www.mathworks.com/help/matlab/ [26] rashki, m. (2018). hybrid control variates-based simulation method for structural reliability analysis of some problems with low failure probability, applied mathematical modelling, 60, pp. 220–234. doi: 10.1016/j.apm.2018.03.009. [27] chen, s., hou, c., zhang, h., haihan, l. and minmu, t. (2020). reliability-based evaluation for concrete-filled steel tubular (cfst) truss under flexural loading, journal of constructional steel research, 169. doi: 10.1016/j.jcsr.2020.106018. [28] zhu, p., shi, l., yang, r. and lin s. (2015). a new sampling-based rbdo method via score function with reweighting scheme and application to vehicle designs, applied mathematical modelling, 39, pp. 4243–4256. doi: 10.1016/j.apm.2014.11.045. [29] rashki, m., azarkish, h., rostamian, m. and bahrpeyma, a. (2019). classification correction of polynomial response surface methods for accurate reliability estimation, structural safety, 81. doi: 10.1016/j.strusafe.2019.101869 [30] dubourg, v. and sudret, b. (2014). meta-model-based importance sampling for reliability sensitivity analysis, structural safety, 49, pp. 27–36. doi: 10.1016/j.strusafe.2013.08.010. [31] sudret, b. (2012). meta-models for structural reliability and uncertainty quantification, asian pacific symposium on structural reliability and its applications, singapore, pp. 1–24. [32] hao, y., rong, x., ma, l., fan, p. and lu, h. (2016). uncertainty analysis on risk assessment of water inrush in karst tunnels, mathematical problems in engineering, 2, pp. 1–11. doi: 10.1155/2016/2947628. [33] kianifar, m.r. and campean, f. (2020). performance evaluation of metamodeling methods for engineering problems: towards a practitioner guide, structural and multidisciplinary optimization, 61, pp. 159–186. doi: 10.1007/s00158019-02352-1. [34] kaymaz, i. (2015). application of kriging method to structural reliability problems, structural safety, 27, pp. 133–51. doi: 10.1016/j.strusafe.2004.09.001. [35] sasena, m. (2002). flexibility and efficiency enhancements for constrained global design optimization with kriging approximation, dissertation university of michigan. [36] box, gep. and wilson, k.b. (1954). the exploration and exploitation of response surfaces: some general considerations and examples, biometrics, 10, pp. 16–60. doi: 10.2307/3001663. [37] gaspar, b., teixeira, a. and guedes soares, c. assessment of the efficiency of kriging surrogate models for structural reliability analysis, probabilistic engineering mechanics, 37, pp. 24–34. doi: 10.1016/j.probengmech.2014.03.011. [38] faravelli, l. (1989). response surface approach for reliability analyses, journal of engineering mechanics, 115, pp. 2763–2781. doi: 10.1061/(asce)0733-9399(1989)115:12(2763). [39] roussouly, n., petitjean, f. and salaun, m. (2013). a new adaptive response surface method for reliability analysis, probabilistic engineering mechanics, 32, pp. 103–115. doi: 10.1016/j.probengmech.2012.10.001. [40] hadidi, a., farahmand azar, b. and rafiee, a. (2017). efficient response surface method for high dimensional structural reliability analysis, structural safety, 68, pp. 15–27. doi: 10.1016/j.strusafe.2017.03.006. https://doi.org/10.1016/j.strusafe.2018.06.001 https://doi.org/10.1016/j.soildyn.2018.09.046 https://doi.org/10.1016/j.jobe.2019.101065 https://doi.org/10.1016/j.jobe.2019.101065 https://doi.org/10.1016/j.engstruct.2020.111370 http://opensees.berkeley.edu/ https://doi.org/10.1016/j.apm.2018.03.009 https://www.sciencedirect.com/science/article/pii/s0143974x19315184#! https://www.sciencedirect.com/science/article/pii/s0143974x19315184#! https://www.sciencedirect.com/science/article/pii/s0143974x19315184#! https://www.sciencedirect.com/science/article/pii/s0143974x19315184#! https://www.sciencedirect.com/science/journal/0143974x https://www.sciencedirect.com/science/journal/0143974x/169/supp/c https://doi.org/10.1016/j.jcsr.2020.106018 https://doi.org/10.1016/j.jcsr.2020.106018 https://doi.org/10.1016/j.apm.2014.11.045 https://doi.org/10.1016/j.strusafe.2019.101869 https://www.sciencedirect.com/science/journal/01674730 https://www.sciencedirect.com/science/journal/01674730 https://doi.org/10.1016/j.strusafe.2013.08.010 https://doi.org/10.1155/2016/2947628 https://doi.org/10.1007/s00158-019-02352-1 https://doi.org/10.1007/s00158-019-02352-1 https://doi.org/10.1016/j.strusafe.2004.09.001 https://doi.org/10.1016/j.probengmech.2014.03.011 https://doi.org/10.1061/(asce)0733-9399(1989)115:12(2763) https://doi.org/10.1016/j.probengmech.2012.10.001 https://doi.org/10.1016/j.strusafe.2017.03.006 a. sadeghi et alii, frattura ed integrità strutturale, 57 (2021) 138-159; doi: 10.3221/igf-esis.57.12 159 [41] shayanfar, m., barkhordari, m.a. and roudak, m.a. (2017). an efficient reliability algorithm for locating design point using the combination of importance sampling concepts and response surface method, communications in nonlinear science and numerical simulation, 47, pp. 223–237. doi: 10.1016/j.cnsns.2016.11.021. [42] guimaraes, h., matos, j.c. and henriques, a.a. (2018). an innovative adaptive sparse response surface method for structural reliability analysis, structural safety, 73, pp. 12–28. doi: 10.1016/j.strusafe.2018.02.001. [43] elhewy, a.h., mesbahi, e. and pu, y. (2006). reliability analysis of structures using neural network method, probabilistic engineering mechanics, 21, pp. 44–53. doi: 10.1016/j. probengmech.2005.07.002. [44] chojaczyk, a.a., teixeira, a.p., neves, l.c., cardoso, j.b. and soares c.g. (2015). review and application of artificial neural networks models in reliability analysis of steel structures, structural safety, 52, pp. 78–89. doi: 10.1016/j.strusafe.2014.09.002. [45] asce 7. (2016). minimum design loads for buildings and other structures, new york: american society of civil engineers. [46] aisc 360. (2016). specifications for structural steel buildings, chicago: american institute of steel construction. [47] mujeeb, m., pasupuleti, v.d.k. and dongre, a. (2020). effect of vehicle impact on reinforced concrete structures. in: subramaniam k., khan m. (editors) advances in structural engineering, lecture notes in civil engineering, 74, springer, singapore. doi: 10.1007/978-981-15-4079-0_17. [48] mestrovic, d., cizmar, d. and miculinic l. (2008). reliability of concrete columns under vehicle impact, journal of wit transactions on the built environment, 98, pp. 157–165. doi: 10.2495/su080161. [49] ellingwood, b., galambos, t.v., macgregor, j.g. and cornell, c.a. (1980). development of a probability based load criterion for american national standard a58 – building code requirement for minimum design loads in buildings and other structures, washington, dc: national bureau of standards, dept. of commerce. [50] jcss. (2001). joint committee on structural safety, probabilistic model code. [51] cen. (1993). european committee for standardization, structural steel i and h sections – tolerances on shape and dimensions, brussels. [52] zhang, x., liu, j., yan, y. and pandey, m. (2019). an effective approach for reliability-based sensitivity analysis with the principle of maximum entropy and fractional moments, entropy, 21. doi: 10.3390/e21070649. [53] conrath, e.j., krauthammer, t., marchand, k.a. and mlakar, p.f. (1999). structural design for physical security – state of the practice, new york: asce. [54] ly, h.b., le, l.m., duong, h.t., nguyen, t.c., pham, t.a., le, t-t., le, v.m., nguyen-ngoc, l. and pham, b.t. (2019). hybrid artificial intelligence approaches for predicting critical buckling load of structural members under compression considering the influence of initial geometric imperfections, applied sciences, 9(11). doi: 10.3390/app9112258. [55] nguyen, h.q., ly, h-b., tran, v.q., nguyen, t-a., le, t-t. and pham, b.t. (2020). optimization of artificial intelligence system by evolutionary algorithm for prediction of axial capacity of rectangular concrete filled steel tubes under compression, materials, 13(5). doi: 10.3390/ma13051205. [56] pham, b.t., nguyen-thoi, t., ly, h.b., nguyen, m.d., al-ansari, n., tran, v.q. and le, t.t. (2020). extreme learning machine based prediction of soil shear strength: a sensitivity analysis using monte carlo simulations and feature backward elimination, sustainability, 12(6). doi: 10.3390/su12062339. [57] park, j. and kim, j. (2010). fragility analysis of steel moment frames with various seismic connections subjected to sudden loss of a column, engineering structures, 32, pp. 1547–55. doi: 10.1016/j.engstruct.2010.02.003. [58] wu, y.t. and mohanty, s. (2006). variable screening and ranking using sampling-based sensitivity measures, reliability engineering & system safety, 91(6), pp. 634–647. doi: 10.1016/j.ress.2005.05.004. [59] sobol', i.m. (1990). sensitivity estimates for nonlinear mathematical models, mat model, 2, pp. 112–8. [60] sobol', i.m. (2001). global sensitivity indices for nonlinear mathematical models and their monte carlo estimates, mathematics and computers in simulation, 55, pp. 271–80. doi: 10.1016/s0378-4754(00)00270-6. [61] arwade, s.r., moradi, m. and louhghalam, a. (2010). variance decomposition and global sensitivity for structural systems, engineering structures, 32, pp. 1–10. doi: 10.1016/j.engstruct.2009.08.011. http://www.journals.elsevier.com/communications-in-nonlinear-science-and-numerical-simulation/ http://www.journals.elsevier.com/communications-in-nonlinear-science-and-numerical-simulation/ https://doi.org/10.1016/j.cnsns.2016.11.021 https://doi.org/10.1016/j.strusafe.2018.02.001 http://dx.doi.org/10.1016/j http://dx.doi.org/10.1016/j.strusafe.2014.09.002 http://dx.doi.org/10.1016/j.strusafe.2014.09.002 https://www.witpress.com/elibrary/wit-transactions-on-the-built-environment https://doi.org/10.3390/e21070649 https://doi.org/10.3390/ma13051205 https://doi.org/10.3390/su12062339 http://dx.doi.org/10.1016/j.engstruct.2010.02.003 https://doi.org/10.1016/j.ress.2005.05.004 http://dx.doi.org/10.1016/s0378-4754(00)00270-6 http://dx.doi.org/10.1016/j.engstruct.2009.08.011 microsoft word 2355 y. khalfi et alii, frattura ed integrità strutturale, 48 (2019) 208-221; doi: 10.3221/igf-esis.48.22 208 mechanical stability investigation of advanced composite plates resting on elastic foundations using a new four-unknown refined theory yassine khalfi université de sidi bel abbes, bp 89 cité ben m’hidi 22000 sidi bel abbes, algérie khalfiyassinesba@yahoo.fr aboubakar seddik bouchikhi, yassine bellebna université de sidi bel abbes, ecole national polytechnique d’oran asbouchiki@yahoo.fr, yassinebellebna@yahoo.fr abstract. a refined and simple shear deformation theory for mechanical buckling of composite plate resting on two-parameter pasternak’s foundations is developed. the displacement field is chosen based on assumptions that the in-plane and transverse displacements consist of bending and shear components, and the shear components of in-plane displacements give rise to the parabolic variation of shear strain through the thickness in such a way that shear stresses vanish on the plate surfaces.therefore, there is no need to use shear correction factor. the number of independent unknowns of present theory is four, as against five in other shear deformation theories.it is assumed that the warping of the cross sections generated by transverse shear is presented by a hyperbolic function. the stability equations are determined using the present theory and based on the existence of material symmetry with respect to the median plane.the nonlinear strain-displacement of von karman relations are also taken into consideration. the boundary conditions for the plate are assumed to be simply supported in all edges. closed-form solutions are presented to calculate the critical load of mechanical buckling, which are useful for engineers in design. the effects of the foundation parameters, side-to-thickness ratio and modulus ratio, the isotropic and orthotropic square plates are presented comprehensively for the mechanical buckling of rectangular composite plates. keywords. rectangular composite plate; critical buckling load; refined shear theory; elastic foundation; non-linear relations of vont karman. citation: khalfi, y, bouchiki, a, s., bellebna, y., mechanical stability investigation of advanced composite plates resting on elastic foundations using a new four-unknown refined theory, frattura ed integrità strutturale, 48 (2019) 208-221. received: 20.01.2019 accepted: 12.02.2019 published: 01.04.2019 copyright: © 2019 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. http://www.gruppofrattura.it/va/48/2355.mp4 y. khalfi et alii, frattura ed integrità strutturale, 48 (2019) 208-221; doi: 10.3221/igf-esis.48.22 209 introduction omposite materials have important advantages over traditional materials. they bring many functional advantages: lightness, mechanical and chemical resistance, reduced maintenance, freedom of forms. they make it possible to increase the lifespan of certain equipment thanks to their mechanical and chemical properties. they contribute to the reinforcement of safety thanks to a better resistance to shocks and fire. they offer better thermal or sound insulation and, for some of them, good electrical insulation. they also enrich the design possibilities by lightening structures and making complex shapes, able to fulfill several functions. in each of the application markets (automotive, building, electricity, industrial equipment, etc.), these remarkable performances are at the origin of innovative technological solutions [1]. they constitute one of the most advanced class of materials whose popularity in industrial applications keeps growing exponentially [2]. their advent has been aided by the development of new processing methods, theoretical approaches of homogenization [3, 4] and numerical simulations of heterogeneous materials [5]. this class of materials is commonly divided into three categories [6] : (i) fibrous composites consisting of continuous fibers embedded in a matrix, (ii)laminated composites consisting of various stacked layers, and (iii) particle-reinforced composites composed of particles in a matrix. the buckling of rectangular plates has been a subject of study in solid mechanics for more than a century. many exact solutions for isotropic and orthotropic plates have been developed, most of them can be found in timoshenko and woinowsky-krieger [7], timoshenko and gere [8], bank and jin [9], kang and leissa [10], aydogdu and ece [11], and hwang and lee [12]. in company with studies of buckling behavior of plate, many plate theories have been developed. the simplest one is the classical plate theory (cpt) which neglects the transverse normal and shear stresses. this theory is not appropriate for the thick and orthotropic plate with high degree of modulus ratio. in order to overcome this limitation, the shear deformable theory which takes account of transverse shear effects is recommended. the reissner [13] and mindlin [14] theories are known as the first-order shear deformation theory (fsdt), and account for the transverse shear effects by the way of linear variation of in-plane displacements through the thickness. however, these models do not satisfy the zero traction boundary conditions on the top and bottom faces of the plate, and need to use the shear correction factor to satisfy the constitutive relations for transverse shear stresses and shear strains. for these reasons, many higher-order theories have been developed to improve in fsdt such as levinson [15] and reddy [16]. shimpi and patel [17] presented a four variable refined plate theory (rpt) for orthotropic plates.this theory which looks like higher-orde theory uses only four unknown functions in order to derive two governing equations for orthotropic plates. the most interesting feature of this theory is that it does not require shear correction factor, and has strong similarities with the cpt in some aspects such as governing equation, boundary conditions and moment expressions. the accuracy of this theory has been demonstrated for static bending and free vibration behaviors of plates by shimpi and patel [17], therefore, it seems to be important to extend this theory to the static buckling behavior. in this paper, the four variable rpt developed by shimpi and patel [17] has been extended to the buckling behavior of isotropic and orthotropic plate resting on two-parameter pasternak’s foundations subjected to the in-plane loading. using the navier method, the closed-form solutions have been obtained. numerical examples involving side-to-thickness ratio, effects of the foundation parameters and modulus ratio are presented to illustrate the accuracy of the present theory in predicting the critical buckling load of isotropic and orthotropic plates. the numerical results obtained by the present theory are compared with solutions of classical theory (cpt) and solutions of first order shear deformation theory (fsdt) and high order shear theory (hsdt). mathematical formulation onsider a rectangular composite plate of thickness h, length a and width b, referred to the rectangular cartesian coordinate system (x, y, z), as shown in fig 1. since in this type of plates there is material symmetry with respect to the median plane (the origin of the coordinate system is appropriately chosen in the direction of the thickness of the composite plate so that it will be confused with the neutral surface) the equations of membranes and bending will be decoupled and therefore equilibrium equations [18]. based on the refined theory of shear deformation [19], the displacement field can be written as: 0( , , ) ( , ) ( )        b sw wu x y z u x y z f z x x (1a) 0( , , ) ( , ) ( )        b sw wv x y z v x y z f z y y (1b) c c y. khalfi et alii, frattura ed integrità strutturale, 48 (2019) 208-221; doi: 10.3221/igf-esis.48.22 210 ( , ) ( , ) ( , ) b sw x y w x y w x y (1c) where u0 and v0 are the mid-plane displacements of the plate in the x and y direction, respectively; wb and ws are the bending and shear components of transverse displacement, respectively. figure 1: coordinate system and geometry for rectangular composite plate on pasternak elastic foundation. this displacement field verifies the nullity of traction boundary conditions on the top and bottom faces of the plate, and leads to a quadratic variation of transverse shear deformations (and therefore stresses) across the thickness. thus, it is not necessary to use shear correction factors. the nonlinear deformation-displacement equations of von karman are as follows: 0 0 0 ( ) , ( ) b s x x x sx yzyzb s y y y y s xz yzb s xy xy xy xy k k z k f z k g z k k                                                                                (2) where 2 2 2 0 0 2 2 1 , , 2                 b sb s b s x x x u w w w w k k x x x x x (3a) 2 2 2 0 0 2 2 1 , , 2                    b sb s b s y x x v w w w w k k y y y y y (3b) 0 0 0                       b s b s xy u v w w w w y x x x y y 2 2 2 2 2 , 2         b sb s xy xy w w k k y y (3c)  / sinh( ) , , ( ) cosh( / ) 1              s ss s yz xz h z z w w hf z y x h ( ) ( ) 1 ( ), ( ) f z g z f z f z z       (3d) the linear constitutive relations of a composite plate can be written as y. khalfi et alii, frattura ed integrità strutturale, 48 (2019) 208-221; doi: 10.3221/igf-esis.48.22 211 12 22 12 22 66 44 55 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 x x y y xy xy yz yz xz xz q q q q q q q                                                    (4) where (σx, σy, τxy, τyz, τyx) and (εx, εy, γxy, γyz, γyx) are the stress and strain components, respectively. qij are the elements of the reduced stiffness matrix that are defined as follows: 1 12 2 2 11 12 22 66 12 44 23 55 13 12 21 12 21 12 21 , , , , , 1 1 1 e e e q q q q g q g q g                 (5) based on the present refined shear plate theory, the stress resultants are related to the stresses by the equations [19]   / 2 / 2 1 , , ( )                          x y xy h b b b x y xy x y xy h s s s x y xy n n n m m m z dz f zm m m (6a) / 2 / 2 ( , ) ( , ) ( )     h s s xz yz xz yz h s s g z dz (6b) using eq. (4) in eq. (6), the stress resultants of the can be related to the total strains by 0 0 , s b s b s s s s s s n a b m d d k s a m b d h k                              (7) where      , , , , , , ,t tt b b b b s s s sx y xy x y xy x y xyn n n n m m m m m m m m   (8a)      0 0 0, , , , , , , ,t t tb b b b s s s sx y xy x y xy x y xyk k k k k k k k      (8b) 11 12 11 12 12 22 12 22 66 66 0 0 0 , 0 0 0 0 0                    a a d d a a a d d d a d (9a) 11 12 11 12 11 12 12 22 12 22 12 22 66 66 66 0 0 0 0 , 0 , 0 0 0 0 0 0 0                                      s s s s s s s s s s s s s s s s s s b b d d h h b b b d d d h h h b d h (9b)     44 55 0 , , , , 0              s t ts s s yz xz yz xz s a s s s a a (9c) y. khalfi et alii, frattura ed integrità strutturale, 48 (2019) 208-221; doi: 10.3221/igf-esis.48.22 212 where aij,dij , etc., are the plate stiffness, defined by 2 2 11 11 11 11 11 11 / 2 2 2 12 12 12 12 12 12 / 2 2 2 66 66 66 66 66 66 22 22 22 22 22 11 (1, , ( ), ( ), ( )) (1, , ( ), ( ), ( )) (1, , ( ), ( ), ( )) ( , , , , ) ( ,                          s s s h s s s h s s s s s s a d b d h q z f z zf z f z a d b d h q z f z zf z f z dz a d b d h q z f z zf z f z a d b d h a d11 11 11 11, , , ) s s sb d h   2/ 2 44 55 / / 2 44 ( )   h s s h a a q g z dz (10) equilibrium and stability equations he equilibrium equations of the rectangular composite plate resting on the pasternak elastic foundation under mechanical loadings may be derived on the basis of the stationary potential energy. the total potential energy of the plate, v, may be written in the form v=u+uf (11) here, u is the total strain energy of the plate, and is calculated as / 2 0 0 / 2 1 2 a b h x x y y xy xy yz yz xz xz h u dzdydx                    (12) and uf is the strain energy due to the pasternak elastic foundation, which is given by [20] 0 0 1 ( ) 2 a b f e b su f w w dydx   (13) where fe is the density of reaction force of foundation. for the pasternak foundation model: 2( ) ( )e w b s g b sf k w w k w w     (14) where kw is the winkler foundation stiffness and kg is a constant showing the effect of the shear interactions of the vertical elements. using eqs. (2), (3), and (7) and employing the virtual work principle to minimize the functional of total potential energy function result in the expressions for the equilibrium equations of plate resting on two parameters elastic foundation as 0      xyx nn x y 0       xy yn n x y 2 22 2 2 2 0           b bb xy yx e m mm n f x yx y t y. khalfi et alii, frattura ed integrità strutturale, 48 (2019) 208-221; doi: 10.3221/igf-esis.48.22 213 2 22 2 2 2 0                 s s ss s xy y yzx xz e m m sm s n f x y x yx y (15) where 2 2 2 2 2 ( ) ( ) ( ) 2b s b s b sxy w w w w w w n nx n ny x yx y                 (16) the stability equations in terms of displacement can be obtained by substituting equation (7) in equation (15). the equations obtained based on the present theory of refined shear deformation of the composite plates resting on two-parameter elastic foundation are four in number and are as follows: 2 2 2 3 3 0 0 0 11 66 12 66 11 12 662 2 3 2 ( ) ( 2 ) 0                   s s ss su u v w wa a a a b b b x yx y x x y 2 2 2 3 3 0 0 0 12 66 66 22 22 12 662 2 3 2 ( ) ( 2 ) 0                    s s ss su v v w wa a a a b b b x y x y y x y 4 4 4 4 4 4 11 12 66 22 11 12 66 224 2 2 4 4 2 2 4 2( 2 ) 2( 2 )                        s s s sb b b s s sw w w w w wd d d d d d d d x x y y x x y y 2( ) ( ) 0      w b s g b sk w w k w w n 3 3 3 3 4 4 0 0 0 0 11 12 66 12 66 22 11 12 663 2 2 3 4 2 2 4 4 4 4 2 2 22 11 12 66 22 55 444 4 2 2 4 2 2 ( 2 ) ( 2 ) 2( 2 ) 2( 2 ) ( )                                               s s s s s s s s sb b s s s s s s sb s s s s s w b s g u u v v w w b b b b b b d d d x x y x y y x x y w w w w w w d h h h h a a k w w y x x y y x y k 2 ( ) 0   b sw w n (17) trigonometric solution to mechanical buckling ectangular plates are generally classified in accordance with the type of support. we are here concerned with the exact solution of eq. (17) for a simply supported rectangular composite plate (figure 2a). the following boundary conditions are imposed for the present refined shear deformation theory at the side edges [21]: 0 0,          b ss b s x x x w v w w n m m at x a y (18a) 0 0,          b ss b s y y y w u w w n m m at y b y (18b) the following approximate solution is seen to satisfy both the differential equation and the boundary conditions 0 0 1 1 cos( ) sin( ) cos( ) sin( ) sin( ) sin( ) sin( ) sin( ) mn mn b bmnm n s smn u u x y v v x y w w x y w w x y                                         (19) where umn, vmn, wbmn, and wsmn are arbitrary parameters to be determined and λ = mπ/a and μ = nπ/b. substituting eq. (19) into eq. (17), one obtains r y. khalfi et alii, frattura ed integrità strutturale, 48 (2019) 208-221; doi: 10.3221/igf-esis.48.22 214    0k   (20) where {δ} denotes the column    , , , tmn mn bmn smnu v w w  (21) and [k] is the symmetric matrix given by   11 12 13 14 12 22 23 24 13 23 33 34 14 24 34 44 a a a a a a a a k a a a a a a a a             (22) figure 2: rectangular plate: (a) boundary condition and (b) in-plane forces. in which 2 211 11 66( )   a a a 12 12 66( )  a a a 13 0a 2 214 11 12 66( 2 )       s s sa b b b 2 222 66 22( )   a a a 23 0a 2 224 12 66 22( 2 )       s s sa b b b 4 2 2 4 0 2 0 2 2 233 11 12 66 22( 2( 2 ) ( ) )                x y g wa d d d d n n k k 4 2 2 4 0 2 0 2 2 234 11 12 66 22( 2( 2 ) ( ) )                 s s s s x y g wa d d d d n n k k y. khalfi et alii, frattura ed integrità strutturale, 48 (2019) 208-221; doi: 10.3221/igf-esis.48.22 215 4 2 2 4 2 2 0 2 0 2 2 2 44 11 12 66 22 55 44( 2( 2 ) ( ) )                     s s s s s s x y g wa h h h h a a n n k k (23) by applying the static condensation approach to eliminate the coefficients associated with the in-plane displacements, eq. (20) can be rewritten as 11 22 12 1 212 0 0t k k k k                                  (24) where 33 3411 12 1411 12 22 34 4412 22 24 0 , , 0                            a aa a a k k k a aa a a (25a) 1 2,                mn bmn mn smn u w v w (25b) equation (24) represents a pair of two matrix equations: 11 1 12 2 0         k k (26a) 12 1 22 2 0          t k k (26b) solving eq. (26a) for δ1 and then substituting the result into eq. (26b), the following equation is obtained: 22 2 0k     (27) where 122 33 3422 12 11 12 34 44 t a a k k k k k a b                            (28a) and 33 3433 34, a a a a 1 243 34 44 44 14 24 0 0 ,    b b a a b a a a b b 20 11 22 12 1 14 22 12 24 2 11 24 12 14, , ,     b a a a b a a a a b a a a a (28b) for nontrivial solution, the determinant of the coefficient matrix in eq. (27) must be zero. this gives the following expression for the mechanical buckling load 2 0 0 33 44 34 2 2 33 44 34 1 2 x y a b a n n a a a       (29) y. khalfi et alii, frattura ed integrità strutturale, 48 (2019) 208-221; doi: 10.3221/igf-esis.48.22 216 clearly, when the effect of transverse shear deformation is neglected, the eq.(29) yields the result obtained using the classical plate theory [22]. it indicates that transverse shear deformation has the effect of reducing the buckling load. for each choice of m and n, there is a corresponsive unique value of n0. the critical buckling load is the smallest value of n0(m, n). results and discussion o illustrate the proposed theory, a simply supported rectangular plate subjected to the different types of loading (or even figure.2), is considered to verify the accuracy of the current theory in the prediction of the critical loads of the mechanical buckling of rectangular composite plates. comparisons are made with different plate theories available in the literature the description of the different displacement models is given in table 1. in order to study the effects of the parameters of the foundation, side-to-thickness ratio (a/h) and the modulus ratios (e1/e2), isotropic square plates and orthotropes are considered. the shear correction factor (k=5/6) and also used for the first order shear deformation theory (fsdt) and a comparison with the current theory is established. figure 3: the loading conditions of square plate for (a) uniaxial compression, (b) biaxial compression. model theory unknown functions cpt fsdt hsdt present classical plate theory first-order shear deformation theory [23] higer order shear deformation theory [24] present refined plate theory 3 5 5 4 table 1: displacement models. it is assumed that the thickness and properties of materials for all laminates are the same. the following engineer constants are used [25]:  for isotropic rectangular plates: e1 = e2= e, g12 = g13= g23 = g = e/2(1+ ν), ν12 = ν13 = ν23= ν = 0.3 (30)  for orthotropic rectangular plates: e1 = e2 varied, g12/e2 = g13/e2 = 0.5, g23/e2 = 0.2, ν12 = 0.25, ν21:=( ν12 e2)/e1 (31) for convenience, the following nondimensional buckling load is used: t y. khalfi et alii, frattura ed integrità strutturale, 48 (2019) 208-221; doi: 10.3221/igf-esis.48.22 217 2 3 2 crn an e h  (32) where a is the length of the square plate and h is the thickness of the plate. the following dimensionless of winkler’s and pasternak’s elastic foundation parameters, as well as the critical buckling temperature difference are used in the present analysis 4 4 1 2,w g a a k k k k d d   (33) where 3 2 2 / 12(1 )d e h     (34) a/h theories k1=0, k2=0 k1=10, k2=0 k1=10, k2=10 k1=0, k2=0 k1=10, k2=0 k1=10, k2=10 isotropic v = 0.3 orthotrophic e1/e2=10 25 40 orthotrophic e1/e2=10 25 40 orthotrophic e1/e2=10 25 40 5 present cpt fsdt hsdt 2.9512 3.0440 4.8755 3.6152 3.7080 5.5395 2.9498 3.0042 3.9345 2.9512 3.0440 4.8755 6.3487 9.1039 10.578 11.1628 23.4949 35.8307 6.1804 8.2199 9.1085 6.3487 9.1039 10.578 6.4378 9.1939 10.6685 11.2528 23.5849 35.9207 6.2265 8.2666 9.1564 6.4378 9.1939 10.6685 8.2156 10.9717 12.4463 13.0306 25.3627 37.6986 7.0759 9.1356 10.0504 8.2156 10.9717 12.4463 10 present cpt fsdt hsdt 3.4224 3.5151 5.3466 3.6152 3.7080 5.5395 3.4222 3.5088 5.1996 3.4224 3.5151 5.3466 9.3732 16.7719 22.2581 11.1628 23.4949 35.8307 9.2733 15.8736 20.3044 9.3732 16.7719 22.2581 9.4632 16.8620 22.3482 11.2528 23.5849 35.9207 9.3531 15.9501 20.3789 9.4632 16.8620 22.3482 11.2410 18.6397 24.1260 13.0306 25.3627 37.6986 10.9144 17.4460 21.8356 11.2410 18.6397 24.1260 20 present cpt fsdt hsdt 3.5650 3.6578 5.4893 3.6152 3.7080 5.5395 3.5650 3.6569 5.4711 3.5650 3.6578 5.4893 10.6534 21.3479 31.0685 11.1628 23.4949 35.8307 10.6199 20.9528 30.0139 10.6534 21.3479 31.0685 10.7435 21.4380 31.1586 12.0634 25.7465 39.4333 10.7085 21.0405 30.1009 10.7435 21.4380 31.1586 12.5212 23.2158 32.9364 13.0306 25.3627 37.6986 12.4555 22.7709 31.8171 12.5212 23.2158 32.9364 50 present cpt fsdt hsdt 3.6071 3.6999 5.5314 3.6152 3.7080 5.5395 3.6071 3.6998 5.5303 3.6071 3.6999 5.5314 11.0780 23.1225 34.9717 11.1628 23.4949 35.8307 11.0721 23.0464 34.7487 11.0780 23.1225 34.9717 11.1681 23.2125 35.0618 11.2528 23.5849 35.9207 11.1621 23.1360 34.8386 11.1681 23.2125 35.0618 12.9458 24.9903 36.8396 13.0306 25.3627 37.6986 12.9379 24.9105 36.6118 12.9458 24.9903 36.8396 100 present cpt fsdt hsdt 3.6132 3.7060 5.5375 3.6152 3.7080 5.5395 3.6132 3.7060 5.5373 3.6132 3.7060 5.5375 11.1415 23.4007 35.6120 11.1628 23.4949 35.8307 11.1400 23.3810 35.5538 11.1415 23.4007 35.6120 11.2315 23.4907 35.7021 11.2528 23.5849 35.9207 11.2300 23.4711 35.6438 11.2315 23.4907 35.7021 13.0093 25.2685 37.4798 13.0306 25.3627 37.6986 13.0076 25.2484 37.4210 13.0093 25.2685 37.4798 table 2: comparison of nondimensional critical buckling load of square plates subjected to uniaxial compression. in order to verify the mechanical buckling solutions determined in this work, the results of composite plates under uniaxial and biaxial loading are obtained and compared with those predicted by cpt, fsdt, and hsdt as indicated in tables 2 and 3.it is clear that the results show significant differences between the shear deformation theories and the classical plate theory, due to the shear deformation effect. in addition, an excellent agreement is obtained between the current theory and the hsdt for all side-to-thickness ratio values a/h and the modulus ratiose1/e2. the disagreement between the present theory rpt and hsdt on the one hand and the first order shear theory fsdt on the other hand increases as the side-tothickness a/h and the modulus ratios e1/e2 increases. it can also be noted that the dimensionless critical load of buckling increases rapidly with the increase of the side-to-thickness ratio a/h, while this dimensionless load ceases to increase when y. khalfi et alii, frattura ed integrità strutturale, 48 (2019) 208-221; doi: 10.3221/igf-esis.48.22 218 this ratio exceeds 25 (the plate becomes thinner more and more), and the results obtained by shear deformation theories (current rpt theory and first-order shear theory fsdt and high order theory hsdt) become identical to that obtained by conventional cpt theory, implying that the effect transverse shear becomes useless. indeed, the non dimensional critical load of the buckling does not depend on the variation of side-to-thickness according to the classical theory which neglects the effect of the transverse shear. it is clear to note the considerable increase in dimensionless critical load of buckling when the plate rests on an elastic foundation. it should be noted that the unknown function in present theory is 4, while the unknown function in fsdt and hsdt is 5. it can be concluded that the present theory is not only accurate but also simple in predicting the critical buckling load of rectangular composite plates. a/h theories k1=0, k2=0 k1=10, k2=0 k1=10, k2=10 k1=0, k2=0 k1=10, k2=0 k1=10, k2=10 isotropic v = 0.3 orthotrophic e1/e2=10 25 40 orthotrophic e1/e2=10 25 40 orthotrophic e1/e2=10 25 40 5 present cpt fsdt hsdt 1.4756 1.5220 2.4378 1.8076 1.8540 2.7698 1.4749 1.5070 2.1138 1.4756 1.5220 2.4378 2.8549 3.3309 3.4800 5.5814 8.4069 10.8715 2.8319 3.1422 3.2822 2.8549 3.3309 3.4800 2.8729a 3.3489a 3.6905a 5.6264 8.4249a 10.8895a 2.8341a 3.1453 a 3.2859a 2.8729a 3.3489a 3.6905a 4.1078 4.2378a 4.5794a 6.5153 9.3138a 11.7783a 2.9976 a 3.3390a 3.4994a 4.1078 4.2378a 4.5794a 10 present cpt fsdt hsdt 1.7112 1.7576 2.6733 1.8076 1.8540 2.7698 1.7111 1.7552 2.6208 1.7112 1.7576 2.6733 4.6718 6.0646a 7.2536 5.5814 8.4069 10.8715 4.6367 5.8370 6.6325 4.6718 6.0646a 7.2536 4.6898a 6.0826a 7.2716a 5.6264 8.4249a 10.8895a 4.6765 5.8491 a 6.6444a 4.6898a 6.0826a 7.2716a 5.5787a 6.9714 a 8.1604a 6.5153 9.3138a 11.7783a 5.2882 a 6.4367 a 7.2181a 5.5787a 6.9714 a 8.1604a 20 present cpt fsdt hsdt 1.7825 1.8289 2.7446 1.8076 1.8540 2.7698 1.7825 1.8286 2.7380 1.7825 1.8289 2.7446 5.3267 7.6643a 9.6614a 5.5814 8.4069 10.8715 5.3100 7.5546 9.3049 5.3267 7.6643a 9.6614a 5.3717 7.6823a 9.6794a 5.6264 8.4249a 10.8895a 5.3542 7.5716a 9.3217a 5.3717 7.6823a 9.6794a 6.2606 8.5711a 10.5682a 6.5153 9.3138a 11.7783a 6.2277 8.4083 a 10.1518a 6.2606 8.5711a 10.5682a 50 present cpt fsdt hsdt 1.8036 1.8500 2.7657 1.8076 1.8540 2.7698 1.8036 1.8499 2.7653 1.8036 1.8500 2.7657 5.5390 8.2784a 10.6576a 5.5814 8.4069 10.8715 5.5361 8.2566 10.5810 5.5390 8.2784a 10.6576a 5.5840 8.2964a 10.6756a 5.6264 8.4249a 10.8895a 5.5810 8.2744a 10.5989a 5.5840 8.2964a 10.6756a 6.4729 9.1853a 11.5645a 6.5153 9.3138a 11.7783a 6.4689 9.1597 a 11.4835a 6.4729 9.1853a 11.5645a 100 present cpt fsdt hsdt 1.8066 1.8530 2.7687 1.8076 1.8540 2.7698 1.8066 1.8530 2.7687 1.8066 1.8530 2.7687 5.5707 8.3744a 10.8172a 5.5814 8.4069 10.8715 5.5700 8.3687 10.7972 5.5707 8.3744a 10.8172a 5.6158 8.3924a 10.8352a 5.6264 8.4249a 10.8895a 5.6150 8.3867 a 10.8151a 5.6158 8.3924a 10.8352a 6.5046 9.2813a 11.7241a 6.5153 9.3138a 11.7783a 6.5038 9.2752a 11.7035a 6.5046 9.2813a 11.7241a a mode for plate is (m, n) = (1,2). table 3: comparison of nondimensional critical buckling load of square plates subjected to biaxial compressive load figures 4 show the effect of the side-to-thickness ratio (a/h) on the dimensionless critical buckling n when the square plate (a/b = 1) without elastic foundation or resting on winkler’s or pasternak’s elastic foundations using the present refined shear deformation theory. it is noted that n increases rapidly with increasing side-to-thickness ratio. however, for the plate without elastic foundation or resting on one parameter winkler’s foundation, the variation of the dimensionless critical buckling n is almost independent of the side-to-thickness ratio (a/h) when this latter is higher than 25 . it can be also seen that the presence of elastic foundations lead to an increase of the dimensionless critical buckling n . figures 5 and 6 show the variation of the critical load of the dimensionless buckling n of the rectangular composite plates without elastic foundation or resting on winkler’s or pasternak’s elastic foundations as a function of the modulus ratio (e1/e2).the plate is assumed to be subjected to axial loading shown in fig. 3 (uniaxial compression and biaxial compression). it is found that the critical load of dimensionless buckling increases monotonically as the the modulus ratio (e1/e2) increases. it is also noted that the critical dimensionless load n of the rectangular composite plates under unaxial compression is greater than that of a plate under biaxial compression. y. khalfi et alii, frattura ed integrità strutturale, 48 (2019) 208-221; doi: 10.3221/igf-esis.48.22 219 figure 4: the effect of side-to-thickness and modulus ratios on the critical buckling load of square plate with or without elastic foundations subjected to uniaxial compression: (a)isotropic,(b)e1/e2 =10, (c)e1/e2 =25 and (d)e1/e2= 40. figure 5: the effect of modulus ratio on the critical buckling load of square plate with or without elastic foundations subjected to uniaxial compression : (a)a =10h and (b)a =20h. y. khalfi et alii, frattura ed integrità strutturale, 48 (2019) 208-221; doi: 10.3221/igf-esis.48.22 220 figure 6: the effect of modulus ratio on the critical buckling load of square plate with or without elastic foundations subjected to biaxial compression: (a)a =10h and (b)a =20h. conclusion refined and simple shear deformation theory is presented for mechanical buckling of rectangular composite plates in contact with two-parameter elastic foundation. unlike the conventional shear deformation theories, the proposed refined shear deformation theory contains only four unknowns and has strong similarities with the cpt in many aspects, accounts for a quadratic variation of the transverse shear strains across the thickness, and satisfies the zero traction boundary conditions on the top and bottom surfaces of the plate without using shear correction factors. to clarify the effect of shear deformation on the critical buckling, the results obtained by the present theory as well as hsdt, s and fsdt are compared with those obtained by cpt. it is shown through the numerical examples that the results of the shear deformation plate theories are lower than those of the cpt, indicating the shear deformation effect. all comparison studies show that the critical buckling mechanical obtained by the proposed theory with four unknowns are almost identical with those predicted by other shear deformation theories containing five unknowns. it can be concluded that the proposed theory is accurate and efficient in predicting the mechanical buckling responses of rectangular composite plates resting on two parameter (pasternak’s model) elastic foundations. due to the interesting features of the present theory, the present findings will be a useful benchmark for evaluating the reliable of other future plate theories. references [1] seyvet, j. (2002). the french composite materials industry (louis berreur, bertrand de maillard & stanislas nösperger., paris). [2] gay, d. (2014). design and applications (composite materials third edition, crc press) . [3] ponte castañeda, p and suquet, p. (1997). nonlinear composites, adv. appl. mech., 34, pp. 171–302. [4] milton, g. w. (2002). the theory of composites cambridge university press. [5] moulinec, h. and suquet, p. (1998). a numerical method for computing the overall response of nonlinear composites with complex microstructure, comput. meth-ods appl. mech. eng. 157, pp. 69–94. [6] jones, r. m. (1998). mechanics of composite materials, crc press. [7] timoshenko, s.p., woinowsky-krieger s. (1959), theory of plates and shells, new york: mcgraw-hill. [8] timoshenko, s. p., gere, j. m. (1961). theory of elastic stability, new york, mcgraw-hill. [9] bank, l., yin, j. (1996). buckling of orthotropic plates with free and rotationally restrained unloaded edges, thin wall struct. 24(1), pp. 83–96. [10] kang, j. h., leissa, a. w. (2005). exact solutions for the buckling of rectangular plates having linearly varying in-plane loading on two opposite simply supported edges, int j solids struct, 42(14), pp. 4220–38. a y. khalfi et alii, frattura ed integrità strutturale, 48 (2019) 208-221; doi: 10.3221/igf-esis.48.22 221 [11] aydogdu, m., ece, m. c. (2006). buckling and vibration of non-ideal simply supported rectangular isotropic plates, mech res commun, 33(4), pp. 532–540. [12] hwang, i., lee, j. s. (2006). buckling of orthotropic plates under various inplane loads, ksce j civ eng, 10(5), pp. 349–356. [13] reissner, e. (1945). the effect of transverse shear deformation on the bending of elastic plates, j appl mech-t asme, 12(2), pp. 69–77. [14] mindlin, r. d. (1951). influence of rotary inertia and shear on flexural motions of isotropic, elastic plates,“. j appl mech-t asme, 18(1), pp. 31–38. [15] levinson, m. (1980). an accurate simple theory of the statics and dynamics of elastic plates, mech res commun, 7(6), pp. 343–350. [16] reddy, j. n. (1984). a simple higher-order theory for laminated composite plates, j. appl. mech. 51, pp. 745–752. [17] shimpi, r. p., patel, h. g. (2006). a two variable refined plate theory for orthotropic plate analysis, int j solids struct 43(22–23), pp. 6783–6799. [18] khalfi, y., houari, m.s.a. and tounsi, a. (2014). a refined and simple shear deformation theory for thermal buckling of solar functionally graded plates on elastic foundation, int. j. comput. method 11(5), 1350077. [19] abdelaziz, h. h., atmane, h. a. mechab, i., boumia, l., tounsi, a. and adda bedia, e. a. (2011). static analysis of functionally graded sandwich plates using an efficient and simple refined theory, chinese j. aeronaut 24, pp. 434–448. [20] aiello, m. a. and ombres, l. (1999). buckling and vibrations of unsymmetric laminates resting on elastic foundations under in-plane and shear forces, compos. struct. 44, pp. 31–41. [21] draiche, k., tounsi, a. and khalfi, y. (2014), a trigonometric four variable plate theory for free vibration of rectangular composite plates with patch mass, steel compos. struct., int. j 17(1), pp. 69-81. [22] seung-eock, k., huu-tai, t., jaehong, l. (2009). buckling analysis of plates using the two variable refined plate theory, thin-walled structures 47, pp. 455–462 [23] whitney, j. m. and pagano, n. j. (1970). shear deformation in heterogeneous anisotropicplates, j. appl. mech. 37, pp. 1031–1036. [24] reddy, j. n. (1984). a refined nonlinear theory of plates with transverse shear deformation, int j solids struct 20(9), pp. 881–896. [25] reddy, j. n. 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/hrv (za stvaranje adobe pdf dokumenata najpogodnijih za visokokvalitetni ispis prije tiskanja koristite ove postavke. stvoreni pdf dokumenti mogu se otvoriti acrobat i adobe reader 5.0 i kasnijim verzijama.) /hun 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can be opened with acrobat and adobe reader 5.0 and later.) >> /namespace [ (adobe) (common) (1.0) ] /othernamespaces [ << /asreaderspreads false /cropimagestoframes true /errorcontrol /warnandcontinue /flattenerignorespreadoverrides false /includeguidesgrids false /includenonprinting false /includeslug false /namespace [ (adobe) (indesign) (4.0) ] /omitplacedbitmaps false /omitplacedeps false /omitplacedpdf false /simulateoverprint /legacy >> << /addbleedmarks false /addcolorbars false /addcropmarks false /addpageinfo false /addregmarks false /convertcolors /converttocmyk /destinationprofilename () /destinationprofileselector /documentcmyk /downsample16bitimages true /flattenerpreset << /presetselector /mediumresolution >> /formelements false /generatestructure false /includebookmarks false /includehyperlinks false /includeinteractive false /includelayers false /includeprofiles false /multimediahandling /useobjectsettings /namespace [ (adobe) (creativesuite) (2.0) ] /pdfxoutputintentprofileselector /documentcmyk /preserveediting true /untaggedcmykhandling /leaveuntagged /untaggedrgbhandling /usedocumentprofile /usedocumentbleed false >> ] >> setdistillerparams << /hwresolution [2400 2400] /pagesize [612.000 792.000] >> setpagedevice microsoft word numero_29_art_1 a. bacigalupo et alii, frattura ed integrità strutturale, 29 (2014) 1-8; doi: 10.3221/igf-esis.29.01 1 focussed on: computational mechanics and mechanics of materials in italy a micropolar model for the analysis of dispersive waves in chiral mass-in-mass lattices a. bacigalupo university of trento andrea.bacigalupo@unitn.it l. gambarotta university of genoa luigi.gambarotta@unige.it abstract. the possibility of obtaining band gap structures in chiral auxetic lattices is here considered and applied to the case of inertial locally resonant structures. these periodic materials are modelled as beam-lattices made up of a periodic array of rigid rings, each one connected to the others through elastic slender ligaments. to obtain low-frequency stop bands, elastic circular resonating inclusions made up of masses located inside the rings and connected to them through an elastic surrounding interface are considered and modeled. the equations of motion are obtained for an equivalent homogenized micropolar continuum and the overall elastic moduli and the inertia terms are given for both the hexachiral and the tetrachiral lattice. the constitutive equation of the beam lattice given by the authors [15] are then applied and a system of six equations of motion is obtained. the propagation of plane waves travelling along the direction of the lines connecting the ring centres of the lattice is analysed and the secular equation is derived, from which the dispersive functions may be obtained. keywords. auxetic materials; chirality; cellular materials; mass-in-mass dynamic systems; dispersive waves. introduction n recent years a considerable interest in acoustic metamaterials was witnessed by several research (see for reference [1]), most of them focused to the design of artificial materials having periodic microstructure conceived to get complete sound attenuation for a certain frequency range, namely acoustic wave spectral gap. sonic crystals with spectral gaps [2] have been developed on the realization that composites with locally resonant structural units may exhibit effective negative elastic constants at certain frequency ranges, as shown by liu et al. [3] and by huang et al. [4,5]. recently, bigoni et al. [6] proposed a periodic metamaterial with internal locally resonant structures that supports tunable lowfrequency stop bands. this effect is associated with localized rotational modes obtained from a chiral microstructure of the periodic cell. tee et al. [7] have recently obtained a band gap structure in periodic tetrachiral materials. spadoni et al. [8] have obtained analogous results with reference to hexachiral lattices. these kind of materials are auxetics [9] and their structure is i a. bacigalupo et alii, frattura ed integrità strutturale, 29 (2014) 1-8; doi: 10.3221/igf-esis.29.01 2 characterized by a periodic array of the rings connected by four or six elastic ligaments. lakes [10], with reference to the planar isotropic case of hexachiral lattice, proposed this microstructure geometry firstly. later prall and lakes [11] showed for this material a poisson’s ratio of -1 under the hypothesis of ignoring the axial strain of the ligaments. further studies on the homogenization of hexachiral auxetic materials have been carried out by spadoni and ruzzene [12] and by liu et al. [13]. liu et al. [14] proposed a hexachiral metacomposite by integrating a two-dimensional hexachiral lattice with elastic resonating inclusions to obtain low-frequency band gap. this metacomposite has been analysed through a numerical model where the ligaments are modelled as multi-beam elements and the inclusions as a two dimensional fem model. in this paper, hexaand tetra-chiral beam lattices are considered having local resonators at the nodes of the periodic array. the model is developed in closed-form and is based on a micropolar homogenization of the lattice. this approach partially relies on the results by bacigalupo and gambarotta [15], which developed and compared the results from the micropolar and a second displacement gradient homogenization for both the hexachiral and the tetrachiral periodic cells in order to evaluate the validity limits of the beam lattice model. the possibility of obtaining band gap structures in chiral auxetic lattices is here considered and applied to the case of inertial locally resonant structures. these structures are obtained following huang et al. [4] and liu et al. [14], by the insertion of a circular mass connected through an elastic surrounding interface to each ring of the microstructure. the equations of motion are given within a micropolar continuum model and the overall elastic moduli and the inertia terms are obtained for both the hexachiral and the tetrachiral lattice. the constitutive equation of the beam lattice given in [15] are then applied and a system of six equations of motion is obtained. the propagation of plane waves travelling along the direction of the lines connecting the ring centres of the lattice is analysed and the secular equation is derived, from which the dispersive functions may be obtained. (a) (b) figure 1: (a) hexachiral lattice; (b) tetrachiral lattice. chiral mass-in-mass periodic material: micropolar homogenization he periodic materials shown in figure 1 are considered as beam-lattices made up of a periodic array of rigid rings, each one connected to the others through n elastic slender ligaments rigidly connected to the rings. in figure 2.a the periodic hexachiral cell (n=6) is shown, while in figure 1.b is shown the tetrachiral cell (n=4). each ligament is tangent to the joined rigid rings and has length l measured between the connection points, with section width t, thickness d and young’s modulus se . both the ligaments and the rings have mass density s , so that the mass and the rotation inertia of the rings are 1m 2 s rt  and 2 1 1j m r , respectively. the two dimensional composite materials are auxetic. the hexachiral lattice is isotropic and its poisson’s ratio becomes negative when increasing the chirality angle  . on the other hand, the tetrachiral material is strongly anisotropic and presents a directional dependency of the chirality on the direction of the applied stress, as shown in [15]. to obtain low-frequency stop bands, a metamaterial inclusion consisting of a softly heavy disk is located inside the ring as shown in figure 3.a. this inclusion plays the role of low-frequency resonator with mass and rotation inertia denoted with 2m and 2j , respectively. the motion of the rigid ring of the beam lattice is denoted by the displacement vector u and the rotation  , respectively (see figure 3.b), while the motion of the mass of the resonator is denoted by the displacement vector v and the rotation  (see figure 3.c). t a. bacigalupo et alii, frattura ed integrità strutturale, 29 (2014) 1-8; doi: 10.3221/igf-esis.29.01 3 (a) (b) figure 2: periodic cell of the (a) hexachiral lattice; (b) tetrachiral lattice. (a) (b) (c) figure 3: (a) internal mass with external elastic thick layer; (b) rigid ring and related dofs; (c) internal mass and related dofs. a soft elastic interface connects the internal mass to the rigid ring. to get a simplified formulation, the constitutive equation of the interface is assumed in the form    , c = dk k      f v u (1) f being the force exerted by the rigid ring on the internal mass and c the corresponding couple (see figure 4). the parameters dk and k are the isotropic translational stiffness and the rotational stiffness, respectively. figure 4: contact force and couple between the rigid ring and the internal mass. the lattice model is here approximated as a micropolar continuum model resulting from a homogenization process based on the macro-homogeneity criterion, involving both the total potential energy and the kinetic energy through the hamilton principle (see [13, 16] for reference). the equations of motion for the homogenized beam-lattice are a. bacigalupo et alii, frattura ed integrità strutturale, 29 (2014) 1-8; doi: 10.3221/igf-esis.29.01 4             11,1 12,2 1 1 1 1 21,1 22,2 2 2 1 2 1,1 2,2 21 12 1 1 1 2 1 2 2 2 2 2 ˆ ˆ ˆ ˆ ˆ ˆ d d d d k v u u k v u u m m k i k u v v k u v v k i                                                  (2) where the stiffnesses ˆd d cellk k a and ˆ cellk k a  are introduced, cella being the area of the periodic cell, together with the mass densities m11 cella   and m 22 cella   , and the micro-inertia terms j11 cell i a and j 2 2 cell i a , respectively. in eq. (2) ij and im are the overall stress components, namely the asymmetric stress components and the microcouples, respectively. in case of hexachiral lattice, one obtains 2 22 3 coscell la   and the following inertial parameters are obtained  1 3 sin 2 24 s       2 21 3 tan sin 24 si l       22 2 3 sin 24 i cell m a       2 2 222 3 sin tan 192 i cell j i l a       for the tetrachiral lattice one obtains 2 2coscell la   and the resulting inertia parameters are  1 sin 2 24 s       , 2 2 1 sin 48 si l      , 222 sin 48 i cell m a       , 2 2 222 sin tan 192 i cell j i l a       . to obtain the displacement formulation of the equations of motion, the compatibility equations involving the macrostrain components 11 1,1u  , 22 2,2u  , 12 1,2u   ,   21 2,1u and the curvatures 1 ,1   and 2 ,2  have to be considered together with the constitutive equation. micropolar constitutive equation for hexaand tetra-chiral lattices he constitutive equation of hexachiral honeycomb corresponds to that obtained in [13, 15] and is written as follows 11 11 22 22 12 12 21 21 1 1 2 2 2 0 0 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 a a a a a a k k a a k k m s m s                                                                             (3) in which the five elastic moduli t a. bacigalupo et alii, frattura ed integrità strutturale, 29 (2014) 1-8; doi: 10.3221/igf-esis.29.01 5            2 2 2 2 2 2 2 2 2 2 2 2 3 1 4 3 1 cos sin 4 3 sin cos 2 3 3sin 4 cos 12 3 1 sin cos 2 s s s s s e e k e s e a a e                                 (4) depend on the young’s modulus, the slenderness ratio t l  and the angle  of inclination of the ligaments. the constitutive eq. (3) show the coupling between the extensional strains 11 and 22 and the asymmetric strains 12 and 21 through the elastic constant a. the elastic moduli, with the exception of parameter  , depend on the parameter of chirality  , but only the constant a is an odd function of this parameter, i.e. it reverses its sign when the handedness of the material pattern is flipped over. in case of symmetric macro-strain fields, the fourth order elastic tensor for the hexagonal system corresponds to that of the transversely isotropic system whose elastic moduli in the plane of the lattice are:          2 4 2 2 3 2 hom 2 2 2 2 hom 2 4 2 2 2 hom 3 cos sin 2 3 1 cos sin 1 3 cos sin 3 = 1 4 s s e e e                           g (5) for the tetrachiral lattice, the constitutive equation is written [15]: 11 11 22 22 12 12 21 21 1 1 2 2 2 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 b b b b m s m s                                                               (6) where four elastic moduli are related to the lattice parameters as follows         2 2 2 2 2 2 2 2 2 2 2 cos sin 2 sin cos 1 sin cos 1 3sin 4 cos 12 s s s s e k e b e s e a                           (7) similarly to the hexachiral honeycomb, a coupling is obtained between the extensional strains and the asymmetric strains through the elastic modulus b which is an odd function of the parameter of chirality  , while the other elastic moduli are even functions. in case of symmetric macro-strain fields, the resulting classical fourth order elasticity tensor has the elastic a. bacigalupo et alii, frattura ed integrità strutturale, 29 (2014) 1-8; doi: 10.3221/igf-esis.29.01 6 moduli of the tetragonal system. the elasticity tensor depends on the chirality parameter, but unlike the hexachiral honeycomb, some elasticities are odd functions of  [15]. plane waves propagation he free wave motion in the hexachiral material is written in terms of the components of the generalized displacement field    1 2 1 2 t u u v v  u x in the following form             1,11 1,12 1,22 2 ,11 2,12 2,22 ,1 ,2 1 1 1 1 1,11 1,12 1,22 2,11 2,12 2,22 ,1 ,2 2 2 1 2 ,11 ,22 1,1 2,2 1,2 2 ( 2 ) 2 2 2 2 ( 2 ) 2 2 2 2 2 2 d d u au k u au k u au a k k v u u au k u au k u au u k a k v u u s s au au ku ku                                                                ,1 1 1 1 2 1 2 2 2 2 2 4 ˆ , ˆ , ˆ . d d k k i k u v v k u v v k i                                  (8) if a harmonic plane wave propagating along axis 1x in an infinite planar micropolar medium is admitted, the generalized displacement field at a point is assumed in the following form  1ˆ expt i qx t   u u , where q and  denote the wave number and the circular frequency, respectively, and  1 2 1 2ˆ ˆˆ ˆ ˆ ˆ ˆt u u v v  u is the vector of the amplitudes  1i   . substituting the assumed generalized displacement field in the equation of motion (8) one obtains the secular equation system for the equivalent continuum model     2 2 2 1 2 2 2 1 2 2 1 2 2 2 2 2 2 2 ˆ2 0 0 ˆ ˆ2 0 0 ˆ 4 ˆ2 2 0 0 ˆ ˆ ˆ0 0 0 0 ˆ ˆ0 0 0 0 ˆ ˆ0 0 0 0 d d d d d d d d q aq iaq k k k q aq ikq k k sq k iaq ikq k k i k k k k k k i                                                                       1 2 1 2 ˆ ˆ ˆ ˆ ˆ ˆ u u v v                            0 (9) the solution of the eigenproblem (9), characterized by a hermitian matrix, provides dispersion functions  q defined in the domain ,q a a        , a being the characteristic size of the cell as shown in figure 2. since the model has six degrees of freedom, it follows that in the general case six plane waves may propagate, each characterized by a dispersion function. it follows that this model exhibits plane waves more complex than those obtained and discussed by parfitt and eringen [17] for isotropic achiral two dimensional micropolar solids and more recently by khurana and tomar [18] for 3d chiral t a. bacigalupo et alii, frattura ed integrità strutturale, 29 (2014) 1-8; doi: 10.3221/igf-esis.29.01 7 micropolar media. since the matrix of the coefficient in the eigenproblem (9) is hermitian, the eigenvalues are real, but not necessarily positive. therefore, for some values of the model parameters is expected a reduced number of dispersive functions. in case of a tetrachiral lattice with internal resonant masses the free wave equation of motion takes the form:           1,11 1,22 2,11 2,22 ,1 ,2 1 1 1 1 1,11 1,22 2,11 2,22 ,1 ,2 2 2 1 2 ,11 ,22 1,1 2 ,2 1,2 2,1 1 1 1 2 1 2 2 2 2 2 2 2 ˆ ˆ ˆ d d d d u ku bu bu b k k v u u bu bu ku u k b k v u u s s bu bu ku ku k k i k u v v k u v v                                                         2 k i                 (10) in this case the secular equation system is written as follows: 2 2 2 1 2 2 2 1 2 2 1 2 2 2 2 2 2 ˆ2 ˆ 0 0 ˆ ˆ0 0 2 ˆ0 0 ˆ ˆ ˆ0 0 0 0 ˆ ˆ0 0 0 0 ˆ ˆ0 0 0 0 d d d d d d d d q k bq ibq k kq k bq ikq k sq k ibq ikq k k i k k k k k k i                                                                         1 2 1 2 ˆ ˆ ˆ ˆ ˆ ˆ u u v v                         0 (11) again the solution of the eigenproblem (11) with hermitian matrix provides dispersion functions  q , defined in the domain ,q a a       . the analytical formulation here derived, which is based on a micropolar continuum model enriched with additional degrees of freedom of the resonating masses located inside the rings, will be developed in future research to analyze the wave propagation and to appreciate the influence of the geometrical and mechanical parameters of the microstructure and of the resonant devices on the frequency spectra and on the conditions of wave attenuation. the reliability of the results has to be evaluated from the comparison with the rigorous solutions obtained from a floquet-bloch analysis of the generalized beam lattice proposed in this paper. finally, it should be noted that the validity of this model relies on the rigidity assumption of the rings [15], a condition that may be easily implemented in the physical model. acknowledgements he authors acknowledge financial support of the (murst) italian department for university and scientific and technological research in the framework of the research miur prin09 project xwlfkw, multi-scale modelling of materials and structures, coordinated by prof. a. corigliano. andrea bacigalupo gratefully thanks financial t a. bacigalupo et alii, frattura ed integrità strutturale, 29 (2014) 1-8; doi: 10.3221/igf-esis.29.01 8 support of the italian ministry of education, university and research in the framework of the firb project 2010, “structural mechanics models for renewable energy applications". references [1] lu, m.h., feng, l., chen, y.-f., phononic crystals and acoustic metamaterials, materialstoday, 12 (2009) 34-42. [2] pennec, y., vasseur, j.o., djafari-rouhani, b., dobrzyński, l., deymier, p.a., two-dimensional phononic crystals: examples and applications, surface science reports, 65 (2010) 229–291. [3] liu, z., zhang, x., mao, y., zhu, y., yang, z., chang, c.t., sheng, p., locally resonant sonic materials, science, 289 (2000) 1734-1736. [4] huang, h.h., sun, c.t., huang, g.l., on the negative effective mass density in acoustic metamaterials, int. j. of engineering science, 47 (2009) 610-617. [5] huang, h.h., sun, c.t., wave attenuation mechanism in an acoustic metamaterial with negative effective mass density, new journal of physiscs, 11 (2009) 013003. [6] bigoni, d., guenneau, s., movchan, a. b., brun m., elastic metamaterials with inertial locally resonant structures: application to lensing and localization, physical review, b 87 (2013) 174303. [7] tee, k.f., spadoni, a., scarpa, f., ruzzene, m., wave propagation in auxetic tetrachiral honeycombs, j. of vibration and acoustics asme, 132 (2010) 031007-1/8. [8] spadoni, a., ruzzene, m., gonella, s., scarpa, f., phononic properties of hexagonal chiral lattices, wave motion, 46 (2009) 435-450. [9] prawoto, y., seeeing auxetic materials from the mechanics point of view: a structural review on the negative poisson's ratio, computational material science, 58 (2012) 140-153. [10] lakes, r. s.,foam structures with a negative poisson’s ratio, science, 235 (1987) 1038-1040. [11] prall, d., lakes, r.s., properties of chiral honeycomb with a poisson ratio of -1, int. j. mechanical sciences, 39 (1997) 305-314. [12] spadoni, a., ruzzene, m., elasto-static micropolar behavior of a chiral auxetic lattice, j. mechanics and physics of solids, 60 (2012) 156-171. [13] liu, x.n., huang, g.l., hu, g.k., chiral effect in plane isotropic micropolar elasticity and it’s application to chiral lattices, j. mechanics and physics of solids, 60 (2012) 1907-1921. [14] liu, x.n., hu, g.k., sun, c.t., huang, g.l., wave propagation characterization and design of two-dimensional elastic chiral metacomposite, j. of sound and vibration, 330 (2011) 2536-2553. [15] bacigalupo, a., gambarotta, l., homogenization of periodic hexaand tetrachiral cellular solids, composite structures, doi 10.1016/j.compstruct.2014.05.033, 2014.to appear. [16] stefanou, i., sulem, j., vardoulakis, i., three-dimensional cosserat homogenization of masonry structures: elasticity, acta geotechnica, 3 (2008) 71–83. [17] parfitt, v.r., eringen, a.c., reflection of plane waves from the flat boundary of a micropolar elastic half-space, j. acoustical society of america, 45 (1969) 1258-1272. [18] khurana, a., tomar, s.k., longitudinal wave response of a chiral slab interposed between micropolar solid halfspaces, int. j. of solids and structures, 46 (2009) 135–150. microsoft word numero_58_art_06_3115 a. bouaricha et alii, frattura ed integrità strutturale, 58 (2021) 77-85; doi: 10.3221/igf-esis.58.06 77 load bearing capacity of thin-walled rectangular and i-shaped steel sections of short both empty and concrete-filled columns amor bouaricha department of mechanical engineering, industrial mechanical laboratory. university of badji mokhtar, annaba, algeria bouarichaa@yahoo.fr naoual handel* department of civil engineering, infrares laboratory, university of mouhamed cherif messadia, souk-ahras, algeria. n.handel@univ-soukahras.dz, https://orcid.org/0000-0002-5711-9999 aziza boutouta mechanics research center (crm), bp n73b, constantine, algeria. boutoutaziza@gmail.com sarah djouimaa department of civil engineering, infrares laboratory, university of mouhamed cherif messadia, souk-ahras, algeria. gc.djouimaa@yahoo.fr abstract. in this experimental work, strength results obtained on short columns subjected to concentric loads are presented. the specimens used in the tests have been made of cold-rolled, thin-walled steel. twenty short columns of the same cross-section area and wall thickness have been tested as follows: 8 empty and 12 filled with ordinary concrete. in order to determine the column section geometry with the highest resistance, three different types of cross-sections have been compared: rectangular, i-shaped unreinforced and, reinforced with 100 mm spaced transversal links. the parameters studied are the specimen height and the cross-sectional steel geometry. the registered experimental results have been compared to the ultimate loads intended by eurocode 3, for empty columns, and by eurocode 4, for compound columns. these results showed that a concrete-filled composite column had improved strength compared to the empty case. among the three crosssection types, it has been found that i-section reinforced is more resistant than the other two sections. moreover, the load capacity and mode of failure have been influenced by the height of the column. also, the ec3 and ec4 predictions were not conservative compared to the experimental strengths of the tested columns. keywords. load; instability; steel; mixed column; cross-section. citation: bouaricha, a., handel, n., boutouta, a., djouimaa, s., load bearing capacity of thin-walled rectangular and ishaped steel sections of short both empty and concrete-filled columns, frattura ed integrità strutturale, 58 (2021) 77-85. received: 25.05.2021 accepted: 10.07.2021 published: 01.10.2021 copyright: © 2021 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. https://youtu.be/7vd14pzrmze a. bouaricha et alii, frattura ed integrità strutturale, 58 (2021) 77-85; doi: 10.3221/igf-esis.58.06 78 introduction ubular steel columns filled with concrete have been widely used in structures around the world. they offer many mechanical advantages such as high ultimate strength, rigidity and high ductility at the same time. several studies have been carried out on the hollow steel columns filled with different types of concrete under axial loads. the studied columns are made of thin-walled cold-rolled steel. these columns have a structure such that the majority of the soliciting load is supported by concrete, which is a very economical material that resists well to compression load. thus, the cross-sectional components of this type of column result in significant economies in the design of buildings with different usages. several researchers have conducted recent experimental studies on the cross-sectional shape of thin-walled steel columns. the behavior and strength of concrete-filled aluminum tube columns using square and rectangular hollow sections under uniform axial compression have been analysed by feng zhou and al [1], it has been found that the shape of the crosssection, the thickness of the tube and concrete strength had a considerable effect on the local buckling of tubular columns. concrete-filled steel tubular columns (cft) under axial and eccentric load, with and without binding bars were studied by zhi-liang zuo and al [2, 3]. they noted that the local buckling could be delayed by the installation of the binding bars. they have also noticed that decreasing the horizontal spacing of the bars increases ductility and strength. as per the study of duarte and al [4], on the geometric effect of the cross-section of steel tubes with different grades and filled with rubber concrete (a.p.c), they concluded that the ductility increasing under axial load depended on the geometry of the crosssection, being more effective for columns with circular sections than those of columns with square or rectangular sections. handel [5] studied the effect of age and type of filler concrete on the ultimate strength of six rectangular thin-walled coldrolled steel hollow tubes under axial loading. three concrete mixtures have been used: ordinary concrete, slag concrete where the gravel and sand have substituted by crystallised slag and, slag sand concrete where dune sand has been substituted by crushed crystallised slag sand. the hollow tubes filled with slag concrete gave the best ultimate resistance. this was due to the high strength of slag concrete. it was also noted that, at the age of 180 days, the axial load capacity of mixed tubes filled with the three types of concrete, increased respectively by 13.98%, 3.71% and 3.10% compared to those found at 28 days age. weiwei wang and al [6] studied eight t-shaped concrete-filled steel tubular (cfst) stub columns with stiffeners to high temperature under the compressive load. they have found that the temperature, thickness of steel tube, yield strength of steel tube and compressive strength of concrete are the key factors contributing to the axial compressive performance of the cfst stub columns and the failure pattern. nineteen lightweight aggregate concrete-filled steel tubular (cfst) columns with circular, square, square with roundended, rhombic, rectangular, rectangular with round-ended, elliptical, hexagonal asymmetric, t-shaped, pentagram, hexagon, octagon, 1/4 circular, semi-circular, d-shaped, fan-shaped, l-shaped and t-shape cross sections, have been tested under axial load by ali hameed naser almamoori and al [7]. all the cfst columns failed due to the crushing of the concrete core with local buckling of the steel tube. they noted that as the number of steel plates welded together to form the section increases, the section becomes more stable and leading to a better confinement. the columns with conventional cross-sectional shapes such as circle and square seem to have a relatively higher ductility index. but, as the shape becomes more irregular, the ductility index decreases. a fully or partially encased composite column is a composite type column that consists of an h-shaped or i-shaped steel section with concrete poured between the opposing flanges. the advantage of this type of column is that it offers a simplified connection between beams and columns, with reduced formwork on two sides of the column. few researches has been conducted on profiles partially filled with concrete. hunaiti and fattah [8], jamkhaneh and al. [9], chicoine.t and al. [10], begum and al. [11] studied the behavior and load-bearing capacity of a new type of composite column partially filled with ordinary concrete and thin-walled welded i-section reinforced with transverse links. the specimen's mode failure was local buckling with deformation of the steel at the flanges and crushing of the concrete. the studies showed the additional reinforcement could improve the column's ultimate load. handel and al [12] have noted that the increase in ultimate load capacity of thin-walled partially encased sections filled with slag concrete under axial loading attributed to the higher strength of the concrete. also, it is confirmed that the length and thickness of the steel profile have a significant effect on the ultimate strength and failure mode. experimental and numerical results of a study of partially encased composite columns under concentric loads conducted by margot f. pereira and al. [13] indicated that the welded wire mesh could replace the transversal links between the flanges. t a. bouaricha et alii, frattura ed integrità strutturale, 58 (2021) 77-85; doi: 10.3221/igf-esis.58.06 79 according to the literature, there was a lack of experimental tests comparing concrete-filled tubular section columns and partially or fully encased profiles to understand which cross-section provided the best strength and stability performance. therefore, an experimental study is performed on short thin-walled steel columns of rectangular cross-section, i-shaped without reinforcement and i-shaped reinforced by transverse links, under axial load, to analyze the ultimate strength and failure mode of these column types. the parameters studied are the height and the shape of the cross-section of the specimens. the recorded experimental results are compared with those given by the prediction of ec3 regulation [14] for empty steel columns and ec 4 [15] for mixed columns. experimental program geometric properties of specimens and their fabrication n this work, a twenty short cold rolled galvanized steel columns with a thickness of 2 mm and a cross-sectional area (100x70) mm² are tested as follows: 8 empty and 12 filled with ordinary concrete, under uniaxial loading, to investigate the effect of column height and cross-section geometry on their load-bearing capacity and failure modes. the studied sections consist of two u-shaped cold-rolled steel obtained by cold bending and joined throughout the height by a continuous weld to form a hollow steel tube and welded back to back to forms an i-shaped steel section. three types of cross-sections are compared: rectangular, unenforced i-shape and, istiffened by transverse links spaced by 100 mm. the heights of the specimens are 200 mm 300 mm 400 mm 500 mm. the test program contains 5 series of columns: the first series represents empty steel specimens with an i-shaped cross-section (fig. 1-a) designated as c1-c2-c3-c4; the second series represent empty hollow rectangular section steel specimens (fig. 1-d) designated as c5-c6-c7-c8; the third series represents the partially encased i-shaped cross-sectional steel specimens (fig. 1-b) designated as c9-c10c11-c12; the fourth series represents the steel i-shaped cross-section specimens partially encased and reinforced horizontally by round steel links of 3.3 mm diameter smooth in u-shape welded to the extremities of the flanges as shown in fig. (1-c) designated as c13-c14-c15-c16. the transverse link spacing of 100 mm (d =100 mm) has been used to increase the confined concrete capacity and to retard local buckling of the thin-walled steel; the fifth series represents hollow rectangular section specimens filled with ordinary concrete (fig. 1-e) designated as c17-c18-c19-c20. figure 1: cross section of test specimens. steel the mechanical properties of the used steel for the short columns are: young’s modulus: ea = 205 000 mpa yield strength: fy = 300 mpa concrete the method used to determine the filler concrete composition is that of the gorisse-dreux method. it is determined with maximum aggregate diameter dmax = 15 mm and a 6 cm slump (according to the nf p 18-451 standard) corresponding to a plastic concrete. the concrete composition is listed in tab. 1. the short steel columns filled with ordinary concrete have been poured in a vertical position in three layers and vibrated on a vibrating table to obtain compact concrete throughout the specimen's height. the concrete compressive strength at 28 days is determined using the nf p 18-406 standard on three cubic specimens of dimension (10x10x10 cm), and the splitting tensile strength of the concrete is determined according to the nf p 18-408 standard on three cylindrical specimens of dimension (16x32 cm). all casted columns i a. bouaricha et alii, frattura ed integrità strutturale, 58 (2021) 77-85; doi: 10.3221/igf-esis.58.06 80 hardened in a vertical position in laboratory ambient air (temperature = 20-25°c and relative humidity = 60 at 70 %) (fig. 2). cement cpj 42.5 watercement ratio w/c sand dune (0/2.5) limestone gravel (5/15) real density slump cubic compressive strength of concrete (28 days) tensile strength of concrete (28 days) unit kg/m3 kg/m3 kg/m3 kg/m3 mm mpa mpa value 350 0.60 811.32 1095.77 2.47 60 25 2 table 1: compositions of the filling concrete. figure 2: a general view of the fabricated specimens. results and discussion ll the specimens are tested to failure under axial compression at 28 days by a universal testing machine, with a capacity of 2000 kn. particular attention is payed in checking the correct position of the columns before loading. the top and bottom faces of composite columns are treated to eliminate surface irregularities to provide a more uniform load distribution across the column cross-section. recorded experimental results are compared with those given by the prediction of ec3 regulation for empty steel columns and ec 4 for mixed columns. experimental strength (nue) of the specimens and their predicted strengths (nuc) according to ec3 and ec4 are presented in tab. 2. the ultimate load is examined under the effect of the geometry of the empty sections (i shape or rectangular) (fig. 3): it is observed that empty specimens (c1, c2, c3 and c4) of the section i record an increase in load capacity of (30.50%, 40.66%, 47% and 52.75%) respectively compared to the empty specimens (c5, c6, c7 and c8) of rectangular sections. in contrast, ultimate loads decrease for specimens c4 and c8 as heights increase. from these results, it can be concluded that the height of thin-walled cold rolled steel columns has a negative influence on the axial load capacity. for the fourth series specimens (c13, c14, c15 and c16) of i-section partially encased and reinforced by horizontal links, it is recorded (see fig. 4) an improvement of their load capacities respectively of the order of 40%, 45.35%, 52.52% and 61.37% compared to those of the non-reinforced specimens of the third series (c9, c10, c11 and c12). this improvement is not very important for their ultimate loads: it is respectively improved of 16.6 %, 17.1 %, 17.4 % and 18 % comparing to the rectangular cross-section specimens of the fifth series (c17, c18, c19 and c20) (fig.4). these results also show the improvement of the load capacity in partially encased steel columns of ratio (b / t = 17.5) and reinforced with links. the ultimate load is inversely proportional to the height of the specimen. fig. 5 illustrates the ratio between experimental loads from the composite columns and the loads from the empty steel columns. the compressive strength of the filler concrete at 28 days is 25 mpa. comparing the ultimate loads of the empty steel i-section specimens (first series) with those of the partially encased i-section specimens with no reinforcement (third series), it is noted that ultimate load increased from 34% to 69%. the fourth series specimens with transverse links show a i-shaped empty i-shaped empty with transversal links concrete filled, i-form with and without links empty and concrete filled, rectangular shape a. bouaricha et alii, frattura ed integrità strutturale, 58 (2021) 77-85; doi: 10.3221/igf-esis.58.06 81 an increase in ultimate load from 116.4 % to 136%. this reflects the advantage of short steel columns filled with concrete. more the transversal links welded at the butt of the footings and spaced 100 mm apart can improve the axial load capacity by 40% to 61.4% compared to the i-shaped section specimens not reinforced. also, an increase of 130% to 153.4% for the ultimate loads of the 5th series rectangular hollow concrete-filled specimens is observed compared to the empty ones (series 2). the concrete containment between the steel walls of the hollow section gives the highest load ratio. test series specimen labels column length (mm) width-tothickness ratio: b/t exp. ult. strength nue (kn) nue/nuc series 1 (empty isection columns) c1 200 17.5 190.89 0.87 c2 300 17.5 192.85 0.86 c3 400 17.5 188.25 0.88 c4 500 17.5 181.32 0.90 series 2 (empty rectangular section columns) c5 200 17.5 146.30 0.61 c6 300 17.5 137.10 0.57 c7 400 17.5 128.00 0.54 c8 500 17.5 118.70 0.50 series 3 (mixed i-section columns) c9 200 17.5 280.00 0.93 c10 300 17.5 258.00 0.88 c11 400 17.5 238.00 0.82 c12 500 17.5 220.00 0.75 series 4 (mixed i-section columns with horizontal link) c13 200 17.5 392.00 1.26 c14 300 17.5 375.00 1.17 c15 400 17.5 363.00 1.09 c16 500 17.5 355.00 1.10 series 5 (mixed rectangular section columns) c17 200 17.5 336.11 1.02 c18 300 17.5 320.00 0.97 c19 400 17.5 309.10 0.94 c20 500 17.5 300.84 0.91 table 2: experimental results of empty steel and composite columns. figure 3: experimental ultimate load (nue) of empty steel columns. a. bouaricha et alii, frattura ed integrità strutturale, 58 (2021) 77-85; doi: 10.3221/igf-esis.58.06 82 figure 4: experimental ultimate load (nue) of composite columns. figure 5: strength gain for cross-section types. according to ec4, the concrete contribution ratio (ccr) is the experimental ultimate load (nue) divided by the yield strength (fy) of steel and the effective cross-sectional area that considers the local buckling of the steel tube (as.eff). fig. 6 shows the ccr of the three composite column series. the results show that the i-shaped cross-section with horizontal links partially encased has a greater positive influence on concrete filling than the rectangular and i-shaped without horizontal links sections. that confirmed the tendency observed for the experimental ultimate load of the series 4 composite columns. the experimental ultimate loads are compared to those given by the prediction of ec3 regulation for empty steel columns and ec 4 for mixed columns. the results presented in fig. 7 showing clearly the experimentally obtained load capacity of empty steel columns is lower than predicted by ec3. although short column experimental loads have expected to be close to those calculated according to ec3, the experimental results gave lower loads for empty columns due to premature buckling. the error of predicting the axial capacity of the composite column is shown in fig. 8. it can be observed that ec4 is not conservative where the error obtained with respect to the experimental load values varies from 0.93 to 0.75. the same observation was noted for rectangular section specimens of heights of 500 mm, 400 mm and 300 mm with an error varying from 0.91 to 0.97. but ec4 is conservative for rectangular section specimen of height 200 mm. ec4 estimates safer predictions with an error varying from 1.10 to 1.17 for i-shaped specimens reinforced with horizontal links. from the results of tests obtained on short thin-walled empty and concrete-filled cold-rolled steel columns under uniaxial loading, it should be noted that the instability of thin-walled local occurred at all specimens with low attenuation for composite columns, this is due to lateral stiffness contribution that prevents the specimens to produce large lateral a. bouaricha et alii, frattura ed integrità strutturale, 58 (2021) 77-85; doi: 10.3221/igf-esis.58.06 83 displacements and therefore lesser the local buckling. also, the length of the column has a significant effect on the local buckling. the typical failure modes for the tested partially encased columns are by fully or partial crushing of concrete, steel web end flange buckling outwards and inwards, with steel-concrete separation. the composite columns reinforced with transversal links of the 4th series have a more ductile mode of failure than the 3rd series columns. the horizontal links prevented concrete-steel separation, premature concrete cracking and minimized local buckling of the specimen flanges (fig. 9). figure 6: concrete contribution ratio (ccr). figure 7: empty columns load ratio (nue/nuc). figure 8: composite columns load ratio (nue/nuc). a. bouaricha et alii, frattura ed integrità strutturale, 58 (2021) 77-85; doi: 10.3221/igf-esis.58.06 84 figure 9: typical failure mode 400 mm high columns empty and filled with concrete). conclusions his study has examined five series tests of cold-rolled, thin-walled short steel columns filled with ordinary concrete under uniaxial loading. from the experimental results of this study, some conclusions can be drawn:  increasing the column height (empty or composite) leads to a decrease in the ultimate strength for all types of studied cross-sections.  the axial load capacity of composite columns filled with concrete is improved compared to empty columns.  transverse reinforcement of the i-shaped section with links improved the experimental ultimate loads of the composite column compared to the i-shaped without links section. partial confinement increased strength gain by 49.81%.  the used column with i-shaped cross-sections and transversal links with a web thickness of 4 mm, gave a higher experimental ultimate load than a rectangular section. this load has been influenced by the steel thickness. the strength gain is about 17.3 % for all the heights of the specimens.  all specimens failed by local buckling with the crushing of the entire or partially concrete. the local buckling becomes less significant as the height of the specimens increases.  multiple experimental tests are required to verify the validity of the ec3 and ec4 predictions for reconstructed crosssectional short columns of thin-walled cold-rolled steel under axial loading. references [1] feng, z. and ben, y. (2008). tests of concrete-filled aluminum stub columns, thin-walled structures, 46(6), pp. 573583. doi: 10.1016/j.tws.2008.01.003. [2] zhi-liang, z., jian, c., chun, y., qing-jun, c. and gang, s. (2012). axial load behavior of l-shaped cft stub columns with binding bars, engineering structures, 37, pp. 88-98. doi: 10.1016/j.engstruct.2011.12.042. [3] duarte, a.p.c., silva, b.a., silvestre, n., de brito, j., júlio, e. and castro, j.m. (2016). tests and design of short steel tubes filled with rubberised concrete, engineering structures, 112, pp. 274-286. doi: 10.1016/j.engstruct.2016.01.018. [4] handel, n. (2019). experimental investigation of the blast furnace slag based concretes filled in the thin walled steel stubs, international review of civil engineering, 10(2), pp. 117-124. doi: 10.15866/irece.v10i2.16418. [5] weiwei, w., xuetao, l., yuzhuo, z., yang, y. and tong, z. (2020). axial compression performance of thin-walled tshaped concrete filled steel tubular columns under constant high temperature: experimental and numerical study, structures , 27, pp. 525-541. doi: 10.1016/j.istruc.2020.06.004. [6] almamoori, a.h.n, naser, f.h. and dhahir, m.k. (2020). effect of section shape on the behaviour of thin walled steel columns filled with light weight aggregate concrete: experimental investigation, case studies in construction materials, 13, pp. 1-13. doi: 10.1016/j.cscm.2020.e00356. t concrete filled empty i-shaped section rectangular section empty concrete filled a. bouaricha et alii, frattura ed integrità strutturale, 58 (2021) 77-85; doi: 10.3221/igf-esis.58.06 85 [7] hunaiti, y. m. and abdel fattah, b. (1994). design considerations of partially encased composite columns, proc. inst. civ. engrs structs and build., 106, pp. 75–82. [8] jamkhaneh, m.e., kafi, m.a., & kheyroddin, a. (2018). behavior of partially encased composite members under various load conditions: experimental and analytical models, pp. 1-18. doi: 10.1177/1369433218778725. [9] chicoine,t., massicotte, m. and tremblay, r. (2003). long-term behavior and strength of partially encased composite columns made with built-up steel shapes, journal of structural engineering, 129(2), pp. 141-150. [10] begum, m., driver, r. g. and elwi, e.a. (2007). finite-element modeling of partially encased composite columns, using the dynamic explicit method, journal of structural engineering, 133(3), pp. 326-334. [11] handel, n., chikh, n.e and achoura, d. (2009). experimental investigation of partially encased composite column axially loaded», international review of mechanic engineering, 3(6), pp. 825-832. [12] pereira, m., de nardin, s. and de cresce el debs, a.l.h. (2016). structural behavior of partially encased composite columns under axial loads, steel and composite structures, 20(6), pp. 1305-1322. doi: 10.12989/scs.2016.20.6.1305. [13] cen en 1993-1-1. (2005). eurocode 3: design of steel structures part 1-1: general rules and rules for buildings. [14] cen en 1994-1. (2004). eurocode 4: design of composite steel and concrete structures. part 1-1: general rules and rules for buildings. [15] zeghiche, j. and handel, n. (2007). experimental behaviour of concrete filled thin welded steel stubs axially loaded case, 8th international conference on concrete technology in developing countries, the african concrete code sympsium, tunisia. [16] handel, n., hafsi, b., touati, a. and djabbar, y. (2011). substitution of the aggregate by solid waste of blast furnance in the preparation of concrete, j. mater. environ. sci, 2(1), pp. 520-525. [17] handel, n. and madi, w. (2015). experimental investigation of slag concrete-filled steel tubular columns axially loaded, 18th international conference on composite structures (iccs18), portugal. [18] ye, y., han, l.h., tao, z. and guo, s.l. (2016). experimental behavior of concrete-filled steel tubular members under lateral shear loads, j. constr. steel res, 122, pp. 226–237. [19] akchurin, t. k., stefanenko, i. v. and yurievna, p.o. (2017). slag wastes from regional metallurgical industry used in construction compositions, international review of civil engineering, 8(5), pp. 197-202. doi: 10.15866/irece.v8i5.12681. [20] xiang, x.y., zhao, r.d. and liu, y. (2017). calculation method of bearing capacity for self-compacting recycled concrete-filled steel-tube short column, railw. eng, pp. 34–37. [21] saleh, s.m. 2017. size effect on the load carrying capacity of normal and lightweight concrete filled square steel tube composite columns, int. j. appl. eng. res, 12, pp. 5261–5266. microsoft word numero_33_art_33 t. itoh et alii, frattura ed integrità strutturale, 33 (2015) 289-301; doi: 10.3221/igf-esis.33.33 289 focussed on multiaxial fatigue evaluation and visualization of multiaxial stress and strain states under non-proportional loading t. itoh, m. sakane ritsumeikan university, japan itohtaka@fc.ritsumei.ac.jp, sakanem@se.ritsumei.ac.jp t. morishita college of science & engineering, ritsumeikan university, japan gr0202xp@ed.ritsumei.ac.jp abstract. this paper presents a simple method of determining stresses and strains and a severity of loading history under non-proportional loadings with defining the rotation angles of the maximum principal stress and strain in a three dimensional stress and strain space. based on the method, non-proportional stress and strain ranges are derived and applicability of the range to the life evaluation for low carbon steel under non-proportional random strain paths are discussed. the strain range taking account of intensity of loading path reducing life can be suitable parameter for multiaxial fatigue life evaluation under multiaxial non-proportional loading. this paper also shows a method of visually presenting the principal stress and strain that assists designers to understand the loading mode whether proportional or non-proportional under 3 dimensional (6 stress/strain components) multiaxial loading. keywords. fatigue; low cycle fatigue; multiaxial loading; non-proportional loading; stress and strain evaluation; random loading; visualization of multiaxial loading. introduction ost design codes use equivalent values to express the intensity of multiaxial stress or strain, like von mises or tresca equivalent stress and strain, and fatigue lives are usually estimated using equivalent values under multiaxial stress and strain states. the equivalent value means a scalar parameter that expresses intensity of a physical phenomenon in multiaxial stress states and should be reduced to be a uniaxial value in uniaxial stress state. most widely used equivalent parameters are the von mises and the tresca equivalent stresses and strains. the von mises equivalent stress physically expresses the intensity of shear strain energy and the tresca equivalent stress that of the maximum shear stress. for example, asme section iii, division 1 nh [1] uses the von mises equivalent strain and asme section viii, division 3 [2] the maximum shear stress. however, the von mises equivalent stress and strain have no negative values so that they have a difficulty of expressing stress and strain ranges. the tresca equivalent stress and strain have negative values but they also have a difficulty to put a sign to the shear stress and strain under multiaxial loading. especially, in non-proportional loading where the principal stress and strain change their directions, giving a sign to them becomes more difficult. a simple and clear method of calculating stress and strain ranges is needed for describing multiaxial fatigue. m http://www.gruppofrattura.it/pdf/rivista/numero33/audioslides/itoh/index.html t. itoh et alii, frattura ed integrità strutturale, 33 (2015) 289-301; doi: 10.3221/igf-esis.33.33 290 low cycle fatigue (lcf) lives are reduced under strain controlled non-proportional loading accompanied by additional cyclic hardening compared with proportional loading [3-8] and an appropriate design method of evaluating the nonproportional fatigue life is needed for a reliable design and maintenance of structural components. classical models particularly applicable in multiaxial fatigue life evaluation under proportional loadings lead to overestimate the lives under non-proportional loadings. for life evaluation under non-proportional loading, commonly proposed models are critical plane approaches that consider specific plane applied the critical damage, such as a simith-watoson-topper [9] and a fatemi-socie [10] models. the authors also proposed a strain parameter (itoh-sakane model) estimating the nonproportional lcf lives for several materials under various strain histories [6, 7, 11-15]. this parameter is the strain based model with introducing two parameters, non-proportional factor and material constant. the former one reflects the intensity of non-proportional loading reducing life and the latter one is related to the material dependence for degree of life reduction due to non-proportional loading. the simith-watoson-topper, the fatemi-socie and the itoh-sakane models have been demonstrated to be applicable to life evaluation under non-proportional loading using hollow cylinder specimens in a laboratory level. that is, these models can be applicable to the life evaluation under limited non-proportional loadings such as the loadings in the plane stress state. however, many components and structures such as turbine blade, pressure vessel and pipe which receive combined thermal and mechanical loadings undergo non-proportional loading in which principal directions of stress and strain are changed into various directions under wider multiaxial stress and strain states [8, 13, 16-18]. therefore, a development of suitable models for the design of actual components where variation in principal directions of stress and strain vs time is changed 3-dimensionally is required. this study presents a method of evaluating the principal stress and strain ranges and the mean stress and strain, and also presents a method of calculating the non-proportional factor which expresses the severity of non-proportional loading in 3-dimantional (3d) stress and strain space (6 stress/strain components). based on the method proposed, nonproportional strain and stress ranges are derived and applicability of the range to the life evaluation of type 304 stainless steel under 15 proportional and non-proportional strain paths are also discussed. this study also shows a method of visually presenting the stress/strain, the non-proportionality of loading and the damage evaluation. stress and strain under non-proportional loading definition of stress and strain ig. 1 illustrates three principal vectors, si(t), applied to a small cube in material at time t in xyz-coordinates (spatial coordinates), where “s” is the symbol denoting either stress “” or strain “”. thus, si(t) are the principal stress vectors for the case of stress and are the principal strain vectors for the case of strain. the subscript, i, takes 1, 2 or 3 in descending order of principal stress or strain. the maximum principal vector, si(t), is defined as si(t) whose absolute value takes maximum one, i.e., si(t)=s1(t) when s1(t) takes maximum magnitude among si(t). the maximum principal value, si(t), is defined as the maximum absolute value of si(t) as, i i 1 2 3( ) ( ) max ( ) , ( ) , ( )t     s s s ss t t t t (1) figure 1: principal stress and strain in xyz coordinates. f t. itoh et alii, frattura ed integrità strutturale, 33 (2015) 289-301; doi: 10.3221/igf-esis.33.33 291 the “max” denotes taking the larger value from the three in the bracket. the maximum value of si(t) during a cycle is defined as the maximum principal value, simax, at t=t0 as follows, i 1 0 2 0 3 0imax 0( ) max ( ) , ( ) , ( )    s s s ss t t t t (2) figure 2: definition of principal stress and strain directions in xyz coordinates. definition of principal stress and strain directions fig. 2 illustrates two angles, (t)/2 and (t), to express the rotation or direction change of the maximum principal vector, si(t), in the new coordinate system of xyz, where xyz-coordinates are the material coordinates taking x-axis in the direction of si(t0) with the other two axes in arbitrary directions. the two angles of (t)/2 and (t) are given by i i i i ( )1 0 0 ( ) ( )( ) cos ( 0 ) 2 ( ) ( ) 2 2 t tt t t t            s s s s (3) i i 1 ( )( ) tan ( 0 ( ) 2 ) ( ) z y t t t t            s e s e (4) where dots in eqs (3) and (4) denote the inner product and ey and ez are unit vectors in y and z directions, respectively. si(t) are the principal vectors of stress or strain used in eq. (1) and the subscript i takes 1 or 3. the rotation angle of (t)/2 expresses the angle between the si(t0) and si(t) directions and the deviation angle of (t) is the angle of si(t) direction from the y-axis in the x-plane. definitions of stress and strain in polar figure fig. 3 shows the trajectory of si(t) in 3d polar figure for a cycle where the radius is taken as the value of si(t), and the angles of (t) and (t) are the angles shown in the figure. a new coordinate system is used in fig. 3 with the three axes of si1, si2 and si3, where si1-axis directs to the direction of si(t0). the rotation angle of (t) has double magnitude compared with that in the specimen shown in fig. 2 considering the consistency of the angle between the polar figure and the physical plane presentation. the principal range, si, is determined as the maximum projection length of si(t) on the si1axis. the mean value, simean, is given as the center of the range. si and simean are equated as,  i i i i iδ max ( )max max mincos ( )s s t s t s s    (5)  i mean i imax min 1 2 s s s  (6) simin is the si(t) to maximize the value of the bracket in eq. (5). the sign of simin in the figure is set to be positive if it does not cross the si2-si3 plane and the sign negative if it crosses the plane. the advantage of the definitions of the maximum principal range and mean value above mentioned is that the two are determinable without human judgments for any loading case in 3d stress and strain space. the range and mean value are consistent used in simple loading cases which are discussed in the case studies in the followings. si(t) can be replaced by equivalent values of stress or strains, such as the von mises and the tresca, in case of necessity from user’s requirement. t. itoh et alii, frattura ed integrità strutturale, 33 (2015) 289-301; doi: 10.3221/igf-esis.33.33 292 si 1  (t)  (t) si (t) si(t0) si 2 si 3 δ s i 0 .5 δ s i s i m ea n simax simin simax ex ey ez er figure 3: definition of principal range and mean principal value. case studies his section discusses a couple of case studies for si and simean under proportional and non-proportional loadings under biaxial plane stress condition. the symbol s takes () in the case studies in the followings. proportional loading fig. 4 (a) illustrates three proportional strain paths for normal and shear strainings under plane stress condition in the normal strain – shear strain (–/3) plot. the path a-a’ is push-pull loading, the b-b’ combined tension and shear loading and the path c-c’ shear loading. figs 4 (b)(d) show the variations of 1(t), 3(t), i(t), (t)/2 and (t) and fig. 4 (e) the strain path in the polar figure presentation. principal strains and their angle change are obtained in the stages of oa-ob-oc and oa’-ob’-oc’ as follows. stage oa-ob-oc:   i i i 21 2 2 2 3 1 1 3 max ( ) 1 1 1 ( ) ( ) 2 2 ( ) ( ) ( ) ( ) ( ) , ( ) 0 , ( ) 0 t t t t t since of t t k k a b or c t t                                 (7.a) stage oa’-ob’-oc’:   i 21 2 2 2 3 3 1 3 ( ) ( ) 1 1 1 ( ) 2 2 ( ) ( ) ( ) ( ) ( ) 180 , ( ) 0 t t t t t since of t t t t                             (7.b)  is the poisson’s ratio. note that /3=0 in the loading stages of oa and oa’ and  =0 in the loading stages of oc and oc’. the maximum principal strains (1(t)) vary along the solid lines in fig. 4 (b) in the loading stages of oa, ob and oc, and the minimum principal strains (3(t)) along the dashed lines in the same loading stages. in these cases, the maximum principal strains all have a positive sign, whereas the minimum principal strains a negative sign. i(t) makes the positive triangle waveforms as illustrated in fig. 4 (c) because i(t) is either 1(t) or 3(t) taking larger absolute strain as shown in eq. (1). the principal strain, i(t), changes its direction by an angle of 180 (/2=90) at the origin o in the reversed t t. itoh et alii, frattura ed integrità strutturale, 33 (2015) 289-301; doi: 10.3221/igf-esis.33.33 293 1(t), 3(t) o o o t 1 max min 3 a b c a’ b’ c’ 90 t (t)/2, (t) o o o (t)/2 (t) t o o o i(t) a b c a’ b’ c’ o aa’  b b’ c c’ 3  a’ a   i i1 o imax imin c’ c b’ b i3 s i m ea n loading stages of aa’, bb’ and cc’, fig. 4 (d). finally, the straight loading lines are obtained in the polar figure as shown in fig. 4 (e). in the proportional loadings in fig. 4 (a), the directions of i(t) are fixed (=0 or 180) and =0. the maximum strain range and mean strain are expressed as i i imax min 1 3( ) ( ')k k         (8)    i mean i imax min 1 3 1 1 ( ) ( ') 2 2 k k        (9) as shown in fig. 4 (e), where k takes a, b or c and k’ a’, b’ and c’. the results agree well with the principal strain range and mean strain we have considered by putting a sign with human operation. (a) (b) (e) (c) (d) figure 4: variations of i(t), i(t) and (t)/2 in proportional straining: (a) strain paths on  /3 plot, (b) variation of i (t), (c) variation of i(t), (d) variation of (t) and (t), (e) strain paths on polar figure. non-proportional loading fig. 5 shows non-proportional loading cases of the cruciform and box shapes. in the figure, imax is assumed to be given by i(a) and i(a) in the cruciform and box shape loadings, respectively. the principal strains and the direction of i(t) in each stage in the figure are expressed as follows. principal strains: stage oa, ob, od and ddaab   i i i i i a a a a                                  21 2 2 2 3 1 1 3 max 1 max 1 ( ) 1 1 1 ( ) ( ) 2 2 ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) t t t t t since of t t for cruciform loading for box shaped loading (10.a) stage oc and bbccd   i 21 2 2 2 3 3 1 3 ( ) 1 1 1 ( ) ( ) 2 2 ( ) ( ) ( ) ( ) t t t t t since of t t                       (10.b) t. itoh et alii, frattura ed integrità strutturale, 33 (2015) 289-301; doi: 10.3221/igf-esis.33.33 294 a o b - c b a dc 3  d t i(t) b c c d da b ba o c do o o 1(t), 3(t) 1 3 to cruciform t 90 -90 (t)/2, (t) (t)/2 (t) ba o c doo o o cruciform t 90 -90 (t)/2, (t) (t)/2 (t) box b acc d da b a b acc d da b 1(t), 3(t) 1 3 t box a a a cruciform box i1   i imax imin b a c d i3 i1   i imax imin b a b c d a d c i3 box o direction of i(t): stage oa, ob, od for cruciform loading ( ) 0 , ( ) 0 ( ) 90 , ( ) 90 ( ) 90 , ( ) 90 t t along oa t t along ob t t along od                    (11.a stage oc for cruciform loading ( ) 180 , ( ) 0t t along oc     (11.b) stage abbcc for box-shaped loading 0 ( ) 180 , ( ) 90t t      (11.c) stage cddaa for box-shaped loading 0 ( ) 180 , ( ) 90t t       (11.d) (a) (b) (e) (c) (d) figure 5: variations of i(t), i(t) and (t)/2 in non-proportional straining: (a) strain paths on  /3 plot, (b) variation of i (t), (c) variation of i(t), (d) variation of (t) and (t), (e) strain paths on polar figure. in the cruciform loading, i(t) makes four triangles shown in figs 5 (b) and (c). the angle of (t) rotates in the range of 0(t)180, fig. 5 (d), and the angle of (t) changes by 90 at the origin o in a cycle. the principal strain path in the polar figure became a cruciform shape as shown in fig. 5 (e). in the box loading, 1(t) takes positive and 3(t) negative values without changing sign in a cycle as shown in fig. 5 (b). then, i(t) in the box loading has large mean value with a small fluctuation during a cycle, fig. 5 (c). the principal strain direction rotates continually in the range of 0(t)180 and (t)=90 and the principal strain path forms rhombus shape, figs 5 (d) and (e). the maximum strain ranges are i i i a c max min 1 3( ) ( )           for cruciform loading (12.a) i i i a c max min 1 3( ) ( )           for box-shaped loading (12.b) the mean strain in the two cases is 0. t. itoh et alii, frattura ed integrità strutturale, 33 (2015) 289-301; doi: 10.3221/igf-esis.33.33 295 definition of non-proportionality he authors proposed the non-proportional strain range expressed in eq. (13) for correlating mlcf lives under non-proportional loading [6, 7, 11-14].   inp np1     f (13) in the equation, i is the principal strain range discussed previously.  is a material constant expressing the amount of additional hardening by non-proportional loading and is defined as the ratio of a saturated principal stress in the circular loading to that in uniaxial push-pull loading at the same principal strain amplitude for additional hardening material. in eq. (13), i also can be replaced by the other equivalent stains based on the user’s requirement although trends of data correlation are different between the strains used which have been discussed in other studies [6, 7, 11-14]. fnp is the non-proportional factor that expresses the severity of non-proportional loading in the form as [6, 7, 11-14],      i0 i max sin t t np b t t dt    f (14) where t is the time for a cycle. b is a constant for making fnp=1 in the circular loading on  /3 plot and b takes /2 when i(t) is employed [6, 7]. in eq. (14), fnp is calculated by measuring the rotation of the maximum principal strain direction and the integration the strain amplitude after the rotation. therefore, fnp evaluates comprehensively the severity of non-proportional cyclic loading based on the amplitude of strain and the direction change of principal strain. this paper proposes a modified non-proportional factor, fnp, to be applicable for 3d stress and strain space defined in chapter 3, which is expressed as, i i path path c ( ) d d 1 ' max | 2 np rc s t s s l l s       f |e e (15) where er is a unit vector directing to si(t), ds the infinitesimal trajectory of the loading path shown in fig. 3. lpath is the whole loading path length during a cycle and “” denotes vector product. the scalars, simax and lpath, before the integration in eq. (15) is set to make fnp unity in the circler loading in 3d polar figure. integrating the product of amplitude and principal direction change of stress and strain by path length in eq. (15) is more suitable for evaluation of fatigue damage rather than the integration by time. type 1 2 3 4 5 6 loading path fnp 0 0.39 0.10 0.20 0.79 0.79 f ’np 0 0.49 0.12 0.24 0.71 0.71 type 7 8 9 10 11 12 loading path fnp 0.53 1.06 f ’np 0.5 1 0.71 0.98 0.49 1.78 si 1 si 3 si 1 si 2 si 3 simax 1 1/2 figure 6: comparing fnp and f ’np under several loadings. t t. itoh et alii, frattura ed integrità strutturale, 33 (2015) 289-301; doi: 10.3221/igf-esis.33.33 296 si---coordinate (polar coordinate) (1) input 6 components of stress or strain at time t s(t)= (t) or  (t) (2) calculating principal stress vector or strain vector at time t si(t) (3) calculating maximum absolute value of si(t) and principal direction change (two angles) si max ,  (t)/2, (t) (4) describing si max ,  (t)/2,  (t) into polar figure (5) calculating si, f’np xyz-coordinate (material coordinate) xyz-coordinate (spatial coordinate) fig. 6 compares the values of fnp with those of fnp for several loading paths for the case of strain. small difference in the value between fnp and fnp is found because of different definition between them. however, fnp has the advantages applicable to 3d stress and strain conditions. fig. 7 shows a flow chart of calculation of stress or strain range and non-proportionality. when 6 components of stress or strain at time t as the data obtained from experiment, numerical analysis such as a finite element analysis or etc., si and fnp are calculated based on the procedures presented in above. then, evaluation of fatigue damage can be analyzed by user’s method or itoh-sakane model [13]. figure 7: flow chart of calculation of stress or strain range and non-proportionality. non-proportional stress and strain ranges for life evaluation he authors analyzed the non-proportional lcf lives of type 304 steel tube specimens fatigued using 15 strain waveforms shown in fig. 8 at 923 k [22]. figs 9 (a)(c) correlate non-proportional fatigue lives with the asme equivalent strain range (asme) and two maximum stress ranges of ie and i. asme is the strain range based on mises equivalent strain and is the strain range recommended in the code case of asme, section iii, division 1 nh [1]. ie is the principal stress range calculated from i multiplied by young’s modulus of 145 gpa. the correlation using ie was made considering that conventional design usually uses stress ranges elastically calculated from strain ranges. i is the maximum principal stress range experimentally obtained at 1/2nf. in the figures, heavy solid lines are drawn based on the case 0 data and two thin solid lines show a factor of 2 scatter band. fig. 9 (a) clearly indicates that asme overestimates the non-proportional fatigue lives in the cases with sever nonproportionalities. for type 304 stainless steel at room temperature, the more drastic reduction in lcf lives due to nonproportional loading beyond a factor of 10 was also reported [4, 5, 7, 12, 15]. the cause of the overestimates results from that asme does not cover the effect of non-proportional loading on life. the correlation with ie shown in fig. 9 (b) appears to be a similar trend to that in fig. 9 (a). ie has larger magnitude than experimental practically because the stress was calculated elastically even in plastic deformation occurred. in the data correlation with i, fig. 9 (c), lcf lives under non-proportional loading are underestimated. the underestimate of the lcf lives under non-proportional loading may result from the additional hardening due to non-proportional loading, because i does not cover the additional hardening due to non-proportional loading resulting in reduction in life. t t. itoh et alii, frattura ed integrità strutturale, 33 (2015) 289-301; doi: 10.3221/igf-esis.33.33 297 102 103 104 105 0.2 0.4 1 2 number of cycles to failure nf, cycles s tr a in ra n g e   a s m e , % sus304, t=923k case0 case1 case2 case3 case4 case5 case6 case7 case8 case9 case10 case11 case12 case13 case14 102 103 104 105 0 1000 2000 3000 number of cycles to failure nf, cycles s tr e ss ra n g e    ie , m p a sus304, t=923k case0 case1 case2 case3 case4 case5 case6 case7 case8 case9 case10 case11 case12 case13 case14 102 103 104 105 200 400 600 800 number of cycles to failure nf, cycles s tr e ss ra n g e    i, m p a sus304, t=923k case0 case1 case2 case3 case4 case5 case6 case7 case8 case9 case10 case11 case12 case13 case14  case 0 case 1 case 2 case 3 case 4 case 5 case 6 case 7 case 8 case 9 case 10 case 11 case 12 case 13 case 14 3 figure 8: 15 strain paths employed in the non-proportional lcf test. (a) (b) (c) figure 9: correlation of non-proportional lcf lives with asme, ie and i: (a) asme  nf, (b) ie  nf, (c) i  nf. fig. 10 correlates the non-proportional lcf lives with np, where material constant, , is set to 0.4. np correlates the non-proportional fatigue lives with a small scatter.  employed was determined from the degree of additional hardening. this result suggests that a suitable strain parameter for multiaxial lcf life evaluation must take account of intensity of non-proportionality of loading and additional hardening due to non-proportional loading. the former is the nonproportional factor, fnp or fnp, and the latter is the material constant, , in np. 102 103 104 105 0.2 0.4 1 2 number of cycles to failure nf, cycles s tr a in ra n g e   n p , % sus304, t=923k case0 case1 case2 case3 case4 case5 case6 case7 case8 case9 case10 case11 case12 case13 case14  = 0.4 figure 10: correlation of non-proportional lcf lives with np. t. itoh et alii, frattura ed integrità strutturale, 33 (2015) 289-301; doi: 10.3221/igf-esis.33.33 298 visualizations and analyses of stress and strain state and life evaluation outline of program for visualization ased on the definition of stress and strain mentioned above, a program is developed to analyze and visualize stress/strain and evaluate the failure life under non-proportional loading. the programming code used is c#. fig. 11 is a flowchart of the program, which is divided into 8 categories as below. (1) input data the stress/strain data vs. time obtained from experimental or calculated result, denoted by s(t), is read into the program. the input data consists of the 6 components of stress/strain and time at each column. additional columns (temperature, pressure, etc.) can be added. as an example, for a butterfly-shape strain path under the combined push-pull and cyclic reversed torsion loadings using a hollow cylinder specimen, figs. 12 (a) and (b) show a strain path in /2 plot and a strain path in polar figure coordinates, respectively, where  and  are the total axial and the total shear strains. in the figures, attached characters ‘a-c’ will be referenced later. fig. 13 is the table of the input data formatted for the program. (2) calculation of si(t) and simax in this step, si(t) and simax are calculated in accordance with the is-method. (3) determination of reference axis the reference axis for defining (t) and (t) is determined. the determination of the reference axis has three methods (method-1, -2 and -3). in method-1, the reference axis corresponds to the direction of simax, which is the maximum amplitude of stress/strain in a cycle. in method-2, the reference direction is put into the direction perpendicular to a critical plane defined as critical plane approach [23, 24]. in this study, the critical plane is determined as the plane where cumulative normal stress/strain becomes the maximum in a cycle under the random loading. in method-3, users can define the reference axis as any direction at their request. the reference axes determined by method-1, -2 and -3 are denoted by the characters a, b and c, respectively, in fig. 12. (4) calculation of ξ(t) and ζ(t) in accordance with the is-method, calculations of ξ(t) and ζ(t), etc. are carried out. (a) (b) figure 12: 4 strain paths of input data: (a) in ε-γ/2 plot. (b) in polar figure. figure 11: calculation flow in the program. figure 13: formatted input data. b t. itoh et alii, frattura ed integrità strutturale, 33 (2015) 289-301; doi: 10.3221/igf-esis.33.33 299 (5) figures of s(t)-t, si(t)-t and si(t)-ξ(t)-ζ(t) by the calculations and analyses in the above categories, descriptions of s(t)-t, si(t)-t and si(t)-ξ(t)-ζ(t) are calculated. fig. 14 shows a graph of the input data for strains, as a function of time, shown in figs. 12 and 13. figs. 15 (a) and (b) illustrate the strain path in the polar coordinates, i.e., si(t)-ξ(t)-ζ(t) and the projection of si(t) and non-proportionality of loading as a function of time t. in fig. 15 (a), attached characters, a, b and c, indicate the directions of the reference axes. tab. 1 shows results as output data and they are strain ranges and non-proportional factors evaluated for each reference axis assuming the axial strain range =1.0%. (6) cycle counting and analysis of si(t) for random loading under the random loading, waveform of stress/strain must be analyzed using a counting method, such as a rain-flow counting method, and damage also has to be evaluated by a cumulative damage rule like miner’s rule. stress/strain waveform under non-proportional loading was already reduced to the simple waveform in the categories (1)-(5), the cycle counting and the cumulative damage rule used in uniaxial loading can be applied to the non-proportional loading. (7) figure and output of results evaluated by the program in this step, all the figures and tables can be graphed and saved to memory. by examining the figures, the users can visually understand the multiaxiality and non-proportionality of stress/strain state simultaneously. (8) damage and life evaluation based on the results obtained in the categories (1)-(7), failure life evaluation can be performed. for the life evaluation, s-n curve base data and the is-method are employed with the rain-flow cycle counting method and cumulative damage rule. method 1 2 3 reference axis oa ob oc δεi 1.26 1.24 1.09 fnp 0.65 0.66 0.78 np 1.87 1.85 1.42 figure 14: strain waveforms of input data. table 1: comparison of evaluated parameters. (a) (b) figure 15: output strain path in polar coordinates and waveforms: (a) strain path in polar coordinates. (b) strain waveforms projected to reference axis. t. itoh et alii, frattura ed integrità strutturale, 33 (2015) 289-301; doi: 10.3221/igf-esis.33.33 300 life evaluation under random loading one example of life evaluation under random loading is presented here. material used is a rolled steel for general structure, type ss400, whose material properties are; yong’s modulus e=206 gpa, tensile strength σb=437 mpa. the failure life curve employed for evaluation is given by eq.(16), which is obtained from experiment. e fδ 69 log 1190n    (16) figs. 16 (a) and (b) show stress waveforms of the input data for 1 block cycles and the calculated stress path in the polar coordinates, respectively. it is clear that the evaluated stress path is proportional loading since the stress path in fig. 15 (b) is shown by a unique straight line. counting method employed was a rain-flow method and 1 block was counted as 30,000 cycles. tab. 2 shows the numerical values of fatigue damage and evaluated life by using a linear cumulative damage low. this analysis was carried out by using the test results under proportional loading, so more discussion about the applicability of the program to the evaluation of fatigue strength under non-proportional loading will be studied after the experimental results under non-proportional loading are obtained. under the non-proportional loading, especially definition of non-proportionality will be required. in there, fnp will be calculated at each separate stress amplitude obtained by the counting method. (a) (b) figure 8: input and output data under random loading: (a) input data, (b) output data in polar coordinates. reference axis oa (ob) σmax (mpa) 447 damage per block 0.161 evaluated life (blocks) 6 experimental life (blocks) 8 table 2: life evaluation under random loading. conclusions 1. this paper proposed a simple method of determining the principal stress and strain ranges together with the mean stress and strain under proportional and non-proportional loading in 3d stress and strain space. it also proposed the method of defining the rotation and deviation angles of the maximum principal stress and strain. 2. the paper extend the non-proportional factor, fnp, from 2d to 3d stress and strain space with the consistency with the previous definition of it in the 2d space. t. itoh et alii, frattura ed integrità strutturale, 33 (2015) 289-301; doi: 10.3221/igf-esis.33.33 301 3. applicability of the non-proportional strain was discussed for describing the high temperature proportional and nonproportional low cycle fatigue lives. 4. based on the is-method to evaluate stress/strain and failure life under non-proportional loading, this study developed a program for visually presenting the stress/strain state, the non-proportionality of loading, and the damage evaluation. it is possible for researchers and engineers to assess the fatigue strength under non-proportional loading without requiring special knowledge and judgment about multiaxial loading. references [1] asme, boiler and pressure vessel code section iii, division 1 nh (2004). [2] asme, boiler and pressure vessel code section viii, division 3 (2004). [3] fatemi, a., socie, d.f., a critical plane approach to multiaxial fatigue damage including out-of-phase loading, fatigue fract engng mater struct, 11(3) (1988) 149-165. [4] nitta, a., ogata, t., kuwabara, k., fracture modes and fatigue life evaluation of sus 304 stainless steel under nonproportional biaxial loading conditions, j society material science, japan, 38(427) (1989) 416-422. [5] doong, s.h., socie, d.f., robertson, i.m., dislocation substructures and nonproportional hardening, trans asme, j engng mater technol, 112 (1990) 456-565. [6] itoh, t., sakane, m., ohnami, m., socie, d.f., nonproportional low cycle fatigue criterion for type 304 stainless steel, trans asme, j engng mater technol, 117 (1995) 285-292. [7] itoh, t., nakata, t., sakane, m., ohnami, m., non-proportional low cycle fatigue of 6061 aluminum alloy under 14 strain path, multiaxial fatigue and fracture (macha et al., eds.), esis-25, (1999) 41-54. [8] socie, d.f., marquis g., eds, ‘multiaxial fatigue’, sae international (2000). [9] smith, r.n., watson, p., topper, t.h., a stress-strain parameter for the fatigue of metals, j materials, 5(4) (1970) 767-778. [10] shamsaei, n., fatemi, a., socie, d.f., multiaxial fatigue evaluation using discriminating strain paths, int j fatigue, 33(4) (2011) 597-609. [11] itoh, t., effect of direction change in maximum principal strain axis on multiaxial low cycle fatigue life of type 304 stainless steel at elevated temperature, j society material science, japan, 49(9) (2000) 988-993. [12] itoh, t., a model for evaluation of low cycle fatigue lives under non-proportional straining, j society material science, japan, 50(12) (2001) 1317-1322. [13] itoh, t., sakane, m., hata, t., hamada, n., a design procedure for assessing low cycle fatigue life under proportional and non-proportional loading, int j fatigue, 28(8) (2006) 495-466. [14] itoh, t., sakane, m., ozaki, t., determination of strain and stress ranges under cyclic proportional and nonproportional loading, j society material science, japan, 60(2) (2011) 88-93. [15] itoh, t., yang, t., material dependence of multiaxial low cycle fatigue lives under non-proportional loading, int j fatigue, 33(8) (2011) 1025-1031. [16] ogata, t., nitta, a., evaluation of multiaxial low-cycle fatigue failure based on new criterion and its application to high temperature structural design, j society material science, japan, 42(472) (1993) 72-77. [17] kobayashi, m., ohno, n., igari, t., thermal ratcheting analysis of cylinders subjected to axial travelling of temperature distribution: comparison with experiments of 316fr steel cylinders, j society material science, japan, 46(8) (1997) 906-913. [18] aoto, k., structural materials development for sodium cooled fast reactor, materia japan, 47(9) (2008) 459-463. [19] sakane, m., ohnami, m., sawada, m., fracture modes and low cycle biaxial fatigue life at elevated temperature, trans asme, j engng mater technol, 109 (1987) 236-242. [20] sakane, m., ohnami, m., hamada, n., biaxial low cycle fatigue for notched, cracked, and smooth specimens at high temperature, trans asme, j engng mater technol, 110 (1988) 48-54. [21] itoh, t., sakane, m., ohnami, m., high temperature multiaxial low cycle fatigue of cruciform specimen, trans asme, j engng mater technol, 116 (1994) 90-98. [22] hamada, n., sakane, m., high temperature nonproportional low cycle fatigue using fifteen loading paths, proceedings of 5th int. conf. on biaxial/multiaxial fatigue and fracture, 1 (1997) 251-266. [23] socie, d.f., multiaxial fatigue damage models, journal of engineering materials and technology, 109 (1987) 293-298. [24] fatemi, a., socie, d.f., a critical plane approach to multiaxial fatigue damage including out-of-phase loading, fatigue & fracture of engineering materials & structures, 11(3) (1988) 149-165. microsoft word numero_56_art_03_2984 s. benaissa et alii, frattura ed integrità strutturale, 56 (2021) 46-55; doi: 10.3221/igf-esis.56.03 46 exploitation of static and dynamic methods for the analysis of the mechanical nanoproperties of polymethylmetacrylate by indentation benaissa soufiane, habibi samir, semsoum djameleddine, merzouk hassen, mezough abdelnour mechanical engineering department, university of mascara, 29000, lgidd laboratory of relizane, 48000, algeria. soufiane.benaissa@univ-mascara.dz, habibismr@univ-mascara.dz, djameleddine.semsoum@univ-mascara.dz, hassen.merzouk@univ-mascara.dz, abdelnour.mezough@univ-mascara.dz boutabout bénali university of djillali liabes, physical mechanics of materials laboratory (lmpm), sidi-bel-abbès, 22000, algeria. bboutabout@yahoo.fr montagne alex national higher school of arts and crafts (ensam), mechanics, surfaces and materials processing laboratory (msmp) of lille, france alex.montagne@ensam.eu abstract. elaborating an instrumented nanoindentation is to exercise nondestructive tests to be applied to volumes of polymethylmetacrylate (pmma) materials in miniature. this work focuses on factors that explain the trends variation of mechanical properties like young's modulus (e), contact hardness (h) and indentation force (p). the evolution of e and h with depth (h) and p shows a 2.77 nm inflection point at low penetrations, separating two zones: the first increasing and the second decreasing. this is respectively explained by the surface hardening induced by preparing the material surface, and the existence of a surface hardness gradient denoted by an indentation size effect (ise) observed at very low depths. moreover, in addition, a critical penetration depth of 9.71 nm below which the surface effect dominates the variation of the penetrating load is detected. e and h results differences between dynamic and static modes are 8.46% and 6.44% inducing an overestimation of 35 mpa in e value, and an underestimation of 1.23 mpa in h value. this tends to affect the expected nanoscale precision of the indentation to determine the nanomechanical properties of pmma. keywords. modulus; hardness; nanometer scale; low indentation depths; indentation size effect. citation: benaissa, s., habibi, s., semsoum, d., merzouk, h., mezough, a., boutabout, b., montagne, a., exploitation of static and dynamic methods for the analysis of the mechanical nanoproperties of polymethylmetacrylate by indentation, frattura ed integrità strutturale, 56 (2021) 46-55. received: 14.01.2021 accepted: 18.01.2021 published: 01.04.2021 copyright: © 2021 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. https://youtu.be/rp6kvfuwoby s. benaissa et alii, frattura ed integrità strutturale, 56 (2021) 46-55; doi: 10.3221/igf-esis.56.03 47 introduction olymers offer interesting technological solutions in many activity fields. due to the attractive mechanical properties of polymethylmetacrylate (pmma) and its ability to be easily shaped, many researchers have focused on it to improve its resistance during the service [1-6]. indeed, pmma is widely used in nanotechnology, especially in mechanical and civil engineering, biomaterials, optical telecommunications, electronics, aeronautics, aerospace, etc. [7-13]. the nanoindentation technique has undergone a great technological evolution for more than a century, with the first tests carried out by brinell [14] making it possible to define the notion of hardness, till today when such technique allows us to determine, at a nano-metric scale, the most commonly measured mechanical properties, such as young's modulus and material hardness [15]. regarding the nanometric scale, several parameters interact like the tip defect [16], instrument complacency [17], flow mode under indenter [18-20], micro-nano scaling-up [21], geometry of indenters, effect of indentation size, etc. all these might influence directly the accuracy of results. many scientists have studied the variation of young's modulus with shallow depth, resulting from a strain rate effect [22], the quality and geometry of the tip on pmma [23] and the compliance of the frame depending on the applied force [24]. in nanoindentation, the size effect is often explained by the strain gradient plasticity (sgp) theory, based on dislocations that are geometrically necessary to accommodate the plastic deformation under the indenter [25, 26]. the main objective of this study is to highlight by experiments the experimental tests of classical indentation at different levels of indentation forces, and the continuous stiffness measurement (c.s.m) via the integrated operating mode. we aim to assess the reliability of software out-puts for processing data, implemented in the instrumented indentation device (in static and dynamic modes), and estimate the measurement difference between both methods. we focus on studying the evolution of modulus and hardness with tip penetration depth and indentation force for very shallow depths, attempting to bring explanatory factors to the behavior of the material examined. specimens and experimental protocol he tests are carried out on an xp, mts nanoindenter, equipped with a dynamic contact module (dcm) head of a very good resolution in force and displacement. the set is placed in an acoustic enclosure to avoid any environmental and acoustic disturbance. the tip used is a diamond berkovich type indenter (e = 1140gpa, ν = 0.3), with a low tip defect hp ≤ 20 nm. the nanoindenter is installed on an anti-vibration springs table, to avoid any parasitic vibration. the imposed force is applied by a magnetic coil, and the displacement is estimated by capacitive measurement, with a surface approach speed of 9nms-1. the dcm head allows using the csm method to obtain the dynamic properties of materials. the xp, mts nanoindenter, which integrates the csm module, allows a continuous measurement of the elasticity modulus and the hardness by successive oscillations of the tip during its movement. without this option, the measurements could be only performed at the maximum penetration depth. the tests are carried out on a pmma plane sample of very low roughness. the sample is fixed with a cyanoacrylate glue on the sample holder, screwed aluminum and cleaned before tests with ethanol. pmma is light, of a density being about half that of glass, resistant to atmospheric agents, easy to work with, and of its transparency greater than that of glass. in nanoindentation, the diameter and thickness of a sample are up to 30 mm and and 10 mm, respectively. the types of tests and the operating conditions are shown in tab. 1. indentation device xp, ts scale nano load range 1-650 mn static mode constant time (30s loading / unloading); waiting time (15s); dynamic mode strain rate (0.05s-1); harmonic shift (2 nm); frequency (45hz); table 1: types of tests and operating conditions. p t s. benaissa et alii, frattura ed integrità strutturale, 56 (2021) 46-55; doi: 10.3221/igf-esis.56.03 48 characterization methodology n instrumented indentation, the hardness (h) is defined as the ratio of maximum load pmax to projected contact area ac: h max c p a (1) the reduced modulus of elasticity er is linked to the slope (or stiffness s) of the curve on unloading by the relationship:   2 r c s e a (2) where er is related to the modulus of elasticity (e and ei) and to the poisson coefficients (ν and νi) of the material and the indenter, respectively:     22 11 1 i r ie e e (3) eqns. (1) and (2) clearly show that the projected contact area (ac) is a key parameter in calculating the mechanical properties. data analysis to obtain such properties is similar for the three scales, with a main difference being in the choice of the function used to estimate ac. in nanoindentation, the most used area function (eq. (4)) is that proposed by oliver and pharr [17], with cn coefficients denoting the least-squares adjustment parameters of the curve obtained from the csm tests on fused silica, ac = 24.5h2c+c1h1c+c2h1/2c +c3h1/4c +...+c8h1/128 (4) the used contact depth (hc) to calculate ac changes depending on the predominant strain mode in the material. the method of oliver and pharr [19] used when the material exhibits a sink-in (eq. (5)), while the method of loubet et al. [20] is exploited when the pile-up is predominant (eq. (6)).   c sink ina       2 0.75 24.56  maxmax b p h h s (5)   c pile upa         2 24.56 1.2 maxmax b p h h s (6) results and analysis n nanoindentation the used area function [17] (eq. (5)), of cn coefficients as the least squares adjustment parameters of the curve obtained from csm tests on pmma, is as follows: ac = 24.4 2 ch +974  ch -2390 1/2  ch -8950h 1/4  ch -72.4. 1/8 ch + 438 1/16  ch + 731 1/32  ch + 888 1/64  ch +969 1/128  ch (7) evaluating the hf/hm ratio to predict the deformation mode of the 48 characteristic points shown in fig. 1 represent the ratios' values obtained at the nanoscale by analysing the curves. we find that for materials with a ratio greater than 0.83, a pile-up was formed on the surface, while the sink-in appears when that was lower. the 0.83 value becomes therefore a i i s. benaissa et alii, frattura ed integrità strutturale, 56 (2021) 46-55; doi: 10.3221/igf-esis.56.03 49 limit value hence pmma adopting an indenter strain in a sink-in form. so, the method of oliver and pharr [19] is used when the material presents a deflection of the faces of the hardness, as shown (eq. 5). figure 1: evaluation of the ratio vs. the indentation force to predict the deformation mode. exploiting conventional nanoindentation was by interpolating results to collect mean hardnesses and modulus, respectively relating to the four ultimate loads ranges (see figs. 2 and 3). for comparison, the evolution of these two properties, obtained by the csm method, is also plotted (see fig. 3 and 4). figure 2: modulus vs. displacement into surface in static mode. figure 3: hardness vs. displacement into surface in static mode. s. benaissa et alii, frattura ed integrità strutturale, 56 (2021) 46-55; doi: 10.3221/igf-esis.56.03 50 the two figs. 2 and 3 illustrate the results of e and h obtained by the static method by interpolation. so that each characteristic point on these two graphical representations designates an ultimate indentation force test. figure 4: modulus vs. displacement into surface in dynamic mode. figure 5: hardness vs. displacement into surface in dynamic mode. the graphical representations (see 4 and 5) illustrate the evolution of the continuous measurement of the properties e and h at each point. in contrary to the two previous ones (see figs. 2 and 3). estimation of nanomechanical properties by using the static method his is a point characterization at maximum progressive loads. the obtained parameters values are given in tab. 2. maxp (mn) emoy (gpa) hmoy (gpa) 50 5.095 0.243 100 5.068 0.251 250 5.056 0.247 650 5.079 0.249 table 2: mechanical properties in static mode. t s. benaissa et alii, frattura ed integrità strutturale, 56 (2021) 46-55; doi: 10.3221/igf-esis.56.03 51 following the four ranges of indentation loads for maximum penetrations between [2000-7300] nm, we obtain an average hardness of 0.247 gpa and an estimated average young's modulus of 5.08 gpa. from the results of the static method originates the fair value of the modulus of elasticity, according to the equation: eit = (5.08±0.02) gpa to the nearest 0.3% (8) and, the estimation of the indentation hardness, as well, as the following equation can show: hit = (0.247 ±0.003) gpa to the nearest 1% (9) by using the dynamic method it is to continuously characterize parameters at loads corresponding to the contact depths at each characteristic point. for low indentation penetrations of the order of (0.8 ÷ 11) nm induced by low indentation forces which vary between (9.83.10-5 ÷ 1.54.10-3) mn generate a young's modulus which varies in the interval of (6.3 ÷ 10) gpa. for low indentation depths between (2.77 ÷ 11) nm induced by low maximum loads which vary between (4.27.10-4 ÷ 1.47.10-3) mn generate a contact hardness which varies in the interval from (0.35 ÷ 0.74) gpa. however, for values of displacement of the tip of the indenter between (11 ÷ 5146) nm, a modulus of elasticity is recorded which varies in the range of (4.5 ÷ 5.5) gpa for values of loads between (1.68.10-3 ÷ 140) mn. and an indentation hardness that varies in the range of (0.25 ÷ 0.30) gpa for forces between (1.54.10-3 ÷ 140) mn. after integrating the csm mode with the classical nanoindentation, we obtain an average hardness of 0.2662 gpa, and a young's modulus estimated at 4.67 gpa (see eqns. 10, 13), which leads to a fair value of the elasticity modulus, according to eq. 10: eit = (4.67±0.02) gpa to the nearest 0.4% (10) and, the estimation of the indentation hardness, as well, as eq. 11 shows: hit = (0.2662±0.0009) gpa to the nearest 0.3% (11) we have treated the obtained results with both methods, by using the statistic tool so-called "standard deviation" to estimate the precision of the central tendency with respect to the mean of the dispersion of the characteristic points. figure 6: radar graphical representation: standard deviation of both methods, estimating (a) young's modulus and (b) contact hardness. by comparing the results consists the difference between both methods static (ms) and dynamic (md) is determined, as shown in eqn. 12 and 13, giving the hardness and modulus, respectively: s. benaissa et alii, frattura ed integrità strutturale, 56 (2021) 46-55; doi: 10.3221/igf-esis.56.03 52 δe% (ms-md) =  * 100 sup inf sup e e e (12) δh% (ms-md) =  * 100 sup inf sup h h h (13) hence, δe% (ms-md) = 8,46% et δh% (ms-md)=6,44% evaluating mechanical nanoproperties at very low loadings and penetrations by using the csm mode exploitation of the results in dynamic mode to examine the behavior of pmma, at low contact depths, between the specimen and the indenter’s tip (see figs .7 (a, b)). (a) (b) figure 7: evolution of (a) e and (b) h by csm vs. the indentation force, at very low point penetrations. the evolution of e shows a significant increase from 5.52 gpa to the peak of 10 gpa for h and pmax respectively less 2.77nm and 0.00044mn (see fig. 7a). this increase in young's modulus with depth, in the shallow depth range should results from a strain rate effect, as reported in the literature [22]. the young's modulus increase in the shallow depth range results, from an overestimation of the contact area, reflecting the fact that the quality of the diamond tip, is not so bad because the young's modulus remains almost constant above 20nm. it is worth noting that these results are in agreement with those obtained [23] on pmma. then, a decrease in e till 5.71 gpa for h and pmax respectively less than 13.92 nm and s. benaissa et alii, frattura ed integrità strutturale, 56 (2021) 46-55; doi: 10.3221/igf-esis.56.03 53 0.0021 mn, was mentioned. knowing that this modulus is an intrinsic property of materials, and assuming that the hypothesis is validated that young's modulus is constant and independent of the applied load [17], this leads to the trend supposing that the device’s compliance is dependent on the applied force, as some researchers have already reported [24]. hence, this difference is probably related to experimental errors during the tests, and the deviation may be related to the relationships used for contact depth and contact area, as mentioned above. however, e converges towards an average constant value for h and respectively pmax less than 5200nm and 146mn. the evolution in h has recorded a significant increase of 0.1 to 0.75gpa for h and pmax respectively less than 2.77nm and 0.00042mn (see fig. 7b), which can be explained by a superficial hardening induced by the preparation of the material surface (brutal mechanical polishing). a sharp decrease is noted in h down to 0.34 gpa for (h, pmax) less than (9.71 nm, 0.0013 mn). such observations can be attributed on the one hand to the role of the surface effect on nanohardness for very low penetration depths, and on the other hand to the existence of a critical penetration depth below which the surface effect dominates the variation of the penetrating load in the vicinity of 9.71 nm. that is the ise generally leading to a decrease in hardness as the indentation load increases. these results confirm the works of zhang and xu [27]. on the other hand, observations can be attributed to the effect of the contact size which is comparable to the grain size of the material [28]. however, the obtained results show that h remains constant when the indentation depth and pmax are respectively less than 5200nm and 146mn. in nanoindentation, the size effect is often explained by the theory of strain gradient plasticity (sgp), based on dislocations that are geometrically necessary to accommodate the plastic deformation under the indenter [25, 27]. now, by comparing the results of dynamic and static modes with those of the literature, we should notice that the estimation of the uncertainties in evaluating the young's modulus and hardness are respectively in orders of 8.46% and 6.44%. therefore, there is a tendency to overlook deviations originating from the evaluations of the measured mechanical properties, and in particular an overestimation of 35mpa in the value of the modulus of elasticity and an underestimation of 1.23mpa in that of the contact hardness. this has likely to affect the expected precision in indentation at nanoscale while determining the nanomechanical properties of the studied polymer. for the berkovich tip, an overestimation of about 5.23% for pmma (4670 vs 4426 mpa [22]) has been recorded. according to briscoe and sebastian [23], the results have to be interpreted as an effect of the high hydrostatic pressure, existing under the berkovich indenter for pmma. conclusion the difference in the results of e and h between the dynamic and static modes are respectively: 8.46% and 6.44% inducing an overestimation of 35 mpa in value of e and an underestimation of 1.23 mpa in value de h. they tend to affect the expected nanometric precision of the indentation to determine the nanomechanical properties of pmma. the indentation mode provided with csm offers several advantages for the mechanical characterization of polymers in particular the external referencing, the optimization of the effort and the time, as well as the high precision for very low loadings compared to the classic technique which does not allow obtaining such efficient results. the evolution of young's modulus and contact hardness shows the existence of a surface hardness gradient called the indentation size effect (ise) observed at very weak penetrations in the vicinity of 2.77 nm. the identification of an estimated critical penetration depth of 9.71 nm below which the surface effect on nanohardness dominates the variation in the penetration charge. in perspective, a comparative study of the different families of materials by the use of the csm mode to explore the effect of indentation size is envisaged to examine indentor plasticity at very low nanometric indentation depths. acknowledgments his research was supported by the general directorate of scientific research and technological development (dgrsdt: direction générale de la recherche scientifique et du développement technologique) of algeria. the authors gratefully acknowledge the scientific support of the two research teams from the lille mechanics unit t s. benaissa et alii, frattura ed integrità strutturale, 56 (2021) 46-55; doi: 10.3221/igf-esis.56.03 54 (france) and the laboratory of industrial engineering and sustainable development (lgidd), university of relizane (algeria). references [1] kaddouri, a., serier, b., kaddouri, k., belhouari, m. (2020). experimental analysis of the physical degradation of polymers – the case of polymethyl methacrylate, frattura ed integrità strutturale, 53, pp. 66-80. doi: 10.3221/igf-esis.53.06. [2] drai, a., aour, b., belayachi, n., talha, a., benseddiq, n. (2020). finite element modeling of the behavior of polymethyl-methacrylate (pmma) during high pressure torsion process, frattura ed integrità strutturale, 52, pp. 181196. doi: 10.3221/igf-esis.52.15. [3] ayatollahi, m.r., rashidimoghaddama, m., razavi, s.m.j., berto, f. (2006). geometry effects on fracture trajectory of pmma samples under pure mode-i loading, engineering fracture mechanics, 163, pp. 449-461. doi: 10.1016/j.engfracmech.2016.05.014. [4] torabi, a.r., campagnolo, a., berto, f. (2015). local strain energy density to predict mode ii brittle fracture in brazilian disk specimens weakened by v-notches with end holes, materials and design, 69 (15), pp. 22-29. doi: 10.1016/j.matdes.2014.12.037. [5] berto, f., cendon, d.a., lazzarin, p., elices.m. (2013). fracture behaviour of notched round bars made of pmma subjected to torsion at −60 °c, engineering fracture mechanics, 102, pp. 271-287. doi: 10.1016/j.engfracmech.2013.02.011. [6] cendón, d.a., berto, f., lazzarin, p., elicescalafat. m. (2013). the cohesive crack model applied to notched pmma specimens obeying a non linear behaviour under torsion loading, key engineering materials, 577-578, pp. 49-52. doi: 10.4028/www.scientific.net/kem.577-578.49. [7] wenhua, y., zeyu, x., yuming, y., jun, y., xiaodan, l., huiqin, w., shuang, w., yufang, x., yunong, y. (2019). aging behavior and lifetime prediction of pmma under tensile stress and liquid scintillator conditions, journal: advanced industrial and engineering polymer research. doi: 10.1016/j.aiepr.2019.04.002. [8] bussi, y., golan, s., dosoretz, cg., eisen, ms. (2018). synthesis, characterization and performance of polystyrene/pmma blend membranes for potential water treatment, journal of desalination. 431, pp.35-46. doi: 10.1016/j.desal.2017.12.024. [9] münker, t.j.a.g., van de vijfeijken, s.e.c.m., mulder, c.s., vespasiano, v., becking, a.g., kleverlaan, c.j., and al. (2018). effects of sterilization on the mechanical properties of poly(methyl methacrylate) based personalized medical devices, journal of the mecchanical behavior of biomedical materials. 81, pp.168-172. doi: 10.1016/j.jmbbm.2018.01.033. [10] kowalonek, j., kaczmarek, h., kurzawa, m. (2016). effect of uv-irradiation on fluorescence of poly (methyl methacrylate) films with photosensitive organic compounds, journal of photochemistry and photobiology a: chemistry. 319-320, pp. 18-24. doi: 10.1016/j.jphotochem.2015.12.017. [11] manjunatha, h.c. (2017). a study of gamma attenuation parameters in poly methylmethacrylate and kapton, journal of radiation physics and chemistry. 137, pp. 254-259. doi: 10.1016/j.radphyschem.2016.01.024. [12] zhong, z.w., wang, z.f., zirajutheen, b.m.p. (2005). chemical mechanical polishing of polycarbonate and polymethylmethacrylate substrates, journal of microelectronic engineering. 81, pp. 117-124. doi: 10.1016/j.mee.2005.04.005. [13] ali, u., karim, k.j.b.a., buang, n.a. (2015). a review of the properties and applications of poly (methylmethacrylate) (pmma), journal of polymer reviews. 55, pp. 678-705. doi: 10.1080/15583724.2015.1031377. [14] tabor, d. (1951). the hardness of metals, monographs on the physics and chemistry of materials, oxford clarendon press; londres: oxford university press. [15] fischer-cripps, a.c. (2002). facteurs affectant les données de test de nanoindentation, nanoindentation, springerverlag new york inc, pp. 77-104. doi: 10.1007/978-1-4419-9872-9. [16] hochstetter, g., jimenez, a., loubet, j.l. (1999). strain-rate effects on hardness of glassy polymers in the nanoscale range. comparison between quasi-static and continuous stiffness measurements, j. macromol. sci. part b-phys. b 38 (5-6), pp. 681-692. doi: 10.1080/00222349908248131. [17] oliver, wc., pharr, gm. (1992). an improved technique for determining hardness and elastic-modulus using load and displacement sensing indentation experiments, journal of materials research, 7(6), pp. 1564-1583. doi: https://doi.org/10.1557/jmr.1992.1564. s. benaissa et alii, frattura ed integrità strutturale, 56 (2021) 46-55; doi: 10.3221/igf-esis.56.03 55 [18] alcala, j., barone, a.c., anglada, m. (2000). l'influence du durcissement plastique sur les modes de déformation de surface autour des vickers et des empreintes sphériques, acta mater, 48, pp. 3451-3464. doi: 10.1016 / s1359-6454 (00) 00140-3. [19] oliver, w.c., pharr, g.m. (2004). mesure de la dureté et du module élastique par indentation instrumentée: progrès de la compréhension et amélioration de la méthodologie, j. mater. res. 19 (1), pp. 3-20. doi: 10.1557/jmr.2004.19.1.3. [20] loubet, j.l., bauer, m., tonck, a., bec, s., gauthier-manuel, b. (1993). nanoindentation with a surface force apparatus, nato advanced study institute series e. m. natasi, 233, pp. 429 447. doi: 10.1007/978-94-011-1765-4_28. [21] hang, w., zhou, l., shimizu, j., yuan, j. (2013). a robust procedure of data analysis for micro/nano indentation. precision engineering, 37, pp. 408-413. doi: 10.1016/j.precisioneng.2012.11.003. [22] hochstetter, g., jimenez, a., cano, j.p., felder, e. (2003). an attempt to determine the true stress-strain curves of amorphous polymers by nanoindentation, tribology international, 36, pp. 973–985. doi: 10.1016/s0301-679x(03)00107-5. [23] briscoe, b.j., sebastian, k.s. (1996). the elastoplastic response of poly(methylmethacrylate) to indentation, proc. r. soc. lond, a 452, pp. 439–57. doi: 10.1098/rspa.1996.0023. [24] cabibbo, m., ricci, p., cecchini, r., rymuza, z., sullivan, j., dub, s., cohen, s. (2012). un protocole international d'étalonnage circulaire pour les mesures de nanoindentation, micron, 43, pp. 215-222. doi: 10.1016/j.micron.2011.07.01. [25] nix, w.d., gao, h. (1997). effets de taille d'indentation dans les matériaux cristallins: une loi pour la plasticité du gradient de déformation, j. mech. phys. solids, 46 (3), pp. 411-425. doi: 10.1016/s0022-5096(97)00086-0. [26] elmustafa, a.a., stone, d.s. (2003). nanoindentation and the indentation size effect: kinetics of deformation and strain gradient plasticity. j. mech. phys. solids, 51 (2), pp. 357-381. doi: 10.1016/s0022-5096(02)00033-9. [27] zhang, t.y., xu, w.h., zhao, m.h. (2004). the role of plastic deformation of rough surfaces in the size-dependent hardness, acta materialia 52, pp. 57–68. doi: 10.1016/j.actamat.2003.08.026. [28] tsui, t.y., pharr, g.m. (1999). substrate effects on nanoindentation mechanical property measurement of soft films on hard substrates, j. mater. res. 14 (1), pp.292-301. doi: 10.1557/jmr.1999.0042. microsoft word numero_34_art_10 c. fischer et alii, frattura ed integrità strutturale, 34 (2015) 99-108; doi: 10.3221/igf-esis.34.10 99 focussed on crack paths influence of local stress concentrations on the crack propagation in complex welded components c. fischer, w. fricke hamburg university of technology, institute of ship structural design and analysis, hamburg, germany w.fricke@tuhh.de abstract. while a long stable crack propagation phase was observed during experiments of complex welded components, very conservative assessments of the fatigue life were achieved in the past. the difference was explained by the stress gradient occurring over the plate thickness. this paper deals with numerical crack propagation simulations which were performed for different geometrical variants. the variants differ related to global geometry, boundary conditions and weld shape. the analyses aim to investigate how the crack propagation is altered if the structural configuration gets more complex. in conclusion, the stress gradient over the plate thickness, the apparent plate thickness and the notch effect slows down the crack propagation rate if the same stress value being effective for fatigue appears at the weld toe. thereby, the load-carrying grade of the weld, the weld flank angle and the geometrical configuration have an impact on both the notch effect and the local stress concentration. keywords. crack propagation simulation; fatigue life; notch effect; stress gradient. introduction omplex welded components can have hot-spots showing high local stresses with steep stress gradients. these could be critical with respect to fatigue. an example is the three-dimensional intersection of plates shown as variant 5 in fig. 1. different variants of this detail were experimentally investigated by means of both large-scale and small-scale fatigue tests over the last decades, see e.g. [2, 11-15]. dijkstra et al. [2] observed an early crack initiation, but a long period of stable crack propagation until the crack had grown through the loaded plate. however, very conservative fatigue assessments were discovered applying the common fatigue approaches to complex structures, see e.g. [6, 7]. lotsberg and sigurdsson [14] explained the disagreement by the stress gradient over the plate thickness which was not covered by the fatigue approach they had selected. fischer and fricke [5] established three additional reasons: the apparent plate thickness, the load-carrying grade of the weld and bending constraints of the detail. they supposed correction factors to account for these influences in the fatigue assessment. generally, the approaches are based on the analysis of tests of small-scale specimens with more or less simple welded joints. here, no three-dimensional complex stress distribution is on hand. this paper deals with different crack propagation analyses at both simple joints and complex welded structures in order to investigate further effects, besides the stress gradient, which affects the crack propagation, shape and fatigue life. at first, a comparison of a transverse attachment and its geometrical modifications with the intersection of plates is presented. four effects which are identified on the basis of different stress distributions and geometry are validated by numerical and analytical crack propagation analyses. in the next step, the geometry is modified to vary the notch effect and the stress c c. fischer et alii, frattura ed integrità strutturale, 34 (2015) 99-108; doi: 10.3221/igf-esis.34.10 100 concentration at the weld toe which depend on the load-carrying-grade of the weld, the weld flank angle and the layout of the intersecting plates. case study selected variants he two-sided transverse attachment (variant 1 in fig. 1) under axial loading represents a simple welded joint. a crack would be initiated at one of the weld toes and would run through the loaded plate. the complex structure (variant 5) is the intersection of various plates joined by fillet welds. here, the local hot-spot at the intersection point is critical since a crack would initiate at the weld toe on the surface of the horizontal plate in the loading condition shown. the other three variants are ‘intermediate’ geometries to separate the effects on crack propagation. they are described and used in the following. corresponding three-dimensional finite element (fe) models taking advantage of the vertical symmetry plane were created in ansys® 13.0. the models consist of solid elements with quadratic shape function (solid186), and the welds were completely modelled in order to account for the local stiffness. the models are 200 mm long, 100 mm wide and 70 mm high. no axial and angular misalignments are present and only the critical weld toe was rounded by a radius rref = 1 mm for the determination of the stress field. the vertical nodal displacements of variants 1 and 5 were suppressed at the bottom. on the symmetry plane corresponding boundary conditions were applied, and the transverse nodal displacement was coupled on the opposite side to represent adjacent structures. the front and back face were loaded by uniform, axial stresses, whereas the axial nodal displacements were suppressed at the back face of the complex structure. f f crack at weld toe crack at weld toe f f m f m f m 100 variant 2 – transverse attachment w. gradient variant 4 – add. long. attachment variant 1 – transverse attachment crack at weld toe crack at weld toe variant 3 supported transverse attachment crack at weld toe variant 5 – complex structure figure 1: selected geometrical variants (variants 1 to 4 are cut in the symmetry plane). structural hot-spot stress and effective notch stress both stresses are commonly used for fatigue assessment of welded joints (see e.g. [10]) and are the basis for comparing the variants. the structural hot-spot stress (hss) σs which appears in front of the rounded weld toe on the symmetry plane consists of the sum of the membrane stress σm and bending stress σb. both σm and σb are determined by linearizing the axial stress component over the plate thickness t = 10 mm according to [10]. moreover, dong [3] characterized a stress gradient occurring over the plate thickness by means of the degree of bending , eq. (1). here,  = 0 denotes pure axial loading and  = 1 pure bending. b m b       (1) t c. fischer et alii, frattura ed integrità strutturale, 34 (2015) 99-108; doi: 10.3221/igf-esis.34.10 101 the effective notch stress σeff accounts for the notch effect and the microstructural support of notches by means of rounding the weld toe or the weld root by a radius rref = 1 mm, see [8]. the highest 1st principal stress on that radius is assumed to be effective for fatigue assessment. the effective notch stress is linked with σs by the weld shape factor kw, eq. (2), which considers the load-carrying grade of the weld and the local weld geometry. eff w sk  (2) comparison of stress distributions in order to reach the same structural hss σs = 176 mpa at the transverse attachment (1) and the complex structure (5), different levels of nominal stresses were required. a uniform axial loading of 100 mpa was sufficient at variant (5) because of the significant stress concentration at the hot-spot which is illustrated by the calculated distributions of the 1st principal stress in fig. 2. x z y f 1st principal stress [mpa] <80 108 136 163 191 219 247 274 302 >330 f x z y f 1st principal stress [mpa] <80 108 136 163 191 219 247 274 302 >330 1 0 m m figure 2: calculated stress distribution at the transverse attachment (left) and the complex structure (right). moreover, the stress distribution over the plate thickness is symmetric in case of transverse attachment (1) due to the weld toe on the opposite side, whereas the stress decreases monotonically for the complex structure (5). these characteristics were represented by different degrees of bending being  = 0 for variant 1 and  = 0.315 for the other. while the stress level is constant over the whole width of the transverse attachment (1), it decreases in variant 5 at first significantly and then slows down when the distance from the symmetry plane rises. the longitudinal plates of the complex structure cause differences as well. the lower plate increases the apparent plate thickness in the symmetry plane; i.e. the cross section is significantly larger than for the transverse attachment. the upper plate affects the load-carrying grade and the level of the effective notch stress. moreover, the vertical support of the lower longitudinal plate results in a bending constraint which is also found in large plated structures. ‘intermediate’ variants three additional variants 2 to 4 according to fig. 1 were defined for the following crack propagation simulation so that the effects on crack propagation life can be separated. in variant 2, the transverse attachment is loaded such that  = 0.315 occurs at the weld toe, while variant 3 is modified by a longitudinal plate below the main plate. the plate is 10 mm thick and 30 mm high. the degree of bending  = 0.315 in the plate is realized by appropriate axial and bending loads. an additional longitudinal plate, having a length l = 100 mm, is added behind the upper transverse attachment in variant 4. due to adjusted loads, the degree of bending is  = 0.315 again. this longitudinal plate increases the load-carrying grade of the welded joint and also the stress concentration in the symmetry plane. this led to a similarly high stress decrease along the weld line as for the complex structure. the c. fischer et alii, frattura ed integrità strutturale, 34 (2015) 99-108; doi: 10.3221/igf-esis.34.10 102 difference between variant 4 and 5 is only the support of the lower longitudinal plate changing also the kind of loading, but not s or eff and  at the hot-spot. computed fatigue lives crack propagation analysis half-circular initial crack is assumed at the critical weld toe for all variants. the crack initiation phase was considered by choosing a small initial crack length ai = 0.15 mm. the crack growth increments da and dc were computed for a defined number of cycles dn via individual integrations of the law by paris and erdogan [16]:  , m i a da c k dn   (3) eq. (3) links the crack propagation rate da/dn to the range of the stress intensity factor (sif) ki,a at the deepest point of the crack by using the material parameter c = 3·10-13 and m = 3 (unit: n and mm). the integrations, however, must be done discretely because the sif varies non-linearly and depends on the crack depth and crack shape. in order to avoid an underor overestimation of cycles, the average value of the cyclic sif was used when the crack grows from one stage (1) to the next (2):      ,1 ,2log 0.5 log logi i ik k k       (4) a separate block of elements was added to the fe models. it includes half of the semi-elliptical crack shape with half crack depth a and width c. the block was connected with the surrounding model by contact elements transferring all kinds of forces and moments (bonded conditions). the block is 10 mm long and high, whereas the width depends on the actual half crack width c. the 20-node solid elements size 0.1·a at the crack front, and the midsize nodes are shifted to the quarter points towards the crack front to improve the accuracy. no weld toe radius was considered to simplify the modelling, but this causes an additional stress singularity and a steep increase of the sif. due to this, the sif ki,c at the plate surface was estimated by extrapolating the sif values computed at the three previous nodes. generally, ki at each node along the crack front was determined individually via the j-integral using six contour integrations. fischer and fricke [4] described the modelling of the crack and the estimation of ki,c in detail. they applied the procedure to a load-carrying cruciform joint and obtained a satisfying agreement with experimental results. 1) transverse attachment 2) transverse attachment w. gradient 3) supported transverse attachment 4) additional longitudinal attachment 5) complex structure degree of bending  0.0 0.315 0.315 0.315 0.315 final crack depth af [mm] 8.48 8.51 8.43 8.44 8.45 final crack width 2cf [mm] 36.1 49.2 42.3 39.8 38.3 fatigue life np 300,000 385,600 452,200 456,200 509,600 rel. fatigue life 1.00 1.29 1.51 1.52 1.70 table 1: computed fatigue life np for the same structural hot-spot stress s = 176 mpa. fatigue lives referring to same structural hot-spot stress between nine and eleven integrations with up to 14 internal loops were performed until the crack had reached the final depth af ≈ 8.5 mm, being close to the opposite plate surface. in this process, smaller increments dn are considered for small cracks. fig. 3 shows the evolution of the crack depth of the variants for the same structural hss s = 176 mpa. here, the additional longitudinal attachment (4) is omitted since the crack grows similarly as for the supported transverse a c. fischer et alii, frattura ed integrità strutturale, 34 (2015) 99-108; doi: 10.3221/igf-esis.34.10 103 attachment (3). first differences in crack growth occur at a small crack depth a ≈ 0.5 mm. this corresponds to ca. 105 cycles. afterwards, faster crack propagation can be observed at variants 1 and 2. the curves of the other two variants deviate beyond a ≈ 1.5 mm. finally, the transverse attachment (1) achieves the shortest fatigue life np, see also tab. 1. the next are the transverse attachment with stress gradient over the plate thickness (2), the supported transverse attachment (3), and, finally, the complex structure (5). tab. 1 also lists in the last line the relative fatigue life referring to that of variant 1. the largest influence (29%) is caused by the stress gradient over the plate thickness (2). both the apparent plate thickness (3) and the bending constraint (5) increase np by about 12%, compared with the previous variants. it is worth noting that the stress gradient along the weld line does not affect the life since the same np is computed for variants 3 and 4. although the two variants differ with respect to the load-carrying grade of the weld, the same stress distribution over the plate thickness occurs. the gradient along the weld line, however, has an impact on the aspect ratios of the crack, see tab. 1. the final ratio is relatively small at variant 2 because the stress level is constant along the weld line, whereas the level decreases over the plate thickness. the final aspect ratio increases from the supported transverse attachment (3) to the complex structure (5) as the stress gradient along the weld line gets more pronounced and slows down the crack growth in this direction. 0 2 4 6 8 0,e+00 1,e+05 2,e+05 3,e+05 4,e+05 5,e+05 quersteife quersteife mit gradient unterstützte quersteife komplexes bauteil 0 105 2∙105 3∙105 4∙105 5∙105 c ra c k d e p th a [m m ] cycles n transverse attachment (1) transverse attachment w. gradient (2) supported transverse attachment (3) complex structure (5) figure 3: determined crack depth vs. applied cycles. 0 4 8 0 4 8 12 16 20 24 r is s tie fe a [m m ] halbe rissbreite c [mm] 0 4 8 0 4 8 12 16 20 24 r is s ti e fe a [m m ] halbe rissbreite c [mm] 0 4 8 0 4 8 12 16 20 24 r is s tie fe a [m m ] halbe rissbreite c [mm] transverse attachment (1) np = 300,000 n = 150,000 0 4 8 0 4 8 12 16 20 24 r is s tie fe a [m m ] halbe rissbreite c [mm] supported transverse attachment (3) transverse attachment w. gradient (2) complex structure (5) n = 360,000 n = 150,000 n = 360,000 n = 150,000 n = 360,000 n = 150,000 np = 385,000 np = 510,000 np = 452,000 half crack width c [mm] half crack width c [mm] half crack width c [mm] half crack width c [mm] c ra c k d e p th a [m m ] c ra c k d e p th a [m m ] c ra c k d e p th a [m m ] c ra c k d e p th a [m m ] figure 4: calculated crack shapes for variants 1 to 3 and 5. 1) transverse attachment 2) transverse attachment w. gradient 3) supported transverse attachment 4) additional longitudinal attachment 5) complex structure weld shape factor kw 2.41 2.24 2.17 2.35 2.43 fatigue life np 297,000 308,500 329,000 418,700 515,000 rel. fatigue life 1.00 1.04 1.11 1.41 1.73 table 2: computed fatigue life np for the same effective notch stress eff = 425 mpa. this influence is also visible when comparing the crack shapes for defined number of cycles, see fig. 4 showing half crack shapes of variant 1 to 3 and 5 for the same number of cycles (np = 150,000; np = 360,000 and at final life) and σs = 176 mpa. the transverse attachment (1) does not reach np = 360,000 since it has the highest crack propagation rate. while the crack shapes of the variants are almost similar for np = 150,000, after this they start to differ obviously between the simple transverse attachments (1 and 2) and the more complex variants 3 and 5. nevertheless, semi-elliptical crack shapes evolve in all cases and the more effects are present, the smaller the computed crack size is. fatigue lives referring to same effective notch stress the computed life can be converted by adjusting the load level in order to consider the same effective notch stress σeff = 425.3 mpa on the radius rref at symmetry plane, see tab. 2. here, the stress gradient over the plate thickness (variant 2) as c. fischer et alii, frattura ed integrità strutturale, 34 (2015) 99-108; doi: 10.3221/igf-esis.34.10 104 well as the apparent plate thickness (variant 3) have only minor influence on fatigue life since the stress concentration factor is smaller for bending loads (see e.g. [17]) and the apparent plate thickness is included in the notch effect by the ratio rref/(h+t) as defined in fig. 1. the lives for the supported transverse attachment (3) and the additional longitudinal attachment (4) differ by about 27% in this comparison. the reason is the load-carrying grade of the fillet weld which is increased by the additional longitudinal attachment. the different load-carrying grades can be seen in the rise of the weld shape factor kw from 2.17 to 2.34. its effect on life can be assessed for e.g. the variants 3 and 4 by raising the ratio of kw to the power of three: 3 ,3 ,3 ,4 ,4 ,1 ,3 1.41 p p w p p w n n k n n k                (5) here, the first term takes into account the increase with respect to the transverse attachment (1). the assessment agrees well with the computed relative lives of tab. 2. moreover, the complex structure reaches even longer life (variant 5 vs. 4), caused by an increased kw and the bending constraint. in general it can be stated that an increased weld shape factor kw results in a decreased crack growth due to the lower stress level in the plate. assessment of the individual influences stress gradient over plate thickness nalytical crack propagation analyses, in which the degree of bending  was varied, were carried out for a transverse attachment having the dimensions of variant 1. by starting with a semi-circular initial crack of ai = ci = 0.15 mm, the life was counted until the crack had reached af = 3 mm. the following propagation phase was neglected since the aspect ratio was small and the increase in life, too. the crack growth increments da and dc were again determined individually via the integration of the paris law. the required sif for the deepest point and for the surface point were taken from [1]. the stress magnification factors mk,c, referring to the surface point, were constant and correspond to the ones for a = 0.15 mm as suggested in [1]. the estimated lives were normalized with respect to the case of pure membrane loading ( = 0). fig. 5 shows the crack depth as a function of the relative fatigue life for different degrees of bending. an increase of nearly 300% is found for  = 1, being in agreement with calculations in [14], and of about 30% for  = 0,315 as in the simulation. d = 0.0 d = 0.2 d = 0.4 d = 0.6 d = 0.8 d = 1.0 relative fatigue life 0 1 2 3 c ra c k d e p th a [m m ] 0 1 2 3 figure 5: computed crack depth at transverse attachment with different degrees of bending  vs. relative fatigue life. 0,6 0,9 1,2 1,5 0 2 4 6 8 quersteife mit gradient unterstützte quersteife n o rm a li z e d s if crack depth a [mm] transverse attachment w. gradient (2) supported transverse attachment (3) figure 6: influence of the remaining cross section on the sif. apparent plate thickness the sif at the deepest point depends among others on the relative crack depth a/t, the effect of which is described by means of the geometry function. if an additional plate is existent, the apparent plate thickness is increased. a c. fischer et alii, frattura ed integrità strutturale, 34 (2015) 99-108; doi: 10.3221/igf-esis.34.10 105 its influence on crack propagation can be illustrated when normalizing ki,a at the deepest point of variant 2 and 3 by means of the structural stress σs, multiplied by √πa, see fig. 6. in the beginning, the normalized sif increases because the semi-circular initial crack becomes flatter (semi-elliptical). with growing crack depth, the stress magnification mk due to the weld toe notch vanishes and the increased apparent plate thickness gains influence. the sif of the two variants show increasing deviations for a > 1 mm. smaller values and a slower increase are obtained for the supported transverse attachment (3), leading to an extended life. in order to assess the effect, the geometry function y for a single edge crack with a/c = 0 in a finite thickness according to tada et al. [18] was integrated discretely from ai = 0.15 mm to af = 8.5 mm. different relative heights h/t of the lower longitudinal plates were considered; see fig. 1 for the definition of h. the influence of the magnification mk was neglected because differences regarding ki,a and, consequently, the crack growth had been found for a > 1 mm, where the mk factors are no more effective, see [9]. the analytical solution for h/t = 3 yields an increase of relative life by about 17% and agrees well with the difference between variant 2 and 3 on the basis of equal structural hss (tab. 1). modified notch effect the local stress concentration at hot-spots and, consequently, the weld shape factor can be additionally affected by the layout of the transverse attachment and the flank angle α of the weld seam. hence, the crack propagation is altered. the intersection of a sloped transverse attachment is a typical detail in cargo holds of bulk carriers, see e.g. [6]. three configurations of the attachment (fig. 7) are selected in the following. the critical weld toe is always arranged vertically above the weld toe on the opposite side. at first, the slope is set to 45° (detail a) and the attachment is shifted so that the flank angle of the critical weld seam remains 45°. thus, the center lines of the plates intersect each other eccentrically. at detail b, the center lines are arranged aligned causing a smaller flank angle α = 25°. a steeper angle α = 33° occurs with a steeper slope of the transverse attachment and by still aligned center lines, see detail c in fig. 7. for each of the three details, fe models of the variants 1 to 3 and 5, shown in fig. 1, are generated and crack propagation is simulated using the previously described conditions. the influence of the bending constraint applied to the complex structure (5) is determined approximatively by comparing variant 3 and 5 and considering the changed weld shape factor by eq. (5) additionally. 7,93 10 10 1 0 7 ,3 detail bdetail a detail c 10 figure 7: considered configuration of a sloped upper transverse attachment: with slope angle of 45° and a) eccentric and b) aligned center lines as well as c) with slope angle of 60° and aligned center lines. 1) transverse attachment 2) transverse attachment w. gradient 3) supported transverse attachment 5) complex structure degree of bending  0.0 0.316 0.316 0.316 weld shape factor kw 2,36 2,21 2,15 2,39 final crack depth af [mm] 8.45 8.48 8.49 8.51 final crack width 2cf [mm] 36.1 46.6 44.9 40.1 fatigue life np 283,800 291,200 306,400 505,00 rel. fatigue life 1.00 1.03 1.08 1.78 table 3: computed fatigue life np for the same effective notch stress σeff = 425 mpa at detail a. c. fischer et alii, frattura ed integrità strutturale, 34 (2015) 99-108; doi: 10.3221/igf-esis.34.10 106 the results referring to equal σeff = 425 mpa are listed in tab. 3 to tab. 5. at detail a, the calculated final crack shapes as well as the weld shape factors are almost similar to the previous simulations (tab. 2), despite of the sloped attachment. additionally, the calculated fatigue lives of the transverse attachment with and without stress gradient (variant 1 and 2) agree with each other. small deviations, however, are obtained for both the supported transverse attachment (3) and the complex structure (5). here, the sloped layout affects the stress distributions over the complete cross section on the symmetry plane which can be recognized by the normalized sif, as illustrated for the two configurations of the supported transverse attachment (3) in fig. 8. higher values appear at the eccentric, sloped layout beyond a > 1.75 mm and lead to faster crack propagation and shorter life finally. in detail b, the weld flank angle is smaller at the same time and reduces the local stress concentration at the weld toe which becomes apparent in generally smaller weld shape factors kw. hence, higher external loadings are required for eff = 425 mpa and the fatigue lives are shorter compared to the other two configurations, see tab. 2 to tab. 4. additionally, the structural hot-spot stresses rise according to eq. (2) since eff is constant and kw smaller. that effect in conjunction with the lower stress concentration decreases the degree of bending at detail b. moreover, the effect of the bending constraint at the complex structure (5) is highly reduced since the relative life rises by only about 21%. n o rm a li z e d s if unterstützte quersteife (c) quersteife mit gradient (b) 0,6 0,9 1,2 1,5 0 2 4 6 8 supported transverse attachment (3) with vertical layout supported transverse attachment (3) with eccentric and sloped layout, detail b crack depth a [mm] figure 8: influence of the layout of the transverse attachment on the sif. c o m p u te d fa ti g u e li fe n p (t h o u s a n d ) 350 250 150 transverse attachment (1) supported transverse attachment (3) 0.93 1.00 1.00 0.96 0.83 0.92  = 4 5 °  = 4 5 °  = 4 5 °  = 4 5 °  = 2 5 °  = 3 3 ° different weld flank angle different slope d e ta il a d e ta il a d e ta il b d e ta il c ve rt ic a l la yo u t ve rt ic a l la yo u t figure 9: influence of slope and weld flank angle on fatigue life, shown for selected variants for equal eff. 1) transverse attachment 2) transverse attachment w. gradient 3) supported transverse attachment 5) complex structure degree of bending  0.0 0.266 0.266 0.266 weld shape factor kw 2,11 2,00 1,93 1,98 fatigue life np 245,500 259,300 266,000 297,000 rel. fatigue life 1.00 1.06 1.08 1.21 table 4: computed fatigue life np for the same effective notch stress σeff = 425 mpa at detail b. in detail, kw at the sloped transverse attachment (1) of detail b, is about 12% smaller compared to the vertical attachment and would shorten fatigue life by about 40% due to increased external loadings. the flatter flank angle, however, compensates the effect partly as the relative lives differ by about 17%. a similar difference is obtained when the effects of the deviating weld shape factors and mk factors referring to the flank angle are considered. at variant 2, the degree of bending decreases and shortens the fatigue life as shown in fig. 5. at the last detail c, the flank angle modifies the stress distribution over the plate thickness and increases weld shape factors but not as much that they agree with the vertical configuration. hence, the required level of the external loading is changed and the fatigue lives of the variants are longer than for detail b but shorter for the other, see tab. 5, tab. 4 and c. fischer et alii, frattura ed integrità strutturale, 34 (2015) 99-108; doi: 10.3221/igf-esis.34.10 107 tab. 2. the different variants of the transverse attachment (variant 1 to 3), both referring to detail c and the vertical layout, deviate from each other by about 10% being caused by a nearly constant difference between the weld shape factors. again, the effect of the bending constraint is reduced. the influence of the flank angle is analytically considered by the stress magnification factor mk being e.g. reported in the iiw guideline [10]. the integration of mk from ai = 0.15 mm to af = 3 mm yields an increasing relative life of about 22% for α = 25° and a/c = 0 compared to α = 45°. the factor is equal one for crack depths a ≥ 3 mm and thus ineffective. the increase of life is about 14% for the steeper flank angle α = 33° of detail c. fig. 9 illustrates the influence of the sloped layout and the weld flank angle for two selected variants. the life of the supported transverse attachment (3) decreases at detail a. the effect is overlaid by the smaller flank angle at the other two details and, hence, omitted. the stress concentration of the transverse attachment (1) is only affected by the flank angle, being smaller at detail b and c. thus, the computed life is reduced. 1) transverse attachment 2) transverse attachment w. gradient 3) supported transverse attachment 5) complex structure degree of bending  0.0 0.3 0.3 0.3 weld shape factor kw 2.27 2.12 2.04 2.18 fatigue life np 274,500 283,000 296,200 390,100 rel. fatigue life 1.00 1.03 1.08 1.42 table 5: computed fatigue life np for the same effective notch stress σeff = 425 mpa at detail c. 1) transverse attachment 2) transverse attachment w. gradient 3) supported transverse attachment 5) complex structure detail a fatigue life np 304,800 382,000 437,300 521,900 rel. fatigue life 1.00 1.25 1.43 1.71 detail b fatigue life np 371,200 457,800 524,700 538,000 rel. fatigue life 1.00 1.23 1.41 1.45 detail c fatigue life np 329,100 416,600 491,300 529,600 rel. fatigue life 1.00 1.27 1.49 1.61 table 6: computed fatigue life np for the same structural hss σs = 176 mpa at three sloped configurations. the influences of both the layout and the flank angle is also directly included in the crack propagation simulation on the basis of the same structural hss s, see tab. 1 and tab. 6, but not in the fatigue assessment using this type of stress. due to the flatter flank angle at detail b and c, the absolute fatigue life is increased by about 25% and 11%, respectively. this agrees with the assessment being based on the integrated mk factor. the relative life of detail a to c does not rise as much as for the vertically supported transverse attachment (3) because the apparent plate thickness is less effective due to the sloped layout. the different influences are suppressed at the complex structure (5) and nearly same absolute fatigue life is achieved. however, the increase of the relative life is rather different because of the sloped layout. conclusions and outlook he paper presents crack propagation simulations which were performed for different welded geometries – from a transverse attachment up to a complex structure. the determined fatigue lives were compared assuming equal structural hss and alternatively effective notch stress in all variants. the complex structures showed longer fatigue life due to a higher stress concentration, resulting in changed stress distribution along the crack path. the following conclusion can be drawn: longer crack propagation phase observed in experiments of complex structures can be found also in numerical crack propagation simulation; t c. fischer et alii, frattura ed integrità strutturale, 34 (2015) 99-108; doi: 10.3221/igf-esis.34.10 108 the crack propagation rate at complex structures is slowed down by: the stress gradient over the plate thickness, the apparent plate thickness, the notch effect and the bending constraint of the detail; the stress gradient along the weld line does not affect the life but the aspect ratio of the semi-elliptical crack shape; the notch effect depends on the load-carrying grade of weld, the flank angle and of the layout of the transverse attachment and it affects the local stress concentration, leading to longer life. the obtained influences should be investigated for further configurations, varying in particular the thickness of the axially loaded plate as well as of the attachments. this would lead to different local support of the critical weld toe, especially if the thicknesses are different. references [1] bs 7910:2005, guide to methods for assessing the acceptability of flaws in metallic structures, british standards institution, london. [2] dijkstra, o, janssen, g., ludolphy, j., fatigue tests on large scale knuckle specimens, in: w.-c. cui, y.-s. wu, g.-j. zhou (eds.), proc. 8th int. symp. on practical design of ships and other floating structures (prads), elsevier, amsterdam, (2001) 1145–1151. [3] dong, p., a structural stress definition and numerical implementation for fatigue analysis of welded joints. int. j. fatigue, 23 (2001), 865–876. [4] fischer, c., fricke, w., realistic fatigue life prediction of weld toe and weld root failure in load-carrying cruciform joints by crack propagation analysis., in: c. guedes soares, j. romanoff (eds.), analysis and design of marine structures – proc. 4th int. conf. on marine structures (marstruct), taylor & francis, london, (2013) 241–248. [5] fischer, c., fricke, w., consideration of stress gradient effects for complex structures in local fatigue approaches, in: c. guedes soares, r.a. shenoi (eds.), analysis and design of marine structures proc. 5th int. conf. on marine structures (marstruct), taylor & francis, london, (2015). [6] fischer, c., fricke, w., rizzo, c.m., n-sif based fatigue approaches of hopper knuckle details, in: e. rizzuto, c. guedes soares (eds.), sustainable maritime transportation and exploitation of sea resources, taylor & francis, london, (2011). [7] fricke, w., recommended hot-spot analysis procedure for structural details of fpso's and ships based on roundrobin fe analysis, in: j.s. chung (ed.), proc. 11th int. offshore and polar engng. conf. (isope), international society of offshore and polar engineers, cupertino, ca, (2001) 89–96. [8] fricke, w., iiw recommendations for the fatigue assessment of welded structures by notch stress analysis, woodhead publishing limited, cambridge (2013). [9] hobbacher, a., stress intensity factors of welded joints, engng. fract. mech., 46 (1993) 173–182. [10] hobbacher, a., recommendations for fatigue design of welded joints and components, welding research council, new york, ny, (2009). [11] iida, k., matoba, m., fatigue strength of hold frame ends in ship hulls. international institute of welding, iiw-doc. xiii-950-80, (1980). [12] kang, j, kim, y., heo, j., fatigue strength of bent type hopper corner detail in double hull structure, in: m.m. salama, p.k. gorf, c.f. mastrangelo, s. balint (eds.), proc. omae specialty symp. on integrity of floating production, storage & offloading (fspo) systems, asme, houston, tx, (2004). [13] kim, w., lotsberg, i., fatigue test data for welded connections in ship-shaped structures, j. offshore mech. and artic eng., 127 (2005) 359–365. [14] lotsberg, i., sigurdsson, g., hot spot stress s-n curve for fatigue analysis of plated structures, j. offshore mech. and artic eng. 128 (2006) 330–336. [15] osawa, n., fatigue assessment of bilge knuckle joint of vlcc according to jtp / jbp rules, in: y. sumi (ed.), comparative studies on the evaluations of buckling/ultimate strength and fatigue strength based on iacs jtp and jbp rules, (2005) 3.1–3.5 [16] paris, p.c., erdogan, f., a critical analysis of crack propagation laws, j. fluid engng. 85, (1963) s. 528–533. [17] peterson, r.e., stress concentration factors, j. wiley & sons, new york, ny, (1974). [18] tada, h, paris, p.c., irwin, g.r., the stress analysis of cracks handbook, del research corporation, st. louis, mo, (1985). microsoft word numero_34_art_23 m. ševčík et al, frattura ed integrità strutturale, 34 (2015) 216-225; doi: 10.3221/igf-esis.34.23 216 focussed on crack paths analytical model of asymmetrical mixed-mode bending test of adhesively bonded gfrp joint m. ševčík, p. hutař institute of physics of materials, academy of sciences of the czech republic, v. v. i., žižkova 22, 616 62 brno, czech republic sevcik@ipm.cz; hutar@ipm.cz a. p. vassilopoulos composite construction laboratory cclab, ecole polytechnique fédérale de lausanne epfl, station 16, ch-1015 lausanne, switzerland anastasios.vasilopoulos@epfl.ch m. shahverdi structural engineering research laboratory, empa, swiss federal laboratories for materials science and technology, überlandstrasse 129, 8600 dübendorf, switzerland moslem.shahverdi@empa.ch abstract. this paper presents new analytical model of asymmetric mixed-mode bending (mmb) specimen of adhesively bonded pultruded gfrp joints. an easily applicable relationship for the calculation of the strain energy release rate of the asymmetric mmb specimens is proposed based on the beam theory. the model is capable to analyze stacking sequence as well as various crack propagation paths. in the paper the effect of the various fiber bridging length and different crack propagation paths is analyzed analytically and supported by experimental results. the methodology and results presented in this paper could be utilized for the design of both joint geometry and lay-up of the laminates constituting the joint or for the prediction of the fracture behavior of such structures. keywords. gfrp materials; mixed-mode bending; fiber bridging; analytical model. introduction iber reinforced polymers are modern kind of materials that benefit from their high stiffness vs. weight ratio. composite materials are being widely used for aeronautical and space applications for decades. despite theirs higher initial price these materials can be used also in the civil engineering applications. material of fibers strongly influences the overall strength of the fiber reinforced polymer materials. glass or aramid fibers are usually used for the civil applications [1] whereas carbon fibers are used mostly for aerospace and automotive applications [2]. connection of composite laminates is typically performed by adhesive joint. the strength of the adhesive should be higher than interlaminar strength of the laminate. therefore, the failure should occur between layers of the laminate rather than in the adhesive layer. unlike the mechanical engineering applications where the adhesive layer thickness is far below f m. ševčík et al, frattura ed integrità strutturale, 34 (2015) 216-225; doi: 10.3221/igf-esis.34.23 217 1 mm in the civil engineering application the adhesive layer thickness can reach up to a few centimeters. this nonnegligible adhesive thickness behaves like additional layer in the adhesive joint and should be taken into account when designing the joint against failure. the main failure mode of the composite materials is delamination of the layers under bending or tension loading and buckling under compression loading [3]. if the crack propagates in the material interface of different materials the crack tip stress field is inherently under mixed-mode behavior [4]. this in fact brings some difficulties for the fracture mechanics analysis of the fiber reinforced polymer materials. the delamination behavior of adhesively bonded gfrp joints is usually studied by variety of specimens doublecantilever-beam (dcb) specimen for pure mode i, end-loaded-split (els) or end notched-flexure (enf) specimen for pure mode ii and mixed-mode bending (mmb) for mixed modes tests. nowadays, the mmb test is one of the standardized test method for evaluation of the interlaminar fracture toughness of unidirectional fiber reinforced polymer matrix composites [5]. the concept of the strain energy release rate (serr) is commonly used for the fracture mechanics description of the failure behavior of adhesively bonded gfrp laminates [6,7]. there exist various expressions for the calculation of the total strain energy release rate for the symmetric mmb specimens but mostly valid only for symmetrical specimens [8]. the asymmetrical specimens are, however, often accompanied by relatively thick adhesive layer or asymmetry of the stacking sequence either in the laminate or in the adhesive joint and therefore there is a need for the development of the new procedures for the calculation of the strain energy release rate components. another way is to describe the delamination behavior using the complex stress intensity factor introduced in [4,9]. in this work the concept of the strain energy release rate as a fracture parameter is utilized. for the accurate description of the crack behavior in asymmetric joints it is necessary to decompose the mode components and explicitly estimate their contribution to the total fracture energy [10–12]. various procedures exist in the literature for the mode separation. most of them are based on the differences between moments [6], displacements [13] or bending stiffnesses [14] of the two arms of the joint. however, the differences between moments or displacements are applicable only for symmetric specimens. the mode separation based on the difference in bending stiffness of the two arms is applicable for the asymmetric specimens, nevertheless, the bending stiffnesses are usually measured on the cracked specimen and it is therefore difficult to predict the behavior of the joint before the test. this paper presents new easily applicable relationship for the calculation of the strain energy release rate of the asymmetric mmb specimens that is proposed based on the beam theory and its ability is validated through comparison with experimental results. materials desription of the mmb specimen he pultruded gfrp laminates, supplied by fiberline a/s, denmark, consisted of e-glass fibers and isophthalic polyester resin. the laminates with 6 mm in thickness consisted of a thin polyester veil in the outer surfaces, two combined mat layers on each side and a roving layer in the middle. each mat layer comprised of 0/90 woven fabric stitched to a chopped strand material. the fiber architecture of the laminate is schematically shown in fig. 1. based on burn-off test, according to astm d3171-11 [15] and fiber density of 2560 kg/m3, the fiber content was 43.3 vol. %. a two-component epoxy adhesive system sikadur 330, sika ag, switzerland, was used for the bonding of the gfrp figure 1: scheme and micrograph of the laminate architecture. figure 2: scheme of the mixed-mode bending test. t m. ševčík et al, frattura ed integrità strutturale, 34 (2015) 216-225; doi: 10.3221/igf-esis.34.23 218 laminates. the polyester resin (matrix) as well as glass fibers exhibit linear elastic behavior in tension up to brittle fracture [16], therefore, allowing the use linear elastic fracture mechanics for the analysis of the results. all the layers of the laminates were modeled according to the thicknesses estimated by the optical microscopy photos. the material properties and thicknesses of all layers of the laminate as well as the adhesive are listed in the tab. 1. one of the failure mechanisms of the adhesively bonded gfrp pultruded laminates is the delamination cracking. the delamination usually occurs between 1st and 2nd combined mat. for the purpose of this paper four crack propagation paths are distinguished for the used laminate: path 0 crack propagation in the middle of adhesive layer path i crack propagation between adhesive and 1st combined mat layer path ii crack propagation between 1st combined mat and 2nd combined mat layer path iii crack propagation between 2nd combined mat layer and roving layer. path 0 represent symmetrical mmb specimen whereas path i, ii and iii represent increasing level of asymmetry. layer thickness [mm] e11 [gpa] e33 [gpa] 13 [-] g13 [gpa] veil 0.05 3.2 3.2 0.38 1.2 1st combined mat 0.63 12.8 3.2 0.36 1.4 2nd combined mat 1.07 15.1 3.2 0.36 1.4 roving 2.5 38.9 3.2 0.35 2.7 adhesive 2 4.6 4.6 0.37 1.7 table 1: material properties and thicknesses of all layers of the laminate and adhesive [17]. analytical model of mmb test here exists analytical expression for the calculation of the total strain energy release rate of the symmetrical mmb specimen derived by reeder and crews in [18,19] in the following form:     22 11 232 22 334 16 3 lclc elhb pa g  (1) this model has been successfully applied for the adhesively bonded laminate joins where the thickness of the adhesive layer was negligibly thin. however, for the structural applications the adhesive layer varies from millimeters to centimeters and therefore the adhesive layer induces asymmetric geometrical configuration and therefore the analytical model for asymmetrical mmb specimen has to be developed. even though the eq. (1) does not take the nonlinear effects (such as rotations of the arms or shear effects) into account it can serve as the reference equation for comparison with the proposed model derived later in this chapter. to derive the total strain energy release rate for the asymmetric mmb specimen following relation can be used [20]: a c b p gtot d d 2 2  (2) where p is the loading force, a is the crack length and c is the compliance of the specimen (c = /p, where  is the displacement of the lever below the applied force p). the displacement of the lever  can be calculated using castigliano’s theorem as follows: p w    (3) where w is total strain energy. to calculate the strain energy maxwell-mohr variant of castigliano’s theorem can be used in general form: t m. ševčík et al, frattura ed integrità strutturale, 34 (2015) 216-225; doi: 10.3221/igf-esis.34.23 219  dxei m w o 2 2 1 (4) where mo is bending moment in the segment, ei is bending stiffness of the segment. the mmb specimen can be virtually divided into three segments, see fig. 3. figure 3: virtual division of the mmb specimen into three segments. figure 4: scheme of location of forces pu and pd. each of these three segments has specific bending stiffness that corresponds to the stacking sequence of the segment. for the mmb specimen the strain energy stored in the system can be calculated as follows.                                   l l d d l a d a u d a u dx ie lxpx p dx ie x p dx ie xp p dx ie xp w 2 4 33 2 44 3 33 2 3 0 2 22 2 2 0 1 11 2 1 2 2 12 2 12 2 1 2 1 (5) where e1,2,3 are bending moduli of each segment calculated by classical laminate theory, pu and pd are components of the loading force p, see fig. 4, that can be calculated from equations [21]: g g u p l c p l c p  (6) g g d p l c p l c p              11 (7) where c, cg, l are dimensions shown in fig. 2, pg is gravity force induced by weight of the loading lever. the displacement of the loading lever below the force p is then:       33 33 22 3 11 3 12 2 12 2 3 ile pclla ile ppcla ile cpa u dudup     (8) where eiii (i = 1,2,3) are bending stiffnesses of the i-th segment of the mmb specimen. as soon as the displacement of the lever below the force p is known it is possible to calculate the compliance of the mmb specimen using following relation: p u c p . (9) finally, the total strain energy release rate can be calculated using eq. (2) in the following form: m. ševčík et al, frattura ed integrità strutturale, 34 (2015) 216-225; doi: 10.3221/igf-esis.34.23 220     33 22 22 22 11 22 88 2 2 ibe ap ibe app ibe ap ag dudutot    (10) it can be proved that the eq. (9) is equivalent to eq. (1) for symmetric mmb specimen (when e1 = e2 = e3, i1 = i2 = i3/8 and gravity force from lever weight pg is neglected. therefore, the eq. (9) is the generalized expression of eq. (1) for the asymmetric mmb specimens. the mmb specimens with geometrical and material properties described in tab. 2, loaded by constant force p = 500 n were used to compare the eq. (10) and eq. (1). fig. 5 presents ratios between eq. (10) and eq. (1) with taking various effects into account. crack position thickness [mm] bending stiffness [gpa×mm4] h1 h2 h e1i1 e2i2 e3i3 path 0 6.7 6.7 13.4 11 695 11 695 181 594 path i 5.7 7.7 13.4 9 776 14 808 181 594 path ii 5.32 8.08 13.4 8 439 19 018 181 594 path iii 4.25 9.15 13.4 5 613 35 581 181 594 table 2: geometry and bending stiffness of mmb specimens for various crack propagation paths (various degree of asymmetry) fig. 5a contains ratio of total strain energy release rate calculated by eq. (10) and by eq. (1) for symmetrical specimen. it is clearly visible that when the weight of the lever is neglected (pg = 0 n) the eq. (10) and eq. (1) are identical. for the present mmb configuration the calculated total strain energy release rate increases at about 9% when the weight of the lever is taken into account. the eq. (1) contains term e11 that is bending modulus in the longitudinal direction. however, the bending modulus of the laminate is different from the bending modulus of the laminate joint. if this change of the modulus and weight of the lever is taken into account the total strain energy release rate increase at about 16% in comparison with eq. (1). fig. 5b shows comparison of total strain energy release rate calculated by eq. (10) and by eq. (1) for asymmetrical specimens where weight of the loading lever is taken into account. here, the asymmetry of the specimen is expressed by crack propagation path where path i is closest to the plane of symmetry (in a distance of 1 mm). the calculated total strain energy release rates for path i and path ii are almost the same as for the symmetrical specimen with various bending moduli shown in fig. 5a. the farther is the crack from the symmetrical plane the higher the strain energy release rate is as document the strain energy release rate for the crack propagating in path iii. based on the derivation described above and successfully compared with available relation derived by reeder and crews it is possible to consider the eq. (10) suitable for the calculation of the total strain energy release rate of the adhesively bonded mixed-mode bending test with asymmetric configuration. figure 5: comparison of total strain energy release rate calculated by proposed eq. (10) with eq. (1) derived by reeder and crews. m. ševčík et al, frattura ed integrità strutturale, 34 (2015) 216-225; doi: 10.3221/igf-esis.34.23 221 fracture criterion he fracture criterion for the crack initiation and crack propagation can be found in the literature [21]. the critical values of the strain energy release rate for the crack initiation and propagation in various crack propagation paths are shown in tab. 3. more information about the experimental measurement of the fracture criterion can be found in [14]. specime n code lever dimensio n [mm] crack initiation crack propagation in path i crack propagation in path ii crack propagation in path iii c cg gi gii gtot gi gii gtot gi gii gtot gi gii gtot mmb-01 227 54 205 85 290 1061 287 1348 102 4 144 1168 mmb-02 166 69 235 410 151 561 963 260 1223 mmb-03 133 55 188 837 226 1063 mmb-04 159 66 225 890 241 1131 mmb-05 163 67 230 497 183 680 924 250 1174 mmb-06 150 38 162 128 290 851 387 1238 383 89 472 mmb-07 210 165 375 550 374 924 1247 567 1814 mmb-08 182 143 325 462 314 776 945 430 1375 mmb-09 182 143 325 1190 541 1731 mmb-10 181 143 324 1012 460 1472 700 164 864 mmb-11 189 149 338 597 406 1003 1302 592 1894 table 3: critical strain energy release rate at various paths under different mixed-mode loading in [j/m2] from [14]. single underlined numbers represent highest recorded values of the group, double underlined values represent lowest recorded values. results he proposed analytical model of the asymmetric mmb test is analyzed in this section. fracture behavior obtained using the proposed model is compared with experimental data recently obtained by authors and well documented in the literature [14,21]. effect of fiber bridging length at first the sensitivity analysis of the fiber bridging length was performed. the total strain energy release rate for crack initiation and crack propagation was kept constant but the fiber bridging length lf was changed in order to study its effect on the load vs. crack length (p-a) diagram. the shape of the fracture criterion used for this analysis is shown in fig. 6. based on the analytical procedure described above it is possible to predict the load vs. crack length diagram assuming that the crack will propagate if the condition gtot(a)=gcrit(a), where gtot(a) is the calculated value of the total strain energy release rate and gcrit(a) is the critical value of the total strain energy release rate that can be measured experimentally, tab. 3. example of such prediction is shown in fig. 7 where experimentally measured and analytically predicted p-a diagrams are plotted when considering fracture in path ii. by inspecting the fig. 7 it is possible to conclude that the analytical model is capable to predict the p-a diagram of the mmb test with sufficient accuracy. the fiber bridging length seems to have strong effect on the maximum loading force, however, it has to be mentioned that in reality the critical serr for the crack propagation gprop depends on the fiber bridging length. generally, the gprop = gini when lf = 0 and gprop increases when lf increases. therefore, if the values of gini and gprop are known the fiber bridging length can be obtained indirectly using this analytical model in comparison with t t m. ševčík et al, frattura ed integrità strutturale, 34 (2015) 216-225; doi: 10.3221/igf-esis.34.23 222 experimental results. for the studied specimen mmb 02 the fiber bridging length is approx. 35 mm which well corresponds to the experimental observation. figure 6: simplified fracture criterion based on the gtot depending on the fiber bridging length. figure 7: the effect of fiber bridging length on the load vs. crack length diagram (c = 227 mm, cg = 54 mm). crack propagation path the fracture of the laminate is often accompanied with delamination in the neighboring layers and interfaces between the layers. this phenomenon is shown in fig. 8 where photograph of the mmb specimen after test is complemented by the crack propagation path description. figure 8: propagation of the crack in multiple paths. the propagation of the crack in various paths brings another complication for the reliable prediction of the p-a diagram. for the comprehensive prediction of the p-a diagram the crack propagation in multiple paths should be captured. one of the possibilities is to plot p-a diagram for all crack propagation paths and therefore to show bounds in which the p-a diagram of the real structure will fall. the preview of such p-a diagram is shown in fig. 9 where fiber bridging length of 20 mm is considered. figure 9: p-a diagram for crack propagating in path i, ii and iii (c = 150 mm, cg = 38 mm). m. ševčík et al, frattura ed integrità strutturale, 34 (2015) 216-225; doi: 10.3221/igf-esis.34.23 223 fig. 9 also contains overall prediction (green curve) that represents crack initiation in path i, crack propagation in path ii and final propagation in path iii. unfortunately, such overall prediction is not possible to construct due to the fact that the crack propagation path is often changed during the crack propagation and sometimes multiple growing cracks in various crack propagation paths can be recorded. on the other hand it is possible to predict upper and lower bounds, see fig. 10. figure 10: comparison of experimental data from [21] with upper and lower predictions of p-a diagram for specimens mmb-06 to mmb-11 (c = 150 mm, cg = 38 mm). fig. 10 shows comparison of experimental data for 6 mmb specimens. the critical values of the strain energy release rate for crack initiation and crack propagation was taken from tab. 3. the upper (lower) bound was obtained in such a way that the highest (lowest) critical strain energy release rates of the group of specimens were taken as the fracture criterion. these values are highlighted in tab. 3. it can be seen that that the upper bound prediction for path ii well fits with experimental results for crack lengths longer than 80 mm whereas lower bound prediction for path i is valid for crack lengths between 50 – 100 mm. for longer cracks the lower bound prediction for path iii is nearest to the lowest experimental results obtained in the mmb test. similar behavior was found also for other groups of specimens. mixed-mode fracture criterion the predictions described in the previous section were based on the total strain energy release rate fracture criterion. the critical strain energy release rate was experimentally measured for every single specimen and served as the input data for the predictions. however, the fracture criterion based on the total strain energy release rate does not consider the mixedmode nature on the crack tip and it is therefore limited to adhesively bonded joints where the crack tip mode-mixity is the same as the experimentally tested mmb specimen. to obtain more general fracture criterion it is important to perform number of mixed-mode delamination tests and experimentally obtain the mixed-mode fracture criterion. such fracture criterion can be generally written in the following form: )g,g,a(g)g,g,a(g crit_iicrit_icritiii  (11) where gi_crit, gii_crit are critical strain energy release rates for pure mode i and pure mode ii. the criterion can have various shapes e.g. linear, semi-linear, elliptical, polynomial etc. preview of the fracture criterion for crack propagation in path ii is shown in fig. 11. similarly to the fracture criterion shown in fig. 11, fracture criteria for crack initiation and crack propagation in various crack propagation paths can be experimentally found. these mixed-mode fracture criteria are necessary for the prediction of p-a diagram using the present analytical model. for the purpose of this paper the exponential power law fracture criterion from [14] was used for the prediction of p-a diagram for various mmb configurations. the components of strain energy release rate in the fracture criterion were calculated using extended global method that was developed for the asymmetrical mixed-mode specimens [21]. the m. ševčík et al, frattura ed integrità strutturale, 34 (2015) 216-225; doi: 10.3221/igf-esis.34.23 224 comparison of the experimental data points and predicted fracture response for the crack propagating exclusively in path ii using mixed-mode fracture criterion is shown in fig. 12. figure 11: experimentally obtained fracture criterion based on the mixed-mode delamination tests [14]. figure 12: comparison of experimental data points of mmb-01 to mmb-05 from [14] with predicted behavior using mixedmode fracture criterion (c = 227 mm, cg = 54 mm). the predicted load vs. crack length diagram using mixed-mode fracture criterion is in both qualitative and quantitative agreement with experimentally obtained data. the scatter in experimental results is far greater than difference between polynomial fit of the experimental data and predicted behavior. utilizing the proposed analytical model of asymmetrical mixed-mode bending test together with the mixed-mode fracture criterion opens possibility for optimization of the laminate lay-up, reduction of the specimen size as well as for the design of adhesively bonded joints of more than two laminates. the only requirement is that the stacking sequence of the laminate remains the same in the vicinity of the crack propagation path otherwise new mixed-mode fracture criterion has to be experimentally obtained. conclusions his paper is focused on the problematic of the mixed-mode bending test of adhesively bonded fiber reinforced polymer composites with special emphasize on the mixed-mode bending test. a new analytical model for the calculation of the total strain energy release rate is derived and compared with well established relation of reeder and crews. on the practical example it is shown that for symmetrical mmb specimens the proposed relation gives equivalent values and it is therefore more generalized and possibly applicable for asymmetric specimens. in the second part of the paper the proposed analytical model is used for the prediction of the load vs. crack length diagram of the mmb test of the real specimens. it is shown that the proposed model can predict the fracture behavior in various layers and therefore to describe the fracture behavior in more details. the methodology and results presented in this paper could be utilized for the design of both joint geometry and lay-up of the laminates constituting the joint or for the prediction of the fracture behavior of such structures. acknowledgements his work was supported through the grant 15-09347s of the czech science foundation and by the ministry of education, youth and sports of the czech republic throughout the project no. cz.1.07/2.3.00/30.0063 “talented postdocs for scientific excellence in physics of materials”. references [1] gowayed, y., types of fiber and fiber arrangement in fiber-reinforced polymer (frp) composites. in: uddin n, editor. developments in fiber-reinforced polymer (frp) composites for civil engineering, woodhead publishing, (2013) 3-17. t t m. ševčík et al, frattura ed integrità strutturale, 34 (2015) 216-225; doi: 10.3221/igf-esis.34.23 225 [2] soutis, c., introduction: engineering requirements for aerospace composite materials. in: irving pe, soutis c, editors. polymer composites in the aerospace industry, woodhead publishing, (2015) 1-18. [3] kachanov, l.m., delamination buckling. delamination buckling of composite materials, springer netherlands, (1988) 19-56. [4] rice, j.r., elastic fracture mechanics concepts for interfacial cracks. j appl mech, 55 (1988) 98-103. doi:10.1115/1.3173668. [5] d30 committee. test method for mixed mode i-mode ii interlaminar fracture toughness of unidirectional fiber reinforced polymer matrix composites. astm international, (2013). [6] williams, j.g., on the calculation of energy release rates for cracked laminates. international journal of fracture, 36 (1988) 101-19. doi:10.1007/bf00017790. [7] kinloch, a.j., wang, y., williams. j.g., yayla, p., the mixed-mode delamination of fibre composite materials. composites science and technology, 47 (1993) 225-37. doi:10.1016/0266-3538(93)90031-b. [8] ducept, f., davies, p., gamby, d., an experimental study to validate tests used to determine mixed mode failure criteria of glass/epoxy composites. composites part a: applied science and manufacturing, 28 (1997) 719-729. doi:10.1016/s1359-835x(97)00012-2. [9] hutchinson, j.w., suo, z., mixed mode cracking in layered materials, in: john w. hutchinson and theodore y. wu, editor. advances in applied mechanics, 29 (1991) 63-191. [10] shahverdi, m., vassilopoulos, a.p., keller, t., a phenomenological analysis of mode i fracture of adhesively-bonded pultruded gfrp joints. engineering fracture mechanics, 78 (2011) 2161-2173. doi:10.1016/j.engfracmech.2011.04.007 [11] bennati, s., fisicaro, p., valvo, p.s., an enhanced beam-theory model of the mixed-mode bending (mmb) test—part i: literature review and mechanical model. meccanica, 48 (2013) 443-462. doi:10.1007/s11012-012-9686-3. [12] bennati, s., fisicaro, p., valvo, p.s., an enhanced beam-theory model of the mixed-mode bending (mmb) test—part ii: applications and results. meccanica, 48 (2013) 465-484. doi:10.1007/s11012-012-9682-7. [13] rybicki, e.f., kanninen, m.f., a finite element calculation of stress intensity factors by a modified crack closure integral, engineering fracture mechanics, 9 (1977) 931-938. doi:10.1016/0013-7944(77)90013-3. [14] shahverdi, m., vassilopoulos, a.p., keller, t., mixed-mode fatigue failure criteria for adhesively-bonded pultruded gfrp joints. composites part a: applied science and manufacturing, 54 (2013) 46-55. doi:10.1016/j.compositesa.2013.06.017. [15] astm d3171-11. test methods for constituent content of composite materials. astm international, (2011). [16] de castro, j., keller, t., ductile double-lap joints from brittle gfrp laminates and ductile adhesives, part i: experimental investigation, composites part b: engineering, 39 (2008) 271-281. doi:10.1016/j.compositesb.2007.02.015. [17] shahverdi, m., vassilopoulos, a.p., keller, t., modeling effects of asymmetry and fiber bridging on mode i fracture behavior of bonded pultruded composite joints, engineering fracture mechanics, 99 (2013) 335-48. doi:10.1016/j.engfracmech.2013.02.001. [18] crews, jr. j.h., reeder, j.r., a mixed-mode bending apparatus for delamination testing, nasa technical memorandum 100662. (1988). [19] reeder, j.r., crews, jr. j.h., redesign of the mixed-mode bending delamination test to reduce nonlinear effects, journal of composites technology and research, 14 (1992) 12-9. [20] zhang, y., vassilopoulos, a.p., keller, t., mode i and ii fracture behavior of adhesively-bonded pultruded composite joints, engineering fracture mechanics, 77 (2010) 128-43. doi:10.1016/j.engfracmech.2009.09.015. [21] shahverdi, m., vassilopoulos, a.p., keller, t., mixed-mode i/ii fracture behavior of asymmetric adhesively-bonded pultruded composite joints, engineering fracture mechanics, 115 (2014) 43-59. doi:10.1016/j.engfracmech.2013.11.014. microsoft word numero_49_art_33_2412 n. kaddouri et alii, frattura ed integrità strutturale, 49 (2019) 331-340; doi: 10.3221/igf-esis49.33 331 focused on fracture mechanics versus environment analysis of the presence of bonding defects on the fracture behavior of a damaged plate repaired by composite patch kaddouri nadia, kouider madani, mohammed amine bellali university of djillali liabes, lmpm laboratory, sidi bel abbes, algeria nadiia_171@hotmail.com, koumad10@yahoo.fr, bmaamine22@gmail.com xavier feaugas lasie, umr7356, laboratory of engineering sciences for the environment, la rochelle university, la rochelle, france. xavier.feaugas@univ-lr.fr abstract.the repair technique has presented its effectiveness in the reduction of the stresses at the level of stresses concentration areas. the search for a patch and suitable adhesive for a good transfer of load has pushed researchers to develop many ideas, which relate the form, the nature, the stacking sequence of the patch and the adhesive type to give a better combination of choice between the patch and the adhesive. our work fits in this context; the objective is to analyze by the method of finite elements the behavior in the rupture of a damaged plate in the presence of defect of bonding. the analysis of j-integral and stresses in the tow substrates adhesive and patch shows clearly that their values depends strongly on the position of the default essentially when it’s located close to the free edge of the free edge of the adhesive or the crack. keywords. j-integral; adhesive defect; peel stress; shear stress. citation: kaddouri n., madani, k., bellali,m a., feaugas, x,. analysis of the presence of defects of bonding on the fracture behavior of a damaged plate repaired by composite patch, frattura ed integrità strutturale, 49 (2019) 331-340. received: 26.02.2019 accepted: 02.06.2019 published: 01.07.2019 copyright: © 2019 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. introduction he use of the technique of bonding in the repair of damage in the aeronautical structures is experiencing a rapid expansion. this technique has shown its advantages compared to the classical technique such as welding or riveting and bolting. one of the most practical solutions for the repair of composite structures is to cover any part of the damaged area and paste patches in composite on the surface of the structure. it can also be noted that the bonding of external patches has been widely used in the repair of metallic structures in order to stop the propagation of a defect. many studies have been redesigned for this type of repair [1]. unfortunately, the repair of laminated composite structures by bonding external patches is much less concerned since it is limited because of its degradation towards environmental conditions [2, 3]. t http://www.gruppofrattura.it/va/49/2412.mp4 n. kaddouri et alii, frattura ed integrità strutturale, 49 (2019) 331-340; doi: 10.3221/igf-esis49.33 332 the patch of composite material bonded on the outside face has been recognized as an effective method for repairing cracks, and consequently extend the service life of structures cracked. considerable research has been done in recent years to develop the technology for bonding composite patches in aeronautical structures. several authors have searched to optimize the composite and the adhesive by the search for mechanical properties that are suitable to absorb as at the crack point is one of the approaches used in the performance analysis of composite material patches. experimental studies, numerical and even analytical, were conducted to study the behavior of cracks repaired by patch in composite. they showed that the crack point stress field, fatigue life and the stress intensity factor depend on several parameters, namely, the mechanical and geometrical properties, the number and thickness of the patch layers, the volume fraction and the orientation of the fibers, the shear modulus of the adhesive, its thickness and its temperature of elaboration and service, the size of much as possible the stresses of the damaged area. other authors have searched to optimize the geometric shape of the patch in order to transfer more and more stress at the crack head or the damaged area [4]. numerical analysis is an important tool for determining the stresses distribution in different substrates. several authors have proposed many methods to model the repaired structure taking into account the mechanical parameters of the adhesive and the composite [5, 6]. the analysis of the stresses in the adhesive layer is important since this latter is the weakest link in the structure or its mechanical properties are the weakest and therefore rapid damage to the latter. however, little research has been devoted to studying the presence of bonding defects. [7,8]. the voids in the adhesive layer are produced during the treatment by the enclosed air or by gas products of the adhesive or adherents. the gas typically forms a bubble in the liquid adhesive and when the adhesive cross-links and solidifies, the bubble remains a void. in other hand, during the realization of a bonded assembly, many types of defects are likely to be created. the nature of the defects that can meet in the bonded assemblies varies according to the phenomena having caused these defects. the concentrations of porosities can lead to the creation of holes or cavities. when they are located in the close vicinity of the interface. the cavities create places of interfaces not related or geometric discontinuities. these may evolve and give birth to preferential sites of initiation of cracking or detachment leading to the rupture of the junction. little research has been done in this area. the objective of our study is to analyze by the finite element method the effect of the presence of a defect of square geometrical shape whose position is variable according to the surface of the adhesive on the value of the j-integral and the different stress in the patch and the adhesive. geometrical model and mechanical properties et consider a 2024-t3 aluminum plate with the presence of a lateral crack repaired by a composite carbon / epoxy patch. this patch is bonded on the damaged area using an adhesive type adekit a-140 as shown in fig. 1. the dimensions of the different substrates are shown in tab. 1. in order to analyze the effect of the presence of defect of bonding on the stresses transfer from the plate to the patch and therefore on the quality of the repair and the value of the j-integral at the level of the crack tip, we have tried to model the presence of a defect in the adhesive layer. it was assumed a defect of square shape of dimension (1*1 mm2) which its position is random. the most defect positions are chosen close to the crack, at the level of the crack and at the level of the adhesive free edges (fig. 2). length (mm) width (mm) thickness (mm) plate h=250 w= 125 ep = 2 adhesif h= 80 w=80 ea =0.2 patch h=80 w=80 er =2 table 1: dimensions of the different substrates. the mechanical properties of the plate (2024-t3 aluminum) and the adhesive (adekit a-140) (tab. 2) are drawn directly of traction tests performed in the laboratory lasie (laboratory of the engineering sciences for the environment) in france [9]. however, for the composite patch, the mechanical properties have been determined by calculation of l n. kaddouri et alii, frattura ed integrità strutturale, 49 (2019) 331-340; doi: 10.3221/igf-esis49.33 333 homogenization between mechanical properties of matrix and fibers using the software cadec designed for materials composites (see tab. 2). figure 1: geometric model. figure 2: some positions of adhesive defect. materials e: young modulus (gpa) g: shear modulus (gpa) : poisson coefficient aluminum : 2024-t3 69 36,92 0,3 adhesive: adekit a-140 2,690 0,99 0,3 table 2: elastic properties of the aluminum plate and adhesive [9]. the composite patch has been modeled as successive multilayer with different orientations. this modeling will allow us to introduce the mechanical properties real for each layer based on the directions of the fibers, which is more real. in this part, it has used the equations of homogenization to determine the mechanical characteristics of composite (see tab.3). n. kaddouri et alii, frattura ed integrità strutturale, 49 (2019) 331-340; doi: 10.3221/igf-esis49.33 334 materials e1 (mpa) e2 (mpa) e3 (mpa) g12 (mpa) g13 (mpa) g23 (mpa) carbon /epoxy 128600 9766 9766 0.346 0.346 0.346 5252 4364 4364 table 3: mechanical properties of the composite patch carbon/epoxy. in order to see the effect of the fibers orientation in the composite patch on the global behavior of the repaired structure, six stacking sequences were selected as shown in the tab. 4. laminates s1 s2 s3 s4 s5 s6 stacking sequence [08]s [02/152/-152/902]s [02/302/-302/902]s [02/452/-452/902]s [02/602/-602/902]s [02/752/-752/902]s table 4: different stacking sequences used in the composite. mesh and boundary condition he boundary conditions for the repaired plate in traction are reproduced in the following manner: • embedding the lower face of the plate u1=u2=u3=ur1=ur2=ur3=0, • pressure at traction to the other face of the amplitude p=50 mpa. figure 3: model of the repaired structure under traction. the numerical analysis has been carried out by the abaqus code using the finite elements methods. the structure been meshed by elements of hexagonal type linear c3d8r (fig. 4). a refined mesh is carried out to the side of the crack and at the level of the patch and the adhesive; the adhesive has been considered as a third material so that one can introduce its mechanicals properties. the contact is considered as being perfect between the different layers (adhesive-patch, adhesiveplate and between the different layers of the composite). an elasto-plastic analysis is considered for the plate and the adhesive by introducing the plastic part of the two curves of the tensile test of the plate and the adhesive. for the composite, the mechanical properties has been varied the sequence of stacking (orientation of the fibers) and the nature of the fibers, for this, one has used the cadec code designed specially to determine the engineers constants of the composite. results and analysis he fig. 5 shows the variation of the j-integral as a function of the length of the crack; we note clearly that the value of the j-integral is low compared to the case of the plate unrepaired. it should be noted that the value of the j-integral increases with the increase in the length of the crack. the slope of the curve becomes more acute and the value of the j-integral increases. t t n. kaddouri et alii, frattura ed integrità strutturale, 49 (2019) 331-340; doi: 10.3221/igf-esis49.33 335 figure 4: mesh details of repaired plate. 0 10 20 30 40 50 0 2 4 6 8 10 12 14 j -i n te g ra l ( m j/m m ²) crack length (mm) plate unrepaired plate repaired figure 5: variation of the j-integral as a function of the length of the crack to the damaged plates and repaired by composite patch. the choice of the laminate sequence for a patch is also important. for this we took 6 laminated with different fibers orientation ( see tab. 4), the variation of the j-integral is similar whatever the sequence of stacking, the value of the jintegral is low for the patch that has the sequence [0]8,this value increases if the sequence of the patch is [02/752/752/902]s, for the laminate sequence [0]8 the patch has the highest mechanical properties according to the loading direction and thus absorbed more stresses. however, if the fibers orientation angle tends toward 90°, the mechanical properties of the patch are declining and therefore less of load transfer from the damaged area. if the length of the crack is too small than the width of the plate, the effect of the sequence of stacking disappears. the j-integral increases with the increase in the size of crack. the lowest values of the j-integral are noted for the case of repair by patch for which the sequence of stacking is [08]s, for this orientation the composite presents the mechanical properties high and therefore a better transfer of charge of the damaged plate through the adhesive. n. kaddouri et alii, frattura ed integrità strutturale, 49 (2019) 331-340; doi: 10.3221/igf-esis49.33 336 5 10 15 20 25 30 35 40 45 50 55 0,10 0,15 0,20 0,25 0,30 0,35 0,40 0,45 0,50 0,55 jin te g ra l ( m j/m m ²) crack length (mm) [0] s [0 2 /15 2 /-15 2 /90 2 ] s [0 2 /30 2 /-30 2 /90 2 ] s [0 2 /45 2 /-45 2 /90 2 ] s [0 2 /60 2 /-60 2 /90 2 ] s [0 2 /75 2 /-75 2 /90 2 ] s figure 6: variation j-integral in function of the length of the crack for a different sequence of stacking. 0 5 10 15 20 25 30 35 40 45 50 55 6 8 10 12 14 16 s h e a r st re ss (m p a ) crack length (mm) [0] s [0 2 /15 2 /-15 2 /90 2 ] s [0 2 /30 2 /-30 2 /90 2 ] s [0 2 /45 2 /-45 2 /90 2 ] s [0 2 /60 2 /-60 2 /90 2 ] s [0 2 /75 2 /-75 2 /90 2 ] s figure 7: variation of the adhesive shear stress τ23 in function of the the length of the crack for a different sequence of stacking. the distribution of shear stresses is the same whatever the sequence of stacking in the composite. the more low stresses are for the patch with a sequence of stacking [08]s this is due to the fact that the majority of stresses in the adhesive are absorbed by the patch. for the other stacking sequences the transfer of stresses is minimal to the patch and therefore of high stresses in the adhesive. by analyzing, the peel stress according to the thickness of the patch. if the length of the crack is minimum than the width of the patch, the peel stresses value is identical, a maximum is on the side in contact with the adhesive and a minimum on the other face which is in contact with the plate. only the sequence [02]8 presents a continuity in the peel stress distribution since the different layers present the same properties and the same orientation of fiber, however for the other stacking sequences the stress distribution is in the n. kaddouri et alii, frattura ed integrità strutturale, 49 (2019) 331-340; doi: 10.3221/igf-esis49.33 337 form of stairs since the mechanical properties of the different layers differ from a layer by report to the other depending on the direction of the fiber. 0,0 0,4 0,8 1,2 1,6 2,0 0 2 4 6 8 10 12 p e e l s tr e s s ( m p a ) patch thickness(mm) crack lenght a= 5 mm crack lenght a= 20 mm crack lenght a= 50 mm 0,0 0,5 1,0 1,5 2,0 0 2 4 6 8 10 12 p e e l s tr e ss ( m p a ) patch thickness(mm) crack lenght a= 5 mm crack lenght a= 20 mm crack lenght a= 50 mm 0,0 0,5 1,0 1,5 2,0 0 2 4 6 8 10 12 14 16 p e e l s tr e s s ( m p a ) patch thickness (mm) crack lenght a= 5 mm crack lenght a= 20 mm crack lenght a= 50 mm [0 2 /45 2 /-45 2 /90 2 ] s [0 2 /75 2 /-75 2 /90 2 ] figure 8: variation of the peel stress σ33 as a function of the thickness of the patch for different length of crack. the value of the j-integral increases considerably if the crack length increases. if the defect is far from the crack and the free edge, the value of the j-integral will be minimal, because, in these places, the presence of the defect will have no effect on the behavior of the adhesive. if the defect is at the level of the free edges of the adhesive, the value of the j-integral will be affected since at these places the concentration of the stresses will be important. the defects that are at the core of the adhesive will have a consequence on the value of the j-integral since they will be close to the crack. these curves show the variation of the j-integral as well as the constraints in the patch and the adhesive in function of the position of the defect. we can see clearly the positions, which induce maximum values of j-integral, and stresses in the patch and the adhesive. the maximum values are for the case or the defect is located at the level of the free edge and a close to the crack. [0 8 ] s n. kaddouri et alii, frattura ed integrità strutturale, 49 (2019) 331-340; doi: 10.3221/igf-esis49.33 338 a) b) c) figure 9: variation of the j-integral in function of the position of the default has a) crack length =10mm, b) crack length =20mm, c) crack length =30mm. conclusion he analysis of the results allowed us to draw the following conclusions: the composite patch considerably reduces the j-integral and the stresses in the different substrates. the stacking sequence plays a decisive role in reducing j-integral and shear stresses in the adhesive and peeling in the patch. the presence of defect significantly affects the value of the j-integral and the stresses in the two substrates. the presence of the defect of bonding, considerably affects the shear stress in the adhesive essentially if the defect is near the crack or at the free edges of the adhesive. the rate of charge transfer increases when stresses are high at the plate and the adhesive. the presence of the defect near a crack of considerable length considerably affects the stresses in the adhesive and j-integral in the plate. if the length of the crack is minimal, the position of the defect has little influence on the value of j-integral. t n. kaddouri et alii, frattura ed integrità strutturale, 49 (2019) 331-340; doi: 10.3221/igf-esis49.33 339 a) 0 1 2 3 4 5 6 7 8 9 10 0,10 0,12 0,14 0,16 0,18 0,20 0,22 defect position jin te g ra l j ( m j/m m ²) crack lenght a= 10 mm crack lenght a= 20 mm crack lenght a= 30 mm 0 2 4 6 8 10 7 8 9 10 11 12 13 14 15 16 17 18 19 sh e a r s tr e ss ( m p a ) defect position crack lenght a= 10 mm crack lenght a= 20 mm crack lenght a= 30 mm b) c) 0 2 4 6 8 1 0 6 8 1 0 1 2 1 4 1 6 1 8 p e e l st re s s ( m p a ) d efect p o sitio n c ra c k le n g h t a = 1 0 m m c ra c k le n g h t a = 2 0 m m c ra c k le n g h t a = 3 0 m m d) figure 10: a) different position of default in the adhesive layer. b) variation of the j-integral in function of the position of the defect c) variation of the shear stress as a function of the position of the defect. d) variation of the peel stress according to the position of the defect. n. kaddouri et alii, frattura ed integrità strutturale, 49 (2019) 331-340; doi: 10.3221/igf-esis49.33 340 references [1] madani, k., touzain, s., feaugas, x., roy, a. a,d cohendoz, s. (2009), analyze of the notch effect on the distribution of the stresses in the adhesive layer between two bonded aluminum 2024-t3 plates. j mater technol; 97, pp. 315– 324. [2] rezgani, l. (2016), influence of water ingress onto the crack propagation rate in an aa2024-t3 plate repaired by a carbon/epoxy patch. aerospace science and technology. [3] rezgani, l. (2017), hygrothermal ageing effect of adekit a140 adhesive on the j-integral of a plate repaired by composite patch. journal of adhesion science and technology. [4] fekih, s. m. (2007), optimization of geometric parameters and mechanical characteristics of patches in composites for the repair of cracked structures. university of sba-udl. [5] wu, z.j., romeijn, a., wardenier, j. (1997), stress expressions of single-lap adhesive joints of dissimilar adherends. compos struct 38, pp. 273. [6] kilic, b., madenci, e., ambur, d.r. (2006), influence of adhesive spew in bonded single-lap joints. eng fractmech 73, pp. 1472–1490. [7] elhannani, m. (2017), statistical study of the influence of different bonding parameters on stress reduction.university of sba-udl. [8] benchiha, a. and madani, k. (2015), influence of the presence of defects on the stresses shear distribution in the adhesive layer for the single-lap bonded joint. structural engineering and mechanics, 53(5). [9] madani, k., touzain, s., feaugas, x., cohendouz, s., & ratwani, m. 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can be opened with acrobat and adobe reader 5.0 and later.) >> /namespace [ (adobe) (common) (1.0) ] /othernamespaces [ << /asreaderspreads false /cropimagestoframes true /errorcontrol /warnandcontinue /flattenerignorespreadoverrides false /includeguidesgrids false /includenonprinting false /includeslug false /namespace [ (adobe) (indesign) (4.0) ] /omitplacedbitmaps false /omitplacedeps false /omitplacedpdf false /simulateoverprint /legacy >> << /addbleedmarks false /addcolorbars false /addcropmarks false /addpageinfo false /addregmarks false /convertcolors /converttocmyk /destinationprofilename () /destinationprofileselector /documentcmyk /downsample16bitimages true /flattenerpreset << /presetselector /mediumresolution >> /formelements false /generatestructure false /includebookmarks false /includehyperlinks false /includeinteractive false /includelayers false /includeprofiles false /multimediahandling /useobjectsettings /namespace [ (adobe) (creativesuite) (2.0) ] /pdfxoutputintentprofileselector /documentcmyk /preserveediting true /untaggedcmykhandling /leaveuntagged /untaggedrgbhandling /usedocumentprofile /usedocumentbleed false >> ] >> setdistillerparams << /hwresolution [2400 2400] /pagesize [612.000 792.000] >> setpagedevice microsoft word numero 23 articolo 2 c. maletta et alii, frattura ed integrità strutturale, 23 (2013) 13-24; doi: 10.3221/igf-esis.23.02 13 scilla 2012 the italian research on smart materials and mems fracture mechanics of pseudoelastic niti alloys: review of the research activities carried out at university of calabria c. maletta, f. furgiuele, e. sgambitterra dept. of mechanical engineering, university of calabria, 87036 rende (cs), italy. carmine.maletta@unical.it abstract. this paper reports a brief review of the research activities on fracture mechanics of nickel-titanium based shape memory alloys carried out at university of calabria. in fact, this class of metallic alloys show a unusual fracture response due to the reversible stress-induced and thermally phase transition mechanisms occurring in the crack tip region as a consequence of the highly localized stresses. the paper illustrates the main results concerning numerical, analytical and experimental research activities carried out by using commercial niti based pseudoelastic alloys. furthermore, the effect of several thermo-mechanical loading conditions on the fracture properties of niti alloys are illustrated. keywords. shape memory alloys; stress-induced martensitic transformation; fracture mechanics. introduction ickel-titanium alloys (niti) are the most useful shape memory alloys, because they combine high recovery capabilities with good mechanical performances and biocompatibility. these alloys are also known as nitinol, which stands for nickel titanium naval ordnance laboratory (white oak, maryland), where in 1961 their shape memory capabilities were discovered. after their discovery niti alloys have attracted the interest of the scientific and engineering community due to their unique properties, namely pseudoelastic effect (pe) and shape memory effect (sme). these functional properties are due to a reversible solid state phase transformation between a parent phase (b2 austenite) and a product phase (b19’ martensite), the so called thermoelastic martensitic transformation (tmt), which can be activated either by temperature (thermally-induced martensitic transformation, tim) or by applied stress (stressinduced martensitic transformation, sim) [1]. as a result of these microstructural changes, niti alloys are able to recover high values of mechanical deformations (up to 12%), by either heating the material above the characteristic transition temperatures (sme) or by removing the mechanical load (pe). however, due to their unique microstructural evolutions elastic and elastic plastic theories cannot be applied to study the mechanical response of niti alloys and, consequently, adhoc models should be developed which take into account the thermally-induced and/or stress induced transformations. in particular, it is widely accepted by the scientific community that crack formation and propagation are significantly affected by the phase transitions mechanisms and, consequently, niti alloys exhibit unusual fatigue and fracture responses with respect to common metals. this topic is of great technological and scientific interest as demonstrated by several recent experimental studies, which have been aimed to evaluate the evolution of cracks under both static [2-8] and cyclic loading conditions [9-12]. furthermore, several numerical studies have been carried out, by using standard finite element codes and plasticity concepts [13-15] as well as by special constitutive models for smas [16-17]. finally, some analytical models have been proposed recently [18-27], which are mainly based on modified linear elastic fracture mechanics concepts. in the present paper a review of the research activities on fracture mechanics of niti alloys, carried out at the department of mechanical engineering at university of calabria (italy), is illustrated. the stress-induced martensitic transformation occurring in the crack-tip region, as a consequence of the high values of local stresses, and the resulting stress distribution n http://www.gruppofrattura.it http://dx.medra.org/10.3221/igf-esis.23.02&auth=true c. maletta et alii, frattura ed integrità strutturale, 23 (2013) 13-24; doi: 10.3221/igf-esis.23.02 14 have been analyzed by numerical simulations [15], analytical modeling [23-26] and experimental measurements [7-8]. in particular, finite element (fe) simulations have been carried out, by using commercial software codes and standard nonlinear plasticity analyses, i.e. by modeling the monotonic stress-strain of smas as a plastic-like behavior. preliminary fe studies have been carried out in [15], where single edge crack specimens (sec) have been analyzed by two-dimensional plane stress fe analyses. in this study the crack tip transformation mechanisms have been analyzed together with their effects on the stress distribution. in addition, a first attempt to model these phase transition mechanisms by modified linear elastic fracture mechanics (lefm) concepts is illustrated. subsequently, an analytical model has been proposed in [23] based on the irwin’s correction of lefm [28] which allows to simulate both the stress-induced crack-tip transformation region and the resulting stress distribution under plane stress conditions. in addition, numerical simulations have been carried out by considering a central crack in a plate subjected to mode i loading conditions; systematic comparison between numerical and analytical results have been carried out and good agreements have been observed. finally, the effects of thermo-mechanical parameters and loading conditions have been analyzed. the model has been subsequently updated in [24] to analyze both plane stress and plane strain conditions, by considering a tri-axial constraint factor for phase transition mechanisms. furthermore, the model prediction have been compared with experimental literature data [5] concerning synchrotron x-ray microdiffraction experiments of miniature ct specimens. the reference analytical model has been also used to define possible fracture control parameters for smas in [25] based on the definition of stress intensity factor in lefm. finally, the reference model has been recently modified in [26] to overcome one of the basic limitation, i.e. the assumption of constant stress transformation. in particular, the stress-strain response is modeled as a tri-linear material with a generic slope of the transformation plateau. experimental tests have been carried out in [7] for a comparative study between base and laser welded materials, by using sec specimens obtained from a commercial pseudoelastic niti sheet (type s, memry, usa). however only the notch strength was calculated for the comparative analysis, and no further considerations have been made about the complex fracture mechanisms in smas. more recently the effects of temperature, within the stress-induced transformation regime, in sec specimens have been analyzed [8], by experimental measurements and analytical studies. the tests were carried out at different values of the testing temperature the critical values of the stress intensity factor were computed, based on lefm theory on the reference analytical model [25]. figure 1: schematic depiction of the crack-tip stress distribution and transformation region in pseudoelastic niti smas. fracture mechanics of smas: basic features he high values of local stresses in the crack tip region of pseudoelastic niti alloys cause a stress-induced martensitic transformation and, consequently, marked differences are observed with respect to common linear elastic or elastic plastic materials as schematically shown in fig. 1. in fact, due to this microstructural evolution t http://www.gruppofrattura.it http://dx.medra.org/10.3221/igf-esis.23.02&auth=true c. maletta et alii, frattura ed integrità strutturale, 23 (2013) 13-24; doi: 10.3221/igf-esis.23.02 15 three different regions are observed in the crack tip region: the austenitic untransformed region (a), the phase transformation region (a→m) and the fully transformed martensitic region (m). the size of the fully transformed martensitic region ( 1m  ) and of the transformation region ( 0 1m  ), along the plane of the crack, are identified by the radii mr and ar , namely martensitic and austenitic radii, respectively. in addition, due to the large transformation strain occurring at the very crack tip, a marked non-linearity and a complex stress distribution are observed, as schematically shown in fig. 1, with respect to common metallic alloys. the figure also illustrates a schematic depiction of the stress-strain response of a pseudoelastic alloy together with the main mechanical parameters: the direct transformation stresses, σams and σ am f , the transformation strain, l , and the effective young’s moduli of austenite, ae , and martensite, me . the transformation strain and the young’s moduli are considered as material constants while the transformation stresses can be expressed as a function of the temperature, t , according to the clausius–clapeyron relation:  0 0σ σam ams s mb t t   (1)  0 0σ σam amf f mb t t   (2) where 0σ am s and 0σ am f are the transformation stresses at the reference temperature 0t and mb is a material constant. numerical modeling he crack tip stress distribution and transformation region in pseudoelastic smas have been studied by finite element (fe) simulations carried out by using commercial software codes and standard non-linear plasticity analyses. in fact, monotonic loads to fracture are generally applied to specimens for toughness measurements and, consequently, the stress-strain hysteretic behavior, observed during loading-unloading cycles, is not taken into account. due to this reason the monotonic nonlinear behavior of smas is treated as a plastic-like response. preliminary fe studies have been carried out in [15], where single edge crack specimens (sec) have been analyzed by two-dimensional plane stress fe analyses, carried out with the commercial finite element code msc marc®. the geometry of the sec specimen is illustrated in fig. 2a, while the corresponding fe model is illustrated in fig. 2b together with an highlight of the crack tip. particularly fine mesh has been adopted to model the crack tip region in order to describe the high stress gradient as well as for an accurate prediction of the non-linear stress distribution due to the stress induced transformation mechanisms (a→ m). a) b) figure 2: sec specimen: a) geometry and b) fe model with an highlight of the crack tip [15] t http://www.gruppofrattura.it http://dx.medra.org/10.3221/igf-esis.23.02&auth=true c. maletta et alii, frattura ed integrità strutturale, 23 (2013) 13-24; doi: 10.3221/igf-esis.23.02 16 several simulations have been carried out for different thermo-mechanical loading conditions as well as by varying the main thermo-mechanical parameters of the alloy, in terms of transformation strain ( l ) and transformation stresses ( σ am s and σamf ). as an example fig. 2a illustrates the transformation region near the crack tip, i.e. the contours of the martensite fraction m , while and the effects of the testing temperature t on the transformation radii, mr and ar , are illustrated in fig. 3.b. these results have been obtained under a remote tensile stress 20.5 mpa   for a sma with young’s moduli 39 ae gpa and 20 me gpa . the figure shows that both mr and ar decrease with increasing the temperature t ; resulting in an overall reduction of the transformation zone. these preliminary results have been confirmed by subsequent numerical simulations carried out in [23] and in [8] where systematic comparison with the estimates of a novel analytical approach have been carried out, as illustrated in the following section. a) b) figure 3: fe results of the crack tip transformation behavior in a pseudoelastic sma: a) contours of the martensite fraction ( m ) and b) transformation radii ( mr and ar ) as a function of the testing temperature [15]. analytical modeling novel analytical approach has been developed recently [23], which is based on a modified irwin’s correction [28] of linear elastic fracture mechanics (lefm). in particular, the model allows to describe the crack tip stress distribution and transformation region in pseudoelastic niti alloys under plane stress conditions. the model has been subsequently improved in [24] to describe both plane stress and plane strain conditions while in [25] two fracture control parameters have been proposed, based on modified stress intensity factors (sif). finally, a new version of the model has been developed in [26] to overcome a limitation of the reference model, i.e. the assumption of constant stress transformation. for the sake of completeness and readability the basic expression of the stress components and of the transformation radii, mr and ar , are given in the following but complete and detailed descriptions of the model are reported in the reference papers [23-24]. eq. 3 gives the expression of the principal stress components along the plane of the crack ( 0  ), in the austenitic region:       1 2 2 δ ie a a k r r r r       (3) the stress equation a is obtained by a modified irwin’s correction [28] of the lefm, i.e. by using effective crack length and sif, namely ea and iek : δea a r  (4) a http://www.gruppofrattura.it http://dx.medra.org/10.3221/igf-esis.23.02&auth=true c. maletta et alii, frattura ed integrità strutturale, 23 (2013) 13-24; doi: 10.3221/igf-esis.23.02 17 ie ek a   (5) where the distance δr is given by: *δ ar r r  (6) with * 1 2 i am tc k r f         (7) where am is the direct a→ m transformation stress and it is assumed to be constant ( am am ams f    ); tcf can be regarded as a transformation constraint factor, i.e. it is defined based on the plastic constraint factor in lefm [29], and varies in the range between 1 and   11 2  , with the lower and upper bounds corresponding to the plane stress and plane strain conditions, respectively. the stress distribution in the martensitic region can be obtained by modified relations for bilinear materials and it is given by the following equation:         1 1 2 1 1 1 2 1 2 2 1 2 amie m m l a tc k r r e f r                        (8) where  represents the young’s modulus ratio ( /m ae e  ) while  1   and 1 / 2  for plane stress and   1 1 2     and 3 / 2  under plane strain conditions. the martensitic radius mr , can be calculated by using the condition  1 amm m tcr f  : 2 21 2 2 2 ie m am tc l a k r f e           (9) the austenitic radius ar can be calculated by imposing the equilibrium condition at the crack tip, as described in [23], and, thus, the following relation can be obtained:    2 * 1 1 1 1 2 /2 1 ie a am am tc l atc k r r f ef                   (10) several analysis have been carried out in [23] by considering a central crack with length 2a in an infinite plate subjected to mode i loading conditions. in particular, the effects of the main thermo-mechanical parameters of the alloy, in terms of the transformation strain ( l ) and stress ( am ), on the crack tip stress distribution and transformation region have been analyzed, as illustrated in fig. 4. in addition, comparisons with fe results are also illustrated in the figure and good agreements are observed. in particular, fig. 4.a illustrates the crack tip stress distribution for a sma with young’s moduli 50 ae gpa and 25 me gpa , while fig. 4.b illustrates the values of /ar a and /mr a as a function of the transformation strain ( l ) for two values of the transformation stress ( am ). a marked decrease of /ar a is clearly observed together with a decrease of /mr a when increasing the transformation stress am , as a direct consequence of the increased values of local stresses near the crack tip in the austenitic region. furthermore, a slight increase of /ar a together with a reduction of /mr a is observed when increasing the transformation strain and these effects become more evident when reducing the transformation stress. the estimates of the analytical model on crack tip stress-induced transformation have been also compared with experimental literature data in [24]; these latter have been obtained by synchrotron x-ray microdiffraction experiments of a miniature ct specimen, under opening mode conditions with a constant load p=2860 n and a crack length-to-width ratio / 0.55a w  [5]. in particular, in fig. 5 the contours of the austenitic radius, ar , under both plane stress and plane strain conditions, are compared with the microdiffraction patterns. the experimentally observed transformation region is between plane stress and plane strain contours and this is the expected result as x-ray observations represents volumehttp://www.gruppofrattura.it http://dx.medra.org/10.3221/igf-esis.23.02&auth=true c. maletta et alii, frattura ed integrità strutturale, 23 (2013) 13-24; doi: 10.3221/igf-esis.23.02 18 averaged data along the specimen thickness (i.e. between plane stress at the specimen surfaces and plane strain in the center). furthermore, the martensitic radius mr is not illustrated as it is about one order of magnitude less than austenitic radius ar and it is not illustrated in the microdiffraction patterns, which show only the region with 30-40% volume fraction of martensite (b19’). a) b) figure 4: comparisons between analytical and fe results: a) crack tip von mises stress and b) transformation radii as a function the transformation strain ( l )and for two values of the transformation stress ( tr am  ) [23]. figure 5: comparison of the crack-tip transformation region between numerical predictions and experimental observations by synchrotron x-ray microdiffraction observations [24]. the analytical model have been also used to define possible fracture control parameters in smas based on the stress equations in both austenitic and martensitic region and on the definition of stress intensity factor in lefm. in particular, two different sifs have been defined in [25]: an austenitic sif, namely iak , and a martensitic or crack tip sif, namely imk . in particular, the austenitic sif, iak , can be directly obtained from the modified irwin’s approach described in the previous section, and it can be regarded as the effective sif iek : 0ˆ lim 2 ˆia a ie r k r k     (11) with ˆ δr r r  ; the martensitic sif, imk , is given by: http://www.gruppofrattura.it http://dx.medra.org/10.3221/igf-esis.23.02&auth=true c. maletta et alii, frattura ed integrità strutturale, 23 (2013) 13-24; doi: 10.3221/igf-esis.23.02 19      10 2 1 lim 2 2 1 1 im m ia r k r k             (12) eq. 12 shows that imk can be expressed ad a function of iak ,  and of the young’s modulus ratio . however, it is worth noting that the knowledge of the extent of transformation region, in terms of ar , is required to calculate both iak and imk and an iterative approach is required to calculate these parameters as described in [25]. fig. 6a shows the values of iak and imk , normalized with respect to the applied sif ik a    , as a function of the transformation strain, l , and for different values of the transformation stress, am , for an alloy with 0.3  , 40 ae gpa and 0.5  . note that the same curves are used to represent iak and imk , as /im iak k is a constant depending on the elastic properties of the alloy, as shown in eq. 12. the figure illustrates that both iak and imk increase with increasing the transformation strain, and this effect is more evident when decreasing the transformation stress, as a direct consequence of the increase of the transformed region near the crack tip [23]. furthermore, iak is always greater than ik  , with / 1ia ik k   when am   and 0l  , i.e. in the case of linear elastic materials. in addition, the martensitic sif, imk , is always smaller than ik  , which indicates a reduction of the stresses at the very crack tip if compared with linear elastic materials. fig. 6b, illustrates the effects of the testing temperature on both iak and imk for a commercial superelastic niti alloy. the figure shows that a decrease of both sifs is observed when increasing the temperature, as a direct consequence of the increase of the transformation stress. in particular, a reduction of about 20% is observed in the temperature range between 273 k and 343 k, which correspond to a range of transformation stress between about 90 mpa and 800 mpa. however, iak and imk decrease rapidly from 273 k to 290 k, while a small variation, i.e. of about 2%, is observed when the temperature is above 290 k. this effect is a direct consequence of the increase of the transformation stress with increasing the temperature, which causes a marked reduction of the transformation region, as discussed in [23], and, consequently, iak approaches to the applied sif ik  , i.e. the alloy behaves like a linear elastic material. furthermore, it is worth noting that the temperature range is limited by a lower bound, mint , which corresponds to a transformation stress equal to zero, and by an upper bound min dt m , which represents a characteristic maximum temperature for stress induced transformation. a) b) figure 6: martensitic and austenitic sifs, iak and imk , normalized with respect to the applied sif, ik  , as a function of: a) the transformation strain( l ) and for different values of the transformation stress ( tam r  ), b) the testing temperature (t) [25]. the reference model has been recently modified in [26] to overcome one of the basic limitation, i.e. the assumption of constant stress transformation. in fact, it has been demonstrated that the slope of the stress-strain transformation plateau increases under specific loading conditions, such when increasing the loading rate or under cyclic loads [30]. to this aim, http://www.gruppofrattura.it http://dx.medra.org/10.3221/igf-esis.23.02&auth=true c. maletta et alii, frattura ed integrità strutturale, 23 (2013) 13-24; doi: 10.3221/igf-esis.23.02 20 the stress-strain response is modeled as a tri-linear material with a generic slope of the transformation plateau. a detailed description of the modified model is out of the scope of the paper, therefore just the main results are reported and discussed here. figs. 7 illustrate the effects of the slope of the stress-strain transformation curve on the crack tip stress distribution (fig. 7a) and on the transformation radii (fig. 7b) for a sma with 40 ae gpa , 0.5  and 4%l  . in particular, two values of the slope of the transformation plateau, with the same average value of the transformation stress   / 2 375am am amavg s s mpa     , are compared with the stress distribution in the case of constant transformation stress. the figures clearly illustrate a marked effect of the slope of the transformation plateau on the austenitic radius ar , which represents the outer contour of the transformation region, while a slight effect on the martensitic radius mr is observed. this is expected to play a role on fracture properties of smas, as the outer transformation contour defines the fracture process zone and it is used to calculate the effective sif based on the modified irwin’s correction (eqs. 4-6). a) b) figure 7: effects of the slope of the stress-strain transformation curve: a) crack tip stress distribution and b) transformation radii [26]. experimental measurements ome experimental studies have been carried out recently to analyze the fracture response of niti pseudoelastic alloys, by using single edge crack specimens obtained from commercial sheets [7, 8]. in particular, the effects of nd: yag laser welding process on the fracture properties of a ni rich ti alloy have been analyzed in [7] by systematic comparison between base and laser welded materials, while the effects of testing temperature have been studied in [8]. ni-49.2 at.% ti pseudoelastic sheets with thickness t=0.75 mm and with a nominal austenite finish temperature af=-7°c (type s, memry, usa) were used. the welding process was carried in open air conditions, by a nd:yag laser source (hl 2006 d) with a maximum power of 2kw, and a shielding/clamping system to avoid chemical contamination of the molten zone and the formation of hot cracks [7]. a set of preliminary tests were carried out in order to identify the optimal values of the process parameters, such as average power and welding rate. to this aim, microscopic observations and hardness tests were executed to evaluate the extension of the heat affected zone (haz) and molten zone (mz), obtained by several values of the aforementioned welding parameters. finally, the following values were chosen: average power of 850 w and welding rate of 2400 mm/min. fig. 9 illustrates a comparison between the load vs crack mouth opening displacement curves of the reference and laser welded materials, obtained from isothermal tests of sec specimens, carried out at room temperature. the notch strength was calculated for a comparative analysis between the fracture resistance of the reference and the laser welded materials, according to the standard astm e338-91, and no further considerations have been made about the complex fracture mechanisms in smas. three different specimens for each type were tested and the results are illustrated in tab. 1; this table clearly illustrates that the welded specimens exhibit a reduction in the notch strength of about 15% with respect to the reference specimens. s http://www.gruppofrattura.it http://dx.medra.org/10.3221/igf-esis.23.02&auth=true c. maletta et alii, frattura ed integrità strutturale, 23 (2013) 13-24; doi: 10.3221/igf-esis.23.02 21 20.0 mm 67.0 mm 7.2 mm edm pre-crack rolling direction a) b) figure 8: sec specimens for fracture tests: a) specimen geometry and b) reference and welded specimens with highlights of the precracks [7]. figure 9: comparison between the load vs crack mouth opening displacement curves of the reference and welded specimens [7]. specimen type maximum load [kn] notch strength [mpa] reference 2.65±0.03 284±3 welded 2.26±0.05 243±5 table 1: mechanical strength of the sec specimens [7]. the fracture path is almost straight along the symmetry plane of both specimens and it is always located in the heat affected zone (haz) of the welded specimens. the fracture surfaces of the sec specimens were analyzed by sem investigations as illustrated in fig. 10, which shows a comparison of the fracture surface of the reference and welded specimens. the figures indicate a ductile fracture surface in the reference material, with dimple size of about 10-30 m, while a more brittle fracture mechanism is observed in the welded specimen with dimple size of about 5 m. http://www.gruppofrattura.it http://dx.medra.org/10.3221/igf-esis.23.02&auth=true c. maletta et alii, frattura ed integrità strutturale, 23 (2013) 13-24; doi: 10.3221/igf-esis.23.02 22 a) b) figure 10: sem observation of the fracture surface: a) reference and b) welded specimen [7]. the effects of temperature, within the stress-induced transformation regime, in single edge crack specimens (sec) have been recently analyzed in [8], by experimental measurements and analytical studies. ni-49.2 at.% ti pseudoelastic sheets with oxide-free surfaces and a thickness of 0.5mm (type s, memry, usa) have been used in this investigation. single edge crack specimens specimen, shown in fig. 11, have been made by electro discharge machining (edm). in particular, fig. 11.a shows the dimensions of the specimen, while fig. 11.b illustrates a picture of the specimen with highlights of the pre-crack. this latter was made by two subsequent steps: 1) electro discharge machining by using a copper wire (=200 m) with a length of about 3 mm and 2) fatigue pre-crack with a length of about 0.3 mm. isothermal fracture tests have carried out by applying a monotonic tensile load until fracture under displacement control condition, at a crosshead speed of 0.005 mm s-1. the tests were carried out at different values of the testing temperature for t>af (t1=303 k, t2=318 k and t3=343 k) and the load-displacement curves were recorded. finally, the mode i stress intensity factor was computed, based on lefm theory, together with modified sifs for smas, based on the reference analytical model [23]. a) b) figure 11: single edge crack (sec) specimen: a) shape and dimensions and b) picture with highlights of the pre-crack [8]. fig. 12 illustrates the results of isothermal mechanical tests of two sec specimens in terms applied load, p, and applied mode i stress intensity factor, ki*, as a function of the crosshead displacement, d, of the testing machine. in particular, fig. 12a has been obtained at the temperature t=303 k while fig. 12b is relative to the temperature t=343 k. it is worth noting that only specimens with crack length to width ratio a/w between 0.3 and 0.4 have been analyzed and the applied http://www.gruppofrattura.it http://dx.medra.org/10.3221/igf-esis.23.02&auth=true c. maletta et alii, frattura ed integrità strutturale, 23 (2013) 13-24; doi: 10.3221/igf-esis.23.02 23 stress intensity factor (ki*) has been calculated by using literature relation for sec specimens [29]; as a consequence ki* is based on classical assumptions of linear elastic fracture mechanics and does not take into account the crack tip transformation mechanisms in smas. a qualitative comparison between figs. 12a and 12b shows that higher non-linear effects are observed in the near peak region of the curves when decreasing the testing temperature. this effect has been observed in all sec specimens and it can be attributed to the decrease of the transformation stresses and, consequently, to the larger size of the crack tip transformation region, when decreasing the testing temperature [23]. a) b) figure 12: isothermal mechanical tests of sec specimens in terms of applied load (p) and mode i stress intensity factor (ki*) as a function of the crosshead displacement (d): a) t=303 k and b) t=343 k [8]. an average value of kic* equal to 33.8 mpa m1/2 has been obtained in the temperature range between 303 k and 343 k and this result is very close to previous literature results [5], where a kic* equal to 34 mpa m1/2 for a pseudoelastic alloy and 31 mpa m1/2 for a martensitic alloy have been measured. however, it is worth noting that these results cannot be directly compared as reference data have been obtained by testing miniature compact tension specimens at a fixed temperature t=295 k. on the contrary, the present results have been obtained for different values of the testing temperature, within the stress induced transformation regime of the alloy, which indicate an slight increase of kic*, with increasing the testing temperature, from about 32 mpa m1/2 at t=303 k to about 35 mpa m1/2 at t=343 k. this trend is in agreement with the predictions of the adopted analytical model, which estimate a reduction of both martensitic and austenitic stress intensity factors (kim and kia) with increasing the temperature, i.e. it indicates a toughening effect. however, further systematic studies should be carried out for a complete validation of this preliminary result, by analyzing different kind of alloys under different values of the testing temperature. conclusions bried review of the research activities on fracture mechanics of shape memory alloys (smas) carried out in the last few years at the department of mechanical engineering of university of calabria is illustrated. in particular, integrated approaches involving numerical simulations, analytical modeling and experimental measurements have been adopted with the aim to understand the role of crack-tip stress-induced martensitic transformation on the fracture properties of smas. comparison between numerical, analytical and experimental results have been carried out and good agreements have been observed. in addition, several case studies have been analyzed in order to understand the effects of the thermo-mechanical parameters and of the loading conditions on the fracture properties of smas. references [1] k. otsuka, x.ren, prog. mater sci, 50(5) (2005), 511. [2] j.h. chen, w. sun, g.z. wang, metall mater trans a phys metall mater sci, 36(4) (2005), 941. a http://www.gruppofrattura.it http://dx.medra.org/10.3221/igf-esis.23.02&auth=true c. maletta et alii, frattura ed integrità strutturale, 23 (2013) 13-24; doi: 10.3221/igf-esis.23.02 24 [3] m.r. daymond, m.l. young, j.d. almer, d.c. dunand, acta mater., 55 (2007) 3929. [4] s. daly, a. miller, a., g. ravichandran, k. bhattacharya, acta mater., 55 (2007) 6322. [5] s. gollerthan, m.l. young, a. baruj, j. frenzel, w.w. schmahl, g. eggeler, acta mater, 57(4) (2009) 1015. [6] s. gollerthan, m.l. young, k. neuking, u. ramamurty, g. eggeler, acta mater, 57 (2009) 5892. [7] c. maletta, a. falvo, f. furgiuele, g. barbieri, m. brandizzi, j mater eng perform, 18(5–6) (2009) 569. [8] c. maletta, f. furgiuele, e. sgambitterra, submitted to fatigue fract eng m, (2012). [9] s.w. robertson, r.o. ritchie, biomaterials, 28(4) (2007) 700. [10] s.w. robertson, r.o. ritchie, j. biomedmater. res. part b appl biomater, 84(1) (2008) 26. [11] s.w. robertson, a. mehta, a.r. pelton, r.o. ritchie, acta mater, 55(18) (2007) 6198. [12] k. gall, j. tyber, g. wilkesanders, s.w. robertson, r.o. ritchie, h.j. maier, mat sci eng a, 486(1–2) (2008) 389. [13] g.z. wang, int j fract, 146(1–2) (2007), 93. [14] g.z. wang, f.z., xuan, s.t. tu, z.d. wang, mater sci eng a, 527 (2010) 1529. [15] c. maletta, a. falvo, f. furgiuele, a. leonardi, j mater eng perform, 18(5–6) (2009) 679. [16] t. baxevanis, y. chemisky, d.c. lagoudas, smart mater struct, 21 (9) (2012) 094012. [17] y. freed, l. banks-sills, j mech phys solids, 55 (2001) 2157. [18] s. yi, s. gao, l. shen, int j solids struct, 38(24–25) (2001) 4463. [19] f. xiong, y. liu, acta mater, 55(16) (2007) 5621. [20] c. lexcellent, f. thiebaud, scripta mater, 59 (2008) 321. [21] c. lexcellent, m.r. laydi, v. taillebot, int j fract., 169(1) (2011) 1. [22] s. desindes, s. daly, int j solids struct, 47 (2010) 730. [23] c. maletta, f. furgiuele, acta mater, 58 (2010) 92. [24] c. maletta, m.l. young, j mat eng perform, 20(4–5) (2011) 597. [25] c. maletta, f. furgiuele, int j solids struct, 48(11–12) (2011) 1658. [26] c. maletta, int j fract, 177(1) (2012) 39. [27] t. baxevanis, d. lagoudas, int j fract, 175(2) (2012) 151. [28] g.r. irwin, in: proceedings of seventh sagamore ordnance materials conference, syracuse university press, syracuse, ny, (1960) 63. [29] p.p. milella, meccanica della frattura elastica e lineare. ansaldo nucleare, italy (1999). [30] c. maletta, a. falvo, f. furgiuele, j.n. reddy, smart mater struct, 18 (2) (2009) 025005. http://www.gruppofrattura.it http://dx.medra.org/10.3221/igf-esis.23.02&auth=true microsoft word numero_30_art_43 m. da fonte et alii, frattura ed integrità strutturale, 30 (2014) 360-368; doi: 10.3221/igf-esis.30.43 360 focussed on: fracture and structural integrity related issues the effect of steady torsion on fatigue crack growth under rotating bending loading on aluminium alloy 7075-t6 m. da fonte idmec & icems, department of mechanical engineering, nautical school fonte@enautica.pt l. reis, m. de freitas idmec & icems, instituto superior técnico, universidade de lisboa luis.g.reis@ist.utl.pt, mfreitas@dem.ist.utl.pt abstract. axles and shafts are of prime importance concerning safety in the transportation industry and railway in particular. design rules for axles and shafts are mainly based on endurance curves for the material used according to the established standards and procedures. recently, the knowledge of fatigue crack growth under typical loading conditions of axles and shafts with rotating bending and steady torsion is being object of research and industrial studies in order to apply damage tolerance concepts, mainly for maintenance purposes. the effect of a steady torsion on fatigue crack growth under rotating bending is focused in this paper. while axles and shafts in the transportation industry are traditionally designed on steels, the need for weight reduction due to fuel economy and eco-design constraints, lightweight materials must be considered for these applications. in this study, fatigue crack growth on rotating bending axles and shafts with or without an applied steady torsion is presented. fracture mechanics approaches are used to analyze the results based on stress intensity factors developed for bending and torsion in shafts and show fatigue crack growth retardation when steady torsion is applied. fractographic observations using sem are presented and helped to explain the fatigue crack growth retardation observed when steady torsion is applied to rotating bending. results are compared for the same loading conditions on steels and relevant differences on fatigue crack growth are commented. keywords. multiaxial fatigue; mixed-mode fatigue crack growth; axles; shafts. introduction ailure of railway axles has been a matter of concern since the development of railway industry and some dramatic failures have been reported from the early decades of the xix century. since the wöhler studies on fatigue failure of railway axles in the middle of the nineteen century, endurance curves determined under rotating bending tests constitute the most important data when designing against fatigue failure and avoid crack initiation. with the development of modern high speed trains, railway axles are submitted to more severe loading conditions and it is still a challenge for the test and design engineers to accurately determine the fatigue lifetime of railway components [1]. nowadays, due to the f m. da fonte et alii, frattura ed integrità strutturale, 30 (2014) 360-368; doi: 10.3221/igf-esis.30.43 361 need of weight reduction in the transportation industry, the use of lightweight materials is being considered and aluminium alloys are one of the most used metals for the weight reduction on mechanical components, therefore their use on axles and shafts may be considered. nevertheless, aluminium alloys are much more sensitive to fatigue crack growth than steels whereby damage tolerance studies must be performed before any industrial application. fatigue failure comprises three distinct phases: (i) crack initiation (including early crack nucleation and small crack growth), (ii) long crack growth and (iii) fast final failure. for long cracks, linear elastic fracture mechanics (lefm) is a powerful tool to predict fatigue crack growth that has been proved with excellent results in aeronautic industry and has been the main tool to perform damage tolerance analysis [2]. to predict fatigue crack growth through lefm, a stress intensity factor (sif) solution for the specific geometry is needed together with materials fatigue crack growth data. besides, shafts are also widely used in railway, automotive, aeronautic and energy industries and in this mechanical component both a torsion and bending load are combined. generally, fatigue failures in power shafts have origin on surface cracks that grow with semi-elliptical shape under cyclic bending, mode i (δki), combined with steady torsion, mode iii (kiii) [3]. large number of power plant systems run with a general steady torsion combined with cyclic bending stress either due to the self-weight bending during the rotation or possible misalignment between journal bearings [4]. in the case of power shafts such as those used in electric power plants, propeller shafts of screw ships, or any other rotary load-transmission devices, the lifetime spent between crack initiation and final fracture is of capital importance to improve the inspection intervals and maintenance procedures. many researchers have studied the influence of a static mode iii loading on cyclic mode i for circumferential notched shafts mainly since 80’s, such as akhurst and lindley [3], hourlier and pineau [5], yates and miller [6]. tschegg [7, 8] has done an important contribution to clarify the influence of steady or cyclic mode iii on fatigue crack propagation behaviour when combined with mode i loading. fonte and freitas [9] have studied the influence of steady torsion on fatigue crack growth of semi-elliptical cracks in shafts under rotating bending, and rotating bending combined with steady torsion. for the purpose a new testing machine was design and constructed. despite the relevant and practical importance of mixed-mode fatigue, the applications of fracture mechanics have been mainly focused on crack growth problems in mode i. several sif solutions have been proposed for semi-elliptical surface cracks under pure bending in round bars [10, 11]. fonte and freitas [12] have also presented sif for semi-elliptical surface cracks in round bars for both pure bending and pure torsion. freitas et al [1] carried out an experimental work in rotary bending specimens to simulate railway axles, and it was shown that the proposed sif are not directly applicable to the fatigue crack growth analysis because the position of fatigue crack front changes continuously during a load cycle. the maximum value of sif is not reached at the same rotation angle for all points along the crack tip profile and it is well-known that crack initiation process in rotor shafts has generally origin on the surface and the crack grows with a semi-elliptical shape. also in [13], both small and long fatigue crack growth data were obtained from rotating or alternate cyclic bending tests on a medium carbon steel (ck45) are presented and results are discussed. for small crack growth, an effective strain-based intensity factor range was proposed as the parameter which correlates small fatigue crack growth data under proportional or non-proportional multiaxial loading conditions. in this paper, the effect of a steady torsion load on fatigue crack growth due to cyclic bending in bars (axles or shafts) is studied for an aluminium alloy. results are commented and compared with previous studies on steels under the same loading conditions, allowing designers to have tools for damage tolerance analysis. experimental procedure material and specimens he material used in this study is the al 7075 t6 in the aged condition. the chemical composition of this aluminium alloy is presented in tab. 1 and the mechanical properties are presented in tab. 2. in rotating bending fatigue tests, classic cylindrical hourglass shaped specimens are used for the determination of s-n curves where the hourglass shape is adopted in order to localize the stress at the crack initiation and final failure. in this study, fatigue crack growth data for long cracks from a precrack will be studied, therefore the specimen geometry adopted was straight cylindrical specimens, fig. 1, with two different diameters, respectively 10 mm and 12 mm. all specimens were machined from round bars of 25 mm diameter. after machining, all specimens were polished and notched on the surface (chordal notch), approximately 3 mm length and 0.1 mm depth. all specimens were pre-cracked under constant amplitude cyclic bending stress until the arc crack length reaches a minimum length of 2 to 3 mm. t m. da fonte et alii, frattura ed integrità strutturale, 30 (2014) 360-368; doi: 10.3221/igf-esis.30.43 362 cu zn mg mn cr si fe ti al 1.267 5.66 2.72 0.05 0.197 0.156 0.228 0.21 bal. table 1: chemical composition of 7075 aluminium alloy. yield strength (mpa) ultimate tensile strength (mpa) a (%) 513 575 10.9 table 2: monotonic mechanical tensile properties of 7075 t6 aluminium alloy. figure 1: specimen used for fatigue crack growth data. testing procedure experiments for fatigue crack growth were performed in a rotating bending fatigue testing machine, fig. 2, which was designed and constructed to model the real conditions of axles and shafts in service [9]. figure 2: schematic of testing machine for rotating bending with or without steady torsion. the fatigue testing machine can perform rotary bending with or without steady torsion under load control either in bending or torsion. due to the load capacity of the machine presented in fig. 1, when higher torsion levels were required, the specimen diameter must be reduced, therefore two specimen diameters, were used, respectively 10 mm and 12 mm. rotating bending fatigue tests were carried out for nominal bending stresses from 140 mpa up to 190 mpa and nominal steady torsion from 60 mpa up to 127 mpa. tab. 3 presents the specimen diameters and loading conditions used on fatigue crack growth tests, representing a wide range of bending stresses and steady torsion. these testing conditions refers to multiaxial loading, with a cyclic normal stress, σ, and a static shear stress, τ, therefore it is helpful to full characterize the stress state during a cycle loading. tab. 3 also presents the ratio between the maximum normal and the maximum shear stress achieved in each loading cycle as well as the maximum and minimum principal stresses, si,max and siii,min, the maximum shear stress τmax and the maximum equivalent (von mises equation) stress σequiv,max. the detection of fatigue crack initiation from the notch and surface crack length measurements were carried out with an optical microscope at a magnification of 80x. measurements of crack length were obtained at constant intervals, interrupting the tests, till the crack depth reaches approximately 3/4 r. in some selected specimens the crack front shape dynamometer m. da fonte et alii, frattura ed integrità strutturale, 30 (2014) 360-368; doi: 10.3221/igf-esis.30.43 363 was marked through beach marks, using a lower bending stress level in order to obtain experimentally the crack shape geometry i. e. crack length vs. crack depth. diameter d (mm) bending σ (mpa) torsion τ (mpa) τ/σ si,max (mpa) siii,min (mpa) τmax (mpa) σeqiv,max (mpa) 10 162 0 0 162 0 81 162 10 162 112 0.691 219 -57 138 252 10 140 127 0.907 215 -75 145 260 12 146 0 0 146 0 73 146 12 152 0 0 152 0 76 152 12 182 0 0 182 0 91 182 12 190 0 0 190 0 95 190 12 152 71 0.467 180 -28 104 195 12 158 60 0.379 178 -20 99 189 12 190 71 0.373 214 24 118 226 table 3: specimen dimensions and loading conditions. results everal torsion stress levels and two specimen diameters were used in order to determine the effect of torsion on fatigue crack growth rates obtained by rotating bending. fig. 3 a) and 3 b) shows two examples of the fracture surface of two different specimens with two different loading cycles, respectively rotating bending, and rotating bending with steady torsion. it is clearly seen that crack initiation starts from the notch, growing in the radial direction under an elliptical shape and when a steady torsion is applied a different crack growth rate is observed for both sides of the semi-elliptical crack shape, as already mentioned in [9] for steels under similar loading conditions. the geometric parameters of cylindrical specimens and semi-elliptical crack dimension are characterized according to shiratori nomenclature [11] as shown in fig. 4 and also adopted in [12], i.e. the semi-arc crack length is denoted by s and the minor semi-ellipse axis corresponding to the maximum crack depth is denoted by b. a) b) figure 3: fracture surfaces for: a) pure rotating bending (symmetrical crack growth); b) rotating bending with steady torsion (nonsymmetrical crack growth). s m. da fonte et alii, frattura ed integrità strutturale, 30 (2014) 360-368; doi: 10.3221/igf-esis.30.43 364 the semi-elliptical crack depth b was related with the total arc crack length 2s and agrees with the equation b=2s/π already found before in previous experimental tests for pure rotary bending and mixed-mode [1, 9] as shown in fig. 3. some deviation for the largest applied torques was found, however for the crack depth b up to r/2 the equation is still valid. figure 4: geometry parameters of semi-elliptical surface crack. fatigue crack growth tests were performed under two different loading conditions respectively: (i) cyclic bending; (ii) cyclic bending with a steady torsion, and results were first analyzed in crack length versus number of cycles. crack growth results determined for two specimens diameters, with and without steady torsion, are presented in fig. 5 a) for the arc crack length, 2s as a function of number of cycles, n after precrack initiation, for 4 specimens of 10 mm diameter, where bxxx denotes the bending stress and txxx the torsion stress levels corresponding to two bending/torsion stress ratios, respectively 0.7 and 0.9. fig. 5 b) presents similar results for 12 mm specimen diamenter ad only one bending/torsion stress ratio. results presented in fig. 5 clearly show that there is an influence of a steady torsion in crack growth under rotating bending, where it can be seen that for lower levels of steady torsion similar trends of crack growth are obtained for both loading conditions, with and without steady torsion; in opposite, for the highest steady torsion applied to rotating bending, a crack growth retardation is observed, which is consistent with previous results from the authors for similar fatigue tests in steels [9]. therefore a significant effect of steady torsion on fatigue crack growth can be observed for the levels of torsion presented. results show that fatigue crack growth rate in rotating bending can decrease in the presence of a steady torsion and this retardation effect increases with the level of steady torsion, even though the von mises equivalent stress increases. a) b) figure 5: arc crack length evolution with number of cycles: a) 10 mm specimen diameter; b) 12 mm specimen diameter. m. da fonte et alii, frattura ed integrità strutturale, 30 (2014) 360-368; doi: 10.3221/igf-esis.30.43 365 discussion stress intensity factors ssuming that cracks have always a semi-elliptical shape as shown in fig. 4, the points on crack front at deepest crack depth (a) and where the crack intersects the external surface (points b and c) are the most important ones. the semi-ellipse axes are obtained according to the equation b=2s/π experimentally obtained [1, 9], and eq. (1) was deducted.  2 2 2 cos1 b r 1 senr a      (1) the major research field of fracture mechanics is the determination of the stress intensity factors. in this study, sif for mode i and mode iii along the crack front of semi-elliptical surface cracks normal to the axis in shafts subjected to bending, torsion and bending-torsion simultaneously, determined by a three-dimensional finite-element analysis [12] will be used. the total arc crack length 2s was chosen as the experimentally obtained crack parameter in fatigue crack growth tests and according to shiratori et al [11] and freitas et al [12]. therefore the mode i stress intensity factor ki for any point along the surface crack was obtained by the equation: sb),,(fk sa b r b ii  (2) where bs is the remote applied bending stress, s is the half arc crack length and fi is the boundary correction factor or the dimensionless sif for mode i which is a function of the semi-elliptical crack shape (b/a), relative crack depth (b/r) and of the position points along the crack front defined by the parametric angle φ, fig. 3, which was determined taking into account the fem calculations presented in [12]. as indicated before, limited results for the sif of semi-elliptical surface cracks in round bars subjected to torsion stress levels are available, and the results presented in [12] are used in this paper. therefore, sif kiii will be obtained using the same geometric parameters that were used for mode i (bending): st),,(fk sa b r b iiiiii  (3) where ts is the remote applied torsion stress on the outer surface of the shaft, s is the half arc crack length and fiii is the boundary correction factor for mode iii which is a function of the semi-elliptical crack shape (b/a), relative crack depth (b/r) and of the position along the crack front determined by the referred parametric angle φ in fig. 3 that was determined taking into account the fem calculations described in [12]. mixed-mode crack growth under multiaxial loading most of fatigue crack growth studies have been done on single-mode loading and usually are performed under mode i loading condition. however, single-mode loading seldom occurs in practice, and in many cases cracks are not normal to the maximum principal stress direction. the multiaxial mixed-mode fatigue crack growth is a common problem in many engineering structures and components. for long cracks, the propagation mechanisms are often analyzed using linear elastic fracture mechanics approach. under combined axial and torsion loading, the surface corner of the semi-elliptical crack has mixed mode i+mode ii, but at maximum depth of the semi-elliptical cracks has only mixed mode i+mode iii [12]. for mixed-mode loading, one can assume that the fatigue crack growth rate may be expressed by the paris law where the stress intensity factor range is replaced by an equivalent sif range, ∆keq:  meqkc dn da  (4) there are many approaches proposed to define the equivalent sif range ∆keq for mixed-mode loadings. one of them is based on the addition of the irwin’s elastic energy release rate, g parameters for the three loading modes:      212iii2ii2i21totaleq kv1kkegk   (5) a m. da fonte et alii, frattura ed integrità strutturale, 30 (2014) 360-368; doi: 10.3221/igf-esis.30.43 366 where δki, δkii and δkiii are the stress intensity factors for mode i, ii and iii respectively and e and ν are the elasticity modulus and the poisson’s ratio. therefore, eq. (4) can be used to correlate the fatigue long crack growth data in a mixedmode loading condition. fatigue crack growth under rotating or alternate (reversed) bending a stress ratio r=-1 exists, therefore δkimax=-δkimin and according to the recommendations specified on astm e647, in this study δki=kimax will be used. for static torsion δkiii=0, therefore eq. (5) is reduced to δki, since only mode i is activated in cyclic loading. fig. 6 shows the fatigue crack growth rate as a function of the mixed-mode equivalent energy release range which in this case reduces to the mode i stress intensity factor range, determined as mentioned before, for several loading conditions and 10 mm and 12 mm diameter specimens: rotary bending, and bending conditions combined with steady torsion. as observed in fig. 6, an effect of steady torsion on fatigue crack growth (fcg) rate is observed. results show that fatigue crack growth in rotating bending decreases with higher levels of steady torsion while for lower levels of steady torsion a small retardation effect is observed. these results represent a similar trend to the one obtained in steels under the same loading conditions that were presented before [9, 13]. a) b) figure 6: fatigue crack growth a) 10 mm specimen diameter; b) 12 mm specimen diameter fractography scanning electron microscopic (sem) observations were carried out for both types of fracture surfaces, pure mode i, due to rotating bending only, and mode (i+iii) due to rotating bending and steady torsion, and the crack growth profiles created by two different types of loading are shown in fig. 7 a) and b) respectively. they correspond to the formation of regular sets of inclined micro facets corresponding to mode i crack growth inclined due to mode iii loading, and are similar to the “factory roof” markings observed in previous similar studies. this “factory roof” crack growth is completely “rubbed” by the strong torque imposed during rotating bending. while some “rubbing” is also visible on crack growth due to rotating bending, this is due to the tension/compression loading cycle observed in rotating bending. the rubbing of the fracture facets is very well observed in fig. 8 a) and b) which shows the fracture surface near the initial phase of fatigue crack growth and much more clearly on fig. 8 b), where the higher amplification clearly shows two types of fracture facies, one strongly “rubbed” at the tip of “factory roof” fracture followed by more “normal” facies characteristic of fatigue crack growth under mode i. m. da fonte et alii, frattura ed integrità strutturale, 30 (2014) 360-368; doi: 10.3221/igf-esis.30.43 367 a) b) figure 7: sem micrographs a) bs=190 mpa; ts=0; b) bs=152 mpa_ts=71 mpa a) b) figure 8: sem micrographs bs=152 mpa_ts=71; a) initial crack growth b) crack growth path conclusions he effects of steady torsion on fatigue crack growth under cyclic bending were studied for long crack growth on aluminium alloy 7075-t6 specimens under multiaxial fatigue loading conditions. for long cracks a superimposed steady mode iii loading to a crack growing in cyclic mode i can lead to significant fatigue crack growth retardation, depending of the ratio between maximum bending stress and maximum steady torsion. crack growth rates decrease with increasing mode iii for cyclic mode i (δki) + static mode iii (kiii) loading. these results are consistent with similar ones obtained for ck45 steels for the same loading conditions, therefore the retardation effect on crack growth can be considered as an effect of the steady torsion on rotating bending. due to steady torsion effect superimposed to rotating bending, the crack path is in zig-zag which creates a helical surface crack morphology. fractographic observations lead to the conclusion that this retardation effect is due to a significant higher irregularity on fatigue crack path which is observed when steady torsion is applied to rotating bending. references [1] de freitas, m., françois, d., analysis of fatigue crack growth in rotary bend specimens and railway axles. fat fract engng mater struct, 18 (1995) 171-78. t m. da fonte et alii, frattura ed integrità strutturale, 30 (2014) 360-368; doi: 10.3221/igf-esis.30.43 368 [2] newman, j. c., philips, e. p., swain, m. h., everett, r. a., fatigue mechanics: an assessment of a unified approach to life prediction. astp stp 1122 (1992), pp 5-27. [3] akhurst, k. n., lindley, t. c., nix, k. j., the effect of mode iii loading on fatigue crack growth in a rotating shaft. fatigue engn struct, 6 (1983) 345-348. [4] fonte, m., de freitas, m., marine main engine crankshaft failure analysis: a case study, engineering failure analysis 16 (2009) 1940–1947. [5] hourlier, f, mclean, d, pineau, a., fatigue crack growth behaviour of ti-5al-2.5sn alloy under complex stress (modei+steady mode iii). metals tech, 1978:154-158. [6] yates, j.r., miller, k.j., mixed mode (i+iii) fatigue thresholds in forging steel. fatigue engng mat struct, 12 (1989) 259-270. [7] tschegg, e.k., stanzl, s., mayer, h., czegley, m., crack face interactions near threshold fatigue crack growth, fatigue fract engng mater struct, 16 (1983) 71-83. [8] tschegg, e.k., mode iii and mode i fatigue crack propagation behaviour under torsional loading, j mat science, 18 (1983) 1604-1614. [9] fonte, m., freitas, m., semi-elliptical crack growth under rotating or reversed bending combined with steady torsion. fat fract engng mater struct, 20 (1997) 895-906. [10] raju, i.s., newman, j.c., stress intensity factors for circumferential surface cracks in pipes and rods under tension and bending loads, fracture mechanics, astm stp 905 (1986) 789-805 [11] shiratori, m., miyoshi, t., sakay, y., zhang, g.r., factors analysis and application of influence coefficients for round bar with a semi-elliptical surface crack. murakami y. editor. handbook of stress intensity factors, ii; pergamon press, oxford, 1987:659-65. [12] fonte, m., freitas, m., stress intensity factors for semi-elliptical surface cracks in round bars under bending and torsion. int j of fatigue, 21 (1999) 457-463. [13] de freitas, m., reis, l., da fonte, m., li, b., effect of steady torsion on fatigue crack initiation a nd propagation under rotating bending: multiaxial fatigue and mixed-mode cracking. engineering fracture mechanics, 78 (2011), 826-835. microsoft word numero 22 articolo 8.doc h. singh et alii, frattura ed integrità strutturale, 22 (2012) 69-84; doi: 10.3221/igf-esis.22.08 69 cold spray technology: future of coating deposition processes harminder singh guru nanak dev university, regional campus, jalandhar, punjab-144007, india harminder10@gmail.com t.s. sidhu shaheed bhagat singh college of engg. & tech., ferozepur, punjab, india s.b.s. kalsi amritsar college of engineering & technology, amritsar, punjab, india abstract. cold spray (cs) belongs to a wide family of thermal spray technology with the difference that it is a solid state process in which spray particles are deposited via supersonic velocity impact at a temperature much below the melting point of the spray material. this paper briefly describes the various aspects of this rapidly emerging technology, with almost all the important parameters which affect the deposition behavior along with advantages and limitations; applications and history of emergence of this process is also reviewed. though this technology emerges three decades ago but still it could not establish itself as viable practical industrial technology. hence, the efforts, along with funding from public/private sources are required to commercialize this coating process. it is expected that next decade will saw the growth of cold spray as a viable coating process around the globe. keywords. cold spray; thermal spray; coating; corrosion. introduction old spray(cs) is a relatively recent spray technology which falls under the larger family of thermal spray processes[1], and there are different approaches known by different names such as: cold gas dynamic spraying, kinetic spraying, high velocity particle consolidation (hvpc), high velocity powder deposition and supersonic particle/powder deposition (spd). the basic principle of the cold spray process is very simple: a high velocity (300 to 1200 m/s) gas jet, formed using a delaval or similar converging/diverging nozzle, is used to accelerate powder particles (1 to 50 µm) and spray them onto a substrate, located approximately 25 mm from the exit of the nozzle. where they impact and form a coating. the kinetic energy of the particles rather than high temperature, helps these particles to plastically deform on impact and form splats, which bond together to produce coatings and thereby avoids or minimizes many deleterious shortcomings of traditional thermal spray methods such as high-temperature oxidation, evaporation, melting, crystallization, residual stresses, gas release. in this process, powder particles are accelerated by the supersonic gas jet at a temperature that is always lower than the melting point of the material, resulting in coating formation from particles in the solid state and hence no melting and solidification process is experienced by the powders like in traditional thermal spray process [2, 3]. c http://dx.medra.org/10.3221/igf-esis.22.08&auth=true http://www.gruppofrattura.it h. singh et alii, frattura ed integrità strutturale, 22 (2012) 69-84; doi: 10.3221/igf-esis.22.08 70 moreover, the footprint of the cold spray beam is very narrow typically around 5 mm diameter due to small size of the nozzle (10-15 mm2) and spray distance (5-25 mm), yielding a high-density particle beam, results in precise control over the area of deposition over the substrate surface. this process is similar to a micro shot peening and hence the coatings are produced with compressive stresses, rather than tensile stresses, which results in dense and ultra thick (5-50 mm) coatings without adhesion failure. the low temperature formation of coating leads to oxides and other inclusions -free coatings with wrought-like microstructure [2]. cold spray (cs) system he cs system can be designed in either portable or manual and robotic or fixed systems. the gasses having aerodynamic properties are generally used to propel the powder particles, as: 1) helium 2) nitrogen 3) mixture of he and n2 4) dry air (79% n2 21% o2) the main components of cs system includes [4]:  powder feeder (powders used are in the range of 1 to 50 μm in diameter)  source of a compressed gas  gas heater to preheat the gas, to compensate for the cooling due to rapid expansion in nozzle  supersonic nozzle (delaval nozzle)  spraying chamber with a motion system  system for monitoring and controlling spray parameters (to measure and control the gas temperature and pressure) types of cs system uring the practical development of cold spray technology, two methods of injecting the spray materials into the nozzle were patented, leading to what is known today as high pressure cold spray (hpcs) and low pressure cold spray (lpcs) system. the two main distinctions of these two systems are; the utilisation of 5-10 bars pressure gas in lpcs instead of 25-30 bars in hpcs and the radial injection of powder in lpcs instead of axial injection in hpcs [1, 4]. low pressure cold spray (lpcs) in low-pressure cold spray the accelerating gas, usually air or nitrogen, at relatively low pressure (5-10 bar) and preheated (up to 550oc), within the gas heater to optimize its aerodynamic properties, and then forced through a ‘delaval’ nozzle. at the diverging side of the nozzle, the heated gas is accelerated to about in the range of 300 to 600 m/s. solid powder particles are radially introduced downstream of the throat section of the supersonic nozzle and accelerated toward the substrate as shown in the fig.1of the lpcs system. the feedstock particles are effectively drawn in from the powder feeder by venturi effect, i.e. by keeping the static pressure within the nozzle below the atmospheric pressure. this is achieved if the ratio of the cross-sectional area of the supersonic nozzle at the powder entry point, ai (m2) to that of the throat (a*) satisfies following equation: ai/a*≥1.3po+0.8 where; po = gas pressure at the nozzle inlet (mpa) [4]. due to the elimination of the need of a high pressure delivery system in lpcs, there is improvement in its operational safety, system is more portable, flexible in automation, and spraying cost also reduced significantly than a hpcs system, but the deposition efficiency with this system typically do not exceed 50%. also in this system the powder particles does not pass through the throat, hence wear of the nozzle walls occurs only in the supersonic portion of the nozzle and, this ensures a longer service life of the nozzle. additionally, a lpcs system is more compatible with a number of system modifications. high pressure cold spray (hpcs) in high-pressure cold spray, the accelerating gas helium or nitrogen at high pressure (25-30 bar) is preheated (up to 1000 °c) to optimise its aerodynamic properties (not to increase particle temperature) and then forced through a convergingdiverging ‘delaval’ nozzle. at the nozzle, the expansion of the gas produces the conversion of enthalpy into kinetic energy, which accelerates the gas flow to supersonic regime (1200 m/s) while reducing its temperature. the solid powder feedstock particles mix with the propellant gas in the pre-chamber zone and are then axially fed into the gas stream, upstream of the converging section of the nozzle at a higher pressure than the accelerating gas to prevent backflow of the carrier gas to the powder feeder as shown in fig. 2. the accelerated solid particles (600 to 1200 m/s) impact the substrate t d http://dx.medra.org/10.3221/igf-esis.22.08&auth=true http://www.gruppofrattura.it h. singh et alii, frattura ed integrità strutturale, 22 (2012) 69-84; doi: 10.3221/igf-esis.22.08 71 with enough kinetic energy to induce mechanical and/or metallurgical bonding. the spray efficiency in this hpsc system is very high, reaching up to 90% as compared to 50 % in lpsc system. moreover, the temperature of particles remain substantially below the initial gas preheat temperature due to short contact time of spray particles with the hot gas called dwell time and hence the name cold spray coating [4]. figure 1: operating principle of low-pressure coldspray [1]. figure 2: operating principle of high-pressure coldspray [1]. history of the invention (1900-2011) he basic idea behind cold spray is fairly simple and the concept has already been patented in the early 20th century. the invention of the cold spray process can be dated back to the time of the invention of the thermal spray process by schoop. though, the idea of using the impact energy of the particles to produce a coating using a carrier gas jet to accelerate solid particles had been in use for a century or more. however, the technology needed to put the idea into practical use was complex at the time and required further development. consequently, it took 80 years for its first demonstration that happened accidentally during a two-phase flow gas dynamic experiment in russia. the cold spray technique can also be viewed as an offshoot of the cold war between the superpowers. while studying models subjected to a supersonic two-phase flow (gas + solid particles) in a wind tunnel at russian academy of science, scientists observed that during the impact of particles of various sizes, impact angles, and velocities on various materials, the solid particles deposited onto the surface when the velocity of impact was higher than certain critical value. since then, efforts have been devoted for the development of this process into a practical industrial technology and the number of related patents and research publications has grown exponentially. a brief view of the development of this process from 1900 to present is as follows [5]: 1902: on august 12, 1902, thurston patented, "a method for carrying out the process of coating one metal with another”. 1915: march 30, 1915 schoop patented thermal spray process. schoop developed the process wherein molten metal droplets are sprayed onto a surface to produce the coating, viz., the thermal spray process, when he observed that if mud balls are shot onto a wall, they get deposited on impact onto the wall forming a mud deposit. however, during this invention he overlooked the impact energy in the mud balls that led to deposit formation. if schoop had taken note of the basic phenomenon of his invention, solid state deposition by impact energy, cold spray would have been the first thermal spray process and not the most recent one. t http://dx.medra.org/10.3221/igf-esis.22.08&auth=true http://www.gruppofrattura.it h. singh et alii, frattura ed integrità strutturale, 22 (2012) 69-84; doi: 10.3221/igf-esis.22.08 72 1970 -1980: in the late 1980s, alkhimov, anatoli papyrin and their team at institute of theoretical and applied mechanics of the siberian division of the russian academy of science (itam of ras) in novosibirisk, developed a "method of applying coating", by converting the wind tunnel experiments into a viable coating technique and patented it. 1990-2000:  a u.s. government sponsored collaborative research and development agreement (crada) under the national center for manufacturing sciences (ncms) brought cold spray out of russia. under this crada, anatoli papyrin, the leader of the cold spray group in russia, moved to the u.s., built a system at ncms, and carried out basic studies. albert kay, asb industries, visited ncms and bought the license to build cold spray systems and use them for supplying industrial coatings.  heinrich kreye, german armed forces university, hamburg, did a large and exhaustive study on all aspects of the cold spray process, including theory, modeling, design and development of guns and nozzles, preparation and characterization of coatings, and development of application coatings. german aerospace industry (eads) also initiated cold spray research directed towards both protective coatings and fabrication of bulk forms. so, during this period the cold spray process developed into an engineered coating process and modeling studies were taken up and various diagnostic techniques were developed to understand and enhance performance of this process. systematic spray optimization experiments were executed to produce and characterize various coating materials. 20002006: germany realized that the availability of a reliable cold spray system to produce reproducible coatings was of paramount importance and that cold spray system development is a multi-disciplinary one. hence, they formed a consortium of federal armed forces university, hamburg; linde r & d; and cgt technologies to pool their respective specialties in materials science, gas technology and process control equipment to evolve the kinetic 3000 cold spray system. a large number of spray experiments were carried out, which resulted in many industrial applications including the world's first mass production application of the cold spray process, viz., thermal management layers on high performance heat sinks. 2006-present: at the present time the cold spray method is recognized by world leading scientists and specialists. a wide spectrum of research is being conducted at many research centres and companies in many countries and it has been established as a viable coating process to produce protective coatings, performance enhancing layers, ultrathick coatings, freeforms, and near net shapes. governments of various countries have realized the importance of this technology and various projects are sanctioned to commercialize this technology. recent study concentrate on optimizing cold spray parameters to produce coatings of many materials with desired microstructures. figure 3: comparison between different thermal spraying processes[30]. http://dx.medra.org/10.3221/igf-esis.22.08&auth=true http://www.gruppofrattura.it h. singh et alii, frattura ed integrità strutturale, 22 (2012) 69-84; doi: 10.3221/igf-esis.22.08 73 advantages of cs oating technology has rapidly advanced with the addition of cold spray coating techniques. the major advantage over thermal spray techniques are the low temperatures involved which minimize any potential phase change and keep the particles in their unmodified solid state. the difference between the cold spray process(hvpc) and other thermal spray processes is illustrated in fig. 3. in the thermal spray process, a coating is formed by melting the coating material and then quenching the molten droplets. hence thermal sprayed coatings in general have microstructures with varying degrees of porosity, oxides and other inclusions, and low corrosion resistance characteristics [2]. however, cs process has advantage of metal deposition with low heat input, local deposition to limited area, and deposition free of oxides and other inclusions can be produced to any metal surface, and due to compressive stresses, the dense uniform deposit of any thickness with wrought-like microstructure are obtained. moreover, the oversprayed expensive raw material can be collected for reprocessing [2, 6]. mechanism of cold spray process he bonding mechanism in thermal spraying can be explained by the occurrence of local adiabatic shear instabilities,at particle-substrate and particle-particle interfaces due to thermal softening, however the true bonding mechanism in cold spray process is still poorly understood [7, 8]. by means of a so-far widely accepted model; during impact, the solid particles undergoes plastic deformation, disrupt thin surface films (oxides), and in turn, intimate conformal contact is achieved and combined with high contact pressure, promotes bonding with the target surface[9, 10].the common phenomena that have been observed during spraying onto various substrates are substrate and particle deformation, and substrate melting as there is evidence for the formation of a metal-jet [7, 11] as shown in fig. 4, in which 20 µm copper sphere impacting an aluminum plate at 650 m/s is modeled. it shows the material adjacent to the interface behave as a viscous fluid-like, results in the formation of interfacial waves, roll-ups, and vortices [11]. figure 4: impact of a cu particle on a cu substrate at successive times:(a)5 ns, (b)20 ns, (c)35 ns, (d)50 ns [11]. it has been suggested that the adhesion strength of the particles in cold spraying is solely to their kinetic energy at impact, which is typically much less than the energy required to melt the particle and hence cold spray is a solid-state process [8, 9]. this concept is explained in the eds image fig.5 of cold sprayed copper deposit on aluminium substrate, examined by champagne et al. [11]. it shows the forced mixing between the deposited copper (light area) and the aluminum substrate (dark region), and that can be achieved through deep-impact penetration of the copper into the aluminium [11]. this theory would also explain the minimum particle velocity necessary to achieve deposition, because sufficient kinetic energy must be available to plastically deform the solid material [9, 10]. an empirical model by champagne et al. [11] shows that interface mixing depends on the substrate hardness and coating material density, and the particle velocity (m/s) vp needed for the attainment of interfacial mixing, as: vp = [(7.5 x 104)(b/ρ)]0.5, where b is the substrate brinell hardness c t http://dx.medra.org/10.3221/igf-esis.22.08&auth=true http://www.gruppofrattura.it h. singh et alii, frattura ed integrità strutturale, 22 (2012) 69-84; doi: 10.3221/igf-esis.22.08 74 number and ρ is the particle density (kg/m3). lupoi et al. [12] examined that during cold spray process cu particles creates more erosion of substrate as compared to al and sn, due to their low specific weight as compared to cu. figure 5: eds image of cu coating on al [11] & schematic of mechanical locking [35]. particle velocity (vp) and critical velocity (vc) t has been widely accepted that particle velocity (vp) prior to impact is one of the most important parameters in cold spraying. it determines whether deposition of a particle or erosion of a substrate occurs on the impact of a spray particle. generally, for a given material, there exists a minimum particle velocity commonly known as critical velocity (vc) which must be achieved for transition from erosion of the substrate to deposition of the particle occurs. only those particles achieving a velocity higher than the critical one can be deposited to produce a coating [2, 7, 13]. the three main stages for the cold spray coating build up and its relation with vp, vc is shown as: first stage/ initial stage induction time or delay timethe time between the beginning of surface treatment by the flow of particles and the beginning of particle attachment to the surface[7]  vp < vc , particles simply reflect (bounce) off the surface. [2]  vp =vc, then solid particle erosion of the surface occurs without any deposition. fig.7 shows three regions, divided by two values of particle velocity: vcr1 and vcr2 [7] 1. vp<vcr1, large number of particle impacts before their adherence to the surface. 2. vcr1 < vp < vcr2, particles adhere to the surface only after some delay. 3. vp > vcr2 (850 m/s), particles adhere to the initial surface without any delay time. second stage particles plastically deform and adhere to the substrate and a first thin layer of the particle material is formed [7], fig.6 vc depends upon the combinations of spray materials and the substrates [14] third stage the particles interact with the surface formed by previously incident particles in second stage it’s a build-up stage, characterized by the growing thickness of the coating layer[7] vc different from the second stage, as this corresponds to the spray material impacting on the substrate of the same compositions as the powder [14] there is the up-limit to the velocity, over which a strong erosion is generated. coating build-up only if vp less than uplimit velocity. with most spray materials the up-limit velocity is higher than 1000 m/s [14] the critical particle velocity, as reported by many authors [2, 7, 13, 14, 15]changes with the spray material, approximately 560– 580, 620–640, 620–640 and 680–700 m/s, for cu, fe, ni and al respectively. however, there is variation in critical velocity is observed like for cu as reported [11] critical velocity of 500m/s and li et al. [16] examined in the range from 298 to 356 m/s. this variation of vc is due to its dependence on many factors mostly on the thermo-mechanical properties of the substrate and the spray powder material and the particle velocity vp is a function of the spray conditions, including physical properties or nature of the driving gas, its operating temperature and pressure and nozzle design of the spray gun and material properties, such as particle diameter, size distribution of particles in powder, density and morphology of powder [2, 7, 13, 14, 15]. i http://dx.medra.org/10.3221/igf-esis.22.08&auth=true http://www.gruppofrattura.it h. singh et alii, frattura ed integrità strutturale, 22 (2012) 69-84; doi: 10.3221/igf-esis.22.08 75 figure 6: the schematic view of different region of particles on substrate [7]. figure 7: induction (deposition delay) time vs. the mean impact velocity of al particles on a polished cu substrate [7]. splat adhesion cold spray process transfers momentum from the supersonic gas jet to the particles results in high velocity particle jet. these powder particles, on impact onto the substrate surface, plastically deform and once bonded to the substrate these particles are known as splats. the interlinking of these splats build up the coating during the process [2, 8]. the relationship between the splat diameter (d) and the diameter of the initial droplet (d) for cold spray is given by lima et al. [10]. the degree of spreading (d/d) is directly proportional to the velocity and inversely proportional to the yield stress (σy ) of the particle as: (d/d)α(ρ, vp , d) α−1(σy ), where ρ, σy and vp are the density, yield stress and the particle impact velocity, respectively. hence, the particles with the same yield stress, density and approximately same size will present larger spreading for higher velocities of impact. so there will be smoother coatings with high impact velocities, which rises with the rise of temperature of the gas. hence, lima et al. [10] reported the decrease of roughness, increase of deposition efficiency, microhardness and elastic modulus of the cold spray coating with the rise of the gun temperature and also with decrease of spray distance for ti cold spray coatings on aluminium pipes. dickinson et al. [8] noticed the increase of splat adhesion with rise of pressure from 0.4 mpa to 1 mpa cold sprayed tio2 particles on a stainless steel substrate. also results shows that smaller splats (< 5 µm) had higher adhesion strengths than larger splats (> 5 µm). also the low yield http://dx.medra.org/10.3221/igf-esis.22.08&auth=true http://www.gruppofrattura.it h. singh et alii, frattura ed integrità strutturale, 22 (2012) 69-84; doi: 10.3221/igf-esis.22.08 76 strength of aluminum and copper may be one of the reasons of highly dense and low porosity of their cold spray coating [10]. effect of particle diameter the particle velocity is inversely related to particle diameter as: vp = k/dn, where vp is the particle velocity, k and n are the coefficients related to driving gas conditions for a certain material [15]. the dependence of vp on the particle diameter under different spray conditions of temperature, pressure for nitrogen (c1, 2, 3) and helium (c4) gas is shown in fig.8 for copper powder [16]. the converging-diverging de laval nozzle with throat diameter 2mm, expansion ratio 9 and downstream length 100 mm is used with same carrier and main gas. it is shown that particle velocity decreases for all conditions with increase of particle diameter and decrease is remarkable when particle size is small particularly in the range of 20µm [15]. figure 8: particle velocity vs. particle diameter for different gas conditions [15]. nature of carrier gas regarding carrier gas type, though pre-heated nitrogen gas is used for a wide diversity of materials, but other hard materials cannot be deposited with nitrogen gas because higher velocity is required. helium provides therefore a solution since it is inert and allows reaching the highest particle velocity. yoon et al. [17] reported the enhancement of deposition efficiency when process gas changed from nitrogen to helium during cold spraying of nitizrsisn amorphous powder. it is reported by li et al. [16] that under all conditions the particles accelerated to higher velocity using helium as compared to nitrogen as driving gas. helium is however 10 times more expensive than nitrogen, making it economically unviable for many applications unless recycled. however, a helium recovery system (hrs) installed at canada, recovers helium from the cold spray chamber with sufficient purity (>99%) allowing for a cost-effective operation by insuring a recovery rate of above 85% [18]. in some applications mixture of helium (he) and nitrogen (n2) is used as carrier gas. nitrogen (n2), being a diatomic gas, and its addition into he increases the enthalpy of the carrier gas for better heat-transfer with spray particles, but it also reduces the velocity due to the heavier atomic mass resulting in coatings with reduced density and hardness[19]. however, high corrosion resistance is reported by balani et al. [19], for cold spray of 1100 al onto 1100 al substrate using he–20 vol.%n2 as carrier gas compared to 100 vol.% he processed coating, though both the cold-sprayed coatings were more corrosion resistant compared to the 1100 al substrate and coating by 100 vol.% he is more hard and dense. effect of temperature the velocity of the gas at the throat (vt) of the laval nozzle is also a function of its temperature as: vt = (γ rtt )0.5, where γ is the ratio of gas specific heats, r is the specific gas constant, tt is the gas temperature at the throat, respectively[10]. hence the particle velocity increases with an increase in gas temperature. though, gas pre-heating provides higher particle velocity but it also raises the risk of oxidation and/or nitridation which in turn can be detrimental for the design functionality of applied coatings[18]. however, it is also reported that at higher temperatures the gas http://dx.medra.org/10.3221/igf-esis.22.08&auth=true http://www.gruppofrattura.it h. singh et alii, frattura ed integrità strutturale, 22 (2012) 69-84; doi: 10.3221/igf-esis.22.08 77 density and viscosity will decrease and hence the drag force of the gas, which is the force responsible for particle acceleration should decrease at higher gas temperatures and hence this area needs to be further explored[10]. it is also reported that critical velocity (vc) decrease with the increase in the particle temperature by about 14m/s with a temperature increment of 100oc, due to the thermal softening effect, shown in fig.9, [16]. figure 9: critical velocity vs. mean particle temperature [16] effect of oxidation condition li et. al.[14], has reported the dependence of critical velocity on the particle oxidation conditions. it is reported that the large discrepancy among the critical velocities for copper particle can be attributed to the difference in oxygen content of the copper powder. the results as shown in fig.10 showed that with copper powder the critical velocity(vc) changed from about 310 m/s at an oxygen content of 0.02 wt.% to 610 m/s at an oxygen content of 0.38 wt.% and with nickelbased monel alloy, the critical velocity was increased from 583 to 632 m/s as the oxygen content was changed from 0.016 to 0.108 wt.%. the study revealed that at high oxygen content, sprayed particles need to break and extrude the oxide scale on impact, therefore the critical velocity is dominated by oxide on the powder and is independent of the material properties as compared to low oxygen content materials. figure 10: effect of oxygen content on the critical velocity of different spray materials [14]. effect of nozzle design however, improvements in nozzle design using gas dynamic models have lead to higher deposition velocities and the ability to deposit larger particles, which results in denser coatings and higher deposition efficiency. so the particle velocity is also influenced by the nozzle design like its nozzle inlet diameter, throat diameter, exit diameter or expansion ratio (i.e., the ratio of the area of the exit to the throat), the entrance convergent section length (upstream length)and the divergent exit length(downstream length). it is found that increasing the length of the nozzle has a significant effect on particle http://dx.medra.org/10.3221/igf-esis.22.08&auth=true http://www.gruppofrattura.it h. singh et alii, frattura ed integrità strutturale, 22 (2012) 69-84; doi: 10.3221/igf-esis.22.08 78 velocity. it is examined that the calculated velocity of a 12 µm copper particle can be increased from 553 m/s to 742 m/s, with a 33% increase in particle velocity by increasing the length of the nozzle from 83mm to 211mm, with nitrogen as the carrier gas. this increased velocity leads to an increase in the deposition efficiency from less than 10% to close to 80%. however, there are fabrication and material constraints that limit the practical length of the nozzles. so new materials need to be tried to improve powder flow through the nozzle and optimization in design is required to minimize the gas flow through the nozzle [20]. karthikeyan [21] used specially designed tungsten carbide nozzle for coating on a special alloy grcop-84 and champagne et al. [22] successfully used thermoplastic nozzle to mitigate the effect of clogging of steel nozzle by al particles. fig. 11 shows the optimum value of 5 mm of nozzle exit diameter for maximum acceleration of particles with different diameters using nitrogen gas at a pressure of 2mpa and temperature of 300oc. li et al. [23], designed a short cold spray gun nozzle for applications in limited internal diameters and calculated the optimal design of expansion ratio of 6.25 with nozzle divergent section length of 40mm for nitrogen or helium gas at the standoff distance of 30mm and found that dense coating can be deposited by the designed short spray gun. figure 11: effect of nozzle exit diameter on velocity of particles of different sizes using nitrogen at a pressure of 2mpa and temperture of 330°c [23] effect on microstructure the particle velocity (vp) also affects the microstructure of the cold sprayed coating .the first layer of the particles on the surface is tamped or ram down hard by the high velocity particles for successive layer and the top layer remain porous as compared to inner region having dense microstructure. the thickness of this top porous layer is influenced by the spray conditions, material properties and the morphology of the particles. since this particle velocity greatly increased with helium as accelerating gas as compared to nitrogen gas under the same operating conditions, so a better tamping effect is reported by li et al. [13] with helium gas, resulted in a thinner top layer than using nitrogen. it is also reported the large top porous layer of titanium coating by cold spray using nitrogen as accelerating gas; even though the deposition efficiency is larger than 80%. deposition efficiency eposition efficiency (de) is one of the most important characteristics of the cold spray coating process. it is the efficiency of deposition of spray powder on the substrate surface and it is practically impossible to obtain 100% deposition efficiency [7], due to the complicated nature of this spray process. deposition efficiency can be calculated experimentally as kd = δms/mp where δms is change of weight of a substrate and mp is weight of all particles interacting with a substrate [7]. de depends upon many factors: delay time, angle of impact of spray particles on the substrate surface, critical velocity, spray powder morphology and substrate surface characteristics like area of the contact surface, crater depth, plastic strain, yield stress, pressure and temperature at the contact boundary, etc [7]. one of the important factors which effect the deposition of particles on the substrate or de, is the critical velocity vc. as practically, only the particles having reached a velocity larger than the critical velocity can be deposited to produce coating. therefore, the critical velocity and particle velocity prior to impact determine the deposition efficiency under a given spray d http://dx.medra.org/10.3221/igf-esis.22.08&auth=true http://www.gruppofrattura.it h. singh et alii, frattura ed integrità strutturale, 22 (2012) 69-84; doi: 10.3221/igf-esis.22.08 79 condition[14]. however, the spray powders used are mostly polydisperse powders having particles of varying diameter from minimum diameter( dmin.) to maximum diameter (dmax.) [15] and as discuss before the particle velocity is inversely related to particle diameter, hence, particle with dmin. will achieve maximum velocity (vmax.) and with dmax will achieve minimum velocity (vmin.). now if vmin. is more than vc then all the particles in the spray powder will be deposited with 100% de and if vmax. is less than vc then no deposition with 0% de. the maximum size of the particles (dc) that can be adhered to the substrate is: dc=(k/vc)1/n, where vc is the critical velocity for the particle to be deposited for a certain material[15]. the relationships between the deposition efficiencies and particle velocity is shown in fig.12 [7]. these calculations of particle velocity are for normal angle between nozzle axis and substrate. as the spray angle decreases from the normal angle called off-normal angle (θ), then deposition of particle depend upon the normal component of the velocity and only the particles with the normal velocity components higher than the vc will be deposited during impact as: dc = (k sin(θ)/vc)1/n,[15]. the variation of de with angle is shown in fig.13. figure 12: the effect of particle velocity on deposition efficiency (de) in cs [7]. figure 13: effect of spray angle on deposition efficiency (de) [7]. effect of material properties on de the deposition of particles and de also depends upon the plastic behavior of the particles and substrate and it is more for metals with high plasticity and the particle adhesion is assumed to be possible if the particle is substantially more plastic than the substrate [7]. metals with the fcc lattice are highly plastic due to more number of slipping planes, hexagonal structure have much fewer slipping planes, which yield a lower plasticity; and metals with the bcc lattice have the lowest plasticity among the three types. during the impact the particle temperature raised to the glass transition temperature (tg) of the amorphous alloys, leading to particle softening and making it possible to achieve very high densities in the coating. it is also reported that for the soft substrates and hard particles, the first impacts will primarily confine the deformation to the substrate material, and after the first layer of undeformed hard particles are created the subsequent impacts provide severe plastic deformation on both substrate and impacting particles [7]. though it is a general postulate that as the substrate deformability decreased, the ease with which particles bond to the surface also decreased, as reported by ghelichi et al. [7], but completely opposite results are also reported and bonding for al particles are seen to be rapid on metallic surface with hardness higher than that of the particles, even when deformation of the substrate was not visible [7]. http://dx.medra.org/10.3221/igf-esis.22.08&auth=true http://www.gruppofrattura.it h. singh et alii, frattura ed integrità strutturale, 22 (2012) 69-84; doi: 10.3221/igf-esis.22.08 80 effect of temperature on de the other important parameter is the particle and substrate temperatures; as the air temperature in the pre-chamber increases, both the particle velocity and the particle and substrate temperatures increase which effects the deposition efficiency, as higher deposition rate of cu particles was noticed for higher substrate temperature, even under the condition where particles were kept at room temperature [7]. the increase in deposition efficiency is reported by li et al. [13] with increase in temperature of carrier gas. during study on titanium powder, no particle deposition occurred for temperature of nitrogen gas below 155 oc and the deposition efficiency increased quickly, especially when the nitrogen temperature becomes higher than 215 oc [13]. lima et al. [10] noticed no change in the deposition efficiencies with the rise of gun temperatures from 370 to 480 oc, for ti coatings on al pipes. effect of surface condition on de it has also been reported by ghelichi et al.[7] that with a greater roughness of the substrate surface (going from polished to grit-blasted), deposition efficiency of metallic powders increases because the impacting particles get deformed more severely on roughened surface as compared to smooth surface of the substrate, which enhanced the mechanical interlocking. kumar et al. [24] suggests that the substrate roughness whose crest size is same as particle size and the trough size is half the particle size creates better bonding. hence, the bond strength values for grit-blasted substrates are higher. so, during cold spray process to improve adhesion, sand blasting is commonly used like other thermal spraying. however, in this spraying process, during delay time the surface is exposed to a large number of particle impacts before particles start to adhere to the surface. so these impacts of the sprayed particles can play an important role for preparation and activation of the substrate surface and this effect can be used in replacing the sand blasting, where it is unacceptable like in spraying on parts with thin walls, parts already coated and parts made of brittle materials and also the effect of interface contamination due to penetration of sand blasting particles into the substrate, especially for soft substrate materials can be avoided [7]. kumar et al. [24] also suggests the need of further research to optimize the roughness value for different materials. applications of cs old spray technology is not here to replace any of the well-established thermal spray methods. instead, cold spray technology is expected to supplement and expand the range of applications for thermal spray [1]. cs applications include both production and restoration [6] in the field of medical, aerospace, electronics, automotive and petrochemical industries [25]. any defect may be easily removed by this process to save production quality. one of the important applications is the repair of the casting defects. both casting defects and machining defects removal by this process can save small-batch or unique production. also casting moulds restoration or modification become easy with this process.  cs is also widely used for the restoration of antique objects both technical as cars and airplanes, and art as metal sculptures [6]. it is used in aerospace industry for aluminum and aluminum alloy coatings for repair/refurbishment of space shuttle solid rocket boosters, in aircraft industry for repair and retrieval of parts and plate stocks used in aircraft structures, repair/refurbishment of casings in gas turbines, corrosion protection coatings in petrochemical, and anti skid coatings [2], sealing up the leakages, shape restoration, defects elimination at small automotive workshops, like repair of vehicle platforms [6]. it is also used for spraying of copper alloys on 'touch' surfaces which are frequently in human contact, such as door knobs, light switches, faucets, bed rails, food preparation areas and other hardware[25]. the continuous seamless titanium pipes can be directly manufactured using cold spray coating technique.  cs coatings are successfully applied to welding lines after the welding of hot galvanized metal structures, anti seizure coatings coats the screws at oil-well tubing and at marine ship propeller shaft. this process is also used for unique coatings to special heating glasses for ships, airplanes and railroad locomotives. also elements of optical electronic devices are created by cold spray[6]. the restoration of defected or worn bearing seats by this process allows avoiding the replacement of the scarce or expensive parts. it is also used to remove defects at the surfaces of the huge rolls for paper and polyethylene film production. hence, the service of worn and old equipment becomes much easy and simple with the use of cold spray process[6].  cold spray technique is used to fabricated the al-tube heat exchanger, used as air conditioning equipments for all types of vehicles these days. it is observed by yoon et al.[26] that high quality coating, which has high corrosion resistance with good brazeability as compared to conventional methods can be obtained by cs process and also with less manufacturing cost. c http://dx.medra.org/10.3221/igf-esis.22.08&auth=true http://www.gruppofrattura.it h. singh et alii, frattura ed integrità strutturale, 22 (2012) 69-84; doi: 10.3221/igf-esis.22.08 81  al-sn alloys are widely used as sliding bearing materials in automobile and shipbuilding industry. tin is a necessary soft phase in the aluminum matrix which can provide suitable friction properties and shear surface during sliding. but due to deleterious effects of high temperature of other thermal processes there is coarsening of sn in the coating. ning et al. [27] successfully prepared al-5sn and al-10sn coatings by cs process, with low porosity and well bonded dense structures and fraction of sn phase is consistent with the feedstock powder. al–5sn coating can be deposited by high pressure cold spray with nitrogen while al–10sn can only be deposited by low pressure cold spray with helium gas. [30]  cs can also be used for the fabrication of complex conductive patterns in solar cells, to enhance surface performance in components made of advanced polymer-matrix composites in wind power generation. architects can create aesthetic metallic patterns on any metal or ceramic substrate by this process [1].  in the medical field, cold spray has already been demonstrated to effectively apply hydroxyapatite (ca10(po4)6(o h)2, also known as (hap), to a number of substrates [1]. hap is widely used in dental and orthopedic implants, due to its chemical and crystallographic similarity with bone minerals and due to lack of cytotoxic effects it can be bonded to the bone directly. but due to poor mechanical strength, the combination of bioactive hap coating and mechanically strong metals is used for surgical implants. though this bioceramic coating is usually done by plasma spray technique, but with deleterious effects of high temperature in the plasma, hence low temperature cold spray coating can remove these harmful effects. the composite coating of ti-hap is successfully deposited using ‘cgt kinetiks 4000 cold spray system’ at asb industries, ohio, with bond strength comparable or better to that of plasma sprayed coating and it is reported that dense composite coatings, containing up to 30% hap can be deposited by this technique. hence the cold spray process has matured from an emerging technology to a viable alternative to thermal spray for selected applications [3,28].  cold spray technology is successfully used to develop high temperature oxidation resistant cucral and nicraly coatings on grcop-84 substrates, at asb industries, ohio, using specially designed tungsten carbide nozzle. grcop-84, a cu-8cr-4nb alloy, developed at nasa glenn research center (grc),for rocket engine liner applications, having very high temperature creep and fatigue capabilities. but for their maximum life additional oxidation protection is required to prevent blanching [21].  cs is used for application of aluminimum barrier coatings for protection from high rate of corrosion and also to restore dimensional tolerances of heat-sensitive materials such as mg alloys ze41a-t5 used in the fabrication of transmission gearboxes in helicopters and fixed-wing aircraft like uh-60 seahawk and mh-60s seahawk. but mg alloys are highly susceptible to galvanic corrosion when coupled to another metal, because magnesium being the most electrochemically active structural metal. also these alloys are very susceptible to damage from excess heat and if coated by conventional thermal spray methods like hvof, then magnesium can reacts with molten material deposited,[22, 29].  cold spray coatings are being used in the power generation plant. these are applied on the boiler tubes to provide resistance from the high temperature corrosion, to provide resistance from the cavitation wear of turbine blades, and the water pump housing, impeller fins, impeller seal section and wear rings. the cold spray of tungsten carbide, chromium oxide and ni-cr coatings can be applied on these parts. also wear rings can be reconditioned by applying bronze by this low temperature spray process. the chromium carbide can be applied to the journal used in coal crusher[30].  one of the important application of cold spray is the coating of copper powder on the aluminium tips of the electric mains to prevent the electrochemical oxidation of contacting elements of copper wire of the transformer and aluminium tip of the cable. the presence of different materials results in circuit breakdown and can be prevented by this method. this problem also occurs in the automotive batteries with contact of copper wire and the aluminium battery terminal[30]. nanostructured coating and smart structures cold spray can be also be used to embed micro-sensors, along with functional coatings, on surfaces for smart structures. these structures would have the ability to provide real-time information related to materials performance or environmental conditions[1]. cold spray can effectively be used for nanostructured coating without compromising their beneficial microstructure. nanostructured (or nanocrystalline) materials have achieved much attention in recent years due to their outstanding properties like having having higher hardness, strength and corrosion resistance as compared to those of micron-size counterparts. these materials are characterized by a microstructural length scale in the1–200 nm regime. it is found that these are sensitive to process temperature because particle size strongly influences the particle thermal history as small http://dx.medra.org/10.3221/igf-esis.22.08&auth=true http://www.gruppofrattura.it h. singh et alii, frattura ed integrità strutturale, 22 (2012) 69-84; doi: 10.3221/igf-esis.22.08 82 particles rapidly heat up and also rapidly cool down. it also affects the interlamellar adhesion of the splats and hence influencing mechanical properties of the coating. nano structured wc-co cermets coatings shows better wear resistance due to the increase of hardness of coatings by the decrease in the particle size of the feedstock powder [31]. jianhong et al. [32] found that the nanostructured coating of cr3c2-25(ni20cr) exhibits a 20.5% increase in microhardness of 1020 hv300 as compared with the corresponding conventional coating of 846 hv300. also these coatings consists of a ductile and a brittle phase that has high potential to improve the corrosion resistance even in the almost hopeless case of high temperature corrosive environment. however, the main hurdle in the nano powder coating is the spray technique, due to the requirement of heating by other thermal spray process like hvof and plasma spray, the properties of nano-sized particles changed. during nano-powder coating by thermal spray process, the feed stock material should exhibit a nanosized structure to get the properties of a nano-structured coating after the spray process .the processing of a nanopowder by means of the standard thermal spray procedure, first of all requires the agglomeration of the nanopowders, in order to form spray particles with appropriate grain size that are suitable for a standard powder feeding device. the agglomerated particles lose their nanostructure, so it is not yet clear if there is any benefit of using nanostructured feed stock materials as compared to using conventional powders. also due to decreasing particle size, the fluidization of the spray powder gets more and more challenging, so it is difficult to decrease the coating thickness below a value in the range of 30 μm by thermal spray process and a reduction of particle sizes in the nano range of below 5 μm needs improvement in powder feeding technique [31]. therefore, cold spray coating technique, being a low temperature and also a solid state process, is foreseen as a viable solution to development of nano-structured coatings, using cold spray process [9, 31, 33, 34]. during the last two decades, research and development on cold spray process and technology, leads to significant progresses on both coating process and technologies [14, 33]. with such progresses, most metals and their alloys can be deposited by cold spraying including coatings using nanostructured powders like cermets wc-co which is a most important wear-resistant coating materials. nanostructured wc-12co coatings are deposited successfully by cold spraying using a nanostructured feedstock with 1800 hv0.3 microhardness of sprayed coating, with critical velocities of about 915 m/s is reported, by nozzle of downstream length 100mm, throat diameter of 2mm and exit diameter of 4mm, standoff distance 20mm and using helium gas at 2mpa pressure and 600oc temperature in the prechamber [33]. lima et al. [9] produce pure and well bonded nanostructured wc-12%co coatings on low carbon steel substrate via cold-spray processing. the coating has a high density and around1225 kgf/mm2 knoop microhardness compared to around 42 kgf/mm2 of the nanostructured feedstock i.e around 2800% increase. the impact of the particles against the substrate at supersonic velocities, promotes a densification in each nanostructured particle, without the presence of porosity. however there is no significant difference between the average grain size of the nanostructured feedstock 109 nm and coating 103nm is reported in the study [9]. hence, the ability of cold spray process to deposit advanced materials onto a diversity of substrates will define the direction and opportunities lying ahead for this technology [1]. conclusion old spray technology is an emerging technology and it should be clear that it is not here for replacement of any of the well-established thermal spray methods. instead, cold spray technology is expected to supplement and expand the range of applications for thermal spray processes as a greener alternative according to stringent environmental and health safety regulations. a number of materials have already proven to be suitable for deposition by cold spray from decorative articles to biomedical, automotive, power plants and space industries. extensive research is required to design the optimum parameters like nature of gas, temperature control, nozzle design and its material and also prediction of critical velocity for different particle/substrate combinations. the research area of mathematical modeling to optimize various design parameters is still open to expand this process to more non-traditional applications. research is required on deposition of hard and brittle ceramic materials by cold spray. the cold spray coating process has huge potential of growth with more applications in new areas like in boiler industry, to increase the life of boiler tubes by prevention from high temperature corrosion in aggressive chlorine and sulphate based environments. coatings by cold spray technique can be beneficial for protection from high temperature oxidation failure of boiler tubes especially of waste-to-energy plants, which are still running at very less efficiency as compared to fossil fuel based plants. this area is explored by the author with a project sponsored by ugc, govt. of india and in collaboration of asb industries ohio and results will be published in future. it is expected that this decade will saw exponential growth of cold spray technology around the globe, through the development of cs coatings for specific applications. c http://dx.medra.org/10.3221/igf-esis.22.08&auth=true http://www.gruppofrattura.it h. singh et alii, frattura ed integrità strutturale, 22 (2012) 69-84; doi: 10.3221/igf-esis.22.08 83 acknowledgement uthor ‘harminder singh’ thankfully acknowledge the research grant under ugc minor project from ugc, new delhi, govt. of india, for carrying out this r&d work on “studies on the behavior of coatings in improving the resistance to hot corrosion degradation in waste incineration environment”, vide f.no. 39-1003/2010(sr). references [1] villafurerte julio, current and future applications of cold spray technology, metalfinishing (2010) [2] j. karthikeyan, cold spray technology:international status and usa efforts, report by asb industries (2004). [3] a. choudhuri, p.s. mohanty, j. karthikeyan, bio-ceramic composite coatings by cold spray technology asbindustries paper 22241 manuscript 3762, (2008). [4] e. tinashe sanyangare, conceptual design of a low pressure cold gas dynamic spray (lpcgds) system, m.s thesis, (2010). [5] j. karthikeyan, advanced materials and processes (2006) [6] a. shkodki, pecularities of the gas dynamic spray applications in russia, ocps, russia, (2010). [7] r. ghelichi, m. guagliano, frattura ed integrità strutturale, 8 (2009) 30. [8] m. e.dickinson, m. yamada, nanoscience and nanotechnology letters, 2(4) (2010) 348. [9] r. s. lima, j. karthikeyan, c. m. kay, j. lindemann, c. c. berndt, thin solid films, 416 (2002) 129. [10] r. s. lima, a. kucuk, c. c. berndt, j. karthikeyan, c. m. kay, j. lindemann, journal of materials science letters, 21 (2002) 1687. [11] v. k. jr.champagne, d. helfritch, p. leyman, s. grendahl, b. klotz, journal of thermal spray technology, 14(3) (2005) 330. [12] r. lupoi, w. o'neill, surface & coatings technology, 205 (2010) 2167. [13] c.-j. li, w.-y. li, surface and coatings technology, 167 (2003) 278. [14] c.-j. li, h.-t. wang, q. zhang, g.-j. yang, w.-y. li, h. l. lio, j. of thermal spray technology 19(1-2) (2010) 95. [15] c.-j. li, w.-y. li, y.-y. wang, g.-j. yang, h. fukanuma, thin solid films, 489 (2005) 79. [16] c.-j. li, w.-y. li, h. lio, j. of thermal spray technology, 15(2) (2006) 212. [17] s. yoon, c. lee, h. choi, h. jo, materials science and engineering, 415 (2006) 45. [18] s. desaulniers, polycontrols, 2010. [19] k. balani, a. agarwal, s. seal, j. karthikeyan, scripta materialia 53 (2005) 845. [20] www.psu.edu (2011) [21] j. karthikeyan, development of oxidation resistant coatings on grcop-84 substrates by cold spray process, nasa/cr—2007-214706, (2007). [22] v. k. champagne, p. f. leyman, d. j. helfritch, magnesium repair by cold spray, arl report no. arl-tr-4438, (2008). [23] w.-y. li, c.-j. li, j. of thermal spray technology, 14(3) (2005) 391. [24] s. kumar, g. bae, c. lee, applied surface science 255 (2009) 3472. [25] m. trexler, cold spray technology application, arl, usa, (2010). [26] s. yoon, h. kim, c. lee, surface & coatings technology, 201 (2007) 9524. [27] x.-j. ning, j.-h. kim, h.j. kim, c. lee, applied surface science, 255 (2009) 3933. [28] j. cizek, k. a. khor, on cold kinetic spraying of hydroxyapatite and tio2 bioceramics onto ti-6al-4v and glass substrates, (2008). [29] b. deforce, t. eden, j. potter, application of aluminum coatings for the corrosion protection of magnesium by cold spray, arl report, 2008. [30] t. goyal, t. s. sidhu, r. s. walia, in: national conference on advancements and futuristic trends in mechanical and materials engineering, (2010) 364. [31] h. singh, t. s. sidhu, s. b. s. kalsi, journal on electronics engineering, 1(1) (2010) 1. [32] jianhong he, julie m. schoenung, nanostructured coatings, materials science and engineering 336 (2002) 274. [33] li chang-jiu, yang guan-jun, gao pei-hu, ma jian, wang yu-yue, li cheng-xin, characterization of nanostructured wc-co deposited by cold spraying, journal of thermal spray technology 16(5-6) (2007) 1011. a http://dx.medra.org/10.3221/igf-esis.22.08&auth=true http://www.gruppofrattura.it h. singh et alii, frattura ed integrità strutturale, 22 (2012) 69-84; doi: 10.3221/igf-esis.22.08 84 [34] singh harminder, sidhu t.s., kalsi s.b.s., scarcity of energy and waste-to-energy (wte) plant: a review, i manager’s journal on mechanical engineering 1(1) (2011) 1. [35] sidhu t.s. phd thesis, 2006. http://dx.medra.org/10.3221/igf-esis.22.08&auth=true http://www.gruppofrattura.it microsoft word 2296 o. plekhov et alii, frattura ed integrità strutturale, 48 (2019) 50-57; doi: 10.3221/igf-esis.48.07 50 focussed on “crack paths” the experimental study of energy dissipation during fatigue crack propagation under biaxial loading oleg plekhov, aleksei vshivkov, anastasia iziumova institute of continuous media mechanics russian academy of sciences ural branch, russia poa@icmm.ru, vshivkov.a@icmm.ru, fedorova@icmm.ru aleksandr zakharov, valery shlyannikov kazan scientific center of russian academy of sciences, russia alex.zakharov88@mail.ru, shlyannikov@mail.ru abstract. the work is devoted to experimental study of heat flux evolution at the fatigue crack tip during biaxial loading with a goal to relate the heat flux to the rate of crack propagation under different loading conditions. the plane samples of titanium alloy (grade 2) 1 mm thick were weakened by notch to initiate fatigue crack at their centers. infrared thermography and the contact heat flux sensor, which is based on the seebeck effect, were used to monitor the dissipated thermal energy. the samples were subject to cyclic loading with constant stress amplitude at different biaxial coefficients. the experimental results confirmed the previous conclusions of the authors about two regime of energy dissipation at fatigue crack tip under paris regime. at the first stage, the power of heat flux is proportional to the product of the crack rate by the crack length. the second stage is characterized by a traditional linear relationship between the crack rate and the heat flux. keywords. fatigue; biaxial loading; crack propagation; dissipated energy. citation: plekhov, o., vshivkov, a., iziumova, a., zakharov, a., shlyannikov, v., the experimental study of energy dissipation during fatigue crack propagation under biaxial loading, frattura ed integrità strutturale, 48 (2019) 50-57. received: 28.11.2018 accepted: 30.01.2019 published: 01.04.2019 copyright: © 2019 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. introduction n the age of rapid technical progress, highly sophisticated mechanisms and technologies and ambitious projects in the field of mechanical engineering, aircraft construction, nuclear energy and space exploration much effort has been put into intensive development of many fields of science and technologies, including fracture mechanics. a number of approaches has been developed to study the processes of nucleation and propagation of fatigue cracks in metals [1-4]. it is well known that real metals have a complex structure, which is a hierarchy of different scale levels. under deformation, the structural changes are observed at all scale levels and leads to irreversible deformation and failure, which is accompanied by accumulation and dissipation of energy. the investigation into thermodynamics of deformation and failure is a key issue of solid mechanics. the analysis of the kinetics of damage accumulation, the process of crack nucleation and kinetics of the crack growth allows specialists to predict the time of structure failure and to perform in i http://www.gruppofrattura.it/va/48/2296.mp4 o. plekhov et alii, frattura ed integrità strutturale, 48 (2019) 50-57; doi: 10.3221/igf-esis.48.07 51 proper time a partial replacement or repair of fractured structural elements. moreover, the repair or replacement of the defective parts on a timely basis is more effective than their complete replacement after mechanical damage. it is therefore very important to know the time during which the flaw size in the ill-behaved areas reach critical values. the actual engineering structures operate under complex types of loading. so, it is of considerable interest to study the behavior of materials under mixed loading conditions that combine mode 1 and mode 2 fractures. in sufficiently plastic structural materials the propagation of the crack begins when the plastic deformation near its tip becomes large (of the order of 10 percent). this irreversible process is accompanied by the release and accumulation of energy, which leads to a local temperature change in the region of the crack tip and the occurrence of a heat flux. for a long time, infrared thermography is regarded as the most effective technique for estimating the power of the heat sources in the process of mechanical testing [5, 6]. a principal solution to the problem of measuring the energy dissipated in the structure under deformation and failure can be obtained by the development of additional system for direct monitoring of the heat flux [7]. the heat generation process depends on both the thermo elastic effect and plastic energy dissipation. the measurement of heat flux near the crack tip allows one to calculate the energy balance during crack propagation and to develop a new equation for its description. attempts to develop a new equation for crack propagation were made by many authors. they used such quantities as the j-integral, the work of plastic deformation, the size of the zone of plastic deformation, the amount of dissipated energy and others [8-11]. the classical assumption of almost complete dissipation of the deformation energy into heat [12] has proved to be correct only in a limited number of cases. the previous authors’ investigations were focused on the problem of crack growth under the opening or mode i fracture mechanism (see [13]). in this work, a relationship for the growth rate of a fatigue crack was developed based on the analysis of the energy balance at its tip. however, failure of most structures occurs under the mixed mode loading. many materials, structures and components subject to uniaxial loads often contain randomly oriented defects and cracks, which lead to a mixed mode state due to rotation about the loading axis. this study is devoted to the investigation of the energy dissipation in the process of crack propagation under biaxial loading. for this purpose, an original contact heat flux sensor was developed to record energy dissipation during crack propagation under biaxial loading and to verify the data of infrared thermography. this sensor made it possible to study in details the dissipated energy evolution in metal samples (titanium alloy grade 2) in bi-axial loading tests and to determine the relationships between the energy dissipation and the fatigue crack rate. experimental setup series of samples made of titanium alloy grade 2 (chemical composition is presented in tab. 1) were tested in the servo-hydraulic biaxial test system biss bi-00-502 at the kazan scientific center of the russian academy of sciences. the photo of experimental setup is given in fig. 2. the geometry of the samples is shown in fig. 1. during tests the samples were subject to cyclic loading of 10 hz at constant stress amplitude and for different biaxial coefficient η=px/py (1, 0.7, 0.5) and stress ratio r=σmin/σmax (0.1, 0.3, 0.5). phases of biaxial loading coincided during the fatigue test. the experimental program is presented in tab. 2. crack length was measured by optic microscope. fe c si n ti o h 0.25 0.07 0.1 0.04 99.24 — 99.7 0.2 0.01 table 1: the chemical composition of titanium alloy. sample sp1 sp2 sp3 sp4 sp5 sp6 biaxial coefficient 1 1 0.5 0 1 1 stress ratio 0.1 0.1 0.1 0.1 0.5 0.5 table 2: experimental program. in the course of the experiment the crack length was measured by the optical microscopy method. to analyze the energy dissipation at the crack tip a contact heat flux sensor was designed and assembled. the sensor is based on the seebeck effect, which is the reverse of the peltier effect. a o. plekhov et alii, frattura ed integrità strutturale, 48 (2019) 50-57; doi: 10.3221/igf-esis.48.07 52 the peltier effect is a thermoelectric phenomenon, in which the passage of electric current through a conducting medium leads to the generation or absorption of heat at the point of contact (junction) of two dissimilar conductors. the quantity of heat and its sign depend on the type of contacting materials, the direction and the strength of the electric current. the quantity of heat absorbed or dissipated by the element is directly proportional to the current intensity and the time of current passage through the element: abp i  (1) where p is the power of heat flux, i is the direct current, ab is the peltier coefficient. figure 1: geometry of samples, thickness is 1 mm (all sizes in millimeters). figure. 2. testing machine biss bi-00-502, biaxial test system. figure 3: schematic representation of the device.1 – testing sample; 2 – “measuring” peltier element; 3 – “cooling” peltier element; 4 – radiator; 5, 6 – thermocouple; 7 – resistor. fig. 3 presents a schematic diagram of the heat flux sensor. here, the following notation is used: 1 stands for a sample, 2 stands for a heat flux sensor. the application of a thermal paste provides good thermal contact between the sample and the sensor. structurally, the sensor comprises two peltier elements ("measuring"2 and "cooling"3), thermocouples 5, 6 and the radiator 4. the measuring peltier element is connected to a low-resistance resistor 7 of 1.2 om. to measure the heat o. plekhov et alii, frattura ed integrità strutturale, 48 (2019) 50-57; doi: 10.3221/igf-esis.48.07 53 flow through the “measuring” peltier element during the experiment, the temperature on its free surface should be kept constant. the “cooling” peltier element coupled with a radiator was connected to the "measuring" peltier element. this cooling system has a feedback and is controlled with the two temperature sensors located between the “measuring” and “cooling” peltier elements. it is placed at a certain distance from the examined sample in the zone with constant temperature. the signal from the sensor (voltage at the resistor 7) is measured by the amplifier and registered by the adc of the microcontroller. the data are transmitted from the microcontroller to the personal computer for further processing. the "cooling" peltier element is controlled via pulse width modulation. this sensor was calibrated using a device with a controlled heat flux. a wire resistor with the preset resistance was glued on a plastic plate, the size of which was equal to that of the test samples. the heat isolating system provided the heat flux only from the resistance to the sensor. the heat flow was calculated using the values of the resistor voltage and the electric current across the resistor. the evolution of the temperature field was recorded by an infrared camera flir sc 5000. the spectral range of the camera was 3-5 µm. the maximum frame size was 320×256 pixels; the spatial resolution was 10-4 meters. the temperature sensitivity was 25 mk at 300 k. calibration of the camera was made based on the standard calibration table. the flir sc5000 mw g1 f/3.0 close-up lens (distortion is less than 0.5%) were used to investigate the plastic zone in details. results uring experiments, a series of samples was subject to biaxial load tests with the aim to record the crack length and the heat flux. the crack propagation rate was 10-7 – 10-4 m/cycle. a comparison of the methods used for estimating the heat flux from the crack tip is given in figs. 4 and 5. the heat flux sensor made it possible to measure the integral heat flux and to verify the infrared thermography data. the infrared thermography method was used to obtain the temperature field and the field of heat source distribution in the crack tip region. fig. 4 presents the characteristic curve describing time variation of the heat flux during the fatigue tests: solid line the heat flux measured by the sensor, circles the heat flux measured by the infrared thermography method with averaging over time and space occupied by the contact sensor. a comparison of heat fluxes measured by the two methods is given in fig.5 (one point of infrared thermography from fig. 4): green line infrared thermography, red line heat flux sensor. figs. 4, 5 confirm the reliability of the heat flow measurement. figure. 4. characteristic time dependence of heat flux. figure. 5. compare the infrared thermography and heat flux sensor. in the previous work [13], the study of the fatigue crack propagation under uniaxial loading in the paris regime revealed two stages of crack propagation differing in the character of energy dissipation. on the curve of the crack length and paris curve, the point of change of the stages is clearly not pronounced. p o w e r o f h e a t fl u x , w d o. plekhov et alii, frattura ed integrità strutturale, 48 (2019) 50-57; doi: 10.3221/igf-esis.48.07 54 the time, at which the type of energy dissipation changes, is determined from the maximum value of the curvature of the function q(t) as: '' ( ) 23 1 ( ') t q t t   (2) where q(t) is the time dependence of the heat flux, t is time. the crack length and crack rate are shown in fig. 6. the heat flux curves illustrating two stages of crack propagation under biaxial loading are shown in fig. 7. circle markers show the point of changes of heat flux stages. a) b) figure. 6. crack length (a) and crack rate (b) during the fatigue test. a) b) figure. 7. two stages of fatigue crack propagation: energy dissipation (a), paris curve (b). the analysis of the experimental data in the light of the hypothesis about the stages of fatigue crack propagation [11] allowed us to derive characteristic relationships between the crack growth rate and the energy dissipation in both stages. c ra ck le n g th , m m c ra ck r a te , m /c yc le c ra ck r a te , m /c yc le o. plekhov et alii, frattura ed integrità strutturale, 48 (2019) 50-57; doi: 10.3221/igf-esis.48.07 55 at the first stage, the crack rate is proportional to the power of heat flux and the crack length 1 1~ da q a dn       , and in the second stage – to the power of heat flux 2~ da q dn       . the characteristic dependences are shown in fig. 8. a) b) figure 8: normalized heat flux and crack rate in the first (a) and second (b) stages. it is worth noting that the relations used for the heat flux and the crack growth rate at both stages are consistent with the classical paris regime. fig. 9 describes the crack growth rate in terms of the stress intensity factor (sif) and energy dissipation (the k index in the legend means the stress intensity factor, q is the energy dissipation, 9a corresponds to the first stage, 9b – to the second stage). a) b) figure 9: comparison between the energy approach and the classical assumption based on the stress intensity factor in the first (a) and second (b) stages. in fig. 9 normalization (3) for heat flux and normalization (4) for stress intensity factor are used: min 1 1 1 1 1 1 max min 1 1 1 1 ,q q a q a a q a q a    min 2 2 2 max min 2 2 ,q q q q q    (3) c ra c k r a te , m /c yc le o. plekhov et alii, frattura ed integrità strutturale, 48 (2019) 50-57; doi: 10.3221/igf-esis.48.07 56 min max min k k k k k         (4) where q1 and a1 are the heat flux and the crack length in the first stage, q2 and a2 are the heat flux and the crack length in the second stage. the superscripts “max” and “min” denote maximum and minimum values during the fatigue test. conclusion series of experiments was carried out to study the energy dissipation at the fatigue crack tip under biaxial loading. the experimental technique for measuring the energy dissipation during fatigue test under biaxial loading was developed based on the contact heat flux sensor and the method of infrared thermography. the results of this study confirm the hypothesis for the existence of two modes of energy dissipation during the fatigue cracks propagation. the first mode corresponds to slowly propagating cracks (10e-7 – 10e-5 m/cycle) and is described by the relation 1 1~ da q a dn       .the point corresponding to a change in the character of energy dissipation lies on the linear section of the paris curve. the obtained experimental results allows us to generalize the hypothesis about the linear relationship between the energy dissipation at the fatigue crack tip and its growth rate to the case of biaxial loading. the study revealed qualitative agreement between the energy approach to the description of the fatigue crack propagation and the classical approach, which is based on the use of the stress intensity factor. acknowledgments his work was supported by the grant of the president of russian federation for support of young russian scientists and leading scientific schools [mk-1236.2017.1] and the russian foundation for basic research [grant number 16-48-590148]. references [1] yates, j.r., zanganeh, m., tomlinson, r.a., brown, m.w., diazgarrido f.a. (2008). crack paths under mixed mode loading, engineering fracture mechanics, 75(3-4), pp. 319-330. [2] mokhtarishirazabad, m., lopez-crespo, p., moreno, b., lopez-moreno, a., zanganeh m. (2017). optical and analytical investigation of overloads in biaxial fatigue cracks, international journal of fatigue, 100(2),pp. 583-590. [3] izumi, y., sakagami, t., yasumura, k., shiozawa, d. (2014). a new approach for evaluating stress intensity factor based on thermoelastic stress analysis, apcfs/sif, pp. 47-51. [4] short, j. s., hoeppner, d. w. (1989). a global/local theory of fatigue crack propagation, engineering fracture mechanics, 33(2), pp. 175-184. [5] meneghetti, g., ricotta, m. (2016). evaluating the heat energy dissipated in a small volume surrounding the tip of a fatigue crack, international journal of fatigue, 92(2), pp. 605-615. [6] risitano, a., risitano, g. (2013). cumulative damage evaluation in multiple cycle fatigue tests taking into account energy parameters, international journal of fatigue, 48, pp. 214-222. [7] pradere, c., joanicot, m., batsale, j-c., toutain, j., gourdon, c. (2006). processing of temperature field in chemical microreactors with infrared thermography, qirt journal, 3, pp. 117-135. [8] matvienko, yu.g., morozov, e m. (2004). calculation of the energy j-integral for bodies with notches and cracks, international journal of fracture, 125, pp. 249-261. [9] rosakis, p., rosakis, a.j., ravichandran, g., hodowany, j. (2000). a thermodynamic internal variable model for the partitional of plastic work into heat and stored energy in metals, j. mech. phys. solids, 48, pp. 581-607. [10] oliferuk, w., maj, m., raniecki, b. (2004). experimental analysis of energy storage rate components during tensile deformation of polycrystals, materials science and engineering, 374, pp. 77-81. [11] izyumova, a., plekhov, o. (2014). calculation of the energy j-integral in plastic zone ahead of a crack tip by infrared scanning, ffems, 37, pp. 1330–1337. a t o. plekhov et alii, frattura ed integrità strutturale, 48 (2019) 50-57; doi: 10.3221/igf-esis.48.07 57 [12] farren, w.s., taylor, g.i. (1925). the heat developed during plastic extension of metals, proc. royal. soc. of london. ser., 107, pp. 422-451. [13] vshivkov, а., iziumova, a., bar, u., plekhov, o. 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can be opened with acrobat and adobe reader 5.0 and later.) >> /namespace [ (adobe) (common) (1.0) ] /othernamespaces [ << /asreaderspreads false /cropimagestoframes true /errorcontrol /warnandcontinue /flattenerignorespreadoverrides false /includeguidesgrids false /includenonprinting false /includeslug false /namespace [ (adobe) (indesign) (4.0) ] /omitplacedbitmaps false /omitplacedeps false /omitplacedpdf false /simulateoverprint /legacy >> << /addbleedmarks false /addcolorbars false /addcropmarks false /addpageinfo false /addregmarks false /convertcolors /converttocmyk /destinationprofilename () /destinationprofileselector /documentcmyk /downsample16bitimages true /flattenerpreset << /presetselector /mediumresolution >> /formelements false /generatestructure false /includebookmarks false /includehyperlinks false /includeinteractive false /includelayers false /includeprofiles false /multimediahandling /useobjectsettings /namespace [ (adobe) (creativesuite) (2.0) ] /pdfxoutputintentprofileselector /documentcmyk /preserveediting true /untaggedcmykhandling /leaveuntagged /untaggedrgbhandling /usedocumentprofile /usedocumentbleed false >> ] >> setdistillerparams << /hwresolution [2400 2400] /pagesize [612.000 792.000] >> setpagedevice microsoft word numero_34_art_54 t. itoh et alii, frattura ed integrità strutturale, 34 (2015) 487-497; doi: 10.3221/igf-esis.34.54 487 focussed on crack paths crack mode and life of ti-6al-4v under multiaxial low cycle fatigue takamoto itoh, masao sakane department of mechanical engineering, college of science & engineering, ritsumeikan university, japan itohtaka@fc.ritsumei.ac.jp, sakanem@se.ritsumei.ac.jp takahiro morishita graduate school of science & engineering, ritsumeikan university, japan gr0202xp@ed.ritsumei.ac.jp hiroshi nakamura engine technology department, aero-engine & space operation, ihi corporation, japan hiroshi_nakamura_2@ihi.co.jp masahiro takanashi structural strength department, research laboratory, ihi corporation, japan masahiro_takanashi@ihi.co.jp abstract. this paper studies multiaxial low cycle fatigue crack mode and failure life of ti-6al-4v. stress controlled fatigue tests were carried out using a hollow cylinder specimen under multiaxial loadings of λ=0, 0.4, 0.5 and 1 of which stress ratio r=0 at room temperature. λ is a principal stress ratio and is defined as λ=ii/i, where i and ii are principal stresses of which absolute values take the largest and middle ones, respectively. here, the test at λ=0 is a uniaxial loading test and that at λ=1 an equi-biaxial loading test. a testing machine employed is a newly developed multiaxial fatigue testing machine which can apply push-pull and reversed torsion loadings with inner pressure onto the hollow cylinder specimen. based on the obtained results, this study discusses evaluation of the biaxial low cycle fatigue life and crack mode. failure life is reduced with increasing λ induced by cyclic ratcheting. the crack mode is affected by the surface condition of cut-machining and the failure life depends on the crack mode in the multiaxial loading largely. keywords. ti-6al-4v; low cycle fatigue; multiaxial loading; crack mode; hollow cylinder specimen; inner pressure introduction i-6al-4v is frequently used as a material in rotating aero engines because it has the properties of high strength, light weight, and excellent corrosion resistance. a rotating aero engine receives cyclic loading under thermal and mechanical stresses which cause multiaxial low cycle fatigue. under non-proportional loading in which the t t. itoh et alii, frattura ed integrità strutturale, 34 (2015) 487-497; doi: 10.3221/igf-esis.34.54 488 principal directions of stress and strain are changed cyclically, previous studies have reported a drastic reduction in the failure life with accompanying additional cyclic hardening [1-16] depending on both the loading path and the material [6, 8, 10, 13, 16]. in addition, some studies about the fatigue property of ti alloys have been reported [17, 18]. meanwhile, only a paper by the authors [19] has dealt with multiaxial low cycle fatigue crack behavior of ti-6al-4v. to evaluate fatigue lives under multiaxial loading conditions, multiaxial fatigue models which relate fatigue lives to uniaxial fatigue properties have been established. equivalent strains and stresses based on the theories of von mises and tresca, which are considered the most commonly used theory, but lead to significant overestimation of fatigue lives under nonproportional loadings from those under proportional loading. therefore, other life evaluation models have been proposed such as critical plane approaches; i) stress based critical plane approaches presented by findley [20] and mcdiarmid [21], ii) strain based critical plane approach by brown and miller [22] and wang and brown [23], iii) strain-stress based critical plane approaches by fatemi and socie [7, 15] and smith, watson and topper [24]. most of these models are success on life evaluation under non-proportional loadings, however, some of them have some limitation on application. itoh et al. [8, 10, 13, 16] proposed a strain parameter taking into account the loading path and material dependencies of life, which shows good correlations with lives under non-proportional loadings for different materials [16]. the studies mentioned above treat the fatigue properties under limited multiaxial loadings of which the principal stress ratio λ range is –1≤λ (=σii/σi)≤0, where σi is the principal stress whose absolute value is the maximum and σii one of which absolute value the middle. the reason why the performable principal stress ratio range was limited to 1≤λ≤0 mainly due to the testing method to apply the axial and twist loads to hollow cylinder specimens. however, to carry out the multiaxial fatigue test beyond the principal stress ratio range, special multiaxial fatigue testing stands must be required. the authors developed a new testing machine which can apply push-pull and reversed torsion loadings and additionally inner pressure onto the hollow cylinder specimen to perform the test in 1λ1 under proportional and non-proportional loadings. in this study, biaxial fatigue tests of the stress ratio range 0≤λ≤1 were carried out using the hollow cylinder specimen of ti-6al-4v by the developed multiaxial fatigue testing machine and properties of failure life and crack mode are discussed. multiaxial loading and testing machine definition of stress and strain multiaxiality ultiaxial stress and strain states can be expressed by using parameters, κ and φ which are the stress and the strain ratios, as equated in eq. (1) and eq. (2),     (1)     (2) where  and  are axial and shear stresses and  and  are axial and shear strains in plane stress state. besides the method above, this paper also employs principal stress ratio, λ, and the principal strain ratio, , to define multiaxial stress and strain states, which are equated in eq. (3) and eq. (4), ii i     (3) ii i     (4) where i and ii are put as principal stresses, 1, 2 or 3 (123) of which absolute values takes the largest and middle ones, e.g., if 1=100mp, 2=50mp and 3=200mp, i=200mpa and ii=100mpa since |3||1||2|. on the other hand, i and ii are principal strains of which principal direction corresponding to those of i and ii, m t. itoh et alii, frattura ed integrità strutturale, 34 (2015) 487-497; doi: 10.3221/igf-esis.34.54 489 respectively. in proportional fatigue test, λ and  have constant values in a cycle. for tension-compression tests using the hollow cylinder specimen, relationships among σ1, σ3, σ, τ and ε1, ε3, ε, γ are shown in eq. (5) and eq. (6). 1 2 2 3 1 4 2 2           (5)  21 2 2 3 1 1 1 2 2                  (6) in eq. (6), ν is the poisson’s ratio. usually, the value of poisson’s ratio is around 0.3 in elastic regime but it is 0.5 in a fully plastic regime. uniaxial and multiaxial stress and strain states a stress state is defined as multiaxial state if the multiple principal stresses operate and a strain state as multiaxial state when the multiple principal strains do. using these definitions, the multiaxial stress state does not always correspond to the multiaxial strain state. for example, fig. 1, an uniaxial tension loading is the uniaxial stress state because only one principal stress operates in tensile direction but this case becomes the multiaxial strain state because the two additional principal strains are caused by the lateral contraction as well as the tensile direction. these definitions of multiaxiality are most consistent for describing the multiaxial stress and strain states compared to using the other stress and strain components, whereas stress multiaxiality does not always correspond to strain multiaxiality. non-proportional loading is defined as the loading where the directions of the principal stresses or strains rotate, and proportional loading when they are fixed. applied load principal stress principal strain applied load principal stress principal strain figure 1: principal stress and principal strain in tension loading.   t 1   t 1 3=-1    t 1 1  xy t 1 1 y x uniaxial loading multiaxial loading tensioncompression reversed torsion tensioncompression and reversed torsion biaxial tensioncompression p ri n c ip a l s tr e ss s ta te a p p lie d s tr e s s type principal stress directions are fixed  =  0.5  = 1  = 1 0  = 1 1   t 1 -1   t 1 -1    t 1  1  xy t 1  1 y x uniaxial loading multiaxial loading p ri n ci p a l s tr a in s ta te a p p lie d s tr a in type principal strain directions are fixed  =  0.5  = 1  = 1    = 1 1 tensioncompression reversed torsion tensioncompression and reversed torsion biaxial tensioncompression (a) (b) figure 2: applied stresses/strains and stress/strain multiaxiality in proportional loading. (a) stress state, (b) strain state. proportional loading figs. 2 (a) and (b) summarize the applied stresses/strains and the stress/strain multiaxiality in various proportional multiaxial testing methods under the plane stress condition. in the tension-compression test, a uniaxial stress () is applied t. itoh et alii, frattura ed integrità strutturale, 34 (2015) 487-497; doi: 10.3221/igf-esis.34.54 490 to the specimen in fig. 2 (a) and a uniaxial strain () is applied to the specimen but the multiple principal strains arise in the specimen thickness direction in fig. 2 (b). the lateral strain is  is applied to the specimen. in the reversed torsion test, the applied stress/strain is only the shear stress/stress (/) but the two principal stresses/strains with the opposite sign are caused in this case. so, the reversed torsion test also becomes a multiaxial test. the combined tension-torsion and the biaxial tension-compression loadings also enable the fatigue test in multiaxial strain states. the former test only covers the stress/strain biaxiality for 10/1 but the latter test does 1, 1. non-proportional loading fig. 3 shows the tension-compression and reversed torsion testing and the biaxial tension-compression testing with phase shift in applied strains. in the tension-torsion test with the phase shift, the direction of the principal strains rotates with time and this loading is non-proportional loading. the phase shift in applied strain in the biaxial tension-compression test causes no rotation of the principal strains but it causes the switch of the principal strain directions. the authors consider that this loading should be classified to a proportional loading because no large additional hardening and little reduction of fatigue life was confirmed in this type of test using type 304 steel cruciform specimens at 823 k [12]. however, another research [25] stated that this loading should be a type of non-proportional tests showing a fair reduction of fatigue lives in experiments. more detailed experimental studies and evidences are needed to have a definite conclusion on the classification of this type of loading.     t 1 1 1 1  = 1 0   y y t 1 1 y y x x biaxial / multiaxial loading tension compression and cyclic torsion biaxial tension compression p ri n c ip a l s tr e s s /s tr a in s ta te a p p lie d s tr e s s /s ta in type principal stress/strain directions rotate continuously. principal stress/strain directions are fixed but they interchange. rotated fixed changed  = 1 1  = 1    = 1 1 1 1 x x   shape of specimen cylinder cruciform cubic type ⅰa type ⅰb type ⅱ type ⅲ axial load shear load axial load shear load in te rn a l p re ss u re e x te rn a l p re ss u re axial load shear load in te rn a l p re ss u re e x te rn a l p re ss u re axial load shear load loadload loadload loadload figure 3: definition of non-proportional loading. figure 4: type of specimens. types of multiaxial fatigue tests fig. 4 shows four types of common used multiaxial fatigue testing methods classified by types of loading and specimen. type ia is the tension-compression and reversed torsion test using the hollow cylinder specimen, which is most widely used testing. type ib is similar to type ia from the point of using the hollow cylinder specimen but type ib is applied with the internal and external pressures in addition to the tension-compression and reversed torsion loadings. type ii is the biaxial tension-compression testing using the cruciform specimen. type iii is the tri-axial tension-compression testing using a cubic specimen. principal stain and stress ratio ranges which can be performed in each type of test are summarized here. type ia have been used widely multiaxial fatigue studies，but the principal stress/strain ratio range performable by this testing is 1<λ0/1<ν. types ib and ii can perform the multiaxial fatigue test under full ranged principal stress/strain ratio range of 1<λ, 1. type iii also does the test under the same multiaxial strain state and tri-axial tension-compression loading, too. however, types ii and iii have no change in principal directions of stress and strain since the directions always fixed into the direction of applied loading. only type ib can perform the multiaxial fatigue test in the full ranged principal stress/strain ratio range with non-proportional loading. multiaxial fatigue testing machine for tension-torsion and inner pressure fig. 5 (a) shows a schematic view of the testing machine used in this study of which type is corresponds to type ib. to generate the inner pressure with tension and torsion loadings, additional hydraulic actuators is installed into the common t. itoh et alii, frattura ed integrità strutturale, 34 (2015) 487-497; doi: 10.3221/igf-esis.34.54 491 used push-pull and reversed torsion testing machine. for measurements of axial, torsional and hoop strains, inductive displacement sensor type extensometers are mounted directly onto the specimen. to measure and evaluate axial, torsional and hoop stresses, load cells for axial load and torque and pressure gauge are installed. the maximum loads are 50kn for push-pull and 250nm for torsion and the maximum inner pressures is 200mpa. by applying these loads, this testing machine can perform the multiaxial fatigue tests under the principal stress ratio range of 1λ1. test control system of this testing machine becomes more complicated than those in common used testing machines since three hydraulic actuators must be controlled simultaneously and independently by employing a test controller program and a system as shown in fig. 5 (b). in order to raise the precision of control, three types of feedback (fb) loop are applied in this testing machine. first one is from load cell to servo amplifier for axial and torsional control, which operates on load-controlled mode. second one is from strain gauge to servo amplifier for axial and torsional control, which operates on displacement-controlled mode. the load or the displacement control can be changed by fb selection switch. the last one is from pressure gauge to servo amplifier to control the inner pressure as test control programed. the specimen employed is the hollow cylinder specimens designed for this testing machine of which shapes and dimensions will be shown later. actuator (torque) specimen actuator (axial load) load cell (axial load & torque) extensometer (axial & shear displacement) actuator (inner pressure) pressure gauge (inner pressure) analog  to  digital  conversion servo amplifiers amplifiers actuators servo  valve axial displacement shear displacement internal pressure sensors axial load torque axial control torque control internal pressure pc digital  to  analog  conversion f e e d b a ck (a) (b) figure 5: multiaxial testing machine for push-pull, reversed torsion and inner pressure. (a) schematic showing of multiaxial testing machine, (b) over view of control system. test material and experimental procedure he material tested was ti-6al-4v, which was subject to solution treatment at 960°c for 1 hour followed by water cooling, annealing at 705°c for 2 hours and air cooling. fig. 6 shows the micro structure, which consists of alpha phases (hexagonal close-packed crystal structure) and the dual alphaand beta-phase mixture (body-centered cubic crystal structure). figure 6: microstructure of ti-6al-4v alloy. t alpha+beta alpha t. itoh et alii, frattura ed integrità strutturale, 34 (2015) 487-497; doi: 10.3221/igf-esis.34.54 492 fig. 7 shows the shape and dimensions of hollow cylinder specimen employed which has a 12 mm inner diameter, a 14 mm outer diameter, and an 8.5 mm parallel at gauge part. in the figure, a coordinate employed are indicated with principal stresses. σ1 is the maximum principal stress, σ2 is the middle principal stress. in this test, σ1 and σ2 are equivalent to axial stress σz and hoop stress σθ equated by the following equations,       2 1 2 2 2 2 4 4 4 i z o i o i            p d f d d d d (7) 2 i o i       p d d d (8) where f and p are axial load and inner pressure, respectively. di and do are inner and outer diameters at gauge part of the specimen. figure 7: shape and dimensions of test specimens (mm) with coordinate. stress controlled low cycle fatigue tests with proportional zero-peak loading were conducted under 4 types of stress paths shown in fig. 8. in the figure, each stress path takes the principal stress ratio, λ=0, 0.4, 0.5 and 1.0. the dashed line shows a constant mises’ equivalent stress at 800 mpa. in the test at =0.4, peak stress was set at 858 mpa. the other ’s test at 800 mpa. m id d le p ri n ci p a l st re ss σ 2 maximum principal stress σ1 (λ=0) (λ=1.0) (λ=0.5) (λ=0.4) mises stress σeq=800mpa o figure 8: principal stress path. fig. 9 shows strain waveforms of axial load (f), inner pressure (p) and axial stress (z), hoop stress (). test frequencies in the uniaxial fatigue test (λ=0) and the biaxial fatigue tests (λ=0.4, 0.5, 1.0) are 0.4 hz and 0.2 hz, respectively. number of cycles to failure (failure life), nf, was determined as the cycle at which the maximum inner pressure was reduced due to leak of oil by initiation of through crack or rupture of the specimen. tab. 1 summarizes test conditions conducted. in the table, z max and  max are maximum values of z and  obtained at the peak load, respectively. eq max a maximum value of mises’ equivalent stress (eq) equated by r θ z σθ=σ2 σz=σ1 σr=σ3=0 t. itoh et alii, frattura ed integrità strutturale, 34 (2015) 487-497; doi: 10.3221/igf-esis.34.54 493      2 2 21 2 eq r r         (9) the inner and outer surfaces at the gauge part of the specimen were ground to an averaged surface roughness 1.6m by honing machine. after the honing, some specimen were also received polishing and buffing to 10m al2o3 denoted by ‘polish’ in tab. 1. s tr e ss time t axial stress σz hoop stress σθ s tr e ss time t axial stress σz hoop stress σθ s tr e ss time t axial stress σz hoop stress σθ a xi a l lo a d , in n e r p re s s u re time t axial load f inner pressure p a xi a l lo a d , in n e r p re ss u re time t axial load f inner pressure p a xi a l lo a d , in n e r p re ss u re time t axial load f inner pressure p load & pressure axial & hoop stresses =0 =0.4, 0.5 =1 figure 9: wave forms of axial load, inner pressure, axial and hoop stresses. stress path maximum stress (mpa) polish/ non-polish uniaxial/biaxial λ axial stress σz max hoop stress σ max mises stress σeq max uniaxial fatigue 0 800 ― 800 non-polish polish biaxial fatigue 0.4 985 400 858 non-polish polish 0.5 924 462 800 polish 1.0 800 800 800 polish table 1: list of fatigue test condition. experimental results and discussion failure life ig. 10 shows a comparison of failure lives. in this figure, failure lives are normalized by the mean value of failure life in the uniaxial fatigue tests (λ=0 tests) tested using polished and non-polished specimens. in comparing the failure lives tested using the polished specimen, failure lives (nf) tend to decrease with increase of the principal stress ratio (λ) although nf at λ=0.4 is slightly shorter than nf at λ=0.5. the shorter life in the λ=0.4 test may come from that the maximum mises’ equivalent stress in the test is slightly larger than those in the other λ’s tests as shown in tab. 1. the specimen polishing effect can be seen in the λ=0 and λ=0.4 tests. in the λ=0 test, nf with non-polished specimen have longer life by about 20 % than that with polished specimen. in the λ=0.4 test, conversely, nf with non-polished specimen is shorter than that with the polished specimen and the reduction ratio is down to approximately 50 % depending on each specimen. the effects of λ and polishing on the failure life will be discussed in following sections. f t. itoh et alii, frattura ed integrità strutturale, 34 (2015) 487-497; doi: 10.3221/igf-esis.34.54 494 0 20 40 60 80 100 120 140 0 20 40 60 80 100 120 140 (%) uniaxial fatigue λ=0 biaxial fatigue λ=0.4 biaxial fatigue λ=0.5 biaxial fatigue λ=1 non-polish polish figure 10: comparison of failure lives at each principal stress ratio’s test. dependence of defamation behavior on multiaxiality fig. 11 shows variation of mean axial strain (z mean) as a function of cycle (n). in the figure, the vertical axis is normalized by mean axial strain at 10 cycles (z mean10) and the horizontal normalized by (n/nf). in all the tests, mean strains increase gradually with increase of cycles, i.e., cyclic ratcheting occurs because the stress amplitude employed was relative high comparing with the yield stress 113 gpa. the degree of the ratcheting becomes larger with increasing  and the larger ratcheting may leads to the reduction in failure life. in structural components using ti-6al-4v, on the other hand, the stress level under service loadings is usually much lower than that employed in this study. in this case, no or small ratcheting will occur resulting in smaller effect of  on failure life. however, the property of failure life under multiaxial loading at lower stress levels is still open question and additional experimental tests at the stress revel are required to confirm them. figure 11: variation of mean axial strains at each principal stress ratio’s test. surface crack and effects polishing on failure life fig. 12 shows cracks observed on specimen surface fatigued at each ’s test. in the figure, the upper side shows surface cracks observed by optical microscope and the lower side schematic showings of the main crack. using the polished specimen, the crack in the λ=0 test shows a zigzag shape crack. each zigzag crack is approximately 100 m in length and has propagation directions of 45 degrees from the specimen axial direction and then the macro-crack formed by linking of each zigzag crack propagated normal to the axial direction. in the tests at λ=0.4 and 0.5, observed cracks are similar to that at λ=0 although length of each zigzag crack is slightly smaller. in the λ=1.0 test, a main crack is observed in the direction of specimen axis and small cracks are also observed around the main crack in various direction. using the non-polished specimen, on the other hand, the crack at λ=0 test is slightly different from that at λ=0 test with the polished specimen. the crack shows the zigzag one but it may be formed by linking cracks propagating along cutting 0 0.2 0.4 0.6 0.8 1 0 1 2 3 4 λ＝0 λ＝0.4 λ＝0.5 λ＝1.0 m e a n a xi a l st ra in n o rm a liz e d b y ε z m e a n 1 0 ε z m ea n /ε z m ea n 1 0 number of cycle normalized by nf n/nf t. itoh et alii, frattura ed integrità strutturale, 34 (2015) 487-497; doi: 10.3221/igf-esis.34.54 495 scratches yielded in machining. in the λ=0.4 test with the non-polishing specimen, a straight crack is observed propagating along the cutting scratch. fig. 13 shows mohr’s stress circles and principal shear stress planes with normal and shear stresses on their planes in each λ state. at λ=0, the equivalent maximum shear stresses planes exists on planes normal and 45 degree incline to free surfaces. these two planes intersect with the surface plane in directions of 45 degree and normal to the specimen axis, respectively. so there are two possibilities of crack propagation which may results in the different crack mode between polish and non-polish specimens. in the λ=0.4 test, the maximum shear stress plane is 45 degree incline to the free surface on which normal and shear stresses are 493 mpa. the second principal shear stress plane is normal to the free surface of which normal and shear stresses are 693mpa and 293mpa, respectively. on this plane, the shear stress is much smaller but the normal stress is larger than those on the maximum shear stress plane. comparing the equivalent mises’ stresses on these planes, the values have a small difference, 985mpa on the maximum shear stress plane and 858mpa on the second principal shear stress plane, which may suggests that which plane cracks propagate is undecidable depending on specimen surface condition. the crack mode may be affected by the specimen surface condition in uniaxial and biaxial fatigue tests and the difference in the crack mode has a possibility affecting on failure lives largely in the biaxial fatigue tests. however, more detail crack observation and discussion will be required about the crack modes in biaxial stress condition. λ λ=0 λ=0.4 λ=0.5 λ=1.0 p o lis h n o n p o lis h axial direction 400 μm figure 12: main crack shape on the surface of specimen.  λ=0 λ=0.4 λ=0.5 λ=1.0 m o h r’ s st re ss c ir cl e s h e a r st re ss p la n e s σ2 σ3 τ σ σ1 σ3 τ σ σ1 σ2 σ3 σ1 τ σ σ2 σ3 σ1 τ σ σ2 400 400 400 400 693 293 462 462 693 231 493 493 400 400 400 400 figure 13: mohr’s stress circle and maximum shear plane in principal stress ratio. t. itoh et alii, frattura ed integrità strutturale, 34 (2015) 487-497; doi: 10.3221/igf-esis.34.54 496 conclusions 1. multiaxial failure lives of ti-6al-4v depend on multiaxiality and decrease with increase of principal stress ratio, λ. the reduction is caused by cyclic ratcheting. 2. crack mode at each λ’s test depends on specimen surface condition of machining. in biaxial loading test, failure life is affected by the crack mode. references [1] kanazawa, k., miller, k.j., brown m.w., cyclic deformation of 1%cr-mo-v steel under out-of-phase loads. fatigue eng mater struct, 2(3) (1979) 217228. [2] mcdowell, f.l., on the path dependence of transient hardening and softening to stable states under complex biaxial cyclic loading. in: desai and gallagher, editors. proc int conf constitutive laws eng mater, (1983) 125-135. [3] krempl, e., lu, h., comparison of the stress response of an aluminum alloy tube to proportional and alternate axial and shear strain paths at room temperature. mechanics of materials, 2(3) (1983) 183192. [4] socie, d.f., multiaxial fatigue damage models. trans am soc mech eng  j eng mater technol, 109(4) (1987) 293298. [5] nitta, a., ogata, t., kuwabara, k., the effect of axial-torsional straining phase on elevated-temperature biaxial lowcycle fatigue life in sus304 stainless steel. j soc mater sci jpn,. 36(403) (1987) 376382. [6] doong, s.h., socie, d.f., robertson, i.m., dislocation substructures and nonproportional hardening. trans am soc mech eng  j eng mater technol, 112(4) (1987)456465. [7] fatemi, a., socie, d.f., a critical plane approach to multiaxial fatigue damage including out-of-phase loading. fatigue eng mate struct, 11(3) (1988) 149165. [8] itoh, t., sakane, m., ohnami, m., socie, d.f., non-proportional low cycle fatigue criterion for type 304 stainless steel. trans am soc mech eng  j eng mater technol, 117(3) (1995) 285292. [9] chen, x., gao, q., sun, x.f., low-cycle fatigue under non-proportional loading. fatigue eng mater struct, 19(7) (1996) 839854. [10] itoh, t., nakata, t., sakane, m., ohnami, m., non-proportional low cycle fatigue of 6061 aluminum alloy under 14 strain path. in: macha et al., editors. multiaxial fatigue and fracture, vol. 25. elsevier international series on structural integrity, (1999) 4154. [11] socie, d.f., marquis, g.b., multiaxial fatigue. sae int, (2000). [12] itoh, t., effect of direction change in maximum principal strain axis on multiaxial low cycle fatigue life of type 304 stainless steel at elevated temperature. j soc mater sci jpn, 49(9) (2000) 988993. [13] itoh, t., a model for evaluation of low cycle fatigue lives under non-proportional straining. j soc mater sci, 50(12) (2001) 13171322. [14] chen, x., an, k., kim, k.s., low-cycle fatigue of 1cr-18ni-9ti stainless steel and related weld metal under axial, torsional and 90°out-of-phase loading. fatigue eng mater struct, 27(6) (2004) 439448. [15] shamsaei, n., gladskyi, m., panasovskyi, k., shukaev, s., fatemi, a., multiaxial fatigue of titanium including step loading and load path alteration and sequence effects. int j fatigue, 32(11) (2010) 1862-1874. [16] itoh, t., yang, t., material dependence of multiaxial low cycle fatigue lives under non-proportional loading. int j fatigue, 33(8) (2011) 10251031. [17] kallmeyer, a.r., krgo, a., kurath, p., evaluation of multiaxial fatigue life prediction methodologies for ti-6al-4v. trans am soc mech eng  j eng mater technol, 124(2) (2002) 229237. [18] mall, s., namjoshi, s.a., porter, w.j., effects of microstructure on fretting fatigue crack initiation behavior of ti-6al4v. materials science and engineering a, 383(2) (2004) 334-340. [19] nakamura, h., takanashi, m., itoh, t., wu, m., shimizu, y., fatigue crack initiation and growth behavior of ti-6al4v under non-proportional multiaxial loading, 33(7) (2011) 842-848. [20] findley, w.n., modified theory of fatigue failure under combined stress. in: proc society experimental stress analysis, 14 (1956) 3546. t. itoh et alii, frattura ed integrità strutturale, 34 (2015) 487-497; doi: 10.3221/igf-esis.34.54 497 [21] mcdiarmid, d.l., a shear stress based critical plane criterion of multiaxial fatigue failure for design and life prediction. fatigue fract eng mater struct, 17(12) (1994) 14751484. [22] brown, m.w., miller, k.j., a theory for fatigue under multiaxial stress-strain conditions. in: proc institution of mechanical engineering, 187 (1973) 745756. [23] brown, m.w., wang, c.h., a path-independent parameter for fatigue under proportional and non-proportional loading. fatigue fract eng mater struct, 16(12) (1993) 1285-1298. [24] smith, r.n., watson, p.p., topper, t.h., a stress-strain parameter for the fatigue of metals. j materials, 5(4) (1970) 767778. [25] ogata, t., nitta, a., evaluation of multiaxial low-cycle fatigue failure based on new criterion and its application to high temperature structural design. japan: journal of the society of materials science, 42 (1993) 7772. microsoft word numero 12 art 3 l. collini, frattura ed integrità strutturale, 12 (2010) 21-36; doi: 10.3221/igf-esis.12.03 21 la modellazione microstrutturale di materiali a struttura eterogenea: princìpi ed applicazioni luca collini università di parma, dipartimento di ingegneria industriale, v.le g.p. usberti 181/a, 43100 parma luca.collini@unipr.it riassunto. molti problemi della meccanica e fisica dei solidi e della scienza dei materiali, non sono facilmente risolvibili con gli approcci tradizionali. oltre allo studio delle proprietà effettive dei solidi eterogenei, vi è la crescente necessità di incorporare un maggiore numero di informazioni sui meccanismi di deformazione e danneggiamento generati alla microscala, anche per i materiali abitualmente considerati omogenei. micromeccanismi di cavitazione e concentrazioni locali di tensione e deformazione, sono indispensabili per spiegare fenomeni non-lineari come la rottura di fatica o il cedimento duttile, altrimenti non inquadrabili con approcci classici di tensioni e deformazioni medie. la micromeccanica si occupa della determinazione precisa, o di una stima accurata, di grandezze di campo microstrutturali locali. in questo lavoro sono illustrati i princìpi che sono alla base dell’approccio micromeccanico, come i concetti di multiscala, di distribuzione statistica delle fasi, di descrizione mediante volumi di riferimento e di omogeneizzazione e localizzazione, e, attraverso alcune applicazioni pratiche delle principali tecniche di modellazione, sono illustrati e discussi criticamente i risultati della ricerca effettuata su varie strutture di ghisa nodulare. abstract. there are many problems in solid mechanics, physics of solids and materials science that can not been solved using conventional approaches. besides the effective properties of non-homogeneous bodies, there is an increasing need for incorporating more physical information about small-scale mechanisms of deformation and damage into phenomenological models of plasticity and rupture of materials which are usually considered homogeneous. cavitation, local stress or strain concentrations at small scale are essential to explain nonlinear phenomena, such as fatigue or ductile rupture, which are not understandable from the simple point of view of average stresses or strains. precise determination or accurate estimation of local fields is the domain of micromechanics. this work treats the basic concepts of the micromechanics in a simple way, with some practical suggestion on the most commonly used modelling techniques and some applications made by the author on various nodular cast iron microstructures. keywords. modellazione micromeccanica; materiali a struttura eterogenea; compositi; comportamento elasto-plastico. introduzione alla meccanica dei materiali microstrutturati materiali microstrutturati e concetto di scala di osservazione a microe meso-meccanica del continuo è una branca relativamente giovane della meccanica dei materiali, che studia il comportamento meccanico dei materiali a livello microstrutturale. molti dei materiali di interesse industriale ed ingegneristico, e la maggior parte dei materiali “naturali”, presentano una struttura eterogenea, formata cioè da più costituenti o “fasi”, distinguibili ad una certa (ridotta) scala di osservazione. in altre parole, ciò che al l http://dx.medra.org/10.3221/igf-esis.12.03&auth=true http://www.gruppofrattura.it l. collini, frattura ed integrità strutturale, 12 (2010) 21-36; doi: 10.3221/igf-esis.12.03 22 nostro occhio può sembrare un solido continuo ed omogeneo, se analizzato ad un’altra lunghezza di scala si rivela formato da più costituenti continui, che a loro volta possono essere eterogenei (per proprietà, orientamento, ecc.) aumentando ulteriormente la definizione della scala di osservazione. è questo un concetto fondamentale nello studio della meccanica dei materiali a livello microscopico. tipici esempi di materiali eterogenei sono i materiali compositi, fibro-rinforzati o particellari, i materiali porosi, gli stessi metalli policristallini, ma anche il legno e l’osso. una diretta conseguenza di questo concetto è l’approccio cosiddetto multiscala allo studio del comportamento meccanico dei materiali microstrutturati, associato a fenomeni e meccanismi peculiari della dimensione in cui si conduce l’analisi [1, 2]. un gran numero di problemi della meccanica dei solidi e della scienza dei materiali non può di fatto essere risolto tramite gli approcci convenzionali, poiché alla base delle effettive proprietà meccaniche di un materiale eterogeneo vi è la crescente necessità di incorporare informazioni fisiche sui micromeccanismi di deformazione e danneggiamento all’interno di modelli fenomenologici di plasticità o rottura, caratteristici dei materiali omogenei. i concetti di nucleazione di vuoti o di localizzazione delle deformazioni a livello microscopico sono alla base di fenomeni non-lineari come la fatica nei materiali, o la rottura duttile, che non sono spiegabili dal solo punto di vista delle tensioni e delle deformazioni medie o mediate. la precisa determinazione delle grandezze di campo locali nel materiale è l’ambito di studio della micromeccanica. i processi di deformazione elasto-plastica sono convenzionalmente trattati facendo riferimento alla meccanica del continuo, che si basa su di una descrizione macroscopica o effettiva del comportamento meccanico del materiale. tale approccio, in cui rientra anche la stessa teoria delle dislocazioni, mostra dei limiti nell’interpretare i meccanismi plastici in un materiale a microstruttura eterogenea. per fare ciò l’analisi deve affinarsi in definizione considerando fattori aggiuntivi a livello microstrutturale, come il comportamento di un singolo elemento del materiale (cristallo, grano, fase…), la mutua interazione tra questi, il comportamento delle zone di confine, la formazione di nuove strutture interne durante la deformazione (ad es. celle, bande di scorrimento, blocchi o altre sottostrutture). da quanto detto appare evidente l’importanza che riveste la dimensione, o scala, alla quale si studia il comportamento di un materiale. la micromeccanica definisce quindi una gerarchia di livelli dimensionali organizzati, appartenenti a diversi ordini di grandezza [3, 4]. ad ogni livello, o scala, si distingue una determinata organizzazione delle fasi. in fig. 1 è schematizzato questo concetto, con diretto riferimento alla struttura tipica di una ghisa nodulare a matrice mista ferriticoperlitica. figura 1: scale di osservazione associate alla struttura di una ghisa nodulare.   la macroscala, fig. 1 a sinistra, identifica il comportamento meccanico macroscopico del materiale, ad esempio la sua resistenza determinata con una prova di trazione, di tenacità a frattura, etc. la fenomenologia associata alla macroscala definisce le proprietà solitamente impiegate nella progettazione meccanica. al livello della microscala, fig. 1 a destra, gli elementi caratteristici sono invece inclusioni, porosità, disposizioni irregolari o difetti della struttura (vacanze, dislocazioni). nel caso illustrato relativo alla ghisa nodulare, alla microscala si manifesta ad esempio il meccanismo di danneggiamento duttile (cavitazione plastica e successiva instabilità della matrice attorno ai noduli di grafite, tipico delle ghise ferritiche): la microscala evidenzia quindi le cause e i meccanismi alla base del comportamento del materiale. una scala intermedia alle precedenti è la mesoscala. fig. 1 al centro mostra una tipica sezione metallografica della ghisa sferoidale. la mesoscala rappresenta il livello in cui s’individuano le fasi presenti o gli elementi caratteristici della microstruttura. la http://dx.medra.org/10.3221/igf-esis.12.03&auth=true http://www.gruppofrattura.it l. collini, frattura ed integrità strutturale, 12 (2010) 21-36; doi: 10.3221/igf-esis.12.03 23 mesoscala possiede una sua peculiarità: essa ammette la descrizione del comportamento di ogni singola fase come un continuo. nella ghisa ad esempio è individuata la fase ferritica (regioni di colore chiaro), quella perlitica (regioni grigio scuro) e la grafite che durante il raffreddamento della massa fusa precipita sotto forma di noduli o sferoidi. in funzione della percentuale delle due fasi – ferrite e perlite – presenti nella matrice, le zone ferritiche sono disposte o attorno ad un singolo nodulo di grafite (configurazione bull’s eye), o in aree più estese racchiudono un numero maggiore di sferoidi. la mesoscala identifica quindi un altro aspetto essenziale del materiale: la disposizione delle fasi. l’analisi del comportamento meccanico di materiali multi-fase o a microstruttura eterogenea su una determinata scala, richiede in genere strumenti di modellazione. i modelli sono volti alla comprensione dei micro-meccanismi che governano il comportamento del solido, manifestato su scala macroscopica. essi forniscono indicazioni sul comportamento d’insieme di un solido disomogeneo, a partire dalla conoscenza del comportamento delle singole fasi e della loro interazione, [5]. la microstruttura della maggior parte dei materiali eterogenei di interesse ingegneristico è solitamente troppo complessa, dal punto di vista puramente geometrico, per essere descritta nel dettaglio in modo deterministico. la disposizione delle fasi deve necessariamente essere trattata in modo statistico, e descritta mediante appropriate funzioni di distribuzione e correlazione. la struttura eterogenea di un materiale può infatti essere considerata “statisticamente omogenea”, e la descrizione statistica dell’arrangiamento non dipende dalla posizione in cui esso è valutato. questo è un altro concetto di fondamentale importanza alla base dell’approccio micromeccanico. per questi sistemi statisticamente omogenei, è lecito definire delle proprietà medie sul volume, indipendenti dalla grandezza e dalla posizione del volume considerato, ammesso che esso sia “abbastanza grande”. un tale volume che contiene tutte le informazioni necessarie e sufficienti per la descrizione statistica di una data microstruttura è detto volume di riferimento, o reference volume element (rve). una microstruttura statisticamente omogenea può essere isotropa se i descrittori statistici sono degli invarianti rotazionali, o statisticamente anisotropa se vi sono direzioni preferenziali nella geometria, orientazione o posizione dei costituenti, [6]. omogeneizzazione e localizzazione. una pratica comune nel trattare i materiali compositi è quella di sostituire idealmente il comportamento della loro struttura disomogenea con quello di un materiale omogeneo equivalente o, per meglio dire, omogeneizzato. la maggior parte delle proprietà macroscopiche può essere determinata sperimentalmente, ma alcune di esse, in pratica, non sono determinabili o sono molto difficili da misurare. un’intera area della meccanica dei solidi si è occupata, negli ultimi 30 anni, della teoria dei compositi e della possibilità di predire le loro proprietà effettive a partire dal comportamento di ciascun costituente, o fase, e dalla loro disposizione, o microstruttura. dai primi lavori di hill [7] e hashin e shtrikman [8], notevoli progressi si sono avuti nello studio del comportamento lineare ed elastico dei materiali, mentre molto meno è stato proposto per quanto riguarda i fenomeni non lineari, come la plasticità e il creep. analizziamo il caso più semplice di materiale microstrutturato a cui sono associate due scale caratteristiche, la macroscala e la scala, molto più piccola, a cui il materiale è eterogeneo, che abbiamo chiamato microscala. alla macroscala il comportamento del materiale è descritto in maniera convenzionale, cioè come quello di un equivalente continuo omogeneo opportunamente scelto. sforzi e deformazioni hanno dunque andamenti continui, che dipendono dalle variazioni di geometria e dalle condizioni di carico. in assenza di macroscopiche variazioni del gradiente di queste grandezze (si parla di slow variations), nessuna variazione è evidente alla microscala, dove l’eterogeneità del materiale produce microscopiche, localizzate fluttuazioni (fast variations). i tensori di tensione e deformazione,  e , funzione del vettore di posizione x, possono essere allora pensati come la somma di grandezze di campo slow (   ,   ) e fast (  ,  ):         ' '           x x x x (1) nel caso, peraltro comune, di materiali eterogenei che mostrano una distinzione sufficientemente definita tra le lunghezze di scala, è possibile scrivere la relazione:    * * * * * * s d          x x (2) valida per ogni campo di tensione statisticamente valido * e campo di deformazione cinematicamente ammissibile *, [7]. nell’eq. (2), il simbolo  indica che una quantità è mediata sul volume di riferimento, e s è il volume di controllo, grande almeno quanto il rve. l’eq.(2) è nota come la condizione di macro-omogeneità di hill o di hill-mandel. essa implica sostanzialmente che la densità media di energia di deformazione sul volume di un solido elastico disomogeneo, http://dx.medra.org/10.3221/igf-esis.12.03&auth=true http://www.gruppofrattura.it l. collini, frattura ed integrità strutturale, 12 (2010) 21-36; doi: 10.3221/igf-esis.12.03 24 possa essere ottenuta da tensioni e deformazioni mediate sul volume, ammesso che le macroe microscale siano sufficientemente diverse. ciò è molto importante, poiché rende possibile il concetto di materiale omogeneo equivalente dal punto di vista energetico al corrispettivo materiale microstrutturato. per ciascuna regione di un materiale disomogeneo, i campi di tensione e deformazione locali (x) e (x) e le corrispondenti risposte macroscopiche  e  , possono essere formalmente messi in relazione mediante le espressioni di localizzazione (o proiezione):               x a x x b x (3) se la regione si presenta sufficientemente estesa e non contiene significativi gradienti nelle distribuzioni di tensione e deformazione macroscopiche, le relazioni di omogeneizzazione possono scriversi nella forma:               1 1 2 1 1 s s s s s s s s d d d d                                 x u x n x u x n x x t x x (4) dove sè la superficie della regione in esame, nγ il vettore normale alla superficie, u il vettore di spostamento, t(x)=(x)n il vettore di trazione sulla superficie, e  il prodotto diadico tra vettori o diade (se a = axi + ayj + azk e b = bxi + byj + bzk, a  b = axbxii + axbyij + axbzik + aybxji + aybyjj + aybzjk + azbxki + azbykj + azbzkk). i tensori a(x) e b(x) sono detti tensori di concentrazione della tensione e della deformazione (o funzioni di influenza). si noti che i campi di tensione e deformazione medie sono univocamente determinati dai campi di spostamento e di trazione, dato che i costituenti sono omogenei e non presentano difetti o discontinuità (come fessurazioni) al loro interno. è importante notare che le equazioni (1) e (4) implicano che per un volume di integrazione abbastanza grande, le medie delle fluttuazioni sul volume si annullino:    1 1 0 s s s s d d           x x . (5) importanti applicazioni delle analisi di omogeneizzazione sono la caratterizzazione di materiali, come ad esempio la simulazione di semplici prove meccaniche di carico (diagramma tensione-deformazione), e modelli costitutivi micromeccanici in grado di riprodurre il comportamento del materiale comunque caricato. data la generale complessità e la casualità delle microstrutture reali, delle semplificazioni ed approssimazioni vengono solitamente impiegate nei processi di omogeneizzazione e localizzazione. le reali espressioni per a(x), b(x), (x), (x), etc. non sono di solito determinabili. tipicamente, tali approssimazioni sono basate sull’ipotesi di ergodicità degli stati di tensione e deformazione (un processo si dice ergodico quando, per un tempo che tende ad infinito, passa in ogni suo stato una percentuale di tempo pari alla probabilità di trovarsi in quello stato, cioè, in altre parole, è statisticamente omogeneo). quindi si considera che volumi di materiale abbastanza estesi, scelti in maniera casuale, rispondano con lo stesso comportamento medio del materiale continuo che, di rimando, rappresenta le proprietà globali o effettive della struttura eterogenea. idealmente, il volume di omogeneizzazione dovrebbe essere scelto come volume di riferimento, ovvero un sotto-volume di s, che è statisticamente rappresentativo della microgeometria del materiale. questo elemento di volume deve essere abbastanza esteso per permettere un campionamento significativo delle grandezze di campo di interesse, ma anche sufficientemente piccolo affinché risultino trascurabili i gradienti macroscopici. nella pratica, può risultare difficoltoso studiare, e, di fatto, anche identificare, un rve adatto a descrivere fedelmente la microstruttura del materiale eterogeneo; devono quindi essere prese in considerazione approssimazioni e ipotesi semplificative, come verrà di seguito mostrato in alcune applicazioni pratiche di modellazione microstrutturale. approcci e metodi della modellazione micromeccanica ome descritto nella precedente sezione, le tecniche di omogeneizzazione sono volte a determinare la risposta di un piccolo volume rappresentativo di un materiale a struttura eterogenea sotto l’azione di prescritte condizioni meccaniche o termiche, deducendo da esso le proprietà effettive del materiale. l’applicazione più tipica di questo c http://dx.medra.org/10.3221/igf-esis.12.03&auth=true http://www.gruppofrattura.it l. collini, frattura ed integrità strutturale, 12 (2010) 21-36; doi: 10.3221/igf-esis.12.03 25 tipo di analisi è la caratterizzazione del materiale, cioè la simulazione della sua risposta complessiva se sottoposto ad un semplice carico, come ad esempio la prova di trazione uniassiale. molte procedure di omogeneizzazione possono essere impiegate anche direttamente sotto forma di modelli costitutivi del materiale, basati sulla microstruttura e atti a descrivere il macro-comportamento mettendo in relazione i tensori di tensione e deformazione completamente omogeneizzati. confrontati con leggi costitutive semi-empiriche, tali modelli micromeccanici possiedono sia una chiara base fisica, sia l’intrinseca capacità di “zoomare” le quantità localizzate in ciascuna fase adottando le procedure di localizzazione. in questo modo è possibile determinare ad esempio il flusso plastico o il danno locali, quando la risposta macroscopica o lo stato di un campione o di una struttura sono noti a priori. oltre alla caratterizzazione di un materiale o alla realizzazione di modelli costitutivi, la micromeccanica del continuo vede altre importanti applicazioni; tra tutte lo studio di fenomeni locali in materiali eterogenei, come l’evoluzione del danno su scala microscopica, l’innesco e la crescita di cricche, gli stati di tensione tra le interfacce macroscopiche e le superfici libere, gli effetti di instabilità locali, l’interazione tra cambiamenti di fase e microtensionamenti. analisi di questo tipo possono venire condotte con diverse tecniche e procedure pratiche; in questa sezione si darà una descrizione di alcune di esse, soffermandosi maggiormente su quelle impiegate dall’autore. è conveniente suddividere le tecniche di modellazione microstrutturale in due grandi categorie. la prima di esse raggruppa i metodi che descrivono microgeometrie di materiali eterogenei sulla base di (limitate) informazioni statistiche, la seconda categoria abbraccia le metodiche di modellazione basate su microstrutture reali discrete. metodi statistici fanno parte di questa categoria gli approcci di tipo mean field e i metodi variazionali. negli approcci di tipo mean field (mfas) le grandezze di campo sono approssimate con le loro medie   p ,  p per ciascuna fase p: si parla in questo caso di piecewise (phasewise) uniform stress and strain fields; le relazioni di localizzazione assumono la forma:         pp pp       a b (6) e quelle di omogeneizzazione:         1 p p p d       x con    pp p v   (7a)         1 p p p d       x con    pp p v   (7b) dove l’indice (p) indica una data fase del materiale, (p) il suo volume, e v(p) = (p)/k(k) la frazione in volume della suddetta fase. si noti che, in contrasto con eq. (3), i tensori di localizzazione a e b non dipendono dal vettore di posizione nel volume di controllo. tra i metodi mfas classici si ricordano quello di mori-tanaka, che è l’approccio più semplice nel descrivere completamente un composito bi-fase; quello di eshelby, che in un lavoro del 1957 studiò il campo di tensione attorno ad un’inclusione ellissoidale immersa in una matrice infinita soggetta a una deformazione uniforme (fig. 2); il metodo di hashin e shtrikman. a titolo di esempio si riportano le espressioni in forma chiusa delle proprietà elastiche di un composito bifase secondo le teorie di eshelby, 1957 eq. (8), hashin-shtrikman, 1962 eq. (9), mori-tanaka, 1963 eq. (10). per la trattazione matematica completa si rimanda alla specifica letteratura, [2, 9-11].          i i mc t ce e         (8)              1 1 * ( ) 0 ( ) 0m m m r mr r hse e l e i l e e e           (9)                1 1 * ( ) ( ) ( ) m r m m r mr r me e i e e s s i e e e               (10) (i) = tensore degli sforzi dell’inclusione; http://dx.medra.org/10.3221/igf-esis.12.03&auth=true http://www.gruppofrattura.it l. collini, frattura ed integrità strutturale, 12 (2010) 21-36; doi: 10.3221/igf-esis.12.03 26 e(i) = tensore di elasticità dell’inclusione; e(m) = tensore di elasticità della matrice; e(r) = tensore di elasticità di un’inclusione ellissoidica; c = deformazione in-situ (constrained deformation) = st (s è noto come il tensore di eshelby); t = autodeformazione (unconstrained deformation);  = autodeformazione equivalente fittizia; e*hs , e*m = tensori di elasticità globali; i = tensore identità; (r) = frazione in volume di inclusioni; l0 = e0[(s0)-1 – i] = overall constraint tensor. i metodi variazionali o di minimo dell’energia (hill [12], hashin-shtrikman [13]), sono spesso impiegati per stimare i limiti superiori e, in molti casi, inferiori dei tensori elastici, dei moduli elastici, di quelli secanti e di altre proprietà di materiali microstrutturati. figura 2: schema del problema di eshelby (1957) di determinazione del campo tensionale in un continuo elastico contenente un’inclusione soggetta alla autodeformazione t. immagine tratta da [14]. metodi basati su microstrutture discrete alla seconda tipologia di metodi di modellazione possono ricondursi le tecniche di studio basate su microstrutture discrete. tra queste le più rilevanti sono la modellazione tramite microcampi periodici (celle unitarie), la modellazione a embedded cell, e la modellazione attraverso “finestre” campionate sulla struttura eterogenea del materiale. nella modellazione tramite microcampi periodici (periodic microfield approaches, pmas), che comprende i metodi a cella unitaria, la microstruttura reale è approssimata mediante un modello discreto che ripetuto uguale a se stesso riproduce una quantità comunque estesa del materiale; le fasi e il loro arrangiamento sono intrinsecamente periodici. tali approcci, nei quali la risoluzione è solitamente affidata a metodi numerici, sono spesso utilizzati per definire dei modelli costitutivi di materiale su base microstrutturale, e per lo studio di fenomeni non-lineari, come il danneggiamento, grazie alla grande definizione che possono offrire senza impiegare grandi risorse di calcolo. gli approcci pmas non sono invece utilizzabili per l’analisi dell’interazione della microstruttura con fenomeni macroscopici, come ad esempio la propagazione di un difetto. la letteratura specifica dei metodi pmas è estesissima, dato il loro ampio utilizzo; si citano qui solo alcuni riferimenti di base, [15-18]. nell’impiego di microcampi periodici risultano particolarmente critiche le fasi di: (i) definizione del microcampo stesso, rappresentativo della struttura; (ii) definizione delle condizioni al contorno (periodicità, simmetria, antisimmetria); (iii) definizione dei carichi meccanici o termici. tali operazioni devono essere interconnesse, come mostrato nello schema di fig. 3, per mantenere una rappresentatività realistica della microcella. fig. 4 chiarisce il concetto di base della modellazione a microcampi periodici, applicato alla microstruttura di una ghisa nodulare quasi interamente perlitica. si noti come la http://dx.medra.org/10.3221/igf-esis.12.03&auth=true http://www.gruppofrattura.it l. collini, frattura ed integrità strutturale, 12 (2010) 21-36; doi: 10.3221/igf-esis.12.03 27 microstruttura eterogenea reale, a sinistra, sia riprodotta come un array regolare di celle unitarie equispaziate, contenenti noduli di uguale dimensione e tutte le informazioni necessarie a descrivere il numero e la disposizione dei costituenti. figura 3: schema di array esagonale periodico di inclusioni circolari (ad esempio fibre di rinforzo immerse in una matrice continua) e definizione di 11 possibili celle unitarie e delle relative condizioni al contorno [2]. figura 4: schema di modellazione a cella unitaria della microstruttura di una ghisa nodulare perlitica. una seconda tecnica è la modellazione tramite embedded cell approaches (ecas). secondo tale approccio, la struttura eterogenea reale è descritta da un modello di materiale costituito da un nucleo (core) contenente un arrangiamento discreto delle fasi, inserito in una regione omogenea a cui sono generalmente applicati i carichi (deformazioni e tensioni). la legge costitutiva della regione esterna al nucleo eterogeneo è solitamente quella macroscopica del materiale, nota a priori o determinabile nel caso di modelli di tipo self-consistent, [19-21]. infine, le tecniche di modellazione che si basano sul windowing approach, prevedono la costruzione di sub-regioni (“windows”) rettangolari o esaedriche ricavate in modo casuale a partire dalla microstruttura reale, e sottoposte ad appropriate condizioni al contorno, [22]. le finestre, che possono essere bidimensionali o tridimensionali, si possono ottenere da micrografie mediante tecniche di analisi digitale, come illustrato ad esempio in [23-25]. questo genere di modellazione non risulta troppo adatta a descrivere la risposta globale di materiali eterogenei, quanto lo sviluppo di fenomeni locali all’interno della finestra di campionamento, come ad esempio localizzazione della deformazione in bande, sviluppo di scorrimenti, interazione tra inclusioni o particelle di rinforzo. data la specificità dei fenomeni che si osservano in funzione della peculiare struttura esaminata, particolare attenzione va riposta nella scelta della grandezza della finestra, nel numero e nella disposizione delle inclusioni, nei tempi di calcolo. dato che la finestra è posta casualmente al di sopra della struttura, questo è noto anche come approccio secondo degli statistical volume elements (sves). uno schema riassuntivo delle tecniche appartenenti a questa tipologia di modellazione microstrutturale è illustrato nella fig. 5. recentemente un’interessante tecnica di modellazione windowing concettualmente nuova è stata proposta dai ricercatori del mpa (staatliche materialprüfungsanstalt) di stoccarda; la tecnica prevede l’applicazione di un campo di spostamenti determinato sperimentalmente, sui bordi di un sve numerico della microstruttura, [26]. sperimentato su un composito al-al2o3, questo approccio consente di creare un link diretto tra modellazione ed evidenza sperimentale, di importanza strategica nello studio di microcampi di deformazione e micromeccanismi di danneggiamento. http://dx.medra.org/10.3221/igf-esis.12.03&auth=true http://www.gruppofrattura.it l. collini, frattura ed integrità strutturale, 12 (2010) 21-36; doi: 10.3221/igf-esis.12.03 28 figura 5: tecniche di modellazione basate su microstrutture discrete: pma, eca e windowing approach (sves) [2]. alcune applicazioni modellazione tramite microcampi periodici: la cella unitaria n questa sezione sono illustrate alcune applicazioni condotte dall’autore nel campo della modellazione del comportamento meccanico della ghisa nodulare, a partire dalla sua microstruttura caratteristica. è anche illustrato lo studio di recente condotto per la riproduzione della microstruttura di una lega di rame a struttura ultrafine dei grani, mediante tassellatura con l’algoritmo di voronoi. come detto in precedenza, uno dei più comuni metodi di studio delle distribuzioni di sforzi e di deformazioni a livello della meso-scala è quello basato sulla riproduzione della struttura del materiale tramite una micro-geometria che si ripete periodicamente, la cella unitaria. l’uso della cella elementare nella modellazione micromeccanica si è diffuso negli ultimi anni poiché costituisce uno strumento semplice per predire la risposta costitutiva o per studiare il danneggiamento duttile di materiali disomogenei a struttura complessa, come materiali porosi o compositi a matrice metallica rinforzati con particelle o fibre. molti lavori recenti riportano lo studio dell’evoluzione delle dimensioni di vuoti in una matrice solida; tra questi, mcclintock [27] ha considerato l’evoluzione di un singolo vuoto cilindrico in una matrice infinita sottoposta a un carico assialsimmetrico; gurson [28] ha derivato in maniera rigorosa una funzione di potenziale plastico per materiali porosi basata su una cella sferica contenente un vuoto anch’esso sferico, tvergaard e needleman [29, 30] hanno fatto uso della modellazione a cella elementare per studiare la localizzazione del flusso plastico ed estendere la validità del cosiddetto modello gtn alla previsione del danneggiamento e della frattura duttile. la microstruttura della ghisa sferoidale bene si presta ad una schematizzazione secondo la ripetizione di una cella elementare che contenga tutte le informazioni necessarie, poiché i noduli di grafite sono distribuiti abbastanza uniformemente nella matrice, le loro dimensioni non sono troppo dissimili, e la distribuzione delle fasi ha una caratteristica ben distinta (ciascun nodulo è incapsulato dalla fase ferritica). diversi lavori sono reperibili in letteratura sull’utilizzo di celle unitarie per lo studio e la previsione del comportamento meccanico della ghisa nodulare, inerenti le proprietà elastiche, la simulazione del danneggiamento, o l’effetto della presenza di tensioni termiche, [31-34]. in un lavoro del presente autore [35] si è presentato un modello a cella unitaria della ghisa nodulare, mostrato in fig. 6, che comprendesse anche la fase perlitica nella matrice ferrosa. lo studio è stato incentrato sulla risposta meccanica della microstruttura al variare dei parametri caratteristici come il contenuto e la disposizione delle fasi. le leggi costitutive delle fasi presenti nel materiale (ferrite, perlite, grafite) sono desunte da dati di letteratura. i risultati della modellazione sono presentati in termini di risposta alla trazione monoassiale della cella, una volta adottata una procedura di omogeneizzazione basata sul volume di riferimento che consenta di rilevare il comportamento del materiale a livello macroscopico. i diagrammi di fig. 7 riportano alcuni dei risultati ottenibili con l’approccio a cella unitaria. per quanto riguarda le proprietà elastiche, il confronto con risultati sperimentali e con tecniche di modellazione mori-tanaka e hashinshtrikman, evidenzia come l’approccio a cella unitaria sia delimitato inferiormente e superiormente dai due metodi mean field, e come d’altra parte i valori sperimentali del modulo elastico effettivo siano dispersi attorno ai risultati delle i http://dx.medra.org/10.3221/igf-esis.12.03&auth=true http://www.gruppofrattura.it l. collini, frattura ed integrità strutturale, 12 (2010) 21-36; doi: 10.3221/igf-esis.12.03 29 modellazioni a causa di altri fattori microstrutturali (concentrazione delle tensioni, micro-plasticizzazioni locali, discontinuità). la predizione della resistenza – fig. 7(b) – evidenzia un maggior accordo con i dati sperimentali, indicando una notevole capacità della cella unitaria di riprodurre i fenomeni plastici in microstrutture abbastanza regolari e ripetitive come quella della ghisa nodulare. figura 6: modellazione della ghisa nodulare mediante cella assialsimmetrica, [35]. altre modellazioni successive a quella descritta in fig. 6 sono state condotte con celle unitarie più raffinate, finalizzate da una parte allo studio comparativo dell’effetto di costrizione della deformazione introdotta dai modelli di tipo assialsimmetrico, e dall’altra all’analisi più dettagliata della microstruttura. con tali modelli, ad esempio, è stata indagata la risposta meccanica di una microstruttura con due diverse dimensioni caratteristiche dei noduli, individuate mediante considerazioni statistiche su micrografie reali, e variando la loro disposizione spaziale reciproca, [37]. (a) (b) figura 7: (a) effetto del contenuto in grafite sulle proprietà elastiche della ghisa nodulare; (b) effetto del contenuto in ferrite sulla resistenza della ghisa nodulare [37]. alcune celle unitarie di questo tipo sono illustrate in fig. 8: qui si hanno celle tridimensionali con percentuale dei costituenti variabile, e disposizione reciproca dei noduli di grafite (riprodotti come cavità sferiche) ad array incrociato o sfalsato. la cella unitaria offre di fatto la possibilità di studiare, impiegando modeste risorse di modellazione e di calcolo, diverse configurazioni (periodiche) delle inclusioni nella matrice, analizzandone gli effetti sulla rigidezza del materiale, sul flusso plastico delle tensioni, e in generale sulla risposta effettiva del materiale. lo studio comparativo di questi diversi microcampi periodici ha evidenziato una certa sensibilità della cella unitaria nel descrivere la risposta meccanica del materiale, come mostrato dai diagrammi di fig. 9. nel confronto, illustrato in fig. 9(a), gli effetti della modellazione tridimensionale su due microstrutture a diverso contenuto della fase ferritica mostrano una sostanziale equivalenza nel descrivere il comportamento elastico, mentre viene riprodotto un incrudimento plastico maggiore nel caso della cella assialsimmetrica. http://dx.medra.org/10.3221/igf-esis.12.03&auth=true http://www.gruppofrattura.it l. collini, frattura ed integrità strutturale, 12 (2010) 21-36; doi: 10.3221/igf-esis.12.03 30 figura 8: microcelle unitarie ad una e due cavità per la modellazione della ghisa nodulare. (a) (b) figura 9: (a) risposta della ghisa nodulare simulata con modelli di cella assialsimmetrica e tridimensionale (modelli 3d a e 3d b); (b) effetto della modellazione a cella assialsimmetrica con doppia cavità [37]. d’altra parte, l’introduzione di una seconda cavità nella cella al fine di valutare l’interazione reciproca di due vuoti con diverso volume, mostra come, a parità del contenuto in grafite, un nodulo piccolo assieme ad un nodulo grande sia una condizione peggiorativa nella risposta plastica rispetto alla presenza di noduli di grandezza uniforme. dal punto di vista sperimentale, si veda fig. 9(b), si deduce che la tipologia di cella assialsimmetrica “più adatta” dipende dalla quantità e disposizione dei costituenti: la cella con singola cavità è un valido strumento interpretativo nel caso di configurazione bull’s eye della struttura (limitata presenza della fase soft ferritica attorno ai noduli), mentre la modellazione mediante celle con doppia cavità trova un maggiore riscontro nel descrivere il comportamento della ghisa nodulare quando viene incrementata la presenza della fase più dura e resistente nella matrice. modellazione di microstrutture discrete: embedded cell e windowing apporaches in questa sezione sono presentati alcuni esempi di modellazione microstrutturale di tipo embedded e windowing applicati alla ghisa nodulare a matrice mista ferritico/perlitica. questi approcci di modellazione si basano sulla riproduzione di microstrutture discrete, generalmente a partire da micrografie o rilevamenti microstrutturali compiuti su sezioni metallografiche. rispetto alla modellazione con microvolumi periodici, i modelli windowing sono impiegati per lo studio di fenomeni locali sui quali hanno grande influenza le caratteristiche morfologiche specifiche della struttura eterogenea. un modello window può essere impiegato ad esempio per valutare la distribuzione delle tensioni a livello microstrutturale responsabili dei meccanismi di danneggiamento tipici della ghisa nodulare, come quelli illustrati in fig. 10. la creazione, la discretizzazione in elementi finiti, e la risoluzione numerica, sono per questi modelli alquanto più laboriose rispetto ai modelli a cella unitaria. in fig. 11 è presentato un modello embedded di una ghisa nodulare con il 9% di contenuto in grafite, il 63% di perlite e il 37% di ferrite, e di caratteristiche meccaniche note. il modello, che consta in http://dx.medra.org/10.3221/igf-esis.12.03&auth=true http://www.gruppofrattura.it l. collini, frattura ed integrità strutturale, 12 (2010) 21-36; doi: 10.3221/igf-esis.12.03 31 circa 50 mila elementi plane strain, viene costruito a partire da una specifica micrografia, inserendo la finestra (embedding) che contiene le informazioni sulla struttura eterogenea in un continuo omogeneo di dimensioni opportune, e la cui legge costitutiva è desunta dalla risposta macroscopica. le leggi costitutive delle fasi microstrutturali, qui nella forma di modelli di ramberg-osgood, sono invece tratte dalla letteratura. questo genere di modellazione offre il doppio vantaggio di imporre automaticamente appropriate condizioni al contorno alla finestra di analisi, e di ottenere una risposta effettiva già omogeneizzata in quanto al perimetro possono essere applicati direttamente degli spostamenti noti. figura 10: meccanismi di danneggiamento in una ghisa nodulare ferritico/perlitica; a = debonding dei noduli; b = localizzazioni di deformazione plastica; c = bridging di microcricche, [38]. figura 11: modello tipo embedded cell, e distribuzione della risultante della deformazione plastica in seguito all’applicazione di un carico in direzione orizzontale. i risultati ottenibili sono generalmente finalizzati allo studio dell’andamento del carico nella microstruttura e della distribuzione della deformazione, nonché dell’interazione reciproca tra i costituenti valutata nella configurazione reale. il contour mostrato a titolo di esempio nella fig. 11, riporta la distribuzione della risultante della componente plastica di deformazione nella microstruttura. esso mostra come la comparsa di fenomeni di localizzazione generino deformazioni ben maggiori di quelle effettive, e come l’interazione tra noduli opportunamente orientati siano responsabili della nascita di bande di scorrimento. fenomeni di danneggiamento microscopico come quelli illustrati nella micrografia di fig. 10, possono trovare con questo modello un’interpretazione quantitativa e stimolare l’ottimizzazione della microstruttura e quindi delle prestazioni del materiale. una valida alternativa alla modellazione di tipo embedded è, come visto nella sezione approcci e metodi della modellazione micromeccanica, la modellazione di tipo windowing. a parità di microstruttura in esame, questa differisce dalla precedente sostanzialmente per l’estensione geometrica del modello, che ne favorisce la rapidità di risoluzione, e per le condizioni al contorno impostate. in fig. 12 sono mostrati due modelli di questo tipo della stessa ghisa nodulare del modello embedded, che differiscono tra loro per la tipologia di vincolo e di carico (spostamenti u1 e u2 applicati uniformemente sui lati l). una questione delicata che sorge quando si adotta questo approccio, è la scelta della dimensione ottimale della finestra di “campionamento”; se da una parte un modello di grande estensione riesce a catturare maggiori informazioni ed è statisticamente più http://dx.medra.org/10.3221/igf-esis.12.03&auth=true http://www.gruppofrattura.it l. collini, frattura ed integrità strutturale, 12 (2010) 21-36; doi: 10.3221/igf-esis.12.03 32 rappresentativo del materiale, dall’altra le risorse e i tempi computazionali richiesti per la sua risoluzione possono diventare proibitivi. le curve in fig. 13(a) mostrano che la risposta meccanica del modello di fig. 12, pressoché analoga lungo le due direzioni di caricamento, differisce sostanzialmente sia nel campo elastico che in quello plastico dalla risposta di un modello windowing delle dimensioni pari a un quarto (small window model). uno studio di questo tipo potrebbe essere utile per determinare la grandezza ideale della finestra di riproduzione. a differenza dell’impiego di micro campi periodici, questi ultimi due tipi di simulazione, comunque, non si prestano in maniera rigorosa a riprodurre la risposta effettiva di una certa microstruttura. uno dei punti deboli delle tecniche embedded e windowing, infatti, è la loro eccessiva cedevolezza a causa dell’assoluta mancanza di costrizione della deformazione; inoltre, con questi modelli è perduta la condizione di periodicità della struttura. uno sforzo in tale direzione è però possibile impostando delle particolari condizioni al contorno di periodicità sul perimetro del modello (periodic window), [39]. figura 12: modello windowing della ghisa nodulare. (a) (b) figura 13: risposte meccaniche della ghisa nodulare simulate con modelli discreti della microstruttura: (a) curve di trazione dei modelli di fig. 12; (b) risposte meccaniche dei modelli a condizioni al contorno periodiche di fig. 14 (1 = 100% fe; 2 = 68% fe; 3 = 19% fe) [37]. con riferimento allo schema di fig. 14, che mostra un altro modello window di una ghisa nodulare a struttura interamente ferrica (gjs400), le condizioni al contorno di periodicità sono esprimibili mediante le eq. (11a-f): 34 4 12 1     c c u u u u (11a) 14 23        n n (11d) 14 1 23 2     c c u u u u (11b) 1 2 2 2  c c u u (11e) 12 34        n n (11c) 3 2 4 1    c c c c u u u u (11f) http://dx.medra.org/10.3221/igf-esis.12.03&auth=true http://www.gruppofrattura.it l. collini, frattura ed integrità strutturale, 12 (2010) 21-36; doi: 10.3221/igf-esis.12.03 33 figura 14: un modello window con condizioni al contorno opportune può riprodurre un microcampo periodico. con la seguente notazione:  1 2,u u u = vettore spostamento; n = vettore normale; c1,2,3,4 = boundaries del modello;  = vettore delle tensioni risultanti. nello specifico, le relazioni scritte impongono la simmetria degli spostamenti nodali sui lati affacciati – eq. (11a) e (11b) – l’equilibrio delle forze che si generano sugli stessi lati – eq. (11c) e (11d) – e vietano la traslazione – eq. (11e) – e la rotazione – eq. (11f) – della finestra. la deformazione nel modello può allora essere originata applicando uno spostamento lungo una direzione a piacere al nodo in c3, che non possiede gradi di libertà costretti. altre informazioni maggiormente specifiche su questa tecnica di modellazione sono reperibili ad esempio in [40]. figura 15: distribuzione dello sforzo in tre microstrutture eterogenea di ghisa nodulare simulate con modelli windowing a condizioni al contorno periodiche (eq. 11). gli aspetti che questo tipo di modellazione mette in luce non differiscono significativamente da quelli già evidenziati dai modelli window appena discussi. in fig 15 sono illustrate le distribuzioni dello sforzo equivalente in tre microstrutture di ghisa nodulare, variabili per percentuali dei costituenti nella matrice, sottoposte ad una deformazione effettiva del 3%. le distribuzioni bene evidenziano la disuniformità degli sforzi, corrispondenti allo stesso livello di deformazione mesoscopica imposta. lo stato locale di sforzo è affetto dalla presenza di cavità, dalla conformazione della microstruttura e dalle http://dx.medra.org/10.3221/igf-esis.12.03&auth=true http://www.gruppofrattura.it l. collini, frattura ed integrità strutturale, 12 (2010) 21-36; doi: 10.3221/igf-esis.12.03 34 discontinuità tra le fasi. la deformazione nella ghisa a matrice interamente ferritica si localizza lungo bande a 45° che rappresentano “punti deboli”; nella microstruttura mista la tensione si localizza in una striscia perlitica che unisce due subregioni ferritiche, mentre nella microstruttura quasi completamente perlitica si presenta un’alta disomogeneità dello sforzo, sebbene la ferrite presente attorno ai noduli sia sottoposta ad uno sforzo pressoché costante. quest’ultimo è di entità ridotta poiché la libera deformazione del materiale è impedita dalle zone perlitiche circostanti. il modello interpreta quindi correttamente i meccanismi di cedimento fragile osservati sperimentalmente anche nella fase ferritica in ghise sferoidali a matrice quasi interamente perlitica, [41, 42]. analizzando la risposta di resistenza a trazione di questi tre modelli, si osserva, a parità delle percentuali di costituenti nella microstruttura, un comportamento sostanzialmente più cedevole rispetto alla cella assialsimmetrica, si vedano le curve di fig 13(b), in particolar modo quando si incrementa la percentuale di ferrite. questo aspetto conferma l’influenza della disomogeneità e della localizzazione della deformazione associate alle discontinuità microstrutturali che con tale tecnica si riescono a riprodurre. generazione di microstrutture statisticamente equivalenti un ultimo cenno vuole essere rivolto al concetto legato alla generazione di microstrutture statisticamente equivalenti di materiali a struttura in qualche modo eterogenea. due strutture si definiscono statisticamente equivalenti quando possiedono uguali valori dei loro descrittori statistici. figura 16: microfrafia tem di una lega di rame a struttura ultrafine del grano e tassellatura voronoi statisticamente equivalente. una delle tecniche maggiormente utilizzate per generare modelli geometrici equivalenti è la tassellatura o decomposizione voronoi (dal nome del matematico georgy voronoi risalente ai primi del ‘900), originariamente applicata in geofisica e meteorologia. l’algoritmo di voronoi consiste nel definire un certo numero di regioni (celle), a partire da un insieme discreto di punti, con la condizione che i lati di ciascuna cella siano equidistanti da tali punti. una tassellatura di voronoi può essere definita con alcune specifiche proprietà, come l’unicità di ciascuna cella, i limiti inferiore e superiore e il valore medio delle dimensioni delle celle, il numero minimo e massimo di lati, i valori estremi degli angoli. la tassellatura voronoi è producibile nel piano o anche nello spazio. la formulazione matematica completa dell’algoritmo di voronoi può essere reperita ad esempio in [43]. le celle di un reticolo così creato sono statisticamente rappresentative, nelle due o tre dimensioni, della struttura a grani di un materiale metallico policristallino. l’equivalenza statistica della tassellatura nei confronti di una struttura reale, può imporsi nella dimensione media dei grani (misurata ad esempio tramite l’area, il lato maggiore, il prodotto lato maggiore http://dx.medra.org/10.3221/igf-esis.12.03&auth=true http://www.gruppofrattura.it l. collini, frattura ed integrità strutturale, 12 (2010) 21-36; doi: 10.3221/igf-esis.12.03 35 per lato minore o l’area del cerchio equivalente), nella loro orientazione, o in altri fattori geometrici. il presente autore è al momento impegnato nella modellazione dell’effetto della dimensione media del grano sulla resistenza alla propagazione di difetti di fatica nel rame. in particolare, con riferimento ad una campagna di prove sperimentali da poco terminate, è in esame la lega di rame a struttura ultrafine mostrata in fig. 16. in questo specifico caso, la generazione delle celle di voronoi è stata effettuata determinando i nodi interni a ciascuna cella a partire dal riconoscimento automatico del gradiente di grigio in una micrografia tem del tutto analoga a quella di fig. 16. ciascun punto viene determinato come un punto di massimo del gradiente di colore in una determinata area, e l’equivalenza statistica della distribuzione della dimensione dei grani, verificata dopo ogni passaggio, è ottenuta tramite la continua modifica del livello di soglia del riconoscimento dei toni di grigio. il lavoro è stato condotto con il programma di analisi digitale “imagej” scaricabile gratuitamente dal sito http://rsbweb.nih.gov/ij. considerazioni conclusive n questo lavoro si sono presentate alcune tecniche di modellazione microstrutturale utilizzate per lo studio della meccanica dei materiali eterogenei. assieme ad alcuni cenni al concetto di “scala di indagine” e alle teorie classiche e di base della mesoe micromeccanica, si sono illustrati i risultati di un certo numero di casi di studio concreti. nella discussione critica degli aspetti più interessanti delle analisi mostrate, si è cercato di evidenziare punti di forza e possibilità di ricerca offerte, ma anche vincoli e limitazioni di ciascun metodo. l’approccio micromeccanico applicato a un materiale a struttura eterogenea come la ghisa nodulare, si dimostra in definitiva uno strumento indispensabile sia per l’analisi e l’interpretazione di fenomeni locali che dipendono dalla microstruttura, sia per la previsione del suo comportamento elastico e plastico. bibliografia [1] s. nemat-nasser, m. hori, micromechanics: overall properties of heterogeneous materials. north-holland, amsterdam (1993). [2] h. j. böhm, mechanics of microstructured materials. cism courses and lectures, springer-verlag, vienna, 464 (2004). [3] l. l. mishnaevsky, s. schmauder, applied mechanics review, 54(1) (2001) 49. [4] s. torquato, theory of composite materials. oxford university press, london (2001). [5] p.v. makarov, s. schmauder, o.i. cherepanov, i.yu. smolin, v.a. romanova, r.r. balokhonov,d.yu. saraev, e. soppa, p. kizler, g. fischer, s. hu, m. ludwig, theoretical and applied fracture mechanics, 37 (2001) 183-. [6] j. aboudi, mechanics of composite materials. elsevier, amsterdam (1991). [7] r. hill, j. mech. phys. solids, 15 (1965) 89. [8] z. hashin, s. shtrikman, j. mech. phys. sol., 11 (1963) 127. [9] t. mori, k. tanaka, acta metall., 21 (1973) 571. [10] j. d. eshelby, in: proc. r. soc. london, a 241 (1957) 376. [11] h. j. böhm, a short introduction to basic aspects of continuum micromechanics. cdl-fmd report, 3 (1998). [12] r. hill, in: proc. phys. soc., a65 (1952) 349. [13] z. hashin, s. shtrikman, j. mech. phys. solids, 10 (1962) 335. [14] p. j. withers, philosophical magazine a, 59(4) (1989) 759. [15] y. bansal, m.-j. pindera, int. j. plasticity, 22 (2006) 775. [16] s. li, a. wongsto, mechanics of materials, 36 (2004) 543. [17] m.-j. pindera, h. khatama, a.s. dragob, y. bansal, composites: part b, 40 (2009) 349. [18] i. saiki, k. teradab, k. ikedab, m. hori, comput. methods appl. mech. engrg., 191 (2002) 2561. [19] n. takano, m. zako, t. okazaki, jsme int. j. srs., a44 (2001) 602. [20] g. l. heness, b. ben-nissan, l. h. gan, y. w. mai, comput. mater. sci., 13 (1999) 259. [21] h. r. chen, q. s. yang, f. w. williams, comput. mater. sci., 2 (1994) 301. [22] m. ostoja-starzewski, int. j. sol. struct., 35 (1998) 2429. [23] z. shan, m. arun, a. m. gokhale, int. j. plasticity, 20 (2004) 1347. [24] z. shan, a. m. gokhale, acta mater., (2001) 2001. [25] n. takano, m. zako, f. kubo, k. kimura, int. j. sol. struct., 40 (2003) 1225. i http://dx.medra.org/10.3221/igf-esis.12.03&auth=true http://www.gruppofrattura.it l. collini, frattura ed integrità strutturale, 12 (2010) 21-36; doi: 10.3221/igf-esis.12.03 36 [26] e. soppa, s. schmauder, g. fischer, j. brollo, u. weber, comput. mater. sci., 28 (2003) 574. [27] f. a. mcclintock, j. appl. mech., 35 (1968) 363. [28] a. l. gurson, j. engng. mater. technol., 99 (1977) 2. [29] v. tvergaard, j. mech. phys. solids, 30 (1982) 265. [30] a. needleman, v. tvergaard, acta metall., 32 (1984) 157. [31] w. brocks, s. hao, d. steglich, j. de physique iv, 6 c6 (1996) 43. [32] m. kuna, d.-z. sun, j. de physique iv, 6 c6 (1996) 113. [33] n. bonora, a. ruggiero, int. j. sol. struct., 42 (2005) 1401. [34] d. steglich, w. brocks, comput. mater. science, 9 (1997) 7. [35] l. collini, g. nicoletto, j. strain analysis, 40 (2005) 107. [36] w. brocks, g. pusch, w. baer, d. steglich, anwendung mikromechanischer modelle der werkstoffschädigung zur gefügeabhängigen bewertung der zähigkeit von duktilen gußeisenwerkstoffen, final report of dfg-project br521/6 and pu104/4, geesthacht and freiberg, germany (1996). [37] l.collini, micromechanical modeling of the elasto-plastic behavior of heterogeneous nodular cast iron. tesi di dottorato in ingegneria industriale, xvii ciclo (2005). [38] l. collini, p. bujnova, in: procs. of 3rd ysesm, porretta terme, italy (2004) 61. [39] l. collini, g. nicoletto, in: atti xxxiv convegno aias, milano (2005). [40] r. j. smit, w. a. brekelmans, h. e. meijer, comput. methods appl. mech. engrg., 155 (1998) 181. [41] g. nicoletto, r. konečna, b. hadzimova, l. collini, in: atti xxxi convegno aias, parma (2002). [42] f. iacoviello, v. di cocco, f. franzese, workshop igf, forni di sopra (2010). [43] v. du, q. faber, m. gunzburger, siam review, 41(4) (1999) 637. http://dx.medra.org/10.3221/igf-esis.12.03&auth=true http://www.gruppofrattura.it microsoft word numero_33_art_39 m.a. meggiolaro et alii, frattura ed integrità strutturale, 33 (2015) 357-367; doi: 10.3221/igf-esis.33.39 357 focussed on multiaxial fatigue on the applicability of multi-surface, two-surface and non-linear kinematic hardening models in multiaxial fatigue m.a. meggiolaro, j.t.p. castro pontifical catholic university of rio de janeiro meggi@puc-rio.br, jtcastro@puc-rio.br h. wu tongji university in shanghai wuhao@tongji.edu.cn abstract. in this work, a comparison between nlk and mróz-garud’s multi-surface formulations is presented. a unified common notation is introduced to describe the involved equations, showing that the mróz-garud model can be regarded as a particular case of the nlk formulation. it is also shown that the classic two-surface model, which is an unconventional simplified plasticity model based on the translation of only two surfaces, can also be represented using this formulation. such common notation allows a direct quantitative comparison among multi-surface, two-surface, and nlk hardening models. keywords. multiaxial fatigue; incremental plasticity; kinematic hardening; non-proportional variable amplitude loads. introduction he bauschinger effect, commonly called kinematic hardening, can be modeled in stress spaces by allowing the yield surface to translate with no change in its size or shape. so, in the deviatoric stress space, kinematic hardening maintains the radius s of the yield surface fixed while its center is translated, changing the associated generalized plastic modulus p that defines the slope between stress and plastic strain increments in the prandtl-reuss plastic flow rule, also known as the normality rule. there are several models to calculate the current value of p as the yield surface translates, as well as the direction of such translation, to obtain the associated plastic strain increments. most of these hardening models can be divided into three classes: mróz multi-surface (or multi-linear), non-linear, and two-surface kinematic models. mróz [1] defined in 1967 the first multi-surface kinematic hardening model to approximately describe the behavior of elastoplastic solids through a family of nested surfaces in the stress space, the innermost being the yield surface associated with the material yield strength. it assumes that p is piecewise constant, resulting in a multi-linear description of the stressstrain curve, i.e. the non-linear shape of the elastoplastic stress-strain relation is approximated by several linear segments. the mróz model can induce a few numerical problems, which can result in hardening surfaces improperly intersecting in more than one point under finite strain increments. garud [2] proposed a geometrical correction that avoids intersection problems even for coarse integration increments. in spite of its limitations, several multiaxial fatigue works use the mróz-garud model to predict the stress-strain behavior under combined loading, especially due to its ability to store plastic memory effects under variable amplitude loading. this t http://www.gruppofrattura.it/pdf/rivista/numero33/audioslides/megg1/index.html m.a. meggiolaro et alii, frattura ed integrità strutturale, 33 (2015) 357-367; doi: 10.3221/igf-esis.33.39 358 popularity is understandable, since the multi-linear stress-strain curves generated by the mróz-garud model provide good results for balanced loadings. however, such multi-linear models cannot predict any uniaxial ratcheting or mean stress relaxation caused by unbalanced loadings, since their idealized hysteresis loops always close because they are unrealistically assumed as perfectly symmetric. in addition, under several non-proportional loading conditions, these models predict multiaxial ratcheting with a constant rate that never decays, severely overestimating the ratcheting effect measured in practice [3]. as a result, multi-surface kinematic hardening models should only be confidently applied to balanced proportional loading histories. to correctly predict the stress-strain history associated with unbalanced loadings, it is necessary to introduce non-linearity in the hardening surface translation equations, the main characteristic of the non-linear kinematic (nlk) models. nlk models are more general than mróz-garud because they use non-linear equations to describe the surface translation direction and the value of p, leading thus to a more precise description of the non-linear stress-strain curves. armstrong and frederick’s original formulation [4] was improved by chaboche [5], which indirectly introduced the mróz nestedsurface idea to nlk models, however in a non-linear instead of multi-linear formulation. therefore, both nlk and mróz-garud formulations have several common features, as discussed further in this work. a third class of kinematic hardening models involves the so-called two-surface models, which use a rather simplified formulation that combines elements of both non-linear and mróz multi-surface kinematic models. in this work, instead of defining the nested hardening surfaces in the 6d stress or 6d deviatoric stress spaces, a 5d reduced order deviatoric stress space e5s is adopted, using the mises yield function to describe each surface. this 5d space has two advantages over the usual 6d formulations: it is a non-redundant representation of the deviatoric stresses, which decreases the computational cost of stress-strain calculations; and the radius s of the yield surface is equal to the yield strength without the need to include the scaling factor 2 3 required in 6d formulations. besides, even though all kinematic hardening equations are presented here in the 5d space, their conversion to 6d versions is trivial. mróz multi-surface models n fig. 1, the first (and innermost) circle is the monotonic yield surface, with radius r1  sy. in addition, m 1 hardening surfaces with radii r1 < r2 < … < rm  1 are defined, along with an outermost failure surface whose radius rm  1 is equal to the true rupture stress u of the material. their centers are located at points cis  with i  2, 3, …, m  1, respectively. these m  1 nested circles cannot cross one another, must have increasing radii, and for a virgin material they all are initially concentric at the origin of the e5s space, i.e. initially their 0cis   . moreover, the failure surface never translates, i.e. its center always remains at the origin of the e5s space, 1 0mcs    . in fact, any stress point that reaches its boundary causes the material to fracture due to ductility exhaustion, which is equivalent to the criterion 1|s | m ur     . figure 1: yield, hardening and failure surfaces in the x  xy3 2d sub-space of e5s (left) and corresponding radii ri and generalized plastic moduli pi obtained from the piecewise linearization of the uniaxial stress versus plastic strain curve (right). i m.a. meggiolaro et alii, frattura ed integrità strutturale, 33 (2015) 357-367; doi: 10.3221/igf-esis.33.39 359 except for the failure surface, all other hardening surfaces can translate as the material strain-hardens, as shown in fig. 1(right). the centers of the hardening surfaces (which are circles in the 2d example from fig. 1) move as the material plastically deforms and hardens, because they are successively pushed by the inner surfaces. the radii ri of the various hardening surfaces are equal to the stress levels associated with the plastic strains xpli that delineate the multi-linear representation of the stress-strain curve, fitted to properly describe the stress-strain  behavior of the material. the difference between the radii of each pair of consecutive surfaces is defined as ri  ri  1  ri. in principle, all hardening surfaces radii ri may change during plastic deformation as a result of isotropic and np hardening effects. the backstress vector   , which locates the current yield surface center 1c s    , can be decomposed as the sum of up to m surface backstresses 1  , …, m  that describe the relative positions 1i ii c c s s         between centers of the consecutive hardening surfaces, see fig. 2. note that the length (norm) i  of each surface backstress is always between 0i   , if the surface centers ic s  and 1ic s   coincide (as in an unhardened condition), and i ir    , if the surfaces are mutually tangent (a saturation condition with maximum hardening). the main rules in the evolution of these yield and hardening surfaces are: (i) they must translate as rigid bodies when the point s  that defines the current deviatoric stress state in the e5s space reaches their boundaries, to guarantee that such stress point is never outside any surface. in other words, neither the yield surface nor any hardening surface translate unless the stress state is at their boundary (|s s | ic i r     ) trying to move outwards; and (ii) the hardening surfaces cannot cross through one another, therefore they gradually become mutually tangent to one another at the current stress point s  as the material plastically deforms. figure 2: yield, hardening, and failure surfaces in the deviatoric space for m  3, showing the backstress vector   that defines location of the yield surface center 1c s    and its components 1  , 2  , and 3  that describe the relative positions between the centers of consecutive surfaces. in the mróz multi-surface formulation, the outermost surface that is moving at any instant is called the active surface, denoted here as the surface with index ia. any changes in the stress state that happen inside the yield surface are assumed elastic, not resulting in any surface translation as long as 1 1 |s s |c r     , therefore no surface would be active in this case and thus ia  0. each surface is associated with a generalized plastic modulus pi (i  1, 2, …, m  1), which altogether define a field of hardening moduli. the value of p is then chosen as the pi from the active surface i ia. fig. 3 illustrates two consecutive surfaces i and i  1 (i  1), with radii ri and ri  1 in the e5s 5d deviatoric stress space. assuming that the m.a. meggiolaro et alii, frattura ed integrità strutturale, 33 (2015) 357-367; doi: 10.3221/igf-esis.33.39 360 current active surface is i  ia, then according to the mróz model all outer hardening surfaces do not translate, therefore the increments of the respective backstresses are 1 2 ... 0i i md d d            , resulting in 1i ic ci ids d ds d          . figure 3: illustration of mróz, garud, and prager-ziegler surface translation rules used to model kinematic hardening in the mróz multi-surface formulation in the e5s space. the mróz multi-surface formulation assumes that, during plastic straining, all inner surfaces 1, 2, …, ia 1 must translate altogether with the active surface i  ia, therefore their centers do not move relatively to each other, resulting in 1 2 1... 0id d d            . thus, translation rules in the mróz multi-surface formulation only need to be applied to the evolution of the backstress id   of the active surface i  ia, giving 1 , if 0, if c c ai i a ds ds d i i d i i              (1) moreover, since these inner hardening surfaces 1, 2, …, ia 1 are all mutually tangent at the current stress state s  perpendicular to the normal vector n  , their backstresses are all parallel to n  and have reached their saturation (maximum) values. the kinematic rule for the translation id   of the active yield surface can be defined from an assumed translation direction iv  . prager [6] assumed that iv  is parallel to the direction of the normal unit vector n  , i.e. id   happens at the current stress state s  in such normal direction n  . ziegler, on the other hand, assumed that id   happens in the radial direction cis s    from the surface center [7]. for the mises yield surface, both prager’s and ziegler’s rules result in the same prager-ziegler direction iv n    , see fig. 3, which can be calculated from the normalized difference between the current stress state s  and the yield surface center cis  : | | c ci i c ii s s s s n rs s                  (2) for mises materials, the translation direction of prager-ziegler’s kinematic rule is then 1( )i i iiv n r r n r          (prager-ziegler) (3) m.a. meggiolaro et alii, frattura ed integrità strutturale, 33 (2015) 357-367; doi: 10.3221/igf-esis.33.39 361 but prager-ziegler’s translation rule is too simplistic to model kinematic hardening. an improved rule was adopted by mróz [1], who assumed that the translation id   of the active surface occurs in a direction iv  defined by the segment that joins the current stress state c iis s n r        with the corresponding “image stress point” 1 1c im is s n r         that has the same normal unit vector n  at the next hardening surface i 1, see fig. 3. the mróz translation direction is then 1 11 1 nt point ( ) ( ) ( ) m i c c c ci i i i i i ii i i i s image poi current r v s n r s n r n r r s s n r                                             (mróz) (4) note that the mróz translation direction is the combination of prager-ziegler’s hardening term with a “dynamic recovery” direction i  . this last term induces the center of the active surface to translate back towards the center of the next hardening surface, attempting to dynamically recover from the hardening state described by the surface backstress i  that separates their centers. this dynamic recovery term is able to consider a fading memory of the plastic strain path, which is necessary to model mean stress relaxation and ratcheting effects. however, the mróz rule can induce a few numerical problems, which can result in surfaces intersecting in more than one point under finite load increments. garud proposed an empirical correction that avoids intersection problems even for coarse integration increments, as detailed in [2]. a major concern of the mróz multi-surface formulation is that the directions of the calculated stress or strain paths may significantly vary depending on the number of surfaces used. even worse, better predictions are not necessarily obtained from using a larger number of surfaces. as a result, the number of hardening surfaces that results in the best calculation accuracy is a finite number that would also need to be calibrated, an undesirable feature. moreover, the multi-linear formulation adopted by mróz and garud models is not able to correctly predict ratcheting and mean stress relaxation effects. a better approach is to replace such multi-linear models with a non-linear kinematic hardening formulation, described next. non-linear kinematic (nlk) hardening models he multi-linear stress-strain curves generated by the mróz and garud multi-surface models provide good results for balanced proportional loadings, which by definition do not induce ratcheting or mean stress relaxation. however, such piecewise linear models cannot predict any uniaxial ratcheting or mean stress relaxation effects caused by unbalanced proportional loadings. this shortcoming is due to the linearity of the mróz and garud surface translation rules and the resulting multi-linearity of the approximated stress-strain representation, which describes all elastoplastic hysteresis loops using multiple straight segments, instead of predicting the experimentally observed curved paths caused by those non-linear effects. such straight segments generate unrealistic perfectly symmetric hysteresis loops that always close under constant amplitude proportional loadings. in addition, for np loadings, the mróz and garud multi-surface models may predict multiaxial ratcheting with a constant rate that never decays, severely overestimating the ratcheting effect measured in practice. as a result, mróz or garud kinematic strain-hardening models should only be applied to balanced loading histories, severely limiting their applicability. another serious flaw of the mróz and garud models becomes evident for a np path example where the stress state s  follows the contour of the active yield surface. in this example, the stress increment ds  would always be tangent to such active surface, therefore it would induce 0tds n     and no plastic strain would be predicted from the normality rule. this conclusion is physically inadmissible, since it would assume zero plastic straining along a load path with radius ra larger than the yield surface radius r1. the mróz and garud models would predict that the yield surface can translate tangentially to the active surface without generating plastic strains. these major drawbacks are a consequence of mróz and garud multi-surface kinematic hardening models being of an “uncoupled formulation” type, as qualified by bari and hassan in [8]. such uncoupling means that the generalized plastic modulus p  pi in this formulation is not a function of the load translation direction iv  , since it is a constant for each surface. such “uncoupled procedure” (where p and iv  are independent) provides undesirable additional degrees of freedom to the mróz and garud models that allow, for instance, 90o out-of-phase tension-torsion predictions of resulting plastic strain amplitudes that are not a monotonic function of the applied stress amplitudes, as they should be [9]. these t m.a. meggiolaro et alii, frattura ed integrità strutturale, 33 (2015) 357-367; doi: 10.3221/igf-esis.33.39 362 wrong mróz and garud predictions are both qualitatively and quantitatively dependent on the number of surfaces adopted in the model, without any clear convergence. to correctly predict the stress-strain history in unbalanced loadings, p and iv  must be coupled, in addition to introducing non-linearity in the surface translation equations, generating the non-linear kinematic (nlk) models discussed next. the first non-linear kinematic (nlk) hardening model was proposed by armstrong and frederick in 1966 [4]. their original single-surface model did not include any hardening surface, but their yield surface already translated according to a nonlinear rule. chaboche et al. [5] significantly improved armstrong-frederick’s model capabilities by indirectly introducing the concept of multiple hardening surfaces. as demonstrated by ohno and wang in [10], this improvement allowed the nlk formulation to use the same representation of the hardening state as the one in the mróz multi-surface formulation, which includes one yield surface, m 1 hardening surfaces, and one failure surface, all of them nested within each other without crossing. therefore, the improved nlk models also adopt a multi-surface formulation, using a “coupled procedure” based on non-linear translation rules. however, unless otherwise noted, the denomination “multi-surface model” is traditionally associated in the literature with the mróz “uncoupled procedure” based on multi-linear translation rules and piecewise-constant generalized plastic moduli pi [8]. in summary, despite their significant differences, both mróz and nlk approaches can be represented using the same multi-surface formulation. as in the mróz models, instead of defining these surfaces in the 6d stress or deviatoric stress spaces, in this work a 5d reduced order deviatoric stress space e5s is adopted, using the mises yield function to describe each surface. in the multi-surface version of nlk models, the backstress   that locates the center of the hardening surface is also decomposed as the sum of m surface backstresses 1 2, , ..., m        , that describe the relative positions 1iii c c s s         between the centers of consecutive surfaces, exactly as in the mróz multi-surface formulation. from these relations, the center of the yield surface (i  1) or of any hardening surface (2  i  m) can be written as the 5d vector 1 2 2 1...ci i i i m m ms                            (5) once again, the length i  of each hardening surface backstress is always between 0 (in the unhardened condition) and its saturation value ri (a maximum hardening condition when these surfaces become tangent, see fig. 3), while the failure surface is always centered at the origin, i.e. 1 0 mc s     . as usual, the hardening surfaces cannot pass through one another, remaining nested at all times, since | |i ir    . but during plastic straining in the nlk multi-surface formulation, the yield and all hardening surfaces do translate, as opposed to the mróz formulation, where all surfaces outside the active one would not move. the nlk models do not use an “active surface” concept, since all hardening surfaces become active during plastic straining. the yield and hardening surfaces from the nlk models behave as if they were all attached to one another with non-linear spring-slider elements, causing coupled translations even before they enter in contact, i.e. even for | |i ir    . therefore, any hardening surface translation causes all surfaces to translate, usually with different magnitudes and directions, even before they become tangent to each other. pairs of consecutive hardening surfaces i and i  1 may eventually become mutually tangent at the saturation condition | |i ir    , when their respective translations have the same magnitude and direction 1 0 i ic ci d ds ds          , so when there is no surface backstress variation for this pair. so, plastic straining causes increments 0id    in all surface backstresses, except for the ones from the saturated surfaces. quantitatively, these surface translation rules state that, during plastic straining, , if | | 0, if | | i i i i i i i p v dp r d r                 (6) for the yield (i  1) and all hardening surfaces i  2, …, m, where ( 2 3) | |pldp de   is the equivalent plastic strain increment, iv  is the surface translation direction vector (in the 5d space e5s), and pi is a generalized plastic modulus coefficient that must be calibrated for every surface, used in the calculation of p. m.a. meggiolaro et alii, frattura ed integrità strutturale, 33 (2015) 357-367; doi: 10.3221/igf-esis.33.39 363 the main difference among the several nlk hardening models proposed in the literature rests in the equation of the hardening surface translation direction iv  , which for most models can be condensed into the general equation [11]   pr cov * * [ (1 ) ( ) ]ti i i i i i i i i ager dynamic radial ziegler re ery return v n r m n n                            (7) where the scalar functions i* and mi* are defined as | | * i i i ir            and | | , if 0 * 0, if 0 imt t i i i i t i n n m n                        (8) the calibration parameters for each surface i are the ratcheting exponent i, the multiaxial ratcheting exponent mi, the ratcheting coefficient i, and the multiaxial ratcheting coefficient i, scalar values that are listed in tab. 1 for several popular nlk hardening models. note that several literature references represent the nlk hardening parameters ri, pi, and i as r(i), c(i), and (i), but this notation is not used in this work to avoid mistaking the (i) superscripts for exponents. year kinematic hardening model i mi i i 1949 prager [6] 0 0 0 1 1966 armstrong-frederick [4] 0 0 0  i  1 1 1967 mróz [1] 0 0 1 1 1983 chaboche [12] 1 0 1 1 1986 burlet-cailletaud [13] 0 0 0  i  1 0 1993 ohno-wang i [14-15] ∞ 1 1 1 1993 ohno-wang ii [14-15] 0  i < ∞ 1 1 1 1995 delobelle [16] 0 0 0  i  1 0  i  1 1996 jiang-sehitoglu [17-18] 0  i < ∞ 0 1 1 2004 chen-jiao [19] 0  i < ∞ 1 1 0  i  1 2005 chen-jiao-kim [20] 0  i < ∞ ∞ < mi < ∞ 1 1 table 1: calibration parameters for the general translation direction from eq. (8). the translation direction iv  of each hardening surface i, shown in eq. (7), can be separated into three components: (i) the prager-ziegler term, in the normal direction n  perpendicular to the yield surface at the current stress point s  ; (ii) the dynamic recovery term, in the opposite direction of the backstress component of the considered surface, which acts as a recall term that gradually erases plastic memory with an intensity proportional to the product of the ratcheting terms i*mi*ii; and (iii) the radial return term, in the opposite direction of the normal vector n  , which mostly affects multiaxial ratcheting predictions. fig. 4 shows the geometric interpretation of these three components. two-surface kinematic hardening model he two-surface model proposed by dafalias and popov [21] and independently by krieg [22] is an unconventional plasticity model based on the translation of only two moving surfaces: a single hardening surface (i  2), usually called bounding or limit surface, and an inner yield surface (i  1), shown in fig. 5. the outer failure surface (i  3) is also present, however it does not translate. t m.a. meggiolaro et alii, frattura ed integrità strutturale, 33 (2015) 357-367; doi: 10.3221/igf-esis.33.39 364 figure 4: geometric interpretation of the three components of the translation direction iv  of hardening surface i: prager-ziegler’s, dynamic recovery, and radial return terms, where the equivalent parameter i*  i*mi*i. in this model, every time an elastic stress state s  reaches the yield surface, the length of the current mróz translation vector between the yield and bounding surfaces is stored as the initial reference length 1| | |s |in mv v s        , where s m  is the mróz (stress) image point, see fig. 5. the generalized plastic modulus p is then calculated at each stress increment from the current length 1| |v  of the mróz translation vector and its initial value vin through: 2 1 1( ) | | ( | |)in inp p f v v v v       (9) where p2 is the value of p calibrated for the bounding surface, and f(vin) is a continuous material function that needs to be calibrated. the generalized plastic modulus p continuously varies in a non-linear way between the elastic value p  ∞ and the saturated p  p2, instead of assuming a piecewise-constant value p  pi (from the active surface i  ia) as in the original mróz multi-surface formulation. some implementations [22] of this model adopt a slightly different metric to define generalized plastic modulus p and the initial reference length vin, replacing 1| |v  with the projection 1 tv n    onto the yield surface normal vector. the translation direction of the surface backstress 1  is defined by 1 1 1mv s s n r              , the mróz surface translation rule, while the translation direction of the yield surface can adopt any linear or non-linear hardening rule such as the ones listed in tab. 1. a non-linear rule is suggested, to avoid the same drawbacks from the mróz and garud multilinear models for unbalanced uniaxial or np loadings, thus allowing the prediction of ratcheting. contrary to the mróz or nlk multi-surface formulations, the two-surface kinematic hardening model does not adopt a rule to explicitly calculate the surface translation direction between surfaces i  2 and i  3 (respectively the bounding and failure surfaces in the two-surface formulation). the continuous definition of the modulus p from eq. (9), as opposed to the piecewise-constant p  pi from the mróz multi-surface formulation, introduces a non-linear component in the twosurface model that allows it to reasonably predict uniaxial and multiaxial ratcheting under constant amplitude loading. however, the quality of such ratcheting predictions strongly depends on the non-linear kinematic hardening rule employed to define the translation direction of the yield surface [8]. in practice, non-linear kinematic models should be preferred over two-surface models for cyclic unbalanced loadings that cause ratcheting or mean stress relaxation. due to its computational simplicity, the two-surface model has been widely adopted for the prediction of the deformation behavior of metals under monotonic and constant amplitude loadings. the need for only m  2 moving surfaces makes it attractive to model pressure-sensitive or even anisotropic materials, whose elaborate yield function would result in a high computational cost in mróz or nlk multi-surface formulations with m >> 2. even though two-surface models are not the best option for unbalanced or variable amplitude loadings, they can provide excellent results for monotonic loading applications, such as in sheet metal forming [23]. m.a. meggiolaro et alii, frattura ed integrità strutturale, 33 (2015) 357-367; doi: 10.3221/igf-esis.33.39 365 figure 5: yield, bounding, and failure surfaces in the s1-s2 deviatoric space for the two-surface model. in summary, the two-surface model and its variations combine elements of both mróz and nlk multi-surface models, as compared in tab. 2. similarly to mróz multi-surface models, it is an “uncoupled formulation” since the generalized plastic modulus p is not a function of the translation directions, only of the distance | |iv  . on the other hand, similarly to nlk multi-surface models, the yield and all hardening surfaces translate, the surface translation direction can (and should) use a non-linear equation, and the generalized plastic modulus p continuously varies instead of being assigned piecewiseconstant values. mróz multi-surface two-surface nlk multi-surface number m of yield and hardening surfaces: m  2 m 2 m  1 surface translation during plastic straining: no translation outside active surface the yield and all hardening surfaces (including the bounding surface) translate surface translation direction iv  : defined by linear rules such as mróz mróz for 1d  ; linear or non-linear rule for 1 2d d     defined by non-linear rules surface backstress variation 1d  during plastic straining: 1d  from the active surface i ia is the only 0id   all surface backstress increments 1d  (for i  1, 2, …, m) are different than zero generalized plastic modulus p: piecewise-constant p  pi from the active surface i  ia non-linear and continuously varying, calculated from relative positions among the yield and all hardening surfaces consistency condition that prevents s  from moving outside any surface: used to calculate the backstress increments 1d  and associated surface translations cids  used to calculate the non-linear p table 2: comparison among the mróz multi-surface, two-surface, and nlk multi-surface model formulations, to predict multiaxial kinematic hardening effects. m.a. meggiolaro et alii, frattura ed integrità strutturale, 33 (2015) 357-367; doi: 10.3221/igf-esis.33.39 366 conclusions n this work, it is concluded that the mróz-garud multi-surface formulation can lead to very poor multiaxial stressstrain predictions in the presence of significant mean stresses, severely limiting their application in multiaxial fatigue analysis. the two-surface model better accounts for unbalanced loadings, however its application is mostly recommended for monotonic plastic processes, since it does not appropriately deal with complex variable amplitude loading histories, with decreasing amplitudes and several layers of hysteresis loops within loops, which are very common under spectrum loading. on the other hand, nlk models can accurately deal with non-proportional loadings, either balanced or unbalanced. moreover, contrary to two-surface models, they deal with complex variable amplitude spectrum loading, as long as a sufficiently high number of backstress components (i.e. number of hardening surfaces) is adopted in a refined nlk formulation, to efficiently store plastic memory effects. therefore, this analysis shows that nlk models should be preferred over multi-surface and two-surface models in multiaxial fatigue calculations under variable amplitude loading. references [1] mróz, z. on the description of anisotropic workhardening, j mech phys solids, 15(3) (1967) 163-175. [2] garud, y.s., a new approach to the evaluation of fatigue under multiaxial loading, j eng mater tech, 103 (1981) 118-125, [3] jiang, y.; sehitoglu, h., comments on the mróz multiple surface type plasticity models, int j solids struct, 33 (1996) 10531068. [4] armstrong, p.j., frederick, c.o., a mathematical representation of the multiaxial bauschinger effect. cegb report rd/b/n731, berkeley nuclear laboratory, (1966). [5] chaboche, j.l., dang van, k., cordier,g. modelization of the strain memory effect on the cyclic hardening of 316 stainless steel. transactions 5th int conf struct mech reactor technology, div. l, berlin, (1979). [6] prager, w., recent developments in the mathematical theory of plasticity, j appl phys, 20 (1949) 235-241. [7] ziegler, h., a modification of prager’s hardening rule, appl math, 17 (1959) 55-65. [8] bari, s., hassan, t., kinematic hardening rules in uncoupled modeling for multiaxial ratcheting simulation, int j plasticity 17 (2001) 885-905. [9] jiang, y., kurath, p. characteristics of the armstrong-frederick type plasticity models, int j plasticity, 12 (1996) 387-415. [10] ohno, n., wang, j.d., transformation of a nonlinear kinematic hardening rule to a multisurface form under isothermal and non-isothermal conditions, int j plasticity, 7 (1991) 879-891. [11] meggiolaro, m.a., castro, j.t.p., wu, h., a general class of non-linear kinematic models to predict mean stress relaxation and multiaxial ratcheting in fatigue problems, in: int conf fatigue damage struct mater x, hyannis, ma, (2014). [12] chaboche, j.l., rousselier, g., on the plastic and viscoplastic constitutive equations part i: rules developed with internal variable concept. j press vess-t asme, 105 (1983) 153-158. [13] burlet, h., cailletaud, g., numerical techniques for cyclic plasticity at variable temperature. eng computation, 3 (1986) 143-153. [14] ohno, n., wang, j.d., kinematic hardening rules with critical state of dynamic recovery, part i: formulations and basic features for ratchetting behavior, int j plasticity, 9 (1993) 375-390. [15] ohno, n., wang, j.d., kinematic hardening rules with critical state of dynamic recovery, part ii: application to experiments of ratchetting behavior, int j plasticity, 9 (1993) 391-403. [16] delobelle, p., robinet, p., bocher, l., experimental study and phenomenological modelization of ratchet under uniaxial and biaxial loading on an austenitic stainless steel, int j plasticity, 11 (1995) 295-330. [17] jiang, y., sehitoglu, h., modeling of cyclic ratchetting plasticity, part i: development of constitutive relations. j appl mecht asme, 63 (1996) 720-725. [18] jiang, y., sehitoglu, h., modeling of cyclic ratchetting plasticity, part ii: comparison of model simulations with experiments. j appl mech-t asme, 63 (1996) 726-733. [19] chen, x., jiao, r., modified kinematic hardening rule for multiaxial ratcheting prediction, int j plasticity, 20 (2004) 871-898. [20] chen, x., jiao, r., kim, k.s., on the ohno-wang kinematic hardening rules for multiaxial ratcheting modeling of medium carbon steel, int j plasticity, 21 (2005) 161-184. [21] dafalias,y.f., popov, e.p., plastic internal variables formalism of cyclic plasticity, j appl mech-t asme, 43 (1976) 645651. [22] krieg, r.d., a practical two-surface plasticity theory, j appl mech-t asme, 42 (1975) 641-646. i m.a. meggiolaro et alii, frattura ed integrità strutturale, 33 (2015) 357-367; doi: 10.3221/igf-esis.33.39 367 [23] yoshida, f., uemori, t., a model of large-strain cyclic plasticity describing the bauschinger effect and workhardening stagnation, int j plasticity, 18 (2002) 661-686. microsoft word numero_56_art_15_3029 i. boudjemaa et alii, frattura ed integrità strutturale, 56 (2021) 187-194; doi: 10.3221/igf-esis.56.15 187 effect of multi-layer prosthetic foam liner on the stresses at the stump–prosthetic interface i. boudjemaa, a. sahli, a. benkhettou, s. benbarek department of mechanical engineering, laboratory mechanics physics of materials (lmpm), university of sidibel abbes, bp 89, cite ben m’hidi, sidibel abbes, 22000, algeria ismailboubou000@gmail.com sahliabderahmen@yahoo.fr, http://orcid.org/0000-0002-5183-1168 aekben.dz@22gmail.com sma_benbarek@yahoo.fr, http://orcid.org/0000-0002-5420-9144 abstract.the prosthetic liner plays a significant role in the redistribution of the pressure between the stump and the socket, as adds a cushioning layer between the stump and the socket which relieves pain and makes the prosthesis more comfortable. this study employed nonlinear finite element analyses to investigate the peak pressure and shear stress at stump–prosthetic interface in the case of multilayer prosthetic foam liner, this liner has an inner polymeric foam layer surrounded by another type of polymeric foam layer, we used three different types of foams in different order to define this liner (flexible polyurethane foam, polyurethane-shape memory polymer foam, and natural rubber latex foam). that allows comparing 6 deferent configurations of multi-layer prosthetic foam liner. keywords. prosthesis; stump; contacts stresses; multi-layer liner; transtibial amputation. citation: boudjemaa, i., sahli, a., benkhettou, a., benbarek, s., effect of multilayer prosthetic foam liner on the stresses at the stump–prosthetic interface, frattura ed integrità strutturale, 56 (2021) 187-194. received: 25.02.2021 accepted: 18.03.2021 published: 01.04.2021 copyright: © 2021 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. introduction ower limb amputations are mainly due to arterial disease problems, often associated with diabetes, and to a lesser extent to trauma and cancer [1], after trans-tibial amputation (tta) patients need prostheses to keep their mobility, this prosthesis should be comfortable and should not cause pain to the patient. lower limb prostheses are generally developed with three principal parts: socket, pylon (leg section), and foot [2], most modern sockets are used with an intermediate liner, this liner helps to redistribute the stresses at the stump-prosthetic interface [3], the contact pressure at the stump–prosthetic interface is the most important parameter to evaluate the comfort of the prosthesis. sockets are customer products, designed to fit the unique geometry of the patient's residual limb [2]. significant trauma can be caused by a poorly fitting socket. the manufacturing process of a socket is based on patient feedback and the l https://youtu.be/qlvagwtcw7u i. boudjemaa et alii, frattura ed integrità strutturale, 56 (2021) 187-194; doi: 10.3221/igf-esis.56.15 188 personal judgment of the prosthetics. this process is long and expensive requiring several prototypes to arrive at the final product. these lead to the high prices of the products [4], and they are built to withstand only three to five years. a low-cost efficient socket design and manufacturing process are required in order to reduce the high price of these products. there are many advantages in using finite element analysis (fea), including the ability to determine the stresses distribution at the whole stump-prosthetic interface. also, these results can be used to design high-performance prosthesis by reducing the contact stresses, several studies have used the element finite method to investigate the pressures at the stump–prosthetic interface, and some model in these studies didn't include a prosthetic liner [4, 5], while others included liner. lin et al (2004) [3] studied the effects of liner stiffness in trans-tibial model, they used an axial load of 600 n (oneleg stance) with linear material properties for all components (bone, soft tissue, liner, socket). jia et al (2004) [6]studied the influence of inertial load on interface pressure and shear stress in this study a prosthetic liner with 4 mm thickness has been used with patellar tendon bearing socket. cagle et al (2018) [7] investigate the pressure distribution at the stump-– prosthetic interface in three different limb shapes (short conical, long conical, and cylindrical) and they used elastomeric liner, the peak contact pressure across all simulations was 98 kpa and the maximum resultant shear stress was 50 kpa in cagle’s study. in this study a trans-tibial element finite model was developed to investigate the effect of the multi-layer prosthetic foam liner on the stresses at the stump–prosthetic interface, this liner has an inner polymeric foam layer surrounded by another type of polymeric foam layer, three different polymeric foams were chosen (flexible polyurethane foam, polyurethaneshape memory polymer foam, and natural rubber latex foam) to get different combinations of liners. method geometries he development of the finite element (fe) model in this study was passed through several stages, the first was to create a 3d trans-tibial model with liner and socket, the limb was generated from computed tomography scans, the socket and the liner was designed using autodesk meshmixer, this software allows to adapt the liner shape and socket with the residual limp and also allows to get rid of cavities in the contact surface between the residual limb and the liner and between the liner and the socket (fig. 1), the model has been converted from stl to igs with mimics 3matic software. figure 1: schematic representation of the stl 3d model and the finite element (ef) model (bone, soft tissue, liner, and socket). the liner was divided into two sections the thickness of each section was 5 mm as shown in fig. 2, by giving each section different mechanical properties, it is possible to simulate different formations of the multi-layer liners as shown in tab. 1. mechanical properties the material properties of the tibia bone, soft tissue, and socket were assumed to be linearly elastic, homogeneous, and isotropic. the bone was assigned with young’s modulus of 10 gpa and poisson’s ratio 0.3 [6], young’s modulus of the soft tissue was 200 kpa, and poisson’s ratio was assumed to be 0.49 [6], the socket was assigned with young’s modulus of 1.5gpa and poisson’s ratio 0.3 [8]. t i. boudjemaa et alii, frattura ed integrità strutturale, 56 (2021) 187-194; doi: 10.3221/igf-esis.56.15 189 figure 2: schematic representation of prosthetic liner (ef). table 1: the different configurations of all six multi-layer foam linersstudied. structure young’s modulus poisson’s ratio bone 10 gpa 0.3 soft tissue 200 kpa 0.49 socket 1.5 gpa 0.3 table 2: details material properties for the (fe) model. for the liners the foam the flexible polyurethane foam, polyurethane-shape memory polymer foam, and natural rubber latex foam were assigned as hyper-elastic materials, the open-cell flexible polyurethane foam was assigned with hyperelastic ogden's model 1=7.27mpa, 1=1.63, 2 = -7.2 mpa, 2 =1.63, 3=8.5e-4mpa,3= 45.75 [9]. fig. 3 shows the mechanical properties of polyurethane shape memory polymer foam [10] and natural rubber latex foam [11] used. boundary and loading conditions the interfaces between the bone and soft tissue were tied, the physical contact between the stump and the liner was represented by using surface-to-surface contact. the coefficient of friction (cof) between the liner and soft tissue was assumed to be 0.5 [3, 6, 8]. a static vertical load equivalent to the half body weight [12] (350 n) was applied on top of the tibial bone, the distal end of the socket was fixed. liner inner layer outer layer liner(a) flexible polyurethane foam polyurethane-shape memory polymer foam liner(b) polyurethane-shape memory polymer foam flexible polyurethane foam liner (c) flexible polyurethane foam natural rubber latex foam liner (d) natural rubber latex foam flexible polyurethane foam liner (e) natural rubber latex foam polyurethane-shape memory polymer foam liner (f) polyurethane-shape memory polymer foam natural rubber latex foam i. boudjemaa et alii, frattura ed integrità strutturale, 56 (2021) 187-194; doi: 10.3221/igf-esis.56.15 190 figure 3: compressive stress strain relationship of natural rubber latex foam and polyurethane-shape memory polymer foam. figure 4: schematic representation of load and boundary conditions. mesh tetrahedral meshes for all components (bone, soft tissue, socket, and liner), was chosen tetrahedral meshes are generally preferred over hexahedral meshes for free-formed complex geometries as the former is computationally more efficient [13]. structure elements number element type bone 32539 c3d4 soft tissue 6411 c3d4 socket 26185 c3d4 liner 33257 c3d4 table 3: mesh properties used i. boudjemaa et alii, frattura ed integrità strutturale, 56 (2021) 187-194; doi: 10.3221/igf-esis.56.15 191 figure 5: mesh of the analyzed (fe) model. results is section outlines the stresses obtained at the interference between the trans-tibial prosthesis and the stump due to the body weight application, this reflects the residual limb reaction with all six cases of multi-layer prosthetic foam liner shown in the tab.1. the results based on the peak contact pressure and peak longitudinal shear stress at the stump interface. the computed contact pressure and the shear stress will help determine which liner produces the least pressure on the stump-prosthetic interface. the vertical displacement recorded in the liners was used to compare their weight-bearing capacity in every case. fig. 6 shows the distributions of contact pressure at the stump–prosthetic interface for all liners cases, the patellar tendon area, and the region under the amputated tibia bone were recorded the highest pressure distributions. the highest contact pressure recorded in the stump between all cases was in the liner (f) up to 52 kpa, the lows contact pressure between all cases was in the cases of liners (a) and (c) up to 31 kpa and 30 kpa respectively as shown in the fig. 8. stump at liner (a) stump at liner (b) stump at liner (c) stump at liner (d) stump at liner (e) stump at liner (f) figure 6: distributions of contact pressure at the stump interface for all six types of multi-layerliners. t i. boudjemaa et alii, frattura ed integrità strutturale, 56 (2021) 187-194; doi: 10.3221/igf-esis.56.15 192 fig. 7 shows the distributions of longitudinal shear stress at the stump–prosthetic interface for all liners cases, the patellar tendon area, and the region under the amputated tibia bone were recorded the highest longitudinal shear stress distributions. the highest longitudinal shear stresses recorded in the stump between all cases was in the cases of liners (b), (e), and (f) up to 22,20 and 26 kpa respectively, the lows longitudinal shear stress between all cases was in the cases of liners (a) and (c)up to15 kpa as shown in the fig. 8. stump at liner (a) stump at liner (b) stump at liner (c) stump at liner (d) stump at liner (e) stump at liner (f) figure 7: distributions of longitudinal shear stress at the stump interface for all six types of multi-layerliners. figure 8: peak contact pressure and longitudinal shear stress at the stump–liner interface for all multi-layer liners cases. the distributions of displacement in all six cases of multi-layer prosthetic foam liner allow knowing the capacity of these liners to support the patient's weight. fig. 9 shows the distributions of vertical displacement at all liners cases, the highest vertical displacement distributions in the liners was located in the area below the tibia end, the highest displacement i. boudjemaa et alii, frattura ed integrità strutturale, 56 (2021) 187-194; doi: 10.3221/igf-esis.56.15 193 between all cases was recorded in the liner (a) up to 9.2 mm, the lows displacement between all cases was in the cases of liners (e) and (f) up to 5.5 and 5.4 mm respectively. liner (a) liner (b) liner (c) liner (d) liner (e) liner (f) figure 9: distribution of displacement along the load axis (u2) in all liners cases. conclusion n this study, a 3d nonlinear fe model was established to predict contact pressure and longitudinal shear stress at the stump interface, a static force equivalent to the half-body weight was applied at the knee joint during a two-leg stance. the effects of multi-layer prosthetic foam liner materials inertia during analysis were estimated by comparing the results of the stresses at the stump–prosthetic interface. based on the study of cagle et al [7] it can be said that the stresses recorded on the prosthesis interface in all cases of multi-layer foam liners in this study were very suitable for patient's comfort, the peak contact pressure values did not exceed in the highest case 52 kpa, and 25 kpa for the longitudinal shear stress. through this simulation, the multi-layer prosthetic foam liners were showed high efficiency in reducing the stress at the stump–prosthetic interface. however, some cases of multi-layer prosthetic foam liners did not show adequate support for the patient's weight, it’s recorded large displacement values (liner (a) and liner(c)). the multi-layer foam liners that have achieved the best balance between low stress values at the stump–prosthetic interface and weight bearing capacity were the liners (b) and (d). references [1] ziegler-graham, k., mackenzie, e. j., ephraim, p. l., travison, t. g., and brookmeyer, r. (2008), “estimating the prevalence of limb loss in the united states: 2005 to 2050”, archives of physical medicine and rehabilitation, 89(3), 422-429. doi: 10.1016/j.apmr.2007.11.005 [2] radcliffe, c. w. (1955). functional considerations in the fitting of above-knee prostheses. biomechanics laboratory, university of california, 2(1), pp. 35 60. i i. boudjemaa et alii, frattura ed integrità strutturale, 56 (2021) 187-194; doi: 10.3221/igf-esis.56.15 194 [3] lin, c. c., chang, c. h., wu, c. l., chung, k. c. and liao, i. c. (2004). effects of liner stiffness for trans-tibial prosthesis: a finite element contact model, medical engineering and physics, 26(1), pp. 1-9. doi: 10.1016/s1350-4533(03)00127-9. [4] zachariah, s. g. and sanders, j. e. (2000). finite element estimates of interface stress in the trans-tibial prosthesis using gap elements are different from those using automated contact, journal of biomechanics, 33(7), pp. 895-899. doi: 10.1016/s0021-9290(00)00022-1. [5] ballit, a., mougharbel, i., ghaziri, h. and dao, t. t. (2020). fast soft tissue deformation and stump-socket interaction toward a computer-aided design system for lower limb prostheses, irbm, 41(5), pp. 276-285. doi: 10.1016/j.irbm.2020.02.003. [6] jia, x., zhang, m. and lee, w. c. (2004). load transfer mechanics between trans-tibial prosthetic socket and residual limb—dynamic effects, journal of biomechanics, 37(9), pp. 1371-1377. doi: 10.1016/j.jbiomech.2003.12.024. [7] cagle, j. c., reinhall, p. g., allyn, k. j., mclean, j., hinrichs, p., hafner, b. j. and sanders, j. e. (2018). a finite element model to assess transtibial prosthetic sockets with elastomeric liners, medical and biological engineering and computing, pp. 56(7), 1227-1240. doi: 10.1007/s11517-017-1758-z. [8] lee, w. c., zhang, m., jia, x. and cheung, j. t. (2004). finite element modeling of the contact interface between trans-tibial residual limb and prosthetic socket, medical engineering and physics, 26(8), pp. 655-662. doi: 10.1016/j.medengphy.2004.04.010. [9] ju, m. l., jmal, h., dupuis, r. and aubry, e. (2014). a comparison among polynomial model, reduced polynomial model and ogden model for polyurethane foam, in advanced materials research, 856, pp. 169-173. doi: 10.4028/www.scientific.net/amr.856.169 [10] tobushi, h., okumura, k., endo, m. and hayashi, s. (2001). thermomechanical properties of polyurethane-shape memory polymer foam, journal of intelligent material systems and structures, 12(4), pp. 283-287. doi: 10.1106/fnsx-ap9v-qp1r-nmwv. [11] karim, a. f. a., ismail, h. and ariff, z. m. (2018). effects of kenaf loading and alkaline treatment on properties of kenaf filled natural rubber latex foam, sainsmalaysiana, 47(9), pp. 2163-2169. doi: 10.17576/jsm-2018-4709-26. [12] wu, c. l., chang, c. h., hsu, a. t., lin, c. c., chen, s. i. and chang, g. l. (2003). a proposal for the pre-evaluation protocol of below -knee socket design-integration pain tolerance with finite element analysis, journal of the chinese institute of engineers, 26(6), pp. 853-860. doi: 10.1080 /02533839.2003.9670840. [13] ramos, a. and simoes, j. a. (2006). tetrahedral versus hexahedral finite elements in numerical modeling of the proximal femur, medical engineering and physics, 28(9), pp. 916-924. doi: 10.1016/j.medengphy.2005.12.006. microsoft word numero_45_art_12 s. harzallah et al, frattura ed integrità strutturale, 45 (2018) 147-155; doi: 10.3221/igf-esis.45.12 147 eddy current modelling using multi-layer perceptron neural networks for detecting surface cracks s. harzallah, r. rebhi, m.chabaat university built environmental research lab., civil engineering faculty, university of sciences and technology houariboumediene, b.p 32 el alia bab ezzouar, algiers 16111 algeria. sharzallah@usthb.dz, r_rebhi @yahoo.fr, m.chabaat@yahoo.com a. rabehi laboratoire de micro-électronique appliquée, université djillali liabès de sidi bel abbés, bp 89, 22000 sidi bel abbés, algeria  rab_ehi@hotmail.fr abstract . a new method for computing fracture mechanics parameters using computational eddy current modelling by multi-layer perceptron neural networks for detecting surface cracks. the method is based upon an inverse problem using an artificial neural network (ann) that simulates mapping between eddy current signals and crack profiles. simultaneous use of ann by mlp can be very helpful for the localization and the shape classification of defects. on the other side, it can be described as the task of reconstructing the cracks and damage in the plate profile of an inspected specimen in order to estimate its material properties. this is accomplished by inverting eddy current probe impedance measurements that are recorded as a function of probe position, excitation frequency or both. in eddy current nondestructive evaluation, this is widely recognized as a complex theoretical problem whose solution is likely to have a significant impact on the detection of cracks in materials keywords. 3d-fem-ec; artificial neural network; inverse problems; cracks; multi-layer perceptron. citation:. harzallah, s., rebhi, r., chabaat, m., rabehi, a., eddy current modelling using multilayer perceptron neural networks for detecting surface cracks, frattura ed integrità strutturale, 45 (2018) 147-155. received: 07.03.2018 accepted: 17.06.2018 published: 01.07.2018 copyright: © 2018 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. introduction etection and characterization of a crack in a plate at its initial stage (before propagation), is a real industrial challenge and a major element in security especially in high-risk areas. it is on the basis of these characterizations that engineers have the means then to analyze such crack behavior and predicting its spread, therefore assess its harmfulness as well as the life of the inspected body [1,2]. d http://www.gruppofrattura.it/va/45/2.mp4 s. harzallah et al, frattura ed integrità strutturale, 45 (2018) 147-155; doi: 10.3221/igf-esis.45.12 148 the (ect) technique works on the principle of electromagnetic induction, and it consists on the detection of the magnetic field due to the eddy current induced on the tested specimen. the presence of the defect modifies the eddy currents pattern and hence gives rise to field perturbation closely related to the position and shape of the defects. the excitation field is carried out by using a coil fed by an alternating current and the changed impedance coil can be computed to account the defect influence on the induced currents. the modeling of a practical configuration of (ec) sensor is generally complex and requires extended analytical or numerical developments. the finite element method (fem) is more general, numerically superior, primarily used for its versatility modeling of material properties, simulations of boundary conditions, modeling arbitrary domain space, and reduces substantially the experimental work [3]. the inverse eddy current problem can be described as the task of reconstructing the electrical conductivity profile of an inspected specimen in order to estimate its material properties. this is accomplished by inverting eddy current probe impedance measurements which are recorded as a function of probe position, excitation frequency or both. in eddy current nondestructive evaluation this is widely recognized as a complex theoretical problem whose solution is likely to have a significant impact on the characterization of conductive materials [4]. the neurons are the fundamental elements in each layer, and every neuron in one layer is associated and interacts with other layers. the outputs of every neuron in the hidden and output layers are determined by the previous output ( ij j  σ w  x , jx is the input signals), activation function (  ij j f σ w  x ), and weighting coefficients ( ijw ) [4]. the mlp network is processed as follows: the information flow is input into the input layer and passes through the hidden and output layers to achieve the output information. the tan-sigmoid activation function is used in the neurons of hidden and output layers in this work [5]. ann is composed of highly interconnected processing elements called neurons. these latest can perform arbitrary mappings between sets of input-output pairs. this is achieved by adjustment of the weights of interconnections after training through the presentation of examples. neural network performance has been proven robustness when faced incomplete, fuzzy or novel data. previous work has shown that ann can also be used as for solving electric and/or magnetic inverse problems. ann is then a tool used to information processing systems which can recognize highly complex patterns within available data. it has recently been applied to solve the electromagnetic non-destructive testing inverse problem and has been proved to have a higher accuracy compared to classical methods [6-8]. fem discretization of 3-d eddy current governing equations he eddy current testing phenomenon can be treated as a quasi-static electromagnetic field problem which is expressed by the governing field equations in terms of electrical scalar and magnetic vector potentials. these equations can be solved by 3-d finite element method. application of the coulomb gauge allows simultaneous solution of the coupled magnetic vector potential and the electric scalar potential equation in the inductor ωi and the conducting region ωc, the non-conducting region representing the air ωa with a current density source. these equations can be written as [9, 10]           0                                              .                                                .             a p s i a in a a j in j a in                  (1)  . . 0j a      (2) where, p the penalty term,  the electric conductivity,  is the magnetic reluctivity and v is the electrical potential, sj the current density source. the integral a v formulation is obtained when applying galerkin’s methods and the weighted residuals for eqns. (1) and (2), using vector ni and scalar αi weighted functions. such a formulation leads to the following integral forms by [11];         .  a  .   . a           vi p i i in n d j n a d                   (3) t s. harzallah et al, frattura ed integrità strutturale, 45 (2018) 147-155; doi: 10.3221/igf-esis.45.12 149       a       .  i i sn d n j d     ∮ ∮ (4)     [ .   v ]   0i ij n a d       (5) sensor impedance calculation he detection of change of the resulting magnetic field is based on two basic methods: the ndt differential mode represented by two separate coils linked magnetically and supplied by the same current and the nde absolute mode which makes use of only one coil. the impedance variation is obtained from comparison with the reference impedance. the impedance variation z is a complex number. the imaginary part is computed with the magnetic energy (wm) in the whole meshed domain and the real part is computed with the joule losses in the conductive media and the imaginary part is computed with the magnetic energy in the whole meshed domain [12]. the coil impedance with an excited current i at a frequency f is obtained by the following expression;       2 22    1        c f jl re z i re z j j d           and       2 22       1      c m f w im z i im z b b              (6)   2 2   1    (     2        .   z r j x j z d j f b h d i               (7) where j, b, and h are the induced magnetic induction, and the magnetic field, respectively [13]. figure 1: vector of induction b. figure 2: density of the induced current. applications or the application, we chose to test a magnetic plate without any crack and characterized by a high conductivity 107 sm-1 with a magnetic permeability μ of 1.2 10-6h/m. the plate is excited by a sinusoidal current of density j = 2.67 106 a/m and a frequency of 10 khz. ec testing problem deals with a pancake coil placed above a flat plate, as t f s. harzallah et al, frattura ed integrità strutturale, 45 (2018) 147-155; doi: 10.3221/igf-esis.45.12 150 shown in fig. 2, with rectangular crack. the coil is placed along the crack length direction, moving in the xoy plan, parallel to the x-axis[9]. figure 3: impedance z vs. the crack’s width. figure 4: impedance z vs. the crack’s depth. results interpretation he results of simulation obtained in the case of a non-magnetic plate without defects are illustrated in the following figures; fig. 1 represents the distribution of the currents induced on the surface of target. it is noticed that their values are high because the conductivity of the non-magnetic target is large (j = σ.2π.f.a) but are relatively weak compared to the primary currents. fig. 2 indicates the distribution of magnetic field. that explains the strong concentration of the vectors of magnetic induction on the level of the cracks without the possibility to penetrate inside the plate due to the characteristics of material and the effect of the frequency. in figs. 3 and 4, one can notice that when the width decreases then, the value of impedance δz decreases at the same rate. the width of the defect has a great influence on the variation of impedance meanwhile the variation depth of the defect has a light influence on δz. it is noticed that the difference of impedance δz has a dependency on the width of the defect, indeed the width of defect increases δz. on the other side, when the width decreases then, δz decreases. the depth of defect has an effect on the impedance. the variation depth of the defect has a light influence on δz. it is noticed that the difference of impedance δz dependents on the width of the defect. the width of defect increases δz and also one can remark that when the width decreases then, δz decreases at the same rate. it is obvious that the depth of defect does not influence the impedance. artificial neural networks lthough this is an oversimplified model of the biological brain, the organization and the information processing strategies of an ann are based on the features of their biological counterparts. the neurons combine the input impulses in several ways, operating in parallel with other neurons to perform a variety of functions. in artificial neural nets, each simple node performs a weighted sum of the inputs and computes a nonlinear function of the results [17]. the prediction methodology by artificial intelligence or machine learning is based on the following key steps [1]: 1. selection of the variable to predict, e.g. global, diffuse or beam solar radiation on horizontal or tilted surface; 2. selection of the input parameters and data collection, e.g. climatologic data, geographical coordinates, past time series, etc.; 3. definition of the training and testing sets; 4. development of the ann model and training phase assessment; 0.04 0.045 0.05 0.055 0.06 0.065 0.07 -1 0 1 2 3 4 5 6 7 8 9 w=1mm w=1.25mm w=1.5mm w=2mm -2 -1.5 -1 -0.5 0 0.5 1 1.5 2 -1 0 1 2 3 4 5 6 7 8 w=2mm w=3mm w=4mm w=5mm w=7mm t a s. harzallah et al, frattura ed integrità strutturale, 45 (2018) 147-155; doi: 10.3221/igf-esis.45.12 151 5. calculation of the prediction error, through statistical indices, adopting the testing set; 6. comparisons and final choice of the best ann configuration. material and method eural networks can be classified into dynamic (e.g. elman) and static (e.g. mlp) categories. mlp is the most commonly used static networks [18], in which the input is presented to the network along with the desired output, and the weights are adjusted so that the network attempts to produce the desired output. the mlp network has three layers of neurons (nodes) an input layer, a hidden layer and an output layer (fig. 5). the neurons are the fundamental elements in each layer, and every neuron in one layer is associated and interacts with other layers. the outputs of every neuron in the hidden and output layers are determined by the previous output ( ij j  σ w  x , jx is the input signals), activation function (  ij j f σ w  x ), and weighting coefficients ( ijw ) [19]. the mlp network is processed as follows: the information flow is input into the input layer and passes through the hidden and output layers to achieve the output information. the tan-sigmoid activation function is used in the neurons of hidden and output layers in this work. in detail, neurons sum the weight-controlled input production to apply the nonlinear activation function as follows: n i ij j  j 1 a w  x    (8)   i i i 2a 2 y f a 1 1 e     (9) where ijw is the weight coefficient, jx is the input signals, ia is the summation of the weighted inputs, and iy . is the output at neuron i of the output layer. figure 5: architecture of mlp neural network. model validation or the estimation of the depth and length, a type of neural network (mlp) is used. fig. 6 represents the steps of inversion. the accuracy and performance of the derived correlations in predicting of global solar radiation was evaluated on the basis of the following statistical error tests which are coefficient of determination r², root mean square error (rmse) and its normalised value (nmbe), relative root mean square error (rrmse), mean absolute error (mae) and its normalised value (nmae). these error indices are defined as [20,21]: n f s. harzallah et al, frattura ed integrità strutturale, 45 (2018) 147-155; doi: 10.3221/igf-esis.45.12 152   n 2 i i i 1 1 rmse y x n    (10)  n 2i ii 1 n ii 1 1 y x nrrmse 100 1 x n        (11) figure 6: inverse problem rn with two inputs and two outputs. the ranges of rrmse define the model performance as: excellent if: rrmse < 10% good if: 10 % < rrmse < 20% fair if: 12 % < rrmse < 30% poor if: rrmse > 30% i i n i 1 1 y x n mae    (12)     i i i i n i 1 n i 1 y x ² y y ² ² r        (13) where: yi and xi are the estimated and the measured values, iy is the average of estimated values and n is data number. figure 7: cost function (mse) vs. number of iterations. x position z direct model by fem stocking data base ann depth of crack length of cracks depth of crack estimated length of cracks estimated s. harzallah et al, frattura ed integrità strutturale, 45 (2018) 147-155; doi: 10.3221/igf-esis.45.12 153 evaluation of the depth or length independently does not lead to a complete characterization of the geometry of such a crack. this is why an evaluation of two sizes (depth and length) will be established at the same time exploiting the previous architecture; but this time the database must contain two vectors of inputs and two vectors for output to estimate. fig. (6) shows a block diagram of a network (mlp) with two inputs and two outputs for the fault characterization. after repeated several times the learning algorithm (for each iteration biases reset, obtained results are different), fig. (7) is drawn showing the cost function (mse). one can notice that it converges to the imposed optimum of 5. 10-7 after 122 iterations. curves in figs. 8 and 9 give an acceptable correlation between the rectangular geometry of a crack by the direct model using the finite element method and those obtained by the neural network and mean absolute error (mae). figure 8: the correlation between the desired exit and the exit of the network. figure 9: mean absolute error (mae). 0.04 0.045 0.05 0.055 0.06 0.065 0.07 0 0.002 0.004 0.006 0.008 0.01 0.012 0.014 0.016 0.018 s. harzallah et al, frattura ed integrità strutturale, 45 (2018) 147-155; doi: 10.3221/igf-esis.45.12 154 results from the fem for every figure have been inversed just for comparisons purposes with the ann optimization and the true profile of the shape crack. these comparisons are shown in the fig. 10 and give good maps representing the nn in very short time. however, the approach described in the paper identifies the problem fairly and effectively of admissible solutions for different shapes. figure 10: comparison results from the nn optimized, fem profile. conclusion neural network approach for solving inverse problem in eddy current testing is presented in this paper. the main idea is the introduction of a categorization for the shape reconstruction using a neural network. results are obtained for a simple eddy current problem using fem method as an experimental support. on the other hand, nn responses which estimate the forms of cracks are given by the inverse model. it is shown herein that the application of artificial intelligence can be a good substitute or a help of the ndt operators’ work. references [1] harzallah, s. chabaat, m. and chabane, k. (2017). numerical study of eddy current by finite element method for cracks detection in structures, frattura ed integrità strutturale, 39, pp. 282-290. doi: 10.3221/igf-esis.39.26. [2] hamia, r., cordier, c. and dolabdjian, c. (2014). eddy-current non-destructive testing system for the determination of crack orientation, ndt & e international, 61, pp.. 24–28. [3] harzallah, s. and chabaat, m. (2017). 3d-fem computation and experimental study of eddy currents for characterization of surface cracks. int. j. of structural integrity, 8(5), pp.603-610, doi: 10.1108/ijsi-02-2017-0013. 0.04 0.045 0.05 0.055 0.06 0.065 0.07 -4.5 -4 -3.5 -3 -2.5 -2 -1.5 -1 -0.5 0 0.5 fem nn optimized 0.04 0.045 0.05 0.055 0.06 0.065 -4 -3.5 -3 -2.5 -2 -1.5 -1 -0.5 0 0.5 fem nn optimized 0.03 0.035 0.04 0.045 0.05 0.055 0.06 0.065 -4 -3.5 -3 -2.5 -2 -1.5 -1 -0.5 0 0.5 nn optimized fem a s. harzallah et al, frattura ed integrità strutturale, 45 (2018) 147-155; doi: 10.3221/igf-esis.45.12 155 [4] zaoui, a., menana, h., feliachi, m. and berthiau, g. (2010). inverse problem in nondestructive testing using arrayed eddy current sensors, journal of sensors, 10(9), pp. 8696-8704. [5] helifa, b., filiachi, m., lefkaier, i.k., boubenider, f., zaoui, a. and lagraa, n. (2016). characterization of surface cracks using eddy current ndt simulation by 3d-fem and inversion by neural network, aces journal, 31(2). [6] rao, b.p.c., raj, b. and kröning, m. (1999). artificial neural network for on-line eddy current testing. in: thompson d.o., chimenti d.e. (eds) review of progress in quantitative nondestructive evaluation. review of progress in quantitative nondestructive evaluation, springer, boston, ma, 18 a. [7] harzallah, s., mimouni, m. l., benissad, s. and chabaat, m. (2018). 3d-fem computational and inverse problem in nondestructive evaluation using neural networks for detection of cracks, transylvanian review, 26, pp. 1-13. [8] uchimoto, t., takagi, t., ichihara, t. and dobmann, g. (2015). evaluation of fatigue cracks by an angle beam emat– et dual probe, ndt & e international, 72, pp. 10–16. [9] harzallah, s. and chabaat, m. (2016). 3-d eddy current modeling for evaluating the fracture parameters by a new method based on the variation of the impedance, international journal of applied electromagnetics and mechanics, 53, pp. 1–15. [10] sakagami, t. (2015). remote nondestructive evaluation technique using infrared thermography for fatigue cracks in steel bridges, fracture of engineering materials & structures, 38(7). [11] notghi, b. and brigham, j. c. a. (2015). computational approach for robust nondestructive test design maximizing characterization capabilities for solids and structures subject to uncertainty, international journal for numerical methods in engineering 104(4). [12] zaidi, h., santandre, l., krebsa, g. and le bihan, y. (2014). finite element simulation of the probe displacement in eddy current testing, international journal of applied electromagnetics and mechanics, 45, pp. 887–893. [13] garcia-martin, j., gomez-gil, j. and vazquez-sanchez, e. (2011). non-destructive techniques based on eddy current testing, sensors, 11(3), pp. 2525-2565. [14] hughes, r., fan, y. and dixon, s. (2014). near electrical resonance signal enhancement (nerse) in eddy current crack detection, journal of nondestructive testing and evaluation, 66, pp. 82–89. [15] babbar, v.k., underhill, p.r., stott, c. and krause, t.w. (2014). finite element modelling of second layer crack detection in aircraft bolt holes with ferrous fasteners present, 65, pp. 64–71. [16] xu, p., huang, s. and zhao, w. (2011). a new differential eddy current testing sensor used for detecting crack extension direction, ndt&e international, 44, pp. 339–343. [17] bortolini, m., gamberi, m. and regattieri, a. (2016). artificial neural network optimisation for monthly average daily global solar radiation prediction. energy conversion and management, 120, pp. 320-329. [18] moghaddamnia, a., remesan, r., kashani, m. h., mohammadi, m., han, d. and piri, j. (2009). comparison of llr, mlp, elman, nnarx and anfis models—with a case study in solar radiation estimation. journal of atmospheric and solar-terrestrial physics, 71(8), pp. 975-982. [19] hassanpour kashani, m. (2008). flood estimation at ungauged sites using a new hybrid model. journal of applied sciences 9, pp. 1744–1749. [20] guermoui, m., rabehi, a., benkaciali, s. and djafer, d. (2016). daily global solar radiation modelling using multi-layer perceptron neural networks in semi-arid region. leonardo electronic journal of practices and technologies, 28, pp. 35-46. [21] rabehi, a., guermoui, m., djafer, d. and zaiani, m. 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can be opened with acrobat and adobe reader 5.0 and later.) >> /namespace [ (adobe) (common) (1.0) ] /othernamespaces [ << /asreaderspreads false /cropimagestoframes true /errorcontrol /warnandcontinue /flattenerignorespreadoverrides false /includeguidesgrids false /includenonprinting false /includeslug false /namespace [ (adobe) (indesign) (4.0) ] /omitplacedbitmaps false /omitplacedeps false /omitplacedpdf false /simulateoverprint /legacy >> << /addbleedmarks false /addcolorbars false /addcropmarks false /addpageinfo false /addregmarks false /convertcolors /converttocmyk /destinationprofilename () /destinationprofileselector /documentcmyk /downsample16bitimages true /flattenerpreset << /presetselector /mediumresolution >> /formelements false /generatestructure false /includebookmarks false /includehyperlinks false /includeinteractive false /includelayers false /includeprofiles false /multimediahandling /useobjectsettings /namespace [ (adobe) (creativesuite) (2.0) ] /pdfxoutputintentprofileselector /documentcmyk /preserveediting true /untaggedcmykhandling /leaveuntagged /untaggedrgbhandling /usedocumentprofile /usedocumentbleed false >> ] >> setdistillerparams << /hwresolution [2400 2400] /pagesize [612.000 792.000] >> setpagedevice microsoft word numero_50_art_56_2433 j.m. vasco-olmo et alii, frattura ed integrità strutturale, 49 (2019) 658-666; doi: 10.3221/igf-esis.50.56 658 focused on crack tip fields experimental characterisation of fatigue crack growth based on the ctod measured from crack tip displacement fields using dic j.m. vasco-olmo, f.a. díaz university of jaén, spain jvasco@ujaen.es fdiaz@ujaen.es f.v. antunes university of coimbra, portugal fernando.ventura@dem.up.pt m.n. james university of plymouth, uk m.james@plymouth.ac.uk abstract. the current work presents an experimental study on the use of the crack tip opening displacement (ctod) to evaluate its ability to characterise fatigue crack growth. a methodology is developed to measure and to analyse the ctod from experimental data. the vertical displacements obtained by implementing digital image correlation (dic) on growing fatigue cracks are used to measure the ctod. two fatigue tests at stress ratios of 0.1 and 0.6 were conducted on compact tension (ct) specimens manufactured from a 1 mm thick sheet of commercially pure titanium. a sensitivity analysis to explore the effect of the position selected behind the crack tip for the ctod measurement was performed. the analysis of a full loading cycle allowed identifying the elastic and plastic components of the ctod. the plastic ctod was found to be directly related to the nonlinear zone (i.e., plastic deformation) generated at the crack tip during fatigue propagation. moreover, a linear relationship between da/dn and δctodp independent of the stress ratio was found. results show that the ctod can be used as a viable alternative to the stress intensity factor range (δk) in characterising fatigue crack propagation since the parameter considers the fatigue threshold and crack shielding in an intrinsic way. keywords. crack tip opening displacement (ctod); fatigue crack growth rate; dic; range of plastic ctod. citation: vasco-olmo, j.m., díaz, f.a., antunes, f.v., james, m.n., experimental characterisation of fatigue crack growth based on the ctod measured from crack tip displacement fields using dic, frattura ed integrità strutturale, 49 (2019) 658-666. received: 11.03.2019 accepted: 23.04.2019 published: 01.07.2019 copyright: © 2019 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. http://www.gruppofrattura.it/va/50/2433.mp4 j.m. vasco-olmo et alii, frattura ed integrità strutturale, 49 (2019) 658-666; doi: 10.3221/igf-esis.50.56 659 introduction atigue crack growth has been traditionally characterised by the paris law [1], that relates the crack growth per cycle, da/dn to the stress intensity factor range, δk. however, there are several controversial issues and unanswered questions in this field. the procedures for analysing constant amplitude fatigue under small-scale yielding conditions are well established, although a number of uncertainties remain. variable amplitude loading, large-scale plasticity, and short cracks introduce additional complications that are not fully understood. in addition, in many materials, it is virtually impossible to characterise the fracture behaviour with linear elastic fracture mechanics (lefm), and an alternative fracture mechanics model is required. elastic-plastic fracture mechanics (epfm) is applied to materials that exhibit nonlinear behaviour (i.e., plastic deformation). hence in authors’ view, the linear elastic δk parameter should be replaced by nonlinear crack tip parameter since fatigue crack growth is governed by nonlinear processes at the crack tip. two elastic-plastic parameters have been proposed to be related with crack tip plastic deformation, the crack tip opening displacement (ctod) and the j contour integral. both parameters describe crack tip conditions in elastic-plastic materials, and they can be used as a fracture criterion. ctod is a local parameter, while the j integral is used as a global criterion based on the quasi-strain energy release rate. critical values of ctod or j give nearly size-independent measurements of fracture toughness, even for relatively large amounts of crack tip plasticity. there are limits to the applicability of these parameters but they are much less restrictive than the validity requirements of lefm. in this work, ctod is the parameter used to characterise fatigue crack growth. ctod was first observed by wells [2] when he was attempting to measure kic values in a number of structural steel. wells found that these materials were too tough to be characterised by lefm. while examining fractured test specimens, wells noticed that the crack faces had moved apart prior to fracture; plastic deformation had blunted an initially sharp crack, resulting in a finite displacement at the crack tip. the degree of crack blunting increased in proportion to the toughness of the material. this observation led wells to propose the opening at the crack tip as a measurement of fracture toughness. nowadays, ctod is a classical parameter in elastic-plastic fracture mechanics and it has a great importance for fatigue analysis. crack tip blunting at maximum load and the crack tip re-sharpening at minimum load were used to explain fatigue crack growth [3]. ctod has been experimentally measured by using extensometers located remotely to the crack tip. thus, in compact tension (ct) specimens an extensometer with blades is located at the mouth of the specimen notch to measure the opening of the specimen [4]. in the case of middle tension (mt) specimens a pin extensometer is placed at the centre of the specimen by fixing it in two small holes [5]. recently, full field optical techniques have become very popular for the analysis of structural integrity problems. among them digital image correlation (dic) technique can be considered because the displacement fields at the vicinity of the crack tip can be measured with high level of accuracy [6]. thus, in this work dic is implemented to measure the ctod from the relative displacement between both crack flanks. moreover, finite element analysis has also been used to measure the ctod numerically. the displacement at the first node behind the crack tip is generally used as an operational ctod [7]. in a previous work, antunes et al. [8] developed a numerical study to quantify the ctod in a mt specimen for two aluminium alloys in order to analyse the applicability of this parameter to characterise fatigue crack growth. a relationship was found between da/dn and the plastic ctod range for the 6082-t6 aluminium alloy independent of stress ratio, showing that the ctod can be a viable alternative to δk in the analysis of fatigue crack propagation. thus, in the current work an experimental study of the ctod is performed by implementing the procedure developed by antunes et al. [8] to evaluate the ability of this parameter to characterise fatigue crack growth. note that the values of δctodp reported in [8] are relatively small, lower than 1 μm, which is certainly a challenge for the experimental determination of plastic ctod since some controversy exists about if dic is able to provide extremely high spatial resolution characterisation of crack tip deformation fields, including crack opening profiles [9]. the vertical displacements measured by dic on growing fatigue cracks are used to measure the ctod as the relative displacement existing between the crack flanks. two fatigue tests at stress ratios of 0.1 and 0.6 were conducted on titanium ct specimens. from the analysis of a full loading cycle, the elastic and plastic ctod could be identified. a linear relationship between da/dn and the plastic ctod was found for both tests, showing therefore that the ctod can be used as a viable alternative in characterising fatigue crack growth. with this work, the authors intend to contribute to a better understanding of the different mechanisms driving fatigue crack propagation and to address the outstanding controversy associated with plasticity-induced fatigue crack closure. f j.m. vasco-olmo et alii, frattura ed integrità strutturale, 49 (2019) 658-666; doi: 10.3221/igf-esis.50.56 660 experimental details wo ct specimens (dimensions shown in fig. 1a) were manufactured from a 1 mm thick sheet of commercially pure grade 2 titanium and tested in constant amplitude fatigue loading with a maximum load of 750 n at stress ratio values of 0.1 and 0.6. figure 1: (a) dimensions (mm) of the ct specimens tested. (b) experimental set-up used for fatigue testing and data acquisition. the two surfaces of each specimen were treated using different methods to enable simultaneous measurements of the displacement field by digital image correlation (dic) on one side and crack length on the other. the surface used for the dic study was sprayed with a random black speckle pattern over a white background, while the other surface of the specimen was ground and polished to allow tracking of the crack tip position with a macro-zoom lens (mlh-10x eo). fatigue tests were conducted on an electropuls e3000 electrodynamic machine (fig. 1b) at a loading frequency of 10 hz. a ccd camera, fitted with a macro-zoom lens similar to that indicated above to increase the spatial resolution at the region around the crack tip, was placed perpendicularly to each face of the specimen. during fatigue testing, the cyclic loading was periodically paused to allow acquisition of a sequence of images at uniform increments through a complete loading and unloading cycle. the ccd camera viewing the speckled surface of the specimen was set up so that the field of view was 17.3 x 13 mm (resolution of 13.7μm/pixel) with the crack path located at the centre of the image. a fibre optic ring placed around the zoom lens provided illumination of the specimen surface (also shown in fig. 1b). methodology for locating the crack tip s indicated above, ctod is a parameter that measures the opening at the crack tip, hence the vertical displacements obtained from experiments are used in analysing its value. examples of dic horizontal and vertical displacement maps for a crack length of 9.40 mm and a load level of 750 n are shown in fig. 2. the method of obtaining the ctod from measurements of the relative displacement between the crack flanks of selected points behind the crack tip is explained below. it is important to note that the accuracy of the results is strongly influenced by location of the assumed crack tip; accurate location is therefore important and this is found in the following manner. firstly, the y-coordinate of the crack tip is found by plotting a set of profiles of vertical displacement perpendicular to the crack plane as all profiles converge onto a single point where they cross the crack plane. this is clearly seen in fig. 3a and the intersection point identifies the location of the crack tip in the y-direction. the corresponding vertical displacement ycoordinate for this point is marked in fig. 3a because it is then used to find the x-coordinate of the crack tip. this is done by plotting a displacement profile in the x-direction, parallel with the crack direction, and locating the point that corresponds with the same displacement value (v = 0.158 mm) previously found for the y-coordinate (fig. 3b). using this procedure, the crack tip was identified as located at the point with coordinates x = 470 pixels and y = 468 pixels, with the coordinate origin being at the upper left corner of the vertical displacement map (fig. 2b). once the crack tip location is established, the ctod can be obtained by defining a suitable pair of measurement points behind the crack tip, and determining the ctod through a complete loading cycle by analysing both the loading and unloading half cycles. from this information, the portion of the cycle during which the crack is nominally closed or open t a (b) (a) j.m. vasco-olmo et alii, frattura ed integrità strutturale, 49 (2019) 658-666; doi: 10.3221/igf-esis.50.56 661 can be found. finally, from analysis of the portion of the load cycle during which the crack is open, both the elastic and plastic components of the ctod can be estimated from the variation in slope observed in the ctod versus load curves. figure 2: (a) horizontal and (b) vertical displacement fields measured with dic for a crack length of 9.40 mm at a load level of 750 n. figure 3: graphs to support the explanation given in the paper of the methodology used for locating the crack tip: (a) y-coordinate and (b) x-coordinate. effect of the position behind the crack tip sensitivity analysis was performed to explore the influence of the distance behind the crack tip of the pair of points selected for the ctod measurements, as this is clearly critical to interpreting ctod data and correlating it with fatigue crack growth rate. the position of these two points behind the crack tip is given in fig. 4 as lx in the direction of the crack plane and ly in the direction perpendicular to the crack. the coordinate axes have been modified establishing their origin at the coordinates found in the previous section for the crack tip. the sensitivity analysis involved measuring the ctod at the maximum load as a function of one of the parameters, whilst maintaining the other one fixed. fig. 5 presents the results of this analysis, with fig. 5a plotting the ctod as a function of lx for various value of ly and fig. 5b giving it as a function of ly for different values of lx. as would be expected, ctod values increase steadily with increasing distance behind the crack tip. the key observation from these data considering fig. 5a is that for any particular ly value >10 pixels (136.9 µm) the ctod reaches an upper bound limit for lx distances behind the crack tip approximately ≥ 120 µm. this is more clearly shown in fig. 5b where for lx values approximately > 8 pixels (82.1 µm) the ctod value attains a plateau at a ly distance of approximately 140 µm. this stable plateau region is the result of rigid body motion and indicates the boundary of the region undergoing crack tip deformation and its onset can hence be used to characterise the ctod. the plateau region is indicated with the rectangle in fig. 5b and encloses the ctod values corresponding to the ranges 5–15 pixels (68.4–205.3 μm) for lx and 10–15 pixels (136.8–205.3 μm) for ly. this analysis demonstrates that the ctod is accurately characterised by using data corresponding with the position of two points with a horizontal position lx = 5 pixels (68.4 μm) and vertical position ly = 10 pixels (136.8 μm) behind the crack tip. x (pixels) y ( p ix el s) mm 200 400 600 800 1000 1200 100 200 300 400 500 600 700 800 900 -0.05 -0.04 -0.03 -0.02 -0.01 0 0.01 0.02 x (pixels) y ( p ix el s) mm 200 400 600 800 1000 1200 100 200 300 400 500 600 700 800 900 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2 100 200 300 400 500 600 700 800 900 0.145 0.15 0.155 0.16 0.165 0.17 0.175 0.18 y (pixels) v er ti ca l d is p la ce m en ts ( m m ) y = 468 pixels (v = 0.158 mm) 0 200 400 600 800 1000 1200 1400 0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2 x (pixels) v er ti ca l d is p la ce m en ts ( m m ) x = 470 pixels v = 0.158 mm a (a) (b) (a) (b) j.m. vasco-olmo et alii, frattura ed integrità strutturale, 49 (2019) 658-666; doi: 10.3221/igf-esis.50.56 662 figure 4: magnified view of the crack tip region illustrating how ctod measurements are based on a particular pair of points behind the crack tip. the coordinate axes have been modified with their origin at the crack tip. figure 5: graphs showing the effect of the location behind the crack tip of the selected points used for the ctod measurement. (a) as a function of the distance along the crack plane lx; (b) as a function of the distance in the perpendicular direction ly to the crack plane. experimental results nce the values of lx and ly were established, the ctod through a loading cycle for any particular crack length could be obtained from analysis of the dic data. a typical plot showing ctod at increments of 25 n throughout a full loading cycle for a crack length of 9.40 mm in the case of the specimen tested at r = 0.1 and a crack length of 9.20 mm in the case of the specimen tested at r = 0.6 is shown in fig. 6. the elastic and plastic ctod values can be obtained from the data given in fig. 6, using an offset procedure similar to that reported by skorupa et al. [10] for compliance measurements. in this process, a least squares straight line was fitted to experimental data over the part of the load cycle that corresponds with elastic deformation (see lines drawn in fig. 6). the elastic portions of the loading cycle were identified using a 3 point sliding average, founding a range between 15% and 55% of the loading range from the minimum applied load for the specimen tested at r = 0.1 and between the minimum applied load and a 40% of the loading range from the minimum load for the specimen tested at r = 0.6. to evaluate how the components of ctod can change depending on the loading range selected, a sensitivity analysis was performed to evaluate the errors made when variations of ±10% for the lower and upper limits are analysed. according to this sensitivity analysis, the variations of the lower limit involved errors between 3–4% for the plastic ctod and 1.0–1.5% for the elastic component. on the other hand, the variations on the upper limit involved errors between 6.5–10% for the plastic ctod and 3–4.5% for the elastic ctod. from these results it is evident that the selection of the upper limit is more restrictive than the lower limit. this is 0.000 0.005 0.010 0.015 0.020 0.025 0 20 40 60 80 100 120 140 160 180 200 220 c t o d ( m m ) distance at the perpendicular direction to the crack, ly (μm) lx=-1 pix (-13.7 microns) lx=-2 pix (-27.4 microns) lx=-3 pix (-41.2 microns) lx=-4 pix (-54.8 microns) lx=-5 pix (-68.4 microns) lx=-6 pix (-82.1 microns) lx=-7 pix (-95.8 microns) lx=-8 pix (-109.5 microns) lx=-9 pix (-123.2 microns) lx=-10 pix (-136.9 microns) lx=-11 pix (-150.6 microns) lx=-12 pix (-164.2 microns) lx=-13 pix (-177.9 microns) lx=-14 pix (-191.6 microns) lx=-15 pix (-205.3 microns) o (a) (b) j.m. vasco-olmo et alii, frattura ed integrità strutturale, 49 (2019) 658-666; doi: 10.3221/igf-esis.50.56 663 not strange since the upper limit establishes the separation between the elastic and plastic components. therefore, these results obtained from the sensitivity analysis strengthen the definition of the loading range for describing the elastic behaviour. the equation obtained from this linear fit was employed to calculate the theoretical ctod value corresponding to all analysed load levels. thus, the ctod offset was obtained from eq. (1). the ranges of the elastic and plastic components of the ctod can then be defined as shown in fig. 6. exp 100 th th ctod ctod ctod offset ctod    (1) figure 6: plot of ctod through a complete loading cycle, showing its elastic and plastic components at a crack length of 9.40 mm for the specimen tested at r =0.1 (a) and 9.20 mm for the specimen tested at r = 0.6 (b) using 5 pixels (68.4 μm) and 10 pixels (136.8 μm) for the distances lx and ly, respectively. figure 7: variation of ctod offset as a function of the applied load at a crack length of 9.40 mm for the specimen tested at r = 0.1 (a) and 9.20 mm for the specimen tested at r = 0.6 (b). a value of 4% was set as the offset criterion to define the region of the curve corresponding to the elastic component of the ctod. the ctod offset is plotted against applied load (fig. 7) and the elastic region is determined in accordance with the standard e 647 [30], where a ctod change of 4% either side of the zero value is taken as representing the offset criterion (marked in fig. 7 and corresponding with a compliance change of ≈4%) and establishes the elastic region in the offset ctod trace. the letters a to d in figs. 6a and 7a define the various regions in the ctod loading cycle for the specimen tested at r = 0.1, where the load range between b and c (175 n to 450 n) defines elastic behaviour. it is clear in fig. 6a that from point c there is a deviation from linearity up to point d, corresponding to the maximum applied load, and this is attributed to plastic deformation. the elastic and plastic ranges of ctod can then be estimated by extrapolating the linear regime to the maximum load (fig. 6). during unloading, there is a linear decrease in ctod between points d and 0.000 0.002 0.004 0.006 0.008 0.010 0.012 0.014 0.016 0.018 0.020 0 100 200 300 400 500 600 700 800 c t o d ( m m ) p (n) loading unloading a b c d δctodp δctodel e r = 0.1 0 0.002 0.004 0.006 0.008 0.01 0.012 0.014 0.016 0.018 0.02 0 100 200 300 400 500 600 700 800 c t o d ( m m ) p (n) loading unloading δctodp δctodel c d e b r = 0.6 0 100 200 300 400 500 600 700 800 -10 0 10 20 30 40 50 60 70 80 90 100 p (n ) ctod offset (%) ±4% offset a b c d r = 0.1 400 450 500 550 600 650 700 750 800 -4 -2 0 2 4 6 8 10 12 14 16 18 20 22 24 26 p (n ) ctod offset (%) ±4% offset b c d r = 0.6 (a) (b) (a) (b) j.m. vasco-olmo et alii, frattura ed integrità strutturale, 49 (2019) 658-666; doi: 10.3221/igf-esis.50.56 664 e with the same slope than that obtained for the elastic regime in the loading half cycle. as is the case for the loading half cycle, there is a change in the linearity during further unloading due to the reversed plastic deformation. the elastic and plastic ranges of ctod during the loading half cycle were therefore obtained from fig. 6a as 13 μm and 6 μm, respectively and the corresponding values for the unloading half cycle were 13.2 μm and 5.8 μm, respectively. the plastic ctod is hence 31.6% (loading) and 30.5% (unloading) of the maximum ctod. the region between points a and b in figs. 6a and 7a is associated with crack opening and closing and additional work could be done to estimate the opening and closing loads; however, any additional information gained on the subjects of crack closure and crack tip shielding is both complex in interpretation of its true effects, and is not germane to the present study. similar procedure can be extrapolated in the case of the specimen tested at r = 0.6 but with the difference that the loading range is between 450 n and 750 n. the elastic and plastic ranges of ctod were 8.7 μm and 2.9 μm, respectively. it is clear the difference between these values and those obtained for r = 0.1. however, these values are coherent since the loading range for the test at high ratio is a 44% of that corresponding to the low ratio. another important difference respect the ctod plot at low r-ratio is that the region between a and b point was not identified. this is not surprising since at r = 0.6 any crack shielding effect was not expected. the methodology described above to obtain the ctod range for the elastic and plastic components was applied to data recorded during crack growth for the tests conducted at the stress ratios of r = 0.1 and 0.6. fig. 8a shows the elastic and plastic ctod data as a function of crack length. significant scatter is observed in the elastic ctod values, being those at r = 0.6 about a half of those values at r = 0.1; while those representing the plastic ctod show a more consistent increment with increase in crack length. plastic ctod demonstrates a faster rate of increase at r = 0.1 than at r = 0.6. however, normalising the elastic and plastic ranges of ctod values by the total range of ctod gives a much more uniform picture at the two stress ratio values (fig. 8b) and the data for the elastic ctod now shows more consistent behaviour. the trends in the ctod curves in fig. 8b appear sensible since, as the crack is propagating, the plastic deformation is increasing and, with it, the plastic ctod, whilst the value of the elastic ctod undergoes a corresponding decrease as a percentage of the total ctod. figure 8: (a) elastic and plastic ctod ranges as a function of the crack length for both tests. (b) elastic and plastic ctod ranges as a percentage of the total ctod range as a function of crack length. fig. 9a presents data for da/dn as a function of the ranges of ctodt, ctodel and ctodp for the specimen tested at r = 0.1. it is clear that only the plastic component of ctod shows a consistent increase with crack growth rate and could therefore be used to characterise fatigue crack growth rate. fig. 9b shows the da/dn versus δctodp curves obtained at both r = 0.1 and 0.6 that demonstrate a very good correlation of fatigue crack growth rate into a single linear relationship. it should be noted that this correlation is obtained without employing logarithmic scales as is necessary when using the paris law. the crack growth rate is then given by linear regression as: 0.2706 p da ctod dn   (2) 0.000 0.002 0.004 0.006 0.008 0.010 0.012 0.014 0.016 3 4 5 6 7 8 9 10 δ c t o d ( m m ) crack length (mm) elastic [ct1 (r=0.6)] elastic [ct2 (r=0.1)] plastic [ct1 (r=0.6)] plastic [ct2 (r=0.1)] 0 20 40 60 80 100 120 3 4 5 6 7 8 9 10 δ c t o d p er ce n ta g e (% ) crack length (mm) elastic [ct1 (r=0.6)] elastic [ct3 (r=0.1)] plastic [ct1 (r=0.6)] plastic [ct3 (r=0.1)] (a) (b) j.m. vasco-olmo et alii, frattura ed integrità strutturale, 49 (2019) 658-666; doi: 10.3221/igf-esis.50.56 665 the constant in eq. (2) does not have units, unlike the constants defined by paris law, and a linear relationship between da/dn and the range of ctod was also observed by guo et al. [11], tvergaard [20] and pippan and grosinger [32]. those works, however, all used the total ctod and they did not distinguish between the plastic and elastic ctod components. a linear relationship between da/dn and δctodp has been reported by antunes et al. [33] in work on 7050-t6 aluminium alloy that combined numerical modelling and experimental data in recently published work. they obtained da/dn data from experiments in middle-tension (mt) specimens for different stress ratios while the plastic ctod data were numerically determined by using the methodology previously reported in [21]. they obtained the relationship da/dn = 0.5246 x δctodp. in contrast, in the experimental work presented here, da/dn data were obtained from measurements of crack length and number of cycles, with the ctod data obtained from analysis of dic measurements of the vertical displacement. to the knowledge of the present authors, this is the first time that plastic ctod data, determined solely by experimentation, has been used to characterise fatigue crack growth rate at two different stress ratio values. figure 9: (a) crack growth rate per cycle (da/dn) as a function of the range of total ctod (δctodt), elastic ctod (δctodel) and plastic ctod (δctodp) for the specimen tested at low stress ratio (r = 0.1). (b) plot of da/dn versus δctodp for the two tests conducted at low (r = 0.1) and high (r = 0.6) stress ratio values. conclusions he plastic range of ctod is clearly linked with the plastic deformation generated at the crack tip during fatigue crack propagation at constant amplitude. the range of plastic ctod (δctodp) has therefore been used to characterise and correlate fatigue crack growth data obtained at two different stress ratio values of 0.1 and 0.6. a linear relationship between da/dn and δctodp, independent of stress ratio was, observed for a cp titanium alloy. the ctod was measured from the relative vertical displacement between the crack flanks. a sensitivity analysis was performed to determine the optimum position behind the crack tip of the points where displacement was measured, and it was found that the ctod value showed a significant dependence on their location in the plane of the crack. however, the influence of the vertical distance from the crack plane was not as restrictive, with a stable value of ctod being obtained at a distance of 136.9 µm. this conclusion was reached using a methodology that analysed different displacement profiles plotted from the vertical displacement map. this work has demonstrated that ctod represents a viable alternative technique to stress intensity factor in characterising fatigue crack growth rate since ctod considers fatigue threshold and crack shielding in an intrinsic way [33]. however, further work is necessary to determine whether the linear relationship observed between da/dn and δctodp may be considered as an intrinsic material property, independent of the geometry and loading conditions. the plastic ctod approach is, however, unlikely to shed light on the physical mechanisms underlying such phenomena as plasticity-induced crack tip shielding and a combination of approaches will be required to advance understanding, e.g. the use of plastic ctod and the cjp model of crack tip fields. 0.0000 0.0002 0.0004 0.0006 0.0008 0.0010 0.0012 0.0014 0.0016 0.0018 0 0.005 0.01 0.015 0.02 da /d n (m m /c y cl e) δctod (mm) total ctod elastic ctod plastic ctod da/dn = 0.2706 δctodp r² = 0.9836 0.0000 0.0002 0.0004 0.0006 0.0008 0.0010 0.0012 0.0014 0.0016 0.0018 0 0.001 0.002 0.003 0.004 0.005 0.006 0.007 da /d n (m m /c y cl e) δctodp (mm) ct1 (r=0.6) ct2 (r=0.1) t (a) (b) j.m. vasco-olmo et alii, frattura ed integrità strutturale, 49 (2019) 658-666; doi: 10.3221/igf-esis.50.56 666 acknowledgements he current work has been conducted with the financial support from gobierno de españa through the project ‘proyecto de investigación de excelencia del ministerio de economía y competitividad mat2016-76951-c2-1-p’. references [1] paris, p.c. (1960). a critical analysis of crack propagation laws, j. basic eng., 85, pp. 528–534. [2] wells, a.a. (1961). unstable crack propagation in metals. cleavage and fast fracture, proceedings of the crack propagation symposium, cranfield, uk, 1, 84. [3] laird, c., smith, g.c. (1962). crack propagation in high stress fatigue, philos. mag. 8, pp. 847–857. [4] vasco-olmo, j.m., díaz, f.a., garcía-collado, a., dorado, r. (2013). experimental evaluation of crack shielding during fatigue crack growth using digital image correlation, fatigue fract. engng mater. struct., 38, pp. 223–237. [5] antunes, f.v., branco, r., costa, j.d., rodrigues, d.m. (2010). plasticity induced crack closure in middle-tension specimen: numerical versus experimental, fatigue fract. engng mater. struct. 33, pp. 673–686. [6] chu, t.c., ranson, w.f., sutton, m.a., peters, w.h. (1985). applications of digital-image correlation technique to experimental mechanics, exp. mech., 25, pp. 232–244. [7] de matos, p.f.p., nowell, d. (2007). on the accurate assessment of crack opening and closing stresses in plasticityinduced fatigue crack closure problems, eng. fract. mech., 74, pp. 1579–1601. [8] antunes, f.v., rodrigues, s.m., camas, d. (2016). a numerical analysis of ctod in constant amplitude fatigue crack growth, theoretical and applied fracture mechanics, 85, pp. 45–55. [9] korsunsky, a.m., song, x., belnoue, j., jun, t., hofmann, f., de matos, p.f.p., nowell, d., dini, d. (2009). aparicio-blanco, o., walsh, m.j., crack tip deformation fields and fatigue crack growth rates in ti-6al-4v, int. j. fatigue, 31, pp. 1771–1779. [10] skorupa, m., beretta, s., carboni, m., machniewicz (2002). an algorithm for evaluating crack closure from local compliance measurements, fatigue fract. engng mater. struct., 25, pp. 261–273. [11] guo, w., wang, c.h., rose, r.f. (1999). the influence of cross-sectional thickness on fatigue crack growth, fatigue fract. engng mater. struct., 22, pp. 437–444. [12] tvergaard, v., (2004). on fatigue crack growth in ductile materials by crack-tip blunting, j. mech. phys. solids, 52, pp. 2149–2166. [13] pippan, r.g., grosinger, w., (2013). fatigue crack closure: from lcf to small scale yielding, int. j. fatigue, 46, pp. 41–48. t << /ascii85encodepages false /allowtransparency false /autopositionepsfiles true /autorotatepages /none /binding /left /calgrayprofile (dot gain 20%) /calrgbprofile (srgb iec61966-2.1) /calcmykprofile (u.s. web coated \050swop\051 v2) /srgbprofile (srgb iec61966-2.1) /cannotembedfontpolicy /error /compatibilitylevel 1.4 /compressobjects /tags /compresspages true /convertimagestoindexed true /passthroughjpegimages true /createjobticket false /defaultrenderingintent /default /detectblends true /detectcurves 0.0000 /colorconversionstrategy /cmyk /dothumbnails false /embedallfonts true /embedopentype false /parseiccprofilesincomments true /embedjoboptions true /dscreportinglevel 0 /emitdscwarnings false /endpage -1 /imagememory 1048576 /lockdistillerparams false /maxsubsetpct 100 /optimize true /opm 1 /parsedsccomments true /parsedsccommentsfordocinfo true 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can be opened with acrobat and adobe reader 5.0 and later.) >> /namespace [ (adobe) (common) (1.0) ] /othernamespaces [ << /asreaderspreads false /cropimagestoframes true /errorcontrol /warnandcontinue /flattenerignorespreadoverrides false /includeguidesgrids false /includenonprinting false /includeslug false /namespace [ (adobe) (indesign) (4.0) ] /omitplacedbitmaps false /omitplacedeps false /omitplacedpdf false /simulateoverprint /legacy >> << /addbleedmarks false /addcolorbars false /addcropmarks false /addpageinfo false /addregmarks false /convertcolors /converttocmyk /destinationprofilename () /destinationprofileselector /documentcmyk /downsample16bitimages true /flattenerpreset << /presetselector /mediumresolution >> /formelements false /generatestructure false /includebookmarks false /includehyperlinks false /includeinteractive false /includelayers false /includeprofiles false /multimediahandling /useobjectsettings /namespace [ (adobe) (creativesuite) (2.0) ] /pdfxoutputintentprofileselector /documentcmyk /preserveediting true /untaggedcmykhandling /leaveuntagged /untaggedrgbhandling /usedocumentprofile /usedocumentbleed false >> ] >> setdistillerparams << /hwresolution [2400 2400] /pagesize [612.000 792.000] >> setpagedevice microsoft word numero_33_art_14 c. bagni et alii, frattura ed integrità strutturale, 33 (2015) 105-110; doi: 10.3221/igf-esis.33.14 105 focussed on characterization of crack tip fields gradient-enriched linear-elastic tip stresses to perform the highcycle fatigue assessment of notched plain concrete c. bagni, h. askes, l. susmel department of civil and structural engineering, the university of sheffield, sheffield s1 3jd, united kingdom c.bagni@sheffield.ac.uk, h.askes@sheffield.ac.uk, l.susmel@sheffield.ac.uk abstract. gradient elasticity (ge) allows the stress analysis to be performed by taking into account the size of the dominant source of microstructural heterogeneity via a suitable length scale parameter. this is done by simply assuming that the material under investigation obeys a linear-elastic constitutive law, albeit equipped with additional spatial strain gradients. from a practical point of view, the most important implication of this modus operandi is that gradient-enriched linear-elastic stresses at the notch tips are always finite, this holding true also in the presence of sharp stress risers (such as cracks). in the present investigation, the accuracy of two different ge based design strategies was checked against a number of experimental results generated by testing, under cyclic four-point bending, plain concrete samples containing different geometrical features. the high level of accuracy which was obtained by directly using gradient-enriched linear-elastic notch stresses strongly supports the idea that ge is a powerful tool suitable for designing notched concrete components against high-cycle fatigue. this result is very promising also because the required stress analysis can directly be performed by using standard finite element (fe) solvers. keywords. concrete; fatigue; notch; gradient elasticity. introduction n the civil infrastructure sector, concrete is the most commonly used material. this explains the reason why the problem of optimising the static assessment of concrete has been studied by the international scientific community for decades. the outcomes from this enormous amount of work allow modern concrete structures to be efficiently designed against static loading via the adoption of low safety factors. by so doing, slender concrete structures can safely be built by remarkably reducing the usage of natural resources, this having positive effects not only on sustainability, but also on carbon emissions. owing to the fact that the magnitude of in-service local stresses increases as the size of concrete structural components decreases, slender concrete structures are obviously more susceptible to fatigue. examination of the state of the art shows that, since the beginning of the 1900s [1, 2], much research work has been done to formalise efficient design methods suitable for estimating the fatigue damage extent in concrete components subjected to timevariable loading. unfortunately, the experimental work carried out so far has resulted in design curves suitable for estimating the fatigue lifetime solely for those specific concrete mixtures that were tested. it has to be highlighted also that, apart from three isolated investigations [3-5], no effort has been made so far to devise and validate (through appropriate experimental investigations) specific techniques capable of modelling the detrimental effect of notches on the overall fatigue strength of plain concrete. in this setting, the aim of the present investigation is to check whether linear-elastic gradient-enriched notch tip stresses are successful in performing the high-cycle fatigue assessment of notched plain concrete. i http://www.gruppofrattura.it/pdf/rivista/numero33/audioslides/susmel1/susmel1.html c. bagni et alii, frattura ed integrità strutturale, 33 (2015) 105-110; doi: 10.3221/igf-esis.33.14 106 fundamentals of gradient elasticity n about the middle of the last century, mindlin [6] investigated the most important features of gradient enriched elasticity by proposing an alternative continuum theory based on the use of a number of non-conventional constitutive parameters. even if this theory is certainly very elegant, its implementation is not straightforward at all due to its intrinsic complexity. in light of the doubtless peculiarities of this approach, since the pioneering work done by mindlin, the international scientific community has made a tremendous effort to try to simplify this theory to make it suitable for being used in situations of practical interest. amongst the different formalisations which have been proposed so far, one of the most appealing solutions is the one proposed by aifantis and co-workers [7-9]. this approach takes as its starting point the assumption that the enriched stress vs. strain relationship can be reformulated by using the laplacian of the strain, i.e.:  2 2c     (1) in constitutive law (1),  and  are second-order tensors with the stress and strain components, respectively, c is a fourthorder tensor containing the material elastic moduli, and l is the length scale parameter which is employed to describe the underlying microstructural features of the material being modelled. thanks to the specific features of the above formalisation of ge, constitutive law (1) can efficiently be implemented numerically, the stress and strain analysis being directly performed by using standard fe solvers [10-12]. in more detail, initially the following conventional fe equation has to be solved: k u f (2) where u is the vector with the nodal displacements, f is the vector containing the nodal forces, and k is the linear-elastic stiffness matrix. the displacements determined from eq. (2) allow the gradient-enriched nodal stresses  to be determined as follows: 2 t t tn nn sn s d n b d u                   (3) where n is the matrix containing the shape functions, b is the matrix containing the derivatives of the displacement, and s is the elastic compliance matrix. it is possible to conclude by highlighting that if constitutive law (1) is adopted to model the stress vs. strain behaviour of engineering materials, the use of material length scale parameter l leads to linear-elastic stress fields which are never singular, this holding true also in the presence of cracks and sharp notches [13]. experimental investigation o assess the accuracy of ge in modelling the high-cycle fatigue behaviour of notched plain concrete, 100mm x 100mm square section beams weakened by different types of notches were tested under cyclic four-point bending. the specimen length was equal to 500 mm and the nominal notch depth to 50 mm. the tested notched specimens contained u-notches with root radius, rn, equal to 25 mm, 12.5 mm, and 1.4 mm, resulting in a net stress concentration factors, kt, equal to 1.47, 1.84, and 4.32, respectively. the un-notched specimens used to determine the reference endurance limits had gauge length width equal to 50mm and thickness equal to 100 mm. the concrete mix used to manufacture the tested samples contained portland cement (strength class equal to 32.5 n/mm2), natural round gravel (10 mm grading), and grade m concrete sand. in order to manufacture specimens having the same microstructural features, but different strength, two values for the water-to-cement ratio were investigated: batch a was manufactured by setting the water-to-cement ratio equal to 0.5, whereas batch b was cast by taking the water-to-cement ratio equal to 0.4. the samples were removed from the moulds 24 hours after casting, being subsequently stored for 28 days in a moist room at 23°c. the static strength of the investigated concrete mixes was determined under three-point bending. the bending strength of batch a was seen to be equal to 4.9 mpa, whereas the bending strength of batch b to 6.5 mpa. i t c. bagni et alii, frattura ed integrità strutturale, 33 (2015) 105-110; doi: 10.3221/igf-esis.33.14 107 the un-notched specimens as well as the notched samples were loaded in cyclic four-point bending at a frequency of 10 hz. for the force-controlled fatigue tests the adopted failure criterion was the complete breakage of the specimens. the experimental results generated according to the above experimental procedure are shown in fig. 1 together with the corresponding endurance limits. in this figure 0,max indicates the un-notched material endurance limits, whilst max denotes the notch endurance limits referred to the nominal net area. the symbol rm is used to indicate the average value of the load ratio characterising any data sets. the above endurance limits were all estimated at 2106 cycles to failure by post-processing the fatigue data according to the up-and-down method proposed by dixon [14]. to conclude, it is worth observing that the determined endurance limits were estimated in terms of 0,max and max because, under either cyclic axial loading or bending, the maximum stress in the cycle is seen to be a stress quantity capable of efficiently taking into account the mean stress effect in concrete fatigue [15]. 1.0 2.0 3.0 4.0 5.0 6.0 7.0 8.0 1 2 3 4 5 6 7 max [mpa] specimen id un-notched specimens failure run out batch a, r=0.11 batch b, r=0.33 0,max=5.1 mpa 0,max=3.3 mpa 1.0 2.0 3.0 4.0 5.0 6.0 7.0 8.0 1 2 3 4 5 6 7 max [mpa] specimen id intermediate notches, rn=12.5 mm failure run out batch a, r=0.09 batch b, r=0.35 max=4.6 mpa max=3.2 mpa 1.0 2.0 3.0 4.0 5.0 6.0 7.0 8.0 1 2 3 4 5 6 7 max [mpa] specimen id blunt notches, rn=25 mm failure run out batch a, r=0.07 batch b, r=0.40 max=4.7 mpa max=3.3 mpa 1.0 2.0 3.0 4.0 5.0 6.0 7.0 8.0 1 2 3 4 5 6 7 max [mpa] specimen id sharp notches, rn=1.4 mm failure run out batch a, r=0.11 batch b, r=0.34 max=4.6 mpa max=3.1 mpa figure 1: summary of the generated fatigue results and endurance limits estimated according to dixon’s technique [14]. gradient-enriched tip stresses to design notched concrete against high-cycle fatigue he accuracy of ge in estimating high-cycle fatigue strength of notched concrete was checked against the generated experimental data by using this approach according to two different strategies as described in what follows. initially ge was applied along with the so-called theory of critical distance (tcd) [16, 17]. the tcd postulates that the high-cycle fatigue strength of a notched component can be estimated via critical distance l which takes on the following value [16]: 2 0 1 thkl          (4) in the above definition kth is the range of the threshold value of the stress intensity factor, whereas 0 is the range of the un-notched material endurance limit. t c. bagni et alii, frattura ed integrità strutturale, 33 (2015) 105-110; doi: 10.3221/igf-esis.33.14 108 by following an articulated reasoning based on non-local mechanics [18], it is possible to prove that characteristic length l can directly be estimated from the tcd’s critical distance as follows: 2 2 l  (5) figure 2: effective stress, eff, determined according to the pm. the simplest formalisation of the tcd is known as the point method (pm) [17]. as shown in fig. 2, the pm postulates that a notched/cracked engineering material is in the endurance limit condition as long as the stress at a distance from the assessed geometrical feature equal to l/2 is lower than (or, at least, equal to) the un-notched material endurance limit, 0. the pm can also be used to determine critical distance l when the range of the threshold value of the stress intensity factor is not available [19, 20]. in particular, assume that a notch endurance limit experimentally determined by testing samples containing a known geometrical feature is available for the material being investigated. according to the pm, at the endurance limit, l/2 is equal to the distance from the notch tip at which the local linear-elastic stress equals the unnotched material endurance limit. as shown in the charts of fig. 3, this alternative strategy was adopted to determine the tcd critical distance for the investigated concrete. this simplified procedure resulted in an l value equal to 5.8 mm for both batches. the fact that the two tested batches of concrete had the same microstructural features with different strength strongly supports the idea that the tcd critical distance value is mainly related to the morphology of the material being assessed. the linear-elastic stress-distance curves plotted in fig. 3 were determined from bi-dimensional fe models solved by using commercial software ansys®. further, these curves were estimated, at the endurance limit, under the maximum stress in the cycle in order to correctly take into account the presence of non-zero mean stresses [15]. fig. 4 shows the linear-elastic gradientenriched stress-distance curves determined, in the endurance limit condition, by taking, according to eq. (5), the material characteristic length, l, equal to: 5.8 2.05 2 2 2 2 l mm   (6) as done when estimating the tcd critical distance l (fig. 3), these curves were determined, by using an in-house fe code, under the maximum loading in the cycle to model the mean stress effect in concrete fatigue [15]. the above charts make it evident that the use of the linear-elastic gradient-enriched notch tip stresses [21] resulted in estimates mainly falling, on the conservative side, within an error interval equal to ±20%. it is worth observing here that, as postulated by the tcd [16, 17], such a satisfactory level of accuracy was reached by using the conventional un-notched material endurance limit as reference fatigue strength. as briefly recalled above, the length scale parameter l allows the underlying material microstructure to be directly incorporated into the stress analysis. a close inspection of the fracture surfaces of the broken samples revealed that in the tested concrete fatigue cracks tended to initiate at the interface between matrix and aggregates, the subsequent propagation mainly occurring in the cement paste. both for batch a and batch b, the average distance between the aggregates was measured to be equal to about 4 mm. accordingly, one may argue that length scale parameter l should c. bagni et alii, frattura ed integrità strutturale, 33 (2015) 105-110; doi: 10.3221/igf-esis.33.14 109 directly be taken equal to the average inter-aggregate distance, the results generated by testing the un-notched specimens being used to determine a suitable value for the reference strength. 0.0 1.0 2.0 3.0 4.0 5.0 6.0 7.0 8.0 9.0 10.0 0 5 10 15 20 y,max [mpa] distance, x [mm] linear-elastic stress fields batch a un-notched material endurance limit 0,max=3.3 mpa l/2=2.9 mm linear-elastic stress-distance curve (kt=4.32) 0.0 1.0 2.0 3.0 4.0 5.0 6.0 7.0 8.0 9.0 10.0 0 5 10 15 20 y,max [mpa] distance, x [mm] linear-elastic stress fields batch b un-notched material endurance limit 0,max=5.1 mpa l/2=2.9 mm linear-elastic stress-distance curve (kt=4.32) figure 3: critical distance l determined for batch a and batch b according to the pm. 0.0 1.0 2.0 3.0 4.0 5.0 6.0 7.0 8.0 9.0 10.0 0 5 10 15 20 y,max [mpa] distance, x [mm] linear-elastic stress fields batch a un-notched blunt intermediate sharp un-notched material endurance limit 0,max=3.3 mpa error= +20% error= -20% l=2.05 mm 0.0 1.0 2.0 3.0 4.0 5.0 6.0 7.0 8.0 9.0 10.0 0 5 10 15 20 y,max [mpa] distance, x [mm] linear-elastic stress fields batch b un-notched blunt intermediate sharp un-notched material endurance limit 0,max=5.1 mpa error= +20% error= -20% l=2.05 mm figure 4: accuracy of ge applied by taking l = 2.05 mm, eq. (6). 0.0 1.0 2.0 3.0 4.0 5.0 6.0 7.0 8.0 9.0 10.0 0 5 10 15 20 y,max [mpa] distance, x [mm] linear-elastic stress fields batch a un-notched blunt intermediate sharp un-notched material endurance limit ge0,max=2.8 mpa error= +20% error= -20% l=4.0 mm 0.0 1.0 2.0 3.0 4.0 5.0 6.0 7.0 8.0 9.0 10.0 0 5 10 15 20 y,max [mpa] distance, x [mm] linear-elastic stress fields batch b un-notched blunt intermediate sharp un-notched material endurance limit ge0,max=4.3 mpa error= +20% error= -20% l=4.0 mm figure 5: accuracy of ge applied by taking l equal to the average inter-aggregate distance (l = 4 mm). the charts reported in fig. 5 show the linear-elastic gradient-enriched stress-distance curves plotted, at the endurance limit, under the maximum loading in the cycle. according to this figure, the reference strength, ge0,max, determined from the results generated by testing the un-notched specimens was equal to 2.8 mpa for batch a and to 4.3 for batch b. these diagrams clearly prove that the use of the gradient-enriched notch tip stresses determined by taking l equal to the average c. bagni et alii, frattura ed integrità strutturale, 33 (2015) 105-110; doi: 10.3221/igf-esis.33.14 110 inter-aggregate distance resulted in highly accurate estimates. owing to the fact that the two batches of concrete were characterised by the same morphology, this remarkable accuracy strongly supports the idea that length scale parameter l in constitutive law (1) is capable of directly incorporating into the stress analysis the underlying material microstructural features. conclusions  ge applied along with the tcd was seen to result in conservative estimates with the level of conservatism decreasing as the sharpness of the notch decreases.  the use of ge with length scale parameter l equal to the average inter-aggregate distance resulted in highly accurate estimates for the fatigue strength. references [1] von ornum, j.l., fatigue of cement products, asce trans., 51 (1903) 443-451. [2] von ornum, j.l., fatigue of concrete, asce trans., 58 (1907) 294-320. [3] ohlsson, u., daerga, p.a., elfgren, l., fracture energy and fatigue strength of unreinforced concrete beams at normal and low temperatures, engng frac. mech., 35 l/2/3 (1990) 195-203. [4] plizzari, g.a., cangiano, s., alleruzzo, s., the fatigue behaviour of cracked concrete, fatigue fract. engng mater. struct., 20 8 (1997) 1195-1206. [5] thun, h., ohlsson, u., elfgren, l., a deformation criterion for fatigue of concrete in tension, structural concrete, 12 3 (2011) 187-197. [6] mindlin, r.d., micro-structure in linear elasticity. arch. rat. mech. analysis, 16 (1964) 52–78. [7] aifantis, e.c., on the role of gradients in the localization of deformation and fracture, int. j. engng. sci., 30 (1992) 1279–1299. [8] altan, s.b., aifantis, e.c., on the structure of the mode iii crack-tip in gradient elasticity, scripta metall. mater. 26 (1992) 319–324. [9] ru, c.q., aifantis, e.c., a simple approach to solve boundary-value problems in gradient elasticity, acta mech. 101 (1993) 59–68. [10] askes, h., gutiérrez, m.a., implicit gradient elasticity, int j numer meth engng, 67 (2006) 400-416. [11] askes, h., morata i., aifantis e.c., finite element analysis with staggered gradient elasticity, comput struct, 86 (2008) 1266-1279. [12] askes, h., gitman, i.m., non-singular stresses in gradient elasticity at bi-material interface with transverse crack, int j fract, 156 (2009) 217-222. [13] askes, h., aifantis, e.c., gradient elasticity in statics and dynamics: an overview of formulations, length scale identification procedures, finite element implementations and new results, int. j. solids struct., 48 (2011) 1962–1990. [14] dixon, w.j., the up-and-down method for small samples. journal of the american statistical association, 60 (1965) 967-978. [15] susmel, l., a unifying methodology to design un-notched plain and short-fibre/particle reinforced concretes against fatigue, int. j. fatigue, 61 (2014) 226–243. [16] taylor, d., geometrical effects in fatigue: a unifying theoretical model, int j fatigue, 21 (1999) 413-420. [17] taylor, d., the theory of critical distances: a new perspective in fracture mechanics, elsevier, oxford, uk (2007). [18] susmel, l., askes, h., bennett, t., taylor, d., theory of critical distances vs. gradient mechanics in modelling the transition from the shortto long-crack regime at the fatigue limit, fatigue fract engng mater struct., 36 9 (2013) 861869. [19] susmel, l., taylor, d., a novel formulation of the theory of critical distances to estimate lifetime of notched components in the medium-cycle fatigue regime, fatigue fract. engng. mater. struct., 30 7 (2007) 567-581. [20] susmel, l., multiaxial notch fatigue: from nominal to local stress-strain quantities, woodhead & crc, cambridge, uk, (2009). [21] askes, h., susmel, l., understanding cracked materials: is linear elastic fracture mechanics obsolete?, fatigue fract. engng. mater. struct., 38 (2015) 154–160. microsoft word numero_55_art_03_2907 k. fedaoui et alii, frattura ed integrità strutturale, 55 (2021) 36-49; doi: 10.3221/igf-esis.55.03 32 on the effect of stiffness/softness and morphology of interphase phase on the effective elastic properties of three-phase composite material kamel fedaoui, lazhar baroura, karim arar university of constantine 1, constantine, algeria kamel.fedaoui@umc.edu.dz, https://orcid.org/0000-0003-0885-6914 barouralaz@yahoo.fr, https://orcid.org/0000-0002-6747-5049 arar_karim@yahoo.fr hichem amrani university of batna 2, batna, algeria amranihichem78@hotmail.fr mohamed said boutaani university of bejaia, bejaia, algeria poutasfr@yahoo.fr, https://orcid.org/0000-0003-2003-2432 abstract. in the present study, composite material consisting of an elastic homogeneous isotropic matrix in which are embedded coated elastic isotropic inclusions, widely used in many applications is investigated by a homogenization approach coupled to the finite element method. a finite element model is proposed to predict the young’s and shear modulus of the three-phase composite containing spherical inclusions surrounded by a spherical or ellipsoid interphase layer. three cases of particle volume fractions and interphase were considered with the addition of two interphase morphologies. young’s modulus of the interphase region was varied from soft to hard than the matrix properties. we note the interphase morphology and properties play an important role in the elastic properties of composite with increasing the volume fraction of inclusions and interphase. the results were compared to the first-order bounds voigt and reuss, and the mean-field homogenization techniques. a sensitive study of the effect of mesh density on the results of the von mises stresses and elastic properties has been made. keywords. three-component composites; interphase; representative volume element; unit cell; effective elastic properties. citation: fedaoui., k., baroura, l., arar, k., amrani, h., boutaani, m.s., on the effect of stiffness/softness and morphology of interphase phase on the effective elastic properties of three-phase composite material, frattura ed integrità strutturale, 55 (2021) 3649. received: 27.08.2020 accepted: 07.10.2020 published: 01.01.2021 copyright: © 2021 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. https://youtu.be/29tuh-ibdis k. fedaoui et alii, frattura ed integrità strutturale, 55 (2021) 36-49; doi: 10.3221/igf-esis.55.03 33 introduction or the industrial need in material characteristics, properties and strength of these materials in their mission can be ameliorated by mastering the design of components properties (improve building energy efficiency [1-6]. various techniques are used to give to the composite a great performance by choice of the inclusions shapes, the inclusions properties or the numbers of inclusions [7-10]. another method is by the creation of interphase between the matrix and other phases. these interphases are formed by a desired or natural chemical reaction between the matrix and particles or the use of protective coatings during manufacturing. the incorporation of an interphase between the constituents of composite affects it elastic properties. although small in thickness, interphases affect the overall mechanical properties of the particle reinforced composites. the effective elastic properties of the composite are related to the constituent’s elastic properties and their volume fraction. numerous experimental, analytical or computational techniques like finite element method were adopted to study the effects of various parameters like the morphology, properties of inclusions on the composite material [11-18]. this interphases phenomena influence was the object of many works and various micromechanical techniques were proposed in the literature. a simple example of the material where interphase is important is the concrete with the creation of the interfacial transition zone (itz) which exists in cement paste near sand particles and aggregates. concrete must be considered as a three-phase composite: (1) cement paste, (2) itz, and (3) aggregates, see [6, 19]. for the ductile cast irons, fatigue crack propagation is strongly influenced by the matrix and by the presence of graphite inclusions. in the work of [20], the role played by the graphite inclusions and interphase during the fatigue crack propagation was investigated by means of light optical microscope observations of transversal sections of metallographically prepared fatigue fracture surfaces. because of their potential, core/shell composites have been the subject of numerous experimental and theoretical investigations as the use of core/shell nanoparticles in different fields such as building materials for energy efficiency, as well as in biomedical and biological fields, for the treatment of tumors [21, 22] and medical imaging. composites with a metal matrix reinforced with particles find their uses for their strength /rigidity ratio in a wide range of products such as the aerospace, weapons, automotive industries [23]. cnt (carbon nanotube) is characterized by a surrounding region which has a significant influence on the mechanical properties of the composite [24]. for this, the properties of the latter must be taken into account in the modeling of these materials. recent research has explored the possibility of having complex composites with controllable particle sizes and morphologies. the properties thus obtained allow the use of these composites in solar energy, photothermal and electronic fields, [25]. for the micromechanical model, voigt and reuss proposed a general expression for all the composites with an upper and lower bounds for the elastic modulus taking into account the volume fractions of phases and their elastic properties [26, 27]. the beginner to investigate the effects of a thin interphase on local fields and the resulting effective properties of composite made of coated ellipsoidal inclusion were walpole and cherkaoui et al. [28, 11], by the self-consistent estimate developed a general expression for the prediction of effective parameters of a particle-filled composite with thin interphase while aboutajeddine and neale [29] proposed a general form of elastic properties taken into account the mori-tanaka method. in other papers, [30, 31], the thermo-elastic behavior of matrix reinforced with long continuous coated fiber was studied. herve and zaoui in [32, 33] generalized the model used for the representation of the three-phase model to a model composed of n-layered spherical inclusion. in [34], lipinski et al. proposed the use of the model proposed by hervé and zaoui’s work for the n-layered spherical inclusion morphology to study the n-layered ellipsoidal inclusion configurations. in berger et al. [35], the effective thermo-mechanical properties of three-phase composites (one of the three-phase is considered an interphase) for different configurations were estimated using a unit cell. alexander et al. studied the prediction of effective thermal conductivity of spherical random distributed core–shell particles distributed in a continuous matrix [36]. in cabeza et al.[6] and benjamin, [12], the effective mechanical properties phase change materials pcm used in building material composed of three-phase were predicted using finite element technique and elastic deformation. benjamin in [12, 13] examined the effects of microencapsulated phase change materials (pcms) on the thermal deformation behavior of cement-based composites. in böhm, [37] material reinforced by coated spheres is investigated by some analytical techniques and the use of periodic homogenization. in all the preceding work, composite material is taken like a periodic array of repetitive unit cells. in this paper, we present a computational micromechanical investigation of the effect of interphase on the mechanical properties and strength of materials. we study a few material configurations (properties, morphology, and volume fraction) using the finite element method to explore how the interface morphology and properties affect the material behavior. the f k. fedaoui et alii, frattura ed integrità strutturale, 55 (2021) 36-49; doi: 10.3221/igf-esis.55.03 34 objective of the current paper is the determination of the effective elastic properties and the study of the effects of interphase on these properties. analysis unit cell and phases properties n our case, composite material is taken like a periodic array of repetitive unit cells, constructed with uniform distribution of the same morphology for the reinforcing phase. the micro-mechanical approach chooses this unit cell as the representative volume element (rve) for the composites. the length of the unit cell is set to 0.1 mm. the proposed rve containing the interphase phase, surrounded by the matrix and the spherical inclusion located at the center is schematically represented in fig. 1, see amraei, [38]. the coated inclusions are formed by spherical inclusions surrounded by the interphase. for the morphology of the interphase, the spherical and ellipsoid form is adopted. figure 1: schematics of unit cells with morphology of interphase, spherical and ellipsoids used for numerical simulations the volume of a hollow sphere (interphase) with radius of the overall sphere r1 and the radius of the hollowed region r2 can be determined as:    3 32 14 * 3 sphe hollowv r r (1) for the ellipsoid interphase we have:     2 314 4* * * 3 3 ellip hollowv a b r (2) tab. 1 shows the cases of rve in this study. in this study,   iv ,  ip and ir represents respectively the volume of inclusions, the volume fraction and the radius of the ith phase. p is the volume fraction of the matrix phase. three cases of volume fraction of the interface are considered in this work. firstly the volume of interphase is equal to the volume of inclusion, secondly is half and finally the volume of interphase is one on three of inclusion volume. three different volume fractions of matrix are considered    95%,   90%p and 70% . in this paper,  0 1ip .  1ip corresponds to 100% of the thi phase. i k. fedaoui et alii, frattura ed integrità strutturale, 55 (2021) 36-49; doi: 10.3221/igf-esis.55.03 35 p is the surface fraction of the matrix phase, so    2 1 1i i p p . table 1: cases of materials. phases elastic properties e [mpa]  matrix 1 0.3 inclusion 5 0.2 interphase 0.1 0.2 0.5 0.8 1 3 5 8 10 0.3 table 2: elastic properties of considered material. all the components are considered isotropic, this means that their combination in the unit cell generates a composite with isotropic behavior. we note that interphase is located between the matrix and inclusion, its elastic properties are affected by the elastic properties of the two phases. the young’s modulus 𝐸 and the poisson’s ratio 𝜈 of all phases are presented in tab. 2. governing equations linear elastic constitutive relationships for an isotropic material are given by [39]. ij ijkl klc  (3) where    , , , 1, 2, 3i j k l  for homogeneous and isotropic materials the tensor c is given by:          ijkl ij kl kl jl il jkc (4) with  and  are the lamé parameters and  denote a kronecker delta. the elastic moduli are expressed by:                    2 ,   1 1 2 3 2 1 e e k g g (5) volume fraction shape cases interphase inclusionv v  / 2interphase inclusionv v  / 3interphase inclusionv v  1 2 2.5%p p sphere interphase r1=0.018mm r2=0.023mm r1=0.018mm r2=0.021mm r1=0.018mm r2=0.02mm ellipsoid interphase r1=0.018mm a=0.019mm b=0.032mm r1=0.018mm a=0.019mm b=0.024mm r1=0.018mm a=0.019mm b=0.021mm  1 2 5%p p sphere interphase r1=0.023mm r2=0.029mm r1=0.023mm r2=0.026mm r1=0.023mm r2=0.025mm ellipsoid interphase r1=0.023mm a=0.024mm b=0.04mm r1=0.023mm a=0.024mm b=0.03mm r1=0.023mm a=0.024mm b=0.036mm  1 2 15%p p sphere interphase r1=0.033mm r2=0.042mm r1=0.033mm r2=0.038mm r1=0.033mm r2=0.036mm ellipsoid interphase r1=0.033mm a=0.035mm b=0.058mm r1=0.033mm a=0.035mm b=0.043mm r1=0.033mm a=0.035mm b=0.038mm k. fedaoui et alii, frattura ed integrità strutturale, 55 (2021) 36-49; doi: 10.3221/igf-esis.55.03 36 this constitutive law can be determined based on the detailed fields in the selected unit cell through an “averaging” procedure. first, the differential equilibrium equation in any component is expressed as (hjelmstad, 2005):  , 0ij j (6) second, the strain–displacement relation in any component is given by:     , ,1 2 i j j i (7) where   , , tu u v w is the displacement vector. finally, the constitutive law for each constituent is given by:  iσ c : ε (8) where   ,   ,  i m inc inter combining eqns. (16)– (18), results in governing equations expressed solely in terms of the displacement field. these equations are referred to as navier’s equations, which, for the present case, are given by:         2( ) . 0i i i i iu u (9) where i and i are the lamé parameters for each component. 𝐸 young’s modulus 𝜈 and 𝜈 poisson’s ratio 𝐸 young’s modulus 𝜈 and 𝜈 poisson’s ratio 𝐸 young’s modulus 𝜈 and 𝜈 poisson’s ratio 𝜇 shear modulus 𝜇 shear modulus 𝜇 shear modulus figure 2: boundary conditions applied to the unit cell it is important to note that continuous/welded contact between the inclusion, interphase and the matrix implied displacement continuity across their interfaces. the stress and strain components were not uniform throughout the heterogeneous structure, and thus were volume-averaged to obtain the average stresses. using fem the volume-averaged stresses and strains can be calculated as:    1 ij ijv dv v (10) k. fedaoui et alii, frattura ed integrità strutturale, 55 (2021) 36-49; doi: 10.3221/igf-esis.55.03 37    1 ij ijv dv v (11) where v is the volume of the rve. the averages are then treated as the effective stress and strain fields in the homogenized rve. the relations between  ij and  ij determine the “effective” constitutive law. boundary conditions in order to fully define the problem at hand, boundary conditions must also be prescribed for the unit-cell domain shown in fig. 2. to do so, six boundary conditions are required, three tensile and three shear loads, which were selected in order to model the elastic deformation of a computational domain. the approach proposed in [35] is used in this work. for instance, to predict the unknown effective elastic coefficients of stiffness matrix we impose the boundary conditions in such away is not equal to zero and all other strains are zero. the remaining that the macroscopic strain coefficients can be determined in a similar way. results and discussions he finite element method is a powerful tool to solve the governing equations over the rve domain that was discretized with satisfactorily mesh using the boundary conditions given in the previous subsection. volume averaged stresses and strains were used for the computation of the effective young’s modulus effe and the effective shear modulus effμ from eqns. (10) and (11). for the verification of the exactitude of results, a case of homogeneous composite was studied by putting the same properties for the three-component composite (inclusion, interphase and matrix) with each component. the numerically predicted effective properties young’s modulus and shear modulus were found to be identical to the values of e and mu of each component. convergence of the results with regard to mesh size first, mesh convergence was verified by analysing the relative difference in the effective young’s modulus and shear modulus between different meshes. we note that the curves of von mises stress in the unit cell in all the different meshes tested here (coarse, coarser and extra coarse) have the same appearance in addition they overlap almost completely with negligible differences, see fig. 3 . the elastic properties and von mises stress are independent from the mesh size chosen or computation. comparison with analytical bounds and estimation the voigt and reuss models give too rough a framework for estimating the effective modules. voigt's model assumes constant deformation. this model leads to an upper bound for the tensor of the modules of the effective medium. the expression is given by:      * * *inter inter inc inc mat matp p p (12)   * * *inter inter inc inc mat mate e p e p e p (13) for the lower bound, reuss uses the constant stress. the expression is given by:        1 inter inc inter inc mat p p p (14)    1 inter inc inter inc mat p p p e e e e (15) t k. fedaoui et alii, frattura ed integrità strutturale, 55 (2021) 36-49; doi: 10.3221/igf-esis.55.03 38 figure 3: von misses stress and shear ratio for the case of 10 % as a function of unit cell length for different mesh density ellipsoid interphase morphology (case 10% case 2) mean-field (mf) homogenization techniques [40, 41] describe the composite rheological behavior based on the average stress and strain tensors on phase level and composite level. in the mf approach, the problem of a composite with coated inclusions can be seen as a three-phase composite. model's prediction in this research is based on the first order mori k. fedaoui et alii, frattura ed integrità strutturale, 55 (2021) 36-49; doi: 10.3221/igf-esis.55.03 39 tanaka homogenization (mth) technique. the inclusions are first homogenized with their coatings (first level of homogenization), and the resulting material, which can be seen as an “effective inclusion”, is then homogenized with the matrix (second level of homogenization), see fig. 4. figure 4: multi-level homogenization the mfh approach is a fast (requires no generation of rve model and meshing) and efficient way to forecast the effective elastic properties of linear elastic composites. the mean-field stress ( σ ) and strain ( ) in each phase i and associated parameters are given in [42]. figs. 5, 6 and 7 plots the ratio of young’s modulus and shear modulus of the composite, to the matrix young’s modulus and shear modulus, as a function of interphase young’s modulus for two different interphase morphology spherical and ellipsoids morphologies. we note that the lower bound of reuss gives very good results compared to the finite elements computation results for the case of prediction of shear modulus. the results are independent of the kinds of interphases morphology. the mean-field (mf) homogenization technique give a good agreement with the finite elements estimation of the young’s modulus but it presents a big difference in the case of shear modulus equal to 25% in the case of spherical interphase morphology. for the case of ellipsoid interphase morphology, it is equal to 15%. figure 5: effect of the interphase young’s modulus intere on the ratio of the composite young's modulus, e to the matrix young's modulus, me for ellipsoid interphase morphology at a constant volume fraction of 30% case 1. deepest level highest level k. fedaoui et alii, frattura ed integrità strutturale, 55 (2021) 36-49; doi: 10.3221/igf-esis.55.03 40 figure 6: effect of the interphase young’s modulus intere on the ratio of the composite shear modulus, µ to the matrix shear modulus, mμ for ellipsoid interphase morphology at a constant volume fraction of 30% case 1. figure 7: effect of the interphase young’s modulus intere on the ratio of the composite young's modulus, e to the matrix young's modulus, me for spherical interphase morphology at a constant volume fraction of 30% case 1. figure 8: effect of the interphase young’s modulus intere on the ratio of the composite shear modulus, µ to the matrix shear modulus, mμ for spherical interphase morphology at a constant volume fraction of 30% case 1. k. fedaoui et alii, frattura ed integrità strutturale, 55 (2021) 36-49; doi: 10.3221/igf-esis.55.03 41 effect of interphase volume fraction figs. 8, 9, 10, 11, 12, 13 and 14 plots the ratio in young’s modulus and shear modulus as a function of the interphase young’s modulus ranging from 0,1 to 10. the ratio m e e and m μ μ is presented for three volume fractions and different interphase morphology. it is interesting to note here that the ratio m e e depends on the interphase young’s modulus and considerably with the morphology of the interphase. for the contrast greather than 3, the curves are nearly linear and stable. but for the contrast less than 3, we note a big gain in elastic properties. it is also observed that for the big volume fractions of inclusions and interphase, the young’s modulus and shape affect considerably the elastic properties of composite materials, see figures. for the cases of soft interphase, the amelioration for the case of 5% in young’s and shear modulus is about 5% compared to the amelioration in other cases study of 10 and 30% are about 10 and 35% respectively. we also note a divergence of results between the cases studied especially for the volume fractions 30% but with less effect for the volume fractions 5 and 10%. figure 9: effect of the interphase young’s modulus intere on the ratio of the composite shear modulus, µ to the matrix shear modulus, mμ for different interphase morphology at a constant volume fraction of 5%. figure 10: effect of the interphase young’s modulus intere on the ratio of the composite young's modulus, e to the matrix young's modulus, me for different interphase morphology at a constant volume fraction of 5%. for the cases of stiff interphase, the amelioration for the case of 5% in young’s and shear modulus is about 8% compared to the amelioration in other cases study of 10 and 30% are about 16 and 60% respectively. k. fedaoui et alii, frattura ed integrità strutturale, 55 (2021) 36-49; doi: 10.3221/igf-esis.55.03 42 figure 11: effect of the interphase young’s modulus intere on the ratio of the composite shear modulus, µ to the matrix shear modulus, mμ for different interphase morphology at a constant volume fraction of 10%. figure 12: effect of the interphase young’s modulus intere on the ratio of the composite young's modulus, e to the matrix young's modulus, me for different interphase morphology at a constant volume fraction of 10%. figure 13: effect of the interphase young’s modulus intere on the ratio of the composite shear modulus, µ to the matrix shear modulus, mμ for different interphase morphology at a constant volume fraction of 30%. k. fedaoui et alii, frattura ed integrità strutturale, 55 (2021) 36-49; doi: 10.3221/igf-esis.55.03 43 figure 14: effect of the interphase young’s modulus intere on the ratio of the composite young's modulus, e to the matrix young's modulus, me for different interphase morphology at a constant volume fraction of 30%. effect of interphase morphology in this section, we discuss the influence of morphological parameters namely interphase shape and volume fraction of this phase on the effective young’s and shear modulus of the three phases material. with the variation of volume of interphase from 1, 1/2 and 1/3 times the inclusion volume, we note here the increase of the elastic properties (bulk and shear modulus) in all the cases for spherical and ellipsoid interphase. in all the cases, for the soft interphase compared to the matrix stiffness, for all the volumes fractions and morphologies, the elastic properties are independent. for the stiff interphase compared to the matrix stiffness, the 1 times for all the volumes fraction and morphology presents better properties compared to the others volume 1/2 and 1/3 times, see fig. 8, 9, 10, 11, 12, 13 and 14. figure 15: von mises stress for the case of 10% as a function of interphase young’s modulus for ellipsoid interphase morphology (case 10%, case 2). effect of interphase young’s modulus on the von mises stress fig. 15, 16 shows the evolution of the vm stress in a section made through the center of the unit cell. this in order to be able to trace the constraint in the three elements (matrix, inclusion and interphase). in the outside of the interphase region, it is important to say that all the curves for different interphase young’s modulus for the two cases of ellipsoid and spherical interphase morphologies have the same appearance. the maximum of von mises stress are observed in the interphase area. k. fedaoui et alii, frattura ed integrità strutturale, 55 (2021) 36-49; doi: 10.3221/igf-esis.55.03 44 this value is located for the case with interphase young modulus equal to 8 and 10 [mpa] for the ellipsoid and spherical interphase morphology. in addition to the interphase, all the von mises stress curves converge towards the value of 1 [mpa], the matrix young’s modulus value. the von mises is small in the interval [0.1, 0.2], while on the other hand in the interval [0.5, 5] they exceed the stress found in the matrix. we note that the value of von mises stress in the two cases of ellipsoid and spherical interphase morphologies nearly present the same value with a small growth for the ellipsoid interphase. figure 16: von mises stress for the case of 10 % as a function of interphase young’s modulus for spherical interphase morphology (case 10%, case 2) fig. 17 plots the stress in the three components of the composite, in the case of shear computation for the von mises stress for the case of 30 % (case 1) for spherical and ellipsoid interphase morphology and interphase young’s modulus equal to 10 [mpa]. unit cell interphase inclusion ellipsoid interphase unit cell interphase inclusion spherical interphase figure 17: von mises stress for the case of 30 % (case 1) for spherical and ellipsoid interphase morphology and interphase young’s modulus e_interphase = 10 [mpa] in the case where the interphase young’s modulus is equal to matrix young’s modulus, fig. 17 presents the stress in the different domains of the unit cell (matrix, interphase and inclusion) in the case of computation of shear modulus (case 30%, k. fedaoui et alii, frattura ed integrità strutturale, 55 (2021) 36-49; doi: 10.3221/igf-esis.55.03 45 case 1). for spherical interphase morphology, the von mises stress value is the same in the two cross-section planes (zx and zy), see fig. 18. ellipsiod e_interphase = 10 [mpa] spherical e_interphase = 10 [mpa] figure 18: von mises stress as a function of interphase young’s modulus for spherical and ellipsoid interphase morphology (case 10%, case 2) ellipsiod e_interphase = 1 [mpa] spherical e_interphase = 1 [mpa] figure 19: von mises stress as a function of interphase young’s modulus for spherical and ellipsoid interphase morphology (case 10%, case 2). k. fedaoui et alii, frattura ed integrità strutturale, 55 (2021) 36-49; doi: 10.3221/igf-esis.55.03 46 for the ellipsoid interphase, we note a difference between the von mises results in the two cross-section planes (zx and zy), see fig.18. it is a logical conclusion because of the shape of the ellipse which has three rays (r, r, r) according to the three dimensions. it is very important to know the location of the maximum stress, for that many simulations were conducted. a lot of parameters are tested in this work by varying the interphase young’s modulus from 0.1 to 10 [mpa]. fig.18 plots the stress for the case where we have a stiff interphase, that means the interphase young’s modulus is equal to 10 times the matrix young’s modulus (e_interphase = 10 [mpa]). in this case, the maximum stress is located in the region of interphase area for all the morphologies. fig. 19 plots the stress for the case of interphase young’s modulus is equal to the matrix young’s modulus (e_interphase = 1 [mpa]). in this case, the maximum stress is located in the region of inclusion inside the interphase area for all the morphologies. ellipsiod e_interphase = 0.1 [mpa] spherical e_interphase = 0.1 [mpa] figure 20: von-mises stress as a function of interphase young’s modulus for spherical and ellipsoid interphase morphology (case 10%, case 2). fig. 20 plots the stress for the case of soft interphase (e_interphase = 0.1 [mpa]). for the soft interphase, the maximum stress is located in the region around the outdoor interphase for all the morphologies. it should be pointed out here that it is according to the direction (planes xy, zy, xz) and the type of loading, the stresses follow the direction. conclusion new model based on the unit cell approach is proposed to the estimation of effective elastic properties of threephase coated spherical inclusion using homogenization techniques and finite elements method for different volume fractions and different interphase morphology. two different representative volume elements were created and finite element analysis using kinematic uniform boundary conditions was performed. the effective elastic constants have been calculated with the finite element model. the numerical results demonstrate that the developed fem approach is very useful and give good and efficient results for the analysis of unit cell models of composite, with the presence of the interphases. a k. fedaoui et alii, frattura ed integrità strutturale, 55 (2021) 36-49; doi: 10.3221/igf-esis.55.03 47 we observed that for the big volume fractions of inclusions and interphase, the young’s modulus and interphase shape affect considerably the elastic properties of composite materials. with the variation of volume of interphase from 1, 1/2 and 1/3 times the inclusion volume, we note here the increase of the elastic properties (bulk and shear modulus) in all the cases for spherical and ellipsoid interphase. we note here that the value of von mises stress in the two cases of ellipsoid and spherical interphase morphologies nearly present the same value with a small growth for the ellipsoid interphase. the maximum of von mises stress are observed in the interphase area. this value is located for the case with interphase young modulus equal to 8 and 10 [mpa] for the ellipsoid and spherical interphase morphology. the present work has laid down a foundation for further applications of micro-mechanical model analysis for problems, such as an investigation of stress field in the interphase for the study of inelastic behavior in this area. in addition, this model offers opportunities to study the behavior of the interphase in temperatures fields. references [1] benjamin, a. y., gaurav, s., amanda, m. f. k., alexander, m. t., aditya, k., ertugrul, t., laurent p., (2016). effective elastic moduli of core-shell-matrix composites, mechanics of materials 92, pp. 94–106. doi: 10.1016/j.mechmat.2015.09.006. [2] benjamin, a. y., zhenhua, w., jose, r. c., gabriel, f., aditya, k., narayanan, n.,gaurav, s., laurent, p., (2017). a general method for retrieving thermal deformation properties of microencapsulated phase change materials or other particulate inclusions in cementitious composites. materials & design, 126, pp. 259-267. doi: 10.1016/j.matdes.2017.04.023. [3] ling, t.c., poon, c.s., (2013). use of phase change materials for thermal energy storage in concrete: an overview. constr. build. mater. 46, pp. 55–62. doi : 10.1016/j.conbuildmat.2013.04.031. [4] ghosh, s. k., (2009). self-healing materials: fundamentals, design strategies, and applications. john wiley & sons. [5] tyagi, v. v., kaushik, s. c., tyagi, s. k., akiyama, t., 2011. development of phase change materials based microencapsulated technology for buildings: a review. renew. sustain. energy rev. 15(2), pp. 1373–1391. doi: 10.1016/j.rser.2010.10.006 [6] cabeza, l. f., castellon, c., nogues, m., medrano, m., leppers, r., zubillaga, o., (2007). use of microencapsulated pcm in concrete walls for energy savings. energ. build. 39(2), pp. 113–119. doi: 10.1016/j.enbuild.2006.03.030. [7] eroshkin, o., tsukrov, i., (2005). on micromechanical modeling of particulate composites with inclusions of various shapes. international journal of solids and structures, 42, pp. 409–427. doi : 10.1016/j.ijsolstr.2004.06.045. [8] ghossein, e., lévesque, m., (2012). a fully automated numerical tool for a comprehensive validation of homogenization models and its application to spherical particles reinforced composites. international journal of solids and structures, 49, pp. 1387–1398. doi: 10.1016/j.ijsolstr.2012.02.021. [9] gusev, a., (2014). effective coefficient of thermal expansion of n -layered composite sphere model: exact solution and its finite element validation. international journal of engineering science, 84, pp. 54–61. doi: 10.1016/0020-7225(86)90162-x. [10] giordano, s., (2016). nonlinear effective behavior of a dispersion of randomly oriented coated ellipsoids with arbitrary temporal dispersion. international journal of engineering science, 98, pp. 14–35. doi: 10.1016/j.ijengsci.2015.07.009. [11] cherkaoui, m., sabar, h., berveiller, m., (1994). micromechanical approach of the coated inclusion problem and applications to composite materials. journal of engineering materials and technology, 116, pp. 274–278. doi: 10.1115/1.2904286 [12] sevostianov, i., kachanov, m., (2007). effect of interphase layers on the overall elastic and conductive properties of matrix composites. application to nanosize inclusion. international journal of solids and structures, 44, pp. 1304–1315. doi: 10.1016/j.ijsolstr.2006.06.020 [13] yang, q. s., tao, x., yang, h., (2007). a stepping scheme for predicting effective properties of the multi-inclusion composites. int. j. eng. sci., 45(12), pp. 997–1006. doi: 10.1016/j.ijengsci.2007.07.005. [14] jia, c., chen, y., and huang, z., (2015), iterative method to predict effective elastic moduli of multiphase particulate composites. j. eng. mech., 10, 1061. doi: 10.1061/(asce)em.1943-7889.0000912. [15] bonfoh, n., hounkpati, v., sabar, h., (2012). new micromechanical approach of the coated inclusion problem: exact solution and applications. computational materials science, 62, pp. 175–183. doi: 10.1016/j.commatsci.2012.05.007. [16] boutaani, m.s., madani, s., fedaoui, k, kanit, t., (2017). evaluation of effective mechanical properties of complex multiphase materials with finite element method, u.p.b. sci. bull., series d, 79(3). k. fedaoui et alii, frattura ed integrità strutturale, 55 (2021) 36-49; doi: 10.3221/igf-esis.55.03 48 [17] surendra, b., meenakshi, s., shashank, b., (2019). mechanical property evaluation of composites based on n + 1 phase model and mori-tanaka theory, j. eng. mech., 145(3), 04018139. doi: 10.1061/(asce)em.1943-7889.0001564. [18] chaibainou, l., boutaani, m. s., fedaoui, k., chebbah, m. s., (2019). evaluation of thermal expansion of (al-sic) material using homogeneization method coupled to finite element method, u.p.b. sci. bull., series d, 81(4). [19] garboczi, e. j., berryman, j. j, (2001), elastic moduli of material containing composite inclusions:effective medium theory and finite element computations, mechanics of materials. 33, pp.455–470. [20] iacoviello, f., cocco, v. d., bellini, c., (2019), fatigue crack propagation and damaging micromechanisms in ductile cast irons international journal of fatigue, 124, pp. 48-54. doi: 10.1016/j.ijfatigue.2019.02.030. [21] kayal, p. s., ramanujan, r. v., (2010). anti-cancer drug loaded iron–gold core–shell nanoparticles (fe/au) for magnetic drug targeting, journal of nanoscience and nanotechnology, 10, pp.5527–5539. doi: 10.1166/jnn.2010.2461. [22] pancorbo, p. m., thummavichai, k., clark, l., tanveer, a. tabish, jessica, m., gardner, b., hong, c., nick, s., yanqiu, z., (2019). novel au–sio2–wo3 core–shell composite nanoparticles for surface-enhanced raman spectroscopy with potential application in cancer cell imaging, adv. funct. mater. 1903549. doi : 10.1002/adfm.201903549 [23] tijun, c., libo, g., he, q., min, g., 2018. core-shell-structured particle reinforced a356 matrix composite prepared by powder-thixoforming: effect of reheating temperature. materials, 11, 1718. doi: 10.3390/ma11091718. [24] abu taqa, a. g., abu al-rub, r. k., senouci, a., al-nuaimi, n., bani-hani, k. a., (2015), the effect of interfacial transition zone properties on the elastic properties of cementitious nanocomposite materials, journal of nanomaterials volume, article id 258384, 13 pages. doi: 10.1155/2015/258384. [25] kim, b. s., randall, l. t., (2015). the development of smart, multi-responsive core/shell composite nanoparticles, nanoparticles technology. doi: 10.5772/61262. [26] voigt, w., (1889). ueber die beziehung zwischen den beiden elasticitätsconstanten isotroper körper. annalen der physik. 274. pp. 573–587. doi : 10.1002/andp.18892741206. [27] reuss, a., (1929). berechnung der fließgrenze von mischkristallen auf grund der plastizitätsbedingung für einkristalle. zeitschrift für angewandte mathematik und mechanik. 9, pp. 49–58. doi: 10.1002/zamm.19290090104. [28] walpole, l. j., (1978), a coated inclusion in an elastic medium, math. proc. cambridge philos. soc.0305-0041, 83, pp. 495–506. doi: 10.1017/s0305004100054773. [29] aboutajeddine, a., neale, k., (2005). the double-inclusion model: a new formulation and new estimates. mechanics of materials, 37, pp. 331–341. doi: 10.1016/j.mechmat.2003.08.016. [30] benveniste, y., (1987). a new approach to the application of mori–tanaka’s theory in composite materials. mechanics of materials, 6, pp. 147–157. doi: 10.1016/0167-6636(87)90005-6. [31] benveniste, y., dvorak, g., chen, t., 1991. on diagonal and elastic symmetry of the approximate effective stiffness tensor of heterogeneous media. journal of the mechanics and physics of solids, 39, pp. 927–946. doi: 10.1016/00225096(91)90012-d. [32] hervé, e., zaoui, a., (1995). elastic behaviour of multiply coated fibre-reinforced composites. international journal of engineering science. 33(10), pp. 1419–1433. doi: 10.1016/0020-7225(95)00008-l. [33] hervé, e., & zaoui, a., (1993). n-layered inclusion-based micromechanical modelling. international journal of engineering science, 31, pp. 1–10. doi : 10.1016/0020-7225(93)90059-4. [34] lipinski, p, barhdadi, e. h., cherkaoui, m., (2006), micromechanical modelling of an arbitrary ellipsoidal multicoated inclusion, philosophical magazine, 86(10), pp. 1305-1326. doi: 10.1080/14786430500343868. [35] berger, h., kurukuri, s., kari, s., gabbert, u., rodriguez-ramos, r., bravo-castillero, j. and guinovart-diaz, r., (2007). numerical and analytical approaches for calculating the effective thermo-mechanical properties of threephase composites', journal of thermal stresses, 30(8), pp. 801-817. doi: 10.1080/01495730701415665. [36] alexander, m. t., aditya, k., gaurav, s., laurent, p., (2014). effective thermal conductivity of three-component composites containing spherical capsules international journal of heat and mass transfer 73, pp. 177–185. doi : 10.1016/j.ijheatmasstransfer.2014.02.002. [37] böhm, h. j., (2019), comparison of analytical and numerical models for the thermoelastic behavior of composites reinforced by coated spheres, international journal of engineering science 142, pp. 216–229. doi: 10.1016/j.ijengsci.2019.06.009. [38] amraei, j., jafar, e j, behrouz, a., roohollah, d. f. a., (2018). effect of interphase zone on the overall elastic properties of nanoparticle reinforced polymer nanocomposites, journal of composite materials 0(0), pp. 1–14. doi: 10.1177/0021998318798443. k. fedaoui et alii, frattura ed integrità strutturale, 55 (2021) 36-49; doi: 10.3221/igf-esis.55.03 49 [39] hjelmstad, k. d., (2005), fundamentals of structural mechanics (second edition). springer. [40] pierard, o., friebel, c., doghri, i., (2004), mean-field homogenization of multi-phase thermo-elastic composites: a general framework and its validation, compos. sci. technol., 64(10-11), p1587–1603. doi: 10.1016/j.compscitech.2003.11.009. [41] friebel, c., doghri, i., legat, v., (2006), general mean-field homogenization schemes for viscoelastic composites containing multiple phases of coated inclusions, international journal of solids and structures, 43(9), pp. 2513–2541. doi: 10.1016/j.ijsolstr.2005.06.035. [42] daramola, o. o., olajide, j. l., adediran, a. a., adewuyi, b. o., ayodele, t. t., sadiku, e. r., desai, d. a., (2020), multiscale analysis and experimental validation of the effective elastic modulus of epoxy-dioctahedral phyllosilicate clay composite, heliyon 6, e04008, doi:10.1016/j.heliyon.2020.e04008. shot peening processes to obtain nanocrystalline surfaces in metal alloys: m. marchelli et alii, frattura ed integrità strutturale, 47 (2019) 437-450; doi: 10.3221/igf-esis.47.34 437 a quick-assessment procedure to evaluate the degree of conservation of rockfall drapery meshes m. marchelli, v. de biagi, d. peila politecnico di torino, turin, italy maddalena.marchelli@polito.it, https://orcid.org/0000-0002-9919-2916 valerio.debiagi@polito.it, http://orcid.org/0000-0003-1866-9362 daniele.peila@polito.it, https://orcid.org/0000-0002-1771-8874 abstract. drapery meshes are protection devices installed on a cliff for mitigating rockfall hazard. they can prevent the detachment of rock fragments and control the dynamics of the falling blocks. during their design working life, drapery meshes are subjected to ageing phenomena, corrosion and impact, which can invalidate the purposes of the protection devices. a novel procedure based on a multi-hierarchical assessment of the damages is proposed. the approach is tailored for two technologies well diffused in the alps. the main components of the system are identified and the effects of each potential damage on the overall behaviour are taken into account through risk analysis approached. a site campaign serving to test the procedure is described. the proposed approach can be modified to consider other drapery mesh installation types. keywords. rockfall; drapery mesh; quick assessment; ageing effects citation: marchelli, m., de biagi, v., peila, d., a quick-assessment procedure to evaluate the degree of conservation of rockfall drapery meshes, frattura ed integrità strutturale, 47 (2019) 437-450. received: 24.09.2018 accepted: 11.12.2018 published: 01.01.2019 copyright: © 2018 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. introduction ockfall represents one of the most hazardous landslide phenomena that can cause fatalities to people and damages to structures and infrastructures [1-3]. protection structures are installed for reducing rockfall risk in inhabited areas. these can be classified into active (if rock block instability is prevented) and passive (if the blocks are intercepted and stopped before reaching the targets). drapery meshes are protection structures that can be classified either passive or both active and passive simultaneously [4]. they generally consist of steel wire mesh panels, suspended from upslope anchors [5], capable to control the movement of rock fragments (acting as an active protection), to withstand the punching force of falling rocks, driving the detached blocks at the foot of the slope in a controlled manner (acting as a passive protection). to achieve such goals, the mesh should be kept as close as possible to the slope and be secured both at the top and the bottom of the slope. this is one of the most adopted solutions in case of cliffs close to transportation route or to inhabited areas [6]. other types of passive protection systems comprise embankment and ditches, rockfall protection galleries and flexible protections systems, such as rockfall barriers [3]. various technical solutions exist [4]. they generally consist of a suspended mesh, with additional horizontal and vertical ropes. in addition, the drapes can be combined also with face bolts or other kind of anchors, which directly act on the stability of the block, connected each other and to the nets through diagonal ropes. this system prevents rockfall and r mailto:maddalena.marchelli@polito.it https://orcid.org/0000-0002-9919-2916 mailto:valerio.debiagi@polito.it http://orcid.org/0000-0003-1866-9362 mailto:daniele.peila@polito.it http://www.gruppofrattura.it/va/47/2331.mp4 m. marchelli et alii, frattura ed integrità strutturale, 47 (2019) 437-450; doi: 10.3221/igf-esis.47.34 438 controls its dynamics containing the small falling fragments into delimited sectors of the mesh. it can be adopted in various situations such as when the degree of fragmentation is high, or when localised unstable blocks are highlighted, it represents a powerful alternative solution to rockfall barriers/fences when the release area is small and the expected rockfall bounce height or kinetic energy are excessive. the recent studies on such rockfall mitigation structures mainly focus on the design methods [7-9] and the numerical modelling [10-14]. experimental studies have been performed on real scale installations [4] or on single components [11, 15]. recently, gratchev and colleagues analysed the friction mechanisms that form between the net and the face, which can be identified as the main contribution to the functioning of the rockfall protection [16]. the effects of snow and ice on the mesh are significant for the design of the anchors as noted by shu et al. [15]. to our knowledge, the efficiency over the time of drapery systems has not been object of study, yet. the majority of the studies focused the attention on the time-dependent effects on a single component of the system: the anchors [17-19]. as any structure, drapery nets are multicomponent protection devices that can be compromised during time. ageing, corrosion, interactions with blocks, vegetation, wild animals, or people can affect the integrity and the structural capabilities of the systems. lacerations or bowings in the net, corrosion, or detachment of the anchors are the most common damages that can occur. in this perspective, periodic surveys are required to investigate performance level over time of such systems. although surveying such systems is often critical, the evaluation of the degree of damage of such structures is, in fact, fundamental for defining a priority scale of maintenance interventions, to be related with rockfall risk, i.e. with rockfall probability of occurrence and exposure in a given area. thus, an assessment of the efficiency of drapery mesh is required. due to the extension and variety of drapery nets systems, e.g. in the alps, the protocol needs to be as general as possible, avoiding time-consuming and expensive ad-hoc survey campaigns, or an ongoing monitoring and surveillance system. with this perspective, the present work aims to introduce an encoded expeditious procedure to evaluate the degree of degradation of drapery mesh systems, assessing their state of conservation. this method represents a compelling solution for both authorities and designers in risk evaluation and management strategies. the presented work is based on a multicriteria analysis, involving an encoded screening survey. efficiency of aged drapery nets espite their worldwide use, no universally recognised guidelines or technical standards exist for the design of drapery systems [4]. their mechanisms of passive or combined passive/active rockfall protection have been under debate for a long time [8]. furthermore, the uncertainties of the loading conditions (snow, debris, etc.) to consider in the design increase the difficulty to encode a standard design procedure. as a consequence, empirical and simplified design approaches have been adopted, based on the geotechnical specialists’ experience, incurring sometimes in under-sized elements [20]. the design procedure needs to account for the influence of the mesh weight, the friction interface between the slope and the mesh and the possible accumulation of debris [21]. the first drapery mesh installations date back to the fifties [12]. at present, the "design guidelines for wire mesh/cable net slope protection" [20] issued by the washington state department of transportation are the only rules for the complete design of a simple drapery system. in 2012, the italian standardisation committee released the uni 11437 standard [22], which describes the punching test procedures on meshes for slope coverage. with particular reference to the tests on the net astm a975 standard [23] must be considered. in the following, the essential components constituting a drapery mesh system are listed in the attempt to create a list as general as possible for the large variety of installations. both simple and reinforced types are investigated. the possible damages on each part were investigated, considering the effects of aging, corrosion, weathering, impacts with blocks, interactions with debris, vegetation, animals and even people. at the end, the influence of degrade on aged components on the global efficiency of the system is discussed. the analyses reported in the following refer to the study cases found in the previously mentioned bibliography. a widespread survey campaign was performed in the northwestern italian alps, where a large variety of rockfall protections are installed. as a consequence, the proposed method is tailored to the common european protection systems. main elements of a drapery net generally speaking, drapery systems can be classified into two main typologies: simple drapery or reinforced wire mesh drapery [4]. simple wire mesh drapery systems (fig. 1.a) are essentially made of metallic nets (wire or ropes) fixed at the top with anchors. a top rope serves for ensuring the stability of the mesh. usually, additional fixing points (and a rope) are present at the bottom of the net. the nets are left unanchored along the slope. they control the dynamics of the falling of debris and rock elements along the slope, preventing their bouncing. sometimes vertical and/or horizontal metallic ropes d m. marchelli et alii, frattura ed integrità strutturale, 47 (2019) 437-450; doi: 10.3221/igf-esis.47.34 439 are present, increasing the adhesion of the net to the slope, but without other specific structural aim. the mesh has to resist tangential and normal forces induced by falling blocks that can tear or puncture the mesh. reinforced drapery meshes (fig. 1.b) are essentially made in the same way as the simple meshes. besides, additional metallic ropes fixed to the cliff through a regular pattern of bolts enforce the adhesion of the net to the rock face. this system allows the small falling blocks to be collected into delimited sectors of the mesh and increases the stability of the fragmented face through the bolts, i.e. exerting an active role. (a) simple drapery net (b) reinforced drapery net figure 1: views and sketches of (a) the simple drapery net and (b) the reinforced drapery net installations. note that the reinforced drapery net follows the shape of the cliff face. the performance of the previously described systems depends on the adopted solutions for the mesh, the ropes, and the anchors. nets are made of steel wire meshes, which can be single-twisted rhomboidal or double twisted hexagonal. other solutions consist in cable net panels made of metallic cables, connected with clips or knots, or ring net panels, laced together with steel cables or other devices. usually, cable net is combined with wire mesh to intercept smaller blocks. panels are m. marchelli et alii, frattura ed integrità strutturale, 47 (2019) 437-450; doi: 10.3221/igf-esis.47.34 440 connected each other with clips or knots, or sewed up with a steel wire or cable passing through the whole panels edges (fig. 2). supporting elements, i.e. the top and the bottom ropes, and the reinforcing ropes, are made of galvanised steel. the anchors are usually grouted bars or injected cables. the connection between the anchor and the ropes can be various according to anchor type. at the ends of grouted bars, eye-bolt solution (with or without plate), bolted anchorage plates with anchor nuts, or a grouted u-bolt are directly connected with the ropes, passing through the hoop. in the injected cable case, the rope directly passes through a rope loop, or it is connected to it by means of a shackle. nevertheless, a large variety of technologies for fixing can be found (fig. 3). the metallic ropes are held in tension through rope clips. a large variety of technologies for fixing and connecting the various components of the system can be found. with the aim to encompass the largest number of drapery types, the elements to consider in the performance evaluation are listed in tab. 1 grouping together a rope with its anchors. it must be noticed that in simple drapery systems the intermediate ropes do not play a structural support function. in this sense, the term “intermediate ropes" was adopted. on the contrary, “support ropes" was chosen for the reinforced systems. “top" and “bottom" ropes are the shortened version of top and bottom boundary ropes, respectively. (a) (b) figure 2: different connections between the panels: (a) a vertical rope with clips, (b) knots (close view). (a) (b) (c) (d) figure 3: different anchors types and connection with the ropes and the mesh: (a) a grouted bar with a screwed steel hoop, (b) an injected cable, (c) a grouted bar with a plate, (d) an anchorage plate. damages on the elements all the possible critical scenarios or damages occurring on the main components of the drapery system, identified in tab. 1, are evaluated. tab. 2 reports a list of potential damages, i.e. the damages that can occur on each component if subjected to certain stress/environmental conditions. in the third column of tab. 2, the observed damages are reported. these are a m. marchelli et alii, frattura ed integrità strutturale, 47 (2019) 437-450; doi: 10.3221/igf-esis.47.34 441 complete list of already occurred damages that can preclude the correct functioning of the drapery system, as detailed in the following. main components mesh top rope: rope, anchors, anchor–rope connections bottom rope: rope, anchors, anchor–rope connections intermediate ropes: ropes, anchors, anchor–rope connections (only simple drapery system) support ropes: ropes, anchors, anchor–rope connections (only reinforced drapery system) connection between mesh panels mesh–top rope connection mesh–bottom rope connection mesh–intermediate ropes connection (only simple drapery system) table 1: main components of a drapery mesh system. effects of the local damages on the global efficiency the local damages identified in the previous section affect the efficiency of the entire drapery system in different ways, depending both on the damaged element and on the type of damage. the elements identified in tab. 1 play different roles in the stability and functionality of the entire system. their damage, or absence, affects and compromises the global efficiency in different ways. as a consequence, identifying a hierarchy across the components and understanding the damage propagation and the failure processes is the key issue in the efficiency evaluation procedure. in order to explain the double hierarchy between the components and system efficiency and between damages and system efficiency should be considered. the core of the protection system is represented by the mesh that actively acts on the statics of the potentially falling blocks and on their dynamics. all system components aimed at sustaining the mesh and keeping it in the right position are fundamental for the correct functioning of the system, and their absence (due to ageing) implies that the protection system is inefficient. these are the top rope, the connection between the wire mesh panels, and the connection between the wire mesh and the top rope for the simple drapery system. in addition, for reinforced drapery systems, the support ropes are added to the list of fundamental elements. note that the term “ropes” refers to the overall components, including the anchorages. trying to find the double hierarchy levels between damages and system efficiency, the mesh is used as an example. its integrity and adherence to the cliff are essential for an efficient protection. in case of lacerations of the mesh, the falling blocks can exit the protection structure. it might happen that the laceration is the result of a previous rock detachment event, i.e. a case in which the protection of the system did not work properly. in addition, the damages can be due to an overload or an undesired (or unexpected) type of loading. a potential damage situation (such as corrosion) can reduce the mechanical properties of the mesh, leading to a similar effect. anyway, the removal of the corrosion protection decreases the efficiency of the system less than a laceration. as an example, other sorts of interference, such as the presence of vegetation in the drapery system, can presuppose an unexpected functioning of the installation, as described in tab. 2. it emerges that the several types of damages on the single elements have different degree of importance for computing the efficiency of the global system. with reference to the fixing to the cliff face, the lack of an anchor increases the failure probability of the system more than the corrosion of the same anchoring element. from a general point of view, it can be inferred that the lack of an element affects the efficiency of the system more than its corrosion, deformation, or interaction with vegetation. as a consequence, for example, during the survey operations, the assessment of the presence and the inspection of the top has to be as much accurate as possible, and the eventual presence of vegetation can prevent a careful survey. methodology he purpose of the proposed approach is the evaluation of the residual efficiency of the investigated drapery net system types when no quantitative data from monitoring is available. the proposed method intends to be an alternative solution to a continuous monitoring, i.e. it is a tool for assessing how ageing affects the protection system. t m. marchelli et alii, frattura ed integrità strutturale, 47 (2019) 437-450; doi: 10.3221/igf-esis.47.34 442 thus, it is hypothesised that at the beginning of its working life, the drapery system has its maximum efficiency. the tool has not been conceived for analysing if there are design or construction errors in the protection structures. similarly, nothing is said about the quality of the project and its effectiveness. component potential damages observed damages mesh the accumulation of debris at the bottom, or in the intermediate parts, can cause excessive stresses in the mesh leading to the yielding of the wire and the rupture of the component. large blocks can cause the punching leading to the laceration of the mesh. the growing vegetation (trees) creates an additional anchor, which might be unsuitable for the protection structure and be the cause of additional failures. brushes can cause water stagnation with consequent corrosion. flowing water can be the cause of corrosion. moisture supports the growing of fungi that can change the chemical environment. salty air and other environmental conditions can promote corrosion 
 
 
 lacerations, bowing, excessive deformations, rust, lack of corrosion protection ropes & anchors bolts cannot create a perfect stop if the traction in the rope is large. rust reduces the resisting cross-section area of the components. rust damages the head of the anchor and the plate. water or moisture can corrode the elements, damaging the grouting, and causing the deterioration the bond between bolts and grouting with the consequent unthreading. excessive forces due to debris accumulation can cause unthreading of the anchors fraying or/and rust ing of the ropes, unconnected ropes, rust on the rope clips, unthreading of anchors, rust on the anchors, rust on the head of the anchors, rust on the plates, lack of the connector, lack of the rope clips connections between mesh panels rust reduces the cross-section area of the connection reduced number of connection devices (e.g. clips or knots), rust on the connector, lack of any sort of connection mesh-rope connections if the rope is sewed up in the mesh, local damages on the mesh can make the connection inefficient table 2: potential and observed damages on the main components of the system. the main idea of the approach is to consider the mutual dependencies between the main components and global failure, and local damages and main component, to quantify the residual capacity. the double hierarchy evaluation process described was automated and encoded. in this perspective, assuming a periodic investigation on the efficiency of the structure, a check list of the issues to consider and assess was provided. depending on the drapery system type, two different lists in which each entry represents a possible local damage or critical situation for an element of the drapery system were proposed. the two left-hand side columns of tab. 3 and 4 report the considered issues for each component of simple and reinforced drapery net systems, respectively. from a technical point of view, it is expected that an expert (say an engineer or a geologist) is called for a periodic survey of the structure, assessing the damage, deterioration, or even to mark the fact that the component is missing. three increasing damage levels were introduced, as described in tab. 5. due to the inherent subjectivity of the approach, which is operator-based, the choice of three levels seems to be a profitable solution. fig. 4 shows examples of damage states according to the authors. m. marchelli et alii, frattura ed integrità strutturale, 47 (2019) 437-450; doi: 10.3221/igf-esis.47.34 443 to consider the different influence of these issues on the maintenance of the system efficiency, different weights were associated to each point of the check list. based on the outcomes of past studies reported in the literature, the highly qualified experience of the authors, and in-situ observations, three importance classes were defined: c1 when the influence of the issue to the overall efficiency is negligible, c2 when the issue might influence the protection system, and c3 when the issue is critical and dramatically reduces the efficiency of the protection system. the right-hand side columns of tab. 3 and 4 report the importance class of each point of the check list. (a) (b) (c) (d) figure 4: examples of different damage levels attributed to various components. different anchors types and connection with the ropes and the mesh: (a) damage on the plate and/or on the head of the anchors – d1, (b) unthreading of the anchors – d2, (c) presence of corrosion and/or removal of the corrosion protections of the mesh – d2, (d) presence of corroded zones and/or significant damage of the rope – d1. definition of the maintenance level of the system the level of damage for each element and the class of importance were matched to evaluate the efficiency of the whole drapery mesh system. the method mimics two techniques adopted in risk assessment: weighted sum and matrix approaches. the former represents one of the most common empirical method to evaluate the hazard associated to a natural disaster. it consists in the assignment of a global score, increasing for higher hazard, obtained as a function of the presence of some predisposing factors, weighted by the importance of each. at each factor, a score is assigned and the global score derives from the weighted sum of the single scores divided by the weighted maximum. the weighted process partially limits the inherent subjectivity of the method [24, 25]. matrix evaluation techniques are a widely employed and are profitable methods for evaluating the risk level. these methods are based on the subdivision in categories for both the probability of occurrence of an event (usually the rows of the risk matrix) and the severity of the consequences (the columns). each cell of the matrix identifies a risk level [24, 26] these two methods were tailored, revised and partially combined to define the efficiency of the whole drapery mesh. tab. 6 details the score assigned to each damage level importance factor. the global score of the drapery mesh is the summation of each single score. the score increases as much as the residual efficiency reduces. the greater the number of elements that exhibit criticality is, the higher the global score. the weighted maximum scores range from 0 to 113 for simple drapery nets, and from 0 to 109 for reinforced drapery nets, provided that all elements are present, while the global score ranges from 0% to 100%. if one (or more) are absent, all the local/potential damages linked to these are not considered in the weighted global maximum, i.e. if a rope is missing, all damages related to anchor and connection are not considered. as previously detailed, it emerges that either the deterioration of several minor components or the damage of a unique principal part of a drapery system can compromise the whole system efficiency. in addition, the system can be ineffective even though a single component is in a highly damaged situation. this occurs if the component is fundamental and the expected consequence is marked as c3. in this particular case, for example, the global score is low, but a sudden maintenance work is needed. as a consequence, another additional qualitative indicator is associated to the system relating to the state of conservation of the system, indicating if a sudden repair is needed to restore the system to its initial condition. a risk-matrix was defined, as shown in tab. 6. three maintenance levels were introduced, depending on both the level of damage and the class of importance of the component: a0 if a long-term maintenance plan is needed, a1 if a short/medium-term maintenance plan is needed, and a2 if urgent maintenance is needed. the maintenance level of the whole system is the worst maintenance level obtained by each component. in this way, if almost one part has maintenance lever a2, the drapery m. marchelli et alii, frattura ed integrità strutturale, 47 (2019) 437-450; doi: 10.3221/igf-esis.47.34 444 mesh system requires a sudden maintenance, while a1 identifies a partial loss of functionality that can be recovered in larger times. in addition, the number of damaged components directly relates to the extent of the required intervention works. component local or potential damage coi wire mesh significant amount of debris in the foot of the slope presence of debris in the mesh presence of weeds, bushes or trees interacting with the mesh lacerations in the mesh deformations or bowing of the mesh presence of corrosion and/or removal of the corrosion protections of the mesh c3 c2 c2 c3 c3 c1 top rope absence of the rope presence of corroded zones and/or significant damage of the rope absence of the anchors missing rope-anchors connection elements corrosion of the anchors damage on the plate and/or on the head of the anchors unthreading of the anchors c3 c3 c3 c3 c1 c2 c3 bottom rope presence of corroded zones and/or significant damage of the rope partially visible rope as hidden by debris/vegetation absence of the rope non-visible anchor absence of the anchors missing rope-anchors connection elements corrosion of the anchors damage on the plate and/or on the head of the anchors unthreading of the anchors c2 c1 c2 c1 c2 c2 c1 c2 c2 intermediate ropes (if present) presence of corroded zones and/or significant damage of the rope partially visible rope as hidden by debris/vegetation absence of the rope non-visible anchor absence of the anchors missing rope-anchors connection elements corrosion of the anchors damage on the plate and/or on the head of the anchors unthreading of the anchors c1 c1 c1 c1 c1 c1 c1 c1 c1 connection between mesh panels missing elements presence of corroded zones and/or damages of the connection elements c3 c2 mesh-top rope connection missing elements presence of corroded zones and/or damages of the connection elements c3 c2 mesh-bottom rope connection missing elements presence of corroded zones and/or damages of the connection elements c2 c1 meshintermediate ropes connection missing elements presence of corroded zones and/or damages of the connection elements c2 c1 table 3: classes of importances (coi) for the assessment of the residual efficiency for all the considered components in simple drapery net systems (maximum equal to 113). m. marchelli et alii, frattura ed integrità strutturale, 47 (2019) 437-450; doi: 10.3221/igf-esis.47.34 445 component local or potential damage coi wire mesh significant amount of debris in a portion defined with 4 anchors presence of debris in the mesh presence of weeds, bushes or trees interacting with the mesh lacerations in the mesh deformations or bowing of the mesh presence of corrosion and/or removal of the corrosion protections of the mesh c3 c1 c1 c3 c3 c1 top rope absence of the rope presence of corroded zones and/or significant damage of the rope absence of the anchors missing rope-anchors connection elements corrosion of the anchors damage on the plate and/or on the head of the anchors unthreading of the anchors c2 c3 c3 c3 c1 c2 c3 bottom rope absence of the rope presence of corroded zones and/or significant damage of the rope partially visible rope as hidden by debris/vegetation non-visible anchor absence of the anchors missing rope-anchors connection elements corrosion of the anchors damage on the plate and/or on the head of the anchors unthreading of the anchors c2 c1 c2 c1 c1 c1 c1 c1 c1 support ropes presence of corroded zones and/or significant damage of the rope absence of the rope absence of the anchors missing rope-anchors connection elements corrosion of the anchors damage on the plate and/or on the head of the anchors unthreading of the anchors c1 c3 c3 c3 c1 c2 c3 connection between mesh panels missing elements presence of corroded zones and/or damages of the connection elements c3 c2 mesh-top rope connection missing elements presence of corroded zones and/or damages of the connection elements c3 c2 mesh-bottom rope connection missing elements presence of corroded zones and/or damages of the connection elements c2 c1 table 4: classes of importances (coi) for the assessment of the residual efficiency for all the considered components in reinforced drapery net systems (maximum equal to 109). damage level mesh & ropes anchors & connectsions d0 the considered damage is absent or limited to a very reduced portion (up to 25%) none of the parts is damaged. the element is present d1 the considered damage is diffused (from 25% to 75%) a slight or intermediate of damage is present, at least in one anchor or connection
 d2 a large part of the component is affected by the considered damage (from 75%) at least one part is damaged. the element is absent. table 5: damage levels on the components of a drapery system. m. marchelli et alii, frattura ed integrità strutturale, 47 (2019) 437-450; doi: 10.3221/igf-esis.47.34 446 c1 c2 c3 d0 0 (a0) 0 (a0) 0 (a0) d1 1 (a0) 2 (a0) 3 (a1) d2 2 (a0) 3 (a1) 5 (a2) table 6: table of the scores and the maintenance level (in square brackets) attributed to each entry of the check lists reported in tabs. 3 and 4, depending on the level of damage and the class of importance. study cases he residual efficiency assessment procedure herein proposed was tested in various sites located in the northwestern italian alps. the campaign serves both for verifying the influence of the single damages on the overall functioning of the rockfall mitigation structures and for testing the capabilities of a matrix approach, evaluating if the proposed procedure is able to minimise the subjectivity, which is intrinsic in such man-made survey operations. the investigated structures are directly placed above local and national roads. their selection was based on the possibility to reach the top of the drapery net. the sites are located at an altitude ranging from 300 to 1100 m a.s.l. the slope angle of the cliffs onto which the surveyed drapery nets are installed is variable: gentle slopes as well as overhanging cliffs were examined. a large heterogeneity in the characteristics of the protective structures was observed. in detail, the size of the nets is between 20 to 500 m in length and 5 and 30 m in height. as expected, various net types and damage levels were observed. in the following, the relevant aspects of the survey campaign are reported. three study cases are illustrated (tab. 7 details the scores attributed to each component). fig. 5.a shows a simple drapery net system (case a) installed in a debris slope, in which a few anchors of the top rope are unthreaded. the assigned damage level at “top rope – unthreading of the anchors” entry of tab. 3 is d2 since the element is missing, i.e. at least one anchor is unthreaded. considering the importance class of this damage, i.e. c3, the maintenance level raises up to a2, requiring urgent intervention works. this outcome of the procedure is confirmed by the fact that the system is no more capable to drive the debris at the foot of the slope in a controlled way. the spacing between two fixing points is large and the top rope is slack engendering an unsuited deformation of the wire mesh, which loses its adhesion to the slope. in this particular case, both signs of corrosion on top and bottom ropes and a significant amount of debris accumulated in the foot of the slope were observed. fig. 5.b shows a reinforced drapery system (case b) installed on a vertical gneiss cliff. the visual inspection reports a wellpreserved anchoring system. the local damages affect the support ropes, with a small degree of corrosion, the connection between the wire mesh panels. the wire mesh is slightly corroded, with vegetation interacting with it. the global maintenance level is a1, i.e. medium plan intervention, while the global score is quite high (32). the observed situation is well represented by the outcomes of the procedure, since the system preserve a certain degree of functionality. fig. 5.c shows a reinforced drapery system (case c) located in a debris slope. the visual inspection reports that no corrosion problems emerge, with a global well-preserved situation. the presence of vegetation interacting with the mesh represents the only critical situation. with the adoption of the proposed method, the global maintenance level is a1, i.e. long term intervention works, and the global score is low (2). this result is in complete agreement with what observed. it is worth noting that case a and case b have similar overall score, meaning that the overall damage level is similar, i.e. in both cases several elements are damaged. anyway, in case a only the damage precludes the correct functioning of the protection system, i.e. the maintenance levels are different. as an overall comment, the driving idea of classifying the components into main categories helps in dealing with the heterogeneity of techniques within the same site. for example, different mesh types (wire mesh and cable net) are sometimes combined, see fig. 6.a, or different anchoring devices are used. more frequently, the two investigated different drapery net systems occur in sequence, i.e. a simple and a reinforced drapery nets, as shown in fig. 6.b. in this case, since the check list is system-dependent, two different analyses must be considered, as the influence of the local damages on the global efficiency varies. t m. marchelli et alii, frattura ed integrità strutturale, 47 (2019) 437-450; doi: 10.3221/igf-esis.47.34 447 (a) case a (b) case b (c) case c figure 5: photos of three installations observed during the site campaign: case a is a simple drapery mesh system, the unthreaded anchor is marked with the white circle. case b and case c refer to reinforced drapery systems. (a) (b) figure 6: in (a) two mesh types are adopted; in (b) the simple and the reinforced drapery systems are adjacent in the same site. m. marchelli et alii, frattura ed integrità strutturale, 47 (2019) 437-450; doi: 10.3221/igf-esis.47.34 448 component case a (maximum 90) case b (maximum 105) case c (maximum 105) wire mesh 12 (a2) 11 (a1) 2 (a0) top rope 15 (a2) 3 (a0) 0 (a0) bottom rope 10 (a1) 4 (a0) 0 (a0) intermediate ropes 0* (a0) support ropes 4 (a0) 0 (a0) connection between mesh panels 0 (a0) 5 (a1) 0 (a0) mesh-top rope connection 0 (a0) 5 (a1) 0 (a0) mesh-bottom rope connection 0 (a0) 0 (a0) 0 (a0) mesh-intermediate rope connection 0* (a0) global score 52% 30% 1% table 7: results of the survey campaign on the three cases commented in the text. the sum of the scores and the most severe maintenance level (in round brackets) are reported for each component. if the component is not present, a sign * is added to the score. conclusions and further outlooks rapery net systems are widely employed and profitable measures to mitigate the risk of rockfall events. nevertheless, their failure or destruction would cause serious consequences, both in term of causalities and economical damages. due to their importance, a continuous monitoring would be profitable to evaluate the maintenance of their efficiency despite ongoing ageing and/or local damages. unfortunately, continuous or periodic monitoring is rarely adopted, as it is high time-consuming, and thus no quantitative data are available for the planning of the maintenance works. as a consequence, the proposed quick-assessment procedure herein reported aims at addressing the problem of estimating the efficiency of a rockfall drapery mesh system and establishing a priority list for intervention works. the presented method is based on a multi-criteria analysis, involving an encoded screening survey. the leading idea is that either the deterioration of several minor elements or the damage of a unique fundamental element of a drapery system can compromise the whole system efficiency. this entails a double hierarchy problem, since the final evaluation depends both on the damaged/deteriorated part and on the magnitude of the damage itself. the process is implemented through a list of observed items that the surveyor must check in analysing the protection structure. a damage level and a class of importance for each entry let to assign a global score and a maintenance level to the structure, indicating if urgent reparation works are needed. the lack in the prescriptions for such kind of hazard mitigation structures lead the authors in fixing the attention on two different drapery types. similarly, the procedure can be implemented on other installation types, keeping fixed the identification of the main components and the effects of damage on the overall behaviour. a site campaign was performed to validate the weights assigned to each issue, despite the valuable range of observed different solutions, indeed, a good agreement between the observed conditions of the system and the obtained results emerges. the double information obtained by the global score and the global maintenance level provided a compelling solution to understand both the severity and the extension of the possible required maintenance intervention. further developments can be achieved, expanding the methodology for other mitigation measures [27]. acknowledgements his work has been supported by regione autonoma valle d’aosta under the framework of red risk evaluation dashboard project. d t m. marchelli et alii, frattura ed integrità strutturale, 47 (2019) 437-450; doi: 10.3221/igf-esis.47.34 449 references [1] ferraiolo, f. (2005). i rivestimenti superficiali. geam geoingegneria ambientale e mineraria, xlii, pp. 45–53. [2] giani, g. (1992). rock slope stability analysis. balkema, rotterdam (nl). [3] volkwein, a., schellenberg, k., labiouse, v., agliardi, f., berger, f., bourrier, f., dorren, l., gerber, w., and jaboyedoff, m. (2011). rockfall characterisation and structural protection – a review, natural hazards and earth system sciences, 11, pp. 2617– 2651, doi: 10.5194/nhess-11-2617-2011. [4] bertolo, p., oggeri, c., and peila, d. (2009). full-scale testing of draped nets for rockfall protection, canadian geotechnical journal, 46, pp. 306–316. doi: 10.1139/t08-126. [5] shu, s., muhunthan, b., badger, t., and grandorff, r. (2005). load testing of anchors for wire mesh and cable net rockfall slope protection systems, engineering geology, 79, pp. 162–176. doi: 10.1016/j.enggeo.2005.01.008. [6] peila, d., pelizza, s., and sassudelli, f. (1998). evaluation of behaviour of rockfall restraining nets by full scale tests, rock mechanics and rock engineering, 31, pp. 1–24. doi: 10.1007/s006030050. [7] blanco-fernandez, e., castro-fresno, d., del coz diaz, j., and lopez-quijada, l. (2011). flexible systems anchored to the ground for slope stabilisation: critical review of existing design methods, engineering geology, 122, pp. 129–145. doi: 10.1016/j.enggeo.2011.05.014. [8] giacchetti, g. and bertolo, p. (2010). approccio al calcolo dei sistemi di reti con chiodi per il consolidamento delle pareti rocciose, geam geoingegneria ambientale e mineraria, xlvii, pp. 33–42. [9] giacchetti, g. and grimod, a. (2015). rockfall mitigation using simple drapery system: design approach. in engineering geology for society and territory, 2, pp. 1881–1884. [10] blanco-fernandez, e., castro-fresno, d., del coz diaz, j., navarro-manso, a., and alonso-martinez, m. (2016). flexible membranes anchored to the ground for slope stabilisation: numerical modelling of soil slopes using sph, computer and geotechnics, 78, pp. 1–10. doi: 10.1016/j.compgeo.2016.04.014. [11] castro-fresno, d., del coz diaz, j., lópez, l., and garcía nieto, p. (2008). evaluation of the resistant capacity of cable nets using the finite element method and experimental validation, engineering geology, 100, pp. 1–10. doi: 10.1016/j.enggeo.2008.02.007. [12] sasiharan, n., muhunthan, b., badger, t., shu, s., and carradine, d. (2006). numerical analysis of the performance of wire mesh and cable net rockfall protection systems, engineering geology, 88, pp. 121–132. doi: 10.1016/j.enggeo.2006.09.005. [13] thoeni, k., giacomini, a., lambert, c., and sloan, s. (2013). numerical investigation on the performance of a rockfall drapery system. in bischoff, m., onate, e., owen, r., ramm, e., and wriggers, p., eds., iii international conference on particlebased methods fundamentals and applications particles 2013, pp. 1–10. [14] valfré, a. (2006). dimensionamento di reti metalliche in aderenza per scarpate rocciose mediante modellazioni numeriche, geam geoingegneria ambientale e mineraria, xliii, pp. 47–53. [15] shu, s., muhunthan, b., and badger, t. (2005). snow loads on wire mesh and cable net rockfall slope protection systems. engineering geology, 81, pp. 15–31. doi: 10.1016/j.enggeo.2005.06.007. [16] gratchev, i., kim, d., and chung, m. (2015). study of the interface friction between mesh and rock surface in drapery system for rock fall hazard control, engineering geology, 199, pp. 12–18. doi: 10.1016/j.enggeo.2015.10.005. [17] chakravorty, m., frangopol, d., mosher, r., and pytte, j. (1995). time-dependent reliability of rock-anchored structures, reliability engineering and system safety, 47, pp. 231–236. [18] jiang, s.-h., li, d.-q., zhang, l.-m., and zhou, c.-b. (2014). time-dependent system reliability of anchored rock slopes considering rock bolt corrosion effect. engineering geology, 175, pp. 1–8. doi: 10.1016/0951-8320(94)00068-y. [19] xia, n., liang, r., payer, j., and patnaik, a. (2013). probabilistic modelling of the bond deterioration of fully-grouted rock bolts subject to spatiotemporally stochastic corrosion, structure and infrastructure engineering, 9, pp. 1161–1176. doi: 10.1080/15732479.2012.670649 [20] muhunthan, b., shu, s., sasiharan, n., hattamleh, o., badger, t., lowell, s., and duffy, j. (2005). analysis and design of wire/mesh cable net slope protection. technical report, washington state transportation commission department of transportation, u.s. department of transportation federal highway administration. [21] giacomini, a., thoeni, k., lambert, c., booth, s., and sloan, s. (2012). experimental study on rockfall drapery system for open pit highwalls, international journal of rock mechanics & mining sciences, 56, pp. 171–181. doi: 10.1016/j.ijrmms.2012.07.030 [22] ente italiano di unificazione (2012). uni 11437:2012 rockfall protective measures tests on meshes for slopes coverage. uni. m. marchelli et alii, frattura ed integrità strutturale, 47 (2019) 437-450; doi: 10.3221/igf-esis.47.34 450 [23] astm (2016). astm a975:2016. standard specification for double–twisted hexagonal mesh gabions and revet mattresses (metallic-coated steel wire or metallic-coated steel wire with poly (vinyl chloride) (pvc) coating). [24] dodgson, j., spackman, m., pearman, a., and phillips, l. (2009). multi-criteria analysis: a manual. technical report, department for communities and local government: london. [25] karsak, e. and ahiska, s. (2005). practical common weight multi-criteria decision-making approach with an improved discriminating power for technology selection, international journal of production research, 43, pp. 1537–1554. doi: 10.1080/13528160412331326478 [26] catrinu, m. and nordgård, d. (2010). incorporating risk analysis and multi-criteria decision making in electricity distribution system asset management. in briš, r., guedes soares, c., and martorell, s., eds., reliability, risk and safety: theory and applications, 1, pp. 393–400. [27] marchelli, m. and de biagi, v. (2018). dynamic effects induced by the impact of debris flows on protection barriers, international journal of protective structures, pp. 1–16. doi: 10.1177/2041419618798378. microsoft word numero_30_art_1 d. taylor, frattura ed integrità strutturale, 30 (2014) 1-6; doi: 10.3221/igf-esis.30.01 1 focussed on: fracture and structural integrity related issues fracture mechanics: inspirations from nature david taylor trinity college dublin, ireland dtaylor@tcd.ie abstract. in nature there are many examples of materials performing structural functions. nature requires materials which are stiff and strong to provide support against various forces, including self-weight, the dynamic forces involved in movement, and external loads such as wind or the actions of a predator. these materials and structures have evolved over millions of years; the science of biomimetics seeks to understand nature and, as a result, to find inspiration for the creation of better engineering solutions. there has been relatively little fundamental research work in this area from a fracture mechanics point of view. natural materials are quite brittle and, as a result, they have evolved several interesting strategies for preventing failure by crack propagation. fatigue is also a major problem for many animals and plants. in this paper, several examples will be given of recent work in the bioengineering research centre at trinity college dublin, investigating fracture and fatigue in such diverse materials as bamboo, the legs and wings of insects, and living cells. keywords. fracture; toughness; fatigue; insect cuticle; bamboo; osteoctyes. introduction n this paper (and accompanying lecture) i will be considering two material properties of vital importance in engineering: fracture toughness and fatigue strength. i will show the results of measurements of these two properties in various materials and discuss the significance of these results for the mechanical structures in which these materials are used. however, the materials and structures that i will consider are not from the world of engineering components; instead, they come from nature. if we look around us we see many natural, biological structures which are load-bearing and which are required to provide mechanical support and to ensure rigidity and long-term durability. these structures have not been designed in the way that engineering parts are designed, rather they have evolved over millions of years. in some ways these materials and structures are very different from their engineering equivalents, but nevertheless it can be interesting and perhaps useful to study them from an engineering perspective. such studies shed light on aspects of the world in which we live, and may also lead to the development of improved engineering materials and components via a biomimetics approach in which nature is seen as an inspiration and starting point for creative design activities. very little such work has been done to date from a fracture mechanics point of view. we have hardly any data on fracture toughness (kc) and fatigue properties for natural materials, and little understanding about how these materials resist crack propagation and other failure mechanisms. in my research group we have been addressing this problem, starting some years ago with work on the fracture of bone, and moving in recent years to some of the other structural biological materials. in what follows i will describe three projects, spanning a large range of sizes from plants (which grow to heights i d. taylor, frattura ed integrità strutturale, 30 (2014) 1-6; doi: 10.3221/igf-esis.30.01 2 of several metres), to insects (of the order of millimetres) and finally to living cells in our bodies where the relevant scale falls below one micron. insect wings ig. 1 shows a crack-propagation test carried out on the wing of an insect – in this case a locust. we cut samples approximately 10mm x 10mm, introduced a notch of length approximately 1mm into one side, and applied axial tension. further details can be found in a recent publication [1]. the wing consists of a sheet of material which is very thin (approximately 3m) and which has veins of thicker material running through it at a spacing of approximately 1mm. we found that these veins improved kc by about 50% and that the spacing of veins was optimal: if they had been more closely spaced this would not have improved the stress to failure because the tensile strength of the material would be exceeded. propagating cracks were seen to arrest at veins; on further loading the crack first blunted and then propagated via void formation on the far side of the vein, as shown in the figure. figure 1: the image on the left shows a fracture toughness test on material from the wing of a locust, with a propagating crack arrested at a vein. the image on the right shows the entire wing; the different colours indicate the local spacings of the veins. this experiment illustrates, in a very simple way, a concept which is applicable to all materials: the idea of a “critical distance”. i have investigated in some detail the theory of critical distances as applied to engineering materials (see for example [2]). the concept that any given material possesses a critical distance l which controls fracture and fatigue behaviour can be difficult to understand when applied to materials with complex microstructures: the insect wing presents a simple, two dimensional example of the essential idea: that materials contain microstructural features which inhibit crack propagation. when considering the effect of a crack or notch it is useful to compare the physical dimensions of the feature, and of the disturbance which it creates in the surrounding stress field, with the critical distance. bamboo he stems of plants must be sufficiently rigid to allow upward growth and support of the leaves, and sufficiently strong and tough to resist mechanical forces, especially periodic wind loading. bamboo is an important engineering material in its own right, extensively used in asia and of great future interest because its fast growth makes it a renewable resource. however there have been relatively few publications on the mechanical properties of the bamboo stem, which is known as a “culm”. culms grow to heights of over ten metres, in the form of hollow tubes of almost constant thickness (see fig. 2), with periodic nodes which carry thin branches to which the leaves are attached. in a recent project (the results of which are currently in review for publication) we assessed the mechanical effect of these nodes, showing that (despite previous assumptions to the contrary) they do not improve the stiffness or strength of the bamboo culm, and that (unlike the veins of the insect wing) they are too far apart to significantly improve toughness. f t d. taylor, frattura ed integrità strutturale, 30 (2014) 1-6; doi: 10.3221/igf-esis.30.01 3 figure 2: (photograph): the bamboo culm consists of a hollow tube with periodic nodes. (a) we measured kc by propagating cracks along the tube axis by means of a pair of point loads. (b) we constructed a finite element model including the layered structure. (c) a typical load/displacement trace from a toughness test. measuring the fracture toughness of this material is quite challenging. it is highly anisotropic, and in fact it always fails by splitting (i.e. propagation of cracks in the longitudinal direction) whatever type of load is applied to it. furthermore the tubular shape of the culm and the graded structure (consisting of layers of material varying in stiffness from outside to inside) make it impossible to use standard fracture toughness specimens. a number of previous studies have been published, reporting kc values which vary greatly, from as little as 0.18mpam1/2 [3] to as much as 200mpam1/2 [4]. in fact, the assessment of these various studies is a good lesson for the student of fracture mechanics, demonstrating how incorrect results can be obtained if one does not fully understand the underlying principles. we measured kc by propagating cracks from notches, using a pair of point loads at one end of a tube sample (see fig. 2a). fracture toughness was estimated in two different ways: (i) using the maximum force at failure, along with a finite element model (fig. 2b) to relate this force to the local stress intensity factor; (ii) using the fracture energy (the area under the force/displacement curve) divided by the area of new crack propagation to obtain the strain energy release rate. the two methods gave slightly different results (by about 30%) and consistently recorded a 55% increase when the crack tip was located at a node, suggesting a mechanical role for the nodes in limiting failure by splitting. however, subsequent calculations showed that the separation of the nodes was much too great: any crack which initiates would be able to propagate through the node on reaching it. our conclusion is that these nodes fulfill a biological function (as branch points) but do not confer any mechanical benefit on the plant. fatigue of natural materials yclic loading is very common in nature, and many biological materials fail by fatigue, but as yet we know very little about their fatigue characteristics. one exception is bone, which has been studied quite extensively [5]: fatigue cracks initiate in bone as a result of normal daily activities but usually do not propagate to failure thanks to bone’s self-healing ability. excessive loading (e.g. in professional athletes) or poor-quality bone (e.g. due to osteoporosis) gives rise to fatigue failures which are referred to by doctors as “stress fractures”. recently we have been carrying out tests to measure, for the first time, fatigue behaviour in three other natural materials: insect cuticle; bamboo and cells. c d. taylor, frattura ed integrità strutturale, 30 (2014) 1-6; doi: 10.3221/igf-esis.30.01 4 fig. 3 shows fatigue data on the legs and wings of insects, from a recent publication [6]. these body parts are made from essentially the same material – known as “cuticle” – but the cuticle found in the legs contains more fibres of chitin and is significantly anisotropic. this is reflected in the smaller fatigue range for leg material, with an endurance limit at one million cycles around 70% of the failure stress, in contrast to the wing material which shows fatigue at less than 50% of its tensile strength. legs (which are essentially hollow, thin-walled tubes) were tested in cyclic cantilever bending and displayed two different failure modes: traditional cracking on the tensile side and progressive buckling on the compression side, suggesting that the evolution of these body parts has generated an optimal structure, equally resistant to failure in compression and tension. figure 3: stress-life fatigue data for insect legs and wings. fig. 4 shows data (as yet unpublished) for bamboo. surprisingly, we could find no fatigue data for this material in the published literature, despite its widespread use. these data were generated by cutting tube samples from the culm and loading them in compression across the diameter, thus generating fatigue failure by longitudinal splitting. a large fatigue range exists, which should be taken into account when this material is employed for structural purposes. figure 4: stress-life data for bamboo culm samples my final example of fatigue in natural materials concerns living cells. our bodies, and those of animals and plants, contain different types of cells, which perform specific functions. many cells experience cyclic loading, so the question arises as to whether they ever fail by fatigue. this is a difficult question to answer by experimental means: cells are small (typically 10100m in diameter) and very soft and flexible, consisting of an outer membrane of lipid molecules supported by a d. taylor, frattura ed integrità strutturale, 30 (2014) 1-6; doi: 10.3221/igf-esis.30.01 5 cytoskeleton consisting of relatively stiff protein molecules which line the membrane and also pass across the cell body, conferring some overall rigidity and allowing the cell to move and change shape. though there have been a number of studies to measure the elastic stiffness and viscoelastic properties of cells, there are only a very few reports of monotonic tests to failure, and no data on fatigue failure for any type of cell. we devised a test which makes use of the fact that a certain type of cell – known as an osteocyte – lives inside our bones. these cells are connected to each other via long, thin extensions of the cell body known as cellular processes (see fig. 5). figure 5: osteocytes are linked together in a network via numerous cellular processes: these images show examples of cells with and without the surrounding bone matrix [7]. we noticed that, where a bone contains cracks, these cellular processes can be seen passing across the open crack. therefore, by applying cyclic loading to the bone, causing these cracks to open and close, we could conduct fatigue tests on individual cellular processes. our initial results were published showing the number of cycles to failure as a function of cyclic crack opening [8]; in more recent work (shortly to be published in the journal of the mechanical behavior of biomedical materials) we used finite element modelling to estimate the cyclic strain and therefore generate the first ever strain-life curve for material taken from a living cell (see fig. 6). figure 6: strain-life data for osteocyte cellular processes. this work has some significant limitations: in order to observe failure of these cellular processes (which are only 200nm in diameter) we had to conduct the tests inside a scanning electron microscope using an in situ loading stage. limits on resolution meant that we were only able to measure relatively large strains and therefore small numbers of cycles to failure, up to 10. interestingly the results are quite similar to fatigue of metallic materials in the very low cycle regime. d. taylor, frattura ed integrità strutturale, 30 (2014) 1-6; doi: 10.3221/igf-esis.30.01 6 these findings are of importance because we believe that the fatigue failure of these cellular processes, at the point where they span an open crack in the bone matrix, could be a crucial step in the complex system by which fatigue cracks in bone are repaired, ensuring the continued integrity of the skeleton. concluding remarks here are perhaps two different reasons for engaging in the type of research described above. the first is simple curiosity. it has been fascinating to discover how nature solves the same problems of structural integrity as those faced by engineering designers and materials scientists. the second reason is that in this way, inspiration may be provided to create new, biomimetic materials and structures. nature’s materials are, in many ways, not as good as modern engineering materials. they tend to have lower fracture toughness values and to suffer from fatigue at least as much. but nature has evolved some clever strategies to overcome these limitations – strategies such as self-repair and the use of functionally graded materials – so that keeping an eye on nature may help us to create new, better solutions for engineering applications. acknowledgements e are grateful to science foundation ireland and to the irish research council for financial support. references [1] dirks, j.-h., taylor, d., veins improve fracture toughness of insect wings, plos one, 7(8) (2012) e43411. [2] taylor, d., the theory of critical distances: a new perspective in fracture mechanics, elsevier, oxford, uk (2007). [3] mitch, d., harries, k. a., sharma, b., characterisation of splitting behavour of bamboo culms, journal of materials in civil engineering, 22 (2010) 1195-1199. [4] amada, s., untao, s., fracture properties of bamboo, composites part b: engineering, 32 (2001) 451-459. [5] taylor, d., hazenberg, j. g., lee, t. c., living with cracks: damage and repair in human bone, nature materials, 2 (2007) 263-268. [6] dirks, j. h., parle, e., taylor, d., fatigue of insect cuticle, journal of experimental biology, 216(10) (2013) 19241927. [7] klein-nulend, j., bacabac, r. g., mullender, m. g., mechanobiology of bone tissue, pathologie biologie, 53(10) (2005) 576-580. [8] dooley, c., cafferky, d., lee, t. c., taylor, d., fatigue failure of osteocyte cellular processes: implications for the repair of bone, european cells and materials, 27(2014) 39-49. t w article a. gryguć et alii, frattura ed integrità strutturale, 55 (2021) 213-227; doi: 10.3221/igf-esis.55.16 213 effect of thermomechanical processing defects on fatigue and fracture behaviour of forged magnesium a. gryguć, s.b behravesh, h. jahed, m. wells university of waterloo (department of mechanical & mechatronics engineering, 200 university ave w, waterloo, on n2l 3g1, canada) agryguc@uwaterloo.ca, https://orcid.org/0000-0003-4138-4859 sbbehravesh@uwaterloo.ca, https://orcid.org/0000-0001-6613-2362 hjahed@uwaterloo.ca, https://orcid.org/0000-0002-0270-9254 mawells@uwaterloo.ca, https://orcid.org/0000-0001-5789-2773 b. williams canmetmaterials (natural resources canada, 183 longwood road south, hamilton, on l8p 0a1, canada) bruce.williams@canada.ca, https://orcid.org/0000-0003-0088-4638 r. gruber, a. duquett, t. sparrow, m. lambrou multimatic engineering (multimatic technical centre, 85 valleywood drive, markham, on, l3r 5e5, canada) rgruber@multimatic.com, aduquett@multimatic.com, tsparrow@multimatic.com, mlambrou@multimatic.com x. su ford motor company (ford research and innovation centre, 2101 village road, dearborn, mi, 48124, usa) xsu1@ford.com, https://orcid.org/0000-0001-8645-1424 abstract. the microstructural origins of premature fatigue failures were investigated on a variety of forged components manufactured from az80 and zk60 magnesium, both at the test specimen level and the full-scale component level. both stress and strain-controlled approaches were used to characterize the macroscopically defect-free forged material behaviour as well as with varying levels of defect intensities. the effect of thermomechanical processing defects due to forging of an industrially relevant full-scale component were characterized and quantified using a variety of techniques. the fracture initiation and early crack growth behaviour was deterministically traced citation: gryguć, a., s.k., behravesh, s.b., jahed, h., wells, m., williams b., gruber, r., duquett, a., sparrow, t., lambrou, m., su, x. effect of thermomechanical processing defects on fatigue and fracture behaviour of forged magnesium, frattura ed integrità strutturale, 55 (2021) 213-227. received: 27.11.2020 accepted: 15.12.2020 published: 01.01.2021 https://youtu.be/zyji2gghsu4 a. gryguć et alii, frattura ed integrità strutturale, 55 (2021) 213-227; doi: 10.3221/igf-esis.55.16 214 back to a combination of various effects having both geometric and microstructural origins, including poor fusion during forging, entrainment of contaminants sub-surface, as well as other inhomogeneities in the thermomechanical processing history. at the test specimen level, the fracture behaviour under both stress and strain-controlled uniaxial loading was characterized for forged az80 mg and a structure-property relationship was developed. the fracture surface morphology was quantitatively assessed revealing key features which characterize the presence and severity of intrinsic forging defects. a significant degradation in fatigue performance was observed as a result of forging defects accelerating fracture initiation and early crack growth, up to 6 times reduction in life (relative to the defect free material) under constant amplitude fully reversed fatigue loading. at the full-scale component level, the fatigue and fracture behaviour under combined structural loading was also characterized for a number of zk60 forged components with varying levels of intrinsic thermomechanical processing defects. a novel in-situ non-contact approach (utilizing digital-image correlation) was used as a screening test to establish the presence of these intrinsic defects and reliably predict their effect on the final fracture behaviour in an accelerated manner compared to conventional methods. keywords. magnesium; forging; fatigue; lcf; hcf; digital image correlation copyright: © 2021 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. introduction he successful utilization of lightweight materials in structural applications is an engineering problem which requires a thorough understanding of the service environment of the component to intelligently engineer a manufacturing process suitable for creating high quality and robust solutions for such applications. typically, mg components manufactured using traditional casting methods offer significant reduction in mass compared to other structural metals (due to mg’s low density) however they are generally utilized in applications where they are not significantly load bearing, due to the presence of casting defects which limit strength, ductility and fatigue performance [1]. generally, wrought forms of magnesium have been renowned for offering improved strength and ductility as they do not suffer from the manufacturing defects and inferior microstructure typical of cast manufacturing methods. forging mg to produce near net shape components can offer substantial performance benefit and facilitate the reliable usage of mg in structural fatigue critical components. this has necessitated an immense work towards understanding the complex structural behaviour of forged magnesium components as well as development of the forging process to optimize the resulting material structure, properties and performance. recent work on investigating the feasibility of forging have been conducted specifically focusing on az80 mg as it has good forgeability, and heat-treatability ideal for near net shape of fatigue critical components [1,2]. characterization of the as-forged properties of forged mg components in recent years has become t a. gryguć et alii, frattura ed integrità strutturale, 55 (2021) 213-227; doi: 10.3221/igf-esis.55.16 215 more widespread in literature. many studies have focused on characterization of the monotonic structural properties of forged az80 and zk60 mg, in open die forgings [3–5] as well as for closed die forged components such as wheels [6–8], aerospace components [5,8–12], and finally, automotive structural components [13–24]. in general, the main focus of these studies was the feasibility of achieving adequate material flow to produce the desired forged shape, whilst characterizing the resulting microstructure and quasi-static material properties. chen et al. utilized a two-step die-forging process of extruded az80 mg at 350°c to produce a complex aerospace component where the second forging step aided in removing underfilling and fold defects that persisted after the first step [10]. matsumoto et al. conducted forging combined with backwards extrusion of zk60 mg to produce simple components with small rib features and found that zk60 has a high propensity for the surface to oxidize at temperatures greater than 400°c, and shear cracks would develop at temperatures below 200°c, however at 300°c they were able to forge a component which was free of macroscopic defects. several recent works by gryguć et al. have investigated varying the processing parameters of mg forging with the specific objective of improving the strength, fatigue performance, and improving the homogeneity of properties throughout the forging [3,4,19–23,25– 27]. despite this, there has been little to no work done on developing a link between the fatigue response and nature of the failure morphology to the forging defects present in an mg component produced via an industrially representative forging process. this work aims to investigate the effects of thermomechanical processing defects on the fatigue behaviour of forged mg components by using the material properties extracted from the small-scale specimens which are free of macroscopic defects from within the forged component whilst comparing and contrasting them with the component level behaviour under in-service loading in a realistic forged component with varying levels of defect intensities. figure 1: plan view of extruded billet during different stages of forging operation to achieve final component (prior to machining of the flash). steps 3 and 4 show simulation predictions with transparent top-dies to allow visualization of the forged shape following each step. experimental setup he material used in this investigation was commercially-available az80 mg extruded billet (al: 8.0 ±0.2%, with other elements composition as per astm b91-12 standard) as well as zk60 mg extruded billet (zn: 5.8%, zr: 0.61%. the az80 and zk60 materials were received from luxfer mel technologies both in the as-fabricated condition. the dimension of the extruded billet were a diameter of 63.5 mm and a length of 1000 mm. the forging was conducted at canmetmaterials (hamilton, canada) using the billets which were cut down to a length of 680 mm. the billets were pre-bent at elevated temperature of 300°c to an angle of 108° in a pre-forming step using a mandrel bender to achieve the rough general shape and curvature of the component (step 2 in fig. 1). they then heated again to 300°c for 3 hours prior to flattening (step 3) to redistribute the material in preparation for the single step closed-die t a. gryguć et alii, frattura ed integrità strutturale, 55 (2021) 213-227; doi: 10.3221/igf-esis.55.16 216 forging. the flattened billet was then heated to the target forging temperature (300°c 450°c) for 1.5 hours (to allow any thermal gradients to decay) and isothermally forged using a 1500-ton hydraulic press using heated upper and lower dies with a complex internal geometry representing an automotive suspension lower control arm (step 4). graphite lubricate was used on the die and billet to reduce friction, sticking and promote material flow. the orientation of the billet to the press was such that the radial direction was along the direction of the press stroke (i.e. the direction of forging was along the radial direction of the billet). forging was carried out in a single step at a displacement rate of 2.1 4.2 mm/sec. following die-forging the component was removed from the die and air cooled to room temperature. a final machining operation (step 5) facilitates the removal of excess material (flash) from the forging and ensures interfacing surface features requiring high dimensional accuracy have a smooth machined surface. all of the full-scale components which were investigated in this study were tested in the as-machined condition, with no additional post treatments or surface coatings. tensile monotonic and fatigue test samples were utilized with geometries according to roostaei et al. [28] and a 4 mm thickness, these were machined from various locations throughout closed die forged component. there were 18 test samples that were extracted from 18 different locations throughout the closed die forging (see fig. 2), all with varying thermomechanical histories. the test samples had a nominal surface finish of ra≤0.2μm within the gauge section, however in practice the actual roughness was substantially less, around 0.05μm these samples were later utilized for quasi-static and cyclic (stress & straincontrolled) testing. the quasi-static tensile tests were performed according to astm standard e8/e8m15a using an mts 810 servo-hydraulic test machine operating in displacement control mode with a displacement rate of 1 mm/min. strain measurement was accomplished using a gom aramis 3d 5mp dic system which passively functioned to measure the average axial strain on the surface of the gauge section of the sample throughout the duration of the test. the fatigue tests were performed as per astm e466-15 for the stress-controlled, and astm e606 for strain-controlled, in an ambient environment using an mts 810 servo-hydraulic test machine operating in stress control mode at a frequency range of 0.5 hz to 60 hz depending on the load amplitude to maintain an approximately consistent loading rate between all tests. the strain was measured throughout the first 10,000 cycles using an mts 632.26 extensometer with an 8-mm gauge and travel of ± 1.2-mm until stabilization of the cyclic hysteresis loop was achieved. the fatigue tests were conducted at a zero mean stress for stress-controlled (i.e., rl = −1, fully reversed stress cycle) or zero mean strain (for strain-controlled) and stress amplitudes of between 140 mpa and 180 mpa and total strain amplitudes between 0.35% to 1.4%. the failure criteria for the specimen level tests were considered to be final rupture of the specimen gauge section. full-scale testing of the die-forged component with a load history which is representative of the in-service fatigue loads was carried out on a bi-axial load apparatus that simulated the longitudinal (ld) and lateral loading (td) on the component and a single load application point. the component was constrained at two other locations using rubber bushings similar to the way it is installed and supported in service. in comparison with the polished fatigue test specimens, the full-scale die-forged component had an asfabricated surface roughness which was substantially higher than the polished lab-specimens (although still quite low for typical as-forged surfaces); ranging from 0.6≤ra≤1.3μm for az80 mg, and 0.5≤ra≤1.7μm for zk60 mg. the loading was carried out as per specification by the automotive original equipment manufacturer (oem), with alternate blocks of high and low amplitude loads with some non-zero mean stress. this differs from the fully reversed constant amplitude loading which was done in the laboratory test-specimen level experiments that were used to characterize the material properties, as the full-scale test is meant to understand the holistic fatigue performance of the component within the physical system under representative service loads. the fatigue loading was bi-axial in nature with various proportionality ratios and phase angles between longitudinal and lateral loading axes, this induced varying levels of multiaxiality and bending stresses in the critical areas of the component (such as the dic screening region). the tests were carried out in an ambient environment with cooling air supplied to stabilize the temperature of the rubber bushings which supported the component as large amounts of repeated deformation can cause a. gryguć et alii, frattura ed integrità strutturale, 55 (2021) 213-227; doi: 10.3221/igf-esis.55.16 217 softening and damage to the rubber due to strain related internal heat generation. the frequency of loading employed was 1 hz under force control for the fatigue loading, then screening cycles were performed at a much lower frequency (quasi-static) at regular intervals which were nominally 10%, 50%, 100%, 150% of the “target fatigue life” defined by the component specifications. these slower screening cycles were utilized to monitor critical areas within the component that had either known or likely thermomechanical processing defects, this was accomplished via non-contact, in-situ strain field monitoring using digital image correlation (dic). once a macroscopic crack nucleation was detected via the dic screening technique, the screening interval increment was generally increased to 10% of target live intervals to provide more temporal resolution to monitor the crack growth behaviour. the failure criteria for the component level tests were considered to be > 40 mm of longitudinal displacement at peak load which would generally correlate to a large crack in the region of interest, normally between 2-40 mm in length. important to note is that this failure criteria was intentionally selected to aid in monitoring the growth of fatigue cracks related to thermomechanical processing defects and differs from that of the specification of the automotive oem for the component. if the support bushings became worn or broken this was not considered a failure of the component, they were replaced with new items and the fatigue loading continued as to find the structural failure within the magnesium die-forged suspension component. investigation of the fracture surfaces of both the specimen and component level samples was accomplished utilizing sem techniques (fei quanta feg 250 with edx), as well as quantitative light optical microscopy (lom) using a keyence vhx 6000 & 7000. figure 2: schematics of die-forged components highlighting (a) sample extraction locations and (b) loading/screening schematic during full-scale component level fatigue testing. ld denotes the longitudinal direction of loading and td transverse direction. results and discussion ue to the complex nature of the forged component investigated here (both from a geometry, process variable evolution and service loading point of view), the nature of the thermomechanical defects were traced using multi-modal approach. these various strategies included, identifying failure initiation locations, and investigating the fracture surface morphology and defect constituents (both geometric and particulate) surrounding the location of initiation and early crack growth. furthermore, these observations were both qualitatively and quantitatively assessed to compare and contrast az80 and zk60 mg forged components under traditional fully reversed fatigue loading in a laboratory style test with “dogbone” specimens extracted from the component in the vicinity of the critical locations, as well as the full-scale testing of the component under the representative service loading. the rationale behind the employed approach is to identify in similar forged components the relative effect of thermomechanical d (b) (a) a. gryguć et alii, frattura ed integrità strutturale, 55 (2021) 213-227; doi: 10.3221/igf-esis.55.16 218 defects by contrasting the material behaviour with and without the presence of a defect, and connecting it with the component level failure mode to determine if premature failure was driven by the presence of a defect. a novel non-contact approach was used to monitor the surface of the critical areas of the component during the fatigue loading to visualize the morphology of the defect, and quantify its severity and evolution over time to the threshold where it causes structural failure. digital image correlation was used to monitor the strain field in the critical area during specific intervals of the fatigue loading, and trace its evolution over time to understand the influence of thermomechanical defects on the nucleation and early growth behaviour of fatigue cracks. although using dic techniques to measure the strain field surrounding the crack tip in notched specimens has been done by other researchers for magnesium alloys [29,30], in this study, conventional techniques for crack detection such as optical microscopy, x-ray scanning, and die-penetrant were not effective at locating the presence of an incipient crack or initial defect, as they generally are done with the component in a resting state under no load [31,32]. furthermore, with the exception of x-ray, these conventional techniques are not typically effective for detection of subsurface defects as they require some evidence of the defect to have nucleated at the surface. as can be seen in fig. 3, even in the very first tensile reversal, the employed dic technique was able to detect saturation of strain in the plane which would eventually become the fatigue fracture surface, as the subsurface defect within the forged material effectively acted like an incipient crack when observed in-situ under the tensile load reversal. the component highlighted in the aforementioned figure had no visible forging defects such as underfill, cold-shuts or surface cracking in this critical location as can be seen in fig. 3a [1,33]. these types of in-situ screening tests can provide industrially relevant quantitative feedback to the forging developers to optimize the process parameters and reduce the detrimental effects of incipient defects caused by the forging process. the local accumulation of strain at the surface is well known to be caused by the stress concentration effect which acts to locally amplify the stresses and strains in the area surrounding the subsurface incipient crack which in the case of fig. 3b, are ~4 times larger than the structural strains in the surrounding area of the gross cross section. figure 3: critical location in zk60 mg component forged at 300°c highlighting area of thermomechanical defect, shown in fig. 2b as “dic screening region” (a) macro image of component in unloaded state following step 4 (die forging) prior to machining and (b) in-situ dic under peak tensile load at first reversal of fatigue loading. the location of the green crosshairs highlights the peak strain of εmax = 0.8% observed using in-situ dic at peak tensile load during first reversal. fracture behaviour in laboratory test-specimens under fully reversed loading fully reversed stress-controlled, and strain-controlled fatigue testing was done on conventional dog-bone type test-specimens which were extracted from various locations within the as-forged component. the nature of the crack initiation and fracture morphology were investigated to better understand if any 10 mm 10 mm (a) (b) a. gryguć et alii, frattura ed integrità strutturale, 55 (2021) 213-227; doi: 10.3221/igf-esis.55.16 219 significant thermomechanical defects were present and their level of contribution on the nucleation, growth and final failure of the material. shiozawa et al. investigated the dependency of stress amplitude level on the fracture surface morphology of extruded az80 mg, and saw virtually no difference in the surface roughness in the area immediately surrounding the fatigue crack initiation (fci) as well the fatigue crack propagation (fcp) zones for samples which were tested at both high and low stress amplitudes [34]. they also observed cracks which initiated at the surface with a singular origin on the sample, which is largely similar to those types of failures which are presented in this current study. the lack of dependence of the surface roughness surrounding the initiation zone on the nominal stress amplitude forms the basis of comparison for highlighting the presence of incipient defects near the fci. more specifically, since the local stresses at the fci will be amplified due to the stress concentration factor (scf) superimposed by the incipient crack like defect, we can still compare the surface roughness to distinguish material which was fractured due to the applied fatigue load, from material which was poorly fused from a cold-shut type defect which behaves like an incipient crack. fig. 4 illustrates the macroscopic morphology of the fracture surface and topological features with roughness assessment using quantitative lom for a laboratory fatigue test specimen with geometry as per gryguć et al [21]. this specimen was extracted from location #8 within the forged component which was free from these aforementioned macroscopic cold-shut/poor fusion defects, and then subsequently underwent fully reversed strain-controlled fatigue testing with a strain amplitude of εa = 0.8% and failed at 568 cycles. the stabilized peak and valley stresses were +285 mpa and -230 mpa respecitvely. it can be observed in fig. 4a that the fci location is in the upper right-hand corner of the image, and that progresses diagonally across the sample cross section. furthermore, the roughness observed in the direction parallel with the crack growth direction highlighted by the red line in fig. 4a, is ra = 0.74µm which corresponds well with that which was observed by shiozawa et al in the crack growth zones (yellow zone in fig. 4b) in the fracture surface in az80 extrusion [34]. fig. 4c highlights the roughness profile of the location denoted by the red line in fig. 4a, large macroscopic fatigue striations can be seen which represent large unstable jumps in the crack growth at those locations within the fcp zone. this roughness profile can be thought of as a normalized surface profile to account for curvature or inclination of the surface in order to highlight the features of the surface topography on a more detailed level. figure 4: fracture surface of strain-controlled fatigue test specimen extracted from location #8 of az80 mg forged component (a) macroscopic view of fracture surface, (b) quantative lom of fracture surface to highlitght macroscopic topological features (c) roughness profile of section a in the fatigue crack growth area of fracture surface with an average surface roughness of ra = 0.74. a. gryguć et alii, frattura ed integrità strutturale, 55 (2021) 213-227; doi: 10.3221/igf-esis.55.16 220 fig. 5 illustrates the fracture surface of a fatigue specimen extracted from location #3 of the forged component of which underwent stress-controlled fatigue testing at a fully-reversed stress amplitude of 160 mpa. the specimen gauge section was intentionally located in the region within the component which had a high propensity for cold-shut/poor fusion defects, in order to benchmark the material behaviour relative to other areas within the component with similar thermomechanical history but without these persistent forging defects. this location was identified to also be the critical area of concern in fatigue testing of the full-scale component, and consistently showed evidence of these persistent forging defects originating from a fold line in forging flash fronts that was partially/poorly fused together during the die forging process. this defect will then act as an incipient crack if there is not favourable local temperature and pressure to facilitate fusion of this aforementioned fold line during the die-forging process. fig. 5b illustrates a detailed view of the secondary cracks in the vicinity of the fci. the proportion of cross sectional area for the final fracture region is ~41%, for reference the bulk forging properties (free of forging defects) spatially vary depending on the local thermomechanical history, and thus a range of σuts between ~328-364 mpa is typical. figure 5: fracture surface of stress-controlled fatigue test specimen extracted from location #3 of an az80 mg forged component (forged at 300°c, σamp = 160 mpa, failure after 46,428 cycles) (a) macroscopic view of fracture surface and (b) detailed view of secondary crack at fci location. figure 6: fracture surface of stress-controlled fatigue test specimen extracted from location #13 of an az80 mg forged component (forged at 300°c, σamp = 160 mpa, failure after 282,092 cycles). fig. 6 illustrates the fracture surface of a fatigue specimen extracted from location #13 of the forged component, which is away from the area which had persistent forging defects. the fully reversed fatigue stress amplitude was also 160 mpa, however, this sample exhibited a life which was over 6 times longer than that from location #3. despite location #3 and #13 having slightly varying thermomechanical histories, this variation in life between the two locations clearly illustrates the detrimental effect that the forging defects have on the fatigue properties of the forged material. furthermore, the authors are cognizant of the (a) (b) fci a. gryguć et alii, frattura ed integrità strutturale, 55 (2021) 213-227; doi: 10.3221/igf-esis.55.16 221 stochastic nature of fatigue, however this observation is supported by the final fracture region being ~26% in the sample extracted from location #13, which agrees well with the degraded strength (and associated fatigue performance) observed in location #3 in the vicinity of the defect. mackie et al. observed a similar detrimental effect to the strength of direct-chill cast az80 mg when comparing defect free material to those with high intermetallic particle density and entrained oxide films under monotonic loading [35]. figure 7: fracture surface of az80 mg forged component after full-scale service loading, with failure occurring at 41% of target durability lifespan. (a) global fracture surface morphology (b) sem image of the fci location (c) detailed sem image of area surrounding the left hand side fci #1 location, highlighting oxides and graphite particles that were entrained subsurface during the forging process. fracture behaviour in full-scale component under representative service loading a multi-scale characterization approach was utilized to develop a microstructural based link between the fatigue and fracture behaviour of forged magnesium laboratory style fatigue test specimens and representative durability testing of full-scale components. the transition between the continuum and component length scales helps to illustrate the combined effects of size, loading protocol, and loading multiaxiality has on the detrimental impact of microstructural defects on the fatigue response of forged magnesium alloy. the representative service loading is composed of alternate blocks (low and high intensity) of constant amplitude non-zero mean bi-axial loading which induce an equivalent fatigue damage to the durability requirement of the component in service. in the test apparatus, the load input and constraints imposed on the component replicate the physical configuration in service, and as such, the alternate low and high intensity lateral and longitudinal loading blocks result in structurally representative deformation modes which induce varying levels of stress multiaxiality depending upon the location within the component. as there is no “gauge section” of the sample as in the typical fatigue test specimen, at the component level, critical location which is prone to fatigue failure results from a combination of factors, firstly, the high levels of local cyclic stresses, which are exacerbated by local stress concentrations induced by geometric features in the component and thermomechanical forging defects. fig. 7 highlights the fracture surface of a forged az80 full-scale component which exhibited failure due to a forging defect at 41% of the target durability lifespan. fig. 7b, illustrates an sem image of the fci location highlighting an underfill defect and entrained graphite particles which were utilized as a lubricant during the forging process. the graphite particles are easily visible in the sem image as they are of high contrast due to their conductive nature and the employed imaging technique. the majority of these graphite particles range in size from 2060µm, with evidence of several being entrained into the material exposed on the fracture surface following failure. the underfill defect is also clearly visible with a depth of ~1.5mm with the fracture initation occuring in the plane of the deepest part of the defect (where the local stress concentration is maximum). fig. 7c is an sem image highlighting the area surrounding the left hand side fci location, further illustrating the abundance of large graphite particles that were entrained subsurface during the forging process. furthermore, evidence of several oxide films were identified as well from their chemical compoisition as well as their lack of contrast and their film like morphology. the presence of these large graphite particles in the immediate vicinity of the fci forms the second portion of the justification for the observed failure location, as these brittle particles act as local stress concentrations within the poorly fused mateiral for which a. gryguć et alii, frattura ed integrità strutturale, 55 (2021) 213-227; doi: 10.3221/igf-esis.55.16 222 fatigue cracks will nucleate more easily. this agrees well with mackie et al. whom investigated the effect of oxide films on dc cast az80 mg alloy and found them to have an embrittling effect, with approximatley half the ductility of the defect free material, which is largely similar to the influence of graphite particles which act to embrittle the material in the current study [35]. further supporting these observations, the second fci location displayed similar initiation morphology, also with large and numerous graphite particles in the vicinity of the crack nucleation location. the size and morphology of these graphite particles as well as their subsurface distribtution can have a profound effect upon the smaller secondary cracks, several of which can be observed in fig. 7b between the fci#1 and #2. the location of these secondary cracks also corresponded with graphite particle contamination, albeit smaller in size and less numerous. figure 8: optical and sem images of the fracture surface of zk60 mg forged component after full-scale service loading, with failure occurring at 184% of target durability lifespan highlighting (a) global fracture surface morphology (b) optical image of the fci location, and (c) sem image of the same fci location with eds chemistry. similar observations can be made on another forged mg component, which underwent identical fatigue loading, yet had a different forging defect intensity at the critical location. fig. 8 illustrates the fracture surface morphology of a zk60 mg forged component after a failure which occurred at 184% of the target durability lifespan. the forging defect intensity, which can be described as a combination of the geometric defects (such as underfill) and thermomechanical defects (such as cold-shut/poor fusion) and embrittling particulate contamination is less significant in this particular forged component (in comparison with the previous forging discussed in fig. 7). although the two mg alloys are different (az80 vs. zk60), their defect free fatigue properties are very similar (for the processing conditions of these two forgings which were both 300°c and a rate of 2.1 4.2 mm/sec) [21,22,36]. the component with a lower forging defect intensity exhibited almost a 4.5x longer life than the one with a higher defect intensity. this agrees well with the degradation in life factor of ~6x that was observed in the laboratory style specimens which were contrasting defect free to high intensity forging defect fatigue response. at the larger scale of the full-scale component the comparison is between a high and low intensity forging defect, and thus the observation of a degradation factor that is slightly lower is reasonable. furthermore, the laboratory style specimens which underwent fully reversed strain-controlled uniaxial loading nominally had little to no strain gradient within the gauge section of the sample, compared to the complex three dimensional shape and variable amplitude multiaxial loading at the full-scale component level. fig. 8b illustrates a detailed optical image of the fci location, which shows no evidence of a geometric underfill defect, multiple fci sites or secondary cracking at the surface. it does however, show evidence of thermomechanical poor fusion defects located ~0.5mm subsurface. further investigation under sem with eds highlighted that dispersed throughout the poor fusion defect is a large zone of graphite contamination with entrained graphite particles (similar to those in fig. 7c) albeit smaller in size and entrained deeper subsurface. this type of defect morphology, although still acts to degrade fatigue performance, is not as detrimental as the high intensity forging defects previously discussed. interesting to note however is the location of fatigue crack initiation is in the same general a. gryguć et alii, frattura ed integrità strutturale, 55 (2021) 213-227; doi: 10.3221/igf-esis.55.16 223 location within the component as the high intensity forging defect case, however in-situ screening measurements which monitored the nucleation and growth of these defect induced cracks revealed multiple critical locations which had high propensity for failure. fig. 9 illustrates the evolution of axial strain fields at the surface of a zk60 mg component that was forged at 300°c at peak tensile load, which were computed using digital image correlation (dic) with the axial direction being parallel to the direction of crack opening. fig. 9a illustrates the strain field at the very first tensile reversal peak of the representative service loading, with no obvious incipient cracks being evident. the evolution of the strain field can be observed through fig. 9b and fig. 9c which were captured at the peak of the tensile reversal at 50% and 150% of the target life respectively. the location of peak axial strain is denoted by the green crosshairs shown in each corresponding figure. the peak axial strain at this location was computed in the axis parallel with the crack opening direction and has magnitudes of (a) εaxial = 0.39% in the first reversal, (b) εaxial = 0.48% at 50% of the target life, and (c) εaxial = 1.96% at 150% of the target life. figure 9: axial strain fields computed using digital image correlation (dic) in the direction of crack opening in a zk60 mg component that was forged at 300°c under peak tensile load at (a) 1st cycle and (b) 50% and (c) 150% of target life during variable amplitude fatigue testing (representative service loading). the location peak strain in the image is denoted by the green cross-hairs in the image. the scale for axial strain is shown on the right with areas with high tensile strain being shown in red and those with high compressive strain being shown in blue. figs. b and c show evidence of nucleation and growth of these incipient crack defects with strain accumulating along planes that are perpendicular to the bending induced alternating axial strains which form a significant portion of the cyclic damage mechanism for forged mg alloys under multiaxial loading [21,22,36]. these incipient crack defects manifest themselves as a local accumulation of strain (indicated by the red needle like elliptical zones) at the surface of the component during the peak of the tensile reversal as that is where the largest distance from the neutral axis of bending occurs. this high strain gradient local to this strain accumulation is further amplified by the fact that the resistance of the subsurface incipient crack to tensile stresses is lower than the surrounding material. the major axis of these incipient cracks increases in length over time as the strain field evolves throughout the duration of the fatigue loading as the forging defect amplifies the local stresses and accelerates the cyclic damage mechanism. this major axis of the red needle like elliptical zones can be roughly correlated to the fatigue crack size within the material, its morphology can also be linked to the shape and evolution of the crack surface. this can be observed in fig. 9b which was the first screening interval which the first crack was detected (at 50% of the target life), where evidence of incipient crack nucleation is shown in the region denoted by the green crosshairs, with no other “physically small” cracks being observed in this critical location in that particular life range [37]. however, fig. 9c illustrates how the growth of the crack evolves at 150% of the target life, as well as a new incipient crack which has developed. within the context of this novel imaging technique, the fatigue indicator parameter (fip) can be considered to be the presence of this inhomogeneous strain accumulation (representing the nucleation of an incipient crack) within the critical region of interest. the usefulness of this fip which has been facilitated by the employed dic imaging technique is the fact that it is a non a. gryguć et alii, frattura ed integrità strutturale, 55 (2021) 213-227; doi: 10.3221/igf-esis.55.16 224 contact in-situ parameter that can be measured with good sensitivity to cracks induced by both surface and subsurface defects, something that is not readily feasible with other more conventional crack monitoring techniques such as optical microscopy, x-ray scanning, and die-penetrant. furthermore, the efficacy of this technique is further enhanced as the measurement is conducted at peak tension, which effectively amplifies the strain gradient in the area affected by the notch induced stress concentration. currently, computed tomography (ct) has been effective at characterizing the size and morphology of both internal defects as well as deformation activity at very high resolutions within mg material, however it is not practical for the larger than specimen level length scales associated with the component level test investigated here [35,38,39]. furthermore, the local stress state within the critical area of the full-scale component can be difficult to replicate in an in-situ ct measurement as scaling down the specimen size poses practical constraints in both the loading, as well as size effect induced defect related stress concentrations on the macroscopic fatigue response. the eventual failure which was illustrated in the fracture surface in fig. 8 occurred in the 2nd location of incipient crack nucleation, identified by the green crosshairs in fig. 9c. the employed technique was effective in identifying the nucleation and propagation of incipient cracks within a mg component which originated from forging defects that were both very high intensity (as shown in fig. 3) as well as comparatively low intensity (fig. 8, fig. 9) even when the origin of the forging defect is subsurface. the fip of inhomogeneous strain accumulation proved to be effective in identifying these critical locations and tracing their evolution over time through periodic screening intervals of the full-scale component. this technique is quite effective in identifying physically small cracks at the component length scale, as well as assessing the influence of forging defects upon the crack incubation and microstructurally small crack growth stages in mg alloys [37]. conclusions he microstructural origins of premature fatigue failures were investigated on a variety of forged components manufactured from az80 and zk60 magnesium, both at the test specimen level and the full-scale system level. the effect of thermomechanical processing defects due to forging of a physical full-scale component were characterized and quantified using a variety of techniques. at the fullscale component level, the fatigue and fracture behaviour under combined structural loading was also characterized for a number of forged components with varying levels of intrinsic thermomechanical processing defects. a multi-scale characterization approach was utilized to develop a microstructural based link between the fatigue and fracture behaviour of forged magnesium laboratory style fatigue test specimens and representative durability testing of full-scale components. through combination of qualitative and quantitative observations regarding the fracture behaviour of forged mg components an effective fatigue indicator parameter (fip) was identified. based on these results the following conclusions can be drawn: 1. for the mg forging investigated here, the forging defect intensity can be described as a combination of the geometric defects (such as underfill) and thermomechanical defects (such as cold-shut/poor fusion) and embrittling particulate contamination all of which are detrimental to fatigue life. 2. in fully reversed stress-controlled fatigue of forged az80 mg at the specimen length scale, the presence of a high intensity forging defect had the detrimental effect of reducing the fatigue life by more than 6 times at a stress amplitude of 160 mpa relative to the defect free material. 3. at the component level, the failure was governed by intrinsic forging defects which were present to some degree in all of the investigated components. in multiaxial representative service loading at the component length scale, the difference in life between a zk60 mg component with a high and (comparatively) low intensity forging defect was found to be ~4.5 times, with the defects that were larger and closer in proximity to the surface being more detrimental to fatigue. t a. gryguć et alii, frattura ed integrità strutturale, 55 (2021) 213-227; doi: 10.3221/igf-esis.55.16 225 4. a novel in-situ non-contact approach (utilizing digital-image correlation) was utilized to detect presence of inhomogeneous strain accumulation forming the basis for a fip which was effective in identifying both surface and subsurface forging defects in mg components. 5. under multiaxial representative service loading, the nucleation and growth of incipient cracks induced by forging defects are characterized by local strain accumulating along planes that are perpendicular to the principal strains which dominate the cyclic damage mechanism in forged az80 and zk60 mg components. acknowledgements he financial support of the natural sciences and engineering research council of canada (nserc) through the automotive partnership canada (apc) under apcpj 459269-13 grant with contributions from multimatic technical centre, ford motor company, and centerline windsor are acknowledged. the authors would also like to acknowledge j. mckinley from canmetmaterials for forging trials. references [1] papenberg, n.p., gneiger, s., weißensteiner, i., uggowitzer, p.j., pogatscher, s. (2020). mg-alloys for forging applications-a review, materials (basel)., 13(4), pp. 1–63, doi: 10.3390/ma13040985. [2] ovsyannikov, b. v. (2007). die-forged disks for automobile wheels in magnesium alloys. magnesium: proceedings ofthe 7th international conference magnesium alloys and their application, pp. 352–356. [3] gryguc, a., shaha, s.k., behravesh, s.b., jahed, h., wells, m., williams, b., su, x. (2017). monotonic and cyclic behaviour of cast and cast-forged az80 mg, int. j. fatigue, 104, pp. 136–149, doi: 10.1016/j.ijfatigue.2017.06.038. [4] gryguc, a., shaha, s.k., behravesh, s.b., jahed, h., wells, m., williams, b. (2020). improvement of fatigue properties of az31b extruded magnesium alloy through forging, frat. ed integrita strutt., 53(si: virtual conference on structural integrity), pp. 152–165, doi: 10.3221/igf-esis.53.13. [5] he, h., huang, s., yi, y., guo, w. (2017). simulation and experimental research on isothermal forging with semi-closed die and multi-stage-change speed of large az80 magnesium alloy support beam, j. mater. process. technol., 246, pp. 198–204, doi: 10.1016/j.jmatprotec.2017.03.015. [6] wang, q., zhang, z.m., zhang, x., yu, j.m. (2008). precision forging technologies for magnesium alloy bracket and wheel, trans. nonferrous met. soc. china (english ed., 18(spec. issue 1), pp. s205– s208, doi: 10.1016/s1003-6326(10)60203-8. [7] zhao, x., gao, p., zhang, z., wang, q., yan, f. (2019). fatigue characteristics of the extruded az80 automotive wheel, int. j. fatigue, 132, pp. 105393, doi: 10.1016/j.ijfatigue.2019.105393. [8] yuan, l., zhao, z., shi, w., xu, f., shan, d. (2015). isothermal forming of the large-size az80a magnesium alloy forging with high mechanical properties, int. j. adv. manuf. technol., 78(9–12), pp. 2037–47, doi: 10.1007/s00170-014-6780-9. [9] su, z., wan, l., sun, c., cai, y., yang, d. (2016). hot deformation behavior of az80 magnesium alloy towards optimization of its hot workability, mater. charact., 122, pp. 90–97, doi: 10.1016/j.matchar.2016.10.026. [10] chen, q., zhang, x., lin, j., zhan, h., zhao, z., xie, z., yuan, b. (2019). isothermal closed-die forming process of magnesium alloy upper receiver: numerical simulation and experiments, int. j. adv. manuf. technol., 102(1–4), pp. 685–694, doi: 10.1007/s00170-018-03209-5. [11] gontarz, a., dziubińska, a. (2014). forming of flat parts with ribs from magnesium alloy, aircr. eng. aerosp. technol., 86(4), pp. 356–360, doi: 10.1108/aeat-10-2012-0188. t a. gryguć et alii, frattura ed integrità strutturale, 55 (2021) 213-227; doi: 10.3221/igf-esis.55.16 226 [12] shan, d., xu, w., han, x., huang, x. (2012). study on isothermal precision forging process of rare earth intensifying magnesium alloy, mater. sci. eng. b solid-state mater. adv. technol., 177(19), pp. 1698–1702, doi: 10.1016/j.mseb.2011.10.006. [13] kevorkijan, v. (2003). az80 and zc71/sic/12p closed die forgings for automotive applications: technical and economic assessment of possible mass production, mater. sci. technol., 19(10), pp. 1386– 1390, doi: 10.1179/026708303225007988. [14] moldovan, p., popescu, g., bojin, d., constantinescu, d., pana, m. (2009). improving the fatigue resistance of magnesium alloys for forged parts in automotive industry, metal. int., 14(spec. iss. 2), pp. 23–26. [15] lee, s.i., lee, j.h., park, s.h., park, s.j., yoon, j.h. (2016). static strength test with as-forged controlarm in automobile with mg-al-sn-zn alloy, j. mech. sci. technol., 30(8), pp. 3793–3798, doi: 10.1007/s12206-016-0741-1. [16] deng, l., ren, z., guo, p., jin, j., wang, x., li, j. (2019). precision forming of long-axis forgings with rib-web sections via billet optimization based on flow characteristics, int. j. light. mater. manuf., 2(2), pp. 97–106, doi: 10.1016/j.ijlmm.2019.04.006. [17] yoon, j., lee, s. (2015). warm forging of magnesium az80 alloy for the control arm in an automobile, proc. inst. mech. eng. part d j. automob. eng., 229(13), pp. 1732–1738, doi: 10.1177/0954407014567909. [18] yoon, j., lee, j. (2015). process design of warm-forging with extruded mg-8al-0.5zn alloy for differential case in automobile transmission, int. j. precis. eng. manuf., 16(4), pp. 841–846, doi: 10.1007/s12541-015-0110-5. [19] gryguc, a., shaha, s.k., behravesh, s.b., jahed, h., wells, m., williams, b. (2017). compression behaviour of semi-closed die forged az80 extrusion, charact. miner. met. mater., pp. 361–369, doi: 10.1007/978-3-319-51382-9_39. [20] gryguc, a., behravesh, s.b., shaha, s.k., jahed, h., wells, m., williams, b., su, x. (2018). low-cycle fatigue characterization and texture induced ratcheting behaviour of forged az80 mg alloys, int. j. fatigue, 116, pp. 429–438, doi: 10.1016/j.ijfatigue.2018.06.028. [21] gryguć, a., behravesh, s.b., shaha, s.k., jahed, h., wells, m., williams, b., su, x. (2019). multiaxial cyclic behaviour of extruded and forged az80 mg alloy, int. j. fatigue, 127, pp. 324–337, doi: 10.1016/j.ijfatigue.2019.06.015. [22] gryguć, a., karparvarfard, s.m.h., roostaei, a., toscano, d., shaha, s., behravesh, b., jahed, h. (2020).on the load multiaxiality effect on the cyclic behaviour of magnesium alloys. magnesium technology 2020, pp. 151–159. [23] gryguc, a., behravesh, s.b., jahed, h., wells, m., williams, b., su, x. (2020). multiaxial fatigue and cracking orientation of forged az80 magnesium alloy, procedia struct. integr., 25(1st virtual conference on structural integrity-vcsi1), pp. 486–495, doi: 10.1016/j.prostr.2020.04.055. [24] kurz, g., swiostek, j., beaven, p.a., letzig, d. (2018). die forging of magnesium materials, 2008(724). [25] gryguc, a., jahed, h., williams, b., mckinley, j. (2015). magforge – mechanical behaviour of forged az31b extruded magnesium in monotonic compression, mater. sci. forum, 828–829, pp. 291–297, doi: 10.4028/www.scientific.net/msf.828-829.291. [26] gryguc, a., shaha, s.k., jahed, h., wells, m., williams, b., mckinley, j. (2016). tensile and fatigue behaviour of as-forged az31b extrusion, frat. ed integrita strutt., 10(38), pp. 251–258, doi: 10.3221/igf-esis.38.34. [27] gryguć, a. (2019).fatigue of forged az80 magnesium alloy. university of waterloo. [28] roostaei, a.a., jahed, h. (2016). role of loading direction on cyclic behaviour characteristics of am30 extrusion and its fatigue damage modelling, mater. sci. eng. a, 670, pp. 26–40, doi: 10.1016/j.msea.2016.05.116. [29] yu, x., li, y., li, l. (2015). fracture mechanism of az31 magnesium alloy processed by equal channel angular pressing comparing three point bending test and tensile test, eng. fail. anal., 58, pp. 322–335, a. gryguć et alii, frattura ed integrità strutturale, 55 (2021) 213-227; doi: 10.3221/igf-esis.55.16 227 doi: 10.1016/j.engfailanal.2015.04.020. [30] orozco-caballero, a., lunt, d., robson, j.d., quinta da fonseca, j. (2017). how magnesium accommodates local deformation incompatibility: a high-resolution digital image correlation study, acta mater., 133, pp. 367–379, doi: 10.1016/j.actamat.2017.05.040. [31] prasad, n.s., naveen kumar, n., narasimhan, r., suwas, s. (2015). fracture behavior of magnesium alloys role of tensile twinning, acta mater., 94, pp. 281–293, doi: 10.1016/j.actamat.2015.04.054. [32] qian, l.f.v., roostaei, a.a., dighrasker, u., glinka, g., jahed, h. (2019). notch plasticity and fatigue modelling of az31b-h24 magnesium alloy sheet, sae tech. pap. ser., 1, pp. 1–11, doi: 10.4271/2019-01-0530. [33] hawryluk, m., jakubik, j. (2016). analysis of forging defects for selected industrial die forging processes, eng. fail. anal., 59, pp. 396–409, doi: 10.1016/j.engfailanal.2015.11.008. [34] shiozawa, k., kashiwagi, t., murai, t., takahashi, t. (2010). fatigue behaviour and fractography of extruded az80 magnesium alloys in very high cycle regime, procedia eng., 2(1), pp. 183–191, doi: 10.1016/j.proeng.2010.03.020. [35] mackie, d., robson, j.d., withers, p.j., turski, m. (2015). characterisation and modelling of defect formation in direct-chill cast az80 alloy, mater. charact., 104, pp. 116–123, doi: 10.1016/j.matchar.2015.03.033. [36] karparvarfard, s.m.h. (2020). characterization and modeling of forged zk60 mg alloys under quasistatic and fatigue loadings, univ. waterloo, pp. 1–247. [37] lugo, m., jordon, j.b., solanki, k.n., hector, l.g., bernard, j.d., luo, a.a., horstemeyer, m.f. (2013). role of different material processing methods on the fatigue behavior of an az31 magnesium alloy, int. j. fatigue, 52, pp. 131–143, doi: 10.1016/j.ijfatigue.2013.02.017. [38] jung, k.h., lee, s., kim, y.b., ahn, b., kim, e.z., lee, g.a. (2013). assessment of zk60a magnesium billets for forging depending on casting methods by upsetting and tomography, j. mech. sci. technol., 27(10), pp. 3149–3153, doi: 10.1007/s12206-013-0835-y. [39] jiang, s., jia, y., wang, x. (2020). in-situ analysis of slip transfer and heterogeneous deformation in tension of mg-5.4gd-1.8y-1.5zn alloy, j. magnes. alloy., pp. 1–12, doi: 10.1016/j.jma.2020.01.002. microsoft word numero_57_art_08_3059 r. n. da cunha et alii, frattura ed integrità strutturale, 57 (2021) 82-92; doi: 10.3221/igf-esis.57.08 82 evaluation of the behaviour of reinforced concrete beams repaired with glass fibre reinforced polymer (gfrp) using a damage variable rafael nunes da cunha, kevin mendonça oliveira, antônio gabriel lisboa rego brito, camila de sousa vieira, david leonardo nascimento de figueiredo amorim laboratory of building materials and structures, post-graduation programme in civil engineering, department of civil engineering, federal university of sergipe, são cristóvão, brazil rafael.cunha@ctec.ufal.br, http://orcid.org/0000-0003-2503-6758 kevin.zero@hotmail.com; http://orcid.org/0000-0002-1685-3636 gabriel.lisboa.eng@gmail.com; http://orcid.org/0000-0002-2075-3208 milavieira@gmail.com, http://orcid.org/0000-0002-5371-191x davidnf@academico.ufs.br, http://orcid.org/0000-0002-9233-3114 abstract. the use of fibre reinforced polymers (frp) for increasing the strength of reinforced concrete (rc) structures became a usual method. frp presents easy application and demands low space and provide significant strength increase. usually, the decision for frp use is made in terms of applied loads and deflections. however, such quantities can vary significantly depending on the characteristics of the structural element e.g. span, effective depth and concrete resistance. therefore, this paper aims to present an alternative control variable to analyse the behaviour of rc beams repaired with glass fibre reinforced polymer (gfrp), called damage. such damage variable accounts for concrete cracking and it was experimentally measured before and after the application of gfrp. note that the application of gfrp increased the ultimate load for all repaired beams. the damage values of such beams also increased when collapse was reached. furthermore, it was observed that the collapse mechanism shifted to shear and did not occurred the failure of the gfrp. keywords. glass fibre reinforced polymer; repair; reinforced concrete beams; damage. citation: cunha, r. n., oliveira, k. m., brito, a. g. l. r., vieira, c. s., amorim, d. l. n. f., evaluation of the behaviour of reinforced concrete beams repaired with glass fibre reinforced polymer (gfrp) using a damage variable, frattura ed integrità strutturale, 57 (2021) 82-92. received: 05.04.2021 accepted: 19.05.2021 published: 01.07.2021 copyright: © 2021 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. introduction he necessity of strengthening or repair of reinforced concrete (rc) structures can emerge of its natural deterioration, as well as changes of loading due to alteration of the structure use. structural strengthening consists in intervention at an existing structure, increasing its loading capacity before reaching its limit state, while repair is the t https://youtu.be/kanvgkutylk r. n. da cunha et alii, frattura ed integrità strutturale, 57 (2021) 82-92; doi: 10.3221/igf-esis.57.08 83 reestablishment of use and security of a previously damaged structure. rc structures degrade over time due to multiple causes, from natural aging to accidents, even due to design errors. the most apparent symptoms of problems in rc structures are cracks, deformations, exposition and corrosion of the steel bars. the methods of strengthening and repair of reinforced concrete structures depend on the accurate analysis of the causes that made them necessary and the detailed study of the produced effects. after this definition, the choice of the appropriate technique is made, including the materials and equipment to be used [1]. traditional techniques of structural strengthening, among which the increase of the cross section and the use of metallic profiles stands out, present disadvantages such as the increase of the structure dead load, change in stiffness, and the need to handle heavy metal components [2]. in order to circumvent such disadvantages, new strengthening and repair techniques were studied and created, some of which use composite materials which have a high strength-to-weight ratio, among other desirable properties [3-7]. one of the most applied strengthening strategies is the use of fibres that can be of different materials e.g. steel and glass. the fibres may be used in the concrete mixture step, providing higher resistance and ductility [8-9]. furthermore, fibre reinforced polymers (frp) may be used to repair structural elements that suffered total or partial collapses [10]. choobbor et al. [11] evaluated the bending performance of reinforced concrete beams strengthened with hybrid carbon and basalt fibre reinforced polymer (cfrp/bfrp) composite sheets. nine beams were tested with different combinations of cfrp and bfrp sheets and the test results indicated clear improvements in the load-carrying capacity and ductility of the strengthened specimens. an experimental investigation was conducted by ali et al. [12] to examine the flexural capacity of continuous reinforced concrete beams with three spans strengthened or repaired by bonding cfrp or glass fibre reinforced polymers (gfrp) sheets. experimental tests with monotonic loading were carried out by varying damaged level of the beams, composite material type and strengthening thickness. the results showed that the ultimate bending moment of the beam can be improved. a study of the behaviour of reinforced concrete beam-column joints repaired with externally bonded frp or fibre reinforced cementitious matrix (frcm) composites were made by faleschini et al. [13]. concrete specimens suffered significant damage, then were repaired. the same loading history was applied to the repaired specimens to identify the contribution of the externally-bonded composites to the overall behaviour of the repaired specimens. usually, the variables controlling the decision-making process for repair or strength structural elements are, among others, applied loads, bending moments, shear forces and deflections. the main issue is that those quantities vary significantly for each practical engineering problem. as an alternative, the lumped damage mechanics (ldm) defines a damage variable that characterises the concrete cracking [14]. therefore, it is possible to affirm that the same damage value means collapse for a rc beam in conventional buildings and bridges. ldm models were suitably developed and applied for rc structures in several conditions, such as buildings under seismic loads [15-19], tunnel linings [20-22] and even impact loaded beams [23-25]. in this paper, the behaviour of reinforced concrete beams pre-loaded with different ultimate load ratios and repaired with glass fibre reinforced polymer is investigated, using such damage variable. the repaired beams were subjected to a cyclic flexural test to assess the influence of the glass fibre fabric on ultimate strength, maximum damage and failure mode. experimental programme he four reinforced concrete beams utilised in the experiments were designed to collapse by bending moment. the beams cross section dimensions are 10 cm of base and 15 cm of height, while its total length is equal to 70 cm and the span (distance between supports) is 60 cm. longitudinal reinforcement is comprised of two steel bars with 10 mm of diameter, which represents area of steel equal to 1.57 cm2, and yield stress of 500 mpa. transversal reinforcement is formed by steel stirrups of yield stress of 600 mpa and 5.0 mm of diameter, which is equivalent of 2.12 cm2/cm of area of steel. fig. 1 shows the reinforcement of one of the beams. the cement used to manufacture the beams was cp ii z-32 (portland cement composed with pozzolanic materials and compressive strength at 28 days equal to 32 mpa) from a brazilian brand whose specific mass is 3.03 g/cm³ determined according to technical standard nbr 16605 [26]. tab. 1 presents the aggregates characterisation. one of the casted beams is experimented up to collapse and the other ones were reinforced with unidirectional glass fibre fabric vew130 (fig. 2), after certain ultimate load ratios. such reinforcement was manufactured in the usa and it was applied with a brazilian brand epoxy resin. the data of the glass fibre, provided by the manufacturer, is described in tabs. 2, 3 and 4. the dosage of the concrete mixture followed the aci/abcp method [31], aiming to obtain a characteristic compressive strength (fck) equal to 30 mpa. thus, was adopted the following proportion of cement, sand, gravel 0 and gravel 1: 1:2.21:1.30:1.30. the water-cement ratio was 0.52. the result of the slump test for the mixture was 120 mm, measured t r. n. da cunha et alii, frattura ed integrità strutturale, 57 (2021) 82-92; doi: 10.3221/igf-esis.57.08 84 according to the technical standard nbr nm 67 [32]. in addition to the beams, two specimens of 200 mm of height and 100 mm of diameter were moulded to determine the compressive strength of concrete in accordance with the technical standards nbr 5738 [33] and nbr 5739 [34]. the four beams were demoulded 24 hours after casting and cured submerged during 28 days. after curing, the reference beam (rb) was subjected to a cyclic 3-point bending test with displacement control (fig. 3), with test velocity of 1 mm/s. in order to obtain the maximum strength, the beam was loaded until to rupture, in 14 loading cycles. then, on the remaining three beams, loads equivalent to 100% (beam #1), 80% (beam #2) and 60% (beam #3) of the maximum force were applied, with 7, 5 and 5 loading cycles, respectively. the tests were performed with universal testing machine emic/instron model dl 2000. figure 1: reinforcement of the beam. aggregate characteristic results technical standard sand specific mass (g/cm³) 2.64 nbr nm 52 [27] maximum diameter (mm) 4.8 nbr nm 248 [28] fineness modulus 2.69 nbr nm 248 [28] gravel 0 specific mass (g/cm³) 2.65 nbr nm 53 [29] maximum diameter (mm) 9.5 nbr nm 248 [28] gravel 1 specific mass (g/cm³) 2.65 nbr nm 53 [29] maximum diameter (mm) 19.0 nbr nm 248 [28] table 1: aggregates characterisation. figure 2: unidirectional glass fibre fabric. property results density (g/cm³) 1.85 fibre percentage (%/peso) 69 thickness (mm) 0.02 table 2: physical properties of fibreglass [30]. r. n. da cunha et alii, frattura ed integrità strutturale, 57 (2021) 82-92; doi: 10.3221/igf-esis.57.08 85 maximum stress results (mpa) longitudinal traction 682.58 longitudinal compression 682.58 transverse traction 220.63 transverse compression 220.63 in-plane shear 103.42 longitudinal bending 689.48 transverse bending 206.84 table 3: resistance of fibreglass [30]. elasticity moduli results (mpa) ex 36.13 ey 11.03 gxy 5.24 ex,bending 34.34 ey,bending 10.48 table 4: elasticity moduli of fibreglass. after the bending tests, the beams were reinforced. initially, a layer of epoxy resin was applied to serve as an interface between the concrete and the glass fibre fabric. after that, the fibre was applied on the entire longitudinal section and, finally, another layer of resin was added (fig. 4). the resin cured after a week and then further tests were made. figure 3: beam during the test. figure 4: glass fibre application. r. n. da cunha et alii, frattura ed integrità strutturale, 57 (2021) 82-92; doi: 10.3221/igf-esis.57.08 86 after the glass fibre reinforcement of the beams, new cyclic 3-point bending tests were made, which were applied 7, 6 and 6 loading cycles in the beams #1, #2 and #3, respectively. this time, all three beams were loaded to collapse in order to visualise its behaviour when compared to the reference beam, which had no fibre-reinforcement. experimental damage measurement he experimental response of the beams can be given by:     pp z d w w (1) where p is the applied load, w is the total deflection, wp is the plastic/permanent deflection that measures the steel reinforcement yielding and z(d) is the current stiffness of the beam (fig. 5), considering concrete cracking, given by:      01z d d z (2) being z0 the initial stiffness, i.e. when the concrete is intact, and d the damage variable which accounts for the concrete cracking. thus, the damage variable can be measured by experiments using the following relation:     0 1 z d d z (3) mathematically, the damage variable is nil if there is no cracks in concrete and tends to one if the beam is about to split in two parts. however, despite this mathematical definition, the collapse is reached for damage values smaller than one [35]. according to lemaitre and chaboche [35], most materials fail for damage values between 0.20 and 0.50. for reinforced concrete beams, the bearing capacity is usually achieved for damage values around 0.60 [14]. such value is defined as ultimate damage (du) and can be calculated by the classic rc theory or experimentally measured. in both cases, such value is associated to the bearing capacity of the element. figure 5: graphical representation of damage measurement. results he cyclic flexural test of the reference beam is presented in fig. 6. the bearing capacity of the beam is 76.62 kn and its ultimate damage is 0.53. the damage for each cycle of the reference beam and the repaired beams #1, #2 and #3 are depicted in fig. 7 in terms of the bending moment at the centre of the beam. t t r. n. da cunha et alii, frattura ed integrità strutturale, 57 (2021) 82-92; doi: 10.3221/igf-esis.57.08 87 before repair, the beam #1 (fig. 8) was loaded up to 76.10 kn and the resulting damage was 0.45. after repair, the beam #1 was loaded up to collapse, which occurred with the applied force of 83.98 kn and the damage at the end of the test was 0.57. beam #2 achieved 0.37 of damage before repair, which consists of 61.01 kn of applied force. when repaired, the beam #2 (fig. 9) reached 86.43 kn of maximum force and 0.52 of measured damage. finally, beam #3 (fig. 10) was loaded up to 46.06 kn and the damage at that point was 0.30. after repaired, such beam presented maximum bearing capacity of 83.98 kn and the damage was 0.50 when the test was concluded. the values of maximum force and damage for all beams are summarised in tab. 5. an important observation during the experiments is that the collapse mechanism of the repaired beams shifted to shear (fig. 11). note that the repaired beams presented similar bearing capacity, which is close to the shear strength of such beams, calculated as fs = 85.54 kn (4) using the brazilian standard code nbr 6118 [36]:       0.27 1 250 ck s ck w f f f b d (4) being bw the basis and d the effective height (10 cm). the behaviour shift is evident for beam #1 since there are cracks at the mid-span characterising flexure failure. these cracks appeared in the pre-loading step i.e. when the beam was without gfrp. then, after repair, such beam presented severe shear cracks (fig. 11). the mid-span cracks at the beams #2 and #3 are not severe, since both were repaired after submitted to loads considerably smaller than the collapse force. however, in these last two beams, the shear cracks occurred as well. figure 6: force-displacement response of the reference beam. figure 7: bending moment and damage values at each cycle. r. n. da cunha et alii, frattura ed integrità strutturale, 57 (2021) 82-92; doi: 10.3221/igf-esis.57.08 88 figure 8: beam #1. figure 9: beam #2. r. n. da cunha et alii, frattura ed integrità strutturale, 57 (2021) 82-92; doi: 10.3221/igf-esis.57.08 89 figure 10: beam #3. beam maximum force before repair (kn) maximum damage before repair maximum force after repair (kn) maximum damage after repair reference 76.62 0.53 \ \ #1 76.10 0.45 83.98 0.57 #2 61.01 0.37 86.43 0.52 #3 46.06 0.30 83.98 0.50 table 5: maximum force and damage values before and after repair. conclusion his paper aimed to investigate the behaviour of reinforced concrete beams, which were repaired with glass fibre reinforced polymer (gfrp), measuring the integrity of the beams with the damage variable. at first, it was obtained the results of displacement and damage for the reference beam (without gfrp), for a comparison with the other ones. the reference beam presented collapse for 0.53 of damage. such value is considered the ultimate damage for these beams i.e. the damage value when the load bearing capacity is reached. the analysed beams were previously loaded with a percentage of the collapse load, obtained in the reference beam, equal to 100% (beam #1), 80% (beam #2) and 60% (beam #3). after the repair using gfrp, these three beams were reloaded up to collapse. note that, for all repaired beams, the ultimate load increased in comparation with the obtained for reference beam, even when preloaded with 100% of its strength. besides that, when analysing the failure mode, it is possible to observe that the collapse mechanism of the repaired beams shifted to shear, without occurring the failure of the gfrp. the damage values for the repaired beams varied from 0.50 (beam #3) to 0.57 (beam #1). such range is near to values considered as collapse for rc beams without frp. however, since those beams were repaired by gfrp and the collapse mechanism shifted to shear, further studies are needed to determine the ultimate damage at these conditions. for future works, it is recommended to carry out an extensive experimental campaign as an attempt to characterise for which damage values the rc beams should be reinforced/repaired with gfrp and other techniques. t r. n. da cunha et alii, frattura ed integrità strutturale, 57 (2021) 82-92; doi: 10.3221/igf-esis.57.08 90 figure 11: cracking pattern of the repaired beams. acknowledgements he authors acknowledge the financial support from fapitec/capes (fundação de apoio à pesquisa e a inovação tecnológica do estado de sergipe/coordenação de aperfeiçoamento de pessoal de nível superior) for the proef grant for the post-graduation programme in civil engineering of the federal university of sergipe (proec/ufs), to the grant proap 47481/2018-82, provided to the post-graduation programme in civil engineering (proec/ufs) by capes (coordenação de aperfeiçoamento de pessoal de nível superior), to laboratory of building materials and structures (lamce/ufs) and to laboratory of mathematical modelling in civil engineering (lamec/ufs) for the physical support during the development of this work. the first author acknowledges capes for the financial support of his m.sc. studies. the third author acknowledges fapitec for the financial support of his m.sc. studies. the fourth author acknowledges pnpd/capes for the financial support of her postdoc studies. references [1] souza, v.c.m. and ripper, t. (2009). patologia, recuperação e reforço de estruturas de concreto, são paulo, pini. [2] gonzalez-libreros, j.h., sneed, l.h., d’antino, t. and pellegrino, c. (2017). behavior of rc beams strengthened in shear with frp and frcm composites, eng struct, 150, pp. 830-842. doi: 10.1016/j.engstruct.2017.07.084. t r. n. da cunha et alii, frattura ed integrità strutturale, 57 (2021) 82-92; doi: 10.3221/igf-esis.57.08 91 [3] micota, d., isaincu, a. and marsavina, l. (2021). micromechanical modeling of glass fiber reinforced plastic material, materials today: proceedings. doi: 10.1016/j.matpr.2020.12.919. [4] attari, n., amziane, s. and chemrouk, m. (2012). flexural strengthening of concrete beams using cfrp, gfrp, and hybrid frp sheets, constr build mater, 37, pp. 746-757. doi: 10.1016/j.conbuildmat.2012.07.052. [5] ebead, u. a., shrestha, k. c., afzal, m. s., refai, a. e. and nanni, a. (2016). effectiveness of fabric-reinforced cementitious matrix in strengthening reinforced concrete beams, j compos constr, 21(2), pp. 04016084. doi: 10.1061/(asce)cc.1943-5614.0000741. [6] pino, v., nanni, a., arbodela, d. and roberts-wollmann, c. (2016). repair of damaged prestressed concrete girders with frp and frcm composites, j compos constr, 21(3), pp. 04016111. doi: 10.1061/(asce)cc.1943-5614.0000773. [7] ajwad, a., aqdas, a., khan, m.a., abbas, a. and baig, z. (2019). using carbon fibre reinforced polymer strips for recuperation of originally fissured concrete beams, pak j e t, 2(1), pp. 36-40. doi: 10.51846/pakistan%20j%20engg%20&%20tech.v2i1. [8] akbari, j. and abed, a. (2020) experimental evaluation of effects of steel and glass fibers on engineering properties of concrete: engineering properties of concrete, frattura ed integrità strutturale, 14(54), pp. 116-127. doi: 10.3221/igf-esis.54.08. [9] triantis, d., tsaousi, d. k., stavrakas, i., pasiou, e. d., douvis, p. and kourkoulis, s. k. (2020). electric and acoustic activity in notched fiber-reinforced concrete beams under three-point bending. materials today: proceedings, 32, 148155. doi: 10.1016/j.matpr.2020.03.785.skype [10] carpinteri, a., lacidogna, g. and manuello, a. (2007). an experimental study on retrofitted fiber-reinforced concrete beams using ae, fracture mechanics of concrete and concrete structures, taylor & francis, london, 2, 1061-1068. [11] choobbor, s.s., hawileh, r.a., abu-obeidah, a. and abdalla, j.a. (2019). performance of hybrid carbon and basalt frp sheets in strengthening concrete beams in flexure, compos struct, 227, pp. 111337. doi: 10.1016/j.compstruct.2019.111337. [12] ali, h., assih, j., and li, a. (2021). flexural capacity of continuous reinforced concrete beams strengthened or repaired by cfrp/gfrp sheets, int j adhes adhes, 104, pp. 102759. doi: 10.1016/j.ijadhadh.2020.102759. [13] faleschini, f., gonzalez-libreros, j., zanini, m.a., hofer, l., sneed, l. and pellegrino, c. (2019). repair of severelydamaged rc exterior beam-column joints with frp and frcm composites, compos struct, 207, pp. 352-363. doi: 10.1016/j.compstruct.2018.09.059. [14] flórez-lópez, j., marante, m.e., picón, r. (2015). fracture and damage mechanics for structural engineering of frames: state-of-the-art industrial applications, engineering science reference. isbn: 978-1466663794. [15] flórez-lópez j. (1993) modelos de daño concentrado para la simulación del colapso de pórticos planos. rev int mét num cálc dis ing., 9(2), pp. 123–139. [16] cipollina, a., lópez-inojosa, a., flórez-lópez, j. (1995). a simplified damage mechanics approach to nonlinear analysis of frames, comput. struct., 54(6), pp. 1113–26, doi: 10.1016/0045-7949(94)00394-i. [17] perdomo, m.e., ramírez, a., flórez-lópez, j. (1999). simulation of damage in rc frames with variable axial forces, earthq. eng. struct. dyn., 28(3), pp. 311–28, doi: 10.1002/(sici)1096-9845(199903)28:3<311::aid-eqe819>3.0.co;2-d. [18] rajasankar j, iyer nr, prasad ap. (2009). modelling inelastic hinges using cdm for nonlinear analysis of reinforced concrete frame structures. comput concr.,6(4), pp. 319–41, doi: 10.12989/cac.2009.6.4.319. [19] teles dvc, cunha rn, amorim dlnf, picón r, flórez-lópez j. (2021). parametric study of dynamic behaviour of rc dual system design with the brazilian standard code using the lumped damage model. j braz soc mech sci, approved paper: forthcoming. [20] amorim, d.l.n.f., proença, s.p.b., flórez-lópez, j. (2013). a model of fracture in reinforced concrete arches based on lumped damage mechanics, int. j. solids struct., 50(24), pp. 4070–9, doi: 10.1016/j.ijsolstr.2013.08.012. [21] amorim, dlnf, proença, s.p.b., flórez-lópez, j. (2014). simplified modeling of cracking in concrete: application in tunnel linings, eng. struct., 70, pp. 23–35, doi: 10.1016/j.engstruct.2014.03.031. [22] brito, t.i.j., santos, d.m., santos, f.a.s., cunha, r.n., amorim, d.l.n.f. (2020) on the lumped damage modelling of reinforced concrete beams and arches, frattura ed integrità strutturale, 54, pp. 1-20, doi: 10.3221/igf-esis.54.01 [23] yang t. -s., wang j. -l. (2010). damage analysis of three-dimensional frame structure suffering from impact. j vib shock, 29(12), pp. 177–180. [24] teles, d.v.c., oliveira, m.c., amorim, d.l.n.f. (2020). a simplified lumped damage model for reinforced concrete beams under impact loads, eng. struct., 205, doi: 10.1016/j.engstruct.2019.110070. [25] oliveira mc, teles dvc, amorim dlnf. (2020). shear behaviour of reinforced concrete beams under impact loads by the lumped damage framework. frattura ed integrità strutturale, 53, pp. 13-25, doi: 10.3221/igf-esis.53.02. r. n. da cunha et alii, frattura ed integrità strutturale, 57 (2021) 82-92; doi: 10.3221/igf-esis.57.08 92 [26] brazilian association of technical standards (abnt). (2017). nbr 16605: portland cement and other powdered material determination of the specific gravity. [27] brazilian association of technical standards (abnt). (2009). nbr nm 52: fine aggregate determination of the bulk specific gravity and apparent specific gravity. [28] brazilian association of technical standards (abnt). (2003). nbr nm 248: aggregates sieve analysis of fine and coarse aggregates. [29] brazilian association of technical standards (abnt). (2019). nbr nm 53: coarse aggregate determination of the bulk specific gravity, apparent specific gravity and water absorption. [30] e-composites. tecido de fibra de vidro unidirecional vew130. available at: http://www.marinecomposites.com.br/wp-content/uploads/datasheets/tecido_de_vidro_vew130.pdf. [31] rodrigues, p. p. f. (1995). parâmetros de dosagem do concreto, são paulo, abcp. [32] brazilian association of technical standards (abnt). (2020). nbr nm 67: fresh concrete slump test. [33] brazilian association of technical standards (abnt). (2016). nbr 5738: concrete procedure for molding and curing concrete test specimens. [34] brazilian association of technical standards (abnt). (2018). nbr 5739: concrete compression test of cylindrical specimens. [35] lemaitre j, chaboche jl (1985). mécaniques des matériaux solides. paris: dunod. isbn: 978-2100013975. [36] brazilian association of technical standards (abnt). (2014). nbr 6118: design of concrete structures procedure. microsoft word 002 plenary berto italy paper f. berto, frattura ed integrità strutturale, 34 (2015) 11-26; doi: 10.3221/igf-esis.34.02 11 focussed on crack paths local approaches for the fracture assessment of notched components: the research work developed by professor paolo lazzarin f. berto university of padova, italy berto@gest.unipd.it abstract. brittle failure of components weakened by cracks or sharp and blunt v-notches is a topic of active and continuous research. it is attractive for all researchers who face the problem of fracture of materials under different loading conditions and deals with a large number of applications in different engineering fields, not only with the mechanical one. this topic is significant in all the cases where intrinsic defects of the material or geometrical discontinuities give rise to localized stress concentration which, in brittle materials, may generate a crack leading to catastrophic failure or to a shortening of the assessed structural life. whereas cracks are viewed as unpleasant entities in most engineering materials, uand v-notches of different acuities are sometimes deliberately introduced in design and manufacturing of structural components. dealing with brittle failure of notched components and summarising some recent experimental results reported in the literature, the main aim of the present contribution is to present a review of the research work developed by professor paolo lazzarin. the approach based on the volume strain energy density (sed), which has been recently applied to assess the brittle failure of a large number of materials. the main features of the sed approach are outlined in the paper and its peculiarities and advantages accurately underlined. some examples of applications are reported, as well. the present contribution is based on the author’s experience over about 15 years and the contents of his personal library. this work is in honor and memory of prof. paolo lazzarin who suddenly passed away in september 2014. keywords. notch stress intensity factors; strain energy density; fracture assessment; fatigue strength. introduction ealing with fracture assessment of cracked and notched components a clear distinction should be done between large and small bodies [1-6]. the design rules applied to large bodies are based on the idea that local inhomogeneities, where material damage starts, can be averaged being large the volume to surface ratio. in small bodies the high ratio between surface and volume makes not negligible the local discontinuities present in the material and the adoption of a multi-scaling and segmentation scheme is the only way to capture what happens at pico, nano and micro levels [4-6]. in this scheme the crack tip has no dimension or mass to speak; it is the sink and source that absorbs and dissipates energy while the stress singularity representation at every level is the most powerful tool to quantify the energy packed by an equivalent crack reflecting both material effect and boundary conditions. this new revolutionary d f. berto, frattura ed integrità strutturale, 34 (2015) 11-26; doi: 10.3221/igf-esis.34.02 12 representation implies also a new definition of mass [4, 6]. the distinction between large and small bodies should ever be considered by avoiding to transfer directly the design rules valid for large components to small ones under the hypothesis that all material inhomogeneities can be averaged [1-6]. keeping in mind the observations above and limiting our considerations to large bodies (i.e. large volume to surface ratio), for which an averaging process is still valid, the paper is addressed to review a volume-based strain energy density approach applied to static and fatigue strength assessments of notched and welded structures [7-14]. the concept of “elementary” volume and “structural support length” was introduced many years ago [15-17] and it states that not the theoretical maximum notch stress is the static or fatigue strength-effective parameter in the case of pointed or sharp notches, but rather the notch stress averaged over a short distance normal to the notch edge. in high cycle fatigue regime, the integration path should coincide with the early fatigue crack propagation path. a further idea was to determine the fatigue-effective notch stress directly (i.e. without notch stress averaging) by performing the notch stress analysis with a fictitiously enlarged notch radius, f, corresponding to the relevant support [15-17]. fundamentals of critical distance mechanics applied to static failure, state that crack propagation occurs when the normal strain [18] or circumferential stress  [19] at some critical distance from the crack tip reaches a given critical value. this “point criterion” becomes a “line criterion” in refs. [20, 21] who dealt with components weakened by sharp v-shaped notches. a stress criterion of brittle failure was proposed based on the assumption that crack initiation or propagation occurs when the mean value of decohesive stress over a specified damage segment d0 reaches a critical value. the length d0 is 2-5 times the grain size and then ranges for most metals from 0.03 mm to 0.50 mm. the segment d0 was called “elementary increment of the crack length”. dealing with this topic a previous paper, ref. [22], was quoted in refs [20, 21]. afterwards, this critical distance-based criterion was extended also to structural elements under multi-axial loading [23, 24] by introducing a non-local failure function combining normal and shear stress components, both normalised with respect to the relevant fracture stresses of the material. dealing with notched components the idea that a quantity averaged over a finite size volume controls the stress state in the volume by means of a single parameter, the average value of the circumferential  stress [25]. for many years the strain energy density (sed) has been used to formulate failure criteria for materials exhibiting both ductile and brittle behaviour. since beltrami [26] to nowadays the sed has been found being a powerful tool to assess the static and fatigue behaviour of notched and un-notched components in structural engineering. different sed-based approaches were formulated by many researchers. dealing here with the strain energy density concept, it is worthwhile contemplating some fundamental contributions [2735]. the concept of “core region” surrounding the crack tip was proposed in ref. [27]. the main idea is that the continuum mechanics stops short at a distance from the crack tip, providing the concept of the radius of the core region. the strain energy density factor s was defined as the product of the strain energy density by a critical distance from the point of singularity [28]. failure was thought of as controlled by a critical value sc, whereas the direction of crack propagation was determined by imposing a minimum condition on s. the theory was extended to employ the total strain energy density near the notch tip [29], and the point of reference was chosen to be the location on the surface of the notch where the maximum tangential stress occurs. the strain energy density fracture criterion was refined and extensively summarised in ref. [30]. the material element is always kept at a finite distance from the crack or the notch tip outside the “core region” where the in-homogeneity of the material due to micro-cracks, dislocations and grain boundaries precludes an accurate analytical solution. the theory can account for yielding and fracture and is applicable also to ductile materials. depending on the local stress state, the radius of the core region may or may not coincide with the critical ligament rc that corresponds to the onset of unstable crack extension [30]. the ligament rc depends on the fracture toughness kic, the yield stress σy, the poisson’s ratio  and, finally, on the ratio between dilatational and distortional components of the strain energy density. the direction of max determines maximum distortion while min relates to dilatation. distortion is associated with yielding, dilatation tends to be associated to the creation of free surfaces or fracture and occurs along the line of expected crack extension [30, 31]. a critical value of strain energy density function (dw/dv)c has been extensively used since 1965 [32-35], when first the ratio (dw/dv)c was determined experimentally for various engineering materials by using plain and notched specimens. the deformation energy required for crack initiation in a unit volume of material is called absorbed specific fracture energy (asfe) and its links with the critical value of jc and the critical factor sc were widely discussed. this topic was deeply considered in refs. [28-30] where it was showed that (dw/dv)c is equivalent to sc/r being sc the critical strain energy density factor and the radius vector r the location of failure. since distributions of the absorbed specific energy w in notched specimens are not uniform, it was assumed that the specimen cracks as soon as a precise energy amount has been absorbed by the small plastic zone at the root of the notch. if the notch is sufficiently sharp, specific energy due to the elastic deformation is small enough to be neglected as an initial approximation [34]. while measurements of the energy f. berto, frattura ed integrità strutturale, 34 (2015) 11-26; doi: 10.3221/igf-esis.34.02 13 in an infinitely small element are not possible, they can be approximated with sufficient accuracy by calculating the fracture energy over the entire fractured cross section of an unnotched tensile specimen [35]. notched components loaded under static loads show that the average asfe decreases with increasing the notch sharpness, with the asfe parameter being plotted as a function of the theoretical stress concentration factor, kt , and the temperature [35]. for a common welded structural steel and kt = 1, the asfe value, obtained by tensile tests, is about 1.0mj/m3 while for values of kt greater than 3.0 a plateau value is visible [35]. depending on the considered welded metal, the plateau approximately ranges between 0.15 and 0.35 mj/m3. these values are not so different from the mean value that characterises the high cycle fatigue strength of welded joints, wc = 0.105 mj/m3 but with reference to a specific control volume [8, 10]. the criterion based on the energy density factor, s, gave a sound theoretical basis to the experimental findings [32-35] and the approach, used in different fields, was strongly supported by a number of researchers [36]. the concept of strain energy density has also been reported in the literature in order to predict the fatigue behaviour of notches both under uniaxial and multi-axial stresses [37-38]. it should be remembered that in referring to small-scale yielding, a method based on the averaged of the stress and strain product within the elastic-plastic domain around the notch was extended to cyclic loading of notched components [39]. in particular in ref. [40] it was proposed a fatigue master life curve based on the use of the plastic strain energy per cycle as evaluated from the cyclic hysteresis loop and the positive part of the elastic strain energy density. the two views, cyclic hysteresis loop concept evaluating the plastic energy for tensile specimens [39, 40] and the criterion evaluating the local accumulated sed near the crack tip [28], although formally different, are strictly connected and both tied to the concept of absorbed specific fracture energy. the averaged strain energy density criterion, proposed in refs [7-14, 41], states that brittle failure occurs when the mean value of the strain energy density over a control volume (which becomes an area in two dimensional cases) is equal to a critical energy wc. the sed approach is based both on a precise definition of the control volume and the fact that the critical energy does not depend on the notch sharpness. such a method was formalised and applied first to sharp, zero radius, v-notches and later extended to blunt uand v-notches under mode i loading [11] and successfully applied to welded joints [10]. the control radius r0 of the volume, over which the energy has to be averaged, depends on the ultimate tensile strength, the fracture toughness and poisson’s ratio in the case of static loads, whereas it depends on the unnotched specimen’s fatigue limit, the threshold stress intensity factor range and the poisson’s ratio under high cycle fatigue loads. the approach was successfully used under both static and fatigue loading conditions to assess the strength of notched and welded structures subjected to predominant mode i and also to mixed mode loading [7-14]. the extension of the sed approach to ductile fracture is possible, with a major problem being the definition of the control volume and the influence of the dilatational and distortional components of the strain energy density. recently, the effect of plasticity in terms of strain energy density over a given control volume has been considered by the present authors, showing different behaviours under tension and torsion loading, as well as under small and large scale yielding [14]. several criteria have been proposed to predict fracture loads of components with notches, subjected to mode i loading [20-21, 42-53]. recently, fracture loads of notched specimens (sharp and blunted u and v notches) loaded under mode i have been successfully predicted, using a criterion based on the cohesive zone model [54-57], and in parallel by applying the local strain energy density [7-14]. the problem of brittle failure from blunted notches loaded under mixed mode is more complex than in mode i loading and experimental data, particularly for notches with a nonnegligible radius, is scarce. the main aim of some recent papers was to generalise the previous results valid for components with blunted notches loaded under mode i, to notched components loaded under mixed mode [58-61]. this generalization is based on the hypothesis that fracture mainly depends on the local mode i and on the maximum value of the principal stress or the strain energy density. the proposal of mode i dominance for cracked plates was suggested first in ref. [62] when dealing with cracked plates under plane loading and transverse shear, where the crack grows in the direction almost perpendicular to the maximum tangential stress in radial direction from its tip. two different methods are used to verify such a hypothesis: the cohesive zone model and the model based on the strain energy density over a control volume [58-60]. both methods allow us to evaluate the critical load under different mixed mode conditions when the material behaviour can be assumed as linear elastic. dealing with the sed approach it is worth noting that the case of pure compression or combined compression and shear, for example, would require a reformulation for the control radius of the volume, r0, and should also take into account the variability of the critical strain energy density wc with respect to the case of uniaxial tension loads. to the best of author’s knowledge, the first contribution that modifies the total strain energy density criterion (beltrami’s hypothesys) to account for the different strength properties exhibited by many materials under pure tension and pure compression uniaxial tests was dated 1926 [63]. dealing with both notched and welded components and summarising the most recent experimental results reported in the literature, the main aim of the present contribution is to present a complete review of the analytical frame of the volume f. berto, frattura ed integrità strutturale, 34 (2015) 11-26; doi: 10.3221/igf-esis.34.02 14 based sed approach together with a final synthesis of more than 1900 experimental data from static and fatigue tests. very different materials have been considered with a control radius, r0, ranging from 0.4 m to 500 m. a wider and complete synthesis of this work can be found in [64]. a summary of the career of prof. paolo lazzarin aolo lazzarin, professor at the university of padova, vicenza (italy), outstanding scientist in theoretical and applied notch mechanics, has passed away on september 14, 2014. paolo lazzarin was born on april 21, 1957 in conegliano near treviso (italy). he was graduated at the university of padova, faculty of mechanical engineering, in 1982 and obtained his phd in ʽmechanical behaviour of materialsʼ at the university of pisa in 1986. in 1992 he became associate professor of ʽmachine designʼ at the university of cassino and, afterwards, at the university of ferrara. since 2000 he has been full professor of ʽmachine designʼ at the university of padova, department of management and engineering in vicenza. in this position, he has presided the master course in mechanical engineering since 2012. paolo lazzarin is the author of about 100 significant scientific articles in renown scientific journals. additionally, he has gained merit in the publication sector as a reviewer on demand of these journals. also, he was a member of the board of the journal ʽfatigue and fracture of engineering materials and structuresʼ since 2002 and became its co-editor in 2012. paolo lazzarin was also the organiser of international conferences which aroused considerable attention – the crack path conference in 2009 and the mesomechanics conference in 2011, both conferences held in vicenza. the appreciation hereafter of paolo lazzarin’s scientific achievements cannot specify the respective collaborators and coauthors because of space restrictions. more than 200 pioneering articles in scientific journals are available, all written together with well-known colleagues or talented disciples. paolo lazzarin’s scientific achievements can be assigned to three areas of notch mechanics: notch stress intensity factors, local strain energy density and fictitious notch rounding. paolo’s scientific career started in the mid-eighties of the last century with bruno atzori as his mentor. his challenge was the mathematical analysis of the stress field at fillet weld toes, modelling them as pointed v-notches for assessment of the fatigue limit of these joints within a worst case scenario. the asymptotic stress distribution ahead of the stress singularity at pointed v-notches was available from williams’ linear-elastic solution. it was later on quantified by means of notch stress intensity factors (nsifs), separating the contribution of the three loading modes (in-plane tensile and shear loading as well as out-of-plane shear loading) to the overall stress distribution ahead of the v-notch tip. the nsifs were derived for weld-like geometries and cross-sectional models of various fillet-welded joints. the scale effect, i.e. the influence of specimen size on the level of the asymptotic stresses is already included in the nsifs. fatigue strength values in terms of the nsif amplitudes dependent on number of loading cycles for fillet-welded joints made of steel or aluminium alloys were presented as a scatterband, evaluating a large body of test results in the open literature. the scatterband widths and the curve gradients were well in agreement with comparable nominal stress relationships in the codes. additionally, a mixed-mode failure criterion in terms of the nsifs was derived. also, the relationship to the standardised structural stress at the wed toe was clarified. the elementary nsif concept for pointed notches has been extended by paolo lazzarin to sharply rounded (blunt) or root-holed v-notches. notch rounding removes the stress singularity, but the asymptotic stress distribution connected with the singularity remains largely unchanged at distances from the notch root larger than one half of the notch radius. it was shown that generalised nsifs can be defined as the governing field parameters. these are related to the maximum notch stresses which constitute the conventional stress concentration factors (scfs). in contrast to the scfs, the generalised nsifs characterise not only the maximum stress at the notch root but the whole stress field in the vicinity of the notch root. the field information is needed for assessing local failure processes, but it is not possible in general to express the fatigue limit of sharply rounded notches solely by critical nsif amplitudes. a remarkable by-product of these efforts were the in-plane and out-of-plane stress field solutions for v-notches with root hole. under certain conditions such as low sheet thickness in lap joints, the radial distance from the slit tip, where the second order approximation of the stresses (inclusive of the t-stress) is appropriate, may be very small, so that higher order approximations are needed. stress equations for the in-plane loading modes at slit tips up to the seventh order have been derived. the conventional loading modes 1, 2 and 3 refer to singular stress fields at v-notches which can be considered as twodimensional (plane or anti-plane). it is presumed that the corresponding nsifs do not vary along the straight notch tip line. at the intersection with lateral free surfaces, an abrupt change of the homogeneous conditions takes place. a complex three-dimensional, generally singular stress state occurs near the intersection point. it may be described by the p f. berto, frattura ed integrità strutturale, 34 (2015) 11-26; doi: 10.3221/igf-esis.34.02 15 applied primary loading mode, locally changed and occasionally superimposed by an induced secondary loading mode. these local coupled effects were analysed by the fe method, using extremely fine meshes near the intersection point. paolo lazzarin has also presented an analytical solution for the v-notch in plates of finite thickness under plane-strain conditions. the linear-elastic nsif concept has been extended by paolo lazzarin to elastic-plastic material behaviour. the stress singularity at pointed notches continues to exist, provided strain hardening occurs. it is described by plastic nsifs with inclusion of plastic strain intensity factors which exist also for non-hardening material behaviour. the theoretical basis is the nonlinear power-law applied to crack tips by hutchinson, rice and rosengreen. the hrr theory was reformulated by paolo lazzarin for application to v-notches. neuber’s nonlinear material law, glinka’s alternative procedure as well as the ramberg‒osgood material law were also considered. a highlight of lazzarin’s derivations is a definite relationship between elastic and plastic nsifs. a uniform analysis of nonlinear notch stress fields was presented based on the totalstrain power-law in comparison to neuber’s different analytical approach. the well-known neuber rule, establishing a simple relationship between the stress and strain concentration factors at elastic-plastically deformed notches, deviates by a factor of 1.0‒2.0 (largest for perfectly-plastic materials) from lazzarin’s solution. the second area of notch mechanics elaborated by paolo lazzarin from 2001 onward is the local strain energy density (sed) concept. since the nsifs represent odd singularities which depend on the notch opening angle, a comparison between the fatigue limits of different weld geometries can only be carried out by using the sed averaged over a small control volume surrounding the point of stress singularity. the averaged sed is always bounded, independent of the notch acuity. the radius of the control volume is understood as a material property which can be determined on a statistical basis evaluating a large body of fatigue test data related to fillet-welded joints of various geometries and dimensions. fatigue strength values in terms of averaged sed amplitudes dependent on number of loading cycles were presented in the form of a scatterband with a width and gradient well in agreement with comparable nominal stress relationships in the codes. the agreement of the parameters just mentioned is resulting from the fact that, in many cases of practical interest, not only the fatigue crack initiation life is correlated with the local sed value but also the total life, provided the major part of the fatigue life can be assigned to microcrack initiation and propagation inside the zone governed by the notch stress singularity. the sed approach for the fatigue assessment of non-codified welded joints, in comparison to alternative local approaches such as nsif, fnr or j-integral, has the advantage that the local sed can easily determined from linearelastic fe models with coarse meshing without major loss in accuracy. the reason is that the nodal point displacements determine directly the sed and not the displacement derivatives. any fe analyst in industry will highly appreciate this feature. a sed-based version of the atzori‒lazzarin diagram correlating notch sensitivity with defect sensitivity related to fatigue loading has been derived. paolo lazzarin has also successfully applied the local sed concept to brittle fractures under monotonic loading, considering especially acrylic glass specimens. the concept was also extended into the elastic-plastic range, to multiaxial fatigue and to blunt notches. the link between the locally averaged sed and rice’s j-integral has been established both for pointed and blunt notches. lazzarin’s last finding in this area was that the j-integrals at the pointed v-notch tip are not identical when modelling the material behaviour by the total-strain power-law and the ramberg‒osgood relationship in comparison. his early death did not allow him to pursue this discrepancy further. the third area of notch mechanics, to which paolo lazzarin contributed substantially, is neuber’s concept of fictitious notch rounding (fnr) combined with radaj’s application to welded joints within a worst case scenario. lazzarin’s idea to use the average linear-elastic sed in a control volume as relevant for fatigue or brittle fracture was stimulated by neuber’s earlier concept to average the linear-elastic stresses over a microstructural support length in the direction of crack initiation. a first comparison between the fatigue limits of typical welded joints estimated according to the two concepts in 2007 was encouraging. in the years thereafter, substantial improvements and extensions of the fnr approach have been achieved. the support factor correlating the fictitious notch radius to the microstructural support length with consideration of the multiaxiality conditions was determined for the in-plane tension and out-of-plane shear loading modes depending on notch opening angle and multiaxial failure criterion. this denotes substantial progress in respect of application to welded joints, because the notch opening angle is a decisive parameter here whereas neuber has neglected this influence. in a further effort, in-plane shear loading was included which necessitates consideration of out-of-bisector crack initiation. paolo lazzarin’s last article in the field of notch mechanics was related to the fnr concept applied to v-notches under f. berto, frattura ed integrità strutturale, 34 (2015) 11-26; doi: 10.3221/igf-esis.34.02 16 mixed-mode in-plane loading conditions. the theoretical derivations and mathematical formulations in this article are of unsurpassable elegance without neglect of the application aspects. they carry on the high quality standard in neuber’s famous book on notch mechanics. figure 1: photo of prof. lazzarin paolo lazzarin’s contributions to theoretical and applied mechanics are of lasting value. they are an indispensable reference for the scientists after him. paolo lazzarin’s scientific achievements were based not only on a profound understanding of continuum mechanics combined with an exceptional talent in applied mathematics, but also on his likeable character. the foremost character trait was warm-heartedness, and his generosity was unsurpassable. he paid full respect to any scientific colleague or disciple, not forgetting emotional uprising where it was justified. scientific questions were always answered without delay and in detail. he was a master in didactic clearness and never forgot to emphasize the historical originators of a concept, a formula or an idea. he has guided many students and young researchers through the confusing multitude of scientific methods and approaches. he shared ideas and knowledge with them as a true friend. some expressions for sed in the control volume ith the aim of clarifying the base of the final synthesis carried out in this paper, this section summarises the analytical frame of sed approach. with reference to the polar coordinate system shown in fig. 2, with the origin located at point o, mode i stress distribution ahead of a v-notch tip is given by the following expressions [65]:     1 1 1 1 1 0 , ,ij ij ij r a r f g r                      (1) where 1>1 and the parameter a1 can be expressed either via the notch stress intensity factor 1k in the case of a sharp, zero radius, v-notch or by means of the elastic maximum notch stress tip in the case of blunt v-notches. in eq. (1) r0 is the distance evaluated on the notch bisector line between the v-notch tip and the origin of the local coordinate system; r0 depends both on the notch root radius r and the opening angle 2 (fig. 2), according to the expression r0 = r[(2)/(2-2)]. the angular functions fij and gij are given in ref. [65]: w f. berto, frattura ed integrità strutturale, 34 (2015) 11-26; doi: 10.3221/igf-esis.34.02 17   1 1 1 1 1 1 1 1 1 1 1 1 1 1 (1 )cos(1 ) cos(1 ) 1 (3 )cos(1 ) (1 ) cos(1 ) 1 1 (1 )sin(1 ) sin(1 ) rr b b r f f f                                                                   (2)     1 1 1 1 1 1 1 1 1 1 1 1 1 1 (1 )cos(1 ) cos(1 ) (3 )cos(1 ) cos(1 ) 4 1 1 1 (1 )sin(1 ) sin(1 ) rr d c b r g q g q g                                                                       (3) the eigenfunctions fij depend only on williams’ eigenvalue,  which controls the sharp solution for zero notch radius [66]. the eigenfunctions gij mainly depend on eigenvalue , but are not independent from . since  < , the contribution of -based terms in eq. (1) rapidly decreases with the increase of the distance from the notch tip. all parameters in eqs.(2,3) have closed form expressions but here, for the sake of brevity, only some values for the most common angles are reported in [65]. under the plane strain conditions, the eigenfunctions fij and gij satisfy the following expressions:  ( ) ( ) ( )zz rrf f f      ( ) ( ) ( )zz rrg g g     (4) whereas    zz zz 0f g   under plane stress conditions. figure 2: notch geometry and coordinate system the sed approach is based on the idea that under tensile stresses failure occurs when cw w , where the critical value wc obviously varies from material to material. if the material behaviour is ideally brittle, then wc can be evaluated by using simply the conventional ultimate tensile strength t, so that 2t / 2cw e . often un-notched specimens exhibit a non-linear behaviour whereas the behaviour of notched specimens remains linear. under these circumstances the stress t should be substituted by “the maximum normal stress existing at the edge at the moment preceding the cracking”, as underlined in ref. [21] where it is also recommended to use tensile specimens with semicircular notches. in plane problems, the control volume becomes a circle or a circular sector with a radius r0 in the case of cracks or pointed v-notches in mode i or mixed, i+ii, mode loading (fig. 3a,b). under plane strain conditions, a useful expression for r0 has been provided considering the crack case [41]: 2 ic 0 (1 )(5 8 ) 4π t k r            (5) if the critical value of the nsif is determined by means of specimens with 20, the critical radius can be estimated by means of the expression: f. berto, frattura ed integrità strutturale, 34 (2015) 11-26; doi: 10.3221/igf-esis.34.02 18 11/( 2 2 )2 1 1c 0 1 c4 (π ) i k r e w           (6) when 2=0, 1ck equals the fracture toughness kic. (a) (b) (c) figure 3: critical volume (area) for sharp v-notch (a), crack (b) and blunt v-notch (c) under mode i loading. distance 0 ( 2 ) / ( 2 2 )r r        . (a) (b) figure 4: critical volume for u-notch under mode i (a) and mixed mode loading (b). distance 0 / 2r r according to refs. [15] and [67]. in the case of blunt notches, the area assumes a crescent shape, with r0 being its maximum width as measured along the notch bisector line (fig. 2c) [11]. under mixed-mode loading, the control area is no longer centred with respect to the notch bisector, but rigidly rotated with respect to it and centred on the point where the maximum principal stress reaches its maximum value [58, 59]. this rotation is shown in figure 4 where the control area is drawn for a u-shaped notch both under mode i loading (fig. 4a) and mixed-mode loading (fig. 4b). the parameter a1 of eq. (1) can be linked to the mode i notch stress intensity factor by means of the simple expression 1 1 2π k a  (7) where k1 assumes the following form according to the definition given in ref.[ 68]:   111 0 2π lim ( , 0) r k r r       (8) f. berto, frattura ed integrità strutturale, 34 (2015) 11-26; doi: 10.3221/igf-esis.34.02 19 in the presence of a notch root radius equal to zero, the distance r0 is also zero, and all -related terms in eq. (1) disappear. it is possible to determine the total strain energy over the area of radius r0 and then the mean value of the elastic sed referred to the area . the final relationship is: 1 2 1 1 1 1 1 04 ( ) i k w e r             (9) where 1 is williams’ eigenvalue and 1k the mode i notch stress intensity factor. the parameter i1 is different under plane stress and plane strain conditions for different values of the poisson’s ratio  [60]. equation (9) was extended to pointed v-notches in mixed, i+ii, mode [7] as well as to cases where mode i loads where combined with mode iii loads [9]. it is important to underline the influence of the poisson’s ratio on the i1 values in the case of sharp notches. for a notch opening angle smaller than 60 degrees, i1 varies strongly from =0.1 to =0.4. this fact confirms the important and not negligible effect of the poisson’s ratio while discussing sharp or quasi-sharp notches in agreement with the effect of this parameter on the kind of singularities, weak or strong, highlighted in ref. [1] in the case of a constrained micro-notch at the front of a free edge macro-crack. in the presence of rounded v-notches it is possible to link the parameter a1 of eq. (1) to the maximum principal stress present at the notch tip: 11 0 1 11 tip r a       (10) where 1 is the parameter already listed in the original paper. by using the elastic maximum notch stress, it is possible to determine the total strain energy over the area  and then the mean value of the sed. when the area embraces the semicircular edge of the notch (and not its rectilinear flanks), the mean value of sed can be expressed in the following form [11]: 2 tip0 1 ( 2 ) ( 2 , ) r w f h r e      (11) where f(2) depend on previously defined parameters    1 22 1 1 1 2π 2 1 q f q                (12) by simply using the definition of the mode i nsif for blunt v-notches [69] a simple relationship between tip and kvr,i can be obtained as follows: 1 1 1 1 1 σ q 1 k 2π r f( 2α) σ r 1 ω q tipv r,i tip           (13) then it is possible to rewrite eq. (11) in a more compact form:   1 2v r,i0 1 2( 1 ) 0 1 ( 2 , ) kr w h r e r       (14) equation (14) will be used to summarise all results from blunt notches (uand v-notches) subjected to mode i loading. f. berto, frattura ed integrità strutturale, 34 (2015) 11-26; doi: 10.3221/igf-esis.34.02 20 as opposed to the direct evaluation of the nsifs, which needs very refined meshes, the mean value of the elastic sed on the control volume can be determined with high accuracy by using coarse meshes [70, 71]. very refined meshes are necessary to directly determined the nsifs from the local stress distributions. refined meshes are not necessary when the aim of the finite element analysis is to determine the mean value of the local strain energy density on a control volume surrounding the points of stress singularity. the sed in fact can be derived directly from nodal displacements, so that also coarse meshes are able to give sufficiently accurate values for it. some recent contributions document the weak variability of the sed as determined from very refined meshes and coarse meshes, considering some typical welded joint geometries and provide a theoretical justification to the weak dependence exhibited by the mean value of the local sed when evaluated over a control volume centred at the weld root or the weld toe. on the contrary singular stress distributions are strongly mesh dependent. the nsifs can be estimated from the local sed value of pointed v-notches in plates subjected to mode i, mode ii or a mixed mode loading. taking advantage of some closed-form relationships linking the local stress distributions ahead of the notch to the maximum elastic stresses at the notch tip the coarse mesh sed-based procedure is used to estimate the relevant theoretical stress concentration factor kt for blunt notches considering, in particular, a circular hole and a u-shaped notch, the former in mode i loading, the latter also in mixed, i + ii, mode [70-71]. other important advantages can be achieved by using the sed approach. the most important are as follows: -it permits consideration of the scale effect which is fully included in the notch stress intensity factor approach -it permits consideration of the contribution of different modes. -it permits consideration of the cycle nominal load ratio. -it overcomes the complex problem tied to the different nsif units of measure in the case of different notch opening angles (i.e crack initiation at the toe (2=135°) or root (2=0°) in a welded joint) -it overcomes the complex problem of multiple crack initiation and their interaction on different planes. -it directly takes into account the t-stress and this aspect becomes fundamental when thin structures are analysed [72]. -it directly includes three-dimensional effects and out-of-plane singularities not assessed by williams’ theory [73-77]. the mean value of the strain energy density (sed) in a circular sector of radius r0 located at the fatigue crack initiation sites has been used to summarise fatigue strength data from steel welded joints of complex geometry (fig. 4). synthesis based on sed in a control volume ocal strain energy density w averaged in a finite size volume surrounding weld toes and roots is a scalar quantity which can be given as a function of mode i-ii nsifs in plane problems [8] and mode i-ii-iii nsifs in three dimensional problems [9]. the evaluation of the local strain energy density needs precise information about the control volume size. from a theoretical point of view the material properties in the vicinity of the weld toes and the weld roots depend on a number of parameters as residual stresses and distortions, heterogeneous metallurgical microstructures, weld thermal cycles, heat source characteristics, load histories and so on. to device a model capable of predicting r0 and fatigue life of welded components on the basis of all these parameters is really a task too complex. thus, the spirit of the approach is to give a simplified method able to summarise the fatigue life of components only on the basis of geometrical information, treating all the other effects only in statistical terms, with reference to a well-defined group of welded materials and, for the time being, to arc welding processes. in a plane problem all stress and strain components in the highly stressed region are correlated to mode i and mode ii nsifs. under a plane strain hypothesis, the strain energy included in a semicircular sector shown in figure 2 is [7, 13] 31 2 2 2 2 3 31 1 2 2 11 1 0 0 0 nn n e ke k e k w e r e r e r                                (15) where r0 is the radius of the semicircular sector and e1, e2 and e3 are functions that depend on the opening angle 2 and the poisson ratio . the material parameter r0 can be estimated by using the fatigue strength a of the butt ground welded joints (in order to quantify the influence of the welding process, in the absence of any stress concentration effect) and the nsif-based fatigue strength of welded joints having a v-notch angle at the weld toe constant and large enough to ensure the non singularity of mode ii stress distributions. l f. berto, frattura ed integrità strutturale, 34 (2015) 11-26; doi: 10.3221/igf-esis.34.02 21 a convenient expression is [7]: 1 1 1 1 1 0 2 na a e k r          (16) where both 1 and e1 depend on the v-notch angle. eq. (16) makes it possible to estimate the r0 value as soon as 1 n ak and a are known. at na = 5106 cycles and in the presence of a nominal load ratio r equal to zero a mean value 1 n ak equal to 211 mpa mm0.326 was found re-analysing experimental results taking from the literature [10]. for butt ground welds made of ferritic steels a mean value a = 155 mpa (at na= 5106 cycles) was found [79]. then, by introducing the above mentioned value into eq.(16), one obtains for steel welded joints with failures from the weld toe r0 =0.28 mm. it is interesting to learn that, for welded joints made of structural steels, different espressions forkth taken from the literature were reported in ref. [79], from which kth = 180 mpa mm (5.7 mpa m1/2). in the case 2=0 and fatigue crack initiation at the weld root eq.(16) gives r0=0.36 mm, by neglecting the mode ii contribution and using e1=0.133, eq.(7), 1k n a = 180 mpa mm0.5, and, once again, a = 155 mpa. this means that the choice to use a critical radius equal to 0.28 mm both for toe and root failures is a sound engineering approximation. by modelling the weld toe regions as sharp v-notches and using the local strain energy, more than 900 fatigue strength data from welded joints with weld toe failure were analysed and the first theoretical scatter band in terms of sed was obtained [8]. the geometry exhibited a strong variability of the main plate thickness (from 6 to 100 mm), the transverse plate (from 3 to 200 mm) and the bead flank (from 110 to 150 degrees). figure 5: fatigue strength of welded joints as a function of the averaged local strain energy density; r is the nominal load ratio. the synthesis of all those data is shown in figure 5, where the number of cycles to failure is given as a function of 1w (the mode ii stress distribution being non singular for all those geometries). the figure includes data obtained both under tension and bending loads, as well as from “as-welded” and “stress-relieved” joints. the scatter index tw, related to the two curves with probabilities of survival ps= 2.3% and 97.7%, is 3.3, to be compared with the variation of the strain energy density range, from about 4.0 to about 0.1 mj/m3. tw=3.3 becomes equal to 1.50 when reconverted to an equivalent local stress range with probabilities of survival ps=10% and 90% (t = 3.3 / 1.21 1.5 ). the scatterband proposed was latter applied in [10] to a larger bulk of experimental data, which included also fatigue failures from the weld root. dealing with static loading, the local sed values are normalised to the critical sed values (as determined from unnotched specimens) and plotted as a function of the r/r0 ratio. the data related to the experimental program of pmma tested at 60°c [56-59] are summarised together with other data taken from a data base due related to pmma tested at room 0.01 0.1 1.0 10 10510 4 106 107 r0=0.28 mm 900 fatigue test data various steels inverse slope k=1.5 p.s. 97.7 % 2d, failure from the weld toe, r= 0 2d, failure from the weld root, r = 0 butt welded joints -1 < r < 0.2 3d, -1 < r < 0.67 hollow section joints, r= 0 a v e ra g e d s tr a in e n e rg y d e n s ity  w [ n m m /m m 3 ] tw= 3.3 0.192 0.105 0.058 r0r0 2  cycles to failure, n f. berto, frattura ed integrità strutturale, 34 (2015) 11-26; doi: 10.3221/igf-esis.34.02 22 temperature [45, 54-55]. the final synthesis has been carried out by normalising the local sed to the critical sed values (as determined from unnotched, plain specimens) and plotting this non-dimensional parameter as a function of the r/r0 ratio. a scatterband is obtained whose mean value does not depend on r/r0, whereas the ratio between the upper and the lower limits are found to be about equal to 1.3/0.8=1.6 (figure 6). the strong variability of the non-dimensional radius r/r0 (notch root radius to control volume radius ratio, ranging here from about zero to about 500) makes stringent the check of the approach based on the local sed. the scatterband presented contains failure data from 20 different ceramics, 4 pvc foams and some metallic materials. figure 6: synthesis of data taken from the literature. conclusions or many years the strain energy density (sed) has been used to formulate failure criteria for materials exhibiting both ductile and brittle behaviour. sed is the most fundamental quantity in mechanics being all physical quantities expressible in terms of it. from pico to macroscopic scale the energy absorption and dissipation can explain the most complex phenomena tied to fracture initiation and propagation. keeping in mind that the design rules valid for large bodies (i.e high volume to surface ratio) can not be directly translated and applied to small bodies where local inhomogeneities play a fundamental role for the material damage initiation and propagation and being also aware of the recent contributions and efforts to develop a multiscaling and segmentation scheme able to capture the complex phenomena that happen at every level from pico to macro, the main purpose of the paper is to present a review of the approach based on the mean value of the local strain energy density. dealing with static loading the approach is applied here to different materials and geometries both, under mode i and mixed mode (i+ii) loading. about one thousand experimental data, taken from the recent literature, are involved in the synthesis. they were from uand v-notched specimens made of very different materials. a scatter band is proposed by using as a synthesis parameter the value of the local energy averaged over control volume (of radius r0), normalised by the critical energy of the material. such a normalised energy is plotted as a function of the notch radius to critical radius ratio, r/r0. the strain energy density (sed) in a circular sector of radius r0 located at the crack initiation sites has successfully been used to summarise also about nine hundred data from fatigue failures of welded joints. under the hypothesis that all material inhomogeneities can be averaged, that ceases to be valid at picoand micro-levels but at the same time is the basis of the volume-based theories applied to structural components , the strain energy density approach is shown to be a powerful tool both for static and fatigue strength assessment of notched and welded structures. f 0 0.4 0.8 1.2 1.6 0.1 1 10 100 1000 ceramic materials pmma data metallic materials and other materials r/r0 about 1000 data from static tests 0.4 m  r0  500m 2.5  t  1200 mpa 0.15  ic  55 mpa m0.5 0.1   0.4 0  r/r0  1000 0  2  150° mode 1 and mixed mode (1+2) r  0 r0 r0 r r0+r0 r0 r0 steel aisi o1 duralluminium pvc cw w acrylic resin f. berto, frattura ed integrità strutturale, 34 (2015) 11-26; doi: 10.3221/igf-esis.34.02 23 references [1] tang, x.s., sih, g.c., weak and strong singularities reflecting multiscale damage: micro-boundary conditions for free–free, fixed–fixed and free–fixed constraints, theor. appl. fract. mech., 43(2005) 5-62. doi: 10.1016/j.tafmec.2004.12.002. [2] sih, g.c. tang, x.s., scaling of volume energy density function reflecting damage by singularities at macro-, meso and microscopic level, theor. appl. fract. mech., 43 (2005) 211-231. doi: 10.1016/j.tafmec.2005.01.006. [3] sih, g.c., multiscaling in molecular and continuum mechanics: interaction of time and size from macro to nano, springer, dordrecht, (2007). doi: 10.1007/978-1-4020-5062-6. [4] sih, g.c., crack tip mechanics based on progressive damage of arrow: hierarchy of singularities and multiscale segments, theor. appl. fract. mech., 51 (2009) 1-32. doi: 10.1016/j.tafmec.2009.01.007. [5] sih, g.c. ideomechanics of transitory and dissipative systems associated with length, velocity, mass and energy, theor. appl. fract. mech., 51(2009) 149-160. doi: 10.1016/j.tafmec.2009.05.008. [6] sih, g.c. energy absorption and dissipation associated with mass activation and deactivation for open systems, theor. appl. fract. mech., 52 (2009), 63-71. doi: 10.1016/j.tafmec.2009.08.008. [7] lazzarin, p. zambardi, r., a finite-volume-energy based approach to predict the static and fatigue behaviour of components with sharp v-shaped notches, int. j. fracture, 112 (2001) 275-298. doi: 10.1023/a:1013595930617. [8] lazzarin, p., lassen, t., livieri, p., a notch stress intensity approach applied to fatigue life predictions of welded joints with different local toe geometry, fatigue fract. eng. mater. struct., 26 (2003) 49-58. doi: 10.1046/j.14602695.2003.00586.x. [9] lazzarin, p., sonsino, c.m., zambardi, r. a notch stress intensity approach to assess the multiaxial fatigue strength of welded tube-to flange joints subjected to combined loadings, fatigue fract. eng. mater. struct., 27 (2004) 127140. doi: 10.1111/j.1460-2695.2004.00733.x. [10] livieri, p., lazzarin, p., fatigue strength of steel and aluminium welded joints based on generalised stress intensity factors and local strain energy values, int. j. fracture, 133 (2005) 247-278. doi: 10.1007/s10704-005-4043-3. [11] lazzarin, p., berto f., some expressions for the strain energy in a finite volume surrounding the root of blunt vnotches. int. j. fracture, 135 (2005) 161-185. doi: 10.1007/s10704-005-3943-6. [12] lazzarin, p., berto, f., from neuber’s elementary volume to kitagawa and atzori’s diagrams: an interpretation based on local energy, int. j. fracture, 135 (2005) l33-l38. doi: 10.1007/s10704-005-4393-x. [13] lazzarin, p., livieri, p., berto, f., zappalorto, m., local strain energy density and fatigue strength of welded joints under uniaxial and multiaxial loading, eng. fract. mech., 75 (2008) 1875-1889. doi: 10.1016/j.engfracmech.2006.10.019. [14] lazzarin, p., berto, f., control volumes and strain energy density under small and large scale yielding due to tensile and torsion loading, fatigue fract. eng. mater. struct., 31 (2008) 95-107. doi: 10.1111/j.1460-2695.2007.01206.x. [15] neuber, h., kerbspannungslehre, 2nd edn, springer-verlag, berlin, (1958). [16] neuber, h., űber die berücksichtigung der spannungskonzentration bei festigkeitsberechnungen. konstruktion, 20 (1968) 245-251. [17] neuber, h., kerbspannungslehre, 3rd edn, springer-verlag, berlin, (1985). [18] mcclintock, f.a., ductile fracture instability in shear, j. appl. mech., 25 (1958) 582-588. [19] ritchie, r.o., knott., j., rice, j.r., on the relation between critical tensile stress in fracture toughness in mild steel, j. mech. phys. sol., 21 (1973) 395-410. doi: 10.1016/0022-5096(73)90008-2. [20] knésl , z., a criterion of v-notch stability, int. j. fracture, 48 (1991) r79-r83. doi: 10.1007/bf00012922. [21] seweryn, a., brittle fracture criterion for structures with sharp notches, eng. fract. mech., 47(1994) 673-681. doi: 10.1016/0013-7944(94)90158-9. [22] novozhilov, v.v., on necessary and sufficient criterion of brittle fracture. prikladnaja matematika i mechanika, 33 (1969) 212-222. [23] seweryn, a., mróz, z, a non-local stress failure condition for structural elements under multiaxial loading. eng. fract. mech., 51(1995) 955-973. doi: 10.1016/0013-7944(94)00335-f. [24] seweryn, a. poskrobko, s., mróz, z, brittle fracture in plane elements with sharp notches under mixed-mode loading. j. eng. mech., 123 (1997) 535-543. doi: 10.1061/(asce)0733-9399(1997)123:6(535). [25] sheppard, s.d., field effects in fatigue crack initiation: long life fatigue strength. trans. asme. j. mech. des., 113 (1991) 188-194. doi:10.1115/1.2912768. [26] beltrami, e., sulle condizioni di resistenza dei corpi elastici, rend. r. ist. lombardo di scienze, lettere e arti, 18 (1885) 704 (in italian). doi: 10.1007/bf02824697. f. berto, frattura ed integrità strutturale, 34 (2015) 11-26; doi: 10.3221/igf-esis.34.02 24 [27] sih, g.c., a special theory of crack propagation: methods of analysis and solutions of crack problems, mechanics of fracture, edited by gc sih noordhoff, international publishing, leyden, (1973). [28] sih, g.c., strain-energy-density factor applied to mixed mode crack problems. int. j. fracture, 10 (1974) 305-321. doi: 10.1007/bf00035493. [29] sih, g.c., surface layer energy and strain energy density for a blunted crack or notch, prospect of fracture mechanics, edited by gc sih, h.c. van elst and d. broek, noordhoff international publishing, leyden, (1974). [30] sih, g.c., mechanics of fracture initiation and propagation: surface and volume energy density applied as failure criterion, kluwer academic publisher, dordrecht, (1991). doi: 10.1007/978-94-011-3734-8. [31] sih, g.c., ho, j.w., sharp notch fracture strength characterized by critical energy density, theor. appl. fract. mech., 16 (1991) 179-214. doi: 10.1016/0167-8442(91)90044-k. [32] sih, g.c., czoboly, e., gillemot, l.f., absorbed specific energy and strain energy density criterion, proceedings of an international symposium on absorbed specific energy and strain energy density criterion, budapest, september 1980. in memory of the late professor lászló gillemot, martinus nijhoff publishers, (1982), the netherlands. [33] gillemot, l.f., brittle fracture of welded materials, in: commonwealth welding conference c.7. (1965) 353-358. [34] gillemot, l.f., criterion of crack initiation and spreading. eng. fract. mech., 8 (1976) 239-253. doi: 10.1016/00137944(76)90089-8. [35] gillemot, l.f., czoboly, e., havas, i., fracture mechanics applications of absorbed specific fracture energy: notch and unnotched specimens, theor. appl. fract. mech., 4 (1985) 39-45. doi: 10.1016/0167-8442(85)90041-2. [36] gdoutos, e.e., fracture mechanics criteria and applications, kluwer academic publishers, dodrecht, boston, london (1990). doi: 10.1007/978-94-009-1956-3. [37] glinka, g., molski, k., a method of elastic-plastic stress and strain calculation at a notch root, mater. sci. eng., 50 (1981) 93-100. doi: 10.1016/0025-5416(81)90089-6. [38] glinka, g., energy density approach to calculation of inelastic strain-stress near notches and cracks. eng. fract. mech., 22 (1985) 485-508. doi:10.1016/0013-7944(85)90148-1. [39] ellyin, f., fatigue damage, crack growth and life prediction, chapman & hall, london, (1997). [40] ellyin, f., kujawski, d. generalization of notch analysis and its extension to cyclic loading, eng. fract. mech., 32 (1989) 819-826. doi: 10.1016/0013-7944(89)90178-1. [41] yosibash, z., bussiba, ar., gilad, i., failure criteria for brittle elastic materials. int. j. fracture, 125 (2004) 307-333. doi: 10.1023/b:frac.0000022244.31825.3b. [42] kipp, m. e., sih, g.c., the strain energy density failure criterion applied to notched elastic solids, int. j. solids struct., 11(1975) 153–173. doi: 10.1016/0020-7683(75)90050-5. [43] carpinteri, a., stress singularity and generalised fracture toughness at the vertex of re-entrant corners, eng. fract. mech., 26 (1987) 143-155. doi: 10.1016/0013-7944(87)90086-5. [44] nui, l.s., chehimi, c. pluvinage, g., stress field near a large blunted tip v-notch and application of the concept of the critical notch stress intensity factor (nsif) to the fracture toughness of very brittle materials, eng. fract. mech., 49 (1994) 325-335. doi: 10.1016/0013-7944(94)90262-3. [45] gómez, f.j., elices, m., valiente, a. cracking in pmma containing u-shaped notches, fatigue fract. eng. mater. struct., 23 (2000) 795-803. doi: 10.1046/j.1460-2695.2000.00264.x. [46] atzori, b., lazzarin, p. notch sensitivity and defect sensitivity: two sides of the same medal, int. j. fracture, 107 (2001) l3-l8. [47] strandberg, m., fracture at v-notches with contained plasticity, eng. fract. mech., 69 (2002) 403-415. doi: 10.1016/s0013-7944(01)00079-0. [48] atzori, b., lazzarin, p., meneghetti, g., fracture mechanics and notch sensitivity, fatigue fract. eng. mater. struct., 26 (2003) 257-267. doi: 10.1046/j.1460-2695.2003.00633.x. [49] gogotsi, g.a., fracture toughness of ceramics and ceramic composites, ceramics int., 7 (2003) 777-884. doi: 10.1016/s0272-8842(02)00230-4. [50] leguillon, d., yosibash, z., crack onset at a v-notch. influence of the notch tip radius, int. j. fract., 122 (2003)1-21. doi: 10.1023/b:frac.0000005372.68959. [51] dini, d., hills, d., asymptotic characterisation of nearly-sharp notch root stress fields, int. j. fracture, 130 (2004) 651-666. doi: 10.1007/s10704-004-2510-x. [52] yosibash, z., priel, e. leguillon, d., a failure criterion for brittle elastic materials under mixed-mode loading, int. j. fracture, 141 (2006) 291-312. doi: 10.1007/s10704-006-0083-6. f. berto, frattura ed integrità strutturale, 34 (2015) 11-26; doi: 10.3221/igf-esis.34.02 25 [53] leguillon, d., quesada, d. putot, c., martin, e., prediction of crack initiation at blunt notches and cavities – size effects, eng. fract. mech. 74 (2007) 2420-2436. doi:10.1016/j.engfracmech.2006.11.008. [54] gómez, f.j., elices, m., fracture of components with v-shaped notches. eng. fract. mech., 70 (2003) 1913-1927. doi: 10.1016/s0013-7944(03)00131-0. [55] gómez, f. j., elices, m., a fracture criterion for sharp v-notched samples, int. j. fracture, 123 (2003) 163-175. doi: 10.1023/b:frac.0000007374.80996.a2. [56] gómez, f.j., elices, m., a fracture criterion for blunted v-notched samples, int. j. fracture, 127 (2004) 239-264. doi: 10.1023/b:frac.0000036832.29429.21. [57] gómez, f.j., elices, m., planas, j., the cohesive crack concept: application to pmma at –60˚c, eng. fract. mech., 72 (2005)1268-1285. doi: 10.1016/j.engfracmech.2004.09.005. [58] gómez, f.j., elices, m., berto, f., lazzarin, p., local strain energy to asses the static failure of u-notches in plates under mixed mode loading. int. j. fracture, 145 (2007) 29-45. doi: 10.1007/s10704-007-9104-3. [59] berto, f., lazzarin, p., gomez, f.j., elices, m., fracture assessment of u-notches under mixed mode loading: two procedures based on the 'equivalent local mode i' concept, int. j. fracture, 148 (2007) 415-433. doi: 10.1007/s10704-008-9213-7. [60] lazzarin, p., berto, f., elices, m., gómez, j., brittle failures from uand v-notches in mode i and mixed, i+ii, mode. a synthesis based on the strain energy density averaged on finite size volumes, fatigue fract. eng. mater. struct., 32 (2009) 671-684. doi: 10.1111/j.1460-2695.2009.01373.x. [61] gómez, f.j., elices, m., berto, f., lazzarin, p., fracture of v-notched specimens under mixed mode (i+ii) loading in brittle materials, int. j. fracture, 159 (2009), 121-135. doi: 10.1007/s10704-007-9104-3. [62] erdogan, f., sih, c.g., on the crack extension in plates under plane loading and transverse shear. j. basic eng., (1963) 519-525. doi: 10.1115/1.3656897. [63] schleicher, f., der spannungszustand an der fliessgrenze (plastizitätsbedingung), zeitschrift für angewandte mathematik und mechanik, 6 (3) (1926) 199–216. [64] berto, f., lazzarin, p., recent developments in brittle and quasi-brittle failure assessment of engineering materials by means of local approaches, 75 (2014) 1-48. doi: 10.1016/j.mser.2013.11.001. [65] filippi, s., lazzarin, p. tovo, r., developments of some explicit formulas useful to describe elastic stress fields ahead of notches in plates, int. j. solids struct., 39 (2002) 4543-4565. doi: 10.1016/s0020-7683(02)00342-6. [66] williams, m.l., stress singularities resulting from various boundary conditions in angular corners on plates in tension, j. appl. mech., 19 (1952), 526-528. [67] creager, m., paris, p.c., elastic field equations for blunt cracks with reference to stress corrosion cracking, int. j. fract. mech., 3 (1967) 247–252. doi: 10.1007/bf00182890. [68] gross, r., mendelson, a., plane elastostatic analysis of v-notched plates, int. j. fract. mech., 8 (1972) 267-27. doi 10.1007/bf00186126. [69] lazzarin, p., filippi, s., a generalised stress intensity factor to be applied to rounded v-shaped notches, int. j. solids struct., 43 (2006) 2461-2478. doi: 10.1016/j.ijsolstr.2005.03.007. [70] lazzarin, p., berto, f., gómez, f.j., zappalorto, m., some advantages derived from the use of the strain energy density over a control volume in fatigue strength assessments of welded joints, int. j. fatigue, 30 (2008) 1345-1357. doi: 10.1016/j.ijfatigue.2007.10.012. [71] lazzarin, p., berto, f. zappalorto, m., mean values of the strain energy density from coarse meshes: theoretical bases of a method suitable for rapid calculations of notch stress intensity factors and fatigue strength of welded joints, int. j. fatigue, 32 (2010) 1559-1567. doi: 10.1016/j.ijfatigue.2010.02.017. [72] lazzarin, p., berto, f., radaj, d. stress intensity factors of welded lap joints: a comparison between pointed slit based and keyhole notch based models, with extensions to strain energy density and j-integral, fatigue fract. eng. mater. struct., 32 (2009) 713-735. doi: 10.1111/j.1460-2695.2009.01379.x. [73] kotousov, a., wang, c.h. three dimensional stress constraint in an elastic plate with a notch, int. j. solids struct., 39 (2002) 4311-4326. doi: 10.1016/s0020-7683(02)00340-2. [74] berto, f., lazzarin, p., wang, c.h. three-dimensional linear elastic distributions of stress and strain energy density ahead of v-shaped notches in plates of arbitrary thickness, int. j. fracture, 127 (2004) 265-282. doi: 10.1023/b:frac.0000036846.23180.4d. [75] kotousov, a., lew, t.l., stress singularities resulting from various boundary conditions in angular corners of plates of arbitrary thickness in extension, int. j. solids struct., 43(2005) 5100-5109. doi: 10.1016/j.ijsolstr.2005.06.037. [76] kotousov, a., fracture in plates of finite thickness, int. j. solids struct, 44 (2007) 8259-8273. doi: 10.1016/j.ijsolstr.2007.06.011. f. berto, frattura ed integrità strutturale, 34 (2015) 11-26; doi: 10.3221/igf-esis.34.02 26 [77] harding, s., kotousov, a., lazzarin, p., berto, f., transverse singular effects in v-shaped notches stressed in mode ii, int. j. fracture, 164 (2009) 1-14. doi: 10.1007/s10704-010-9449-x. [78] b. atzori, v. dattoma, a comparison of the fatigue behaviour of welded joints in steels and in aluminium alloys. iiw doc xxxiii, (1983) 1089-1983. 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can be opened with acrobat and adobe reader 5.0 and later.) >> /namespace [ (adobe) (common) (1.0) ] /othernamespaces [ << /asreaderspreads false /cropimagestoframes true /errorcontrol /warnandcontinue /flattenerignorespreadoverrides false /includeguidesgrids false /includenonprinting false /includeslug false /namespace [ (adobe) (indesign) (4.0) ] /omitplacedbitmaps false /omitplacedeps false /omitplacedpdf false /simulateoverprint /legacy >> << /addbleedmarks false /addcolorbars false /addcropmarks false /addpageinfo false /addregmarks false /convertcolors /converttocmyk /destinationprofilename () /destinationprofileselector /documentcmyk /downsample16bitimages true /flattenerpreset << /presetselector /mediumresolution >> /formelements false /generatestructure false /includebookmarks false /includehyperlinks false /includeinteractive false /includelayers false /includeprofiles false /multimediahandling /useobjectsettings /namespace [ (adobe) (creativesuite) (2.0) ] /pdfxoutputintentprofileselector /documentcmyk /preserveediting true /untaggedcmykhandling /leaveuntagged /untaggedrgbhandling /usedocumentprofile /usedocumentbleed false >> ] >> setdistillerparams << /hwresolution [2400 2400] /pagesize [612.000 792.000] >> setpagedevice microsoft word numero_29_art_27 p. casini et alii, frattura ed integrità strutturale, 29 (2014) 313-324; doi: 10.3221/igf-esis.29.27 313 focussed on: computational mechanics and mechanics of materials in italy crack detection in beam-like structures by nonlinear harmonic identification paolo casini, fabrizio vestroni university of rome la sapienza p.casini@uniroma1.it, vestroni@uniroma1.it oliviero giannini university niccolò cusano oliviero.giannini@unicusano.it abstract. the dynamic behavior of beam-like structures with fatigue cracks forced by harmonic excitation is characterized by the appearance of sub and super-harmonics in the response even in presence of cracks with small depth. since the amplitude of these harmonics depends on the position and the depth of the crack, an identification technique based on such a dependency can be pursued: the main advantage of this method relies on the use of different modes of the structure, each sensitive to the damage position in its peculiar way. in this study the identification method is detailed through numerical examples tested on structures of increasing complexity to evaluate the applicability of the method to engineering applications. the amount of data to obtain a unique solution and the optimal choice of the observed quantities are discussed. finally, a robustness analysis is carried out for each test case to assess the influence of measuring noise on the damage identification. keywords. fatigue crack; damage identification; nonlinear dynamics; cracked beam model. introduction he occurrence of cracks in civil or mechanical systems leads to dangerous effects for the structural integrity and causes anomalous behaviors. to not compromise the safety, the detection of a crack in the early stage is of great interest. the presence of a crack not only causes a local variation in the mechanical characteristics of the structure at its location, but it also has a global effect involving the entire structure. for this reason, the dynamic characterization of cracked structures can be used for damage detection in non-destructive tests and, among the various techniques, vibration-based methods provide an effective means of detecting fatigue cracks in structures [1-7]. the vibration-based detection methods exploit the fact that damage in a structure alters its dynamic properties: in particular the presence of cracks can be disclosed by modifications in the linear response (i.e., modal frequencies, damping and shapes associated with each natural frequency, curvature of mode shapes etc.) as well as by the occurrence of nonlinear effects (suband super-harmonics, bifurcations, internal resonances etc.). there are two main categories of crack models used in vibration-based detection methods: open crack and breathing crack models. in the first case it is assumed that the crack in a structural member remains open during vibration. this assumption is usually satisfied in notched beams and when the damage is rather large; this model avoids the complexity resulting from nonlinear behavior when a breathing crack is presented. on the contrary, breathing behavior is generally t p. casini et alii, frattura ed integrità strutturale, 29 (2014) 313-324; doi: 10.3221/igf-esis.29.27 314 reported in the case of fatigue cracks, also when the damage affects only a small portion of the cross section of the structural element; it requires a nonlinear model to take into account its effect on the system dynamics. in fact the breathing crack model considers that, during the vibration cycle of a structure, the edges of the crack come into and out of contact, leading to sudden changes in the dynamic response of the structure. depending on the crack model, vibration based methods are also classified into two categories: the linear and the nonlinear approaches. the first group of methods can identify only the open cracks once at a developed stage, once changes in modal parameters become significant [6, 7]. for this reason, refined studies focus on the nonlinear response characteristics that can be investigated to identify the presence of the crack in an early stage. in fact, the structures with breathing cracks behave similarly to bilinear systems and hence exhibit nonlinear phenomena in the dynamic response even for low damage. therefore in the second group of methods the identification can be obtained by assuming as damage indicators some peculiar characteristics of the nonlinear dynamic response such as the presence of sub and super harmonics [8-11], the changes in the phase diagrams [11, 12], the rise of superabundant nonlinear normal modes [13-15] and non-smooth bifurcations [16]. while these nonlinear effects make the response of beams more difficult to model with respect to notched beams, their appearance clearly marks the boundary between undamaged and damaged behaviour. in fact, as known [17], when a system with a breathing crack is excited by a single harmonic force, distinctive nonlinear features appear in the response. the excitation, in fact, forces the crack to open and close and the resulting clapping of the crack’s edges produces harmonics that are integer multiple or fractional multiple of the forcing frequency. these harmonics are commonly referred to as superharmonics and sub-harmonics, respectively. these features are easily detectable when the excitation frequency is in an integer ratio or is a multiple of a resonance frequency of the system; moreover, these would be much more sensitive to cracks characteristics than the modal properties of a linear system. for this reason, increasingly over recent years [11, 12, 18, 19], attentions have been focused on the investigations of the nonlinear effects caused by the presence of breathing cracks and on the associated applications to the problem of damage detection. according to the previous observations, the dynamic behavior of beam-like structures with fatigue cracks forced by harmonic excitation is characterized by the appearance of sub and super-harmonics in the response even in presence of cracks with small depth. since the amplitude of these harmonics depends on the position and the depth of the crack, an identification technique based on such a dependency has been developed by the authors [19]. the main advantage of this method relies on the combined use of different modes of the structure, each sensitive to the damage position depending on the curvature of the mode at its location. in this paper the identification method proposed in [19] is extended and detailed through numerical examples tested on structures with a single breathing crack and of increasing complexity to evaluate the applicability of the method to engineering applications. dynamic vibrations of small amplitude will be considered so that the crack can be assumed to be stable. the amount of data to obtain a unique solution and the optimal choice of the observed quantities are discussed. finally, a robustness analysis is carried out for each test case to assess the influence of measuring noise on the damage identification; the robustness of the identification, evaluated through a monte carlo simulation, is shown to be quite strong to both measuring and modeling errors envisioning the possibility for in-field applications of this method even in the case of very small cracks. as future developments of this study, another field of investigation will cover the robustness of the procedure with respect to other realistic disturbances such as those caused by constraints imperfections or random distributed mass. two test cases are studied in the present paper: a simply supported beam and a spanned beam; on the first case, the difficulties in detecting the damage in symmetric systems are addressed, while on the second case the difficulties concerning more complex systems with localized modes are considered. systems under investigation generalities ig. 1a,b present the systems under consideration: a simply supported beam, fig. 1a, and a spanned beam, fig. 1b. both cases have been modeled using standard one dimensional finite elements, while the crack is modeled as explained in the following subsection. it is assumed that only one element has a single sided edge breathing crack and that the switching between open and closed behavior of the crack occurs in the equilibrium configuration. furthermore it is supposed that the opening and closing of the crack is primarily driven by the flexural dynamics of the beam and that the crack is the only source of nonlinearity in the structure. the considered beams are made of steel with a total length l = 0.6 m, and a constant rectangular cross-section a, of height h=0.04 m and width w=0.02 m; the properties of the material are: e=206 gpa,  =7800 kg/m3,  =0.3. the beams have a breathing crack of depth a at distance d from the left-end constraint; p = d/l is the non dimensional position f p. casini et alii, frattura ed integrità strutturale, 29 (2014) 313-324; doi: 10.3221/igf-esis.29.27 315 and s = a/h is the non dimensional severity of the crack. the simple supported beam, fig. 1a, has been forced under two different loading condition: almost symmetric 0.45f l l      and asymmetric 0.06f l l      . also for the spanned beam two different locations for the load are considered: 2 3 fl l and 2 5 fl l , where 1 2l l l  . the beams are modeled using standard one dimensional euler-beam elements, with three degrees of freedom for each node, as well as the damaged element; the mesh consists of 60 finite elements. a) b) figure 1: systems under investigation. a) simple supported beam, l=0.6 m, lf=0.26 m (quasi symmetric) or lf=0.04 m (asymmetric). b) spanned beam, l1=0.4 m, l2=0.2 m, lf=0.3 m or lf=0.5 m. to characterize the dynamic properties of the structure, distinction should be made between the first natural frequencies, 1 1 2u ut    and 1 1 2d dt    , of the two constituent sub-models (open crack, superscript d, and closed crack, superscript u) and the first natural frequency 1 of the system: this frequency can be obtained as the average of the natural periods of the two sub-models 1 ut and 1 dt : 1 11 1 1 1 4 u d u d u d it t          . this relation strictly holds for a single-degree-of-freedom oscillator with a bilinear stiffness and is therefore called first bilinear frequency of the system [3]. as demonstrated in the literature [3, 20, 21] the same equation approximates with good accuracy the natural frequencies of a structures with a breathing crack. in conclusion the resonance of the damaged systems occurs at the bilinear frequency i given by: u d i i i u d i i        (1) where ui is the ith natural frequency of the undamaged system and d i is the ith natural frequency of the linear damaged system when crack is always open. model of the breathing crack in several applications, the equilibrium configuration of the system coincides with the switching condition between closed and open behaviour for the crack. under this condition, the cracked zone of the beam can be modelled with a finite element that has a bilinear element matrix with the discontinuity passing through the origin: this leads to an overall bilinear model where the nonlinear characteristics are independent of the vibration amplitude [3, 4, 21]. the standard element stiffness matrix k for a plane beam element with three degrees of freedom per node, collected in the vector u, once shear deformability is neglected, is described by: 2 2 2 / 0 0 0 0 /  6 / 0  12 / 12 / 6 /     4     0 6 /     0 ,             / 0     0       12 / 6 /              4 iu u i i u ju j j ua i a i vll l l lei k u ua il vsymm l l                                   (2) p. casini et alii, frattura ed integrità strutturale, 29 (2014) 313-324; doi: 10.3221/igf-esis.29.27 316 where e is the young's modulus, ui is the moment of inertia of the undamaged beam section, and l is the length of the element. the presence of the breathing crack in the beam is modelled through a particular finite element at the location of the crack. considering a crack propagating from the upper side of the beam, the damaged element is described by a damaged moment of inertia di obtained by superimposing to the healthy element another element that has the following stiffness matrix: 2 2 2 0 0 0 0 0 0     6 / 0  12 /    12 / 6 /           4   0 6 /     0 ,               0 0     0                   12 / 6 /              4 u u d c u ll l l lei i i k l i symm l l                       (3) where  represents the non dimensional flexural damage and ranges between 0 for the healthy section and 1 for the completely damaged section; in eq. (3) the effect of the crack on the axial stiffness is neglected. assuming that the opening mechanism is triggered only by the rotations at the nodes of the element as already proposed in [5, 18], the breathing mechanism is obtained by the damaged element matrix dk with bilinear behavior:     1,              0,   i j d i j c i j i j k k h k h                 (4) where h is the heaviside step function dependent on the relative rotations between the sections i and j. in order to compare the results of the proposed model with the results found in literature that often consider as damage parameter the non dimensional crack severity s = a/h, the results are presented by appropriately scaling the damaged axis. the relation between  and s is obtained through a nonlinear compliance function ( )g s : ( )u d u i i g s i    (5) the particular form of the compliance function  g s is either derived in the literature from theoretical models or from experimental or numerical data. in this work, the compliance function is obtained from a fe model of the open-cracked beam element; it is important to note that ( )g s depends on the length of the damaged element but the results of the identification will not be affected by the particular choice of the compliance function: this function is merely used to graph the results as a function of s rather than  . the proposed crack model, while being sufficiently simple, can capture several practical situations and, in particular, fatigue crack are reported to behave in such this way. moreover, this crack model allows for a consistent reduction of the numerical efforts which is very useful in the solution of the inverse problem. harmonic damage surfaces (hds) efore tackling the damage identification problem, the direct analysis of the effect of a breathing crack on the dynamics of the beam is developed, by applying the procedure described in [19] and synthetically recalled in the following. first, the amplitude of the sub and super-harmonics of the forcing frequency ω are evaluated. in practice, as far as a bilinear system is considered, a large harmonic content emerges at a bilinear frequency of the system, eq. (1), when the driving frequency approaches an integer ratio or a multiple of that frequency. the amplitude of the harmonics of interest is obtained by numerically solving the equations of motion of the finite element model of the structure subjected to a point force applied at the loading points shown in fig. 1. b p. casini et alii, frattura ed integrità strutturale, 29 (2014) 313-324; doi: 10.3221/igf-esis.29.27 317 the amplitude of the j-th order super-harmonic is then normalized with respect to the main harmonic amplitude, obtaining the normalized spectrum * ( )s  around i . its maximum value is labeled as ijr and it depends on crack position and severity: * * ( ) max( ),       ( / ) i ij i s r s s s j     (6) the value of ijr depends on the particular choice of the excited harmonic: for instance 22r is obtained by considering for the second mode the second order harmonic, when the driving frequency is half of the 2nd frequency. the nondimensional ratio ijr is obviously a function of both the crack depth and its location but, because of the normalization and the bilinear behaviour, is not dependent on the used excitation amplitude, as explained at the beginning of the previous subsection. to characterize a j-th order sub-harmonic it is sufficient to replace in the above equations 1/ j to j ; as an example 2½r is obtained by considering for the second mode the second order sub-harmonic, when the driving frequency is twice the 2nd frequency. as the crack position and its severity change, ijr describes a surface that can be computed by performing a parametric analysis. we will refer to this kind of surface as harmonic damage surface (hds). in particular, fig. 2a and 2b present the hds for 22r for the simple supported beam obtained for symmetric and asymmetric loading condition respectively; it is worth noticing that in the first cases the ijr coefficients are considerably smaller, since the loading position is close to the modal shape node. a) b) figure 2: simple supported beam: harmonic damage surfaces r22 order 2 super-harmonic component for = /2; a) symmetric loading condition; b) asymmetric loading condition. similarly, fig. 3a and 3b present the hds for 32r for the spanned beam obtained for two different load locations: 0.3fl  m and 0.5fl  m. it can be observed that the loading conditions can significantly affect the hds. the amplitude of ijr reflects the influence that the damage has on the particular mode: therefore, the surface has a monotonic behaviour with respect to the damage severity whereas, along the p axis, the surface should resemble the curvature of the corresponding mode. in this paper the hds related to 12r , 22r , 32r are used for the simple supported beam and 12r , 22r , 32r , 42r for the spanned one. p. casini et alii, frattura ed integrità strutturale, 29 (2014) 313-324; doi: 10.3221/igf-esis.29.27 318 a) b) figure 3: spanned beam: harmonic damage surfaces r32 order 2 super-harmonic component for ω = 3 /2; a) 2 3 fl l ; b) 2 . 5 fl l nonlinear harmonic identification method description or the damage identification purpose, using the information obtained from direct simulations, the excitation and measurement points can be chosen; the test is carried out exciting the system with a sine sweep and measuring only the response signals. the time histories recorded from the sensors are then post processed adopting the same algorithm used for numerical data produced by the fe model to evaluate the corresponding value of mijr , where the superscript m stands for measured. according to eq. (6), the fourier transform of the signal is computed and the harmonic peak value around i is divided by the peak value of the excitation frequency ( /i j ). the measured ratio mijr defines a sectioning plane for the corresponding hds that intersects it along a curve representing an iso-harmonic-content-curve. this curve collects all the combination of damage-severity and damage-position identified by the performed measure mijr . as an example, fig. 2a reports a representation (dashed line) for the hds surface of 22r furnished by the model sectioned by the plane 22 mr = 0.0135; this value corresponds to a damage located at p = 0.27 and with severity s = 0.1, that is a point of the curve.. the damage identification is obtained by computing, the error function ije for each ijr surface       ,1 1,,, ,      n q mm ij l l ij kij ij m l k ij ijm ij r p s rr p s r e p s r n qr         (7) where  ,ije p s depends on the particular choice of the hds and it is a function of both the damage severity and the damage position. in eq. (7), 1, ,l n  is the index of the computed n points  ,l lp s during the direct analysis to build the corresponding hds, while 1, ,k q  is the index of the q measurements taken on the structure for the identification. finally, the functional to be minimized represents a global normalized error between the model results and the measured data: 2 , ( , ) ( , )ij i j f p s e p s  (8) the values of p and s for which ( , )f p s is minimum, represent the position and the severity of the damage. robustness of the method in the real world, the identification is affected by measuring errors which originate from different sources such as noise in the measures, environmental excitation, error in the positioning of the sensors etc. the proposed method is intrinsically f p. casini et alii, frattura ed integrità strutturale, 29 (2014) 313-324; doi: 10.3221/igf-esis.29.27 319 robust with respect to random errors, because the mijr indicators are normalized quantities. in particular, even a large white noise on the measured response will not lead to significant error in the identification. on the contrary, mijr is sensitive to noise affecting the limited band around either the excitation frequency or the considered super harmonic or other source of nonlinearity present in the system. the amplitude of these errors will be independent of the level of the harmonic ratio due to the damage but they will be dependent on the frequency, on the considered mode, and on the considered harmonic. in [19] the robustness of the method has been tested by considering a cantilever beam and assuming that each measured harmonic mijr has, independently from the other, an error that is gaussian, with a mean value equal to zero, and a standard deviation  that is 15% of the average value of the corresponding hds surface. this level of harmonic error should realistically account for any nonlinearity due to material or non-perfect constraints. the quantification of the error on the identified damage was obtained through a monte carlo simulation performed by building a large 50.000 samples set of triplets mijr , and for each of them the identification was carried out. the robustness of the methodology was evaluated through the statistics on the resulting set of position and severity identified. since the robustness is also very dependent on the position and on the level of the damage, the monte carlo simulation was performed for different combinations of the two parameters. a) b) figure 4: standard deviation of the errors on the identified damage as the damage position and the severity changes for a 15% gaussian random error on the measured harmonics. a) standard deviation of the position error; b) standard deviation of the severity error. as shown in fig. 4, it has been found that in all the considered cases the mean value of error is always below 2.5% and reaches 0.1% as soon as the damage severity exceeds 10%; on the contrary, the standard deviation of the error, which measures how the data spread around their mean values, exhibit a different behavior. in the worst scenario i.e. when the damage is far from the constraint and with very low depth (s < 10%), the standard deviation of the position error, reaches 15%, but falls below 1% as the damage severity reaches 10%. the deviation of the identified severity is generally very low, between 1% and 0.5% of the beam height, and is largely independent on the location and severity. the results show that the procedure is able to fully identify damages in any position when s>0.1, and, for very small damage (0.05<s<0.1), the position remains uncertain but the severity is still well assessed. moreover, results show that in general, the dispersion of all the 50000 data samples of the monte carlo simulation remains quite close to the correct value improving confidence on the proposed technique. numerical applications generalities he present study deals with specific aspects and characteristics of the identification method. in particular, three different numerical tests are carried out to highlight each a specific problem: a) improving the identification by using more than one sensor; b) how to identify the damage in a symmetric structure; c) how the identification t p. casini et alii, frattura ed integrità strutturale, 29 (2014) 313-324; doi: 10.3221/igf-esis.29.27 320 changes as the structure becomes more complex. it is here important to recall that the method detects the damage level through the response of a selected mode of the systems thus, by considering just one mode, a large damage close to a curvature node of that mode has the same effect of a small damage in a curvature antinode. a) b) figure 5: nonlinear harmonic identification on the simply supported beam. the system is excited at lf/l=0.45 ; a) p = 0.27, s = 0.1; b) p =0.73 s = 0.1. damage detection in symmetric structures when a symmetric structure is considered, in this case a simply supported beam, the modes are either symmetric or anti symmetric. thus, in principle, it is difficult for the harmonic identification method to distinguish between the real damage position and its symmetric, while the correct evaluation of the damage severity should not be affected. in practice, however, the presence of the damage breaks the symmetry of the system and this can be exploited in the identification by using a non symmetric excitation of the structure. in particular in fig. 5 two different damage positions are considered: p=0.27 and its symmetric position p=0.73 for a quite low damage s=0.1. the system is excited at 0.45f l l  and the hds related to 12r , 22r , 32r are used. the figures show the value of the functional ( , )f p s as colormap where warmer colors relate to lower values. it is interesting to notice that even if the force position is quite close to center of the beam, the ( , )f p s is not symmetric. however especially when the damage is at 0.73, there are two, almost symmetric zones of damage detected: the correct one at 0.73 and its symmetric at 0.2, being the latter slightly larger. under the same damage conditions, p=0.27 or its symmetric position p=0.73 and s=0.1, if one uses a strong non symmetric position of the force 0.06f l l  , the results do not show any symmetric image of the damage position for both cases, as illustrated in fig. 6. a) b) figure 6: nonlinear harmonic identification on the simply supported beam. the system is excited at lf/l=0.06 ; a) p = 0.27, s = 0.1; b) p =0.73 s = 0.1. p. casini et alii, frattura ed integrità strutturale, 29 (2014) 313-324; doi: 10.3221/igf-esis.29.27 321 information from sensors located at different points the effect of the position of the sensors is illustrated using the simply supported beam. fig. 7a-g shows the results of the identification for different positions of the sensors ps=[0.12 0.26 0.32 0.4 0.6 0.68 0.8] the vertical line shows for each plot the sensor position. as it can be seen all the sensors highlight the correct position and severity of the damage, however some of them, which in general depend on the relative position between damage, force, considered mode and position of the sensor, can produce some other zone of damage. for example, in the particular case of fig. 7e, with the sensor located at ps=0.6, a spurious zone of detected damage around p=0.85, s=0.2 appears. in order to avoid this misleading result, the use of an average between the several results provided by all the sensors can be used, fig. 7h. figure 7: nonlinear harmonic identification on a simply supported beam with damage p = 0.27, s = 0.1 excited at lf/l=0.06. a)-g) results with one sensor located at different points; h) average of the results provided by all the cases a)-g). in order to account for several input sensors the  ,ijr p s becomes also a function of the sensor position:  , , kij sr p s p where ksp is the non-dimensional position of the kth sensor. in that case eq. (7) and (8) become:       ,1 1 , , ( ) , , ( ) , , ,      ( ) ( ) n qk m k k m k ij s ij s ij l l s ij h sk m k l h ij s ij sm k ij s r p s p r p r p s p r p e p s p r p n qr p          (9) and 2 , , ( , ) ( , , )kij s i j k f p s e p s p  (10) respectively. it is clear that more information is available at a reasonable low cost being, in general, quite inexpensive to use more than one sensor in the analysis. moreover, the use of 8 sensors allows an identification that is able to locate the damage, unless it is close to a constraint, from 10% severity down to just 5%. a) b) figure 8: nonlinear harmonic identification on a spanned beam with damage p=0.4, s=0.1 excited at lf/l=0.5. a) three mode identification; b) four mode identification. p. casini et alii, frattura ed integrità strutturale, 29 (2014) 313-324; doi: 10.3221/igf-esis.29.27 322 complex structures more complex systems lead to more complex modal shapes and the presence of constraints produces a zone with low modal response and thus small sensitivity of the method to the damage. moreover, the method has difficulties to distinguish between different zones where the response is quite low. these aspects are investigated by conducting identification of the damage on the spanned beam presented in fig. 1b. the obtained identification degrades quite dramatically and even moderate damage severity, especially if located close to a constraint, leads to an overestimation of damage positions and severity. in particular, the case of a spanned beam with a damage characterized by p=0.68, s=0.1 and a loading condition 0.5f l l  is considered in fig. 8. in fig. 8a the identification procedure is performed by using the 2nd order harmonic of the first three frequency: 12r , 22r , 32r . as it can be observed, besides the correct identification (p=0.4, s=0.1), erroneous solutions appear that can be avoided by adding in the procedure the fourth mode: this is done in fig. 8b where 12r , 22r , 32r , 42r are considered. another unlucky case scenario, among the possible positions of the damage, was at p=0.85 and s=0.18, fig. 9; in this case the identification with three modes (using 12r , 22r , 32 )r produces together with the correct position two other erroneous identifications. in particular there is an identified damage at p=0.5 and s=0.12, that is quite troublesome because also the severity is misleading. by considering also a 4th mode of the system, the performance of the method comes back to the level of accuracy previously obtained as it can be inferred by comparing fig. 8b with fig. 8a and fig. 9b with fig. 9a. a) b) figure 9: nonlinear harmonic identification on a spanned beam with damage p=0.85, s=0.18 excited at lf/l=0.5. a) three mode identification; b) four mode identification. concluding remarks he paper investigates specific aspects of a novel methodology for the identification of breathing cracks in beams structures that is able to detect simultaneously the location and the depth of the damage. the method exploits the nonlinear features in the response of the structure that are caused by the presence of even very small damage. in particular, suband super-harmonics of the forcing frequency appear in the response; these can be easily detected and measured through tests on the system by forcing it with a narrow-band excitation that causes one of the system mode to be predominant. the proposed method uses a set of numerical tests, each exciting one mode and, by combining the obtained information, a sharp identification is achieved through a minimization problem. it was previously shown how on a cantilever beam the nonlinear harmonic identification method, in contrast to other techniques that need a crack depth larger than 15%-20% of the beam’s height to achieve a satisfactory identification, is able to detect the presence and the level of the damage just exceeding 5% depth, while at only 10% damage, the identification of the position is also correctly obtained. t p. casini et alii, frattura ed integrità strutturale, 29 (2014) 313-324; doi: 10.3221/igf-esis.29.27 323 in this paper, the problem of symmetric structures is also addressed and it is shown how, even the small asymmetry caused by the presence of the damage can be exploited, by exciting the system with a non-symmetric load to correctly obtain the damage identification. moreover, the use of more than one sensor on the structure is investigated, considering in the minimization process the information from each measured point. the obtained results, show that with sensors in different positions the method is able to locate the damage, unless it is close to a constraint, starting at just 5% severity finally, the case of a more complex structure with multiple constraints is addressed. the tests show that using three modes is not sufficient to identify the damage at any location. the use of a fourth mode is necessary to identify the damage in any position. this aspect will be the subject of further investigation, increasing also the complexity of the system; moreover, it is planned to verify with an experimental campaign the effectiveness of the proposed method on the controlled laboratory test cases. references [1] rizos, p.f., aspragathos, n., dimarogonas, a.d., identification of crack location and magnitude in a cantilever beam from the vibration modes, journal of sound and vibration 138 (3) (1990) 381-388. [2] shen, m.h.h., chu, y.c., vibrations of beams with a fatigue crack, computers and structures 45 (1) (1992) 79-93. [3] chu, y.c., shen, m.h.h., analysis of forced bilinear oscillators and the application to cracked beam dynamics, journal of american institute of aeronautics and astronautics 30 (10) (1992) 2512-2519. [4] chati, m., rand, r., mukherjee, s.j., modal analysis of a cracked beam, journal of sound and vibration 207 (1997) 249-270. [5] bovsunovsky, a.p., surace, c., considerations regarding superharmonic vibrations of a cracked beam and the variation in damping caused by the presence of the crack, journal of sound and vibration 288 (2005) 865-886. [6] morassi, a., crack-induced changes in eigenparameters of beam structures, journal of engineering mechanics, 119(9) (1993) 1798-1803. [7] morassi, a., vestroni, f., dynamic methods for damage detection in structures, springer-verlag, isbn: 3211787763, (2008). [8] kisa, m., brandon, j.a., the effects of closure of cracks on the dynamics of a cracker cantilever beam, journal of sound and vibration 238 (1) (2000) 1–18. [9] nandi, a., neogy, s., modelling of a beam with a breathing edge crack and some observations for crack detection, journal of vibration and control 8 (5) (2002) 673-693. [10] andreaus, u., casini, p., vestroni, f., nonlinear features in the dynamic response of a cracked beam under harmonic forcing proceedings of the asme international design engineering technical conferences and computers and information in engineering conference detc2005, 6 c, (2005) 2083-2089. [11] andreaus, u., casini, p., vestroni, f., nonlinear dynamics of a cracked cantilever beam under harmonic excitation, international journal of non-linear mechanics 42 (3) (2007) 566-575. [12] andreaus, u., baragatti, p., experimental damage detection of cracked beams by using nonlinear characteristics of forced response, mechanical systems and signal processes 31 (2012) 382404. [13] giannini, o., casini, p., vestroni, f., experimental evidence of bifurcating nonlinear normal modes in piecewise linear systems, nonlinear dynamics 63 (4) (2011) 655-666. [14] casini, p., giannini, o., vestroni, f., persistent and ghost nonlinear normal modes on the forced response of nonsmooth systems, physica d 241 (2012) 2058–2067. [15] casini, p., giannini, o., vestroni, f., effect of damping on the nonlinear modal characteristics of a piecewise-smooth system through harmonic forced response, mechanical systems and signal processing 36 (2) (2013) 540-548. [16] casini, p., giannini, o., vestroni, f., experimental evidence of non-standard bifurcations in non-smooth oscillator dynamics, nonlinear dynamics 46 (3) (2006) 259-272. [17] nayfeh, a. h., mook t., nonlinear oscillations, wiley ed. isbn: 0471121428 (1995) [18] benfratello, s., cacciola, p., impollonia, n., masnata, a., muscolino, g., numerical and experimental verification of a technique for locating a fatigue crack on beams vibrating under gaussian excitation, engineering fracture mechanics 74 (2007) 2992-3001. [19] giannini, o., casini, p., vestroni, f., nonlinear harmonic identification of breathing cracks in beams, computer and structures, 129 (2013) 166-177. p. casini et alii, frattura ed integrità strutturale, 29 (2014) 313-324; doi: 10.3221/igf-esis.29.27 324 [20] spanos, p.d., koh, a.s., rocking of rigid blocks due to harmonic shaking, journal of engineering mechanics 110 (1984)1627–1642. [21] casini, p., vestroni, f., characterization of bifurcating non-linear normal modes in piecewise linear mechanical systems, international journal of non-linear mechanics 46 (1) (2011) 142-150. microsoft word numero_30_art_44 p. lorenzino et alii, frattura ed integrità strutturale, 30 (2014) 369-374; doi: 10.3221/igf-esis.30.44 369 focussed on: fracture and structural integrity related issues application of digital image correlation (dic) in resonance machines for measuring fatigue crack growth p. lorenzino dpto. de ingeniería de los materiales. insa de lyon, francia. pablo.lorenzino@insa-lyon.fr g. beretta, a. navarro escuela técnica superior de ingeniería, universidad de sevilla. navarro@us.es abstract. this paper presents a simple experimental procedure that greatly facilitates the use of digital image correlation (dic) techniques in fatigue test conducted in resonant testing machines, without the need of test interruptions. this is possible due to the implementation of usb interface optical microscopes of very small dimensions, so that they can be mounted on the specimen as a contact extensometer. thus, the microscopesample assembly oscillates at the resonance frequency of the test. this is how, although the resonant testing machine is in motion, and although the specimen is subjected to fatigue, changing its dimensions according to the applied load, the acquired image is completely static. this allows the evaluation of the plastic deformations generated by the crack growth, avoiding the elastic ones. preliminary results on monitoring cracks with this technique on flat specimens with cylindrical notches of 1050 aluminium alloy are also presented. keywords. digital image correlation; fatigue test; resonance machines; crack growth. introduction here is a growing interest in using digital image correlation (dic) to characterize materials for mechanical properties. dic techniques allow the strain fields arising from application of a stress to a component to be defined. the procedure involves producing a spot pattern on the surface of the target component and assessing relative motion in the spots between the initial and final states in order to characterize the resulting strain fields. this requires taking photographs of the target element before and after loading (see fig. 1), and using an appropriate algorithm to assess relative motion between spots to obtain detailed information about the resulting strain fields [1-3]. successful implementation of dic entails minimizing any relative motion between the image acquisition system and the testing machine in order to avoid errors in calculating strain fields. this hinders use of the technique with resonance machines because they are mounted on springs and hence in continuous motion. notwithstanding this difficulty, dic has aroused much interest for fatigue mechanics studies as it provide the means for analyzing plastic deformations arising during crack propagation. t p. lorenzino et alii, frattura ed integrità strutturale, 30 (2014) 369-374; doi: 10.3221/igf-esis.30.44 370 in this work, we developed a simple, effective dic technique for monitoring deformations throughout a fatigue test while avoiding the typical errors due to relative displacements of the image acquisition system from the testing machine even in resonance machines. reference image deformed state figure 1: changes in a spot pattern upon application of a specific strain. experimental difficulties digital images correlation s noted earlier, successful analysis of experimental deformations entails exercising some cautions. thus, • if a single camera is used (i.e., with 2d dic), specimens should be planar. • the camera should be positioned normal to the specimen surface. • any deformations should be planar (i.e., the distance between the camera and specimen should be constant throughout the acquisition time). • even slight motion out of the plane can lead to substantial errors in calculated deformations (see fig. 2). such errors can be minimized by maximizing the distance between the camera and specimen (l) or minimizing displacement of the specimen from the plane (w). figure 2: error resulting from changes in the camera–specimen distance.  there is the additional experimental difficulty arising from high magnifications. as can be seen from fig. 3, the translation δy resulting from application of a load caused the target zone to fall outside the microscope acquisition field. figure 3: using a high magnification can displace the target zone outside the microscope observation field. a p. lorenzino et alii, frattura ed integrità strutturale, 30 (2014) 369-374; doi: 10.3221/igf-esis.30.44 371 resonance machines resonance testing machines provide a simple means for tests involving a large number of fields. these machines can operate at much higher frequencies than servohydraulic machines and have other salient advantages including reduced size, servicing requirements and energy consumption (1/100)[4]. however, resonance machines pose some problems in implementing dic on fatigue loaded specimens. thus, the resonance frequency cannot be accurately controlled by the user as it depends on the rigidity of the target specimen and changes lengthwise and widthwise in it. also, the specimen cross-section decreases as cracks grow, which alters its rigidity and hence its resonance frequency. the inability to accurately set and maintain the resonance frequency throughout a test hinders the use of stroboscopic cameras, which are frequently used on servohydraulic machines. stroboscopic cameras can take photographs at userdefined frequencies. in fixed-frequency tests, this allows the camera to be set at the test frequency and a static video filmed for subsequent dic processing with a view to calculating deformations due to crack formation and growth [3]. one other technique used with servohydraulic machines involves periodic halting of the test to photograph the specimen. this technique is difficult to implement with resonance machines because they are mounted on springs and hence in continuous motion. the oscillations are insubstantial to the naked eye but can have a considerable impact on dic results. as stated above, in this work we developed a simple solution to the above-described problems. new acquisition system he difficulties encountered in applying dic to a resonance testing machine were overcome by developing a new method to acquire images involving the use of very small digimicro microscopic cameras with magnifications of 10–100× and 40–200× (see fig. 4). figure 4: microscope with a usb interface used for in situ measurements of crack growth. this type of camera had previously been successfully used to monitor crack growth uninterruptedly in planar specimens [6–8]. with dic, however, even a very small displacement can lead to error in calculating deformations. this required altering the cameras for sticking to the specimen in roughly the same manner as a contact extensometer in order to prevent relative motion between the specimen and acquisition system. fig. 5 depicts the camera assembly used, which included two cameras in order to allow both sides of the specimen to be photographed at once. the cameras were mounted by means of elastic bands and fixed by means of two small metal pins along their equator. figure 5: microscopes attached to the specimen surface. t p. lorenzino et alii, frattura ed integrità strutturale, 30 (2014) 369-374; doi: 10.3221/igf-esis.30.44 372 fig. 6 shows the target surface (both specimen sides). the inside of the notch was filled with plasticine in order to avoid light from one microscope interfering with the photographs acquired by the other. figure 6: view of the notch during the test as acquired with the microscopes. test ests were conducted on a rumul testronic 100 kn testing machine using loads of the tensile–tensile type (r = 0.1). the target material was 2 mm thick aluminum alloy 1050 cut into 300×42 mm sheets. notches were 1, 2 or 4 mm in size. some specimens were subjected to a thermomechanical treatment described elsewhere [6] to obtain abnormally large grains (8.22 mm) in order to detect microstructural interactions with the plastic zones around the cracks. results ig. 7 shows an event of crack growth as examined by dic. the target specimen had a grain size of 0.07 mm and a cylindrical notch 2 mm in diameter. the figure shows 6 photographs taken at different crack growth stages. propagation of the resulting plastic zone is clearly apparent. these results are quite promising as they confirm that the dic technique allows the above-described experimental difficulties to be overcome simply by altering the way the cameras are arranged. figure 7: crack growth as determined by digital image correlation (dic). number of cycles (n): (a) 100 000, (b) 130 000, (c) 160 000, (d) 180 000, (e) 210 000, (f) 230 000. t f p. lorenzino et alii, frattura ed integrità strutturale, 30 (2014) 369-374; doi: 10.3221/igf-esis.30.44 373 below are also discussed the results of other studies currently under way at the university of seville [6–8] on the influence of specimen microstructure on crack propagation. these studies are aimed at confirming the differences in propagation between “short” cracks, which are comparable to the specimen grain size in length, and “long” cracks, which are much longer. below is commented on the experimental contribution of the proposed technique in this respect. figure 8: image of the specimen immediately before plastic collapse. grain size = 8.22 mm [8]. fig. 8 shows the situation for a specimen of grain size 8.22 mm. the specimen was 2 mm thick and the grain size across its thickness coincided with the specimen physical thickness. this allowed the microstructure of the material to be assimilated to a two-dimensional arrangement of aluminium single crystals. we used dic to examine one side only —the other was used to extract microstructural information (viz., the position of grain boundaries). thus, the notch, the crack and the grain boundaries —which were outlined to facilitate analysis— are shown at the top, and the deformation fields resulting from propagation of the crack at the bottom. clearly, this example is one case of “short” cracks as the cracks propagated through active sliding of the grains they spanned. in order to propagate from one grain to the next, the crack must switch to a different propagation plane (specifically, to the active sliding plane in the adjacent grain). the active sliding plane is dictated by schmid’s factor. this leads to non-symmetric cracks that propagate at dissimilar rates by effect of successive acceleration and deceleration [6-8]. fig. 9 provides a detailed depiction of fig. 7f. the deformation field shown is that occurring immediately before plastic collapse. this example is one of “microstructurally long” cracks, where the specimen microstructure has no influence. thus, cracks grow symmetrically on both sides of the notch, in a plane at 90º with the loading axis. visual comparison of figs 8 and 9 exposes the influence of microstructure on the way cracks and their associated plastic zones propagate. thus, the crack of fig. 9, corresponding to the specimen with the smaller grain size, exhibited a typical propagation pattern (viz., horizontal growth from the notch equator). on the other hand, growth in the crack of fig. 8 was strongly dependent on microstructure. as can be seen, there was little symmetry. thus, immediately before plastic collapse, the crack on the left and its plastic zone stopped at the grain boundary. also, the new plastic zone did not start at the next grain, but rather at one below that was probably more favorably arranged with respect to the loading direction. finally, let us highlight the sturdiness of the microscopes, which were used without problem to acquire images over more than 20 tests. also, they are very inexpensive to replace (less than 50 € each) if they fail. p. lorenzino et alii, frattura ed integrità strutturale, 30 (2014) 369-374; doi: 10.3221/igf-esis.30.44 374 figure 9: analysis of the specimen immediately after plastic collapse. grain size = 0.07 mm. conclusions n this work, we developed a simple procedure for implementing digital image correlation (dic) on resonance fatigue testing machines. the experimental difficulties typically encountered with this type of machine were easily circumvented and deformation resulting from crack growth was analyzed without the need to stop the tests in order to acquire images. the dic technique affords high magnifications with no image displacement errors. preliminary results for crack propagation and its plastic zone were obtained. under special conditions, it is even possible to study crack–microstructure interactions and observe how grain boundaries act as barriers to propagation of the crack and its plastic zone. our group is currently engaged in refining the surface spot pattern in order to increase the precision of the technique, and in using microscopes of similar size and weight but higher resolution and magnification. acknowledgements he authors are grateful to spain’s ministry of education and science for funding this work through projects dpi2008-01100 and dpi2011-27019, and to the andalusian regional government for additional support through project p07-tep-03045. references [1] http://www.correlatedsolutions.com. (january 2014). [2] sun, z., lyons, j. s., mcneill, s. r. measuring microscopic deformations with digital image correlation optics and lasers in engineering, 27 (1997) 409-428. [3] vanlanduit, s., vanherzeele, j., longo, r., guillaume, p., a digital image correlation method for fatigue test experiments optics and lasers in engineering, 47 (2009) 371-378. [4] http://www.rumul.ch comparision of costs between resonant testing machine and servohydraulic testing machine. (january 2014) [5] carroll, j. d., abuzaid, w., lambros, j., sehitoglu, h., high resolution digital image correlation measurements of strain accumulation in fatigue crack growth, international journal of fatigue, 57 (2013) 140-150. [6] lorenzino, p., navarro, a., krupp, u., naked eye observations of microstructurally short fatigue cracks, international journal of fatigue, 56 (2013) 8-16. [7] lorenzino, p., fatiga en componentes con concentradores de tención bajo carga en modo i, tesis doctoral, sevilla, españa, (2012) 17. [8] lorenzino, p., navarro, a, initiation and growth behavior of very-long microstructurally short fatigue cracks, frattura ed integrità strutturale, 25 (2013) 138-144. i t microsoft word numero_49_art_6_2488 g. meneghetti et alii, frattura ed integrità strutturale, 49 (2019) 53-64; doi: 10.3221/igf-esis.49.06 53 focused on crack tip fields averaged strain energy density estimated rapidly from the nodal stresses by fem for cracks under mixed mode loadings including the t-stress contribution giovanni meneghetti, alberto campagnolo university of padova, department of industrial engineering, via venezia 1, 35131, padova, italy giovanni.meneghetti@unipd.it, http://orcid.org/0000-0002-4212-2618 alberto.campagnolo@unipd.it, http://orcid.org/0000-0001-8685-6210 filippo berto ntnu, department of mechanical and industrial engineering, richard birkelands vei 2b, 7491, trondheim, norway filippo.berto@ntnu.no, http://orcid.org/0000-0001-9676-9970 abstract. the present contribution reviews a recently proposed method to rapidly estimate the averaged sed at the tip of short as well as long cracks under in-plane i+ii and long cracks under out-of-plane i+iii mixed mode loadings. short cracks are distinguished from long cracks by considering that the stress fields within the control volume of short cracks are no longer governed solely by the stress intensity factors (sifs), but also the contribution of higher order terms, and primarily the t-stress, becomes significant to estimate the averaged sed. according to the proposed method, the averaged sed is calculated using the linear elastic nodal stresses evaluated by fem either at the crack tip, to account for the sifs contribution, and at selected fe nodes of the crack free edges, to include the t-stress contribution. the advantage of the proposed approach is two-fold: coarse fe meshes can be adopted; moreover, geometrical modelling the control volume is no longer necessary. to validate the approach, cracked plates subjected to in-plane i+ii mixed mode loading as well as bars weakened by circumferential outer cracks subjected to out-of-plane mixed mode i+iii loading have been analysed. a comparison between approximate values of the averaged sed according to the nodal stress approach and those derived directly from the fe strain energy adopting very refined fe meshes has been successfully performed. keywords. stress intensity factors; t-stress; strain energy density; finite elements; coarse mesh; peak stress. citation: meneghetti, g., campagnolo, a., berto, f., averaged strain energy density estimated rapidly from the nodal stresses by fem for cracks under mixed mode loadings including the t-stress contribution, frattura ed integrità strutturale, 49 (2019) 53-64. received: 17.04.2019 accepted: 23.04.2019 published: 01.07.2019 copyright: © 2019 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. http://www.gruppofrattura.it/va/49/2488.mp4 g. meneghetti et alii, frattura ed integrità strutturale, 49 (2019) 53-64; doi: 10.3221/igf-esis.49.06 54 introduction ealing with cracks under in-plane mixed mode i+ii loading conditions, according to williams [1], the local stress fields expressed in terms of cartesian stress components as functions of the polar coordinates (r,θ), with origin at the crack tip (fig. 1a), can be written in the following form:             xx i ii yy xy θ 1 3 θ 1 3 cos sin θ sin θ -2sin sin θ cos θ 2 2 2 2 2 2 σ k kθ 1 3 1 3 σ = cos + sin θ sin θ + sin θ cos θ 2 2 2 2 22πr 2πr τ 1 3 θ 1 3 sin θ cos θ cos sin θ sin 2 2 2 2                                                                        1/2 1 +t 0 +o(r ) 0 θ 2                               (1) with reference to cracks under mode iii loading conditions, the asymptotic, singular stress distributions have been determined by qian and hasebe [2], following williams’ procedure [1]. the local stress field in terms of cartesian stress components as functions of the polar coordinates (r,θ), with origin at the crack tip (fig. 1b), is the following: xz 1/2iii yz θ -sin τ 2k = +o(r ) τ θ2πr cos 2                         (2)   figure 1: cartesian stress components and polar coordinates with origin at the crack tip for (a) in-plane mixed mode i+ii crack problem and (b) out-of-plane mixed mode i+iii crack problem. the mode i and mode ii stress intensity factors (sifs) can be defined according to gross and mendelson [3] by means of eqns. (3) and (4), respectively.   0.5 00 2 limi yy r k r           (3)   0.5 00 2 limii xy r k r           (4) d σnom τnom 2a w = 10 ·2a l = w (a) r crack bisector σxx σyy τxy θ τnom y x a d = 10 ·a l = d crack bisector mt a 2α=0° mt f f r θ τyz σyy σxx τxy τxz σzz y x z (b) g. meneghetti et alii, frattura ed integrità strutturale, 49 (2019) 53-64; doi: 10.3221/igf-esis.49.06 55 similarly, by extending previous definitions, the mode iii sif can be defined by means of eqn. (5).   0.5 00 2 limiii yz r k r           (5) the constant term t in eqn. (1) is a slit-parallel tensile or compressive stress, named “t-stress” by larsson and carlsson [4], and can be defined according to the following equation:    0 00lim xx yyrt         (6) where θ = 0 in eqns. (3)-(6) identifies the crack bisector line. in the context of fracture mechanics it is largely assumed that the stress field in the close neighborhood of the crack tip can be properly characterized by means of the coefficients of the leading order terms, i.e. the sifs. however, detailed analyses reported in the literature have highlighted the fundamental role of the t-stress in defining the stress state close to the crack tip [4–8]. larsson and carlson [4] and later rice [5] argued on the effect of t-stress on the plastic zone ahead of the crack tip in materials characterized by elastic–plastic behaviour. the influence of t-stress on failure mechanisms of brittle materials was investigated by ayatollahi et al. [6,8] and fett and munz [7], who employed a modified maximum tangential stress approach (mts), taking into account mode i and mode ii sifs, t-stress and a material-dependent length parameter. the combined effects of sifs and t-stress on structural strength problems of cracked components under mixed mode i+ii+iii loadings can be easily evaluated by means of the strain energy density (sed) averaged over a control volume, thought of as a material property and modelled as a circular sector of radius r0, as shown in fig. 2, according to lazzarin and zambardi [9]. the averaged sed criterion has been widely adopted in the recent literature for static [10] and fatigue [911] strength assessments.   figure 2: strain energy density averaged over a control volume (area) of radius r0 surrounding the crack tip, . w w= a . for (a) in-plane mixed mode i+ii crack problem and (b) out-of-plane mixed mode i+iii crack problem. dealing with a general mixed mode crack problem, the averaged sed can be expressed in closed-form as a function of the sifs, i.e. ki, kii and kiii, and of the t-stress, i.e. t, according to the following analytical expression [11,12]:      2 2 2 2 231 i 2 ii iii i an 3/2 0 0 0 0 1+ν 2-5νee k e k k k t1-ν 8 2 w = + + + t + e r e r e r 2e e r15 π    (7) σnom τnom 2a w = 10 ·2a l = w (a) τnom a=π r02 r0 w a d = 10 ·a l = d mt a 2α=0° mt f f r0 a=π r02 w (b) g. meneghetti et alii, frattura ed integrità strutturale, 49 (2019) 53-64; doi: 10.3221/igf-esis.49.06 56 in the above equation, e1, e2 and e3 are three known parameters dependent on the opening angle of a general sharp v-notch and on the poisson’s ratio ν [9], while e is the young’s modulus of the considered material. the use of eqn. (7) in engineering problems presents a major drawback, since very refined meshes are required to evaluate the sifs and the t-stress on the basis of definitions (3)-(5) and (6), respectively, applied to a number of stress-distance fe data. this is due to the fact that the entire local stress field must be determined accurately. the practical application is even more time-consuming in the case of 3d fe models. however, the averaged sed can be evaluated directly from the fe results, femw , by summing the strain-energies wfem,i calculated for each i-th finite element belonging to the control volume and by dividing by the volume (or area in 2d problems, a in fig. 2): ,fem ia fem w w a   (8) equation (8) represents the so-called direct approach to calculate the averaged sed. according to a recent contribution of lazzarin et al. [13] coarse fe meshes within the control volume a can be used. recently, a method to rapidly estimate the averaged sed at the tip of short as well as long cracks under in-plane i+ii [14,15] and long cracks under out-of-plane i+iii [16] mixed mode loadings has been proposed. it is based on the nodal stresses evaluated from finite element (fe) analyses, according to the nodal stress approach: the averaged sed is calculated using the linear elastic nodal stresses evaluated by fem either at the crack tip, to account for the sifs contribution according to the peak stress method (psm), and at selected fe nodes of the crack free edges, to include the t-stress contribution. the advantage of the proposed approach is two-fold: there is no need of mesh refinements in the close neighbourhood of the points of singularity, so that coarse fe meshes can be adopted; moreover, geometrical modelling the control volume in fe models is no longer necessary. the present contribution reviews the nodal stress approach and its validation, which is based on the fe analyses of cracked plates subjected to in-plane i+ii mixed mode loading as well as bars weakened by circumferential outer cracks subjected to out-of-plane mixed mode i+iii loading, while varying (i) the crack lengths, (ii) the mode mixity and (iii) the finite element size adopted in the numerical analyses. parameter cracks under i+ii loading – fig. 1a cracks under i+iii loading – fig. 1b a [mm] 0.5, 0.75, 1…2.25, 2.5, 5, 10…75, 80 3, 4, 6, 8, 10, 15…45, 50 d [mm] 0.0125, 0.03125, 0.05, 0.125, 0.25, 0.5, 1…9, 10 0.05, 0.1, 0.2, 0.5, 1, 2, 3, 4, 5, 10 mm 0, 0.2, 0.4, 0.5, 0.6, 0.8, 1 0, 0.2, 0.4, 0.5, 0.6, 0.8, 1 r0 [mm] 0.28 0.28 table 1: geometrical and loading parameters taken into consideration in refs. [14–16]. all combinations have been analysed, provided that the ratio a/d was greater than the minimum feasible one, i.e. a/d = 1. range of applicability of the sed expression (7) in-plane i+ii mixed mode loading onsidering the in-plane i+ii mixed mode crack problem of fig. 1a, exact values of the averaged sed, femw (eqn. (8)), have been evaluated for the geometrical and loading cases reported in tab. 1, by adopting the direct approach with very refined meshes (patterns with about 500 fe within the reference volume). the ‘exact’ ki and kii sifs and t-stress have been evaluated for the same crack problems by using definitions (3), (4) and (6), respectively, applied to fe results of numerical analyses characterized by very refined meshes, where the element size close to the crack tip was reduced to approximately 10-5 mm. after that, also the analytical sed, anw has been calculated from eqn. (7) and deviated from the exact value, femw , by less than 5% for all considered cases. it should be noted that when the t-stress contribution is negligible, only ki and kii contribute to the averaged sed, kiii being null, and eqn. (7) simplifies to: 2 2 1 2 , 0 0 i ii an i ii e k e k w e r e r    (9) c g. meneghetti et alii, frattura ed integrità strutturale, 49 (2019) 53-64; doi: 10.3221/igf-esis.49.06 57 fig. 3a plots the ratio an,i+ii femw /w for three mode mixity ratios mm, i.e. 0 (pure mode i), 0.5 and 0.8, where mm = kii/(ki + kii). the figure highlights that for a crack size equal to the radius of the material dependent control volume (a/r0 = 1) and pure mode i loading (mm = 0) the error in the averaged sed calculation is about 42% if the t-stress contribution is neglected, i.e. if eqn. (9) is used in place of eqn. (7). however, for the same crack size to control radius ratio, the error is decreased to 17% if mm = 0.5 and further reduced to only 2% if mm = 0.8. fig. 3a shows that when reduced crack size to control radius ratios (a/r0 < 10) are considered, eqn. (7), which includes the t-stress, must be adopted. accordingly, the condition a/r0 < 10 identifies the short crack case, while the condition a/r0  10 identifies the long crack case. out-of-plane i+iii mixed mode loading dealing with the out-of-plane i+iii mixed mode crack problem of fig. 1b, exact values of the averaged sed, femw (eqn. (8)), have been evaluated for the geometrical and loading cases reported in tab. 1, by adopting the direct approach with very refined meshes. it is worth noting that when the t-stress contribution is negligible, only ki and kiii contribute to the averaged sed, kii being null, and eqn. (7) simplifies to: 2 2 31 i iii an,i+iii 0 0 ee k k w = + e r e r (10) once evaluated the ‘exact’ ki and kiii sifs by using definitions (3) and (5), respectively, applied to fe results of numerical analyses characterized by very refined meshes, also the analytical sed, an,i+iiiw can be calculated from (eqn. (10)). fig. 3b plots the ratio an,i+iii femw /w for pure mode i (mm = 0) and pure mode iii (mm = 1) loading, where mm = kiii/(ki + kiii). the figure highlights that for a crack size equal to the radius of the material dependent control volume (a/r0 = 1) the error in the averaged sed estimation is about -15% for pure mode i loading (mm = 0), while it increases to about +30% for pure mode iii loading (mm = 1). these deviations are due to the contribution not only of the t-stress, but also of further higher order non-singular terms, o(r1/2) in eqns. (1) and (2), which are needed to account for the free-edge boundary conditions as discussed in detail in [16], but they are disregarded in the analytical expression, eqn. (7). it should be noted that averaged sed expressions which account for the contribution of further higher-order, non-singular terms, o(r1/2) in eqns. (1) and (2), are not currently available in the literature. that said, it can be observed from fig. 3b that the analytical sed, w , (eqn. (10)), deviates from the exact value, w (eqn. (8)), by less than 5% for a ratio a/r0 ≥ 10, i.e. the long crack case. under this condition, the contribution of higher-order, non-singular terms are believed to be negligible from an engineering point of view, so that eqn. (7) is applicable. therefore, cracks under out-of-plane i+iii mixed mode loading characterised by a/r0 > 10 will be analysed in the following, in order to comply with the range of applicability of eqn. (7), according to results shown in fig. 3b.   figure 3: ratio between analytical ( an,i+iiw or an,i+iiiw ) and exact ( femw ) averaged sed values for (a) in-plane mixed mode i+ii crack problem and (b) out-of-plane mixed mode i+iii crack problem. 0,00 0,25 0,50 0,75 1,00 1,25 1,50 1,75 2,00 1 10 100 w a n ,i + ii /w f e m a/r0 pure mode i mm = 0 mixed mode i+ii mm = 0.5 mixed mode i+ii mm = 0.8 a/r0 < 10 short cracks treated in [15] a/r0 > 10 long cracks treated in [14] 2a = 0° fig. 1a (a) 0,00 0,25 0,50 0,75 1,00 1,25 1,50 1,75 2,00 1 10 100 w a n ,i + ii i/ w f e m a/r0 pure mode i mm = 0 pure mode iii mm = 1 2a = 0° fig. 1b (b) δ  5% a/r0 < 10 short cracks not treated a/r0 > 10 long cracks treated in [16] g. meneghetti et alii, frattura ed integrità strutturale, 49 (2019) 53-64; doi: 10.3221/igf-esis.49.06 58    figure 4: averaged sed evaluated according to the nodal stress (ns) approach (eqn. (17)); (a) and (c) geometry and loading conditions. coarsest fe mesh to obtain a reduced error of 10% in the cases: (b) in-plane mixed mode i+ii crack problem with 2a = 3 mm and mm = 0.50 and (d) out-of-plane mixed mode i+iii crack problem for any mode mixity ratio mm and crack length a. the peak stress method to rapidly evaluate ki, kii and kiii he peak stress method (psm) is an approximate numerical technique to evaluate the sifs. the psm takes its origins by a numerical technique proposed by nisitani and teranishi [17] to rapidly estimate by fem the mode i sif of a crack emanating from an ellipsoidal cavity. a theoretical justification to the psm has been provided later on and the method has been extended also to sharp and open v-notches in order to rapidly evaluate the mode i notch stress intensity factor (nsif) [18]. subsequently, the psm has been formalised to include also cracked components under mode ii loading conditions [19] and open v-notches subjected to pure mode iii (anti-plane) stresses [20]. t σnom τnom 2a = 3 mm w = 10 ·2a l = w σyy,peak τxy,peak (a) τnom y x r θ (b) d ≅ 0.15 mm crack tip a d = 10 ·a l = d (c) mt a 2α=0° mt f f r θ y x z σyy,peak σyy,peak τyz,peak τyz,peak d = a/3 (d) a crack tip g. meneghetti et alii, frattura ed integrità strutturale, 49 (2019) 53-64; doi: 10.3221/igf-esis.49.06 59 in more detail, the psm enables to rapidly estimate the sifs ki, kii and kiii (eqns. (3)-(5)) from the crack tip singular, linear elastic, opening, sliding and tearing fe peak stresses σyy,peak, τxy,peak and τyz,peak, respectively, which are referred to the bisector line according to fig. 4a, concerning the in-plane stress components, and fig. 4c, as to the out-of-plane stress component. more precisely, the following expressions are valid [18–20]: * 0.5 , 1.38ife yy peak k k d    (11) ** 0.5 , 3.38iife xy peak k k d    (12) *** 0.5 , 1.93iiife yz peak k k d    (13) where d is the so-called ‘global element size’ parameter to input in ansys® fe code, i.e. the average fe size adopted by the free mesh generation algorithm available in the fe code. eqns. (11)-(13) were derived using particular 2d or 3d finite element types and sizes, so that a range of applicability exists, which has been presented in detail in previous contributions [18–20], to which the reader is referred. here it is worth recalling that for mode i loading (eqn. (11)) the mesh density ratio a/d that can be adopted in numerical analyses must be a/d  3, a being the minimum between the crack and the ligament lengths; for mode ii loading (eqn. (12)) more refined meshes are required, the mesh density ratio a/d having to satisfy a/d  14; in case of mode iii loading (eqn. (13)) the condition a/d  3 must again be satisfied. as an example, fig. 4b shows a free mesh where d = 0.15 mm was input in ansys® software, while fig. 4d shows a free mesh where the average fe size d is in constant proportion with the crack length a, i.e. a/d = 3. the mesh patterns shown in figs. 4b,d are as coarse as possible to estimate the averaged sed with a 10% error using next eqn. (17). it is important to underline that no additional input parameters other than d and no additional special settings are required to generate an fe mesh according to the psm. when eqns. (11)-(13) were calibrated [18–20], the ‘exact’ ki, kii and kiii sifs were evaluated using definitions (3)-(5), respectively, applied to fe results of numerical analyses characterized by very refined meshes, where the element size close to the crack tip was reduced to approximately 10-5 mm. therefore, the fe size required to estimate ki, kii and kiii from σyy,peak, τxy,peak and τyz,peak, respectively, is likely to be some orders of magnitude larger than that needed to directly calculate the local stress fields in order to apply definitions (3)-(5). moreover, while eqns. (3)-(5) require to process a number of stress-distance numerical results, the psm requires a single stress value to evaluate the sifs. a fe-based technique to evaluate rapidly the t-stress he analytical expressions of the stress components σxx along the crack free edges are obtained substituting the polar coordinate θ = +π and –π in eqn. (1) and are given in eqns. (14a) and (14b), respectively [12]:   1/2iixx θ=π 2k σ =+t+o(r ) 2πr (14a)   1/2iixx θ=-π 2k σ =+ +t+o(r ) 2πr (14b) therefore, the t-stress contribution can be derived according to eqn. (15), as previously highlighted by ayatollahi et al. [6], lazzarin et al. [11] and radaj [21]:    xx xxθ=π θ=-πσ + σt= 2 (15) t g. meneghetti et alii, frattura ed integrità strutturale, 49 (2019) 53-64; doi: 10.3221/igf-esis.49.06 60 equation (15) suggests to evaluate the t-stress numerically using the nodal stresses σxx along the crack free edges. the obtained results are shown in fig. 5a for a mesh density ratio a/d = 2 applied to the crack problem of previous fig. 1a. fig. 5a show that due to numerical errors caused by the crack tip singularity, eqn. (15) based on fe results is satisfied with a reduced error lower than 3% only at a distance from the crack tip r ≥ 2d. on the basis of the obtained results, a fe-based technique to rapidly evaluate the t-stress can be defined according to the following expression:    xx xxθ=π,r=2d θ=-π,r=2dσ + σnodal t-stress= 2 (16) to verify the applicability of eqn. (16) to the considered small cracks subjected to mixed mode i+ii loading (see tab. 1), the ratio between the nodal t-stress according to eqn. (16) and the exact t-stress is shown in fig. 5b for a mode mixity ratio mm = 0.50, the results for other mm values being identical. fig. 5b shows that in all cases the minimum feasible mesh density ratio a/d = 2 assures the applicability of eqn. (16), because all numerical results fall within a restricted scatter-band of ±3%.   figure 5: in-plane mixed mode i+ii crack problem: t-stress evaluated according to the nodal stress approach (eqn. (16)). (a) fe stresses σxx along the crack free edges by adopting a mesh density ratio a/d = 2. considered case 2a = 3 mm and mm = 0.50. (b) ratio between approximate and exact t-stress versus the mesh density ratio for the case mm = 0.50. the nodal stress approach to rapidly estimate the averaged sed with inclusion of the t-stress n this section, the nodal stress (ns) approach to estimate the averaged sed for short as well long cracks under inplane i+ii [14,15] and long cracks under out-of-plane i+iii [16] mixed mode loading is recalled. the technique is referred to as the nodal stress approach that can immediately be formalized by substituting eqns. (11)-(13) and (16) into the appropriate analytical sed formulation, eqn. (7):             ns psm nodal-t 2 2 20.5 0.5 0.5 * ** ***31 2 ns fe yy,peak fe xy,peak fe yz,peak 0 0 0 2 2 xx xxθ=π,r=2d θ=-π,r=2d 3/2 w = w + w ee ed d d w = k σ + k τ + k τ + e e er r r σ + σ 1+ν 2-51-ν 8 2 + 2e 2 15 π                                                         0.5 xx xxθ=π,r=2d θ=-π,r=2d* fe yy,peak 0 σ + σν d k σ e 2r                   (17) -10 -8 -6 -4 -2 0 2 4 6 8 10 0,00 0,50 1,00 1,50 2,00 n o rm al iz ed s tr es se s r/d 1 2 3 (σxx)θ=π/t-stress (σxx)θ=-π/t-stress ((σxx)θ=π+(σxx)θ=-π)/t-stress fig. 1a 2α = 0° 2a = 3 mm mm = 0.50 a/d = 2 (a) 0,00 0,25 0,50 0,75 1,00 1,25 1,50 1,75 2,00 1 10 100 1000 n o da l t -s tr es s/ t -s tr es s a/d fig. 1a 2α = 0° mm = 0.50 +3% -3% (b) i g. meneghetti et alii, frattura ed integrità strutturale, 49 (2019) 53-64; doi: 10.3221/igf-esis.49.06 61 figure 6: selected fe nodal stresses to rapidly evaluate the averaged sed according to the nodal stress approach (eqn. (17)). equation (17) shows that only few selected nodal stresses calculated from coarse fe mesh patterns can be used to estimate the averaged sed. fig. 6 shows a sketch of the five nodal stresses involved in eqn. (17): the crack tip, linear elastic opening (σyy,peak), sliding (τxy,peak) and tearing (τyz,peak) peak stresses referred to the crack bisector line and the linear elastic stresses σxx evaluated at the fe nodes located along the crack free edges at r = 2d. coarse fe mesh patterns with an average fe size equal to d are adopted. validation of the nodal stress approach to estimate the averaged sed short as well long cracks under in-plane i+ii mixed mode loading [14,15] o validate the nodal stress approach based on eqn. (17), an infinite plate weakened by a central crack and subjected to in-plane mixed mode loading was considered according to fig. 1a. several crack lengths 2a (from 1 to 160 mm) have been considered, while width w and length l of the plate were set both equal to 10 times the crack length. the mean fe size d to evaluate σyy,peak, τxy,peak, σxx,θ=π,r=2d and σxx,θ=-π,r=2d (see fig. 6) in eqn. (17) was varied from 0.0125 to 10 mm. all different geometrical and loading parameters taken into account are listed in tab. 1. according to the psm, fe analyses have been carried out by using ansys® software and by adopting free mesh patterns consisting of 4-node quadrilateral elements (plane 182 with k-option 1 set to 3). exact values of the averaged sed, w (eqn. (8)), have been evaluated by adopting the direct approach with very refined meshes (patterns with about 500 fe within the reference volume). figs. 7a,b,c report the ratio between approximate ( nsw , nodal stress approach eqn. (17)) and exact ( femw , direct approach eqn. (8)) averaged sed values for selected mode mixity ratios mm. the ratio w /w is seen to converge to unity inside a ±10% scatter-band for all considered mms. in particular, figs. 7a,b,c show that convergence occurs for mesh density ratios a/d greater than 3 for mm = 0, 10 for mm = 0.50 and 14 for mm = 1. the obtained results show that the minimum mesh density ratio a/d to apply the nodal stress approach increases with increasing the mode mixity ratio mm. the minimum mesh density ratio to apply eqn. (17) with a given level of approximation has been determined in [14,15] depending on the mode mixity ratio (mm) and it is not reported here for sake of brevity. long cracks under out-of-plane i+iii mixed mode loading [16] to validate the nodal stress approach based on eqn. (17) under out-of-plane mixed mode loading, numerical analyses have been performed by considering a bar weakened by a circumferential outer crack according to fig. 1b. several crack lengths a (from 3 to 50 mm) have been considered, while diameter d and length l of the bar were set both equal to 10 times the crack length. the average fe size d to evaluate the peak stresses σyy,peak and τyz,peak (see fig. 6, nodal stresses σxx,θ=±π,r=2d are not required, t-stress contribution being negligible for long cracks) in eqn. (17) was varied from 0.05 to 10 mm. all different geometrical and loading parameters taken into account are listed in tab. 1. according to the psm, fe analyses have been carried out by means of ansys® software and by adopting free mesh patterns consisting of two-dimensional, harmonic, 4t (σxx)r=2d,θ=π (σxx)r=2d,θ=-π d ≅ 0.30 σyy,peak σyy,peak τyz,peak τyz,peak τxy,peak τxy,peak y x g. meneghetti et alii, frattura ed integrità strutturale, 49 (2019) 53-64; doi: 10.3221/igf-esis.49.06 62 node linear quadrilateral elements (plane 25 of ansys® element library). exact values of the averaged sed, w (eqn. (8)), have been evaluated by adopting the direct approach with very refined meshes. fig. 7d reports the ratio between approximate (w , nodal stress approach eqn. (17)) and exact ( femw , direct approach eqn. (8)) averaged sed values for all mode mixity ratios mm. the ratio w /w is seen to converge to unity inside a ±10% scatter-band. in particular, fig. 7d shows that convergence occurs for a mesh density ratio a/d greater than 3 for all mode mixity ratios mm taken into account. the obtained results show that the minimum crack size to fe size ratio a/d to apply the nodal stress approach (eqn. (17)) remains constant regardless of the mode mixity ratio mm. this differs from what was obtained previously dealing with cracks subjected to in-plane mixed mode i+ii loading, for which the minimum mesh density ratio a/d to apply the nodal stress approach increased with increasing the mode mixity ratio mm, since mode ii loading is more demanding in terms of mesh density ratio a/d than mode i loading.   figure 7: ratio between approximate (w ) and exact (w ) averaged sed versus the mesh density ratio for (a), (b) and (c) the inplane mixed mode i+ii crack problem of fig. 1a and (d) the out-of-plane mixed mode i+iii crack problem of fig. 1b. w according to the nodal stress approach, eqn. (17); w according to the direct approach, eqn. (8). conclusions he present contribution has reviewed the nodal stress approach recently proposed to estimate the averaged strain energy density (sed) of mixed-mode i+ii and i+iii crack tip fields including the t-stress contribution. the method takes five fe nodal stresses calculated with coarse fe meshes made of four-node, linear quadrilateral finite elements: three of them are the singular, linear elastic crack tip opening, sliding and tearing peak stresses, respectively, which take into account the stress intensity factor contribution; the remaining two ones are the nodal stresses evaluated along the crack free edges at a selected distance from the crack tip and take into account the t-stress contribution. the conclusions can be summarised as follows:  taking advantage of the closed-form expression of the averaged sed (eqn. 7), the nodal stress approach has been formalised according to eqn. (17); 0,00 0,50 1,00 1,50 2,00 2,50 3,00 1 10 100 1000 w n s/ w f e m a/d 2α = 0° mm = 0 r0 = 0.28 mm a/r0>1 +10% -10% (a)  3 0,00 0,50 1,00 1,50 2,00 2,50 3,00 1 10 100 1000 w n s/ w f e m a/d 2α = 0° mm = 0.50 r0 = 0.28 mm a/r0>1 +10% -10% (b)  10 0,00 0,50 1,00 1,50 2,00 2,50 3,00 1 10 100 1000 w n s/ w f e m a/d 2α = 0° mm = 1.00 r0 = 0.28 mm a/r0>1 +10% -10% (c)  14 0,00 0,50 1,00 1,50 2,00 2,50 3,00 1 10 100 1000 w n s/ w f e m a/d 2α = 0° 0 ≤ mm ≤ 1 r0 = 0.28 mm a/r010 +10% -10%  3 (d) t g. meneghetti et alii, frattura ed integrità strutturale, 49 (2019) 53-64; doi: 10.3221/igf-esis.49.06 63  for short as well as long cracks under in-plane i+ii mixed mode loading, more refined fe mesh patterns are required, the higher the mode mixity ratio mm is. in particular, the minimum ratio a/d between the semi-crack length a and the average fe size d to apply the nodal stress approach with a level of approximation equal to 10% is found to be equal to 3 in the case of pure mode i (mm = 0), 10 in the case of mixed mode i+ii with mm = 0.50 and 14 for pure mode ii loading (mm = 1).  for long cracks under out-of-plane i+iii mixed mode loading, the minimum mesh density ratio a/d to apply the nodal stress approach with a level of approximation equal to 10% is equal to 3, independent of the mode mixity.  even though the averaged sed can be evaluated directly by means of fe analyses using coarse meshes inside the control volume, the t-stress contribution being automatically included, nonetheless some additional advantages of the nodal stress approach to estimate the averaged sed can be singled out: (i) only the linear elastic nodal stresses calculated at selected fe nodes are necessary; (ii) geometrical modelling the control volume in fe models is no longer necessary; (iii) the adopted fe meshes are coarse. references [1] williams, m.l. (1957). on the stress distribution at the base of a stationary crack, j. appl. mech., 24, pp. 109–114. [2] qian, j., hasebe, n. (1997). property of eigenvalues and eigenfunctions for an interface v-notch in antiplane elasticity, eng. fract. mech., 56(6), pp. 729–734, doi: 10.1016/s0013-7944(97)00004-0. [3] gross, b., mendelson, a. (1972). plane elastostatic analysis of v-notched plates, int. j. fract. mech., 8(3), pp. 267–276. doi: 10.1007/bf00186126. [4] larsson, s.g., carlsson, a.j. (1973). influence of non-singular stress terms and specimen geometry on small-scale yielding at crack tips in elastic-plastic materials, j. mech. phys. solids, 21(4), pp. 263–277. doi: 10.1016/0022-5096(73)90024-0. [5] rice, j.r. (1974). limitations to the small scale yielding approximation for crack tip plasticity, j. mech. phys. solids, 22(1), pp. 17–26, doi: 10.1016/0022-5096(74)90010-6. [6] ayatollahi, m.r., pavier, m.j., smith, d.j. (1998). determination of t -stress from finite element analysis for mode i and mixed mode i/ii loading, int. j. fract., 91(3), pp. 283–298. [7] fett, t., munz, d. (2003). t-stress and crack path stability of dcdc specimens, int. j. fract., 124(1/2), pp. l165–1170. doi: 10.1023/b:frac.0000009324.91532.fb. [8] smith, d.j., ayatollahi, m.r., pavier, m.j. (2001). the role of t-stress in brittle fracture for linear elastic materials under mixed-mode loading, fatigue fract. eng. mater. struct., 24(2), pp. 137–150. doi: 10.1046/j.1460-2695.2001.00377.x. [9] lazzarin, p., zambardi, r. (2001). a finite-volume-energy based approach to predict the static and fatigue behavior of components with sharp v-shaped notches, int. j. fract., 112, pp. 275–298. doi: 10.1023/a:1013595930617. [10] berto, f., lazzarin, p. (2014). recent developments in brittle and quasi-brittle failure assessment of engineering materials by means of local approaches, mater. sci. eng. r reports, 75, pp. 1–48. doi: 10.1016/j.mser.2013.11.001. [11] lazzarin, p., berto, f., radaj, d. (2009). fatigue-relevant stress field parameters of welded lap joints: pointed slit tip compared with keyhole notch, fatigue fract. eng. mater. struct., 32(9), pp. 713–35. doi: 10.1111/j.1460-2695.2009.01379.x. [12] berto, f., lazzarin, p. (2013). multiparametric full-field representations of the in-plane stress fields ahead of cracked components under mixed mode loading, int. j. fatigue, 46, pp. 16–26. doi: 10.1016/j.ijfatigue.2011.12.004. [13] lazzarin, p., berto, f., zappalorto, m. (2010). rapid calculations of notch stress intensity factors based on averaged strain energy density from coarse meshes: theoretical bases and applications, int. j. fatigue, 32(10), pp. 1559–1567. doi: 10.1016/j.ijfatigue.2010.02.017. [14] meneghetti, g., campagnolo, a., berto, f., atzori, b. (2015). averaged strain energy density evaluated rapidly from the singular peak stresses by fem: cracked components under mixed-mode (i+ii) loading, theor. appl. fract. mech., 79, pp. 113–124. doi: 10.1016/j.tafmec.2015.08.001. [15] campagnolo, a., meneghetti, g., berto, f. (2016). rapid finite element evaluation of the averaged strain energy density of mixed-mode (i + ii) crack tip fields including the t-stress contribution, fatigue fract. eng. mater. struct., 39(8), pp. 982–998. doi: 10.1111/ffe.12439. [16] meneghetti, g., campagnolo, a., berto, f. (2016). averaged strain energy density estimated rapidly from the singular peak stresses by fem: cracked bars under mixed-mode (i+iii) loading, eng. fract. mech., 167, pp. 20–33. doi: 10.1016/j.engfracmech.2016.03.040. [17] nisitani, h., teranishi, t. (2001).ki value of a circumferential crack emanating from an ellipsoidal cavity obtained by g. meneghetti et alii, frattura ed integrità strutturale, 49 (2019) 53-64; doi: 10.3221/igf-esis.49.06 64 the crack tip stress method in fem. in: guagliano, m., aliabadi, m.h., (eds.), proceedings of the 2nd international conference on fracture and damage mechanics, pp. 141–146. [18] meneghetti, g., lazzarin, p. (2007). significance of the elastic peak stress evaluated by fe analyses at the point of singularity of sharp v-notched components, fatigue fract. eng. mater. struct., 30(2), pp. 95–106. doi: 10.1111/j.1460-2695.2006.01084.x. [19] meneghetti, g. (2012). the use of peak stresses for fatigue strength assessments of welded lap joints and cover plates with toe and root failures, eng. fract. mech., 89, pp. 40–51, doi: 10.1016/j.engfracmech.2012.04.007. [20] meneghetti, g. (2013). the peak stress method for fatigue strength assessment of tube-to-flange welded joints under torsion loading, weld. world, 57(2), pp. 265–275, doi: 10.1007/s40194-013-0022-x. [21] radaj, d. (2010). t-stress corrected notch stress intensity factors with application to welded lap joints, fatigue fract. eng. mater. struct., 33(6), pp. 378–389, doi: 10.1111/j.1460-2695.2010.01454.x. << /ascii85encodepages false /allowtransparency false /autopositionepsfiles true /autorotatepages /none /binding /left /calgrayprofile (dot gain 20%) /calrgbprofile (srgb iec61966-2.1) /calcmykprofile (u.s. web coated \050swop\051 v2) /srgbprofile (srgb iec61966-2.1) /cannotembedfontpolicy /error /compatibilitylevel 1.4 /compressobjects /tags /compresspages true /convertimagestoindexed true /passthroughjpegimages true /createjobticket false /defaultrenderingintent /default /detectblends true /detectcurves 0.0000 /colorconversionstrategy /cmyk /dothumbnails false /embedallfonts true /embedopentype false /parseiccprofilesincomments true /embedjoboptions true /dscreportinglevel 0 /emitdscwarnings false /endpage -1 /imagememory 1048576 /lockdistillerparams false /maxsubsetpct 100 /optimize true /opm 1 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/hrv (za stvaranje adobe pdf dokumenata najpogodnijih za visokokvalitetni ispis prije tiskanja koristite ove postavke. stvoreni pdf dokumenti mogu se otvoriti acrobat i adobe reader 5.0 i kasnijim verzijama.) /hun 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/pdfxoutputintentprofileselector /documentcmyk /preserveediting true /untaggedcmykhandling /leaveuntagged /untaggedrgbhandling /usedocumentprofile /usedocumentbleed false >> ] >> setdistillerparams << /hwresolution [2400 2400] /pagesize [612.000 792.000] >> setpagedevice microsoft word numero_34_art_11 g meneghetti et alii, frattura ed integrità strutturale, 34 (2015) 109-115; doi: 10.3221/igf-esis.34.11 109 focussed on crack paths a link between the peak stresses and the averaged strain energy density for cracks under mixed-mode (i+ii) loading g. meneghetti, b. atzori university of padova, department of industrial engineering, via venezia 1, 35131, padova (italy) giovanni.meneghetti@unipd.it, bruno.atzori@unipd.it a. campagnolo, f. berto university of padova, department of management and engineering, stradella s. nicola 3, 36100, vicenza (italy) campagnolo@gest.unipd.it, berto@gest.unipd.it abstract. in this work, a link between the averaged strain energy density (sed) approach and the peak stress method in the case of cracks subjected to mixed mode (i+ii) loading has been investigated. some closed-form expressions of the strain energy density, averaged in a volume of radius r0, as function of the stress intensity factors are provided for plane strain conditions under mixed mode i+ii loadings. on the basis of the peak stress method (psm) some expressions useful to estimate the mode i and mode ii stress intensity factors (sifs) have been recently derived. these relationships take advantage of the elastic peak stresses from fe analyses carried out by using a given mesh pattern where the element size and type are kept constants. the evaluation of the sifs from a numerical analysis of the local stress field usually requires very refined meshes and then large computational effort. the usefulness of the psm-based expressions is that (i) only the elastic peak stresses numerically evaluated at the crack tip are needed and not a set of stress–distance data; (ii) the employed meshes are rather coarse if compared to those necessary for the evaluation of the whole local stress field. by substituting the psm-based relationships in the closed-form expressions of the averaged sed it appears that the latter can be directly estimated by means of the elastic peak stresses evaluated at the crack tip. several fe analyses have been carried out on cracked plates subjected to tension loading considering different geometrical combinations, varying the length 2a and the inclination ϕ of the crack (i.e. the mode mixity) as well as the size d of the adopted finite elements, with the aim to evaluate the local sed and the elastic peak stress components σpeak and τpeak. in all cases the numerical values of the sed derived from the fe analyses have been compared with those analytically obtained by using the expressions for the sed based on the elastic peak stresses, in order to verify the range of applicability of the proposed relationships. keywords. local approaches; stress intensity factors; strain energy density; finite elements; coarse mesh. introduction otch stress intensity factors (nsifs) play an important role in static strength assessments of components made of brittle or quasi-brittle materials and weakened by sharp v-shaped notches [1]. this holds true also for components made of structural materials undergoing high cycle fatigue loading [2] as well as for welded joints n g meneghetti et alii, frattura ed integrità strutturale, 34 (2015) 109-115; doi: 10.3221/igf-esis.34.11 110 [3,4]. in plane problems, the mode i and mode ii nsifs for sharp v-notches, which quantify the intensity of the asymptotic stress distributions in the close neighbourhood of the notch tip, can be expressed by means of the gross and mendelson’s definitions [5]:   111 002 limrk r             (1)   212 002 lim rrk r             (2)  rr r    notch bisector r a=r0 2 r0 figure 1: (a) polar coordinate system centred at the notch tip. (b) control volume (area) of radius r0 surrounding the v-notch tip. where (r,θ) is a polar coordinate system centred at the notch tip (fig. 1a), σθθ and τrθ are the stress components according to the coordinate system and λ1 and λ2 are the mode i and mode ii first eigenvalues in william’s equations [6], respectively. the condition θ = 0 characterizes all points of the notch bisector line. when the v-notch angle 2α is equal to zero, λ1 and λ2 equal 0.5 and k1 and k2 match the conventional stress intensity factors of a crack, ki and kii, according to the linear elastic fracture mechanics (lefm). the main practical disadvantage in the application of the nsif-based approach is that very refined meshes are needed to calculate the nsifs by means of definitions (1) and (2). the modelling procedure becomes particularly time-consuming for components that cannot be analysed by means of two-dimensional models. recently, nisitani and teranishi [7,8] presented a new numerical procedure suitable for estimating ki for a crack emanating from an ellipsoidal cavity. such a procedure is based on the usefulness of the linear elastic stress σpeak calculated at the crack tip by means of fe analyses characterized by a mesh pattern having a constant element size. in particular nisitani and teranishi [7,8] were able to show that the ratio ki/σpeak depends only on the element size, so that the σpeak value can be used to rapidly estimate ki, provided that the adopted mesh pattern has been previously calibrated on geometries for which the exact value of ki is known. this approach has been theoretically justified and extended also to sharp v-shaped notches subject to mode i loading [9] giving rise to the so-called peak stress method (psm), which can be regarded as an approximate fe-based method to estimate the nsifs. later on, the psm has been extended to cracks subjected to mode i as well as mode ii stresses [10]. the element size required to evaluate k1 and k2 from σpeak and τpeak, respectively, is several orders of magnitude greater than that required to directly evaluate the local stress field. the second advantage of using σpeak and τpeak is that only a single stress value is sufficient to estimate k1 and k2, respectively, instead of a number of stress-distance fe data, as usually made by applying definitions (1) and (2). since the units of the mode i and mode ii nsifs, k1 and k2, depend on the notch opening angle, a direct comparison of the nsif values cannot be performed. this problem was overcome by lazzarin and zambardi [11], who proposed to use the total elastic strain energy density (sed) averaged over a sector of radius r0 (fig. 1b) for static [11-14] and fatigue [11,15,16] strength assessments. with reference to plane strain conditions, the sed value can be evaluated as follows: 1 2 2 2 1 1 2 2 1 1 0 0 e k e k w e r e r                (3) where e1 and e2 [11] are two parameters which depend on the notch opening angle 2α and the poisson’s ratio ν. in principle, eq. (3) is valid when the influence of higher order, non-singular terms can be neglected inside the control volume. in the case of short cracks or thin welded lap joints, for example, the t-stress must be included in the local sed evaluation [17]. g meneghetti et alii, frattura ed integrità strutturale, 34 (2015) 109-115; doi: 10.3221/igf-esis.34.11 111 aims of the present contribution are as follows:  to recall the fundamental concepts of the psm for pure modes of loading;  to present the extension of the psm to the case of mixed mode (i+ii) loading;  to investigate a link between the sed approach and the psm in the case of mixed mode (i+ii) loading. the peak stress method for pure modes of loading he peak stress method (psm) is a simplified numerical method to estimate the nsifs parameters. originally it was formulated for cases where only mode i singular stresses exists (i.e. k2 = 0 or mode ii stresses are negligible). it has been based on a link between the exact value of mode i nsif k1, see eq. (1), and the linear elastic opening peak stress σpeak calculated at the v-notch tip according to the following expression [9]: 1 * 1 1 1.38fe peak k k d      (4) the psm according to eq. (4) was applied to correlate the fatigue strength of fillet-, full penetration and butt welded joints subjected to mode i loading [18-20]. recently the peak stress method has been extended also to mode ii crack problems, linking the exact value of mode ii nsif k2, see eq. (2) with 2 = 0° and 2 = 0.5, and the linear elastic sliding peak stress τpeak calculated at the crack tip according to the following expression [10]: 2 ** 2 1 3.38fe peak k k d      (5) in previous expressions d is the mean finite element size adopted when using the free mesh generation algorithm available in ansys numerical code, while “exact nsif values” must be meant as the values obtained using very refined fe mesh patterns in the numerical analyses and applying definitions (1) and (2) to the numerical results. eqs. (4) and (5) are useful in practical applications because if the mean element size d is kept constant, then also k1/σpeak and k2/τpeak ratios are constant. eqs. (4) and (5) are valid under the following conditions:  use of 4-node linear quadrilateral elements, as implemented in ansys® numerical code (plane 42 of ansys element library or alternatively plane 182 with k-option 1 set to 3);  the pattern of finite elements around the v-notch tip must be that shown in fig. 2b (see also [9, 10]); in particular, four elements share the node located at the crack tip;  concerning eq. (4), v-notches characterised by an opening angle 2 ranging from 0° to 135°;  the ratio a/d must be greater than 3 in order to obtain * 1.38 3%fek   , a being the semi-crack length (or the notch depth when dealing with open v-notches). when mode ii (sliding) stresses are of interest, meshes are more refined such that the ratio a/d must be greater than 14 in order to obtain ** 3.38 3%fek   . the peak stress method for mixed mode (i+ii) loading n the present paragraph the peak stress method is extended to mixed mode (i+ii) crack problems. consider a crack (2α = 0°) centred in a plate having the geometry reported in fig. 2a and subjected to tensile loading. by varying the inclination angle ϕ of the crack it is possible to obtain different mode mixities, from pure mode i (ϕ = 0°) to mixed mode i+ii (ϕ > 0°) loading. different geometrical combinations have been considered, varying the projected crack length 2h (from 5 to 80 mm) and the inclination ϕ (from 0° to 60°) as well as the size of the element d, with the aim to investigate to what extent the psm holds true. finite element analyses have been performed by using the commercial code ansys® and 4-node quadrilateral element (plane 42). the free mesh algorithm has been used in all numerical analyses and the sole control parameter set to generate the mesh has been the so-called ‘global element size’, i.e. the mean element size of the finite elements, which ranged from 0.5 mm to 10 mm. with the purpose of obtaining the pattern of finite t i g meneghetti et alii, frattura ed integrità strutturale, 34 (2015) 109-115; doi: 10.3221/igf-esis.34.11 112 elements oriented along the crack bisector line (see fig. 2b), the geometry of the plate has been divided into six areas, such that each crack tip is shared by four areas, as shown in fig 2a. by so doing four elements (each one belonging to a different area) share the node located at the crack tip. for the considered case, k1 = ki, k2 = kii, λ1 = λ2 = 0.5, while σpeak and τpeak represent the maximum elastic normal and tangential stress referred to the bisector line and evaluated at the crack tip according to fig. 2a. the exact values of the mode i and mode ii sif, ki and kii, have been evaluated by means of further finite element analyses performed on the same geometries, but adopting very refined meshes (size of the smallest element of the order of 10-5 mm) in the close neighbourhood of the crack tip. fig. 3 plots the results of the numerical analyses in terms of the non-dimensional parameters k*fe and k**fe defined in eqs. (4) and (5). the results for the cases ϕ = 10°, 45°, 30° and 60° have been reported. from fig. 3, k*fe and k**fe are seen to converge to the previously calibrated values, that is 1.38 [9] and 3.38 [10], respectively, within a scatter band of the numerical results of ±3% also in the case of mixed mode (i+ii) loading. this occurs for a ratio a/d greater than a value between 3 and 6, for mode i loading, and between 12 and 21, for mode ii loading. it can be observed that the minimum a/d ratios to assure the validity of psm under mixed mode (i+ii) loading are only slightly greater than the results obtained in [9], in the case of pure mode i (a/d  3), and the results reported in [10] with reference to pure mode ii (a/d  14). furthermore, as highlighted in [10], it should be noted that the mode ii loading is more critical to analyse with the psm than the mode i loading because it requires more refined finite element mesh patterns. figure 2: (a) geometry and loading condition of the analysed mixed mode crack problem. 2w = 200 mm. (b) pattern of finite elements around the singularity point: four elements share the node located at the crack tip. a link between the peak stresses and the averaged value of the local strain energy density n the present paragraph, a link between the averaged sed [11,12] and the peak stresses [9,10] in the case of cracks subjected to mixed mode (i+ii) loading is investigated. by substituting the psm-based relationships, eqs. (4) and (5), in the closed-form expression of the averaged sed, eq. (3), it appears that the latter can be directly estimated by means of the elastic peak stresses evaluated at the crack tip, σpeak and τpeak: -1 2 2 21 1 * **1 2 0 0 psm fe peak fe peak e ed d w k k e r e r                                  (6) i g meneghetti et alii, frattura ed integrità strutturale, 34 (2015) 109-115; doi: 10.3221/igf-esis.34.11 113 several refined fe analyses have been carried out on the same cracked plates taken into consideration in the previous paragraph, with the aim to evaluate the local sed averaged over a control volume centred at the crack tip. different geometrical combinations have been considered, varying the length 2a and the inclination ϕ of the crack (i.e. the mode mixity), while the radius of the control volume r0 has been kept constant and equal to 0.1 mm. 0.00 0.50 1.00 1.50 2.00 2.50 3.00 3.50 4.00 1 10 100 a/d k * f e , k * * f e k*fe k**fe +3% -3% 1.38  6 2 = 0° = 10° 3.38 +3% -3%  12 (a) k*fe k**fe 0.00 0.50 1.00 1.50 2.00 2.50 3.00 3.50 4.00 1 10 100 a/d k * f e , k * * f e k*fe k**fe +3% -3% 1.38  4 2 = 0° = 30° 3.38 +3% -3%  14 k*fe k**fe (b) 0.00 0.50 1.00 1.50 2.00 2.50 3.00 3.50 4.00 1 10 100 a/d k * f e , k * * f e k*fe k**fe +3% -3% 1.38  5 2 = 0° = 45° 3.38 +3% -3%  21 (c) k*fe k**fe 0.00 0.50 1.00 1.50 2.00 2.50 3.00 3.50 4.00 1 10 100 a/d k * f e , k * * f e k*fe k**fe +3% -3% 1.38  3 2 = 0° = 60° 3.38 +3% -3%  16 k*fe k**fe (d) figure 3: calibration of the psm approach for a crack (2α = 0°) under mixed mode (i+ii) loading: (a) ϕ = 10°; (b) ϕ = 30°; (c) ϕ = 45°; (d) ϕ = 60°. non-dimensional sifs related to mode i and mode ii. the mode mixity ratio (mm) has been evaluated according to the following definition: ii i ii k mm k k   (7) eq. (7) provides as master cases mm = 0 for pure mode i with ϕ = 0°, mm = 0.5 for mixed mode with ϕ = 45° and mm = 1 for pure mode ii loading. in all cases the numerical values of the sed calculated from the fe analyses have been compared with those analytically obtained by using the expressions for the sed based on the elastic peak stresses, eq. (6), in order to verify the range of applicability of the proposed method. being the exact values of the sifs available, the mean value of the sed has been evaluated also according to eq. (3). in particular the maximum difference between the sed parameter evaluated analytically (eq. (3)) and numerically (by fem) resulted about 5%, that means that the influence of higher order terms, as the t-stress, can be neglected in these cases, at least from an engineering point of view. the ratio between the sed based on the elastic peak stresses (eq. 6, psmw ) and the sed calculated from the fe analyses ( femw ) has been reported in fig. 4, with reference to an inclination ϕ of the crack equal to 0°, 30°, 45° and 60°. from fig. 4, it can be observed that the ratio /psm femw w converges to unity, within a scatter band of ±10% for all different mode mixities taken into consideration. this occurs for a ratio a/d greater than 3 for the case mm = 0 (ϕ = 0°), 8.50 for g meneghetti et alii, frattura ed integrità strutturale, 34 (2015) 109-115; doi: 10.3221/igf-esis.34.11 114 mm = 0.37 (ϕ = 30°), 11 for mm = 0.50 (ϕ = 45°) and 16 for mm = 0.63 (ϕ = 60°). in particular the minimum a/d ratio to assure the validity of the proposed method increases as the mode ii loading becomes dominant, that is as the mode mixity ratio (mm) defined by eq. (7) increases. a similar behavior has been observed in the previous paragraph and in [10], with reference to k*fe and k**fe. 0.00 0.50 1.00 1.50 2.00 2.50 3.00 3.50 1 10 100 1000 a/d w p s m /w f e m   rmm    a 0.00 0.50 1.00 1.50 2.00 2.50 3.00 3.50 1 10 100 1000 a/d w p s m /w f e m   rmm    b 0.00 0.50 1.00 1.50 2.00 2.50 3.00 3.50 1 10 100 1000 a/d w p s m /w f e m 2 = 0° = 45° r0 = 0.1 mm   c  0.00 0.50 1.00 1.50 2.00 2.50 3.00 3.50 1 10 100 1000 a/d w p s m /w f e m   rmm    d figure 4: ratio between the sed based on the elastic peak stresses ( psmw ) and the sed derived from the fe analyses ( femw ) for a crack (2α = 0°) under mixed mode (i+ii) loading: (a) ϕ = 0° (mm = 0), (b) ϕ = 30° (mm = 0.37), (c) ϕ = 45° (mm = 0.50) and (d) ϕ = 60° (mm = 0.63). conclusions n the present contribution (*), a link between the averaged sed approach and the peak stress method in the case of cracks subjected to mixed mode (i+ii) loading has been investigated:  on the basis of the peak stress method, some expressions useful to estimate the mode i and mode ii sifs, recently derived for pure modes of loading, have been verified also in the case of mixed mode (i+ii) crack problems.  since the normal and tangential peak stresses are proportional to the mode i and mode ii sifs, a link can immediately be established with the sed parameter by means of eqs. (3), (4) and (5). by substituting the psm-based relationships in the closed-form expressions of the averaged sed it appears that the latter can be directly estimated by means of the elastic peak stresses evaluated at the crack tip.  the ratio between the sed based on the elastic peak stresses and the sed derived from the fe analyses converge to a unit value for a ratio a/d greater than a value between 3 (mm = 0) and 16 (mm = 0.63). the minimum a/d ratio to assure the validity of the proposed method increases with increasing the mode mixity ratio (mm).  the usefulness of the sed expression based on the elastic peak stresses is that (i) only the elastic peak stresses numerically evaluated at the crack tip are needed and the definition of a control volume is no longer required; i g meneghetti et alii, frattura ed integrità strutturale, 34 (2015) 109-115; doi: 10.3221/igf-esis.34.11 115 (ii) the employed meshes are rather coarse if compared to those necessary for sed calculation, because the mean element size can be significantly greater than the radius of the control volume adopted for sed evaluation. (*) a version of the present contribution has already been presented at the third ijfatigue & ffems joint workshop on "characterisation of crack tip fields" organized by the italian group of fracture (igf). references [1] seweryn, a., brittle fracture criterion for structures with sharp notches, eng. fract. mech., 47 (1994) 673–681. [2] boukarouba, t., tamine, t., nui, l., chemini, c. and pluvinage, g., the use of notch stress intensity factor as a fatigue crack initiation parameter. eng. fract. mech., 52 (1995) 503–512. [3] lazzarin, p., tovo, r., a notch intensity factor approach to the stress analysis of welds, fatigue fract. eng. mater. struct., 21 (1998) 1089–1104. [4] atzori, b., meneghetti, g., fatigue strength of fillet welded structural steels: finite elements, strain gauges and reality, int. j. fatigue, 23 (2001) 713–721. [5] gross, r., mendelson, a., plane elastostatic analysis of v-notched plates, int. j. fract. mech., 8 (1972) 267–272. [6] williams, m. l., stress singularities resulting from various boundary conditions in angular corners on plates in tension, j. appl. mech., 19 (1952) 526–528. [7] nisitani, h., teranishi, t., ki value of a circumferential crack emanating from an ellipsoidal cavity obtained by the crack tip stress method in fem, in: guagliano, m., aliabadi, m. h., editors. proceedings of the 2nd international conference on fracture and damage mechanics, (2001) 141–146. [8] nisitani, h., teranishi, t., ki value of a circumferential crack emanating from an ellipsoidal cavity obtained by the crack tip stress method in fem, engng. fract. mech., 71 (2004) 579–585. [9] meneghetti, g., lazzarin, p., significance of the elastic peak stress evaluated by fe analyses at the point of singularity of sharp v-notched components, fatigue fract. engng. mater. struct., 30 (2007) 95-106. [10] meneghetti, g., the use of peak stresses for fatigue strength assessments of welded lap joints and cover plates with toe and root failures, eng. fract. mech., 89 (2012) 40-51. [11] lazzarin, p., zambardi, r., a finite-volume-energy based approach to predict the static and fatigue behavior of components with sharp v-shaped notches, int. j. fract., 112 (2001) 275-298. [12] berto, f., lazzarin, p., recent developments in brittle and quasi-brittle failure assessment of engineering materials by means of local approaches, mater. sci. eng. r, 75 (2014) 1-48. [13] lazzarin, p., campagnolo, a., berto, f., a comparison among some recent energyand stress-based criteria for the fracture assessment of sharp v-notched components under mode i loading, theor. appl. fract. mech., 71 (2014) 2130. [14] torabi, a. r., campagnolo, a., berto, f., experimental and theoretical investigation of brittle fracture in key-hole notches under mixed mode i/ii loading, acta mech., 226 (2015) 2313-2322. [15] livieri, p., lazzarin, p., fatigue strength of steel and aluminium welded joints based on generalized stress intensity factors and local strain energy values, int. j. fract., 133 (2005) 247-276. [16] berto, f., campagnolo, a., lazzarin, p., fatigue strength of severely notched specimens made of ti-6al-4vunder multiaxial loading, fatigue fract. engng. mater. struct., 38 (2015) 503-517. [17] berto, f., lazzarin, p., multiparametric full-field representations of the in-plane stress fields ahead of cracked components under mixed mode loading, int. j. fatigue, 46 (2013) 16-26. [18] meneghetti, g., the peak stress method applied to fatigue assessments of steel and aluminium fillet welded joints subjected to mode-i loading, fatigue fract. engng. mater. struct. 31 (2008) 346–369. [19] meneghetti, g., atzori, b., manara, g., the peak stress method applied to fatigue assessments of steel tubular welded joints subject to mode-i loading, engng. fract. mech., 77 (2010) 2100–2114. [20] meneghetti, g., campagnolo, a., berto, f., fatigue strength assessment of partial and full‐penetration steel and aluminium butt‐welded joints according to the peak stress method, fatigue fract. engng. mater. struct. (in press) doi: 10.1111/ffe.12342. microsoft word numero 2 art 3.doc l. andena et al., frattura ed integrità strutturale, 2 (2007) 17-24; doi: 10.3221/igf-esis.02.03 17 1 introduzione il polibutene-1 isotattico (i-pb1) viene sempre più frequentemente usato come materiale per la fabbricazione di tubi per applicazioni quali riscaldamento e distribuzione di acqua potabile. secondo la polybutene piping systems association (pbpsa), l’utilizzo dell’i-pb1 comporta diversi vantaggi rispetto ai concorrenti più tradizionali, ad esempio per quanto riguarda le sue proprietà meccaniche nel lungo periodo ed il comportamento a temperature elevate. vi sono studi approfonditi che riguardano la transizione dell’i-pb1 tra le sue due forme cristalline (denominate i e ii) in seguito alla fusione [1, 2]. di contro le proprietà meccaniche dell’i-pb1 non sono state finora oggetto di grande attenzione in letteratura. un fenomeno di sicuro interesse per i tubi in pressione in materiale polimerico è quello dell’innesco e successiva propagazione lenta di cricche a partire da difetti superficiali. la resistenza del materiale a questo tipo di cedimento può essere caratterizzata mediante prove accelerate su tubi in pressione ad elevata temperatura. un andamento tipico è riportato schematicamente in fig. 1. si distinapplicazione della meccanica della frattura viscoelastica alla previsione della vita di tubi in polibutene luca andena, marta rink, roberto frassine politecnico di milano, dipartimento di chimica, materiali e ingegneria chimica “g. natta” riassunto. il polibutene-1 isotattico (i-pb1) è un materiale polimerico usato per la produzione di tubi per il trasporto di fluidi in pressione. in questo lavoro si sono studiati due tipi di i-pb1 prodotti da basell che differiscono per grado di isotatticità. si sono condotte prove di frattura a diverse temperature e velocità di spostamento imposte. si è utilizzata una configurazione di flessione su provini con singolo intaglio (senb) unitamente a quella di doppia trave a sbalzo (dcb), quest’ultima limitatamente allo studio della fase di propagazione. al fine di individuare con precisione l’innesco della frattura e la velocità di propagazione della stessa si è fatto ricorso a metodi ottici. dal punto di vista fenomenologico durante la propagazione si assiste alla formazione di zone in cui il materiale risulta fortemente stirato. la frattura in esse avanza con una lacerazione continua che si alterna a salti repentini in occasione del brusco cedimento di queste zone, associato a conseguenti cadute del carico. questa parziale instabilità è stata osservata sui due materiali per entrambe le configurazioni di prova. i risultati ottenuti sono stati interpretati seguendo l’approccio della meccanica della frattura e applicando uno schema di riduzione di tipo tempo-temperatura che ha permesso di descrivere il comportamento viscoelastico del materiale su un intervallo temporale di diverse decadi. i risultati hanno permesso di applicare un modello analitico per la previsione della vita utile di tubi in pressione. il modello si è mostrato in buon accordo con i dati sperimentali disponibili da prove condotte su tubi dello stesso materiale. abstract. isotactic polybutene-1 (i-pb1) is a polymer used for the manufacturing of pressurized pipes. in this work two grades of i-pb1 with a different degree of isotacticity have been investigated; they have been supplied by basell polyolefins. fracture tests have been performed at various temperatures and testing speeds. two configurations have been used, single edge notch bending (senb) and double cantilever beam (dcb), the latter only to study crack propagation. optical methods have been used to detect crack initiation and measure propagation speed. from the phenomenological point of view, the formation of highly stretched material regions has been observed during crack propagation. a continuous tearing of these regions as the crack advances has often been interrupted by their sudden rupture, with the load decreasing accordingly. this partial instability has been observed on both material grades, with both testing configurations. results of the tests have been interpreted using the fracture mechanics framework; a time-temperature superposition scheme has been adopted to represent viscoelastic behavior over several decades. an analytical model has been applied to predict the lifetime of pressurized pipes. a good agreement has been reported between model predictions and experimental data obtained from tests on polybutene pipes. parole chiave. polibutene; frattura; viscoelasticità; polimero http://www.gruppofrattura.it http://www.gruppofrattura.it http://dx.medra.org/10.3221/igf-esis.02.03&auth=true l.andena et al., frattura ed integrità strutturale, 2 (2007) 17-24 18 guono due regioni: a valori di sforzo (e quindi pressione) elevati si assiste al cedimento duttile della sezione resistente del tubo mentre per valori inferiori si ha il campo effettivamente interessato dalla frattura per propagazione lenta di una cricca (“frattura fragile “). estrapolando i risultati ottenuti ad alta temperatura [3] è possibile prevedere la vita utile dei tubi alla temperatura di esercizio. purtroppo queste prove sono molto costose per via della lunga durata (1-2 anni). la meccanica della frattura (mf) può fornire un approccio alternativo al problema. in particolare è possibile caratterizzare il comportamento a frattura del materiale attraverso prove di laboratorio. una volta note le proprietà del materiale è possibile prevedere la vita utile di un qualunque manufatto (ad esempio un tubo in pressione). passoni et al. [4] hanno studiato i due materiali oggetto anche del presente lavoro effettuando prove di creep ad alta temperatura della durata di alcune settimane, dunque assai più brevi delle prove sui tubi discusse in precedenza. gli autori hanno poi applicato un modello analitico per prevedere la vita utile di tubi in pressione. il confronto delle previsioni con le curve di cedimento riportate sulla norma iso 12230 [5] ha mostrato risultati promettenti. figura 1. andamento schematico della relazione tra sforzo circonferenziale e tempo di vita utile per un tubo in pressione realizzato in materiale polimerico. andena et al. [6] hanno invece studiato il comportamento a frattura degli stessi due materiali a temperatura ambiente. dal punto di vista fenomenologico si è evidenziata la presenza di due diversi meccanismi di frattura, uno dei quali responsabile di una parziale instabilità durante la propagazione. si sono poi determinate le proprietà all’innesco in accordo con la mf ed è stato applicato un approccio numerico di modellazione coesiva [7, 8]. lo strumento di calcolo ha prodotto risultati in buon accordo con i dati sperimentali relativi all’innesco. si è tentato di simulare anche la propagazione ma il modello coesivo adottato non è abbastanza sofisticato per riprodurre adeguatamente una fenomenologia complessa quale quella osservata nell’i-pb1. nel presente lavoro si è nuovamente fatto ricorso alla mf per caratterizzare il comportamento dell’i-pb1 durante la propagazione. si sono svolte prove di laboratorio a diverse temperature di durata variabile da alcuni secondi a poco più di un’ora: questi tempi sono assai più brevi di quelli richiesti dalle prove di creep o da quelle sui tubi. in questo modo è stato possibile effettuare previsioni adottando un modello analogo a quello utilizzato in [4] e verificarne l’attendibilità attraverso il confronto con dati sperimentali ottenuti da prove su tubi. 2 aspetti teorici la mf identifica nel fattore di intensificazione degli sforzi ki la grandezza che esprime l’intensità del campo di sforzi all’apice di un difetto, indipendentemente dalla configurazione geometrica del corpo in esame. il suffisso primo si riferisce al fatto che si sta qui considerando il modo di frattura di apertura, solitamente più critico per la maggior parte delle applicazioni; d’ora in avanti il pedice verrà omesso. k è funzione dello sforzo nominale σ (conseguente al carico applicato al contorno, la pressione interna nel caso di un tubo) e dell’entità del difetto a, attraverso un fattore di forma che tiene conto della geometria effettiva: ayk ⋅⋅= σ (1) diversi autori tra cui williams [9] e schapery [10] hanno suggerito possibili approcci per applicare la mf a materiale viscoelastici, quali i polimeri. in particolare williams ha mostrato, sotto opportune ipotesi semplificative, la validità delle seguenti relazioni tra il fattore di intensificazione degli sforzi k, il tempo di innesco ti e la velocità di avanzamento della cricca a& : p i kbt −⋅= (2) qkaa ⋅=& (3) in cui a, b, p e q sono proprietà del materiale ed in generale dipendono dalla temperatura di prova. esse possono essere determinate a partire da prove di frattura condotte su campioni opportunamente intagliati. schapery [11] ha inoltre dimostrato che a& dipende dal valore istantaneo di k ma non dai suoi valori passati e ciò permette di applicare la relazione (3) a qualunque storia di carico. è così possibile formulare una previsione della vita utile tf di un tubo in pressione avente spessore di parete s: (4) nella (4) tp rappresenta il tempo necessario perché dopo l’innesco della frattura un difetto di dimensione iniziale a0 divenga passante. k0 è il valore del fattore di intensifi∫ ⋅+⋅=+= − s a q p pif ka da kbttt 0 0 l.andena et al., frattura ed integrità strutturale, 2 (2007) 17-24 19 cazione degli sforzi (corrispondente ad a0) che rimane costante durante la fase di innesco della frattura, essendo costante la pressione (e dunque lo sforzo) nel tubo. 3 dettagli sperimentali si sono studiati due polibuteni per tubi forniti da basell polyolefins, aventi diverso grado di isotatticità e dunque di cristallinità. i due materiali sono gli stessi studiati in [4] e in analogia al precedente lavoro verranno nel seguito indicati come pb1 e pb2 (quest’ultimo con cristallinità maggiore). entrambi, forniti sotto forma di granuli, sono stati stampati a compressione in lastre di dimensione 170x120x10 mm. in seguito al raffreddamento da fuso l’i-pb1 cristallizza in forma ii, avente simmetria tetragonale. questa forma è metastabile ed a temperatura ambiente transisce spontaneamente nella forma i, che possiede un reticolo esagonale. onde permettere il completamento della transizione i campioni sono stati tagliati dalle lastre e fresati dopo un’attesa di almeno 15 giorni dallo stampaggio [4]. per studiare la propagazione in modo i si è scelto di utilizzare due configurazioni di prova, double cantilever beam (dcb) e single edge notched bending (senb), mostrate rispettivamente in fig. 2 e fig. 3. le dimensioni dei campioni per entrambe le geometrie sono indicate in tab 1. sono stati praticati intagli con raggio di curvatura all’apice pari a 13μm. in entrambi i casi sono state realizzate scanalature laterali per guidare l’avanzamento della frattura lungo il piano desiderato. le scanalature, non mostrate in figura, sono state generate alla fresa con un utensile avente profilo a v di 60° procedendo su ciascun lato dei campioni fino ad una profondità pari al 10% dello spessore nominale. figura 2. provino dcb figura 3 provino senb dcb senb 2h 45 mm w 20 mm l 165 mm l1 88 mm a 60 mm a 10 mm b 10 mm b 10 mm ø 7.5 mm l2 80 mm c 90 mm tabella 1. dimensioni dei campioni dcb e senb le prove di frattura sono state condotte su un dinamometro elettromeccanico instron. si sono utilizzate velocità di spostamento imposte di 1, 10 e 100 mm/min. il dinamometro equipaggiato con una camera termostatica ha permesso di svolgere le prove alle temperature di 23, 50, 70 e 90°c. per ogni condizione di prova (configurazione, velocità e temperatura) si sono effettuate almeno due ripetizioni. la lunghezza di cricca è stata rilevata attraverso misure ottiche effettuate riprendendo con una telecamera i campioni, sui quali era stato posto un opportuno riferimento di calibrazione. 4 risultati durante le prove si è osservata una parziale instabilità nella propagazione della frattura. questo fenomeno si manifesta anche nell’aspetto molto irregolare che le curve carico-spostamento per i due materiali hanno successivamente all’innesco. a titolo di esempio in fig. 4 sono riportate le curve relative alle prove senb a 23°c e 1 mm/min, unitamente ai valori dei parametri critici di mf all’innesco. si osserva che il pb2, caratterizzato da un maggior grado di isotatticità, è più tenace del pb1. attraverso le riprese effettuate durante le prove è stato possibile osservare la peculiare fenomenologia di frattura di questi materiali (v. fig. 5). davanti all’apice della cricca si formano una o più regioni in cui il materiale è fortemente stirato. la frattura procede attraverso una lacerazione continua di queste zone (propagazione stabile) le quali di tanto in tanto cedono bruscamente (propagazione instabile). questo secondo meccanismo determina discontinuità nella propagazione della cricca, visibile in fig. 6. a questo fenomeno è associata la presenza di aree scure e lisce sulle superfici di frattura il cui aspetto differisce molto da quello delle regioni in cui la propagazione è avvenuta in modo stabile [6]. dalla fig. 6 si può però osservare come il fattore di intensificazione degli sforzi si mantenga su valori pressoché costanti, nonostante la velocità di avanzamento della cricca subisca variazioni considerevoli per la presenza delle discontinuità. in virtù di questo fatto si è ritenuto più significativo considerare per ogni prova un unico valore medio di a& rapportandolo al valore medio di k l.andena et al., frattura ed integrità strutturale, 2 (2007) 17-24 20 durante la fase di propagazione, come indicato schematicamente in fig. 6. il grafico in scala bilogaritmica di fig. 7 mostra i risultati ottenuti dalle prove dcb, condotte a temperatura ambiente. l’andamento lineare ipotizzato dall’equazione (3) è confermato dai dati sperimentali. è anche possibile osservare come il pb2 oltre ad essere più tenace all’innesco offra una maggiore resistenza all’avanzamento della frattura. per entrambi i materiali la pendenza delle curve è molto bassa, segno di una modesta influenza della viscoelasticità sul comportamento durante la propagazione. determinata la relazione tra k e a& è stato possibile applicare il modello analitico proposto in [4] per prevedere il tempo di vita di tubi in pressione e confrontarlo con i dati sperimentali disponibili. nel modello si è considerato un difetto piano di forma semicircolare situato sulla superficie interna del tubo e giacente in un piano radiale, ammettendo che la sua forma non cambi durante la propagazione. si sono ipotizzati un diametro interno del tubo di 100mm, uno spessore di parete di 10mm e un raggio iniziale del difetto di 50μm. in analogia con quanto fatto in [4] nel calcolo si è trascurato il tempo di innesco, formulando quindi una previsione conservativa della vita utile del tubo. per validare il modello si sono confrontate le sue previsioni con dati sperimentali ottenuti da prove su tubi in pressione eseguite applicando valori di sforzo circonferenziale fino a 20 mpa. in corrispondenza di questo valore massimo di sforzo i valori di log k calcolati per il modello vanno da -0.66 (per a~a0) fino a 0.48 (per a~s). durante le prime fasi della propagazione questi valori sono molto più bassi di quelli rilevati durante le prove di laboratorio (v. fig. 7). si è così effettuata una estrapolazione ipotizzando valida l’equazione (3): a causa della bassa pendenza delle curve k a& si ottengono valori estremamente bassi di a& , dell’ordine di 10-30 mm/s al limitare inferiore del campo di k considerato. ciò determina previsioni di tempi lunghissimi (nell’ordine di 1020 h) per figura 4. risultati delle prove senb a 23°c, 1 mm/min 0 5 10 0 50 100 150 200 250 innesco c ar ic o [n ] spostamento [mm] pb1 pb2 pb2 gc = 7.6 kj/m² kc = 1.70 mpam0.5 pb1 gc = 5.2 kj/m² kc = 1.32 mpam0.5 innesco figura 5. meccanismi di propagazione stabile/instabile in una prova senb su pb2 a 50°c e 1 mm/min: le immagini sono prese ad intervalli regolari di 16 s. tra 4b e 4c si può osservare un episodio di propagazione instabile che si sovrappone a quella stabile (visibile tra 4a e 4b, tra 4c e 4d). si può notare chiaramente la zona di materiale stirato antistante l’apice della cricca l.andena et al., frattura ed integrità strutturale, 2 (2007) 17-24 21 osservare il cedimento del tubo, assolutamente non realistiche. per esplorare il campo dei valori inferiori di k si sono quindi svolte, sul solo pb2, prove di frattura in configurazione senb a temperature superiori a quella ambiente, in particolare 50, 70 e 90°c. i risultati sono mostrati in fig. 8: si può notare un netto cambiamento nell’andamento della curva k – a& all’aumentare della temperatura. è stato applicato uno schema di riduzione dei dati secondo l’equivalenza tempo-temperatura traslando le curve ottenute a temperature diverse in modo da costruire una curva maestra ad una temperatura di riferimento (si veda ad esempio [12]). in questo modo è stato possibile ottenere una curva estesa su sei decadi di velocità di avanzamento con una buona sovrapposizione dei dati (come mostrato in fig. 9) alle diverse temperature. l’andamento del fattore di spostamento è pressoché lineare in un grafico di tipo arrhenius. come detto l’applicazione del modello al tubo in pressione richiede l’estrapolazione dei dati sperimentali a valori di k inferiori: questa è stata eseguita sulla base del ramo della curva originato dai dati ad alta temperatura. in questo caso i valori di a& calcolati all’inizio della propagazione sono dell’ordine di 10-10 mm/s, superiori di ordini di grandezza rispetto a quelli calcolati in precedenza. le previsioni della vita utile del tubo così ottenute sono in buon accordo con i dati sperimentali disponibili sia per quanto riguarda il posizionamento delle curve in assoluto 100 200 300 400 500 60 70 80 90 100 110 120 da/dt media a k tempo (s) a (m m ) 0.0 0.5 1.0 1.5 2.0 2.5 3.0 k (m p a m ½) k medio figura 6. andamento di k e a durante una prova dcb su pb1 a 23°c e 10 mm/min -5 -4 -3 -2 -1 0 1 -0.10 -0.05 0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40 pb1 pb2 lo g k ( m p a m ½ ) log da/dt (mm/s) figura 7. risultati delle prove dcb a 23°c per i due materiali l.andena et al., frattura ed integrità strutturale, 2 (2007) 17-24 22 che per l’effetto della variazione di temperatura (v. fig. 10). è da rilevare che nelle prove sui tubi si è osservata quasi esclusivamente frattura duttile mentre il modello rappresenta il comportamento del materiale durante la propagazione lenta di una cricca. idealmente queste due situazioni corrispondono ai due distinti rami della curva mostrata in fig. 1. le previsioni del modello suggeriscono una transizione da comportamento duttile a fragile che dovrebbe essere osservata a tempi di poco superiori a quelli rilevati sperimentalmente: ciò potrebbe essere confermato qualora si rendessero disponibili dati relativi al cedimento di tubi in prove condotte a valori di sforzo più bassi. è bene notare che nelle previsioni del modello si è trascurato il tempo di innesco: qualora se ne tenesse conto si avrebbero curve spostate verso tempi maggiori. inoltre le previsioni sono influenzate dalle ipotesi fatte su forma e dimensioni iniziali del difetto, che potrebbero influenzare la posizione delle curve. -5 -4 -3 -2 -1 0 1 -0.10 -0.05 0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40 dcb 23°c senb 50°c senb 70°c senb 90°c lo g k ( m p a m ½ ) log da/dt (mm/s) figura 8. risultati delle prove dcb e senb su pb2 a diverse temperature. per le prove senb i punti rappresentano la media dei valori ottenuti -5 -4 -3 -2 -1 0 1 -0.10 -0.05 0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40 0.0028 0.0030 0.0032 0.0034 -3 -2 -1 0 dcb 23°c senb 50°c senb 70°c senb 90°c lo g k ( m p a m ½ ) log da/dt (mm/s) lo g a2 3° c t 1/t (k-1) figura 9. curva maestra di log k da/dt a 23°c e relativo fattore di spostamento. in figura è anche indicata la retta di estrapolazione utilizzata nell’applicazione del modello del tubo. l.andena et al., frattura ed integrità strutturale, 2 (2007) 17-24 23 5 conclusioni i risultati ottenuti hanno confermato la validità di un approccio di meccanica della frattura per la caratterizzazione di polibutene utilizzati per la realizzazione di tubi in pressione. lo strumento della mf appare del tutto adeguato a mettere in luce differenze di comportamento a lungo termine tra materiali diversi attraverso una caratterizzazione di laboratorio estremamente più rapida ed economica di quella sul manufatto finale. questa caratterizzazione permette inoltre l’applicazione di modelli in grado di prevedere direttamente in modo attendibile la vita utile dei tubi in pressione. naturalmente non si può pensare di sostituire completamente questo approccio alle prove sui tubi, soprattutto in vista dei severi controlli normativi previsti per la certificazione dei materiali per queste applicazioni. con la mf è però possibile discriminare fra materiali diversi accelerando notevolmente lo sviluppo di nuove formulazioni. una volta giunti alla definizione della formulazione più idonea è possibile avviare la campagna di sperimentazione sui tubi per la verifica delle previsioni della mf. le indagini svolte hanno confermato la complessa natura del comportamento a frattura del polibutene, già messa in luce in precedenti lavori. lo schema di riduzione tempotemperatura è stato applicato con successo per la descrizione della propagazione della frattura dell’i-pb1. ulteriori prove sperimentali attualmente in corso potranno confermare la bontà dell’approccio. sviluppi futuri di sicuro interesse sono l’approfondimento dello studio della fase di innesco e un chiarimento dei diversi meccanismi di frattura in atto alle diverse temperature. 6 ringraziamenti si ringrazia l’ing. paolo redondi per il prezioso supporto fornito durante l’esecuzione delle prove dcb. 7 bibliografia [1] am. chatterjee, butene polymers. in: encyclopaedia of polymer science and engineering, 1985. p. 590. [2] f. azzurri, a.flores, gc. alfonso, fj.baltà calleja, polymorphism of isotactic poly(1-butene) as revealed by microindentation hardness. 1. kinetics of the transformation. macromolecules. 2002;35:9069 [3] plastics piping and ducting systems — determination of the long-term hydrostatic strength of thermoplastics materials in pipe form by extrapolation. iso9080:2003(e) [4] p. passoni, r.frassine, a.pavan, small scale accelerated tests to evaluate the creep crack growth resistance of polybutene pipes under internal pressure. proceedings of plastics pipes xii milan 2004. [5] polybutene (pb) pipes – effect of time and temperature on the expected strength. iso12230:1996(e) [6] l. andena, m. rink, jg. williams, cohesive zone modelling of fracture in polybutene. engineering fracture mechanics. 2006;73:2476-2485. [7] s. bianchi, a. corigliano, r. frassine, m. rink, modelling of interlaminar fracture processes in composites using interface elements. compos. sci. technol. 2006;66:255-63. [8] l. andena, m. rink, fracture of rubber-toughened poly (methyl methacrylate): measurement and study of 1 10 101 102 103 104 105 106 107 108 90°c 70°c 23°c 23°c 70°c 90°c modello tempo (h) sf or zo ( m p a) figura 10. confronto tra i dati sperimentali ottenuti da prove su tubi con le previsioni del modello ottenute in base ai dati mostrati in fig. 9. l.andena et al., frattura ed integrità strutturale, 2 (2007) 17-24 24 cohesive zone parameters. proceedings of icf xi turin 2005. [9] jg. williams, the use of fracture mechanics in design with polymers. plasticon 81. engineering design with plastics: principles and practice, university of warwick. 1981. [10] ra. schapery, a theory of crack initiation and growth in viscoelastic media. i. theoretical development. international journal of fracture. 1975;11:141-159. [11] ra. schapery, a theory of crack initiation and growth in viscoelastic media. iii. analysis of continuous growth. international journal of fracture. 1975;11:549562. [12] p. mariani, r. frassine, m. rink, a. pavan, viscoelasticity of rubber-toughened poly(methyl methacrylate). part ii: fracture behavior. polymer engineering and science. 1996;36:2758-2764 microsoft word numero_57_art_26_3096 s. derouiche et alii, frattura ed integrità strutturale, 57 (2021) 359-372; doi: 10.3221/igf-esis.57.26 359 mixed finite element computation of energy release rate in anisotropic materials based on virtual crack closure-integral method sami derouiche civil engineering department, university of august 20, 1955, skikda, algeria. sami.derouiche25@gmail.com, http://orcid.org/0000-0002-3171-1265 salah bouziane, hamoudi bouzerd civil engineering department, university of august 20, 1955, skikda, algeria. laboratory of civil engineering and hydraulics, university of may 8, 1945, guelma, algeria. bouziane_21@yahoo.fr, http://orcid.org/0000-0002-0831-1167 bib_ham@yahoo.fr, http://orcid.org/0000-0002-8216-2980 abstract. the material with anisotropic properties are becoming widely essential due to the ease to manipulate their mechanical properties to obtain a particular quality, insure safety or a specific behavior. those kinds of materials are considered anisotropic because their characteristics and behavior are dependent on every direction of the material’s orientation. in this work, the virtual crack closure-integral technique is implemented to a mixed finite element, in addition to the stiffness derivative procedure, to evaluate the err of crack extension in anisotropic materials. a simulation of a cracked edge rectangular plate with anisotropic characteristics is taken for example. the results obtained are in good agreement with the analytical results, making the proposed technique a good model for fracture investigation and allow it to study more complicated cases in future works. keywords. fracture mechanics; finite element method; anisotropy; energy release rate; virtual crack closure-integral method. citation: derouiche, s., bouziane, s., bouzerd, h., mixed finite element computation of energy release rate in anisotropic materials based on virtual crack closure-integral method, frattura ed integrità strutturale, 57 (2021) 359-372. received: 12.05.2021 accepted: 16.06.2021 published: 01.07.2021 copyright: © 2021 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. introduction n the study of fracture mechanics problems, the anisotropic media represent the most general material characteristics and the most hazardous ones, making them challenging to the procedures of studying the crack propagation problems. in nature, most materials are anisotropic and in the recent works on industrial fields tends to focus on those type of materials [1–5]. i https://youtu.be/xhp9mewtcgq s. derouiche et alii, frattura ed integrità strutturale, 57 (2021) 359-372; doi: 10.3221/igf-esis.57.26 360 several works on the crack propagation in anisotropic material made their reliability, where it is investigated with the linear elastic fracture mechanics [6] and the j-integral [7] but the phase-field modeling developed for the anisotropic surface energy [8] is getting popular for brittle anisotropic material [9,10] and in crystalline material [11,12]. the finite element method is also known for treating the fracture mechanics problems, the stroh formalism is used with an enriched boundary element method to offer better results for any degrees of anisotropy [6]. the extended finite element method (xfem) also was enriched to treat the anisotropy [13]. the recently developed edge-based smoothed finite element method es-fem [14] and the singular edge-based smoothed finite element method ses-fem [15,16] present a significantly improved accuracy of the finite element method fem [17,18] without changing much of the fem settings. the rotating material axes investigate the anisotropy of material and help to approves the new finite element methods [19] such as the scaled boundary finite element method [20], fractal two-level finite element method [21], the element-free galerkin method with the fractal finite element method [22] and the es-fem [16]. the deviation of the principal direction of a crack is defined as kinking of the crack which can be seen as the first step of the propagation, evaluated either with the err [23–26] or more often with the stress intensity factor [27]. it’s taken into account for the fatigue crack growth [28] the effect of the t-stress [27] and different other cases. among the diverse techniques for fracture investigation, the standard irwin’s crack closure integral is widely used for the computation of the err. ronald made a historical approach and a review of the virtual crack closure technique and its parent technique the crack closure integral [29]. the study of the kinked crack phenomenon with the virtual crack closure technique gave also great results [30]. the same method is implemented on developed finite elements such as the cell-based smoothed finite element [31], the floating node method [32], or also for three-dimensional elements such as the tetrahedral finite element [33]. the main purpose of this current work is to solve fracture mechanics problems of anisotropic media with a special mixed finite element rmq7 (reissner’s modified quadrilateral with 7-nodes). this element has been associated with the virtual crack closure-integral technique to evaluate the err for anisotropic materials. the present mixed finite element has the particularity to contain seven nodes, two stress nodes with two degrees of freedom (σ12,σ22) and five displacement nodes with also two degrees of freedom (u1,u2). the rmq7 is created with the purpose to investigate mainly the fracture mechanics-related problems with enough efficiency and easier steps of the calculation, giving by that a significant gain of time. this element was, at first, created by bouzerd [34] with a setup in a physical (x, y) plane. bouziane et al. [35] redevelop the element beginning from the parent element in a natural (ξ, η) plane. that added a rationalization of the calculations and a huge benefit of modeling distinctive types of cracks with different orientations. the method gave great precision on the paperwork of bouziane et al. [36], where a numerical example of a center cracked plan with uniaxial tension was investigated in two cases of homogenous materials and bi-materials. also the study of mohamed ben ali et al.[37] on sandwich structures with two cases of symmetrical double cantilever beam and asymmetrical double cantilever beam. for the work of benmalek et al. [38], the exactitude of the results was highly remarkable. reissner’s modified quadrilateral element he rmq7 is the final element proposed by bouzerd [34] with 7 nodes and 14 degrees of freedom (fig. 1.d). it is reduced from the rmq11, an element with 11 nodes and 22 degrees of freedom (fig. 1.c), with a static condensation procedure, that merges the internal degrees of freedom by reducing the size of equations per elimination of a certain number of variables. bouziane et al. [35] introduced the design of the finite element in a natural (ξ, η) plane. the rmq11 itself is gotten from the parent element rmq5 by re-localization of certain variables and by displacement of the static nodal unknown of the corners toward the side itself. in which, the rmq5 is obtained by adding a displacement node to the reissner mixed element to get an element with 5 nodes and 22 degrees of freedom (fig. 1.b). finally, the reissner element is a four-nodded element with five degrees of freedom at each (fig. 1.a); its formulation is based on reissner’s mixed variational principle bouziane et al.[35]. three of its sides are compatible with linear traditional elements and present a displacement node at each corner. the last side, furthermore on its two displacement nodes about corner (node 1 and node 2), offers three extra nodes: a median node (node 5) and two middle nodes in the medium on each half-side (nodes 6 and 7), presenting the components of the stress vector along with the interface. bouziane et al. [35] have presented the formulation and the validation of the element. the element displacement component is estimated as: t s. derouiche et alii, frattura ed integrità strutturale, 57 (2021) 359-372; doi: 10.3221/igf-esis.57.26 361     u n q (1) where:    1 1 2 2 3 3 4 4 5 51 2 1 2 1 2 1 2 1 2, , , , , , , , ,tq u u u u u u u u u u (2) {q}t is the vector of nodal displacements and [n] is the matrix of interpolation functions for displacements. figure 1: different stages for the mixed finite element formulation. the shape functions are: s. derouiche et alii, frattura ed integrità strutturale, 57 (2021) 359-372; doi: 10.3221/igf-esis.57.26 362                                           1 2 3 4 2 5 1 1 1 2 1 1 1 4 1 1 1 4 1 1 1 4 1 1 1 2 n n n n n (3) the stress field in any point is written       m (4) where m is the matrix of interpolation functions for stresses and {τ} vector of nodal stresses. in the configuration of fig. 1, the shape functions used to estimate 𝜎 are given by:                                 8 11 9 11 10 11 11 11 1 1 2 1 2 4 1 1 2 1 2 4 1 1 2 1 2 4 1 1 2 1 2 4 m m m m (5) the shape functions used to calculate 𝜎 and 𝜎 is given as follows:                                  6 2 7 2 8 2 9 2 1 1 2 1 2 6 1 1 2 1 2 6 1 1 2 1 3 1 1 2 1 4 1, 2 i i i i m m m m i (6) the nodal estimation of the displacement and stress fields is expressed by:                                       0 0 m qb (7) where [b] is the strain-displacement transformation matrix. s. derouiche et alii, frattura ed integrità strutturale, 57 (2021) 359-372; doi: 10.3221/igf-esis.57.26 363 the element matrix [ke] is given by                     0 u e t u k k k k (8) where           e t e a k h m s m da (9) and         e t e u a k h m b da (10) [s] is the compliance matrix; [kσσ] is a block on the reduced element stiffness matrix that depends on the stress interpolation functions only and [kσu] is a block on the reduced element stiffness matrix that depends on the stress interpolation functions and the strain displacement transformation matrix. otherwise, the relation to define the relationship between the forces and the displacement on the nodes is:     ef k u (11) computation of energy release rate he virtual crack closure-integral method, in addition to the stiffness derivative procedure, has been associated with the present mixed finite element to calculate the err for anisotropic materials. this section is reserved for the presentation of the methodology adopted for the calculation of the err. virtual crack closure-integral method (cci) the computation of the err can be evaluated with the crack closure integral technique [30,31,39] which, for a homogenous material, considers the strain energy released for a small crack extension is equal to the energy essential to close the crack. figure 2: the two configurations to consider for the crack closure-integral technique: a) the crack opening at the tip for a length of δl. b) the stress needed to close the crack for the same length. the err for this technique is expressed by irwin [40] for mode i, as:     00 1 lim , 0 , 2 l i y l g l r v r dr l           (12) t s. derouiche et alii, frattura ed integrità strutturale, 57 (2021) 359-372; doi: 10.3221/igf-esis.57.26 364 where σy is the normal stress applied in the closed crack, δl is the small crack extension. δv is the displacement of two points on the crack lips along the y-axis (fig. 2). for mode ii:     00 1 lim , 0 , 2 l ii y l g l r u r dr l           (13) where δu is the displacement of two points of the crack lips along the x-axis, and τ is the shear stress along the closed crack. the application of the eqns. (12) and (13) can be executed by computing the stresses for closing the crack and calculate the displacements corresponding, which could be expressed by: ( 1) ( 2 ) 0 1 2 l i yg v dx l       (14) ( 1) ( 2 ) 0 1 2 l ii xyg u dx l       (15) considering the implementation of the two eqns. (14) and (15) in the finite element rmq7 proposed, it is mandatory to define the nodes that will help in getting the value of the err. first, the forces that are submitted on the nodes (5, 6, 5’ and 7’) which represent the first step of the crack closer integral technique and are determined by the eqn. (11), then the second step is to determine the displacement on the nodes (4, 3’, 7 and 6’) (fig. 3) as: 43' 4 3' 76' 7 6' 43' 4 3' 76' 7 6' u u u u u u v v v v v v             (16) figure 3: the two configurations of the crack closure integral technique occurred in rmq7: a) forces that act to extend the crack lips. b) displacements resulted from the crack extension. s. derouiche et alii, frattura ed integrità strutturale, 57 (2021) 359-372; doi: 10.3221/igf-esis.57.26 365 defining the forces and the displacement will allow the evaluation of the err for the modes i and ii as:     5 43' 6 76' 5 43' 6 76' 1 2 1 2 i y y ii x x g f v f v l g f u f u l           (17) the addition gives the total err: i iig g g  (18) stiffness derivative procedure (sdp) the potential energy π of a cracked body containing a crack is given: 1 2 t tu ku u f   (19) the force f is due to external loads acting on the boundaries other than the crack faces, knowing that the body forces are absent and f does not vary with length proper to the cracked body; then, in conclusion, the err is obtained only by the derivative of the stiffness, as follow: 1 2 t kg u u l l        (20) or as bouziane et al. [36] states it:                1 1 2 nf t f f f f k g v v a (21) where: a : initial crack length. δa: crack length extension. nf: total number of elements concerned by the disturbance δa. {ν}f: vertical vector containing the nodal values of the element concerned by the disturbance. the derivative δk is obtained from the two-state of the crack body (before and after crack extension), it is the difference between the stiffness of the elements around the crack tip in the configuration m0 and the stiffness of the same elements of the configuration m1 (fig. 4). the computation of the strain-err occurs with an extension crack-length δa very small and the nodal displacements are obtained from the configuration m1. elastic constants for a new coordinate system or a given body, the elastic constants that are known in a certain system will be different in another system. considering a body in a local cartesian coordinate system (x,y) with its elastic constants known or defined; a different cartesian coordinate system (x’,y’) would have a different value. in general, the principal elastic constant is given for an orthotropic media in the principal coordinate system and can be recalculated for another coordinate system. such as, the two-dimensional strain-stress relation for an orthotropic media in the principal coordinate system is f s. derouiche et alii, frattura ed integrità strutturale, 57 (2021) 359-372; doi: 10.3221/igf-esis.57.26 366 (22) figure 4: the two configurations for the energy-release-rate calculation with the stiffness derivative procedure. figure 5: an arbitrary body with its material properties in the (x,y) coordinate system and an (x',y') coordinate system inclined with φ from the principal axes with a change of the values of the material properties. where:                                  12 1 1 11 12 13 21 12 22 23 2 2 13 32 33 12 1 0 1 0 1 0 0 e es s s s s s s e e s s s g   (23)       s s. derouiche et alii, frattura ed integrità strutturale, 57 (2021) 359-372; doi: 10.3221/igf-esis.57.26 367 note that subscripts 1, 2, and 3 denote the components corresponding to the tension in the two main axes and the in-plane shear, respectively. the stresses for the coordinate system (x,y) and the stresses for the coordinate system (x’,y’) are related by the transformation matrix [t] such as:  { } [ ]{ '}t (24) where the transformation matrix [t] is given:            2 2 cos ² sin ² 2 cos sin [ ] sin ² cos ² 2 cos sin cos sin cos sin cos sin t               (25) it is now possible to have the relation between the two compliance matrices of the two coordinate systems, such as:        1's t s t (26) moreover, the stress-strain relation of the same body in a coordinate system oriented at an angle φ is considered as anisotropic and defined as:      ' ' 's (27) where                                            21 1 121 2 11 12 13 12 2 12 22 23 121 2 13 32 33 1 2 12 12 12 1 1 ' 1 ge e s s s s s s s ge e s s s g g g       (28) here ei’,νi’ and g’12 are the young’s modulus, poisson’s coefficient, and shear modulus respectfully for the orientated axes plane, and ηi’ is the coefficient of mutual influence of the first type [41][42] (i = 1; 2). these modules and coefficients for the new axes are well determined by reversing every element of the new stiffness matrix as follow: 1 1 4 2 2 41 111 12 2 1 cos ( 2 )sin cos sin e e e es g e             (29) 2 2 4 2 2 42 222 21 1 1 cos ( 2 )sin cos sin e e e es g e             (30) 12 12 4 4 2 212 1233 12 1 2 1 2 2 sin cos 2( (1 2 ) 1)sin cos g g g gs e e               (31) s. derouiche et alii, frattura ed integrità strutturale, 57 (2021) 359-372; doi: 10.3221/igf-esis.57.26 368 and so on for every elastic constant: 2112 22 s s       (32) 12 121 12 11 2 s e s e           (33) 131 33 s s      (34) 232 33 s s      (35) note that both of the methods of voyiadjis [41] and lekhnitskii [43] were used to obtain the elastics constants for the oriented coordinate system, and the values were slightly different from the actual technique presented, which made a significant impact on the final results of the err. numerical validation n this part, a demonstration is required to approve the results proposed by the method mentioned above. a plate of 1mm width and 2 mm length with a central crack edge crack, is been submitted to a traction σ= 1.0 pa pulling the plate upward while the plate is clamped at the bottom left corner and the displacement along the y axis is blocked for the rest of the bottom edge. the material of the plate is a graphite-epoxy composite (fig. 6) with a young’s modulus in the two main principal directions of the fiber e1 = 144.8 gpa and e2 = 11.7 gpa, poisson’s ratio of ν12 =0.21and a shear modulus of g12 = 9.66 gpa. the material is considered orthotropic when its orientation is at 0°. to get the anisotropic properties out from the same material, orientation with an angle φ varying from -90° to 90° changes its elastic constants giving e’1, e’2, ν’12, and g’12. (tab. 1). chen et al. [16] have presented different finite element method applications on this problem, in tab. 2 fem represents the finite element method and es fem is the edge smoothed finite element method. the analytical results are provided from the work of bowie and freese [44]and the results for the finite element methods proposed on the paper were compared to those last. figure 6: an edge central cracked plate submitted to traction. i s. derouiche et alii, frattura ed integrità strutturale, 57 (2021) 359-372; doi: 10.3221/igf-esis.57.26 369 the medialization is made with an elaborated program in mathlab r2014b, the number of elements adopted is 450, and the number of nodes generated is 1201. the values of the err are calculated using the eqn. (21) for the stiffness derivative procedure with the integration relative domain “δa/a” stable at 10-6 to 10-13. moreover, for the crack closure technique the eqn. (17) is used. ϕ e1(gpa) e2(gpa) ν1 g(gpa) η1 η2 0° 144.8 11.7 0.21 9.66 0 0 30° 35.6 14.84 0.1066 10.27 -0.38 -0.33 60° 14.84 35.6 0.0445 10.27 -0.33 -0.37 90° 11.7 144.8 0.016968 9.66 0 0 table 1: the elastic constants for orientated axes by 30°, 60°, and 90°. angle fem [16] es fem [16] rmq7 analytical solution sdp cci -90° 4.1599 4.2818 4.3033 4.296 4.3505 -60° 6.3409 6.7759 6.8659 6.966 7.0432 -30° 10.682 11.432 11.5916 11.604 11.827 0° 13.228 13.783 14.7764 14.197 14.251 15° 12.451 13.11 13.5575 13.355 13.568 30° 10.682 11.432 11.4859 11.604 11.827 45° 8.4684 9.1359 9.1907 9.288 9.4331 60° 6.3409 6.7759 6.8454 6.966 7.0432 90° 4.1599 4.2818 4.3033 4.296 4.3505 table 2: err (10-2 j/m²) for the anisotropic plate under tension with different axes rotations. figure 7: chart of the err for the five finite element methods compared to the analytical ones. s. derouiche et alii, frattura ed integrità strutturale, 57 (2021) 359-372; doi: 10.3221/igf-esis.57.26 370 the results are compared with the analytical ones giving error gaps for the stiffness derivative procedure as1.09% for 90°, 2.80% for 60°, 2.57% for 45°, 2.88% for 30°, 0.08% for 15° and 3.69% for 0°. and the error gap for the crack closure integral are 1.25% for 90°, 1.10% for 60°, 1.54% for 45°, 1.89% for 30°, 1.57% for 15° and 0.38% for 0°. as the chart in (fig. 7) shows, the results of both of the methods are the closest to the analytical results, which proves their efficiency and accuracy. conclusion n this paper, a special mixed finite element rmq7 is adopted to resolve discontinuity problems in anisotropic media. to simulate the anisotropy, an orthotropic media is oriented with an angle, which results in anisotropic elastic properties that are different from an oriented ax to another. in the computation of the err after a crack extension with the current element, two techniques were compared side by side. the crack closure integral gave closer values to the analytics results compared to the stiffness derivative method values, the implementation of those two techniques on the rmq7 represent an accurate evaluation and computation efficiency of the err and outperform the standard fem and the es fem. the rmq7 present one mesh for the calculation of the err, which represent a considerable profit in computing times and set in data compared to the traditional methods, which use two meshes. the stiffness derivative procedure computation is dependent on the domain size, as it is considered between 10-6 and 10-13 of the crack length “δa/a”. acknowledgment his work was supported by the laboratory of civil engineering and hydraulic (lgch) of the university of may 8, 1945 –guelma, algeria. references [1] akinwande, d., brennan, c.j., bunch, j.s., egberts, p., felts, j.r., gao, h., huang, r., kim, j.s., li, t., li, y., liechti, k.m., lu, n., park, h.s., reed, e.j., wang, p., yakobson, b.i., zhang, t., zhang, y.w., zhou, y., zhu, y. (2017). a review on mechanics and mechanical properties of 2d materials—graphene and beyond, extrem. mech. lett., 13, pp. 42–77, doi: 10.1016/j.eml.2017.01.008. [2] liu, n., hong, j., pidaparti, r., wang, x. (2016). fracture patterns and the energy release rate of phosphorene, nanoscale, 8(10), pp. 5728–36, doi: 10.1039/c5nr08682e. [3] larijani, n., brouzoulis, j., schilke, m., ekh, m. (2014). the effect of anisotropy on crack propagation in pearlitic rail steel, wear, pp. 1–12, doi: 10.1016/j.wear.2013.11.034. [4] leitner, t., hohenwarter, a., pippan, r. (2019). anisotropy in fracture and fatigue resistance of pearlitic steels and its effect on the crack path, int. j. fatigue, 124, pp. 528–536, doi: 10.1016/j.ijfatigue.2019.02.048. [5] toribio, j., gonzález, b., matos, j.c. (2015). crack tip fields and mixed mode fracture behaviour of progressively drawn pearlitic steel, frat. ed integrita strutt., 9(33), pp. 221–228, doi: 10.3221/igf-esis.33.28. [6] hattori, g., alatawi, i.a., trevelyan, j. (2017). an extended boundary element method formulation for the direct calculation of the stress intensity factors in fully anisotropic materials, int. j. numer. methods eng., 109(7), pp. 965– 981, doi: 10.1002/nme.5311. [7] tafreshi, a. (2017). an analytical expression for the j 2 -integral of an interfacial crack in orthotropic bimaterials, doi: 10.1111/ffe.12587. [8] eggleston, j.j., mcfadden, g.b., voorhees, p.w. (2001). a phase-field model for highly anisotropic interfacial energy, phys. d nonlinear phenom., 150(1–2), pp. 91–103, doi: 10.1016/s0167-2789(00)00222-0. [9] li, b., peco, c., millán, d., arias, i., arroyo, m. (2014). phase-field modeling and simulation of fracture in brittle materials with strongly anisotropic surface energy, doi: 10.1002/nme. [10] zhang, s., jiang, w., tonks, m.r. (2020). a new phase field fracture model for brittle materials that accounts for elastic anisotropy, comput. methods appl. mech. eng., 358, pp. 112643, doi: 10.1016/j.cma.2019.112643. [11] nguyen, t.t., réthoré, j., baietto, m.c. (2017). phase field modelling of anisotropic crack propagation, eur. j. mech. i t s. derouiche et alii, frattura ed integrità strutturale, 57 (2021) 359-372; doi: 10.3221/igf-esis.57.26 371 a/solids, 65, pp. 279–288, doi: 10.1016/j.euromechsol.2017.05.002. [12] shanthraj, p., svendsen, b., sharma, l., roters, f., raabe, d. (2017). elasto-viscoplastic phase field modelling of anisotropic cleavage fracture, j. mech. phys. solids, 99, pp. 19–34, doi: 10.1016/j.jmps.2016.10.012. [13] hattori, g., rojas-díaz, r., sáez, a., sukumar, n., garcía-sánchez, f. (2012). new anisotropic crack-tip enrichment functions for the extended finite element method, comput. mech., 50(5), pp. 591–601, doi: 10.1007/s00466-012-0691-0. [14] liu, g.r., nguyen-thoi, t., lam, k.y. (2009). an edge-based smoothed finite element method (es-fem) for static, free and forced vibration analyses of solids, j. sound vib., 320(4–5), pp. 1100–1130, doi: 10.1016/j.jsv.2008.08.027. [15] chen, l., liu, g.r., nourbakhsh-nia, n., zeng, k. (2010). a singular edge-based smoothed finite element method (esfem) for bimaterial interface cracks, comput. mech., 45(2–3), pp. 109–125, doi: 10.1007/s00466-009-0422-3. [16] chen, l., liu, g.r., jiang, y., zeng, k., zhang, j. (2011). a singular edge-based smoothed finite element method (esfem) for crack analyses in anisotropic media, eng. fract. mech., 78(1), pp. 85–109, doi: 10.1016/j.engfracmech.2010.09.018. [17] peng, f., huang, w., zhang, z.q., fu guo, t., ma, y.e. (2020). phase field simulation for fracture behavior of hyperelastic material at large deformation based on edge-based smoothed finite element method, eng. fract. mech., 238, doi: 10.1016/j.engfracmech.2020.107233. [18] surendran, m., lee, c., nguyen-xuan, h., liu, g.r., natarajan, s. (2021). cell-based smoothed finite element method for modelling interfacial cracks with non-matching grids, eng. fract. mech., 242, pp. 107476, doi: 10.1016/j.engfracmech.2020.107476. [19] ayatollahi, m.r., nejati, m., ghouli, s. (2020). the finite element over-deterministic method to calculate the coefficients of crack tip asymptotic fields in anisotropic planes, eng. fract. mech., 231, pp. 106982, doi: 10.1016/j.engfracmech.2020.106982. [20] song, c., wolf, j.p. (2002). semi-analytical representation of stress singularities as occurring in cracks in anisotropic multi-materials with the scaled boundary finite-element method, comput. struct., 80(2), pp. 183–197, doi: 10.1016/s0045-7949(01)00167-5. [21] su, r.k.l., sun, h.y. (2003). numerical solutions of two-dimensional anisotropic crack problems, int. j. solids struct., 40(18), pp. 4615–35, doi: 10.1016/s0020-7683(03)00310-x. [22] rajesh, k.n., rao, b.n. (2010). two-dimensional analysis of anisotropic crack problems using coupled meshless and fractal finite element method, int. j. fract., 164(2), pp. 285–318, doi: 10.1007/s10704-010-9496-3. [23] yang, y., chu, s.j., huang, w.s., chen, h. (2020). crack growth and energy release rate for an angled crack under mixed mode loading, appl. sci., 10(12), doi: 10.3390/app10124227. [24] leguillon, d., murer, s. (2008). a criterion for crack kinking out of an interface, key eng. mater., 385–387, pp. 9–12, doi: 10.4028/www.scientific.net/kem.385-387.9. [25] gosz, m., okyar, a.f., nair, s. (2003). a crack driving force criterion for the prediction of interface crack kinking in thin-film composites, interface sci., 11(3), pp. 329–338, doi: 10.1023/a:1025100507702. [26] argatov, i.i., nazarov, s.a. (2002). energy release caused by the kinking of a crack in a plane anisotropic solid, j. appl. math. mech., 66(3), pp. 491–503, doi: 10.1016/s0021-8928(02)00059-x. [27] cornetti, p., sapora, a., carpinteri, a. (2014). t-stress effects on crack kinking in finite fracture mechanics, eng. fract. mech., 132(1), pp. 169–176, doi: 10.1016/j.engfracmech.2014.10.011. [28] spagnoli, a., carpinteri, a., vantadori, s. (2013). on a kinked crack model to describe the influence of material microstructure on fatigue crack growth, frat. ed integrita strutt., 7(25), pp. 94–101, doi: 10.3221/igf-esis.25.14. [29] krueger, r. (2004). virtual crack closure technique: history, approach, and applications, appl. mech. rev., 57(2), pp. 109, doi: 10.1115/1.1595677. [30] xie, d., waas, a.m., shahwan, k.w., schroeder, j.a., boeman, r.g. (2004). computation of energy release rates for kinking cracks based on virtual crack closure technique, c. comput. model. eng. sci., 6(6), pp. 515–24. [31] zeng, w., liu, g.r., jiang, c., dong, x.w., chen, h.d., bao, y., jiang, y. (2016). an effective fracture analysis method based on the virtual crack closure-integral technique implemented in cs-fem, appl. math. model., 40(5–6), pp. 3783– 800, doi: 10.1016/j.apm.2015.11.001. [32] de carvalho, n. v., krueger, r. (2016).modeling fatigue damage onset and progression in composites using an element-based virtual crack closure technique combined with the floating node method. american society for composites thirty-first technical conference, 1102. [33] okada, h., kamibeppu, t. (2005). a virtual crack closure-integral method (vccm) for three-dimensional crack problems using linear tetrahedral finite elements, c. comput. model. eng. sci., 10(3), pp. 229–38, doi: 10.3970/cmes.2005.010.229. s. derouiche et alii, frattura ed integrità strutturale, 57 (2021) 359-372; doi: 10.3221/igf-esis.57.26 372 [34] bouzerd, h. (1992).elémént fini mixte pour interface cohérente ou fissurée. université de claude bernard, lyon i, france. [35] bouziane, s., bouzerd, h., guenfoud, m. (2009). mixed finite element for modelling interfaces, eur. j. comput. mech., 18(2), pp. 155–75, doi: 10.3166/ejcm.18.155-175. [36] salah, b., hamoudi, b., noureddine, b., mohamed, g. (2014). energy release rate for kinking crack using mixed finite element, struct. eng. mech., 50(5), pp. 665–677, doi: 10.12989/sem.2014.50.5.665. [37] mohamed ben ali, a., bouziane, s., bouzerd, h. (2021). computation of mode i strain energy release rate of symmetrical and asymmetrical sandwich structures using mixed finite element, frat. ed integrità strutt. ed integrità strutt., 15(56), pp. 229–239, doi: 10.3221/igf-esis.56.19. [38] benmalek, h., bouziane, s., bouzerd, h. (2021). mixed finite element for the analysis of fgm beams, int. rev. mech. eng., 15(1), pp. 36, doi: 10.15866/ireme.v15i1.19680. [39] rybicki, e.f., kanninen, m.f. (1977). a finite element calculation of stress intensity factors by a modified crack closure integral, eng. fract. mech., 9(4), pp. 931–938, doi: 10.1016/0013-7944(77)90013-3. [40] irwin, g.r. (1957). analysis of stresses and strains near the end of a crack traversing a plate. j. applied mechanics, 24,(1957) 361–364. [41] voyiadjis, g.z., kattan, p.i. (2005). mechanics of composite materials with matlab, 1. [42] hwu, c. (2010). anisotropic elastic plates, vol. 01, boston, ma, springer us. [43] lekhnitskii, s.g. (1968). anisotropic plates, gordon and breach,. [44] bowie, o.l., freese, c.e. (1972). central crack in plane orthotropic rectangular sheet, int. j. fract. mech., 8(1), pp. 49– 57, doi: 10.1007/bf00185197. microsoft word numero_58_art_19_3231.docx m. utzeri et alii, frattura ed integrità strutturale, 58 (2021) 254-271; doi: 10.3221/igf-esis.58.19 254 focussed on steels and composites for engineering structures modelling of low-velocity impacts on composite beams in large displacement m. utzeri*, m. sasso università politecnica delle marche department of industrial engineering and mathematics, italy m.utzeri@pm.univpm.it, m.sasso@univpm.it g. chiappini università degli studi ecampus, italy gianluca.chiappini@uniecampus.it s. lenci università politecnica delle marche department of civil and building engineering, and architecture, italy s.lenci@univpm.it abstract. the paper provides an evaluation of the nonlinear dynamic response of a cantilever beam made of composite material subjected to low-velocity impacts. the structure is assumed to respond in a quasi-static manner and modelled by a continuous beam in large displacement with a lumped mass attached. first, an analytical model was developed to study the free vibrations of a beam, taking into account the nonlinearities due to large displacements and inertia. then, the analytical findings were compared with experimental test data. the vibration of a real composite beam has been acquired through high-speed imaging technique. the displacements of the beam were extracted by digital image analysis; then, the nonlinear parameters of the analytical model were determined by the fitting time history technique. the results obtained by the analytical model and the experimental test are compared with numerical analysis. the validated analytical model was adapted to study a low-velocity impact; the lumped mass was associated with a rigid projectile, whose initial speed represents the impact velocity. keywords. impact dynamics; composite beam; nonlinear frequencies; nonlinear dynamics. citation: utzeri, m, sasso, m., chiappini, g., lenci, s.., modelling of low-velocity impacts on composite beams in large displacement, frattura ed integrità strutturale, 58 (2021) 254-271. received: 18.08.2021 accepted: 01.09.2021 published: 01.10.2021 copyright: © 2021 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. introduction n the last few years, composite materials (e.g. carbon fiber reinforced polymer, glass fiber reinforced polymer) are used extensively in widely impact engineering applications. the mains composite materials peculiarities are the high specific strength and flexibility. therefore, a composite structure can undergo large deflection without breaks when a foreign object hits it. the theory behind the low-velocity impacts has been hugely discussed by abrate with several works i https://youtu.be/nk2pw5hy7-4 m. utzeri et alii, frattura ed integrità strutturale, 58 (2021) 254-271; doi: 10.3221/igf-esis.58.19 255 on this topic [1, 2]. the aim of his work is to extend the known model to predict the contact force history and the overall response of the structure in large displacements. the relevant models used to study the low-velocity impact are spring-mass and energy balance models [3]. in this study the spring-mass approach was used to describe the overall response of a slender cantilever beam which undergoes the impact of a projectile. starting from the abrate theory, the spring associated with the structure is analytically modelled as a continuous euler-bernoulli beam. the indentation phenomenon was neglected because the overall deflection of the beam is much larger than local. in this way, the mass of projectile can be added to the continuous cantilever beam. however, the slender beam reaches large deflection to absorb the projectile energy during the impact so only the nonlinear vibration theory allows establishing the correct dynamical behaviour. many theoretical and experimental investigations of nonlinear vibrations of beams have appeared over the years [4, 5, 6, 7]. in general, the nonlinearity may be attributed to geometry (stiffness and inertia), and material (constitutive equation and damping) [8]. firstly, geometric nonlinearities are caused by large displacements and slopes. consequently, it is not possible to use the small-angle assumption, which would reduce the nonlinear curvature to the simple linear form [9, 10, 11]. for a deeper discussion on the nonlinear curvature the reader is referred to [12, 13]. nonlinear inertia effects may be caused by the presence of concentrated or distributed masses. actually, for transversal vibrations of an initially straight beam there are transversal and axial (linear and nonlinear) inertial effects; while the former can never be neglected, in certain cases (for example for axially immovable boundary conditions), the latter are negligible [5, 14]. according to hamdan [15, 16, 17], the nonlinear stiffness induces nonlinear features of the hardening type, i.e., the vibration frequencies increase by increasing the amplitude of motion; on the contrary, the inertial nonlinearity, which is related to the inextensibility condition and to the lumped mass, determines a softening behaviour of the so-called “backbone curve”. consequently, the nonlinear effects which modify the frequencies act also on the time in which the impact occurs. therefore, the impact time is strictly connected with the amplitude reached during the impact. for instance, a hardening behaviour on the nonlinear frequency clearly reduces the impact time and the maximum amplitude reaches a lower amplitude than linear form. accordingly, in this paper, the effects of nonlinearity in a cantilever beam were addressed further elaborating and extending the analytical approach of the works [16, 15, 18]. analytical model takes into account the nonlinearity derived by large amplitude vibration and inertia. starting from the energy definition, the equation of motion is determined including nonlinear terms associated to geometrical nonlinearity up to the fifth order. hence, enforcing stationarity of the lagrangian of the system yields to the unimodal equation, which can be solved by multiple scale method [19]. this analytical approach gives the approximate solution of the transversal displacement and the first nonlinear frequency where the nonlinear terms are up to fifth order. then, the results of an experimental tests were compared with the the analytical findings to validate the nonlinear model. free vibration experimental tests were done on a rectangular beam made of twill laminated carbon fiber reinforced polymer, whose vibration displacement amplitude was measured by high-speed imaging; indeed, the image analysis allows measuring the vibration displacement amplitude of any point of the beam. the obtained results were post-processed by the fitting time history (fth) technique, which is based on the least square approximation of general damped sinusoidal function with the measured free damped vibrations of the specimen. this technique allows to determine the main natural frequencies, the related modal damping coefficients, and damping and frequency nonlinearities [20, 21]. finally, the projectile impact against a cantilevered beam has been simulated through the commercial finite element software abaqus ©. exploiting the nonlinear euler-bernoulli beam coupled with implicit solver, the data about speed and displacement were exported and compared with the analytical findings. analytical model n according to abrate [3], impacts can be modelled through spring-mass models. they provide accurate solution for low-velocity impacts. the most complete model consist in two-degree of freedom model which the projectile and the hit beam are associated with masses. the spring links each other represents the nonlinear contact stiffness. instead, the second spring is associated with the linear and nonlinear stiffness of the structure. this kind of model can be exploited to describe the impact dynamics of projectile against a slender beam. the stiffness of the structure can be associated with the bending stiffness of euler-bernoulli beam. however, the hit beam undergoes a large deflection because of the slenderness. therefore, the indentation is smaller than the overall deformation of the structure and can be neglected. the models assumes the single-degree of freedom form which the masses of the projectile and the beam are added together, as shown in fig. (2). the low-velocity impacts models exist only when the waves phenomena inside the beam due to the hitting are neglected. in this case, flexural waves appear from the bending action of the impacted projectile. the euler–bernoulli theory of bending assumes that plane sections remain plane as the bending deformation. shear deformation and rotary i m. utzeri et alii, frattura ed integrità strutturale, 58 (2021) 254-271; doi: 10.3221/igf-esis.58.19 256 inertia effects are ignored. considering a uniform beam of mass per unit length m, the elastic modulus e and the area moment of inertia i that undergoes a flexural wave motion with vertical displacement, the flexural waves speed is given by           1 4 f ei c m (1) where γ is the wavenumber and ω is the frequency [22, 23]. from the eqn. (1) can be deduce the flexural waves speed is function of frequency thus they are also called dispersive waves. the phenomenon of flexural wave propagation can be neglected when the interested time is bigger than the time of flexural wave takes to travel inside the beam, fwt =  fc l . fig. (1) shows a simplified motion of slender cantilever beam during an impact of projectile. when the projectile hit the beam fig. (1b), flexural waves start to travel inside the beam and have a velocity fc . fc is not constant as in axial waves but it is depended to the impact. more rapidly is the impulse and more is the waves speed. after the early stages, multiple reflections occur, and the bending motion is established. as the beam is bending, flexural waves keep traveling but their effects can be neglected. consequently, the beam motion can be completely described through multi-modal superposition technique as in fig. (1c). (a) (b) (c) figure 1: simplified motion of slender cantilever beam during an impact of projectile. (a) before the impact. (b) after the impact and  fwt t (flexural waves predominant). (c)after the impact and  fwt t (multi-modal superposition) multi-modal nonlinear response the beam under consideration is shown in fig. (2). it is homogeneous, i.e. the cross-section, the density, and all other properties are constant along the beam axis. the lumped mass is fixed symmetrically with respect to the beam center line to maintain the symmetry with respect to the 𝑋 reference line. figure 2: sketch of cantilever beam with intermediate mass m. utzeri et alii, frattura ed integrità strutturale, 58 (2021) 254-271; doi: 10.3221/igf-esis.58.19 257 in order to describe the nonlinear response of the impacted beam in large deflection, the equations of motion are determined starting from the definition of the energies. the formulation takes into account large vibrations, the inextensibility of the beam, and the lumped mass inertial terms. as proposed by hamdan [17], the kinetic (𝐸 ) and potential (𝐸 ) energy of the beam are defined as                    3 1 2 2 2 2 2 0 | | 2 k ml e x y d x y j (2)    1 2 0 ( , ) 2 p ei e k t d l (3) where dot means derivative with respect to time,   s l is the dimensionless distance from the left boundary,  x x l and  y y l .   ,x t and   ,y t are the deformed position of the generic point   , 0 in the reference straight configuration.   d l is the given dimensionless position of the lumped mass.   m ml and  3 j j ml are the inertia dimensionless parameters of the lumped mass. the term   ,k t is the curvature of the neutral axis of the beam, and is given by:  'k (4) here prime means derivative with respect to  , and  is the rotation (equal to the beam slope, since we are considering an euler-bernoulli beam) [24],             2 2 2 ' '' ' ' ''1 tan     tan ' '     ' ' cos( ) ' ' y y x y x x x y (5) in this work, as in [6], the axis of the beam is considered inextensible. this implies that:  2 2' ' 1x y (6) namely,         2 4 6 2 ' ' '' 1 ' 1 ... 2 8 16 y y y x y (7) where in the last expression a taylor approximation is considered. by means of eqn.(7) we obtain, up to the due order,      3 5' 3 ' ' ... 6 40 y y y (8)       2 2 2 4' 1 ' ' ...y y y (9) (use is made of the boundary condition   0 0x )            2 4 2 '' ' 3 ' '' 1 ... 2 81 ' y y y k y y (10) m. utzeri et alii, frattura ed integrità strutturale, 58 (2021) 254-271; doi: 10.3221/igf-esis.58.19 258 note that the higher order terms are positive, meaning that the curvature increases (with respect to the linear case) for increasing amplitudes. this is the motivation for the hardening behaviour due to the geometric stiffness nonlinearity. the expression of the kinetic energy of the system then becomes:                                                            2 3 53 1 2 0 0 2 3 5 2 0 2 2 4 ' 3 ' ' ' 2 2 8 ' 3 ' ' ' 2 8 ' 1 ' ' k y yml e y y y d d y y y y y d j y y y (11) likewise, the potential energy becomes:           22 4 1 2 0 ' 3 ' ' ' 1 2 2 8 p y yei e y d l (12) the vibration motion is assumed to have linear modes. the vibration of the beam with a concentrate intermediate mass is governed by the equation         ¨ '''' 1 0 m y y ei (13) assuming a solution of eqn.(13) in the form      , φ i ty t e (14) substituting the eqn.(14) into eqn.(13) gives               2 φ '''' 1 φ 0 m ei (15) and the boundary condition at  0x and  1x are           φ 0 0    φ 0 ' 0     φ 1 '' 0     φ 1 ''' 0ei ei (16) taking the laplace transformation of eqn. (15), using the boundary conditions (16) and then taking the inverse laplace transformation yields the eigenfunction of the beam with an intermediate concentrated mass                                                  2 3 2 φ 0 '' φ 0 ''' φ cosh cos sinh sin 2 2 φ sinh sin 2 k kl kl k kl kl kl h kl kl (17) where   2 4 mk ei . hence the unknown constants 0φ'' and 0φ''' can be determined imposing the boundary condition in eqn.(17). substituting 0φ'' and 0φ''' into eqn. (17), and then letting   to eliminate  φ , gives the characteristic equation m. utzeri et alii, frattura ed integrità strutturale, 58 (2021) 254-271; doi: 10.3221/igf-esis.58.19 259                                                1 cos cosh ( cos sinh cosh sin cos cosh 1 2 cos sinh cosh sin cos cosh 1 ) 0 kl kl kl kl kl kl kl bk bk bk bk bk bk kl kl (18) where   1b l [25]. note that the  φ guarantees that   φ 1max . the eqn.(18) can be simplified assuming   0 to obtain the characteristic equation of clamped-free beam case      cosh cosh 1 0kl kl (19) we consider that the arbitrary motion of a beam undergoing free vibration may be expressed as a superposition of its free vibration mode shapes (φ 𝜁 ), each undergoing simple harmonic motion with frequency 𝜔 , namely we assume that: 𝑦 𝜁,𝑡 ∑ 𝑢 𝑡 φ 𝜁 (20) where φ 𝜁 is a given function and 𝑢 𝑡 is the unknown. the lagrangian of the system is defined as ℒ 𝐸 𝐸 . inserting the eqn.(20) in ℒ and enforcing stationariety, yields to the equation of motion of each mode defined as ℒ ℒ . after some computations we get [16, 26]: 𝑢 𝛼 𝛼 𝑢 𝛼 𝑢 𝑢 𝛼 𝑢 2𝛼 𝑢 𝛽 𝛼 𝑢 2𝛼 𝑢 3𝛼 𝑢 0 (21) where 𝛼 φ 𝜁 𝑑𝜁 𝜇φ 𝜂 𝑗φ 𝜂 , 𝛼 φ 𝜒 𝑑𝜒 𝑑𝜁 𝜇 φ 𝜒 𝑑𝜒 𝑗φ 𝜂 , 𝛼 φ 𝜒 𝑑𝜒 φ 𝜒 𝑑𝜒 𝑑𝜁, 𝜇 φ 𝜒 𝑑𝜒 φ 𝜒 𝑑𝜒 𝑗φ 𝜂 , 𝛼 φ 𝜁 𝑑𝜁, 𝛼 φ 𝜁 φ 𝜁 𝑑𝜁, 𝛼 φ 𝜁 φ 𝜁 𝑑𝜁 𝛽 (22) the nonlinear inertial terms are clearly visible. the accuracy of the proposed approximate solution is expected to diminish when the mass ratio  exceeds the value of 3 [16], since the spatial shapes  φn is only considered in linear form. the eqn.(21) is solved by the multiple scale method [19], and the approximate solution is given by                           35 2 1 2 4 1 1 sin sin 3 ... 16 n n nl n n nl nu t a t a t (23) the nl is the nonlinear frequency, and can be written in the form       2 40 2 4 ...nl n n n n na a (24) m. utzeri et alii, frattura ed integrità strutturale, 58 (2021) 254-271; doi: 10.3221/igf-esis.58.19 260 where:                                          4 0 1 0 5 2 2 4 1 2 2 0 5 2 5 6 32 4 2 2 1 4 4 14 1 , 3 , 4   15 18 9 60 12 64   n n n n n (25) eqn.(24) is the analytical expression of the backbone curve, approximated up to the fifth order. considering only the first term in eqn.(23), we remind that the physical tranvsersal position of the beam, which is needed for comparison with numerical and experimental results, is given by                       1 1 , φ s in φn n n nl n n n n y t l u t l a t (26) in low-velocity impact dynamics the analytical model provides two boundary condition. the initial displacement of the system is zero. secondly, the initial velocity of the system coincides with the impact velocity 0v . in a continuous eulerobernoulli beams with a intermediate lumped mass the boundary conditions can be imposed through the dirac function. thereby the initial velocity along the beam is zero except in the point where the impact occurs.                 0, 0 0     , 0y y g v (27) if the impact occurs in a portion of the beam, the  g can be described through boxcar function or rectangular function as                                                    0 0π 2 2 imp imp imp g v v h h (28) where the  imp is the adimensional portion of the beam impacted. then, substituting the eqn.(20) in eqn.(27) yields             1 1 , 0 s in φ 0,n n n n y a (29)                     0 1 1 , 0 c os φn n n n n y v a (30) the initial displaced shape have to be equal to zero so the elementary solution is  1 0n . thus, in this work the na is only function of impact velocity. the magnitudes represents the strengths in which the various modes participate in the subsequent motion [27]. multiplying both sides of eqn.(30) by the m -th eigenfunction, integrating both sides over the length of the beam, and taking advantage of the well-known orthogonality property of the eigenfunctions yields to na , the amplitude coefficients of the n -th mode                             1 1 00 0 1 12 2 0 0 φ φ φ ( ) φ ( ) n n n n n n n g d v d a d d (31) m. utzeri et alii, frattura ed integrità strutturale, 58 (2021) 254-271; doi: 10.3221/igf-esis.58.19 261 experimental method he aim of the experimental test is to validate the analytical model proposed in the previous section. the model can be validated through a comparison with the vibration of cantilever beam with an intermediate fixed mass. in this way a more complex experimental test as gas gun test is avoided [28, 29]. the specimen is subjected to an impulse at its free end and the history of the oscillation amplitude is measured. during beam oscillations, the longitudinal section was recorded by a high speed camera (model fastcam photron  sa4) at frame rate of 10000 hz. by means of the matlab image processing toolbox, each photo has binarized and processed to obtain the profile of beam longitudinal section, as shown in fig.3. more detail of the experimental test can be found in utzeri et al. work [15]. the specimen is a rectangular beam made of carbon fibre reinforced polymer pre-preg t700 twill. the linear density of the beam m is 0.0681 kg m . the flexural young’s modulus, i.e. e , are determined experimentally through the standard test method for flexural properties of polymer matrix composite materials (astm d7264/d7264m), and it is 44951 2 n mm . the beam cross-section is rectangular, where the base is 25.05 mm and the height is 1.85 mm. figure 3: image processing which shows the transverse vibration of the beam. the blue lines represents the upper and lower profiles of the beam. the circle line and the red line can be associated with the the neutral axis and the trajectory of one beam point, respectively. nonlinearities identification ollowing [20, 21], the results were post-processed by the fitting time history (fth) technique, which is based on the least square approxi-mation of the measured free damped vibrations. fth technique permits to reveal how the natural frequencies as well as the modal damping coefficients depend nonlinearly on the excitation amplitude in each i -th mode. consequently, this technique is coherent with the analytical method involved in analytical section, i.e. multimodal approach. according to eqn.(23), and retaining only the term proportional to a, during the free oscillations the amplitude iq of the i -th mode is given by              0, s in φi il i n n i q t l a t (32) where     i i ti ia t b e represents the oscillation amplitude, which is assumed to vary in time because of the damping.     1il i i is the damped frequency, i is the natural frequency, i is the damping coefficient and ib and i are the starting amplitude and the phase delay, respectively, that depend on the initial conditions. the linear frequency is initially t f m. utzeri et alii, frattura ed integrità strutturale, 58 (2021) 254-271; doi: 10.3221/igf-esis.58.19 262 computed by the fast fourier transform (fft). the nonlinear frequency is a function of the amplitude thus, according to eqn.(24), we assume:           2 40 2 4il i i i i it a t a t (33) where  0i is the linear (natural) frequency and ij are the nonlinear correction terms of j -th order for the i -th mode. consistently with the above explained approach, the nonlinear damping has been assumed as:            20 1 2il i i i i it a t a t (34) fth optimization needs a cost or error function to be minimized. therefore, the normal root means square deviation (nrsmd) between analytical function and experimental measures is used:           21 ( ) , , ,   ˆ n k kk ij ij i i q y nnrsmd b max y (35) where n is the number of acquired samples, ky is the k -th experimental observation, kq is the value of the analytical function at the same time. the nrsmd provides the optimal estimation of the vibrational properties of the system (linear,  0i and  0i , and nonlinear,  2i ,  4i ,  1i and  2i ). the minimization algorithm was created in-house with matlab  . finally, the nonlinear damping an frequency coefficients were progressively introduced into the matlab optimization algorithm: first, only linear terms where considered, then a second term was added, and so on. the performance of the optimization algorithm was observed to improve increasingly. numerical model he aim of the numerical modelling is to validate the analytical model proposed in the analytical section. the model can be validated through a comparison with the outcomes obtained by the impact of concentrate mass against the cantilever beam. the fem analysis was carried out by means abaqus  software. the elements such as b23, b23h, b33, and b33h allow to model an euler-bernoulli beam in abqus. so, they do not allow for transverse shear deformation; plane sections initially normal to the beam’s axis remain plane (if there is no warping) and normal to the beam axis. in this study, 10000 b23 beam was used to model the length of the beam. the concentrate mass is considered rigid with specific initial condition. the mass has a initial speed 0v and is located transversely at the beam at d distance from the clamped end. the nonlinear transient analysis coupled with implicit solver has been used to compute the time history of the entire beam deflection. two load step was used and a very small time step, i.e. 0.00001 s, was imposed in the fem simulation. the first step defines the initial condition of the beam and the mass. in the second step the condition on the mass speed was deleted. so, the mass can impact against the beam and loose its velocity during the bending motion of the beam. to avoid the indentation effect and rebounds the mass was imposed to be bonded to the beam. after the simulation the data about speed and displacement were exported and compared with the analytical findings. results and discussions he results obtained by the analytical model were compared with experimental data to validate the nonlinear model. after all, the boundary conditions associated with low-velocity impact were imposed to the model. the analytical findings were discussed and compared to the numerical solutions. experimental validation the fth technique has been applied to the displacement signals measured in the experiment described in experimental method section. a concentrate mass with a mass ratio   0.5 was fixed along to the beam at   0.95 . the vibration response is analyzed through fth technique. t t m. utzeri et alii, frattura ed integrità strutturale, 58 (2021) 254-271; doi: 10.3221/igf-esis.58.19 263 unimodal linear unimodal first order nonlinearities unimodal second order nonlinearities multimodal nrmsd 4.14% 2.64% 1.07% 0.76% 10 149.205 149.145 148.954 148.898 12 0 4.125 4.815 4.232 14 0 0 15.5231 12.6589 10 0.0091 0.0088 0.0063 0.0076 11 0 0.1910 0.3431 0.1793 12 0 0 -6.0519 -4.0536 1b 0.2426 0.2433 0.2451 0.2475 1 1.3219 1.3184 1.3170 1.2907 20 0 0 0 1296.5 20 0 0 0 0.0041 2b 0 0 0 -0.0012 2 0 0 0 3.0167 table 1: fth fitting coefficients for the signal at   0.95 of the beam length the coefficients of the fth fittings, which synthetize the experimental results and thus are the most important results of this part, are reported in tab. 1, together with the achieved nrsmd values. it can be noted that, as expected, the nrsmd values reduces as the modeling is enhanced from linear unimodal to multimodal nonlinear. the  2 2 1 1, , ,b b terms do not have a role in the system characterization. they compare only in the minimization algorithm, and are reported for completeness of information. figure 4: comparison of backbone curve of the first nonlinear frequency in analytical and experimental results. it can be noted that the backbone curve obtained by experimental method is very similar to that obtained with the analytical formulation. moreover, the multi-modal identification increases the performance of the fth. indeed, inserting the second mode with its relative nonlinearities, the backbone curve of first frequency approaches that obtained analytically. the analytical model was able to describes correctly the first nonlinear frequency and therefore it was validated. further information about the efficiency of fth technique in experimental tests can be found in these works [15, 14]. m. utzeri et alii, frattura ed integrità strutturale, 58 (2021) 254-271; doi: 10.3221/igf-esis.58.19 264 analytical findings first of all, the backbone curve of the first three modes are computed by means of eqn. (24). the fig. (5) shows the first nonlinear frequency and the influence of impacted distance  of a projectile with a mass ratio  of 50% and 200%. in both of cases, the nonlinear behaviour is hardening so the frequency increase with the vibration amplitude. the impacted distance  changes the nonlinear hardening trend. especially, the hardening trend decrease up to the impact distance reaches the half of the beam. instead, the increase of mass leads to an further hardening behaviour in all of case. figure 5: backbone curve of first nonlinear frequency. (a) influence of impacted distance  of a projectile with a mass ratio  of 50%. (b)influence of impacted distance  of a projectile with a mass ratio  of 200%. on the contrary the backbone curve of second and third modes are softening type, as shown in fig. (6) and fig. (7) respectively. even in this cases were evaluated the influence of impacted distance  of a projectile with a mass ratio  of 50% and 200%. the impacted distance  changes the nonlinear trend. figure 6: backbone curve of second nonlinear frequency. (a) influence of impacted distance  of a projectile with a mass ratio  of 50%. (b)influence of impacted distance  of a projectile with a mass ratio  of 200% m. utzeri et alii, frattura ed integrità strutturale, 58 (2021) 254-271; doi: 10.3221/igf-esis.58.19 265 figure 7: backbone curve of third nonlinear frequency. (a) influence of impacted distance  of a projectile with a mass ratio  of 50%. (b)influence of impacted distance  of a projectile with a mass ratio  of 200% figure 8: trend of adimensional impact duration in function of mass ratio  . the impact occurs at   0.75 the nonlinear behaviour of the frequency affects the response of the beam during the impacts. following the spring-mass theory the projectile has the initial velocity and the beam is relaxed. then, the projectile hits the beam and reduces its velocity up to the beam reaches the maximum deflection. the potential energy of the beam is equal to the initial kinetic energy of the projectile. after the maximum deflection point the projectile is pushed backward. the impact ends when the projectile overcomes the line of the clamped beam end. in large displacement the time of the impact can be reduced or augmented in function of the hardening or softening trend of nonlinear frequency. as the increase of the deflection of the beam this phenomenon becomes more and more relevant. the first nonlinear vibration is the most involved vibration when the impact occurs close to the free end of the beam. the amplitude due to the projectile impact with a velocity 0v can be found through the eqn.(31). the amplitude associated with the first modes increase as the velocity impact increasing. therefore, the impact time is affected by the nonlinear frequency which is function of the amplitude. starting from the eqn.(24) and the assumption of first vibration response, the impact time is defined as m. utzeri et alii, frattura ed integrità strutturale, 58 (2021) 254-271; doi: 10.3221/igf-esis.58.19 266            2 41 10 12 1 14 1 imp l t a a (36) fig. (8) shows how the adimensional impact duration depends by the mass ratio  . surely, the impact time is bigger as the increase of projectile mass. moreover, the influence of nonlinearities is more relevant at high mass ratio with the same impact velocity. the explanation is related to the amplitude reached during the impact. the initial kinetic energy is strictly dependent to the mass ratio, so inevitably the beam has to deflect more at high mass ratio to absorb the impact at the same impact velocity. likewise, can be evaluated the impact velocity in function of the maximum impact deflection. starting from the eqn.(31) and the assumption of first vibration response, the impact velocity can be computed as follows                 1 2 10 0 1 101 10 φ ( )      , φ d v a linear d (37)                       1 2 1 2 40 0 1 10 12 1 14 11 10 φ ( )      φ d v a a a nonlinear d (38) figure 9: impact velocity in function of the maximum deflection of the beam. (a) the projectile has a mass ratio  of 50%. (b) the projectile has a mass ratio  of 200%. fig. (9) shows how the impact velocity depends by the maximum deflection of the beam with two different mass ratio  . in large displacement the impact velocity is not linear but follow the nonlinear frequency trend. therefore, the hardening behaviour of the first frequency leads to an increase of impact velocity to obtain the predicted amplitude in the linear theory. as the mass ratio increase the hardening behaviour persists and the nonlinear terms have more relevance, as shown in fig. (9)b). the changing of the impact distance  leads to an increase in slope of the impact velocity-amplitude relationship. even in these case, the hardening behaviour persists but the nonlinear terms have less relevance. in impact dynamics the absorption energy on the impact is the key information as well as the displacements, and reactions forces. all information can be obtained by means of analytical model but the mono-modal approach is not able to describe the real time history of the system. for instance, the boundary conditions in eqn.(30) impose the displacement is zero and the velocity is 0v only in the position where the impact occurs. taking into account only the first vibration mode is not possible to have this trend m. utzeri et alii, frattura ed integrità strutturale, 58 (2021) 254-271; doi: 10.3221/igf-esis.58.19 267 because the speed is function of only first mode shape. following multi-modal superposition approach, a trend quite similar to the dirac function can be achieved. therefore, a superposition of 10 modes is computed where only the first three modes takes into account nonlinear behaviour because of computational efforts. fig. (10) shows the energy time history in a impact of projectile with   0.9 ,   0.5 , and 0 5 m v s . figure 10: energy time history. figure 11: deflection history of the free-end beam during the impact of projectile at   0.95 . (a) influence of projectile mass with an initial speed of 5 m s . (b) influence of projectile speed with a mass ratio  of 50%. in order to confirm the validation of the model, the kinetic energy of the system is split between the beam and the projectile. at  0t the kinetic energy of the projectile corresponds to the kinetic energy of free projectile with speed 0v . at the same time, the kinetic energy of the beam is very close to zero because it is relaxed. increasing the numbers of modes into the model the beam reaches zero. in early stages, the beam undergoes the influence of the projectile velocity and starts to deflect. at the end of the impact, the beam continues to oscillate. the sum of the kinetic and potential energies represents the total energy of the system. the fig. (10) shows the average of the total energy is constant. however, there are some fluctuations due to the numerical approximation in multi-modal approach and nonlinear equations. the effect of geometrical m. utzeri et alii, frattura ed integrità strutturale, 58 (2021) 254-271; doi: 10.3221/igf-esis.58.19 268 nonlinearities are noticeable in the displacement history as shown in fig. (11). the displacement in linear and nonlinear response are quite similar in the trend. however, the time of impact is clearly reduced due to the hardening behaviour in the first nonlinear frequency. the effect also involves the peak of deflection. in the nonlinear model, the maximum amplitude reaches a lower amplitude than linear form. it is reduced because of the increase of stiffness in large displacement or rather the hardening behaviour in the first nonlinear frequency. numerical results first of all, the natural frequency obtained by the analytical model was compared with the numerical model. tab.(2) shows this comparison in which some combination of  and  were set. the frequencies in the tables confirm the accuracy of the analytical model. the first frequencies are the best approximated by the analytical model. instead the second and third frequencies are slightly greater than numerical ones.   mode n analytical [hz] fem [hz] 0 0 1° 39.333 39.331 2° 246.39 246.39 3° 690.20 690.20 0.75 0.5 1° 28.771 28.770 2° 243.98 243.94 3° 583.38 582.65 0.5 1 1° 32.328 32.326 2° 159.04 158.99 3° 690.03 689.30 0.75 2 1° 18.575 18.572 2° 242.1731 242.01 3° 531.9391 531.21 1 3 1° 11.697 11.697 2° 176.49 176.43 3° 563.31 562.80 table 2: comparison of natural frequency between analytical and numerical model the numerical analysis was carried out on the impact of a mass with   0.5 at the impact distance   0.9 with a initial velocity 0 5 m v s . firstly, the early stages of the impact was evaluated. the flexural waves start to travel inside the beam after the impact of the projectile. the flexural waves is showed in fig. (12) at two instant of time, 0.00006 second and 0.00009 s. in this time the flexural wave travels along to the beam and runs a distance of 40.58 mm, δ wavex in fig. (12). the analytical flexural waves speed along the beam can be computed following the eqn.(1). the impact occurs in a time about 0.00001 s. hence, the flexural wave speed is 1362.362 m s and the theoretical δ wavex is 40.87 mm. consequently, the flexural wave speed is verified. it is greater than the impact velocity and therefore the low-velocity assumption to model the impact is confirmed. after the early stages, the projectile and the beam start to motion following the multi-modal theory. in order to assess the compatibility of the analytical and numerical models, a comparison between the models results was evaluated. fig. (13) shows the displacement and velocity histories of the impacted distance. the deflection computed with the analytical model overlaps the numerical ones, fig. (13a). the impact time is perfectly described as well as the maximum deflection. also, the analytical trend of velocity is consistent with the numerical one. however, the analytical signal appears smoother than the numerical solution, fig. (13b). m. utzeri et alii, frattura ed integrità strutturale, 58 (2021) 254-271; doi: 10.3221/igf-esis.58.19 269 figure 12: flexural waves propagation in early stages of impact ( δ 0.00003 t s and scale factor 100). figure 13: impact of a mass with   0.5 at the impact distance   0.9 with a initial velocity 0 5 m v s ; comparison of fem and analytical results.(a) deflection history. (b) velocity history conclusion his paper investigated the nonlinear impact response in large displacements of a slender cantilever beam which undergoes the impact of a projectile. the spring-mass approach was used to describe the overall response and the indentation phenomenon was neglected because the overall deflection of the beam is much larger than local. the analysis compared the results coming from analytical approach with numerical model and experimental observations. as the nonlinear frequencies behaviour is function of the amplitude, the impact time is affected by the velocity impact. the hardening behaviour of the first frequency leads to a decrease of impact time as the velocity impact increase. moreover, the hardening behaviour leads to an increase of impact velocity to obtain the same predicted amplitude in the linear theory. the experimental tests confirm the hardening behaviour of the first backbone curve. so, the analytical model was validated by the experimental findings. the numerical analysis also confirm the analytical outcomes. consequently, the low-velocity assumption to model the impact is confirmed also in continuous beam hit by a projectile. references [1] beléndez t., neipp c., beléndez a., 2002. large and small deflections of a cantilever beam. european journal of physics 23, 371. doi: 10.1088/0143-0807/23/3/317. t m. utzeri et alii, frattura ed integrità strutturale, 58 (2021) 254-271; doi: 10.3221/igf-esis.58.19 270 [2] zheng y., shabana a. a., zhang d., 2018. curvature expressions for the large displacement analysis of planar beam motions. journal of computational and nonlinear dynamics 13. doi: 10.1115/1.4037226. [3] abrate, s., 1998. low-velocity impact damage, in: impact on composite structures. cambridge university press, pp. 135–160. doi: 10.1017/cbo9780511574504.005. [4] abrate, s., 2001. modeling of impacts on composite structures. composite structures 51, 129–138. doi: 10.1016/s0263-8223(00)00138-0. [5] abrate, s., 2011. impact engineering of composite structures. springer vienna. doi: 10.1007/978-3-7091-0523-8.  [6] anderson t. j., nayfeh a. h., balachandran b., 1996. experimental verification of the importance of the nonlinear curvature in the response of a cantilever beam. journal of vibration and acoustics 118, 21–27. doi: 10.1115/1.2889630.  [7] awrejcewwicz j., kryosko a. v., soldatov v., 2012. analysis of the nonlinear dynamics of the timoshenko flexible beams using wavelets. journal of computational and nonlinear dynamics 7. doi: 10.1115/1.4004376.  [8] babilio e., lenci s., 2017. on the notion of curvature and its mechanical meaning in a geometrically exact plane beam theory. international journal of mechanical science 128-129, 277–293. doi: 10.1016/j.ijmecsci.2017.03.031.  [9] crespo da silva m. r. m., glynn c. c., 1978. nonlinear flexural-torsional dynamics of inextensional beams ii. forced motions. journal of structural mechanics 6, 449–461. doi: 10.1080/03601217808907349.  [10] eisley j. g., 1964. nonlinear deformation of elastic beams, rings and strings. wear 7, 225–312. doi: 10.1016/00431648(64)90095-x. [11] goel, r.p., 1973. vibrations of a beam carrying a concentrated mass. journal of applied mechanics 40, 821–822. doi: 10.1115/1.3423102.  [12] graff, k., 1991. wave motion in elastic solids. dover publications, new york.   [13] hamdan m. n., dado m. h. f., 1997. large amplitude free vibrations of a uniform cantilever beam carrying an intermediate lumped mass and rotary inertia. journal of sound and vibration 206, 151–168. doi: 10.1006/jsvi.1997.1081.  [14] hinnant h. e., hodges d. h., 1988. nonlinear analysis of a cantilever beam. aiaa journal 26, 1521–1537. doi: 10.2514/3.10072.  [15] leissa, a., sonalla, m., 1991. vibrations of cantilever beams with various initial conditions. journal of sound and vibration 150, 83–99. doi: https://doi.org/10.1016/0022-460x(91)90403-7.  [16] lenci, s., clementi, f., 2019. flexural wave propagation in infinite beams on a unilateral elastic foundation. nonlinear dynamics 99, 721–735. doi: 10.1007/s11071-019-04944-4.  [17] lenci s., clementi f., rega g., 2016. a comprehensive analysis of hardening/softening behavior of shearable planar beams with whatever axial boundary constraint. meccanica 51, 2589–2606. doi: doi.org/10.1007/s11012-016-0614-9.  [18] lenci s., consolini l., clementi f., 2017a. the use of the fitting time histories method to detect the nonlinear behaviour of laminated glass. journal of vibration testing and system dynamics 1, 1–14. doi: 10.5890/jvtsd.2017.03.001.  [19] lenci s., consolini l., clementi f., cocchi g., 2017b. revealing nonlinear dynamical behaviour of laminated glass. procedia engineering 199, 1454–1459. doi: 10.1016/j.proeng.2017.09.394.  [20] navaee s., elling r. e., 1991. large deflections of cantilever beams. transactions of the canadian society for mechanical engineering 15, 91–107. doi: 10.1139/tcsme-1991-0005.  [21] nayfeh a. h., 2000. perturbation methods. john wiley & sons.  [22] schwalbe d., wagon s., 1997. the duffing equation. john wiley & sons.  [23] hamdan m. n.and shabaneh n. h., 1997. on the large amplitude free vibrations of a restrained uniform beam carrying an intermediate lumped mass. journal of sound and vibration 199, 711–736. doi: 10.1006/jsvi.1996.0672.  [24] utzeri, m., bhagavatam, a., mancini, e., dinda, g., sasso, m., newaz, g., 2021a. quasistatic and dynamic behavior of inconel 625 obtained by laser metal deposition: experimental characterization and constitutive modeling. journal of engineering materials and technology 143. doi: 10.1115/1.4051087.  [25] utzeri, m., farotti, e., coccia, m., mancini, e., sasso, m., 2021b. high strain rate compression behaviour of 3d printed carbon-pa. journal of materials research doi: 10.1557/s43578-021-00248-9.  [26] utzeri, m., sasso, m., chiappini, g., lenci, s., 2020. nonlinear vibrations of a composite beam in large displacements: analytical, numerical, and experimental approaches. journal of computational and nonlinear dynamics 16. doi: 10.1115/1.4048913.  [27] wagner h., 1964. large-amplitude free vibrations of a beam. journal of applied mechanics 32, 887–892. doi: 10.1115/1.3627331.  m. utzeri et alii, frattura ed integrità strutturale, 58 (2021) 254-271; doi: 10.3221/igf-esis.58.19 271 [28] warminski, j., kloda, l., lenci, s., 2020. nonlinear vibrations of an extensional beam with tip mass in slewing motion. meccanica 55, 2311–2335. doi: 10.1007/s11012-020-01236-9.  [29] zavodney l. d., nayfeh a. h., 1989. the non-linear response of a slender beam carrying a lumped mass to a principal parametric excitation: theory and experiment. international journal of non-linear mechanics 24, 105–125. doi: 10.1016/0020-7462(89)90003-6.    microsoft word numero_33_art_24 j.m. vasco-olmo et alii, frattura ed integrità strutturale, 33 (2015) 191-198; doi: 10.3221/igf-esis.33.24 191 focussed on characterization of crack tip fields experimental evaluation of plasticity-induced crack shielding from crack tip displacements fields j.m. vasco-olmo, f.a. díaz university of jaén, departamento de ingeniería mecánica y minera, campus las lagunillas, edificio a3, 23071, jaén, spain jvasco@ujaen.es, fdiaz@ujaen.es abstract. in this work it is proposed a methodology for the evaluation of plasticity-induced crack shielding from the analysis of the crack tip displacements fields measured by digital image correlation. this methodology is based on the evaluation of the stress intensity factors determined from the displacements fields measured at the vicinity of the tip of a growing fatigue crack. for the characterisation of the crack tip displacements field, cjp model has been implemented. this model considers the shielding effects due to plasticity generated during fatigue crack growth. for the purpose of the current work, several fatigue experiments at different r-ratios have been conducted on al2024-t3 compact tension specimens. in addition, compliance based methods have been adopted to perform a comparison of the results with those obtained by dic. results show a good level of agreement, illustrating the enormous potential of dic technique for the study of fracture mechanics problems. keywords. plasticity-induced crack shielding; fatigue; stress intensity factor; digital image correlation. introduction atigue crack growth generates a plastic zone at the crack tip and along the crack flanks, which may induce plasticity-induced crack closure [1]. this phenomenon is one of the crack tip shielding mechanisms that reduces the stress intensity factor range originated at the crack tip. however, there are still some issues that remain unresolved or misunderstood regarding crack closure, which are mainly associated with problems in its measurement and interpretation [2]. recently, the use of digital image correlation (dic) has become very popular for the analysis of structural integrity problems. thus, different methodologies based on the calculation of stress intensity factors (sifs) from the displacement fields measured around a tip of growing cracks have been developed [3 – 6]. in particular, the method developed by james et al. (cjp model) [6] which takes into account the effect of plasticity generated around the crack tip during fatigue growth. thus, it considers an analysis of the shielding effect over the surrounding elastic field. in the current work, it has been performed an experimental evaluation of plasticity-induced crack shielding from the displacements fields measured at the vicinity of the crack tip using dic. thus, cjp model [6] has been implemented for the characterisation of the crack tip displacements fields. moreover, for the purpose of this work, fatigue tests at different r-ratios on al2014-t3 ct (compact-tension) specimens have been conducted. results have been compared with those obtained using the strain offset calculation, showing a good level of agreement which highlights the potential of dic to evaluate the shielding effect during fatigue crack growth. f j.m. vasco-olmo et alii, frattura ed integrità strutturale, 33 (2015) 191-198; doi: 10.3221/igf-esis.33.24 192 fundamentals of the model for characterising crack tip displacements fields jp model is a novel mathematical methodology developed by christopher, james and patterson [6] based on muskhelishvili’s complex potentials [7] which considers that the plastic enclave that exists around a fatigue crack tip and along the crack flanks will shield the crack from the full influence of the applied elastic stress fields. crack tip shielding includes the effect of crack flank contact forces and a compatibility-induced interfacial shear stress at the elastic-plastic boundary. fig. 1 illustrates schematically the forces acting at the interface of the plastic zone and the surrounding elastic field material. fax and fay are the reaction forces to the applied remote load. this load generates the t-stress and the corresponding force ft. the above forces cause a plastic zone at the crack tip, deforming permanently the material and inducing the forces fpx and fpy during unloading. fs is the induced force by the interfacial shear at the elastic-plastic boundary of the crack wake. fc is the force generated when the plastic wakes contact during unloading, so the crack closes under the action of the elastic field. figure 1: schematic idealisation of the forces acting at the elastic-plastic boundary [6]. according to this model, the crack tip displacements field can be described as follows:       1 1 1 2 2 2 1 1 2 2 1 1 1 2 2 2 2 2 2 4 2 ln 4 2 ln 4 ` ln 2 4 c f g u iv b e z z ez z z c f z b e z ez z c f az dz z dz z                              (1) where  2 1 y g    is the shear modulus, y and ν are the young’s modulus and the poisson’s ratio of the material respectively, 3 1       for plane stress or 3 4   for plane strain, z is the complex coordinate and a, b, c, d, e and f are unknown coefficients. thus, this new model employs four parameters to characterise the stress and displacement fields around the crack tip generated by the forces as indicated in fig. 1. where kf is an opening mode stress intensity factor, kr a retardation stress intensity factor, ks shear stress intensity factor and t the t-stress. kf is characterised by the driving crack growth force fa generated by the remote load: c j.m. vasco-olmo et alii, frattura ed integrità strutturale, 33 (2015) 191-198; doi: 10.3221/igf-esis.33.24 193  3 8 2 fk a b e     (2) kr is characterised by fc and fp that induce a shielding effect on the crack tip and therefore a retardation effect of fatigue crack growth:   3 2 3 2 rk d e    (3) ks is characterised by fs that acts in the interfacial boundary between the generated plastic zone and the surrounding elastic field:   2 sk a b    (4) finally, the t-stress is characterised by ft generated by the remote load: ;x yt c t f    (5) experimental procedure he main objective of the current work is the experimental evaluation of the retardation effect on fatigue crack growth. for this purpose, two fatigue tests at different r-ratios on ct al2024-t3 specimens (fig. 2a) were conducted. the first test was conducted at low r-ratio (r = 0), while the second one was at high r-ratio (r = 0.5). thus, a loading cycle between 5 and 600 n was used for the first test, and between 600 and 1200 n for the second one. both tests were conducted at a cycling frequency of 10 hz employing a 100 kn mts 370.10 servohydraulic machine (fig. 2b). figure 2: ct specimen (a) and experimental set-up (b) used for fatigue testing. as it was indicated above, the retardation effect was evaluated from the analysis of the sifs calculated from the displacements field measured around the crack tip using 2d-dic. thus, for the implementation of the technique a sequence of images was captured with a monochromatic ccd camera (allied vision technologies, model stingray f504b/c) placed perpendicularly to the specimen surface with a 75 mm lens controlled by an e6510 intelcore i5 delllatitude laptop with the aid of a fwb-ec3402 video. in addition, the specimen surface was prepared to obtain a random speckle pattern by spraying it with black paint over a previously painted white background. in addition, an extra camera (allied vision technologies, model pike f-032b/c) was located at the back of the specimen to track the crack tip and monitor the crack growth during fatigue experiments. moreover, results from dic were compared with those obtained from the implementation of strain offset technique. thus, the opening and closing loads were estimated from the analysis of crack opening displacement (cod) data collected from an mts 632.03f-30 extensometer with a data sampling of 5 hz. t (b)(a) j.m. vasco-olmo et alii, frattura ed integrità strutturale, 33 (2015) 191-198; doi: 10.3221/igf-esis.33.24 194 experimental methodology for sif calculation n this work, the evaluation of plasticity-induced crack shielding was made from the analysis of the sifs calculated from the displacements fields measured around the crack tip. hence, the development of an experimental methodology to calculate sifs was essential. the first step in the methodology was capturing a sequence of images during fatigue experiments from a reference state (undeformed) until a deformed state at different loading steps. after capturing the sequence of images and before its processing, the areas corresponding to the notch and the grips were masked since these areas did not add any relevant information. the next was the image processing, for this task the commercial software package vic-2d [8] was employed. as an example, fig. 3 shows the displacements fields measured for a 34.10 mm crack at a load of 600 n. figure 3: horizontal (a) and vertical (b) displacement fields measured for a 34.10 mm and a load level of 600 n. according to eq. 1, the relationship between the displacements and the unknown coefficients is linear. therefore sifs can be obtained solving a system of linear equations. thus, an error function was defined to relate the experimental data (displacement fields) with a mathematical expression according to the model. it is important to indicate that rigid body motion was considered in the formulation (horizontal and vertical translation, and rotation), otherwise the adopted dic algorithm would consider it as a virtual displacement induced by the applied load. finally, experimental sifs have been compared with those nominal values predicted by astm e647-99 [10] according to the following expression: 3 2 2 3 42 0.886 4.64 13.32 14.72 5.6 1 nom a p a a a awk w w w wt w a w                                  (6) where δp is the loading range, t and w are the thickness and the width of the specimen, respectively, and a is the crack length. experimental results and discussion n this section, experimental results obtained from the analysis of the displacement fields measured on the specimens tested are presented and discussed. fig. 4 shows the experimental kf and kr values along the loading cycle for a specimen tested at low r-ratio at a crack length of 34.10 mm. in addition, nominal ki values according to eq. 6 have been also presented. from the analysis of kf, it is observed that from a load level of 150 n, the experimental values agree with the nominal values. however, below the load level above indicated kf values are higher than ki values. it is observed a gradual change in the trend followed by kf values as the load decreases. this behaviour is similar to that reported by elber when defining plasticity-induced crack closure phenomenon. he noticed an anomaly in the elastic compliance of several fatigue specimens. thus, he argued that this change in compliance was due to the contact between crack surfaces at low load levels higher than zero. according to this, opening (kop) and closing (kcl) stress intensity factors can be estimated from kf trend as that value corresponding to x (pixels) y ( p ix el s) mm 50 100 150 200 250 300 50 100 150 200 250 -0.03 -0.02 -0.01 0 0.01 0.02 x (pixels) y ( p ix el s) mm 50 100 150 200 250 300 50 100 150 200 250 -0.2 -0.15 -0.1 -0.05 0 0.05 0.1 i i  (a) (b) j.m. vasco-olmo et alii, frattura ed integrità strutturale, 33 (2015) 191-198; doi: 10.3221/igf-esis.33.24 195 the minimum applied load (red line in fig. 4) for the loading and unloading branch respectively. moreover, from the analysis of kr, a sign change is observed as the load reaches 100 n. thus, below this load kr takes positive values, while above this load kr changes its sign. therefore, it can be established that kr values divide the loading cycle in two portions, thus the first portion corresponds to the loading interval at which the crack is closed, while the second portion corresponds to the interval at which the crack is open. according to this, there is a correspondence between the change in the kf trend and the sign change in kr. figure 4: sifs obtained for the specimen tested at low r-ratio corresponding to a crack length of 34.10 mm the adopted methodology can be extrapolated to estimate kop and kcl as a function of the crack length. in fig. 5, estimated kop and kcl values at the different analysed crack lengths for the specimen tested at low r-ratio have been plotted. it can be observed a gradual increase of kop and kcl values along the crack length. these are above kmin and hence, it highlights that the crack opens or closes at a load higher than the minimum applied load. in addition, it can be observed that there are not big differences between kop and kcl values. moreover, crack opening (pop) and closing (pcl) loads can be calculated from kop and kcl values previously estimated using eq. 6. thus, results have been plotted in fig. 6 together with the minimum and maximum loads of the applied loading range. it is observed that as the crack grows pop and pcl values are within a load range (75 n ≤ pop, pcl ≤ 125 n) which corresponds to a percentage of 12.5 and 21 % of the maximum applied load. nevertheless, some scatter is observed which can be attributed to the fact that crack opens or closes in a gradual way, and consequently, it is difficult to establish a single value for pop or pcl. thus, there is an interval at which crack changes from fully closed to fully open. once dic results have been analysed, results from the strain offset calculation are exposed and discussed. the signal collected from the extensometer was divided into two data sets corresponding to the loading and unloading branches of the applied load. in addition, the cod signal was filtered to minimise the influence of noise. for the implementation on the method, the two branches are represented on a load versus cod plot, and a least-squares straight line is fit to experimental data at the part of the loading cycle at which the crack is fully open. for this purpose, a segment that spanned a range of approximately 25 % of the loading cycle range is selected to represent a fully open crack configuration. then, a linear fit corresponding to the load range to fully open crack is employed to calculate the theoretical cod for a particular load value. the difference between theoretical and experimental cod values is calculated to obtain the strain offset. finally, the strain offset is presented as a function of the applied load, and pop from the loading branch and pcl from the unloading one are obtained as the load value at which the strain offset reaches the zero value. fig. 7 shows the results obtained from strain offset method for a 35.47 mm crack corresponding to the specimen tested at low r-ratio. plots located on the left correspond to results for the loading branch, while those located on the right correspond to the unloading branch. top plots show the applied load versus the measured cod for loading (left) and unloading (right) branches. in both plots, it can be observed raw data, filtered data and a fitted line corresponding to no closure. this line has been obtained considering data results above 150 n (corresponding to a 25 % of the load range) and performing a least squares fitting. j.m. vasco-olmo et alii, frattura ed integrità strutturale, 33 (2015) 191-198; doi: 10.3221/igf-esis.33.24 196 figure 5: estimated kop and kcl values as a function of the crack length for the specimen tested at low r-ratio. figure 6: pop and pcl at different crack lengths for the specimen tested at low r-ratio. from top plots, it can be observed a change in the slope of experimental data for load values between 100 and 110 n, which indicates that crack starts opening. however, from bottom plots, it is observed that for load values higher than 100 n (for loading branch) and 115 n (for unloading branch) the strain offset is almost 0, which indicates that the crack is completely open. according to this, pop and pcl values can be estimated for all the analysed crack lengths (fig. 8). in fig. 8 it can be observed that pop and pcl values are between 75 n and 125 n, with no apparent differences between pop and pcl values. therefore, these results show great level of agreement with those obtained from cjp model, so the experimental methodology proposed to estimate pop and pcl values from kf trend can be considered as validated. figure 7: results obtained from strain offset method for a crack length of 35.47 mm corresponding to the specimen tested at low rratio. a) applied load versus cod for loading branch, b) applied load versus cod for unloading branch, c) applied load versus strain offset for loading branch and d) applied load versus strain offset for unloading branch. in a similar way, results from the specimen tested at high r-ratio have been also analysed. kf and kr values obtained as a function of the loading cycle at crack lengths of 34.64 and 41.09 mm are shown in fig. 9. it is observed that kf values show total level of agreement throughout the whole loading cycle with those calculated from eq. 6. therefore, there is no change in the slope of kf as in the case of the specimen tested at low r-ratio, which indicates the absence of the shielding effect and consequently, the crack remains fully open during the loading cycle. in addition, this behaviour is also observed loading branch unloading branch -0.05 0 0.05 0.1 0.15 0.2 0.25 0.3 0 100 200 300 400 500 600 cod (mm) lo a d ( n ) raw data smoothed data no closure (a) -0.05 0 0.05 0.1 0.15 0.2 0.25 0.3 0 100 200 300 400 500 600 cod (mm) lo a d ( n ) raw data smoothed data no closure (b) -0.02 -0.015 -0.01 -0.005 0 0.005 0.01 0.015 0.02 0 100 200 300 400 500 600 strain offset lo a d ( n ) smoothed data (c) -0.02 -0.015 -0.01 -0.005 0 0.005 0.01 0.015 0.02 0 100 200 300 400 500 600 strain offset lo a d ( n ) smoothed data (d) a) b) c) d) j.m. vasco-olmo et alii, frattura ed integrità strutturale, 33 (2015) 191-198; doi: 10.3221/igf-esis.33.24 197 from the analysis of kr, where there is no change in its sign during the loading cycle, which is interpreted as no variation in crack configuration and therefore, the crack keeps fully open throughout loading cycle. figure 8: pop and pcl values obtained at different crack lengths for the specimen tested at low r-ratio using the strain offset method. figure 9: experimental kf and kr corresponding to the specimen tested at high r-ratio for two different crack lengths (34.64 and 41.09 mm). conclusions igital image correlation has been employed to evaluate plasticity-induced crack shielding from the analysis of the stress intensity factors defined in cjp model and calculated from the measured crack tip displacement fields on al-2024 ct specimens. an experimental methodology to estimate pop and pcl values has been proposed, being based on the analysis of kf trends for the loading and unloading branches respectively. shielding effect during fatigue crack growth has been observed in the specimen tested at low r-ratio. however, this phenomenon has not been observed for the specimen tested at high r-ratio. results from dic have been compared with those obtained from a compliance based method, showing a good level of agreement and illustrating the potential that both dic technique and cjp model present to evaluate the plasticity-induced crack shielding effect and consequently, fracture mechanics problems. references [1] elber, w., fatigue crack closure under cyclic tension, eng. fract. mech., 2, 1 (1970) 37-45. [2] james, m.n., some unresolved issues with fatigue crack closure measurement, mechanisms and interpretation problems, advance in fracture research, proceedings of the ninth international conference on fracture. edited by b.l. karihaloo et al., pergamon press, 5 (1996) 2403-14. [3] ewalds, h.l., wanhill, r.j.h., fracture mechanics, edward arnold, london, uk (1991). [4] yates, j.r., zanganeh, m., tai, y.h., quantifying crack tip displacement fields with dic, eng. fract. mech., 77 (2010) 2063-76. [5] lópez-crespo, p., sheterenlikht, a., patterson, e.a., withers, p.j., yates, j.r., the stress intensity factors of mixed mode cracks determined by digital image correlation, j. strain anal. eng. design, 43 (2008) 769-80. [6] james, m.n., christopher, c.j., lu, y., patterson, e.a., local crack plasticity and its influences on the global elastic stress field, int. j. fatigue, 46 (2013) 4-15. [7] muskhelishvili, n.i., some basic problems of the mathematical theory of elasticity, noordhoff international publishing, groningen, netherlands (1977). [8] http://www.correlatedsolutions.com/vic-2d/ [9] sanford, r.j., dally, j.w., a general method for determining the mixed-mode stress intensity factors from isochromatic fringe pattern, eng. fract. mech., 11 (1979) 621-33. [10] e647-99, standard test method for measurement of fatigue crack growth rates. philadelphia: american society for testing and materials (1999). d j.m. vasco-olmo et alii, frattura ed integrità strutturale, 33 (2015) 191-198; doi: 10.3221/igf-esis.33.24 198 [11] elber, w., fatigue crack closure under cyclic tension, eng. fract. mech., 2, 1 (1970) 37-45. [12] skorupa, m., beretta, s., carboni, m., machniewicz, t., an algorithm for evaluating fatigue crack closure from compliance measurements, fatigue fract. eng. mater. struct., 25 (2002) 261-73. microsoft word numero 25 art 3 a.s. chernyatin et alii, frattura ed integrità strutturale, 25 (2013) 15-19; doi: 10.3221/igf-esis.25.03 15 special issue: characterization of crack tip stress field combining experimental and numerical analysis to estimate stress fields along the surface crack front a.s. chernyatin, yu.g. matvienko, i.a. razumovsky mechanical engineering research institute of the russian academy of sciences, moscow, russia abstract. combining experimental and computational method for determination of the singular and the nonsingular stress terms along the front of the 3d surface crack is proposed. evaluation of the terms is based on comprehensive comparison between deformation responses (for measurement points on the surface) obtained experimentally and from numerical solutions of the corresponding boundary problem of solid mechanics. the proposed approach allows carrying out an adequate and a comprehensive assessment of stress fields in the vicinity of the surface crack front. keywords. 3d surface crack; stress intensity factors; t-stresses; fem; minimization problem; numerical experiment. introduction ne of the main trends in the development of methods for assessing of strength and lifetime of damaged structures, working under extreme loading conditions, is the application of fracture mechanics and, in particular, the methods for an analysis of the crack initiation process in the engineering structure. in this case, it is very important to estimate the singular and the non-singular stress terms in the williams series solution along the crack front. it should be noted that these stress terms are dependent on crack and body configurations as well as loading conditions (e.g., [1, 2]). at the same time, operational loading conditions of engineering components can strongly differ from design conditions due to crackor notch-like defects, assembly and residual stress, etc. to solve this problem, combining experimental and computational method can be employed for estimating operational loading conditions, the singular and the non-singular stress terms along the 3d surface crack front. the present paper deals with the approach which is based on comprehensive comparison between deformation responses (for measurement points on the surface of the engineering components) obtained experimentally and from numerical solutions of the corresponding boundary problem of solid mechanics. as a result, loading conditions, distribution of the singular (ki, kii) and the non-singular (txx, tzz) terms along the surface crack front can be estimated. statement of the problem he object of research and numerical simulation (by means of fem) is an elastic half-space with a semi-elliptical crack (length 2a, depth b) orthogonal to the surface. homogeneous tensile stresses σx, σy are applied in two orthogonal directions. displacement fields on the surface for certain specimen configuration can be measured by electronic speckle interferometry (esi) or computed by numerical experiment. it is necessary to estimate the stress intensity factor and the t-stress terms along the crack front by means of an analysis of these displacement fields. the problem can be solved by two steps. firstly, the parameters b, σx, σy should be estimated by the following procedure [3]:  generation of the experimental data (ei*) for the displacement fields; o t http://www.gruppofrattura.it http://dx.medra.org/10.3221/igf-esis.25.03&auth=true a.s. chernyatin et alii, frattura ed integrità strutturale, 25 (2013) 15-19; doi: 10.3221/igf-esis.25.03 16  creation so-called “response bank” which is mathematical analog of the fe model of the half-space with the surface crack. it allows calculating the values of the displacements in measurement points (ei) corresponding to ei* in case arbitrary values of the searching parameters (b, σx, σy);  solution of a minimization problem. variation of the searching parameters is carrying out for achievement of the minimum of objective function which describes a discrepancy between ei* and ei;  assessment of ei*-scatter effect on determination accuracy of the searching parameters at different conditions of experimental measurements and minimization problem solution. the second step is connected with calculation of stress fields in the vicinity of the crack front at the parameters b, σx, σy which are defined by the first step. as results, distribution of the singular (ki, kii) and the non-singular (txx, tzz) terms along the crack front are calculated. numerical simulation he proposed method is realized in the case of a numerical experiment. generation of the original data for the displacement fields is performed by numerical simulation of the probe hole in the vicinity of the surface crack. the finite element model of the elastic half-space under biaxial loading (fig. 1a) is built in ansys software environment in the form of a prismatic body of finite dimensions, including the surface crack and volume of the probe hole (fig. 1b). it should be noted that standard ansys procedure does not allow building a crack in this area, because its front is located over several volumes. therefore, special multipurpose macros are created to build the planar crack with arbitrarily 3d-orientation and front geometry along which grid of singular elements is constructed in finite element model. loading conditions are the following: σx = 100 mpa, σy = 200 mpa. the following sizes are also used in numerical simulation: the length of semi-elliptical crack 2a =20 mm and the depth b =(2/3)a = 6.67 mm, the diameter and depth of the probe hole d = t = 2 mm. figure 1: the elastic half-space with a semi-elliptical crack and a probe hole (a) and finite element model of the output crack on the surface (b). (a) (b) (c) figure 2: the displacement field u, v, w (a, b, c, respectively) due to the to the formation of the hole in the vicinity of the surface crack tip. t http://www.gruppofrattura.it http://dx.medra.org/10.3221/igf-esis.25.03&auth=true a.s. chernyatin et alii, frattura ed integrità strutturale, 25 (2013) 15-19; doi: 10.3221/igf-esis.25.03 17 the computed fields of tangential (u, v) and normal (w) displacement (fig. 2), analogues of which in practice can be measured using the esi, are obtained from the solution of the direct problem including calculation of stress and strain states due to the formation of the hole in the vicinity of the surface crack tip (fig. 1a). further, the displacement fields u, v, w are used as the original experimental data to compute the strain response ei* at corresponding points of the body under external load. the resulting array ei* is employed for the calculation of parameters pj = {b, σx, σy} by minimization of the objective function i(ei*,ei) comparing experimental and numerical data. the details of the above-mentioned procedure are given in ref. [3]. accuracy of the results he objective function i(ei*,ei) reached the minimum magnitude at the following condition pj = pj *. the objective function i is taken as root-mean square norm (irms) or maximum norm (imax) reflecting the divergence between calculated ei and experimental ei* data. the procedure of searching the minimum of the objective function is based on simplex method for function minimization [4] which is widely used in practice. to analyze the stability of the solution and to assess the sensitivity of the procedure to the error of the experimental data, series of numerical experiments were carried out to determine the parameters pj under various conditions of experimental measurements and solution of the minimization problem. variation of the experimental error (δe), the number of measurement points (n), and the area of their location (described by normalized radius vector r / ρ , where ρ is radius of the hole) is used to estimate the accuracy of the obtained results. some numerical results for the expectation and variation of the normalized parameters * * * x x x y y yb b / b , / , /        are summarized in tab. 1. it can be seen that the proposed method gives very high accuracy. conditions expectation variation № r / ρ n δ, % i b x y b x y 1 [2; 3] [2; 3] 55 55 55 55 10 10 10 10 irms 1.013 0.998 0.988 0.081 0.036 0.049 2 imax 1.010 0.996 0.988 0.109 0.061 0.067 3 [1; 2] [1; 2] irms 1.049 0.994 0.982 0.216 0.091 0.116 4 imax 1.075 0.989 0.975 0.262 0.093 0.128 5 [2; 3] [2; 3] [2; 3] [2; 3] 110 110 110 10 irms 1.003 0.992 0.992 0.051 0.023 0.030 6 20 20 irms 1.030 0.970 0.959 0.124 0.055 0.071 7 imax 1.054 0.093 0.932 0.097 0.040 0.055 8 60 20 irms 0.996 0.978 0.078 0.081 0.048 0.054 table 1: the influence of the experimental error on the values of the unknown parameters (numerical example). calculation of the stress intensity factors and the t-stresses he final step of a comprehensive analysis is estimation of the distribution of the singular (ki, kii) and the nonsingular (txx, tzz) terms along the crack front on a basis of the calculated parameters b, σx, σy. the first and the second terms in a series expansion of the three-dimensional elastic stress components can be presented as follows [5]: xx i ii xx 1 3 3 k cos 1 sin sin k sin 2 cos cos t 2 2 2 2 2 22 r                          yy i ii 1 3 3 k cos 1 sin sin k sin cos cos 2 2 2 2 2 22 r                        (1) xy i ii 1 3 3 k sin cos cos k cos 1 sin sin 2 2 2 2 2 22 r                        t t http://www.gruppofrattura.it http://dx.medra.org/10.3221/igf-esis.25.03&auth=true a.s. chernyatin et alii, frattura ed integrità strutturale, 25 (2013) 15-19; doi: 10.3221/igf-esis.25.03 18 zz i ii zz zz zz xx 2 k cos k sin t 2 22 r t e t                here, k is the elastic stress intensity factor, r and  are the polar coordinates in plane x0y, zz is the strain in the zdirection, e and ν are the young modulus and poisson’s ratio, respectively. the terms xxt and zzt are the amplitudes of the second order terms in the three-dimensional series expansion of the crack-front stress field in the xand z-directions, respectively. the stress intensity factor is calculated in a number of points (at variable values of r a / 20 ) using the following equation  i xx 0 xx xx r k 2 | | | 2              (2a)  ii xx xx r k | | 8          (2b) the obtained values of the stress intensity factor are extrapolated to the point r=0. to evaluate the distribution of the stress intensity factors along the crack front, this procedure is used for a number of orthogonal to the front of the crack plane (x0y). their location is characterized by local coordinate s along the front which starts from the center of the crack front and finishes at the point located on the body surface. the magnitude of the t-stress terms is defined through stress components for the points on the crack surface as follows xx xx xx 1 t 2             (3a) zz zz zz 1 t 2             (3b) the determination of the non-singular txxand tzz-stress is similar to the calculation procedure for the stress intensity factor including extrapolation to the point r=0. the distribution of the singular (ki, kii) and the non-singular (txx, tzz) terms along the crack front (in the absence of the probe hole) is shown in fig. 3. the stress intensity factor kii is negligible as it is expected for the surface crack and loading conditions under consideration. it can be also seen that the non-singular terms are significantly changed along the surface crack front. in contrast to the txx-stress, the tzz-stress approaches the maximum value at the center of the crack front. conclusions t was shown that combining experimental and computational method can be employed for estimating operational loading conditions, the singular and the non-singular stress terms in a series expansion of the three-dimensional elastic stress components along the surface crack front. the proposed method is based on comprehensive comparison between deformation responses (for measurement points on the surface of the engineering components) obtained experimentally and from numerical solution of the corresponding boundary problem of solid mechanics. the distribution of the singular (ki, kii) and the non-singular (txx, tzz) terms along the surface crack front is computed. acknowledgement he authors acknowledge the support of the russian foundation of basic research (grant n 12-08-91158nsfc_а). i t http://www.gruppofrattura.it http://dx.medra.org/10.3221/igf-esis.25.03&auth=true a.s. chernyatin et alii, frattura ed integrità strutturale, 25 (2013) 15-19; doi: 10.3221/igf-esis.25.03 19 figure 3: the distribution of the stress intensity factors (a) and the non-singular stresses (b) along the crack front. references [1] gonzalez-albuixech, v.f., giner, e., fernandez-saez, j., fernandez-canteli, a. influence of the t33-stress on the 3-d stress state around corner cracks in an elastic plate, engng. fract. mech., 78 (2011) 412-427. [2] matvienko, yu.g., shlyannikov, v.n., boychenko, n.v. in-plane and out-of-plane constraint parameters along a three-dimensional crack-front stress field under creep loading, fatigue fract. engng. mater. struct., 36 (2013) 1424. [3] razumovsky, i.a., chernyatin, a.s. experimental numerical method to estimate loading conditions for structures with surface cracks, journal of machinery and reliability, 3 (2009) 247-254. [4] nelder, j.a., mead, r. a simplex method for function minimization. computer journal, 7 (1965) 308–313. [5] nakamura, t., parks, d. m. determination of elastic t-stress along three-dimensional crack fronts using an interaction integral, int. j. solids struct., 29 (1992) 1597–1611. http://www.gruppofrattura.it http://dx.medra.org/10.3221/igf-esis.25.03&auth=true microsoft word numero_49_art_27_2481 o. naimark, frattura ed integrità strutturale, 49 (2019) 272-281; doi: 10.3221/igf-esis.49.27 272 focused on russian mechanics contributions for structural integrity duality of singularities of multiscale damage localization and crack advance: length variety in theory of critical distances oleg naimark institute of continuous media mechanics ub ras, russia naimark@icmm.ru abstract. the existence of two singularities related to the stress field at the crack tip and blow-up kinetics of damage localization is considered as the physical basis for the interpretation of the theory of critical distances. the free energy metastability of solid with defects and corresponding free energy release explain the conception of the finite fracture mechanics in the presence of the finite amplitude energy barrier. the variety of crack paths is analyzed as duality of inherently linked two types of singularities related to the singularity of multiscale damage kinetics under crack nucleation and singularity of stress field at the crack tip as the classical framework of fracture mechanics. the singularity of multiscale damage kinetics is a natural precursor of crack nucleation that could provide in some cases the totally independent scenario of fracture from the stress singularity at the crack tips. the influence of two singularities with the nature of intermediate asymptotical solutions for stress at the crack tip and damage localization kinetics over the set of spatial scales represents two attractors, which provides the variety of crack paths for corresponding loading conditions. keywords. singularity duality; critical distance theory. citation: naimark, o., duality of singularities of multiscale damage localization and crack advance: length variety in theory of critical distances, 49 (2019) 272-281. received: 12.04.2019 accepted: 29.05.2019 published: 01.07.2019 copyright: © 2019 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. introduction onlinear aspects of multiscale damage evolution in the presence of stress concentration, cracks and notches are the subject of intensive experimental and theoretical studies in the problem of damage-failure transition for quasi-static, fatigue and dynamic statements, which generally are inherently linked. the phenomenological statements of this problem was formulated by the theory of critical distances (tcd), which combines the approaches based on conventional material toughness and material strength parameters for the definition of material characteristic lengths [1]. however, there is a permanent question concerning physical basis for the tcd and the definition of characteristic lengths. the material length scales are the key parameters of physically based theories of fracture. these lengths correlate with microstructure scales (grain or inclusion sizes, spacing) and responsible for the susceptibility of material to multiscale damage accumulation [2]. n http://www.gruppofrattura.it/va/49/2481.mp4 o. naimark, frattura ed integrità strutturale, 49 (2019) 272-281; doi: 10.3221/igf-esis.49.27 273 the tcd had independent inventions in different forms for the prediction of quasi-brittle fracture [3, 4]. the theory of critical distances operates with the phenomenological estimation of the process zone l arising from the continuum mechanics models. commonly used length scale l in the tcd is given by 2 0 1 ckl          , (1) where ck is the fracture toughness of the material, and 0 is material tensile strength. in fatigue problems the same equation has used, replacing these material constants with the relevant cyclic ones: the crack propagation threshold thk and fatigue limit 0 . estimated by (1) the values of l for fracture and fatigue of brittle and ductile materials (silicon carbide and alumina [5], steel [6, 7], fiber composite laminate [4]) separate the “damage induced” and “crack induced” fracture scenario: for small cracks the experimental data deviate from the linear fracture mechanics (lfm) line towards tensile strength 0 . scale of l occurs in the middle of transient region for “fracture stress” versus “defect size” curve [1].the value of l determines structure-induced damage and fracture processes and are related to a microstructural parameter, for example, the grain size for ceramic materials. for metal fatigue l is associated with the length of nonpropagating cracks [8]. critical distance approach is generalization of the griffith energy balance theory assuming a finite amount of crack extension, that is so-called as the finite fracture mechanics (ffm) [9,10]. this ffm can be formulated in the form: 2 2 2 0 2 l ck da k l  . (2) three-point bending analysis showed the deviation both lfm and ffm for “normalized strength” 0   versus “normalized beam height” 2h l at the vicinity of l : the lm and ffm tend to opposite extremes as the beam height approaches l . however, a combined approach, in which both lfm and ffm criteria apply, show realistic results supporting numerous structural observations revealing the variety of length l . using this approach it was the prediction of the size effect in notched and un-notched beams [10] and the fracture criterion was proposed with application to laminate cracking analysis [11,12]. comparing experimental data on fracture strength as a function of crack length revealed the similarity in form for both monotonic fracture in brittle materials such as ceramics, and for fatigue limit behavior in metals. it is the cases, when linear fracture mechanics breaks down at short-cracks scale, that are significant in predicting the material responses to small defects such as manufacturing flaws, and in estimating the number of cycles needed for small fatigue cracks to grow. the anomalous short-crack behavior highlights more general problem of size effects or scaling effects. the tcd is useful for the applications, when the size of the sample is approaching to l [1, 9, 10]. it is important observation that the effect of notch-root radius has also interpretation in tcd phenomenology to introduce a critical root radius for crack-like behavior. this characterization of notch effects is based on the tcd phenomenology and has important applications for more complex effects related to multiaxial loading and finite life predictions [2, 8]. the interpretation of variation in specimen strength when the size of the entire specimen is changed (saving the shape) is another complex problem addressing to tcd with applications to high cycle fatigue and the fracture of quasi-brittle materials necessitating a modified form of the approach in which l becomes a variable quantity [13,14]. the power of tcd approach in predicting a wide range of phenomena in different materials, and capability of engineering applications stimulate the question – why does this theory work and what is the ranges [1]? theoretical basis of the tcd is the finite fracture mechanics (ffm) formulation that is combined the criticality features related to two stress-based factors: strength and fracture toughness [9]. understanding of the scientific basis of the tcd includes the study of the nature of cohesive (process) zone, applications of local and non-local approaches. there is the question concerning the range of validity of the tcd since ffm formulation shares common features of singularities with lfm. it means, that the underlying scaling phenomena are related to the smallscale yielding criterion. the smallscale yielding criterion, for instance, for the notch-root plastic zone assumes a small fraction of specimen dimensions providing crack instability. the structural and mechanical basis of fmm and the “critical distances” conception is the existence of characteristic length providing the discontinuous and branching scenario of crack growth on the distances determined by o. naimark, frattura ed integrità strutturale, 49 (2019) 272-281; doi: 10.3221/igf-esis.49.27 274 the microstructure and deformation behavior of the material. the tcd provides two new material parameters: the distance l and the stress ratio 0 u  , where u is the tensile stress, u is, the so-called, characteristic strength of materials. these parameters are recognized as potential characteristics of a material’s brittleness, notch sensitivity and susceptibility to size effects. the tcd is recognized as the approach providing a bridge between continuum-mechanics and micromechanical models, stress-based methods and stress-intensity methods, fatigue failure and brittle fracture with application to different classes of materials. some results in crack mechanics and failure he subject of variety of crack paths is one whose roots go back to the classical work of griffith [15]. with a goal to study the crack path problem and the interaction of the main crack with the defect ensemble in the process zone we will consider briefly the classical results in the crack mechanics, where much analytical progress has been made in assuming that the medium behaves according to the equations of linear elasticity. according to the griffith theory the additional characteristics of the crack resistance were introduced in the form of the energy of the development of the new surface at the crack tip. the energy u of elastic materials with a crack is represented in the form (fig.1, curve 1) 2 2 2 2 4 a u a e            , (3) where  is the surface energy;  is the applied stress; a is the crack length; e is the elastic modulus. figure 1: the griffith (1) and fraenkel (2) energy form of elastic solid with a crack. irwin [16] developed the griffith conception and proposed the force version of the crack stability (the stress intensity factor) related to the intermediate self-similar singular solution for the stress field at the crack tip area 1 2 ( )ik i ijk r f    ik a  , (4) where ik is the stress intensity factor, ,r  are the coordinates of point, ( )ijf  is the  dependence in the first term of asymptotical solution. two classical treatments are based on the griffith criterion and stress-intensity factor criterion and reflect the physical contradiction related to incorrectly prediction of an infinite load at failure due to the global instability (singularity) of stress field at the crack tip. barenblatt [17] proposed a variant of the force version of the crack stability that reflects another view on the role of stress in the crack tip area. it was assumed the existence of the cohesion forces ( )bg s at the process (cohesive) area with the size d  0 s d  . the self-similarity of the crack tip evolution are the consequence of the small ratio of the applied stress  and the cohesion force bg : 1bg  . this fact reflects the intermediate-asymptotic character of quasi-brittle failure theories and the material parameter was introduced, the so-called the cohesive modulus, as the independent strength property of materials: b bk g d . despite the similar form of the cohesive modulus bk and the stress intensity t o. naimark, frattura ed integrità strutturale, 49 (2019) 272-281; doi: 10.3221/igf-esis.49.27 275 factor ik there is a difference between the irwin criteria and the cohesive modulus. the cohesive modulus determines the steady-state character of crack propagation, but not the catastrophic one corresponding to the griffith-irwin approach. non-local formulation of stress criterion was proposed by novozhilov [3] to introduce the fracture “quantization” scale. according to this formulation the crack propagation condition in mode i reads: 0 2 d yy cdx d  , (5) where yy is the normal stress perpendicular to the atomic layer with the space d , c is the critical stress. the space d is the fracture quantum. the criterion (5) can be used if the complete expression of the stress-field, and not only its asymptotic term, is taken into consideration. the non-local stress criterion can be also used for the interpretation of the cohesion forces ( )bg s , when the fracture quantum not restricted to be the atomic spacing. the qualitative difference between above mentioned approaches can be shown taking in view the remarks by fraenkel [18] under the critical analysis of the griffith approach. fraenkel wrote that the physically realistic form of the energy u must contain the local minimum ( )e eu a (fig. 1, curve 2). the difference in the energy c eu u u   determines the work of the stress field at the crack tip under transition from the steady-state to the unstable regime of crack propagation. this work provides the overcoming of the energy barrier. it is natural to assume that the cohesive modulus, non-local approach, the finite fracture mechanics and the tcd are the force version of this energy barrier. we will show in the following that the metastable energy form, assumed by fraenkel, has the relationship to the collective behavior of the defect ensemble in the process zone and to the interaction of the defects ensemble with the main crack. origin of characteristic lengths and crack variety paths tatistical theory of typical mesoscopic defects (microcracks, microshears) allowed us to establish specific type of critical phenomena in solid with defects – the structural-scaling transitions and propose the phenomenology of damage-failure transition [19]. one of the key results of the statistical approach and statistically based phenomenology are the establishment of two “order parameters” responsible for the structure evolution – the defect density tensor ikp (defect induced deformation) and the structural scaling parameter   3 0r r  , which represents the ratio of the spacing between defects r and mean size of structural heterogeneity 0r , and characterizes the current susceptibility of material to the defects growth [20,21]. statistically predicted non-equilibrium free energy f represents generalization of the ginzburg-landau expansion in terms of mentioned order parameters, defect induced deformation   yyp x p in uni-axial loading in y-direction and structural scaling parameter  :       2 2 4 6 * 1 1 1, ,2 4 6 c pf a p bp c p d p x            , (6) where yy  is the stress,  is the non-locality parameter, , , ,a b c d are the material parameters, * and c are characteristic values of structural-scaling parameter (bifurcation points) that define the areas of typical nonlinear material responses on the defect growth (quasi-brittle, ductile and fine-grain states) in corresponding ranges of  : * *1, , 1.3c c            . free energy form (6) represents multi-wall potential with qualitative different metastability in the ranges *c    and 1c   [19]. free energy release kinetics allows the presentation of damage evolution equation in the form      3 5*, ,p c p pp a p bp c p d x x                 , (7) s o. naimark, frattura ed integrità strutturale, 49 (2019) 272-281; doi: 10.3221/igf-esis.49.27 276 where p are the kinetic coefficients. kinetic equations (7) and the equation for the total deformation ĉ p   ( ĉ is the component of the elastic compliance tensor) represent the constitutive equations of materials with defects. material responses include the generation of characteristic collective modes – the autosolitary waves in the range of *c    and the “blow-up” dissipative structure in the range 1c   . the generation of these collective modes under the loading provides the defect induced mechanisms of structural (ductile) relaxation in the range *c    and specific mechanisms of damage localization on the set of spatial scales with the blow-up defect growth kinetics. the “blow-up” damage localization kinetics follows to the self-similar solution [21]    p g t f  , hx l  , ( ) (1 ) m cg t g t    , (8) and can be considered as the precursor of crack nucleation. the parameters in (8) are: c is the so-called "peak time" ( p   at ct  for the self-similar profile  f  of defects localized on the scale hl ), 0, 0g m  are the parameters of non-linearity, which characterize the free energy release rate for c  . the blow-up self-similar solution (8) describes damage kinetics for ,c ct p p  (fig.2) on the set of spatial scales , 1, 2,...h cl kl k k  , where cl and hl corresponds to the so-called “simple” and “complex” blow-up dissipative structures. the scales cl represent natural measure of the quantization length in the process zone providing the variety of the crack paths in the presence of two singularities: intermediate asymptotic solution for stress distribution at the crack tip area and the blow-up damage localization kinetics in the process zone. 0 a p p  c   c  c c p 1 p 2 1 f p p p p   c 1 c 21 a b figure 2 : a. nonlinear responses of material on defect density p in different ranges of structural-scaling parameter  ; b. free energy metastability for 1c   [19]. duality of singularities. the tcd lengths he existence of two singularities related to the stress field at the crack tip (4) and blow-up kinetics of damage localization (8) represents the physical basis for the interpretation of phenomenological assumption of the theory of critical distances. the free energy metastability of solid with defects and corresponding free energy release explain the conception of the finite fracture mechanics in the presence of the finite amplitude energy barrier. the out-ofequilibrium system “solid with defects” realizes the transition in the areas of metastabilities ( *c    and 1c   ) due to the generation of collective modes of defects (autosolitary waves of strain localization transforming into the blowup dissipative structures), which provides finally singular damage kinetics on the set of spatial lengths , 1, 2,...h cl kl k k  . different nature of these singularities, related to spatial (geometrical) basis for stress intensity factor and temporal one for damage localization, leads to the variety of transition scenario to failure in wide range of load intensity. experimental study of dynamic crack instability in pmma revealing the transition from steady to branching regimes of crack dynamics with qualitative changes of fracture surface morphology [19, 20], fig.3; the “resonance” excitation of selected blow-up modes (equal size of mirror-like damage localization zones in different spall cross-sections of shocked pmma rod [21,22]), the limit case of resonance damage localization under the “failure wave” initiation [23, 24], temporal and spatial scaling under dynamic fragmentation [25] supported the competitive role of two mentioned t o. naimark, frattura ed integrità strutturale, 49 (2019) 272-281; doi: 10.3221/igf-esis.49.27 277 singularities (attractor types) and allow the discussion of the area, when the tcd can be effectively used. the area of competition between two attractors belongs to the intermediate temporal scales of the loading rate, that is close to 6 510 10t s   [23]. a b figure 3: typical fractographic images of fracture surface for steady-state (a) and branching (b) regime of crack dynamics [24]. the tcd is based on the “force” version of failure criteria and, as a consequence, the large class of load conditions (with characteristic times approaching to the time of blow-up damage kinetics) could not be considered in the framework of the tcd phenomenology. characteristic example for such situation is the transition from the steady-state to the branching crack dynamics in pmma with qualitative changes of the fracture surface morphology: continuously mirror fracture surface for the steady-state crack dynamics and pronounced roughness with numerous mirror zones having different characteristic sizes (fig.3). steady-state crack dynamics and mirror morphology corresponds to the lfm asymptotical solution (4). the branching crack scenario corresponds to the set of collective modes of damage localization (the set of mirror zones), that represents the “degrees of freedom” responsible for the creation of the “process zone length” providing the crack advance. the formation of the “process zone length” is the consequence of the free energy metastability and “decomposition” of the metastable states due to the generation of collective blow-up defects modes corresponding to the self-similar solution (8) [26]. the existence of self-similar profile of damage distribution  f  , localized on the set of scales ( , 1, 2,...h cl kl k k  ), explains the nature of the critical distances, that provides both scenario of damage-failure transition corresponding to stress-based and stress-intensity phenomenology. the selection of wide spectrum of scales in the range , 1, 2,...h cl kl k k  is realized under dynamic and shock wave loading according to the presence of wide spectrum of finite amplitude stress modes and, as the consequence, corresponding spectrum of blow-up damage localization modes. phenomenological basis of the dct approach corresponds to the quasistatic loading conditions, when the “complex” blow-up mode can be initiated with the length h cl kl . namely this scale can be associated with the effective length in the theory of critical distance in the framework of elasto-plastic models. fatigue length scales. interpretation of bathias-paris’s diagram of fatigue crack growth pplication of the tcd to fatigue problems assumes that fatigue damage depends on the stress field distribution in the vicinity of the stress concentrator and the appropriate stress field parameter responsible for the damage in fatigue process zone could be introduced. it was proposed the calculation of the effective stress field parameter in the process zone according to the following relationship [27]:    1 0 0 1 0, 1 effl eff eff r r dr l              , (9) where  is the stress gradient of the elasto-plastic stress field:    1 1 0,1 0, d r r dr          . (10) a 1 mm o. naimark, frattura ed integrità strutturale, 49 (2019) 272-281; doi: 10.3221/igf-esis.49.27 278 eq. (9) defines the effective stress using a weighted average of the elasto-plastic stress field damaging the fatigue process zone over a line having length equal to effl . it is evident that the length effl , as the integration path, is assumed to be dependent on the notch geometry. the non-locality effect is the key structural factor responsible for the characteristic length effl providing the correct predictions for the application of the tcd [28]. there is data concerning the tcd application in predicting the high-cycle fatigue strength of real mechanical components. the effl value in fatigue damage is associated somehow with the grain size, but, in general, its value is of an order of magnitude higher than the average grain size. this experimental observation in the fatigue process zone leads to the definition of structural volume concept for the interpretation of link between the linear-elastic stress distribution within such a volume and the initial crack path. the structural volume idea takes as starting point for the assumption that all physical processes resulting in the formation of fatigue cracks are confined within a finite volume. the size of this volume is assumed to be constant (but different for different materials) and it depends on the stress field damaging the fatigue process zone. mentioned features of fatigue damage and fatigue crack advance in the interpretation of the tcd can be explained in terms of singularity dualities. the illustration of both these approaches (the tcd and duality of singularities) can be given by the interpretation of the bathias-paris diagram of fatigue crack growth, when both, stress and stressintensity based scenario of damage-failure transition, are presented. the solutions (4) and (8) represent two types of singularities (two attractors corresponding to intermediate asymptotic solutions for stress distribution and damage kinetics), which provide the interpretation of the bathias-paris diagram of fatigue crack initiation and growth, fig.4. the blow-up damage kinetics is the consequence of specific nonlinearity (metastability) of free energy release in the presence of non-locality effects of defects interaction that allows the explanation of transition from damage localization to the fatigue crack nucleation stage. figure 4. crack advance diagram in hcf [29]: is the burgers vector, 0k and effk are stress intensity factors corresponding to the crack lengths 0a and ia . the k independent area of fatigue crack initiation corresponds to the transition to the blow-up damage kinetics with explosive jump from structure dependent scales of defects inta to macroscopically recognized 0a . the power law   2int n da dn b a a reflects the self-similar (blow-up) stage of damage kinetics over cl scale that allows to estimate 0a ~ cl . this length is related to the stress based scenario of fatigue crack nucleation. starting from this scales 0a the singularity related to the stress intensity factor 0k is combined with the blow-up singularity (6), that provides fatigue crack kinetics up to the scale la . the drop of the crack velocity is the consequence of subjection of crack kinetics to the stress intensity factor thk according to the paris law. the process zone scale in this o. naimark, frattura ed integrità strutturale, 49 (2019) 272-281; doi: 10.3221/igf-esis.49.27 279 case is associated with the hl length. this analysis allows the natural conclusion that variety of crack paths and characteristic lengths are related to duality of singularities caused by asymptotic self-similar solution for stress distribution at the crack tip and intermediate singular (blow-up) damage kinetics in the process zone. mentioned scenario can be illustrated by the morphological images of crack nucleation and propagation in the conditions of very high cycle fatigue, fig.5 [29]. figure 5. fracture surface of ti6al4v alloy in very high cycle fatigue regime with the images of characteristic areas of fracture surface [30]. different mechanisms related to above mentioned scenario were supported studing the scaling (spatial invariance) properties of characteristic area of fracture surface rughness. the surface roughness was analysed by nterferometerprofiler new view 5010 to establish quantitative characteristics of the fracture surface in terms of the scaling hurst exponent. three distinct zones with strongly different exponent were observed (fig. 5): the area 1 of the size ~ 100-300 μm corresponds to the zone of damage localization (associated with cl ); the area 2 representing the image of crack advance in the presence of two singularities, given by the solutions (4) and (8), with the following re-subjection of crack kinetics (area 3) to the stress intensity fator. discussion he existence of two singularities related to the stress field at the crack tip and blow-up kinetics of damage localization is considered as the physical basis for the interpretation of the theory of critical distances. the free energy metastability of solid with defects and corresponding free energy release explain the conception of the finite fracture mechanics in the presence of the finite amplitude energy barrier. the variety of crack paths is analyzed as duality of inherently linked two types of singularities related to the singularity of multiscale damage kinetics under crack nucleation and singularity of stress field at the crack tip as the classical framework of fracture mechanics. the singularity of multiscale damage kinetics is a natural precursor of crack nucleation that could provide in some cases the totally independent scenario of fracture from the stress singularity at the crack tips. the influence of two singularities with the nature of intermediate asymptotical solutions for stress at the crack tip and damage localization kinetics over the set of spatial scales represents two attractors, which provides the variety of crack paths for corresponding loading conditions and the existence of characteristic scales that could be associated with the critical distance lengths. t o. naimark, frattura ed integrità strutturale, 49 (2019) 272-281; doi: 10.3221/igf-esis.49.27 280 acknowledgements uthor thanks prof. valery matveyenko for the proposal to present the paper in the issue. research was supported by the russian foundation of basic research (project n. 17-01-00687a). references [1] taylor, d. (2008). the theory of critical distances, engng, fract. mech., 75, pp. 1696-1705. [2] susmel, l., taylor, d. (2008). on the use of the theory of critical distances to predict static failures in ductile metallic materials containing different geometrical features, engng. fract. mech.,75, pp. 4410–4421. [3] novozhilov, v.v. (1969). on a necessary and sufficient criterion for brittle strength, prik. mat. mek., 33, pp.201– 210. [4] whitney, j.m, nuismer, r.j. (1974). stress fracture criteria for laminated composites containing stress concentrations, j, compos. mater. 8, pp. 253–265. [5] taylor, d. (2004). predicting the fracture strength of ceramic materials using the theory of critical distances, engng. fract. mech., 71, pp. 2407–2416. [6] taylor, d, wang, g. (2000). the validation of some methods of notch fatigue analysis. fatigue fract. engng. mater. struct., 23, pp.387–94. [7] el haddad, m.h., topper, t.h., smith, k.n. (1979). prediction of non propagating cracks. engng. fract. mech., 11, pp.573–84. susmel, l. (2008). the theory of critical distances: a review of its applications in fatigue. engng. fract. mech., 75, pp. 1706-1724. [8] taylor, d., cornetti, p., pugno, n. (2005). the fracture mechanics of finite crack extension. engng. fract. mech., 72, pp. 1021–38. [9] taylor, d, cornetti, p. (2005). finite fracture mechanics and the theory of critical distances. in: aliabadi m.h., editor. advances in fracture and damage mechanics iv. ec, eastleigh uk, pp. 565–70. [10] hashin, z. (1996). finite thermoelastic fracture criterion with application to laminate cracking analysis. j. mech. phys. solids, 44. pp. 1129–45. [11] leguillon, d. (2002). strength or toughness? a criterion for crack onset at a notch. eur j mech a/solids, 21, pp.61– 72. [12] cornetti, p., pugno, n, carpinteri a., taylor d. (2006). finite fracture mechanics: a coupled stress and energy criterion. engng fract mech., 73, pp. 2021–2033. [13] taylor, d., bologna, p., bel knani, k. (2000). prediction of fatigue failure location on a component using a critical distance method. int. j. fatigue, 22, pp. 735–742. [14] griffith, a.a. (1921) the phenomena of rupture and flow in solids. phil. trans. roy. soc. london, ser. a. 221, pp. 163-198. [15] irwin, g.r., (1957). analysis of stresses and strains near the end of a crack traversing a plate. journal of applied mechanics, 24, pp. 361-364. [16] barenblatt, g.i. (1962). the mathematical theory of equilibrium cracks in brittle fracture. advances in applied mechanics, 7, pp. 55 -129. [17] fraenkel, ya..i. (1952). theory of reversible and non-reversible cracks in solid. journal of technical physics, 22, pp. 1857-1866. [18] naimark, o.b. (2000). collective behavior of cracks and defects (plenary lecture) in : d miannay, p.costa, d. francois, a. pineau, eds. advances in mechanical behavior, plasticity and damage. elsevier, 1, pp.15-28. [19] naimark, o.b. (2004). defect induced transitions as mechanisms of plasticity and failure (plenary lecture). in: g. capriz and p. mariano, eds. advances in multifield theories of continua with substructure, birkhäuser, boston, pp.75-114. [20] beljaev, v.v., naimark, o.b. (1990). kinetics of multi-hotspot failure under shock wave loading sov. phys. doklady, 312, pp.289-293. [21] bellendir, e.n., beljaev, v.v., naimark, o.b. (1989). kinetics of multi-hotspot failure in the spall conditions. jetph letters, 15, pp. 90-93. a o. naimark, frattura ed integrità strutturale, 49 (2019) 272-281; doi: 10.3221/igf-esis.49.27 281 [22] naimark, o.b. (2016). energy release rate and criticality of multiscale defects kinetics. int. j. fracture, 202, pp. 271279. [23] naimark, o.b., and uvarov, s.v. (2004). nonlinear crack dynamics and scaling aspects of fracture (experimental and theoretical study), int. j. fracture, 128, pp. 285-292. [24] naimark, o.b., uvarov, s.v., davydova, m.m., bannikova, i.a. (2017). multiscale statistical laws of dynamic fragmentation. physical mesomechanics, 20, pp. 90-101. doi: 10.1134/s1029959917010088. [25] kurdyumov, s.p. (1988). evolution and self-organization laws of complex systems. international journal of modern physics, 1, pp. 299-327. [26] qylafku, g., azari, z., kadi, n., gjonaj, m., pluvinage, g. (1999). application of a new model proposal for fatigue life prediction on notches and key-seats. int j fatigue, 21, pp.753–60. [27] atzori, b., meneghetti, g., susmel, l. (2005). material fatigue properties for assessing mechanical components weakened by notches and defects. fract. engng. mater. struct., 28, pp. 83–97. [28] huang, z., wagner, d., bathias, c., paris, p.c. (2010). subsurface crack initiation and propagation mechanisms in gigacycle fatigue, acta materialia, 58, pp. 6046–6054. [29] betekhtin, v.i., kadomtsev, a.g., narykova, m.v., bannikov, m.v., naimark, o.b., abaimov, s.g., akhatov, i.s., palin-luc, t. 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/pdfxoutputintentprofileselector /documentcmyk /preserveediting true /untaggedcmykhandling /leaveuntagged /untaggedrgbhandling /usedocumentprofile /usedocumentbleed false >> ] >> setdistillerparams << /hwresolution [2400 2400] /pagesize [612.000 792.000] >> setpagedevice microsoft word numero_58_art_16_3142 .docx g. gomes et alii, frattura ed integrità strutturale, 58 (2021) 211-230; doi: 10.3221/igf-esis.58.16 211 a new methodology to predict damage tolerance based on compliance via global-local analysis gilberto gomes, thiago arnaud a oliveira, alvaro martins delgado neto, luciano mendes bezerra university of brasilia, brazil ggomes@unb.br, http://orcid.org/0000-0002-8385-9042 eng.thiagoarnaud@gmail.com, http://orcid.org/0000-0002-8220-5557 alvaro.martins.bok@gmail.com, http://orcid.org/0000-0002-4900-9116 lmbz@unb.br, http://orcid.org/ 0000-0002-5789-9649 abstract. over the years several design philosophies to address fatigue have been developed trying to combine structural safety and economy with aircraft manufacturing and operating processes. the safe-life approach consists of designing and manufacturing an aeronautical structure to be safe throughout its useful life. this approach results in factors that oversize structural elements to prevent possible failure and evidently incurs high design costs. alternatively, a damage tolerance concept-based approach assumes that the structure, even when damaged, is able to withstand the actions for which it was designed until the detection of a crack due to fatigue or other defects during its operation. this research proposes a new methodology to address the damage tolerance problem in which twodimensional global-local analysis at different levels of external requests will be made by means of compliance, aimed at finding a relationship between fatigue life and the paris’ constant. moreover, the study uses the bemcracker2d program for simulating two-dimensional crack growth. this methodology has proved to be an efficient alternative applicable to damage tolerance analysis. keywords. compliance; damage tolerance; fatigue; global-local analysis aircraft fuselage; bem. citation: gomes, g., oliveira, t. a. a., delgado neto, a. m., bezerra, l. m., a new methodology based on compliance to predict damage tolerance by the boundary element method, frattura ed integrità strutturale, xx (2021) 211-230. received: 15.06.2021 accepted: 27.07.2021 published: 01.10.2021 copyright: © 2020 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. introduction he national transportation safety board [1] and wanhill [2], have highlighted a number of documented studies to interpret the cause of airplane accidents due to fatigue processes such as those with the comet and the boeing 737-200. sanford [3] states that all such structures are subject to fatigue, with cracks starting at the edges and growing until reaching critical size for brittle failure to occur, even when subjected to permanent loads only. unlike t https://youtu.be/nbacqnmrfyk g. gomes et alii, frattura ed integrità strutturale, 58 (2021) 211-230; doi: 10.3221/igf-esis.58.16 212 structures that are plastically overloaded, where large deformations occur before failure, those caused by fatigue occur suddenly, without warning (brittle failure). this proves to be a big problem as it makes it impossible to take preventive measures before the complete rupture, so information related to the variable load over time and, particularly, its effect on cracks is of fundamental importance for predicting the behavior of the structure as a whole. over the years, several fatigue design philosophies have evolved trying to combine structural safety and economy in aircraft manufacturing and operating processes. the first approach, called safe-life, consists of designing and manufacturing an aircraft structure that is safe for its entire lifetime. to that end, the most extreme situations of foreseeable fatigue requirements arising during operation must be considered in the prototype tests. this methodology results in factors that oversize the structural elements in order to prevent the possibility of failure. it is an approach that evidently leads to high design costs and is not capable of guaranteeing security as to whether an unforeseen failure may occur during project life. rationally, a new philosophy has been developed based on the concept of damage tolerance. in this methodology, it is assumed that the structure, even when damaged, is able to withstand the actions for which it was designed until the detection of a fatigue crack or other defects during its operation. the unit is then checked, repaired and put back into service until the end of its useful life. palmberg [4] has been a pioneer in this new concept, performing a statistical analysis to control fatigue crack propagation and considering inspection intervals to keep the probability of complete failure low. later, wanhill [5,6] examined damage tolerance in the use of aluminum alloys for aircraft structural applications. newman jr. [7,8] has suggested that fatigue damage can be characterized by crack size. schijve [9] proposed some aspects of the design, predictions and experiments associated with the same concept in aircraft structures. barter and molent [10] showed that the load cycles have a direct linear relationship with the logarithm of the crack size and that the largest cracks formed grow approximately exponentially (the so-called "main crack" methodology) [11] from small discontinuities inherent to the material, as soon as an aircraft enters into service [12]. currently, the concept of damage tolerance is applied to aircraft with composite structures [13–16] in multiple crack analysis [17] and in shape optimization projects [18,19]. probabilistic studies on damage tolerance are based on fabrication components [20] and fatigue life dispersion from an initial defect distribution [21]. other works relate damage tolerance to computational methods, using finite element method [22] and extended finite element method (xfem) [23], boundary element method (bem) [24] and dual boundary element method (dbem) [25]. in an aircraft fuselage, the evaluation of fracture mechanics (fm) parameters such as stress intensity factor (sif), number of load cycles and stress and displacement fields becomes difficult due to the complex nature of the panel details: brackets, shear clips, rivets, etc. on the other hand, knowledge of those parameters is of paramount importance for understanding the nature of the damage process, especially under the action of dynamic loads. thus, designers are always looking for fast and reliable simulation methods that can produce accurate average data from these parameters to avoid damage processes and, consequently, the occurrence of accidents. automation is seen as a key point, allowing for the evaluation of various analyzes as a means for conducting parametric studies and resulting in design optimization [26]. among the several numerical methods for fracture modeling and analysis, dbem has been consolidated and has the following advantages: simplified modeling of the crack area, direct sif calculation, reduced execution times and accurate simulation of crack growth [27–29]. the behavior of a solid, discretizing only its contours, enables the analysis of the thousands of simulations necessary for a probabilistic study and, using dbem, it is possible to study the defects, predicting the fatigue behavior, especially the damage process, multiple sites damage and reliability analysis, among others [30–34]. this work aims to find a solution for the damage tolerance problem detected in [35]. for that, two-dimensional globallocal analyzes will be carried out under different levels of external demands through compliance. the method aims to find a relationship between fatigue life and paris’ constants. furthermore, a homemade software called bemcracker2d and its gui bemlab2d version will be used for modeling and analysis of two-dimensional elastostatic problems involving cracks, which are based on the bem and dbem. literature review opez [36] presents an extensive review of the uncertainties involved in the monitoring of structural damage in aircraft addressing the existing methods developed for the problem of uncertainty in the areas of damage diagnosis, prognosis and control. newman jr. [8] predicts the fatigue life of various metallic materials under different loading conditions. this study made it possible to express crack growth as a function of the effective stress intensity factor interval. the results obtained were compared with experiments on notched and unnotched specimens of aluminum and steel alloys. fatigue is commonly represented by the study of [37]. those authors made a fundamental l g. gomes et alii, frattura ed integrità strutturale, 58 (2021) 211-230; doi: 10.3221/igf-esis.58.16 213 contribution to the modeling of cracks in solids subjected to cyclic loads from the paris-erdogan law, also called da/dn, which relates the number of fatigue cycles with the crack size. palmberg [4] is one of the pioneers when it comes to considering the concept of damage tolerance. that author performs a statistical analysis to control the propagation of fatigue cracks and considers inspection intervals in order to ensure that the probability of complete failure of the structure is always kept low. pyo [38] deals with an alternative method for analyzing fatigue damage in aircraft structures. the author developed a methodology called elastic finite element alternating method (efeam) to predict the maximum load capacity in cracked panels highlighting the multi site damage (msd) effect. also in the same study, an analytical solution for a crack line in an infinite metal sheet is developed and as a result the author demonstrates that the classical lefm approximation overestimates the load capacity. jeong [39] presents a method for predicting the msd threshold and also widespread damage to fuselages saying that the problem of widespread damage is the reduction in the residual strength of the structure below the tolerance while the msd threshold refers to the point in useful life when there is fatigue coalescence (linkup) of two adjacent cracks still at the allowable stress level. the presented methodology determines a threshold value from the analysis of the combination of residual strength and fatigue crack growth results evaluated through laboratory tests. for that model, the results for the fatigue damage threshold were between 32,000 and 40,000 cycles and for the msd threshold, about 70,000 cycles. platz [40] points out that fatigue cracks in lightweight shells or panel structures can lead to major failures when used for sealing or cargo transport. in his research, that author investigates the application of piezoelectric systems applied to the surface of a thin cracked aluminum panel to reduce fatigue crack propagation. with the reduction of propagation, uncertainties in the strength of the structure, which remain even when the structure is used under damage tolerance conditions such as in an aircraft fuselage, can be reduced. piezoelectrics act by inducing compressive forces at the crack tip to reduce cyclic sif. as a result, it has been statistically highlighted using experimental samples that the crack propagation rate significantly reduces. khan [41] has examined low cycle fatigue in aluminum al 2024-t351 plate. experimental analysis was performed for both monotonic and cyclic loading, using imaging technology to detect the crack start site. breitbarth [42], based on biaxial tests with samples arranged in a cross, studied cracks in fuselage sections between the wing and tail of the aircraft, obtaining maximum sif's values for metallic parts. the experimental results from digital images were compared with the analytical ones, obtaining studies of sif's, j-integral, plastic zone, and crack closure effects. finally, the publications of [9] and [43] revealed that a fuselage subjected to compression testing to the ultimate limit state (uls) and then fatigue tested had improved results due to residual compressive stresses. those tensions were able to delay the development of cracks. figure 1: double cantilever beam specimen requested by traction. basic formulation his section presents the basic formulation of the main topics related to the methodology, namely, compliance and fatigue life. compliance compliance is the magnitude that represents the inverse of rigidity. mathematically it is determined by: t g. gomes et alii, frattura ed integrità strutturale, 58 (2021) 211-230; doi: 10.3221/igf-esis.58.16 214  c p (1) where 𝛿 is the displacement from an applied load p. in fig. 1, 𝛿 ∆/2. fatigue life fatigue life can be represented by the paris’ law. this law relates the crack propagation rate (da/dn) to the variation of the stress intensity factor (δk):  . m da c k dn (2) where c and m are material constants, determined experimentally, a is the crack size, n is the number of loading cycles and k is the variation of the stress intensity factor. developing eqn. (2), the classic condition of the number of cycles, which varies from an initial crack 0a that can be detected by conventional methods, to a critical length ca , as determined by:    0 1 ca totma da n n c k (3) where n is the number of cycles needed to increase the initial size crack and totn is the expected number of cycles over the life. this variation between the number of cycles of the initial crack 0n and the critical   cn , when a safety factor (sf) is applied, is defined as the inspection interval to be adopted, mathematically represented by:  0cn n sf (3) material and methods his section presents the computational technique developed for optimizing the fatigue life of aircraft fuselage parts through compliance. the technique aims to find the relationship between the physical parameters of the paris’ law material (c, m), such that the fatigue life equals that defined in the project. moreover, a brief description will be made of the computational tools used in the global-local modeling and analysis process (bemlab2d and bemcracker2d softwares) in order to corroborate the presented methodology. this technique is based on the four steps of the following algorithm: 1) from the model in bemlab2d gui by the user, the number of cycles required, or project, is defined (n*); 2) the algorithm computes the stress field in the macro analysis and locates the stress peak before reaching plastification, thus enabling the elastic analysis; 3) the algorithm positions the micro element at the stress peak found in step 2, and calculates the number of cycles for which compliance reaches 3c (n3c); 4) the algorithm, considering the initial fuselage defects (hole size and crack lengths), obtains a series of physical parameters of the material to be used (c and m) taking the number of cycles of the minimum instability compliance (n3c) to be that defined by the user (n*). for example, if the designer wants to obtain the instability at n*=6x1012, the optimization will show which series of physical parameters (c and m) the material needs to have so that it takes n3c to the number of cycles defined in the design (n*), as illustrated in fig. 2. bemlab2d gui the bemlab2d software [44] is a graphic interface for manipulating two-dimensional models of boundary elements, allowing geometric information, boundary conditions and physical attributes to be managed in an efficient and userfriendly way. bemlab2d works both as a pre-processor when defining the geometric model of the problem, by associating physical attributes to the geometry and by generating the boundary elements mesh, and as a post-processor t g. gomes et alii, frattura ed integrità strutturale, 58 (2021) 211-230; doi: 10.3221/igf-esis.58.16 215 when used to visualize the data provided by bemcracker2d, as deformed graphs, sif's, number of cycles and crack propagation, among others. fig. 3 illustrates these features. figure 2: optimization of the minimum number of cycles (n3c) (fatigue life) for the number of design cycles (n*). (a) (b) (c) figure 3: bemlab2d gui; a) modelling; b) crack growth view; c) deformed mesh view. this graphical interface, for preand post-processing, is able to represent the macro and micro models by boundary elements, as detailed in the following sections. bemcracker2d program bemcracker2d [45–48] is the processor program for elastostatic analysis of 2d problems. it is written in c++ language and entirely structured on the concepts of object oriented programming (oop) in order to perform analyzes using the boundary elements method. here, the module iii (dbem with propagation) of bemcracker2d is used, which consists in: stress analysis with standard bem sif’s evaluation (j-integral) direction/correction of crack growth fatigue life evaluation (paris’ law) and coalescence of multiple cracks (linkup). this software was developed from the standard bem modeling and the incremental analysis strategy for problems with cracks [49,50]. for analysis of fracture mechanics problems, bemcracker2d calculates elastic stresses using the conventional bem and performs incremental analysis of the crack extension using the dbem. sifs are computed for each increment through the j-integral, the propagation direction by the three classical criteria in the literature, although g. gomes et alii, frattura ed integrità strutturale, 58 (2021) 211-230; doi: 10.3221/igf-esis.58.16 216 here the maximum circumferential stress is used, and the crack growth rate by one modified paris’ equation, which uses an equivalent sif considering fracture modes i and ii. computational technique he technique developed is divided into two analyses: macro, which shows the place where the stress peak occurs; and micro, which shows the number of critical fatigue life cycles. in this case, there is a main program that performs the interaction between the global and local analyses, as well as the link between the bemlab2d interface and the processing by bemcracker2d. macro analysis – pre-processing initially, the modeling of the fuselage is performed in bemlab2d, obtaining the data referring to the physical parameters and the boundary element mesh, such as the nodal coordinates, mesh topology, traction and displacement boundary conditions, etc. as an example, the model in fig. 4 was adopted, which consists of a plate with normal p and shear q external loads and displacement restriction in the other nodes. figure 4: global model and internal points. from the initial model in fig. 4, the algorithm creates the internal points for the calculation of the stress field, by bemcracker2d. the generated set of internal points is only intended to obtain a uniform grid of points to enable the plots of stress field and, therefore, it is not a mandatory requirement of the bem. macro analysis – post-processing after obtaining the internal stress fields of the macro model, by bemcracker2d, the stress fields σx, σy and τxy are obtained, as illustrated, respectively, in figs. 5, 6 and 7. with these stress fields, one can find the critical location, or a peak that considers the three stresses together. for this, the von mises criterion is used – see fig. 8. it is noteworthy that the von mises criterion was adopted only to identify the peak, still in the elastic regime; there is no plasticity analysis, since the algorithm is recommended for the elastic regime. thus, if other criteria such as tresca are adopted, for example, there will be no significant change in the position of the peak. from the stress peak obtained in the macro model highlighted in fig. 8, the micro model analysis is shown in the following item. t g. gomes et alii, frattura ed integrità strutturale, 58 (2021) 211-230; doi: 10.3221/igf-esis.58.16 217 figure 5: x-normal stress field (x). figure 6: y-normal stress field (y). figure 7: shear stress field (xy). g. gomes et alii, frattura ed integrità strutturale, 58 (2021) 211-230; doi: 10.3221/igf-esis.58.16 218 figure 8: local of stress peak. micro analysis the micro model represented has a square shape with an edge size of 1 cm with initial flaws characterized by a central hole of radius r and two cracks with sizes l1 and l2 representing the upper and lower cracks, respectively. the micro-model size and the initial defects are among the main problems in a multi-scale analysis, especially in techniques in which physical quantities are transferred from the micro-scale to the global scale, as performed in homogenization techniques [51]. numerous researchers have addressed this problem over the years [52–56]. in this work, the values used reflect the effective size of supposed initial faults, however, a probabilistic methodology with bem – using bemcracker2d, allows the initial defects to be modeled under different sizes. thus, the micro analysis is performed at the peak location of the stress field, since, as this is the most unfavorable situation, all other positions would naturally be met. continuing with the example adopted in [35], the peak is shown in fig. 8 and the positioning of the micro model is shown in fig. 9 (a). in this case, the stresses are taken from the stress field at this point and applied on the right and upper edge with a fatigue load ratio (r) equal to 0.5 and displacement constraint on the left and lower edges, fig. 9 (b). here, 64 elements and 128 geometric nodes were considered, with quadratic continuous elements arranged on the edges and in the central circular hole, and quadratic discontinuous elements representing the cracks in the proportion 0.2-0.3-0.3-0.2. the elements were distributed as follows: 10 on each outer edge, adding 40, with a distance of 0.05 between them; 8 in the central circular hole and 8 in each crack, as shown in fig. 9 (c). (a) (b) (c) figure 9: micro model; a) local of stress peak; b) micro model modelling; c) bem mesh. from the micro model, bemcracker2d processes the incremental analysis and, at each crack advance, it brings as results the number of cycles and the mesh displacement, necessary for the compliance calculation from the average of the displacements of each edge and the respective tension on the considered edge (right or upper). g. gomes et alii, frattura ed integrità strutturale, 58 (2021) 211-230; doi: 10.3221/igf-esis.58.16 219 fig. 10 (a) shows the propagation path and the respective number of cycles and, and fig. 10 (b) shows the mesh deformation. in fig. 11, each point, from left to right, represents an increment of the crack from fig. 10 (a). the initial compliance, before the crack propagation, is on the abscissa axis, and, with each propagation increment, the plate loses rigidity and exponentially increases the compliance versus cycles ratio. from these points, a curve fit corresponding to a spline is created, resulting in the curves in fig. 12, from which it is obtained the number of cycles corresponding to 2x initial compliance and 3x initial compliance. the number of cycles referring to 3x initial compliance is considered unstable, as from this point onwards compliance tends to infinity. the results in fig. 12 refer to tip 1 of crack 1 (crack 1 tip 1), see fig. 9 (b). fig. 13 presents the cycle number results for the four crack tips. for the purpose of damage tolerance, the smallest number of cycles that reach instability in 3x initial compliance (n3c) should be considered. (a) (b) figure 10: micro model results; a) crack propagation; b) deformed mesh. (a) (b) figure 11: relation number of cycles versus compliance points for each increment; (a) upper edge; (b) right edge. g. gomes et alii, frattura ed integrità strutturale, 58 (2021) 211-230; doi: 10.3221/igf-esis.58.16 220 (a) (b) figure 12: load cycles versus compliance curves; (a) upper edge; (b) right edge. figure 13: load cycles versus compliance curves for all crack tips. application his section presents two applications based on the model presented in [57], in order to demonstrate the accuracy of the proposed methodology, as well as to validate the robustness of the bemcracker2d program as part of it. for simplification purposes, the results of the macro and micro models regarding the mesh, stress field and deformed shape will not be shown, but only those related to the stress peak location, number of cycles, compliance and the respective curves. in both applications, p and q represent the normal and shear loads, respectively; r is the radius of the central hole; l1 and l2 are the size of the top and bottom cracks, respectively. a1 application tab. 1 presents the macro and micro values for the first application, whose external request produces the location of the voltage peak as illustrated in fig. 14. next, the algorithm positions the micro element at the peak composed of the stresses arranged in tab. 2 and executes the fatigue test to evaluate the respective number of cycles at each propagation crack until the last increment before reaching an edge. finally, at each increment, there are the points for the construction of the fatigue life curve (n) versus the average compliance of the edges, as illustrated in fig. 15. thus, as this element was executed at the point of stress peak, these curves correspond to the worst situation, the n3c minimums. t g. gomes et alii, frattura ed integrità strutturale, 58 (2021) 211-230; doi: 10.3221/igf-esis.58.16 221 for this application, the values of c=5e-11 and m=2.5 of the paris’s constants were considered to calculate the number of cycles. however, by varying these values, the number of cycles also varies, thus making it possible to create the curve that relates the variables c and m with the number of cycles, as will be shown below. curve n(c, m) for a1 application adopting c and m from paris’s law in the form of a grid in the domain c = [5e-11, 9.5e-11] and m = [2.7, 3.2], the points that relate them to the number of cycles are obtained, as illustrated in fig. 16. macro variables micro variables p (mpa) 360.47 r (cm) 0.089 q (mpa) 92.78 l1 (cm) 0.074 l2 (cm) 0.086 table 1: variable values for a1 application. figure 14: peak stress location. stresses σx (mpa) -30.66 σy (mpa) 360.00 τ (mpa) 92.00 table 2: peak stresses values for a1 application. next, through the interpolation of the points obtained in fig. 16, the surface that represents the function that relates c in with the number of cycles is obtained, fig. 17. with that, to find the values of the constants that carry the number of minimum cycles to the design value, the intersection between the relationship curves with the surface of the required number of cycles must be found. for example, considering the number of cycles defined in the project as 1e+04, the intersection is shown in the red line, as shown in fig. 18 (a). in fig. 18 (b), in the c x m plane, the curve that shows the parameters c and m that the material must have for the number of cycles requested by the user is obtained, thus originating the graph in fig. 19 showing that it supports 10,000 cycles. g. gomes et alii, frattura ed integrità strutturale, 58 (2021) 211-230; doi: 10.3221/igf-esis.58.16 222 figure 15: load cycles versus compliance curves. figure 16: relation (c, m) versus load cycles (n) points. figure 17: relation (c, m) versus load cycles (n) curve. g. gomes et alii, frattura ed integrità strutturale, 58 (2021) 211-230; doi: 10.3221/igf-esis.58.16 223 (a) (b) figure 18: intersection between n(c, m) curve versus design load cycles curve (n*). figure 19: relation (c, m) with 1e+04 design number cycles. furthermore, by modifying the value of the number of design cycles n* (black color surface of fig. 18), it is possible to obtain the variation of c and m for each value of n* requested in design, as shown in fig. 20. figure 20: relation (c, m) resulting in 1e+04, 2e+04, 2.5e+04 design number cycles. g. gomes et alii, frattura ed integrità strutturale, 58 (2021) 211-230; doi: 10.3221/igf-esis.58.16 224 a2 application tab. 3 presents the macro and micro values for the second application, while the location of the stress peak is seen in fig. 21. the stress peak is displayed in tab. 4 and, finally, at each increment, there are the points for the construction of the fatigue life curve (n) versus average compliance of the edges, as illustrated in fig. 22. macro variables micro variables p (mpa) 343.58 r (cm) 0.112 q (mpa) 90.70 l1 (cm) 0.081 l2 (cm) 0.093 table 3: variable values for a2 application. figure 21: peak stress location. stresses σx (mpa) -36.06 σy (mpa) 343.58 τ (mpa) 90.70 table 4: peak stress values for a2 application. curve n(c,m) for a2 application fig. 23 shows the domain c = [5e-11, 9.5e-11] and m = [2.7, 3.2] relating them to the number of cycles. fig. 24 (a) illustrates the surface that represents the function relating c and m with the number of cycles. thus, considering the number of cycles defined in the project as 1e+04, for example, the intersection is shown in the red line. in fig. 24 (b), in the c x m plane, the curve that shows the parameters c and m that the material must have for the number of cycles requested by the user is obtained, thus originating the graph in fig. 25, showing that it supports 10,000 cycles. furthermore, by modifying the value of the number of design cycles n* (black color surface of fig. 24), it is possible to obtain the variation of c and m for each value of n* requested in design, as shown in fig. 26. g. gomes et alii, frattura ed integrità strutturale, 58 (2021) 211-230; doi: 10.3221/igf-esis.58.16 225 figure 22: load cycles versus compliance curves. figure 23: relation (c, m) versus load cycles (n) points. g. gomes et alii, frattura ed integrità strutturale, 58 (2021) 211-230; doi: 10.3221/igf-esis.58.16 226 (a) (b) figure 24: intersection between n(c, m) curve versus design load cycles curve (n*). figure 25: relation (c, m) with 1e+04 design number cycles. figure 26: relation (c, m) that results 1e+04, 2e+04 design number cycles. application/variables a1 a2 p (mpa) 360.47 343.58 q (mpa) 92.78 90.70 r (cm) 0.089 0.112 l1 (cm) 0.074 0.081 l2 (cm) 0.086 0.093 table 5: comparison between a1 and a2 applications. comparisons between a1 and a2 applications here, the curves c and m between applications a1 and a2 are compared. tab. 5 shows the values of the variables for each application and, in fig. 27, the respective curves are illustrated. in this table, one can observe the difference in the choice of paris’ values when we change the input variables p, q, r, l1, l2. g. gomes et alii, frattura ed integrità strutturale, 58 (2021) 211-230; doi: 10.3221/igf-esis.58.16 227 figure 27: comparison between a1 and a2 (c, m) curves for 1e+04 design load cycles. final remarks he proposed methodology is an alternative to the classical damage tolerance analysis in which the evaluation of damage is done through the critical crack size. in this research, the critical size is disregarded and compliance is evaluated as the defining variable of instability. the use of the boundary elements method (bem), as a numerical method, has been essential because of its flexibility, precision and mesh simplicity. with the bem, the proposed numerical fatigue life technique was programmed without complex re-meshing processing as in the fem. the suggested formulation was useful to evaluate both the location of the stress peak and the compliance of the edges of the local analysis elements. this research presents the relationship between the paris' constants (c and m) and damage tolerance, through curves relating the paris' constants to the desired number of cycles. a function is presented with the parametric data of c and m related to the desired number of cycles in a conservative way to avoid instability. the automation of the technique presented in this research with the use of the computer programs bemlab2d and bemcracker2d enable the analysis of fatigue tolerance in two-dimensional geometries and under plain stress or strain. the programs allow damage analyses throughout the parametric data of c and m of paris' law to ensure damage tolerance and avoid the undesired limit state. this research is an initial contribution and more work is needed and encouraged. acknowledgment he authors are grateful to the brazilian national research council (cnpq) and to the brazilian coordination for the improvement of higher education personnel (capes) for the supporting funds for this research. the authors also thank the graduate programme in structural engineering and civil construction in the department of civil and environmental engineering at the university of brasilia. references [1] ntsb, n.t.s.b. (1989). aircraft accident report, aloha airlines, flight 243, boeing 737-200, n73711, near maui, hawaii, april 28, 1988. [2] wanhill, r., molent, l., barter, s. (2016). milestone case histories in aircraft structural integrity. reference module in materials science and materials engineering, elsevier. [3] sanford, r.j. (2002). principles of fracture mechanics. [4] palmberg, b., blom, a.f., eggwertz, s. (1987). probabilistic damage tolerance analysis of aircraft structures. probabilistic fracture mechanics and reliability, dordrecht, springer netherlands, pp. 47–130. t t g. gomes et alii, frattura ed integrità strutturale, 58 (2021) 211-230; doi: 10.3221/igf-esis.58.16 228 [5] wanhill, r. (1994). flight simulation fatigue crack growth testing of aluminium alloys specific issues and guidelines, int. j. fatigue, 16(2), pp. 99–110, doi: 10.1016/0142-1123(94)90100-7. [6] wanhill, r. (1994). status and prospects for aluminium-lithium alloys in aircraft structures, int. j. fatigue, 16(1), pp. 3–20, doi: 10.1016/0142-1123(94)90441-3. [7] newman, j.c. (1998). the merging of fatigue and fracture mechanics concepts: a historical perspective, prog. aerosp. sci., 34(5–6), pp. 347–390, doi: 10.1016/s0376-0421(98)00006-2. [8] newman, j. (1999). fatigue-life prediction methodology using small-crack theory, int. j. fatigue, 21(2), pp. 109– 119, doi: 10.1016/s0142-1123(98)00058-9. [9] schijve, j. (2009). fatigue damage in aircraft structures, not wanted, but tolerated?, int. j. fatigue, 31(6), pp. 998– 1011, doi: 10.1016/j.ijfatigue.2008.05.016. [10] barter, s., molent, l., goldsmith, n., jones, r. (2005). an experimental evaluation of fatigue crack growth, eng. fail. anal., 12(1), pp. 99–128, doi: 10.1016/j.engfailanal.2004.04.002. [11] molent, l., barter, s.a. (2010). the lead fatigue crack concept for aircraft structural integrity, procedia eng., 2(1), pp. 363–377, doi: 10.1016/j.proeng.2010.03.041. [12] barter, s.a., molent, l., wanhill, r.j.h. (2012). typical fatigue-initiating discontinuities in metallic aircraft structures, int. j. fatigue, 41, pp. 11–22, doi: 10.1016/j.ijfatigue.2011.10.017. [13] molent, l., forrester, c. (2017). the lead crack concept applied to defect growth in aircraft composite structures, compos. struct., 166, pp. 22–26, doi: 10.1016/j.compstruct.2016.12.076. [14] chowdhury, p., sehitoglu, h., rateick, r. (2018). damage tolerance of carbon-carbon composites in aerospace application, carbon n. y., 126, pp. 382–393, doi: 10.1016/j.carbon.2017.10.019. [15] chowdhury, n.m., chiu, w.k., wang, j., chang, p. (2016). experimental and finite element studies of bolted, bonded and hybrid step lap joints of thick carbon fibre/epoxy panels used in aircraft structures, compos. part b eng., 100, pp. 68–77, doi: 10.1016/j.compositesb.2016.06.061. [16] pegorin, f., pingkarawat, k., mouritz, a.p. (2015). comparative study of the mode i and mode ii delamination fatigue properties of z-pinned aircraft composites, mater. des., 65, pp. 139–146, doi: 10.1016/j.matdes.2014.08.072. [17] smith, l., pilarczyk, r., feiger, j. (2016). validation testing and analysis of cracked-hole continuing damage solutions, mater. perform. charact., 5(3), pp. mpc20150055, doi: 10.1520/mpc20150055. [18] sonmez, f.o. (2007). shape optimization of 2d structures using simulated annealing, comput. methods appl. mech. eng., 196(35–36), pp. 3279–3799, doi: 10.1016/j.cma.2007.01.019. [19] chintapalli, s., elsayed, m.s.a., sedaghati, r., abdo, m. (2010). the development of a preliminary structural design optimization method of an aircraft wing-box skin-stringer panels, aerosp. sci. technol., 14(3), pp. 188– 198, doi: 10.1016/j.ast.2009.12.007. [20] gorelik, m. (2017). additive manufacturing in the context of structural integrity, int. j. fatigue, 94, pp. 168–177, doi: 10.1016/j.ijfatigue.2016.07.005. [21] ciavarella, m., papangelo, a. (2018). on the distribution and scatter of fatigue lives obtained by integration of crack growth curves: does initial crack size distribution matter?, eng. fract. mech., 191, pp. 111–124, doi: 10.1016/j.engfracmech.2018.01.019. [22] carta, f., pirondi, a. (2011). damage tolerance analysis of aircraft reinforced panels, frat. ed integrità strutt., 5(16), pp. 34–42, doi: 10.3221/igf-esis.16.04. [23] srivastava, a.k., arora, p.k., kumar, h. (2016). numerical and experiment fracture modeling for multiple cracks of a finite aluminum plate, int. j. mech. sci., 110, pp. 1–13, doi: 10.1016/j.ijmecsci.2016.02.010. [24] wen, p.h., aliabadi, m.h., young, a. (2004). crack growth analysis for multi-layered airframe structures by boundary element method, eng. fract. mech., 71(4–6), pp. 619–631, doi: 10.1016/s0013-7944(03)00021-3. [25] salgado, n.k., aliabadi, m.h. (1997). the analysis of mechanically fastened repairs and lap joints, fatigue fract. eng. mater. struct., 20(4), pp. 583–593, doi: 10.1111/j.1460-2695.1997.tb00290.x. [26] ju, j., you, x. (2013). dynamic fracture analysis technique of aircraft fuselage containing damage subjected to blast, math. comput. model., 58(3–4), pp. 627–633, doi: 10.1016/j.mcm.2011.10.044. [27] portela, a., aliabadi, m.h., rooke, d.p. (1992). the dual boundary element method: effective implementation for crack problems, int. j. numer. methods eng., 33(6), pp. 1269–1287, doi: 10.1002/nme.1620330611. [28] portela, a., aliabadi, m.h., rooke, d.p. (1992). dual boundary element analysis of cracked plates: singularity subtraction technique, int. j. fract., 55(1), pp. 17–28, doi: 10.1007/bf00018030. [29] blandford, g.e., ingraffea, a.r., liggett, j.a. (1981). two-dimensional stress intensity factor computations using the boundary element method, int. j. numer. methods eng., 17(3), pp. 387–404, doi: 10.1002/nme.1620170308. g. gomes et alii, frattura ed integrità strutturale, 58 (2021) 211-230; doi: 10.3221/igf-esis.58.16 229 [30] citarella, r. (2011). msd crack propagation by dbem on a repaired aeronautic panel, adv. eng. softw., 42(10), pp. 887–901, doi: 10.1016/j.advengsoft.2011.02.014. [31] citarella, r., carlone, p., sepe, r., lepore, m. (2016). dbem crack propagation in friction stir welded aluminum joints, adv. eng. softw., 101, pp. 50–59, doi: 10.1016/j.advengsoft.2015.12.002. [32] price, r.j., trevelyan, j. (2014). boundary element simulation of fatigue crack growth in multi-site damage, eng. anal. bound. elem., 43, pp. 67–75, doi: 10.1016/j.enganabound.2014.03.002. [33] morse, l., khodaei, z.s., aliabadi, m.h. (2017). multi-fidelity modeling-based structural reliability analysis with the boundary element method, j. multiscale model., 08(03n04), pp. 1740001, doi: 10.1142/s1756973717400017. [34] huang, x., aliabadi, m.h., khodaei, z.s. (2014). fatigue crack growth reliability analysis by stochastic boundary element method, c. model. eng. sci., 102(4), pp. 291–330, doi: 10.3970/cmes.2014.102.291. [35] oliveira, t.a.a., gomes, g., evangelista jr, f. (2019). multiscale aircraft fuselage fatigue analysis by the dual boundary element method, eng. anal. bound. elem., 104, pp. 107–119, doi: 10.1016/j.enganabound.2019.03.032. [36] lopez, i., sarigul-klijn, n. (2010). a review of uncertainty in flight vehicle structural damage monitoring, diagnosis and control: challenges and opportunities, prog. aerosp. sci., 46(7), pp. 247–273, doi: 10.1016/j.paerosci.2010.03.003. [37] paris, p., erdogan, f. (1963). a critical analysis of crack propagation laws, j. basic eng., 85(4), pp. 528–533, doi: 10.1115/1.3656900. [38] pyo, c.r., okada, h., atluri, s.n. (1995). an elastic-plastic finite element alternating method for analyzing widespread fatigue damage in aircraft structures, comput. mech., 16(1), pp. 62–68, doi: 10.1007/bf00369886. [39] jeong, d.y., tong, p. (1997). onset of multiple site damage and widespread fatigue damage in aging airplanes., int. j. fract., 85, pp. 185–200, doi: 10.1023/a:1007452712730. [40] platz, r., stapp, c., hanselka, h. (2011). statistical approach to evaluating reduction of active crack propagation in aluminum panels with piezoelectric actuator patches, smart mater. struct., 20(8), pp. 085009, doi: 10.1088/0964-1726/20/8/085009. [41] khan, s., kintzel, o., mosler, j. (2012). experimental and numerical lifetime assessment of al 2024 sheet, int. j. fatigue, 37, pp. 112–122, doi: 10.1016/j.ijfatigue.2011.09.010. [42] breitbarth, e., besel, m., reh, s. (2018). biaxial testing of cruciform specimens representing characteristics of a metallic airplane fuselage section, int. j. fatigue, 108, pp. 116–126, doi: 10.1016/j.ijfatigue.2017.12.005. [43] brot, a., peleg-wolfin, y. (2008).the damage tolerance behavior of integrally stiffened metallic structures. 48th israel annual conference on aerospace sciences. [44] delgado neto, a.m., oliveira, t.a.a., gomes, g. (2019). an efficient gui update for bem-fem mixed mesh generation, int. j. comput. methods eng. sci. mech., 20(3), pp. 256–267, doi: 10.1080/15502287.2019.1632975. [45] gomes, g., miranda, a.c.o. (2018). analysis of crack growth problems using the object-oriented program bemcracker2d, frat. ed integrità strutt., 12(45), pp. 67–85, doi: 10.3221/igf-esis.45.06. [46] gomes, g., delgado neto, a.m., wrobel, l.c. (2016). modelling and 2d cracks view using dual boundary integral equation. xxxcii iberian latin american congress on computational methods in engineering cilamce, brasília-df. [47] gomes, g., oliveira, t.a.a., delgado neto, a.m. (2019). bemcracker2d: a software package for two-dimensional fatigue crackgrowth analysis. xl ibero-latin-american congress on computational methods in engineering cilamce, natal-rn. [48] oliveira, t.a.a., gomes, g., evangelista jr, f., delgado neto, a.m. (2018). multiscale analysis of multiple cracks in aircraft fuselage. xxxix ibero-latin american congress on computational methods in engineering, university of technology compiégne. [49] brebbia, c.a. (1978). the boundary element method for engineers., london/new york: pentech press/halstead press. [50] wrobel, l.c., aliabadi, m.h. (2002). the boundary element method, 2: applications in solids and structures, wiley. [51] pavliots g. a., stuart a. (2008). multiscale methods, vol. 53, new york, ny, springer new york. [52] ranganathan, s.i., ostoja-starzewski, m. (2009). towards scaling laws in random polycrystals, int. j. eng. sci., 47(11–12), pp. 1322–1330, doi: 10.1016/j.ijengsci.2009.05.003. [53] song, w., krishnaswamy, v., pucha, r. v. (2016). computational homogenization in rve models with material periodic conditions for cnt polymer composites, compos. struct., 137, pp. 9–17, doi: 10.1016/j.compstruct.2015.11.013. g. gomes et alii, frattura ed integrità strutturale, 58 (2021) 211-230; doi: 10.3221/igf-esis.58.16 230 [54] zabihyan, r., mergheim, j., javili, a., steinmann, p. (2018). aspects of computational homogenization in magneto-mechanics: boundary conditions, rve size and microstructure composition, int. j. solids struct., 130– 131, pp. 105–21, doi: 10.1016/j.ijsolstr.2017.10.009. [55] zhu, f.-y., jeong, s., lim, h.j., yun, g.j. (2018). probabilistic multiscale modeling of 3d randomly oriented and aligned wavy cnt nanocomposites and rve size determination, compos. struct., 195, pp. 265–275, doi: 10.1016/j.compstruct.2018.04.060. [56] carniel, t.a., klahr, b., fancello, e.a. (2019). on multiscale boundary conditions in the computational homogenization of an rve of tendon fascicles, j. mech. behav. biomed. mater., 91, pp. 131–138, doi: 10.1016/j.jmbbm.2018.12.003. [57] johnson, k.l. (1985). contact mechanics, cambridge university press. microsoft word numero_34_art_56 k. nowak, frattura ed integrità strutturale, 34 (2015) 507-514; doi: 10.3221/igf-esis.34.56 507 focussed on crack paths paths of interactive cracks in creep conditions k. nowak cracow university of technology, faculty of civil engineering, institute of structural mechanics, ul. warszawska 24, 31-155 krakow, poland kn@limba.wil.pk.edu.pl abstract. the paper contains plane strain analysis of uniformly stretched plate working in creep condition. the plate contains initial defects in forms of central and/or edge cracks working in mode i. these cracks are modelled by attributing critical value of damage parameter to preset points and therefore resulting in stresses set to zero (material does not support any loading). the continuum damage mechanics constitutive equations are used to describe the creep crack growth problem and finite element method abaqus system is applied to solve corresponding boundary and initial value problem. analysis of different initial cracks configuration has been performed. the crack path is defined by points in which damage parameter equals to critical one. time to failure of the plate with single initial crack is achieved when the crack path spans its width. this time is calculated and compared to the time to failure of initially uncracked structure. for the plate with multiple cracks the paths starting from different cracks can develop independently until they merge and/or span the plate width. in each case the damage field is analysed and the direction of crack path development is determined. the analysis of crack propagation allows for determination of a distance between initial cracks for which the interaction between them is negligible. it is demonstrated that continuum damage mechanics approach allows not only to model the development of initially existing cracks but also initiation of new, cross-spanning cracks and their kinking and branching. keywords. creep damage; crack paths; cracks interaction; integrity assessment. introduction valuation of remaining life time of a structure working in creep condition is important engineering problem. it is especially crucial if some initial flaws exist what may influence the cracks and their pattern development causing premature failure of the structure. for the structure working in elastic regime, the flaws can be modelled by the cracks and the structure can be analysed by linear fracture mechanics (lfm) tools. each single crack can be modelled independently and critical length of it can be evaluated. much more complicated is the problem of cracks interaction. if distance between neighbouring cracks is comparable with the length of the cracks, they should be analysed together. this problem was analysed by many authors (e.g. [4, 5, 6, 9, 10, 12]). in frame of lfm the interaction is expressed in terms of stress intensity factor (sif). the cracks interaction can cause amplification of sif or its decreasing. the former effect occurs mainly for coplanar cracks, the latter for parallel cracks due to shielding effect. in both cases the interacting cracks can be replaced by single substitute crack which size depends on dimensions and relative position of original cracks (cf. e.g. [10]). e k. nowak, frattura ed integrità strutturale, 34 (2015) 34 (2015) 507-514; doi: 10.3221/igf-esis.34.56 508 if the structure works at elevated temperature, that is in creep conditions, the analysis using sif is limited to a few cases. it can be applied if the stress redistribution from elastic state to steady creep state is small. for steady state creep condition the c*-integral (analogous to j-integral) can be used (cf. e.g. [14, 15, 17]). thanks to this parameter different configurations of cracks can be compared and parameters of single equivalent crack can be determined. but in this method the steady state stress field is considered as constant and the stress redistribution due to damage development is not taken into account. another method is that by means of continuum damage mechanics. it allows for tracing stress and damage history, and to determine the most probable crack development. this methodology was successfully applied to creep growth of single crack by [7, 13] and is used by authors in this paper to determine the paths of interacting multiple cracks in creep conditions. creep versus elastic safety of structures or perfect elastic structures its loading capacity can be evaluated basing on two limit cases: ultimate strength for uncracked members or critical load to propagate existing defects. the first one is standard procedure for newly projected structure, the second one for structures which contain one or multiple cracks. in creep conditions, however, which has to be taken into account when structures is expected to work in a severe environmental conditions (e.g. high temperature or chemically aggressive media), the concept of critical loading must be replaced by the notion of critical time to failure. the latter is an effect of material structure deterioration which occurs at any level of mechanical load. this is similar to the effect of sloping of both part of wöhler diagrams and fatigue limit absence in high temperature applications. in the case of appearance of multiple linear defects (cracks) a new approach has to be developed because of interaction between individual cracks. in elasticity it requires solving a troublesome individual bvp (boundary value problem) for each initial crack configuration. this procedure can be neglected when cracks interaction is weak, and critical load can be calculated basing on the sif value for most dangerous crack. the assumption of nonexistence of cracks interaction can not hold in creep conditions. the material deterioration will grow for any load, even for initially flawless structures, causing the slowly movement of cracks which will always grow albeit not necessarily dangerous and may coalescence with catastrophic result. in the present paper the methodology of dealing with such a situation will be developed and illustrated by an simple example of a plane rectangular specimen subjected to uniaxial tension with two symmetric edge cracks and/or a central one. constitutive equations used and numerical methodology nalytical modelling of material deterioration in creep conditions became possible due to l.m. kachanov works initiated in late 50-ties of last century [8]. when damage is coupled with stress-strain rate equation (cf. [2]) it yields a set of differential nonlinear equations: 1 c ij ijkl kl ijd     , (1a) 1 nc ij eff eff ijt                , (1b)  max 1 1 1 eff a t                 , (1c) where ij , c ij are total and creep strain tensors, ij is stress tensor, dijkl is elastic constants matrix,  , n, a, ,  are steady-state creep and damage material constants, max, eff main positive principal stress and huber-mises effective stress,  scalar damage parameter (0  1), t time. this approach has been used in several investigations [1, 2, 3] and presented also at the series of conferences “crack paths”. the picture below demonstrates effectiveness of this approach used in analysis of crack paths in 3d bending plates [3]: f a k. nowak, frattura ed integrità strutturale, 34 (2015) 507-514; doi: 10.3221/igf-esis.34.56 509 (a) (b) figure 1: crack patterns on upper (a) and lower (b) surfaces of a 3d plate without initial damage. the above methodology allows for evaluation all three characteristic stages of damage growth terminated by: t1 time when first failure occurs in a point, t2 time when failure occurs across of structures characteristic length, t3 time when the cracks system makes structure unstable. it is worthwhile to notice the ‘kachanov paradox’, which follows his approach, that for uniform stress distribution (uniaxial tension) the damage in all points grows simultaneously causing the specimen to ”evaporate” at time t1 = t2 = t3! this is not the case when stress field in a structure is non-homogeneous one like in plates, for example and which is particularly strong in the case of initial discontinuities (cracks) existing in a structure. because of its nonlinearity and complexity the problems considered below will be solved by means of numerical analysis. time integration of eq. (1) is done by euler explicit method. plane strain fourand three-node solid elements are used. a diversification of a fe mesh has been made in damage affected zones. the numerical solution of the problem is very strong mesh depended (cf. e.g. [14]), so the results can be considered as qualitative ones. the initial cracks are defined as the set of gauss integration points in which initial value of damage parameter ω=1 (failure in a point). specimen geometry, loading and material characteristics rectangular plate of dimensions shown in fig. 2a is subjected to uniformly distributed loading q on its end edges. the plane strain condition is assumed and the problem is solved as 2d one, the times t2 and t3 are equal. the following configurations of initial crack will be considered: two symmetric edge cracks (fig. 2b), two symmetric central cracks (fig. 2c), and combination of two previous configurations (fig. 2d), where the distance denoted as h will be used as a problem free parameter. only quarter part (right upper) of the plate is modelled due to symmetry. unlikely to elastic considerations, for creep conditions an interaction between multiple cracks will always exists as damage field extends over the whole structure. the critical distance will be sought for which the interaction of edge and central cracks can be neglected (it is when they will span plate width independently). it is necessary to emphasise that this critical distance has to be understood as that corresponding to the situation when cracks which span specimen edges at time t2 will be different form cases 2c and 2d by a small, arbitrarily defined amount. the material parameters used for simulation was that of type 316 stainless steel at 650°c according to [11]: e=0.144·106mpa, ν=0.314, =2.13·10-13(mpa)-n h-1, n=3.5, a=3.42·10-9(mpa)-μ h-1, =2.8, =1.0. the loading was assumed to be 50 mpa and is kept constant for all experiments. for the structure shown in fig. 2b the length of initial edge crack is assumed to be le=15 mm. sif for this crack and assumed loading is 12.3 mpam0.5. this value is about one order less than critical value of sif, so the structure is safe in elastic conditions. for the structure shown in fig. 2c the length of initial central cracks are assumed to yield the same critical elastic load as in the case of central crack and equals to 18 mm (sif is equal to 12.3 mpam0.5, too). for the initially non-cracked structure (fig. 2a) the time to failure can be calculated independent of deformation since the stress σx (the only nonzerocomponent of stress matrix) is from equilibrium equal to loading q. simple integration of the eq. (1c) in uniaxial stress state with initial condition ω=0 and failure at ω=1 yields: 0 1 5115 h ( 1) t aq     . (2) a k. nowak, frattura ed integrità strutturale, 34 (2015) 34 (2015) 507-514; doi: 10.3221/igf-esis.34.56 510 (a) (b) (c) (d) figure 2: initial uncracked structure (a), structure with edges cracks (b), with central cracks (c) and with both cracks types (d). dimensions are in millimetres. due to symmetry the calculations are performed in the greyish quadrant of the plate. analysis of a plate with single initial crack edge crack or the structure with edge crack (fig. 2b) the time of first failure occurrence is found to be t1e=99.1h. then the crack develops due to damage growth and finally spans the width of the plate in time t2e=795h. as the damage is driven by the maximum principal stress (=1.0) the path of the crack is straight. the rate of the crack growth at the beginning is equal to 1.84e-5m/h and it is increasing as the crack becomes longer. when the crack length achieves its critical value in creep condition the rate of the growth becomes relatively high and is equal to 1.22e-2m/h (marked in fig. 3 by a red point). the critical length of the crack at this instant is close to 68mm. 0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0 200 400 600 800t [h] lo c u s o f th e c ra c k t ip [ m ] figure 3: development in time of the edge crack. small variations of the curve shown in fig. 3 is because the crack growth rate is subjected to small fluctuations as the constitutive model consists of two parts, elastic and creep ones. the elastic stress is very high at crack tip and due to relaxation this high value is decreasing in time. simultaneously the damage is developing, the crack tip changes its position and new elastic stress is raised. f k. nowak, frattura ed integrità strutturale, 34 (2015) 507-514; doi: 10.3221/igf-esis.34.56 511 single central crack the next structure analysed is that with a single central crack (parameter h=0 in fig. 2c). the time of first damage occurrence and ultimate time to failure are: t1c=94.1 h and t2c=715 h. the differences to the previous case are very small 5% and 10% respectively. the critical length of the crack is 67mm, so it is also very close to critical length of edge crack. plate with two central cracks he structure with two central cracks (fig. 2c) exhibits the presence of shielding effect. in elastic regime for infinite plate the sif is going to sif of single crack when h is going to infinity (c.f. e.g. [9, 16]); for smaller value of h the structure becomes more safe due to shielding. the analysed values of parameter h are from 1 to 25mm with step 1mm for h<5mm, and 5mm for larger h. the cracks in first two cases (h=1mm and h=2mm) are joining together producing single central crack (see fig. 4). the structure becomes unstable due to cutting off the central part. obtained times to failure are of the order of time to failure of single central crack t2c (see fig. 5). the intermediate cases (h from 3 to 15mm) produce straight cracks and greater times to failure (about 800h). for the larger distance (h>15mm) the times to failure are smaller and do not differ much from the time to failure of single central crack t2c. so the shielding effect is the most pronounced for h in its medium range. for larger distance the long term behaviour is similar to behaviour of single crack so crack interaction can be dealt as negligible. slightly different situation is for time of first failure occurrence t1 (see fig. 6). except the case h=0mm the time t1 monotonically decreases with growing h. this situation corresponds to growing sif in elastic regime as the time t1 depends partly on elastic stress distribution in contrast to the time t2. the critical length of crack, defined as the length of crack with rate growth going to infinity, is almost constant and is equal to about 67mm (see fig. 7). figure 4: damage distribution close to final failure for the quarter central part of the plate for central crack h=1mm. 0 200 400 600 800 1000 1200 0 5 10 15 20 25h [mm] t2 [ h ] edge central multiple 0 20 40 60 80 100 120 0 5 10 15 20 25h [mm] t1 [ h ] edge central multiple figure 5: time to failure. figure 6. time to first failure occurrence. t k. nowak, frattura ed integrità strutturale, 34 (2015) 34 (2015) 507-514; doi: 10.3221/igf-esis.34.56 512 plate with multiple initial cracks he multiple crack configuration consists of two edge cracks and two central ones (see fig. 2d). the numerical analysis is performed for values of h parameter from 0 to 25mm. the crack paths for all examined configurations are shown in fig. 8. it can be noticed that for small values of distance h, the crack remains straight until the central and edge cracks meet together, and kink to join. for larger values of h, the cracks are bypassing each other, but damage field develops in area between cracks, causing them to join together. in some situations a new crack arises, transverse to main ones. for large values of h the central crack keeps developing in its main direction, as the edge crack stops its straightforward growth and becomes the transversal crack. the area behind the central crack is not stretched and value of damage parameter is close to 0, all the time. the interactions of both cracks is always visible in all examined configurations (also for time t1). so the distance h of not interacting cracks should be greater than 25 mm. this is in contradiction to commonly used ‘rule of thumb’ in elastic conditions, that for distance greater than crack length (18 mm) the interaction of cracks is negligible. 0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0 5 10 15 20 25h [mm] lc ri t [m ] edge central multiple central multiple edge figure 7. critical length of cracks. figure 8. crack paths for multiple cracks configurations. red are initial cracks, dark grey crack at time to failure, light grey crack opening area. comparison of times to failure (fig. 5) for cases 2c and 2d shows that the edge crack in all configurations shortens significantly the specimen life (except the h=1 and 2 mm cases, but here another failure mechanism determines the time t2 for central crack configuration). the reduction in time is close to 60%. it is much larger than reduction of time t1 which is up to 20% (fig. 6). it can be concluded that the evolution of damage field in time multiplies the effect of cracks interaction. t k. nowak, frattura ed integrità strutturale, 34 (2015) 507-514; doi: 10.3221/igf-esis.34.56 513 analysis of critical lengths of cracks (fig. 7) shows that the final crack growth acceleration for small values of h is only when the cracks meet together the calculated critical length is close to half of the plate width. for larger values of h this length is not constant. therefore, it is difficult to propose any formula for equivalent length. thus in time dependent analysis and for multiple crack configurations the failure criterion based on critical length of the crack is meaningless. final remarks he solutions obtained demonstrate ability of adopted methodology to show creep crack paths in the case of existence of interactive initial cracks. different cracks behaviour like its merging, kinking and branching become possible. the next step one should consider influence of geometry of structure (width and length of a specimen under tension) as well as the length of initial cracks making this analysis useful in engineering practice. references [1] bodnar, a., chrzanowski, m., on creep rupture of rectangular plates, zeitschrift für angewandte mathematik und mechanik, 82 (2002) 201-205. doi: 10.1002/1521-4001(200203)82:3<201::aid-zamm201>3.0.co;2-g [2] bodnar, a., chrzanowski, m., nowak, k., brittle failure lines in creeping plates, int. j. pres. ves. & piping, 66 (1996) 253-261. doi: 10.1016/0308-0161(95)00100-x [3] bodnar, a., chrzanowski, m., nowak, k., latus, p., influence of small variations of initial defects upon crack paths in creeping plates – continuum damage mechanics description, eng. fract. mech., 75 (2008) 526-533. doi: 10.1016/j.engfracmech.2007.01.014 [4] carpinteri, a., brighenti, r., vantadori, s., a numerical analysis on the interaction of twin coplanar flaws, eng. fract. mech., 71 (2004) 485-499. doi: 10.1016/s0013-7944(03)00040-7 [5] daud, r., ariffin, a.k., abdullah, s. et al., mathematical model of elastic crack interaction and two-dimensional finite element analysis based on griffith energy release rate, advanced materials research, 795 (2013) 587-590. doi: 10.4028/www.scientific.net/amr.795.587 [6] gope, p.c., bisht, n., singh, v.k., influence of crack offset distance on interaction of multiple collinear and offset edge cracks in a rectangular plate, theor. and applied fracture mechanics, 70 (2014) 19-29. [7] hayhurst, d.r., brown, p.r., morrison, c.j., the role of continuum damage in creep crack growth, phil. trans. r. soc. lond. a, 311 (1984) 131-158. [8] kachanov l.m., on the time of the rupture in creep conditions (in russian), izv. akad. nauk. ssr, 8 (1958) 26-31. [9] kachanov m., a simple technique of stress analysis in elastic solids with many cracks, int. j. fract., 28 (1985) r11r19. [10] kamaya m., growth evaluation of multiple interacting surface cracks. part ii: growth evaluation of parallel cracks, eng. fract. mech., 75 (2008) 1350-1366. [11] mizuno m., murakami s., analysis of creep crack growth under neutron irradiation, in: m. jono t. inoue (eds.), mechanical behavior of materials vi, 3, pergamon press, oxford, (1991) 853-858. [12] moussa w.a., bell r., tan c.l., the interaction of two parallel non-coplanar identical surface cracks under tension and bending, int. j. pres. ves. & piping, 76 (1999) 135-145. [13] murakami s., hirano t., liu y., asymptotic fields of stress and damage of a mode i creep crack in steady-state growth, int. j. sol. struct., 37 (2000) 6203–6220. [14] murakami s., liu y., mizuno m., computational methods for creep fracture analysys by damage mechanics, comput. methods appl. mech. engng, 183 (2000) 15-33. doi: 10.1016/s0045-7825(99)00209-1 [15] si, j., xuan, f. z., tu s. t., creep crack interaction of high temperature structure with multiple cracks, key engineering materials, 327-325 (2006) 105-108. doi: 10.4028/www.scientific.net/kem.324-325.105 [16] tada, h., paris, p.c., irwin, g.r., the stress analysis of cracks handbook, asme press, (2000). [17] xuan, f. z., si, j., tu, s. t., evaluation of c* integral for interacting cracks in plates under tension, eng. fract. mech., 76 (2009) 2192-2201. doi: 10.1016/j.engfracmech.2009.06.012 t microsoft word numero_58_art_25_3188.docx s. çalışkan et al.ii, frattura ed integrità strutturale, 25 (2021) 344-364; doi: 10.3221/igf-esis.58.25 344 determining the endurance limit of aisi 4340 steels in terms of different statistical approaches salim çalışkan, rıza gürbüz department of metallurgical and materials engineering, middle east technical university, 06800 ankara, turkey caliskan.salim@metu.edu.tr, https://orcid.org/0000-0002-9276-8492 rgurbuz@metu.edu.tr, https://orcid.org/0000-0002-8369-4639 abstract. in engineering applications, fatigue phenomenon is a key issue and needs to be analyzed in the beginning of design phase in case of any component exposed to alternating loading on operation otherwise catastrophic fatigue failure may cause. component can be designed with safelife, fail-safe, and damage tolerant approach based on whether redundant load path and damage sensitive. before starting analyzing the structure, material allowable data needs to be presented in a reliable way to predict fatigue life of components. sn curves with presented confidence levels are the robust approach to make a prediction on safe life of a structure in terms of fatigue. in this point, there are so many approaches to determine fatigue limit of materials and issue shall be handled by statistical manner. in literature, different staircase and curve fitting methods were presented to estimate endurance limit of materials and some reliability manuscript published. in this paper, fatigue limit of aisi 4340 steel will be investigated through most convinced staircase and curve fitting approaches and their reliability will be queried. keywords. steels; fatigue; staircase; curve fitting; reliability citation: çalışkan, s., gürbüz, r., determining the endurance limit of aisi 4340 steels in terms of different statistical approaches, frattura ed integrità strutturale, 58 (2021) 344-364. received: 14.07.2021 accepted: 13.09.2021 published: 01.10.2021 copyright: © 2021 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. introduction n curves have been firstly used by german engineer, wöhler and stress-life was formulated in linear equation; hereby, logarithm of life is correlated with oscillating stress [1]. then, basquin proposed new model by using each side natural logarithm of stress and life [2]. however, addition of initial boundary data point (ultimate stress) to sn curve resulted in poor estimation. so, non-linear model was presented by stromeyer by smoothing previous models [3]. to enhance best fit of sn curve, researchers continued to propose new models basically same approach stated above by adding parameters or changing complexity of the relation. some of them are accepted as common standard in constructing of sn curves. in the literature, many approaches have been presented best fit of data with large number of specimens however inconsistency results in case of small specimen data sets [4]. even though new technologies enable performing fatigue tests with ultras https://youtu.be/4m7k2bvbcns s. çalışkan et al.ii, frattura ed integrità strutturale, 25 (2021) 344-364; doi: 10.3221/igf-esis.58.25 345 high-test frequency on resonant test systems these days, sn curve models need to be compatible with small data sets due to time limitation for uhcf [5]. fatigue failure caused by surface feature is attributed to crack initiation; on the other hand, crack propagation is because of bulk characteristic of material. therefore, crack is easily formed at high stress values and resulted as less scatter; however, large scatter is observed around fatigue limit because of local circumstances in the reverse condition [6]. although coupon level testing provides information about scatter, it can be difficult to predict in service conditions. sn curves are affected by grain size and direction of grains, composition of material, surface finish after machining and heat treatment [7]. therefore, scatter caused by variation in material and production-based reasons cannot be overestimated for products in service and needs to be verified by component level testing. it is commonly used method to perform tests at least twice covering operation life in service in order to observe critical locations in terms of crack susceptibility. in literature, scatter effect is covered by confidence levels by statistical approaches [8]. unless specified sn curves in the literature presented as mean curve with 50% quantile. designers use 95% confidence level to be sure safe fatigue limit and 95% meets their requirements [9]. design curves are commonly obtained by curve fitting methods based on log-normal or weibull distribution. sn curve fitting can be evaluated simply through two parameters because of not dealing with complexity and it offers well suited and results are adequately accurate [10]. fatigue data of metallic materials exhibit log-normal or weibull distribution based on analytic equations with certain inconsistency; therefore, all approaches need to verify by fatigue testing to get reliable data [11]. even though fatigue strength exhibits normal distribution extensively, coefficient of variance in fatigue limit reflects lognormal distribution and scatter is greater than initiation dominant life region compared to propagation one that is under high stress loading. previous one is well fitted with weibull distribution and latter is exhibited by log-normal distribution. standard deviation changes with applied stress; accordingly, decreasing stress or strain results in increasing standard deviation. maximum likelihood method covers run-out data points by linear regression to estimate observed data. least square estimation is a method that minimizes the residuals (sum of squared deviation) of experimental data. for smooth specimen run-out criteria can be chosen as 2e+06 cycles because of not existing stress concentration [12]. barbosa et al. studied different estimated fatigue models to exhibit good adjustment between observed and fitted data. difference of this models is to provide best fit from ultra-low cycles to high cycles; however, medium and high cycle region is the focus for design issue for a structure. schijve et al. investigated fatigue limits statistical point of view and resulted in weibull is better suited than log-normal distribution. another approach is proposed by stüssi and non-linear equation is formulated with stress and life relation taking ultimate and infinite endurance stress into formulation. by linear regression, model parameters can be estimated however combined stüssi and weibull distribution approach which is proposed by caiza et al. results in good fit in all regions of sn curve due to better estimation of model parameter [13]. burhan et al. also investigated different curve fitting methods for fatigue data characterization in terms of competence of sn curve, estimation of fitting parameter consistency, adjustment to other stress ratios, presented as fatigue damage estimation and curve shape ability covering ultimate stress point. kim et al. found that micro-crack density scales up logarithmically with fatigue cycles increases rather than micro-crack length [14]. differently, lipski et al. studied constructing sn curve based on thermography analysis and provides an advantage to stop test before catastrophic failure based on temperature change [15]. astm e739-91 proposes simple linear relation between stress and life in log scale. model uses log-normal distribution and it can be solved by linear regression based on maximum likelihood approach. it also gives information about how many specimens are needed to get reliable data. accordingly, recommended data set shall be between 12-24 specimens. as a guideline, confidence level shall be 5% and 95% to estimate confidence band that covers observed experimental data. because of limitation of model, very low cycle regions are out of consideration and therefore astm e739-91 model is suitable for medium and high cycle fatigue regions. according to dixon, the idea behind of staircase is based on concentrating of data points around mean value. sample size needs to be large enough accordingly dixon suggested at least 40 specimens are required for accurate data evaluation. increment range shall be between 0.5σ and 2σ for good estimation if standard deviation is known; otherwise, small interval results in spending time unless starting point close to mean value [16]. this approach is modified by dixon and proposed that increment step can be estimated as σ and maximum 50% error of standard deviation can be tolerated. therefore, increment step may be 2/3σ and 3/2σ for likely guess since small interval produces smaller covariance in case of given mean value previously; however, large step size results in decreased number of trials around mean value [17]. even though it is recommended to make analysis through 15 specimens by staircase method, test set is generally managed by 6 specimens many discussions are available to estimate fatigue limit of material with less number by preserving reliability of data [18]. fatigue limit of material generally follows normal distribution. in engineering applications, it also exhibits log-normal distribution. primary condition of staircase method is to estimate by normal distribution; however, safety factor needs to be evaluated through log-normal distribution to prevent oversizing. s. çalışkan et al.ii, frattura ed integrità strutturale, 25 (2021) 344-364; doi: 10.3221/igf-esis.58.25 346 according to zheng’s study, intermediate and long-life regions of sn curve follow normal and log-normal distribution respectively. rabb studied whether starting point has effect on staircase method or not and resulted as little influence. the most popular approach is starting with estimated fatigue limit to increase accuracy of analysis. in case logarithmic stress values are equally spaced, the log-normal and weibull distribution can be used as an analyzing of staircase method. to estimate mean value and confidence level of fatigue data, choosing increment level between 2/3σ and 3/2σ provides well-established analysis [19]. basically, it can be assumed that there exists threshold above fatigue limit and facilitates crack initiation under applying higher stress than endurance limit [20]. reduction of fatigue limit requires knowledge of mean strength and standard error. although fatigue strength is insensitive to increment size, standard deviation is affected markedly. the value of coefficient of variation is a key parameter for fatigue limit analysis since almost similar results rise for low values of cov but not satisfactory results for high values therefore dixon-mood is the best option in this case [21]. lin at al studied that method used to determine endurance limit can be chosen based on covariance of data; in case of small covariance ray projected method (extrapolating through low cycles data) gives better result but dixon-mood method (based on maximum likelihood estimate) is advised for large covariance. however, projection method is not reliable below 104 cycles therefore stress level is critical for accelerated analyses. even though most popular approach is maximum likelihood estimate for staircase method, wallin justify this approach because scatter exhibits weibull distribution not normal distribution which is underlying assumption for mle. monte carlo method is proposed by iterating of data points in terms of arithmetical operation [22]. similarly, pollak et al. used bootstrapping method to decrease standard error for small sample data sets as an alternative to dixon-mood method since latter method gives accurate results in case of large specimens (at least 40 specimens) however underestimated results with small data sets. bootstrap is an alternative method by counting standard deviation and confidence level around the mean value. the advantage is no need to use distribution hypothesis like classical methods nevertheless it presents same results and data points develop with replacing data points through replication [23]. as different approach, fatigue strength of material is governed by inhomogeneous distribution of different types of defects. it has proved that non-propagating cracks ahead of micro-notches exist below the stress level of endurance limit. based on murakami and endo assumption, analysis for fatigue limit gave similar results for annealed condition steel; however, it will be different for hardened steel because of non-metallic inclusions effect. beretta et al. studied fatigue properties in terms of statistical manner and minimum number of defects inside microstructure and resulted as maximum likelihood is the best estimator because of having less standard deviation of excessive defects [24]. experimental procedure isi 4340 steel with a composition (in wt%) of .38% c, .65%mn, .7% cr, 1.65% ni, .2% mo, .025% p and s, bal. fe, was chosen as a research material because it exhibits a constant endurance limit after a certain fatigue life. additionally, it shows high fatigue strength and toughness therefore it is considered as a good candidate for aircraft material. a set of smooth round fatigue specimens with 22 mm gage diameter and 130 mm length was manufactured from aisi 4340 steel with optimum machining parameters. before specimen preparation, material was heat treated per ams 2759-1d for optimum condition for machining. firstly, material was normalized at 899 °c for 90 minutes then austenitized at 816°c for 60 minutes and finally tempered at 593°c for 3 hours. normalizing removed internal stress and provided microstructural homogeneity. austenitizing and tempered provided desired microstructure in terms of strength and hardness. after quenching, martensite phase forms because of not allowing enough time for diffusion of carbon atoms because of rapid cooling and resulting bct crystal structure. later, tempering results in bainite (intermediate phase) and ferrite phases in the microstructure by allowing transformation of martensite to bainite phase. as a result, crystal structure is composed of bcc after this transformation. the microstructure of material is given on fig. 1. mechanical properties of material results in 1080 mpa ultimate strength and 29 hrc hardness after heat treatment process. a total of 14 specimens were used to determine endurance limit of material. all of them were out from rolling directionr90 orientation. crack initiation was observed in r90-transverse plane which is perpendicular to applied stress along rolling direction. in this research, sn curves were constructed by using different methods providing data points for finite and infinite life regions. entirely 14 specimens were sequentially tested, 8 of them were assigned for establishing endurance limit of material with applying less stress range and 6 of them were used to focus on finite fatigue region. fatigue tests were performed under constant amplitude cyclic loading in laboratory conditions (23±2°c and 50±5 rh) per astm e466-96. round fatigue specimens were alternately axial loaded by applying sinusoidal wave form with stress ratio r of 0.1 (tension-tension) under constant 150 hz test frequency on rumul resonant test system. a s. çalışkan et al.ii, frattura ed integrità strutturale, 25 (2021) 344-364; doi: 10.3221/igf-esis.58.25 347 figure 1: micrograph of aisi 4340 steel staircase analysis staircase or up-and-down method is commonly used method for determining fatigue limit of material at a specified life value. accordingly, run-out criterion is firstly stated (say 107cycles) and first specimen is roughly tested around mean value then if the specimen failed at this stress level. next specimen will be tested at less stress level with defined stress increment otherwise, stress level increased in case of run-out case. hence, applied stress for next specimen depends on foregoing test results. stress increment is determined based on standard deviation and rest of the specimens are tested in this manner. dixon-mood method dixon-mood method derived from maximum likelihood theory is a common approach to determine endurance limit of materials. tests are carried out by increasing or decreasing stress level with defined increment based on standard deviation and generated the sequence also called up-down method. the purpose is to focus around median value to determine accurate fatigue strength with defined confidence levels. sample mean and standard deviation can be estimated by given equations:         0 1 2 a s s d f when less periodic event becomes failures (1)         0 1 2 a s s d f when less periodic event becomes run-outs (2)           2 2 1.62 0.029 f b a s d f n case of    2 2 0.3 b f a f (3)  0.53  s d . in case of    2 2 0.3 b f a f (4) where s0 is the lowest stress level of dataset, d is the stress increment, f=∑fi, a=∑i·fi, b=∑i2·fi, i is the numbering of stress level and fi is the number of samples corresponding to the stress level. if estimated stress increment is extremely higher than standard deviation; then sample mean will be higher than reality and standard deviation will be less. in case of reverse condition, higher standard error and lower sample mean will be obtained. it was expected to choose stress increment around 2/3σ and 3/2σ before starting test. sample mean with 50% confidence level and standard deviation for dixon-mood method can be computed as 585 mpa and 23.21 mpa based on equations given above and variables can be seen on fig. 2. mean value needs to be defined with confidence interval since every set of test specimen will give different mean values because of scatter and confidence interval for sample mean will provide to present conservative data for endurance limit. it can be used that 95% confidence interval for sample mean to stay safe side meaning that 95% of test results will be upwards of mean value. confidence interval with unknown coefficient of variance is distributed per t-distribution meaning that defined confidence interval ((1-α) · 100%) is symmetric around empirical sample mean and underside boundary can be expressed as given equation below:      % , 1x n s s s t n . (5) s. çalışkan et al.ii, frattura ed integrità strutturale, 25 (2021) 344-364; doi: 10.3221/igf-esis.58.25 348 figure 2: staircase sequence per dixon-mood method in this way, limits of probability of failure are taken into consideration with reduced endurance limit. accordingly, mean value with 95% confidence interval can be calculated as 563.8 mpa. similarly, confidence interval for standard deviation needs to be calculated to validate standard deviation below the upper limit of empirical standard deviation coming from fatigue test data with defined confidence level. it obeys chi-square right tailed probability of distribution and it is calculated by given equation:     % 2 , 1 1 x n n s s (6) eventually, standard deviation with 95% confidence interval is found to be 56.92 mpa as shown in fig. 3. this value will be used to determine endurance limit of material as the limits for probability of failure taking place. figure 3: mean value for 50% probability of failure and 95% confidence level with given standard deviations. iabg method another approach for staircase method is iabg method proposed by hück [26]. accordingly, it is like dixon-mood method in terms of evaluation of data. iabg method starts with second test specimens’ data and first one is discarded and not evaluated rather fictitious data is added at the end of data set as shown in fig. 4. additionally, evaluation cover all failed and survived specimens on specified stress range and based on logarithmic values of data. same data above will be evaluated in same manner with given equations presented by iabg method [27].      0log log( ) log a s s d f (7) s. çalışkan et al.ii, frattura ed integrità strutturale, 25 (2021) 344-364; doi: 10.3221/igf-esis.58.25 349       2 2 *  0 5   f b a f elsek .    2 2   f b a f 0.5;   0.889521  4.579494a f ;   0.4052297.235548b f (8)       log log log 10a bs d k (9) hereby, s and s are the mean value and standard deviation of data set respectively, d is stress increment on logarithmic base and k, a and b are the auxiliary variables. figure 4: staircase sequence per iabg method (δ: fictitious data). mean value with 50% confidence level and standard deviation for iabg method can be computed as 585.11 mpa and 14.54 mpa, respectively based on equations specified above and logarithmically shown in fig. 5. figure 5: mean value and standard deviation with given 95% confidence level based on iabg method. bootstrapping method another approach is bootstrapping method introduced by efron [28] which is based on data simulation providing many unreal data in other words re-sampling from original data. standard deviation of random distribution of a population is perpetually indeterminate; therefore, most popular approach is to use estimated standard error and correlating standard deviation. since bootstrapping covers all present information about the distribution, it could be a good choice to estimate standard error of data set. samples are normally distributed as shown in fig. 6. the idea behind of approach is to decrease scatter by allowing less biased standard error. s. çalışkan et al.ii, frattura ed integrità strutturale, 25 (2021) 344-364; doi: 10.3221/igf-esis.58.25 350 figure 6: normal distribution of staircase data based on bootstrapping method. standard error estimation of re-sample distribution for bootstrapping method is originated by monte-carlo approach. approximating population with larger sample size is advanced at least 200 times re-sampling from original data [28]. during analysis, 200 times original data was re-sampled and only 10 of them can be seen on tab. 1. b x(1) x(2) x(3) x(4) x(5) x(6) x(7) x(8) x* 1 580 580 600 580 580 580 600 600 587.5 2 580 620 600 620 600 560 600 580 595 3 580 580 560 620 580 620 560 620 590 4 560 560 580 580 560 560 580 560 567.5 5 560 600 600 580 560 580 580 560 577.5 6 560 560 600 560 560 560 560 560 565 7 580 580 580 600 560 560 580 580 577.5 8 600 580 620 580 560 620 600 600 595 9 620 560 600 600 600 560 600 600 592.5 10 580 600 580 620 580 620 560 560 587.5 table 1: bootstrapping algorithm. mean value and estimated standard deviation of bootstrap replications can be seen from following equations:    b * i i 1 1 x x b (10)           1 22* 1 1 1 b i i s x x b (11) similarly, standard deviation of monte carlo approximation based on bootstrapping replications can be calculated by following equation:      2 1 s n n (12) standard deviation of 200 means is the bootstrapped standard error of the mean. mean value can be calculated as 585.11 and estimated standard deviation is 7.09 after bootstrapping analysis in fig. 7. standard deviation based on monte carlo approximation is 9.19 which is close to bootstrapping method. by using bootstrapping re-sampling, confidence intervals s. çalışkan et al.ii, frattura ed integrità strutturale, 25 (2021) 344-364; doi: 10.3221/igf-esis.58.25 351 could be established for given population. bootstrap t-interval and standard confidence interval (1-α) can be found with given equations, respectively:      , 1 x lower n x t s . (13)   /2x  * lowerx z s (14) figure 7: mean curve (solid line) along with 95% bootstrap t-interval (dash line) and standard (long dash dot) lower confidence limit weibull method function of random variable with unknown parameter can be associated with fatigue data. weibull distribution facilitates estimating low probability of failures compared to normal distribution and fatigue limit can also be obtained by 2-parameter weibull distribution (location parameter not used). most popular optimizing technique to estimate scale (α) and shape (β, weibull slope) parameters is maximum likelihood estimator by correlating variables with most likely observed data. all of data (failed and runout) can be evaluated during analysis and not necessarily to specify constant stress increment for mle method. therefore, the advance of mle is treating censored data correctly with any distribution. maximized likelihood function for staircase tests is given in eqn. 15.               1 1 , . 1 , n m i j i j l f s p f s p (15) where n and m are failed and run-out specimens respectively, {p} is the parameters describing distribution and f is the cumulative density function. by optimizing l, scale and shape parameters can be estimated using newton raphson method which is an iterative technique for weibull distribution function. accordingly, β and α can be estimated by given iteration method as shown in fig. 8.                                            1 1 1 1 2 2 1 1 2 2 11 1  β   1 n n i i ii i n ii k k n n i ii i ii nn iiii lnx x lnx n x x lnx x lnx xx (16) s. çalışkan et al.ii, frattura ed integrità strutturale, 25 (2021) 344-364; doi: 10.3221/igf-esis.58.25 352              1/ 1 n ii x n (17)          1 αг 1 (18)                1/2 2 22г 1 (19) figure 8: weibull distribution of staircase data based on newton rapson technique. mean value and standard deviation can be estimated 584.13 and 23.64 based on weibull distribution. jsme method another method used as a standard that is jsme (japan society of mechanical engineers) requiring 14 specimens for analysis and constructs whole of the sn curve. eight of them are used in linear region and six specimens are enough to determine fatigue limit of data set. first stress point is taken as highest non-failed (run-out) point in data set. rest of them is constructed up-and-down method based on previous test result by a certain stress increment. stress increment for staircase sequence is estimated by assuming standard deviation equals to stress increment. linear region is associated with following parameters:    log α β*n s (20)                8 1 8 2 1 *(log log ( ) i ii ii s s n n s s ,        8 1 1 log log 8 i i n n and    8 1 1 8 i i s s (21) mean and standard deviation can be estimated with given equations:    7 2 1 6 j j s s (22)            8 2 1 1 1 ( log( log 6 i i i s n s (23) after calculation, mean and standard deviation were calculated as 583.3 and 26.01 respectively. s. çalışkan et al.ii, frattura ed integrità strutturale, 25 (2021) 344-364; doi: 10.3221/igf-esis.58.25 353 curve fitting analysis in engineering applications, sn curves are constructed by linear regression of stress versus life data with given standard deviation. this procedure is also known as curve fitting of fatigue data by executing goodness-of-fit. weibull and log-normal distribution are suitable for metallic materials data to determine life of material. life prediction is carried out by modelling of sn curve and constructing design curves with estimated confidence band, then fatigue limit is estimated based on probabilistic fatigue life model. basquin method firstly, wöhler formulated sn curve with regression parameters to get linear relationship between stress and life. sn curve in finite region is represented by linear correlation between stress and life in logarithmic scale. then, another and most common approach was proposed by basquin and it interrelates stress as a function of life.    . 2 ba f fn (24)  2 2 110b scov (25) these equations based on log-normal distribution, σa, σf, and b are the applied stress, fatigue strength coefficient and fatigue strength exponent respectively. coefficient of variance is calculated by correlation of fatigue strength coefficient with standard deviation (s). standard deviation is estimated by log (2nf) over log (a ). by using least square method, sn curve with finite life can be estimated with 50% reliability. accordingly, mean value for %50 probability of failure in 107 cycles (assumed as run-out criterion) and standard deviation are calculated as 592.89 mpa and 34.7 respectively as shown in fig. 9. figure 9: sn curve per basquin method. stromeyer proposed a new equation for estimating stress by addition of σ∞ term even though endurance limit at defined σ∞ not exist.       σfn (26) where σ is applied stress, α and β are fitting parameters, nf is the number of cycles and σ∞ is stress at infinity. based on this assumption, stromeyer’s model is not linear as in the case of basquin. it practically smooths linear methods by adding new parameter that makes estimation more complicated. similarly, palmgren and weibull later proposed new methods by addition of a dependent term and static stress respectively [3]. the idea behind these models is to provide smoother curve with given fitting parameters to estimate fatigue behavior of materials. astm e739-91 method astm e739-91 defines a correlation between stress and life in linear region by sizing experimental data not extrapolating outside the data with given confidence intervals. the linear relation is established with failed specimens (run-out not included) and evaluated on logarithmic scale. it suggests that at least 12 specimens are required to get reliable data for allowable purposes [29]. s. çalışkan et al.ii, frattura ed integrità strutturale, 25 (2021) 344-364; doi: 10.3221/igf-esis.58.25 354     log *n a b log (27)                         1 2 1 (log log ) * (log log ) (log log ) n i ii n ii n n b (28)            21(log log ) 2 n ii n n s n (29) in given equations, life (n) is the random variable, a and b are the fitting parameters, n is number of specimens, s is standard deviation and stress (σ) is the independent variable.  and n are mean values for stress and life respectively. eventually, linear fit is estimated by regression. the confidence intervals for entire sn curve are estimated for 90 and 95% probability of failure.                              1/2 2 2 1 (log log )1 2 (log log ) p n ii a b log f s n (30) where snedecor distribution value (fp) is tabulated per degree of freedoms in astm e739-91. figure 10: sn curve per astm e731-91 method after calculation, mean value for %50 probability of failure in 107 cycles (assumed as run-out criterion) was found 584.05 and 95% confidence bands were plotted in fig. 10. kim and zhang method differently kim and zhang proposed fatigue damage concept while constructing sn curve. accordingly, fatigue damage rate has a correlation with maximum stress and defined fitting parameters. by applying best fit between damage rate and stress in logarithmic base fitting parameters can be calculated. only finite data points are used to estimate sn curve. damage rate (∆dfi/∆nfi) is calculated by given equation below:        1 maxf ultimate s d s (31)            max ( ) f i i f i d s n (32) where (i) represents each stress level on finite region and average life value can be taken in case of multiple test points on each stress level to present best fit relation. ∆df(i)=df(i-1)-df(i) for the case of df(i-1)>df(i) and similarly ∆nf(i)=nf(i-1)-nf(i) for nf(i1)>nf(i). s. çalışkan et al.ii, frattura ed integrità strutturale, 25 (2021) 344-364; doi: 10.3221/igf-esis.58.25 355 to estimate fitting parameters (α and β), log (     /f i f id n ) and log  max ( is ) are plotted and the slope gives β value. ten to power of intercept gives α value. after the parameters are calculated, sn curve is constructed with following equation:                        1 1 0 . . 1 1 f max ult ult n n s s s (33) where n0 is the hypothetical value and indicates life of material under alternatingly loading. the corresponding smax for n0 equals to sult and n0 is considered to be between 0 and 1. after curve fitting, mean value for %50 probability of failure in 1.0e+07 cycles is 592.1 mpa as shown in fig. 11. figure 11: sn curve per kim and zhang method. bilinear method as an alternative method to random fatigue limit approach which optimizes parameters to get best-fit based on maximum likelihood method, bilinear random fatigue limit model is proposed [5]. it assumes that the sn curve consists of two distinct regions and linear region can be estimated by basquin method via incorporating number of cycles in transition region and fatigue limit terms into stress equation:      * limits m logn n s . for  *n n . (34)  limits s . for  *n n (35) where m is the slope of curve in low cycle region and n* are the transition cycles from finite part to infinite part of sn curve. figure 12: sn curve by bilinear method s. çalışkan et al.ii, frattura ed integrità strutturale, 25 (2021) 344-364; doi: 10.3221/igf-esis.58.25 356 basically, it is recommended to use large experimental data for good fit. therefore, it is a rough estimate of fatigue limit with small datasets because of not introducing smooth transition. therefore, there is a weak correlation between high cycle and low cycles fatigue regions. based on bilinear method, fatigue limit value for 50% probability of failure is 592 mpa as shown in fig. 12. therefore, regression models provide less bias with strong estimation of fatigue data. stussi method by addition of run-out data on data, non-linear models present unbiased estimation by linear regression. stussi proposed a non-linear model to estimate sn curve in low and high cycle fatigue region by introducing tensile strength and fatigue stress at infinity into equation. this formulation is based on log-log scale and optimized by fitting parameters. accordingly,          1 b m b r n s s n (36) where rm is the tensile strength of material, a and b are fitting parameters and s is the infinite stress. figure 13: sn curve by stussi estimation this model is compatible with 3-parameter weibull distribution and provides well-fitting not only on endurance region but also on low cycle fatigue region compared to previous methods specified. based on this approach, mean value for %50 probability of failure which is decided as run-out criterion in 1.0e+07 cycles is 594.6 mpa as shown in fig. 13. agard-ag-292 method another method is agard-ag-292, a comprehensive handbook for helicopter design, and sub-chapter 4.4 describes statistical analysis of small samples by presenting 4 parameters regression including censored data by considering constant scatter of fatigue data along all the regions of the sn curve. accordingly, it is assumed that fatigue data is well fitted by weibull distribution with four parameters fitting. best fit is done with least square technique and log scale is used to make variable in linear form; however, increasing number of fitting parameters increases difficulties in calculating parameters. extending curve beyond the data points cannot be conservative for endurance limit of material therefore data shall be used with reduced curve by introducing confidence interval.      c s s a n b (37) where s is the stress, s is infinite stress, a, b and c are constant fitting parameters, n is the fatigue life of specimen at corresponding stress level. based on this approach, two-sided confidence interval (t-value of student variable) is used when estimating reduced curve. accordingly, the mean and standard deviation are calculated assuming normal distribution of population. then the variable tα is calculated as given equation:     * 1 s x t n (38) s. çalışkan et al.ii, frattura ed integrità strutturale, 25 (2021) 344-364; doi: 10.3221/igf-esis.58.25 357 to estimate 95% confidence interval for the population, sn curves are plotted for each specimen using same fitting parameters and ensuring passing over the observed test data for each specimen. eventually, standard deviation is calculated on 107 cycles (chosen as run-out criterion) with known stress points coming from each curve. figure 14: constructing sn curve by agard-ag-292 method. accordingly, mean value with 50% probability of failure is 593.4 mpa and standard deviation is 33.3. fatigue limit was estimated as 574.3 mpa by applying tα -variable for 95% confidence interval. fatigue reliability analysis it is important to present accurate data without any bias providing theoretical data after analysis that meets the requirement of desired lifetime of a component. reliability is basically to intends to the probability of data without failure in real life conditions. fatigue life evaluation through statical analysis is carried out to prevent fatigue failure under operation with accurate estimation. negative relationship exists between fatigue life and reliability such that decreasing reliability results in increased fatigue life meaning that probability decreases and fatigue failure change increases. sn curve can be generalized such that there is a linear relationship between life and applied stress in logarithmic base. by applying linear regression, model minimizes error by optimizing prediction. after estimation of observation, outliers shall be defined for reliable data by calculating residuals which is the difference between test data and prediction. for the sake of simplicity, standardized residuals are identified for each data point as corresponding error ( ie ) divided by an estimate of standard deviation.    1 i i ii e r mse h (39)    2 1 1 n i i mse e n (40)          2 2 1 1 i ii n ii x x h n x x (41) where ri is the standardized residuals, ei is the standard error, hii is leverage, ix is fatigue life of corresponding specimen, �̅� is mean life of specimens and mse is the mean square error. outliers can be detected by looking at residuals and influential point is accepted an outlier if standardized residuals are greater than three in absolute value. presence of potential outlier in data set influences regression model and results in biased predictor coefficients; therefore, studentized residuals are introduced by removing i-th observation from regression model. then the formula becomes: s. çalışkan et al.ii, frattura ed integrità strutturale, 25 (2021) 344-364; doi: 10.3221/igf-esis.58.25 358      1 i i iii e t mse h (42)                       2 1 1 1 2 i i ii n ke mse mse h n k n k (43) where k is the number of independent variables, n is the number of specimen and ei is the error between estimated and observed data. as shown in fig. 15, there are no outliers for this data set. figure 15: standardized residual vs studentized residuals. another method to identify outliers is to construct normal probability plot. the points in line with normal probability plot line projects standard variation however outside of the line suspicious or outlier data. normal probability plot is basically presenting relative cumulative rate of fatigue data. samples are ordered in ascending manner and cumulative distribution function is calculated in the form of f(s)=[(s-μ)/σ] where s, μ and σ are stress in logarithmic base, mean value and standard deviation respectively. probability plot is constructed log-stress versus zi=f-1(pi) that is inverse function of cumulative distribution function. pi is called as plotting position and most used explanation proposed by hazen [30] as follows:   0.5 i i p n (44) accordingly, theoretical data is plotted with 95% confidence interval as shown in fig. 16 and no outliers are found for normal probability plot. figure 16: normal probability plot. s. çalışkan et al.ii, frattura ed integrità strutturale, 25 (2021) 344-364; doi: 10.3221/igf-esis.58.25 359 fatigue data contains scatter because of nature of material and scatter band is covered by confidence interval. in the same manner, fatigue lifetime is identified at given probability of survival that determines necessary service time by assuming constant standard deviation though whole curve. accordingly, fatigue curves for a probability of survival can be identified by destinating standard deviation following the probability of survival based on gaussian log-normal distribution on given tab. 2. probability of survival (%) standard deviation factor 99.9 -3 97.7 -2 84 -1 50 0 16 1 2.3 2 0.1 3 table 2: probability of survival based on standard deviation. it is explicit that having higher probability of survival eventuated higher reliability of data. in engineering applications sn curves are typically affiliated with 97,7% probability of survival meaning that offsetting from mean curve (50%) by 2 times standard deviation to obtain fatigue data in a conservative way instead of 95% probability of survival stated in astm e73991 [29]. figure 17: sn curve with probability of failure by bilinear method 97.7% probability of failure (survival) is generally used when estimating limits for design curves associated one-sided distribution. mean and standard deviation of sample were considered same for entire population. accordingly, design curve was constructed based on bi-linear method as an example and 26.5 % reduction in fatigue limit was observed as shown in fig. 17.    297.7 50 10 sn n (45) where s is the standard deviation and n50 is the life of the working curve over specified stress range. discussion atigue damage in metals typically starts on surface and propagated perpendicular to applied load because of cyclic plasticity and isotropic properties of material. fatigue mechanism behind of crack initiation is surface phenomenon on the other hand propagation is affiliated bulk phenomenon. fatigue limit confirmed by sn curve acts as a threshold and below the endurance it allows crack initiation therefore it is affiliated with crack initiation phenomenon. essentially it is not realistic to determine fatigue limit of material because of having randomly distribution of fatigue data however distribution of fatigue limit with correct bias can be estimated. to obtain good estimate of mean value with very f s. çalışkan et al.ii, frattura ed integrità strutturale, 25 (2021) 344-364; doi: 10.3221/igf-esis.58.25 360 small interval is only possible with handling large specimens while determining fatigue limit of material; otherwise, estimate will be biased in case of using small samples. nevertheless, available methodologies proposed to advance accuracy of results with reduced number of specimens. basically, staircase methods are easy to handle while estimating mean value of data set with 50% probability of failure; however, standard deviation is complicated because of small data set and needs to be severely reduced with safety factor to get conservative value. to analyze staircase test results, different methodologies was used by finding parameters of distribution that maximizes probability of test data. maximum likelihood method is the most efficient method in terms of estimation with less standard deviation compared to other methodologies. mle usage gives advantage by providing closer confidence level to nominal ones compared to normal approximated intervals for staircase methods. it is advised to use stress increment is around 0.5σ and 1.5σ while performing staircase since small interval leads to waste observations on the other hand precision of mean decreases while increasing stress interval. bootstrapping method resulted in too small standard deviation around mean that means less frequent occurrence and not presenting optimum confidence intervals. iabg method is better estimation than dixon-mood because of omitting first specimen’ test results during analysis that means reduced sample size is used with bias correction. also, weibull distribution resulted in more suitable estimation for standard deviation compared to dixon-mood method. however, dixon-mood method gives best results in case of existence for very large coefficient of variance of data set. astm e739 is advised for metallic materials with the efficiency in medium and high cycle region, stussi is effective also in low cycle fatigue region. method formula fatigue limit (mpa) st. dev. staircase dixon-mood         0 1 2 a s s d f when less event failure         0 1 2 a s s d f when less event run-outs 585.0 31.7 iabg      0( ) a log s log s log d f 585.1 14.5 bootstrapping    b * i i 1 1 x x b 585.1 7.1 weibull          1 αг 1 584.1 23.6 jsme    7 2 1 6 j j s s 583.3 26.0 curve fitting basquin    . 2 ba f fn 592.9 34.7 astm e739-91      log n a b log 584.1 43.9 kim and zhang                      0 . . 1 1 f max ult ult n n s s s 592.1 57.2 bilinear      * limits m logn n s for  *n n  limits s for  *n n 591.0 40.6 stussi       1 b m b r n s s n . 594.6 32.1 agard-ag-292       1 b m b r n s s n 593.4 33.3 table 3: different approaches to determine fatigue limit of material. s. çalışkan et al.ii, frattura ed integrità strutturale, 25 (2021) 344-364; doi: 10.3221/igf-esis.58.25 361 in engineering applications, it is accepted that fatigue strength and corresponding life follow log-normal or weibull distribution; therefore, linear regression was operated to determine sn curve that allows estimation of fatigue limit as well. curve fitting techniques were used in correlation between fatigue life and stress by optimizing fitting parameters. by increasing number of parameters to improve predictability of approach, solving equation becomes difficult because of increased iteration by least square technique and needs to be given necessary efforts. linear regression gives mean value with 50% probability of failure and data needs to be reduced with defined probability of survival and confidence interval for resulting design data. if the presented distribution not fit data as desired, reliability estimation will be inexact. basquin equation estimated poorly because of limited capabilities in case of addition of ultimate strength of data as an input that regression models provide good estimation with goodness of fit. bilinear model can be used for materials showing fatigue behavior of sharp transition between infinite and finite region with relatively constant scatter though sn curve. other models exhibited closer estimation for medium and high cycle fatigue region. exceptionally kim and zhang resulted in high covariance because of limited data on low cycle fatigue region such that this method is more suitable for stress level higher than four on finite region. nevertheless, prediction of fatigue limit data agreed with observed data sensibly. scatter band is caused by inhomogeneous defect size in microstructure of material, production, environment, operator, and misalignment of test specimen on machine [6]. in general scatter is observed larger on low cycle fatigue region and lower on infinite region of sn curve. probability distribution of fatigue data was studied for reliability assessment. inverse correlation exists between fatigue life and reliability, fatigue reliability decreases when increased fatigue life. after estimation of fatigue data in terms of stress and life relationships, residual analysis needs to be performed for reliable data in structural design. in this point, outliers can be detected to present more accurate data by employing standard deviation for normal probability plot and standard/ studentized residuals which is calculated by least square estimation based on minimizing sum of squared deviations. significance level denoted as 0.05 meaning that 5% risk of data and confidence level and probability of survival for fatigue lifetime was calculated for 95% and 97.7 respectively for this study. in this paper, it was attempted to determine endurance limit of material using staircase and curve fitting methods and their results were tabulated on tab. 3. figure 18: variation of design curve after probabilistic analysis (c.i.: confidence interval, p. of s.: probability of survival). to qualify fatigue test data coming from coupon tests, design curves need to be constructed by applying reduction factor to present conservative data as shown in fig. 18. in this way, probabilistic nature of fatigue data can accurately be estimated accounting for scatter effects with confidence. conclusions atigue strength of a material can be determined by evaluation of staircase or curve fitting methods statistically. the idea is to present more accurate data with specified confidence intervals such that conservative data needs to be used in design side. the following conclusions drawn from this study are listed below:  weibull and iabg method resulted in better fit compared to other methods in terms of fatigue limit and standard deviation for limited data set. f s. çalışkan et al.ii, frattura ed integrità strutturale, 25 (2021) 344-364; doi: 10.3221/igf-esis.58.25 362  total number of specimens (14) seems appropriate to construct sn curve, 8 of which are finite and 6 for infinite regions which makes it possible to determine endurance limit for small sample data analysis.  even though analyses have been carried out for aisi 4340 coupon test data, it can be commissioned for any material that exhibits fatigue limit behavior.  staircase method is easy to operate for estimating fatigue limit of material and proposed methods exhibit similar results in terms of 50% probability of failure; however, standard deviation is complicated so large safety factors are inevitable to get reliable results for small samples.  scatter band of sn curve at 95% confidence level and 97.7% probability of survival needs to be studied for accurate and reliable data for design curves.  curve fitting methods can be used to determine sn curve shape by allowing estimation of fatigue strength for corresponding number of cycles and estimated fatigue limit at 1e+07 cycles resulted in close agreement with staircase methods.  coupon level testing is carried out in laboratory conditions and results give an idea about fatigue behavior of material; however, components in service can have unforeseen risks and this is not easy to estimate in terms of scatter therefore additional safety (knock-down) factors are needed. acknowledgments uthors acknowledge turkish aerospace inc. references [1] burhan, i., and kim, h. (2018). s-n curve models for composite materials characterisation: an evaluative review. journal of composites science, 2(3), 38. doi: 10.3390/jcs2030038. [2] murakami, y., takagi, t., wada, k., and matsunaga, h. (2021). essential structure of s-n curve: prediction of fatigue life and fatigue limit of defective materials and nature of scatter. international journal of fatigue, 146, 106138. doi: 10.1016/j.ijfatigue.2020.106138. [3] barbosa, j. f., correia, j. a. f. o., freire júnior, r. c. s., zhu, s.-p., and de jesus, a. m. p. (2019). probabilistic s-n fields based on statistical distributions applied to metallic and composite materials: state of the art. advances in mechanical engineering, 11(8), 168781401987039. doi: 10.1177/1687814019870395. [4] leonetti, d., maljaars, j., and snijder, h. h. (b. (2017). fitting fatigue test data with a novel s-n curve using frequentist and bayesian inference. international journal of fatigue, 105, pp. 128–143. doi: 10.1016/j.ijfatigue.2017.08.024. [5] pollak, r., palazotto, a., and nicholas, t. (2006). a simulation-based investigation of the staircase method for fatigue strength testing. mechanics of materials, 38(12), pp. 1170–1181. doi: 10.1016/j.mechmat.2005.12.005. [6] schijve, j. (2005). statistical distribution functions and fatigue of structures. international journal of fatigue, 27(9), pp. 1031–1039. doi: 10.1016/j.ijfatigue.2005.03.001. [7] pascual, f. g., and meeker, w. q. (1999). estimating fatigue curves with the random fatigue-limit model. technometrics, 41(4), pp. 277–289. doi: 10.1080/00401706.1999.10485925. [8] rabb, b.r. (2003). staircase testing – confidence and reliability. trans. eng. sci. 40, 447–464. [9] sutherland, h. and veers, p. (2000). the development of confidence limits for fatigue strength data. wind energy asme/aiaa. 10.2514/6.2000-63. [10] sakai, t., nakajima, m., tokaji, k., and hasegawa, n. (1997). statistical distribution patterns in mechanical and fatigue properties of metallic materials. journal of the society of materials science, japan, 46(6appendix), pp. 63–74. doi: 10.2472/jsms.46.6appendix_63. [11] li, h., wen, d., lu, z., wang, y., and deng, f. (2016). identifying the probability distribution of fatigue life using the maximum entropy principle. entropy, 18(4), 111. doi: 10.3390/e18040111. [12] schneider, c. r. a., and maddox, s. j. (2003). best practice guide on statistical analysis of fatigue data. the welding institute, cambridge, uk. a s. çalışkan et al.ii, frattura ed integrità strutturale, 25 (2021) 344-364; doi: 10.3221/igf-esis.58.25 363 [13] toasa c., and ummenhofer, t. (2018). a probabilistic stüssi function for modelling the s-n curves and its application on specimens made of steel s355j2+n. international journal of fatigue. 117. doi: 10.1016/j.ijfatigue.2018.07.041. [14] kim, h. s., and zhang, j. (2001). fatigue damage and life prediction of glass/vinyl ester composites. journal of reinforced plastics and composites, 20(10), pp. 834–848. doi: 10.1177/073168401772678959. [15] lipski, a. (2018). determination of the s-n curve and the fatigue limit by means of the thermographic method for ductile cast iron. doi: 10.1063/1.5066398. [16] dixon, w. j., and mood, a. m. (1948). a method for obtaining and analyzing sensitivity data. journal of the american statistical association, 43(241), pp. 109–126. doi: 10.1080/01621459.1948.10483254. [17] dixon, w. j. (1965). the up-and-down method for small samples. journal of the american statistical association, 60(312), pp. 967–978. doi: 10.1080/01621459.1965.10480843. [18] lin, s. (2001). evaluation of the staircase and the accelerated test methods for fatigue limit distributions. international journal of fatigue, 23(1), pp. 75-83. doi: 10.1016/s0142-1123(00)00039-6. [19] little, r. e. (1972). estimating the median fatigue limit for very small up-and-down quantal response tests and for. probabilistic aspects of fatigue. doi: 10.1520/stp35403s. [20] loren, s. (2003). fatigue limit estimated using finite lives. fatigue fracture of engineering materials and structures, 26(9), pp. 757-766. doi: 10.1046/j.1460-2695.2003.00659.x. [21] minak, g. (2007). comparison of different methods for fatigue limit evaluation by means of the monte carlo method. journal of testing and evaluation, 35(2), 100122. doi: 10.1520/jte100122. [22] nicholas m., and ulam s. (1949). the monte carlo method, journal of the american statistical association, 44, pp. 335341 [23] johnson, r. w. (2001). an introduction to the bootstrap. teach. stat. 23, pp. 49–54. [24] beretta, s., and murakami, y. (1998). statistical analysis of defects for fatigue strength prediction and quality control of materials. fatigue fracture of engineering materials and structures, 21(9), pp. 1049-1065. doi: 10.1046/j.1460-2695.1998.00104.x. [25] wallin, k. r. w. (2011). statistical uncertainty in the fatigue threshold staircase test method. international journal of fatigue, 33(3), pp. 354–362. doi: 10.1016/j.ijfatigue.2010.09.013. [26] hück, m. (1983). ein verbessertes verfahren für die auswertung von treppenstufenversuchen. materialwissenschaft und werkstofftechnik, 14(12), 406-417. doi: 10.1002/mawe.19830141207. [27] müller, c., wächter, m., masendorf, r., and esderts, a. (2017). accuracy of fatigue limits estimated by the staircase method using different evaluation techniques. international journal of fatigue, 100, pp. 296-307. doi: 10.1016/j.ijfatigue.2017.03.030. [28] efron, b., and tibshirani, r. (1986). bootstrap methods for standard errors, confidence intervals, and other measures of statistical accuracy: rejoinder. statistical science, 1(1). doi: 10.1214/ss/1177013815. [29] astm e739-91 (1998). available at: https://www.astm.org/database.cart/historical/e739-91r98.htm. [30] hazen, a. (1914). storage to be provided in impounding municipal water supply. transactions of the american society of civil engineers, 77(1), pp. 1539–1640. doi: 10.1061/taceat.0002563. [31] beretta, s., clerici, p., and matteazzi, s. (1995). the effect of sample size on the confidence of endurance fatigue tests. fatigue and fracture of engineering materials and structures, 18(1), pp. 129-139. doi: 10.1111/j.1460-2695.1995.tb00147.x. [32] molina, a., piña-monarrez, m. r., and barraza-contreras, j. m. (2020). weibull s-n fatigue strength curve analysis for a572 gr. 50 steel, based on the true stress—true strain approach. applied sciences, 10(16), 5725. doi: 10.3390/app10165725. [33] engler-pinto, c. c., lasecki, j. v., frisch, r. j., dejack, m. a., and allison, j. e. (2005). statistical approaches applied to fatigue test data analysis. sae technical paper series. doi: 10.4271/2005-01-0802. [34] zheng, x., lü, b., and jiang, h. (1995). determination of probability distribution of fatigue strength and expressions of p-s-n curves. engineering fracture mechanics, 50(4), pp. 483-491. doi: 10.1016/0013-7944(94)00218-7 [35] boylan, g. l., and cho, b. r. (2011). the normal probability plot as a tool for understanding data: a shape analysis from the perspective of skewness, kurtosis, and variability. quality and reliability engineering international, 28(3), pp. 249264. doi: 10.1002/qre.1241. [36] sivák, p., and ostertagová, e. (2012). evaluation of fatigue tests by means of mathematical statistics. procedia engineering, 48, pp. 636-642. doi: 10.1016/j.proeng.2012.09.564 [37] jamalkhani k., m., and azadi, m. (2018). reliability prediction, scatter-band analysis and fatigue limit assessment of high-cycle fatigue properties in en-gjs700-2 ductile cast iron. matec web of conferences, 165, 10012. doi: 10.1051/matecconf/201816510012 s. çalışkan et al.ii, frattura ed integrità strutturale, 25 (2021) 344-364; doi: 10.3221/igf-esis.58.25 364 [38] najim, a., and anwar t. (2015). comparison four methods for estimating the fatigue life distribution parameters through simulation. international journal of science and research, pp. 2319-7064. [39] agard-ag-292 (1983). helicopter fatigue design guide. [40] kepka, m. (2018). using design sn curves and design stress spectra for probabilistic fatigue life assessment of vehicle components. [41] fan, j. l., guo, x. l., wu, c. w., and zhao, y. g. (2011). research on fatigue behavior evaluation and fatigue fracture mechanisms of cruciform welded joints. materials science and engineering: a, 528(29-30), pp. 8417–8427. doi: 10.1016/j.msea.2011.08.037. [42] astm e466-96 (1996). standard practice for conducting force controlled constant amplitude axial fatigue tests of metallic materials, astm international, west conshohocken, pa, available at: www.astm.org. [43] ams 2759-1d (2007). heat treatment of carbon and low-alloy steel parts minimum tensile strength below 220 ksi (1517 mpa), sae international. microsoft word numero 12 art 5 f. frendo, frattura ed integrità strutturale, 12 (2010) 48-56; doi: 10.3221/igf-esis.12.05 48 analisi del cedimento strutturale del braccio di una gru portuale francesco frendo università di pisa, dipartimento di ingegneria meccanica, nucleare e della produzione frendo@ing.unipi.it riassunto. nel presente lavoro vengono discusse le cause del cedimento strutturale del braccio di una gru portuale a portata variabile. l’ispezione delle sezioni di rottura ha mostrato in particolare la presenza di una grossa fessura preesistente al momento del crollo, che si estendeva per circa metà sezione di uno degli elementi tubolari principali che costituiscono il traliccio del braccio. al fine di stabilire le modalità del crollo, nel lavoro vengono presentati un modello per l’analisi della propagazione della fessura, che fa uso del metodo delle weight functions ed un modello per l’analisi di collasso della sezione. le analisi condotte hanno permesso di concludere che il crollo si è verificato per collasso plastico della sezione ed hanno messo in evidenza come la fessura in esame, per una parte considerevole della vita, sia propagata in condizioni stabili con velocità di avanzamento circa costante. abstract. in the present paper the structural failure of a crane arm is analysed and discussed. during inspections, a significant pre-existing crack was observed, which extended to about half the cross section of one of the main tubular elements which constitute the arm frame. in order to determine the failure cause, a model for the crack growth analysis and a model for the plastic collapse were developed; the model for the analysis of crack growth is based on the weight functions method. the analyses allowed to conclude that the failure was due to plastic collapse and to asses how, for a considerable part of the life, the crack propagated under stable conditions with an almost constant rate. parole chiave. integrità strutturale; apparecchi di sollevamento; meccanica della frattura; collasso plastico. introduzione modelli di calcolo dell’integrità strutturale ed i modelli fenomenologici che descrivono il danneggiamento dei materiali rappresentano uno strumento fondamentale per l’ingegnere sia nelle fasi di progettazione, che per l’analisi e l’interpretazione delle modalità di cedimento delle parti di una macchina che svolgono le funzioni strutturali. vale la pena di osservare come, in particolare nel secondo caso, le difficoltà maggiori risiedono spesso nella conoscenza della storia operativa effettiva della macchina; nonostante ciò, tali modelli permettono di fare delle stime utili, relative ad esempio alla fase di propagazione di un difetto o alla vita del componente e alle cause di collasso. la problematica affrontata nel presente lavoro riguarda l’analisi del crollo del braccio di una gru portuale a portata variabile. il braccio è costituito da un traliccio di tubi saldati; più in particolare vi sono tre correnti longitudinali principali tubolari, disposti ai vertici di un triangolo equilatero e degli elementi tubolari di sezione minore che realizzano il traliccio di collegamento. il materiale del braccio è l’acciaio api 5l x52, un acciaio al carbonio tipicamente impiegato per la produzione di tubi utilizzati nella realizzazione di gasdotti. il crollo del braccio è avvenuto in prossimità della zona di collegamento alla parte fissa della gru (fig. 1); l’esame delle sezioni di rottura ha mostrato in particolare la presenza di un grosso difetto preesistente in uno dei correnti principali, che al momento del crollo interessava circa metà sezione (fig. 2). come risulta evidente dalla figura, il difetto si è originato in i http://dx.medra.org/10.3221/igf-esis.12.05&auth=true http://www.gruppofrattura.it f. frendo, frattura ed integrità strutturale, 12 (2010) 48-56; doi: 10.3221/igf-esis.12.05 49 corrispondenza del bordo di una saldatura di un elemento di rinforzo ed è poi propagato nel materiale in un piano ortogonale all’asse del tubo. obiettivi principali dello studio sono stati l’analisi della fase di propagazione per fatica del difetto e valutare se il cedimento è avvenuto per raggiungimento del valore critico del fattore di intensificazione degli sforzi o per il collasso della sezione residua. l’analisi della fase di propagazione è servita a valutare quella che può essere stata l’evoluzione temporale del difetto; tuttavia, non essendo disponibile una registrazione dei cicli di carico effettivi, è stato possibile effettuare una stima per eccesso della velocità di propagazione assumendo un ciclo di riferimento relativamente severo. la disponibilità delle caratteristiche di resistenza e della tenacità a frattura del materiale costituente il tubo ha invece permesso di identificare con certezza la causa del crollo; a questo riguardo, le caratteristiche meccaniche del materiale costituente il braccio sono state determinate con delle prove standard di trazione secondo normativa uni, utilizzando dei campioni estratti da uno dei correnti principali del traliccio costituente il braccio; la tenacità a frattura del materiale è stata reperita in letteratura (si veda ad es. [1, 2, 6]). figura 1: zona di rottura del traliccio costituente il braccio della gru. figura 2: immagine della sezione di uno dei correnti principali del braccio; è evidente l’ossidazione di una grossa porzione della sezione. propagazione del difetto a fessura osservata rappresenta un difetto passante in un tubo sollecitato in trazione e flessione; in questi casi la modalità di danneggiamento è riconducibile alla nucleazione di un difetto sulla superficie esterna, alla sua crescita all’interno dello spessore del tubo sino a quando la fessura non diventa passante; successivamente si ha l http://dx.medra.org/10.3221/igf-esis.12.05&auth=true http://www.gruppofrattura.it f. frendo, frattura ed integrità strutturale, 12 (2010) 48-56; doi: 10.3221/igf-esis.12.05 50 l’avanzamento della fessura in un piano ortogonale all’asse del tubo (modo i), che va ad interessare una porzione sempre maggiore della sezione del tubo. nel caso specifico la fase di nucleazione e crescita del difetto iniziale è stata condizionata dalla presenza di un elemento di rinforzo, un piatto saldato sulla superficie esterna del tubo visibile in fig.2; questa fase dell’avanzamento risulta complessa per effetto della geometria e delle proprietà del materiale nella zona della saldatura. si è deciso quindi di restringere l’analisi alla sola fase di avanzamento del difetto passante e si è presa a riferimento una dimensione iniziale del difetto pari alla larghezza dell’elemento di rinforzo (fig.3); non è stata quindi analizzata la fase antecedente di crescita di una o più cricche al bordo del cordone di saldatura sino a che non si è avuta la fessura passante di tale estensione. ciò rappresenta evidentemente una semplificazione che ha portato ad ottenere una stima per difetto del tempo di crescita della fessura; tale stima risulterà per difetto anche per il fatto che, come è già stato accennato, si è preso a riferimento un ciclo di carico relativamente severo. figura 3: modello di avanzamento del difetto. con riferimento alla fig.3 si è indicata con  la semiestensione angolare della fessura; si indicherà con  la coordinata angolare generica (stessa convenzione utilizzata per . la fase di propagazione del difetto può essere descritta tramite la legge di paris; sono state prese in considerazione le due formulazioni seguenti: 11 mkc dn da  (1) con c1=4·10-11 m/ciclo ed m1=3 (dati ricavati per un acciaio al carbonio da [1]);   22 mthkkc dn da   (2) con c2=2·10-10 m/ciclo, kth=8 mpa m0.5, m2=2.4 per il materiale api 5l gr x52 [5]. in entrambe le relazioni, per studiare l’avanzamento della fessura è stata considerata la parte positiva del k ottenuto sulla base del ciclo di carico. i fattori di intensificazione degli sforzi, necessari per il calcolo del k, sono stati valutati con il metodo delle weight functions (si veda ad es. [3, 4]); il fattore di intensificazione degli sforzi può essere ottenuto con il seguente integrale:     a dxxamxwk 0 , (3) nel quale w rappresenta lo spessore, waa / rappresenta la larghezza adimensionalizzata della fessura,  x l’andamento della tensione agente in corrispondenza del piano in cui è presente la fessura, valutata nel pezzo integro ed  xam , l’espressione della weight function. il caso in esame, già schematizzato in fig.3, è riconducibile per motivi di simmetria a quello mostrato in fig.4 (la figura si riferisce alla geometria effettiva, non adimensionalizzata), relativo ad una serie periodica di fessure in una lastra infinita, con le seguenti trasformazioni: http://dx.medra.org/10.3221/igf-esis.12.05&auth=true http://www.gruppofrattura.it f. frendo, frattura ed integrità strutturale, 12 (2010) 48-56; doi: 10.3221/igf-esis.12.05 51 ra  , rw  , rx  ove r rappresenta il raggio medio del tubo e  la coordinata angolare. figura 4: serie periodica di fessure passanti in una lastra infinita (tratta da[3]). la weight function per il caso di fig.4 è stata presa da [3]. l’applicazione del metodo al caso in esame ha però richiesto un passaggio intermedio, in quanto, essendo il braccio della gru una struttura internamente iperstatica, le caratteristiche di sollecitazione agenti sul corrente ove si è avuto l’avanzamento della fessura, sono funzione della dimensione del difetto; per questo motivo anche la tensione normale che compare nella (3), agente nel tubo integro, risulta funzione della dimensione del difetto. per il calcolo del fattore di intensificazione degli sforzi va quindi considerata la relazione seguente al posto della precedente (3):     a dxxamxawk 0 ,, (4) figura 5: modello impiegato per valutare le caratteristiche di sollecitazione nella sezione contenente il difetto. per studiare l’avanzamento della fessura è stato quindi precedentemente ricostruito l’andamento  ,a x utilizzando la seguente procedura: è stato sviluppato un modello agli elementi finiti del braccio della gru, contenente un difetto di dimensioni variabili ( 0 max    ) nella sezione di tubo corrispondente al caso reale (fig.5); il modello è stato interamente realizzato con elementi pipe, tranne la porzione di corrente ove è presente la fessura, che è stata modellata con elementi shell. a partire dai carichi nodali agenti negli elementi a monte e a valle della porzione modellata con elementi shell, sono state valutate le caratteristiche di sollecitazione (sforzo normale e momento flettente) agenti nella sezione in cui è presente il difetto; tali caratteristiche, riferite alla sezione integra, sono mostrate nelle fig. 6 e 7 per varie estensioni del difetto. vale la pena osservare che, per effetto del tiro delle funi agenti in punta al braccio, la condizione più gravosa per l’avanzamento del difetto, quella cioè in cui si ha l’apertura massima della fessura, si ha quando le strutture del braccio sono sottoposte all’azione della gravità; tale considerazione rende verosimili le ipotesi fatte sul ciclo di carico, in quanto http://dx.medra.org/10.3221/igf-esis.12.05&auth=true http://www.gruppofrattura.it f. frendo, frattura ed integrità strutturale, 12 (2010) 48-56; doi: 10.3221/igf-esis.12.05 52 porta a considerare equivalenti tutte le condizioni di carico (dovute al sollevamento del carico da parte della gru) a partire da quella che provoca la chiusura del difetto. figura 6: sforzo normale agente nella sezione del tubo in funzione della semiampiezza del difetto; le due curve si riferiscono alle due condizioni utilizzate per definire il ciclo di carico. figura 7: momento flettente valutato rispetto al baricentro della sezione integra in funzione della semiampiezza del difetto; le curve si riferiscono alle due condizioni di carico. con queste caratteristiche di sollecitazione è stato possibile valutare la tensione normale, da impiegare nella (4), utilizzando semplicemente la teoria delle travi ed utilizzando le caratteristiche della sezione integra:        xr j am a an xa y  cos,  (5) è interessante osservare come all’aumentare dell’estensione del difetto lo sforzo normale vari lievemente, mentre più rilevante è la variazione del momento flettente, che nella condizione relativa al peso proprio cambia segno, per una semiestensione della fessura pari a circa 53°; questi andamenti hanno un’influenza determinante sulla velocità di avanzamento della fessura. le fig. 8, 9 e 10 mostrano il k , la velocità di propagazione e la semiestensione della fessura che si ottengono utilizzando le precedenti relazioni (1) e (2) e la procedura precedentemente descritta, assumendo un difetto iniziale di semiestensione pari a circa 25°, corrispondente alla larghezza del piatto di rinforzo; come si può osservare le due leggi di propagazione forniscono risultati in ragionevole accordo, sebbene la (1) fornisca velocità di avanzamento superiori. -3.e+05 -2.e+05 -1.e+05 0.e+00 1.e+05 2.e+05 3.e+05 4.e+05 5.e+05 0 20 40 60 80 100 semiestensione fessura (°) s fo rz o n o rm a le ( n ) sotto carico peso proprio -2.e+07 -2.e+07 -1.e+07 -5.e+06 0.e+00 5.e+06 1.e+07 2.e+07 0 20 40 60 80 100 semiestensione fessura (°) m o m e n to f le tt e n te ( n m m ) sotto carico peso proprio http://dx.medra.org/10.3221/igf-esis.12.05&auth=true http://www.gruppofrattura.it f. frendo, frattura ed integrità strutturale, 12 (2010) 48-56; doi: 10.3221/igf-esis.12.05 53 la linea tratteggiata rappresentata in fig. 10 rappresenta la semiestensione della fessura osservata nella sezione di rottura rappresentata in fig. 2. se ne ricava quindi che, con il ciclo di carico ipotizzato, la fase di crescita del difetto a partire dalla estensione iniziale, utilizzando la (1), ha richiesto poco più di 80000 cicli; dalle fig. 8 e 9 si deduce inoltre che la propagazione è avvenuta con un k ed una velocità di avanzamento circa costanti; ciò è dovuto alla variazione delle caratteristiche di sollecitazione e della tensione normale da impiegare nella (4) all’aumentare delle dimensioni del difetto; la velocità di avanzamento media, stimata utilizzando la relazione (1), è risultata pari a circa 1.8 m/ciclo; il k in questa fase è compreso tra 30 e 37 mpa m0.5, significativamente inferiore rispetto al kic del il materiale in questione. prendendo a riferimento la (2) si ha che la fase di avanzamento è durata circa 260000 cicli, la velocità di avanzamento in questa fase è stata pari a circa 0.6 m/ciclo, mentre il k risulta analogo a quello precedente. figura 8: parametro k di sollecitazione della fessura; in blu ed in verde le curve relative alla (1) e alla (2) rispettivamente. figura 9: velocità di avanzamento; in blu ed in verde le curve relative alla (1) e alla (2) rispettivamente. modalità di cedimento ’analisi dei risultati ottenuti al paragrafo precedente ha messo in evidenza come in presenza di un difetto di semiestensione pari a circa 85°, quale quello osservato sulla sezione di rottura, con il ciclo di sollecitazione assunto non si raggiunga il valore critico kic, che per il materiale in questione è circa 70 mpa m0.5 (si veda [2, 6]); infatti, l http://dx.medra.org/10.3221/igf-esis.12.05&auth=true http://www.gruppofrattura.it f. frendo, frattura ed integrità strutturale, 12 (2010) 48-56; doi: 10.3221/igf-esis.12.05 54 affinché il k cresca rapidamente e raggiunga valori comparabili con la tenacità a frattura bisogna che la fessura superi l’ampiezza complessiva di 220°, cosa che non trova conferma nell’osservazione diretta della sezione di rottura. è stato quindi sviluppato un modello di collasso plastico della sezione per valutare se il meccanismo di cedimento potesse essere spiegato con questa modalità. il modello è illustrato in fig.11 in cui è mostrato anche il sistema di riferimento avente origine nel centro della sezione integra; come prima,  indica la semiampiezza del difetto e  (<<) la posizione della cerniera plastica. si è ipotizzato quindi che in tutti i punti della sezione del corrente si raggiunga una tensione di scorrimento sc, convenzionalmente assunta come media tra la tensione di snervamento e la tensione di rottura; la caratterizzazione sperimentale del materiale ha fornito per questo parametro il valore di 460 mpa (fig.12). figura 10: semiestensione della fessura; in blu ed in verde le curve relative alla (1) e alla (2) rispettivamente. figura 11: modello di collasso della sezione. detti r e t il raggio medio della sezione e lo spessore del tubo rispettivamente (si considera per semplicità t/r<<1), è possibile valutare le caratteristiche geometriche della sezione; in particolare, la posizione del baricentro della sezione residua rispetto al sistema di riferimento mostrato in figura si ottiene dalla seguente espressione:                r dr yg 2 sin2     senr yg (6) http://dx.medra.org/10.3221/igf-esis.12.05&auth=true http://www.gruppofrattura.it f. frendo, frattura ed integrità strutturale, 12 (2010) 48-56; doi: 10.3221/igf-esis.12.05 55 in maniera analoga è facile determinare lo sforzo normale n ed il momento flettente mg, valutato rispetto al baricentro della sezione residua, risultanti dal profilo di tensione ipotizzato in fig. 11. si ha rispettivamente:        2222 scscsc rtrtrtn , (7)                                                       22 sinsin22 sinsin 2 sinsinsin 2 2 sc scscg tr rr rt rr rtm figura 12: curve  ottenute dalla caratterizzazione sperimentale del materiale effettuata mediante prove di trazione effettuate su provini estratti da uno degli elementi costituenti il braccio. le espressioni precedenti mostrano la dipendenza delle caratteristiche di sollecitazione dai parametri che rappresentano la semiestensione della fessura e la posizione della cerniera plastica; utilizzando tali espressioni è possibile costruire la mappa mostrata in fig.13, che mostra il legame tra lo sforzo normale ed il momento flettente al collasso; le diverse curve si riferiscono a diversi valori della semiapertura  della fessura, mentre i diversi punti di una curva si riferiscono a diversi valori del parametro  che indica la posizione della cerniera plastica; all’aumentare del parametro  aumenta il valore dello sforzo normale, come risulta evidente anche dalla distribuzione di tensioni mostrata in fig.11. figura 13: relazione tra sforzo normale e momento flettente al collasso e sollecitazioni effettive. 0 100 200 300 400 500 600 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 deformazione t e n s io n e ( m p a ) http://dx.medra.org/10.3221/igf-esis.12.05&auth=true http://www.gruppofrattura.it f. frendo, frattura ed integrità strutturale, 12 (2010) 48-56; doi: 10.3221/igf-esis.12.05 56 se si considera la singola curva del grafico di fig.13 che, essendo univocamente determinata dal parametro , corrisponde ad una certa ampiezza della fessura, si può dire che, se le condizioni effettive di carico (sforzo normale e momento flettente) sono rappresentate da un punto sul grafico posto al di sotto della curva, queste non sono sufficienti per far collassate la sezione; viceversa se il punto rappresentativo dei carichi agenti sulla sezione è posto al di sopra della curva si può avere il collasso. le varie curve tracciate per diversi valori del parametro  mostrano che, come è ragionevole aspettarsi, all’aumentare dell’ampiezza della fessura presente nella sezione diminuiscano i valori minimi delle caratteristiche di sollecitazione che provocano il collasso plastico della sezione. nello stesso grafico di fig. 13 sono anche riportati i valori delle caratteristiche di sollecitazione che si verificano nella sezione in cui è presente il difetto, per diversi valori del parametro nella condizione in cui il braccio è sottoposto alla sola azione del proprio peso. questi dati sono stati ottenuti con il modello agli elementi finiti già descritto; il valore del momento flettente, in particolare, differisce da quello già mostrato nella fig. 7, che si riferiva alla sezione integra. come si può osservare, all’aumentare della dimensione della fessura, lo sforzo normale diminuisce leggermente mentre il momento flettente aumenta. il grafico di fig. 13 dimostra chiaramente come con fessure di estensione complessiva compresa tra i 140° e i 180° si hanno effettivamente le condizioni per le quali si può verificare il collasso plastico della sezione del corrente. l’analisi delle curve mostra inoltre che il collasso si verifica con un valore dell’angolo , che rappresenta la posizione della cerniera plastica, dell’ordine dei 140°. conclusioni el presente lavoro sono state presentate alcune metodologie di analisi applicate ad un caso reale per stabilire quale sia stato il meccanismo di cedimento della struttura a traliccio del braccio di una gru portuale a portata variabile. le analisi svolte hanno permesso di concludere che il crollo del braccio si è verificato per il meccanismo di collasso plastico della sezione di uno dei correnti principali, nella quale era presenta una fessura che interessava circa metà sezione. la fessura si è originata al bordo del cordone di saldatura ed è propagata in condizioni stabili a velocità di avanzamento circa costante sino alla dimensione finale. la durata della fase di avanzamento del difetto è stata stimata utilizzando due diverse formulazioni della legge di paris, in cui si è fatto uso del metodo delle weight functions per valutare il fattore di intensificazione degli sforzi; tale analisi ha inoltre permesso di ricavare come il valore critico del kic reperito in letteratura risultasse significativamente superiore al fattore di intensificazione degli sforzi che si verificava per i carichi agenti e per le dimensioni della fessura prese a riferimento. il collasso plastico della sezione in cui era presente il difetto, ha prodotto il cedimento degli altri elementi portanti e quindi il crollo del braccio della gru. bibliografia [1] m. kleesnil, p. lukas, fatigue of metallic materials, elsevier (1992). [2] f. bolzoni, m. guagliano, l. lazzari, l. vergani, m. vimercati, in: atti del xxxi convegno nazionale aias (associazione italiana per l’analisi delle sollecitazioni), parma (2002). [3] xue-ren wu, a. jane carlsson, weight functions and stress intensity factor solutions, london pergamon press (1991). [4] t. fett, d. munz, stress intensity factors and weight functions, computational mechanics publications, southampton (1997). [5] j.t.p. de castro, m.a.meggiolaro, a.c. de oliveira miranda, computational materials science, 46(1) (2009) 115. [6] j. capelle, j. gilbert, i. dmytrakh, g. pluvinage, structural integrity and life, 9(1) (2009) 9. n http://dx.medra.org/10.3221/igf-esis.12.05&auth=true http://www.gruppofrattura.it microsoft word numero_34_art_40 o.ševeček et alii, frattura ed integrità strutturale, 34 (2015) 362-370; doi: 10.3221/igf-esis.34.40 362 focussed on crack paths understanding the edge crack phenomenon in ceramic laminates o. ševeček, m. kotoul brno university of technology, institute of solid mechanics, mechatronics and biomechanics, faculty of mechanical engineering, technická 2, 616 69 brno (czech republic) sevecek@fme.vutbr.cz, kotoul@fme.vutbr.cz d. leguillon institut jean le rond d'alembert, cnrs umr 7190, sorbonne universités, upmc, f-75005 paris (france) dominique.leguillon@upmc.fr e. martin laboratoire des composites thermo-structuraux, cnrs umr 5801, université de bordeaux, f-33600 pessac (france) martin@lcts.u-bordeaux1.fr r. bermejo montanuniversität leoben , institut für strukturund funtionskeramik, peter-tunner straße 5, 8700 leoben (austria) raul.bermejo@unileoben.ac.at abstract. layered ceramic materials (also referred to as “ceramic laminates”) are becoming one of the most promising areas of materials technology aiming to improve the brittle behavior of bulk ceramics. the utilization of tailored compressive residual stresses acting as physical barriers to crack propagation has already succeeded in many ceramic systems. relatively thick compressive layers located below the surface have proven very effective to enhance the fracture resistance and provide a minimum strength for the material. however, internal compressive stresses result in out-of plane stresses at the free surfaces, what can cause cracking of the compressive layer, forming the so-called edge cracks. experimental observations have shown that edge cracking may be associated with the magnitude of the compressive stresses and with the thickness of the compressive layer. however, an understanding of the parameters related to the onset and extension of such edge cracks in the compressive layers is still lacking. in this work, a 2d parametric finite element model has been developed to predict the onset and propagation of an edge crack in ceramic laminates using a coupled stress-energy criterion. this approach states that a crack is originated when both stress and energy criteria are fulfilled simultaneously. several designs with different residual stresses and a given thickness in the compressive layers have been computed. the results predict the existence of a lower bound, below no edge crack will be observed, and an upper bound, beyond which the onset of an edge crack would lead to the complete fracture of the layer. keywords. edge crack; residual stresses; ceramic laminate; fe analysis; coupled criterion. o.ševeček et alii, frattura ed integrità strutturale, 34 (2015) 362-370; doi: 10.3221/igf-esis.34.40 363 introduction eramics have been used for many decades as structural elements, but due to their inherent brittleness they have been mainly utilized under compressive loading conditions. nowadays, most of the new engineering designs need to withstand tensile stresses which imply potential limitations for ceramics due to their low fracture toughness and the sensitivity of ceramic material strength to the presence of defects [1-3]. the brittle fracture of glasses and ceramics is a consequence of the material defects located either within the bulk or at the surface, resulting from the processing and/or machining procedures [4, 5]. under external applied stress, the stress concentration associated with such defects is the common source of failure of ceramic components. if each defect is considered as a crack or a potential source for crack initiation, then obviously the size and type of these defects determine the mechanical strength of the material [6]. the distribution of defects of different sizes within a ceramic component yields a statistically variable strength which can be described by the weibull theory [7, 8]. as a consequence of such behaviour there remains a (small) probability of failure even at very small applied loads (i.e., no lower threshold for strength). since flaws are intrinsic to processing and in most cases unavoidable, the mechanical reliability of ceramic components is associated with such a flaw distribution. in order to reduce both the defect population and the defect size, many studies have been devoted in the past to improve ceramic processing [9]. another approach to increase strength has been to introduce compressive residual stresses at the surface. a successful example can be found in strengthened glass [10] and more recently gorilla glass [11]. however, a significant reduction of strength variability cannot be achieved with these approaches. in an attempt to reduce the level of uncertainty in mechanical strength and to overcome the lack of toughness of structural and functional ceramics, newer approaches have been developed in which knowledge about the energy release mechanisms has resulted in the creation of “flaw tolerant” (strength reliable) materials, with improved fracture toughness [9, 10, 12-27]. layered ceramic materials (also referred to as “ceramic laminates”) are becoming one of the most promising areas of materials technology. they have been proposed as an alternative for the design of structural ceramics with improved fracture toughness, strength and mechanical reliability. among all, laminates designed with strong interfaces and compressive residual stresses have led to an increase in fracture energy, thermal shock resistance and, in some cases, a decrease in the sensitivity of the material strength to the different size of defects. the utilization of tailored compressive residual stresses acting as physical barriers to crack propagation has succeeded in many ceramic systems [17, 23, 25, 2831]. however, a limiting factor in the design of these multilayer systems is the fact that the beneficial compressive stresses in one type of layers have to be balanced by (potentially) critical tensile stresses in the other layers. therefore, the use of relatively high residual stresses to enhance the mechanical behaviour can lead to the onset of initial cracks in the layers, which may later propagate in service under external applied stresses, leading to failure of the component. fig. 1 illustrates typical surface cracks associated with residual stresses in planar ceramic-ceramic multilayer systems. an example is that of “tunnelling cracks”, which may appear at the free surface of the layers with tensile stresses and are oriented perpendicular to the layer plane [32, 33]. another type of cracks are the so-called “edge cracks”, which initiate from pre-existing flaws at the free surface of compressive layers, oriented parallel to the layer plane [34, 35]. the third type is delamination, mainly occurring at the corner interface between adjacent layers. figure 1. schematic of surface cracks in ceramic laminates designed with tensile (t) and compressive (c) residual stresses. experimental observations have shown that edge cracking may be associated not only with the magnitude of internal compressive stresses but also with the thickness of the compressive layer [26]. some authors have speculated that this phenomenon may be related to crack bifurcation observed in some laminates with relatively high compressive residual stresses [36, 37]. in a recent work, the authors applied a stress-energy criterion to set the conditions for edge cracking formation and extension in a particular laminate [38]. however, an understanding of the parameters related to the onset c o.ševeček et alii, frattura ed integrità strutturale, 34 (2015) 362-370; doi: 10.3221/igf-esis.34.40 364 and extension of such edge cracks in the compressive layers is still lacking. in this work, a 2d parametric finite element model has been developed to predict the onset and propagation of an edge crack in ceramic laminates. the fe model utilizes the coupled stress-energy criterion [39], which considers simultaneously the necessary stress and energy conditions for the onset of the edge/tunnelling cracks and their further propagation. several cases have been computed to show the effect of the compressive residual stresses on the onset and extension of edge cracks in ceramic laminates. experimental observations he ceramic laminate of study consists of 9 alternated layers combining two ceramic materials: (i) alumina with 5% tetragonal zirconia, named as atz, (ii) alumina with 30% monoclinic zirconia, referred to as amz. fig. 2 shows a schematic of a prismatic bending bar with approx. dimensions of (lxbxh) 45mm x 4mm x 3mm. due to the different thermal strains during cooling down from the sintering temperature, elastic strains are generated in the atz and amz layers, which lead to internal (in-plane) residual stresses. in this particular case, the atz layers have tensile stresses and the amz layers compressive stresses. for more details on the estimation of residual stresses see [26, 35]. in fig. 2 an edge crack along the centre of the amz layer can be clearly seen. this is due to the tensile stress component generated at the free surface, having its maximum value at the edge, and decreasing into the material (see [34] for more details). figure 2. experimental observation of the edge crack phenomenon in compressive amz layer, and stress redistribution at the free surface of the thinner compressive layer. numerical analysis of edge cracking in laminates fe model he fe model prepared for the studies has been designed as a fully parametric model which enables automatic creation of any arbitrary laminate configuration with different volume ratios of particular material components (leading to different levels of residual stresses) or different thicknesses of the amz layer. based on the real specimens, the considered model consists of nine layers composed by alternating atz and amz materials. the height and width of the laminate was fixed for all simulations to be h=3mm and w=4mm, respectively. the thickness of the inner amz layer was varied in the interval (30-350m) and the thicknesses of the atz layers correspondingly tailored to reach the total thickness of 3mm. the material properties for the atz and amz layers needed for the numerical simulation are listed in tab. 1. to simulate (i) the nucleation and (ii) the propagation of the edge crack and its dependency on the layer thickness and level of residual stress inside the layer, a 2d fe model of the laminate cross-section was created – see fig. 3. quadratic plane183 elements with generalized plane strain option were used to correctly capture the thermoelastic stress state in the laminate. fe software ansys 15.0 was used for this purpose. an example of the fe mesh is shown in fig. 3. the t t edge (surface) crack atz layer amz layer x z y t laminate cross-section atz amz atz a o.ševeček et alii, frattura ed integrità strutturale, 34 (2015) 362-370; doi: 10.3221/igf-esis.34.40 365 thickness of the inner amz layer is set to values between 30m and 350m; the length (depth) of the edge crack into the amz layer can be set in the interval 0m to 400m. for every thickness of the amz layer, a large number of simulations with different edge crack lengths was done. in the first step, when the edge crack length is equal to 0m (no edge crack) the stresses yy along the prospective crack path and potential energy of the uncracked body are calculated and saved for further postprocessing. in the next simulations, the edge crack of a given length is introduced in the model and the actual potential energy of the cracked body (for each crack length) is calculated again and used later for calculation of the incremental energy release rate ginc(a) and the energy release rate (err) g(a) at the crack tip as follows:       ( ) (0) ( ) / ( ) ( ) / incg a w w a a g a dw a da , (1) where w is the potential energy which depends on the crack length – see [38]. for verification purposes, the err g(a) at the crack tip was also calculated in ansys simulation using the implemented cint function (employing j-integral). it was found that it leads to practically same curves of errs as the energy approach based on eq. (1). the biggest advantage of the energy approach is that we can directly calculate the incremental err ginc(a) as well as the err at the crack tip g(a). if the contour integral method is to be used, more care about the used mesh is necessary and also a recalculation of g(a) to ginc(a) has to be made in the postprocessing. figure 3. schematic of the fully parametric fe model, developed to study the propagation of edge cracks in the compressive amz layers. material e [gpa]  [-]  x106 [k-1] c [mpa] kic [mpa.m1/2] gc [j/m2] atz 39010 0.22 9.80.2 422±30 3.20.1 252 amz 28010 0.22 80.2 90±20 2.60.1 232 table 1: material properties of the atz and amz layers [40]. coupled stress-energy criterion in order to determine the suitable conditions for the onset of the edge crack, the coupled stress-energy criterion was employed – see [39, 41]. this criterion states that a crack originates if two conditions (i.e. stress and energy conditions) are fulfilled simultaneously – namely ginc(a)≥gc(amz) and yy≥c. the first condition means that there is enough energy x z y laminate cross-section circumferential edge cracks h=const.=3mm 2d fe model (1/4 symmetry) t1 t1 t2 a w=4mm fe parametric study:  t2=30-350m (step 10 m)  a=0-400m (step 1 m) t2=100m t2=350m element size 0.5m t1= t(atz) t2= t(amz) o.ševeček et alii, frattura ed integrità strutturale, 34 (2015) 362-370; doi: 10.3221/igf-esis.34.40 366 available to create a crack, and the second condition stipulates that the tensile stress is greater than the tensile strength all along the new presumed crack path. to predict the onset of such an edge crack, the coupled criterion [39, 41] allows getting rid of any assumption on the existence of flaws able to trigger cracking [36, 37]. there is no adjustable parameter in the coupled criterion, whereas in the other case the flaw size is selected so as to fit with the experimental measures. this choice is somewhat arbitrary because it does not rely on micrographic observations. moreover the flaw approach analyses the early stage of the edge cracking and assumes a further crack growth in depth and along the specimen faces (channelling) to reach the observable state. on the other hand, with the coupled criterion we make the assumption that the crack appears almost simultaneously all around the specimen and then grows in depth. application to ceramic laminates for demonstration, let us consider our laminate of study, where the thickness of the amz layer is selected as 0.150mm. after the sintering process the laminate is cooled down from the reference (sintering) temperature lying between 12001500°c to room temperature which results in origination of compressive residual stresses inside the amz layer (and tensile stresses in atz layer). in case that the difference to the reference temperature is relatively low (e.g. ≈ 700°c), the magnitude of compressive residual stresses will be relatively low (in this particular case ≈-400mpa) and no edge crack can be initiated, because at no point both energy and stress criterion is fulfilled (yy≥c and ginc(a)≥gc(amz)) – see fig. 4a). if the specimen is further cooled down until a value of residual stress res(amz)=-432mpa inside the amz layer, then a first point of satisfaction of both criteria is reached (namely ginc(a)=gc(amz)) and the edge crack is originated with a sudden jump from zero length to length a1=0.059mm as depicted in the fig. 4b). after continuation of the cooling down process, the residual stresses inside the amz layer become yet lower and can theoretically reach values around -700mpa. this state is demonstrated in the fig. 4c). once the crack is nucleated, then it propagates through the amz layer as long as the err at the crack tip g(a) is greater than gc(amz). the final crack length after the cooling down process is thus determined by point 3 in the fig. 4c) and reaches a value of a3. if the curve of g(a) become higher than gc(amz) at all points along the possible edge crack path, then the amz layer should break totally in the whole plane of the specimen. this can thus indicate not suitable laminate configurations for which the processing of the specimens would become problematic. results ith the introduced model a parametric study involving an influence of the amz layer thickness and level of residual stress inside this layer on the origination and propagation of the edge crack has been carried out. the aim was to understand how the mentioned parameters influence the edge cracking phenomenon. a large number of different laminate configurations were calculated in order to obtain general insight into the problem. let us consider now several laminate configurations with different thicknesses of the amz layer, ranging from 50 to 350m. if the total height of the laminate is kept constant, then these configurations will result in different volume ratios of atz and amz components and thus also in different levels of residual stresses (upon the assumption of a complete cooling down process from 1300°c to room temperature). in order to enable a comparative study for a given level of residual stress, a corresponding t has to be first calculated for each laminate configuration. then a further set of simulations is performed by introducing an edge crack with a length between 0m and 400m (with a step of 1m), enabling the estimation of g, ginc and yy (along the prospective crack path) as a function of the edge crack length a. consider now a level of residual stress in the amz layer to be res(amz)=-200mpa. the dimensionless err and tangential stress yy ahead the crack tip are plotted together in fig. 5a. this plot clearly shows that no edge cracking is possible. if the level of compressive stress is increased to the value res(amz)=-300mpa as shown in fig. 5b, we can clearly see that for amz layers thicker or equal to 285m edge cracking can be predicted, since both conditions yy≥c  and ginc(a)≥gc(amz) are fulfilled simultaneously to certain length of the edge crack indicated by point 1 in the referred graph. once the edge crack is created, it propagates until err at the crack tip is higher than the fracture toughness of the material g(a) ≥gc(amz). again for layer thicknesses lower than 285m no edge cracking is to be expected. w o.ševeček et alii, frattura ed integrità strutturale, 34 (2015) 362-370; doi: 10.3221/igf-esis.34.40 367 (a) (b) (c) figure 4. the dimensionless incremental energy release rate ginc(a)/gc(amz), the dimensionless energy release rate g(a)/gc(amz) and the dimensionless tensile stress yy(a)/c(amz) for t(amz)=0.15mm and compressive residual stress in amz layer: a) res(amz)=-400mpa, b) res(amz)=-432mpa, c) res(amz)=-700mpa (a) (b) figure 5. the dimensionless incremental energy release rate ginc(a)/gc(amz), the dimensionless energy release rate g(a)/gc(amz) and the dimensionless tensile stress yy(a)/c(amz) for different thicknesses of the compressive amz layer at certain level of residual compressive stress: a) res(amz)=-200mpa, b) res(amz)=-300mpa. o.ševeček et alii, frattura ed integrità strutturale, 34 (2015) 362-370; doi: 10.3221/igf-esis.34.40 368 outlook he model can be applied to study the combined effect of residual stress and thickness of the compressive embedded layers, which can define lower and upper bounds for the absence or presence of edge cracks in ceramic laminates. based upon this model, recommendations on layer architectural design can be given, which should prevent the formation of edge cracking in laminate systems designed with internal residual stresses. an extension of this model will be the study of edge crack formation and extension considering the combination of residual stresses and layer thickness as design parameters. in such case, several possibilities for improvement in the mechanical properties of the system (i.e. fracture resistance and strength) are to be expected. conclusions his work presents a novel approach to predict the onset and propagation of surface cracks (namely edge cracks) in ceramic laminates, associated with the residual stresses developed after cooling down from the sintering step. a full parametric 2d finite element model was developed to simulate the initiation and propagation of the edge crack in the compressive layers. the conditions for crack initiation/propagation were assessed using a coupled stressenergy criterion. the analysis only requires the values of the elastic moduli and poisson’s ratio of the layers, the coefficient of thermal expansion, the toughness and the tensile strength of the compressive layer. there is no adjustable parameter and there is no need to assume the presence of surface defects to initiate fracture. it was further found that, for a given thickness of the compressive layer, no edge crack is to initiate for relatively low internal (in-plane) compressive residual stress in the layer. for higher stress values, edge crack may initiate and grow in a stable manner. finally, for relatively higher stress values, the formation of edge cracks will be followed by the fracture of the entire layer in an unstable fashion. in future work, we will focus on the validation of the obtained results on different real specimens with various thicknesses and levels of residual stresses, aiming to provide guidelines for the fabrication of layered ceramics with controlled surface cracks. acknowledgements he work has been supported by the netme centre established thanks to a financial support of the european regional development fund under the operational program research and development for innovation. the presented results have been obtained within netme centre plus (lo1202) project co-funded by the czech ministry of education, youth and sports within the support program national sustainability program i. a financial support of the czech science foundation under the project no. 14-11234s is also gratefully acknowledged. references [1] griffith, a.a., the phenomenon of rupture and flow in solids, phil. tran. roy. soc. london, a221 (1920) 163-198. [2] kingery, w.d., bowen, h.k., uhlmann, d.r., introduction to ceramics. new york: john wiley & sons., (1976) 1032. [3] danzer, r., a general strength distribution function for brittle materials, journal of the european ceramic society, 10 (1992) 461-472. [4] morrell, r., fractography of brittle materials. teddigton: national physical laboratory, (1999) 86. [5] danzer, r., mechanical failure of advanced ceramics: the value of fractography, key engineering materials, 223 (2002) 1-18. [6] lawn, b., fracture of brittle solids. 2nd ed. solid state science, new york, usa: cambridge university press. (1993) [7] munz, d., fett, t., ceramics. mechanical properties, failure behaviour, materials selection. materials science, ed. r. hull, et al., berlin: springer (1999). [8] danzer, r., lube, t., supancic, p., damani, r., fracture of advanced ceramics, advanced engineering materials, 10(4) (2008) 275-298. t t t o.ševeček et alii, frattura ed integrità strutturale, 34 (2015) 362-370; doi: 10.3221/igf-esis.34.40 369 [9] lange, f.f., powder processing science and technology for increasing reliability, j. am. ceram. soc., 72(11) (1989) 315. [10] green, d.j., tandon, r., sglavo, v.m., crack arrest and multiple cracking in glass through the use of designed residual stress profiles, science, 283(5406) (1999) 1295-1297. [11] qi, y.e., zhang, y.s., fang, y., hu, l.t., design and preparation of high-performance alumina functional graded self-lubricated ceramic composites, composites part b: engineering, 47(0) (2013) 145-149. [12] clegg, w.j., kendall, k., alford, n.m., button, t.w., birchall, j.d., a simple way to make tough ceramics, nature, 347 (1990) 455-457. [13] marshall, d.b., ratto, j.j., lange, f., enhanced fracture toughness in layered microcomposites of ce-zro2 and al2o3, j. am. ceram. soc., 74(12) (1991) 2979-2987. [14] chartier, t., merle, d., besson, j.l., laminar ceramic composites, journal of the european ceramic society, 15 (1995) 101-107. [15] cutler, w.a., zok, f.w., lange, f.f., mechanical behavior of several hybrid ceramic-matrix-composite laminates, journal of the american ceramic society, 79(7) (1996) 1825-1833. [16] clegg, w.j., design of ceramic laminates for structural applications, material science and technology, 14 (1998) 483495. [17] rao, m., sanchez-herencia, j., beltz, g., mcmeeking, r.m., lange, f., laminar ceramics that exhibit a threshold strength, science, 286 (1999) 102-105. [18] mcmeeking, r.m., hbaieb, k., optimal threshold strength of laminar ceramics, zeitschrift metallkunde, 90(12) (1999) 1031-1036. [19] moon, r.j., et al., r-curve behavior in alumina-zirconia composites with repeating graded layers, engineering fracture mechanics, 69(2002) (2002) 1647-1665. [20] orlovskaya, n., et al., robust design and manufacturing of ceramic laminates with controlled thermal residual stresses for enhanced toughness, journal of materials science, 40 (2005) 5483-5490. [21] sglavo, v.m., paternoster, m., bertoldi, m., tailored residual stresses in high reliability alumina-mullite ceramic laminates, j. am. ceram. soc., 88(10) (2005) 2826-2832. [22] bueno, s., baudín, c., layered materials with high strength and flaw tolerance based on alumina and aluminium titanate, j. eur. ceram. soc., 27(2-3) (2007) 1455-1462. [23] bermejo, r., et al., threshold strength evaluation on an al2o3–zro2 multilayered system, journal of the european ceramic society, 27(2-3) (2007) 1443-1448. [24] tomaszewski, h., weglarz, h., wajler, a., boniecki, m., kalinski, d., multilayer ceramic composites with high failure resistance, journal of the european ceramic society, 27 (2007) 1373-1377. [25] bermejo, r., pascual, j., lube, t., danzer, r., optimal strength and toughness of al2o3–zro2 laminates designed with external or internal compressive layers, journal of the european ceramic society, 28(8) (2008) 1575-1583. [26] bermejo, r., baudin, c., moreno, r., llanes, l., sanchez-herencia, a.j., processing optimisation and fracture behaviour of layered ceramic composites with highly compressive layers, composites science and technology, 67(9) (2007) 1930-1938. [27] bermejo, r., et al., residual stresses, strength and toughness of laminates with different layer thickness ratios, acta materialia, 54(18) (2006) 4745-4757. [28] lugovy, m., slyunyayev, v., subbotin, v., orlovskaya, n., gogotsi, g., crack arrest in si3n4-based layered composites with residual stress, composite science and technology, 64(13-14) (2004) 1947-1957. [29] lugovy, m., et al., apparent fracture toughness of si3n4-based laminates with residual compressive or tensile stresses in surface layers, acta mater., 53 (2005) 289-296. [30] sglavo, v.m., bertoldi, m., design and production of ceramic laminates with high mechanical resistance and reliability, acta mater., 54(18) (2006) 4929-37. [31] bermejo, r., torres, y., anglada, m., llanes, l., fatigue behavior of alumina-zirconia multilayered ceramics, journal of the american ceramic society, 91(5) (2008) 1618-1625. [32] ho, s., suo, z., tunneling cracks in constrained layers, journal of applied mechanics, 60 (1993) 890-894. [33] hillman, c., suo, z., lange, f., cracking of laminates subjected to biaxial tensile stresses, journal of the american ceramic society, 79(8) (1996) 2127-2133. [34] ho, s., hillman, c., lange, f.f., suo, z., surface cracking in layers under biaxial, residual compressive stress, journal of the american ceramic society, 78(9) (1995) 2353-2359. o.ševeček et alii, frattura ed integrità strutturale, 34 (2015) 362-370; doi: 10.3221/igf-esis.34.40 370 [35] bermejo, r., sanchez-herencia, a.j., baudin, c., llanes, l., residual stresses in al2o3-zro2 multilayered ceramics: nature, evaluation and influence on the structural integrity, boletin de la sociedad espanola de ceramica y vidrio, 45(5) (2006) 352-357. [36] hbaieb, k., mcmeeking, r., lange, f., crack bifurcation in laminar ceramics having large compressive stress, international journal of solids and structures, 44(10) (2007) 3328-3343. [37] chen, c.r., bermejo, r., kolednik, o., numerical analysis on special cracking phenomena of residual compressive inter-layers in ceramic laminates, engineering fracture mechanics, 77(13) (2010) 2567-2576. [38] leguillon, d., sevecek, o., martin, é., bermejo, r., edge cracking due to a compressive residual stress in ceramic laminates, comptes rendus mécanique, 343(3) (2015) 192-198. [39] leguillon, d., strength or toughness? a criterion for crack onset at a notch, european journal of mechanics a/solids, 21(1) (2002) 61-72. [40] bermejo, r., et al., fracture behaviour of an al2o3-zro2 multi-layered ceramic with residual stresses due to phase transformations, fatigue & fracture of engineering materials & structures, 29(1) (2006) 71-78. [41] martin, e., leguillon, d., energetic conditions for interfacial failure in the vicinity of a matrix crack in brittle matrix composites,, international journal of solids and structures, 41 (2004) 6937-6948. microsoft word numero_34_art_24 l. e. kosteski et alii, frattura ed integrità strutturale, 34 (2015) 226-236; doi: 10.3221/igf-esis.34.24 226 focussed on crack paths applications of lattice method in the simulation of crack path in heterogeneous materials l. e. kosteski prof. at unipampa university, alegrete, rio grande do sul, brazil luiskosteski@gmail.com f. s. soares student of promec/ufrgs, mechanical post-graduation program, federal univ. rio grande do sul brazil szs.fernando@gmail.com i. iturrioz prof. of promec/ufrgs, brazil ignacio@mecanica.ufrgs.br abstract. the simulation of critical and subcritical crack propagation in heterogeneous materials is not a simple problem in computational mechanics. these topics can be studied with different theoretical tools. in the crack propagation problem it is necessary to lead on the interface between the continuum and the discontinuity, and this region has different characteristics when we change the scale level point of view. in this context, this work applies a version of the lattice discrete element method (ldem) in the study of such matters. this approach lets us to discretize the continuum with a regular tridimensional truss where the elements have an equivalent stiffness consistent with the material one wishes to model. the masses are lumped in the nodes and an uni-axial bilinear relation, inspired in the hilleborg constitutive law, is assumed for the elements. the random characteristics of the material are introduced in the model considering the material toughness as a random field with defined statistical properties. it is important to highlight that the energy balance consistence is maintained during all the process. the spatial discretization lets us arrive to a motion equation that can be solved using an explicit scheme of integration on time. two examples are shown in the present paper; one of them illustrates the possibilities of this method in simulating critical crack propagation in a solid mechanics problem: a simple geometry of grade material. in the second example, a simulation of subcritical crack growth is presented, when a pre-fissured quasi-brittle body is submitted to cyclic loading. in this second example, a strategy to measure crack advance in the model is proposed. finally, obtained results and the performance of the model are discussed. keywords. lattice model; dynamic crack propagation; subcritical propagation. introduction he crack propagation in heterogeneous materials has some particular issues, as the localization phenomenon and the influence of clusters of microfissures which are some of the effects that characterize this problem. the study of this problem from a continuum mechanics point of view let advance, but it is necessary to overpass the homogenization of anisotropic damage with a non-homogeneous distribution. an alternative to the continuum approach is to simulate t l. e. kosteski et alii, frattura ed integrità strutturale, 34 (2015) 226-236; doi: 10.3221/igf-esis.34.24 227 damage development through a discrete element model. in this context, this paper presents a method of discrete elements formed by bars. this method consists essentially in representing the continuum through a set of uniaxial elements whose stiffness is equivalent to the solid that must be modeled, model masses are lumped in the nodes connecting the elements. the non-linear behavior is captured using a very simple bilinear constitutive law applied in each element. the area below this constitutive law is coherent with the energy balance of the system. the governing equations obtained as result of the spatial discretization are integrated in the time domain using an explicit scheme of integration (central difference method). in the present paper two applications are presented. in the first one, a plate of functionally grade material is studied when the variation of the critical crack path is simulated for different levels of heterogeneity in the mechanical properties. the functionally graded materials (fgm) are a new generation of engineering composites characterized for having a smooth variation of mechanical/thermal, or electromagnetic properties. they are new advanced multifunctional materials, which are tailored to take advantage of their constituents, for example, in a ceramic/metal fgm, heat and corrosion resistance of ceramics works together with mechanical strength and toughness of metals. to carry out an application of fgms, scientific knowledge of fracture and damage tolerance are important for improving their structural integrity. for this kind of problems, the finite element method with cohesive interfaces is usually employed (xu and needleman [1]; paulino and zanhg [2]). in the second application, the lattice discrete element method here presented is applied in the simulation of subcritical crack growth in a heterogeneous material. in this example, the proposed strategy to measure crack propagation velocity is commented. other approaches in the simulation of subcritical crack propagation due to fatigue can be quoted, among them the works of xu and yuan [3] and unger et al [4], using the extended finite elements method, and the works of yang & cheng [5], yamaguchi et al [6] and siegmund [7], that combine the finite elements method with cohesive interface techniques. discrete element model description he discrete element method employed in this paper was proposed by riera [8] and is based on the representation of a solid by means of a cubic arrangement of elements able to carry only axial loads. the discrete elements representation of the orthotropic continuum was adopted to solve structural dynamic problems by means of explicit numerical integration of the equations of motion, assuming the mass lumped at the nodes. each node has three degrees of freedom, corresponding to the nodal displacements in the three orthogonal coordinate directions. fig. 1a,b illustrates the basic bar arrangement used in this approach. the equations that relate the properties of the elements to the elastic constants of an isotropic medium are:       2 29 89 2    ,           ,          ,      4 8 18 24 3 l da e l e a e l e               (1) in which e and  denote the young’s modulus and the poisson’s ratio, respectively, while la and da represent the areas of longitudinal and diagonal elements. the resulting equations of motion may be written in the well-known form:     0rm x c x f t p t         (2) in which x  represents the vector of generalized nodal displacements, m is the diagonal mass matrix, c is the damping matrix, also assumed diagonal,  rf t  is the vector of internal forces acting on the nodal masses and  p t  is the vector of external forces. obviously, if m and c are diagonal, eq. 2 is not coupled. then the explicit central finite differences scheme may be used to integrate eq. 2 in the time domain. since the nodal coordinates are updated at every time step, large displacements can be accounted for in a natural and efficient manner. non-linear constitutive model for material damage the softening law for quasi-brittle materials, proposed by hillerborg [9], was adopted to handle the behavior of the materials simulated here by means of the triangular constitutive relationship for the ldem bars, presented in fig. 1c, which allows accounting for the irreversible effects of crack nucleation and propagation. the area under the force vs. strain curve (the area of the triangle oab) is related to the energy density necessary to fracture the element area of influence. thus, for a given point p on the force vs. strain curve, the area of the triangle oap quantifies the energy density dissipated by damage. t l. e. kosteski et alii, frattura ed integrità strutturale, 34 (2015) 226-236; doi: 10.3221/igf-esis.34.24 228 once the damage energy density equals the fracture energy, the element fails and loses its load carrying capacity. on the other hand, under compression the material is assumed linearly elastic. thus, failure in compression is induced by indirect tension. figure 1: ldem discretization strategy: (a) basic cubic module, (b) generation of a prismatic body, (c) bilinear constitutive law adopted for ldem uniaxial elements. constitutive parameters and symbols shown in fig. 1c are defined below: the element axial force f depends on the axial strain ε. the area associated to each element was given in eq. 1 for longitudinal and diagonal elements. an equivalent fracture area, fia , of each element is defined in order to satisfy the condition that the energy dissipated by fracture of the continuum and by its discrete representation are equivalent. with this purpose, fracture of a cubic sample of dimensions lll is considered. the energy dissipated by fracture of a continuum cube due to a crack parallel to one of its faces is presented in eq. 3: 2 f fг g g l   (3) 21 24 4 4 3 dem f a a aг g c c c l                (4) in eq. 3, λ represents the actual fractured area, i.e., l2. on the other hand, the energy dissipated when a ldem module of dimensions lll fractures in two parts consists of the contributions of five longitudinal elements (four coincident with the module edges and one internal element) and four diagonal elements. then, the energy dissipated by a ldem module can be written as shown in eq. 4 (kosteski et al [10]). the first term between brackets, in eq. 4, accounts for the four edge elements, the second term for the internal longitudinal element, while the third term represents the contribution of the four diagonal elements. the coefficient ca is a scaling parameter used to establish the equivalence between γ and γdem. thus: 2 222 3 f f ag l g c l       (5) 2 23 4 ,   22 22 f f l da l a l             (6) from eq. 5 it follows that 3 / 22ac  . finally, the equivalent fracture areas of the longitudinal and the diagonal elements are presented in eq. 6. the critical failure strain ( p ) is defined as the largest strain attained by the element before damage initiation (point a in fig. 1c). the relationship between p and the specific fracture energy, fg , is given in terms of linear elastic fracture mechanics as:  21 f p f g r e     (7) l. e. kosteski et alii, frattura ed integrità strutturale, 34 (2015) 226-236; doi: 10.3221/igf-esis.34.24 229 1 fr y a  (8) in which fr is the so-called failure factor, which may account for the presence of an intrinsic defect of critical size a . fr may be expressed in terms of critical fracture dimension of a , as presented in eq. 8, where y represents the dimensionless parameter that depends on both the specimen and the crack geometry. notice that, if the characteristic dimension of the simulated body, l, is smaller than the intrinsic critical crack size, a , the collapse will be stable. on the other hand, if l > a , an instable global collapse is expected. also, one could write the failure factor, fr , in terms of the fragility number, s , proposed by carpinteri [11], this dimensionless parameter measures the fragility quality of a determined structure. in the expressions presented in eq. 9, one can see the fragility number, s , in terms of the critical stress intensity factor, ick , and the critical stress, p ; or in terms of the critical specific fracture energy, fg , and the critical strain, p ; or, using eq. 7 and eq. 8, in terms of the ldem parameters, as shown in eq. 10. fic p p g ek s l e l    (9) 1 f a s y lr l   (10) if two models are built with different materials and different dimensions, one can expect similar global mechanical behavior if both models have the same s value.; the element loses its load carrying capacity when the limit strain, r , is reached (point b in fig. 1c). this value must satisfy the condition that, upon failure of the element, the dissipated energy density equals the product of the element fracture area, fa , and the specific fracture energy, ,fg divided by the element length. hence:   2 0 2 r f f i r p i i g a k ea f d l       (11) 2 2ff i r p i i g a k e a l              (12) 22 f f i cr p i g a l e a           (13) in which the sub index i is replaced by l or d depending on whether the element under consideration is longitudinal or diagonal. the coefficient rk is a function of the material properties and the element length il . in order to guarantee the stability of the algorithm, the condition    1rk  must be satisfied. in this sense, it is interesting to define the critical element length crl (see eq. 13).  3 / 22fl l a a        (14)  3 / 11f d d a a        (15) l. e. kosteski et alii, frattura ed integrità strutturale, 34 (2015) 226-236; doi: 10.3221/igf-esis.34.24 230 in the special case of an isotropic continuum with 0.25  , the value of the coefficients shown above are 1.125  and 0.4  , which lead to    * */      /     0.34l l d da a a a  . thus, for practical purposes, a single value of the critical length can be used for longitudinal and diagonal elements. therefore, the stability condition is expressed by eq. 16 and the limit strain by eq. 17. 1 cr r i cr i l k l l l          (16) r r pk  (17) the random distribution of material parameters in the ldem environment is modelled, defining the toughness, fg , as a random field with a type iii (weibull) extreme value distribution. details of the implementation can be found in kosteski et al [12]. figure 2: (a) layout and boundary condition of the rectangular plate with central fissure and imposed constant strain velocity; (b) the mechanical properties adopted for the ldem model; (c) the constitutive uniaxial law adopted for the bars; (d) the characteristic of the analyzed cases. first application: simulation of critical crack propagation in functional graded materials he present example shows a rectangular plate of polimetilmetacrilate (pmma) with a central fissure. the plate dimensions are show in fig. 2.a. this plate is submitted to constant strain velocity of 5m/s in its borders. paulino and zhang [2] studied the influence that the functionally graded material (fgm) has in dynamic crack propagation in this same geometry using the finite element method with cohesive interfaces. the cohesive elements were implemented in the region where fissure propagation could take place. the quoted authors studied the influence of three different types of fgm in the crack propagation event. in case 1 the homogeneous property was considered. in case 2 a hypothetic fgm material was proposed, where just the cohesive properties graded linearly in y axis direction. finally, in case 3 not only the cohesive properties, but also the finite element properties were graded. dem model only the middle of the plate was modeled due to the geometry and load symmetries of the problem. the plate was discretized with 60 modules on each side and one module in the thickness direction. the boundary conditions applied permit to represent the left border as a symmetry axis. the plane strain condition was imposed fixing the displacements in t l. e. kosteski et alii, frattura ed integrità strutturale, 34 (2015) 226-236; doi: 10.3221/igf-esis.34.24 231 the thickness direction; the half of the fissure was discretized using 6 cubic modules. the material properties and the main model characteristics are presented in fig. 2b. fig. 3 shows the constitutive law adopted for the material, considered homogeneous in the vertical direction of the plate. the critical step time is related to the time that an elastic wave takes to pass through the normal elemental bar. in the present case, for homogeneous material, the step critical time was δtcrit =1.82 e-8 s. the main difference between paulino and zhang’s [2] analysis and the present study is the poisson coefficient value, in dem model when one works with the cubic arrangement (see fig.1) one is limited to work with poisson’s coefficient of 0.25, if the goal is to model an elastic isotropic and homogeneous material. if one wishes to model elastic and isotropic materials with other poisson’s coefficient, it will be necessary to employ another kind of geometric arrangement. in fig.2d the case characteristics studied by paulino and zhang [2] are presented. the uniaxial constitutive law used in this work in the case 1 is also presented in fig 2.c. obtained results case 1, homogeneous case: the homogeneous material is considered in this first case. thus, in this case, there isn’t any spatial variation in the elements constitutive law in dem model. the fig. 4(i) shows a fracture configuration obtained by paulino and zhang [2] (a), the main crack begins to branch when it reaches a length of 1.05mm, with an approximate angle of 29° in relation to the horizontal direction. in the case of the ldem simulation (b) the branching begins when the main crack reaches a length of 1.0mm with an angle of 32° in relation to the horizontal direction. in both simulations it is possible to verify another characteristic that is seen in fig.4(i) (a) and (b) which is the similarity between the two final configurations, for example, it is possible to observe a secondary branching in both figures. the lack of symmetry in the final configuration of ldem simulation characterizes an unstable propagation process. this method has been verified sensitive to disturbances that occur during the process. these disturbances could be produced by rounding errors in the calculus and due to little changes in the step integration time. case 2, graded gc : in the present case only the toughness parameter cg is graded in vertical direction. the cohesive interface of the finite element model used by paulino and zhang [2] is characterized by three parameters that are: the normal maximum tensile in the interface maxnt , the critical opening displacement n and the area closed by the curve that is proportional to the toughness cg . the grade in the interface properties that was implemented to modify the curve is illustrated in fig. 3(a). the graded material proposed in case 2, for ldem simulation, was carried out modifying the uniaxial curve as indicated in fig. 3b. the elastic modulus that is directly linked with the initial slope is maintained constant. the cg graduation is obtained modifying the critical strain p, maintaining r constant to facilitate the comparison with the cohesive model. the material properties in the bottom boundary are: gc = 176.1 n/m and p = 0.0125, r = 0.06, these values grade linearly up to gc = 528.4 n/m, p = 0.0375 and r = 0.06 in the top boundary. as the minimum value of toughness occurs in the bottom boundary and the maximum one occurs in the top boundary, it is expected that crack propagation take place in the inferior region of the plate, as it is possible to observe in fig. 3(ii) (a) and (b). the comparison between paulino and zhang’s [2] results and ldem, in terms of final configuration, show a significant similarity. -0.15 0.00 0.15 0.30 0.45 0.60 0.75 -0.04 -0.02 0.00 0.02 0.04 0.06 0.08 0.10 0.12 0.14 cer for -1/2w cer midle cer for 1/2w f ( n )  (%) (a) (b) (c) figure 3: a) the cohesive interface laws used by paulino and zhang [2]; the elemental constitutive law used in ldem implementation: (a) for the graded material in case 2; (b) for the graded material in case 3. -0.15 0.00 0.15 0.30 0.45 0.60 0.75 -0.04 -0.02 0.00 0.02 0.04 0.06 0.08 0.10 0.12 0.14 cer for -1/2w cer m idle cer for 1/2w f ( n )  (%) l. e. kosteski et alii, frattura ed integrità strutturale, 34 (2015) 226-236; doi: 10.3221/igf-esis.34.24 232 case 3, graded e and gc : in case 3, the elasticity modulus e and the toughness parameter gc are changed simultaneously in vertical direction. in paulino and zhang’s [2] work, a graduation was proposed to the interface properties in the vertical direction, in the same manner of case 2, and the elasticity modulus e in the elements was modified. in dem approach for case 3, the constitutive elemental law was modified as shown in fig. 3(c). in fig.4(iii) the comparison between paulino and zhang’s [2] implementation (a) and ldem implementation (b), in terms of final configurations, is shown. in the present case, the similarity between both configurations is not too clear, but both show the same general tendency. (i) (ii) (iii) figure 4: (i) final configuration for the case 1, homogeneous material. final configuration for the graded materials (ii) for the case 2, (iii) for the case 3, (in all cases (i-iii) (a) the paulino and zhang’s [2] config., (b) the ldem config. (a) (b) (c) d) figure 5: a) energy balance during the simulated process in case 1; b) the elastic energy; c) kinetic energy; d) damage dissipated energy for the three analyzed cases. comparison in terms of energy balance: here the results in terms of energy balance during the whole fracture process are discussed. in fig. 5(a) the complete balance of energy during the whole process for case 1 is shown. in fig. 5 (b), (c), and (d), the elastic, kinetic and dissipated energy through all the damage process are shown for the three cases. it can be verified in fig. 5(d) that case 1 shows high level of dissipated energy due to the greater fracture area generated during the simulation. in fig. 5(c), the abrupt change in kinetic energy in cases 2 and 3 shows a sensitive change in the crack propagation velocity during the whole process. this is in accordance with the final configuration obtained, where branching and secondary cracks appear more than in case 1. 0.0 2.0x10 -6 4.0x10 -6 6.0x10 -6 8.0x10 -6 1.0x10 -5 1.2x10 -5 1.4x10 -5 0.0 5.0x10 -5 1.0x10 -4 1.5x10 -4 2.0x10 -4 2.5x10 -4 3.0x10 -4 3.5x10 -4 4.0x10 -4 4.5x10 -4 5.0x10 -4 elastic energy kinetic energy internal energy damage disipated energy e n e rg y (j ) t (s) 0.0 2.0x10 -6 4.0x10 -6 6.0x10 -6 8.0x10 -6 1.0x10 -5 1.2x10 -5 1.4x10 -5 0.0 5.0x10 -5 1.0x10 -4 1.5x10 -4 2.0x10 -4 2.5x10 -4 3.0x10 -4 3.5x10 -4 4.0x10 -4 case 1 case 2 case 3 e la st ic e n e rg y (j ) t (s) 0.0 2.0x10 -6 4.0x10 -6 6.0x10 -6 8.0x10 -6 1.0x10 -5 1.2x10 -5 1.4x10 -5 0.0 5.0x10 -5 1.0x10 -4 1.5x10 -4 2.0x10 -4 2.5x10 -4 3.0x10 -4 3.5x10 -4 4.0x10 -4 case 1 case 2 case 3 k in e tic e n e rg y (j ) t (s) 0.0 2.0x10 -6 4.0x10 -6 6.0x10 -6 8.0x10 -6 1.0x10 -5 1.2x10 -5 1.4x10 -5 0.0 5.0x10 -5 1.0x10 -4 1.5x10 -4 2.0x10 -4 2.5x10 -4 3.0x10 -4 3.5x10 -4 4.0x10 -4 case 1 case 2 case 3 d a m a g e d is ip a te d e n e rg y (j ) t (s) l. e. kosteski et alii, frattura ed integrità strutturale, 34 (2015) 226-236; doi: 10.3221/igf-esis.34.24 233 second application: the subcritical crack growth using ldem ldem model ith the goal of studying the subcritical crack propagation in a rectangular plate built with quasi-brittle material, a model was developed using the lattice discrete element method (ldem) presented before. the rectangular plate model has a pre-crack that emanates from a lateral border. the loads and boundary conditions used are illustrated in fig 6(left). in the present case, plane strain condition was adopted; this condition is implemented in ldem using only one cubic module of thickness and restraining of displacements in out of plane direction (dir. y). the plate was also fixed in the right boundary as indicated in fig. 6 (left). a pre-crack was introduced in the model with the goal of favoring subcritical crack growth through the middle of the plate. it is important to highlight that the goal here is not to characterize a specific material, but to explore the capacity of ldem in simulating the subcritical propagation of a preexistent fissure. with the considered parameters, the ratio between rupture and critical strain will be r/p = 60. for this analysis, material toughness gf was considered as a random field characterized by means of a variation coefficient. it will also be considered that the correlation length of the random field is of the same order of the discretization level. implementations regarding the unlinking of discretization level and correlation length of random field are presented in puglia et al [13]. figure 6: (left) ldem model used with details of how the loads and boundary conditions are applied, where b=0.75m (100 modules) and h=0.3075m (41 modules); (right) force transmitted to a normal bar element close to pre-crack tip versus percentage of simulation time. the load was applied in the central nodes of the cubic cells that constitute the top and bottom surfaces of the plate, as indicated in fig. 6 (left). in fig. 6 (right) the graphic shows the tensile force transmitted to a normal bar element placed in the middle of the plate’s high, h, and close to the pre-crack tip versus percentage of simulation time. in this model, a cubic cell length of l = 0.0075 m was adopted, the model has 100 modules in the x direction, 1 module in y direction and 41 modules in z direction. the material properties are characterized for poisson coefficient of  = 0.25, the young modulus is e = 35 gpa, the density value is  = 2400 kg/m3 and the critical strain p = 2.18 10-4. the toughness random field is characterized by a mean value of(gf) = 1155 n/m and a variation coefficient of cv(gf)=5%. in fig. 6 (right), it can be verified that, in a first moment, load rises according to an exponential function, until a stable magnitude is achieved, so that inertial effects are none. after that, oscillation begins and amplitude grows, also according to an exponential function, until stable loading cycle amplitude is reached. this oscillation does not induce considerable dynamic effects in the model, and after 880 cycles loading amplitude is assumed constant. the applied loads produce remote stress acting in the plate of 2.93mpa before oscillation starts, ranging later between a top value of 3.34mpa and lower value of 2.52mpa. obtained results in fig. 7 (left), six crack configurations obtained during propagation process are ilustrated. the elements in darker shade of grey, siding the main crack, are parilly damaged. broken elementes constitute main crack and are not shown. the applied version of ldem constitutive law does not take residual strain into account. constitutive laws that account for such effects are presented in kosteski [10]. the cluster of microfissures that precedes the main fissure in fatigue crack growth (characteristic in quasi-brittle materials) can be clearly seen in the partial configurations illustrated in fig. 7 (left). it is also important to observe that crack propagation does not influence in a significant way the discrete element mesh. w l. e. kosteski et alii, frattura ed integrità strutturale, 34 (2015) 226-236; doi: 10.3221/igf-esis.34.24 234 in fig.7 (right) the graphic illustrates fluctuations of kinetic, elastic and dissipated energy during all the damaged process, where abrupt changes in such values of energy are associated to local instabilities in main crack grow, denoting the spasmodic character of simulated subcritical growth. aiming to improve visualization of the energetic fluctuations during simulated crack growth, the dissipated energy curve (red) is multiplied by a 0.02 scaling factor and elastic energy (green) by a 0.04 scaling factor. kinetic energy curve (blue) is shown in original scale. observing fig. 7 it is possible to conclude that the macro crack propagates in subcritical way from (t/tmax=0,70) untill (t/tmax=0.96) when the process becomes unstable. within subcritical growth, in the next subsection, fatigue life is characterized according to the classic paris law. figure 7: (left) main crack configuration during six moments of simulation, where  * / max 100t t t  ; (right) the fluctuations of kinetic, elastic and dissipated energy during simulated damage process. fatigue life characterization: the paris law, based in a potencial law, presents subcritical crack growth velocity (da/dn) as a function of the delta of stress intensity factor (k) acting at the main crack tip. for this work, was computed using the expresion presented in gdoutos [14] which is adequate to the model geometry, boundary conditions and pre-crack configuration here adopted. the value of kchanges (grows) during the simulation process, ask also depends on the crack length, a. having obtained crack propagation velocity (da/dn) and stress intensity factor (k) by mean of the ldem tool, the values can be subtituted in paris equation [(da/dn) = ckm] to model fatigue life during subcritical crack growth. applying log operation in both sides of paris expression it is possible to obtain the constants and that characterize fatigue behavior for the simulated material. the velocity (da/dn) is obtained in the ldem model using the x coordinate of every element and the instant in time when it reaches the critical strain value p, becoming damaged. this strategy implies in assuming that the microfissure cluster which precedes the main crack advances through the plate in the same velocity as the crack itself. thus, (da/dn) is measured computing the time in which each bar reaches the critical strain p, versus the x coordinate of the element central point. also, the same procedure is realized when rupture strain r is achieved. the resulting graphic is seen in fig. 8 (left). figure 8: (left) normalized time versus the x coordinate of the central points of elements that reached (red dots) and (blue dots) during the simulation, the curve equivalent to is denoted by the green dots; (right) plot versus where the straight line indicates subcritical crack growth. the velocity is expressed in µm per cycle. l. e. kosteski et alii, frattura ed integrità strutturale, 34 (2015) 226-236; doi: 10.3221/igf-esis.34.24 235 in fig. 8 (left) the curve denoted by the green dots corresponds to the first elements to become damaged in a given x coordinate. therefore, this set of points forms a curve linked with the damage propagation velocity at the crack tip and the propagation velocity of the main crack itself, according to the previous assumption made. thus, 10 representative points were selected to carry out the curve a versus n. the cycle count begins in the normalized time t*=70, when the loading reaches permanent regime (see fig. 6 right). knowing the crack propagation velocity (da/dn) during the simulation process, it is possible to plot fig. 8 (right), where the log(da/dn) versus log(k) is presented. the tendence line of this curve models the region in crack propagation known as region of stable growth or region ii (see gdoutos [14]). the applied tendence line gives the straight line equation: log(da/dn)  0.22 log(k) -4.37, this means m = 0.22 and c = 4.26  10-5. therefore, it is possible to characterize the modeled material according to paris law as: da/dn = 4.26  10-5 k0.22. pointing out that calculation procedure to obtain the constants c and m was carried out with stress values in pascal [pa] and length in meters [m]. as previously said, the present work focus on exploring the possibilities of the ldem tool in simulating and characterizing fatigue damage development. matters regarding real material modeling are topics for future works. conclusions n this work, two applications of the lattice discrete element method for studying damage development in quasi-brittle materials were presented. in the first example, unstable crack propagation in functional graded material was analyzed. in the second example, subcritical crack propagation due to fatigue damage was studied. in both examples it was possible to verify the great potential of the applied discontinuous mechanics tool in the study of damage development. acknowledgement he authors acknowledge the support of cnpq and capes (brazil). references [1] xu, x., needleman, a., numerical simulations of dynamic crack growth along an interface, international journal of fracture, 74 (1995) 289-324. [2] paulino, g.h., zhang, z., cohesive zone modeling of dynamic crack propagation in functionally graded materials, 5th gracm international congress on computational mechanics. limassol, (2005). [3] xu, y., yuan, h., computational analysis of mixed-mode fatigue crack growth in quasi-brittle materials using extended finite element methods, engineering fracture mechanics, 76 (2009) 165-181. [4] unger, f. j., eckardt, s., könke, c.: modelling of cohesive crack growth in concrete structures with the extended finite element method, comput. methods appl. mech. engrg., 196 (2007) 4087-4100. [5] yang, z. j., chen, j., finite element modelling of multiple cohesive discrete crack propagation in reinforced concrete beams, engineering fracture mechanics, 72 (2005) 2280-2297. [6] yamaguchi, t., okabe, t., kosaka, t., fatigue simulation for ti/gfrp laminates using cohesive elements, advanced composite materials, 19 (2010) 107-122. [7] siegmund, t., cyclic crack growth and length scales. school of mechanical engineering, purdue university, indiana, usa, (2007a). [8] riera, j.d., local effects in impact problems on concrete structures. conference on structural analysis and design of nuclear power plants, 3 (1984). [9] hillerborg, a., a model for fracture analysis. division of building materials, lund institute of technology, tvbm3005 (1978) 1-8. [10] kosteski, l.e., iturrioz, i., batista, r.g., cisilino, a.p., the truss-like discrete element method in fracture and damage mechanics, engineering computations, 6 (2011) 765787. i t l. e. kosteski et alii, frattura ed integrità strutturale, 34 (2015) 226-236; doi: 10.3221/igf-esis.34.24 236 [11] carpinteri, a., mechanical damage and crack growth in concrete: plastic collapse to brittle fracture. martinus nijhoff publishers, dordrecht, xiii+234 (1986). [12] kosteski, l.e., barrios, r., iturrioz, i., crack propagation in elastic solids using the truss-like discrete element method. international journal of fracture, 174 (2012) 139-161. [13] puglia, v.b., iturrioz, i, riera, j.d., kosteski, l., random field generation of the material properties in the truss-like discrete element method, mec. comp., cilamce-mecom, xxix (2010) 6793-6807. [14] gdoutos, e. e., fracture machanics, an introduction, springer, xanthi, greece, (2005). microsoft word numero_49_art_72ex15_2452 s.a. bochkarev et alii, frattura ed integrità strutturale, 49 (2019) 814-830; doi: 10.3221/igf-esis.49.15 814 focused on russian mechanics contributions for structural integrity analysis of spatial vibrations of piezoceramic eccentric cylindrical shells interacting with an annular fluid layer s.a. bochkarev, s.v. lekomtsev, a.n. senin institute of continuous media mechanics, ural branch russian academy of sciences, perm (russian federation) bochkarev@icmm.ru, http://orcid.org/0000-0002-9722-1269 lekomtsev@icmm.ru, http://orcid.org/0000-0002-8331-2979 senin.a@icmm.ru, https://orcid.org/0000-0002-7537-0001 abstract. the work is devoted to a numerical study of the behavior of vertically oriented eccentric (non-coaxial) electroelastic shells, containing a fluid in the gap between them. the solution of the problem is found in the framework of a three-dimensional formulation using the finite element method. the shells are made of the piezoelectric material polarized in the radial direction. thin-walled structures are considered in the framework of the classical theory based on the kirchhoff – love hypotheses, as well as the equations of linear electroelasticity. the distribution of the electric potential through the thickness is assumed linear. the fluid is considered within the framework of a potential theory. the study of the low natural frequencies and vibration modes is carried out for different variants of the boundary conditions at the edges of the shells, the level of fluid in the gap and the eccentricity of the inner shell. the influence of the electric boundary conditions specified on the parts of the shells surfaces covered with electrodes is estimated. keywords. piezoceramics; potential fluid; partial filling; eccentric cylindrical shells; finite element method; natural vibrations. citation: bochkarev, s.a., lekomtsev, s.v., senin a.n., analysis of spatial vibrations of piezoceramic eccentric cylindrical shells interacting with an annular fluid layer, frattura ed integrità strutturale, 49 (2019) 814-830. received: 01.04.2019 accepted: 22.05.2019 published: 01.07.2019 copyright: © 2019 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. introduction n the last few decades, the wide-spread use of structural elements in the form of nested shells with parallel axes, interacting with a fluid or gas contained in the gap between them, gave an impetus to the appearance of many publications, in which such systems are the subject of research. an extensive bibliography, covering recent studies into the dynamic behavior of coaxial shells interacting with both stationary and flowing fluids, is given in review [1] and monograph [2]. smaller reviews extending this list of cited papers and including some unlisted pioneering studies are given in recent articles of the authors [3, 4]. however, in the context of this study, the matter of particular current interest is a few works that take into account the axis misalignment of the inner and outer shells [5–9]. in [5], it was shown that the i http://www.gruppofrattura.it/va/49/2452.mp4 s.a. bochkarev et alii, frattura ed integrità strutturale, 49 (2019) 814-830; doi: 10.3221/igf-esis.49.15 815 axial eccentricity affects the vibration process only in the case of a narrow annular gap between infinite shells. the analysis of the added liquid masses for two infinite cylinders with eccentricity, containing either an ideal or a viscous fluid in the gap between them, was performed in [6] and [7]. as noted in [7], the added masses and viscous damping coefficients, which grow with increasing eccentricity, are of greater practical interest, because they are widely used in studying hydroelastic vibrations and stability of structures in various engineering applications. the analysis of natural frequencies of cylindrical shells with an eccentricity immersed in a rigid cylindrical container was performed in works [8, 9]. the first of these papers considers the system, in which the non-viscous compressible fluid is contained only in the annular gap between the container and the shell, whereas the second paper examines the situation when the inner shell also contains a fluid. it has been demonstrated that with increasing eccentricity, the frequency of vibrations decreases, which is most significant for low circumferential and axial modes. particular attention should also be paid to publications dealing with the analysis of coaxial shells partially filled with a fluid [10–15]. in all these papers, the studies of the dynamic behavior of coaxial shells are made with account of the free-surface sloshing effect, but do not include numerical simulation, which would allow one to estimate the effect of this boundary condition. note that here we cite only those works which analyze the effect of partial filling of shells on the dynamic characteristics of the system. it is shown that an increase in the fluid level causes a decrease in the natural vibration frequencies. a more general review of papers aimed at studying hydroelastic vibrations of partially filled coaxial cylindrical shells is given in monograph [16]. in the above mentioned works, the solution of the problem is searched for in the context of a two-dimensional (flat) or axisymmetric problem formulation. in the case when non-coaxial structures are set in the vertical or horizontal position and partial filled with fluid, their symmetry with respect to the circumferential coordinate is disturbed, which necessitates the use of more complex spatial models. as far as the authors know, such studies, including those that take into account the elasticity of both shells, are not presented in the literature. electroelastic materials embedded in or attached to engineering structures have been used for rather long time in various fields of technology in order to improve the performance characteristics of a product. intellectual systems of passive or active control of dynamic behavior built on the basis of their peculiar properties serve to reduce the level of mechanical vibrations or acoustic noise. the bibliography of basic works dealing with the analysis of various approaches used in modeling the structures with piezoelectric elements, and presenting examples of their practical use can be found in monograph [17]. in [18], the authors come to a conclusion that successful practical application of piezoelectric elements coming in contact with a fluid or gaseous medium is possible only with an adequate description of their coupled response. in the case of thin-walled structures this can be achieved with the model proposed in [19]. the model is based on a singlelayer representation of the elastic body displacements and a layered description of piezoelectric properties. this approach was used for modeling the plates and single shells, including those interacting with a quiescent fluid, and also the elastic structures with external patches made completely or partially from the electroelastic material [20–23]. for a linear distribution of electrical properties through the body thickness, this method, when used in the framework of finite element modeling, allows us to simplify the solution by eliminating the electrical components at the element level. in the literature, there are no papers describing the application of the above method to coaxial shells. thus, the purpose of this work is to analyze the natural frequencies and the corresponding modes of vibrations of elastic and piezoelastic eccentric (non-coaxial) cylindrical shells at different values of the annular gap width and different levels of ideal compressible fluid contained in this gap. the solution of the problem is found using a modified version of the finite element algorithm developed in the previous works for evaluating the hydroelastic interaction of single shell structures with arbitrary cross section completely or partially filled with fluid [24–26]. statement of the problem and constitutive relations e consider a structure consisting of two vertically located eccentric (non-coaxial) shells of length l, radiuses (1)r and ( 2)r , and thicknesses ( 1 )h and ( 2 )h (fig. 1) made of electroelastic material (piezoceramics). hereinafter, the superscripts “(1)” and “(2)” characterize the inner and outer shells, respectively. the axis of rotation of the inner shell is displaced laterally with respect to rotation axis of the outer shell by the value a  ( 2 ) ( 1)( )a r r , and the space between them is filled with an ideal compressible fluid to the level h  (0 )h l . it is necessary to investigate the natural frequencies and modes of vibrations of the system under different kinematic and electric boundary conditions, and geometric parameters (the size of the annular gap, the height of the fluid, eccentricity). w s.a. bochkarev et alii, frattura ed integrità strutturale, 49 (2019) 814-830; doi: 10.3221/igf-esis.49.15 816 figure 1: schematic representation of the computational domain. an ideal compressible fluid is considered in the framework of a potential theory, in which the wave equation in the case of small perturbations takes the following form [27]:     2 2 1 tc   , (1) where  is the velocity potential, c is the speed of sound in the liquid,  is the differential nabla operator,  t is the time derivative. using the perturbation velocity potential as an unknown function allows to take into account both the flow or the rotation of the inviscid compressible fluid with a slight modification of the numerical algorithm. in the case of complete filling of the shell with a fluid, the following boundary conditions are prescribed for the velocity potential:    0, : 0x l x . (2a) in the case of partial filling, it is assumed that the free surface of the fluid frees remains stationary and is free from the dynamic pressure and surface tension. the corresponding boundary condition is given as [28]  : 0x h  . (2b) on the wetted surfaces  ( ) ( )i if ss s s the impermeability conditions hold true      ( ) ( ) i i w tn , (3) where ( )in is the vector of the normal to the shell surface; ( )iw is the normal component of shell displacements; fs and ( )i ss are the surfaces that bound the volumes of the fluid fv and shell ( )i sv . in what follows,  1, 2i . the hydrodynamic pressure p exerted on the elastic structures by the fluid is calculated using the bernoulli equation: s.a. bochkarev et alii, frattura ed integrità strutturale, 49 (2019) 814-830; doi: 10.3221/igf-esis.49.15 817    ( )i fp t   , (4) where f is the fluid density and the sign of the right-hand parts of eqns. (3)–(4) depends on the direction of the vectors of the normal to the external surfaces of the shells. eqn. (1) together with the boundary conditions (2)–(3) are converted by the bubnov – galerkin method to a weak form [26]                   ( 1) ( 2 ) 2 (1) ( 2 ) 2 2 ˆ ˆ ˆ1ˆd d d d 0, 1, f f n n n n f v v s s w w f v f v f s f s n m t tc t , (5) where ̂ and ( )ˆ iw are the approximations of the velocity potential and the normal components of the vectors of shell displacements; nf and fm are the basis functions and their number, respectively. in the general case, the behavior of the electroelastic body is described by the equations of state, piezoelectric effect, and the electrostatic relations [29, 30]   tcε e e , (6)  d eε de , (7)   0d , (8)  e . (9) here: , ε are the stress and linear strain tensors; e and d are the vectors of electric field intensity and electrical induction; c, e, d are the matrices of elastic constants, piezoelectric and dielectric coefficients;  is the electrostatic potential. in the case when a thin-walled structure with a radially polarized field is in the plane stress state, eqns. (6)–(9) can be simplified. in particular, of all components the vectors of the electric field strength and nonzero electrical induction retain only 3e and 3d , and eqns. (6) and (7) are written as follows [31, 32]:                                                            11 11 31 11 12 22 22 32 21 22 12 12 3 66 0 0 0 0 0 0 0 , 0 0 0 0 0 0 e c c e c c e c c c , (10)                                            11 22 3 31 32 12 33 3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0d e e d e    , (11) where           23 3 33 66 66 3 3 33 3 33 33 33 33 33, , , , , 1, 2lm lm l m m m mc c c c c c c e e e c c d d e c l m (12) here we proceed from the assumption that the shell surface is covered with thin weightless electrodes, which can either be shorted, which corresponds to the boundary condition 3 0e (short circuited) or disconnected 3( 0,d open circuited). from eqns. (6)–(9) the following integral relation can be obtained [21] s.a. bochkarev et alii, frattura ed integrità strutturale, 49 (2019) 814-830; doi: 10.3221/igf-esis.49.15 818        t t d d 0 s sv v v ve eε e de . (13) in the shell simulation, it is assumed that their curved surfaces can be represented with a reasonable degree of accuracy as a set of flat segments [33]. the strains in each segment are determined according to the classical theory of thin plates [34]. the corresponding relations in the cartesian coordinates  , ,x y z , which are tied in with the lateral surfaces of thinwalled structures, are written as                                                     t( ) ( ) ( ) ( ) ( ) ( ) 11 22 12 t( ) ( ) ( ) ( ) t( ) ( ) ( ) ( ) 11 22 12 t2 ( ) 2 ( ) 2 ( ) t( ) ( ) ( ) ( ) 11 22 12 2 2 , , , , , , , , , , , , 2 . i i i i i i i i i i i i i i i i i i i i i z u v u v x y y x w w w x yx y ε ε ε (14) hereinafter, the over-line means that the quantity is defined in the coordinates  , ,x y z , and ( ) ( ), i iu v and ( )iw is the meridional, circumferential and normal components of the displacement vectors of the middle surfaces of the shells in these coordinates. taking into account the accepted simplifications, the physical relations interconnecting the vectors of generalized forces and moments ( )it , generalized deformations ( )i and electric field strength ( )ie , can be written in the matrix form as                          t( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) 11 22 12 11 22 12 ( ) ( ) t( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) 11 22 12 11 22 12( ) ( ) , , , , , , , , , , , , , , i i i i i i i i i i i i i i i i i i i i i i i i t t t m m mt d ε g e t a b d ε b c (15) where the coefficients entering into the stiffness matrix  ( )id are calculated as          ( ) ( ) 2 ( ) ( ) ( ) 2 ( ) 2 , , 1, , d i i h i i i i h z z za b c c , (16) and the structure of the matrix ( )ig will be presented below. a mathematical formulation of the problem of the dynamics of elastic shells is based on the variational principle of virtual displacements, which, with account of relation (4) and the work made by the inertial forces, can be written in the matrix form as                           ( ) ( ) ( ) t t t( ) ( ) ( ) ( ) ( ) ( ) ( ) t t( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) , , , , , , , 0, 0, , 0, 0, 0 , i i i s s i i i i i i i s v v s i i i i i i i i i x y z dv dv ds u v w p ε t u u u p 0 u p (17) where ( )is are the densities of shell materials, ( )iu are the vectors of the displacements and rotation angles of shells, and ( )ip are the vectors of loads acting on the shell surfaces. s.a. bochkarev et alii, frattura ed integrità strutturale, 49 (2019) 814-830; doi: 10.3221/igf-esis.49.15 819 numerical implementation ollowing [21], let us decompose the shells through its thickness into n layers and represent the component of the electric field 3e for each layer as    ( ) ( ) ( )3 i i i k kk e v h , (18) where   ( ) ( ) ( ) 1 i i i k k kh z z is the thickness of the k -th layer;    ( ) ( ) ( ) ( )( 2 2)i i i iz h z h is the coordinate measured from the middle surface of the shell;   ( ) ( ) ( ) 1 i i i k k kv   is the difference in the electrostatic potentials between the upper and lower surfaces of the layer, which, as well as the components of the vectors of shell displacements ( )iu and the velocity potential  , turns to be an unknown variable. the numerical solution of the problem is found using the finite element method (fem) [33]. to describe the velocity potential ˆ, the basic functions nf , and membrane displacements of shells ( ) ( )( , )i iu v we use the lagrange shape functions with linear approximation, and for bending deflections of shells ( )iw we use the hermite non-conformal shape functions the discretization of the fluid and shell regions is made using spatial prismatic (8-node brick) and flat quadrangular (4-node plane) finite elements, respectively. expressing the unknown variables in terms of their nodal values, we arrive at the following matrix relations     ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ), , ,i i i i i i i i ie e e e eu n u f ε b u e b φ  , (19) where f and ( )in are the shape functions for the velocity potential of the fluid and the vectors of the nodal displacements of the shell, ( )ieu and e are the vectors of the nodal values, ( )ib are the gradient matrices which are determined by eqn. (14) and relate the strain vectors to the shell displacements,     t( ) ( ) ( ) ( )1 , , ,i i i ie k ne e ee     t( ) ( ) ( ) ( )1 , , ,i i i ie k nv v vφ    ( ) ( ) ( ) ( )1diag 1 , ,1 , 1 .i i i ik nh h hb using the introduced relations the matrix ( )ig in eqn. (15) is generated in the following way                                     ( ) ( ) ( ) 11 1 1 ( ) ( ) ( ) 21 2 2 ( ) ( ) ( ) ( ) 11 1 1 ( ) ( ) ( ) 21 2 2 ˆ ˆ ˆ ˆ ˆ ˆ 0 0 0 0 0 0 i i i k n i i i k n i i i i k n i i i k n g g g g g g g g g g g g g , (20) where        2 2( ) ( ) ( ) ( ) ( ) ( ) ( )3 1 31ˆ , , 1, , 1, 2. 2 i i i i i i i lk k l lk k k lk k g h e g z z e k n l           (21) from eqns. (5), (13) and (17) taking into account (18)–(20), we derive with the aid of the standard fem operations a coupled system of equations, which can be used to describe the interaction of electroelastic shells with an ideal compressible fluid. the system can be represented in a matrix form as f s.a. bochkarev et alii, frattura ed integrità strutturale, 49 (2019) 814-830; doi: 10.3221/igf-esis.49.15 820                                                            (1) (1)(1)(1) (1) (1) ( 2 )( 2 ) ( 2 )( 2 ) ( 2 ) ( 2 ) (1) ( 2 ) 0 0 0 00 0 0 0 0 0 0 0 00 0 0 0 0 0 0 0 00 0 0 0 0 0 0 0 00 0 0 0 0 0 0 0 0 0 0 0 sfs sfs f fs fs u ucm cu um m c c                                          (1) (1) (1) t(1) (1) (1) ( 2 ) ( 2 ) ( 2 ) t ( 2 )(1) ( 2 ) 0 0 0 0 0 0 0,0 0 0 0 0 0 0 0 0 0 s s s s s f       k k u k k k k u k k k    (22) where ( ) , iu  and ( )i are the generalized vectors of the shell displacements and rotation angles, the perturbation velocity potential of the fluid and the difference in the electrostatic potentials of the shells. the typical stiffness (k), mass (m) and damping (c) matrices for individual finite elements are generated as follows:         ( ) ( ) ( ) ( ) ( ) t t t t ( ) t ( ) 2 t t t( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) t( ) ( ) ( ) ( ) ( 1 d , d , d , d , d , d , d , i f f i i i s s i s i i f f fs w v v s i i i i i i i i i i s s s sf f w v v s i i i i i s v v v s x x y y z z c v v s v                                        f f f f f f k m f f c f n k b d b m n n c n f k b g b k           ( ) t) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) 1 33 33 331 d , diag , , , , . i s i i i v i i i i i i i k nk n v h d h d h d     b h b h     (23) here ( )iwn are the shape functions for the normal component of the nodal displacement vector of the shells. since some matrices in (23) are written in the cartesian coordinates  , ,x y z , the derivation of the solution in the global coordinates, which have been used to specify the problem geometry and to write the constitutive equations for the fluid, involves the transformation of the displacements and rotation angles using the matrix of the directional cosines γ of size 3 3 in the following way:        ( ) ( )0 0 i iu u   . (24) during the numerical implementation, at each node of the finite element of the shell it is necessary to determine six unknowns (three displacements and three angles of rotation). therefore, the transformation of conventional matrices is performed using the diagonal matrix         diag , , , , , ,l :              t t t( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) t( ) ( ) ( ) ( ) ( ) ( ) , , , , . i i i i i i i i i i i s s s s sf sf i i i i i i s s fs fs  k l k l m l m l c l c k l k c c l (25) expressing the quantities associated with the electrostatic potential in terms of the shell displacements s.a. bochkarev et alii, frattura ed integrità strutturale, 49 (2019) 814-830; doi: 10.3221/igf-esis.49.15 821      1 t( ) ( ) ( ) ( )i i i is k k u , (26) yields, instead of (22), the system of equations with respect to the displacements of electroelastic bodies and the velocity potential of the fluid                                                                     (1) (1) (1) (1) ( 2 ) ( 2 ) ( 2 ) ( 2 ) (1) ( 2 ) 1 t(1) (1) (1) (1) 1 t( 2 ) ( 2 ) ( 2 ) ( 2 ) 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 s sf s sf f fs fs s s s s s s f       m u c u m u c u m c c k k k k k k k k k               (1) ( 2 ) 0, u u  (27) which can be written in a more compact form       t(1) ( 2 )0, , ,mx cx kx x u u  . (28) representing the motion of shells and fluid in the exponential form     ( ) ( ), ( , , ), ( , , ) exp( )i i x y z x y z tu u  , (29) we obtain instead of (28) the following expression   2 0 mx cx kx . (30) here,  ( )iu and  ( )i are some functions of the coordinates;   i   is the characteristic coefficient, in which  is the natural frequency of vibrations,  is the quantity responsible for the system damping, and  i 1 is the imaginary unit. the system of eqns. (30) is reduced to an asymmetric generalized eigenvalue problem                     0 0 0 0   c k m x i i x , (31) where i is the unit matrix. the calculation of the eigenvalues of the system of eqns. (31) is carried out using the arpack procedures, which are based on the implicitly restarted arnoldi method [35]. results few numerical examples were considered to investigated the behavior of vertically oriented coaxial cylindrical shells, containing an ideal compressible fluid in the annular gap between them. the system parameters are listed in tab. 1. the shells were made of pzt-5h piezoceramics, the physical and mechanical characteristics of which are given in tab. 2. as the boundary conditions for thin-walled bodies, we chose rigid clamping        ( 0)x y zu v w at one end (cantilever, cf) or at both ends (clamped-clamped, cc). the calculations were a s.a. bochkarev et alii, frattura ed integrità strutturale, 49 (2019) 814-830; doi: 10.3221/igf-esis.49.15 822 performed at different values of the dimensionless annular gap k, filling level  and displacement (eccentricity) of the inner shell         ( 2 ) ( 1) ( 1) ( 2 ) ( 1), ,k r r r h l a r r  . (32) note that the radius of the outer shell ( 2 )( )r is fixed, and the radius of the inner shell (1)( )r varies and depends on the parameter k. geometric data fluid properties parameter value parameter value l, m 1 f , kg/m3 1000 ( 2 )r , m 0.1 c, m/s 1500  (1) ( 2 )h h h , m  45 10 table 1: geometrical parameters of the shells and physical properties of the fluid. parameter value parameter value c11, gpa 126 e15, c/m2 17 c12, gpa 79.5 e24, c/m2 17 c13, gpa 84.1 e31, c/m2 -6.5 c22, gpa 126 e32, c/m2 -6.5 c23, gpa 84.1 e33, c/m2 23.3 c33, gpa 117 d11  1010 , f/m 150.3 c44, gpa 23 d22  1010 , f/m 150.3 c55, gpa 23 d33  1010 , f/m 130 c66, gpa 23.3 s , kg/m3 7500 table 2: properties of piezoceramics pzt-5h. verification of the numerical model the assessment of reliability of the constructed algorithm for the numerical investigation of an electroelastic thin-walled body was made by comparing its performance with the results of work [21]. here the simply supported at both ends  ( 0)v w shell made of pzt-5h piezoceramics was investigated (tab. 3). the boundary conditions for the fluid were specified as follows: 0  at  0x and  .x l geometric data fluid properties parameter value parameter value l, m 5 f , kg/m3 1000 r, m 1 c, m/s 1500 h, m 0.02 table 3: geometrical parameters of electroelastic shells and physical properties of the fluid [21]. a comparison between the natural frequencies of the empty shell and the shell filled with an ideal compressible fluid is given in tab. 4. the number of half-waves in the circumferential and meridional directions is denoted by j and m, respectively. according to the data presented in the table, there is good agreement between the results obtained by analytical and numerical solution of the problem. the assessment of the reliability of the results obtained for coaxial shells  ( 0) made of isotropic elastic material and containing fluid in the gap between them was carried out by comparison with the results of analytical solution presented in [36]. in this case, the matrices ( )ik and ( )i sk in eqn. (27) are excluded from the calculation, and the stiffness matrices s.a. bochkarev et alii, frattura ed integrità strutturale, 49 (2019) 814-830; doi: 10.3221/igf-esis.49.15 823  ( )id are generated in the known fashion using young's modulus se and poisson’s ratio  . geometrical and physicomechanical parameters of the problem are summarized in tab. 5, and a comparison of the obtained results is given in tab. 6. without fluid with fluid wave numbers short circuited open circuited wave numbers short circuited open circuited j m [21] present [21] present j m [21] present [21] present 1 1 88.2310 88.1261 93.7900 93.7266 1 1 44.7600 44.6100 48.2710 48.1062 2 216.260 217.239 228.227 229.386 2 107.390 107.797 115.614 115.968 0 275.956 280.586 275.956 280.586 3 154.131 154.925 166.065 166.705 3 311.647 313.207 330.649 332.755 4 189.327 190.099 204.211 204.721 4 366.968 368.502 392.134 393.952 5 217.190 217.515 234.469 234.471 2 1 37.3160 36.8135 40.1090 39.6043 2 1 19.9160 19.5781 21.4640 21.3157 2 114.210 114.107 122.677 122.616 2 62.5970 62.3712 67.6230 67.4905 3 193.791 194.308 207.916 208.565 3 108.575 108.650 117.248 117.433 4 259.346 260.087 278.434 279.316 4 149.022 149.255 160.912 161.282 5 308.464 308.553 331.551 331.658 5 182.817 182.814 197.400 197.590 table 4: a comparison of the natural vibration frequencies  (hz) of a simply supported shell with or without fluid at different combinations of electrical boundary conditions. geometric data material properties fluid properties parameter value parameter value parameter value l, m 0.3  (1) ( 2 )s s se e e , gpa 69 f , km/m 3 1000 (1)r , m 0.1  (1) ( 2 )   0.3 c, m/s 1483 ( 2 )r , m 0.15   (1) ( 2 ) s s s   , kg/m3 2700  ( 1) ( 2 )h h h , m 0.002 table 5: physicomechanical and geometrical parameters of the system, consisting of elastic coaxial shells and a fluid. j m [36] phase mode present j m [36] phase mode present 1 1 391.1 out-of-phase 390.3 2 1 435.6 out-of-phase 434.9 2 846.7 out-of-phase 846.3 2 907.1 out-of-phase 905.2 3 1397.5 out-of-phase 1396.5 1 996.8 in-phase 995.2 1 1736.6 in-phase 1732.5 3 1401.3 out-of-phase 1399.7 4 1908.5 out-of-phase 1907.3 * 1822.2 mixed phase 1819.1 5 2317.2 out-of-phase 2312.5 * 1892.6 mixed phase 1891.2 * 2623.4 mixed phase 2579.5 * 2265.3 mixed phase 2262.2 3 1 403.0 out-of-phase 403.2 4 1 382.5 out-of-phase 383.3 1 671.3 in-phase 671.4 1 561.9 in-phase 562.9 2 858.30 out-of-phase 857.7 2 791.0 out-of-phase 792.0 2 1344.8 in-phase 1343.8 2 1075.5 in-phase 1076.7 3 1352.4 out-of-phase 1351.5 3 1267.5 out-of-phase 1268.8 4 1810.7 out-of-phase 1811.1 3 1676.9 in-phase 1678.0 3 2010.6 in-phase 2008.6 4 1729.2 out-of-phase 1731.3 table 6: a comparison of the natural vibration frequencies  (hz) of clamped-clamped coaxial shells containing an ideal compressible fluid in the annular gap between them. note that in [36], it was first shown that for two elastic coaxial shells, along with the in-phase (the direction and number of meridional half-waves m coincide) and out-of-phase (opposite directions) vibration modes there also exist mixed modes (the number of half-waves varies). from the data presented in tab. 6, we may conclude that the results obtained in the framework of the model used in this paper agree fairly well with the data of the analytical solution presented in [36]. s.a. bochkarev et alii, frattura ed integrità strutturale, 49 (2019) 814-830; doi: 10.3221/igf-esis.49.15 824 natural frequencies of electroelastic shells fig. 2 shows the graphs of the lowest natural frequencies of vibrations  as a function of the dimensionless displacement of the inner shell  at different filling levels  for the gap  1 10.k the results were obtained for two configurations of electroelastic bodies under different boundary conditions. as is evident from the presented data, in the presence of eccentricity the frequencies decrease regardless of the choice of electrical and kinematic boundary conditions at the edges of the shells. according to refs. [6, 7, 9], the reason for such a behavior is the growth of the added fluid mass. in this case, a decrease in the level of a fluid and, consequently, a decrease in its the added mass contributes to a stronger dependence of the lowest vibration frequency on the axial misalignment of the shells and eventually leads to their greater relative decrease. the cantilevered structures are less sensitive to the eccentricity of the inner shell, so that over a fairly wide range of the parameter  a decrease in the frequencies is inessential. similar dependencies for other values of the annular gap k do not demonstrate qualitative differences, which is supported by the data given in tab. 7. (a) (b) figure 2: the dependences of the lowest vibration frequencies  (hz) on the eccentricity  obtained at different filling levels and electrical boundary conditions (shaded symbols — short circuit mode, unshaded symbols — open circuit mode) for clamped-clamped (a) and cantilevered (b) shells,  1 10 .k due to an additional contribution of the associated stiffness, the electrical boundary conditions corresponding to the open-circuited configuration, lead to an increase in frequencies compared to the case of short-circuited configuration. the relative differences between these two variants ( ) as a function of eccentricity  are presented in figs. 3–5 for different values of the annular gap k. it can be seen from the above data that the curves are of a qualitatively different character, which is associated with the boundary conditions at the edges of the shells, the size of the annular gap and the level of filling with a liquid. the higher is the fluid level in the annular gap between the shells, the larger is the relative difference in frequencies  . fig. 6 shows the dependences, which allow us to estimate the variation in the lowest natural frequencies of vibrations with the level of the fluid in the gap at  1 10k and various kinematic boundary conditions. the curves presented in the figure reflect the growth of frequencies with a decrease in the filling level. it can be seen that they are of qualitatively similar character for shells with different boundary conditions. however, in the case of rigid clamping at both ends (fig. 6a), there is a range of the fluid levels, at which the frequencies practically do not change regardless of the displacement of the inner shell . for cantilevered shells (fig. 6b), such a behavior is not observed. in this case, the differences in the frequencies obtained at different electrical boundary conditions are insignificant. figs. 7, 8 show the mode shapes of the shells ( 1 10 ,k  open circuited, cc) obtained for different variants of the inner shell displacement and the fluid level in the annular gap. in the figures, displaying the transverse and longitudinal sections of the system, the dotted lines represent the shells in the undeformed state, and the solid line — the shells in the deformed state. the liquid is shown by light grey. 0.0 0.2 0.4 0.6 0.8  0 10 20 30 40  ●, ○  = 0.25 ▲, δ  = 0.50 ■, □  = 1.00 0.0 0.2 0.4 0.6 0.8  0 12 24 36 48  ●, ○  = 0.25 ▲, δ  = 0.50 ■, □  = 1.00 s.a. bochkarev et alii, frattura ed integrità strutturale, 49 (2019) 814-830; doi: 10.3221/igf-esis.49.15 825 k     clamped-clamped shells clamped-free shells short circuited open circuited  , % short circuited open circuited  , % 1/2 1.00 0.00 32.7722 36.6289 11.7682 8.58148 9.65366 12.4942 0.50 28.0167 30.9768 10.5657 7.78148 8.71879 12.0455 0.95 15.9592 17.8405 11.7885 5.22212 5.88609 12.7145 0.50 0.00 44.0368 49.0209 11.3179 28.3814 31.4965 10.9758 0.50 38.5264 42.7049 10.8459 26.7499 29.7033 11.0407 0.95 21.5175 24.0634 11.8313 17.2344 19.2967 11.9662 0.25 0.00 89.2623 98.0454 9.83972 39.1212 43.3674 10.8539 0.50 81.4270 90.0862 10.6343 39.0705 43.3060 10.8407 0.95 45.0888 49.9111 10.6952 37.8442 41.8567 10.6027 1/10 1.00 0.00 15.4716 17.2113 11.2443 3.81831 4.25959 11.5569 0.50 13.3385 14.7800 10.8069 3.47482 3.87567 11.5359 0.95 7.13355 7.97309 11.7689 2.24936 2.52362 12.1930 0.50 0.00 21.7425 24.0692 10.7013 15.8505 17.4368 10.0074 0.50 18.7429 20.7607 10.7661 14.1066 15.5642 10.3326 0.95 9.70433 10.8434 11.7380 7.85436 8.76154 11.5500 0.25 0.00 53.0114 57.4618 8.39530 36.5821 40.5511 10.8496 0.50 43.6699 47.9169 9.72512 35.7320 39.4371 10.3692 0.95 20.7597 22.9591 10.5944 20.0218 22.0848 10.3036 1/100 1.00 0.00 4.97846 5.50687 10.6138 1.22342 1.35737 10.9483 0.50 4.27499 4.72525 10.5323 1.11144 1.23392 11.0193 0.95 2.25033 2.51305 11.6749 0.71178 0.79643 11.8917 0.50 0.00 7.08603 7.80343 10.1242 5.42042 5.92045 9.22498 0.50 6.04697 6.68328 10.5228 4.69234 5.15888 9.94261 0.95 3.06832 3.42595 11.6555 2.50227 2.78760 11.4030 table 7: natural vibration frequencies  (hz) of the system of coaxial shells at different values of the annular gap k, eccentricity , and filling level  and varying electrical and kinematic boundary conditions. (a) (b) figure 3: the relative difference in the frequencies  as a function the eccentricity  at different levels of the fluid in the annular gap  for clamped-clamped (a) and cantilevered shells (b),  1 10 0.k 0.0 0.2 0.4 0.6 0.8  8.0 8.8 9.6 10.4 11.2 , %  = 1.00  = 0.50  = 0.25 0.0 0.2 0.4 0.6 0.8  7.5 8.4 9.3 10.2 11.1 , %  = 1.00  = 0.50  = 0.25 s.a. bochkarev et alii, frattura ed integrità strutturale, 49 (2019) 814-830; doi: 10.3221/igf-esis.49.15 826 (a) (b) figure 4: the relative difference in the frequencies  as a function the eccentricity  at different levels of the fluid in the annular gap  for clamped-clamped (a) and cantilevered shells (b),  1 10 .k (a) (b) figure 5: the relative difference in the frequencies  as a function the eccentricity  at different levels of the fluid in the annular gap  for clamped-clamped (a) and cantilevered shells (b),  1 2 .k from the presented data it is clear that the amplitude of the displacements on the wetted areas of the shell surfaces exceeds the displacement amplitude on the areas not contacting with the fluid. a decrease in the level of the fluid also leads to a decrease in the maximum amplitudes of the displacements occurring in the shells. moreover, in the case of the eccentricity, the displacement maximum occurs in the areas where the distance between the thin-walled bodies is minimal  ( 2 ) (1)( )r r a and gradually decreases towards the region where the spacing between them is maximum  ( 2 ) (1)( )r r a . the behavior described above is the result of a change in the added mass of the fluid in the corresponding regions of the shells. 0.0 0.2 0.4 0.6 0.8  10.5 11.0 11.5 12.0 12.5 , %  = 0.50  = 1.00  = 0.25 0.0 0.2 0.4 0.6 0.8  9.5 10.0 10.5 11.0 11.5 , %  = 0.50  = 1.00  = 0.25 0.0 0.2 0.4 0.6 0.8  9.4 10.0 10.6 11.2 11.8 , %  = 1.00  = 0.25  = 0.50 0.0 0.2 0.4 0.6 0.8  8.0 8.8 9.6 10.4 11.2 , %  = 1.00  = 0.50  = 0.25 s.a. bochkarev et alii, frattura ed integrità strutturale, 49 (2019) 814-830; doi: 10.3221/igf-esis.49.15 827 (a) (b) figure 6: variation in the lowest natural frequencies  (hz) with the level of the fluid in the annular gap between the shells  at different values of the eccentricity  and various electrical boundary conditions (shaded symbols — short-circuit mode, unshaded symbols — open-circuit mode) for clamped-clamped (a) and cantilevered (b) shells: k = 1/10. (a) (b) (c) figure 7: the lowest vibration mode of the electroelastic shell interacting with a fluid in the transverse ( 2)x l and longitudinal ( 0)y sections at different levels of the fluid in the annular gap  (cc, open-circuit mode,  1 10, 0)k  : (a)  1.0; (b)  0.5; (с)  0.25. 0.0 0.2 0.4 0.6 0.8  0 10 20 30 40  ●, ○  = 0.00 ▲, δ  = 0.50 ■, □  = 0.95 0.0 0.2 0.4 0.6 0.8  0 28 56 84 112  ●, ○  = 0.00 ▲, δ  = 0.50 ■, □  = 0.95 s.a. bochkarev et alii, frattura ed integrità strutturale, 49 (2019) 814-830; doi: 10.3221/igf-esis.49.15 828 (a) (b) (c) figure 8: the lowest vibration mode of the electroelastic shell interacting with a fluid in the transverse ( 2)x l and longitudinal ( 0)y sections at different levels of the fluid in the annular gap  (cc, open-circuit mode,  1 10 , 0.5)k  : (a)  1.0; (b)  0.5; (с)  0.25. conclusion he dynamic behavior of eccentric (non-coaxial) electroelastic cylindrical shells, containing a quiescent fluid in the annular gap between them, was studied in a three-dimensional formulation with the use of the proposed mathematical model, the numerical implementation of which was based on the finite element method. the analysis of the obtained results allowed us to estimate the influence of the size of the annular gap between the shell, the level of the fluid in it, the eccentricity of the inner shell, and the electrical and kinematic boundary conditions on the lowest natural frequencies of vibrations and the corresponding mode shapes. it was demonstrated that both an increase in the misalignment of the shells and the fluid level in the annular gap and a decrease in the size of the gap itself are responsible for a decay of the lowest vibration frequencies. the growth of the lowest frequencies is provided by setting on the electrode covered surfaces of the shells the electrical boundary condition peculiar to the open-circuited configuration. acknowledgments he study was supported by the grant of the russian scientific foundation (project no. 18-71-10054). references [1] brown, s.j. (1982). a survey of studies into the hydrodynamic response of fluid-coupled circular cylinders, j. press. ves. tech., 104(1), pp. 2-19. doi: 10.1115/1.3264181 t t s.a. bochkarev et alii, frattura ed integrità strutturale, 49 (2019) 814-830; doi: 10.3221/igf-esis.49.15 829 [2] païdoussis, m.p. (2016). fluid-structure interactions: slender structures and axial flow, vol. 2, 2nd edn., london, elsevier academic press. [3] bochkarev, s.a., lekomtsev, s.v. and senin, a.n. (2018). analysis of spatial vibrations of coaxial cylindrical shells partially filled with a fluid, comput. continuum mech., 11(4), pp. 448-462. doi: 10.7242/1999-6691/2018.11.4.35 [4] bochkarev, s.a., lekomtsev, s.v., matveenko, v.p. and senin, a.n. (2019). hydroelastic stability of partially filled coaxial cylindrical shells, acta mech. (in press) [5] buivol, b.n. and guz, a.n. (1966). oscillations of two cylindrical eccentrically arranged shells in a stream of inviscid liquid, rep. as ukr. ssr, no. 11, pp. 1412-1415. [6] chung, h. and chen, s.-s. (1977). vibration of a group of circular cylinders in a confined fluid, j. appl. mech., 44(2), pp. 213–217. doi: 10.1115/1.3424026 [7] mateescu, d., païdoussis, m.p. and sim, w.-g. (1994). spectral solutions for unsteady annular flows between eccentric cylinders induced by transverse oscillations, j. sound vib., 177(5), pp. 635–649. doi: 10.1006/jsvi.1994.1458. [8] jeong, k.-h. (1999). dynamics of a concentrically or eccentrically submerged circular cylindrical shell in a fluid-filled container, j. sound vib., 224(4), pp. 709-732. doi: 10.1006/jsvi.1999.2209. [9] jeong, k.-h., lee g.-m. and chang, m.-h. (2001). free vibration analysis of a cylindrical shell eccentrically coupled with a fluid-filled vessel, comput. struct., 79(16), pp. 1517-1524. doi: 10.1016/s0045-7949(01)00031-1. [10] baghdasaryan, g.ye. (1968). the vibrations of coaxial cylindrical shells with a clearance partially filled with fluid, mechanics. proc. as arm. ssr, 21(4), pp. 40-47. [11] tani, j. and haiji, h. (1986). the free vibration of free-clamped fluid-coupled coaxial cylindrical shells, trans. jpn. soc. mech. eng. part c, 52(484), pp. 3137-3144. doi: 10.1299/kikaic.52.3137. [12] tani, j., sakai, t. and chiba, m. (1989). dynamic stability of fluid-coupled coaxial cylindrical shells under vertical excitation, trans. jpn. soc. mech. eng. part c, 55(512), pp. 870-877. doi: 10.1299/kikaic.55.870. [13] okazaki, k., tani, j. and sugano, m. (2002). free vibrations of a laminated composite coaxial circular cylindrical shell partially filled with liquid, trans. jpn. soc. mech. eng. part c, 68(671), pp. 1942–1949. doi: 10.1299/kikaic.68.1942. [14] gavrilova, e. (2003). a study of the vibration of fluid coupled coaxial cylindrical shell, in: benaroya h., wei t.j. (eds) iutam symposium on integrated modeling of fully coupled fluid structure interactions using analysis, computations and experiments. fluid mechanics and its applications, 75, pp. 363-374. doi: 10.1007/978-94-007-0995-9_26. [15] baghdasaryan, g.ye. and marukhyan, s.a. (2011). dynamic behavior of a coaxial cylindrical shells, with a gap partially filled with fluid, mechanics. proc. nas arm., 64(3), pp. 10-21. [16] ibrahim, r.a. (2005). liquid sloshing dynamics: theory and applications, cambridge, cambridge university press. [17] abramovich, h. (2016). intelligent materials and structures, berlin, de gruyter. [18] kaljevic, i. and saravanos, d.a. (1997). steady-state response of acoustic cavities bounded by piezoelectric composite shell structures, j. sound vib., 204(3), pp. 459–476. doi: 10.1006/jsvi.1996.0911 [19] saravanos, d.a. (1997). mixed laminate theory and finite element for smart piezoelectric composite shell structures, aiaa j., 35(8), pp. 1327–1333. doi: 10.2514/2.264. [20] lammering, r. and mesecke-rischmann, s. (2003). multi-field variational formulations and related finite elements for piezoelectric shells, smart mater. struct., 12(6), pp. 904–913. doi: 10.1088/0964-1726/12/6/007. [21] larbi, w., deü, j.-f. and ohayon, r. (2007). vibration of axisymmetric composite piezoelectric shells coupled with internal fluid, int. j. num. meth. eng., 71(12), pp. 1412–1435. doi: 10.1002/nme.1987. [22] deü, j.-f., larbi, w. and ohayon, r. (2008). piezoelectric structural acoustic problems: symmetric variational formulations and finite element results, comp. meth. appl. mech. eng., 197(19–20), pp. 1715–1724. doi: 10.1016/j.cma.2007.04.014. [23] larbi, w., deü, j.-f. and ohayon, r. (2012). finite element formulation of smart piezoelectric composite plates coupled with acoustic fluid, compos. struct., 94(2), pp. 501–509. doi: 10.1016/j.compstruct.2011.08.010. [24] bochkarev, s.a., lekomtsev, s.v. and matveenko, v.p. (2013). numerical modeling of spatial vibrations of cylindrical shells, partially filled with fluid, comput. technologies, 18(2), pp. 12-24. [25] bochkarev, s.a., lekomtsev, s.v. and matveenko, v.p. (2015). natural vibrations of loaded noncircular cylindrical shells containing a quiescent fluid, thin-walled struct., 90, pp. 12-22. doi: 10.1016/j.tws.2015.01.001 [26] bochkarev, s.a., lekomtsev s.v. and matveenko, v.p. (2016). natural vibrations and stability of elliptical cylindrical shells containing fluid, int. j. struct. stab. dyn., 16(10), 1550076. doi: 10.1142/s0219455415500765. [27] vol’mir, a.s. (1979). shells in liquid and gas flow. hydroelastisity problems, moscow, nauka. [28] amabili, m. (1996). free vibration of partially filled, horizontal cylindrical shells, j. sound vib., 191(5), pp. 757-780. s.a. bochkarev et alii, frattura ed integrità strutturale, 49 (2019) 814-830; doi: 10.3221/igf-esis.49.15 830 doi: 10.1006/jsvi.1996.0154. [29] grinchenko, v.t., ulitko, a.f. and shul’ga, n.a. (1989). mechanics of coupled fields in elements of structures. vol. 5. electroelasticity, kiev, naukova dumka. [30] rogacheva, n.n. (1994). the theory of piezoelectric shells and plates, london, crc press. [31] sheng, g.g. and wang, x. (2010). thermoelastic vibration and buckling analysis of functionally graded piezoelectric cylindrical shells, appl. math. model., 34(9), pp. 2630-2643. doi: 10.1016/j.apm.2009.11.024. [32] yao, g. and li, f.-m. (2014). the stability analysis and active control of a composite laminated open cylindrical shell in subsonic airflow. j. intel. mat. sys. struct., 25(3), pp. 259-270. doi: 10.1177/1045389x13491020. [33] zienkiewicz, o.c. (1971). finite element method in engineering science, new york, mcgraw-hill. [34] reddy, j.n. (2015). an introduction to nonlinear finite element analysis, 2nd edn, oxford, oxford university press. [35] lehoucq, r.b. and sorensen, d.c. (1996). deflation techniques for an implicitly restarted arnoldi iteration, siam j. matrix anal. appl., 17(4), pp. 789–821. doi: 10.1137/s0895479895281484. [36] jeong, k.-h. (1998). natural frequencies and mode shapes of two coaxial cylindrical shells coupled with bounded fluid, j. sound vib., 215(1), pp. 105–124. doi: 10.1006/jsvi.1998.1648. << /ascii85encodepages false /allowtransparency false /autopositionepsfiles true /autorotatepages /none /binding /left /calgrayprofile (dot gain 20%) /calrgbprofile (srgb iec61966-2.1) /calcmykprofile (u.s. web coated \050swop\051 v2) /srgbprofile (srgb iec61966-2.1) /cannotembedfontpolicy /error /compatibilitylevel 1.4 /compressobjects /tags /compresspages true /convertimagestoindexed true /passthroughjpegimages true /createjobticket false /defaultrenderingintent /default /detectblends true /detectcurves 0.0000 /colorconversionstrategy /cmyk /dothumbnails false /embedallfonts true /embedopentype false /parseiccprofilesincomments true /embedjoboptions true /dscreportinglevel 0 /emitdscwarnings false /endpage -1 /imagememory 1048576 /lockdistillerparams false /maxsubsetpct 100 /optimize true /opm 1 /parsedsccomments 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/hrv (za stvaranje adobe pdf dokumenata najpogodnijih za visokokvalitetni ispis prije tiskanja koristite ove postavke. stvoreni pdf dokumenti mogu se otvoriti acrobat i adobe reader 5.0 i kasnijim verzijama.) /hun 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can be opened with acrobat and adobe reader 5.0 and later.) >> /namespace [ (adobe) (common) (1.0) ] /othernamespaces [ << /asreaderspreads false /cropimagestoframes true /errorcontrol /warnandcontinue /flattenerignorespreadoverrides false /includeguidesgrids false /includenonprinting false /includeslug false /namespace [ (adobe) (indesign) (4.0) ] /omitplacedbitmaps false /omitplacedeps false /omitplacedpdf false /simulateoverprint /legacy >> << /addbleedmarks false /addcolorbars false /addcropmarks false /addpageinfo false /addregmarks false /convertcolors /converttocmyk /destinationprofilename () /destinationprofileselector /documentcmyk /downsample16bitimages true /flattenerpreset << /presetselector /mediumresolution >> /formelements false /generatestructure false /includebookmarks false /includehyperlinks false /includeinteractive false /includelayers false /includeprofiles false /multimediahandling /useobjectsettings /namespace [ (adobe) (creativesuite) (2.0) ] /pdfxoutputintentprofileselector /documentcmyk /preserveediting true /untaggedcmykhandling /leaveuntagged /untaggedrgbhandling /usedocumentprofile /usedocumentbleed false >> ] >> setdistillerparams << /hwresolution [2400 2400] /pagesize [612.000 792.000] >> setpagedevice shot peening processes to obtain nanocrystalline surfaces in metal alloys: f. iacoviello et alii, frattura ed integrità strutturale, 33 (2015) 111-119; doi: 10.3221/igf-esis.33.15 111 focussed on characterization of crack tip fields fatigue crack tip damaging micromechanisms in a ferritic-pearlitic ductile cast iron francesco iacoviello, vittorio di cocco università di cassino e del lazio meridionale, dicem, via g. di biasio 43, 03043 cassino (fr), italy iacoviello@unicas.it, v.dicocco@unicas.it mauro cavallini università di roma “sapienza”, dicma, via eudossiana 18, rome, italy mauro.cavallini@uniroma1.it abstract. due to the peculiar graphite elements shape, obtained by means of a chemical composition control (mainly small addition of elements like mg, ca or ce), ductile cast irons (dcis) are able to offer the good castability of gray irons with the high mechanical properties of irons (first of all, toughness). this interesting properties combination can be improved both by means of the chemical composition control and by means of different heat treatments(e.g. annealing, normalizing, quenching, austempering etc). in this work, fatigue crack tip damaging micromechanisms in a ferritic-pearlitic dci were investigated by means of scanning electron microscope observations performed on a lateral surface of compact type (ct) specimens during the fatigue crack propagation test (step by step procedure), performed according to the “load shedding procedure”. on the basis of the experimental results, different fatigue damaging micromechanisms were identified, both in the graphite nodules and in the ferritic – pearlitic matrix. keywords. ferritic-pearlitic ductile cast irons; fatigue damaging mechanism; crack tip. introduction uctile iron discovery in 1948 gave a new lease on life to the cast iron family. in fact, these cast irons (dcis) combine the good castability of gray irons and high toughness values of steels and they are also characterized by an interesting fatigue crack propagation resistance. considering their interesting mechanical properties, dcis are widely used in the critical automotive parts (e.g., crankshafts, truck axles, etc.), and in many other application, like pumps, pipes or turbine components [1, 2]. dcis can be considered as natural composites, with graphite nodules embedded in a metal matrix. the dcis performances are strongly affected by the graphite elements morphological peculiarities (e.g., graphite elements nodularity, volume fraction, density, distribution, dimension). different combinations of the mechanical properties can be obtained depending on the matrix microstructure [3]: ranging from ferritic to pearlitic dcis, different combination of ductility or tensile strength values can be obtained (anyway, equivalent to the values offered by low carbon steels); martensitic dcis are characterized by a very high strength, but low levels of toughness and ductility; bainitic grades are characterized by a high hardness; austenitic dcis show good corrosion resistance, good strength and dimensional stability at high temperature; finally, austempered grades (adi) show d http://www.gruppofrattura.it/pdf/rivista/numero33/audioslides/iacoviello1/iac1.html f. iacoviello et alii, frattura ed integrità strutturale, 33 (2015) 111-119; doi: 10.3221/igf-esis.33.15 112 a very high wear resistance and fatigue strength. difference between dcis and low carbon steels tensile properties are summarized in fig. 1, considering the microstructure influence on uts and elongation [4]. figure 1: uts-elongation for different dci and low carbon alloys [4]. focusing on the fatigue crack propagation resistance, microstructure influence is more evident corresponding to higher values of the stress ratio and the applied stress intensity values [5], fig. 2, where ferritic-pearlitic dci (50% f – 50% p) shows a fatigue crack propagation resistance that is analogous to the investigated adi. cavallini et alii [5, 6] proposed that this behaviour is due to an enhanced crack closure effect, due to the graphite nodule presence and to the different phases distribution and mechanical properties. considering that pearlite (or bainite, in adi) is characterized by a reduced ductility and higher uts (ultimate tensile strength) values, if compared to ferrite, this second peculiar crack damaging mechanism can be described as follows (fig. 3):  corresponding to kmax values, ferritic shields are more deformed than pearlitic (or bainitic in adi) matrix (considering an equivalent stress level);  corresponding to kmin values, pearlitic (or bainitic in adi) matrix induces on ferritic shields a residual compression stress condition with a consequent enhancing of the closure effect. 10 10 -10 10 -9 10 -8 10 -7 10 -6 r = 0.1 100% f 50% f + 50% p 5% f + 95% p adi r = 0.5 100% f 50% f + 50% p 5% f + 95% p adi r = 0.75 100% f 50% f + 50% p 5% f + 95% p adi d a /d n [m /c y c le ] k [mpa m 1/2 ] 3 50 figure 2: microstructure and stress ratio influence on fatigue crack propagation in dcis [5]. figure 3: ductile and fragile graphite elements debonding influence on crack closure effect in ductile irons [5]. in this work, fatigue crack tip damaging micromechanisms in a ferritic-pearlitic dci were investigated by means of scanning electron microscope (sem) observations of the lateral surface of metallographically prepared compact type (ct) specimens, focusing both the role played by the graphite nodules and the influence of the phases distribution. f. iacoviello et alii, frattura ed integrità strutturale, 33 (2015) 111-119; doi: 10.3221/igf-esis.33.15 113 investigated material and experimental procedure n as cast ferritic – pearlitic dci, with analogous ferrite and pearlite volume fraction and showing a peculiar “bull’s eye” morphology (fig. 4) and characterized by a high graphite elements nodularity, were considered (chemical composition is shown in tab. 1). figure 4: investigated ferritic-pearlitic ductile iron: phases distribution (obtained by means of chemical composition control; nital 3). c si mn s p cr mg sn 3.65 2.72 0.18 0.010 0.03 0.05 0.055 0.035 table 1: investigated ferritic-pearlitic dci chemical composition. 10 mm thick ct specimens were metallographically prepared and etched (nital 3), and fatigue crack propagation tests were run according to astm e647 standard [7], considering one stress ratio value (e.g. r=pmin/pmax = 0.1). tests were performed using a computer controlled servohydraulic machine in load controlled conditions, considering a 20 hz loading frequency, a sinusoidal loading waveform and laboratory conditions. crack length measurements were performed by means of a compliance method using a double cantilever mouth gage and controlled using an optical microscope (x40). after the precracking procedure (measured crack length equal to 3 mm) a decreasing k values were applied according to the relationship:  0 0 c a a k k e      (1) where 0 k is the initial k at the beginning of the test (20 mpam), a0 is the corresponding crack length, a is the crack length during the test and c is equal to -0.291. this procedure allowed to obtain a propagating crack with a decreasing crack tip plastic zone radious, up to threshold conditions (about 8 mpam), corresponding to a negligible crack tip plastic zone. during the fatigue crack propagation tests, sem crack path observations were performed with a step by step procedure. furthermore, fracture surfaces were analysed by means of a scanning electron microscope, focusing both the graphite nodules and the metal matrix. results and comments atigue crack path is microscopically tortuous (fig. 5a). this behaviour and the consequent fracture surface roughness were already extensively investigated [8, 9]: this parameter increases with the increase of the applied k. superposing white spots to the fatigue crack path corresponding to the intersections between the crack path and the graphite nodules (fig. 5b), it is evident that crack path tortuosity is strongly affected by the graphite nodules distributions: graphite nodules are not mere voids embedded in the metal matrix but they influence the crack path increasing the fracture surface roughness and, consequently, the importance of the roughness induced crack closure effect [10]. a f f. iacoviello et alii, frattura ed integrità strutturale, 33 (2015) 111-119; doi: 10.3221/igf-esis.33.15 114 (a) (b) figure 5: (a) fatigue crack path; (b) fatigue crack path intersections with graphite nodules (with or without crack path deviations). http://www.gruppofrattura.it/video/fis33/iacoviello/v1/v1.html f. iacoviello et alii, frattura ed integrità strutturale, 33 (2015) 111-119; doi: 10.3221/igf-esis.33.15 115 (a) (b) figure 6: fatigue crack path deviations corresponding to graphite nodules (crack growths from left to right). (a) k = 15 mpam; (b) k = 19 mpam. figure 7: fatigue crack path: phases influence (crack growths from left to right). k = 17 mpam. figure 8: secondary crack (crack growths from left to right). k = 13 mpam. figure 9: intergranular crack path crack (crack growths from left to right). k = 14 mpam. higher magnification sem observations allow to confirm the behaviour described in fig. 5, with evident crack deviations due to the graphite nodules presence (fig. 6). in addition, it is possible to observe that, corresponding to the graphite nodules, the main damaging micromechanisms is the debonding between the graphite nodule and the matrix (mainly ferrite, see also fig. 4), although, seldom, the crack pass through the graphite nodules (fig. 6b). this behaviour is f. iacoviello et alii, frattura ed integrità strutturale, 33 (2015) 111-119; doi: 10.3221/igf-esis.33.15 116 completely different with respect to the damaging micromechanisms observed during tensile tests [11, 12], where the mechanical properties gradient inside the graphite nodules plays a key role and secondary cracks inside graphite nodules nucleate and propagate (“onion-like” mechanism). considering the crack path in the ferritic-pearlitic matrix, crack mainly propagates transgranularly, with slip bands that emanate from the crack tip (more evident in the ferritic matrix, at least according to the sem observation). ferrite-pearlite interfaces influence on crack path is evident in fig. 7. the intersection between the crack path and the ferrite-pearlite interfaces always implies a crack path direction modification, with a consequent increase of the fracture surface roughness (and of the roughness induced crack closure effect). in addition, both secondary cracks (fig. 8) and intergranular crack path (fig. 9) are seldom observed. considering the fracture mechanics principles, and, as first approximation, assuming the investigated dci as an homogeneous and linear elastic material, it is possible to roughly describe the stress state at the crack tip. fig. 10 [13] shows the different zones ahead the crack tip during a fatigue loading: reverse/cyclic plastic zone (orange, rpz): fatigue loading implies a stress hysteresis loop depending upon the stress ratio r and the applied value of k. monotonic plastic zone (yellow, mpz): plastic deformation occur during monotonic loading and, after that, elastic loading-unloading takes place elastic zone (grey, ez): the deformation is completely elastic. figure 10: fatigue crack propagation: rpz (reversed plastic zone); mpz (monotonic plastic zone); ez (elastic zone). figure 11: rpz and mpz compared to graphite nodules corresponding to lower k values (e.g. 10 mpam). figure 12: rpz and mpz compared to graphite nodules corresponding to higher k values (e.g. 20 mpam). corresponding to the lateral surface (plane stress conditions): 2 1 2 y y k r            (2) the “reversed” or “cyclic” plastic zone ( rpzr ), the volume which undergoes yielding due to both tensile and compressive stress, is four times lower than the monotonic value corresponding to kmax. considering the investigated loading conditions, for k values ranging between 10 and 20 mpam, the corresponding rpzr values range between about 30 and about 120 m, or rather between the half and the double of the maximum measured graphite nodules diameters. instead, considering the matrix, rpzr values are lower or comparable to the ferrite grains or pearlite colonies diameters. as a consequence, fatigue crack propagation in the investigated ferritic-pearlitic dci can be analysed with the k parameter only as first approximation, being the material non homogenous, at least at the scale of the fatigue damaging processes at the crack tip. considering lower k values, two conditions are possible: f. iacoviello et alii, frattura ed integrità strutturale, 33 (2015) 111-119; doi: 10.3221/igf-esis.33.15 117 graphite nodules free zone (fig. 10): rpz and mpz are lower than the ferritic grain or pearlitic colonies diameters. material can be considered as microscopically homogeneous and the propagation is mainly influenced by the metal matrix (e.g., with slip bands in ferritic grains). graphite nodules ahead the crack tip (fig. 11 and 13): mpz interact with the matrix-graphite nodule interface. considering the nodule ahead the mpz in fig. 13, the left side is plastically stress, with the right side that is still elastically stressed. matrix and graphite nodules different mechanical behaviour implies the activation of the nodule-matrix debonding (fig. 13b). when crack propagates up to the graphite nodule (fig. 13c), the debonding can be completely developed and the graphite nodule can only influence the closure effect, according to the mechanism described in fig. 3 [5]. (a) (b) (c) figure 13: fatigue crack propagation. interaction between rpz, mpz and graphite nodules (lower k values). considering higher k values, two conditions are still possible: graphite nodules free zone (fig. 10): rpz and mpz are larger than the ferritic grain or pearlitic colonies diameters. material can be considered as microscopically homogeneous and as a polycrystalline material. graphite nodules ahead the crack tip (fig. 12 and 14): larger rpz and mpz allows an interaction also with graphite nodules that are not exactly ahead the crack tip. graphite nodules in the mpz “attract” the crack path due to the influence of their presence on the crack tip stress filed, with an increase of the crack path tortuosity and a consequent increase of the fracture surface roughness. (a) (b) (c) figure 14: fatigue crack propagation. interaction between rpz, mpz and graphite nodules (higher k values). sem fracture surface analysis confirms this behaviour: corresponding to all the observed graphite nodules, it is possible to observe both not damaged nodules, or voids without graphite residuals (fig. 15). f. iacoviello et alii, frattura ed integrità strutturale, 33 (2015) 111-119; doi: 10.3221/igf-esis.33.15 118 figure 15: sem fracture surface analysis (k = 10 mpam) conclusions n this work, fatigue crack propagation micromechanisms in a ferritic-pearlitic dci have been investigated, focusing on both the graphite nodules role and the crack tip stress condition. considering as first approximation the dci as an homogenous material, the analysis of the experimental results allows to summarize the following conclusion: the main contribution of the graphite nodules to the damaging micromechanisms is the graphite nodules – matrix debonding. this is due to the interaction of the rpz and mpz with the graphite nodule/matrix interface. the increase of the applied k implies an increase of the number of graphite nodules that can be embedded in the mpz. as a consequence the increase of the k implies a more tortuous crack path with a consequent increase of the crack surface roughness and of the roughness induced crack closure effect. if the mpz and rpz are nodule free, the crack propagates generating slip bands at the crack tip, more evident in ferrite grains. this propagation micromechanism is compatible with the “spheroid presence induced” crack closure effect described in [5]: also this mechanism becomes more evident with the increase of the applied kmax (and, as consequence, of the mpz radious). references [1] jeckins, l.r., forrest, r.d., ductile iron, in properties and selection: iron, steels and high performance alloys. asm handbook, metal park (oh) asm international, 1 (1993) 35-55. [2] canzar, p., tonkovic, z., kodvanj, j., microstructure influence on fatigue behaviour of nodular cast irons, materials science and engineering a, 556 (2012) 88-99. [3] labrecque, c., gagne, m., review ductile iron: fifty years of continuous development, can. metall. quart., 37 (1998) 343-378. [4] www.advancedcast.com/adi-advantages.htm (2015). [5] cavallini, m., di bartolomeo, o., iacoviello, f., fatigue crack propagation damaging micromechanisms in ductile cast irons, engineering fracture mechanics, 75 (2008) 694-704. doi: 10.1016/j.engfracmech.2007.02.002. [6] cavallini, m., di bartolomeo, o., iacoviello, f., fatigue damaging micromechanisms in ductile cast irons, in: proceedings of international conference on fatigue crack paths (cp2006), parma, italy, (2006) 13. [7] astm standard test method for measurements of fatigue crack growth rates (astm e647 13ae1). annual book of astm standards. 0301, american society for testing and materials, (2013). [8] iacoviello, f., polini, w., influenza della matrice sulla propagazione di cricche di fatica nelle ghise sferoidali, la metall. ital., 7/8 (2000) 31–34. [9] iacoviello, f., di cocco, v., ductile cast irons: microstructure influence on fatigue crack propagation resistance, frat. ed integrità strutt. 13 (2010) 3–16. doi: 10.3221/igf-esis.13.01. i f. iacoviello et alii, frattura ed integrità strutturale, 33 (2015) 111-119; doi: 10.3221/igf-esis.33.15 119 [10] elber, w., the significance of fatigue crack closure, damage tolerance in aircraft structures, astm stp 486, american society for testing and materials, (1971) 230 – 242. [11] di cocco, v., iacoviello, f., rossi, a., damaging micromechanisms characterization in a ferritic-pearlitic ductile cast iron, frat. ed integrità strutt., 8 (2014) 62–67. doi: 10.3221/igf-esis.30.09 [12] di cocco, v., iacoviello, f., rossi, a., iacoviello, d., macro and microscopical approach to the damaging micromechanisms analysis in a ferritic ductile cast iron, theor. appl. fract. mech. 69 (2014) 26–33. doi: 10.1016/j.tafmec.2013.11.003. [13] paul, s. k., tarafder, s., cyclic plastic deformation response at fatigue crack tips, international journal of pressure vessels and piping 101, (2013) 81-90. doi: 10.1016/j.ijpvp.2012.10.007. [14] iacoviello, f., di cocco, v., rossi, a., cavallini, m., fatigue crack propagation damaging micromechanisms in pearlitic ductile cast irons, fatigue fract. eng. mater. structures, 38 (2015) 238–245. doi: 10.1111/ffe.12215. microsoft word numero_33_art_4 l. malíková et alii, frattura ed integrità strutturale, 33 (2015) 25-32; doi: 10.3221/igf-esis.33.04 25 focussed on characterization of crack tip fields estimation of the crack propagation direction in a mixed-mode geometry via multi-parameter fracture criteria l. malíková, v. veselý brno university of technology, faculty of civil engineering, institute of structural mechanics, brno, czech republic malikova.l@fce.vutbr.cz, vesely.v1@fce.vutbr.cz s. seitl academy of sciences of the czech republic, v. v. i., institute of physics of materials, brno, czech republic seitl@ipm.cz abstract. the presented work introduces a numerical parametric study on the crack propagation direction under mixed-mode conditions (mode i + ii). it is conducted for the geometry of an eccentric asymmetric fourpoint bending of a single edge notched beam specimen; various levels of mode-mixity are ensured by modifications in the crack length and crack eccentricity. the direction of crack propagation is estimated semianalytically using both the maximum tangential stress criterion and the strain energy density criterion (implemented as a procedure within the used finite element computational code) as well as numerically (from verification reasons). multi-parameter fracture mechanics is employed in the presented work for precise analytical evaluation of the stress field in the cracked specimen. this theory is based on description of the stress and deformation fields in the cracked body by means of their approximation using several initial terms of the williams power series. recent studies show that utilization of only first term of the series, which corresponds to the stress intensity factor (sif), the single controlling parameter for the crack initiation and propagation assessment in brittle materials, is insufficient in many crack problems. it appears also in this study that the higher-order terms of the asymptotic crack-tip field are of great relevance for the conducted analysis, similarly to a number of other fracture phenomena (near-crack-tip stress field approximation, non-linear zone extent estimation, etc.). keywords. near-crack-tip fields; williams expansion; crack propagation direction; multi-parameter fracture criteria; finite element analysis. introduction t is well known that the classical (one-parameter) fracture mechanics concept is based on the existence of the stress intensity factor that expresses the amplitude of the singular term describing the stress distribution in a cracked specimen. nevertheless, this approach exhibits several limitations and one of them is the extent of the zone of nonlinear behavior that has to be small enough in comparison to the typical structural dimensions. it is obvious that this restriction is too strong for a large group of materials, such as the quasi-brittle or the elastic-plastic ones. fracture processes occurring in these cases are more complicated and many works have been concerned with developing i l. malíková et alii, frattura ed integrità strutturale, 33 (2015) 25-32; doi: 10.3221/igf-esis.33.04 26 approaches that will allow their precise description, see e.g. [1–3]. it can be shown that it is reasonable to take into account more parameters for the stress field approximation and the so-called multi-parameter fracture mechanics approach seems to be a very useful tool for assessment of fracture behavior of a wide range of materials. the introduced approach is based on the williams solution of the crack-tip stress field distribution in a cracked specimen, see [4]. extensive investigations in this field have been performed by the authors, see e.g. [5–8]. it can be noted that what is referred to as the so-called overdeterministic method has been used for estimation of values of the coefficients of the higher-order terms of the williams expansion (we). more details about the method can be found for instance in [9], or in some of the authors’ works, e.g. [10]. in this work, a parametric study is carried out on a mixed-mode geometry and the initial kink angle of a crack is investigated for a wide range of mode-mixity situations. the multi-parameter form of two commonly used fracture criteria is introduced and tested. the main focus is on the discussion of the influence of considering the higher-order terms of the we. note that this work is only a part of the extensive ongoing research of the authors on the application of this multiparameter approach in more advanced fracture mechanics tasks. williams expansion and multi-parameter fracture mechanics concept he multi-parameter fracture mechanics concept consists in the idea that the crack-tip stress field is described by means of the williams expansion [4]. originally, the infinite power series was derived for a homogeneous elastic isotropic cracked body with an arbitrary remote loading and it can be written in the form:      yxjimgrmbnfrna m ij m m n ij n nij ,,,, 2 , 2 1 , 1 2 1 , 1 2          (1) similarly, the equation for the displacement vector components can be expressed as:      yxiemgbrenfaru m uim m n uin n i ,,,,,,,, 1 , 2 1 , 2        (2) eq. 2 is important with regard to the method used for evaluation of the series coefficients, see the text below. note that the approximation of the individual stress tensor and displacement vector components via a truncated series is used. the meaning of the symbols used in eq. 1 and 2 is: ij and ui represent the stress tensor and displacement vector components, respectively; r,  symbolize the polar coordinates (provided the centre of the coordinate system at the crack tip and the crack faces lying on the negative x-axis); fij, ,gij, and fi,u , gi,u stand for the known functions and their expressions can be found in classical textbooks on fracture mechanics; e and  represent young’s modulus and poisson’s ratio, respectively. the only unknown symbols are the coefficients an and bm – their values depend on the relative crack length or generally, on the cracked specimen configuration. therefore, it is necessary to calculate these parameters numerically and the method used within this work is described in the following text. over-deterministic method the authors point out that there exist several methods suggested for estimation of the coefficients of the terms of the we. in this paper, the so-called over-deterministic method (odm) was chosen, taking into account its appreciable advantages. whereas the use of hybrid crack elements (hce, see e.g. [11,12]) or boundary collocation method (bcm, see e.g. [13]) requires advanced numerical procedures and special elements, odm is based only on the knowledge of the displacement field around the crack tip and therefore, the conventional finite element analysis (fea) is sufficient. particularly, the displacements are determined in a set of nodes in the vicinity of the crack tip (usually at a ring around the crack tip) and together with polar coordinates of the nodes are then substituted as inputs into the eq. 2. thus, when k nodes are selected, a system of 2k algebraic equations for the variables an and bm is created. more details, recommendations and/or restrictions regarding the application of the method can be found for instance in [9,14,15]. fracture criteria the literature survey of mixed mode fracture criteria can be find in [16]. for research in this contribution, two fracture criteria were chosen for estimation of the initial crack propagation direction: maximum tangential stress (mts) criterion [17] and strain energy density (sed) criterion [18,19]. both of them are well known and often used when the crack path shall be investigated. t l. malíková et alii, frattura ed integrità strutturale, 33 (2015) 25-32; doi: 10.3221/igf-esis.33.04 27 the mts criterion is independent on the plane stress or plane strain conditions (it is stress-based criterion) and it assumes that a crack will propagate in the direction where the tangential stress  is maximal: 0,0 2 2            (3) when the classical one-parameter fracture mechanics concept is preferred, an explicit equation for the crack propagation direction γ can be derived: 2 ii 2 ii ii 8 2 arctan2 kkk k    (4) ki and kii represent the stress intensity factors and are directly related to the first williams expansion terms: 21i ak  and 21ii bk  (5) note that when the multi-parameter fracture mechanics approach is utilized, the stress component  in eq. 3 is approximated via the we and the maximum needs to be sought numerically. contrary to the mts criterion, the sed criterion states that a crack will grow in the direction where the strain energy density s reaches its minimum: 0,0 2 2        ss , where          22 8 1 2 1     rrrrr s (6) again, the williams series expansion is used for approximation of the stress tensor components and the minimum is sought through numerical methods. particularly, a procedure for searching for the extreme of the function is programmed in wolfram mathematica code [20]. the relevant quantities are expressed by means of the we considering both various we terms numbers (n = m = 1, 2, 3,... ,10) and various distances from the crack tip where the criterion is applied (rc = 0.2, 0.4, 1.0, 1.5, 1.8 and 3.2 mm). for each configuration, the angle where the derivative of the corresponding quantity is zero is sought via an iterative method (newton’s method is default in the mathematica code). specimen geometry and numerical model mixed mode geometry of an eccentric asymmetric four point bending specimen (ea4pb), see a diagram of the geometry in fig. 1, was chosen for the investigations presented. figure 1: eccentric asymmetric four point bending of a notched beam specimen under study. a set of 45 various geometrical configurations was modelled and analyzed; the following dimensions were considered: half specimen length l = 100 mm, half span between the applied forces d = 20 mm, specimen width w = 40 mm, the relative crack length a/w varied from 0.1 up to 0.9 (in steps equal to 0.1) and the ratio between the crack eccentricity and the specimen width e/w was modelled in the range between 0 and 0.4 (with step 0.1). the idea was to cover a large range of mode-mixities; particularly, the ratio between the stress intensity factors of mode i and ii varied from approximately 0 up to ca. 12. note that the relation between the sifs and the coefficients of the we terms is described in eq. 5. although the ki/kii ratio is used very often in fracture mechanics works, its using within this work is not fully correct with regard to a l. malíková et alii, frattura ed integrità strutturale, 33 (2015) 25-32; doi: 10.3221/igf-esis.33.04 28 the generalized/multi-parameter fracture mechanics concept applied. nevertheless, no other more relevant parameter is known yet. all the numerical simulations have been done in ansys finite element software [21]. for the two-dimensional linear elastic numerical model created, the following material properties were used: young’s modulus e = 40 gpa, poisson’s ratio  = 0.2 and the loading force was f = 4 kn. plane strain conditions were set. the specimen was meshed with plane82 elements, only the vicinity of the crack tip was specially refined: one row of special crack elements with shifted mid-side nodes was used around the crack tip and six more regular rings of nodes were modelled at the distances of rc = 0.2, 0.4, 1.0, 1.5, 1.8 and 3.2 mm from the crack tip. these rings were utilized for the analyzes performed, particularly:  the displacements and coordinates of the nodes at the defined rings were used for the evaluation of the initial 10 terms of the we by means of the odm, as it is described in the text above;  the corresponding stress tensor components in the nodes at the defined rings were used for the direct evaluation of the fracture criteria. in the following chapter, the values of the initial crack propagation angles are presented. particularly, the angles calculated from the multi-parameter form of the fracture criteria (considering various numbers of the initial terms of the we; n = m = 1, 2, 4, 7 and 10) are compared to the fem results determined purely numerically from the nodal solution performed in ansys. results for all the cracked specimen configurations investigated are introduced and the influence of the distance from the crack, where the fracture criteria are applied, is discussed. note that existence of the new/additional length parameter (rc, the distance from the crack tip, where the criterion is applied) is a phenomenon connected to the application of the multi-parameter fracture mechanics approach. generally, it is assumed that this value should be a material property, i.e. it should be constant for the particular material and should be related to material characteristics, see several suggestions in [22–24]. results and discussion his chapter is devoted to the presentation of the results obtained on the introduced mixed-mode cracked geometry. particularly, the initial kink angle was investigated. the main attention is devoted to description and discussion of potential advantages of the application of the multi-parameter form of the fracture criteria suggested. the results are presented in the form of dependences of the initial crack propagation direction angle γ on the relative crack length ( = a/w = 0.1  0.9). the plots are displayed for various relative crack eccentricities (e/w = 0.0, 0.1, 0.2, 0.3 and 0.4) and furthermore, the application of the fracture criteria at various distances (rc = 0.2, 0.4, 1.0, 1.5, 1.8 and 3.2 mm) is studied. the data presented are of two kinds:  the purely numerical results, denoted as "fem": crack propagation direction angle γ is determined directly from the nodal solution of the fe analysis, i.e. the maximum of the tangential stress and minimum of the strain energy density, respectively is being sought at a given distance rc from the crack tip;  the semi-analytical results, denoted as "n = m = 1, 2, 4, 7 and 10": crack propagation direction angle γ is determined from the multi-parameter/generalized form of the fracture criteria, i.e. the maximum of the tangential stress and minimum of the strain energy density, respectively is being sought iteratively from eq. 3 and 6 when the stress tensor components are expressed by means of the we (see eq. 1) considering various numbers of the initial terms of the series. the results obtained from the mts criterion can be found in fig. 2, those from the sed criterion in fig. 3. the dependences plotted in fig. 2 and 3 enable to summarize the following statements and conclusions: 1) general results, fig. 2 and 3:  the results validate the theory that the fracture criteria in its classical one-parameter form (n = m = 1) are independent on the length parameter, i.e. on the radial distance.  the dependences obtained via sed criterion are not so sensitive to changing of the parameters (radial distance from the crack tip, crack eccentricity, number of the we terms in the fracture criterion, etc.) as the dependences obtained via mts criterion.  the larger distance from the crack tip, the worse agreement of the kink angles calculated by means of the multiparameter fracture criteria considering a low number of the we terms (n = m = 1, 2) with the kink angles determined numerically via fem.  scatter of all the data presented grows with increasing rc for each approximation. this effect is much more evident for long cracks, which is connected with the influence of the free surface and the necessity of the stress redistribution. t l. malíková et alii, frattura ed integrità strutturale, 33 (2015) 25-32; doi: 10.3221/igf-esis.33.04 29 -70 -50 -30 -60 -40 -20 0 -50 -30 -10 -40 -30 -20 -10 0 -40 -30 -20 -10 0 0.0 0.5 1.0 0.5 1.0 0.5 1.0 0.5 1.0 0.5 1.0 0.5 1.0 e w/ = 0 .0 e w/ = 0 .1 e w/ = 0 .2 e w/ = 0 .3 e w/ = 0 .4 rc = 0.2 rc = 0.4 rc = 1.0 rc = 1.5 rc = 1.8 rc = 3.2 c ra c k p ro p a g a ti o n d ir e c ti o n a n g le � [d e g .] relative crack length � [-] n m= = 1 n m= = 2 n m= = 4 n m= = 7 n m= = 10 fem figure 2: dependences of the initial crack propagation direction angle γ on the relative crack length  for various relative crack eccentricities e/w obtained from the mts fracture criterion at various radial distances from the crack tip rc; the purely numerical results ("fem") are compared to the semi-analytical results ("n = m = 1, 2, 4, 7 and 10") calculated via the multi-parameter form of the fracture criterion. 2) mts fracture criterion, fig. 2:  whereas the dependences of the kink angle calculated via fem fluctuate at several points, the results obtained by means of the we approximation seems to be more stable.  the kink angle dependence calculated via fem is changing with increasing rc and this phenomenon can be well described by means of the multi-parameter form of the fracture criterion; n = m = 4 is sufficient up to rc = 1.5 mm, n = m  7 needs to be considered for larger distances from the crack tip. l. malíková et alii, frattura ed integrità strutturale, 33 (2015) 25-32; doi: 10.3221/igf-esis.33.04 30  prediction of the crack propagation angle by means of one or two terms of the we is accurate enough if the distance from the crack tip is small enough (let's say up to rc = 0.4 mm). the deviations from the numerical solution increase with larger distances. -70 -50 -30 -60 -40 -20 0 -50 -30 -10 -40 -30 -20 -10 0 -40 -30 -20 -10 0 0.0 0.5 1.0 0.5 1.0 0.5 1.0 0.5 1.0 0.5 1.0 0.5 1.0 e w/ = 0 .0 e w/ = 0 .1 e w/ = 0 .2 e w/ = 0 .3 e w/ = 0 .4 rc = 0.2 rc = 0.4 rc = 1.0 rc = 1.5 rc = 1.8 rc = 3.2 c ra c k p ro p a g a ti o n d ir e c ti o n a n g le � [d e g .] relative crack length � [-] n m= = 1 n m= = 2 n m= = 4 n m= = 7 n m= = 10 fem figure 3: dependences of the initial crack propagation direction angle γ on the relative crack length  for various relative crack eccentricities e/w obtained from the sed fracture criterion at various radial distances from the crack tip rc; the purely numerical results ("fem") are compared to the semi-analytical results ("n = m = 1, 2, 4, 7 and 10") calculated via the multi-parameter form of the fracture criterion. 3) sed fracture criterion, fig. 3:  the dependences of the kink angle calculated via fem behave more stably, value of the angle doesn’t change so much as when the mts criterion is applied. l. malíková et alii, frattura ed integrità strutturale, 33 (2015) 25-32; doi: 10.3221/igf-esis.33.04 31  if the crack eccentricity is small (e/w = 0.0 or 0.1), the prediction of the crack propagation angle by means of the multi-parameter form of the criterion considering one or two terms of the we seems to be accurate enough; the differences increase with growing crack eccentricity (especially for larger distances from the crack tip).  the multi-parameter form of the sed fracture criterion is unavoidable if both the crack eccentricity and the distance from the crack tip are large. conclusions he paper is focused on the application of the multi-parameter fracture mechanics approach to the task of the determination of the initial crack propagation angle. a parametric study is performed on an eccentric asymmetric four point bending specimen. various mode-mixities (combinations of the mode i and ii) are ensured by means of varying geometrical parameters of the cracked specimen (crack length and crack eccentricity). two fracture criteria, mts and sed, are presented. the kink angle calculated exclusively from the numerical solution by means of the fem is compared to the angle calculated from the fracture criteria considering the we approximation of the stress tensor components. especially the influence of assuming various numbers of the initial we terms is investigated and discussed. it can be concluded that the sed criterion is much less sensitive to variations in all the parameter studied and with the exception of the configuration with large crack eccentricity and large distances from the crack tip (where the criterion is applied) seems to be accurate enough in its classical one-parameter form. on the other hand, the mts criterion exhibits much larger differences from the numerical results if only the first term of the we is considered for the crack-tip stress field approximation. again, this is essential especially if the criterion is applied farther from the crack tip. therefore, it can be concluded that several more higher-order terms of the we should be used for the stress field description when the distance from the crack tip is not small enough. this statement can be generalized not only for the crack propagation angle estimation task but also for more complicated issues within the nonlinear fracture mechanics field, when the nonlinear zone extent is comparable to the typical structural dimensions. acknowledgements inancial support from the czech science foundation (project no. 15-07210s and 15-19865y) is gratefully acknowledged. references [1] berto, f., lazzarin, p., on higher order terms in the crack tip stress field, int. j. fract., 161 (2010) 221–226. [2] du, z.z., hancock, j.w., the effect of non-singular stresses on crack tip constraint, j. mech. phys. solids, 39 (1991) 555–567. [3] karihaloo, b.l., size effect in shallow and deep notched quasi-brittle structures, int. j. fract., 95 (1999) 379–390. [4] williams, m.l., on the stress distribution at the base of a stationary crack, j. appl. mech. (asme), 24 (1957) 109– 114. [5] malíková, l., veselý, v., the influence of higher-order terms of williams series on a more accurate description of stress fields around the crack tip, fatigue fract. engng mater. struct., 38 (2014) 91–103. doi: 10.1111/ffe.12221. [6] šestáková, l., using the multi-parameter fracture mechanics for more accurate description of stress/displacement crack tip fields, key engng. mat., 586 (2014) 237–240. [7] veselý, v., frantík, p., sobek, j., malíková (šestáková), l., seitl, s., multi-parameter crack tip stress state description for estimation of nonlinear zone width in silicate composite specimens in component splitting/bending test geometry, fatigue fract. engng. mater. struct., (2014), doi: 10.1111/ffe.12170. [8] veselý, v., sobek, j., šestáková, l., frantík, p., seitl, s. multi-parameter crack tip stress state description for estimation of fracture process zone extent in silicate composite wst specimens, frattura ed integrità strutturale, 25 (2013) 69–78. [9] ayatollahi, m.r, nejati, m. an over-deterministic method for calculation of coefficients of crack tip asymptotic field from finite element analysis, fatigue fract. engng mater. struct., 34 (2010) 159–176. t f l. malíková et alii, frattura ed integrità strutturale, 33 (2015) 25-32; doi: 10.3221/igf-esis.33.04 32 [10] šestáková, l., how to enhance efficiency and accuracy of the over-deterministic method used for determination of the coefficients of the higher-order terms in williams expansion, appl. mech. mater., 245 (2013) 120–125. [11] karihaloo, b.l., xiao, q.z. accurate determination of the coefficients of elastic crack tip asymptotic field by a hybrid crack element with p-adaptivity, engng fract. mech., 68 (2001) 1609–1630. [12] tong, p., pian, t.h.h., lasry, s.j. a hybrid element approach to crack problems in plane elasticity, int. j. num. methods engng., 7 (1997) 297–308. [13] xiao, q.z., karihaloo, b.l., liu, x.y. direct determination of sif and higher order terms of mixed mode cracks by a hybrid crack element, int. j. fract., 125 (2004) 207–225. [14] šestáková (malíková), l. how to enhance efficiency and accuracy of the over-deterministic method used for determination of the coefficients of the higher-order terms in williams expansion, appl. mech. mater., 245 (2013) 120–125. [15] šestáková (malíková), l., veselý, v. convergence study on application of the over-deterministic method for determination of near-tip fields in a cracked plate loaded in mixed-mode, appl. mech. mater., 249–250 (2013) 76–81. [16] qian, j., fatemy, a. mixed mode fatigue crack growth: a literature survey, engng. fract. mech., 55(6) (1996) 969– 990. [17] erdogan, f., sih, g.c. on the crack extension in plates under plane loading and transverse shear, j. basic engng., 85 (1963) 519–525. doi:10.1115/1.3656897. [18] sih, g.c. some basic problems in fracture mechanics and new concepts, engng. fract. mech., 5 (1973) 365–377. [19] sih, g.c. strain energy density factor applied to mixed mode crack problems, int. j. fract. mech., 10 (1974) 305–321. [20] wolfram mathematica documentation center. wolfram research, inc., champaign (2007). [21] ansys program documentation. user’s manual version 10.0. swanson analysis system, inc., houston (2005). [22] seweryn, a., lukaszewicz, a. verification of brittle fracture criteria for elements with v-shaped notches, engng. fract. mech., 69 (2002) 1487–1510. [23] sih, g.c., ho, j.w. sharp notch fracture strength characterized by critical energy density, j. theor. appl. fract. mech., 16 (1991) 179–214. [24] susmel, l., taylor, d. the theory of critical distances to predict static strength of notched brittle components subjected to mixed-mode loading, engng. fract. mech., 75 (2008) 534–550. microsoft word 2356 o. a. mocian et alii, frattura ed integrità strutturale, 48 (2019) 230-241; doi: 10.3221/igf-esis.48.24 230 low velocity failure and integrity assessment of foam core sandwich panels oana alexandra mocian, dan mihai constantinescu, ştefan sorohan, marin sandu university politehnica of bucharest, department of strength of materials, 060042 bucharest, romania mocianoana@gmail.com, https://orcid.org/0000-0003-3093-7788 dan.constantinescu@upb.ro, https://orcid.org/0000-0001-5400-7804 stefan.sorohan@upb.ro, https://orcid.org/0000-0002-9400-5843 marin.sandu@upb.ro, https://orcid.org/0000-0002-9183-5104 abstract. impact resistance and energy absorbing capability are of great interest in the design of composite sandwich structures. this paper experimentally studies damage, failure and energy absorption properties of foam core sandwich panels with aluminum and glass fiber reinforced plastic (gfrp) facesheets subjected to low velocity impact. tests are performed using a drop weight impact tower at different impact velocities. the energy absorbing capabilities of aluminum and composite facesheet sandwich panels with pur and ps foam core are evaluated by means of absorbed energy-time histories and by specific parameters as normalized absorbed energy, specific energy absorption, and crush force efficiency. stiffer panels behave better at lower impact velocities, while more ductile ones do better if impact energy is increased. keywords. low velocity impact; sandwich panels; skin and core damage; energy absorption parameters. citation: mocian, o.a., constantinescu, d.m., sorohan, şt., sandu, m., low velocity failure and integrity assessment of foam core sandwich panels, frattura ed integrità strutturale, 48 (2019) 230-241. received: 20.01.2019 accepted: 15.02.2019 published: 01.04.2019 copyright: © 2019 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. introduction ne of the main design drivers of modern engineering is weight reduction whilst still ensuring high level of operational safety. lightweight design can protect human life, avoid financial losses and reduce vehicles emissions. seeking suitable lightweight materials has led to the development of composite materials, plastics and alternative new materials and sandwich construction. the last, usually consists of two strong and stiff facesheets separated by a lowdensity core. faces are generally made of metal alloys [1], fiber reinforced composites [2] or fiber metal laminates [3] and are responsible for carrying the transverse loads or bending moments. the core of sandwich structures comprises of honeycombs [4], corrugated materials [5], polymeric/metallic foams [6, 7], lattices [8] or balsa wood [9] and is responsible for absorbing the impact energy by local plastic deformation whilst still offering enough overall support to prevent high local bending strains in the facesheets. a comprehensive review of the current trends in the research and applications of sandwich structures is done by birman and kardomateas, [10]. during service life, sandwich structures may be subjected to o http://www.gruppofrattura.it/va/48/2356.mp4 o. a. mocian et alii, frattura ed integrità strutturale, 48 (2019) 230-241; doi: 10.3221/igf-esis.48.24 231 several severe impacts arising from operational events like collision, flying debris, tool drop or bird strike. among these, low velocity impacts can severely reduce the strength of the whole structure due to indentation and localized internal skin and/or core damage [11, 12], without any perception on the impacted side, [13-15]. as mentioned by feng and aymerich [15] the low velocity impact can develop various damage patterns in sandwich composites as resulting from different failure mechanisms as: matrix cracking, fiber fracture, face-core debonding through delaminations, and core crushing. all of them interact through complicated synergies when increasing the impact energy. many research results can be found in the aspects of quasi static, dynamic and energy absorption characteristics. in the studies of steeves et al. [16], jiang et al. [17] and vitale et al. [18], the collapse of a sandwich beam under three-point bending was analyzed through several types of failure events: core shear, face micro buckling, facesheet indentation and core crushing, depending on the geometry and density of the foam core. the dominant regimes of each collapse mode were marked out by drawing failure maps. the predictions were found close to the experimental results. sokolinsky et al. [19] used linear higher-order sandwich panel theory (hsapt) to describe the mechanical response of sandwich beams with aluminum facesheets and pvc foam core. they showed that the linear hsapt can be efficiently used to estimate vertical displacements of soft-core sandwich beams up to high load levels with great accuracy. zhang et al. [20] studied the flexural performance of composite sandwich beams with different gfrp ribs in four-point bending tests and concluded that beams failed due to skin compressive failure when positioned edgewise and in core shear failure when positioned flatwise. styles et al. [21] investigated the effect of core thickness on the failure behavior of aluminum foam core sandwich structures under flexural loading using the 3d digital image correlation method. a full field strain analysis for each core thickness was conducted and different failure mechanisms were found. regarding the dynamic impact investigations of sandwich structures, attention has gradually shifted from experimental testing to analytical analysis and numerical simulation due to the high cost of testing and the inability to accurately capture the damage states, especially in the case of low velocity impact where damage is nearly imperceptible. extensive studies have been recently made on sandwich structures with composites as facesheets. in [22] analytic and semi-analytic solutions have been obtained for the quasi-static case in studying the problem of damage progression and interaction in a sandwich beam with laminated facesheets and a homogeneous core. it was shown that core/facesheet interactions generate energy barriers to the propagation of delaminations in the facesheet; this explains the experimental findings of low velocity impact tests showing that in some cases multiple delamination damage in the facesheet typically remains localized near the striker. a procedure to numerically simulate the low-velocity impact tests and residual flexural strength tests of sandwich structures was developed by the vumat subroutine in abaqus/explicit, [23]. the damage morphology of both facesheets and the corrugated core was clearly identified. the numerical and experimental load-displacement characteristics for all cases were compared and there was a reasonably good agreement between them, except for the prolonged load plateau stage when the predicted load overestimated the experimental result, probably because the interface debonding was not considered in the numerical simulation. funari et al. [24] developed a much more refined numerical technique by incorporating in the model moving mesh cohesive modelling, crack initiation and nucleation at core/skin interfaces. arbitrary lagrangian–eulerian (ale) interface elements were used for the sandwich structure combined with a cohesive fracture approach where debonding phenomena may occur in presence of multiple delaminations. it is therefore realized a reduction of the computational costs, required to predict crack onset and progressive evolution of debonding phenomena. cohesive models for sandwich core/skin interfaces were calibrated by means of comparisons with numerical and experimental data for mode i and mode ii configurations. they also studied, [25], the influence of inertial effects on debonding phenomena and crack propagation in different core typologies of sandwich structures based on fracture parameters determined experimentally on commercially available foams. park et al. [26] investigated the force-time history curves of impacted sandwich structures and concluded that the damage resistance appears to be dependent on both the facesheet materials and core thickness: the lower the stiffness becomes, the greater the core thickness affects the impact resistance. crupi et al. [27] conducted a theoretical and experimental analysis for the impact response of glass fiber reinforced aluminum honeycomb sandwiches. they used 3d computed tomography to investigate the failure mode and internal damage and demonstrated that the use of glass-epoxy reinforcement on aluminum honeycomb sandwiches enhanced the energy absorption and load carrying capacities. zhu et al. [28] studied through theoretical, experimental and numerical methods the damage and failure mode maps of composite sandwich panels subjected to quasi-static indentation and low velocity impact. the effect of facesheet thickness was found to be vital contribution to the failure mode and its corresponding ultimate load, while core density affected only the failure mode. dawood et al. [29] demonstrated through experimental and numerical means that the punching resistance of gfrp sandwich panels with balsa wood cores can be increased by locally stiffening the panels near the location of the concentrated load. the low velocity impact response in metallic facesheets such as titanium, stainless steel and aluminum is different from composites as metals are ductile under localized deformation. xie et al. [30] studied the low velocity impact response of o. a. mocian et alii, frattura ed integrità strutturale, 48 (2019) 230-241; doi: 10.3221/igf-esis.48.24 232 titanium honeycomb sandwich structures through experimental and numerical investigations. the identified failure modes were permanent indentation on the impacted facesheet and localized honeycomb core crush under the impact location. sun et al. [31] studied the effect of skin thickness, core thickness, core height and cell size on indentation characteristics, such as peak forces, failure modes and energy absorption, for sandwich panels with aluminum facesheets and honeycomb core. the principal failure mechanisms identified were shear and tension damage for the facesheets and plastic folding and buckling for the honeycomb core. the parametric studies conducted through numerical analysis revealed that by modifying the cell size changed considerably the failure modes and by increasing the core height decreased the peak forces. despite the extensive research conducted in low velocity impact of sandwich structures, a considerable amount of research is still needed to reveal their complex damage and failure characteristics. in this study, the damage and failure mechanism and energy absorption properties of foam core sandwich panels with aluminum and gfrp facesheets subjected to low velocity impact are investigated. drop weight impact tests are carried out to induce damage into the sandwich panels. different impact velocities are selected as to cause different damage response of the sandwich panels, from barely visible impact damage to complete perforation. damage characteristics are evaluated by measuring the damaged area or depth of indentation of the impactor and energy absorption is evaluated by using specific parameters as: normalized absorbed energy, specific energy absorption and crush force efficiency. experimental methodology materials and specimens ll tested sandwich panels consist of two identical facesheets and a foam core. facesheets are of two major types: aluminum and composite. the aluminum is al 6082-t6, which is one of the strongest alloys from the 6xxx series, due to the heat-treated and artificially aged processes. the thickness of the aluminum facesheets is 1.5 mm. the composites are made from 8 layers of fiber glass roving of 500 g/m2 and a general-purpose epoxy system, epolam 2017. three different types of composite facesheets were obtained by adding different amounts of short glass fibers in the resin matrix: type a 0 g of short glass fibers / 100 g resin, type b 6.4 g of short glass fibers / 100 g resin and type c 9.3 g of short glass fibers / 100 g resin. thickness of the facesheets slightly varies around 2 mm due to the manual manufacturing process. the foams used as core for the sandwich panels are polyurethane (pur) necuron 100 of density 100 kg/m3 and commercial extruded polystyrene (ps) of density 32 kg/m3, both having thicknesses of 12 mm. facesheets were bonded to the core using an epoxy adhesive, type araldite aw106 (huntsman). the panels were cut into square specimens of 140x140 mm. low velocity impact testing impact tests were conducted according to iso 6603-2:2000 [32] and astm 7136 [33] standards, using an instrumented impact tower presented in fig. 1. the instron ceast 9340 is a gravitationally accelerated impact drop tower that can reach impact velocities up to 4.6 m/s and impact energies of almost 430 j. it is equipped with an instrumented impactor, having a hemispherical head of 20 mm diameter, which can directly measure the impact force using a strain gauge transducer which is mounted inside, on an elastic element. the sandwich plates are placed on an adjustable in height test specimen support with a circular hole of 100 mm diameter (fig. 1), which eventually allows the striker to fall if the plate is perforated. a clamping ring is pressed over the sandwich plate by a pneumatic system with a maximum force of 3 kn. this force cannot be adjusted during testing. the machine's software allows the user to obtain other impact characteristics such as: absorbed energy, displacement of the impactor, and of course the measured contact force during impact. therefore force-time and force-displacement plots can be easily obtained. data acquisition was done with a frequency of 200 khz for a maximum estimated time of 40 ms which proved as being sufficient to follow all the significant events. only the first impact was considered for monitoring the impact phenomena and comparisons of the responses of the sandwich panels which were tested. details of the experimental procedure can be found in previous work [34, 35]. the objective of the impact tests was to cause impact damage to the panels, from barely visible impact damage to complete perforation. several specimens were tested at impact velocities ranging between 1.5 and 4.5 m/s in order to select the impact velocities that manage to cause various failure mechanisms. three impact velocities were selected hereby: 3 m/s, 3.5 m/s and 4 m/s and a constant mass of the impactor as 13.15 kg. the corresponding impact energies and drop heights are presented in tab. 1. the impacted sandwich panels were abbreviated as following: sandwich panel (sp) with composite type (a, b or c) or aluminum (al) facesheets, foam core type (pur or ps) and impact velocity. therefore, as an example, spa_pur_3 means a o. a. mocian et alii, frattura ed integrità strutturale, 48 (2019) 230-241; doi: 10.3221/igf-esis.48.24 233 sandwich panel with composite facesheets type a and polyurethane foam core impacted at 3 m/s. figure 1: instron ceast 9340 drop tower impact system. impact velocity [m/s] impact energy [j] drop height [mm] 3 59.17 460 3.5 80.54 625 4 105.2 815 table 1: impact characteristics of the drop weight tests: impact velocity, impact energy and drop height. results and discussions uring an impact test, the variation of the impact force in time is recorded by the drop tower impact system. using these data, the software calculates other variations such as impact energy in time and impact force as a function of impactor displacement. it also determines some impact parameters such as peak force, corresponding to the maximum value on the force-time curve, and absorbed energy, calculated as the area under the force-displacement curve. the average values of mass, maximum impact force and absorbed energy of the impacted sandwich panels are listed in tab. 2. sandwich panel mass [g] fmax [n] eabs [j] sandwich panel mass [g] fmax [n] eabs [j] pur ps pur ps pur ps pur ps pur ps pur ps spa_3 162 137 5563 4336 57.97 57.88 spc_3 172 173 5804 4847 59.47 58.25 spa_3.5 163 138 5705 4442 76.02 66.54 spc_3.5 163 165 5463 5185 76.63 83.03 spa_4 161 144 6151 4825 84.82 80.30 spc_4 172 174 5839 6015 86.26 92.66 spb_3 175 168 5850 4669 57.78 57.18 spal_3 198 184 10981 6985 50.84 58.03 spb_3.5 165 160 5555 5025 81.11 78.35 spal_3.5 199 185 11789 8261 78.45 76.62 spb_4 170 164 6045 4935 85.00 78.14 spal_4 193 184 11061 10030 99.20 100.30 table 2: parameters of impacted sandwich panels. d o. a. mocian et alii, frattura ed integrità strutturale, 48 (2019) 230-241; doi: 10.3221/igf-esis.48.24 234 energy absorption fig. 2 presents typical energy variation curves as a function of time for all tested sandwich panels. results are presented comparatively in terms of core type and impact velocity, for each type of facesheet. a) b) c) d) figure 2: variation of energy in time for different facesheet types: a) composite type a; b) composite type b; c) composite type c; d) aluminum. three important particularities can be identified in the energy-time variation curve: the impact energy corresponding to the maximum value on the curve, the absorbed energy corresponding to the constant value on the curve after the decrease of energy and the elastic recovered energy represented by the difference between the impact and absorbed energy. if the curve shows an increase of the energy in time it results that the panel has been perforated (figs. 2 a, b, c at 4 m/s and pur foam core, as an example). in all cases the absorbed energy increases with increasing impact energy. for sandwich panels with aluminum facesheets there is always a recovery of energy regardless the impact velocity. instead, for sandwich panels with composite facesheets, a recovery of energy is achieved only for the smallest impact velocity of 3 m/s. not only the impact velocity influences the absorbed energy but also the facesheet and core type (see fig. 3). when using pur foam as core, for the impact velocity of 3 m/s, the sandwich panels with aluminum facesheets absorb approximately 13 % less impact energy than those with composite facesheets. on the contrary, sandwich panels with ps core absorb almost the same amount of energy, regardless the facesheet type, due to its elastic behavior. at 3.5 m/s all panels with pur foam core (fig. 3a) absorb almost the same amount of impact energy. for panels with ps foam core (fig. 3b), the highest amount of energy is absorbed by those with composite facesheets type c, approximately 25% more than those with composite facesheets type a, which absorb the smallest amount of energy. for the highest impact velocity, sandwich panels with aluminum facesheets absorb the same amount of energy, regardless the foam core type. composite sandwich panels absorb considerably less energy, approximately 14 % less, since they are completely perforated at this impact velocity, except the case of sandwich panel with composite facesheets type c and ps foam core. the energy absorption can also be quantified by several parameters, such as: normalized absorbed energy (nae ratio between absorbed energy and initial impact energy), specific energy absorption (sea ratio between absorbed energy and mass) and crush force efficiency (cfe ratio between average crushing force and peak force), [36]. these parameters are comprised in tab. 3 and graphically illustrated in fig. 4. 0 30 60 90 120 0 5 10 15 20 25 30 35 e n er g y [ j ] time [ms] spa_pur_3 spa_ps_3 spa_pur_3.5 spa_ps_3.5 spa_pur_4 spa_ps_4 0 30 60 90 120 0 5 10 15 20 25 30 35 e n er gy [ j ] time [ms] spb_pur_3 spb_ps_3 spb_pur_3.5 spb_ps_3.5 spb_pur_4 spb_ps_4 0 30 60 90 120 0 5 10 15 20 25 30 35 e n er g y [ j ] time [ms] spc_pur_3 spc_ps_3 spc_pur_3.5 spc_ps_3.5 spc_pur_4 spc_ps_4 0 30 60 90 120 0 5 10 15 20 e n er gy [ j ] time [ms] spal_pur_3 spal_ps_3 spal_pur_3.5 spal_ps_3.5 spal_pur_4 spal_ps_4 o. a. mocian et alii, frattura ed integrità strutturale, 48 (2019) 230-241; doi: 10.3221/igf-esis.48.24 235 a) b) figure 3: comparison of absorbed impact energy as a function of facesheet type: a) pur foam core; b) ps foam core. sandwich panel nae [%] sea [j/kg] cfe [-] sandwich panel nae [%] sea [j/kg] cfe [-] pur ps pur ps pur ps pur ps pur ps pur ps spa_3 97.96 97.81 357.97 423.7 0.47 0.54 spc_3 98.78 98.45 346.68 336.82 0.43 0.50 spa_3.5 94.39 82.62 465.46 483.73 0.54 0.58 spc_3.5 95.15 99.42 468.99 504.58 0.59 0.67 spa_4 80.63 76.33 526.05 556.13 0.56 0.62 spc_4 82.00 88.07 500.52 531.55 0.59 0.60 spb_3 97.65 96.63 329.40 339.73 0.43 0.58 spal_3 85.94 98.06 257.23 315.62 0.56 0.60 spb_3.5 98.37 97.27 492.25 490.85 0.62 0.63 spal_3.5 97.41 95.13 393.54 414.44 0.36 0.60 spb_4 80.81 74.28 499.72 473.67 0.55 0.61 spal_4 94.30 95.32 514.49 545.86 0.49 0.59 table 3: energy absorption quantifying parameters. for sandwich panels with composite facesheets, irrespective of core type, the normalized absorbed energy decreases with increasing impact velocity, respectively with increasing impact energy (see fig. 4). this happens because the impact energy exceeds the saturation energy, which represents the maximum impact energy that can be absorbed by a structure until it completely loses its load carrying capacity. as it will be further seen in this study, most of the sandwich panels with composite facesheets are perforated at higher impact velocities, meaning that they absorbed only a part of the total impact energy. the rest remained in the impactor as residual velocity. in the case of sandwich panels with aluminum facesheets, at higher impact velocities, nae slightly increases for panels with pur foam core and decreases for panels with ps foam core. due to its elastic behavior the ps foam core manages to better absorb the impact energy at lower impact velocities than the pur core. the higher values of sea for sandwich panels with composite facesheets indicate that these panels absorb more energy per unit mass than those with aluminum facesheets. this is because the average weight of sandwich panels with composite facesheets is approximately 15 % less than of those with aluminum facesheets. also, sandwich panels with composite facesheets absorb a greater amount of energy than those with aluminum facesheets, especially for the lowest impact velocity, due to the different and complex energy absorption mechanisms: matrix cracking, debonding, fiber rupture, core crushing and delaminations. this type of failure determines a small value for the cfe parameter. for a structure to have good energy absorption capabilities, both sea and cfe parameters should have high values. from fig. 4 b) and c) although aluminum sandwich panels with both pur and ps foam core have the highest values for cfe at 3 m/s, they have the smallest value for sea. consequently, even though they fail in a progressive mode they do not manage to absorb enough impact energy per unit mass. at this impact velocity, the sandwich panel with composite facesheets type a and ps foam core proves to be the most efficient, with sea of almost 425 j/kg and cfe as 0.54. though, as it will be later seen in this study, this panel is also the most damaged one at 3 m/s. the cfe parameter for aluminum sandwich panels with pur foam core considerably reduces its value at higher impact velocities. for example, at 3.5 m/s reaches a value of 0.36, which is 35 % less than for the lowest impact velocity of 3 m/s. instead, the value of the cfe parameter for sandwich panels with aluminum facesheets and ps foam core remains almost the same, around 0.60, irrespective of impact velocity. for impact velocities of 3.5 m/s and 4 40 60 80 100 120 3 3.5 4 a b so rb ed e n er g y [j ] impact velocity [m/s] spal_pur spa_pur spb_pur spc_pur 40 60 80 100 120 3 3.5 4 a b so rb ed e n er g y [j ] impact velocity [m/s] spal_ps spa_ps spb_ps spc_ps o. a. mocian et alii, frattura ed integrità strutturale, 48 (2019) 230-241; doi: 10.3221/igf-esis.48.24 236 m/s, composite sandwich panels have higher values for both sea and cfe than those with aluminum facesheet. though, at 4 m/s they completely lose their load bearing capacity, being completely perforated. a) b) c) figure 4: comparison of energy absorption quatifying parameters as a function of impact velocity: a) nae; b) sea; c) cfe. 0 20 40 60 80 100 120 n a e [ % ] sandwich type 3 m/s 3.5 m/s 4 m/s 0 100 200 300 400 500 600 s e a [ j /k g ] sandwich type 3 m/s 3.5 m/s 4 m/s 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 c f e [ -] sandwich type 3 m/s 3.5 m/s 4 m/s o. a. mocian et alii, frattura ed integrità strutturale, 48 (2019) 230-241; doi: 10.3221/igf-esis.48.24 237 damage assessment impact damage assessment of the tested sandwich panels was carried out through visual inspection on the front and back facesheets of the panels. high resolution photographs were taken to assess the damage extension for all adopted impact velocities. this images were used to measure the damaged areas in sandwich panels with composite facesheets using the imagej software [37], which is an open source image processing program designed for scientific multi-dimensional images. for panels with aluminum facesheets the indentation depth, defined as the residual depth of the depresion of the aluminum facesheet surface caused by the impactor during the impact event, was measured. results are presented in tab. 4 and tab. 5. facesheet perforation is marked with “”, while for sign “x” a no perforation situation appeared. moreover, close up images of the central part of the impacted sandwich panels are presented in fig. 5 and fig. 6. sandwich panel damage area [mm2] facesheet perforation top bottom top bottom pur ps pur ps pur ps pur ps spa_3 737.76 649.97 270.43 388.051   x x spa_3.5 690.00 544.17 746.63 821.64   x  spa_4 746.73 576.23 872.05 872.55     spb_3 726.05 733.07 165.06 243.40   x x spb_3.5 641.78 658.91 653.25 776.02   x x spb_4 662.14 614.95 822.31 895.89     spc_3 741.74 654.18 58.93 185.14 x  x x spc_3.5 650.87 738.33 581.15 607.92   x x spc_4 646.28 746.26 826.03 907.75    x table 4: summary of damage events induced by impact loading in sandwich panels with composite facesheets. sandwich panel indentation depth [mm] facesheet perforation top bottom pur ps pur ps pur ps spal_3 8.23 13.38 x x x x spal_3.5 12.61 15.13  x x x spal_4 15.84 16.87  x x x table 5: summary of damage events induced by impact loading in sandwich panels with aluminum facesheets. for the lowest impact velocity of 3 m/s, the upper facesheet of all sandwich panels with composite facesheets is perforated, irrespective of core type, except for the spc_pur panel, which is the most rigid one due to the pur core and the composite facesheets with the highest amount of short glass fibers. the bottom facesheets present only matrix cracking, debonding and some fiber rupture, with no perforation (see fig. 5). composite sandwich panels with pur foam core have a larger damage area on the upper facesheet and a smaller damage area on the bottom facesheet than those with ps foam core. the increased rigidity of the pur foam reduces the absorption capability of the core and thus most of the impact energy is absorbed by the upper facesheet, which is more damaged. the sandwich panels with aluminum facesheets present a small indentation on the upper facesheet, with no perforation, and no visible damage on the bottom facesheet (see fig. 5). by increasing the impact velocity to 3.5 m/s determines an important increase of the damage area in the bottom facesheets, almost 76% for pur panels and 64 % for ps panels,while uppper facesheet perforation and debonding is almost the same for all composite sandwich panels. moreover, the bottom facesheet of the less rigid composite sandwich panel, the spa_ps panel, is perforated. the aluminum sandwich panels with pur foam core, present local indentation and perforation of the o. a. mocian et alii, frattura ed integrità strutturale, 48 (2019) 230-241; doi: 10.3221/igf-esis.48.24 238 upper facesheet, and a small bulge deformation on the bottom facesheet. same as composite sandwiches, these panels with ps foam core show less damage on the upper facesheet, with no perforation, but a larger bulge deformation on the bottom facesheet. as a consequence, the indentation depth for sandwich panels with ps foam core is larger than those with pur foam core (tab. 5). spa_pur spb_pur spc_pur spal_pur t o p b o t t o m a) spa_ps spb_ps spc_ps spal_ps t o p b o t t o m b) figure 5: failure of sandwich panels impacted at 3 m/s: a) pur foam core; b) ps foam core. at an impact velocity of 4 m/s both facesheets of all composite sandwich panels are perforated (fig. 6a), except for the bottom facesheet of the spc_ps panel. the damage area on this facesheet reaches the highest value of all, close to 908 mm2, that is 4.6 % of the total area of the sandwich panel. in all other cases, the damage areas on the upper and bottom facesheets are almost the same. it must be noticed that upper composite facesheets fail both through thickness shear mode and tension mode. though, sandwich panels with pur core fail mostly under shear mode, due to the brittle behavior of the polyurethane foam, while sandwich panels with ps core fail mostly in tension mode. moreover, the elastic behavior of the ps foam core allows the impactor to push apart the ruptured fibers and hence create a bigger perforation cavity (see fig. 6b). the upper facesheet of the aluminum sandwich panels with pur foam core is perforated and damage is concentrated in the impact zone. while for the ps panels there is no perforation of the panel, but the upper facesheet, among local indentation, undergoes plastic deformation due to bending on random directions from the center to the margins of the panel. o. a. mocian et alii, frattura ed integrità strutturale, 48 (2019) 230-241; doi: 10.3221/igf-esis.48.24 239 spa_pur spb_pur spc_pur spal_pur t o p b o t t o m a) spa_ps spb_ps spc_ps spal_ps t o p b o t t o m b) figure 6: failure of sandwich panels impacted at 4 m/s: a) pur foam core; b) ps foam core. concluding remarks his paper experimentally investigated the low velocity impact behavior of foam core sandwich panels with aluminum and glass fiber reinforced composite facesheets. the energy absorption capabilities and failure characteristics of these sandwich panels were analyzed in detail. based on the results and discussions, the following conclusions can be drawn: (1) the energy-time variation curves indicate a recovery of energy in the case of aluminum sandwich panels irrespective of impact velocity; for sandwich panels with composite facesheets this energy recovery is barely noticeable only at the lowest impact velocity. (2) the energy absorbing capability of the sandwich panels is affected by the initial impact velocity on one hand, and facesheets and core type on the other hand. for the lowest impact velocity, pur sandwich panels with aluminum facesheets absorb less energy than those with composite facesheets, while ps sandwich panels absorb almost the same amount of energy for both types of facesheets. for the highest impact velocity, the aluminum facesheets panels absorb the highest amount of energy regardless the core type. (3) three normalized parameters are used to quantify the effectiveness of impact energy absorption of the sandwich panels with pur and ps core by using composite and aluminum facesheets. they are: normalized absorbed energy (nae), specific energy absorption (sea), and crush force efficiency (cfe). higher they are, better it is from the point of view of engineering applications. that is, for the same core, the main question is: what is it better to use as facesheet with similar thickness: aluminum or gfrp? or, for the same type of facesheet, pur or ps foams are t o. a. mocian et alii, frattura ed integrità strutturale, 48 (2019) 230-241; doi: 10.3221/igf-esis.48.24 240 preferable? it looks like each normalized parameter gives specific information on the sandwich response and therefore the obtained information from all of them must be corroborated. at lower impact speeds composite facesheets do better than the aluminum ones; more rigid the facesheet and core (type c and pur) are, the outcome is that the composite panel is surpassing the aluminum one in terms of sea, but not so evidently for nae and cfe. at the highest impact speed of 4 m/s the parameter sea is about the same for both types of facesheets, nae increases using aluminum facesheets and cfe decreases. (4) for composite facesheets panels the damaged area of the top facesheet is reduced if the facesheet is stiffer – type c versus type a, and by using the more rigid core – pur versus ps. on the bottom facesheet, in the cases without perforation at 3 and 3.5 m/s, an important decrease of the damaged surface is produces by using pur foam core instead of ps foam core (more than 3 times for type c facesheet at 3 m/s). at 4 m/s perforation of bottom facesheet is almost produced even for type c facesheet and the surface of the damaged area is greater for ps foam core than for pur foam core, actually about the same regardless the type of the composite facesheet for each foam core type. acknowledgements iss oana alexandra mocian acknowledges the phd student scholarship given by the ministry of national education from romania through the contract no. 06.40/2014 which made possible the present researches. all the authors acknowledge that this work was supported by a grant from the romanian national authority for scientific research and innovation, cccdi-uefiscdi, project number 11/2015. references [1] gilioli, a., sbarufatti, c., manes, a., giglio, m. (2014). compression after impact test (cai) on nomex™ honeycomb sandwich panels with thin aluminum skins, compos. part b-eng., 67, pp. 313-325. doi: 10.1016/j.compositesb.2014.07.015. [2] zhang, y., zong, z., liu, q., ma, j., wu, y., li, q. (2017). static and dynamic crushing response of cfrp sandwich panels filled with different reinforced materials, mater. design, 117, pp. 396-408, doi: 10.1016/j.matdes.2017.01.010. [3] tan, c.y., akil, h.m. (2012). impact response of fiber metal laminate sandwich composite structure with polypropylene honeycomb core, compos. part b-eng., 43, pp. 1433-1438, doi: 10.1016/j.compositesb.2011.08.036. [4] wang, h., ramakrishnan, k.r., shankar, k. (2016). experimental study of the medium velocity impact response of sandwich panels with different cores, mater. design, 99, pp. 68-82, doi: 10.1016/j.matdes.2016.03.048. [5] wei, k., peng, y., qu, z., he, r., cheng, x. (2017). high temperature mechanical behaviors of lightweight ceramic corrugated core sandwich panels, compos. struct., 176, pp. 379-386, doi: 10.1016/j.compstruct.2017.05.053. [6] jing, l., xi, c., wang, z., zhao, l. (2013). energy absorption and failure mechanism of metallic cylindrical sandwich shells under impact loading, mater. design, 52, pp. 470-480, doi: 10.1016/j.matdes.2013.05.090. [7] zhang, s., dulieu-barton, j.m., thomsen, o.t. (2015). the effect of temperature on the failure modes of polymer foam cored sandwich structures, compos. struct., 121, pp. 104-113, doi: 10.1016/j.compstruct.2014.10.032. [8] mcshane, g.j., radford, d.d., deshpande, v.s., fleck, n.a. (2006). the response of clamped sandwich plates with lattice cores subjected to shock loading, eur. j. mech. a-solids, 25, pp. 215-229, doi: 10.1016/j.euromechsol.2005.08.001. [9] jover, n., shafiq, b., vaidya, u. (2014). ballistic impact analysis of balsa core sandwich composites, compos. part beng., 67, pp. 160-169, doi: 10.1016/j.compositesb.2014.07.002. [10] birman, v., kardomateas, g.a. (2018). review of current trends in research and applications of sandwich structures, compos. part b-eng., 142, pp. 221-240, doi: 10.1016/j.compositesb.2018.01.027. [11] chai, g.b., zhu, s. (2011). a review of low-velocity impact on sandwich structures, p. i. mech. eng. l-j. mat., 225(4), pp. 207-230, doi: 10.1177/1464420711409985. [12] pathipaka, r.k., namala, k.k., sunkara, n., bandaru, c.r. (2018). damage characterization of sandwich composites subjected to impact loading, j. sandw. struct. mater., doi: 10.1177/1099636218792717. [13] siivola, j.t., minakuchi, s., mizutani, t., takeda, n. (2016). evaluation of damage detectability in practical sandwich structure application conditions using distributed fiber optic sensor, struct. health monit., 15, pp. 3-20, doi: 10.1177/1475921715620002. [14] akatay, a., bora, m.o., coban, o., fidan, s., tuna, v. (2015). the influence of low velocity repeated impacts on residual compressive properties of honeycomb sandwich structures, compos. struct., 125, pp. 425-433, m o. a. mocian et alii, frattura ed integrità strutturale, 48 (2019) 230-241; doi: 10.3221/igf-esis.48.24 241 doi: 10.1016/j.compstruct.2015.02.057. [15] feng, d., aymerich, f. (2013). damage prediction in composite sandwich panels subjected to low-velocity impact, compos. part a-appl. sci. manuf., 52, pp. 12-22, doi: 10.1016/j.compositesa.2013.04.010. [16] steeves, c., fleck, n. (2004). collapse mechanisms of sandwich beams with composite faces and a foam core, loaded in three-point bending. part ii: experimental investigation and numerical modeling, int. j. mech. sci., 46(4), pp. 585608, doi: 10.1016/j.ijmecsci.2004.04.004. [17] jiang, b., li, z., lu, f. (2015). failure mechanism of sandwich beams subjected to three-point bending, compos. struct., 133, pp. 739-745, doi: 10.1016/j.compstruct.2015.07.056. [18] vitale, j., francucci, g., xiong, j., stocchi, a. (2017). failure mode maps of natural and synthetic fiber reinforced composite sandwich panels, compos. part a-appl. s., 94, pp. 217-225, doi: 10.1016/j.compositesa.2016.12.021. [19] sokolinsky, v.s., shen, h., vaikhanski, l., nutt, s.r. (2003). experimental and analytical study of nonlinear bending response of sandwich beams, compos. struct., 60(2), pp. 219-229, doi: 10.1016/s0263-8223(02)00293-3. [20] zhang, f., liu, w., fang, h., jia, z. (2019). flexural behavior of composite sandwich beams with different kinds of gfrp ribs in flatwise and edgewise positions, compos. part b-eng., 156, pp. 229-239. doi: 10.1016/j.compositesb.2018.08.053 [21] styles, m., compston, p., kalyanasundaram, s. (2007). the effect of core thickness on the flexural behavior of aluminum foam sandwich structures, compos. struct., 80(4), pp. 532-538, doi: 10.1016/j.compstruct.2006.07.002. [22] massabò, r., cavicchi, a. (2012). interaction effects of multiple damage mechanisms in composite sandwich beams subject to time dependent loading, int. j. solids struct., 49, pp. 720–738, doi: 10.1016/j.ijsolstr.2011.11.012. [23] he, w., liu, j., wang, s., xie, d. (2018). low-velocity impact response and post-impact flexural behaviour of composite sandwich structures with corrugated cores, compos. struct., 189, pp. 37-53, doi: 10.1016/j.compstruct.2018.01.024. [24] funari, m.f., greco, f., lonetti, p. (2018). sandwich panels under interfacial debonding mechanisms, compos. struct., 203, pp. 310–320, doi: 10.1016/j.compstruct.2018.06.113. [25] funari, m.f., greco, f., lonetti, p., spadea, s. (2019). a numerical model based on ale formulation to predict crack propagation in sandwich structures, frattura ed integrità strutturale, 47, pp. 277-293, doi: 10.3221/igf-esis.47.21. [26] park, j.h., ha, s.k., kang, k.w., kim, c.w., kim, h.s. (2008). impact damage resistance of sandwich structure subjected to low velocity impact, j. mater. process. tech., 201(1-3), pp. 425-430. doi: 10.1016/j.jmatprotec.2007.11.196. [27] crupi, v., kara, e., epasto, g., guglielmino, e., aykul, h. (2016). theoretical and experimental analysis of glass fibre reinforced aluminium honeycomb sandwiches, j. sandw. struct. mater., 20(1), pp. 42-69. doi: 10.1177/1099636216629375. [28] zhu, s., chai, g.b. (2013). damage and failure mode maps of composite sandwich panel subjected to quasi-static indentation and low velocity impact, compos. struct., (101), pp. 204-214, doi: 10.1016/j.compstruct.2013.02.010. [29] dawood, m., ballew, w., seiter, j. (2011). enhancing the resistance of composite sandwich panels to localized forces for civil infrastructure and transportation applications, compos. struct., 93(11), pp. 2983-2991, doi: 10.1016/j.compstruct.2011.05.004. [30] xie, z., zhao, w., wang, x. (2017). low-velocity impact behaviour of titanium honeycomb sandwich structures, j. sandw. struct. mater., 20(8), pp. 1009-1027, doi: 10.1177/1099636217728421. [31] sun, g., chen, d., huo, x., zheng, g., li, q. (2018). experimental and numerical studies on indentation and perforation characteristics of honeycomb sandwich panels, compos. struct., 184, pp. 110-124, doi: 10.1016/j.compstruct.2017.09.025. [32] iso 6603-2:2000, plastics -determination of puncture impact behaviour of rigid plastics -part 2: instrumented impact testing, international organization for standardization, geneva, switzerland [33] astm d7136/d7136m-15. standard test method for measuring the damage resistance of a fiber-reinforced polymer matrix composite to a drop weight impact event, west conshohocken, pa, usa: astm international, 2015. [34] mocian, o.a., constantinescu, d.m., sandu, m., sorohan, st. (2018). experimental and numerical analyses of the impact response of lightweight sandwich panels, mater. today-proc., 5(13), pp. 26634-26641, doi: 10.1016/j.matpr.2018.08.128. [35] mocian, o.a., constantinescu, d.m., sandu, m., sorohan, st. (2018). experimental evaluation of the response of sandwich panels in low-velocity impact, p. i. mech. eng. l-j. mat., doi: 10.1177/ 1464420718798168. [36] lakshmana, c.r., narayanamurthy, v., simha, k.r.y. (2016). applied impact mechanics, john wiley & sons ltd, united kingdom. 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can be opened with acrobat and adobe reader 5.0 and later.) >> /namespace [ (adobe) (common) (1.0) ] /othernamespaces [ << /asreaderspreads false /cropimagestoframes true /errorcontrol /warnandcontinue /flattenerignorespreadoverrides false /includeguidesgrids false /includenonprinting false /includeslug false /namespace [ (adobe) (indesign) (4.0) ] /omitplacedbitmaps false /omitplacedeps false /omitplacedpdf false /simulateoverprint /legacy >> << /addbleedmarks false /addcolorbars false /addcropmarks false /addpageinfo false /addregmarks false /convertcolors /converttocmyk /destinationprofilename () /destinationprofileselector /documentcmyk /downsample16bitimages true /flattenerpreset << /presetselector /mediumresolution >> /formelements false /generatestructure false /includebookmarks false /includehyperlinks false /includeinteractive false /includelayers false /includeprofiles false /multimediahandling /useobjectsettings /namespace [ (adobe) (creativesuite) (2.0) ] /pdfxoutputintentprofileselector /documentcmyk /preserveediting true /untaggedcmykhandling /leaveuntagged /untaggedrgbhandling /usedocumentprofile /usedocumentbleed false >> ] >> setdistillerparams << /hwresolution [2400 2400] /pagesize [612.000 792.000] >> setpagedevice microsoft word numero_49_art_57_2414 m. hadj miloud et alii, frattura ed integrità strutturale, 49 (2019) 630-642; doi: 10.3221/igf-esis.49.57 630 coupled identification of the hardening behavior laws and gurson– tvergaard–needleman damage parameters validation on tear test of 12nicr6 ct specimen mohamed hadj miloud, ibrahim zidane, mohammed mendas laboratoire de rhéologie et mécanique lrm, université hassiba benbouali de chlef, algeria m.hadjmiloud@univ-chlef.dz, i.zidane@univ-chlef.dz, m.mendas@univ-chlef.dz abstract. this work is devoted to the application of the micromechanical gurson-tvergaard-needleman (gtn) model to study the ductile tearing of 12nicr6 steel. gtn model is widely used to describe the three stages of ductile tearing: nucleation, growth and the coalescence of micro-voids. a new approach based on the identification of the gtn damage model coupled or not with hardening laws using inverse analysis. after identification, the obtained results show a good agreement between the experimental curve tensile test of an axisymetric notched bar (an2) and those numerically obtained for gtn model coupled with the hardening laws. in order to validate the identified gtn parameters, a simulation of tear test is conducted on 12 nicr6 steel ct specimen. the numerical results are compared with experimental results found in the literature and a good agreement is obtained. this identification procedure is more accurate than when the damage parameters are identified independently of the hardening laws. keywords. gtn model; hardening laws; inverse analysis; fe modeling; vuhard; ductile fracture. citation: hadj miloud, m., zidane, i., mendas, m., coupled identification of the hardening behavior laws and gurson– tvergaard–needleman damage parameters validation on tear test of 12nicr6 ct specimen, frattura ed integrità strutturale, 49 (2019) 630-642. received: 28.02.2019 accepted: 03.03.2019 published: 01.07.2019 copyright: © 2019 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. introduction any accidental failures of bridges, ships, tanks, pipes, etc., occur that are due to defects generated by: material processing, engineering design process, and the lack of knowledge of some problems as fatigue, corrosion, etc. scientific researches carried out numerical model/experimental investigations to understand and prevent such accidents. this gave birth of fracture mechanics, which aims to study the propagation of pre-existing cracks within a material. the local approach based on the micromechanical modeling is one of the several methods used in the damage analysis. numerous models based on a coupling between plasticity and damage has been proposed, notably that of gurson model [1], which describes the behavior of a porous ductile material. many variants of this model have been formulated m http://www.gruppofrattura.it/va/49/2414.mp4 m. hadj miloud et alii, frattura ed integrità strutturale, 49 (2019) 630-642; doi: 10.3221/igf-esis.49.57 631 subsequently [2-4]. the modified gurson-tvergaard-needeleman (gtn) model is widely used in the modeling of ductile fracture. metallographic studies [5-6] demonstrate that the ductile fracture process of a metal is basically characterized by three mechanisms of void evolution as represented in the fig. 1. a) nucleation of voids due to the debonding of particle–matrix interface, fracture of the particle or micro-cracking of the matrix surrounding the inclusion (part iii); b) growth of voids leading to an enlargement of existing cavities (part iv); c) finally, coalescence of micro-cracks initiated from voids leading to the drop of the load-carrying capacity of the material, when the void volume fraction (vvf) reaches to its final value (part v). from fig. 1, we note also that part i represents the elastic zone and part ii represents the lüder bands. figure 1: schematic representation of different stages of ductile fracture. gurson [1] developed a constitutive model for porous metal plasticity. this model was derived from an approximated one through an upper bound approach limit-analysis of a hollow sphere made of ideal plastic mises material. tvergaard et al. [4] perceived that the gurson model give adequate results for high triaxiality rates of the stresses but overestimate the fracture strains (ductility) for low triaxialities. therefore, they introduced the constitutive parameters: q1, q2 and q3 in the gurson model as: 2 eq 2m eq y 1 2 32 yy σ σ (σ ,σ , f) q f q ( q f ) 0 σσ 3 φ 2 cosh 1 2            (1) where: σeq von mises stress, σy matrix yield limit, σm hydrostatic stress, f the porosity for the previous yielding criteria and to take into account the fast softening of the material during the coalescence stage (fig. 1-stage v), tvergaard and needleman [2-4] introduced the f*(f) function. the yield surface of the gurson-tvergaardneedleman (gtn) model is written with the following form: 2 eq * 2 * 2m eq 1 2 12 σ σ3 φ(σ ,σ,f) 2q f cosh q (1 q f ) 2 σσ 0          (2) where: σ is an equivalent tensile flow stress representing the actual microscopic stress-state in the matrix material, [4]. f* is the modified porosity follows the law below: m. hadj miloud et alii, frattura ed integrità strutturale, 49 (2019) 630-642; doi: 10.3221/igf-esis.49.57 632     c * c c c f * u f f if f f f f f δ f f if f f f f if f f           (3) with: * u c f c f f f f     , called the coalescence acceleration fc is the critical porosity corresponding to the beginning of the coalescence ff designate the porosity corresponding to the final fracture of the material. the ultimo value *uf is reached when the macroscopic fracture occurs by loss of the bearing load and is calculated by the following equation * 1 1 f q u  when 2 3 1q q . during the plastic flow, the porosity evolution is due to both the voids growth and the voids nucleation: croissance nucléationf f f    (4) assuming the matrix incompressibility, the term due to the voids growth is given by the following equation: p croissance kkf (1 f )ε   (5) p kk is the trace of the macroscopic strain rates tensor. when the nucleation is controlled by the plastic strain, its contribution is as follow: p nucléationf aε  (6) where p represents the equivalent plastic strain. chu and needleman [7] assumed that the priming of the voids follows a normal distribution with a mean strain n and a standard deviation sn: 2p n n nn f ε ε1 a exp 2 ss 2π             (7) the gtn model parameters can be subdivided in three subsets as: constitutive parameters: q1, q2 and q3. commonly, these parameters are fixed as: q1=1.5, q2=1 and q3= (q1)2 [2, 8]. nucleation parameters: εn, sn and fn. generally, the εn and sn values are 0.3 and 0.1 respectively for most materials. thus, they are considered as constants of the statistical distribution law and not as intrinsic material characteristics. the void volume fraction fn is the volume fraction of particles available for void nucleation, while the initial void volume fraction f0 concerns all the inclusions [9, 10]. the porosities f0, fc and ff are considered as material parameters. the initial vvf parameter f0 characterizes the initial state of the material. generally, this parameter is evaluated by microscopic analysis of the undamaged material. for the studied material, the initial void volume fraction f0 is small (f0=10-5) [9]. there are several methods to determine the critical void volume fraction fc. from a physical point of view, there is a threshold of porosity from which the specimen rigidity drops suddenly. but its determination is very difficult. sun et al. [11-13] have suggested that fc can be numerically obtained by fitting the numerical curve with the experimental one. the final void volume fraction ff describes the state of the material at the fracture phase. this parameter is considered as constant and can be determined experimentally [14]. it has been considered as an unimportant parameter, it is interesting to know whether it is a constant zhang et al. [15]. in this work, the final failure void volume fraction is preset to ff =0.1. m. hadj miloud et alii, frattura ed integrità strutturale, 49 (2019) 630-642; doi: 10.3221/igf-esis.49.57 633 the critical void volume fraction fc signifies the onset of coalescence. in most investigations, only the critical void volume fraction fc is considered as a material parameter. it is obtained by fitting the numerical curves, determined by finite element (fe) modeling, with experimental data of notched tensile bar tests [16-21]. a method is proposed for the determination of fn and fc, using the experimental fracture strain εf [9]. the experimental parameter εf is extracted from the load–diametric reduction curve of an axisymmetric notched tensile bar test an2. the inverse method is also widely used to identify the gtn-model. in the work of springmann and kuna [8, 22], the damage mechanical constitutive laws parameters are identified by locally measured displacement fields and measured force– displacement curves. for the material parameter identification a non-linear optimization algorithm is applied, to render the objective function to a minimum by means of a gradient based method. the force-displacement curves are obtained from tensile tests on notched flat specimens of ste690 steel, which allows the material parameters to be identified [8]. in the work of jouabi et al. [23], a coupled elastic–plastic/damage is adopted in order to describe tensile behavior with validation on the deep-drawing test of a dp980 dual phase steel sheet. the gtn damage model is used. the used hardening laws are those of swift (non-saturating law), voce (saturating law) and hockett-sherby (saturating law). an identification method for elastic–plastic parameters and gtn damage model parameters has been presented using the software modefrontier [23]. in the literature, there are consistent methods to determine gtn model parameters, but with a pre-defined hardening laws i.e. without identification of hardening laws in the same processes of gtn parameters determination. recently, many works [24-26] are devoted to identify simultaneously gtn model and hardening laws parameters. other interesting works of [27 and 28] consist to link the micro-scale to the macro-scale by studying the crack propagation using the gtn model and then determining the r-curves for cracked specimens. in the first part of this work, we propose a numerical inverse procedure to determine the gtn damage model with and without hardening laws. this procedure is carried out on the software package abaqus [29]. within this software, a vuhard subroutine is implemented to carry out the hardening laws. the experimental data, used in the inverse analysis, are extracted from the load-diametric contraction curve of an axisymmetric notched tensile bar test (an2) made with 12nicr6 steel [20]. in the second part, and in order to validate the identified parameters of the gtn model, a numerical simulation of the ductile tear test of a ct25 specimen was performed. the numerical results of the force-displacement curve are compared to those determined experimentally by wilsius [30]. gtn and hardening parameters identification he aim of the first step of this work is to identify simultaneously the gtn model and the hardening laws of the 12nicr6 steel. hence, a numerical procedure of the inverse analysis, based on the fe method, is used to model the tensile test of an axisymmetric notched bar (fig. 2). this numerical model is coupled with an optimization tool. figure 2: specimen geometry and fe model of axisymetric notched bar with 2 mm radius (an2). t m. hadj miloud et alii, frattura ed integrità strutturale, 49 (2019) 630-642; doi: 10.3221/igf-esis.49.57 634 tensile tests on notched specimen an2 the nickel chromium steel used in this investigation is the 12nicr6 steel. the tensile test was carried out on the notched round tensile bar an2 [9]. these specimens type have been originally developed for analyzing the hydrostatic stress effect on the failure by ductile tear. the onset necking of those specimens occur at the notch. on this latter a diametric extensometer was set up to measure the diametric reduction. the experimental data obtained from those tests allow to a successful fe identification of damage models [31]. the specimen geometry (fig. 2-a) and fe model are represented in the fig. 2-b and c. fe model of the uniaxial tensile test of an2. from the data obtained by [9], the objective is to identify simultaneously the hardening laws and the gtn model of the studied material. the tensile test of an2 is simulated using the fe software abaqus/explicit with taking into account the experimental conditions. in order to compare the numerical results with those experimental obtained in [9], the same specimen dimensions (fig. 2-a) are considered in the numerical model. given the symmetry of specimen geometry, only the specimen quarter is modelled in an axis-symmetry case. the quadrilateral elements, type four nodes cax4r, are used in the meshing. a refined mesh is adapted at the notch zone of the specimen (fig. 2-c). it should be noted that the element size could be important in fe damage analysis. the number of elements in fe mesh was 660. a velocity v(t) boundary condition was applied to the top of the fe model (fig. 2-b). the test was performed in the quasi static case and the same velocity of 0.3mm/min is used in the numerical modelling. the resulting tensile load was determined from nodal forces versus displacement. the material of the specimen, 12nicr6, is assumed have an isotropic elasto-plastic behavior. the density of the material is 7.8 × 10-6 kg /mm3. the elastic part is described by using hooke’s model with young’s modulus of e=194gpa and a poisson’s ratio of ν = 0.3. for the plastic domain, the von mises yield criteria is used. it’s added to the plastic part of the gtn damage parameters. this model already exists in the software abaqus/dynamic explicit in porous metal plasticity option [29]. in the literature, several formulated laws exist to describe the hardening behaviors from numerous parameters. the adopted laws in this inverse identification procedure are those of voce and ludwick. the difference between those laws is that the voce law is characterized by a saturated yielding stress σs for high strains. however, the ludwick law is characterized by a continuous evolution of the yielding stress. the lüder bands are taken also into account in the hardening laws following the below equations: voce hardening law: 0 0 ( ) 0 if else ( ) ( ) l l l s s e                              (8) ludwick hardening law: 0 0 n 0 if else ( ) k ( ) l l l                        (9) where: s saturated yielding stress, 0 yielding stress, 0 yielding strain,  material dependent adimensioned parameter, k material consistency, n hardening exponent and l strain limit of lüder bands. the different behavior laws are implemented through a vuhard type subroutine in the software abaqus/dynamic explicit. identification strategy the inverse procedure is used to determine the hardening law and the gtn parameters of studied 12nicr6 steel, using the numerical model described above. this numerical procedure using the fe model is coupled to an optimization tool in order to minimize the gap between numerical results and experimental data. the optimization tool used « optpar » was developed by gavrus [32]. the optimal gtn parameters are obtained using the gauss-newton iterative algorithm by minimizing the cost function (q). this tool was widely used in previously research works [32-35] mainly for characterizing the behavior of metallic alloys under static, dynamic, uniaxial and biaxial solicitation. the general scheme of the inverse procedure is shown in the fig. 3. m. hadj miloud et alii, frattura ed integrità strutturale, 49 (2019) 630-642; doi: 10.3221/igf-esis.49.57 635 figure 3: scheme of identification procedure by inverse analysis. the cost function to minimize is given by:     2 1 2 1 f f q f np i i exp num i np i exp i       (10) with: fexp (or fnum ) = { f i } with i=1, 2, … np: total number of experimental measures (or computed), η: allowable error. the numerical/experimental comparison is conducted on the load versus diameter reduction of notched axisymmetric specimen. parameters identification procedure generally, the determination of gtn model parameters usually consists of a phenomenological procedure which requires a hybrid methodology of comparison between experimental data and numerical results. hence, the gtn parameters, as it is also indicated in [8, 9, 23 and 31] are obtained by the best fit of the numerical curve with the experimental curve. the nucleation void volume fraction fn and the critical void volume fraction fc play a crucial role in the ductile failure process. thus, the gtn model response is strongly influenced by these two parameters. then, the identification by inverse analysis will be conducted on the fn and fc parameters. to show the effect of the hardening laws on the gtn parameters identification, in a first step, the gtn model parameters are identified separately of the hardening law σ(ε). the hardening behavior is determined from standard uniaxial tensile test then it is introduced by tabulation in abaqus (predefined hardening law). secondly, the two hardening laws are included (eqs. 8 and 9) in the inverse identification using a vuhard subroutine coupled with gtn model. q ≤ η experimental data yes numerical model (vuhard, abaqus) rheological test (an2 tensile test) new parameters set comparison: cost function (q) no initial parameters set test conditions material observables: numerical results optimal parameters set (gtn and hardening laws) m. hadj miloud et alii, frattura ed integrità strutturale, 49 (2019) 630-642; doi: 10.3221/igf-esis.49.57 636 results and discussions fig. 4 shows the load-diametric reduction curve for the notched specimens (an2) and that obtained from numerical simulation. at the point ‘p’, there is a sharp change in the slope and drastic fall in load showing the final step of failure process(fracture). the results (fig. 4 and tab. 1) present the identification by inverse analysis of the fn and fc parameters of gtn model. the plastic behavior part of the material 12nicr6 is modeled with introducing the experimental hardening curve into the software abaqus by tabulated form. this hardening curve was obtained from a smooth tensile bar test [30]. the gtn parameters identified do not allow the best description of the fracture point because there is a gap between the experimental and numerical hardening zone of the load-diametric reduction curves. in addition, the fracture point is not clearly observed in the numerical curve. figure 4: numerical/experimental comparison of the load vs. diametric reduction curve in the case of gtn model identification with a pre-defined hardening σ(ε). initial parameters interval of variation identified parameters fixed ff 0.1 0.1 0.1 fc 0.0100 0.0100 to 0.0800 0.0100 fn 0.0040 0.0005 to 0.0070 0.0011 cost function 19.75% ----------------------5.51% table 1: gtn parameters identified with pre-defined σ(ε). the comparison between identification and experiment of load/diametric contraction is shown in the fig. 5 and the tab. 2. in this identification process, the gtn model is coupled with voce hardening law. starting by the hardening parameters, we note that l  =0.0214 parameter which characterizes the lüder bands allows a good representation of the yielding zone. the yielding stress is about 0 =339.8 mpa. the plastic parameters of voce ( =9.380 and s =659mpa) let to a good agreement in hardening zone between experimental and numerical curves. the gtn damage parameters (fc=0.048 and fn=0.0065) give the best description of the fracture point ‘p’ (fig. 5). for the following results, the comparison (fig. 6 and tab. 3) is done for gtn model coupled with ludwick hardening law. the strain at the lüder band limit l  =0.026 is close to that identified for voce law. the yielding stress is about 0 =339.8mpa. and it’s exactly the same obtained for the voce law. the plastic parameters of ludwick (k=428.6mpa and n=0.3) give also a good agreement in hardening zone between numerical and experimental curves. the gtn damage parameters (fc=0.052 and fn=0.0088) are also close for the voce law to describe the fracture point ‘p’ (fig. 6). the results of the used inverse identification are summarized in the tab. 4. the global comparison between experimental and computed load versus diametric contraction curve is also presented in fig. 7. we note that the gtn parameters identified (fc and fn) with voce and ludwick hardening laws are similar to those of the reference [9] and give approximately the same experimental fracture point. 0 5 10 15 20 25 0 0,5 1 1,5 2 l o a d ( k n ) diametric reduction (mm) experimental data[9] gtn identification with predifined σ(ε) p m. hadj miloud et alii, frattura ed integrità strutturale, 49 (2019) 630-642; doi: 10.3221/igf-esis.49.57 637 figure 5: numerical/experimental comparison of the load vs. diametric reduction curve in the case of the coupled identification of gtn model and voce hardening law. initial parameters interval of variation identified parameters 0 (mpa) 420.0 300.0 to 460.0 339.8  15.0 5.0 to 70.0 9.38 s (mpa) 800.0 500.0 to 900.0 659 l  0.015 0.01 to 0.05 0.021 fixed ff 0.1 0.1 0.1 fc 0.01 0.005 to 0.08 0.048 fn 0.004 0.0005 to 0.007 0.0065 cost function 32.32% ----------------------4.01% table 2. identified gtn and voce parameters. figure 6: numerical/experimental comparison of the load vs. diametric reduction curve in the case of the coupled identification of gtn model and ludwick hardening law. 0 5 10 15 20 25 0 0,5 1 1,5 2 l o a d ( k n ) diametric reduction (mm) experimental data[9] gtn identification with voce law 0 5 10 15 20 25 0 0,5 1 1,5 2 l o a d ( k n ) diametric reduction (mm) experimental data[9] gtn identification with ludwick law p p m. hadj miloud et alii, frattura ed integrità strutturale, 49 (2019) 630-642; doi: 10.3221/igf-esis.49.57 638 initial parameters interval of variation identified parameters 0 (mpa) 420.00 300.0 to 450.0 339.70 k (mpa) 350.00 150.0 to 600.0 428.6 n 0.20 0.150 to 0.50 0.3 l  0.015 0.01 to 0.05 0.026 fixed ff 0.1 0.1 0.1 fc 0.010 0.005 to 0.08 0.052 fn 0.0040 0.0005 to 0.007 0.0088 cost function 18% ---------------------4.13% table 3. identified gtn and ludwick parameters. figure 7: global comparison between experimental data and numerical results. gtn parameters with predefined σ(ε) voce and gtn parameters ludwick and gtn parameters ref. [9] hardening law prameters ------ 0 =339.8 mpa 0 =339.7 mpa ------------ =9.380 k = 428.6 mpa ------------ s =659 mpa n=0.3 ------------ l =0.0214 l =0.026 ------fixed ff 0.1 0.1 0.1 0.1 fc 0.0100 0.048 0.052 0.06 fn 0.0012 0.0065 0.0088 0.004 cost function 5.51% 4.01% 4.13% ------ table 4. identified material parameters. the comparison in the fig. 7 shows a good agreement between the experimental curve and those obtained for gtn model with voce and ludwick hardening laws rather than with predefined hardening σ(ε). the fig. 8 presents the evolution of cost function with the iteration number. as it is indicated below, the number of identified parameters, in the case of gtn model identification with tabulated hardening law is lower than the other cases. therefore, the number of iterations allowing a stagnation of cost function (of 5%) is reached after only two iterations, but low parameters accuracy is observed (tab. 4). in the two other cases (gtn-ludwick/voce) of identification, a high parameters precision is obtained relatively to those found in ref. [9]. the cost function stagnation is reached after five iterations. we note that, on the one hand, the number of iterations for gtn model identification with predefined σ(ε) is less than with voce and ludwick hardening laws, but on the other hand, the obtained parameters are more accurate. m. hadj miloud et alii, frattura ed integrità strutturale, 49 (2019) 630-642; doi: 10.3221/igf-esis.49.57 639 figure 8: global comparison between experimental data and numerical results. figure 9: fe model and geometry of the experimental ct25 specimen. ductile tear on ct specimen experiment he tear tests were carried out on an instron-type hydraulic test machine at room temperature on ct specimens precracked (fig. 9). the test was conducted to reach a ratio a/w≈0.5, with ‘a’ the crack length and ‘w’ the specimen width. the ct specimen was pre-cracked by fatigue. after pre-cracking, except one, the specimens were grooved laterally with a depth of 2.5 mm on each side to guide the crack propagation and to have the most rectilinear crack path possible [30]. the tests were carried out under the following experimental conditions: • notch opening speed 0.1 mm/min, • opening interval of the notch 0.1 mm. during the test, the loading and the opening of the crack lips were recorded simultaneously. the displacement was measured using a blade extensometer located between the two fixed blades at the front of the specimen [7]. numerical model the tear test, described previously, is modeled using the fe software abaqus/explicit. in order to compare the numerical results with the experimental data of ref. [7], the same geometry of the specimen (fig. 9) is modeled in cartesian coordinates. 0% 5% 10% 15% 20% 25% 30% 35% 0 1 2 3 4 5 6 7 c o st f u n ct io n number of iterations cost function of gtn ident with predifined σ(ε) cost function of gtn ident with voce cost function of gtn ident with ludwik t symmetry condition / y free area (pre-crack) affined mesh in crack propagation zone loading (w) a m. hadj miloud et alii, frattura ed integrità strutturale, 49 (2019) 630-642; doi: 10.3221/igf-esis.49.57 640 given the symmetry of the specimen and the use of an isotropic material, only half of the specimen is modeled considering the crack plane as plane of symmetry. a 3d mesh is adopted and the hexahedral elements, c3d8r type, are used. an affined mesh is adopted in the crack propagation zone of the specimen (fig. 9). in order to validate the identified gtn model and voce law by the inverse numerical procedure, the parameters values indicated in tab. 2 are used in the numerical simulation of the tear test. the loading is applied along a line as shown in the fig. 9; this represents the pin location where the specimen is loaded. the behavior of this area is considered rigid. results and discussions fig. 10 gives the evolution of the applied load as a function of the displacement on the load line for specimens with and without lateral grooves. the obtained results show an experimental dispersion globally caused by the different ratios of precrack length a/w according to [30]. the curve corresponding to the test ct1 without lateral notch has a great load than the other specimen. this difference is justified by the difference in thicknesses between the uncut specimen (25 mm) and those with grooves (20 mm). there is an average dispersion of 7 kn between the results of ct tests with grooves. in our opinion, this dispersion is not significant, and it results to the machining effects of the notch. the comparison of the experimental curves with numerical results (fig. 10: -solid line) shows a good agreement and proves the relevance of the developed numerical model. figure 10: comparison between loaddisplacement curves: experimental [30] and obtained numerical results. fig. 11 represents the comparison of the crack propagation observed on the experimental failure facies [30] and that obtained from the numerical results. from this, the crack propagation is materialized by a map of the elements where the final volume fraction is reached ff =0.1. in our case, when this value ff equal to 0.1, the element loses completely its rigidity. both numerical and experimental results are qualitatively comparable and the two fronts show the same aspect of propagation. a well-known crack propagation tunnel phenomenon [30] in the case of plane strains is observed. in fact, when there are no lateral notches, the crack propagation is more developed in the specimen centre rather than at the lateral sides. figure 11: crack propagation comparison. m. hadj miloud et alii, frattura ed integrità strutturale, 49 (2019) 630-642; doi: 10.3221/igf-esis.49.57 641 conclusion n this work, an inverse identification procedure is adopted to identify fn and fc parameters of gtn damage model coupled with and without hardening laws. the model was built under the software package abaqus. despite the high number of parameters, the approach applied made it possible to determine them simultaneously with good accuracy. this is verified comparatively with the experimental results found in the literature. in the inverse procedure, the experimental results data are extracted from the load-diametric reduction curve of an axisymmetric notched an2 of 12nicr6 steel bar tensile test. after identification, we noticed that the identified gtn parameters, fc and fn, with voce or ludwik hardening law are similar to those of ref [9] and approximately the same fracture point is obtained. the best fit is obtained with the work hardening law of voce. the small difference between numerical results in the case of coupled identification and those obtained experimentally highlights the mutual interaction between the hardening and damage parameters in the mechanical behavior of the materials. thereafter, the identified gtn parameters are used in the numerical model of tear test on a ct specimen. in order to validate them, the numerical load-displacement curve was compared to the experimental results performed by [30]. this comparison shows a good agreement between the experimental and the numerical results. this indicates the relevance of the developed fe model. the crack propagation is materialized numerically by the elements where the final porosity is reached. all of these elements represent the fracture facies profile. in our case, this facies corresponds to that of a ct specimen without grooves. this indicates that it is imperative to take into account the notch in numerical modeling. references [1] gurson, a.l. (1977). continuum theory of ductile rupture by void nucleation and growth: part i – yield criteria and flow rules for porous ductile media, j eng mater tech, 99, pp. 2–15. doi: 10.1115/1.3443401 . [2] tvergaard, v. (1981). influence of voids on shear band instabilities under plane strain conditions, international journal of fracture, 17, pp. 389–407. doi: 10.1007/bf00036191. [3] tvergaard, v. (1982). on localization in ductile materials containing spherical voids, international journal of fracture, 18, pp. 237–52. doi: 10.1007/bf00015686. [4] tvergaard, v. and needleman, a. (1984). analysis of the cup-cone fracture in a round tensile bar, acta metallurgica, 32(1), pp. 157–169. doi: 10.1016/0001-6160(84)90213-x. [5] hancock, j.w. and mackenzie, a.c. (1976). on the mechanisms of ductile failure in high-strength steels subjected to multiaxial stress-states, j mech phys solids, 24(2–3), pp. 147–160. doi:10.1016/0022-5096(76)90024-7 [6] thomason, p.f. (1990). ductile fracture of metals. oxford: pergamon press. https://trove.nla.gov.au/version/20721090 [7] chu, c. and needleman, a. (1980). void nucleation effects in biaxially stretched sheets, journal of engineering materials and technology,102, pp. 249–56. doi: 10.1115/1.3224807 . [8] springmann, m. and kuna, m. (2006). determination of ductile damage parameters by local deformation fields: measurement and simulation, arch appl mech, 75, pp. 775–797. doi: 10.1007/s00419-006-0033-9 [9] hadj miloud, m. imad, a. benseddiq, n. bachir bouiadjra, b. bounif, a. and serier, b. (2013). a numerical analysis of relationship between ductility and nucleation and critical void volume fraction parameters of gurson– tvergaard– needleman model, proc imeche part c: j mechanical engineering science, imeche, 227(11), pp. 2634–2646. doi: 10.1177/0954406213476232. [10] cox, t. and low, j.j. (1974). an investigation of the plastic fracture of aisi4340 and 18nickel-200 grade maraging steels, metall trans a, 5, pp. 1457–1470. doi: 10.1007/bf02646633. [11] sun, d.z., siegele, d., voss, b. and schmitt, w. (1989). application of local damage models to the numerical analysis of ductile rupture, fatigue fract eng mater, 12(3), pp. 201–212. doi: 10.1111/j.1460-2695.1989.tb00527.x. [12] sun, d.z., siegele, d., voss, b. and schmitt, w. (1991). numerical prediction of ductile fracture resistance behaviour based on micromechanical models, in: jg blauel and kh schwalbe(eds) defect assessment in components – fundamentals and applications (esis/egf9), london: mechanical engineering publications, pp. 447–458. [13] sun, d.z., kienzler, r,. voss, b. and schmitt, w. (1992). application of micro-mechanical models to the prediction of ductile fracture, fracture mechanics, in: sn atluri (ed.) 22nd symposium (ii), astm stp 1131. philadelphia, pa: american society for testing and materials, pp. 368–378. i m. hadj miloud et alii, frattura ed integrità strutturale, 49 (2019) 630-642; doi: 10.3221/igf-esis.49.57 642 [14] guillemer-neel, c., feaugas, x. and clavel, m. (2000). mechanical behavior and damage kinetics in nodular cast iron: part i. damage mechanisms, metall mater trans a, 31, pp. 3063–3074. doi : 10.1007/s11661-000-0085-3. [15] zhang, z.l., thaulow, c. and ødegård, j. (2000). a complete gurson model approach for ductile fracture, eng fract mech, 67, pp. 155–168. doi: 10.1016/s0013-7944(00)00055-2. [16] bernauer, g. and brocks, w. (1999). numerical, round robin on micro-mechanical models: conclusions of part a (ductile tearing) and first results of part b (cleavage fracture), in: esis tc1 and tc8 meeting, statoil research centre, 26 august. [17] oh, c.k. kim, y.j. baek, j.h. kim, y.p. and kim, w. (2007). a phenomenological model of ductile fracture for api x65 steel. int j mech sci, 49, pp. 1399–1412. doi: 10.1016/j.ijmecsci.2007.03.008. [18] pavankumara, t.v. samala, m.k. et al. (2005). transferability of fracture parameters from specimens to component level, int j press vessels pip, 82, pp. 386–399. doi: 10.1016/j.ijpvp.2004.10.003. [19] acharyya, s. and dhar, s. (2008). a complete gtn model for prediction of ductile failure of pipe, j mater sci, 43, pp. 1897–1909. doi: 10.1007/s10853-007-2369-0 . [20] rakin, m., cvijović, z., grabulov, v. and miloš, k. (2000). micromechanism of ductile fracture initiation: void nucleation and growth, facta univer ser: mechanical engineering; 1(7), pp. 825–833. [21] rakin, m., cvijović, z., grabulov, v., putic, s. and sedmak, a. (2004). prediction of ductile fracture initiation using micromechanical analysis, eng fract mech, 71, pp. 813–827. doi: 10.1016/s0013-7944(03)00013-4. [22] springmann, m. and kuna, m. (2005). identification of material parameters of the gurson–tvergaard–needleman model by combined experimental and numerical techniques, computational materials science, 33, pp. 501–509. doi: 10.1016/j.commatsci.2004.09.010. [23] djouabi, m. ati, a. and manach, p.y. (2018). identification strategy influence of elastoplastic behavior law parameters on gurson–tvergaard–needleman damage parameters: application to dp980 steel, international journal of damage mechanics, 3, 1–28. doi: 10.1177/1056789518772130. [24] zhao, p.j., chen, z.h. and dong, c.f. (2016). experimental and numerical analysis of micromechanical damage for dp600 steel in fine-blanking process, journal of materials processing technology, 236, pp. 16–25. doi: 10.1016/j.jmatprotec.2016.05.002. [25] li, h., yang, h., lu, r.d. and fu, m.w. (2016). coupled modeling of anisotropy variation and damage evolution for high strength steel tubular materials, international journal of mechanical sciences, 105, pp. 41–57. doi: 10.1016/j.ijmecsci.2015.10.017. [26] chen, y., zhang, c. and vare, c. (2017). an extended gtn model for indentation-induced damage, computational materials science, 128, pp. 229–235. doi: 10.1016/j.commatsci.2016.11.043. [27] cricrì, g. (2013). a consistent use of the gurson-tvergaard-needleman damage model for the r-curve calculation, frattura ed integrita strutturale, 24, pp. 161-174. doi: 10.3221/igf-esis.24.17 . [28] sepe, r., lamanna, g., caputo, f. (2016). a robust approach for the determination of gurson model parameters, frattura ed integrita strutturale, 10 (37), pp. 369-381. doi: 10.3221/igf-esis.37.48. [29] abaqus; version 6.12 (2012). user’s manual, hibbitt, karlson & sorensen inc. [30] wilsius, j. (1999). étude expérimentale et numérique de la déchirure ductile basée sur des approches locales en mécanique de la rupture, phd thesis, université des sciences et technologies de lille, france. [31] hadj miloud, m. (2017). modélisation de la rupture ductile de l’acier 12nicr6 par le modèle micromécanique de gurson, phd thesis, ust oran, alegria. [32] gavrus, a. (1996). identification automatique des paramètres rhéologiques par analyse inverse, phd thesis, ecole des mines de paris. [33] zidane, i. (2009). développement d'un banc d'essai de traction biaxiale pour la caractérisation de formabilité et du comportement élastoplastique de tôles métalliques, phd thesis, insa rennes, france. [34] diot, s., guines, d., gavrus, a. and ragneau, e. (2009). minimization of friction influence on the evaluation of rheological parameters from compression tests – application to a forging steel behavior identification, journal of engineering materials and technology, 131, pp. 1-10. doi: 10.1115/1.3026543 [35] zidane, i., guines, d., léotoing, l. and ragneau, e. 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can be opened with acrobat and adobe reader 5.0 and later.) >> /namespace [ (adobe) (common) (1.0) ] /othernamespaces [ << /asreaderspreads false /cropimagestoframes true /errorcontrol /warnandcontinue /flattenerignorespreadoverrides false /includeguidesgrids false /includenonprinting false /includeslug false /namespace [ (adobe) (indesign) (4.0) ] /omitplacedbitmaps false /omitplacedeps false /omitplacedpdf false /simulateoverprint /legacy >> << /addbleedmarks false /addcolorbars false /addcropmarks false /addpageinfo false /addregmarks false /convertcolors /converttocmyk /destinationprofilename () /destinationprofileselector /documentcmyk /downsample16bitimages true /flattenerpreset << /presetselector /mediumresolution >> /formelements false /generatestructure false /includebookmarks false /includehyperlinks false /includeinteractive false /includelayers false /includeprofiles false /multimediahandling /useobjectsettings /namespace [ (adobe) (creativesuite) (2.0) ] /pdfxoutputintentprofileselector /documentcmyk /preserveediting true /untaggedcmykhandling /leaveuntagged /untaggedrgbhandling /usedocumentprofile /usedocumentbleed false >> ] >> setdistillerparams << /hwresolution [2400 2400] /pagesize [612.000 792.000] >> setpagedevice microsoft word numero_54_art_19_2909 t. nehari et alii, frattura ed integrità strutturale, 54 (2020) 275-281; doi: 10.3221/igf-esis.54.19 275 numerical analysis of the influence of maximum residual thermal stresses on the intensity factor between the matrix and particle interfaces in metal matrix composite nehari taieb smart structures laboratory (ssl) university centre of ain témouchent-belhadj bouchaib, po box 284,46000, algeria. nehari1976@gmail.com, https://orcid.org/0000-0002-4525-0105 bahram kaddour, nehari driss university centre of ain témouchent-belhadj bouchaib, department of mechanical engineering, po box 284,46000, algeria, kadero_7@hotmail.com, https://orcid.org/0000-0002-2338-1438 smart structures laboratory (ssl) university centre of ain témouchent-belhadj bouchaib, po box 284,46000, algeria. nehari_dr@yahoo.fr, https://orcid.org/0000-0003-2524-424x marni sandid abdelfatah smart structures laboratory (ssl) university centre of ain témouchent-belhadj bouchaib, po box 284,46000, algeria. abdelfatahsandid@hotmail.com, https://orcid.org/0000-0001-7592-967 abstract. a critical problem in the application of metal matrix composites is the presence of high residual thermal stresses induced during the development process. these thermally induced stresses are generally detrimental to the service life of this type of composite. this article discusses the influence of maximum residual stresses on the intensity factor. the results interpreted in terms of damage, allowed us to identify the risk zones; characterized by a significant level of maximum residual stresses (s11max, s22max, s33max), namely the particle/matrix interface. the results also show that the loading conditions and the inter-distance between matrix and particle with two interfacial cracks have an important effect on max residual stresses and stress intensity factors. keywords. maximum residual stresses; crack; intensity factor. citation: nehari, t., bahram, k., nehari, d., marni sandid, a., numerical study of the analysis influences the maximum residual thermal stresses on the intensity factor between the matrix/particle interfaces in cmm, frattura ed integrità strutturale, 54 (2020) 275-281. received: 08.05.2020 accepted: 05.09.2020 published: 01.10.2020 copyright: © 2020 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. introduction oday, metal matrix composite materials (mmc) are highly concerned materials in engineering applications mainly because of their mechanical properties and characteristics in general, these materials often have very high specific rigidity, strength and low density. t https://youtu.be/brclnlxekhc t. nehari et alii, frattura ed integrità strutturale, 54 (2020) 275-281; doi: 10.3221/igf-esis.54.19 276 however, during the planning of the composites at relatively high temperatures, residual stresses arise during the process of cooling these temperatures to room temperature. they are essentially due to the difference in the coefficients of thermal expansion between the particle and the matrix. a gap that is too large delicate the adhesion between these two constituents and consequently favors the initiation and propagation of fatigue microcracks. fatigue microcracks can start in one of these two constituents and their propagation leads to the ruin of the composite. interfacial cracks, responsible for disbanding, may be due either to poor mechanical bonding or to the existence of internal shear stresses at the reinforcement-matrix interface that are too high. in this work, we study the variation of the stress intensity factor (sif) in the opening modes (mode i) and in the shearing modes (modes ii and iii). under the effect of the residual stress, a matrix crack, oriented, relative to the axis of the fibre, propagates at the heart of the matrix, in mixed modes i, ii and iii. such a crack crosses the fibre-matrix interface by shearing of its lips (modes ii and iii). the instability of the crack increases with the increment in the temperature of the elaboration of the composites. under the effect of the tension of putting into service of the composite, the crack of the matrix develops in pure mode i and penetrates into the fibre by opening its lips. the propagation kinetics are strongly slowed when its front approaches very proximity to the fibre-matrix interface, and then develops rapidly in the fibre. this behaviour is all more accentuated as these tensions are stronger [1]. using a simple cubic cell model with square reinforcement forms was developed to study its effect on the mechanical properties of mmc. the objective is to calculate stress intensity factors ki and kii for cracks in the matrix and particles. the results also show that the loading conditions and the inter-distance between two particles with two inter-facial cracks have a significant effect on the stress intensity factors ki and kii, kiii [2]. in this study, the analysis of the residual thermal stresses of boron fibre reinforced epoxy matrix composite and the effect of fibre inter-distance. the strongest constraints are located in the immediate vicinity of the interface. its state and level, radial stresses promote adhesion between the matrix and the fibre. the increase in the fibre fraction implies a reduction of the internal stresses of the reinforcing material and its increase in the matrix. the interaction of two fibres, plays an important role on the internal plane: in the matrix if low inter-distance implies an amplification of longitudinal stresses of about four times and circumferential stresses of thirty times, and also leads a fall of the internal longitudinal stress in reinforcing material. a reduction of the fibre–fibre distance implies a decrease in the amplitude of the induced fibre stress circumference [3]. in the 1960s, hashin and shmuel [4] developed analytical models that predict the elastic thermomechanical properties of perfect multi-phase materials: cohesive and free of damage. however, most of these materials have numerous micro-cracks resulting from the thermal expansion disagreement between the phases involved. these micro-cracks, also called damage, result from the thermal history, usually complex, of the material studied. these damages strongly influence the thermomechanical macroscopic properties of these materials and can have a strong influence on their service life. the present work concerns the numerical study by the finite element method of residual stresses in a metal matrix composite reinforced by spherical particles (sic). these composites are elaborate at relatively high temperatures. their cooling (from the working temperature to the ambient temperature), leads to the creation of residual stresses, the distribution and amplitude of which are closely linked to the gap between the physical and mechanical properties of the matrix and the particle. the first part is to highlight the effect of the crack inter-distance on the maximum residual stresses (in the matrix and particle) and the second part presents the effect of crack size on the intensity factors of constraint ki, kii, and kiii. model used three-dimensional analysis by the finite element method has been developed for the simulation of maximum residual stresses in the al / sic couple. the mechanical behaviour of the metal analysed is purely elastic. fig. 1 shows the model of the structure composed of a matrix-particle assembly and the meshing used for the analysis of the distribution and the level of the stresses in the vicinity close to the interface. due to the symmetry of the studied structure, only half of it has been considered and modelled (to reduce the calculation time). with a width crack a=10µm, and inter-distance d=0.1µm. the calculation code used for this analysis is abaqus (6.11) standard, using general purpose c3d4 (a 4-node linear tetrahedral type element, 1 integration point, uses a linear shape function; this is first order element of stress / displacement analysis; the number of elements is 52750). this element provides precise results only in general cases with a very fine mesh [5]. the thermal cycle used for the calculation consists of heating at a given high temperature up to 600°c followed by cooling to the ambient temperature of 20°c at a constant velocity. a t. nehari et alii, frattura ed integrità strutturale, 54 (2020) 275-281; doi: 10.3221/igf-esis.54.19 277 the internal stresses are a function not only of the deviation between the coefficients of thermal expansion of the matrix and the particle, of the deviation between the temperature at which the thermoplastic deformation disappears and the temperature at which it is formed, but also the modulus of elasticity and poisson coefficient of the two constituents (particle and matrix):   0 1 21 2 m f r fm m f t t vv e e         (1) the effect of internal stresses on crack behaviour is analyzed in terms of variation of the stress intensity factor in opening modes (mode i) and shear modes (modes ii and iii). figure 1: distribution of the residual stress of von mises d=0.1μm, a=10μm, t=300°c property matrix particle material aluminum sic coefficient of thermal expansion (k-1) 23.4e-6 5.12e-6 modulus of elasticity (gpa) 70 408 poisson ratio 0.3 0.2 yield strength mpa 275 0 table 1: mechanical and physical properties of the materials used in the simulation. results and discussion he results of the numerical simulations at for purpose study the influence of temperature variation and inter-distance (d) between crack and particle on maximum residual stresses and stress intensity factors. the numerical code "abaqus 6.11" was valid by comparing the numerical results with those collected in the literature [1, 2]. the fig. 5 show the stress intensity factor values ki, kii, kiii. which attest to the good agreement of the results with a small gap. t t. nehari et alii, frattura ed integrità strutturale, 54 (2020) 275-281; doi: 10.3221/igf-esis.54.19 278 effect of crack penetration on maximum stresses the residual stresses on the surface of the matrix-particle junction are shown in fig.2, which represents the von mises stress distribution for the case (a=10µm, d=0.1µm and t=300°c). this stress is very important at the crack tip when propagating to particle; it is of the order of 286 mpa. in the same direction, the effect of the very close crack of the particle on the stress levels of von mises at the interface of the matrix and particle expressed in fig. 2 which also shows a high stress concentration approximately the crack tip and which extends to particle. it is should be noted that the maximum stresses in the particle are at the bottom while those of the matrix are close at the bottom; this is mainly due to the interaction effect and difference of the mechanical properties of the materials. figure 2: crack-particle interaction (a=10µm, d=0.1 µm, t=300°c). level of maximum residual thermal stresses residual thermal stresses in a composite subjected to a thermomechanical load such as three-dimensional. the distribution of the maximum residual stresses relative to the principal axes of a well-defined reference point, obtained by the finite element method is illustrated in the figs. 3 and 4 the distribution of maximum residual stresses in the matrix and particle can be seen from these figures. analysis of the distribution of maximum residual stresses revealed that they are more intense in the centre of the junction than at the edge. in addition, the interface can be easily identified as the interface most affected by these constraints. for a best of this illustration of these results, the distribution of maximum stresses reported for the zones of the matrix to the particle, according to the two positions. fig. 3 reports the variation in maximum residual stress as a function of the crack-particle inter-distance. we notice that following this configuration, the particle is in compression and the matrix in tension. this behavior is due to the velocity of cooling which is more in the matrix compared to the particle (αmatrix > αfibre). the interface on the matrix subjected to high circumferential tension, mainly at the edge. in combination with compaction defects, this stress usually elicits radial cracks in the matrix, which can significantly affect the material. on the other side in the particle, this constraint is more intense than in the matrix, its amplitude is the same level as that radial, and remains almost invariable what that whether of the interface-particle distance. the state of the stresses and their distribution in the particle, the analysis shows that the composite material behaves like a homogeneous material. the state of the stresses and their distribution in the particle, the analysis shows that the composite material behaves like a homogeneous material. figs. (3.a), (3.b), illustrate the variation of the maximum residual stresses recorded in the particle (sic), the analysis of these figures shows clearly that a proportionality between the maximum residual stress decrease, and the temperature. in addition, there is an acceleration in the level of these maximum residual stresses by exceeding inter-distance (d=0.4µm). for fig. (3.c) illustrates the variation of the maximum residual stresses according to the direction s33max, we note that the maximum stresses increase progressively sensibly afield from the inter-distance that is to say (d = 0.4µm) contrary to the centre. this observation explained by a low energy characterizing this zone. fig. 4 shows the variation of the maximum residual stresses generated in the three directions s11max, s22max, s33max of the matrix as a function of the crack width. this figure shows that the residual stresses intensively localized at the matrix interface. the level of these constraints progressively increases us near of the link interface. in the vicinity very near of the interface, these residual stresses reach their maximum intensity. the maximum residual stress according to s11max of about three times s33max. t. nehari et alii, frattura ed integrità strutturale, 54 (2020) 275-281; doi: 10.3221/igf-esis.54.19 279 figure 3: level of maximal residual stress s11max, s22max, s33max in particle following the path line (a=10μm, d=0.1 μm). figure 4: level of maximal residual stress s11max, s22max, s33max in matrix following the path line (a=10μm, d=0.1 μm). t. nehari et alii, frattura ed integrità strutturale, 54 (2020) 275-281; doi: 10.3221/igf-esis.54.19 280 the effect of residual stresses on the intensity factor the results obtained in this part of the work show that under the effect of residual stress, a crack, initiated in the matrix, propagates in pure mode i when its front is located relatively far from the interface with the particle and in mixed mode i, ii and iii when its front approaches this interface. fig. 5a shows that the residual tensile stresses in the matrix act as crack opening stresses. in mode i, the stress intensity factor values increase when the crack size passes through the interface at (d=0.1µm) and temperature. in the particle, the residual stresses are in the form of compression stresses that act as the closing stresses of the crack. in mode ii, the crack tends to the interface and passes through the interface up to inter-distance (d = 0.1μm), beyond a size the crack propagates in the particle is in pure mode i. the propagation kinetics is all the stronger as the composite is elaborate at high temperatures the stress intensity factor is all the more important, as the temperature is high. the factor intensity of stress parameter evenly distributed over the two crack fronts. indeed, the values of the factors resulting from these two points are identical and what is the temperature. the results shown in this figure show that internal stresses promote crack instability in mode ii (fig. 5.b). fig. 5.c shows the effect of temperature on the mode iii stress intensity factor resulting from the two cracking fronts. this figure clearly shows that an increase in the working temperature leads to an intensification of this fracture criterion. we noted however that the residual stresses favor the crack development in mode iii. the values of this factor obtained in this case are much more significant. this clearly illustrates that such a crack propagates in mode ii and iii shear mode and essentially in mode iii. mechanical energy is repartee fairly in points a and b of the cracking defect. figure 5: variation of the stress intensity factors in mode (i, ii, iii) as a function width of the crack t. nehari et alii, frattura ed integrità strutturale, 54 (2020) 275-281; doi: 10.3221/igf-esis.54.19 281 conclusion his work, focused on the analysis of the thermomechanical behaviour of a composite cubic cell with a metal matrix, is part of a very current scientific and technological context.  it should be noted that the maximum stresses in particle are at the bottom while those of the matrix are near at the bottom; this is mainly due to the interaction effect and difference of the mechanical properties of the materials. for a zero inter-distance, the increase in temperature gradient elicit the transformation of residual tensile stresses to residual compressive stresses.  with regard to the s11max and s22max constraints, we note that the matrix supports the greatest load of these constraints. the stresses s11max are three times significant in the matrix than particle. reverse behaviour occurs for the s22max.and s33max stresses, they are maximum in particle. the increase in temperature gradient decreases the stresses.  it should also be noted that the effect of the inter-distance is significant for the low values of "d" and less than 0.4 μm for the two cases namely on the interface of the matrix and on the external area of the particle.  the growth of a crack initiated in the composite matrix al/sic perpendicular to the interface favours its instability very strongly. growth kinetics grow very rapidly as the crack tends towards the interface  for maximum residual stress at d=0.1µm and δt = 600°c. the difference in thermal expansion coefficient shows that the crack is more unstable in three modes, and that the stress intensity factor values increase when the crack size crosses the interface at the inter-distance (d=0.1µm) for all three modes. references [1] zaoui, b., baghdadi m., serier b., belhaouari m. (2020). finite element analysis of the thermomechanical behavior of metal matrix composites (mmc). frattura ed integrità strutturale, 51, pp. 174-188; doi: 10.3221/igf-esis.51.14. [2] aicha, m., madani k., abdelkader l. (2018). effect of crack position and size of particle on sif in sic particles reinforced al composite. frattura ed integrità strutturale, 48, pp. 152-160. doi: 10.3221/igf-esis.48.18. [3] metehri, a., serier, b., bachir bouiadjra, b., belhouari, m. and mecirdi m.a.(2009). numerical analysis of the residual stresses in polymer matrix composites. materials and design journal, 30, pp. 2332-2338. doi: 10.1016/j.matdes.2008.11.009. [4] hashin, z., shmuel, s., (1963). a variational approach to the theory of the elastic behaviour of multiphase materials. journal of the mechanics and physics of solids, 11(2), pp. 127–140; doi:10.1016/0022-5096(63)90060-7. [5] simulia, dassault systems. abaqus software. version 6.11. (2011) [6] sellam, s., serier, b., bouafia, f., bachir bouidjra, b. and sardar, s. h. (2013). analysis of the stresses intensity factor in alumina–pyrex composites. journal computational materials science, 72, pp. 68–80. doi: 10.1016/j.commatsci.2013.01.030. [7] nehari, t., (2018). numerical study of residual thermal stresses in mmc. mechanics and mechanical engineering 22(4), pp. 1099–1109. [8] mecirdi, m.a., serier b. (2015). calcul des facteurs d'intensité de contraintes (fic) pour les fissures interfaciales dans les composites fibreux. revue des composites et des matériaux avancés, 25, pp.311-325. [9] victor, n. k., emilios, s., john, v., chrysoula, r. (2019). a sem-x-ray assisted experimental approach for the determination of mechanical and thermal load – induced damage in mmcs. frattura ed integrità strutturale, 50, pp. 414-422. doi: 10.3221/igf-esis.50.35. [10] hadj, b. r, boutabout b. (2020). three-dimensional numerical analysis of a joint bonded reinforced with silica nanoparticles (sio2). frattura ed integrità strutturale, 52, pp. 128-136. doi: 10.3221/igf-esis.52.11. [11] hu, g k. and weng g j. (1998). influence of thermal residual stresses on the composite macroscopic behavior, mechanics of materials, 27, pp. 229–240. doi: 10.1016/s0167-6636(97)00050-1. [12] ouinas, d., bachir bouiadjra b., benderdouche n. (2008). interaction effect of a main crack emanating from a semicircular notch and a microcrack, comput. mater. sci. 43, pp. 1155–1159; doi: 10.1016/j.commatsci.2008.03.014. [13] ouinas, d., bachir bouiadjra b., benderdouche n., ait saadi b., vina j. (2011). numerical modelling of the interaction macro–multimicrocracks in a plate under tensile stress’ journal of computational science, 2, pp. 153-164. doi: 10.1016/j.jocs.2010.12.009. [14] bouafia, f., serier b., bachir bouiadjra b. (2012). finite element analysis of the thermal residual stresses of sic particle reinforced aluminum composite, computational materials science, 54, pp. 195-203. doi:10.1016/j.commatsci.2011.10.030. t << /ascii85encodepages false /allowtransparency false /autopositionepsfiles true /autorotatepages /none /binding /left /calgrayprofile (dot gain 20%) /calrgbprofile (srgb iec61966-2.1) /calcmykprofile (u.s. web coated \050swop\051 v2) /srgbprofile (srgb iec61966-2.1) /cannotembedfontpolicy /error /compatibilitylevel 1.4 /compressobjects /tags /compresspages true /convertimagestoindexed true /passthroughjpegimages true /createjobticket false /defaultrenderingintent /default /detectblends true /detectcurves 0.0000 /colorconversionstrategy /cmyk /dothumbnails false /embedallfonts true /embedopentype false /parseiccprofilesincomments true /embedjoboptions true /dscreportinglevel 0 /emitdscwarnings false /endpage -1 /imagememory 1048576 /lockdistillerparams false /maxsubsetpct 100 /optimize 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/pdfxoutputintentprofileselector /documentcmyk /preserveediting true /untaggedcmykhandling /leaveuntagged /untaggedrgbhandling /usedocumentprofile /usedocumentbleed false >> ] >> setdistillerparams << /hwresolution [2400 2400] /pagesize [612.000 792.000] >> setpagedevice microsoft word 2297 t. profant et alii, frattura ed integrità strutturale, 48 (2019) 503-512; doi: 10.3221/igf-esis.48.48 503 focussed on “crack paths” microcrack interaction with circular inclusion and interfacial zone tomas profant, miroslav hrstka brno university of technology, technická 2896/2, 616 69 brno, czech republic profant@fme.vutbr.cz, mira.hrstka@gmail.com jan klusák ceitec ipm, institute of physics of materials; zižkova 22, 616 62, brno, czech republic klusak@ipm.cz abstract. a geometrically simplified plane elasticity problem of a finite small crack emanating from a thin interfacial zone surrounding the circular inclusion situated in the finite bounded domain is investigated. the crack is arbitrarily oriented and modelled using the distribution dislocation technique. this model represents the inner solution of the studied problem. the corresponding fundamental solution is based on the application of muskhelishvili complex potentials in the form of the laurent series. the coefficients of the series are evaluated from the compatibility conditions along the interfaces of the inclusion, the interfacial zone and the enclosing matrix. the fundamental solution is also used in the solution of the boundary integral method approximating the stress and strain relations of the so-called outer solution. the asymptotic analysis at the point of the crack initiation combines the inner and the outer solution and results in the evaluation of the stress intensity factors of the crack tip, which lies in the matrix. the topological derivative is subsequently used to approximate the energy release rate field associated with the perturbing crack in the matrix. the extreme values of the energy release rate allow one to assess the crack path direction of the initiated microcrack. keywords. crack path assessment; complex potentials; interfacial zone; circular inclusion; fundamental solution; topological derivative. citation: profant, t., hrstka, m., klusák, j., microcrack interaction with circular inclusion and interfacial zone, frattura ed integrità strutturale, 48 (2019) 503-512. received: 29.11.2018 accepted: 22.01.2019 published: 04.01.2019 copyright: © 2019 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. introduction icrocracking is a phenomenon appearing in the vicinity of some stress rising features, where relatively short cracks rise and grow. an inclusion whose material properties differ from the ones of the surrounding matrix can be taken into account as a potential generator of such stresses [1], [2], [3]. the stress distribution generated by the presence of the inclusion can be influenced by its interfacial zone between the inclusion and the matrix. in spite of m http://www.gruppofrattura.it/va/48/2297.mp4 t. profant et alii, frattura ed integrità strutturale, 48 (2019) 503-512; doi: 10.3221/igf-esis.48.48 504 the idealization of the problem geometry, the analytical mathematical tools can propose an energetic balance at the crack tip initiated in this stress field. the energy consideration is a basic concept widely used not only in the fracture mechanics. the energy release rate (err) associated with a finite small and arbitrary oriented crack initiation at the interface between the interfacial zone of the circular inclusion and the matrix is considered to assess the direction of the crack path influenced by the presence of the inclusion and its interfacial zone. the topological derivative field indicates the variation of a response functional when an infinitesimal hole is introduced into the body, where the response functional is the total potential energy of the fractured matrix. as the first, it is introduced the fundamental solution in the form of the unit point force or edge dislocation interacting with the inclusion and the interfacial zone, [4]. the fundamental solution is found in the form of the laurent series whose coefficients are evaluated from the compatibility conditions between the inclusion, interfacial zone and infinity matrix. the fundamental solution is applied to the boundary integral method and the continuously distributed dislocation method [5]. under the assumption of a relatively short crack with respect to the inclusion and matrix dimensions, the asymptotic analysis [6] introduces the outer and inner solution of the problem represented by the uncracked finite matrix and cracked infinity matrix, respectively. the asymptotic analysis also demonstrates that the mismatch between the stress values along the outer boundary of the uncracked matrix and the stresses at the same points of the unbounded cracked matrix is proportional to the crack length. the energy momentum tensor [7], [8] and the approximation of the energy release rate for any crack size and orientation by means of a topological derivative can be evaluated from the inner solution and the corresponding stress intensity factors at the crack tip lying in the matrix. figure 1: the problem formulation. the cracked matrix under the statically equilibrated external load and containing the inclusion with thin zone. the length of the crack is small with respect to the dimension of the inclusion. figure 2: the point force f and the dislocation with burgers vector b at the circular inclusion with the interfacial zone. fundamental solution he derivation of the fundamental solution, see fig. 2, describing the interaction between the unit point force f or dislocation with burgers vector b and the circular inclusion with an interfacial zone is based on [4], but contrary to its results it is supplemented by a rigid displacement of the body, because the fundamental solution is also to be t t. profant et alii, frattura ed integrità strutturale, 48 (2019) 503-512; doi: 10.3221/igf-esis.48.48 505 applied in the method of the boundary integral equations as the outer solution of the problem. the basis for the expression of the fundamental solution is the complex analysis in the plane elasticity represented by muskhelishvili’s complex potentials, e.g. [10], which for the matrix 1w can be written in the form (the series of complex potential for domains 2w and 3w can be found in [3], [4]) ( ) ( ) ( ) ( ) ( )1 0 0 ; ; , ; ln , ;s n nn n n n z z h k z z h k zf z f z g z g z g g z ¥ ¥ = = = + =+å å , (1) ( ) ( ) ( ) ( ) ( )1 0 0 ; ; , ; ln , ;s n nn n n n z z p k z k z p k z z z y z y z g z g z g g g z z ¥ ¥ = = = + =+ + å å , (2) where ( )1 1 1 1 , for point force, 2 1 i 1, for dislocation. 1 f k b k k g p k m g k ìïï ==ïï +ïí ïï = =ïï +ïî and 1m is shear modulus and 1k is kolosov’s constant of the material of the domain 1w . the functions ( ); s zf z and ( );s zy z are the well-known complex potentials giving at the point iz x y  the response of the point force ix yf f f  or edge dislocation ix yb b b  situated at point iz x h= + in the infinite complex plane. the coefficients  , ;nh k   and  , ;np k   are determined from the conditions of the continuity of displacements and the resultants of the tractions along the interfaces among the matrix 1w , interfacial zone 2w and inclusion, see [3], [4]. asymptotic analysis and stress intensity factor evaluation he purpose of using the methods analyzing the path of the crack initiated from interface between the interfacial zone 2w and the matrix 1w follows from the stress composite expansion applied at the point of the crack initiation represented by the parameter a , see fig. 1. the composite expansion, i.e. an asymptotic expansion with respect to the small parameter e , is introduced under the assumption that the crack eg is small with respect to the dimensions of the inclusion 3w and can be written as follows, see [3], ( ) ( ) ( ) ( ) ( )0( 0 ) ( 0 )ˆ, / ,e e= + +t x t x t x t x (3) where [ ],x yºx ,  ( 0 )t x is the outer stress,  ( 0 ) /t x  is the inner stress and  ( 0 )t̂ x is an error when the members associated with ne , where 0n  , are neglected in the asymptotic expansion of the stress  ,t x  . the outer stress  ( 0 )t x is defined in the crack-free domain 1w as the solution of the following boundary problem ( )( 0 ) 0⋅ =t x for î wx (4) ( )( 0 ) p⋅ =t x n t for î ¶wx (5) where ( ) ( ) ( ) ( ) 1 2 , 0 for 1, 0 , 0, for 0, 1 p t t ì = ïï=í ï = ïî n t n (6) t t. profant et alii, frattura ed integrità strutturale, 48 (2019) 503-512; doi: 10.3221/igf-esis.48.48 506 and 1 2 3w = w èw èw with outward normal n . the boundary problem (4), (5) and (6) can only be solved using some numerical methods the boundary element method in this case. this method ensures that the boundary conditions in (6) are fulfilled at discrete points along the boundary of the domain w . on the other hand, the conditions of the stress and displacement compatibility at the interfaces of 1w , 2w and 3w are satisfied automatically via the fundamental solution described in previous section. the fundamental solution also makes it possible to express the boundary conditions for the inner problem represented in (3) by the stress tensor    0 /t x  , which must be independent of the crack length parameter e . the inner problem can be formulated in such a way that a crack of the unit length 1 1e eg g =º is initiated in arbitrary direction along the scaled ˆ ˆ /x x e= -axis from the interface between the unloaded matrix 1 ¥w and the interfacial zone 2w . the domain 1 ¥w is a domain 1w with an outer boundary extended to infinity. the crack faces are loaded with radial and tangential stresses ( )( 0 )tqq x and ( ) ( 0 ) rt q x from the outer problem (4), (5) and (6), which are generated in the uncracked matrix 1w at points of the crack eg . thus, ( )( 0 ) 0⋅ =t x for e ¥îwx (7) ( )( 0 ) ˆe= ⋅t t x n for 1gîx (8) ( )( 0 ) 0t x for  ¥x (9) where e ¥w is a cracked domain 1 2 3 ¥ ¥w = w èw èw . the inner problem is due to the scaled coordinate /x x e= independent of the parameter e . similarly to [9], the crack in (7), (8) and (9) is modelled using the continuously distributed dislocation technique [3], [5]. if the dislocation with burgers vector ix yb b b= + is situated at the point 1/z e ¥z = îw , then the stress tensor components yyt and xyt appearing at the point 1/z e ¥= îwz can be written as follows using the potentials (1) and (2), ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) 1 2 1 1 1 0 2 1 i 1 1 ; i ; 2 1 , ; , ; 1 , ; , ; yy xy n n n n n n n n n t t b b b n bh k bh k b n h k bp k m k g g g g ¥ = é -zêz + z = + + +ê+ -z -z-zêë é+ z + z +êë ùù+ + z z úúûû å z z z z zz z z zz z (10) the dislocations will be distributed along the ˆ ˆ /x x e= -axis, i.e. for ˆ ˆ / 0y y e= = , see fig. 1. hence the standard transformations of vectors and tensors with respect to the rotations through angles a and q in xy and ˆ ˆxy planes, respectively, must be applied to the eqn. (10), see [5]. the singular part represented by the first three expressions in (10) is simply transformed to the cauchy type singular kernel. the transformed regular part of (10) represented by the infinite sum can be written as ( ) ( ) ( ) ( ) ( ) ( ) ( ) 2 3 ˆ ˆ ˆ 3 2 ˆˆ ; ; cos sin ; cos ; cos sin 2 ; sin ; cos sin ; sin sin 2 , xxx xyy xxyxyy yxx yyy yxy h x h h h h h h q q q q q q q q q q x = + + + + x ξ x ξ x ξ x ξ x ξ x ξ (11) ( ) ( ) ( ) ( ) ( ) ( ) ( ) 3 2 ˆ ˆ ˆ 2 3 ˆˆ ; ; sin ; cos sin ; sin sin 2 ; cos sin ; cos ; cos sin 2 , xxx xyy xxyyyy yxx yyy yxy h x h h h h h h q q q q q q q q q q x =+ + + + x ξ x ξ x ξ x ξ x ξ x ξ (12) t. profant et alii, frattura ed integrità strutturale, 48 (2019) 503-512; doi: 10.3221/igf-esis.48.48 507 ( ) ( ) ( ) ( ) ( ) ( ) ( ) 2 2 ˆ ˆ ˆ 2 2 ˆˆ ; ; cos sin ; cos sin ; cos cos 2 ; cos sin ; cos sin ; cos 2 sin , xxx xyy xxyxxy yxx yyy yxy h x h h h h h h q q q q q q q q q q q q x =+ + x ξ x ξ x ξ x ξ x ξ x ξ (13) ( ) ( ) ( ) ( ) ( ) ( ) ( ) 2 2 ˆ ˆ ˆ 2 2 ˆˆ ; ; cos sin ; cos sin ; cos 2 sin ; cos sin ; cos sin ; cos cos 2 , xxx xyy xxyyxy yxx yyy yxy h x h h h h h h q q q q q q q q q q q q x = + + x ξ x ξ x ξ x ξ x ξ x ξ (14) where 1 1 1 1 ˆ ˆˆ ˆcos cos , sin sin , cos cos , sin sinr x r x r ra q a q a q a qé ùé ù= + + = + x + xê ú ê úë û ë ûx ξ (15) and ( ) ( ) ( ){ ( ) ( ) ( ) } 1 1 1 2 1 ; , ; , ; 1 , ; , ; , n n xxx n n n n n n n h n h k h k n h k p k g g g g ¥ = = á z z + + + z z åx ξ z z zz z (16) ( ) ( ) ( ){ ( ) ( ) ( ) } 1 1 1 2 1 ; , ; , ; 1 , ; , ; , n n xyy n n n n n n n h n h k h k p n h k p k g g g g ¥ = = á z z + z + z åx ξ z z zz z (17) ( ) ( ) ( ){ ( ) ( ) ( ) } 1 1 1 2 1 ; , ; , ; 1 , ; , ; , n n xxy n n n n n n n h n h k h k n h k p k g g g g ¥ = = â z + z + + + z z åx ξ z z zz z (18) ( ) ( ) ( ){ ( ) ( ) ( ) } 1 1 1 2 1 ; , ; , ; 1 , ; , ; , n n yxx n n n n n n n h n h k h k n h k p k g g g g ¥ = = â z + z + + + z z åx ξ z z zz z (19) ( ) ( ) ( ){ ( ) ( ) ( ) } 1 1 1 2 1 ; , ; , ; 1 , ; , ; , n n yyy n n n n n n n h n h k h k n h k p k g g g g ¥ = = â z + z + z + z åx ξ z z zz z (20) ( ) ( ) ( ){ ( ) ( ) ( ) } 1 1 1 2 1 ; , ; , ; 1 , ; , ; . n n yxy n n n n n n n h n h k h k n h k p k g g g g ¥ = = á z + z + z + z åx ξ z z zz z (21) the symbols { }.â and {}.á mean real and imaginary value of the complex expression. the dislocation is continuously distributed along the ˆ /x e -axis in the interval ( )ˆ 0,1x î . this process is modelled by introducing the density of the burgers vector ( )ˆ ˆyb x and ( )ˆ ˆxb x , which is in relation with burgers vector ( )ˆ ˆ,x yb b=b as follows ( ) ( ) ( ) ( )ˆ ˆ ˆ ˆ ˆ ˆd d ˆ ˆ, , ˆ ˆd d y x y x b b b b x x x = x = x x (22) t. profant et alii, frattura ed integrità strutturale, 48 (2019) 503-512; doi: 10.3221/igf-esis.48.48 508 where ˆ ˆ cos sin , sin cos . x yx x yy b b b b b b q q q q = + = + (23) figure 3: the stress tensor component xxt of the fundamental solution ( )* , ; xt x h compared with the fem solution along the positive x axis for the unit point force 1f fh= = situated at the point [ ],x h . figure 4: the stress tensor components xyt of the fundamental solution ( )* , ; xt x h compared with the fem solution along the positive x axis for the unit point force 1f fh= = situated at the point [ ],x h . figure 5: the stress tensor components yyt of the fundamental solution ( )* , ; xt x h compared with the fem solution along the positive x axis for the unit point force 1f fh= = situated at the point [ ],x h . figure 6: the energy release rate ge as a function of the crack inclination q and the outer stress 1t when 0a =  . t. profant et alii, frattura ed integrità strutturale, 48 (2019) 503-512; doi: 10.3221/igf-esis.48.48 509 figure 7: the energy release rate ge as a function of the crack inclination q and the crack initiation angle a . figure 8: the energy release rate ge as a function of the crack inclination q , the crack initiation angle a and elastic modulus of the interfacial zone 2e . finally, the boundary conditions (8) and (9) in the inner problem formulation (7), lead to the solution of the following system of the singular integral equations following from the above mentioned transformations of (10) ( ) ( ) ( ) ( ) ( ) ( ) 1 ( 0 ) 1 ˆ ˆ ˆ ˆ ˆ ˆ ˆ ˆˆˆ 1 0 2ˆ ˆ ˆ ˆ ˆˆ ˆ ˆ; ; d ˆˆ1 yy x xyy y yyy t x b h x b h x x m e p k é ùæ ö÷çê ú= x x + x + x x÷ç ÷çê úè ø+ -xë û ò , (24) ( ) ( ) ( ) ( ) ( ) ( ) 1 ( 0 ) 1 ˆ ˆ ˆ ˆ ˆ ˆ ˆ ˆˆ̂ 1 0 2ˆ ˆ ˆ ˆ ˆˆ ˆ ˆ; ; d ˆˆ1 xy x xxy y yxy t x b h x b h x x m e p k é ùæ ö÷çê ú= x + x + x x x÷ç ÷çê úè ø+ -xë û ò (25) and integral equations ensuring the closed crack tips ( ) ( ) 1 1 ˆ ˆ 0 0 ˆ ˆ ˆ ˆd 0, d 0. x y b bx x = x x =ò ò (26) the outer stresses ( )( 0 )ˆˆ ˆyyt x , ( ) ( 0 ) ˆˆ ˆxyt x are the solution of (4), (5) and (6) at the points ˆx̂ xe= of the crack eg in the case of the loaded but uncracked matrix 1w and also linearly transformed with respect to the local coordinate system ˆ̂xy . the unknown burgers vector densities ( )ˆ ˆxb x and ( )ˆ ˆyb x are found in the form ( ) ( ) ( ) ( ) ( ) ( ) 1 1 2 2 ˆ ˆ ˆ ˆ ˆ ˆ ˆ ˆ ˆ ˆ ˆ1 , 1 y y x x b bl lc c x = x -x x x = x -x x , (27) where the value of the exponent l is different from the value -0.5 due to the mismatch of the materials of the matrix 1w and interfacial zone 2w . the functions ( )ˆ ˆyc x and ( )ˆ ˆxc x are continuous in the interval ( )ˆ 0,1xî and approximated by jacobi polynomials. the stress intensity factors ik and iik at the crack tip lying in the matrix 1w can be evaluated from the dislocation densities ( )ˆ ˆyb x and ( )ˆ ˆxb x as follows ( ) 1 12 ˆ ˆ, , 1 2 1 1 i ii y x k l m p c k + = + , (28) t. profant et alii, frattura ed integrità strutturale, 48 (2019) 503-512; doi: 10.3221/igf-esis.48.48 510 energy release rate evaluation or the purpose of the assessment of the crack path direction, the knowledge of the stress intensity factors at the tips of the just existing crack is insufficient and the change of the energy state of the unit crack advance is necessary. the shape optimization methods tender an interesting way to eliminate the problem of the complexity of the geometry of the presented problem. the shape functional ( )u ew plays an important role in the following method, because represents the potential energy of the fracture problem (3). the change of the shape functional with respect to the small perturbation de of the crack eg at its tip x̂ e= can be expressed by its asymptotic expansion, see [3], [8] and [9], ( ) ( ) ( ) ( ) ( ) ˆ ˆ , x u u g j x oe de e ede de+ =w = w + + (29) where j is the topological derivative of u on the perturbed domain e de+w . it is supposed that ( )g e is the positive function such that ( ) 0g de  with 0de  . the additional requirements about the remainder of (29) can be found in [8]. in [8] it is also shown the relation between the shape derivative of  u  and the topological one in the sense to the domain variation produced by an uniform expansion of some perturbation. this method, the so-called topological-shape sensitivity method, uses the concept of shape sensitivity analysis as an intermediate step in the topological derivative calculation. from the combination of the topological and shape sensitivity one gets the expression of the energy release rate, [3], [9], ( ) ( ) ( ) 2 2ˆˆ ˆ 0 ˆ ˆ lim dx i iix x b g x j x s k k e σ n e de e ee e de e = =  ¶ é ù= =⋅ ⋅ = +ë ûò (30) where 1 1/ (1 )e e n= for plane strain, 1e e= for plane stress, ( )ˆj x is a derivative of  ˆj x with respect to de , σe is the eshelby’s momentum tensor [7], x̂e is a basis vector of x̂ -axis and n is an unit normal to the boundary bde¶ of the stress-free circular shaped perturbation bde at the crack tip x̂ e= . numerical results correct description of the stress field surrounding the inclusion 3w with the interfacial zone 2w situated in the matrix 1w is conditioned by the fundamental solution (1) behavior at the inclusion, interfacial zone and matrix interfaces. the figs. 3-5 show a numerical example of the convergence and the fulfilling of the compatibility conditions of the stress component xxt , xyt and yyt of the stress tensor   * , ;t x  along the positive x -axis ( [ ], 0x=x , 0x > ) generated by the fundamental solution (1) for the domain 1w and its additional forms for the domain 2w and 3w along their interfaces. the applied values of elastic moduli, geometry and degree of laurent series are also added. the unit point force f is parallel with respect to y hº -axis and situated at a point [ ],x h . the graphs show the matching of the laurent approximation of the fundamental solution and the fem solution along the positive x -axis for series degree  10n (especially in the interval   10,11x mm, where the interfacial zone is situated). in the next numerical example, see fig. 6, the case of the assessment of the crack path direction 0q of the crack initiated from the point on the interface between the matrix and interfacial zone corresponding to 0a =  is considered. the elastic moduli of the used materials ( )1 1,e n , ( )2 2,e n , ( )3 3,e n , the finite crack size e , geometry 1r , 2r and degree of laurent series are also given in the graph. the graph shows the dependence of the corresponding energy release rate ge on q , where the external load 1t varies from zero value to the negative value of 2t to model the shear loading of the cracked matrix. the crack initiation direction corresponding to the local maximum value of ge is of course fairly f a t. profant et alii, frattura ed integrità strutturale, 48 (2019) 503-512; doi: 10.3221/igf-esis.48.48 511 influenced by the sheer stresses and mode ii loading. it is worth mentioning that the maximum value of the angle 50q  is due to the value of the stress singularity exponent l , which becomes complex for the 50q >  . the complex value of l requires different approach of the stress field description. the graph also shows that for some combination of the external stresses 1t getting some specific value from the range ( )1 80, 60t î mpa it is difficult to assess the crack path direction, because the dependence of the energy release rate ge is rather flat without the clear local extremal value. the fig. 7 shows the position of the crack initiation at the interface between the interfacial zone and matrix represented by the angle a and the crack inclination q . the elastic moduli of the used materials ( )1 1,e n , ( )2 2,e n , ( )3 3,e n , the finite crack size e , geometry 1r , 2r and degree of laurent series are again given in the graph. the external load 1t is zero in this case, while 2 100 mpat  . the local maximum value of ge is for 40a  and the crack path direction 0q is near the zero value, i.e. the crack growth under the mode i loading. similarly to the previous example, the maximum values of ge are limited due to the real values of the stress singularity exponent l . the influence of the interfacial zone on the crack initiation position and potentially crack growing direction shows fig. 8. the width of the interfacial zone 2w plays an unimportant role in the crack behavior and it is not illustrated there. on the other hand, the material properties of 2w influence the point of the crack initiation as well as the crack path direction. the grey curves represent the material of the interfacial zone with elastic moduli similar to those of the stiffer particle 3w , the black ones similar to the material softer then the matrix 1w . on can see that the position of the point of the crack initiation represented by the angle a tends to the lower values for the stiffer material of 2w and the crack path direction 0q moves to the positive values. conclusions he energy release rate associated with the arbitrary oriented finite small crack initiating at the interface between the interfacial zone of the circular inclusion and the matrix was evaluated. the scheme of the energy release rate evaluation was adopted from [9] but modified to the presented problem. the proposed procedure combines traditional as well as modern analytical approaches with a numerical one. the most important part of the analysis is the establishing of the fundamental solution given by the interaction between the edge dislocation or point force and circular inclusion with an interfacial zone. a numerical example of the convergence of the approximating series of the fundamental solution was shown. the asymptotic analysis, where the crack perturbs the matrix only and the crack has to have a finite small length, allows one to apply the fundamental solution to model as the cracked infinity as the uncrack finite loaded matrix containing the inclusion. the numerical results showed the influence of the external loads on the crack path direction but also the position of its point of initiation along the interface between the interfacial zone and matrix. the influence of the material properties of the interfacial zone on the cracking of the matrix was also shown. even that the character of the presented results is theoretical only and their validation is desirable, the applied procedure offers an interesting tools to solve the fracture problems of the composites with sound mathematical background. acknowledgments his research has been financially supported by the czech science foundation through the grant 16-18702s and by the ministry of education, youth and sports of the czech republic under the project ceitec 2020 [lq1601]. references [1] krepl, o., klusák, j. (2017). the influence of non-singular terms on the precision of stress description near a sharp material inclusion tip, theor. appl. fract. mech., 90, pp. 85–99, doi: 10.1016/j.tafmec.2017.03.007. [2] krepl, o., klusák, j. (2016). reconstruction of a 2d stress field around the tip of a sharp material inclusion, procedia struct. integr., 2, pp. 1920–7, doi: 10.1016/j.prostr.2016.06.241. t t t. profant et alii, frattura ed integrità strutturale, 48 (2019) 503-512; doi: 10.3221/igf-esis.48.48 512 [3] profant, t., hrstka, m., klusák, j. (2019). an asymptotic analysis of crack initiation from an interfacial zone surrounding the circular inclusion, compos. struct., 208, pp. 479–97, doi: 10.1016/j.compstruct.2018.10.020. [4] cheeseman, b.a., santare, m.h. (2001). the effect of the interphase on crack-inclusion interactions, int. j. fract., 109(3), pp. 303–23, doi: 10.1023/a:1011092801013. [5] hills, d., kelly, p., dai, d., korsunsky, a. (1999). solution of crack problems: the distributed dislocation technique, amsterdam, kluwer academic publishers. [6] kozlov, v., maz’ya, v., movchan, a. (1999). asymptotic analysis of fields in multi-structures, oxford, oxford university press. [7] eshelby, j.d. (1975). the elastic energy-momentum tensor, j. elast., 5(3–4), pp. 321–35, doi: 10.1007/bf00126994. [8] novotny, a.a., sokołowski, j. (2013). topological derivatives in shape optimization, springer-verlag berlin heidelberg. [9] silva, m., geubelle, p.h., tortorelli, d.a. (2011). energy release rate approximation for small surface-breaking cracks using the topological derivative, j. mech. phys. solids, 59(5), pp. 925–39, doi: 10.1016/j.jmps.2011.03.005. [10] muskhelishvili, n.i. 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can be opened with acrobat and adobe reader 5.0 and later.) >> /namespace [ (adobe) (common) (1.0) ] /othernamespaces [ << /asreaderspreads false /cropimagestoframes true /errorcontrol /warnandcontinue /flattenerignorespreadoverrides false /includeguidesgrids false /includenonprinting false /includeslug false /namespace [ (adobe) (indesign) (4.0) ] /omitplacedbitmaps false /omitplacedeps false /omitplacedpdf false /simulateoverprint /legacy >> << /addbleedmarks false /addcolorbars false /addcropmarks false /addpageinfo false /addregmarks false /convertcolors /converttocmyk /destinationprofilename () /destinationprofileselector /documentcmyk /downsample16bitimages true /flattenerpreset << /presetselector /mediumresolution >> /formelements false /generatestructure false /includebookmarks false /includehyperlinks false /includeinteractive false /includelayers false /includeprofiles false /multimediahandling /useobjectsettings /namespace [ (adobe) (creativesuite) (2.0) ] /pdfxoutputintentprofileselector /documentcmyk /preserveediting true /untaggedcmykhandling /leaveuntagged /untaggedrgbhandling /usedocumentprofile /usedocumentbleed false >> ] >> setdistillerparams << /hwresolution [2400 2400] /pagesize [612.000 792.000] >> setpagedevice microsoft word numero_58_art_07_3116 m. emara et al, frattura ed integrità strutturale, 58 (2021) 86-104; doi: 10.3221/igf-esis.58.07 86 enhancement of circular rc columns using steel mesh as internal or external confinement under the influence of axial compression loading mohamed emara structural engineering dept., faculty of engineering, zagazig university, zagazig, 44519, egypt mremara@eng.zu.edu.eg, http://orcid.org/0000-0003-4936-5257 mostafa s. rizk el-arish high institute for engineering and technology, el-arish, north sinai, egypt mostafasalah@zu.edu.eg, https://orcid.org/0000-0002-9026-897x heba a. mohamed, mahmoud zaghlal structural engineering dept., faculty of engineering, zagazig university, zagazig, 44519, egypt hebawahbe@zu.edu.eg, https://orcid.org/0000-0002-8292-720x myazaghlal@zu.edu.eg, https://orcid.org/0000-0003-2579-6132 abstract. reinforced concrete (rc) columns cannot get supreme confinement by using the customary steel stirrups reinforcement because of the requirements for the spacing distances between the stirrups in addition to concrete continuance problem. for this, steel mesh (sm) externally wrapped around the outer perimeter of the column as contributory confinement is being widely used due to its features. limited tests focused on using sm for the internal confinement around the reinforcing cage of rc columns. moreover, no experimental comparison was presented between rc columns internally and externally confined using sm. this paper investigates experimentally the behavior of circular rc columns confined internally or externally by sm. six short rc columns have been subjected to axial loading until failure. the main studied parameters were sm schemes, number of sm wraps, sm position (internally or externally), and the steel stirrups existence. results demonstrated that sm could decrease the crack opening, diminish the concrete spalling, increase the maximum failure load, and enhance the ductility, energy absorption, and column stiffness. furthermore, the partial internal confinement using two wraps of sm around the steel ties presented the maximum capacity with reasonable ductility. in general, internally confined columns showed better behavior than the externally confined one. keywords. rc columns; steel mesh; internal confinement; external confinement; axial loading. citation: emara, m., rizk, m. s., mohamed, h. a., zaghlal, m., enhancement of circular rc columns using steel mesh as internal or external confinement under the influence of axial compression loading, frattura ed integrità strutturale, 58 (2021) 86-104. received: 26.05.2021 accepted: 26.07.2021 published: 01.10.2021 copyright: © 2021 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. https://youtu.be/3hddwygrqui m. emara et al, frattura ed integrità strutturale, 58 (2021) 86-104; doi: 10.3221/igf-esis.58.07 87 introduction umerous strategies of the bending retrofitting for reinforced concrete (rc) elements were presented, such as bonded high strength fiber reinforced-polymer (frp) sheets and steel plates on the outside of the concrete, and near-surface mounted (nsm) reinforcement using frp or steel bars [1–6]. even though these strategies have demonstrated efficiency in enhancing the bending strength of rc elements, each strategy has its drawbacks, nsm causes negative influences on the adjacent concrete. bonded frp strips and steel plates on the outside of the concrete are exposed to debonding problems from the external surfaces of concrete. moreover, weak resistance to fire was noticed in the technique of externally bonded frp that produces harmful vapors in the fire [7]. frp materials are also broadly used in columns strengthening and repair because of their easy handling and lightweight. many previous researches have demonstrated that the columns, which confined using frp showed an improvement in their ductility and compressive strength [8-11]. notwithstanding, due to the high industrialization and implementation costs of frp materials, other confinement materials have been verified [12]. steel mesh (sm) is a favorable material that is being utilized as another method for column strengthening because of its features such as lightweight, satisfactory fire resistance, low cost, high strength, fast execution, and no need for skilled workers [7, 13]. prior researches have demonstrated that using sm as circumferential confinement for rc columns increases the strain value at the failure and the column ductility, and distributes stress regularly. additionally, sm boosts the capacity of energy absorption and changes the mode of failure from a brittle pattern to a ductile one [14–17]. kim and choi [18] examined a repairing technique for deteriorated rc columns due to the earthquake. three columns were initially exposed to the periodic load, and then the repairing technique was applied by wrapping steel wire mesh (swm) around the columns. after that, the tested columns were re-exposed to an earthquake load similar to an actual one. the results proved that the swm has a mightily effective repair technique for rc columns that have insufficient lap splices under earthquake load, where the peak load, flexural strength, energy dispersion, stiffness, and the displacement ductility of the rehabilitated columns were larger than those of the unrepaired columns. kim and kim [19] tested rc bridge columns retrofitted using sm and a porous polymer mortar. this study indicated that the improvement in the retrofitted columns ductility was greatly satisfactory, and their seismic behavior was extremely enhanced compared to the original columns without sm. nevertheless, this retrofitting technique (with sm in addition to polymer mortar) has some defects. for instance, the polymer mortar possesses a slight ability to control the cracks, which leads to reduce the rc elements' toughness. abo-alanwar [20] suggested a new procedure to strengthen twenty-one rectangular rc columns under the effect of eccentric compression represented in using various dimensions of steel plates and/or steel angles wrapped with swm at the outer compression side. the results of this strengthening procedure showed that augmentation of the dimensions of steel plates and steel angles leads to a high increase in the maximum capacity and remarkable amelioration in the ductility for the retrofitted columns. furthermore, in the case of the strengthened columns, steel plates and/or steel angles could carry forces from the peak loads more than steel reinforcement. kumar and patel [21] tested several numbers of concrete column specimens strengthened using stainless steel wire mesh (sswm) under compression to evaluate the effectiveness of sswm in the strengthening. it was noticed that when column specimens were strengthened using single and double layers of sswm, the increase in the compressive strength reached 61% and 86%, respectively. additionally, the strengthened specimens showed lower lateral displacements and higher ultimate load than the unstrengthened specimens because of the confinement effect using sswm, which was more economical compared to using frp. el-kholy and dahish [22] proposed an actual confinement arrangement consisted in using one layer of expanded mesh that was warped over the stirrups, which were used with different volumetric ratios in square rc columns. the confined columns showed higher plastic deformation, larger failure load, superior ductile performance, a greater capacity of energy absorption, and a larger decrease in the stirrups volumetric ratio compared to the unconfined columns. el-kholy et al. [23] studied experimentally several short square rc columns confined with two types of steel meshes; welded mesh and expanded mesh. post-heating and preloading were taken into consideration in this test to simulate the fire and natural conditions to obtain an actual evaluation for the suggested confinement. the results confirmed that the metal meshes increased the ductility, failure load, and fire resistance of the confined columns compared to the unconfined columns. due to the high strength of welded mesh, the influence of expanded mesh was lower than welded mesh on the loading capacity enhancement of the confined columns. marthong et al. [24] presented an experimental test on various column forms represented in rectangular, square, circular, and polygon shapes confined using swm under the effect of axial loading. the findings of this test showed a noticeable n m. emara et al, frattura ed integrità strutturale, 58 (2021) 86-104; doi: 10.3221/igf-esis.58.07 88 increase in ultimate load, displacement ductility, stiffness, energy dissipation, and deformation in all wrapped columns compared to their control columns. the highest and the lowest load values were observed in the circular and polygon columns, respectively, which refers to the effect importance of the shape parameter of the confined columns on the load capacity. elsamny et al. [25] investigated theoretically and experimentally the performance of the strengthened deteriorated rc columns with various slenderness and aspect proportions. the columns were confined externally using both spiral stirrups and swm, then covered by grout mortar. the proposed strengthening pattern contributed to increasing the columns carrying capacities and decreasing the transverse displacements. additionally, the failure location was changed from the midheight of the column to its upper and lower parts or both after applying the proposed reinforcement technique. the used strengthening pattern was not affected by changing the slenderness proportions. in addition, numerous tests were performed on rc beams strengthened using swm in shear or in flexure/bending. the results confirmed that swm could improve shear and flexural behaviors for the beams and enhance the beam flexibility. moreover, using sm increased the peak load of the beam and its ultimate deflection [2629]. as noted in the literature, the research work utilized the steel mesh (sm) around the outer perimeter of the column as extra confinement. there are limited tests about using sm for the internal confinement around the ordinary steel stirrups of rc columns, especially the circular columns. no experimental comparison was presented between using the steel mesh as internal confinement around the reinforcing cage and using it as external confinement around the outer surface of the column. this requires the submission of new studies to establish the advantages of this confinement technique for the columns. this paper tested circular short rc columns confined internally or externally by sm subjected to axial loading to evaluate the effect of applying sm as transverse reinforcement on the column's performance. the influence of new parameters such as sm schemes, number of sm wraps, the volumetric ratio of the lateral confining reinforcement including lateral reinforcement (stirrups) and sm reinforcement, sm position (internally or externally), and the steel stirrups' existence was considered in this research. for comparison, there is an unconfined column as a reference specimen. the parameters influence in terms of mode of failure and crack pattern, load-vertical shortening curve, maximum load, ductility index, the capacity of energy absorption, and the stiffness were studied. experimental study program s stated above, the literature review has indicated the requirement for additional investigation about the employment of sm for the internal reinforcement around the ordinary steel stirrups in the circular rc columns. for this, the current paper investigates the behavior of circular concrete columns, confined using sm, under centric axial loads. the specimens details and test approach, material properties, and specimens preparation, including particular circular formworks, and concrete blending and casting, as well as loading configuration, and test setup for the current experimental study, are presented in the next sections. specimens details and test approach in the present experimental program, six short circular steel-reinforced columns subjected to central static load were tested. all the prepared columns possess analogous cross-sections of 200 mm in diameter and 1000 mm in height as a small scale from the real column. the dimensions of the rc columns were selected according to the egyptian code for design and construction of concrete structures (ecp 203/2010) [30] which recommended that the column diameter shall not be less than 200 mm for the circular section with a height at least five times the cross-sectional diameter. the experimental program was designed as follows: one column was kept as a control specimen without confinement, as shown in fig. 1, with a volumetric ratio of the lateral reinforcement of 0.513 %. three more columns were internally reinforced and confined using two different schemes; partial confinement with one and two wrapping layers of sm with 325 mm length at the top and bottom of the specimen, as indicated in fig. 2, with a volumetric ratio of the lateral confining reinforcement of 0.578 % and 0.645 %, respectively, and full confinement with a single wrap of sm material along the height of the reinforcing cage, as shown in fig. 3, with a volumetric ratio of 0.609 %. the overlap length of the wrapped steel mesh reinforcement was 70 mm; fig. 4. the last two specimens were fully confined using one sm layer along the column height; one specimen internally fully confined with sm material around the full height of the main reinforcing bars (about 0.24 % volumetric ratio) instead of the ordinary steel stirrups (without stirrups) to investigate the confinement influence of sm and its extent of compensation for using the stirrups in the columns, as indicated in fig. 5. the circular profile of steel mesh was maintained using 6 mm a m. emara et al, frattura ed integrità strutturale, 58 (2021) 86-104; doi: 10.3221/igf-esis.58.07 89 circular steel stirrups at both ends and mid-height of the main reinforcement for keeping the circular shape of the reinforced cage, and consequently the steel mesh; fig. 5. whereas the other specimen externally fully confined with sm material around the full height of the outer perimeter of the column with total a volumetric ratio of the lateral confining reinforcement of 0.621 %. initially, the surface of the circular column specimen was roughened, then the sm layer was wrapped around the specimen surface, and the endings of the wrapping layer were firmly tied to each other using a tying steel wire. finally, a 20 mm thickness cement mortar layer with a ratio of 1:2, (cement to sand) was utilized to bond sm to the concrete surface and to envelope sm to protect it from the environmental effects; fig. 6. to maintain the sm position during concrete casting, the wrapped sm layers were tied to the lateral stirrups and main reinforcement in the case of the internal confinement by using tying steel wire, as shown in fig. 7. thus, the space between the longitudinal bars and the mesh became very small and has no negative effect. six vertical steel bars with a diameter of 12 mm were utilized for the longitudinal reinforcement for all the samples. 8 mm steel stirrups were utilized, in five columns, for the transverse reinforcement at 180 mm spacing. transverse and longitudinal reinforcements of the tested columns were adopted according to es 262-1/2009 [31] and es 262-2/2009 [32], respectively. the stirrups were installed around the vertical bars after leaving a 25 mm distance from the ends of the bars. the dimensions of the tested specimens and their reinforcement details are shown in fig. 8. additionally, the lengths of sm wraps in the partial and full confinement of the columns are illustrated in fig. 9. tab. 1 presents the full details of the prepared column specimens and their confinement specifications. each specimen was identified using letters and numbers as follows: the letter c at the beginning of the label symbolizes the matrix type, which here is conventional (normal) concrete. the next two letters s and f refer to the sm schemes; s for strip (partial) internal confinement over the traditional stirrups and f for full confinement whether this confinement is internally over the entire reinforcing cage height or externally around the full height of the outer column perimeter. the first number (if any) in the specimen label denotes the sm wraps number. the next two letters oc at the end of the specimen label indicate that the sm layers have been wrapped around the outer core of the column (over the stirrups). while if the letters ed was found at the end of the specimen label, it means that the sm layers have been wrapped around the external diameter of the column as extra confinement (the outer perimeter of the column). finally, the absence of the stirrups in the tested sample is expressed by adding the letter w to the specimen label. (a) longitudinal view (b) indication of the number of wraps (a) longitudinal view (b) cross-section view figure 1: the column without confinement. figure 2: sm schemes (partial internal confinement). figure 3: sm schemes (full internal confinement). single wrap double wraps m. emara et al, frattura ed integrità strutturale, 58 (2021) 86-104; doi: 10.3221/igf-esis.58.07 90 (a) single layer of emm (b) double layer of emm figure 4: the lap in the single-layer and the double layer of mesh reinforcement. (overlap length of emm layer) (a) longitudinal view (b) cross-section view (a) before using the cement mortar layer (b) after using the cement mortar layer figure 5: sm schemes (full internal confinement but without stirrups). figure 6: sm schemes (full external confinement). figure 7: tying sm layer to the stirrups and main reinforcement. tying sm layer to the stirrups and main reinforcement using tying steel wire m. emara et al, frattura ed integrità strutturale, 58 (2021) 86-104; doi: 10.3221/igf-esis.58.07 91 (a) the column in 3d view (b) cross section (a) partial confinement (b) full confinement figure 8: dimensions of the tested column specimens and their reinforcement details (dimensions in mm). figure 9: the lengths of sm wraps (dimensions in mm). specimen no specimen label longitudinal reinforcement (mm) transverse reinforcement (mm) sm schemes∗ number of sm wraps volumetric ratio of lateral reinforcement % height of the wraps (mm) 1 c control 6∅12 ∅8@180 0.513 2 cs1oc 6∅12 ∅8@180 pc around upper & lower portion of oc of the column sample one 0.578 325 3 cs2oc 6∅12 ∅8@180 pc around upper & lower portion of oc of the column sample two 0.645 325 4 cfoc 6∅12 ∅8@180 fc around the full height of oc of the column sample one 0.609 950 5 cwfoc 6∅12 fc around the full height of oc of the column sample one 0.24 950 6 cfed 6∅12 ∅8@180 fc around the full height of ed of the column sample one 0.621 950 note: (*) ‘‘pc” denotes the partial confinement, ‘‘oc” denotes the outer core of the column, ‘‘fc” denotes the full confinement, and ‘‘ed” denotes the external diameter of the column. table 1: full details of the specimens and their confinement specifications. material properties crushed stone with 14 mm maximum size and 2.78 specific gravity was used as coarse aggregate. the medium-sized sand, with 2.53 specific gravity and 2.91 fineness modulus, was utilized as fine aggregate. both coarse and fine aggregates (crushed stone and sand) are compatible with the egyptian standards [33]. the portland cement, which has a strength grade of 42.5 mpa and identical to cement type 1 in the egyptian standards [34] and british standards [35], was utilized in the preparation of the concrete admixture. m. emara et al, frattura ed integrità strutturale, 58 (2021) 86-104; doi: 10.3221/igf-esis.58.07 92 the vertical bars and horizontal stirrups used in the column samples are high-strength steel and mild steel, respectively. the material properties of used steel bars, as well as stirrups, were listed in tab. 2. among available types of expanded metal mesh, the most two common types, which could be used for rc column confinement, are the standard expanded metal and the flattened expanded metal. in the current study, the standard expanded metal mesh was selected due to its versatility and economic characteristics. the mesh openings have a diamond shape with 15 mm 20 mm strand spacing and 1.6 mm diameter; fig. 10. the yield tensile stress, ultimate tensile stress, and elastic modulus of the emm were obtained through the direct tensile test, which was conducted on coupon specimens cut from the metal mesh. the specimen was prepared by immersing the two ends of a metal mesh coupon in a mortar along a length equal to the specimen width; fig. 11. both ends were embedded in the mortar that acted as gripping pads and the test specimen was represented by the non-embedded part of the metal mesh. as recommended by batson et al. [36], the test specimen has a width of 120 mm (at least six times the wire spacing) and a length of 360 mm (more than or equal to three times of specimen width); fig. 11. after performing this tensile test on the emm, it turned out that the emm has 350 mpa yield stress, 400 mpa ultimate stress, and 185×10 mpa modulus of elasticity. the emm was prepared in this research to be significantly spotless and free from detrimental/harmful materials like oil, rust, paint coating, dust, or analogous substances, as previously advised by batson et al. [36]. the crushed stone was washed with pure water to obtain clean coarse aggregate before the blending, as indicated in fig. 12. the target characteristic compressive strength of concrete considered for mixture design is 30 mpa. the ratio of the mixture by weight in the current study for concrete components including cement, fine aggregate, and coarse aggregate are 1, 1.63, and 3.79, respectively, as indicated in tab. 3. for the existing experimental study, a water-cement ratio of 0.46 was considered. the slump test was performed during the concrete pouring process to ensure the desired workability of the concrete was achieved, as illustrated in fig. 13, displaying a 77 mm slump value. as shown in fig. 14, the concrete cubes of standard dimensions (150 150 150 mm) were cast, treated for 28 days, and then subjected to the compression test, displaying 30.67 mpa compressive strength. diameter (mm) yield stress fy (mpa) ultimate stress fu (mpa) modulus of elasticity es (gpa) 8 361 497 195 12 531 640 204 table 2: properties of reinforcing steel. cement fine aggregate coarse aggregate water weight 350 kg/m 568.77 kg/m 1327.13 kg/m 161 kg/m ratio 1 1.63 3.79 0.46 table 3: mixture ratio designed for columns casting. specimens preparation for the casting of the concrete mix in the vertical direction of the column-like construction in the site, particular circular formworks with 200 mm internal diameter and 1000 mm height were prepared and constructed, as shown in fig. 15. the prepared formworks were vertically placed over horizontal circular bases of wood; fig. 16. the designed reinforcing cage has been accurately positioned in the prepared formwork to start pouring of concrete. the components of the concrete mix have been designed to pass naturally from the column sample core through the expanded mesh's diamond openings using a mechanical vibrator to create the concrete cover of the sample without forming voids where the size of coarse aggregate is compatible with the mesh openings. for the blending of concrete components with the specified proportions, which previously mentioned, an electric mixer of concrete was utilized. for obtaining good concrete, an electric vibrator was used to consolidate the concrete and prevent the formation of voids in the column samples. every column sample was extracted from its formwork after 24 h of casting then was wrapped using wet burlap for curing for 28 days. finally, the samples were uncovered after the end of the curing period to dry at room temperature to be prepared for testing, as indicated in fig. 17. m. emara et al, frattura ed integrità strutturale, 58 (2021) 86-104; doi: 10.3221/igf-esis.58.07 93 figure 10: the used emm with a diamond shape. figure 11: the used coupon specimens from the metal mesh for the direct tensile test (dimensions in mm). figure 12: the used crushed stone. figure 13: slump test of fresh concrete. figure 14: cube specimens of compressive strength test. the crushed stone before washing the crushed stone after washing after cutting the mesh roll illustration of the mesh m. emara et al, frattura ed integrità strutturale, 58 (2021) 86-104; doi: 10.3221/igf-esis.58.07 94 (a) before concrete casting (b) after concrete casting figure 15: the used formworks in the current test. figure 16: the prepared wooded circular bases. figure 17: column samples after drying. loading configuration and test setup fig. 18 shows the loading configuration and test setup. the hydraulic testing machine with a capacity of 2000 kn was utilized for testing the desired column samples under the effect of centric loading. to guarantee the precision of the results, the machine was calibrated before testing. stiff steel plates were installed below and over the column sample. steel collar was coiled and bolted using high strength bolts around supporting and loading ends of the sample for adequate confinement; fig. 19. the centric load at the failure was promptly determined using a load cell at the testing machine. to monitor the stiffeners of galvanized sheets m. emara et al, frattura ed integrità strutturale, 58 (2021) 86-104; doi: 10.3221/igf-esis.58.07 95 vertical shortening of the column sample at each loading step, a single displacement transducer, fixed to the steel base plate, was mounted at the vertical orientation of the sample over its entire height. moreover, an electrical strain gauge was installed at the bottom third of the column height of every tested column specimen for measuring the vertical strain. the centric load, its corresponding displacement and axial strain were registered automatically using the data logger system. figure 18: loading configuration and test setup. figure 19: steel collar at the ends. results and analysis ab. 4 indicates the fundamental experimental outcomes for each tested column. the outcomes include the maximum load, axial shortening at both yield and ultimate loads, energy absorption, ductility index, and stiffness. besides, this table shows the improvement of the maximum load over the control column specimen due to partial/full confinement using sm. fig. 20 presents crack patterns and modes of failure for tested columns. fig. 21 illustrates the comparison between the load-vertical shortening curve of the control specimen and that of the confined specimens under the effect of the studied parameters. fig. 22 shows also a comparison between load-vertical shortening curves of full internal and full external confinement. figs. 23, 24, 25, and 26 display the increases in maximum load, ductility index, energy absorption as well as stiffness, respectively, for the confined column specimens (with respect to the control column specimen). t m. emara et al, frattura ed integrità strutturale, 58 (2021) 86-104; doi: 10.3221/igf-esis.58.07 96 crack patterns and failure modes for all tested rc columns, vertical cracks began to appear in the longitudinal direction at about 70 % of the column failure load. these cracks spread and became wider with rising the axial loading of the columns. as a result, the concrete cover spalling of the column samples was observed before reaching their ultimate capacity. lastly, concrete crushing was noticed in many of the studied column samples at the bottom third of the sample height, and the ability to bear loads was dropped; fig. 20. this is identical to the failure position of the tested columns by kim and choi [18] and yanhua et al. [37]. the failure mode for the control specimen (c control) was a somewhat brittle failure, while the rest of the specimens showed a remarkable deformation capacity due to the help of internal or external jacketing using sm. it was found that the domain of concrete cover spalling or the deterioration level of concrete crushing at the failure was larger for the control column specimen (c control), which was confined using stirrups only, and for the column specimen (cwfoc), which was internally confined using only emm as full confinement without stirrups, as indicated in fig. 20 (a) and (e). the partial confinement with a single wrap of emm above the stirrups (internal confinement) as in specimen cs1oc showed a slight improvement in the deterioration degree of concrete crushing compared to the control rc column specimen at the loading end, as shown in fig. 20 (b). moreover, the use of two emm layers as partial confinement around the stirrups or a single emm layer as full confinement around the reinforcing cage significantly reduced the concrete cover spalling zone and diminished the severity of concrete crushing, as shown in fig. 20 (c) and (d); for specimens cs2oc and cfoc, respectively. this shows that the internally confined columns that have a higher volumetric ratio of lateral confining reinforcement enhance the confinement efficiency of the tested columns and present more ductile failure compared to the column specimens that have a lower volumetric ratio of lateral confining reinforcement. consequently, using sm in addition to the stirrups gives better confinement. rupture of some strands in the emm was only observed in the specimen cs2oc, which achieved thef largest ultimate load. externally fully jacketing using a single wrap of emm around the outer perimeter of the column presented effective confinement, where the spalling occurred in the external cement mortar layer around the steel mesh, and the internal core stayed intact, as well as the cracks did not permeate within the column, as shown in fig. 20 (f), this represents an acceptable failure mode for the column element. specimen no specimen label p (kn) 𝞓y (mm) 𝞓u (mm) pmax / pc control capacity of energy absorption (kn.mm) 𝐷𝐼 stiffness (kn/mm) 1 c control 680 2.84 3.27 1 1675.44 1.15 244.44 2 cs1oc 748.2 2.63 3.39 1.1 3004.69 1.29 277.33 3 cs2oc 788.2 2.35 3.11 1.16 4404.10 1.32 314.03 4 cfoc 770.92 1.78 3.33 1.13 4392.69 1.78 369.52 5 cwfoc 674.1 2.12 2.51 0.99 1996.23 1.18 305.48 6 cfed 749.73 1.96 3.23 1.103 4200.65 1.65 361.27 note: ‘‘pmax” stands for maximum load, ‘‘𝞓y” represents the axial shortening at the yield load, ‘‘𝞓u” represents the axial shortening at the ultimate load, ‘‘pmax / pc control” indicates the change in the maximum load after using sm compared to the control specimen, and ‘‘di” refers to ductility index. table 4: fundamental experimental outcomes for every tested column specimen. load versus vertical shortening curves and maximum load the vertical shortening increases swiftly with raising the value of the applied load prior to reaching the maximum load. then, due to the concrete cover spalling and the starting of concrete crushing, the column compression load dropped after overtaking the maximum load with increasing the vertical shortening; fig. 21. the diminishing trend of the load-shortening curve for the control concrete column specimen was more obvious after the peak of the curve being reached than that for the concrete column specimens, which were confined using both stirrups and steel mesh, as indicated in fig. 21. this shows the increase of deformation capacity for confined column specimens using sm compared to the control column specimen. thus, the deformability beside the energy absorption increased remarkably by reinforcing the circular column using steel mesh. the highest deformability after the maximum load being achieved was observed by wrapping either double wraps from the steel mesh over the stirrups as a partial confinement pattern or a single wrap from the steel mesh around the reinforcing cage as a full confinement pattern; specimens (cs2oc and cfoc), respectively, as shown in fig. 21(a). m. emara et al, frattura ed integrità strutturale, 58 (2021) 86-104; doi: 10.3221/igf-esis.58.07 97 cover spalling on the other side     (a) c control (b) cs1oc (c) cs2oc   (d) cfoc (e) cwfoc (f) cfed figure 20: crack patterns and failure modes of column specimens. fig. 23 and tab. 4 reveal that all the studied parameters in the applying of sm as transverse confinement in addition to the stirrups for circular column samples could bear higher loading capacity with adequate ductility over the control circular column sample (including stirrups only without steel meshes), where the sm gives perfect confinement. fig. 23 and tab. 4 show that the heights load carrying capacity was observed in the case of specimen partially confined using two layers of steel mesh around the stirrups (specimen cs2oc). this result confirms that the load capacity of internally confined columns increases when the volumetric ratio of lateral confining reinforcement increases. for the control column specimen the experimental load carrying capacity was about 680 kn which was 2.7% higher than the theoretical load carrying capacity (662 kn) calculated according to the egyptian standards. in the case of the internal confinement, the maximum load for the confined column specimens using single or double wrapping layers of sm as partial confinement over the stirrups surpassed that of the control column sample by 10.03% and 15.91%, respectively; specimens (cs1oc and cs2oc), as shown in fig. 21 (a) and fig. 23. the maximum load also increased when reinforcing the column using sm as full confinement over the stirrups (internal confinement); specimen (cfoc) by about 13.37%; fig. 21 (a) and fig. 23. concrete crushing concrete crushing on the other side cover spalling on the other side concrete crushing concrete crushing on the other side limited cover spalling and slight crushing limited cover spalling and slight crushing on the other side limited rupture of emm strands spalling of cement mortar layer spalling of cement mortar layer on the other side slight crushing very slight crushing on the other side cover spalling and concrete crushing on the other side concrete crushing m. emara et al, frattura ed integrità strutturale, 58 (2021) 86-104; doi: 10.3221/igf-esis.58.07 98 using sm as full internal confinement rather than the classical stirrups; specimen (cwfoc) resulted in a very slight decrease in loading capacity by about 0.87% less than the original control column capacity (with stirrups only), where this specimen achieved a loading capacity of about 674.1 kn, as indicated in fig. 21(b) and tab. 4. this demonstrates the superb efficiency of steel mesh to confine the concrete circular column core rather than the classical stirrups, which has a higher cost than the steel mesh. in other words, a large reduction in the volumetric ratio of the stirrups with no significant loss in ultimate capacity could be achieved by wrapping the emm layer around the main reinforcement. in the case of the external jacketing, using one wrap of sm around the outer perimeter of the column; specimen (cfed), increased the maximum load by 10.25% compared to the original specimen, as shown in fig. 21(c) and fig. 23. in general, the analysis of the test results above showed that the utilization of the steel mesh in reinforcing the circular concrete column internally over the classical stirrups or in strengthening it externally enhanced the column behavior; fig. 21. the results also exhibited that using steel mesh as full internal confinement achieved a relatively greater effect in increasing the loading capacity for the circular column than that achieved by using steel mesh as a full external jacketing; figs. 22 and 23. this result agrees with the research introduced by el-kholy and dahish [22], which showed a significant improvement in the ultimate load of the rc columns by using steel mesh as internal confinement. (a) effect of internal confinement using sm. (b) effect of replacing the stirrups with sm. (c) effect of external jacketing using sm. figure 21: load versus mid-hight vertical shortening curves for the tested columns. ductility index the ductility of the structures is the capability of the member in the structure to withstand inner forces with high deformation, where the calculation of the ductility value can be a forthright reflection for the determination of the capacity of plastic deformation respecting the column samples. for this reason, a common method was used in the present analysis to get the ductility factor. this method is a calculation of the proportion between the axial shortening at the ultimate load m. emara et al, frattura ed integrità strutturale, 58 (2021) 86-104; doi: 10.3221/igf-esis.58.07 99 figure 22: comparison between load-vertical shortening curves of full internal and full external confinement for the circular column using sm. figure 23: percentage increase in the maximum load of the confined column specimens compared to the control column specimen. ‘‘𝞓u” and that at the yield load ‘‘𝞓y” as shown in eq. (1). this method is known as ductility index ‘‘di”. the load-shortening curves in fig. 21 demonstrate that the column specimens which were confined with the various schemes of steel mesh beside the classical stirrups showed enhanced ductility compared to that of the control column specimen. the ductility index increments of all the studied confined specimens were indicated in fig. 24, and its values were illustrated in tab. 4. the enhancement was very significant in case of the full confinement over the stirrups; specimen (cfoc), and medium in case of the partial confinement (single or double wraps of sm) over the stirrups; specimens (cs1oc and cs2oc). where the ductility index for the specimens cs1oc, cs2oc, and cfoc increased by about 12.17%, 14.78%, and 54.78% compared to the control specimen (c control), respectively, while replacing the stirrups with a single wrap of steel mesh around the entire longitudinal reinforcing steel as in the specimen (cwfoc) not only maintained the ductility level of the column but there was a slight improvement in the value of the ductility index by about 2.61%; fig. 24. this shows the effectiveness of increasing the volumetric ratio of mesh reinforcement as lateral confining in the same position of the reinforcement in increasing the ductility index of the column specimen, as in the specimens cs1oc and cs2oc. it should be noted that the full external jacketing around the outer perimeter of the column; specimen (cfed) also improved the ductility index by 43.48 %. this refers to that using steel mesh as full internal reinforcement for the circular column can enhance the ductility by a greater ratio to some extent than that accomplished by using it as full external strengthening, as shown in fig. 24. this may be attributed to the fact that the full internal reinforcement greatly reduced the regions of concrete cover spalling and diminished the severity of concrete crushing; fig. 20(d). m. emara et al, frattura ed integrità strutturale, 58 (2021) 86-104; doi: 10.3221/igf-esis.58.07 100   /u ydi (1) energy absorption another method for calculating ductility factor, which is known as energy absorption capacity, was considered in the current study. this method is a computation of the entire area under the load-vertical shortening curve via numerical integration to foresee the sample ductility based on the study presented by hadi [38, 39]. all internally or externally confined column specimens absorbed energy larger than that for the control specimen, as fig. 25 and tab. 4 clarify. fig 25 displays that the increase in energy absorption of column specimen cs2oc was more than those for other column specimens due to the slight deterioration of this specimen. the highest loading capacity was provided via the same specimen, as mentioned earlier. the percentages of energy absorption increase in the case of the internal confinement beside the traditional stirrups were 79.34% for specimen cs1oc (partial confinement using a single wrap of steel mesh), 162.86% for specimen cs2oc (partial confinement using a double wrap of steel mesh), and 162.18% for specimen cfoc (full confinement using a single wrap of steel mesh) compared to control specimen; fig. 25. while the energy absorption in the case of absence of the stirrups; specimen cwfoc (full internal confinement using a single wrap of steel mesh without stirrups) increased slightly by about 19.15%, this may be attributed to the crushing in this specimen was higher than other confined column specimens. the full external jacketing using sm; specimen cfed also increased the energy absorption by 150.72 %, as indicated in fig. 25. stiffness in the current study, the stiffness value of rc column specimens was calculated as the slope of the load-vertical shorting curve in the elastic region (linear region). where the stiffness is the ratio between the change in load capacity to change in the shortening. fig. 21 and tab. 4 showed that the cs1oc specimen could present slight enhancement (or no degradation at least) in the stiffness, while the cs2oc specimen and the cwfoc specimen revealed medium enhancement in column stiffness over that of the control specimen (c control). finally, whether the full internal or external confinement, in addition to the classical stirrups; specimens cfoc and cfed, presented a noticeable enhancement in the stiffness. these results illustrate that the confinement of circular columns using steel mesh has an effective role in their stiffness. where using the steel mesh led to increasing the stiffness of all tested column samples. for further clarification, the stiffness of specimens cs1oc, cs2oc, cfoc, cwfoc, and cfed increased by 13.46%, 28.47%, 51.17%, 24.97%, and 47.79 %compared to the control specimen, respectively; fig. 26. figure 24: percentage increase in the ductility index of the confined column specimens compared to the control column specimen. figure 25: percentage increase in the energy absorption of the confined column specimens compared to the control column specimen. m. emara et al, frattura ed integrità strutturale, 58 (2021) 86-104; doi: 10.3221/igf-esis.58.07 101 figure 26: percentage increase in the stiffness of the confined column specimens compared to the control column specimen. load versus axial strain fig. 27 confirms that using double layers of emm as a partial internal confinement pattern for the column specimen presented the highest vertical strain increment; specimen cs2oc compared to the other confined specimens with respect to control column specimen (c control). also, it should be noted that the case of using emm layer as full confinement either internally or externally led to a significant increase in the vertical strain value of the confined columns; specimens cfoc and cfed. the increments of vertical strain for the column specimens partially confined using the emm was greatly affected by the number of mesh layers, where the vertical strain increase was 26.69 % in case of using a single layer of emm; specimen cs1oc and 45.63 % in case of using double layers of emm; specimen cs2oc. whereas the increments of vertical strain for the column specimens fully confined using the emm layer were 42.72 % for the internal confinement; specimen cfod, and 36.89 % for the external confinement; specimen cfed. a small reduction was observed in the vertical strain value with about 6.31 % when using a single layer of emm around the main reinforcing steel instead of the traditional stirrups; specimen cwfoc. figure 27: load-vertical strain relationship for the tested column specimens. m. emara et al, frattura ed integrità strutturale, 58 (2021) 86-104; doi: 10.3221/igf-esis.58.07 102 conclusions his paper presented an experimental test to evaluate the behavior of circular rc columns that were confined internally or externally using steel mesh (sm). six short rc circular column specimens were tested under central loading until the failure, including one as a reference specimen, and the rest were confined with steel mesh. various parameters including, sm schemes, number of sm wraps, sm position (internally or externally), and the steel stirrups existence, were studied in the current research. as a result of the experimental test procedure in this study, the subsequent conclusions were obtained: the failure mode for the control column specimen was a somewhat brittle failure, whereas using sm as internal or external jacketing for the remaining column specimens presented a noticeable deformation capacity and enhanced ductility, where the diminishing trend of the load-shortening curve for the confined column specimens was less obvious after the peak of the curve being reached than that for the control column specimen. using sm in addition to the stirrups gives better confinement than that in the case of using the stirrups only. where using double wraps of expanded metal mesh (emm) as partial internal confinement or using a single wrap of it as full internal confinement led to reducing the zones of concrete cover spalling, decreasing the severity of the deterioration of concrete crushing, and presenting the highest deformability after the maximum load being achieved. externally fully jacketing using a single wrap of emm showed influential confinement, where the failure occurred in the cement mortar layer around the steel mesh, but the internal core stayed intact. the confined column specimens could bear higher loading capacity with adequate ductility over the control specimen. the largest capacity was obtained by using double wraps of sm over the stirrups as a partial confinement pattern, where the maximum load surpassed that of the control specimen by about 15.91%. however, the maximum ductility was observed in the case of the full internal confinement (54.78% increase over the control specimen). using sm as full internal confinement rather than the classical stirrups demonstrated a superb efficiency to confine the rc circular column, where the column could recover 99.13% of the original control column capacity without a reduction in the original ductility value. using sm as full internal confinement achieved a relatively greater effect in increasing the loading capacity and the ductility for the circular column than that achieved by using it as a full external jacketing. in general, increasing the volumetric ratio of mesh reinforcement in the same position of the confinement increases the effectiveness of the reinforcement and thus increases the value of the column capacity and enhances the ductility. all confined column specimens absorbed energy larger than that for the control sample, especially when using double wraps of sm as partial internal confinement, where the energy absorption increased by 162.86% due to the slight deterioration in this arrangement. confinement of the circular rc column specimens using the sm led to increasing the column stiffness over the control specimen, especially when using sm as a full jacketing either internally or externally. references [1] lorenzis, l. d. and teng, j. g. (2007). near-surface mounted frp reinforcement: an emerging technique for strengthening structures, composites part b: engineering, 38(2), pp.119–143. doi: 10.1016/j.compositesb.2006.08.003. [2] jumaat, m. z. and alam, m. a. (2009). strengthening of r.c. beams using externally bonded plates and anchorages, australian journal of basic and applied sciences, 3(3), pp. 2207-2211. http://eprints.um.edu.my/6081. [3] wu, y. f. and jiang, c. (2013). quantification of bond-slip relationship for externally bonded frp-to-concrete joints, journal of composites for construction, 17(5), pp. 673–686. doi: 10.1061/(asce)cc.1943-5614.0000375. [4] zhou, y., fan, z., du, j., sui, l. and xing, f. (2015). bond behavior of frp-to-concrete interface under sulfate attack: an experimental study and modeling of bond degradation, construction and building materials, 85, pp. 9–21. doi: 10.1016/j.conbuildmat.2015.03.031. [5] zhang, s.s., yu, t. and chen, g.m. (2017). reinforced concrete beams strengthened in flexure with near-surface mounted (nsm) cfrp strips: current status and research needs, composites part b: engineering, 131, pp. 30–42. doi: 10.1016/j.compositesb.2017.07.072. t m. emara et al, frattura ed integrità strutturale, 58 (2021) 86-104; doi: 10.3221/igf-esis.58.07 103 [6] hadad, h. a., erickson, b. and nanni, a. (2020). flexural analysis and design of frcm strengthened rc beams, construction and building materials, 244, pp. 118371. doi: 10.1016/j.conbuildmat.2020.118371. [7] yuan, f., chen, m. and pan, j. (2020). flexural strengthening of reinforced concrete beams with high-strength steel wire and engineered cementitious composites, construction and building materials, 254, pp. 119284. doi: 10.1016/j.conbuildmat.2020.119284. [8] hadi, m. n. s. (2007a). behavior of frp strengthened concrete columns under eccentric compression loading, composite structures, 77(1), pp. 92–96. doi: 10.1016/j.compstruct.2005.06.007. [9] hadi, m. n. s. (2007b). the behavior of frp wrapped hsc columns under different eccentric loads, composite structures, 78(4), pp. 560–566. doi: 10.1016/j.compstruct.2005.11.018. [10] wu, h. l., wang, y. f., yu, l. and li, x. r. (2009). experimental and computational studies on high-strength concrete circular columns confined by aramid fiber-reinforced polymer sheets, journal of composites for construction, 13(2), pp. 125–134. doi: 10.1061/(asce)1090-0268(2009)13:2(125). [11] chellapandian, m., prakash, s. s. and rajagopal, a. (2018). analytical and finite element studies on hybrid frp strengthened rc column elements under axial and eccentric compression, composite structure, 184, pp. 234-248. doi: 10.1016/j.compstruct.2017.09.109. [12] hadi, m. n. s. and zhao, h. (2011). experimental study of high-strength concrete columns confined with different types of mesh under eccentric and concentric loads, journal of materials in civil engineering, 23(6), pp. 823-832. doi: 10.1061/(asce)mt.1943-5533.0000234. [13] meng, q., chen, w. and hao, h. (2017). numerical and experimental study of steel wire mesh and basalt fibre mesh strengthened structural insulated panel against projectile impact, advances in structural engineering, 21(8), pp.11831196. doi: 10.1177/1369433217733762. [14] kondraivendhan, b. and pradhan, b. (2009). effect of ferrocement confinement on behavior of concrete, construction and building materials, 23(3), pp. 1218–1222. doi: 10.1016/j.conbuildmat.2008.08.004 [15] tawab, a. a., fahmy, e. h. and shaheen, y., b. (2012). use of permanent ferrocement forms for concrete beam construction, materials and structures, 45(9), pp. 1319–1329. doi: 10.1617/s11527-012-9834-1. [16] fahmy, e. h., shaheen, y. b. i., abdelnaby, a. m. and zeid, m. n. a. (2014). applying the ferrocement concept in construction of concrete beams incorporating reinforced mortar permanent forms, international journal of concrete structures and materials, 8(1), pp. 83–97. doi: 10.1007/s40069-013-0062-z. [17] chen, g. f. (2010). experimental study on axial compression behavior of steel wire confined concrete [master thesis]. china: zhengzhou university. [18] kim, s. h. and choi, j. h. (2010). repair of earthquake damaged rc columns with stainless steel wire mesh composite, advances in structural engineering, 13(2), pp. 393–402. doi:10.1260/1369-4332.13.2.393. [19] kim, s. h. and kim, d. k. (2011). seismic retrofit of rectangular rc bridge columns using wire mesh wrap casing, ksce journal of civil engineering, 15(7), pp. 1227–1236. doi: 10.1007/s12205-011-0881-x. [20] abo-alanwar, m. m. (2015). an experimental study on strengthening rectangular reinforced concrete columns under eccentric loads by steel wire mesh and external vertical steel bars, civil engineering research magazine (cerm), al-azhar university, faculty of engineering, department of civil engineering, cairo, egypt, 36(4), pp. 280– 296. https://www.researchgate.net/publication/329452895. [21] kumar, v. and patel, p. v. (2016). strengthening of axially loaded circular concrete columns using stainless steel wire mesh (sswm) – experimental investigations, construction and building materials, 124, pp. 186–198. doi: 10.1016/j.conbuildmat.2016.06.109. [22] el-kholy, a. m. and dahish, h. a. (2016). improved confinement of reinforced concrete columns, ain shams engineering journal, 7(2), pp. 717-728. doi: 10.1016/j.asej.2015.06.002. [23] el-kholy, a. m., abd el-mola, s., abd el-aziz, m. a. and shaheen, a. a. (2018). effectiveness of combined confinement with metal meshes and ties for preloaded and post-heated rc short columns, arabian journal for science and engineering, 43, pp. 1875–1891. doi: 10.1007/s13369-017-2782-x. [24] marthong, c., sutnga, d., kharshandi, o., khryiemmujat, i. g. and shangpliang, a. (2019). mechanical strength of galvanized steel wire mesh (gswm) as a strengthening material of short rc column, iop conference series materials science and engineering, 491, pp. 012014. doi:10.1088/1757-899x/491/1/012014. [25] elsamny, m. k., elbatal, s. a., abo-alanwar, m. m. and abdel-mohsen, a. m. (2020). retrofitting of damaged rc columns using spiral stirrups, new york science journal, 13(3), pp.16–38. doi:10.7537/marsnys130320.02. [26] griezic, a., cook, w. d. and mitchell, d. (1994). tests to determine performance of deformed welded wire fabric stirrups, structural journal, 91(2), pp. 211–220. https://trid.trb.org/view/389106. m. emara et al, frattura ed integrità strutturale, 58 (2021) 86-104; doi: 10.3221/igf-esis.58.07 104 [27] el debs, m. k. and naaman, a. e. (1995). bending behavior of mortar reinforced with steel meshes and polymeric fibers, cement and concrete composites, 17(4), pp. 327–338. doi: 10.1016/0958-9465(95)00031-7. [28] paramasivam, p., lim, c. t. e. and ong, k. c. g. (1998). strengthening of rc beams with ferrocement laminates, cement and concrete composites, 20(1), pp. 53–65. doi: 10.1016/s0958-9465(97)00068-1. [29] nithin, k. r. and kumar, n. s. (2016). flexural behaviour of self-compacting concrete beam using welded wire mesh as shear reinforcement, international journal of science and research (ijsr), 5(6), pp. 189–194. doi: 10.21275/v5i6.nov164026. [30] egyptian code committee. egyptian code for design and construction of concrete structures; ecp 203-2007. cairo (egypt): housing and building national research center, hbrc; (2010). [31] egyptian standards – ferrous products committee. steel for the reinforcement of concrete part1: – plain bars; es 2621. cairo (egypt): egyptian organization for standards and quality, eos; (2009). [32] egyptian standards – ferrous products committee. steel for the reinforcement of concrete part2: – ribbed bars; es 262-2. cairo (egypt): egyptian organization for standards and quality, eos; (2009). [33] egyptian standards – building materials committee. aggregates for concrete; es 1109. cairo (egypt): egyptian organization for standards and quality, eos; (2008). [34] egyptian standards-building materials committee: cement part 1: composition, specifications and conformity criteria for common cements (es 4756-1). egyptian organization for standards and quality (eos), cairo (2013). [35] british standards – b/516/6 cement specifications committee. cement part1: composition, specifications and conformity criteria for common cements; bs en 197-1. london (unitedkingdom): british standards institution, bsi; (2011). [36] batson, g. b., castro, j. o., guerra, a. j., iorns, m. e., johnston, c. d., naaman, a. e., ...and tilsen, b. l. (1988). guide for the design, construction, and repair of ferrocement, aci structural journal, 85(3), pp. 325-351. https://www.concrete.org/publications/internationalconcreteabstractsportal/m/details/id/3527. [37] yanhua, s., xiaoyong, w. and guangjing, x. (2013). seismic behaviour of rc columns strengthened with steel bar/wire mesh mortar, key engineering materials, 539, pp. 108-114. doi: 10.4028/www.scientific.net/kem.539.108. [38] hadi, m. n. s. (2006). behaviour of frp wrapped normal strength concrete columns under eccentric loading, composite structures, 72(4), pp. 503-511. doi: 10.1016/j.compstruct.2005.01.018. [39] hadi, m. n. (2007). behaviour of frp strengthened concrete columns under eccentric compression loading, composite structures, 77(1), pp. 92-96. doi: 10.1016/j.compstruct.2005.06.007. microsoft word numero_57_art_06_3068 m. moreira et alii, frattura ed integrità strutturale, 57 (2021) 63-69; doi: 10.3221/igf-esis.57.06 63 impact response of different materials for sports mouthguards maria moreira, joão carlos ramos fmuc, dep. of dental medicine, university of coimbra, coimbra, portugal mariamoreira.portugal@gmail.com; joao.ramos@ipmd.pt, https://orcid.org/0000-0003-1965-1092 ana messias, maria augusta neto, ana amaro, p.n.b. reis university of coimbra, cemmpre, dep. of mechanical engineering, coimbra, portugal ana.messias@uc.pt, https://orcid.org/0000-0003-4019-9379 augusta.neto@dem.uc.pt, https://orcid.org/0000-0003-3030-0146 ana.amaro@dem.uc.pt, https://orcid.org/0000-0001-5237-0773 paulo.reis@dem.uc.pt, http://orcid.org/0000-0001-5203-3670 abstract. up to this moment, there is no guideline regarding the materials to produce mouthguards. the most used is ethylene-vinyl acetate (eva). studies indicate that laminating eva sheets with rigid components could increase the protection capacities of the mouthguards. on the other hand, other studies suggest that only replacement of the material within its structure can increase energy absorption. therefore, this work aims to evaluate the impact response of four different foils when compared to a 4 mm thickness eva sheet. five different materials were subjected to impact tests with energies of 1.72 j, 2.85 j and 4.40 j. in this context was considered the following materials: eva foils (g1), eva foils with an eva foam core (g2), eva foils with an acetate core (g3), foils of erkoloc-pro (g4) and foils of ortho ibt resin (g5). comparisons between the materials were made by qualitative analysis of the average energy-time and load-displacement curves, as well as by comparison of the peak load, maximum displacement, contact time and absorbed energy using the kruskal-wallis test. it was possible to conclude that statistically significant differences were found in the energy absorbed (p=0.001). laminated foils with a soft core (g2) are a good option to produce mouthguards, while eva foils with an acetate core (g3) and foils of ortho ibt resin (g5) were declared unsuitable. keywords. mouthguard; impact response; thermoforming foil; mechanical testing. citation: moreira, m., ramos, j.c., messias, a., neto, m. a., amaro, a., reis, p.n.b., impact response of different materials for sports mouthguards, frattura ed integrità strutturale, 57 (2021) 63-69. received: 29.04.2021 accepted: 13.05.2021 published: 01.07.2021 copyright: © 2021 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. https://youtu.be/95lku3jyfiu m. moreira et alii, frattura ed integrità strutturale, 57 (2021) 63-69; doi: 10.3221/igf-esis.57.06 64 introduction t is known that collision or contact sports and some recreational activities can expose practitioners to harmful impacts in the orofacial region, with the associated risk of injury. despite the current call for prevention in the health area, studies developed by green [1] and knapik et al. [2] reveal that the incidence and prevalence of orofacial lesions tend to increase. bourguignon and sigurdsson [3] estimated, for example, that 14% to 25% of children, adolescents and young adults can be the target of at least one traumatic episode in their lifetime. therefore, in particular, athletes who practice collision or contact sports are advised to use safety devices, such as mouthguards, to minimize the risk of traumatic injuries. several authors even claim that properly adjusted mouthguard reduces the incidence of orofacial injuries in sports [4-6]. for this purpose, there are three types of mouthguards: ready-made or stock mouth guard; the mouth-formed “boil-and bite” and the custom-fitted mouth guard, which is considered the best protection for teeth, lips and jaw, because it is done by a dentist or dental technician and can be adapted to the athlete’s mouth [7]. according to bastian et al. [8] the boil andbite mouthguards were the most recommended by orthodontists. however, most patients who used these mouthguards reported forgetfulness as the most frequent reason for not always using them due to the discomfort created. on the other hand, some athletes do not use mouthguards because they consider that it affects performance and promotes some discomfort [9], but ferreira et al. [10] clarify that mouthguards do not impair the athlete’s performance. according to american dentistry association council (see https://www.ada.org/en/member-center/oral-healthtopics/mouthguards), a mouthguard should not only protect teeth and surrounding structures but also prevent ingestion or inhalation in case of loss or fractured teeth. also, it must be made of resilient materials able to dissipate the forces applied during an impact and to reduce the deflection transmitted to the underlying structures. the open literature [1, 3, 11, 12] also reports that such devices should be psychologically and physically comfortable for the patient. however, up to this moment, there is no guideline regarding the materials to produce mouthguards, but green [1] and fukasawa et al. [13] indicate that ethylene-vinyl acetate (eva), a thermoplastic co-polymer, is the most used material in these components. nevertheless, the higher vinyl acetate content promotes greater flexibility for eva foils, which is reflected in lower stiffness and hardness. on the other hand, higher damping capacity and, consequently, better energy absorption. in this context, knapik et al. [2] report that, although latex rubber was a material widely used in the first mouthguards, it has less shock absorption, less hardness and less tear and tensile strength than eva or polyurethane. kadota et al. [14] use mouthguards with 3 mm of eva to protect weak periodontal tissue of children, in which the thickness of the sheet is considered a determining factor for the reduction of the external force to teeth. however, for westerman et al. [15] this minimum thickness must be between 3 and 4 mm to absorb energy and reduce the forces transmitted when impacted. these authors also mention that there is an inverse proportion between the shock absorption capacities and the thickness of the mouthguard. nevertheless, according to australian dental association, a minimum thickness of 4 mm is required for the labial flange of a mouthguard. moreira et al. [16] developed studies using a custom-made mouthguard produced by the erkoform 3d motion with the occluform-3 accessory considering two plaques of ethyl vinyl acetate 4 mm and 2 mm thick and found that there were no statically significant differences concerning the retention parameters. on the other hand, takeda et al. [17] and lunt et al. [18] report that higher values of thickness for mouthguards improve the protection because they increase the absorbed energy, but excessive thicknesses impair the athletes’ comfort and performance. consequently, it compromises the use of mouthguards in critical situations. besides that, lunt et al. [18] concluded that only the combination of different materials, eva with rigid laminates sandwiches and/or additional air spacing, is possible to promote significant improvements in the level of protection. eva polymeric foams have gained increasing importance due to a unique combination of properties, such as good damping performance, lightness, good ageing, chemical resistance and inertness. in this context, the open literature reports significant benefits in terms of absorbed energy when air cells are introduced within the eva sheet thickness or with the addition of foaming agents [1, 3, 13, 19]. however, the main disadvantage of the current standard of production of customized mouthguards is the fabrication process that requires two appointments one for impression-taking and another for insertion and athlete instruction – and implies wasting the excess of the material, increasing the associated costs. 3d printing could be the solution to overcome this limitation. new materials with shore a hardness similar to that of eva foils have become available and could be useful to produce mouthguards, guaranteeing the required precision and preventing material waste [1, 2]. although all options have been widely used in other sports or even in the development of passive safety mats for athletes, from a scientific point of view, there are still few studies regarding the mechanical characterization of these materials for application in mouthguards. therefore, this study intends to evaluate the response to the impact of five materials to obtain an architecture with better performance. in this context, it can replace the conventional eva in mouthguards. for this i m. moreira et alii, frattura ed integrità strutturale, 57 (2021) 63-69; doi: 10.3221/igf-esis.57.06 65 purpose, the following materials will be considered: eva foils, eva foils with an eva foam core, eva foils with an acetate core, foils of erkoloc-pro and foils of ortho ibt resin. impact tests were carried out with energies of 1.72 j, 2.85 j and 4.40 j, and the results compared with those obtained with eva. experimental procedure ive groups of thermoforming foils, conveniently described in tab. 1, were prepared to perform low velocity impact tests by drop-weight. the first group used eva, considered a generic foil with a vinyl acetate ratio <0.3 % and shore a 82 hardness. for the eva_soft and eva_hard groups, laminated foils were produced using a hot press machine and by the moulding technique. erkoloc-pro foils (with the hard side of petg and the soft side of tpu) from erkodent® with 3 mm were used in the erkoloc group. finally, in the resin_ibt group, the foils were printed on the nextdent™ 5100 3d printer. the chosen material was nextdent indirect bonding tray (ortho ibt), a monomer based on acrylic esters with shore a hardness similar to eva. group/material thickness structure eva eva 4 mm eva_soft eva + eva foam 1.5 mm eva+2 mm eva foam+1.5 mm eva eva_hard eva + acetate 2 mm eva+0.5 mm acetate+2 mm eva erkoloc petg co-polyester + therm. polyurethane 2 mm petg+1 mm tpu resin_ibt aliphatic urethane acrylate oligomer 4 mm table 1: materials analysed in this study. the low velocity impact tests were carried out using a drop weight-testing machine instron-ceast 9340. a 10 mm diameter impactor with a mass of 3.4 kg was used. the test was performed on circular section samples of 55 mm and the impactor strokes at the center of the samples obtained by centrally supporting the 120x120 [mm] samples. impact energies of 1.72 j, 2.85 j and 4.40 j were applied, which correspond to impact velocities of 1 ms-1, 1.29 ms-1 and 1.61 ms-1, respectively. the tests were carried out at room temperature and, for each group/condition, five specimens were tested. finally, comparisons between mouthguard materials were made by qualitative analysis of the average energy-time and loaddisplacement curves, as well as by comparison of the peak load (n), maximum displacement (mm), impact time (ms) and absorbed energy (j) using the kruskal-wallis test. results and discussion rom the impact tests carried out, fig. 1 shows the typical curves obtained for all materials tested for the impact energy of 4.4 j. however, the profile of these curves is representative of all others obtained for 1.72 j and 2.85 j. however, it is noted higher energies than 4.4 j for eva and eva_soft, which are a consequence of these materials' mechanical properties. in fact, the plates produced with these materials have a very elastic behaviour. consequently, the displacement is superior, producing, in this case, higher energy values. fig. 1a) shows typical energy-time curves, which show that the impact energy was not high enough to promote full penetration, because the impactor sticks into specimens and rebound always. the beginning of the plateau is coincident with the loss of contact between the striker and the specimen. hence, this energy coincides with the absorbed energy by the f f m. moreira et alii, frattura ed integrità strutturale, 57 (2021) 63-69; doi: 10.3221/igf-esis.57.06 66 specimen [20, 21]. therefore, the difference between this energy and the energy at peak load is the elastic energy. on the other hand, fig. 1b) shows typical load-displacement curves, where it is possible to observe that the load increases up to a maximum value (pmax) followed by a drop after the peak load. this drop is due to the loss of contact between the striker and specimen. during unloading it is possible to see the influence of the different foils structure. based on the results obtained in these tests, tab. 2 presents the maximum load, maximum displacement, contact time and absorbed energy, in terms of average values and standard deviation for all materials. a statistical analysis was also performed resorting to ibm spss® statistics version 23. group comparisons were made with the kruskal-wallis test and all post-hoc comparisons considering bonferroni correction. the significance level was set at 0.05. statistically significant differences were found in the energy absorbed (p=0.001), regardless of the impact energy. fig. 2. impact test with 4.40 j (a) variation of energy in time; (b) relation between load and displacement. figure 1: for all materials, typical: a) energy versus time curves; b) load versus displacement curves. group/material peak load [n] max displacement [mm] contact time [ms] absorbed energy [j] eva 511.8 (±25.6)a 20.1 (±0.6)a 18.8 (±0.5)a 3.5 (±0.3) eva_soft 455.5 (±10.5)b,c 23.2 (±0.8)b 21.4 (±0.5)b,c 3.5 (±0.2) eva_hard 858.3 (±32.4)c 11.9 (±0.6) 12.7 (±0.6)b 4.1 (±0.1)a erkoloc 1549 (±24.9)a,b 7.2 (±0.1)a,b 6.5 (±0.1) 2.9 (±0.2)a,b resin_ibt 796.2 (±51.3) 11.9 (±0.9) 11.7 (±0.9)c 4.4 (±0.1)b p <0.001* <0.001* <0.001* <0.001* values represent average (± ) standard deviation. similar superscript letters indicate groups that present statistically significant differences at the 0.05 level. table 2: average values of the peak load, maximum displacement, and elastic recuperation at impacts of 4.4 j pairwise comparisons indicate that eva_soft is statistically superior to erkoloc regarding maximum displacement (p=0.006 and p<0.001, respectively) and contact time (p=0.006 and p<0.001, respectively). the eva_soft group simultaneously presented the highest contact time and the lowest values of peak impact load. as reported by verdejo and mills [22] and mocian et al. [23], soft damping systems, like this laminated foil, tend to increase the contact time of impacts and, consequently, spread energy over a larger area, decreasing the damage in a local area. erkoloc presents a mean peak impact force, statistically superior to eva (p=0.017) and eva_soft (p<0.001). eva_hard and resin_ibt presents the higher energy absorption by the impactor statistically superior to erkoloc (p=0.001 and p<0.001, respectively). from tab. 2, for example, it is possible to find an increase of about 41.4% in the absorbed energy when the eva_hard material is compared with erkoloc, but in terms of maximum load there is a decrease around 44.6%. this evidence can be reported in fig. 2, where is shown the impact damage observed on all materials with 4.4 j impact. a close observation of the contact area of the impactor reveals barely noticeable permanent deformation in eva (a) and eva_soft (b) foils. eva_hard (c) foils were perforated and showed a wide area of delamination surrounding the impact. erkoloc (d) showed the narrowest area of contact associated with puncture type permanent association. though no permanent deformation was visible on the surface of resin_ibt (e) it was clear that the foil fractured. (a) (b) m. moreira et alii, frattura ed integrità strutturale, 57 (2021) 63-69; doi: 10.3221/igf-esis.57.06 67 finally, tab. 3 presents the restored energy for all materials and the impact energies to compare the impact performance in a wider range of energies. of all the tested materials, it is possible to verify that the ones that presented the highest restored energy were eva and erkolock. therefore, when comparing them, it appears that for the lowest impact energy (1.72 j) erkoloc presents a restored energy around 7.5% lower than that obtained with eva. however, when the impact energy increases, the restored energy obtained with the erkolock material is higher than the values observed with eva. in this case, compared to eva, increases of around 9.7% and 26.7% were observed for erkolock, respectively, for impact energies of 2.85 j and 4.4 j. therefore, for higher energies, erkoloc shows more tendency to restore energy after impact. on the other hand, it is noticed that for the impact energy of 4.4 j, eva_soft was the second material that presented the highest restored energy, which means that these foils have a good impact absorption capacity for impacts with high energy levels. these results are in good agreement with those obtained by mocian et al. [24]. figure 2: impact damages observed for an impact energy of 4.4 j and for: (a) eva; (b) eva_soft; (c) eva_hard; (d) erkoloc; (e) resin_ibt. impact energy [j] restored energy [%] eva eva_soft eva_hard erkoloc resin_ibt 1.72 53.4 (±6.4) 31.5 (±3.4) 28.0 (±2.0) 48.6 (±3.4) 7.3 (±0.9) 2.85 41.4 (±6.3) 25.6 (±5.1) 23.0 (±3.7) 45.0 (±0.7) 11.3 (±1.1) 4.4 30.2 (±6.5) 31.8 (±3.9) 14.4 (±2.3) 37.8 (±3.3) 7.3 (±0.8) table 3: restored energy obtained for all materials and impact energies. possible mechanical improvements in hard layers or their inserts in mouthguards materials have also been studied. in this case, when the impact energy increases, the sheet is perforated, which means that the energy is higher than the material can absorb. in fact, only very small amounts of energy are absorbed in these cases. although acetate presents adequate energy absorption under low impact energies, delamination of the foil was observed experimentally, which makes this material unsafe because, in these conditions, the peak load is transmitted to the oral structures. green [1], takeda et al. [25] and westerman et al. [26] also showed that sandwiching hard layers with softer eva did not improve shock absorption ability. in the present study, this phenomenon occurred with an impact energy of 4.4 j in eva_hard material. 10mm a b c e d m. moreira et alii, frattura ed integrità strutturale, 57 (2021) 63-69; doi: 10.3221/igf-esis.57.06 68 regarding the erkoloc-pro foils, they contain polyester and thermoplastic polyurethane (tpu). these foils have high stability, biocompatibility, good elastomeric properties, good resistance to fatigue loads and low water absorption. for this study, 3 mm foils were chosen. materials that had higher impact loads (as seen on fig. 1), like erkoloc, correspond to more brittle materials. the load, in these cases, drops suddenly because of the damage and the material is severely punctured. lower impact load values indicate less impact shock and, therefore, impact attenuation, as reported by mocian et al. [23], westerman et al. [26] and alexandra et al. [27]. although delamination didn’t happen, the lower part of the skin was damaged with impacts of 4.4 j. these findings are corroborated by the level of penetration seen in fig. 2. 3d printing is becoming popular among clinicians. mcglumphy et al. [28] and liang et al. [29], for example, agree that the possibility of reducing material waste, costs and improve accuracy make this technology attractive. the material used in this study, ortho resin ibt, is a monomer based on acrylic esters, and its selection was based on a hardness shore similar to eva (a 85). therefore, from tabs. 2 and 3, it is possible to conclude that resin_ibt is the material with the highest absorbed energy and, consequently, the material with the lowest restored energy (elastic energy). similar to the study developed by mocian et al. [24], these results indicate that this material has a weak damping capacity. although no delamination is observed, it is noticed a cohesive fracture of the foil. according to the authors' best knowledge, there are no data available in the literature for comparison. conclusions t was found that the insertion of an intermediate layer with less stiffness than eva (eva_soft) is a good option to produce customized mouthguards, taking into account its high values of displacement. rigid and thinner materials (erkoloc) were found to be unsuitable due to the damage associated, even though they exhibit high levels of elastic energy. it was also found that thermoformed foils made with semi-rigid core using acetate suffer delamination and, as the three-dimensionally printed materials used in this study, are not suitable for the production of mouthguards. it is important to consider that other materials might suit as semi-rigid core and may not suffer delamination, which would make them suitable for this purpose. acknowledgements this research is sponsored by feder funds through the program compete – programa operacional factores de competitividade – and by national funds through fct – fundação para a ciência e a tecnologia –, under the project uidb/00285/2020. references [1] green, j.i. (2017) the role of mouthguards in preventing and reducing sports-related trauma, prim. dent. j., 6, pp. 27-34. doi: 10.1308/205016817821281738. [2] knapik, j.j., marshall, s.w., lee, r.b., darakjy, s.s., jones, s.b., mitchener, t.a., cruz, g.g., jones, b.h. (2007) mouthguards in sport activities: history, physical properties and injury prevention effectiveness, sport med. 37, pp. 117-144. doi: 10.2165/00007256-200737020-00003. [3] bourguignon, c., sigurdsson, a. (2009) preventive strategies for traumatic dental injuries. dent. clin. north am. 53, pp. 729-749. doi: 10.1016/j.cden.2009.06.002. [4] kang, y., franco, c.s. (2014) a story of dental injury and orthodontics. oral health dent. manag. 13, pp. 243-253. doi: 10.4172/2247-2452.1000572. [5] labella, c.r., smith, b.w., sigurdsson, a. (2002) effect of mouthguards on dental injuries and concussions in college basketball. med. sci. sports exerc. 34, pp.41-44. [6] lieger, o., von arx, t. (2006) orofacial/cerebral injuries and the use of mouthguards by professional athletes in switzerland. dent. traumatol. 22, pp. 1-6. doi: 10.1111/j.1600-9657.2006.00328.x. [7] pawar, p.g., suryawanshi, m.m., patil, a.k., purnale, p.s., ali, f.m. (2013) importance of mouth guards in sports: a review. j. evol. med. dent. sci. 2pp. 8903-8908. doi: 10.14260/jemds/1546. i m. moreira et alii, frattura ed integrità strutturale, 57 (2021) 63-69; doi: 10.3221/igf-esis.57.06 69 [8] bastian, n.e., heaton, l.j., capote, r.t., wan, q., riedy, c.a., ramsay, d.s. (2020) mouthguards during orthodontic treatment: perspectives of orthodontists and a survey of orthodontic patients playing school-sponsored basketball and football. am. j. orthodo. dentofacial orthop. 157, pp. 516-525.e2. doi: 10.1016/j.ajodo.2019.04.034. [9] ahmed, i., fine. p. (2021) injury prevention versus performance: has the time come to mandate the use of mouthguards in all contact sports? bmj open sport exerc. med. 7, pp. e000828. doi: 10.1136/bmjsem-2020-000828. [10] ferreira, g.b., guimarães, l.s., fernandes, c.p., dias, r.b., coto, n.p., antunes, l.a.a., antunes, l.s. (2019) is there enough evidence that mouthguards do not affect athletic performance? a systematic literature review. int. dent. j. 69, pp. 25-34. doi: 10.1111/idj.12406. [11] bochnig, m.s., oh, m.j., nagel, t., ziegler, f., jost-brinkmann, p.g. (2017) comparison of the shock absorption capacities of different mouthguards. dent. traumatol. 33, pp. 205-213. doi: 10.1111/edt.12324. [12] parker, k., marlow, b., patel, n., gill, d.s. (2017) a review of mouthguards: effectiveness, types, characteristics and indications for use. br. dent. j. 222, pp. 629-633. doi: 10.1038/sj.bdj.2017.365. [13] fukasawa, s., churei, h., chowdhury, r.u., shirako, t., shahrin, s., shrestha, a., wada, t., uo, m., takahashi, h., ueno, t. (2016) difference among shock-absorbing capabilities of mouthguard materials. dent. traumatol. 32, pp. 474-479. doi: 10.1111/edt.12275. [14] kadota, t., okawa, r., otsugu, m., ohata, j., hanaoka, i. nakano, k. (2021) mouthguards for a childhood hypophosphatasia patient to protect periodontal tissue of immature permanent teeth-case report. pediatr. dent. j. 31, pp. 117-122. doi: 10.1016/j.pdj.2021.01.004. [15] westerman, b., stringfellow, p.m., eccleston. j.a. (2002) eva mouthguard: how thickness should they be? dent traumatol. 18, pp. 24-27. doi: 10.1034/j.1600-9657.2002.180103.x. [16] moreira, a., mendes, j., fonte, e., ferreira, d., clemente, m., vasconcelos, m. (2019) implementation of a custommade mouthguard in a professional basketball team. journal of mechanical engineering and biomechanics 3, pp. 2532. doi: 10.24243/jmeb/3.4.195. [17] takeda, t., ishigami, k., jun, h., nakajima, k., shimada, a., ogawa, t. (2004) the influence of the sensor type on the measured impact absorption of mouthguard material. dent. traumatol. 2004, pp. 29-35. doi: 10.1111/j.1600-4469.2004.00220.x. [18] lunt, d.r., mendel, d.a., brantley, w.a., beck f.m., huja, s., schriever, s.d., grentzer, t.h., alapati, s.b. (2010) impact energy absorption of three mouthguard materials in three environments. dent. traumatol. 26, pp. 23-29. doi: 10.1111/j.1600-9657.2009.00848.x. [19] genina, n., holländer, j., jukarainen, h., mäkilä, e., salonen, j., sandler, (2016) n. ethylene vinyl acetate (eva) as a new drug carrier for 3d printed medical drug delivery devices. eur. j. pharm. sci. 90, pp. 53-63. doi: 10.1016/j.ejps.2015.11.005. [20] aktas, m., atas, c., icten, b.m., karakuzu, r. (2009) an experimental investigation of the impact response of composite laminates, compos. struct., 87, pp. 307–13. doi: 10.1016/j.compstruct.2008.02.003. [21] reis, p.n.b., ferreira, j.a.m., santos, p., richardson, m.o.w., santos, j.b. (2012). impact response of kevlar composites with filled epoxy matrix, compos. struct., 94, pp. 3520–8. doi: 10.1016/j.compstruct.2012.05.025. [22] verdejo, r., mills, n.j. (2004) heel-shoe interactions and the durability of eva foam running-shoe midsoles. j. biomech. 37, pp. 1379-1386. doi: 10.1016/j.jbiomech.2003.12.022. [23] mocian, o., constantinescu, d.m., sandu, m., sorohan, ş. (2017) impact response of polyurethane and polystyrene sandwich panels. procedia struct. integr. 5, pp. 653-658. doi: 10.1016/j.prostr.2017.07.035. [24] mocian, o.a., constantinescu, d.m., sorohan, ş., sandu, m. (2019) low velocity failure and integrity assessment of foam core sandwich panels. frat. ed integrita strutt. 13, pp. 230-241. doi: 10.3221/igf-esis.48.24. [25] takeda, t., ishigami, k., handa, j., naitoh, k., kurokawa, k., shibusawa, m., nakajima, k., kawamura, s. (2006) does hard insertion and space improve shock absorption ability of mouthguard? dent. traumatol. 22, pp. 77-82. doi: 10.1111/j.1600-9657.2006.00361.x. [26] westerman, b., stringfellow, p.m., eccleston, j.a. (2000) the effect on energy absorption of hard inserts in laminated eva mouthguards. aust. dent. j. 45, pp. 21-23. doi: 10.1111/j.1834-7819.2000.tb00237.x. [27] alexandra, m.o., mihai, c.d.a.n., marin, s., ştefan, s. (2018) low-velocity impact testing of foam core sandwich panels. j. engineering sciences and innovation 3, pp. 93-106. [28] mcglumphy, k.c., mendel, d.a., yilmaz, b., seidt, j.d. (2014) pilot study of 3d image correlation photogrammetry to assess strain and deformation of mouthguard materials. dent. traumatol. 30, pp. 236-239. doi: 10.1111/edt.12076. [29] liang, k., carmone, s., brambilla, d., leroux, j.-c. (2018) applied sciences and engineering 3d printing of a wearable personalized oral delivery device: a first-in-human study. sci. adv. 4, eaat2544. doi: 10.1126/sciadv.aat2544. shot peening processes to obtain nanocrystalline surfaces in metal alloys: a. yankin et alii, frattura ed integrità strutturale, 55 (2021) 327-335; doi: 10.3221/igf-esis.55.25 327 influence of different loading paths on the multiaxial fatigue behavior of 2024 aluminum alloy under the same amplitude values of the second invariant of the stress deviator tensor a.s. yankin, a.i. mugatarov, v.e. wildemann center of experimental mechanics, perm national research polytechnic university, perm, russian federation yas.cem@yandex.ru, https://orcid.org/0000-0002-0895-4912 cem_mugatarov@mail.ru, https://orcid.org/0000-0002-2229-8181 wildemann@pstu.ru, https://orcid.org/0000-0002-6240-4022 abstract. 2024 aluminum alloy is a common aeronautic material. during operations, construction elements made of aluminum alloys undertake complex cyclic loadings. therefore, it is important to estimate the influence of these loadings on the durability of the material. hereby, multiaxial fatigue tests with the same amplitude values of the second invariant of the stress deviator tensor are conducted, and test data are analyzed. the modified sines method is utilized to predict fatigue experimental data. results show that the model is accurate enough to fatigue behavior prediction of 2024 aluminum alloy. keywords. multiaxial fatigue; tension; torsion; 2024 aluminum alloy. citation: a.s. yankin, a.i. mugatarov, v.e. wildemann, influence of different loading paths on the multiaxial fatigue behavior of 2024 aluminum alloy under the same amplitude values of the second invariant of the stress deviator tensor, frattura ed integrità strutturale, 55 (2021) 327-335. received: 16.12.2020 accepted: 24.12.2020 published: 01.01.2021 copyright: © 2021 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. introduction uring operations the greatest number of critical components of construction elements undertake complex cyclic loadings, thus the estimation of their influence on the durability of metal materials is a problem to be solved [14]. also, the need in studying fatigue processes under complex stress state brought a number of experimental works in this area, which used specialized equipment and methods of multiaxial loading. the main loading conditions referred to the literature when studying multiaxial fatigue are biaxial tension of cross-shaped specimens, tension with torsion and bending with torsion of cylindrical specimens. meanwhile, attention is paid not only to the proportional cyclic loading but also to more complex modes with phase shifting, different frequencies and other characteristics [5-9]. apart from testing standard hourglass and tubular specimens, one can also test weld joint specimens [10, 11], specimens with grooves [12] and other stress raisers [13]. d https://youtu.be/xzbtrwia5dg a. yankin et alii, frattura ed integrità strutturale, 55 (2021) 327-335; doi: 10.3221/igf-esis.55.25 328 there are a large number of factors that can influence the fatigue behavior of materials under the multiaxial influence. these include the change in the ratio of stress amplitudes [14-16], the phase angle between the modes of influence [14-17], the ratio of loading frequencies [18-19], average stresses in the cycle [20-24] and others. moreover, real structures have a complex geometry and consequently stress raisers that might influence the fatigue resistance. also, notches are a reason of inherent multiaxiality [25]. in this case, even if the loading is uniaxial, the stress or strain fields in the vicinity of stress or strain raiser are multiaxial. for different materials, different dependencies of fatigue behavior on loading factors can be observed. for example, an increase in the mean stress leads to a decrease in fatigue strength. this effect is quite strong for brittle materials (e.g. cast iron) both in axial and in torsion [26]. however, this effect is lower in torsion than in axial for ductile materials such as steels and aluminum alloys [27]. nowadays, there are different criteria of multiaxial fatigue that can be used to describe the regularities of the fatigue behavior of various materials. these approaches can be classified as energy-based, based on a critical plane and static criteria. also, probabilistic fatigue models should be noted that allow taking into account different sources of uncertainty in prediction such as material properties and microstructures (e.g. large inclusions or defects) or geometrical features of structures. the most frequently mentioned models in the literature include the fatemi socie [28], smith watson topper [29], brown miller [30], crossland [31], sines [22], generalized strain energy/amplitude [32] methods and various their modifications [20, 27, 33, 34]. some reviews of multiaxial criteria are presented in works [35, 36]. all these approaches might be more or less accurate for various materials at different loading paths, therefore it is important to validate multiaxial fatigue models in particular cases. in addition, it is also important to check the applicability of models for notched and cracked bodies. in previous work, the marin, modified crossland and sines models were compared by using non-proportional fatigue test data (with superimposed static mean stress) of 2024 aluminum alloy [37]. as a result, it was shown that the modified sines method described the experimental data in the most accurate way. the present work is aimed at checking the modified sines method by means of biaxial fatigue data of the 2024 aluminum alloy at the different ratio of stress amplitudes, angle of phase shift between the modes of influence and ratio of frequencies of biaxial (tension-compression and torsion) influences. experiments material and specimen xperimental studies to assess the durability of metallic materials under multiaxial cyclic loading were carried out on samples of the 2024 aluminum alloy, manufactured taking into account the requirements of gost 25.502. the 2024 alloy is one of the main structural materials in aviation, astronautics and other areas of mechanical engineering and is often used in various tests for fatigue life [38-41]. the chemical composition of the alloy consists of cu 4.28, mg 1.48, mn 0.75, fe 0.28, si 0.29, zn 0.12, ni 0.009, ti 0.06, cr 0.017, pb 0.05. mechanical properties for the material are listed in tab. 1. fatigue tests were performed on hourglass specimens. the specimen geometry is shown in fig. 1. the specimens are designed in accordance with recommendations of national standard gost 25.502. stresses used in calculating were in accordance with the minimum cross-section of specimen. property symbol 2024 aluminum alloy unit 0.2% tensile yield strength σy 336 mpa 0.3% torsional yield strength τy 153 mpa modulus of elasticity e 75.4 gpa shear modulus g 30.0 gpa shear fatigue strength coefficient τ'f 445 mpa shear fatigue strength exponent b0 -0.0765 fatigue strength coefficient σ'f 1290 mpa fatigue strength exponent b -0.1254 table 1: mechanical properties of 2024 aluminum alloy. e a. yankin et alii, frattura ed integrità strutturale, 55 (2021) 327-335; doi: 10.3221/igf-esis.55.25 329 figure 1: specimen geometry (in mm). experimental procedure and results all tests were carried out in the instron electropuls e10000 at room temperature in the center of experimental mechanics (russia). the electropuls e10000 linear-torsion is an all-electric test instrument with a dynamic linear load capacity of ±10 kn and a dynamic torque capacity of ±100 nm. more information you can find in [21]. as part of the work, fatigue tests were carried out to determine the durability of the 2024 aluminum alloy at various values of the ratio of stress amplitudes, the angle of phase shift between the modes of influence and the ratio of the frequencies of biaxial loading. thus, the study concentrates on uniaxial under tension-compression or torsion and multiaxial loading situations involving mixtures of tension-compression and torsion (out-of-plane shear): mode i and mode iii in the terminology of fracture mechanics.the loading conditions and the results of the experiments are shown in tab. 2. in all experiments, the amplitude of equivalent von mises stress, σma = (σa2 + 3τa2)1/2, was the same. the average number of cycles before failure was determined by the formula ( ) =  = 1 1 log 50 10 n i i n n n . the fatigue curves obtained in tension-compression and torsion for an aluminum alloy have different slope angles [14, 20, 42], that is, the ratio σa(ni) / τa(ni) is not constant. this means that for the same values of the stress amplitude, σma, the number of cycles before failure can be different. the results presented in this article do not contradict the above. thus, from tab. 2 (loadings 1-15) it can be seen that with proportional loadings with the same values of the stress amplitude, σma, with an increase in the angle between the normal and share axes, the average number of cycles before failure increases almost in 3 times. nex is the experimental fatigue life, npr is the predicted fatigue life according to the sines++ model, τa is the amplitude of share stress, σa is the amplitude of normal stress, φ is the phase shift angle between loading modes, υτ is the frequency of loading in the shear mode, υσ is loading frequency in the normal mode. if we plot the fatigue curves obtained in tension-compression and torsion, in the form of the dependence of the amplitude on the number of cycles before failure σma(n), then the curves intersect at the point where σa(n1) = √3τa(n1). this is the only point where the number of cycles to failure will be constant for the same amplitude values , σma, for proportional loadings. the data from tab. 2 (loads 5-8 and 16-23) show the dependence of the number of cycles to failure on the phase angle between the loading modes. with an increase in the phase shift angle from 0 to 45 degrees, an increase in the number of cycles is observed by about 1.4 times, with an increase to 90 degrees, a return to approximately the original values is observed. the results, available in the literature, show different patterns. thus, in [17, 38, 42], with an increase in the phase shift angle, a decrease in the number of cycles was observed, in [14], an increase, and in [20], no significant changes were observed. it should be noted that the alloys presented in [14, 17, 20, 38, 42] were similar in composition, but differed in heat treatment. the final part of the study was aimed at studying the effect of changing the frequency ratio of biaxial loading on fatigue life. for loadings 5-8 and 24-28 from tab. 2, it can be seen that in one cycle a load with the same maximum values of the second invariant of the stress deviator tensor acts on the sample, but the loading paths are different (for 24-28 from tab. 2, the path is more complicated). due to the complication of the type of impact, there is a decrease in the number of cycles to destruction by about 2.3 times. fig. 2 shows typical photographs of fractures of fractured specimens for different loading cycles. fatigue tests for uniaxial tension-compression (fig. 2 a) are characterized by a complex fracture with sections located at angles of 90° and 45° to the sample axis. tests for proportional tension-compression with torsion are characterized by a complex fracture, located at an angle of about 45° to the sample axis (fig. 2 b, τa = 116 mpa, σa = 180 mpa) and about 80-90° to the sample axis (fig. 2 c, τa = 147 mpa, σa = 90 mpa). in pure torsion, the fracture is perpendicular to the rod axis (fig. 2 d). with a phase shift of 90°, 45° and loading with different frequencies of the normal and tangential components, complex fractures are observed, shown in figs. 2 e-g. a. yankin et alii, frattura ed integrità strutturale, 55 (2021) 327-335; doi: 10.3221/igf-esis.55.25 330 no. loading path loading path scheme τа, mpa σа, mpa φ, deg υτ, hz υσ, hz σmа, mpa nex, cyc n50, cyc npr, cyc 1 uniaxial 0 270 0 0 30 270 135,143 120,073 130,057 2 0 270 0 0 30 270 74,913 3 0 270 0 0 30 270 137,680 4 0 270 0 0 30 270 149,129 5 in-phase 1 116 180 0 10 10 270 131,981 137,472 171,892 6 116 180 0 10 10 270 108,475 7 116 180 0 10 10 270 126,773 8 116 180 0 10 10 270 196,782 9 in-phase 2 147 90 0 10 10 270 169,777 205,848 252,640 10 147 90 0 10 10 270 200,086 11 147 90 0 10 10 270 256,769 12 torsion 156 0 0 10 0 270 328,000 358,041 451,253 13 156 0 0 10 0 270 350,437 14 156 0 0 10 0 270 491,539 15 156 0 0 10 0 270 290,863 16 90 op 116 180 90 10 10 270 122,679 117,035 171,892 17 116 180 90 10 10 270 153,960 18 116 180 90 10 10 270 96,749 19 116 180 90 10 10 270 102,668 20 45 op 116 180 45 10 10 270 241,930 196,996 171,892 21 116 180 45 10 10 270 144,247 22 116 180 45 10 10 270 192,814 23 116 180 45 10 10 270 223,818 24** 3 fr 116 180 0 10 30 270 33,488* 60,318* 99,242* 25 116 180 0 10 30 270 100,039* 26 116 180 0 10 30 270 82,689* 27 116 180 0 10 30 270 56,810* 28 116 180 0 10 30 270 50,736* table 2: summary of fatigue tests. (for loadings 24-28, cycles were counted in a tangential mode; test result no. 24 is outside the ±2factor error). a. yankin et alii, frattura ed integrità strutturale, 55 (2021) 327-335; doi: 10.3221/igf-esis.55.25 331 a b c d e f g figure 2: specimens after fatigue failure. a. yankin et alii, frattura ed integrità strutturale, 55 (2021) 327-335; doi: 10.3221/igf-esis.55.25 332 in the article [37], the authors considered multiaxial fatigue models and compared them based on the results of biaxial nonproportional tests with a constant component of the shear and normal loading axes. among the models, the most accurate is the modified sines++ model. this model allows to take into account the beneficial effect of the mean compressive axial stresses, the higher mean stress effect in the axial direction compared with the torsion case and different slopes of the s-n curves under tension-compression and torsion. simplistically, the model can be represented as follows: ( ) ( )+ + +  2 2 2 2 1 1 1a m m aa i b i ci di (1) ( ) ( ) ( ) ( )        = − + − + − + + + 2 2 2 2 2 21 2 11 22 22 33 11 33 12 23 136 6a a a a a a a a a ai (2) ( ) ( ) ( ) ( )        = − + − + − + + + 2 2 2 2 2 21 2 11 22 22 33 11 33 12 23 136 6m m m m m m m m m mi (3)   = + +1 11 22 33m m m mi (4)   = + +1 11 22 33a a a ai (5) where i2a and i2m are the amplitude and the mean value of the second invariant of the stress deviator tensor, i1m and i1a are the amplitude and the mean value of the first invariant of the stress tensor. the model parameters a, b, c and d were determined as follows:  = 1 '(2 ) bo f eq a n ; = 1 ub ;   = − 1 1 3u u c ;   = − 1 1 '(2 ) 3 '(2 ) b bo f eq f eq d n n (6)  =eqn n n ;       =n n (7) where neq is the equivalent fatigue life, nσ and nτ are values of the predicted fatigue life (normal and shear axis), σu is the ultimate tensile strength, τu is the shear strength, τ'f is the shear fatigue strength coefficient, b0 is the shear fatigue strength exponent, σ'f is the fatigue strength coefficient, b is the fatigue strength exponent, υσ and υτ are load frequencies for normal and shear axis. discovering the number of cycles to failure using the sines ++ model is an iterative process. in this regard, a program was developed in python software: https://github.com/yanicen1/multiaxial-fatigue-modified-model-sines-. the prediction results are shown in tab. 2 and fig. 3. in addition, the standard error was calculated using the formula: ( )( ) == −  2 1 log 2 n pr ex i n n se n (8) where n is a number of tests. according to the results of the study, only 1 experimental point out of 28 (or 3.6%) lies outside the ±2-factor error and not a single point outside the ±3-factor error. the standard error was 0.175 or ±1.5 factors (±50 %). it should be noted that although the model describes the experimental data quite well, it does not describe the change in the number of cycles when changing the values of the phase shift angle between loading modes, i.e. the predicted number of cycles remains constant (see tab. 2, loading no. 5-8 and 16-23). however, for the 2024 alloy, this dependence is not essential, which allows the a. yankin et alii, frattura ed integrità strutturale, 55 (2021) 327-335; doi: 10.3221/igf-esis.55.25 333 sines ++ model to achieve high accuracy. it is also worth noting that it was proposed to use the equivalent number of cycles neq to describe the fatigue behavior of the material at different loading frequencies. figure 3: comparison of model prediction with experimental results lastly, it should be noted that for notched bodies modes ii and iii at the crack tip cannot exist in isolation (for a poisson’s ratio greater than zero): mode ii causes mode iii and vice versa. these modes are named coupled modes [43, 44]. according to that, considered in this research multiaxial loads might also induce coupled modes. thus, one should pay attention to this problem in the future dealing with such loads when modes i and iii applied in combinations. conclusions n the current study, the multiaxial fatigue study was performed to assess the effect of different loading schemes on the fatigue life of the 2024 aluminum alloy under the condition of the same amplitude of the second invariant of the stress deviator tensor in all tests. in the experiments, the phase shift angle between the modes of influence, the ratio of the stress amplitudes of the normal and shear axes, and the ratio of the frequencies of the normal and shear loading axes were varied. as a result, the following conclusions can be summarized from the current research: 1. the loading paths might influence significantly the fatigue life results even if the amplitude of the second invariant of the stress deviator tensor is maintained the same in all tests. 2. a modified sines fatigue model is proposed for multiaxial fatigue analysis, in which additional material parameters are introduced to describe the patterns of the fatigue behavior observed for the 2024 aluminum alloy. 3. a program for using the modified sines model is presented that allows determining the number of cycles to failure by means of loading path parameters. 4. for all performed fatigue tests, the modified sines model demonstrates good fatigue life predictions: only 1 experimental point lies outside the ±2-factor error and not a single point outside the ±3-factor error. acknowledgements he work was carried out in perm national research polytechnic university with the financial support of the russian foundation for basic research (grants 19-01-00555 a). the experimental studies were conducted within the state assignment of the ministry of science and higher education of the russian federation (no. fsnm-2020-0027). i t a. yankin et alii, frattura ed integrità strutturale, 55 (2021) 327-335; doi: 10.3221/igf-esis.55.25 334 references [1] serensen, s.v. (1985). fatigue of materials and structural elements, kiev, naukova dumka. [2] troshhenko, v.t. and sosnovskij, l.a. (1987). fatigue resistance of metals and alloys, kiev, naukova dumka. [3] terent`ev, v.f. and korableva, s.a. (2015) metal fatigue, moscow, nauka. [4] matvienko, yu.g. (2006). models and criteria for fracture mechanics, moscow, fizmatlit. [5] anes, v., reis, l. and de freitas, m. (2015). asynchronous multiaxial fatigue damage evaluation. proc. engineering, 101, pp. 421-429. doi: 10.1016/j.proeng.2015.02.051. [6] anes, v., reis, l. and de freitas, m. (2015). multiaxial fatigue damage accumulation under variable amplitude loading conditions. proc. engineering, 101, pp. 117-125. doi: 10.1016/j.proeng.2015.02.016. [7] marciniak, z., rozumek, d. and macha, e. (2008). fatigue lives of 18g2a and 10hnap steels under variable amplitude and random non-proportional bending with torsion loading, int. j. fatigue, 30(5), pp. 800-813. doi: 10.1016/j.ijfatigue.2007.07.001. [8] shamsei, n., gladskyi, m., panasovskyi, k., shukaev, s. and fatemi, a. (2010). multiaxial fatigue of titanium including step loading and load path alteration and sequence effects, int. j. fatigue, 32(11), pp. 1862-1874. doi: 10.1016/j.ijfatigue.2010.05.006. [9] xia, t. and yao, w. (2013). comparative research on the accumulative damage rules under multiaxial block loading spectrum for 2024-t4 aluminum alloy, int. j. fatigue, 48, pp. 257-265. doi: 10.1016/j.ijfatigue.2012.11.004. [10] sonsino, c.m., kueppers, m., eibl, m. and zhang, g. (2006). fatigue strength of laser beam welded thin steel structures under multiaxial loading, int. j. fatigue, 28(5-6), pp. 657-662. doi: 10.1016/j.ijfatigue.2005.09.013. [11] susmel, l. and askes, h. (2012). modified wohler curve method and multiaxial fatigue assessment of thin welded joints, int. j. fatigue, 43, pp. 30-42. doi: 10.1016/j.ijfatigue.2012.01.026. [12] li, j., zhang, z., sun, q. and li, c. (2011). multiaxial fatigue life prediction for various metallic materials based on the critical plane approach, int. j. fatigue, 33(2), pp. 90-101. doi: 10.1016/j.ijfatigue.2010.07.003. [13] gates, n. and fatemi, a. (2014). notched fatigue behavior and stress analysis under multiaxial states of stress, int. j. fatigue, 67, pp. 2-14. doi: 10.1016/j.ijfatigue.2014.01.014. [14] zhang, j., shi, x., fei, b. (2012). high cycle fatigue and fracture mode analysis of 2a12-t4 aluminum alloy under outof-phase axial-torsion constant amplitude loading, int. j. fatigue, 38, pp. 144-154. [15] wang q., xin c., sun q., xiao l., sun j. (2018). biaxial fatigue behavior of gradient structural purity titanium under in-phase and out-of-phase loading, int. j. fatigue, 116, pp. 602-609. [16] liu, t., shi, x., zhang, j., fei, b. (2019). crack initiation and propagation of 30crmnsia steel under uniaxial and multiaxial cyclic loading, int. j. fatigue, 122, pp. 240-255. [17] wang y.-y., yao w.-x. (2006). a multiaxial fatigue criterion for various metallic materials under proportional and nonproportional loading, int. j. fatigue, 28(4), pp. 401-408. [18] skibicki d., pejkowski l. (2017). low-cycle multiaxial fatigue behaviour and fatigue life prediction for cuzn37 brass using the stress-strain models, int. j. fatigue, 102, pp. 18-36. [19] pejkowski, l., skibicki, d., seyda, j. (2018). stress-strain response and fatigue life of a material subjected to asynchronous loadings, aip conference proceeding, 2028, 020016. [20] gates, n.r., fatemi, a. (2017). on the consideration of normal and shear stress interaction in multiaxial fatigue damage analysis, int. j. fatigue, 100, pp. 322-336 [21] wildemann v.e., tretyakov m.p., staroverov o.a., yankin a.s. (2018). influence of the biaxial loading regimes on fatigue life of 2024 aluminum alloy and 40crmnmo steel, pnrpu mechanics bulletin, 4, pp. 169-177. doi: 10.15593/perm.mech/2018.4.16 [22] sines, g. (1955). failure of materials under combined repeated stresses with superimposed static stress, washington, national advisory committee for aeronautics (n.a.c.a), 6. [23] mocilnik, v., gubeljak, n. and predan, j. (2017). the influence of a static constant normal stress level on the fatigue resistance of high strength spring steeltheor. appl. fract. mech., 91, pp. 139-147. doi: 10.1016/j.tafmec.2017.06.002. [24] papuga, j., halama, r. (2018). mean stress effect in multiaxial fatigue limit criteria. arch. appl. mech., pp. 1-12. doi: 10.1007/s00419-018-1421-7. [25] susmel l. multiaxial notch fatigue: from nominal to local stress-strain quantities. cambridge, uk: woodhead; 2009. a. yankin et alii, frattura ed integrità strutturale, 55 (2021) 327-335; doi: 10.3221/igf-esis.55.25 335 [26] tovo, r., lazzarin, p., berto, f., cova, m. and maggiolini, e. (2014). experimental investigation of the multiaxial fatigue strength of ductile cast iron, theor. appl. fract. mech., 73, pp. 60-67. doi: 10.1016/j.tafmec.2014.07.003. [27] pallarés-santasmartas, l., albizuri, j., avilés, a., saintier, n. and merzeau, j. (2018). influence of mean shear stress on the torsional fatigue behaviour of 34crnimo6 steel, int. j. fatigue, 113, pp. 54-68. doi: 10.1016/j.ijfatigue.2018.04.008. [28] fatemi a, socie d.f. (1988). a critical plane approach to multiaxial fatigue damage including out-of-phase loading, fatigue fract. engng mater. struct. 1(3), pp. 149-165. [29] smith rn, watson p, topper th. (1970). a stress-strain parameter for the fatigue of metals. j. mater, 5(4), pp. 767778. [30] brown mw, miller kj. (1973). a theory for fatigue failure under multiaxial stress-strain conditions, proc inst mech eng, 187, pp. 745-755. [31] crossland b. (1956). effect of large hydrostatic pressures on the torsional fatigue strength of an alloy steel, in proceedings of the international conference on fatigue of metals (institution of mechanical engineers, london), pp. 138-149. [32] ince a, glinka g. (2014). a generalized fatigue damage parameter for multiaxial fatigue life prediction under proportional and non-proportional loadings, int. j. fatigue, 62(2), pp. 34-41. doi: 10.1016/j.ijfatigue.2013.10.007 . [33] zhu, s.-p., yu, z.-y., correia, j., de jesus, a., and berto, f. (2018). evaluation and comparison of critical plane criteria for multiaxial fatigue analysis of ductile and brittle materials, int. j. fatigue, 112, pp. 279-288. doi: 10.1016/j.ijfatigue.2018.03.028. [34] correia, j., apetre, n., arcari, a., de jesus, a., muñiz-calvente, m., calcada, r., berto, f. and fernández-canteli, a. (2017). generalized probabilistic model allowing for various fatigue damage variables, int. j. fatigue, 100, pp. 187-194. doi: 10.1016/j.ijfatigue.2017.03.031. [35] milella p. p. (2013). fatigue and corrosion in metals, springer, 844 p. [36] carpinteri, a., spagnoli, a., and vantadori, s. (2017). a review of multiaxial fatigue criteria for random variable amplitude loads, fatigue fract. engng mater. struct, 40(7), pp. 1007-1036. doi: 10.1111/ffe.12619. [37] yankin a.s. et alii. (2020). influence of static mean stresses on the fatigue behavior of 2024 aluminum alloy under multiaxial loading, frattura ed integrità strutturale, 14(51), pp. 151-163. doi: 10.3221/igf-esis.51.12. [38] xia t.x., yao w.x., ji y.f., wang c.j. (2015). study on the accumulative fatigue damage rules under multiaxial twostage step spectra constructed by loadings with similar lives, fatigue fract. engng mater. struct, 38(7), pp. 838-850. [39] han z.-y., huang x.-g., cao y.-g., xu j.-q. (2014). a nonlinear cumulative evolution model for corrosion fatigue damage, journal of zhejiang university: science a, 15(6), pp. 447-453. [40] chang h., pang x.c., li z.j., tang w.j., chen f.m. (2014). monitoring corrosion fatigue damage process of ly12cz aluminum alloy with and without coating by acoustic emission, applied mechanics and materials, 552, pp. 145-148. [41] wang y., zhang d., yao w. (2014). fatigue damage rule of ly12cz aluminium alloy under sequential biaxial loading, science china: physics, mechanics and astronomy, 57(1), pp. 98-103. [42] wang, x.-w., shang, d.-g. (2016). determination of the critical plane by a weight-function method based on the maximum shear stress plane under multiaxial high-cycle loading, int. j. fatigue, 90, pp. 36-46. [43] pook, l. p., campagnolo, a., and berto, f. (2016). coupled fracture modes of discs and plates under anti-plane loading and a disc under in-plane shear loading, fatigue fract. engng mater. struct, 39(8), pp. 924-938. doi: 10.1111/ffe.12389. [44] berto, f., lazzarin, p., and kotousov, a. (2011). on higher order terms and out-of-plane singular mode, mechanics of materials, 43(6), pp. 332-341. doi: 10.1016/j.mechmat.2011.03.004. microsoft word numero_56_art_08_2988 n. miloudi et alii, frattura ed integrità strutturale, 56 (2021) 94-114; doi: 10.3221/igf-esis.56.08 94 temporal analysis of the performance of an elevated concrete tank considering the corrosion of the steel reinforcement. nassima miloudi, karima bouzelha, hocine hammoum department of civil engineering, mouloud mammeri university, 15000 tizi ouzou, algeria. nassima.miloudi@ummto.dz, karima.bouzelha@ummto.dz hocine.hammoum@ummto.dz , https://orcid.org/0000-0002-1481-6241 younes aoues laboratoire d’optimisation et fiabilité en mécanique des structures, insa de rouen, france. younes.aoues@insa-rouen.fr ouali amiri institut de recherche en génie civil et mécanique ieg gem, polytech nantes, france. ouali.amiri@univ-nantes.fr abstract. reinforced concrete water storage tanks are civil engineering structures subject to very aggressive atmospheric conditions that expose them to harmful corrosion risk. this dangerous phenomenon caused by the penetration of chloride ions causes pitting corrosion and leads to the reduction of the section of the reinforcements and consequently to the loss of strength and the structure performance. in this study, we are interested in analyzing the performance of an elevated storage tank, taking into account the corrosion of the reinforcements subjected to tensile stress, by considering environments with different rates of aggressiveness. a method based on housner's model is used to evaluate the tension stresses in the reinforced concrete (rc) pedestal (supporting system) of the tank, subjected to the seismic actions. a pitting corrosion model is developed in order to determine the evolution in time of the reinforcements section in different environments. several parameters influencing corrosion are taken into account, such as concrete cover and the concentration of chlorides ions. keywords. rc elevated tank; pitting corrosion; reinforcement; performance; seismic actions; lifetime. citation: miloudi, n., bouzelha, k., hammoum, h., aoues, y., amiri, o., temporal analysis of the performance of an elevated concrete tank considering the corrosion of the steel reinforcement, frattura ed integrità strutturale, 56 (2021) 94-114. received: 16.01.2021 accepted: 26.02.2021 published: 01.04.2021 copyright: © 2021 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. https://youtu.be/x13zlj9nbt0 n. miloudi et alii, frattura ed integrità strutturale, 56 (2021) 94-114; doi: 10.3221/igf-esis.56.08 95 introduction hether one is interested in the management of existing structures or the design of new structures, one of the major issues is the control of their lifespan, while maintaining a guarantee of optimal response to performance requirements. these are conditioned by the response of the structures to physical and chemical attacks from the environment [1], as well as by the ability of the constituent materials to protect themselves against these attacks. the prediction of the lifetime of a structure has become a fundamental requirement, particularly for those of vital importance, such as rc storage tanks, classified as structures of great importance, from class 1b according to algerian seismic code (rpa) [2]. they are considered to be extremely stressed structures, intended to storage water for distribution to subscribers. in order to ensure a sufficient hydraulic pressure in drinking water supply networks, tanks are preferably located on sites such as hilltops and mounds, exposing them to very harsh conditions of aggressiveness. these extreme conditions expose them to the corrosion risk of the reinforcements, thus reducing the performance of their resistant elements [3]. in addition, this type of structure is particularly vulnerable to the hydrodynamic effect under seismic action. the hydrodynamic behaviour of water storage tanks has been the subject of several researches in order to improve their design and their strength to high seismic loads. the first published work in this field was carried out by hoskin and jacobsen [4] who, based on the work of westergaard [5] on rigid rectangular gravity dams, conducted theoretical and experimental studies to evaluate the hydrodynamic pressures developed in rectangular tanks subjected to seismic excitation. subsequently, housner's work [6,7] made it possible to formulate the simplified analytical method, according to which the reservoirs are replaced by an equivalent system with two degrees of freedom, concentrating the mass of the structure at two points (impulsive and convective). this method, which is still used nowadays by practical engineers, has largely answered the problematic of the seismic response of liquid storage tanks. later, in the 1970s, epstein [8], based on housner's model, developed formulas and dimensioning curves to estimate bending and overturning moments in rectangular and cylindrical tanks subjected to seismic action. still based on housner's model, hammoum et al. [9] were interested in the analysis of circular and elevated rc reservoirs, and proposed a modelling of the hydrodynamic effect, taking into account the seismic action represented by a response spectrum given by rpa [2]. these authors show that the negligence of the hydrodynamic phenomenon would considerably underestimate the normal vertical tensile stresses acting in the rc pedestal. indeed, contrary to what is stated in the rpa [2], the consideration of the hydrodynamic effect in the dimensioning calculations is necessary whatever their storage capacity and seismic zone. aliche et al. [10] presented a probabilistic approach, based on the monte carlo simulation method, to develop fragility curves to represent the failure probability of rc elevated tanks at different levels of seismic acceleration and for different soil types. however, reinforcement’s corrosion is considered to be one of the main causes of deterioration of rc structures over time [11]. this corrosion does not develop as long as the concrete ensures physical or chemical protection to the reinforcements [12]. indeed, the hydration of the cement produces a basic interstitial solution with a high ph (about 13) which gives permanent stability to the rust layer adhering to the reinforcements embedded in the concrete; which phenomenon is called passivation. steel can be depassivated by two main mechanisms: the carbonation of concrete by carbon dioxide (c02) from the atmosphere or the penetration of chloride ions coming from sea water, sea spray or deicing salts [13]. concrete carbonation corrosion affects large zones of reinforcement with a more or less uniform loss around the perimeter of the reinforcing bars, whereas pitting corrosion is localized on small areas and results in a substantial reduction in their cross section [14]. this study will focus on pitting corrosion because it is more dangerous than uniform corrosion. in the lifetime of a rc structure, we can distinguish two phases of corrosion: a corrosion initiation phase and a propagation phase. the duration of the initiation phase is determined by the speed of neutralisation of the cover concrete, or the speed of penetration of aggressive agents, such as chlorides [15]. when the chloride concentration in the steel bars reaches the threshold concentration, the propagation phase begins, the steel corrodes, its section decreases causing the ruin of the structure [12]. tutti's diagram (fig.1) summarizes in two stages (initiation, propagation) the corrosion mechanism that leads to the deterioration of structures [16]. the initiation time is defined by portuguese researchers group [18] for uniform corrosion and by duracrate [15] for pitting corrosion. in order to estimate the loss of section induced by corrosion in concrete, several models have been proposed to express the uniform corrosion current (duracrete, li and lawanwisut, gonzales et al., gonzales et al., tuutti) and the pitting corrosion current (liu and weyers, vu and stewart, vu et al., gonzales et al., tuutti) [19]. the choice of the model depends on the input parameters which must be modelled so that the results are realistic. few researches have been done on estimating the durability and performance of rc storage tanks considering the reinforcement corrosion. we can cite the work of bouzelha et al. [20] treating the analysis of the performance of a storage w n. miloudi et alii, frattura ed integrità strutturale, 56 (2021) 94-114; doi: 10.3221/igf-esis.56.08 96 tank posed on the ground, taking into account the corrosion phenomenon of the reinforcements and considering environments with different rates of aggressiveness. figure 1: schematic degradation of steel reinforcement over time [17]. the research work presented in this paper is a continuation of the work carried out by bouzelha et al. [20]. the objective is the analysis of the vertical tensile stresses of the pedestal of an elevated concrete tank, under seismic action, taking into account corrosion by penetration of chloride ions, inducing pitting corrosion. for the evaluation of these tensile stresses, the housner’s model [9] is thus used to simulate the hydrodynamic effect, which will be briefly presented in section 2. in section 3, we study the evolution of pitting corrosion rates in tensile stress steels, using the model of liu and weyers [21], which is quite entire because it takes into account several parameters of environmental influence. as for the initiation time, it is evaluated with the model proposed by duracrete [15]. in section 4, we present a practical application, where the lifetime of the elevated tank is estimated by considering environments with different aggressiveness, as well as different seismic zones. the influence of different parameters on corrosion is analysed, such as cover concrete, chlorides concentration, cement content and environmental parameters. relevant conclusions and recommendations are thus provided in the final section. deterministic approach for the evaluation of vertical tensile stresses in the support ousner's model decomposes the action of the water contained in the storage tank into two actions: an impulsive action causing impulsive efforts and convective action causing convective efforts [22]. thus, the modelling of the entire reservoir is represented by its mechanical equivalent and its mathematical model with two degrees of freedom, as shown in fig. 2. figure 2: elevated tank equivalent mechanical and mathematical models. h n. miloudi et alii, frattura ed integrità strutturale, 56 (2021) 94-114; doi: 10.3221/igf-esis.56.08 97 in the adopted mathematical model, the mass m0 representing the part of the water oscillating, is connected to the structure by a rod of the same stiffness k1 forming a direct coupling with m1.  aiki i k ki s f .γ .m .a g (1) sai : ground acceleration in "i" mode; mk: level "k" mass; aki: mass amplitude "k" in mode "i"; γi: modal distribution coefficient (mode i), given by the following formula:      2 k kik 1 i 2 2 k kik 1 m .a γ m .a (2) the resultant of the calculated seismic force applied to each mass mk is given by:    2 2 k ki i 1 f f (3) the pedestal is subjected to a normal vertical stress noted n, representing the weight of the empty storage tank augmented by the weight of the water it contains as well as the weight of the support tower, and to a bending moment noted m, due to lateral seismic forces (f0 and f1). the pedestal is then stressed in compound bending (m, n). normal compressive and tensile stresses are developed on the extreme fibres of the pedestal. in this study, we are interested in the tensile stresses; they are estimated using the following relation:   n m σ v  ω i (4) v represents the distance of the most tense fibre of the pedestal from an axis passing through the gravity centre of the tank. the section of the pedestal noted ω has the shape of a ring, and its horizontal section is given by:   2 2ext intπω d d 4 (5) where, dint and dext refer respectively to the internal and external diameter of the pedestal. the moment of inertia of the pedestal, with respect of an axis passing through the gravity centre of the tank, is given by:   4 4ext intπi d d 64 (6) the vertical tensile stress at the base of a fully tensioned linear band of the support, of thickness es, is expressed at the serviceability limit state (sls) by the following relationship: s st  σ. e (7) the necessary reinforcements section is thus deduced from the serviceability limit state by the following relation:  snec st t a σ (8) n. miloudi et alii, frattura ed integrità strutturale, 56 (2021) 94-114; doi: 10.3221/igf-esis.56.08 98 stσ , is the tensile stress limit of steels, considering very detrimental cracking according to fascicule 74 [23], is defined as follows:      est e tj f2 σ 0.8 min f  ;  max ; 90 ηf 3 2 (9) where fe and ft28 respectively denote the elastic limit of steels and the tensile strength of concrete at 28 days. in practice, the reinforcements section initially adopted (at t=0) for a unit band (1 linear meter) is given by:     2 00 4 s b d a n (10) where: bn : is the number of bars adopted on a unit band of the pedestal. 0  d : is the initial diameter of a steel bar. mechanical model of reinforcements corrosion n this study, we put forward the hypothesis that the state of corrosion progress at a given time t, is uniform on the bars of the same unit band, since they are subjected to the same aggression from the environment. it then comes that the section of longitudinal reinforcements tended at time t which we denote  sa t of a unit band at the base of the pedestal, is expressed as follows:    s b ra t n a t (11)  ra t is the residual section of a steel bar at time t, given by the eqn. (12), as a function of the initial bar diameter d0 and the pitting depth p(t) [14], as shown in fig. 3 : figure 3: pit configuration [24].                        2 0 0 1 2 0 1 2 0 0                                      4 2                                              2 0                                                               r d d a a if p t d a t a a if p t d if p t d (12) i n. miloudi et alii, frattura ed integrità strutturale, 56 (2021) 94-114; doi: 10.3221/igf-esis.56.08 99 where:               22 0 0 1 1 0 1    2 2 2 p td d a a d (13)            2 2 2 2 0 p t1  a   α p t 2 d a (14)           2 0 p t 2 p t 1 d a (15)         1 0 2 arcsin a d (16)          2 a α 2 arcsin 2p t (17) val et al. [24] suppose a spherical shape of the pitting (fig. 3) and define its maximum depth by the following relation:     ini t corrt p t  0.0116 α i dt (18) where α is the pitting factor that takes into account the non-uniform corrosion along the reinforcement bars. the corrosion current density icorr is estimated as proposed by liu and weyers model [21]:             cor s c 0.215 ini 1 3034 2.32 i exp 8.37 0.618 ln 1.69 c 0.000105r 1.08 t t (19) this model takes into account several parameters, such as the concentration of chlorides on the surface of the steels (cs),the ambient temperature (t), the resistivity of concrete (rc) and the corrosion initiation time ( init ) . the latter is obtained from the second law of fick, which express the diffusion of chloride in concrete using the partial differential equation in the following form:         2 cl 2 c x, t c x, t d t x (20) c(x,t) is the concentration of free chlorides inside the concrete at carbonation depth (x) and time (t), and dcl is the effective chloride diffusion coefficient. the resolution of fick's second law is carried out, taking into account the following hypotheses [15]: isotropic, saturated and semi-infinite domain; diffusion coefficient independent of time and space; chloride concentration at the surface is constant and chloride concentration in the concrete at the initial time (t=0) is zero. thus, the concentration of chlorides is given by:              s cl x c x, t c 1 erf 2 d t (21) n. miloudi et alii, frattura ed integrità strutturale, 56 (2021) 94-114; doi: 10.3221/igf-esis.56.08 100 erf(.) is the error function defined by mcgee [25]:                2 3 5 7 x t 0 2 2 1.x 1.x 1.x 1.x  erf x e  dt   0 !.1 1!.3 2 !.5 3!.7π π (22) the diffusion coefficient of chlorides dcl depends mainly on the composition of the concrete. it is influenced by the mixing proportions (water, aggregate and cement), by the environment (relative humidity and temperature) and is variable as a function of time, as given by duracrete [15]:     n n0 0cl cl 0 e t c 0 ini ini t t d t   d t  ( ) k .k .k .d . ( ) t t (23) where: d0 : diffusion coefficient effected at the reference time t0 (m2/s) ; ke : factor taking into account the characteristics of the environment ; kt : factor used to determine d0 ; kc : factor taking into account the cure time ; t0 : time for which d0 was measured (days) ; n : aging factor. corrosion is initiated when the concentration of chloride ions c(x,t) reaches the threshold limit or critical concentration ccr, and the carbonation depth (x) reaches the concrete cover (e). this combined effect of chlorides and carbonation leads to a depassivation of steel reinforcement. the result is:                       1 2 1 n2 1 cr ini n se t  c   0 0  ce t erf 1 c4k k k d (t ) (24) note that the diffusion coefficient of chlorides dcl is expressed mainly in 10-12 m2/s or more rarely in [mm2/year]. the units should be consistent with those of depth x and time t. practical application he practical application presented here concerns the analysis of an elevated water storage tank with a capacity of 200 m3 posed on a pedestal (tower support) (fig. 4). the geometric characteristics of the tank are shown in tab. 1. figure 4: the studied elevated tank with the adopted reinforcement of the pedestal in a very high seismicity zone. t n. miloudi et alii, frattura ed integrità strutturale, 56 (2021) 94-114; doi: 10.3221/igf-esis.56.08 101 internal diameter of the tank [m] 8.20 average water height in the tank [m] 4.95 height of the pedestal [m] 14.50 internal diameter of the tower support [m] 5.00 external diameter of the tower support [m] 5.40 tower support thickness [m] 0.20 real tank volume [m3] 200.50 concrete cover [mm] 40 table 1: geometrical characteristics of the tank [9]. evaluation of the vertical reinforcements section of the pedestal the tensioned reinforcement sections are evaluated using the method outlined in section 2 for the unit band of the concrete pedestal for various seismic zones defined by rpa [2]. the necessary reinforcements sections obtained from the stress analysis as well as those adopted are shown in tab. 2. table 2: results of reinforcement sections for a 1 ml band of the pedestal. influence of corrosion on the section of the reinforcements to study the effect of pitting corrosion on the section of reinforcements, we consider that the tank is located in a socalled atmospheric zone and we analyse four environments with different levels of aggressiveness to which correspond different chloride ion concentrations (cs) (see tab. 3). in this so-called atmospheric zone, the reservoir is not directly exposed to seawater; wind-borne spray is the main source of chlorides [26]. the data used for the corrosion model are summarized in tab. 4, for a portland cement with a content of 400 kg/m3. environment description cs (kg/m3) 1 environment of low aggressiveness 1.80 2 environment of moderate aggressiveness 3.50 3 environment of high aggressiveness 5.30 4 environment of extreme aggressiveness 7.40 table 3: average values of the parameters (cs) depending on the environment [27]. seismic zones zone i low seismicity zone iia average seismicity zone iib high seismicity zone iii very high seismicity seismic acceleration coefficient 0.12 0.20 0.25 0.30 developed tensile effort (kn/m) 19.74 196.51 307.00 417.48 necessary section anec(cm2) 1.23 12.28 19.19 26.09 adopted reinforcement 14 ɸ 10 14 ɸ 12 14 ɸ 14 14 ɸ 16 adopted section a0 (cm2) 10.99 15.83 21.55 28.14 n. miloudi et alii, frattura ed integrità strutturale, 56 (2021) 94-114; doi: 10.3221/igf-esis.56.08 102 variable units values reference ambient temperature t k 25+273 [21] resistivity of the concrete cover rc ohm 1500 [21] diffusion coefficient d0 m2/s 7·10-12 [15] coefficient α 5.65 [28] critical concentration of chlorides ccr kg/m3 0.5 [15] factor ke 0.676 [15] aging factor n 0.65 [15] test type factor kt 0.832 [15] factor kc (28 days) 4.445 [15] cure time t0 days 28 [15] table 4: the used parameters in corrosion model. the results of the pitting corrosion initiation time, obtained for the different considered environments and for a concrete cover equal to 40 mm, are presented in tab. 5. these results show that the initiation of corrosion is very sensitive to the aggressiveness of the surrounding environment, which decreases considerably as its moves from an environment of low aggressiveness to an extreme aggressiveness. except for the low-aggressivity environment, the reservoir's lifetime is above the provisional lifetime of a civil engineering structure (50 to 100 years) [26]. environment aggressiveness tini (years) environment of low aggressiveness 213.0459 environment of moderate aggressiveness 38.3382 environment of high aggressiveness 17.9740 environment of extreme aggressiveness 10.8350 table 5: corrosion initiation time values for each environment. the evolution over time of the residual section of reinforcement as(t), of the most tense unit band, after corrosion is shown in fig. 5 for the different environments and for each seismic zone. we note that the intersection of the residual section of reinforcement with the necessary section corresponds to the critical threshold beyond which this residual section becomes smaller than the necessary section, thus causing the failure of the structure. this critical threshold therefore defines the lifetime of the tank. a s (t ) (c m 2 ) n. miloudi et alii, frattura ed integrità strutturale, 56 (2021) 94-114; doi: 10.3221/igf-esis.56.08 103 figure 5: evolution of the reinforcements section as a function of time for different seismic zones. a s (t ) (c m 2 ) 0 100 200 300 400 500 600 time (years) 0 5 10 15 20 25 30 (c) zone iib low agressiveness moderate agressiveness high agressiveness extrem agressiveness necessary section a s (t ) (c m 2 ) n. miloudi et alii, frattura ed integrità strutturale, 56 (2021) 94-114; doi: 10.3221/igf-esis.56.08 104 based on the estimate of val et al. [26], we propose in tab. 6 a classification of reservoir life, divided into three levels of safety. safety level red orange green lifetime ( years) 1 49 50 100 ≥ 100 estimated lifetime critical good very good table 6: classification of service life. from fig. 4, we extract the lifetime of the tank as a function of the environment aggressiveness and the seismic zone (tab. 7). we note that the reservoir has a lifetime far beyond the provisional lifetime in an environment of low and moderate aggressiveness for any seismic zone, and in an environment of high aggressiveness for a low seismicity zone (fig.5.a). this lifetime decreases significantly in a high aggressiveness environment and moves away from its provisional lifetime dictated by standards in an environment of extreme aggressiveness in medium, high and very high seismicity zones (fig.5.b, fig.5.c and fig.5.d). aggressiveness rate seismic zone low moderate high extreme zone i 460 155 94 63 zone iia 338 100 59 39 zone iib 314 91 52 33 zone iii 306 87 50 30 table 7: tank lifetime as a function of the environment aggressiveness and the seismic zone. the results presented above are obtained for fixed values of the calculation parameters for reinforcement’s corrosion, such as concrete cover, diffusion coefficient, critical concentration of chloride ions, environment temperature and concrete resistivity. in order to distinguish between parameters that promote the initiation and propagation of corrosion as well as the handicapping parameters, we are interested, in what follows, in the study of the influence of each of these parameters on the lifetime of the elevated tank. effect of concrete cover the evolution of the initiation time as a function of the concrete cover is shown in fig. 6 and this for different levels of aggressiveness of environments. the results show that the initiation time increases with the increase in concrete cover, regardless of the considered environment, which clearly explains why the concrete cover has a handicapping effect on the ability of the chloride ions to diffuse in the concrete. thus, by increasing the value of the concrete cover, we can increase the initiation time and thus increase the life of the tank. however, this increase is less pronounced in environments of high aggression and even less so in environments of extreme aggression. figure 6: evolution of initiation time as a function of concrete cover, for different environments. n. miloudi et alii, frattura ed integrità strutturale, 56 (2021) 94-114; doi: 10.3221/igf-esis.56.08 105 in practice, and as a measure of constructive dispositions, the civil engineer refers to the french standards bael 99 [29], to fix the concrete cover according to the aggressiveness of the environment, as shown in tab. 8. the initiation time for each concrete cover recommended by the bael [29], and deduced from fig. 6, is very short, especially in environments of high and low aggressiveness. we conclude that these concrete covers are insufficient to protect the reinforcements from the penetration of chloride ions and therefore from corrosion. environment description cs (kg/m3) e (mm) tini(years) 1 environment of low aggressiveness 1.8 10 0,1 2 environment of high aggressiveness 5.30 30 3 3 environment of extreme aggressiveness 7.40 50 39 table 8: average values of the parameters (cs and e) depending on the environment [26, 28]. the evolution over time of the residual section of reinforcement as(t) of the most tense unit band, for the environments considered and for the different concrete covers recommended by bael [29], is shown in fig. 7 for two seismic zones (iia and iii). by analyzing the critical corrosion threshold, we find that the corrosion propagation is accelerated and that the tank enters into failure at less than 10 years and 30 years respectively in the low and high aggressiveness environment; which confirms that the concrete covers recommended by the bael [29] are insufficient to protect the structure. inversely, the concrete cover of 5cm recommended in an extremely aggressive environment is sufficient to ensure the provisional lifetime of such structure, given that the critical threshold was recorded at 75 years. since the results observed for the two seismic zones are similar, we have chosen the very high zone for the rest of our analysis. figure 7: evolution of the reinforcements section for different concrete covers recommended by bael [29]. 0 10 20 30 40 50 60 70 80 90 100 110 120 130 140 150 160 time (years) 0 2 4 6 8 10 12 14 16 (a) zone iia low agressiveness (c=10mm) high agressiveness(c=30mm) extrem agressiveness (c=50mm) necessary section 0 20 40 60 80 100 120 140 160 180 200 time (years) 0 5 10 15 20 25 30 (b) zone iii low agressiveness (c=10mm) high agressiveness(c=30mm) extrem agressiveness (c=50mm) necessary section n. miloudi et alii, frattura ed integrità strutturale, 56 (2021) 94-114; doi: 10.3221/igf-esis.56.08 106 effect of the diffusion coefficient to study the effect of the diffusion coefficient noted d0, we refer to the values defined by duracrate [14] according to the cement content and the ratio w/c. these values vary from 200 mm2/year to 800 mm2/year for good and bad concrete respectively. the evolution of the initiation time as a function of the diffusion coefficient is illustrated in fig. 8 for the considered environments and for a concrete cover of 40 mm. we notice that for a diffusion coefficient lower than 500 mm2/year, the initiation time decreases with the increase in the aggressiveness of the environment. however, above 500 mm2/year, and except for the low aggressiveness environment, corrosion initiation is immediate in the other three environments. indeed, the research work of hobbs et al. [30] has shown that the diffusion coefficient is mainly a function of the w/c ratio, which has a very great influence on the porosity of concrete. more the diffusion coefficient is important, more the concrete's porosity is greater, thus facilitating the penetration of aggressive elements to accelerate the corrosion of the reinforcement [31]. figure 8: effect of diffusion coefficient and chloride ion concentration on corrosion initiation time. the evolution of the residual section of reinforcements over time for different diffusion coefficients is shown in fig. 9 for a moderate and aggressiveness environment. we find that the propagation of corrosion decreases with reduction of diffusion coefficient. the lifetime of the tank is approximately 100 years in the moderate aggressiveness environment (fig.9.a). however, in environment of extreme aggressiveness (fig.9.b), it stays below the provisional duration of 50 years, regardless of the values of the diffusion coefficient. this explains why, in an aggressive environment, in order to increase the lifetime of the structure it is necessary to reduce the capillary porosity of the concrete by reducing the w/c ratio. in practice, careful curing of the concrete considerably improves the waterproofing of the surface. in it ia ti o n t im e t in i ( ye a rs ) a s (t ) (c m 2 ) n. miloudi et alii, frattura ed integrità strutturale, 56 (2021) 94-114; doi: 10.3221/igf-esis.56.08 107 figure 9: evolution of residual section of reinforcements for different diffusion coefficients. influence of concrete quality the quality of the concrete is linked to the cement content. the higher is the cement content, more concrete strength is increased. in order to study the impact of cement content on the initiation time of a pitting corrosion and on the lifetime of the tank, we combined two parameters that are depending on the cement content according to the literature, namely the diffusion coefficient and the critical concentration of chloride ions. to this effect, duracrate [15] proposes values of the diffusion coefficient as a function of cement content (tab. 9). as for the maximum content of chloride ions (ccr), it is given according to the cement content, by the formula proposed by the french standard [32]:  0.2 % crc c (25) the initiation time (tab. 9) is calculated for each cement content considering a concrete cover of 40 mm and a moderate aggressiveness environment. the initiation time increases with the cement content and the critical concentration of chlorides ions. this increase corresponds to a decrease in the diffusion coefficient. the latter decreases as the quality of the concrete increases, thus limiting the penetration of chlorides and consequently the risk of corrosion. nature of the concrete c (kg/m3) d0 (10-12 m2/s) e (mm) ccr (kg/m3) tini (years) poor concrete 300 15 40 0.6 6.44 ordinary concrete 350 10 40 0.7 29.74 good concrete 400 7 40 0.8 117.72 table 9: average values of the critical concentration of chlorides ions and the diffusion coefficient for each quality of concrete [15, 32]. the evolution of the initiation time as a function of the concrete cover is illustrated in fig. 10 for different qualities of concrete. we notice that beyond a concrete cover of 30 mm, the initiation time increases as the concrete cover increases. furthermore, this increase is more pronounced for better quality concrete. however, for a concrete cover smaller than 30 mm, corrosion is immediately initiated for the different qualities of concrete. thus, the initiation of corrosion of the reinforcements is subordinated to the use of an adequate concrete cover, and to a better quality of the concrete, which is governed by the increase of the cement content, the increase of the critical concentration and the decrease of the diffusion coefficient. fig. 11 show the temporal variation of the residual section of reinforcement for different qualities of concrete in a moderate and extreme environment. we notice that the propagation of corrosion is slowed down as the cement content is increased. however, for the same quality of concrete, the lifetime of the tank in a moderate aggressiveness environment (fig.11.a) is twice as long as that of a tank evolving in an extreme aggressiveness environment (fig.11.b). for this reason, fascicule 74 [23] recommends a minimum cement content of 400 kg/m3 for the concrete used to build tanks. 0 20 40 60 80 100 120 time (years) 0 5 10 15 20 25 30 (b) environment of extreme aggressiveness d 0 = 200 mm 2 /year d 0 = 400 mm2/year d 0 = 600 mm 2 /year d 0 = 800 mm 2 /year necessary section (zone iii) n. miloudi et alii, frattura ed integrità strutturale, 56 (2021) 94-114; doi: 10.3221/igf-esis.56.08 108 figure 10: effect of concrete cover, and quality of concrete on initiation time of corrosion. figure 11: evolution of residual section of reinforcements as a function of time for different cement contents. influence of critical concentration of chlorides the presence of clions in the vicinity of steel surfaces does not automatically induce corrosion. accumulation of chlorides until the critical concentration is reached in the vicinity of the reinforcements is necessary for the passive layer in iti a tio n t im e t in i ( ye a rs ) 0 50 100 150 200 250 300 350 400 time (years) 0 5 10 15 20 25 30 (a) environment of moderate aggressiveness good concrete ordinary concrete poor concrete necessary section (zone iii) a s (t ) (c m 2 ) n. miloudi et alii, frattura ed integrità strutturale, 56 (2021) 94-114; doi: 10.3221/igf-esis.56.08 109 that protects the steel to fail and corrosion to initiate [12]. fig. 12 shows the initiation time of corrosion as a function of the critical concentration of chlorides ions in the vicinity of the reinforcements for environments of different aggressiveness. the initiation time increases as the critical concentration increases, thus slowing down the corrosion initiation. however, we notice that this increase is less pronounced in environments of high and extreme aggressiveness, whereas for these two environments the critical concentration of chlorides ions is important. figure 12: evolution of the residual section of reinforcements for different values of the critical concentration. the evolution of the residual section of reinforcement for different critical chlorides ions concentration values is shown in fig. 13 for moderate and extreme environment. we find that the lifetime of the tank is all the longer as the critical concentration of chloride ions is important. however, in the environment of extreme aggressiveness (fig.13.b), the lifetime still very short compared to the environment of moderate aggressiveness (fig.13.a). we notice that for critical concentrations of 0.50 kg/m3 and 0.75 kg/m3, the provisional lifetime is not reached. influence of the temperature it is known that temperature promotes the corrosion process [3]. according to liu and weyers [21], an increase in temperature increases the speed of corrosion. this phenomenon can be explained by the fact that the anodic (oxidation of steel components) and cathodic (reduction of protons in an acid environment) processes are thermally activated. this results in an exchange current, i.e. a corrosion rate increasing with temperature. an increase in temperature from 10 to 20°c multiplies by two the corrosion rate in an active corrosion situation. for this reason, we judged it useful to evaluate the corrosion rate at different temperatures for different environments (fig. 14). we notice that the corrosion rate increases with the increase of temperature. this promotes the propagation of corrosion and increases the diffusivity of chlorides ions. for a given temperature, the corrosion rate is more pronounced in high and extreme aggressiveness environments. the evolution of the residual section of reinforcements in a moderate and extreme environment is illustrated in fig. 15 for different temperature values. the curves show that the increase of temperature accelerates the propagation of corrosion following the increase of the diffusivity of chlorides, especially in an extreme aggressiveness environment (fig.15.b) where the presence of chlorides is important, which induces a reduction in the lifetime of the structure. influence of concrete resistivity the resistivity of concrete represents its capacity to prevent electrons from moving and significantly affects the corrosion of reinforcements in concrete [33]. this depends on the composition of the concrete interstitial solution, its microstructure (pore size and pore distribution), humidity, salt content, and ambient temperature [34]. fig. 16 shows the influence of concrete resistivity on the corrosion rate, for different rates of aggressiveness and for a temperature of 25 °c. we find that corrosion of the reinforcement increases as the electrical resistivity of the concrete decreases. however, for a given resistivity, the corrosion rate is much more important in the environment of high and extreme aggressiveness and tends towards zero in the environment of low aggressiveness. in an aggressive environment, even if the resistivity of the concrete is high, the density of chloride ions remains always high. n. miloudi et alii, frattura ed integrità strutturale, 56 (2021) 94-114; doi: 10.3221/igf-esis.56.08 110 figure 13: evolution of the residual section of reinforcements for different values of the critical concentration. figure 14: effect of temperature on corrosion rate for different concentrations of chlorides ions. 0 100 200 300 400 500 600 time (years) 0 5 10 15 20 25 30 a s (t ) (c m 2 ) environment of moderate aggressiveness c cr =0.5 kg/m3 c cr =0.75 kg/m3 c cr =1.00 kg/m3 necessary section (zone iii) c o rr o si o n r a te i c o r ( a /c m 2 ) n. miloudi et alii, frattura ed integrità strutturale, 56 (2021) 94-114; doi: 10.3221/igf-esis.56.08 111 figure 15: evolution of the residual section of reinforcements for different temperature values. figure 16: effect of the concrete resistivity and the concentration of chlorides ions on the corrosion rate. the evolution of the residual section of reinforcement for different resistivity values is shown in figs. 17 for moderate and extreme environment. it is noticed that the resistivity of concrete has an handicapping effect on the propagation of 0 50 100 150 200 250 300 time (years) 0 5 10 15 20 25 30 (a) environment of moderate aggressiveness temperature =20 °c temperature =25 °c temperature =30 °c temperature =35 °c necessary section (zone iii) 0 20 40 60 80 100 120 140 time (years) 0 5 10 15 20 25 30 (b) environment of extreme aggressiveness temperature =20 °c temperature =25 °c temperature =30 °c temperature =35 °c necessary section (zone iii) c o rr o si o n r a te i c o r ( a /c m 2 ) n. miloudi et alii, frattura ed integrità strutturale, 56 (2021) 94-114; doi: 10.3221/igf-esis.56.08 112 corrosion. in fact, if the electrical resistivity of concrete is important, the last will be less conductive, and thus the passage of chloride ions will be limited, and the lifetime of the structure will be prolonged. however, it is noticed that in an aggressive environment (fig.17.b), even if the resistivity of the concrete is quite important, the penetration of chloride ions is still high and the tank lifetime remains less than the provisional duration of 50 years. figure 17: evolution of the residual section of reinforcements for different resistivity values. conclusion itting corrosion of reinforcements is one of the most serious pathologies affecting concrete tanks and leading them to failure. this corrosion induced by the penetration of chloride ions is aggravated by the aggressiveness of the surrounding environment which accelerates its initiation and propagation. through a deterministic analysis of an elevated concrete tank located in an atmospheric environment, we have shown that in same conditions, the lifetime of the tank decreases considerably, going from a low to an extreme aggressiveness environment, whatever the seismic zone. in addition, a parametric study has shown that concrete cover, cement content, resistivity and the critical concentration of chlorides ions are factors that slow down the initiation and propagation of corrosion. in fact, the results have highlighted the importance of covering in the protection of the reinforcements against the aggressiveness of the environment. its disabling effect reduces considerably the ability of chloride ions to diffuse in concrete, thus prolonging the corrosion initiation time as well as the lifetime of the structure. however, the covering values recommended by bael 99 [29] in an environment of low and high aggressiveness are insufficient for the steels protection against corrosion. the results also showed the importance of respecting the cement content, especially in environments of high and extreme aggressiveness; this justifies the recommendation in fascicule 74 [23] which imposes a content of 400 kg/m3 for tanks. as for resistivity, a s (t ) (c m 2 ) p n. miloudi et alii, frattura ed integrità strutturale, 56 (2021) 94-114; doi: 10.3221/igf-esis.56.08 113 this has a direct influence on the conductivity of the concrete as well as on the diffusion of oxygen in the material. higher is the resistivity of the concrete, more limited is the diffusion of aggressive ions and lower is the corrosion current. however, in an aggressive environment, even if the resistivity of the concrete is high, the density of chloride ions always remains high, hence the necessity to increase the concrete cover. finally, if the reinforcement in concrete has a low critical concentration of chlorides, the initiation of corrosion is fast, so increasing the critical concentration will lead to a reduction of corrosion. several studies have shown that the critical concentration is influenced by the quality of the steel. among parameters favouring the propagation of corrosion, we can mention the temperature and the diffusion coefficient. a high temperature increases the diffusivity of chloride ions, especially in environments of high and extreme aggressiveness, where the concentration of chlorides on the surface of steels is high. in addition, the diffusion coefficient is a parameter linked to the w/c ratio; it is all the more important as the porosity of the concrete, facilitating the penetration of aggressive species that subsequently cause corrosion of the reinforcements. the phenomenon of corrosion is quite complex to be taken lightly, as so many parameters are interdependent, hence the importance of integrating it in standards and readjusting the concrete cover for each environment. it is a necessary to consider, in the design step, certain requirements such as the quality and properties of the concrete composition, its implementation conditions, climatic and environmental conditions. it is also recommended to include these criteria with their variability in design codes as sources of aggression in the definition of exposure classes, in order to design more sustainable structures in aggressive environments. acknowledgements he authors wish to thank the algerian ministry of higher education and scientific research for funding the university education research project (prfu – n° a01l02un150120180002) and tassili project (phc – 18mdu121). declaration of interest statement n behalf of all authors, the corresponding author states that there is no conflict of interest. references [1] gerengi, h. (2018). the use of dynamic electrochemical impedance spectroscopy in corrosion inhibitor studies, j. prot. met. phys. chem. surf, 54(3), pp. 536–540. doi: 10.1134/s2070205118030267. [2] règlement parasismique algérien (rpa 99/version 2003). document technique réglementaire dtr bc 2 48. centre national de recherche appliquée en génie parasismique, ministre de l’habitat, alger, algérie. [3] bastidas arteaga, e. and stewart, m.g. (2015). damage risks and economic assessment of climate adaptation strategies for design of new concrete structures subject to chloride-induced corrosion, j. struct .saf., 52, pp.40–53. doi: 10.1016/j.strusafe.2014.10.005. [4] hoskin, l.m. and jacobsen, l.s. (1934). water pressure in a tank caused by a simulated earthquakes, j. bull. seismol. soc. am., 24, pp. 1–32. [5] westergaard, h.m. (1933). water pressures on dams during earthquakes, trans, asce 98., 47, pp. 418–472. [6] housner, g.w. (1957). dynamic pressures on accelerated fluid containers, j. bull. seismol. soc. am., 47, pp.15-35. [7] housner, g.w. (1963). the dynamic behavior of water tanks, j. bull. seismol. soc. am., 53, pp. 381-387. [8] epstein, h.i. (1976). seismic design of life liquid storage tanks, j. struct.div., 102(9), pp. 1659–1673. [9] hammoum, h., bouzelha, k. and slimani, d. ed., (2016). seismic risk of rc water storage elevated tanks: case study, in: handbook of materials failure analysis with case studies from the chemicals, concrete and power industries, new york, elsevier ed., pp. 187–216. doi: 10.1016/b978-0-08-100116-5.00008-9. [10] aliche, a., hammoum, h. and bouzelha, k. (2019). mecano-reliability analysis applied to rc tank under seismic loads according to the algerian seismic standard, asian. j. civ. eng., 20, pp.395–408. t o n. miloudi et alii, frattura ed integrità strutturale, 56 (2021) 94-114; doi: 10.3221/igf-esis.56.08 114 doi: 10.1007/s42107-018-00113-x. [11] nguyen, p.t., bastidas arteaga, e., amiri, o. and el soueidy, c.p. (2017). an efficient chloride ingress model for long-term lifetime assessment of reinforced concrete structures under realistic climate and exposure conditions, int. j. concr. struct. mater.,11, pp. 199–213. doi: 10.1007/s40069-017-0185-8. [12] stewart, m.g. and rosowsky, d.v. (1998). time-dependent reliability of deteriorating reinforced concrete bridge decks, j.struct. saf., 20, pp. 91–109. doi:10.1016/s0167-4730(97)00021-0. [13] aoues, y. (2008). optimisation fiabiliste de la conception et de la maintenance des structures. thèse de doctorat en genie civil, université blaise pascal-clermont ii, france. [14] duprat, f. (2006). reliability of rc beams under chloride-ingress, j. constr. build. mater.,21, pp.1605–1616. doi: 10.1016/j.conbuildmat.2006.08.002. [15] duracrete. (2000). statistical quantification of the variables in the limit state functions. tech rep, the european union brite euram iii contract brpr-ct95-0132 project be95-1347/r9. [16] güneyisi, e.m., mermerdaş, k., güneyisi, e. and gesoglu, m. (2015). numerical modeling of time to corrosion induced cover cracking in reinforced concrete using soft-computing based methods, j. mater struct.,48, pp.1739– 1756. doi: 10.1617/s11527-014-0269-8. [17] tuutti, k. (1982). corrosion of steel in concrete, stockholm: swedish cement and concrete research institute, cbi forsking research report.,82(4). [18] national laboratory of civil engineering lnec e 465. (2009). resistance of concrete to carbonation. predicted and measured values in natural exposure, lisbon, portugal., 8. [19] otieno, m., beushausen, h. and alexander, m. (2012). prediction of corrosion rate in reinforced concrete structures a critical review and preliminary results, j. mater. corros., 63(9). doi:10.1002/maco.201106282. [20] bouzelha, k., amazouz, l., miloudi, n. and hammoum, h. (2019). temporal analysis of the performance of a rc storage tank considering the corrosion. first international symposium on risk and safety of complex structures and components (iras 2019), procedia struct integrity., 22, pp. 259–266. doi: 10.1016/j.prostr.2020.01.033. [21] liu, y. and weyers, r.e. (1998). modeling the time to corrosion cracking in chloride contaminated reinforced concrete structures, aci. mater. j., 95(6), pp. 675–680. [22] davidovici, v. and haddadi, a. (1982). calcul pratique de réservoirs en zone sismique, annales de l’itbtp, paris., (409). [23] fascicule 74 texte officiel. (1998). construction des réservoirs en béton-cahier des clauses techniques générales. ministère de l’équipement des transports et du logement, paris, france. [24] val, d.v. and melchers, r.e. (1997). reliability of deteriorating rc slab bridges, j. struct. eng (asce)., 123(12), pp. 1638–1644. doi: 10.1061/(asce)0733-9445(1997)123:12(1638). [25] mcgee, r.w. (2001). on the service life modelling of tasmanian concrete bridges. phd thesis in civil and mechanical engineering, university of tasmania. [26] val, d.v. and stewart, m.g. (2003). life-cycle cost analysis of reinforced concrete structures in marine environments, j. struct. saf., 25, pp. 343–362. doi: 10.1016/s0167-4730(03)00014-6. [27] weyers, r.e. (1993). concrete bridge protection, repair, and rehabilitation relative to reinforcement corrosion: a methods application manual. washington: strategic highway research program, national academy of sciences dc 20418.,(202), pp. 334–3774. [28] aoues, y. and bastidas arteaga, e. (2011). conception optimale des structures en béton soumises à la pénétration d’ions de chlorures. 29éme rencontres universitaires de génie civil, tlemcen, 187-195. [29] bael 91 modifiées 99. (2000). règles techniques de conception et de calcul des ouvrages et constructions en béton armé suivant la méthode des états limites. fascicule 62, france, dtu p 18-702. [30] hobbs, d.w. (1999). aggregate influence on chloride ion diffusion into concrete, j. cement concrete. res.,29, pp. 1995–1998. doi: 10.1016/s0008-8846(99)00188-x. [31] baroghel bouny, v. (2005). nouvelle approche performentielle et prédictive fondée sur les indicateurs de durabilité. laboratoire central des ponts et chaussées, paris, france.,4. [32] norme française homologuée. (2002). béton-partie 1: spécification, performances, production et conformité. france: nf en., 206-1. [33] nguyen, p.t. (2014). étude multiphysique du transfert de chlorures dans les bétons insaturés : prédiction de l’initiation de la corrosion des aciers. thèse de doctorat en génie civil, université de la rochelle, france. [34] blankwoll, a. (1997). history of the gimsoystaumen bridge repair project. international conference-repair of concrete structures, from theory to practice in a marine environment, norvége, 53. microsoft word numero_33_art_34 m.kurek et alii, frattura ed integrità strutturale, 33 (2015) 302-308; doi: 10.3221/igf-esis.33.34 302 focussed on multiaxial fatigue estimation of fatigue life of selected construction materials under cyclic loading m. kurek, t. łagoda opole university of technology, poland ma.kurek@po.opole.pl, t.lagoda@po.opole.pl s. vantadori university of parma, italy sabrina.vantadori@unipr.it abstract. in the literature, there are many criteria of multiaxial fatigue. they are based on various assumptions and parameters describing the process of fatigue. among them, there is a special group of criteria based on the concept of critical plane. some of them in their equations take into account the ratio of normal and shear stresses. macha has formulated the criterion of maximum normal and shear stress in fracture plane which can be generalised for the scope of random loading of numerous criteria. in the present study authors estimated the fatigue life of several construction materials. for the purposes of the analysis, the authors proposed modified carpinteri et al. method to find orientation of critical plane, which is used in multiaxial fatigue criterion defined in critical plane. this plane is turned through the angle of β in relation to the plane defined by maximum normal stresses. in this study authors analyzed the variability calculation of fatigue life, depending on the angle β. simulation studies were conducted in which it was assumed that β  <0°, 45°>. for each of the 46 angles, we calculated parameters b and k appearing in the formula defining equivalent stress. then we calculated fatigue life according to the proposed model for each of the obtained angles β. fatigue life analysis was carried out in order to verify which angle β gives the most similar results. keywords. fatigue life; multiaxial criteria. introduction he phenomenon of fatigue of materials and structures is a significant issue of the day. fatigue occurs in various fields of industry, i.e. aerospace, machinery, mining or transport. the main objective of the bulk of research on predicting the fatigue strength is to identify a method of estimating the fatigue strength already on the stage of design and construction of components of machines and devices. the fatigue criterion in multiaxial loading is based on establishing such equivalent value that would enable comparison of multiaxial load with uniaxial loading. literature of the subject provides a number of multiaxial fatigue criteria [6]. such criteria are based on various assumptions and parameters of the fatigue process. a separate group of criteria among them are based on the critical plane concept [4]. some of the criteria include the ratio of bending fatigue to torsional fatigue. the paper discusses estimation of fatigue strength depending on the changing orientation of the critical plane of proportional torsional bending for specific construction t m.kurek et alii, frattura ed integrità strutturale, 33 (2015) 302-308; doi: 10.3221/igf-esis.33.34 303 materials. the paper also compares the calculation and experimental results for fatigue strength of specific materials, using multiaxial fatigue criteria and various methods for determining critical plane orientation that take into account the ratio of fatigue limits. fatigue strength algorithm o estimate calculation fatigue life used standard model, which consists of several stages. the first step includes measurement, generation or calculation of component of stress tensor, according to the following equations: ( ) sin( )t t xx a    (1) ( ) sin( )t t xy a      (2) where: σa – amplitude of normal stress induced by bending, τa – amplitude of shear stress induced by torsion, ω – angular frequency, φ – angle of phase shift, t time. in the discussed model, the course of normal stress σxx(t) refers to stress induced by bending, while τxy(t) refers to torsioninduced stress. the next step involves determination of the orientation angle of the critical plane, which can be done using one of three established methods: weight functions, damage accumulation or variance. in this paper, the orientation of the critical plane was determined using damage accumulation method. if the criterion proposed by carpinteri et al. [2] is used, the inclination angle of the critical plane is increased by the angle 2 2 3 1 1 45 2 b               (3) with respect to the angle determined by maximum normal stress, where: 2 af af b    (4) where σaf, τaf are fatigue limits for bending and torsion respectively. the relationship (4) was proposed for some selected constructional materials, and the group for which this relationship is constant was determined. in such a case, hypotheses allow to calculate the fatigue life. as for other materials, there is no one universal criterion of fatigue life calculation because it is necessary to include variation of the ratio σa/τa depending on a number of cycles to the fatigue failure [5, 16]. there is a number of multiaxial fatigue criteria. here, we are discussing the group based on the critical plane concept. macha [8] has formulated the criterion of maximum normal and shear stress in fracture plane which can be generalised for the scope of random loading of numerous criteria. the general form can be written down as ( ) ( ) ( )eq st b t k t     (5) where: b, k – constants used for selection of specific criterion form [7] in this paper, in order to verify the highest conformity of results, three different criteria of multiaxial fatigue were used: 1. criterion in the maximum normal stress plane, in the following form 1( ) ( ) ( )eq st b t t     (6) where: b1 – constant depending on material type, ση(t) is the course of normal stress orientated at angle α towards σxx, expressed by the following equation 2( ) ( )cos ( )sin 2t t t xx xy        (7) whereas τηs(t) is the course of shear stress 1 ( ) ( )sin 2 ( )cos 2 2 t t t s xx xy         (8) t m.kurek et alii, frattura ed integrità strutturale, 33 (2015) 302-308; doi: 10.3221/igf-esis.33.34 304 where:     (9)  is the angle defined by normal stress using the damage accumulation method or by finding an angle, for which normal stress variance reaches maximum [13, 15]    21 ot n o o t dt t      (10) where to is time of observation, in constant amplitude loading it is one cycle. 2. criterion in the maximum shear stress plane, in the following form 2 22eq ηs ησ (t) b τ (t) ( b )σ (t)   (11) where in general case: b2 =    /a fi a fin n  (12) fin is number of cycles, for which amplitude ratio is defined. when characteristics are parallel, we take fatigue limit as defined in formula (4) [6, 16]. 3. criterion using determination of critical plane orientation according to the carpinteri et al. method as defined in (3), where weighing factors can be defined as: 2 2 2 sin(90 2 ) cos sin 2 sin(90 2 ) cos(90 2 ) 2 cos o o o b b             (13) 2 2 sin 2 2 cos b k     (14) the final step is the calculation of fatigue strength. for fixed amplitude loadings (cyclical), the fatigue strength is calculated using basquin’s fatigue characteristics, in compliance with the relevant astm standard [1]. the formula for calculation strength under cyclical loading is expressed as , lg 10 eg acal a m n   (15) analysed materials the analysis used the results of fatigue tests of the following materials: two aluminium alloys: pa4 (6082) [10], pa6 (2017a) [3] , 10hnap [11] and 30crnimo8 [14] steels, ggg40 cast iron [9], and brass cuzn40pb2 [5]. the results were also used to calculate the regression equations for oscillatory bending (or unixial push-pull), as per the astm recommendations [1], in the following form log nf = aσ+ mσ logσa. (16) for bilateral torsion, the regression equation takes the form of log nf = aτ+ mτ logτa, (17) where: aσ, mσ, aτ, mτ coefficients of regression equation for oscillatory bending and bilateral torsion, respectively. tab. 1 lists the values of coefficients of regression equation for the analysed materials. fig. 1 shows fatigue diagram for oscillatory bending and bilateral torsion on the example of the pa4 aluminum alloy. m.kurek et alii, frattura ed integrità strutturale, 33 (2015) 302-308; doi: 10.3221/igf-esis.33.34 305 figure 1: fatigue diagram for oscillatory bending and bilateral torsion for the 6082-t6 aluminum alloy (where a, a are stress amplitudes generated by torsional moment and bending moment, respectively). material bending torsion nfi σa/τa (nfi) a m a m cycles pa6 (2017a) 21.87 -7.03 19.94 -6.87 2000000 1.696 ggg40 32.39 -10.95 35.48 -12.41 1000000 1.11 10hnap 30.88* 9.5* 25.28 8.2 2000000 1.874 pa4 (6082) 23.8 -8.0 21.4 7.7 2000000 1.68 30crnimo8 27.54 8.05 69.56 24.62 100000 1.5 cuzn40pb2 19.99 5.86 45.3 17.17 1000000 0.92 table 1: coefficients of regression equation for analysed materials. 0 , 45    . for each of the 46 angles calculated parameters b and k in accordance with the formulas (13) and (14). fig. 2 presents b and k constants depending on the angle β for the pa4 aluminum alloy. , lg 10 eg acal a m n   . 0 5 10 15 20 25 30 35 40 45 -40 -35 -30 -25 -20 -15 -10 -5 0 x: 13 y: -2.935 , 0 b 0 5 10 15 20 25 30 35 40 45 0.35 0.4 0.45 0.5 0.55 x: 41 y: 0.4393 , 0 k (a) (b) figure 2: the dependence of the parameter a) b, b) k from the angle β for aluminum alloy 6082 (pa4). 10 4 10 5 10 6 10 7 50 150 250 350 450 500 n f , cykle  a ,  a , m p a  a = 0  a = 0 log(n f )=23,8-8log( a ) log(n f )=21,4-7,7log( a ) m.kurek et alii, frattura ed integrità strutturale, 33 (2015) 302-308; doi: 10.3221/igf-esis.33.34 306 verifications of proposed criteria and analysis of obtained results n order to perform the correct analysis of the fatigue life scatter, the logarithmic dependence of the ratios of experimental and calculation strength should be used. a new method of determination the fatigue life scatter has been proposed by [12], defined as the root mean square error: exp2 1 log n i cal n n e n   (18) therefore, the scatter can be determined as: t = 10e (19) tab. 2 compares plane rotation angles according to the carpinteri et al. method. moreover, the angle β was found for minimum scatter according to the formula (19). fig. 3 shows the relationship between scatter value (19) and the angle β for the selected pa4 aluminum angle. for this alloy, the least scatter (global minimum) was achieved for β=420 (t=2.366). additionally, local minimum was obtained for β =190 (t=2.391). 0 5 10 15 20 25 30 35 40 45 2 3 4 5 6 7 8 9 10 x: 42 y: 2.366 , o t figure 3: relationship between scatter values t (19) and the angle β. material βc (3) tmin β (tmin) β (21) pa6 44 1.9972 44 42 ggg40 13 2.583 1 16 10hnap * 1.932 43 44 pa4 44 2.366 42 42 30crnimo8 38 1.992 40 39 cuzn40pb2 ** 4.335 11 →0 table 2: the values of rotation angles β and minimum scatters of fatigue life (*out of range > 3 ; ** out of range <1 the carpinteri et al. method concerning determination of the angle β is based on the assumption that we deal with materials ranging from resilient-brittle to resilient-plastic state. considering this, the author assumes that in the first case coefficient b2 is 1, and in the second extreme case its value is 3 . therefore, it has been assumed that the plasticization criterion according to the heber-mises-hencke hypothesis is right in the boundary case for materials in resilient-plastic state. as we see, this ratio (tab. 1) for the 10hnap steel exceeds that value. considering this, it has been proposed to i m.kurek et alii, frattura ed integrità strutturale, 33 (2015) 302-308; doi: 10.3221/igf-esis.33.34 307 introduce the boundary plasticization value according to the tresca hypothesis (max. {b} = 2). thus, the formula analogical to (3) is as follows:                 45 1 1 3 4 2 2b  (20) when we analyse the data shown in fig. 4, we can see that the points defined as scatter minimum for individual materials, lie along the more convex curve. considering this, a new curve has been proposed, satisfying the same boundary conditions as the formula (20) with the arguments fitting within range <0, 2>, in the following form:                 45 1 1 15 16 4 2b  (21) figure 4: the relationship between the angle β and the parameter b2 according to different models. conclusions nalysing the results of fatigue tests and calculations, it can be concluded that: 1. the multiaxial fatigue criterion proposed for life estimation is applicable to wide range of materials from resilient-brittle to resilient-plastic state. 2. the carpinteri et al. hypothesis has proven to be right. the hypothesis concerns orientation rotation for the critical plane defined by normal stresses by the angle dependent on the ratio of fatigue boundaries for bending and torsion. 3. the tresci criterion has been taken as the boundary condition for materials in resilient-plastic state. the new form of formula for the critical plane orientation rotation angle has been proposed on the basis of this condition. 4. further verification is required for other materials and other loading conditions. a m.kurek et alii, frattura ed integrità strutturale, 33 (2015) 302-308; doi: 10.3221/igf-esis.33.34 308 references [1] astm e 739–91, standard practice for statistical analysis of linearized stress–life (s–n) and strain life fatigue data, in: annual book of astm standards, vol. 03.01, philadelphia (1999) 614–628. [2] carpinteri, a., spagnoli, a., vantadori, s., multiaxial fatigue assessment using a simplified critical plane-based criterion, international journal of fatigue, 33(8) (2011) 969-976. doi: 10.1016/j.ijfatigue.2011.01.004. [3] kardas d., kluger, k., łagoda, t., ogonowski, p., fatigue life under proportional constant amplitude bending with torsion in energy approach basic on aluminium alloy 2017(a), physicochemical mechanics of materials, 4(2008) 68-74, materials science, 541-549 [4] karolczuk, a., macha, e., a review of critical plane orientations in multiaxial fatigue failure criteria of metallic materials, international journal fracture, 134 (2005) 267-304. [5] kurek, m., łagoda, t., comparison of fatigue characteristics for some selected structural materials under bending and torsion, materials science, 47(3) (2011) 334-344. [6] kurek m., łagoda t., , estimation of fatigue life of materials with out-of-parallel fatigue characteristics under block loading, materials science forum trans tech publications, switzerland, 726 (2012) 181-188. [7] łagoda, t., ogonowski, p., criteria of multiaxial random fatigue based on stress, strain and energy parameters of damage in the critical plane, mat.-wiss. u. werkstofftech, 36(9) (2005) 429-437. [8] macha, e., generalization of fatigue fracture criteria for multiaxial sinusoidal loadings in the range of random loadings, in: biaxial and multiaxial fatigue, egf 3 (edited by m.w. brown and k.j. miller), mechanical engineering publications, london, (1989) 425–436 [9] muller, a., zum festigkeitsverhalten von mehrachsig stochastisch beanspruchten gußeisen mit kugelgraphit und tempergu, fraunhofer – institut fur betriebsfestigkeit, darmstadt, (1994). [10] niesłony, a., łagoda, t., walat, k., kurek, m., multiaxial fatigue behaviour of aa6068 and aa2017a aluminium alloys under in-phase bending with torsion loading condition, mat.-wiss. u. werkstofftech., 45 (2014) 947-952. [11] pawliczek, r., badanie wpływu parametrów obciążenia i geometrii karbu na trwałość przy zmiennym zginaniu i skręcaniu, rozprawa doktorska, politechnika opolska, opole (in polish) (2001). [12] walat, k., łagoda, t., lifetime of semi ductile materials through the critical plane approach, international journal of fatigue, 67 (2014) 73-77. [13] kluger, k., łagoda, t., fatigue life of metallic material estimated according to selected models and load conditions, journal of theoretical and applied mechanics, 51(3) (2013) 581-592. [14] sanetra, c., untersuchungen zum fetigkeitsvwrhalten bei mehrachsiger randombeanspruchung unter biegung und torsion, dissertation, technische universitat clausthal, (1991). [15] walat, k., kurek, m., ogonowski, p., łagoda, t., the multiaxial random fatigue criteria based on strain and energy damage parameters on the critical plane for low-cycle range, int. j. fatigue, 37 (2012) 100-111. [16] kurek, m., łagoda, t., fatigue life estimation under cyclic loading including out-of-parallelism of the characteristics, applied mechanics and materials, 104 (2012) 125-132. microsoft word numero_57_art_03_3030 f. boursas et alii, frattura ed integrità strutturale, 57 (2021) 24-39; doi: 10.3221/igf-esis.57.03 24 parametric study of i-shaped shear connectors with different orientations in push-out test farid boursas, djamel boutagouga laboratory of mine, department of civil engineering, university of tébessa, algeria farid.boursas@univ-tebessa.dz, d.boutagouga@yahoo.fr abstract. a great deal of research has been conducted to improve the understanding of the behavior of new types of shear connectors. this article presents the study of i-shaped connectors behavior under monotonic load welded in four different orientations in order to get the position which gives the high shear strength and the best ductility. for this purpose, eight push-out test specimens with i-shaped shear connectors with different orientations and dimensions were tested in c20/25 and c30/37 concrete classes. the load-slip behavior and failure modes of the tested connectors are presented and discussed. furthermore, a non-linear 3d finite element modelling of the pushout test is performed in order to further investigate the influencing parameters on the i-shaped connectors behavior. hence, a parametric study is carried out by using the established 3d finite elements model to study the influence of concrete strength, connector’s steel grade, reinforcements, height and length of the connector. both experimental and numerical results show that there is a privilege orientation for which the shear strength of an i-shaped shear connector is significantly higher than that of all other tested orientations. keywords. i-shaped connectors; shear strength; ductility; 3d finite element modelling; failure modes. citation: boursas, f., boutagouga, d., parametric study of i-shaped shear connectors with different orientations in push-out test, frattura ed integrità strutturale, 57 (2021) 2439. received: 26.02.2021 accepted: 18.04.2021 published: 01.07.2021 copyright: © 2021 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. introduction owadays, steel-concrete composite structures are increasingly used in many structural applications. these structures combine the steel and concrete materials to extract their best performances through the adequate coupling of these materials into an integral cross-section. by the rational structural use of the right materials at the right places, mixed beams can offer highly efficient and lightweight units commonly used in structures like multi-story buildings and large-span bridges. the composite behavior of these structures is largely influenced by the amount of interfacial slip. in order to limit the slip between steel and concrete, both materials are mechanically joined together using n https://youtu.be/gt0w1rtdkt8 f. boursas et alii, frattura ed integrità strutturale, 57 (2021) 24-39; doi: 10.3221/igf-esis.57.03 25 mechanical connection elements, known as connectors. consequently, the behavior of composite beams is greatly affected by shear connectors strength and ductility. in practice, several forms of shear connectors are widely used. however, only few are proposed in the eurocode 4 [1], therefore, push-out tests are used in order to study the behavior of shear connectors and their efficacity. shear connectors are generally divided into two classes, rigid, and flexible “ductile” connectors depending on the distribution of shear forces and the functional relationship between force and interfacial slip [2]. note that, the various studies carried out on shear connectors for more than 50 years, have shown that there is no ideal connector [3]. the choice of this or that type of connector depends on the cost, the implementation difficulties, and the mechanical performances of the connector. several research works have focused on studying new types of shear connectors that can be used instead of the ones proposed by eurocode 4 [1]. it was revealed that these new shear connectors offer better resistance, structural safety, welding quality, constructability, cost-effectiveness, etc. the v-shaped angle shear connector [4], for instance, exhibits several satisfactory proprieties such as ductility, elevated resistance, high shear transmission, and it is more economical than other shear connectors [4]. the newly suggested lshaped, c-shaped, and i-shaped shear connectors [5–7] can efficiently provide adequate mechanical performances. furthermore, high-strength friction-grip bolts were proposed as shear connectors [8]. they can be easily unbolted during deconstruction and structural modification. another new shear connector is developed from the reforming of a part of the steel section flange to be embedded inside the concrete to resist slippage between steel and concrete [8]. hollow steel tube (hst) shear connectors and web opening (wo) shear connectors were also studied [9]. it should be also noted that the steel pipe has been recently studied as a new shear connector [10]. experimental push-out tests are expensive and time-consuming. that is why reliable numerical modeling can be a good alternative to experimental tests. finite element models of the push-out test have been developed to investigate the bearing capacity of shear connectors in many research works. timber-concrete composite beams under long-term loading has been modeled by fragiacomo and ceccotti [11]. all anomalies affecting the long-term behavior of timber, concrete and the attachment system, such as creep, mechano-sorptive creep, shrinkage/swelling and variations in temperature were considered. another model using the finite element software ansys was proposed by queiroz et al [12]. the proposed fe model can simulate the whole flexural loadings of composite beams which are subject to simple support. its covers load-deflection behavior, longitudinal slip at interface between the steel and concrete, stud shear force distribution, and modes of failure. nguyen and kim [13] developed a finite element model of the push-out test to investigate the load capacity of large stud shear connectors. the material nonlinearities of concrete, steel beam, headed studs, and rebar were included in the finite element model. a parametric fem analysis was carried out by xu and sugiura [14] to investigate “the mechanical performances of group studs”, in which, damage plasticity was introduced to simulate material nonlinear behavior of concrete. in order to study composite beams with profiled sheeting oriented perpendicularly to its axis, a three-dimensional nonlinear finite element model was established in [15]. the push-out test analysis was performed using abaqus/explicit with a very slow load program to guarantee a quasi-static solution. an elasto-plastic behavior was used for all steel components while the concrete damaged plasticity model was adopted for the concrete slab [15]. a three-dimensional quarter-scale finite element model for headed stud connectors pushout test was developed by bouchair et al [16] using the software atena. han et al [17] used damage plasticity model for concrete and contact algorithms available in abaqus software to numerically investigate composite beams with crumb rubber concrete slabs. paknahad et al [18] recently estimated experimentally and analytically the effect of high-strength concrete (hsc) on the shear capacity of the channel shear connectors (csc) in the steel concrete composite floor system [18]. an interesting connector type known as an “i-shaped” shear connector was tested under static loading [7,19]. the test results show that in composite beams, i-shape connectors can be used to transfer the longitudinal shear forces and limit the interfacial slippage between the steel and concrete. in these works, the lowest inertia of the i-shaped connector was employed to resist the interfacial shear force. indeed, in the previous works, the i-shaped connector was oriented in the way that its axis of lowest inertia was against shear force action axis, see fig. (1). as the i-shaped shear connector has three distinct principal axes of inertia, it can take several orientations within the concrete slab, which can offer different stiffness and ductility, which can be more advantageous in resisting the interfacial slip and shear forces. therefore, this work aims to investigate the i-shaped shear connector load-slip behavior when the i-shaped connector takes different orientations in the concrete slab plane. several experimental tests and numerical analysis were performed in order to attain the best orientation that gives the superior shear strength. we have also investigated, in this study, the main influential factors on the behavior of the i-shaped connectors. f. boursas et alii, frattura ed integrità strutturale, 57 (2021) 24-39; doi: 10.3221/igf-esis.57.03 26 experimental program he main idea of this work is to test i-shaped steel shear connectors in different orientations within the concrete slab relative to the steel beam axis, which is, the main axis of action in a steel-concrete mixed beam. this section is devoted to highlight the undertaken experimental program, describe the tested push-out specimens, and test set-up. specimens presentation four orientations of the connector axes relative to the steel beam longitudinal axis as shown in fig. (1) are investigated in this study. (a) p01 (b) p02 (c) p03 (d) p04 figure 1: the i-shaped connector in different configurations in this study, the composite beam is composed by an heb160 steel beam connected to a concrete slab of dimensions (36×32×12 cm3) reinforced by 4 rebars of 8 mm in diameter so 4φ8 in both directions, as shown in fig. (2). the connection is made up by means of an ipe120 shear connector. the standard dimensions according to eurocode 4 of the whole specimen [1] are presented in fig. (3). two concrete classes c20/25 and c30/37 that correspond to the desired compressive strengths of 20 mpa and 30 mpa respectively were adopted t f. boursas et alii, frattura ed integrità strutturale, 57 (2021) 24-39; doi: 10.3221/igf-esis.57.03 27 in this study for the push-out tests. we adopted the steel grade s355 (fy = 355 mpa) for the heb160 steel beam and s235 (fy = 235 mpa) for the ipe120 steel connectors. figure 2: push-out specimens’ preparation. figure 3: dimensions and details of the push-out specimens in the configuration p03. material properties two steel tensile coupon specimens were taken out from the ipe120 flange and web in order to determine the stress-strain curve of the ipe120 connector through standard tensile testing of the taken coupons. the dimensions of the specimen are taken according to iso 6892-1 [20]. the obtained material properties, including the yield stress, the ultimate tensile stress and young’s modulus of elasticity of the ipe120 connector, are listed in tab. (1). type fy (mpa) fu (mpa) e (mpa) ipe120 flange plate 217 352 205000 ipe120 web plate 248 368 208000 table 1: mechanical properties of the connector’s steel. f. boursas et alii, frattura ed integrità strutturale, 57 (2021) 24-39; doi: 10.3221/igf-esis.57.03 28 in this study, two desired compressive strengths of 20 mpa and 30 mpa for the concrete slab were obtained using a plasticizer adjuvant as water reducer. these two classes of concrete were formulated by using the dreux-gorisse method [21]. the used concrete mixes are listed in tab. (2). concrete mixes component c20/25 c30/37 gravel (3/8) 263.111 kg 263.111 kg gravel (8/15) 708.117 kg 708.117 kg sand 630.937 kg 630.937 kg cement 350 kg 350 kg water 208.538 l 157.150 l super plasticizer 5.25 l 5.25 l table 2: the concrete mixes. in order to avoid the disparity of concrete compressive strength from one slab to another, the slabs of all the push-out specimens were cast vertically; the friction effect at the steel-concrete interface was eliminated by oiling the steel flanges before casting the slabs. during the concrete cast of the push-out specimens, four concrete cylinders of 160 mm in diameter and 320 mm of length were casted from the concrete mixture. these concrete specimens were tested for compressive strength on the same day of the push-out tests. the experimental program considers eight push-out specimens. all the tested specimens are shown in the tab. (3). series specimens fc (mpa) average fc (mpa) serie a p01-a 21.980 p02-a 19.538 p03-a 20.077 20.487 p04-a 20.354 serie b p01-b 28.882 p02-b 29.435 p03-b 30.143 30.037 p04-b 31.689 table 3: the obtained concrete compressive strength. test setup a concentrated monotonic loading is applied at the top of the heb160 cross section of the push-out specimens, as shown in fig. (4). the load is applied using a calibrated hydraulic jack connected with an electric hydraulic pump. the capacity of hydraulic jack is 500 kn. the relative displacements between the heb160 steel section and the concrete slab is measured using a linear variable differential transformer (lvdt) connected with data acquisition system installed at the top center of heb160 web to measure the relative displacement between the connector and the heb160 top which is the total displacement applied during the push-out test. two rigid steel plates of 20 mm thickness were used as base plates during the test. one of theme was placed between the heb160 steel section and the hydraulic jack in order to distribute the applied load on the whole heb160 transverse section. the second one was placed under the concrete slabs to serve as a rigid base. the test was carried out in accordance with eurocode 4 [1]. the load was applied in increments of 10 kn from 0 to 100 kn (40% of the expected failure load), then returned back to 12.5 kn (5% of the expected failure load). after that, the loading cycle between 12.5 kn and 100 kn was repeated 25 times to remove any lack of fit in the test set up. then, the applied load continued monotonically up to the failure. f. boursas et alii, frattura ed integrità strutturale, 57 (2021) 24-39; doi: 10.3221/igf-esis.57.03 29 figure 4: test setup. experimental results the ultimate load (ptest), ultimate displacement (δtest), failure modes, and the load–slip curves for each tested specimen are the main obtained results from the carried out experimental push-out tests. the obtained results will be presented and discussed in details in this section. to obtain the bearing capacity of one connector (ptest), the ultimate load carried by the two shear connectors placed on both sides (flanges) of the heb160 steel section is divided by the number of connectors (which is two in this case). δtest is the maximum slip recorded between the steel and concrete measured at the connector level. figure 5: experimental test results f. boursas et alii, frattura ed integrità strutturale, 57 (2021) 24-39; doi: 10.3221/igf-esis.57.03 30 the obtained relationship between the applied load and the recorded interfacial slip for all tested specimens are shown in fig. (5). it is easy to notice from the obtained results listed in tab. 4 that there is a privilege orientation for which the shear capacity of an i-shaped connector is significantly larger than that of all other tested orientations in both concrete classes. on the other hand, with the increase of the concrete class from c20/25 to c30/37, it is observed that the ultimate load (ptest) in configuration p01 increases by 14.28 %, in configuration p02 increases by 21.17 %, in configuration p03 increases by 11.78 %, and in configuration, p04 increases by 23.88 %. however, this increase of resistance is companied by a loss in ductility especially in the configurations p03 and p04. concrete class positions shear ultimate loads (kn) increment of ultimate load refer to p01 configuration. failure mode c20/25 p01 84 / concrete crushing p02 78.9 -0.06 % concrete crushing p03 121 44.05 % concrete crushing p04 82.5 -0.01 % concrete crushing c30/37 p01 96 / concrete crushing p02 95.6 -0.00 % shearing of the connector p03 135.25 40.89 % concrete crushing p04 102.2 0.06 % concrete crushing table 4: shear ultimate loads and failure modes. the obtained test results clearly show that the i-shaped connector exhibits a ductile behavior (δtest > 6 mm) in all the tested configurations. it is noticed from the analysis of the test results obtained with c20/25 concrete class that the maximum slip δtest decreases by 8.95 % with the change of connector orientation from the configuration p01 for which δtest = 13.28 mm to the configuration p03 for which δtest = 12.23 mm. a decrease of slip by 8.65 % can also be noticed with the change of connector orientation from the configuration p01 to p04. the decrease of ductility is more remarkable with c30/37 concrete class compared to the maximum slip obtained with the c20/25 concrete class, especially in p03 and p04 configurations. the observed failure modes for the tested specimens can be classified into two types, the first one is the cracking and crushing of concrete slab, while the second is the shearing of connector with a remarkable cracking of the surrounding concrete. the first failure mode has been observed in all specimens with c20/25 concrete class as shown in fig. (6.a). the shearing of connector was noticed in the connector orientation p02 with c30/37 concrete class. a form of shear cutting in the connector’s web embedded inside the concrete as shown in fig. (6.b). (a) (b) figure 6: failure modes. (a) concrete crushing, (b) shearing of the connector. f. boursas et alii, frattura ed integrità strutturale, 57 (2021) 24-39; doi: 10.3221/igf-esis.57.03 31 finite element modelling n this study, the finite element software abaqus [22] was used to simulate the non-linear push-out test. in this modelling, the composite beam is composed of an heb160 steel beam and a reinforced concrete slab of dimensions (36 cm × 32 cm × 12 cm) connected by means of an ipe120 shear connector. in composite beams, any component (concrete slab, steel beam, rebars and shear connectors) can significantly influence the load-slip behavior of the shear connection. in order to investigate in details, the interaction mechanism arising between the steel beam and the concrete core, a 3d fe model has been established, in which, the interaction stresses arising between the i-shaped connector and the surrounding concrete were taken into account. in this model, the geometrical, material and contact nonlinearities were considered. material constitutive models the nonlinear compressive and tensile stress-strain behavior of concrete is presented by an equivalent uniaxial stress-strain curve as shown in fig. (7). the concrete damage plasticity model available in abaqus material library was adopted to model the non-elastic behavior of reinforced concrete. this material model is suitable for modelling concrete failure and other quasi-brittle materials with strength degradation. the material dilation angle (ψ) was taken 30.5, and the eccentricity (ε) was taken 0.1. the ratio of biaxial compressive strength to uniaxial compressive strength (fb0/fc0) was taken as 1.16, and tensile-to-compressive meridian ratio (k) is 0.667. (a) (b) figure 7: stress-strain relationship for concrete [23]. (a) compression, (b) tension. figure 8: stress-strain relationship stress for i connectors, structural and reinforcement steel [24] geometry and mesh due to the symmetry of geometry, loading and boundary conditions, only one-half of the push-out test specimen was modelled as shown in fig. (9). the numerical model of the one-half push-out specimen consists of five components, which are, one concrete slab, one half of steel beam, one i-shaped connector, reinforcement rebars and a rigid base. i f. boursas et alii, frattura ed integrità strutturale, 57 (2021) 24-39; doi: 10.3221/igf-esis.57.03 32 figure 9: push-out test specimen model each component was modelled as an independent part. the concrete slab, the steel beam and the i-shaped connector was modelled using the 8-node linear brick element with reduced integration “c3d8r” available in abaqus library [22]. this brick element can be efficiently used in nonlinear analysis including plasticity, contact, large displacements and failure. the rebar part was modelled by using the truss element t3d2, which is, a linear truss element with two nodes. the rigid base is modelled by using the discrete rigid element r3d4. in order to reduce the computational effort, a finer mesh was applied at the connector and the surrounding concrete region while, a reasonable mesh was applied to the rest of the model. in order to validate the finite element mesh of the numerical model, a mesh refinement convergence test is conducted to determine the required mesh size. an example of the finite element mesh of the modelled specimen is presented in fig. (10). figure 10: finite element mesh of the specimen interactions and constraint conditions the whole model was made by assembly of the five parts in their proper location. appropriate constraints were used to describe the different interactions between components. as shown in fig. (11), the bottom surface of the i-shaped f. boursas et alii, frattura ed integrità strutturale, 57 (2021) 24-39; doi: 10.3221/igf-esis.57.03 33 connector’s flange is tied to the top flange surface of steel beam. according to pushout test procedure proposed by eurocode 4 the steel beam flange surface that is in contact with the concrete slab is greased to reduce friction resistance between them and testing only the shear resistance of the connector, in finite elements analysis, a frictionless contact interaction was applied to the steel flange and concrete slab interface. the contact between concrete and the i-shaped connector was modelled through a contact interaction with tangential friction applied at the concrete and i-shaped connector interface. the friction coefficient value of 0.20 is adopted. the embedded-region constraint was applied to the rebars located inside the concrete slab as shown in fig. (11). frictionless contact interaction was applied at the interface between the concrete slab and the rigid base. (a) (b) (c) figure 11: interaction and constrain conditions of the specimen. (a) interaction contact, (b) rebars embedded constraint and (c) tie constraint loading and boundary conditions the symmetric boundary condition (bc) was applied to the heb160 web’s transverse section surface at the symmetry plane of the specimen as shown in fig. (9). the rigid base was assumed to be fixed, so all dofs of the reference point of the rigid base were restrained. in this analysis, the displacement control method was adopted in which a uniform displacement is applied to the top transverse section surface of the steel beam as shown in fig. (12). the slip was measured as the relative displacement between the nodes on the steel flange of the i-shaped connector. the acting load was measured as the total reaction acting on the loading surface. figure 12: symmetry and loading of the specimen. f. boursas et alii, frattura ed integrità strutturale, 57 (2021) 24-39; doi: 10.3221/igf-esis.57.03 34 finite element results the obtained numerical results shown in fig. (13) were compared against the experimental test results. the comparison in tab. (5) shows that the 3d finite element model established during this study is able to predict the ultimate shear capacity and the load-slip curve for the push-out test with i-shaped connectors efficiently. figure 13: finite element results. it is shown that in the linear regime the finite element results are in good agreement with the test results and slightly diverge from the test results in the nonlinear regime for the tests p03 and p04. however, the numerical curves take the form of plastic flow and diverge from the experimental curves after reaching the ultimate load for all specimens. this behavior can be explained by the adopted steel material behavior in the finite element model that was a bi-linear elastic perfectly plastic behavior. tab. (5) shows the experimental load capacity and maximum slip results versus finite elements analysis results. according to the results listed in tab. (5), the mean values of the ratios (ptest/pfe) and (δtest/δfe) are 0.957 and 0.988 respectively. stress and deformation distributions have been recorded. for instance, the stress distribution on the shear connector and on the whole model are shown in fig. (14) for the models p01 and p03. (a) (b) figure 14: stress distribution and deformations. (a) stress distribution and deformations in p01, (b) stress distribution and deformations in p03. f. boursas et alii, frattura ed integrità strutturale, 57 (2021) 24-39; doi: 10.3221/igf-esis.57.03 35 positions specimens experimental results fe results comparison vertical slip δtest (mm) ultimate load ptest (kn) vertical slip δfe (mm) ultimate load ptest (kn) δtest/δfe ptest/pfe p01 p01-a 13.28 84 13.16 84.38 1.01 1.00 p01-b 10.2 96 9.17 102.35 1.11 0.94 p02 p02-a 13.1 78.9 13.1 85.46 1.00 0.92 p02-b 8.84 95.6 9.24 99.34 0.96 0.96 p03 p03-a 12.23 121 11.58 123.7 1.06 0.98 p03-b 7.28 135.25 7.54 142.58 0.97 0.95 p04 p04-a 12.13 82.5 12.73 85 0.95 0.97 p04-b 7.08 102.2 8.29 108.37 0.85 0.94 table 5: comparison between experimental results fe results. parametric study n order to accomplish this study, after validating the established 3d finite elements model, certain parameters related to the push-out test such as concrete strength, connector ‘s steel grade, reinforcements, height and length of the connector are investigated by means of the finite elements model. figure 15: evaluated parameters. effect of the concrete compressive strength three compressive strengths of concrete which are 20, 30 and 40 mpa are investigated in this study. it is observed that the increase in the compressive strength of the slab’s concrete provides a considerable increase in the bearing capacity of the connector as confirmed by the experimental results, see tab. (4). the increase of the compressive strength of concrete from 20 mpa to 30 mpa provides an increase in the ultimate load capacity of the i-shaped connector from 123.70 kn to 142.58 kn which is approximately more than 15.26% gain in the load capacity. when the concrete strength is further increased from 30 mpa to 40 mpa, the ultimate load capacity of i-shape connector increased by 16.52% to attain 166.14 kn. however, the gain in the load capacity is accompanied by a considerable loss in ductility. the increase of the compressive strength of concrete from 20 mpa to 30 mpa decreases the maximum slip from 11.58 mm to 7.55 mm which corresponds to a loss of 34.80%. when the concrete strength is further increased from 30 mpa to 40 mpa, the maximum slip decreases by 17.35% as shown in fig. (16). effect of the steel grade in order to evaluate the influence of the connector’s steel grade on the ultimate load capacity of the i-shaped connector, three steel grades which are s235, s275 and s355 were investigated. fig. (17) presents the load-slip curves of the i-shaped connector in configuration p03 with the three steel grades. it can be seen that the increase of the connector’s steel grade provides a non-significative increase in the connector’s load capacity. this increase of the load capacity is also accompanied by a non-significative decrease in the connector’s ductility. i f. boursas et alii, frattura ed integrità strutturale, 57 (2021) 24-39; doi: 10.3221/igf-esis.57.03 36 figure 16: effect of the concrete compressive strength figure 17: effect of connectors steel grade. effect of the height the influence of the height of the i-shaped connector on the ultimate load capacity is shown in fig. (18). by increasing the connector’s height from 60 mm up to 70 mm, a considerable increase of the ultimate load from 123.70 kn up to 139.50 kn is attained. this gain represents 12.77% from the initial ultimate load. however, any further increase of the connector’s height does not provide any significant increase of the ultimate load, as shown in fig. (18). it can be easily noticed that an increase of the connector’s height brings a remarkable increase of the connector’s ductility. the maximum slip increases from 11.58 mm to 14.81 mm then to 17.07 mm when the connector’s height increases from 60 mm to 70 mm then to 80 mm respectively, which is a 47.40% increase from the initial slip capacity. f. boursas et alii, frattura ed integrità strutturale, 57 (2021) 24-39; doi: 10.3221/igf-esis.57.03 37 figure 18: effect of height. effect of the length the effect of the connector’s length on the ultimate load capacity is similar to the effect of the connector’s height. increasing the length from 120 mm up to 140 mm leads to an increase of 16% from the initial ultimate load. but when we increase the connector’s length to 140 mm there is an increase of the ultimate load by18%, as shown in fig. (19). however, the increase of the connector’s length results in a slight decrease of ductility, as shown in fig. (19). figure 19: effect of length effect of concrete reinforcement three diameters of reinforcement rebars (φ8, φ 10 and φ 12) were investigated in order to study the influence of this parameter on the ultimate load capacity and ductility of the i-shaped connector. it appears that a slight increase of the f. boursas et alii, frattura ed integrità strutturale, 57 (2021) 24-39; doi: 10.3221/igf-esis.57.03 38 reinforcement rebars diameter yields a considerable increase in both strength and ductility. the ultimate load increased to 137.40 kn and 139.52 kn when using φ10 and φ12 rebars, respectively. at the same time, the maximum interfacial slip attains 13.39 mm and 14.56 mm respectively. figure 19: effect of concrete reinforcement conclusion n this study, the i-shaped shear connector’s behavior with different orientations in the concrete slab was investigated. several push-out tests and finite elements modelling were conducted, in which, several influential parameters were studied. a good agreement was obtained between the finite elements’ analysis and experimental tests which gives high reliability to the presented numerical parametric study. the obtained results show that there is a privilege orientation for which the bearing capacity of an i-shaped shear connector is significantly higher than that of all other tested orientations in terms of the ultimate load capacity and interfacial slip. in this orientation, named by p03 in this study, the web surface of the i-shaped connector is parallel to the web surface of the steel beam while the flanges of the connector and the steel beam are perpendicular. thus, the parametric study was interested by studying the effect of material and geometric parameters on the connector’s behavior in this particular orientation. according to the experimental and numerical parametric study we can conclude as follows:  the orientation of the i-shaped connector has a significant influence on the shearing load capacity.  the i-shaped shear connectors exhibit sufficient ductility in all the tested orientations.  failure was dominated by the concrete crushing failure mode.  the steel grade of the i-shaped connector has a non-significative influence on the connector’s load capacity and ductility.  increasing the concrete strength significantly increases the connector’s load capacity. this increase of the load capacity is accompanied by a significant decrease of ductility.  increasing the rebars diameter, the height and the length of the i-shaped connector provides an increase of the connector’s load capacity. there is a threshold from which the increasing of the rebars diameter, the height and the length of the i-shaped connector is non-significative. i f. boursas et alii, frattura ed integrità strutturale, 57 (2021) 24-39; doi: 10.3221/igf-esis.57.03 39 references [1] cen (european commitee for standardization). (2004). eurocode 4 design of composite steel and concrete structures part 1.1: general rules and rules for buildings eurocode. [2] rankovi, s. and drenic, d. (2002). static strength of the shear connectors in steel-concrete composite beams regulations and research analysis, facta universitatis, 2(4), pp. 251–259. [3] loubna, b. (2005). contribution à l’étude expérimentale et théorique de structures mixtes acier-béton assemblées par collage. université de reims champagne ardenne, ecole doctorale sciences technologies santé. [4] mansouri, i., shariati, m., safa, m., ibrahim, z., tahir, m.m., petković, d. (2019). analysis of influential factors for predicting the shear strength of a v-shaped angle shear connector in composite beams using an adaptive neuro-fuzzy technique, j. intell. manuf., 30(3), pp. 1247–1257, doi: 10.1007/s10845-017-1306-6. [5] kim, y.h., cho, h., lee, s., yoon, s.j. (2011). experimental and analytical investigations on the hat shaped shear connector in the steel-concrete composite flexural member, int. j. steel struct., 11(1), pp. 99–107, doi: 10.1007/s13296-011-1009-3. [6] mazoz, a., benanane, a., titoum, m. (2014). push-out tests on a new shear connector of i-shape, int. j. steel struct., 13(3), pp. 519–28, doi: 10.1007/s13296-013-3011-4. [7] titoum, m., mazoz, a., benanane, a., ouinas, d. (2016). experimental study and finite element modelling of push-out tests on a new shear connector of i-shape, adv. steel constr., 12(4), pp. 487–506, doi: 10.18057/ijasc.2016.12.4.7. [8] liu, x., bradford, m.a., chen, q.j., ban, h. (2016). finite element modelling of steel-concrete composite beams with high-strength friction-grip bolt shear connectors, finite elem. anal. des., 108, pp. 54–65, doi: 10.1016/j.finel.2015.09.004. [9] baharom, s., hosseinpour, e., badaruzzaman, w.h.w. (2018).hollow steel tube versus web opening as shear connectors in hollow steel tube versus web opening as shear connectors in slim-floor steel beam. 13th international conference on steel, space and composite structure, perth, australia. [10] nasrollahi, s., maleki, s., shariati, m., marto, a., khorami, m. (2018). investigation of pipe shear connectors using push out test, steel compos. struct., 27(5), pp. 537–543, doi: 10.12989/scs.2018.27.5.537. [11] fragiacomo, m., ceccotti, a. (2006). long-term behavior of timber–concrete composite beams. i: finite element modeling and validation, j. struct. eng., 132(1), pp. 13–22, doi: 10.1061/(asce)0733-9445(2006)132:1(13). [12] queiroz, f.d., vellasco, p.c.g.s., nethercot, d.a. (2007). finite element modelling of composite beams with full and partial shear connection, j. constr. steel res., 63(4), pp. 505–521, doi: 10.1016/j.jcsr.2006.06.003. [13] nguyen, h.t., kim, s.e. (2009). finite element modeling of push-out tests for large stud shear connectors, j. constr. steel res., 65(10–11), pp. 1909–1920, doi: 10.1016/j.jcsr.2009.06.010. [14] xu, c., sugiura, k., wu, c., su, q. (2012). parametrical static analysis on group studs with typical push-out tests, j. constr. steel res., 72, pp. 84–96, doi: 10.1016/j.jcsr.2011.10.029. [15] qureshi, j., lam, d., ye, j. (2011). effect of shear connector spacing and layout on the shear connector capacity in composite beams, j. constr. steel res., 67(4), pp. 706–719, doi: 10.1016/j.jcsr.2010.11.009. [16] bouchair, a., bujnak, j., duratna, p., lachal, a. (2012). modeling of the steel-concrete push-out test, procedia eng., 40, pp. 102–107, doi: 10.1016/j.proeng.2012.07.063. [17] han, q., wang, y., xu, j., xing, y. (2015). static behavior of stud shear connectors in elastic concrete-steel composite beams, j. constr. steel res., 113, pp. 115–126, doi: 10.1016/j.jcsr.2015.06.006. [18] paknahad, m., shariati, m., sedghi, y., bazzaz, m., khorami, m. (2018). shear capacity equation for channel shear connectors in steel-concrete composite beams, steel compos. struct., 28(4), pp. 483–494, doi: 10.12989/scs.2018.28.4.483. [19] mazoz, a. (2015). développement du système de connexion dans les poutres mixtes (acier-béton), thèse de doctorat, université abdelhamid ibn badis mostaganem. [20] européenne, n. (2016). metallic materials — tensile testing bsi standards publication en iso 6892-1. [21] festa, j., dreux, g. (2012). nouveau guide du béton et de ses constituants, eyrolles éditions, paris-france. [22] duval, a., al-akhras, h., maurin, f., elguedj, t., duval, a., al-akhras, h., maurin, f., elguedj, t. (2014). abaqus/cae 6.14 user’s manual, dassault systémes inc. provid. ri, usa, iv(june), pp. 1–6. [23] norme européenne, n. française. (2005). eurocode 2 calcul des structures en béton partie 1-1: règles générales et règles pour les bâtiments. [24] (cen), e.c. for s. (2005). eurocode 3: design of steel structures part 1-1 general structure rules. microsoft word numero_30_art_36 m. n. james, frattura ed integrità strutturale, 30 (2014) 293-303; doi: 10.3221/igf-esis.30.36 293 focussed on: fracture and structural integrity related issues fracture-safe and fatigue-reliable structures m. n. james university of plymouth, school of marine science & engineering, plymouth, pl4 8aa, england nelson mandela metropolitan university, department of mechanical engineering, port elizabeth, south africa mjames@plymouth.ac.uk abstract. learning from history is, by popular account, something at which human beings are not particularly good; george bernard shaw having stated that “we learn from history that we learn nothing from history”, while the spanish philosopher george santayana apparently claimed that “those who cannot learn from history are doomed to repeat it”.1 this is certainly true in the field of structural integrity where, some 150 years after the first full-scale structural fatigue tests were carried out, fracture-safe and fatigue-reliable design can be achieved to a statistical probability in complex and sophisticated structures, such as aircraft. alongside this, however, failures of large, and expensive, welded structures can still occur from such simple causes as inadequate communication, and lack of awareness of the importance of the design of structural details to the overall fatigue life and failure. this paper considers several examples of such difficulties in the context of the development of fatigue design philosophies and the success or otherwise of learning from the history of failures. keywords. structural failure; fatigue-reliable; fracture-safe; fatigue design; design failure. introduction ome 170 years after the term fatigue2 was first coined and 150 years after the first full-scale structural fatigue tests were carried out, many large and expensive structures still experience very early fracture compared with their design fatigue lives. this paper will explore some of the reasons why this can occur with nominally well-designed and fabricated structures and draws some conclusions regarding the lessons to be learnt and how these might be disseminated to working engineers. this will be done using, as the main example, two large rotating shells with a replacement capital cost of some $20m, which should have been designed to provide a service fatigue life of 20 years, and which experienced severe shell fracture within 5-7 months of commencing service. this example is instructive, as at first sight it seems a fairly straightforward case of inadequate fatigue design, while on closer inspection it became clear that a number of interacting factors were involved which made a replace/repair decision 1 at least according to the web site age-of-the-sage.org, see the web page http://www.age-of-the-sage.org/philosophy/history/learning_from_history.html 2 the origin of the term ‘fatigue’ is uncertain; some papers have ascribed the first use of the term fatigue to j. v. poncelet in his book introduction à la mécanique industrielle: physique ou expérimentale published in paris in 1839 (or to lectures given by him around that time). this volume appears to rather discuss the work and fatigue of ‘living motors’, i.e. horses and human beings, rather than mechanical components under cyclic loads. neither do the seminal papers by c. hood [1] or w. j. m. rankine [2] appear to use the term. s m. n. james, frattura ed integrità strutturale, 30 (2014) 293-303; doi: 10.3221/igf-esis.30.36 294 rather difficult and which complicated the design of a replacement. these factors mainly derived from inadequate communication between the various parties, and included:  imprecise specification of the operating conditions and design codes by the owner of the process technology;  internal fixtures in high stress areas that caused high local stress concentrations and which were, in the main, eventually found to be superfluous;  inadequate consideration of the variable amplitude and biaxial stresses arising from ovality induced in the shell during rotation;  lack of a detailed finite element analysis of the internal fixtures;  unauthorised alloy substitution for some parts of the internal design fixtures that led to an increased chance of weld defects, especially hydrogen cracking;  poor weld documentation and poorly controlled preheat, which led to increased residual stresses and weld defects;  inadequate consideration of the maintenance requirements in terms of the duty cycle of the composters, which led to excessive erosion of the shell occurring. the ultimate outcome from these interacting aspects of the failure was the instigation of legal proceedings that continued for some 5 years and cost a similar amount to the original capital cost, by which time repair of the structures had been made impossible through shell erosion. all of these issues could have been easily avoided had the various parties understood and shared more information regarding the requirements of the process for which the structures were designed, fatigue cracking, weld design and the influences of a corrosive environment. the paper will also discuss the historical background to the development of fracture-safe and fatigue-reliable structures to set in context the main tenet of the paper, namely that learning from history is extremely good in certain industrial sectors and surprisingly poor in others. historical background to fatigue ailure of components and structures under varying or cyclic loading patterns has been discussed in the literature since at least 1843, when rankine delivered a paper to the institution of civil engineers in london entitled “on the causes of the unexpected breakage of the journals of railway axles; and on the means of preventing such accidents by observing the law of continuity in their construction” [2]. this was one of the first recorded papers which used the term “gradual deterioration” to describe failures of rotating or reciprocating components that occurred under cyclic loading after a period of time in service. subsequently, in a series of papers between 1858 and 1870 wöhler established several fundamental principles of the safe-life, or s-n, approach to fatigue design [e.g. 3, 4]. these included acquiring s-n data from full-scale tests of railway axles (reference 3, whose title translates as “report about the experiments, which have been carried out with instruments to measure the tension and the torsion of the axles of carriages of the koeniglichen niederschlesischen-maerkischen railway during travel”), and determining the effect of a notch on fatigue life (reference 4, whose title is “about experiments concerning the cohesiveness of iron and steel”). wöhler observed the occurrence of a fatigue limit stress for steels at lives > 5 x 105 cycles of loading and also explored the effect of a notch on the s-n curve. the s-n philosophy is still widely used today for component fatigue design, albeit with a much more sophisticated understanding of interactions among the service environment (temperature, chemistry, loads and displacements), materials (composition, processing and microstructure), and their static and dynamic performance. fig. 1 shows some of the fatigue data reported by wöhler in reference [4]. early examples of failure by fatigue and fracture were strongly influenced by the low metallurgical quality of cast iron and puddled or wrought steel [5]; the puddling furnace was an open-hearth metal-making technology used to create wrought iron or steel from the pig iron produced in a blast furnace. the major advantage of a puddling furnace was in keeping the impurities of the fuel separated from the pig iron charge. puddled steel still contained, however, a high level of elongated manganese sulphide (mns) inclusions (which are then crack-like defects) as shown below in fig. 2 and 3. early steels also exhibited low notched toughness and a high ductile-to-brittle transition temperature, meaning that failure occurred in an apparently brittle (rock candy) fashion in the presence of relatively small fatigue cracks or crack-like defects even at moderate temperatures (e.g. as illustrated in fig. 4). this observation of apparently brittle fracture in an alloy that showed ductile tensile behaviour led to a longstanding controversy over the mechanism of fatigue cracking; the erroneous crystallinity theory advanced by hood [1] (the concept that after a certain number of load repetitions the material became f m. n. james, frattura ed integrità strutturale, 30 (2014) 293-303; doi: 10.3221/igf-esis.30.36 295 ‘tired’ of carrying the load and became crystalline in nature) versus the correct progressive fissuring mechanism proposed by rankine [2]. the notion of the material having ‘tired’ of carrying the load led to the term ‘fatigue’ being coined to describe failures under cyclic loading. the charpy notched bar impact test was subsequently developed as a simple means of assessing the notched toughness of steels. figure 1: fatigue data reported by wöhler in 1870 [4] from s-n tests on notched and unnotched iron specimens. whilst the crystallinity theory was completely discredited by 1903 (through microscopic observations of crack initiation and growth via ‘persistent’ slip band cracking made by humphreys and ewing [6]) the term ‘fatigue’ has remained in use to the present day to describe the process of crack initiation and/or growth under cyclic loading. figure 2: micrograph of puddled steel circa 1880 showing sharp elongated mns inclusions. the two phenomena of fatigue and fracture remain of prime concern in ensuring structural integrity and reliability, even though the last 150 years have seen an enormous world-wide effort devoted to understanding, explaining and predicting failure from crack growth and fracture. a strong focus on fracture-safe and fatigue-reliable design is required by the sophistication and complexity of modern engineering components and structures, and their increasingly arduous service requirements. the term ‘fracture-safe and fatigue-reliable design’ was apparently first used by pellini in guidelines intended for steel structures [7]. m. n. james, frattura ed integrità strutturale, 30 (2014) 293-303; doi: 10.3221/igf-esis.30.36 296 figure 3: confocal laser scanning microscope image of a sharp crack-like mns inclusion in puddled steel. figure 4: example of brittle intergranular (rock candy) fracture during fatigue loading in cast steel. the particular example shown is due to aluminium nitride embrittlement. fracture control and fatigue design strategies atigue is a process of crack initiation and growth by microplasticity in metallic alloys or, more generally, a nonlinear constitutive stress-strain (σ-ε) response leading to hysteresis in the cyclic σ-ε curve and an associated input of energy into the material via damage mechanisms (in the case of metallic alloys this is the movement and interaction of dislocations in the crystal lattice). fracture is sudden, catastrophic collapse under either an applied static load (certain cases), a steadily increasing load or as the final stage in the fatigue process. the defining characteristics of these two phenomena are often that:  applied loads are much less than general yield (i.e. plasticity is highly localised to cracks or sharp defects)  there is little prior evidence of imminent failure, i.e. the overall structure is still behaving in a linear elastic fashion. in this context, however, it should be noted that there are now standardised processes for structural design which explicitly consider the possibility of failure by the conjoint mechanisms of plastic collapse and fast fracture [e.g. 8]. this two-parameter approach to fracture control uses a failure assessment diagram (fad), and has been driven by the use of high toughness metallic alloys often operating at high temperatures. it has been made possible through a detailed f m. n. james, frattura ed integrità strutturale, 30 (2014) 293-303; doi: 10.3221/igf-esis.30.36 297 understanding of the response of materials to loading and by the development of fracture mechanics, which is the branch of applied mechanics dealing the behaviour of cracked bodies. fracture control and fatigue design strategies have developed alongside greatly enhanced analytical, numerical and experimental techniques to understand and characterise the response and behaviour of components and structures subject to applied loads and displacements. a brief outline of the historical development of these fracture control strategies is also given, as a precursor to considering the successes and failures in “learning from history”. safe-life design this philosophy is underpinned firstly, by experimental testing to establish the stress-life or strain-life (s-n) curve for the material under conditions that match those anticipated in service. as noted above, the first data of this type was reported by wöhler who was the locomotive superintendent of the royal lower silesian railways in the second half of the 19th century [3, 4]. the second important requirement is the application of a so-called ‘factor of safety’ to ensure that the design level of stress or strain experienced by the component or structure is significantly less than the value from the s-n curve corresponding to the required cyclic fatigue life. this parameter is actually a ‘factor of uncertainty’ reflecting imprecise data on:  material properties and condition (e.g. heat treatment, notches, surface damage)  service environment and conditions  applied loads and displacements early structural testing of fatigue loaded structures often relied on simply factoring the measured yield, proof or tensile strength of the material, e.g. by loading the wings of wooden framed aircraft with bags of lead shot until fracture occurred. interestingly, this technique is still widely applied to the wings of homebuilt aircraft, and it is worth noting that this simple approach works best with composite structural materials, such as wood, where the fatigue strength can be a high percentage (≈70-80%) of the tensile strength at lives ~106 cycles [9]. ferritic alloys tend to show a ‘fatigue limit’ stress where the sustainable stress becomes asymptotic with the x-axis for lives typically greater than about 2 x 106 cycles. this is related to pinning of dislocations in the crystal lattice by interstitial atoms, such as carbon, nitrogen or boron. nonferrous alloys do not exhibit this fatigue limit behaviour and it is usual to refer to an ‘endurance limit’ stress for these alloys that is applicable to a specific cyclic life. the s-n approach is still widely and successfully used on such important components as crankshafts and connecting rods. the key requirement is that the conditions used in fatigue testing closely match those of the component in service. it is now routine practice in several industries to use computer-controlled testing applying a load spectrum that replicates the measured service load spectrum. failures can still occur when there has been:  incorrect assessment of: o service loads (including incorrect assessment of different load state contributions) o environment o vibration or resonant frequency problems  implementation of new materials/technology with a priori unforeseen or unknowable consequences  unanticipated changes in: o usage (loads or type of service duty) o environment (corrosion and temperature) o surface condition (including inadvertent damage)  human error o inadequate communication amongst relevant parties o inadequate fabrication/machining o inadequate inspection/maintenance fail-safe design this uses the same basic philosophy as safe-life design but takes account of the possibility of cracking of critical components. these are defined as parts whose failure would lead to catastrophic loss of the structure, e.g. wing or tail plane spars in an aircraft. widespread manufacture and operation of aircraft with metallic structures, and a consequent relatively high number of failures was the main driving force behind this advance. the new developments included:  redundant load paths in critical areas which can redistribute the load in the event of a partial failure of the structure and/or act as crack arrestors m. n. james, frattura ed integrità strutturale, 30 (2014) 293-303; doi: 10.3221/igf-esis.30.36 298  explicit consideration of inspection intervals at the design stage  identification of critical areas in the structure via full-scale testing  feed-back into design from failure analysis  codified design procedures the success of this type of approach, when coupled with the use of fracture mechanics and defect-tolerance, can be illustrated by contrasting the consequences of fatigue cracking and subsequent structural damage in two famous aircraft failures:  de havilland comet 1 in 1954, where growth of a fatigue crack led to rupture of the fuselage and complete break-up of the aircraft in the air through explosive decompression at an altitude of about 35,000 feet [10, 11, 12].  aloha airlines boeing 737 in 1988, in which a fatigue crack caused an explosive decompression and structural failure at an altitude of 24,000 feet [11]. according to the official us national transportation safety board report [13], approximately 5.5 m of the pressure cabin skin and structure aft of the cabin entrance door and above the passenger floor line separated from the aircraft during flight. the flight crew made an emergency descent and landed the aeroplane safely. the fail-safe approach is attempting to design ‘defect-tolerant’ structures, although prior to the development of fracture mechanics it was not possible to predict crack growth rates or remnant life in the presence of a defect. fracture mechanics and the quantification of defect-tolerance the development of fracture mechanics was spurred by some notable failures that occurred over the period 1940 to 1980. these ranged across ships, aircraft, bridges and pressure vessels. several useful reviews of the development of defect tolerant methodologies in these various industries are available, including the us air force handbook for damage tolerant design [14] and a review of strategies to combat aircraft structural failures by brot [15]. the basic concepts in fracture mechanics are that:  crack tip stresses, strains or displacements reach a critical value (which under a specific set of conditions is represented by a material constant value of resistance to crack growth, the fracture toughness).  the rate of energy absorption in incremental crack advance is < the rate of energy supplied by release through crack growth of the stored strain energy in the structure. a critical factor in fast fracture is that the presence of a crack or sharp crack-like defect induces a triaxial stress field near the crack tip. this makes plastic deformation more difficult and increases the constraint on plastic flow, particularly in thicker sections of material. extensive work in the period between 1950-1975 led to the definition of parameters to characterise crack tip fields, and to the development of standardised fracture toughness tests which give ‘material constant’ values (under specified conditions) for the resistance to crack growth of a material [16]. the three usual characterising parameters are the stress intensity factor k, the crack tip opening displacement cod, and the j-integral. k is an elastic parameter which characterises critical and subcritical crack growth under conditions of macroscopically elastic behaviour in a cracked body, i.e. constrained and limited plasticity. the j-integral is a nonlinear elastic parameter based on energy integration along a path around the crack tip, which has been shown to characterise macroscopically elastic-plastic behaviour. cod is a parameter which explicitly considers the existence of extensive plasticity at the crack tip. current codes for the engineering assessment of criticality of defects in structures [8] allow for use of any of the three, depending on the level of plasticity experienced during fracture. the codes also consider a twoparameter failure mode where the possibilities of fracture and plastic collapse are assessed independently and the probability of failure is then plotted on a failure assessment diagram (fad). work in the 1960’s established that, in a similar manner that k characterises the onset of fracture in the presence of a ‘critical’ crack, the range of the applied stress intensity factor δk characterised the growth of stable cracks under cyclic loading, i.e. ‘subcritical’ cracks. for the first time, quantitative predictions of remnant life were possible once a crack was detected. thus defect-tolerant design involves living with defects and an explicit acceptance that manufacturing and fabrication processes introduce cracks or crack-like defects so that a structure enters service in a ‘flawed’ state. the steps in the procedure generally include:  size the initial defect population on service entry via ndt (perhaps coupled with proof testing to establish a possible maximum size of defect that could be present but has not been detected)  perform a fracture mechanics based life assessment  set inspection intervals and the level of inspection required m. n. james, frattura ed integrità strutturale, 30 (2014) 293-303; doi: 10.3221/igf-esis.30.36 299  this procedure requires fracture mechanics based crack growth rate data and a k-calibration for the region of interest in the structure or component, plus knowledge of an appropriate fracture toughness parameter. fea may be necessary to establish the stresses present in the region of interest  extensive full-scale structural testing as well as specimen testing may be necessary to assure structural integrity assessment procedures this type of assessment may represent around 5-12% of the capital cost of a sophisticated structure, which is likely to be cost-effective when considering that the percentage of failures associated with crack or fracture problems remains rather high in both engineering structures and in aircraft [17]. table 1 presents information from reference 17 on frequency of occurrence of these failure mechanisms. percentage of failures structures aircraft corrosion 29 16 fatigue 25 55 brittle fracture 16 overload 11 14 high temperature corrosion 7 2 scc/corrosion fatigue/he 6 7 creep 3 wear/abrasion/erosion 3 6 table 1: frequency of failure mechanisms in structures and aircraft [17]. in this table, he represents hydrogen embrittlement and scc stands for stress corrosion cracking. the complexity of structural testing on a modern airliner is indicated in data provided in the boeing airliner magazine [18] which indicates that one hundred hydraulic actuators simultaneously apply flight spectrum loads, measured via 4,300 strain gauges, to a complete 777 airframe. the effectiveness of defect-tolerant design, coupled with this type of testing programme, in reducing the maintenance costs of aircraft has been discussed in a paper by goranson [19] in terms of labour hours expended on maintenance as a function of aircraft type and manufacturing production line position. ‘maintenance labour hours per aircraft’ is a measure of the effectiveness of design improvements resulting from the development and application of durability standards [19]. reference 19 demonstrates significant order of magnitude improvements in maintenance labour costs between first and second generation wide and standard body aircraft. learning from history: success and failure n enormous amount of literature has been published on fatigue design, the application of fracture mechanics to structural design and on failure analysis, and the reliability achieved in the key industrial sectors of transport, energy extraction and generation, and pressure vessels is truly outstanding. the 2011 edition of injury facts published by the us national safety council [20] indicates the average death rate over the ten year period from 1999 to 2008 was 0.01 per 100,000,000 passenger miles for scheduled airlines and 0.05 for rail and buses. in other industrial sectors, particularly where structures are fabricated by welding, there remains a greater potential for cracking problems to occur through fatigue or fracture. reasons for this higher incidence of cracking-related problems include:  insufficient attention to environmental influences  lack of awareness of the importance of detail design to the fatigue performance of major structures (geometry and fabrication practice)  inadequate communication between the various parties involved in major design projects (end user, fabricator, design team and process owner)  insufficient knowledge of the requirements of, and limitations inherent in, current fatigue design codes the remainder of this paper will briefly present some case study examples of the type of problems that occur and their underlying root causes which, very often, include lack of communication and/or inadequate knowledge of the interactions a m. n. james, frattura ed integrità strutturale, 30 (2014) 293-303; doi: 10.3221/igf-esis.30.36 300 amongst materials, welding fabrication and fatigue and fracture. such difficulties may also include misinterpretation of the requirements and constraints imposed by fatigue design codes. failure case studies the main example of such problems in the present paper centres on two large horizontal rotating cylindrical shells in which author was recently involved as an expert witness. each cylindrical shell rotates at 1 rpm, and is around 65 m long and 4.5 m in diameter. there is a significant corrosive distributed load inside the shell at any time as well as a substantial self-weight. the capital cost of the installation was around $24m and the design life was specified to be 20 years against fatigue and corrosion. a large through-shell crack was discovered in one cylinder within 5 months from the date of practical completion whilst the second cylinder experienced similar cracking within a further 2 months. the initial cause of the failure was identified as fatigue cracking from internal detail attachment welds associated with two process-related features: firstly knife features designed to assist the internal process taking place in the cylinders. forty of these features were arranged in an array inside the shell from low stress entry positions to high stress positions further along the cylinder. secondly, wear bars in the form of channel sections were stitch welded to the inside of the shell as the internal process was known to be abrasive. the problem was ascribed to inadequate fatigue design, as the stress concentrating effect of these features, in particular the knives whose geometry created large stiffness transitions at their attachment points, had not been considered in the original stress calculations done for the shells. further design issues were identified as:  transition tapers between shell segments of different thickness (25 mm to 40 mm to 70 mm) that did not meet the requirements for the weld class used in the fatigue life calculations of the circumferential butt welds between cylindrical strakes. there was high concern at this point as further fatigue life calculations indicated that in a free corrosion environment, cracks of the size found (in a very limited survey undertaken of the large number of internal welds) would very quickly lead to further through-shell cracks.  there was a 35 m unsupported span of 25 mm shell in the central region of each cylinder, which a strain gauging and fe analysis showed became oval during rotation and that therefore led to two biaxial stress cycles occurring during each revolution of a shell. short-term remedial measures were accordingly implemented which included removing all the knives except those in low stress areas of the shell along with associated repair work, and a long-term re-design process was commenced along with a court case by the operators. it was interesting that the removal of the bulk of the knives had no discernible effect on the efficacy of the internal process inside the cylinders. this raises the interesting question as to why they had been specified as part of the original design. it was a point of note that the original design specification from the process owners made no mention of a highly corrosive internal environment, although it was clear from operational measurements that such an environment was present in at least some parts of the cylinder. further investigation demonstrated that additional problems had also contributed to the very short observed fatigue life. these included alloy substitution for the knife backing plates, which were fillet welded to the shell, from grade 250 steel (yield strength around 250 mpa) which had been specified for all knives except those in low stress positions, to abrasion resistant steel with typical yield strength of 1,200 mpa. the backing plates of knives in low stress positions had been specified by the designers to be fabricated from abrasion resistant steel with a 0.2% proof strength of around 1,070 mpa. this alloy substitution meant that tightly controlled welding procedures should have been followed by the fabricator in terms of consumables, pre-heat and interpass temperatures. in the event, the procedures followed were not fully documented, while the hardness values and their variation across the weld zone implied that hydrogen cracking was a distinct possibility (this was supported by the observed positions of some cracks at the attachment welds). in addition, solidification cracks were present at some of the detail attachment welds. the final issue of relevance to the ongoing legal argument regarding responsibility, replacement or repair, emerged from semi-annual non-destructive monitoring of sections of the shells, using automated ultrasonic inspection. it became apparent that significant shell abrasion was occurring between the wear bars, although the process design was supposed to lead to an adherent abrasion-resistant coating being deposited on the inner surface of the cylindrical shell between the wear bars. it is interesting to note that annual maintenance of these shells was supposed to occur in a very short shutdown period of about a week. these difficulties could have been avoided through better communication amongst process owner, designers, fabricators and operator and by better familiarity with the requirements of weld design and fabrication for fatigue. the legal argument and associated preparation of reports from a variety of experts eventually pushed the settlement costs of the case to perhaps $40m and extended the time taken for achieving a long-term solution to more than 5 years, by which point the only option was total replacement. m. n. james, frattura ed integrità strutturale, 30 (2014) 293-303; doi: 10.3221/igf-esis.30.36 301 the second example of a large structure that failed because of deficient communication concerns a 40 tonne portal crane operating in a harbour. portal cranes are a form of crane where a large rectangular framework forms a flat-topped arch with a gantry across the top. this whole portal frame can move on tracks via a railway bogie attached under each end. the lifting gear itself is on a small trolley that can move crossways along the horizontal gantry. a driver’s cabin was also positioned under the gantry. in common with many other shipyard gantry cranes, the design consisted of twin overhead box girders rigidly fixed to rectangular box section legs at one end and hinged at the other end to an a-frame structure. the crane failed during service whilst lifting a shipping container, and the mode of failure of the crane was by fracture through a welded joint between the bottom plate and the vertical members of the gantry box girder; this allowed collapse of the horizontal beams to occur over the fixed legs causing the other set of hinged legs to pivot outwards. the net result was that the driver’s cabin was crushed in the collapse. figure 5: fracture surface of the failed box section which led to collapse of the portal crane. the letter ‘o’ indicates the outer edge of the section, where the cracking started. the fracture surface is shown in fig. 5 where the symbol ‘o’ marks the outer side of the leg. the bottom plate of the gantry box girder was 17 mm thick, with the end plate at position ‘o’ being 8 mm thick and the side plates 6.5 mm thick. examination of the failed joint indicated that final fracture had occurred from a pre-existing fatigue crack that had a length of the order of 1 metre at the time of failure. heavy corrosion on the fracture surface indicated that the crack had been growing for a considerable period of time before the final fracture occurred. no unusual defects could be observed at the presumed initiation site for the fatigue cracking. the crane had been in operation for about 7.5 years and had last been inspected by an authorised inspection agency some 2 months before the failure. it was designed as a class 2 crane for medium material handling duty, supposedly intended to work 2,000 hours per annum with a design lifetime of 20 years, i.e. 40,000 hours. at the time of failure the crane had been operating for some 22,515 hours, well inside the design life but with a greater number of hours, pro-rata, for the 7.5 year service life. there were two main points of interest regarding this failure, firstly, that the design should have been done to class 3 for heavy material handling duty, based on the operational service conditions and, secondly, that the inspection methodology had not taken account of the likely mechanism of failure of this portal crane. with respect to the first point, the manufacturer was aware that this crane was intended for harbour operation, moving shipping containers and should have queried the operator’s specification of a class 2 crane for this duty. it is worth noting that more recent designations of crane classes indicate that class 2 equates to 100,000 to 500,000 load cycles while class 3 equates to 500,000 to 2,000,000 load cycles. this crane was definitely in a class 3 environment. lack of clear and full communication between operator and designer regarding the duty cycle and crane class was therefore a prime cause in this failure. with respect to inspection, the existence of a crack around a metre in length at the time of the failure should have implied that it would have been detected at the last inspection which took place 2 months before the failure. speaking with the person who carried out the inspection of the crane, he stated that this critical joint (in terms of structural integrity) had been visually inspected from the ground level. it was also clear that the paint coating on this crane structure was flexible and of high quality; thus it was detached from the steel structure at this positon on other parts of the structure but was o m. n. james, frattura ed integrità strutturale, 30 (2014) 293-303; doi: 10.3221/igf-esis.30.36 302 uncracked. in summary, despite the existence of a metre long fatigue crack at the time of the inspection, the paintwork would have been uncracked and the problem would not have been detected except by detailed inspection of the joint itself. conclusions earning from failure remains highly relevant to achieving fracture-safe and fatigue-reliable design, particularly as the cost-driven requirements for life extension and lower design margins are, to some extent, mutually exclusive. failure analysis therefore forms an important part of the repertoire of successful design and inspection, and should be included in the education and training of engineering students, as well as forming part of the requirement for continuing professional development of practising engineers. further advances in achieving fatigue-reliable and fracturesafe design is, at least in part, contingent on closing the loop between failure analysis and engineering design. this is turn appears likely to require some changes to current undergraduate engineering curricula which focus more on materials as ideal homogeneous, isotropic continua, rather than the reality of polycrystalline media joined by ‘defective’ processes. in such ‘real’ media fatigue and fracture properties reflect the crystaland micro-structure, and hence their heat treatment and manufacturing/fabrication processes, as well as their defect population, surface condition and environment. nonetheless, the advances in engineering capability in reliable probabilistic fatigue and fracture design for complex structures, made over the last 40 years, is a tribute to the combined input from metallurgists and materials scientists, and mechanical and welding engineers. references [1] hood, c., on some peculiar changes in the internal structure of iron, independent of, and subsequent to, the several processes of its manufacture, minutes of the proceedings (institution of civil engineers), 2 issue 1842 (january 1842) 180-181. [2] rankine, w.j.m., on the causes of the unexpected breakage of the journals of railway axles; and on the means of preventing such accidents by observing the law of continuity in their construction, minutes of the proceedings (institution of civil engineers), 2 issue 1843 (january 1843) 105-107. [3] wöhler, a., bericht über die versuche, welche auf der königl. niederschlesisch-märkischen eisenbahn mit apparaten zum messen der biegung und verdrehung von eisenbahnwägen-achsen während der fahrt, angestellt wurden, zeitschrift für bauwesen, 8 (1858) 641-652. [4] wöhler, a., ueber die festigkeits-versuche mit eisen und stahl, zeitschrift für bauwesen, 20 (1870) 73-106. [5] tylecote, r.f., a history of metallurgy, second ed., institute of materials, london, (1992). [6] ewing, j.a., humfrey, j.c.w., the fracture of metals under repeated alternations of stress, philosophical transactions of the royal society, 200 (1903) 241-266. [7] pellini, w.s., guidelines for fracture-safe and fatigue-reliable design of steel structures, british welding research association, cambridge (1983). [8] bs 7910:2013, guide to methods for assessing flaws in metallic structures, third ed., british standards institution, london (2013). [9] watanabe, a., sasaki, y., yamasaki, m., bending fatigue of wood: strain energy-based failure criterion and fatigue life prediction, wood and fiber science, 46 (2) (2014) 1-12. [10] withey, p.a., fatigue failure of the de havilland comet 1, engineering failure analysis, 2 (4) (1997) 47-154. [11] wanhill, r.j.h., milestone case histories in aircraft structural integrity, comprehensive structural integrity, editors-inchief: milne, i., ritchie, r.o., karihaloo, b., elsevier science ltd, (2003) 61-72. [12] swift, t., damage tolerance in pressurized fuselages, new materials and fatigue resistant aircraft design, ed. d. l. simpson, engineering materials advisory services, warley, (1987) 1–77. [13] national transportation safety board, air accident report: aloha airlines, flight 243, boeing 737-200, n73711, near maui, hawaii, april 28, 1988, ntsb/aar-89/03 (1989). [14] handbook for damage tolerant design, us air force structural integrity program, http://www.afgrow.net/ (2014). [15] brot, a., developing strategies to combat threats against the structural integrity of aircraft, proceedings of the 52nd israel annual conference on aerospace sciences, 1, 29 february 1 march 2012, tel-aviv and haifa, israel. l m. n. james, frattura ed integrità strutturale, 30 (2014) 293-303; doi: 10.3221/igf-esis.30.36 303 [16] british standards institution, bs 7448-1:1991 (1991), fracture mechanics toughness tests; method for determination of kic, critical ctod and critical j values of metallic materials. [17] findlay, s.j., harrison, n.d., why aircraft fail, materials today, (november 2002), 18-25. [18] seidel, b., 777 full-scale static and fatigue structural tests, boeing airliner magazine, july-september 1995. [19] goranson, u.g., fatigue issues in aircraft maintenance and repairs, international journal of fatigue, 20 (6) (1997) 413-431. [20] us national safety council, injury facts, 2011 edition, itasca, illinois. accessed 11 august 2014. http://www.nsc.org/documents/injury_facts/injury_facts_2011_w.pdf microsoft word numero_49_art_24_2447 yu. bayandin et alii, frattura ed integrità strutturale, 49 (2019) 243-256; doi: 10.3221/igf-esis.49.24 243 focused on russian mechanics contributions for structural integrity steady plastic wave fronts and scale universality of strain localization in metals and ceramics yuriy bayandin, natalia saveleva, oleg naimark institute of continuous media mechanics ural branch russian academy of sciences, 1, ac. korolev str., perm 614013, russia buv@icmm.ru, https://orcid.org/0000-0002-1824-1940 saveleva@icmm.ru, https://orcid.org/0000-0003-3756-7695 naimark@icmm.ru, https://orcid.org/0000-0001-6537-1177 abstract. mechanisms of structural relaxation are linked with the metastability of nonequilibrium potential of solid with defects and the generation of collective modes of defects responsible for the plastic strain and damage localization. it is shown that spatial-temporal dynamics of collective modes (auto-solitary and blow-up dissipative structures) provide the anomalous relaxation ability of nonlinear system “solid with defects” in the conditions of the specific type of criticality – structural-scaling transition. these modes have the nature of self-similar solutions of evolution equations for damage parameter (defect-induced strain) and represent the “universality class” providing the four power law for a steady plastic front, splitting of an elastoplastic shock wave front, and elastic precursor decay kinetics. widerange constitutive equations reflecting the linkage between defect-induced mechanisms and structural relaxation are used in the numerical simulation for shock wave loading of metals and ceramics in the comparison with experiments. keywords. metals, ceramics; shock waves; self-similarity; defects; spall strength. citation: bayandin, yu., saveleva, n., naimark, o., steady plastic wave fronts and scale universality of strain localization in metals and ceramics, frattura ed integrità strutturale, 49 (2019) 243-256. received: 31.03.2019 accepted: 29.05.2019 published: 01.07.2019 copyright: © 2019 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. introduction hysical mechanisms leading to the fracture of solids are associated with multiscale structural relaxation phenomena caused by mesoscopic defects. the conditions of dynamic high-speed loading of solid with characteristic times close to the relaxation times of structural stresses provide a unique opportunity to study experimentally the kinetics of the processes of failure and deformation in the strain rate range of 103-108 s-1. the deformation and failure of solids under shock wave loading are accompanied by pronounced self-similar regularities. in the experimental investigation of barker [1], swegle and grady [2, 3] the self-similarity of plastic wave fronts in metals and non-metals at strain rates of ~ 105 s-1 was established. modern statements about the mechanisms of deformation and fracture, the experimental possibilities of using the technique of shock wave experiment and high time resolution p http://www.gruppofrattura.it/va/49/2447.mp4 yu. bayandin et alii, frattura ed integrità strutturale, 49 (2019) 243-256; doi: 10.3221/igf-esis.49.24 244 recording systems can be the basis for the development of universal methods for investigating the rheological properties and the destruction of condensed matter due to multiscale structural effects. experimental data on structured plane shock front are presented for a wide class of materials – both metals and nonmetallic materials [2, 3]. the description of mechanical properties of solid over a range of strain rates about 103-108 s-1 due to multiscale mechanisms of structural relaxation mechanisms was proposed in the form of the corresponding constitutive equations of elastoviscoplastic material, as well as the kinetic equations of damage accumulation. this approach is combined with advanced experimental methods that allow the “in-situ” study of relaxation properties and damage accumulation stages (up to failure) using the doppler interferometry. the measurements are realized on time scales close to the times of structural relaxation and reflecting the multilevel kinetics of nucleation and growth of defects, the kinetics of phase transformations in shocked materials. the peculiarity of deformation behavior and the development of failure under intense loadings is the proximity of the times of structural relaxation caused by the kinetics of defects with relaxation times that determine the development of plastic deformation and damage in the material. these features and the nonlinear kinetics of defects play a major role and are linked with key problems of describing the self-similar structure of wave fronts, the relaxation of an elastic precursor and the stages of failure. the investigation of authors [4] is devoted to the development of structural-phenomenological models that take into account the link of structural changes caused by defects [5] and the relaxation properties of metals. in the paper [6] an relaxation model is proposed that reflects the influence of dislocation ensemble kinetics on plastic flow taking into account the dependence of stress relaxation times on the dislocation density parameter according to the activation kinetics. this model, which reflects the kinetics of defects nucleation and growth, allows the quantitative description of shock wave fronts propagation in metals. wide-range constitutive equations of plastic flow (strain rates 103108 s-1) are proposed in [7, 8] for the interpretation of phenomenological assumptions of the mts-ptw model related to the metastability of the thermodynamic potential for solid with defects, the nature of threshold flow stresses in the moderate range of strain rates of 104-105 s-1 and the links the with asymptotic (self-similar) behavior of the plastic wave fronts (the barker-swegle-grady fourth power law). a special part is devoted to the study of the mechanisms of plastic strain localization and the stages of failure as a special type of critical behavior of solid with mesoscopic defects − structural-scaling transitions accompanied by the formation of collective modes of mesoscopic defects. these collective modes have the nature of self-similar solutions for the evolutionary equation of damage kinetics (autosoliton modes in the case of the development of plastic instability and dissipative structures for damage localization) and play the role of “collective variables” that subordinate the spatialtemporal dynamics of the behavior of condensed matter under intense impacts. the formation of self-similar plastic wave fronts [2, 3], instability and damage-failure transitions in metals and ceramics [9-15], kinetic regularities of spall fracture in metals and ceramics [12, 15, 16] can be regarded as the most striking manifestations of such space-time dynamics. the listed effects are studied theoretically [6, 11, 13, 16-22] on the basis of developed continuum models reflecting the role of metastability, collective modes of defects on the relaxation properties of solid and damage-failure transition scenario. numerical simulation results are compared with the data of original experiments [23-28], which are used to identify the parameters and the explanation of the self-similar patterns of solid responses on shock wave loading. present study includes an analysis of the models of elastoplastic materials under shock wave loading taking into account the link between the relaxation mechanisms and the stages of failure with the nonlinear kinetics of mesoscopic defects (microcracks, microshears); identification of model parameters based on the results of dynamic experiments; numerical simulation of plane shock wave loading; verification of the model based on the comparison with the results of original experiments on shock wave loading of samples (metals and ceramics); substantiation on the basis of the results of numerical simulations and experimental data of self-similar propagation of shock wave fronts, the stages of failure in metals and ceramics. with reference to numerical simulation, the behavior of materials under dynamic and shock wave loading, the justification of the model in a wide range of load intensities are related to elastic-plastic transition under the formation of shock wave fronts and damage kinetics. relaxation times he phenomenology of solid with defects contains a description of the thermodynamic state of the system based on the introduction of parameters that characterize the behavior of the ensemble of defects and have the meaning of independent thermodynamic variables. within this approach, irreversible deformation is divided into plastic (dissipative) strain and structural strain, which allows us to separate the physical mechanisms underlying each of them. in t yu. bayandin et alii, frattura ed integrità strutturale, 49 (2019) 243-256; doi: 10.3221/igf-esis.49.24 245 this case, both the processes of defect accumulation and plasticity contribute to stress relaxation. stress relaxation is determined by the nucleation and growth of defects in the shock front and should depend on the effective viscosity, which is the main stress relaxation factor that needs to be identified from experimental data. in the present paper, these parameters depend in general on many thermodynamic variables and can be represented by following the approach of the kinetic theory [29] as 0 0 expi i u            (1) where  is the temperature factor, 0u is the characteristic value of the energy of the interatomic bond rupture, 0 i is the characteristic relaxation times,  is the generalized thermodynamic force, which in the zhurkov model coincides with the applied stresses [12, 14]. in the works of the authors [6, 18], the dependence of the relaxation times on the accumulated strain in the form 2 0exp h h              t (2) where  ,  – the intensity of strains and stresses, respectively, t – yield stress, h , h – the hardening and depletion coefficients, respectively. the generalized thermodynamic force depends on both stress and strain. it is necessary to assume the influence on the relaxation times of only the structural (inelastic) component, for example, in polymers practically coincides with the total strain [18]. the relaxation times for inelastic strain can depend on the accumulated structural strain due to defects [6]. in this case, the energy factor in eqn. (1) is the thermodynamic force, which tends to return the system to the equilibrium state. therefore, the relaxation times will be less than the system is further from the equilibrium state. then eqn. (1) for the model of solid with mesoscopic defects can be represented by 0 0 exp p i i u j e                    σ (3) where ( )j  is the intensity of the tensor argument, σ is the stress tensor,  is the specific free energy,  p is the nonlinear component of the thermodynamic force, which depends only on the inelastic strain p due to the defects. comparison of eqs. (2) and (3) shows that the energy contribution to the relaxation processes is divided into the effect of applied stresses and the structural component, expressed in nonlinear dependence on the characteristic deformations, as a polynomial for the model presented in [1, 9, 18] or as nonlinear dependence of the component of the thermodynamic force due to defects [6]. structural-statistical model of elastoviscoplastic deformation and failure of solid with mesoscopic defects he approach developed by the authors is based on the description of the collective behavior of an ensemble of mesoscopic defects using the effective field theory for multiscale interaction between defects [5, 30]. based on the geometric features of defects as a local changing in the symmetry of the distortion field (deformation) the nucleation and the growth of defects are associated with the contribution of induced by defects strain that is introduced as an additional structural variable. taking into account the interaction of defects within the framework of the developed statistical-thermodynamic model it was possible to propose a continual description of solid with defects to formulate a system of constitutive equations linking the mechanisms of structural relaxation caused by the nucleation and growth of defects with the kinetics of elastic-plastic transitions and the stages of failure. an important point in the describing of mechanical properties of elastoplastic material is the established relationship between the formation of collective modes of defects ensembles related to the kinetics of plastic strain and damage localization. variables for characterizing of defects t yu. bayandin et alii, frattura ed integrità strutturale, 49 (2019) 243-256; doi: 10.3221/igf-esis.49.24 246 (microcracks and microshears) are introduced like dislocation density tensors and are described by symmetric strain tensors in the case of microcracks ik i ks sv v and microshears  1 2ik i k i ks s v l l v  . here v is the unit vector to the base plane of the microcrack or slip plane of the microscopic shear, l is the unit vector in the direction of the shift, s is the volume of the microcrack or the microshear intensity. the averaging of the microscopic tensor iks gives a macroscopic tensor of microcracks (microshears) density (defect density tensor) ik ikp sn (4) which coincides with macroscopic strain induced by defects, where n is the concentration of defects. statistical theory for mesoscopic defects has established various qualitative reactions of the material represented in the nonlinear form of out-of-equilibrium free energy of solid with defects f depending on defect density tensor ikp and the structural-scaling parameter c characterizing the current susceptibility of the material to the nucleation and growth of defects. this parameter represents the ratio of the characteristic structural scales  30~ r r , where r is the distance between the defects, 0r is the average size of the defect nuclei. it was shown that in the intervals *1, 1.3c c         the responses of the material are characteristic for quasi-brittle, ductile and fine grain state, respectively [5, 30]. figure 1: characteristic material reactions on the growth of defects: (a) for microshears, (b) for microcracks the curves in fig. 1 demonstrate the solutions of the equation 0f p   for simple shear (  d  ,  dp p ) and uni-axial strain (  s  ,  sp p )states. metastability for stresses ci  ( cd  for microshears, cs  for microcracks) is a consequence of the effect of the ordering (orientation transition) in the ensemble of defects. the value of stress  cs  for  c  defines the dynamic elastic limit (hel) for quasi-brittle materials. the stress in the metastable area *c    corresponds to the range of the elastic limit for materials with a plastic response (fig. 1) [5]. figure 2: self-similar solutions of the kinetic equation for strain induced by defects: periodic spatial structures ( *  ), autosoliton waves ( *c    ) and localized dissipative structures (  c  ) yu. bayandin et alii, frattura ed integrità strutturale, 49 (2019) 243-256; doi: 10.3221/igf-esis.49.24 247 for the interval of the structural scaling parameter *c    , the metastability regions in the continuum with defects appear. at a certain value of stress, an orientation transition occurs in the defects ensemble that leads to a sharp jump of plastic strain. this transition has a dynamic image (self-similar solution [5]) of an autosoliton wave (fig. 2). the transition through the critical value c is accompanied by the formation of localized blow-up modes (fig. 2), characterized by rapid kinetics of nucleation and growth of defects. the blow-up regime is the final stage of damage accumulation before the transition to fracture. numerical simulation of vanadium behavior under shock-wave loading he mathematical modeling of dynamic loading of materials need the correct formulation of a system of equations that reflects physical and mechanical aspects for carrying out a computational experiment. it is of fundamental reason to establish the connection between the mechanisms of structural relaxation caused by the collective behavior of defects, the kinetics of the elastic-plastic transition and failure to describe the qualitative changes in the deformation reactions of materials with increasing load intensity (strain rates). in this section, a mathematical statement of the collision of two plates is formulated using the constitutive equations taking into account the results of the statistical thermodynamic description of the collective behavior of defects (microshears, microcracks) and transition to elastoviscoplastic response and failure of metals (vanadium) due to defect induced metastability of thermodynamic responses of solid. mechanisms of plasticity and damage localization caused by the collective behavior of ensembles of defects are described taking into account the kinetics of two structural variables: the defect density tensor (defect-induced strain) and the structural-scaling parameter which determines the current susceptibility" of solid to the nucleation and growth of defects. mechanisms of plastic deformation are associated with the kinetics of these two variables (microshears and microcracks density tensor) in the presence of metastability of thermodynamic potential providing a different scenario of defectinduced (structural) relaxation of stress in material. the kinematic relation for solid with defects is given for the strain rates in the frame of small strains     e pε ε εp (5) where eε is the elastic strain, p is the strain induced by defects and pε is the viscoplastic strain. here and below, the tensor quantities are indicated in bold. the thermodynamic description of the behavior of solid with defects is based on the phenomenological representation of the free energy using independent thermodynamic variables eε , p and  . nonlinearity of thermodynamic potential in the helmholtz form reflects the collective behavior of defects [5]. taking into account the introduced thermodynamic variables and following the second law of thermodynamics the dissipative function of an elastoviscoplastic material with defects can be represented in the form                     0p f f ts   ε p p σ (6) where f is the free energy,  is the parameter of structural scaling, s is the entropy, t is the temperature, σ is the total stress. following the onsager's principle the thermodynamic forces can be represented as linear combinations of thermodynamic fluxes                     4 , , a , p pf f   1 2 3 2 a ε a p a p a ε p σ (7) t yu. bayandin et alii, frattura ed integrità strutturale, 49 (2019) 243-256; doi: 10.3221/igf-esis.49.24 248 here , ,1 2 3a a a are positive definite fourth-rank tensors, 4a is a positive kinetic coefficient, which in the general case can depend on all the thermodynamic parameters. stress and strain tensors are represented as the sum of the bulk (index s) and deviator (index d) parts s d  σσ σ (8) s d p p p (9) hooke's law in high-speed form was used    1( ) 2 e ei gσ ε i ε (10) where  is the lame's first parameter, g is the lame's second parameter (the shear modulus), 1( ) ei ε is the first invariant of the elastic strain rate tensor and i is the unit tensor of the second rank. the equation of balance for mass is taken in the form     v (11) where  is the density, v is the particle velocity. the equation for momentum conservation is given as  σu = (12) where  is the density, u is the displacement vector. as a result, the system of constitutive eqs. (7), (10) together with the balance eqs. (11),(12) for an elastoviscoplastic material with defects complete the formulation of the mathematical modeling problem [25]. the system of differential eqs. (7) (12) describes the relationship of the relaxation mechanisms with the kinetics of the microshear and microcracks defects, with the laws governing the evolution of elastoviscoplastic flow and damage localization for the plate impact statement. the developed model has eleven scalar parameters that require the realization of identification procedures. the approach for identification of material parameters was developed in [31] and based on the minimizing of the difference between the numerical simulation and the experimental data for quasi-static and dynamic tests. to provide the correctness of the optimization procedure (according to hadamard) the solution was realized using a series of initial conditions. mathematical statement for optimization procedure is presented below                                                   1 2 2 * 0 1 0 ... min, , , , , , , , 1 , , , . n k n k n pd d cd cd d k k p d d d d pd d p d d d d d j j j j j p p                      (13) yu. bayandin et alii, frattura ed integrità strutturale, 49 (2019) 243-256; doi: 10.3221/igf-esis.49.24 249 the estimation of the model parameters was carried out by the stress-strain diagrams over a strain rate range of quasistatic and dynamic tests. a modified search method was used for solving the optimization problem. the initial vector of parameter values and the initial step were chosen to calculate the optimizing function at each iteration step. an indicator that has a value  -1, 0,1 allows the determination of the step value. if the point corresponds to the value of the indicator equal zero, then the step decreases, otherwise the current point becomes the minimum. the procedure stops when the step becomes less than the specified accuracy. this method was previously used to determine model parameters for various materials [31]. fig. 3 shows a comparison for the stress-strain diagrams in the experiment [32] and numerical calculations obtained as a result of identification of model parameters for vanadium at different strain rates. figure 3: experimental stress-strain diagrams for vanadium at different strain rates (dotted line − 10-1 s-1, dashed line − 103 s-1) and corresponded numerical simulation (□ − 10-1 s-1, ○ − 103 s-1) it should be noted that the developed model makes it possible to describe stress-strain diagrams for wide-range strain rates (10-1−103 s-1) for the same values of model parameters. the procedure for verification of the model for vanadium was carried out from the shock-wave experiment in the conditions of a plate impact. fig. 4 presents the results of numerical simulation and experiment [33]. fig. 4 shows the particle velocity profiles for vanadium sample at different values of the stress amplitude that revealed the correspondence of numerical and experimental tests [33]. the profiles reflect the splitting of the shock wave front into an elastic precursor and the plastic front. the unloading of shock-compressed material behind the shock wave front leads also to the separation of the profile into an elastic wave and a wave of plastic unloading. in this zone, the numerical results do not agree well with the experimental profile, that can be linked with difficulty in recording the unloading wave front in the experiment. the mathematical statement allows the modeling of the behavior of metals under shock wave loading in the presence of damage accumulation to predict the critical state of shocked material (damage localization as spall failure precursor). the spall failure is linked with the final stage of damage kinetics corresponding to the initiation of blow-up localized damage structures [5]. this stage occurs when the value of the bulk component sp of the defect-induced strain reaches the critical value сsp and appropriate distribution over the spatial scale according to blow-up (self-similar) collective modes. the problem of spall failure for the plate impact test was studied numerically for vanadium. the simulation showed a significant dependence of the spall strength on the strain rate and typically (fig. 5) the increase in spall strength for increasing strain rates [25]. 0 0.02 0.04 0.06 0.08 0.1 0 1 2 3 4 5 6 7 x 10 -3   / 2g yu. bayandin et alii, frattura ed integrità strutturale, 49 (2019) 243-256; doi: 10.3221/igf-esis.49.24 250 figure 4: particle velocity profiles for vanadium sample. the solid line is stress amplitude value about 9.7 gpa (numerical calculation), the dashed line − 6.4 gpa (numerical calculation), ○ − 9.7 gpa (experiment), □ − 6.4 gpa (experiment) [33] figure 5: dependence of spall strength versus strain rate: ● − experiment [25], − model calculation, ▼ − experiment [24] the results of numerical simulation for the spall fracture are in accordance with the experiment and have established an increasing of spall stress with the increase of strain rate. that is the consequence of the pronounced damage localization with the avalanche kinetics of defect growth and weak sensitivity of the blow-up damage kinetics to the current value of stress amplitude. during the numerical simulation, the velocity profiles were reconstructed at different parts of the sample in order to study the connection between the structural relaxation laws due to nonlinear defect kinetics, elastic-plastic transitions and the formation of viscoplastic wave fronts. fig. 6 shows the results of numerical simulation and experimental dependencies of the elastic precursor amplitude for different thickness of the sample. 0 0.2 0.4 0.6 0.8 1 0 50 100 150 200 250 time, s p ar ti cl e ve lo ci ty , m / s 10 4 10 5 10 6 10 7 10 8 0 1 2 3 4 5 6 7 8 strain rate, s-1 sp al l s tr en gt h , g p a yu. bayandin et alii, frattura ed integrità strutturale, 49 (2019) 243-256; doi: 10.3221/igf-esis.49.24 251 figure 6: dependence of the dynamic elastic limit on the thickness of the vanadium sample. marker ● is the minimum value (experiment) [25], ○ − maximum value (experiment) [25], ▼ − minimum value (experiment [24]), ∇ − maximum value (experiment [ 25]), − numerical calculation, solid line – approximation. figure 7: free surface velocity profiles for silicon carbide samples in normalized time coordinates: ○ − experiment [15], lines − numerical simulation for different target thicknesses (8.32 mm, 3.81 mm, 2.15 mm) [22]. the model describes the elastic precursor decay under the path of the elastoplastic wave in the sample (fig. 6) that is in the agreement with the experimental data. the results of the simulation were approximated (solid line) by an exponential dependence in the form    3.349 exp 1.707 exp 0.0360.962hel h h     , where h is the thickness of the sample. numerical simulation shows that the relaxation mechanisms of the elastic precursor can be associated with the effects of energy absorption due to the defects as a new “phase” of the material. this is based on the nonlinear kinetics of 0 2 4 6 8 10 1 10 thickness, mm e la st ic p re cu rs o r lim it , g p a 50 70 90 110 130 0 200 600 1000 1400 time/thickness, ns/mm f re e su rf ac e ve lo ci ty , m / s yu. bayandin et alii, frattura ed integrità strutturale, 49 (2019) 243-256; doi: 10.3221/igf-esis.49.24 252 nucleation and growth of defects with pronounced transitions at metastability area in terms of the structural variable (the defect density tensor and structural scaling parameter). numerical simulation of silicon carbide behavior under shock-wave loading he wide applications of ceramics have been found due to the high dynamic elastic limit and the ability to absorb the energy at high load intensities. ceramics show a low level of plastic (viscoplastic) deformation and the elasticplastic transition in ceramic are associated with the “geometric” contribution of defects to the total strain. fig. 7 shows a comparison of simulation and experimental results for silicon carbide under shock wave loading [15, 22]. the presented velocity profiles demonstrate the splitting of the shock wave into an elastic precursor and a plastic front. the value of plastic strain for ceramics is much smaller than that observed for metals. weak sensitivity of the plastic front to the pulse intensity reflects the low contribution of the viscoplastic component, which is associated with low mobility of defects in ceramics. it was noted in [15] that some spall experiments in ceramics show weakly expressed spall pulse. this feature can be associated with a very short time of initiation and size of damage localization zone leading to small changes in the mechanical impedance during the formation of the spall surface. the self-similarity of wave fronts in sic ceramics was established in [15] and it was shown that the value of the dynamic elastic limit does not depend on time. in this connection, velocity profiles were constructed in time-normalized coordinates for different thicknesses of the samples (fig. 7). this result demonstrates the self-similarity of shock wave fronts in ceramics, which is due to self-similar patterns of damage kinetics in the metastability area of the nonequilibrium thermodynamic potential for solid with defects. self-similarity of shock wave fronts in metals and ceramics or a wide class of materials (metals [1-3] and nonmetals [2]), the fourth power-law universality of plastic wave fronts is established (fig. 8 and fig. 9)  * 0a p  (14) where 0p is the stress amplitude,  is the exponent equal to four in the strain rate range  * ~ 105−107 s-1 [3]. an explanation for the power universality of plastic wave fronts was proposed in [4], associated with the subjection of relaxation mechanisms to multiscale collective autosolitary modes of defects. it is established that the fourth power-law is violated for vanadium [3, 33]. comparison of the results of the numerical simulation with experimental data is shown in fig. 10. with an increase of strain rate at the wave front an asymptotic approximation to the fourth power-law is possible (in the graphs it is indicated by a solid line). conclusions he mechanisms of structural relaxation are associated with collective behavior of mesoscopic defects related to the metastability of nonequilibrium potential of solid with defects and the generation of collective modes responsible for plastic strain and damage localization. these modes represent the self-similar solutions of the evolution equation for the structural variable (defect-induced strain), which determines the relaxation properties of material and scenario of elastic-plastic transition. spatial-temporal dynamics of these modes (autosolitary and blow-up dissipative structures) can be initiated at appropriate load condition (shock wave rise) and could provide the anomalous relaxation ability of nonlinear system “solid with defects” in the conditions of the specific type of criticality – structural-scaling transition. the metastability “decomposition” leads to the splitting of the wave front on the elastic precursor, the transient area of elastic precursor decay and the steady plastic front due to continuous (structural-scaling) transition between similar types of metastability depending on the shock wave amplitude. autosolitary wave modes which subject the relaxation properties of shocked materials represent the “universality class” providing the four power universality at the steady shock wave front. the splitting of the wave front starts at the onset of critical behavior in the presence of metastability caused by the t f t yu. bayandin et alii, frattura ed integrità strutturale, 49 (2019) 243-256; doi: 10.3221/igf-esis.49.24 253 initial material structure. as the consequence, the elastic decay dynamics could be sensitive to the qualitative different relaxation kinetics: exponential kinetics with characteristic times that are close to the acoustic times and intermittent “slow” relaxation leading to the power law plastic wave fronts. figure 8: dependences of the stress amplitude versus the strain rate at the shock front for metals figure 9: dependences of the amplitude of stresses versus the strain rate at the front of the shock wave for nonmetals 10 5 10 6 10 7 10 0 10 1 d/dt, s-1  a , g p a fe [2] cu [2] al [2] al simulation [31] d/dt~ a 4 10 5 10 6 10 7 10 0 10 1 d/dt, s-1  a , g p a mgo [2] sio 2 [2] sic simulation sic experiment [15] d/dt~ a 4 yu. bayandin et alii, frattura ed integrità strutturale, 49 (2019) 243-256; doi: 10.3221/igf-esis.49.24 254 figure 10: dependences of the stress amplitude versus the strain rate at the front of the shock wave for vanadium an explanation of the influence of the spatial-temporal dynamics of defects leading to the plastic strain instability (selfsimilar plastic wave fronts, adiabatic plastic shear) was proposed in [4, 34, 35], on the kinetics of spall failure in metals and ceramics in [22, 25]. the listed effects were studied theoretically on the basis of developed continuum models reflecting the role of metastability in the formation of collective modes and their relation to the relaxation properties of solid with defects. the results of the simulation are supported by original experiments that are used to identify the parameters and the results of the simulation to explain the self-similar features of deformation and fracture for metals and ceramics under shock wave loading. acknowledgments his work was supported by the russian foundation for basic research (project no. 17-01-00867). references [1] barker, l.m. (1968). behavior of dense media under high dynamic pressures, gordon and breach, new york. [2] swegle, j.w., grady, d.e. (1985). shock viscosity and the prediction of shock wave rise times, j. appl. phys., 58(2), pp. 692-701. doi: 10.1063/1.336184. [3] grady, d.e. (2010). structured shock waves and the fourth-power law, j appl phys, 107, pp. 013506. doi: 10.1063/1.3269720. [4] bayandin, yu.v., leontiev, v.a., mikhailov, e.v., naimark, d.o., savinykh, a.s., skakun, s.n. (2004). experimental study of wave fronts and structural scaling in copper upon shock-wave loading, phys. mesomech., 7(1-2), pp. 97-101. [5] naimark, o.b. (2003). collective properties of defect ensembles and some nonlinear problems of plasticity and fracture, phys. mesomech., 6(4), pp. 39-63. 10 4 10 5 10 6 10 0 10 1 d/dt, s-1  a , g p a v [33] v simulation d/dt~ a 4 t yu. bayandin et alii, frattura ed integrità strutturale, 49 (2019) 243-256; doi: 10.3221/igf-esis.49.24 255 [6] merzhievskii, l.a., paletsky, a.v. (2001). calculations for diagrams of dynamic deformation of metals and alloys, phys mesomech., 4(3), pp. 85-96. [7] preston, d., tonks d. (2003). model of plastic deformation for extreme loading conditions, j app phys., 93(1), pp. 211-220. doi: 10.1063/1.1524706 [8] follansbee ps, kocks uf. (1988) a constitutive description of the deformation of copper based on the use of the mechanical threshold stress as an internal state variables, acta metall., 36(1), pp. 81-93. doi: 10.1016/0001-6160(88)90030-2 . [9] makarov, p.v. (2004). on the hierarchical nature of deformation and fracture of solids and media, phys. mesomech., 7(3-4), pp. 21-29. [10] kanel, g.i., razorenov, s.v., fortov, v.e. (2004). shock-wave phenomena and the properties of condensed matter, springer, new york. [11] bayandin, yu.v., naimark, o.b., uvarov, s.v. (2010). numerical simulation of mesodefect induced spall failure under shock wave loading of metals, computational continuous media mechanics, 3(1), pp. 13-23 (in russian). doi: 10.7242/1999-6691/2010.3.1.2. [12] petrov, y.v., smirnov, v.i. (2010). interrelation between the threshold characteristics of erosion and spall fracture, tech. phys., 55(2), pp. 230-235. doi: 10.1134/s1063784210020118. [13] saveleva, n.v., bayandin, yu.v., naimark, o.b. (2012). modeling of deformation and failure of metals in plate impact test, computational continuum media mechanics, 5(3), pp. 300-307 (in russian). doi: 10.7242/1999-6691/2012.5.3.35. [14] petrov, yu.v., gruzdkov, a.a., bratov, v.a. (2012) structural-temporal theory of fracture as a multiscale process, phys. mesomech., 15(3-4), pp. 232-237. doi: 10.1134/s1029959912020117. [15] savinykh, a.s., razorenov, s.v., kanel, g.i., rumyantsev, v.i. (2013). evolution of shock waves in sic ceramic, tech. phys., 58(7), pp. 973-977. doi: 10.1134/s1063784213070207. [16] bayandin, yu.v., saveleva, n.v., savinykh, a.s., naimark, o.b. (2013). numerical simulation of shock wave loading of metals and ceramic, physics of extreme states of matter, pp. 64-67. [17] merzhievskii, l.a., tyagel’skii, a.v. (1994). modeling of dynamic compression of porous iron, combustion, explosion and shock waves, 30(4), pp. 522-530. doi: 10.1007/bf00790160. [18] makarov, p.v. (2008). mathematical theory of evolution of loaded solids and media, phys. mesomech., 11(5-6), pp. 213-227. doi: 10.1016/j.physme.2008.11.002. [19] malygin, g.a., ogarkov, s.l., andriyash, a.v. (2013). on the power-law pressure dependence of the plastic strain rate of crystals under intense shock wave loading, physics of the solid state, 55(4), pp. 780-786. doi: 10.1134/s1063783413040197. [20] malygin, g.a., ogarkov, s.l., andriyash, a.v. (2013). two-wave structure of plastic relaxation waves in crystals under intense shock loading, physics of the solid state, 55(11), pp. 2280-2288. doi: 10.1134/s1063783413110152. [21] malygin, g.a., ogarkov, s.l., andriyash, a.v. (2014). dislocation structure of plastic relaxation waves in polycrystals and alloys under intense shock wave loading, physics of the solid state, 56(11), pp. 2239-2246. doi: 10.1134/s1063783414110183. [22] bayandin, yu.v., saveleva, n.v., savinykh, a.s., naimark, o.b. (2014). numerical simulation of multiscale damagefailure transition and shock wave propagation in metals and ceramics, journal of physics: conference series, 500, p. 152001. doi: 10.1088/1742-6596/500/15/152001. [23] kanel, g.i., savinykh, a.s., garkushin, g.v., razorenov, s.v. (2015). dynamic strength of tin and lead melts, journal of experimental and theoretical physics letters (jetp letters), 102(8), pp. 548-551. doi: 10.1134/s0021364015200059. [24] zaretsky, e.b., kanel, g.i. (2014). tantalum and vanadium response to shock-wave loading at normal and elevated temperatures. non-monotonous decay of the elastic wave in vanadium, j. appl. phys., 115(24), pp. 243502. doi: 10.1063/1.4885047. [25] saveleva, n.v., bayandin, yu.v., savinykh, a.s., garkushin, g.v., lyapunova, e.a., razorenov, s.v., naimark, o.b. (2015). peculiarities of the elastic-plastic transition and failure in polycrystalline vanadium under shock-wave loading conditions, tech. phys. lett., 41(6), pp. 579-582. doi: 10.1134/s1063785015060292 [26] kanel, g.i., garkushin, g.v., razorenov, s.v. (2016). temperature-rate dependences of the flow stress and the resistance to fracture of a vt6 titanium alloy under shock loading at a temperature of 20 and 600○c, tech. phys., 61(8), pp. 1229-1236. doi: 10.1134/s1063784216080132. [27] kanel, g.i., zaretsky, e.b., razorenov, s.v., ashitkov, s.i., fortov, v.e. (2017). unusual plasticity and strength of metals at ultra-short load durations, physics-uspekhi, 60(5), pp. 490-508. doi: 10.3367/ufne.2016.12.038004. yu. bayandin et alii, frattura ed integrità strutturale, 49 (2019) 243-256; doi: 10.3221/igf-esis.49.24 256 [28] petrova, a.n., brodova, i.g., razorenov, s.v. (2017). strength properties and structure of a submicrocrystalline almg-mn alloy under shock compression, physics of metals and metallography, 118(6), pp. 601-607. doi: 10.1134/s0031918x17060072. [29] zhurkov, s.n. (1984). kinetic concept of the strength of solids, int j fract., 26(4), pp. 295–307. doi: 10.1007/bf00962961. [30] naimark, o.b., bayandin, y.v., zocher, m.a. (2017). collective properties of defects, multiscale plasticity, and shock induced phenomena in solids, phys mesomech., 20(1), pp. 10-30. doi: 10.1134/s1029959917010027. [31] bayandin, y.v., naimark, o.b., uvarov, s.v. (2008). structural-scaling transitions under dynamic and shock wave loads in solids, physics of extreme states of matter, pp. 122-124 (in russian). [32] tonks, d.l. (1991). the datashop: a database of weak-shock constitutive data, los alamos, new mexico. [33] chhabildas, l.c., hills, c.r. (1986). in metallurgical applications of shock-wave and high-strain-rate phenomena, marcel dekker, inc. [34] bilalov, d., sokovikov, m., bayandin, yu., chudinov, v., oborin, v., naimark, o. (2015). numerical simulation and experimental investigation of strain localization in almg6 alloy under dynamic loading, aip conference proceedings, 1683, pp. 020025. doi: 10.1063/1.4932715. [35] bilalov, d., sokovikov, m., bayandin, yu., chudinov, v., oborin, v., naimark, o. 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can be opened with acrobat and adobe reader 5.0 and later.) >> /namespace [ (adobe) (common) (1.0) ] /othernamespaces [ << /asreaderspreads false /cropimagestoframes true /errorcontrol /warnandcontinue /flattenerignorespreadoverrides false /includeguidesgrids false /includenonprinting false /includeslug false /namespace [ (adobe) (indesign) (4.0) ] /omitplacedbitmaps false /omitplacedeps false /omitplacedpdf false /simulateoverprint /legacy >> << /addbleedmarks false /addcolorbars false /addcropmarks false /addpageinfo false /addregmarks false /convertcolors /converttocmyk /destinationprofilename () /destinationprofileselector /documentcmyk /downsample16bitimages true /flattenerpreset << /presetselector /mediumresolution >> /formelements false /generatestructure false /includebookmarks false /includehyperlinks false /includeinteractive false /includelayers false /includeprofiles false /multimediahandling /useobjectsettings /namespace [ (adobe) (creativesuite) (2.0) ] /pdfxoutputintentprofileselector /documentcmyk /preserveediting true /untaggedcmykhandling /leaveuntagged /untaggedrgbhandling /usedocumentprofile /usedocumentbleed false >> ] >> setdistillerparams << /hwresolution [2400 2400] /pagesize [612.000 792.000] >> setpagedevice microsoft word numero 2 art 1 finale.doc e. lucon, frattura ed integrità strutturale, 2 (2007) 2-9; doi: 10.3211/igf-esis.02.01b 2 1 introduzione in determinate circostanze, il tempo può diventare una variabile importante nelle problematiche relative allo studio della meccanica della frattura. in condizioni di ve locità di deformazione1 elevata, due fenomeni possono influenzare e complicare la valutazione della tenacità a frattura dinamica per un materiale metallico: 1 in questo lavoro, il termine "velocità di deformazione" è usato come sinonimo di "velocità di carico" o "velocità di caricamento" (traduzione letterale dell'inglese "loading rate"). misure di tenacità a frattura su acciai utilizzando velocità di deformazione elevate enrico lucon institute of nuclear material science, centro di studi nucleari del belgio, sck•cen, boeretang 200, b-2400 mol (belgio), e-mail: elucon@sckcen.be riassunto. la conoscenza delle proprietà meccaniche di tipo dinamico per i materiali metallici è utile ogniqualvolta la sensibilità alla velocità di deformazione è di rilevanza per un acciaio, e qualora le condizioni reali di carico per una struttura (in caso di normale esercizio o di situazioni d'emergenza) siano diverse dal caso statico. inoltre, in alcuni studi l'aumento della velocità di deformazione serve a simulare gli effetti di altri meccanismi di fragilizzazione quali l'invecchiamento termico (thermal ageing) o l'irraggiamento. la presente memoria fornisce una panoramica dell'esperienza maturata al centro nucleare belga (sck•cen) nel campo delle misure di tenacità a frattura su acciai in condizioni di velocità di deformazione elevata, con particolare riguardo alle prove di resilienza strumentata su provini charpy precriccati (pcvn). dopo una breve dissertazione sui meccanismi fondamentali che aiutano a comprendere gli effetti della velocità di deformazione sulla tenacità degli acciai in regime fragile e duttile, vengono presentate le procedure sperimentali ed analitiche per misurare la tenacità a frattura con velocità di deformazione elevata, prendendo in considerazione da un lato le principali normative internazionali (astm e iso) e dall'altro il lavoro di normazione attualmente in corso sotto il coordinamento di sck•cen: la revisione della norma astm e1921 (metodo della master curve per la misura della tenacità in regime di transizione duttile/fragile) e lo sviluppo di una nuova norma iso sulle prove di tenacità dinamica con provini pcvn. quest'ultimo documento è presentato in maggior dettaglio, concentrando l'attenzione sulla determinazione della tenacità dinamica in campo fragile con il metodo dell'impact response curve e in campo duttile (curve di resistenza j-r) mediante l'uso di metodi monoe multi-campione. in conclusione, vengono presentati alcuni esempi tratti dalla banca dati sviluppata da sck•cen per le misure di tenacità dinamica, prevalentemente su acciai da vessel di uso nucleare (rpv steels). abstract. the knowlegde of dynamic mechanical properties is useful in all cases where the strain rate sensitivity of metallic materials is an issue, and whenever the actual loading conditions for a structure (either in normal operation or under accidental circumstances) are different from static. furthermore, in some investigations increasing the loading rate is used to simulate other embrittling mechanisms such as thermal aging or neutron exposure. this paper provides an overview of sck•cen experience on measuring fracture toughness of steels at elevated loading rates, with specific emphasis on instrumented impact tests on precracked charpy (pcvn) specimens. after briefly dwelling on the basic mechanisms which explain loading rate effects on cleavage and ductile fracture toughness, the experimental and analytical procedures for measuring fracture toughness at elevated loading rates are addressed, both in terms of official astm and iso test standards and considering standardization efforts currently in progress under sck•cen coordination: revision of astm e1921 (master curve methodology for measuring fracture toughness in the ductile-to-brittle transition region) and a future iso standard on instrumented pcvn testing. this latter document is examined in more detail, focussing the attention on the dynamic evaluation of brittle fracture toughness (impact response curve) and the determination of crack resistance curves using multiple and single-specimen techniques. finally, selected examples from sck•cen database of dynamic toughness measurements will be illustrated, mainly relevant to reactor pressure vessel (rpv) steels. http://www.gruppofrattura.it http://www.gruppofrattura.it http://dx.medra.org/10.3221/igf-esis.02.01b&auth=true e. lucon, frattura ed integrità strutturale, 2(2007) 2-9 3 • la variazione delle proprietà meccaniche in funzione della velocità di deformazione (nella maggior parte dei metalli, le proprietà tensili aumentano sensibilmente quando la velocità di deformazione aumenta di alcuni ordini di grandezza); • effetti inerziali, che possono assumere grande importanza quando la forza varia bruscamente o quando una cricca avanza rapidamente (parte del lavoro speso sul provino è convertita in energia cinetica). la velocità di deformazione di un materiale metallico vicino all'apice di una cricca è di solito misurata come dove ki è il fattore di intensità delle sollecitazioni in modo i e t è la variabile tempo. per velocità di deformazione fino a • k = 106 mpa√m/s, generalmente entrambi gli effetti sono significativi e devono essere presi in considerazione nelle misure di tenacità a frattura. 2 effetti qualitativi di un aumento della velocita’ di deformazione qualitativamente, le conseguenze di un aumento della velocità di deformazione sulla tenacità a frattura di un acciaio possono essere schematizzate nel modo seguente, in funzione del regime di frattura (fragile/transizione/duttile) nel quale il materiale si trova ad operare: • comportamento fragile (lower shelf): un aumento della velocità di deformazione provoca una diminuzione della tenacità a frattura (kid < kic)2; • comportamento parzialmente fragile e parzialmente duttile (regime di transizione): la temperatura di transizione aumenta all'aumentare della velocità di deformazione (to,d > to,s)3; • comportamento duttile (upper shelf): una velocità di deformazione più elevata tende ad aumentare la resistenza del materiale all'innesco e alla propagazione duttile di una cricca (jid > jic). in termini grafici, le conseguenze di un aumento della velocità di deformazione sull'intera curva della tenacità a frattura in funzione della temperatura per un acciaio ferritico possono essere rappresentate come in fig. 1. in condizioni prevalentemente fragili, un aumento della velocità di deformazione rende più difficoltoso il movimento delle dislocazioni all'interno del materiale, con conseguente aumento dello sforzo di snervamento (indurimento, o hardening). lo spostamento verso l'alto della curva di snervamento ha per effetto un aumento della temperatura alla quale si realizza la condizione di clivaggio, che corrisponde all'intersezione con la curva dello 2 il pedice "d" indica un parametro "dinamico". 3 il pedice "s" indica un parametro "statico". sforzo di frattura (che dipende in maniera modesta dalla la velocità di deformazione o dalla temperatura). tale incremento della temperatura di clivaggio corrisponde al fenomeno della fragilizzazione (embrittement), che può anche essere causato dall'irraggiamento neutronico. quanto descritto è illustrato graficamente nella fig. 2. anche quando il comportamento dell'acciaio è di tipo duttile, un incremento della velocità di deformazione rende più difficoltoso il movimento delle dislocazioni e di conseguenza la deformazione plastica del materiale. in tali circostanze, i fenomeni tipici associati all'innesco e alla propagazione duttile di una cricca (nucleazione, crescita e coalescenza di vuoti) avvengono a livelli più elevati di lavoro speso, e quindi la tenacità del materiale aumenta. figura 1. effetto qualitativo di un aumento della velocità di deformazione sulla tenacità a frattura di un acciaio ferritico (curva blu: velocità quasi-statica; curva rossa: velocità dinamica). figura 2. effetti di indurimento e fragilizzazione causati da un aumento della velocità di deformazione in un acciaio con comportamento fragile. 3 misura sperimentale della tenacita’ a frattura dinamica nei paragrafi seguenti, si farà principalmente riferimento alle normative di prova già pubblicate o in via di pubblicazione da parte dell'astm (american society for testing and materials) e dell'iso (international standardisation organization). • = i dk k dt diminuzione tenacità in campo fragile aumento della temperatura di transizione aumento della tenacità di innesco t en ac it à k i (m pa √m ) temperatura (°c) diminuzione tenacità in campo fragile aumento della temperatura di transizione aumento della tenacità di innesco t en ac it à k i (m pa √m ) temperatura (°c) aumento velocità deform. sforzo di frattura (modesta dipendenza da velocità di deformazione o temperatura) δt aumento snervamento (indurimento) sf o rz o temperatura aumento sforzo di snervamento causato dalla maggior difficoltà di movimento delle dislocazioni aumento temperatura clivaggio (fragilizzazione) δσy condizioni di clivaggio aumento velocità deform. sforzo di frattura (modesta dipendenza da velocità di deformazione o temperatura) δt aumento snervamento (indurimento) sf o rz o temperatura aumento sforzo di snervamento causato dalla maggior difficoltà di movimento delle dislocazioni aumento temperatura clivaggio (fragilizzazione) δσy condizioni di clivaggio e. lucon., frattura ed integrità strutturale, 2 (2007) 2-9 4 3.1 comportamento fragile (lower shelf) l'intervallo di velocità di deformazione per prove in condizioni quasi-statiche è definito come 0.55-2.75 mpa√m/s nelle norme astm e399 [1] e e1820 [2] e come 0.55-3 mpa√m/s nella norma iso 12135 [3]. il medesimo intervallo è prescritto anche dalla norma british standard bs 7448:3 [4]. in caso di velocità di deformazione più elevate, le normative si limitano a raccomandare di determinare accuratamente i valori di forza applicata e prescrivono un tempo totale di prova non inferiore a 1 ms. inoltre, nei calcoli della tenacità a frattura si richiede l'uso di un valore di sforzo di snervamento corrispondente alla velocità di prova. è interessante osservare che entrambe le norme astm (e399 e e1820) escludono la possibilità di eseguire prove di impatto utilizzando masse cadenti, quindi prove di resilienza charpy o pellini (drop weight). inoltre, viene esplicitamente affermato che "diminuzioni significative della tenacità possono essere osservate all'aumentare della velocità di deformazione". 3.2 comportamento misto fragile/duttile la norma astm e1921 [5], che descrive la ben nota metodologia della master curve per la misura della tenacità a frattura di acciai ferritici in regime di transizione fragile/duttile, prevede che per una determinazione quasistatica della temperatura di riferimento to, la velocità di deformazione sia compresa tra 0.1 e 2 mpa√m/s. tale requisito consente di limitare a un massimo di 10 °c la variazione di to per effetto della velocità di prova [6]. è consentito altresì eseguire la prova al di sotto del limite inferiore (0.1 mpa√m/s), purchè gli effetti ambientali siano trascurabili o assenti. la versione attuale della norma (2005) non prevede la possibilità di eseguire prove con velocità di deformazione più elevate; tuttavia, l'autore della presente memoria sta preparando una revisione della e1921 nella quale sarà consentito applicare velocità di prova superiori, sino a poter testare provini charpy precriccati utilizzando un pendolo strumentato [7-10]. esiste infatti una consistente base sperimentale che dimostra senza ombra di dubbio che il metodo della master curve è pienamente applicabile alle misure di tenacità dinamica eseguite su provini charpy precriccati; un chiaro esempio è fornito dalla fig. 3, che mostra i risultati di un round-robin (prova interlaboratorio) recentemente organizzato nell'ambito del coordinated research project phase 8 (crp-8) dell'iaea (international atomic energy agency) [11,12]. nell'ambito del medesimo crp-8, è attualmente in corso uno studio sulla sensibilità alla velocità di deformazione degli acciai ferritici [11]; lo studio si basa sulla raccolta ed analisi di valori della temperatura di riferimento to ottenuti a diverse velocità di deformazione mediante la metodologia della master curve. la fig. 4 mostra i risultati di prove eseguite da sck•cen su tre acciai (due acciai da vessel – jsps e jrq e un acciaio ferritico/martensitico – e97) variando la velocità di prova; le pendenze variabili delle curve di regressione in scala semilogaritmica evidenziano la diversa sensibilità degli acciai considerati. in assenza di misure sperimentali, una stima dell'incremento della temperatura di riferimento conseguente all'aumento della velocità di deformazione può essere ottenuta dalla seguente correlazione empirica, proposta da wallin [13]: 0 50 100 150 200 250 -50 -40 -30 -20 -10 0 10 20 30 temperatura (°c) k j c, 1t (m p a√ m ) lab #1 lab #2 lab #3 lab #4 lab #5 lab #6 lab #7 lab #8 master curve complessiva 95% 5% lb mc 0 50 100 150 200 250 -50 -40 -30 -20 -10 0 10 20 30 temperatura (°c) k j c, 1t (m p a√ m ) lab #1 lab #2 lab #3 lab #4 lab #5 lab #6 lab #7 lab #8 master curve complessiva 95% 5% lb mc figura 3. prove di tenacità dinamica su provini charpy precriccati dell'acciaio da vessel jrq (a533b cl.1), analizzati mediante il metodo della master curve. dati del round-robin del crp-8 dell'iaea [12]. e. lucon, frattura ed integrità strutturale, 2(2007) 2-9 5 (1) dove la funzione γ è data da: (2) con σys,tos = limite di snervamento alla temperatura to,s (temperatura di riferimento corrispondente a velocità di deformazione quasi-statiche). la correlazione (1) è stata sviluppata su 59 acciai, per velocità di prova comprese tra 10-1 e 106 mpa√m/s, limiti di snervamento tra 200 e 1000 mpa e valori to,s tra -180 e 0 °c. 3.3 comportamento duttile (upper shelf) all'interno della norma astm e1820 [2], e più precisamente nell'annex a14, vengono fornite indicazioni per l'esecuzione di prove con elevata velocità di deformazione. affinché la prova sia analizzabile, si richiede che la parte iniziale del grafico forza/spostamento sia sufficientemente ben definita e che la durata della prova non sia inferiore a un valore minimo tw che dipende dalla rigidità del provino e dalla massa totale del sistema di prova. nel caso che la prova duri meno di tw, le equazioni per il calcolo dell'integrale-j sono da considerarsi inaccurate. nel caso si debba determinare la curva di resistenza alla propagazione duttile (j-r curve), la norma raccomanda l'uso della tecnica della normalizzazione (normalization data reduction), descritta nell'annex a15. da notare che nella norma e1820 si afferma esplicitamente che "la curva j-r e la tenacità critica jic(t) aumentano al crescere della velocità di prova". 4 la futura norma iso sulle prove di tenacita’ dinamica utilizando provini charpy precriccati in ambito iso e con il coordinamento di sck•cen, una normativa di prova è attualmente in preparazione per prove di tenacità dinamica su provini charpy precriccati testati mediante un pendolo strumentato [14]. tale norma è quasi interamente basata sull'ultima versione della procedura di prova scritta dal comitato tecnico tc5 dell'esis (european structural integrity society) [15]. la norma tratta tutti e tre i regimi di comportamento a frattura (fragile / transizione / duttile), identificando il diagramma forza/tempo in base a quattro tipologie (fig. 5): • essenzialmente lineare elastico (tipo i); • frattura fragile per clivaggio senza crescita duttile significativa (δa ≤ 0.2 mm) (tipo ii); • frattura fragile per clivaggio con crescita duttile significativa (0.2 mm < δa ≤ 1.6 mm) (tipo iii); • frattura fragile per clivaggio con δa > 1.6 mm o propagazione duttile in assenza di clivaggio (tipo iv). 4.1 provini rispetto alle prove di tipo quasi-statico, la lunghezza minima ammessa della precriccatura di fatica è ridotta da σ⎡ ⎤⎛ ⎞⎛ ⎞⎢ ⎥γ = + ⎜ ⎟⎜ ⎟ ⎜ ⎟⎢ ⎥⎝ ⎠ ⎝ ⎠⎣ ⎦ 1.091.66 ,,9.9 exp 190 722 ys toso st 1.e-01 1.e+00 -120 -100 -80 -60 -40 -20 0 20 40 1.e-02 1.e+01 1.e+02 1.e+03 1.e+04 1.e+05 1.e+06 dk/dt (mpa√m/s) to (° c ) astm e1921-05 jrq jsps e97 prove di impatto (1-1.5 m/s) 1.e-01 1.e+00 -120 -100 -80 -60 -40 -20 0 20 40 1.e-02 1.e+01 1.e+02 1.e+03 1.e+04 1.e+05 1.e+06 dk/dt (mpa√m/s) to (° c ) astm e1921-05 jrq jsps e97 prove di impatto (1-1.5 m/s) figura 4 – influenza della velocità di prova sulla temperatura di riferimento per due acciai da vessel (jsps, jrq) e un acciaio ferritico/martensitico (e97). prove eseguite da sck•cen nell'ambito del crp-8 dell'iaea [11]. • ⋅ γ = ⎛ ⎞ γ − ⎜ ⎟ ⎝ ⎠ , , log o s o d t t k e. lucon., frattura ed integrità strutturale, 2 (2007) 2-9 6 0.45w a 0.3w, con w = larghezza del provino (10 mm). l'applicazione di scanalature laterali (side-grooves) è ammessa ed anzi raccomandata nel caso si voglia determinare la curva j-r. 4.2 macchine di prova svariate tipologie di macchine di prova sono ammesse nella futura norma, benché l'attrezzatura consigliata sia un pendolo strumentato con angolo di caduta – e quindi velocità d'impatto – variabile. e' comunque consentito l'uso di macchine a massa cadente (drop-weight), macchine di prova di tipo servoidraulico, pendoli speciali con appoggi mobili e provino fisso ecc. il percussore (striker) strumentato può essere conforme alla geometria prevista sia dalla norma iso 148-2 (raggio del coltello: 2 mm) sia dalla norma astm e23 (raggio del coltello: 8 mm). 4.3 velocità d'impatto qualsiasi velocità d'impatto è consentita, fino a valori dell'ordine di 5 m/s o superiori. nel caso di un pendolo charpy, la velocità di prova può essere ridotta sino a circa 1 m/s. in caso di comportamento fragile, se la velocità è tale che il tempo di frattura è inferiore a 5 volte il periodo di oscillazione naturale del sistema provino/macchina (tf < 5τ), la tenacità a frattura non può essere calcolata a partire dal grafico forza/spostamento della prova; in tal caso, deve utilizzarsi il metodo dinamico di calcolo della tenacità dinamica dell'impact response curve, descritto nella sezione successiva. 4.4 metodo dinamico di calcolo della tenacità dinamica in regime di clivaggio il metodo detto impact response curve (curva di risposta all'impatto) [16], prevede la determinazione della tenacità dinamica kid a partire dal tempo a frattura tf, utilizzando una curva universale che è rappresentata dalla funzione (3) in cui: r è funzione della cedevolezza della macchina di prova, vo è la velocità d'impatto e t" è tabulato in funzione di tf. per l'individuazione del tempo di frattura tf, nell'ipotesi tf < 5τ, si raccomanda di strumentare il provino con un estensimetro (strain gage) applicato in prossimità dell'apice della cricca (fig. 6); una brusca diminuzione del segnale elettrico dell'estensimetro consente di individuare l'istante della frattura [17]. in alternativa, è possibile esaminare la variazione nel tempo di altri segnali, ad es. un segnale magnetico o la caduta di potenziale attraverso il provino percorso da corrente (potential drop). figura 5. possibili tipologie del diagramma forza/tempo per una prova di tenacità dinamica su provino charpy precriccato. = "id ok rv t e. lucon, frattura ed integrità strutturale, 2(2007) 2-9 7 4.5 metodi per la misura della tenacità dinamica in regime duttile l'approccio consigliato per determinare la curva j-r in condizioni dinamiche prevede l'uso di una metodologia di tipo multi-provino; la futura norma iso cita i seguenti metodi di prova: • low-blow test: la velocità d'impatto viene variata da una prova all'altra in modo da ottenere quantità variabili di crescita duttile δa; l'energia potenziale deve figura 6. esempi di metodi per l'individuazione del tempo di frattura in caso di frattura fragile. temperatura di riferimento normalizzata, t – to (°c) te na ci tà di na m ic a no rm al iz za ta , k jc ,1 t (m p a√ m ) temperatura di riferimento normalizzata, t – to (°c) te na ci tà di na m ic a no rm al iz za ta , k jc ,1 t (m p a√ m ) figura 7. banca dati sck•cen costituita da misure di tenacità dinamica su provini pcvn di acciai da vessel (cerchi) e ferritici/martensitici (triangoli). le prove, eseguite in regime di transizione fragile duttile, sono state analizzate mediante il metodo della master curve (rappresentata nella figura insieme a diversi livelli statistici di probabilità di frattura). e. lucon., frattura ed integrità strutturale, 2 (2007) 2-9 8 essere sufficiente a far propagare la cricca, senza tuttavia provocare la rottura completa del provino. • stop block test: valori differenti di crescita duttile tra un provino e l'altro vengono ottenuti variando la posizione d'arresto del martello, anche in questo caso evitando di rompere completamente il provino. il metodo è tuttavia sconsigliato per macchine di prova standard, in quanto esiste il rischio di danneggiare la cella di carico. • cleavage r-curve method: le prove sono eseguite in regime di transizione fragile/duttile, facendo variare la temperatura di prova in modo da ottenere valori δa variabili. le differenze tra le temperature di prova vengono ignorate [18]. in aggiunta, sono anche disponibili metodologie monoprovino, quali il metodo della key curve [19], l'approccio analitico a 3 parametri di schindler [20] e la già citata tecnica della normalizzazione descritta nella norma astm e1820. un recente studio eseguito da sck•cen ha evidenziato un buon accordo tra metodi multie mono-provino per alcuni tipici acciai da vessel [21]. 5 esempi di misure di tenacità dinamica tratti dalla banca dati di sck•cen per concludere, vengono presentati alcuni risultati di prove di tenacità dinamica eseguite da sck•cen su provini charpy precriccati, provenienti in prevalenza da acciai da vessel per uso nucleare. la fig. 7 mostra la nostra banca dati costituita da 113 prove condotte in regime di transizione fragile/duttile su 7 acciai in 11 diverse condizioni (per alcuni acciai, sono presenti misure su materiale sia non irraggiato che irraggiato). figura 8. misure di resistenza alla frattura duttile, ottenute per due acciai da vessel con velocità di deformazione quasi-statiche (curve blu) e dinamiche (curve rosse). e. lucon, frattura ed integrità strutturale, 2(2007) 2-9 9 i valori di tenacità dinamica (normalizzati allo spessore di riferimento – 1 pollice) sono rappresentati in funzione della differenza tra la temperatura di prova e la temperatura di riferimento to calcolata per il relativo materiale; questo tipo di rappresentazione consente di riunire sullo stesso grafico materiali diversi tra loro. la fig. 7 costituisce un'ulteriore dimostrazione che il metodo della master curve è perfettamente applicabile a misure di tenacità dinamica su provini pcvn. esempi di misure dinamiche di resistenza alla frattura duttile, ottenute mediante la metodologia low blow test precedentemente descritta, sono mostrati per due tipici acciai da vessel nella fig. 8, dove le curve dinamiche (in rosso) sono confrontate alle curve j-r ottenute in condizioni quasi-statiche (in blu) alle stesse temperature di prova. la fig. 8 consente di apprezzare chiaramente l'incremento della resistenza alla frattura duttile, conseguente ad un aumento della velocità di deformazione. 6 bibliografia [1] astm e399-05, standard test method for linearelastic plane-strain fracture toughness kic of metallic materials, annual book of astm standards 2006, vol. 03.01. [2] astm e1820-05a, standard test method for measurement of fracture toughness, annual book of astm standards 2006, vol. 03.01. [3] iso 12135:2002, metallic materials -unified method of test for the determination of quasistatic fracture toughness. [4] bs 7448-3:2005, method for determination of fracture toughness of metallic materials at rates of increase in stress intensity factor greater than 3.0 mpa√m/s, british standards institution. [5] astm e1921-05, standard test method for determination of reference temperature, to, for ferritic steels in the transition range, annual book of astm standards 2006, vol. 03.01. [6] j.b. hall e k.k. yoon, quasi-static loading rate effect on the master curve reference temperature of ferritic steels and implications, proceedings of the 2003 asme pressure vessels and piping conference (cleveland, oh, 28-31 luglio 2003). [7] t.j. koppenaal, dynamic fracture toughness measurements of high-strength steels using precracked charpy specimens, astm stp 563, 1974, pp. 92-117. [8] k.r. iyer and r.b. miclot, instrumented charpy testing for determination of the j-integral, astm stp 563, 1974, pp. 146-165. [9] htgr fracture toughness program, epri np-120, project 337-1, final report, aprile 1976. [10] proceedings of c.s.n.i. specialist meeting on instrumented precracked charpy testing, epri np-2102ld, palo alto, california, 1-3 dicembre 1980. [11] h.-w. viehrig e e. lucon, iaea coordinated research project on master curve approach to monitor fracture toughness of rpv steels: effect of loading rate, proceedings of pvp2007, asme pressure vessels and piping division conference, 22-26 luglio 2007, san antonio, texas. [12] e. lucon e h.w. viehrig, round-robin exercise on instrumented impact testing of precracked charpy specimens (iaea coordinated research program phase 8), proceedings of pvp2007, asme pressure vessels and piping division conference, 22-26 luglio 2007, san antonio, texas. [13] k. wallin, effect of strain rate on the fracture toughness reference temperature to for ferritic steels, in: recent advances in fracture (ed. r.k. mahidhara et al.; the minerals, metals & materials society, 1997). [14] iso tc 164/sc4 n465.3, steel measurement of fracture toughness at impact loading rates using precracked charpy v-notch test pieces, ultima revisione: 27 ottobre 2006. [15] esis tc5, proposed standard methods for instrumented pre-cracked charpy impact testing of steels and other metallic materials, draft 25.4: dicembre 2005. [16] j.f. kalthoff, s. winkler and w. böhme, a novel provedure for measuring the impact fracture toughness kid with precracked charpy specimens, journal de physique, colloque c5, supplement au n°8, tome 46, agosto 1985, pp 179-186. [17] h. j. macgillivray e d. f. cannon, the development of standard methods for determining the dynamic fracture toughness of metallic materials, astm stp 1130, 1992, pp. 161-179. [18] w. böhme, experience with instrumented charpy tests obtained by a dvm round robin and further developments, esis 20, ed. e. van valle, mep publications, london, 1996, pp. 1-23. [19] j.a. joyce, static and dynamic j-r curve testing of a533b steel using the key-curve analysis technique, astm stp 791, 1983, pp. i-543-i560. [20] h.j. schindler, estimation of fracture toughness from charpy tests – theoretical relations, astm stp 1380, 1999, 340ff. [21] e. lucon, the use of single-specimen techniques for measuring upper shelf toughness properties under impact loading rates, rapporto blg-1016, sck•cen, settembre 2005. microsoft word numero_49_art_62_2490 e. abdelouahed et alii, frattura ed integrità strutturale, 49 (2019) 690-697; doi: 10.3221/igf-esis.49.62 690 pipeline repair by composite patch under temperature and pressure loading e. abdelouahed, h. benzaama laboratoire labab, ecole nationale polytechnique maurice audin, oran, algeria heabamine@gmail.com, habenza@yahoo.fr m. mokhtari laboratoire lartfm, ecole nationale polytechnique maurice audin, oran, algeria mokhtarimohamed44@yahoo.fr b. aour laboratoire labab, ecole nationale polytechnique maurice audin, oran, algeria ben_aour@yahoo.fr abstract.in this study, the three-dimensional finite element method is used to analyze an api 5l x70 steel cylindrical pipeline subjected to an internal pressure load by calculating the stress intensity factors and the integral j at the peak of crack in elastic and elastoplastic behavior. the effectiveness of composite patch repair bonded to the cracked surface is highlighted. the effects of the geometrical and mechanical properties of the composite patch and the adhesive on the effectiveness of the repair were highlighted. the variation of the stress intensity factor at the crack tip is used to evaluate the repair performance. the results obtained show that the residual heat stress significantly increases the stress intensity factor at the bottom of the crack, which reduces the effectiveness of the repair. keywords. fem; repair by composite patch; pipeline; cracking; thermal stress; internal pressure; temperature; stress intensity factor. citation: e. abdelouahed, h. benzaama, m. mokhtari, b. aour, pipeline repair by composite patch under temperature and pressure loading, frattura ed integrità strutturale, 49 (2019) 690-697. received: 21.04.2019 accepted: 15.05.2019 published: 01.07.2019 copyright: © 2019 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. introduction lobal energy demands continue to rise with the rapid development of the global economy. [1] pipeline transportation of oil and gas is the safest and cheapest way for hydrocarbon transportation companies. [2] to increase the profitability of a pipeline, the flow is often increased by increasing the service pressure. [3] considerable research work is available in the literature on the various aspects of bonded composite joints. several design parameters play an important role in the technology of composite patches, [4] such as patch size, patch shape, material selection, patch, ambient temperature, size of heating zones, etc.., the importance and effects of some of the design parameters discussed. g http://www.gruppofrattura.it/va/49/2490.mp4 e. abdelouahed et alii, frattura ed integrità strutturale, 49 (2019) 690-697; doi: 10.3221/igf-esis.49.62 691 for pipeline repair, a number of technical design issues must be considered that may be important depending on the repair circumstances. the application of a bonded repair to a pipeline poses a number of technical design problems with materials that may be important depending on the circumstances of repair. [5] one example is the development of residual stresses when a high cure temperature adhesive is used to bond a repair patch to a substrate with a different coefficient of thermal expansion. [6] the main drawback of the use of gr / ep (graphite / epoxy), b / ep (boron / epoxy) and g / p (glass / epoxy) results from a discrepancy in the coefficients of thermal expansion between the composite and the metal. [7] residual thermal stresses are particularly important when high temperature curing adhesives are used to bond the patch. for example, in a typical repair applied to pipeline structures, the reinforced region is initially heated to a temperature of about 100-120 ° c under pressure for about 1 hour and then cooled to room temperature after curing of the adhesive. 8] due to the differences between the elastic properties and the thermal expansion properties of the composite patch and the metallic pipeline, residual thermal stresses may occur. it has long been recognized that in some cases, residual heat stress is a serious problem for the effectiveness of composite patch repair. [9] if the repair material is different from the substrate, the residual stress level must be calculated during the design process. [10] numerous attempts have been made in recent years to estimate the values of these residual stresses. köpple et al. [11] used an analytical method based on linear elastic fracture mechanics and finite element method and considered a steel pipeline with a through-wall defect repaired by a composite material. zarrinzadeh et al. [12] used the abaqus software to better simulate the experimental results of cracked aluminum pipe with patch repair under fatigue load. t. nateche et al. [13] used a composite patch to repair damaged pipelines. it is a fast and economical method without interruption of service. mhamdia et al. [14] analyzed the effects of residual thermal stress on the variation of the stress intensity factor in an aluminum plate repaired with a composite boron / epoxy patch. according to albedah et al. [15] the residual thermal stress caused the reduction of the fatigue life of repaired aeronautical structures. to mitigate the effects of residual heat stress on repair performance, cure temperature and adhesive properties must be optimized. lam et al. [16] also considered a circular tube that is repaired by a composite patch to study the effect of the patch on reducing stress intensity factors. the purpose of this study is to analyze the effect of the variation of the stress stress factor of repaired crack in steel pipelines with aadhesived composite patch. the novelties of this work are the parametric studies of the effects of the geometric, thermal and mechanical properties of the composite on the variation of the stress intensity factor at the end of cracks repaired with aadhesived composite patch. finite element model he cracked steel pipeline that is repaired by a composite patch under an internal pressure load as shown in fig. 1. the api 5l x70 elastic cylindrical steel pipeline having the following dimensions: dpipe=304,8mm, lpipe=1000 mm, epipe=4mm. a transverse crack of length 2a to the pipe axis is assumed to exist in the pipeline. this crack is repaired with a composite patch of boron / epoxy 2 mm thick, and length 4a. the adhesive used for bonding is fm-73 with a thickness ea = 0.2 mm, inside diameter equal to the outside diameter of composite patch. the inside diameter of the composite patch is equal to the outside diameter of the pipeline. the adhesive is cured at 120° c and the ambient temperature is considered to be 20° c. the elastic and thermal properties of the pipeline and the composite are given in tab.1. analysis by the finite element method of the configuration illustrated in fig. 1 is performed using the calculation code abaqus [17]. in order to avoid the degrees of complexity in the finite element model of this three-dimensional structure, we have formulated some simplifying assumptions that allowed us to capture the essential characteristics of the response. these assumptions are: each part of the model is considered as a three-dimensional structure. no bonding property at the interface between the adhesive and the two other structures (pipe, patch). at the interface, each mesh node is common between the adjacent structures. the adhesive is homogeneous elastic and isotropic [18]. the deformation of the adhesive is under the effect of shearing and peeling. the patch is unidirectional composite oriented perpendicular to the crack. the adhesive is modeled as a third layer. the nodes are common between the patch/adhesive and adhesive/pipe interfaces for continuity of deformation and stress. the advantage is to be able to capture the necessary characteristics of the adhesive such as the transfer of charges between the pipe and the patch. the finite element model consists of three subsections; cracked pipeline, adhesive and composite patch. due to symmetry, only half of the repaired pipeline is considered. to generate the crack front, a number of elements originally created around the crack tip are replaced by a "crack block". this crack block is meshed with quadratic elements, which are mapped in the space of the original elements and merged with a quadratic mesh. the mesh was refined near the crack end zone using at t e. abdelouahed et alii, frattura ed integrità strutturale, 49 (2019) 690-697; doi: 10.3221/igf-esis.49.62 692 least 10 elements at the front and near the crack tip. we have refined the mesh proportionally to the number of elements which gives the convergence of the results. we used quadratic elements based on quadratic interpolation functions in order to have a low calculation cost. a gauss point is used per element which allows us to have a reduced integration scheme. figure 1: diagram of a cracked aluminum pipe repaired by composite patch. e1 (gpa) e2 (gpa) e3 (gpa) g12 (gpa) g13 (gpa) g23 (gpa) 12γ 13γ 23γ 12α (10-6°c) 12α (10-6°c) 12α (10-6°c) api 5l x70 207 0.33 22.5 adhesive (fm-73) 0.42 0.30 bore/époxy 200 19.6 19.6 7.2 5.5 5.5 0.3 0.28 0.28 4.5 23 23 glass/époxy 50 14.5 14.5 2.56 2.56 2.24 0.33 0.33 0.33 5.5 15 15 carbone/époxy 134 10.3 10.3 5.5 5.5 3.2 0.33 0.33 0.53 -1.2 34 34 table 1: elastic and thermal prosperity for different materials 18000 19000 20000 21000 22000 23000 18 20 22 24 26 28 k i( m p a .m 0 .5 ) number of nodes of structure element type c3d20r c3d15 c3d10 pipeline steel api 5l x70 , epipe = 4 mm composite patch, epatch= 2 mm adhesive fm 73, ea = 0.2 mm crack length a=5mm figure 2: mesh convergence of the structure. e. abdelouahed et alii, frattura ed integrità strutturale, 49 (2019) 690-697; doi: 10.3221/igf-esis.49.62 693 the virtual crack closure technique is based on the energy balance proposed by irwin. in this technique, the stress intensity factors are obtained for the three fracture modes using the equation: gi=ki²/e (1) where gi is the energy release rate for mode i, ki is the stress intensity factor for mode i, and e is the modulus of elasticity (i, ii and iii). in numerical elemental computations, the mesh choice results in the number of nodes and their arrangement that characterize the element and its density in the mesh structure. a series of calculation launching is opted in the first places in order to reach the convergence of computation with an optimization in the density of mesh, three different types of mesh were used: c3d20r: (a 20-node quadratic brig), (c3d15 : a 15-node quadratic triangular prism), (c3d10: a 10-node quadratic tetrahedron). stabilization of the result such as the stress intensity factor expresses the optimal choice of number and type of elements. it is also important to refine the mesh at the crack levels in order to better capture the value of the stress intensity factor. the number of elements used in the structure is 21414 elements in the pipeline, 2176 in the patch and 2176 in the adhesive. fig. 3 shows the architecture of the mesh used for the calculations. figure 3: overall mesh of the sample results and discussion effect of internal pressure ig. 4 shows the variation of the stress intensity factor in the cracked and repaired pipeline by three types of composite patch (boron / epoxy, glass / epoxy and carbon / epoxy) as a function of the change in internal pressure in the pipeline rift. the stress intensity factor (ki) is calculated in the direction of the fiber (parallel to the direction of the applied load). we can see that the adhesive curing process involves a relatively high level of sif at the crack front in the pipeline. this means that the adhesive and the patch are in tension. the pressurized pipeline exerts the tensile stresses. the intensity of the constraints in the patch is less significant compared to the constraint in the pipeline. this is because the coefficient of thermal expansion for steel is greater than that of (boron/epoxy, carbon/epoxy and glass/epoxy). however, the stresses in the composite are relatively large because there is a transfer of stresses from the steel pipeline to the composite part through the adhesive layer. on the other hand, it can also be said that the best composite for repair under high pressures is boron/epoxy. this linear variation of the stress intensity factor as a function of the internal pressure clearly reflects the linear behavior of the composite patch, the more rigid the composite, the greater the repair. temperature effect fig.5 uses the variation of the stress intensity factor in the cracked and repaired pipeline by three different types of composite patches (boron / epoxy, glass / epoxy and carbon / epoxy) as a function of the temperature in the external environment of the composite cracked pipeline. we notice that the stress intensity factor is higher when the temperature increases; it means that the increase of the temperature reduces the quality of the repair. from the graph (fig. 4), it can be said that among the f e. abdelouahed et alii, frattura ed integrità strutturale, 49 (2019) 690-697; doi: 10.3221/igf-esis.49.62 694 three composites, boron / epoxy and the most resistant patch in areas where the temperature is high for the repair of cracked transport pipelines. pipeline steel api 5l x70 , epipe = 4 mm composite patch epatch=2mm, pint=variable adhesive fm-73, e a = 0.2 mm crack length a=5mm pint(bar) 0 20 40 60 80 100 k 1 (m p a .m 0 .5 ) 0 10 20 30 40 50 60 boron/epoxy glass/epoxy carbon/epoxy figure 4: sif variation according to the internal pressure t(°c) 0 10 20 30 40 50 60 70 k 1 (m p a .m 0 .5 ) 0 2 4 6 8 10 12 14 16 18 boron/epoxy carbon/epoxy glass/epoxy pipeline steel api 5l x70 , e pipe = 4 mm composite patch, epatch=2 mm adhesive fm-73, ea = 0.2 mm crack length a=5mm figure 5: sif variation according to the temperature of the external environment the temperature of the external environment as well as the type of the patch composite clearly played a determining effect on the stress intensity factor levels. on one side the temperature weaken the adhesive accumulating the load on the pipeline and on the other hand the quality of the composite of the patches conditions the absorbed quantity of the loads, the more the composite is rigid more it allows the adhesive to transfer more than charge. however, this transfer is limited by the capacity of the adhesive, which will be limited even more by the presence of temperature as a climatic load on the structure. effect of crack depth fig. 6 shows the evolution of the stress intensity factor at the bottom of the composite patch repaired api 5l x70 steel pipe crack as a function of the crack depth change with respect to the thickness of the pipeline. we noticed that the ki increases when increasing the depth of the emerged crack, so the stresses are very important at the front of the crack. it is deduced that the quality of the repair decreases in cases where the crack is very deep. it is also noted that the effect of the composite quality of the patch follows the same variation as that of the stress intensity factor. this effect also retains the advantage of its quality regardless of the parameters analyzed. the more the crack depth increases, the more the repair affects its effect. e. abdelouahed et alii, frattura ed integrità strutturale, 49 (2019) 690-697; doi: 10.3221/igf-esis.49.62 695 depthcrack(%) 20 40 60 80 100 120 k 1 (m p a .m 0 .5 ) 0 5 10 15 20 25 boron/epoxy carbon/epoxy glass/epoxy pipeline steel api 5l x70 , epipe = 4 mm composite patch, epatch=2 mm adhesive fm-73, ea = 0.2 mm crack length a=5mm figure 6: variation of sif as a function of the crack depth of the pipeline effect of the thickness of the patch fig. 7 shows the evolution of the stress intensity factor at the crack front of the repaired steel pipe api 5l x70 as a function of the thickness variation of the composite part independently of the boron/epoxy, the glass/epoxy or carbon/epoxy. we note that the ki decreases as the thickness of the patch increases in the three different cases of repair and the smallest value is when the thickness of the patch is equal to the thickness of the pipeline. epatch 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 k 1 (m p a .m 0 .5 ) 5.6 5.7 5.8 5.9 6.0 6.1 6.2 6.3 6.4 boron/epoxy carbon/epoxy glass/epoxy pipeline steel api 5l x70 , epipe = 4 mm composite patch, epatch=variable adhesive fm 73, ea = 0.2 mm crack length a=5mm figure 7: sif variation according to composite patch thickness likewise, the reduction of the stress intensity factor follows the same variation as a function of the thickness of the patch, and always keeps the advantage of its quality (boron, carbon, glass) between them. the more the patch increases in thickness, the greater the charge transfer by the adhesive. this considerably reduces the sif, but remains conditioned by the strength of the adhesive. effect of change in crack length fig. 8 shows the variation of the stress intensity factor at the crack front in a pipeline repaired by three different types of composite patches (boron/epoxy, glass/epoxy and carbon/epoxy) as a function of the length of the crack. from this fig. 5, we notice that the development of the crack gives us larger values of ki, which means that the quality of the repair by composite patches decreases. we also note that the most effective material for repair in case of long cracks is boron/epoxy. reducing the stress intensity factor is always possible with a more rigid composite choice but it is clearly e. abdelouahed et alii, frattura ed integrità strutturale, 49 (2019) 690-697; doi: 10.3221/igf-esis.49.62 696 shown in this figure that the more the crack increases the more the repair becomes useless. this can be explained by the fact that the working area (transfer) of the adhesive is limited when the crack increases. lcrack 0 2 4 6 8 10 k 1 (m p a .m 0 .5 ) 5.6 5.8 6.0 6.2 6.4 6.6 6.8 7.0 boron/epoxy carbon/epoxy glass/epoxy pipeline steel api 5l x70 , epipe = 4 mm composite patch, epatch=2mm, lpatch=c st adhesive fm 73, ea = 0.2 mm crack length a=variable figure 8: sif variation according to the crack length of the pipeline conclusion his study has been focused by a numerical simulation on the evaluation of the stress intensity factor under different effect of: temperature variation, pressure variation, patch variation, patch thickness variation, and crack size variation of a structure steel pipe cracked and repaired by composite patch. the following conclusions could be deduced from the obtained results: • patches and adhesive play a crucial role on the repair. any reduction efficiency is limited by the ability of the adhesive to resist. • the efficiency repair is directly related to the stiffness of the composite patch. if the composite is more rigid, the repair efficiency is elevated. • an increase in the thickness of the patch increases the rigidity, the consequence, the increase in the efficiency. • the reparation efficiency decreases with the increasing length and crack depth. which subsequently undermines the work of the adhesive. • thermal stresses weaken the capacity of the adhesive by accumulating loads, which explains the increase in the stress intensity factor. references [1] manne, a., mendelsohn, r., richels, r. (1995). a model for evaluating regional and global effects of ghg reduction policies, energy policy, 23 (1), pp. 17-34. [2] sydney, t., richard a. d. (2003). review of ways to transport natural gas energy from countries which do not need the gas for domestic use, energy, (28), pp. 1461–1477. [3] ibrahim, h., ilinca, a., perron, j. (2008). energy storage systems—characteristics and comparisons, renewable and sustainable energy reviews, (12), pp. 1221 – 1250. [4] katnam, k.b., da silva, l.f.m., young, t.m. (2013). bonded repair of composite aircraf t structures: a review of scientific challenges and opportunities, progress in aerospace sciences, (61), pp. 26–42. [5] wu, m., johannesson, b., geiker, m. (2012). a review: self-healing in cementitious materials and engineered cementitious composite as a self-healing material, construction and building materials, (28), pp. 571–583. [6] djokic, d., rogers, a., lee-sullivan, p., mrad, n. (2002). residual stress development during the composite patch bonding process: measurement and modeling, composites, (a33), pp. 277-288. t e. abdelouahed et alii, frattura ed integrità strutturale, 49 (2019) 690-697; doi: 10.3221/igf-esis.49.62 697 [7] baker, a. (1999). bonded composite repair of fatigue-cracked primary aircraft structure, composite structures, (47), pp. 431-443. [8] komonen, j., penttala, v. (2003). effects of high temperature on the pore structure and strength of plain and polypropylene fiber reinforced cement pastes, fire technology, (39), pp. 23–34. [9] chow, w. t., atlim, s. n. (1997). composite patch repairs of metal structures: adhesive nonlinearity, thermal cycling, and debonding, aiaa journal, 35 (9), pp. 1528-1535. [10] gu, d.d., meiners, w., wissenbach, k., poprawe, r. (2012). laser additive manufacturing of metallic components: materials, processes and mechanisms, international materials reviews, 57 (3), pp. 133-164. [11] köpple, m., lauterbach, s., wagner w. (2013). composite repair of through-wall defects in pipework –analytical and numerical models with respect to iso/ts 24817, compos. struct, (95), pp. 173 –178. [12] zarrinzadeh, h., kabir, m.z., deylami, a. (2017). crack growth and debonding analysis of an aluminum pipe repaired by composite patch under fatigue loading, thin-walled structures, (112), pp. 140–148. [13] nateche, t., hadjmeliani, m., shafique, m.a., khan, matvienko, y.g., merah, n., pluvinage, g. (2015). residual harmfulness of a defect after repairing by a composite patch, engineering failure analysis, (48), pp. 166–173. [14] mhamdia, r., bachir bouadjra, b., serier, b. et al. (2011). contrainte intensity factor for repaired crack with bonded composite patch under thermo-mechanical loading. j reinf plastic compos, (30), pp. 416–424. [15] albedah, a., bachir bouiadjra, b., aminallah, l., et al. (2011). numerical analysis of the effect of thermal residual contraintees on the performances of bonded composite repairs in aircraft structures. compos, b (4), pp.511–516. [16] lam, c., cheng, j., yam, c. (2011). finite element study of cracked steel circular tube repaired by frp patching, procedia eng, (14), pp. 1106 –1113. [17] abaqus finite element programs. abaqus standard 5.6. hibbitt. pawtucket, ri 028: karlsson and sorensen, inc. [18] madani, k., touzain, s., feaugas, x., cohendouz, s., ratwani ,m. (2010). experimental and numerical study of repair techniques for panels with geometrical discontinuities. computational materials science, (48), pp. 83–93. << /ascii85encodepages false /allowtransparency false /autopositionepsfiles true /autorotatepages /none /binding /left /calgrayprofile (dot gain 20%) /calrgbprofile (srgb iec61966-2.1) /calcmykprofile (u.s. web coated \050swop\051 v2) /srgbprofile (srgb iec61966-2.1) /cannotembedfontpolicy /error /compatibilitylevel 1.4 /compressobjects /tags /compresspages true /convertimagestoindexed true /passthroughjpegimages true /createjobticket false /defaultrenderingintent /default /detectblends true /detectcurves 0.0000 /colorconversionstrategy /cmyk /dothumbnails false /embedallfonts true /embedopentype false /parseiccprofilesincomments true /embedjoboptions true /dscreportinglevel 0 /emitdscwarnings false /endpage -1 /imagememory 1048576 /lockdistillerparams false /maxsubsetpct 100 /optimize true /opm 1 /parsedsccomments true 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/hrv (za stvaranje adobe pdf dokumenata najpogodnijih za visokokvalitetni ispis prije tiskanja koristite ove postavke. stvoreni pdf dokumenti mogu se otvoriti acrobat i adobe reader 5.0 i kasnijim verzijama.) /hun 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can be opened with acrobat and adobe reader 5.0 and later.) >> /namespace [ (adobe) (common) (1.0) ] /othernamespaces [ << /asreaderspreads false /cropimagestoframes true /errorcontrol /warnandcontinue /flattenerignorespreadoverrides false /includeguidesgrids false /includenonprinting false /includeslug false /namespace [ (adobe) (indesign) (4.0) ] /omitplacedbitmaps false /omitplacedeps false /omitplacedpdf false /simulateoverprint /legacy >> << /addbleedmarks false /addcolorbars false /addcropmarks false /addpageinfo false /addregmarks false /convertcolors /converttocmyk /destinationprofilename () /destinationprofileselector /documentcmyk /downsample16bitimages true /flattenerpreset << /presetselector /mediumresolution >> /formelements false /generatestructure false /includebookmarks false /includehyperlinks false /includeinteractive false /includelayers false /includeprofiles false /multimediahandling /useobjectsettings /namespace [ (adobe) (creativesuite) (2.0) ] /pdfxoutputintentprofileselector /documentcmyk /preserveediting true /untaggedcmykhandling /leaveuntagged /untaggedrgbhandling /usedocumentprofile /usedocumentbleed false >> ] >> setdistillerparams << /hwresolution [2400 2400] /pagesize [612.000 792.000] >> setpagedevice microsoft word numero_34_art_41 s. keck et alii, frattura ed integrità strutturale, 34 (2015) 371-378; doi: 10.3221/igf-esis.34.41 371 focussed on crack paths investigation of crack paths in natural fibre-reinforced composites s. keck, m. fulland university of applied sciences zittau/görlitz, germany s.keck@hszg.de, m.fulland@hszg.de abstract. nowadays, fibre-reinforced composite materials are widely used in many fields, e.g. automotive and aerospace. natural fibres such as flax and hemp provide good density specific mechanical properties. additionally, the embodied production energy in natural fibres is much smaller than in synthetic ones. within this paper the fracture mechanical behaviour of flax fibre-reinforced composites is discussed. especially, this paper focuses on the determination and investigation of crack paths in compact tension specimens with three different fibre directions under a static as well as fatigue load. differences and similarities in the obtained crack paths under different loading conditions are presented. due to the pronounced orthotropic behaviour of those materials the crack path is not only governed by the stress state, but practically determined by the fibre direction and fibre volume fraction. therefore, the well-known stress intensity factor solutions for the standard specimens are not applicable. it is necessary to carry out extensive numerical simulations to evaluate the stress intensity factor evolution along the growing crack in order to be able to determine fatigue crack growth rate curves. those numerical crack growth simulations are performed with the three-dimensional crack simulation program adapcrack3d to gain energy release rates and in addition stress intensity factors. keywords. natural fibre-reinforced composites; orthotropic material behaviour; crack paths; fatigue crack growth rate curves; adapcrack3d. introduction ue to their mechanical properties (stiffness and strength) and their small densities fibre-reinforced composite materials are widely used in many fields such as automotive and aerospace. hence, their utilisation for lightweight applications is suitable. furthermore, it is of great importance to take renewable resources into account which are comparable in terms of mechanical properties with conventional materials. concerning this matter natural fibres need to be considered. the embodied production energy in natural fibres is in the order of 10 times smaller than in synthetic ones. additionally, the production of greenhouse gases is enormously reduced [1]. within this paper the fracture mechanical behaviour of natural fibre-reinforced composites is discussed. in this work composites are defined as petrochemical polymers reinforced with flax-fibres. the fibres take up forces. the matrix transfers forces to fibres, fixes, and protects those from surrounding conditions. the ratio of fibre volume and composite volume defines the fibre volume fraction. thereby, tailored construction components and structures can be built. due to the pronounced orthotropic behaviour of those materials the crack path is not only governed by the stress state, but practically determined by the fibre direction and the fibre volume fraction. d s. keck et alii, frattura ed integrità strutturale, 34 (2015) 371-378; doi: 10.3221/igf-esis.34.41 372 at first, materials and specimens are explained. then experimental investigations and numerical computations are described. later on the identified crack paths and fatigue crack growth curves are illustrated. finally, conclusions of the obtained results and an outlook are given. material and specimens n this work the composite is reinforced with flax-fibres, which are semi-finished products (yarn and twisted yarn). their density is about 1,450 kg/m³ [1]. for the polymer matrix an epoxy resin is used. the fibres get rolled on a frame to achieve a unidirectional alignment (fig. 1). due to the orthotropic behaviour of the fibres and the unidirectional alignment the composites are orthotropic, too. unnotched specimens and compact tension specimens were taken from plates (geometric dimensions: 500 mm x 470 mm x 10 mm). the size of an unnotched specimen is 150 mm x 15 mm x 10 mm. the geometric dimensions of the compact tension specimens (fig. 2) are chosen according to the astm standard e647-13 [2]. due to the smaller mechanical properties (fig. 3) compared to metallic materials the drill holes are reduced. the specimen depth is set to 10 mm. a postcuring process provides a higher strength of the polymer matrix. for each compact tension specimen the pre-crack initiation is produced with a razor blade (razor sawing). figure 1: semi-finished product consisting of flax. figure 2: geometric dimensions of the investigated compact tension specimen (dimensions in mm). i s. keck et alii, frattura ed integrità strutturale, 34 (2015) 371-378; doi: 10.3221/igf-esis.34.41 373 experimental investigations mechanical properties he young’s moduli are measured by a universal testing machine (zwick roell z250) under ambient temperature. tensile tests were conducted to characterize the mechanical properties, which are required to execute the numerical simulations with real values. the mean values and the standard deviations of the young’s moduli of the unnotched specimens with different fibre directions and fibre volume fractions are plotted in fig. 3. thereby, character ’f’ stands for flax. the number left to the slash describes the yarn count (unit: meters per gram). a ’1’ behind the slash marks a yarn and a ’2’ would mean a twisted yarn. subsequently, fibre volume fraction and fibre direction are named. the fibre directions are illustrated schematically in fig. 4. both constituents (fibres and polymer matrices) and composites have brittle fracture behaviour. additionally, tensile test results show that there is a non-linear behaviour of the composites. figure 3: young’s moduli of unnotched specimens. figure 4: schematic illustration of compact tension specimens with different fibre directions (0°, 45°, 90°). crack paths the crack paths of the compact tension specimens were determined under static as well as cyclic loading conditions. in fatigue tests the stress ratio r is set to 0.1. different values of remote tensile forces were applied, thus, the initial crack is in mode i. fig. 5 shows the crack paths of the specimens (fibre volume fraction 35%) under constant amplitude cyclic loading. after executing fatigue tests those were loaded until failure. if the fibre direction is perpendicular to the loading direction, the fatigue crack grows along the fibres (fig. 5, right hand side). this particular crack path is identical with a path in homogeneous isotropic materials. if the angle between fibre direction and loading direction is about 45°, the crack path kinks at the crack tip and grows along the fibre direction (fig. 5, middle). if the reinforced direction is parallel to the loading direction, the fatigue crack kinks at the crack tip in fibre direction and grows along the fibres (fig. 5, left hand t s. keck et alii, frattura ed integrità strutturale, 34 (2015) 371-378; doi: 10.3221/igf-esis.34.41 374 side). in either case the crack paths are determined by the fibre direction and there are inter-fibre failures. the same crack paths were obtained by testing compact tension specimens under static loading. figure 5: compact tension specimens with different directions after cyclic loading (fibre volume fraction 35%). further investigations showed that there is a relation between fibre volume fractions and crack paths. the dependence on the fibre volume fraction using compact tension specimens (0° fibre direction, constant amplitude cyclic loading, r = 0.1) is illustrated in fig. 6. the more fibres are contained, the faster the crack path tends to grow in fibre direction. figure 6: compact tension specimens with different fibre volume fractions (0° fibre direction). fatigue crack growth rate curves he fatigue tests were conducted on a resonance testing machine (roell amsler 100 hfp 5100) under constant amplitude cyclic loading and ambient temperature. the stress ratio r is set to 0.1 and the frequencies are about 30 hz. the fatigue crack growth rate curves were determined by experimental investigations and application of numerical simulations. the crack length a is detected by an optical measuring system. in conjunction with the recorded load cycles n the crack growth rates da/dn can be calculated. the equivalent stress intensity factors keq and the cyclic equivalent stress intensity factor δkeq are calculated according to richard [3] as 2 2 2 1 2 1 4( ) 4( ) 2 2 i eq i ii iii k k k k k     (1) where α1 = kic/kiic and α2 = kic/kiiic. there is no formula available to calculate the stress intensity factors for such anisotropic material. hence, those are determined by the three-dimensional crack simulation program adapcrack3d. the program uses the modified virtual crack closure method to determine the energy release rates and corresponding values of stress intensity factors [4]. the correlation function according to the astm standard e647-13 [2] to examine the crack length in order to the crack tip opening displacement is not applicable. therefore, it is necessary to calculate the stress intensity factors corresponding to the determined crack lengths. a three-dimensional finite elements model of the specimen is constructed in the t s. keck et alii, frattura ed integrità strutturale, 34 (2015) 371-378; doi: 10.3221/igf-esis.34.41 375 commercial finite element program abaqus. the simulations are performed with abaqus and adapcrack3d. using the latter, the numerical simulations of the fatigue crack growth and the fracture mechanical analysis are computed. for crack propagation it is assumed that linear elastic fracture mechanics is valid [4]. for executing the numerical simulations young’s moduli are required. those were needed, among other things, for calculating fracture mechanical parameters. thus, values are chosen according to the determined ones (cf. tab. 1). consequently, due to reasonable simulation the inhomogeneous orthotropic material is approximated as a homogeneous orthotropic continuum. fibre direction e1 [gpa] e2 [gpa] e3 [gpa] 0° 3 20 3 45° 3 4.2 4.2 90° 3 3 20 table 1: mechanical properties for numerical simulations. the fatigue crack growth rate curve for specimens with fibre direction perpendicular to the loading direction is illustrated in fig. 7. the da/dn versus δkeq data are plotted on logarithmic scales. the fatigue crack growth rate curves for other directions are shown in figs. 8 (45°) and 9 (0°). for each curve a fit of the necessary forman/mettu equation parameters (tab. 2) has been carried out. this crack growth equation [5] is given by max 1 1 1 1 p th n eq fm eq q c k kda c k dn r k k                      (2) parameter fibre direction 0° 45° 90° cfm 5e-04 2e-04 9e-05 γ 0 0 0 r 0.1 0.1 0.1 δkth 0.8 0.9 1.0 kc 4.5 9.0 9.0 n 3.5 2.0 2.5 p 5.0 3.0 2.5 q 0.50 0.25 0.25 table 2: forman/mettu equation parameters. it can be seen that near-threshold values can hardly be found due to the material and the sensitivity of the measurement system. therefore, the threshold values can only be regarded as extrapolations. the data for the linear intervals are well-recorded, so that a fit of the parameters was possible. the slope of the fatigue crack growth rate curve for specimens with 0° fibre direction is much steeper than the other ones. the crack growth rate data for 45° specimens and 90° specimens are very similar. s. keck et alii, frattura ed integrità strutturale, 34 (2015) 371-378; doi: 10.3221/igf-esis.34.41 376 figure 7: fatigue crack growth rate data for compact tension specimens (90° fibre direction, r = 0.1). figure 8: fatigue crack growth rate data for compact tension specimens (45° fibre direction, r = 0.1). figure 9: fatigue crack growth rate data for compact tension specimen (0° fibre direction, r = 0.1). s. keck et alii, frattura ed integrità strutturale, 34 (2015) 371-378; doi: 10.3221/igf-esis.34.41 377 geometry correction factor functions he evolution of the cyclic equivalent stress intensity factors with the growing crack does not follow the wellknown stress intensity factor solution for compact tension specimens proposed by srawley [6] since the material is no longer homogeneous and isotropic, in consequence the crack is not only governed by the stress state. it is necessary to carry out extensive numerical simulations to evaluate the stress intensity factor evolution along the growing crack in order to be able to determine fatigue crack growth rate curves. for numerical simulations experimentally determined crack lengths are required to calculate the corresponding stress intensity factors. hence, special functions for calculating the geometry correction factors for each fibre direction and fibre volume fraction are needed. here, the geometry correction factor y is computed with the equivalent stress intensity factor keq, the specimen thickness b, the length of the ligament (specimen width) x, and the applied force p to eqk b x y p    (3) the single geometry correction factors can be expressed by a mathematical function. commonly, the function depends on the crack length a and the length of the ligament, mostly named with the character w. here, those lengths are denoted with the character x to point out that x is a directional parameter. for example, if the fibre direction is perpendicular to the loading direction (90°), x is assumed as the originally length of the ligament w. the function is described by 2 3 4 5.5 2 20 8 70 a a a a a a y y x w w w w w                                         (4) by means of the geometry correction factor functions it is possible to calculate values of the stress intensity factor and obtain fatigue crack growth rate curves for different fibre directions. the geometry correction function data for a compact tension specimen with 90° fibre direction are plotted in fig. 10. for further fibre directions functions need to be developed. therefore, it is suitable to only modify the parameter x in eq. (4). concerning this matter the length of the ligament x could be changed directional. figure 10: geometry correction factor data for compact tension specimen (90° fibre direction). conclusions and outlook n this paper mechanical and fracture mechanical behaviour of natural fibre-reinforced composites were presented. thereby, crack paths for compact tension specimens with different fibre directions and fibre volume fraction were under consideration. both fibre direction and fibre volume fraction influence the crack path. the more fibres are t i s. keck et alii, frattura ed integrità strutturale, 34 (2015) 371-378; doi: 10.3221/igf-esis.34.41 378 contained, the faster the crack path tends to grow in fibre direction. here the ratio of the elasticity mismatch plays an important role. also, as a first approach a formula for calculating the geometry correction factors for compact tension specimens where the fibre direction is perpendicular to the loading direction was described. the geometry correction factor functions for further fibre directions need to be developed. therefore, it is necessary to consider the possibility to only modify the parameter concerning the length of the ligament. acknowledgement his publication has been partially funded with support from the european union, the european social fund (esf) and the free state of saxony. references [1] dicker, m.p.m., duckworth, p.f., baker, a.a., francois, g., hazzard, m.k., weaver, p.m., green composites: a review of material attributes and complementary applications, composites: part a: applied science and manufacturing, 56 (2014) 280–289. [2] astm standard e647-13, standard test method for measurement of fatigue crack growth rates. american society for testing and material, west conshohocken, pa, (2013). [3] richard, h.a., fulland, m., sander, m., theoretical crack path prediction, fatigue & fracture of engineering materials and structures, 28 (2015) 3–12. [4] fulland, m., steigemann, m., richard, h.a., specovius-neugebauer, m., development of stress intensities for cracks in fgms with orientation perpendicular and parallel to the gradiation, engineering fracture mechanics, 95 (2012) 37– 44. [5] kuna, m., finite elements in fracture mechanics. theory-numerics-applications, springer, heidelberg, (2013). doi: 10.1007/978-94-007-6680-8. [6] srawley, j.e., wide range stress intensity factor expressions for astm e399 standard fracture toughness specimens, international journal of fracture, 12 (1976) 475. t microsoft word numero_58_art_08_3154 b. v. s. kumar et alii, frattura ed integrità strutturale, 58 (2021) 105-113; doi: 10.3221/igf-esis.58.08 105 influence of oxidation on fracture toughness of carbon-carbon composites for high-temperature applications b.v. sunil kumar department of mechanical engineering, canara engineering college, mangalore, vtu, karnataka, 574219, india. sunilbv777@gmail.com , https://orcid.org/0000-0002-3115-2141 v. neelakantha londe, m. lokesha department of mechanical engineering, mangalore institute of technology and engineering, moodabidri, vtu, karnataka, 574225, india. s.n. vasantha kumar department of mechanical engineering, canara engineering college, mangalore, vtu, karnataka, 574219, india. a.o. surendranathan department. of metallurgical and materials engineering, nitk, surathkal, karnataka, 575025, india. abstract. carbon-carbon composites (c-cc), used as composites for their remarkable qualities in the space industry and in many other industry sectors. c-cc has proven to be the most efficient material in extreme temperature situations. they are one among the best high-temperature materials with good thermal quality, such as high-temperature stability, outstanding thermal conductivity and low-temperature expansion coefficients. in aircraft, railways, trucks and even race vehicles, c-cc brake disks are in high demand. compared to the favorable thermal and mechanical qualities of c-cc, their great sensitivity to oxidation in an oxidizing environment at temperatures even around 400°c is a major restriction with these composites. in particular, a study of the c-cc oxidation mechanism helps to create protective measures for these composites. the present experimental study explores the influence of oxidation in static air on the fracture toughness of c-cc. at a temperature of around 400°c to 700°c in an increment of 100°c, an oxidation evaluation of the material is carried out. results show that there was a significant decrease in the fracture toughness when there was an increase in temperature from 400°c to 700°c. we can observe that c-cc fracture toughness is severely affected by oxidation. the decrease in the fracture toughness value in comparison with room temperature was 6% for 400°c and 45% for 700°c. keywords. carbon-carbon composites; fracture toughness; oxidation; senb specimen; astm d5045. citation: kumar b. v., s., londe, v. n., lokesha, m., vasantha kumar, s.n., surendranathan, a.o., influence of oxidation on fracture toughness of carbon-carbon composites for high-temperature applications, frattura ed integrità strutturale, xx (2021) 105-113. received: 27.06.2021 accepted: 17.07.2021 published: 01.10.2021 copyright: © 2021 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. https://youtu.be/qqouyo5y5do b. v. s. kumar et alii, frattura ed integrità strutturale, 58 (2021) 105-113; doi: 10.3221/igf-esis.58.08 106 introduction ecause of its excellent long-durability, we employ composites for several applications, including architecture, cars, electronics, and biomedical engineering. composites are employed in our daily lives. in recent decades, improved composite materials are used in the field of study, and novel fiber composites are being developed constantly. in the space sector and many other industries, carbon-carbon composites (c-cc) are used as composites because of their unique characteristics. c-cc has been showed to be the most efficient material in extreme temperature conditions [1,2]. this special material was created at the end of the 1950s and designed for space travel only for the use of spatial programs until the late 1960s when space shuttles required materials such as lightweight, high thermal shock resistance, low heat expansion coefficients, high resistance to impact, high hardness, etc. [1–3]. the c-cc is one of the best high-temperature materials, with strong thermal properties such a high thermo stability (melting point > 3000 °c), excellent thermal conductivity and low-temperature expansion coefficients. mechanical efficiency can be maintained even at severe temperatures. the good frictional properties with less wear are maintained throughout the temperature range [4–6]. these properties make it suitable for applications in high-speed airplanes such as the airbus, concord and mirage. c-cc is a popular material for nose entrance tips, state-of-the-art wing material, rocket systems, highperformance turbojet engines, intercontinental ballistic rocket nose cones, vehicle braking systems, and other applications. thanks to its unique quality and very low density. in fig. 1. some of the applications are shown [7–10]. a b c d figure 1: (a) c-cc brake disc [10] (b) nose cone for missile [16] (c) plates and liners [1] (d) turbine rotor [1]. in aircraft, railways, vehicles, even racing automobiles, carbon brake disks are in high demand. for brake disks, around 60% of the applications are c-cc. c-cc are used in other fields and in aeronautical applications in recent years [7–10]. c-cc extends to challenging applications such as earthquakes and lightweight concrete systems in the building sector and infrastructure. they also have significant potential in the oil business, especially in crushing lines, drilling and deep oceans b b. v. s. kumar et alii, frattura ed integrità strutturale, 58 (2021) 105-113; doi: 10.3221/igf-esis.58.08 107 [1–3]. compared to the favorable thermal and mechanical qualities of c-cc, their great sensitivity to oxidation in an oxidizing environment at temperatures even around 400°c is a major restriction with these composites. in particular, a study of the c-cc oxidation mechanism helps to create protective measures for these composites. the mechanical properties of the c-cc recessed because of oxidation which were found in certain investigations. the effect of oxidation on mechanical proprieties is shown to be catastrophic. in the meantime decrease in flexural strength was attributed primarily to a decrease in fracture toughness rather than an increase in flaw size. the more the mass loss, the lower the failure stress. a significant number of studies have been carried out in order to understand the oxidation mechanisms for the oxidation behavior of c-cc. it was shown furthermore that the overall surface area other than porosity or gradual density and porous entry were controlled for the oxidation of c-cc. the oxidation took place at the contact between the fiber and matrix and subsequently advanced through the micro-cracks between the interfaces [11,12]. fracture mechanics is considered the field of research related to engineering fractures and failures. the development of technical structures, materials, and installations, to ensure their technical safety, durability, and dependability, is based on fractures and damage prevention and evaluation [13,14]. fracture toughness is a quantitative means of quantifying fracture resistance when there is a crack. this is an important feature of all materials, sometimes referred to as crack resistance, and used in all design applications in the fracture mechanic domain. the fact that fracture mechanics apply to common isotropic materials was also successfully established. intralaminar fracture toughness is one of the problems with polymer composites (fiber-intensive cracking or matrix cracking). astm d 5045 [15] (plastic/particular polymer composites) testing methodologies for strain fracturing toughness are applied by investigators. these testing techniques based on astm d 5045 include loading pre-cracked specimen in tension or the three-point bending, which is shown in fig. 2. [15,16]. tension specimen is related as compact tension (ct) and three-point bending as single edge notch bend (senb). in comparison to other specimen configurations, ct and senb geometries are recommended since they feature mostly bending stress levels that allow smaller sample sizes for plane stress. the specimen thickness is denoted as ‘b’ and ‘w’ is specimen width ‘w=2b’. the crack length ‘a’ is selected such that 0.45 < a/w < 0.55 for both these configuration [16,17]. a b figure 2: (a) ct specimen (b) senb specimen [15,16] at 400°c and above, c-cc interacts with oxygen. these materials have long-term usage at high temperatures, so they must therefore be evaluated for the fracture toughness in this respect. the oxidation test of the samples in static air at temperature of around 400°c to 700°c was carried out in the current investigation. the temperature was raised in an increment of 100°c. the heating of specimens was carried out in a tubular furnace for about 10 to 15 minutes until the required temperature was attained and a thermocouple monitored and controlled the temperature. senb specimen configuration having a thickness (b) of 10 mm is used in mode i loading conditions. (a/w) ratio taken for the study is 0.45. materials and experimental methods fabrication and specimen preparation of carbon-carbon composite he liquid phase impregnation technology is utilized to manufacture the composites. the material having a ‘2d’ fiber architecture is used in the fabrication process. this process impregnates liquid impregnates such charcoal tar, oil pitches, and thermosetting resins which provide high carbon content. initially, a compression mold procedure t b. v. s. kumar et alii, frattura ed integrità strutturale, 58 (2021) 105-113; doi: 10.3221/igf-esis.58.08 108 formed the carbon and phenolic laminates from carbon materials in the form of a disk. the combined phenolic and 2d carbon fibers in a pitch are impregnated over 300°c. laminates are carbonized at 1000°c in an inert environment (very pure nitrogen) and then pitched in petrol (densification). the densification process contains 3 phases, pitch impregnation, up to 700°c high-pressure carbonizations at a pressure of about 1000 bar, and above 2000°c graphitization. the densification cycles are repeated to achieve the required 1.8 g/cc density. the test specimen employed is senb as discussed and created by produced laminates per astm d 5045 standards [15,16]. fracture toughness testing laminates fabricated are machined to make senb specimens. the first portion of the ‘v’ notch is made with a cutter and a starting crack known as ‘pre-crack’ is placed at the root of the notch with a fine jewel saw. the (a/w) ratio taken for the study is 0.45. five samples have been examined for each condition. the testing is conducted by united calibration corporation made universal testing equipment with a crosshead speed of 1 mm/min, under standard astm d5045. tests were carried out at room temperature (28°c) initially and later to find an effect of oxidation, samples were heated in a tubular furnace in static air at a temperature of around 400°c to 700°c in an increment of 100°c. the heating of specimens was carried out for about 10 to 15 minutes until the required temperature was attained and a thermocouple monitored and controlled the temperature. later the samples were removed from the furnace and cooled to room temperature to carry out the fracture toughness testing. load against displacement curves are entered and the load pq is computed as illustrated in fig. 3a for calculating fracture toughness. using eqn.1 [15,16] fracture toughness (kic) is calculated based on geometrical parameters of samples as shown in fig. 3b.  1/ 2 q ic p k f x bw        (1)          2 1/ 2 3/ 2 1.99 1 2015 3.93 2.7 6 1 2 1 x x x x f x x x x        (2) where, x = (a/w) a b figure 3: (a) determination of pq [15] (b) geometrical parameters for senb specimen testing results and discussion fracture toughness oad to displacement curve is obtained for room temperature and oxidation temperatures discussed as shown in fig. 4 and calculated corresponding fracture toughness is tabulated in tab. 1 and shown in fig. 5. l b. v. s. kumar et alii, frattura ed integrità strutturale, 58 (2021) 105-113; doi: 10.3221/igf-esis.58.08 109 figure 4: load to displacement curve for various temperatures sl no. temperature (°c) pmax (kn) pq (kn) fracture toughness kic ( mpa m ) variation in kic to room temp. 1 28°c (room temperature) 1.35 1.28 8.27 2 400°c 1.27 1.20 7.75 6 % 3 500°c 1.17 1.05 6.78 18 % 4 600°c 1.06 0.90 5.81 29 % 5 700°c 0.81 0.70 4.52 45 % table 1: fracture toughness results at various temperatures figure 5: fracture toughness at various temperatures b. v. s. kumar et alii, frattura ed integrità strutturale, 58 (2021) 105-113; doi: 10.3221/igf-esis.58.08 110 from the results, we observed that there was a significant decrease in the fracture toughness when there was an increase in temperature from 400°c to 700°c. we can observe that c-cc fracture toughness is severely affected by oxidation. the decrease in the fracture toughness value in comparison with room temperature was 6% for 400°c and 45% for 700°c . the fracture toughness was drastically reduced. weight loss is readily demonstrated by oxidation in c-cc. oxidation protection, therefore, has to be done by various techniques for c-cc in this respect. scanning electron microscope (sem) analysis sem micrographs were obtained using the scanning electron microscope (model: s 3500, make: hitachi). the fractured ccc surface at room temperature depicted in fig. 6 shows the brittle behavior of fractures. in certain regions, porosity is seen. the fracture results from the extraction of fiber and the decomposition of fiber are processes that consume energy. a b c d figure 6: fractured sem images of c-cc at room temperature for different magnifications (a) x 200 (b) x 500 (c) x 2k (d) x 2k. b. v. s. kumar et alii, frattura ed integrità strutturale, 58 (2021) 105-113; doi: 10.3221/igf-esis.58.08 111 a b c d figure 7: fractured sem images of c-cc after oxidation fractured sem images of c-cc after oxidation for different magnifications (a) x 200 (b) x 500 (c) x 500 (d) x 2k. we can observe from fig. 7 that the c-cc burning away very rapidly due to oxidation. the burning started above 500°c and the creation of holes and cracks in the matrix has gradually taken place. we may witness the formation of huge pores between the fiber bundles. fiber and matrix were oxidized at the same time, however, the matrix was first burnt resulting in quick damage to the oxygen penetration in the fibers. the fiber diameter is also dramatically reduced and ends are sharply reduced when compared to the starting diameter following oxidation. the coefficient of thermal expansion between fiber and matrix shows a difference and this causes potential stress on the interface. the tensile stress may lead to little fractures known as debonding. the cracks allow oxygen to enter and oxidization to accelerate. as a result, when oxidation took place, the circumferential gap depth was increased. the breadth of the gaps is increased by increasing the oxidation temperature. furthermore, the spaces are gradually linked. b. v. s. kumar et alii, frattura ed integrità strutturale, 58 (2021) 105-113; doi: 10.3221/igf-esis.58.08 112 conclusions he following conclusions are formed from the results, discussion, and analysis.  the heat treatment procedure plays an extremely important part in the manufacture of c-cc. it is necessary to densify through pitch impregnation. if the composites are not appropriately densified, composites with less density will not be suitable for several applications.  from the results, we observed that there was a significant decrease in the fracture toughness when there was an increase in temperature from 400°c to 700°c. we can observe that c-cc fracture toughness is severely affected by oxidation. the decrease in the fracture toughness value in comparison with room temperature was 6% for 400°c and 45% for 700°c. the fractured c-cc surface at room temperature shows the brittle behavior of fractures. in certain regions, porosity is seen. the fracture results from the extraction of fiber and the decomposition of fiber are processes that consume energy.  the creation of holes and cracks in the matrix has gradually taken place. we may witness the formation of huge pores between the fiber bundles. fiber and matrix were oxidized at the same time, however, the matrix was first burnt resulting in quick damage to the oxygen penetration in the fibers.  the fracture toughness has drastically reduced and weight loss is readily demonstrated by oxidation in c-cc. oxidation protection, therefore, has to be done by various techniques for c-cc in this respect. acknowledgments he author sunil kumar b.v. would like to thank advanced systems laboratory, hyderabad for providing research facilities and study support. references [1] fitzer, e., manocha, l.m. (2001).carbon reinforcements and carbon/carbon composites. annales de chimie science des materiaux, 26, pp. 93–4. [2] savage, g. (1993).applications of carbon-carbon composites. carbon-carbon composites, springer, pp. 323–59. [3] devi, g.r., rao, k.r. (1993). carbon carbon composites: an overview., def. sci. j., 43(4), pp. 369. [4] windhorst, t., blount, g. (1997). carbon-carbon composites: a summary of recent developments and applications, mater. des., 18(1), pp. 11–5. [5] das, t.k., ghosh, p., das, n.c. (2019). preparation, development, outcomes, and application versatility of carbon fiber-based polymer composites: a review, adv. compos. hybrid mater., pp. 1–20. [6] arabab, s. (2015). research in carbon-carbon composites, open siuc. [7] manocha, l.m. (2003). high performance carbon-carbon composites, sadhana, 28(1–2), pp. 349–58. [8] scarponi, c. (2016).carbon--carbon composites in aerospace engineering. advanced composite materials for aerospace engineering, elsevier, pp. 385–412. [9] lim, d.-w., kim, t.-h., choi, j.-h., kweon, j.-h., park, h.-s. (2008). a study of the strength of carbon--carbon brake disks for automotive applications, compos. struct., 86(1–3), pp. 101–6. [10] gadow, r., jiménez, m. (2019). carbon fiber-reinforced carbon composites for aircraft brakes, am. ceram. soc. bull., 98(6), pp. 28–34. [11] mckee, d.w. (1987). oxidation behavior and protection of carbon/carbon composites, carbon n. y., 25(4), pp. 551– 7. [12] zhang, c., yan, k., qiao, s., li, m., han, d., guo, y. (2012). effect of oxidation on fracture toughness of a carbon/carbon composite, j. wuhan univ. technol. sci. ed., 27(5), pp. 944–7. [13] kuna, m. (2013). finite elements in fracture mechanics, 10, springer. [14] gdoutos, e.e. (2020). fracture mechanics: an introduction, vol. 263, springer nature. [15] d5045--14. (2014). standard test methods for plane-strain fracture toughness and strain energy release rate of plastic materials 1, astm j, 99, pp. 1–9. [16] kumar, b.v.s., londe, v.n., lokesha, m., anilas, m., surendranathan, a.o. (2021). experimental investigation on t t b. v. s. kumar et alii, frattura ed integrità strutturale, 58 (2021) 105-113; doi: 10.3221/igf-esis.58.08 113 mode-i fracture toughness of carbon-carbon composites fabricated by preformed yarn method, mater. today proc.. [17] zhu, x.-k., joyce, j.a. (2012). review of fracture toughness (g, k, j, ctod, ctoa) testing and standardization, eng. fract. mech., 85, pp. 1–46. microsoft word numero_34_art_12 l. náhlík et alii, frattura ed integrità strutturale, 34 (2015) 116-124; doi: 10.3221/igf-esis.34.12 116 focussed on crack paths estimation of stepwise crack propagation in ceramic laminates with strong interfaces l. náhlík, k. štegnerová institute of physics of materials, academy of sciences of the czech republic, zizkova 22, 616 62 brno, czech republic and faculty of mechanical engineering, brno university of technology, technicka 2, 616 69 brno, czech republic nahlik@ipm.cz, stegnerova@ipm.cz p. hutař institute of physics of materials, academy of sciences of the czech republic, zizkova 22, 616 62 brno, czech republic hutar@ipm.cz abstract. during the last years many researchers put so much effort to design layered structures combining different materials in order to improve low fracture toughness and mechanical reliability of the ceramics. it has been proven, that an effective way is to create layered ceramics with strongly bonded interfaces. after the cooling process from the sintering temperature, due to the different coefficients of thermal expansion of individual constituents of the composite, significant internal residual stresses are developed within the layers. these stresses can change the crack behaviour. this results to the higher value of so-called apparent fracture toughness, i.e. higher resistance of the ceramic laminate to the crack propagation. the contribution deals with a description of the specific crack behaviour in the layered alumina-zirconia ceramic laminate. the main aim is to clarify crack behaviour in the compressive layer and provide computational tools for estimation of crack behaviour in the field of strong residual stresses. the crack propagation was investigated on the basis of linear elastic fracture mechanics. fracture parameters were computed numerically and by author’s routines. finite element models were developed in order to obtain a stress distribution in the laminate containing a crack and to simulate crack propagation. the sharp change of the crack propagation direction was estimated using sih’s criterion based on the strain energy density factor. estimated crack behaviour is qualitatively in a good agreement with experimental observations. presented approach contributes to the better understanding of the toughening mechanism of ceramic laminates and can be advantageously used for design of new layered ceramic composites and for better prediction of their failure. keywords. ceramic laminates; crack behaviour; residual stresses; strain energy density factor; crack propagation direction. introduction aterial interfaces play an important role in material (composite) behaviour and its properties. the presence of regions with different material and mechanical properties and the existence of an interface between them have a pronounced influence on the stress distribution of composite bodies. the influence of material interfaces was m l. náhlík et alii, frattura ed integrità strutturale, 34 (2015) 116-124; doi: 10.3221/igf-esis.34.12 117 intensively studied during last years for different material combinations, from both theoretical and experimental sides, see e.g. [1-8] for detailed information. the specific stress distribution of layered composites can be used in design of new composite materials with improved mechanical properties, e.g. with higher flexural strength or higher resistance to crack propagation, etc. the existence of interfaces and their toughening effect are, with the advantage, used in the manufacturing of “flaw tolerant” multilayer ceramic composites [9]. there is a new class of ceramic materials under development, the ceramic laminates with controlled crack resistance and crack propagation [10-12]. the paper is focused on ceramic laminates with strongly bonded layers. the toughening mechanism of strongly bonded laminates is based on deflection and/or bifurcation of crack path caused by internal residual stresses inside the layers [13,14]. mechanism of internal stresses evolution is based on unequal shrinkage of physically bonded materials during sintering [15]. this mechanism was experimentally proved for different kinds of ceramic laminates with strongly bonded interfaces [16-27], however only few works exists dealing with the prediction of laminate properties [28] or explaining specific crack behaviour in the ceramic laminates [29-32]. this paper focuses on the crack behaviour in the compressive layer of the laminate and describes by use of linear elastic fracture mechanics specific crack propagation (see fig. 1) in this layer. figure 1: crack bifurcation in amz layer. with courtesy of r. bermejo [23]. the basic principle of the toughening of the layered ceramic composite is based on selection of two ceramics with different values of coefficients of thermal expansion. the ceramics are layered by system a-b-a symmetrically and parallelly to the axis of symmetry of the layered composite body. cooling down from the sintering temperature leads to the development of residual stresses, which are usually of tensile nature in the outside layers. description of the studied layered ceramic composite for the study material system based on alumina and zirconia was chosen. these two constituents can be taken as typical examples of convenient materials for layered ceramics. behaviour of such kind of laminates were studied e.g. in [20-23]. considered ceramic laminate was created by 9 layers. 5 were made of al2o3/5vol.%t-zro2 (alumina with tetragonal zirconia, reffered as atz) and 4 were made of al2o3/30vol.%m-zro2 (alumina with monoclinic zirconia, reffered as amz). material characteristics were taken from literature [20,21] and are summarized in tab. 1. the laminate was subjected to four-point bending (4pb) test, see fig. 2. property atz amz young´s modulus e [gpa] 390 280 poisson´s ratio ν [-] 0.22 0.22 fracture toughness kic [mpa.m0.5] 3.2 2.6 coefficient of thermal expansion t [10 -6 k -1 ] 9.8 8.0 strength f [mpa] 422 90 table 1: material properties of studied laminate [20,21]. l. náhlík et alii, frattura ed integrità strutturale, 34 (2015) 116-124; doi: 10.3221/igf-esis.34.12 118 figure 2: scheme of studied ceramic laminate with typical crack path (dimensions in [mm]) and orientation of residual stresses in composite layers. the magnitude of residual stresses in the case of crack absence in the layered composite can be estimated from forces balance in individual layers. this leads to following expressions [33]:  0 , 1 1 1 ' ' 1 sf t amz atz t res atz atz amz dt n e e n             , , , 1 1 res amz res atz n n          , (1) where: atz amz t t   , ' 1 amz amz amz e e    , ' 1 atz atz atz e e    , tsf [°c] is stress free temperature, t0 [°c] room temperature, α [10-6k-1] coefficient of thermal expansion, n [-] number of layers, t [mm] thickness of layer, e [mpa] young´s modulus and ν [-] poisson´s ratio. calculated values of residual stresses for studied configurations are shown in the tab. 2. tatz : tamz tatz [mm] tamz [mm] σres,atz [mpa] σres,amz [mpa] 2 : 1 0.4288 0.2140 236.6 -592.6 5 : 1 0.5170 0.1038 109.8 -683.6 7 : 1 0.5384 0.0770 80.6 -704.6 10 : 1 0.5556 0.0556 57.7 -721.0 table 2: residual stresses calculated for different ratio of layer thicknesses (tatz : tamz) by eq. 1. it is evident from the tab. 2 that the compressive residual stresses in the amz layers are circa six hundred megapascals and higher for all considered cases. these stresses are responsible for typical stepwise crack propagation like is shown in the scheme in fig. 2. model of crack propagation estimation of crack propagation direction ih´s criterion [34,35] based on strain energy density factor s was used for the determination of crack propagation direction due to brittle nature of the composite. the criterion was implemented in finite element system ansys [36] to perform calculations with small crack increments automatically: 2 211 12 222i i ii iis a k a k k a k   , (2) where ki and kii are stress intensity factors corresponding to mode i and ii respectively, s l. náhlík et alii, frattura ed integrità strutturale, 34 (2015) 116-124; doi: 10.3221/igf-esis.34.12 119   11 1 1 cos cos 16 a k        ,  12 1 sin 2 cos 1 16 a k        ,      22 1 1 1 cos 1 cos 3cos 1 16 a k             , constant 3 4k   for plane strain or 3 1 k      for plane stress,  2 1 e     is shear modulus,  is polar coordinate originating from the crack tip. the criterion postulates that the crack will propagate in the direction where factor s is the minimum. the angle of next crack propagation direction 0 can be determined from the conditions: 0 0 2 2 0  0 s s                      (3) the crack will propagate under angle 0 if the value of s will reach its critical value scr, i.e. for s = scr. in special case (pure mode i) can be the critical value scr related to fracture toughness kic:   21 2 4 ic cr k s     for plane strain condition. (4) fracture toughness of amz layer is 2.6 mpa.m0.5. corresponding value of scr = 825.10-8 mpa.m. figure 3: detail of fine mesh around the crack tip. numerical model for the numerical modelling finite element (fe) method was chosen. numerical models were developed in commercial system ansys. models contained circa 100 000 elements plane 183. boundary conditions corresponding to 4pb, i.e. vertical displacements on the lower side in the locations of rigid supports were equal to zero and the loading forces p/2 on the upper side of the models were applied, see fig. 2 for details. thermal load by change of temperature from 1200°c to 20°c was applied together with mechanical loading to generate residual stresses in the layers. material characteristics written in the tab. 1 were used. all calculations were performed under condition of plane strain. very fine mesh was used around the crack tip to well describe the stress distribution there (see fig. 3), which is of crucial importance for determination of crack behavior. the size of smallest elements was circa 1.10-5 mm. on the base of former experience [28] the crack propagation was modelled from first atz/amz interface through the amz layer. the initial crack l. náhlík et alii, frattura ed integrità strutturale, 34 (2015) 116-124; doi: 10.3221/igf-esis.34.12 120 increment was chosen 1 m to describe crack path precisely and model was remeshed after each step. stress intensity factors were calculated by author’s routine from displacements close to the crack tip in each step. new crack propagation direction was determined on the base of author´s ansys macros based on eqs. 2 and 3 after each step. hundreds of calculations were performed to obtained realistic crack path in compressive amz layer during each simulation. pc based workstations were used for extensive numerical calculations. results and discussion ifferent material layers create regions with different material properties. it was shown in the former work of authors [7] that suitable selection of materials with different elastic properties can lead to the higher values of applied load for crack propagation through interface. this value of applied load can be higher than the one for crack propagation in the individual composite constituents. the effect of crack retardation is stronger in the studied case due to acting of residual stresses developed in the layers during sintering process. these residual stresses have pronounced influence on the crack behaviour in the composite, damage mechanism of the composite and consequently on the value of apparent fracture toughness of the composite body. in the numerical fe studies four different ratios of layer thicknesses were considered (see tab. 2). the calculations performed were focused on the description of mechanism leading to the higher apparent fracture toughness of ceramic laminate with strongly bonded interfaces. sih’s criterion (eq. 3) was applied in each step of the simulations. the crack started to strongly deflect in certain depth a´ under the first atz/amz interface due to acting of compressive stresses in all simulations. in this moment an additional external load was necessary for the crack propagation. the depth of deflection and values of external force p are shown in the tab. 3. tatz : tamz a’ [mm] pmax [n] 2 :1 0.046 16.2 5 : 1 0.020 24.8 7 : 1 0.017 34.6 10 : 1 0.024 48.0 table 3: the depth a´ in amz layer under the first atz/amz interface, where the crack changes mode of propagation and values of the force p acting in the moment of crack deflection. hundreds of calculations (steps) were performed in each simulation to obtain crack path in the amz layer. results of simulations are shown in the fig. 4. on the base of results obtained the crack behaviour in the compressive layer can be divided to four stages, see fig. 5 for the explanation: 1) after passing perpendicularly through the atz/amz interface the crack is retarded (the stress intensity factor and the strain energy density factors decrease). an external load is necessary for further crack propagation. the compressive stresses don’t allow further direct crack propagation under mode i like in tensile loaded atz layer. 2) in the depth a´ under the interface the character (mode) of crack propagation changes from mode i to mode ii. the stress distribution around the crack tip in the depth a´ enables crack deflection or bifurcation. further crack propagation is controlled by compressive stresses. the crack propagates parallel or nearly parallel to the material interfaces. 3) when the crack tip is close to the next amz/atz interface the presence of tensile stresses in the atz layer growths in importance and the controlling mode of crack propagation starts to be again mode i and the crack deflect to the direction (nearly) perpendicular to amz/atz interface. 4) the crack passing through (nearly) perpendicularly the amz/atz interface. the resistance to the crack propagation is the highest between stages 3 and 4. behaviour of the crack at the stage 4 was studied in [28]. d l. náhlík et alii, frattura ed integrità strutturale, 34 (2015) 116-124; doi: 10.3221/igf-esis.34.12 121 a) result for tatz : tamz = 2. crack path in the amz layer after 270 steps (left), detail of crack deflection after 33 steps. b) result for tatz : tamz = 5. crack path in the amz layer after 491 steps (left), detail of crack deflection. c) result for tatz : tamz = 7. crack path in the amz layer after 315 steps (left), detail of crack deflection. d) result for tatz : tamz = 10. crack path in the amz layer after 306 steps (left), detail of crack deflection. e) detail of stress distribution in the laminates: tatz : tamz = 2 (left), tatz : tamz = 10. figure 4: simulation of crack propagation in the compressive layer for different ratio of layer thicknesses. magnitude of longitudinal stress component is displayed. l. náhlík et alii, frattura ed integrità strutturale, 34 (2015) 116-124; doi: 10.3221/igf-esis.34.12 122 figure 5: scheme of stages of crack propagation in the compressive layer of ceramic laminate with strongly bonded interfaces. the crack can relatively easy propagate in the outside layers from some flaws, scratches or initial notches under external bending load of the composite. in the tensile layers the crack propagation corresponds to the mode i and cracks propagate perpendicularly to the material interface. due to this fact it is necessary to prepare the composite with low tensile stresses, i.e. with wide tensile layer (atz in studied case) and thin compressive layer (amz) with high compressive stresses. the resistance to the crack propagation in the tensile layer is lower due to tensile residual stresses than in the case of crack propagation in the homogeneous ceramics, see e.g. [28]. when the crack passed through the interface to the compressive layer (amz) acting compressive residual stresses change the mode of crack propagation from mode i to shear mode ii. this causes strong crack deflection or can lead to bifurcation of the propagating crack. crack propagation parallel to the material interface in the compressive layer is evident from experiments published in [37]. this phenomenon is supported by results obtained as well. the parallel crack propagation is controlled by specific stress distribution in the compressive amz layer and influenced by the vicinity of tensile layers. after some propagation the bending nature of loading, existence of material imperfections (flaws, pores) and the vicinity of material interface lead to the other change of crack propagation direction close to amz/atz interface [32]. these effects contribute to the characteristic stepwise crack propagation in the strongly bonded ceramic laminates. conclusions he paper presented focuses on the crack behaviour in the multilayered ceramic composite subjected to the bending load. crack propagation in the compressive layer responsible for higher apparent fracture toughness of the composite was investigated by means of finite element method. sih’s criterion based on strain energy density factor was used for estimation of the crack behaviour in the layers and for the estimation of crack path. it was shown that the crack after passing through the first material interface between tensile and compressive layer retards due to acting of strong residual stresses and the crack is sharply deflected. an additional external load is necessary for further crack propagation at this moment. the depth of crack deflection was determined for different thicknesses of the composite layers. the stress distribution allows in this moment bifurcation of the crack as well, like was shown e.g. in the works [29,31]. further crack propagation in the compressive layer is more or less parallel to the material interface. the stages leading to the stepwise crack propagation were described in detail. finite element method implemented in commercial system ansys with author’s routines was used for numerical simulations. the paper contributes to the better understanding of damage of strongly bonded ceramic laminates and their toughening mechanism. acknowledgement his work was supported through the grant no. 15-09347s of the czech science foundation and the specific academic research grant (k. štegnerová) no. fsi-s-14-2311 provided to brno university of technology, faculty of mechanical engineering. t t l. náhlík et alii, frattura ed integrità strutturale, 34 (2015) 116-124; doi: 10.3221/igf-esis.34.12 123 references [1] kolednik, a., predan, j., gubeljak, n., fischer, d.f., modeling fatigue crack growth in a bimaterial specimen with the configurational forces concept, mat. sci. eng. a, 519 (2009) 172–183. doi: 10.1016/j.msea.2009.04.059. [2] marsavina, l., sadowski, t., knec, m., crack propagation paths in four point bend aluminium–pmma specimens, eng. frac. mech., 108 (2013) 139-151. doi: 10.1016/j.engfracmech.2013.02.029. [3] leguillon, d., martin, e., the strengthening effect caused by an elastic contrast—part i: the bimaterial case, int. j. fract., 179 (2013) 157–167. doi: 10.1007/s10704-012-9787-y. [4] he, m.y., hutchinson, j.w., crack deflection at an interface between dissimilar elastic materials, int. j. solids struct., 25 (1989) 1053–1067. [5] he, m.y., evans, a.g., hutchinson, j.w., crack deflection at an interface between dissimilar elastic materials: role of residual stresses, int. j. solids struct., 31 (1994) 3443-3455. doi: 10.1016/0020-7683(94)90025-6. [6] sistaninia, m., kolednik, o., effect of a single soft interlayer on the crack driving force, eng. frac. mech., 130 (2014) 21–41. doi: 10.1016/j.engfracmech.2014.02.026. [7] knésl, z., náhlík, l., radon, j., influence of interface on fatigue threshold values in elastic biomaterials, comp. mater. sci., 28 (2003) 620–627. doi:10.1016/j.commatsci.2003.08.018. [8] wang, b., siegmund, t., simulation of fatigue crack growth at plastically mismatched bi-material interfaces, int. j. plasticity, 22 (2006) 1586-1609. doi: 10.1016/j.ijplas.2005.09.004. [9] minatto, f.d., milak, p., de noni jr., a., hotza, d., montedo, o. r. k., multilayered ceramic composites – a review, adv. appl. ceram., 114 (2015) 127-138. doi: 10.1179/1743676114y.0000000215. [10] šestáková, l., bermejo, r., chlup, z., danzer, r., strategies for fracture toughness, strength and reliability optimisation of ceramic–ceramic laminates, int. j. mat. res., 102 (2011) 1-14. doi: 10.3139/146.110523. [11] bermejo, r., chlup, z., šestáková, l., ševeček, o., danzer, r., strategies to optimize the strength and fracture resistence of ceramic laminate, mechanical properties and performance of engineering ceramics and composites vii: ceramic engineering and science proceedings, 33 (2012) 163-174. [12] she, j., inoue, t., ueno, k., multilayer al2o3/sic ceramics with improved mechanical behaviour, j. eur. ceram. soc., 20 (2000) 1771-1775. doi:10.1016/s0955-2219(00)00048-0. [13] hadraba, h., drdlík, d., chlup, z., máca, k., dlouhý, i., cihlář, j., layered ceramic composites via control of electrophoretic deposition kinetics, j. eur. ceram. soc., 33 (2013) 2305–2312. doi:10.1016/j.jeurceramsoc.2013.01.026. [14] hadraba, h., klimeš, j., maca, k., crack propagation in layered al2o3/zro2 composites prepared by electrophoretic deposition, j. mater. sci., 42 (2007) 6404–6411. doi: 10.1007/s10853-006-1197-y. [15] oechsner, m., hillman, c., lange, f. f., crack bifurcation in laminar ceramic composites, j. am. ceram. soc., 79 (1996) 1834-1838. [16] lugovy, m., slyunyayev, v., orlovskaya, n., blugan, g., kuebler, j., lewis, m., apparent fracture toughness of si3n4-based laminates with residual compressive or tensile stresses in surface layers, acta mater., 53 (2005) 289–296. doi:10.1016/j.actamat.2004.09.022. [17] wei, p., chen, l., okubo, a., hirai, t., tough multilayered α–β si3n4 ceramics prepared by spark plasma sintering, mater. lett., 49 (2001) 239–243. doi: 10.1016/s0167-577x(00)00377-3. [18] tomaszewski, h., weglarz,h., wajler, a., boniecki, m., kalinski, d., multilayer ceramic composites with high failure resistence, j. eur. ceram. soc., 27 (2007) 1373–1377. doi:10.1016/j.jeurceramsoc.2006.04.030. [19] chlup, z., hadraba, h., slabáková, l., drdlík, d., dlouhý, i., fracture behaviour of alumina and zirconia thin layered laminate, j. eur. ceram. soc., 32 (2012) 2057–2061. doi:10.1016/j.jeurceramsoc.2011.09.006. [20] bermejo, r., danzer, r., high failure resistance layered ceramics using crack bifurcation and interface delamination as reinforcement mechanisms, eng. frac. mech., 77 (2010) 2126–2135. doi: 10.1016/j.engfracmech.2010.02.020. [21] bermejo, r., llanes, l., anglada, m., supancic, p., lube, t., thermal shock behavior of an al2o3/zro2 multilayered ceramic with residual stresses due to phase transformation, key engineering materials, 290 (2005) 191-198. doi: 10.4028/www.scientific.net/kem.290.191. [22] bermejo, r., torres, y., baudín, c., sánchez-herencia, a.j., pascual, j., anglada, m., llanes, l., threshold strength evaluation on an al2o3-zro2 multilayered system, j. eur. ceram. soc., 27 (2007) 1443–1448. doi:10.1016/j.jeurceramsoc.2006.05.037. [23] bermejo, r., baudín, c., moreno, r., llanes, l., sánchez-herencia, a.j., processing optimisation and fracture behaviour of layered ceramic composites with highly compressive layers, compos.sci. technol., 67 (2007) 1930–1938. doi:10.1016/j.compscitech.2006.10.010. l. náhlík et alii, frattura ed integrità strutturale, 34 (2015) 116-124; doi: 10.3221/igf-esis.34.12 124 [24] gotor, f.j., bermejo, r., córdoba, j.m., chicardi, e., medri, v., dalle fabbriche, d., torres, y., processing and characterisation of cermet/hardmetal laminates with strong interfaces, materials and design, 58 (2014) 226–233. doi: 10.1016/j.matdes.2014.01.076. [25] kuo, d.h., kriven, w.m., fracture of multilayer oxide composites, mat.sci. eng. a, 241 (1998) 241–250. [26] zhou, p., hu, p., zhang, x., han, w., laminated zrb2–sic ceramic with improved strength and toughness, scripta mater., 64 (2011) 276–279. doi:10.1016/j.scriptamat.2010.10.005. [27] bermejo, r., sánchez-herencia, a.j., llanes, l., baudín, c., high-temperature mechanical behaviour of flaw tolerant alumina–zirconia multilayered ceramics, acta mater., 55 (2007) 4891–4901. doi:10.1016/j.actamat.2007.05.005. [28] náhlík, l., šestáková, l., hutař, p., estimation of apparent fracture toughness of ceramic laminates, comp. mater. sci., 46 (2009) 614–620. doi:10.1016/j.commatsci.2009.04.005. [29] ševeček, o., bermejo, r., kotoul, m., prediction of the crack bifurcation in layered ceramics with high residual stresses, eng. frac. mech., 108 (2013) 120–138. doi: 10.1016/j.engfracmech.2013.03.013. [30] kotoul, m., ševeček, o., vysloužil, t., crack growth in ceramic laminates with strong interfaces and large compressive residual stresses, theor. appl. frac.mech., 61 (2012) 40–50. doi: 10.1016/j.tafmec.2012.08.005. [31] chen, c.r., bermejo, r., kolednik, o., numerical analysis on special cracking phenomena of residual compressive inter-layers in ceramic laminates, eng. frac. mech., 77 (2010) 2567–2576. doi:10.1016/j.engfracmech.2010.06.020. [32] náhlík, l., šestáková, l., hutař, p., bermejo, r., prediction of crack propagation in layered ceramics with strong interfaces, eng. frac. mech., 77 (2010) 2192–2199. doi:10.1016/j.engfracmech.2010.02.023. [33] oel, h.j., fréchette, v.d., stress distribution in multiphase systems: i, composites with planar interfaces. j. am. ceram. soc., 50 (1967) 542–549. doi: 10.1111/j.1151-2916.1967.tb14992.x. [34] sih, g.c., in: g.c. sih (ed.), a special theory of crack propagation: methods of analysis and solutions of crack problems, mechanics of fracture, noordhoff, international publishing, leyden, (1973) 21–45. [35] berto, f., lazzarin, p., recent developments in brittle and quasi-brittle failure assessment of engineering materials by means of local approaches, mat. sci. eng. r, 75 (2014) 1–48. doi: 10.1016/j.mser.2013.11.001. [36] ansys v14.5, ansys, inc., (2012). [37] tarlazzi, a., roncari, e., pinasco, p., guicciardi, s., melandri, c., de portu, g., tribological behaviour of al2o3/zro2-zro2 laminated composites, wear, 244 (2000) 29–40. doi:10.1016/s0043-1648(00)00429-4. microsoft word numero_49_art_49_2319 r. suresh kumar et alii, frattura ed integrità strutturale, 49 (2019) 526-535; doi: 10.3221/igf-esis.49.49 526 focused on showcasing structural integrity research in india specimen level and component level simulations of fatigue crack growth behavior under cyclic bending r. suresh kumar indira gandhi centre for atomic research, homi bhabha national institute, kalpakkam, india – 603 102, india ersureshkr@gmail.com b.n. rao indian institute of technology madras, chennai, india bnrao2018@gmail.com k. velusamy, s. jalaldeen indira gandhi centre for atomic research, kalpakkam kvelu@igcar.gov.in, jalal@igcar.gov.in abstract. this paper describes a benchmark analysis that was performed to demonstrate numerical simulation capability on fatigue crack growth (fcg) behaviour under cyclic bending. economic design of a piping system against the leak-before-break (lbb) criteria require an accurate estimate of crack growth behaviour. to this end, two representative geometries were selected. the first model was a plate-type geometry with a specimen-type feature, and the other model was a prototype pipe bend geometry with the component feature. the numerically simulated fcg behaviour was found to agree with published data within engineering accuracy for both the specimen-level and the component-level geometries. details of the fcg simulation, its validation against benchmark data, and plausible reasons the difference observed in the fcg behaviour of the specimen-level and full-scale component-level geometries are presented in this paper. the results of the fcg simulation strengthen the argument for performing component-level fcg simulation for an accurate demonstration of lbb for the power plant piping systems. keywords. leak-before-break; fatigue crack growth; stress intensification factor. citation:suresh kumar, r., rao, b., n., velusamy, k., jalaldeen, s., specimen level and component level simulation of fatigue crack growth behavior under cyclic bending, frattura ed integrità strutturale, 49 (2019) 526-535. received: 30.11.2018 accepted: 28.05.2019 published: 01.07.2019 copyright: © 2019 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. http://www.gruppofrattura.it/va/49/2319.mp4 r. suresh kumar et alii, frattura ed integrità strutturale, 49 (2019) 526-535; doi: 10.3221/igf-esis.49.49 527 introduction ipings are critical systems in power plants and chemical industries. in coal-fired and nuclear power plants, these systems are subjected to many cyclic operating conditions during their service. it is known that cyclic loads exceeding specific magnitudes have a strong potential to cause crack initiation and propagation. however, in the case of sodium-cooled fast reactor (sfr), where the piping system is made up of ss 316ln material, it is possible to detect sodium leakage, (i) due to the ductile nature of ss 316ln and (ii) elaborate sodium leak detection provision. these conditions made sfr design more favourable in demonstrating leak-before-break (lbb) criteria [1]. in the case of sfr piping system, these conditions are respected as per the design criteria given in rcc mrx a16 [2]. the highly conservative method detailed in rcc mrx a16 poses challenges in demonstrating the lbb criteria for small-size low-pressure piping system. conducting full-scale experiments at the required temperature on all the sizes of the piping system is expensive and time-consuming. hence, there is a strong need for the development of a reliable numerical method for a quick and economical design of power plant components for lbb. this is the focus of the present paper wherein; benchmark analysis has been carried out towards validation of numerical fatigue crack growth (fcg) simulation. it may be highlighted that the characteristics of fcg had been investigated by many researchers in the past [3-11]. in the present research, two representative geometries studied in the open literature [4-5] have been selected. the selected geometries are (i) a typical plate-type geometry with a specimen-type feature and (ii) a prototype pipe bend with the component feature. as already mentioned that an sfr piping system is subjected to cyclic bending stress variation during its service conditions [1]. the bending stress variation in the sfr piping system has a positive load ratio (r), which is defined as the ratio of the minimum stress (min) to maximum stress (max) during the cyclic load. towards comparing the fcg behaviour of the specimen level plate-type geometry, data reported in [4] is used, and for the prototype geometric simulation, the full-scale pipe bend test data reported in [5] is used. benchmark data plate specimen data hapuliot et al. [4] have investigated fcg behaviour in a plate specimen, by detailed experimentation. the geometric and loading details are given in fig.1. the dimensions of the test specimen are 350 mm wide, 250 mm height and 20 mm thickness. an elliptical initial surface crack is provided at the centre of the plate as depicted in fig.1. figure 1: geometric and loading of the plate specimen [4] the plate specimen is made up of ss 316 ln material. the essential data required for modelling the fcg behaviour of this geometry are presented in tab. 1. p c   a   b r. suresh kumar et alii, frattura ed integrità strutturale, 49 (2019) 526-535; doi: 10.3221/igf-esis.49.49 528 e (mpa) maximum load fmax (kn) minimum load fmin (kn) a0 (mm) 2c0 (mm) 195500 22.5 3.1 2.0 80.0 table 1: essential data used for modelling fcg in a plate specimen [4]. the plate has been subjected to cyclic load variation with a maximum load of 22.5 kn and a minimum load of 3.1 kn, with a load ratio of 0.138. the measured crack length as a function of the number of cycles is presented in fig.2. these data are used for assessing the validity of computational prediction of fcg behaviour in plate specimen. figure 2: benchmark data for the plate specimen [4] figure 3: geometrical and loading details of the pipe bend r. suresh kumar et alii, frattura ed integrità strutturale, 49 (2019) 526-535; doi: 10.3221/igf-esis.49.49 529 pipe bend data the data from literature includes the experimental study on fcg behaviour of a full-scale pipe bend of 219 mm outer diameter and thickness of 15.12 mm [5], made of carbon steel (sa333 gr.6 grade) material. the schematic of the test pipe specimen is shown in fig. 3. the cyclic test was carried out with a load ratio of 0.1, and other relevant data considered in the computational modelling of the fcg behaviour are presented in tab. 2. the measured crack length as a function of the number of cycles is depicted in fig. 4. material maximum load fmax (kn) minimum load fmin (kn) a0 (mm) 2c0 (mm) sa350lf2 -150 -15 2.0 87.0 table 2: data used in modelling fcg in a pipe bend [5-6]. figure 4: benchmark data for pipe bend geometry [5] static analysis t the outset, static analysis has been carried out for both the plate as well as the pipe bend geometries, to check the correctness of the numerical model. these results are presented below: plate specimen the plate geometry has been modelled using 3-dimensional solid element along with the associated rigid loading connections for the application of the required bending moment. as already indicated that the maximum load of 22.5 kn is applied [4]. the mode-1 stress distribution under the application of the external load is shown in fig.5. it is clear that the inner surface of the plate is under the maximum tensile stress (319 mpa), while the outer surface is under the maximum compressive stress (-290 mpa). thus, for the fcg simulation, the crack is provided at the inner surface of the plate in the horizontal direction, as shown in fig. 1. pipe bend geometry the 219 mm outer diameter, 15.1 mm thick pipe bend with a radius of 219 mm is also modelled using 3-d solid element. the pipe bend is subjected to the maximum load of 150 kn [5]. application of this force in the direction as indicated in fig.6 with a moment arm of 485 mm, creates an in-plane bending moment in the pipe bend, which leads to a closing of the pipe bend, and thereby the pipe cross-section becomes oval. at this condition, the stress distribution responsible for the mode-i crack propagation is presented in fig.6. it is clear that the preferred location and the orientation to insert the initial defect on the pipe bend is at the crown location along the longitudinal direction. a r. suresh kumar et alii, frattura ed integrità strutturale, 49 (2019) 526-535; doi: 10.3221/igf-esis.49.49 530 figure 5: mode-i crack initiation stress (mpa) distribution in the plate specimen figure 6: mode-i crack initiation stress (mpa) distribution in the pipe bend specimen fatigue crack growth (fcg) simulation he fcg simulation for both the plate, as well as pipe bend specimen, has been performed using the franc3d software. this software is adopted as it can simulate 3-d fcg analysis together with the general-purpose finite element (fe) solvers. the magnitude and direction of the crack growth depend upon the stress intensity factor (sif) and the local ‘kink angle’ respectively. kink angle is defined as the angle that maximises the ratio between maximum sif (kimax) computed based on the maximum tensile stress at the crack front and the directionality dependent material resistance to crack growth (kc). the convergence of the crack growth simulation is decided by maximising the ratio kimax/kc. the direction of crack propagation is determined based on the ‘kink angle’ measurement at the base of the crack front. the sif is computed based on the m-integral concept at mid-side nodes along the crack front using the maximum tensile stress [12]. the sub modelling concept, deployed in the franc3d, helps in local mesh-refinement at the cracked portion of the component geometry for efficient computation. higher mesh density is provided for a shallow crack. also, a pattern of elements with controlled mesh size and shapes are placed around the crack front for accurate estimation of sif. t r. suresh kumar et alii, frattura ed integrità strutturale, 49 (2019) 526-535; doi: 10.3221/igf-esis.49.49 531 these elements take the form of generalised cylindrical tubes with the crack fronts serving as the axes. 3-d wedge shaped elements are placed immediately adjacent to the crack fronts, and rings of brick elements surround the crack front. the magnitude of sif depends upon the crack dimensions, applied stress and other geometrical parameters. the local direction of crack advancement is determined based on the local ‘kink’ angle. the fcg simulation is performed as per the paris law, defined as da/dn = c (k)m, where da/dn is in m/cycle, k is in mpam and c & m are the respective fcg material parameters. the values of c and m used for the plate geometry are 1.2 x 10-8 and 2.84, respectively [4]. the corresponding values for the plate geometry are 3.982 x 10-12 and 3.188, respectively [5]. the results of the fcg analysis are presented below. fcg on plate specimen for the plate specimen, the initial elliptical surface crack length (2c0) is 80 mm, and the crack depth (a0) is 2 mm. the locations a and b in fig.7 represent the crack surface location (crack length ‘c’ direction) and the deepest crack location (crack depth ‘a’ direction). the orientation of the initial crack is along the x-direction (ref. fig. 7) such that the applied bending stress will enhance the mode-1 crack propagation. the finite element model of the cracked geometry is shown in fig.7. there are 245964 elements in the specimen. it houses a combination of the 3d tetrahedron, hexahedron and wedge elements. figure 7: fe sub-model of the cracked plate geometry figure 8: sif variation for plate geometry at the critical location b r. suresh kumar et alii, frattura ed integrità strutturale, 49 (2019) 526-535; doi: 10.3221/igf-esis.49.49 532 as already indicated, the crack growth rate depends upon the sif at the crack front. the numerically obtained ki along the crack front indicates that kib (sif at location b in fig.7) is higher than kia (sif at location a in fig.7). this is due to the high crack size aspect ratio (c/a). subsequently, the critical location sif (kib) variation during the advancement of the crack is presented in fig.8. it shows that ki increases with an increase in ‘a/t’ ratio up to 0.6, and then it decreases, which is attributed to the influence of neighbouring compressive stress zone, as shown in fig.5. the predicted fcg behaviour of the plate specimen is compared with the experimental data [4] in fig.9. it shows that the numerically estimated crack growth is in good agreement with the experimental results. figure 9: comparison of ‘a’ vs ‘n’ for a plate specimen figure 10: fe sub-model of the cracked pipe bend geometry fcg on pipe bend the fcg analysis for the pipe bend geometry is carried out with an initial elliptical surface crack length (2c0) of 87 mm and depth (a0) of 2 mm. the locations a and b in fig.10 represent the crack surface location (crack length ‘c’ direction) and the crack deepest location (crack depth ‘a’ direction). cyclic bending stress is applied with a load ratio of 0.1. the large shallow surface crack is introduced in the hoop tensile stress region (outer surface at the crown location from fig. 6) of the pipe bend. simulation of a crack along the axial direction on the outer surface, as shown in fig.3, will enhance the mode-1 crack propagation. the sub-model concept is adopted in this case and the respective fe mesh given in fig.10. the difference between the full model and the sub-model will be clear with the comparison of figs. 6 and 10, respectively. the sub model contains a combination of the 3d tetrahedron, hexahedron and wedge elements. in total, there are 167969 elements against r. suresh kumar et alii, frattura ed integrità strutturale, 49 (2019) 526-535; doi: 10.3221/igf-esis.49.49 533 245964 in the case of plate geometry. the total number of elements can also be further reduced by adjusting the boundary of the sub model without affecting the results. the sif variation extracted from franc3d at the critical location (b from fig.10) during fcg is shown in fig.11. it indicates that ki increases with an increase in ‘a’ up to ‘a/t’ ratio of 0.4 (a = 6 mm) and then it decreases, due to the influence of the neighbourhood compressive stress zone as evident from fig.6. figure 11: sif variation for the pipe bend at the critical location-b the numerically predicted estimate of fcg behaviour of the pipe bend is compared with the experimental data and depicted in fig.12. it is clear that the numerically predicted crack growth is in good agreement with the experimental results. the reduction in the rate of crack growth beyond 6 mm is due to the influence of low ki value. figure 12: comparison of ‘a’ vs ‘n’ on pipe bend summary and conclusions wo representative geometries have been selected from the literature towards validating numerical simulation of fcg behaviour. the selected geometries are a plate specimen and a representative full-scale pipe bend. the important observations are summarised below.  sif is computed at the mid-side nodes along the crack front based on m-integral concept. the deployment of submodelling concept has made the computation of fcg behaviour more effective. the crack growth direction is decided by maximising the ‘kink angle’ measurement at the base of the crack front using the maximum tensile stress. this also enhances the accuracy of the numerical model. t r. suresh kumar et alii, frattura ed integrità strutturale, 49 (2019) 526-535; doi: 10.3221/igf-esis.49.49 534  the numerical crack growth estimates at both specimen level as well as the component level, have been validated with better engineering accuracy with the available experimental data.  the sif is seen to exhibit a non-monotonic variation to the crack depth ratio, attaining a peak value at a critical ‘a/t’ ratio. the estimated results show that the variation of ki for the pipe geometry decreases earlier than that of the plate geometry. this early reduction is due to the influence of the global compressive stress present at the leading edge of the crack propagation.  fatigue crack growth rate is found to be lower for the pipe geometry than that of the plate geometry under cyclic bending condition. this is due to the presence of the higher amount of asymmetric bending stress variation in the case of the pipe bend geometry than that of the plate geometry under the application of bending moment.  the difference in material property may also influence the fcg behaviour. this can be confirmed by simulating fcg for both the plate and pipe bend geometries with identical material properties, load ratio and cyclic stress variation. in the case of the sfr piping system, the leading cause of fatigue load for crack propagation is the cyclic bending stress. the above results indicate that a prototype level simulation is essential for an accurate estimation of parameters used in the lbb demonstration. acknowledgements uthors acknowledge the support rendered by shri. santhosh n l & shri. kaushik, dhio research and engineering, bangalore for their service related to franc3d software. references [1] suresh kumar, r., jalaldeen, s., selvaraj, p., chellapandi, p.(2011). high temperature design of class-1 piping systems in sodium cooled fast breeder reactor. transactions, smirt 21, 6-11 november, 2011, new delhi, india, p. div-vi: paper id# 792. [2] afcen. (2012). section iii – tome 1 – subsection z appendix a16 : guide for prevention of fast fracture , leak before break analysis and defect assessment, rcc mrx. [3] chellapandi, p., srinivasan, r., biswas, a., chetal, s.c., bhoje, s.b. (2003).leak before break investigation on sodium piping for prototype fast breeder reactor. transactions of the 17th international conference on structural mechanics in reactor technology (smirt 17) prague, czech republic, p. 3216. [4] chapuliot, s., chaudat, t., mineau, v., moulin, d. (1996). fatigue growth of semi-elliptical cracks in plates subjected to bending, asme pvp, fatigue & fracture, 323, pp 291-298. [5] arora, p., singh, p.k., bhasin, v., vaze, k.k., pukazhendhi, d.m., gandhi, p., raghava, g. (2013). fatigue crack growth behavior in pipes and elbows of carbon steel and stainless steel materials, procedia eng., 55, pp. 703–709. doi: 10.1016/j.proeng.2013.03.318. [6] singh, p.k., bhasin, v., vaze, k.k., ghosh, a.k., kushwaha, h.s., murthy, d.s.r., gandhi, p., sivaprasad, s. (2008). fatigue studies on carbon steel piping materials and components: indian phwrs, nucl. eng. des., 238(4), pp. 801– 813, doi: 10.1016/j.nucengdes.2007.09.002. [7] chattopadhyay j., b. dutta, and h.kushwaha. (1999). leak-before-break qualification of primary heat transport piping of 500 mwe tarapur atomic power plant, int. j. press. vessel. pip., 76(4), pp. 221–243, doi: 10.1016/j.nucengdes.2016.02.013. [8] sethuraman, r., c. l. rao, and p.kameswara r. (1999). fatigue crack growth of semielliptical surface cracks in curved geometries, j. structuctral eng., 26(1), pp. 81–86, doi: 10.1177/0021998305055549. [9] riddell, w.t., ingraffea, a.r., wawrzynek, p.a. (1997). experimental observations and numerical predictions of threedimensional fatigue crack propagation, eng. fract. mech., 58(4), pp. 293–310, doi: 10.1016/s0013-7944(97)00122-7. [10] rao, c.l., sethuraman, r., bhoje, v., chellapandi, p. (2000). fatigue crack propagation studies on a semi-elliptical surface crack in a plate subjected to bending loads, asmepvp, 404, pp. 37–44. [11] nagapadmaja, p., kalyanaraman, v., kumar, s.r.s., chellapandi, p. (2008). experimental study on lbb behaviour of a r. suresh kumar et alii, frattura ed integrità strutturale, 49 (2019) 526-535; doi: 10.3221/igf-esis.49.49 535 lmfbr pipe elbows, int. j. fatigue, 30(3), pp. 574–84. [12] liang, r.z., rui, z.c., liang, z.y., bo, z.h., zuo, j., engineering, d.u., zhou, x. (2010).m-integral for stress intensity factor based on xfem. proceedings of the third international symposium on electronic commerce and security workshops(isecs ’10), pp. 226–30. << /ascii85encodepages false /allowtransparency false /autopositionepsfiles true /autorotatepages /none /binding /left /calgrayprofile (dot gain 20%) /calrgbprofile (srgb iec61966-2.1) /calcmykprofile (u.s. web coated \050swop\051 v2) /srgbprofile (srgb iec61966-2.1) /cannotembedfontpolicy /error /compatibilitylevel 1.4 /compressobjects /tags /compresspages true /convertimagestoindexed true /passthroughjpegimages true /createjobticket false /defaultrenderingintent /default /detectblends true /detectcurves 0.0000 /colorconversionstrategy /cmyk /dothumbnails false /embedallfonts true /embedopentype false /parseiccprofilesincomments true /embedjoboptions true /dscreportinglevel 0 /emitdscwarnings false /endpage -1 /imagememory 1048576 /lockdistillerparams false /maxsubsetpct 100 /optimize true /opm 1 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can be opened with acrobat and adobe reader 5.0 and later.) >> /namespace [ (adobe) (common) (1.0) ] /othernamespaces [ << /asreaderspreads false /cropimagestoframes true /errorcontrol /warnandcontinue /flattenerignorespreadoverrides false /includeguidesgrids false /includenonprinting false /includeslug false /namespace [ (adobe) (indesign) (4.0) ] /omitplacedbitmaps false /omitplacedeps false /omitplacedpdf false /simulateoverprint /legacy >> << /addbleedmarks false /addcolorbars false /addcropmarks false /addpageinfo false /addregmarks false /convertcolors /converttocmyk /destinationprofilename () /destinationprofileselector /documentcmyk /downsample16bitimages true /flattenerpreset << /presetselector /mediumresolution >> /formelements false /generatestructure false /includebookmarks false /includehyperlinks false /includeinteractive false /includelayers false /includeprofiles false /multimediahandling /useobjectsettings /namespace [ (adobe) (creativesuite) (2.0) ] /pdfxoutputintentprofileselector /documentcmyk /preserveediting true /untaggedcmykhandling /leaveuntagged /untaggedrgbhandling /usedocumentprofile /usedocumentbleed false >> ] >> setdistillerparams << /hwresolution [2400 2400] /pagesize [612.000 792.000] >> setpagedevice microsoft word numero_29_art_28 e. grande et alii, frattura ed integrità strutturale, 29 (2014) 325-333; doi: 10.3221/igf-esis.29.28 325 focussed on: computational mechanics and mechanics of materials in italy a data fusion based approach for damage detection in linear systems ernesto grande, maura imbimbo university of cassino and southern lazio, depart. of civil and mechanical engineering e.grande@unicas.it, mimbimbo@unicas.it abstract. the aim of the present paper is to propose innovative approaches able to improve the capability of classical damage indicators in detecting the damage position in linear systems. in particular, starting from classical indicators based on the change of the flexibility matrix and on the change of the modal strain energy, the proposed approaches consider two data fusion procedures both based on the dempster-shafer theory. numerical applications are reported in the paper in order to assess the reliability of the proposed approaches considering different damage scenarios, different sets of modes of vibration and the presence of errors affecting the accounted modes of vibrations. keywords. damage identification; modal strain energy; flexibility matrix; data-fusion introduction umerous studies concerning the development of damage indicators mainly based on the modal parameters of systems derived from identification processes, in some cases combined with finite-element model update algorithms, are available in the current literature [1-3]. some of these indicators, coupled with innovative algorithms, provide information on the position and the severity of damage [4-6]. among these, the relative damage indicator (rdi) and the modal strain energy change ratio (msecrj) indicators, respectively based on the change of the flexibility matrix and the modal strain energy of systems before and after the damage, are widely used for damage detection in linear systems [7, 8]. they are defined as:  de e e diag f f rdi diag f   (1)  1 1 max n ij j i ij j msecr msecr n msecr   (2) where fe and fed is the elemental flexibility matrix of the system before and after damage respectively, msecrij is the modal strain energy change ratio corresponding to the ith mode of vibration and to the jth element of the system and n is the number of elements composing the system. n e. grande et alii, frattura ed integrità strutturale, 29 (2014) 325-333; doi: 10.3221/igf-esis.29.28 326 the studies available in literature show the ability of these indicators to detect the presence, the position, and in some cases, the severity of damage. nevertheless, the same studies have also underlined some drawbacks generally arising when multiple damages occur or noises/errors affect the identified dynamic properties of the systems. in these cases, a reliable prediction of damage requires a significant number of information particularly in terms of number of modes. recently, in order to improve the ability of classical damage indicators, data information fusion techniques have been extended to structural damage identification [6, 9-11]. the fusion of information derived from different sources allows, indeed, to improving the ability of damage indicators particularly in detecting the damage position. in this paper, two approaches for damage detection in linear systems based on the use of the rdi and msecrj indicators combined with the dempster-shafer data fusion theory are presented. in particular, while the first approach, denoted in the following df as data fusion, is based on the fusion of the information derived separately from the msecrj and rdi indicators, considered as separate and independent sources, the second approach is an innovative procedure, denoted in the following mdf as multi-stage data fusion, consisting in a data fusion implemented in a multi-stage process where the sources are based on the same damage indicator, either rdi or msecrj, but evaluated on the basis of different combinations of modes of vibration. numerical applications are presented in the paper to assess the reliability of the proposed approach considering different damage scenarios, different sets of modes of vibration and presence of noise. dempster-shafer theory empster-shafer theory [12] represents the first data fusion theory developed by dempster and shafer in 1976 and, still, one of the most valuable. some key definitions of the theory, those used in the approach proposed in the paper, are summarized in the following. considering a finite set  , ,a b c  of mutually exclusive and exhaustive propositions, the corresponding power set 2 is defined as the set of all the subsets of  which also includes the null set. the theory of evidence assigns a basic probability assignment function, named bpa or m(x), to any subset of 2 , defined as: : 2 [0,1]m   (3) being: ( ) 1 and (m x m o ) 0 x   (4) in the framework of the dempster-shafer theory [12] the bpa can be interpreted as a generalization of the probability concept being the probability assigned not only to one hypothesis but to a set of hypotheses without any information on how it is distributed among the elements of the set itself. the dempster’s rule provides a method for combining the basic probabilities assignment of different information sources is . in particular, given 1s and 2s two information sources and 1m and 2m the bpas given by the two sources, the fused bpa is given by: 1 2 1 1 1 2 2 1 ( ) ( ) ( ) 1 s s s m s m s m s q       (5) where q represents a measure of the degree of conflict between the two sources defined as: 1 2 1 1 2 2( ) ( ) s s q m s m s     (6) df and mdf proposed techniques for damage detection he approaches presented in this paper for damage identification of linear systems are developed by combining the use of classical damage indicators based on the modal strain energy through the modal strain energy change ratio index (msecr) and on the flexibility matrix through the relative damage indicator (rdi) with the dempstershafer data fusion theory. in particular, two different approaches are presented. the df approach is simply based on the x d t e. grande et alii, frattura ed integrità strutturale, 29 (2014) 325-333; doi: 10.3221/igf-esis.29.28 327 fusion of the information derived separately from the msecr and rdi indices, while the mdf approach is an innovative procedure using only of the indexes rdi and msecr in a multi-stage data fusion (fig. 1). in the case of the df approach, modal strain energy change ratios (msecr) and rdi are evaluated by accounting all the available modes of vibration and assumed as two separate sources of information (s1rdi and s2mse). then, the obtained msecr and rdi are converted in local decisions m1(s1), m2(s2) and involved in df process which provides the bpas which can be assumed as indices able to detect the damage location. regarding the mdf approach, the procedure is developed by considering the rdi index and the msecr index separately. the main differences with respect to the df procedure consists in the fact that the sources are composed by the same index (msecr or rdi) and each source differ from the others by the number of accounted modes of vibrations. indeed, considering n identified modes of vibration for both the undamaged and damaged state of the system, a group of n firstlevel sources, denoted as si with i = 1,…, n, is defined by considering different sets of undamaged/damaged couples of mode shapes , i d i i       , according to the scheme reported in fig. 1.b and fig. 1.c. for each first-level source si, it is possible to evaluate the rdi and the msecr of the jth element (j = 1…n), named rdij[si] and msecrj[si]. the local decision mi(si) associated to the ith first-level source si for both the use of rdi and msecr are, then, obtained:       1 1 i i s j i i n s k k j n rdi m s rdi                (7)       1 1 i i s j i i n s k k j n msecr m s msecr                (8) a second group of n-1 second-level sources, denoted as is , is introduced and, for each is , the corresponding local decisions  im s are obtained from subsequent data-fusion operations according to the scheme shown in fig. 1. a) b) c) figure 1: schematization of the proposed data fusion procedures for the optimization of the damage detection: a) df fusion technique; b) df technique based on the rdi indicator; c) mdf technique based on the msecrj indicator. e. grande et alii, frattura ed integrità strutturale, 29 (2014) 325-333; doi: 10.3221/igf-esis.29.28 328 therefore, the derivation of the second-level sources is based on the fusion of couples of local decisions. in fact, starting, for example, from the first two first-level sources, s1 and s2, a first fusion, developed through the dempster’s rule, provides the vector of local decisions associated to the second-level source 1s as follows: 1 2 1 1 2 1 1 2 2 1 1 1 2 2 ( ) ( ) 1 ( ) ( ) s s s s s m s m s m s m s          1 m ( s ) (9) the subsequent fusions for obtaining the local decision vectors of the second-level sources are characterized by the peculiarity that one of the vector of local decisions refers to a first-level source ( is ) whilst, the other one corresponds to the second-level source derived from the previous fusion ( 2is  ), as shown in fig. 1. the vector of local decisions corresponding to the last source ( 1ns  ) is just the vector accounted for deriving information on the damaged members of the system according to the proposed approach:           2 1 2 2 2 2 2 n n n n n n n n n s s s n 1 n 1 n n n n s s m s m s m s m s m s                    (10) the greatest components of this vector indicate the members where the damage is located. numerical applications he numerical applications reported in the paper are devoted to assess the capability of the dempster-shafer theory to improve the ability of classical indices in detecting damages in structures on the basis of the variation of their dynamic properties. in particular, both the df and mdf techniques proposed by the authors are analyzed with reference to the fixed end beam shown in fig. 2 [6]. the beam is composed of 12 elements and 13 nodes characterized by only vertical displacements as available dofs. each element has a length of 0.6 m, modulus of elasticity of 7.5x10 n/m2, cross sectional area of 0.001 m2, moment of inertia of 7.56x10.7 m4, and mass density of 7800 kg/m3. two damage patterns are considered and, for both of them, the damage is simulated by a reduction of the stiffness of some elements. the first pattern is a single damage case where only one single element, that is no. 6, is damaged by reducing its stiffness of 15% (denoted in the following as “s6d15”); the second pattern is a multiple damage case where two elements, no. 6 and 11, are both damaged by reducing their stiffness of 10% (denoted in the following as “s6,11d10”). the mode shapes and the frequencies of vibration have been numerically derived through the eigenvalue problem for both undamaged and damaged cases. the df and the mdf techniques have been applied to the beam in the different damage patterns considering a limited number of identified mode shapes and not consecutives mode shapes. moreover, in order to simulate the presence of noises that in real applications generally affect the signals used in the identification process, df and mdf have been also applied by introducing errors in the numerically evaluated mode shapes. figure 2: fem of fixed-end beam single damage case: s6d15 the results concerning the single damage scenario are shown in fig. 3 for the case of df technique and in fig. 4 for the case of mdf technique, considering in both cases different sets of modes of vibration. in particular, in fig. 3 are also reported the results deduced by applying the classical damage identification technique based on the use of the rdi and msecrj indices. from the figures it is possible to observe that both df and mdf technique allow to improving the detection of damage with respect to the classical damage identification technique. indeed, graphically it is evident that the bars corresponding t e. grande et alii, frattura ed integrità strutturale, 29 (2014) 325-333; doi: 10.3221/igf-esis.29.28 329 to the use of df and mdf more clearly underline the damaged element n.6, particularly in the case of mdf where for all the accounted sets of modes the most significant bpa just corresponds to the damaged element. in the case of the use of the classical techniques, it is possible to observe that for many sets of modes the damaged element is not identified (it is characterized by a bpa less than the ones corresponding to other undamaged elements) and it seems that more than one of the elements composing the beam is affected by damage. for these cases, although the application of the df technique leads to an increase of the bpa corresponding to the damaged element, the corresponding bar results the highest one, significant values of the bpa also characterize the other elements. also in the case of the mdf technique the sets of modes =[3,5,7], =[3,4,6] are characterized by a less accurate damage identification although a significant difference characterize the bpa corresponding to the damage element and the bpa of the undamaged ones. this effect clearly underlines the role of the identified modes of vibration before and after the damage. indeed, the sets characterized by the better identification of damage are the ones composed of the modes of vibration with significant values of the modal participating mass and by the more sensibility to the damage in terms of variation of the frequency. =[1,2,3] =[1,5,7] =[3,5,7] =[3,4,6] figure 3: rdi and msecrj index vs. df technique – s6d15 damage case multiple damage case: m6,11d10 in fig. 5 and 6 are reported the same results considering the multiple damage scenario. also for this damage scenario it is possible to observe the capability of the df and mdf in improving the damage detection with respect to traditional techniques, and, also in this case, it is evident the importance of the selected sets of modes. this last effect becomes more important in the case of multiple damage scenarios. effect of noise the capability of data fusion to improve the damage detection is further assessed by introducing errors in the modes of vibration generally arising when noises affect the signals at the basis of the identification process. in the paper, this effect is simulated by perturbing each mode shape, accounted in the damage identification, as follows:  1 1,..,i i ir i n      (11) 1 2 3 4 5 6 7 8 9 101112 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 elements rd i 1 2 3 4 5 6 7 8 9 101112 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 elements m s e c r j 1 2 3 4 5 6 7 8 9 101112 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 elements b p a s datafusion df 1 2 3 4 5 6 7 8 9 101112 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 elements rd i 1 2 3 4 5 6 7 8 9 101112 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 elements m s e c r j 1 2 3 4 5 6 7 8 9 101112 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 elements b p a s datafusion df 1 2 3 4 5 6 7 8 9 101112 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 elements rd i 1 2 3 4 5 6 7 8 9 101112 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 elements m s e c r j 1 2 3 4 5 6 7 8 9 101112 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 elements b p a s datafusion df 1 2 3 4 5 6 7 8 9 101112 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 elements rd i 1 2 3 4 5 6 7 8 9 101112 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 elements m s e c r j 1 2 3 4 5 6 7 8 9 101112 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 elements b p a s datafusion df e. grande et alii, frattura ed integrità strutturale, 29 (2014) 325-333; doi: 10.3221/igf-esis.29.28 330 being ri a normally distributed random variable with zero mean and  the noise level in terms of percentage. in fig. 7-10 are reported the results derived from the damage identification considering df and mdf technique, the single damage and the multiple damage scenarios and by accounting 100 samples with a 0.5% noise level. the obtained results confirm the capability of both df and mdf to improve the damage detection with respect to traditional approach. at the same, greater dispersion of results characterizes both df and mdf. this evidence is due to the fact that df and mdf techniques use several times the same mode of vibration and, consequently, the corresponding errors. =[1,2,3] =[1,5,7] =[3,5,7] =[3,4,6] figure 4: mdf technique – s6d15 damage case =[1,2,3] =[1,5,7] =[3,5,7] =[3,4,6] figure 5: rdi and msecrj index vs. df technique – m6,11d10 damage case 1 2 3 4 5 6 7 8 9 10 11 12 0 0.2 0.4 0.6 0.8 1 elements b p a s( rd ie 2) multiple datafusion mdf rdie 2 index 1 2 3 4 5 6 7 8 9 10 11 12 0 0.2 0.4 0.6 0.8 1 elements b p a s( m s e c r j) multiple datafusion mdf msecr j index 1 2 3 4 5 6 7 8 9 10 11 12 0 0.2 0.4 0.6 0.8 1 elements b p a s( rd ie 2) multiple datafusion mdf rdie 2 index 1 2 3 4 5 6 7 8 9 10 11 12 0 0.2 0.4 0.6 0.8 1 elements b p a s( m s e c r j) multiple datafusion mdf msecr j index 1 2 3 4 5 6 7 8 9 10 11 12 0 0.2 0.4 0.6 0.8 1 elements b p a s( rd ie 2) multiple datafusion mdf rdie 2 index 1 2 3 4 5 6 7 8 9 10 11 12 0 0.2 0.4 0.6 0.8 1 elements b p a s( m s e c r j) multiple datafusion mdf msecr j index 1 2 3 4 5 6 7 8 9 10 11 12 0 0.2 0.4 0.6 0.8 1 elements b p a s( rd ie 2) multiple datafusion mdf rdie 2 index 1 2 3 4 5 6 7 8 9 10 11 12 0 0.2 0.4 0.6 0.8 1 elements b p a s( m s e c r j) multiple datafusion mdf msecr j index 1 2 3 4 5 6 7 8 9 101112 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 elements rd i 1 2 3 4 5 6 7 8 9 101112 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 elements m s e c r j 1 2 3 4 5 6 7 8 9 101112 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 elements b p a s datafusion df 1 2 3 4 5 6 7 8 9 101112 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 elements rd i 1 2 3 4 5 6 7 8 9 101112 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 elements m s e c r j 1 2 3 4 5 6 7 8 9 101112 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 elements b p a s datafusion df 1 2 3 4 5 6 7 8 9 101112 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 elements rd i 1 2 3 4 5 6 7 8 9 101112 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 elements m s e c r j 1 2 3 4 5 6 7 8 9 101112 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 elements b p a s datafusion df 1 2 3 4 5 6 7 8 9 101112 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 elements rd i 1 2 3 4 5 6 7 8 9 101112 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 elements m s e c r j 1 2 3 4 5 6 7 8 9 101112 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 elements b p a s datafusion df e. grande et alii, frattura ed integrità strutturale, 29 (2014) 325-333; doi: 10.3221/igf-esis.29.28 331 =[1,2,3] =[1,5,7] =[3,5,7] =[3,4,6] figure 6: m df technique – m6,11d10 damage case =[3,5,7] =[3,4,6] figure 7: rdi and msecrj index vs. df technique – s6d15n0.5 damage case (100 simulations) =[3,5,7] =[3,4,6] figure 8: mdf technique – s6d15n0.5 damage case (100 simulations). 1 2 3 4 5 6 7 8 9 10 11 12 0 0.2 0.4 0.6 0.8 1 elements b p a s( rd ie 2) multiple datafusion mdf rdie 2 index 1 2 3 4 5 6 7 8 9 10 11 12 0 0.2 0.4 0.6 0.8 1 elements b p a s( m s e c r j) multiple datafusion mdf msecr j index 1 2 3 4 5 6 7 8 9 10 11 12 0 0.2 0.4 0.6 0.8 1 elements b p a s( rd ie 2) multiple datafusion mdf rdie 2 index 1 2 3 4 5 6 7 8 9 10 11 12 0 0.2 0.4 0.6 0.8 1 elements b p a s( m s e c r j) multiple datafusion mdf msecr j index 1 2 3 4 5 6 7 8 9 10 11 12 0 0.2 0.4 0.6 0.8 1 elements b p a s( rd ie 2) multiple datafusion mdf rdie 2 index 1 2 3 4 5 6 7 8 9 10 11 12 0 0.2 0.4 0.6 0.8 1 elements b p a s( m s e c r j) multiple datafusion mdf msecr j index 1 2 3 4 5 6 7 8 9 10 11 12 0 0.2 0.4 0.6 0.8 1 elements b p a s( rd ie 2) multiple datafusion mdf rdie 2 index 1 2 3 4 5 6 7 8 9 10 11 12 0 0.2 0.4 0.6 0.8 1 elements b p a s( m s e c r j) multiple datafusion mdf msecr j index 0 2 4 6 8 10 12 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 elements rd i i nd ex 0 2 4 6 8 10 12 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 elements m s e in de x 0 2 4 6 8 10 12 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 elements in de x fro m fu si on rdi index mse index datafusion 0 2 4 6 8 10 12 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 elements rd i i nd ex 0 2 4 6 8 10 12 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 elements m s e in de x 0 2 4 6 8 10 12 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 elements in de x fro m fu si on rdi index mse index datafusion 0 5 10 0 0.2 0.4 0.6 0.8 1 elements b p a s( rd ie 2) multiple datafusion mdf rdie 2 index 0 5 10 0 0.2 0.4 0.6 0.8 1 elements b p a s( m s e c r j) multiple datafusion mdf msecr j index 0 5 10 0 0.2 0.4 0.6 0.8 1 elements b p a s( rd ie 2) multiple datafusion mdf rdie 2 index 0 5 10 0 0.2 0.4 0.6 0.8 1 elements b p a s( m s e c r j) multiple datafusion mdf msecr j index e. grande et alii, frattura ed integrità strutturale, 29 (2014) 325-333; doi: 10.3221/igf-esis.29.28 332 =[3,5,7] =[3,4,6] figure 9: rdi and msecrj index vs. df technique – m6,11d10n0.5 damage case (100 simulations). =[3,5,7] =[3,4,6] figure 10: mdf technique – m6,11d10n0.5 damage case (100 simulations) conclusions he approaches here proposed combines the use of some damage indicators with the evidence theory based on the dempster’s rule of combination through a procedure devoted to obtain more reliable and evident information concerning the position of damage in linear systems. the results carried out with reference to the numerical applications reported in the paper have clearly underlined the ability of the proposed approach in improving the performances of damage indicators both in the case of single damage scenarios and in the case of multiple damage scenarios. in particular, the mdf have underlined a better capability to detect the location of damage with respect to the df where a simple fusion is performed. indeed, it has been observed that the mdf particularly emphasizes the values of damage indicators corresponding to the damaged members and, at the same time, leads to a significant reduction of the value of the indicators of the undamaged members. this peculiarity is indeed mainly due to the subsequently data-fusion multiple steps procedure which allows to refine the vectors of local decisions. the ability of the proposed approach has been also confirmed in the presence of scenarios characterized by damages with lower damage severity (stiffness reduction less than 5%). nevertheless, although this aspect has not been analyzed in the present paper, in this case it has been observed a greater sensibility of the data fusion to the set of the selected modes of vibration. although the proposed approaches have shown a sensibility to errors affecting the identified modes, as occurs for the classical approach based on the rdi and the msecr, it has been observed that the most significant variations concern the only indicators corresponding to the damaged members; on the contrary, in the case of the classical approach, the indicators of all the members are significantly affected by the noise. finally, as underlined in [6], the ability of the proposed approach in providing an efficient detection of the damage position in structures represents an important basis for the further step of the identification process that is the determination of the damage severity. indeed, the precision of most of the methods available in the current literature [13] in detecting the damage amount is strongly dependent on the correct identification of the damage position. moreover, the proposed data fusion approach could be generalized in order to improve not only the identification of the damage position but also the damage extent. 0 2 4 6 8 10 12 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 elements rd i i nd ex 0 2 4 6 8 10 12 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 elements m s e in de x 0 2 4 6 8 10 12 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 elements in de x fro m fu si on rdi index mse index datafusion 0 2 4 6 8 10 12 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 elements rd i i nd ex 0 2 4 6 8 10 12 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 elements m s e in de x 0 2 4 6 8 10 12 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 elements in de x fro m fu si on rdi index mse index datafusion 0 5 10 0 0.2 0.4 0.6 0.8 1 elements b p a s( rd ie 2) multiple datafusion mdf rdie 2 index 0 5 10 0 0.2 0.4 0.6 0.8 1 elements b p a s( m s e c r j) multiple datafusion mdf msecr j index 0 5 10 0 0.2 0.4 0.6 0.8 1 elements b p a s( rd ie 2) multiple datafusion mdf rdie 2 index 0 5 10 0 0.2 0.4 0.6 0.8 1 elements b p a s( m s e c r j) multiple datafusion mdf msecr j index t e. grande et alii, frattura ed integrità strutturale, 29 (2014) 325-333; doi: 10.3221/igf-esis.29.28 333 references [1] salawu, o., detection of structural damage through changes in frequencies: a review, engineering structures, 19-9 (1997) 718-723 [2] farath, c., hemez, f., updating finite-element dynamic models using an element-by-element sensitivity methodology, aiaa journal, 31-9 (1993) 1702-1711. [3] de angelis, m., imbimbo, m., a procedure to identify the modal and physical parameters of a classically damped system under seismic motions, adv. acoust. vib., (2012), article id 975125. [4] doebling, s., hemez, f., peterson, l., farath, c., improved damage location accuracy using strain energy based on mode selection criteria, aiaa journal, 35-4 (1997) 693-699. [5] grande, e., imbimbo, m., a data-driven approach for damage detection: an application to the asce steel benchmark structure, journal of civil structural health monitoring, 2 (2012) 73-85. [6] grande, e., imbimbo, m., a multi-stage data-fusion procedure for damage detection of linear systems based on modal strain energy, journal of civil structural health monitoring, 4 (2014) 107–118. [7] shi, z., law, s., zhang, l., structural damage detection from modal strain energy change, journal of engineering mechanics, 128-5 (2002) 521-529. [8] pandey, a.k., biswas, m., damage detection in structures using changes in flexibility, journal of sound and vibration, 169-1 (1994) 3–17. [9] fei, q., li, a., han, x., simulation study on damage localization of a beam using evidence theory, procedia engineering, 1 (2009) 147-150. [10] guo, h., li, z., a two-stage method to identify structural damage sites and extents by using evidence theory and micro-search genetic algorithm, mechanical systems and signal processing, 23 (2009) 769-782. [11] bao, yq., li, h., an, y., ou, jp., dempster-shafer evidence theory approach to structural damage detection, struct. health monit. 10-3 (2011) 235-246. [12] g., shafer, a mathematical theory of evidence, princeton university press, princeton, nj, (1976). [13] shi, z., law s., zhang l., structural damage detection from elemental modal strain energy change, journal of engineering mechanics, 126-12 (2000) 1216-1223. shot peening processes to obtain nanocrystalline surfaces in metal alloys: a. regad et alii, frattura ed integrità strutturale, 56 (2021) 115-122; doi: 10.3221/igf-esis.56.09 115 repair and rehabilitation of corroded hdpe100 pipe using a new hybrid composite a. regad, d. benzerga, h. berrekia lscmi, university of sciences and technology of oran, mechanical department, b.p. 1505, 31000 oran, algeria abdelmalekregad@yahoo.fr, djeb_benz@yahoo.fr, habib.doctorat@hotmail.com haddi abdelkader univ. artois, ulr 4515, laboratoire de génie civil et géo-environnement (lgcge), béthune, f-62400, france abdelkader.haddi@univ-artois.fr chekhar nourredine production director pti polymer transformation innovation, oran, algeria nourdine.chakh@gmail.com abstract. the good management of drinking water begins with a supply network, with a low rate of leakage. currently, the pipes used in the water transport system are mainly made of polymeric materials, such as hdpe. the corrosion degradation of this type of pipe has received a lot of attention from the drinking water supply companies. it is therefore important to understand the effect of pressure on an hdpe pipe with a surface defect. to answer this problem, we will first study the mechanical behavior at failure of hdpe pipes in the presence of a surface defect using a finite element method. for the rehabilitation of pipe in presence of surface defect, we try to use a new composite. this new laminated composite is reinforced with a natural organic load. it is obtained from a laminated composite woven by incorporating a natural non-polluting organic load (granulates of date cores) which becomes hybrid composite. the new economical hybrid composite material is made of an organic matrix containing methyl methacrylate, a woven reinforcement including a reinforcing glass fiber and a fabric perlon having an absorbing role. the textile reinforcement made up of several folds reinforcing laid out according to the orientations (90, 452, and 0). a numerical simulation with the ansys workbench software is carried out to study the behavior of the hdpe pipe with surface defect and with defect repaired by the new hybrid composite material in the form of rings to consolidate the cracked area of the tube. the numerical results will allow us to decide on a real practical use of the new hybrid composite. citation: regad, a., benzarga, d., haddi, a., chekhar, n., repair and rehabilitation of corroded hdpe100 pipe using a new hybrid composite, frattura ed integrità strutturale, 56 (2021) 115-122. received: 24.01.2021 accepted: 08.03.2021 published: 01.04.2021 copyright: © 2021 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. https://youtu.be/2zujws8mshq a. regad et alii, frattura ed integrità strutturale, 56 (2021) 115-122; doi: 10.3221/igf-esis.56.09 116 keywords. rehabilitation; pipe hdpe; superficial defect; finite element method; new hybrid composite. introduction oday, the deterioration of underground drinking water supply pipes has become a growing concern of industrial and environmental sectors. the global water crisis and the scarcity of water resources require good management of this precious resource. good management begins with a reliable drinking water supply system with a low leakage rate. leaks caused by the rupture of pipes, a fairly common phenomenon in urban areas, are initiated by a corrosion or other defects. the severity of these phenomena depends on several parameters including the nature of the material of the pipes. polymeric materials, such as hdpe, occupy a large part of the water transport market, thanks to their multiple qualities (reduced cost, ease of installation, flexibility). in fact, the annual growth in the number of accidents occurring in water supply networks (aqueducts) and the huge rehabilitation budgets that result from it are at the origin of the search for innovative techniques in terms of assessment and prevention against corrosion damage. currently, the pipes used in the water transport system are mainly made of polymeric materials, such as hdpe. the corrosion degradation of this type of pipe has received a great deal of attention from drinking water supply companies and also from producers of these materials. the soil where these pipes are located is a favorable environment which accentuates all types of defects despite the protection of these pipes. the unfavorable environment and the damage in the pipes led to explore different repair options for functional maintenances such as reinforcements in composite materials. the concern of pipeline network managers is to see the breaks that represent a potential threat because of their economic and social transformations [1-5]. in addition, the repair of faults and premature replacement of pipes leads to significant financial losses [6-10]. therefore, the evaluation of the residual strength of pipes with defects should be as accurate as possible and based on confirmed experimental and numerical methods [11-18]. the objective of our work is to assess cracked hdpe pipes considering the crack size effect on the burst pressure. for this purpose, a finite element model is developed in ansys software. the model is validated with experimental data [19]. the maximum service pressure that an hdpe pipe with surface defect could be computed from the numerical model and used for comparison. then, we studied the behavior of the tube with the new hybrid composite material. the hybrid composite that served as a ring strengthening on the weakened area by the corrosion. the numerical results obtained are important for practical use of the new hybrid composite for rehabilitating drinking water supply pipes in hdpe. numerical modeling o model the pipeline we used the ansys workbench 2020r1 software. a model has been developed that simulates the behavior of a hdpe pipe following an increase in internal pressure while taking into account the presence of a longitudinal crack in its outer wall. given the symmetry of the hdpe 100 tube, we modeled a half cylinder. the dimensions of the structure are: length, radius and thickness. thus we were able to model the surface defect of the hdpe tube by taking into account the geometry of the defect, the boundary conditions and the mesh [20]. for the simulation, we used the experimental results presented in [19]. initially, we modeled a pipe in pehd100 without defect presenting the same characteristics as those presented in [19] and we calculated the rupture pressure which corresponds to the value of the von mises stress when this one reaches the tensile strength of the material. then we modeled a tube of the same grade with a parabolic defect with variable lengths and depths and calculated for each type of defect the corresponding rupture pressure. only a tube with a diameter of 125 mm and a thickness of 12 mm was simulated. the effect of the depth of the defect was studied by varying the depth "a" for each specimen. the length of the defect "c" varies as a function of "a". the width of the defect remains very small compared to the other dimensions (see fig. 1). the results obtained are compared with the experimental results. the geometry studied is an hdpe 100 tube with an outside diameter of 125 mm and a thickness of 12 mm containing a longitudinal defect on its outside surface of length c and depth a. different sizes of the defect are treated (see tab. 1) for the model with superficial defect (crack), a cavity was created which represents the defect on the tube. to do this, we create a parabolic half-surface at the end of the tube. the volume of the defect is obtained by a rotation of 90 ° around the upper line of the tube wall. this volume is subtracted from the volume of the original tube without defect, which gives t t a. regad et alii, frattura ed integrità strutturale, 56 (2021) 115-122; doi: 10.3221/igf-esis.56.09 117 us a quarter-tube with a quarter-defect [21] (see fig. 2). figure 1: geometry of the defect table 1: geometric characteristics of the surface defects figure 2: pipe with elliptical defect figure 3: hdpe 100 tube meshing. a(mm) a/e c(mm) 2 0 .167 25 4 0 .333 34.87 6 0.5 42.14 8 0.667 48 10 0.833 52.91 a. regad et alii, frattura ed integrità strutturale, 56 (2021) 115-122; doi: 10.3221/igf-esis.56.09 118 pressure : 10 bars pressure : 20 bars pressure : 25 bars figure 4: the variation of the von mises stress at the surface of the defect as a function of the increase in pressure with parabolic default (c = 25mm, d = 2 mm) a mesh sensitivity study was conducted to choose the appropriate mesh size (see fig. 3a). the stress-number of elements curve allows us to choose the size of the elements. in the case of the parabolic hdpe pipe, we have chosen a size of 1.3 10-2 m which corresponds to 28,443 nodes and 14,911 elements. in the vicinity of the defect, the mesh has been further refined for better results. a sphere of radius 0.1 m was located at the level of the defect with a size of 5.5 to 10-3 m of the elements (see fig. 3b). then, the analysis was conducted considering different levels of pressure. increased pressure von mises stress (pa) prevision of the rupture the von mises stress reaches the reference stress along the entire ligament von mises stress (pa) von mises stress (pa) a. regad et alii, frattura ed integrità strutturale, 56 (2021) 115-122; doi: 10.3221/igf-esis.56.09 119 numerical results o obtain the results, the pressure is increased until the von mises stress is close to the tensile strength of the material which is 27.62 mpa [22]. the values of the depth and the length of the defect are varied, and the value of the pressure is recorded each time. the numerical simulation was carried out in the same way for the other superficial defects. the resulting pressures after simulation are shown in tab. 2. table 2: burst pressure vs crack initiation pressure. δ1: offset between the value of the burst pressure determined by the formula (ref.19) and that calculated by finite elements. δ2: offset between the crack initiation pressure and the burst pressure. the values given by the formula are in good agreement with the values of the starting pressure calculated numerically with an error δ1 which does not exceed 23% and an average error of 16%. the crack initiation pressures are lower than the burst pressures with an offset δ2 varying between 32% and 52%. the numerically determined crack initiation pressures and those given by the proposed formula as well as the experimentally determined burst pressures are shown in fig. 5. figure 5: comparison between burst pressures and initiation crack pressures. the initiation crack pressure is the minimum loading level involving the initiation of the crack. the initiation crack pressure depends on the one hand on the mechanical characteristics of the material, and on the other hand it is related to the geometric parameters (geometry of the pipe and the size of the defect). fig. 5 shows that the numerically calculated initiation crack pressure are in agreement with the pressure values given by the formula proposed in [19] the initiation t a (mm) a/e c(mm) burst pressure (mpa) crack initiation pressure (mpa) formula (ref. 19) numerical crack initiation pressure (mpa) δ1 (%) δ2 (%) 2 0.167 25 [5.36 ; 5.11] 3.9 3.555 4.858 33.71 4 0.333 34.87 [4.58 ; 4.84 ; 4.81] 3.417 3.220 6.740 38.50 6 0.5 42.14 [4.25; 4.03 ; 4.1] 2.8 2.300 10.34 49.47 8 0.667 48 [3.52 ; 3.59; 3.58] 2.4 1.843 19.75 54.93 10 0.833 52.91 [3.11] 2.167 1.470 28.01 52.75 a. regad et alii, frattura ed integrità strutturale, 56 (2021) 115-122; doi: 10.3221/igf-esis.56.09 120 crack pressures are lower than the burst pressures with a variable offset. this offset comes from the crack propagation phase. in fact, the initiation of the crack is followed by a phase of propagation of the crack on the remaining ligament until complete bursting. new hybrid composite repair system repair with composite materials can be an effective leak containment solution to repair defects that can cause leaks in potable water supply pipes due to future deterioration such as corrosion and erosion. benefits associated with composite repair systems include short length of time needed to complete a repair, undisrupted product transmission in the piping system while the repair is made and eliminating the possibility of welding or cutting of the pipeline is required. industry analysis shows composite repair systems are, on average, 73% cheaper than replacing the damaged section completely [23]. for the reinforcement of the corroded hdpe 100 pipe with a surface defect, and in order to give it the mechanical characteristics of a healthy and flawless tube, we used the new hybrid composite. in order to achieve this, we used the ansys workbench 2020 r1 code to create the layers of composite that will be used to repair the defective tube. the new hybrid composite (90/452/0) consists of two layers of perlon, two layers of glass fiber and ten grams of granulated of dates. the mechanical characteristics of the new hybrid composite are presented in the table below [24]. yield strength (mpa) ultimate tensile strength (mpa) young modulus (mpa) elongation a% normal bending stress (mpa) maximum interlaminar shear stress (mpa) 29.628 31.63 10.829 3.94 42.1 1.26 table 3: the mechanical characteristics of the new hybrid composite. the von mises stress in the vicinity of the defect was compared for hdpe 100 tube without and with composite repair. the new hybrid composite layer with a thickness 1.2mm was utilized (see fig. 6). the contact between composite and pipe surfaces is assumed to be perfectly bonded. figure 6: corroded hdpe 100 pipe reinforced with the new hybrid composite. the results obtained after simulation show that the von mises stress of the structure is modified when the hdpe 100 pipe with a (parabolic) defect is repaired by the new hybrid composite (tab.4). it can be seen from the results of tab. 4 that: ✓ the maximum von mises stress decreases when the hdpe 100 pipe is repaired using the hybrid composite. ✓ the hybrid composite, if its thickness is increased or the number of its layers is multiplied can restore the tube to the mechanical characteristics of a healthy tube. a. regad et alii, frattura ed integrità strutturale, 56 (2021) 115-122; doi: 10.3221/igf-esis.56.09 121 these results show that the new hybrid composite can be used in the rehabilitation and repair of hdpe pipes used for the transport of drinking water. the acceptance of composite materials as an alternative to conventional repair materials is indicated through the recent development of several codes and standards [25]. the standards recognize composites as a legitimate repair material. long-term performance is a main concern for composite repair system. defect maximum value of von mises stress (mpa) a (mm) a/e c(mm) pipe non repaired pipe repaired by one layer pipe repaired by two layers pipe repaired by three layers pipe repaired by four layers pipe repaired by five layers pipe repaired by six layers 2 0.167 25 14.39 13.11 11.94 10.88 9.91 9.03 8.22 4 0.333 34.87 18.68 18.31 17.94 17.59 17.24 16.90 16.56 6 0.5 42.14 22.374 21.913 21.46 21.01 20.58 20.16 19.74 8 0.667 48 24.377 23.015 21.72 20.51 19.36 18.28 17.26 10 0.833 52.91 25.667 24.893 24.14 23.411 22.70 22.02 21.33 table 4: hdpe 100 pipe repaired with new hybrid composite. conclusion dpe 100 pipes for the transport of drinking water are subject to corrosion failure resulting in surface defects that weaken the pipe. this study focuses on the assessment of hdpe 100 pipes in the presence of surface defects as well as a proposal of a composite reinforcement using a new hybrid composite material. for this purpose, a numerical model validated with experimental data is developed in ansys. the results of the numerical analysis showed that the presence of defects may increase significantly the level of stress near the crack tip (stress concentration zone). a propagation of this anomaly would generate the ruin of the structure which will lead to a downtime of the network and require repairs. the numerical results of the reinforcement based on the new hybrid composite material showed that the von mises stress decreases when the tube is reinforced with a composite layer as preventive measure (before ruin). a parametric study showed that the von mises equivalent stress increases with increasing defect length and depth. the repair by this system of new hybrid composite, which has the qualities of being economical and non-polluting, can be very effective in practice because it helps to restore corroded hdpe pipe to its initial service pressure. long-term performance is a main concern for composite repair system. in response to that, a large research program sponsored by pti polymer transformation innovation is conducted to better understand the long-term performance of composite repair systems using this new hybrid composite. references [1] rubeiz, c. (2010). impact of potable water disinfectants on pe pipe, technical report: jana laboratories inc., pp.1 34 [2] khelif, r. (2007). analyse de la rupture et évaluation de la durée de vie basée sur la fiabilité des tubes en polyéthylène pour le transport du gaz, (doctoral dissertation, université blaise pascal-clermont-ferrand ii). [3] krishnaswamy, r. k. (2005). analysis of ductile and brittle failures from creep rupture testing of high-density polyethylene (hdpe) pipes, polymer, 46(25), pp. 11664-11672. [4] guide d’étude des réseaux en polyéthylène. (2012).2011th–2012th ed. association pluridisciplinaire réso-pe. [5] gabriel, l. h., & bennett, o. (2010). the complete corrugated polyethylene pipe design manual and installation guide. plastics pipe institute (ppi). [6] history of hdpe and hdpe pipe products, pe specialisten technology, pp. 1–2. h a. regad et alii, frattura ed integrità strutturale, 56 (2021) 115-122; doi: 10.3221/igf-esis.56.09 122 [7] ziegler, k. (1965). consequences and development of an invention. rubber chemistry and technology, 38(1), pp. 23-36. [8] brömstrup, h. (ed.). (2004). pe 100 pipe systems. vulkan-verlag gmbh. [9] addiego, f. (2006). caractérisation de la variation volumique du polyéthylène au cours de la déformation plastique en traction et en fluage (doctoral dissertation, institut national polytechnique de lorraine). [10] guidara, m. a. (2016). analyse des conditions de rupture des conduites d’adduction d’eau potable en polyéthylène, sous l’effet d’écoulement transitoire, en présence d’un défaut, (doctoral dissertation, université de lorraine; université de sfax (tunisie)). [11] arieby, r. (2007). caractérisation mécanique et modélisation thermodynamique du comportement anisotrope du polyéthylène à haute densité. intégration des effets d’endommagement, (doctoral dissertation, institut national polytechnique de lorraine). [12] ferhoum, r. (2012). etude expérimentale et modélisation numérique du comportement du pehd à l'état vierge et après vieillissement thermique, (doctoral dissertation, université mouloud mammeri). [13] cazenave, j. (2005). sur le compromis rigidité/durabilité du polyéthylène haute densité en relation avec la structure de chaîne, la microstructure et la topologie moléculaire issues de la cristallisation, (doctoral dissertation, lyon, insa). [14] peterlin, a. (1971). molecular model of drawing polyethylene and polypropylene, journal of materials science, 6(6), pp. 490-508. doi: 10.1007/bf00550305 [15] zhang, c., & moore, i. d. (1997). nonlinear mechanical response of high-density polyethylene. part i: experimental investigation and model evaluation, polymer engineering & science, 37(2), pp. 404-413. doi: 10.1002/pen.11683. [16] zhang, c., & moore, i. d. (1997). nonlinear mechanical response of high-density polyethylene. part ii: uniaxial constitutive modeling, polymer engineering & science, 37(2), pp. 414-420. doi: 10.1002/pen.11684 [17] ouardi, a., majid, f., mouhib, n., & elghorba, m. (2018). residual life prediction of defected polypropylene random copolymer pipes (ppr), frattura ed integrità strutturale, 12(43), pp. 97-105. doi: 10.3221/igf-esis.43.07 [18] majid, f., nattaj, j., elghorba, m. (2016).pressure vessels design methods using the codes, fracture mechanics and multiaxial fatigue, frattura ed integrità strutturale, 38, pp. 273–280. doi: 10.3221/igf-esis.38.37. [19] bouaziz, m. a. (2016). sécurité des réseaux d’adduction d’eau potable en présence de défaut superficiel sous l’effet du phénomène de coup de bélier, (doctoral dissertation, université de lorraine; université de sfax (tunisie)). [20] h. berrekia, d. benzerga, a. haddi, (2019). behavior and damage of a pipe in the presence of a corrosion defect depth of 10% of its thickness and highlighting the weaknesses of the asme/b31g, frattura ed integrità strutturale,49, pp. 643-654; doi: 10.3221/igf-esis.49.58 [21] benzerga, d. (2015).burst pressure estimation of corroded pipeline using damage mechanics, mmssd, isbn 978-3 319-14531-0. doi: 10. 1007/978-3-319-14532-7 springer. [22] chouiter, a., benzerga, d., haddi, a. and tamine, t. (2019).prediction of cycle life of expansion bellows for fixed tube sheet heat exchanger, frattura ed integrità strutturale, 47 30-38; doi: 10.3221/igf-esis.47.03 [23] lim, k. s., siti nur afifah, a., norhazilan, m. n., & nordin, y. (2016). systems for repair and rehabilitation of corroded oil & gas pipelines, jurutera 13 [24] k. tadjine. (2007). contribution à l'étude et à l'amélioration du comportement mécanique des matériaux composites stratifiés à usage biomécanique, (thèse de doctorat. université d’artois). [25] repair of pressure equipment and piping, (2011). the american society of mechanical engineers, asme pcc-22011. microsoft word numero_33_art_5 g. meneghetti et alii, frattura ed integrità strutturale, 33 (2015) 33-41; doi: 10.3221/igf-esis.33.05 33 focussed on characterization of crack tip fields some relationships between the peak stresses and the local strain energy density for cracks subjected to mixed-mode (i+ii) loading g. meneghetti university of padova, department of industrial engineering, via venezia 1, 35131, padova (italy) giovanni.meneghetti@unipd.it a. campagnolo, f. berto university of padova, department of management and engineering, stradella s. nicola 3, 36100, vicenza (italy) campagnolo@gest.unipd.it, berto@gest.unipd.it abstract. in this work, a link between the averaged strain energy density (sed) approach and the peak stress method in the case of cracks subjected to mixed mode (i+ii) loading has been investigated. some closed-form expressions of the strain energy density, averaged in a volume of radius r0, as function of the stress intensity factors are provided for plane strain conditions under mixed mode i+ii loadings, the material being thought of as isotropic and linear elastic. on the basis of the peak stress method (psm) some expressions useful to estimate the mode i and mode ii stress intensity factors (sifs) have been recently derived. these relationships take advantage of the elastic peak stresses from fe analyses carried out by using a given mesh pattern where the element size and type are kept constants. the evaluation of the sifs from a numerical analysis of the local stress field usually requires very refined meshes and then large computational effort. the usefulness of the psm-based expressions is that (i) only the elastic peak stresses numerically evaluated at the crack tip are needed and not a set of stress–distance data; (ii) the employed meshes are rather coarse if compared to those necessary for the evaluation of the whole local stress field. by substituting the psm-based relationships in the closed-form expressions of the averaged sed it appears that the latter can be directly estimated by means of the elastic peak stresses evaluated at the crack tip. several fe analyses have been carried out on cracked plates subjected to tension loading considering different geometrical combinations, varying the length 2a and the inclination ϕ of the crack (i.e. the mode mixity) as well as the size d of the adopted finite elements, with the aim to evaluate the local sed and the elastic peak stress components σpeak and τpeak. in all cases the numerical values of the sed derived from the fe analyses have been compared with those analytically obtained by using the expressions for the sed based on the elastic peak stresses, in order to verify the range of applicability of the proposed relationships. keywords. local approaches; stress intensity factors; strain energy density; finite elements; coarse mesh. g. meneghetti et alii, frattura ed integrità strutturale, 33 (2015) 33-41; doi: 10.3221/igf-esis.33.05 34 introduction otch stress intensity factors (nsifs) play an important role in static strength assessments of components made of brittle or quasi-brittle materials and weakened by sharp v-shaped notches [1]. this holds true also for components made of structural materials undergoing high cycle fatigue loading [2] as well as for welded joints [3, 4]. in plane problems, the mode i and mode ii nsifs for sharp v-notches, which quantify the intensity of the asymptotic stress distributions in the close neighbourhood of the notch tip, can be expressed by means of the gross and mendelson’s definitions [5]:   111 002 limrk r             (1)   212 002 lim rrk r             (2)   rr  r    notch bisector r a=r0 2 r0 (a) (b) figure 1: (a) polar coordinate system centred at the notch tip. (b) control volume (area) of radius r0 surrounding the v-notch tip. where (r,θ) is a polar coordinate system centred at the notch tip (fig. 1a), σθθ and τrθ are the stress components according to the coordinate system and λ1 and λ2 are respectively the mode i and mode ii first eigenvalues in william’s equations [6]. the condition θ = 0 characterizes all points of the notch bisector line. when the v-notch angle 2α is equal to zero, λ1 and λ2 equal 0.5 and k1 and k2 match the conventional stress intensity factors of a crack, ki and kii, according to the linear elastic fracture mechanics (lefm). the main practical disadvantage in the application of the nsif-based approach is that very refined meshes are needed to calculate the nsifs by means of definitions (1) and (2). the modelling procedure becomes particularly time-consuming for components that cannot be analysed by means of two-dimensional models. recently, nisitani and teranishi [7, 8] presented a new numerical procedure suitable for estimating ki for a crack emanating from an ellipsoidal cavity. such a procedure is based on the usefulness of the linear elastic stress σpeak calculated at the crack tip by means of fe analyses characterized by a mesh pattern having a constant element size and type. in particular nisitani and teranishi [7, 8] were able to show that the ratio ki/σpeak depends only on the element size for a given element type, so that the σpeak value can be used to rapidly estimate ki, provided that the adopted mesh pattern has been previously calibrated on geometries for which the exact value of ki is known. this approach has been theoretically justified and extended also to sharp v-shaped notches subject to mode i loading [9] giving rise to the so-called peak stress method (psm), which can be regarded as an approximate fe-based method to estimate the nsifs. later on, the psm has been extended to cracks subjected to mode i as well as mode ii stresses [10]. the element size required to evaluate k1 and k2 from σpeak and τpeak, respectively, is several orders of magnitude greater than that required to directly evaluate the local stress field. the second advantage of the use of σpeak and τpeak is that only a single stress value is sufficient to estimate k1 and k2, respectively, instead of a number of stress-distance fe data, as usually made by applying definitions (1) and (2). since the units of the mode i and mode ii nsifs, k1 and k2, depend on the notch opening angle, generally a direct comparison of the nsif values cannot be performed. this problem was overcome by lazzarin and zambardi [11], who proposed to use the total elastic strain energy density (sed) averaged over a sector of radius r0 (fig. 1b) for static [11-14] and fatigue [11,15,16] strength assessments. with reference to plane strain conditions, the sed value can be evaluated as follows: n g. meneghetti et alii, frattura ed integrità strutturale, 33 (2015) 33-41; doi: 10.3221/igf-esis.33.05 35 1 2 2 2 1 1 2 2 1 1 0 0 e k e k w e er r                (3) where e1 and e2 [11] are two parameters which depend on the notch opening angle 2α and the poisson’s ratio ν. in principle, eq. (3) is valid when the influence of higher order, non-singular terms can be neglected inside the control volume. in the case of short cracks or thin welded lap joints, for example, the t-stress must be included in the local sed evaluation [17]. aims of the present contribution are as follows:  to recall the fundamental concepts of the psm for pure modes of loading;  to present the extension of the psm to the case of mixed mode (i+ii) loading;  to investigate a link between the sed approach and the psm in the case of mixed mode (i+ii) loading. the peak stress method for pure modes of loading he peak stress method (psm) is a simplified numerical method to estimate the nsifs parameters. originally it was formulated for cases where only mode i singular stresses exists (i.e. k2 = 0 or mode ii stresses are negligible). it has been based on a link between the exact value of mode i nsif k1, see eq. (1), and the linear elastic opening peak stress σpeak calculated at the v-notch tip according to the following expression [9]: 1 * 1 1 1.38fe peak k k d      (4) the psm according to eq. (4) was applied to correlate the fatigue strength of filletand full penetration welded joints subjected to mode i loading [18,19]. recently the peak stress method has been extended also to mode ii crack problems, linking the exact value of mode ii nsif k2, see eq. (2) with 2 = 0° and 2 = 0.5, and the linear elastic sliding peak stress τpeak calculated at the crack tip according to the following expression [10]: 38.3 dτ k k 2λ1 peak 2** fe     (5) in previous expressions d is the mean finite element size adopted when using the free mesh generation algorithm available in ansys numerical code, while “exact nsif values” must be meant as the values obtained using very refined fe mesh patterns in the numerical analyses and applying definitions (1) and (2) to the numerical results. eqs. (4) and (5) are useful in practical applications because if the mean element size d is kept constant, then also k1/σpeak and k2/τpeak ratios are constant. eqs. (4) and (5) are valid under the following conditions:  use of 4-node linear quadrilateral elements, as implemented in ansys® numerical code (plane 42 of ansys element library or alternatively plane 182 with k-option 1 set to 3);  the pattern of finite elements around the v-notch tip must be that shown in fig. 2b (see also [9, 10]); in particular, four elements share the node located at the crack tip;  concerning eq. (4), v-notches characterised by an opening angle 2 ranging from 0° to 135°;  the ratio a/d must be greater than 3 in order to obtain %338.1* fek , being a the semi-crack length (or the notch depth when dealing with open v-notches). when mode ii (sliding) stresses are of interest, meshes must be more refined such that the ratio a/d must be greater than 14 in order to obtain %338.3** fek . the peak stress method for mixed mode (i+ii) loading n the present paragraph the peak stress method is extended to mixed mode (i+ii) crack problems. consider a crack (2α = 0°) centred in a plate having the geometry reported in fig. 2a and subjected to tensile loading. by varying the inclination angle ϕ of the crack it is possible to obtain different mode mixities, from pure mode i (ϕ = 0°) to mixed mode i+ii (ϕ > 0°) loading. different geometrical combinations have been considered, varying the projected crack length t i g. meneghetti et alii, frattura ed integrità strutturale, 33 (2015) 33-41; doi: 10.3221/igf-esis.33.05 36 2h (from 5 to 80 mm) and the inclination ϕ (from 0° to 60°) as well as the size of the element d, with the aim to investigate to which extent the psm holds true. finite element analyses have been performed by using the commercial code ansys® and 4-node quadrilateral element (plane 42). the free mesh algorithm has been used in all numerical analyses and the sole control parameter set to generate the mesh has been the so-called ‘global element size’, i.e. the mean element size of the finite elements, which ranged from 0.5 mm to 10 mm. with the purpose of obtaining the pattern of finite elements oriented along the crack bisector line (see fig. 2b), the geometry of the plate has been divided into six areas, such that each crack tip is shared by four areas, as shown in fig 2a. by so doing four elements (each one belonging to a different area) share the node located at the crack tip. for the considered case, k1 = ki, k2 = kii, λ1 = λ2 = 0.5, while σpeak and τpeak represent the maximum elastic normal and tangential stress referred to the bisector line and evaluated at the crack tip according to fig. 2a. the exact values of the mode i and mode ii sif, ki and kii, have been evaluated by means of further finite element analyses performed on the same geometries, but adopting very refined meshes (size of the smallest element of the order of 10-5 mm) in the close neighbourhood of the crack tip. figs. 3-4 plot the results of the numerical analyses in terms of the non-dimensional parameters k*fe and k**fe defined in eqs. (4) and (5). for the sake of brevity, only the results for the cases ϕ = 30° and 60° have been reported. from figs. 3-4, k*fe and k**fe are seen to converge to the previously calibrated values, that is 1.38 [9] and 3.38 [10], respectively, within a scatter band of the numerical results of ±3% also in the case of mixed mode (i+ii) loading. this occurs for a ratio a/d greater than a value between 3 and 4, for mode i loading, and between 14 and 16, for mode ii loading. it can be observed that the minimum a/d ratios to assure the validity of psm under mixed mode (i+ii) loading confirm the results obtained in [9], in the case of pure mode i (a/d  3), and the results reported in [10] with reference to pure mode ii (a/d  14). furthermore, as highlighted in [10], it should be noted that the mode ii loading is more critical to analyse with the psm than the mode i loading because the former requires more refined finite element patterns. (a) (b) figure 2: (a) geometry and loading condition of the analysed mixed mode crack problem. 2w = 200 mm. (b) pattern of finite elements around the singularity point: four elements share the node located at the crack tip. a link between the peak stresses and the averaged value of the local strain energy density n the present paragraph, a link between the averaged sed [11,12] and the peak stresses [9,10] in the case of cracks subjected to mixed mode (i+ii) loading is investigated. by substituting the psm-based relationships, eqs. (4) and (5), in the closed-form expression of the averaged sed, eq. (3), it appears that the latter can be directly estimated by means of the elastic peak stresses evaluated at the crack tip, σpeak and τpeak: i g. meneghetti et alii, frattura ed integrità strutturale, 33 (2015) 33-41; doi: 10.3221/igf-esis.33.05 37 -1 2 2 21 1 * **1 2 0 0 psm fe peak fe peak e ed d w k k e er r                                  (6) several fe analyses have been carried out on the same cracked plates taken into consideration in the previous paragraph, with the aim to evaluate the local sed averaged over a control volume centred at the crack tip. different geometrical combinations have been considered, varying the length 2a and the inclination ϕ of the crack (i.e. the mode mixity), while the radius of the control volume r0 has been kept constant and equal to 0.1 mm. figure 3: calibration of the psm approach for a crack (2α = 0°) under mixed mode (i+ii) loading (ϕ = 30°). normalized sif related to (a) mode i and (b) mode ii. the mode mixity ratio (mm) has been evaluated according to the following definition: ii i ii k mm k k   (7) eq. (7) provides as master cases mm = 0 for pure mode i with ϕ = 0°, mm = 0.5 for mixed mode with ϕ = 45° and mm = 1 for pure mode ii loading. g. meneghetti et alii, frattura ed integrità strutturale, 33 (2015) 33-41; doi: 10.3221/igf-esis.33.05 38 in all cases the numerical values of the sed calculated from the fe analyses have been compared with those analytically obtained by using the expressions for the sed based on the elastic peak stresses, eq. (6), in order to verify the range of applicability of the proposed method. figure 4: calibration of the psm approach for a crack (2α = 0°) under mixed mode (i+ii) loading (ϕ = 60°). normalized sif related to (a) mode i and (b) mode ii. being available the exact values of the sifs, the mean value of the sed has been evaluated also according to eq. (3). in particular the maximum difference between the sed parameter evaluated analytically (eq. (3)) and numerically (by fem) results to be about 5%, which means that the influence of higher order terms, as the t-stress, can be neglected in these cases, at least from an engineering point of view. the ratio between the sed based on the elastic peak stresses (eq. 6, psmw ) and the sed calculated from the fe analyses ( femw ) has been reported in fig. 5, with reference to an inclination ϕ of the crack equal to 0°, 30° and 60°. from fig. 5, it can be observed that the ratio fempsm ww / converges to unity, within a scatter band of ±10% for all different mode mixities taken into consideration. this occurs for a ratio a/d greater than a value equal to 3 for the case mm = 0 (ϕ = 0°), 8.50 for mm = 0.37 (ϕ = 30°) and 16 for mm = 0.63 (ϕ = 60°). in particular the minimum a/d ratio to assure the validity of the proposed method increases as the mode ii loading becomes dominant, that is increasing the mode mixity ratio (mm) defined by eq. (7). this confirms the behavior observed in the previous paragraph and in [10], with reference to k*fe and k**fe. g. meneghetti et alii, frattura ed integrità strutturale, 33 (2015) 33-41; doi: 10.3221/igf-esis.33.05 39 figure 5: ratio between the sed based on the elastic peak stresses (wpsm) and the sed derived from the fe analyses (wfe) for a crack (2α = 0°) under mixed mode (i+ii) loading: (a) ϕ = 0° (mm = 0), (b) ϕ = 30° (mm = 0.37) and (c) ϕ = 60° (mm = 0.63). g. meneghetti et alii, frattura ed integrità strutturale, 33 (2015) 33-41; doi: 10.3221/igf-esis.33.05 40 conclusions n the present contribution, a link between the averaged sed approach and the peak stress method in the case of cracks subjected to mixed mode (i+ii) loading has been investigated:  on the basis of the peak stress method, some expressions useful to estimate the mode i and mode ii sifs, recently derived for pure modes of loading, have been verified also in the case of mixed mode (i+ii) crack problems, considering different mode mixities.  since the normal and tangential peak stresses are proportional to the mode i and mode ii sifs, a link can immediately be established with the sed parameter by means of eqs. (3), (4) and (5). by substituting the psmbased relationships in the closed-form expressions of the averaged sed it appears that the latter can be directly estimated by means of the elastic peak stresses evaluated at the crack tip.  the ratio between the sed based on the elastic peak stresses and the sed derived from the fe analyses converge to a unit value for a ratio a/d greater than a value between 3 (mm = 0) and 16 (mm = 0.63). the minimum a/d ratio to assure the validity of the proposed method increases with increasing the mode mixity ratio (mm), confirming the behavior observed with reference to k*fe and k**fe.  the usefulness of the sed expression based on the elastic peak stresses is that (i) only the elastic peak stresses numerically evaluated at the crack tip are needed and the definition of a control volume is no longer required; (ii) the employed meshes are rather coarse close to the crack tip, indeed the mean element size can be significantly greater than the radius of the control volume adopted for sed evaluation. references [1] seweryn, a., brittle fracture criterion for structures with sharp notches, eng. fract. mech., 47 (1994) 673–681. [2] boukarouba, t., tamine, t., nui, l., chemini, c., pluvinage, g., the use of notch stress intensity factor as a fatigue crack initiation parameter. eng. fract. mech. , 52 (1995) 503–512. [3] lazzarin, p., tovo, r., a notch intensity factor approach to the stress analysis of welds, fatigue fract. eng. mater. struct. 21 (1998) 1089–1104. [4] atzori, b., meneghetti, g., fatigue strength of fillet welded structural steels: finite elements, strain gauges and reality, int. j. fatigue, 23 (2001) 713–721. [5] gross, r., mendelson, a., plane elastostatic analysis of v-notched plates, int. j. fract. mech., 8 (1972) 267–272. [6] williams, m. l., stress singularities resulting from various boundary conditions in angular corners on plates in tension, j. appl. mech., 19 (1952) 526–528. [7] nisitani, h., teranishi, t., ki value of a circumferential crack emanating from an ellipsoidal cavity obtained by the crack tip stress method in fem, in: guagliano, m., aliabadi, m. h., editors. proceedings of the 2nd international conference on fracture and damage mechanics, (2001) 141–146. [8] nisitani, h., teranishi, t., ki value of a circumferential crack emanating from an ellipsoidal cavity obtained by the crack tip stress method in fem, engng. fract. mech., 71 (2004) 579–585. [9] meneghetti, g., lazzarin, p., significance of the elastic peak stress evaluated by fe analyses at the point of singularity of sharp v-notched components, fatigue fract. engng. mater. struct., 30 (2007) 95-106. [10] meneghetti, g., the peak stress method applied to fatigue assessments of steel and aluminium fillet welded joints subjected to mode-i loading, fatigue fract. engng. mater. struct., 31 (2008) 346–369. [11] meneghetti, g., atzori, b., manara, g., the peak stress method applied to fatigue assessments of steel tubular welded joints subject to mode-i loading, engng. fract. mech., 77 (2010) 2100–2114. [12] lazzarin, p., zambardi, r., a finite-volume-energy based approach to predict the static and fatigue behavior of components with sharp v-shaped notches, int. j. fract., 112 (2001) 275-298. [13] berto, f., lazzarin, p., recent developments in brittle and quasi-brittle failure assessment of engineering materials by means of local approaches, mater. sci. eng. r, 75 (2014) 1-48. [14] lazzarin, p., campagnolo, a., berto, f., a comparison among some recent energyand stress-based criteria for the fracture assessment of sharp v-notched components under mode i loading, theor. appl. fract. mech., 71 (2014) 2130. i g. meneghetti et alii, frattura ed integrità strutturale, 33 (2015) 33-41; doi: 10.3221/igf-esis.33.05 41 [15] torabi, a. r., campagnolo, a., berto, f., local strain energy density to predict mode ii brittle fracture in brazilian disk specimens weakened by v-notches with end holes, mater. design, 69 (2015) 22-29. [16] livieri, p., lazzarin, p., fatigue strength of steel and aluminium welded joints based on generalized stress intensity factors and local strain energy values, int. j. fract., 133 (2005) 247-276. [17] berto, f., campagnolo, a., lazzarin, p., fatigue strength of severely notched specimens made of ti-6al-4vunder multiaxial loading, fatigue fract. engng. mater. struct., (2015). doi: 10.1111/ffe.12272. [18] berto, f., lazzarin, p., multiparametric full-field representations of the in-plane stress fields ahead of cracked components under mixed mode loading, int. j. fatigue, 46 (2013) 16-26. [19] meneghetti, g., the use of peak stresses for fatigue strength assessments of welded lap joints and cover plates with toe and root failures, eng. fract. mech., 89 (2012) 40-51. microsoft word numero_34_art_25 t.-t.-g. vo et alii, frattura ed integrità strutturale, 34 (2015) 237-245; doi: 10.3221/igf-esis.34.25 237 focussed on crack paths modelling 3d crack propagation in ageing graphite bricks of advanced gas-cooled reactor power plant thi-tuyet-giang vo university of manchester – the modelling and simulation centre, uk. philippe martinuzzi, van-xuan tran edf energy r&d uk centre – the modelling and simulation centre, george begg building, university of manchester, m139pl manchester, uk. philippe.martinuzzi@edfenergy.com neil mclachlan, alan steer edf energy generation abstract. in this paper, crack propagation in advanced gas-cooled reactor (agr) graphite bricks with ageing properties is studied using the extended finite element method (x-fem). a parametric study for crack propagation, including the influence of different initial crack shapes and propagation criteria, is conducted. the results obtained in the benchmark study show that the crack paths from x-fem are similar to the experimental ones. the accuracy of the strain energy release rate computation in a heterogeneous material is also evaluated using a finite difference approach. planar and non-planar 3d crack growth simulations are presented to demonstrate the robustness and the versatility of the method utilized. finally, this work contributes to the better understanding of crack propagation behaviour in agr graphite bricks and so contributes to the extension of the agr plants’ lifetimes in the uk by reducing uncertainties. keywords. 3d crack propagation; advanced gas-cooled reactor; graphite brick; extended finite element method; code_aster; strain energy release rate. introduction gr cores are composed of thousands of graphite bricks. after years of service, the heterogeneous irradiation and temperature fields gradually modify both the microstructure and internal stresses of the bricks. this modification may lead to crack initiation and propagation. one goal of the plant life extension (plex) program, developed by edf energy, aims at understanding the crack propagation in graphite bricks for the coming years. part of the research program conducted at edf energy r&d uk centre relies on studying the capabilities to model graphite brick crack propagation using the x-fem in code_aster, an open source finite element software package developed by edf r&d since 1989. x-fem’s major advantage is that it represents the crack without explicitly meshing it. this method of crack propagation allows many steps of crack propagation to be performed using a single mesh and enables a more accurate calculation of the stress intensity factors and the strain energy release rate around the crack front. recent developments in a t.-t.-g. vo et alii, frattura ed integrità strutturale, 34 (2015) 237-245; doi: 10.3221/igf-esis.34.25 238 code_aster enable modelling of the behaviour of ageing graphite (spatial heterogeneity of the young’s modulus and internal stresses). in this paper, crack propagation in agr graphite bricks with ageing properties is studied using the x-fem. the accuracy of the strain energy release rate computation in a heterogeneous material is evaluated using a finite difference approach. a parametric study for crack propagation, including the influence of different initial crack shapes and propagation criteria, is then conducted. the robustness and the consistency of the propagation are also presented. in section 2, the implementation of x-fem model is given. a description of the methodology for crack propagation in ageing graphite bricks is presented in section 3. the benchmark study, the numerical simulation results for planar and non-planar crack problem on the graphite bricks appear in section 4 with the discussions. and finally, in section 5, some conclusions and prospects are provided. crack propagation using x-fem basics of level set method and x-fem he level set method (lsm) is the numerical scheme developed by osher and sethian [1] to track the evolution of interfaces and shapes. in the lsm the interface is represented as the zero level set of a function of one higher dimension. to describe a crack, two level set functions are required [2]. the normal level set (lsn) represents the signed distance to the crack surface and the tangent level set (lst) represents the distance to the crack front. the x-fem allows modelling the crack growth without having to modify the original mesh. in cracking, the discontinuity of displacement due to the crack is introduced by a generalized heaviside function and the addition of the asymptotic fields near the crack tip in order to improve the accuracy in elastic fracture mechanics. the formula used for the displacement approximation uh(x) at point x is given in eq. (1). the first term is the standard one (continuous). the second term brings the discontinuity of displacement for the elements crossed by the crack (heaviside enrichment) and the third term brings the singularities for the elements around the crack tip (asymptotic enrichment). fig. 1a shows a representation of a crack with additional degrees of freedom for enriched elements. note that the crack passes through the elements and that the crack is not explicitly meshed [4]. 4 ( ) ( ) ( ) 1 ( ) ( ) ( ) ( ( )) ( ) ( ( ), ( )) n n n h i i j j k k i n x j n x k k n x l u x a x b x h lsn x c x f lsn x lst x                 (1) where ai are the traditional displacement degrees of freedom associated with node i, φ i is the linear shape function of node i, bj are the enriched degrees of freedom associated with node j, kc  are the enriched degrees of freedom associated with node k. the function h(x) is a heaviside function, which is discontinuous across the crack surface. consider an element that is crossed by the crack, h(lsn(x))=1 for the nodes located on the side where lsn(x)>0, whereas h(lsn(x))=-1 for those located on the other side where lsn(x)<0. only one layer of elements is enriched. note that a geometrical (fixed area) enrichment can also be done. the expressions of the function f  , α = 1.4, are the following [3]:  sin , cos , sin sin , cos sin2 2 2 2f          (2) the local polar co-ordinates (  ,  ) can be expressed in terms of the level sets at the crack tip as (see fig. 1b): 2 2 1; tan lst lsn lst lsn            (3) the propagation of crack thus consists in updating the level sets and determining the new crack front. the mesh is refined in the area near the crack front (the distance is evaluated by the values of the level sets) to improve the accuracy of the stress intensity factors and the strain energy release rate computation. the flowchart for a code_aster model with xfem crack propagation is presented in fig. 1c. t t.-t.-g. vo et alii, frattura ed integrità strutturale, 34 (2015) 237-245; doi: 10.3221/igf-esis.34.25 239 (a) (b) (c) figure 1: a representation of a crack with additional degrees of freedom for enriched elements (circle symbols represent the elements enriched by the heaviside function and square symbols represent the elements enriched by the singular functions) (a), global cartesian coordinate system (r,z), local cartesian coordinate system (n,t), local polar coordinate system (  , ) and representation of the level sets (b) and flowchart for code_aster model with x-fem crack propagation (c). [4] criteria of propagation – the maximum hoop stress criterion erdogan and sih [5] proposed the maximum hoop stress criterion. the maximum hoop stress criterion assumes that the crack will propagate where the hoop stress  is maximised. near the crack front, a good approximation of the hoop stress field is given by eq. (4). 2 1 1 1 3 cos cos sin 2 2 22 i iik k r                    (4) the angle of propagation is deduced by differentiating the eq. (4) and is given in eq. (5).   2 1 12 tan 8 4 i i ii ii ii k k sign k k k                  (5) where ki, kii are the values of the stress intensity factors. for non-planar crack propagation, at each point along the crack front, a plane perpendicular to the crack front at this point will be considered. the directions of the non-planar crack paths are also computed using eqs. (4) and (5). crack propagation in ageing graphite bricks algorithms of crack propagation in ageing graphite bricks using x-fem he analysis is done in two steps (see fig. 2). the first one is the ageing analysis. in order to perform this calculation, the complex abaqus user material (umat) routine, developed by amec foster wheeler since the 1990s, was used (code_aster being able to directly read umat routines). from this calculation, it is possible to extract the different material properties at any instant tcrack which also vary in space. for this study, the assumption is made that the crack will propagate instantly, therefore the properties of graphite are not evolving during crack propagation and the behaviour can be considered elastic. the important values from the umat calculation are the young’s modulus and t t.-t.-g. vo et alii, frattura ed integrità strutturale, 34 (2015) 237-245; doi: 10.3221/igf-esis.34.25 240 the stress state at instant tcrack that will be considered as the initial stress state in the crack propagation analysis. these values are extracted and passed into the second step. this step is based on an algorithm where the lsm is coupled with the x-fem to introduce and represent the crack and perform the crack propagation (see fig. 2). step 1 step 2 irradiation and oxidation of graphite crack propagation (xfem) introduction of the crack (xfem) extraction of: material properties: e(x,y,z,tcrack) stress state: σ_ij(x,y,z,tcrack) non linear behaviour (umat) crack propagates when g=gc automatic mesh refinement figure 2: description of the analysis done for crack propagation in ageing agr graphite bricks. the computation of the energy release rate g is done by using the g-theta method [7]. when g is smaller than gc (the critical strain energy release rate), there is no crack propagation. when g reaches gc, there is propagation. heterogeneous young’s modulus in space regarding the heterogeneity of the young’s modulus, developments have been made in code_aster in order to enable the calculation despite some theoretical approximations: indeed, the spatial variation of young’s modulus in the component is taken into account but there is a missing term, in gradient of e, which is not calculated. in fact, the generic definition of g which is derived from the evolution of the potential energy (ep) with the increase of the crack surface (a) with propagation is described in eq. (6). pe g a     (6) therefore, in a 2d model, by simply calculating the potential energy for a crack of length l and then for a crack of length l+dl (where dl is small compared to l), it is possible to approximate g with eq. (7). this value will be called gdiff. ( ) ( )p p diff e l dl e l g dl     (7) the previous results of martinuzzi and al. [6] had shown that the missing term in the calculation of g appeared to be negligible in the considered case of agr bricks. results and discussions benchmark of crack propagation tools on virgin graphite bricks ig. 3 represents the geometry of graphite bricks used in agr. depending on the reactors, the dimensions and the geometry may slightly vary. a benchmark was conducted in order to test the ability of four potentially interesting methods – x-fem with griffith adapted criteria, cohesive zone models (czm) [8], damage modelling (these three first methods are developed in code_aster) and configurational forces (developed at the university of glasgow) – to model crack propagation. fig. 4 shows the results of the crack paths obtained from these four methods on the first and simplest case: a 100 mm slice of f t.-t.-g. vo et alii, frattura ed integrità strutturale, 34 (2015) 237-245; doi: 10.3221/igf-esis.34.25 241 brick is slotted and externally loaded in order to replicate the internal stress state of graphite bricks after years of service and exposition to oxidation and irradiation. the crack path is two-dimensional and planar. figure 3: geometry of the graphite bricks. section (a), lateral view (b), and representation of the methane holes (c). figure 4: crack propagation methods tested for agr graphite bricks: x-fem, czm, damage modelling and configurational forces. from the results obtained in the benchmark study, the most promising one developed in code_aster was the use of the x-fem. in this case, the crack paths were similar to the experimental ones. incremental crack growth was based on energetic criteria relevant to quasi brittle materials: the direction of propagation along the crack front was based on the maximum hoop stress criterion, and the length of propagation for each step of calculation depends on the value of the strain energy release rate along the crack front. the crack paths are presented in fig. 5 for different loading scenarios using x-fem, and compared with their experimental counterparts. planar crack propagation in ageing agr graphite brick the behaviour of these ageing graphite bricks has been studied for many years. fast neutron irradiation causes graphite to shrink initially before expanding again to exceed its original volume. the attenuation in dose between the bore and the outside causes differential rates of graphite shrinkage that generate internal stresses that vary through life. fast neutron irradiation also causes the elastic modulus of the material to increase significantly early on, while oxidation causes   a)  b) c)  t.-t.-g. vo et alii, frattura ed integrità strutturale, 34 (2015) 237-245; doi: 10.3221/igf-esis.34.25 242 progressively increasing weight loss that reduces the elastic modulus. these changes occur more rapidly close to the fuel channel walls, so there is a significant variation in elastic modulus across the thickness of the brick. many numerical analyses were performed using umat routines in abaqus. these umat routines use material properties that depend on three different field variables (temperature, irradiation dose, and weight loss due to oxidation). developments in code_aster have been made to enable stress analysis to be run by directly reading the umat routines. figure 5: crack paths obtained for the different test cases of the benchmark using the x-fem (left) and experimental method (right). simulation of internal loading on slotted sliced bricks (a), simulation of external loading on sliced bricks (b), external loading on fullsize bricks (c), and the brokenshire test [9] (d). figure 6: evolution of the strain energy release rate (g) with crack propagation obtained by code_aster and abaqus. the values of g have been calculated in three different ways in code_aster, two local approaches (g0 and gav) and a global approach (gdiff). abaqus calculation is based on a global approach t.-t.-g. vo et alii, frattura ed integrità strutturale, 34 (2015) 237-245; doi: 10.3221/igf-esis.34.25 243 a parametric analysis has also been conducted using x-fem in code_aster on a full-size brick with initial stresses representing post stress-reversal state of an agr graphite brick when there are tensile stresses at the keyway corners. the influences of initial crack shape, propagation criteria, and the choice of the fracture mechanics post-processing tools are studied. a first comparison with an abaqus model gives good agreement between both codes. particularly, the evolution of the strain energy release rate with crack propagation is similar (see fig. 6). additionally, a good agreement between the local approach and the global approach is seen in fig. 7. 0 2 4 6 8 10 12 14 16 0 0.01 0.02 0.03 0.04 0.05 0.06 e m e rg y  r e le a se  ( j) crack area (m2) code_aster abaqus figure 7: evolution of the strain energy release rate with crack propagation obtained by code_aster and abaqus. fig. 8 shows the full-size brick and the evolution of a crack path under planar propagation. simulations are performed for 94 steps. the study stopped when the crack propagated fully along the brick height. all crack propagations steps were automatically performed in code_aster. it took 7 hours to perform the entire study. step 2 step 60 step 94 figure 8: photograph of a fuel brick (a) and evolution of a planar crack path using x-fem on a full-size graphite brick with stresses coming from umat analysis (b). nonplanar crack propagation in virgin graphite brick the non-planar crack propagation model is also conducted by using x-fem. an initial elliptic crack, representing a large, postulated, initial defect, is introduced with initial stresses representing the post stress-reversal state of an agr graphite a) b) t.-t.-g. vo et alii, frattura ed integrità strutturale, 34 (2015) 237-245; doi: 10.3221/igf-esis.34.25 244 brick. the influences of mesh size, propagation criteria, and the choice of the fracture mechanics post-processing tools are studied. crack propagation simulations are conducted, and the different stages in the crack growth paths are depicted in fig. 9. the angle of propagation is defined by eq. (5). simulations are performed over 16 steps, until the crack reaches the interstitial keyway and reaches the outer boundary of graphite brick. the simulations reveal the non-planar character of propagation and the results clearly demonstrate the capabilities of x-fem. ongoing work will be to improve the robustness of 3d non-planar crack propagation in ageing agr graphite bricks. step 1 step 4 step 8 step 12 step16 figure 9: evolution of a non-planar crack path using x-fem on a full-size graphite brick with stresses coming from umat analysis. conclusion n this paper, numerical applications of x-fem are presented to demonstrate the crack propagation modelling method in code_aster and to show the capabilities of solving the challenging problem in computational fracture mechanics in ageing agr graphite bricks. the results obtained in the benchmark study shows that the crack paths from x-fem were similar to the experimental ones. the accuracy of the strain energy release rate computation in a heterogeneous material is evaluated using a finite difference approach. the evolution of the planar crack path on an ageing agr graphite brick and the non-planar crack path on virgin graphite brick reveal the robustness and the consistency of the propagation. further work to improve the robustness of 3d non-planar crack propagation in agr graphite bricks is ongoing. this work contributes to the better understanding of crack propagation behaviour in service, and so contributes to the extension of the agr plants’ lifetimes in the uk by reducing uncertainties. acknowledgements his work was done as part of a tsb collaborative project between edf energy r&d uk centre, edf energy generation, edf r&d in france and the university of manchester. the authors gratefully acknowledge edf energy generation for their valuable input data and support. the views expressed in this paper are those of the i t t.-t.-g. vo et alii, frattura ed integrità strutturale, 34 (2015) 237-245; doi: 10.3221/igf-esis.34.25 245 authors, and not necessarily those of edf energy generation. technical support for this work from edf r&d is greatly appreciated. references [1] osher, s., sethian, j.a., fronts propagating with curvature dependent speed: algorithms based on hamilton-jacobi formulations, journal of computational physics, 79 (1988) 12–49. [2] stolarska, m., chopp, d.l., moës, n., belytschko, t., modelling crack growth by level sets in the extended finite element method, int. j. numer. methods eng., 51 (2001) 943–960. [3] geniaut, s., galenne, e., a simple method for crack growth in mixed mode with x-fem, international journal of solids and structures, 49 (2012) 2094–2106. [4] tran, v-x, geniaut, s., development and industrial applications of x-fem axisymmetric model for fracture mechanics, engineering fracture mechanics, 82 (2012) 135–157. [5] erdogan, f., sih, g.c., on the crack extension in plates under plane loading and transverse shear, asme journal of basic engineering, 85 (1963) 519–527. [6] martinuzzi, p., pellet, l., geoffroy, d., modelling crack propagation in irradiated graphite, the 4th edf energy nuclear graphite symposium: engineering challenges associated with the life of graphite reactor cores, (2014). [7] code_aster, analysis of structures and thermomechanics for surveys and research. [8] park, k., paulino, g. h., cohesive zone models: a critical review of traction-separation relationships across fracture surfaces, applied mechanics reviews, (2011) 64(6) 060802. [9] brokenshire, d.r., a study of torsion fracture tests, ph.d. thesis, cardiff university, (1996). f.v. antunes et alii, frattura ed integrità strutturale, 33 (2015) 199-208; doi: 10.3221/igf-esis.33.25 199 focussed on characterization of crack tip fields a numerical study of non-linear crack tip parameters f.v. antunes cemuc, department of mechanical engineering, university of coimbra, 3030-129 coimbra, portugal fernando.ventura@dem.uc.pt r. branco cemuc, depart. of mechanical engineering, polytechnic institute of coimbra rbranco@isec.pt l. correia, al ramalho cemuc, escola superior de tecnologia do inst. politécnico de castelo branco, av. do empresário, 6000 767 castelo branco lcorreia@ipcb.pt, aramalho@ipcb.pt abstract. crack closure concept has been widely used to explain different issues of fatigue crack propagation. however, different authors have questioned the relevance of crack closure and have proposed alternative concepts. the main objective here is to check the effectiveness of crack closure concept by linking the contact of crack flanks with non-linear crack tip parameters. accordingly, 3d-fe numerical models with and without contact were developed for a wide range of loading scenarios and the crack tip parameters usually linked to fatigue crack growth, namely range of cyclic plastic strain, crack tip opening displacement, size of reversed plastic zone and total plastic dissipation per cycle, were investigated. it was demonstrated that: i) lefm concepts are applicable to the problem under study; ii) the crack closure phenomenon has a great influence on crack tip parameters decreasing their values; iii) the keff concept is able to explain the variations of crack tip parameters produced by the contact of crack flanks; iv) the analysis of remote compliance is the best numerical parameter to quantify the crack opening level; v) without contact there is no effect of stress ratio on crack tip parameters. therefore it is proved that the crack closure concept is valid. keywords. fatigue crack propagation; plasticity induced crack closure; non-linear crack tip parameters; keff introduction odern design methodologies consider that inherent defects are always present in components. fatigue life is therefore defined as the number of load cycles required to propagate these defects up to a critical size. engineering analysis of fatigue crack propagation is usually performed by relating the crack advance per unit cycle, da/dn, to the stress intensity factor range, k. initially it was surprising that this linear-elastic parameter could successfully describe the rate of plastic processes at the crack tip. rice 1 showed that the small-scale cyclic plasticity at the crack tip is, indeed, controlled by k. according to paris law, da/dn is uniquely determined by one loading m http://www.gruppofrattura.it/pdf/rivista/numero33/audioslides/antunes/antunes.html f.v. antunes et alii, frattura ed integrità strutturale, 33 (2015) 199-208; doi: 10.3221/igf-esis.33.25 200 parameter, the stress intensity factor range, k. however, the large amount of work developed showed that other parameters influence da/dn, like stress ratio or load history. christensen 2 proposed the concept of fracture surface interaction leading to a decrease of stress intensity at the crack tip and to an increase of fatigue life. elber 3 discussed the concept in terms of fracture mechanics parameters, promoting a strong research effort into the mechanisms and phenomena associated with fatigue crack closure. ritchie et al 4 and suresh 5,6 identified the main closure mechanisms, which are plasticity induced crack closure (picc), oxide-induced crack closure and roughness induced crack closure. according to elber’s understanding of crack closure, as the crack propagates due to cyclic loading, a residual plastic wake is formed. the deformed material acts as a wedge behind the crack tip and the contact of fracture surfaces is forced by the elastically deformed material. crack closure concept seemed to be able to explain the influence of mean stress in both regimes i and ii of crack propagation 7, the transient crack growth behaviour following overloads 8, the growth rate of short cracks 9 and the effect of thickness 10, 11, among other aspects. this success in explaining different issues of fatigue crack propagation has been used to validate the crack closure concept. pippan and grosinger 12 demonstrated that crack closure is not only important under small scale yielding conditions, it is also essential in the regions of low cycle fatigue. the effect of specimen geometry on crack closure has been accounted for using the t-stress concept 13. complementary concepts have been proposed by different authors. dai and li 14 considered that the plastic deformation modifies the elastic stress field and defined a plasticity-corrected k to account for the effect of plasticity. this kpc was proposed as a new mechanical driving force parameter for predicting fcg rate, able to explain important phenomena associated with the plastic zone around a fatigue crack tip, such as the effects of load ratio r, single overload and the fcg behavior under cyclic compression. ranc et al. 15 quantified the effect of heterogeneous temperature on stress intensity factor. the energy dissipated in the cyclic plastic zone ahead of crack tip produces thermal expansion of the material which affects the stress field. the stress intensity factor has to be corrected by a negative value which reduces the crack driving force. pokluda 16 states that the effective stress field at the crack tip is a superposition of remote and local sifs. the internal stresses created by dislocation configurations and secondary phases are to be considered as an important additional factor affecting the crack propagation rate in fatigue. christopher et al. 17, 18 proposed a novel mathematical model of the stresses around the tip of a fatigue crack, which considers the effects of wake contact and compatibility-induced stresses at the elastic–plastic boundary. four parameters were considered to characterize the stress field: an opening mode stress intensity factor kf, the shear stress intensity factor ks, the retardation stress intensity factor kr, and the t-stress. kr characterizes the effect of crack tip shielding arising due to plasticity both at the crack tip and in the wake. however, several questions have been raised questioning the crack closure concept, therefore the importance and even the existence of crack closure effect have been questioned by different authors. donald and paris 19 and kujawski 20 introduced the concept of partial crack closure, which indicates that the contact of crack flanks at some distance from crack tip has a relatively low effect on fcgr. some researchers suggested that closure can only occur under plane stress 21, while others believe that it may not occur at all. since 1993 sadananda and vasudevan 22-24 have advocated that because the closure occurs behind the crack tip, it has a rather limited effect on the damage process, which takes place at the ‘process zone’ in front of the crack. according to these researchers the approaches to fatigue behavior based on crack closure (i.e. on what happens behind the crack tip) should be replaced by approaches based on what happens ahead of the crack tip. they argued that closure effects on fcg behavior have been greatly exaggerated, and suggested that the fatigue crack propagation rate is controlled by a two parameter driving force, which is a function of the maximum stress intensity factor, kmax, and total stress intensity factor range, k. these two parameters account for both the applied load and the residual stress contributions. kujawski 25 proposed a new driving force parameter for crack growth: keffk=(kmaxk+)0.5, being k+ the positive part of k. he found that without using the crack closure concept, it is possible to explain the stress ratio effect, even better than using this concept. however, noroozi et al. 26, 27 pointed out that these models are strictly empirical and cannot explain the influence of the compressive part of the load history on fatigue crack growth. they formulated a unified two-parameter model to correlate kmax and k with the actual elasticplastic crack tip stress–strain field. in their investigation, the difference in the stress–strain concentration at the crack tip associated with the compressive part of the loading cycle was taken into account. clearly there is no general agreement among researchers regarding the significance of closure concept on fatigue crack behavior. the contact of crack flanks is accepted by all, because it was observed numerically and using experimental techniques, namely, digital image correlation 28, x-ray diffraction 28,29, potential drop 30,31 and sem 31. the great disagreement is about the effect of this contact on fatigue crack growth. in fact, the direct link between crack closure and crack tip fields has not been totally exploited. this might be due to experimental difficulties in measuring quantitative f.v. antunes et alii, frattura ed integrità strutturale, 33 (2015) 199-208; doi: 10.3221/igf-esis.33.25 201 strain/stress fields near a fatigue crack tip 30. anyway, different studies may be found in literature 32-34. the link between crack closure and non-linear crack tip parameters is however rare. further work is therefore necessary to quantify the effect of the contact of crack flanks on the process zone where the propagation effectively happens. the main objective of this paper is therefore to check the effectiveness of crack closure concept by linking the contact of crack flanks to the non-linear crack tip parameters. a m(t) specimen made of 6016-t4 aluminium alloy was modeled and submitted to different load scenarios using the finite element method. the numerical tests were done with and without contact of crack flanks. the numerical approaches are very interesting for the elimination of contact in order to study its effect, however no studies were reported in literature by the authors. non-linear crack tip parameters (nlp) ig. 1 shows the four different zones that can be identified ahead of a fatigue crack tip 35. in the elastic zone (regions i and ii), which is far ahead of crack tip, the material is deformed in purely elastic manner. the stress intensity factor controls the magnitude of stress and strain fields in region ii. region iii is known as monotonic plastic zone. plastic deformation occurs during monotonic loading and after that elastic loading-unloading is taking place. in region iv, close to fatigue crack-tip, known as reverse/cyclic plastic zone, hysteresis loop occurs. the small scale yielding hypothesis justifies the use of k as the crack driving force. however, it provides no information about the physical phenomena happening during crack propagation, namely in the reversed plastic zone. it is widely accepted by the scientific community that crack advance in metals is mainly determined by the damage of a highly localized volume immediately ahead of the crack tip, called the process zone. a literature review was made to identify the crack tip parameters that may be expected to control crack tip progression due to cyclic loading. figure 1: schematic diagram of crack tip zones, parameters and stress-strain response. pokluda 16 stated that the crack driving force in fatigue is directly related to the range of cyclic plastic strain. the crack tip opening displacement (ctod or cod) is another main crack tip parameter. note that the cod is equal to cod since the crack re-sharpens during unloading 36. pelloux 37, using microfractography, showed that the concept of cod allowed the prediction of fatigue striations spacing and therefore the crack growth rate. nicholls 38 assumed a polynomial relation between crack growth rate and ctod: 1/( ) p da b ctod dn  (1) where b and p are constants. tvergaard 39 and pippan and grosinger 12 indicated a linear relation between da/dn and ctod for very ductile materials: da c ctod dn   (2) f residual plastic wake iv iii ctod p energy crack closure (keff) k kmax ii i regions i,ii region iii region iv f.v. antunes et alii, frattura ed integrità strutturale, 33 (2015) 199-208; doi: 10.3221/igf-esis.33.25 202 being c a constant. in numerical studies the ctod is usually defined as the distance between two points found by intersecting the finite element model with two (+45º and -45º) lines originated from the crack tip. the size of reversed plastic zone has also been considered a main parameter of crack growth 40, 41. ould chick et al. 42 showed that da/dn has a linear variation with the square of the cyclic plastic zone size (rpc2): 2( )pc da a r dn  (3) where a depends on the yield stress. other authors suggested that the total plastic dissipation per cycle occurring in the reversed plastic zone is a driving force for fatigue crack growth in ductile solids, and can be closely correlated with fatigue crack growth rates 43, 44. dissipated energy approaches to fatigue crack growth prediction have since been the subject of numerous analytical 45, 46 and experimental 47, 48 investigations. numerical model middle-tension specimen was considered to predict the crack opening level, having w=60 mm and a straight crack with an initial size a0 of 5 mm (a0/w=0.083). a small thickness was considered (t=0.1 mm) to simulate the plane stress state. two materials were considered in this research: the 6016-t4 aluminium alloy and a high strength steel (dp600). since picc is a plastic deformation based phenomenon, the hardening behaviour of the material was carefully modelled. the hardening behaviour of this alloy was represented using an isotropic hardening model described by a voce type equation, combined with a non-linear kinematic hardening model described by a saturation law. table 1 indicates the load parameters defined in the different sets of constant amplitude tests considered for 6016-t4 aluminium alloy and dp600 steel, respectively. sets with constant kmin, kmax, k and r were studied, as can be seen. set 1 (kmin=0) set 2 (kmax=6.4) set 3 (kmax=2.2) set 4 (kmax=4.6) k r k r k r k r 2.9 0 3.8 0.43 2.2 0 2.3 0.5 3.8 0 5.7 0.14 4.4 -1 4.6 0.0 4.8 0 7.7 -0.14 6.6 -2 6.8 -0.5 6.7 0 9.6 -0.43 8.9 -3 9.1 -1 8.6 0 11.5 -0.71 11.0 -4 12.5 -1.75 9.6 0 13.4 -1.00 13.6 -5 13.3 -2 10.5 0 15.3 -1.29 15.9 -6 14.8 -2.25 set 5 (r=0.2) set 6 (k=4.8) set 7 (k=6.7) set 8 (kmax=9.1) k r k r k r k r 3.1 0.2 4.8 -2 6.7 -2 1.4 0.88 3.8 0.2 4.8 -1 6.7 -1 2.5 0.75 4.6 0.2 4.8 -0.5 6.7 -0.5 4.6 0.5 5.4 0.2 4.8 0 6.7 0 6.9 0.25 6.1 0.2 4.8 0.25 6.7 0.25 9.1 0 6.9 0.2 4.8 0.5 6.7 0.5 11.3 -0.25 table 1: loading parameters for 6016-t4 aluminium alloy (k, kmax, kmin=mpa.m1/2) a f.v. antunes et alii, frattura ed integrità strutturale, 33 (2015) 199-208; doi: 10.3221/igf-esis.33.25 203 the finite element mesh considered was refined near the crack tip and enlarged at relatively remote positions. square elements with 88 μm2 were defined in the refined region, while only one layer of elements was considered along the thickness. crack propagation was simulated by successive debonding of nodes at the minimum load. each crack increment corresponded to one finite element and two load cycles were applied between increments. in each cycle, the crack propagates uniformly over the thickness by releasing both current crack front nodes. the opening load, fop, necessary for the determination of the closure level was obtained considering the contact status of the first node behind the current crack tip. the numerical simulations were performed with the three-dimensional elastic-plastic finite element program (dd3imp), originally developed to simulate deep drawing. further details of this numerical procedure may be found in literature 49. the analysis of the effect of contact flanks was developed comparing the crack tip parameters obtained with and without contact. for each load condition, the crack was submitted to 160 crack increments and 320 load cycles, which corresponds to a global crack increment a=1608μm=1.280 mm. this is enough to stabilize the crack opening values. after that, 30 load cycles were applied without crack propagation. this procedure was done with and without the symmetry plane used to simulate the contact of crack flanks. three non-linear crack tip parameters were measured at the end of this procedure: the crack tip opening displacement (cod), the range of plastic strain (p,yy), and the energy dissipated per cycle. these last two quantities were measured at the gauss point immediately ahead of the last crack tip position, and in the last load cycle applied. the energy is the area of the last stress-strain loop. note that da/dn is usually correlated with the total energy dissipated ahead of crack tip. anyway the energy at the point immediately ahead of the crack tip is related with the total energy. the size of cyclic plastic zone was determined from the analysis of equivalent plastic strain ahead of crack tip. the increase of plastic deformation with the decrease of load, down to its minimum value, indicates the occurrence of reversed plasticity. the cod was assumed to be the vertical displacement of the node behind crack tip at maximum load. the same approach was used by ellyin and wu 50 to quantify the cod. numerical results validity of lefm he linear elastic fracture mechanics (lefm) assume that the crack tip process zone is controlled by the elastic field around it, i.e., that the k concept is valid. small-scale plasticity must however exist, otherwise k will not be the controlling parameter. the validity of lefm was checked here, verifying the relation between k and the nonlinear crack tip parameters. fig. 2a plots the plastic strain perpendicular to crack flank, p,yy, and the crack opening displacement, cod, versus k. these predictions were obtained without contact of crack flanks. the results for different load cases give well defined curves, which clearly point to the validity of the lefm. both the plastic strain range and cod increase linearly with the square of k, i.e., pl, cod  k2. note that the numerical cod was obtained at maximum load, therefore it includes elastic and plastic components. the magnitude of the values found here is according to pippan and grosinger 12 who said that in the mid and upper paris regime the cyclic crack tip opening displacements are in the order of micrometers. validity of crack closure concept fig. 3 plots the plastic strain range ahead of crack tip versus the stress intensity factor range. without contact, there is a well defined trend between energy and k. however, there is a great scatter when the energy obtained with contact is plotted versus k. the controversy about the effect of contact has therefore a clear answer: the contact has a significant effect on non-linear crack tip parameters and therefore on fatigue crack growth rate. nevertheless, when the p with contact is plotted versus effective k (keff), a well defined trend is obtained once again. moreover, there is a coincidence of the curves energy without contact versus k and energy with contact versus keff. the other two crack tip parameters showed similar results. this coincidence of results clearly shows that the concept of keff is able to explain the variations of crack tip parameters produced by the contact of crack flanks. the results of crack tip parameters versus k may be seen as master curves, free of the influence of crack closure. additionally, the results show that without contact of crack flanks there is no effect of stress ratio. klingbeil 44 also observed that without crack closure, the stress ratio has a negligible effect on total energy dissipation per cycle. sunder et al. 51 observed no effect of stress ratio on crack growth rate of long cracks in 2014-t6511 aluminium alloy (r=0.64; 0.69 and 0.73). t f.v. antunes et alii, frattura ed integrità strutturale, 33 (2015) 199-208; doi: 10.3221/igf-esis.33.25 204 0 0.0005 0.001 0.0015 0.002 0 0.01 0.02 0.03 0.04 0.05 0 5 10 15 20   p k [mpa.m0.5] c o d [m m ] cod c o d [m m ] p 0 0.01 0.02 0.03 0.04 0 5 10 15 20   p ,y y k, keff [mpa.m0.5] no contact; versus contact; versus contact; versus k k keff figure 2: effect of k on range of plastic strain and crack opening displacement (no contact). figure 3: effect of effective stress intensity factor range, keff, on plastic strain range. effect of mesh size the finite element mesh is a major parameter of numerical crack closure models. therefore, the influence of mesh refinement on non-linear crack tip parameters was studied here. fig. 4 shows the effect of using square elements with 16 m2 at the crack tip (mesh m16), instead of 8 μm2 elements (mesh m8), on the plastic strain range. there is a significant decrease of p, which is explained by the position of the gauss point relatively to the crack tip. in fact, the decrease of mesh size approaches the gauss point to the crack tip, as is illustrated in fig. 4. anyway, a well defined trend still was observed for mesh m16, which confirms once again the validity of lefm. the plastic strain range also showed a significant decrease with the increase of mesh size. on the other hand, the cod increased with mesh size. this is explained by the position of the node behind crack tip where the cod was measured. the increase of mesh size departs the node from the crack tip, which increases the cod. 0 0.0005 0.001 0.0015 0.002 0.0025 0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0 20 40 60 80 100   p energy [n.mm/mm3] strain e; no contact strain e; contact cod e; no contact cod e; contact c o d [m m ] figure 4: effect of mesh on plastic strain range. figure 5: crack opening displacement versus energy and plastic strain range versus energy. relations between non-linear crack tip parameters robust relations between the non-linear crack tip parameters were found, with a relatively low influence of mesh refinement. fig. 5 shows the relations between the specific energy dissipated immediately ahead of crack tip (e) and the crack opening displacement, and between the energy and the plastic strain range. as can be seen, the contact of crack flanks does not affect the relation between the crack tip parameters, which indicates that these are quite robust f.v. antunes et alii, frattura ed integrità strutturale, 33 (2015) 199-208; doi: 10.3221/igf-esis.33.25 205 effect of overloads after an overload the crack growth rate has usually a sudden increase followed by a progressive decrease down to a minimum value, and a progressive increase to the pre-overload fcgr. several mechanisms have been proposed to explain crack growth retardation, namely residual stresses 52, crack closure 3, crack tip blunting, strain hardening 53, crack branching 54 and reversed yielding 55. the non-linear crack tip parameters were considered here to analyze the effectiveness of crack closure concept to explain the variations of fatigue crack growth after an overload. several overloads were considered, which are indicated in tab. 2. fig. 6 plots the results obtained for the maximum energy ahead of crack tip. the master curve was obtained without contact of crack flanks. when the energy is plotted versus k there is a great scatter. however, the consideration of keff moves the points towards the master curves. this indicates that the crack closure concept is able to explain the variations of non-linear crack tip parameters after an overload, and therefore the variations of da/dn. there is a slight difference between some of the energy-keff points and the master curve, which may be explained by partial closure. further work is required to clarify this issue. min,bl max,bl max,ol 20 46.7 60 -6.7 46.7 60 -33.3 46.7 60 -46.7 46.7 60 table 2: overload parameters (min,bl, max,bl, max,ol,=mpa) 0 5 10 15 20 25 30 35 40 45 50 0 2 4 6 8 10 12 14 e n er gy k [mpa.m0.5] energy versus k energy versus k   eff master curve (no contact) figure 6: effect of effective stress intensity factor range, keff, on dissipated energy after overloads. conclusions numerical study was developed to understand the effect of crack flank contact on crack tip parameters and therefore on da/dn. one of the main outcomes of this work is that the crack closure concept is valid, at least for plane stress state. additional conclusions resulting from this investigation are: a f.v. antunes et alii, frattura ed integrità strutturale, 33 (2015) 199-208; doi: 10.3221/igf-esis.33.25 206 the stress intensity factor was found to control the non-linear crack tip parameters (cod, p, rpc, energy). therefore the lefm concepts are applicable to the problem being studied. the contact of crack flanks, i.e. the crack closure, has a great influence on crack tip parameters that are supposed to control fatigue crack growth rate. the contact decreases the values of the different crack tip parameters. the keff concept is able to explain the variations of crack tip parameters produced by the contact of crack flanks. the crack tip parameters versus k obtained without contact may be seen as master curves. additionally, without contact of crack flanks there is no effect of stress ratio, and k is the controlling parameter. the change of mesh size modifies the relations between non-linear crack tip parameters and k, however the validity of lefm and of keff concept still are verified. the relations between non-linear crack tip parameters were found to be independent of mesh size. the crack closure concept is able to explain the variations of non-linear parameters (and therefore of da/dn) after an overload. the crack tip parameters proved to be a fundamental tool to understand the crack closure phenomenon. in fact, they supply a link between crack closure and fatigue crack growth rate. a close look to non-linear crack tip parameters, like plastic strain range or dissipated energy, is the key for a deeper understanding of fcg and the establishment of physically based relations with loading parameters. acknowledgments he authors are indebted to the portuguese foundation for the science and technology (fct) and compete program from feder (european regional development fund) for the financial support under the projects ptdc/ems-pro/3148/2012 and pest-c/eme/ui0285/2013. references [1] rice, j.r., mechanics of crack tip deformation and extension by fatigue, astm stp 415 (1967) 256–71. [2] christensen, r.h., fatigue crack growth affected by metal fragments wedged between opening-closing crack surfaces, appl. mater. res. 2(4) (1963) 207-210. [3] elber, w., fatigue crack closure under cyclic tension, eng. fracture mechanics, 2 (1970) 37-45. [4] ritchie, r.o., suresh, s., moss, c.m., near-threshold fatigue crack growth in 2(1/4)cr-1 mo pressure vessel steel in air and hydrogen, journal of engng materials and technology, 102 (1980) 293-299. [5] suresh, s., ritchie, r.o., on the influence of fatigue underloads on cyclic crack growth at low stress intensities”, materials science and engng, 51 (1981) 61-69. [6] suresh, s., ritchie, r.o., a geometric model for fatigue crack closure induced by fracture surface roughness, metallurgical transactions, 13a (1982) 1627-1631. [7] blom, a.f., holm, d.k., an experimental and numerical study of crack closure, eng fract mech, 22 (1984) 997-1011. [8] borrego, l.p., ferreira, j.m., costa, j.m., fatigue crack growth and crack closure in an almgsi alloy, fatigue fract eng mater struct, 24 (2001) 255-265. [9] rao, k.t.v., yu, w., ritchie, r.o., on the behaviour of small fatigue cracks in commercial aluminium lithium alloys, eng fract mech, 31(4) (1988) 623-635. [10] bao, h., mcevily, a.j., on plane stress-plane strain interactions in fatigue crack growth, int. j fatigue, 20(6) (1998) 441-448. [11] costa, j.d.m., ferreira, j.a.m., effect of stress ratio and specimen thickness on fatigue crack growth of ck45 steel, theoretical and applied fracture mechanics, 30 (1998) 65-73. [12] pippan, r., grosinger, w., fatigue crack closure: from lcf to small scale yielding, int journal of fatigue, 46 (2013) 41–48. [13] tong, j., t-stress and its implications for crack growth, engng fracture mechanics 69 (2002) 1325–1337. [14] dai, p., li, z., a plasticity-corrected stress intensity factor for fatigue crack growth in ductile materials, acta mater, 61 (2013) 5988–95. [15] ranc, n., palin-luc, t., paris, p.c., saintier, n., about the effect of plastic dissipation in heat at the crack tip on the stress intensity factor under cyclic loading, int journal of fatigue 58 (2014) 56–65. t f.v. antunes et alii, frattura ed integrità strutturale, 33 (2015) 199-208; doi: 10.3221/igf-esis.33.25 207 [16] pokluda, j., dislocation-based model of plasticity and roughness-induced crack closure, int journal of fatigue, 46 (2013) 35-40. [17] christopher, c.j., james, m.n., patterson, e.a., tee, k.f., towards a new model of crack tip stress fields, int j fract 148 (2007) 361–371. [18] christopher, c.j., james, m.n., patterson, e.a., tee, k.f., a quantitative evaluation of fatigue crack shielding forces using photoelasticity, eng fract mech, 75 (2008) 4190–4199. [19] donald, k., paris, p.c., an evaluation of keff estimation procedure on 6061-t6 and 2024-t3 aluminum alloys, int j fatigue, 21 (1999) s47–57. [20] kujawski, d., enhanced model of partial crack closure for correlation of r-ratio effects in aluminum alloys, int j fatigue, 23 (2001) 95–102. [21] alizadeh, h., hills, d. a., matos p.f.p., nowell, d., pavier, m.j., paynter, r.j., smith, d.j., simandjuntak, s., a comparison of two and three-dimensional analyses of fatigue crack closure, int. j. fatigue, 29 (2007) 222–231. [22] louat, n., sadananda, k., duesbery, m., vasudevan, a.k., a theoretical evaluation of crack closure, metallurgical transactions, 24a (1993) 2225-2232. [23] vasudevan, a.k., sadananda, k., louat, n., a review of crack closure, fatigue crack threshold and related phenomena, mater sci eng a, a188 (1994) 1–22. [24] sadananda, k., vasudevan, a.k., multiple mechanisms controlling fatigue crack growth, fatigue fract eng mater struct, 26 (2003) 835–45. [25] kujawski, d., a new (k+kmax)0.5 driving force parameter for crack growth in aluminum alloys, int j fatigue, 23 (2001) 733–740. [26] noroozi, a.h., glinka, g., lambert, s., a two parameter driving force for fatigue crack growth analysis, int j fatigue, 27 (2005) 1277–1296. [27] noroozi, a.h., glinka, g., lambert, s., a study of the stress ratio effects on fatigue crack growth using the unified two-parameter fatigue crack growth driving force, int journal of fatigue, 29 (2007) 1616–1633. [28] lopez-crespo, p., withers, p.j., yusof, f., dai h., steuwer, a., kelleher, j.f., buslaps, t., overload effects on fatigue crack-tip fields under plane stress conditions: surface and bulk analysis, fatigue fract engng mater struct, 36 (2012) 75–84. [29] steuwer, a., santisteban, j., turski, m., withers, p.j., buslaps, t., high-resolution strain mapping in bulk samples using full-profile analysis of energy dispersive synchrotron x-ray diffraction data, nucl. instr. meth. phys. res. b, 238 (2005) 200–204. [30] lee, s.y., liaw, p.k., choo, h., rogge, r.b., a study on fatigue crack growth behavior subjected to a single tensile overload part i. an overload-induced transient crack growth micromechanism, acta materialia 59 (2011) 485–494. [31] andersson, m., persson, c., melin, s., experimental and numerical investigation of crack closure measurements with electrical potential drop technique, int j fatigue, 28 (2006) 1059–68. [32] james, m.n., pacey, m.n., wei, l.-w. patterson, e.a., characterisation of plasticity-induced closure—crack flank contact force versus plastic enclave, engng fracture mechanics 70 (2003) 2473–2487. [33] vasco-olmo, j.m., díaz, f.a., garcía-collado, a., dorado-vicente, r., experimental evaluation of crack shielding during fatigue crack growth using digital image correlation, fatigue fract engng mater struct, 38 (2015), 223–237. [34] roychowdhury, s., dodds jr., r.h., a numerical investigation of 3-d small-scale yielding fatigue crack growth, engng fracture mech, 70 (2003) 2363-2383. [35] paul, s.k., tarafder, s., cyclic plastic deformation response at fatigue crack tips, int journal of pressure vessels and piping, 101 (2013) 81-90. [36] pippan, r., zelger, c., gach, e., bichler c., weinhandl h., on the mechanism of fatigue crack propagation in ductile metallic materials, fatigue fract engng mater struct, 34 (2010) 1–16. [37] pelloux, r.m., crack extension by alternating shear, engng fracture mechanics 1 (1970) 170-174. [38] nicholls, d.j., the relation between crack blunting and fatigue crack growth rates, fatigue fract eng mater struct, 17(4) (1994) 459-467. [39] tvergaard, v., on fatigue crack growth in ductile materials by crack–tip blunting, journal of the mechanics and physics of solids, 52 (2004) 2149–2166. [40] heung, b.p., kyung, m.k., byong, w.l., plastic zone size in fatigue cracking, int. j. pres. ves. piping, 68 (1996) 279– 285. [41] zhang, j., he, x.d., du, s.y., analyses of the fatigue crack propagation process and stress ratio effects using the two parameter method, int journal of fatigue, 27 (2005) 1314–1318. f.v. antunes et alii, frattura ed integrità strutturale, 33 (2015) 199-208; doi: 10.3221/igf-esis.33.25 208 [42] ould chikh, b., imad, a., benguediab, m., influence of the cyclic plastic zone size on the propagation of the fatigue crack in case of 12nc6 steel, computational materials science, 43 (2008) 1010–1017. [43] rice, j.r., mechanics of crack tip deformation and extension by fatigue. astm stp 415 (1967) 247–311. [44] klingbeil, n.w., a total dissipated energy theory of fatigue crack growth in ductile solids, int journal of fatigue, 25 (2003) 117–28. [45] bodner, s.r., davidson, d.l., lankford, j., a description of fatigue crack growth in terms of plastic work. engng fracture mechanics, 17 (1983) 189–191. [46] wang, w., hsu, c-t.t., fatigue crack growth rate of metal by plastic energy damage accumulation theory, journal of engng mechanics, 120 (1994) 776–795. [47] liaw, p.k., kwun, s.i., fine, m.e., plastic work of fatigue propagation in steels and aluminum alloys, metallurgical transactions a, 12a (1981) 49–55. [48] ranganathan, n., jendoubi, n., benguediab, m., petit. j., effect of r-ratio and �k level on the hysteretic energy dissipated during fatigue crack propagation, scripta metallurgica, 21 (1987) 1045–1049. [49] antunes, f.v., correia, l., ramalho, a.l. a parameter for quantitative analysis of plasticity induced crack closure, int. j. fatigue, 71 (2015) 87–97 [50] ellyin, f., wu, j., a numerical investigation of the effect of an overload on fatigue crack opening and closure behaviour, fatigue and fracture of engng materials and structures, 22 (1999) 835-847. [51] sunder, r., porter j., ashbaugh, n.e., the effect of stress ratio on fatigue crack growth rate in the absence of closure, int journal of fatigue 19 (1997) s211-s221. [52] shijve, j., broek, d., the result of a test program based on a gust spectrum with variable amplitude loading, aircraft engng, 34 (1962) 314–316. [53] jones, r.e., fatigue crack growth retardation after single-cycle peak overload in ti–6al–4v titanium alloy, engng fract mech, 5 (1973) 585–604. [54] suresh, s., micromechanisms of fatigue crack growth retardation following overloads, engng fract mech, 18 (1983) 577–593. [55] nicoletto, w., fatigue crack-tip mechanics in 7075-t6 aluminium alloy from high-sensitivity displacement field measurements, astm stp 995 (1989) 415–432. microsoft word numero_49_art_73_2357 h.m. cao, frattura ed integrità strutturale, 49 (2019) 831-839; doi: 10.3221/igf-esis.49.73 831 analysis of mechanical properties of transition segment of road and bridge based on high-strength foam concrete hongmei cao sichuan college of architectural technology, deyang, sichuan 618000, china hongmc_hm@aliyun.com abstract. the settlement difference in the transition section of road and bridge may lead to traffic accidents, which has many negative effects. back filling of foam concrete behind abutment is a good method of treatment. in this study, a kind of high-strength foam concrete was designed for back filling of transition section of road and bridge, and the mechanical properties of the transition section of road and bridge were analyzed using finite element analysis method. it was found that only a large number of micro cracks grew in high-strength concrete under a large number of load cycles, and structural damage did not happen, indicating the high-strength foam concrete had high strength and long service life; the static base pressure was about 40 kpa, indicating a small burden on the structure. under the vehicle load, the vertical displacement of the transition section of road and bridge with back filling of high-strength foam concrete behind abutment was about 0.7 m and the maximum vertical stress was about -40 kpa, which was significantly lower than that of the ordinary concrete, and the stability was favourable and the settlement was small, indicating that the high-strength foam concrete had good vibration absorption effect. the analysis results verifies the value of the high-strength foam concrete as the backfill material of the transition section of road and bridge and proves that it can effectively solve the problem of differential settlement of the transition segment of road and bridge, providing some theoretical bases for its application and popularization. keywords. foam concrete; transition section of road and bridge; settlement difference; back filling behind abutment; mechanical properties. citation: cao, h.m., analysis of mechanical properties of transition segment of road and bridge based on high-strength foam concrete, frattura ed integrità strutturale, 49 (2019) 831-839. received: 21.01.2019 accepted: 29.04.2019 published: 01.07.2019 copyright: © 2019 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. introduction ifferential settlement of transition segment of road and bridge is a common problem. soft soil foundation in coastal areas is prone to deformation, which will result in the compression of filling behind abutment and settlement difference problem. the rigidity difference between abutment and roadbed will also cause settlement difference [1]. abutment which has large rigidity has small settlement, but roadbed which has loose filling is easy to d http://www.gruppofrattura.it/va/49/2357.mp4 h.m. cao, frattura ed integrità strutturale, 49 (2019) 831-839; doi: 10.3221/igf-esis.49.73 832 deform and cause settlement. the settlement difference in the transition segment of road and bridge will make vehicles bump when passing; the faster the vehicle speed, the stronger the vibration [2], which will not only make the driver and passenger feel uncomfortable, but also damage car components and increase fuel consumption, even causing traffic accidents. vehicle bumping will also bring great impact to the transition section of road and bridge, especially at the expansion joint of bridge deck, which will damage bridge deck and roadbed [3], affect the stress distribution of pavement [4], increase the human and financial resources in pavement maintenance, and seriously affect the service life of pavement [5], i.e., have negative effects in aspects of economics and safety. how to effectively solve the problem of settlement difference and ensure driving stability is of great significance [4] and has become a major problem in engineering construction [7]. at present, there are many methods to solve the settlement difference problem in china and abroad, such as using bridge end transition slab [8], i.e., connecting bridge abutment with roadbed through reinforced concrete slab [9], improving the degree of density of roadbed and reducing deformation by using civil engineering material with reinforced bars and loading preload, increasing rigidity of foundation by piling, and filling foundation with lightweight materials. greco et al. [10] regarded vehicle and bridge as an integrated system based on moving mesh strategy and analyzed the moving load of vehicle and bridge interaction using finite element model. lonetti et al. [11] analyzed the dynamic properties of tied-arch bridge under the action of moving load and evaluated the interaction between deformation of bridge and moving load, including the impact of the external quality of mobile system on dynamic bridge. sun et al. [12] suggested application of deep reinforced concrete plate to solve the differential settlement of transition segment of road and bridge and found that the method had great advantage in controlling settlement and could effectively reduce bump at bridge-head through finite element analysis. liu et al. [13] made a finite element analysis of the pavement settlement and stress change of the transition section of road and bridge under dynamic and static loads and found that the maximum stress decreased significantly, with an average decrease value of 34.82%, when rubber concrete was used as the material of transition section of road and bridge. wu et al. [14] designed a lightweight backfilling method which cost less and avoided road closure. field measurements showed that the method had a very significant effect in reducing settlement, the total land settlement decreased by 36% and the average settlement rate decreased by 40%. luo et al. [15] applied the properties of expanded polystyrene (eps) material to fill embankment and found that the use of eps material could greatly reduce the foundation pressure and settlement of pavement and increase the strength and had a good stability. lightweight materials have been widely applied in the differential settlement treatment of transition section of road and bridge. foam concrete is a very good lightweight material. it is a kind of concrete and has been applied in building and garden construction. foam concrete with low thermal conductivity, good heat insulation effect, moderate sound absorption capacity and low elastic modulus plays an important role in solving the settlement difference problem of transition section of bridge and road. in this study, foam concrete was applied to deal with the settlement difference problem. in order to improve the material properties, a high-strength foam concrete was designed, and the good strength and stability of the material were proved by the analysis of mechanical properties. it should be further popularized in settlement difference treatment. method of back filling behind abutment with foam concrete n interchange in sichuan province, china, has poor bearing capacity because of powder sand layer in foundation. there was problem of differential settlement in the transition of road and bridge. back filling behind abutment with foam concrete was planned (figure 1). the technical standards were wet density of 0 ~ 80 cm road base ≦ 600 kg/m3, and strength after 28 days ≧ 0.6 mpa; wet density of 80 cm above road base ≦ 650 kg/m3, strength after 28 days ≧ 0.8 mpa, and fluidity was 180 mm. manufacturing of high-strength foam concrete raw materials used in the experiment included p.o52.5 ordinary portland cement (pangu group, china), gs-1 foaming agent (guansheng civil engineering technology co., ltd., china), silicon ash (shunde ruitong chemical engineering co., ltd., china), grade i fly ash (xiangtan power plant, china), s95 slag (shaogang jiayang novel material co., ltd., china) and polycarboxylene based superplasticizer. the preparation method of foam concrete was as follows. firstly the diluted foaming agent was stored in a liquid storage pot, and the pressure was added to 0.5 mpa using an air compressor. foam was obtained by mixing air with foaming a h.m. cao, frattura ed integrità strutturale, 49 (2019) 831-839; doi: 10.3221/igf-esis.49.73 833 agent (figure 2). cement, silica fume, slag and fly ash were weighed and taken and stirred by a stirrer for two minutes. water reducer dissolved in water was poured to the mixing pot and stirred for three to five minutes. after foam was added, it was mixed evenly immediately. the test specimen was obtained after casting. it was maintained in water at 80 ℃ for 48 h and maintained in a standard maintenance room for 28 days after cooling. figure 1: the cross section of foam concrete at the transition section of road and bridge. figure 2: air compressor and foaming device. to obtain high-strength foam concrete, the proportion of different materials was adjusted to compare the properties of test specimens. finally the optimal mix proportion of materials was obtained, as shown in tab. 1. cement 1 silicon ash 0.3 slag 0.1 fly ash 0.4 water reducer 1.5% water-binder ratio 0.18 table 1: the mix proportion of materials. mineral admixtures in appropriate proportion formed grain composition in the paste, improving the density of the paste and adjusting the hole wall structure of concrete. the small water-cement ratio (0.6-0.65 usually) under the action of water reducer not only ensured the fluidity of the paste, but also improved the strength of concrete. the test results showed that the density of the specimens was 1319 kg/m3 and the strength of the specimens was 25.8 mpa after 28 days, which fully meet the requirements of back filling behind abutment. back filling behind abutment with foam concrete foam concrete was transported using pump pipe. the pouring gate of the pouring pipe was put outside the casting area and moved to the casting area after the output foam concrete was confirmed normal. the casting started from one end. multiple pouring pipes worked at the same time. after reaching the predetermined height, the pump pipe was artificially lifted and slowly dragged after the surface was swept. the above actions were repeated until the casting finished. h.m. cao, frattura ed integrità strutturale, 49 (2019) 831-839; doi: 10.3221/igf-esis.49.73 834 the following matters needed to be paid attention to in the construction process. the casting area was cleaned before construction, and whether there was water on the foundation was checked. the casting area was covered in rainy days, and defoaming surface was shoveled. casting stopped when rain was heavy. in winter, construction was allowed when the temperature was above 0 ℃; high temperature in the noon was avoided in summer. long-time staying was avoided during casting. the pipe was washed if the staying time exceeded 10 min, and time of pipe washing was no less than 30 min. thin film was timely covered after casting for moisture preservation, and walking on the concrete was not allowed within seven days. analysis of mechanical properties of transition section of road and bridge analysis of high-strength foam concrete oad cycle test was performed on concrete test specimens in a size of 100 mm × 10 0mm × 100 mm using an electro-hydraulic servo static/dynamic universal testing machine; the loading frequency was 6 hz, the amplitude value was 3 kn, and the mean value was -4 kn. the times of load cycle increased from 0 to 1,200,000 times, with an increase of 200,000 each time. the changes of mechanical properties of the test specimen is shown in figure 3 and 4. figure 3: curve of changes of number of micro cracks. figure 4: the sketch map of micro cracks (a: load cycles for 200,000 times; b: load cycles for 600,000 times; c: 1,000,000 times). times of load cycles/ten thousand times 0 20 40 60 80 100 120 residual strength/mpa 1.12 1.03 0.9 7 0.8 9 0.74 0.6 2 0.51 table 2: changes of residual strength. l h.m. cao, frattura ed integrità strutturale, 49 (2019) 831-839; doi: 10.3221/igf-esis.49.73 835 figure 2 shows the number of micro cracks on the high-strength foam concrete specimens under the action of load cycle. the black spots in figure 3 represented the micro cracks produced in the specimens. it was found that the number of micro cracks increased with the increase of load cycles, and the increase speed became higher and higher. after 1.2 million times (about 60 years of service), there were more than 100,000 micro cracks in the specimens, and the residual strength decreased from 1.12 mpa to 0.51 mpa, but no structural damage occurred. it could meet the basic requirements of use. analysis of mechanical properties of transition section of road and bridge establishment of finite element model the model of transition section of road and bridge after processing of back filling behind abutment with high-strength concrete was established using finite element analysis method. load such as house was ignored as the focus of the study is the changes of mechanical properties of the transition segment of road and bridge. pavement, foam concrete and foundation adopted linear elastic model, and the others adopted mohr-coulomb plastic model. the structure of the model is shown in figure 5. figure 5: the sketch map of back filling behind abutment. the parameters of the model are shown in table 3. material mass per unit volume (kn/m3) bulk modulus (mpa) shear modulus (mpa) cohesive force (kpa) internal friction angle (°) highstrength foam concrete 6 290 226 366 5.1 ordinary concrete 2 12500 12500 3180 54.9 table 3: parameters related to the model. the load of vehicle was simplified as impact surface source load, and the specific parameters of vehicle load are shown in table 4. h.m. cao, frattura ed integrità strutturale, 49 (2019) 831-839; doi: 10.3221/igf-esis.49.73 836 wheel base/m 3.5+1.5 gravity of front axle/kn 2×30 gravity of middle axle/kn 2×120 wheel base/m 1.8 length and width when front wheels touch the ground 0.2×0.3 length and width when rear wheels touch the ground 0.2×0.6 table 4: parameters of vehicle load. analysis of static base pressure figure 6 shows the change of base pressure of transition section of road and bridge under the deadweight pressure of soil body. it was found that the base pressure was small, about 10 kpa, around the bridge abutment, i.e., 0 m away from the expansion joint, and large when away from the bridge abutment, i.e., away from the expansion joint; the overall base pressure of the high-strength foam concrete was smaller than that of ordinary concrete; the base pressure of the highstrength foam concrete increased from 10 kpa to 40 kpa, with the increase of the distance with the expansion joint; the base pressure of ordinary concrete increased from 10 kpa to 80 kpa, which was significantly higher than that of the highstrength foam concrete. it indicated that the base pressure of the transition section of road and bridge was relatively small when the high-strength foam concrete was taken as the material of back filling behind abutment. figure 6: analysis of change of base pressure. stress analysis under vehicle load fig. 7 shows that the curve of changes of vertical displacement of the transition section of road and bridge under vehicle load. the vertical displacement was the largest when vehicle load was exerted in 0.1 s, and gradually decreased. the fluctuation of vertical displacement of ordinary concrete was significantly larger than that of the high-strength concrete. the maximum vertical displacement of ordinary concrete was 0.7 m, and it tended to be stable at 0.35 s. the vertical displacement of the high-strength foam concrete was smaller than 0.1 m and tended to be 0 m at 0.15 s. it indicated that the stability of transition section of road and bridge was better when the high-strength foam concrete was taken as the material of back filling behind abutment. h.m. cao, frattura ed integrità strutturale, 49 (2019) 831-839; doi: 10.3221/igf-esis.49.73 837 figure 7: the curve of changes of vertical displacement. figure 8 shows the curve of changes of vertical stress. it was found that the vertical stress of ordinary concrete was significantly larger than that of the high-strength foam concrete and the maximum vertical stress was about 45 kpa. the maximum vertical stress of the high-strength foam concrete was about -40 kpa and became 0 kpa after 0.1 s. the vertical stress of ordinary concrete was close to 0 kpa after 0.1 s, but still fluctuated, indicating that the damping effect of the high-strength foam concrete was better. figure 8: the curve of changes of vertical stress. analysis of ground surface settlement figure 9 shows the changes of settlement amount along the longitudinal center line of the road 300 days after the simulated transition segment of road and bridge opened to traffic. it was found that the settlement amount of the road beside bridgehead was large and increased gradually as time went by, the maximum settlement amount was about 0.04 m, and the overall settlement of the road was stable, without bumping at bridge head. it showed that the back filling of highstrength foam concrete behind abutment was stable. h.m. cao, frattura ed integrità strutturale, 49 (2019) 831-839; doi: 10.3221/igf-esis.49.73 838 discussion he analysis of the high-strength foam concrete suggested that the material generated a large number of micro cracks under the action of load cycle, and the number of micro cracks increased significantly with the increase of load cycles; after 1 million 200 thousand cycles of loading, there were more than 100 thousand micro cracks in the specimen, and the residual strength was 0.51 mpa, but there was no structural damage. it indicated that it had a long service life and could fully meet the requirements of the transition section of road and bridge. the analysis of the mechanical properties of the transition section of road and bridge suggested that the static base pressure of transition section of road and bridge which was processed by the high-strength foam concrete was about 40 kpa, which was much smaller than that of ordinary concrete, indicating that the load on the transition section of road and bridge was small. under the action of vehicle load, the mechanical properties of the high-strength foam concrete were better than those of ordinary concrete. the maximum vertical displacement of the high-strength foam concrete was less than 0.1 m, and the maximum vertical stress value was about -40 kpa, which was smaller than that of ordinary concrete, and it became stable in a relatively short time. it showed that the high-strength foam concrete could reduce the impact load of vehicle driving on the transition section of road and bridge and increase the service life of transition section of road and bridge. in addition to better mechanical properties, back filling of foam concrete can also reduce side pressure on bridge abutments and improve bridge safety and service life. the construction difficulty is also low. it can effectively reduce settlement difference and avoid bridgehead jumping. economically, in the construction using traditional materials, compactor will be used to compact the road surface, which takes long construction time, and moreover the cost of foundation treatment is also high. dynamic compaction and rolling compaction are not needed for high-strength foam concrete, which shortens the construction period and production and transportation cost [16]; the cost of foundation treatment is low as it can be integrated directly with bridge abutment. in addition, although the price of high-strength foam concrete is higher than that of ordinary concrete, the comprehensive cost of high-strength foam concrete is significantly lower than the traditional material, and moreover it can be recycled. the use of recycled foam concrete can significantly reduce the treatment cost. in the aspect of environmental protection, the dust produced by the backfill materials such as lime soil and coal ash during the construction process is serious, which will cause great pollution to the surrounding environment. a large amount of dust may also lead to the production reduction of the surrounding farms. foam concrete can effectively avoid dust pollution during construction and reduce the impact of construction on the environment, and will not cause adverse environmental consequences. in the aspect of durability, high-strength foam concrete can ensure a service time of at least 60 years of the transition segment of bridge and road, which can completely satisfy the requirement on age limit of road. conclusion n this paper, the mechanical properties of transition section of road and bridge based on high-strength foam concrete were analyzed, and the preparation and back filling method of high-strength foam concrete were briefly introduced. the mechanical analysis suggested that the high-strength foam concrete had better strength and longer service life. compared with ordinary concrete, the high-strength foam concrete had smaller base pressure and structure load. moreover its vertical displacement and stress under the action of vehicle load were both small. therefore it has good vibration and energy absorption effects. it is an ideal material for back filling behind abutment and deserves further promotion. references [1] kaewunruen, s. and mirza, o. (2017). hybrid discrete element finite element simulation for railway bridge-track interaction, mater. sci. eng. conf. ser., pp. 012016. doi: 10.1088/1757-899x/251/1/012016. [2] hu, c., qiang, l., liang, z., et al. (2014). test analysis of vibration characteristics of high-speed railway on crts ⅱ slab ballastles strack bridge-subgrade transition, j. vib. shock, 33(1), pp. 81-88. t i h.m. cao, frattura ed integrità strutturale, 49 (2019) 831-839; doi: 10.3221/igf-esis.49.73 839 [3] yan, w., deng, l. and yin, x. (2016). allowable slope change of approach slabs based on the interacted vibration with passing vehicles, ksce j. civil eng., 20(6), pp. 2469-2482. doi: 10.1007/s12205-015-0466-1. [4] (2016). impact factors for fatigue design of steel i-girder bridges considering the deterioration of road surface condition, j. bridge eng., 21(5), pp. 04016011. [5] zhang, j., zheng, j.j., zhao, d.j., et al. (2016). field study on performance of new technique of geosyntheticreinforced and pile-supported embankment at bridge approach, sci. china technol. sc., 59(1), pp. 162-174. doi: 10.1007/s11431-015-5995-9. [6] huang, c.f., li, q., wu, s.c., et al. (2017). application of the richards model for settlement prediction based on a bidirectional difference-weighted least-squares method, arab. j. sci. eng., (2), pp. 1-9. doi: 10.1007/s13369-017-2909-0 [7] li, h.l., jin, c.z., yang, c.f., et al. (2014). research on the stress-strain law of abutment approach embankment filled with liquid fly ash, adv. mater. res., 1065-1069, pp. 536-539. doi: 10.4028/www.scientific.net/amr.1065-1069.536. [8] yasrobi, s.y., ng, k.w., edgar, t.v., et al. (2016). investigation of approach slab settlement for highway infrastructure, transp. geotech., 6, pp. 1-15. doi: 10.1016/j.trgeo.2015.12.002. [9] xiang, y.q., yun, s., jin, f.g., et al. (2010). case study of the deep-seated concrete slab for settlement control at bridge approach embankment, j. harbin instit. tech., 42(1), pp. 158-162. doi:10.1007/978-3-642-04460-1_124. [10] greco, f. and lonetti, p. (2018). numerical formulation based on moving mesh method for vehicle-bridge interaction, adv. eng. softw., 121, pp. 75-83. doi: 0.1016/j.advengsoft.2018.03.013. [11] lonetti, p., pascuzzo, a. and davanzo, a. (2016). dynamic behavior of tied-arch bridges under the action of moving loads, math. probl. eng., 2016, pp. 1-17. [12] sun, y., xiang, y.q., guo, d.m., et al. (2010). analysis of the deep-seated concrete slab for settlement control at bridge approach embankment, adv. environ. geotech. springer berlin heidelberg, pp. 935-939. doi:10.1007/978-3-642-04460-1_124. [13] liu, x., liu, p., wang, q., et al. (2016). feasibility analysis on application of modified concrete contains rubber powder of straddle type monorail train waste tire, proc. environ. sci., 31, pp. 804-811. doi: 10.1016/j.proenv.2016.02.078. [14] wu, y.d., zeng, c.c., liu, j., et al. (2016). measured settlement of highways improved by lightweight backfilling without road closure, arab. j. sci. eng., 41(10), pp. 1-8. doi:10.1007/s13369-015-2017-y. [15] luo, y.h., hu, h.y., huang, z.x., et al. (2014). characteristics of eps materials and the application in road and bridge projects, appl. mech. mater., 501-504, pp. 1418-1423. doi:10.4028/www.scientific.net/amm.501-504.1418. [16] amran, y.h.m., farzadnia, n. and ali, a.a.a. 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/hrv (za stvaranje adobe pdf dokumenata najpogodnijih za visokokvalitetni ispis prije tiskanja koristite ove postavke. stvoreni pdf dokumenti mogu se otvoriti acrobat i adobe reader 5.0 i kasnijim verzijama.) /hun 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<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> /enu (use these settings to create adobe pdf documents best suited for high-quality prepress printing. created pdf documents can be opened with acrobat and adobe reader 5.0 and later.) >> /namespace [ (adobe) (common) (1.0) ] /othernamespaces [ << /asreaderspreads false /cropimagestoframes true /errorcontrol /warnandcontinue /flattenerignorespreadoverrides false /includeguidesgrids false /includenonprinting false /includeslug false /namespace [ (adobe) (indesign) (4.0) ] /omitplacedbitmaps false /omitplacedeps false /omitplacedpdf false /simulateoverprint /legacy >> << /addbleedmarks false /addcolorbars false /addcropmarks false /addpageinfo false /addregmarks false /convertcolors /converttocmyk /destinationprofilename () /destinationprofileselector /documentcmyk /downsample16bitimages true /flattenerpreset << /presetselector /mediumresolution >> /formelements false /generatestructure false /includebookmarks false /includehyperlinks false /includeinteractive false /includelayers false /includeprofiles false /multimediahandling /useobjectsettings /namespace [ (adobe) (creativesuite) (2.0) ] /pdfxoutputintentprofileselector /documentcmyk /preserveediting true /untaggedcmykhandling /leaveuntagged /untaggedrgbhandling /usedocumentprofile /usedocumentbleed false >> ] >> setdistillerparams << /hwresolution [2400 2400] /pagesize [612.000 792.000] >> setpagedevice microsoft word 003 plenary gates & fatemi usa paper 8-25-15 final n.r. gates et alii, frattura ed integrità strutturale, 34 (2015) 27-41; doi: 10.3221/igf-esis.34.03 27 focussed on crack paths crack paths in smooth and precracked specimens subjected to multiaxial cyclic stressing nicholas r. gates mechanical, industrial and manufacturing engineering department, the university of toledo, 2801 w. bancroft street, toledo, oh 43606, usa ngates@eng.utoledo.edu ali fatemi mechanical, industrial and manufacturing engineering department, the university of toledo, 2801 w. bancroft street, toledo, oh 43606, usa afatemi@eng.utoledo.edu abstract. the understanding of shear-mode crack growth mechanisms and crack branching phenomena is of great interest for a variety of practical engineering situations. despite this fact, relatively little research is available regarding these topics. of the studies that have been performed, few provide a means of quantifying such effects and most consider crack growth starting from a precrack. the current study is aimed at trying to fill some of the research voids in these areas by investigating the effects of microcrack coalescence, loading level, and superimposed normal stresses on the mode ii crack behavior of naturally initiated fatigue cracks. based on the experimental results and subsequent analyses, it was determined that microcrack networks and coalescence have little to no effect on the experimentally observed crack paths regardless of the applied loading level. instead, the preferred crack growth mode is shown to have a dependence on the applied shear stress magnitude and stress normal to the crack plane, indicating a significant role of fiction and roughness induced crack closure effects in the crack growth process. a simple model is then proposed to quantify these effects based on the idea that crack face interaction reduces the effective mode ii sif by allowing a portion of the nominally applied loading to be transferred through a crack. the model agrees qualitatively with the experimentally observed trends for pure torsion loading and predicts crack branching lengths within a factor of 2 for all loadings considered. keywords. fatigue; crack growth; mode ii; friction; branching; closure. introduction atigue crack growth often represents a significant portion of a component’s total fatigue life. therefore, a fundamental understanding of the mechanisms that govern crack propagation and the development of accurate crack growth modeling techniques are essential to a complete fatigue life analysis. this is especially true in f n.r. gates et alii, frattura ed integrità strutturale, 34 (2015) 27-41; doi: 10.3221/igf-esis.34.03 28 situations where a damage tolerant design philosophy has been employed. crack growth mechanisms and their influence on crack growth rate have been researched extensively over the years for uniaxial loadings and mode i crack extension. most of these studies, however, utilize specimens which promote ideal crack growth conditions. in practical applications, where components are often subjected to complex multiaxial loading histories, these ideal conditions usually don’t exist. instead, naturally initiated fatigue cracks can grow in a complex and mixed-mode manner which is not easy to predict or quantify. one of the complexities involved in mixed-mode crack growth is predicting crack path by determining in what direction a crack will grow throughout different stages of its development [1]. for example, cracks initiated naturally at a mechanical notch tend to nucleate and grow a short distance, usually comparable to the length of a few grains, on planes of maximum shear, but almost always turn so that long crack growth occurs on planes of maximum tensile stress [2–5]. in this case, well established mode i crack extension models can be employed to predict growth rates for a given loading history. on the other hand, long cracks in un-notched (smooth) specimens have been shown to propagate on maximum shear planes, maximum tensile planes, or a combination of both. the preferred growth plane has been shown to depend on material, nominally applied loading, and/or loading magnitude [6]. in general, cracks in the low cycle fatigue regime tend to grow on maximum shear planes while cracks at longer lives tend to transition into mode i growth [7–11]. one explanation offered for the discrepancy between crack growth in smooth and notched specimens is that a fundamental difference in crack growth mechanism exists. in the smooth specimens, the uniformly stressed gage section allows for a large number of microcracks to develop and form “crack networks” across the specimen surface. the growth of these cracks is driven primarily by far field stresses and plasticity of the gage section. each small crack can grow to a different length and at a different rate due to microstructural variations, shielding, and other interaction with adjacent cracks in the network. these cracks grow individually and remain relatively small until near fracture where they coalesce to form a failure crack which retains the same orientation of the individual cracks. shamsaei and fatemi [12] observed that the development of microcrack networks in smooth specimens is more prominent in the low cycle fatigue regime due to increased plasticity in the gage section activating more slip systems. this observation agrees with the higher tendency for macroscopic shear-mode crack growth in this regime. they also observed a larger number of microcracks initiating in more ductile behaving materials, as opposed to higher strength materials, for solid cylindrical specimens, as opposed to tubular specimens, and for in-phase axial-torsion loadings, as opposed to 90° out-of-phase loadings. for the notched specimens, in contrast to the smooth, only a small number of dominant cracks nucleate at the location(s) of maximum stress around the notch, typically on the maximum shear plane. with the absence of microcrack networks, unable to develop in the lower stressed material surrounding the notch, the cracks quickly turn into the mode i direction and grow independently, driven by the stress and plasticity fields at the crack tip. therefore, cracks initiated from notches generally grow in a continuous manner and lack the retardation or acceleration effects observed for the smooth specimens due to crack interaction. this is also the case for cracks growing in smooth specimens tested at lower stress amplitudes. as early as the 1950s, marco and starkey [13] noted a difference between these two types of crack growth mechanisms and termed the growth of long cracks through microcrack coalescence a type r crack system, whereas crack growth dominated by the propagation of a single crack was termed a type s crack system. knowing by which mechanisms and on which planes a crack will grow is essential to performing accurate crack growth analysis. there are many parameters that can influence mixed-mode crack growth behavior, some of which include loading magnitude and r ratio, loading sequence, material strength, and crack closure [14]. to account for these effects, several prediction models or correlation parameters for both mixed-mode growth direction and growth rate have been proposed. for example, the maximum tangential stress criterion [15] has been found to give close predictions of the experimentally observed crack growth path [3], and equivalent stress intensity factor parameters, such as that proposed by tanaka [16] can satisfactorily correlate the experimental growth rate data [4]. however, these models are most effective in the absence of crack coalescence and cannot account for differences in crack path for such cases. for example, the maximum tangential stress criterion would predict a mode ii crack initiated under pure torsion loading to immediately branch at an angle of 70.5° to the crack growth direction and grow in mode i regardless of the applied loading magnitude [8, 17]. this prediction is not in agreement with the shear-mode crack growth observed in many smooth specimens from initiation up until fracture. owing to the complexity of the task, little research is available on models which attempt to quantify when or if cracks will grow by type r mechanisms, type s mechanisms, or whether or not these two mechanisms are even responsible for the differences in smooth and notched specimen crack paths. to simplify this problem for the following discussion, it will be assumed that naturally occurring fatigue cracks always tend to initiate on planes of maximum shear stress. this is an assumption backed by both the physics of fatigue crack initiation and by large amounts of experimental evidence [12]. n.r. gates et alii, frattura ed integrità strutturale, 34 (2015) 27-41; doi: 10.3221/igf-esis.34.03 29 this then leaves two possibilities for subsequent crack growth; the crack can either branch and grow in mode i on maximum tensile planes, or the crack can remain coplanar and grow in mode ii or mixed-mode conditions until failure. concerning the first possibility, there is a reasonable amount of literature available describing the processes governing the transition from stage i to stage ii crack growth. murakami and takahashi [17] studied the behavior of small mode ii cracks growing under near threshold conditions for pure torsion loading of medium carbon steel solid cylindrical specimens. they observed three different conditions for crack growth from a precrack. cracks either started to grow in both modes i and ii from the precrack tip, with the mode ii cracks stopping after a short distance to give way to the more dominant mode i cracks, or only mode i cracks were observed to grow from the precrack tip, or the crack propagated in mode ii for a short distance before eventually branching to grow in mode i. crack branching was attributed to a higher threshold stress intensity factor (sif) value for modes ii and iii as compared to mode i. they argued that this led to an arrest of shear-mode cracks as they dropped below their threshold value which gave way to mode i growth as cracks were still above the mode i threshold sif value [7]. they concluded that the mode i sif of the branched cracks governed the fatigue limit for small cracks in torsion and were able to predict the fatigue limit using an extension of the square root of area parameter [17]. makabe and socie [18] studied crack growth in precracked specimens of 4340 steel under torsion loading with and without the influence of static axial stresses. they observed that cracks grew longer in mode ii before branching as the applied shear strain and/or static axial stress increased. this was attributed to decreased contact and friction between opposing crack faces and the resulting change in slip band density surrounding the crack tip. the eventual branching mechanism was described as a zig-zagging between perpendicular slip bands generated in the vicinity of the crack tip. it was concluded that in order for a crack to continue to grow in shear-mode, the driving force for shear deformation at the crack tip must be large enough to overcome the friction between crack faces. considering the effects of crack face friction, tong et al. [19] proposed a model to describe changes in local stress intensity factors during shear-mode crack growth based on an idealized crack face asperity angle and coefficient of friction. the model was developed for a two-dimensional edge crack growing nominally in pure mode ii and relates theoretical crack sliding displacements computed using finite element analysis (fea) to local displacement components due to wedging of crack face asperities. the local displacements are then used to compute a local reduction in mode ii sif due to friction and a local increase in mode i sif due to wedging. comparing the effective mode ii sif to the local mode i sif provides a means of predicting crack branching. the model predictions were not compared directly to experimental results, but the predicted trends agreed with experimental observations. in an extension of the same work [20], the model was applied to mixed-mode i and ii loadings and could be extended to other crack geometries as well, provided the appropriate weight functions and crack face loading distributions are known. more recently, künkler et al. [21] predicted the two-dimensional crack propagation behavior of short cracks under uniaxial loading in the region of stage i to stage ii transition using a microstructure sensitive modeling technique. they found that mode ii growth occurs primarily on single slip systems within individual grains. once the crack reaches a length where its plastic zone is large enough to activate additional slip systems in neighboring grains, the crack begins to transition to mode i growth by switching from a single slip mechanism to a double slip propagation mechanism. in double slip crack growth, shear displacements on the two different slip systems cause a crack tip opening which promotes mode i crack extension. the crack length at this transition was considered dependent upon crack geometry, grain size, and the orientation of slip systems in neighboring grains. in 2014, pokluda et al. [10] reviewed research on shear-mode crack behavior in metallic materials. it was concluded that the main factor driving the branching of mode ii cracks is crack face friction and wedging caused by surface asperities. these asperities result from microstructural level crack meandering due to differing orientations of slip systems, and their average inclination angle was shown to vary based on the crystallographic structure of the material. when mode ii sliding displacements occur between opposing crack faces, the wedging effect of these asperities acts to simultaneously reduce the effective value of the mode ii sif and introduce a local mode i sif component. when the conditions are such that the local mode i sif value exceeds the mode i threshold, crack branching is considered to occur. the authors applied a simple crack branching criterion to predict whether or not crack branching would occur in the threshold region before a crack became non-propagating. they compared the predictions to experimental data of four different metals and reported good agreement. while the aforementioned studies deal with describing or predicting the development of a mode i branch from a mode ii crack in the near threshold regime, far less literature is available concerning the conditions for continuous coplanar shearmode propagation of a crack. tschegg [11] discussed this issue in a study of mode iii crack growth behavior in circumferentially grooved cylindrical specimens of 4340 steel. the change in fracture mode was found to coincide with the intersection of the mode i and mode iii crack growth curves. at lower stress intensity values, where crack branching and n.r. gates et alii, frattura ed integrità strutturale, 34 (2015) 27-41; doi: 10.3221/igf-esis.34.03 30 factory roof fracture surfaces were observed, it was speculated that the mode i loading of favorably oriented microcracks in the crack tip plastic zone would produce higher crack growth rates than the effective mode iii loading of the main crack. therefore, whichever loading mode produced the highest crack growth rate values for a given combination of loading conditions and crack length was considered to control the crack growth process. using a similar “maximum growth rate” approach, doquet and bertolino [8] addressed the fracture mode issue by considering a local approach based on elastic-plastic crack tip stresses and strains derived via non-linear incremental fea. two multiaxial fatigue damage parameters, one predicting tensile dominated failure (smith-watson-topper) and one predicting shear dominated failure (fatemi-socie) were then applied to predict crack path based on which mode would produce the most damage (based on the shortest predicted life and highest growth rate). the damage parameter values were averaged over an arbitrary length (between 0.020 – 0.100 mm) along a radial line emanating from the crack tip along either plane experiencing the maximum normal strain or maximum shear strain range. a transition in growth mode from tensile dominated to shear dominated was successfully predicted at higher applied loading, but no quantitate comparison was made to experimental results. a major drawback of this approach, however, is the need to perform non-linear fea over an entire cycle for each crack length and loading level being considered. tanaka [9], in an investigation on shear crack growth in circumferentially grooved specimens of a stainless and carbon steel, speculated that a criterion for coplanar versus branched crack growth could be related to the shear strain range ahead of the crack tip. for higher loading levels, it was suggested that increased plasticity at the crack tip could lead to the initiation of local shear oriented microcracks ahead of the crack tip which would encourage coplanar crack growth through local coalescence. however, no quantitative analysis was provided. this study is similar in some regards to those mentioned previously, but presents some aspects typically not considered in shear-mode crack growth studies. for example, nearly all of the aforementioned studies deal exclusively with mode ii cracks growing from precracks or circumferential notches. this study, on the other hand, places a strong emphasis on the behavior of naturally initiated fatigue cracks in smooth specimens. one problem with studying growth from precracks is that residual stresses in the crack tip region, resulting from the precracking procedure, have the potential to influence the subsequent mode ii crack growth. even if specimens are annealed following precracking to eliminate these effects, the crack face topography still varies from that of a naturally occurring crack. in addition, growing a mode ii crack from a precrack can significantly alter the length scale required for branching mechanisms to occur and eliminates any influence on crack path from microcrack coalescence. the present study compares crack path evolution between both natural cracks and cracks growing from artificial precracks in order to evaluate the effect of microcrack coalescence on overall crack path. the role of crack face friction and roughness induced crack closure on shear-mode crack growth is evaluated as well. an emphasis is placed on crack paths in the low to intermediate fatigue life regime where mode ii cracks may or may not branch to grow in mode i. in an attempt to quantify the experimental observations, a model is proposed to account for reductions in effective mode ii sif due to crack face interaction effects. material and testing procedures ll tests performed for this study utilized thin-walled tubular specimens of 2024-t3 aluminum alloy, a common aerospace alloy since the 1930s. mechanical properties for the material were generated experimentally and include a yield strength (0.2% offset) of 330 mpa, ultimate tensile strength of 495 mpa, and modulus of elasticity of 73.7 gpa. the specimens, machined from drawn tubing with nominal dimensions of 34.9 mm outside diameter and 4.75 mm wall thickness, were designed in accordance with astm standard e2207 [22] and feature a 30 mm long gage section with an outside diameter of 29 mm and an inside diameter of 26 mm, resulting in a wall thickness of 1.5 mm. the specimen geometry and dimensions are shown in fig. 1(a). for precracked specimens, the term precrack is used to refer to a small notch machined in the specimen meant to resemble, as closely as possible, the profile of a naturally occurring fatigue crack. no actual precracking procedure was performed on this notch prior to applying the testing loads. it is referred to as a precrack simply as a means of differentiating it from other notched specimens, containing non crack-like notches, which are referred to in the introduction. all precrack notches were machined by means of a 0.127 mm diameter ball mill and were semi-elliptic in shape. the precracks were of a length and depth equal to approximately 1 mm and 0.2 mm, respectively, and were aligned with a plane of maximum shear stress for each applied loading condition. a sectioned view of a precrack notch is shown in fig. 1(b). all smooth specimens were fully polished, inside and out, to eliminate any adverse effects from machining marks. final polishing was performed with a 3 micron lapping film. precracked specimens were polished similarly, but external polishing was only performed in the crack growth region surrounding the precrack. a n.r. gates et alii, frattura ed integrità strutturale, 34 (2015) 27-41; doi: 10.3221/igf-esis.34.03 31 all fatigue tests were carried out in a closed loop servo-hydraulic axial–torsion load frame with a dynamic rating of 100 kn axial load and 1 kn·m torsional load. load train alignment was verified in accordance with astm standard e1012 [23] prior to the beginning of, and periodically throughout, testing. crack initiation and growth were monitored via cellulose acetate replication for smooth specimen tests, and by using a 2.0 megapixel digital microscope camera, capable of 10–230x optical zoom levels, for precracked specimens. crack lengths were measured using an eyepiece scale affixed to an optical microscope for the surface replicas, and by means of image analysis software for the digital microscope images. (a) (b) figure 1: test specimen details for (a) thin-walled tubular specimen geometry and (b) sectioned view of machined precrack notch. all dimensions are in mm. all tests were performed in load control and include fully-reversed (r = -1) pure torsion and in-phase axial-torsion tests for both smooth and precracked specimens. additional smooth specimen tests were also performed for pure torsion loading, with and without the addition of a static tensile or compressive stress, to evaluate the effect of mean stresses on mode ii crack growth. experimental results and discussion lthough surface replicas have shown the development of small microcrack networks in a number of the smooth specimen fatigue tests performed in this study, crack coalescence was only observed in a limited number of these tests and usually occurred relatively early in the crack growth life. therefore, questions were raised on whether or not crack coalescence played a large role in determining overall crack path for these tests. thus the effect of microcrack networks and coalescence was investigated through the testing of smooth and precracked specimens under identical loading conditions. two load levels each were used for tests under fully-reversed pure torsion loading, in-phase axialtorsion loading, pure axial loading, and 90° out-of-phase axial-torsion loading. however, results from the latter two loading conditions are not included in this study because the difference between mode i and mode ii growth cannot be observed from the outer surface of the specimen. a future three-dimensional analysis would be required to interpret those results. therefore, only the experimentally observed crack paths for the two torsion loading levels and two in-phase axialtorsion load levels are shown in fig. 2. by comparing crack paths between the smooth and precracked specimens in fig. 2, it is easy to see that they are very similar. this is true even for complex crack paths where cracks initiate in mode ii, branch into mode i cracks, and eventually transition back to mode ii after growing for some distance (fig. 2(b-d)). this suggests that microcrack networks and their coalescence did not play a significant role in determining the crack paths for these tests. if dominant cracks, growing without the influence of crack coalescence, were expected to always branch into mode i growth regardless of the applied loading (as predicted by traditional crack growth direction criteria), then the crack path for the precracked specimen subjected to the higher level pure torsion load (fig. 2(a)) would certainly not have remained vertical for its entire growth life. this, combined with the transition back to shear-mode growth after a period of mode i growth observed for the other precracked specimen tests, supports findings from many smooth specimen surface replicas where shear dominated crack growth occurred even in the absence of any observable crack coalescence. although the existence of the type r crack growth mechanism is certainly not being rejected, it is clear that in the case of this study, coalescence was most likely not responsible for the shear dominated crack paths observed in the smooth specimen tests. therefore, there must be some other mechanism by which crack growth behavior transitions from being mode i to mode ii dominated. by studying the crack paths in fig. 2, a correlation between the loading level and/or sif and the crack growth direction is observed. to help illustrate this point, tab. 1 was constructed and contains all available a n.r. gates et alii, frattura ed integrità strutturale, 34 (2015) 27-41; doi: 10.3221/igf-esis.34.03 32 crack orientation data from pure torsion, torsion with static axial stress, and in-phase axial-torsion fatigue tests of smooth specimens. nominally applied loadings are given along with shear stress amplitude and maximum normal stress on the maximum shear plane. specimen suffixes indicate the loading conditions as follows: st are pure torsion tests, stsa are torsion tests with static axial stress, and sc are in-phase axial-torsion tests. the table is sorted based on decreasing shear stress amplitude on the maximum shear plane. within each shear stress level, tests are sorted by decreasing level of maximum normal stress on the maximum shear plane. approximate crack plane orientation is then listed for different ranges of overall tip-to-tip crack length, 2c (in mm), as well as the total number of cycles to failure, nf, at which point the final crack lengths were approximately 15-20 mm. the dependence of crack growth direction on loading level is easy to see from tab. 1. above a shear stress amplitude of 188 mpa, all significant ranges of crack growth for all loading conditions took place in mode ii on planes of maximum shear. below this level, cracks begin to transition to mode i growth shortly after initiation and continue growing in mode i until near failure. the only exception to this trend comes when a tensile normal stress exists on the maximum shear plane. in these cases, cracks spend more time in mode ii growth than specimens tested at the same shear stress amplitude without a tensile normal stress. in all but one case, both crack initiation and final failure were observed to be shear-mode processes. figure 2: superimposed crack paths for precracked specimens (black) and smooth specimens (green) tested under identical loading conditions for (a) higher load level pure torsion, (b) lower load level pure torsion, (c) higher load level in-phase axial torsion, and (d) lower load level in-phase axial-torsion tests. relative load level is indicated by the ratio of von mises equivalent stress to yield strength. (a) (b) (c) (d) n.r. gates et alii, frattura ed integrità strutturale, 34 (2015) 27-41; doi: 10.3221/igf-esis.34.03 33 nominal loading (mpa) on τmax plane (mpa) crack orientation vs. length (mm) specimen id† τamp σamp σmean τamp σmax initiation 0.2 <2c <1 1 <2c <2 2c >2 nf tm56-st 248.3 0 0 248.3 0 τmax τmax τmax τmax 736 tm63-sc 178.0 300.0 0 232.8 150.0 τmax τmax τmax τmax 2009 tm100-stsa 187.8 0 92.0 187.8 92.0 τmax τmax τmax τmax 6742 tm101-stsa 187.8 0 92.0 187.8 92.0 τmax τmax τmax τmax 15177 tm1-st* 187.8 0 0 187.8 0 τmax τmax τmax τmax 72397 tm58-st 187.8 0 0 187.8 0 τmax τmax τmax τmax 68105 tm103-stsa 187.8 0 -92.0 187.8 0 τmax τmax τmax τmax 15283 tm106-stsa 187.8 0 -92.0 187.8 0 τmax τmax τmax τmax 21191 tm53-sc* 130.3 225.0 0 172.1 112.5 τmax σ1 τmax τmax 25555 tm4-st 168.2 0 0 168.2 0 τmax σ1 σ1 τmax 180288 tm78-st 150.1 0 0 150.1 0 τmax σ1 τmax τmax 181299 tm96-stsa 140.3 0 150.0 140.3 150.0 τmax τmax τmax τmax 35095 tm99-stsa 140.3 0 150.0 140.3 150.0 τmax τmax τmax τmax 58046 tm67-st 140.3 0 0 140.3 0 τmax σ1 σ1 τmax 531716 tm105-stsa 140.3 0 -150.0 140.3 0 τmax σ1 σ1 τmax 770431 tm37-sc 106.4 175.0 0 137.8 87.5 τmax σ1 τmax τmax 147725 tm54-sc 90.3 156.0 0 119.3 78.0 σ1 σ1 σ1 σ1 213138 tm62-sc 90.3 156.0 0 119.3 78.0 τmax σ1 σ1 τmax 867295 †suffix indicates loading condition as follows: st (pure torsion), stsa (torsion with static axial stress), and sc (in-phase axial-torsion) *crack orientations refer to a secondary crack, not the failure crack table 1: loading conditions, crack orientation vs. crack length, and fatigue life (to crack lengths of approximately 15-20 mm) for smooth specimen fatigue tests. all stresses are given in mpa and all crack lengths are given in mm. these observations support the idea that friction and roughness induced crack closure, caused by crack face interaction, play a key role in determining crack path. at the lower loading levels, the combined effect of friction and roughness seem to reduce the effective mode ii driving force at the crack tip until it drops below a critical level. this critical level could either represent a mode ii threshold condition, or a value at which the potential for mode i growth exceeds that of the existing mode ii crack. at this point, the crack then turns to maximum tensile planes where there is less resistance to mode i crack propagation. this idea echoes the conclusions drawn in several of the studies reviewed in the introduction. at the higher loading levels, however, these factors do not appear to play as large of a role in determining crack path. this is likely due to a combination of factors. for example, at higher stress levels, the effect of friction may not be large enough to drop the effective mode ii driving force below its critical value. additionally, increased plasticity at the crack tip can result in the deformation and destruction of the crack face asperities which would otherwise restrict the effective mode ii driving force. fig. 3 shows that as the shear stress amplitude was increased in the pure torsion tests, a longer mode ii crack length was observed before branching occurred. this trend was also reported in refs. [8, 18] and suggests that the mode ii driving force increases at a faster rate than the attenuation effect due to crack face interaction, which eventually leads to a non-branching condition. such a dependence on load level is consistent with the observed differences between crack paths in smooth and notched specimens. because of the stress concentration effect in notched specimens, they are often tested at much lower nominal stress amplitudes than smooth specimens. therefore, once an initial mode ii crack propagates out of the notch affected zone and into the lower stressed gage section, frictional effects would significantly restrict its growth and lead to a tendency for the crack to transition into mode i where there is less resistance to crack extension. the same is true for crack growth tests where crack growth is evaluated from a precrack. because data for a large range of growth rates and stress intensity factors are typically desired in these types of test, they are performed at the lower nominal loadings conducive to mode i growth. n.r. gates et alii, frattura ed integrità strutturale, 34 (2015) 27-41; doi: 10.3221/igf-esis.34.03 34 figure 3: initial mode ii crack length before mode i branching vs. shear stress amplitude for fully-reversed pure torsion tests. vertical arrows indicate a non-branching condition. the mean stress effect on crack path that was observed in these tests further emphasizes the role of crack face interaction in the crack growth process. for two different values of shear stress amplitude, specimens were tested with a static compressive stress, no normal stress, and a static tensile stress. it should be noted that static normal stresses were used so as to not introduce mixed-mode growth effects through a nonzero mode i sif range. the fatigue lives for these tests, to various tip-to-tip crack lengths, are shown in fig. 4. for both shear stress levels, the addition of the tensile normal stress reduced the overall fatigue life by around an order of magnitude. much of this difference can be attributed to a decrease in crack growth life which would logically stem from a reduction in crack face friction and roughness induced closure effects. as a result, crack paths for these tests were always observed to be in the specimen circumferential direction, perpendicular to the applied tensile stress (fig. 5(a)). for the tests in which a static compressive stress was applied, the crack growth plane switched from the specimen circumferential direction to the longitudinal direction (fig. 5(b)). although both are planes of maximum shear stress, the compressive normal stress acts to increase crack face interaction and inhibit crack growth on the circumferential plane. as a result, longitudinal cracks developed and grew under the same nominal loading and in a similar manner to those for torsion only tests. for specimens tested at the lower shear stress amplitude, crack branching and mode i growth was observed over the same range of crack lengths for both the compressive normal stress and pure torsion cases (although not for the specimen pictured in fig. 5). the decrease in fatigue life observed in fig. 4(b) for the static compression tests compared to pure torsion tests may be due to an increase in plastic zone size and crack driving force as a result of the additional compressive tangential stress (t-stress) at the crack tip. although also present for tests performed at the lower shear stress amplitude, the effect of t-stress is expected to have a larger effect as stress levels increase. also, the addition of the static stresses at the higher shear stress amplitude results in a general yielding condition throughout the specimen gage section which greatly increases the probability of crack initiation compared to the pure torsion test. for the lower shear stress amplitude, all loading conditions result in nominally elastic stresses throughout the gage section. figure 4: fatigue lives to various crack lengths for smooth specimens tested at shear stress amplitudes of (a) 140 mpa and (b) 188 mpa with and without static axial stresses. specimens for which no crack growth data were available are shown as solid gray columns. (a) (b) n.r. gates et alii, frattura ed integrità strutturale, 34 (2015) 27-41; doi: 10.3221/igf-esis.34.03 35 figure 5: final crack paths for selected smooth specimen tests under (a) torsion with static tensile stress, (b) torsion with static compressive stress, and (c) pure torsion loadings. modeling of friction effects s evidenced by the experimental results, the role of friction and roughness induced closure effects on mode ii crack growth is a complex, yet significant, issue. because of the many factors involved and their inherent variability, quantification of these effects is challenging. this section will aim to reproduce some of the crack growth trends observed in experiments by presenting a simplified model to predict and quantify crack growth attenuation due to crack face friction and roughness. the proposed model takes as its starting point the idea that friction and roughness induced crack face interaction allow a portion of the nominally applied loading to be transferred through a crack. consider two extremes for pure torsion loading: an uncracked volume of material can transmit all of the nominal loading and creates no stress concentration effect, while a geometrically ideal mode ii crack cannot transfer any load between crack faces and produces the theoretical mode ii sif value at its crack tip. therefore, it would seem logical that an effective mode ii sif could be determined by taking into account the amount of loading transferred between crack faces in an actual cracked component. the model should be able to account for experimentally observed trends such as normal stress effect and loading level dependence and should also depend on quantities relative to crack face friction and roughness such as coefficient of friction and crack face asperity angle. for ease of implementation, it should also ideally only depend on readily available material properties and not require the use of geometry dependent functions, other than those used in sif calculations. in order to compute the proposed effective mode ii sif, the first step is to determine the nominal stress state. nominal, in this case, refers to the stress state that would exist in the volume of material surrounding a crack if the crack were not present. this is assumed to be a two dimensional stress state aligned with the direction of overall crack growth. loads transferred through the crack face are considered on an averaged basis along the entire length of the crack. if significant stress gradients exist along the length and/or depth of the crack, average stress values should be considered. the nominal coordinate system (x-y) is shown schematically in fig. 6 along with other expressions relevant to the following discussions. once the appropriate stress state is known, it is transformed into a coordinate system (subsequently named x'-y') aligned with the average effective crack face asperity angle, αeff , the calculation of which will be explained later. of the stresses in the transformed coordinate system, the crack can only directly transfer a compressive stress, σx’, normal to the asperity face. however, a resulting friction induced stress component allows for additional loads to be transferred as well. it should be noted that the model will not correctly predict frictional attenuation for asperity angles exceeding 45°. above this angle, attenuation starts to become more of a function of mechanical interlocking than friction. additionally, shielding from the alternating asperity angles will begin to have an effect on stresses at the crack interface above this angle. a (a) (b) (c) n.r. gates et alii, frattura ed integrità strutturale, 34 (2015) 27-41; doi: 10.3221/igf-esis.34.03 36 figure 6: schematic showing coordinate systems and nomenclature relevant to the proposed frictional attenuation model the friction stress acting at the crack interface is calculated by multiplying the compressive normal stress, σx’, by a coefficient of friction, µ, which represents the friction between opposing crack faces under ideal contact conditions. coefficients of friction for various materials can be readily found in machinery handbooks such as [24] and typical reported values for static coefficients include 1.1-1.3 for aluminum on aluminum contact, 0.7-0.8 for steel on steel, and 1.0 for copper on copper. although sliding coefficients of friction are harder to find, typical values range from 50-80% of the value of the static coefficient for the same material. since relative motion occurs between crack faces in mode ii crack growth, a sliding coefficient of friction should be assumed. this friction stress then serves to react all or part of the transformed shear stress, τxy’. if the value of the friction stress is greater than the transformed shear stress, then the entire value of τxy’ is considered to be acting at the crack interface as the local shear stress component, τnt. if the available friction stress is less than the transformed shear stress, on the other hand, then τnt assumes the value of the friction stress. however, if local normal stress component, σx’, is tensile, then no contact occurs between opposing crack faces, no load is transferred through the crack, and both σn and τnt are zero. additionally, because crack faces perpendicular to local stress component σy’ are not in contact, this stress component is not transferred through the crack (i.e. σt = 0). this can be expressed mathematically by eqs. (1) and (2):          0x 0x if0 ifx n ' ''    (1)                       '''' ''' ' ' ' ' xyxxxy xyxx xy xy x x and0if and0if 0if0 nt        (2) the macaulay brackets in eq. (2) represent the following function: ‹x› = (x+|x|)/2. by taking the local crack face stress components, in n-t coordinates, and transforming them back into the original x-y coordinate system, a new shear stress component, τfrict, can be obtained. this quantity reflects the portion of the nominally applied shear stress that is transferred through the crack due to friction and crack roughness. therefore, an effective shear stress value, τeff, can be calculated by subtracting the frictional shear stress from the nominal value, i.e. τeff = τxy – τfrict. this effective value of shear stress is then used to compute the effective mode ii sif acting at the crack tip. to this point, the proposed model only relies on two parameters in addition to the nominal loading: the average effective crack face asperity angle and the coefficient of friction. the coefficient of friction is assumed to be a constant, while the average effective asperity angle is allowed to evolve in order to reflect changes in crack face contact conditions. an equation describing the variation in effective asperity angle is proposed as follows: n.r. gates et alii, frattura ed integrità strutturale, 34 (2015) 27-41; doi: 10.3221/igf-esis.34.03 37 ic nomql2 c eff k k 1e1 4 ,                    (3) where α is the natural/undeformed asperity angle, c is the crack length, l is a material characteristic length, kq,nom is the nominally applied equivalent sif (not accounting for friction effects), kic is the material plane-strain fracture toughness, and the parameter, β, describes the influence of loading level on crack face interaction. although eq. (3) is phenomenological in nature, it is designed to reflect the complex changes that occur at the crack interface as a crack grows and provides a simple means of quantifying these changes. the undeformed asperity angle, α, is independent of the applied loading and can either be determined through experimental measurements or estimated based on crystallographic structure [10]. assuming a constant value of average asperity angle, however, would result in a nearly constant frictional effect on effective shear stress. in reality, variations in asperity angle will cause the value of friction stress to change, which will affect the load transfer through the crack interface. this phenomenon is reflected in the current model through a variation in asperity angle with crack length. the idea behind the first bracketed term in eq. (3) is that initially, when cracks are on the order or a grain size or two, there is not much deviation in their ideal path. this is because there has not been a sufficient amount of growth to encounter slip system misalignment from one grain to the next and/or other microstructural obstacles which lead to crack meandering and the development of crack face asperities. therefore, the effective asperity angle at zero crack length is reduced to zero by this term and allowed to gradually increase with crack length until it approaches its saturated value at a length equal to that of a few grains. this produces a behavior which agrees with the decreasing crack growth rates observed for short cracks in the constant sif controlled tests reported in ref. [11]. the material characteristic length, l, can be considered equal to the average grain size in the direction of crack growth. similarly, long cracks may also experience a reduction in frictional stresses due to changes in crack face asperities. unlike short cracks, however, these changes are brought about as a result of asperity destruction due to plasticity and fretting along the crack interface. additionally, the coefficient of friction is more prone to a reduction in long cracks as well, due to the formation of oxide and/or debris layers between crack faces. since the effects of these processes generally increase with an increase in local stresses and/or crack length, the second bracketed term in eq. (3) reflects changes in frictional attenuation by decreasing the effective asperity angle as the ratio of nominal sif to fracture toughness increases. a linear relationship was chosen based on trends reported in ref. [25]. the application of this model is fairly straight forward in cases of fully-reversed pure torsion loading, but it can also be applied to cases where nonzero mean and/or mixed-mode loading conditions exist. because it is based on the stress state at the crack location, it is applicable to any type of loading and the predicted frictional attenuation is sensitive to both the applied shear stress and normal stress components. a simple mohr’s circle analysis reveals that the model will correctly predict a decrease or increase in crack face interaction due to the presence of an applied tensile or compressive stress, respectively. for situations where loading is not fully reversed, the model can be applied at both the minimum and maximum loadings in a cycle to compute the effective sif range. however, care should be taken when determining the sign of the stress transformation angle to ensure that the transformed stress, σx’, is perpendicular to the appropriate crack interface (related to the shear stress direction on crack growth plane) at each loading state considered. comparisons with experimental results egardless of how well a model qualitatively agrees with experimental observations, its real value comes from the ability to predict crack growth behavior in a quantitative manner. the following section will evaluate the proposed model’s ability to do so by analyzing the experimental data presented earlier. correlations will be made concerning both crack branching and crack growth rate. due to time constraints, however, the analysis presented in this section is only applied to situations involving fully-reversed pure torsion loadings. the effectiveness of the model when applied to situations involving static axial stresses or mixed-mode loadings will be evaluated in a future study. the first step in analyzing the experimental data was to gather the relevant material parameters for the proposed model. the average undeformed crack face asperity angle was measured from the surface crack replicas of several specimens when crack lengths, 2c, were less than 1 mm. fifteen measured values ranged from 16° to 60° with an average of 36° and standard deviation of 14°. a value for sliding coefficient of friction under ideal conditions could not be found and was instead estimated as being 0.67 times the average reported static values for aluminum on aluminum contact, i.e. 0.67(1.2) r n.r. gates et alii, frattura ed integrità strutturale, 34 (2015) 27-41; doi: 10.3221/igf-esis.34.03 38 = 0.8. the parameter, β, in eq. (3), was assumed to be 4 loosely based on data and trends reported in ref. [24]. this predicts that the frictional attenuation due to crack face interference disappears after the nominal sif exceeds one quarter of the value of the material’s plane-strain fracture toughness. the value for latter was considered to be 34 mpa(m) [26] and an average grain size of 0.075 mm was used based on data reported in ref. [27] for 2024-t3 aluminum alloy. to compute nominal and effective sif values, the ideal mode ii crack geometry was considered to be a semi-elliptic surface crack in a finite thickness plate growing with a constant aspect ratio (a/c) of 0.5. this aspect ratio corresponds to a condition where the mode ii sif at the specimen surface is approximately equal to the mode iii sif at the crack’s maximum depth, a, [28]. therefore, an ideal crack growing in shear-mode would be expected to maintain this aspect ratio throughout its growth life. this agrees well with the experimental crack shape data presented in ref. [29] for pure torsion loading of inconel 718. with this aspect ratio, cracks do not become through thickness for any of the lefm applicable crack lengths considered in this analysis. appropriate geometry factor functions were obtained through the fitting of linear fea results, derived using the xfem crack technique in abaqus/cae 6.11-1, for several crack lengths. with all of the model inputs known, calculations for effective mode ii sif were carried out using the previously described procedure. since the loading considered was fully reversed, sif values were only calculated at the maximum applied loading and were doubled to obtain the effective mode ii sif range. fig. 7 shows crack growth rate versus both the nominally applied and effective mode ii sifs calculated for all available lefm applicable pure torsion crack growth data. growth rates were computed using a three point polynomial reduction technique. it can be seen from the figure that the model predicts a significant effect from frictional attenuation on the effective sif values while at the same time improving correlation between the various loading levels. the effective sif decreases by around a factor of 3 at the lower crack growth rates and begin to merge with the nominal values at around 10-7 m/cycle. reductions in effective sif of a similar order were measured experimentally in refs. [20, 30]. figure 7: experimentally measured lefm applicable crack growth rates vs. nominal and effective mode ii sif for fully-reversed torsion tests. another application of the proposed model is in predicting whether or not crack branching will occur for a given loading condition. in order to do this, the effective mode ii sif value must be compared to a crack branching criterion. for this analysis, a maximum growth rate criterion was considered and was evaluated at the outer surface location of the specimen where the growth is pure mode ii. since reliable data on crack growth kinetics (in the absence of closure effects) were not readily available for the tested material, an equivalent sif formulation was used as the basis to compare crack growth potential for each mode. equivalent sif was computed using eq. (4), which is based on the summation of energy release rates due to each crack extension mode: n.r. gates et alii, frattura ed integrità strutturale, 34 (2015) 27-41; doi: 10.3221/igf-esis.34.03 39 2 iii 2 ii 2 iq k1kkk  )(  (4) according to this equation, mode i and mode ii sifs have the same contribution to the equivalent sif value. therefore, for this analysis, whichever loading mode produced the highest sif was considered the preferred crack growth mode. mode i sif values were based on the normal stress component, as calculated from the nominally applied stresses, acting on the maximum principal stress plane at the location of the crack. to account for differences in effective crack length due to plane orientation, the overall crack length was projected onto the maximum principal plane prior to calculating the mode i sif. only the tensile portion of the normal stress cycle was considered for the calculation of sif range, as the crack is assumed to be closed under compression. the mode i geometry factor function was obtained using the same crack geometry and procedures described for mode ii. although there is likely some degree of error in these calculations due to the difference in profile between the projected crack and an ideal mode i crack, this effect has not yet been evaluated. fig. 8 shows analysis results for the four different lefm applicable pure torsion loading levels applied in the experimental program. each plot shows the effective mode ii sif range, computed using the proposed model, along with the mode i potential sif range versus half crack length. the effective asperity angle is also plotted for reference. the vertical dotted lines on each plot enclose the regions of experimentally observed mode i growth for each loading level and experimental mode ii growth regions are highlighted in red. by studying this figure, it can be seen that this type of analysis is able to reflect the trend observed in fig. 3 of an increase in initial mode ii crack length before branching with increasing loading level. additionally, the predicted crack length at this transition is within a factor of 2.5 of the experimentally measured value for all loadings cases considered. it is also worth noting that a further increase in applied loading would have resulted in the correct prediction of a non-branching crack condition and that a transition back to shear-mode growth after a period of mode i growth, which was observed in experiments, was predicted by the analysis. although in the latter case, quantitative results can vary due to the potential for a mode i branch to cause significant deviation from the idealized mode ii path assumed by the model. fig. 9 shows a fairly reasonable agreement between the experimental and predicted crack paths for the fatigue tests represented in fig. 8(a) and 8(c). figure 8: effective mode ii sif, local mode i sif, and effective coefficient of friction vs. crack length for fully-reversed pure torsion loadings of (a) 140 mpa, (b) 150 mpa, (c) 168 mpa, and (d) 188 mpa. all results represent lefm applicable regions of crack growth. mode i mode i (b)(a) τa = 140 mpa τa = 150 mpa τa = 168 mpa τa = 188 mpa mode i mode i (c) (d) n.r. gates et alii, frattura ed integrità strutturale, 34 (2015) 27-41; doi: 10.3221/igf-esis.34.03 40 figure 9: experimental vs. predicted crack path based on maximum growth rate criterion and proposed crack friction model. these initial results are promising because they demonstrate the ability of the proposed model to predict experimentally observed trends in shear-mode crack growth. however, because this model is new, further investigation is needed to determine its robustness and general applicability. future application to the torsion with static axial and in-phase axialtorsion data presented in this study will provide a means for some of this verification, but additional analyses for different materials and loading conditions would be necessary as well. in addition, a preliminary analysis of the sensitivity of the model to the various input parameters indicates a fairly strong dependence on the β value, a more moderate dependence on coefficient of friction and asperity angle, and a smaller effect of the average grain size only at shorter crack lengths. a more in depth sensitivity study should be performed as well to help quantify these effects. conclusions espite the significance of shear-mode crack growth mechanisms and crack branching phenomena in practical applications, relatively little research is available regarding these topics. of the studies that have been performed, few provide a means of quantifying such effects and even fewer consider the natural initiation of fatigue cracks in smooth specimens. the current study was aimed at trying to fill some of the research voids in these areas. based on the experimental results and analysis presented herein, the following conclusions can be drawn: 1. microcrack networks and coalescence do not appear to have an effect on the experimentally observed crack paths for the smooth specimen fatigue tests performed in this study, regardless of the applied loading level. 2. the preferred crack growth mode is shown to have a dependence on the applied shear stress magnitude as well as the stress normal to the crack plane. this indicates that fiction and roughness induced crack closure effects play a significant role in the shear-mode crack growth process. 3. an increase in initial mode ii crack length before branching is observed with an increase in pure torsion loading level. this indicates that the mode ii driving force increases at a higher rate than the attenuation effect due to crack face interaction, which eventually leads to a non-branching condition. 4. a simple model is proposed in an attempt to quantify the complex phenomena involved in crack growth attenuation due to friction and roughness induced closure effects. the model is based on the idea that crack face interaction reduces the effective mode ii sif by allowing a portion of the nominally applied loading to be transferred through a crack interface. resulting crack path predictions are shown to agree relatively well, both qualitatively and quantitatively, with experimentally observed trends for pure torsion loading. although the model shows promise for application to more complex loading conditions, more analysis is needed for such cases to verify its robustness. references [1] carpinteri, a., pook, l. p., susmel, l., vantadori, s., fatigue crack paths 2012, int. j. fatigue, 58 (2014) 1. [2] fatemi, a., gates, n. r., socie, d. f., phan, n., fatigue crack growth behaviour of tubular aluminum specimens with a circular hole under axial and torsion loadings, eng. fract. mech., 123 (2014) 137–147. d n.r. gates et alii, frattura ed integrità strutturale, 34 (2015) 27-41; doi: 10.3221/igf-esis.34.03 41 [3] tanaka, k., small fatigue crack propagation in notched components under combined torsional and axial loading, procedia eng., 2 (2010) 27–46. [4] zhang, h., fatemi, a., short fatigue crack growth behaviour under mixed-mode loading, int. j. fract., 165 (2010) 1– 19. [5] qian, j., fatemi, a., fatigue crack growth under mixed-mode i and ii loading, fatigue fract. eng. mater. struct., 19:1 (1996) 1277–1284. [6] socie, d. f., marquis, g. b., multiaxial fatigue, society of automotive engineers, inc., warrendale, pa, (2000). [7] murakami, y., takahashi, k., kusumoto, r., threshold and growth mechanism of fatigue cracks under mode ii and iii loadings, fatigue fract. eng. mater. struct., 26 (2003) 523–531. [8] doquet, v., bertolino, g., local approach to fatigue cracks bifurcation, int. j. fatigue, 30 (2008) 942–950. [9] tanaka, k., small crack propagation in multiaxial notch fatigue, proceedings of the 4th international conference on crack paths (cp 2012), gaeta, italy, (2012) 31–45. [10] pokluda, j., pippan, r., vojtek, t., hohenwarter, a., near-threshold behaviour of shear-mode fatigue cracks in metallic materials, fatigue fract. eng. mater. struct., 37 (2014) 232–254. [11] tschegg, e. k., mode iii and mode i fatigue crack propagation behaviour under torsion loading, j. mater. sci., 18 (1983) 1604–1614. [12] shamsaei, n., fatemi, a., small fatigue crack growth under multiaxial stresses, int. j. fatigue, 58 (2014) 126–135. [13] marco, s. m., starkey, w. l., a concept of fatigue damage, trans. asme, 76 (1954) 627–632. [14] qian, j., fatemi, a., mixed mode fatigue crack growth: a literature survey, eng. fract. mech., 55 (1996) 969–990. [15] erdogan, f., sih, g. c., on the crack extension in plates under plane loading and transverse shear, asme j. basic eng., 85 (1963) 519–525. [16] tanaka, k., fatigue crack propagation from a crack inclined to the cyclic tensile axis, eng. fract. mech., 6 (1974) 493–507. [17] murakami, y., takahashi, k., torsional fatigue of a medium carbon steel containing an initial small surface crack introduced by tension-compression fatigue: crack branching, non-propagation and fatigue limit, fatigue fract. eng. mater. struct., 21 (1998) 1473–1484. [18] makabe, c., socie, d. f., crack growth mechanism in precracked torsional fatigue specimens, fatigue fract. eng. mater. struct., 24 (2001) 607–615. [19] tong, j., yates, r., brown, m. w., a model for sliding mode crack closure part i: theory for pure mode ii loading, eng. fract. mech., 52:4 (1995) 599–611. [20] tong, j., yates, r., brown, m. w., a model for sliding mode crack closure part ii: mixed mode i and ii loading and application, eng. fract. mech., 52:4 (1995) 613–623. [21] künkler, b., düber, o., köster, p., krupp, u., fritzen, c.-p., christ, h.-j., modelling of short crack propagation transition from stage i to stage ii, eng. fract. mech., 75 (2008) 715–725. [22] astm standard e 2207-08: standard practice for strain-controlled axial-torsional fatigue testing with thinwalled tubular specimens, in: bailey, s. j., baldini, n. c. (eds.), annual book of astm standards, vol. 03.01, astm international, west conshohocken, (2009) 1258–1265. [23] astm standard e 1012-05: standard practice for verification of test frame and specimen alignment under tensile and compressive axial force application, in: bailey, s. j., baldini, n. c. (eds.), annual book of astm standards, vol. 03.01, astm international, west conshohocken, pa, (2009) 797–807. [24] oberg, e., jones, f. d., horton, h. l., ryffel, h. h., machinery’s handbook, twenty-sixth ed., industrial press inc., new york, (2000). [25] doquet, v., bertolino, g., a material and environment-dependent criterion for the prediction of fatigue crack paths in metallic structures, eng. fract. mech., 75 (2008) 3399–3412. [26] military handbook: metallic materials and elements for aerospace vehicle structures: mil-hdbk-5h, united states department of defense, (1998). [27] merati, a., a study of nucleation and fatigue behavior of an aerospace aluminum alloy 2024-t3, int. j. fatigue, 27 (2005) 33–44. [28] murakami, y., fukushima, y., toyama, k., matsuoka, s., fatigue crack path and threshold in mode ii and mode iii loadings, eng. fract. mech., 75 (2008) 306–318. [29] beer, t., crack shapes during biaxial fatigue, report no. 106, university of illinois at urbana-champaign, urbana, il, (1984). [30] vaziri, a., nayeb-hashemi, h., the effect of crack surface interaction on the stress intensity factor in mode iii crack growth in round shafts, eng. fract. mech., 72 (2005) 617–629. << /ascii85encodepages false /allowtransparency false /autopositionepsfiles true /autorotatepages /none /binding /left /calgrayprofile (dot gain 20%) /calrgbprofile (srgb iec61966-2.1) /calcmykprofile (u.s. web coated \050swop\051 v2) /srgbprofile (srgb iec61966-2.1) /cannotembedfontpolicy /error /compatibilitylevel 1.4 /compressobjects /tags /compresspages true /convertimagestoindexed true /passthroughjpegimages true /createjobticket false /defaultrenderingintent /default /detectblends true /detectcurves 0.0000 /colorconversionstrategy /cmyk /dothumbnails false /embedallfonts true /embedopentype false /parseiccprofilesincomments true /embedjoboptions true /dscreportinglevel 0 /emitdscwarnings false /endpage -1 /imagememory 1048576 /lockdistillerparams false /maxsubsetpct 100 /optimize true /opm 1 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can be opened with acrobat and adobe reader 5.0 and later.) >> /namespace [ (adobe) (common) (1.0) ] /othernamespaces [ << /asreaderspreads false /cropimagestoframes true /errorcontrol /warnandcontinue /flattenerignorespreadoverrides false /includeguidesgrids false /includenonprinting false /includeslug false /namespace [ (adobe) (indesign) (4.0) ] /omitplacedbitmaps false /omitplacedeps false /omitplacedpdf false /simulateoverprint /legacy >> << /addbleedmarks false /addcolorbars false /addcropmarks false /addpageinfo false /addregmarks false /convertcolors /converttocmyk /destinationprofilename () /destinationprofileselector /documentcmyk /downsample16bitimages true /flattenerpreset << /presetselector /mediumresolution >> /formelements false /generatestructure false /includebookmarks false /includehyperlinks false /includeinteractive false /includelayers false /includeprofiles false /multimediahandling /useobjectsettings /namespace [ (adobe) (creativesuite) (2.0) ] /pdfxoutputintentprofileselector /documentcmyk /preserveediting true /untaggedcmykhandling /leaveuntagged /untaggedrgbhandling /usedocumentprofile /usedocumentbleed false >> ] >> setdistillerparams << /hwresolution [2400 2400] /pagesize [612.000 792.000] >> setpagedevice microsoft word numero_49_art_61_2484 l. restuccia, frattura ed integrità strutturale, 49 (2019) 676-689; doi: 10.3221/igf-esis.49.61 676 fracture properties of green mortars with recycled sand luciana restuccia politecnico di torino, turin, italy luciana.restuccia@polito.it, https://orcid.org/0000-0002-6999-0466 abstract. urbanisation is consuming huge amounts of sand, being the basic element of concrete and glass, two of the most popular construction materials. unfortunately, sand mining is causing environmental damage and drastically reducing the amount of raw resources. the main topic of this research is to investigate the use of construction and demolition waste finer fraction namely recycled sand to totally replace the standard one into traditional mortars. from the analysis of the mechanical characterization of specimens, it is possible to state that recycled sand could represent a new resource for green and sustainable mortars. keywords. mortar; superplasticizer; recycled sand; cdw; fracture properties. citation: restuccia, l., fracture properties of green mortars with recycled sand, frattura ed integrità strutturale, 49 (2019) 676-689. received: 15.04.2019 accepted: 31.05.2019 published: 01.07.2019 copyright: © 2019 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. introduction ggregates like sand and gravel represent the largest volume of solid material globally extracted. the amount of their use is constantly increasing, due to the global economic growth: every year, between 47 and 59 billion tons of aggregates is mined [1], since they are used in a wide range of sectors. however, their largest use is in construction sector, because they are the main elements for the concrete production: for each ton of cement, building industry needs about six to seven times more tons of sand and gravel [2]. the problem becomes even environmental: 1 kg of cement produced gives an equivalent of 0.9 carbon dioxide tons in atmosphere. there are some ways for reducing the extraction and the consumption of sand, for example by including quarry dust [3-5] or fly ash [6,7] in substitution of sand. furthermore, materials by cdw could be used to avoid the use of aggregates. nowadays, however, the major cdw use is for road construction (unbound sub-base and base layers, bituminous surface pavements), due to their uncertain quality [8]. moreover, as regard to the fine fraction (sand), the general opinion is that it has limited application due to its negative effect on concrete properties [9]. in fact, the fine fraction of cdw strongly influence the rheological properties and workability of concretes [10], for its intrinsic properties and amount. dapena et al. [11] studied the mechanical behaviour of mortars by using recycled sand (rs) contents of 0%, 5%, 10%, 15%, 20% and 50% by weight. the results showed that the use of up to 20% recycled aggregates caused a drop in the compressive and flexural strength. braga et al. [12] showed that it is feasible to use up to 15% of fine concrete recycled aggregates (maximum amount tested) in mortar production. in fact, this percentage caused an improvement in the reference mortar properties. zhao [13] analysed the influence of recycled sand saturation state on mortar properties, then evaluated a http://www.gruppofrattura.it/va/49/2484.mp4 l. restuccia, frattura ed integrità strutturale, 49 (2019) 676-689; doi: 10.3221/igf-esis.49.61 677 the influence of either replacement percentage or replacement fraction of natural sand by recycled sand, by volume (slump, compressive and flexural strength, itz microstructure). the results showed that the slump of mortars containing dried recycled sand is always larger than the one of the mortars with saturated one (pre-saturated 24h before the mix), because water is not immediately adsorbed into the cement paste at the initial time [13]. moreover, results also showed that the compressive strength of mortars with recycled sand is always lower than the reference mortar, with a quasi-linear decrease as the replacement percentage of recycled sand increases [13]. two parameters to be taken into account for the realisation of construction materials with fine recycled sand are the amount of fine content, which influence its workability, water absorption and shrinkage [14-16] and the amount of superplasticizer, which prevents the flocculation of cement particles when recycled aggregates are used [17]. miranda and selmo [18] analysed the effect of materials finer than 75 m on mortar properties and they found that the distribution of the pore sizes generated by the presence of fines in the mixtures had a higher effect on drying shrinkage than those of the porosity introduced by the effective water/cement ratio itself. bravo et al. [19] studied the superplasticizer efficiency on the mechanical properties of recycled aggregates concrete founding that incorporation of 1% of polycarboxylic-based superplasticizers has been beneficial in all percentages used, but the extent of its effect was dependent on the aggregate composition. cartuxo et al. [20] studied the rheological behaviour of concrete made with fine recycled concrete aggregates founding that the addition of high-performance superplasticizers (a fixed proportion of 1% of cement mass was used) can offset the negative effects of fine recycled aggregates concrete introduction in mixtures. the fine fraction of cdw can be used like a filler to produce engineered cement composites [21] or for preparing self-compacting concrete mixes, but 20% is the maximum replacement level [22] while its use only as a replacement of standard sand is almost impossible. therefore, the objective of this study is the utilisation of fine cdw (also called recycled sand) to reproduce the granulometric distribution of the standard one, to completely replace it in traditional mortar. the authors, in their first investigation about recycled sand in mortars [23], have analysed its effect in different compositions without additions of superplasticizer. as expected, the large water demand has been the main problem and it has not been possible to replace over 50% of standard sand. for this reason, superplasticizer has been used to obtain a workable mixture: it was added with respect to the weight of cement, nevertheless the problem of workability has not been resolved. on the contrary, the authors achieved quite satisfactory results through the recycled sand washing process, which allows the elimination of finer particles of poor quality, by using water and sieves, limiting the problem of water absorption [24]. another important result obtained was related to the percentage of superplasticizer, added on the basis of the weight of the recycled sand (the quantity usually varies according to the weight of the cement): this solution was suitable to go beyond the complexity of the exact prediction of required w/c ratio for attaining the desirable mechanical performances. in this research paper, the prosecution of the previous research [24] has been carried out: the percentages of substitution reach up to 100% to promote the sustainable use of recycled sand into traditional mortars. moreover, the recycled sandbased composites have been characterized not only from a mechanical point of view, but they were also analysed considering the fracture behaviour and the variation in the phase compositions via x-ray diffraction analysis. material and methods materials and specimen’s preparation n this work, recycled sand provided by cavit s.p.a. has been used (fig. 1). it is characterized by particle size less than 8mm, with a plasticity index and a liquid limit equal to 0.9 and 26.4 respectively (atterberg limits). in the declaration of conformity of this product (ce marking) drawn up by the cavit s.p.a., according to uni en 13242:2013 “aggregates for unbound and hydraulically bound materials for use in civil engineering work and road construction”, the parameters are indicated in tab. 1 below: density of particle 2.5 mg/m3 fine granular content fine granular quality water absorption se≥ 28 mb 1.25 4 ≤ wa24 ≤ 6 table 1: “recycled 0-8” (uni en 13242). i l. restuccia, frattura ed integrità strutturale, 49 (2019) 676-689; doi: 10.3221/igf-esis.49.61 678 figure 1: cdw waste treatment plant, cavit s.p.a., la loggiaturin. the determination of particle size distribution of ss and rsw has been realized through dry sieve, according to uni en 933-1 (fig. 2). figure 2: particle size distribution of standard sand (ss) and recycled washed sand (rsw). the retained rsw residue at each sieve (0.08; 0.16; 0.50; 1.00 and 1.60 mm) has been analysed by means of x-ray diffraction (xrd). this kind of analysis, even if does not provide direct information on the sample chemical composition, allows defining and quantifying the crystalline phases present in the first 20 m of the sample surface. xrd patterns has been recorded with a pan analytical x’pert pro diffractometer, between 5° and 70° in 2θ, with a step width of 0.026° and 1 s data collection per step (cukα radiation and graphite secondary monochrome). moreover, a surface morphology study by fesem zeiss supra-40 (field emission scanning electron microscopy) has been carried out to identify the microstructure and the particle size of rsw grains. mortars with standard sand have been prepared as references and, according to the previous studies [24], experimental recycled mortars have been casted by using recycled washed sand (rsw), as washing process helps to eliminate the finer particles that affect workability and water absorption. 0 5 10 15 20 25 30 35 0 1 2 3 4 5 6 7 8 r et ai n ed [ % ] sieve size [mm] standard sand ss recycled sand rsw l. restuccia, frattura ed integrità strutturale, 49 (2019) 676-689; doi: 10.3221/igf-esis.49.61 679 sand packets have been realized through remixing of each granular fraction of standard sand ss with the corresponding granular fraction of recycled washed sand rsw, using four different percentages (25%, 50%, 75% and 100%) of replacement. in tab. 3, the four different mix compositions with the specific amounts of both of them are reported: square mesh size [mm] cumulative retained [%] retained [%] retained mass [g] 2.00 0 0 0 1.60 7 7 94.5 1.00 33 26 351 0.50 67 34 459 0.16 87 20 270 0.08 99 12 162 filler 100 1 13.5 table 2: cen standard sand – granular fractions. size 25% 50% 75% 100% ss rsw ss rsw ss rsw ss rsw [mm] [g] [g] [g] [g] [g] [g] [g] [g] 1.60 70.9 23.6 47.25 47.25 23.6 70.9 0 94.5 1.00 263.3 87.8 175.5 175.5 87.8 263.3 0 351 0.50 344.25 114.75 229.5 229.5 114.75 344.25 0 459 0.16 202.5 67.5 135 135 67.5 202.5 0 270 0.08 121.5 40.5 81 81 40.5 121.5 0 162 < 0.08 10.1 3.4 6.8 6.8 3.4 10.1 0 13.5 table 3: mix compositions of sand packets with recycled washed sand rsw. the specimens have been manufactured in accordance with uni en 196-1:2005 (standard procedure). after 24 hours from the moulding procedure, all the specimens have been cured in water for 7 days. in tab. 4, the main characteristics of the specimen series produced are reported. it is important to underline that, after washing process, it was very hard to collect a sufficient quantity of < 0.08 mm fraction. for this reason, a calcium carbonate filler named vg1 has been used for replacing the filler fraction (in total 13.5 g as shown in tab. 2); this substitution does not involve any substantial change, as it only accounts for 1% of the total amount of sand used. in order to achieve an optimal mix-design, two parameters have been modulated: the amount of superplasticizer (sp1, acrylic polymer of mapei dynamon sp system) and water/cement ratio. in tab. 4, the mix-design summary for each composition: the strategy adopted is to gradually decrease both the amount of superplasticizer and the water/cement ratio, in order to obtain mortars with better mechanical performances. it is important to specify that for only standard sand mortar (m-ss), the sp1 has been added with respect to the weight of cement, while for the other compositions it has been varied according to the quantity of recycled washed sand rsw. l. restuccia, frattura ed integrità strutturale, 49 (2019) 676-689; doi: 10.3221/igf-esis.49.61 680 #series id specimen w/c [-] cement [g] water [g] composition sand [g] sp1 [%] sp1 [g] vg1 [g] ss rsw 1 m-ss 0.5 450 225 1350 0 0 0 0 m-rsw_25% 0.5 450 225 1002.4 334.1 1* 3.34* 13.5 m-rsw_50% 0.5 450 225 668.2 668.2 1* 6.68* 13.5 m-rsw_75% 0.5 450 225 334.1 1002.4 1* 10.24* 13.5 m-rsw_100% 0.5 450 225 0 1336.5 1* 13.36* 13.5 2 m-ss 0.5 450 225 1350 0 0 0 0 m-rsw_25% 0.5 450 225 1002.4 334.1 0.75* 2.50* 13.5 m-rsw_50% 0.5 450 225 668.2 668.2 0.75* 5.02* 13.5 m-rsw_75% 0.5 450 225 334.1 1002.4 0.75* 7.51* 13.5 m-rsw_100% 0.5 450 225 0 1336.5 0.75* 10.02* 13.5 3 m-ss 0.45 450 202.5 1350 0 1 4.50 0 m-rsw_25% 0.45 450 202.5 1002.4 334.1 1* 3.34* 13.5 m-rsw_50% 0.45 450 202.5 668.2 668.2 1* 6.68* 13.5 m-rsw_75% 0.45 450 202.5 334.1 1002.4 1* 10.24* 13.5 m-rsw_100% 0.45 450 202.5 0 1336.5 1* 13.36* 13.5 4 m-ss 0.40 450 180 1350 0 1 4.50 0 m-rsw_100% 0.40 450 180 0 1336.5 1* 13.36* 13.5 *= % added with respect to rsw weight for each composition table 4: series of experimental mortars. id specimen rsw [g] sp1 – 0.75% [g] sp1 1% [g] m-rsw_25% 334.1 2.50 3.34 m-rsw_50% 668.2 5.02 6.68 m-rsw_75% 1002.4 7.51 10.24 m-rsw_100% 1336.5 10.02 13.36 table 5: mix-design of superplasticizer for each composition. theory and test methods he classical linear elastic fracture mechanics (lefm) theory is inadequate for cement-based materials [25], due to the development of a relatively large fracture process zone (fpz), which undergoes progressive softening damage due to mechanisms such as micro-cracking, crack branching, crack-deviation. one method developed to account for the fpz in cement-based materials is the two-parameters fracture method [26], used in this research to understand the fracture process of mortars. the experimental determination of the young’s modulus e, the fracture toughness kic and the fracture energy gf has been carried out by the evaluation of load-cmod curve for each specimen, during the threepoint bending tests, as indicated in rilem tc 89fmt methods [27]. the young’s modulus e for the different mixes has been calculated by the following equation:  0 1 2 2 6             i la v e n m c d b      (1) in which ci is the initial compliance of the load-cmod curve [m n-1] and v1(α) is equal to: t l. restuccia, frattura ed integrità strutturale, 49 (2019) 676-689; doi: 10.3221/igf-esis.49.61 681     2 3 1 2 0.66 0.76 2.28  3.87 2.04 1 v            (2) where α= (a0 + ho)/(d + ho), and l, a0, ho, d and b are those indicated in fig. 3: figure 3: testing configuration and geometry of specimen [27]. the critical stress intensity factor, kic, represents the resistance opposed by the material for a crack extension in plane strain condition for stress state near the crack tip, with limited plastic deformation. in case of mode i, the stress intensity factor kic can be expressed as:   3 2 2 3( 0.5 )                           2 max ic p w l a k f n m d b           (3) where:         2 3 2 1.99 1 2.15 3.93 2.7 1 2 1 3 f                (4) and α = a/d, pmax = maximum load [n], l, d and b are the span, depth and width, respectively [27]. after the determination of kic, the fracture energy, gf, has been evaluated according rilem tc50-fmc [21] as: 0 0                         f lig w mg n g a m       (5) figure 4: set up and test of experimental mortars: three-point bending test. l. restuccia, frattura ed integrità strutturale, 49 (2019) 676-689; doi: 10.3221/igf-esis.49.61 682 to evaluate the fracture properties for the different mixes, standard three-point bending (tpb) tests have been performed according to rilem recommendations [27,28]. the specimens had dimension of 160x40x40 mm, with a span/depth ratio equal to 4 and a notch/depth ratio equal to 1/3. a single column displacement-controlled testing machine zwick line-z050, with load cell of 50 kn was used with a crosshead speed of 0.01 mm/min. crack mouth opening displacement (cmod) has been controlled by using a clip-ongauge, placed across the notch and held in position by two steel knife-edges glued to the specimen (fig. 4). after flexural testing, each halves of the broken prism have been subjected to compression test by using an mts servohydraulic machine (a modified zwick machine), by loading its side faces through auxiliary plates of tungsten carbide of thickness 10 mm and surface (40 x 40 mm). the tests have been performed with 0.05 mm/s test speed (fig. 5). figure 5: set up and test of experimental mortars: compression test. results and discussion results by xrd and fesem analysis rd patterns of rsw showed the presence in all the samples of calcite (jcpds card #05-0586) and quartz (jcpds card #46-1045) as major constituents. paragonite (a sodium aluminum silicate hydroxide, jcpds card #24-1047), phlogopite (a potassium magnesium aluminum silicate hydroxide, jcpds card #10-0493) and clinochlore (a magnesium aluminum iron silicate hydroxide, jcpds card #07-0078) were secondary phases. gismondine (a calcium aluminum silicate hydrate, jcpds card n°39-1373), probably due to hydrated cement residues, was found as traces (fig. 6). paragonite and clinochlore came from the aggregate fraction of former concrete, while calcite could have different origins: from aggregates, as cement filler, and from concrete degradation process (carbonation). field emission scanning electron microscopy analysis (fesem) were carried out for observing the shape of different fraction and for evaluating the capability of these recycled washed grains to ensure a good adherence to the cement paste. generally, it seems that the smaller fraction has a sharpener shape (0.08 and 0.16 mm), which could ensure a better adhesion with the cement matrix (fig. 7). the larger grains (≥ 1.00 mm) instead have a more rounded form (fig. 8). x l. restuccia, frattura ed integrità strutturale, 49 (2019) 676-689; doi: 10.3221/igf-esis.49.61 683 figure 6: s results of xrd analysis for all the retained fraction of recycled washed sand. figure 7: particular of a grain of 0.16 mm of rsw. figure 8: particular of a grain of 1.00 mm of rsw. c=calcite, cl=clinochlore, pa=paragonite, p=phlogopite, q= quartz l. restuccia, frattura ed integrità strutturale, 49 (2019) 676-689; doi: 10.3221/igf-esis.49.61 684 results of mechanical tests the mechanical experimental results showed very interesting indications, as sign that recycled washed sand rsw could be used as replacement of standard sand ss in mortar. the results of series 1, series 2 and series 3 are reported in tabs. 6-8. each batch is composed of three specimens and the results correspond to the mean values ± standard deviation. id batch pmax e kic gf σf σc [n] [gpa] [mpa√m] [n/m] [mpa] [mpa] m-ss 871.48±33.59 5.72±0.71 3.53±0.73 5.62±8.91 6.67±0.26 59.16±0.79 m-rsw_25% 529.31±20.77 3.67±1.49 3.05±1.20 4.06±9.77 4.05±0.16 32.61±0.98 m-rsw_50% 685.54±24.99 4.43±1.53 3.90±1.31 5.70±11.16 5.25±0.19 40.10±0.29 m-rsw_75% 820.71±75.25 5.19±6.95 3.66±3.58 6.38±8.81 6.28±0.58 56.49±2.10 m-rsw_100% 871.41±13.33 4.70±2.55 4.05±3.97 7.46±11.05 6.67±0.10 56.20±1.37 table 6: mechanical and fracture results, series 1 (w/c = 0.5; 1.00 % sp1). id batch pmax e kic gf σf σc [n] [gpa] [mpa√m] [n/m] [mpa] [mpa] m-ss 871.48±33.59 5.72±0.73 3.53±0.73 5.62±8.91 6.67±0.26 59.16±0.79 m-rsw_25% 551.81±33.85 3.92±1.71 3.25±1.72 4.03±6.65 4.22±0.26 34.79±0.57 m-rsw_50% 611.54±15.72 4.10±2.94 3.54±7.57 4.83±4.81 4.68±0.12 38.50±0.19 m-rsw_75% 684.99±49.19 4.07±2.41 3.68±1.92 5.94±5.21 5.24±0.32 46.23±0.68 m-rsw_100% 816.37±22.20 4.13±2.91 4.06±1.22 7.03±2.02 6.25±0.17 50.20±1.39 table 7: mechanical and fracture results, series 2 (w/c = 0.5; 0.75 % sp1). id batch pmax e kic gf σf σc [n] [gpa] [mpa√m] [n/m] [mpa] [mpa] m-ss 895.79±50.21 6.46±2.08 3.77±1.59 7.32±3.05 6.86±0.38 55.00±2.19 m-rsw_25% 653.00±15.98 4.52±1.63 3.73±1.31 5.02±2.69 5.00±0.12 38.14±0.43 m-rsw_50% 685.83±15.00 4.25±1.44 3.99±1.40 5.77±5.34 5.25±0.11 38.33±0.50 m-rsw_75% 881.68±62.57 5.02±1.86 4.31±3.41 7.12±1.23 6.75±0.48 55.98±0.88 m-rsw_100% 893.78±30.17 4.84±3.41 4.22±1.91 7.58±4.79 6.84±0.23 56.31±2.97 table 8: mechanical and fracture results, series 3 (w/c = 0.45; 1.00 % sp1). according to tabs. 6-8, it is evident that the greater is the percentage of rsw in mortars, the greater are mechanical performances, with very similar values to those of traditional ones. this can be explained by the fesem results: the particles of rsw appear highly irregular and indented, while those of standard sand by definition “are generally isometric and rounded in shape" [29]. therefore, in compositions with higher percentages of rsw, it is possible to hypothesize more non-homogeneity grains, which surely increase the ability to create a strong bond with the matrix. furthermore, the washing process allows removing the fine powders (< 0.08 mm) and l. restuccia, frattura ed integrità strutturale, 49 (2019) 676-689; doi: 10.3221/igf-esis.49.61 685 impurities, reducing the higher absorption rate of recycled sand that influences workability of fresh state and mechanical properties of hardened state [30]. the second observation is that decreasing the amount of superplasticizer (series 2), the results undergo a decrease for all the percentages. in fact, with the sp1 percentage of 0.75% there is a great decrease in terms of mechanical results between the series 1 and the series 2: this indicates that, fixed the w/c ratio, the correct amount of superplasticizer to use is equal to 1%. the drop both in mechanical and fracture parameters can be related to the lack of cement grain and recycled washed sand dispersion because of the fewer amount of sp1. by the series 3 analysis, it is not surprising to find an improvement for all the compositions: the superplasticizer was brought back to optimum condition (1%) and the w/c ratio has been decreased (from 0.50 to 0.45), which have great influence on workability and hardened properties of mortars [31]. in figs. 9-11 are reported the load-cmod curves, obtained by tpb tests for mortars with ss and mortars with rsw, for each series considered. from the observation of experimental curves, it is possible to note that mortars with recycled sand percentage replacement above 75% behave in a "more ductile" manner with respect to the standard mortar. this can be attributed to the presence of the superplasticizer, which counterbalances the detrimental effects associated with the use of recycled sand in compositions. as found in literature, if superplasticizer is used to reduce the w/c ratio, the fine recycled fraction can be as good as the conventional type [32]. for this reason, in series 3 (w/c = 0.45; 1.00 % sp1), the best results can be found. moreover, the improvement in ductility at 75% rsw might be linked to the increase in elongated grains of recycled sand replacing the more spherical standard sand grains in cementitious matrix. figure 9: load-cmod curves, series 1. figure 10: load-cmod curves, series 2. l. restuccia, frattura ed integrità strutturale, 49 (2019) 676-689; doi: 10.3221/igf-esis.49.61 686 figure 11: load-cmod curves, series 3. to produce completely recycled materials, series 4 has been done only for mortar with standard sand (m-ss) and for mortar with 100% of recycled sand (m-rsw 100%). in this case, the amount of sp1 has been maintained at 1% dose, while the w/c ratio has been lowered. in tab. 9 the results concerning the mechanical tests are reported. the improvement trend follows that of the previous series, as a sign that the increased presence of recycled sand grains can ensure a strong bond with the matrix: this might explain, in fact, the substantial increase in terms of fracture energy gf. table 9: mechanical and fracture results, series 4 (w/c = 0.40; 1.00 % sp1). figure 12: load-cmod curves, series 4. id batch pmax e kic gf σf σc [n] [gpa] [mpa√m] [n/m] [mpa] [mpa] m-ss 1021.14±53.22 6.02±3.98 4.79±3.52 6.40±3.41 7.81±0.41 45.88±2.30 m-rsw_100% 909.10±65.64 4.71±1.21 4.38±1.45 8.65±6.73 6.96±0.50 52.68±5.08 l. restuccia, frattura ed integrità strutturale, 49 (2019) 676-689; doi: 10.3221/igf-esis.49.61 687 in fig. 12, the curve load-cmod for two experimental specimens of the series 4 is shown, through which it is possible to explain the enhancement of fracture energy, by evaluating the ductility factor μ. ductility factor is defined as the ratio between the ultimate displacement δu and displacement corresponding to the peak load δp:  μ  δu /  δp (6) and, in this case, it is equal to 1.92 for m-ss (specimen#2) and 2.47 for m-rsw_100% (specimen#2). analysing the values of young’s modulus e reported in tab. 9 and observing fig. 12, a little change of slope of the first portion of the load cmod curves can be seen. in literature, the lowest young's modulus is attributed to the residues adhered of recycled aggregates [33], but probably in this case there is still a correlation with the amount of superplasticizer used. in fact, in the traditional mortar 4.5 g of sp1 have been used while 13.5 g in the mortar with 100%rsw (as reported in tab. 3). this lead to a difference in density of the two mixtures, which may explain the small decrease in the elastic modulus, according to mehta and monteiro [34]. conclusions n this research work, an investigation regarding the feasibility of replacing in traditional mortars the fine fraction of cdw waste has been conducted. this topic has still little relevance in scientific literature, as it is believed that the greater water absorption of recycled sand could compromise mechanical properties of both fresh and hardened states. the importance of this research lies in the fact that, through the washing process, it is possible to obtain suitable sand to be re-used in building materials. mechanical and fracture properties of mortars with rsw are extremely similar to those of traditional mortars, even exhibiting an improvement regarding fracture toughness and fracture energy. based on the test results, the main conclusions are as follows:  the higher the percentage of recycled washed sand in mortars, the higher mechanical performances. this is probably related to a huge presence of irregular and indented grains of recycled sand, which ensure a more cohesive bond with cement matrix;  the presence of the superplasticizer counterbalances the detrimental effects associated with the use of recycled sand. their joint use is a solution to offset the negative effects caused by recycled sand incorporation [19] and, if superplasticizer has being varied with respect to the weight of recycled sand for each composition, then the workability is ensured; this is a critical parameter for the performance of fresh and hardened states;  it is possible to evaluate not only the fineness of the recycled sand used in correlation with water requirement, but also the quality of the superplasticizer as parameters for the mix-design of the mixture [19-21].  although specific studies are required in order to obtain an optimal mix-design of mortars made with fine recycled sand, it can be stated that it is technically feasible to use it for mortar production, especially when powder of < 0.08 mm fraction is eliminated. abbreviations ss, standard sand; rs, recycled sand; sp, superplasticizer; rsw, recycled washed sand, cdw, construction and demolition waste; m-ss, mortar with standard sand; m-rsw, mortar with recycled washed sand; itz, interfacial transition zone. references [1] steinberger, j.k., krausmann, f. and eisenmenger, n. (2010). global patterns of materials use: a socioeconomic and geophysical analysis, ecological economics 69, pp. 1148-1158. doi: 10.1016/j.ecolecon.2009.12.009. i l. restuccia, frattura ed integrità strutturale, 49 (2019) 676-689; doi: 10.3221/igf-esis.49.61 688 [2] usgs (2013). cement, statistics and information. u.s. geological survey, reston. [3] gameiro, f., de brito, j. and correia da silva, d. (2014). durability performance of structural concrete containing fine aggregates from waste generated by marble quarrying industry, eng struct 59, pp. 654–662. doi: 10.1016/j.engstruct.2013.11.026. [4] galetakis, m., piperidi, c., vasiliou, a., alevizos, g., steiakakis, e., komnitsas k. and soultana, a. (2016). experimental investigation of the utilization of quarry dust for the production of microcement-based building elements by self-flowing molding casting, constr build mater 107, pp. 247-254. doi: 10.1016/j.conbuildmat.2016.01.014. [5] schankoski, r.a., pilar, r., prudêncio jr., l.r. and douglas ferron, r. (2017). evaluation of fresh cement pastes containing quarry by-product powders, constr build mater 133, pp. 234-242. doi: 10.1016/j.conbuildmat.2016.12.056. [6] bilir, t., gencel, o. and topcu, i. b. (2015). properties of mortars with fly ash as fine aggregate, constr build mater 93, pp. 782-789. doi: 10.1016/j.conbuildmat.2015.05.095. [7] thomas, j. and harilal, b. (2015). properties of cold bonded quarry dust coarse aggregates and its use in concrete, cem concr compos 62, pp. 67-75. doi: 10.1016/j.cemconcomp.2015.05.005. [8] cedr (2012). recycling: road construction in a post-fossil fuel society, transnational road research programme call; [9] westerholm, m., lagerblad, b., silfwerbrand, j. and forssberg, e. (2008). influence of fine aggregate characteristics on the rheological properties of mortars, cem concr compos 30, pp. 274-282. doi: 10.1016/j.cemconcomp.2007.08.008. [10] katz, a. and baum, h. (2006). effect of high levels of fines content on concrete properties, aci mater j 103, pp. 474482. [11] dapena, e., alaejos, p., lobet, a. and pérez, d. (2010). effect of recycled sand content on characteristics of mortars and concretes, j mater civil eng 23, pp. 414–422. doi: 10.1061/(asce)mt.1943-5533.0000183. [12] braga, m., de brito, j. and veiga, r. (2012). incorporation of fine concrete aggregates in mortars, constr build mater 36, pp. 960-968. doi: 10.1016/j.conbuildmat.2012.06.031. [13] zhao, z., remond, s., damidot, d. and xu, w. (2015). influence of fine recycled concrete aggregates on the properties of mortars, constr build mater 81, pp. 179-186. doi: 10.1016/j.conbuildmat.2015.02.037. [14] lahuerta, j.v. and monterde, g.j.c. (2012). estudio teorico y experimental sobre los morteros para muros resistentes de fabrica de ladrilho para la actualizacion de la norma basica mv 201-1972; 1 parte: memoria del estudio. materiales de construccion 34, pp. 33–41. doi: 10.3989/mc.1984.v34.i196.936. [15] le, t., rémond, s., le saout, g. and garcia-diaz, e. (2016). fresh behavior of mortar based on recycled sand – influence of moisture condition, constr build mater 106, pp. 35-42. doi: 10.1016/j.conbuildmat.2015.12.071. [16] li, l., zhan, b. j., lu, j. and sun poon, c. (2019). systematic evaluation of the effect of replacing river sand by different [17] particle size ranges of fine recycled concrete aggregates (frca) in cement mortars, constr build mater 209, pp. 147– 155. doi: 10.1016/j.conbuildmat.2019.03.044. [18] pacheco, j., de brito, j., ferreira, j. and soares, d. (2015). destructive horizontal load tests of full-scale recycled aggregate concrete structures, aci struct. j. 112 (6), pp. 815–826. doi: 10.14359/51687800. [19] miranda, l. and selmo, s. (2006). cdw recycled aggregate renderings: part i – analysis of the effect of materials finer than 75 m on mortar properties, constr build mater 20, pp. 615-624. doi: 10.1016/j.conbuildmat.2005.02.025. [20] bravo, m., de brito, j., evangelista, l. and pacheco, j. (2017). superplasticizer’s efficiency on the mechanical properties of recycled aggregates concrete: influence of recycled aggregates composition and incorporation ratio, constr build mater 153, pp. 129-138. doi: 10.1016/j.conbuildmat.2017.07.103. [21] cartuxo, f., de brito, j., evangelista, l., jiménez, j.r. and ledesma, e.f. (2015). rheological behaviour of concrete made with fine recycled concrete aggregates – influence of the superplasticizer, constr build mater 89, pp. 36-47. doi: 10.1016/j.conbuildmat.2015.03.119. [22] li, j. and yang, e-h. (2017). macroscopic and microstructural properties of engineered cementitious composites incorporating recycled concrete fines, cem concr compos 78, pp. 33-42. doi: 10.1016/j.cemconcomp.2016.12.013. [23] vinay kumar, b.m., ananthan, h. and balaji, k.v.a. (2017). experimental studies on utilization of coarse and finer fractions of recycled concrete aggregates in self-compacting concrete mixes, journal of building engineering 9, pp. 100–108. doi: 10.1016/j.jobe.2016.11.013. [24] ferro, g.a, spoto, c., tulliani, j.m. and restuccia, l. (2015). mortars made of recycled sand from c&d, procedia engineering 109, pp. 240 – 247. doi: 10.1016/j.proeng.2015.06.224. [25] restuccia, l., spoto, c., ferro, g.a. and tulliani, j.m. (2016). recycled mortars with c&d waste, procedia structural integrity 2, pp. 2896–2904. doi: 10.1016/j.prostr.2016.06.362. [26] bažant, z.p. and oh, b.h. (1983). crack band theory for fracture concrete, mater. struct 16, pp. 155-177. doi: 10.1007/bf02486267. [27] jenk, y. and shah, s.p. (1985). two parameter fracture model for concrete, j. eng. mech. 111, pp. 1227-1241. l. restuccia, frattura ed integrità strutturale, 49 (2019) 676-689; doi: 10.3221/igf-esis.49.61 689 [28] shah, s.p. (1990). rilem tc 89-fmt, determination of fracture parameters (kic and ctodc) of plain concrete using three-point bend tests, mater. struct. 23, pp. 457-460. [29] rilem tcs (1985). determination of the fracture energy of mortar and concrete by means of three-point bend tests on notched beams, mater. struct. 18, pp. 285-290. [30] cen standard sand en 196-1: 2005 (iso standard sand iso 679: 2009). [31] evangelista, l. and de brito, j. (2014). concrete with fine recycled aggregates: a review. eur j environ civ eng 18, pp. 129–172. doi: 10.1080/19648189.2013.851038 [32] haach, v.g., vasconcelos, g. and lourenço, p.b. (2011). influence of aggregates grading and water/cement ratio in workability and hardened properties of mortars, constr build mater 25, pp. 2980-2987. doi: 10.1016/j.conbuildmat.2010.11.011. [33] pereira, p., evangelista, l. and de brito, j. (2012). the effect of superplasticisers on the workability and compressive strength of concrete made with fine recycled concrete aggregates, constr build mater 28, pp. 722–729. doi: 10.1016/j.conbuildmat.2011.10.050. [34] hansen, t. (1992). recycling of demolished concrete and masonry, rilem report 6, london, uk: e&fn spon. doi: 10.1201/9781482267075. [35] mehta, p.k. and monteiro, p.j.m. 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can be opened with acrobat and adobe reader 5.0 and later.) >> /namespace [ (adobe) (common) (1.0) ] /othernamespaces [ << /asreaderspreads false /cropimagestoframes true /errorcontrol /warnandcontinue /flattenerignorespreadoverrides false /includeguidesgrids false /includenonprinting false /includeslug false /namespace [ (adobe) (indesign) (4.0) ] /omitplacedbitmaps false /omitplacedeps false /omitplacedpdf false /simulateoverprint /legacy >> << /addbleedmarks false /addcolorbars false /addcropmarks false /addpageinfo false /addregmarks false /convertcolors /converttocmyk /destinationprofilename () /destinationprofileselector /documentcmyk /downsample16bitimages true /flattenerpreset << /presetselector /mediumresolution >> /formelements false /generatestructure false /includebookmarks false /includehyperlinks false /includeinteractive false /includelayers false /includeprofiles false /multimediahandling /useobjectsettings /namespace [ (adobe) (creativesuite) (2.0) ] /pdfxoutputintentprofileselector /documentcmyk /preserveediting true /untaggedcmykhandling /leaveuntagged /untaggedrgbhandling /usedocumentprofile /usedocumentbleed false >> ] >> setdistillerparams << /hwresolution [2400 2400] /pagesize [612.000 792.000] >> setpagedevice microsoft word numero_49_art_4_2416 yu. g. matvienko, frattura ed integrità strutturale, 49 (2019) 36-43; doi: 10.3221/igf-esis.49.04 36 focused on crack tip fields comparison of the constraint parameters in elastic-plastic fracture mechanics yu. g. matvienko mechanical engineering research institute of the russian academy of science. 4 m. kharitonievsky per.,101990 moscow, russia. matvienko7@yahoo.com, http://orcid.org/0000-0003-2367-0966 abstract. to describe the effect of crack-tip constraint on the stress field for finite cracked bodies, the following most widely used constraint parameters can be employed in elastic-plastic fracture mechanics, namely, local triaxiality parameter, constraint parameter q, the second fracture mechanics parameter a using a three-term elastic-plastic asymptotic expansion. to establish the relationship between different constraint parameters, the crack-tip stress fields are employed. relationship between the crack-tip constraint parameters a, a2, q and ps of elastic-plastic fracture mechanics is investigated. keywords. constraint parameters; elastic-plastic fracture mechanics. citation: matvienko, yu. g., comparison of the constraint parameters in elastic-plastic fracture mechanics, frattura ed integrità strutturale, 49 (2019) 36-43. received: 01.03.2019 accepted: 23.04.2019 published: 01.07.2019 copyright: © 2019 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. introduction t present time, it becomes obvious that classical one-parameter fracture mechanics based on traditional parameters, such as the stress intensity factor, the j-integral, etc., is not sufficient for describing the stress field in the vicinity of the crack tip for finite cracked bodies. it is necessary to take into account the crack-tip constraint effect, i.e. to employ models and criteria of two-parameter fracture mechanics. to describe the effect of crack-tip constraint in elastic-plastic two-parameter fracture mechanics, the following possible constraint parameters should be introduced into basic equations and criteria of fracture mechanics in the case of small scale yielding and large scale yielding conditions, namely, local triaxiality parameter [1], constraint parameter q [2, 3], the second fracture mechanics parameter a of a three-term elastic-plastic asymptotic expansion [4-6]. some aspects of the relationship between most widely used crack-tip constraint parameters have been discussed [7, 8]. solutions of the parameter a for 2d test specimens are obtained by extensive finite element analysis [7]. moreover, an engineering method of estimating the second parameter a in three-term elastic–plastic asymptotic expansion is developed to cover small-scale yielding to large-scale yielding loading conditions [9]. in particular, it was shown that the parameter a can be calculated through the elastic non-singular t-stress in the case of small-scale yielding. some aspects of application of the j-a approach in elastic-plastic fracture mechanics as well as solutions of the parameter a for 3d test specimens are discussed in refs. [8, 10, 11]. a http://www.gruppofrattura.it/va/49/2416.mp4 yu. g. matvienko, frattura ed integrità strutturale, 49 (2019) 36-43; doi: 10.3221/igf-esis.49.04 37 the constraint parameter q in the j-q approach proposed by o’dowd and shih [2, 3] has been widely used in engineering applications. this parameter can be estimated as the deviation of the crack-tip stress field from that based upon possible reference fields. relationship between the parameter q and the non-singular t-stress was also established. to quantify in-plane and out-of-plane constraints and their interaction, a unified constraint characterization parameter ap was proposed [12-14]. this parameter is based on the plastic area surrounded by the equivalent plastic strain isoline in the vicinity of the crack tip. a sole linear relation between the normalized fracture toughness in terms of the j-integral and √𝐴 was observed. the present paper concentrates on relationship between some crack-tip constraint parameters of elastic-plastic fracture mechanics. two-parameter j-a concept the j-a asymptotic elastic-plastic crack-tip stress field and fracture criterion n the case of the elastic-plastic material deformed according to the ramberg–osgood power-law strain hardening curve 0 0 0 n                (1) the stress field in the vicinity of the mode i plane strain crack is described by the three-term asymptotic expansion [5, 6] (fig. 1) 2 ( 0 ) (1) 2 ( 2 ) 0 0 0 ( ) ( ) ( ) ij s t t s ij ij ij a a a a                 (2) here, 0 σ0 is the yield stress,  is the hardening coefficient, n is the hardening exponent (n > 1), 0 0 / e  is the yield strain and e is young's modulus, j is the energetic integral proposed by cherepanov [15] and rice [16], a is the second fracture parameter, ij are stress components r ,  and r in the polar coordinate system r with origin at the crack tip, ( )kij are dimensionless angular stress functions obtained from the solution of asymptotic problems of order (0), (1) and (2). angular stress functions ( 0 )ij and (1) ij are scaled so as maximal equivalent mises stress is equal to unity, i.e. ( 0 ) (1)max max 1e e     . exponent s has closed form expression 1/ ( 1)s n   . exponent t is a numerically computed eigenvalue that depends on strain hardening exponent n. for materials with n=5 and 10 that are used in this paper values of exponent t are: t(5) = 0.05456, t(10) = 0.06977. coefficient a0 is specified as 0 0( ) s na i . dimensionless radius  is defined by the following formula 0/ r j    (3) comparing eqn. (2) and the crack-tip stress field proposed by hutchinson [17] and rice and rosengren [18] ((so-called the hrr field), it is easy to see that the first term of the asymptotic expansion (2) is exactly the hrr field. it can be seen that the hrr field does not describe correctly stresses in the region 01 / 5r j  (fig. 1) that is significant for fracture process. finite element solutions of elastic-plastic crack problems show that the j-a stress field is much closer to finite element results than the hrr field [8]. the three terms of expansion (2) are controlled by two parameters, namely, the j-integral and the parameter a. the parameter a is a measure of stress field deviation from the hrr field. assuming that cleavage fracture of a specimen and a cracked structure occurs when stress fields near the crack tip are same it is possible to formulate two-parameter j-a fracture criterion. this assumption also justifies the use of a as a constraint parameter [8]. the two-parameter fracture i yu. g. matvienko, frattura ed integrità strutturale, 49 (2019) 36-43; doi: 10.3221/igf-esis.49.04 38 criterion implies comparison of computed j-integral for a cracked structure and the experimental fracture toughness jc corresponding to computed value of the constraint parameter a figure 1: comparison of the j-a stress field and the hrr field for edge cracked plate. ( )| ( )a cj p j a (4) determination of the dependency jc(a) can be accomplished by testing cracked specimens with different constraint at fracture load. change of the constraint conditions is achieved by varying crack length in the specimen. to avoid numerous experiments it is desirable to develop computational approaches for predicting the fracture toughness as a function of the constraint parameter a. estimating change of the fracture toughness jc with variation of the constraint parameter a can be based on an assumption that fracture under different constraint conditions corresponds to constant fracture probability pf [19]. numerical estimation of the j-integral and parameter a the equivalent domain integral method (edi) [20, 21] is employed for computing the j-integral. determination of the constraint parameter a is based on stress calculation in the vicinity of the crack tip by means of the finite element method. if stresses are known at points ( ),i i  then the value of the parameter a at ith point is found from the following quadratic equation [6] 2 2 ( 2 ) (1) ( 0 ) 0 0 0 0 ( , ) ( ), ( ), ( ) i i i t s fem t si i i i i i i i i i i a a b a c a b c a a                         (5) where fem is stress calculated by the finite element method. solution of eqn. (5) produces different a values at different points due to deviation of actual stress field from the three term asymptotic expansion. better estimate of a for the set of points is obtained by minimizing sum of squares of deviations of the j-a asymptotic field from the finite element results. application of the least squares method leads to a cubic equation for the parameter a [6]   3 2 3 2 1 0 2 2 3 2 1 0 0 2 3 2, , ,i i i i i i i i d a d a d a d d a d a b d a c b d b c             (6) usually values of the stress  at finite element integration points inside region 1 4  , 0 45   are used for estimation of the parameter a. yu. g. matvienko, frattura ed integrità strutturale, 49 (2019) 36-43; doi: 10.3221/igf-esis.49.04 39 relationship between the parameter a and other elastic-plastic constraint parameters he most widely used constraint parameters mentioned in the introduction of this paper can be employed in engineering applications. to establish the relationship between these parameters, the crack-tip stress fields can be very useful. relationship between the constraint parameters a, a2 and q was discussed in refs. [7, 8]. a constraint characterization parameter pa [12-14] is also analyzed in connection with the constraint parameter a. relationship between the parameters a and a2 the well-known j-a2 approach for two-dimensional body with a mode i crack under plane strain conditions is based on the following expression of the three-term asymptotic expansion for stress in the vicinity of the crack tip in elastic-plastic material [22]             1 2 3 1 2 32 1 2 2 0 s s s ij ij ij ij r r r a a a l l l                                   (7) here, a1=    10 0 1/ , 1/ 1 s ni l j s n     and 3 2 12s s s  . comparing eq. (2) and eq. (7), it should be noted that three corresponding dimensionless angular functions  kij are the same in eq. (2) and eq. (7). moreover, there is the connection between exponents ks and t in eq. (2), namely, 1 2 3, s , 2s s t s t s    . therefore, the following relationship between the constraint parameters a and a2 in the three-term asymptotic expansions of elastic-plastic crack-tip stress field can be written  2 0 0 s t s n j a i a l             (8) thus, j-a and j-a2 approaches are mathematically equivalent. the difference of these approaches is in distance scaling of r according to eqs. (2) and (7). comparison of parameters a and a2 is shown in fig. 2. dependencies of both parameters are plotted for 3pb specimen with cracks of same aspect ratios a/w. in contrast to the parameter a, the parameter a2 does not have its small-scale yielding value. it can be seen that the parameter a2 tends to infinite value with load decrease. it is less convenient for constraint interpretation and engineering application. relationship between the parameters a and q the constraint parameter q in the j-q approach [2, 3] is defined by the deviation of the crack-tip stress field under consideration from a reference stress field. possible reference fields can be the hrr field or field corresponding to smallscale yielding conditions   0 0 ijij ssyq      or   0 0 ijij hrrq      (9) the following relationship between the parameters a and q can be obtained from eq. (2) and eq. (9)       2 1 2 2 0 t t saq a a            at 0, 2.   (10) fig. 3 presents dependencies of a and q as functions of the applied load for cracks of different depth in 3pb specimen. constraint parameters a and q demonstrate similar behavior and can be used in engineering applications. but, the q parameter can be considered as a qualitative measure of crack-tip constraint, because small errors in the crack-tip stress t yu. g. matvienko, frattura ed integrità strutturale, 49 (2019) 36-43; doi: 10.3221/igf-esis.49.04 40 obtained by finite element method lead to the significant error in the value of q [23]. the j and a parameters allow describing the elastic-plastic stress field near the crack tip with sufficient accuracy. figure 2: comparison of the parameters a and a2 as functions of applied load p. figure 3: comparison of the parameters a and q as functions of applied load p. relationship between the parameters a and p ps a a parameter /p peeq refa a a is introduced into consideration as the unified constraint parameter to characterize inplane and out-of-plane crack-tip constraint [12-14]. the parameter peeqa is the area surrounded by the equivalent plastic strain contour with specified value of strain p , the parameter refa is peeqa with same strain p measured in a standard specimen test. finite element method based on gurson-tvergaard-needleman damage model was used to calculate the equivalent plastic strain p distribution ahead of the crack tip for specimens with different in-plane and out-of-plane constraints. the following plastic strains p =0.1, 0.2 and 0.3 were employed for determination of plastic contours. it was found that p =0.2 and 0.3 provides approximately linear dependencies /c refj j versus pa [13]. this is not a surprising result since the area inside specified strain p is proportional to 2j . so, the j-integral is compared to the quantity that is yu. g. matvienko, frattura ed integrità strutturale, 49 (2019) 36-43; doi: 10.3221/igf-esis.49.04 41 proportional to the j-integral. in our opinion the parameter p ps a is not suitable for using as a constraint parameter because plastic zone areas and j values are proportional. to avoid direct dependence of these parameters on each other, it is proposed to replace coordinate r (as well as x and y) with dimensionless coordinate  0/ /r j  [8]. in this case, the area inside equivalent plastic strain becomes dimensionless  20/ /peeq peeqa a j  (11) therefore, a normalized constraint parameter pa can be introduced into consideration by means of the following expression p ps a , where /p peeq refa a a . (12) the parameter pa is denoted as ps . the modified constraint parameter ps should be less dependent on the j-integral. in this case, the separation of the constraint parameter and the j-integral improves the quality of a fracture criterion that is based on these parameters. behavior of the parameter ps as a function of a/assy is investigated using the j-a elastic-plastic asymptotic field. the area surrounded by the equivalent plastic strain contour with specified value of strain p is estimated with the following algorithm [8]. stress p corresponding to specified plastic strain p can be represented as 1/ 1/ 0 0 0 n n p p pe                    (13) the rectangular area in the vicinity of the crack tip is divided into square cells. equivalent stress is computed at each cell by means of the j-a elastic-plastic asymptotic field. if this stress is larger than p , the cell area is added to peeqa . computation of the plastic area is performed in coordinates 0 /x j and 0 /y j , so the resulting area is peeqa . fig. 4 summarizes the computed results for plastic zones inside plastic strain contours corresponding to p =0.1, 0.2 and 0.3 and relationships between parameters ps and a for a material with 1  and 5n  . smallest plastic zone corresponds to small scale yielding value of the constraint parameter a (assy (n=5) = 0.3803). intermediate plastic zone is computed for the value of  max / 2ssya a . largest plastic zone is related to amax (shown in fig. 4). it can be seen that there is a unique relationship between the constraint parameters ps and a in a wide range of specified values of strain p . conclusions elationship between the crack-tip constraint parameters a, a2, q and ps of elastic-plastic fracture mechanics is based on analysis of the stress fields in the vicinity of the crack tip. the following conclusions can be drawn. it was demonstrated that j-a and j-a2 approaches are mathematically equivalent. the difference of these approaches is in distance scaling r. but, in contrast to the parameter a, the parameter a2 does not have its value under small scale yielding conditions. constraint parameters a and q show similar behavior. at the same time, it should be noted that small errors in the crack-tip stress obtained by finite element method lead to the significant error in the value of q. the constraint parameter p ps a based on the area surrounded by the equivalent plastic strain p contour ahead of the crack tip is not suitable as a crack-tip constraint parameter because plastic zone areas and j values are proportional. to avoid direct dependence of these parameters on each other, the constraint characterization parameter pa is modified as r yu. g. matvienko, frattura ed integrità strutturale, 49 (2019) 36-43; doi: 10.3221/igf-esis.49.04 42 follows p pa s . in this case, the separation of the constraint parameter and the j-integral improves the quality of a fracture criterion in two-parameter elastic-plastic fracture mechanics. it was shown that there is a unique relationship between the constraint parameters ps and a in a wide range of specified values of strain p . a) b) c) figure 4: equivalent plastic strain isolines for a/assy with minimal, average and maximal values (left); the constraint parameter ps as a function of the parameter a (right): n=5, p =0.1 (a), p =0.2 (b) and p =0.3 (c). yu. g. matvienko, frattura ed integrità strutturale, 49 (2019) 36-43; doi: 10.3221/igf-esis.49.04 43 acknowledgements he authors acknowledge the support of the russian science foundation (project n 18-19-00351). references [1] henry, b.s., luxmoore a.r. (1997). the stress triaxiality constraint and the q-value as ductile fracture parameter, eng. fract. mechanics, 57, pp. 375-390. [2] o’dowd, n. p., shih, c. f. (1991). family of crack-tip fields characterized by a triaxiality parameter i. structure of fields, j. mech. phys. solids, 39, pp. 989-1015. [3] o’dowd, n. p., shih, c. f. (1992). family of crack-tip fields characterized by a triaxiality parameterii. fracture applications, j. mech. phys. solids, 40, pp. 939-963. [4] yang, s., chao, y.j., sutton, m.a. (1993). higher-order asymptotic fields in a power law hardening material, eng. fract. mechanics, 45, pp. 1-20. [5] nikishkov, g.p. (1995). an algorithm and a computer program for the three-term asymptotic expansion of elastic– plastic crack tip stress and displacement fields, eng. fract. mechanics, 50, pp. 65–83. [6] nikishkov, g.p., bruckner-foit, a., munz, d. (1995). calculation of the second fracture parameter for finite cracked bodies using a three-term elastic-plastic asymptotic expansion, eng. fract. mechanics, 52, pp. 685-701. [7] ding, ping, wang, xin. (2010). solutions of the second elastic–plastic fracture mechanics parameter in test specimens, eng. fract. mechanics, 77, pp. 3462-3480. [8] matvienko, yu.g., nikishkov, g.p. (2017). two-parameter j-a concept in connection with crack-tip constraint. theor. appl. fract. mech., 92, pp. 306-317. [9] ding, ping, wang, xin. (2012). an estimation method for the determination of the second elastic–plastic fracture mechanics parameters, eng. fract. mechanics, 79, pp. 295-311. [10] nikishkov, g.p., matvienko, yu.g. (2016). elastic-plastic constraint parameter a for test specimens with thickness variation, fatig. fract. eng. mater. struct., 39, pp. 939-949. [11] matvienko, yu.g., nikishkov, g.p. (2016). j-a elastic-plastic crack tip field and the two-parameter fracture criterion, structural integrity procedia 2 26–33. [12] yang, j., wang, g.z., xuan, f.z., tu, s.t. (2013). unified characterisation of in-plane and out-of-plane constraint based on crack-tip equivalent plastic strain, fatig. fract. eng. mater. struct., 36, pp. 504–514. [13] mu, m.y., wang, g.z., xuan, f.z., tu, s. t. (2015). unified correlation of in-plane and out-of-plane constraint with cleavage fracture toughness, theor. appl. fract. mech., 80, pp. 121-132. [14] mu, m.y., wang, g.z., xuan, f.z., tu, s. t. (2017). fracture assessment based on unified constraint parameter for pressurized pipes with circumferential surface cracks, eng. fract. mechanics, 175, pp. 201-218. [15] cherepanov, g.p. (1967). the propagation of cracks in a continuous medium, j. appl. math. mech., 31, pp. 503-512. [16] rice, j.r. (1968). a path independent integral and the approximate analysis of strain concentration by notches and cracks, j. appl. mech. asme, 35, pp. 379-386. [17] hutchinson, j.w. (1968). singular behavior at the end of a tensile crack in a hardening material, j. mech. phys. solids, 16, pp. 13-31. [18] rice, j.r., rosengren, g.f. (1968). plane strain deformation near a crack tip in a power law hardening material, j. mech. phys. solids, 16, pp. 1-12. [19] nikishkov, g.p. (2016). prediction of fracture toughness dependence on constraint parameter a using the weakest link model, eng. fract. mech., 152, pp. 193-200. [20] nikishkov, g.p., atluri, s.n. (1987). calculation of fracture mechanics parameters for an arbitrary three-dimensional crack by the equivalent domain integral method, int. j. numer. meth. eng., 24, pp. 1801-1821. [21] nikishkov, g.p., vershinin, a.v., nikishkov, y.g. (2016). mesh-independent equivalent domain integral method for j-integral evaluation, adv. eng. softw., 100, pp. 308–318. [22] chao, y.j., yang, s., sutton, m.a. (1994). on the fracture of solids characterized by one or two parameters: theory and practice, j. mech. phys. solids, 42, pp. 629-647. [23] lee, m.m.k., boothman, d.p., luxmoore, a.r. 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/hrv (za stvaranje adobe pdf dokumenata najpogodnijih za visokokvalitetni ispis prije tiskanja koristite ove postavke. stvoreni pdf dokumenti mogu se otvoriti acrobat i adobe reader 5.0 i kasnijim verzijama.) /hun 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can be opened with acrobat and adobe reader 5.0 and later.) >> /namespace [ (adobe) (common) (1.0) ] /othernamespaces [ << /asreaderspreads false /cropimagestoframes true /errorcontrol /warnandcontinue /flattenerignorespreadoverrides false /includeguidesgrids false /includenonprinting false /includeslug false /namespace [ (adobe) (indesign) (4.0) ] /omitplacedbitmaps false /omitplacedeps false /omitplacedpdf false /simulateoverprint /legacy >> << /addbleedmarks false /addcolorbars false /addcropmarks false /addpageinfo false /addregmarks false /convertcolors /converttocmyk /destinationprofilename () /destinationprofileselector /documentcmyk /downsample16bitimages true /flattenerpreset << /presetselector /mediumresolution >> /formelements false /generatestructure false /includebookmarks false /includehyperlinks false /includeinteractive false /includelayers false /includeprofiles false /multimediahandling /useobjectsettings /namespace [ (adobe) (creativesuite) (2.0) ] /pdfxoutputintentprofileselector /documentcmyk /preserveediting true /untaggedcmykhandling /leaveuntagged /untaggedrgbhandling /usedocumentprofile /usedocumentbleed false >> ] >> setdistillerparams << /hwresolution [2400 2400] /pagesize [612.000 792.000] >> setpagedevice microsoft word numero_59_art_10_3189.docx h. rezzag et alii, frattura ed integrità strutturale, 59 (2022) 129-140; doi: 10.3221/igf-esis.59.10 129 tribological performance and corrosion behavior of cocrmo alloy hadda rezzag laboratory of metallurgy & materials engineering (lmgm), university badji mokhtar, b. p. 12, annaba 23000, algeria. research center in industrial technologies crti, p. o. box 64, cheraga 16014 algiers, algeria rezzagbiom@gmail.com latifa kahloul, hacène chadli laboratory of mines, metallurgy, and materials (l3m), national school of mines and metallurgy.annaba, 23000, algeria. latifabiomat@gmail.com, chadli_hacene@yahoo.fr alima mebrek research center in industrial technologies crti, p. o. box 64, cheraga 16014 algiers, algeria a.mebrek@crti.dz adel saoudi centre de recherche scientifique et technique en analyses physico-chimiques crapc, zone industrielle bou-ismail, tipaza, po 384, rp 42001, algeria saoudi_dl@yahoo.com abstract. the present work focuses on the tribological properties and corrosion behavior evaluation of sintered cocrmo alloy. the cocrmo alloy was elaborated by powder metallurgy process at various sintering temperatures (1200°c, 1250°c and 1300°c). the structural properties were characterized by x-ray diffraction and scanning electron microscopy. the tribological characteristics were measured using a dry disc-ball tribometer. the corrosion behavior of the samples was studied using different electrochemical tests in a simulated physiological environment (hank’s solution). the obtained results show that higher sintering temperatures have a positive impact on the tribological behavior as well as the corrosion resistance of cocrmo alloys. the sintered samples at 1300°c showed a better resistance to friction wear and a lower corrosion rate. keywords. cocrmo alloy; powder metallurgy; wear; electrochemical properties. citation: rezzag, h., kahloul, l., chadli, h., mebrek. a., saoudi, a. tribological performance and corrosion behavior of cocrmo alloy, frattura ed integrità strutturale, 59 (2022) 129-140. received: 14.07.2021 accepted: 14.10.2021 published: 01.01.2022 copyright: © 2022 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. https://youtu.be/ftfvs3if6v4 rh. rezzag et alii, frattura ed integrità strutturale, 59 (2022) 129-140; doi: 10.3221/igf-esis.59.10 130 introduction obalt-based alloys are widely used in the biomedical field. the cobalt-chromiummolybdenum alloy (cocrmo) is mainly used for orthopedic implants and dental devices [1]. they represent the preferred choice for artificial joints and metal-to-metal contact [2] because of their excellent properties in terms of wear and corrosion resistance aligned with a good biocompatibility with the human tissues [3]. the high biocompatibility of these alloys is related to the immediate formation of a protective passive film on the surface. this film is mainly composed of chromium oxide cr2o3[4], with a small contribution of co and mo oxides [5]. several techniques were used for the development of co-based alloys such as casting and forging [6]. however, these techniques present the disadvantages of solidification defects and precipitation [7] including a coarse microstructure, low resistance and elongation. hence, it was a great interest to improve the mechanical reliability of these cocrmo alloys in order to achieve high durability of medical implants. powder metallurgy (pm) methods have been commonly employed to produce high-purity alloys, with accurate chemical composition, targeted structures and controlled porosity [8]. indeed, several studies have emphasized the pm effect on the tribological and electrochemical properties of cocrmo alloys. recently, there was a particular focus on improving the tribological behavior of implant materials [9]. the electrochemical characterization and corrosion resistance of cocrmo alloys were studied by zuraidawani che daud et al. they verified the electrochemical behavior of cocrmo alloy in a 0.9% sodium chloride solution and found that the sintering regime had a significant impact on the corrosion resistance [10]. in addition, a study was carried out on the electrochemical properties of the cocrmo alloy elaborated by the powder metallurgy process. the obtained results have shown that the main parameter to be monitored is the sintering temperature. in fact, the sintering temperature significantly affects the mechanical strength and electrochemical behavior of these alloys in the ringer's solution [11]. the aim of this work is to study the structural and tribological properties as well as the electrochemical corrosion behavior of the cocrmo alloy elaborated by sintering. experimental methods materials preparation he cocrmo alloy was synthesized by the powder metallurgy (pm) process. the initial powders are cobalt, chromium and molybdenum with a particle size: co (99.5% purity, 45μ m), cr (99.9% purity, 32μm) and mo (99.9% purity, 2μm). the chemical composition of this alloy is given in the tab. 1. all the samples were prepared according to astm f75 [2]. the elementary powders mixture was first kneaded in a ball mill at room temperature. next, they were dried in an oven for 2 h at 80°c to eliminate all the moisture molecules adsorbed on the surface. after that, the mixture was uniaxial cold compacted in a tungsten carbide matrix carbide die under a seven ton load to produce cylindrical specimens (13 mm in diameter and 4 mm in height). to prevent samples contamination, the pellets were placed into ceramic crucibles, and sintered at different temperatures of 1200°c, 1250°c and 1300°c for 2 h, with subsequent cooling in the oven at an average speed of 20 °c/min to avoid oxidation. the sintering was carried out in an electric furnace under a hydrogen atmosphere. in order to perform the analytical tests, all specimens were polished after sintering. element co cr mo impurities weight ⦋%⦌ bal. 28 6 fe, cu<1 table 1: chemical composition of the cocrmo alloy powder (wt. %). characterizations: microstructure, x-ray diffraction (xrd) and mechanical properties the microstructure of cocrmo alloys were analyzed by jeol jsm-6830 scanning electron microscope (sem). the phase identification was done by x-ray diffraction using a rigakuultima iv type diffractometer with a conventional radiation source copper cu kα (λ=1.5418 å) applying a voltage of 40 kv and a current of 40 ma. the x-ray diffraction patterns were compared to the icsd database. for mechanical characterization, vickers microhardness measurements were carried out c t h. rezzag et alii, frattura ed integrità strutturale, 59 (2022) 129-140; doi: 10.3221/igf-esis.59.10 131 under 100g load (hv0.1, dwell time 15 seconds) using a microdurometer tester (innovatest). the porosity rate was calculated using formula (1)[12]:                 % 1 .100   p th (1) where: 𝜌th: theoretical density and 𝜌: experimental density. characterizations: tribological tests in accordance with astm g 99-95a and din 50324 standards, the tribological characteristics were assessed using a csminstrument tribometer in the ball-disc configuration, and the tests were performed in dry conditions. the alumina ball (al2o3) was selected as an antagonist with a hardness of 16 gpa and 6mm in diameter. after each friction test, the surface condition was analyzed by scanning electron microscope analysis. a profilometer 3d cyber technology ct100 model (laser source) was employed to measure the depth and the width of the wear groove. tab. 2 summarizes the tribological test parameters. the wear rate was calculated using formula (2) proposed by archard [13]. the ball-disc standard configuration is illustrated in fig. 1.         v w f s (2) where: w: wear rate (mm3/n.m); v: the wear volume (mm3); f: applied load (n); s: total rotation distance (m). applied load⦋n⦌ 5 linear speed ⦋cm/s⦌ 1.08 stop conditions ⦋m⦌ 30 radius ⦋mm⦌ 4.90 atmosphere air temperature ⦋°c⦌ 20.00 humidity ⦋%⦌ 40.00 table 2: parameters of tribological tests. figure 1: standard configuration of the ball-disc. characterizations: electrochemical corrosion tests the electrochemical measurements were performed using a biologic sp300 type potentiostat/galvanostat controlled by an ec-lab v10.40 analyzer to study the corrosion behavior of cocrmo alloy in simulated body fluid. the experiments were conducted using a conventional three-electrode cell with the saturated calomel electrode (sce) as the reference electrode, platinum wire (pt) as the auxiliary electrode, and cocrmo alloy as the working electrode. the electrochemical experiments were performed in a physiological medium () [14]. the composition of the hank’s solution is shown in tab. 3. rh. rezzag et alii, frattura ed integrità strutturale, 59 (2022) 129-140; doi: 10.3221/igf-esis.59.10 132 the potential monitoring was made in open circuit (ocp) for 60 min. the potentiodynamic polarization tests were performed by scanning the applied potential from -1 to 1.2 v / sce at a scan rate of 1mv. s−1. the corrosion potential ecorr as well as the current density of corrosion icorr were extrapolated from the tafel curves slope using ec-labv11.20 software. the electrochemical impedance spectroscopy (eis) tests were carried out in the frequency range of 100 khz to 10 mhz with amplitude of 0 ± 10 mv. table 3: composition of hank’s solution. results and discussions xrd analysis and microstructure -ray patterns of cocrmo samples (fig. 2) show that the three samples (a, b, c) are mainly composed of two phases: the γ-co phase with a cubic structure, fcc (jcpds 00-001-1277) and the ε-co phase with a hexagonal structure, hcp (jcpds 00-015-0806). the results are in good agreement with existing phases in the co-cr binary equilibrium diagram [1]. for all samples, the peak intensity of (111) fcc is higher than that of the (101) hcp. moreover, the presence of diffraction peak with low intensity corresponding to the ε-co phase (101) indicates that all the samples contain a small amount of ε-co phase [15]. figure 2: x-ray diffraction patterns of cocrmo alloys sintered: (a) 1200°c, (b) 1250°c, (c) 1300°c. otherwise, no additional diffraction or offset peaks were observed for the studied cocrmo samples sintered at different temperatures. the microstructure of the sintered cocrmo alloy at different temperatures is given in fig. 3. these figures show that depending on the contrast, there were three types of phases in the cocrmo alloy, i.e. gray, dark and shiny phases. calculations of the volume proportions of each of the obtuse phases are done using the highscore plus software version (3.0.4). the results of the phase volume fractions obtained show a variation in the volume proportion of the ε-co phase ranging from 51.1%, 58.7% and 63.1% for the samples sintered at 1200 ° c, and 1250 ° c and 1300 ° c. respectively. we note the presence of the majority co phase which constitutes the matrix of gray color. in the matrix, we also notice regions of dark lamellar morphology rich in chromium and light zones rich in molybdenum. no carbides are present in the microstructure, which corresponds well to the drx of the cocrmo alloy identified in fig. 2. the sintering temperature in our sample does not affect the nature of the formed phases, but rather the volume fraction of the existing phases. substance nacl kcl nahco3 nah2po4. h2o na2hpo4. 2h2o cacl2.2h2o mgcl2 mgs4.7h2o glucose composition [g/ l] 8.0 0.4 0.35 0.25 0.06 0.19 0.19 0.06 1 x h. rezzag et alii, frattura ed integrità strutturale, 59 (2022) 129-140; doi: 10.3221/igf-esis.59.10 133 figure 3: sem images of cocrmo alloys sintered: (a) 1200°c, (b) 1250°c, (c) 1300°c. density evolution and microhardness tab. 4 summarizes the experimental values of density and micro-hardness of the sintered samples. one observes that these two properties increase with the sintering temperature. the highest values of relative density 91% and hardness of 384hv0.1 were obtained for the sample sintered at 1300°c. this is mainly due to an increased formation of collars between the particles (depends on the diffusion phenomena). as more necks were forming with increasing sintering temperature. diffusion mechanisms become active at higher temperatures during heating process. this fact leads to porosity reduction and automatically affects hardness. table 4: experimental density, porosity and microhardness of the cocrmo alloy the hardness result from our samples is greater than that obtained from zuraidawani che daud et al [16]. the highest rate in terms of porosity is obtained from a sample sintered at 1200°c. in fact, mechanical and microstructural properties of the sintered alloy cocrmo are strongly dependent on the heat treatment parameters (sintering). generally biomedical materials require a certain degree of porosity, pores are important for tissue formation, as they allow cell migration and proliferation, as well as vascularization [17]. tribological behavior: coefficient of friction the evolution of the coefficient of friction (cof) in the cocrmo alloy as a function of the friction distance for various temperatures is presented in fig. 4(a). the analysis of these curves makes it possible to distinguish four successive periods of friction. the first period (i) of friction corresponds to the running-in regime, because the surfaces adapt to each other and the surface roughness is reduced by the plastic deformation. the second period (ii) corresponds to a slight decrease in the coefficient of friction, as the wear particles cannot easily anchor a polished surface due to the decrease in roughness deformation. the third period (iii) is defined by a substantial rise in the coefficient of friction. the third body which sintering temperature ⦋°c⦌ 1200 1250 1300 experimental density ⦋g/cm³⦌ 7. 520 7.710 8.020 porosity ⦋%⦌ 15 13 9 microhardness hv0.1 219 334 384 rh. rezzag et alii, frattura ed integrità strutturale, 59 (2022) 129-140; doi: 10.3221/igf-esis.59.10 134 fragments and oxidizes most possibly to serve an abrasive role and, finally the fourth period (iv) corresponds to the stationary phase or the stabilized regime corresponding to the stabilization of the coefficient of friction where its value is maintained constant during the test[18]. . (a) (b) figure 4: (a) evolution of coefficient of friction and (b) average friction coefficients of the cocrmo alloy sintered at different temperatures. the average values of the friction coefficient of the samples cocrmo sintered at different temperatures are shown in fig. 4(b). a slight decrease in friction coefficient values, with the sintering temperature increasing from 1200°c to 1250°c. this is mainly due to the increase in the sintering temperature which leads to the increase in hardness and density. so, for a sample sintered at 1200°c, we go from a hardness of 219 hv to a hardness of 334 hv for a sample sintered at 1250 ° c. on the other hand, for the sample sintered at 1300 ° c, it has a high coefficient of friction although it has a higher hardness. this is probably due to the formation of solid wear debris (third-body particles) during the friction process and thus contributes to the increase in the coefficient of friction. in addition, this fact is indicative of the beginning of the particle detachment from the metallic material to the alumina ball’s outer surface (fig. 5). in fact, the contact form changes every time from two bodies (alumina-sample) to that of three bodies (debris-alumina-sample) [19] wear rate fig. 5 depicts the evolution of the specific wear rate of the cocrmo samples elaborated by pm as a function of the different sintering temperatures. it can be shown that the sintering temperature has a positive effect on the reduction in the wear. the wear phenomenon is a surface degradation by friction during operating cycle. when the system is subject to stresses, various types of damage can take place according to the intensity of the stresses applied. since these stresses locally exceed the yield strength of one of the two materials in contact, the latter is deformed either plastically (ductile material) or going to flake or crack (brittle material) after a few operating cycles. on the other hand, the wear behavior can be explained by the effect of porosity, the presence of pores within sintered materials decreases the actual contact area between the two materials in contact, thus increasing the contact pressure and promote the detachment of particles during sliding. as a result, causing wear debris to form during sliding, cracks appear next to the pores. the wear resistance and the coefficient of friction are thus reduced, this is mainly due to an increased formation of collars between the particles (depends on the diffusion phenomena). as more necks formed with increasing sintering temperature. diffusion mechanisms become active during the high temperature heating process, cause porosity reduction and automatically affect hardness. as can be seen in fig. 5, the wear rate decreases from 2.394x10-4 mm3/ (nm) to 2.233x10-4 mm3/ (nm) when the sintering temperature increases from 1200°c to 1250°c. for samples sintered at 1300 °c, exhibits a porosity rate of around 9%, this sample exhibits a porosity that is mostly closed. it therefore behaves like a dense material, which explains the low values obtained for the wear rate (0.987x10-4mm3 / nm). a good correlation between the wear rate values and the mechanical properties obtained for the sintered compacts at h. rezzag et alii, frattura ed integrità strutturale, 59 (2022) 129-140; doi: 10.3221/igf-esis.59.10 135 different temperatures in this analysis. the higher the sintering temperature, the more the porosity decreases, which provides good wear resistance for the sample sintered at the highest temperature (1300 °c). in fact, the structure and hardness have been reported to have a significant impact on the wear behavior of this alloy [20]. in our work, we predict that a fraction of the wear debris can remain attached to against an alumina ball. transfer of material to the contact surface of the counterface (alumina ball) was clearly visible in fig. 6. the findings of the 3d surface analysis of the worn surface's wear traces are shown in the fig. 7. these findings support the presence of a contact trace on the sample's surface. this illustration depicts numerous grooves of various widths and depths. figure 5: wear rate after dry friction test of cocrmo alloy sintered at different temperatures. figure 6: optical micrographs of wear marks on the alumina ball: (a) 1200°c, (b) 1250°c and (c) 1300°c. rh. rezzag et alii, frattura ed integrità strutturale, 59 (2022) 129-140; doi: 10.3221/igf-esis.59.10 136 figure 7: 3d images of the worn surface of the cocrmo alloy samples sintered: (a) 1200°c, (b) 1250°c and (c) 1300° c. wear surface and wear mechanism the sem images (fig. 8) shows the morphology of the worn surfaces of the samples allowing the identification of the wear mechanisms that intervene during friction. all of the sintered samples studied show significant damage to their surfaces, with a distorted appearance (fig. 8a, 8b and 8c). indeed, grooves parallel to the direction of sliding or imprints left by hard particles on the surface of the samples are clearly visible, wear debris (third body) was also observed in the two samples sintered at 1200 ° c and 1250 °c. examination of these tracks reveals the presence of scratches and grooves parallel to the sliding direction that are typical characteristics of abrasive wear [21]. we also note for the sample sintered at 1300 ° c (fig. 8c), that the scratches parallel to the sliding direction are always present. a detachment of small chips was observed on the surface, especially at the periphery of the trace of contact. this phenomenon indicates a degradation mechanism based on plastic deformation and brittle fracture of the surface linked to the hardness of the alloy. figure 8: sem micrographs of the wear tracks on the surface of the cocrmo alloy sintered at different temperatures: (a) 1200°c, (b) 1250°c and (c) 1300°c. h. rezzag et alii, frattura ed integrità strutturale, 59 (2022) 129-140; doi: 10.3221/igf-esis.59.10 137 in this work we introduce the plowing effect that occurs when one of the two materials in contact is much more difficult to create furrows on the contact surface of the softer material. the hardness ratios (ball of alumina / cocrmo) at different temperatures are (2400/219 hv), (2400/334 hv) and (2400 / 384hv), respectively. in addition, tough roughness can sink into the soft body, creating a groove through the plastic flow of the material. this phenomenon induces resistance to movement [22]. corrosion behavior: electrochemical properties in order to study the corrosive behavior of cocrmo alloy samples sintered at different temperatures, we started by tracking the abandonment potential (eocp) using plotting potential-time curves (fig. 9 a). these curves suggest that a stable value is not immediately reached by the open circuit potential. experiments show that it stabilizes after 15 minutes of immersion. for the samples sintered at 1300°c, the equilibrium potential increases towards positive values, and then it stabilizes at -497mv. however, the potential for samples sintered at 1200°c and 1250°c increases sharply and then decreases to stabilize at -512mv and -499mv, respectively. therefore, we can conclude that the increase in the potential at the beginning of the experiments is related to the electrochemical reaction that occurs between the sample surface and the solution. (a) (b) figure 9: electrochemical curve of cocrmo alloy in hank’s solution: (a) eocp curves,(b) potentiodynamic polarization curves. moreover, obtaining the constant ocp value after immersion means that the formation of the protective layer of oxide (passive film formation of cr2o3) has been completed [23]. the potentiodynamic curves provide useful information on the kinetics of the multiple-composed corrosion mechanism (charge transfer, mass transfer, and species adsorption). fig. 9.b. represents the potentiodynamic curves of cocrmo alloys sintered at different temperatures. three typical potential domains can be observed in the anodic region. a short passivation zone accompanied by an increase in current density due to the passive film rupture corresponds to the first domain. the current density related to the reformation of passive film in the third region and its stability [24]. tab. 5 lists the various electrochemical parameters obtained from these curves, such as the corrosion potential (ecorr), the corrosion current (icorr) and the corrosion rate (vcorr). the highest corrosion current density (14.08 µa/cm2) was obtained for cocrmo sample sintered at 1200°c, while, the lowest value was obtained for the alloy sintered at 1300°c (0.775 µa/cm2). this fact may be attributed to the influence of the porosity on the corrosion resistance. table 5: corrosion parameters of cocrmo alloy after electrochemical tests. temperature ⦋°c⦌ ecorr ⦋mv⦌ icorr ⦋µa/cm2⦌ vcorr ⦋mm/year⦌ rp ⦋ohm⦌ 1200 -420 14.087 0.0850 2642 1250 -698 1.070 0.0064 31387 1300 -563 0.775 0.0047 34527 rh. rezzag et alii, frattura ed integrità strutturale, 59 (2022) 129-140; doi: 10.3221/igf-esis.59.10 138 the higher the sintering temperature, the lower the porosity, which results higher corrosion resistance. therefore, the corrosion rate is proportional to the density of the corrosion current [25]. it should be noted that for a sample sintered at 1300°c, the shift of the corrosion potential towards more noble. values can be due to two factors [26]. the first factor refers to the higher surface energy of the alloy. the second factor is related to the surface layer oxidation. in this case, the protection is provided by the thickening of the oxide film. in fact, the passivation of the cocrmo alloy is linked to the formation of a thin layer mainly formed of chromium oxide (cr2 o3) and certain hydroxides [27]. this layer prevents the exchange of oxygen and metal ions. electrochemical impedance spectroscopy the eis measurements were carried out at the open circuit potential (ocp) after 360 minutes of immersion in hank's solution. fig. 10 (a) illustrates the nyquist diagram for the cocrmo alloy sintered at different temperatures. it can be seen that the impedance spectra exhibit an incomplete semi-circle at mid and high frequencies. the absolute impedance curve at high frequencies (10,000 0.1 hz) is almost independent of frequency with a phase angle of 0°, chowing electrolyte resistance (rs). this suggests a capacitive behavior of the cocrmo electrode in the corrosion solution. it is well known that the radius of the semicircular arc is linked to the polarization resistance of the passive film. this behavior indicates the formation of a stable oxide film on the surface of the alloy. according to the impedance measurements, the best passive properties were obtained from the alloy sintered at 1300°c compared to other samples sintered at 1250°c and 1200°c, respectively. figure 10: nyquist diagram sintered alloy in the hank’s solution and equivalent electrical circuit used for the simulation of the impedance data of the cocrmo alloy. the results thus obtained confirm the positive influence of the sintering temperature on the corrosion resistance. in a previous study, the capacitive behavior at the metal/electrolyte interface was shown to be primarily due to the formation of an oxide film on the surface of these alloys [28]. the closing appearance of the capacitive loop indicates that the surface is covered with a two-layer oxide film, mainly a compact inner layer and a porous outer layer. tab. 6 summarizes the analysis of experimental impedance data using the ec-lab software. the goodness-of-fit was evaluated by the values of (χ 2) that were in the range of 10-3. the data were adjusted with the equivalent electrical circuit (eec) depicted in fig. 10 (b). this circuit has already been proposed by many authors [29]. table 6: electrical parameters of the equivalent circuit of the sintered cocrmo alloy in hank's solution. the proposed model is composed of the solution resistance (rs) arranged in series with two parallel combinations resistance/capacity, each composed of a r1 (the outer layer resistance)/cpe1 (the elementary phase constant of the external film) and r2 (the inner layer resistance)/cpe2 (the elementary phase constant of the internal film). the resistance values of the inner layer that acts as a compact barrier are much higher than those of the outer porous layer. this indicates that the temperature ⦋°c⦌ rs ⦋ωcm2⦌ cpe1.10-3 ⦋fcm-2⦌ n1 r1 ⦋ωcm2⦌ cpe2.10-3 ⦋fcm-2⦌ r2 ⦋ωcm2⦌ n2 1200 26 0.573 0.9 445 0.230 1300 0.7 1250 23 0.721 0.9 1 978 0.196 3 309 0.8 1300 20 0.746 0.9 264 0.133 5 823 0.8 h. rezzag et alii, frattura ed integrità strutturale, 59 (2022) 129-140; doi: 10.3221/igf-esis.59.10 139 protection offered by the passive layer is mainly due to that of the internal barrier layer [45]. the larger capacitive loop usually leads to better corrosion resistance [30]. so, it should be noted that the sample sintered at 1300°c exhibited a higher polarization resistance. in fact, this resistance is the sum of two resistances: namely the resistance of the porous layer and the compact barrier resistance. the results thus obtained are in a good agreement of those obtained from the polarization curves. conclusion his paper investigates the influence of the sintering temperature on the microstructural, tribological and electrochemical properties of the cocrmo alloy. the main conclusions are listed below: 1. higher densification (porosity of up to 9%) was obtained at high sintering temperature of 1300°c compared to 1200°c and 1250°c. 2. the samples sintered at 1300°c exhibited better wear resistance with a wear rate of 0.987x10-4 mm3/nm. 3. in terms of electrochemical behavior, the samples sintered at 1300°c displayed higher corrosion resistance with a corrosion rate of 0.0047mm/year compared to samples sintered at 1200°c and 1250°c, respectively. 4. the results of the electrochemical impedance tests in the hank’s solution confirmed the capacitive behavior of the alloy by the formation of a film composed of two layers, a compact inner layer and another porous outer one. 5. the cocrmo alloy sintered at 1300°c yielded the best performance in terms of tribological and electrochemical. 6. the assessment of the effect of the sintering temperature is an important feature for alloy development. references [1] bandyopadhyay, a., shivaram, a., isik, m., avila, j. d., dernell, w. s. and bose, s. (2019). additively manufactured calcium phosphate reinforced cocrmo alloy: bio-tribological and biocompatibility evaluation for load-bearing implants. addit. manuf, 28, pp. 312–324. doi: 10.1016/j.addma.2019.04.020. [2] toh, w. q., tan, x., bhowmik, a., liu, e. and tor, s. b. (2017). tribochemical characterization and tribocorrosive behavior of cocrmo alloys: a review. materials, 11(1). doi: 10.3390/ma11010030. [3] liu, y.,& gilbert, j. l. (2017). the effect of simulated inflammatory conditions and ph on fretting corrosion of cocrmo alloy surfaces. wear, 390, pp. 302–311. doi: 10.1016/j.wear.2017.08.011. [4] stojanović, b., bauer, c., stotter, c., klestil, t., nehrer, s., franek, f. and rodríguez ripoll, m. (2019). tribocorrosion of a cocrmo alloy sliding against articular cartilage and the impact of metal ion release on chondrocytes. acta biomater, 94, pp. 597–609. doi: 10.1016/j.actbio.2019.06.015. [5] de castro girão, d., béreš, m., jardini, a. l., filho, r. m., silva, c. c., de siervo, a., araújo, w. s. (2020). an assessment of biomedical cocrmo alloy fabricated by direct metal laser sintering technique for implant applications. mater. sci. eng. c, 107, pp. 110305. doi: 10.1016/j.msec.2019.110305 [6] li, h., wang, m., lou, d., xia, w. and fang, x. (2020). microstructural features of biomedical cobalt–chromium– molybdenum (cocrmo) alloy from powder bed fusion to aging heat treatment. j. mater. sci. technol, 45, pp. 146– 156. doi: 10.1016/j.jmst.2019.11.031. [7] yamanaka, k., mori, m. and chiba, a. (2013). nanoarchitectured co-cr-mo orthopedic implant alloys: nitrogenenhanced nanostructural evolution and its effect on phase stability. acta biomater, 9(4), pp. 6259–6267. doi: 10.1016/j.actbio.2012.12.013. [8] hermawan, h., ramdan, d. and p. djuansjah, j. r. (2011). metals for biomedical applications. biomedical engineering from theory to applications. doi: 10.5772/19033. [9] varano, r., bobyn, j. d., medley, j. b. and yue, s. (2006). effect of microstructure on the dry sliding friction behavior of cocrmo alloys used in metal-on-metal hip implants. j. biomed. mater. res. part b appl. biomater, 76(2), pp. 281– 286. doi: 10.1002/jbm.b.30370. [10] daud, z. c., jamaludin, s. b., derman, m. n. and wahab, j. a. (2013). the corrosion studies of powder metallurgy cocr-mo (f-75) alloy. adv. environ. biol, 7, pp. 3716–3719. [11] rodrigues, w. c., broilo, l. r., schaeffer, l., knörnschild, g. and espinoza, f. r. m. (2011). powder metallurgical processing of co-28%cr-6%mo for dental implants: physical, mechanical and electrochemical properties. powder technol, 206(3), pp. 233–238. doi: 10.1016/j.powtec.2010.09.024. t rh. rezzag et alii, frattura ed integrità strutturale, 59 (2022) 129-140; doi: 10.3221/igf-esis.59.10 140 [12] thümmler, f. and oberacker, r. (1993). an introduction to powder metallurgy (series edi). the institute of materials, london. [13] ren, f., zhu, w. and chu, k. (2016). fabrication, tribological and corrosion behaviors of ultra-fine grained co-28cr6mo alloy for biomedical applications. j. mech. behav. biomed. mater, pp. 60, 139–147. doi: 10.1016/j.jmbbm.2015.12.039. [14] manivasagam, g., dhinasekaran, d. and rajamanickam, a. (2010). biomedical implants: corrosion and its prevention a review,recent patents corros. sci, 2(1), pp. 40–54. doi: 10.2174/1877610801002010040. [15] mehmet yıldırım, ak. (2018). production of co-cr-mo biomedical alloys via investment casting technique. turk. j. electrom. energ, 3(1). [16] daud, z. c., jamaludin, s. b. and bari, f. (2011). characterization of co-cr-mo (f-75) alloy produced by solid state sintering. adv. mater. res, 173, pp. 106–110. doi: 10.4028/www.scientific.net/amr.173.106. [17] mour, m., das, d., winkler, t., hoenig, e., mielke, g., morlock, m. m. and schilling, a. f. (2010). advances in porous biomaterials for dental and orthopaedic applications. materials, 3(5), pp. 2947–2974. doi: 10.3390/ma3052947. [18] buciumeanu, m., bagheri, a., souza, j. c. m., silva, f. s. and henriques, b. (2016). tribocorrosion behavior of hot pressed cocrmo alloys in artificial saliva. tribol. int, 97, 423–430. doi: 10.1016/j.triboint.2016.02.007. [19] fellah, m., aissani, l., iost, a., zairi, a., montagne, a. and mejias, a. (2018). friction and wear behavior of biomaterials alloys aisi 316l and ti-6al-7nb for total hip prosthesis. mater. tech, 106(4). doi: 10.1051/mattech/2018051 [20] saldívar-garcía, a. j. and lópez, h. f. (2005). microstructural effects on the wear resistance of wrought and as-cast co-cr-mo-c implant alloys. j. biomed. mater. res. part a, 74(2), pp. 269–274. doi: 10.1002/jbm.a.30392. [21] cuao-moreu, c. a., hernández-sanchéz, e., alvarez-vera, m., garcia-sanchez, e. o., perez-unzueta, a. and hernandez-rodriguez, m. a. l. (2019). tribological behavior of borided surface on cocrmo cast alloy. wear, pp. 426– 427(september 2018), 204–211. doi: 10.1016/j.wear.2019.02.006. [22] matthews, a. holmberg, k. (1994). coatings tribology: properties, techniques and applications in surface engineering, elsevier. 28, pp. 33-124. doi: 10.1016/s0167-8922(08)70753-3. [23] abbass, m. k. yagoob, j. a. (2019). corrosion behavior and mechanisms of co-cr-mo alloy fabricated by powder metallurgy route in ringer's solution. tikrit journal for dental sciences, 7(1), pp. 11-19. [24] thornley, b., beadling, r., bryant, m. and neville, a. (2020). investigation of the repassivation process of cocrmo in simulated biological fluids. corrosion, 76(6), pp. 539–552. doi: 10.5006/3423 [25] ortega-saenz, j. a., hernandez-rodriguez, m. a. l., ventura-sobrevilla, v., michalczewski, r., smolik, j. and szczerek, m. (2011). tribological and corrosion testing of surface engineered surgical grade cocrmo alloy. wear, 271(9–10), pp. 2125–2131. doi: 10.1016/j.wear.2010.12.062. [26] songür, m., çelikkan, h., gökmeşe, f., şimşek, s. a., altun, n. ş. and aksu, m. l. (2009). electrochemical corrosion properties of metal alloys used in orthopaedic implants. j. appl. electrochem., 39(8), pp. 1259–1265. doi: 10.1007/s10800-009-9793-6. [27] lashgari, h. r., kong, c., asnavandi, m. and zangeneh, s. (2018). the effect of friction stir processing (fsp) on the microstructure, nanomechanical and corrosion properties of low carbon cocr28mo5 alloy. surf. coatings technol, 354, pp.390–404. doi: 10.1016/j.surfcoat.2018.09.039 [28] vidal, c. v. and muñoz, a. i. (2009). effect of thermal treatment and applied potential on the electrochemical behaviour of cocrmo biomedical alloy. electrochim. acta, 54(6), pp. 1798–1809. doi: 10.1016/j.electacta.2008.10.018. [29] metikoš-huković, m., pilić, z., babić, r. and omanović, d. (2006). influence of alloying elements on the corrosion stability of cocrmo implant alloy in hank’s solution. acta biomater, 2(6), pp. 693–700. doi: 10.1016/j.actbio.2006.06.002. [30] liu, c., zhou, z. and li, k. y. (2017). improved corrosion resistance of cocrmo alloy with self-passivation ability facilitated by carbon ion implantation. electrochim. acta, 241, pp. 331–340. doi: 10.1016/j.electacta.2017.04.127. << /ascii85encodepages false /allowtransparency false /autopositionepsfiles true /autorotatepages /none /binding /left /calgrayprofile (dot gain 20%) /calrgbprofile (srgb iec61966-2.1) /calcmykprofile (u.s. web coated \050swop\051 v2) /srgbprofile (srgb iec61966-2.1) /cannotembedfontpolicy /error /compatibilitylevel 1.4 /compressobjects /tags /compresspages true /convertimagestoindexed true /passthroughjpegimages true /createjobticket false /defaultrenderingintent /default /detectblends true /detectcurves 0.0000 /colorconversionstrategy /cmyk /dothumbnails false /embedallfonts true /embedopentype false /parseiccprofilesincomments true /embedjoboptions true /dscreportinglevel 0 /emitdscwarnings false /endpage -1 /imagememory 1048576 /lockdistillerparams false /maxsubsetpct 100 /optimize true 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/hrv (za stvaranje adobe pdf dokumenata najpogodnijih za visokokvalitetni ispis prije tiskanja koristite ove postavke. stvoreni pdf dokumenti mogu se otvoriti acrobat i adobe reader 5.0 i kasnijim verzijama.) /hun 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can be opened with acrobat and adobe reader 5.0 and later.) >> /namespace [ (adobe) (common) (1.0) ] /othernamespaces [ << /asreaderspreads false /cropimagestoframes true /errorcontrol /warnandcontinue /flattenerignorespreadoverrides false /includeguidesgrids false /includenonprinting false /includeslug false /namespace [ (adobe) (indesign) (4.0) ] /omitplacedbitmaps false /omitplacedeps false /omitplacedpdf false /simulateoverprint /legacy >> << /addbleedmarks false /addcolorbars false /addcropmarks false /addpageinfo false /addregmarks false /convertcolors /converttocmyk /destinationprofilename () /destinationprofileselector /documentcmyk /downsample16bitimages true /flattenerpreset << /presetselector /mediumresolution >> /formelements false /generatestructure false /includebookmarks false /includehyperlinks false /includeinteractive false /includelayers false /includeprofiles false /multimediahandling /useobjectsettings /namespace [ (adobe) (creativesuite) (2.0) ] /pdfxoutputintentprofileselector /documentcmyk /preserveediting true /untaggedcmykhandling /leaveuntagged /untaggedrgbhandling /usedocumentprofile /usedocumentbleed false >> ] >> setdistillerparams << /hwresolution [2400 2400] /pagesize [612.000 792.000] >> setpagedevice microsoft word numero 23 articolo 4 m. bocciolone et alii, frattura ed integrità strutturale, 23 (2013) 34-46; doi: 10.3221/igf-esis.23.04 34 scilla 2012 the italian research on smart materials and mems application of martensitic sma alloys as passive dampers of gfrp laminated composites m. bocciolone, m. carnevale, a. collina, n. lecis, a. lo conte, b. previtali politecnico di milano, department of mechanical engineering, via la masa, 1 milano (italy) c.a. biffi, p.bassani, a. tuissi national research council cnr, institute for energetics and interphases, corso promessi sposi, 29 lecco (italy) abstract. this paper describes the application of sma (shape memory alloy) materials to enhance the passive damping of gfrp (glass fiber reinforced plastic) laminated composite. the sma has been embedded as reinforcement in the gfrp laminated composite and a sma/gfrp hybrid composite has been obtained. two sma alloys have been studied as reinforcement and characterized by thermo-mechanical tests. the architecture of the hybrid composite has been numerically optimized in order to enhance the structural damping of the host gfrp laminated, without significant changes of the specific weight and of the flexural stiffness. the design and the resultant high damping material are interesting and will be useful in general for applications related to passive damping. the application to a new designed lateral horn of railway collector of the italian high speed trains is discussed. keywords. sma hybrid composite; structural damping; laser micro-cutting; railway collector. introduction ver the past few years, due to the increasing technological demand for the passive suppression of mechanical vibrations, there has been a growing interest in developing high damping materials. while a consistent amount of literature on the damping of smas (shape memory alloys) has focused on the active damping of smallamplitude vibrations devoted either to applications of pseudoelasticity or during the superelastic phase, less attention has been paid to the passive damping behaviour at small amplitude harmonic vibrations with varying frequency ranges. small amplitude and passive vibration damping can be important in mechanical applications, where random broadband excitations are present in a typical operational environment. shape memory alloys are characterized by two phases: an austenitic phase, obtained at high temperatures and a martensitic one, obtained at low temperatures; the direct and reverse phase transformation between the two phases occurs in a certain temperature range, depending on the composition and heat treatment of the alloy [1]. high damping can be observed during direct and reverse transformations, and, consequently, during limited temperature intervals. several types of shape memory alloys, such as cu based smas, show high values of internal friction, even in the martensitic state [2-4]. the fairly high intrinsic damping of these martensitic phases has been associated with the atoms and defect motion and with the re-orientation of the martensite twin variants under stress [5]. from a practical point of view, this intrinsic energy dissipation mechanism of the martensitic phase over wider temperature ranges offers an interesting perspective for the application of sma alloys in the martensitic state as passive dampers of low amplitude mechanical vibrations for automotive, aerospace and other dynamic applications [6, 7] the idea of adopting the damping properties of the martensitic state means that the service temperature has to be lower than the transformation temperature. o http://www.gruppofrattura.it http://dx.medra.org/10.3221/igf-esis.23.04&auth=true m. bocciolone et alii, frattura ed integrità strutturale, 23 (2013) 34-46; doi: 10.3221/igf-esis.23.04 35 the high cost, the relatively high specific weight, and the relatively low specific modulus preclude the use of monolithic sma as a bulk material in many structures; however, interesting examples of composites or hybrid composites, designed for damping, can be found in literature [8, 9]. since the concept of sma hybrid composites was first proposed in 1988 by rogers et al. [10], these composites have attracted enormous attention in terms of improving creep and fatigue properties [11], strength [12] and damping capacity [13], as well as to control the shape or vibration response property [14]. among these materials, the sma/glass-fiber reinforced plastic (gfrp) hybrid composite in which the embedded sma is used to improve structural damping, thereby saving weight and stiffness, is especially important due to the wide potential or effective technological application of gfrp in all, real-life engineering environments [15, 16]. this paper describes a new architecture of sma/gfrp hybrid composite numerically optimized in order to enhance the structural damping of the host gfrp laminated, without significant changes of the specific weight and of the flexural stiffness [7]. two sma alloys have been studied as reinforcement and characterized by termo-mechanical tests. the design and the resultant high damping material are interesting and will be useful in general for applications related to passive damping, i.e. wind turbine blades or automotive components. since the research began from studies about the dynamic optimization of the collector of the italian high speed trains, this application is the guideline of the paper. design considerations he flexural modes of the collector of the high-speed train (fig. 1) play a significant role in terms of its dynamic behaviour and its lateral horns usually made of fiber glass/epoxy resin laminated are not able to guarantee the required level of structural damping. to optimize the dynamic behaviour of the collector, structural damping must be enhanced, in order to avoid in-depth modification in terms of mass and stiffness [17, 18]. figure 1: italian high-speed train collector. to enhance the damping of a glass fiber reinforced polymer (gfrp) beam and shell through passive vibration suppression, a shape memory alloy (sma) can either be embedded as reinforcement in the gfrp part. unlike gfrp, sma alloys have a higher storage modulus and a higher specific damping [19, 20]. due to its higher storage modulus and, assuming that the interface guarantees the right load transfer, the sma material is capable of storing more specific elastic energy than the gfrp and, as consequence, is able to take maximum advantage of its higher specific damping in order to enhance the structural damping of the hybrid composite. therefore the partial substitution of the gfrp material with sma material in various shapes and forms is expected to significantly increase the damping properties of the hybrid composite. in [21], thanks to the high damping of the niti in its martensitic the authors proposed the application of ti-ni sma alloy wires as ‘‘smart fibers’’ embedded in this conventional gfrp material in order to create new horns with an enhanced flexural damping capacity related to the first flexural mode. two series of 13 wires, with a diameter of 0.56 mm, were embedded below the upper and the lower surfaces of the horn as shown in fig. 2. figure 2: lateral horn made from a gfrp laminated composite with two layers of embedded niti wires. t http://www.gruppofrattura.it http://dx.medra.org/10.3221/igf-esis.23.04&auth=true m. bocciolone et alii, frattura ed integrità strutturale, 23 (2013) 34-46; doi: 10.3221/igf-esis.23.04 36 a first prototype of the horn was manufactured and then tested dynamically in a laboratory. experimental results showed that not only do the niti wires collaborate in the composite but also that the non-dimensional damping of the first flexural mode increases by about 11% with respect to the non-dimensional damping of the original horn made only of gfrp. conversely, the first natural frequency increases by about 5%. according to these results, it can be expected that the higher level of the vibration damping, required for real application of the proposed architecture of the horn, can be obtained with a proper volume fraction of the sma wires; however, the conflicting consequences of the introduction of sma wires between increasing of the structural damping and increasing of the first natural frequencies is addressed. for this reason, the same paper also discusses the implementation of a fe model of the horn in order to perform a dynamic analysis and to calculate the related non-dimensional damping. the results are presented for three configurations: the horns in their original configuration (only grfp), the horns made from grrp with two series of 13 embedded wires, as in the real prototype shown in fig. 3, and the horn made from grrp with two series of 20 embedded wires. as expected, by increasing the number of wires, the vibration damping of the horn increases; however, the undesirable side effect of the niti wires is that the flexural frequency increases by 10%, thus indicating that the requirements of the renewed design cannot be satisfied. additionally, some consideration should also be given to the architecture of the lateral horn with embedded sma wires. the manufacturing process involved in positioning the wires within the matrix is very complex. furthermore, when the horn is cooled to room temperature, high residual stresses in the sma wires are expected, due to the mismatch between the thermal expansion coefficients of the sma material and the laminated gfrp composite. as a consequence, sma fiber pull-out can easily occur [22]. the information generated and the experience gained in our previous paper will be used to propose a new sma/gfrp hybrid composite, based on a synergistic contribution of the parameters associated with the sma material such as specific damping, specific stiffness and volume fraction as well as those associated with the host, including flexural rigidity, sma through-the-thickness location and sma-host interfacial strength. particular attention has been paid to manufacturability and the cost-effectiveness of the component made with the proposed new composite. the architecture of the new hybrid composite he architecture of the new proposed hybrid composite is shown in fig. 3. the base composite is a symmetric angle-ply laminated of fiber glass/epoxy resin (3m-sp250 s29a). the elastic properties of the unidirectional layer are shown in tab. 1. the sequence of lamination is [45/-45]15. the elastic modulus (e11=e22) of the laminated fiber glass/epoxy resin with this sequence of lamination is 17 gpa. the loss factor, obtained by performing dma tests (q800 dma, ta instruments) on a 35x11.36x1.29 mm3 sample with a lamination sequence of [45/-45]3 at room temperature (indicatively 20 °c), is 0.8 % and, in the range (1-70 hz) results not dependent on the frequency value. two sma sheets are embedded below the upper and the lower surface of the layered gfrp. moreover, patterning of the sma sheets is introduced to improve adhesion between the sma sheets and gfrp layers, to avoid the delamination of the composite and to maximize the mechanical energy transmission to the sma element. the geometry of the patterning is optimized with respect to the improvement in terms of the composite damping and the adhesion at sma/glass fiber interface [15]. figure 3: architecture of the new proposed hybrid composite. t http://www.gruppofrattura.it http://dx.medra.org/10.3221/igf-esis.23.04&auth=true m. bocciolone et alii, frattura ed integrità strutturale, 23 (2013) 34-46; doi: 10.3221/igf-esis.23.04 37 traction compression exx [gpa] eyy [gpa] exx [gpa] eyy [gpa] gxy [gpa] nxy 45.7 13.5 47.8 12.8 5.4 0.27 table 1: elastic properties of the fiber glass/epoxy resin 3m-sp250 s29a. sma materials niticu and cuznal alloys are proposed for the reinfocement. niticu is a well-known system, obtained by partial substitution of ni with copper, whose damping capacity is high and stable versus the vibration time and aging effect of martensite. cuznal alloy has the highest damping capacity of all high damping metals [3] as well as a relatively high and appropriate modulus of elasticity. the niticu and cuznal alloys were prepared by means of a vacuum induction melting system. the nominal atomic composition of the smas produced are ni40ti50cu10 and cu66zn24al10. the ingots were hot forged and hot and cold rolled to achieve sheets boasting a thickness of 0.3 mm (30mm in width and 400-mm in length). the final heat treatments were 450°c for 1h, followed by a water quench and 750 °c for 30 min followed by a water quench, respectively. small samples, weighing about 15 mg, were subjected to differential scanning calorimetry (dsc), with a heating and cooling rate of 10 °c/min in the range 10-110 °c (q100 dsc, ta instruments). the thermographs shown in fig. 4, outline the characteristic transformation temperatures: mf=32 °c; ms=49 °c; as=52 °c and, af=61 °c for the ni40ti50cu10 and mf=50 °c; ms=63 °c; as=60 °c and, af=68 °c for the cu66zn24al10. the dsc scan confirms, for both materials, the martensitic structure at room temperature. the damping properties of the alloy were evaluated by means of dynamic mechanical analyses (q800 dma, ta instruments) carried out on thin sheet (12x1x0.15 mm3) of examined materials. different values of the frequency and strain amplitude were analysed. the specimen was subjected to a sinusoidal strain () with amplitude of 0.01%, 0.05%, and 0.1% and to a oscillation frequency (f) of 2, 10, 20, and 35 hz. the phase lag () between the applied stress and the resultant strain were measured in the temperature range [-20 °c÷120 °c] with a cooling/heating rate of 1 °c/min. as a result, the intrinsic damping (tan  of the sma was obtained as a function of the temperature. figure 4: dsc scan of the investigated materials, heating/cooling rate: 10 °c/min. figure 5: tan δ vs. temperature. dma analysis: heating rate 1°c/min, frequency 10 hz, strain amplitude 0.05%. fig. 5 shows the intrinsic damping tan δ as a function of temperature for an 0.05% strain amplitude, at a 10 hz frequency. the high damping capacity of the martensite phase can be observed at temperatures of below the as temperature, while, at higher temperatures, the parent phase (austenite phase) exhibits low tan δ values. no significant influence of frequency was observed in the range (2÷35 hz) tested. owing to the fact that only a few grains were present in the cross section of the dma specimens, results were validated through cyclic stress strain tests on larger samples. a http://www.gruppofrattura.it http://dx.medra.org/10.3221/igf-esis.23.04&auth=true m. bocciolone et alii, frattura ed integrità strutturale, 23 (2013) 34-46; doi: 10.3221/igf-esis.23.04 38 a mts quasi-static testing machine with a load cell of 10 kn is used for cyclic tension tests, at room temperature, on specimens measuring 200x20 mm2. the cycle frequency is fixed as equal to 0.05 hz, based on the assumption that the sma damping properties do not vary significantly at low frequencies. a series of 16 tests was performed by controlling the cyclic elongation using a 50 mm gage length extensometer. the deformation amplitude ranges between 2 104 and 1 103, while the minimum value is about 3 104. in each test, 10 cycles were run at the specified deformation amplitude. fig. 6 reports a comparison of the stress-strain hysteresis loop at 0.075% strain amplitude for the ni40ti50cu10 and cu66zn24al10 alloys. the highest damping capacity of the cu66zn24al10 are clearly shown. figure 7: stress-strain hysteresis loop for cuznal and niticu during mts tensile test at 0.075% strain amplitude. the following parameters have been calculated at each strain amplitudes: 1) tan δi value, obtained from the single cycle as: tan 2 i i i w w     (1) where δwi is the energy dissipated in the ith cycle of oscillation for unit volume, representing the area enclosed within the stress–strain hysteresis loop, and wi is the maximum stored energy in the same cycle of oscillation per unit volume; 2) storage modulus ei, evaluated as δσ/δε from the ith hysteresis loop; 3) sma specific damping capacity tan δ and sma storage modulus, obtained as the average values over the ten stress– strain loops performed. the results are shown in figs. 7 and 8 both for ni40ti50cu10 and cu66zn24al10. the loss factor shows an almost linear increase of the damping as a function of the strain amplitude. for cu66zn24al10 a nonlinear increase at about 0.06% of strain was observed. the tan d discontinuity at 0.05% strain amplitude was also observed during dma tests. this confirms that this particular trend of tan  is associated with a certain behaviour of the cu based sma. in order to understand this phenomenon better, accurate experiments will be performed in future developments. by comparison of results of fig. 7 with dma results of fig. 5 at a frequency of 10 hz, a good agreement can be observed. as shown by the results of fig. 8, the storage modulus decreases as the strain amplitude increases. numerical analyses inite element analysis was used in conjunction with a modal strain energy approach to study the change in the natural frequencies and the loss factor of a beam or shell, made from angle-ply laminated fiber glass/epoxy resin ([45/-45]15), when two thin sheets of the examined sma alloy are embedded in the hybrid composite based on the architecture of fig. 3. the hybrid composite is orthotropic with 1, 2, 3 as axes of orthotropy. the finite element model of the hybrid composite is a solid, beam-shaped model. the fiber glass/epoxy resin base composite (200x20x4.6 mm3) is modelled using 20node brick elements with reduced integration; the thin sma sheets are modelled with eight node shell elements. the constraint between the upper and lower surface of the gfrp laminated composite and the thin sma sheet is a tie constraint. the beam is clamped at one end (see fig. 9). f http://www.gruppofrattura.it http://dx.medra.org/10.3221/igf-esis.23.04&auth=true m. bocciolone et alii, frattura ed integrità strutturale, 23 (2013) 34-46; doi: 10.3221/igf-esis.23.04 39 figure 7: tan δ vs. strain amplitude. tensile test: f=10 hz, room temperature. figure 8: storage modulus vs. strain amplitude. tensile test: f=10 hz, room temperature. a linear elastic, undamped, modal finite element analysis was performed using the abaqus 6.7 code to extract the first natural frequency of the beam. the fiber glass/epoxy resin laminated composite has been assumed as an homogenous material having an appropriate density value and a linear elastic behaviour with an elastic modulus equal to the elastic modulus e=e11 of the gfrp base composite, and a poisson coefficient equal to 12, of the angle-ply laminated fiber glass/epoxy resin (see tab. 2). the behaviour of the sma material has also been assumed as being linear elastic with the properties shown in tab. 2. figure 9: fem model of the hybrid composite and first flexural deformed shape with superimpose the vertical displacement when the displacement of the free end is 1 mm. cu66zn24al10ni40ti50cu10 ni40ti50cu10 cu66zn24al10 http://www.gruppofrattura.it http://dx.medra.org/10.3221/igf-esis.23.04&auth=true m. bocciolone et alii, frattura ed integrità strutturale, 23 (2013) 34-46; doi: 10.3221/igf-esis.23.04 40 input data niticu cuznal glass fiber young modulus e [mpa] 23000 78000 17000 poisson coefficient [-] 0.30 0.20 0.35 density [kg/mm3] 6.50 10-6 7.40 10-6 1.86 10-6 table 2: input data for the fem analyses. figure 10: thin sheets following laser micro-cutting with three different patterns, having a different sma surface/total surface ratio. three different patterns of thin sma sheets, characterized by the same elliptical shape, but having a different hole surface/sma surface ratio are proposed (fig. 10). the hole surface/sma surface ratio is equal to 2.4, 2.25 and 0.65 for the pattern named large ellipses, few small ellipses and many small ellipses respectively. likewise, for comparison, the case of thin, un-patterned sma sheets were also considered. given the two selected material of tab. 2 and the geometries of the patterns shown in figura 10, the effect of the thin sheet thickness on the first natural frequency of the beam and on the splitting of the modal strain energy between gfrp laminated composite and reinforcement was numerically investigated. the preliminar result of the numerical analyses is about the first natural frequency. as the thickness of the fiber glass/epoxy resin base composite is kept constant (4.6 mm), if the thicknesses (t) of the sma equal to 0.1, 0.2 and 0.3 mm, the specific weight () of the hybrid composite is slightly affected by the presence of the sma insert, and the increase of the first natural frequency with thin, patterned sma-large ellipse, sma-many small ellipse, and sma-few small ellipse, sheets is limited and almost independent on the thickness. only for the unpatterned sma the first natural frequency is thickness dependent and the maximum variation is about 5% when the thickness is 0.3 mm. results are reported in tab. 3 for the first vibrational mode of the hybrid composite with, sma-large ellipses, smamany small ellipses and sma-not patterned, ni40ti50cu10 thin sheets embedded. t [mm] f [hz] athin sheets [%] agfrp laminated composite [%] tan  [%] fiber glass/ epoxy resin -71.1 -100 0.84 sma -large ellipse 0.1 0.2 0.3 73.9 74.1 74.2 4.9 8.5 11.6 95.1 91.5 88.4 0.92 1.10 1.30 smasmall ellipse 0.1 0.2 0.3 74.1 74.3 74.3 6.2 10.7 14.4 93.7 89.3 85.6 1.04 1.18 1.30 sma-not patterned 0.1 0.2 0.3 75.5 76.6 77.5 15.5 26.7 35.3 84.5 73.2 64.6 1.76 1.68 1.94 table 3: fem analysis estimated loss factor of the hybrid composite with ni40ti50cu10 thin sheets embedded. http://www.gruppofrattura.it http://dx.medra.org/10.3221/igf-esis.23.04&auth=true m. bocciolone et alii, frattura ed integrità strutturale, 23 (2013) 34-46; doi: 10.3221/igf-esis.23.04 41 the second aspect investigated by numerical analyses is the percentage of modal strain energy stored in the thin sma sheets (thin sheet) and in the gfrp laminated composite (gfrp laminated), for the first flexural mode, that is directly associated to the calculation of the loss factor of the hybrid composite (tan ). the modal strain energy approach gives us [23]: tetedcomposigfrplaminatetedcomposigfrplamina tantantan   thinsheetsthinsheets (1) where thin sheet and gfrp laminated are respectively the percentage of the modal strain energy stored in the thin sheets and in the gfrp laminated composite; tanthin sheet and tangfrp laminated are the loss factors of the corresponding materials. the loss factor of the hybrid composite was calculated according to eq. (1) are also reported in tab. 3. as can be observed in the sixth column of tab. 3, when the ni40ti50cu10 patterned sheets are embedded in the composite, the loss factor is significantly enhanced. the composites with unpatterned inserts perform very well in terms of damping, but are likely to delaminate during service life [24]. as opposed to the fiber glass/epoxy resin beam, the composites with thin, inserted patterned sheets show a significant improvement in terms of damping capacity, provided that the thickness of the sma layer is greater than 0.2 mm. thanks to the presence of hollow ellipses, a significant improvement in the insert/gfrp adhesion is also expected. the beam having many small ellipses, patterned sma sheets gives a better performance in terms of damping. as regards the thickness effect, it is necessary to point out that the composite loss factor increases with the thickness of the thin sma sheets. on the other hand, technological aspects related to the laser micro-cutting process have to be considered when the sheet thickness used in the layered composite is increased. laser cutting becomes more difficult when the thickness is considerably increased owing to the fact that the process speed has to be reduced and a multi pass strategy adopted. both actions decrease cutting edge quality in terms of dross, roughness and thermal damage. since finishing operations, targeted at removing the layer affected by the laser beam are intentionally disregarded because they increase process costs and time, a thickness of 0.2 mm seems to be a good compromise between damping and workability. a comparison between the damping performance of the hybrid composite with ni40ti50cu10 and cu66zn24al10 thin sheets, is reported in tab. 4. cu66zn24al10 thanks to its higher storage modulus stores up to 25 % of the elastic energy of the deformed beam with respect to the 10% of the modal strain energy stored by the ni40ti50cu10 reinforcement with the same many small ellipses patterns. as consequence the higher specific damping of the cu66zn24al10 alloy participate with a greater contribution to the enhancement of the structural damping of the hybrid composite moreover a modification of the pattern, from the sma_many small ellipses to the sma_few small ellipses, with a hole surface/sma surface ratio is equal to 0.65 (see fig. 11), allows a further significant increase of the modal strain energy stored in the sma thin sheets and of the final structural damping of the composite. t [mm] f [hz] thin sheets [%] gfrp laminated composite [%] tan  [%] ni40ti50cu10 – many small ellipse 0.2 74.3 10.7 89.3 1.18 cu66zn24al10 – many small ellipse 0.2 66.1 25 75 1.60 cu66zn24al10 – few small ellipse 0.2 69 37 69 2.04 table 4: fem analysis estimated loss factor of the hybrid composite, comparison between ni40ti50cu10 and cu66zn24al10 thin sheets embedded. these numerical results have been validated by experimental decay tests performed on sample of the proposed new composite. the experimental tests are described in detail in [13, 25]. http://www.gruppofrattura.it http://dx.medra.org/10.3221/igf-esis.23.04&auth=true m. bocciolone et alii, frattura ed integrità strutturale, 23 (2013) 34-46; doi: 10.3221/igf-esis.23.04 42 sma/gfrp lateral horn he new architecture of a sma/gfrp hybrid composite profile is proposed for the design of an sma/gfrp lateral horn. in this case the host composite is a symmetric angle-ply laminate of fiber glass/epoxy resin with a stacking sequence of (45/-45)n, where n varies, thus accounting for the variation in the horn thickness, ranging from 49 (thicker section) to 24 at the opposite end. on the basis of the results of the previous paragraph a cu66zn24al10 material and the few small ellipses pattern has been selected for this application. as regards the thickness effect, it is necessary to point out that the composite loss factor increases with the thickness of the sma sheets. even if laser micro-cutting becomes more difficult when the thickness increases, a thickness of 0.3 mm has been adopted in order to take the maximum advantage from the passive damping of the sma reinforcements. figure 11: architecture of the sma//gfrp hybrid composite horn. grey [-45/+45]n layered gfrp host composite. brown: embedded cuznal sma thin patterned sheets. a prototype of the horn has been made. firstly, the regular pattern of elliptical holes has been produced by means of laser cutting using a pulsed nanosecond fiber laser (ipg photonics ylp50). the process parameters used to perform the micro-cutting process of the elliptical pattern are shown in tab. 5. the maximum average power available, together with the highest pulse frequency and process speed were chosen to ensure through cutting and reduced thermal damage. a double laser pass strategy was required in order to guarantee stable cutting through the entire thickness of the sma sheet [26]. process speed [mm/s] average power [w] pulse frequency [khz] shielding gas 5 50 80 argon at 5 bar table 5: main process parameters used in laser micro-cutting of the elliptical pattern. in the second step, the laminated composite is assembled. the horn mould is filled first with four layers [+45/-45]4 of unidirectional fiber glass/epoxy resin and covered with the first patterned thin sma sheet; the sequence of lamination [+45/-45]n is added and covered by the second thin sma sheet and by an additional four layers [+45/-45]4 of unidirectional fiber glass/epoxy resin. as previously reported, parameter n is dependent on the thickness of the cross section along the axis of the horn. any air bubbles are eliminated by means of a vacuum bag and the hybrid composite is then cured in an autoclave. in order to study the dynamic properties of the proposed hybrid layered architecture and to evaluate the improvement of the damping capacity due to the introduction of the sma insert, three samples of the horn were produced. the first one was manufactured as described, while the second one was produced using the same architecture as the first one. however, in this case, commercial brass sheets were used in the place of the sma sheets. the third one was only made with gfrp. manufacture of an extra horn with a commercial brass insert is targeted at evaluating/excluding any possible contribution of a metal sheet/host composite interface to the damping of the sma hybrid composite horn. as shown in fig. 12, following the cure cycle in an autoclave, the three horn samples are completed. t http://www.gruppofrattura.it http://dx.medra.org/10.3221/igf-esis.23.04&auth=true m. bocciolone et alii, frattura ed integrità strutturale, 23 (2013) 34-46; doi: 10.3221/igf-esis.23.04 43 figure 12: final appearance of the three horn samples. experimental tests he non-dimensional damping, related to the first flexural mode of the three horns manufactured, was experimentally measured by performing a series of decay tests with the horn in a single cantilever configuration. during the tests, the end of the horn, designed to be connected to the structure of the collector, was clamped on a steel fixture, while the other end was loaded with an initial vertical displacement and then released to oscillate freely [22]. the transient response was recorded in terms of the vertical displacement of the section of the horn at a distance of 150 mm from the clamp. the displacement was measured by means of a lase-triangulation sensor (mel m5l/10). the non dimensional damping was evaluated as follows: 1 ln 2 wheren nn n n x h x             (2) where n is the logarithmic attenuation coefficient, xn is the vertical displacement amplitude of the horn at 150 mm from the clamping at the nth oscillation of the transient response and xn+1 is the same displacement amplitude at the (n+1)th oscillation. during transient decay, the amplitude of each successive oscillation decreases, meaning that eq. (2) allows us to obtain the dependence of the non-dimensional damping from the displacement amplitude. in order to compare the non-dimensional damping (h) with the loss factor (tan ), assumed as an index of the intrinsic damping in section design considerations, the following consideration can be made. the loss factor (tan ) of the oscillatory beam, considered as a single degree of freedom system, is defined as the ratio tan 2 de u    (3) where ed is the energy loss per cycle and u is the strain energy. assuming that the motion is entirely due to the first flexural mode 2 1 1 1 2 u k q (4) 2 1 1 1de c q   (5) where k1 is the modal stiffness, q1 is the modal coordinate, c1 is the modal damping, and  is the frequency of the first flexural mode of the beam. on account of 21 1 1k m where m1 is the modal mass of the beam and, from the definition of non-dimensional damping  1 1 1 12c h m , eq. (3) can be rewritten as: 2 2 1 1 1 1 1 1 1 1 2 2 2 1 1 1 1 1 (2 ) tan 2 1 2 2 c q h m q h m qk q            (6) t http://www.gruppofrattura.it http://dx.medra.org/10.3221/igf-esis.23.04&auth=true m. bocciolone et alii, frattura ed integrità strutturale, 23 (2013) 34-46; doi: 10.3221/igf-esis.23.04 44 eq. (6) recalls that the loss factor is equal to twice the non-dimensional damping value. the natural frequency of vibration of the first flexural mode can be identified by fourier transform of the waveform of the transient response of the horns acquired during the decay tests reported in fig. 13. in this figure, the transient response of the horn with a commercial brass patterned insert is actually superimposed on the only gfrp horn and, for sake of clarity, is not reported. the first natural frequencies of the three horn samples are shown in tab. 6 and are not affected by the integration of the sma/commercial brass. the total weight of the horns is also reported in the same table and is only slightly affected by the integration of the sma/commercial brass. as will be shown below, the reduced thickness of the sma/commercial brass sheets and the patterns with a ratio between the surface of the holes and the total surface of the sma sheet, equal to 0.65, not only allows us to maintain the structural and dynamic behaviour of the component but also to improve the damping capacity. the beneficial effect of the integration of an sma insert in the host gfrp horn on its damping capacity is apparent in fig. 13. the horn manufactured as an sma/gfrp hybrid composite has a larger logarithm attenuation coefficient of the first flexural mode both as regards the horn made only from gfrp as well as the one manufactured as a commercial brass/gfrp hybrid composite. as previously mentioned in fig. 13, the transient response of the latter two is practically superimposed. the results of experimental non-dimensional damping, associated with the first flexural mode, calculated from the logarithmic decrement of fig. 13 when the displacement is equal to 1mm, are shown in tab. 7. the comparison between the non dimensional damping of the only gfrp horn and the non dimensional damping of the horn with commercial brass reinforcement allows us to exclude any significant contribution of the metal sheet/host composite interface to the damping of the sma hybrid composite horn. when the sma patterned sheets is embedded in the composite, due to its high specific damping the non-dimensional damping of the horn is significantly enhanced. first natural frequency [hz] total weight of the horn [g] only gfrp 75.5 168 commercial brass/gfrp 75.3 182 sma/ gfrp 74.8 180 table 6: first natural frequency and total weight of the three horn samples. 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 -1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1 time [s] d is p lc e m e n t [m m ] only gfrp sma/gfrp figure 13: transient of the displacement in the section at 150 mm from the clamped section, for the horn with a sma patterned insert and for the horn made only from gfrp. http://www.gruppofrattura.it http://dx.medra.org/10.3221/igf-esis.23.04&auth=true m. bocciolone et alii, frattura ed integrità strutturale, 23 (2013) 34-46; doi: 10.3221/igf-esis.23.04 45 horn tan  h only gfrp 0.8 0.4 commercial brass 0.84 0.42 cu66zn24al10/gfrp 1.4 0.7 table 7: tan  e non-dimensional damping (h) for the three horns when the displacement is equal to 1 mm. conclusions o enforce the application of sma alloys for passive damping in mechanical systems, shape memory alloy-based composites with thin, embedded, patterned sma sheets were numerically optimized and fabricated. it has be shown that the new architecture of the hybrid composite is applicable to improve the structural damping of the host gfrp laminated, without significant changes of the specific weight and of the flexural stiffness. a salient result of this study is that the proposed hybrid composite architecture can be used for passive control of gfrp slender structure. patches of patterned sma thin sheets can be embedded only in the area of highest deformation of the gfrp structure according to the considered modal shape, to improve their passive damping capacity without any design modification and significant effects on the dynamic behaviour. the pattern of the thin sma sheets proved to be a key feature in the optimization process of the flexural stiffness, weight and damping capacity of the hybrid composite. at the same time, this feature plays a positive role in the improvement of adhesion, and in the load transfer, between the gfrp laminated composite and the sma reinforcements. the application of the proposed hybrid composite for a new design of a gfrp lateral horn of a railway pantograph has been proposed. a first prototype of the horn was manufactured. the salient points of the manufacturing process included the production of a cuznal sma alloy having an appropriate transformation temperature; the laser microcutting of the cuznal sma sheets and the fabrication of the component without any purpose-made alignment device. acknowledgment he authors would like to thank mako shark s.r.l–viale montecuccoli 18, 23843 dolzago (lc), italy, for manufacture of the laminated horns. references [1] k. otsuka, c.m. wayman, shape memory materials, cambridge university press, cambridge, (1998). [2] a. biscarini, b. coluzzi, g. mazzolai et al., j. alloys compd., 356 (2003) 669. [3] m.o. moroni, r. saldivia, m. sarrazin, a. sepulved, material science and engineering, a335 (2002) 313. [4] y.h. li, s.w. liu, h.c. jiang, et al., journal of alloy and coumponds, 430 (2007) 149. [5] j. van humbeeck, j. alloys compd., 355 (2003) 58. [6] j. van humbeek, s. kustov, smart mater. struct., 14 (2005) 171. [7] j. raghavan, t. bartkiewicz, s. boyko, m. kupriyanov, et al., composites: part b, 41 (2010) 214. [8] ya xu, k.otsuka, h.yoshida, h.nagai, r.oishi, h.horikawa, t.kishi, intermetallics, 10 (2002) 361. [9] r. zhang, q. q. ni, a. masuda, t. yamamura, m. iwamoto, composite structures, 74 (2006) 389. [10] rogers ca, liang c, barker d. in: proceedings of us army research office workshop on smart materials, structures, and mathematical issues, blacksburg, usa (1988) 39. [11] m. dolce, d. cardone, int. j. of mechanical sciences, 47 (2005) 1693. [12] d.s. li, x.p. zhanga, z.p. xionga, y.-w. mai, journal of alloys and compounds, 490 (2010) l15. [13] c.a. biffi, p. bassani, a. tuissi, m. carnevale, n. lecis, a. lo conte, b previtali, functional materials letters, 5(1) (2012) 1250014. [14] g. zhou, p. lloyd, composites science and technology, 69 (2009) 2034. [15] y. matsuzaki, t. ikeda, c boller, smart mater. struct., 14 (2005) 343 t t http://www.gruppofrattura.it http://dx.medra.org/10.3221/igf-esis.23.04&auth=true m. bocciolone et alii, frattura ed integrità strutturale, 23 (2013) 34-46; doi: 10.3221/igf-esis.23.04 46 [16] f. taheri-behrooz, f taheri, r. hosseinzadeh, material and design, 32 (2011) 2023. [17] a. collina, s. melzi, in: aitc-ait, conference, parma, italy, (2006). [18] a. collina, a. lo conte, m. carnevale, proc. imeche part f: j. rail and rapid transit, 223 (2009) 1. [19] s.k. wu, h.c. lin, journal of alloys and compounds, 355 (2003) 72. [20] c. remillat, m. r. hassan, f. scarpa, transactions of the asme, 128, (2006), 260. [21] a. tuissi, p. bassani, a. casati, m. bocciolone a. collina, m. carnevale, a. lo conte, b. previtali, jmepeg, 18 (2009) 612. [22] k.t. lau, a. w.chan, s. q. shi, l. m. zhou, materials and design, 23 (2002) 265. [23] g. lepoittevin, g. kress, materials and design, 31 (2010) 14. [24] q. q. ni, r. zang, t. natsuki, m. iwamoto, composites structures, 2007 (79) 501. [25] p. bassani, c.a. biffi, m. carnevale, n. lecis, b. previtali, a. lo conte, materials and design, 45 (2013) 88. [26] b. previtali, s. arnaboldi, p. bassani, et al., in: 10th biennial conference on engineering systems design and analysis, esda 2010, istanbul (2010). http://www.gruppofrattura.it http://dx.medra.org/10.3221/igf-esis.23.04&auth=true microsoft word numero_49_art_48_2299 a. kumar et alii, frattura ed integrità strutturale, 49 (2019) 515-525; doi: 10.3221/igf-esis.49.48 515 focused on showcasing structural integrity research in india structural integrity assessment of weld for joining waveguide to annular linear induction pump subjected to vibration ashish kumar, y.v. nagaraja bhat, b.k. sreedhar, s.i. sundar raj, v.prakash, p. selvaraj indira gandhi centre for atomic research, kalpakkam, tamil nadu-603102, india. ashishkumar@igcar.gov.in, yvnb@igcar.gov.in, bksd@igcar.gov.in, sisr@igcar.gov.in abstract.annular linear induction pump (alip) is employed for low flow rate pumping of liquid metals because of its maintenance free operation. in order to monitor pump vibration during operation, a waveguide with accelerometer combination is employed. the waveguide is a stainless steel (ss) rod of 300 mm length and 20 mm diameter which is provided with a threaded provision at one end for mounting the accelerometer. the other end of the waveguide is welded to the shell of the alip of 3 mm thickness. these waveguides are to be attached to the alip in different orientations. the weld connecting the waveguide to the shell of alip is subjected to fatigue loading caused due to pump vibration. this paper discusses the analysis carried out to determine the fatigue life of the weld using asme section viii division 2. keywords. alip; vibration; waveguide; weld; fatigue. citation: kumar, a., bhat, y.v.n., sreedhar, b.k., sundar raj, s.i., prakash, v., selvaraj, p., structural integrity assessment of weld for joining waveguide to annular linear induction pump subjected to vibration, frattura ed integrità strutturale, 49 (2019) 515-525. received: 29.11.2018 accepted: 04.06.2019 published: 01.07.2019 copyright: © 2019 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. introduction nnular linear induction pump (alip) is used to circulate liquid metals at low flow rates. these pumps are used because they are maintenance free due to the absence of moving parts. however, it is reported in literature [1] that the pumps may experience vibrations from magneto hydrodynamic instability, especially at large flow rates. online vibration monitoring of these pumps may be carried out using a specially designed vibration monitoring device consisting of a waveguide and accelerometer combination. the construction of the waveguide indicating locations for mounting accelerometers on these waveguide is shown in fig. 1. these waveguides have a conical end (fig. 1) at which it is attached to the alip and these waveguides are to be attached under different orientations as shown in fig. 2, but the configuration which would result in the most severe stresses is the one in which the horizontal axis of the waveguide is perpendicular to gravity (waveguides 2 and 3 in fig. 2). the thickness of alip body where waveguide 2 is attached is 6 mm while at the location of attachment of waveguide 3, thickness of alip body is 3 mm. hence, the configuration shown for waveguide 3, being the most critical, has been analyzed. a http://www.gruppofrattura.it/va/49/2299.mp4 a. kumar et alii, frattura ed integrità strutturale, 49 (2019) 515-525; doi: 10.3221/igf-esis.49.48 516 figure1: details of waveguide and location of accelerometers figure 2: location and orientation of waveguides on the alip body the objective of this study is to estimate the fatigue life of the weld which is acted upon by stresses arising due to selfweight and excitation of its base. a suitable finite element model has been identified to carry out numerical simulation. studies have been carried out to estimate the static stress at the weld arising due to self-weight of the waveguide. natural frequency of the waveguide is found to ensure that it does not lie close to expected frequency of vibration of pump. a transient analysis is finally carried out to estimate the stress response of the weld under time varying displacements. the a. kumar et alii, frattura ed integrità strutturale, 49 (2019) 515-525; doi: 10.3221/igf-esis.49.48 517 stress response obtained under time varying displacements is studied and it is utilized to estimate fatigue life of the weld using codal formula. weld details and process of welding to obtain the higher frequencies signals, the waveguide must be attached to the component uniformly such that no air gap is present between them, as air gaps tend to reflect back the signals. to achieve a strong uniform attachment without air gaps, welding is considered to be most appropriate. the minimum thickness of the alip body, where the waveguide is to be attached is only 3mm, hence, a weld of size that is sufficient to provide enough strength with minimal distortion of the thin alip body is to be selected. due to this reason, a 3mm groove weld has been chosen to weld the waveguides to alip. location of weld, waveguide and alip body is shown in fig. 3. tungsten inert gas (tig) welding is ideal to weld the waveguide end to alip body. the filler metal used for this welding shall be filler wire (electrode rod) er316l conforming to sfa 5.9 of asme section ii of part c for ss 316l material. for initial passes, in which gap to be filled is less, filler wire having diameter 1.6mm shall be used while the subsequent passes can be completed using 2.5 mm diameter filler wire. this welding shall be carried by qualified welder in accordance to section ix of asme. after completion of the weld, it will be properly ground followed by 100% radiography and liquid penetrant examination to ensure that the weld has no defects. design of waveguide material and dimensions of waveguide hoice of material for construction of alip has been decided mainly based upon material’s compatibility with sodium, temperature of operation, creep properties, economics etc. keeping these criteria in mind for alip, the most appropriate material is (stainless steel) ss 316l or ss 304l [2]. in this study, it has been assumed that alip is constructed of ss 316l and corresponding material properties have been selected from reference 3. waveguides to be attached to alip is made of same material (ss 316l in this case) to facilitate similar metal weld. the length of the waveguide is the result of a compromise between the temperatures required for proper functioning of accelerometers mounted at the extreme end of these waveguides and the displacement at that end due to vibrations. whereas the temperature at the location of accelerometers in these waveguides should be close to the ambient temperature, the displacements due to vibration should be minimal. use of insulation on the alip body also poses an additional limitation on the shortest length of the waveguide, which should be greater than insulation thickness. the diameter of the waveguide can vary depending upon space available for mounting the accelerometers. to meet these criteria, a 300 mm long waveguide has been chosen with diameter of 20 mm (fig. 1). determination of maximum stress under static condition the weld location of the waveguide is subjected to stresses as a result of attachment of the waveguide under the given orientation. the bending stress acting on the weld is given as: σb = m/z (1) where, σb = bending stress m = moment due to self-weight at weld location z = section modulus of the weld the weight of waveguide is 0.9 kg and centre of mass is at a distance of 169 mm from tip of the weld; so, m = 1.49 n-m z = i/y =2.12×10-8 m3 hence, σb = 1.49/2.12×10-8 = 70 mpa the effect of stress concentration factor has been neglected in the above calculation. the increment in stress due to this has been estimated using finite element method (fem). finite element model commercially available finite element method (fem) based code is used to carry out the numerical simulation. a complete solid model of the waveguide has been used as symmetry advantage could not be taken due to geometry and c a. kumar et alii, frattura ed integrità strutturale, 49 (2019) 515-525; doi: 10.3221/igf-esis.49.48 518 boundary conditions. the model is shown in fig. 3. the portion of alip body selected for simulation is discussed under following section. figure 3: model of waveguide, weld and alip body this model is discretized using 10 node solid tetrahedral elements and mesh independent study has been carried out by refining the mesh near the weld location, until the difference in the result (maximum stress) between two consecutive trials was negligible. using fem, the maximum equivalent stress at the weld location has been found to be around 96 mpa. the deformed shape is shown in fig. 4 while the detailed equivalent (von mises) stress around the weld is shown in fig. 5. figure 4: deformed shape under self-weight of the waveguide figure5: equivalent (von-mises) stress around the weld location due to self-weight of the waveguide modeling of alip body t the point of attachment, the waveguide (waveguide 2 and 3) is oriented with its horizontal axis perpendicular to gravity as shown in fig. 2. in order to carry out the analysis, instead of completely considering the entire alip body, only a small portion of the alip body has been considered. the size of this portion of the alip has been a a. kumar et alii, frattura ed integrità strutturale, 49 (2019) 515-525; doi: 10.3221/igf-esis.49.48 519 estimated with the concept of “beam on elastic foundation” [4], such that the effect of attachment of waveguide on the alip body is negligible beyond this region. this region is represented approximately by a circle whose radius is equal to 1/β. 1/β is the distance beyond the application of load after which factors like deflection, slope, bending moment, etc. are negligible [4]. 2 4 2 2 3(1 ) r h     (2) where, ν = poisson ratio r = radius of curvature h = thickness substituting ν = 0.3, 1.285 rh   for r= 0.189 m and h=0.003 m, β = 54m-1 = 0.054 mm-1 hence, 1/β = 18.53 mm this is illustrated with the help of fig. 6. figure 6: isometric view of modeled alip body and waveguide attached with weld dynamic analysis carried on model he vibration in the alip sets the waveguide also into vibration and the welded region experiences maximum alternating stress cycles. to estimate the stresses under vibration, first of all, natural frequency of the waveguide has been estimated. natural frequency of waveguide the waveguide consists of different cross-sections and hence, its natural frequency needs to be estimated using fem. in order to confirm the correctness of the modeling exercise using fem, the natural frequency of a simple cantilever of 20 mm diameter and length of 300 mm was calculated using analytical formula as well as using fem analysis. the natural frequency of a cantilever beam is given by the formula 3 [5]: 2 4 ( )n n e i l l        (3) where, ω = angular velocity/ frequency n = mode number e = young’s modulus of the material l = length of the cantilever t a. kumar et alii, frattura ed integrità strutturale, 49 (2019) 515-525; doi: 10.3221/igf-esis.49.48 520 i = moment of inertia  = mass per unit length β = number which depends on the boundary conditions of the problem the value of (βnl)2 for a cantilever[5] is given in tab. 1. (β1l)2 (β2l)2 (β3l)2 3.52 22.0 61.7 table 1: values of (βnl)2 for e = 2×1011 n/m2 l = 0.3 m i = 7.854 ×10-9 m4  = 2.466 kg/m ω1 = 987.07 rad/s = 157.09 hz ω2 = 6169.24 rad/s = 981.86 hz the natural frequencies determined by fem are as follows, ω1 = 156.97 hz ω2 = 969.31 hz this shows that the results obtained through fem are in close agreement to that obtained using analytical method. the actual 20 mm waveguide, as shown in fig. 1, which has to be analyzed has a conical end where a 3 mm groove weld is present; hence the diameter at this location is 6 mm. this change in cross-section results in decrease of the natural frequency, which has been estimated using fem and is tabulated in tab. 2. mode frequency(hz) 1 32.2 2 567.7 table 2: natural frequencies of vibration of waveguide fig. 7 and 8 shows the first two mode shapes of the waveguide figure 7: first mode shape of vibration of waveguide at 32.2 hz figure 8: second mode shape of vibration of waveguide at 567.7 hz reference 1 indicates that the dominant low frequency (lf) pressure pulsation lies in the range of 0-10 hz and at an ac supply frequency of 50 hz, a double supply frequency (dsf) pressure pulsation lies at 100 hz. these frequencies arising a. kumar et alii, frattura ed integrità strutturale, 49 (2019) 515-525; doi: 10.3221/igf-esis.49.48 521 due to magneto-hydrodynamic instability lie far away from both the estimated natural frequency of the waveguide. hence resonance of waveguide, which may lead to large amplitudes, is not expected during its operation. transient analysis at 10 hz frequency: assuming that the vibration of alip sets the waveguide under harmonic vibration, the weld would be subjected to maximum stress cycle. to estimate these stresses, the modeled alip body was set under harmonic motion governed by eqn. (4) in vertical direction. displacement cycle the maximum acceleration (i.e. 0.5 m/s2) and expected frequency of vibration (i.e. 10 hz) due to magneto-hydrodynamic instability has been chosen based on details given in reference 1. given maximum acceleration ‘ao’ =0.5 m/s2 = 500 mm/s2 frequency of vibration ‘ω’ =10 hz = 2π×10 rad/s displacement equation, ‘y’ = (ao/ω2) sin (ωt) putting the numerical values,    2 500 sin 2 10 2 10 y time mm       (4) the effect of damping has been considered in obtaining the response of the system by incorporating a proportional damping ‘c’[6], as given by rayleigh: c = α m + β k (5) where, m is mass matrix and k is the stiffness matrix α, β are constants which are related to natural frequency (ωi) and damping ratio (ζ) as, 2ζωi = α + ωi2β (6) the first two natural frequencies and damping of 2% for both frequencies are used for determining these damping constants. six cycle of operation, as shown in fig. 9 were given as input to the extreme left of the alip body at the location as shown in fig. 10. figure 9: input displacement cycles under these displacement cycle, given at the location as shown in fig. 7, the maximum equivalent stress at a location in the weld region was obtained as a function of time and is shown in fig. 11. a. kumar et alii, frattura ed integrità strutturale, 49 (2019) 515-525; doi: 10.3221/igf-esis.49.48 522 figure 10: location of input displacement cycle at the alip body figure 11: variation of maximum equivalent stress at the weld location as a function of time fatigue life estimation the stress cycles has an initial exponentially decaying amplitude region in which peak stress at the critically loaded location in the first cycle is 161.66 mpa. the eventual steady state stress cycle at the same location has alternating stress range=10.6 mpa, about a mean stress of 93.3 mpa. under such loading, in order to find the reliable period of operation, estimation of fatigue life of the weld is critical. in order to find out the fatigue life, asme section viii division 2 [7] has been used, which lays out the procedure for estimation of fatigue life of weld. it is to be noted that the initial exponentially decaying stress amplitude corresponds to the solution of complementary part of the governing differential equation [6], which occurs during start up of alip. the number of cycles, hence calculated for this stress range would indicate the number of start up of alip which the weld can withstand. alip is supposed to operate continuously without shutdown for the incessant supply of sodium to purification circuit and to make up for various leakages and hence, it will not be shutdown unless there exists a need for maintenance. the number of cycles, n as per 2010 asme section viii, division 2, 3.f.2.2 for welded joint, is given as 1 , . hmti e ess k f cf n f s        (7) where, fi = fatigue improvement method correction factor for welded joint fatigue curve this factor has been taken as 1 assuming that no fatigue improvement method has been used. if any improvement method is adopted then the factor can be changed as per formula given in reference 7. fe = environmental correction factor to the welded joint fatigue curve this factor is taken as 4 as per reference 7. fmt = material temperature correction factor this is the ratio of modulus of elasticity of the material under evaluation at average temperature of cycle being evaluated to modulus of elasticity of carbon steel at ambient temperature. c , h = given in tab. 3.f.11 of asme 2010 section viii, division 2 in this calculation c is taken as 11577.9 considering lower prediction interval (-3σ) for design unless while h is taken as 0.31950. a. kumar et alii, frattura ed integrità strutturale, 49 (2019) 515-525; doi: 10.3221/igf-esis.49.48 523 ∆sess,k = equivalent structural stress range parameter, given as , 2 1 2. , ss ss ss k ess k m m m ess m k s t i f                     (8) where, ∆σk = stress range mss = exponent used in a fatigue analysis based on the structural stress this factor has been taken as 3.6 as per reference 7 tess = structural stress effective thickness this factor has been taken as 16 as per reference 7 i =correction factor used in the structural stress evaluation fm,k = mean stress correction factor for the kth cycle the detailed procedure for estimation of these i and fm,k is given in reference 7. the calculation given here corresponds to estimation of number of allowable cycles for the weld under constant stress amplitude, which has the following stress range, mean stress, σmean = 93.3 mpa stress range, ∆σk = 10.6 mpa number of cycles, n = 2.247×108 cycles i.e. the welded joint can withstand a continuous operation for 260 days, if it continues to vibrate at 10 hz at room temperature. in the next set of calculation, initial exponentially decaying stress response has been considered. for each cycle allowable number of cycles has been estimated and finally the number of overall cycles (i.e. maximum number of start up of alip which the weld can withstand) is arrived at, in such a way that total fatigue usage fraction remains less than one. allowable cycles for each stress range are tabulated in tab. 3. cycle no. σ min σ max ∆ σ σ mean allowable no. of cycles 1 7.57 161.66 154.08 84.615 36967 2 32.311 132.82 100.509 82.566 114980 3 58.009 122.56 64.551 90.284 1651157 4 77.205 114.0 36.795 95.6025 1275653 5 82.115 101.30 19.185 91.707 7966562 6 80.786 94.60 13.514 87.543 19726942 7 86.03 98.521 12.491 92.275 22320979 table 3: allowable cycles for various stress cycles during exponentially decaying period assuming the number of startups of alip = n calculation for total fatigue fraction to be less than 1, 1 36967 114980 1651157 1275653 7966562 19726942 22330979 n n n n n n n        hence, n ≤ 26767 cycles hence, the weld can withstand more than 25000 startups at a temperature of 200°c. a. kumar et alii, frattura ed integrità strutturale, 49 (2019) 515-525; doi: 10.3221/igf-esis.49.48 524 reduction in length of waveguide he main purpose of waveguide is to transmit signal from the vibrating body to which it is attached at one end (alip in present case) to the accelerometer mounted at its other end. an insulation of thickness 150 mm covers the alip body, and hence, the minimum length of waveguide must be greater than this. initially it has been proposed to use a 300 mm waveguide for which fatigue life has been estimated. with the objective of obtaining lower stresses and hence, higher fatigue life, a 200 mm long waveguide has been analyzed. this decrease in length is assumed to have no appreciable increase in the temperature at the accelerometer region as compared to original length. analysis the bending stress at the weld location for 200 mm long waveguide was found to be 47.84 mpa, whereas the natural frequency of this waveguide is shown in following table: mode frequency (hz) 1 56.20 2 876.21 table 4: different mode shape frequency of the waveguide stress due to vibration for finding out the stress response, 3 cycles were analyzed in this case at a frequency of 10 hz and maximum amplitude of 0.5 m/s2. the stress response is shown in the figure below. figure 12: stress at the weld location as a function of time estimation of fatigue life of the weld in this case the mean stress has reduced to about 48 mpa while the stress range has become 5.8 mpa. under such condition and neglecting the exponentially decaying amplitude region the fatigue life of the weld has been estimated to be n = 1.483 × 109 cycles i.e. the welded joint can withstand a continuous operation for 1716 days or approximately 4.7years, if it continues to vibrate at 10 hz at 200°c. with a decrease in stress range as well as mean stress the number of start up which the weld can withstand, due to initial exponentially decaying stress amplitude, would be higher than those calculated for 300 mm length. t a. kumar et alii, frattura ed integrità strutturale, 49 (2019) 515-525; doi: 10.3221/igf-esis.49.48 525 response at 100 hz frequency a further estimation of fatigue life was done by exciting the alip body at 100 hz to consider double supply frequency (dsf) [1]. as the frequency of excitation is high, the analysis was run for about 30 cycles. a similar transient simulation was done as described earlier to estimate the transient stress response. the mean stress in this case remains the same as earlier i.e. ~ 48 mpa while the stress range has reduced to 3.29 mpa. the fatigue life under the constant stress amplitude is, n= 8.784 × 109 cycles i.e. the welded joint can withstand a continuous operation for 1016 days or approximately 2.78 years, if it continues to vibrate at 100 hz at 200°c. conclusion he stress response obtained under the sinusoidal excitation given near the base comprises of two parts. in the first part, stress amplitudes are high and decreases exponentially with time and its frequency is equal to the natural frequency of the waveguide. this response is governed by solution of homogenous part of the governing differential equation and it limits the number of start-ups (or sudden transients) that the weld can withstand. the second part, which is the solution of particular integral, is stabilized stress cycle with same frequency as the frequency of excitation. the stress amplitude in this region remains constant and hence it limits the time for which the weld can be continuously subjected to such vibrations. it is evident that the fatigue life of the weld is the determining criteria for a reliable period of operation of the waveguide. the fatigue life of the weld has been estimated and the minimum fatigue life of weld for 300 mm long waveguide vibrating at 10 hz continuously is around 260 days. in an attempt to enhance this fatigue life, a reduction in the overall length by 100 mm was done and its effect on stress and life were obtained. this modification leads to a reduction in the stress due to self-weight from 96 mpa to 48 mpa. the constant stress range has reduced from 10.6 mpa to 5.8 mpa when the alip vibrates at 10hz thereby increasing the minimum fatigue life of the weld to 1716 days, however for 100 hz frequency the life of the weld has been estimated as 1016 days under continuous operation. hence, the use of a 200 mm long waveguide is a preferable choice. references [1] hideo, araseki et.al. (2004). magnetohydrodynamic instability in annular linear induction pump part i. experiment and numerical analysis, nuclear engineering and design 227 (2004) 29–50 [2] mannan, s.l. et. al. (april, 2003). selection of materials for prototype fast breeder reactor, transactionsindian institute of metals 56(2) [3] boiler and pressure vessel code (bpvc) asme (2013). ii materials part d properties (customary) [4] harvey,john f. theory and design of pressure vessels, van nostrand reinhold company, new york. [5] thomson,w. t. theory of vibration, cbs publishers and distributors, new delhi, third edition. [6] rao, singiresu s. (2004). mechanical vibrations, pearson education pte. ltd. [7] boiler and pressure vessel code (bpvc) asme (2010). section viii, division 2, part 5, fatigue assessment of weld-elastic analysis and structural stress. t << /ascii85encodepages false /allowtransparency false /autopositionepsfiles true /autorotatepages /none /binding /left /calgrayprofile (dot gain 20%) /calrgbprofile (srgb iec61966-2.1) /calcmykprofile (u.s. web coated \050swop\051 v2) /srgbprofile (srgb iec61966-2.1) /cannotembedfontpolicy /error /compatibilitylevel 1.4 /compressobjects /tags /compresspages true /convertimagestoindexed true /passthroughjpegimages true /createjobticket false /defaultrenderingintent /default /detectblends true /detectcurves 0.0000 /colorconversionstrategy /cmyk /dothumbnails false /embedallfonts true /embedopentype false /parseiccprofilesincomments true /embedjoboptions true /dscreportinglevel 0 /emitdscwarnings false /endpage -1 /imagememory 1048576 /lockdistillerparams false /maxsubsetpct 100 /optimize true /opm 1 /parsedsccomments true 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can be opened with acrobat and adobe reader 5.0 and later.) >> /namespace [ (adobe) (common) (1.0) ] /othernamespaces [ << /asreaderspreads false /cropimagestoframes true /errorcontrol /warnandcontinue /flattenerignorespreadoverrides false /includeguidesgrids false /includenonprinting false /includeslug false /namespace [ (adobe) (indesign) (4.0) ] /omitplacedbitmaps false /omitplacedeps false /omitplacedpdf false /simulateoverprint /legacy >> << /addbleedmarks false /addcolorbars false /addcropmarks false /addpageinfo false /addregmarks false /convertcolors /converttocmyk /destinationprofilename () /destinationprofileselector /documentcmyk /downsample16bitimages true /flattenerpreset << /presetselector /mediumresolution >> /formelements false /generatestructure false /includebookmarks false /includehyperlinks false /includeinteractive false /includelayers false /includeprofiles false /multimediahandling /useobjectsettings /namespace [ (adobe) (creativesuite) (2.0) ] /pdfxoutputintentprofileselector /documentcmyk /preserveediting true /untaggedcmykhandling /leaveuntagged /untaggedrgbhandling /usedocumentprofile /usedocumentbleed false >> ] >> setdistillerparams << /hwresolution [2400 2400] /pagesize [612.000 792.000] >> setpagedevice microsoft word numero_55_art_19_2969 f. cucinotta et alii, frattura ed integrità strutturale, 55 (2021) 258-270; doi: 10.3221/igf-esis.55.19 258 thermal emission analysis to predict damage in specimens of high strength concrete filippo cucinotta university of messina, italy filippo.cucinotta@unime.it, http://orcid.org/0000-0002-0304-4004 antonino d’aveni university of catania, italy daveni@dica.unict.it, http://orcid.org/0000-0002-7178-1495 eugenio guglielmino university of messina, italy eguglie@unime.it, http://orcid.org/0000-0001-7793-7406 antonino risitano c.r.p.s., italy arisitan@gmail.com giacomo risitano, dario santonocito university of messina, italy giacomo.risitano@unime.it, http://orcid.org/0000-0002-0506-8720 dsantonocito@unime.it, http://orcid.org/0000-0002-9709-9638 abstract. in this paper thermal analysis was applied to determine the “critical stress” of concrete, different from its ultimate strength, able to produce the first damage in the structures under compressive loads. the critical stress can be thought as the stress able to produce the beginning of fatigue rupture within the material. several specimens of high strength concrete were tested in order to define the incipient crack phenomena, also in internal part of the specimen not accessible by direct inspections, with the aid of infrared thermography. a finite element analysis completes the study and compares, for the same static loading conditions, the stress state with the experimental thermographic images. the final results show as the coupling of normal compressive test and the acquisition of the thermal images can be a useful aid to estimate a security stress value, indeed the critical stress, before the ultimate serviceability limit (slu) of the structure, defined as the maximum load condition before its failure. keywords. crack; critical stress; fem; infrared thermography. citation: cucinotta, f., d’aveni, a., guglielmino, e., risitano, a., risitano, g., santonocito, d., thermal emission analysis to predict damage in specimens of high strength concrete, frattura ed integrità strutturale, 55 (2021) 258-270. received: 19.11.2020 accepted: 18.12.2020 published: 01.01.2021 copyright: © 2021 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. https://youtu.be/usitfyyaawk f. cucinotta et alii, frattura ed integrità strutturale, 55 (2021) 258-270; doi: 10.3221/igf-esis.55.19 259 introduction everal bridges and civil structures disasters, like genova morandi’s viaduct, alert that the cyclical creep may have been an additional cause of the catastrophic collapse of these structures. fatigue phenomena on civil structures, subjected to dynamic loads over time (atmospheric phenomena, alternate loads and vibrations induced by vehicular traffic) lead to dangerous cracking, limiting the life of the structures. indeed, during the design phase it is necessary to know not only the breaking limit of the concrete, but also the value of the “critical stress”, lower than ultimate stress, for which irreversible cracking phenomena begins. it is also known that the fatigue characterization of the concrete and of the pre-compressed concrete is not easy to perform due to the cost over time and to the necessary equipment for significant fatigue tests. in the last thirty years, many studies have shown that the temperature variation of a mechanical component under stress is a good parameter for estimate the energetic release, hence the residual fatigue life of the material [1–3]. different papers showed as the thermal analysis applied to steel specimens [4–6], to composite specimens [7–9], to welding joints [10] permit to estimate the fatigue limit of the materials in easy and rapid way. indeed, according to the thermo-elastic theory, under adiabatic conditions, there is a direct link between the applied stress and the temperature of the material. in monoaxial tests, it is possible to define three phases of the temperature variation on the specimen surface in relation to the applied stress (figure 1):  a first phase where there is a linear correspondence between the applied load and temperature;  a second phase where it is possible to observe the loss of linearity with a change of the slope in the temperaturestress (or deformation) curve;  a third phase in which there is a sudden increase in temperature up to the specimen breakage. the transition from the first to the second phase gives information about critical stress: this stress, if applied in a cyclical way, will lead to failure. the concrete life is affected by different factors, such as geometric ones, temperature variations, environmental and atmospheric effects and vibration phenomena. therefore, as for aeronautical structures, it is necessary to define more accurate and programmed controls for some specific components during the design phase. the italian technical construction code (ntc 2018) [11] defines the ultimate serviceability limit (slu) as the overload and breakage condition for a structure, even for fatigue damage. the same code defines the serviceability limit state (sls) as the concrete limit stress state which produces cracks, excessive deformation and fatigue damage that may locally affect the structural integrity. no information is given about the concrete strength under cyclic loads, except for bridges. in the present paper, the authors propose a procedure to estimate the critical stress of the concrete in laboratories. although it is lower than the ultimate stress, it must be taken into consideration during the design phase. furthermore, finite element analyses (fea) were performed to qualitatively compare the stress maps (numerical) with the related surface temperature maps (experimental). finally, a careful image analysis procedure has been carried out with the matlab® software. physical and theorical background n this work, the procedure used to define the critical stress of the concrete is based on the effect discovered by lord kelvin. under adiabatic conditions, the law of variation of the solid temperature (δt) for mono axial mechanical stress is (eqn. 1): m 0 mδt= k t σ (1) where km is the thermoelastic coefficient (pa-1), t0 the specimen initial temperature (k) and σm the average stress in the specimen cross section (mpa). the thermoelastic phenomenon has also been studied by g. caglioti et al. in [12]. the authors defined the temperature vs. time diagram (δt-t) for a steel sample during a mono axial tensile test in order to determine the yield strength (y) of the material. they defined the yield strength as the corresponding stress for which the temperature tangent is horizontal (point b, figure 1). s i f. cucinotta et alii, frattura ed integrità strutturale, 55 (2021) 258-270; doi: 10.3221/igf-esis.55.19 260 figure 1: qualitative δts trend vs machine time (t) vs applied stress (σ). melvin et al. studied in detail the heat generated during mono axial tensile test of steel [13,14]. they observed that the formation of micro cracks in the steel material can be defined by the loss of linearity of the temperature vs time (t-t.) diagram (point a, figure 1). in fact, the temperature has a linear trend in the first part of tensile test (phase i, elastic zone), but as the load increases it changes its trend (phase ii, mainly elastic zone; phase iii, plastic zone). they, applying the thermodynamic theory, evaluated the entropy of the phenomena as the sum of the thermodynamic forces and the fluxes (eqn. 2):      2 0tt dσ-χ t=-γ 1-2ν t e dt (2) where χ is the thermal diffusivity (m2/s) and γ the gruneisen parameter. in the case of mono axial static tensile stress for a homogeneous material, eqn. 2 becomes eqn. 3 for a cylindrical sample with a constant stress rate (stress / time), not fast enough to neglect the viscous effects: 2 m m 0 m v σ δt=k t σ -b 3c e (3) the mathematical modelling is not easy to apply in practical cases due to the uncertainty in the assessment of coefficients, particularly for b, linked to the burges vector b (b= mbmv*/s). in melvin's analytical model, the loss of linearity in the temperature vs time diagram (t-t) occurs at the first micro-plasticity. this occurs before yielding as verified by numerous experimental tests. nowadays, the use of high precision ir sensors allows to precisely estimate the variation of the surface temperature during a monoaxial tensile test in order to define exactly the stress at which linearity is lost. furthermore, the stress rate must be chosen very high in order to achieve adiabatic conditions. the study of the stretch of line a’–b’ in figure 1 is very important in engineering field. it is possible to link the stress at which the temperature changes during tensile (compressive) static tests to a critical stress on the stress vs time diagram (-t). in fact, the critical stress coincides with the macro stress value able to produce irreversible local micro-plasticity in the material. in this case, under repeated loads, the micro plastic area increases up to produce micro cracks and fatigue failure. at the same time, it is possible to affirm that a macro stress applied during tensile (compressive) static tests produces likewise irreversible local micro-plasticity that will lead the material to fatigue failure if repetitive cycles at critical stress level are applied. if it is possible to identify when the linearity of thermoelastic phase is lost in the temperature vs time diagram (t-t) during static tensile (compressive) test, it is possible to go back to the corresponding macro stress linked to the critical stress. f. cucinotta et alii, frattura ed integrità strutturale, 55 (2021) 258-270; doi: 10.3221/igf-esis.55.19 261 in the case of high strength concrete, although the homogeneity of the material is not completely realistic, the experimental tests showed some important indications about the concrete critical stress. in particular, during compression tests it has been possible to identify the first slope in the temperature vs time diagram (t-t) and define the corresponding value of the critical stress. material and methods he 14 specimens were concrete cube of 15 cm side; the mix design per cubic meter is:  inert for 1820 dan (4-16 size for 25%, 0-4 size for 65%, 0-2 size for 10%);  cement cem i 52.5 r for 410 dan; water for 172 litres;  additive mapei "dynamon nsg 1022" for 3.5 litres;  density of the concrete 2404 kg/m3;  class of consistency s4 with slamp tests 210 cm. the tests were made with the controls c7600 machine with full scale of 5000 kn. the applied uniaxial compression stress rate was 1 mpa/s. the tests were carried out in load control at constant speed (n/s). the thermal images were acquired by flir sc300 ir camera. figure 2 shows a concrete specimen loaded at left side (a) and thermal image of the same specimen surface at the beginning of the test at right side (b). in figure 2b the analysed zones (square) and the reference temperature of the tests (image zero) are indicated. (a) (b) figure 2: a) adopted specimen; b) thermal image of one face at the beginning of the test with the analysed areas (square). the maximum value of temperature within the five detection areas (ar01 to ar05) was recorded during the execution of the tests with an acquisition frequency of 10 hz. in order to correlate the thermal images with the stress map of the specimen, a static finite element analysis was conducted using ansys® apdl. a cubic concrete specimen (figure 3a) with the same geometry of the ones adopted for experimental tests was modelled. as in the experimental tests, the specimen was bonded with two rigid plates and the uniaxial load was applied on it through the rigid top plate. the concrete specimen was modelled with hexa solid186 element type and the material characteristics of high strength concrete (e= 30 gpa, ν= 0,2) with linear elastic behaviour were used. the contact zones between the plates of the test machine and the specimen were modelled as a surface-to-surface contact using conta174 elements for the specimen surfaces and targe170 for the rigid plates. in the fe analysis a “rough” contact model was taken into account since, as observed by dai and lam [15] on compressive tests of short concrete-filled elliptical steel columns, a large friction model between the plates and the surface of the specimen seems to adequately predict the contact behaviour in tangential direction. the rigid top plate was loaded at its pilot node and was fixed in all its d.o.f. except in the vertical displacement direction, while the bottom rigid plate was totally fixed (all the six d.o.f. are blocked) through its pilot node. t f. cucinotta et alii, frattura ed integrità strutturale, 55 (2021) 258-270; doi: 10.3221/igf-esis.55.19 262 a convergence analysis (figure 3b) on the vertical displacement of the central node of the specimen was conducted with different lengths of the finite elements, ranging from 5 mm to 25 mm. in order to obtain a better resolution of the stress field on the external specimen surface, 31.114 finite elements of 5 mm size were chosen for an appropriate comparison with the thermal images. (a) (b) figure 3: a) finite element model of the cubic concrete specimen and b) convergence analysis on the vertical displacement of the specimen central node. for a better presentation of the results, the image analysis of the acquired thermal maps has been carried out, adopting a procedure developed in matlab®, as follows:  subtraction of the ambient temperature in order to emphasize the difference in temperature of the sample surface. the ambient temperature was detected as the average temperature inside a rectangular area outside the sample but with the same reflectivity.  noise reduction by gaussian filter with standard deviation sd= 8. the gaussian filter replaces the value of each pixel with the weighted average value of the contiguous pixels. in this way the thermal map is smoother and less influenced by noise and anisotropies.  displaying by means of isotherm contours. the contours highlight better the different thermal areas and help to better understand the behaviour of the specimen. in figure 4, an example of image analysis of the specimen surface temperature has been reported for a determined load condition. it is evident how the image processing allows to clearly improve the ability to distinguish the colder areas from the warmer ones. furthermore, the 3d surface mapping help to clearly render the heat distribution on the external surface of the specimen, as in figure 5. the 3d surface of the equivalent stress on the external surface of the sample, as predicted by the fea, is reported in figure 6. it shows the expected hourglass shape due to compressive loads. results and analysis thermal analysis on concrete specimens during classic compressive static test was performed. the temperature vs. time vs. stress diagrams shown: 1. a linear trend typical of the thermoelastic phase. at this stage, there are no microcracks and, therefore, the second term of eqn. 3 is not relevant. 2. a second phase in which the points are well interpolated by means of a second straight line with a different slope. the intersection of the two lines defines the critical stress; where micro-faults begin to appear in the internal structure of the concrete sample. in fact, the heat is released by plastic deformations. in the analytical model, the contribution of the a f. cucinotta et alii, frattura ed integrità strutturale, 55 (2021) 258-270; doi: 10.3221/igf-esis.55.19 263 second term of eqn. 3 increases more and more due to the effect of the applied compressive mean stress (m) with a clearly visible temperature variation that continues until the specimen fails. figs. 7-10 show the temperature recorded in characteristic points of the specimen surface during the loading phase. figure 4: thermal image processing steps: a) absolute temperature detected by ir camera; b) the ambient temperature is subtracted; c) noise reduction by means of a gaussian filter (sd=8); d) the isotherm contours are plotted. figure 5: 3d rendering of the experimental thermal map on the specimen surface. f. cucinotta et alii, frattura ed integrità strutturale, 55 (2021) 258-270; doi: 10.3221/igf-esis.55.19 264 figure 6: 3d rendering of the equivalent stresses estimated by fem on the specimen surface. in figure 7, related to second tested specimen, the temperature data for the centre (ar05, area no. 5 of figure 2) of specimen surface is reported. the intersection of the two straight lines (in black) define the critical stress for the concrete cl at 44.2 mpa. figure 7: t vs time curve (blue points) and stress vs time curve (red line) for area ar05 of specimen 2. in figure 8, the data for the area located in the upper right corner (ar04, area no. 4 of the specimen of figure 2) are reported. the corner area ar04 shows a different trend compared to the central area ar05 for the same concrete specimen; in fact, the temperature drops continuously. for area ar04, the change in slope is much less noticeable than in area ar05. f. cucinotta et alii, frattura ed integrità strutturale, 55 (2021) 258-270; doi: 10.3221/igf-esis.55.19 265 these behaviours are perfectly congruent with the stresses in the two examined areas: compressive stress for the central area ar05 and tensile stress for the upper right corner area ar04. the next two figures (figure 9 and figure 10) are related to a different area of the test performed on specimen no. 11. also in this case, the previously seen phenomena are shown again. it can be summarized that in all tests, a temperature trend similar to the one already described was observed. in particular, the temperate trend of area ar05 was used to determine the critical stress on the stress-time diagram. figure 8: t vs time curve (blue points) and stress vs time curve (red line) for area ar04 of specimen 2. . figure 9: t vs time curve (blue points) and stress vs time curve (red line) for area ar05 of specimen 11. f. cucinotta et alii, frattura ed integrità strutturale, 55 (2021) 258-270; doi: 10.3221/igf-esis.55.19 266 figure 10: t vs time curve (blue points) and stress vs time curve (red line) for area ar04 of specimen 11. figure 11 shows a comparison of the picture taken after the breakage (a), the original ir image (b) and the processed ir image (c) recorded immediately before the breakage of the specimen no. 14. it is possible to observe the distribution of temperatures, linked to the stresses. in the centre of the specimen it is completely different from the four corner areas (ar01-04). this is due to the plate of the testing machine that activate a distorted stress state. the value of the critical load at the corner, related to the intersections point of two temperature interpolating straight lines, is about 1000 kn, despite the plate effect on the corner areas. this value is practically comparable with the one recorded on the central area ar05. (a) (b) (c) figure 11: a) picture after the breakage of the specimen; b) original ir image and c) processed ir image before of the breakage. in summary, the thermoelastic effect (first phase) of concrete is perfectly visible and the cubic critical stress can be determined from the t vs time curves cl≈ 36 mpa). this cubic critical stress is slightly less than the italian code compressive stress limit (c,max=0.60xrck=43,57 mpa, with rc cubic compressive strength of concrete at 28 days) at the limit state serviceability (sls) for the load characteristic combination (italian code ntc 2018 paragraph 4.1.2.2.5.1). this small difference in values suggests to investigate the effects of cyclical loads (wind effect for instance) also on the durability of civil structures. f. cucinotta et alii, frattura ed integrità strutturale, 55 (2021) 258-270; doi: 10.3221/igf-esis.55.19 267 specimen no. strength rc [mpa] concrete critical stress σcl [mpa] r= σcl/ rc at the center at the corner at the center at the corner 1 82 45 43 0.55 0.52 2 77 54 46 0.70 0.60 3 88 68 58 0.77 0.66 4 79 51 46 0.64 0.58 5 84 47 53 0.55 0.63 6 79 47 44 0.59 0.56 7 84 43 44 0.51 0.53 8 73 52 53 0.72 0.73 9 101 60 38 0.60 0.38 10 80 51 53 0.64 0.67 11 89 49 36 0.55 0.40 12 84 47 42 0.55 0.50 13 82 31 40 0.38 0.49 14 82 53 42 0.65 0.51 average (rcm) 83.3 49.8 45.7 0.60 0.554 standard deviation (sd) 6.51 8.42 6.56 0.0982 0.0996 characteristic value 72.62 35.99 34.94 rck=(rcm-1,64xsd) table 1: cubic strength rc and critical stress σcl of the concrete. in order to correlate the thermal images with the internal stress of the cubic concrete specimen, a finite element analysis was conducted with a load equal to the previously found critical load of about 1000 kn. the equivalent von mises stresses on the external surface of the cubic specimen, calculated by the fe analysis (on right) and compared with the thermal map (on left), are reported in figure 12. the values of the stress agree with the ones found experimentally and reported in table 1 (about 50 mpa, central area), therefore the finite element model is well calibrated. in both the images reported in figure 12 it is possible to highlight: the corner area (1) in which there are both the maximum of temperature and stress; the central area (2) in which there are the relative minimum values of the temperature and the relative maximum of the equivalent stress; the lateral area (3) in which there are the relative maximum of temperature and the relative minimum of stress; the contact area with the plates (4) in which there is the negative peak of temperature, due to the heat dissipation caused by the steel plates and the local contact stresses. basically, the two colormaps have a roughly mirrored behaviour. this is because, where there is an increase of the stresses due to an expansion of the material, there is a consequent lowering of the temperature. this behaviour is more evident on a median horizontal section, in which the curve temperature and the correspondent equivalent stress curve appear almost reflected (figure 13). f. cucinotta et alii, frattura ed integrità strutturale, 55 (2021) 258-270; doi: 10.3221/igf-esis.55.19 268 (a) (b) figure 12: a) thermal map and b) fem equivalent von mises stress for the critical load (1000 kn). the examination of the thermal images of all the specimens shows the possibility to identify the lines and the areas in which the concrete material shall begin to fail locally. in figure 14, the stress distributions of four different load levels (500, 1000, 1500 and 1900 kn) calculated by fem are compared with the experimental ir images of a specimen at the same load levels. the colormaps of temperature and the equivalent stress at the four different load conditions are reported using the same colormap. the load equal to 1900 kn corresponds to the beginning of failure. in all the maps it is possible to observe the expected hourglass shape, due to the freedom of expansion of the lateral specimen surfaces and to the constraints of the plates of the machine. figure 13: experimental temperature and fem equivalent von mises stress curves on a median horizontal section of the specimen. f. cucinotta et alii, frattura ed integrità strutturale, 55 (2021) 258-270; doi: 10.3221/igf-esis.55.19 269 (a) (b) (c) (d) figure 14: comparison between a) experimental thermal and b) equivalent stress distribution on the specimen. for loads much lower than the ultimate load of the material (500 and 1000 kn), it is difficult to identify the possible failure area, while the temperature line become more marked close to the ultimate load. the temperature gives indications about the possible beginning of cracking within the concrete specimen as is well shown for 1500 and 1900 kn loads. in particular, for loads close to the concrete ultimate load it is easy to identify the path along which the specimen should break. the stress maps reported in figure 12 and figure 14 show the hourglass shape, as it was observed in the concrete specimens after the breakage (figure 11a). conclusions n order to identify the critical stress value cl, coinciding with the first local plasticization (not visible to human eye), a test campaign was performed on 14 samples of high strength concrete under classic uniaxial static compression tests using the thermographic technique. the examination of the heat maps developed for four different load levels and of the related stress maps obtained through fem confirms the validity of the proposed procedure. according to an experimental protocol, already adopted for other materials by risitano et al. [4,5], the critical stress cl (load/area of the cross section) can be defined. the results of the research shown how the thermal analysis permits to identify the stress that produces the first local cracking in the specimen, with loads different and lower (50% -70%) from the breaking load rck. in addition, the loss of linearity in the temperature-stress (strain) diagram, permits to associate the critical stress of concrete to the stress value that defines the beginning of fatigue phenomena. on the basis of the results, it is possible to state also: 1. the italian code ntc 2018 (paragraph 4.1.2.2.5.1) for concrete, which identifies for the serviceability state limit (sls) the limit compressive stress σc ≤ (0.45 to 0.60) fck, seems to be adequate. 2. the procedure adopted permits, by means of static uniaxial compression test, to define in a more accurate way the allowable stress in the legal field (0.45 to 0.60 fck). 3. a suitable protocol test may be adopted, both in the testing stage and in the working stage, as non-destructive method to determine the critical stress of the concrete specimen or structure components. 4. the proposed method can be very useful in the pre-project phase in which the designer, with easy compression tests, can know the value of the allowable compressive stresses for the load combination at serviceability state limit (sls). i f. cucinotta et alii, frattura ed integrità strutturale, 55 (2021) 258-270; doi: 10.3221/igf-esis.55.19 270 acknowledgements hanks for the supply of concrete specimens to i.c.e.a. companies ltd industry and premixed concrete s.p. n. 3 km 0:30 zona industriale piano tavola 95032 belpasso (ct) references [1] risitano, a., risitano, g. (2010). cumulative damage evaluation of steel using infrared thermography. theor appl fract mech 54, pp. 82–90. doi: 10.1016/j.tafmec.2010.10.002. [2] clienti, c., fargione, g., la rosa, g., risitano, a., risitano, g. (2010). a first approach to the analysis of fatigue parameters by thermal variations in static tests on plastics. eng fract mech 77, pp. 2158–2167. doi: 10.1016/j.engfracmech.2010.04.028. [3] risitano, a., risitano, g. (2013). cumulative damage evaluation in multiple cycle fatigue tests taking into account energy parameters. int j fatigue 48, pp. 214–222. doi: 10.1016/j.ijfatigue.2012.10.020. [4] risitano, a., risitano, g. (2013). determining fatigue limits with thermal analysis of static traction tests. fatigue fract eng mater struct 36, pp. 631–639. doi: 10.1111/ffe.12030. [5] ricotta, m., meneghetti, g., atzori, b., risitano, g., risitano, a. (2019). comparison of experimental thermal methods for the fatigue limit evaluation of a stainless steel. metals (basel) 9, pp. 677. doi: 10.3390/met9060677. [6] corigliano, p., cucinotta, f., guglielmino, e., risitano, g., santonocito, d. (2020). fatigue assessment of a marine structural steel and comparison with thermographic method and static thermographic method. fatigue fract eng mater struct 43, pp. 734–743. doi: 10.1111/ffe.13158. [7] colombo, c., vergani, l., burman., m. (2012). static and fatigue characterisation of new basalt fibre reinforced composites. compos struct 94, 1165–1174. doi: 10.1016/j.compstruct.2011.10.007. [8] palumbo, d., de finis, r., demelio, p.g., galietti, u. (2017). early detection of damage mechanisms in composites during fatigue tests. conf. proc. soc. exp. mech. ser., 8, p. 133–141. doi: 10.1007/978-3-319-42195-7_19. [9] crupi, v., guglielmino, e., risitano, g., tavilla, f. (2015). experimental analyses of sfrp material under static and fatigue loading by means of thermographic and dic techniques. compos part b eng 77, pp. 268–277. doi: 10.1016/j.compositesb.2015.03.052. [10] corigliano, p., epasto, g., guglielmino, e., risitano, g. (2017). fatigue analysis of marine welded joints by means of dic and ir images during static and fatigue tests. eng fract mech 183, pp. 26–38. doi: 10.1016/j.engfracmech.2017.06.012. [11] norme tecniche per le costruzioni (ntc 2018). italy: gazzetta ufficiale n.42 del 20/02/2018, supplemento ordinario n.8; 2018. [12] caglioti, g., ferro, milone, a. (1982). società italiana di fisica. mechanical and thermal behaviour of metallic materials: varenna on lake como, villa monastero, north-holland pub. co. [13] melvin, a.d., lucia, a.c., solomos, g.p., volta, g., emmony, d. (1990). thermal emission measurements from creep damaged specimens of aisi 316l and alloy 800h. proc 9th int conf exp mech 2, pp. 765-773. [14] melvin, a.d., lucia, a.c., solomos, g.p. (1993). the thermal response to deformation to fracture of a carbon/epoxy composite laminate. compos sci technol 46, pp. 345–51. doi: 10.1016/0266-3538(93)90180-o. [15] dai, x., lam, d. (2010). numerical modelling of the axial compressive behaviour of short concrete-filled elliptical steel columns. j constr steel res 66, pp. 931–42. doi: 10.1016/j.jcsr.2010.02.003. t microsoft word numero_55_art_04_2913 m. mani et alii, frattura ed integrità strutturale, 55 (2021) 50-64; doi: 10.3221/igf-esis.55.04 50 experimental characterization of a new sustainable sand concrete in an aggressive environment mohammed mani department of hydraulic and civil engineering, faculty of technology, university of el-oued, 39000, algeria m.mani39@gmail.com meriem fakhreddine bouali department of civil engineering, faculty of sciences & technology, university of mohamad cherif messaadia, souk ahras, 41000, algeria m.bouali@univ-soukahras.dzb.meriemfakhreddine@gmail.com,http://orcid.org/0000-0002-6986-980x abdelouahed kriker laboratory of exploitation and valorisation of natural ressources in arid arears (e.v.r.n.z.a), university of kasdimerbah, ouargla, 30000, algeria a_kriker@yahoo.fr abdelkader hima department of electrical engineering, faculty of technology, university of el-oued, 39000, algeria abdelkader-hima@univ-eloued.dz, http://orcid.org/0000-0002-5533-3991 abstract. the scarcity of building materials and the shortage of coarse aggregates which represent the main component of concrete is a problem of particular urgency in most third world countries, especially in the vast desert of algeria. in desert conditions where the environment suffers from the rising water phenomenon and soil aggressivity; the evaluation of existing abundant sand dune could be a very good economic solution. several national and international researches show that sand dunes could be exploited in concrete after a granular correction. in this paper, a new sand resource is proposed as an alternative of natural sand to perform a sand concrete. this experimental study shows that the sand concrete based on this new resource of sand dunes of the algerian desert has a good resistance when used in the ambient saharan aggressive conditions. keywords. durability; economic; sand concrete; sand dune; naturel sand. citation: mani, m., bouali, m. f., kriker, a., hima, a., experimental characterization of a new sustainable sand concrete in an aggressive environment, frattura ed integrità strutturale, 55 (2021) 50-64. received: 06.09.2020 accepted: 07.10.2020 published: 01.01.2021 copyright: © 2021 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. https://youtu.be/dr8yaqim4da m. mani et alii, frattura ed integrità strutturale, 55 (2021) 50-64; doi: 10.3221/igf-esis.55.04 51 introduction lgeria has a vast desert that contains large quantities of sand dunes. the abundance of sand dunes causes various environmental problems, such as disappearance of reefs and valleys buried in those untapped sand. these regions suffer from a serious environmental phenomenon called ‘’water rise phenomenon’’ 1 which destroys thousands of oases of palm trees 2 that’s considered the source of food in the region. this phenomenon also destroyed and ruined buildings gradually 3. the sand used for construction is almost non-existent in those desolate deserts that don’t have neither natural stream, valleys, coasts, nor other sand resources that enable building constructions. developed countries monitor their national income to support and establish infrastructure construction. in algeria, the need for this substance during 2012 was about 9millions cubic meters, and some sources indicate that the consumption rate has reached 20millions cubic meters 4, which made it very expensive: the cubic meter may exceed 3000 dzd (25 usd) 5, while it does not exceed 7usd in egypt, but in the united states, it does not exceed 3.5 usd. several scientific experiments were conducted to study the phenomenon of water rise and its impact on buildings in one hand 6, 7. several studies showed the use of sand dunes (sd) as a material in concrete 8, 9 in condition that it must have a granular correction 10, 11.the main objective of this experimental investigation was the exploitation of existing resources such as the sand of the dunes in the algerian desert. in the other hand, sand of oued el-ratm (sr) was studied and it is known that this type of sand was never used previously in construction fields. these two types of sand are used to produce a sand concrete by trying to reveal the effect of rising waters under aggressive conditions on the sand concrete produced by the mixtures. materials characterization n this experimental investigation, oued souf sand dunes that come from oasis situated in the south east of algeria was used and improved its properties with naturel sand found in oued el-ratm region in order to obtain a formula to improve the sand dunes at a lowest cost. oued el-ratm desert region is also located in the heart of the algerian oases close to five big cities named: biskra, djelfa, ouargla, el-oued and ain touta cement. the experiments were carried out in the laboratory of ouargla and el-oued university (algeria). the tested are carried out on a number of samples which varies between 06 and 08. sand the sand used in this study is the dune’s sand in guemar (el-oued) (gsd) and the natural sand from oued el-ratm (nsr) area, which was mixed in order to improve the sand dune properties, this technique is used by several researchers 12. in table 1 are presented the determined characteristics of these types of sand. type bulk volumetric mass (kg/m3) absolut volumetric mass (kg/m3) fineness modulus (fm) (%) sand equivalent se (%) guemar sand dune (gsd) 15403 26202 1.610.1 951 naturel sand oued el-ratm (nsr) 15854 25001 2.350.15 80.091.5 60% naturel sand (nsr) + 40% sand dune (gsd) 1609.22 2609.66 2.240.12 870.5 table 1: experimental characteristics of different types of used sand. according to the results mentioned in table 1, it appears that the guemar’s sand dune (gsd) has the smaller coefficient of smoothness (1.61%) which is outside the acceptable margin areas in building a, b and c. while the natural sand of a i m. mani et alii, frattura ed integrità strutturale, 55 (2021) 50-64; doi: 10.3221/igf-esis.55.04 52 oued el-ratm (nsr) and the mixed sand 60% nsr and 40% gsd, have coefficients of smoothness equal to 2.35% and 2.24% respectively lactated in the margin areas in building. fig. 1 shows the grain size distribution of natural sand (nsr) dune, guemar sand dune (gsd) and the mixture sand (40% gsd + 60% nsr) used in the experimental program. figure 1: the grain size distribution of sands used in the experimental program. it is noted from fig. 1 that the gsd curve is mostly located outside the reference fields and it tends to the smooth side, while the nsr curve is located within the reference curve and is proposed to correct the first curve. the mixture 40% gsd+60% nsr is within the reference areas which make it acceptable. cement the used cement is i 42.5 (crs). this cement is specially made to resist sulfate as stipulated in the technical card and as indicated by its name (crs) i.e. sulfate resistant cement. this type of cement contains a low percentage of tri-calcium aluminate and is characterized by a greater ability to resist sulfate because of the components 13, or because of the process used in the manufacturing. so it is used in cases that requires high resistance to sulfate, and is widely available in the local market. it is produced in ain-touta cement factory, which is in compliance with the rules na 442 000 and na 433: 2002.the values of experimental volumetric mass were computed for the hardened mortars. experiences bulk volumetric mass (kg/m3) absolute volumetric mass (kg/m3) primary stiffness time (min) withdrawal 28 days (m/m) cement 2120 3034 60 1000 table 2: used cement experimental characteristics 14. water in mixing this concrete tap water is used from the civil engineering laboratory of el-oued university, which is free of harmful substances such as materials, salts, oils, greases, acids, alkalis, and the soft material as seen in table 3. m. mani et alii, frattura ed integrità strutturale, 55 (2021) 50-64; doi: 10.3221/igf-esis.55.04 53 salinity ph hco3so4no3clna++ k++ mg++ ca++ 2799 7.75 124 755 14.5 755 536 31 125 242 table 3: chemical characteristics of used the water in the sand concrete mixture. environment conditions the studied concrete samples, after removing them from the molds, are kept in water for 28 days, then removed after a while. in order to study the effect of the aggressive medium on the sand concrete, two type of water are considered. the first one is ordinary water (tap water) while the second is aggressive water. since the most dangerous elements to concrete are chlorine (cl-) and sulfur ions (so4-), a medium that contains these two elements is used. the chlorine ions concentration is higher in region (1) (sidi mestour region) that contains 1640.23 mg/l, and the higher concentration of sulfur ions is in the region (2) (hotel of louss region) that contains a concentration of sulfur equal to 3373 mg/l. a most dangerous medium is used considering these two higher concentrations of chlorine and sulfur existing respectively in the region (1) and (2). the concentrations are tripled by the authors to speed up the results of its effect on sand concrete. in this study, those concrete samples were re-positioned in a medium that simulates a rising water layer that’s capable of affecting the upstream facility at a later time. chemical composition of the aggressive water layer characterized by our university’s team is illustrated in table 4 according the regions. n° of point ca++ (mg/l) mg++ (mg/l) nh4+ (mg/l) cl (mg/l) so4 (mg/l) hco3 (mg/l) no3 (mg/l) no2 (mg/l) cond (micro s/cm) sal ‰ tds (mg/l) ph region (1) 617.23 104.51 0.15 1640.23 3363.00 51.24 64.65 0.05 7270 4.5 4390 7.43 region (2) 637.27 75.35 0.10 588.22 3373.00 420.00 47.81 0.01 5110 3.1 3010 7.31 table 4: chemical composition of the ascending aquatic layer in oued souf. to properly judge the durability of the obtained concrete’s body and the good suitability of the sand for possible use in construction, a study of the effect of this medium on the chemical composition of the concrete and on its resistance will be carried out. mix proportions regular sand concrete (witness) n order to obtain a formula for the regular sand concrete that will be used as a witness, a sample of cement and sand was taken as a stipulated according to en 196-1 rule. the temperature was (202)°c and the relative humidity was greater or equal to 50%. we take an amount of 01 part of cement with 03 parts of sand, while the percentage of water is determined by the experience of operations. after conducting the experiment, we obtain the formulation listed in table 5. this experiment was performed according to specifications of nfp 18-452 as described in table 6. duration in seconds type of concrete t ≥ 40 unwieldy dry concrete 20 < t ≤ 30 concrete with good workability 10 < t ≤ 20 very plastic concrete t ≤ 10 very fluid concrete table 5: type of concrete in function of workability. i m. mani et alii, frattura ed integrità strutturale, 55 (2021) 50-64; doi: 10.3221/igf-esis.55.04 54 after performing the experiment, we have the following results as illustrated in table 6. then, all the tested concretes are considered flexible according to the standard env 206: 1990. composition w/c time in seconds sand dune 100% (gsd) 0.6 30.52 natural sand 100% (nsr) 0.55 232 40% sand dune (gsd) + 60% natural sand (nsr) 0.55 252 table 6: the obtained results of the workability test. various sand concrete studied the composition of the samples used in our cubic meter of sand concrete is presented in table 7 according to different used types of sand. composition sand (kg) cement (kg) water (l) w/c time of streaming operational sand dune 100% (gsd) 1396.63 465.54 279.32 0.6 230.5 s natural sand 100% (nsr) 1390.04 463.34 254.84 0.55 225 s 40% sand dune (gsd) + 60% natural sand (nsr) 1392.39 464.13 255.27 0.55 225 s table 7: composition of the sand concrete for the studied samples. the experimental volumetric mass of the studied concrete are shown in table 8 relative to each type of used sand. samples sand dune 100% (gsd) natural sand 100% (nsr) 40% sand dune (gsd) + 60% natural sand (nsr) volumetric mass (kg/m3) 2141.5 2132.4 2135 table 8: volumetric mass of studied sand concrete. test methods the experiment is conducted according to en 196-1 as shown in fig. 2. the test is carried out using a solid material compression device. this later comes from the sample breaking experiment by bending with a section of (40x40)mm. this sample that’s placed between two hard metal plates where the latter is located 1cm from the side edges as shown in fig. 2. the strength is measured by using the following equation (1):  ² c c f r b (1) cr : compressive strength (mpa) cf : load of rupture (n) ²b : cross-sectional area (b=40mm) m. mani et alii, frattura ed integrità strutturale, 55 (2021) 50-64; doi: 10.3221/igf-esis.55.04 55 figure 2: device in compression test. results and discussions granulometric correction o simulate the effect of the rising water phenomenon in aggressive environment, the tested concretes were preserved in two type of water. the first one is a tap water (fig. 3a) and the second corresponds to aggressive water (fig. 3b) as indicated above. to distinguish the samples preserved in tap water to those preserved in the aggressive water, the symbol (con) is used to indicate those conserved in the aggressive medium. (a) samples preserved in plain water (b) samples preserved in aggressive water figure 3: samples preserved in different medium conditions. effect on compressive strength the compressive strengths are measured for the concretes made with various sands: 100% guemar sand dune (gsd), 100% natural sand oued el-ratm (nsr) and a mixture of 40% gsd+ 60% nsr. the evolution of compressive t m. mani et alii, frattura ed integrità strutturale, 55 (2021) 50-64; doi: 10.3221/igf-esis.55.04 56 strength with age for the concrete preserved in plain water and those preserved in the aggressive water are shown in fig. 4 and fig. 5 respectively. figure 4: compressive strength of concretes preserved in plain water in terms of age. figure 5: the effect of aggressive water on compressive strength in terms of age. the figs. 4-5 showed clearly that the compressive strength of sand concrete mixed between sand dune (gsd) and natural sand (nsr) has improved if compared with sand concrete made by sand dune about 23.13%. this difference in resistance is due to the difference in granular gradient and the smoothness factor of each type of sand used in these concretes. the smaller coefficient of smoothness indicates that the sand is smooth, which makes the concrete made of it less resistant as described in 10, 15. it is well noted from figs. 4-5 that the type of medium has a similar effect on the tested concretes. as shown in fig. 4; the highest compressive strength is recorded for the sand concrete made by the natural sand of oued el-ratm (nsr), while sand concrete made with guemar sand dunes (gsd) gives the lowest and the mixture gives the intermediate compressive strength. this order of compressive strength magnitude is always valid in the case of concretes stored under aggressive conservations conditions (fig. 5). effect on flexural strength the flexural strengths are measured for the concretes made with various sands: 100% guemar sand dune (gsd), 100% natural sand oued el-ratm (nsr) and a mixture of 40% gsd+ 60% nsr. the evolution of flexural strength with age for the concrete preserved in plain water and those preserved in aggressive water are shown in fig 6 and fig. 7 respectively. m. mani et alii, frattura ed integrità strutturale, 55 (2021) 50-64; doi: 10.3221/igf-esis.55.04 57 figure 6: flexural strength of concretes preserved in plain water in terms of age. figure 7: the effect of aggressive water on flexural strength in terms of age. similarly to the case of compression, it is noted that the concrete made of 100% natural sand of oued el-ratm (nsr) gave the best resistance to bending. the flexural strength obtained by the sand concrete made by 40% gsd+ 60% nsr is better than the giving by 100% guemar sand dune (gsd). the resistance of bending increases about 30.20% if compared with those obtained by 100% guemar sand dune (gsd) which is the lowest resistance. this improvement in resistance is due to the combination of the two types of sand 16, which led to improvement in the coefficient of smoothness, as this mixture contained sand particles of larger dimensions than that of the dune sand, which led to a good granular distribution resulting in the closure of the voids 17 that are in the concrete sand dune and thus increase in bending resistance 18. effect on the environmental conditions the aim of this part is to study the effect of the preservation medium on each type of sand concrete separately. according to fig. 8, it appears clearly that the effect of the preservation medium on concrete was very weak. this effect on sand dunes concrete (gsd) was 6.67% did not exceed 0.69% for oued el-ratm concrete (nsr) and achieved just 0.688% for the mixed sand concrete. this is noticeable in all mechanical resistance, especially compression and flexion. 0 1 2 3 4 5 6 7 0 50 100 150 200 f le x u ra l st re n g th ( m p a) age (days) %100gsd 40%gsd+60%nsr 100%nsr 0 1 2 3 4 5 6 7 0 50 100 150 200 f le x u ra l st re n g th ( m p a) age (days) %100gsd(con) 40%gsd+60%nsr(con) 100%nsr(con) m. mani et alii, frattura ed integrità strutturale, 55 (2021) 50-64; doi: 10.3221/igf-esis.55.04 58 (a) guemar sand dune concrete (gsd) (b) mixed sand concrete (gsd+nsr) (c) natural sand oued el-ratm sand concrete (nsr) figure 8: impact of preservation medium in the case of compressive strength. 0 5 10 15 20 0 28 90 180 c o m p re ss iv e s tr en g th ( m p a) age (days) %100gsd %100gsd(con) 0 5 10 15 20 0 28 90 180 c o m p re ss iv e st re n g th ( m p a) age (days) 40%gsd+60%nsr 40%gsd+60%nsr(con) 0 5 10 15 20 25 0 90 28 180 c o m p re ss iv e s tr en g th ( m p a) age (days) 100%nsr 100%nsr(con) m. mani et alii, frattura ed integrità strutturale, 55 (2021) 50-64; doi: 10.3221/igf-esis.55.04 59 (a) guemar sand dune concrete (gsd) (b) mixed sand concrete (gsd+nsr) (c) natural sand dune oued el-ratm concrete (nsr) figure 9: impact of preservation medium in the case of flexural strenght. m. mani et alii, frattura ed integrità strutturale, 55 (2021) 50-64; doi: 10.3221/igf-esis.55.04 60 effect on sand grains here, we cannot be sure unless we know how this medium affects each type of sand, so we saved sand samples in this medium in parallel with concrete samples and treated them with dental x-rays (drx) and revealed with an electronic detector mb. the obtained results for the gsd and nsr sand concrete are shown in figs. 10 and 11 respectively as follows: figure 10: x-ray processing curve for guemar sand dune (gsd) grains. figure 11: x-ray processing curve for natural sand oued el-ratm (nsr) grains. the x-ray treatment drx for sand dunes and natural sand for oued el-ratm (figs. 10 and 11) shows that its nature is mainly from sio2 silicates as quatrz is the main metal of its compostion, and on a secondary basis there are some elements such as caco3 and gypsum with traces of clay minerals in the other one. according to 19, the absence of traces of active carbon rocks or stones such as dolomite or magnesite in fine debris means that the sands studied have a chemically stable composition, and are capable of producing slurry or concrete without alkali-alkaline reaction. nor did the effects of harmful substances that make up the preservation medium appear on these sand compositions, which indicate their non-interaction with them and thus the stability of this substance in this medium and with studied concentration. the effect on the bond resulting from the rehydration of cement after removing the samples from the preservation medium, it was noticed that a thin white layer formed on the surface of the samples, which it was processed with x-ray. the results of this treatment are shown in figs. 12, 13 and 14 for 100% gsd samples, 40% gsd + 60% nsr and 100% nsr samples respectively. m. mani et alii, frattura ed integrità strutturale, 55 (2021) 50-64; doi: 10.3221/igf-esis.55.04 61 figure 12: x-ray treatment curve for sediments on 100% gsd samples. figure 13: x-ray treatment curve for sediments on samples 40% gsd + 60% nsr. figure 14: x-ray treatment curve for sediments on 100% nsr samples. the results of x-ray treatment shown in figs. 12, 13 and 14 allows us to say that these white deposits are made of trangite known by its chemical formula 3cao. al2o3. 3caso4. 31h2o as it showed a new compound containing elements from the aggressive medium, which is cacl2, as well as the gypsum substance known as caso4. 2h2o. as a result of the interaction of c-s-h and cac, the basic components of cementation hydration with the harmful ions cl and so4— gives a new white substance deposited on the surface of the samples according to the following reaction equation: gypsum h2so4 + ca(oh)2------------------------caso4.2h2o this has been transformed into trangit in the presence of tri calcium yemenite c3a according to the formula: m. mani et alii, frattura ed integrità strutturale, 55 (2021) 50-64; doi: 10.3221/igf-esis.55.04 62 3caso4 + 3 cao. al2o3. 6h2o + 25h2o--------------3cao. al2o3.3caso4.31h2o the presence of gypsum may be through the interaction of sulfate acid with the calcium element in the sand used in mixing the concrete. as for calcium chlorides, they were produced through the reaction: calcium chloride hcl + ca (oh)2-------------h2o + ca(cl)2 these precipitates, which formed a white layer, have weak pressure resistance compared to concrete resistance. this layer was superficial and thin, but it affected the resistance with a weak degree as well 20-23. this layer is natural to form because a type of cement that is resistant to the sulfate material 24 was used. the behavior of the products of this cement’s interaction with water is known to be a white layer consisting of these compounds (caso4.2h2o and cacl2) and others to play the role of guard for the concrete core from entering and penetrating harmful materials from the aggressive medium surrounding the concrete body 20, 25, 26. conclusion and concrete has a large interest in many countries for the resources available. several national and international researches show that sand dunes could be exploited in concrete after a granular correction. sand of oued el-ratm (sr) was never used previously in construction fields in algeria. the phenomenon of rising aggressive water existing in the desert of algeria is simulated in this experimental investigation by conserving the sand concretes samples in aggressive water with high concentration of chlorine (cl-) and sulfur ions (so4-) which simulates the water existing in the desert area of algeria.three types of concrete made with various sands: 100% guemar sand dune (gsd), 100% natural sand oued el-ratm (nsr) and a mixture of 40% gsd+ 60% nsr are considered in this study. the evolution of compressive and flexural strength with age for the concrete preserved in plain water and those preserved in the aggressive water are measured experimentally and the effect of the aggressive water is studied for all types of sand concretes considered in this work. the main objective of this experimental investigation was the exploitation of existing resources such as the sand of the dunes in the algerian desert. the key findings of this experimental investigation are:  natural oued el-ratm sand (nsr) has an acceptable coefficient of smoothness equal to 2.35, and its graininess is within the reference range.  guemar sand dune (gsd), its fineness coefficient is acceptable equal to 1.61, which is small if the sand is fine, and its grainy gradation is mostly outside the reference range, so we corrected it by mixing it with natural oued el-ratm sand (nsr).  the mixing ratios that gave an acceptable value for smoothness factor are 60% (nsr) + 40% (gsd), which gave a coefficient of smoothness equal, to 2.24, and we curved it within the reference curve.  the resistance of sand concrete made with 100% (nsr) of natural oued el-ratm sand is good compared to the resistance of regular mortar. this opens new horizons to take advantage of this abundant mine, which will yield significant returns for investing countries and companies.  compression resistance improved when 60% of natural oued el-ratm sand (nsr) was added to guemar sand dune (gsd), an acceptable improvement of 23.13% compared to witness concrete (dune sand concrete).  the bending resistance improved when adding 60% 60% of natural oued el-ratm sand (nsr) was added to guemar sand dune (gsd) was an acceptable improvement of 30.20% compared to witness concrete (dune sand concrete). using the sands of oued el-ratm sand (nsr) alone or mixed with sand dunes gives concrete resistance to the aggressive media present in the oases of oued souf if we use cement anti-sulfate crs. this means that the used sand was not affected by the aggressive environment, which enables us to exploit it in construction. this means valuing the sand of the dunes in the algerian desert, using them in construction, to provide us with two important things: 1. preserving the environment from the movement of this sand by utilizing it and thus reducing its quantities. 2. contributing to providing new building sand to cover the shortage of natural sand suitable for construction. s m. mani et alii, frattura ed integrità strutturale, 55 (2021) 50-64; doi: 10.3221/igf-esis.55.04 63 such a study, which deals with discovering new mines and resources for building materials, would open fields of competition for various international companies to invest in the exploitation of such new resources and thus benefit the countries that own them. nomenclature sd: sand dunes sr: sand of oued el-ratm gsd: guemar sand dune (el-oued) nsr: natural sand from oued el-ratm fm: fitness modulus se: sand equivalent crs: sulfate resistant cement w/c: water/cement ratio rc: compressive strength (mpa) fc: load of rupture (n) b²: cross-sectional area drx: dental x-rays mb: electronic detector references [1] boualem, b. and salah, b. m. (2018). gestion du phénomène de la remontée des eaux dans la région d’el oued (se algérie) et la possibilité d’utilisée les eaux usées épurées en irrigation. international journal of environment and water (issn 2052-3408), 7(2), pp. 82–91. [2] miloudi, a. m. and remini, b. (2018). the ghout of souf: an original hydroagricultural system. geoscience engineering (issn 1802-5420), lxiv (3), pp. 30-37 . [3] abimouloud, y. and kriker, a. (2016, july). effect of exposure delay of concrete into aggressive environment. in aip conference proceedings 1758(1), p. 030008. aip publishing llc. [4] riad, kh. (2013). 20 milliards de dinars les pertes du trésor public par an en raison du vol de sable, newspaper elbiled. [5] mhamed, m. (2015). les projets de logement sont menaces d’arret en raison des prix élevés des matériaux de construction, newspaper el khabar. [6] djedid, t., guettala, a. and mani, m. (2019). study of the workability and mechanical strength of concrete in the face of upwelling (case of the el oued region of algeria). journal of fundamental applied science. 11(1), pp. 368-384. [7] logbi, a., kriker, a. and snisna, z. (2017, february). effects of mineral additions on durability and physicomechanical properties of mortar. in aip conference proceedings 1814(1), p. 020032. aip publishing llc. [8] belferrag, a. (2016). contribution à l’amélioration des propriétés mécaniques et rhéologiques des bétons de sable de dunes (doctoral dissertation, université mohamed khider-biskra). [9] tafraoui, a. (2009). contribution à la valorisation du sable de dune de l’erg occidental (algérie) (doctoral dissertation, toulouse, insa). [10] belferrag, a., kriker, a., abboudi, s. and bi, s. t. (2016). effect of granulometric correction of dune sand and pneumatic waste metal fibers on shrinkage of concrete in arid climates. journal of cleaner production, 112, pp. 30483056. [11] mohammed, m., abdelouahed, k. and allaoua, b. (2017, february). compressive strength of dune sand reinforced concrete. in aip conference proceedings 1814(1), p. 020023. aip publishing llc. [12] bilal, h., yaqub, m., rehman, s. k. u., abid, m., alyousef, r., alabduljabbar, h. and aslam, f. (2019). performance of foundry sand concrete under ambient and elevated temperatures. materials, 12(16), 2645. [13] centre d’information sur le cimente et ses application (2009). guide de prescription des ciments pour des constructions durables ". [14] fiche technique de cimenterie ain-touta. (2018).algeria. m. mani et alii, frattura ed integrità strutturale, 55 (2021) 50-64; doi: 10.3221/igf-esis.55.04 64 [15] claude, b., gérard, b. and pierre-claude, a. (1984). role des caractéristiques physico-mecaniques des granulats sur la resistance en compression de betons a trés haute resistance. bulletin of the international association of engineering geology-bulletin de l'association internationale de géologie de l'ingénieur, 30(1), pp. 187-191. [16] awoyera, p., wisdom, a., chukwudi, o., ekedum, k., adediran, a. and mebitaghan, c. (2018). curing, thermal resistance and bending behaviour of laterised concrete containing ceramic wastes. cogent engineering, 5(1), 1485476. [17] mavroulidou, m. and lawrence, d. (2019). can waste foundry sand fully replace structural concrete sand? journal of material cycles and waste management, 21(3), 594-605. [18] zhang, m., liu, h., sun, s., chen, x. and doh, s. i. (2019). dynamic mechanical behaviors of desert sand concrete (dsc) after different temperatures. applied sciences, 9(19), 4151. [19] seif, a. and sedek, e. s. (2013). performance of cement mortar made with fine aggregates of dune sand, kharga oasis, western desert, egypt: an experimental study. jordan journal of civil engineering, 159(3164), pp. 1-15. [20] laoufi, l., senhadji, y., benazzouk, a., langlet, t., mouli, m., laoufi, i. and benosman, a. s. (2016). evaluation de la durabilité de mortiers pouzzolaniques exposés à une attaque chimique (assessment of pozzolanic mortars sustainability exposed to chemical attack). j. mater. environ. sci, 7(5), pp. 1835-1845. [21] huang, q., wang, c., zeng, q., yang, c., luo, c. and yang, k. (2016). deterioration of mortars exposed to sulfate attack under electrical field. construction and building materials, 117, pp. 121-128. [22] harbi, r. (2018). propriétés physico-mécaniques et durabilité des mortiers avec additions minérales (doctoral dissertation). [23] melais, f. z. (2016). durabilité des bétons de sable fibres dans les différents milieux agressifs « effets de la nature des fines d’ajouts et fibres". dunes (doctoral dissertation, université badji mokhtar annaba). [24] salhi, a., kriker, a., tioua, t., abimiloud, y. and barluenga, g. (2016, july). durability of visitable concrete sewer gallery under the effect of domestic wastewater. in aip conference proceedings 1758(1), p. 030025. aip publishing llc. [25] khelifa, m. r. (2009). effet de l'attaque sulfatique externe sur la durabilité des bétons autoplaçants (doctoral dissertation). [26] nasser, a. (2010). la corrosion des aciers dans le béton à l'état passif et par carbonatation: prise en compte des courants galvaniques et des défauts d'interface acier-béton (doctoral dissertation, université de toulouse, université toulouse iii-paul sabatier). microsoft word numero_49_art_38_2453 m. bannikov et alii, frattura ed integrità strutturale, 49 (2019) 383-395; doi: 10.3221/igf-esis.49.38 383 focused on russian mechanics contributions for structural integrity damage evolution in the almg6 alloy during high and very high cycle fatigue mikhail bannikov, dmitry bilalov, vladimir oborin, oleg naimark institute of continuous media mechanics ub ras, russia mbannikov@icmm.ru, http://orcid.org/0000-0002-5737-1422 ledon@icmm.ru, http://orcid.org/ 0000-0003-1541-2246 oborin@icmm.ru, https://orcid.org/0000-0003-2836-2073 naimark@icmm.ru, https://orcid.org/0000-0001-6537-1177 abstract. paper presents the “in situ” method for determining of irreversible fatigue damage accumulation, based on the analysis of nonlinear manifestations of the feedback signal in a closed system of an ultrasonic fatigue system. during very high cycle (gigacycle) fatigue, the anomalies of the elastic properties of the material are appear, which leads to a nonlinearity effect in the amplitude of oscillations. this effect increases with the initiation and growth of fatigue cracks. the technology was applied to samples of almg-6 alloy with preliminary dynamic deformation to determine the moment of initiation and growth of the fatigue crack in very high cycle fatigue regime. this method is applicable for the early detection of fatigue cracks both on the surface and inside the material under cyclic loading in the ultrasonic mode. on the basis of wide-range defining relations for a deformable solid body with mesoscopic defects, a mathematical model has been proposed that can adequately describe behavior of the material during fatigue failure. the results of mathematical modeling are in good agreement with the experimental data keywords. damage accumulation; scaling; highand very high cycle fatigue; mathematical modeling; destruction, mesoscopic defects. citation: bannikov, m., bilalov, d., oborin, v., naimark, o., damage evolution in the almg6 alloy during high and very high cycle fatigue, frattura ed integrità strutturale, 49 (2019) 383-395. received: 01.04.2019 accepted: 14.06.2019 published: 01.07.2019 copyright: © 2019 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. introduction he determination of fatigue cracks origin nature is one of the most important fundamental problem for various application areas, especially speaking about ultrahigh-cycle (gigacycle) [1-3] fatigue, when crack forms inside the material. the series of catastrophes caused by the fatigue destruction of gas turbine engines [4-6], combined with the high cost of resource assessment and the potential cost of developing new structures, stimulated promising concepts of national programs in the field of high and very high cycle fatigue, based on the use of new fundamental results in t http://www.gruppofrattura.it/va/49/2453.mp4 m. bannikov et alii, frattura ed integrità strutturale, 49 (2019) 383-395; doi: 10.3221/igf-esis.49.38 384 assessing fatigue strength. special attention should be paid to the foreign object damage (fod) research section, which deals with the destruction of engine parts after preliminary dynamic loading [7-11]. at present, after several decades of research, it is becoming clear that fatigue damage is the result of accumulation of microplastic deformations, which lead to irreversible microstructural and topological changes [12] that determine critical states of damage and the transition to destruction. general knowledge of the mechanisms of microstructural changes leading to fatigue failure allows us to associate these critical states with the development of an ensemble of microcracks originating in localized shifts. the interest to fundamental problems of fatigue damage has sharply increased in connection with the possibility of attaining a fatigue resource corresponding to the so-called very high (gigacycle) fatigue [1-10]. the results of these studies raised, in particular, the question of the existence of a fatigue limit in the transition from high cycle to gigacycle loading conditions. the formation of fatigue damage is traditionally associated with microplastic deformations [1-2, 12], which are occur under cyclic loading conditions, initiating various microstructural mechanisms that control durability and depend on the nature and initial structure of the material. for ductile metals, a special type of fatigue (cyclic) deformation localization (persistent slip bands psb) is observed, the development of which traditionally leads to the initiation of cracks in the near-surface zone. the second common case, for example, in the fatigue fracture of high-strength steels, is the onset of damage (microcracks), in the vicinity of inclusions at low load amplitudes corresponding to very high cycle fatigue. a characteristic feature of destruction under gigacycle fatigue conditions is the decisive effect of the initiation stage of a fatigue crack on the fatigue life. at the same time, a qualitative difference is the formation of a fatigue crack in the bulk of the material, which decisively changes the formulation of the problem of assessing the fatigue life, methods for studying the stages of fracture development. in contrast to the established traditions in the field of high-cycle fatigue, where central attention is paid to the crack propagation stage, a fundamental problem arises about formation of the fatigue crack during multiscale damage development processes associated with defects of various nature (inclusions, localized plastic shear bands, microcracks, pores). the staging of destruction is characterized by the effects of “irreversibility”, initiated by the formation of localized shifts that play a key role in the initiation of a fatigue crack [13-15], which can manifest itself in signs of nonlinearity of the elastic behavior of materials, “anomalies of elastic compliance” of fatigue samples. the role of the initiation stage is especially important for gigacyclic loading regimes, which are characterized by "fish-eye" crack formed in the bulk of the material [13-14]. this article presents a method for monitoring the kinetics of accumulation of defects by analyzing the amplitude of the second harmonic of oscillations of the free end of the sample. with the appearance of internal defects, nonlinearity effects arise, which significantly increase with their correlated interaction and the formation of a fatigue crack. material and experiment condition n this research were investigated samples of aluminum alloy amg-6, the chemical composition and mechanical characteristics of which are presented in tabs. 1 and 2. the material was subjected to dynamic deformation performed by split hopkinson pressure bar set-up at the strain rates of ~103 s-1 [16]. the material was pre-deformed in order to specify a certain degree of initial damage to assess further of the defects development kinetics. samples with a geometry corresponding to fig. 1. al cu mg mn si fe zn be ti 91.1-93.68 0.10 5.8-6.8 0.5-0.8 0.4 0.4 0.20 0.0002-0.005 0.02-0.1 table 1: the chemical composition of amg6 (as a percentage) elastic modulus (gpa) yield strength (mpa) tensile strength (mpa) maximum elongation (%) 71 180 355 25 table 2: quasi-static tensile properties of amg6 i m. bannikov et alii, frattura ed integrità strutturale, 49 (2019) 383-395; doi: 10.3221/igf-esis.49.38 385 figure1: geometry of the samples (scales in mm) the fatigue loading was carried out on an ultrasonic shimadzu usf-2000 resonant-type testing machine (fig. 2) at stress levels of 90-162 mpa and a symmetrical cycle r = -1. the principle of operation testing machine is based on formation of standing wave in the generator-horn-sample system [2]. in this case, the maximum amplitude of displacements occurs at the ends of the sample, and the maximum amplitude of stresses at its center. on the side of the free end of the specimen, an inductive sensor is fixed, which makes possible to determine the displacement of the end with an accuracy of tenths of a micron and a frequency of up to 1 mhz. the machine allows testing materials on the basis of 109-1010 cycles with amplitude from the 1st to several tens of microns with a frequency of 20 khz, which reduces the test time to several days, in contrast to the classical fatigue installations, where this number of cycles is achieved during the years of testing. figure 2: the experimental setup: 1 horn, 2 sample, 3 displacement sensor, 4 cooling system. the formation of cracks in cylindrical samples undergoing high cycle loading in the range 106-107 cycles begins from the surface. for the dynamic preloading samples almg6 subject to cyclic loads in the range exceeding 108 cycles the crack formation is started in the bulk of the sample. the fracture surface in this case exhibits a fatigue zone known as a “fisheye” which is a distinguishing feature of such fatigue regimes. the central part of this region comprises a fracture nucleus surrounded by the region of refined (submicrocrystalline) structure so-called fga [13] (fig. 3a). m. bannikov et alii, frattura ed integrità strutturale, 49 (2019) 383-395; doi: 10.3221/igf-esis.49.38 386 a) (b) figure 3: (a) characteristic surface relief of a gigacycle fatigue fracture zone of almg6, (b) scaled-up fragment of the «fish-eye» zone obtained by the scanning electron microscope hitachi s3400 (σ=138 mpa nf=7.51108), the region 1 is the center of crack initiation, the region 2 is fga zone. nonlinear acoustics method for non-destructive testing of fatigue failure he method is based on the initiation of a longitudinal finite-amplitude perturbation a0 with a frequency ω0 on one side of the sample, while its other end remains free [17-19]. oscillations of the free end of the sample will contain a number of harmonic components: components with amplitude a1 at the fundamental frequency ω0, amplitude a2 of the second harmonic with frequency 2ω0, and so on. the nonlinearity parameter βe is determined experimentally by measuring the absolute amplitudes of the signals of the first a1 and second a2 harmonics corresponding to the nonlinear law of elasticity: 2 21 1 ... ...2 3 22 2 u u u ue e e ea a a a a a a                                              (1) where σ is the stress, u is the displacement, a is the spatial coordinate, 2 ea and 3 ea are the second and third order elastic coefficients, respectively. by introducing the nonlinearity coefficient: 3 2( / ) e e ea a   and the wave equation can be represented as: 2 2 2 1 e u u u c a at                     (2) where u is the component of the displacement vector in the direction, c is the longitudinal speed of sound, t is time. its solution, given that the end oscillation u =u1cos(ωt), will be: 0 1 2cos( ) sin 2( ) ...u u u t u t ka      (3) that the amplitude of the second harmonic 2 22 1(1/ 8) eu k u a , where 0 /k   – wave number, we can derive: 2 22 18 / e u k u a  (4) in the study of nonlinear phenomena in the gigaclic fatigue regime, the relative parameter is determined by measuring the amplitudes of the main and second harmonics: t m. bannikov et alii, frattura ed integrità strutturale, 49 (2019) 383-395; doi: 10.3221/igf-esis.49.38 387 relative 0/   (5) where β0 refers to intact material. measurement of nonlinearity coefficient o determine the nonlinearity coefficient, we prologue both parts of the eqn. (4): 2 1log( ) log( ) log( ) 2 log( )k u u    (6) the amplitude of the oscillations is measured in decibels at scales  1 20 1a log u and (2 20 2)a log u , then the ratio takes the form: 2 120 log( ) 20 log( ) 20 log( ) 40 log( ),k u u    (7) 2 120 log( ) 2k a a    (8) thus, the relative nonlinearity parameter β can be found from the formula: 0 2 1 2 1 020 log( / ) ( 2 ) ( 2 )a a a a      (10) the authors developed a software and hardware complex which analyzes the signal in real time with a variable duration and performs a fast fourier transform to search for the amplitudes of the fundamental and second harmonics. when a trend is detected to increase the amplitude of the second harmonic, the software stops the experiment and reports the possible occurrence of a fatigue crack. a) b) figure 4: the change in the non-linearity factor βrelative (db) during testing of the sample with an internal crack (a) σ = 138 mpa, nf = 7.51 • 108 (fish-eye) and a sample with a surface crack (b) σ = 140 mpa, nf = 2.72 • 108. the dependences of the non-linearity coefficient βrelative on the loading amplitude during fatigue life for aluminum alloy amg-6 are given. during the experiment, βrelative increases slightly at the initial stage, which is usually attributed to the effect of heating the sample and, as a result, changing its linear dimensions [17-19], then most of the time of the experiment, the amplitude of the second harmonic remains constant and increases significantly with the formation of a fatigue crack and its growth (fig. 4, a). the amplitude of the second harmonic is associated with the deformation due to defects. for given loading parameters, the system is macroscopically in the elastic region, and all deformations are t m. bannikov et alii, frattura ed integrità strutturale, 49 (2019) 383-395; doi: 10.3221/igf-esis.49.38 388 reversible. the defects weakly correlate with each other, and the amplitude of the second harmonic is small and varies little. however, in the process of cyclic loading, irreversible microdamages are appeared, which begin to interact with each other, which subsequently leads to the formation of a fatigue crack. in one of the samples, which were destroyed with the formation of a surface crack, a monotonic decrease in the amplitude of the second harmonic uncharacteristic for others was found during the testing process (fig. 4.b). this is supposed to be due to the fact that the initial structure of the material was saturated with defects, since the samples were pre-deformed. during cyclic loading, a small amplitude in the material resulted in relaxation of internal stresses [20], which reduced the nonlinearity of the signal. when a stress relaxation resource is depleted, an avalanche-like growth of the second harmonic amplitude is observed, which indicates a high correlation of defects and their interaction on a large scale compared with the internal nucleation of a fatigue crack. in the fig. 5 the growth of the amplitude of the second harmonic is shown. at the time point of 5.415 * 10 ^ 4, the software stopped the experiment on the basis of a significant increase in the amplitude of the second harmonic (6 times), which indicated the formation of a fatigue crack. later, the experiment was started again, which allowed us to observe how the amplitude of the second harmonic increases with increasing crack length. thus, the βrelative parameter can be used not only as an indicator of the appearance of a fatigue crack, but also to determine its size, as it was done in [21]. figure 5. the amplitude of the second harmonic of prestrained sample amg-6. the difference in the number of cycles between the moment of detection of the nucleation of a fatigue crack and its exit to macroscopic destruction (the output of the system from resonance) was more than 2 • 106 cycles. mathematical model he wide-range constitutive equations [22-24], describing the relationship between the kinetics of damage caused by defects and the relaxation properties of materials, were used to construct a mathematical model that is capable of describing the deformation behavior of metals and alloys under fatigue loading. to describe the evolution of the structure of the material, two parameters are introduced: tensor: ( ) 2 s  s lb bl and scalar: 3 0 ( ) r δ r  where: s tensor of microshears [23]; s shear intensity; l unit normal vector to the shear plane; b unit vector in the direction of shear; δ scale-invariant, structural parameter; r the distance between defects, 0r the characteristic size of the nuclei of defects. t m. bannikov et alii, frattura ed integrità strutturale, 49 (2019) 383-395; doi: 10.3221/igf-esis.49.38 389 averaging s over an elementary volume gives a tensor of microshears density [23]: ( , , )w s dv p s l b (10) where: v volume, ( , , )w s l b distribution function of orientation and intensity of microshears. in its physical meaning p is a strain due to defects. the total strain rate ( ε ) consists of three components: plastic ( pε ), elastic ( eε ) and due to defects ( p ): e p  ε ε ε p    from the second law of thermodynamics, it follows that the energy dissipation can be represented as: : : 0p f f ts δ δ         σ ε p p    , (11) where: t temperature; s rate of change of entropy; σ stress tensor; no equilibrium free energy. according to the onsager principle, еhe following relations are obtained from (11): 1 2 pl l σ ε p  (12) 2 3 pf l l       ε p p   (13) 4 f l δ δ      (14) where: 1l , 2l , 3l , 4l kinetic coefficients, in the general case, depending on state parameters, satisfying the constraint: 2 1 3 2 0l l l  . relations (12)-(14) are complemented by hooke's law in the rate formulation and approximation for non-equilibrium free energy. thus, the complete system of constitutive equations looks as follows: ( : ) 2 ( )pλ g   σ d e e ε ε p    (15) 1 2 p d f      ε σ p  (16) 2 3d f      p σ p  (17) 4 f δ δ      (18) 2 2 2 1 2 3 4 : ln( ) 2 2 2 d m p pf c p c c c p p f δ g        σ p (19) d s σ σ σ , 1 ( : ) 3 s σ σ e e m. bannikov et alii, frattura ed integrità strutturale, 49 (2019) 383-395; doi: 10.3221/igf-esis.49.38 390 where: 31 2 1 3 2 l l l l    , 22 2 1 3 2 l l l l    , 13 2 1 3 2 l l l l    , 4 4 1 l   ; e the unit tensor, dσ and sσ the deviator and spherical parts of the stress tensor; mf , 1c 4c – potential approximation constants, g – shear modulus; λ – the first parameter lame; :p  p p . in general, kinetic coefficients depend on state parameters and are representable as follows: 1 i ig   where i the characteristic relaxation times, which in general can be represented as dependencies: 0 ( , , , , , , , , )exp( ) p p i i i u δ t kt    σ ε ε ε ε p p   , where: k is the boltzmann constant, ( )iu  is the characteristic activation energy. the hypothesis is accepted that for the studied processes the relaxation times have the following dependencies: 0 0 0exp( ) in i i i u ε u kt       , 1, 2, 3i  (20) 0 4 0 0 4 4 exp( ) nu p u kt        (21) where: 0 2 : 3 c ε ε  ε ε    , 1cε  s-1 is the dimensionless factor; 0u kt , iu , 1...3i  are the constants that have the meaning of the characteristic energy of overcoming barriers, after which new relaxation mechanisms are activated; 0 : c p ε  p p   ; 1 2 3, , ,n n n n constants, characterizing the rate sensitivity of the material. the meaning of this hypothesis is that the physicomechanical characteristics of the material depend on the strain rate, and the evolution of damage under cyclic loading with small stress amplitudes depends only on the parameter, which in this case can be interpreted as the growth rate of a fatigue crack, related to its characteristic scale. assuming a weak strain rate sensitivity of the relaxation times, we can expand the expression (20) into a taylor series with an accuracy of the second term: 0 0 0 0 0 0 0exp( ) 1 1 i i i in n n n i i i iu ε u u ε u u ε u u ε kt kt kt kt kt             then we get: 0 0 0 0 0 1 i i i u i i i i n n n i i kt u ε u ε ε kt          similarly, for the expression (21): m. bannikov et alii, frattura ed integrità strutturale, 49 (2019) 383-395; doi: 10.3221/igf-esis.49.38 391 0 0 0 04 0 0 4 4 4 4 4 4 4 0 0 4 0 0 4 0 0 1 1 exp( ) exp( ) 1 n u n n n n u p u kt kt u p u u p u u p p kt kt                           . then the kinetic coefficients will have the following form: 0 in i u i ε g    , 1...3i  , 04 4 n u p g      . we introduce the notation: 1 1 0 nε    , 22 0 n p ε    , 33 0 n pε    , 4 0 np     , 1 2n n n   , 2 3pn n n  . the final determining equation is the fracture criterion. in the framework of the proposed model, we can enter a criterion based on the structural scaling parameter: 0δ  (22) the meaning of this criterion is that the percentage ratio of the volume of material occupied by defects tends to 100%, which can be achieved by tending to zero the distance between defects or tending to infinity of the size of defects. the second option is impossible, and the first has a clear physical meaning. in the calculation, the condition (22) is not realizable due to the instability, as it is, therefore, we can replace it with a softer one: fδ δ (23) where 0.4fδ  is the critical value [22], after which the avalanche-like growth of defects begins and the material is considered destroyed. this value is universal for all plastic materials for the proposed model. critical value fδ δ corresponds to critical value cp . model parameter identification the identification of the parameters of the constructed model (15)-(19) was carried out in the uniaxial case: 2 ( )pσ λ g p         (24) 0 ( ) np p f ε σ p            (25) 0 ( ) pn p p f p ε σ p          (26) 0 n fδ p δ          (27) 2 2 2 1 2 3 4ln( ) 2 2 2m p p σpf c p c c c p p f δ g        (28) m. bannikov et alii, frattura ed integrità strutturale, 49 (2019) 383-395; doi: 10.3221/igf-esis.49.38 392 where:  , σ , pl , p are the corresponding components of the tensors ε , σ , pε , p . at the first stage of identification, the problem of minimizing the discrepancy between the experimental and calculated stress-strain diagrams is solved. this determines the parameters  , p , p ; dimensionless strain rate 0 1ε  (static loading), 1.15δ const  . at the second stage, using the known values  , p , p the problem of minimizing the discrepancy between the experimental and calculated stress-strain diagrams at different strain rates is solved. this determines the parameters n and pn , 1.15δ const  . an illustration of optimization problem solving is presented in tab. 3. strain rate, s-1 yield strength, mpa (the experiment, [25, 26]) yield strength, mpa (the calculation) 0.0001 165 166 520 175 176 1210 210 213 table 3: the yield strength in the experiment [25, 26] and the calculation at different strain rates. the final step in identifying the parameters of the model is to determine the values of  and n that are found using experimental fatigue loading data. two characteristic points on the wöhler curve were selected: (300,000 cycles, 190 mpa) and (300,000,000 cycles, 156 mpa). parameters  and n were chosen in such a way that at the loading amplitude of 190 mpa the material was destroyed after 300,000 cycles, and at 156 mpa after 300,000,000 cycles, respectively. the frequency of loading in this case was equal to 20 000 hz, as in the experiment. thus, the complete set of constants for the almg6 alloy is as follows: constants known from literature [24]: 2670ρ  kg / m3, 41  gpa, 27g  gpa. constants that were defined: 529  (pa·s)-1, 38.5p  (pa·s)-1, 2.9p  (pa·s)-1, 3.46  (pa·s)-1, 0.967pn n   , 1.985n  . numerical simulation results a numerical study of the behavior of a real structure and even a laboratory specimen in the very high cycle fatigue mode is not possible due to the requirement of huge computational and time resources. therefore, instead of solving the boundary value problem, the problem of loading a representative material volume (24)-(28) with loading conditions in the form of applied cyclic stresses (29) with amplitude a and frequency 20000  hz, as well as initial conditions (21) is considered. ( ) sin( 2 )at t   (29) 00 00 0 0, 0, 0, 1.15p t tt t p δ δ          (30) the loading condition (19) can be written in terms of strain: ( ) ( )sin( 2 )aε t ε σ t (31) where ( )ε σ is the function that converts stresses into strains for almg6 alloy. differentiating (31) by time, we get: ( ) ( )2 cos( 2 )aε t ε σ t  (32) the numerically constructed wöhler curve and its comparison with experimental data of authors and experiment [27] with similar experiment conditions (almg-6, r=-1, frequency 10 khz) are presented in fig. 6. m. bannikov et alii, frattura ed integrità strutturale, 49 (2019) 383-395; doi: 10.3221/igf-esis.49.38 393 figure 6: wöhler curve for almg6 alloy. solid line numerical calculation, points experimental data of the authors, squares experiment [27] with conditions: frequency 10 khz, r=-1. due to the amplitudes of the applied stresses below the yield strength, the material is macroscopically in the elastic region, and the applied deformations can be considered small. then expression (24) can be rewritten in the form: 2 ( )pσ λ g p      (33) since macroplastic strain is not observed, then in the very high cycle fatigue mode, the parameter p is responsible for the accumulation of damage and destruction. the growth of defects leads to a gradual change in the amplitude of the applied voltages, and consequently to a change in the amplitude of the applied displacements, since for some displacement amplitude au in the loading machine is always assigned aσ : ( ) 2 ( ( ) )a a aσ λε σ g ε σ p   (34) after reaching the parameter p of some critical value pc (which corresponds to 0, 4fδ  ), an avalanche-like growth of defects occurs, leading to the destruction of the material, which in the experiment corresponds to an avalanche-like change in the amplitude of the second harmonic of displacements (fig. 7.). figure 7: defect kinetics (dashed line) in the calculation and change in the amplitude of the second harmonic of displacements in the experiment (solid line) . in fig. 7 shows the normalized curves of variation of the parameter p, referred to pc and the amplitude of the second harmonic of displacements, referred to its maximum value. figure 7 shows the experimental data corresponding to the preloaded specimen. according to the proposed model, the change in structure due to preloading is described in terms of the parameter δ. namely, a smaller value of the initial condition δ0 corresponds to the preloaded specimen. to obtain the dotted curve (fig. 7), the eqns. (24-29, 30, 32) was solved with the initial condition δ0 = 1.02. thus, the proposed model is able to adequately describe the behavior of the material in the modes of highand very high cycle fatigue. based on the results of numerical simulation, we can conclude that the change in the amplitude of the m. bannikov et alii, frattura ed integrità strutturale, 49 (2019) 383-395; doi: 10.3221/igf-esis.49.38 394 second harmonic of displacements in the experiment gives adequate information about the accumulation of damage in the material. conclusion n analysis of the free end oscillations during gigacyclic tests showed a significant increase in the second harmonic amplitude and nonlinearity coefficient during the formation of fatigue cracks. in conjunction with the simulation results, we can conclude that the deviation from the linear-elastic law (“anomaly of elastic compliance”) is due to the accumulation of defects in the material, and the avalanche-like growth of the second harmonic displacement corresponds to the avalanche-like growth of defects and the formation of a macroscopic crack. thus, it is possible to judge the accumulation of damage, including in the amount of material based on the acoustic signal. using the proposed equations, it can to predict the fatigue life of the material and identify internal defects and cracks before macroscopic destruction occurs. acknowledgments uthors thank prof. valery matveyenko for the proposal to present the paper in the issue. this work was supported by the russian science foundation, grant number 18-72-00142. references [1] botvina, l.r. (2004) gigacycle fatigue is a new problem in physics and mechanics of destruction // factory laboratory. diagnostics of materials 70(4), pp. 41. (in russian). [2] bathias, c., paris, p.c. (2005), gigacycle fatigue in mechanical practice, marcel dekker publisher co., pp. 328. [3] oborin, v., bannikov, m., naimark, o., palin-luc, t. (2010). scaling invariance of fatigue crack growth in gigacycle loading regime, technical physics letters, 36 (11), pp. 1061-1063. doi: 10.1134/s106378501011026x. [4] cowles, b.a. (1996). high cycle fatigue in aircraft gas turbines an industry perspective, international journal of fracture 80, pp.147-163. doi: 10.1007/bf00012667. [5] shanyavsky, a.a. (2007) simulation of fatigue damage of metals. synergetic in aviation, ufa: monograph llc. (in russian). [6] nicholas, t. (2006). high cycle fatigue. a mechanics of material perspective, elsevier., pp. 641. [7] peters, j.o., ritchie, r.o. (2000). influence of foreign object damage on crack initiation and early crack growth during high-cycle fatigue of ti-6al-4v, eng. fract. mech. 67, pp. 193-207. doi: 10.1016/s0013-7944(00)00045-x. [8] spanrad, s., tong, j. (2011). characterisation of foreign object damage (fod) and early fatigue crack growth in laser shock peened ti–6al–4v aerofoil specimens, materials science and engineering a, 528, pp. 2128–2136. doi: 10.1016/j.msea.2010.11.045. [9] oakley, s.y., nowell, d. (2007) prediction of the combined highand low-cycle fatigue performance of gas turbine blades after foreign object damage, international journal of fatigue, 29, pp. 69–80. doi: 10.1016/j.ijfatigue.2006.02.042. [10] chen, xi (2005). foreign object damage on the leading edge of a thin blade, mechanics of materials, 37, pp. 447–457. doi: https://doi.org/10.1016/j.mechmat.2004.03.005. [11] nowell, d., duó, p., stewart, i.f. (2003). prediction of fatigue performance in gas turbine blades after foreign object damage, international journal of fatigue, 25, pp. 963-969. doi: 10.1016/s0142-1123(03)00160-9. [12] mughrabi, h. (2015). microstructural mechanisms of cyclic deformation, fatigue crack initiation and early crack growth, philosophical transactions of the royal society a: mathematical, physical and engineering sciences, 373(2038), 20140132. doi: 10.1098/rsta.2014.0132. [13] zhang, li-li, et al. (2016). on the formation mechanisms of fine granular area (fga) on the fracture surface for high strength steels in the vhcf regime, international journal of fatigue, 82, pp. 402-410. doi: 10.1016/j.ijfatigue.2015.08.021. a a m. bannikov et alii, frattura ed integrità strutturale, 49 (2019) 383-395; doi: 10.3221/igf-esis.49.38 395 [14] oborin, v., sokovikov, m., bilalov, d., & naimark, o. (2016). multiscale study of morphology of the fracture surface aluminum-magnesium alloy with consecutive dynamic and gigacycle loading, procedia structural integrity, 2, pp. 10631070. doi: 10.1016/j.prostr.2016.06.136. [15] froustey, c., naimark, o., bannikov, m., oborin, v. (2010). microstructure scaling properties and fatigue resistance of pre-strained aluminium alloys (part 1: alcu alloy), european journal of mechanics a/solids, 29, pp. 1008-1014. doi: 10.1016/j.euromechsol.2010.07.005. [16] oborin, v.a., bayandin, yu. v., bilalov, d. a., sokovikov, m. a., chudinov, v. v, naimark, o. b. (2018). self-similar laws of damage development and evaluation of the reliability of alloys d16t and amg6 under combined dynamic and gigacycle loading, phys. mezomekh, 21(6), pp. 135-145 doi: 10.1134/s1029959919020048. [17] john h. cantrell, william t. yost (2001) nonlinear ultrasonic characterization of fatigue microstructures, int. j. of fatigue, 23, pp.487–490. doi: 10.1016/s0142-1123(01)00162-1. [18] kumar, a., torbet, j.c. pollock, m.t., jones, w.j. (2010). in situ characterization of fatigue damage evolution in a cast al alloy via nonlinear ultrasonic measurements, actamaterialia, 58(6), pp. 2143-2154. doi: 10.1016/j.actamat.2009.11.055 [19] kumar a. et al. (2011) in situ damage assessment in a cast magnesium alloy during very high cycle fatigue. scriptamaterialia, 64(1), pp.65-68. doi: 10.1016/j.scriptamat.2010.09.008 [20] nazarov a.a., (2018). nonequilibrium grain boundaries in bulk nanostructured metals and their recovery under the influences of heating and cyclic deformation. review, letters on materials 8 (3), 2018 pp. 372-381 (in russian). doi: 10.22226/2410-3535-2018-3-372-381 [21] w. li, h. cui, w. wen, x. su, c. c. engler-pinto jr.: (2015). in situ nonlinear ultrasonic for very high cycle fatigue damage characterization of a cast aluminum alloy. materials science and engineering a, 645, pp. 248-254. doi: 10.1016/j.msea.2015.08.029. [22] bilalov, d.a., bayandin, yu.v., naimark, o.b. (2018). mathematical modeling of failure process of almg2.5 alloy during highand very high cycle fatigue, computational continuum mechanics. 11(3), pp. 323-334. (in russian). doi: 10.7242/1999-6691/2018.11.3.24. [23] naimark, o.b. (2003) collective properties of defects ensembles and some nonlinear problems of plasticity and fracture, physical mesomechanics, 6(4), pp. 39-63. [24] froustey c., naimark o.b., panteleev i.a., bilalov d.a., petrova a.n., lyapunova e.a. (2017) multiscale structural relaxation and adiabatic shear failure mechanisms, physical mesomechanics, 20(1), pp. 31-42. doi: 10.1134/s1029959917010039. [25] glushak, b.l., ignatova, o.n., pushkov, v.a., novikov, s.a., girin, a.s., sinitsyn, v.a. (2000). dynamic deformation of aluminum alloy amg-6 at normal and higher temperatures, journal of applied mechanics and technical physics., 41(6), pp. 1083-1086. doi: 10.1023/a:1026662824249. [26] frolov, k.v. (2001). mechanical engineering. encyclopedia. volume ii-3: non-ferrous metals and alloys. composite metallic materials. moscow, mechanicalengineering, 880 p. (in russian). [27] yakovleva, t. yu., matokhnyuk, l.e. (2004). prediction of fatigue metal resistance characteristics at different loading frequencies, strength problems, 4, pp. 145-155. 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/hrv (za stvaranje adobe pdf dokumenata najpogodnijih za visokokvalitetni ispis prije tiskanja koristite ove postavke. stvoreni pdf dokumenti mogu se otvoriti acrobat i adobe reader 5.0 i kasnijim verzijama.) /hun 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can be opened with acrobat and adobe reader 5.0 and later.) >> /namespace [ (adobe) (common) (1.0) ] /othernamespaces [ << /asreaderspreads false /cropimagestoframes true /errorcontrol /warnandcontinue /flattenerignorespreadoverrides false /includeguidesgrids false /includenonprinting false /includeslug false /namespace [ (adobe) (indesign) (4.0) ] /omitplacedbitmaps false /omitplacedeps false /omitplacedpdf false /simulateoverprint /legacy >> << /addbleedmarks false /addcolorbars false /addcropmarks false /addpageinfo false /addregmarks false /convertcolors /converttocmyk /destinationprofilename () /destinationprofileselector /documentcmyk /downsample16bitimages true /flattenerpreset << /presetselector /mediumresolution >> /formelements false /generatestructure false /includebookmarks false /includehyperlinks false /includeinteractive false /includelayers false /includeprofiles false /multimediahandling /useobjectsettings /namespace [ (adobe) (creativesuite) (2.0) ] /pdfxoutputintentprofileselector /documentcmyk /preserveediting true /untaggedcmykhandling /leaveuntagged /untaggedrgbhandling /usedocumentprofile /usedocumentbleed false >> ] >> setdistillerparams << /hwresolution [2400 2400] /pagesize [612.000 792.000] >> setpagedevice q.-c. li et alii, frattura ed integrità strutturale, 58 (2021) 1-20; doi: 10.3221/igf-esis.58.01 1 factors affecting reorientation of hydraulically induced fracture during fracturing with oriented perforations in shale gas reservoirs qing-chao li school of energy science and engineering, henan polytechnic university, jiaozuo, henan 454000, china. school of petroleum engineering, china university of petroleum (east china), qingdao, shandong 266580, china. liqingchao2020@hpu.edu.cn, b16020053@s.upc.edu.cn, http://orcid.org/0000-0001-7373-4046 liang zhou well testing branch, cnpc bohai drilling engineering company limited, langfang, hebei 065007, china. zhouliang8@cnpc.com.cn zhi-min li no.3 drilling engineering company, cnpc bohai drilling engineering company limited, tianjin 300280, china. lzhimin@cnpc.com.cn zhen-hua liu oil production plant no.2, petrochina changqing oilfield company, qingcheng, gansu 745100, china. liuzhenhua3186@163.com yong fang well testing branch, cnpc bohai drilling engineering company limited, langfang, hebei 065007, china. fang_yong@cnpc.com.cn lei zhao no.4 drilling engineering branch company, cnpc bohai drilling engineering company limited, renqiu, hebei 062550, china. zhaolei9@cnpc.com.cn ying han* school of energy science and engineering, henan polytechnic university, jiaozuo, henan 454000, china. hyhpu@hpu.edu.cn abstract. hydraulic fracturing with oriented perforations is an effective technology for gas development from shale reservoirs. however, fracture reorientation during fracturing operation can affect the fracture conductivity and hinder the effective production of shale gas. in addition, factors such as perforation azimuth, in-situ stresses, fracturing fluid viscosity and injection rate can affect fracture reorientation during fracturing operation, and the first citation: li, q.c., zhou, l., li, z.-m.-, liu, z.-h., fang., y., zhao, l., han., y., factors affecting fracture reorientation during fracturing operation with oriented perforations in shale gas reservoirs, frattura ed integrità strutturale, 58 (2021) 1-20. https://youtu.be/dday-bmxfvi q.-c. li et alii, frattura ed integrità strutturale, 58 (2021) 1-20; doi: 10.3221/igf-esis.58.01 2 three factors are controllable factors. in the present work, a numerical simulation model for investigating fracture reorientation during fracturing with oriented perforations was established, and it was verified to be suitable for all investigations in this paper. based on this simulation model, factors affecting both initiation and reorientation of the hydraulically induced fractures were investigated. the investigation results show that the fluid viscosity has little effect on initiation pressure of hydraulically induced fracture during fracturing operation, and the initiation pressure is mainly affected by perforation azimuth, injection rate and the stress difference. moreover, the investigation results also show that perforation azimuth and difference between two horizontal principal stresses are the two most important factors affecting fracture reorientation. based on the investigation results, the optimization of fracturing design can be achieved by adjusting some controllable factors. however, the regret is that the research object herein is a single fracture, and the interaction between fractures during fracturing operation needs to be further explored. keywords. hydraulic fracturing; oriented perforation; fracture initiation; fracture reorientation; fracture propagation; shale reservoir. received: 11.03.2021 accepted: 03.07.2021 published: 01.10.2021 copyright: © 2021 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. introduction hale is the fragile and fine grain sedimentary layer that is composed of clastic particles with particle size less than 6.35×10-5 m, clay and organic matter [1]. according to u.s. energy information administration (eia), the global technically recoverable shale gas resources are 206.68×1012 m3 by 2013, and china has the largest recoverable reserves all over the world [2]. moreover, the eia predicts that shale gas will be the main driving force for increase of global natural gas production in the future. by 2040, the average daily production of shale gas is expected to be four times that of 2015, reaching 4.76×109 m3 [3]. therefore, although tight shale formations have been generally considered as the caprock of oil and gas reservoirs, they have received increasing attention as unconventional reservoir in recent years. however, shale reservoirs generally have lower permeability (usually between 1.0×10-21 m2 and 1.0×10-19 m2), and belong to ultra-low permeability reservoirs [4]. hydraulic fracturing operations are generally considered to be effective measures to stimulate the physical properties of shale reservoirs, increasing natural gas production [5, 6]. perforations around wellbore region can effectively reduce the initiation pressure that is needed to overcome in hydraulic fracturing operations, which is conducive to the initiation of hydraulically induced fractures [7-9]. accordingly, hydraulic fracturing with oriented perforations has become an effective measure to stimulate shale reservoir. ideally, to ensure the high fracture conductivity, the direction of perforation should be consistent with the direction of the maximum horizontal main stress. in fact, the geologic conditions of formation are often complicated and it is difficult to accurately determine the direction of the maximum horizontal principal stress σh [7, 10]. as shown in fig.1a, stress concentration at the perforation tip due to injection of fracturing fluid results in the microhydraulically-induced fracture at the beginning of fracturing operation. as the fracturing fluid continues to be injected, the micro-fracture will propagate along the initial perforation for a certain distance (see fig.1b). then, fracture reorientation will occur if there is an angle between the perforation and the maximum horizontal principal stress (fig.1c). the parameter l in fig.1c is defined as reorientation radius herein, which is used for describing fracture reorientation. in addition, the bending fractures formed during hydraulic fracturing will lead to retention of proppant in the reorientation position (see fig.1d), which brings difficulty to the transport of proppant within fracture. therefore, in-depth investigation on the reorientation of hydraulically induced fractures during hydraulic fracturing operation with oriented perforations is of great importance for the design and optimization of hydraulic fracturing in oilfields. at present, most investigations on hydraulic fracturing technology mainly focus on the analysis of post-fracturing productivity. in comparison, there are fewer studies on the behavioral evolution of fractures during fracturing. recently, considerable advancements have already been made in behavior evolution of hydraulically induced fractures numerically and/or s q.-c. li et alii, frattura ed integrità strutturale, 58 (2021) 1-20; doi: 10.3221/igf-esis.58.01 3 experimentally during hydraulic fracturing operations. li et al. [11] numerically investigated factors affecting fracture propagation during the multi-cluster staged fracturing for shale reservoir using cohesive elements with abaqus fem software. the investigation reveals that the cluster spacing between the adjacent hydraulic-induced fractures is the most important factor. chang et al. [12] carried out a series of laboratory experiments to investigate the effectiveness of oriented perforation fracturing, and it showed that the fractures formed by oriented perforation fracturing technology tend to stimulate more reservoir volume. zhu et al. [13] studied the factors affecting initiation pressure of unconventional reservoirs with a finite element model of hydraulic-induced fracture for the cased wells with the oriented perforations. li et al. [14] analyzed the reorientation mechanism of hydraulically induced fracture with the coupling finite element model, and the investigation results showed that difference between the maximum and the minimum horizontal principal stresses affects the fracture morphology large. although these investigations are particularly useful and helpful, there is a lack of detailed research on factors affecting reorientation of fractures during hydraulic fracturing operations with oriented perforation in shale reservoirs. in other words, investigation on the fracture reorientation during reservoir stimulation through hydraulic fracturing is not deep enough. therefore, it is important and necessary to conduct relevant research. figure 1: schematic of fracture reorientation during hydraulic fracturing operation with oriented perforations. a: fracture initiation; b: fracture propagation; c: fracture reorientation; d: proppant retention within fracture. in addition, the interaction between fractures during fracturing operation is also an important factor affecting the final fracture morphology in reservoir. therefore, in-depth analysis of the interaction between fractures is valuable for understanding the formation mechanism of complex fracture network during the fracturing operation. up till now, some progress has been made by so many scholars in this area. however, current investigations focus on the interaction between natural fractures and hydraulic fractures during fracturing operation, rather than interaction between hydraulically induced fractures. zhou et al. [15] analyzed crack coalescence in rocks with defects by uniaxial compression experiments and found that crack coalescence can occur in nearly all samples, but the mechanism is different for different types of rocks. yu et al. [16] numerically analyzed the interaction between fractures during fracturing in tight sandstone reservoir. it was found that obvious interaction occurs between hydraulically induced fractures, and the reservoir pressure is the dominant factor affecting the interaction between fractures. zhang et al. [17] analyzed factors affecting propagation of natural fracture by xfem method, it is found that natural fracture propagates easily with the decrease of dip angle and stress difference. arash [18] investigated the effect of natural fracture on propagation of hydraulically induced fractures, and the investigation results show that interaction between natural fracture and hydraulically induced fracture is the key condition resulting in complex fracture network. nevertheless, considering that interaction between hydraulic fractures is not the focus of the present work, so related investigation is not carried out herein. in the present work, the coupled finite element model (fem) used for investigating reorientation of the hydraulically induced fracture in shale reservoirs was developed by using the extended finite element method (xfem). in this coupled model, some important aspects in the q.-c. li et alii, frattura ed integrità strutturale, 58 (2021) 1-20; doi: 10.3221/igf-esis.58.01 4 hydraulic fracturing operations (such as injection of fracturing fluid, fluid flow in hydraulically induced fractures and fracture reorientation) were considered. based on this, factors affecting fracture reorientation during fracturing in shale reservoirs are then studied, regarding fracture initiation pressure and reorientation radius as the research target. the study in this paper will provide reference for fracturing design of unconventional oil and gas reservoirs. elementary theory for hydraulic fracturing by xfem hale reservoirs are generally heterogeneous and anisotropic, which brings difficulties to practical research [19]. to highlight the research focus, the research model for investigating fracture reorientation in shale reservoirs is assumed to be a homogeneous, isotropic 2d plane strain model. furthermore, it is considered that the fracture propagation is quasi-static and there is no fluid hysteresis within fractures. finally, the incompressible newton fracturing fluid is injected into the wellbore at a constant flow rate during fracturing. therefore, in-depth study of fracture reorientation in hydraulic fracturing process needs to thoroughly understand the basic theories of seepage mechanics, rock mechanics and damage mechanics involved in the process. in this section, the elementary theories were presented. stress balance equation of rock in shale reservoir rock deformation occurs under the dual action of the in-situ stresses and the fluid pressure during fracturing. weak form is the ultimate equation form for solving multi-field coupling problems by using finite element method. therefore, the weak form of equations for both the seepage field (pore pressure) and the deformation field (stress and displacement) were obtained herein. the weak form of stress balance equation can be expressed by eqn. (1) when seepage in porous media of shale reservoir was considered [20, 21]. ( )   =  +   :w v s v p dv ds dvσ i ε t u f u (1) where, σ is the effective stress, mpa; f is the unit body force, mpa; t is the unit surface force, mpa; pw is the fluid pressure at the fracture, mpa; δε is the virtual stain, dimensionless; δu is the virtual displacement, m; dv is the volume of the micro-element, m3; and ds is the area of the micro-element, m2. seepage flow equation in shale gas reservoir simulation of fluid seepage in shale reservoir can be realized by applying pore pressure at each node and then applying the boundary condition of pore pressure at a certain boundary. the law of mass conservation is the law that all physical processes follow. therefore, the mass conservation equation of fracturing fluid in porous medium can be written as [22, 23]       +  =        0w w v s d dv ds dt n v (2) where, ρw is the density of fracturing fluid, kg/m3; φ is the porosity, dimensionless; n is the normal vector of surface s, dimensionless. at present, only single-phase incompressible seepage can be properly realized in abaqus software, and the calculation of complex multi-phase seepage cannot be achieved. just as eqn. (3), the seepage of fracturing fluid in shale reservoir is assumed to satisfy darcy's law [21].   = −  1 w dp g v k (3) where, v is the seepage velocity, m/s; k is the permeability of shale reservoir, m2; g is gravity acceleration, 9.8 m/s2; dp is pressure difference between two ends of micro-element, mpa. s q.-c. li et alii, frattura ed integrità strutturale, 58 (2021) 1-20; doi: 10.3221/igf-esis.58.01 5 initiation and propagation of hydraulically induced fracture the constitutive model of elements used for simulating fracture initiation satisfies the traction-separation criteria. that is to say, the constitutive relationship of elements within the investigation model herein is linear elastic before damage, and its stiffness drops to zero when the damage occurs. up till now, a variety of different damage criteria (such as the maximum principal stress and the maximum principal strain criterion) have been embedded in the abaqus finite element software [11, 24]. among them, the maximum stress criterion has been proved to be more effective and accurate [24]. therefore, in this paper, the maximum principal stress criterion shown in eqn. (4) is used as the damage criterion [25].     =     max 0 max f (4) where, σ0max and σmax are the critical maximum principal stress and the maximum principal stress respectively, mpa. once the principal stress criterion was adopted, the critical maximum principal stress should be given, and the element damage begins to occur when the maximum principal stress σmax exceeds the critical maximum principal stress σ 0 max. the damage evolution of the unit follows the benzeggagh-kenane criteria [25, 26] shown in the following equation ( )    + − =    s nc sc nc c t g g g g g g (5) where, gnc, gsc, gs and gt are the normal critical energy release rate, tangential critical energy release rate, the first tangential fracture energy release rate and the second tangential fracture energy release rates respectively, mpa·m; η is a constant, 2.284. fluid flow in fracture during fracturing fluid flow in fracture can be divided into the normal flow and the tangential flow. the tangential flow ensures the continuous propagation of fracture during fracturing, and the following cubic-law can be adopted to describe the tangential flow in hydraulically induced fracture.  =  3 12 d q p (6) where, q is the fluid flow required for 1m of fracture propagation, m3; d is the fracture width, m; μ is the fluid viscosity, pa·s. normal fluid flow within the hydraulically induced fracture results in the leak-off of fracturing fluid, and the leak-off of fracturing fluid from fracture into reservoir is defined as ( )−= −leak-off leak off w surfc p pv (7) where, vleak-off is the leak-off velocity, m/s; cleak-off is the leak-off coefficient, m/(mpa·s); psurf is the pore pressure in shale reservoir adjacent to the fracture surfaces, mpa. numerical modeling of single fracture reorientation model geometry and mesh generation lthough the establishment of simulation model is the basic for investigation of fracture reorientation during fracturing operation, a series of assumptions need to be made before the model is constructed. firstly, shale reservoir is assumed to be homogeneous, and the reservoir properties at any node within the model are the same. secondly, only single-phase seepage of fracturing fluid occurs in shale, and it satisfies darcy's law. moreover, shale is a q.-c. li et alii, frattura ed integrità strutturale, 58 (2021) 1-20; doi: 10.3221/igf-esis.58.01 6 assumed to be elastic and its plastic failure during fracturing is ignored. finally, wellbore used for shale gas production and fracturing operation is a vertical one (see fig.2a). based on these assumptions, a 2d plane strain model for investigating fracture reorientation during hydraulic fracturing with oriented perforations in shale reservoirs is established with abaqus finite element software (see fig.2). therefore, only the maximum and the minimum horizontal principal stress exist within the 2d simulation model before simulation. as shown in fig.2b, the investigation model is a full-size square model, and its side length is200 m. generally speaking, the half-length of fractures during fracturing operation is within 100 meters [11]. therefore, the model size in this paper is sufficient to avoid the influence of boundary effects on the simulation results [11, 27-29]. moreover, the borehole with a radius of 0.2 m is located in the center of the simulation model. as can be seen from fig.2a and fig.2b, the simulation area "abcd" corresponds to a plane in shale reservoir that is perpendicular to the wellbore axis. in order to improve the simulation accuracy, the element size at the outer boundaries is 25 times as large as that around wellbore (see fig.2b and fig.2c), and the reservoir model is finally discretized into 17,500 cpe4p elements. the cpe4p elements can realize coupling analysis of fracturing fluid seepage and borehole deformation in simulation of hydraulic fracturing. another important reason for meshing in this way is that both the initiation and propagation of fractures mainly occur in the near-wellbore region around wellbore. as can be seen in fig.2c, two perforations are designed centrosymmetrically in different azimuth angles around borehole herein, and the perforation depth is 0.50 m. in the model, reservoir and two perforations are three separate parts, and the perforations should be discretized separately during simulation. therefore, two centrosymmetrical perforations around wellbore are discretized into 10 t2d2 elements and interact with the reservoir elements. during simulation with this model, when the pressure in perforation reaches reservoir strength, the fracture will initiate at the perforation tip. load type objects type and value fluid injection two injection nodes in fig.2c injection rate q=10m3/min boundary conditions boundary ab and cd displacement u1=0 boundary bc and da displacement u2=0 boundary ab, bc, cd and da pore pressure pp=18mpa borehole displacement u1=u2=0 initial conditions whole model pore pressure pp=18mpa whole model σh=43mpa, σh=33mpa and σv=35mpa table 1: the loads, boundary conditions and initial conditions in the investigation. boundary conditions and basic simulation parameters the loads, boundary conditions and initial conditions adopted herein have been presented in tab.1. as can be seen in tab.1, the normal displacement of both the outer boundaries and the borehole should all be set to 0 throughout the simulation, and the pore pressure at the outer boundaries should also be fixed to the original reservoir pressure. before the fracturing simulation, the initial in-situ stresses and reservoir pressure within the model need to be initialized. furthermore, it should be emphasized that the two perforation tips are regarded as injection points of fracturing fluid. the fracturing fluid is injected into the perforation holes at a constant rate during the fracturing operation. q.-c. li et alii, frattura ed integrità strutturale, 58 (2021) 1-20; doi: 10.3221/igf-esis.58.01 7 figure 2: schematic diagram of hydraulic fracturing with oriented perforation in shale reservoir and the established finite element model. (the perforation azimuth angle is 30°, and the perforation depth is 0.50 m) (a): formation model; (b): 2d finite element meshing model; (c): meshing elements around borehole. parameter value parameter value elastic modulus e, gpa 18 poisson's ratio υ, dimensionless 0.25 maximum horizontal principal stress σh, mpa 43 minimum horizontal principal stress σh, mpa 33 vertical principal stress σv, mpa 35 water saturation sw, % 100 tensile strength ts, mpa 3 initial porosity φ, % 4 initial pore pressure pp0, mpa 18 leak-off coefficient cleak-off, m/(mpa·s) 1×10-12 permeability k, m2 5×10-17 side length l, m 200 viscosity of fracturing fluid μ, mpa·s 30 injection rate q, m3/min 10 borehole radius r, m 0.20 perforation depth pd, m 0.50 total fracturing time t, min 10 reservoir depth d, m 2000 perforation azimuth θ, ° 40 table 2: basic parameters for simulation. although tab.1 has presented how loads, boundary conditions and initial conditions are applied, no specific values are given. for this purpose, tab.2 gives the basic data required for simulation. based on these data, the simulation can be conducted in this paper. implementation of fracture initiation and reorientation in abaqus although most of the simulation involved in this paper can be done directly by cae interface in abaqus software, secondary development is required for some settings. in this work, a text file with extension .inp is outputted after inputting basic parameters to the simulation software, and secondary development can be conducted by manually modifying this file. fig.3 shows what needs to be modified in the *.inp file. as can be clearly seen in fig.3, two contents need to be modified to achieve secondary development: ➢ the fluid injection parameters need to be added into the *.inp file. the content (1) in fig.3 means that the fracturing fluid is continuously injected at a rate of 5×10-6 m3/s at two nodes numbered 180 and 181 within the instance named part-1-1. q.-c. li et alii, frattura ed integrità strutturale, 58 (2021) 1-20; doi: 10.3221/igf-esis.58.01 8 (a) before modification (b) after modification figure 3: comparison of the *.inp file before and after modification. ➢ in addition, some simulation results need to be manually outputted. contents (2) in fig.3 are some output variables that need to be manually edited in file with extension .inp. modification (2) in fig.3 are pfopenxfem: width of the hydraulically induced fracture; leakvrtxfem and leakvrbxfem: leak-off flow rate of two interfaces of fracture in 2d model; aleakvrtxfem and aleakvrbxfem: total leak-off flow volume from two interfaces of fracture within a 2d model; porpres: pore pressure of the element damaged by the hydraulically induced fracture. the relevant results of hydraulically induced fracture are read from the result file in the form of *.odb when the simulation has been completed, thereby obtaining the initiation pressure and the reorientation radius. in addition, as can be seen in tab.2, the injection rate is a constant value. however, in order to prevent the non-convergence caused by the sudden change of injection rate at the beginning of simulation, some measures need to be taken. as shown in fig.4, the injection rate is gradually increased from 0 to the set value during the first 10 seconds. in this way, injection evolution of fracturing fluid at the beginning of fracturing operation becomes smoother, and the simulation process is more stable. of course, the injection pattern displayed in fig.4 needs to be realized by the amplitude function. q.-c. li et alii, frattura ed integrità strutturale, 58 (2021) 1-20; doi: 10.3221/igf-esis.58.01 9 figure 4: evolution of injection rate during fracturing operation. verification of the simulation model model validation refers to exploring the applicability of the established model to investigations. the applicability of the investigation model used in this paper has been verified numerically and/or experimentally in several studies [14, 30]. in the present work, the applicability of the investigation model given in fig.2 is verified by comparing the experiment in references [31] with the simulation in this paper. however, it should be noted that the simulation conditions (of course, numerical scaling is required according to dimensional analysis.) should be all consistent with experimental conditions in reference [31]. the experimental conditions are summarized in tab.3. figure 5: comparison of the experimental result in reference [31] with the simulation result. fig.5 illustrates the comparison of the experimental result with the simulation result. by fig.5, we can clearly see that the fracture morphology obtained by experiment (see fig.5a) and simulation (see fig.5b) is similar, which can qualitatively verify the applicability of the investigation model. in order to quantitatively verify the applicability, tab.4 compares the experiment and the simulation by two parameters, i.e. initiation pressure and reorientation radius. by comparison, it can be found that the initiation pressure in simulation is only 0.29mpa lower than that in experiment, and the redirection radius in simulation is also only 0.18cm shorter than that in experiment. all the above comparisons show that the investigation model in this paper can be used for analysis of both the initiation and the redirection of hydraulically induced fractures during fracturing operation. q.-c. li et alii, frattura ed integrità strutturale, 58 (2021) 1-20; doi: 10.3221/igf-esis.58.01 10 conditions value unit viscosity of fracturing fluid 73 mpa·s maximum horizontal principal stress 6 mpa minimum horizontal principal stress 1 mpa tensile strength 2.59 mpa porosity 1.85 % permeability 1×10-16 m2 elastic modulus 8.402 gpa poisson's ratio 0.23 injection rate 2.1×10-9 m3/s perforation depth 0.05 m perforation azimuth 60 ° table 3: experimental conditions in reference [31]. parameter experiment in reference [31] simulation initiation pressure, mpa 15.55 15.26 redirection radius, cm 8.30 8.48 table 4: verification results of the simulation model. results and discussions n order to deeply understand both the initiation and the reorientation of hydraulically induced fractures during fracturing operation with oriented perforations, influences of different factors on them were investigated. therefore, all data in tab.2 are the benchmark data. when investigating the influence of certain factor on fracture reorientation, it is only necessary to adjust the corresponding data based on tab.2. for example, if the effect of perforation azimuth on fracture reorientation was investigated, the perforation azimuth can be expanded from 40° to five values of 0°, 20°, 40°, 60° and 80° based on tab.2. effect of perforation azimuth as mentioned above, hydraulically induced fractures will eventually propagate along the maximum horizontal principal stress during hydraulic fracturing. if the perforation does not follow the direction of the maximum horizontal principal stress, the fracture reorientation will occur, affecting the fracture morphology. herein, fracture reorientation under five different perforation azimuths of 0°, 20°, 40°, 60°, and 80° was investigated. fig.6 shows the final fracture morphology with changing the perforation azimuth. it can be seen from fig.6 that regardless of the perforation azimuth, all fractures are initiated at the perforation tip after the fracturing operation has started for a period. then, it propagates outward and gradually reorients to the x direction (direction of the maximum principal stress), eventually forming a double-wing reoriented fracture. this indicates that perforation azimuth has little influence on the direction of fracture propagation, and the maximum principal stress is the main factor affecting the propagation direction. moreover, with the increase of perforation azimuth, fracture reorientation becomes more obvious. although the influence of perforation azimuth on fracture reorientation can be described intuitively and qualitatively from fig.6, the quantitative conclusion can’t be obtained. i q.-c. li et alii, frattura ed integrità strutturale, 58 (2021) 1-20; doi: 10.3221/igf-esis.58.01 11 figure 6: the final fracture morphology when the perforation azimuth is different. therefore, fig.7 shows the effects of perforation azimuth on pressure evolution at injection node, fracture initiation and fracture reorientation during fracturing operation. fracture initiation occurs when the pressure at injection node reaches a certain value, and the pressure at the injection node then gradually decreases from this time and eventually stabilizes [32]. the highest point of pressure evolution curve obtained in fig.7a is usually defined as the initiation pressure [23]. therefore, fig.7b presented the relationship between the initiation pressure during fracturing and perforation azimuths. it can be clearly seen from fig.7b that the initiation pressure increases with the increase of perforation azimuth. the initiation pressure is approximately 38.26mpa when the perforation coincides with the direction of the maximum horizontal principal stress. however, the initiation pressure reaches 52.57mpa when the perforation azimuth is 80°, which is 37.40% higher than that when the perforation azimuth is 0°. the main reason for this is that the bigger the perforation azimuth is, and the more energy is needed to overcome the shear stress to promote the fracture initiation. if fracture reorientation is described by the parameter of redirection radius, the large reorientation radius of hydraulically induced fracture indicates the severe fracture reorientation. we can see from fig.7c that the redirection radius increases non-linearly with the increase of perforation azimuth, and the perforation azimuth of about 62.5° is the inflection point in fig.7c. the increase rate of fracture reorientation radius is 0.42 m/° when the perforation azimuth is less than 62.5°, but it reaches 1.60 m/° when the perforation azimuth exceeds 62.5°. this is because that the area where stress changes during fracturing increases with the increase of perforation azimuth angle, so the hydraulically induced fracture propagates for longer path through this area. therefore, based on the numerical simulation in this section, we can draw the conclusion that perforation azimuth is preferably designed in the range of 0° to 40° during fracturing operation. this is because if the perforations are designed within this range, both the initiation pressure and the fracture pressure are relatively low, so that the operation efficiency can be effectively improved and the operation cost can be reduced. effect of injection rate of fracturing fluid the injection rate is also an important factor affecting both the fracture reorientation and the final fracture morphology. in this section, seven injection rates, 4m3/min, 6m3/min, 8m3/min, 10m3/min, 12m3/min, 14m3/min and 16m3/min, are set to explore the influence of injection rate on fracture initiation and fracture reorientation. moreover, the perforation azimuth adopted in these simulations is 40°. fig.8 shows the final fracture morphology when the injection rate is different. from fig.8, we can qualitatively see that the injection rate of fracturing fluid has little effect on the reorientation of fractures during fracturing operation, but it will affect the propagation of fractures. in fig.8a, when the injection rate is 4m3/min, the half-length of fracture is only about 50m. however, it reaches about 90m when the injection rate has been q.-c. li et alii, frattura ed integrità strutturale, 58 (2021) 1-20; doi: 10.3221/igf-esis.58.01 12 increased to 16m3/min, which is nearly twice as long as the fracture length when the injection rate is 4m3/min (see fig.8g). as what we can see from fig.8g, the numerical model in this paper is almost fractured into the upper and lower parts at the end of fracturing operation when the whole operation is carried out at a larger injection rate. (a): pressure evolution at the injection node during fracturing when the perforation azimuth is 40° (b): effects of perforation azimuth on fracture initiation (c): effects of perforation azimuth on and fracture reorientation figure 7: effects of perforation azimuth on initiation pressure and fracture reorientation. q.-c. li et alii, frattura ed integrità strutturale, 58 (2021) 1-20; doi: 10.3221/igf-esis.58.01 13 figure 8: the final fracture morphology when the injection rate of fracturing fluid is different. to quantitatively clarify the effects of injection rate on both fracture initiation and fracture reorientation, fig.9 gives the initiation pressure and the reorientation radius when the fracturing fluid was injected at different injection rates during fracturing. we can see from fig.9a that a larger injection rate results in the higher initiation pressure. the initiation pressure has increased from 37.26mpa to 53.03mpa when the injection rate was increased from 4m3/min to 16m3/min. as expected, the simulation results show that fracture initiation occurs much earlier at a larger injection rate than that at a smaller one. this is because, for large injection rate, leak-off of fracturing fluid from perforation to reservoir can be almost completely neglected, less time is needed to increase the pressure of injection point to the initiation pressure. fig.9b displays the relationship between reorientation radius and injection rate. although the effect of injection rate on fracture reorientation is not as pronounced as that of perforation azimuth, it can be seen from fig.9b that the increasing injection rate of fracturing fluid can also worsen the fracture reorientation. the reorientation radius is only 13.05m when the injection rate is designed as 16m3/min. although large injection rate can effectively accelerate the fracturing operation and lengthen the fracture length, too large injection rate will increase the cost of fracturing operation. of course, too small injection rate is still inappropriate for fracturing in shale reservoir. therefore, the injection rate of 8 to 12 m3/min under the simulation conditions in this paper is more appropriate. effect of difference between two horizontal principal stresses in this part, on the premise of keeping other basic parameters unchanged, the effect of difference between two horizontal principal stresses on fracture reorientation has been investigated by changing the minimum horizontal principal stress. the minimum horizontal principal stress is sequentially set to 33mpa, 35mpa, 37mpa, 39mpa, 41mpa, and 43mpa in the form of an arithmetic progression. the maximum horizontal principal stress is a fixed value in the whole fracturing q.-c. li et alii, frattura ed integrità strutturale, 58 (2021) 1-20; doi: 10.3221/igf-esis.58.01 14 simulation. in other words, the difference between the two horizontal principal stresses is an arithmetic sequence with a tolerance of 2mpa between 0mpa and 10mpa. (a): effect of injection rate on fracture initiation (b): effect of injection rate on fracture reorientation figure 9: effect of injection rate on initiation pressure and redirection radius during fracturing operation with oriented perforations in shale reservoirs. the final fracture morphology when the difference between two horizontal principal stresses is different is shown in fig.10. we can qualitatively see from fig.10a that the hydraulically induced fracture is almost a straight-line propagating along the perforations during fracturing operation when the two horizontal principal stresses are equal to each other. on the contrary, fracture reorientation occurs more pronouncedly when the difference between two horizontal principal stresses is greater (see fig.10b to fig.10f). although it can be clearly seen from fig.10 that the difference between two horizontal principal stresses will significantly affect fracture reorientation, the quantitative description is necessary. therefore, fig.11 quantitatively describes the influence of stress difference on initiation pressure (see fig.11a) and reorientation angle (see fig.11b) during fracturing operation. we can see from fig.11a that when the minimum horizontal principal stress is 43mpa (i.e., stress difference is 0mpa), the initiation pressure is 52.24mpa. moreover, with the increase of difference between the two horizontal principal stresses, initiation of hydraulically induced fracture becomes easier and easier. the initiation pressure decreases to 43.81mpa when the minimum horizontal principal stress is 33mpa (i.e., stress difference is 10mpa). this is due to the strong stress concentration at the tip of the perforation when the difference between two horizontal principal stresses is significant, which is conducive to the initiation of hydraulically induced fracture. q.-c. li et alii, frattura ed integrità strutturale, 58 (2021) 1-20; doi: 10.3221/igf-esis.58.01 15 figure 10: the final fracture morphology when the difference between two horizontal principle stresses is different. as can be seen in fig.11b, the reorientation of hydraulically induced fracture will be aggravated with the increase of difference between the two horizontal principal stresses. as described in fig.10a, no fracture reorientation occurs (i.e., reorientation angle is 0°) when the difference between two horizontal principal stresses is 0mpa. however, the reorientation angle is 41.73° when the minimum horizontal principal stress is 33.00mpa (i.e., stress difference is 10mpa). from this, we can know that the difference between two horizontal principal stresses is the most important factor that determines whether the fracture reorientation can occur during fracturing operation. although in-situ stresses are not a human intervention factor, the simulation results can be used to properly guide the design of fracturing operations. effect of fluid viscosity the viscosity of hydraulic fluid can also affect the initiation and reorientation of fractures during fracturing operation. based on the parameters listed in tab.2, the initiation pressure and reorientation radius are investigated respectively when the fluid viscosity is 30mpa·s, 60mpa·s, 90mpa·s, 120mpa·s, 150mpa·s and 180mpa·s. q.-c. li et alii, frattura ed integrità strutturale, 58 (2021) 1-20; doi: 10.3221/igf-esis.58.01 16 (a): effect of stress difference on fracture initiation (b): effect of stress difference on fracture reorientation figure 11: effect of difference between two horizontal principal stresses on initiation pressure and reorientation radius during fracturing. figure 12: effect of fluid viscosity on fracture initiation during fracturing operation with oriented perforations in shale reservoirs. fig.12 exhibits the influence of fluid viscosity on initiation pressure during fracturing with oriented perforations when fluid viscosity is different. from fig.12, we can see that the initiation pressure will increase with the increase of fluid viscosity, but the fluid viscosity has little effect on the fracture initiation pressure. the initiation pressure has increased from 45.22mpa to 45.60mpa when the fluid viscosity changes from 30mpa·s to 180mpa·s, with an increase of 0.38mpa. with the help of fig.13, the mechanism of the effect of fluid viscosity on the initiation pressure for fracturing operation can be well explained. from fig.13a, we can see that when the fluid viscosity is low, the fracturing fluid in perforation will more easily invade into shale reservoir, and the seepage resistance of fracturing fluid with lower viscosity in shale reservoir is also smaller. when the fluid viscosity is 30mpa·s, the invasion distance is 12.52cm around perforation. it is not so easy to maintain the pressure in perforation at the beginning of fracturing operation, a large amount of fracturing fluid will invade into reservoir before fracture initiation occurs at the perforation tip. in this case, the initiation pressure will be small when the fracturing fluid viscosity is low. on the contrary, as shown in fig.13b, when the fluid viscosity is high, it is difficult for fracturing fluid to invade into reservoir, and pressure holding in perforation is easy to achieve [33]. when the fluid viscosity is 30mpa·s, the invasion distance is 4.63cm around perforation. therefore, when the fluid viscosity is high, fracture initiation has already begun to occur before the fracturing fluid in perforation invades into the reservoir violently, and the initiation pressure is high. q.-c. li et alii, frattura ed integrità strutturale, 58 (2021) 1-20; doi: 10.3221/igf-esis.58.01 17 (a): low fluid viscosity (b): high fluid viscosity figure 13: fluid invasion from perforation to reservoir during fracturing operation with oriented perforations in shale reservoirs. figure 14: effect of fluid viscosity on reorientation radius during fracturing operation with oriented perforations in shale reservoirs. fig.14 displays the influence of fluid viscosity on reorientation radius of hydraulically induced fracture during fracturing operation with oriented perforations in shale reservoirs. we can see from fig.14 that the reorientation radius of hydraulically induced fracture will nonlinearly become longer with the increase of fluid viscosity. when the fluid viscosity is 30mpa·s, the reorientation radius is only 10.32m. however, the reorientation radius has increased to 14.34m when the fluid viscosity is 180mpa·s, which is 4.02m longer than that when the fluid viscosity is 30mpa·s. this can also be explained by fig.13. as shown in fig.13, when the fluid viscosity is high, fluid within the perforation is difficult to invade into the reservoir, and the pressure in perforation is high. therefore, when the fluid viscosity is high, the fracture has propagated a long distance before reorientation. q.-c. li et alii, frattura ed integrità strutturale, 58 (2021) 1-20; doi: 10.3221/igf-esis.58.01 18 conclusions and future work n the present work paper, factors (such as the injection rate and the in-situ stresses) affecting fracture initiation and fracture reorientation have been numerically investigated by the xfem-based cohesive zone method with abaqus software. the main conclusions are summarized as follows: (1) model verification is necessary and important for the numerical simulation. in the present work, model verification was conducted by comparing the experiment in public article and the simulation herein. through comparison, it is found that the simulation results are almost consistent with the experimental results, which shows that the simulation model herein is suitable for all investigations in the present work. (2) perforation around wellbore facilitates fracture initiation during fracturing operation, and the fracture typically initiates at the perforation tip. although the perforation azimuth has little influence on the direction of fracture propagation, it severely affects fracture initiation and fracture reorientation. investigation on the effects of perforation azimuth on fracture initiation and reorientation shows that both the initiation pressure and the reorientation radius increase sharply with the increase of perforation azimuth. although larger perforation azimuth is beneficial to the formation of complex fractures, it cannot be designed to be very large. considering the cost and effectiveness of the operation, the perforation azimuth is recommended to be in the range of 0° to 40°. (3) as we all know, the driving force for initiation and propagation of hydraulic fractures in fracturing operation mainly comes from the fluid injection into the perforations. therefore, injection rate of fracturing fluid is also an important factor affecting the fracture morphology. investigation results show that increasing the injection rate of fracturing fluid can not only increase the initiation pressure during fracturing operation, but also make the fracture reorientation more difficult. (4) as the difference between the two horizontal principal stresses increases, the shear stress at the tip of the perforation easily reaches the tensile strength and fracture occurs. if the initial pressure is used to reflect the influence of the stress difference on the initiation of the fracture, the initial pressure will decrease as the stress difference increases. moreover, the reorientation radius becomes longer as the stress difference increases. although the in-situ stress is not a factor we can control, the investigation can provide reference for engineering design by adjusting some other factors (such as injection rate and perforation azimuth). (5) fluid viscosity affects the initiation and reorientation of fractures by affecting the invasion of fracturing fluid from perforation into reservoir during fracturing. the investigation results show that both the initiation pressure and the reorientation radius increase with the increase of fluid viscosity. all the investigations herein are aimed at factors affecting the initiation and reorientation of the single fracture, but the interaction between fractures will affect the fracture morphology. therefore, in the following investigation, we will focus on the interaction between fractures during fracturing. acknowledgements his work is supported by the postdoctoral program of henan polytechnic university (grant no. 712108/210) and the national key research and development program (grant no. 2016yfc0304005). references [1] zou, c., zhao, q., dong, d., zhao, q., dong, d., yang, z., qiu, z., liang, f., wang, n., and huang, y. (2017). geological characteristics, main challenges and future prospect of shale gas, journal of natural gas geoscience, 2(56), pp. 273-288. doi: 10.1016/j.jnggs.2017.11.002. [2] technically recoverable shale oil and shale gas resources: an assessment of 137 shale formations in 41 countries outside the united states. https://www.eia.gov/analysis/studies/worldshalegas/pdf/overview.pdf (2013). [3] iea. world energy outlook 2017. https://iea.blob.core.windows.net/assets/4a50d774-5e8c-457e-bcc9-513357f9b2f b/world_energy_outlook_2017.pdf (2017). [4] miguel, m. (2015). hydraulic fracturing: an overview and a geomechanical approach, master thesis, lisbon university. i t q.-c. li et alii, frattura ed integrità strutturale, 58 (2021) 1-20; doi: 10.3221/igf-esis.58.01 19 [5] vengosh, a., jackson, r. b. and warner, n. (2014). a critical review of the risks to water resources from unconventional shale gas development and hydraulic fracturing in the united states, environmental science & technology, 48(15), pp. 8334-8348. doi: 10.1021/es405118y. [6] kumar, d., gutierrez, m., frash, l. p., and hampton, j. (2015). numerical modeling of experimental hydraulic fracture initiation and propagation in enhanced geothermal systems. 49th u.s. rock mechanics/geomechanics symposium, american rock mechanics association, arma 15-253. [7] biao, f., liu, h., zhang, j., zhang, s., and wang, x. (2011). a numerical study of fracture initiation pressure under helical perforation conditions, journal of university of science & technology of china, 41(3), pp. 219-226. (in chinese) doi: 10.3969/j.issn.0253-2778.2011.03.006. [8] zhang, g., chen, m., yin, y., and sun, h. (2003). study on influence of perforation on formation fracturing pressure, chinese journal of rock mechanics and engineering, 22(1), pp. 40-44. (in chinese) [9] zhu, h., deng, j., liu, s., and peng, c. (2013). a prediction model for the hydraulic fracture initiation pressure in oriented perforation, acta petrolei sinica, 34(3), pp. 556-562. doi: 10.7623/syxb201303021. [10] wright, c., and leen, w. (2001). hydraulic fracture reorientation: does it occur? does it matter?, the leading edge, 20(10), pp. 1185-1189. doi: 10.1190/1.1487252. [11] li, q., cheng, y., zhou, d., li, q., and ansari, u. (2018). effect of inter-cluster interference on the fracture morphology in multi-cluster staged fracturing for shale reservoir, frattura ed integrità strutturale, 12(44), pp. 35-48. doi: 10.3221/igf-esis.44.04. [12] chang, x., wang, h., cheng, y., and han, x. (2015). experimental study of fracture propagation mechanisms by oriented perforation technology for srv fracturing, advances in petroleum exploration and development, 10(2), pp. 44-49. doi: 10.3968/7621. [13] zhu, h., deng, j., jin, x., hu, l., and bo, l. (2015). hydraulic fracture initiation and propagation from wellbore with oriented perforation, rock mechanics & rock engineering, 48(2), pp. 585-601. doi: 10.1007/s00603-014-0608-7. [14] li, q., li y., cheng, y., wang, f., wei, j., liu, y., zhang, c., song, b., yan, c., and ansari, u. (2018). numerical simulation of fracture reorientation during hydraulic fracturing in perforated horizontal well in shale reservoirs, energy sources, part a: recovery, utilization, and environmental effects, 40(15), pp. 1807-1813. doi: 10.1080/15567036.2018.1486920. [15] zhou, x., lian, y., wong, l., and berto, f. (2018) understanding the fracture behavior of brittle and ductile multiflawed rocks by uniaxial loading by digital image correlation, engineering fracture mechanics, 199, pp. 438-460. doi: 10.1016/j.engfracmech.2018.06.007. [16] yu, y., zhu, w., li, l., wei, c., yan, b., and li, s. (2019) multi-fracture interactions during two-phase flow of oil and water in deformable tight sandstone oil reservoirs, journal of rock mechanics and geotechnical engineering, 12, pp. 821-849. doi: 10.1016/j.jrmge.2019.09.007. [17] zhang, h., pu, c., and sun, c. (2020) study on the interaction between hydraulic fracture and natural fracture based on extended finite element method. engineering fracture mechanics. 230, pp. 106981. doi: 10.1016/j.engfracmech.2020.106981. [18] arash, d. (2009) analysis of hydraulic fracture propagation in fractured reservoirs: an improved model for the interaction between induced and natural fractures, doctoral dissertation, university of texas at austin. [19] mahdi, h., and kamy, s. (2016). xfem-based czm for the simulation of 3d multiple-cluster hydraulic fracturing in quasi-brittle shale formations, rock mechanics and rock engineering, 49, pp. 4731-4748. doi: 10.1007/s00603-016-1057-2. [20] ren, q., dong, y., and yu, t. (2009). numerical modeling of concrete hydraulic fracturing with extended finite element method, science in china series e: technological sciences, 52(3), pp. 559-565. doi: 10.1007/s11431-009-0058-8. [21] renshaw, c., and pollard, d. (1995). an experimentally verified criterion for propagation across unbounded frictional interfaces in brittle, linear elastic materials, international journal of rock mechanics and mining sciences & geomechanics abstracts, 32(3), pp. 237-249. doi: 10.1016/0148-9062(94)00037-4. [22] zhang, g. m., liu, h., zhang, j., wu, h., and wang, x. (2010). three-dimensional finite element simulation and parametric study for horizontal well hydraulic fracture, journal of petroleum science & engineering, 72(3-4), pp. 310317. doi: 10.1016/j.petrol.2010.03.032. [23] feng, y., and gray, k. e. (2017). parameters controlling pressure and fracture behaviors in field injectivity tests: a numerical investigation using coupled flow and geomechanics model, computers & geotechnics, 87, pp. 49-61. doi: 10.1016/j.compgeo.2017.02.002. [24] simulia. (2016). abaqus version 2016 analysis user’s guide, providence (ri,usa): dassault systèmes. https://doi.org/10.1021/es405118y https://doi.org/10.3969/j.issn.0253-2778.2011.03.006 https://doi.org/10.7623/syxb201303021 https://doi.org/10.1190/1.1487252 https://doi.org/10.3221/igf-esis.44.04 https://doi.org/10.3968/7621 https://doi.org/10.1007/s00603-014-0608-7 https://doi.org/10.1080/15567036.2018.1486920 https://doi.org/10.1016/j.engfracmech.2018.06.007 https://doi.org/10.1016/j.jrmge.2019.09.007 https://doi.org/10.1016/j.engfracmech.2020.106981 https://doi.org/10.1007/s00603-016-1057-2 https://doi.org/10.1007/s11431-009-0058-8 https://doi.org/10.1016/0148-9062(94)00037-4 https://doi.org/10.1016/j.petrol.2010.03.032 https://doi.org/10.1016/j.compgeo.2017.02.002. q.-c. li et alii, frattura ed integrità strutturale, 58 (2021) 1-20; doi: 10.3221/igf-esis.58.01 20 [25] benzeggagh, m. l., and kenane, m. (1996). measurement of mixed-mode delamination fracture toughness of unidirectional glass/epoxy composites with mixed-mode bending apparatus, composites science and technology, 56(4), pp. 439-449. doi: 10.1016/0266-3538(96)00005-x. [26] guo, t., qu, z., gong, f., and wang, x. (2017). numerical simulation of hydraulic fracture propagation guided by single radial boreholes, energies, 10, pp. 1680: 1-22. doi: 10.3390/en10101680. [27] gong, d, chen, j., qu, z., and guo, t. (2018). effect of radial well guidance on hydraulic fracturing crack propagation mechanism, journal of southwest petroleum university (science & technology edition), 40(5), pp. 122130. (in chinese) doi: 10.11885/j.issn.1674-5086.2017.10.27.02. [28] qu, z., tian, y., li, j., guo, t., li, x., and liu, x. (2017) numerical simulation study on fracture extension and morphology of multi-cluster staged fracturing for horizontal wells, journal of china university of petroleum (edition of natural science), 41(1), pp. 102-109. (in chinese) doi: 10.3969/j.issn.1673-5005.2017.01.013. [29] gong, d., qu, z., li, j., qu g., cao, y., and guo, t. (2016) extended finite element simulation of hydraulic fracture based on abaqus platform, rock and soil mechanics, 37(5), pp. 1512-1520. (in chinese) doi: 10.16285/j.rsm.2016.05.036. [30] mahdi, h., and sepehrnoori, k. (2015) simulation of hydraulic fracturing in quasi-brittle shale formations using characterized cohesive layer: stimulation controlling factors, journal of unconventional oil and gas resources, 9, pp. 65-83. doi: 10.1016/j.juogr.2014.10.001. [31] jiang, h., chen, m., zhang, g., jin, y., zhao, z., and zhu, g. (2009). impact of oriented peroration hydraulic fracture initiation and propagation, chinese journal of rock mechanics and engineering, 28(7), pp. 1321-1326. doi: 10.3321/j.issn:1000-6915.2009.07.004. [32] fatahi, h., hossain, m., and fallahzadeh, s. (2016). numerical simulation for the determination of hydraulic fracture initiation and breakdown pressure using distinct element method, journal of natural gas science and engineering, 33, pp. 1219-1232. doi: 10.1016/j.jngse.2016.03.029. [33] ishida, t., chen, q., mizuta, y., and roegiers, j. (2004). influence of fluid viscosity on the hydraulic fracturing mechanism, journal of energy resources technology, 126(3), pp. 190–200. doi: 10.1115/1.1791651. https://doi.org/10.1016/0266-3538(96)00005-x https://doi.org/10.3390/en10101680 https://doi.org/10.11885/j.issn.1674-5086.2017.10.27.02 https://doi.org/10.3969/j.issn.1673-5005.2017.01.013 https://doi.org/10.16285/j.rsm.2016.05.036 file:///i:/phd%20dissertation/@成果及想法/已取得成果/期刊论文/16-已录用-2021-ei-fracture%20and%20structural%20integrity裂缝转向/2021-07-05修改/10.1016/j.juogr.2014.10.001 file:///i:/phd%20dissertation/@成果及想法/已取得成果/期刊论文/16-已录用-2021-ei-fracture%20and%20structural%20integrity裂缝转向/2021-07-05修改/10.3321/j.issn:1000-6915.2009.07.004 https://doi.org/10.1016/j.jngse.2016.03.029 https://doi.org/10.1115/1.1791651 microsoft word numero_33_art_35 v. anes et alii, frattura ed integrità strutturale, 33 (2015) 309-318; doi: 10.3221/igf-esis.33.35   309   focussed on multiaxial fatigue random accumulated damage evaluation under multiaxial fatigue loading conditions v. anes, l. reis, m. de freitas idmec, instituto superior técnico, university of lisbon, av. rovisco pais, 1049-001 lisbon, portugal. e-mail: luis.g.reis@tecnico.ulisboa.pt abstract. multiaxial fatigue is a very important physical phenomenon to take into account in several mechanical components; its study is of utmost importance to avoid unexpected failure of equipment, vehicles or structures. among several fatigue characterization tools, a correct definition of a damage parameter and a load cycle counting method under multiaxial loading conditions show to be crucial to estimate multiaxial fatigue life. in this paper, the ssf equivalent stress and the virtual cycle counting method are presented and discussed, regarding their physical foundations and their capability to characterize multiaxial fatigue damage under complex loading blocks. moreover, it is presented their applicability to evaluate random fatigue damage. keywords. fatigue; multiaxial random loading; cycle counting method; fatigue life; damage accumulation. introduction sually, structures and mechanical components are subjected to random fatigue loadings. car suspensions, wind towers for energy harvest or offshore structures are three examples, among others, that are subjected to this type of loading during service. random loadings are quite different from the ones usually used in lab to evaluate fatigue strength, because they have unknown time histories. therefore, damage assessment of these loadings is quite difficult, because exists an aleatory behaviour that is difficult to simulate. nevertheless, in service conditions nothing is totally random; for instance, when a car suspension travels in the same path every day, the random forces of the car suspension will have similar patterns each day, but they do not have the same pattern. thus, typical loading spectra are used in design stages of components and structures for reliability, where it is required reliable fatigue criteria. multiaxial random fatigue is the ultimate stage in fatigue life assessment; it takes into account several multiaxial fields that usually/traditionally are studied separately. in this stage, it is needed to cover a broad number of concepts related to multiaxial fatigue. in fact, it is not possible to deal with random accumulated damage without considering all of them. fig. 1 shows the fatigue pyramid concept for random fatigue characterization. in this pyramid, each level depends of all levels below and each level deals with a wide number of material science concepts. this is a very complex issue that has been handled in a segmented manner, i.e. each level of the fatigue pyramid has been studied and analysed without an evident interconnection between them. in literature, it can be gathered information related to each subject inherent to each fatigue level, but they are usually studied and presented separately. therefore, issues like damage accumulation, damage parameters, cyclic properties, multi-axial cycle counting among others, are concepts that capture partially fatigue phenomena when considered separately, however they have not been u v. anes et alii, frattura ed integrità strutturale, 33 (2015) 309-318; doi: 10.3221/igf-esis.33.35   310   synergistically presented in literature on a regular basis. nevertheless, to analyse and estimate random multi-axial fatigue life it is necessary to account with all of them. figure 1: fatigue levels of random fatigue characterization. at the base of the fatigue pyramid, shown in fig. 1, one can find level 1, here it is studied the loading effects on the material cyclic response, such as cyclic hardening, cyclic softening, non-proportional hardening, ratcheting, among others. essentially, level 1 is focused on elastic-plastic cyclic models that cyclically update stress-strain states accordingly to the material cyclic properties and loading type, the outcomes of level 1 are the input of level 2. level 2 takes into account the damage parameter concepts. there are mainly four types of criteria to evaluate multiaxial fatigue; they are the critical plane criteria (which are stress-based, strain-based, and energy-based)[1–4], the equivalent stress criteria (mostly invariant-based)[5], the integral criteria, [6] and the spectral criteria [7]. the objective of these criteria is to capture multi-axial fatigue damage resulting from stress levels and several loading path types such as: sequential, proportional, non-proportional, stress gradient effects, mean stress effects, among others. these criteria are used to obtain multiaxial fatigue estimates based on reference damage curves such as uniaxial shear/axial s_n curves. among these criteria, the most appreciated one is the equivalent stress, because they reduce complex stress states (stress tensors) to a scalar (equivalent stress), which is a very suitable feature widespread in finite element packages. although, their success in static mechanical design, they have huge limitations regarding fatigue damage assessment. for instance, the equivalent stress concept under multi-axial loading conditions is independent from the loading path type, i.e. it can be reached the same equivalent stress in respect to different combinations of normal, and shear stresses, regarding the same stress level. however, experimental results show that the fatigue strength varies with different combinations of normal and shear stress amplitudes, even for the same equivalent stress amplitude. thus, fatigue life estimates of equivalent stress criteria under multi-axial loading conditions give inconsistent results. at level 3, cycle counting techniques are used to account for variable amplitude and loading blocks damage using the damage parameters of level 2. there are very few cycle counting methods for multiaxial loading conditions [8,9]. most of them are very complex to implement and consumes too much computational resources, which can be a shortcoming in damage assessment in random loading conditions. also multiaxial cycle counting methods based on rainflow method do not show, so far, good correlations with experimental lab data even for well-defined loading paths. thus, level 3 is the fatigue level that has less contribution in literature despite having equal importance. finally, in level 4, it is focused in damage accumulation rules. damage accumulation rules translate an important procedure to estimate fatigue strength under complex loading paths [10]. usually, they compute the unitary damage captured by the damage parameter in association with a cycle counting method. thus, if a damage parameter and cycle counting method really capture the unitary damage of a loading block, thus the damage accumulation rule should be linear. it is found in literature some examples of non-linear damage accumulation rules, but in the present authors’ opinion, those approaches aim to capture the damage accumulation without having into account the physical damage mechanisms within the material. therefore, damage accumulation rules based in the palmgren-miner must be able to capture damage accumulation under random loading conditions. v. anes et alii, frattura ed integrità strutturale, 33 (2015) 309-318; doi: 10.3221/igf-esis.33.35   311   this synergistic way to account with each pyramid level is an important feature because under random multi-axial loadings all of these pyramid levels may be activated in a sequential or simultaneous way. fig. 2 summarizes the synergistic process of evaluating random multi-axial fatigue. figure 2: fatigue estimates process under random loading conditions. in this paper is presented by the present authors a contribution to levels 2, 3, and 4. for level 2, it was developed the ssf equivalent shear stress, and for level 3 it was developed the virtual cycle counting method, which is deeply dependent on the ssf equivalents stress time histories. regarding level 4, it is presented the block extraction methodology, where loading blocks are extracted from loading spectra in order to be evaluated with the virtual cycle counting (vcc) technique and damage accumulation rules. ssf equivalent stress (level 2) ssf physical foundations t is well-know that normal and shear stresses have different damage scales [11,12]. this is so because in experiments it is obtained different fatigue lives regarding the same stress amplitude in both uniaxial loading conditions (shear and axial). usually, for structural materials, the uniaxial axial sn curve stands above the shear one. thus, to obtain the same fatigue life in both loading conditions it is required higher normal stress amplitude comparatively to the shear stress amplitude. (a) (b) (c) (d) figure 3: illustration of different deformation patterns from different loading types. a) without applied loads, b) axial loading, c) shear loading, and d) biaxial loading.  under multiaxial loading conditions, fatigue damage results from the combination of both axial/normal and shear loading components of a multiaxial loading where it is necessary to account the axial and shear damage contribution to the overall damage. to do that, it is necessary to have both axial and shear damages in the same damage scale. for example, the von i v. anes et alii, frattura ed integrità strutturale, 33 (2015) 309-318; doi: 10.3221/igf-esis.33.35   312   mises equivalent stress uses the 3 constant to reduce shear damage to the axial one. this procedure can be found in a wide range of multiaxial fatigue criteria being a common practice to account combined fatigue damage [13]. fig. 3 illustrates these damage patterns. fig. 3 a) depicts a grid at rest without any load (it can be imagined as a material grain). now, consider fig. 3 b), in this case the grid is loaded with an axial loading with an elongation pattern. fig. 3 c) presents the same grid but now with a uniaxial shear loading causing a distortion deformation. as can be seen, the deformation pattern is quite different in both loading conditions. consider now a material grain structure loaded with the loading conditions shown in fig. 3. under these loading conditions, the grain structure will have different deformation patterns like the ones depicted in fig. 3, under axial, shear, and multiaxial loadings. due to the different deformation patterns, the material strength will be different for each loading conditions. now, consider a biaxial loading having simultaneously two types of deformation patterns (axial and shear) above represented in fig. 4 d). in this case, the deformation pattern is a mixture of axial deformation and shear distortion. to account the contribution of each damage pattern from axial and shear deformations (different deformation mechanisms), it is required reduce both damages to the same scale, because they cause different types of deformation within the material grain structure. from experiments it was found that the contribution percentage of each axial and shear loading components of a multiaxial loading to the overall damage does influence the material fatigue strength results [11]. the predominance of an axial damage over the shear one or vice versa causes different cyclic damage rates and therefore different fatigue lives are obtained. for each loading direction depicted in a stress space, given by the stress amplitude ratio a a   , there will be a damage scale that reduces axial damages to the shear damage scale. zhang et al. published an interesting work that correlates proportional loadings, with different stress amplitude ratios, with their crack initiation planes on a 2a12–t4 aluminium alloy [11]. fig. 4 shows the crack opening paths obtained by zhang et al. in respect to the stress amplitude ratios within the range  0; where it can be found different damage mechanisms associated to each stress amplitude ratio. these results corroborate the premise in which different stress amplitude ratios have different damage scales being required their assessment to account combined axial and shear damages. (a) = 0 (b) = 3/2 (c) = 3 (d) = 3 (e)= ∞ figure 4: in-phase fracture appearance under different stress amplitude ratios [11].  (a) = 0° (b) = 24° (c) = 46° (d) = 68° (e)= 90° figure 5: out-of-phase () fracture appearance for a constant stress amplitude ratio, 3 [11].  fig. 5 shows the phase angle variation effect on the crack opening, here the stress amplitude ratio was maintained equal to 3 in each phase-shift . based on these results, it can be concluded that the phase-shift variation also induces different crack opening paths indicating different fatigue damage mechanisms. these mechanisms are related to the material sensitivity to non-proportional loadings, which is a level 1 issue. the present authors developed the y non-proportional sensitivity factor to account with this phenomenon in the ssf multiaxial fatigue package, which can be found in [14]. v. anes et alii, frattura ed integrità strutturale, 33 (2015) 309-318; doi: 10.3221/igf-esis.33.35   313   the stress scale factor (ssf) concept in the von mises equivalent stress criterion, where the stress scale factor is a constant 3 and is defined under static loading conditions, it is not possible to capture the relation between axial, and shear damages for different stress amplitude ratios. it is assumed that the axial and shear damage relation given by the stress scale factor is constant for any stress amplitude ratios which has led to poor fatigue life estimates under multiaxial loading conditions. fig. 6 depicts the reasoning that supports the damage scale concept used in the ssf method to reduce axial damage to the shear damage scale. fig. 6 presents a new way to represents sn curves. instead of using the usual practice where it is represented a damage parameter vs fatigue life ( fn ) it is depicted the axial and shear stress amplitudes (of a multiaxial loading) vs their fatigue life. thus, fig. 6 has three sn curves, one is the uniaxial shear sn curve ( _ 1uniaxial ), used here as reference damage across the fatigue life range, and the other two are the sn curves of the axial ( _ 2load ) and shear ( _ 2load ) loading components of a multiaxial loading. now, suppose that a fatigue lifetime is selected, for example at 4e5 loading cycles, as shown in fig. 6. the selected fatigue life can be achieved by using both loadings presented in fig. 6 (the uniaxial shear loading (loading 1) and the multiaxial loading, loading 2). thus, in the shear uniaxial loading it will be needed the 1 shear stress amplitude, and in the biaxial loading it will be needed the axial stress amplitude 2 and the shear stress amplitude 2 . note that, the 2 value is not enough to cause failure, it is required 2 . therefore, the damage difference between 1 and 2 , is given by the damage caused by 2 . having this in mind, the damage from bc in the shear damage scale, is equal to the damage from ad in the axial damage scale. figure 6: sff damage scale concept. ssf equivalent stress eq. (1) represents the ssf equivalent shear stress damage parameter [12], where the axial stress component of a multiaxial loading is reduced to the shear damage scale by a ssf damage function, the  ,assf   .  . ,aeq ssf      (1) the ssf damage function has as input the stress amplitude ratio and the axial stress amplitude where the stress amplitude ratios defines the axial and shear damage relation and the axial stress defines the stress level within a multiaxial loading; please see eq. (2).   2 3 2 3 4 5,a a a assf a b c d f g h i                       (2) where, a is the axial component of the biaxial loading and  is the stress amplitude ratio (sar), see fig. 7. the constants from “a” to “i" are determined through the experimental tests discussed above. therefore, the objective of the ssf damage function is to update the damage scale accordingly to each loading direction (sar) under cyclic loading conditions. the ssf damage function is determined based in proportional sn curves for the loading paths presented in v. anes et alii, frattura ed integrità strutturale, 33 (2015) 309-318; doi: 10.3221/igf-esis.33.35   314   fig. 7 considering the damage concept depicted in fig. 6. these loadings have stress amplitude ratios that cover different relations between axial and shear damages, starting from pure axial (0º) and ended with the pure shear loading condition (90º). the ssf damage function is a material cyclic property, and like many others should be determined by experimental tests. there are some directions, between the ones depicted in fig. 7, where it was not performed any experimental test. in these directions , the ssf damage function was established by using interpolation techniques between known experimental values of the ssf damage function. eq. (3) shows the ssf criterion for fatigue life assessment.     max ,a b fssf a n     (3) the left side of eq. (3), represents the maximum value of the ssf equivalent shear stress found within the loading period, where the shear component of a biaxial loading,  , is added to the axial component previously reduced to the shear damage scale,  ,assf    . then, the fatigue lifetime is estimated using the uniaxial shear sn curve, represented in the right side of eq. (3). figure 7: loading paths used in experiments to calculate the ssf damage function.  cycle counting (level3) he equivalent ssf shear stress only captures the damage inherent to the ssf maximum value found in a loading cycle, thus it is not captured the damage associated to all local ssf equivalent stress reversals within a loading history. however, the damage estimated for loading blocks considering only the maximum equivalent stress found in that same loading block is smaller than it should be leading to un-conservative fatigue life results. thus, the ssf equivalent stress criterion requires a cycle counting technique to evaluate fatigue damage for multiaxial variable amplitude loadings. limitations of maximum equivalent stress concept usually variable amplitude time histories are transformed into an equivalent stress spectrum where each loading block is identified based on their stress amplitude level [15], please see fig. 8. the equivalent spectrum approach is suitable to be used in damage accumulation rules based in the palmgren-miner concept, however, the transformation from variable amplitude time histories to constant amplitude load spectrum (as one can see in fig. 8 b), lead to lose the real damage monitoring found in the stress time histories. this means that the stress or damage parameter spectrum will hardly capture the fatigue damage, especially under multiaxial loading conditions. fig. 9 shows two different loadings with the same loading period and maximum stress level. despite, the same maximum stress during the load period is obtained in both loading cases; the fatigue damage inherent to each loading is quite different. however, this is the approximation performed when it is used an equivalent stress spectrum where the varying amplitude is reduced to a constant one. the loading depicted in fig. 9 a) cannot be considered a loading block because the unitary damage is related to one load cycle which is repeated until reach time t , thus in damage accumulation rules the t v. anes et alii, frattura ed integrità strutturale, 33 (2015) 309-318; doi: 10.3221/igf-esis.33.35   315   unitary damage is computed for one loading cycle and then is multiplied by the number of loaded cycles. on the other hand, the load depicted in fig. 9 b), can be considered as a loading block and the inherent damage unity is related to all load cycles performed during the loading period. none of these loading cycles have the same fatigue damage because they have different amplitudes and load sequence. thus in order to quantify a unitary damage from a general loading it is necessary to account with all the loading cycles. (a) (b) figure 8: variable amplitude loadings, a) time history, b) equivalent stress spectrum. (a) (b) figure 9: two different loading paths with same maximum stress. unitary block damage concept the main idea that supports the unitary block damage concept is based in the relation between the maximum equivalent stress fatigue life estimates (for a loading block) and the experimental results. this relation is given in eq. (4). exp re _ estimated erimental f block f n lative damage n  (4) the unitary damage concept aims to establish the loading block damage, which under cyclic loading conditions can be linearly added as if it was a simple sinusoidal loading cycle, like the ones used to obtain the uniaxial sn curves. it is expected that the experimental fatigue life be less than the estimated one; thus, the block unitary damage can be estimated as follows in eq. (5). exp 1 re _erimental estimated f f block n n lative damage  (5) where 1 re _ block lative damage is the block unitary damage. in order to estimate the relative damage without falling back on experimental tests, it was developed the virtual cycle counting method based in the ssf equivalent shear stress time histories. v. anes et alii, frattura ed integrità strutturale, 33 (2015) 309-318; doi: 10.3221/igf-esis.33.35   316   virtual cycle counting concept the virtual cycle counting (vcc) [16] is a non-rainflow approach to evaluate loading block damage and it is based on the ssf equivalent shear stress previously presented. in the present authors´ opinion, equivalent stress approaches are much more suitable to account block damages than other ones, because they condensed in one damage parameter the instantaneous values of axial and shear damages, and also it allows in an easy way to implement cycle counting techniques in finite element packages. the concept and use of the vcc approach is much easier than other methods usually adopted to quantify block damage accumulation. basically, the vcc method estimates the relative damage described in the previous section and is presented in eq. (6). in the numerator of eq. (6), it is added all ssf equivalent stress absolute values at each peak and valley found between two consecutive zero stress points along the ssf equivalent shear stress time history of a loading block. in denominator hold two times the maximum ssf equivalent shear stress found in the entire ssf time history. fig. 10 illustrates the vcc method and their variables.   , ssf,max,2 ssf peak valley block abs vcc      (6) (a) (b) (c) figure 10: virtual cycle counting variables identification. the block fatigue life is estimated as follows in eq. (7), 1 ,max, _ b ssf block f block a n vcc       (7) where a, and b are the power law regression variables obtained from pure shear fatigue life results from the considered material. ,max,ssf block it the maximum ssf equivalent stress within a loading block, and vcc is the virtual cycle counting. random loadings (level 4) damage assessment of loading spectra ne way to deal with random loadings is to extract loading blocks from the random loading time history in order to estimate multiaxial random accumulative damage. in order to do that, the ssf equivalent stress criterion in association with the virtual cycle counting method can be used. the paradigm that supports the block extraction methodology presented here is based in the ssf equivalent stress time histories and is described in the following. fig. 11, shows a multiaxial loading represented with the ssf equivalent shear stress time evolution. here the block extraction is based on the ssf maximum peak, the first maximum peak is settled as the reference damage on the ssf virtual cycle procedures, see block 1 on fig. 11, until that peak be exceeded, see block 2 on fig. 11, at this point the block 1 ends and starts the second block region with a new damage scale given by the ssf time evolution new peak, block 3, in fig. 11. the same methodology is used to extract the other blocks. o v. anes et alii, frattura ed integrità strutturale, 33 (2015) 309-318; doi: 10.3221/igf-esis.33.35   317     figure 11: block extraction methodology for random loadings. during the block extraction, it can be established the inherent unitary damage of each block as follows in eq. (8): _ ,max,ssf,block 1 unitary block f block d n vcc  (8) eq. (8) shows the methodology to estimate the unitary damage within a loading block. on the left, in numerator the number 1 is related to the number of loaded blocks, which in this context is 1. in the denominator, it is represented the material fatigue strength when subject to a loading block, where ,max,ssf,blockfn is the fatigue life estimate based in the maximum value of the ssf equivalent stress within a loading block, and blockvcc is the virtual cycle counting regarding each extracted block. in order to estimate the instantaneous accumulated damage, the palmgren-miner rule concept can be used as follows in eq. (9). . 1 ,max,ssf,block 1i ssf random f block i d n vcc         (9) eq. (9) represents the instantaneous accumulated damage value, which is updated block by block until .ssf randomd reaches the value 1, which is the reference condition, considered here to estimate a high fatigue failure probability. final remarks n this paper was discussed and analysed several aspects related to random multiaxial fatigue. first, it was discussed the importance of having multiaxial fatigue packages in which is contained multiaxial fatigue models synergistically linked, in order to deal with all fatigue phenomena in multiaxial random fatigue. second, it was presented the ssf equivalent shear stress damage parameter where it was focused the ssf physical foundations. third, it was presented the virtual cycle counting method to evaluate a block damage and finally it was presented how the ssf equivalent stress in synergy with the virtual cycle counting method can be used to estimate random accumulated damage under multiaxial loading conditions. acknowledgements he authors gratefully acknowledge financial support from fct – fundação para a ciência e tecnologia (portuguese foundation for science and technology), through the project ptdc/eme-pme/104404/2008 and through idmec, under laeta, project uid/ems/50022/2013. i t v. anes et alii, frattura ed integrità strutturale, 33 (2015) 309-318; doi: 10.3221/igf-esis.33.35   318   references [1] fatemi, a., socie, d.f., a critical plane approach to multiaxial fatigue damage including out-of-phase loading, fatigue & fracture of engineering materials & structures, 11 (1988) 149–165. [2] socie, d., critical plane approaches for multiaxial fatigue damage assessment, astm special technical publication, 1191 (1993) 7–7. [3] carpinteri, a., spagnoli, a., vantadori, s., a multiaxial fatigue criterion for random loading, fatigue & fracture of engineering materials & structures, 26 (2003) 515–522. [4] carpinteri, a., spagnoli, a., multiaxial high-cycle fatigue criterion for hard metals, international journal of fatigue, 23 (2001) 135–145. [5] cristofori, a., susmel, l., tovo, r., a stress invariant based criterion to estimate fatigue damage under multiaxial loading, international journal of fatigue, 30 (2008) 1646–1658. [6] sonsino, c.m., multiaxial fatigue assessment of welded joints–recommendations for design codes, international journal of fatigue, 31 (2009) 173–187. [7] lagoda, t., macha, e., nieslony, a., fatigue life calculation by means of the cycle counting and spectral methods under multiaxial random loading, fatigue & fracture of engineering materials & structures, 28 (2005) 409–420. [8] wang, c.h., brown, m.w., a path-independent parameter for fatigue under proportional and non-proportional loading, fatigue & fracture of engineering materials & structures. 16 (1993) 1285–1297. [9] langlais, t.e., vogel, j.h., chase, t.r., multiaxial cycle counting for critical plane methods, international journal of fatigue, 25 (2003) 641–647. [10] fatemi, a., yang, l., cumulative fatigue damage and life prediction theories: a survey of the state of the art for homogeneous materials, international journal of fatigue, 20 (1998) 9–34. [11] zhang, j., shi, x., fei, b., high cycle fatigue and fracture mode analysis of 2a12–t4 aluminum alloy under out-ofphase axial–torsion constant amplitude loading, international journal of fatigue, 38 (2012) 144–154. [12] anes, v., reis, l., li, b., fonte, m., de freitas, m., new approach for analysis of complex multiaxial loading paths, international journal of fatigue, 62 (2014) 21–33. [13] pitoiset, x., preumont, a., spectral methods for multiaxial random fatigue analysis of metallic structures, international journal of fatigue, 22 (2000) 541–550. [14] anes, v., reis, l., li, b., freitas, m., new approach to evaluate non-proportionality in multiaxial loading conditions, fatigue & fracture of engineering materials & structures, 37 (2014) 1338–1354. [15] lee, y.-l., fatigue testing and analysis: theory and practice, butterworth-heinemann, (2005). [16] anes, v., reis, l., li, b., de freitas, m., new cycle counting method for multiaxial fatigue, international journal of fatigue, 67 (2014) 78–94. microsoft word numero_57_art_18_3117 c. lupi et al., frattura ed integrità strutturale, 57 (2021) 246-258; doi: 10.3221/igf-esis.57.18 246 railway overhead contact wire monitoring system by means of fbg sensors carla lupi, ferdinando felli, erwin ciro dicma, sapienza università di roma, via eudossiana 18, 00184 roma, italy carla.lupi@uniroma1.it, http://orcid.org/0000-0003-4096-3592 ferdinando.felli@uniroma1.it, https://orcid.org/0000-0002-7527-8096 erwin.ciro@uniroma1.it, https://orcid.org/0000-0002-7673-3556 claudio paris centro ricerche enrico fermi, via panisperna 89a, 00184 roma, italy claudio.paris@centrofermi.it, https://orcid.org/0000-0003-3137-1456 cristian vendittozzi faculty unb gama, universidade de brasília unb, brasília, 72444-240 gama brasília-df, brazil vendittozzi@unb.br https://orcid.org/0000-0003-0793-4052 abstract. safety of infrastructures represents one of the most significant concerns for governments and service providers to preserve people's wellbeing. one of the main ways to keep safe facilities (buildings, bridges, railways, etc.) involves the use of monitoring sensor systems in charge of measuring critical operating conditions. those measurements together with periodical maintenance, contribute to minimize potential risks that the infrastructure faces. the paper aims at designing, developing, and testing a monitoring system for mechanical stresses acting on the overhead contact wire (ocw) to ensure the operational safety of the railway network. in this regard, the paper proposes two fiber bragg grating (fbg) sensors-based solutions, relying on the ability of these sensors to allow real-time and continuous data acquisition. the first one consists of a polyimide-coated sensor bonded on an ocw clamp, the second one is a copper-coated sensor hanging between the two separated halves of an ocw clamp. significant results have been obtained mechanically testing both solutions, trying to simulate the operative conditions. keywords. fbg; ocw; embedded sensory system; electrodeposited metal coating; strain measuring. citation: lupi, c., felli, f., ciro, e., paris, c., vendittozzi, c., railway overhead contact wire monitoring system by means of fbg sensors, frattura ed integrità strutturale, 57 (2021) 246-258. | received: 14.05.2021 accepted: 10.06.2021 published: 01.07.2021 copyright: © 2020 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. https://youtu.be/c1pqog-vadg c. lupi et al., frattura ed integrità strutturale, 57 (2021) 246-258; doi: 10.3221/igf-esis.57.18 247 introduction n the railway system several components undergo constant monitoring and frequent maintenance due to severe working and environmental conditions. particularly, the rails and the overhead contact wires (ocw) require permanent monitoring. in the current paper a system for monitoring the ocw is presented. the most common configuration involved in overhead contact system (ocs) comprises a complex electric structure consisting of tension-carrying wires to provide power transmission to trains. some of these cable wires are ocw and messenger wire. these two wires are longitudinally supported by a cantilever array describing a zig-zag distribution along the electric system (overhead catenary). both the ocw and messenger wire are distanced by dropper cables responsible to minimize falls and maintain the vertical elasticity [1-3], (fig. 1). figure 1: overhead contact system (also known as catenary) on an italian railway. the most important problems regarding ocw can be normally summarized in contact loss and excessive wear with pantographs. the continuous friction between the pantograph and the ocw produces wear that reduces the effective cross section of the wire (fig. 2). figure 2: ocw cross section detail showing the wire before (on the left) and after (on the right) wear action. the excessive wear issue often leads to energy interruptions and consequently to local arcing formation once operations restart. these conditions result in an undesirable combination of electrical and mechanical effects causing the performance deterioration of both systems, overcharges, and an inability to provide proper service. although both the contact and the energy collection capabilities might be enhanced, it is also true that both systems suffer rapid wear. several studies have been carried out to understand and measure the wear mechanism [1-4], and to develop new chemical compositions of ocw, shifting from pure copper to copper-based carbon composites [5-7]. in order to ensure railway service quality and safety, ocw wear measurements are required. thus, several investigations are aimed at designing an automatic monitoring system for detecting early-stage deterioration of ocw, resulting in excessive wear, through continuous and in real-time monitoring, of the mechanical and thermal load variations acting on the ocw. in this context different contactless measurement i c. lupi et al., frattura ed integrità strutturale, 57 (2021) 246-258; doi: 10.3221/igf-esis.57.18 248 techniques have been investigated (based on magnetic fields analysis, microwave reflection analysis, electrical and optical detection systems) for solving the wear issues [7-10]. this investigation seeks to monitor the mechanical stresses that deteriorate ocws by means of an easy-to-install smart clamp (sc) provided by a copper-coated sensor. this paper neglects the effect of temperature, which is another fundamental parameter that affects the ocw's stress state (wire tensions vary somewhat unpredictably with temperature variations). this is because temperature has a critical effect on the operative performance of the railway network when exceeding the thermal ranges (-40°c and 60°c) [11, 12]. the study of the interaction between the ocw and its thermal field will be the focus of forthcoming investigations. in unstressed conditions with no passing trains, an increase of stress on the contact wire means a wire-section reduction. if a cross-section reaches a reduction of 20%, the wire should be replaced in compliance with railway regulations, [13]. in the present paper all references to railway nomenclature and regulations refer to the italian railway network (rfi, that stands for rete ferroviaria italiana). to evaluate mechanical stresses of the ocw, two smart measuring systems were developed integrating fiber bragg grating (fbg) sensors into standard railways clamps. previous laboratory observations suggest that directly bonding the sensors on the contact wire can cause their failure, mainly because of its intrinsic brittleness. some critical issues of fbg sensors bonded to the ocw could be: i) measurements of temperature and strain are unreliable when the collector plate of the pantograph passes close to the sensor, ii) thermal compensation in the sensor strain measurements can be difficult to be achieved, iii) preservation of sensor-system from environmental effects, iv) no possibility to remove the fgb from ocw, if required. the vision is that of an intelligent system capable of monitoring the ocw continuously and in real time, consisting of an array of sensors that can be easily integrated into existing systems on the national railway network and perfectly compliant with standard operating conditions. the whole monitoring system includes a control room from which several sensors chains branch out, covering railway stretches of tens of km, as shown in fig. 3. figure 3: ocw monitoring system overview this paper focuses attention on the sensitive part of this system, the ocw monitoring clamp. for that reason, an easy to install and remove system was designed, based on standard railway components and performing copper-coated fbg sensor (for allowing a safer handling and a better thermal and electrical conductivity). two fbg-based clamps were developed, with two different geometries, two different materials and two fbg that differ in coating. the paper is divided in two main sections, the first one describes the peculiarities that make the fbg the most suitable sensor for this application, the electrolytic process used to coat the optical fiber with a thin copper layer and a detailed description of the two clamps. the second section presents the experimental setup implemented to characterize the performance of the two clamps and summarizes the results of the tests. c. lupi et al., frattura ed integrità strutturale, 57 (2021) 246-258; doi: 10.3221/igf-esis.57.18 249 materials and methods fbg sensing system iber optic sensors such as fbgs, [14], offer an excellent solution for being integrated into an ocw monitoring system for measuring strains, due to its unique features that are not commonly encountered in electrical monitoring systems. among them, high strain and temperature sensitivity, electromagnetic immunity, minimum cabling, minimum weight and intrusiveness, and multiplex large number of sensors along the same (single) fiber capability and longdistance safe data acquisition are the most acknowledged. furthermore, a feature that is very important for the aim of our research, is the possibility of coating the fbg by means of electrodeposition (ed) [15] with a thin layer of copper (cu). in addition to mechanically reinforcing the fiber (and allowing their easier handling), the cu coating increases the sensor thermal sensitivity [16]. moreover, a metal coating makes fbgs more compatible for embedding within a metal matrix, such as in the case of ocs wires and of the cu matrix of the clamps used as a gripping system in the italian ocs. fbg sensors represent a technology, largely mature for measuring deformations in structures, as they are already used in many industrial applications, [17-20]. fiber optic monitoring has been introduced in many engineering fields showing promising results even in the railways network field, providing very interesting performance while applied on smart railways projects [21, 22], or as an effective monitoring system for hard impacts on the ocw, in order to ensure efficient operation, [11]. bragg gratings act as wavelength (wl) filters that are essentially defined by the microstructure spatial period and the refraction index of the fiber core [23]. the microstructure works as a wl selective mirror: light passing the fiber is partially backscattered and reflections are returned down in a narrow band. max reflectivity occurs at the bragg wavelength (λb) and depends on the grating period, λ, and on the effective index of refraction, neff, according to the bragg condition:   2b effn (1) the grating’s wl changes with strain (ε) and temperature (t) according with:          0  k t (2) where δλ is the wl shift from the wl reference λ0), k is the grating gauge factor and αδ is the change in refraction index due to temperature change (t). for the grating that have been used in this test campaign the k is 0.89. the sensing system applied on the ocw consists of optical fibers, integrated into the contact wire, along the existing connections, and an acquisition system that can be placed conveniently far from sensor locations. the fiber bragg grating sensors are bonded directly on the clamps, as shown in figs. 4 and 5, and the clamps are installed in selected places along the railways network. copper coating electrodeposition on fbg sensor the fbgs that were used in the test campaign, were copper coated by means of the ed technique. the coating was performed to increase the fiber toughness resistance, the thermal conduction, to protect it from environmental conditions and to enhance the fbg sensitivity. dummy (sensor-less fiber) samples were used for optimizing the ed process, while coated fbg samples (sensorized samples) were used for testing the proposed systems. the sample preparation (whether it is equipped with fbg or not) starts with the gilding of about 5 cm of fiber length by means of the sputtering technique (by using an edwards sputter coating, model s150b) that was carried out in order to ensure the electrical conductivity of the outer surface (fused silica) of the fibers, that is necessary for the ensuing ed process. after the gold deposition, the cylindrical conductive surface is used as a cathode, while a custom-designed cylindrical lead anode is used to close the ed system. the metal ed was carried out by sinking the cathode-anode pair inside a glass electrolytic cell with radius and height of 3 and 12 cm, respectively. the gilded fiber is kept on axis, at the center of the cylindrical cathode, and held vertically inside the cell, by means of a dedicated holder, in order to obtain a uniform thickness on the cylindrical surface, minimizing the occurrence of unwanted anisotropies or radial stresses in the coating. the presence of these defects can induce disturbances affecting the grating's spectrum. the maximum possible homogeneity of coating is required. the copper ed process was carried out using amel galvanostat and an electrolyte composition of 50 g/l cu and 20 g/l h2so4 by fixing the initial current density and temperature at 250 a/m2 and 50 °c, respectively. these ed process physical parameters affect: (i) thickness and (ii) grain size of the electrodeposited coating. the parameters values were selected by an optimization procedure performed on dummy samples, then used to produce the fbg samples. finally, samples were examined by f c. lupi et al., frattura ed integrità strutturale, 57 (2021) 246-258; doi: 10.3221/igf-esis.57.18 250 scanning electronic microscopy equipped with energy-dispersive x-ray spectroscopy (sem-eds) to determine the morphological aspect of the coatings. smart clamps for laboratory tests, two different clamp configurations were expressly designed and manufactured. the two configurations, called smart clamp 1 (sc1) and smart clamp 2 (sc2) differ in support geometry and in grating arrangement. the two scs are shown in figs. 4 and 5 and are described in detail in the following subsections. in developing the monitoring system, looking for a solution that was quickly removable, it was decided to use components off the shelf, i.e., components that were already used and approved by current legislation. two different types of clamps already used in catenaries have been selected. a dropper jumpers clamp, that is made of copper, was used for sc1 and an electrical continuity jumpers clamp, that is in bronze, was used for sc2. both items were instrumented with an fbg sensor, prepared with different coatings and arrangement. a method for installing sensors and preparing scs was selected to allow easy mounting of the corresponding clamp, ensuring the standardization of the installation processes on the ocw. the fbg has been bonded on the external side of the clamps (closest as possible to the contact wire), in order to avoid its rupture possibly caused by the tightening torque of 25 nm that was used for installing the clamp on the contact wire. figure 4: a) sc1; b) detail of the fbg bonded on sc1 copper clamp. scs performance tests a mechanical tests campaign was performed on both scs. it consists of three mechanical tests carried out to compare the performance of the two configurations. all tests were performed at room temperature (rt). a first tensile test involves a single loading phase and was carried out to check the response of the two scs to the mechanical tensile stress exerted on a ocw sample (a copper beam of 550 mm in length). the second test is a cyclic tensile test. in this case, the copper beam simulating the ocw was loaded and unloaded six times in a row to check the tightness of the scs' bolts. tensile tests simulate the system of counterweights that keeps the contact wire under tension. the maximum load imposed in these tests is 3 kn, that is the maximum target value of the instron® 3375 tensile testing machine that was used during these tests. the copper alloys clamps are characterized by a high conductivity, therefore allowing a good detection of local temperature variations. nevertheless, some preliminary qualitative observations were performed. a polyimide recoated fbg was used on the sc1, which was bonded using a two-component thermo-conductive epoxy glue. the sensor was bonded below the bolt to ensure maximum proximity to the ocw, fig. 4.b. the cu-coated sensor, described above, was installed on the sc2. in this case, the bronze clamp commonly used in electrical continuity jumpers was chosen. the original clamp was modified to reduce its stiffness, removing a central section, and keeping only the bolted ends, suspending the sensor between these two parts, as shown in fig. 5. thus, the mechanical stresses acting on the ocw (in particular those due to bending) are amplified. furthermore, the cu-coated grating being not in direct contact with the ocw, should be also slightly thermally isolated. furthermore, a bending test was performed on the setup shown in fig. 6, to simulate the bending induced by the pantograph on the contact wire. the purpose of this simulation is to check the sensitivity of the two configurations in response to a minor mechanical stress, if compared with the pantograph motion, in accordance with the standard en 50367:2006 that defines the range of application of the static force, between 60 and 70 n, and the nominal value of the applied load, equal to 70 n. the figure shows how the ocw sample, 550 mm long, has been suspended and fixed to the test-bench by means of a vice-clamp that prevents all its movement, blocking the beam's 6 degrees of freedom. the load was applied to the free c. lupi et al., frattura ed integrità strutturale, 57 (2021) 246-258; doi: 10.3221/igf-esis.57.18 251 end of the ocw while the scs were mounted on it with a tightening torque of 25 nm at three successive positions from the joint, z1, z2 and z3 as it is shown in fig. 6. for both scs the same load-conditions were applied (three different masses corresponding to 0.5 kg, 1 kg and 2 kg). in all tests the load was applied and maintained in each position for 20 seconds, once the load was removed, the next load was applied after a 20-second break. figure 5: sc2 configuration, the grating is hanging between the two clamps. figure 6: bending test set-up. this cantilever beam configuration represents a simplified model that allows to check the scs sensitivity (i.e., their capability to measure even a smaller deformation induced on the ocw by a small load) and to compare the two scs results with the calculated theoretical values. simulating the wire as a cantilever beam, with well-known geometrical and mechanical characteristics, allows to effectively calculate the stress (σ), through the typical equation:   f maxf f x m y m w l (3) where mf is the bending moment and wf is the bending modulus (ymax/lx, calculated as the ratio between the moment of inertia of the section with regard to the neutral axis and the furthest point of the section from the neutral axis). the strain (ε) can be calculated by the equation that maintains its validity in the elastic field:    e (4) where e is the ocw-alloy elastic modulus, that is 120 gpa for the copper alloy considered during the tests, in compliance with national railway regulations. since the strain decreases as the distance from the joint increases, different strain values were measured at the three different positions shown in fig. 6 (z1, z2 and z3). c. lupi et al., frattura ed integrità strutturale, 57 (2021) 246-258; doi: 10.3221/igf-esis.57.18 252 results and discussion his section presents and discusses the results concerning the ed of the copper coating on the optic fiber and how it affects the fbg’s wl. furthermore, the results of the test campaign that was carried out on the two scs are presented. sensor coating the dummy coated samples were used in destructive tests and sem observations to evaluate the deposit quality in terms of both compactness and thickness uniformity on the cylindrical surface of the fiber. fig. 7 provides several details of the dummy sample. the optical macrograph of a copper-coated sensor of fig. 7a shows a good cylindrical shape, terminating in a truncated cone. that geometrical configuration indicates the conductive zone ending; fig. 7b shows a complete view of the copper-coated sample appearing quite regular in its cylindrical form if considering the ed production process; fig. 7c shows a sample cross section where in the right upper part a magnification of the sample emphasizes the gold thinner layer of about 3 μm. the cross-section shows a thick copper deposit of approximately 300 μm with a consistent radius. fig. 7d highlights the dummy sample morphology where irregular and randomly disposed grains are evident, but the surface is compact and presents very few voids, as it is expected considering the copper positive deposition potential, that hinders the hydrogen evolution reaction (her). figure 7: optical macrographs and sem micrographs showing geometrical and morphological aspects of the copper coated fiber: (a) optical general view, (b) sem micrograph general view, (c) cross section and (d) surface morphology. fig. 8 shows the transformation of the grating spectrum following the various steps of sample coating production. after gilding (the blue line in fig. 8), no relevant variations of the spectrum are revealed, while after cu ed (the red line in fig. 8), the spectrum experiences a broad shift toward lower wavelengths (wls), with a small increase in intensity. the main effect of the thickness growth seems to be an appreciable wls shift with quasi-unchanged spectral shape, that can be fully explained by a homogeneous axial contraction of the bragg grating after the cu ed. tensile test the contact wire is usually tensioned by a system of counterweights in order to balance the deformations caused by temperature changes. tensile tests were performed to simulate that operating conditions. the tests were carried out by mounting both scs on the contact wire at the same time (fig. 8) and associating a traditional extensometer to compare the maximum strain (εmax) achieved during tests. t c. lupi et al., frattura ed integrità strutturale, 57 (2021) 246-258; doi: 10.3221/igf-esis.57.18 253 figure 8: fbg spectrum shift due to the whole coating process. figure 9: sc1(in blue) and sc2 (in red) mounted on the ocw segment undergoing tensile test. the test setup (tensile test equipment and optical acquisition system) was set as follows: ● imposed displacement: 0.5 mm/min ● maximum applied load: 3 kn ● contact wire length: 550 mm ● clamp tightening torque: 25 nm ● sampling frequency: 100 hz the strain measured on sc1 and sc2 was recorded and reported in fig. 10a and b, respectively. the two scs measured different strains and, once again, the sc2 was more accurate. the wls plots (fig. 10a and b) show that sc2 has a higher sensitivity than sc1, being δλ around 0.2 and 0.01 nm, respectively. the exact values for λ0, λmax, δλ, which are respectively the value at rest, the maximum reached value and the wavelength increment of the installed fbg, are reported in tab. 1. the table also comes with the εmax that is compared to the one obtained by tensile test machine’s extensometer. the latest comparison shows that the sc2 strain and that measured by the extensometer are of the same order of magnitude while the c. lupi et al., frattura ed integrità strutturale, 57 (2021) 246-258; doi: 10.3221/igf-esis.57.18 254 sc1 measured strain is negligible. fig. 10 highlights the latest observation, the sensor bonded on sc2 (fig. 10b) records a maximum strain value 20 times higher than that measured by sc1 (fig. 10a). figure 10: tensile test on a) sc1 and on b) sc2. in a) the response profile of sc1 is highlighted even on a larger scale. sc 1 sc 2 extensometer λ0 [nm] 1555.216 1560.642 λmax load [nm] 1555.227 1560.861 δλ [nm] 0.011 0.220 εmax [µm/ m] 7.75 158.12 169.61 table 1: tensile test strain comparison. cyclic tensile test a dynamic test was then carried out, using the same set-up and alternating 6 consecutive loading and unloading cycles, in order to verify the capability of the system to return to its starting (original) value in case of cyclic (repeated) stress. this cyclic tensile test is not a simulation of the real behavior of the ocw, which is subjected almost exclusively to bending, but rather a stress test carried out to check the tightness of the clamp bolts. the dynamic test confirms the previous observations and reveals an anomalous behavior of sc1, as shown in fig. 11. the two scs were tested simultaneously, yet the response to the same stress is different. the sensitivity of sc2 is visibly higher (fig. 11b) than that of sc1 (fig. 11a) and is emphasized by the same representation scale of 250 pm of the vertical axis. the recorded wl variation is almost constant for both scs but the sensitivity of sc2 is about 17 times higher than that of sc1. this ratio was calculated by considering the maximum wl increase reached by the two sensors at the maximum applied load (3 kn). the strain results comparison of the cyclic tensile test is resumed in tab. 2. the sc1 signal shows a marked trend of decreasing throughout the test, while sc2 remains stable. based on these results, it can be assumed that the cause of the different behavior of the two clamps is due to a thermal effect. although the two clamps are both mounted at the same time on the same ocw section during the cyclic test, their configuration induces a different response to a probable small local temperature variation. a local increase in temperature may have occurred during the test. fig. 4 shows that the sc1 fbg is bonded directly onto the clamp (rigid and massive body), below the bolt, very close to the ocw. the sc2 sensor is hanging between two half clamps, in a position that is more distant from the ocw. it is also worth remembering that the thermal conductivity of copper is higher than that of bronze. these configurations make sc2 less responsive to temperature variations than sc1, which is more sensitive to thermal stress and less affected by mechanical stress. a second hypothesis could exclude temperature variation as a cause c. lupi et al., frattura ed integrità strutturale, 57 (2021) 246-258; doi: 10.3221/igf-esis.57.18 255 of the anomalous response of sc1 and instead could link it to the surface stress state induced by the very proximity of the bolt. in sc1 the grating is bonded very close to the bolt in an area that is probably under a compressive effect that makes unstable the perception of any other external mechanical stress. figure 11: cyclic tensile test on a) sc1 and b) sc2. fbg 1 fbg 2 extensometer λ0 [nm] 1555.1895 1560.637 λmax load [nm] 1555.2012 1560.8468 δλ [nm] 0.01165 0.19678 εmax [µm/ m] 8.42 151.03 167.44 table 2: cyclic tensile test. bending test the pantograph motion was simulated by means of a bending test, according to the setup shown in fig. 6. this consists of a beam, made of an ocw segment, which was clamped at one end. the scs were placed in the three positions indicated by z1, z2 and z3, which correspond to a distance of 30, 120 and 240 mm from the vise. in each test, a load (p) of 0.5, 1.0 and 2.0 kg was hung at the free end of the beam. in this case the two scs were not tested at the same time to ensure that they were positioned with the center of the grating at the indicated position. the diagrams of figs. 12, 13 and 14 show the wl variation recorded by the sc1 (plotted in blue) and sc2 (plotted in red) during the tests, with a sampling rate of 100 hz. each graph was represented in a vertical range (wl) of 300 pm. figure 12: bending test @z1 sampling rate: 100 hz. a) sc1 and b) sc2. tabs. 3 and 4 resumes the results collected during the bending tests, performed at z1, z2 and z3 respectively on sc1 and sc2. the experimental values were compared with the values calculated by eq. (3) e (4). c. lupi et al., frattura ed integrità strutturale, 57 (2021) 246-258; doi: 10.3221/igf-esis.57.18 256 figure 13: bending test @z2 sampling rate: 100 hz. a) sc1 and b) sc2. figure 14: bending test @z3 sampling rate: 100 hz. a) sc1 and b) sc2. z1 (30 mm) z2 (120 mm) z3 (240 mm) applied load [kg] 0.50 1.00 2.00 0.50 1.00 2.00 0.50 1.00 2.00 mf(z) [nmm] 2650.00 5300.00 10600.00 2150.00 4300.00 8600.00 550.00 1100.00 2200.00 σ(z) [mpa] 5.21 10.42 20.84 4.23 8.45 16.91 1.08 2.16 4.32 λ0 [nm] 1554.855 1554.851 1554.845 1554.977 1554.957 1554.958 1555.126 1555.116 1555.105 λload [nm] 1554.859 1554.857 1554.859 1554.982 1554.977 1554.971 1555.128 1555.12 1555.111 δλ [nm] 0.004 0.006 0.013 0.005 0.019 0.013 0.001 0.003 0.006 ε [µm/m] 43.41 86.83 173.65 35.22 70.44 140.89 9.01 18.02 36.04 εfbg [µm/m] 2.75 4.22 9.62 2.29 4.12 5.96 1.00 2.40 4.15 ε/εfbg [%] 15.81 20.57 18.05 15.37 17.10 23.62 8.97 7.51 8.69 table 3: bending test results on sc1. z1 (30 mm) z2 (120 mm) z3 (240 mm) applied load [kg] 0.50 1.00 2.00 0.50 1.00 2.00 0.50 1.00 2.00 mf(z) [nmm] 2600.00 5200.00 10400.00 1700.00 3400.00 6800.00 500.00 1000.00 2000.00 σ(z) [mpa] 5.11 10.22 20.45 3.34 6.68 13.37 0.98 1.97 3.93 λ0 [nm]  1561.343 1561.343 1561.343 1561.314 1561.314 1561.314 1560.977 1560.977 1560.977 λload [nm]  1561.395 1561.441 1561.528 1561.362 1561.402 1561.471 1560.989 1561 1561.021 δλ [nm] 0.052 0.098 0.185 0.048 0.088 0.157 0.012 0.023 0.044 ε [µm/m]  42.59 85.19 170.38 27.85 55.70 111.40 8.19 16.38 32.76 εfbg [µm/m]  37.34 70.44 133.03 34.50 63.51 113.30 8.94 16.55 31.73 ε/εfbg [%]  1.14 1.21 1.28 0.81 0.88 0.98 0.92 0.99 1.03 table 4: bending test results on sc2. c. lupi et al., frattura ed integrità strutturale, 57 (2021) 246-258; doi: 10.3221/igf-esis.57.18 257 the last row of both tables shows the comparison between the strain recorded by the scs and the theoretical (calculated) strain. sc2 recorded values very close to the calculated value. the bending tests confirm the findings of the tensile tests. sc2 shows a higher sensitivity to mechanical stress than sc1. even in this case, the plot of the wls of sc1 shows a barely perceptible reaction to the mechanical stress (i.e., load application at the free end of the beam), while it seems to react with a decreasing trend to a small local variation of the temperature. sc2, on the contrary, responds in a clear way to the application of the load and seems not to be influenced by the thermal stress. final remarks resent paper is aimed at seeking a smart solution for ocw continuous monitoring, a solution that meets the railway network requirements. the rfi demands a versatile sensor system capable of being easily installed (and removable) to existing networks, with no extra embedding procedures. this investigation proposes two easy to install and remove solutions (sc1 and sc2), both using the railways standard cu-alloys clamps. the sc1consists of a single copper element placed at the end of a dropper cable that hooks on the cable and remains in place by means of a single bolt; the sensor is an fbg coated only with polyimide coating and is bonded to the bottom of the clamp, very close to the ocw. the sc2 consists of two bronze half-clamps (obtained by cutting the original clamp in two parts) and a copper coated fbg sensor, which is hung between the two halves. the operating conditions, simulated via bending and tensile tests, were evaluated using the scs grabbed on an ocw used in the italian rfi. the ocw was simulated using a copper (cu-0.1wt.%ag alloy) beam segment of 55 cm in length, geometrically defined by the standard en 50149/2013. the strain measurements carried out by sc1 have shown unsatisfying results measuring strain values 20 times lower than that measured with sc2 (which recorded values that are very close to the calculated ones). moreover, sc1 showed another issue concerning the difficulty of returning to its original wl. plotted wl-time curve of both bending and tensile tests showed an anomalous descending trend. two hypotheses have been proposed to understand this behavior, in both cases it should be recalled that the two scs were tested under the same conditions and the response of sc2 was always consistent with the calculated values, responding linearly to the applied stresses and with a very low background noise. the copper coating plays a key role in the superior performance of the sc2. the electrodeposited cu-coating confers greater rigidity to the grating which, combined with the configuration in which it is hanging between two half-clamps, allows the clamp to perform as a mechanical stress amplifier. an in-depth metallographic analysis was performed on copper-coated optical fiber samples to check the good quality of the ed and to improve the deposition process. references [1] zhang, w., zou, d., tan, m., zhou, n., li, r., mei, g. (2018). review of pantograph and catenary interaction, front. mech. eng., 13(2), pp. 311–22, doi: 10.1007/s11465-018-0494-x. [2] cho, c.j., park, y. (2016). new monitoring technologies for overhead contact line at 400 km·h−1, engineering, 2(3), pp. 360–365, doi: 10.1016/j.eng.2016.03.016. [3] antunes, p., ambrósio, j., pombo, j., facchinetti, a. (2020). a new methodology to study the pantograph–catenary dynamics in curved railway tracks, veh. syst. dyn., 58(3), pp. 425–452, doi: 10.1080/00423114.2019.1583348. [4] shimanovsky, a., yakubovich, v., kapliuk, i. (2016). modeling of the pantograph-catenary wire contact interaction, procedia eng., 134, pp. 284–90, doi: 10.1016/j.proeng.2016.01.009. [5] bucca, g., collina, a. (2009). a procedure for the wear prediction of collector strip and contact wire in pantographcatenary system, wear, 266(1–2), pp. 46–59, doi: 10.1016/j.wear.2008.05.006. [6] mańka, a., hełka, a., ćwiek, j. (2020). influence of copper content on pantograph contact strip material on maximum temperature of railroad wire, sci. j. silesian univ. technol. ser. transp., 106, pp. 97–105, doi: 10.20858/sjsutst.2020.106.8. [7] ambrósio, j., pombo, j., pereira, m. (2013). optimization of high-speed railway pantographs for improving pantographcatenary contact, theor. appl. mech. lett., 3(1), pp. 013006, doi: 10.1063/2.1301306. [8] borromeo, s., aparicio, j.l., martõâ, p.m. (2003). proceedings of the institution of mechanical engineers part f, j. rail rapid transit, 217(3), pp. 167–75, doi: 10.1243/095440903769012876. [9] müller, r. (1997). contact wire wear measurement devices. a system comparison. wcrr, vol. c, firenze, pp. 245–50. p c. lupi et al., frattura ed integrità strutturale, 57 (2021) 246-258; doi: 10.3221/igf-esis.57.18 258 [10] tan, m., ning zhou, jiangwen wang, dong zou, w.z.& g.m. (2018). a real-time impact detection and diagnosis system of catenary using measured strains by fibre bragg grating sensors, veh. syst. dyn., pp. 1–23, doi: 10.1080/00423114.2018.1556396. [11] en 50125-1:2014. (2014). railway applications. environmental conditions for equipment. rolling stock and on-board equipment. [12] en 50155:2017. (2017). railway applications. electronic equipment used on rolling stock. [13] en 50149:2012. (2012). railway applications. fixed installations. electric traction. copper and copper alloy grooved contact wires. [14] measures, r.m. (2001). structural monitoring with fibre optic technology, meas. sci. technol., 12(9), pp. 1609–10, doi: 10.1088/0957-0233/12/9/708. [15] lupi, c., felli, f., dell’era, a., ciro, e., caponero, m.a., kalinowski, h.j., vendittozzi, c. (2019). critical issues of double-metal layer coating on fbg for applications at high temperatures, sensors artic., 19, pp. 3824, doi: 10.3390/s19183824. [16] vendittozzi, c., felli, f., lupi, c. (2018). modeling fbg sensors sensitivity from cryogenic temperatures to room temperature as a function of metal coating thickness, opt. fiber technol., 42(february), pp. 84–91, doi: 10.1016/j.yofte.2018.02.017. [17] ramzyzan ramly, wahyu kuntjoro, m.k.a.r. (2012). using embedded fiber bragg grating (fbg) sensors in smart aircraft structure materials, procedia eng., 41, pp. 600–6, doi: 10.1016/j.proeng.2012.07.218. [18] al-fakih, e., abu osman, n.a., mahamd adikan, f.r. (2012). the use of fiber bragg grating sensors in biomechanics and rehabilitation applications: the state-of-the-art and ongoing research topics, sensors, 12, pp. 12890–926, doi: 10.3390/s121012890. [19] regina c. s. b. allil, marcelo m. werneck, b.a.r. and f.v.b. de n. (2013). application of fiber bragg grating sensors in power industry, current trends in shortand long-period fiber gratings, intechopen. [20] allwood, g.; wild, g.; hinckley, s. (2017). fiber bragg grating sensors for mainstream industrial processes, electronics, 6(92), doi: 10.3390/electronics6040092. [21] vendittozzi, c., ciro, e., felli, f., lupi, c., marra, f., pulci, g., astri, a. (2020). static and dynamic weighing of rolling stocks by mean of a customized fbg-sensorized-patch, int. j. saf. secur. eng., 10(1), doi: 10.18280/ijsse.100111. [22] tam, hwa & liu, shun-yee & guan, bai-ou & chung, weng-hong & chan, tommy & cheng, l. (2005). fiber bragg grating sensors for structural and railway applications. proceedings of spie the international society for optical engineering. [23] k. o. hill and g. meltz. (1997). fiber bragg grating technology fundamentals and overview, light. technol., 15(8), pp. 1263–76, doi: 10.1109/50.618320. microsoft word numero_30_art_4 r. louks et alii, frattura ed integrità strutturale, 30 (2014) 23-30; doi: 10.3221/igf-esis.30.04 23 focussed on: fracture and structural integrity related issues static assessment of brittle/ductile notched materials: an engineering approach based on the theory of critical distances r. louks, h. askes, l. susmel department of civil and structural engineering, the university of sheffield, sheffield s1 3jd, united kingdom r.louks@sheffield.ac.uk, h.askes@sheffield.ac.uk, l.susmel@sheffield.ac.uk abstract. engineering components often contain notches, keyways or other stress concentration features. these features raise the stress state in the vicinity of their apex which can lead to unexpected failure of the component. the theory of critical distances has been proven to predict accurate results, but, conventionally, requires two key ingredients to be implemented: the first is a stress-distance curve which can be obtained relatively easily by means of any finite element software, the second is two additional material parameters which are determined by running appropriate experiments. in this novel reformulation, one of these additional parameters, namely the critical distance, can be determined a priori, allowing design engineers to assess components whilst reducing the time and cost of the design process. this paper investigates reformulating the theory of critical distances to be based on two readily available material parameters, i.e., the ultimate tensile strength and the fracture toughness. an experimental data base was compiled from the technical literature. the investigated samples had a range of stress concentration features including sharp v-notches to blunt u-notches, and a range of materials that exhibit brittle, quasi-brittle and ductile mechanical behaviour. each data set was assessed and the prediction error was calculated. the failure predictions were on average 30% conservative, whilst the non-conservative predictions account for less than 10% of the tested data and less than 2% of the non-conservative error results exceed -20%. it is therefore recommended that a safety factor of at least 1.2 is used in the implementation of this version of the theory of critical distances. keywords. theory of critical distances; static fracture; notches; design. introduction tructural and mechanical engineering components will often contain notches or keyways that act as stress concentrators, raising the local stress ahead of the stress raiser apex. predicting the failure of engineering components accurately has been the goal of many engineers in the last century, as improved accuracy leads to less unexpected failure and more efficient usage of materials. examination of the state of the art suggests that the tcd produces very accurate predictions of failure in components that contain stress concentration features, typically predicting within ±20% error [1]. the tcd is a group of theories which use a common critical distance, l, to assess the local stresses ahead of a stress concentrator apex. the tcd have been formalised into four methods which include the point method (pm), the line method (lm), the area method (am), and the volume method (vm)[2]. historically, critical distance analysis was first proposed in the 1930s and by the 1950s neuber [3] had developed and published a method which is equivalent to the tcd lm. neuber’s method averages the elastic stress ahead of the stress concentrator over a material dependent length. a few years later, peterson [4] developed a simpler method which is the equivalent to the tcd pm. peterson’s approach assumes that the component would fail when the elastic stress at a s r. louks et alii, frattura ed integrità strutturale, 30 (2014) 23-30; doi: 10.3221/igf-esis.30.04 24 material dependent distance from the stress concentrator reaches a critical value. neuber and peterson were investigating the fatigue life of notched metallic components, but since these early works, critical distance analysis has also been adapted to predict static fracture. neuber and peterson faced two problems with implementing their critical distance methods, namely: 1. what value of l should be ascribed to each material? peterson hypothesised that the critical distance was related to grain size, however, this posed some measuring difficulties. both neuber and peterson determined the critical distance empirically, fitting predictions to data. 2. obtaining accurate stress-distance curves in real components. neuber suggested various elegant solutions for some standard notch geometries but they only offer approximations when applied to real components. in 1974, whitney and nuismer [5] investigated the problem of monotonic failure of fibre composite materials containing stress raising features. with seemingly no knowledge of the early work, they developed identical theories to the lm and pm but with different names. in their research they made the useful link between continuum mechanics and linear elastic fracture mechanics (lefm) allowing them to express the critical distance as a function of the fracture toughness, kic. figure 1: critical local stress-distance curves ahead of two geometrically different stress concentrators. the mathematical definition of l is shown by eq. (1), 2 0 1  ic k l          (1) where σ0 is the so-called materials inherent strength and kic is the plane strain fracture toughness. in the conventional application of the tcd for assessing components made from materials that exhibit some ductility prior to failure, the critical distance and inherent strength are not known a priori, meaning l and σ0 have to be determined experimentally for each material. as shown in fig. 1, by plotting, in the incipient failure condition, the critical stress-distance (s-d) curve for two like components containing different stress concentration features, the tcd parameters can be obtained. the material inherent strength, , will often be greater than the material ultimate tensile strength (uts) [1]. if the inherent strength is greater than the uts, the tcd cannot be used to design plain components as it would predict failures with large non-conservative errors. in 2007, david taylor published his book entitled “the theories of critical distances, a new perspective in fracture mechanics” [2]. in the chapter on ceramics, which is based on his earlier work [6], it is said that some very brittle engineering ceramics take the inherent strength, σ0, equal to the material uts, σuts. this finding is in agreement with whitney and nuismer’s work [5]. in particular, they used the uts as σ0 for some quasi-brittle composite materials, achieving good results for both the pm and lm. on the contrary, it has been proven [7] that adopting σ0=σuts to calculate the critical distance does not return accurate results in comparison to the conventional tcd when assessing materials that exhibit, prior to failure, limited plasticity in the vicinity of the stress raiser apex (such as, for instance, pmma [3]). r. louks et alii, frattura ed integrità strutturale, 30 (2014) 23-30; doi: 10.3221/igf-esis.30.04 25 figure 2: failure stress and critical distance relationship. formed simplifying hypothesis to calculate the critical distance value he aim of the present work is to reformulate the tcd to use it to assess mode i fracture in brittle, quasi-brittle and ductile notched materials by determining the required critical distance via standard mechanical properties. in more detail, independently from the level of ductility characterizing the material being assessed, an engineering value for the critical distance is proposed here to be calculated as: 2 1 ic e uts k l          (2) where uts is the conventional ultimate tensile strength and kic the plane strain fracture toughness. therefore, according to the pm, the component is assumed to fail when the effective stress at le/2 along the notch bisector reaches the uts. since the required material properties are supplied by most manufactures, definition (2) makes it evident that critical distance le can be determined without the need for running complex and expensive experimental investigations. this obviously would make the tcd even more appealing to those structural engineers engaged in designing real components against static loading. however, definition (2) raises an obvious and unavoidable question: does the tcd still work? the schematic s-d curve plotted, in the incipient failure condition, in the chart of fig. 2 shows the way the pm assesses notch static strength when the critical distance is calculated according to definition (1) as well as to definition (2). as briefly recalled earlier, when final breakage is preceded by localised plastic deformations, 0 is seen to be larger than uts [2, 3]. this implies that, kic being constant, the critical distance value becomes larger than the corresponding value which would be calculated by applying the tcd rigorously. having pointed out this theoretical argument, it is evident that the only way to answer the above key question, and therefore the validity of adopting eq. (2), is by checking the accuracy of the tcd against appropriate experimental data, the critical distance being directly calculated according to definition (2). this will be done in the next section. methodology review of technical literature containing experimental data on static fracture was compiled. from the built database, all mode i fracture data of notched components made of brittle, quasi-brittle and ductile materials were assessed. tab. 1 summarises the different materials which were investigated and, where necessary, the temperature at which the tests were conducted. this table lists also the type of stress concentration feature being considered (which include external and internal u and v-notches) and the type of tests used (i.e., three/four point bending tests, tension tests, and testing done using blunt and sharp notched brazilian/half brazilian disks). the sharpness of the stress concentration features are also provided in the form of the notch root radii (which varied in the range 0.017.07mm). the geometry of each data was modelled using finite element software ansys®. after applying appropriate boundary conditions to each model, including the application of a unitary load/stress, the solution for each model was calculated by t a r. louks et alii, frattura ed integrità strutturale, 30 (2014) 23-30; doi: 10.3221/igf-esis.30.04 26 assuming that that the investigated materials were linear-elastic, isotropic and homogeneous. the mesh density in the vicinity of stress concentration features apex was refined until convergence occurred at the critical distance (i.e., at le/2). the typical mesh spacing for convergence was between 1-10μm. the local effective stress calculated according to the pm was extracted from along the focus path, the focus path being coincident with the notch bisector under mode i loading. the required s-d curves were calculated by fea in terms of maximum principle stress. it is worth observing here that, under mode i loading, the first principal stress is coincident with the maximum opening stress. further, for the quasibrittle and ductile materials, the s-d curves were calculated and post-processed also in terms of von mises equivalent stress. the s-d curves for each investigated geometrical feature were post-processed according to the pm. finally, the failure prediction was compared with the experimental results, the error being calculated according to definition (3),  %   100validation uts uts error       (3) where   validation is either the maximum principal stress or the von mises stress obtained, at a distance from the notch tip equal to le/2, from the finite element results calculated for the failure stress of the data. the error calculation for each data will show if the proposed method predicts the failure conservatively or non-conservatively by assigning either positive or negative results, respectively. results hown in figs 3 and 4 are the error predictions against changes in the material characteristic behaviour (i.e., from brittle to ductile) using the maximum principal stress and von mises equivalent stress, respectively. material class reference material notch type test type σ uts (mpa) kic (mpa.m0.5) le (mm) ρ range (mm) b1 [8] soda-lime glass v bd 14 0.6 0.585 1 4 b2 [9] alumina7%zirconia v fpb 290 5.5 0.114 0.0310.1 b3 [10] isostatic graphite key u tension 46 1.06 0.169 0.25 4 b4 [11] polycrystalline graphite v tpb & bd 46 1.06 0.169 1 4 b5 [12] isostatic graphite internal bean tension 46 1.06 0.169 0.25 4 b6 [13] pmma -60°c u tension 128.4 1.7 0.056 0.047.07 qb1 [14] pmma 20°c v tpb 111.8 1.12 0.032 0.030.25 qb2 [15] pmma 20°c u tpb 71.95 2.03 0.253 0.012.5 qb3 [16] pmma 20°c cvt tension 67 2.2 0.343 0.2 4 qb4 [17] pmma 20°c v tpb 75 1 0.057 0.080.08 qb5 [18] pmma 20°c u tpb 75 1 0.057 0.11 – 4 d1 [19] high strength steel u tpb 1285 33 0.210 0.1 – 1 d2 [7] en3b u-v tpb 638.5 97.4 7.407 0.1 5 table 1: summary of experimental data (b=brittle, qb=quasi-brittle and d=ductile, bd=brazilian disk, tpb=three point bending, fpb=four-point bending) s r. louks et alii, frattura ed integrità strutturale, 30 (2014) 23-30; doi: 10.3221/igf-esis.30.04 27 figure 3: error results using 1st principal stress as effective stress. figure 4: error results using von mises equivalent stress as effective stress for quasi-brittle and ductile materials. figure 5: error % against ratio of notch root radius, ρ, and the critical distance, le (local stress fields post-processed in terms of maximum principal stress). initially the database was assessed by extracting the maximum principal stress s-d curve from the fea for each of the data. the calculated error results are shown in fig. 3. using the maximum principal stress as the effective stress, the error scatter appears to increase with ductility. the results on the non-conservative side, negative error, do not exceed -27%. to counteract the apparent increasing conservatism with ductility, von mises effective stress s-d curves were extracted and r. louks et alii, frattura ed integrità strutturale, 30 (2014) 23-30; doi: 10.3221/igf-esis.30.04 28 post-processed. the results are presented in fig. 4 for semi-ductile and ductile materials. the scatter and conservatism of the predictions is reduced for the ductile materials, however, the non-conservative error increases. discussion he predictions made for the data set assessed using the maximum principal stress as effective stress (fig. 3) show a maximum non-conservative error of -27%, the majority of the data being on the conservative side. this suggests that the pm applied along with the maximum principal stress criterion can safely be used in situations of practical interest by directly estimating the required critical distance according to definition (2). it has been proven [1] that the tcd applied along with von mises equivalent stress is successful in estimating the static strength of notched ductile materials subjected to both uniaxial and multiaxial static loading, provided that, both inherent strength 0 and critical distance l are determined experimentally. as shown in fig. 4, the use of uts and le, eq. (2), to assess notched ductile components results in a lower level of scattering, the maximum non-conservative error reaching 50%. this suggests that, as far as notched ductile materials subjected to mode i loading are concerned, the use of the simplified methodology proposed here to calculate the critical distance values results in the largest level of accuracy when the tcd is applied along with the maximum principal stress criterion. fig. 5 plots the errors obtained by using the maximum principal stress against the ratio of notch root radius, ρ, and the critical distance, le. as the notch root radius decreases, the stress concentrator is considered to be more like a crack; as the critical distance reduces, the material is considered to be more sensitive to defects and/or machined stress raisers. by using a dimensionless abscissa, the error predictions can be treated independently of the materials sensitivity to defects/notches and the stress concentration feature, which is considered to be mostly governed by the notch root radii, making this version of the tcd suitable to design components containing any geometrical feature and constructed of any material. this diagram confirms that the accuracy of the tcd applied by calculating critical distance via definition (2) is independent from ratio ρ/le. the error results are plotted as a cumulative probability distribution, displayed in fig. 6. it can be seen that, as far as the maximum principal stress is concerned, less than 10% of the predictions fall on the non-conservative side and do exceed 27%. less than 2% of the non-conservative error results exceed -20%, it is therefore recommended that a safety factor of at least 1.2 be implemented with the maximum principal stress assessment. the use of von mises stress to assess semiductile and ductile data is also shown in fig. 6. the results show an increase of non-conservatism but a decrease in the scatter, therefore, using von mises stress in this assessment of components experiencing mode i loading should be incorporated with a safety factor of at least 1.5. figure 6: probability distribution of the error predictions using the maximum principal stress for all data and von mises stress for semi-ductile and ductile data. the simplified engineering method proposed in the present paper is suitable for the design of engineering components that experience mode i loading, without the need for expensive testing. if the level of conservatism is an important factor such as high performance components where weight and/or size are crucial, it is recommended that the rigorous t r. louks et alii, frattura ed integrità strutturale, 30 (2014) 23-30; doi: 10.3221/igf-esis.30.04 29 application of the tcd be used, the conventional method has been proven to predict static failures with an accuracy of ±15% [7]. it should also be highlighted that the tcd has been reported to give similar levels of accuracy, typically ±20%, when used to assess other fracture and fatigue problems [2]. finally, it is worth mentioning that predictions made in practical applications may have increased conservatism. this is due to engineering values supplied by manufacturers typically being given as minimum values compared to the average values typically reported in technical literature, from the design engineers point of view this should be seen as a positive factor in achieving a safe design. conclusions  the proposed method was validated using over 200 mode i test data, however, many test data were presented as an average of up to 5 tests.  using the maximum principal stress for the assessment of components subjected to mode i loading should be incorporated with a safety factor of at least 1.2.  using von mises stress for the assessment of components subjected to mode i loading should be incorporated with a safety factor of at least 1.5.  further work is required to extend this engineering approach to predict failure under multiaxial loading conditions. references [1] susmel, l., taylor, d., the theory of critical distances to estimate the static strength of notched samples of al6082 loaded in combined tension and torsion. part ii: multiaxial static assessment, eng. fract. mech., 77 (3) (2010) 470– 478. [2] taylor, d., the theory of critical distances: a new perspective in fracture mechanics. elsevier ltd, (2007). [3] neuber, h., theory of notch stresses, second. heidelberg: springer-verlag, (1958). [4] sines, g., peterson, r. e., metal fatigue, new york; london; mcgraw-hill, (1959) 293–306. [5] whitney, j. m., nuismer, r. j., stress fracture criteria for laminated composites containing stress concentrations, j. compos. mater., 8(3) (1974) 253–265. [6] taylor, d., predicting the fracture strength of ceramic materials using the theory of critical distances, eng. fract. mech., 71(16–17) (2004) 2407–2416. [7] susmel, l., taylor, d., on the use of the theory of critical distances to predict static failures in ductile metallic materials containing different geometrical features, eng. fract. mech., 75(15) (2008) 4410–4421. [8] ayatollahi, m. r., torabi, a.r., experimental verification of rv-mts model for fracture in soda-lime glass weakened by a v-notch, j. mech. sci. technol., 25(10) (2011) 2529–2534. [9] yosibash, z., bussiba, a., gilad, i., failure criteria for brittle elastic materials, int. j. fract., 125(1957) (2004) 307–333. [10] lazzarin, p., berto, f., ayatollahi, m. r., brittle failure of inclined key-hole notches in isostatic graphite under inplane mixed mode loading, fatigue fract. eng. mater. struct., 36(9) (2013) 942–955. [11] ayatollahi, m. r., torabi, a. r., tensile fracture in notched polycrystalline graphite specimens, int. j. carbon, 48(8) (2010) 2255–2265. [12] berto, f., lazzarin, p., marangon, c., brittle fracture of u-notched graphite plates under mixed mode loading, mater. des., 41 (2012) 421–432. [13] gómez, f. j., elices, m., planas, j., the cohesive crack concept: application to pmma at −60°c, eng. fract. mech., 72(8) (2005) 1268–1285. [14] priel, e., bussiba, a., gilad, i., yosibash, z., mixed mode failure criteria for brittle elastic v-notched structures, int. j. fract., 144(4) (2007) 247–265. [15] cicero, s., madrazo, v., carrascal, i. a., analysis of notch effect in pmma using the theory of critical distances, eng. fract. mech., 86 (2012) 56–72. [16] susmel, l., taylor, d., the theory of critical distances to predict static strength of notched brittle components subjected to mixed-mode loading, eng. fract. mech., 75(3–4)(2008) 534–550. [17] gómez, f. j., elices, m., fracture of components with v-shaped notches, eng. fract. mech., 70(14) (2003) 1913– 1927. r. louks et alii, frattura ed integrità strutturale, 30 (2014) 23-30; doi: 10.3221/igf-esis.30.04 30 [18] gomez, f. j., elices, m., valiente, a., cracking in pmma containing u-shaped notches, fatigue fract. eng. mater. struct., 23(9) (2000) 795–803. [19] gómez, f. j., elices, m., valiente, a., fracture of a high strength steel containing u-notches, in: ecf13, san sebastian, espana, (2000). microsoft word numero_57_art_23_3072 m. słowik, frattura ed integrità strutturale, 57 (2021) 321-330; doi: 10.3221/igf-esis.57.23 321 analysis of fracture processes in reinforced concrete beams without stirrups m. słowik lublin university of technology, poland m.slowik@pollub.pl, http://orcid.org/0000-0001-9627-3625 abstract. the analysis of fracture processes which led to shear failure in reinforced concrete beams without transverse reinforcement was performed on the basis of test results from the author’s own experimental investigation and numerical simulations. the variable parameters during the experiment were a beam’s length and a shear span. it was observed that the character of failure in the beams depended on the beam’s length and the span-to-depth ratio. in slender beams characterized by the shear span-to-depth ratio 3.4 and 4.1, the formation of the critical diagonal crack caused a brittle, sudden failure and the shear capacity was low. in short beams, when the shear span-to-depth ratio was 1.8 and 2.3, the failure process had a more stable character with a slow developing of inclined cracks and the significantly higher load capacity was reached. the activation of various shear transfer mechanisms was examined with regard to the slenderness of the member and the transition between a beam action which took place in slender beams to an arch action which predominated in short beams was described. keywords. fracture process; reinforced concrete; shear failure. citation: słowik m., analysis of fracture processes in reinforced concrete beams without stirrups, frattura ed integrità strutturale, 57 (2021) 321-330. received: 14.04.2021 accepted: 14.06.2021 published: 01.07.2021 copyright: © 2021 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. introduction everal scientific works on shear capacity of structural concrete members were conducted all around the world. the shear transfer model for reinforced concrete members with transverse reinforcement is well recognized for static loading and some new researches are carried out according to impact loading, for instance [1]. nevertheless, there is still no consensus on the general theory for a rational shear design of reinforced concrete members without transverse reinforcement although numerous experimental investigations have been dedicated to beams without stirrups. one of the first broad-scale test results were reported in the middle of the 20th century by leonhardt and walther [2], and kani [3]. then experiments were being continued and an effort was being undertook to improve the understanding of a load transfer in reinforced concrete members due to shear forces, for example [4-10]. despite these works, the shear capacity for members without transverse reinforcement is often calculated on the basis of empirical formulas (for example like in the european recommendation eurocode 2 [11] and the american standard aci 318 [12]). however, empirical formulas s https://youtu.be/rr0xjxdlc3q m. słowik, frattura ed integrità strutturale, 57 (2021) 321-330; doi: 10.3221/igf-esis.57.23 322 can bring some doubts connecting with unsafe estimates for the structural members which are outside of empirical calibration. therefore, the problem of shear capacity of members without transverse reinforcement is still attracted the interest of many researchers. several works have been published recently, for instance [13-17]. the growing knowledge of shear behaviour in beams without stirrups brought the grounds for developing mechanical models of shear transfer mechanisms. particularly, two theories, e.g. the modified compression field theory [18] and the critical shear crack theory [19], helped to work out the shear design concepts which were put into practice, for instance in the latest recommendation of international federation for structural concrete – fib model code 2010 [20] and in a few national codes [21, 22]. it must be emphasized that these new design methods are dedicated to predict the shear capacity of typical slender beams. there are several potential shear transfer actions recognized by the researchers. because the shear failure is affected by various factors, a theoretical description of shear transfer mechanisms is very complicated. the important parameter which influences the failure process in the beams is the ratio of longitudinal reinforcement. the influence of the longitudinal reinforcement ratio on the character of failure in flexural members has been analyzed in depth in [17]. slightly reinforced concrete beams fail soon after appearing of a few flexural cracks and the failure process has a brittle character. in moderately reinforced concrete beams, a stable growth of several flexural cracks is usually observed and the full flexural capacity is reached. in higher reinforced concrete beams, the shear failure predominates due to shear forces and the propagation of inclined cracks. the shear failure often causes dangerous, brittle damage. however, the stable process of developing inclined cracks can also be observed and a relatively high shear capacity can be obtained in some kind of higher reinforced concrete beams [24]. the experimental results of shear capacity in reinforced concrete beams presented in professional literature show a big scatter. the question arises as to whether the shear capacity depends on the beam’s length and as to what contribution of the longitudinal reinforcement in the shear transfer is. when analyzing shear behaviour of longitudinally reinforced concrete beams without transverse reinforcement not only shear capacity should be of interest but also the progress of failure process should be examined. the development of cracks, the propagation of a critical crack and the stress distribution are of primary importance. therefore, the author’s own experimental investigation was performed to analyze the failure process in longitudinally reinforced concrete beams. the experiment was focused on the observation of the cracks formation and propagation in the beams of a higher reinforcement ratio. variable length of the beams and the arrangement of loading allowed to research into the effect of the beam’s span and the shear span-to-depth ratio on the load capacity and the fracture process in reinforced concrete beams without transverse reinforcement. experimental investigation he experimental investigation was performed on four beams: two slender beams: oi-1, oi-2 and two short beams: pi-1, pi-2. the beams had a rectangular cross-section of the width b = 0.12 m, the total height h = 0.25 m and the effective depth (depth measured from the compression edge to the level of longitudinal steel bars) d = 0.22 m. two deformed steel bars of the diameter 18 mm were used as longitudinal reinforcement in the beams. the reinforcing steel was of rb500 category and it was characterized by the yield stress fy = 545 mpa and the tensile strength ft = 631 mpa. the ratio of longitudinal reinforcement was  = 1.8%. transverse reinforcement was not used in the beams. the cross section of the beams is shown in fig. 1. figure 1: cross section of the beams. t m. słowik, frattura ed integrità strutturale, 57 (2021) 321-330; doi: 10.3221/igf-esis.57.23 323 the beams had a different total length and span (distance between the supports) during the test. the span for two slender beams oi-1 and oi-2 was the same leff = 1.8 m whereas the span in short beams differed and it was leff = 1.0 m in the beam pi-2 and leff = 0.8 m in the beam pi-1. the beams were simply supported during the test. the external force was applied from the testing machine in the middle of the span when testing three beams oi-1, pi-2, pi-1 and in case of the beam oi-2 the applied force was symmetrically distributed into two forces, as it is presented in fig. 2. a different scheme of load applying in the beam oi2 (two forces) compering to a load arrangement in rest of beams (one force) was used in order to obtain a different shear span a (distance between the applied force and the support) in slender beams. such arrangement of loading caused that the shear span during the test was also a changing parameter and the beams were characterized by a different shear span-to-depth ratio a/d (see tab. 1). figure 2: static scheme of tested beams. beam span, leff [m] shear span, a [m] shear span-to-depth ratio, a/d [-] oi-1 1.8 0.90 4.1 oi-2 1.8 0.75 3.4 pi-2 1.0 0.50 2.3 pi-1 0.8 0.40 1.8 table 1: tested members. the beams were made by the same constructional concrete. the dolomite aggregate of the maximum size 16 mm was used to produce the concrete mixture. concrete properties were tested on standardized specimens and at standard conditions. the compressive strength of concrete and the modulus of elasticity were measured on cylindrical specimens 150/300 mm whereas the tensile strength of concrete was tested using the splitting test on cubic specimens 150/150/150 mm. the obtained results are presented in tab. 2. the uniaxial tensile strength of concrete was calculated on the basis of the splitting tensile strength as it is recommended in eurocode 2 [10]: fct = 0.9fct,sp = 3.15 mpa. property number of specimens, [-] mean value, [mpa] standard deviation, [mpa] coefficient of variation, [%] compressive strength fc 27 35 5.6 16 tensile splitting strength fct,sp 32 3.5 0.4 11 modulus of elasticity ec 19 41400 93650 9 table 2: concrete properties. m. słowik, frattura ed integrità strutturale, 57 (2021) 321-330; doi: 10.3221/igf-esis.57.23 324 the beams were loaded up to failure. the applied load increased gradually and the cracks’ appearing and developing were monitored, and the cracks’ widths were measured in the following steps of loading. the bond between steel bars and concrete was monitored during the test. for this purpose, steel bars were lengthened out of the beam and dial test gaudes were placed on the ends of bars having the contact with the beam’s edge. the slip of steel bars was not observed during the experiment what confirmed that steel bars were correctly bonded and an un-anchor failure had no place. the instrumentation for bond checking is presented in fig. 3. figure 3: bond checking. all beams failed due to the propagation of inclined cracks and the shear governed the failure. the load applied on the beams at the failure was read from the testing machine pult and the ultimate shear force vult was calculated according to the schemes presented in fig. 2 (p = 2 f). the ultimate loads pult and ultimate shear forces vult of tested beams are presented in tab. 3. a significantly lower shear capacity vult were observed in longer beams characterized by the shear span-to-depth ratio 4.1 and 3.4 comparing to the shear forces at failure in short beams, in which a/d was 2.3 and 1.8. the obtained results were juxtaposed with some test results reported by kani [2]. although both experiments were performed in similar conditions, the shear forces at failure could not be compared directly because the dimensions of the beams tested by kani and the dimensions of the beams from the own test differed a little. therefore, the relationships of the ultimate shear stress ult = vult /(bd) versus the shear span-to-depth ratio a/d were confronted. the comparison which is demonstrated in fig. 4 revealed satisfactory agreement of test results. beam shear span-to-depth ratio, a/d [-] applied load, pult [kn] shear capacity, vult [kn] ultimate shear stress, ult = vult /(bd) [mpa] slender beam oi-1 4.1 90.0 45.0 1.50 slender beam oi-2 3.4 87.0 43.5 1.45 short beam pi-2 2.3 142.0 71.0 2.34 short beam pi-1 1.8 180.0 90.0 3.00 table 3: shear capacity of the beams. figure 4: comparison of test results. m. słowik, frattura ed integrità strutturale, 57 (2021) 321-330; doi: 10.3221/igf-esis.57.23 325 when analyzing test results presented in fig. 4 it was concluded that the shear span-to depth ratio had a considerable influence on the ultimate shear stress of reinforced concrete beams without transverse reinforcement. it was observed that the decrease in the shear span-to-depth ratio resulted in the increase in the ultimate shear stress and this tendency appeared to be more significant when a/d < 2.5. when the shear span to-depth ratio was a/d 2.5 (such a/d is typical for slender beams) the shear capacity was relatively low whereas when the shear span-to-depth ratio did not exceed 2.5 (such a/d characterizes short beams) the shear capacity was noticeable higher. in order to explain a significantly higher load capacity obtained in short beams comparing to shear capacity in slender beams, the analysis of failure process in the beams according to the beams’ span and the shear span-to-depth ratio was performed. analysis of crack propagation and type of failure hen monitoring the cracks appearance and development in tested beams as well as analyzing crack widths, several observations were made. flexural cracks appeared as first in all beams. due to a relatively high ratio of longitudinal reinforcement, the steel bars provided considerable resistance to the opening of the flexural cracks in the region of the maximum bending moment. therefore, several flexural cracks developed and the number of flexural cracks depended on the beams’ length. with the increase of the beam’s length the number of flexural cracks increased and the flexural cracks propagated deeper towards the compression edge of the beam. as the longitudinal reinforcement stabilized the propagation of flexural cracks, with the further load increase diagonal cracks started to form in the support regions. the inclination of cracks was associated with the trajectories of principal stress due to the shear force and the bending moment acting simultaneously in cross sections, see fig. 5. figure 5: trajectories of principal stress. the inclinations and widths of diagonal cracks as well as the development of the critical crack were influenced by the shear span-to-depth ratio. in slender beams oi-1 and oi-2 (characterized by the shear span-to-depth ratio 4.1 and 3.4) the critical diagonal crack formed in one side of the beam, in the middle of the support zone. shear failure in slender beams was caused by the critical crack growth which developed from the flexural-shear crack. in the region where the longitudinal reinforcement could not control the propagation of the inclined shear crack, the crack turned out to be unstable. it led to the brittle collapse of the member. a different shear-transfer action was observed in short beams pi-2 and pi-1 (characterized by the shear span-to-depth ratio 2.3 and 1.8) in which the load was applied at a short distance to the supports. two main inclined cracks propagated in the direction between the load application point and the supports the development of cracks had a stable character and finally one of the inclined cracks predominated and provoked the failure of the beam. fig. 6. illustrates the crack patterns and the failure crack in the beams. it should be pointed that in all tested beams the failure was connected with the propagation of the inclined crack. w m. słowik, frattura ed integrità strutturale, 57 (2021) 321-330; doi: 10.3221/igf-esis.57.23 326 figure 6: crack patterns in the beams. the results of the performed experimental investigation showed that considerable differences existed between short and slender beams not only according to the shear capacity but also to the development of cracks and the character of failure. therefore, the analysis of shear behaviour should not be limited to determine the shear capacity in a critical cross section but different shear transfer actions in the support zone of the beams should be widely examined. shear transfer actions he main mechanisms of shear stress transfer in typical slender beams without shear reinforcement which were recognized up till now are as following: shear transfer in the compression zone, residual tensile stress in the fracture process zone (strain softening effect), aggregate interlock and dowel action of reinforcing bars. they are demonstrated in fig. 7. the distribution of residual stress in tensile concrete in front of the crack was described in [24]. the analysis presented in [17], has confirmed that the strain softening of concrete in tension has the most important contribution in the crack initiation in case of flexural cracks. the empirical model for estimating dowel action was proposed in [4]. several models for describing the effect of aggregate interlock were developed, among them well known model derived by walraven [25] and new propositions presented recently in [26, 27]. however, the activation of the individual shear transfer mechanism seems to be depended on the width of the inclined crack. in case of slender beams a brittle failure was observed and the quick development of the first diagonal crack followed to the beam collapse. the maximum crack width before failure did not exceed 0.1 mm. the shear transfer mechanisms: strain softening effect, aggregate interlock and dowel action of steel bars occurred during the diagonal crack formation but the contribution of the aggregate interlock on the shear transfer seemed to be the most important. t m. słowik, frattura ed integrità strutturale, 57 (2021) 321-330; doi: 10.3221/igf-esis.57.23 327 figure 7: shear mechanisms in slender beams. in case of short beams the influence of the aggregate interlock on the shear transfer was not predominant. the maximum measured crack width before failure reached 0.7 mm. the large opening of the critical diagonal crack reduced the interlock of aggregate particles. the direction of inclined cracks suggested that the main stream of stress transfer ran from the applied load directly to the supports, as it is demonstrated in fig. 8. it gave the evidence that an arch action appeared and the longitudinal steel bars, acting as a tensile tie, had an important influence on the shear resistance. figure 8: shear failure mechanisms in short beams. in order to look deeper into the phenomenon governing cracks distribution in the investigated beams, a numerical simulation was performed. the numerical calculations were provided using the finite element program ansys. two beams were modelled: the short beam which corresponded to the tested member pi-1 of a/d = 1.8 and the longer beam of a/d = 2.5 because the shear span to depth ratio 2.5 has been found to be critical one which separates beams for slender and short. eight-node solid elements were used to model the concrete and three-dimensional bar elements were taken from the library of the ansys program for modelling steel bars. the discrete model of reinforcement was applied and the bond between concrete and steel was modelled as the identical displacement of connected nodes. the nonlinear characteristic of concrete, in particular the strain softening of tensile concrete, was taken into account. a three dimensional stress-strain state was considered by using the willam-warnke limit surface. the newton-raphson method of solving the finite element system of equations was used. the detailed description of the procedure applied to the finite element simulation was presented in [28]. as the results of the numerical calculations, trajectories of total strain were generated. in fig. 9 the obtained distributions of total strain are presented for both beams examined in case of two loading levels: the load level which correspond to the formation of the first diagonal crack (v = 30 kn) and the load level before failure. the significant differences can be observed when comparing the obtained numerical results for both beams. in case of the short beam (a/d = 1.8), two inclined struts transferring the load directly to the supports were generated. the strain concentration in the narrow struts was clearly observed in the load level before failure but the tendency of the struts formation was seen also in the load level v = 30 kn connecting with the formation of diagonal cracks. this finding brought the evidence that the arch action took place in the short beam. quite different progress of strain distribution was observed in the longer beam a/d = 2.5. the streams of total strain pointed that, before the formation of diagonal cracks, m. słowik, frattura ed integrità strutturale, 57 (2021) 321-330; doi: 10.3221/igf-esis.57.23 328 several flexural cracks were able to develop in the mid-span of the beam, in the region where bending moment predominated. then, the stronger concentration of strain in the support zone suggested the failure which was connected with the formation of the critical diagonal crack. such development of strains confirmed that the beam action predominated in the beam of a/d = 2.5. the total strain distributions presented in fig. 9 showed a reasonable agreement with the experimental observation of crack patterns. the obtained numerical results have confirmed that the different work action can be observed in longitudinally reinforced concrete beams in dependence of the member’s length. finally, it can be recapitulated that the higher shear capacity of short beams can be explained by the transfer from the beam action in slender beams to the arch action in short beams. therefore, the adequate shear models should be consider in reinforced concrete beams without transverse reinforcement according to their length. design methods do predict the shear capacity which are used for slender beams are not suitable for short beams. longer beam a/d = 2.5 v = 30 kn v = 51 kn short beam a/d = 1.8 v = 30 kn v = 66 kn figure 9: total strain distribution – fem results. conclusions ased on the performed analysis of cracking process and the character of failure in longitudinally reinforced concrete beams without transverse reinforcement, the following conclusions can be drown: 1. the significant influence of the beam’s length and the shear span-to-depth ratio on the shear capacity and the character of failure is observed in reinforced concrete beams without transverse reinforcement. 2. different character of failure is noticed in short beams comparing to typical slender beams. in slender beams a brittle shear failure is caused by a sudden development of the first diagonal crack. the load capacity is low and it depends on the shear force which causes diagonal cracking. in short beams a more stable growth of two inclined cracks is observed and a significantly higher load capacity is reached. 3. the fracture process in the beams changes also according to the shear span-to-depth ratio a/d. in the beams characterized by a/d 2.5, the beam shear-transfer action takes place whereas in the beams of a/d < 2.5 the arching action predominates. the transfer from the beam action to the arch action is the main factor which causes a different character of fracture process in reinforced concrete beams without transverse reinforcement. the special fib report [29] was dedicated to shear in structural concrete in 2018, where in the concluding remarks [30] it has been pointed that: “… the hypotheses underlying existing models for the shear behavior of structural concrete are mainly based on interpreted (rather than measured) data from experiments that are not representative of real-lifestructures. hence, the existing models are biased and may not capture the real mechanical behaviour. consequently, no general accepted theory, in particular for members with very little or no stirrup reinforcement, is available today. however, b m. słowik, frattura ed integrità strutturale, 57 (2021) 321-330; doi: 10.3221/igf-esis.57.23 329 such a theory is essential, in particular to avoid unnecessary strengthening of countless existing infrastructure objects that are “structurally deficient” according to current codes. …”. the performed experiments presented in the paper provide more insight in recognizing the failure processes in reinforced concrete members without shear reinforcement of different length. taking into account the obtained results it can be concluded that failure and load carrying capacity in slender beams and short beams should be analyzed separately. the design methods to predict the shear capacity of reinforced concrete members without transverse reinforcement should rely on a comprehensive understanding of failure processes which are connected with different shear transfer mechanisms in short beams comparing to mechanisms observed in typical slender beams. acknowledgments his work was supported by lublin university of technology. references [1] oliviera m. c., da cunha teles d. v., de figueiredo amorin d. l. n. (2020). shear behaviour of reinforced concrete beams under impact loads by the lumped damage framework. frattura ed integrità strutturale, 53, pp. 13-25. doi: 10.3221/igf-esis.53.02. [2] leonhardt f., walther r. (1962). beiträge zur behanndlung der schubprobleme im stahlbetonbau. in: schubversuche an einfeldrigen stahlbetonbalken mit und ohne schubbewehrung, deutscher ausschuss für stahlbeton, berlin, heft 151. [3] kani g.n.j. (1966). basic facts concerning shear failure. journal of the american concrete institute, june, pp. 675692. [4] baumann t., rüsch h. (1970). versuche zum studium der verdubelungswirkung der biegezugbewehrung eines stahlbetonbalken. deutscher ausschuss für stahlbeton, no. 210, ernst & sohn, berlin, pp. 43-83. [5] jelić i., pavlović m.n., kotsovos m.d. (1999). a study of dowel action in reinforced concrete beams. magazine of concrete research, 51, no. 2, pp. 131-141. doi: 10.1680/macr.1999.51.2.131. [6] carmona j.r., ruiz g., viso j.r. (2007). mixed-mode crack propagation through reinforced concrete. engineering fracture mechanics, 74, pp. 2788-2809. doi: 10.1016/j.engfracmech.2007.01.004. [7] hamrat m., boulekbache b., chemrouk m., amziane s. (2010). shear behaviour of rc beams without stirrups made of normal strength and high strength concretes. advances in structural engineering, 13, pp. 29-41. [8] carpinteri a., carmona j.r., ventura g. (2011). failure mode transitions in reinforced concrete beams part 2: experimental tests. aci structural journal, 3, pp. 286-292. doi: 10.1260/1369-4332.13.1.29. [9] caldentley a.p., padilla p., muttoni a., ruiz m.f. (2012). effect of load distribution and variable depth on shear resistance of slender beams without stirrups. aci structural journal, 5, pp. 595-603. [10] reineck k., bentz e.c., fitic b.,. kuchma d.a, bayrak o. (2013). aci-dafstb database of shear tests on slender reinforced concrete beams without stirrups. aci structural journal, 110 (5), pp. 867-876. [11] en 1992-1-1 (2004). eurocode 2. design of concrete structures – general rules and rules for buildings. cen, brussels. [12] aci 318-14, (2014). building code requirements for structural concrete. american concrete institute, farmington hills, michigan. [13] cavagnis f., ruiz m. f., muttoni a. (2015). shear failures in reinforced concrete members without transverse reinforcement: an analysis of the critical shear crack development on the basis of test results. engineering structures, 103, pp. 157-173. doi: 10.1016/j.engstruct.2015.09.015. [14] tung n.d., tue n.v. (2016). a new approach to shear design of slender reinforced concrete members without transverse reinforcement. engineering structures, 107, pp. 180-194. doi: 10.1016/j.engstruct.2015.04.015. [15] tung n.d., tue n.v. (2016). effect of support conditions and loading arrangement on the shear response of reinforced concrete beams without transverse reinforcement. engineering structures, 111, pp. 370-382. doi: 10.1016/j.engstruct.2015.12.022. t m. słowik, frattura ed integrità strutturale, 57 (2021) 321-330; doi: 10.3221/igf-esis.57.23 330 [16] avagnis f., ruiz m.f., muttoni a. (2018), a mechanical model for failures in shear of members without transverse reinforcement based on development of a critical shear crack. engineering structures, 157, pp. 300-315. doi: 10.1016/j.engstruct.2017.12.004. [17] słowik m. (2019). the analysis of failure in concrete and reinforced concrete beams with different reinforcement ratio. archive of applied mechanics, 89, pp. 885-895. doi: 10.1007/s00419-018-1476-5. [18] vecchio f.j., collins m.p. (1986). the modified compression field theory for reinforced concrete elements subjected to shear. journal of aci, 83 (2), pp. 219-231. [19] muttoni a., ruiz m.f. (2008). shear strength of members without transverse reinforcement as function of critical shear crack width. aci structural journal, 105 (2), march-april, pp. 163-172. [20] fib model code for concrete structures 2010, (2013). ernst & sohn, berlin. [21] csa committee a23.3-14, (2014). design of concrete structures. canadian standards association. [22] sia 262:2003, (2003). concrete structures. code. swiss society of engineers and architects. [23] słowik m., smarzewski p. (2012) study of the scale effect on diagonal crack propagation in concrete beams. computational materials science, 64, pp. 216-220. doi: 10.1016/j.commatsci.2012.05.068. [24] hillerborg a., modeer m., petersson p.e. (1976). analysis of crack formation and crack growth in concrete by means of fracture mechanics and finite elements. cement and concrete research, 6, pp. 773-782. [25] walraven j.c. (1981). fundamental analysis of aggregate interlock. journal of the structural division, asce, 107 (st11), pp. 2245-2270. [26] pundir m. at al. (2019). review of fundamental assumptions of the two-phase model for aggregate interlocking in cracked concrete using numerical methods and experimental evidence. cement and concrete research, 125, 105855. doi: 10.1016/j.cemconres.2019.105855. [27] huber t., huber p., kollegger j. (2019). influence of aggregate interlock on the shear resistance of reinforced concrete beams without stirrups. engineering structures, 186, pp. 26-42. doi: 10.1016/j.engstruct.2019.01.074. [28] słowik m., smarzewski p. (2014). numerical modeling of diagonal cracks in concrete beams, archive of civil engineering, 60 (3), pp. 307-322. doi: 10.2478/ace-2014-0021. [29] fib bulletin 85: (2018). towards a rational understanding of shear in beams and slabs. technical report, fédération internationale du béton. [30] kaufmann w., mata-falcón j., beck a. (2018) future directions for research on shear in structural concrete. in: fib bulletin 85: towards a rational understanding of shear in beams and slabs. pp. 323-338. microsoft word numero_34_art_14 y. hos et alii, frattura ed integrità strutturale, 34 (2015) 133-141; doi: 10.3221/igf-esis.34.14 133 focussed on crack paths measurement and simulation of crack growth rate and direction under non-proportional loadings y. hos technische universität darmstadt, materials mechanics group, franziska-braun-str. 3, d-64287 darmstadt, germany hos@wm.tu-darmstadt.de m. vormwald technische universität darmstadt, materials mechanics group, franziska-braun-str. 3, d-64287 darmstadt, germany vormwald@wm.tu-darmstadt.de abstract. a series of fatigue experiments on thin-walled tubes under tension and torsion, the experimental results – crack path and crack growth life – are measured and compared. it is observed that the cracks follow a curvature from a tensile to a shear dominated growth with increasing crack length. the results are enforced by the high amplitudes applied to the specimens causing large cyclic plastic deformations and crack growth rates in the order of 10-3 mm/cycle. the non-linear nature of the cyclic deformation has been taken into account by applying a cyclic plasticity model, and plasticity-induced crack closure is captured by a contact formulation. already for the uniaxial reference case the current limitations in modelling plasticity induced crack closure – a prerequisite for achieving realistic simulation results – have become obvious. measurements have shown that friction and roughness induced closure processes come up, especially for non-planar crack surfaces, challenge to be met in the future. keywords: multiaxial fatigue; mixed mode; fatigue crack growth. introduction he fatigue crack growth under non-proportional mixed-mode loading depends on many influence factors besides the mode-mixity. increasing mode-mixity creates a tendency for a shear dominated crack growth instead of a tensile stress dominated one, the latter being the usual case. with increasing cyclic plastic deformation the shear dominated fatigue crack growth becomes more important. the cyclic plastic deformation is also the origin of the plasticity induced crack closure. especially in non-proportional cases, the roughness and friction induced crack closure occurs and interacts with the plasticity induced crack closure. these influence factors are closely interrelated, therefore a study of individual factors is hard to achieve. originating from information gathered from a literature overview [1], a research project was launched, seeking further knowledge on the mechanisms. results achieved so far are the subject of this paper. in order to connect the results to the state of the art the experimental methods are first applied to cases with proportional and mode i dominated fatigue crack growth. t y. hos et alii, frattura ed integrità strutturale, 34 (2015) 133-141; doi: 10.3221/igf-esis.34.14 134 description of the problem onstant amplitude fatigue tests have been performed using thin-walled tubes under tension-compression (force f) and torsion (moment m). the specimen geometry is shown in fig. 1. the specimens were machined from longitudinally welded tubes. the individual specimens were saw-cut and the notches were milled. two holes, diameter 4 mm, were drilled with the distance of 10 mm of the centres of the holes (length of an arc measured at the outer surface). the notch was positioned opposite to the longitudinal weld. the material is the construction steel s235 with mechanical properties as given in tab. 1. besides young’s modulus, e, plastic offset stress, rp0.2, ultimate tensile strength, rm, the parameters of the cyclic stress-strain curve, 1 ' n a a a e k           , (1) are given. for use in finite element calculations the cyclic stress-strain curve is reformulated in terms of chaboche’s model [2],    5 pl 1 1 expiy i i c                , (2) with the parameters listed in tab. 2. figure 1: specimen geometry. e in mpa rp0.2 in mpa rm in mpa k’ in mpa n 214000 310 435 1170 0.239 table 1: mechanical properties of s235 [3]. y in mpa c1 in mpa 1 c2 in mpa 2 c3 in mpa 3 c4 in mpa 4 c5 in mpa 5 58.2 13442 46 39134 400 72245 1904 603494 7404 800707 104861 table 2: chaboche parameters for representing the cyclic stress strain curve of s235. two series of experiments have been performed. in the first series of experiments, the fatigue crack lengths were monitored automatically by taking photographs of the specimen at predefined numbers of applied cycles. three cameras were installed, one directly facing the slit of width 14 mm from front, one with 45° angle on one side and one with 45° angle on the other side. at regular, pre-defined intervals the test was interrupted automatically. the specimen was c y. hos et alii, frattura ed integrità strutturale, 34 (2015) 133-141; doi: 10.3221/igf-esis.34.14 135 unloaded completely. then, a static load of 90% of the maximum fatigue load was applied. during the short hold time the cameras took pictures of the specimen’s surface. the specimen was unloaded again and the cyclic loading continued. the pictures were inspected after the test. in order to ease the optical evaluation of the crack tip coordinates the specimens were branded with a 1 mm laser-dot pattern prior to testing. the five different loading sequences have been applied: pure tension-compression loading, pure torsion loading, proportional loading resulting from the superposition of these two and out-of-phase loading with phase angles of 45° and 90°. the load ratio was rf = rm = -1. the experiments have been conducted under load control and moment control, respectively, using a servo-hydraulic, four-pillar tension-torsion testing machine with frequencies between 0.25 hz and 2 hz. in the air conditioned laboratory, a temperature of 21°c and a relative air humidity of 50% were kept constant. the cracks were assumed to be through-wall cracks with a straight crack front. the crack length is defined as the arc length with the arc starting at the crack initiation location. here, the scheme of presenting the results was adopted from references [4] an [5] with crack 1 being left and crack 3 being right. in the second series of experiments the tests were occasionally interrupted and the deformation field was measured applying the digital image correlation (dic) technique. more details on the measurement technique can be found in references [6,7]. some results of these investigations are used later when dealing with crack closure. uniaxial loading the specimen r-001 has been tested under pure tension-compression loading with max 45 knf  and 1fr   . two symmetric cracks grew in the centre cross section plane, fig. 2. the crack growth curve is shown in fig. 3. figure 2: cracks in the specimen r-001, pure tension-compression with max 45 knf  and 1fr   , steel s235. figure 3: crack growth curve of specimen r-001, pure tension-compression with max 45 knf  and 1fr   , steel s235. the results of this experiment serve as a reference for determining the basic material crack growth properties and for calibrating numerical procedures. y. hos et alii, frattura ed integrità strutturale, 34 (2015) 133-141; doi: 10.3221/igf-esis.34.14 136 multiaxial loading three specimens were tested under proportional loading, 90° out-of-phase loading and 45° out-of-phase loading, namely the specimens r-004, r-005 and r-006 respectively. the amplitudes of the loadings are max 33 knf  , max 382 nmm  and 1f mr r   . the nominal stresses in the gross section are ,max 101.5 mpan  and ,max 62.6 mpan  . again, two cracks initiated at the notch. only for the very early stage of short fatigue crack growth it can be assumed that the crack grows in the uniaxial stress field prevailing at the notch surface. the different crack paths can be seen in figs. 4 to 6 with a summary in fig. 7. for proportional loading, fig. 4, the principal axis calculated from the nominal stresses is 25.5° inclined against the specimen axis. the crack growth direction, however, is only inclined approximately 14° against the cross section plane. some cyclic mode ii loading could have contributed to the fatigue crack growth. the specimen does not show the conventional and expected growth behaviour under pure mode i. figure 4: cracks in specimen r-004, proportional loading with max 33 knf  , max 382 nmm  and 1f mr r   , steel s235. for out-of-phase loading with phase angle 90° the two cracks show unsymmetrical growth behaviour, fig. 5. while crack 1 grows straight at nearly 45° inclined to the specimen axis, crack 3 starts curving almost immediately after initiation. the crack has at least two options for choice which path to follow and both options are nearly equilibrate. the crack growth life – the comparison is shown in fig. 8 – under the 90° out-of-phase loading is longest. figure 5: cracks in specimen r-005, out-of-phase loading with max 33 knf  , max 382 nmm  and 1f mr r   , phase angle 90°, steel s235. under out-of-phase loading with phase angle 45° crack 1 is inclined in average 26° during its first 13 mm of growth and afterwards turns to a direction perpendicular to the specimen axis. contrary to crack 1 the crack 3 shows an initial steep crack path inclined 58° against the cross section plane. after 12 mm of crack growth a sharp kink to the cross section plane growth occurs. the stepwise crack growth, see fig. 6, is related to the various kinks in the crack growth direction. after the occurrence of a kink the growth rate is decelerated. as a consequence of the variety of kinks the crack surface becomes very rough. in total, the crack growth is slower than under proportional loading which might be due to increased roughness induced crack closure. the frequency of kinks and the unsymmetrical growth of the two cracks may again indicate that the crack path has at least two options for choice which are nearly equilibrate. in its early stage the mode i growth around the notch surface dominates. with increasing crack length a fracture mode ii gains priority and is enforced after approximately 13 mm of crack growth. y. hos et alii, frattura ed integrità strutturale, 34 (2015) 133-141; doi: 10.3221/igf-esis.34.14 137 figure 6: cracks in specimen r-006, out-of-phase loading with max 33 knf  , max 382 nmm  and 1f mr r   , phase angle 45°, steel s235. figure 7: crack growth curve of specimens r-004, r-005 and r-006 with max 33 knf  , max 382 nmm  and 1f mr r   , steel s235. figure 8: crack growth curve of specimens r-004, r-005 and r-006 with max 33 knf  , max 382 nmm  and 1f mr r   , steel s235. y. hos et alii, frattura ed integrità strutturale, 34 (2015) 133-141; doi: 10.3221/igf-esis.34.14 138 fatigue crack growth simulation n the experiments presented in the previous chapter the applied load amplitudes have been so large and the crack growth rates have been so fast that a fatigue crack growth simulation is expected to fail when based on the stress intensity factor range of the linear elastic fracture mechanics. from the variety of crack driving force parameters of the elastic-plastic fracture mechanics [8] the cyclic j-integral was selected for describing fatigue crack growth, i i ( ) d d u j w y t s x          (3) with ij ij ij 0 d( )w         . (4) the symbol  preceding the stress tensor, strain tensor, traction vector and displacement vector components designates the changes of these quantities. these changes must be evaluated referring to a reference state. it serves as the new origin for defining the increments of the field variables, the latter preceded by the symbol . the stress and displacement state at the moment of load reversal is a natural reference state. then the symbol  designates the increments from the respective reference values. at the moment of the next reversal, these increments become the conventional cyclic ranges. however, the symbol  in j and w does not represent changes of j and w; instead j and w are functions of their arguments as defined by eqs. (3) and (4). for non-proportional loading the theoretical background is widely lost. nevertheless, hertel et al. [9] proposed an algorithm which delivers practically path-independent values when solving eq. (3). due to this path independence the thereby obtained value should be valid crack driving force. in case of non-proportional loading the load reversal points, in terms of j, are detected by the following algorithm. if the change in j after the integration of eq. (3) turns out to be negative, it is presumed that the last equilibrium state was a load reversal point. in consequence, the reference variables are redefined with stress, strain and displacement values of the last equilibrium state. thereupon, the integration is continued. this procedure provides the monotonic increase of j for every load step. hertel’s algorithm was extended here to take crack closure into account. only the portions of a cycle with open crack surfaces have been considered. therefore, the values obtained here can be labelled effective cyclic j-integral, jeff. the loading step associated with the onset of crack closure was determined by applying a finite element based crack growth simulation. in the present paper only results for the tension-compression can be reported. the simulation started with three cycles applied to the uncracked structure. at maximum load of the next cycle, a crack growth step for 1 mm crack advance was executed. for this purpose the boundary condition of the relevant nodes on the crack growth plane was changed from fixed to unrestrained. additionally, a contact plane was inserted at the new crack surface to prevent negative displacements of the crack surface nodes during subsequent cyclic loading. after the new equilibrium was found three cycles without crack growth were calculated. the node release procedure – 1 mm crack growth followed by three cycles – was repeated until reaching 5 mm crack length. further repetitions of this scheme followed until reaching a crack length of 6 mm. however, the crack growth per repetition was continuously reduced. growth steps of 0.5 mm, 0.25 mm and two times 0.125 mm were used. it is admitted that sound recommendations, see e.g. herz et al. [10,11] and zerres and vormwald [12], for achieving a converged result are violated. however, with the plasticity model at hand converged results cannot be achieved either due to its ratcheting properties. a first estimate is expected to provide inside anyway. in fig. 9 an example is shown for the dependence of jeff from the stress range . the calculations were stopped on the occurrence of the first crack surface contact. recently, hos et al. [6,7] showed that due to severe ratcheting the crack opening displacements increase from cycle to cycle without any trend of stabilization. this behaviour is typical for the chaboche model. as a consequence of the large ratcheting the crack opening and closure loads are too low when compared to measured values using the digital image correlation technique. in contrast to the simulations presented in [7] the node release scheme was modified to reduce ratcheting. in especially, no intermediate cycles without a crack growth i y. hos et alii, frattura ed integrità strutturale, 34 (2015) 133-141; doi: 10.3221/igf-esis.34.14 139 step were applied. nevertheless, before dealing with the more complicated combined loading cases producing nonproportional mixed mode a realistic cyclic plasticity model has to be implemented. such models are available [13]; however, their application requires determination of material’s ratcheting behaviour first and identification of the corresponding material parameters second. such work is ongoing. the numerical as well as the experimental determination of crack closure is accompanied by some uncertainties which are transferred to the effective ranges of the crack driving force parameter. fig. 10 is shown here with the intension to unravel the uncertainties. first, an expected crack growth rate as function of the effective cyclic is plotted as solid line. a power law is assumed to correlate both variables. eff d d ma c j n   (5) the parameters c and m are determined following an older recommendation [14] that the exponent might be set to m = 1.5 and the coefficient can be estimated from a fatigue crack growth rate of 10-5 mm/cycle at jeff = e/(5.105 mm-1). second, the experimentally determined crack growth rates of specimen r-001 are plotted as lineconnected symbols over jeff where this effective crack driving force is estimated based on both numerically and experimentally determined effective ranges. it can be concluded that the measured effective ranges provide more realistic estimates of the crack driving force. figure 9: jeff as function of the applied nominal stress range , specimen r-001, pure tension-compression with max 45 knf  and 1fr   , steel s235. conclusions he path of fatigue cracks in thin walled tubes under combined tension/compression and torsion has been experimentally determined for proportional and non-proportional loading. as a general trend, it is observed that the cracks follow a curvature from a tensile to a shear dominated growth with increasing crack length. this behaviour had been observed also in previous investigations, however, an influence of the specimen geometry explaining the effect had bee postulated because the former specimens were shouldered. here, it must be stated that the change of the growth mode is a property of the material itself. this change was observed to occur either in a continuous way or abruptly producing a kink. both phenomena could appear in the same specimen at the both crack tips. the results summarized above are probably enforced by the high amplitudes applied to the specimens causing large cyclic plastic deformations and crack growth rates in the order of 10-3 mm/cycle. any fracture mechanics based model for t y. hos et alii, frattura ed integrità strutturale, 34 (2015) 133-141; doi: 10.3221/igf-esis.34.14 140 describing the process should therefore be based on a crack driving force parameter of the elastic-plastic fracture mechanics. here, the closure-free cyclic jeff is applied first to the uniaxial case. even for this relatively simple case the problem of realistically estimating the effective ranges becomes apparent. the simulation with a finite element based node release scheme requires the application of an advanced plasticity model which is superior to the chaboche model as it is supplied in commercial software. especially ratcheting should be described realistically as this process occurs near the crack tips in a very pronounced way. otherwise the predicted plasticity induced crack closure is unrealistic. without a satisfactory solution for determining the plasticity induced crack closure the non-proportional mixed mode case is hard to tackle. first measurements have shown that – and this is obvious – friction and roughness induced closure processes come up, especially for non-planar crack surfaces. this modelling challenge will have to be met in the future. 10 -4 10 -3 10 -2 d a/ d n i n m m /c y cl e 1 5 10 50 100 jeff in n /mm open sy m bols: crack closure from simulation closed sy mbols: crack closure from measurement circles: left crack squares: right crack figure 10: experimentally determined fatigue crack growth rates from specimen r-001, pure tension-compression with max 45 knf  and 1fr   , steel s235, plotted over jeff the latter calculated for measured and simulated effective ranges. acknowledgement he german research foundation (deutsche forschungsgemeinschaft) is greatly acknowledged by the authors for financial support under grant vo729/13-1. references [1] zerres, p., vormwald, m., review of fatigue crack growth under non-proportional mixed-mode loading, international journal of fatigue 58 (2014) 75–83. [2] chaboche, j.l., dang van, k., cordier, g., modelization of the strain memory effect on the cyclic hardening of 316 stainless steel, 5th int. conf. struct. mech. in reactor techn., l (1979) l11/3. [3] boller, chr., seeger, t., materials data for cyclic loading, elsevier, 1 (1987). [4] zerres, p., brüning, j., vormwald, m., risswachstumsverhalten der aluminiumlegierung almg4.5mn unter proportionaler und nichtproportionaler schwingbelastung, materials testing, 53 (2011) 109-117. [5] zerres, p., brüning, j., vormwald, m., fatigue crack growth behavior of fine-grained steel s460n under proportional and non-proportional loading, engineering fracture mechanics, 77 (2010) 1822-1834. [6] hos, y., vormwald, m., freire, j.l.f., using digital image correlation to determine mixed mode stress intensity factors in fatigue cracks, proceedings of coteq 2015, conference on technology of equipment, organized by abendi, brazilian society for ndt and inspection, (2015). [7] hos, y., vormwald, m., freire, j.l.f., measurement and simulation of strain fields around crack tips under mixedmode fatigue loading, frattura ed integrità strutturale, 42 (2015) 42-55. doi: 10.3221/igf-esis.33.06. t y. hos et alii, frattura ed integrità strutturale, 34 (2015) 133-141; doi: 10.3221/igf-esis.34.14 141 [8] vormwald, m., fatigue crack propagation under large cyclic plastic strain conditions, procedia materials science, 3 (2014) 301-306. [9] hertel, o., döring, r., vormwald, m., cyclic j-integral under nonproportional loading, proc. 7th int. conf. biaxial/multiaxial fatigue fract., dvm berlin, (2004) 513-518. [10] herz, e., hertel, o., vormwald, m., numerical simulation of plasticity induced fatigue crack opening and closure for autofrettaged intersecting holes, engineering fracture mechanics, 78 (3) (2011) 559-572. [11] herz, e., thumser, r., bergmann, j.w., vormwald, m. endurance limit of autofrettaged diesel-engine injection tubes with defects, engineering fracture mechanics, 73 (2006) 3-21. [12] zerres, p., vormwald, m., finite element based simulation of fatigue crack growth with a focus on elastic–plastic material behavior, computational materials science, 57 (2012) 73–79. [13] döring, r., hoffmeyer, j., seeger, t., vormwald, m., a plasticity model for calculating stress-strain sequences under multiaxial nonproportional cyclic loading, computational material science, 28 (2003) 587-596. [14] vormwald, m., anrißlebensdauervorhersage auf der basis der schwingbruchmechanik für kurze risse, institut für stahlbau und werkstoffmechnaik der technischen universität darmstadt, report 47 (1989). microsoft word numero_56_art_18_3036 m. k. wasekar et alii, frattura ed integrità strutturale, 56 (2021) 217-228; doi: 10.3221/igf-esis.56.18 217 analysis of the influence of reinforcements on the microstructure and mechanical characterization of the al-flyash composites milind k. wasekar, mohan p. khond department of mechanical engineering, college of engineering, pune, india. wasekarmk14.mech@coep.ac.in, http://orcid.org/0000-0002-9499-6042 mpk.mech@coep.ac.in, https://orcid.org/0000-0003-3852-5366 abstract. the aim of this work is to investigate the influence of the addition of silicon carbide and molybdenum disulfide on the microstructure and the tensile strength of the al-flyash hybrid composites prepared using the stir casting technique. the composite with aluminum 6061 alloy as the matrix and flyash as the reinforcement, with different weight fractions, is investigated to study its microstructure and the tensile strength. the same has been compared with the hybrid composites with aluminum-flyash/sic and aluminum-flyash/mos2 for different weight fractions of the reinforcements. the tensile tests were conducted as per astm standard testing procedures at room temperature. from the results it is identified that tensile strength of the al6061-flyash composite is lesser than the al6061-flyash/sic and al6061flyash/mos2 hybrid composites. it is also observed that increment in the composition of the sic and mos2 causes the increment in the tensile strength of the hybrid composite. this increment in the tensile strength is due to good interface bonding and uniform distribution of the reinforcements in the composite. keywords. flyash; tensile strength; molybdenum disulfide; silicon carbide; microstructure. citation: wasekar, m. k., khond, m. p., analysis of the influence of reinforcements on the microstructure and mechanical characterization of the al-flyash composites, frattura ed integrità strutturale, 56 (2021) 217-228. received: 04.03.2021 accepted: 21.03.2021 published: 01.04.2021 copyright: © 2021 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. introduction aterials selected so far are particulate reinforced metal matrix composites (mmcs) which have the advantage that they are nearly isotropic [1]. silicon carbide, al2o3, boron carbide (b4c), and graphite are common reinforcements for aluminum matrices. however, the flyash as reinforcement in the aluminum matrix has the wide range of scope in area of mechanical behavior [2-3] of the composites. aluminum matrix with flyash particulate reinforced composite has also a lower density than aluminum which leads to weight reductions in the areas of aerospace and automobiles. however the increment in the flyash leads to decrement in the strength of the aluminum composite. thus it is recommended to use the hybrid aluminum metal matrix composites such that the other reinforcements gives the better strength to the composites. m https://youtu.be/1jqid60uec8 m. k. wasekar et alii, frattura ed integrità strutturale, 56 (2021) 217-228; doi: 10.3221/igf-esis.56.18 218 many authors prepared the metal matrix composites using stir casting route [4-5] however the stir casting route is also utilized to prepare the hybrid mmcs [6-9]. since, stir casting method was considered to be of low cost and effective method and also gives the uniform distribution of the reinforcement even at higher weight percentages. mechanical properties, tensile fracture behavior of aluminum matrix composites with graphite [10-11], fly ash [12] etc was studied by the different authors and many authors made an attempt to compare the obtained results with the unreinforced aluminum alloy. some authors studied the aluminum matrix composites with single reinforcement [10-12] and concluded that the required results were not obtained. e. gikunoo et al [12] studied the al-fly ash composites and found that the density of the composite decreases thus the weight reduction is possible however the tensile strength of the composite decreases. thus, many researchers concentrating on the research in the field of hybrid metal matrix composites [13-14]. to keep the reduced weight of the composite one reinforcement used such as flyash [15-18], rice husk ash [19] and to increases the strength of the composites second reinforcement such as graphite [15-17], silicon carbide [18-19] has been utilized. the main idea to utilize the graphite in the metal matrix composites is to gain the reduced co-efficient of friction of the composites. since the graphite act as the self lubricant material, the wear rate of the composite has been reduced. researchers [20-23] utilized the molybdenum disulfide (mos2) as the reinforcement in aluminum matrix composites. however, adding of mos2 more than 5wt% in the aluminum matrix decreases tensile as well as wear properties of the composites [22-23]. thus the hybrid metal matrix composites were utilized in order to increases the tensile strength using the silicon carbide and reduce the wear rate using the self lubricants such as graphite [24-25] and mos2 [26-30]. researchers also compared the al-sic mmcs with hybrid al-sic/mos2 mmcs and recommended that hybrid mmcs have better mechanical properties in contrast with the single reinforced mmcs. it is identified from the literature that more research work has been done on the mechanical behavior of aluminum matrix reinforced with silicon carbide or graphite [31-32], tib2 [33] particulate and laminated [34], polymer [35] composites. on the other hand it is also observed that the systematic evaluation of mechanical behavior of hybrid aluminum matrix composites has to carry out. in this background, there is a scope for the study the mechanical characterization of hybrid aluminum composite with fly ash as reinforcement. through this investigation, an attempt has been made to investigate effect of addition of the sic and mos2 separately on the microstructure of the al6061-flyash hybrid composites. through the material characterization an attempt has been made to compare the al6061-fly ash composite with al6061-fa/sic and al6061-fa/mos2 hybrid composite. methodology he methodology adopted in this work is mentioned below: (1) the stir casting method will be used to prepare the aluminum matrix composites for the various compositions of the reinforcement/s. the compositions considered in this work are composite a al6061-fly ash for 4, 8, 12, 16, and 20wt.% of the reinforcement; composite b al6061-fa/sic composite for the 2, 4, 6, 8, and 10wt.% of flyash, and 1, 2, 3, 4 and 5wt.% of sic; and composite c al6061-fa/mos2 composite for the 2, 4, 6, 8 and 10wt% of flyash and 1, 2, 3, 4 and 5wt% of mos2. (2) the energy-dispersive x-ray spectroscopy (edx) experimental setup, shown in fig.1(a), will be utilized to determine the presence of reinforcing elements in the composites. the scanning electron microscope (sem) analysis will be used to analyze the microstructure of the composites. these analysis techniques will be utilized to study the microstructure of the said composites due to the availability, low cost, ease to examine and analyze, etc. (3) for all the compositions of composite a, composite b and composite c, hardness, tensile test specimens will be prepared as per the astm standard testing procedure. (4) to analyze the failure of the composites, the fractography examination will be carried out using sem. material and preparation he materials chosen in this work are aluminum alloy 6061 as matrix material, particles of flyash, and silicon carbide/molybdenum disulfide as reinforcements. the motivation to use fly ash as the reinforcement is to gain the advantage of its weight reduction properties. the use of sic gives the increased hardness, tensile, impact strength, etc. the addition of mos2 gives better wear resistance properties to the aluminum composite. it is identified that the addition of the flyash reinforcement to the aluminum decreases the density of the composites [1216]. thus this can be utilized in applications in automobile industries where it requires weight reduction properties. on t t m. k. wasekar et alii, frattura ed integrità strutturale, 56 (2021) 217-228; doi: 10.3221/igf-esis.56.18 219 the other hand, the increment in the weight percentage of flyash increases the hardness and strength of the composites whereas there is a decrement in the same has been observed after 10wt% of the fly ash reinforcement. hence in the present investigation, the weight percentage of the flyash is considered are 2, 4, 6, 8, and 10wt%. from the literature, it is also observed that the addition of a higher percentage of sic in the aluminum matrix has not given significant hardness and tensile properties and also increases the weight of the composite. whereas the lower weight fractions of the sic will give the better properties of the composites. also at a low weight fraction of sic will give the increased hardness, lower density, reduced weight, increased strength of the composites. hence in the present investigation, the weight percentage of the sic is considered to be 1, 2, 3, 4, and 5wt%. molybdenum disulfide is silver black in appearance, occurs as molybdenite. mos2 is unreactive and unaffected by dilute acids. it is similar to graphite in appearance, and also it is used as a solid lubricant as it has a low coefficient of friction. it is also reported in the literature that the density of the mos2 is 5.06 g/cc. thus the addition of the higher weight fractions of the mos2 increases the weight of the composites as well as the tensile strength also decreases [22]. hence in the present investigation, the weight percentage of the mos2 is considered to be 1, 2, 3, 4, and 5wt%. from the literature [13] it is identified that flyash has higher silicon oxide. thus it gives better properties when mixed with aluminum. in the present work, the flyash is used as main reinforcement with 2, 4, 6, 8, and 10wt% with silicon carbide/mos2 as additional reinforcements 1, 2, 3, 4, and 5wt% in the aluminum hybrid mmcs. most of the researchers [4-9] utilized stir casting method in the fabrication of particulate hybrid mmcs. tab. 1 shows the various configurations of materials and the casting parameters used to prepare the composites. . sl no al6061 flyash sic mos2 composite temperature stirring speed 1 96, 92, 88, 84 and 80% 4, 8, 12, 16 and 20wt% al6061-fa 720°c 500rpm 2 97, 94, 91, 88 and 85% 2, 4, 6, 8 and 10wt% 1, 2, 3, 4 and 5wt% al6061-fa/sic 720°c 500rpm 3 97, 94, 91, 88 and 85% 2, 4, 6, 8 and 10wt% 1, 2, 3, 4 and 5wt% al6061-fa/mos2 720°c 500rpm table 1: material compositions and the processing parameters the al6061 is super heated to the temperature 720oc in a graphite crucible. while stirring, with four blade stirrer, at 500rpm the reinforcements such as flyash and sic particles were added to the molten aluminum. since the al6061 in liquid state is very reactive to oxygen, thus stirring is done in the closed chamber with nitrogen gas. the degasifier and flux has been added to remove the gases from the liquid melt (if any) and magnesium is added to increase the wettablitiy of flyash particles. the liquid melt is poured to the graphite mold and allowed to solidify. the al6061-fa/sic composite bars taken from the mold were machined to prepare the testing specimens (edx, sem, hardness, tensile test specimens). the similar casting experimentation is repeated to prepare the composite a and composite c for the said compositions. experimentation n this experimental work on al6061-fly ash, al6061-fly ash/sic, and al6061-fly ash/mos2 particulate composite, for various weight percentages of reinforcement/s. these composites produced using the stir casting technique to determine the mechanical properties such as hardness, tensile strength.for all the combinations, i.e. composite a, composite b, and composite c,specimens are prepared to examine the material properties. fig.1(b) shows the experimental setup for tensile testing whereas fig.1(c-d) shows the tensile test specimens of al6061-flyash composites before and after a fracture. i m. k. wasekar et alii, frattura ed integrità strutturale, 56 (2021) 217-228; doi: 10.3221/igf-esis.56.18 220 (a): edx and sem experimental setup (c): before test (b): tensile testing experimental setup (d): after test figure 1 (a): edx and sem setup, (b) tensile testing setup, (c-d): tensile test specimens al6061-flyash composites. results and discussion edx analysis o confirm the formation of al6061-fa, al6061-fa/sic, and al6061-fa/mos2 composites, edx analysis was performed. the existence of these composites generally influences the mechanical properties of al6061-fa hybrid composites. to confirm the formulation of the aluminium-flyash composites the analysis of different areas was focused, corresponding peaks, and results are shown in fig.2(a-c). the microstructure of the composite demonstrates the uniform distribution of flyash content in the aluminum matrix. fig.2(a) shows the edx analysis of the al6061-flyash composite with 8wt% of the reinforcement. the table inside the figure shows the elements present in it. the presence of aluminum is common whereas the presence of si and mg shows that, the aluminum used is al6061 alloy. the elements fe and o indicate the presence of the flyash reinforcement. the main constituents in the flyash are sio2, al2o3, and fe2o3, it also has a little quantity of mgo. however the si and mg in the al6061 alloys were 0.6 to 0.8%, and the increased percentage of those elements shows the addition of flyash in the composite. fig.2(b) shows the edx analysis of the al6061-flyash with sic as the additional reinforcement in the hybrid composite with 8wt% of the reinforcement. the table inside the figure shows the elements present in it. the presence of the percentage of al, si, and mg shows that the aluminum used is al6061 alloy. the elements fe and o indicate the presence of the flyash reinforcement and the increased percentage of the si is obtained from the addition of the sic reinforcement. element c shows the presence of carbide obtained from the sic which gives the strength to the said composite. fig.2(c) shows the edx analysis of the al6061-flyash with mos2 as the additional reinforcement in the hybrid composite with 8wt% of the reinforcement. the table inside the figure shows the elements present in it. the presence of the percentage of al, si, and mg shows that the aluminum used is al6061 alloy. the elements fe and o indicate the presence of the flyash reinforcement and the increased percentage of the si is obtained from the addition of the flyash reinforcement. the element mo and s show the presence of reinforcement mos2. however, the presence of sulfide is not obtained from the edx profile, because in the hot condition the mos2 reacts with oxygen and forms the molybdenum trioxide and sulfur oxide. the presence of molybdenum gives the increased ductility, density and provides a little increment in the hardness. t m. k. wasekar et alii, frattura ed integrità strutturale, 56 (2021) 217-228; doi: 10.3221/igf-esis.56.18 221 figure 2(a): edx spectrum of the al6061-8wt%flyash figure 2(b): edx spectrum of the al6061-6wt%fa/ 3wt%sic composite. from the edx spectra, it is seen that the interface is very smooth and it also shows the existence of the elements aluminum, carbon, silicon, magnesium, mo, o, and fe phase at the interface. from the sem/eds spectrum analysis, the results confirm the required composition of the tailored composites. fig 3(a-d) shows the edx spectrum respectively at the marked location at the particle-matrix interface of flyash particles, al6061-8wt.%flyash, al6061-6-wt.%fa/3wt.%sic, and al6061-6wt%fa/3wt%mos2 composite respectively. from fig 3 (b-d), through the mapping of particles, it is clear that the distribution of the reinforced particles (sic and mos2) in the aluminum-flyash composites is uniform. hence, the uniform distribution of the reinforced particles may give improved mechanical properties. m. k. wasekar et alii, frattura ed integrità strutturale, 56 (2021) 217-228; doi: 10.3221/igf-esis.56.18 222 figure 2(c): edx spectrum of the al6061-6wt%fa/ 3wt%mos2 composite. (a) flyash particles (b) al6061-8%flyash (c) al6061-6%fa/ 3%sic composite (d) al6061-6wt%fa/ 3wt%mos2 composite figure 3: sem of hybrid aluminum matrix composites m. k. wasekar et alii, frattura ed integrità strutturale, 56 (2021) 217-228; doi: 10.3221/igf-esis.56.18 223 density of the hybrid composites density values of hybrid composites may increase or decrease from the matrix material. which is mainly depends on the density of the reinforcement material. the density of the hybrid composites increases with increment in weight fractions of the reinforcements of higher densities whereas, for the lower density reinforcement, it decreases. the density of both sic and mos2 is higher than that of al6061 whereas the density of the flyash is lesser than that of the al6061 and other reinforcements. thus to investigate the effect of the addition of different reinforcements on the hybrid mmc on its density has to be determined. the archimedes principle is used to determine the same. the result of the experimentation is given in fig.4. from fig.4 it is observed that the density of the al6061-fa composite decreases with increment in the flyash content whereas the addition of sic in the al6061-fa maintains the density as equal to the al6061 and the addition of mos2 in the al6061-fa increases the density of the hybrid composites. figure 4: density of hybrid aluminum matrix composites hardness of the hybrid composites the hardness experimentation has been carried out using the vickers’ micro-hardness testing machine. the result of the experimentation has been shown in the fig.5 for different composition of the hybrid composites. figure 5: micro-hardness of hybrid aluminum matrix composites from fig 5 it is observed that the hardness of the al6061-fa composites increases up to 8wt% of the reinforcement and further increment in the flyash decreases the hardness of the composites. this decrement is due to the increased particles of the flyash which forms the clustering and failed to form the uniform distribution which in turn decreases the resistance to the indentation. the hardness of the al6061-fa/sic and al6061-fa/mos2 hybrid composites is observed to be higher m. k. wasekar et alii, frattura ed integrità strutturale, 56 (2021) 217-228; doi: 10.3221/igf-esis.56.18 224 than the al6061-fa composites. the hardness of the al6061-fa/mos2 hybrid composite increases with increment in the mos2 up to 4wt% and later decreases whereas the hardness of the al6061-fa/sic hybrid composite increases up to the 3wt% of sic and decreases on the further increment of the sic. however the as compared to the al6061-fa and al6061fa/mos2 hybrid composite the hardness of the al6061-fa/sic hybrid composite is higher. the maximum hardness obtained, for al6061-6%fa+3%sic, is 87.9 vhn and it is 13% higher than the other composites. the addition of the sic and mos2 particles increases the hardness of the hybrid composites. however, the maximum hardness is obtained at the 6 to 8wt% of the flyash, as observed in the al6061-fa composites. tensile strength of the hybrid composites the tensile test has been carried out using the universal testing machine. the result of the experimentation has been shown in fig.6 for different compositions of the hybrid composites. from fig.6 it is observed that the tensile strength of the al6061-fa composites increases up to 8wt% of the reinforcement and further increment in the flyash decreases the tensile strength of the composites. this decrement is due to the increased particles of the flyash which forms the clustering and failed to form the uniform distribution in the aluminum matrix which in turn decreases the strength. figure 6: tensile strength of hybrid aluminum matrix composites. the tensile strength of the al6061-fa/sic and al6061-fa/mos2 hybrid composites is observed to be higher than the al6061-fa composites. the tensile strength of the al6061-fa/mos2 and al6061-fa/sic hybrid composite increases with increment in the mos2 and sic, respectively, up to 4wt% and later decreases. however, as compared to the al6061fa and al6061-fa/mos2 hybrid composite the tensile strength of the al6061-fa/sic hybrid composite is higher. the maximum hardness obtained, for al6061-8%fa+4%sic, is 273.8n/mm2 and it is 20% higher than the other composites. the addition of the sic and mos2 particles increases the tensile strength of the hybrid composites. however, the maximum tensile strength is obtained at the 8wt% of the flyash, as observed in the al6061-fa composites. thus the addition of the flyash up to 8wt% in the al6061 matrix increases the hardness and tensile strength of the composites. fig 7 shows the comparison of the hardness and tensile strength of the al6061-fa, al6061-fa/sic, and al6061-fa/mos2 composites at 8wt% of the flyash reinforcement. from fig.7 it is also identified that the hardness of al-8%fa is nearly the same as the al-8%fa/4%mos2 whereas the tensile strength of the al-8%fa/4%mos2 is lesser than the al-8%fa. this indicates the addition of mos2 has no impact on the hardness and decreases the tensile strength. this decrement in the tensile strength is due to the layered microstructure of the mos2 which unable to take the applied load or its interlayer sliding due to the applied stress dissipates the energy. thus the entire load will act on the matrix and thus reduces the strength of the composite. in contrast with the al-8%fa and al-8%fa/4%mos2, the al-8%fa/4%sic has high hardness and high tensile strength. this enhancement in hardness and tensile strength is due to the hard particles of the sic reinforcement, which take the applied load. from fig 7 it is observed that, at 8wt% of the flyash, the hardness and the tensile strength of the al6061-fa/sic is high in contrast with the al6061-fa and al6061-fa/mos2 composites. thus the 8wt% of flyash and 4wt% of sic is to be considered the optimized composition and can be used as the potential material for the replacement of aluminum-flyash, aluminum-flyash/mos2 for automobile applications. some of the specific applications of flyash composites include pistons, bearings surfaces [4], bushes, cylinder liners, pistons, camshafts [9] as well as the disc brake of two-wheelers. m. k. wasekar et alii, frattura ed integrità strutturale, 56 (2021) 217-228; doi: 10.3221/igf-esis.56.18 225 figure 7: comparison of hardness and tensile strength of composites at 8wt% of the flyash fig 8 shows the fractured surfaces of the aluminum hybrid metal matrix composites for different compositions. fig.8(a-b) shows the fractured surfaces of the al6061-flyash composites for 8wt% and 16wt% of the reinforcement. from the fractography, it is clear that the al6061-flyash composites have microvoids and crack, propagation of those leads to the failure of the matrix. it is also observed that higher percentages of the flyash reinforcement weaken the bonding thus leads to the formation of the cracks at the interfaces. fig.8(c-d) shows fractography of al6061-8%fa/4%sic and al6061-10%fa/5%sic composites. it is observed that al lower percentages of reinforcement the bonding between the matrix and the reinforcement is good and increased reinforcements such as flyash and sic causes the debonding and voids at the interfaces. thus decreases the properties of the hybrid composites. fig.8(e-f) shows the fractographs of al6061-8%fa/4%mos2 and al6061-10%fa/5%mos2 composites. it is also observed that at the lower percentages of the flyash, up to 8wt%, the voids formed are lesser whereas, at higher percentages, 10wt% of fa and 5wt% of mos2, the more number of cracks were formed which further leads to the propagation of crack upon loading. thus reduces the mechanical properties of the said hybrid composites. conclusions n this experimental work, the influence of the addition of the sic and mos2 on the hardness and tensile properties of the al6061-fa has been studied. from the results, it is observed that with the addition of sic and mos2 particles in the al6061-fa composite, the hardness and the tensile strength of the composite increase. however, this increment is limited to the 8wt% of flyash reinforcement in the aluminum matrix. the hardness and the tensile strength of the al6061-fa/sichybrid composite are higher than the al6061-fa and al6061-fa/mos2 composites. thus for the application like disc brake, which requires lesser weight and high strength and hardness the al6061-fa/sichybrid composite can be potential material.in further analysis, for the disc brake application in an automobile, the wear behavior of the al6061-fa/sic hybrid composite has to be carried out. in future work, this experiment also be conducted in the thermal environment, to find the effect of temperature on the mechanical properties of the said composites. funding his research received no specific grant from any funding agency in the public, commercial, or not-for-profit sectors. i t m. k. wasekar et alii, frattura ed integrità strutturale, 56 (2021) 217-228; doi: 10.3221/igf-esis.56.18 226 conflict of interest he authors declare that they have no conflict of interest. (a) al6061-8%fa (b) al6061-16%fa (c) al6061-8%fa/4%sic (d) al6061-10%fa/5%sic (e) al6061-8%fa/4%mos2 (f) al6061-10%fa/5%mos2 figure 8: sem of fractured surfaces of the aluminum hybrid composites t cracks at the interface of al-fa voids cracks cracks voids cracks cracks voids cracks m. k. wasekar et alii, frattura ed integrità strutturale, 56 (2021) 217-228; doi: 10.3221/igf-esis.56.18 227 references [1] asm handbook, composites, asm international, 21 (2001). [2] anderson, t. l. (2013). fracture mechanics-fundamentals and applications. 3rd edition, taylor & francis group, new york. [3] asm international (2000). mechanical testing and evaluation, asm handbook, 8, pp. 1302-1326. [4] doddamani, s. and kaleemulla, m. (2019). comparisons of experimental fracture toughness testing methods of al6061-graphite particulate composites, journal of failure analysis and prevention, springer, 19(3), pp.730-737. doi: 10.1007/s11668-019-00652-8. [5] dhummansure, v., kalyanrao, a. a., doddamani, s. (2020). optimization of process parameters for fracture toughness of al6061-graphite composites, structural integrity and life, 20(1), pp 51–55. [6] rajesh, a. m., kaleemulla, m., doddamani, s. (2019). generation of mechanically mixed layer (mml) in hybrid aluminum metal matrix composites under as-cast and age hardened conditions, sn aplied science, springer, 1(8), 860. doi:10.1007/s42452-019-0906-5. [7] rajesh, a. m., kaleemulla, m., doddamani, s. (2019). development and characterization of hybrid aluminum metal matrix composites, acta technica corviniensis – bulletin of engineering, 12(3), pp 63-66. [8] rajesh, a. m., kaleemulla, m., doddamani, s. (2019). effect of heat treatment on wear behavior of hybrid aluminum metal matrix composites, tribology in industry, 41(3), pp.344-354. doi: 10.24874/ti.2019.41.03.04. [9] rajesh, a. m., kaleemulla, m., doddamani, s., bharath k. n. (2019). material characterization of sic and al2o3 reinforced hybrid aluminum metal matrix composites on wear behavior, advanced composite letters, sage, 28, pp.1-10. doi: 10.1177/0963693519856356. [10] doddamani, s. and kaleemulla, m. (2015). review of experimental fracture toughness (kic) of aluminium alloy and aluminium mmcs, international journal of fracture and damage mechanics, journals pub, 1 (2), pp.38-51. [11] doddamani, s. and kaleemulla, m. (2016). indentation fracture toughness of alumnum6061-graphite composites, international journal of fracture and damage mechanics, journals pub, 1 (1), pp.40-46. [12] gikunoo, e., omotoso, o. and oguocha, i. n. a. (2005). effect of fly ash particles on the mechanical properties of aluminium casting alloy a535, materials science and technology, 21(2), pp-143-152. [13] dey, a. and pandey, k. m. (2016). characterization of fly ash and its reinforcement effect on metal matrix composites: a review, rev.adv. mater. sci. 44, pp-168-181. [14] imran, m. and anwar khan, a. r. (2019). characterization of al-7075 metal matrix composites: a review, journal of material research and technology, 8(3), pp.3347–3356. doi: 10.1016/j.jmrt.2017.10.012. [15] kumar, v., dev gupta, r. and batra, n. k. (2014). comparison of mechanical properties and effect of sliding velocity on wear properties of al 6061, mg 4%, fly ash and al 6061, mg 4%, graphite 4%, fly ash hybrid metal matrix composite, procedia materials science 6, pp.1365 – 1375. doi: 10.1016/j.mspro.2014.07.116. [16] haider, u., bittnar, z., kopecky, l., bittnar, p., němeček, j., ali, a., pokorny, j. (2016). mechanical behaviour and durability of high volume fly ash cementitious composites, frattura ed integrità strutturale, 38, pp. 289-302. doi: 10.3221/igf-esis.38.41. [17] prakash kumarasamy, s., vijayananth, k., thankachan, t., pudhupalayam muthukutti, g. (2017), investigations on mechanical and machinability behavior of aluminum/flyashcenosphere/gr hybrid composites processed through compocasting, journal of applied research and technology 15, pp. 430–441. doi: 10.1016/j.jart.2017.05.005. [18] raja selvam, d., robinson smart, j., dinaharan, d. s. (2013). synthesis and characterization of al6061-fly ashpsicp composites by stir casting and compocasting methods, energy procedia 34, pp. 637 – 646. doi: 10.1016/j.egypro.2013.06.795. [19] ravikumar, m., reddappa, h.n., suresh, r., sreenivasareddy, m., (2021), experimental studies of different quenching media on mechanical and wear behavior of al7075/sic/al2o3 hybrid composites, frattura ed integrità strutturale, 55, pp. 20-31. doi: 10.3221/igf-esis.55.02 . [20] bizhan rahmati, a., sarhan, a. d., and sayuti, m. (2014). investigating the optimum molybdenum disulfide (mos2) nanolubrication parameters in cnc milling of al6061-t6 alloy, int j adv manuf technol, 70, pp. 1143–1155. doi: 10.1007/s00170-013-5334-x. [21] geeta rani, m., parameswararao, ch.v.s., rama kotaiah, k. (2017). studies on characterization of al6061/ mos2 metal matrix composite, international journal of mechanical engineering and technology (ijmet), 8(8), pp. 998– 1003. m. k. wasekar et alii, frattura ed integrità strutturale, 56 (2021) 217-228; doi: 10.3221/igf-esis.56.18 228 [22] yadav, r., prakash sharma, j., rekha yadav, g. (2017). prediction of mechanical and wear properties of al6061/mos2 (molybdenum disulphide) composites, international journal of innovative research in science, engineering and technology, 6( 8), pp. 1583915849. doi: 10.15680/ijirset.2016.0608039. [23] marachakkanavar, m., patil, s., rao, r., patil, h., banne, g. (2018). a review on tribological and mechanical characterization of al6061 reinforced with mos2, journal of emerging technologies and innovative research (jetir), 5(2) pp.244-246. [24] vamsi krishna, m., xavior, a.m. (2014). an investigation on the mechanical properties of hybrid metal matrix composites, 12th global congress on manufacturing and management, procedia engineering 97, pp. 918 – 924. doi: 10.1016/j.proeng.2014.12.367. [25] vijaya, m., srinivas, k. (2019). investigation on mechanical properties of aa6351/sic and aa6351/sic/gr composites fabricated by stir casting method, international journal of recent technology and engineering (ijrte), 8(1), pp.705-708. [26] rouhi, m., moazami-goudarzi, m. and ardestani, m. (2019). comparison of effect of sic and mos2 on wear behavior of al matrix composites, trans. nonferrous met. soc. china 29, pp. 1169−1183. doi: 10.1016/s1003-6326(19)65025-9. [27] janbozorgi, m., shamanian, m., sadeghian, m. sepehrinia, p. (2017). improving tribological behavior of friction stir processed a413/sicp surface composite using mos2 lubricant particles, trans. nonferrous met. soc. china, 27, pp. 298−304. doi: 10.1016/s1003-6326(17)60034-7. [28] maruthi varun, k. and raman goud, r. (2019). investigation of mechanical properties of al 7075/sic/mos2 hybrid composite, materials today: proceedings, doi: 10.1016/j.matpr.2019.08.131. [29] daniel, s. a. a., ananth, s. v., parthiban, a. (2019). optimization of machining parameters in electro chemical machining of al5059/sic/mos2 composites using taguchi method, materials today: proceedings, doi: 10.1016/j.matpr.2019.06.750. [30] kumar bannaravuri, p., kumar birru, a., shanker dixit, u. (2020). effect of laser surface melting on surface integrity of al−4.5cu composites reinforced with sic and mos2, trans. nonferrous met. soc. china, 30, pp. 344−362. doi: 10.1016/s1003-6326(20)65217-7. [31] doddamani, s., kaleemulla, m., (2017). fracture toughness investigations of al6061graphite particulate composite using compact specimens, frattura ed integrità strutturale, 11(41), pp. 484-490. doi:10.3221/igf-esis.41.61. [32] doddamani, s., kaleemulla, m. (2017). experimental investigation on fracture toughness of al6061–graphite by using circumferential notched tensile specimens, frattura ed integrità strutturale, 11(39), pp. 274-281. doi: 10.3221/igf-esis.39.25. [33] bolzon, g., bocciarelli, m., chiarullo, e.j. (2009). mechanical characterization of metal-ceramic composites, frattura ed integrità strutturale, 10, pp. 56-63; doi: 10.3221/igf-esis.10.07. [34] bellini, c., di cocco, v, iacoviello, f., sorrentino, l. (2019). experimental analysis of aluminium carbon/epoxy hybrid laminates under flexural load, frattura ed integrità strutturale, 49, pp. 739-747. doi: 10.3221/igf-esis.49.66. [35] nurullaev, e., ermilov, a. s., lyubimova, n. yu. (2017). dependence of mechanical characteristics from composition and structure and optimization of mechanical fracture energy of polymer composite material based on high-molecular rubbers, frattura ed integrità strutturale, 41, pp. 369-377. doi: 10.3221/igf-esis.41.48. microsoft word numero_30_art_45 o. sucharda et alii, frattura ed integrità strutturale, 30 (2014) 375-382; doi: 10.3221/igf-esis.30.45 375 focussed on: fracture and structural integrity related issues numerical modelling of reinforced concrete beams with fracture-plastic material o. sucharda, j. brozovsky vsb-tu ostrava, faculty of civil engineering oldrich.sucharda@vsb.cz, jiri.brozovsky@vsb.cz abstract. this paper describes the use of models of fracture-plastic materials for reinforced concrete in numerical modelling of beams made from reinforced concrete. the purpose of the paper is to use of a model of concrete for modelling of a behaviour of reinforced concrete beams which have been tested at the university of toronto within re-examination of classic concrete beam tests. the original tests were performed by breslerscordelis. a stochastic modelling based on lhs (latin hypercube sampling) has been performed for the reinforced concrete beam. an objective of the modelling is to evaluate the total bearing capacity of the reinforced concrete beams depending on distribution of input data. the beams from the studied set have longitudinal reinforcement only. the beams do not have any shear reinforcement. the software used for the fracture-plastic model of the reinforced concrete is the atena. keywords. concrete; beam; bearing capacity; reinforced; non-linear analysis; fracture-plastic. introduction oncrete ranks among modern building materials. it is used, in particular, in bearing structures in structural and civil engineering. these are, for instance, beams, walls, slabs, shell or volume enclosing sections. as the concrete is very specific, extensive research has been carried out. for instance, the concrete behaves differently if subject to tension or if subject to compression. for this reason, a non-linear analysis should be used in calculations. more intensive use of the concrete and the need to carry out a detailed analysis have resulted in availability of many source documents and computational models for the concrete. creation of such source documents have been among topics addressed by the international federation for structural concrete (ceb-fib) which issues recommendations and publications that are regarded as the starting point for creation of standards. in european standards, the recommendations of model code 1990 [3] are taken as a basis for designing of concrete and reinforced concrete structures. the latest recommendation is model code 2010 [4] which mentions several approaches applicable to the nonlinear analysis. this paper aims at validating the use of one of such approaches to the non-linear analysis. because the design standards require that uncertainty should be considered in input data, the non-linear analysis is supported by the stochastic modelling which makes it possible to describe better the real behaviour and bearing capacity of the structure. c o. sucharda et alii, frattura ed integrità strutturale, 30 (2014) 375-382; doi: 10.3221/igf-esis.30.45 376 material models of the concrete n order to choose the model of the concrete correctly, it is necessary to consider the purpose and area where the concrete should be used because the concrete models require different data and accuracies of the models are different. this is, for instance, the case of details in the computational model. in most of advanced models the following is true: the more precise is the model, the higher are the demands in terms of quantity and quality of the complex data, this making, in turn, the computational process more demanding. a non-linear analysis of the concrete and reinforced concrete structures is often combined with other types of the task. such tasks could, for instance, simulate dynamic loads or earthquakes [14]. constitutive models of the concrete are implemented in several software applications [10], [18] and [21]. [1] and [21] deal also with the modelling and analysing of the concrete structures they describe possible approaches to the behaviour of concrete elements and concrete models. [5] and [22] provide a good summary of the topic under study. one of advanced models fracture plastic material [9] in atena [6] has been chosen for numerical modelling of the behaviour of the reinforced concrete beam. a predecessor of this concrete model is sbeta which is among widely-used models. the numerical analysis of stress and deformation in concrete structures uses the finite element method [20]. stochastic modelling n numerical analyses it is recommended to consider, in some cases, the random character of input data. the most common random inputs are material properties of the concrete. this is, for instance, the compression strength, tensile strength or modulus of elasticity of the concrete. in those cases, it is possible to use the stochastic modelling. responses of the structure are calculated for individual sets of stochastic input parameters which describe uncertainty of input data [7] and [8]. the input values should be properly described, e.g. with a mean value, standard deviation, or type of distribution. the analysis output are processed typically in histograms. stochastic modelling is performed in freet [17] which is a lhs software application. lhs (latin hypercube sampling) and possible use are described in an theoretical manual [7] and user manual [8]. freet is compatible with atena. the both software applications are supplied together as sara. when selecting the random variables, it is recommended to follow jcss [12] and iso [11] and use a correlation matrix. the number of simulations depends on complexity of the task. typically, it takes tens of hours to calculate the task. experiments ore than sixty years ago one of the first important scientific work focused on the concrete appeared. the authors was bresler-scordelis [2] and his works has been supported by several experiments which have been properly documented. these were three-point bending tests of the reinforced concrete beams. the beam span and reinforcement were different. the work dealt with shear failures and total bearing capacity of the beams. the tests were used later for validation of several papers and recommendations. twelve beams in four series were tested. each series had a specific reinforcement and span. the shape was rectangular. the basic length of the beam was 3.66, 4.57 or 6.4 mm. each beam was ca. 552 mm long. fig. 1 shows principles of the experiment. more details about the test and numerical calculations are provided in [2]. figure 1: scheme of the experiment. i i m o. sucharda et alii, frattura ed integrità strutturale, 30 (2014) 375-382; doi: 10.3221/igf-esis.30.45 377 the data obtained in the experiments were used for the testing software at the university of toronto. the goal was to repeat the bresler-scordelis’s tests of the reinforced concrete beams. the number, size and reinforcement of the beams were as close as possible and in line with current capabilities of the equipment. differences in production dimensions were very little. figure 2: cross-section of the beams. again, the purpose was to describe the behaviour of the reinforced concrete beams during the loading process and to determine collapse of the structure. the experiments were also used for the fem numerical modelling [20]. results of the experiments and numerical modelling are described in [19]. bar size area [mm2] fy [mpa] fu [mpa] es [mpa] m25a 500 440 615 210000 m25b 500 445 680 220000 m30 700 436 700 200000 table 1: material properties of steels. beam number l [mm] span [mm] bottom steel oa1 4100 3660 2 m30, 2 m25 oa2 5010 4570 3 m30, 2 m25 oa3 6840 6400 4 m30, 2m25 table 2: detail of beams. beam number fc [mpa] es [mpa] fsp [mpa] oa1 22.6 36500 2.37 oa2 25.9 32900 3.37 oa3 43.5 34300 3.13 table 3: material properties of concrete. the beams identified as oa were chosen for the numerical modelling in this paper. they are shown in fig. 2. the beam is reinforced with the reinforcement identified as m25 and m30. the material properties of steel are described in tab. 1. an elastic-plastic model of steel with reinforcement was chosen for the numerical modelling. m25b was used as a reinforcement for the beams 1 and 3, while the beam 2 was reinforced with steel identified as m25a. more details about dimensions and reinforcement of the beam are in tab. 2. original properties of concrete are described in tab. 3. specific features were calculated in atena [10] using the recommended values. o. sucharda et alii, frattura ed integrità strutturale, 30 (2014) 375-382; doi: 10.3221/igf-esis.30.45 378 it follows from the test that the collapse in the beams without shear reinforcement occurs as a diagonal-tension failure. this is similar as in tests performed by bresler-scordelis. examples of the failures are shown in [19]. this also shows the process of testing and the collapse. numerical modelling he numerical modelling was performed in atena [10] which uses fem as a basis. that software includes a number of constitutive models of the concrete. it was decided to use a fracture-plastic material model for concrete and 2d computational models for the numerical analyses. considering the numerical calculations performed in [19], very similar calculation models of the beams were created. the calculation model is a regular mesh of four-node finite elements. the finite elements in the concrete form a grid: 16x46, 16x56 and 15x66. because the non-linear analysis depends much on the modelled boundary conditions, supports and loading plate from a linear elastic materials were also modelled. the calculation models were formed by a symmetric half of the real beams. in order to solve a system of non-linear equations, the newton-raphon method and deformation loads were chosen in atena [10]. fig. 3 shows the final calculation models. the reinforcement was included into the calculation model as a smeared reinforcement. beam oa1 beam oa2 beam oa3 figure 3: computer models of beam (oa1, oa2, oa3). the analysis focused on development of cracks during the loading, maximum bearing capacity pu and deformation wu. the calculations have been performed in two alternatives in tab. 4 a 5. the first alternative includes all properties of the concrete which are mentioned in tab. 3, while the second alternative takes the compressive strength of the concrete as a basis. the basis is the recommended values for standard concrete. the remaining values are calculated in atena [10]. the software calculates also the tensile strength and modulus of elasticity of concrete. those data are not so frequently available and their values are rather distributed in practical engineering. beam number ultimate load midspan deflection pu, test [kn] pu, calc [kn] pu, test /pu, calc wu, test [mm] wu, calc [mm] wu, test /wu, calc oa1 331 332 1.00 9.1 6.8 1.35 oa2 320 358 0.89 13.2 13.2 1.00 oa3 385 374 1.03 32.4 30.6 1.06 mean 0.97 mean 1.14 table 4: comparison of the numerical calculations and experiments – alternative 1. t o. sucharda et alii, frattura ed integrità strutturale, 30 (2014) 375-382; doi: 10.3221/igf-esis.30.45 379 beam number ultimate load midspan deflection pu, test [kn] pu, calc [kn] pu, test /pu, calc wu, test [mm] wu, calc [mm] wu, test /wu, calc oa1 331 315 1.05 9.1 6.7 1.37 oa2 320 308 1.04 13.2 11.2 1.18 oa3 385 334 1.15 32.4 24.5 1.32 mean 1.08 mean 1.29 table 5: comparison of the numerical calculations and experiments – alternative 2. load 48 kn oa1 load 224 kn oa1 load – collapse oa1 figure 4: failure in a beam, oa1. figure 5: load – displacement diagram for beams oa load 76 kn oa2 load 31 kn oa3 load 220 kn oa2 load 212 kn oa3 load collapse oa2 load collapse oa3 figure 6: failure in a beam. oa2 (left) and oa3 (right). fig. 5 shows the final comparison of work diagrams for the beams obtained in the numerical calculation. fig. 4 and 6 show three typical loading conditions where cracks develop in each beam. the first condition is development of cracks next to the lower edge of the beam. the second condition is development of tensile cracks along the lower edge immediately before creation of a shear crack. the third condition is a collapsing beam. stochastic modelling ehaviour of beams under load was analysed in detail in a stochastic modelling. the objective was to find out impacts of some input data which enter the calculation as a histogram onto the total bearing capacity. the stochastic modelling was carried out using lhs as a method and freet [7] as a software application. statistic parameters were described using the recommendations specified in jcss [12] and iso [11]. tab. 6 and 7 list the chosen b o. sucharda et alii, frattura ed integrità strutturale, 30 (2014) 375-382; doi: 10.3221/igf-esis.30.45 380 histogram parameters and cov for the input variables of concrete and steel. the initial value was the compressive strength of the concrete. tab. 8 shows the correlation matrix used for the concrete in the stochastic modelling. input ec fc ft gf distribution lognormal lognormal weibull weibull cov 0.15 0.10 0.18 0.2 table 6: material properties in the stochastic modelling concrete. input fy fu histogram lognormal lognormal cov 0.05 0.05 table 7: material properties in the stochastic modelling steel. input ec fc ft gf ec 1 0.7 0.9 0.5 fc 0.7032 1 0.8 0.9 ft 0.8972 0.7987 1 0.6 gf 0.5021 0.8991 0.6014 1 table 8: correlation matrix of concrete. figure 7: final histogram, estimate ultimate load. discussion he university of toronto tested the beams without shear reinforcement. three basic phases of load can be identified in working diagrams and photos published in [19]. it follows from the comparison of the working diagrams, photos and numerical calculations that these are the three basic phases of the loading process. at the beginning of the loading process, cracks appear at the lower edge in the middle of the span. then, shear cracks appear. they become dominant, until the beam collapses. the collapse occurs fast. in case of beams with a big span (oa2 and oa3), the crack is located towards the loading point and is almost horizontal. the crack propagates in places where the reinforcement is located. in each numerical calculation the final way of collapse in a beam was same as in the experiment. these were diagonaltension failures. the comparison of the total bearing capacity obtained in calculations and that obtained in experiments shows very good correlation for both the first and second alternatives. the medium values of pu, test /pu, calc are 0.97 and t o. sucharda et alii, frattura ed integrità strutturale, 30 (2014) 375-382; doi: 10.3221/igf-esis.30.45 381 1.08. in case of the maximum deformation the correlation was not so good. the mean value of wu, test /wu, calc for the first and second alternatives is 1.14 and 1.29, respectively. the conclusion, however, is that the results are satisfactory with respect to the input data. it follows from the results that the worst correlation was obtained for the oa1 beam for which the stochastic analysis was performed. fig. 7 shows the final estimate of the histogram for the total bearing capacity. it follows from the evaluation of the histogram data and comparison with results of the numerical analysis that the bearing capacity ranges in a rather interval from 204.8 kn until 368.4 kn, provided that normal distribution is assumed. the resulting histogram is assumed normal distribution, the mean value is 302.5 kn. it should be also pointed out that the results could be influenced by the modelling of supports and loads, by the size of the loading step or by the size of the finite element. conclusion he numerical analysis indicate that the calculations performed using the fracture-plastic material [9] for concrete describe the loading process of reinforced concrete beams without shear reinforcement very well, the final bearing capacity correlating well with the experiments. the maximum deformation of the beam also proved good correlation between the calculation and experiment. the calculation was, however, too sensitive to input properties of the concrete. this was the evaluation of results of the stochastic modelling where the final deformation and bearing capacity lied in a rather big interval. calculations which used the compressive strength of concrete only described well the real behaviour of a beam, with respect to the quantity of estimated input data. the results of the numeric calculation and stochastic modelling can be used in calculation in line with the proposed standards. with this procedure, it is, however, necessary to use a suitable the global safety limits for the design values. the authors will focus now on the stochastic modelling and probabilistic methods which include, for instance, [13], [15] and [16]. the reason is that the stochastic calculations take much time and this makes them inconvenient for wide use and for drawing conclusions. in general, the model of concrete describes well the total bearing capacity of a concrete beam and development of failure during loading. the reason for difference between the experiments and numerical analyses is probably approximation of specific parameters and uncertainty in input data. acknowledgement he works were supported from sources for conceptual development of research, development and innovations for 2014 at the všb-technical university of ostrava which were granted by the ministry of education, youths and sports of the czech republic. references [1] asce, finite element analysis of reinforced concrete, state of-the-art, (1982) 545. [2] bresler, b., scordelis, a. c., shear strength of reinforced concrete beams, journal of american concrete institute, 60 (1) (1963) 51-72. [3] ceb fip model code 1990: design code. by comite euro-international du beton, thomas telford, (1993). [4] ceb – fip model code 2010, first complete draft, draft model code. 1 (2010) [5] chen, w. f., plasticity in reinforced concrete. mc. new york, graw hill, (1982). [6] computer program atena: theory manual. praha, červenka consulting, (2000). [7] computer pragram freet (computer program for statistical, sensitivity and probabilistic analysis): theory manual. brno, (2002). [8] computer pragram freet (computer program for statistical, sensitivity and probabilistic analysis): user manual. brno, (2004). [9] červenka, j., papanikolaou, v. k., three dimensional combined fracture-plastic material model for concrete. int. j. plasticity, 24(12) (2008) 2192-2220. t t o. sucharda et alii, frattura ed integrità strutturale, 30 (2014) 375-382; doi: 10.3221/igf-esis.30.45 382 [10] červenka, v., červenka, j., pukl, r., atena a tool for engineering analysis of fracture in concrete, sadhanaacademy proceedings in engineering sciences, (2002) 485-492. [11] iso 2394 general principles on reliability for structures, iso (1998). [12] jcss: probabilistic model code. jcss working material [online], http://www.jcss.ethz.ch/, (2012) [13] králik, j., a rsm method for probabilistic nonlinear analysis of reinforced concrete bubbler tower structure integrity, in: proc. european safety and reliability conference, esrel 2009, reliability, risk and safety, theory and applications, crc press/a.balkema book, taylor francis group, prague, 2 (2009) 1369-1372. [14] kralik, j., kralik, j., seismic analysis of reinforced concrete frame-wall systems considering ductility effects in accordance to eurocode, engineering structures, 31(12) (2011) 2865-2872. [15] králik, j., deterministic and probabilistic analysis of steel frame bracing system efficiency. in: 4th international conference on mechanical and aerospace engineering, icmae 2013, applied mechanics and materials, 390 (2013)s 172-177. [16] krejsa, m., janas, p., čajka, r., using doproc method in structural reliability assessment. in: mechatronics and applied mechanics ii, pts 1 and 2, 2nd international conference on mechatronics and applied mechanics (icmam2012), applied mechanics and materiále. 300-301 (2013) 860-869. doi: 10.4028/www.scientific.net/amm.300-301.860. [17] novák, d., vořechovský, m., rusina, r., small-sample probabilistic assessment software freet,” icasp 9, in: 9th international conference on applications of statistics and probability in civil engineering, san francisco, usa, (2003) 91-96 [18] release 11 documentation for ansys, sas ip, inc., (2007). [19] vecchio, f. j., shim, w., experimental and analytical re–examination of classic concrete beam tests, asce j. of struct. eng., 130(3) (2004) 460-469. [20] rombach, g., anwendung der finite-elemente-methode im betonbau. 2. auflage. berlin, ernst & sohn, (2007). [21] sucharda, o., brožovský. j., bearing capacity analysis of reinforced concrete beams. international journal of mechanics, 7(3) (2013) 192-200. [22] willam, k., tanabe, t., finite element analysis of reinforced concrete structures, aci special publ. no. sp-205, 399 (2001). microsoft word numero_34_art_43 l. marsavina et alii, frattura ed integrità strutturale, 34 (2015) 387-396; doi: 10.3221/igf-esis.34.43 387 focussed on crack paths on the crack path under mixed mode loading on pur foams l. marsavina, e. linul, t. voiconi university politehnica timisoara, romania liviu.marsavina@upt.ro, tudor_2015@yahoo.com, linul_emanoil@yahoo.com d. m. constantinescu, d. a. apostol university politehnica bucharest, romania dan.constantinescu@upb.ro, apostolda@yahoo.com abstract. in this paper are presented the crack initiation angles obtained in polyurethane (pur) foams under mixed mode loading. closed cell rigid pur foams having three different densities 100, 145, and 300 kg/m3 were investigated. experiments were performed using asymmetric semi-circular bend and single edge crack specimens. the obtained crack initiation values were compared with four fracture criteria to introduce: maximum tensile stress, strain energy density, maximum energy release rate and equivalent stress intensity factor, and a good agreement was observed. this allow to conclude that the theoretical fracture criteria developed for solid material could be used with success to predict the crack propagation angles in cellular materials like pur foams. keywords. pur foams; crack path; mixed mode. introduction he main characteristics of polyurethane (pur) foams are lightweight, high porosity and good energy absorption capacity, [1,2]. one of the main application of foam materials is their utilization as cores in sandwich structures. of particular interest is the fracture toughness in mixed modes because foam cracking weaknesses the capacity of carrying load of the sandwich structure. there are several studies to determine the mode i fracture toughness and to investigate the influence of density, loading speed and loading direction [3-11]. a linear correlation between mode i fracture toughness kic and relative density of the foam was observed by danielsson [7] on pvc divinycell foams, viana and carlsson on diab h foams [8]. brittle fracture without yielding in mode i loading was observed by kabir et al. [9] for pvc and pur foams applying the procedure described by astm d5045. they investigated the effect of density, effect of specimen size, effect of loading rate and effect of cell orientation. density has a significant effect on fracture toughness, which increases more than 7 times when the foam density increases 3.5 times. burman [10] presented fracture toughness results for two commercial foams rohacell wf51 (density 52 kg/m3) and divinycell h100 (density 100 kg/m3). the mode i fracture toughness kic was obtained on single edge notch bending specimens and has values 0.08 mpam0.5 for wf51, respectively 0.21 mpam0.5 for h100. he also determined the mode ii fracture toughness using end-notch flexure (enf) specimen with values of 0.13 mpam0.5 for wf51, respectively 0.21 mpam0.5 for h100. poapongsakorn and carlsson [11] also presented fracture toughness results for pvc foams determined on three (tpb) and four point bending (fpb), investigating the cell size t l. marsavina et alii, frattura ed integrità strutturale, 34 (2015) 387-396; doi: 10.3221/igf-esis.34.43 388 and loading rate. their results show that the value of fracture toughness obtained in fpb loading configuration is higher with a factor of 2 comparing with those obtained on tpb. only few studies present the mixed mode fracture of polymeric foams, and only for pvc foams. hallsttröm and grenestedt [12] investigated mixed mode fracture of cracks and wedge shaped notches in expanded pvc foams. different types of specimens made of divinycell h100 were investigated and the non singular t-stress was considered in formulation of fracture criteria. it was concluded that for predominantly mode ii the use of t-stress improved the facture predictions. three different densities of pvc foams were investigated using a compact tensile specimen with arcan fixtures to produce mixed mode conditions, [13]. the ratio between mode ii and mode i fracture toughness kiic/kic was found to be between 0.4 and 0.65 depending on foam density. for mixed mode loading the richard fracture criterion gives better predictions of fracture limit and crack initiation angle. marsavina el. al. [14, 15] and linul et al. [16] presented results mixed mode fracture toughness of pur foams. they highlighted that the foam density is the major factor influencing fracture toughness, loading speed and loading direction having minor influence. the anisotropy of the foam was explained trough the cellular topology of foams. however, the crack initiation angle is less investigated [13, 15, 16]. present study assessed the theoretical fracture criteria for crack initiation angle in pur foam materials under mixed mode loading, using an asymmetric semi-circular bend and single edge crack specimens. analytical models for crack propagation he fracture initiation for a crack in-plane mixed mode conditions is described by:  the angle of crack initiation c,  a critical combination of stress intensity factors (ki and kii) and fracture toughness (kic) in the form:   , , 0i ii icf k k k (1) the four most used fracture criterion are summarized below. maximum tensile stress criterion (mts) erdogan and sih [17] criterion, based on maximum tensile stress, consider that crack initiation starts radially from the crack tip at an angle c perpendicular to the maximum tensile circumferential tensile stress ,max. the crack propagation becomes unstable when ,max reaches a critical value cr, which is a material parameter at a radius r:     ,max 2 ic cr k r (2) the equation for crack initiation angle and the relationship between stress intensity factors (sif's) ki, kii and fracture toughness kic for mts criterion are presented in tab. 1. condition mathematical formulation crack initiation angle           2 2 2 2 2 3 8 arccos 9 ii i i ii c i ii k k k k k k (3)  , ,i ii icf k k k         2 3cos cos sin 2 2 2 c c i ii c ick k k (4) table 1: the mts criterion. minimum strain energy density criterion (sed) sih [18] postulated that the fracture occurs in the direction where the strain energy density s is minimum, at a critical distance r0:     2 1 8 cr ics k (5) t l. marsavina et alii, frattura ed integrità strutturale, 34 (2015) 387-396; doi: 10.3221/igf-esis.34.43 389 with  the shear modulus,  for plane strain, for plane stress, and  is the poisson's ratio. based on sed criterion the crack initiation angle and the relation between ki, kii and kic are presented in tab. 3. condition mathematical formulation crack initiation angle                            2 2 2 sin 2 cos 1 2 cos ( 2 cos 1) 2sin sin 6 cos 1 0 i i ii ii k k k k (6)  , ,i ii icf k k k                                       2 2 2 1 1 cos cos 2 sin 2 cos 1 2 1 1 1 cos 1 cos 3 cos 1 c c i c c i ii c c c ii ic k k k k k (7) table 2: the sed criterion. table 3: the gmax criterion. condition mathematical formulation crack initiation angle                                                                                            2 2 2 2 22 2 2 2 2 32 1 6 sin cos 8 cos sin 10 sin cos 1 cos 3 1 4 sin cos (3 cos 1) 8 sin cos 9 5 cos 1 cos 3 1 1 ln 1 1 i i ii ii i i ii ii k k k k k k k k                                                                                       1 2 2 2 2 2 22 1 1 1 11 1 3cos 1 8 sin cos 9 5 cos 0 cos 3 i i ii iik k k k (9)  , ,i ii icf k k k                                   2 2 2 2 2 2 2 1 1 4 3 cos 1 1 3 cos 8 sin cos 9 5 cos c c cc c i i ii c c c ii ick k k k k (10) l. marsavina et alii, frattura ed integrità strutturale, 34 (2015) 387-396; doi: 10.3221/igf-esis.34.43 390 maximum energy release rate criterion (gmax) hussain et al. [19] postulate that the crack propagation initiates when the energy release rate g reaches a critical value gic and expressed the energy release rate g in terms of stress intensity factors of initial crack:     2 ' ic c ic k g g e (8) with e’=e young's modulus for plane stress, and e'=e/(1-2) for plane strain. the crack initiation angle could be found by solving eq. (9) from tab. 3, while the functional relationship between ki, kii and kic is represented by eq. (10). equivalent stress intensity factor criterion (esif) richard [20, 21] proposed a generalized fracture criterion, based on the equivalent stress intensity factor keq, which is defined as:     221 4 2 2 i eq i ii k k k k (11) with =kic/kiic. crack starts to propagate when keq reaches the fracture toughness of the material kic. for the crack initiation angle richard proposed an empirical expression (12), which represents a correlation with a considerable number of experiments. condition mathematical formulation crack initiation angle                   2 0 0155.5 83.4ii iic i ii i ii k k k k k k (12)  , ,i ii icf k k k    221 4 2 2 i i ii ic k k k k (13) table 4: the esif criterion. materials and methods materials rack propagation studies were performed on rigid pur foams having a closed cell microstructure. three foam densities, manufactured by necumer gmbh (germany), were investigated 100 kg/m3 (necuron 100), 145 kg/m3 (necuron 160) and 300 kg/m3 (necuron 301). a statistical analysis of the foams microstructure is presented in [14]. the main properties provided by the manufacturer are listed in tab. 5, [22]. according to the manufacturer the main applications of these foams are test models, draw dies, large volume models, back filling of moulds and patterns, and substructure for hard styling clay. property units of measure necuron 100 160 301 density kg/m3 100 145 300 temperature resistance 0c 120 120 65 compressive strength mpa 2 3 5 flexural strength mpa 1.5 2.5 6 table 5: material properties according to manufacturer [22] (approximate values). c l. marsavina et alii, frattura ed integrità strutturale, 34 (2015) 387-396; doi: 10.3221/igf-esis.34.43 391 determination of density the density determination of the considered foams was performed according with astm d 1622-03 [23]. a sartorius gd 503 class balance was used for the mass determination, and the dimensions of the specimens (84 x 35 x 10 mm) were measured using a digital caliper mitutoyo digimatic. fracture toughness determination and mixed mode loading tests the fracture toughness kic and kiic of pur foams were determined using two types of specimens: asymmetric semicircular bend (ascb) and single edge crack (sec), fig. 1. the choice of using these specimen types was that with the same shape is possible to produce from pure mode i loading to pure mode ii loading, and intermediate mixed modes only by changing the position s2 of one support for ascb specimens or by changing the loading direction  for sec specimens. the ascb specimen with radius r, which contains an edge crack of length a oriented normal to the specimen edge, loaded with a three point bend fixture, was proved to give a wide range of mixed modes from pure mode i (s1=s2) to pure mode ii (s1≠s2), only by changing the position of one support. the considered geometry of the specimen has: r=40 mm, a=20 mm, t=10 mm, s1 = s2=30 mm (for symmetric loading and mode i fracture toughness determination), 12 mm, 8 mm, 6 mm, 4 mm (for mixed mode loading) and s2=2.66 mm (for mode ii fracture toughness determination). the dimensions of the sec specimens were w = 75 mm, t = 8 mm and a = 33.75 mm and the loading angle was  = 00 for mode i tests, 300, 450, 600 for mixed mode loading, respectively  = 900 for mode ii tests. tests were carried out at room temperature (20 0c) on a 5 kn zwick proline testing machine, using displacement control with 2 mm/min loading speed, fig. 2. typical load displacement curves are shown in fig. 3: a. the effect of applied mixed mode on ascb specimens for the foam with density 145 kg/m3, and b. the influence of density on sec specimens loaded in mode i. all tested specimens show a linear behaviour and a brittle fracture, which was confirmed by the fact that no plastic deformations remain after testing. the determination of fracture toughness is presented in more detail in [14, 15] for ascb specimens and in [16] for sec specimens. the experimental results for density and fracture toughness of investigated foams are presented in tab. 6. it should be mentioned that the fracture toughness results are determined for specimens obtained in the rise direction (in plane). a discussion regarding the foams anisotropy is presented elsewhere, [14]. a. ascb specimen b. sec specimen figure 1: specimens used from fracture toughness and mixed mode loading tests. it could be observed that fracture toughness kic and kiic increases with density. the maximum relative differences between fracture toughness values obtained by ascb and sec specimens was 28% for foam with density 100 kg/m3 for mode ii, while minimum relative difference was obtained for the same density for kic 1.1%. also, it could be observed that the mode ii fracture toughness values are lower than the mode i ones for all foam densities and specimen type, with the exception of 300 kg/m3 foam density using ascb specimens. l. marsavina et alii, frattura ed integrità strutturale, 34 (2015) 387-396; doi: 10.3221/igf-esis.34.43 392 figure 2: experimental set up with details of ascb specimen in three point bending grips (top right), respectively with sec specimen in arcan grips (left and middle right). property units of measure necuron 100 160 301 density kg/m3 100.35±0.25* 145.53±0.22* 300.28±1.38* mode i fracture toughness (ascb) mpa·m0.5 0.087 0.131 0.372 mode ii fracture toughness (ascb) mpa·m0.5 0.049 0.079 0.374 mode i fracture toughness (sec) mpa·m0.5 0.088 0.108 0.337 mode ii fracture toughness (sec) mpa·m0.5 0.069 0.095 0.319 table 6: material properties determined experimentally (* standard deviation values). 0 50 100 150 200 0.0 0.5 1.0 1.5 2.0 2.5 3.0 l o a d [ n ] displacement [mm] 2.66 4 6 8 12 30 ascb specimens 145 kg/m3 density 0 50 100 150 200 250 300 350 0.0 0.5 1.0 1.5 2.0 2.5 l o a d [ n ] displacement [mm] 300 145 100 300 145 100 density [kg/m3] a) b) figure 3: typical load displacement curves: a) influence of applied mixed mode for ascb specimens; b) influence of density for sec specimens loaded in mode i. l. marsavina et alii, frattura ed integrità strutturale, 34 (2015) 387-396; doi: 10.3221/igf-esis.34.43 393 results and discussions his paper is focused on the determination the crack initiation angle and the obtained crack paths under mixed mode loading of pur foams. the obtained crack paths were digitized using a nikon d5100 digital camera. fig. 4 presents the crack paths for ascb specimens for six loading configurations: a. mode i, b.-e. mixed modes, f. mode ii. except for the mode i case, when the crack propagates like a straight line, all other cases show curvilinear crack paths. figure 4: crack paths resulted from testing ascb specimens. in fig. 5 the crack paths for sec specimens are shown. more straight crack trajectories resulted on testing the sec specimens for all loading configurations. a. 0 0c b. 0 0c c. 45 0c d. 0 0c e. 0 0c figure 5: crack paths resulted from testing sec specimens. figure 6: measurement of crack initiation angle. the crack initiation angle c was measured on each specimen using sigma scan pro software as the angle between the tangent (red line) to the crack at the initiation point and the crack initial direction (blue line) in fig. 6. fig. 7 presents the mean values and the range (minimum to maximum values) of the crack initiation angle c measured on the specimens versus applied mixed mode loading me = arctg(kii/ki) side by side with the predicted crack propagation angles by the four theoretical criteria. it could be observed that for predominantly mode i loadings me < 450 the measured values are in good agreement with the predicted ones. for predominantly mode ii loading (me > 450) the t l. marsavina et alii, frattura ed integrità strutturale, 34 (2015) 387-396; doi: 10.3221/igf-esis.34.43 394 experimental crack propagation angles differ from the predicted values. it can be also observed that the foam with density 300 kg/m3, with a microstructure close to a porous solid gives closer propagation angles to theoretical predictions (especially to mts and esif), developed for brittle solid materials. noury et al. [13] also found, investigating pvc foams in mixed mode loading, that mts criterion gives the closest crack initiation angles to experimental values. comparing the two type of specimens the crack initiation angles obtained on sec specimens are above those results for testing ascb specimens, and closer to the theoretical predictions. 0 15 30 45 60 75 90 0 15 30 45 60 75 90  c [d eg re es ] me [degrees] density 100 kg/m3 0 15 30 45 60 75 90 0 15 30 45 60 75 90  c [d eg re es ] me [degrees] density 145 kg/m3 a. density 100 kg/m3 b. density 145 kg/m3 0 15 30 45 60 75 90 0 15 30 45 60 75 90  c [d eg re es ] me [degrees] density 300 kg/m3 c. density 300 kg/m3 legend figure 7: comparison between experimental and theoretical crack initiation angles. in order to investigate the effect of density, the mean value of crack initiation angle is plotted versus the support position s2 for ascb specimens in fig. 8.a, respectively versus loading angle  for sec specimens, fig. 8.b. the crack initiation angles are slightly different for the investigated densities. this is more pronounced for ascb specimen, where maximum relative difference between densities 145 and 300 kg/m3 and mode ii loading (s2=2.66 mm) is 22.3%. the maximum relative difference for sec specimens was observed for loading angle = 300 is 7.2% and this could be considered in the range of experimental determination. conclusions rack initiation angle on mixed mode loading for pur foams of three different densities was investigated experimentally. two specimens ascb and sec were considered, which allow to produce mixed mode loading only by changing some loading configurations. the obtained values were compared with four most used fracture c l. marsavina et alii, frattura ed integrità strutturale, 34 (2015) 387-396; doi: 10.3221/igf-esis.34.43 395 criteria mts, sed, gmax, respectively esif, and a good agreement was observed. this allows to conclude that the theoretical fracture criteria developed for a solid material could be used with success to predict the crack propagation angles in cellular materials like pur foams. crack paths presented in figs. 4 and 5 show that crack initiates in mixed mode or mode ii, but grows to regain the symmetry and to eliminate mode ii. 0 10 20 30 40 50 60 70 80 90 2.66 4 6 8 12 30 c [ d eg re es ] support position s2 [mm] ascb specimens 100 145 300 density 0 10 20 30 40 50 60 70 80 90 0 30 45 60 90  c [d eg re es ] loading angle [degrees] sec specimens 100 145 300 density a. ascb specimens b. sec specimens figure 8: effect of density on crack initiation angle. acknowledgments his work was supported by a grant of the romanian national authority for scientific research, cncs – uefiscdi, project pn-ii-id-pce-2011-3-0456, contract number 172/2011. dr. e. linul was partially supported by the strategic grant posdru/159/1.5/s/137070 (2014) of the ministry of national education, romania, co-financed by the european social fund – investing in people, within the sectoral operational programme human resources development 2007-2013. dr. d.a. apostol was partially supported by the strategic grant posdru/ posdru/159/1.5/s/137390/ (2014) of the ministry of national education, romania, co-financed by the european social fund – investing in people, within the sectoral operational programme human resources development 20072013. references [1] gibson, l.j., ashby, m.f., cellular solids, structure and properties, second edition, cambridge university press, (1997). [2] srivastava, v., srivastava, r., on the polymeric foams: modeling and properties, j. mater. sci., 49 (2014) 2681-2692. [3] marsavina, l., fracture mechanics of foams, in h. altenbach, a. ochsner (eds.), cellular and porous materials in structures and processes, springer, wien, (2010) 1-46. [4] marsavina, l., constantinescu, d.m., failure and damage in cellular materials, in h. altenbach, t. sadowski (eds.), failure and damage analysis of advanced materials, springer, wien, (2015) 119-190. [5] huang, j.s., gibson, l.j., fracture toughness of brittle foams, acta metall. mater., 39 (1991) 1627-1636. [6] choi, s., sankar, b.v. fracture toughness of carbon foam, j. compos. mater., 37 (2003) 2101-2116. [7] danielsson, m., toughened rigid foam core material for use in sandwich construction, cell. polym., 15 (1996) 417435. [8] viana, g.m., carlsson, l.a., mechanical properties and fracture characterisation of cross-linked pvc foams, j. sandw. struct. mater., 4 (2002) 91-113. [9] kabir, m.e., saha, m.c., jeelani, s., tensile and fracture behavior of polymer foams, mat. sci. eng. a-struct., 429 (2006) 225-235. t l. marsavina et alii, frattura ed integrità strutturale, 34 (2015) 387-396; doi: 10.3221/igf-esis.34.43 396 [10] burman, m., fatigue crack initiation and propagation in sandwich structures, report no.98-29, stockholm (1998). [11] poapongsakorn, p., carlsson, l.a., fracture toughness of closed-cell pvc foams: effect of loading configuation and cell size, compos. struct., 102 (2013) 1-8. [12] hallstrom, s., grenestedt, j.l., mixed mode fracture of cracks and wedge shaped notches in expanded pvc foam, int. j. fract, 88 (1997) 343-358. [13] noury, p.m., shenoi r.a., sinclair, i., on mixed-mode fracture of pvc foam, i j fracture, 92 (1998) 131-151. [14] marsavina, l., constantinescu, d.m., linul, e., apostol, d.a., voiconi, t., sadowski, t., refinements on fracture toughness of pur foams, eng. fract. mech., 129 (2014) 54-66. [15] marsavina, l., constantinescu, d.m., linul, e., voiconi, t., apostol, d.a., sadowski, t., evaluation of mixed mode fracture for pur foams, procedia materials science, 3 (2014) 1342-1352. doi:10.1016/j.mspro.2014.06.217. [16] linul, e., voiconi, t., marsavina, l., determination of mixed mode fracture toughness of pur foams, structural integrity and life, 14 (2014) 87-92. [17] erdogan f., sih g. c., on the crack extension in plates under plane loading and transverse shear, j basic engng, 85 (1963) 519-525. [18] sih g. c., strain-energy-density factor applied to mixed mode crack problems, i j fract, 10 (1974) 305-321. [19] hussain m. a., pu s. l., underwood j., strain energy release rate for a crack under combined mode i and mode ii. in: fracture analysis, p.c. paris, g.r. irwin (edts), astm stp560, philadelphia, (1974) 2-28. [20] richard h. a., bruchvorhersagen bei uberlagreter normalund schubbeanspruchung von rissen, vdi-verlag, dusseldorf, (1985). [21] richard h. a., fulland m., sander m., theoretical crack path prediction, fatigue fract engng. mater. struct., 28 (2005) 3-12. [22] http://necumer.com/index.php/en/produkte-2/board-materials/modelling, (2014). [23] astm d1622-03 test method for apparent density of rigid cellular plastics. microsoft word numero_33_art_16 v. veselý et alii, frattura ed integrità strutturale, 33 (2015) 120-133; doi: 10.3221/igf-esis.33.16 120 focussed on characterization of crack tip fields multi-parameter approximation of stress field in a cracked specimen using purpose-built java applications v. veselý, j. sobek, d. tesař, p. frantík, t. pail brno university of technology, faculty of civil engineering, institute of structural mechanics, brno, czech republic vesely.v1@fce.vutbr.cz, sobek.j@fce.vutbr.cz, tesar.d1@study.fce.vutbr.cz, kitnarf@centrum.cz, pail.t@fce.vutbr.cz s. seitl academy of sciences of the czech republic, v. v. i., institute of physics of materials, brno, czech republic seitl@ipm.cz abstract. a quality of multi-parameter approximation of the stress and displacement fields around a crack tip in a non-brittle material test specimen is studied in the paper. the stress field approximation using williams power series is intended to be utilized for estimation of the nonlinear zone extent which potentially plays a role within methods for determination of true values of fracture parameters of materials exhibiting nonlinear failure. considering the fact that in the case of elastic-plastic and especially quasi-brittle materials the size of this zone is substantial in comparison to the specimen dimensions, it is necessary to take a large region around the crack tip into account for this task. an automatic utility created to determine the values of coefficients of the higher order terms of williams power series by usage of over-deterministic method applied on results of finite element analysis of arbitrary mode i test geometry is one of the tested procedures. the second one provides a backward reconstruction of the crack-tip stress field analytically by means of truncated williams expansion. the developed procedures are based on the support of java programming language and considerably simplify analyses of the mechanical fields’ description in a farther distance from the crack-tip. the presented research is focused on optimization of selection of fe nodal results for improvement of accuracy of the approximation. keywords. cracked specimen; near-crack-tip fields; williams expansion; higher order terms; stress field reconstruction; finite element analysis, java application. introduction he concept of fracture process zone (fpz) has been introduced into analysing fracture behaviour of nonlinearly failing (especially softening) materials already several decades ago [1-3]. estimation of the size, shape and other relevant properties of the fpz evolving at the tip of propagating crack in these materials is not commonly utilized within fracture analyses of these materials; however, the situation has changed recently. the fpz issue is also among the main goals of the presented research. this is motivated by the fact that fracture properties of softening materials exhibit strong size-dependence, know under the term size-effect, linked mainly to the mutual proportions of the internal length of their coarse material structure, the extent of their large fpz which varies during the crack propagation, and the structural dimensions. thus, properties of the fpz are prospected to be utilized, t v. veselý et alii, frattura ed integrità strutturale, 33 (2015) 120-133; doi: 10.3221/igf-esis.33.16 121 among others, within methods for evaluation of fracture parameters and subsequently the mechanical characterization of these materials. due to this effect (connected also with geometry and boundary effect), investigation the role of fpz in the fracture of quasi-brittle materials, particularly concrete, has attracted lot of interest from engineering community in the field of concrete fracture mechanics. for the fpz extent estimation, a precise description of the stress state in the cracked body is necessary. for that purpose, multi-parameter fracture mechanics is employed as the proportion of sizes of the fpz and the whole specimen is much larger in the case of the quasi-brittle materials than e.g. plastic zone in metals [4], and therefore the stress field farther from the crack trip must be described precisely. main focus of the contribution is on testing of two own developed automatic utilities; the first enables computation of values of coefficients of the higher order terms of williams power series using the over-deterministic method (odm) applied to results of fem analysis, the second provides analytical approximation of the stress field in the cracked body via truncated williams power expansion taking into account the values of coefficients of the higher order terms calculated using the first programmed application. from this point of view the latter utility provides a kind of backward reconstruction of the stress field analysed by fem and processed via odm. the influence of the number of terms considered for the power series reconstruction of stress field as well as the way of selection of the fem nodes for the calculation of the values of coefficients of those terms are investigated in the paper. verification of the overall analysis results is conducted on an example of the wedge splitting test specimen as it has become very frequently used in the field of testing of silicate-based composites (let us name e.g. [5-7] from recent period). multi-parameter fracture mechanics concept near-crack tip fields for mode i fracture problem he stress and displacement fields in a two-dimensional homogeneous elastic isotropic body with a crack loaded by an arbitrary remote loading can be expressed in a form of an infinite power series, the williams expansion [8]. for the stress tensor  and displacement vector u it holds:     1 2 , 1 , , , , 2 n ij n ij n n a r f n i j x y       (1) and    2 , 1 , , , , , n i n i u n u r a f n e i x y      (2) respectively, where r and θ are polar coordinates (with their beginning placed at the crack tip and the crack propagation direction corresponds with the x-axis), fij, and fi,u are known functions, e and  represent young’s modulus and poisson’s ratio. values of coefficients an depend on the cracked specimen geometry (crack length, specimen shape and boundary conditions) and they are usually determined numerically at present. typically, coefficients an are expressed as functions of the relative crack length  and transformed (normalized with respect to loading and appropriate power of the specimen’s dimension) into the form of dimensionless functions [9, 10] as follows    2 22 2 nom nom 4 ( ) for 1, 3, 4 , and ( ) n n n a a g w n n g t            (3) where nom is the nominal stress in the central plane of the specimen due to the applied load, w and b is the specimen’s width and breadth, respectively. the nominal stress is usually considered as being caused only by the splitting component psp of the load imposed to the specimen via the wedge (see fig. 1a, i.e. nom = psp/bw ), although it has been shown by the authors [11] that also the vertical component pv plays a significant role in many cases. note that the approximations of the individual stress tensor components presented further in this paper are expressed using truncated forms of the williams series. over-deterministic method computation of the values of the an coefficients of terms of the williams expansion is conducted using the technique solving the system of equations resulting from the displacement field expression in eq. (2) referred to as the overt v. veselý et alii, frattura ed integrità strutturale, 33 (2015) 120-133; doi: 10.3221/igf-esis.33.16 122 deterministic method (odm, [12-14]). basically, the odm is a linear least-squares formulated regression, it provides the solution of system of 2k equations, where k means the number of selected nodes around the crack tip, for first n selected terms of the power series. components of the displacement vector u a v in the selected nodes of the finite-element mesh and also their coordinates serve as inputs to this technique and values of the coefficients of the terms of the series an, where 1,n n present its outputs. in the case of this study, the number of the selected nodes k was set to 49 (due to keeping consistence with previous studies in [15, 16]) and maximal order of the williams series term was n = 12, so the system of equations was strongly over-determined (the condition of the over-determination is 2k > n). for the fe calculations the ansys computational software [17] was employed. own developed java applications odemapp he odm procedure has been implemented in java programming language [18] as a multi-platform and objectoriented computational tool, referred to as odemapp (over deterministic method application). design of each class of the software application came out from the requirement of transparency and further extensibility. it is a command line operated tool; the user specifies the path to external input files containing necessary fe parameters (the coordinates of selected nodes and their displacements) and additional input information (parameters of material and geometrical description of the test specimen) for performing the solution using the odm procedure. the program then allows defining the type of the solved 2d problem (plane strain or plane stress). in the next step the user enters the highest index of the williams series term up to which the coefficients shall be calculated. then the odm procedure takes place. the calculated values of an coefficients are eventually converted to their dimensionless form gn within this procedure. refrapro refrapro is a java application programmed for the advanced determination of the fracture characteristics of silicate-based materials failing in a quasi-brittle manner [19]. the tool reconstructs the progress of quasi-brittle fracture from the measured load-displacement curve and the knowledge of basic mechanical properties of the material (refrapro si an acronym for reconstruction of fracture process). the application implements a developed technique for estimation of the size and shape of the fpz [20-22]. the technique is based on an amalgamation of several modelling concepts dealing with the failure of structural materials, i.e. multi-parameter linear elastic fracture mechanics, classical non-linear fracture models for concrete (equivalent elastic crack and cohesive crack models), and the plasticity approach. the application utilizes the description of the stress field in a cracked body considering the higher order terms of the williams power expansion so that the field in a larger distance from the crack tip is well approximated. this description allows creating graphical representations of stress fields (presented below) for particular set of terms of william expansion which are used for this study of the dependency. this paper presents only the part of the application that deals with the analytical reconstruction of the stress field by means of the truncated williams series (similarly as in [23, 24]), other capabilities are presented in e.g. [19, 22]. study of the stress field in a body with crack – wedge splitting test specimen he wedge-splitting test (wst, [25-27]) specimen in one of its variant is used for the study – see fig. 1a. a cubeshaped specimen with the edge length of w = 100 mm is supported in two points and loaded through steel platens. specimen dimensions provided in fig. 1a are of following values: f = 30 mm, dn = 20 mm, h = 15 mm, wef = 85 mm, i = 25 mm. the crack length a is considered as the vertical distance from the crack tip to the loading bearings’s axles, i.e. a = c + dn – h. variable relative crack length ef/ 0.075; 0.95a w   with step of 0.025 is used to simulate stages of the progressive fracture through the specimen ligament. numerical model the created fe model of the studied test, namely its symmetrical half, with typical applied boundary conditions (the vertical and horizontal components of the applied load; fixed nodes in both directions at the support and perpendicular to the axis of symmetry along the ligament) is illustrated in fig. 1b. the test specimen is considered to be made of quasit t v. veselý et alii, frattura ed integrità strutturale, 33 (2015) 120-133; doi: 10.3221/igf-esis.33.16 123 brittle cementitious composite material, e.g. concrete, with modulus of elasticity e = 35 gpa and poisson’s ratio  = 0.2 and the loading platens of elastic isotropic material with e = 210 gpa,  = 0.3. the fe mesh of the task is formed from almost 70,000 fe nodes in order to enable fine enough nodal selection for the odm application in all directions from the crack tip. details of the fe mesh around the crack tip and the support is shown in fig. 1c and d. figure 1: a) used wst geometry, b) fe model (symmetrical half of the specimen with loading platen), c) and d) details of fe mesh. description of parametric study the parametric study is constructed in a way that shall reflect the two main issues of this research: i) which number of terms of the williams power series is suitable to consider for reconstruction of stress field in relevant fracture analyses and ii) how to determine the values of coefficients of those terms with sufficient accuracy. in both these issues the distance from the crack tip plays a significant role. the odemapp application is created for arbitrary number of nodes picked from the fe model; however, k was set to 49 in this study (explained above, adopted from [15, 16]). the space of the parametric study presented in the paper consists of several directions/axes. the basic two are formed by the radial and the tangential (using angular sections) way of fe nodes selection for the odm technique. the nodal selection concerning the angle range can be optional from 0° to 180° (in the case of the used symmetrical half of the specimen, i.e. 360° for the whole model). in this study, four sub-variants were considered as is shown on fig. 2a to d (representing models with different values of relative crack length ). particularly, the fig. 2a shows the case marked as 90°(10°) which describes sector of angular measure equal to 90° with initial side of the sector being rotated from the crack propagation direction by 10°. analogically, cases marked as 90°(45°), 90°(80°), and 180°(10°) are depicted in fig. 2b, c and d, respectively. note that especially in the cases 90°(10°) and 90°(80°) the sectors are oriented to directions, where boundary conditions are imposed, i.e. in the case of 90°(10°) towards the groove with loading platens and the 90°(80°) case to support on the bottom surface. for the distance distribution of the nodal selection, three options are considered in this study: the constant (f(x) = const., marked as con), the quadratic (f(x) = x2, marked as qua) and the exponential (f(x) = ex, marked as exp) function. for clarity, the distributions are sketched in fig. 2 as well to complete the graphical description of the conducted study. particular expression of the functions depends on the chosen number of nodes within the length interval between the crack tip and the boundary for individual directions. in this case four nodes, i.e. nodes in four layers from the crack tip, were chosen. thus, altogether 12 cases of the fe nodes selection are taken into account in the study: four cases of tangential selection × three cases of radial distribution. selection of nodes whose state variables’ values (displacements) are used within the odm technique for calculation of the values of coefficients of the higher order terms of the williams series is performed from a regular fe mesh (see fig. 1c and d). the procedure of selection of the nodes according to the two above-described criteria was programmed within the post-processing of results in the used ansys computational software. coordinates and displacements of the selected nodes for each considered nodal selection case (for a model of each value of relative crack length) are written in a text file after the run of fe analysis. these created data files are then loaded into odemapp and processed. a) b) c) d) v. veselý et alii, frattura ed integrità strutturale, 33 (2015) 120-133; doi: 10.3221/igf-esis.33.16 124 several examples of the nodal selection are shown in fig. 3 – the selected fe nodes are displayed as dots within the modelled specimen body. n o da l d is ta n ce length interval constant distribution n o da l d is ta n ce length interval x2 distribution n o da l d is ta n ce length interval ex distribution a) angle selection with 90° wedge, initial angle 10°,  = 0.45 b) angle selection with 90° wedge, initial angle 45°,  = 0.3 c) angle selection with 90° wedge, initial angle 80°,  = 0.55 d) angle selection with 180° wedge, initial angle 0°,  = 0.7 distance selection with: e) constant, f) quadratic, and g) exponential distribution figure 2: variants of selection of nodes within an angle range and distance from the crack tip. a) constant distance distribution, 90° wedge, initial angle 10°,  = 0.3 b) exponential distance distribution, 90° wedge, initial angle 45°,  = 0.5 c) quadratic distance distribution, 90° wedge, initial angle 80°,  = 0.3 d) constant distance distribution, 180° wedge, initial angle 0°,  = 0.5 figure 3: examples of performed nodal selection within the fe model. results and discussion geometry functions ig. 4 shows the results from the odemapp procedure, the dimensionless values of williams terms coefficients gn (for 1;12n  ) as functions of the relative crack length  determined for all considered variants of nodal selection. it can be seen that trends of the g-functions for individual nodal selection variants are not uniform, especially in the cases of short and long cracks (the short cracks are represented by  < 0.2 and the long ones by  > 0.8). in the case of short cracks the 90°(10°) variants significantly differ from the rest. on the other hand, the 90°(80°) variants exhibit different trends in the long cracks region, especially for n > 6 (see fig. 4g to l). the nodal distance distribution function also plays a role; there can be seen a substantial difference between the exponential distribution in comparison f 90° 10° 45° 90° 90° 180° 80° 0° a) b) c) d) e) f) g) a) b) c) d) qua, 90° (80°)exp, 90° (45°)con, 90° (10°) con, 180° (0°) v. veselý et alii, frattura ed integrità strutturale, 33 (2015) 120-133; doi: 10.3221/igf-esis.33.16 125 with the other two variants. the most suitable distribution function of nodal selection is the constant one – it seems to be best for the majority of angle selections. the most stable angle selection variant is 180° (0°). these statements are in consistence with fig. 5 where the g-functions with stable progress are kept while the fluctuating variants are deleted. the selection of variants that are regarded as incorrect was based only on visual judgement, no rigorous criterion was applied. however, according to opinion of the authors, such an approach is sufficient for the presented study. it can be stated that: the way of angular selection of nodes has greater effect than the distance distribution function for the progress of g-functions captured by the following graphs in fig. 4 and 5; the progress of g-function is strongly influenced by the used type of distance distribution and the place of interest (determined by the initial angle, the selection sector and the relative crack length). in this aspect the results are in accordance with the conclusions in [16]; this is the reason for choosing three different values of  for stress the field analysis using the refrapro application. note that the fe model, before it was used for evaluation of the stress field via odm, was successfully verified for the value of the first term of william expansion in previous works (e.g. [28]) via its comparison to results from literature [9, 10, 29, 30]. stress field reconstruction by means of truncated williams series for presentation of the stress fields approximation using the refrapro application, three values of the relative crack length were selected to cover the whole interval, from the short cracks with  = 0.25, the middle ones with  = 0.5, and the long ones with  = 0.75. results of this rather thorough numerical study on the stress fields’ approximation are displayed in figs. 6 to 11. contour plots of the 1 principal stress and the normal stress components (in this case marked as yy because of rotated coordinate system) are displayed; they were taken into account as they might serve as the equivalent stress thresholds in the simplest failure condition for estimation of the nonlinear zone (plastic zone) extent. nomenclature in tables in these figures is as follows: main columns represent the number of the higher-order terms (variants with n = 1, 2, 4, 7, 11 were selected) considered for the backward reconstruction of stress field by refrapro application. each of these columns has three sub-columns for the considered nodal distance distribution functions (con, qua, exp); rows represent the angle selection variants (90°(10°), 90°(45°), 90°(80°), 180°(0°)). in the left column, a corresponding finite-element solution using ansys software (considered as the exact one, or in other words that one which takes into account theoretically infinite number of william series terms) is given for comparison. it is obvious from fig. 6 that variants of nodal selection have almost no effect on the stress field reconstruction if only first or first two terms were taken into account. therefore, contour plots of the selected stress tensor components calculated for n = 4, 7, 11 are in shown figs. 7 to 11. the contour plots provided by both tools, the ansys fe software and the refrapro application, are created for the same load (psp = 2.9 kn considering the wedge slope angle equal to 15°). the stress scale is uniform for all displayed contour plots: grey colour for values < 0 mpa, blue for interval (0;0.5) mpa, cyan for (0.5;1.25) mpa, green for (1.25;2.5) mpa, yellow for (2.5;5.0) mpa and red for values > 5 mpa. discussion of the results of the stress field reconstruction is based again only on the visual comparison of the contour plots in this paper. it is intended to apply a suitable method for the inaccuracy quantification in further research. after detailed observations of the results, it can be stated that: determination of a particular number of terms that allows a correct enough approximation of the stress field is tricky in a real case since it depends also on the distance from the crack tip at which the field is characterized. using a low number of parameters, for example only the first two parameters, the stress intensity factor (corresponding to g1) and the t-stress (g2), the area of reasonably accurate approximation is very small, see the red colour contour in the vicinity of crack tip for n = 1 or 2 (in fig. 6). if the knowledge of stress field from a larger distance of the crack tip is necessary, one must take into account several terms of the williams power series. however, it’s not possible to determine a certain number, because it depends, particularly in the studied wst specimen, on the relative crack length, the investigated component of the stress tensor and the distance from the crack tip. it can be expected that it is dependent also on the shape and boundary conditions of the cracked body. but generally for this study, the number of terms should be greater than 4. considering the facts from previous paragraph, it is evident that the attention should be paid to the choice of the nodal selection. from the g-function graphs can be seen that the usage of nodal selection from the whole test specimen with constant distance distribution provides the most stable and accurate results. v. veselý et alii, frattura ed integrità strutturale, 33 (2015) 120-133; doi: 10.3221/igf-esis.33.16 126 0 10 20 30 40 0 0.2 0.4 0.6 0.8 g1 [] � [-] con 180° (0°) con 90° (10°) con 90°(45°) con 90° (80°) qua 180° (0°) qua 90° (10°) qua 90° (45°) qua 90° (80°) exp 180° (0°) exp 90° (10°) exp 90° (45°) exp 90° (80°) -20 0 20 40 60 80 100 0 0.2 0.4 0.6 0.8 g2 [] � [-] con 180° (0°) con 90° (10°) con 90° (45°) con 90° (80°) qua 180° (0°) qua 90° (10°) qua 90° (45°) qua 90° (80°) exp 180° (0°) exp 90° (10°) exp 90° (45°) exp 90° (80°) -250 -200 -150 -100 -50 0 0 0.2 0.4 0.6 0.8 g3 []  [-] con 180° (0°) con 90° (10°) con 90° (45°) con 90° (80°) qua 180° (0°) qua 90° (10°) qua 90° (45°) qua 90° (80°) exp 180° (0°) exp 90° (10°) exp 90° (45°) exp 90° (80°) a): dimensionless g1 function b): dimensionless g2 function c): dimensionless g3 function -25 0 25 50 75 100 125 150 0 0.2 0.4 0.6 0.8 g4 [] � [-] con 180° (0°) con 90° (10°) con 90° (45°) con 90° (80°) qua 180° (0°) qua 90° (10°) qua 90° (45°) qua 90° (80°) exp 180° (0°) exp 90° (10°) exp 90° (45°) exp 90° (80°) -400 -300 -200 -100 0 0 0.2 0.4 0.6 0.8 g5 [] � [-] con 180° (0°) con 90° (10°) con 90° (45°) con 90° (80°) qua 180° (0°) qua 90° (10°) qua 90° (45°) qua 90° (80°) exp 180° (0°) exp 90° (10°) exp 90° (45°) exp 90° (80°) -100 100 300 500 700 0 0.2 0.4 0.6 0.8 g6 [] � [-] con 180° (0°) con 90° (10°) con 90° (45°) con 90° (80°) qua 180° (0°) qua 90° (10°) qua 90° (45°) qua 90° (80°) exp 180° (0°) exp 90° (10°) exp 90° (45°) exp 90° (80°) d): dimensionless g4 function e): dimensionless g5 function f): dimensionless g6 function -1500 -1250 -1000 -750 -500 -250 0 250 0 0.2 0.4 0.6 0.8 g7 [] � [-] con 180° (0°) con 90° (10°) con 90° (45°) con 90° (80°) qua 180° (0°) qua 90° (10°) qua 90° (45°) qua 90° (80°) exp 180° (0°) exp 90° (10°) exp 90° (45°) exp 90° (80°) -500 0 500 1000 1500 0 0.2 0.4 0.6 0.8 g8 [] � [-] con 180° (0°) con 90° (10°) con 90° (45°) con 90° (80°) qua 180° (0°) qua 90° (10°) qua 90° (45°) qua 90° (80°) exp 180° (0°) exp 90° (10°) exp 90° (45°) exp 90° (80°) -5000 -4000 -3000 -2000 -1000 0 1000 0 0.2 0.4 0.6 0.8 g9 [] � [-] con 180° (0°) con 90° (10°) con 90° (45°) con 90° (80°) qua 180° (0°) qua 90° (10°) qua 90° (45°) qua 90° (80°) exp 180° (0°) exp 90° (10°) exp 90° (45°) exp 90° (80°) g): dimensionless g7 function h): dimensionless g8 function i): dimensionless g9 function -2000 0 2000 4000 6000 0 0.2 0.4 0.6 0.8 g1 0 [] � [-] con 180° (0°) con 90° (10°) con 90° (45°) con 90° (80°) qua 180° (0°) qua 90° (10°) qua 90° (45°) qua 90° (80°) exp 180° (0°) exp 90° (10°) exp 90° (45°) exp 90° (80°) -9000 -6000 -3000 0 3000 0 0.2 0.4 0.6 0.8 g 11 [] � [-] con 180° (0°) con 90° (10°) con 90° (45°) con 90° (80°) qua 180° (0°) qua 90° (10°) qua 90° (45°) qua 90° (80°) exp 180° (0°) exp 90° (10°) exp 90° (45°) exp 90° (80°) -5000 0 5000 10000 15000 20000 0 0.2 0.4 0.6 0.8 g1 2 [] � [-] con 180° (0°) con 90° (10°) con 90° (45°) con 90° (80°) qua 180° (0°) qua 90° (10°) qua 90° (45°) qua 90° (80°) exp 180° (0°) exp 90° (10°) exp 90° (45°) exp 90° (80°) j): dimensionless g10 function k): dimensionless g11 function l): dimensionless g12 function figure 4: dimensionless values of gn as functions of the relative crack length determined by odm; plots of all considered variants of the node selection are displayed. v. veselý et alii, frattura ed integrità strutturale, 33 (2015) 120-133; doi: 10.3221/igf-esis.33.16 127 0 10 20 30 40 0 0.2 0.4 0.6 0.8 g1 [] [-] con 180° (0°) con 90° (10°) con 90°(45°) con 90° (80°) qua 180° (0°) qua 90° (10°) qua 90° (45°) qua 90° (80°) exp 180° (0°) exp 90° (10°) exp 90° (45°) exp 90° (80°) -20 0 20 40 60 80 0 0.2 0.4 0.6 0.8 g 2 []  [-] con 180° (0°) qua 180° (0°) exp 180° (0°) exp 90° (10°) -250 -200 -150 -100 -50 0 0 0.2 0.4 0.6 0.8 g 3 []  [-] con 180° (0°) con 90° (10°) con 90° (45°) qua 180° (0°) qua 90° (10°) qua 90° (45°) exp 180° (0°) exp 90° (10°) exp 90° (45°) a): dimensionless g1 function b): dimensionless g2 function c): dimensionless g3 function -20 0 20 40 60 80 100 120 0 0.2 0.4 0.6 0.8 g 4 []  [-] con 180° (0°) con 90° (45°) qua 180° (0°) qua 90° (45°) exp 180° (0°) -400 -300 -200 -100 0 0 0.2 0.4 0.6 0.8 g 5 []  [-] con 180° (0°) con 90° (10°) con 90° (45°) qua 180° (0°) qua 90° (45°) exp 180° (0°) -100 100 300 500 700 0 0.2 0.4 0.6 0.8 g 6 [] � [-] con 180° (0°) con 90° (45°) qua 180° (0°) qua 90° (45°) exp 180° (0°) exp 90° (45°) d): dimensionless g4 function e): dimensionless g5 function f): dimensionless g6 function -1500 -1250 -1000 -750 -500 -250 0 0 0.2 0.4 0.6 0.8 g 7 []  [-] con 180° (0°) con 90° (10°) con 90° (45°) qua 180° (0°) qua 90° (45°) exp 180° (0°) exp 90° (45°) -300 0 300 600 900 1200 1500 0 0.2 0.4 0.6 0.8 g 8 []  [-] con 180° (0°) con 90° (10°) con 90° (45°) qua 180° (0°) qua 90° (45°) exp 90° (45°) -5000 -4000 -3000 -2000 -1000 0 0 0.2 0.4 0.6 0.8 g 9 []  [-] con 180° (0°) con 90° (10°) con 90° (45°) qua 180° (0°) exp 180° (0°) g): dimensionless g7 function h): dimensionless g8 function i): dimensionless g9 function -1000 1000 3000 5000 7000 0 0.2 0.4 0.6 0.8 g 10 []  [-] con 180° (0°) con 90° (45°) qua 180° (0°) exp 180° (0°) -10000 -7500 -5000 -2500 0 0 0.2 0.4 0.6 0.8 g 11 []  [-] con 180° (0°) con 90° (45°) qua 180° (0°) exp 180° (0°) -2500 2500 7500 12500 17500 0 0.2 0.4 0.6 0.8 g 12 []  [-] con 180° (0°) con 90° (10°) con 90° (45°) qua 180° (0°) exp 180° (0°) j): dimensionless g10 function k): dimensionless g11 function l): dimensionless g12 function figure 5: dimensionless values of gn as functions of the relative crack length determined by odm; only plots of variants of the node selection without a significant error are displayed. v. veselý et alii, frattura ed integrità strutturale, 33 (2015) 120-133; doi: 10.3221/igf-esis.33.16 128 fem n = 1 n = 2 n = 4 n = 7 n = 11 con. qua. exp. con. qua. exp. con. qua. exp. con. qua. exp. con. qua. exp. 90 ° (1 0° ) 90 ° (4 5° ) 90 ° (8 0° ) 18 0° ( 0° ) figure 6: contour plots of the approximation of 1 principal stress in the test specimen with the relative crack length  = 0.25 for all the considered variants of the nodal selection and number of williams series terms n = 1, 2, 4, 7, 11 compared to the fem solution. conclusions n the present work, issues regarding the stress field approximation around the crack tip in a 2d body loaded in mode i are discussed. two own developed java applications are utilized for the task; one (odemapp) for determination of the values of coefficients of the williams power series terms from results of fem analysis using a square-root regression based technique, the second (refrapro) for reconstruction of the crack-tip fields via the williams series considering the values of the terms coefficients determined using the former one. these developed software tools are employed with convenience in a study concerning the way of selection of the nodal results from the fem solution on the quality of the stress field capturing (using odemapp) and reconstruction (using refrapro). several variants of way of for selecting of the nodes were compared and discussed with regard to accuracy of the stress field approximation. significant advantages of the usage of multi-parameter description in the analysis of the stress field are reported; large errors of the approximation caused by a limited number of terms are demonstrated. results of this study have significant implications to intentions on estimations of the fpz extents in quasi-brittle materials. the technique of the fpz estimation implements the crucial parts of the above-mentioned procedure; functioning of the technique is currently being verified via numerical simulations of the fracture process in the test specimens by means of a lattice-particle (spring network) model and is planned to be validated with the help of acoustic emission technique and/or dynamical x-ray radiography in future research. acknowledgements inancial support from the czech science foundation (projects no. 13-09518s and no. 15-07210s) is gratefully acknowledged. this paper has been worked out under the “national sustainability programme i” project “admas up – advanced materials, structures and technologies” (no. lo1408) supported by the ministry of education, youth and sports of the czech republic. i f v. veselý et alii, frattura ed integrità strutturale, 33 (2015) 120-133; doi: 10.3221/igf-esis.33.16 129 fem n = 4 n = 7 n = 11 con. qua. exp. con. qua. exp. con. qua. exp. 90 ° (1 0° ) 90 ° (4 5° ) 90 ° (8 0° ) 18 0° ( 0° ) figure 7: contour plots of the approximation of 1 principal stress in the test specimen with the relative crack length  = 0.5 for all the considered variants of the nodal selection and number of williams series terms n = 4, 7, 11 compared to the fem solution. references [1] mindess, s., fracture process zone detection. in: shah sp, carpinteri a, (eds.) fracture mechanics test methods for concrete, london: chapman & hall; (1991) 231–61. [2] shah, s.p., swartz, s.e., ouyang, c., fracture mechanics of structural concrete: applications of fracture mechanics to concrete, rock, and other quasi-brittle materials, new york: john wiley & sons, inc; (1995). [3] karihaloo, b.l., fracture mechanics and structural concrete, new york: longman; (1995). [4] anderson, t. l., fracture mechanics: fundamentals and applications, new york, crc press, (1995). [5] merta, i., tschegg, e.k., fracture energy of natural reinforced concrete, const. build. mat., 40 (2013) 991–997. [6] korte, s., boel, v., de corte, w., de schutter, g., static and fatigue fracture mechanics properties of selfcompacting concrete using three-point bending tests and wedge-splitting tests, const. build. mat, 57 (2014) 1–8. [7] cifuentes, h., karihaloo, b., determination of size/independent specific fracture energy of normaland highstrength self/compacting concrete from wedge splitting tests. const. build. mat., 48 (2013) 548–553. [8] williams, m.l., on the stress distribution at the base of a stationary crack. j. appl. mech. (asme), 24 (1957) 109– 114. v. veselý et alii, frattura ed integrità strutturale, 33 (2015) 120-133; doi: 10.3221/igf-esis.33.16 130 fem n = 4 n = 7 n = 11 con. qua. exp. con. qua. exp. con. qua. exp. 90 ° (1 0° ) 90 ° (4 5° ) 90 ° (8 0° ) 18 0° ( 0° ) figure 8: contour plots of the approximation of 1 principal stress in the test specimen with the relative crack length  = 0.75 for all the considered variants of the nodal selection and number of williams series terms n = 4, 7, 11 compared to the fem solution. [9] karihaloo, b.l., abdalla, h., xiao, q.z., coefficients of the crack tip asymptotic field for wedge splitting specimen, engng. fract. mech., 70 (2003) 2407–2420. [10] karihaloo, b.l., xiao, q.z., higher order terms of the crack tip asymptotic field for a wedge-splitting specimen. int. j. fract., 112 (2001) 129–137. [11] veselý, v., bedáň, j., sobek, j., seitl, s., work of fracture due to compressive component of loading in wedge splitting test on quasi-brittle cementitious specimens, key eng. mat., 627 (2015) 317–320. [12] ayatollahi, m.r., nejati, m., an over-deterministic method for calculation of coefficients of crack tip asymptotic field from finite element analysis, fatigue fract. engng. mater. struct., 34 (2010) 159–176. [13] šestáková (malíková), l. how to enhance efficiency and accuracy of the over-deterministic method used for determination of the coefficients of the higher-order terms in williams expansion, appl. mech. mater., 245 (2013) 120–125. [14] šestáková (malíková), l., veselý, v., convergence study on application of the over-deterministic method for determination of near-tip fields in a cracked plate loaded in mixed-mode, appl. mech. mater., 249–250 (2013) 76–81. [15] veselý, v., sobek, j., šestáková, l., seitl, s., accurate description of near-crack-tip fields for the estimation of inelastic zone extent in quasi-brittle materials, key eng. mat., 525–526 (2013) 529–532. v. veselý et alii, frattura ed integrità strutturale, 33 (2015) 120-133; doi: 10.3221/igf-esis.33.16 131 fem n = 4 n = 7 n = 11 con. qua. exp. con. qua. exp. con. qua. exp. 90 ° (1 0° ) 90 ° (4 5° ) 90 ° (8 0° ) 18 0° ( 0° ) figure 9: contour plots of the approximation of yy stress in the test specimen with the relative crack length  = 0.25 for all the considered variants of the nodal selection and number of williams series terms n = 4, 7, 11 compared to the fem solution. [16] sobek, j., pail, t., veselý, v., evaluation of crack tip stress field using combination of advanced implementation of over-deterministic method and fe analysis, key eng. mat., 627 (2015) 273–276. [17] ansys program documentation. user’s manual version 11.0. swanson analysis system, inc., houston (2007). [18] javatm. programming language. http://www.java.com/en/about/. [19] veselý, v., frantík, p., an application for the fracture characterization of quasi-brittle materials taking into account fracture process zone influence, adv. eng. softw., 72 (2014) 66–76. [20] veselý, v., frantík, p., reconstruction of a fracture process zone during tensile failure of quasi-brittle materials, appl. comp. mech., 4 (2010) 237–50. [21] veselý, v., frantík, p., keršner, z., cracked volume specified work of fracture. in: topping b.h.v., costa neves l.f., barros r.c. (eds.), in: proceedings of the 12th int. conf. on civil, structural and environmental engineering computing. stirlingshire: civil-comp press (2009). [22] frantík, p., veselý, v., keršner, z., parallelization of lattice modelling for estimation of fracture process zone extent in cementitious composites, adv. eng. softw., 60-61 (2013) 48–57. [23] veselý, v., sobek, j., šestáková, l., frantík, p., multi-parameter crack tip stress state description for estimation of fracture process zone extent in silicate composite wst specimen, frattura ed integrità strutturale, 25 (2013) 69–78. v. veselý et alii, frattura ed integrità strutturale, 33 (2015) 120-133; doi: 10.3221/igf-esis.33.16 132 fem n = 4 n = 7 n = 11 con. qua. exp. con. qua. exp. con. qua. exp. 90 ° (1 0° ) 90 ° (4 5° ) 90 ° (8 0° ) 18 0° ( 0° ) figure 10: contour plots of the approximation of yy stress in the test specimen with the relative crack length  = 0.5 for all the considered variants of the nodal selection and number of williams series terms n = 4, 7, 11 compared to the fem solution. [24] veselý, v., frantík, p., sobek, j., malíková (šestáková), l., seitl, s., multi-parameter crack tip stress state description for estimation of nonlinear zone width in silicate composite specimens in component splitting/bending test geometry, fatigue fract. engng. mater. struct., 38(2) (2014) 200-214, doi: 10.1111/ffe.12170. [25] tschegg, e.k. equipment and appropriate specimen shapes for tests to measure fracture values, austrian patent at no. 390328, austrian patent office, austria, 31. 1. 1986. [26] linsbauer, h.n., tschegg, e.k., fracture energy determination of concrete with cube-shaped specimens, zement und beton, 31 (1986) 38–40. [27] brühwiler, e., wittmann, f.h., the wedge splitting test, a new method of performing stable fracture mechanics test, engng. fract. mech., 35 (1990) 117–125. [28] seitl, s., veselý, v., řoutil, l., two-parameter fracture mechanical analysis of a near-crack-tip stress field in wedge splitting test specimens, comp. struct., 89 (2011) 1852–1858. [29] guinea, g.v., elices, m., planas, j., stress intensity factors for wedge-splitting geometry, int. j. fract., 81 (1996) 113– 124. [30] tada, h., paris, p.c., irwin, g.r., the stress analysis of cracks handbook, 3rd ed. bury st. edmunds, uk: professional engineering publishing, ltd., (2000). v. veselý et alii, frattura ed integrità strutturale, 33 (2015) 120-133; doi: 10.3221/igf-esis.33.16 133 fem n = 4 n = 7 n = 11 con. qua. exp. con. qua. exp. con. qua. exp. 90 ° (1 0° ) 90 ° (4 5° ) ;9 0° ( 80 °) 18 0° ( 0° ) figure 11: contour plots of the approximation of yy stress in the test specimen with the relative crack length  = 0.75 for all the considered variants of the nodal selection and number of williams series terms n = 4, 7, 11 compared to the fem solution. microsoft word numero_56_art_17_2991 k.c. nehar et alii, frattura ed integrità strutturale, 56 (2021) 203-216; doi: 10.3221/igf-esis.56.17 203 experimental study and modeling of the mechanical behavior of recycled aggregates-based high-strength concrete kheira camellia nehar laboratory of mechanics and materials development at the university of djelfa, pobox 3117, 17000 djelfa algeria camellia90@hotmail.fr , c.nehar@univ-djelfa.dz , https://orcid.org/0000-0002-9188-2496 dalila benamara laboratory of civil engineering at the university of djelfa, pobox 3117, 17000 djelfa algeria benamaradalila2018@gmail.com , d.benamra@univ-djelfa.dz abstract. the concrete constitutes a material of prime importance which is widely used in different works and infrastructures. among the raw materials component the concrete are the aggregates which take the first place. it is widely acknowledged that the consumption of natural aggregates increases with the growth in the amount of concrete needed. it has recently emerged that concrete waste can be recycled and reused in civil engineering works after a series of treatments. moreover, in order to protect the environment and based on the principles of sustainable development, it was considered urgent to produce a high strength concrete incorporating recycled materials in addition to silica fume and a high-efficiency superplasticizer. this would certainly help to establish a harmonious sustainable development that guaranties the ecological balance and environmental protection, and prevents the depletion of natural resources. this study is part of a larger research program that that seeks to recover, recycle and valorize construction and demolition wastes. the main objective sought in this article is firstly to use aggregates from demolition concrete in the manufacture of a new concrete with high mechanical and rheological performance, and secondly, to model the behavior of this type of concrete using the finite element method. this modeling aims to evaluate the maximum compressive strengths and compare them with those obtained experimentally. keywords. high strength concrete; recycled aggregates; environment; modelization; finite element method. citation: nehar, k.c.., benamara d., experimental study and modeling of the mechanical behavior of recycled aggregatesbased high-strength concrete, frattura ed integrità strutturale, 56 (2021) 203-216. received: 19.01.2021 accepted: 18.03.2021 published: 01.04.2021 copyright: © 2021 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. https://youtu.be/bsklrmifwea k.c. nehar et alii, frattura ed integrità strutturale, 56 (2021) 203-216; doi: 10.3221/igf-esis.56.17 204 introduction he refurbishment and reconstruction of civil engineering works produce enormous amounts of waste every year. algeria, like many other countries around the world, produces between 20 and 30 million tons of demolition debris per year [1]. considering the accelerated depletion of building material resources, in addition to the new economic, environmental, and political requirements, it has been necessary to envisage recycling waste building materials with a view to using them as substitute materials to manufacture a new type of concrete. in general, many substitute aggregates have been developed through recycling throughout the world in order to preserve the natural aggregates which are constantly decreasing. the first quality benchmark in this field dates from the second world war (nixon, 1977). the two most important and interactive points in these studies are the fields of application of recycled concrete waste and their classification with respect to their quality. recycled materials, sometimes called secondary materials, are numerous and this is why it has become urgent to classify them according to their characteristics [2]. various types of recyclable materials are currently used in civil engineering applications. these include, recycled concrete, fly and bottom ash, blastfurnace slag, steel slag, cement kiln dust, silica fume, crushed glass, reclaimed asphalt pavement, and rice husk ash. reutilization of these recyclable materials is especially beneficial in civil engineering applications that require large volumes of materials. when these waste products are used in place of other conventional materials, natural resources and energy are preserved and expensive and/or potentially harmful waste disposal is avoided. it has been established that it is no longer required to use high quality elements to manufacture strong and efficient materials. nowadays, more and more attention is paid to the choice of materials to be used in the design and construction of these structures. furthermore, it is no longer necessary to use high quality materials to make a strong and resistant structure, because safety and economic factors do not have the same importance for the different types of structures. indeed, economic factors (i.e. supply, demand and market saturation) beside the concept of recycling, which consists of avoiding the exhaustion of supply sources, are now inciting us to revalorize recyclable materials of similar sectors [3]. the previously mentioned factors tend to increasingly encourage the recovery of construction and demolition waste to be recycled in the form of substitute aggregates for the development of new concretes. therefore, using recycled products is perfectly justified. in this context, the right approach consists in using the right material for the right purpose under the right conditions [4]. in construction, the demand annually amounts to more than 30 million tons of cubic meters of aggregates. furthermore, much of the waste from construction sites is increasingly transformed into aggregates to be utilized in the formulation of concrete. it can be predicted that in the future about 4 ‰ of buildings will be destroyed each year, which is expected to generate roughly 1 million of cubic meters of concrete waste [5]. in algeria, the entire production of concrete in construction and public works is made up only of natural aggregates. over the past few years, constraints related to the growth in demand for aggregates have surfaced, which incited researchers and practitioners to design and develop new aggregates as alternatives to replace natural aggregates. moreover, it is worth indicating that demolition or construction materials are being increasingly produced in very large quantities. these wastes are generally used as backfill or discharged to the environment which engenders a very bad impact on the ecosystem [6]. as these new aggregates can be recycled on site, all the expenses and costs associated with the transport of natural aggregates on the one hand, and the disposal of demolition waste, on the other, can be saved, which represents a considerable economic advantage. consequently, this procedure would contribute to reducing the depletion of natural resources and enhancing the concept of sustainable development. the valorization and the use of aggregates issues from concrete for the manufacturing of a resistant and an efficient hydraulic concrete would help to extend their current field. to the best of our knowledge, few studies have been carried out to date on the possibility of recycling construction demolition waste in order to formulate a high-strength concrete (hsc). moreover, not many researchers have tried to numerically model this type of concrete. [7]. for these reasons, we have endeavored to explore the above-mentioned subject in order to provide a deeper insight into the topic of construction waste recovery. according to some authors, zhang et al. [8], and abid et al. [9], the effect of bentonite on mechanical and durability behaviour of both natural aggregates concrete (nac) and recycled aggregates concrete (rac) was investigated and compared. results of testing revealed that with the incorporation of bentonite, rac showed significant improvement in the durability and strength. to understand the degradation of mechanical properties of recycled aggregate concrete (rac) after acid rain exposure, the effect of recycled coarse aggregate (rca) replacement ratios, the acidity (ph value) of the simulated acid rain solution and mineral admixtures on compressive strength and elastic modulus of rac are investigated in the study of lu et al. [10]. t k.c. nehar et alii, frattura ed integrità strutturale, 56 (2021) 203-216; doi: 10.3221/igf-esis.56.17 205 however, several researchers have conducted studies on in the numerical modeling of concrete sections in recent years. deshpande et al. [11] presented the findings of a study which carried out for modeled compressive strength of concrete using the techniques of artificial neural network (ann), model tree (mt) and non-linear regression. the prediction of compressive strength of concrete by data-driven models was used by khademi et al. [12]. nitka et tejchman [13] studied the modelling of the behaviour of plain concrete during uniaxial compression and tension using the discrete element method dem. an advanced finite element model using the general-purpose fe software ansys to simulate the behaviour of the initially damaged concrete beams was studied by berezoug et al. [14]. peng et al. [15] have studied the numerical simulation of recycled concrete using convex aggregate model and base force element method (bfem), they show this combination can be used for simulating the relationship between microstructure and mechanical properties concrete. the numerical modeling of a circular concrete columns has presented by havlásek [16] he used the nonlinear finite element simulations which allow for arbitrary loading configuration and the topology into the design process. all these research works have conducted the studies on a numerical modeling of concrete behaviour using various approaches based on software simulations. however, this modeling can be done by using the programming of the finite element method (fem) theory [17, 18]. this method is now widely used in the engineering field and which is adopted in this work to model the recycled aggregate concrete [19]. the objective of the present work is, on the one hand, to supply an economical resistant concrete, based on recycled aggregates, having very high mechanical, physical and elastic properties, by adding silica fume and a superplasticizer and, on the other hand, to evaluate and compare the maximum compressive strengths using the finite element method. to achieve these goals, it was decided to divide the work into four stages: • the first step consisted in optimizing the high-strength concrete (hsc) with 100% natural aggregates; this was used as reference concrete, • the second step aimed to optimize the recycled hsc while varying the contents of recycled and natural aggregates, • the third step was about determining an optimal formulation that could give the maximum strength, • the last step consisted in comparing the strength obtained with that provided by the finite element method; it also sought to identify the distribution of stresses in the various samples of concrete used. used materials aggregates wo types of aggregates were used in this study:  natural aggregates (na) class 3/8 and 8/15 crushed limestone gravels were used. these gravels have a specific gravity equal to 2.65, with 3.70% impurity and 0.30% humidity with, and a los angeles coefficient of 19.20%. as for sand, it has a specific weight of 2.70 and a fineness modulus of 3.20.  recycled aggregates the recycled aggregates (ra) were prepared in the civil engineering laboratory at the university of djelfa, in algeria. the following table shows the chemical characteristics of the aggregates. chemical characteristics p.a.f. % sio2 % ai2o3 % fe2o3 % cao % mgo % so3 % k2o % na2o % na 1.47 11.35 4.59 3.52 78.89 1.10 1.22 0.41 0.13 ra 47.17 -0.63 0.85 49 1.02 1.30 0.50 table 1: chemical characteristics of aggregates. tab. 1 above summarizes the chemical composition of the different aggregates. it was found that the recycled sand included silica and limestone (47% of silica and 49% of carbonate) with a small amount of alumina (al2o3) which was due to the presence of cement paste around the sand grains. however, natural aggregates were calcareous in nature, with a fairly high percentage of carbonates (around 78%). therefore, it can be said that in general recycled aggregates are of a lime-silicate nature. however, this is not always true because it can vary according to the type of the recycled waste. for example, some researchers [20, 21] found out that their recycled aggregates had a rather siliceous nature. t k.c. nehar et alii, frattura ed integrità strutturale, 56 (2021) 203-216; doi: 10.3221/igf-esis.56.17 206  physical and mechanical characteristics: the water absorption test was carried out according to standard nf en 18-554, and the results obtained are summarized in the table below. type of aggregate los angeles (%) water absorption (%) sand equivalent (%) absolute density apparent density na ra na ra na ra na ra na ra 8/15 19.20 31 1.35 1.1 2.48 2.45 0.78 5.20 3/8 21 33 1.38 1.21 2.57 2.60 0.92 6.30 0/5 1.20 0.9 2.89 2.80 80 76 table 2: physical and mechanical characteristics of aggregates. the findings revealed that the densities decreased as the granular fraction augmented. in addition, natural aggregates and recycled aggregates exhibited nearly the same absolute densities. on the other hand, the apparent densities of recycled aggregates were found lower than those of natural aggregates due to the presence of pores in the recycled aggregates because the concrete waste had a high porosity. furthermore, the water absorption test helped to see the difference between the two types of aggregates from the density viewpoint, since the recycled aggregates showed a greater water absorption coefficient (approximately 8%) than that of natural aggregates (about 2%). this difference is primarily attributed to the fact that recycled aggregates had a higher porosity than that of natural aggregates [4, 6]. cement the cement (c) used is a portland cement with high resistance to sulphates (cem i 42.5 hrs). its mineralogical composition is such that c3s = 60%, c2s = 25.55%, c3a = 2% and c4af = 12.45%. the density of anhydrous cement is 3.23 g / cm3 and its specific surface is 3880 (cm2 / g). adjuvant the adjuvant used is a new generation high-water-reducing superplasticizer of the medaflow 145 type. it is a solution of polycarboxylates, 31% dry extract, light pitch color, and ph between 5 and 6. silica fume the actual density of silica fume is 2194 (kg/m3) and its blaine specific surface is greater than 15000 (cm²/g). the chemical compositions of cement and silica fume (sf) used in this study are given in tab. 3. the samples p.a.f. % sio2 % ai2o3 % fe2o3 % cao % mgo % so3 % k2o % na2o % cement (c) 1.47 22.31 4.39 5.52 63.89 0.80 1.11 0.41 0.09 silica fume (sf) 93.17 0.60 1.25 1.40 1.02 2.30 1.00 table 3: chemical compositions of the constituents. the blaine specific surface area of cement is ssb = 3304 (cm² / gr). the blaine specific surface area of silica fume is ssb > 20000 (cm² / gr). the abbreviations used: nc: normal concrete rc: recycled concrete c (n + r): normal concrete + recycled concrete hsc: high strength concrete a: aggregates na: natural aggregates ra: recycled aggregates sf: silica fume k.c. nehar et alii, frattura ed integrità strutturale, 56 (2021) 203-216; doi: 10.3221/igf-esis.56.17 207 adj: adjuvant c: cement (w/c): (water/cement) ratio (s/g): (sand/gravel) ratio (w/b): (water/binder) ratio cs 28d: compressive strength at 28 days. fem: finite element method. experimental study of the composition of concrete formulation of reference concrete enerally, the formulation methods do not all provide the same results, because each of them must simplify the hypotheses and rely only on a few of them. the assumptions are not always the same. note, however, that none of these hypotheses leads with certainty to an accurate composition. this is certainly due to the fact that the numerous parameters which have an impact on concrete are difficult to evaluate. with regard to the formulation of the reference concrete, it was decided to use the baron-lesage method, but the aggregate content should be known in advance in order to have an optimal mineral skeleton. according to baron and lesage [22], the following two assumptions must be respected: • for a fixed dosage of cement and water at the beginning (fixed ratio w/c), the most workable and compact concrete is the one that is the most compact with an optimal skeleton. • the optimal dosage of aggregates does not depend on the contents of water and cement. it is worth noting that in order to achieve the optimal composition of concrete, several parameters, such as the cement content, water content and aggregate content (s/g = sand/gravel) should be considered. therefore, in order to simplify our study and satisfy the hypotheses of the method, only the (s/g) ratio was varied. the cement dosage and the ratio (w/c) were kept unchanged at the beginning. according to gorisse [23], the optimal ratio (s/g) is between 0.50 and 0.83. in the present work, seven values of this ratio were selected and tested (step: 0.05) for the purpose of obtaining seven different compositions. the abrams cone sag, corresponding to the values of the ratio (s/g) = 0.50, 0.55, 0.60, 0.65, 0.70, 0.75, and 0.80, was measured for each composition. types of concrete c (kg/m3) a (kg/m3) w (l/m3) w/b 8/15 3/8 0/5 nc (100%) 350 905 200 670 192.5 0.55 rc (100%) 350 905 200 670 245 0.70 (70%na+30%ra) 350 905 200 670 210 0.60 (50%na+50%ra) 350 905 200 670 227.5 0.65 table 4: optimal composition of reference concrete. the compressive strength at 28 days with these types of concrete are presented in the fig. 1. formulation of the concretes under study once the reference concrete was prepared, a formulation method was established in order to find the optimal composition of the high performance concretes (hpc). it should be noted that the formulation method adopted for the mixture of constituents entering into the composition of high performance concrete is the one that was developed by aïtcin [2] at the university of sherbrooke. this is a simple and practical method. it consists in combining the empirical results and those obtained using the absolute volume method. the amount of water contained in the superplasticizer is considered to be part of the amount of mixing water. the data used for the optimal formulation which gave the maximum strength with acceptable workability for one cubic meter of concrete are presented in the tab. 5. g k.c. nehar et alii, frattura ed integrità strutturale, 56 (2021) 203-216; doi: 10.3221/igf-esis.56.17 208 figure 1: the compressive strength at 28 days of reference concrete. types of concrete c (kg/m3) a (kg/m3) sf (%) adj. (%) w/b sagging (cm) fresh density8/15 3/8 0/5 nc+sf 450.70 950 200 670 60.2 10.5 0.30 5.0 2567 rc+sf 522.46 950 200 670 70.4 14.2 0.37 5.7 2389 (70%na+30%ra+sf) 472.13 950 200 670 65.6 11.7 0.32 4 2465 (50%na+50%ra+sf) 484.60 950 200 670 72.3 13.4 0.35 3 2332 table 5: composition of concrete mixes. figure 2: the compressive strength at 28 days of concrete mixes. fig. 2 shows the compressive strength at 28 days obtained with this optimal formulation. n c (1 00 % ) rc (1 00 % ) (7 0% n a+ 30 % ra ) (5 0% n a+ 50 % ra ) 0 10 20 30 40 c o m p re ss iv e st re n gt h a t 28 d ay s (m p a) n c+ sf rc +s f (7 0% n a+ 30 % ra +s f) (5 0% n a+ 50 % ra +s f) 0 10 20 30 40 50 60 70 80 90 c o m p re ss iv e st re n gt h a t 28 d ay s (m p a) k.c. nehar et alii, frattura ed integrità strutturale, 56 (2021) 203-216; doi: 10.3221/igf-esis.56.17 209 figure 3: flowchart of the numerical simulation model. discussion and interpretation the table above shows that: it is possible to manufacture high strength concretes with a compressive strength exceeding 70 mpa (at 28 days) and adequate plasticity, provided that the recycled aggregates are used up to 30% of the total amount of aggregates in ordinary high-strength concrete. partial substitution of natural aggregates with recycled aggregates for the manufacture of the new concrete offers a new aggregate resource and allows saving natural materials. the findings were encouraging since the strength drop of concrete incorporating recycled gravel only does not exceed 17% for a target characteristic strength of 70 mpa. these results confirm the trend evoked by the antecedent studies of revilla-cuesta et al. [25], and masood et al. [26], their researches is presented into recycled concrete aggregate properties and the mix-design of the self-compacting concretes that contain them, as well as relevant results on the fresh state (workability, rheology), the hardened state (compressive strength, splitting tensile and flexural strength, modulus of elasticity, density, and porosity), durability (resistance to aggressive agents), long-term properties of concrete (shrinkage, creep), and structural elements manufactured with selfmesh construction. introduction of applied loading. form the force vector {f} computation of displacement {u} = [k] /{f} computation of stresses computation of the elementary stiffness matrix  [ ] [ ] [ ][ ] t e v k b c b dv assembly: construction of the global stiffness matrix [k]. introduction of boundary conditions: embedding, single or double support depending on the study case. begin data input: geometric: geometry dimension b, h, ep. number of elements in x and y direction mechanics: young's modulus e. poisson's ratio ν. treatment end -initialization of the elementary stiffness matrix [ke]. computation of interpolation functions [n]. computation of the derivatives of interpolation functions [dn]. computation of the matrix [b]. computation of the elasticity matrix [c]. k.c. nehar et alii, frattura ed integrità strutturale, 56 (2021) 203-216; doi: 10.3221/igf-esis.56.17 210 compacting concrete containing recycled concrete aggregate. the results under review reaffirm that the incorporation of recycled concrete aggregate can produce a suitable self-compacting recycled concrete, on the basis of careful designs that are essential for successful performance. numerical study of concrete samples modeling by the finite element method he finite element approximation was programmed under matlab [27] for the finite element modeling of concrete specimens. it is represented by the organization chart in fig. 3. numerical application the samples investigated in the present work were modeled and evaluated using our finite element calculation code. these are concrete elements of width b = 10 cm, height h = 10 cm and thickness ep = 10 cm, as shown in fig. 4 (a), and plane strain conditions are adopted. in the design procedure, it was decided to apply a compression loading similar to that used in the experimental part with a quadrangle mesh density of 100 x 100 elements for all types of concrete (fig. 4 (b)). figure 4: (a) geometric configuration of the concrete samples studied, (b) modeled sample. several types of concrete were prepared and investigated in this study. their mechanical characteristics are summarized in the following table: types of concrete young’s modulus e(mpa) poisson's ratio ν nc (100%) 29000 0.20 rc (100%) 24000 0.19 (70%na+30%ra) 27000 0.20 (50%na+50%ra) 25000 0.20 (na+ sf) 46000 0.25 (ra +sf) 38000 0.23 (70%na+30%ra+sf) 42000 0.24 (50%na+50%ra+sf) 39000 0.22 table 6: mechanical properties of concretes used in this study. results and discussion the finite element method (fem) was programmed and applied to the previously prepared specimens. the results obtained were compared with those provided by the experimental study for the purpose of highlighting the performance of the developed program. t (b) (a) k.c. nehar et alii, frattura ed integrità strutturale, 56 (2021) 203-216; doi: 10.3221/igf-esis.56.17 211 fig. 5 displays the results of the comparison between the experimental compressive strengths and those predicted numerically by the finite element method (fem), at 28 days, for all types of concrete studied. figure 5: experimental and numerical compressive strength values at 28 days. it is quite clear that the compressive strength values obtained at 28 days using our finite element calculation code are in good agreement with those resulting from the experimental tests. consequently, the data obtained for the compressive strength are quite satisfactory and encouraging. in order to better understand the distribution of compressive stresses in our concrete samples, the evolution of these stresses was presented for each type of concrete as follows: (nc (100%), rc (100%), (70% na + 30% ra), (50% na + 50% ra), (na + sf), (ra + sf), (70% na + 30% ra + sf), (50% na + 50% ra + sf)), and which are shown in figs. 6 (a), (b), (c), (d), (e), (f), (g), (h), respectively. figs. 6 (a), (b), (c), (d), (e), (f), (g) and (h) present the mapping of the equivalent stress field resulting from numerical simulations using the finite element method (fem). the distribution of stress is symmetrical about the loading application point. the stress field is maximal at the center of the test specimen. however, the mapping shows the presence of stress concentrations (circled in black in fig. 6) in the loading application regions which are located at the edge of the specimens. these concentrations were in fact expected due to the presence of the compressive loading at the edge of the specimens. furthermore, this mapping also showed that the addition of 30% natural aggregates along with silica fume in the concrete makes it possible to achieve a better distribution of stresses compared to normal concrete. conclusions he experimental results obtained indicate that: it is quite possible to manufacture a highly resistant concrete, by the partial substitution of natural aggregates with recycled aggregates (70% na + 30% ra), with a compressive strength of about 70.80 mpa at 28 days. this value is not too far from that of concrete incorporating natural aggregates only (100% na); its compressive strength was found approximately equal to 83 mpa for the same age. these findings are attributed to the fact that the super plasticizer was very effective in reducing the water-to-binder (w/b) ratio below 0.30. in addition, the use of additions, such as the finely ground silica fume, considerably helped to make the cement paste denser and to further reduce the amount of water, especially that the cement used contains a very small amount of tricalcium aluminate (ca3). recycled aggregates could be used up to 30% of the total amount of aggregates for most environments. if recycled sand is used, then the amount used should be less than 30%. t nc (10 0% ) rc (10 0% ) (70 %n a+ 30% ra ) (50 %n a+ 50% ra ) (n a+ sf ) (ra +s f) (70 %n a+ 30% ra +s f) (50 %n a+ 50% ra +s f) 0 10 20 30 40 50 60 70 80 90 c o m p re ss iv e st re n gt h a t 28 d ay s (m p a) experimental results numerical results k.c. nehar et alii, frattura ed integrità strutturale, 56 (2021) 203-216; doi: 10.3221/igf-esis.56.17 212 figure 6: distribution of compressive stresses in the samples using matlab [27]: (a) nc (100%), (b) rc (100%), (c) (70% na+ 30% ra), (d) (50% na + 50 % ra), (e) (na+ sf), (f) (ra + sf), (g) (70% na+ 30% ra + sf), and (h) (50% na+ 50 % ra + sf). (a) (b) (c) (d) (e) (f) (g) (h) k.c. nehar et alii, frattura ed integrità strutturale, 56 (2021) 203-216; doi: 10.3221/igf-esis.56.17 213 moreover, good workability can easily be achieved despite the low ratio (w/b) = 0.35 thanks to the good quality superplasticizer (media flow 145) used. it is useful to remember that this superplasticizer has fairly high rheological and mechanical performance. the use of recycled aggregates is of paramount importance from the environmental point of view. this allows getting rid of the materials resulting from the demolition of old buildings and the destruction of structures following natural disasters. moreover, this study allowed us to model the concrete samples prepared, using the finite element method. a simple comparison helped to confirm the good correlation between the results obtained by our calculation code and those obtained by the experimental study, for all types of concrete. it can therefore be concluded that the addition of 30% of recycled aggregates and silica fume into concrete allows achieving a better distribution of stresses in comparison with ordinary concrete. references [1] ministère de l’aménagement du territoire et de l’environnement (mate), algeria. [2] tayeh, b. a., al saffar, d. m. and alyousef, r. (2020). the utilization of recycled aggregate in high performance concrete: a review. j. of mat. res. and tech., 9(4), pp. 8469–8481. doi: 10.1016/j.jmrt.2020.05.126. [3] ali, a. a. m., zidan, r. s. and ahmed, t. w. (2020). evaluation of high-strength concrete made with recycled aggregate under effect of well water. case stu. in const. mat., 12, e00338. doi:10.1016/j.cscm. 2020.e00338. [4] jin, r., li, b., elamin, a., wang, s., tsioulou, o. and wanatowski, d. (2018). experimental investigation of properties of concrete containing recycled construction wastes. int. j. of civ. eng., 16(11), pp. 1621–1633. doi: 10.1007/s40999-018-0301-4. [5] guo, h., shi, c., guan, x., zhu, j., ding, y., ling, t. c., zhang, h. and wang, y. (2018). durability of recycled aggregate concrete–a review. cem. and conc. comp., 89, pp. 251–259. doi: 10.1016/j.cemconcomp.2018.03.008. [6] verian, k. p., ashraf, w. and cao, y. (2018). properties of recycled concrete aggregate and their influence in new concrete production. res. conserv. and recyc., 133, pp. 30–49. doi:10.1016/j.resconrec.2018.02.005. [7] siempu, r. and pancharthi, r. k. (2017). bond characteristics of concrete made of recycled aggregates from building demolition waste. mag. of conc. res., 69(13), pp. 665–682. doi:10.1680/jmacr.16.00400. [8] zhang, y., luo, w., wang, j., wang, y., xu, y., & xiao, j. (2019). a review of life cycle assessment of recycled aggregate concrete. const. and build. mat., 209, pp. 115-125. doi: 10.1016/j.conbuildmat.2019.03.078. [9] abid, s. r., nahhab, a. h., al-aayedi, h. k. and nuhair, a. m. (2018). expansion and strength properties of concrete containing contaminated recycled concrete aggregate. case stud. in constr. mat., 9, pp. e00201. doi: 10.1016/j.cscm.2018.e00201. [10] lu, c., wang, w., zhou, q., wei, s. and wang, c. (2020). mechanical behavior degradation of recycled aggregate concrete after simulated acid rain spraying. jour. of clea. produc., 262, pp. 121237. doi: 10.1016/j.jclepro.2020.121237. [11] deshpande, n., londhe, s., and kulkarni, s. (2014). modeling compressive strength of recycled aggregate concrete by artificial neural network, model tree and non-linear regression. int. j. of sust. bui. env., 3(2), pp. 187-198. doi: 10.1016/j.ijsbe.2014.12.002. [12] khademi, f., akbari, m., and jamal, s. m. m. (2015). prediction of compressive strength of concrete by data-driven models. i-manager’s j civ eng, 5, pp. 16. [13] nitka, m. and tejchman, j. (2015). modelling of concrete behaviour in uniaxial compression and tension with dem. granu. mat., 17(1), pp. 145–164. doi: 10.1007/s10035-015-0546-4. [14] berrezoug zidani, m., belakhdar, k. and tounsi, a., adda bedia, e. (2015). finite element analysis of initially damaged beams repaired with frp plates. compo. struc., 134, pp. 429–439. doi: 10.1016/j.compstruct.2015.07.124. [15] peng, y., chu, h., and pu, j. (2016). numerical simulation of recycled concrete using convex aggregate model and base force element method. adv. in mat. scien. and eng., 2016. doi: 10.1155/2016/5075109. [16] havlásek, p. (2020). numerical modeling of axially compressed circular concrete columns. eng. struc., 227, pp. 111445. doi: 10.1016/j.engstruct.2020.111445. [17] pradhan, k. k. and chakraverty, s. (2019). chapter four—finite element method. in computational structural mechanics, academic press, pp. 25–28. k.c. nehar et alii, frattura ed integrità strutturale, 56 (2021) 203-216; doi: 10.3221/igf-esis.56.17 214 [18] baaser, h. (2010). development and application of the finite element method based on matlab. springer science & business media. [19] tekkaya, a.e. and soyarslan, c. (2018). finite element method. in: int. academy for production engineering, chatti s., tolio t. (eds) cirp encyc. of prod. eng. springer, berlin, heidelberg. doi:10.1007/978-3-642-35950-7_16699-3 [20] xiao, j. (2018). recycled aggregate concrete structures, springer-verlag berlin heidelberg, pp. 65–98. doi: 10.1007/978-3-662-53987-3. [21] babu, v. s., mullick, a. k., jain, k. k. and singh, p. k. (2015). strength and durability characteristics of high-strength concrete with recycled aggregate-influence of processing. j. of sust. cem.-bas. mat., 4(1), pp. 54-71. doi: 10.1080/21650373.2014.976777. [22] baron, j. (1997). les additions normalisées pour béton, ecole française du béton, édition eyrolles. [23] gorisse, d., festa, j. (1998). nouveau guide du béton et de ses constituants, huitième édition, edition eyrolles, france. [24] aïtcin, p.c. (2001). bétons haute performance, edition eyrolles, paris. [25] revilla-cuesta, v., skaf, m., faleschini, f., manso, j. m. and ortega-lópez, v. (2020). self-compacting concrete manufactured with recycled concrete aggregate: an overview. jour. of clea. produc., 262, pp. 121362. doi: 10.1016/j.jclepro.2020.121362. [26] masood, b., elahi, a., barbhuiya, s. and ali, b. (2020). mechanical and durability performance of recycled aggregate concrete incorporating low calcium bentonite. constru. and build. mat., 237, pp. 117760. doi: 10.1016/j.conbuildmat.2019.117760. [27] matlab (1984). script language with a development environmental for numerical calcul, version 16.0, mathworks, california, united states. annex fem modeling in order to model the concrete samples, the finite element approximation is used [12]. we consider a quadrilateral element (fig. a.1) the element is defined by four nodes in natural coordinates (ξ, η). the coordinates are interpolated and given as follows [15]:      4 4 1 1 i i i i i i u n u v n v (1) where u, v represents the displacements fields at any point of the element and ui, vi; the nodal displacements. figure a.1. quadrilateral q4 element in natural coordinates (ξ, η). ni represents the standard interpolation functions which are given by:         1 1 1 1 ( , ) ( ) ( ) (1 )(1 ) 4 n l l (2)         2 2 1 1 ( , ) ( ) ( ) (1 )(1 ) 4 n l l (3) k.c. nehar et alii, frattura ed integrità strutturale, 56 (2021) 203-216; doi: 10.3221/igf-esis.56.17 215         3 2 2 1 ( , ) ( ) ( ) (1 )(1 ) 4 n l l (4)         4 1 2 1 ( , ) ( ) ( ) (1 )(1 ) 4 n l l (5) in matrix form:                          (1 )(1 ) (1 )(1 )1 (1 )(1 )4 (1 )(1 ) t in (6) the derivatives of the interpolation functions ni are:                      (1 ) (1 )1 (1 )4 (1 ) t in ,                      (1 ) (1 )1 (1 )4 (1 ) t in (7) these derivatives are transformed by a function f(x, y) with respect to ξ and η:                                                                                               [ ] yf yf f x x f f yx x x j f ff f x y yf x y yx y (8) where j is the jacobian operator, connecting the natural and global coordinates. the derivatives with respect to the global coordinates can be found as follows:                              1[ ] ff x j f f y (9) the stiffness matrix is then obtained by:  [ ] [ ] [ ][ ] t v k b c b dv (10) where [b] is the strain matrix derived from the interpolation functions:                                                   1 0 [ ] 0 , [ ] i ii i i i i i n nnx n x b j n ny yn n x y (11) k.c. nehar et alii, frattura ed integrità strutturale, 56 (2021) 203-216; doi: 10.3221/igf-esis.56.17 216 [c] is the elasticity matrix:              2 1 0 [ ] 1 0 1 0 0 2(1 ) e c , in plane strains (12)                        1 0 [ ] 1 0 (1 ) 1 2 (1 2 )0 0 2 e c , in plane stresses (13) the volume of the element dv is given by:   .det . .dv h j d d (14) where detj is the determinant of the jacobian matrix and h the thickness of the element. the surface dξ.dη at the point (ξ, η) of the reference element is transformed into the surface da at the point (x ((ξ, η)), y ((ξ, η))) of the natural element. were:   det . .da j d d (15) the integral in the stiffness matrix on the real element is:  [ ] [ ]. v k f dv (16) therefore, becomes on the reference element:  [ ] .[ ]. a k h f da (17) taking: [ ] [ ] [ ][ ]tf b c b (18) the integral in the stiffness matrix is then calculated numerically by gaussian quadrature in two dimensions. in the fournode element, we can use a 2 × 2 numerical integration for exact integration.                1 1 1 11 1 , . . , p q i j i j i j f d d w w f (19) where p, q are the number of integration points in the directions ξ, η, respectively, and wi, wj are the corresponding weights. the stiffness matrix can be calculated using 2 × 2 gauss points as:                                   1 1 1 1 2 2 1 1 . . . det . . . . det . t t e a t i j i j k h b c b da h b c b j d d h b c b j w w (20) microsoft word numero_34_art_27 yu.g. matvienko et alii, frattura ed integrità strutturale, 34 (2015) 255-260; doi: 10.3221/igf-esis.34.27 255 focussed on crack paths the concept of the average stress in the fracture process zone for the search of the crack path yu.g. matvienko, m.m. semenova mechanical engineering research institute of the russian academy of sciences, russia. ygmatvienko@gmail.com abstract. the concept of the average stress has been employed to propose the maximum average tangential stress (mats) criterion for predicting the direction of fracture angle. this criterion states that a crack grows when the maximum average tangential stress in the fracture process zone ahead of the crack tip reaches its critical value and the crack growth direction coincides with the direction of the maximum average tangential stress along a constant radius around the crack tip. the tangential stress is described by the singular and nonsingular (t-stress) terms in the williams series solution. to demonstrate the validity of the proposed mats criterion, this criterion is directly applied to experiments reported in the literature for the mixed mode i/ii crack growth behavior of guiting limestone. the predicted directions of fracture angle are consistent with the experimental data. the concept of the average stress has been also employed to predict the surface crack path under rolling-sliding contact loading. the proposed model considers the size and orientation of the initial crack, normal and tangential loading due to rolling–sliding contact as well as the influence of fluid trapped inside the crack by a hydraulic pressure mechanism. the mats criterion is directly applied to equivalent contact model for surface crack growth on a gear tooth flank. keywords. crack path; maximum average tangential stress; t-stress; mixed mode; rolling-sliding. introduction eneral aspects of the concept based on calculation of the average stress over the length of the process zone are described in refs. [1-6] for a solid with cracks or notches. these references demonstrate an advantage of the critical average stress criterion over the classical elastic and elastic-plastic fracture mechanics criteria because this criterion avoids the confusion of applying the unrealistic continuum mechanics stress singularity to the fracture process zone in the vicinity of the crack (or notch) tip. for example, the failure criterion of the average stress within an effective distance has been successfully employed to relate the apparent fracture toughness in specimens with notches to the fracture toughness obtained from deeply cracked specimens (e.g., [4]). in this case, the effective distance corresponds to the point with a minimum of the stress gradient which requires finite element analysis to obtain the effective distance [5]. it should be noted that the effect of the high stress gradient ahead of the crack/notch tip can be taken into account by means of the theory of critical distance using the stress at some critical distance [6]. the theory of critical distances was very successful in predicting the fracture strength of ceramic materials. thus, the concept based on averaging the stress over the fracture process zone length can be successfully applied to cracks or notches. the concept of the average stress has been employed to propose the maximum average tangential stress (mats) criterion under mixed mode i/ii loading for predicting the direction of fracture angle. the effect of the g yu.g. matvienko et alii, frattura ed integrità strutturale, 34 (2015) 255-260; doi: 10.3221/igf-esis.34.27 256 constant term of the series of williams has been expressed by the parameter t and it is incorporated into the basic criterion equation. to demonstrate the validity of the proposed mats criterion, this criterion is directly applied to experiments reported in the literature for the mixed mode i/ii crack growth behavior. maximum average tangential stress (mats) criterion he tangential crack-tip stress under mixed mode i/ii loading can be characterized by the singular (the first order term) and the nonsingular term (the t-stress) in polar coordinate following to williams [7] 2 21 3cos cos sin sin 2 2 22 i iik k t r               (1) here, r and  are the crack tip coordinates, ik and iik are mode i and mode ii stress intensity factor, respectively. the maximum average tangential stress (mats) criterion is assumed to be applicable and can be expressed mathematically as follows [8] 0      , 2 2 0      . (2) this criterion states that a crack grows when the maximum average tangential stress  in the fracture process zone ahead of the crack tip reaches its critical value and the crack growth direction coincides with the direction of the maximum average tangential stress along a constant radius around the crack tip. combining eq. (1) with eq. (2), the mats criterion leads to predicting the direction of fracture angle 0 [8]  00 0 0 8 sin 3 cos 1 2 cos sin 0 3 2 i ii t k k d             (3) 0,0 0,2 0,4 0,6 0,8 0 10 20 30 40 50 60 mats criterion experimental results [9] d ir e ct io n o f f ra ct u re a n g le , o 0 me figure 1: the predicted and experimental directions of fracture angle for the mixed mode i/ii crack growth behavior of guiting limestone. validation of the mats criterion o validate the proposed mats criterion, eq. (3) is directly applied to the experimental results [9] for the mixed mode i/ii crack growth behavior of guiting limestone. different combinations of modes i and ii are characterized by a mixity parameter em t t yu.g. matvienko et alii, frattura ed integrità strutturale, 34 (2015) 255-260; doi: 10.3221/igf-esis.34.27 257 2 arctan ie ii k m k        (4) the values of em were varied through 1 (pure mode i), 0.75, 0.5, 0.25, 0 (for pure mode ii). according to the mats criterion (eq. (3)), four parameters ik , iik , t and d at fracture need to be known for each mode mixity. the local strength of this brittle material and the fracture process zone length d are treated as a function of the tensile strength [8] which is equal to 2 mpa. the fracture toughness matk is 0.24 mpa m . these values were assumed to be constant for all mixities. the fracture trajectories predicted using the mats criterion (eq. (3)) are consistent with those observed in the broken specimens under various mode mixities (fig. 1). the surface crack path under rolling-sliding contact loading ssuming the singular and non-singular (t-stress) terms are sufficient to characterize the crack tip stress under mode i/ii loading in the case of rolling-sliding contact, the tangential stress  is written in polar coordinate as follows [10] -2 2 2 1 3 ( , ) cos cos sin sin sin 2 cos 2 2 22 c c i ii xy yyr k k t r                     . (5) here, the tractions cxy and c yy are defined at the crack tip and their distribution is smooth enough along the crack surface. this equation is valid, if the crack surfaces are loaded with constant pressure ( , )p x y   . the stress component c yy is then equal to the – yp while c xy =− xp . averaging the tangential stress over the fracture process zone, which is characterised by a critical distance d , the maximum average tangential stress (mats) criterion leads to the following mathematical expression 0 0 0 0 0 0 cos 24 8 sin (3cos 1) 2 ( ) 2 cos sin 0 3 3 2cos 2 xy yy c c i iik k d t d                     (6) the fracture process zone size d in the above-mentioned equation can be determined for critical state 0  as follows        2 2 20 00 0 0 0 0 3 2 sin sin 2 cos cos cos sin 2 2 2 c c xy yy i iit k k d                                     (7) in general case, the local strength 0 is dependent on the model of a solid and can be treated for plane strain according to von mises yield criterion as a property of both the yield stress y and the t-stress which quantifies constraint in different geometries and type of loading [11, 12]       22 2 0 2 1 / 11 2 4 1 2 y y y tt t                   , (8) where . .is poisson’s ratio. according to zafošnik et al. [10], the real contact geometry (e.g. gear tooth flanks) can be transformed into a pair of equivalent contacting cylinders with the radii corresponding to curvature radii of analyzed mechanical elements. for small a yu.g. matvienko et alii, frattura ed integrità strutturale, 34 (2015) 255-260; doi: 10.3221/igf-esis.34.27 258 coefficients of friction the distribution of tangential contact loading q(x) due to relative sliding can be estimated with a simple coulomb friction law within the hertzian model [13] ( ) ( )xq x p p x   , (9) where μ is the coefficient of friction between contacting elements. following loading configurations have been considered to investigate the effect of a moving contact on the crack propagation angle (fig. 2). all configurations have the same normal  p x and tangential  q x contact loading distributions which are applied at different positions with reference to the crack mouth. the pressure on the crack faces is considered to be equal to that at the crack mouth, and is equal to 2 0 0( ) 1y x p x p p b        , (10) where 0 /x b is moving contact load position (fig. 2). figure 2: simulation of the moving contact. the following mechanical properties of carburized steel 16mncr5 are used in the computational model: young’s modulus 206e gpa  , poisson’s ratio 0.3  , yield strength 2200y мpа   and fracture toughness 521matk mpa m [10]. the hertzian contact pressure distribution p(x) has the following parameters, namely, maximum value of 0 1779p mpa  and the half-length of the contact area 0.228 b mm . the influence of different contact sliding is simulated with three different coefficients of friction (μ=0.04, 0.065 and 0.1). initial length of the crack is equal to 0 20a m  with the initial inclination angle towards the contact surface 20 o  . the computational data published by zafošnik et al. [10] is employed in calculation to illustrate the variation of observed parameters in the region of maximum stress intensity factors 0i ik k p b  , 0ii iik k p b  and 0t t p for moving contact load over the crack mouth. the computational results (fig. 3) determined by the mats criterion illustrate the variation of crack propagation angle 0 in the region of maximum stress intensity factors ik , iik and t-stress for moving contact load over the crack mouth, which is given in terms of a relative position of the loading case with respect to the half-contact width b. it can be seen that the influence of coefficient of friction on crack propagation angle is negligible. to evaluate the analytical results obtained by the proposed maximum average tangential stress (mats) criterion, the maximum tangential stress (mts) criterion [10] is also employed. the obtained results illustrate the following. the mats criterion gives slightly largest crack propagation angles as compared with the mts criterion for load position corresponding to 0 / 0.94x b   (fig. 4). at the same time, the predicted crack propagation angles are smaller for contact load position corresponding to 0 / 0.94x b   . yu.g. matvienko et alii, frattura ed integrità strutturale, 34 (2015) 255-260; doi: 10.3221/igf-esis.34.27 259 figure 3: crack propagation angle determined with the mats criterion. figure 4: crack propagation angle determined with mats and mts criteria (coefficient of friction 0.1  ). further investigation should be connected with numerical and experimental research to validate the proposed mats criterion for estimation of crack propagation angles under the rolling-sliding contact loading. conclusions he maximum average tangential stress (mats) criterion, based on the concept of the average stress within the fracture process zone, has been proposed for predicting the direction of fracture angle. the effect of the constant term of the series of williams has been expressed by the parameter t and it is incorporated into the mats criterion. the predicted directions of fracture angle are good consistent with the experimental data for the mixed mode i/ii crack growth behavior of guiting limestone. the criterion of the maximum average tangential stress, taking into account the non-singular t-stress and the lubricant hydraulic pressure on crack surfaces, is also spread to estimate the surface crack path under the rolling-sliding contact loading. the effect of coefficient of friction and load position on the crack path has been analysed. it is shown that the influence of coefficient of friction on crack propagation angle is negligible. at the same time, there is significant effect of contact load position on the crack propagation angle. t yu.g. matvienko et alii, frattura ed integrità strutturale, 34 (2015) 255-260; doi: 10.3221/igf-esis.34.27 260 acknowledgements he author acknowledges the support of the russian science foundation (project n 14-19-00383). references [1] dyskin, a.v., crack growth criteria incorporating non-singular stresses: size effect in apparent fracture toughness, int. j. fract., 83 (1997) 191–206. [2] matvienko, yu.g., local fracture criterion to describe failure assessment diagrams for a body with a crack/notch, int. j. fract., 124 (2003) 107–112. [3] matvienko, yu.g., erratum: local fracture criterion to describe failure assessment diagrams for a body with a crack/notch, int. j. fract., 131 (2005) 309. [4] kim, j.h., kim, d.h., moon, s.i., evaluation of static and dynamic fracture toughness using apparent fracture toughness of notched specimens, mater. sci. engng. a, 387-389 (2004) 381–384. [5] pluvinage, g., fracture and fatigue emanating from stress concentrators, kluwer academic publishers, dordrecht, (2003). [6] taylor, d., the theory of critical distances, elsevier, amsterdam, (2007). [7] williams, m.l., on the stress distribution at the base of a stationary crack, j. appl. mech., 24 (1957) 109-114. [8] matvienko, yu.g., maximum average tangential stress criterion for prediction of the crack path, int. j. fract., 176 (2012) 113–118. [9] aliha, m.r.m., ayatollahi, m.r., smith, d.j., pavier, m.j., geometry and size effects on fracture trajectory in a limestone rock under mixed mode loading, engng. fract. mech., 77 (2010) 2200-2212. [10] zafošnik, b., ren, z., flašker, j., mishuris, g., modelling of surface crack growth under lubricated rolling–sliding contact loading, int. j. fract., 134 (2005) 127–149. [11] matvienko, yu.g., on the cohesive zone model for a finite crack, int. j. fract., 98 (1999) l53–l58. [12] matvienko, yu.g., two-parameter fracture mechanics in contemporary strength problems, journal of machinery manufacture and reliability, 42 (2013) 374-381. [13] ren, z., glodez, s., fajdiga, g., ulbin, m., surface initiated crack growth simulation in moving lubricated contact, theor. appl. fract. mech., 38 (2002) 141–149. t d. shiozawa et alii, frattura ed integrità strutturale, 33 (2015) 56-60; doi: 10.3221/igf-esis.33.07 56 focussed on characterization of crack tip fields 3d analyses of crack propagation in torsion d. shiozawa kobe university, 1-1, rokkodai, nada-ku, kobe, japan shiozawa@mech.kobe-u.ac.jp i. serrano-munoz, s. dancette, c. verdu, j. lachambre, j.-y. buffiere insa-lyon mateis bat saint exupery 25 av. jean capelle f-69621 villeurbanne cedex jean-yves.buffiere@insa-lyon.fr abstract. the initiation and propagation of fatigue cracks during cyclic torsion loading was studied in a cast al alloy (a357) with a relatively large (~500 µm) grain size. 2d observations, revealed that multi site crack initiation occur on the {111} slip planes exhibiting the highest slip activity (iso-strain taylor analysis), preferentially on planes nearly perpendicular to the sample axis. within the first grain, the cracks have a pronounced crystallographic propagation mode (mode ii crack growth) and strongly interact with the grain boundaries. in situ 3d monitoring of torsion fatigue tests using synchrotron x-ray tomography reveal that propagation towards the interior of the samples occurs first along the sample periphery in mode ii leading to relatively shallow cracks which penetrate towards the sample center only after a large number of cycles is reached .the values of mode i, ii and iii stress intensity factors have been calculated from finite element simulation at the tip of the shallow mode ii crack. those values are used to analyse the bulk propagation of the observed cracks. keywords. torsion; cracks; 3d imaging; stress intensity factors; mode iii mode ii. introduction ince most machine components are operated under complex cyclic stress states, it is important to understand the propagation behavior of fatigue cracks under mixed loading. one of the most typical mixed mode crack propagation behavior arises under cyclic torsion. compared to tensile uni-axial loading, in torsion, the planes of the specimen showing the largest of shear stresses values are not submitted to any normal stress. besides, the level of the shear stresses is maximum at the sample surface and decreases towards the bulk of the sample. those two distinctive features have a strong influence on the initiation and propagation of fatigue cracks. experimentally, in metals, fatigue crack propagation mechanisms in torsion have been mainly studied through surface observations [1, 2] or by post mortem fractographic analyses [3]. the link between surface observations and fracture surfaces where crack growth can be very complex is however difficult to establish and the detailed chronology of crack growth in the sample interior is lost. the 3d shape of a fatigue crack growing inside a ti alloy has been analyzed using x ray tomography [4]; although this is a considerable improvement compared to the aforementioned observations the images were obtained during ex situ experiments providing pictures of unloaded cracks. in this paper, we report results on the initiation and propagation of fatigue cracks during cyclic torsion loading of a cast al alloy (a 357). in situ experiments have been performed on macroscopic samples (surface monitoring by optical microscopy) and on smaller ones (bulk s http://www.gruppofrattura.it/pdf/rivista/numero33/audioslides/buffiere/index.html d. shiozawa et alii, frattura ed integrità strutturale, 33 (2015) 56-60; doi: 10.3221/igf-esis.33.07 57 characterisation by synchrotron x-ray tomography), providing a chronology of crack development with this loading mode both at the surface and in the bulk of the material. the observed crack paths are analysed in light of the mode i, ii and ii stress intensity factors obtained from finite element simulations. experimental set up he material used in this study is a cast aluminium alloy a357. the fatigue samples were cut from the central part of cylindrical rods (30 mm diameter) obtained by permanent mold casting. after a t6 treatment (solution treatment at 540°c for 10h followed by water quench and 8h at 160°c) the average secondary dendrite arm spacing (sdas) was found equal to 38 μm and the average grain size to 501 μm; the value of the 0.2% yield stress obtained from tensile tests was 275 mpa. macroscopic torsion fatigue specimens were machined according to iso-13522011 standard [5] and reversed torque-controlled fatigue tests were carried out using a mts 809 axial/torsional servohydraulic machine at a frequency of 10 hz. a polished flat surface was produced along the cylindrical sample gage length in order to monitor crack development by in situ optical microscopy. electron back scattered diffraction observations of this surface were performed post mortem. in situ reversed torque controlled torsion tests were also carried out at the european synchrotron radiation facility (esrf) on beamline id19 on smaller samples (3mm diameter) in order to monitor crack initiation and growth in the bulk using x-ray tomography. the samples were cycled in situ with a dedicated rig and observed under load at the two extreme values of torque (+ max and – max). the sample shown here had been submitted to 195 kcycles at |max|=120 mpa before a first imaging scan was performed. then a scan was recorded every 10 or 20 kcycles until 305 kcycles. experimental results and discussion the first scan at 195 000 cycles at a=120 mpa, vertical cracks (ie cracks which intersection with the sample surface is aligned with the cylindrical sample axis) and horizontal cracks (ie crack perpendicular or nearly perpendicular to the sample axis) were observed. an optical image of one horizontal crack is shown on fig. 1. figure 1: optical micrograph of a mode ii intragranular crack fatigue crack observed after 100 000 kcycle (max=95 mpa). the sample axis is vertical on the figure. the plane of the crack correspond to a {111} plane the white lines show the grain boundaries with two neighbouring grains. figure 2: 3d rendering of a crack perpendicular to the sample axis similar to the one shown in fig. 1 at two different numbers of cycles.(195k cycles and 215k cycles). t o d. shiozawa et alii, frattura ed integrità strutturale, 33 (2015) 56-60; doi: 10.3221/igf-esis.33.07 58 ebsd analysis has revealed that such cracks form on the {111} planes which experience the highest slip activity (iso strain taylor analysis) [5]. a strong interaction with the grain boundaries is observed, generally accompanied by a pronounced change of direction. the sub-surface development of such a crack can be observed at 195,000 and 215,000 cycles in fig. 2. from the various images recorded in 3d, we observed that mode ii growth (at the intersection of the crack tip with the surface) was faster than mode iii growth (in the bulk). this is shown in fig. 3 where one can observe that the crack length on the surface c increases rapidly with increasing in number of cycles n and tends to saturate when a crack length of the order of 3mm is reached. the sub surface crack length a increases almost linearly, and less rapidly, as a function of n. the crack arrest and/or decrease in crack propagation rate in mode ii crack has been linked in the literature to crack tip shielding [6, 7] induced by the friction between the crack surfaces (some debris between the crack surfaces have been observed in the interior of the sample as well as at the surface). figure 3: crack growth curve of the crack shown in fig. 2: surface growth (mode ii) is more rapid than bulk growth. after a rapid intragranular propagation below the surface in mode ii, cracks similar to those shown in fig. 1 and 2 will eventually grow toward the interior of the sample. this second stage of propagation corresponds however to a change in mode as can be seen on fig. 4. fig. 4(c) show reconstructed images parallel to the z-axis, and at various depth within the bulk as indicated by the white lines shown in fig. 4(a). one can clearly see that when moving from the surface towards the interior the cracks evolve from a (nearly) horizontal orientation towards a 45° orientation (with respect to the z-axis) corresponding to a gradual change from mode iii towards mode i opening. figure 4: (a) and (b): projection along the z axis of the minimum intensity in the reconstructed volume of the sample after 265k cycles, (c) vertical slice at the positions indicated by the white lines. fig. 4(a) shows a projection of the minimum intensity of the voxels of the reconstructed volume of the sample along the z direction. a crack (or a porosity) which shows little attenuation appears in black on such projections and a darker grey d. shiozawa et alii, frattura ed integrità strutturale, 33 (2015) 56-60; doi: 10.3221/igf-esis.33.07 59 level corresponds to a larger opening of the crack (or to a larger porosity) and vice versa. with this type of rendering, the closing/opening of some parts of the crack open in mode i below the surface under the application of the positive or negative torque can clearly be observed. to discuss the change of crack propagation mode from mode iii to mode i in the bulk of the sample, the values of stress intensity factors for a crack in torsion have been calculated by fem analysis. the fem model used is shown in fig. 5: a crack of depth aii ( aii =180m) similar to the crack shown in fig. 2 is modeled. the distribution of the stress intensity factor values along the crack tip for a circumferential length c=0.25mm is shown in fig. 6. as expected, ki is equal to 0 all along the crack front. on the contrary, kii is maximum at the point corresponding to the intersection between the crack tip and the surface and is equal to 0 inside the sample. kiii is maximum inside the sample. several calculations have been performed with increasing values of c. it is found that when c increases, ki remains equal to 0 and, after a slight increase, the kii values saturate . although the change in crack propagation mode inside the sample cannot be correlated to the calculated distribution of ki, the saturation in crack growth rate observed for intragranular growth could be the result of the saturation observed for kii values when c increases.the stress intensity values found from our model cannot therefore account for the transition between mode iii to mode i observed in the bulk. however, it can clearly be observed from fig. 1 that when meeting a grain boundary the observed fatigue cracks can be strongly deflected. this could also happen in the bulk. if a small kink crack forms at the crack tip in the bulk (or at the surface), because of the local crystallography, the values of the mode i stress intensity factor will increase rapidly [4] and mode i growth can take place. figure 5: fem model (aii=0.18mm, d=3.5mm). figure 6: stress intensity factor of stress intensity factor along crack front for a circumferential length c=0.25mm, =120mpa. d. shiozawa et alii, frattura ed integrità strutturale, 33 (2015) 56-60; doi: 10.3221/igf-esis.33.07 60 conclusions he mechanisms of crack initiation and propagation during cyclic reversed torque controlled experiment have been studied in situ. surface observations (optical microscopy and ebsd) show that intragranular cracks initiate in mode ii and have a strong cristallographic character. the planes of these cracks correspond to highly activated {111} slip planes. strong deviations are often observed when those mode ii cracks encounter some grain boundaries. the bulk development of those cracks has been imaged inside the sample bulk by synchrotron x-ray tomography. the crack growth rate at the surface (mode ii) is faster than in the bulk (mode iii) leading to a shallow crack. friction between the crack surfaces might impede mode iii growth in the bulk for low values of the applied torque. when the number of cycles is increased, however, the growth in the bulk resumes but in mode i. the values of the mode i, ii and iii stress intensity factors computed from a fe simulation cannot account for this transition from mode iii to mode i unless some kink appears at the crack tip. such a kink might be produced by a change in the local crystallography (grain boundary) as observed for the mode ii cracks at the surface. references [1] murakami y, takahashi k, toyama k., mechanism of crack path morphology and branching from small fatigue cracks under mixed loading. fatigue fract engng mat struct, 28(1–2) (2005) 49–60. [2] sawada m, bannai k, sakane m., crack propagation of type 304 stainless steel in torsion low cycle fatigue, j soc mat sci jpn, 54(6) (2005) 615–21. [3] murakami, y., takahashi, k., kusumoto, r., threshold and growth mechanism of fatigue cracks under mode ii and iii loading, fatigue fract engng mater struct 26(2003), 523–531. [4] shiozawa, d., nakai, y., murakami, t., nosho, h., observation of 3d shape and propagation mode transition of fatigue cracks in ti–6al–4v under cyclic torsion using ct imaging with ultra-bright synchrotron radiation, int. j. fatigue, 58 (2013) 158-165. [5] phd i.serrano munoz insa lyon (2014), http://theses.insa-lyon.fr/publication/2014isal0117/these.pdf (in english) [6] matsunaga, h., muramoto, s., shomura, n., endo, m., shear mode growth and threshold of small fatigue cracks in suj2 bearing steel, j soc mat sci jpn, 58(9) (2009) 773–80. [7] campbell, jp, ritchie, ro. mixed-mode, high-cycle fatigue-crack growth thresholds in ti–6al–4v: ii. quantification of crack-tip shielding, eng fract, mech, 67 (2000) 229–49. t microsoft word numero_50_art_13_2495 a. tijani et alii, frattura ed integrità strutturale, 50 (2019) 141-148; doi: 10.3221/igf-esis.50.13 141 corrosion’s impact on wire rope strand response – comparison with a theoretical predictive model amal tijani laboratory of atmosphere’s physics, materials and modeling, fst mohammedia, hassan ii university of casablanca, bp 146 mohammedia, morocco amaltijani@gmail.com, http://orcid.org/0000-0003-4543-1253 meryam meknassi laboratory of control and mechanical characterization of materials and structures, national higher school of electricity and mechanics (ensem), hassan ii university of casablanca, b.p 8118 oasis – casablanca, morocco hassan chaffoui laboratory of atmosphere’s physics, materials and modeling, fst mohammedia, hassan ii university of casablanca, bp 146 mohammedia, morocco mohamed elghorba laboratory of control and mechanical characterization of materials and structures, national higher school of electricity and mechanics (ensem), hassan ii university of casablanca, b.p 8118 oasis – casablanca, morocco abstract in this work, we investigate the behavior of wire ropes when they are subject to corrosion damage. the method is based on accelerated corrosion using experimentation as well as a theoretical predictive model. the experimental approach used static tensile tests on corroded strands. a loss in rigidity and decrease of the ultimate force was observed. for the predictive model, the residual ultimate force was evaluated at a time t in function of the initial diameter, the residual diameter at time t and the ultimate force of the original strand. given that the obtained residual force evolution depending on the strand’s fraction of life matched for both methods, the proposed predictive model can be used by engineers to assess if the wire rope needs to be changed to ensure a good maintainability of structures. actually, when the applied force on the wire rope approaches its residual bearing force determined by a measure of the residual diameter, the wire rope removal is mandatory. keywords wire rope; accelerated corrosion; damage; residual force; reliability; predictive maintenance. citation: tijani, a., meknassi, m., chaffoui, h., elghorba, m., effect of corrosion on wire rope strand response comparison with a theoretical predictive model, frattura ed integrità strutturale, 50 (2019) 141-148. received: 24.05.2019 accepted: 19.07.2019 published: 01.10.2019 copyright: © 2019 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. http://www.gruppofrattura.it/va/50/2495.mp4 a. tijani et alii, frattura ed integrità strutturale, 50 (2019) 141-148; doi: 10.3221/igf-esis.50.13 142 introduction lot of civil engineering structures use wire ropes [1] like suspended bridges, cable stayed bridges, prestressed concrete structures or cableways. being involved in the structure of a large part of road and rail networks, these elements are subject to mechanical, thermal and environmental solicitations. thus, regular monitoring and maintenance are mandatory in order to avoid any consequent economic and social disagreement due to the closure of the supported structure. the main function of a wire rope in an engineering structure is to transmit the traction load from the deck to the piles (suspended and cable stayed bridges) or to compress the concrete (prestressed structures). according to their use, wire ropes are exposed to variable loading levels in more or less aggressive environment. these cables are made of drawn steel wires which have a very high tensile strength and a carbon content close to the eutectoid [2]. wire drawing is a process of wire transformation which consists in hardening the machine wire and then improving their mechanical characteristics by reducing their diameters when passing through dies. thus, wire ropes have high yield strength and can support high axial loads. thanks to their multi-component nature, the cable can continue to ensure its function in spite of the breakage of one or more wires. indeed, in a multi-stranded cable, a broken wire has the ability to re-anchor by friction and to recover its load capacity [3]. moreover, their flexibility makes it possible to store them on coils, which facilitates their implementation on structures, but also promotes their use in lifting gear thanks to the possibility of passage through pulleys. during their service life, broken wires appear on the wire ropes. in that respect, most codes and regulations use the number of broken wires as a criterion for quantifying the degradation level [4]. moreover, regarding the low alloy steel composition and the environmental conditions (marine atmosphere, pollution, rain, etc.), the cables have an "ordinary" predisposition to corrosion [5]. so far, it is still difficult to quantify the impact of corrosion on the state of the structure and its safety of use. drawn steel corrosion has been investigated in conditions simulating the wire rope loading in prestressed concrete structures (stress corrosion) [6] and in bridges (fretting-fatigue corrosion) [7]. the fatigue strength reduction due to corrosion was studied in the case of bolted joins using an accelerated process of the marine-industrial environment [8]. fretting fatigue of wire ropes used in coal mines has been studied in four different corrosive medias [9]. this work was carried out at the scale of the wire. other research focused on the breakage of wires in wire ropes and their impact on the cable behavior. beltrán and de vico used numerical modeling for the study of wire ropes behavior with asymmetric damage [10,11].wang et al [12] investigated the wire failure mechanisms by acoustic emission, torkar and arzensi [13] investigated the failure of a crane wire rope. the main reasons were fatigue and lack of inspection. this work is a contribution to the methods of predicting the wire ropes behavior and life time. the influence of corrosion is investigated at the strand’s scale. the choice of carrying out our study on the strand’s scale is justified by the following points: the strand is representative of the wire rope. this is, in fact, a specific case of wire rope construction (strand wire). the results obtained for a strand can therefore be extended to the case of the cable; taking into account the evolution by layers of the corrosion [14], it is necessary to have data not only on the corrosion of the constitutive wires but also on that of the strands. the proposed method is based on accelerated corrosion by immersing strands in sulfuric acid for different lengths of time. besides, damage estimation is obtained by only static tensile tests. material and methods he wire rope used for this research is manufactured by bridon, of type 19*7 (1 * 7 + 6 * 7 + 12 * 7), rotation resistant, 10 mm diameter, with independent wire rope core (iwrc), right hand lay and preformed. general characteristics of the cable are given on table 1. specimens preparation samples are prepared in accordance with the iso standard 6892 [15] relative to tensile tests on metal materials. strands are extracted from the external layer of the wire rope cut beforehand to a length of 300 mm (200 mm according to the iso standard over 100 mm required for mooring). this operation is carried out with particular care so as not to damage the specimens. then, in the same way, wires are extracted from the strands. a t a. tijani et alii, frattura ed integrità strutturale, 50 (2019) 141-148; doi: 10.3221/igf-esis.50.13 143 cable diameter 10 mm construction 19x7 strand diameter of external layer 1.9 mm strand diameter of internal layer 2.1 mm wire rope core diameter 2.4 mm strand wire diameter 0.58 mm strand core diameter 0.68 mm strand construction 6/1 coating galvanized core metallic approximate mass 40.4 kg/100 m lubrication a2/w-3 breaking force 68.6 kn table 1. wire rope general information corrosive solution the objective of studying the behavior of corroded wire ropes is reminded in the iso standard 7539 [16]: ‘’the objective of corrosion tests is, in general, to provide information faster than this obtained from experience in service and in the same time, to predict the behavior in service’’. every kind of material has a susceptibility to corrosion in a specific media. in our case, we have the choice between the solutions below: ‐ solution naoh ‐ nitrate solution ‐ carbonate solution ‐ sea water ‐ h2s in their paper, wang et al [17] studied the corrosion fatigue phenomena under 4 different medias : hydrochloric acid, sulfuric acid, water sea and neutral solution. the research demonstrated the influence of the sulfuric acid on the drawn wires. it was the media which reduces the most the life time of the material. for this purpose, we choose to use a corrosive solution based on sulfuric acid. furthermore, in a precedent research aimed in the determination of the critical acid concentration, meknassi et al [18] experimented the corrosion of drawn wires from a 19x7 wire rope in solutions of different concentration of sulfuric acid (from 10% to 90% with a step of 10%). the critical concentration was found for 30% of sulfuric acid. strands and wires chemical damage in order to damage the central part of the strands and wires, the specimens are immerged in the acid solution according to the scheme in figure 1. the depth of the solution is fixed such as we obtain a corroded length of 100 mm for each sample. the immersion time is: 4 h, 8 h, 16 h, 24 h and 32 h. figure 1. accelerated corrosion procedure a. tijani et alii, frattura ed integrità strutturale, 50 (2019) 141-148; doi: 10.3221/igf-esis.50.13 144 tensile tests tensile tests are made under imposed displacement corresponding to a speed of 1.5 mm/min [19] on a zwick roell machine with a loading capacity of ±10 kn. photos of the testing machine and a strand specimen after tensile test are represented on figure 2. figure 2. fitting of test specimens on the testing machine – zoom on the fixing jaws overview of a strand after the tensile test figure 3. wire’s pit configuration corrosion strength calculation n this section, we propose to estimate the strands loss of strength after their corrosion in function of the fraction of lifetime. to do so, we will estimate the loss of strength according to the stewart model [20] based on the loss of corroded section. i a. tijani et alii, frattura ed integrità strutturale, 50 (2019) 141-148; doi: 10.3221/igf-esis.50.13 145 corroded section calculation according to val et al [21], the section consumed by corrosion ap(t) is expressed in formula 1. it uses a probabilistic analysis of experimental data to determine the maximum corrosion depth p(t) and the geometrical shape of the corroded wire section. 0 1 2 2 0 0 1 2 0 2 0 0 if ( ) 2 ( ) if ( ) 4 2 if ( ) 4 p d a a p t d d a t a a p t d d p t d                 (1) with: 2 2 0 0 1 1 0 ( ) 0.5 2 2 d d p t a b d             2 2 2 2 0 ( ) 0.5 ( ) p t a p t b d         2 0 ( ) 2 ( ) 1 p t b p t d        1 0 2 arcsin b d         2 2 arcsin 2 ( ) b p t         the residual surface of the wire is then: 2 0( ) ( ) 4 a p d a t a t    (2) tensile strength reduction of the corroded wires structures are designed to withstand permissible loads. when attacked by corrosion, the decrease of wires’s cross-section induces a reduction in their strength. thus, irreversible damage can occur leading to the collapse of the structure. it is therefore important to take into account the reduction of the resistance of the corroded elements if it is desired to keep them in service. the model described by stewart et al. [20] expresses the strength of the corroded wires fpy (t) as a function of the strength of the undamaged wires fpy0: 0 ( ) ( ) 1 ( ) p py y py a a t f t f a t         (3) a. tijani et alii, frattura ed integrità strutturale, 50 (2019) 141-148; doi: 10.3221/igf-esis.50.13 146 where αy is a coefficient of a mean value to consider equal to 0,005. results and discussion predictive force loss he multi-component nature of the strand does not allow us to clearly measure the section of the corroded samples. to this end, wire samples extracted from the cable subject to this study were subjected to corrosion under the same conditions as the strands. the diameter loss ratio was recorded for different lifetimes [18]. corrosion time (in hours) 0 4 8 16 24 32 40 diameter loss ratio (in %) 0 7 15 25 35 50 80 table 2. diameter loss ratio in function of the immersion time in the corrosive solution instead of using the probabilistic model of the consumed section by corrosion ap(t) which can change in function of the material [20], we change the formula (3) and express it in function of the residual diameter, the ultimate and residual force of the wire. thus, the experimental data relative to our wire will be used. the expression becomes: 2 2(1 )ur r y r uf d d f     (4) where: urf is the residual force of the corroded wire; uf is the ultimate force of the undamaged wire; rd is the residual diameter ratio; it represents the balance of the diameter loss ratio. experimental strands force loss the resulting tensile tests on the corroded strands are represented on figure 4. the mean residual tensile forces obtained for each immersion time are illustrated on table 3. in addition to the reduction of the residual force which increases with the acid immersion time, a decrease in the rigidity of the strands is observed. this has also been noted in other studies[22][23]. figure 4. representative tensile curves of the corroded strands t a. tijani et alii, frattura ed integrità strutturale, 50 (2019) 141-148; doi: 10.3221/igf-esis.50.13 147 immersion time (in hours) 0 4 8 16 24 32 residual ultimate force (in n) 3770 3397 3130 1960 1160 834 table 3. residual ultimate forces of corroded strands for different immersion times thus, we draw the theoretical and experimental curves of the ultimate force reduction rate as a function of the life fraction (fig. 5). the ultimate force reduction rate is equal to the ratio between the ultimate residual force of the corroded material at time t and the ultimate strength of the original material. the fraction of life corresponds to the ratio between the time t in hours and the total time corresponding to the loss of total resistance of the material which was set to 40 h. figure 5. ultimate force reduction rate in function of the life fraction of the strands loss of experimental and theoretical force from the figure, we can see that the curves obtained experimentally and deduced theoretically correspond overall. thus, the correspondence between the wire’s scale and the strand’s scale can be established. conclusion n this paper, we were interested in evaluating the impact of corrosion on the wire rope behavior. the choice of the corrosive solution was based on the material sensibility and preliminary tests aimed to set the critical acid concentration. static tensile tests were made on the virgin and corroded strands. the high resistance of the material was confirmed. the ultimate strength was up to 1935 mpa with yield strength of 1800 mpa. as a fact, the drawn wires work essentially on elastic phase. tensile tests on the corroded strands showed a decreasing ultimate force with the increasing corrosion time. a loss in strand’s rigidity was also observed in the corroded strands. besides, theoretical formulation was developed to predict the corrosion influence on the wire ropes strength. the formulation gives the residual ultimate force estimation at time t in function of the initial diameter, the residual diameter at time t and the ultimate force of the original strand (before corrosive damage). a monitoring at the wire’s scale gave us the diameter ratio loss corresponding to each corrosion time. thus, the estimated rate of ultimate force loss is drawn in function of the fraction of life. the comparison is made with the experimental curve obtained from tensile test on the corroded strands. a good matching appears between the two curves. as a result, by evaluating the bearing force of wire rope affected by corrosion during its life service, engineers can assess the possibility of maintaining the structure in service and define the time of removal. this way conciliation is ensured between optimization and reliability of the structure. i a. tijani et alii, frattura ed integrità strutturale, 50 (2019) 141-148; doi: 10.3221/igf-esis.50.13 148 references [1] calgaro, j.-a., bernard-gely, a. (2009). conception des ponts démarche de conception, tech. l’ingénieur les routes, les ponts les joints, c4496. [2] brevet, p., olivie, f., guilbaud, j.p., raharinaivo, a. (2004). microstructure et propriétés mécaniques des aciers pour câbles, bull. ddes lab. des ponts chaussées, pp. 35–48. [3] raoof, m., kraincanic, i. (1998). determination of wire recovery length in steel cables and its practical applications, comput. struct., 68(5), pp. 445–59, doi: 10.1016/s0045-7949(98)00088-1. [4] chaplin, c.r. (1995). failure mechanisms in wire ropes, eng. fail. anal., 2(1), pp. 45–57, doi: 10.1016/1350-6307(95)00004-a. [5] brevet, p. (2005). pathologie des haubans et cables fatigue – corrosion, journée câbles 2005, laboratoire central des ponts et chaussées. [6] perrin, m., gaillet, l., tessier, c., idrissi, h. (2010). hydrogen embrittlement of prestressing cables, corros. sci., 52(6), pp. 1915–26, doi: 10.1016/j.corsci.2010.02.041. [7] périer, v., dieng, l., gaillet, l., tessier, c., fouvry, s. (2009). fretting-fatigue behaviour of bridge engineering cables in a solution of sodium chloride, wear, 267(1–4), pp. 308–14, doi: 10.1016/j.wear.2008.12.107. [8] zampieri, p., curtarello, a., pellegrino, c., maiorana, e. (2017). fatigue strength of corroded bolted connection, frat. ed integrità strutt., 12(43), pp. 90–96, doi: 10.3221/igf-esis.43.06. [9] wang, d., zhang, d., zhao, w., ge, s. (2014). quantitative analyses of fretting fatigue damages of mine rope wires in different corrosive media, mater. sci. eng. a, 596, pp. 80–88, doi: 10.1016/j.msea.2013.12.047. [10] beltrán, j.f., williamson, e.b. (2011). numerical procedure for the analysis of damaged polyester ropes, eng. struct., 33(5), pp. 1698–1709, doi: 10.1016/j.engstruct.2011.02.007. [11] beltrán, j.f., de vico, e. (2015). assessment of static rope behavior with asymmetric damage distribution, eng. struct., 86, pp. 84–98, doi: 10.1016/j.engstruct.2014.12.026. [12] wang, d., zhang, d., ge, s. (2012). effect of displacement amplitude on fretting fatigue behavior of hoisting rope wires in low cycle fatigue, tribol. int., 52, pp. 178–89, doi: 10.1016/j.triboint.2012.04.008. [13] torkar, m., arzenšek, b. (2002). failure of crane wire rope, eng. fail. anal., 9(2), pp. 227–233, doi: 10.1016/s1350-6307(00)00047-9. [14] elachachi, s.m., breysse, d., yotte, s., cremona, c. (2006). a probabilistic multi-scale time dependent model for corroded structural suspension cables, probabilistic eng. mech., 21(3), pp. 235–45, doi: 10.1016/j.probengmech.2005.10.006. [15] iso 6892. (1984). matériaux métalliques essai de traction, ,. [16] iso 7539-1. (2012). corrosion of metals and alloys stress corrosion testing part 1: general guidance on testing procedures. [17] wang, s., zhang, d., chen, k., xu, l., ge, s. (2014). corrosion fatigue behaviors of steel wires used in coalmine, mater. des., 53, pp. 58–64, doi: 10.1016/j.matdes.2013.06.059. [18] meknassi, m., mouhib, n., tijani, a., el ghorba, m. (2015). experimental study of wires extracted from steel wire rope and exposed to sulfuric acid, ipasj int. j. mech. eng., 3(11), pp. 47–53. [19] tijani, a., meknassi, m., chaffoui, h., elghorba, m. (2017). combined effect of broken rope components and corrosion on damage evolution through its lifetime, j. mater. civ. eng., 29(7), pp. 04017035, doi: 10.1061/(asce)mt.1943-5533.0001846. [20] stewart, m.g., al-harthy, a. (2008). pitting corrosion and structural reliability of corroding rc structures: experimental data and probabilistic analysis, reliab. eng. syst. saf., 93(3), pp. 373–382, doi: 10.1016/j.ress.2006.12.013. [21] val, d. v., melchers, r.e. (1997). reliability of deteriorating rc slab bridges, j. struct. eng., 123(12), pp. 1638–44, doi: 10.1061/(asce)0733-9445(1997)123:12(1638). [22] périer, v., dieng, l., gaillet, l. (2007). modélisation de la fatigue de contact dans les câbles corrodés, 18ème congrès français de mécanique. [23] françois, r., arliguie, g., escadeillas, g., francy, o. (1998). optimisation des structures en béton armé vis-à-vis de la corrosion, rev. française génie civ., 2(8), pp. 949–968, doi: 10.1080/12795119.1998.9692221. << /ascii85encodepages false /allowtransparency false /autopositionepsfiles true /autorotatepages /none /binding /left /calgrayprofile (dot gain 20%) /calrgbprofile (srgb iec61966-2.1) /calcmykprofile (u.s. web coated \050swop\051 v2) /srgbprofile (srgb iec61966-2.1) /cannotembedfontpolicy /error /compatibilitylevel 1.4 /compressobjects /tags /compresspages true /convertimagestoindexed true /passthroughjpegimages true /createjobticket false /defaultrenderingintent /default /detectblends true /detectcurves 0.0000 /colorconversionstrategy /cmyk /dothumbnails false /embedallfonts true /embedopentype false /parseiccprofilesincomments true /embedjoboptions true /dscreportinglevel 0 /emitdscwarnings false /endpage -1 /imagememory 1048576 /lockdistillerparams false /maxsubsetpct 100 /optimize true /opm 1 /parsedsccomments true 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can be opened with acrobat and adobe reader 5.0 and later.) >> /namespace [ (adobe) (common) (1.0) ] /othernamespaces [ << /asreaderspreads false /cropimagestoframes true /errorcontrol /warnandcontinue /flattenerignorespreadoverrides false /includeguidesgrids false /includenonprinting false /includeslug false /namespace [ (adobe) (indesign) (4.0) ] /omitplacedbitmaps false /omitplacedeps false /omitplacedpdf false /simulateoverprint /legacy >> << /addbleedmarks false /addcolorbars false /addcropmarks false /addpageinfo false /addregmarks false /convertcolors /converttocmyk /destinationprofilename () /destinationprofileselector /documentcmyk /downsample16bitimages true /flattenerpreset << /presetselector /mediumresolution >> /formelements false /generatestructure false /includebookmarks false /includehyperlinks false /includeinteractive false /includelayers false /includeprofiles false /multimediahandling /useobjectsettings /namespace [ (adobe) (creativesuite) (2.0) ] /pdfxoutputintentprofileselector /documentcmyk /preserveediting true /untaggedcmykhandling /leaveuntagged /untaggedrgbhandling /usedocumentprofile /usedocumentbleed false >> ] >> setdistillerparams << /hwresolution [2400 2400] /pagesize [612.000 792.000] >> setpagedevice microsoft word 2332 a. fesenko et alii, frattura ed integrità strutturale, 48 (2019) 768-792; doi: 10.3221/igf-esis.48.70 768 an uncoupled thermoelasticity problem for a semi-infinite layer with regard to its proper weight a. fesenko, n. vaysfel’d faculty of mathematics, physics and information technologies, odessa i. i. mechnikov national university, ukraine 81anna81@gmail.com, vaysfeld@onu.edu.ua abstract. the exact solution of the uncoupled thermoelasticity problem for a semi-infinite elastic layer with regard to its proper weight was constructed. the originality of the proposed paper is based on reducing lame equations to two jointly and one separately, solvable equations. it allows the application of integral transformations directly to the transformed equations of equilibrium and makes it possible to reduce the initial problem to a one-dimensional vector boundary problem. a special technique is given to calculate multiple integrals containing oscillating functions that appear during the inversion of the transforms. the character of the temperature and proper weight influence on the value of normal stress on the lateral face of the semi-infinite layer, the zone of tensile stress depending on the shapes of the distributed load section and the temperature and poisson's ratio is established. the parameters of dimensionless mechanical load and temperature, when the separation of the side wall of the semi-infinite layer can be eliminated, were established. a study of the influence of the layer’s proper weight on the stress emerging on the layer’s edge is conducted. the constructed exact solution can be used as a model for solving a similar class of problems by numerical methods. keywords. uncoupled thermoelasticity problem; semi-infinite layer; proper weight; tensile stress. citation: fesenko, a., vaysfel’d, n. an uncoupled thermoelasticity problem for a semi-infinite layer with regard of its proper weight, frattura ed integrità strutturale, 48 (2019) 768-792. received: 12.12.2019 accepted: 14.03.2019 published: 01.04.2019 copyright: © 2019 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. introduction number of methods of three-dimensional problem studies in elasticity are based on representations of homogeneous lame equation solutions using harmonic and biharmonic functions. such representations were given by j. v. boussinesq, w. thomson (lord kelvin), and p. g. tait [1] where the possibility of reducing the number of harmonic functions to three was also considered. b. g. galerkin presented the general solution of homogeneous equilibrium equations for an isotropic body through three biharmonic functions. in the works of p. f. papkovich [2] and h. neuber [3] a solution form containing four harmonic functions reducing the lame equations to a harmonic sequence with unshared boundary conditions was proposed. a http://www.gruppofrattura.it/va/48/2332.mp4 a. fesenko et alii, frattura ed integrità strutturale, 48 (2019) 768-792; doi: 10.3221/igf-esis.48.70 769 using functions of a complex variable and integrals of cauchy type in monographs g.v. kolosov [4] and i. i. muskhelishvili [5] developed an effective method for solving plane boundary problems of elasticity, which later became classical. although this method is not directly applicable to the spatial problems of elasticity, the apparatus of functions of a complex variable is also used in solving problems of this class. so, g. n. polozhii [6] proposed a method for solving axisymmetric spatial problems in elasticity, it involves using two p-analytic functions and is an analog of kolosov muskhelishvili's complex potential method. another way to investigate three-dimensional problems is the method of integral equations, with its help, the existence and unique theorems for the solution of boundary value problems can be proved. this method often serves as a basis for developing algorithms for the numerical solution of elasticity problems. the monograph [7] is devoted to the method of integral equations. the method of integral transforms is widely used in spatial problems of elasticity. with the help of the corresponding integral transform, a transition is made to a simpler problem in the domain of transforms. an extensive bibliography of papers on the use of this method in problems of elasticity theory is given in the monograph by ya. s. uflyand [8]. thus, the above methods, using different representations’ solutions through auxiliary harmonic and biharmonic functions, which, on one hand, facilitated solving in terms of these functions, but on the other hand it causes difficulties during the calculation of the original functions these difficulties in itself present a complex mathematical problem. one of the basic methods to construct an exact solution for spatial problems of elasticity is the fourier method, which is based on the use of curvilinear orthogonal coordinate systems that allow the separation of variables in the threedimensional laplace equation for static problems. one notes that solutions obtained by the fourier method are the initial steps to construct solutions for problems of finite bodies bounded by surfaces described by canonical coordinate systems. using the method of variable separation demands different representations of the equilibrium equations solutions through the stress functions. with the help of such representations, the original problem is reduced to solving differential equations of a simpler structure. each stress function in these equations is not related to the others, but it is presented in the boundary conditions together with the others. the solution in the form of papkovich neuber is used most often, because it allows the application of classical solutions of the potential theory by solving boundary value problems, represented in the form of series and integrals containing special functions. another way to investigate spatial problems is the method of eigenvector functions, which is a vector analog of the fourier method, this was proposed in [9]. it involves the construction of vector structure eigen functions on the boundary surface of the bodies. with the help of this method, solutions were obtained for complex three-dimensional problems of elasticity. in paper [10] a method of two-dimensional singular equations for three-dimensional problems of stationary thermal conductivity and thermoelasticity for bodies with cracks was developed, and several problems for a semi-infinite body with cracks were solved. a new approach proposed by g. ya. popov in [11] is used in this paper. the method is based on reducing lame equations to one independently solvable and two jointly solved equations. moreover, the boundary conditions are also separated, which greatly simplifies the calculation technique in comparison with traditional methods. by the method of integral transforms applied directly to the transformed equations of equilibrium and the boundary conditions of the initial stated problem, one reduces it to a one-dimensional vector boundary value problem, which is solved exactly. the problem of elasticity for a quarter space was solved with this method in [12]. the elastic layer, as an important and frequently used model object, has been studied by many authors. thus, in a static formulation, the axisymmetric contact problems for an elastic layer and strip are considered in [13-15], various mixed boundary-value thermoelasticity problems for a half-layer and a half-space in [16-23], layers with thermal loadings were considered in [24] with no static loading, where the conformal mapping method was used, dynamic problems were investigated in [25-27]. the papers [28, 29] are devoted to solving elasticity problems for bodies with their proper weight. in paper [30] the authors investigated the propagation of thermoelastic waves through the layers and analyzed the importance of thermally nonlinear generalized thermoelastic analysis. in [31] the size-dependent quality factor of thermoelastic damping in a microbeam resonator, based on modified strain gradient elasticity was analyzed. the generalized thermoelasticity theory of the lord–shulman model was used to derive the equation of coupled thermoelasticity. the paper [32] is devoted to study functionally graded nanodisks under thermoelastic loading based on the strain gradient theory, where the effects of external load at the inner and outer radii on radial displacement as well as stress components were considered. in [33] the influence of measurement errors on the accuracy of the estimated heat flux and mechanical load on laminated functionally graded plate was investigated. thermo-elasticity problems of functionally graded materials were evaluated in [34]. in [35] an exact solution for thermoelastic deformations of functionally graded thick rectangular plates was derived. the contact problem of two semi-infinite kirchhoff plates on the a. fesenko et alii, frattura ed integrità strutturale, 48 (2019) 768-792; doi: 10.3221/igf-esis.48.70 770 elastic layer is considered in [36]. the contact stresses concentrations between the plates and the layer was studied, as it can induce destruction of the engineering structure. the advances in the use of thermoelastic stress analysis for fracture mechanics assessment were reviewed in [37]. the development of techniques to determine stress intensity factor was presented, followed by the application of these techniques to fatigue crack growth. the work [38] investigates the behavior of a transvers crack tensile specimen undergoing fatigue loading, by means of a thermoelastic stress analysis experimental setup. the information on the stress distribution settling near the crack tips and its evolution with crack growth under fatigue is provided. a review of the above papers shows that the problem of constructing an exact solution for problems of an elastic layer remains open, despite the variety of methods and in particular numerical solutions. the results obtained, based on the exact solution of the spatial problem can be used as the basis for solving problems by approximate numerical methods. this dictates an increasing interest in the development of analytical methods to solve three-dimensional elasticity problems and in particular for a layer as the most important model object. the purpose of this paper is to establish the changes in the fields of displacements and stress of the semi-infinite elastic layer for the effects of different types of loading, in particular temperature, mechanical loads and proper weight. earlier in paper [16], the problem of stationary heat conduction and the elasticity problem for a layer were solved separately. it was stated that using this technique makes it is possible to solve the problem of uncoupled thermoelasticity, which was accomplished in this work. solving this task requires use of the green function apparatus, moreover, the green matrix function, which has not been used for the problems of this type. the proposed work consists of a new approach that makes it possible to obtain an exact solution of mixed uncoupled thermoelasticity, which can be also applied to solve analogical problems with much more complicated boundary conditions. the statement of the mixed uncoupled thermoelasticity problem et’s consider the elastic semi-infinite layer (fig. 1) occupying the area          0 , , 0x y z h (1) , ,x y z are the cartesian’s coordinate system figure 1: geometric model of the problem the conditions of an ideal contact are given at the layer’s edge  0x and at the lower face  0z by this, the authors mean frictionless contact conditions. at the same time, these faces are thermo-isolated. the known temperature ( , , )t x y z , found earlier from the corresponding thermoconductivity problem, and pressure load ( , )p x y both l a. fesenko et alii, frattura ed integrità strutturale, 48 (2019) 768-792; doi: 10.3221/igf-esis.48.70 771 distributed on the segments   [0, ], [ , ]x a y b b are applied at the upper face z h . the proper weight of the layer should be taken into consideration. the stated problem for the semi-infinite layer is formulated in terms of the boundary value problem                                  * * * , , u ( ) ( , , ) (3 2 ) v ( ) ( , , ) (3 2 ) w ( ) ( , , ) (3 2 ) g g x x y z g t g g y x y z g t g g z x y z g t (2) here           2 2 2 2 2 2x y z is a laplace's differential operator, *u ( , , )xu x y z ,  *v ( , , )yu x y z ,  *w ( , , )zu x y z unknown displacements,           ,, , f f f f f f x y z , , ,x y z are the components of the proper weight force. λ, g are lame's constants and    u ( , , ) v ( , , ) w ( , , ),x y z x y z x y z is a volume expansion, α is a coefficient of linear expansion. one must solve the boundary value problem with the following boundary conditions. the conditions of an ideal contact are given at the layer’s edge  0x and at the lower face  0z        * 0 0 0 u 0, 0, 0xz xyx x x (3)       * 0 00 w 0, 0, 0zx zyz zz (4) the pressure load ( , )p x y distributed on the segments   [0, ], [ , ]x a y b b is applied at the upper face z h          ( , ), 0, 0z zx zyz h z h z hp x y (5) the authors propose to solve the previously the stated problem for the subcase when the unit normal loading is applied to an arbitrary point on the upper face of the layer. the solution to this problem could be used as an influence function to construct the solution for the stated loading. for this subcase the boundary conditions (5) take the form             ( ) ( ), 0, 0z zx zyz h z h z hx a y b (6) ( )x dirac’s function. the field of displacements and stress should be found. the temperature ( , , )t x y z , on the right hand parts of lame’s equations (2), is unknown. it’s needed to solve the corresponding thermoconductivity problem for the layer (1) with the same lame’s constants. these values will be used as known in further calculations. statement and solving the corresponding thermoconductivity problem for a semiinfinite layer t’s necessary to construct a solution to laplace's equation decreasing on infinity  ( , , ) 0t x y z ,           2 2 2 2 2 2x y z (7) it is supposed that edges  0x and  0z are thermo isolated i a. fesenko et alii, frattura ed integrità strutturale, 48 (2019) 768-792; doi: 10.3221/igf-esis.48.70 772     0 ( , , ) 0 x t x y z x ,     0 ( , , ) 0 z t x y z z (8) here function ( , , )t x y z is the unknown temperature of the layer. at the upper face z h of the layer, the temperature is given along the segment   [0, ], [ , ]x a y b b ( , , ) ( , )t x y h f x y ,   [0, ], [ , ]x a y b b (9) the integral transform method is used to derive the one-dimensional boundary problem. the fourier cosine transform with regard to the variable x and full fourier’s transform with regard to the variable y are applied consecutively to the laplace equation (7) and boundary conditions (8, 9). it leads to the one-dimensional problem at the transforms' domain     2( ) ( ) 0t z n t z , (0, )z h (10)  (0) 0t ,  ( )t h f where          0 ( , )cos i yf f x y x e dydх ,   2 2 2n ,  , are fourier’s transform parameters. usage of the general solution of the equation (10)   1 2( )t z c shnz c chnz ,  1 20, /c c f chnh leads to the final solution in the transform domain, where the inverse integral transform was applied               2 12 0 ( , , ) cos i y chnz t x y z f x e d d chnh (11) the final solution of the stated conductivity problem (7-9) is presented in the form                     2 2 2 1 0 sin 1 sin( )2 ( , , ) cos 1 cos( ) ( ) 1 n k k k k k k k ta tbch tzc t x y z tx ty dt n ch ht ta b (12) where ( )nk are zeros of chebyshov polynomials of the first kind, c is the constant value of temperature, distributed along the segment   [0, ], [ , ]x a y b b . a more detailed derivation of the formula (12) is given in the appendix 1. an important property                     2 2 2 2 1 11 ln 2 1 1 bn k ka b k k k k ka c c n (13) was obtained based on solution (12) and will be used for calculating stress at the corner point of a layer. a more detailed derivation of the formula (13) is given in appendix 2. the next step is to find the solution of the problem for the elastic layer           , , 0x y z h under its proper weight. a. fesenko et alii, frattura ed integrità strutturale, 48 (2019) 768-792; doi: 10.3221/igf-esis.48.70 773 the deriving of normal stress with regard to its proper weight o solve this problem, the displacements   u , v , w will be searched as the function depending on the variable z     0 1 2u ( ), v ( ), w ( )f z f z f z (14) because of problem’s symmetry one can take   u 0, v 0 . hence, the tangent stress   0xy . that’s why the displacements were taken in the form (14), the boundary condition of the ideal contact (3) is satisfied automatically at the edge of the layer. the function w satisfies the lame's equation          0w w 0 , (15) where   / ,z zq g q is the weight of an elastic material,     10 (1 2 ) . the face z h is supposed free of stress          0, 0, 0z zx zyz h z h z h the lower face  0z is in ideal contact conditions         0 00 w 0, 0, 0zx zyz zz finally, one gets the boundary problem       0 2(1 ) ( ) 0, 0f z z h  2 2(0) 0, ( ) 0f f h the solution has the form      1 20w (1 ) 2hz z hence, the stress x for the layer with regard to its proper weight is constructed     1(1 ) ( )x zq h z (16) the solution of the initial stated problem (2-5) will be searched in the form              * * * *u u u , v v v , w w w , x x x (17) here u( , , ), v( , , ), w( , , ), ( , , )xx y z x y z x y z x y z are displacements and stress appearing in a body without regard to its proper weight. t a. fesenko et alii, frattura ed integrità strutturale, 48 (2019) 768-792; doi: 10.3221/igf-esis.48.70 774 reduction of the initially stated uncoupled thermoelasticity problem to a onedimensional vector boundary problem ne neglects the volume forces , ,x y z . so, lame's equations (2) can be written in the vector form              •0 , ,u,v,w , , , ,t t t (18) here         10 1 0 *2 (1 ) . the boundary conditions are                             0 0 0 0 00 ( ) ( ), 0, 0 u 0, 0, 0 w 0, 0, 0 z zx zyz h z h z h xz xyx x x zx zyz zz x a y b (19) let's reformulate the boundary conditions (19) in terms of displacements, taking into consideration well known formulas connecting the displacements and stresses [20]               1 0 0 ,u ( , , ) v ( , , ) +(1 ) w ( , , ) ( 2 ) ( , , ) ( ) ( ) / ( 2 )x y h x y h x y h t x y h x a y b g  ,u ( , , ) w ( , , ) 0x y h x y h ,   ,w ( , , ) v ( , , ) 0x y h x y h (20)    u(0, , ) v (0, , ) w (0, , ) 0y z y z y z w( , , 0) 0x y ,  ,u ( , , 0) w ( , , 0) 0x y x y ,   ,w ( , , 0) v ( , , 0) 0x y x y . the idea is to reduce the lame's equations (18) to one independently and two simultaneously solving equations, subjected by separated conditions (20). the unknown functions   •( , , ) u ( , , ) v ( , , )z x y z x y z x y z ,   •s( , , ) v ( , , ) u ( , , )x y z x y z x y z (21) are input accordingly to [11]. the lame's equations system (18) is separated on the system of two equations                         2 2 2 20 0 w , w w , ,,, xy xy xy x y z z t z t (22) and independently solving equation   0s . the boundary conditions (20) after separation procedure will take the form with regard to the new functions (21)    (0, , ) 0(0, , ) 0, w (0, , ) 0, y zz y z y z s   ( , , 0) 0 , ( , , 0) 0, w( , , 0) 0,z x yx y x y s (23)   w( , , ) ( , , ) 0 , , ( , , ) 0,xy x y h z x y hx y h s o a. fesenko et alii, frattura ed integrità strutturale, 48 (2019) 768-792; doi: 10.3221/igf-esis.48.70 775                 1 10 02 ( ) ( ) 2 ( , , ) , ( , , ) (1 )w ( , , ) g x a y b t x y hz x y h x y h . in the domain of fourier’s transforms (the cosine transform with regard to the variable x and full fourier transform with regard to the variable y) one can derive two boundary problems. first, it is formulated for the unknown function ( , , )s x y z           2( ) ( ) 0, 0 , ( ) 0, (0) 0s sz n z z h s h s it’s obvious, that this problem has a trivial solution  ( ) 0s z , and, hence, ( , , ) 0s x y z . for the functions  ( ), w ( )z z z the one dimensional boundary problem is stated               2 0 0 1 1 ( ) ( ), 0 ( ) , ( ) l z z z h u z u z y f y γ y γ (24) here 2l is the differential operator of second order          " 2 0 2( ) ( ) '( ) ( ) ( ), 0l z z z n z z z hy i y q y p y f i is unit matrix,          1 * 2 0 0n q ,        1 * * 0 0 р ,          2 ( ) ( ) ( ) z z n z t t f ,             w ( ) ( ) ( ) z z z zy is the unknown vector of transforms. the boundary functionals , 0,1iu i are written in the corresponding forms      0 1 2 0[ ] ( ) ( )u z zy i y i y γ      1 1[ ] ( ) ( )u z zy ay by γ                        2 1 2 1 0 0 0 0 10 , , , 0 0 0 1 1 00 n i i a b 0 0γ ,               1 1 1 0 0 0 ( )( 2 cos (2) )i b t hg a e γ . the solution of the problem (24) is searched in the form [37]               βα 0 0 1 1 βα 0 w ( ) ( ) ( , ) ( ) ( ) ( ) ( ) hz z z d z z z z y g f ψ γ ψ γ (25) where ( , )zg іs green matrix function, ( ), 0,1i z iψ are the basis matrices. a. fesenko et alii, frattura ed integrità strutturale, 48 (2019) 768-792; doi: 10.3221/igf-esis.48.70 776 the construction of the matrix fundamental solution system, the matrix basic solution system, the fundamental matrix and green matrix function ccording to [39] the basic matrices are the solutions of the boundary matrix problems    2 ( ) 0, ( )j i j ijl z u zψ ψ δ (26) ijδ is kronecker’s symbol. the basic matrices are constructed in the form     0 1( ) ( ) ( ) , 0,1i i iz z z iψ y c y c where  ( ), ( )z zy y are the matrix fundamental solutions of the homogeneous equation (26) correspondingly decreasing and increasing in infinity. the algorithm of fundamental solutions ( )zy derivation is described in [37], where the method of fundamental matrix equation is also indicated. according to this approach, the solution is searched as the contour integral [39, 40]    112( ) ( )szi c z e s dsy m (27) where contour c covers all poles of the matrix 1( )sm , where    2 20( )s s s nm i q p ,    22 2det ( )s s nm ,  s n . let’s calculate matrix  1 *( ) ( ) / det ( )s s sm m m , so (27) will be transformed      *12 22 2( ) ( ) sz i c e z s ds s n y m here * ( )sm is a union matrix. with the help of the residual theorem, one derives                        2 ( ) 2 2 0 3 1 3 1 ( ) ( ), ( ) re , ( ) ( ) ( ) (4 ) ( 1), ( ) (4 ) ( 1) j sz j j nz nz d e z y z y z s s n dz s n s n y z n e nz y z n e nz y γ here, to find matrices ( ) , 0, 2j jγ one uses the fact, that     2 1 ( ) 04 1 ( ) ( ) i i i s s p s m γ ,   4 2 2 44 ( ) 2p s s s n n or     2 ( ) 4 0 ( ) ( ) i i i p s s si m γ . using that coefficient near the same exponents should be equal, the matrixes ( ) , 0, 2j jγ are found     ( 2 ) (1) ( 0 ) 2 10, , nγ i γ q γ p . as a result, the fundamental matrix system is derived                   1 * 0 2 1 * (z) ( ) nz nz ze n z nz y a a. fesenko et alii, frattura ed integrità strutturale, 48 (2019) 768-792; doi: 10.3221/igf-esis.48.70 777    3 4 . the unknown constant matrices 0 1, , 0,1i i ic c and  ( )zy are shown in appendix 3. the basic matrices are expressed by the formulas after transformations          ( 11) ( 12 ) ( 21) ( 22 ) 1 ( ) i ii n i i z d ψ (28) where   2 2 4nd sh nh nh . the components of the matrix (28) are shown in appendix 4. the expression for green’s matrix function is proposed in [39]            0 0 1 1( , ) ( , ) ( ) ( , ) ( ) ( , )z z z u z z u zg φ ψ φ ψ φ (29) where ( , )zφ is a fundamental matrix of the corresponding homogeneous equation (26). for the construction of the fundamental matrix ( , )zφ , let’s continue the function ( )y z on all the real axes and apply the fourier integral transform       ( ) i zy y z e dz (30) the same transform (30) should be applied to the equation in (24)         2 0 2y i y n yi q p f hence, one derives     1( )iy m f after the inverse integral fourier transform the correspondence for ( )y z is obtained                1 ( )12 ( )( ) i zi e d dy z m f (31) according to the fundamental matrix definition, this matrix is              1 ( )12( ) ( ) i zz i e dφ m or after changing the variable   s i , the matrix has the form             * ( )1 2 2 2 2 0( ) ( ) , 0( ) s z i c zs z e zs n m φ (32) here c are the closed contours that cover the poles  s n or   in . the residuals at   in and   in are correspondingly equal             3 1 3 1(4 ) (1 ), (4 ) (1 ),ny nye n ny e n ny y z (33) a. fesenko et alii, frattura ed integrità strutturale, 48 (2019) 768-792; doi: 10.3221/igf-esis.48.70 778 the matrices φ are searched with the help of the matrices (32)           20 nφ i q p (34) after substitution of the expressions (33) into the equations (34), uniting these results, the fundamental matrix is constructed in the form                          1 *0 2 1 * ( ) ( , ) ( ) ( )4 n z n z ze z n z n zn φ (35) according to the formula (29) the green’s matrix has the form                                   1 ( 11) ( 12 ) *0 0 2 1 ( 21) ( 22 ) * ( ) ( ) ( , ) ( ) ( )4 2 n z n n z ze z n z n zn nd g (36) where components  ( ) , , 1, 2ij i j are shown at appendix 4. finally, the solution of the vector boundary problem (24) in fourier’s transform domain is constructed with the formulas                                         1 20 βα βα * βα 0 βα( 11) 2 ( 12 )0 βα βα 1 1 0 w ( ) ( ) ( ) ( ) 4 ( )cos ( ) ( ) ( , ) ( , ) 2 2 2 h n z h i b n n n z e n z t z n t d n t ha e t n t d f n z f n z nd gd d (37)                                         10 βα βα * βα 0 βα( 21) 2 ( 22 )0 βα βα 2 2 0 ( ) ( ) ( ) ( ) 4 ( )cos ( ) ( ) ( , ) ( , ) 2 2 2 h n z h i b n n n z z e n z t n z t d t ha e t n t d f n z f n z nd gd d where                           11 1 12 11 2 02 1 ( , ) ( ) ( ) ( ) ( ) ( ) ( ) ( , ) ( ) ( ) ( ) ( ) ( ) ( ) f n z z h shn h z h z shn h z chn h z shn h z n f n z n z h chn h z n h z chn h z shn h z shn h z   2 2 4nd sh nh nh deriving the displacements and stress formulas in the transform domain and their inversion o, the transformation of the solution is constructed in the form of superposition          3 3 1 1 w ( ) w ( ), ( ) ( ),k k k k z z z z z z where s a. fesenko et alii, frattura ed integrità strutturale, 48 (2019) 768-792; doi: 10.3221/igf-esis.48.70 779              1 β 1βα 1 2βα ( , )w ( ) cos ( , )( ) 2 i b n f n zz a e f n zz z gd , (38)               2 βα 1βα 2 2βα ( ) ( , )w ( ) , ( , )( ) 2 n t h f n zz f n zz z d (39) functions 1 2( , ), ( , )f n z f n z , nd are defined in (37).                                   3 1 20 βα βα * βα 0 ( 11) 2 ( 12 )0 βα βα 0 w ( ) ( ) ( ) ( ) 4 ( ) ( ) , 2 h n z h n z e n z t z n t d n t n t d nd (40)                                   3 10 βα βα * βα 0 ( 21) 2 ( 22 )0 βα βα 0 ( ) ( ) ( ) ( ) 4 ( ) ( ) . 2 h n z h n z z e n z t n z t d t n t d nd in detail, the inversion of the fourier transform for terms of the form (39) is described using the example of the term 2 βαw ( )z . proceeding from the boundary condition in (10) of the stationary heat conduction problem considered in part 3 of the article, one gets            βα βα 0 ( ) ( , ) cosit h f f e d d . then the representation of the term 2βαw ( )z will take the form                          2 1 2 0 0 ( , ) w ( , , ) ( , ) cos cos 2 i i y n f n z x y z f e e xd d d d d changing the order of integration, using the formula (401.06.,[41]), and application of the euler formula allows to simplify the term 2βαw ( )z . the temperature is assumed to be constant, distributed over a finite interval       , 0b b a , which leads to the expression                              2 ( ) ( ) ( )1 2 0 ( , ) w ( , , ) 8 b a i y i x i x nb f n zc x y z e e e d d d d d (41) further, using formula (a3) in the appendix 1, correspondence (41) can be written as              2 *1 0 0 0 ( , ) w ( , , ) ( , , , , ) 4 b a tb t f t zc x y z j t x y d d dt d ,   2 2td sh t t applying the procedure for calculating multiple integrals of the bessel function to internal integral, one gets            2 2 ,1 2 0 0 ( , )2 w ( , , ) ( )cos( cos )cos( sin )a bt t t f t zc x y z s tx ty d dt d a. fesenko et alii, frattura ed integrità strutturale, 48 (2019) 768-792; doi: 10.3221/igf-esis.48.70 780 the formulas  2βα βαu ( ) α ( )z n z z ,  2βα βαv ( ) β ( )z i n z z were used to find the originals of the displacements 2 2u ( , , ), v ( , , )x y z x y z so,      βα βα2 2βα 2 βα 22 2 ( ) ( ) β u ( ) ( , ), v ( ) ( , ) 2 2n n t h t h i z f n z z f n z d n d n . by analogy, it was found                               2 2 2 ,2 2 0 0 2 ,2 2 0 0 ( , )2 u ( , , ) ( )cos( cos )cos( sin ) , ( , )2 v ( , , ) ( )cos( cos )cos( sin ) . a b t t a b t t f t zc x y z s tx ty d dt x t d f t zc x y z s tx ty d dt y t d let’s consider the terms containing the integrals in (37). using the solution of the stationary thermal conductivity problem (10), the temperature transformation and its derivative are written in the form   βα βα( ) , chn t f chnh    βα βα( ) . shn t nf chnh after substitution of this transform into (40), the formula for 3βαw ( )z was constructed      3 0βα βα 0 w ( ) ( , , ) 4 h z f f z n d where                      ( 11) (12 ) 1 * 1 ( , , ) ( ) .n z n shn n chn f z n e n z shn z n chn chnh d in order to find final expression for displacement (40)                  3 0 βα2 0 0 w ( , , ) ( , , ) cos 4 h i yx y z f f z n e xd d d (42) the representation of the function f should be substituted into (42)                             3 0 2 0 0 0 w ( , , ) ( , ) ( , , ) cos cos . 4 h i y ix y z f f z n e e x d d d d d using formula (a3) in the appendix 1 and (401.06., [41]), it was derived                  3 *0 0 0 0 0 w ( , , ) ( , , ) ( , , , , ) 8 b a h b c x y z t f z t j t x y d d dtd , where the temperature is defined on a finite interval and supposed to be constant c . further, after changing the order of integration, and calculating the double integral of the bessel function, the integral is represented in the form a. fesenko et alii, frattura ed integrità strutturale, 48 (2019) 768-792; doi: 10.3221/igf-esis.48.70 781                    3 20 22 1 0 0 ( , , )1 1 w ( , , )= ( , )cos 1 cos( ) 2 1 hn k k k k k k c f z t x y z f t tx ty dtd n t                        2 3 20 1 32 1 0 0 ( , , / )1 1 u ( , , )= ( , )cos 1 cos( ) . 2 1 hn yx k k kh h k k k h c f zh h t h x y z f t t t dtd x n t the expression for displacement 3v ( , , )x y z can be constructed by analogy. the expressions (38) correspond to the solution of the problem of a semi-infinite layer loading. the normal stress is constructed by the formula [20] in the form                      2 1 0 1 ( , )2 ( , , ) ( 1) (1 ) (1 ) (1 ) n kab k x k k t f t x y z z cht z z cht z dt n d                     1 2 0 2 1 0 1 ( , ) (1 ) (1 ) 1 n k k k tk k f t sht z sht z dt d t the final solution of the initially stated uncoupled thermoelasticity problem for a semi-infinite layer with its proper weight was derived in the form       * ( , , ) ( , , ) 2 (1 ) (1 ),t abx x zx y z x y z q h z       ( , , ) ( , , ) (1 )t ab abx xx y z x y z g c                              1 12 1 2 0 0 1 22 2 1 10 0 0 0 2 1 ( , ) ( , )1 , 1 1 n n k k k k kk k k k g c f t f t f d dt f d dt n cht cht where the functions 1 2,f f are defined in аppendix 5,   * ,  is a coefficient of linear expansion,  2 2td sh t t ,             2 2( , ) sin 1 sin cos 1 cos( )k h k h k h k h kf t ta tb tx ty . discussion and numerical results uring the calculations, two types of materials were selected: copper − µ = 1/3, g = 44.7 gpa, α = 16.5 · 10-6 1/с0, qz = 0.00896 kg/м3; glass − µ = 1/4, g = 26.2 gpa, α = 6 ·10-6 1/с0, qz = 0.00119 kg/м3; the layer’s thickness h = 1 м; in all diagrams and tables, the units of measurement for stress are pa; the investigation of the influence of the load area shape on the stress was carried out for the case of unit temperature. for glass, in figures 2, 3 the distributions of normal stress  ,abx ab tx along the lateral wall of the layer for  0 z h depending on the shapes of the distributed load section and the temperature are represented. here abx indicates the normal stress caused by mechanical loading, distributed over the site   [0, ], [ , ]x a y b b , ab tx − normal stress under the action of distributed load and temperature influence. the case  2b a corresponds to the distribution of compression loading on the layer’s face z h along the rectangle, elongated along the axis y ;  / 4b a − along a rectangle elongated along the axis x ;  / 2b a − quadratic spread. these graphs correspond to the case for glass. the stress graphs for copper, where   1/ 3 , are similar, but with larger absolute values. so, they are not shown here. as it can be seen from the graphs, in the case of a shape  / 2b a , maximal compressing stress is observed. in the case d a. fesenko et alii, frattura ed integrità strutturale, 48 (2019) 768-792; doi: 10.3221/igf-esis.48.70 782 of size  2b a the stress has minimal values and the separation of the layer from the side wall takes place. stretching stresses are greater for the case of size  2b a in comparison with the form  / 2b a . taking into account the temperature influence, one can note increasing compressing stress values and reducing tensile stress values. figure 2: distribution of normal stress  (0, 0, )abx z figure 3: distribution of normal stress  (0, 0, )ab tx z it was also important to establish for which materials and loading sites a delamination of the side wall of the layer occurs. it was found that the separation of a semi-infinite layer from the side wall is not observed when the ratio / 12p c , where р – the dimensionless intensity of constant mechanical loading, с – the dimensionless temperature. the side edge of the semi-infinite layer is detached for poisson's ratio values   0 0.33 at the size  2b a and for values   0 0.23 at the size  / 2b a (fig. 4). figure 4: distribution of normal stress depends on poisson's ratio values -0.4046 0.0531 -0.0085 1 -0.0073 0.40.2 -0.5008 -0.5073 z -0.4122 0.0482 -0.0140 1 -0.0108 0.4 0.2 -0.5948 -0.5008 z b = 2a b = a/4 b = a/2 0.1 0.2 0.3 0.4 -0.3671 -0.2018 0.1276 µ в = 2а в = а/2 b = 2a b = a/4 b = a/2 a. fesenko et alii, frattura ed integrità strutturale, 48 (2019) 768-792; doi: 10.3221/igf-esis.48.70 783 the layer separation was observed in different cases of poisson's ratio values. it was established which values of coefficient lead to the delamination of the lateral face of the semi-infinite layer. in these cases, the linearity of the problem is violated and the statement of the problem is not correct.  / 2b a z 0 0.2 0.4 0.6 0.8 1  (0, 0, )lx z   1/ 4 -0.0085 -0.0217 -0.0646 -0.1454 -0.2708 -0.5008   1/ 3 -0.0340 -0.0493 -0.0991 -0.1934 -0.3421 -0.6006  (0, 0, )l wx z   1/ 4 -0.0081 -0.0213 -0.0644 -0.1452 -0.2707 -0.5008   1/ 3 -0.0295 -0.0457 -0.0964 -0.1917 -0.3411 -0.6006  (0, 0, )l тx z   1/ 4 -0.0140 -0.0262 -0.0689 -0.1501 -0.2771 -0.5086   1/ 3 -0.1087 -0.1145 -0.1609 -0.2584 -0.4193 -0.6981   (0, 0, )l т wx z   1/ 4 -0.0135 -0.0259 -0.0686 -0.1498 -0.2766 -0.5086   1/ 3 -0.1042 -0.1109 -0.1582 -0.2566 -0.4183 -0.6981 table 1: normal stress along the axis z  2b a z 0 0.2 0.4 0.6 0.8 1  (0, 0, )lx z   1/ 4 0.0531 0.0379 -0.0085 -0.0853 -0.1860 -0.4046   1/ 3 0.0283 0.0130 -0.0336 -0.1109 -0.2120 -0.4317  (0, 0, )l wx z   1/ 4 0.0535 0.0382 -0.0082 -0.0851 -0.1859 -0.4046   1/ 3 0.0327 0.0166 -0.0309 -0.1091 -0.2111 -0.4317  (0, 0, )l тx z   1/ 4 0.0482 0.0339 -0.0120 -0.0889 -0.1903 -0.4122   1/ 3 -0.0313 -0.0367 -0.0778 -0.1578 -0.2709 -0.5292   (0, 0, )l т wx z   1/ 4 0.0486 0.0342 -0.0118 -0.0888 -0.1902 -0.4122   1/ 3 -0.0268 -0.0332 -0.0752 -0.1561 -0.2700 -0.5292 table 2: normal stress along the axis z the values of the normal stress are given in the tables (1)-(3) for the following parameters: the thickness of the layer h = 1 and unit temperature. they are investigated depending on the form of the load and temperature distribution. for convenience, the following notations are introduced:  lх the stress that occurs under the action of a compressive load; a. fesenko et alii, frattura ed integrità strutturale, 48 (2019) 768-792; doi: 10.3221/igf-esis.48.70 784  l wх the stress that occurs under the action of a compressive load with regard to the proper weight of the layer;  l тх the stress that occurs under the action of a compressive load with a distributed temperature;   l т wх the stress that occurs under the action of a compressive load with a distributed temperature with regard to the proper weight of the layer;  / 4b a z 0 0.2 0.4 0.6 0.8 1  (0, 0, )lx z   1/ 4 -0.0073 -0.0156 -0.0439 -0.1042 -0.2291 -0.5737   1/ 3 -0.0220 -0.0318 -0.0656 -0.1389 -0.2952 -0.7276  (0, 0, )l wx z   1/ 4 -0.0069 -0.0153 -0.0436 -0.1041 -0.2290 -0.5737   1/ 3 -0.0295 -0.0282 -0.0629 -0.1372 -0.2943 -0.7276  (0, 0, )l тx z   1/ 4 -0.0108 -0.0186 -0.0471 -0.1501 -0.2771 -0.5948   1/ 3 -0.0706 -0.0783 -0.1193 -0.2135 -0.4141 -0.9970   (0, 0, )l т wx z   1/ 4 -0.0104 -0.0182 -0.0468 -0.1085 -0.2368 -0.5948   1/ 3 -0.0661 -0.0747 -0.1166 -0.2117 -0.4132 -0.9971 table 3: normal stress along the axis z it can be seen from analysis of these tables that the separation of the layer from the rigid wall arises in the case of the size  2b a . this case corresponds to the distribution of temperature and loading elongated along the y axis by a rectangular spot. here the stresses are higher for the case of poisson's value µ=1/4. the influence of loading begins to have a significant effect on the absolute value of the stress at about 2 / 3 of the layer h height. this pattern can be traced for any shape of the loading area and poisson's ratio. the investigation of the loading spot’s shape was provided with the aim to establish what ratio of length and width causes the maximal value of normal stress. it was established that maximal stress, equal to 0.7276 , arises on the side wall of the layer as a result of the mutual action of the distributed load and proper weight of the layer. it has place in the case when the load is distributed along a rectangle elongated along the axis x , when   1/ 3 . the maximal value, equal to 0.9971, the stress reaches when  / 4b a , when the load, temperature influence and proper weight are taken into account, i.e. the stress practically becomes equal to the acting load. in all cases it is clear that taking into account the proper weight of the layer reduces the values of the compressive normal stresses on the side wall. the combined influence of temperature and external load increases the stress on the lateral face of the layer compared with the case when only the external mechanical action is taken into account. conclusions he proposed new method, based on the green’s matrix function apparatus, made it possible to obtain the exact solution of the uncoupled thermoelasticity problem for a semi-infinite layer taking into account its proper weight. the engineering computational formulas for the displacements and stress of the layer were obtained and the t a. fesenko et alii, frattura ed integrità strutturale, 48 (2019) 768-792; doi: 10.3221/igf-esis.48.70 785 mechanical characteristics that arise at certain ratios of the distribution spot, where mechanical loading and temperature are acting, were revealed. the resulting formulas can be used as models for estimating the validity of the new approximate numerical methods to solve mechanical problems. the analysis of the calculations establishes the geometrical parameters of the loading spots shape sections, when the effect of the layer’s edge separation from the wall is observed. it was found that the appearance of the tensile stress is sufficiently dependent on each material from the shape of the loading spot. it was also revealed at what values of the poisson's ratio the separation of the layer’s wall is observed and the problem’s statement becomes incorrect. it was determined that taking into account the layer’s proper weight reduces the stress values. the presence of temperature load increases the value of stress in comparison with the case, when only a mechanical load is applied. the analyses of stress for different shapes of the loading spots as with, so and without layer proper weight indicates that maximal the value of the stress is observed when the shape of loading spot is quadratic. it should be emphasized that the frictionless contact conditions at the layer’s edge made it possible to obtain an exact solution of the problem. in the case when the edge is rigidly fixed to the wall, the initial problem is reduced to an integral singular equation. the developed methodology allows a number of extensions. this approach can be used to solve a wider class of problems, when different boundary conditions are fulfilled on the faces of the layer or when the load is nonstationary one. analysis of some cases of steady-state loading is already in progress. references [1] eubanks, r. a. and sternberg, e. (1956). on the completeness of the boussinesq-papkovitch stress functions, j. rat. mech. and anal. 5, pp. 735-746. [2] papkovitch, p. f. (1932). a representation of the general integral of the basic differential equations of elasticity theory in terms of harmonic functions, izv. akad. nauk sssr. otd. mat. est. nauk., 10. pp. 1425-1435. [3] neuber, h. (1973). kerbspanungslehre, berlin, springer. [4] kolosov, g. v. (1935). application of complex diagrams and the theory of functions of complex varable to elasticity theory [in russian], leningrad-moscow, onti. [5] muskhelishvili, n. i. (1953). some basic problems of mathematical theory of elasticity, groningen, noordhoff. [6] polozhii, g. n. (1963). on the boundary-value problems of axisymmetric elasticity theory. the method of p – analytic functions of complex variable, ukr. mat. zh., 15 (1), pp. 25-45. [7] kupradze, v. d., gegeliya, t. g., basheleishvili, m. o. and burchuladze, t. v. (1976). threediminsional problems of mathematical elasticity theory and thermoelasticity [in russian], moscow, nauka. [8] uflyand, ya. s. (1968). integral transformations in problems of elasticity theory [in russian], leningrad, nauka. [9] ulitko, a. f. (1979). the method of vector eigenfunctions in spatial problems of elasticity theory [in russian], kiev, naukova dumka. [10] kit, h. s. (2008). problems of stationary heat conduction and thermoelasticity for a body with heat release on circular domain (crack), mat. met. fis.-mech. polya, 51 (4), pp. 120-128; english translation: (2010). j. math. sci. 167 (2), pp. 141-153. [11] popov, g. ya. (2003). new transforms for the resolving equations in elastic theory and new integral transforms, with applications to boundary value problems of mechanics, prikl. mekh., 39 (12), pp. 46-73. english translation: (2003). int. appl. mech., 39 (12), pp. 1400-1424. [12] vaisfeld, n. d., popov, g. ya. (2009). mixed boundary value problem of elasticity for a quarter space, mech. solids. 44: 712. doi: 10.3103/s0025654409050082 original russian text: (2009). izvestiya akademii nauk. mekhanika tverdogo tela, 5, pp. 68-89. [13] takhar, h. s., chamkha, a. j., nath, g. (1999). unsteady flow and heat transfer on a semi-infinite flat plate with an aligned magnetic field, int. j. engineering sci. 37, pp. 1723-1736. [14] tokovyy, y., ma, c.-c. (2015). an analytical solution to the three-dimensional problem on elastic equilibrium of an exponentially-inhomogeneous layer, j. mech. 31 (5), pp. 545-555. [15] vaysfel’d, n., zhuravlova, z. (2015). on one new approach to the solving of an elasticity mixed plane problem for the semi-strip, acta mechanica, 226: 4159. doi: 10.1007/s00707-015-1452-x [16] fesenko, а. а. (2015). mixed problems of stationary heat conduction and elasticity theory for a semiinfinite layer, j. math. sci., 205 (5), pp. 706-718. doi: 10.1007/s10958-015-2277-9 [17] haji-sheikh, a., donald, e. a., beck, j. v. (2009). temperature field in a moving semi-infinite region with a prescribed wall heat flux, int. j. heat and mass transfer, 52 (7), pp. 2092-2101. a. fesenko et alii, frattura ed integrità strutturale, 48 (2019) 768-792; doi: 10.3221/igf-esis.48.70 786 [18] kit, h. s., mykhas' kiv, v. v., khai, m. v. (1996). the method of potentials in three-dimensional static and dynamical problems of the theory of cracks, materials science, 32 (1), pp. 14-24. [19] matysiak, s. j., perkowski, d. m. (2010). on heat conduction in a semi-infinite laminated layer. comparative results for two approaches, int. communications in heat and mass transfer, 37, pp. 343-349. [20] nowacki, w. (1957). a dynamical problem of thermoelasticity, archiwum mechaniki stosowanej, 9 (3), pp. 325-334. [21] rabinovich, a., dagan, g., miloh t. (2012). heat conduction in a semi-infinite medium with a spherical inhomogeneity and time-periodic boundary temperature, int. j. heat and mass transfer, 55, pp. 618-628. [22] tokovyy, y., ma, c.-c. (2013). three-dimensional temperature and thermal stress analysis of an inhomogeneous layer, j. therm. stresses, 36 (8), pp. 790-808. [23] kulchytsky-zhyhailo, r., matysiak, s. j. & perkowski, d. m. (2007). on displacements and stresses in a semi-infinite laminated layer: comparative results, meccanica, 42: 117. doi: 10.1007/s11012-006-9026-6 [24] chen, y.z. (2016). numerical solution for thermal confocal elliptic dissimilar layers in plane elasticity, acta mechanica, 227: 2233-2244. doi: 10.1007/s00707-016-1626-1 [25] menshykov, o., menshykova, m. and vaysfeld, n. (2017). exact analytical solution for a pie-shaped wedge thick plate under oscillating load, acta mechanica, 228 (12), pp. 4435-4450. doi: 10.1007/s00707-017-1938-9 [26] vorovich, i. i. and babeshko, v. a. (1979). dynamical mixed problems of the elasticity theory for the no classical areas [in russian], moscow, nauka. [27] taein, yeo and barber, j. r. (1996). finite element analysis of the stability of static thermoelastic contact, j. thermal stresses, 19 (2), pp. 169-184 doi: 10.1080/01495739608946168 [28] popov, g. ya., kebli, b. (2012). exact solution of the mixed boundary value elasticity problem for an infinite wedgeshaped plate with regard for its proper weight, j. math. sci., 187 (6), pp. 758-771. [29] popov, g. ya., protserov, yu. s. (2016). axisymmetric problem for an elastic cylinder of finite length with fixed lateral surface with regard for its weight, j. math. sci., 212 (1), pp. 67-82. [30] bateni, m. and eslami, m. r. (2018). thermally nonlinear generalized thermoelasticity: a note on the thermal boundary conditions, acta mechanica, 229, pp. 807-826. doi: 10.1007/s00707-017-2001-6 [31] bostani, m. and karami mohammadi, a. (2018). thermoelastic damping in microbeam resonators based on modified strain gradient elasticity and generalized thermoelasticity theories, acta mechanica, 229, pp. 173-192. doi: 10.1007/s00707-017-1950-0 [32] shishesaz, m., hosseini, m., naderan tahan, k. et al. (2017). analysis of functionally graded nanodisks under thermoelastic loading based on the strain gradient theory, acta mechanica, 228, pp. 4141-4168. doi: 10.1007/s00707-017-1939-8 [33] ebrahimi, h. z. and haghighi, m. r. g. (2016). estimation of heat flux and mechanical loads on laminated functionally graded plate, acta mechanica, 227, pp. 2075-2097. doi: 10.1007/s00707-016-1596-3 [34] kugler, s., fotiu, p.a. and murin. (2016). thermo-elasticity in shell structures made of functionally graded materials, acta mechanica, 227: 1307. doi: 10.1007/s00707-015-1550-9 [35] senthil, s. vel and batra, r. c. (2002). exact solution for thermoelastic deformations of functionally graded thick rectangular plates, aiaa journal, 40 (7), pp. 1421-1433. doi: 10.2514/2.1805 [36] babeshko, v., evdokimova, o., babeshko, o. (2017). action of the semi-infinite plates on the elastic layer, procedia iutam, 20, pp. 50-55. doi: 10.1016/j.piutam.2017.03.007 [37] marsavina, l., tomlinson, r. a. (2014). frattura ed integrità strutturale, 8 (27), pp. 13-20. doi: 10.3221/igfesis.27.02 [38] pitarresi, g., scalici, t., catalanotti, g. (2018). thermoelastic stress analysis of modified transverse cut tensile composite specimens under pure mode ii fatigue delamination, procedia structural integrity, 8, pp. 474-485. doi: 10.1016/j.prostr.2017.12.047 [39] popov, g. ya., abdimanov, s. a. and ephimov, v. v. (1999). green’s functions and matrices of one-dimensional boundary value problems [in russian], almaty, rauan. [40] popov, g. ya. (1982). the elastic stress concentration around dies, cuts, thin inclusions and reinforcements [in russian], moscow, nauka. [41] gradshtein, i. s. and rygik, i. m. (1980). tables of integrals, series and products, new york, acad. press. [42] bateman, h. and erdelyi, a. (1954). higher transcendental functions, new york, mcgraw-hill. a. fesenko et alii, frattura ed integrità strutturale, 48 (2019) 768-792; doi: 10.3221/igf-esis.48.70 787 appendix 1. deriving the formula (12) for the temperature function the corresponding formula for f ,          0 ( , )cos i yf f x y x e dydх is substituted at (11) and the order of integration operators is changed at (11). to calculate the integrals exactly, the formula (1.314(3), [41]) is used                             21 0 0 ( , , ) ( , )cos cos i yi chnz t x y z f e d d x e d d chnh (a1) let’s consider the internal integrals at formula (a1). one must use the fact that function  ( , )f is the even one and to use euler’s formula. after some additional transforms the solution of the boundary value problem (7-9) is written as                                    2 ( ) ( ) ( )14 0 ( , , ) ( , ) i x i x i y chnz t x y z f e e e d d d d chnh (a2) one should note that value n at the solution (a2) is defined as   2 2 2n . it gives opportunity to simplify the expression (a2) with the formula [40]                      2 2 2 21 02 0 ( )i x i yf e d d t f t j t x y dt (a3) where 0 ( )j t is a bessel’s function of the first kind. with regard of formula (a3), the solution (a2) will be transformed                      *1 02 0 0 ( , , ) ( , ) ( , , , , ) chtz t x y z f t j t x y dt d d chth (a4) where           * 2 2 2 20 0 0( , , , , ) ( ) ( ) ( ) ( )j t x y a b j t x a y b j t x a y b . if at the boundary condition (9) one takes   ,f c c is constant, then exact solution of boundary value problem (7-9) will be obtained                  *02 0 0 ( , , ) ( , , , , ) a b c b chtz t x y z t j t x y dt d d chth . (a5) let’s simplify the internal integral at the equality (a5), using the known integral representation of bessel function [42]                      2 2 2 0 0 2 ( ) ( ) cos cos ( ) cos sin ( )j t x y t x t y d after some elementary transformations one obtains          2 , 2 0 0 4 ( , , ) ( )cos( cos )cos( sin )a bt chtzab t x y z c t s tx ty d dt chth a. fesenko et alii, frattura ed integrità strutturale, 48 (2019) 768-792; doi: 10.3221/igf-esis.48.70 788 here       , 1 1( ) ( cos ) sin( cos )( sin ) sin( sin )a bts ta ta tb tb as it may be seen function , ( )a bts is continuously differentiated function with regard of variable  . this function is even also, so after changing the variable   sin one can obtain the correspondence         1 , , ,2 2 1 2 ( , ) ( , ) 1 a b a b t t ab d j x y f x y , (a6) where                2 , 2 , 2 sin 1 sin ( , ) cos 1 cos( ) 1 a b t ta tb f x y tx ty tbta . based on the quadrature formula of the highest degree of accuracy, one can obtain for (a6)      ( ), ,, 1 2 1 ( , ) ( , )n k n a b a b t t k ab j x y f x y n ,    ( ) 2 1 cos , 2 n k k n  1,k n ( )nk are zeros of the chebyshov polynomials of the first kind. so, after substitution we get                     2 2 2 1 0 sin 1 sin( )2 ( , , ) cos 1 cos( ) ( ) 1 n k k k k k k k ta tbch tzc t x y z tx ty dt n ch ht ta b appendix 2. deriving the formula (13) for the analysis of the reliability of the calculations, we perform a test based on the obtained formula (12) for the fulfillment of the boundary condition of the problem. to this end, we consider the temperature (12) in the corner point of the layer   0, 0,x y z h                      2 , , 2 1 10 0 sin 1 sin2 2 (0, 0, ) (0, 0) 1 n n k k a b t k k k k ta tbc c t h t f dt dt n n ta b (a7) using the formula (3.741(1), [41])         2 0 sin sin 1 ln , 0, 0, 4 mx nx m n dx m n m n x m n (a8) gives                    2 2 2 2 1 1 ( / )1 (0, 0, ) ln 2 1 1 ( / ) n k k k k k k k b ac t h n b a . (a9) a. fesenko et alii, frattura ed integrità strutturale, 48 (2019) 768-792; doi: 10.3221/igf-esis.48.70 789 we note that when  0m ,  0n or  0n ,  0m the formula (a8) is not contradictory, it is also possible  0n (  0m ). to calculate with this formula, an essential condition is the requirement m n , i.e    21 k ka b . if / 1b a , then, to be definite, it is necessary that the condition     21 0 , or based on the replacement   sin :   cos sin , i.е    / 4 or   1/ 2 . let’s consider the case  .a b taking into account formula (a9), we get                    2 2 2 2 1 1 ( / )1 (0, 0, ) ln 2 1 1 ( / ) n k k k k k k k b ac t h n b a . (a10) if n – is an even number, then proceeding from the properties of the logarithm, the expression for the temperature (a10) takes the form                    2 2 2 2 2 1 1 ( / )1 (0, 0, ) ln 1 1 ( / ) n k k k k k k k b ac t h n b a . here we use the property of zeros of the chebyshev polynomial:   1n ,   1 2n ,…, i.е. there are exactly n roots, arranged symmetrically in the gap ( 1,1) . it can be noted that when n – is odd, there will be a root  ( 1)/2 0n , which leads to a singularity in formula (a10). for this case we consider the passage to the limit   0         , 0, ( 1) / 2k k k k n . using the lopital rule, we have                             2 2 2 2 1 ( 1)/2 1 ( / )1 1 (0, 0, ) 2 ln 2 1 1 ( / ) n k k k k k k k k n b ac b t h n a b a . let us consider three cases of local temperature distribution over sections of different sizes: 1) / 1/ 2b a ; 2) / 2b a ; 3) / 1/ 4b a . for the case when the number of nodes n in the formula (a10) was chosen equal to n = 70 аnd the constant of the temperature с = 1, for three cases, the temperature at the corner point of the layer was equal to: 1) (0, 0, )t h = 0.999445, 2) (0, 0, )t h = 0.999444, 3) (0, 0, )t h = 0.998545. the reliability of the results obtained was verified on the basis of formula (3.364(2), [41]). we can justify the result directly, considering the boundary condition (9) of the problem. proceeding from the applied integral transformations, one can find the transformation of the given function             0 0 sin ( ) ( , )cos cos a a f y f x y xdx c xdx c ,                              2sin sin sin sin ( ) 2 . 2 i b i bb i y i y b e ea a a b f f y e dy c e dy c c i we substitute the resulting transform into formula (12), and find the value at the point (0, 0, )h                    2 2 0 2 sin sin 4 (0, 0, ) . 2 2 c a b c t h d d c a. fesenko et alii, frattura ed integrità strutturale, 48 (2019) 768-792; doi: 10.3221/igf-esis.48.70 790 here we used the parity of the integrand with respect to the variable β and formula (3.721(1), [41]). thus, the numerically obtained results are justified analytically, by the relation                     2 2 2 2 1 11 ln 2 1 1 bn k ka b k k k k ka c c n . appendix 3. derivatives of the solutions ( )zy and constant matrices                       1 1 0 * 0 2 1 1 * 1 ( 2 ) ( 1) ( ) ( 1) ( 2 ) nz n nz nzz e n nz n nz y ,                     1 1 0 * 0 2 1 1 * 1 ( 2 ) ( 1) ( ) ( 1) ( 2 ) nz n nz nzz e n nz n nz y                               11 11 0 1 0 0 0 1 1 0 1 1 0,u u u u u uc y y y y c y y c                               11 11 0 1 1 1 1 0 0 1 0 0 1,u u u u u uc y y y y c y y c                                                      2 1 1 2 2 1 2 1 2 2 1 2 * 1 1 1 * 0 1 1 0 2 2 2 1 1 2 2 1 1 0 2 2 2( ) 4 2 2( ) ( ) ( ) 2 1 2( ) 2 2( ) 2 nh nh nh nh nh n n e nh nh n e nhe nd n e nh nh e nh nh c                                                  2 1 2 1 2 1 2 1 2 1 * 1 1 1 * 0 1 0 0 2 2 1 2 2 21 1 2 2 ( ) 2 2( ) ( ) ( )1 2 2( ) 2 1 2( ) 2 nh nh nh n n nh nh e n nh nd n nh nh e nh nh e c                                        1 1 1 1 * 0 0 * 10 * 1 2 1 1 2 1 0 1 0 ( ) 2 ( 2 (n nh shnh chnh n nh shnh chnh n d n nh shnh chnh n nh chnh shnh c                                        1 1 1 1 * 0 0 * 11 * 1 2 1 1 2 1 0 1 0 ( ) 2 2n nh shnh chnh n nh chnh shnh n d n nh shnh chnh n nh chnh shnh c   2 2 4nd sh nh nh . appendix 4. components of the basic matrices ( ), 0,1i z iψ                         1 ( 11) 2 1 1 1 0 1 1 2 1 1 1 2 ( ) (1 2 ) 4 2 ( 2 ) 2 ( 2 ), h h z shnz nz chnz nh chnz shnz nz chn h z shn h z n                  1 ( 12 ) 1 1 2 11 0 0 12 ( ) 2( ) ( 2 )h h z shnz n z chnz n shnz n z chn h z , a. fesenko et alii, frattura ed integrità strutturale, 48 (2019) 768-792; doi: 10.3221/igf-esis.48.70 791                          1 ( 21) 2 1 1 0 1 1 1 1 0 2 ( ) (1 2 ) 2 ( ) ( 2 ) ( 2 ) , n n h h z chnz nz shnz nh shnz chnz nz shn h z chn h z                   21 ( 22 ) 1 11 1 0 22 ( ) (2 ) (2 ) (2 )h h z chnz h z shnz n chnz z shn h z n chn h zn ,                    (11) 1 2 1 1 * 0 0( ) ( ) ( ) ( ) ( ) ( ) ( )n n h z chn h z n h z chn h z shn h z shn h z                  ( 12 ) 1 1 1 * 12 ( ) ( ) ( ) ( ) ( ) ( )n h z shn h z n h z shn h z chn h z chn h z ,                  ( 21) 1 1 1 * 12 ( ) ( ) ( ) ( ) ( ) ( )n h z shn h z n h z shn h z chn h z chn h z ,                   ( 22 ) 1 2 1 1 * 0 04 ( ) ( ) ( ) ( ) ( ) ( )n n h z chn h z n h z chn h z shn h z shn h z . appendix 5. functions 1 2,f f in the solution of the thermoelasticity problem   21 1 , 2 t f f f d      4 5 6 72 3 , 2 t f f f f f f d             1 11 * *( ) ( ) ( ) ( )t zf e t t z sh t t z ch t ch t ,      2 21 22( ) ( ),f f sh t f ch t                                                           21 2 1 1 0 ( 2 ) ( 2 )1 1 2 2 1 ( 2 )1 1 1 0 2 2 2 (1 ) ( 2 ) 2 (1 ) 2( ) ( 2 ) (1 ) 2 2 2( ) (1 ) (1 ) t t t z t z t z t f e t t z shtz chtz cht z t z chtz tzshtz chtz tzsht z e t tchtz tzshtz chtz e e tchtz tzshtz chtz t z e t z e ( 2 ) ,z                                                          2 2 1 22 * 2 1 2 1 ( 2 ) ( 2 )1 1 * 2 2 ( 21 1 2 2 2 (1 ) ( 2 ) 2 (1 ) ( 2 ) ( 2 ) ( 2 ) (1 ) 2 2 (1 ) t t t z t z t f e t t z shtz chtz cht z t z chtz t z shtz chtz tzsht z cht z e t tchtz tzshtz chtz e e tchtz tzshtz chtz t z e    ) ( 2 )12 (1 ) ,z t zt z e                  1 1 13 0 * *2 sgn( ) ( ) ( ) ( ) ( ) ( )t zf e z sh t t z ch t ch t t z sh t ,                                            2 ( 2 ) ( 2 )1 1 4 1 2 2 ( 2 ) ( 2 )1 1 2 2 1 ( 2 ) 1 ( 2 )1 1 0 02 2 (1 ) 2( 1 ) 2 ( 1 ) (1 ) (1 ) , t t z t z t z t z t z t z f e t t chtz tzshtz e e t chtz tzshtz t z e t z e e e a. fesenko et alii, frattura ed integrità strutturale, 48 (2019) 768-792; doi: 10.3221/igf-esis.48.70 792                                            2 5 1 2 1 1 2 1 2 1 1 2 1 0 0 1 1 ( 2) 2 (1 ) ( 2 ) 2 2 (1 ) 2 ( 2 ) ( 2 ) 2 ( ) , tf e t chtz t z shtz cht z tshtz t z chtz chtz tzshtz tshtz tzsht z chtz cht z chtz chtz                            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can be opened with acrobat and adobe reader 5.0 and later.) >> /namespace [ (adobe) (common) (1.0) ] /othernamespaces [ << /asreaderspreads false /cropimagestoframes true /errorcontrol /warnandcontinue /flattenerignorespreadoverrides false /includeguidesgrids false /includenonprinting false /includeslug false /namespace [ (adobe) (indesign) (4.0) ] /omitplacedbitmaps false /omitplacedeps false /omitplacedpdf false /simulateoverprint /legacy >> << /addbleedmarks false /addcolorbars false /addcropmarks false /addpageinfo false /addregmarks false /convertcolors /converttocmyk /destinationprofilename () /destinationprofileselector /documentcmyk /downsample16bitimages true /flattenerpreset << /presetselector /mediumresolution >> /formelements false /generatestructure false /includebookmarks false /includehyperlinks false /includeinteractive false /includelayers false /includeprofiles false /multimediahandling /useobjectsettings /namespace [ (adobe) (creativesuite) (2.0) ] /pdfxoutputintentprofileselector /documentcmyk /preserveediting true /untaggedcmykhandling /leaveuntagged /untaggedrgbhandling /usedocumentprofile /usedocumentbleed false >> ] >> setdistillerparams << /hwresolution [2400 2400] /pagesize [612.000 792.000] >> setpagedevice microsoft word numero_58_art_26_3156.docx m. achoui et alii, frattura ed integrità strutturale, 58 (2021) 365-375; doi: 10.3221/igf-esis.58.26 365 influence of themo-mechanical treatments and microstructural state on the fatigue behaviour of a weld seam: case of api x60 steel mohammed achoui, fethi sebaa university of tlemcen, ingeniery of mechanical systems and materials laboratory, tlemcen, algeria achoumedi@yahoo.fr , http://orcid.org/0000-0001-2345-6789 sebaafeth@yahoo.fr , https://orcid.org/0000-0001-5630-7819 benattou bouchouicha university djillali liabes of sidi bel abbes, reactive materials and systems laboratory (lmsr), sidi bel abbes, algeria benattou_b@yahoo.fr , https://orcid.org/0000-0002-6051-5108 abstract. the aim of this work is the study of the fatigue behaviour of api x60 steel and the influence of thermal and mechanical treatments. the evaluation of the integrity and safety of welded structures dictates the approach taken in this research. the microstructural observations on the different zones of the weld seam indicates that the variation of heterogeneous structure is a progressive destruction of the strips of lamination which cause a new phase leading to a drop in the mechanical properties requiring treatment after welding. the fatigue cracking rate diverges beyond the threshold of , but no deviation of the crack from its propagation axis was noticed, which confirms the correct choice of filler metal over that of the base metal with an overmatching m = 1.1, and the treatments applied to the structure. this fatigue cracking rate transversal to the welding direction initially presents an aspect similar to that of bm but registers a delay as soon as the crack tip enters the second zone (haz) then it progresses rapidly. this evolution is characterized by a disturbance due to the repeated change of microstructure. keywords. fatigue crack; thermal-mechanical treatment; microstructure of welded joints; crack propagation; mechanical properties of api x60 steel; chemical composition. citation: achoui, m., sebaa, f., f bouchouicha, b., influence of themomechanical treatments and microstructural state on the fatigue behaviour of a weld seam: case of api x60 steel, frattura ed integrità strutturale, 58 (2021) 365-375. received: 28.06.2021 accepted: 19.09.2021 published: 01.10.2021 copyright: © 2021 this is an open access article under the terms of the ccby 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. introduction enerally, industrial structures, consist of elements assembled by welding, show geometric discontinuities near which areas of stress concentration are formed. these areas are the prime sites for the initiation and propagation of fatigue cracks which are the real causes for the damage to these structures. when designing mechanical structures or pipelines, it is essential to have tools capable of predicting their fatigue resistance under conditions close to actual operation. g https://youtu.be/3whyemztaxw m. achoui et alii, frattura ed integrità strutturale, 58 (2021) 365-375; doi: 10.3221/igf-esis.58.26 366 cracks in weld joints, base metal, overloads due to vibratory movements, corrosion, maintenance and rehabilitation work can also lead to nicks or scratches and indentations in structures [1-3] . rupture prevention is built on an in-depth knowledge based on tangible facts and on data to support them. it starts with the engineering and design of the pipelines, during the exploitation and manufacturing of the structures. these latter will continue to deteriorate over time; they will be subjected to variable environmental conditions and to external events that their manufacturers could not, always, predict. several studies have discussed the factors affecting the life of welded structures, including heterogeneity, welding conditions and of course the filler metal [4-5]. the right choice of this latter improves, considerably, fatigue resistance of structures [69]. the microstructure of the material has a considerable effect on the propagation behaviour of fatigue cracks in structures, which has become the center of attention of researches for many years. these microstructural effects are associated with welding conditions especially the position of the weld seam according to the orientation of loads and stresses [10-11]. the thermal effect of the welding cycle gives microstructural heterogeneity in this zone (haz) made up of several subzones with different microstructures that can cause different behaviours [12-14]. a ferrite-bainitic microstructure offers better resistance to crack propagation in the welded zone than the martensitic or bainitic structures [15]. indeed, a better combination of resistance and fatigue crack growth instead of rupture was observed for steel containing more than 70% of martensite and low carbon content. this study deals with the influence of the thermal and mechanical treatment on the fatigue behaviour of a welded joint. this is a useful step in assessing the integrity and safety of welds. on the other hand, the microstructure and effects of reducing internal stresses using the advance fatigue crack ligament pre-compression method were also analysed. experimentation material presentation ur study focuses on api x60 steel, used for the manufacturing of gas tanks (liquefied petroleum gas lpg) and the construction of pipelines. welding is performed by submerged arc welding (saw) with coated electrodes gmosi. the basic chemical composition and mechanical properties of the two materials are given by tab. 1 and 2 respectively. c% mn% p% si% s% v% mo% base material (bm) api x60 0.22 1.4 0.03 0.03 < 0.01 filler metal fm gmosi 0.1 1.15 0.6 0.52 table 1: chemical composition of bm and fm (wm). re (mpa) rm (mpa) a % k n base material (bm) api x60 414 517 25 578 0.1 filler metal fm gmosi 460 560 22 836 0.3 table 2: mechanical properties du bm et fm (wm). micrographic examinations micrographic examinations on polished cuts (1 μm) then attacked with 3% nital, were carried out using a microscope. the aim is to observe the structures in very localized areas on the surface and transversal perpendicular to the welded seam in the three areas illustrated by fig. 1 the transformations that the haz undergoes cannot be simulated to the heat treatments applied to steels. indeed, after a welding operation, there is the appearance of bainite and intergranular ferrite in the junction zone and the transformation zones.  zone z1 (bm): the observation shows the presence of ferrite and ferrite-perlite (an alternating structure of ferrite and perlite characteristic of bands of lamination (fig. 2 a). o m. achoui et alii, frattura ed integrità strutturale, 58 (2021) 365-375; doi: 10.3221/igf-esis.58.26 367  zone (z3) fm (wm): in the last pass, the arrangements of the ferritic areas and of the carburized constituents similar to ferrite present a marked arrangement linked to solidification. observation shows the presence of a dendritic structure with islets (ferrite-perlite) and fairly large grains (fig. 2b).  zone haz: this zone presents a variation of heterogeneous structure and a progressive destruction of the bands of lamination (fig. 2 c). in the area near the fusion line, an overheated structure appears with a particular aspect and disposition of the ferrite. we notice the presence of a new phase which is the acicular ferrite (in the form of needles). this microstructure presents islets of slatted bainite separated by ferrite and has good mechanical properties. recent works [16-17] practically detect similar observations. figure 1: polished cuts orientation for micrographic exams. figure 2: the structure of the three zones with different magnifications: a bm, b – fm (or wm), c – haz. figure 3: border junction between the three zones. m. achoui et alii, frattura ed integrità strutturale, 58 (2021) 365-375; doi: 10.3221/igf-esis.58.26 368 the small, punctual "brown spots" distributed over the entire micrograph are localized chemical attacks. fig. 3 shows the border junction between the three zones. fatigue cracking test conditions and instrumentation he cracking tests were carried out on 07 mm thick ct 50 test specimens compliant to the astm-e-647 standard. the tests were carried out in ambient air and for the same value of load ratio r = 0.1, and we used 3 test tubes for each case studied. the sampling of the test tubes was done according to fig. 4. figure 4: schematic representation of the sampling process. calculation method of the cracking rate the smoothing of the curves is based on an incremental polynomial method that uses the smoothing of a series of successive points by a polynomial whose growth is monotonic in this interval [18]. the equation of the smoothed curve is of the form:                2 1 1 1 1 1    0 1 2 2 2   n c n c a b b b c c (1) 0 1 2b , b et b : regression parameters determined by the least square’s method in an interval of seven points. parameters c1 and c2 are used to normalize the data.    1 1 3 1 3 1         2 c n n (2)    2 1 3 1 3 1         2 c n n (3) the cracking rate at point ia is obtained from the derivative of the first expression. t m. achoui et alii, frattura ed integrità strutturale, 58 (2021) 365-375; doi: 10.3221/igf-esis.58.26 369         1 1 1 2 2 2 2   2 b n cda b dn c c (4) elimination of residual stresses by local pre-compression during a fatigue cracking test on a weld seam, it is noted that the propagation of the fatigue crack is disturbed by the existing residual stress field. to remedy this problem, we used the local pre-compression method to limit the plastic deformation to a few percentages of the thickness in order to modify the progression of the crack. fig. 5 schematically shows the principle of the method with the dimensions of the punches to be used. fig. 6 represents the photo taken on the studied test tubes. the applied pressure and the penetration of the punch into the ligament are given respectively by relations (5) and (6):  20.4. .p re b (5) with: re: elastic limit of the material (mpa) b: test tubes thickness (mm)   0.5% t b (totalised on both sides) (6) figure 5: pre-compression method principal. figure 6: pre-compressed ligament. crack’s advance ligament treatment this operation went through two important phases, a preheating before the welding operation and a stress relieving annealing consisting of a slow lowering of the temperature. this treatment must guarantee perfect safety and reliability at the weld level depending on the thicknesses and the quality of the material while reducing internal stresses. in fact, this treatment was carried out in an oven at a maximum temperature of 580 °c for 2 hours, followed by a slow cooling to 320 °c, then an exposure to a temperature below 200 ° c, all the process took place at a temperature below ac1. other techniques and procedures are also used [19-20]. m. achoui et alii, frattura ed integrità strutturale, 58 (2021) 365-375; doi: 10.3221/igf-esis.58.26 370 results and discussion study on the three zones he obtained results concern the different test tubes in the three zones (bm fm haz) represented by fig. 4. tab. 3 encompasses the values of c and m of the paris law (formula 7) of the explored domain exhibiting an almost straight appearance.       mda c k dn (7) designation paris law k bm da/dn=1.25e-11k4.3 20 to 62 mpa m fm (wm) da/dn=9.76e-12k4.6 28 to 64 mpa m haz da/dn=6.33e-12k5.8 18 to 66 mpa m fm after tth da/dn=6.53e-10k3.1 18 to 60 mpa m transversal seam da/dn=1.42e-14k6.2 17 to 65  mpa m fm before comp da/dn=6.77e-15k6 22 to 50 mpa m table 3: c and m values of paris law in the different studied zones. fig. 7 represents the crack growth rate da⁄dn compared to  of the 3 zones with a load ratio r = 0.1. the results show that for low rates of , the growth of fatigue cracks is similar. however, for values of  greater than 30 mpa.m, this crack growth becomes more important respectively in the fm and the haz.  for the values of > 50 mpa.m, the cracking rate presents a significant difference (15%) between the 3 cases, which means that:  in this studied area, the cracking rate presents an almost similar rate in the three zones.  even if the speeds differ in the three zones, but no deviation of the crack from its axis of propagation has been noticed, contrary to certain authors [21-23] who have shown that beyond a certain value of  the cracking speed is usually accompanied by a deviation of the crack from its initial plane towards base metal. this confirms that the weld was seine and the choice of a filler metal over that of the base metal is adequate. usually, the deviation is due to the difference in mechanical characteristics between the three zones; the crack moves from a harder microstructure to a softer one. fig. 8 represents the cracking speed da⁄dn according to in the molten metal after relaxation by heat treatment with the aim of eliminating the internal stresses arising from the solidification of the cooled welded parts. the results show that the crack growth is initiated at a lower level of  than the state without heat treatment. and even for larger values of , a decrease in this speed was recorded with a regular growth of the fatigue crack. this means the elimination of internal stresses caused by solidification after welding. transversal welding position the variation da⁄dn, in the plate containing a transversal weld joint, follows a pace similar to that of bm, but records a delay as soon as the crack tip enters the second zone (haz) then it progresses rapidly with a slope m close of 7. this evolution is characterized by a disturbance due to the repeated change of the microstructure. in addition, the weld seam had a higher resistance to crack growth than the base metal, especially in the low range . as the growing crack propagated through haz and fm this resistance dropped (fig. 9). t m. achoui et alii, frattura ed integrità strutturale, 58 (2021) 365-375; doi: 10.3221/igf-esis.58.26 371 figure 7: crack speed evolution da/dn=f()in the three zones (bm, fm et haz).    figure 8: comparison of the evolution of da/dn=f() before and after tth. 10 20 30 40 50 60 70 80 90100 1e-6 1e-5 1e-4 1e-3 0,01 da/dn=5,6e-4(mm/cycle) da/dn=1,4e-3(mm/cycle) kc=60mpa m 1/2 k(haz) k(bm) k(w m) difference w m/bm bm w m haz d a /d n ( m m /c yc le ) k (mpa m 1/2 ) difference haz/w m da/dn=3,33e-3(mm/cycle) 1 0 2 0 3 0 4 0 5 0 6 0 7 0 8 0 9 0 1 0 0 1 e -6 1 e -5 1 e -4 1 e -3 0 ,0 1 b m (d ire c tio n o f w e ld in g ) 3 zo n e s (tra n s v e rs e d ire c tio n o f th e w e ld ) d a /d n ( m m /c yc le s) k (m p a m 1 /2 ) m. achoui et alii, frattura ed integrità strutturale, 58 (2021) 365-375; doi: 10.3221/igf-esis.58.26 372 figure 9: comparison 𝑑𝑎 𝑑𝑁⁄ =f() of fm longitudinal and transversal direction. figure 10: comparison 𝑑𝑎 𝑑𝑁⁄ = f () of fm with and without pre compression of the ligament. 10 20 30 40 50 60 70 80 90100 1e-6 1e-5 1e-4 1e-3 0,01 difference difference w ma/w m kc=60mpa m 1/2 w m (befor tth) w ma (after tth) d a /d n ( m m /c yc le s) k (mpa m 1/2 ) 10 20 30 40 50 60 70 80 90 100 1e-6 1e-5 1e-4 1e-3 0,01 0,0 2,0x10 5 4,0x10 5 6,0x10 5 8,0x10 5 0 4 8 12 16 20 24 28 number of cumulative cycles before propagation nc = 280,000 cycles wm wm (without precompression) d a /d n ( m m /c yc le s) k (mpa m 1/2 ) a-n (wm without precompression ) a-n (wm) a -a 0 m m n (cycle) m. achoui et alii, frattura ed integrità strutturale, 58 (2021) 365-375; doi: 10.3221/igf-esis.58.26 373 cracking on fm without pre compression fig. 10 represents the evolution of the cracking speed before the relaxation of internal welding stresses at the pre-compression crack point. indeed, this behaviour is in accordance with the residual stresses and the evolution of the closing of cracks. when the residual traction stresses act to fully open the crack, the test tube adopts a crack growth behaviour comparable to the base metal but with a large accumulation of number of fatigue cycles. the results show that the crack growth is very important after the delay recorded due to the closure by internal stresses and exhibits a practically constant deviation during the advance of the crack. the slope m is increased and is comparable to the slope obtained in the haz. other authors have drawn the same conclusions on x70 steel [23-25]. conclusion he influence of local treatment and the effects of reducing internal stresses on the fatigue behaviour of a weld joint have been dealt with in this study. the following conclusions have been drawn: (1) appearance of bainite and intergranular ferrite in the junction zone and the transformation zones after a welding operation and before heat treatment.  far from the weld seam, the observation shows an alternating structure of ferrite and perlite characteristic of lamination strips. but on the seam and in the last pass, the observation shows the presence of a dendritic structure with isles (ferrite perlite) and fairly large grains. this phase can be assimilated to ferrite exhibiting a marked disposition linked to solidification.  in the haz, we notice a gradual destruction of the lamination strips, resulting in a variation of heterogeneous structure. this justifies the obtained mechanical properties. (2) fatigue cracks show that for low rates of , crack growth is similar. but for  greater than 30 mpa.m, this crack growth becomes more important respectively in the fm and the haz. approaching the third stage, the crack rate shows an important difference (15%) between the 3 cases, which means that:  after the initiation and exit from the wake of the residual stresses, the crack rate presents an almost similar pattern in the three zones.  the adequate choice of the fm melted metal and the treatment of the crack tip ligament avoided deviating the crack from its propagation axis for the different configurations. contrary to certain authors [26] showing that beyond a certain value of , the crack rate is generally accompanied by a deviation of the crack from its initial plane towards the base metal. (3) for the position of the transversal weld, the crack propagates perpendicular to the welding direction. we remark an evolution characterized by a disturbance due to the repeated change of microstructure. this case allows to have a similar appearance to that of bm but registers a delay as soon as the crack tip enters the second zone (haz) then it progresses rapidly. the mechanical properties drop as the crack propagates through the haz and fm. conflict of interests he authors declare that there is no conflict of interests regarding the publication of this paper. references [1] tirenifi, m., chikh, b. o., bouchouicha, b., and bensari, a. (2019). numerical comparison of cruciform weld and butt weld simulation and a study of fracture mechanics on two types of welds. frattura e integrita strutturale, 13(48), pp. 357-369; doi: 10.3221/igf-esis.48.34. t t m. achoui et alii, frattura ed integrità strutturale, 58 (2021) 365-375; doi: 10.3221/igf-esis.58.26 374 [2] bensari, a., ould chikh, b., bouchouicha, b., and tirenifi m., (2019). numerical simulation of a steel weld joint and fracture mechanics study of a compact tension specimen for zones of weld joint. frattura ed integrità strutturale, 13(47), pp. 17-29. doi: 10.3221/igf-esis.47.02. [3] arsic, m., savic, z., sedmak, a., bosnjak, s., and sedmak, s. (2016). experimental examination of fatigue life of welded joint with stress concentration. frattura ed integrità strutturale, 10(36), pp. 27-35. doi: 10.3221/igf-esis.36.03 . [4] chaib, m., slimane, a., slimane, s. a., ziadi, a., and bouchouicha, b. (2021). optimization of ultimate tensile strength with doe approach for application fsw process in the aluminum alloys aa6061-t651 and aa7075-t651. frattura ed integrità strutturale, 15(57), pp. 169-181. doi: 10.3221/igf-esis.57.14. [5] slimane, a., slimane, s., kebdani, s., chaib, m., dahmane, s., bouchouicha, b., sardi, n. and adjim, s. (2019). parameters effects analysis of rotary ultrasonic machining on carbon fiber reinforced plastic (cfrp) composite using an interactive rsm method. international journal on interactive design and manufacturing (ijidem), 13(2), pp. 521-529. doi: 10.1007/s12008-018-0518-0. [6] chattopadhyay, a., glinka, g., el-zein, m., qian, j., and formas, r. (2011). stress analysis and fatigue of welded structures. welding in the world, 55(7), pp. 2-21. doi: 10.1007/bf03321326. [7] bouchouicha, b., zemri, m., zaim, a., and chikh, b. o. (2015). estimation of the energy of crack propagation in different zones of a welded joint by the local technique. international journal of fracture, 192(1), pp. 107-116. doi 10.1007/s10704-015-9989-1. [8] deliou, a., and bouchouicha, b. (2018). fatigue crack propagation in welded joints x70. frattura ed integrità strutturale, 12(46), pp. 306-318. doi: 10.1007/bf02586155. [9] kainuma, s., and mori, t. (2008). a study on fatigue crack initiation point of load-carrying fillet welded cruciform joints. international journal of fatigue, 30(9), pp. 1669-1677. doi: 10.1016/j.ijfatigue.2007.11.003. [10] camagic, i., vasic, n., cirkovic, b., burzic, z., sedmak, a., and radovic, a. (2016). influence of temperature and exploitation period on fatigue crack growth parameters in different regions of welded joints. frattura ed integrità strutturale, 10(36), pp. 1-7. doi: 10.3221/igf-esis.36.0. [11] slimane, a., kebdani, s., bouchouicha, b., benguediab, m., slimane, s., bahram, k., ... and sardi, n. (2018). an interactive method for predicting industrial equipment defects. international journal of advanced manufacturing technology, 95(9-12), pp. 4341-4351. doi: 10.1007/s00170-017-1416-5. [12] kaddour, b., bouchouicha, b., benguediab, m., and slimane, a. (2018). modeling and optimization of a cracked pipeline under pressure by an interactive method: design of experiments. international journal on interactive design and manufacturing (ijidem), 12(2), pp. 409-419. doi 10.1007/s12008-017-0385-0. [13] wei, s., and liu, x. (2018). high cycle fatigue assessment of steel load-carrying cruciform welded joints: an overview of recent results. frattura ed integrità strutturale, 12(46), pp. 94–101. doi: 10.3221/igf-esis.46.10. [14] ferro, p., peron, m., razavi, s. m. j., berto, f., and torgersen, j. (2017). the fatigue behavior of v-notches in presence of residual stresses: recent developments and future outcomes. frattura ed integrità strutturale, 11 (42), pp. 189-195. doi: 10.3221/igf-esis.42.20. [15] slimane, a., bouchouicha, b., benguediab, m., and slimane, s. a. (2015). contribution to the study of fatigue and rupture of welded structures in carbon steel-a48 ap: experimental and numerical study. transactions of the indian institute of metals, 3(68), pp. 465-477. doi: 10.1007/s12666-014-0477-5. [16] chrysanthopoulos, m.k. and righiniotis, t.d. (2006). fatigue reliability of welded steel structures, journal of constructional steel research, 62, 2006, pp.1199–1209. doi: 10.1016/j.jcsr.2006.06.007. [17] bordbar, s., alizadeh, m., and hashemi, s. h. (2013). effects of microstructure alteration on corrosion behavior of welded joint in api x70 pipeline steel. materials and design, 45, pp. 597-604. doi: 10.1016/j.matdes.2012.09.051. [18] messabih, f. z., and bouchouicha, b. (2018). coupling between welding conditions and thermal cycling for identification of the mechanical heterogeneity of a weld joint. periodica polytechnica mechanical engineering, 62(3), pp. 226-232. doi: 10.3311/ppme.12065. [19] alioua, a., bouchouicha, b., zemri, m., and abdellatif, i. m. a. d. (2018). effect of filler metal mechanical properties on fatigue behaviour welded joints. transactions of the indian institute of metals, 71(4), pp. 977-984. doi:10.1007/s12666-017-1231-6 [20] alioua, a., bouchouicha, b., zemri, m., and abdellatif, i. m. a. d. (2017). fatigue behavior of mechanical structures welded with different filler metal. advances in materials research, 6(3), 233. doi: 10.12989/amr.2017.6.3.233. [21] slimane, s. a., slimane, a., guelailia, a., boudjemai, a., kebdani, s., smahat, a., and mouloud, d. (2021). hypervelocity impact on honeycomb structure reinforced with bi-layer ceramic/aluminum facesheets used for spacecraft shielding. mechanics of advanced materials and structures, pp. 1-19. doi: 10.1080/15376494.2021.1931991. m. achoui et alii, frattura ed integrità strutturale, 58 (2021) 365-375; doi: 10.3221/igf-esis.58.26 375 [22] tsay, l. w., liu, c. c., chao, y. h., and shieh, y. h. (2001). fatigue crack propagation in 2.25 cr–1.0 mo steel weldments in air and hydrogen. materials science and engineering: a, 299(1-2), pp. 16-26. doi: 10.1016/s09215093(00)01420-9. [23] akita, m., nakajima, m., tokaji, k., and shimizu, t. (2006). fatigue crack propagation of 444 stainless steel welded joints in air and in 3% nacl aqueous solution. materials and design, 27(2), pp. 92-99. doi: 10.1016/j.matdes.2004.10.004. [24] deliou, a., and bouchouicha, b. (2018). fatigue crack propagation in welded joints x70. frattura ed integrità strutturale, 12(46), pp. 306-318. doi: 10.3221/igf-esis.46.28. [25] hwang, b., kim, y. g, lee, s., kim, y. m., kim, n. j. and yoo, j. y. (2005). effective grain size and charpy impact properties of high-toughness x70 pipeline steels, metallurgical and materials transactions a, 36a, pp. 2107-2114. [26] bahram, k., bouchouicha, b., benguediab, m. and slimane, a. (2017). admissibility of external cracks in a pipeline api x60 using the sintap procedure, periodica polytechnica mechanical engineering, 61(4), pp. 261-265. doi: 10.3311/ppme.1051612:409-419. microsoft word numero_33_art_26 x. zhou et alii, frattura ed integrità strutturale, 33 (2015) 209-214; doi: 10.3221/igf-esis.33.26 209 focussed on characterization of crack tip fields load history effects on fatigue crack propagation: its effect on the r-curve for threshold x. zhou materials center leoben forschungs gmbh, roseggerstraße 12, 8700 leoben, austria austria erich schmid institute of the austrian academy of sciences, jahnstraße 12, 8700 leoben, austria xiang.zhou@mcl.at a. hohenwarter, t. leitner department of material physics of the montanuniversity leoben, jahnstraße 12, 8700 leoben, austria anton.hohenwarter@unileoben.ac.at, t.leitner@stud.unileoben.ac.at h.p. gänser materials center leoben forschungs gmbh, roseggerstraße 12, 8700 leoben, austria hans-peter.gaenser@mcl.at r. pippan erich schmid institute of the austrian academy of sciences, jahnstraße 12, 8700 leoben, austria department of material physics of the montanuniversity leoben, jahnstraße 12, 8700 leoben, austria reinhard.pippan@oeaw.ac.at abstract. the study deals with the effect of load history during threshold and fatigue crack propagation measurements in the near threshold regime. the compression pre cracking and the stepwise increasing load amplitude test was applied. the effects of pre-cracking as well as the effect of compression and tension overloads after the pre-cracking on the long crack threshold and on the r-curve of the threshold of stress intensity range are analysed. keywords. threshold of stress intensity range; r-curve; crack closure; compression pre-cracking. introduction he propagation of a fatigue crack in ductile materials is caused by the cyclic plastic deformation at the crack tip, which is governed by the plastic properties of the material and the crack driving force. the discovery of elber [1] of the premature contact of the crack flanks during the unloading sequence reduces cyclic the plastic deformation, which can be expressed by a reduction of the crack driving force k or the cyclic j integral to an effective crack driving force keff or jeff. this phenomenon is usually called crack closure effect. both, the cyclic plastic properties of a material and the effect of crack closure can be significantly affected by the loading history. there are a vast number of papers dealing with the effect of loading history during variable amplitude loading for fatigue crack propagation in the paris regime [2]. t x. zhou et alii, frattura ed integrità strutturale, 33 (2015) 209-214; doi: 10.3221/igf-esis.33.26 210 this paper will focus the attention to the effect of loading history in the threshold regime and especially to the phenomena occurring it the so-called stepwise increasing load amplitude test, which permits the determination of the crack length dependence of the threshold of stress intensity range kth. the paper is organized in the following way: at first, the stepwise increasing load amplitude test is shortly introduced, then the different applied loading procedures and the obtained results are described, and finally a simple estimation of the extension of the crack where the results are affected by the pre-cracking procedure is presented. the stepwise increasing load amplitude test: he threshold of fatigue crack propagation test is usually measured by a load decreasing technique [3]. in this case a fatigue crack is generated in the paris regime and then the stress intensity range is slowly reduced till kth is reached. in order to avoid a history effect a very small reduction rate of k should be chosen. a complete different technique has been proposed by pippan [3] and later by newman [5]. the pre-crack in this case is produced in cyclic compression. such pre-crack is surely open in the unloaded state. the crack closure during cyclic tension loading has to build-up during crack extension in the following fatigue crack experiment. figure 1: illustration of the used stepwise increasing constant load amplitude method. the specimens with existing pre-cracks were loaded with a constant amplitude step-by-step. (a) schematic of the loading procedure. the amplitude was increased to the next step, when the crack stopped to propagate. the final crack extension δa and the final stress intensity δk are plotted in diagram (c) which characteristics the material resistance against crack propagation (the r-curve). for the last step where stable crack extension occurs, the crack growth rate was measured as a function of δk depicted in (b). the load at the start of the stable crack growth corresponds to the long crack threshold value in literature. the loading procedure to determine the threshold kth and fatigue crack propagation behavior is schematically depicted in fig. 1. after pre-cracking in compression, the load amplitude at the desired stress ratio, r, is increased in steps until the threshold value of the long crack is reached. if no crack extension takes place, the applied k is smaller than the effective threshold (because the crack is open, the closure stress intensity at the beginning is in compression, kcl is smaller than keffth [6]. if k is larger than keffth a crack extension takes place. if during crack extension sufficient crack closure develops, the crack will stop the propagation. when k is sufficient that the crack closure stress intensity at the threshold t x. zhou et alii, frattura ed integrità strutturale, 33 (2015) 209-214; doi: 10.3221/igf-esis.33.26 211 is build up, no further stopping of the crack propagation will be observed and the standard long crack growth behavior can be measured. in addition to the standard fatigue crack propagation behavior of a long crack, also the r-curve [7, 8] for the threshold of stress intensity range kth can be estimated from such experiments, by plotting the stress intensity factor range as a function of the corresponding extension of the crack where stopping takes place. however, this r curve for kth is only an estimation because the residual stresses induced by the pre-cracking can affect the shape of the r-curve. effect of compressive overloads on the r-curve for kth n order to visualize the effect of residual stresses in front of the compression pre-cracked samples the r-curve for kth for specimens pre-cracked in cyclic compression with different additional compression overloads at the end of the pre-cracking have been investigated. the material was a quenched and tempered steel with a yield strength of 630mpa. single edge notch eight point bending specimens (width 20mm, thickness 6mm and a notch depth of 5mm) are used. to sharpen the notch root, a razorblade polishing technique had been applied. the pre-cracks were generated at a k = 18mpa√m at r=10 (in pure cyclic compression), 20000 cycles were applied. the length of the pre-cracks was about 30µm, which is significantly larger than the notch root radius. therefore the standard equations for the determination of the kvalues can be used. on 2 specimens in addition at the end of the cycling compression pre-cracking a single compression overload with a kmax of 30 and 40mpa√m were applied. on specimens with these additional compression overloads and without the overloads a stepwise increasing load amplitude experiment was performed at a stress ratio r of -1. the resulting r-curve for kth and the observed long crack fatigue crack growth behavior are shown in fig. 2 and fig. 3. from these results it is clearly evident that the fatigue crack growth curves and the long crack threshold are not affected by the pre-cracking procedure and the overloads. however, the r-curve for kth for the samples with overloads is significantly shifted to larger crack extension. this shift increases with increasing overloads. figure 2: the r-curves for the threshold of stress intensity range at a load ratio of r=-1 for a specimen with pre-cracks generated in cyclic compression and specimens with additional compression overloads. figure 3: the experimentally obtained long crack fatigue crack growth behavior for a specimen with pre-cracks generated in cyclic compression and specimens with additional compression overloads. the explanation of this shift of the r-curve is simple. the compressive overloads induce local tensile residual stresses in front of the crack tip. this residual tensile stresses increases the r-ratio locally. the crack can propagate if k is larger than keffth till the residual stresses are not sufficient high enough to compensate the building-up of crack closure. when the crack is grown over the regime of this residual stress zone generated by the compression loading the typical transition i x. zhou et alii, frattura ed integrità strutturale, 33 (2015) 209-214; doi: 10.3221/igf-esis.33.26 212 to the long crack behavior is observed. this includes also the building-up of the long crack closure contribution, which also takes place on closure free pre-cracks without residual stresses [7]. it should be noted that the sample, which is only compression pre-cracked, contains also residual tensile stresses in front of the pre-crack. they can be reduced if the number of loading cycles is enhanced in order to increase the crack length till the crack stops the propagation. this reduces then the size of zone with residual tensile stress. another possibility is also to reduce the load amplitude for the compression pre-cracking [6]. estimation of affected zone finite element analysis can be used to predict the evolution of the effect of the residual stresses induced by the cyclic compression as well as the compression overload on the local stress intensity ratio or the stress intensity factor induced by the residual plastic deformation. a careful analysis of the growing fatigue crack in such a zone is however quite cumbersome. the concept of dislocation shielding or anti-shielding is a very simple tool to estimate the effect of the wake plasticity induced by such compression overload, especially in the case of plane strain condition which one usually have always in the near threshold regime. under plane strain condition and small scale yielding the plastic deformation in front of a crack or in front of a very sharp notch is mainly realized by plastic shear inclined between 60° and 100° to the crack plane. therefore the effect of an edge dislocation (which is geometrically necessary to realize the mentioned plastic shear deformation) inclined with 70° and 90° as a function of the distance behind the crack will be discussed in the following. fig. 4 shows a geometrical arrangement of a single dislocation generated during the compression loading of a very sharp notch. such notch can be considered as a crack which does not come into contact during compression loading. figure 4: schematic representation of the geometrical arrangement of a single dislocation generated during the compression loading. the real effect of the compression loading can be calculated by a simple linear superposition of all geometrically necessary dislocation to realize the necessary plastic deformation. since all the geometrically necessary dislocations have similar burgers’ vectors and the mentioned linear superposition, it is sufficient to show the effect of a single dislocation. the mode i shielding (if k is negative) or anti-shielding (if the resulting k is positive) stress intensity for the arrangement of the edge dislocation as depicted in fig. 4 can be calculated by: parallel to the crack propagation direction: cos( )xb b   (1) perpendicular to the crack propagation direction: sin( )yb b   (2) 1 3 1 1 3 sin cos ( 2 cos sin sin ) 2 2 2 2 22(1 ) 2(1 ) yx b gb g k r r                (3) where g is the shear modulus, r is the distance from crack tip to the dislocation [9]. the burgers vector b is separated into two parts which are parallel (bx) and perpendicular (by) to the crack propagation direction, respectively. ν is the poisson’s ratio,  is the angle between the connection line from crack tip to the position of dislocation and the crack plan. this expression is identical also with the solution presented in [10]. a x. zhou et alii, frattura ed integrità strutturale, 33 (2015) 209-214; doi: 10.3221/igf-esis.33.26 213 in fig. 5 and 6 the anti-shielding effect of a single dislocation generated during the compression overload as a function of its distance in the wake of the crack x is shown. the anti-shielding stress intensity is displayed for two inclination angles of the edge dislocation, 70°and 90°. the values are calculated for a shear modulus of 80000mpa, a burgers’ vector b = 0.3nm, a distance of the dislocation rpl = 1µm. figure 5: the stress intensity factors induced for 70° and 90° inclined dislocations as a function of the distance to the crack tip in the wake. figure 6: magnified stress intensity factors induced for 70° and 90° inclined dislocations as a function of the distance to the crack tip in the wake. for x larger than 2rpl, the stress intensity of the 70° inclined dislocation becomes somewhat shielding compares to the 90° inclined dislocation which remains antishielding. from fig. 5 it is clearly evident that for crack extensions a or x smaller than r the dislocation generated during the compression loading induces a significant anti-shielding, this is the reason that cracks can propagate under pure cyclic compression. however, for x larger than r the k values becomes very small, they remain anti-shielding for the inclination angle 90° and becomes shielding for inclination angle 70°, but the values are very small and disappear relatively fast. the consequence of this estimation is that the increase of the local r-ratio induced by the compression overload should be significant only for crack extensions comparable to the size of the generated plastic zone. using the estimation of irwin for the size of the plastic zone under plane strain condition 2 pl 2 y k r 3  gives a plastic zone size of 0.241mm and 0.428 mm for the 30 and 40mpa√m overload, respectively. a comparison of the r-curves for kth in fig. 2 shows that the shift of the r-curves for the 30 and 40mpa√m compression overloads agree quite well with the estimation of the size of the plastic zone. hence as a simple estimation of the pre-cracking affected zone is the size of the plastic zone. conclusion compression overloads of pre-cracks can significantly affect the fatigue crack propagation behavior of short fatigue cracks. such compressive overloads can shift the r-curve for kth to large crack extension. this is also important for practical application, because each crack or flaw has load history. the shift can be explained by the anti-shielding induced by the plastic deformation generated during the compression overload. the crack propagation rate is affected over a distance comparable to the size of the plastic zone. x. zhou et alii, frattura ed integrità strutturale, 33 (2015) 209-214; doi: 10.3221/igf-esis.33.26 214 references [1] elber,w., fatigue crack closure under cyclic tension, eng fract mech, 2 (1970) 37-45. [2] suresh, s., fatigue of materials, cambridge university press, (1998). [3] pippan, r., plochl, l., klanner, f., stuwe, h. p., use of fatigue specimens precracked in compression for measuring threshold values and crack growth, astm j test eval, 22 (1994) 98-103. [4] standard test method for measurement of fatigue crack growth rates, astm international e-647, (2006). [5] newman jr., j., schneider, j., daniel, a., mcknight, d., compression pre-cracking to generate near threshold fatiguecrack-growth rates in two aluminum alloys, int j fatiuge, 27 (2005) 1432-40. [6] tabernig, b., pippan, r., determination of the length dependence of the threshold for the fatigue crack propagation, eng fract mech, 69 (2002) 899-907. [7] pippan, r., berger, m., stuewe, h., influence of crack length on fatigue crack growth in deep sharp notches, metall trans a, 18 (1987) 429-435. [8] tanaka, k., akiniwa, y., resistance-curve method for predicting propagation threshold of short fatigue cracks at notches, eng fract mech, 30 (1988) 863-876. [9] weertman, j., dislocation based fracture mechanics, world scientific, (1996). [10] riemelmoser, pippan, r., discussion of error in the analysis of the wake dislocation problem, metall trans a, 29 (1998) 1357-1360. microsoft word numero_56_art_11_3001 m. m. konieczny et alii, frattura ed integrità strutturale, 56 (2021) 137-150; doi: 10.3221/igf-esis.56.11 137 influence of the applied layer on the state of stress in a bimetallic perforated plate under two load variants mateusz marcin konieczny, henryk achtelik, grzegorz gasiak opole university of technology, poland mateuszmarcinkonieczny@wp.pl, kmpkm@po.edu.pl, g.gasiak@po.edu.pl abstract. the paper presents the results of the analysis of the influence of the applied plate layer on the state of stress in the bimetallic perforated plate. the finite element method ansys program was used for numerical calculations. the paper presents the results of stress tests for a single-layer clad plate made of s355j2 steel and a bimetallic perforated plate consisting of layers made of s355j2 steel and titanium. in addition, the study presents the results of the research on the influence of the method of loading, i.e. the concentrated force p in the geometric center of the plate and the external pressure q on the entire surface of the plate, and the method of support, i.e. free support and fixed, on the location of stress concentration zones in the bimetallic circular perforated plate. it has been shown that the presence of a perforated layer in the plate reduces the value of the equivalent von mises stress by a minimum of approximately 30% in the base (steel) layer. keywords. applied layer; base layer; stress analysis; numerical calculations; fem. citation: konieczny, m. m., achtelik, h., gasiak g., influence of the applied layer on the state of stress in a bimetallic perforated plate under two load variants, frattura ed integrità strutturale, 56 (2021) 137-150. received: 25.01.2021 accepted: 08.03.2021 published: 01.04.2021 copyright: © 2021 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. introduction n engineering structures, e.g. process equipment [1] or energy equipment [2], elements consisting of many layers and of many materials are used, i.e. bimetallic (plated) elements (fig. 1) [3, 4], laminated elements [5] and composite elements [6]. such structural elements may include layers made of structural steel, titanium alloys, brass, aluminum, nickel, but also of non-metallic materials such as polyethylene, glued wood, glass fibers and carbon fibers. these types of elements are most often used due to the improvement of corrosion resistance, appropriate frictional properties or special properties of thermal conductivity as well as the mechanical parameters of the structure in which such elements are present. the thickness of the applied layers, depending on the type of use of the plated sheet, may vary from 1.5–15% of the substrate thickness. layering methods can be divided into two groups: cold plating, i.e. cold rolling, explosion [7, 8, 9] or hot plating, i.e. hot rolling, broaching, sintering. the use of elements consisting of many types of materials and multiple layers allows to obtain a material with specific properties that a single-layer material does not have. i https://youtu.be/toqfo4qudc8 m. m. konieczny et alii, frattura ed integrità strutturale, 56 (2021) 137-150; doi: 10.3221/igf-esis.56.11 138 figure 1: model of bimetallic perforated plate [3]. in the works [10. 11], an analytical solution was presented using mathematical formulas enabling engineers to estimate the effort of the designed plated perforated plates subjected to various types of load. the results of these calculations were compared with the results obtained numerically using the finite element method and a good agreement was obtained. on the other hand, the work [12] presents the results of experimental research of the state of stress in a bimetallic perforated plate consisting of two layers, i.e. a steel and a titanium layer. it was found that the use of the ansys program enables the determination of the state of stress of the plated perforated plate at any point of the plate, i.e. on the bridge between the holes, around the holes, along the thickness of the titanium and steel layers. it also enables the determination of stress concentration zones, and thus the location of dangerous places in the designed plate. experimental methods based on tensometry do not offer such possibilities. in this work, among others, influence of the applied layer on the state of stress in a bimetallic circular perforated plate, freely supported at the edge and fixed at the edge, and loaded in the first case with a centrally concentrated force p perpendicular to the plate surface and in the second case with external pressure q over the entire surface of the plate. the research carried out at work was carried out on the basis of the application of the finite element method (fem). the test results in the form of stress values presented in the paper can be used by engineers in the design of bimetallic perforated plates loaded perpendicular to their surface. material and geometry or the calculations in the first case, a bimetallic perforated plate with dimensions: diameter d = 300 mm consisting of two layers, i.e. the base layer b in the form of structural steel with a thickness of h = 10 mm and the applied layer a in the form of titanium with a thickness of a = 2.5 mm was adopted. (fig. 2, 4b, 4d, 4f, 4h). however, in the second case, a perforated plate with the following dimensions was adopted: diameter d = 300 mm consisting of one layer, i.e. the base layer b in the form of structural steel with a thickness of h = 10 mm (fig. 2, 4a, 4c, 4e, 4g). 100 holes with different radii located on the plate. these holes were arranged in five circles with 20 holes in each circle. on the first outer circle, the plate had holes d1 = 20.5 mm in diameter and on the fifth, inner circle holes d5 = 9.5 mm in diameter (fig. 2). steel plate grade s355j2 was adopted as the base material, and titanium sheet was adapter as the applied material with the following mechanical and material parameters (tab. 1) [13]. the materials used in the work, titanium and steel included in the bimetallic perforated plate, were modeled as elastic materials. f m. m. konieczny et alii, frattura ed integrità strutturale, 56 (2021) 137-150; doi: 10.3221/igf-esis.56.11 139 figure 2: model of bimetallic perforated plate consisting of steel thickness perforated plate h and titanium perforated plate thickness a containing holes with diameters d1,…,d5. s355j2 steel and titanium applied layer a titanium re [mpa] rm [mpa] e [gpa] 𝑣 [-] g [gpa] a5 [%] 189-215 308-324 100 0.37 36.5 43-56 c fe h n o ti 0.10 0.20 0.015 0.03 0.18 all base layer b s355j2 steel re [mpa] rm [mpa] e [gpa] 𝑣 [-] g [gpa] a5 [%] 382-395 598-605 220 0.30 84.6 24-34 c si mn p s cu fe 0.22 0.55 1.60 0.025 0.025 0.45 all table 1: strength properties and chemical composition of s355j2 steel and titanium, where: re – yield strength [mpa], rm – tensile strength [mpa], e – young’s modulus [gpa], 𝑣 – poisson’ s ratio [-], a5 – tensile elongation [%]. m. m. konieczny et alii, frattura ed integrità strutturale, 56 (2021) 137-150; doi: 10.3221/igf-esis.56.11 140 calculation method umerical calculations were carried out using the ansys finite element method software. it is a program for advanced numerical calculations using the finite element method (fem). the three-dimensional 3d computational model of a circular plated perforated plate was created and discretized with the use of modeling and finite element mesh modeling in ansys [14]. finite elements used for discretization were solid186 finite elements. elements of the solid185 type are higher-order elements with a square shape function and well suited for modeling curved model boundaries without losing computational accuracy. finite elements of this type are defined in the case of a tetrahedron-shaped element by 10 nodes with three degrees of freedom per node (ux, uy, uz), i.e. translations in the nodes in the x, y, and z directions and in the case of a cube-shaped element by 20 nodes ( i, j, k, l, m, n, o, p, q, r, s, t, u, v, w, x, y, z, a, b) with three degrees of freedom per node (ux, uy , uz), i.e. translations in nodes in the x, y and z directions. these elements can have any spatial orientation as well as take into account plasticity, creep, stress stiffness, large deflection and large strain. the calculation model for the clad perforated plate with the ring support had a total number of 3379707 finite elements, while the total number of nodes was 7027927. the entire plate had 25 finite element layers (twenty base plate layers and five layers of add-on plate) (fig. 3). on the other hand, the calculation model in the case of a clad perforated plate without a support contained the total number of finite elements 2927283, while the total number of nodes was 5029189. tab. 2 shows the number of finite elements and nodes for each plate layer, i.e. for the steel plate layer and the titanium plate layer, and ring support (fig. 3). number of finite elements and nodes support base layer b steel applied layer a titanium nodes 1998738 3428852 1600337 elements 452424 2019704 907579 table 2: number of finite elements and nodes in the analyzed plate. figure 3: finite elements of a bimetallic circular perforated plate in ansys program. n m. m. konieczny et alii, frattura ed integrità strutturale, 56 (2021) 137-150; doi: 10.3221/igf-esis.56.11 141 the base layer of the b – steel plate is combined with the applied layer of the a – titanium plate by using the "connections" function, providing the option to bond two or more elements [14]. details are presented in appendix a. the calculations were made with an accuracy of 5%. the method of supporting and loading the perforated plate t was assumed that the analyzed circular perforated plate is freely supported along its entire perimeter. the free support of the plate was achieved by designing a annular support on which a plated perforated plate was placed. minimal friction contact is applied between the plate and the support. then, in the first case, the analyzed plate was loaded centrally with the concentrated force p, normal to its surface. the load was applied around a hole with a diameter of d = 12 mm located in the central part of the plate. the load was distributed over the diameter of b1 = 14 mm from the center of the plate with the use of a pressure stemp (fig. 4a and 4b). in the second case, the analyzed plate was loaded with external pressure q over the entire plate surface (fig. 4c and 4d). in the further part of the work, it was assumed that the analyzed circular plated perforated plate is fixed along its entire perimeter. the plate was fixed by limiting all degrees of freedom to the finite elements located on the outer contour of the perforated plate. then, in the first case, the analyzed plate was loaded centrally with the concentrated force p, normal to its surface. the load was applied around a hole with a diameter of d = 12 mm located in the central part of the plate. the load was distributed over a diameter of b1 = 14 mm from the center of the plate with a pressure stamp (fig. 4e and 4f). in the second case, the analyzed plate was loaded with the external pressure q over the entire plate surface (fig. 4g and 4h). figure 4: the method of supporting and loading the perforated plate. i m. m. konieczny et alii, frattura ed integrità strutturale, 56 (2021) 137-150; doi: 10.3221/igf-esis.56.11 142 state of stress calculation bimetallic perforated plate (fig. 4b – 4h) xamples of the equivalent von mises stress distributions 𝜎 given in [mpa] along the thickness of the bimetallic perforated plate are shown in fig. 5. the figure shows the stress distribution in the perforated plate in the first case, simply supported on the annular support and loaded with a force p = 10 kn (fig. 5a), in the second case, simply supported on a annular support and loaded with external pressure q = 0.4 mpa (fig. 5b), in the third case fixed on the perimeter and loaded with a force p = 10 kn (fig. 5c), and in the fourth case fixed on the perimeter and loaded external pressure q = 0.4 mpa (fig. 5d) in the applied boundary zone a’ titanium, in the base boundary zone b’ steel and in the applied layer a and base layer b. the presented stress distribution was determined on the radius r = r5 = 60 mm. the points ap and bp denote the maximum value of stress in the area of the hole in the layer of the applied plate a titanium and in the base layer of plate b steel, respectively. on the other hand, the points ap’ and bp’ represent the maximum values of stress in the boundary zone of the plate, respectively in the boundary zone of the applied a’ titanium plate and in the boundary zone of the base b’ steel plate. figure 5. the distribution of the equivalent von mises stresses 𝜎 in a bimetallic perforated plate on the radius r = r5 = 60 mm. the most hazardous place in the considered circular bimetallic perforated plate with various methods of support and loading, where the highest stress concentration occurs, is at the hole radius d5 = 9.5 mm and the circle radius r = r5 = 60 mm. tab. 3 summarizes the values and locations of stress concentration. e m. m. konieczny et alii, frattura ed integrità strutturale, 56 (2021) 137-150; doi: 10.3221/igf-esis.56.11 143 values and locations of stress concentrations points equivalent von mises stress 𝜎 [mpa] point with coordinates x [mm] y [mm] z [mm] load p = 10 kn – free supported ap 97.99 6.0 68.51 0.0 bp 168.83 6.0 68.51 12.5 load q = 0.4 mpa – free supported ap 114.39 -5.83 63.04 0.0 bp 188.29 -5.83 63.04 12.5 load q = 0.4 mpa – free supported ap 51.16 8.88 -54,.91 0.0 bp 91.82 8.88 -54.91 12.5 load p = 10 kn – fixed supported ap 30.98 5.32 62.50 0.0 bp 54.43 5.32 62.50 12.5 table 3: values and locations of stress concentrations in bimetallic perforated plate. single-layer perforated plate (fig. 4a – 4g) examples of the equivalent von mises stress distributions 𝜎 given in [mpa] along the thickness of a single-layer perforated plate are shown in fig. 6. the figure shows the stress distribution in the first case, simply supported on a annular support and loaded with a force p = 10 kn (fig. 6a), in the second case, simply supported on a annular support and loaded with external pressure q = 0.4 mpa (fig. 6b), in the third case fixed on the perimeter and loaded with a force p = 10 kn (fig. 6c), and in the fourth case fixed on the perimeter and loaded external pressure q = 0.4 mpa (fig. 6d) in the base layer b. the presented stress distribution was determined on the radius r = r5 = 60 mm. the bp point is the maximum value of stress in the hole zone in the base layer of the steel plate b. m. m. konieczny et alii, frattura ed integrità strutturale, 56 (2021) 137-150; doi: 10.3221/igf-esis.56.11 144 figure 6. the distribution of the equivalent von mises stresses 𝜎 in a single-layer perforated plate on the radius r = r5 = 60 mm. the most hazardous place in the considered circular single-layer perforated plate with different methods of support and load, where the highest stress concentration occurs, is at the hole radius d5 = 9.5 mm and the circle radius r = r5 = 60 mm. tab. 4 summarizes the values and locations of stress concentration. values and locations of stress concentrations points equivalent von mises stress 𝜎 [mpa] point with coordinates x [mm] y [mm] z [mm] load p = 10 kn – free supported bp 224.77 13.84 61.70 10.0 load q = 0.4 mpa – free supported bp 245.83 14.24 60.78 10.0 load q = 0.4 mpa – free supported bp 121.14 -8.51 -54.85 10.0 load p = 10 kn – fixed supported bp 70.77 -14.20 61.37 10.0 table 4: values and locations of stress concentrations in single-layer perforated plate. results of the research igs. 7-10 show the equivalent von mises stresses  nred along the radius r given in [mpa], determined by the finite element method, both in the bimetallic and single-layer perforated plate. in the first case, simply supported on a annular support and loaded with a force p = 10 kn (fig. 7), in the second case simply supported on a annular support and loaded with external pressure q = 0.4 mpa (fig. 8), in the third case restrained on perimeter and loaded with a force p = 10 kn (fig. 9) and in the fourth case, fixed on the perimeter and loaded with an external pressure q = 0.4 mpa (fig. 10). f m. m. konieczny et alii, frattura ed integrità strutturale, 56 (2021) 137-150; doi: 10.3221/igf-esis.56.11 145 figure 7: courses of equivalent von mises stress  nred in: a) a bimetallic perforated plate; b) a single-layer perforated plate, simply supported on a annular support and subjected to a load of p = 10 kn. figure 8: courses of equivalent von mises stress  nred in: a) a bimetallic perforated plate; b) a single-layer perforated plate, simply supported on a annular support and subjected to a load of q = 0.4 mpa. figure 9: courses of equivalent von mises stress  nred in: a) a bimetallic perforated plate; b) a single-layer perforated plate, fixed on the perimeter and subjected to a load of p = 10 kn. m. m. konieczny et alii, frattura ed integrità strutturale, 56 (2021) 137-150; doi: 10.3221/igf-esis.56.11 146 figure 10: courses of equivalent von mises stress  nred in: a) a bimetallic perforated plate; b) a single-layer perforated plate, fixed on the perimeter and subjected to a load of q = 0.4 mpa. whereas, figs. 11 14 show the percentage difference of changes in equivalent von mises stresses δ nred determined along the radius r given in [mpa], both in the bimetallic and single-layer perforated plate. in the first case, it is simply supported on a annular support and loaded with a force p = 10 kn (fig. 11), in the second case simply supported on a annular support and loaded with external pressure q = 0.4 mpa (fig. 12), in the third case it is fixed on perimeter and loaded with a force p = 10 kn (fig. 13) and in the fourth case, fixed along the perimeter and loaded with an external pressure q = 0.4 mpa (fig. 14). figure 11: percentage difference of changes in equivalent von mises stresses δ nred determined in the bimetallic plate  n red b and in the single-layer plate  nreds , simply supported on the annular support and with a load of p = 10 kn. the analysis of the courses of equivalent von mises stress in the perforated plates presented in figs. 7-10 shows that in all cases of loading and edge support, the equivalent von mises stress  b n red is lower in the base layer of the bimetallic steel plate compared to the equivalent von mises stress  s n red in the same layer of a single-layer steel plate. the presence of a perforated titanium layer in the plate significantly increases the load-bearing capacity of the plate. moreover, figs. 11-14 show the courses of the percentage difference in the changes of the equivalent von mises stresses δ nred determined in the m. m. konieczny et alii, frattura ed integrità strutturale, 56 (2021) 137-150; doi: 10.3221/igf-esis.56.11 147 bimetallic plate  b n red and the single-layer plate  s n red along its radius r the percentage difference in equivalent von mises stress for bimetallic and single-layer plates was determined from the relationship:      δ * 100%b s b n n red redn red n red where:  b n red – value of equivalent von mises stress in the base layer b steel bimetallic perforated plate;  s n red – the value of the equivalent von mises stress in a single-layer perforated plate with a thickness equal to the base layer b bimetallic steel plate. figure 12: percentage difference of changes in equivalent von mises stresses δ nred determined in the bimetallic plate  b n red and in the single-layer plate  s n red , simply supported on the annular support and with a load of q = 0.4 mpa. figure 13: percentage difference of changes in equivalent von mises stresses δ nred determined in the bimetallic plate  b n red and in the single-layer plate  s n red , fixed on the perimeter and with a load of p = 10 kn. m. m. konieczny et alii, frattura ed integrità strutturale, 56 (2021) 137-150; doi: 10.3221/igf-esis.56.11 148 figure 14: percentage difference of changes in equivalent von mises stresses δ nred determined in the bimetallic plate  b n red and in the single-layer plate  s n red , simply fixed on the perimeter and with a load of q = 0.4 mpa. the diagram in fig. 11 shows that the maximum difference in the value of the equivalent von mises stress is about 46% and occurs at the radius r = 130 mm in the case of a simply supported plate loaded with a concentrated force p = 10 kn. in the case of a simply supported plate and loaded with external pressure q = 0.4 mpa, the maximum difference occurs at the radius r = 120 mm (fig. 12) and amounts to approx. 47%. fixed the plate edges causes the maximum difference in the equivalent von mises stress in the case of p = 10 kn δ nred = 48% on the radius r = 90 mm (fig. 13). however, in the case of the load q = 0.4 mpa δ nred = 38% on the radius r = 80 mm (fig. 14). from the design engineer's point of view, the zone of the least influence of the state of stress of the applied layer a titanium on the effort of the bimetallic perforated plate is interesting. figs. 11-14 show that this is the central zone of the plate from the radius r = 6 mm to r = 50 mm and is approx. δ nred = 30%. this reserve of strength due to the presence of the a titanium applied layer increases the safe operation of the bimetallic perforated plate. it should be mentioned that the main purpose of introducing an applied (titanium) layer in a bimetallic perforated plate is to improve the properties of the plate, such as: corrosion resistance, thermal transmittance, while the task of the base layer is to transfer the load applied to the bimetallic perforated plate. it can be seen from the above that the superimposed layer a titanium additionally plays a positive role in the effort of the bimetallic perforated plate. conclusions ased on the tests of the state of stress of bimetallic and single-layer perforated plates and their analysis, the following conclusions can be drawn: 1) it has been shown that in a bimetallic perforated plate subjected to bending compared to a single-layer perforated plate, the equivalent von mises stress minimally; 2) as the applied layer titanium was introduced for the purposes of, among others, corrosion resistance, its contribution to the improvement of the strength of the bimetallic perforated plate should be considered a positive feature; 3) it should be noted that the share of the titanium layer in the bimetallic perforated plate contributes to the improvement of the operational safety of structures made of these plates, e.g. process equipment. appendix a he base layer of the b – steel plate is combined with the applied layer of the a – titanium plate by using the "connections" function, providing the option to bond two or more elements [14]. it was assumed that the combination of the titanium layer and the steel layer of the plates is excellent. modeling the connection of these two b t m. m. konieczny et alii, frattura ed integrità strutturale, 56 (2021) 137-150; doi: 10.3221/igf-esis.56.11 149 layers, contact was used in the form of inseparable bonding – as both layers were bonded permanently. this type of feature is a default configuration and applies to all contact regions (surfaces, solids, lines, faces, edges, etc.). if the contact areas are stuck together, no shifting or separation between the surfaces or edges is possible. this type of contact allows a linear solution since the contact length / area will not change when the load is applied. a plate made of titanium was used as the contact element, while a steel plate was used as the target element. details are shown in fig. a.1. figure a.1: application of the connections function between the base layer of the plate and the applied layer of the plate, where: a) contact object view, b) target object view. references [1] gomez, e., ruiz, r. and wilson, r. (2013). asme section iii stress analysis of a heat exchanger tubesheet with a misdrilled hole and irregular or thin ligaments. proceedings of the asme 2013 pressure vessels and piping conference paris, france, pp. 18. [2] saraçoğlu, m. and albayrak, u. (2015). linear static analysis of perforated plates with round and staggered holes under their self-weights. research of engineering structures and matirials, 2 (1), pp. 39 – 47 [3] kurek, a., niesłony, a. and szulc, z. (2013). design of process equipment made from explosively cladded materials, including the imposed material thickness in calculations. przegląd mechaniczny, 12, pp. 22-27. [4] konieczny, m., achtelik, h. and gasiak, g. (2020). rozkład naprężeń w platerowanej płycie perforowanej obciążanej centralnie siłą skupioną. studia i monografie z. 540, zmęczenie materiału w eksploatacji maszyn roboczych, oficyna wydawnicza politechniki opolskiej, 2, ss. 47-69 (in polish). [5] chaudhuri, r.a. (1987). stress concentration around a part through hole weakening laminated plate. computers and structures, 27 (2), pp. 601 – 609, doi: 10.1016/0045-7949(87)90075-7. [6] shaikh, e.n., panchal, k.c. and patel, d.b. (2015). stress analysis of an infinite plate with different shaped cutouts in composite plate. international journal of science, technology and management, 4(1), pp. 307-312. [7] kurek, a., niesłony, a. and kurek, m. (2014) stress concentration resulting from irregular shape of explosively cladded materials connections – fem simulation. acta mechanica at automatica, 8(2), pp. 103-106. doi 10.2478/ama-2014-0019. [8] walczak, w. (1989). metal explosion welding. wtn, warsaw (in polish). [9] čížek, l., ostroushko, d. and szulc, z. (2010). properties of sandwich metals joined by explosive cladding method. archives of materials science and engineering, 43, pp. 21–29. m. m. konieczny et alii, frattura ed integrità strutturale, 56 (2021) 137-150; doi: 10.3221/igf-esis.56.11 150 [10] konieczny, m., achtelik, h. and gasiak, g. (2021). location of stress concentration zones in a two-layer axially symmetrical perforated plate with force applied normally to its surface. engineering structures, 226, pp. 1-14. doi: 10.15199/28.2019.2.4. [11] konieczny, m., achtelik, h. and gasiak, g. (2021). research of stress distribution in the cross-section of a bimetallic perforated plate perpendicularly loaded with concentrated force. frattura ed integrità strutturale, 55, pp. 241-257. doi: 10.3221/igf-esis.55.18. [12] konieczny, m., achtelik, h. and gasiak, g. (2021). experimental analysis of the state of stress in a steel – titanium perforated plate loaded with concentrated force. frattura ed integrità strutturale, 55, pp. 277-288. doi: 10.3221/igf-esis.55.21. [13] data from explomet company research (z.t.w. explomet, gałka, szulc, sp. j. ul. oświęcimska 100h, 45-641 opole, poland). [14] user’s guide ansys 2020 r1, ansys, inc., usa. shot peening processes to obtain nanocrystalline surfaces in metal alloys: x.-g. huang et alii, frattura ed integrità strutturale, 48 (2019) 481-490; doi: 10.3221/igf-esis.48.46 481 durability method on corrosion fatigue performance of ah 32 steel xiao-guang huang, zhi-qiang wang college of pipeline and civil engineering, china university of petroleum (east china), qingdao, 266580, china. huangxg@upc.edu.cn abstract. a durability method in view of cathodic protection is proposed to improve the corrosion fatigue resistance of ah 32 steel in seawater. by aid of corrosion fatigue tests, the effects of thermal spraying zn (zinc) and cr (chromium) coating corrosion fatigue lives are quantitatively determined, respectively, and electrochemical measurement and fracture analysis are used to analyze the life-prolonging mechanism of these two coatings on corrosion fatigue. the results show that both zn and cr coating improve the corrosion fatigue resistance of ah 32 steel, and the effect enhances with the decrease of stress. the effect of cr coating on corrosion fatigue of ah 32 steel mainly reflects in extending the crack initiation life for its better corrosion resistance. while the effect of zn coating on corrosion fatigue lies in not only inhibiting the initiation of corrosion fatigue but also restraining crack propagation as cathodic protection materials. to sum up, cr coating has a better durability effect than zn coating at higher stress level, while zn exceeds cr at low stress level. keywords. durability method; corrosion fatigue; thermal spraying; crack nucleation; crack propagation. citation: huang, x. g., wang, z. q., durability method on corrosion fatigue performance of ah 32 steel, frattura ed integrità strutturale, 48 (2019) 481-490. received: 02.12.2018 accepted: 04.03.2019 published: 01.04.2019 copyright: © 2018 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. introduction ailure accidents of marine structures result in huge casualties, economic losses, and regional environmental pollution. therefore, safety and reliability is always a top priority for the design of these marine structures. according to the swedish damage situation report in 1972, about 70.4% of the damages of marine ships were induced by fatigue [1]. with the increasing capacity and the large–scale construction of the ships and offshore platform, the risk of fatigue damage is becoming more and more prominent. in marine corrosive environment, corrosion, fatigue and their concomitant injuries to the ships and ocean engineering structures cannot be underestimated, although the ships and ocean engineering structures are already equipped with a strict corrosion protection system to ensure the corrosion controlled within the theoretically acceptable range [2-4]. according to the real-time detection, the corrosion protection system is not effective enough in the service period [5]. what’s the worse, when the marine engineering structures are subjected to the combined action of fatigue load and corrosion environment, the service time will be shortened obviously. the interaction and coupling of the corrosion environment and fatigue load results in that the corrosion fatigue damage is much severe than the single action of corrosion or fatigue load [6-8]. according to the statistical data, corrosion fatigue f http://www.gruppofrattura.it/va/48/2322.mp4 x.-g. huang et alii, frattura ed integrità strutturale, 48 (2019) 481-490; doi: 10.3221/igf-esis.48.46 482 failure accounted for nearly 30% of the total number of accidents of ocean engineering structures [9]. in recent years, more and more attentions have been attached to the corrosion fatigue of ship and marine structure, and corrosion fatigue mechanism and durability design has been a hot research on the account. ah 32 steel is a hot rolled steel mainly used in the manufacture of hull and deck of the ships and offshore platforms, etc. due to the large demand of marine shipbuilding industry for ah 32 steel, the mechanical properties and corrosion resistance are the critical factors to ensure the integrity of the ships. li et. al. [10] studied the hot ductility and strength of ah 32 steel during the continuous casting process, and determined the cracking sensitivity of ah 32 steel under different temperatures and strain rates. jia et. al. [11] tested the mechanical properties of ah 32 opened plate improved by advanced production equipment and csp rolling process control. zhang et.al. [12] performed the fatigue tests of the tshaped welded specimen for ah 32 steel. dong et. al. [13] experimentally investigated the low cycle fatigue failure and accumulative plastic damage, as well as their interaction of ah 32 steel in uniaxial cyclic loading. also, they studied the fatigue crack growth behavior of ah-32 steel with the experimental application of ctod [14]. sun et. al. [15] revealed the characteristics of the plastic strain accumulation behavior of ah 32 steel under the combined effect of the cyclic stress and corrosion factors. minoru [16] clarified the pitting corrosion mechanism through onboard research of ah 32 steel by various corrosion tests, and developed a new corrosion resistant steel (crs) with trace amounts of alloying elements. however, the failure of ah 32 steel in marine environment is often caused by the interaction of load and corrosion, the researches of interaction mechanism and durability of corrosion fatigue of this material are relatively insufficient. numerical studies have testified the accelerating effect of corrosion process on fatigue failure [17-20]. therefore, the methods of inhibiting corrosion have been widely adopted to extend the corrosion fatigue life, such as, surface enhancement by laser [21-22], low plasticity burnishing [23], and cathodic protection [24-25]. in this paper, we propose a method of thermal coating technology to improve the corrosion fatigue durability of ah 32 steel. arc spraying zn and cr coating are performed respectively, to improve corrosion fatigue life of ah 32 steel in marine environment. the effects of coatings on corrosion fatigue of ah 32 are quantitatively analyzed in virtue of rotating bending corrosion fatigue tests, and the mechanisms of these two coatings’ improving corrosion life are discussed in details. experimental program samples and experimental preparation he selected ah 32 steel for rotary bending fatigue test were manufactured by anshan iron and steel. it contains (w.t. %) 0.09 c, 1.2 mn, 0.28 cu, 0.36 si, 0.37 ni, 0.006 p, 0.002 s, 0.09 cr, and fe rem. the tensile curve of ah 32 is shown in fig. 1. the yield strength and tensile strength of ah 32 are 358 mpa and 441mpa, respectively. the rod specimens are machined from ah 32 steel bar (φ24mm) by wire-cutting and fine grinding to achieve the accuracy requirements. figure 1: stress-strain relation of ah 32 steel. the fatigue and corrosion fatigue failure tests of ah 32 steel are carried out on cardan low-frequency rotating bending fatigue testing machine. according to the strength characteristics of the steel, eight different stress levels 179 mpa (0.5σs), 191mpa, 203mpa, 215mpa (0.6σs), 233mpa, 251mpa, 269mpa and 286 mpa (0.8σs), are selected for fatigue test. the 0 100 200 300 400 500 0 0.02 0.04 0.06 0.08 坐 标 轴 标 题 坐标轴标题 ah32  / m p a  t https://www.sciencedirect.com/topics/materials-science/strain x.-g. huang et alii, frattura ed integrità strutturale, 48 (2019) 481-490; doi: 10.3221/igf-esis.48.46 483 loading frequencies are set as 0.5, 1 and 2hz, respectively. to ensure the interaction of sample and corrosion solution during the fatigue test. a special designed circulating device of seawater is used to maintain the circulation and renewal of the seawater, as shown in fig. 2. the pump drives corrosive liquid circulate in the tube, and spray it on the test section of the samples through the shower. the surface of testing section of the sample is strapped with a layer of absorbent fiber to ensure the full immersion of the samples in the absorbed solution during the experiment. figure 2: setup of circulation device of corrosion solution. results of corrosion fatigue tests fig. 3 shows the number of cycles to fatigue and corrosion fatigue failure for bare ah 32 steel in seawater under different stress amplitudes. it can be seen corrosion environment impose an obvious influence on fatigue life, and this effect becomes more significant at low stress level. stress amplitude is the dominant factor determining fatigue and corrosion fatigue life, and fatigue lives increase with the decrease of stress amplitude. the stress frequency also has a significant effect on the corrosion fatigue life, and the corrosion fatigue lives decrease at lower frequencies under the same stress amplitude. it can be explained that the interaction between sample and corrosion environment is more effective in each cycle at low frequencies, which accelerates the evolution of corrosion fatigue damage per cycle [26-27]. in contrast, the effect of frequency on fatigue life is not as significant as corrosion fatigue. figure 3: results of fatigue and corrosion fatigue tests. fig. 4 shows the typical fracture surface of the sample under low stress amplitude. from the overall morphology of the fracture shown in fig. 4(a), there shows symmetry of the morphological development on both sides, and the crack initiation zone, extension zone and fracture zone are in turn from the two sides to the central axis. fig. 4 (b) shows the morphology of crack nucleation zone, and it can be seen clearly that the corrosion pit promotes the formation fatigue flow direction chuck recycling pump corrosive solution storage box tube seal ring shower fatigue sample absorbent fiber chamber 160 200 240 280 320 10000 100000 1000000 10000000 s /m p a n /cycle f=0.5hz(fatigue) f=1hz(fatigue) f=2hz(fatigue) f=0.5hz(corrosion fatigue) f=1hz(corrosion fatigue) f=2hz(corrosion fatigue) x.-g. huang et alii, frattura ed integrità strutturale, 48 (2019) 481-490; doi: 10.3221/igf-esis.48.46 484 crack. fig. 4 (c) is about the crack propagation zone and there exist a series of irregular fatigue crack striations. but the fracture surface is almost covered a layer of corrosion product for the corrosion process. figure 4: fracture morphology (a. overall appearance; b. crack nucleation zone; c. crack propagation zone). durability technology thermal spraying of zinc and cr coating hrough the above analysis, it is found that the corrosion environment has a significant effect on the fatigue life of the structure. therefore, anti-corrosion treatment always serves as an effective way to prolong the corrosion fatigue life. there are several ways to control corrosion commonly used in engineering, such as reasonable design of engineering structures, selection of anti-corrosion materials, change of corrosion environment, use of corrosionresistant coatings, electrochemical protection, and substitution of metal structures with non-metallic structures with better corrosion resistance. compared with the above methods, for ah 32 steel in marine environment, the feasible methods are electrochemical protection by surface coating of cathodic materials. here, to ensure adhesion between coating and substrate, arc spraying of zn and cr coatings are adopted respectively to evaluate their effects on corrosion fatigue. figure 5: cross-section microstructures of coated specimens (a. zn coating; b. cr coating). a crack nucleates from corrosion pits crack propagation striations b a b c t x.-g. huang et alii, frattura ed integrità strutturale, 48 (2019) 481-490; doi: 10.3221/igf-esis.48.46 485 according to the iso 2063 standard, zn and cr coating are deposited by cmd-as1620 arc spray system. before spraying, the rust of samples has been removed, and the surface have been blasted by 0.5mm corundum to achieve the roughness of 50-80 µm. the blasting pressure is 0.6 mpa and the blasting distance is 150 mm. after several trials on spray conditions, the filamentary zn and cr are heated to the melting state, and blown into a mist by compressed nitrogen gas to form a uniform particle flow and sprayed on the substrate surface. the stand-off distance (distance between the nozzle and the substrate) is kept constant at 150 mm. the stagnation pressure is 0.7mpa and the powder feed rate is 27.78 g/min. during the spraying process, the process parameters are finely adjusted to obtain a constant thickness of 500 ± 30 µm. the crosssections of ah 32 substrate and zn and cr coating interface are obtained by optical electron microscope, as shown in fig.5. it can be clearly observed that a lamellar structure with lamellas parallel to the substrate surface, with a good bonding with close to no porosity. the coating-substrate interface is quite irregular, possibly due to the impact of the high velocity particles that constitute the coating, on the ah 32 substrate. before deposition, it is evident that the substrate had undergone a severe plastic deformation during the coating process. however, such deformation enhances the mechanical bonding and adhesion of the coating to the substrate. both zn and cr coating show a good build-up and had a final roughly uniform thickness in the range of 470 to 530 μm. effect of coating on corrosion fatigue the corrosion fatigue tests of bare steel, and zn and cr coated specimens are carried out under the same test condition, and the s-n curves at 1hz frequency are shown in fig. 6. for comparison purposes, and to provide a better understanding of the effect of the corrosive environment on fatigue life of the ah 32, the s-n curve of fatigue testing is also shown in the same figure. it can be seen that both zn and cr coating can greatly improve the corrosion fatigue of ah 32 steel, and this effect enhances with the decrease of stress. this is attributed to the interaction of physical isolation, compressive residual stresses induced by arc spray and electrochemistry function of the coating materials [28-30]. an interesting phenomenon is that the effects of zn and cr coating on fatigue life extension are dramatically dependent on the stress level. the comparison of corrosion fatigue lives of zn and cr coated samples show that cr coating has better performance than zn coating at higher stress level, but the opposite is true at low stress amplitude. this can be explained from the contribution of these two coatings to crack nucleation and crack propagation at different stress levels. however, their contributions of each part to corrosion fatigue life is difficult to be quantitatively determined, and we will discuss in detail from the mechanism analysis. figure 6: s-n curves of corrosion fatigue tests the pre-corrosion fatigue tests of zn and cr coated specimens are also carried out to investigate their corrosion resistance. the bare samples, zn and cr coated specimens are respectively emerged in the seawater for period of 15 d and 30 d, and the typical corroded samples with a period of 15 d are shown in fig. 7. it can be seen the surface corrosion of test section of bare ah 32 samples is the most serious, followed by zn coated and cr coated samples. the fatigue behaviors of the pre corroded samples are tested under the same load as the corrosion fatigue, with results shown in fig. 8. the fatigue lives of pre corroded cr coating samples are apparently larger than that of zn coated samples, and the difference between 160 200 240 280 320 10000 100000 1000000 10000000 s /m p a n /cycle f=1hz(corrosion fatigue) f=1hz(corrosion fatigue-cr coating) f=1hz(corrosion fatigue-zn coating) f=1hz(fatigue) x.-g. huang et alii, frattura ed integrità strutturale, 48 (2019) 481-490; doi: 10.3221/igf-esis.48.46 486 which become obvious with the prolongation of period of pre corrosion and the decrease of stress amplitude. it follows that corrosion resistance of cr coating is stronger than that of zn coating. with the prolongation of pre-corrosion time, the surface corrosion of zinc coating is more serious than cr coating, and corrosion defects are more likely to induce fatigue crack nucleation under fatigue load, thus accelerating the fatigue failure of zinc coating samples. figure 7: morphology of the corroded samples. figure 8: s-n curves of corrosion fatigue. mechanism of zn and cr coating on corrosion fatigue to make insight into the mechanism of zn and cr coating improving corrosion fatigue resistance of ah 32 steel. the electrochemical measurements of the two coating materials and ah 32 substrate in the seawater are performed by a perkin-elmer m283 three-electrode-cell constant potential electrochemical testing system. cyclic potentiodynamic tafel polarization are measured starting from -250mv (vs open circuit potential), and scanned toward more positive direction with scanning rate of 0.5mv/s. figure 9: tafel polarization curves of coatings and substrate the instantaneous tafel polarization curves of ah 32, zn and cr in seawater are depicted in fig. 9, and the electrochemical parameters from polarization analysis are listed in table 1. the corrosion current densities at different immersion periods are also listed in table 2 for comparison. compared with ah 32 substrate, zn has a more negative corrosion potential than cr, while cr has a better corrosion resistance. therefore, zn is more suitable for cathodic protection, and often mixed with aluminum or magnesium to form an alloy coating for cathodic protection of engineering materials [32-34]. while cr is often added to the substrate material as alloy element, to improve the corrosion resistance of the substrate [35-36]. bare ah32 zn coating cr coating 160 200 240 280 320 10000 100000 1000000 10000000 s /m p a n /cycle 15 d zn coating 15 d cr coating 30 d-zn coating 30 d-cr coating 15 d-bare 30 d-bare -1.2 -1 -0.8 -0.6 -0.4 -0.2 0 -7 -6 -5 -4 -3 -2 -1 0 坐 标 轴 标 题 lgi (a.cm2) ah32 cr coating zn coating 2 lg( ) /a.cmi s e c / v e x.-g. huang et alii, frattura ed integrità strutturale, 48 (2019) 481-490; doi: 10.3221/igf-esis.48.46 487 material ecorr (v) icorr (macm2) ba(v.dec-1) bc(v.dec-1) rp (ω.cm2) ah 32 -0.510 0.0489 0.405 0.157 1005.962 zn -1.103 0.0110 0.572 0.203 592.203 cr -0.411 0.0078 0.128 0.281 4901.968 *polarization resistance (rp): rp= ba* bc/[2.3×icorr×(ba+bc)] [31] table 1: the instantaneous electrochemical parameters from polarization curve. test period material 0h 15 d 30 d ecorr (v) icorr (macm2) ecorr (v) icorr (macm2) ecorr (v) icorr (macm2) ah 32 -0.510 0.0489 -0.557 0.0187 -0.564 0.0125 zn -1.103 0.0110 -1.176 0.0073 -1.192 0.0065 cr -0.411 0.0078 -0.427 0.0062 -0.430 0.0059 table 2: comparison of corrosion current density of ah32 and coating materials in different immersion periods. figure 10: morphology of crack propagation zone (a. zn coating, b. cr coating). through the above research, it is not difficult to find that the mechanisms of zn and cr coating to improve ah 32 corrosion fatigue resistance are different. the effect of zn coating on corrosion fatigue prolongation embodies in not only crack nucleation but also crack propagation. before crack nucleation, the zn and cr coating only acts as physical isolation. because of the interaction of electrochemical process and fatigue, zn coated specimens are more likely to form crack on the surface. in comparison, the surface corrosion of cr coating samples develops more slowly for the better corrosion resistance, as obtained from pre-corroded tests. therefore, cr coated samples have longer crack nucleation lives than that of zn coated ones, under the same corrosive load. once cracks nucleate and propagate, zn transform its role from physical isolation to sacrificial anode material, to a certain extent, to restrain the corrosion reaction of crack surface and crack tip and to avoid the acceleration effect of corrosion products on crack propagation. however, the electrochemical activity of chromium is not as good as ah 32, but worse than zn. cr coating cannot play the role as sacrificial anode to protect crack propagation of the substrate. fig. 10 shows the crack propagation zone of zn and cr coated samples, respectively. in the fracture surface of zn coated sample, the crack striations in crack propagation is very clear, and the corrosion status is not serious. while the corrosion at the fracture of cr coated sample is serious covered with a layer of corrosion fatigue. what’s more, there also exists several deep secondary cracks. it has been testified that the corrosion products and secondary cracks have close relation with the crack propagation behavior [37-38]. therefore, the phenomena in fig. 6 can be explained as the superposition of the contribution of zn and cr coating to crack nucleation and crack propagation. at low stress level, corrosion fatigue crack propagation life is relatively longer, so the effect of zn coating on a fatigue striations b corrosion product secondary cracks x.-g. huang et alii, frattura ed integrità strutturale, 48 (2019) 481-490; doi: 10.3221/igf-esis.48.46 488 crack propagation is remarkable and the overall improvement effect of zn exceeds that of cr coating. conversely, at high stress level, cr coating has better effect because of its contribution to crack nucleation. conclusion n the present study, durability method to improve corrosion fatigue resistance of ah 32 steel in seawater are conducted by arc spraying zn and cr coatings. pre-corrosion fatigue and corrosion fatigue tests are carried out to quantitatively determine the effect of coatings on corrosion fatigue behavior of ah 32 steel in seawater, and the mechanism of coating improving corrosion fatigue characteristics are investigated. the main results obtained can be concluded as follows: (1) corrosion fatigue failure always initiates from corrosion defects at the surface of the specimen, because the stress concentration occurs at these corrosion defects, under cyclic loading, accelerates the nucleation of fatigue crack. the effect of corrosion in fatigue life of ah32 steel become more obvious at low stress level. the effect of loading frequency which determine the corrosion time at every cycle on corrosion fatigue life also cannot be ignored. (2) the results of corrosion fatigue and pre corrosion fatigue tests of zn and cr coated ah32 steel show that both zn and cr coating can greatly improve the corrosion fatigue of ah 32 steel, and the effect enhances with the decrease of stress. cr coating on corrosion fatigue of ah 32 steel mainly reflects in extending the crack initiation life because of its better corrosion resistance. while the effect of zn coating on corrosion fatigue of ah 32 steel mainly lies in not only inhibiting the initiation of corrosion fatigue but also restraining crack propagation as cathodic protection materials. to sun up, cr coating has better durability effect than zn coating at higher stress level, while zn exceeds cr at low stress level. acknowledgments he research work is supported by the national natural science foundation of china (no.51404286), and the fundamental research funds for the central universities of china (no.17cx02065). the authors are also grateful for the financial support from china scholarship council (no. 201806455016). references [1] kjellander, s. l. (1972). hull damage on large swedish-built ships. styrelsen for teknisk utveckling. report no. 701272/u981, stockholem, sweden. [2] jordan c. r., and cochran c. s. (1978). further survey of in-service performance for structural details. ssc-272. [3] folorunso o. m., salau m. a., and esezobor d. e. (2013). offshore steel structures corrosion damage model. international journal of scientific & engineering research, 2(10), pp.1-6. [4] melchers r. e. (2006). recent progress in the modeling of corrosion of structural steel immersed in seawater. journal of infrastructure systems, 12(3), pp.154-162. doi: 10.1061/(asce)1076-0342(2006)12:3(154). [5] melchers r. e. (1999). corrosion uncertainty modeling for steel structures. journal of constructional steel research, 52, pp. 3-19. doi: 10.1016/s0143-974x(99)00010-3. [6] alamilla j. l., espinosa-medina m. a., and sosa e. (2009). modelling steel corrosion damage in soil environment. corrosion science, 51, pp. doi: 2628-2638. 10.1016/j.corsci.2009.06.052. [7] maeng w. y., kang y. h., nam t. w., ohashi s., and ishihara t. (1999). synergistic interaction of fatigue and stress corrosion crack growth behavior in alloy 600 in high temperature and high pressure water. journal of nuclear materials, 275, pp. 194-200. doi: 10.1016/s0022-3115(99)00114-2. [8] pérez-mora r., palin-luc t., bathias c., and paris p. c. (2015). very high cycle fatigue of a high strength steel under sea water corrosion: a strong corrosion and mechanical damage coupling. international journal of fatigue, 74, pp.156-165. doi: 10.1016/j.ijfatigue.2015.01.004. i t http://xueshu.baidu.com/s?wd=author%3a%28omotoso%20matthew%20folorunso%29%20&tn=se_baiduxueshu_c1gjeupa&ie=utf-8&sc_f_para=sc_hilight%3dperson http://xueshu.baidu.com/s?wd=author%3a%28salau%20m.%20a%29%20&tn=se_baiduxueshu_c1gjeupa&ie=utf-8&sc_f_para=sc_hilight%3dperson http://xueshu.baidu.com/s?wd=author%3a%28esezobor%20d.%20e%29%20&tn=se_baiduxueshu_c1gjeupa&ie=utf-8&sc_f_para=sc_hilight%3dperson http://xueshu.baidu.com/s?wd=paperuri%3a%28774c093eab0771d1c92090554c8a6a1d%29&filter=sc_long_sign&sc_ks_para=q%3doffshore%20steel%20structures%20corrosion%20damage%20model&sc_us=1491027810281844296&tn=se_baiduxueshu_c1gjeupa&ie=utf-8 http://xueshu.baidu.com/s?wd=author%3a%28robert%20e.%20melchers%29%20&tn=se_baiduxueshu_c1gjeupa&ie=utf-8&sc_f_para=sc_hilight%3dperson https://doi.org/10.1061/(asce)1076-0342(2006)12:3(154) x.-g. huang et alii, frattura ed integrità strutturale, 48 (2019) 481-490; doi: 10.3221/igf-esis.48.46 489 [9] emi h., yuasa m., kumano a., arima t., yamamoto n., and umino m. (1992). a study on life assessment of ships and offshore structures: 2nd report: risk assessment of fatigue failures of hull structures. journal of society of naval architects of japan, 172, pp.627-35. [10] li g. y., li x. f., and ao l. g. (2006). investigation on hot ductility and strength of continuous casting slab for ah 32 steel. acta metallurgica sinica, 19(1), pp.75-78. doi: 10.1016/s1006-7191(06)60026-4. [11] jia j. l., dong z. q., yuan j. l., and han t. w. (2013). study on mechanical properties of ah 32 opened plate. advanced materials research, 631-632, pp. 354-357. doi: 10.4028/www.scientific.net/amr.631-632.354. [12] zhang z. f., li l. b., and li y. z. (2013). research of test and simulation on fatigue strength of t welded joint for ah 32 steel. ship science and technology, 35(6), pp.57-60. [13] dong q., yang p., xu g., and jiang w. (2018). experimental study on interaction of low cycle fatigue and accumulative plastic damage of ah 32 steel in uniaxial cyclic loading. journal of ship mechanics, 22(6), pp. 771-782. [14] dong q., yang p., and xu g. (2019). low cycle fatigue analysis of ctod under variable amplitude loading for ah32 steel. marine structures, 63, pp.257-268 doi: 10.1016/j.marstruc.2018.10.002. [15] sun y., li h. m., wang c. x., and shao g. j. (2018). plastic strain accumulation behaviour of ah 32 steel in a cyclic stress-corrosion environment. journal of constructional steel research, 2018, 145: 1-9. doi: 10.1016/j.jcsr.2018.02.011. [16] ito m., kaneko m., nishimura s., and sato h. (2012). development of corrosion resistant steel for bottom plates of crude oil tankers and onboard evaluation results. asme international conference on ocean, 77, pp. 549-551. doi: 10.1115/omae2012-83821. [17] arzaghi e., abbassi r., garaniya v., binns j., chin c., khakzad n., and reniers g. (2018). developing a dynamic model for pitting and corrosion-fatigue damage of subsea pipelines. ocean engineering, 150(15), pp.391-396. doi: 10.1016/j.oceaneng.2017.12.014. [18] han z. y., huang x. g., and cao y. g.(2014). a nonlinear cumulative evolution model for corrosion fatigue damage. journal of zhejiang university-science a, 15(6), pp. 447-453. doi: 10.1631/jzus.a1300362. [19] hazra m., and singh s. (2018). corrosion-induced fatigue failure of a first-stage flow straightener vane of an aeroengine. journal of failure analysis and prevention, 2018, 18(4): 819-827. doi: 10.1007/s11668-018-0467-8. [20] he x. l., wei y. h., hou l. f., yan z. f., guo c. l., and han p. j. (2014). investigation on corrosion fatigue property of epoxy coated az31magnesium alloy in sodium sulfate solution. theoretical and applied fracture mechanics, 70, pp. 39-48. doi: 10.1016/j.tafmec.2014.03.002. [21] mhaede m. (2012). influence of surface treatments on surface layer properties, fatigue and corrosion fatigue performance of aa7075 t73. materials and design, 41, pp. 61-66. doi: 10.1016/j.matdes.2012.04.056. [22] chan c., yue t., and man h. (2003). the effect of excimer laser surface treatment on the pitting corrosion fatigue behavior of aluminium alloy 7075. journal of materials science, 38 (12), pp. 2689-2702. doi: 10.1023/a:1024498922104. [23] prevey p., and cammett j. (2001). the influence of surface enhancement by low plasticity burnishing on the corrosion fatigue performance of aa7075-t6. international journal of fatigue, 26 (9), pp.975-982. doi: 10.1016/j.ijfatigue.2004.01.010. [24] ahnia f., and demri b. (2013). evaluation of aluminum coatings in simulated marine environment. surfaces & coating technology, 220(15), pp. 232-236. doi: 10.1016/j.surfcoat.2012.12.011. [25] ahn s. h., park k. j., oh k. n., hwang s. d., park b. j., kwon h. s., and shon m. y. (2015). effects of sn and sb on the corrosion resistance of ah 32 steel in a cargo oil tank environment. metals and materials international, 21(5), pp. 865-873. doi:10.1007/s12540-015-5164-5. [26] wang r. (2008). a fracture model of corrosion fatigue crack propagation of aluminum alloys based on the material elements fracture ahead of a crack tip. international journal of fatigue, 30, pp.1376-1386. doi: 10.1016/j.ijfatigue.2007.10.007. [27] huang x. g., xu j. q., and feng m. l. (2013). energy principle of corrosion environment accelerating crack propagation during anodic dissolution corrosion fatigue. journal of shanghai jiao tong university (sci.), 18(2), pp. 190-196. doi: 10.1007/s12204-013-1382-5. [28] kim s. j., lee s. j., park y. s., jeong j. y., and jang s. k. (2014). influence of sealing on damage development in thermally sprayed al–zn–zr coating. science of advanced material, 6 (9), pp. 2066-2070. doi: 10.1166/sam.2014.2118. https://doi.org/10.1016/s1006-7191(06)60026-4 https://doi.org/10.4028/www.scientific.net/amr.631-632.354 https://doi.org/10.1016/j.marstruc.2018.10.002 https://www.sciencedirect.com/science/journal/0143974x http://xueshu.baidu.com/s?wd=author%3a%28minoru%20ito%29%20&tn=se_baiduxueshu_c1gjeupa&ie=utf-8&sc_f_para=sc_hilight%3dperson http://www.researchgate.net/publication/267648712_development_of_corrosion_resistant_steel_for_bottom_plates_of_crude_oil_tankers_and_onboard_evaluation_results http://www.researchgate.net/publication/267648712_development_of_corrosion_resistant_steel_for_bottom_plates_of_crude_oil_tankers_and_onboard_evaluation_results http://xueshu.baidu.com/usercenter/data/journal?cmd=jump&wd=confuri%3a%28acb0fc3280201d96%29%20asme%20international%20conference%20on%20ocean&tn=se_baiduxueshu_c1gjeupa&ie=utf-8&sc_f_para=sc_hilight%3dpublish&sort=sc_cited https://www.sciencedirect.com/science/article/pii/s0029801817307369#! https://www.sciencedirect.com/science/article/pii/s0029801817307369#! https://www.sciencedirect.com/science/article/pii/s0029801817307369#! https://www.sciencedirect.com/science/journal/00298018 http://xueshu.baidu.com/s?wd=author%3a%28mrityunjoy%20hazra%29%20defence%20metallurgical%20research%20laboratory%20%28dmrl&tn=se_baiduxueshu_c1gjeupa&ie=utf-8&sc_f_para=sc_hilight%3dperson http://xueshu.baidu.com/s?wd=author%3a%28satyapal%20singh%29%20defence%20metallurgical%20research%20laboratory%20%28dmrl&tn=se_baiduxueshu_c1gjeupa&ie=utf-8&sc_f_para=sc_hilight%3dperson https://link.springer.com/journal/11668 x.-g. huang et alii, frattura ed integrità strutturale, 48 (2019) 481-490; doi: 10.3221/igf-esis.48.46 490 [29] mcgrann r., greving d., shadley j., rybicki e., kruecke t., and bodger b. (1998). the effect of coating residual stress on the fatigue life of thermal spray coated steel and aluminum. surface and coatings technology, 108-109, pp.59-64. doi: 10.1016/s0257-8972(98)00665-3. [30] zhao t. l., liu z. y., du c. w., sun m. h., and li x. g. (2018). effects of cathodic polarization on corrosion fatigue life of e690 steel in simulated seawater. international journal of fatigue, 110, pp. 105-114. doi: 10.1016/j.ijfatigue.2018.01.008. [31] tang j. w., shao y. w., zhang t., meng g. z., wang f. h. (2011). corrosion behaviour of carbon steel in different concentrations of hcl solutions containing h2s at 90 oc [j]. corrosion science, 53 (5), pp.1715-1723. doi: 10.1016/j.corsci.2011.01.041 [32] chavan n. m., jyothirmayi a., phani p. s., and sundararajan g. (2013). the corrosion behavior of cold sprayed zinc coatings on mild steel substrate. journal of thermal spray technology, 22 (4), pp.463-470. doi: 10.1007/s11666-013-9893-z. [33] hamlaoui y., tifouti l., and pedraza f. (2010). on the corrosion resistance of porous electroplated zinc coatings in different corrosive media. corrosion science, 52, pp.1883-1888. doi: 10.1016/j.corsci.2010.02.024. [34] bonabi s. f., ashrafizadeh f., sanati a., and nahvi s. m. (2018). structure and corrosion behavior of arc-sprayed zn-al coatings on ductile iron substrate. journal of thermal spray technology, 27(3), pp. 524–537. doi: 10.1007/s11666-018-0694-2. [35] xiao d. h., zhou p. f., wu w. q., diao h. y., gao m. c., song m., and liaw p. k. (2017). microstructure, mechanical and corrosion behaviors of alcocufeni-(cr,ti) high entropy alloys. materials & design, 116(15), pp. 438-447. doi: 10.1016/j.matdes.2016.12.036. [36] kandavel t. k.，sacs k. p., and krishna m. v. (2018). experimental investigation on corrosion behaviour of fe-ccr p/m alloy steels. materials and corrosion, 69, pp.1355-1367. doi: 10.1002/maco.201810155. [37] khan z. (1996). effect of corrosive environment on the fatigue crack initiation and propagation behavior of al 5454-h32. journal of materials engineering and performance, 5(1), pp.78–83. doi: 10.1007/bf02647273. [38] stannard t. j., williams j. j., singh s. s., singaravelu a. s. s., xiao x. h., and chawla n. (2018). 3d time-resolved observations of corrosion and corrosion-fatigue crack initiation and growth in peak-aged al 7075 using synchrotron x-ray tomography. corrosion science, 138(1), pp. 340-352. doi: 10.1016/j.corsci.2018.04.029. https://doi.org/10.1016/j.corsci.2011.01.041 http://xueshu.baidu.com/s?wd=author%3a%28naveen%20manhar%20chavan%29%20&tn=se_baiduxueshu_c1gjeupa&ie=utf-8&sc_f_para=sc_hilight%3dperson http://xueshu.baidu.com/s?wd=author%3a%28a%20jyothirmayi%29%20&tn=se_baiduxueshu_c1gjeupa&ie=utf-8&sc_f_para=sc_hilight%3dperson http://xueshu.baidu.com/s?wd=author%3a%28p%20sudharshan%20phani%29%20&tn=se_baiduxueshu_c1gjeupa&ie=utf-8&sc_f_para=sc_hilight%3dperson http://xueshu.baidu.com/s?wd=author%3a%28g%20sundararajan%29%20&tn=se_baiduxueshu_c1gjeupa&ie=utf-8&sc_f_para=sc_hilight%3dperson http://xueshu.baidu.com/usercenter/data/journal?cmd=jump&wd=journaluri%3a%281c19f0cf1c259cd4%29%20%e3%80%8ajournal%20of%20thermal%20spray%20technology%e3%80%8b&tn=se_baiduxueshu_c1gjeupa&ie=utf-8&sc_f_para=sc_hilight%3dpublish&sort=sc_cited https://link.springer.com/journal/11666 https://www.sciencedirect.com/science/article/pii/s0264127516315532#! https://www.sciencedirect.com/science/article/pii/s0264127516315532#! https://www.sciencedirect.com/science/article/pii/s0264127516315532#! https://www.sciencedirect.com/science/article/pii/s0264127516315532#! https://www.sciencedirect.com/science/article/pii/s0264127516315532#! https://www.sciencedirect.com/science/article/pii/s0264127516315532#! https://www.sciencedirect.com/science/article/pii/s0264127516315532#! https://www.sciencedirect.com/science/journal/02641275 http://xueshu.baidu.com/s?wd=author%3a%28t.%20k.%20kandavel%29%20school%20of%20mechanical%20engineeringshanmugha%20arts%2c%20science%2c%20technology%20and%20research%20academythanjavur%20613401tamil%20naduindia&tn=se_baiduxueshu_c1gjeupa&ie=utf-8&sc_f_para=sc_hilight%3dperson http://xueshu.baidu.com/s?wd=author%3a%28k.%20praveen%20sacs%29%20school%20of%20mechanical%20engineeringshanmugha%20arts%2c%20science%2c%20technology%20and%20research%20academythanjavur%20613401tamil%20naduindia&tn=se_baiduxueshu_c1gjeupa&ie=utf-8&sc_f_para=sc_hilight%3dperson http://xueshu.baidu.com/s?wd=author%3a%28m.%20venkat%20krishna%29%20school%20of%20mechanical%20engineeringshanmugha%20arts%2c%20science%2c%20technology%20and%20research%20academythanjavur%20613401tamil%20naduindia&tn=se_baiduxueshu_c1gjeupa&ie=utf-8&sc_f_para=sc_hilight%3dperson http://onlinelibrary.wiley.com/doi/10.1002/maco.201810155/abstract http://onlinelibrary.wiley.com/doi/10.1002/maco.201810155/abstract https://link.springer.com/journal/11665 https://www.sciencedirect.com/science/article/pii/s0010938x17319790#! https://www.sciencedirect.com/science/article/pii/s0010938x17319790#! https://www.sciencedirect.com/science/article/pii/s0010938x17319790#! https://www.sciencedirect.com/science/article/pii/s0010938x17319790#! https://www.sciencedirect.com/science/article/pii/s0010938x17319790#! https://www.sciencedirect.com/science/article/pii/s0010938x17319790#! https://www.sciencedirect.com/science/journal/0010938x https://doi.org/10.1016/j.corsci.2018.04.029 microsoft word numero_58_art_10_3097 w. frenelus et alii, frattura ed integrità strutturale, 58 (2021) 128-150; doi: 10.3221/igf-esis.58.10 128 long-term degradation, damage and fracture in deep rock tunnels: a review on the effect of excavation methods wadslin frenelus, hui peng, jingyu zhang department of hydraulic engineering, college of hydraulic and environmental engineering, china three gorges university, yichang 443002, china wadslin@ctgu.edu.cn, https://orcid.org/0000-0002-9084-2548 406955991@qq.com, 304428211@qq.com abstract. rocks are frequently host materials for underground structures, particularly for deep tunnels. their behavior plays a fundamental role in the overall stability of these structures. in fact, the erection of deep tunnels imposes rocks excavations around the defined routes. these excavations are generally carried out by various methods of which the most used are drilland-blast (db) and tunnel boring machine (tbm). however, regardless of the tunnelling method used, the impacts such as the perturbation of the initial stress field in rocks and the release of the stored energy are always significant. the impacts produce damage, fractures and deformations which are generally time-dependent and influence the long-term stability of deep tunnels built in rocks. thus, by considering the aforementioned excavation methods, this paper identifies, reviews and describes the relevant factors generated during and after rock excavations. interestingly, such factors directly or indirectly influence the long-term stability and therefore the structural integrity of deep rock tunnels. in addition, some recommendations and proposals for future works are presented. this paper can provide useful references in understanding the degradations, damage and fractures generated by tunnelling methods and facilitate suitable actions to ensure long-term stability of deep underground structures. keywords. excavation methods; excavation impacts; rocks behavior; deep tunnels; structural integrity; long-term stability. citation: frenelus, w., peng, h., zhang, j., long-term degradation, damage and fracture in deep rock tunnels: a review on the effects of excavation methods, frattura ed integrità strutturale, 58 (2021) 128-150. received: 13.05.2021 accepted: 03.08.2021 published: 01.10.2021 copyright: © 2021 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. introduction espite many challenges generally encountered in underground excavations, engineering projects for the construction of deep tunnels continue to grow. indeed, the underground space needs are necessary from day to day particularly in developed countries. it is thereby widely known that deep tunnels can be built for various purposes such as water conveyance, reservoirs emptying, hydropower stations, sanitary drainage, etc. as a result, the longterm stability of these tunnels must be guaranteed, so that they can perform their roles correctly throughout their period of operation. however, this long-term stability is influenced by many potential factors, including the methods used to excavate these tunnels. d https://youtu.be/fqtvo3dd7gy w. frenelus et alii, frattura ed integrità strutturale, 58 (2021) 128-150; doi: 10.3221/igf-esis.58.10 129 it is quite obvious that, when excavating deep rocks tunnels, the virgin rock mass properties are modified [1, 2], and there are disturbances or alteration of the existing stresses in the rock massifs [3, 4]. there is then an imbalance in the stresses state of rocks which mainly surround the generated openings. for that, a new state of stress equilibrium is inevitable to prevent any early collapse of the excavations. it greatly depends on geological and geotechnical characteristics of the rocks and also on the excavation methods used. according to kaiser et al. [5], stress changes strongly influence the stability of underground projects. their impacts could be even more considerable when tunnels are constructed at great depth and when the lithology is variable. for instance, long deep tunnels generally cross heterogeneous rocky environments. so, one of the main challenges to be faced is the lack of information on geological structures of the areas to be excavated [6]. this would therefore entail a risk during tunnelling. the risks globally provoked by the tunnelling methods are numerous, both on the quality of rocks and on their properties. rocks instability caused by excavations affect the overall safety and even sometimes the feasibility or the continuation of deep underground projects. barton [7] has showed that the hybrid solution of tbm and db methods can reduce risk in long deep tunnels. on their side, based on microseismic monitoring technology, tang et al. [8] revealed that the speed balancing of tbm can attenuate the risk of surrounding rocks instability during excavations. but anyway, tunnelling by tbm and db led to the creation of impacted zones in which there are generally permanent modifications of rocks properties in the vicinity of deep tunnels. the aim of this paper is to describe the stages reflecting the influences of excavation methods on the long-term stability of deep tunnels built in rocky mediums. in fact, many studies have been carried out on the stability of underground structures, but attention has not been drawn sufficiently to the influence of tunnelling methods on long-term stability of deep tunnels. to address this issue, this review is presented in order to highlight the relevant factors generated during and after tunnels excavations. each of these factors influence directly or indirectly the lifetime of tunnels. their adequate consideration could constitute a source of ideas that could lead to the development of solutions to minimize their impacts on long-term stability of tunnels. it should be noted that the excavation operations of deep long tunnels can take years. in addition, due to stress factors, the strength of natural rocks is time-dependent [9]. the longer the excavations last, the greater the risk of deterioration of rocks properties due to the time effect. accordingly, the more the tunnels created are unstable. thus, study the influence of excavation methods on long-term stability of deep rocks tunnels is of tremendous importance. general rocks excavations methods overview he main methods for rocks excavations are drill-and-blast (db), and tunnel boring machine (tbm) [10, 11]. the process of rocks removal is very different in the two mentioned tunnelling methods. in db method, there are holes creation using long drill, and blasting the holes previously filled with explosives; while in tbm, the work is done thanks to the digging force of the machine equipped with rolling cutters operating at high pressure [12]. tabs. 1 and 2 summarize the relevant advantages and disadvantages of the main tunnelling methods. excavation method general relevant advantages general relevant disadvantages authors (year) db good progression rate for tunnels of small diameters. low advancing rate for tunnels of big diameter. suorineni et al. (2008) [13] generate crack fracture morphology. high degree of damage in surrounding rocks. larger relaxation depth. impose usually considerable strengthening measures. ji et al. (2012) [11] comprehensive flexibility and strong adaptability for many geological conditions. complex tunnelling procedures. considerable disturbances to surrounding rocks. rough excavation perimeter. slow progression rate. huang et al. (2018) [14] possible use for all types of rocks blast damage are unavoidable and persist zareifard (2020) [15] table 1: relevant advantages and disadvantages of db excavations t w. frenelus et alii, frattura ed integrità strutturale, 58 (2021) 128-150; doi: 10.3221/igf-esis.58.10 130 excavation method general relevant advantages general relevant disadvantages authors (year) fastest advancing rates in good ground conditions. tunnel route quite straight. complex operation for complex tunnelling geometry. not too applicable for short tunnels. low steering capacity suorineni et al. (2008) [13] inflexibility yan et al. (2012) [10]; mazaira and konicek (2015) [16] tbm favourable to the surrounding rocks stability control. construction efficiency. favourable for environmental protection. high progression rate, depending on in-situ stress intensity. low adaptability to geological conditions. possibility of trapping due to possible accidents and geohazards. huang et al. (2018) [14] smaller relaxation depth generate shear fracture morphology. existence of a certain degree of damage for surrounding rocks. ji et al. (2012) [11] progression rate considerable applicable for slope  10.5% ( 6 ) ma et al. (2020) [17] table 2: relevant advantages and disadvantages of tmb excavations rock mass excavation, as pointed out by bao et al. [18], affects strongly the safety and the stability of tunnels. referring to liu et al. [19], it is assumed that tunnels shall be severely damaged when deformations induced by the excavations exceed established tolerable limits. hence, for ensuring the long-term stability of deep tunnels, proper measurements of deformations caused by excavations are extremely important. degradation of properties of surrounding rocks unnel excavation is regarded as an unloading process that can cause degradation of the main properties of surrounding rocks. more broadly, qiu et al. [20] and niu et al. [21] have reported that the surrounding rocks endure a complex unloading-loading process during deep tunnelling. this process affects the main properties of rocks, and generates instability around tunnels. cai and kaiser [22] related that there is alteration of mechanical, hydraulic and geochemical properties of surrounding rocks when excavating underground openings. in their research, based on unloading effect, luo et al. [23] studied the deterioration of the mechanical properties of surrounding rocks for deep tunnels and have found that the main mechanical properties (cohesion, internal friction angle, elastic modulus, and poisson’s ratio) exhibit nonlinear degradation features. rocks strength around tunnels is reduced due to the degradation of their properties. the degradation of rocks properties is an unfavourable indicator for the long-term stability of tunnels. any excavation method (db, tbm) generates degradations in the rocks surrounding the openings. although the degree of rocks degradation varies depending on the excavation method used, in all cases the rock properties remain altered in the vicinity of the tunnels. the extent of degradations generated by tunnelling on relevant rocks properties needs to be deeply investigated. this would help to elucidate in depth the influence of excavation methods on long-term stability of deep tunnels constructed in rocky environments. excavation loose zone and excavation disturbed zone he zones that directly influence the service life of deep tunnels are mainly the excavation loose zone (elz), also called excavation damaged zone (edz), and the excavation disturbed zone (edz) (see figs. 1 & 2). they play a key role in the understanding of the long-term stability of these structures. in the elz (edz), the physical, t t w. frenelus et alii, frattura ed integrità strutturale, 58 (2021) 128-150; doi: 10.3221/igf-esis.58.10 131 mechanical, hydraulic and geochemical properties of rocks are considerably degraded [24, 25, 26]. consequently, in these zones, there is irreversibility of deformations. the elz or edz could also be called failed zone, referring to eberhardt et al. [27], where slabbing failure can occur. it should also be noted that in edz, according to verma et al. [28], not only there is degradation of the main properties of rocks, but there is also an increase in transferability properties. that is, in edz, transmissibility or transferability properties of rocks are augmented due to the degradations that could engender cracks and fractures. the evolution of edz (elz) strongly influence the stability of surrounding rocks around deep tunnels. factors favorable to the formation and growth of edz must be identified and controlled. according to yang et al. [29, 30], three main aspects may contribute to the formation of edz namely in-situ stress or excavation process, time-dependent behavior of rocks, and rock mass quality or evolution of fractured zones in rock mass. in fact, the edz is particularly formed when concentrated compressive or tensile in-situ stress is higher than the rock strength [31, 32, 33]. under geostress environment, referring to yang et al. [30], edz can provoke at the same time cracks growth and stress redistribution around tunnels. it also facilitate the flow of groundwater inside deep tunnels, increasing the risk of instability of said structures [34]. the extent of edz depends on several factors, but mainly on the excavation method used. it could be thicker in drill-and-blast tunnelling than tbm [35, 36]. the edz is the expansion of stress redistribution at some regions near the openings. in these zones, rocks are weakened [27]. in the edz, also called excavation influence zone (eiz), the hydromechanical and geochemical properties of rocks are not change considerably [35, 26]. for circular tunnels, according to du et al. [37], the extent of edz depends on the tunnels radius and generally limited to 3 times of their radius (≤3r). figure 1: edz and edz surrounding a circular tunnel subjected to the stresses 1 and 3 , adapted from eberhardt et al. [27] figure 2: diagram of failure zones during and after excavation. reprinted from [26], copyright 2019 elsevier bv w. frenelus et alii, frattura ed integrità strutturale, 58 (2021) 128-150; doi: 10.3221/igf-esis.58.10 132 it is important to note that, as said by perras and diederichs [38], in in-situ measurements, the distinction between eiz and edz is not obvious, and the transition between them is gradual. their impacts on long-term stability of deep tunnels are significant. the extent evaluation of these zones must be taken into account since they can change with time [39, 40, 41, 18]. in addition, they influence considerably the stress field in roof region of tunnels [42]. the view of stress-strain curve (fig. 3) can show the irreversibility of deformations in the edz by triaxial compression test. figure 3: stress-strain curve showing the location of edz and eiz, adapted from [43] and [44], copyright 2011 & 2015, elsevier as revealed by kwon et al. [2], the characteristics of the edz are seriously influenced by the excavation method used. in fact, additional damage is generated by any excavation method. however, there are more supplemental edz provoked by the db method than that of tbm method. regarding the edz or eiz, the effects of excavations are habitually minor, as outlined by satici and topal [45], but exist nonetheless. depending on the magnitude of the stress disturbances beyond the edz, the amplitude of edz may vary and become significant, and its effects may therefore become considerable. it should thus be recognized that both tbm and db excavations increase the magnitude of edz and edz in the surrounding rocks of tunnels. energy release during rocks excavations uring rocks excavations, the stored energy is disturbed. these excavations can lead to the release of elastic strain energy suddenly [46, 47]. the perturbations can induce serious damage and affect the stability of rocks located in the vicinity of deep tunnels. based on the work of yan et al. [10], tab. 3 presents the characteristics of the relevant factors for the energy release during db and tbm tunnelling. relevant factors db tbm behavior of the stress paths process transient unloading quasi-static unloading energy release magnitude larger smaller energy release extent higher lower energy release rate (err) higher lower energy release speed (ers) higher lower table 3: relevant factors of the energy release during db and tb tunnelling. d w. frenelus et alii, frattura ed integrità strutturale, 58 (2021) 128-150; doi: 10.3221/igf-esis.58.10 133 according to yang et al. [29], the elastic stress energy depends on various factors such as principal stresses, number of elements contained in the rocks, and the mechanical properties of rocks. rocks with more elements can release more strain energy. the most significant damage is related to the higher releases of the elastic strain energy. the strain energy released in the rocks is extremely essential to understand the sudden structural failure of the rocks [48]. as shown in tab. 3, the energy release by the unloading stress during db excavations is transient and higher. the db tunnelling may cause more perturbation and more degradation in the surrounding rocks of tunnels. moreover, as reported by fan et al. [49], the energy release during the transient unloading of the in-situ stress is not only highest, but also fastest. so, db tunnelling can deteriorate the surrounding rocks of tunnels faster than the tbm excavations. however, the effects of both tunnelling methods are permanent in the edz. damage and failure ne manner to take account of damage in a material is to use the concept of net stresses. as noted by hoxha et al. [50], the ‘‘net stresses’’ concept is used to describe how damage influences the mechanical response of a damaged material. lemaitre and chaboche [51] have shown that, for a solid under a constant uniaxial tensile stress ( ), the “net stress” ( * ), which depends on the damage factor ( d ), is given by    * / 1  d (1) rocks damage can be associated with creep (see fig. 4) which are both time-dependent phenomenon. according to brantut et al. [52], during creep, the damage parameter can take values from 0 (intact) to 1 (broken) and can be expressed as follows:     1e (2) where the applied stress is  , the young modulus is e , and the creep strain is  . the constant  is called damaged parameter. when rock is deformed by creep, the elastic modulus is decreased owing to damage [53, 54]. by equating   d , the last equation is    1e d (3) more broadly, rocks damage can also be expressed using the energy dissipation concept. referring to yang et al. [55], the global damage equation of rocks using the energy dissipation concept is as follows:                         0 0 0 0 0 0 0                                                          ( 1  )           1               1                           d u u u u d u u u u d u u (4) 0u is the critical strain energy corresponding to the initial damage; u is the strain energy expressed by     0 ij ij iju d (5) where  , ij ij are stress tensor and strain tensor respectively, (  1, 2, 3ij ); the principal stresses are 1 , 2 , 3 ; for positive compression    1 3 2 . the principal strains are 1 , 2 , 3 ;  is a parameter related to the materials properties. the relationship between damage and energy release can explain that greater energy corresponds to greater damage. in other words, the more energy the rocks release, the greater the damage is. in fact, great damage evolution lead to instability o w. frenelus et alii, frattura ed integrità strutturale, 58 (2021) 128-150; doi: 10.3221/igf-esis.58.10 134 of structures, and can affect the bearing capacity of rocks. mu et al. [56] have reported that the instability of structure is the macroscopic result of damage evolution and strength degradation in microstructures. damage and failure are closely linked. any damage generates a form of structural instability which can lead to failure. tang et al. [57] pointed out that the failure of rocks is caused by the damage evolution from initial defects. the latter, when they exist, are even more vulnerable during excavations. accumulation or evolution of damage in structures always results in failure when they exceed their allowable limit. according to jiang et al. [58], the time-dependent damage affects the major safety of surrounding rocks when it is severe. in fact, failure process in tunnels is composed by 3 stages (fig. 5) including initiation, propagation and coalescence of cracks [59, 20]. when it is completed, partial or total failure can occur in deep tunnels. . figure 4: rock damage evolution trend related to creep. reprinted from [55], copyright 2018 mdpi. figure 5: illustration of excavation failure and damage evolution in deep rock tunnel; a): crack initiation and propagation in tension; b): crack initiation and propagation in shear; c) coalescence. reprinted from [20], copyright 2013 springer-verlag wien. tunnels failure usually occurs by loss of rocks strength, or by excessive deformations or by serious damage of the support systems. any type of failure mode can occur during and after excavations. when rocks are subjected to stress, fracture toughness and fracture energy are two important characteristics that must be taken into account. in fact, it should be noted that there is an energy consumption or dissipation during the initiation of cracks. the energy dissipation increases with the evolution of cracks [60]. cracks and fractures evolution depends on fracture toughness of rocks. fracture toughness of rocks is the resistance to cracks expansion [61, 62]. fracture energy of rocks is the energy release rate which could be related to the disturbances generated by the excavation methods. more precisely, fracture energy refers to the energy required to cause fractures in rocks [62]. as related by dong et al. [60], when the fracture energy is considerable up to its critical value, w. frenelus et alii, frattura ed integrità strutturale, 58 (2021) 128-150; doi: 10.3221/igf-esis.58.10 135 cracks can propagate in the surrounding rocks of tunnels. toughness and fracture energy values can indicate how resistant rocks or structures are to the propagation of cracks or fractures. the most stable structures are those built with materials that have the highest fracture energies. tunnels built in rocky environments with high fracture energies may have higher degree of integrity during and after excavations by tbm or db. in plane strain condition, fracture energy and fracture toughness ( ick ) and can be linked as follows [60]:        2 2 1 c icg k e (6) where cg is the critical fracture energy; ick is the mode i fracture toughness;  is the poisson’s ratio; e is the elastic modulus. some quantitative values of the fracture toughness and fracture energy of rocks based on the performed tests conditions are summarized in tabs. 4 and 5, in mode i. in fact, according to kusch et al. [63], cracks can be propagated by mode i, ii and iii in loaded and stressed materials, but mode i is of paramount importance. note that fracture toughness and fracture energy of rocks vary with different factors such as depth, geometry, temperature, confining pressures, etc. rock type fracture toughness, ick ( mpa m ) testing method source (year) tage tuff 0.30-2.4 scb and senrbb funatsu et al. (2004)[64] schist 2.70 senb momber (2015)[65] limestone 1.21 senb momber (2015)[65] mudstone 0.73 0.85 scb yang et al. (2019)[66] andesite 2.04  0.66 fbd keles and tutluoglu (2011)[67] granite 1.65 secbd zhang (2002) [68] sandstone 0.67 bdt zhang (2002) [68] shale 0.38-1.38 bdt nezhad et al. (2018)[69] marble 1.11-1.36 scb ghouli et al. (2021) [70] table 4: quantitative values of fracture toughness for certain types of rocks rock type fracture energy, cg (mode i) ( 2/j m ) testing method or type source (year) limestone 50 femdem guo et al. (2017) [71] shale 30 femdem guo et al. (2017) [71] andesite 35-152 sr and dcb karpuz and bozdag (1996) [72] granite 28-56 scb nejati el al. (2021) [73] sandstone 2.4-13.9 cccd zhang et al. (2021) [74] marble 7.5 – 12.5 bdt feng et al. (2020) [75] table 5: quantitative values of fracture energy for certain types of rocks after the tunnelling, as already mentioned, the physical, mechanical and hydraulic properties of rocks are permanently damaged in the edz. the extent of these degradations evolves with the magnitude of edz. for instance, as experimented by kwon et al.[2], the elastic modulus can reach a huge reduction of up to 56% due to stress redistribution from blasting w. frenelus et alii, frattura ed integrità strutturale, 58 (2021) 128-150; doi: 10.3221/igf-esis.58.10 136 effects. toughness and fracture energy are usually greatly reduced when rocks are subjected to various dynamic loads of excavations. for example, by analyzing marble samples under dynamic three-point bending tests, yu et al. [76] showed the drastic change in toughness and fracture energy which decrease to 65.27% and 76.23% respectively of their initial values. they demonstrated that the deterioration of these properties increases with the evolution of damage in rocks. it is important de remember that, tunnel excavations generate dynamic perturbations in the surrounding rocks [20]. it should therefore be understood that the greater the damage generated by the excavations, the greater the risk of degradation of rock properties. thereby, more cracks and fractures can be spread in the surrounding rocks of tunnels. this increasingly increases the degree of damage to rocks and the risk of tunnel failure. rockbursts ockbursts are considered as frequent form of damage or disaster that can occur during excavations of deep tunnels. they are caused by excavation when unloading the in-situ stress [77, 78]. their risk is considerable during and after underground excavations. it increases when there is more elastic energy stored in the elastic zone, and less dissipated in the plastic zone [79, 80]. in fact, rockbursts are related to the strain energy that exists in the surrounding rocks of tunnels [81]. they can thus crop up when there is the highest release of that energy. in deep excavations, rockbursts are dangerous phenomenon mainly generated by the brittle failure of rocks related with induced seismic events [79, 82]. although it remains a challenge particularly at great depth, rockbursts control and assessment are extremely important in the analysis of the longterm stability for deep tunnels. indeed, wu et al. [83] reported that rockbursts can generate strong decrease in the stability of surrounding rocks. rockbursts impacts on the stability of structures vary with their intensity. based on elastic energy index ( etw ), zhou et al. [84] classified rockbursts into 4 groups for hard rocks, namely none rockburst (  2etw ), light rockburst (  2 5etw ), medium rockburst (  5 10etw ), and heavy rockburst (  10etw ). this classification corresponds respectively to minor rockburst, moderate rockburst, intensive rockburst and extreme rockburst, according to xie et al. [85]. fractures or damage of surrounding rocks during and after excavation could be closely related to the intensity of generated rockbursts. it is obvious that heavy rockbursts produce more damage and more fractures. many studies have been conducted about rockbursts prediction. li et al. [86] have realised a study permitting to predict rockbursts based on seismic techniques. one of their findings is that the excavation rate influence the frequency of rockbursts. this frequency is an important factor in the stability of surrounding rocks. some previous studies explained that rockbursts frequency increase as the excavation depth increases. they established empirical formulas [87] permitting to calculate a critical depth from which rockbursts frequency can be estimated. rockbursts can occur frequently when the excavation depth is greater than the established critical depth. on their side, based on acoustic emission and on field measurements, cheng et al. [88] have found that rockbursts signals are closely related to the adjustment of rock stresses. xue et al. [89] established a hierarchical evaluation system for rockbursts prediction based on a set of index and criterion. recently, he et al. [90] explained that one of the rockbursts method prevention, is to avoid high stress concentration areas as early as possible when selecting the tunnel route. indeed, rockbursts prediction could be used for a better control of the rockburst-induced damage during excavations. tab. 6 presents the key factors and conditions favorable for rockbursts occurrence. key factors and conditions favorable for rockbursts occurrence authors year strain energy accumulation and stress concentration pu et al.2018 [91] rock heterogeneity, disturbance and newly-fractured zones ma et al. – 2018 [92] stress regime influenced by the excavation unloading liu et al. – 2018 [93] adjustment of stress field and loading system manouchehrian & cai-2018 [94] hard and rigid rocks under high levels stress mazaira & konicek – 2015 [16] high in-situ stress zhang et al. – 2014 [6] in-situ stresses influenced by geological structure yan et al. – 2012 [10] critical depth and current tectonic stress field li et al. – 2007 [46] environment for stress concentration and strain energy accumulation wang and park – 2001 [95] table 6: key factors and conditions favorable for rockburst occurrence r w. frenelus et alii, frattura ed integrità strutturale, 58 (2021) 128-150; doi: 10.3221/igf-esis.58.10 137 to sum up, rockburst occurrence is linked to the stress and strength of surrounding rocks [96], and thus mainly depends on the excavation methods. when considering, for instance, the readjustment of stress or the unloading of the in-situ stress, they are also factors on which the occurrence of rockburst depends. nevertheless, such factors depend on rock excavation methods. in fact, in deep underground spaces, the significance of the stress adjustment varies according to the rocks excavation methods. on another hand, the geological characteristics and conditions of rocks can also play a role in the rockburst occurrence. here again, it’s the excavation method used that can make this occurrence possible to any extent. when excavating deep rocks, the sudden and delayed occurrence of rockbursts is governed by the excavation methods [97]. prompt rockbursts are typically generated during db excavation method, while delayed rockbursts are mostly provoked by tbm excavations. indeed, the in-situ stress is unloaded differently in the two excavation methods, as shown in tab. 3. taking as example the diversion tunnel of jinping ii hydropower station located at the southwestern of china, xie et al. [85] demonstrated that in both tunnelling methods, minor and moderate rockburst can occur during excavations. nevertheless, moderate rockbursts are predominantly frequent in db excavations. likewise, as also revealed by par yan et al. [10], intensive rockbursts occur mostly in db tunnelling (fig. 6). it is important to emphasise that under the effects of tunnelling methods, geological structures also influence the intensity and the frequency of rockbursts, as reported by fan et al. [97]. figure 6: rockbursts occurrence in rocks excavations by tbm and db methods. reprinted from [85], copyright 2018 springer. basically, the control of the energy release process in surrounding rocks during excavations is the best way to control rockbursts [98]. the greater the energy released, the larger the rockbursts and the greater the damage recorded in surrounding rocks. thereby tunnels built in hard and brittle rocks executed by db methods can generate a lot of rockbursts. this can increase damage and deformations of surrounding rocks and influence the long-term stability of deep tunnels. consideration on adverse geological conditions dverse geological conditions can affect the whole parameters of surrounding rocks during and after excavations, particularly when tunnelling by tbm. therefore, a good knowledge of the geological conditions is strongly recommended prior to excavations, in order to foresee the necessary precautions. for ensuring adequate excavations, the main adverse geological should be known. among these adverse geological conditions, we can mention: cavities, fractured and faults areas [99], high water inflow, spalling, squeezing and swelling ground [100]. they strongly a w. frenelus et alii, frattura ed integrità strutturale, 58 (2021) 128-150; doi: 10.3221/igf-esis.58.10 138 influence the tunnelling and the long-term stability of deep tunnels. huang et al. [14] reported that instability and collapse of the surrounding rocks are frequent when tbm excavations are done in zones with high fractures and faults. active faults can cause partial or total collapse of tunnels. more specifically, some parts of tunnels can be collapsed when deformations produced by tbm excavation are enormous in faults areas [101]. as shown in tabs. 1 and 2, one of the advantages of db excavations is their great flexibility and adaptability in many geological conditions, while tbm are disadvantageous for unfavorable geological conditions. such disadvantages of tbm must be seen both from a safety and an economic point of view. in fact, it is always reported by many scholars and researchers that there is high entrapment risk of tbm during excavations in adverse geological conditions. tbm entrapment generally cause serious excavations delays, and increase considerably the instability risk of tunnels and economic losses. referring to zhang et al. [6], due to unfavorable geological conditions, the tbm excavating the yacambú–quíbor deep tunnel in venezuela was blocked and it took several years to remove its remains. in taiwan, it took 15 years to complete the syueshan tunnel. these examples can illustrate the complexity associated with tunnelling in adverse geological conditions. in fact, under these conditions, the surrounding rocks parameters become even more weakened by any excavation method. nonetheless, db excavations could produce less instability in the tunnels under such conditions. figure 7: illustration of the effects of water in rocks creep behavior. figs. (a) and (b) show the creep behavior of red sandstones in dried state and in water soaked state at 2, 4, 6 and 8 days, at same stress conditions. the longer the rock samples are immersed, the shorter the lifetime is, and the faster the creep strain rate is. in dried state, the samples exhibit longer time-to-failure and the creep strain rate evolves slowly with time. the figs. (a-1) and (b-1) in the left part are the zoomed-in view of the strain and strain rate curves for the rocks samples immersed in water at 4 days, 6 days and 8 days. reprinted from [108], copyright 2018 springer-verlag austria consideration on high groundwater pressures and flow t great depth, high groundwater pressures can infiltrate into the excavated areas and attack the stability of surrounding rocks. according to hoek [102] and stille and palmström [1], groundwater pressures generated overall instability and reduced rock strength and shear. likewise, liu et al. [103] reported that the unexpected groundwater inflow at tunnel head generate uncontrollable effects like for example mechanical instability and environmental impacts. a w. frenelus et alii, frattura ed integrità strutturale, 58 (2021) 128-150; doi: 10.3221/igf-esis.58.10 139 the fight against heavy water pressure infiltration during tunnelling is frequent particularly for deep long tunnels, and requires much sustained attentions. in fact, as noted by hwang and lu [104] and zhang et al. [6], one of the challenges to be faced in deep tunnels is the high groundwater pressure. the problems induced by these inflows are usually assigned to water-rich fracture zones, particularly when using tbm [105]. thereby, prediction and identification of high groundwater pressures must be done. then, an adequate treatment is required to ensure tunnels stability. referring to zhang et al. [6] and zhang et al. [106], some techniques (pre-excavation, decompression, blocking, and radial grouting) are generally used in order to fight against high-groundwater pressure around deep long tunnels. but the impacts of these pressures and water flows are not negligible in the long-term. when studying the long-term stability of deep underground structures, emphasis should be placed on the creep behavior of their surrounding rocks. as pointed out by zhou et al. [107], the long-term strength criterion can be considerably described by the creep failure of rocks. the time-dependent creep behavior of rocks is influenced by water and hydraulic pressures. thus, taking into account the groundwater pressures and flows generated during excavations is important for a real evaluation of rocks creep strength. fig. 7 illustrates uniaxial creep curves of red sandstone samples studied by tang et al. [108] in order to reveal the influence of water on creep behavior of this rock type. the red sandstone samples was initially immersed in water at different durations like 2 days, 4 days, 6 days and 8 days. in the figure, the symbol “d” refers to days, the times are multiplied by 410  s , the creep strain rates are multiplied by 510 1s . s refers to second. the literature reveals that the creep behavior of all types of rocks is significantly influenced by water. tab. 7 presents the relevant effects of water on creep behavior for different types of rocks. rock type effects of water on creep behavior of rocks testing method reference (year) tage tuff creep behavior of water-saturated tage tuff is shortened uniaxial compression creep tests okubo et al. (2010) [109] green-schist the increase in instantaneous axial and lateral strains is caused by the increase of water content. biaxial compression creep tests xiong (2014) [110] limestone the increase in water and hydraulic pressure results in an increase in creep strain and creep strain rate. triaxial compression creep tests liu et al. (2015) [111] mudstone the reduction in short-term mechanical properties and the increase in both creep strain and creep strain rate are caused by the presence of water. uniaxial compression tests and multistage creep tests lu and wang (2017) [112] andesite the creep lifetime is drastically reduced by the presence of water. it is about 180 times shorter in wet conditions than in dry conditions, under the same stress conditions. uniaxial compression tests hashiba et al. (2018) [113] shale with the presence of water, the mechanical behavior of shale is remarkably affected in triaxial test. under uniaxial tests, there is reduction from 58% to 62% for the compressive modulus and strength. the latter also decrease in 36% under bdt. uniaxial, triaxial and bdt tests li et al. (2020) [114] granite, marble and sandstone water considerably affects the mechanical characteristics of rocks, and mainly decreases elastic modulus, critical strain and uniaxial compressive strength. uniaxial compression tests ad acoustic emission cai et al. (2019) [115] table 7: effects of water on the creep behavior of different types of rocks. indeed, groundwater pressures and flow generated by the tunnelling methods (db and tbm) lead to an increase of water content in the surrounding rocks of tunnels. as shown in fig. 7 and tab. 7, the presence of water deteriorates the mechanical and creep properties of rocks. accordingly, under the effect of excavation methods, water engenders long-term degradation in tunnels built in rocky environments. w. frenelus et alii, frattura ed integrità strutturale, 58 (2021) 128-150; doi: 10.3221/igf-esis.58.10 140 convergence deformation s already mentioned, during and after excavations, the initial stress field always tries to stabilize by itself. as a result, rocks tend to closure around the openings. this closure is the deformation that called convergence of the rocks surrounding the tunnels. convergence deformation is one of the severe effects of excavations which can be spectacular. it evolves as time increase owing to the time-dependent behavior of rocks [116, 4]. convergence is inevitable, as revealed by kontogianni et al. [117], since it is part of tunnels deformations mechanisms. according to them, due to the natural rocks behavior, tunnels convergence can be manifested in 3 stages: an accumulation rate, an evolution, and finally a stabilization. furthermore, tunnel convergence can be limited to a distance less than twice the diameter of the openings. in other words, when an underground opening is created, the convergence deformation is naturally observable owing to the rocks behavior. however, the extent of such a deformation is influenced by the degree of rocks damage during and after excavations. in addition to the properties of rocks, any excavation method has impact on the tendency and extent of convergence. paraskevopoulou and diederichs [116] have showed that both tunnelling methods (db and tbm) influence the convergence of tunnels. by considering an elasto-visco-elastic rock mass and the cvisc (visco-elastic-plastic) model, they numerically demonstrated that db and tbm excavations effects increase the total displacement of rocks surrounding the tunnels. however, under similar duration of the excavation sequences, when rock mass conditions are favorable and tunnels length is considerable, tbm excavations can generate fewer additional displacements than that of db. otherwise, in adverse geological conditions, the additional wall displacements of tunnels are greater under tbm tunnelling. convergence is an essential factor in the study of tunnels stability. in fact, tunnel performance depends on it [118]. consequently, tunnel convergence should be seriously controlled since the earlier stage of excavations, and throughout the lifetime of tunnels. as explained above, both tunneling methods influence the extent of tunnel convergence deformation by increasing it. the influence of excavation methods on tunnel convergence can be reduced if proper measures are taken as soon as possible. it is therefore extremely important to understand in depth such tunnel behavior and to adopt suitable solutions to limit it considerably. tab. 8 presents an overview of the salient details in the study of convergence deformations for deep tunnels. type of rocks or rock mass convergence measurement method used salient findings references (year) all type differentiation of effects reflecting the convergence tunnels convergence describing by wall displacements depends on the time-dependent behaviour of rocks and the face advance effect. sulem et al. (1987) [119] sandstones fields monitoring in viscous media, there are relaxation path of rocks, and delayed tunnels convergence. consequently, tunnels convergence law is not assimilated to the creep law. pellet et al. (2000) [120] broken soft rocks multi-point extensometers floor heave represents 65% of the total roof and floor deformation. there is huge deformation with rapid speed, and unevenly distributed in the entire deep tunnel cross section. wang jin-xi et al. (2009) [121] soft rocks under high stress fields monitoring the average value of the convergence deformation in roof and floor can at least double that of sidewalls. yu et al. (2015) [122] deep buried composite rocks finite element difference & similar theory surrounding rocks convergence deformations of tunnels are composed in 2 parts: instantaneous and continuous creep deformations. soft rocks exhibit maximum convergence deformations. yang et al. (2019) [123] hard rocks multi-point extensometers tunnel convergence could be divided in 3 stages: initial, rapid and stable convergence. wang et al. (2019) [124] good rock mass quality advance borehole monitoring & numerical inversion analysis deformations characteristics of surrounding rocks are traduced by the convergence deformations. the surrounding rocks crown convergence deformation can be well analysed during tunnelling for double-shield tbm tunnels. li et al. (2020) [125] table 8: salient details about convergence deformations due to tunnelling a w. frenelus et alii, frattura ed integrità strutturale, 58 (2021) 128-150; doi: 10.3221/igf-esis.58.10 141 fig. 8 illustrates that the deformations wall-wall (which is assimilated to convergence) of tunnels increases with the increasing of time after the excavation period. this rheological behavior is strictly related to the rocks types and excavation methods. huge rocks perturbations during excavations can involve huge convergences over time for deep tunnels. figure 8: illustration of the evolution of convergence deformations in tunnels. reprinted from [56], copyright 2020 elsevier ltd discussion and propositions he analysis of papers highlights different potential factors of excavations methods which impact the stability of deep tunnels. these factors evolve over time, and their influence on the above structures stability will be for longterm. the extent of these influences depends firstly on the characteristics of the encountered rocks at the excavations depth and the geological conditions, and secondly on the excavations methods used. in fact, unfavourable geological conditions delay tunnelling [126], and consequently lead to additional impacts to the rocks around tunnels. for example, initially fractured rocks are generally more vulnerable to excavations and more damaged than that of unfractured. zhang et al. [106], revealed that the damage generated by the fractures of rocks are frequent. when tunnelling in these rocks, damage would be added to the initial damage increasing the instability of deep underground structures. adverse effects exist in all tunnelling method. in order to design adequate tunnels supports and reduce the excavations impacts, adequate control and measurement of damage or deformations should be done. in fact, the duration of the excavation operation is an important factor. some tunnels collapse during the period of their excavation [127]. the excavation time depends on several parameters including the geotechnical characteristics of rocks, the tunnelling methods as well the capacity and speed of work. from an intact deep rock mass until the setup of support systems for deep tunnels, potential factors illustrating the influence of excavations methods are in the diagram hereinafter (fig. 9). figure 9: diagram showing the influence of excavation methods on long-term stability of tunnels t w. frenelus et alii, frattura ed integrità strutturale, 58 (2021) 128-150; doi: 10.3221/igf-esis.58.10 142 the lifespan of tunnels could be influenced by the manner in which the surrounding rocks have been disturbed, damaged and deformed during and after excavations. indeed, the least durable tunnels could be those whose surrounding rocks were the most severely damaged and deformed during and after excavations. considering a saturated viscoplastic rock mass by referring to deleruyelle et al. [128], the life cycle of deep tunnels can be detailed in four stages such as excavation, tunnel unlined, lining emplacement, and post-closure (fig. 10). the post-closure stage is the total destruction of tunnels which mainly depends on the extent of convergence deformation accumulated in the first three stages, and over time. figure 10: illustration of tunnels life cycle. reprinted from [128], copyright 2016 elsevier masson sas in order to mitigate the influence of excavation methods in deep tunnels, the following steps are proposed: firstly, a good evaluation of the geological and hydrogeological properties of the areas to be excavated is crucial. secondly, an evaluation of the tunnelling methods to be used should always be made. indeed, especially for deep long tunnels, combined actions of two tunnelling methods could be beneficial at certain levels, and unfavourable in some points. so a good assessment of their impacts are required prior to tunnelling. thirdly, a good selection of excavation sequences and direction is extremely important for the surrounding rocks stability. it also plays a great role in the stability of different components of tunnels. fourthly, field monitoring and measurements are necessary throughout the tunnelling periods, in order to control damage fractures and rockbursts signals. all cracks and deformations generated during the excavations periods of deep tunnels should be well identified and assessed and all actions should be optimized during and after tunnelling. this will limit damage evolution by putting in place suitable support systems as quickly as possible in order that tunnels be stable during their service life. the aforementioned steps can be performed through different methodologies and instrumentations such as: fields monitoring and relevant surveys, relevant empirical and/or analytical formulas, adequate experimental tests and numerical methods. more precisely, steps 1 and 2 can be effectuated by in-situ measurements, experimental tests, as well as numerical methods. in fact, both experimental tests and numerical methods can be employed to determine the hydro-mechanical properties of rocks. to ensure reliability, in many cases, numerical results can be compared with experimental results. referring to wang et al. [129], we outline that machine learning techniques can also be used to determine or predict mechanical properties of rocks. for the step 3, pertinent numerical methods can provide goods results regarding the excavations sequences and directions of deep rock tunnels. step 4 can be performed using field measurements and relevant numerical methods. note also that the support systems or linings can be calculated using appropriated empirical or analytical formulas and numerical methods. fig. 11 illustrates the steps in more detail. future research needs he long-term stability of deep rocks tunnels built in rocky mediums must always be sought. despite that many previous studies are conducted, there are still several areas of research which deserve further studies in order to support accurate predictions of deep tunnel’s long-term stability. although it remains as challenge tasks, it is of tremendous importance to accurately estimate: t w. frenelus et alii, frattura ed integrità strutturale, 58 (2021) 128-150; doi: 10.3221/igf-esis.58.10 143 the extent of degradations of the mechanical properties for surrounding rocks and its influence on long-term stability of deep tunnels. the overall magnitude of edz and its influence on long-term life of deep rocks tunnels based on unloading effect. how excavations methods influence the rocks bearing capacity of deep tunnels based on time-dependent effect. the total damage and deformations generated in the surrounding rocks after tbm and/or drill-and-blast excavations based on creep effect. comparison of the convergence deformations magnitude between tunnels excavated by tbm and db under same geological and hydrogeological conditions. long-term stability analysis of deep tunnels based on post-excavation evaluation. the degradation of the fracture toughness and fracture energy in deep rocks tunnels after tbm and dill-and-blast excavations. figure 11: proposed methodologies to control and mitigate the effects of excavations methods on the long-term stability of deep rocks tunnels. conclusions he excavations methods have considerable influence on long-term stability of deep rock tunnels. the main conclusions related to this paper are summarized as follows: t w. frenelus et alii, frattura ed integrità strutturale, 58 (2021) 128-150; doi: 10.3221/igf-esis.58.10 144 a) the long-term stability of deep tunnels is influenced by the long-term stability of its surrounding rocks. any excavation method has adverse effects on the properties of rocks, and impact the durability of deep rocks. thereby it influences the long-term stability of deep tunnels owing to the degradation of the physical, mechanical, and hydraulic properties of the surrounding rocks. b) owing to the energy release during excavations, rockbursts are inevitable, especially during hard and brittle rocks excavations. in engineering practice, the tunnelling rate must well be controlled to prevent intensive rockbursts. the latter cause generally more damage and weaken much more the surrounding rocks of tunnels. consequently the life time of these tunnels can be more impacted. c) for deep long tunnels crossing complicated geological zones, when a combination of drill-and-blast and tbm methods is employed, high stress concentrations in the intersection areas will also influence the lifetime of deep tunnels. d) the proper design of the lining systems depends on the conditions of surrounding rocks after excavations. thus, the excavation methods used govern on the long-term the support systems of deep rock tunnels. the greater the damage or deformation, the more resistant the support systems must be. e) after rocks excavations, deformations increase continuously and failure can occur over time due to the timedependent behavior of natural rocks. hence, the total convergence deformation caused by the excavations should be predicted minutely considering all the relevant factors. indeed, long-term monitoring is necessary during the lifetime of deep tunnels. f) all tunnelling methods impose additional deformations on surrounding rocks of deep tunnels. these deformations can be minimized if actions are optimized during the tunneling period. however in any case they influence the tunnels long-term stability. g) to ensure the long-term stability of deep rocks tunnels, a high degree of structural integrity is required. nomenclature db: drill-and-blast tbm: tunnel boring machine elz: excavation loose zone edz: excavation damaged zone eiz: excavation influence zone edz: excavation disturbance zone err: energy release rate ers: energy release speed. scb: semi-circular bend senrbb: single edge-notched round bar in bending senb: single edge notch bend fbd: flattened brazilian disc secbd: single edge cracked brazilian disk in diametric compression bdt: brazilian disk test femdem: combined finite-discrete element method sr: short rod dcb: double cantilever beam cccd: center-cracked circular disc cvisc: visco-elastic-plastic or burger constitutive viscoplastic. acknowledgements he work is supported by the china scholarship council (csc no.2019gbj008203). t w. frenelus et alii, frattura ed integrità strutturale, 58 (2021) 128-150; doi: 10.3221/igf-esis.58.10 145 references [1] stille, h., palmström, a. (2008). ground behaviour and rock mass composition in underground excavations. tunnelling and underground space technology, 23 (1), pp. 46–64. doi: 10.1016/j.tust.2006.11.005 [2] kwon, s., lee, c., cho, s., jeon, s., cho, w. (2009). an investigation of the excavation damaged zone at the kaeri underground research tunnel. tunnelling and underground space technology, 24 (1), pp.1-13. doi:10.1016/j.tust.2008.01.004 [3] hefny, a. m., lo, k.y. (1999). analytical solutions for stresses and displacements around tunnels driven in crossanisotropic rocks. int. j. num. anal. meth. geomech., 23, pp. 161-177. doi: 10.1002/(sici)1096-9853(199902)23:2<161::aid-nag963>3.0.co;2-b [4] fu t.-f., xu, t., wasantha, p.l.p, et al. (2020). time-dependent deformation and fracture evolution around underground excavations. geomatics, natural hazards and risk, 11 (1): pp. 2615-2633. doi: 10.1080/19475705.2020.1856202 [5] kaiser, p.k., yazici, s., maloney, s. (2001). mining-induced stress change and consequences of stress path on excavation stability – a case study. int. journal of rock mechanics and mining sciences, 38(2), pp. 167-180. doi: 10.1016/s1365-1609(00)00038-1 [6] zhang, g.-h., jiao, y.-y., wang, h. outstanding issues in excavation of deep and long rock tunnels: a case study (2014). can. geotech. j., 51 (9), pp. 984-994. doi: 10.1139/cgj-2013-0087 [7] barton, n. (2012). reducing risk in long deep tunnels by using tbm and drill-and-blast methods in the same project– the hybrid solution. journal of rock mechanics and geotechnical engineering, 4 (2), pp. 115-126. doi: 10.3724/sp.j.1235.2012.00115. [8] tang, z., liu, x., xu, q., et al. (2018). stability evaluation of deep-buried tbm construction tunnel based on microseismic monitoring technology. tunnelling and underground space technology. 81, pp. 512-524. doi: 10.1016/j.tust.2018.08.028. [9] deng, p., liu, q., ma, h., et al. (2020). time-dependent crack development processes around underground excavations. tunnelling and underground space technology, 103, 103518. doi: 10.1016/j.tust.2020.103518. [10] yan, p., lu, w., chen, m. et al. (2012). energy release process of surrounding rocks of deep tunnels with two excavation methods. journal of rock mechanics and geotechnical engineering, 4 (2), pp. 160-167. doi: 10.3724/sp.j.1235.2012.00160. [11] ji, f., lu, j., shi, y., zhou, c. (2013). mechanical response of surrounding rock of tunnels constructed with the tbm and drill-blasting method. nat hazards, 66, pp. 545-556. doi: 10.1007/s11069-012-0500-2 [12] cai, m. (2008). influence of stress path on tunnel excavation response numerical tool selection and modeling strategy. tunnelling and underground space technology, 23: pp. 618-628. doi: 10.1016/j.tust.2007.11.005. [13] suorineni, f.t., kaiser, p.k., henning, j.g. (2008). safe rapid drifting – support selection. tunnelling and underground space technology, 23, pp. 682-699. doi: 10.1016/j.tust.2008.01.002. [14] huang, x., liu, q., shic, k., pan, y., liu, j. (2018). application and prospect of hard rock tbm for deep roadway construction in coal mines. tunnelling and underground space technology, 73, pp. 105-126. doi: 10.1016/j.tust.2017.12.010. [15] zareifard, m. r. (2020). a new semi-numerical method for elastoplastic analysis of a circular tunnel excavated in a hoek–brown strain-softening rock mass considering the blast-induced damaged zone. computers and geotechnics, 122, 103476. doi: 10.1016/j.compgeo.2020.103476 [16] mazaira, a., and konicek, p. (2015). intense rockburst impacts in deep underground construction and their prevention. canadian geotechnical journal, 52, pp. 1426-1439. doi: 10.1139/cgj-2014-0359 [17] ma, h., wang, j., man, k., et al. (2020). excavation of underground research laboratory ramp in granite using tunnel boring machine: feasibility study. journal of rock mechanics and geotechnical engineering, 12, pp. 1201-1213. doi: 10.1016/j.jrmge.2020.09.002. [18] bao, h., zhang, k., yan, c., et al. (2020). excavation damaged zone division and time-dependency deformation prediction: a case study of excavated rock mass at xiaowan hydropower station. engineering geology, 272, 105668. doi: 10.1016/j.enggeo.2020.105668. [19] liu, b., zhang, d.-w., yang, c., et al. (2020). long-term performance of metro tunnels induced by adjacent large deep excavation and protective measures in nanjing silty clay. tunnelling and underground space technology, 95, pp. 103147. doi: 10.1016/j.tust.2019.103147. [20] qiu, s.-l., feng, x.-t., xiao, j.-q., et al. (2014). an experimental study on the pre-peak unloading damage evolution of marble. rock mech rock eng, 47, pp. 401-419. doi:10.1007/s00603-013-0394-7 w. frenelus et alii, frattura ed integrità strutturale, 58 (2021) 128-150; doi: 10.3221/igf-esis.58.10 146 [21] niu, l., zhu, w., cheng, z., et al. (2017). numerical simulation on excavation-induced damage of rock under quasistatic unloading and dynamic disturbance. environ earth sci. 76, pp. 614. doi:10.1007/s12665-017-6955-4 [22] cai, m., kaiser, p.k. (2005). assessment of excavation damaged zone using a micromechanics model. tunnelling and underground space technology, 20, pp. 301-310. doi: 10.1016/j.tust.2004.12.002. [23] luo, t., wang, s., zhang, c., liu, x. (2017). parameters deterioration rules of surrounding rock for deep tunnel excavation based on unloading effect. dyna, 92 (6), pp. 648-654. doi: 10.6036/8554 [24] yan, c., yuan, t., wang, k. (2014). unloading phenomena characteristics in brittle rock masses by a large-scale excavation in dam foundation. the open civil engineering journal, 8, pp. 177-182. [25] wu, z., jiang, y., liu, q et al. (2018). investigation of the excavation damaged zone around deep tbm tunnel using a voronoi-element based explicit numerical manifold method. international journal of rock mechanics and mining sciences, 112, pp. 158-170. doi: 10.1016/j.ijrmms.2018.10.022. [26] tian, m., han, l., meng, q. et al. (2019). in situ investigation of the excavation-loose zone in surrounding rocks from mining complex coal seams. journal of applied geophysics, 168, pp. 90-100. doi: 10.1016/j.jappgeo.2019.06.008. [27] eberhardt, e., stead, d., stimpson, b. (1999). quantifying progressive pre-peak brittle fracture damage in rock during uniaxial compression. international journal of rock mechanics and mining sciences, 36, pp. 361-380. doi: 10.1016/s0148-9062(99)00019-4. [28] verma, h.k, samadhiya, n.k., singh, m., goel r.k., singh, p.k. (2018). blast induced rock mass damage around tunnels. tunnelling and underground space technology, 71, pp. 149-158. doi: 10.1016/j.tust.2017.08.019 [29] yang, h., huang, d., yang x., et al. (2013). analysis model for the excavation damage zone in surrounding rock mass of circular tunnel. tunnelling and underground space technology, 35, pp. 78-88. doi: 10.1016/j.tust.2012.12.006 [30] yang, h.q., zeng, y.y., lan, y.f., et al. (2014) analysis of the excavation damaged zone around a tunnel accounting for geostress and unloading. international journal of rock mechanics & mining sciences, 69, 59-66. doi: 10.1016/j.ijrmms.2014.03.003. [31] martino, j.b., chandler, n.a. (2004). excavation-induced damage studies at the underground research laboratory. int. j. of rock mechanics & mining sciences, 41, pp. 1413-1426. doi: 10.1016/j.ijrmms.2004.09.010 [32] siren, t., kantia, p., rinne, m. (2015). considerations and observations of stress-induced and construction-induced excavation damage zone in crystalline rock. international journal of rock mechanics & mining sciences, 73, pp. 165174. doi: 10.1016/j.ijrmms.2014.11.001 [33] yang, j.h, jiang, q.h, zhang, q.b. et al. (2018). dynamic stress adjustment and rock damage during blasting excavation in a deep-buried circular tunnel. tunnelling and underground space technology, 71, pp. 591-604. doi: 10.1016/j.tust.2017.10.010 [34] gao, c., zhou, z., li, z., et al. (2020). peridynamics simulation of surrounding rock damage characteristics during tunnel excavation. tunnelling and underground space technology, 97, pp. 103289. doi: 10.1016/j.tust.2020.103289 [35] tsang, c.-f., bernier, f., davies, c. (2005). geohydromechanical processes in the excavation damaged zone in crystalline rock, rock salt, and indurated and plastic clays in the context of radioactive waste disposal. international journal of rock mechanics & mining sciences, 42, pp. 109-125. doi: 10.1016/j.ijrmms.2004.08.003. [36] zareifard, m.r., fahimifar, a. (2016). analytical solutions for the stresses and deformations of deep tunnels in an elasticbrittle-plastic rock mass considering the damaged zone. tunnelling and underground space technology, 58, pp. 186196. doi: 10.1016/j.tust.2016.05.007 [37] du, x., zhang, p., jin, l., lu, d. (2019). a multi-scale analysis method for the simulation of tunnel excavation in sandy cobble stratum. tunnelling and underground space technology, 83, pp. 220-230. doi: 10.1016/j.tust.2018.09.019. [38] perras, m.a., diederichs, m.s. (2016). predicting excavation damage zone depths in brittle rocks. journal of rock mechanics and geotechnical engineering, 8, 60-74. doi: 10.1016/j.jrmge.2015.11.004. [39] malan, d.f. (1999). time-dependent behaviour of deep level tabular excavations in hard rock. rock mech. rock engng., 32 (2), pp. 123-155. doi: 10.1007/s006030050028. [40] malan, d.f. (2002) manuel rocha medal recipient simulating the time-dependent behaviour of excavations in hard rock. rock mech. rock engng, 35(4), pp. 225-254. doi: 10.1007/s00603-002-0026-0 [41] barla, g., debernardi, d., sterpi, d. (2012). time-dependent modeling of tunnels in squeezing conditions. international journal of geomechanics. 12, pp. 697-710. doi: 10.1061/(asce)gm.1943-5622.0000163. [42] tao, m., hong, z., peng, k., sun, p., cao, m., du, k. (2019). evaluation of excavation-damaged zone around underground tunnels by theoretical calculation and field test methods. energies, 12(9), pp. 1682. doi: 10.3390/en12091682 [43] renaud, v., balland, c., verdel, t. (2011). numerical simulation and development of data inversion in borehole ultrasonic imaging. journal of applied geophysics, 73, pp. 357-367. doi: 10.1016/j.jappgeo.2011.02.007 w. frenelus et alii, frattura ed integrità strutturale, 58 (2021) 128-150; doi: 10.3221/igf-esis.58.10 147 [44] wang, h., jiang, y., xue, s., et al. (2015). assessment of excavation damage zone around roadways under dynamic pressure induced inactive mining process. int. journal of rock mechanics &mining sciences, 77, pp. 265-277. doi: 10.1016/j.ijrmms.2015.03.032 [45] satici, o., topal, t. (2021). assessment of damage zone thickness and wall convergence for tunnels excavated in strainsoftening rock masses. tunnelling and underground space technology, 108, 103722. doi: 10.1016/j.tust.2020.103722 [46] li, t., cai, m.f., cai, m. (2007). a review of mining-induced seismicity in china. international journal of rock mechanics & mining sciences, 44, pp. 1149-1171. doi: 10.1016/j.ijrmms.2007.06.002. [47] yang, j., lu, w., chen, m., et al. (2013). microseism induced by transient release of in situ stress during deep rock mass excavation by blasting. rock mech rock eng, 46, pp. 859-875. doi: 10.1007/s00603-012-0308-0 [48] xie, h., li, l., peng, r., et al. (2009). energy analysis and criteria for structural failure of rocks. journal of rock mechanics and geotechnical engineering. 2009, 1, pp. 11–20. doi: 10.3724/sp.j.1235.2009.00011. [49] fan, y., zheng, j., hu, x., et al. (2020). study on energy release of surrounding rock under the multiple unloading disturbance during tunnel excavation. mathematical problems in engineering, 6486815. doi: https://doi.org/10.1155/2020/6486815 [50] hoxha, d., giraud, a., homand, f. (2005). modelling long-term behaviour of a natural gypsum rock. mechanics of materials, 37, pp. 1223-1241. doi: 10.1016/j.mechmat.2005.06.002. [51] lemaitre, j., chaboche, j.-l. (1990). mechanics of solid materials. cambridge university press, cambridge. [52] brantut, n., heap, m.j., meredith, p.g., baud, p. (2013). time-dependent cracking and brittle creep in crustal rocks: a review. journal of structural geology, 52, pp. 17-43. doi: 10.1016/j.jsg.2013.03.007. [53] tang, s., yu, c., tang, c. (2018). numerical modeling of the time-dependent development of the damage zone around a tunnel under high humidity conditions. tunnelling and underground space technology, 76, pp. 48–63. doi: 10.1016/j.tust.2018.03.012. [54] yang, s.-q., hu, b., ranjith, p. g., et al. (2018). multi-step loading creep behavior of red sandstone after thermal treatments and a creep damage model. energies, 11(1), 212. doi: 10.3390/en11010212 [55] mu, w., li, l., chen, d., et al. (2020). long-term deformation and control structure of rheological tunnels based on numerical simulation and on-site monitoring. engineering failure analysis, 118, pp. 104928. doi: 10.1016/j.engfailanal.2020.104928. [56] tang, c., tang, s. (2011). applications of rock failure process analysis (rfpa) method. journal of rock mechanics and geotechnical engineering, 3 (4), pp. 352-372. doi: 10.3724/sp.j.1235.2011.00352. [57] jiang, q., cui, j., chen, j. (2012). time-dependent damage investigation of rock mass in an in situ experimental tunnel. materials, 5 (8), pp. 1389-1403. doi: 10.3390/ma5081389 [58] zhu, w.c, liu, j., tang, c.a., et al. (2005). simulation of progressive fracturing processes around underground excavations under biaxial compression. tunnelling and underground space technology, 20, pp. 231-247. doi: 10.1016/j.tust.2004.08.008 [59] sun, j.-s., zhu, q.-h., lu, w.-b. (2007). numerical simulation of rock burst in circular tunnels under unloading conditions. j. china univ mining & technology, 17 (4), pp. 0552-0556. [60] dong, x., karrech, a., basarir, h., et al. (2019). energy dissipation and storage in underground mining operations. rock mechanics and rock engineering, 52, pp. 229–245. doi: 10.1007/s00603-018-1534-x [61] nasseri, mhb, mohanty, b., young, r.p., (2006). fracture toughness measurements and acoustic emission activity in brittle rocks. pure appl. geophys, 163, pp. 917-945. doi 10.1007/s00024-006-0064-8 [62] peng, k., lv, h., zou, q., et al. (2020). evolutionary characteristics of mode-i fracture toughness and fracture energy in granite from different burial depths under high-temperature effect. engineering fracture mechanics, 239, 107306. doi: 10.1016/j.engfracmech.2020.107306 [63] kusch, a., salamina, s., crivelli, d., berto. f. (2021). strain energy density criterion as failure assessment for quasi-static uni-axial tensile load, frattura ed integrità strutturale, 57, pp. 331-349. doi: 10.3221/igf-esis.57.24 [64] funatsu, t., seto, m., shimada, h., et al. (2004). combined effects of increasing temperature and confining pressure on the fracture toughness of clay bearing rocks. international journal of rock mechanics & mining sciences, 41, pp. 927938. doi: 10.1016/j.ijrmms.2004.02.008 [65] momber, a.w. (2015). fracture toughness effects in geomaterial solid particle erosion. rock mechanics and rock engineering, 48, pp. 1573-1588. doi: 10.1007/s00603-014-0658-x [66] yang, j., li, l., lian, h. (2019). experimental evaluation of the influences of water on the fracture toughness of mudstones with bedding. advances in materials science and engineering, 5693654. doi: 10.1155/2019/5693654 [67] keles, c., tutluoglu, l. (2011). investigation of proper specimen geometry for mode i fracture toughness testing with flattened brazilian disc method. int j fract, 169, pp. 61–75. doi: 10.1007/s10704-011-9584-z w. frenelus et alii, frattura ed integrità strutturale, 58 (2021) 128-150; doi: 10.3221/igf-esis.58.10 148 [68] zhang, zx. (2002). an empirical relation between mode i fracture toughness and the tensile strength of rock. international journal of rock mechanics & mining sciences, 39(3), pp. 401-406. doi: 10.1016/s1365-1609(02)00032-1 [69] nezhad, mm., fisher, qj, gironacci, e., rezania, m. (2018). experimental study and numerical modeling of fracture propagation in shale rocks during brazilian disk test. rock mechanics and rock engineering, 51, pp. 1755-1775. doi: 10.1007/s00603-018-1429-x [70] ghouli, s., bahrami, b., ayatollahi, m.r. et al. (2021). introduction of a scaling factor for fracture toughness measurement of rocks using the semi-circular bend test. rock mech rock eng, may 2021. doi: 10.1007/s00603-021-02468-1 [71] guo, l., latham, j.p., xiang, j. (2017). a numerical study of fracture spacing and through-going fracture formation in layered rocks. international journal of solids and structures, 110-111, pp. 44–57. doi: 10.1016/j.ijsolstr.2017.02.004 [72] karpuz, c., bozdag, t. (1996). a comparison on the double cantilever beam and short rod fracture toughness test results of ankara andesite. isrm international symposium eurock 96, turin italy, september 1996. [73] nejati, m., bahrami, b., ayatollahi, m.r., driesner, t. (2021). on the anisotropy of shear fracture toughness in rocks. theoretical and applied fracture mechanics, 113, 102946. doi: 10.1016/j.tafmec.2021.102946 [74] zhang, s., an, d., zhang, x., et al. (2021). research on size effect of fracture toughness of sandstone using the centercracked circular disc samples. engineering fracture mechanics, 251, 107777. doi: 10.1016/j.engfracmech.2021.107777 [75] feng, f., chen, s., li, d., et al. (2020). excavation unloading‐induced fracturing of hard rock containing different shapes of central holes affected by unloading rates and in situ stresses. energy sci eng., 8, pp. 4-27. doi: 10.1002/ese3.486. [76] yu, l., fu, a., yin, q., et al. (2020). dynamic fracturing properties of marble after being subjected to multiple impact loadings. engineering fracture mechanics, 230, 106988. doi: 10.1016/j.engfracmech.2020.106988 [77] zhu, w.c, liu, j., tang, c.a., et al. (2005). simulation of progressive fracturing processes around underground excavations under biaxial compression. tunnelling and underground space technology, 20, pp. 231-247. doi: 10.1016/j.tust.2004.08.008 [78] sun, j.-s., zhu, q.-h., lu, w.-b. (2007). numerical simulation of rock burst in circular tunnels under unloading conditions. j. china univ mining & technology, 17 (4), pp. 0552-0556. [79] xiao, y.x., feng, x. t., li, s.j., et al. (2016). rock mass failure mechanisms during the evolution process of rockburst in tunnels. international journal of rock mechanics & mining sciences, 83, pp. 174-181. doi: 10.1016/j.ijrmms.2016.01.008 [80] kaiser, p.k., cai, m. (2012). design of rock support system under rockburst condition. journal of rock mechanics and geotechnical engineering, 4 (3), pp. 215-227. doi: 10.3724/sp.j.1235.2012.00215. [81] zhang, j., wang, y., sun, y., et al. (2020). strength of ensemble learning in multiclass classification of rockburst intensity. int j numer anal methods geomech., 44, pp. 1833-1853. doi: 10.1002/nag.3111 [82] naji, a.m., emad, m.z., rehman, h., et al. (2019). geological and geomechanical heterogeneity in deep hydropower tunnels: a rock burst failure case study. tunnelling and underground space technology, 84, pp. 507-521. doi: 10.1016/j.tust.2018.11.009. [83] wu, s., wang, g. (2011). rock mechanical problems and optimization for the long and deep diversion tunnels at jinping ii hydropower station. journal of rock mechanics and geotechnical engineering, 3 (4), pp. 314-328. doi: 10.3724/sp.j.1235.2011.00314. [84] zhou, j., li, x., mitri, h.s. (2018). evaluation method of rockburst: state-of-the-art literature review. tunnelling and underground space technology, 81, pp. 632-659. doi: 10.1016/j.tust.2018.08.029. [85] xie, l.t., yan, p., lu, w.b., et al. (2018). effects of strain energy adjustment: a case study of rock failure modes during deep tunnel excavation with different methods. ksce journal of civil engineering, 22(10), pp. 4143-4154. doi: 10.1007/s12205-018-0424-9. [86] li, p.-x., feng, x.-t., feng, g.-l., et al. (2019). rockburst and microseismic characteristics around lithological interfaces under different excavation directions in deep tunnels. engineering geology, 260, 105209. doi: 10.1016/j.enggeo.2019.105209. [87] li, x.-b., zhou, j., wang, s.-f., et al. (2017). review and practice of deep mining for solid mineral resources. chin. j. nonferrous metals, 27 (6), pp. 1236-1262. doi: 10.19476/j.ysxb.1004.0609.2017.06.021 [88] cheng, w., wang, w., huang, s., ma, p. (2013). acoustic emission monitoring of rockbursts during tbm-excavated headrace tunneling at jinping ii hydropower station. journal of rock mechanics and geotechnical engineering, 5, pp. 486-494. doi: 10.1016/j.jrmge.2011.09.001. [89] xue, y., bai, c., kong, f., qiu, d., li, l., et al. (2020). a two-step comprehensive evaluation model for rockburst prediction based on multiple empirical criteria. engineering geology, 268, 105515. w. frenelus et alii, frattura ed integrità strutturale, 58 (2021) 128-150; doi: 10.3221/igf-esis.58.10 149 doi: 10.1016/j.enggeo.2020.105515. [90] he, s., lai, j., zhong, y., et al. (2021). damage behaviors, prediction methods and prevention methods of rockburst in 13 deep traffic tunnels in china. engineering failure analysis, 121, 105178. doi: 10.1016/j.engfailanal.2020.105178. [91] pu, y., apel, d.b., lingga, b. (2018). rockburst prediction in kimberlite using decision tree with incomplete data. journal of sustainable mining, 17, pp. 158-165. doi: 10.1016/j.jsm.2018.07.004. [92] ma, t.-h., tang, c.a., tang, s.b., et al. (2018). rockburst mechanism and prediction based on microseismic monitoring. international journal of rock mechanics and mining sciences, 110, pp. 177-188. doi: 10.1016/j.ijrmms.2018.07.016. [93] liu, f., ma, t., tang, c.a., et al. (2018). prediction of rockburst in tunnels at the jinping ii hydropower station using microseismic monitoring technique. tunnelling and underground space technology, 81, pp. 480-493. doi: 10.1016/j.tust.2018.08.010. [94] manouchehrian, a., cai, m. (2018). numerical modeling of rockburst near fault zones in deep tunnels. tunnelling and underground space technology, 80, pp. 164-180. doi: 10.1016/j.tust.2018.06.015. [95] wang, j.a., park, h.d. (2001). comprehensive prediction of rockburst based on analysis of strain energy in rocks. tunnelling and underground space technology, 16 (1), pp. 49-57. doi: 10.1016/s0886-7798(01)00030-x. [96] zhang, w., feng, x.-t., xiao, y.-x., et al. (2020).a rockburst intensity criterion based on the geological strength index, experiences learned from a deep tunnel. bulletin of engineering geology and the environment, 79, pp. 3585-3603. doi: 10.1007/s10064-020-01774-2. [97] fan, y., lu, w., zhou, y., et al. (2016). influence of tunneling methods on the strainburst characteristics during the excavation of deep rock masses. engineering geology, 201, pp. 85-95. doi: 10.1016/j.enggeo.2015.12.015. [98] yan, p., zhao, z., lu, w., et al. (2015). mitigation of rock burst events by blasting techniques during deep-tunnel excavation. engineering geology, 188, 126-136. doi: 10.1016/j.enggeo.2015.01.011 [99] shang, y., xue, j., wang, s., et al. (2004). a case history of tunnel boring machine jamming in an inter-layer shear zone at the yellow river diversion project in china. engineering geology, 71, pp. 199-211. doi: 10.1016/s0013-7952(03)00134-0 [100] yagiz, s., karahan, h. (2015). application of various optimization techniques and comparison of their performances for predicting tbm penetration rate in rock mass. international journal of rock mechanics and mining sciences, 80, 308-315. doi: 10.1016/j.ijrmms.2015.09.019 [101] xu, z.h., wang, w.y., lin, p., et al. (2021). hard-rock tbm jamming subject to adverse geological conditions: influencing factor, hazard mode and a case study of gaoligongshan tunnel. tunnelling and underground space technology, 108, 103683. doi: 10.1016/j.tust.2020.103683. [102] hoek, e. (2001). big tunnels in bad rock. journal of geotechnical and geoenvironmental engineering. 127 (9), pp. 726-740. [103] liu, x.-x., shen, s.-l., xu, y.-s., et al. (2018). analytical approach for time‐dependent groundwater inflow into shield tunnel face in confined aquifer. int. j. numer. anal. methods geomech., 42, 655-673. doi: 10.1002/nag.2760. [104] hwang, j.-h., lu, c.-c. (2007). a semi-analytical method for analyzing the tunnel water inflow. tunnelling and underground space technology, 22, pp. 39-46. doi: 10.1016/j.tust.2006.03.003. [105] font-capó, j., suñé, e.v., carrera, j., et al. (2011). groundwater inflow prediction in urban tunneling with a tunnel boring machine (tbm). engineering geology, 121, pp. 46-54. doi: 10.1016/j.enggeo.2011.04.012. [106] zhang, c., liu, n., chu, w. (2016). key technologies and risk management of deep tunnel construction at jinping ii hydropower station. journal of rock mechanics and geotechnical engineering, 8, pp. 499-512. doi: 10.1016/j.jrmge.2015.10.010. [107] zhou, x.-p., huang, x.-c., berto, f., (2018). an innovative micromechanics-based three-dimensional long-term strength criterion for fracture assessment of rock materials, frattura ed integrità strutturale, 44, 64-81. doi: 10.3221/igf-esis.44.06 [108] tang, s.b., yu, c.y., heap, m.j., chen, p.z., ren, y.g. (2018). the influence of water saturation on the short and long-term mechanical behavior of red sandstone. rock mechanics and rock engineering, 51, pp. 2669-2687. doi: https://doi.org/10.1007/s00603-018-1492-3 [109] ]okubo, s., fukui, k., hashiba, k. (2010). long-term creep of water-saturated tuff under uniaxial compression. international journal of rock mechanics mining sciences, 47, pp. 839-844. doi: 10.1016/j.ijrmms.2010.03.012. [110] xiong, l., li, t., yang, l. (2014). biaxial compression creep test on green-schist considering the effects of water content and anisotropy. ksce journal of civil engineering, 18(1), pp. 103-112. doi 10.1007/s12205-014-0276-x [111] liu, y., liu, c., kang, y., et al. (2015). experimental research on creep properties of limestone under fluid–solid coupling. environ earth sci, 73, pp. 7011-7018. doi: 10.1007/s12665-015-4022-6 w. frenelus et alii, frattura ed integrità strutturale, 58 (2021) 128-150; doi: 10.3221/igf-esis.58.10 150 [112] lu, y., wang, l. (2017). effect of water and temperature on short-term and creep mechanical behaviors of coal measures mudstone. environ earth sci, 76, 597. doi 10.1007/s12665-017-6941-x [113] hashiba, k., fukui, k., kataoka, m., chu, s.y. (2018). effect of water on the strength and creep lifetime of andesite. international journal of rock mechanics and mining sciences 108, pp. 37-42. doi: 10.1016/j.ijrmms.2018.05.006 [114] li, z., liu, s., ren, w., et al. (2020). multiscale laboratory study and numerical analysis of water-weakening effect on shale. advances in materials science and engineering, 5263431. doi: 10.1155/2020/5263431 [115] cai, x., zhou, z., liu, k., et al. (2019). water-weakening effects on the mechanical behavior of different rock types: phenomena and mechanisms. applied sciences, 9, 4450. doi: 10.3390/app9204450 [116] paraskevopouloua, c., diederichs, m. (2018). analysis of time-dependent deformation in tunnels using the convergence-confinement method. tunnelling and underground space technology, 71, 62-80. doi: 10.1016/j.tust.2017.07.001. [117] kontogianni, v., papantonopoulos, c., stiros, s. (2008). delayed failure at the messochora tunnel, greece. tunnelling and underground space technology, 23, pp. 232-240. doi: 10.1016/j.tust.2007.04.005. [118] chen, s.-h. (2015). hydraulic structures, springer-verlag berlin heidelberg. doi 10.1007/978-3-662-47331-3_13 [119] sulem, j., panet, m., guenot, a. (1987). closure analysis in deep tunnels. international journal of rock mechanics and mining science, 24 (3), pp. 145-154. doi: 10.1016/0148-9062(87)90522-5 [120] pellet, f., sahli, m., boidy, e., et al. (2000). modelling of time-dependent behavior of sandstones for deep underground openings. international symposium on civil engineering in the 21th century, pp. 431-438. [121] wang, j.-x., lin, m.-y., tian, d.-x., zhao, c.-l. (2009). deformation characteristics of surrounding rock of broken and soft rock roadway. mining science and technology, 19(2), pp. 205-209. doi: 10.1016/s1674-5264(09)60039-9 [122] yu, w., wang, w., chen, x., du, s. (2015). field investigations of high stress soft surrounding rocks and deformation control. journal of rock mechanics and geotechnical engineering, 7 (4), pp. 421-433. doi: 10.1016/j.jrmge.2015.03.014 [123] yang, s.-q., tao, y., xu, p., chen, m. (2019). large-scale model experiment and numerical simulation on convergence deformation of tunnel excavating in composite strata. tunnelling and underground space technology, 94, 103133. doi: 10.1016/j.tust.2019.103133 [124] wang, j., li, e., chen, l., wang, j., tan, y., et al. (2019). measurement and analysis of the internal displacement and spatial effect due to tunnel excavation in hard rock. tunnelling and underground space technology, 84, pp. 151165. [125] li, c., hou, s., liu, y., qin, p., et al. (2020). analysis on the crown convergence deformation of surrounding rock for double-shield tbm tunnel based on advance borehole monitoring and inversion analysis. tunnelling and underground space technology, 103, 103513. doi: 10.1016/j.tust.2020.103513 [126] farrokh, e., rostami, j. (2009). effect of adverse geological condition on tbm operation in ghomroud tunnel conveyance project. tunnelling and underground space technology, 24, pp. 436-446. doi: 10.1016/j.tust.2008.12.006. [127] huang, f., wang, y., wen, y., lin, z., zhu, h. (2019). the deformation and failure analysis of rock mass around tunnel by coupling finite difference method and discrete element method. indian geotech j., 49(4), pp. 421-436. doi: 10.1007/s40098-018-0348-9 [128] deleruyelle, f., bui, t.a., wong, h., dufour, n., tran, d.k., zhang, x.s. (2016) analytical study of the postclosure behavior of a deep tunnel in a porous creeping rock mass. c. r. mechanics, 344, pp. 649-660. doi: 10.1016/j.crme.2016.05.003 [129] wang, y.-t., zhang, x., liu, x.-s. (2021). machine learning approaches to rock fracture mechanics problems: mode-i fracture toughness determination. engineering fracture mechanics, 253, 107890. doi: 10.1016/j.engfracmech.2021.107890. microsoft word numero_33_art_44 f. fremy et alii, frattura ed integrità strutturale, 33 (2015) 397-403; doi: 10.3221/igf-esis.33.44 397 focussed on multiaxial fatigue crack tip fields in elastic-plastic and mixed mode i+ii+iii conditions, finite elements simulations and modeling f. fremy, s. pommier lmt (ens cachan / cnrs / université paris saclay) flavien.fremy@ens-cachan.fr, sylvie.pommier@ens-cachan.fr e. galenne edf r&d erwan.galenne@edf.fr s. courtin areva np stephan.courtin@areva.com abstract. this paper is devoted to the analysis of the load path effect on i+ii+iii mixed mode fatigue crack propagation in a 316l stainless steel. experiments were conducted in mode i+ii and in mode i+ii+iii. the same maximum, minimum and mean values of the stress intensity factors were used for each loading path in the experiments. the main result of this set of experiments is that very different crack growth rates and crack paths are observed for load paths that are however considered as equivalent in most fatigue criteria. the experiments conducted in mode i+ii and in mode i+ii+iii, also allowed to show that the addition of mode iii loading steps to a mode i+ii loading sequence is increasing the fatigue crack growth rate, even when the crack path is not significantly modified. keywords. fatigue crack growth; mixed mode; mode i; mode ii; mode iii. introduction ost cyclically loaded machines are subjected to multi-axial loadings. for example, power shafts are usually subjected to a combination of torsion and bending due to the transmission of the torque, the self-weight of the shaft and its rotation speed. for components loaded in proportional multi-axial conditions, the fracture mechanics concepts are normally used to determine the crack path for which the crack is loaded in mode i [1-7]. then, the growth rate is usually predicted using the paris’ law determined in mode i conditions. when non-proportional multiaxial loading conditions are encountered, various approaches have been derived from the paris’ law, to predict the growth rate in mixed mode conditions [1-3]. most of them are based on an equivalent stress intensity factor (eq. 1), whose expression varies according to the authors, but is usually function of the stress intensity factor ranges (eq. 2). da m eqck dn  (1) m f. fremy et alii, frattura ed integrità strutturale, 33 (2015) 397-403; doi: 10.3221/igf-esis.33.44 398   1 n n n n eq i ii iiik k k k        (2) corrections are required to account for the closure effect, or for the in-phase or out-of-phase nature of the fatigue cycles. as a matter of fact, most papers devoted to fatigue crack growth under out-of-phase or sequential mixed mode loading conditions indicate a detrimental effect of the mode-mixity variation during the fatigue cycle and do underline the role of crack tip plasticity [1-7]. a set of experiments was therefore conducted in order to characterize specifically the importance of the load path effect on mixed mode fatigue crack growth, all the other effects being as far as possible kept the same. in these experiments, the stress intensity factor ranges and mean values are the same for each mode and each load path. a static mode i load is always applied so as to limit the effect of crack closure. the tests were conducted with different load paths, yet both "in phase" or both "out of phase", in the sense that the extremes values of the stress intensity factors in each mode are attained simultaneously or not. experiments material & experimental setup he tested material is an aisi 316 l austenitic stainless steel. this material is employed in power plants to produce various components such as pumps, mixing tees and taps because of its excellent resistance to corrosion, its good formability and ductility. the elastic-plastic behavior of this material has been extensively studied in uniaxial and multiaxial conditions [8]. the experiments were conducted on the multiaxial servo-hydraulic testing machine astree, available at lmt-cachan. six actuators are used simultaneously to perform the tests (fig. 1). three pairs of actuators are used to load the specimen along three orthogonal axes and to keep fixed the intersection of the three loading axes fixed. each horizontal loading axis is load controlled. figure 1: six actuators servo-hydraulics testing machine astree, experimental set-up. a cruciform specimen was used for the experiments (fig. 2). a centered 30 mm long slit is machined in the specimen (fig. 2), the slit plane being inclined at 45° with the loading axes of the specimen. linear elastic finite element analyses were conducted in order to determine the relations between the loads fx, fy and fz applied along the three axes of the specimen (fig. 2) and the stress intensity factors ki, kii and kiii at mid-thickness for a coplanar crack propagating from the slit. a mode i stress intensity factor is obtained by applying the same load along the two in-plane axes of the specimen (fx=fy). a mode ii stress intensity factor is obtained by applying fx=-fy. a mode iii stress intensity factor is obtained by applying an out-of-plane load fz. the mode i+ii+iii loading cycles used in the experiments do always include a positive mean value of ki, for three main reasons. first of all, a positive mean value of ki allows limiting the crack closure effects. second, the mean value of ki was determined so that the in-plane loads fx and fy will always remain positive during cycling so as to avoid any buckling of the specimen. third, when an out-of-plane load fz is applied onto the specimen, it induces a bending of the t f. fremy et alii, frattura ed integrità strutturale, 33 (2015) 397-403; doi: 10.3221/igf-esis.33.44 399 specimen and hence it induces a mode i stress intensity factor variation along the crack front. this variation was determined using finite element analyses. it was checked that, for the mixed mode i+ii+iii fatigue cycles used in these experiments, the mode i stress intensity factor induced by the application of the out-of-plane load fz could be neglected with respect to the mode i stress intensity factor induced by the application of the in-plane loads fx=fy. figure 2: schematics of the specimen and of the boundary conditions. loading cases each specimen was pre-cracked in mode i at 10 to 20 hz and at r=0.33 (fx=fy=33.1 kn, fz=0 kn) up to a crack length 2a=34 mm. for this crack length, the stress intensity factors used to pre-crack the specimen corresponds to kimin=5 mpam and kimax=15 mpam. each load path considered in this set of experiments is defined by means of evolutions of the stress intensity factors ki(t), kii(t) and kiii(t). for a crack length 2a=34 mm, the load sequences fx(t), fy(t) and fz(t) that corresponds to the desired evolutions of the stress intensity factors ki(t), kii(t) and kiii(t), are determined using fe simulations. the load sequences fx(t), fy(t) and fz(t) determined for 2a=34 mm are then applied to grow the crack by fatigue up to a length of about 2a=38 mm. in the following, when values of the stress intensity factors are given, they correspond to the start of the test when 2a=34mm. four mixed mode i+ii loadings cases have been studied (fig. 3). each of them is centered around the same mean value for each mode ki = 10 mpam and k  0ii  , and has the same stress intensity factor amplitude for each mode ki=kii=10 mpam. these four cases are all equivalent with respect to the criteria based on an equivalent stress intensity factor (eq. 2) determined in linear elastic conditions. the load paths were constructed as follows:  first, the peak values of ki and kii are attained simultaneously for the “proportional” (fig. 3c), the “square” (fig. 3a) and the “windmill” (fig. 3d) load paths,  second, the cumulative “lengths” of the “square” (fig. 3a) and the “cross” (fig. 3b) load paths are the same, and is one half of that of the “windmill” (fig. 3d) load path,  third, there is one cycle with an amplitude ki=kii=10 mpam in each load path for the “proportional” (fig. 3c), the “square” (fig. 3a) and the “cross” (fig. 3b) load paths. the case of the “windmill” (fig. 3d) load path is somehow different, since we may either count, per load path, two cycles, with an amplitude ki=kii=10 mpam, or, the sum of one cycle with an amplitude 1/2δk δk 10 . . i ii mpa m  and two smaller cycles with an amplitude ki=kii=5 mpam. as in mixed mode i+ii conditions, the loading cases studied in mixed mode i+ii+iii conditions (fig. 4) are centered around the same mean value for each mode ki=10 mpam, kii=0 and kiii=5 mpam, and have the same stress intensity factor amplitude for each mode ki=kii=kiii=10 mpam. they are also equivalent with respect to the criteria in eqs. 2. in addition,  the peak values of ki, kii and kiii are attained simultaneously for the “proportional” (fig. 4b) and the “cube” (fig. 4a) load paths,  the cumulative “lengths” of the “cube” (fig. 4a) and the “star” (fig. 4c) load paths are the same, f. fremy et alii, frattura ed integrità strutturale, 33 (2015) 397-403; doi: 10.3221/igf-esis.33.44 400  the contribution of mode iii to mixed mode fatigue crack growth can be determined by comparing pairs of load cases, namely the two “proportional” load paths (fig. 3c and fig. 4b), the “square” and the “cube” load paths (fig. 3a and fig. 4a) and finally the “cross” and the “star” load paths (fig. 3b and fig. 4c). figure 3: loading cases applied in mixed mode i+ii conditions. a –« square » load path, b – « cross » load path c – « proportional » load path, d – « windmill » load path. figure 4: loading cases applied in mixed mode i+ii+iii conditions. a – « cube » load path, b – « proportional » load path, c – « star» load path. results he results of the fatigue crack growth experiments conducted in mixed mode i+ii conditions indicate that there is a significant load path effect in mixed mode fatigue crack growth (fig 5a). first of all, the crack path is significantly different according to the load path selected. these observations show a significant tilt of the crack path (40°) for the “proportional” load path, after 1 mm of coplanar crack growth in mixed mode conditions. on the contrary, the tilt of the crack path is found to be moderate for the “square” load path (10°) and very small for the two other cases. t f. fremy et alii, frattura ed integrità strutturale, 33 (2015) 397-403; doi: 10.3221/igf-esis.33.44 401 second, in all mixed mode i+ii experiments, below 1 mm of crack propagation, the crack path remained coplanar even for the “proportional” load path. the crack growth rate variations from one test to another can thus be attributed to a load path effect only. the number of cycles required to get a crack extent of 0.65 mm, for instance can typically varies by a factor 3, according to the load path applied in the experiment, though the extreme values and the mean values of the stress intensity factors are kept the same in each experiment. (a) (b) figure 5: (a) evolutions of the crack lengths with the number of cycles applied for each load case in mixed mode i+ii conditions. two curves are plotted for the « windmill » load path, the curve 1, was plotted considering 1 cycle per load path, and the curve 2 considering 2 cycles per load path. (b) evolutions of the crack lengths with the number of cycles applied for each load case in mixed mode i+ii+iii conditions. the results of the fatigue crack growth experiments conducted in mixed mode i+ii+iii conditions are plotted in fig. 5b as in mixed mode i+ii, a very significant load path effect is observed. however, the load path effect is smaller when the extreme values of the stress intensity factors are attained simultaneously for each mode (“cube” and “proportional” load paths). the largest difference is observed between the “cube” and the “star” load paths. as in mixed mode i+ii, below 0.5 mm the crack path remains coplanar and the variations of the growth rate from one test to the other can solely be attributed to the load path effect. the number of cycles required to grow the crack by a=0.5 mm in each mode i+ii+iii test are gathered in tab. 1. according to the loading path the crack growth rate is found to vary by more than a factor 2.in addition, in mixed mode i+ii+iii, the crack path is also significantly varying with the loading case. the effects are more pronounced in mixed mode i+ii+iii than in mixed mode i+ii. the overall inclination of the crack path was roughly characterized at the end of the test, by two angles, the tilt angle () and the twist angle (). f. fremy et alii, frattura ed integrità strutturale, 33 (2015) 397-403; doi: 10.3221/igf-esis.33.44 402 load path number of cycles δni to get δa=0.5 mm δni/δnc 1 m eq n k c a       cube na=4678 0.43 30.82 proportional nb=6216 0.57 28.08 star nc=10920 1.00 23.34 table 1: number of cycles required to grow the crack by fatigue by a=0.5 mm in each experiment, equivalent stress intensity factor  eqk   mpa m   required to get a growth rate  ia / n   m / cycle  assuming eq. 1, with m=3 and c=3.08 10-12. load path “prop.” “ cube ” “ star ” tilt angle  -10° none 40° twist angle  50° 15° 10° table 2: twist angle () through the thickness of the specimen (5 mm) and tilt angle () after the crack has propagated in mixed mode by a=2mm. effect of the load path on the crack path, after the crack has propagated in mixed mode i+ii+iii from 2a=34mm up to 2a=38mm. . the “proportional” loading path has promoted the most severe change in the crack path, since the crack plane has twisted by an angle of about 50°. on the contrary, the fatigue crack growth remains more or less coplanar under the “cube” load path. most surprisingly, the “star” load path is producing a significant tilt and a small twist, while no bifurcation was observed in mode i+ii under the “cross” load path. adding mode iii loading steps (“star”) to a mixed mode i+ii loading cycle (“cross”) did not promote the twisting of the crack path, but induced a tilt. conclusions xperiments were conducted in mode i+ii and in mode i+ii+iii non-proportional loading conditions in order to characterize the load path effect in fatigue crack propagation in a 316l stainless steel and the contribution to fatigue crack growth of mode iii loadings. since the same maximum, minimum and mean values of the stress intensity factors were applied in each experiments, the load paths are all considered as “equivalent” with respect to most of the fatigue crack growth criteria, in particular with those based on   1 n n n n eq i ii iiik k k k        . the main result of this set of experiments is that very different crack growth rates are observed even though the extreme values and the mean values of the stress intensity factors are the same in each test. a variation by up to a factor three of the crack growth rate according to the loading path was observed in these experiments, even when the crack path remained coplanar. in addition, it was shown that the crack path is also significantly dependent of the load path. for instance, the crack path remains coplanar for the “square” load path while a tilt is observed for the “proportional” load path in mixed mode i+ii. in these two cases, the extreme values of the mode i and mode ii stress intensity factors are attained simultaneously. references [1] qian, j., fatemi, a.,mixed mode fatigue crack growth: a literature survey. engineering fracture mechanics, 55(6) (1996) 969‐990. e f. fremy et alii, frattura ed integrità strutturale, 33 (2015) 397-403; doi: 10.3221/igf-esis.33.44 403 [2] hourlier, f., pineau, a., propagation of fatigue cracks under polymodal fatigue, fatigue of engineering materials and structures, 5 (4) (1982) 287-302. [3] bold, p. e., m. w. brown, a review of fatigue crack‐growth in steels under mixed mode‐i and mode‐ii loading, fatigue & fracture of engineering materials & structures, 15(10) (1992) 965‐977. [4] plank, r., kuhn, g., fatigue crack propagation under non-proportional mixed mode loading. engineering fracture mechanics, 62(2‐3) (1999) 203‐229. [5] brown, m. w. b., s. l. wong, fatigue crack growth rates under sequential mixed‐mode i and ii loading cycles. fatigue & fracture of engineering materials & structures, 23(8) (2000) 667‐674. [6] doquet, v., abbadi, m., influence of the loading path on fatigue crack growth under mixed‐mode loading. international journal of fracture, 159(2) (2009) 219‐232. [7] doquet, v., pommier, s:, fatigue crack growth under non-proportional mixed‐mode loading in ferritic‐pearlitic steel. fatigue & fracture of engineering materials & structures, 27(11) (2004) 1051‐1060. [8] benallal, a., legallo, p., an experimental investigation of cyclic hardening of 316‐stainless steel and of 2024‐ aluminum alloy under multiaxial loadings. nuclear engineering and design, 114(3) (1989) 345‐353. microsoft word numero_29_art_29 v. zega et alii, frattura ed integrità strutturale, 29 (2014) 334-342; doi: 10.3221/igf-esis.29.29 334 focussed on: computational mechanics and mechanics of materials in italy integrated structure for a resonant micro-gyroscope and accelerometer v. zega, c. comi, a. corigliano department of civil and environmental engineering, politecnico di milano, piazza leonardo da vinci 32, 20133 milano, italy. valentina.zega@polimi.it, claudia.comi@polimi.it, alberto.corigliano@polimi.it c. valzasina ams division, stmicroelectronics, via tolomeo 1, 20010 cornaredo, (milano), italy carlo.valzasina@st.com abstract. this paper presents the study of the mechanical behavior of a microstructure designed to detect acceleration and angular velocity simultaneously. the new resonant micro-sensor proposed, fabricated by the thelma© surface-micromachining technique, bases detection of two components of external acceleration (one in-plane component and one out-of plane component) and two components of angular velocity (roll and yaw) on the variation of frequency of several elements set in resonance. the device, despite its small dimensions, provides a differential decoupled detection of four external quantities thanks to the presence of four slender beams resonating in bending and four torsional resonators. keywords. mems; gyroscope; accelerometer; resonators. introduction icro-electro-mechanical systems (mems) or microsystems, are micro-sized devices (see e.g. [1, 2]) nowadays largely used in the consumer and automotive market. their diffusion is exponentially increasing in the biomedical market; their use is also growing in structural engineering as efficient and low-cost devices for structural health monitoring. typical examples of widely diffused mems are accelerometers, gyroscopes, pressure sensors. the fast evolution of mems technology is mainly driven by the attempt to reduce the total size of the microsystem, while keeping the power consumption low and the sensitivity high enough for the specific applications. to reduce the cost and the dimensions required to embed several sensors for detecting the various external quantities, there is a trend to integrate a number of detection structures within the same device. several proposals consists in integrating in a single die several sensors with different proof masses, a review of multi-dof inertial mems is presented in [3]. some interesting proposals also exist of multi-axial inertial sensors with a single proof mass: in [4] a five-axis sensor (3-axis accelerometer and 2-axis gyroscope) with capacitive detection was fabricated using silicon bulk micromachining; in [5] a six-axis vortex sensor (3-axis accelerometer and 3-axis gyroscope) with piezo-resistive detection was proposed. in this line of research, in the present work we study an integrated structure for a micro-gyroscope and accelerometer. the device is fabricated by the thelma© surface-micromachining technique [6] that makes it possible to obtain planar suspended structures with relatively small thickness, anchored to the substrate through flexible parts (springs) and m v. zega et alii, frattura ed integrità strutturale, 29 (2014) 334-342; doi: 10.3221/igf-esis.29.29 335 consequently able to displace with respect to the underlying silicon substrate. the proposed four-axis sensor makes use of differential resonant detection for both in-plane and out-of plane acceleration components and roll and yaw velocity components. resonant detection, as compared to other measuring techniques, has the advantage of affording a direct frequency output, of a quasi-digital type, a high sensitivity and a wide dynamic range. while several resonant accelerometers have been proposed in the literature [7-10] there exist a few examples of micro-gyroscopes with resonant detection [11-12]. the proposed device makes simultaneous use of two different operating principles typical of resonant mems: the frequency shift due to the presence of axial stresses in slender resonating beams and the frequency shift due to variations of the so-called electrical stiffness in torsional resonators. in particular, external in-plane acceleration or yaw velocity make the proof masses translate and induce axial forces in bending resonators, while external out-of-plane acceleration or roll velocity make the proof masses tilt and change the electrical stiffness of torsional resonators. the paper is organized as follows. the first section presents the device design, discusses the mechanical behavior of the resonating parts and provides an analytical estimate of the sensitivity. the second section focuses on the fabricated device and presents the results of numerical modal simulations. experimental characterization of the integrated sensor is currently under development. device design device structure he proposed structure is schematically shown in fig. 1. the device is constituted by two moving proof masses attached to the substrate by means of folded springs which allow their translation in the plane and their tilting around the axes a-a. four bending resonators (labelled i, ii, iii and iv in fig. 1) are located beside the masses and attached to them through the external springs and four torsional resonators (labelled 1, 2, 3 and 4 in fig. 1) are directly attached to the masses. the variation of the resonance frequency in the flexural resonators is induced by the presence, upon translation of the inertial mass, of axial stresses while in the torsional resonators it is induced by variations of the so-called “electrical stiffness” to which the resonator mass is subjected. the simultaneous use of these two different type of resonators allows realizing of a four-axis sensor with reduced dimensions. by means of the flexural resonator elements, the integrated detection structure enables differential detection of an angular velocity acting about an out-of-plane direction, the yaw angular velocity ωz, and of a linear acceleration ay along the y-axis. in addition, by means of the torsional resonator elements, the integrated detection structure enables differential detection of an angular velocity acting about the y-axis, the roll angular velocity ωy, and of a linear out-of-plane acceleration az. figure 1: schematic plan view of the structure, for detection of acceleration and angular velocity. t v. zega et alii, frattura ed integrità strutturale, 29 (2014) 334-342; doi: 10.3221/igf-esis.29.29 336 bending and torsional resonators we first focus on the modelling of the two types of resonator which constitute the sensing elements of the integrated structure. the flexural resonators are very thin beams attached to the substrate at one end and to the springs at the other end, at a certain distance h from the anchor point (see fig. 2(a)). the optimal length of h is selected to maximize the sensitivity of the device. the electrostatic driving of the resonator is done by means of an electrode attached to the substrate with initial gap d0; another parallel electrode allows for the sensing. during functioning a polarization voltage vp is applied to the resonator while a small oscillating signal va(t) applied to the driving plate drives the beam to resonance. in the absence of external input, the resonator has the nominal frequency 0f 0 1 2 m ek kf m   (1) where mk , ek and m are the equivalent mechanical and electrostatic stiffness and the equivalent mass, respectively. figure 2: schematic views of the resonators: (a) in-plane view of bending resonator, (b) in-plane and side view of torsional resonator their expressions can be obtained as in [13] making use of the hamiltonian’s principle and searching for the solution, in terms of transverse displacement of the beam, in the form ( , ) ( ) ( )w y t y w t . using as ( )y the eigenfunction of a doubly clamped beam these equivalent properties read:  2 30 2 2 0 02 3 30 0 0 2 0 198.492 2 2 0.397 0.397 h m h p p e h ei k ei dy h sv sv k dy h d d m a dy ah                 (2) where e is the young’s modulus, a and i the area and the momentum of inertia of the cross section, 0 is the dielectric permittivity, s is the out of plane thickness and  the mass density. v. zega et alii, frattura ed integrità strutturale, 29 (2014) 334-342; doi: 10.3221/igf-esis.29.29 337 when, due to an external acceleration or yaw angular velocity, the in-plane inertia force or the coriolis’ force is applied to the proof masses, an axial force n is exerted on the resonators and their frequency changes according due to an additional geometric stiffness term gk  2 0 4.88h gk n dy n h    (3) in the case of a tensile axial load n the beam oscillation frequency increases while in the case of a compressive load it decreases [14-16] according to the relation: 0 1 4.88 1 2 ( ) m g e m e k k k f f n m h k k       (4) since the resonating beam is very slender and the gap d0 is very small, nonlinear effects can appear due to both geometrical and electrostatic effects. however, the presence of the little horizontal part of length h, see fig. 2(a), partially releases the axial constraint, thus lowering the higher order mechanical stiffness terms and widening the regime of linear oscillation. the electrostatic stiffness nonlinearities can be reduced by lowering the actuation voltage va(t); the sensor proposed in this work will be actuated in the linear regime. a detailed discussion on the nonlinear behavior of the resonator can be found in [13,17]. the other resonators included in the device are torsional resonators constituted by a small mass of in-plane dimensions 2b l and out-of-plane thickness s connected to the proof mass by two folded torsional springs, which allow for its outof-plane rotation ( , )x t (see fig. 2(b)). when in the rest position, the mass is at distance 0g from both the electrodes (see fig. 2(b)) and the torsional resonator has the nominal frequency 0 0 1 2 m e mass k k j      (5) with  2 3 30 3 0 22 , 3 m e p lgj k k v b c l g     where j is the torsional momentum of inertia, massj is the centroidal mass moment of inertia of the rigid mass, l is the total length of one of the folded torsional springs and g is the shear elastic modulus. the sensing electrode is usually connected to a virtual ground at zero voltage while the mass is kept at the polarization fixed voltage vp (see fig. 2(b)). by applying a small variable voltage va(t) to the driving electrode the mass is electrostatically actuated and can dynamically vibrate. when, due to external actions, the proof masses tilt, there is a change of gap 0g between the resonators and the electrodes and the frequency changes according to equation (5). as for the bending resonators nonlinear effects can appear for high values of va(t) due to higher order terms in the electrostatic stiffness. the nonlinear behavior and the range of actuation available to ensure operation in the linear regime are studied in [18]. device operation principle during the gyroscope-accelerometer functioning the inertial proof masses are kept in resonance according to their inplane translational mode in x direction by means of electrostatic driving implemented by the respective driving electrodes (see fig. 1). also the bending resonator elements (labeled i, ii, iii, iv in fig. 3) are kept in resonance according to the first flexural mode in the plane along the first axis x, by means of electrostatic interaction with the driving electrodes. in absence of an external angular velocity or linear acceleration, all resonators have the same nominal frequency 0f , see eq. (1). when an external yaw angular velocity ωz is applied, two coriolis’ forces fc originate on the two inertial masses; they are directed along the axis y, have opposite signs (see fig. 3(a)) and have modulus: 2c zf m x   (6) where x is the linear velocity of the inertial masses due to resonant driving and m is their mass. v. zega et alii, frattura ed integrità strutturale, 29 (2014) 334-342; doi: 10.3221/igf-esis.29.29 338 consequently, the resonators, are subjected to an axial action: in particular, two of them, for instance resonators i and iv, are subjected to a compressive force, whereas the other two, for instance ii and iii, are subjected to a tensile force of the same intensity, n, 2 c ii iii i iv f n n n n       (7) where  is a force-amplification factor, depending on the geometry of the resonator and in particular on h. because of the axial stress, the frequency of oscillation of the resonators subjected to compression decreases, whereas the frequency of oscillation of the resonators subjected to tension increases, according to the relation (4). figure 3: schematic plan view of the structure: (a) detection of the yaw angular velocity ωz, (b) detection of the linear acceleration ay combining the readings of frequency of the four bending resonators from equation (4), linearized around the nominal frequency f0, one can compute the external yaw angular velocity ωz 0 0 1 4.88 1 4.88 2 1 1 2 ( ) 2 ( ) 4.88 2 ( ) iii ii i iv z z m e m e z m e f f f f f m x m x h k k h k k f m x h k k                          (8) on the other hand, when an external linear acceleration ay is applied, as shown in fig. 3(b), the inertial masses are subjected to inertia forces fa directed in the y direction, with the same sign and with modulus a yf ma (9) as a result of the inertia forces fa, the bending resonators are again subjected to axial stresses, but in this case, these axial stresses are of the same sign in the resonators i and iii, and they are of the same sign in the resonators ii and iv. 2 a ii iii i iv f n n n n       (10) combining the readings of the four resonators starting once again from equation (4) linearized around the nominal flexural oscillation frequency f0, one obtains a measure of the external acceleration ay: 0 0 1 4.88 1 4.88 4.88 2 1 1 4 ( ) 4 ( ) ( ) i iii ii iv y y y m e m e m e f f f f f m a m a f m a h k k h k k h k k                   (11) therefore, via a different combination of the quantities supplied by the same resonator elements it is possible to detect simultaneously the yaw angular velocity ωz and the linear in-plane acceleration ay; both measures are of differential type. the measure of the roll angular velocity ωy and of the linear out-of-plane acceleration az is performed by means of the torsional elements labeled 1, 2, 3, 4 in fig. 4, kept in resonance according to their torsional natural mode through the driving electrode located below them on the substrate. when an external roll angular velocity ωy is applied, two coriolis’ forces, labeled fc in fig. 4(a), originate on the inertial masses which are oscillating in the x-direction. these forces are directed along the out-of-plane axis z, have opposite signs and the modulus is given by v. zega et alii, frattura ed integrità strutturale, 29 (2014) 334-342; doi: 10.3221/igf-esis.29.29 339 xmf yc ω2 (12) as a result, the two inertial masses rotate about their respective axis of rotation a-a in the same direction (see fig. 4(a)) of the angle: ω 3 3 l tsg rxm β gy  (13) where rg is the distance between the a-a axis of rotation of a proof mass and the center of gravity of the same mass, is the total length of one folded torsional spring attaching the mass to the substrate and t its in-plane thickness. figure 4: schematic plan view of the structure: (a) detection of the roll angular velocity ωy, (b) detection of the linear acceleration az in particular, a first resonator element approach the substrate and its gap reduces to 0g r while the other resonator element move away from the same substrate and its gap increases to 0g r , r being the distance between the a-a axis and the torsional resonator’s axis of rotation. the torsional resonators change their natural frequencies according to (5) as a consequence of their electrostatic stiffness variation  2 3 30 3 1 3 2 3( )1 2 m p mass l k v b c g r j            ,  2 3 30 3 2 4 2 3( )1 2 m p mass l k v b c g r j            (14) by combining the readings of the four torsional resonators and linearizing one obtains the frequency shift which provides a differential measure of the roll angular velocity ωy: 2 1 4 3 0 0 3 0 0 6 18 ge e y m e m e m x rk kr r l k k g k k g g s t                (15) in the presence of linear out-of-plane acceleration az, (see fig. 4(b)), two forces of inertia fa originate on the two inertial masses directed along the axis z, which have in this case the same sign. because of these forces, one inertial mass rotates counterclockwise, while the other rotates clockwise by an angle: 3 3 2 z gm a r l g s t   (16) in this case, therefore, frequency variations of the same sign occur in the torsional resonator elements 1 and 4, and in the torsional resonator elements 2 and 3. similarly to what done for the measure of the roll velocity, combining the readings of the four torsional resonators, the following expression is obtained, allowing for the measure of the external acceleration az : v. zega et alii, frattura ed integrità strutturale, 29 (2014) 334-342; doi: 10.3221/igf-esis.29.29 340 2 1 3 4 0 0 3 0 0 6 9 ge e z m e m e m rk kr r l a k k g k k g g s t              (17) fabricated device he designed integrated structure has been produced with the surface micromachining process thelma© which has been developed by stmicroelectronics to realize silicon inertial sensors and actuators. the main process phases are substrate thermal oxidation, deposition and patterning of horizontal interconnections, deposition and patterning of a sacrificial layer, epitaxial growth of the structural layer, structural layer patterning by trench etch and sacrificial oxide removal and contact metallization deposition (see [6] for more details). the inertial masses of the integrated structures and the proof masses of the torsional resonators have holes to allow the complete oxide removal below it. the produced integrated structure is shown in the sem micrograph of fig. 5. the integrated structure is packed at the pressure of 1mbar with getter to avoid degasing. figure 5: sem image of the integrated structure for a resonant micro-gyroscope and accelerometer numerical analyses the eigenmodes of the device have been calculated through a three dimensional finite element analysis performed by the commercial code comsolmulthyphisics©: the first 6 modes together with the first bending mode of the beam resonators (21st mode for the whole structure) are reported in tab. 1 along with small pictures of the corresponding modal shape. for the sake of an easier visualization, the contours of the magnitude of the displacement are shown on the modal shapes. the driving modes for the inertial masses is around 10 khz, the natural frequency of the torsional resonators is 22.5 khz and the natural frequency of the bending resonators is 243 khz. note that the resonators have been designed to oscillate at very different frequencies in order to obtain similar sensitivities for the out-of-plane and in-plane external acceleration and angular velocity components. the separation of the frequencies also ensure a very low cross-talk in sensing. with a size of the two inertial masses of approximately 420 µm x 470 µm x 22 µm and a bias voltage of 6v, the expected sensitivity as accelerometer in both of the directions y and z is higher than 350 hz/g, while the sensitivity as gyroscope is approximately 0.15 hz/°/s. the experimental characterization of the device is currently under development. t v. zega et alii, frattura ed integrità strutturale, 29 (2014) 334-342; doi: 10.3221/igf-esis.29.29 341 mode # frequency (khz) description 1 1.33 in-plane translation of the whole mass along y-axis 2 2.26 out-of –plane rotation of the whole mass around axis a–a 3 10.11 in-plane translation of the whole mass along x-axis (driving mode) 4 12.61 in-plane rotation of the whole mass around z-axis 5 13.44 torsional mode of the proof mass 6 22.52 first mode of torsional resonators 21 243 first mode of bending resonators table 1: principal modes of the device. because of the device’s symmetry only one half of it is plotted. x y z a a v. zega et alii, frattura ed integrità strutturale, 29 (2014) 334-342; doi: 10.3221/igf-esis.29.29 342 conclusion n the present work, an innovative resonant four-axis inertial sensor has been designed, modelled and fabricated. analytical and numerical finite elements simulations have been used during the design phase for the evaluation of the device performances and for the maximization of its sensitivity. the resulting structure has only two inertial masses and, despite its extremely reduced dimensions, enables differential detection of two different angular velocities and of two different linear acceleration components. resonant detection is used for the four axis, with two different kind of resonators respectively oscillating in bending and in torsion. the differential reading enables detection of the external quantities even in the presence of eigenstresses due e.g. to temperature variations. moreover, the differential reading increases the range of linearity and the sensitivity of the proposed inertial sensor. references [1] senturia, s.d., microsystem design, kluwer academy, dordrecht (2002). [2] gardner, j.w., varadan, v.k., awadelkarim, o.o., microsensors mems and smart devices, wiley, chichester (2001). [3] ayazi, f., multi-dof inertial mems: from gaming to dead reckoning, proc. 16th international solid-state sensors, actuators and microsystems conference, transducers'11, (2011) 2805-2808. [4] watanabe, y., mitsui, t., mineta, t., kobayashi, s., taniguchi, n., okada, k., five-axis motion sensor with electrostatic drive and capacitive detection fabricated by silicon bulk micromachining, sens. actuator a, 97-98 (2002) 109-115. [5] xie, z., chang, h., yang, y., li, x., zhou, p., yuan, w., design and fabrication of a vortex inertial sensor consisting of 3-dof gyroscope and 3-dof accelerometer, in: proc. of the ieee international conference on micro electro mechanical systems (mems), (2012) 551-554. [6] corigliano, a., masi, b.d., frangi, a., comi, c., villa, a. and marchi, m., mechanical characterization of polysilicon through on chip tensile tests, j. microelectromech. syst., 13 (2004) 200-219. [7] zhu, r., zhang, g., chen, g., a novel resonant accelerometer based on nanoelectromechanical oscillator, in: proc. mems 2010, hong kong, (2010) 440-443. [8] comi, c., corigliano, a., langfelder, g., longoni, a., tocchio, a., simoni, b., a resonant micro-accelerometer with high sensitivity operating in an oscillating circuit, j. microelectromech. syst., 19 (2010) 1140 – 1152. [9] kim, h.c., seok, s., kim, i., choi, s-d. , chun, k., inertial-grade out-of-plane and in-plane differential resonant silicon accelerometers (drxls), in: proc. transducers05, seoul, (2005) 172-175. [10] comi, c., corigliano, a., ghisi, a., zerbini, s., a resonant micro accelerometer based on electrostatic stiffness variation, meccanica, 48 (2013) 1893–1900. [11] seshia, a.a., howe, r.t., montague, s., an integrated microelectromechanical resonant output gyroscope, in: proc. mems2002, (2002) 722-726. [12] li, j., fang, j., dong, h., tao, y., structure design and fabrication of a novel dual-mass resonant output micromechanical gyroscope, microsyst. technology, 16, 4 (2010) 543552. [13] comi, c., on geometrical effects in micro-resonators, latin american j. solid and structures, 6 (2009) 73-87. [14] ferrari, v., ghisla, a., marioli, d., taroni, a., silicon resonant accelerometer with electronic compensation of inputoutput cross-talk, sens. actuator a, phys., 123-124 (2005) 258-266. [15] stokey, w., vibration of systems having distributed mass and elasticity. shock and vibration handbook, c. harris, ed. new york: mcgrawhill, 1988. [16] bokaian, a., natural frequencies of beams under tensile axial load, j.sound vib., 142 (1990) 481–498. [17] tocchio, a., comi, c., langfelder, g., corigliano, a., longoni a., enhancing the linear range of mems resonators for sensing applications, ieee sensors journal, 11(12) (2011) 3202-3210. [18] caspani, a., comi, c., corigliano, a., langfelder, g., zega, v., zerbini, s., dynamic non-linear behaviour of torsional resonators in mems, in preparation. i microsoft word numero_51_art_16_2449 s. merdaci et alii, frattura ed integrità strutturale, 51 (2020) 199-214; doi: 10.3221/igf-esis.51.16 199 influence of porosity on the analysis of sandwich plates fgm using of high order shear-deformation theory. slimane merdaci university of sidi bel abbes, bp 89 cité ben m’hidi 22000 sidi bel abbes, algeria. slimanem2016@gmail.com adda hadj mostefa university of rélizane, institut des sciences & technologie, rélizane, algeria. hadj9510@gmail.com abstract. in this article, the analytical solutions for static of bending analysis of functionally graded sandwich plates using four-variable high order shear-deformation theory is presented. during manufacture of these plates, defects such as porosities can appear. the objective of this paper is to develop a model to employ the new function for analysis the static of functionally graded sandwich plates. however, the material properties of the sandwich plate varies according to a power law p-fgm form through the thickness coordinate depending on the volume fraction of the constituent material. equilibrium and stability equations are derived based on the present theory. the solution of the problem is derived by using navier’s technique. the influences of many sandwich plate parameters such of the variation and influences of porosity coefficient, aspect ratio, side-to-thickness ratio and exponent volume fraction will be investigated. keywords. sandwich plates; bending; fgm; porosity; high order theory citation: merdaci, s., hadj mostefa, a., influence of porosity on the analysis of sandwich plates fgm using of high order shear theory, frattura ed integrità strutturale, 51 (2020) 199-214. received: 30.03.2019 accepted: 24.11.2019 published: 01.01.2020 copyright: ©2020 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. introduction omposite materials are known as the modern materials which are composed of two or more different materials, to have the desired properties in specified applications. the lightweight composite materials known as fiber-matrix laminated composites have been used successfully in aircraft, automotive, marine industries and other engineering applications. however, the mismatch in mechanical properties across the interface of two different materials may cause large inter-laminar stresses. functionally graded materials (fgms) are microscopically inhomogeneous spatial composite materials, typically composed of a ceramic-metal or ceramic-polymer pair of materials. therefore, it is important to investigate the behaviors of engineering structures such as beams and plates made from fgms when they are subjected to thermal loads for c http://www.gruppofrattura.it/va/51/2449.mp4 s. merdaci et alii, frattura ed integrità strutturale, 51 (2020) 199-214; doi: 10.3221/igf-esis.51.16 200 appropriate design. frequently, fg plates are made from a mixture of two phases (metallic and ceramic) in which volume fraction of phases changing through the thickness. to remedy such defects, functionally graded materials (fgms), within which material properties vary continuously, have been proposed. the concept of fgm was proposed in 1984 by a group of materials scientists, in sendai, japan, for thermal barriers or heat shielding properties [1]. functionally graded materials (fgms) are recently developed advanced composite materials and are being widely used in various engineering appliances such as nuclear reactors and high speed spacecraft industries. in recent years, these materials have found other applications in electrical appliances, energy transformation, biomedical engineering, optics, etc. [2]. however, in the manufacture of fgm, porosities may occur in the materials during the sintering process. this is due to the large difference in coagulation temperature between the components of the material [3]. wattanasakulpong et al. [4] discussed the porosities that occur in lateral fgm samples made with a multistage sequential filtration technique. so, it is important to take under consideration the porosity effect when designing fg components under the effect of dynamic loadings. based on the open literature, it seems that many investigators have paid attention to the analysis of fgm structures with porosities. most of these investigations are concerned with the vibration behavior of fg porous structures [5–19]. the objective of this article is to present the static of bending behavior of sandwich plates fgm having porosities. the sandwich plate may be either perfectly porous homogeneous or has a perfect homogeneity shape depending on the values of the volume fraction of voids (porosity) or of the graded factors. the sandwich plate is assumed isotropic at any point within the plate, with its young’s modulus varying across its thickness in accord with a power law p-fgm in terms of the volume fractions of the sandwich plate constituents while the poisson’s ratio remains constant. the present theory satisfies equilibrium conditions at the sandwich plate’s top and bottom faces without using shear correction factors. a navier’s solution is used to obtain closed-form solutions for simply supported sandwich plates fg symmetrical. several important aspects, i.e. aspect ratios, thickness ratios, exponent graded factor as well as porosity volume fraction, which affect deflections and stresses, are investigated. this paper explores the following elements:  formulation of the problem (structural model and displacement field and constitutive equations)  equilibrium equations  analytical solutions for fgm sandwich plate  numerical results and discussions formulation of the problem structural model onsider a fg thick rectangular plate of length a, width b and thickness h made of functionally graded material as shown in fig.1 together with the adopted coordinate system. the material properties of the fg plate, such as young’s modulus e, are assumed to be function of the volume fraction of constituent materials. figure 1: geometry and coordinates of the porous sandwich plate fgm. let the sandwich plate fgm be subjected to a transverse load q(x, y), and a rectangular cartesian coordinate of x and y is introduced for the deformation analysis of the plate. the plate under study is bounded by the co-ordinate planes 0 ≤x ≤ a and 0 ≤y ≤ b. the reference surface is the middle surface of the plate defined by z =0, and z denotes the thickness coordinate measured from the un-deformed middle surface. c s. merdaci et alii, frattura ed integrità strutturale, 51 (2020) 199-214; doi: 10.3221/igf-esis.51.16 201 let the present plate is converted from lower to upper surfaces according to an exponential or polynomial laws. we will consider firstly a non-homogeneity material with a porosity volume function, α (0 ≤ α ≤ 1). in such a way, the efficient material properties, as young’s modulus, can be expressed as: 1 2 2 1 0 p z he e e         (1) where p (p ≥ 0) represents a factor that points out the material variation through the thickness. note that the plate is perfectly porous homogeneous when k equals zero and it gets the perfect homogeneity shape when p = α = 0. the functional relationship between e(z) for the ceramic and metal fgm plate is assumed to be is ref. [30-31].    ( ) 2 c m m c me z e e v e e e       and 1 2 p z v h       (2) where ec and em are the corresponding properties of the ceramic and metal, respectively, and “p ” is the volume fraction exponent which takes values greater than or equal to zero. the above power-law p-fgm assumption reflects a simple rule of mixtures used to obtain the effective properties of the ceramic-metal sandwich plate. the rule of mixtures applies only to the thickness direction. note that the volume fraction of the metal is high near the bottom surface of the plate, and that of the ceramic is high near the top surface. furthermore, eqn. (2) indicates that the bottom surface of the plate (z = −h/2) is metal whereas the top surface (z = h/2) of the plate is ceramic. in which n represents number of layers of sandwich plate and (1) ( 2 ) ( 3) 41 1 2 2 3 3 4 2 1 3 4 , [ , ] ; 1 , [ , ] ; , [ , ] pp z hz h v z h h v z h h v z h h h h h h                  (3) table 1: displacement models displacement field and constitutive equations n the present analysis, the shear deformation plate theory is suitable for the displacements (merdaci et al [20-25]): model theory transverse shear function unknown variables cpt classical plate theory   0f z  3 fsdpt first-order shear deformation theory [26]   zf z  5 esdpt exponential shear deformation plate theory [28]   2 2 /( ) . z hf z z e  5 ssdpt sinusoidal shear deformation plate theory [27] ( ) sin zh f z h         5 hsdpt higher-order shear deformation theory[29] 2 2 4 ( ) 1 3 z f z z h        5 present present higher-order shear deformation theory 2 2 51 ( ) 4 3 z f z z h        4 i s. merdaci et alii, frattura ed integrità strutturale, 51 (2020) 199-214; doi: 10.3221/igf-esis.51.16 202 0 0 ( , , ) ( , ) ( ) ( , , ) ( , ) ( ) ( , , ) ( , ) ( , ) b s b s b s w w u x y z u x y z f z x x w w v x y z v x y z f z y y w x y z w x y w x y                 (4) the number of unknown functions is only four, while five or more in the case of other shear deformation theories (tab. 1). the strains associated with the displacements in eqn. (5) are 2 2 2 2 ( ) 1 3 '( ) ( ) 1 '( ) 4 4 5 5df z f z and g z f z dz z z h h       (5) 2 2 0 2 2 2 2 0 2 2 2 2 0 0 ( ) ( ) 2 ( ) 2 ( ) ; ( ) 0 b s x b s y b s xy s s yz xz z u w w z f z x x x v w w z f z y y y u v w w z f z y x x y x y w w g z g z and y x                                                           (6) for elastic and isotropic fgms, the constitutive relations can be written as 11 12 44 12 22 55 66 0 0 0 , 0 0 0 x x yz yz y y zx zx xy xy q q q q q q q                                                (7) where ( x , y , xy , yz , yx ) and ( x , y , xy , yz , yx ) are the stress and strain components, respectively. using the material properties defined in eqn.(1), the stiffness coefficients, ijq , can be expressed as  11 22 11 22 12 44 55 662 2 2 ( ) ( ) ( ) ( ) , , , 2 11 1 1 e z e z e z e z q q q q q q q q                (8) equilibrium equations he static equations can be obtained by using the principle of virtual displacements. it can be stated in its analytical form /2 /2 0 h x x y y xy xy yz yz xz xz h d dz q w d                               (9) where  is the top surface. by substituting eqns. (6) and (7) into eqn. (9) and integrating through the thickness of the plate, eqn. (14) can be rewritten t s. merdaci et alii, frattura ed integrità strutturale, 51 (2020) 199-214; doi: 10.3221/igf-esis.51.16 203   0 0 0 0 b b b b b b s s x x y y xy xy x x y y xy xy x x s s s s s s s s y y xy xy yz yz xz xz b n n n m k m k m k m k m k m k s s d q w ws d                                        (10) where the stress resultants n, m, and s are defined by   /2 ( ) /2 , , 1 , , , , , ( ), , x y xy h nb b b x y xy x y xy hs s s x y xy n n n m m m z dz f zm m m                                /2 ( ) /2 , , ( ) . h ns s xz yz xz yz h s s g z dz      (11) where a is the top surface, and the stress resultants n, m, and s are defined by: , , s b s b s s s s s s n a b b m a d d k s a m b d h k                              (12) 0 12 11 1211 12 11 0 12 22 12 22 12 22 11 12 11 12 11 12 12 22 12 22 12 22 11 12 11 12 11 12 12 22 12 22 12 22 s s x x s sy y b bs s x x b s s y s s s s s s s x s s s s s s s y n b b ba a b n a a b b b b m b b d kd d d m kb b d d d d m b b d d h h m b b d d h h                                             0 11 66 66 66 66 66 66 66 66 44 55 0 0 b y s x s y s xy xy b s b xy xy s s ss s xy xy s s yz yz ss xzxz k k n a b b m b d d k b d hm k s a as                                                                                 (13) where aij , bij , etc. are the plate stiffness defined by   1 11 11 11 11 11 11 3 ( ) 2 2 ( ) 12 12 12 12 12 12 11 1 ( ) 66 66 66 66 66 66 1 1, , , ( ), ( ), ( ) 1 2 n n s s s h s s s n n n hs s s n a b d b d h a b d b d h q z z f z z f z f z dz a b d b d h                                  (14a)     ( )22 22 22 22 22 22 11 11 11 11 11 11 11 2 ( ) , , , , , , , , , , , 1 s s s s s s n e za b d b d h a b d b d h q     (14b)     13 2 44 55 1 ( ) ( ) , 2 1 n n h s s n h e z a a g z dz         (14c) s. merdaci et alii, frattura ed integrità strutturale, 51 (2020) 199-214; doi: 10.3221/igf-esis.51.16 204 the governing equations of equilibrium can be derived from eqn.(10) by integrating the displacement gradients by parts and setting the coefficients δu, δv, δwb, and δws zero separately. thus, one can obtain the equilibrium equations associated with the present shear deformation theory, 2 22 2 2 2 22 2 2 : 0 : 0 : 2 0 : 2 0 xyx xy y b bb xy yx b s s s ss xy y xz yzx s nn u x y n n v x y m mm w q x yx y m m s sm w q x y x yx y                                        (15) analytical solutions for fgm sandwich plate he following simply-supported boundary conditions are imposed at the side edges of the fg sandwich plate:          0, 0, 0, 0, 0, 0b sb s w w v y w y w y y y y y          (16a)          , , , , , 0b sb s w w v a y w a y w a y a y a y y y          (16b)            0, 0, 0, , , , 0b s b sx x x x x xn y m y m y n a y m a y m a y      (16c)          , 0 , 0 , 0 , 0 , 0 0b sb s w w u x w x w x x x x x          (16d)          , , , , , 0b sb s w w u x b w x b w x b x b x b x x          (16e)            , 0 , 0 , 0 , , , 0b s b sy y y y y yn x m x m x n x b m x b m x b      (16f) figure 2: boundary conditions for full plate. t s. merdaci et alii, frattura ed integrità strutturale, 51 (2020) 199-214; doi: 10.3221/igf-esis.51.16 205 the external force according to navier’s solution can be expressed as 1 1 ( , ) sin( )sin( )mn m n q x y q x y        (17) where /m a  and /n b  , « m » and « n »are mode numbers. for the case of a sinusoidally distributed load, we have 1m n  and 11 0q q (18) where q0 represents the intensity of the load at the plate center. following the navier solution procedure, we assume the following form of solution for (u,v,wb,ws) that satisfies the boundary conditions cos( )sin( ) sin( )cos( ) , sin( )sin( ) sin( )sin( ) mn mn b bmn s smn u u x y v v x y w w x y w w x y                                    (19) where umn, vmn,wbmn, and wsmn are arbitrary parameters. eqn.(15) in combination with eqn. (16) can be combined into a system of first order equations as:     ,k f  (20) where   and  f denotes the columns    , , , ,t mn mn bmn smnu v w w  and    0, 0, , t mn mnf q q   (21) and   11 12 13 14 12 22 23 24 13 23 33 34 14 24 34 44 a a a a a a a a k a a a a a a a a             (22) the elements aij = aji of the coefficient matrix [k]. the elements of the symmetric matrix [k] presented in eqn. (23) are given by  2 211 11 66a a a     12 12 66 a a a    2 213 11 12 66 [ ( 2 ) ]a b b b     2 214 11 12 66 [ ( 2 ) ] s s sa b b b     (23) s. merdaci et alii, frattura ed integrità strutturale, 51 (2020) 199-214; doi: 10.3221/igf-esis.51.16 206         2 2 22 66 22 2 2 23 12 66 22 2 2 24 12 66 22 4 2 2 4 33 11 12 66 22 4 2 2 4 34 11 12 66 22 4 2 2 4 2 2 44 11 12 66 22 55 44 [( 2 ) ] [( 2 ) ] 2( 2 ) 2( 2 ) 2( 2 ) s s s s s s s s s s s s s a a a a b b b a b b b a d d d d a d d d d a h h h h a a                                                 numerical results and discussions n this section, the present refined theory is applied to the bending analysis of sandwich plates fgm and. the poisson’s ratio is fixed at ν = 0.3, and comparisons are made with available solutions. numerical case studies are used to verify the accuracy of the present analysis. the fg plate is taken to be made of aluminum and alumina with the following material properties: • metal (aluminum, al): em = 70 gpa; ν = 0.3. • ceramic (alumina, al2o3): ec = 380 gpa; ν = 0.3. the various non-dimensional parameters used are: 2 0 2 2 0 0 0 10 10 , , , , , , , 2 2 2 2 2 2 2 3 x yx y he a b h a b h h a b h w w a q a q a q                       0 0 0 0, , 0 , , 0, , 0, 0, , / 2 2 6 3 xz yz xyxz yz xy h b h a h h h z z h aq aq aq                           the deflections and the dimensionless stresses of the square fg plate (a/h = 10) for different values of the volume fraction p are presented including tab.2. the present predictions (present refined theory) are compared with the cpt, first-order shear deformation theory (fsdpt) [26], higher-order (hsdpt) [29], exponential (esdpt) [28] and sinusoidal (ssdpt) [27]. it should be noted that all theory (cpt, fsdpt, esdpt, hsdtt and ssdpt) were obtained on the basis of sinusoidal variation of both in-plane and transverse displacements across the thickness. it can be seen that ssdpt [27] presented sinusoidal theory with five unknowns. the present non-porous results (α = 0) almost more accurate than those generated by other theories. also, the present results are compared well with those of other solution. the deflections dimensionless of the square plate (a=b=1) symmetrical and unsymmetrical sandwich plate fgm (a/h = 10) for different values of the volume fraction p are presented in fig.3. this figure shows that the displacement variation increases as p and α=0 (noporosity) increases, as we notice that the displacement variation of symmetrical fg and bigger than compared the symmetrical and unsymmetrical sandwich plate fgm. in fig.4, the effect of the material index p on the adimensional displacement w of the perfect and imperfect fgm plate for values of the thickness ratio (a/h = 10) of the sandwich plate and different values of porosity coefficient using the present high order shear theory are illustrated in fig.3. it should be noted that the dimensionless displacement increases with the increase of the value of the power law index for the perfect and imperfect sandwich plate fgm and that for the thickness ratio. displacements are higher for metal plates while displacements are lower for all-ceramic plates (p = 0). there is a rapid variation in displacements for the low values of the ratio a/h where the plate is considered thick. exceeding this ratio of the material index p = 2, the displacements keep a more or less constant look and this for the i s. merdaci et alii, frattura ed integrità strutturale, 51 (2020) 199-214; doi: 10.3221/igf-esis.51.16 207 different values of coefficient of the porosity. fig. 4 shows that the deflection increases as α and p increases. for greater values of α, the differences in deflections may be more than double. theories p w x y yz xz xy cpt ceramic 0.07722 1.97576 1.31718 0.15915 0.15915 0.70925 fsdpt(k =5/6)[26] 0.07722 1.97576 1.31718 0.15916 0.15916 0.70925 ssdpt[27] 0.07769 1.98392 1.31508 0.18995 0.20359 0.70812 esdpt[28] 0.07770 1.98428 1.31502 0.19090 0.20740 0.70809 hsdpt[29] 0.07709 1.97408 1.31761 0.15111 0.14874 0.70948 present 0.07791 1.99432 1.31236 0.21206 0.23857 0.70666 cpt p=1 0.19586 0.93765 1.54787 0.19570 0.26880 0.83347 fsdpt(k =5/6)[26] 0.19586 0.93765 1.54787 0.19570 0.26880 0.83347 ssdpt[27] 0.19610 0.94056 1.54745 0.20986 0.30894 0.83324 esdpt[28] 0.19610 0.94070 1.54751 0.20974 0.31299 0.83327 hsdpt[29] 0.19577 0.93697 1.54798 0.19104 0.25827 0.83353 present 0.19609 0.94370 1.54687 0.21637 0.33433 0.83293 cpt p=2 0.28509 1.36934 1.36210 0.19078 0.34892 0.73344 fsdpt(k =5/6)[26] 0.28509 1.36934 1.36210 0.19078 0.34892 0.73344 ssdpt[27] 0.28514 1.37294 1.36172 0.19822 0.38854 0.73324 esdpt[28] 0.28511 1.37311 1.36177 0.19739 0.39220 0.73326 hsdpt[29] 0.28502 1.36847 1.36220 0.18759 0.33768 0.73349 present 0.28490 1.37662 1.36123 0.19888 0.40919 0.73297 cpt p=3 0.336721 1.61758 1.25527 0.17464 0.41003 0.67591 fsdpt(k =5/6)[26] 0.33672 1.61758 1.25527 0.17464 0.41003 0.67591 ssdpt[27] 0.33666 1.62155 1.25475 0.17975 0.45234 0.67564 esdpt[28] 0.33660 1.62171 1.25478 0.17864 0.45568 0.67565 hsdpt[29] 0.33667 1.61661 1.25541 0.17195 0.39739 0.67599 present 0.33624 1.62552 1.25415 0.17844 0.47133 0.67531 cpt p=4 0.36538 1.75385 1.23316 0.15823 0.45817 0.66401 fsdpt(k =5/6)[26] 0.36538 1.75385 1.23316 0.15823 0.45817 0.66401 ssdpt[27] 0.36527 1.75807 1.23249 0.16289 0.50554 0.66365 esdpt[28] 0.36519 1.75823 1.23251 0.16173 0.50878 0.66366 hsdpt[29] 0.36532 1.75281 1.23333 0.15568 0.44369 0.66410 present 0.36474 1.76229 1.23174 0.16129 0.52541 0.66325 cpt p=5 0.3818576 1.83097 1.24289 0.14497 0.49709 0.66925 fsdpt(k =5/6)[26] 0.38186 1.83097 1.24289 0.14497 0.49709 0.66925 ssdpt[27] 0.38175 1.83541 1.24208 0.14989 0.55087 0.66881 esdpt[28] 0.38166 1.83557 1.24209 0.14877 0.55423 0.66882 hsdpt[29] 0.38177 1.82984 1.24307 0.14228 0.48020 0.66935 present 0.38116 1.83989 1.24120 0.14864 0.57337 0.66834 cpt metal 0.41919 1.97576 1.31718 0.15916 0.15916 0.70925 fsdpt(k =5/6)[26] 0.41919 1.97576 1.31718 0.15916 0.15916 0.70925 ssdpt[27] 0.42172 1.98392 1.31508 0.18995 0.20359 0.70812 esdpt[28] 0.42180 1.98428 1.31502 0.19090 0.20740 0.70809 hsdpt[29] 0.41847 1.97408 1.31761 0.15111 0.14874 0.70948 present 0.42294 1.99432 1.31236 0.21206 0.23857 0.70666 table. 2: comparative study of deflections and stress non-dimensional of sandwich plate fgm for different volume fraction value. s. merdaci et alii, frattura ed integrità strutturale, 51 (2020) 199-214; doi: 10.3221/igf-esis.51.16 208 figure 3: displacement variation as a function of the power index p and the porosity factor α=0 of sandwich plate fgm. figure 4: displacement variation w as a function of the power index p and the different porosity factor α of sandwich plate fgm figure 5: dimensionless displacement variation as a function of the thickness ratio a/h for the different values of porosity coefficient for plate sandwich fgm. s. merdaci et alii, frattura ed integrità strutturale, 51 (2020) 199-214; doi: 10.3221/igf-esis.51.16 209 figure 6: variation of dimensional displacement as a function of the geometric ratio a/b for the different values of porosity coefficient for plate sandwich fgm. fig.5, shows the increase in dimensionless displacements, which is explained by the influence of material stiffness, ie an increase in the value of the power index p, leads to a decrease in the modulus of elasticity of the material plate. in other words, the plates become flexible as the power law index increases, and thus increase the displacement values. in addition, the porosity (α) leads to a remarkable increase in plate displacement. an increase in the ratio (a/h) leads to an increase in adimensional displacements. we can also say that the thickness ratio (a/h) has a considerable effect on dimensionless displacement. in fig.6, we study adimensional displacement variation as a function of the geometric ratio (a/b) for the different values of porosity coefficient with a ratio of equal thickness (a/h = 10) and a material index p = 2 for this plate sandwich fgm. decreasing of said ratio makes lowering of displacement. figure 7: variation of stress non-dimensional x as a function of the power index p and the different porosity factor α of sandwich plate fgm. now, the results for the fg thick (a/h = 10), square (b = a) sandwich plates are presented for various values of the porosity (α) and the graded p parameters. fig. 7 shows the variation of stress x of the sandwich plate embedding an fg s. merdaci et alii, frattura ed integrità strutturale, 51 (2020) 199-214; doi: 10.3221/igf-esis.51.16 210 core for different exponential factor p. this figure shows that the stress x increases as p and α=0 (no porosity)increases, as we notice that the stress will have a decrease in the presence of porosity factor α≠0. in fig.8 shows the variation of stress non-dimensional y of the sandwich plate embedding an fg core for different exponential factor p and for different porosity factor α (0.1, 0.2 and 0.3) for the stress non-dimensional y . it should be noted that the stress dimensionless increases with the increase of the value of the power law index p and the different porosity factor α for the perfect and imperfect fgm plate sandwich and that for the thickness ratios (a/h=10). figure 8: variation of stress non-dimensional as a function of the power index p and the different porosity factor α of sandwich plate fgm. in figs.9, 10 and 11 , contains the variation of the transverse shear stress across the exponent of the volume fraction p for the sandwich plate fgm. the effect of the porosity of the fgm plate was taken into account by means of the introduction of the coefficient (α). four values are therefore retained (α = 0, 0.1, 0.2 and 0.3). for figs.6 the transverse shear stress non-dimensional xy has an increase with respect to power index p = 1 afterwards one observes a decrease of these transverse shear stress according to the decrease of factor of porosity which has an influence this plate sandwich. in figs.10 and 11 it can be seen that the increase in the index of porosity (α) leads to an increase in stresses. this can be justified by the fact that the porosity reduces the rigidity of the plate. the stresses are tensile above the median plane and compression below the median plane. it is important to observe that the maximum stress depends on the value of the exponent of the volume fraction p. figure 9: variation of tangential stress non-dimensional xy as a function of the power index p and the different porosity factor α of sandwich plate fgm. s. merdaci et alii, frattura ed integrità strutturale, 51 (2020) 199-214; doi: 10.3221/igf-esis.51.16 211 figure 10: variation of tangential stress non-dimensional xz as a function of the power index p and the different porosity factor α of sandwich plate fgm. figure 11: variation of tangential stress non-dimensional yz as a function of the power index p and the different porosity factor α of sandwich plate fgm. conclusion new simple for four-variable theory of high order shear and normal deformation theory is developed for functionally graded sandwich plates fgm. the principle of virtual displacements is used to derive the governing equations and boundary conditions. then, analytical solutions for functionally graded porous square sandwich plates are presented. the inclusions of porosity parameters and exponent of the volume fraction p are investigated. the effects of various parameters, such as thickness ratio, gradient index, and volume fraction of porosity on the flexion of fgm ceramic-metal sandwich plates symmetrical are all discussed. many validations examples are reported and numerical results of the present high order shear and normal deformation theory is accurate in predicting the static of bending response of non-porous sandwich plates. in addition, the present theory gave control results that can be used to evaluate various plate theories, and also to compare with the results obtained by another solution (cpt, fsdpt, esdpt, ssdpt and hsdpt). from this work, it can be said that the present and simple theory for the resolution of the mechanical behavior of fgm plates sandwich with porosity that presses manufacturing defects. a s. merdaci et alii, frattura ed integrità strutturale, 51 (2020) 199-214; doi: 10.3221/igf-esis.51.16 212 references [1] koizumi, m. (1997). fgm activities in japan[j]. composites;28(1–2): pp.1–4. doi: 10.1016/s1359-8368(96)00016-9 [2] suresh, s., mortensen, a. (1998). fundamental of functionally graded materials. london: maney. doi: 10.1016/j.compscitech.2007.08.029 [3] zhu, j., lai, z., yin, z., jeon, j., lee, s. (2001). fabrication of zro2–nicr functionally graded material by powder metallurgy. mater chem phys 68, pp.130–5. doi: 10.1016/j.msea.2009.01.066 [4] wattanasakulpong, n., prusty, b.g., kelly, d.w., hoffman, m. (2012). free vibration analysis of layered functionally graded beams with experimental validation 36, pp.182–90. doi:10.1016/j.matdes.2011.10.049 [5] rezaei, a.s., and saidi, a.r. (2015). exact solution for free vibration of thick rectangular plates made of porous materials, compos. struct. 134, pp.1051–1060. doi: 10.1016/j.compstruct.2015.08.125 [6] behravan rad, a., shariyat, m. (2015). three-dimensional magneto-elastic analysis of asymmetric variable thickness porous fgm circular plates with non-uniform tractions and kerr elastic foundations, compos. struct. 125, pp.558– 574. doi: 10.1016/j.compstruct.2015.02.049 [7] rezaei, a.s., and saidi, a.r.. (2016). application of carrera unified formulation to study the effect of porosity on natural frequencies of thick porous-cellular plates, composites, part b, eng. 91, pp.361–370. doi: 10.1016/j.compositesb.2015.12.050 [8] chen, d., yang, j., kitipornchai, s. (2016). free and forced vibrations of shear deformable functionally graded porous beams, int. j. mech. sci. 108–109, pp.14–22. doi: 10.1016/j.ijmecsci.2016.01.025 [9] chen, d., kitipornchai, s., yang, j. (2016). nonlinear free vibration of shear deformable sandwich beam with a functionally graded porous core, thin-walled struct. 107, pp.39–48. doi: 10.1016/j.tws.2016.05.025 [10] ebrahimi, f., jafari, a., barati, m.r. (2017). vibration analysis of magneto–electro-elastic heterogeneous porous material plates resting on elastic foundations, thin-walled struct. 119, pp.33–46. doi:10.1016/j.tws.2017.04.002 [11] rezaei, a.s., saidi, a.r., abrishamdari, m., pour mohammadi, m.h. (2017). natural frequencies of functionally graded plates with porosities via a simple four variable plate theory: an analytical approach, thin-walled struct. 120, pp. 366–377. doi: 10.1016/j.tws.2017.08.003. [12] rezaei, a.s., and saidi, a.r. (2017). on the effect of coupled solid–fluid deformation on natural frequencies of fluid saturated porous plates, eur. j. mech. a, solids 63, pp. 99–109. doi:10.1016/j.euromechsol.2016.12.006. [13] lhoucine, b., khalid, e., and rhali, b. (2017). thermal behavior analysis at large free vibration amplitudes of thin annular fgm plates with porosities, proc. eng. 199, pp.528–533. doi: 10.1016/j.proeng.2017.09.148. [14] al rjoub, y.s., and hamad, a.g. (2017). free vibration of functionally euler–bernoulli and timoshenko graded porous beams using the transfer matrix method, ksce j. civ. eng. 21(3), pp.792–806. doi:10.1007/s12205-016-0149-6 [15] ghorbanpour arani, a., khani, m., and khoddami maraghi, z. (2017). dynamic analysis of a rectangular porous plate resting on an elastic foundation using high-order shear deformation theory, j. vib. control. 24(3), pp.1–16. doi: 10.1177/1077546317709388. [16] chen, d., kitipornchai, s., and yang, j. (2018). dynamic response and energy absorption of functionally graded porous structures, mater. des. 140, pp.473–487. doi: 10.1016/j.matdes.2017.12.019. [17] barati, m.r. (2018).a general nonlocal stress–strain gradient theory for forced vibration analysis of heterogeneous porous nanoplates, eur. j. mech. a, solids 67, pp.215–230. doi: 10.1016/j.euromechsol.2017.09.001. [18] barati, m.r. (2018).vibration analysis of porous fg nanoshells with even and uneven porosity distributions using nonlocal strain gradient elasticity, acta mech. 229, pp.1183–1196. doi:10.1007/s00707-017-2032-z. [19] barati, m.r., and shahverdi, h. (2018). nonlinear vibration of nonlocal four-variable graded plates with porosities implementing homotopy perturbation and hamil-tonian methods, acta mech. 229, pp. 343–362. doi: 10.1007/s00707-017-1952-y [20] merdaci, s., tounsi, a., houari, m.s.a., mechab, i., hebali, h., and benyoucef, s. (2011). two new refined shear displacement models for functionally graded sandwich plates. arch appl mech, 81, 1507e22. doi: 10.1007/s00419-010-0497-5 [21] merdaci, s., tounsi, a., bakora, a. (2016). “ a novel four variable refined plate theory for laminated composite plates” ; an international journal steel & composite structures. 22(4), pp.713-732. doi: 10.12989/scs.2016.22.4.713 [22] merdaci, s. (2017). “study and comparison of different plate theory”; international journal of engineering research and advanced technology (ijerat); 3(8), pp.49-59. doi: 10.7324/ijerat.3130. s. merdaci et alii, frattura ed integrità strutturale, 51 (2020) 199-214; doi: 10.3221/igf-esis.51.16 213 [23] hadj mostefa, a., merdaci, s., and mahmoudi, n. (2018). an overview of functionally graded materials «fgm», proceedings of the third international symposium on materials and sustainable development, pp.267–278. doi:10.1007/978-3-319-89707-3. [24] merdaci, s. (2018). analysis of bending of ceramic-metal functionally graded plates with porosities using of high order shear theory, advanced engineering forum, 30, pp.54-70. doi: 10.4028/www.scientific.net/aef.30.54. [25] merdaci, s., and belghoul, h. (2019). high order shear theory for static analysis functionally graded plates with porosities, comptes rendus mecanique, 347(3), pp.207-217. doi: 10.1016/j.crme.2019.01.001. [26] timoshenko, p. and gere, j.m. (1972). mechanics of materials. new york: d.van nostrand company. https://www.worldcat.org/title/mechanics-of-materials/oclc/251209 [27] karama, m., afaq, k.s., and mistou, s. (2003). mechanical behaviour of laminated composite beam by the new multilayered laminated composite structures model with transverse shear stress continuity, int. j. solids structures; 40 (6), pp.1525-1546. doi: 10.1016/s0020-7683(02)00647-9 [28] touratier, m. (1991). an efficient standard plate theory. engng sci, 29(8), pp. 901-916. doi: 10.1016/0020-7225(91)90165-y. [29] reddy, j.n. (1984). asimple higher-order theory for laminated composite plates. trans. asme j. appl. mech. 51, pp.745–752. doi:10.1115/1.3167719. [30] praveen,g.n., and reddy, j.n. (1998). nonlinear transient thermoelastic analysis of functionally graded ceramic– metal plates. int. j. solids struct. 35, pp.4457–4476. doi:10.1016/s0020-7683(97)00253-9. [31] najafizadeh, m.m., eslami, m.r. (2002). buckling analysis of circular plates of functionally graded materials under uniform radial compression.int. j. mech. sci. 44, 2479–2493. doi: 10.1016/s0020-7403(02)00186-8 [32] merdaci, s., belmahi, s., belghoul, h., and hadj mostefa, a. (2019). free vibration analysis of functionally graded plates fg with porosities, (ijert), 8(3), pp.143-147. https://www.univusto.dz/site_divers/ajrt/article2/analysisofbendingfunctionallygradedplateswithporositiesusin ghighordersheartheory.pdf [33] merdaci, s., (2019). free vibration analysis of composite material plates "case of a typical functionally graded fg plates ceramic/metal" with porosities, nano hybrids and composites (nhc), 25, pp.69-83. doi: 10.4028/www.scientific.net/nhc.25.69. [34] merdaci, s. (2018). analysis of bending of functionally graded plates with porosities using of high order shear theory, algerian journal of research and technology ajrt, 2, pp. 54-69. https://www.ijert.org/research/freevibration-analysis-of-functionally-graded-plates-fg-with-porosities ijertv8is030098.pdf. [35] merdaci, s., boutaleb, s., hellal, h., and benyoucef, s. (2019). analysis of static bending of plates fgm using refined high order shear deformation theory, j. build. mater. struct. 6(1), pp.32-38. doi: 10.5281/zenodo.2609306. nomenclature a : length of the plate aij : rigidity terms in membrane of the plate b : width of the plate bij : rigidity terms of coupling the plate h : total thickness of the plate dij : rigidity terms of bending the plate q : intensity of load s ija : rigidity terms of the plate in shear u, v, w : displacement in x, y and z directions, respectively s ijb : rigidity terms of the plate in shear uo, vo, wo : mid-plane displacements in x, y and z directions, respectively s ijd : rigidity terms of the plate in shear x, y, z : cartesian co-ordinates s ijh : rigidity terms of the plate in shear ec and em are the corresponding properties of the ceramic and metal n : normal membrane efforts v: volume fraction mb : moments of pure bending p : exponent graded factor ms : additional bending moment due to transverse shear α : porosity volume fraction s : pure shearing effort. s. merdaci et alii, frattura ed integrità strutturale, 51 (2020) 199-214; doi: 10.3221/igf-esis.51.16 214 f(z) : warping function (transverse shear function)  : the upper surface. f ’(z) : the first derivative of the warp function with respect to z qij : the stiffness coefficients x , y , z : normal stresses i, j : natural numbers. xy , yz , yx : shear stress [k]: symmetrical matrix x , y : deformation in the x, y and z direction   : vector of generalized displacements xy , yz , yx : distortion deformation {f} : vector of generalized efforts u , v , bw , sw : virtual field of displacement w : non-dimensional central deflection wb: flexural components x , y , xy , xz , yz : non-dimensional stresses ws: shear components z : coordinate thickness m, n : mode numbers. << /ascii85encodepages false /allowtransparency false /autopositionepsfiles true /autorotatepages /none /binding /left /calgrayprofile (dot gain 20%) 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/hrv (za stvaranje adobe pdf dokumenata najpogodnijih za visokokvalitetni ispis prije tiskanja koristite ove postavke. stvoreni pdf dokumenti mogu se otvoriti acrobat i adobe reader 5.0 i kasnijim verzijama.) /hun 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can be opened with acrobat and adobe reader 5.0 and later.) >> /namespace [ (adobe) (common) (1.0) ] /othernamespaces [ << /asreaderspreads false /cropimagestoframes true /errorcontrol /warnandcontinue /flattenerignorespreadoverrides false /includeguidesgrids false /includenonprinting false /includeslug false /namespace [ (adobe) (indesign) (4.0) ] /omitplacedbitmaps false /omitplacedeps false /omitplacedpdf false /simulateoverprint /legacy >> << /addbleedmarks false /addcolorbars false /addcropmarks false /addpageinfo false /addregmarks false /convertcolors /converttocmyk /destinationprofilename () /destinationprofileselector /documentcmyk /downsample16bitimages true /flattenerpreset << /presetselector /mediumresolution >> /formelements false /generatestructure false /includebookmarks false /includehyperlinks false /includeinteractive false /includelayers false /includeprofiles false /multimediahandling /useobjectsettings /namespace [ (adobe) (creativesuite) (2.0) ] /pdfxoutputintentprofileselector /documentcmyk /preserveediting true /untaggedcmykhandling /leaveuntagged /untaggedrgbhandling /usedocumentprofile /usedocumentbleed false >> ] >> setdistillerparams << /hwresolution [2400 2400] /pagesize [612.000 792.000] >> setpagedevice microsoft word numero_34_art_47 v. oborin et alii, frattura ed integrità strutturale, 34 (2015) 422-426; doi: 10.3221/igf-esis.34.47 422 focussed on crack paths multiscale study of fracture in aluminum-magnesium alloy under fatigue and dynamic loading vladimir oborin, mikhail bannikov, oleg naimark, mikhail sokovikov, dmitry bilalov institute of continuous media mechanics of ural branch of ras, 614013, perm, russia oborin@icmm.ru, mbannikov@icmm.ru, naimark@icmm.ru, sokovikov@icmm.ru, ledon@icmm.ru abstract. in this paper we investigated the influence of consecutive dynamic and gigacycle fatigue loads on the lifetime of aluminum-magnesium alloy almg6. preloading of samples was achieved during dynamic tensile tests in the split-hopkinson bar device. fatigue tests were conducted on shimadzu usf-2000 ultrasonic fatigue testing machine. this machine provides 109-1010 loading cycles with the amplitude from 1 to several dozens of microns and frequency of 20 khz, which reduces dramatically the testing time in the comparison to the classical fatigue testing machines. the new-view 5010 interferometer–profiler of high structural resolution (resolution of 0.1 nm) was used for qualitative fracture surface analysis, which provided the data allowing us to find correlation between mechanical properties and scale-invariant characteristics of damage induced roughness formed under dynamic and gigacycle fatigue loading conditions. original form of the kinetic equation was proposed, which links the rate of the fatigue crack growth and the stress intensity factor using the scale invariant parameters of fracture surface roughness. the scale invariance characterizes the correlated behavior of multiscale damage provides the link of crack growth kinetics and the power exponent of the modified paris law. keywords. fracture; gigacycle fatigue; scaling; surface morphology; fractal analysis; paris law. introduction he assessment of the lifetime of critical engineering structures, in particular those for aircraft engines, poses qualitatively new fundamental problems related to evaluation of the reliability of materials under cyclic loading in excess of 109–1010 cycles corresponding to the so-called gigacycle fatigue range. this interest is caused by the fact that the fatigue lifetime of critical structures operating under cyclic loading conditions exceeds a gigacycle fatigue range. the gigacycle fatigue range can be characterized by some features, where of special interest is the range pertaining to the number of cycles n≈109. the behavior of materials in this range reveals some qualitative changes in the mechanisms governing both the nucleation of cracks and their propagation. the influence of random statistic and dynamic loads on the lifetime of materials under gigacycle fatigue regime is a subject of much current interest for aircraft motor companies in the context of solving the problem of reliability (longevity) of materials under real operating conditions [1]. for instance, that concerns to the lifetime estimation of gas turbine engine blades during their collision with solid particles usually called foreign object damage. the solution to this problem needs t v. oborin et alii, frattura ed integrità strutturale, 34 (2015) 422-426; doi: 10.3221/igf-esis.34.47 423 the understanding of fundamental aspects of multi-scale damage evolution in large range of load intensity for the prediction of the kinetics of nucleation and propagation of cracks in the damaged material with the purpose to optimize the material structure and finding the materials with low sensitivity to random dynamic loads under highand gigacycle fatigue conditions. in this paper, aluminum-magnesium alloy (almg6) samples (fig. 1) are tested. kinetic equation for fatigue-crack growth he universal character of kinetic law establishing a relationship between the growth rate dl/dn of a fatigue cracks and a change in the stress intensity coefficient δk has been extensively studied both experimentally and theoretically. the power laws originally established by paris [2] (and presently referred to as the paris law) reflect the self-similar nature of fatigue crack kinetics. this law is related to a nonlinear character of damage evolution in the vicinity of the crack tip (called the “process zone”):  mdl a k dn   (1) where a and m are the experimentally determined constants. for a broad class of materials and wide range of crack propagation velocities under high cycle fatigue conditions, the exponent is typically close to m = 2–4. the self-similar aspects of the fatigue crack growth were studied by barenblatt, ritchie [3,4] using the assumption concerning intermediate self-similarity of fatigue crack kinetics to introduce the following variables for the representation of the crack growth rate a = dl/dn (where l is the crack length and n is the number of cycles): a1 = δk is the stress intensity factor; a2 = e is the young modulus; a3 = lsc is the scale related to the correlated behavior in the ensemble of defects on the scale a4 = lpz associated with the process zone. 3d new view roughness data within the crack process zone (fig.2) supported the existence of mentioned characteristic scales: the scale of process zone lpz and correlation length lsc that is the scale when correlated behavior of defect induced roughness has started. using the π-theorem and taking into account the dimensions of variables [dl/dn] = l, [δk]=fl–3/2, [lsc]=[lpz] = l, and [e] = fl–2, the kinetic equation for the crack growth: ф( , , , )sc pzdl dn k e l l  , (2) can be written as: 1 , pz sc scsc ldl k dn l le l         . (3) estimation of the values ( ) 1sck e l  and / 1pz scl l  allowed one to suggest an intermediate-asymptotic character of the crack growth kinetics for eq. (3) in the following form: sc pz sc ld l k dn le l             , (4) where / scl l l   . introducing the parameter  /pz scc l l   , we can reduce the scaling relation (4) to the following form analogous to the paris law: c sc d l k dn e l         , (5) t v. oborin et alii, frattura ed integrità strutturale, 34 (2015) 422-426; doi: 10.3221/igf-esis.34.47 424 where is a universal exponent. this form is similar to the equation proposed by hertzberg for scl b , where b is the burgers vector. materials and experimental conditions ynamic preloading of aluminum-magnesium alloy (almg6) samples (fig. 1) was realized using the split hopkinson pressure bar set-up at the strain rates of ~103 s-1, after which the samples were subject to cyclic loading at room temperature. then the fractography of fracture surface pattern was studied using the roughness data by interferometer–profiler new-view 5010. fatigue tests were carried out using the resonance type of testing machine of (shimadzu usf-2000) that provides the cyclic loading using the generator transforming the frequency of 50 hz into ultrasonic electrical sinusoidal signal of frequency 20 khz by piezoelectric transducer, generating longitudinal ultrasonic waves at a frequency 20 khz and the mechanical stress with maximum amplitude in the gauge length (mid-section) of the sample. deviation of the frequency by 0.5 khz was associated with the damage critical stage and considered as failure precursor related to the initiation of a crack with characteristic size of ~2 mm. the level of applied stresses allowed us to investigate fatigue life up to the values associated with 1010 cycles. the fatigue scenario was studied for the stress amplitude 105, 120, 130 mpa corresponding to a critical number of cycles of about ~1010 estimated for initially unstressed materials subject to gigacycle fatigue tests. figure 1: sample geometry (sizes are given in millimeters). the roughness of fracture surfaces was measured by the high-resolution new-view 5010 interferometer-profiler (providing x2000 magnification) and then was analyzed using the assumption concerning fractal geometry of fracture surface profile associated with correlated behavior of multiscale defect structures on the scale of process zone pzl that preceded to the crack growth. the fatigue tests provided the fractured samples of two types. the samples of the first type were broken during the fatigue test. the samples of the second type revealed pronounced variations in the resonance frequency associated with fatigue crack origin. the fracture surfaces of the samples of the first and second type were uncovered by cooling the samples with liquid nitrogen and breaking them in the minimal cross-section of samples. it is assumed that the fatigue fracture surface of the samples subjected to gigacycle loading has already been formed during fatigue tests and occupies the largest part of the fracture surface, which is determined by a change in the resonance frequency. the crack origin in cylindrical samples undergoing high cycle loading in the range 106-107 is started from the surface (fig. 2a). for the samples subject to cyclic loads in the range exceeding 108 cycles the crack formation is started in the bulk of the sample. the fracture surface in this case exhibits a fatigue zone known as a “fish-eye” which is a particular feature of such fatigue regimes. the central part of this region comprises a fracture nucleus surrounded by the region of refined (submicrocrystalline) structure (region 2 in fig. 2b). the new-view scanning was realized over the zones of fatigue crack growth (fig. 2a) and one-dimensional profiles of the surface relief were made in the radial direction starting from zone 1 to zone. within each “window” about 12 onedimensional profiles were analyzed to ensure representativeness of the data along the defect-induced relief with vertical resolution of 0.1 nm and horizontal resolution of ~ 0.5 µm. a minimum (critical) scale lsc that corresponds to beginning of multiscale long-range correlation in defect ensembles is determined by the computing of the hurst exponent. the function k(r) is calculated for one-dimensional profiles of fracture surface relief according to the formula [5,6]: d v. oborin et alii, frattura ed integrità strutturale, 34 (2015) 422-426; doi: 10.3221/igf-esis.34.47 425   1/22( ( ) ( )) h x k r z x r z x r    , (6) where k(r) is the averaged difference between the values of surface relief heights z(x+r) and z(x) in the window of size r, and h is the hurst exponent (surface roughness index). representation of the function k(r) in logarithmic coordinates allowed one to evaluate the lower boundary of the scaling range lsc, and the value of upper boundary considering one as the characteristic scale of the process zone lpz , i.e. the area of correlated behavior of multiscale defect structures (fig.3). (a) (b) figure 2: characteristic surface relief of a fatigue fracture zone: high cycle fatigue (a); gigacycle fatigue (b). (a) (b) figure 3: characteristic one-dimensional profiles for zone 1 (a), plot lnk(r) vs. ln(r) for zone 1 (b). the values of the hurst exponent h and the scales lpz and lsc for different loading conditions are given in tab. 1. conclusion he comparative analysis of the scaling characteristics of samples loaded under conditions of high and gigacycle fatigue shows a significant decrease in the range of spatial scales, where the hurst exponent remains constant for dynamically loaded samples in the «fish-eye» (0.5-10.9 mkm) zone. this result confirms our assumption that mentioned characteristic scales lpz and lsc play an important role in the list of variables for the kinetic equation fatigue of t v. oborin et alii, frattura ed integrità strutturale, 34 (2015) 422-426; doi: 10.3221/igf-esis.34.47 426 crack growth and can be used for the identification of phenomenological parameters (power index) providing self-similar law for the crack path. sample number elongation (mm) striker velocity (m/s) , mpa , cycles zone number lsc, mkm lpz , mkm h 1 0.89 28.4 130 7.33·10+6 2 1.4 20.6 0.57 2 1.77 40.3 120 7.82·10+8 2 3 0.5 0.8 10.9 21.4 0.63 0.62 3 1.27 32.1 120 5.72·10+7 2 1.0 18.2 0.60 4 2.21 40.3 105 5.83·10+6 2 1.0 14.2 0.46 table 1: the values of the hurst exponent h and scales lpz and lsc at various levels of fatigue longevity. acknowledgement his study was supported by the russian science foundation, project № 14-19-01173. references [1] peters, j. o., influence of foreign object damage on crack initiation and early crack growth during high-cycle fatigue of [2] ti-6al-4v, eng. fract. mech., 67 (2000) 193-207. [3] paris, p., lados, d., tad, h., reflections on identifying the real keffective in the threshold region and beyond, eng. [4] fract. mech., 75 (2008) 299–3052. [5] barenblatt, g.i., scaling phenomena in fatigue and fracture, int. j. of fracture, 138 (2006) 19–35. [6] ritchie, r.o., incomplete self-similarity and fatigue-crack growth, int. j. of fracture, 132 (2005) 197–203. [7] bouchaud, e., scaling properties of cracks, j. phys. condens. matter, 9 (1997) 4319– 4344. [8] froustey, c., naimark, o., bannikov, m., oborin, v., microstructure scaling properties and fatigue resistance of [9] prestrained aluminium alloys (part 1: al-cu alloy), european journal of mechanics a/solids, 29 (2010) 1008–1014. t microsoft word numero_57_art_25_3045 h. s. patil et alii, frattura ed integrità strutturale, 57 (2021) 350-358; doi: 10.3221/igf-esis.57.25 350 age-hardening heat treatment behavior of as-cast mg–zn–al alloys h. s. patil, d. c. patel mechanical department, gidc degree engineering college, abrama, navsari, gujarat, india hspatil28@gmail.com, pateldcp@gmail.com abstract. magnesium alloys have generated renewed interest as a light alloys; replacing some conventional structural materials for weight reduction in applications like aerospace, automotive and electronics industries. in interior components and powertrains, cast alloys are widely used and represent more than 99% of magnesium alloys used today, whereas only a few wrought products are used. mostly in automotive applications, mg-engine block can noticeably reduce the weight and consequently its fuel consumption and environmental impact. due to solid-state precipitates, these alloys are strong in nature and are produced by an age-hardening heat treatment process. in the present work the age-hardening behavior of the as cast mg– zn–al alloys (za85 alloy) in the composition of 8 wt. %zn, 5 wt. %al has been investigated. through the differential thermal analysis (dta) studies, it has been found out that dissolution temperature of ternary eutectic precipitates is present in the alloy. based on the dta results, the as cast samples have been solutionised at 360 °c temperature for different intervals of time. solutionising time has been optimized from the enthalpy values of un-dissolved precipitates. the solution treated samples have been then aged at temperature of 180° c for different time intervals. from the peak hardness values, the ageing conditions have been optimized. keywords. magnesium alloy za85; dta; solution treatment; ageing; microstructure; hardness. citation: patil,. h. s., patel, d. c, agehardening heat treatment behavior of the ascast mg–zn–al alloys, frattura ed integrità strutturale 57 (2021) 350-358. received: 19.03.2021 accepted: 19.06.2021 published: 01.07.2021 copyright: © 2021 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. introduction agnesium alloys is a promising material for the fabrication of automotive, aerospace and electronics components. so far, most mg alloys have been used in automotive components like the steering wheels, disk wheels, gear box, chain locker instrument panels, and seat frames and crank cases where, the operating temperature is low, due to its light weight could help car manufacturers to reduce the amount of emissions generated per automobile and to meet present and future regulations looking for more environmentally friendly vehicles [1, 2]. for m https://youtu.be/imkrdm-pimu h. s. patil et alii, frattura ed integrità strutturale, 57 (2021) 350-358; doi: 10.3221/igf-esis.57.25 351 instance, its usage for automotive parts requiring low mass and low specific weight has been found to reduce fuel consumption by 20-25% [2]. however, the low strength of magnesium alloys compared to aluminium and steel have limited its use in many areas. in order to improve the hardness of magnesium alloys, solid solution, grain size and dislocation density strengthening which either depends on the composition and thermal treatment processes had been widely studied, but precipitation strengthening mechanism has the highest strengthening effect. the precipitation hardening involves the addition of alloying elements along with heat treatments in order to synergistically bring about the strengthening required for the mg alloy. these had been the focus of numerous investigations in recent times. among the mg-based alloys, magnesium-zinc (mg-zn) alloys shows the highest precipitation hardening response; therefore, it has been found that the properties of this alloy improved significantly when combined with calcium (ca) [1]. the mg-zn alloys with addition of ca has been reported to increase the effectiveness of precipitation hardening when the alloy is exposed to ageing, causing a higher quantity of finer and uniformly dispersed precipitates, that influences the final texture of the alloy significantly [2-5] and ca addition also decreases the grain size in microstructure that leads to improvement in mechanical properties of the alloy [6], moreover it decreases the flammability of the alloy and increases creep and oxidation resistance [7-11]. it is difficulty to process mg-alloys; different deformation mechanism present and anisotropy when loaded under tension/compression are major challenges, which limit their application in automotive industries [1215]. that can be overcome by using mg-alloys with rare earth (re) elements such as ce, gd, nd and y developed for high temperature applications in the aerospace industries but these alloys are very expensive[16]. hence, the development of heat resistant mg-alloy at low cost is the major challenge in automotive sector. recent studies [17-18] have reported that the mg­zn-al system having zn-al composition in the ratio of 2:1 has sound creep resistance. it is also reported that za85 alloy is one such alloy system having superior elevated temperature behaviour and satisfies the requirement of other corrosion and foundry properties [19]. the mechanical properties such as strength, ductility and fracture toughness of this alloy can be further improved by adopting suitable heat treatment procedure. however, each heat treatment procedure such as solutionising temperature, time and the ageing conditions significantly influence properties and microstructural changes [20]. differential thermal analyser (dta) is a powerful tool which is normally used to measure the rate of phase transformation in the alloys such as, precipitation of additional volume fraction of precipitates through fresh nucleation or growth of existing precipitates, progressive dissolution of precipitates, on-going coarsening of precipitates and precipitation of new phases [21-22]. the present work investigated the age-hardening behaviour of the as cast mg–zn– al alloys (za85 alloy) using dta studies and other conventional methods. figure 1: image of mg-alloy casting materials and experimental methods alloy preparation and casting procedures n experiments, permanent cast iron mold castings method was used and initially, no pouring basin attachment with the sprue was there, which led to a restriction in pouring speed as higher pouring speed led to the spilling of molten metal into the floor. before the casting, the properly cleaned mold was given a graphite coat and preheated to 310°c in a heating oven for 60-70 minutes. resistance box furnace was used for melting of magnesium alloys. the preheated i h. s. patil et alii, frattura ed integrità strutturale, 57 (2021) 350-358; doi: 10.3221/igf-esis.57.25 352 flux was sprinkled in the bottom and side of the cleaned crucible and kept inside the furnace. after the complete melting of the metals in the crucible, the refining of melt was carried out at a temperature of 700°c. after the refining and settling process was over, the molten metal was poured into the pre heated molds. pouring was carried out smoothly without any jerk in the melt, as excessive jerk disturbs the settled oxide inclusions in the bottom. the flux layer near the lip of the crucible was pulled back softly by using a skimmer for smooth flow of molten metal. the oxygen around the melt jet was removed by sulfur dusting. three fourth of the melt in the crucible was poured into the preheated mould. the remaining metal was poured separately as a scrap. fig. 1 shows an image of one such mg-alloy casting samples. the chemical compositions of mg-alloy za85 are presented in tab. 1. zn al mn mg 8 5 0.2 balanced table 1: chemical compositions of mg-alloy za85 (wt. %). thermal analysis the differential thermal analysis (dta) measurements were carried out on as cast samples of za85 alloy to find out the dissolution temperature of eutectic ternary phase using differential thermal analyzer under argon atmosphere with a heating rate 10 °c min-1. from the dta results, solutionising temperature was identified as 360 °c. then, the samples were solution treated using the heat treatment schedule presented in tab. 2. the dta measurements were performed on all the samples immediately after solution treatment to find out the time required for maximum dissolution of the precipitates into the matrix. at least three runs were carried out to confirm the results. heat treatment the samples (cylindrical pieces of 20mm15mm) were machined out from the castings of za85. these samples were heat treated in a muffle furnace under carbon dioxide atmosphere for different schedules given in tab. 2. table 2: heat treatment schedule for mg-alloy za85. the samples were solution treated for optimum condition and they were aged at 180°c for 36 hours. every 2 hours, samples were drawn from the furnace and the hardness measurements were carried out. hardness testing sigma hardness machine was used for brinell hardness measurement of as cast and heat-treated samples. for hardness measurement one side of the specimen was polished with 600 grit size emery paper to remove the oxide and other scales in order to see the edges of the indentation mark clearly. a 3 mm ball was used to make indentation. load was fixed at 100 kg with a dwell time of 30 sec. on an average five indentations were made and average value is recorded. microstructure both the cast and heat-treated samples were initially paper polished with different grit size 100, 220, 400 and 600 m silicon carbide emery papers, subsequently they were polished with 0.25 micrometres diamond paste then they were etched with solution containing 5 g of picric acid, 5 ml acetic acid, 100 ml ethanol and 10 ml distilled water. the 2~3s alloy code heat treatment parameters z1 as cast z2 solution treated at 360°c for 24 hours, quenched in water at 32°c z3 solution treated at 360°c for 48 hours, quenched in water at 32°c z4 solution treated at 360°c for 72 hours, quenched in water at 32 c z5 solution treated at 360°c for 96 hours, quenched in water at 32°c h. s. patil et alii, frattura ed integrità strutturale, 57 (2021) 350-358; doi: 10.3221/igf-esis.57.25 353 etched samples were viewed under microscope with image analysis software. sem was used to analyse the microstructure of mg, zn and al ternary intermetallic. x-ray diffraction (xrd) xrd was applied to analyse the phases present in heat treated samples using panalytical x-ray diffractometer. x-rays are electromagnetic waves with short wavelength. the interaction of the x-ray beam and the electrons in atoms causes diffraction. the energy dispersive spectroscope (eds) studies were also carried out using jeol sem to analyse the compositions of mg, zn and al bearing intermetallic. results and discussion microstructure analysis he optical micrographs of permanent mould as cast za85 alloy is represented in fig. 2(a). from this, it is observed that, the microstructure of mg-alloy za85 contains (hcp) mg-matrix, coarse ternary intermetallic phases and γ (mg4-zn11-al) stable phase at the grain boundaries. in za85 alloy, the solidification starts with crystallization of -mg in the dendrite region and forms mg17al12 eutectic compound at moderate temperature. on further cooling, the metastable mg17-al12 phase reacts with zn in the liquid and forms many possible mg-zn-al ternary intermetallic compounds [18]. similar investigations on za84 (mg-8zn-4al) alloy confirm that the ternary intermetallic found in this alloy is a metastable icosahedra quasi-crystal of point group m35 with a small fraction of equilibrium γ-phase [19]. in the present work, x-ray diffraction of quasi-crystal ternary intermetallic could not be identified because of the imperfect match of its standard spectrum in the diffraction data software. however, the eds result as shown in fig. 2(b) confirms the presence of coarse intermetallic phase of mg/zn/al having ratio 66/16/17. it is further noticed that this ternary intermetallic phase ratio varies with different locations in the microstructure of mgx-zny-alz type. figure 2: (a) sem micrograph of as cast mg-alloy (b) sem-eds of eutectic ternary phase effect of solution treatment the differential thermal analysis (dta) thermograph of za85 alloy is shown in fig. 3. it is observed from this figure that the endothermic peak at 361.08°c for the as cast sample corresponding to the ternary eutectic dissolution temperature. it is difficult to identify the other peaks of many possible mgx-zny-alz phases present in the alloy mainly because oxidation of this alloy starts above 450°c. it can be further observed from the dta results that liquidus temperature of za85 alloy is 597.17 °c which is equivalent to liquidus temperature of commercial az91 alloy (598 °c), entailing good castability of alloy. from the dta investigation, the solutionising temperature of the alloy is determined as 360 °c, which is slightly lower than the dissolution temperature. during solution treatment, the intermetallics present in the alloy get dissolved into the -mg matrix and form a supersaturated solution while quenching. however, the homogenization and micro-segregation depend upon the solutionising temperature, time and the solubility range. fig. 4 shows the x-ray diffraction (xrd) analysis for the as cast t h. s. patil et alii, frattura ed integrità strutturale, 57 (2021) 350-358; doi: 10.3221/igf-esis.57.25 354 and st samples at 360°c for different intervals of times. it is observed from the fig. 4 that complete dissolution of mg4zn11al has taken place after 24 hours of holding. figure 3: dta thermograph (heating rate of 10 °c min-1) figure 4: x-ray diffraction pattern of as cast and solution treated samples fig. 5 presents the micrographs of za85 alloy with respect to different solutionizing times. it is noticed from this figure, that there is significant change in the microstructure with increase in solutionising time. even though, the microstructure of z2 condition reveals the complete dissolution of γ-phase to supersaturated solid solution, however the presence of mgmatrix with some eutectic ternary phases can be seen. the microstructures of z3 and z5 conditioned alloys presented in figures 5b-c show the presence of considerable volume fraction of precipitates, which are distributed along the grain boundaries even after increasing the solutionising time. further, dta analyses have been carried out to find out the time required for dissolution of maximum number of precipitates. the dta studies carried out on the as cast and the solution treated samples at 360 °c for varying time intervals (24, 48, 72 and 96 hrs) are exhibited in fig. 6. the peak temperature for eutectic dissolution and the enthalpy calculated from the dta thermographs for all the samples are given in tab. 3. it is observed from the dta results that the enthalpy decreases with increase in solutionising time due to dissolution of precipitates into the matrix. the reduction in enthalpy from 0 to 24 hrs is marginal because of the insufficient time given for dissolution of precipitates into the matrix but the reduction in enthalpy is drastic from 24-48hrs. for prolonged time (up to 96 hrs) of solution treatment, considerable amount of endothermic reaction observed in the in dta studies confirm the presence of precipitates but in a lower h. s. patil et alii, frattura ed integrità strutturale, 57 (2021) 350-358; doi: 10.3221/igf-esis.57.25 355 volume observed in the microstructure. this can be further explained that the maximum solid solubility of (6.22 wt %) zn atoms contributing to the dissolution of precipitates into matrix; the residual zn atoms (beyond 6.22 wt %) does not respond to the solution treatment temperature and time. (a) as cast (b) solution treated at 360 °c for 48 hours (c) solution treated at 360 °c for 96 hours figure 5: micrographs of mg-alloy za85. figure 6: dta curve of as cast and solutionised samples at different time intervals. h. s. patil et alii, frattura ed integrità strutturale, 57 (2021) 350-358; doi: 10.3221/igf-esis.57.25 356 table 3: peak temperature (±1 °c) and enthalpy values for endothermic reaction in the as cast and solutionised samples the brinell hardness values of the solution treated samples also show similar trend as shown in fig. 7. it is evident from the hardness results that the minimum time required for dissolution of maximum ternary eutectic phase in the solution treated conditions is 48 hours at 360 °c. figure 7: brinell hardness for as cast and st samples figure 8: hardness variation with different aging time effect of age-hardening the hardness values as a function of ageing time at 180 °c are shown in fig. 8. it is observed from this figure that the hardness increases with increasing ageing time and the maximum hardness is obtained at 17 hours of aging; beyond that it decreases. this maximum hardness attained is associated with the optimum temperature and time. while increasing ageing time, the particles become coarser and they are less effective in retarding the dislocation motion during deformation. the formation of particles to an optimum size and uniform inter particle spacing thereby increase the strain field of alloy code peak temperature in 1 °c enthalpy (j/g) z1 361.08 63.9112 z2 362.87 44.9931 z3 353.06 18.0056 z4 360.05 15.9620 z5 359.89 14.9629 h. s. patil et alii, frattura ed integrità strutturale, 57 (2021) 350-358; doi: 10.3221/igf-esis.57.25 357 phase/matrix interface. the microstructure of optimum aged (180 °c for 17 hours) za85 alloy displayed in fig. 9 shows the presence of fine eutectic ternary phases distributed uniformly along the grain boundaries, which act as an effective straddle to dislocation motion thereby improving the properties of za85 alloy. figure 9: micrographs of optimum aged sample. conclusions n this research work, experimentation was conducted to investigate age-hardening heat treatment behaviour of the as-cast mg-alloy-za85. based on the experimental results, the conclusions drawn are: a. the liquidus temperature of mg alloy za85 is 597.17°c, whereas the dissolution temperature of ternary eutectic precipitate is 360 °c b. to achieve the maximum strength properties in mg alloy za85, the following heat treatment process needs to be followed: solution treatment: 360 °c ± 5 °c for 48 hours water quenching at 32 °c age-hardening: 180 °c ± 2 °c for 17 hours c. the hardness values increases with increasing ageing time and the maximum hardness is attained at 17 hours of aging beyond that hardness values decreases. this maximum hardness attained is associated with the optimum temperature and time. references [1] clark, j.b. (1965). transmission electron microscopy study of age hardening in a mg-5 wt.% zn alloy, acta metallurgica, 13(12), pp. 1281-1289. [2] gibson, m.a., venkatesan, k., and bettles, c.j. (2004). enhanced age-hardening behaviour in mg–4 wt.% zn, scripta materialia, 51, pp. 193-197. [3] oh-ishi, k., hono, k. and mendis, c.l. (2007). enhanced age-hardening in a mg–2.4 at.% zn alloy by trace additions of ag and ca, scripta materialia, pp. 485-488. [4] watanabe, r., mendis, c.l., hono k. and oh-ishi (2009). age-hardening response of mg–0.3at.% ca alloys with different zn contents, materials science and engineering a, 526, pp. 177-184. [5] zheng, m., qiao, x., wang, d., peng, w., wu, k., jiang, b., and du, y. (2016). improving microstructure and mechanical properties in mg–6 mass %zn alloys by combined addition of ca and ce, materials science and engineering a, 656, pp. 67-74. [6] qiao, x.g., zheng, m.y., wu, k., xu, s.w., and du, y.z. (2015). the microstructure, texture and mechanical properties of extruded mg–5.3zn–0.2ca–0.5ce (wt%) alloy, materials science &engineering a, 620, pp. 164-171. i h. s. patil et alii, frattura ed integrità strutturale, 57 (2021) 350-358; doi: 10.3221/igf-esis.57.25 358 [7] parka, w.w, chung, i.s., and youa, b.s. (2000). the effect of calcium additions on the oxidation behavior in magnesium alloys, scripta materialia, 42(11), pp. 1089-1094. [8] czerwinski, f. (2014). controlling the ignition and flammability of magnesium for aerospace applications, 86. [9] akiyama, s., ogi, k., and sakamoto, m. (1997). suppression of ignition and burning of molten mg alloys by ca bearing stable oxide film, journal of materials science letters, 16(12), pp. 1048 1050. [10] kraft, o., arzt, e., and vogel, m. (2005). effect of calcium additions on the creep behavior of magnesium die cast alloy za85, 36(7). [11] zhu, s.m., muddle, b.c., nie, j.f. and gao, x. (2005). precipitation-hardened mg–ca–zn alloys with superior creep resistance, scripta materiala, 53(12), pp. 1321–1326. [12] lee, j.h., moon, b.g., you, b.s., and park, h. s. (2014). tension–compression yield asymmetry in as-cast magnesium alloy, journal of alloys and compounds, 617, pp. 277–280. [13] al-samman, t., molodov, a.d., gottstein, g., and molodov, d.k. (2016). on the role of anomalous twinning in the plasticity of magnesium, acta materialia, 103, pp. 711–723. [14] xin, r., shu, x., wang, c., liu, q., and liu, g. (2016). the mechanism of twinning activation and variant selection in magnesium alloys dominated by slip deformation, journal of alloys and compounds, 687, pp. 352–359. [15] krajewski, p.e., luo, a.a., and powell, b.r. (2010). magnesium alloys for lightweight powertrains and automotive structures, materials, design and manufacturing for lightweight vehicles, pp. 114-173. [16] wenwen, d., yangshan, s. and oengym, w. (2003). microstructure and mechanical properties of mg-al based alloy with calcium and rare earth additions, materials science and engineering, a356, pp. 1-7. [17] vogel, m., kraft, o., and artz, e. (2003). creep behavior of magnesium die cast alloy za85, scripta materialia, 48, 985-990. [18] vogel, m., kraft, dehm, g., and artz, e. (2001). quasicrystalline grain boundary phase in the magnesium die cast alloy za85, scripta materialia., 45, 517-524. [19] bourgeois, l., muddle, b.c., and nie, j.f. (2001).the crystal structure of the equilibrium $ phase in mg-zn-al casting alloys, acta materialia, 49, 2701-2711. [20] hossain, a. and kurny, a.s.w. (2013). effects of strain rate on tensile properties and fracture behavior of al-simg cast alloys with cu contents, materials science and metallurgy engineering., 1(2), pp. 27-30. [21] li, q., shenoy, r.n. (1997). dsc and tem characterizations of thermal stability of an al–cu–mg–ag alloy. journal of materials science 32, pp. 3401–3406. [22] boettinger, w.j. and kattner, u.r. (2002). on differential thermal analyzer curves for the melting and freezing of alloys, metallurgical and material transactions. a, 33a, pp. 1779-1794. microsoft word numero_57_art_13_3074 i.boudjemaa et alii, frattura ed integrità strutturale, 57 (2021) 160-168; doi: 10.3221/igf-esis.57.13 160 preliminary results on the effects of orthopedic implant stiffness fixed to the cut end of the femur on the stress at the stumpprosthetic interface i.boudjemaa, a. sahli, a. benkhettou, s.benbarek department of mechanical engineering, laboratory mechanics physics of materials (lmpm), university of sidibel abbes, bp 89, cite ben m’hidi, sidibel abbes, 22000, algeria ismailboubou000@gmail.com sahliabderahmen@yahoo.fr, http://orcid.org/0000-0002-5183-1168 aekben.dz22@gmail.com sma_benbarek@yahoo.fr, http://orcid.org/0000-0002-5420-9144 abstract. people with trans-femoral amputation often experience skin breakdown due to the pressures and shear stresses in the stump-prosthesis interface. in this study, a finite element model was employed to investigate the stresses at the stump interface in the case of an orthopedic implant fixed to the cut end of the femur. by changing the stiffness of this implant, we aim to see how the stiffness of this implant affects the stresses in the interface between the amputated limb and the prosthesis. to find out the effects of implant stiffness, five values for the elastic modulus, ranging from 0.1 to 0.5 mpa, with an interval of 0.1 mpa were employed in the implant structure of the fe model. obtained results show that the implant played important role in reducing the stresses at the stump-prosthesis interface where the contact pressure did not exceed 53 kpa and 17.3 kpa for shear stress in the stiffer case of an implant, while the contact pressure in the case of femur without an implant exceeded 79 kpa and 42 kpa for shear stress. we also noted that the intensity of the contact pressure and the shear stress is proportional to the stiffness of the implant, as the greater the implant stiffness, the higher the peak of these stresses. keywords. prosthesis; stump interface; stiffness; contacts stresses; implant. citation: boudjemaa, i., sahli, a. benkhettou, a., benbarek, s., preliminary results on the effects of orthopedic implant stiffness fixed to the cut end of the femur on the stress at the stump-prosthetic interface, frattura ed integrità strutturale, 57 (2021) 160-168. received: 16.04.2021 accepted: 06.06.2021 published: 07.01.2021 copyright: © 2021 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. introduction ower limb amputations are mainly due to traffic accidents, particularly motorcycle accidents [1], diabetes and cancer are also major causes of amputation [2, 3]. after lower limb amputation the patients need a prosthesis to retain upright mobility capabilities, unfortunately, many of them remain dissatisfied with the performance of this l https://youtu.be/w792g8tn7bq i.boudjemaa et alii, frattura ed integrità strutturale, 57 (2021) 160-168; doi: 10.3221/igf-esis.57.13 161 prosthesis [4], some patients also suffer from deep problems with this prosthesis, like discomfort, redness, sores, and inability to stand for a long time [5]. the stresses at the stump-prosthetic interface are primarily responsible for these problems. several studies have discussed the stresses at the residual limb interface using the finite element method (ffm) [6-18]. the models developed in these studies can be divided into three types. the first type involves linear static analysis established under assumptions of linear material properties, the second type can be referred to as nonlinear analysis, taking into consideration the nonlinear material properties, and the third type involves dynamic models. analyses of this type consider not only dynamic loads but also material inertial effects and time-dependent material properties [19, 20]. jia et al (2004) [18] performed a (fe) study on the influence of inertial load on interface pressure and shear stress, the socket was modeled as rigid in the study, and all materials were assumed linear. lacroix et al (2011) [14], developed five ef models from five different patients to study the effect of the socket donning process on the stress-strain state at the outer residual limb interface. the main goal of the study performed by zhang et al (2013) [13] was to predict the stress distribution between the socket and the residual limb, in this study a prosthetic liner with 5 mm thickness has been used. meng et al (2020) [7] investigated the residual limb stress of trans-femoral amputees compression/release stabilized (crs) socket by finite elemental modeling. most of these studies applied a load equivalent to half or full body weight at the bone head or they apply forces equivalent to the reaction forces extracted from larger (fe) models. medical implants are devices that can place inside or on the surface of the body, these implants can replace body parts and function or provide support to organs and tissues. a soft implant under the cut end of the femur bone (fig. 1) could be one of the suggested solutions, as it helps the bone to increase the ability to carry weight and thus reduce stresses on the stump-prosthetic interface also help to cushion the end of the femur bone. 2d simulation of this type of orthopedic implant has previously been performed in chillale’s study [11]. in this study, an implant that is fixed to the cut end of the amputated femur bone (fig. 2) was simulated, we aim by employing a 3d finite element model to investigate the effect of this orthopedic implant stiffness on the stresses at the stump-prosthetic interface. to find out the effects of implant stiffness, five values for the elastic modulus, ranging from 0.1 to 0.5 mpa, with an interval of 0.1 mpa were employed in the implant structure of the fe model. figure 1: schematic representation of the (ef) model, (a) bone with implant parts, (b) the different sections of the 3d (ef) model geometry (bone, soft tissues, implant, liner, and socket). method geometry finite element (fe) model for a virtual patient was developed to simulate an above-the-knee amputation, this model is composed of a limb (soft tissue, bone, implant, and implant support) and a prosthesis with a prosthetic liner and socket. the liner and the socket were designed using autodesk meshmixer this software allows to adapt a soft tissue femur bone with implant liner (6 mm) socket (2 mm) femur bone implant support soft implant (a) (b) i.boudjemaa et alii, frattura ed integrità strutturale, 57 (2021) 160-168; doi: 10.3221/igf-esis.57.13 162 the prosthetic liner shape to the residual limp, the liner was considered to be 6 mm thick, as for the socket, it was 2 mm. the model has been converted from stl to igs with mimics 3matic software. the different parts are shown in fig 1. the implant was developed in the (ef) model with two principal parts, the top was the support part for the soft implant with a height of 45.5 mm, and the diameter of the soft implant was 45 mm [11] as shown in fig. 2. figure 2: schematic representation of implant geometry mechanical properties the material properties of the femur bone, soft tissue, implant support, implant, liner, and socket were assumed to be linearly elastic, homogeneous, and isotropic. the list of the values of elastic modulus and poisson’s ratio used in the finite was shown in tab. 1. the young’s modulus of the implant was changed from 0.1 to 0.5 [17] to predict how the stiffness of the implant affected the stresses at the limb-prosthetic interface. material young’s modulus poisson’s ratio bone [16] 10 gpa 0.3 soft tissue [18] 0.2 mpa 0.49 implant support [11] 5.5 mpa 0.38 implant [17] 0.1 to 0.5 mpa 0.49 liner [18] 0.38 mpa 0.39 socket [16] 1.5 gpa 0.3 table 1: details material properties for the (fe) model [11, 16, 17, 18] boundary and loading condition in this study, a non-linear finite element static analysis method was used. this analysis employed multiple finite element techniques, including geometric non-linearity due to large deflections, non-linear contacts due to friction between the contact surfaces of the stump and the prosthetic. the interfaces between the femur bone with the implant and soft tissue were tied; the physical contact between the stump and the liner and between the liner and the socket was represented by using surface-to-surface contact condition, which impede the residual limb nodes (slave nodes) to trespass or penetrate into the socket (master surface) during the displacement caused by the application of body weight. the coefficient of friction between the liner and soft tissue was assumed to be 0.5 [13, 20]. although the bone is considered quasi-brittle material [21, 22], however, it is responsible for carrying human weight. in this study static vertical load equivalent to the half body weight [23] 350 n (two-leg stance) was applied on the femoral bone head, the distal end of the socket was fixed. implant support soft implant i.boudjemaa et alii, frattura ed integrità strutturale, 57 (2021) 160-168; doi: 10.3221/igf-esis.57.13 163 figure 3: schematic representation of load and boundary conditions mesh the reliability of the results obtained requires a very refined mesh. the meshing was performed using c3d4 tetrahedral elements (c-continuum, 3d-three dimensional element, and 4four noded element) for all components (bone, stump, liner, socket, and implant), tetrahedral meshes are generally preferred over hexahedral meshes for free-formed complex geometries as the former are computationally more cost-effective [24]. the total number of elements and element types for all components are specified in tab. 2. parts elements number element type soft tissue 53214 c3d4 liner 17933 c3d4 socket 19413 c3d4 bone with implant 12749 c3d4 bone without implant 8984 c3d4 table 2: mesh properties used figure 4: mesh of the analyzed (fe) model axial load 350 n the distal end of the socket was fixed i.boudjemaa et alii, frattura ed integrità strutturale, 57 (2021) 160-168; doi: 10.3221/igf-esis.57.13 164 results esults represent the predictions of residual limb reaction after patient weight application in all cases in this simulation. distribution of von misess stress in the femur bone and the soft tissue with implant 0.1 and without implant was shown in fig 5. the maximum von mises in the femur in the case with the implant was 65.9 kpa almost double of von mises recorded in the case without an implant (36.3 kpa), this proves that the soft implant increases the weight carrying ability of the amputated femur. the maximum von mises stress in the soft tissue in the case with implant 0.1 was 11.5 kpa this is less than that recorded in the case without implant that was 42 kpa. the stresses in the case of residual limb without implant recorded high concentration under the truncated femur bone region, this proves that the soft implant was played an important role in cushioning the end of the amputated bone and reducing the stresses on the soft tissue. figure 5: von mises stress distribution (mpa) on the limb with and without implant r bone without implant bone with implant 0.1 mpa (young’s modulus) soft tissue in the case of implant 0.1 mpa (young’s modulus) soft tissue in the case without implant i.boudjemaa et alii, frattura ed integrità strutturale, 57 (2021) 160-168; doi: 10.3221/igf-esis.57.13 165 fig 6 shows the distribution of contact pressure at the stump-prosthetic interface in all cases of implant stiffness and the case without an implant. in the case without an implant, we get a high concentration of contact pressure under the truncated femur region; the peak pressure, in this case, was 79.7 kpa. in the case of the implant below the amputated bone, we noticed that the intensity of the contact pressure at the outer stump interface rises with the increase of stiffness of this implant. the highest peak contact pressure between the implant cases was 53 kpa at the implant (0.5 mpa young’s modulus). the lowest peak contact pressure was recorded in the limb in the case of the least stiffness implant (0.1 mpa young’s modulus) up to 45 kpa. figure 6: contact pressure distribution (mpa) on the stump-prosthetic interface for all implant stiffness cases and the case without implant. fig 7 shows the distribution of longitudinal shear stress at the stump-prosthetic interface in all cases of implant stiffness and the case without an implant. it can be noticed that the case of limb without implant was recorded the highest values of shear stresses up to18.4 kpa the lowest shear stress was recorded in the limb in case of the least stiffness implant (0.1 mpa young’s modulus) up to 6.8 kpa. the stump at implant 0.3 mpa (young’s modulus) the stump at implant 0.2 mpa (young’s modulus) the stump at implant 0.1 mpa (young’s modulus) the stump at implant 0.4 mpa (young’s modulus) the stump at implant 0.5 mpa (young’s modulus) the stump without implant i.boudjemaa et alii, frattura ed integrità strutturale, 57 (2021) 160-168; doi: 10.3221/igf-esis.57.13 166 figure 7: longitudinal shear stress distributio (mpa) on the stump-prosthetic interface for all implant stiffness cases and the case without implant. figure 8: peak contact pressure(kpa) on the stump-prosthetic interface for all implant stiffness cases and the case without implant. figure 9: resultant shear stress (kpa) on the stump-prosthetic interface for all implant stiffness cases and the case without implant. the stump at implant 0.1 mpa (young’s modulus) the stump at implant 0.2 mpa (young’s modulus) the stump at implant 0.3 mpa (young’s modulus) the stump at implant 0.4 mpa (young’s modulus) the stump at implant 0.5 mpa (young’s modulus) the stump without implant i.boudjemaa et alii, frattura ed integrità strutturale, 57 (2021) 160-168; doi: 10.3221/igf-esis.57.13 167 fig. 8 shows a histogram of the relationship between the peak contact pressure at the stump-prosthesis interface and the implant stiffness (elastic modulus, ranging from 0.1 to 0.5 mpa), the relationship between implant stiffness below the amputated bone and the contact pressure on the interface between the stump and the prosthesis was a direct relationship, as the higher the implant stiffness, the greater the stresses at the interface. fig. 9 shows a histogram of the relationship between the peak resultant shear stress at the stump-prosthesis interface and the implant stiffness. the resultant shear stress is the magnitude of the combination of longitudinal and circumferential components of shear stresses in the contact interface. the maximum resultant shear stress was recorded in the case of femur without implant up to 42.16 kpa. while the resultant shear stress increase from 13.3 kpa in the case of implant 0.1 to 17.3 kpa in the case of implant 0.5. conclusions y employing a non-linear finite element method (efm) to investigate the stresses after trans-femoral amputation in the case of a soft implant below the amputated bone. we came out with conclusions, including that the implant under the amputated bone had a very clear effect in reducing stresses caused by body weight, whether inside the muscle tissue in the area below the amputated bone or on the interface between the limb and the prosthetic, as the difference between the peak contact pressure in the case without an implant (79.7 kpa) and the case with implant 0.1(45 kpa) was 34.7kpa. we observed also that the relationship between implant stiffness below the amputated bone and the contact pressure on the interface between the stump and the prosthesis was a direct relationship, as the higher the implant stiffness, the greater the stresses at the interface. this simulation predicted that the soft implant under an amputated bone is a very promising technique for relieving the patient's pain, problems of skin degradation, and even the inability to stand for a long time, as the contact pressures and the shear stress recorded were much less than those causing problems for the patient, according to cagle study [6]. the results of this study reinforce the results of previous studies such chillale’s study [11] about the efficiency of this implant below the bone in reducing stresses at the stump-prosthetic interface. this implant may be a solution to the great problems suffered by amputee patients. these results remain hypothetical despite the efficiency of the finite element method further work is necessary to validate this result. references [1] ebskov, l. b. (1992). level of lower limb amputation in relation to etiology: an epidemiological study. prosthetics and orthotics international, 16(3), pp. 163-167.doi:10.3109/03093649209164335. [2] adler, a. i., boyko, e. j., ahroni, j. h., and smith, d. g. (1999). lower-extremity amputation in diabetes. the independent effects of peripheral vascular disease, sensory neuropathy, and foot ulcers. diabetes care, 22(7), pp. 1029-1035. doi: 10.2337/diacare.22.7.1029. [3] ziegler-graham, k., mackenzie, e. j., ephraim, p. l., travison, t. g., and brookmeyer, r. (2008), estimating the prevalence of limb loss in the united states: 2005 to 2050, archives of physical medicine and rehabilitation, 89(3), pp. 422-429.doi: 10.1016/j.apmr.2007.11.005. [4] ali, s., osman, n. a. a., naqshbandi, m. m., eshraghi, a., kamyab, m., and gholizadeh, h. (2012). qualitative study of prosthetic suspension systems on transtibial amputees' satisfaction and perceived problems with their prosthetic devices. archives of physical medicine and rehabilitation, 93(11), pp. 1919-1923. doi: 10.1016/j.apmr.2012.04.024. [5] meulenbelt, h. e., dijkstra, p. u., jonkman, m. f., and geertzen, j. h. (2006). skin problems in lower limb amputees: a systematic review. disability and rehabilitation, 28(10), pp. 603-608. doi: 10.1080/09638280500277032. [6] cagle, j. c., reinhall, p. g., allyn, k. j., mclean, j., hinrichs, p., hafner, b. j., and sanders, j. e. (2018). a finite element model to assess transtibial prosthetic sockets with elastomeric liners. medical and biological engineering and computing, 56(7), pp.1227-1240. doi: 10.1007/s11517-017-1758-z. [7] meng, z., wong, d. w. c., zhang, m., and leung, a. k. l. (2020). analysis of compression/release stabilized transfemoral prosthetic socket by finite element modelling method. medical engineering and physics, 83, pp. 123129. doi: 10.1016/j.medengphy.2020.05.007. [8] ballit, a., mougharbel, i., ghaziri, h., and dao, t. t. (2020). fast soft tissue deformation and stump-socket interaction toward a computer-aided design system for lower limb prostheses. irbm, 41(5), pp. 276-285. doi 10.1016/j.irbm.2020.02.003. b i.boudjemaa et alii, frattura ed integrità strutturale, 57 (2021) 160-168; doi: 10.3221/igf-esis.57.13 168 [9] boudjemaa, i., sahli, a., benkhettou, a., and benbarek, s. (2021). effect of multi-layer prosthetic foam liner on the stresses at the stump–prosthetic interface. frattura ed integrità strutturale, 15(56), pp. 187-194. doi: 10.3221/igf-esis.56.15. [10] mbithi, f. m., chipperfield, a. j., steer, j. w., and dickinson, a. s. (2019, july). predictive control for an active prosthetic socket informed by fea-based tissue damage risk estimation. in 2019 41st annual international conference of the ieee engineering in medicine and biology society (embc) (pp. 2073-2076). ieee. doi: 10.1109/embc.2019.8857155. [11] chillale, t. p., kim, n. h., and smith, l. n. (2019). mechanical and finite element analysis of an innovative orthopedic implant designed to increase the weight carrying ability of the femur and reduce frictional forces on an amputee’s stump. military medicine, 184(supplement_1), pp. 627-636. doi: 10.1093/milmed/usy382. [12] vélezzea, j. a., bustamante góez, l. m., and villarraga ossa, j. a. (2015). relation between residual limb length and stress distribution over stump for transfemoral amputees. revista eia, (23), pp. 107-115. [13] zhang, l., zhu, m., shen, l., and zheng, f. (2013, july). finite element analysis of the contact interface between trans-femoral stump and prosthetic socket. in 2013 35th annual international conference of the ieee engineering in medicine and biology society (embc), pp. 1270-1273. doi: 10.1109/embc.2013.6609739. [14] lacroix, d., and patiño, j. f. r. (2011), finite element analysis of donning procedure of a prosthetic transfemoral socket, annals of biomedical engineering, 39(12), 2972. doi: 10.1007/s10439-011-0389-z. [15] ramírez, j. f., and vélez, j. a. (2012). incidence of the boundary condition between bone and soft tissue in a finite element model of a transfemoral amputee. prosthetics and orthotics international, 36(4), pp. 405-414. doi:10.1177/0309364612436409. [16] lee, w., zhang, c.c., ming, j.i.a., xiaohong, et al. (2004). finite element modeling of the contact interface between trans-tibial residual limb and prosthetic socket. medical engineering & physics, 26(8), pp. 655-662. doi: 10.1016/j.medengphy.2004.04.010. [17] lin, c. c., chang, c. h., wu, c. l., chung, k. c., and liao, i. c. (2004). effects of liner stiffness for trans-tibial prosthesis: a finite element contact model. medical engineering & physics, 26(1), pp. 1-9. doi: 10.1016/s1350-4533(03)00127-9. [18] jia, x., zhang, m., and lee, w. c. (2004). load transfer mechanics between trans-tibial prosthetic socket and residual limb—dynamic effects. journal of biomechanics, 37(9), pp. 1371-1377. doi: 10.1016/j.jbiomech.2003.12.024. [19] mak, a. f., zhang, m., and boone, d. a. (2001). state-of-the-art research in lower-limb prosthetic biomechanicssocket interface: a review. journal of rehabilitation research and development, 38(2), pp. 161-174. [20] dickinson, a. s., steer, j. w., and worsley, p. r. (2017). finite element analysis of the amputated lower limb: a systematic review and recommendations. medical engineering & physics, 43, pp. 1-18. doi: 10.1016/j.medengphy.2017.02.008. [21] vantadori, s., carpinteri, a., fortese, g., ronchei, c., scorza, d., and berto, f. (2016). two-parameter fracture model for cortical bone. fratturaedintegritàstrutturale, 10(37), pp. 215-220. doi: 10.3221/igf-esis.37.28. [22] aliha, m. r. m., ghazi, h., and ataei, f. (2019). experimental fracture resistance study for cracked bovine femur bone samples. fratturaedintegritàstrutturale, 13(50), pp. 602-612. doi: 10.3221/igf-esis.50.51. [23] surapureddy, r., schönning, a., stagon, s., and kassab, a. (2016). predicting pressure distribution between transfemoral prosthetic socket and residual limb using finite element analysis. international journal of experimental and computational biomechanics, 4(1), pp. 32-48. [24] ramos, a., and simoes, j. a. (2006), tetrahedral versus hexahedral finite elements in numerical modelling of the proximal femur, medical engineering & physics, 28(9), pp. 916-924. doi: 10.1016/j.medengphy.2005.12.006. microsoft word numero 23 articolo 1 r. casati et alii, frattura ed integrità strutturale, 23 (2013) 7-12; doi: 10.3221/igf-esis.23.01 7 scilla 2012 the italian research on smart materials and mems on the preparation and characterization of thin niti shape memory alloy wires for mems riccardo casati, maurizio vedani department of mechanical engineering, politecnico di milano, via la masa 34, milano, italy syed a. m. tofail, calum dikinson materials and surface science institute, university of limerick, limerick, ireland ausonio tuissi national research council (cnr-ieni), corso promessi sposi 29, lecco, italy abstract. shape memory alloy (sma) wires are employed as actuators in small devices for consumer electronics, valves and automotive applications. because of the continued miniaturization of all the industrial products, nowadays the tendency is to produce mems (micro electromechanical systems). among the most promising functional mems materials, the thin sma wires that are offering a rapid actuating response with high power/weigh ratio of the material, are attracting a world wide interest. this paper is aimed at showing the production process and the characterizations of thin niti shape memory wires. the activity was focused on drawing procedure and on functional and tem characterizations of the final products. in particular, it was evaluated the performance of the sma wires for actuators in terms of functional fatigue and thermo-mechanical properties by means of an experimental apparatus design ad hoc for these specific tests. keywords. shape memory alloys; sma; mems; thin wire; actuators; tem. introduction mas are basically functional materials which exhibit peculiar thermo-mechanical properties such as the shape memory effect and the superelasticity. these properties are consequence of a reversible thermo-elastic martensitic transformation occurring at the solid state [1]. because the martensite phase shows a strong amplitude-dependent internal friction, sma have also an high damping capacity [2, 3]. when sma is used as actuator, it can be classified as “smart material” because it combines both sensor and actuator functions. sma alloys are applied with success in several commercial fields: biomedical (stents, orthodontic arc wire, orthopaedics devices, surgical tools); sensor/actuator (valves, active actuators, on/off devices); coupling (pipe fastener, electric fastener); sport; manufactures; antennas, gadgets etc. [4,5]. in the modern world, great emphasis has been placed in miniaturization and huge research efforts are oriented to develop mems (micro electro-mechanical systems) to perform a multitude of tasks [6]. among mems materials the sma, in form of films or thin wires, are attracting a particular interest for the development of new highly functionalized devices on micro/meso scale [7-10]. sma elements are characterized by a significant amount of actuation with an extremely small total volume over conventional actuator mechanisms. another advantage that shape memory alloys have is the versatility since they can be actuated thermally or electrically [7-10]. in this work, ti rich niti alloy, with high transformation temperatures, is produced by vacuum induction melting and thin wire are manufactured by hot and cold working. the main processing aspects of thin niti wire manufacturing are reported with specific reference to the effect s http://www.gruppofrattura.it http://dx.medra.org/10.3221/igf-esis.23.01&auth=true r. casati et alii, frattura ed integrità strutturale, 23 (2013) 7-12; doi: 10.3221/igf-esis.23.01 8 of cold drawing steps on the wire characteristics. the process can be scale down to diam. 10 micron wire for the developing of sma device within meso/micro scale. for both the drawn and the trained wires, longitudinal cracks, localized around inclusions, were highlighted by tem analyses. again, functional properties of the produced wires are studied by both dsc scans and electrically actuated thermal cycling under constant applied stress up to 300.000 cycles. experimental methods t was chosen a ni rich ni49ti51 (at.%) composition, which is very commonly employed for the production of shape memory materials for actuators with transformation temperature above room temperature. electrolytic grade nickel and pure titanium (grade 1) were melted by vim (vacuum induction melting) furnace in carbon crucible under argon atmosphere [11]. the ingot was hot forged and hot rolled at 950°c and finally cold drawn with intermediate annealing. the first steps of the drawing process (down to the diameter of 0.5 mm) were performed by means of a conventional drawing machine reaching values of area reduction of about 10-20% before each thermal annealing (700 °c). the final steps of drawing were indeed carried out employing a special experimental drawing system (mgs mod. trf 6/25 m) modified to prevent breakings of wires (fig. 1a). this machine was equipped by a controlled drawing speed system, an electrical clutch coiler and a laser sensor-controlled spooling system for correct distribution of the wire on the spool (fig. 1b), diamond dies, load cell, die cooling system, camera for checking correct wire pay-on (fig. 1b). in tab. 1, the die used and the heat treatments parameters carried out during the cold drawing process are resumed. the evolution of functional properties, in particular of the residual strain, during thermo-mechanical cycling by means of an experimental apparatus designed ad hoc for these specific tests is here reported. specimens (100 mm in length) were vertically gripped in the testing equipment and axially loaded (250 mpa). they were heated by electrical pulses (see fig.2 for details of pulse parameters) and cooled by natural air convection. the wire displacement was measured by lvdt and relative strain was continuously monitored and evaluated as l/lo (lo wire length for each cycle before heating). the same experimental apparatus detailed reported elsewhere [13] was used in order to carried out the first 500 thermal cycles under 250 mpa as well as fatigue tests under 200 mpa. for the latter the total recovered strain was set at 3.8% and the stress at 200 mpa. (a) (b) figure 1: a) experimental drawing system b) laser sensor-controlled spooling system for correct distribution of the wire on the spool and camera for checking correct wire pay-on . before and after thermo-mechanical cycling calorimetric test were carried out by dsc seiko 220c. the temperature range investigated was 223k/403k (-50°c/130°c). thermo-mechanical loop was performed by dma ta q800 equipped with tension clamps for uniaxial tests. the temperature range investigated was 273k/423k (0°c/150°c), the heating and cooling rate was 5k/min and the applied stress was 200 mpa. microstructural analysis was executed by jeol jem-210 operating at 80 200 kv. thin slice for tem investigation were extracted from the center of the wire by focus ion beam fei 200 (fig.3a). in fig.3b a picture of a thin slice fib cutting is depicted. i http://www.gruppofrattura.it http://dx.medra.org/10.3221/igf-esis.23.01&auth=true r. casati et alii, frattura ed integrità strutturale, 23 (2013) 7-12; doi: 10.3221/igf-esis.23.01 9  die (m) area reduction 200 heat treatment: 300s 550°c + water quenching 175 23,4% 150 26,5% heat treatment: 300s 550°c + water quenching 130 24,9% 110 28,4% heat treatment: 300s 550°c + water quenching 100 17,4% 90 19,0% 80 21,0% heat treatment: 1200s 400°c + water quenching table 1: drawing steps and corresponding area reduction. figure 2: step waveform electrical pulse: ton = 0,4 s, toff = 2,5 s, imax = 0.13 a figure 3: a) scheme of tem sample preparation. b) niti thin slice used for tem analysis. results he whole working process was carried out without any formation of macroscopic cracks on the surfaces of the bars and the wires. the microstructure of the final product (80 μm wire) after heat treatment (400°c, 1200s) was investigated by tem. this analysis revealed a very fine polycrystalline microstructure (grain size was about 20nm) and the presence of inclusions (fig.4). t http://www.gruppofrattura.it http://dx.medra.org/10.3221/igf-esis.23.01&auth=true r. casati et alii, frattura ed integrità strutturale, 23 (2013) 7-12; doi: 10.3221/igf-esis.23.01 10 figure 4: tem images of the wire after the last heat treatment (1200 s, 400°c). figure 5: thermal cycling under constant stress (250mpa). this process is performed to stabilize the sm properties of the material. a high content of ti4ni2ox confirmed by selected area electron diffraction (saed) were observable. the drawing procedures caused the breaking of these ceramic compounds into fine inclusions that lined up in the drawing direction inducing significant amount of cracks into the matrix (fig.4). the inset diffraction pattern indexed space group fd-3m and lattice parameter 1.19 nm viewed down the [01-1] zone axis (in this respect, see the previous work by tuissi and coworkers [12]). before their application, smas must be thermo-mechanical cycled to stabilize their functional properties [13]. in order to reproduce a standard process of stabilization of the material, 500 thermal cycles under an applied stress of 250 mpa were carried on the wires (fig.5). during the first few hundreds cycles, the material accumulates irreversible plastic deformation. from the curve in fig.5 the lengthen of the wire is noticeable (about 2%). this phenomenon involves the increase of transition temperatures. fig.6a shows the results of calorimetric analyses performed on two samples of the wire taken before and after the thermo-mechanical cycling. both the samples exhibit a single-stage inverse transformation (between b19’ and b2) and a two-stage direct transformation (from b2 to r-phase and then to b19’). the main gap between the two curves consists in the transformation peaks broadening and in a increasing of transition temperature due to the cycling. similar results were obtained by thermal loop under constant stress (200 mpa) by dma. as depicted in fig.6b, the t-ε curves show a double inflexion on the cooling branch due to a two-stage direct transformation. the load leads to an increase in all transition temperatures, this is in according with the clausius-clapeyron relationship [1]. the increase in transformation temperature due to thermo-mechanical cycling is detectable even under an applied constant load. the cycling promoted an increase of rm transition temperature which, summed to the effect of the applied load, implies the disappearance of r-phase during the cooling and then a narrow thermal hysteresis. 20 um http://www.gruppofrattura.it http://dx.medra.org/10.3221/igf-esis.23.01&auth=true r. casati et alii, frattura ed integrità strutturale, 23 (2013) 7-12; doi: 10.3221/igf-esis.23.01 11 in fig. 7 the strain-cycles curves are reported: the wire was subjected to 300,000 cycles under constant stress (200 mpa) and the strain recovered was set at 3.8%. this fatigue test shows that even if the metal matrix exhibits a significant amount of cracks, the wire could withstand a very high number of thermo-mechanical cycles, indeed no wire failure occurred. (a) (b) figure 6: a) dsc curves and b) thermal loop under constant load before and after 500 cycles figure 7: fatigue test: thermal cycling under constant stress (200 mpa). conclusions he results obtained through this research can be summarized as follow:  80 μm ni49ti51 (at.%) wire was produced without any formation of macroscopic cracks on the surfaces of the final product. then, the procedure revealed to be suitable for the production of very thin shape memory wire employable in mems, actuators and other applications.  tem analysis revealed a mean grain size of few tens nanometers and the presence of rather big inclusions (less than 1 μm). saed pattern revealed these particles to be ti4ni2ox inclusions. these ceramic compounds did not impaired significantly the fatigue behavior of the sma wire, since it could reach 300000 cycles without failing.  the wire shows characteristic transformation temperature higher than room one. thermo-mechanical cycling leads to a reduction of thermal hysteresis. these are good points for the using of the material as shape memory actuator. acknowledgements he authors would like to thanks marco pini; nicola bennato; enrico bassani (cnr ieni lecco) for melting and technical assistance serguei belochapkines (university of limerick) for tem assistance. t t http://www.gruppofrattura.it http://dx.medra.org/10.3221/igf-esis.23.01&auth=true r. casati et alii, frattura ed integrità strutturale, 23 (2013) 7-12; doi: 10.3221/igf-esis.23.01 12 references [1] k. otsuka, c.m. wayman, shape memory materials. cambridge university press, (1998). [2] j.van humbeek, journal of alloys and compounds, 355(1–2) 30 (2003) 58. [3] b. coluzzi, a. biscarini, g. mazzolai, f.m. mazzolai, a. tuissi, e. villa, key engineering materials, 319 (2006) 1. [4] t. duerig, a. pelton, d. stöckel, materials science and engineering a, 273-275 (1999) 149. [5] j. van humbeck, materials science and engineering a, 273-275 (1999) 134. [6] t. hsu, in: ieee/asme international conference on advanced manufacturing technologies and education in the 21st century, chia-yi, taiwan, republic of china, (2002). [7] k. ikuta, micro/miniature shape memory alloy actuator. iee-icra (1990). [8] l. sun, w.m. huang, z. ding, y. zhao, c.c. wang, h. purnawali, c. tang, materials and design 33 (1) (2012) 577. [9] a. nespoli, s. besseghini, s. pittaccio, e. villa, s. viscuso, sen actuators, a158 (2010) 149. [10] y. fu, h. du, w. huang, s. zhang , m. hu, sensors and actuators a, 112(2-3) (2004) 395. [11] a. tuissi, p. bassani, a. mangioni, l. toia, in: proceedings smst 2004, asm international, materials park, oh, (2006) 501. [12] r. casati, a. tuissi, s. belochapkine, c. dickinson, s.a.m. tofail, functional materials letters, 5(1) (2012) 1250009. [13] r. casati, a. tuissi, journal of materials engineering and performance, 21(12) (2012) 2633. http://www.gruppofrattura.it http://dx.medra.org/10.3221/igf-esis.23.01&auth=true microsoft word numero_55_art_10_2915 v. yu. popov et alii, frattura ed integrità strutturale, 55 (2021) 136-144; doi: 10.3221/igf-esis.55.10 136 assessment of the strength reliability of high-temperature heat exchangers with long service life at the design stage v.yu. popov moscow aviation institute, russia quazzar.89@mail.ru, https://orcid.org/0000-0002-9290-8627 v.v. kashelkin, m.yu. fedorov jsc "krasnaya zvezda", russia reentry@redstaratom.ru a.s. demidov moscow aviation institute, russia demidov@mai.ru abstract. the article describes a method for assessing the strength reliability of high-temperature heat exchangers with service life of several tens of thousands of hours at the design stage, when there is not enough statistical data on the operating time of elements and material properties. the method shows, how to determine the coefficients of variation for calculating reliability and build the function of the probability of failure-free operation, considering the change of the properties of the structural material over time. the method of visualizing the distribution of zones, both satisfying and not satisfying reliability criteria at the nodes of any finite element model, is also described. keywords. reliability; strength; heat-exchanger; assessment. citation: popov, v. yu., kashelkin, v. v., fedorov, m.yu., demidov a.s., assessment of the strength reliability of high-temperature heat-exchangers with long service life at the design stage, frattura ed integrità strutturale, 55 (2021) 136-144. received: 08.09.2020 accepted: 10.11.2020 published: 01.01.2021 copyright: © 2021 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. introduction he energy supply of high-power systems requires the use of heat exchangers (he) for various purposes as part of a power plant. in the case when the service life of the plants is several tens of thousands of hours, and the temperatures reach the creep temperatures of the structural material, it becomes necessary to take into account changes in the properties of materials (reduction of long-term static strength), as well as changes in the stress state of the structure (stress relaxation) over time, which is directly affects strength reliability. thus, the substantiation of the strength reliability of he with long service life is a rather difficult engineering task. t https://youtu.be/uxzokescbv8 v. yu. popov et alii, frattura ed integrità strutturale, 55 (2021) 136-144; doi: 10.3221/igf-esis.55.10 137 there are several works devoted to reliability of he. however, in [1] the authors use statistical data on similar serial heat exchangers that have been working for a long time and determine other parameters. in work [2], the authors use a similar method in content, however, they carry out calculations in the software package and do not indicate data on the coefficients of variation and the principle of their choice. in [3], considered a technique for analyzing the reliability of complex mechanical systems at the design stage, however, the authors consider other aspect of this problem. in this paper, the authors consider a method for determining the coefficients of variation for calculating the reliability of complex systems, such as he, at the design stage. object of study s an example, considered a shell-and-tube type he with a cylindrical body in which a tube packet (tp) is enclosed. the tubes in packet are connected to the tube boards by welding. in the general case, the structure is under the influence of pressure drops in various cavities and under the influence of high temperature fields distributed according to a certain law both along the length of the structure and in the radial direction along he sections. the thermal isolation of the casing and the tube package is carried out using a bellows (fig. 1). all parts are made of steel 08cr16n11m3 (russian classification). the structural model and the finite element model ig. 2 shows the finite element model (fem) built in the «fidesys» software package. fig. 3 shows the distribution of the temperature field in the heat exchanger. figure 1: structural model of he figure 2: variant of finite element model of the he a f v. yu. popov et alii, frattura ed integrità strutturale, 55 (2021) 136-144; doi: 10.3221/igf-esis.55.10 138 figure 3: temperature field applied to he, °c estimation of long-term static strength considering the effect of stress relaxation he study of the stress state of the structure using the fem showed the presence of high stresses in the compensator,  = 200 mpa (figs. 4, 5), which exceeds the long-term static strength mtr for the material used at a temperature of 600 °c, and a resource of 1×105 hours:  80mtr mpa, however, does not exceed the limit of short-period (about tens of hours) long-term static strength ltsr according to [4]:  273ltsr mpa. figure 4: calculation results. fragments with the highest stresses, mpa. figure 5: calculation results. compensator of temperature displacements, mpa to calculate the relaxation process, the equation of steady creep was used in the form proposed by shesterikov s. a. and yumasheva m. a. [4], which best way describes the experimental data for the considered steel:            n cr lts a r (1) where ltsr the limit of short-period long-term static strength according to [4], for 600 °c: ltsr = 273 mpa;  – the calculated stresses in the element under study, mpa; a and n – temperature-dependent constants obtained by processing the results of steel creep tests; on which based method of processing of experimental data in [4]:              lg( ) 17 lg( ) lg ap lts lts a t d r n r (2) t v. yu. popov et alii, frattura ed integrità strutturale, 55 (2021) 136-144; doi: 10.3221/igf-esis.55.10 139 where  a – the applied stress in experiment; pt – time to sample failure and               17 lg n a p lts lts a d t r r (3) in accordance with [4], after processing the test results of 08cr16n11m3 steel, for 600 °c: a = 2.0725×10-6 and n = 2.238. based on relation (1), the relaxation equation is obtained following way. if the total strain (elastic + creep) is constant, then it can be argued that the strain rate is zero:        ˙ 0el cr (4) equation for elastic strain:     el е (5) and eqn. (4) takes the following form:                n lts а е r 0 (6) or            1   0   n lts d а е dt r (7) after transformation of eqn. (7), the relaxation equation is obtained:                0 1 n ltsrt d ae (8) where e – the young’s modulus of steel at the corresponding temperature, for 600 °c: e = 1.63×105 mpa;  0 – the stress at the initial instant of time. the relaxation curve for the initial stresses σ0 = 200 mpa and the long-term strength curve are presented in fig. 6. it can be seen that the relaxation curve lies below the long-term strength curve constructed from the values from [5] over the entire considered time period. formally, a comparison of these curves is enough to satisfy the criteria of long-term static strength, however, in the general case, the magnitude of the acting stresses, considering relaxation, is a random variable. also, a random variable is the value of the long-term static strength, therefore, to assess functional reliability, the use of probabilistic methods is necessary. v. yu. popov et alii, frattura ed integrità strutturale, 55 (2021) 136-144; doi: 10.3221/igf-esis.55.10 140 figure 6: relaxation and long-term strength curves for 08cr16n11m3 steel for the initial stress of 200 mpa and the temperature of 600 °c. reliability assessment method n the general case, the strength reliability is determined through the probability of failure-free operation p, which is gotten by integrating the probability density function  ψp of the difference of random variables r alleged failure stresses, with the mathematical expectation r and f of the calculated stresses, with the mathematical expectation f :  ψp =  p r f (fig. 7), in the interval determining the failure-free operation, on which the values of r ≥ f, i.e. from 0 to +.                 2 20 ψ1 22 p exp d (9) where  – the integration variable;   – standard deviation of a random variable  , according to the rule of summation of random variables, the square of which  2ψ is equal to the sum of the variances dr =  2 r and df =  2 f :     2 2 2 ψ r f [6], from where               2 22 2 r f r fr f (10) where  r and  f are the object of the investigation are the coefficients of variation of the random variables r and f; ψ the mathematical expectation of a random variable, in this case, the meaning of the mathematical expectation difference  ψ r f . to take into account the change in the reliability characteristics over time, use the relaxation curve as a function describing the change in the calculated stresses  f t , and the long-term strength curve as a function describing the change in the stress of the alleged failure  r t , and obtain       ψ t r t f t . then can be built (for example, in matlab or python) a three-dimensional function of probability density over time, taking into account the change in time of all its parameters (fig. 8) [7, 8] and the function of changing the probability of failure-free operation over time (fig. 9). i v. yu. popov et alii, frattura ed integrità strutturale, 55 (2021) 136-144; doi: 10.3221/igf-esis.55.10 141 figure 7: example of probability density  ψp figure 8: example of probability density dependence function on time figure 9: example of function of the dependence of the reliability indicator on time determination of coefficient of variation the determination of the coefficients  r and  f is a key problem in the probabilistic assessment of reliability, because there are no general methods for their determination for cases where there are no statistical data from which it would be possible to determine the variances of the dr , df values and standard deviations r and  f . the best way to determine the value characterizing the deviation of the failure stresses from the mathematical expectation is to test the steel samples that are supposed to be used and obtain data on the scatter of values, and then determine the coefficient of variation of material properties based on them, but it is often not available. in this case, the coefficient of variation for welded joints can be included in the value as a term, according to [9]: νwld = 0.05, which characterizes the deviations associated with the peculiarities of changing the properties of the material in the welding area. as the second term characterizing the deviations of the properties of the material, can be taken the value of the coefficient of variation of the properties of the material, equal to 0.1, from the russian regulatory document “gost 25.504 “calculations and strength tests. methods for calculating fatigue resistance characteristics.” the final coefficient of variation for the allowable stresses will be determined as the sum of these terms:    0.1 0.05 0.15r (11) next, it is necessary to determine the coefficient of variation  f for the stresses obtained as a result of the load, which determines the possible deviation of the load value from the calculation. this coefficient cannot be found in the literature and the main question becomes how to determine and justify its value. considering that stresses are determined as a result of calculations, it would be logical to use the error of the methods by which these calculations were performed as the coefficient of variation. for "manual calculation", can be considered the error associated with cutting off the decimal places. using the fem, a number of test calculations can be performed on t ×104, h , мpа allowable level estimated index of reliability t ×104, h p(, t) v. yu. popov et alii, frattura ed integrità strutturale, 55 (2021) 136-144; doi: 10.3221/igf-esis.55.10 142 simple problems and compared with the exact analytical solution. from experience can be said, that as a rule, with proper preparation of the model, the fem error does not exceed 5-6% (i.e., a variation coefficient of  f 0.05 or 0.06 can be used), however, the calculation error for a complex model may increase due to the influence of other mathematical factors (such as an increase in stresses in the zones of “mathematical concentrators”), which will require the use of a posteriori estimation methods for the error of fem calculation and the use of data obtained on their basis. in calculating the fem, the following method can also be used. in this calculation, there is an element whose reliability is the subject of research a compensator. using the method of submodeling, this element is "cut out", after which the problem is solved many times with mesh refinement with each new calculation until the asymptotic convergence of the results is obtained. on example of compensator from previous section we get following results (see tab. 1). number of elements by thickness 2 3 4 5 6 7 stress in the compensator, mpa 200 175.3 179 170.6 169.7 170.1 table 1: the results of fem calculations for the strength of the compensator after that, using data from tab. 1, can be calculated the sample average value, which is taken as the mathematical expectation     1 1 n i i f n = 177.45 mpa (12) selective (unbiased) variance as        2 1 1 1 n f i i d f n = 135.31 mpa2 (13) and get  2f fd . from where:    22 2/ 135.31/ 177.45f f f 0.065 (14) accordingly, the more results after the solution is established, the higher the accuracy and less  f , which is not required in this formulation of the problem. on the contrary, in order to obtain a more conservative result, it is necessary to obtain the minimum and maximum value of the calculated stresses for the model under study in order to determine the calculation error “relative to oneself” for further calculation of the values necessary for assessing reliability f and  f necessary for assessing reliability. as variation coefficient of load  f for structures that will subsequently be subjected to mechanical tests, can be taken the total error rounded up for all metrological characteristics of the equipment on which loading conditions will be implemented. such information is usually contained in the certificate of verification of equipment and this value can be about 3.5% (i.e., a variation coefficient of 0.035 can be used). if it is impossible to obtain data of  f other way, this approach can be considered quite acceptable. in the general case, the coefficients  r and  f can also depend on time; however, it is rather difficult to justify the function of their change without sufficient statistics on the properties of the material. results of reliability assessment n the case of designing complex structures, it is necessary that simple elements (parts) had a reliability indicator equal to 1 (in the mechanical sense, when we get as a result of the calculation 0.999999…. an infinite number of nines after the decimal point). i v. yu. popov et alii, frattura ed integrità strutturale, 55 (2021) 136-144; doi: 10.3221/igf-esis.55.10 143 using the method from “reliability assessment” section of this article, to assess the reliability of the compensator taking into account the values of the coefficients, can be obtained the field of nodes of the fe-model of the compensator with estimates of the satisfaction of the reliability criterion. after the fem calculation, data on the coordinates of the nodes and the values of the von mises stresses in these nodes can be downloaded from any software package. further, using algorithms written in matlab (or in another language), can be implemented the estimates from “reliability assessment” paragraph, and then load the converted results back into the software package (if it allows it) or implement graphical construction through the function “scatter3(x,y, z, d, d, 'o', 'filled')” from matlab, where x, y, z are the vectors of the coordinates of the nodes, and d are the values of the reliability estimates. as a result, it is possible to obtain a visualization of areas whose reliability does not meet the requirements at any of the time points of the resource, for example, less than 0.9999, as shown in fig. 10 (zones with p <0.9999 at a certain time point of the resource are highlighted). figure 10: nodal reliability assessment by fe model in matlab having received the results of the reliability assessment in this form, they can be used to build algorithms for automatic optimization of the structure with a change in the geometric and physical parameters of the model. conclusion he reliability assessment method given in this article is a convenient tool for assessing the reliability of structures at the design stage when there are no statistical data on operating hours and it is necessary to take into account the change in material properties and load over the service life. references [1] lingeswara, s. (2016). reliability analysis on a shell and tube heat exchanger, iop conf. ser.: earth environ. sci. 36, 012012 [2] amirat, a., bounamous, b., khelif, r., chateauneuf, a. and chaoui, k. (2008). reliability assessment of pipelines using phimeca software. in safety reliability and risks associated with water, oil and gas pipelines, springer netherlands, dordrecht, pp. 233-259. [3] covino, m. m., rodgers, p. a., smith, j. s., clarkson, j. p. (2000). assessing reliability in mechanical systems, society for design and process science, 4(2), pp. 67-84. [4] demidov, a.s., kashelkin, v.v., kashtanov, a.d., yakovlev, v.a. (2015). forecast of reactor steel 08х16н11м3-пд mechanical properties under creep conditions with regard for irradiation and without irradiation. bulletin of the moscow state technical university named after n.e. bauman, pp.18-26. [5] norms for calculating the strength of equipment and pipelines of nuclear power plants (pnae g-7-002-86) / ussr gosatomnadzor. –m .: energoatomizdat, (1989). p. 525. (rules and regulations in nuclear energy). [6] melchers, r. e., beck, a. t. (2018). structural reliability analysis and prediction: edition 3, john wiley & sons, p. 528. [7] ostreykovsky, v. (2008). reliability theory: textbook for universities, 2nd ed., p. 463. t v. yu. popov et alii, frattura ed integrità strutturale, 55 (2021) 136-144; doi: 10.3221/igf-esis.55.10 144 [8] system analysis reference: reliability, availability & optimization. url: http://reliawiki.com/index.php/timedependent_system_reliability_(analytical)(addressed october 23, 2019). [9] reshetov, d.n., ivanov, a.s., fadeev, v.z. (1988). reliability of machines / m.: "higher school", p. 237. [10] aguirre esponda, g.j. and wallace, k.m. (1990) evaluation of technical systems at the design stage. in: international conference on engineering design (iced'90), dubrovnik, croatia. shot peening processes to obtain nanocrystalline surfaces in metal alloys: k. okuda et alii, frattura ed integrità strutturale, 48 (2019) 125-134; doi: 10.3221/igf-esis.48.15 125 focussed on “crack paths” influence of microstructure on fatigue property of ultra high-strength steels kanji okuda, kazuhiro ogawa, yuji ichikawa tohoku university, japan kanji.okuda@rift.mech.tohoku.ac.jp, kogawa@rift.mech.tohoku.ac.jp, ichikawa@rift.mech.tohoku.ac.jp tsuyoshi shiozaki, naoki yamaguchi jfe steel corporation, japan t-shiozaki@jfe-steel.co.jp, n-yamaguchi@jfe-steel.co.jp abstract. ultra-high-strength steels (with tensile strength higher than 980 mpa) are widely used in automobile manufacturing owing to their lightweight that contributes to fuel efficiency. the fatigue strength of ultra-high-strength steels with a notch tends to decrease, which is known as the effect of notch sensitivity. in this study, 4-point bending fatigue tests were performed to examine the fatigue strength and notch sensitivity of four steels; namely 590 mpa class steel, 980 mpa class martensitic steel, 980 mpa class bainitic steel, and 980 mpa class precipitation hardening steel plates with three different stress concentration factors. the results indicate that the fatigue strength and notch sensitivity of 980 mpa class steel specimens were higher than those of 590 mpa class steel specimens. the notch sensitivities of tested plate specimens were lower than those reported for cylindrical specimens of bainitic ultra-high-strength steels. fatigue crack observation revealed that the cracks initiated in 590 mpa class steel, 980 mpa class bainitic, and martensitic steel propagated vertically from the lowest bottom of notch. although similar initial crack propagation pattern was detected in precipitation hardening steel, the crack changed direction when it reached the central part of the specimen. keywords. ultra-high-strength steel; fatigue; 4-point bending; fatigue crack. citation: okuda, k., ogawa, k., ichikawa, y., shiozaki, t., yamaguchi, n., influence of microstructure on fatigue property of ultra high-strength steels, frattura ed integrità strutturale, 48 (2019) 125-134. received: 30.11.2019 accepted: 18.02.2019 published: 01.04.2019 copyright: © 2019 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. introduction ecently, automobile fuel efficiency has been receiving worldwide attention to reduce automotive carbon emissions and to surpress global warming. reducing the vehicle weight is one of the most efficient methods to improve fuel efficiency. hence, this can be achieved by adopting lightweight steel with higher strength. for example, a similar r mailto:kanji.okuda@rift.mech.tohoku.ac.jp mailto:kogawa@rift.mech.tohoku.ac.jp mailto:t-shiozaki@jfe-steel.co.jp http://www.gruppofrattura.it/va/48/2304.mp4 k. okuda et alii, frattura ed integrità strutturale, 48 (2019) 125-134; doi: 10.3221/igf-esis.48.15 126 performance can be obtained with 1/3 of the vehicle weight using three times stronger lightweight steel than conventional steel. ultra-high-tensile-strength steel (uhts) exhibits lightweight properties with relatively high tensile strength, higher than 980 mpa, compared to conventional mild steel with tensile strength of approximately 300 mpa. multiple methods can be used to enhance the tensile strength of steels, such as heat treatment and microstructural control. these methods allow producing uhts with varying properties, including extension rates and yield stress values. however, despite the high fatigue strength of uhts compared to conventional steel, its applications in vehicle parts are limited owing to the significant decrease in uhts fatigue strength when it is subjected to any stress concentration. the fatigue strength of uhts used in fillet welded joint has shown a behavior similar to that of conventional steel because of the high stress concentration factor between the welded metal and substrate. using uhts in lap fillet joint of a suspension frame is critical owing to the limitation of producing it using butt welding; however, uhts may be susceptible to large vibrations owing to the position of suspension frames. the reduction in fatigue strength caused by stress concentration is known as notch sensitivity. this fatigue property is inherent to each material. notch sensitivity is quantified by the fatigue notch factor kf, defined as n c f s s k = (1) where sc is the fatigue limit of smooth specimen and sn is the fatigue limit of notched specimen [1]. notch sensitivity is generally evaluated using cylindrical specimens. the evaluations have revealed that the higher strength steel typically exhibits higher notch sensitivity. fig. 1, which shows the notch sensitivity of cylindrical carbon steel with different strengths in rotating bending fatigue test [2], indicates that the notch sensitivity of uhts is seen to be higher than that of a 787 mpa class specimen. also, fig. 1 shows that kf increases at a rate proportional to stress concentration factor kt up to 2. similar trend was observed in the latest bainitic uhts [3]. then, kf values become almost stagnant as the kt value increases. notch sensitivity must be considered when using high-strength material in parts subjected to stress concentration because the value of kf for high-strength materials tends to increase to approx. 3. however, most of the notch sensitivity evaluations described above are obtained by a rotary bending fatigue test. rotating bending test requires a cylindrical specimen which is not feasible make out of steel sheets that are used in automobiles. thus, any difference in notch sensitivity related to the shape of the specimen must be considered to determine the appropriate design. in this design stage, the fatigue notch factor is determined and the fatigue characteristics are evaluated using a thin steel plate sample. in particular, when a high-strength material like uhts with high notch sensitivity is used for automobile parts using thin steel plates, its fatigue characteristics must be evaluated using a thin steel plate specimen with the existence of a stress concentration. figure 1: relationship between kt and kf of carbon steels with different tensile strengths [2]. the microstructure of materials must be considered in order to evaluate their fatigue properties because the crack propagation behavior and fatigue strength can be changed based on the microstructural changes [4~6]. however, many studies aimed at improving the fatigue strength of welded joints focused on the development of residual stresses induced k. okuda et alii, frattura ed integrità strutturale, 48 (2019) 125-134; doi: 10.3221/igf-esis.48.15 127 by hammer peening [7] or shot peening [8] as methods to improve fatigue strength. however, in recent years, new uhts with different microstructures are developed to improve fatigue strength of uhts by microstructural control. thus, further studies are required to evaluate the fatigue properties of uhts welded joints with different microstructures. in this study, fatigue tests and crack observations have been performed to evaluate the fatigue properties of uhtss and ultimately improve the fatigue properties of steels. in order to improve the fatigue characteristics of uhts plates with different tensile strengths and microstructures were evaluated using flat specimens with notches simulating the stress concentration factor at the toe of the overlap fillet joint. experimental procedure materials and specimens urface notch specimens, which simulate lap fillet joint, and smooth specimens were used in this study. current material (590 mpa class ferrite-bainitic steel), and 3 types of uhts (980 mpa class bainitic steel, 980 mpa class martensitic steel, and 980 mpa class precipitation hardening steel) are prepared for the fatigue test. fig. 2 shows microstructures of 4 types of steels. bainitic steel has low ratio of martensitic phase inside bainitic based steel, while martensitic steel consists of full martensitic phase. precipitation hardened steel of this study was a precipitate of nano-sized particles in full-ferrite steel. the mechanical properties of the tested steels are listed in tab. 1. steels tensile strength [mpa] yield stress [mpa] elongation [%] vickers hardness [hv 1kg] 590 mpa class steel 610 464 26.0 192 bainitic steel 988 860 15.0 307 martensitic steel 1095 1008 11.1 356 precipitation hardened steel 1059 1014 17.6 333 table 1: mechanical properties of four types of steel. figure 2: microstructures of 4 types of steels (a) 590 mpa class steel, (b) bainitic steel, (c) martensitic steel, (d) and (e) precipitation hardened steel [9]. fig. 3 shows the sizes of fatigue test specimens. the notch depth is 1 mm, and the bottom of notch was processed with a curvature radius of 0.1 mm or 0.2 mm. the stress concentration factor of lap fillet joint in suspension frame, shown in fig. s k. okuda et alii, frattura ed integrità strutturale, 48 (2019) 125-134; doi: 10.3221/igf-esis.48.15 128 4, which had been estimated using finite element method, was approximately 2–3 using 1/4 sized model described in fig. 5. each samples notch was prepared with a stress concentration higher than that of a general lap fillet.. thus, kt values of 2.6, and 3.6 were obtained for the specimens with the curvature radii of the notch bottom 0.2 mm and 0.1 mm, respectively. surfaces of smooth specimens were electro-polished to eliminate or reduce the roughness. finite element analysis has been performed to calculate stress concentration factor of welded joint and surface notch specimen using nastran. pulsating load-controlled 4-point bending fatigue tests were conducted with stress ratio r = 0 (10–14 hz). the definition of fracture was of 0.25 mm deformation. cyclic tests were stopped when the cross-head displacement reaches 0.25 mm or the number of cycles reaches 3 x 106. the stress range of non-fractured specimens under 3 x 106 cycles was used as fatigue limit to calculate the fatigue notch factor kf.. the strain value was measured at 2000 cycles each points using strain gage. figure 3: sizes of tested specimens (mm). figure 4: cross section image of lap fillet joint supposed in this study. k. okuda et alii, frattura ed integrità strutturale, 48 (2019) 125-134; doi: 10.3221/igf-esis.48.15 129 figure 5: model used for fem calculation. fatigue tests the fatigue test results are shown in fig. 3. the fatigue limits when kt = 1 for all of the steel specimens are almost equivalent to their tensile strengths. the fatigue strength of notched specimens decreased with increasing stress concentration factor. however, the fatigue strength of notched 980 mpa class steel specimen was higher than that of notched 590 mpa class steel specimen. though similar fatigue strength were obtained for notched bainitic steel and martensitic steel specimens, the precipitation hardening steel is approximately 100 –150 mpa stronger than either of those steels. this result indicates the significant effect of microstructure on the fatigue strength of steels. the fatigue limit of precipitation hardening steel when kt = 3.6 was estimated as 500 mpa. the estimated fatigue limit value with the data obtained from the fatigue test were used to calculate the notch sensitivities of all the tested specimens, as shown in fig. 4. the notch sensitivities of the steel plates were far lower than those of cylindrical specimens. this can be attributed to the shape of surface notch specimen with one-side notch, and easiness of trapping of retention cracks. materials with high stress gradient is known to be easy to retain crack of crack tip [10]. steel plate with 3 mm thickness in this study has high stress gradient compared to conventional cylindrical specimens with 10 mm diameter used for evaluation of relationship between kt and kf [2]. figure 6: influence of specimen dimensions on fatigue strength (a) kt = 1, (b) kt = 2.6, (c) kt = 3.6. evaluation of data of strain gage in order to elucidate the cause of high fatigue strength of precipitation hardened steel, evaluation on strain gage data was conducted. the measured results by strain gage against the number of cycles in fig. 8 indicated that crack propagation which initiated at a, continued to propagate until the sample finally fractured at b. a is defined as the first point when the gradient (calculated by the least square method) of the last 6000 cycles were lower than 0, a value which was calculated from adjacent data point, starting from the fracture point, b to a. k. okuda et alii, frattura ed integrità strutturale, 48 (2019) 125-134; doi: 10.3221/igf-esis.48.15 130 figure 7: relationship between kt and kf, of tested specimens. figure 8: measured data of strain gage with increasing number of cycles (precipitation hardened steel (688 kn, 82023 fraction) fig. 9 shows the s-n curves of the test samples from beginning of the test until a. the results shown the crack propagation occurred faster for the precipitation hardened steel samples, then followed by bainitic steel samples and martensitic steel samples, respectively. these results were coherent with the s-n curves shown in fig. 6. as a results, the precipitation hardened steel samples had shown high fatigue strength attributed to the numerous nano-sized precipitates inside its grains, which intercept the movement of dislocation required for crack generation. fig. 10 shows the s-n curves of the same test samples used in fig. 9, but from a to b, representing the length of crack propagation of each samples. coherent to results obtained in fig. 9, the cycle range of crack propagation of precipitation hardened steel was the slowest, followed by bainitic steel and martensitic steel. to elucidate the cause of delay in crack propagation speed in precipitation hardened steel, sem observation and ebsd analysis was conducted. sem observation and ebsd analysis of cracks fig. 11 indicates the scanning electron microscope (sem) images of fatigue crack growth in each specimen when kt = 2.6. the fatigue cracks initiated in 590 mpa class steel, 980 mpa class bainitic steel, and martensitic steel specimens propagated k. okuda et alii, frattura ed integrità strutturale, 48 (2019) 125-134; doi: 10.3221/igf-esis.48.15 131 vertically from the bottom of notch. meanwhile, a similar initial propagation pattern was detected for the crack initiated in the precipitation hardening steel specimen; however, secondary cracks branched out in opposite directions when it reached the central part of the specimen. the cracks initiated in the 980 mpa class bainitic steel and martensitic steel specimens propagated straight from the bottom of notch. however, the curve of fatigue crack of precipitation hardening steel intercepted the crack propagation by spreading the energy of repeated stress. in order to observe the resulting microstructural changes and eventually understand the crack propagation mechanism that caused the fatigue crack, an electron back scattered diffraction (ebsd) analysis was conducted. figs. 12 and 13 illustrated the results of ebsd analysis performed for five crack points that initiated in the precipitation hardening steel specimen. figure 9: s-n curves of crack propagation start figure 10: s-n curves of cycle range of crack propagation ebsd analysis revealed the fatigue crack characteristics of each steel. a linear crack growth pattern with numerous repeated small refractions was observed in the 590 mpa class steel specimen. the crack propagation direction may change and grow in grains when the crack propagates into adjacent crystal grain with different orientation, such as grain a shown in fig. 12. meanwhile, the ebsd analysis of 980 mpa class bainitic steel specimen revealed a nearly vertical crack propagation pattern with repeated small branches and refractions from the bottom of notch; however, some of these refractions were intercepted by certain grains such as grain b shown in fig. 12. based on the sem observations carried out after etching, it was confirmed that this crystal grain was a martensitic phase. the fracture morphology formed during crack propagation in the 980 mpa class martensitic steel specimen was of transgranular character. when the crack changed its direction in the 980 mpa precipitation hardening steel specimen, the fracture morphology also changed. since nano-sized precipitation strengthen the ferrite grains in the precipitation hardened steel, the intergranular strength is relatively weaker than that of transgranular. hence, the transgranular crack was observed. detailed ebsd analysis of the precipitation hardening steel specimen is shown in fig. 13. the arrow indicates the direction of fatigue crack propagation. point b is an enlarged image of the crack between the bottom of notch and its branch point, where the fatigue crack grew with transgranular fracture. point c shows the intergranular fracture occurred when the crack propagated in the longitudinal direction after the crack k. okuda et alii, frattura ed integrità strutturale, 48 (2019) 125-134; doi: 10.3221/igf-esis.48.15 132 branch was formed. the crack may change its direction in vertical direction of specimen, as shown in point d, at which transgranular fracture morphology was detected while the crack propagated vertically. a fracture morphology of intergranular character was observed at point e at the end of crack. this indicates that the fracture morphology is influenced by microstructural control technique, which may delay the crack propagation range of material. fig. 14 indicates the result of ebsd analysis near the point b in fig. 13. before the crack reaches the branch point, many small cracks propagates in horizontal direction. the fracture morphology of the small crack was of transgranular character. these small cracks is also considered to spread the energy of repeated stress. furthermore, concerning the refraction of the crack, it is considered that the crack tip is blunted due to the sliding deformation of the slant crack [11]. figure 11: sem images of fatigue cracks growth. figure 12: results of ebsd analysis. k. okuda et alii, frattura ed integrità strutturale, 48 (2019) 125-134; doi: 10.3221/igf-esis.48.15 133 figure 13: result of ebsd analysis of precipitation hardening steel. figure 14: result of ebsd analysis of precipitation hardening steel near point b. conclusions n this study, 4-point bending fatigue tests were performed for four types of steel plates with surface notch (590 mpa class current material, 980 mpa class bainitic steel, martensitic steel, and precipitation hardening steel). the notch sensitivity of each steel specimen was evaluated in comparison to smooth plate specimens. in addition, sem observations and ebsd analysis of the cracks growth and propagation patterns were conducted. the following conclusions were drawn: i k. okuda et alii, frattura ed integrità strutturale, 48 (2019) 125-134; doi: 10.3221/igf-esis.48.15 134 the fatigue strength of all the 980 mpa class steel plates were higher than that of 590 class steel plate. an almost equivalent fatigue strength was obtained for the martensitic steel and bainitic steel specimens; however, the fatigue strength of precipitation hardening steel was 100–150 mpa higher than either of these steels. hence, the fatigue strength was considered to be influenced by the microstructural control technique. based on the results of notch sensitivity evaluation, the descending sequence of the tested steel specimens shows similar values for the 980 mpa class martensitic steel and 980 mpa class bainitic steel specimens, which are higher than that of the 590 mpa class steel. meanwhile, the notch sensitivity of 980 mpa class precipitation hardening steel is the lowest amongst all tested specimens. however, the obtained notch sensitivity values were lower than those obtained with cylindrical specimens. crack initiation of precipitation hardened steel is later than the other steels since nano-sized precipitates prevents the movement of dislocation require to the crack initiation. crack propagation speed was slowest in precipitation hardened steel, followed by bainitic steel, martensitic steel and 590 mpa class steel, respectively. sem observations confirmed that similar crack propagation patterns were detected in the 590 mpa class steel, bainitic steel, and martensitic steel specimens. however, the crack of bainitic steel was intercepted by martensitic phase inside the steel, this phenomenon is considered to be the cause of delay in crack propagation. the fatigue crack formed in the precipitation hardening steel specimen showed quite different propagation pattern, with changes in the crack direction after approximately 500 m propagation. ebsd analysis revealed the different fatigue crack propagation patterns in each steel. in particular, the change in the fracture morphology of precipitation hardening steel from transgranular fracture into intergranular fracture was revealed. references [1] weixing, y, kaiqua, x. (1995). on the fatigue notch factor, kf, int. j. fatigue, 17(4), pp. 245–251. doi: 10.1016/01421123(95)93538-d [2] ishibashi, t. (1984). kinzokuhirou to hakaino boushi, yokendo. ncid: ba43331546/ [3] yoshikawa, n., kobayashi, j., sugimoto, k. (2012). notch-fatigue properties of advanced trip-aided bainitic ferrite steels, metallurgical and materials transactions a, 43(11), pp. 4129–4136. doi: 10.1007/s11661-012-1246-x [4] riemer, a., leuders, s., thone, m., rechard, h.a., troster, t. niendorf, t. (2014). on the fatigue crack growth behaviour in 316l stainless steel, engineering fracture mechanics 120, pp. 15–25. doi:10.1015/j.engfracmech.2014.03.008. [5] nikulin, i., sawaguchi, t., i ogawa, k., tsuzaki, k. (2016). effect of  to  martensitic transformation on low-cycle fatigue behaviour and fatigue microstructure of fe-15mn-10cr-8ni-xsi austenitic alloys, acta materialia15, pp 207– 218. doi: 10.1016/j.actmat.2015.12.002. [6] krueger, d. d., antolovich, s. d., van stone, r. h. (1987). effects of grain size and precipitate size on the fatigue crack growth behavior of alloy 718 at 427 °c, metallurgical transactions a 18(8), pp. 1431 –1449. doi: 10.1007/bf02636657. [7] branco, c. m., infante, v., bapitista, r. (2004). fatigue behavior of welded joints with cracks, repaired by hammer peening, fatigue & fracture of engineering materials 27(9), pp. 785–798. doi: 10.1111/j.1460-2695.2004.00777.x. [8] sidhom, n., laamouri, a., fathallah, r., braham, c. lieurade, h.p. (2005). fatigue strength improvement of 5083 h11 al-alloy t-welded joint by shot peening: experimental characterization and predictive approach, international journal of fatigue 27, pp. 729–745. doi: 10.1016/j.ijfatigue.2005.02.001. [9] yoshitake, a., kinoshita, m., osawa, k., ogawa, k., nakagawa, h., kabasawa, m. (1994) pp. 1-2. [10] fatigue properties of fillet welded lap joints of high strength steel sheet for automobiles, the engeneering society for adbancing mobility land sea air and space, 1994. [11] vallellano., c, navarro., a, dominguez., j. (2009). fatigue failure assessment under stress gradients using small crack fatigue concepts, engineering failure analysis 16, pp 2646-2657. doi: 10.1016/j.engfailanal.2009.04.018. [12] okamura, h. (1976). senkei hakai rikigaku nyumon, baihukan, pp. 139, asin:b000ja0vdc. microsoft word numero_33_art_37 v. shlyannikov et alii, frattura ed integrità strutturale, 33 (2015) 335-344; doi: 10.3221/igf-esis.33.37 335 focussed on multiaxial fatigue surface crack growth in cylindrical hollow specimen subject to tension and torsion v. shlyannikov, r. yarullin, i. ishtyryakov kazan scientific center of russian academy of sciences shlyannikov@mail.ru, yarullin_r@mail.ru, ivan_200999@mail.ru abstract. the subject for studies is an aluminium cylindrical hollow specimen with external axial and part circumferential semi-elliptical surface crack undergoing fatigue loads. both the optical microscope measurements and the crack opening displacement (cod) method are used to monitor and calculate both crack depth and crack length during the tests. the variation of crack growth behaviour is studied under cyclic axial tension, pure torsion and combined tension+torsion fatigue loading. for the particular surface flaw geometries considered, the elastic and plastic in-plane and out-of-plane constraint parameters, as well as the governing parameter for stress fields in the form of in-integral and plastic stress intensity factor, are obtained as a function of the aspect ratio, dimensionless crack length and crack depth. the combined effect of tension and torsion loading and initial surface flaw orientation on the crack growth for two type of aluminium alloys is made explicit. the experimental and numerical results of the present study provided the opportunity to explore the suggestion that fatigue crack propagation may be governed more strongly by the plastic stress intensity factor rather than the magnitude of the elastic sifs alone. one advantage of the plastic sif is its sensitivity to combined loading due to accounting for the plastic properties of the material. keywords. surface crack; tension; torsion; crack growth. introduction n order to provide operation in a safe condition, it is necessary to perform fracture mechanics assessment of a structural component under cyclic loading. the fatigue growth analysis of surface cracks is one of the most important elements for structural integrity prediction of the circular cylindrical metallic components (bars, wires, bolts, shafts, etc.) in the presence of initial and accumulated operation damages. in most cases, part-through flaws appear on the free surface of the cylinder and defects are approximately considered as semi-elliptical cracks. multiaxial loading conditions including tension/compression, bending and torsion are typical for the circular cylindrical metallic components of engineering structures. the problem of residual fatigue life prediction of such type of structural elements is complex and the closed solution is often not available because surface flaws are three-dimensional in nature. the fatigue failure of cylindrical specimens often develops from surface flaws, and thus several analyses have been carried out to determine the stress intensity factors along the front of an edge defects and crack growth rate study on this base [1-4]. an actual surface crack may usually be replaced by an equivalent circular arc or elliptical-arc edge flaw. the elastic stress intensity factors have been published for part-circular, part-elliptical, or straight fronted cracks in a cylindrical specimen. in this paper, firstly experimental results of fatigue crack growth for a crack starting from a semi-elliptical edge notch in an cylindrical hollow specimens under axial loading with or without cyclic torsion are given. the influence of different i v. shlyannikov et alii, frattura ed integrità strutturale, 33 (2015) 335-344; doi: 10.3221/igf-esis.33.37 336 loading conditions on fatigue life of cylindrical specimens is discussed. the relations of crack opening displacement and crack length on the free surface of specimens are obtained and it is shown that the growth of the crack fronts is dependent on the initial notch form. using the aforementioned relations, the crack front shape and crack growth rate in the depth direction can be predicted. the simulations for the crack path assessment are based on the constrain parameters behaviour. the computational 3d fracture analyses deliver a governing parameter of elastic-plastic stress field distributions along the crack front. on this base crack growth interpretation is performed using the traditional elastic and new plastic stress intensity factors [5-7]. different crack growth rate is observed in the direction of the deepest point of the crack front with respect to the free surface of the hollow cylindrical specimen. specimens and material properties he test materials are aluminum alloys d16t and b95 which main mechanical are listed in tab. 1 where e is the young’s modulus, b is the nominal ultimate tensile strength, 0 is the monotonic tensile yield strength, u is the true ultimate tensile strength,  is the elongation,  is the reduction of area, n is the strain hardening exponent and α is the strain hardening coefficient. aluminum alloy 0.2 mpa b mpa  %  % u mpa e gpa n α d16t 439 590 9 9 645 75.922 5.88 1.5 438 598 12 13 686 77.191 5.85 1.58 b95at 442 604 11 11 658 77.734 5.79 1.66 470 637 10 15 731 74.135 6.62 1.62 table 1: main mechanical properties of aluminum alloys. figure 1: details of the hollow specimen geometry and initial notches. the hollow cylindrical specimen geometry configuration is shown in fig. 1. the diameter is equal to 28 mm in the test section and the length is equal to 130 mm. using linear cutting machine surface edge cracks were cut with initial flaw depths b0 3.0 mm for both a circular arc and elliptical-arc initial edge notch. the geometric parameters of the specimen test section and of the growing crack are shown in figs. 1 and 2. in these figures, b is the current crack depth, with the crack front approximated by an elliptical curve with major axis 2c and minor axis 2a. the crack length b is obtained by measuring the distance between the advancing crack break through point and the notch break through point, as shown in fig. 2. the depth of the initial curvilinear edge notch is denoted by a and the initial notch length by h. the crack opening displacement is measured on the free hollow specimen cylindrical surface, in the central plane of symmetry as shown in fig. 2. the axial torsion test system bi-00-701 is used for axial-torsional fatigue and fracture testing of the hollow cylindrical specimens. this system is equipped with: fatigue rated axial-torsional dynamic load cell with axial capacity 100 kn and torsional capacity 2 kn-m; bi-06-3xx series axial extensometers and torsional strain measurement fixture. the crack length on the specimen lateral surface were monitored using the optical instrumental zoom microscope whereas, to fix the crack opening displacement of specimen at the gauge length, a pulley arrangement with an externally axial encoder t v. shlyannikov et alii, frattura ed integrità strutturale, 33 (2015) 335-344; doi: 10.3221/igf-esis.33.37 337 is introduced (fig. 2). all tests are carried out with sinusoidal loading form, with load and torque moment control. for the simple cyclic tension fatigue tests, the specimens are tested with an applied maximum nominal stress equal to 80 mpa and with a frequency value 10 hz. the combined tension/torsion tests are performed with the same stress ratio, applying synchronous and in-phase tensile and shear stresses whose maximum values are respectively equal to 75 and 59 mpa.   figure 2: test equipment for measuring cod and edge crack geometric parameters. a0/c0 = 0.9 a0/c0 = 0.37 a) b) c) figure 3: aspect ratio versus crack depth under tension for different initial surface flaw geometries. a) b) c) figure 4: surface crack paths under torsion for (a) transverse and (b,c) longitudinal initial notches. v. shlyannikov et alii, frattura ed integrità strutturale, 33 (2015) 335-344; doi: 10.3221/igf-esis.33.37 338 two different stress ratio rf values (0.1 and 0.5) were applied several times to the specimens in order to highlight the crack front geometry during propagation: during each test, beach marks were produced on each specimen by increasing the applied stress ratio from 0.1 to 0.5 at constant value of maximum cyclic nominal stress, when the surface crack length was approximately increased to a  0.1mm. the typical beach marks on the post mortem cross section of different specimens are shown in figs. 3 and 4 for tension and torsion, respectively. from the crack front shape obtained in this way, the relations between the relative crack depth a/d and the surface crack chord length c/d can be measured using a comparison microscope. in addition, based on periodically measured increments of surface crack chord length b, the curve of surface crack propagation versus cycle numbers db/dn can be obtained. afterwards, utilizing the relation of crack depth versus surface crack chord length, it is possible to obtain the crack growth rates da/dn in the depth direction. another interesting result pointed out in the present study is the crack front and aspect ratio stabilization (fig.3,b) with respect to different initial notch geometry, when considering the analyzed multiaxial loading condition. it can be seen that the crack propagation paths differ with diverse initial flaw forms, but converge to the same configuration when the crack depth ratio is larger than about 0.25. numerical results dimensionless coordinates rom figs. 3 and 4 can be seen that the length of the arc of semi-elliptical crack front depends on the loading conditions of the hollow specimens. moreover, the crack propagation process in hollow samples can be divided into two stages. during the first stage a semi-elliptical crack is a part-through-thickness. on the second stage semielliptical crack completely crosses the cylinder wall and becomes a through-thickness. to compare the parameter distributions along the semi-elliptical crack front is convenient to introduce the dimensionless coordinates in the following form: 0 0cosx    , 0 0siny    (1) cosc cx    , sinc cy    cosi ix    , sini iy    ,  0 , i c   , 0c     0 0 i i c x x x x x    ; 0 0 i i c y y y y y    (2) 2 21 2 i iir x y  ,  0, 1r  (3) where 0 is angle determining position of initial point of the semi-elliptical crack front whereas c is angle corresponding to the deepest point of the crack front. in the following representation of numerical results, we will use variable r changing in the range from 0 to 1. constraint parameters recently, several two parameter models describing elastic-plastic fracture mechanics were introduced to explain some of the restrictions inherent in the one parameter approach based on the j-integral. the different sources of changes in the inplane and out-of-plane constraint are associated with the crack size, the geometry of the specimen and the loading conditions and notch effects on the fracture resistance characteristics of structural materials. characterization of the constraint effects in the present study was performed using the non-singular t-stresses, the local triaxiality parameter h and the tz-factor of the stress-state in a 3d cracked body to illustrate the features of the behavior of surface cracks in the hollow specimen. t-stress the t-stress has been recognized to present a measure of the constraint for the small-scale yielding conditions. few methods have been proposed for calculating t. this study explores the direct application of fem analysis by using the crack flank nodal displacements for calculating t-stress. using this technique, the t-stress distributions in various specimen geometries were determined from numerical calculations. to this end, the commercial finite element code, ansys [8], was used to calculate the stress distributions ahead of the crack tips. in this part of the fea calculations, the material is assumed to be linear elastic and characterized by e=74 gpa and =0.3. f v. shlyannikov et alii, frattura ed integrità strutturale, 33 (2015) 335-344; doi: 10.3221/igf-esis.33.37 339 tz-factor the tz factor [9] has been recognized to present a measure of the out-of-plane constraint and can be expressed as the ratio of the normal elastic-plastic stress components zz z xx yy t      (4) where zz is the out-of-plane stress, and xx and yy are the in-plane stresses. the variation of this parameter is important to characterize the thickness effect on the crack front stress distribution and the changes of the plastic zone size. stress triaxiality as a secondary fracture parameter, a local parameter of the crack-tip constraint was proposed by the authors [10] because the validity of some of the above-mentioned concepts depends on the chosen reference field. this stress triaxiality parameter is described as follows:   3, , 3 2 kk ij ijh r z s s         (5) where kk and sij are the hydrostatic and deviatoric stresses, respectively. being a function of both the first invariant of the stress tensor and the second invariant of the stress deviator, the stress triaxiality parameter is a local measure of the inplane and out-of-plane constraint that is independent of any reference field. the distributions of the elastic and elastic-plastic constraint parameters along the crack front in the hollow specimen under cyclic tension are plotted in fig. 5 under pure mode i loading. these distributions correspond to the crack front positions at the accumulated number of loading cycles n1=0 (initial front), n2= 21000 (intermediate front), n3= 50000 (intermediate front), n4= 131500 (final failure front). the constraint parameter is plotted against the normalized coordinate r. in this plot r = 0.0 is the crack border (the specimen free surface) while r = 1.0 is the mid-plane of the hollow specimen thickness. it can be observed that all constraint parameters essentially changed along the crack front from the free surface toward the mid-plane. it should be noted that the front of the number four in the fig. 5 corresponds to the second stage of crack propagation when it becomes completely through-thickness and intersects the cylinder wall. а) b) с) figure 5: constraint parameter distributions under cyclic tension along crack front (1-initial, 2-3-intermediate, 4-final). plastic stress intensity factor here, our primary interests are to obtain an accurate description for the distribution along the crack front of the governing parameter for the elastic-plastic solution in the form of an in-integral and to determine the accuracy that this type of calculation, which will later be used for the general 3d problem, provides for the plastic stress intensity factor (sif). the method developed here for combining the knowledge of the dominant singular solution with the finite element technique to obtain accurate solutions in the neighborhood of a crack tip is also applicable to the treatment of problems involving cracks in finite bodies. v. shlyannikov et alii, frattura ed integrità strutturale, 33 (2015) 335-344; doi: 10.3221/igf-esis.33.37 340 in accordance with the approach of hutchinson [11], the plastic stress intensity factor pk in pure mode i (or pure mode ii) can be expressed directly in terms of the corresponding elastic stress intensity factor using rice’s j-integral. that is      2 2 1 10 ; ' ' n n p k j i k e e      (6)             ; 11 2 1 2 0 11 2 0 2 1                       n n n n p i way i k k       wayk 11   (7) where wkk 11  is normalized by a characteristic size of cracked body elastic stress intensity factor and 'e e for plane stress and  2' 1e e   for plane strain. in the above equations,  and n are the hardening parameters, wa is the dimensionless crack length, w is characteristic size of specimen (for our case that is specimen diameter),  is the nominal stress, and 0 is the yield stress. the numerical constant  ni  is obtained from the singularity analysis by means of the conjugation solutions for the far and near fields. for small-scale yielding, i.e., when the plastic zone near the crack tip is quite small compared with the crack length, the amplitude of the singularity pk can be determined directly by application of the j-integral. in the framework of the present work, the conditions at the crack tip are described using the j-integral and an inherent parameter in that must be determined for the tested hollow specimens as well as for the structural elements to enable the applicability of the results. to address the theoretical aspects relevant to the experiments, finite element analysis is used to determine the governing parameter in of the asymptotic behavior of the stresses at the crack tip. in the classical first-term singular hrr-solution [11], the numerical parameter in is a function of only the material strain hardening exponent n. shlyannikov and tumanov [5] reconsidered the hrr-solution for both plane strain and plane stress and supposed that under small-scale yielding, the expression for in depends implicitly on the dimensionless crack length and the specimen configuration. in this section, we extend the analysis to the in-integral behavior in an infinitely sized cracked body [11] to treat the test specimen’s specified geometries. the use of the hutchinson’s theoretical definition for the in-factor directly adopted in the numerical finite element analyses leads to [5]     , , , ( , , ,fem femn p pi m n a w m n a w d         (8)     1, , , cos sin 1 fem fem femfem n fem fem fem femr p e rr r r du dun m n a w u u n d d                                      1 cos . 1 fem fem fem fem rr r ru u n         in this case, the numerical integral of the crack tip field in changes not only with the strain hardening exponent n but also with the relative crack length b/d and the relative crack depth a/d. more details to determine the in factor for different test specimen configurations are given by refs. [5-7]. the distribution of the elastic-plastic constraint parameters along the crack front in the direction from the free surface toward the mid-plane is plotted in fig. 6 for the hollow specimens under different loading conditions. the left picture in fig. 6 depicts the behavior of the in-factor, whereas the right picture in fig. 6 gives us the distribution of the stress triaxiality parameter h for the fixed curvilinear crack front position. the constraint parameters are plotted against the normalized coordinate r. in these plots r = 0.0 is the crack border (the specimen free surface) while r = 1.0 is the midplane of the specimen. it can be observed from these figures that both constraint parameters sufficiently changed along the crack front from the free surface toward the mid-plane as a function of loading conditions. fig. 7 represents the distributions of the in-factor for the pure tension and pure torsion as well as the combined loading conditions for different crack front position in hollow specimens. the last part of the numerical calculations of the present study is devoted to the determination of the plastic stress intensity factors in hollow samples. in fig.8 shown the distributions of the elastic and plastic sif's for the same tensile loading conditions along the same crack front. fig. 8 gives a clear illustration of the necessity to take into account the v. shlyannikov et alii, frattura ed integrità strutturale, 33 (2015) 335-344; doi: 10.3221/igf-esis.33.37 341 plastic properties of the material in the interpretation of the characteristics of the material resistance to crack propagation. the data shown in fig. 9 confirm this suggestion in more details for several other crack fronts. recall that the front of the number four in the fig. 9 corresponds to the second stage of crack propagation when it becomes completely throughthickness and intersects the hollow cylinder wall. figure 6: in-factor and stress triaxiality parameter distributions along crack front under different loading conditions. figure 7: in-factor distributions along crack front under different loading conditions (1-initial, 2-3-intermediate, 4-final crack front). figure 8: elastic and plastic stress intensity factor behavior for initial crack front under tension. v. shlyannikov et alii, frattura ed integrità strutturale, 33 (2015) 335-344; doi: 10.3221/igf-esis.33.37 342 а) b) с) figure 9: elastic (a) and plastic stress intensity (b-b95, c-d16) factor distributions along crack front (1-initial, 2-3-intermediate, 4-final). experimental results and discussion he evolution of the crack growth rate of the elliptical-fronted edge cracks during the tests is determined using cod and the microscope. in order to study the crack growth under fatigue tension loading with superimposed cyclic torsion, several hollow specimens of both aluminum alloys b95 and d16 are tested with an initial notch depth equal to 3 mm. fig. 10 shows plot of the break through point advances b and of cod against the number of cycles n under pure tension and combined loads, respectively. as shown in fig. 10, in-phase cyclic torsion loading superimposed on cyclic tension leads to different effects on the relationship between crack length on the free surface of the specimen and crack opening displacement under combined cyclic loading which depend on the material properties. nevertheless there is a strong correlation between these two parameters that can be very useful for automation of experimental studies of fatigue and fracture under multiaxial stress state. on the base of this experimental data, polynomial functions can be used to express the cod as a function of the superficial crack length. fig. 11 represents the superficial crack growth rate db/dn versus cod on the hollow cylindrical specimens undergoing pure tension and combined loading. it is found that the crack growth rate along the external surface direction as a function of cod fit into a single curve with a small scatter band of the experimental results under different loading conditions for both tested aluminum alloys. however, looking at figs.3,4 and considering changes in the general durability of the specimens in pure tension and combined loading, significant differences in the crack growth rate in the depth direction a and on the free surface b of hollow specimens under the above types of loading conditions are expected. figure 10: relationship between cod and crack length on free surface of hollow specimen under different loading conditions. figure 11: crack growth rate on free surface of hollow specimen versus cod under different loading conditions. t v. shlyannikov et alii, frattura ed integrità strutturale, 33 (2015) 335-344; doi: 10.3221/igf-esis.33.37 343 fig. 12 shows the typical experimental fatigue fracture diagrams in the coordinates of the crack growth rate versus the values of the stress intensity factors for the hollow cylindrical specimens tested under pure tensile loading. the left picture in fig. 12 depicts the behavior of the db/dn as a function of the elastic sif k1, whereas the right picture in fig. 12 gives us the crack growth rate depending on of the dimensionless plastic stress intensity factor kp. to determine the experimental values of the elastic and plastic sif's for two main points of the crack front, namely, the free surface and midplane section, was used the distributions represented in fig. 9. looking at fig.12 it should be noted that increasing of the crack growth rates is observed in the direction of the deepest point of the crack front with respect to the crack front intersection with the free surface of the hollow cylindrical specimens in terms of the elastic and plastic sif's. а) b) figure 12: crack growth rate as a function of (a) elastic and (b) plastic sifs under tension for different crack front points. in contrast to the elastic sif k1, the plastic sif kp shows very useful effect of the sensitivity to the plastic properties of the tested materials. it can be seen from fig. 12 that the plastic sif gradually increases by increasing the crack length and crack depth at fixed elastic properties of the aluminum alloys characterized by e=74 gpa and =0.3. the data presented very obvious advantages of using the plastic stress intensity factors to characterize the material's resistance to cyclic crack growth. this conclusion is confirmed by the relative position of crack growth curves in fig.12 for both tested aluminum alloys under pure cyclic tension in the terms of the elastic and plastic sif"s. conclusions atigue crack growth for an elliptical arc-fronted edge crack with two different initial notch form in hollow cylindrical specimens of b95 and d16 aluminum alloys is studied. experiments and calculations made under axial cyclic tension with and without cyclic torsion are described. all the experimental and numerical results are shown: for the same specimen configuration and different the crack front position as a function of cyclic tension and torsion loading, the following constraint parameters were analysed, namely, the non-singular t -stress, zt -factor and the stress triaxiality parameter h in the 3d series of elastic-plastic computations for aluminum alloys different properties; the governing parameter of the elastic-plastic stress fields in-factor distributions along various crack fronts was also determined from numerical calculations, this governing parameter is used as the foundation of the elastic-plastic stress intensity factor; under pure cyclic tension loading, it can be seen that the crack propagation paths differ with diverse initial flaw forms, but converge to the same configuration when the crack depth ratio is larger than about 0.25; it is found that there is one general relationship between the crack growth rate on the free surface of specimen and cod for both tested aluminum alloys and loading conditions including the case when the torsion loading is superimposed on the cyclic tension; f v. shlyannikov et alii, frattura ed integrità strutturale, 33 (2015) 335-344; doi: 10.3221/igf-esis.33.37 344 increasing of the crack growth rates is observed in the direction of the deepest point of the crack front with respect to the crack front intersection with the free surface of the hollow cylindrical specimens; the experimental and numerical results of the present study background provide an opportunity to explore the suggestion that crack growth rate may be represented by the plastic stress intensity factor, rather than the magnitude of the elastic sifs alone; it is stated that the elastic-plastic stress intensity factor, which is sensitive to the constraint effects and elastic-plastic material properties, is attractive as the self-dependent unified parameter for characterization of the material fracture resistance properties. acknowledgment he authors gratefully acknowledge the financial support of the russian scientific foundation under the project 1419-01716. references [1] newman, j.c., raju, i.s., an empirical stress-intensity factor equation for the surface crack, eng. fract. mech., 15 (12) (1981) 185-192. [2] carpinteri, a., brighenti, r., part-through cracks in round bars under cyclic combined axial and bending loading, int. j. fatigue, 18 (1) (1996) 33-39. [3] yang, f.p., kuang, z.b., shlyannikov, v.n., fatigue crack growth for straight-fronted edge crack in a round bar, int. j. fatigue, 28 (2006) 431–437. [4] citarella, r., lepore, m., slyannikov, v., yarullin, r., fatigue surface crack growth in cylindrical specimen under combined loading, eng. fract. mech., 131 (2014) 439-453. [5] shlyannikov, v.n., tumanov, a.v., characterization of crack tip stress fields in test specimens using mode mixity parameters, int. j. fract., 185 (2014) 49-76. [6] shlyannikov, v.n., zakharov, a.p., multiaxial crack growth rate under variable t-stress, eng. fract. mech., 123 (2014) 86–99. [7] shlyannikov, v.n., tumanov, a.v., zakharov, a.p., the mixed mode crack growth rate in cruciform specimens subject to biaxial loading, theoret. appl. fract. mech., 73 (2014) 68-81. [8] ansys mechanical apdl theory reference release 14.5// ansys, inc. southpointe, 275 technology drive, canonburg, pa 2012. [9] guo, w.l., elasto-plastic three dimensional crack border field-i, eng. fract. mech., 46 (1993) 93-104. [10] henry, b.s., luxmoore, a.r., the stress triaxiality constraint and the q-value as ductile fracture parameter, eng. fract. mech., 55 (1997) 375-390. [11] hutchinson, j.w., singular behaviour at the end of a tensile crack in a hardening material, journ. mech. phys. solids, 16 (1968) 13-31. t microsoft word numero_33_art_8 d. a. hills et alii, frattura ed integrità strutturale, 33 (2015) 61-66; doi: 10.3221/igf-esis.33.08 61 focussed on characterization of crack tip fields fretting in complete contacts the use of williams’ solution d. a. hills, r. flicek university of oxford, uk david.hills@eng.ox.ac.uk, robert.flicek@eng.ox.ac.uk abstract. williams’ solution may be used to characterize the corners of ‘complete’ fretting contacts. here we look at the practicalities of conducting fretting tests using a range of different kinds of apparatus and the kind of results they can reveal of practical relevance to establishing a fretting database. keywords. fretting, complete-contacts; williams’ solution. introduction t the second ijfatigue & ffems joint workshop held in 2013, in malaga (spain), we developed quite extensively a framework for understanding the fretting fatigue of complete contacts, using williams’ solution to characterize the local behaviour [1]. this can sometimes be quite a complicated process, as the stress intensity contributions from mode i and mode ii loading may change sign, giving rise to local separation, and there are the competing non-linear local effects of slip (giving rise to fretting damage) and plasticity (giving rise to crack nucleation) [2,3]. for background material, these two papers should be consulted. they give, first, detailed consideration to length scales; all notch asymptotes subject to combined-mode loading have an internal length scale, even if the notch is semi-infinite extent. this is the quantity we have designated do, and is defined as 1 0 i iiii i k d k    (1) where ki, kii are the mode i, mode ii generalized stress intensity factors respectively, and λi, λii are the corresponding williams’ exponents [1]. observation points nearer to the contact corner than do are mode i dominated, whilst those further away are either mode ii dominated or may be subject to the influence of higher order terms in the series (in which case the field is not ‘small scale’ in character). there are two non-linear local effects, both forms of slip. first, there is the process zone within which non-linear effects give rise to the accumulation of damage, which is wholly analogous to the process zone at the root of a sharp v-notch. secondly, there is the possibility of frictional slip (fretting itself), which clearly causes at least some local damage including surface finish degradation. if the process zone envelopes the frictional slip extent, we would say that the contact corner is ‘notch-like’ (and this remark applies a fortiori if the contact corner is actually adhered). in contrast, if the slip zone envelopes the process zone, we would argue that fretting damage is likely to be very important in controlling the strength of the contact corner. in this paper, we want to take a more practical look at what these observations tell us about the properties of various fretting tests which are widely used, and what the range of test parameters should be so as to obtain the maximum useful output from the tests. it should be recalled that the notch-root generalized stress intensity factors act as a ‘filter’, and that, whatever the actual loading in the experiment, the locally experienced stresses can ‘see’ only the ki,kii fields. also, different types of tests probe different regions of ki, kii space. so, in general terms, normal loading drives the state of a d. a. hills et alii, frattura ed integrità strutturale, 33 (2015) 61-66; doi: 10.3221/igf-esis.33.08 62 stress into the (ki<0,kii>0) quadrant, implying, as intuitively expected, firm closure of the contact corner, whereas the application of a shear force or tension drives the state of stress into either the (ki>0,kii>0) or (ki<0,kii<0) quadrants. these imply some degree of local opening [2, 3]. choice of test ll of the early ‘complete’ fretting tests conducted at oxford were carried out on a modified version of the group’s general purpose fretting-fatigue apparatus, originally designed to conduct ‘incomplete’ (mainly hertzian) fretting tests, which is shown in fig. 1. one of the features which was thought to be very desirable was to use pad holders that could swivel, so intimate contact was made between the pad ends and the dogbone specimen faces. at the same time, the geometry was carefully arranged so as to attempt to ensure that the applied shear force was imposed strictly through the plane of the interface to ensure that there was no moment present tending to ‘tip’ the pads. very large numbers of tests were carried out (over one hundred) on super-cmv steel, but the spread of results obtained was disappointing [4]. figure 1: fretting-fatigue test rig at the university of oxford for studying both incomplete and complete contacts [2]. one difficulty was that the usual increase in the coefficient of friction experienced during the first few cycles of loading typically increased the friction coefficient from about 0.4 to 0.7. in the case of hertzian contacts, this simply has the result of reducing the width of the slip zones, and this happens in a smooth manner. but, in the case of sharp-edged contacts, it can make the difference between edge slip and a fully adhered contact, so the steady state problem is little more than a notch incorporating an interface. the interface, including asperities, is still likely to be a source of weakness, so the fatigue strength of the pair will be lower than that of a monolithic component incorporating a notch. a further feature of the contact pair is that, because all surfaces are machined prior to assembly, the contact corner is truly sharp, whereas, in the case of a notch, an internal corner is present which, no matter how careful the machining process, will always have some finite radius. a principal advantage of the pad-on-dogbone arrangement is that it is possible to control three separate external loads – the normal force, p, which is normally held constant; the shear force, q; and the bulk stress, t, which are both controlled by servo-hydraulic actuators as shown in fig. 2. all three components of load excite both mode i and mode ii loading, and the first really thorough derivation of the contact corner stress intensity factors was carried out by flicek [5], with the following results a d. a. hills et alii, frattura ed integrità strutturale, 33 (2015) 61-66; doi: 10.3221/igf-esis.33.08 63 1 1 1 1 2 1 0.1537 0.1223 0.0609 0.0751 / 0.1280 0.1610 0.1109 0.1562 / 0.1534 0.2116 0.2731 0.0752 / 0.1285 0.4236 0.4737 0.1564 t/ i i i i a i a ii b i b ii k a p a k a q a q ak a ak a                                         (2) where kia, kiia correspond to the left corner in fig. 2, and kib, kiib correspond to the right corner. by careful choice of the mix of normal, bulk, and shear loads, a wide range of ki, kii space may be probed by this experiment. figure 2: idealised diagram of the pad-on-dogbone test rig [5]. cantilever specimen wholly different kind of very simple test was conducted by juoksukangas et. al. [6]. this employs a simple cantilever strip, clamped between blocks, subject to a cyclically imposed tip deflexion. juoksukangas et. al. obtained a very good set of results using this apparatus, and a smooth ‘s-n’ type curve was plotted. in their original paper, these authors used the notional stress at the root of the cantilever implied by elementary bending theory. it is, however, a simple step to obtain the calibration for the cantilever-root stress intensity factors. this is an important step because it means that the quantity being employed now represents the true state of stress at the critical point (here the cantilever root edges). thus, what is being revealed is a true material property, which may applied to any other geometry where there is an internal right angle, with possible attendant interface slip, at the critical point. a limitation of the technique is that there are only two loads – the clamping force, which is kept constant, and the cantilever tip deflexion, which provides the oscillatory component of load. also, it is assumed that the static load has only a secondary effect on the fatigue strength, and it is the oscillatory load which controls the contact strength. we obtained calibrations for the contact corner stress intensities in a discussion paper [7], and these were used to re-plot the experimental results found on a plot of δki versus n1 (number of cycles to macroscopic crack initiation), which is reproduced in fig. 3. this figure may be thought of as displaying a definitive material property curve, with a fatigue limit, kifl, which might be adopted to solve any fretting-fatigue strength problem involving sharp-edged contacts. figure 3: plot of δki versus cycles to macroscopic crack initiation, n1, [7]. a d. a. hills et alii, frattura ed integrità strutturale, 33 (2015) 61-66; doi: 10.3221/igf-esis.33.08 64 bridge type specimens ong before our understanding of partial slip contact problems had developed to the point it has now, and before clear separation of the nucleation and propagation phases of crack growth were considered, materials scientists were conducting fretting tests in which ‘bridges’ were clamped to either rotating-bending or simple tension dogbone specimens. the oscillating values of surface strain meant that shear forces were developed beneath the feet of the bridges, and this usually produced some slip, and hence fretting damage. the principal advantages of the arrangement were: (i) the fretting components were relatively easy to make, and (ii) particularly in the case of rotating-bending, the assembly was maintained in balance, so it could be operated at high speed, and the number of cycles could be clocked up very quickly. on the other hand, although the tests are easy and quick to conduct, their interpretation is correspondingly very difficult. there have been a number of attempts to analyse the bridge-foot contact problem, notably by hattori and nakazawa using a boundary element method [8,9]. recently, noraphaiphipaksa et. al. [10] have made a very good analysis of bridge-style contact pads clamped to a dogbone specimen subject to oscillatory tension, which is shown in fig. 4. figure 4: idealised diagram of one quarter of the bridge-style test rig [11]. this test rig has the advantages of: (i) two-way symmetry, and (ii) all deformation occurs in the plane of analysis, which therefore is strictly two-dimensional in nature. the nature of the contact is such that the application of a bulk tension produces a shear force on each ‘foot’ of the bridge. this enables a single actuator servo-hydraulic test machine to be used to conduct fretting-fatigue tests. noraphaiphipaksa et al.'s analysis is extremely revealing and shows that at the loads which were typically employed, sufficient twisting of the feet occurred for there to be significant receding of the contact as the outside of the foot separated, which significantly complicates interpretation of the results. this is because during part of the load cycle the contact of the foot is ‘complete’ with an attendant singular contact pressure, and during part of the loading cycle the contact has shrunk and is incomplete in nature, so there will certainly be at least some partial slip occurring. we re-analysed noraphaiphipaksa et al.'s results in a discussion paper [11] and fitted generalized stress intensity factors to the contact edge solutions. the calibrations found are given here 1 1 0 1 0 1 0.1693 0.1669 0.3656 0.5092 0.5617 0.6163 0.3034 0.2770 i i i i a i a ii b i b ii k a k a p k a k a                                     (3) where kia, kiia correspond to the left corner in fig. 3, and kib, kiib correspond to the right corner. we are then in a position to show very easily the conditions under which the feet remain in intimate (complete) contact and when they recede (and become incomplete), and this information is shown in fig. 5. as will be clear, the situation is quite different for the ‘inside’ and the ‘outside’ of the feet. it is clear that in the tests which mutoh carried out, a very complicated load cycle existed, and the loads would have to be ‘backed off’ considerably in order for his investigation to probe strictly ‘complete’ contacts. equally, the philosophy developed here shows that it is perfectly possible to devise forms of the ‘bridge’ which do maintain intimate contact up to higher loads, and this would seem to be a viable way to go, but with a more restrictive probing of ki,kii space than is possible using the two-actuator and single-pad arrangement. l d. a. hills et alii, frattura ed integrità strutturale, 33 (2015) 61-66; doi: 10.3221/igf-esis.33.08 65 figure 5: diagram of kii versus ki showing the implications of williams' solution for contact behaviour [11]. shrink fit problems recent set of experiments intended to investigate the fretting-fatigue strength of shrink-fit joints is being developed by bertini et. al. [12]. these tests are still at an early stage of refinement but show promise. summary ur ambition is to produce a viable laboratory technique which reveals the fretting-fatigue strength of materials in a laboratory test, and which may be applied to a wide range of practical problems. at the outset, a distinction should be made between incomplete contacts and complete contacts. for the former of these, the relevant asymptotic forms take a particular form (square-root bounded), and the tremendous amount of data generated in many laboratories throughout the world has been very satisfactorily correlated [13]. in contrast, complete contacts are much more challenging to characterise, and an important starting point is to think of them not as contacts between two components brought together, but as a monolithic entity which may be split, even separated, along small parts of the contact, especially the edges. the domain in which the analysis is carried out is therefore very different, and the problems are notch-like. indeed, in some cases, when the edge is adhered, they are virtually indistinguishable from a sharp notch. nevertheless, the presence of slip will have some influence on the propensity of the contact edge to start a crack. we do not attempt to speculate what this might precisely be, but instead rely on a laboratory experiment to determine the contact strength. here, we have reviewed the relatively modest amount of data available, together with its sources. acknowledgements .c. flicek would like to thank rolls-royce plc and the technology strategy board for financial support under the programme siloet-ii. the authors wish to thank rolls-royce plc for granting permission to publish this work. references [1] hills, d.a., flicek, r.c., dini, d., sharp contact corners, fretting and cracks. frattura ed integritá strutturale (fracture and structural integrity), 25 (2013) 27-35. doi:10.3221/igf-esis.25.05 a o r d. a. hills et alii, frattura ed integrità strutturale, 33 (2015) 61-66; doi: 10.3221/igf-esis.33.08 66 [2] flicek, r., hills, d.a., dini, d., progress in the application of notch asymptotics to the understanding of complete contacts subject to fretting fatigue. fatigue. fract. eng. m., 36 (2013) 56-64. doi:10.1111/j.1460-2695.2012.01694.x [3] flicek, r.c., hills, d.a. dini, d., sharp edged contacts subject to fretting: a description of corner behaviour. int. j. fatigue, 71 (2015) 26-34. doi:10.1016/j.ijfatigue.2014.02.015 [4] mugadu, a.e.b., studies in fretting fatigue of complete contacts. university of oxford d.phil. dissertation, trinity term 2002. [5] flicek, r.c. analysis of complete contacts subject to fatigue. university of oxford d.phil. dissertation, michaelmas term 2014. [6] juoksukangas, j., lehtovaara, a., mäntylä, a., development of a complete contact fretting test device. p. i. mech. eng. j-j. eng., 227 (2013) 570-578. doi:10.1177/1350650112466162 [7] hills, d.a., flicek, r.c., dini, d., a discussion of: development of a complete contact fretting test device by j juoksukangas et al. p. i. mech. eng. j-j. eng., 228 (2014) 123-126. doi:10.1177/1350650113500946 [8] hattori, t., nakamura, m., ishizuka, t., fretting fatigue analysis of strength improvement models with grooving or knurling on a contact surface. in attaia, m. h. and waterhouse, r. b. (eds.) standardization of fretting fatigue test methods and equipment, astm stp 1159. race street, philadelphia. astm (1992) 101-114 [9] nakazawa, k., sumita, m., maruyama, n. effect of contact pressure on fretting fatigue of high strength steel and titanium alloy. in attaia, m. h. and waterhouse, r. b. (eds) standardization of fretting fatigue test methods and equipment, astm stp 1159. race street, philadelphia. astm (1992) 115-125 [10] noraphaiphipaksa, n., kanchanomai, c., mutoh, y., numerical and experimental investigations on fretting fatigue: relative slip, crack path, and fatigue life. eng. fract. mech., 112 (2013) 58-71. doi:10.1016/j.engfracmech.2013.10.007 [11] hills, d.a., flicek, r.c., a discussion of “numerical and experimental investigations on fretting fatigue: relative slip, crack path, and fatigue life” by n. noraphaiphipaksa, c. kanchanomai, and y. mutoh. eng. fract. mech., 113 (2015) 52-55. doi:10.1016/j.engfracmech.2014.10.024 [12] bertini, l., beghini, m., santus, c., baryshnikov, a., resonant test rigs for fatigue full scale testing of oil drill string connections. int. j. fatigue, 30 (2008) 978-988. doi:10.1016/j.ijfatigue.2007.08.013 [13] hills, d.a, thaitirarot, a., barber, j.r., dini, d., correlation of fretting fatigue experimental results using an asymptotic approach, int j. fatigue 43 (2012) 62-75. doi:10.1016/j.ijfatigue.2012.02.006. microsoft word numero_33_art_27 p. lorenzino et alii, frattura ed integrità strutturale, 33 (2015) 215-220; doi: 10.3221/igf-esis.33.27 215 focussed on characterization of crack tip fields synchrotron 3d characterization of arrested fatigue cracks initiated from small tilted notches in steel p. lorenzino, j.-y. buffiere insa-lyon mateis cnrs umr 5510 pablo.lorenzino@insa-lyon.fr, jean-yves.buffiere@insa-lyon.fr s. okazaki, h. matsunaga, y. murakami kyushu university okazaki.saburo.983@s.kyushu-u.ac.jp, matsunaga.hisao.964@m.kyushu-u.ac.jp, murakami.yukitaka.600@m.kyushu-u.ac.jp h. matsunaga international institute for carbon-neutral energy research matsunaga.hisao.964@m.kyushu-u.ac.jp abstract. high resolution synchrotron x-ray tomography has been used to obtain 3d images of arrested cracks initiated at small artificial defects located on the surface of cylindrical steel specimens subjected to mode i fatigue loading. these defects consist in small semi-circular slits tilted at 0°, 30° or 60° with respect to the plane normal to the loading axis; all of them had the same defect size, area = 188 μm, where the area denotes the area of the domain defined by projecting the defect on a plane normal to the loading axis. arrested cracks initiated from the notch were observed for all tilt angles at the surface of samples cycled at the fatigue limit (stress amplitude at which the specimen does not fail after 1×107 cycles). high resolution synchrotron x-ray tomography has been used to obtain 3d images of those small defects and non-propagating cracks (npc). despite the fact that steel is a highly attenuating material for x rays, high resolution 3d images of the cracks and of the initiating defects were obtained (0.65 m voxel size). the values of surface crack length measured by tomography are the same as those obtained by optical microscope measurements. the area values present the same tendency as the surface length of npc, i.e. larger non-propagating cracks areas were observed in the softer steel. in the extreme case of 60º tilted defect, the crack fronts appear much more discontinuous with several cracks propagating in mode i until arrest. keywords. x-ray tomography; notch; arrested crack; 3d. introduction n a previous work we reported an experimental test campaign that was carried out in order to clarify the effect of defect orientation on the fatigue limit of three types of steels; jis-s15c, jis-s45c and jis-sncm439 [1]. the average vickers hardness hv of each material measured with a load of 9.8 n was 117, 186 and 293, respectively. a semicircular slit or hole was introduced into a cylindrical specimen with a diameter of 7 mm by electro-discharge machining or drilling. the slits were tilted at 0° 30° or 60° with respect to the plane normal to the loading axis, but all of them had the i p. lorenzino et alii, frattura ed integrità strutturale, 33 (2015) 215-220; doi: 10.3221/igf-esis.33.27 216 same defect size,  area = 188 µm, where the area denotes the square root of the size of projection of the defect on a plane normal to the loading axis. fully reversed tension-compression fatigue tests were carried out at a test frequency of 150 hz. the fatigue limit fl was determined as the stress amplitude at which the specimen does not fail after 1×107 cycles. for every material and notch tilt angle a non-propagating crack was found at the fatigue limit. after performing fatigue tests, and carrying out fatigue crack propagation studies, the following conclusions were obtained: in jis-s15c and jis-s45c, the fatigue limits were nearly independent of the tilting angle, and were found in good agreement with the predicted values by the area parameter model [1-2]. on the other hand, in jis-sncm439, the fatigue limit was also in agreement with the prediction at the tilting angle of 0°, but it increased with an increase in the tilting angle. as shown on fig. 1, a typical growth behavior of small crack was observed irrespective of the tilt angle; when the stress amplitude was slightly above the fatigue limit, the growth first decelerated to a certain crack length, and then started accelerating with fatigue cycles until the final failure. (a) (b) figure 1: propagating and non-propagating cracks found above and below the fatigue limit in case of jis s45c steel and 30º notch (a) crack length vs. number of cycles (b) crack growth rate vs. crack length. the length of non-propagating cracks varied greatly according to the steel types, i.e. longer non-propagating cracks were observed in softer steel. the crack length measured at the surface was also found to be independent of the tilting angle in the case of jis-s15c and jis-s45c, whereas in the case of jis-sncm439, the length increased with an increase in the tilting angle. the observed crack paths were in good agreement with the direction normal to the maximum principle stress near the defect (2d analysis). to complement the information reported above and understand the phenomenon in more detail, it was noted that further investigation was needed to clarify the three dimensional shapes of the non-propagating cracks. as a step forward in this direction, this paper shows 3d experimental characterization of the non-propagating fatigue cracks using high resolution x-ray tomography. experimental specimens n order to perform the x-ray analysis of non-propagating fatigue cracks, a smaller specimen with a square crosssection ranging from 0.8 to 1 mm2 was cut from the larger sample, such that it contained the notch and the nonpropagating fatigue crack. as the cross sectional area of the small samples cannot be larger than 1 mm2 due to experimental restrictions and some of the samples contained cracks measuring up to 700 μm in surface length, extreme care was taken when cutting the sample. the procedure consisted in extracting a larger sample containing the notch plus crack and then applying successive steps of polishing and microscope observation until the final geometry was reached. i p. lorenzino et alii, frattura ed integrità strutturale, 33 (2015) 215-220; doi: 10.3221/igf-esis.33.27 217 fig. 1 details the shapes and dimensions of the samples at various stages of preparation (a) fatigue specimens (b) tomography specimen extracted from the fatigue specimen (c) notch and non-propagating cracks located in the small specimen (d) types of defects and tilting angles. figure 1: (a) fatigue specimen (b) tomography specimen extracted from the fatigue specimen (c) notch and non-propagating cracks located in the small specimen (d) types of defects and tilting angles. synchrotron x-ray microtomography the tomography experiments were performed on id19 beamline at the european synchrotron radiation facility (esrf) located in grenoble, france. at it is shown in fig. 2, a monochromatic x-ray “pink beam” having a photon energy of 60 kev is used. a pco edge ccd camera with a 2160 x 2560 pixel chip was used. in order to load the samples for producing crack opening, a dedicated in situ tensile rig was mounted onto the rotation stage of the beamline. 2000 radiographs were taken while the sample was rotating over 180º along its vertical axis; with an exposure time of 0.07 s. (scan acquisition time of 3.68 min). reconstruction of the tomographic data was performed with a standard filtered back-projection algorithm. a 0.65 m voxel size was obtained, allowing a good detection of the notch plus cracked areas. fiji and paraview open softwares were used for post-processing the images obtaining separately the notch and crack geometries for every steel and defect tilting angle. figure 2: schematic view of the tomographic acquisition process, volume reconstruction and 3d crack analysis. p. lorenzino et alii, frattura ed integrità strutturale, 33 (2015) 215-220; doi: 10.3221/igf-esis.33.27 218 results 3d crack analysis 3d image of the small initiating defect and of the non-propagating fatigue crack was obtained for every defect geometry and steel type. fig. 3 shows the results in the case of the annealed jis-s45c steel. figures on the left show 3d images of non-propagating cracks found at the fatigue limit and figures on the right corresponds to the crack projection (minimum intensity values) in to z, y and x planes, z being the direction parallel to the loading axis. figure 3: left: 3d images of non-propagating cracks found at the fatigue limit. right: crack projections in to z, y and x axis (minimum intensity). material: annealed jis-s45c steel. s15c s45c sncm 435 o.m. (m) 3d (m) diff. (%) area (m) o.m. (m) 3d (m) diff. (%) area (m) o.m. (m) 3d (m) diff. (%) area (m) 652 658 -0.9 320 497 492 1.0 265 356 357 -0.2 219 650 655 -0.8 332 495 515 -4.0 278 433 440 -1.6 249 730 756 -3.6 334 485 497 -2.4 252 409 411 -0.4 226 table 1: non-propagating crack length measured by optical microscope (o. m.) and the analysis of 3d images (3d). the area values were obtained analyzing z projection images (i.e. fig. 3 right). tab. 1 shows a comparison between the length of non-propagating crack measured at the specimen surface by optical microscope and the surface length obtained by analyzing the 3d images. these measurements are very similar, having a maximum difference of 4 % for the case of s45c steel, 30º notch. regarding the different materials, the npc size varied a p. lorenzino et alii, frattura ed integrità strutturale, 33 (2015) 215-220; doi: 10.3221/igf-esis.33.27 219 greatly according to the steel types, i.e. larger non-propagating cracks observed in the softer steel. this observation is consistent with the previous 2d crack analysis performed at the surface in previous work. the area values corresponding to the square root of the total defect area (notch plus crack) projected on a plane normal to the loading axis are also shown in tab. 1. these values present the same tendency as the surface length of npc. these results give confidence in the ability of tomography to measure reliably the length of those small cracks. from these images it can clearly be seen that longer cracks are always observed at the surface where larger sif values are found, for every notch tilt angle. in case of the 60º semi-elliptical slit, the crack observed at the notch root seems to be smaller but the projected area of the defect plus crack is similar to those obtained for 0º and 30º. furthermore in the case of 60º tilted defects, irrespectively of the steel type, cracks do not merge in to a single crack front, propagating in mode i leading to a much more discontinuous front. on the z projection the npc presents discontinuities, showing deviations from the typical semi-elliptical single-front shape. fem mesh reconstruction as mentioned before, a calculation of the sif values for 3d cracks will be helpful for a better understanding of the experimental results. in previous work, a first 2d approach was carried out where the sifs of two-dimensional cracks were calculated by using finite element analyses and implementing the stress extrapolation method [3]. ki values where obtained for the different tilt angles and results showed that ki values of the cracks grown from tilted cracks do not significantly differ from that of non-tilted crack with equivalent projected crack lengths. the maximum difference was about 6% in the crack length range where non-propagating cracks were observed. of course this is a basic analysis in comparison with the actual notch 3d geometry. in order to extend these results to the 3d field, a fem analysis including the 3d defect geometry is necessary. as a first step, a fem mesh of the actual defect was obtained by treating with aviso software the 3d x-ray images of defects, at it is shown in fig. 4. figure 4: fem mesh of the actual notch geometry. this mesh will be a starting point for computing k values near the crack tips for every tilt angle; those values will be used to analyze the 3d shapes of the cracks reported here. conclusions igh resolution (0.65 μm voxel size) synchrotron tomography was used to obtain 3d images of arrested cracks initiated from artificial defects in 3 different steels. good contrast level between crack and bulk facilitates accurate measurements. surface crack length measured by this technique gave the same results as optical microscope measurements. the area values present the same tendency as the surface length of npc, i.e. larger non-propagating cracks were observed in the softer steel. in the case of 60º tilted defect, the crack fronts appear much more discontinuous with several cracks propagating in mode i until arrest. h p. lorenzino et alii, frattura ed integrità strutturale, 33 (2015) 215-220; doi: 10.3221/igf-esis.33.27 220 3d imaging allowed us to generate fem mesh that will be used to perform 3d fem calculation of sifs values for more detailed analysis. references [1] lorenzino, p., okazaki, s., matsunaga, h., murakami, y., effect of orientation of small defects on fatigue limit of steels, web of conferences. edp sciences, 12 (2014). [2] murakami, y., metal fatigue: effects of small defects and nonmetallic inclusions, elsevier ltd., oxford, uk, (2002). [3] lorenzino, p., okazaki, s., matsunaga, h., murakami, y., effect of small defect orientation on fatigue limit of carbon steels, ffems, under review, (2015). microsoft word numero_49_art_55_2358 d. e. belhadri et alii, frattura ed integrità strutturale, 49 (2019) 599-613; doi: 10.3221/igf-esis.49.55 599 stress intensity factors analyses for external semi-elliptical crack for repaired gas-pipeline by composite overwrap under pressure d. e. belhadri, m. belhamiani, w. n, bouzitouna, w. oudad smart structures laboratory univ ctr of ain témouchent, po box 284,46000, algeria djamelins@hotmail.fr, mbelhamiani@gmail.com, hibanesrine@outlook.fr oudadw@gmail.com, https://orcid.org/0000-0002-3283-1322 abstract. the purpose of this article is to present the stress intensity factors (sif) solutions for semi-elliptic crack in pipelines under internal pressures, the stress intensity factors are calculated by the three-dimensional finite element method (fem) for cracked pipelines and repaired pipe by composite patch. the distribution of normalized stress intensity factors (ki, kii and kiii) along the crack front for different crack lengths, crack depth, crack geometry, lap length and composite thickness was obtained by nodal calculations. our results show the presence of three failure modes along the semi elliptical crack front and has three zones in which the stress intensity factor in mixed mode (kii) the higher-values comparing to ki and kiii. it can also be noted that the composite repair reduces the sif ki by 46% and the kii by 55% and the kiii by 72% near the outside diameter of the pipe in each zone. however, the reduction of the sif ki is more significant for the rectangular crack than for the semi-elliptic crack, from which it is concluded that the composite repair is very effective for a rectangular crack with respect to the semi-elliptic crack. thereby, the fracture behavior of the semi-elliptic crack is governed by the three modes of failure and not only by mode i. keywords. stress intensity factor; crack; composite; adhesive; pipeline, api 5l x65. citation: belhadri, d. e, belhamiani, m., bouzitouna, w. n., oudad, w., stress intensity factors analyses for external semielliptical crack for repaired gas-pipeline by composite overwrap under pressure, frattura ed integrità strutturale, 49 (2019) 599-613. received: 21.01.2019 accepted: 09.05.2019 published: 01.07.2019 copyright: © 2019 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. introduction round the world, more than 1.7 million kilometers of pipeline are used to transport gas, crude oil and petroleum products [1]. many of these pipelines have been in service since the 1940s and 1950s [2]. therefore, each year between 2 and 3.3 billion $ dollars in the us alone is lost to corrosion in the gas and oil pipelines that need to be repaired or replaced. [3] the large amount of external corrosion of pipeline increases ultimately the cost of energy. faced with the phenomena of ruins of structures or components with signs of rupture, the industry has to offer effective solutions to enhance or prolong the life of the damaged structure or even valued the equipment [4]. the composite repairs were used in the transmission pipeline industry for the past 20 years for the repair and strengthening of permanent sections of the tube wall that have been weakened due to corrosion. [5] most repair codes internationally a http://www.gruppofrattura.it/va/49/2358.mp4 d. e. belhadri et alii, frattura ed integrità strutturale, 49 (2019) 599-613; doi: 10.3221/igf-esis.49.55 600 recognized, such as asme b31.4 [6] and b31.8 [7], accept the use of composite materials for the repair function. most oil and gas pipeline operators are familiar with composites and the health, safety, technical and commercial benefits they provide. composite repairs are a proven and accepted technology for repairing high pressure pipelines. for example, clock spring has completed more than 100,000 repairs in more than 62 countries around the world [5]. pipeline defects can be permanently repaired using composites technology in a safer, faster and cheaper way than any other technique. c. alexander and b. francini [8] had developed a detailed state of the art assessment of composite systems used to repair transmission pipelines. many researches had used the stress intensity factor as a criterion to evaluate the efficiency of the composite repair system. many crack configurations are used to calculate the sif such as the rectangular and the semi elliptical crack. newman and raju (1984) [9] detailed an analytical study of the stress intensity factor equations for an embedded elliptical crack, a semi elliptical surface crack, a quarter-elliptical corner crack, a semi elliptical surface. crack along the bore of a circular hole and a quarter elliptical corner crack at the edge of a circular hole in finite plate. the equations give stress intensity factor as a function of parametric angle, crack depth, crack length, plate thickness, and where applicable, hole radius. a. saffih and s. hariri studied elliptical cracks in a cylinder with a thickness transition. they found that sif calculations in the transition, assuming a uniform thickness cylinder are conservative but not precise. the comparative study shows that the cylinder with a thickness transition is more vulnerable to a defect [10]. another study of the u.s. department of transportation presents an investigation to determine the mode i stress-intensity factors, along two symmetric surface cracks emanating from a centrally located hole in a rectangular plate using the domain integral method [11]. excellent agreement was obtained with those of newman and raju (1983). all these researches are focused on the study of the behavior in rupture in opening mode (mode i). the objective of the present work is to highlight the behavior of a semi-elliptic crack governed by the three failure modes in pipe subjected to internal pressure, after that the study extends on the estimation of the efficiency of repair of the pipe by a carbon-epoxy composite. stress intensity factors calculation he stress intensity factor (sif) is one of the most important parameters in fracture mechanics. brittle fracture in cracked engineering components is usually examined by sif. after the crack detection in a structure, sif can be calculated by various experimental or theoretical methods such as finite element analysis. once sif is known the risk of brittle fracture can be evaluated by using an appropriate fracture criterion. the mode i and mode ii stress intensity factors (ki and kii ) can be calculated from finite element analysis based on the displacement functions (u and v) in a local coordinate system fixed to the crack tip [12] . figure 1: local cartesian coordinates on crack tip.  2   2    1 i v rg k k r     (1)  2   2 1 ii u rg k k r     (2) where r is the radial distance from the crack front in the polar coordinates, g is the shear modulus, υ is poisson’s ratio, and k can be defined for plane strain and plane stress problems as follows: t d. e. belhadri et alii, frattura ed integrità strutturale, 49 (2019) 599-613; doi: 10.3221/igf-esis.49.55 601   3 4                  3 / 1      plane strain k plane stress        (3) for three dimensional models, different subscripts are used to designate the stress intensity factor for the three different modes. these factors are formally defined as [13]   0  lim 2 , 0i yy r k r r      0  lim 2 , 0ii yx r k r r    (4)   0  lim 2 , 0iii yz r k r r    for cylinders subjected to axisymmetric loading, a decomposition of stresses in a polynomial form of third or fourth degree is usually used [14–18]. the sif can be written in the form:                1, 2, 3 j j j j j a k i a j t         (6) recently an interesting study, published in 2018 has been proposed for rapidly estimating notch stress intensity factors using the singular linear elastic peak constraints named: peak stress method (psm) [19,20]. geometry and loading of cracked pipe he pipe analyzed in this study is shown in fig. 2 where r=350mm, l is the longitudinal length l= 1000 mm, and t =12.7mm is the wall's thickness. the crack was repaired by using a glass-epoxy composite patch bonded cylinder form with an adhesive cylinder eadh=02mm ,ladh=lp=100mm, ep=4mm . the end sections pipeline was subjected to no displacement in the longitudinal direction (u3=0). the material properties of the pipeline, patch, and adhesive are summarized in tab. 1. the pipe was made of x65 grade steel per api 5l psl2 [21] specifications. the pipe is subjected to an internal pressure of 7mpa. the material model is considered as an elastic material. figure 2: geometry of the pipe with an external axial crack of semi-elliptical shape. a range of ratios of a/t, c/t, patch length (lp), patch thickness(ep) as well as single and multi-laps of composite are highlighted in this study. t d. e. belhadri et alii, frattura ed integrità strutturale, 49 (2019) 599-613; doi: 10.3221/igf-esis.49.55 602 table 1: material’s properties. figure. 3: mesh type of the model and a geometry of the repaired pipe. finite element modeling he cracked pipe was modeled using abaqus 6.14 [24], and meshed using a structured mesh with three-dimensional hex-dominated quadratic elements with a focused mesh surrounding the crack-tip of 0.02 mm element [24, 25, 26, 27, 28]. a meshed pipe is shown in fig. 3. the reduced, c3d20r integration elements are used in this modelization to compute the stress intensity factors. only a quarter of the specimen was modeled due to symmetry conditions. the procedure used in the finite element analysis involved the following steps: (i) the internal pressure was applied to the api 5l x65 properties [21] young’s modulus (gpa) 205 poisson’s ratio 0.3 minimum yield stress (mpa) 415 yield strain 0.5% glass epoxy composite properties [22] young’s modulus e1(gpa) 55 young’s modulus e2, e3(gpa) 15.2 poisson’s ratio υ12, υ13 0.254 poisson’s ratio υ23 0.428 shear modulus g12, g13 (gpa ) 4.7 shear modulus g23 (gpa) 3.28 adhesive (fm73) properties [23] young’s modulus (gpa) 3.28 poisson’s ratio 0.45 t d. e. belhadri et alii, frattura ed integrità strutturale, 49 (2019) 599-613; doi: 10.3221/igf-esis.49.55 603 specimen; (ii) general static ‘step’-option was used for analysis with abaqus; (iii) automatic increment of steps was used with maximum increments number of 100. minimum increment size was 10−5 and maximum increment size was 1. nevertheless, the abaqus solver code could override matrix solver choice according to the ‘step’-option. the von mises yield criterion is used to predict plastic deformation. incremental plasticity theory is introduced to model the material nonlinearity. the fe simulations are carried out using the static general procedure to analyze this problem. results and discussion a) evaluation of the failure mode: in this part, we will focus on the crack failure. fig. 4 presents the variation of the stress intensity factors in mode i, ii, and iii as a function of normalized line of the crack front for an unrepaired cracked pipe. we note that the behavior of the sif is non-linear and that there are three areas. zone 1 is influenced by shear mode ii, which gives importance to circumferential stresses; in zone ii, k1 has larger values than k2 and k3 until the end of the crack comes the appearance of mode iii but of low intensity. we conclude that 75% of the crack front is controlled by mode ii, 20% by mode i and only 5% of the crack front for mode iii. -10 0 10 20 30 40 50 60 70 80 90 100 110 -5 0 5 10 15 20 25 30 35 normalized distance from the crack front k ( m p a .m m 0 ,5 ) zone 1 zone 2 zone 3 k i k ii k iii figure 4: variation of the sif along the front of the elliptical crack for an unrepaired pipe (c = 60mm, a = 5mm). in fig. 4, composite repair does not change the configuration. fig. 5 shows the variation of the sif along the crack front for a repaired pipe fig 3, indeed the zone 1 is still controlled by kii but with more or less variable reductions for the three modes. to verify this reduction, each mode has been traced separately to quantify the rates of improvement knowing that these rates change from one crack to another. in what follows we will use the variables *k i (sif*), which will represent the improvement provided by the repair where: *               , ,   unrep rep i i i unrep i k k k i i ii iii k    (6) fig. 6 (a) shows the distribution of the mode i stress intensity factor along the crack front for a repaired and unrepaired pipe. there is a net reduction of the ki in the crack tip with a maximum of 46%, this fall of the sif decreases as the front touches the edge of the pipe. in fig. 6 (b) is shown the effectiveness of the repair expressed by k*, the latter confirms the fig. (a) since it is clear that the efficiency decreases towards the edge of the crack. crack front d. e. belhadri et alii, frattura ed integrità strutturale, 49 (2019) 599-613; doi: 10.3221/igf-esis.49.55 604 -10 0 10 20 30 40 50 60 70 80 90 100 110 -4 0 4 8 12 16 20 24 28 normalized distance ( ) k iii k ii k i figure 5: variation of the sif along the front of the elliptical crack for a repaired pipe (c = 60mm, a = 5mm). figure 6: variation of the sif and *ik along the front of the elliptical crack pipe (c = 60mm, a = 5mm). figure 7: variation of the sif and *iik along the front of the elliptical crack pipe (c = 60mm, a = 5mm). d. e. belhadri et alii, frattura ed integrità strutturale, 49 (2019) 599-613; doi: 10.3221/igf-esis.49.55 605 the kii variation on the crack front for a repaired and unrepaired pipe is shown in fig. 7(a). it is visible that the composite repair also reduces the kii for a rate of only 17% for the median position of the elliptical crack. conversely, at *k i , the *k ii repair efficiency increases towards the extreme edge of the elliptical crack to reach 55%. fig. 7(b) for kiii fig. 8 shows the variation of the kiii along the crack front for a cracked pipe and a repaired pipe, it can be clearly seen that there is no effect of the repair at the bottom of the crack for the kiii on the other hand is approaching the end of the crack the effect of the repair is more marked with a reduced rate of 81%. -10 0 10 20 30 40 50 60 70 80 90 100 110 -2 0 2 4 6 8 10 12 14 16 18 20 22 24 k ii i ( m p a .m m 0 ,5 ) normalized distance repaired pipe unrepaired pipe figure 8: variation of the kiii along the front of the elliptical crack pipe (c = 60mm, a = 5mm). b) effect of the crack dimensions: the durability of composite patch repairs of damaged structures depends on the nature and size of the defects. the application of this technique will not be reliable if the size of the defect repaired exceeds a critical value. in this part, the effect of the crack size is represented by the crack progression in the thickness for the evaluation of the variation of the sif. figure 9: variation of the ki along the front of the elliptical crack pipe for different crack depth (c = 60mm). position 1 position 2 position 3 0 10 20 30 40 50 60 70 80 90 100 -20 -15 -10 -5 0 5 10 15 20 25 k i(m p a m m 0 ,5 ) normalized distance a/t=0,39 a/t=0,55 a/t=0,71 a/t=0,79 a/t=0,87 d. e. belhadri et alii, frattura ed integrità strutturale, 49 (2019) 599-613; doi: 10.3221/igf-esis.49.55 606 fig. 9 shows the behavior of the ki along the crack front for different values of crack depth (a) and for a repaired pipe. we can say that the sif keeps the same behavior regardless of the depth, but we also note that there are three areas as already mentioned before where there is a variation of the sif and to illustrate this effect, we trace fig. 10 to differentiate the variation of ki as a function of the depth (a) for the three zones noted in fig. 9. the ki is inversely proportional to the depth (a) for the three positions, this is essentially due to the composite's behavior towards the deformation caused by the opening of the crack.; this confirms the beneficial effect of the composite repair even at 86% of the thickness of the pipe. figure 10: variation of the ki along the front of the elliptical crack pipe for different crack depth in position 1, 2 and 3 (c = 60mm). fig. 11 shows the variation of the kii at the crack front as a function of the depth (a), the results show that the depth a/t=0.87 presents a major risk of rupture with a maximum value of 57 mpa mm0.5. this observation confirms that the failure behavior of the progress of the crack is more influenced by shear mode (kii) without neglecting the presence of the two other modes. 0 10 20 30 40 50 60 70 80 90 100 -15 -10 -5 0 5 10 15 20 25 30 35 40 45 50 55 60 65 a/t=0,39 a/t=0,55 a/t=0,71 a/t=0,79 a/t=0,87 k ii (m p a m m 0 ,5 ) normalized distance figure 11: variation of the kii along the front of the elliptical crack pipe for different crack depth (c = 60mm). 5 6 7 8 9 10 11 12 -5 0 5 10 15 20 a (mm) k im p a .m m 0 .5 position 1 position 2 position 3 d. e. belhadri et alii, frattura ed integrità strutturale, 49 (2019) 599-613; doi: 10.3221/igf-esis.49.55 607 the behavior of the kiii along the crack front is shown in fig. 12 (a)for different values of (a). the median position of the crack is not sensitive to the variation of the kiii . on the other hand, and as already pointed out, this variation becomes more and more marked where kiii progresses proportionally as a function of depth (a). fig. 12 (b) asserts that kiii reaches maximal values at the outer limit of the elliptical crack. figure 12: variation of kiii along the front for different crack depth (a) variation of kiii for position (4) of the crack (b). repaired pipe with c = 60mm. figure 13: variation of the sif: ki , kii and kiii along the crack front for different length. repaired pipe with a = 7mm a second analysis is presented in the following for a constant depth a = 7mm and we change the length of the crack 2c. in these results it was found that the three stress concentration factors keep almost the same behavior noticed for the depth a with respect to the crack length 2c. the appearance of the ki shows the presence of three zones, the kii is independent d. e. belhadri et alii, frattura ed integrità strutturale, 49 (2019) 599-613; doi: 10.3221/igf-esis.49.55 608 the length of the crack except for the length 2c = 50mm, finally the kiii proves its sensitivity to the longitudinal advancement of the crack always to the outer side of the crack which is in contact with the repair composite. c) effect of crack shape: in this part the effect of the crack shape is expressed. it is important to note that the values of kii and kiii are negligible compared to ki for a rectangular crack. fig. 14 shows the variation of the ki for a rectangular crack and an elliptical crack along the fronts, it is clear that the rectangular crack marks a maximum higher than the elliptical crack; this is mainly due to the singularity of the rectangular crack, which has a 90 ° angle (hot point ) that amplifies the stress. the presence of this singularity is confirmed by the appearance of k  maxi at 65% of the normalized distance. in addition, the rectangular crack is governed only by mode 1, while the semi elliptic crack knows the interaction of the three modes of fractures i, ii and iii . -10 0 10 20 30 40 50 60 70 80 90 100 110 5 10 15 20 25 30 35 40 k i(m p a .m m 0 ,5 ) normalized distance rectangular crack semi-elliptical crack figure 14: variation of ki for rectangular and semi-elliptic crack of an unrepaired pipe (2c = 60mm, a = 5mm) for composite repair, the distribution of the ki on the crack front is shown in fig. 15, we can say that the composite repair is much more obvious for the rectangular crack than for the elliptical crack since we see that the repair brings the two curves to the same maximum 22 mpa mm0.5 for mode i. it is concluded that the composite repair technique is effective for the two crack geometries studied. figure 15: variation of ki for rectangular and semi-elliptic crack of a repaired pipe (2c = 60mm, a = 5mm) rectangular crack semi-elliptical crack hot point d. e. belhadri et alii, frattura ed integrità strutturale, 49 (2019) 599-613; doi: 10.3221/igf-esis.49.55 609 d) effect of composite thickness: fig. 16 shows the variation of the ki as a function of the thickness of the composite. the crack front describes a nonlinear behavior or one can distinguish four zones, to make out the effect of the thickness is drawn fig. 17 which shows the variation of the ki for different thickness and for each zone.               figure 16: ki distribution along the front for different composite thickness. repaired pipe (2c = 45mm, a = 7mm).   5 figure 17: ki variation versus composite thickness for the four zones it is clear from fig. 17 that increasing the thickness of the patch leads to the decrease of the ki for internal and external crack positions. a thick patch allows a good absorption of the stresses, this is more marked for zone 3 whereas the ki tends to stabilize for zones 1 and 2, for zone 4 the ki is independent of the thickness of the composite. fig. 18 (a) shows the kii distribution along the front as a function of the thickness of the composite. for the kii the behavior remains more intensive at the bottom of the crack and takes weak values towards the end of the crack, the effect of the thickness of the composite is significant only for bottom of the crack whereas it is independent of the limit of composite dimension crack. from fig. 18 (b) it can be seen that in zone 1 the kii reaches its maximum for a thickness of 4 mm from which it decreases. -10 0 10 20 30 40 50 60 70 80 90 100 110 0 4 8 12 16 20 24 28 zone 4 zone 3 zone 2 ep composite =2mm ep composite =4mm ep composite =6mm ep composite =8mm ep composite =10mm normalized distance k i ( m p a .m m 0 ,5 ) zone 1 d. e. belhadri et alii, frattura ed integrità strutturale, 49 (2019) 599-613; doi: 10.3221/igf-esis.49.55 610 figure 18: distribution of the kii along the front for different thickness of the composite (a) variation of the kii as a function of the thickness of the composite (b) repaired pipe (2c = 45mm, a = 7mm).     figure 19: distribution of the kiii along the front for different thickness of the composite (a) variation of the kii as a function of the thickness of the composite (b) repaired pipe (2c = 45mm, a = 7mm). fig. 19 (a) shows the distribution of kiii along the front as a function of the thickness of the composite. from this figure, it is noted that the mode iii is not sensitive to the thickness of the composite at the bottom of the crack whereas it varies significantly with the thickness of the composite on the outer side of the crack or it is in direct contact with the patch, however it increases with the thickness of the composite up to a maximum value of 85mpa.mm0.5 for a value of 8mm, beyond this value the kiii decreases and the patch resumes its role of absorption of constraints at the edge of the crack. e) effect of the composite length: fig. 20 describes the variation of the sif as a function of the length of the composite patch along the crack front. it is observed that increasing the length of the patch does not reduce much the sif. except for the kiii, or it can be said that it is sensitive to increasing the length of the composite, the sif in external position is reduced by 20%. this result confirms that the choice of a long patch does not necessarily increase the effectiveness of the repair of the blow reduces the cost of the maintenance operation. d. e. belhadri et alii, frattura ed integrità strutturale, 49 (2019) 599-613; doi: 10.3221/igf-esis.49.55 611 figure 20: variation of the sif: ki , kii and kiii along the crack front for different overwrap length. repaired pipe with 2c=45mm, a = 7mm. figure 21: variation of ki, kii and kiii along the crack front for a single layer of composite and for four sub-layers of the composite. repaired pipe with (2c = 60mm, a = 7mm). d. e. belhadri et alii, frattura ed integrità strutturale, 49 (2019) 599-613; doi: 10.3221/igf-esis.49.55 612 f) effect of the repair method: in reality, the composite does not have a single thickness but is wound around the pipeline by several layers. by taking this evidence we have assumed two repair configurations, at first, we consider a single layer of a composite of 4mm thick, the second, we apply a repair with four (4) layers of composite and four (4) layers of adhesives to the same thickness. fig. 21 shows the distribution of sif along the front of cracks, it is clear that the two configurations do not present a big difference for the three modes. this result presents an excellent agreement with those of m. m. benziane et al[29] conclusion he results obtained numerically by the three-dimensional finite element method enable us to draw the following conclusions: 1. we note the presence of three failure modes along the semi elliptical crack front. the maximum value of the sif along the crack tip is that of the mode kii. 75% of the crack front is influenced by the mode ii, 20% by mode i and only 5% of the crack front is commanded by the mode iii. 2. for longitudinal elliptical cracks the risk of rupture of pipelines is more dangerous on the internal fronts than for external ones. 3. the repair on the external side is better with an efficiency of 81% for the mode iii. this is mainly due to the direct contact of the lips of the crack with the composite which ensures a good transfer of the concentrations of the constraints of the pipe through the adhesive to the composite. 4. the composite repair technique is effective for the two crack geometries studied. 5. the rectangular crack is governed only by mode 1, while the semi elliptic crack knows the interaction of the three modes of fractures i, ii and iii. 6. the reduction of stress intensity factor by the composite patch leads us to conclude that the fatigue life can be improved. 7. the increase of the thickness of the patch leads to the decrease of the sif for the internal and external crack positions. a thick patch allows a good absorption of the constraints. 8. it is necessary to optimize the characteristic and geometric (thickness, length) of the composite to have an effective repair. this can lead to low cost repair and hence decrease the cost of energy. 9. the use of a layer of composite or the decomposed in several layers to simulate the real case showed that there is not a big difference compared to our results. this confirms that only the first layer of the composite which absorb the maximum stress of the pipe. references [1] mohitpour, m., golshan, h., murray, a. (2003). pipeline design and construction: a practical approach. 2nd ed. new york, ny: asme press; 2003. pp. 499–518. [2] chapetti m.d., otegaui, j.l., manfredi, c., martins, c.f. (2001). full scale experimental analysis of stress states in sleeve repairs of gas pipelines. international journal of pressure vessels and piping, 78, pp. 379–87. [3] koch gh, brongers mp, tompson ng, virmani yp, payer jh. (2001). corrosion cost and preventative strategies in the united states. federal highway administration, office of infrastructure research and development, pp. 260–311. [4] matheas, j.d. (2005). etude du comportement mécanique de patchs composites utilisés pour le renforcement de structures métalliques aéronautiques. pp. 13-21. phd thesis. n d’ordre : d.u. 1587 edspic : 323. [5] andrew, j., patrick., compositescase studies of pipeline repair applications, clock spring company, l.p., huntingdon, uk. [6] asme b31.4. (2003). liquid transportation system for hydrocarbons, liquid petroleum gas, anhydrous ammonia and alcohols. new york: american society of mechanical engineers; 2003. [7] asme b31.8. (2003). gas transmission and distribution piping systems. new york: american society of mechanical engineers; 2003. [8] alexander, c.r., francini, r. (2006). state of the art assessment of composite systems used to repair transmission pipelines. paper no. ipc2006-10484. in: proceedings of the 16th international pipeline conference, calgary, canada september. pp. 25–29. t d. e. belhadri et alii, frattura ed integrità strutturale, 49 (2019) 599-613; doi: 10.3221/igf-esis.49.55 613 [9] newman, j.c., j.r. and raju, i.s. (1983). stress intensity factor equations for cracks in three dimensional finite bodies. fracture mechanics: fourteenth symposium––volume i: theory and analysis, astm stp 791, j. c. lewis and g. sines, eds. american society for testing and materials. pp. i-238 i-265. [10] a. saffih, s. hariri. (2006). numerical study of elliptical cracks in cylinders with a thickness transition, international journal of pressure vessels and piping. 83. pp. 35–41. [11] gosz, m. and moran, b. (1997). stress-intensity factors along three-dimensional elliptical crack fronts, office of aviation research washington, d.c. 20591-dot/faa/ar-96/97. [12] khoramishad, h. and ayatollahi, m. r. (2009). finite element analysis of a semi-elliptical external crack in a buried pipe. transactions of the canadian society for mechanical engineering, vol. 33, no. 3, 2009 [13] rooke, d.p. & cartwright, d.j. (1976). compendium of stress intensity factors. hmso ministry of defence. procurement executive. [14] heliot, j., labbens, r.c., pelissier-tanon, a. (1979). semi elliptical cracks in a cylinder subjected to stress gradient. am soc test mater. pp. 341–64. [15] mcgowan, j.j., raymund m. (1979). stress intensity factor solutions for internal longitudinal semi-elliptical surface flaws in a cylinder under arbitrary loadings. am soc test mater. pp. 365–80. [16] rsem. (1997). rules for in service inspection on nuclear power plant components. afcen, tour framatome, f92084 paris la défense cedex; edition . [17] chapuliot, s., lacire, m.h. (1998). stress intensity factors for internal circumferential cracks in tubes over a wide range of radius over thickness ratios. proceedings of the asme pvp conference, vol. 365; 1998. pp. 95–106. [18] chapuliot, s., lacire, m.h. (1999). stress intensity factors for external circumferential cracks in tubes over a wide range of radius over thickness ratios. proceedings of the asme pvp conference, vol. 388; 1999. pp. 3–12. [19] meneghetti, g., campagnolo, a., avalle, m., castagnetti, d., colussi, m., corigliano, p., de agostinis, m., dragoni, e., fontanari, v., frendo, f., goglio, l., marannano, g., marulo, g., moroni, f., pantano, a., rebora, a., scattina, a., spaggiari, a., zuccarello, b. (2018). rapid evaluation of notch stress intensity factors using the peak stress method: comparison of commercial finite element codes for a range of mesh patterns, fatigue fract. eng. mater. struct., 41(5), doi: 10.1111/ffe.12751. [20] campagnolo, a., meneghetti, g. (2018). rapid estimation of notch stress intensity factors in 3d large-scale welded structures using the peak stress method, matec web conf., 165, doi: 10.1051/matecconf/201816517004. [21] api 5l. specification for line pipe. apl specification 5l, 42nd ed. usa: the american petroleum institute; 2000. [22] walker, a.c., williams, k.a.j. (1995). strain based design of pipelines. in: proceedings of the asme 14th international conference on ocean, offshore and arctic engineering, vol. v, copenhagen, denmark; 1995. pp. 345–50. [23] hyer, m.w. (2008). stress analysis of fiber-reinforced composite materials. new york (usa): mcgraw-hill; 2008. [24] dassault systèmes simulia corp abaqus/cae 6.14 user's manual. [25] dake, y., sridhar, i., zhongmin, x., kumar, s.b. (2012). fracture capacity of girth weldedpipelines with 3d surface cracks subjected to biaxial loading conditions. int jpress vessels pip. pp. 92-115. [26] anderson, t.l. (2005). fracture mechanics: fundamentals and applications 3rd edition,crc press; 2005. [27] mcmeeking, r.c., parks, d.m. (1979). on criteria for j-dominance of crack tip fields in large-scale yielding. philadelphia: astm stp 668; 1979. pp. 175e194 [28] bezzerrouki, m., albedah, a., bachir bouiadjra, b., ouddad, w., benyahia, f. (2011). computation of the stress intensity factor for repaired cracks with bonded composite wrap in pipes under traction effect. journal of thermoplastic composite materials. doi: 10.1177/0892705711430428. [29] madjid meriem-benziane , sabah, a., wahab, a., hamou, z., benoauda, b., mohamed, h.m., guy, p. (2015). finite element analysis of the integrity of an api x65 pipeline with a longitudinal crack repaired with singleand doublebonded composites. composites part b 77 . pp. 431-439 << /ascii85encodepages false /allowtransparency false /autopositionepsfiles true /autorotatepages /none /binding /left /calgrayprofile (dot gain 20%) /calrgbprofile (srgb iec61966-2.1) /calcmykprofile (u.s. web coated \050swop\051 v2) /srgbprofile (srgb iec61966-2.1) /cannotembedfontpolicy /error /compatibilitylevel 1.4 /compressobjects /tags /compresspages true /convertimagestoindexed true /passthroughjpegimages true /createjobticket false /defaultrenderingintent /default /detectblends true /detectcurves 0.0000 /colorconversionstrategy /cmyk /dothumbnails false /embedallfonts true /embedopentype false /parseiccprofilesincomments true /embedjoboptions true /dscreportinglevel 0 /emitdscwarnings false /endpage -1 /imagememory 1048576 /lockdistillerparams false /maxsubsetpct 100 /optimize true /opm 1 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/pdfxoutputintentprofileselector /documentcmyk /preserveediting true /untaggedcmykhandling /leaveuntagged /untaggedrgbhandling /usedocumentprofile /usedocumentbleed false >> ] >> setdistillerparams << /hwresolution [2400 2400] /pagesize [612.000 792.000] >> setpagedevice microsoft word numero_55_art_21_2971 m. m. konieczny et alii, frattura ed integrità strutturale, 55 (2021) 277-288; doi: 10.3221/igf-esis.55.21 278 experimental analysis of the state of stress in a steel – titanium perforated plate loaded with concentrated force mateusz marcin konieczny, henryk achtelik, grzegorz gasiak opole university of technology, poland mateuszmarcinkonieczny@wp.pl, kmpkm@po.edu.pl, g.gasiak@po.edu.pl abstract. the paper presents an experimental analysis of the state of stress, free supported on the edge of a steel – titanium circular perforated plate loaded with a centrally concentrated force, created in the technological process of explosion welding. for this purpose, a special test stand was designed and a methodology for testing the perforated plate was developed. resistance strain gauges were used to measure the state of strain. the load was applied in the center of the plate to a pressure stamp. as a result of the research, the values of radial, circumferential and equivalent von mises stress were obtained as a function of the radius of the plate perforation circle and its load. the stress distribution topography revealed the zones of maximum stress of the steel – titanium perforated plate. the proposed method of experimental research can be used by engineers to verify the state of stress, e.g. in the designed tube sheet walls of reactors for ammonia synthesis. keywords. perforated plate; concentrated force; stress analysis; experimental research. citation: konieczny, m. m., n., achtelik, h., gasiak, g., experimental analysis of the state of stress in a steel – titanium perforated plate loaded with concentrated force, frattura ed integrità strutturale, 55 (2021) 277-288. received: 12.12.2020 accepted: 23.12.2020 published: 01.01.2021 copyright: © 2021 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. introduction n the work of a designer, a frequent problem is the proper determination of the level of stresses and strains. experimental tests are used to assess the correctness of the design of a given structure element in terms of its strength. the assessment is based on the material effort determined by the states of stress and strain. research on these states can be carried out on real objects, as well as on their models made of various materials. on the basis of these tests, information is obtained that allows for a possible improvement of a structural element and for checking its behavior under operational loads [1]. in the literature, there are many works related to the analysis of the state of stress and strain in perforated plates [2, 3, 4, 5, 6, 7, 8]. an experimental verification of the mathematical model obtained in [9] is presented in [10], where the methodology of experimental tests was developed, which would allow to determine the value of stresses in perforated plates loaded centrally by concentrated force. the diameters of the holes, as well as the topography of their arrangement in the plate prepared for the tests, ensured the stability of the section weakening coefficients. resistance strain gauges were placed between the holes to measure the strain. the axially symmetrical perforated plate has been bent with a concentrated force applied centrally. additionally, plate bending was monitored with a dial gauge during deformation measurements. based on the measured deformation values, the values of radial, circumferential and equivalent von mises stresses in the plate were i https://youtu.be/-vjzghrfjd4 m. m. konieczny et alii, frattura ed integrità strutturale, 55 (2021) 277-288; doi: 10.3221/igf-esis.55.21 279 obtained. an experimental approach to the analysis of perforated plates was also proposed by the authors of [11], where they analyzed the state of stress and deflection of a circumferentially freely supported, circular-symmetric perforated plate, loaded with static pressure. for this purpose, a special test stand was designed and a methodology for testing the perforated plate was developed. the load on the perforated plate was carried out by means of a special elastic cushion, similar to that of duncan [12]. tensometric rosettes were used to measure the plate state of deformation. the load on the plate was determined by the deflection of its center. as a result of the research, the values of stresses were obtained as a function of the radius of the plate perforation circle and its load. in addition, the experimental approach related to the analysis of the state of deformation and stress in single-layer square perforated plates made of steel with specific geometric parameters was the subject of works [13, 14, 15]. currently, more and more often in engineering structures are used elements consisting of many layers and of many materials, i.e. plated elements [16, 17]. such structural elements may include layers made of structural steel, titanium, brass, aluminum, nickel, but also of non-metallic materials such as polyethylene, kevlar, glass fibers and carbon fibers. elements of this type are most often used due to the improvement of thermal properties, chemical properties (e.g. corrosion resistance) as well as the mechanical parameters of the structure in which such elements are present. in the works [16, 17] an analytical solution was presented with the use of mathematical formulas enabling engineers to estimate the effort of the designed cladded perforated plates subjected to various types of load. it was found that both the finite element method and the analytical method make it possible to determine the stress values in plated perforated plates in the transition layers, i.e. in the transition layer on the titanium side and in the transition layer on the steel side. experimental methods based on strain gauges do not offer such possibilities. the presented work proposes an experimental approach to determining the stress values in a steel – titanium circular perforated plate, freely supported on the edge and loaded centrally with a concentrated force pi perpendicular to the plate surface. the research carried out at work was based on the use of resistance strain gauges. the results of the research presented in the paper can be used by engineers to design bimetallic perforated plates loaded perpendicular to their surface. figure 1: model of bimetallic perforated plate consisting of steel thickness perforated plate h and titanium perforated plate thickness a containing holes with diameters d1,…,d5. m. m. konieczny et alii, frattura ed integrità strutturale, 55 (2021) 277-288; doi: 10.3221/igf-esis.55.21 280 subject of the research he experimental research was based on a bimetallic circular axisymmetric perforated plate with dimensions: diameter d = 300 mm and comprising two layers, i.e. the base layer b in the form of structural steel with a thickness of h = 10 mm and the applied layer (plating) in the form of titanium with the thickness of a = 2.5 mm. 100 holes with different radii located on the plate. these holes were arranged in five circles with 20 holes in each circle. on the first outer circle, the plate had holes d1 = 20.5 mm in diameter and on the fifth, inner circle holes d5 = 9.5 mm in diameter. the scheme of the plate is shown in fig. 1, and the plate in fact in fig. 2. the perforated plate adopted for experimental research was made of a metallic composite called a platter, obtained during the so-called explosive plating. explosive plating, also known as bonding or welding, consists in joining two or more metal elements with the use of energy released during the detonation of an explosive (fig. 2) [18]. this technology is mainly used for materials that are difficult to join or cannot be joined by other methods. in this case, it was a steel sheet with a titanium layer applied to it. the plate prepared in this way was subjected to a rolling process to obtain a circular plate. then, holes were drilled in the plate, positioned as shown in fig. 1. the base material of the plate was steel sheet of the s355j2 grade, and the applied material was titanium sheet with the following mechanical and material parameters (tab. 1) [19]. figure 2: model of bimetallic perforated plate. s355j2 steel and titanium applied layer a titanium re [mpa] rm [mpa] e [gpa] v [-] g [gpa] a5 [%] 189-215 308-324 100 0.37 36.5 43-56 c fe h n o ti 0.10 0.20 0.015 0.03 0.18 99.5 base layer b s355j2 steel re [mpa] rm [mpa] e [gpa] v [-] g [gpa] a5 [%] 382-395 598-605 220 0,30 84,6 24-34 c si mn p s cu fe 0.22 0.55 1.60 0.025 0.025 0.45 all table 1: strength properties and chemical composition of s355j2 steel and titanium, where: re – yield strength [mpa], rm – tensile strength [mpa], e – young’s modulus [gpa], v – poisson’ s ratio [-], a5 – tensile elongation [%]. t m. m. konieczny et alii, frattura ed integrità strutturale, 55 (2021) 277-288; doi: 10.3221/igf-esis.55.21 281 research method he aim of the experimental tests was to determine the state of stress in a steel – titanium circular perforated plate. this plate was loaded with a concentrated force pi applied in its geometric center perpendicular to its surface, and the boundary conditions were assumed in the form of free support of the plate on its edge. on a previously prepared steel – titanium perforated plate, tokyo sokkia kenkyujo co ltd, fla-1-11 strain gauges with a measuring base of 1 mm and a strain gauge constant k = 2.14 (fig. 3) were attached, on two plate layers, i.e. on base layer b steel and on the applied layer a titanium at 20 measuring points on the bridges between the holes in the circumferential direction, i.e. from ac1 to ac5 and from bc1 to bc5, and in the radial direction, i.e. from ar1 to ar5 and from br1 to br5. this situation is illustrated in figs. 4 and 5. wooden pegs (fig. 2), to which clamps are screwed, were placed in the appropriate holes of the experimental plate. in this way, the cables connecting the strain gauge with the measuring system of the wheatstone bridge were immobilized and thus secured against breaking. as the plate is axially symmetrical with an axially-symmetrical distribution of holes (the hole spacing is 18 degrees), fig. 5 show the actual arrangement of the strain gauges for a quarter of the plate. figure 3: strain gauges type: tokyo sokkia kenkyujo co ltd, fla-1-11. figure 4: arrangement of strain gauges on a bimetallic circular perforated plate: a) on the applied layer a – titanium; b) on the base layer b – steel (schematically). t m. m. konieczny et alii, frattura ed integrità strutturale, 55 (2021) 277-288; doi: 10.3221/igf-esis.55.21 282 figure 5: arrangement of strain gauges on a bimetallic circular perforated plate: a) on the applied layer a – titanium; b) on the base layer b – steel (schematically). figure 6: view of the testing machine prepared for testing in the case of plate loading with concentrated force p, where: 1 computer, 2 universal testing machine, 3 steel-titanium circular axially symmetrical perforated plate, 4 annular support, 5 strain gauge, 6 sensor dial, 7 pressure pin, 8 distribution box, 9 strain gauge bridge, 10 dial gauge. research position suitable test stand was prepared to measure the topography of deformations in a steel – titanium circular perforated plate. for this purpose, an appropriately designed annular support was made to ensure the boundary conditions of free support. the zdm 10 universal testing machine from werkstoff preufmaschinnen leipzig was used for the tests. the annular support was mounted on the machine in such a way that the axis of the loading pin passes through its axis of symmetry. the test plate with the strain gauges glued on was placed on the thus prepared support in such a way that the lower layer of the plate, i.e. the base layer b steel, touched the support, while the upper layer, i.e. the layer a titanium, a m. m. konieczny et alii, frattura ed integrità strutturale, 55 (2021) 277-288; doi: 10.3221/igf-esis.55.21 283 was in contact with the mandrel of the testing machine . the experimental plate was loaded in the form of a concentrated force. this type of load was realized directly by the mandrel of the testing machine, which corresponds to a case of concentrated force pi applied at the geometric center of the plate normal to its surface. the test stand used for the experiment is shown in fig. 6. the measurement of deformation in the plate was made with the use of a set consisting of a distribution box and a t2-type strain gauge bridge with a reading unit value of 0.005 ‰. however, the plate deflection was controlled with a dial gauge with an indication accuracy of 0.01 mm and a measuring range of 10 mm. the dial indicator was attached to the annular support in such a way that the axis of the stylus passes through the center of the experimental plate and lies in the axis of the loading pin of the testing machine. after the experimental plate was properly placed on a specialized support, the axiality of the sensor's measuring pin and the loading pin of the testing machine was checked. after resetting the measuring devices, the test stand was ready for the experiment. figure 7: scheme of a steel – titanium circular perforated plate mounted on a ring support and loaded with a concentrated force pi applied in the geometric center of the plate normally to its surface: a) from the layer of the applied plate a titanium; b) from the side of the base layer of the b plate steel, where: 1 – bimetallic circular perforated plate, 2 the applied layer of the plate a titanium, 3 base layer of the plate b steel, 4 annular support, 5 stand support, 6 pi load, 7 dial gauge, 8 pressure stamp. course of research n the first case, a steel – titanium circular perforated plate was loaded with a concentrated force pi applied in the geometric center of the plate perpendicularly to the surface of the applied a titanium plate, and the boundary conditions were assumed in the form of free support of the plate on its edge. the diagram of fastening and loading of the perforated plate for the analyzed case is shown in fig. 7a. in the second case, a steel – titanium circularsymmetrical i m. m. konieczny et alii, frattura ed integrità strutturale, 55 (2021) 277-288; doi: 10.3221/igf-esis.55.21 284 perforated plate was loaded with a concentrated force pi applied in the geometric center of the plate perpendicularly to the base surface of the b steel plate, and the boundary conditions were assumed in the form of free support of the plate on its edge. the diagram of fastening and loading of the perforated plate for the analyzed case is shown in fig. 7b. then, the plate was initially subjected to a load p0 causing a deflection w0 in its center. after obtaining the initial load and deflection, readings of strain gauges on each of the radial circles in the radial and circumferential directions were read and recorded as the initial reading marked with the index "p". then the plate was loaded with the force pi, which caused the deflection. the readings of the strain gauges were read again and marked with the index "k" as the final reading. a similar measurement procedure was used for the successive forces p2, p3 and p4, which corresponded to the deflections w2, w3 and w4. the following values of the pi load were adopted: p1 = 5 kn, p2 = 10 kn, p3 = 15 kn, p4 = 20 kn. the readings of strain gauges during measurements and the strains calculated on their basis in the circumferential direction εθ and in the radial direction εr were used to determine the appropriate stresses. research results and their analysis t was assumed that a plane state of stress occurs in a steel – titanium circular perforated plate. for the elastic state of strains, the relationships between strains and stresses result from the generalized hooke's law. if the principal directions 1 and 2 are known, the relationship between the strains 1 and 2 , and the stresses 1 and  2 , takes the following form [20]:        1 1 221 e (1)         2 2 121 e (2) where: e – young’s modulus [mpa]; v – poisson’s ratio [-]. in our case, the main directions of the axially symmetrical perforated plate are radial direction r and circumferential direction 𝛳. therefore, having determined the deformations in the radial direction r and in the circumferential direction  , the main stress components in the radial direction  r and in the circumferential direction  were determined from the following relationships:        21 r r e (3)         21 r e (4) after determining the radial stress values r and circumferential stresses values θ, these values were introduced into the formula for equivalent von mises stress red , in the form:         2 2 red r r (5) figs. 8 and 9 shown the values of stresses in the radial direction  r and circumferential direction  and equivalent von mises stress red at the designated measurement points of the plate on the surface of the applied layer of the plate a titanium (fig. 4a and 5a) and on the surface of the base layer of the plate b steel (fig. 3b and 4b) with different loading forces, i.e. p1 = 5 kn, p2 = 10 kn, p3 = 15 kn, p4 = 20 kn. in this case, the load was applied from the side of the titanium layer as shown in fig. 7a. figs. 10 and 11 shown the values of stresses in the radial direction  r and circumferential direction i m. m. konieczny et alii, frattura ed integrità strutturale, 55 (2021) 277-288; doi: 10.3221/igf-esis.55.21 285  and the equivalent von mises stress red at the designated measurement points of the plate on the surface of the applied layer of the plate a titanium (fig. 4a and 5a) and on the surface of the base layer of the plate b steel (fig. 4b and 5b) with different loading forces, i.e. p1 = 5 kn, p2 = 10 kn, p3 = 15 kn, p4 = 20 kn. in this case, the load was applied from the side of the steel layer, as shown in fig. 7b. figure 8: summary of the stress values, respectively:  , r red determined on the surface of the applied layer of the plate a – titanium, in this case, the load was applied from the side of the titanium layer. figure 9: summary of the stress values, respectively:  , r red determined on the surface of the base layer of the plate b steel., in this case, the load was applied from the side of the steel layer. m. m. konieczny et alii, frattura ed integrità strutturale, 55 (2021) 277-288; doi: 10.3221/igf-esis.55.21 286 figure 10: summary of the stress values, respectively:  , r red determined on the surface of the applied layer of the plate a – titanium, in this case, the load was applied from the side of the titanium layer. figure 11: summary of the stress values, respectively:  , r red determined on the surface of the base layer of the plate b – steel, in this case, the load was applied from the side of the steel layer. fig. 12 shows the results of measurements of deflection w for a steel – titanium circular perforated plate, freely supported and loaded with a concentrated force pi applied in the geometric center of the plate, determined experimentally in its m. m. konieczny et alii, frattura ed integrità strutturale, 55 (2021) 277-288; doi: 10.3221/igf-esis.55.21 287 geometric center, in the case where the load was applied from the side of the titanium layer – 1w and if the load was applied from the steel layer – 2w . figure 12: results of measurements of deflection in the center of the slab, at various loads with concentrated force pi in the geometric center of the slab, normal to its surface, where: 1w – the load was applied from the side of the titanium layer, 2w – the load was applied from the side of the steel layer. figs. 8 – 11 summarize the stress values in a bimetallic perforated plate centrally loaded with a concentrated force pi. the strains measurement concerned points on the bridges between the plate holes, arranged according to the diagrams shown in figs. 4 and 5. these are points in zones with a significant stress concentration compared to a homogeneous plate. the comparison of the stress results presented in figs. 8 – 11 shows that when the plate load is applied from the side of the applied layer, i.e. the titanium, stress values differ slightly from the stresses obtained for the same plate but loaded from the side of the base layer, i.e. steel . this is the result of residual stresses in the bimetallic perforated plate. in practice, such bimetallic plates are not subject to heat treatment due to their large size. in industry, such plates are used in the raw state [19], for example as heat exchanger tube sheets [10]. the deformation measurements were made in the plate perforation zone (figs. 4 and 5), where in the process of making holes, the residual stresses should be reduced. however, the conducted tests showed that the residual stresses cause discrepancies in the determination of stresses resulting from the load on the perforated plate. moreover, it can be seen from fig. 12 that when the load is applied from the side of the base layer, i.e. the steel layer, the deflection 1w is greater than the deflection obtained when the load was applied from the side of the applied layer, i.e. the titanium layer 2w . it also indicates that residual stresses occur in the bimetallic perforated plate in the area where the titanium plates are connected to the steel plate [21]. the deflection concerns the point of the geometric center of the plate, which consists of a perforated zone (60 mm ⩽ r ⩽ 130.5 mm) and a homogeneous zone (6 mm ⩽ r ⩽ 60 mm) (fig. 1). conclusions he following conclusions can be drawn from the above analysis: 1) the distribution of stresses in the plate perforation zone was determined in the places of stress concentration; 2) it has been shown that despite the holes made in the plate, we deal with the presence of residual stresses arising in the process of explosive joining of steel sheet with titanium sheet; t m. m. konieczny et alii, frattura ed integrità strutturale, 55 (2021) 277-288; doi: 10.3221/igf-esis.55.21 288 3) the proposed method of experimental research can be used by engineers to verify the state of stress, e.g. in the designed tube sheet walls of reactors for ammonia synthesis. references [1] niezgodziński, m.e. (1973). obliczenia grubości ścian sitowych w zbiornikach ciśnieniowych, przegląd mechaniczny, 3, ss. 102-105 (in polish). [2] chen, k.t., ting, k. and yang, w.s. (2000). stress analysis of two-dimensional perforated plates using boundary element alternating method, computers and structures, 75, pp. 515 – 527, doi: 10.1016/s0045-7949(99)00103-0. [3] kang, j. h. (2014). exact solutions of stresses, strains, and displacements of a perforated rectangular plate by a central circular hole subjected to linearly varying inplane normal stresses on two opposite edges, international journal of mechanical sciences, 84, pp. 18 – 24, doi: 10.1016/j.ijmecsci.2014.03.023. [4] mirji, p. (2013). optimization of rectangular plate with two holes subjected to in plane static loading, international journal of scientific and engineering research, 4(6), pp. 1470 1473. [5] bhattacharya, a. and venkat, r. (2003). peak stress multipliers for thin perforated plates with square arrays of circular hole, international journal pressure vessels and piping, 80, pp. 379 – 388, doi: 10.1016/s0308-0161(03)00067-x. [6] bhattacharya, a. and venkat, r. (2004). yield surfaces for perforated plates with square arrays of holes, nuclear engineering and design, 231, pp. 219 – 233, doi: 10.1016/j.nucengdes.2004.04.001. [7] niezgodziński, m.e. and zwoliński, w. (1973). obliczenie den sitowych usztywnionych przez płaszcz zbiornika, przegląd mechaniczny, 8, (in polish). [8] konieczny, m., achtelik, h. and gasiak, g. (2020). finite element analysis (fea) and experimental stress analysis in circular perforated plates loaded with concentrated force, frattura ed integrità strutturale, 51, pp. 164-173, doi: 10.3221/igf-esis.51.13. [9] achtelik, h., gasiak, g.and grzelak, j. (2008). strength tests of axially symmetric perforated plates for chemical reactors: part 1—the simulation of stress state, international journal of pressure vessels and piping, 85, pp. 248 – 256, doi: 10.1016/j.ijpvp.2007.08.009. [10] achtelik, h., gasiak, g. and grzelak, j. (2008). strength tests of axially symmetric perforated plates for chemical reactors: part 2—experiments, international journal of pressure vessels and piping, 85, pp. 257 – 264, doi: 10.1016/j.ijpvp.2007.08.010. [11] ledwoń ,w. and achtelik, h. (2017). experimental analysis of the state of stress of the axisymetric perforated plates loaded with hydrostatic pressure, proceedings of the 13th international scientific conference: computer aided engineering, pp. 331 341. [12] duncan, j. p. (1955). the structural efficiency of tube – plates for head exchangers, proceedings of institute of mechanical engineers, 169, pp. 789-802. [13] gasiak, g. and sojka, m. (2005). wytężenie płyt perforowanych, studia i monografie, 224, politechnika opolska, ss. 95 – 108 (in polish). [14] andh, u., chavan, s., kulkarni, s. and khurd, s. (2016). stress analysis of perforated plates under uniaxial compression using fea and photoelasticity, international research journal of engineering and technology, 3 (11), pp. 239 – 244, doi: 10.1007/978-3-030-16848-3_90. [15] andh, u., chavan, s., kulkarni, s. and khurd, s. (2017). stress analysis of perforated plates under uniaxial compression using experimentation and finite element analysis, international journal of current engineering and technology, 7(2), pp. 431 437. [16] konieczny, m., achtelik, h. and gasiak, g. (2020). stress distribution in plated perforated plate loaded centrally with concentrated force, zmęczenie materiału w eksploatacji maszyn roboczych, po, 2, pp. 47-62. [17] konieczny, m., achtelik, h. and gasiak, g. (2021). location of stress concentration zones in a two-layer axially symmetrical perforated plate with force applied normally to its surface, engineering structures, 226, pp. 1-14. [18] walczak, w. (1989). metal explosion welding, wtn, warsaw (in polish). [19] data from explomet company research (z.t.w. explomet, gałka, szulc, sp. j. ul. oświęcimska 100h, 45-641 opole, poland). [20] thimoshenko, s. strengh of materials, princeton d. van nostrand co, inc. part 1 (1956), part 2 (1957). [21] karolczuk, a. and kowalski, m. (2013). residual stress determination based on the hole drilling method in explosively welded bimetallic composite, 13th international conference on material modelling, warsaw, p. 140. microsoft word numero_30_art_46 a. fernández-canteli et al., frattura ed integrità strutturale, 30 (2014) 383-393; doi: 10.3221/igf-esis.30.46 383 focussed on: fracture and structural integrity related issues determining fracture energy parameters of concrete from the modified compact tension test a. fernández-canteli, l. castañón, b. nieto, m. lozano university of oviedo, gijón, spain afc@uniovi.es, labres@uniovi.es t. holušová, s. seitl institute of physics of materials, academy of science of the czech republic, brno, czech republic and brno university of technology, faculty of civil engineering, institute of structural mechanics, brno, czech republic holusova.t@fce.vutbr.cz, seitl@ipm.cz abstract. the modified compact tension (mct) test, though not yet recognized as a valid test for determining fracture energy of concrete, is believed to represent a plausible and suitable alternative versus other well established procedures, such as the wedge-splitting test (wst) and the three point (3pb) or four point bending (4pb) tests, due to its simplicity and low cost. the aim of the paper is twofold: firstly, to demonstrate the necessary correspondence between the experimental mct test setup and finite element simulations and secondly, to initiate the way of establishing the desirable conversion between the fracture energy parameter values resulting from the mct test and the standard conventional procedures. mct tests are carried out and compared with the numerical results from 2-d and 3-d finite element calculations using the commercial codes abaqus and atena, the latter being specifically developed for applications on concrete structures and elements. in this way, the usability of the modified compact tension test for practical purposes is confirmed. keywords. concrete fracture energy; modified compact tension test; concrete; numerical simulation. introduction and motivation ne of the relevant parameters that characterize concrete fracture is its fracture energy. the most extended procedure for it to be obtained is the three point bending test [1 3], whose guidelines are collected in rilem draft recommendation (50-fmc) [4, 5]. the wedge-splitting test [6, 7] represents some advantages compared to the three point bending test and it is also often used [8]. from any of those tests, the load-displacement or load-cod (crack open displacement) curve is obtained (fig. 1) [9, 10], the area under which represents the work of fracture (wf ), from which the fracture energy (gf ) is defined as: f f ligg w a (1) where alig is a ligament area. that previous kind of tests are carried out in testing machines implying specific devices and auxiliary tooling; moreover, the manufacture of such specimens is not simple; the test execution is far from being trivial and, finally, a relatively large o a. fernández-canteli et al., frattura ed integrità strutturale, 30 (2014) 383-393; doi: 10.3221/igf-esis.30.46 384 amount of material (especially for 3pb and 4pb) is needed. searching for an alternative and simpler way of testing, the idea of using a compact tension (ct) specimen has emerged. figure 1. load figure 1: load-displacement curve of concrete specimens in metallic materials, testing ct specimens represents a usual procedure to determine fracture parameters. thus, astm standard e-399 [11, 12] specifies the geometry and general configuration of this kind of tests in metallic materials. the idea of its application to testing concrete on fracture is not new: previous researchers, like wagoner et al. [13], attempt to perform this kind of tests in concrete according to the above mentioned standard though they ran into troubles obtaining premature failures in 50% of the tests at the pulling load holes thus evidencing the disability of the new procedure. with the purpose of avoiding such a high percentage of invalid tests, a different ct test methodology, denoted modified compact tension test (mct), is developed by the authors getting practically nil quote of premature failures. basically, the new procedure consists in applying the pulling force by means of reinforced bars built in the specimen, which are clamped in the machine during testing [7, 14]. in this way, the need of providing holes in the specimen, as in the metallic materials, dismissed. modified compact tension test: configuration he modified compact tension test (mct) solution was initially developed for slide shaped specimens cut off from cylindrical specimens used in standard compression tests, which can be obtained as a drill core from real constructions for evaluating age and conditions of the material. the holes are drilled into the specimens in perpendicular direction to the milled notch into which the pulling bars are allocated and glued. nevertheless, in the meantime more advanced, practical and simple solutions, the denoted “ad-hoc” specimens, have been developed that facilitate its preparation in the laboratory. in the two above mentioned mct solutions, i.e. “drill-out” and “ad-hoc” specimens, the geometry is apparently the same consisting in notched cylinders of a suitable thickness b furnished with the pulling bars, see fig. 2, but they result from two different manufacturing procedures. the characteristic dimensions of the two specimens tested in this work are summarized in tab. 1, where: cs: specimen diameter [mm], sb: pulling bar diameter [mm], w: specimen width, i.e., distance from the load axis to the back side of the specimen [mm] a: notch length measured from load axis [mm], b: specimen thickness [mm], e: notch width [mm], alig: ligament area [mm2], and α : relative notch length [-]. with these values, the ligament area, defined as the area of specimen that has to be fractured, is calculated, as the product of the length of the ligament times the thickness of the specimen. on its turn, the relative notch length α, defined as the dimensionless parameter in eq. (2) like in the original compact tension tests [15], is considered a reference parameter to be studied in the modified compact tension tests of concrete. a w  (2) t displacement (mm) load (n) a. fernández-canteli et al., frattura ed integrità strutturale, 30 (2014) 383-393; doi: 10.3221/igf-esis.30.46 385 with the same meaning of the parameters , a and w as above. figure 2: characteristic specimen’s dimensions in [mm]. cs [mm] sb [mm] w [mm] a [mm] b [mm] e [mm] alig [mm2] α [-] specimen 1 153 8 116.4 40.2 63.5 4 4838.70 0.3454 specimen 2 153 8 114.3 32.9 68.6 4 5584.04 0.2878 table 1: measured dimensions of the two specimens tested. experimental procedure he fabrication of the specimens is as follows: firstly, concrete is prepared as a mixture of the components. then, the concrete is poured into the mold, in this case a pvc pipe of internal diameter d = 153 mm, i.e. the required for the specimen. the curing process lasted for 21 days after which the bars are allocated into the drill holes and glued to the specimen using a strong epoxy adhesive. lastly, the notch is mechanized. this procedure can be also applied for fracture characterization of concrete when drilling cores are extracted from real structures. all tests were performed with a servohydraulic test machine mts bionix 25 kn of load capacity, see fig. 3. one of the bars is anchored to the lower clamps, which stay fixed. the other bar is anchored to the upper clamps, which move vertically up and transmit the load to the specimen. thus, as the displacement of the upper clamp increases, a crack is generated starting in the tip of the notch, until the complete rupture of the specimen. tests are performed by displacement control of the machine with a rate of 0.5 mm/min. numerical simulation umerical simulations are performed using two different codes based on the finite element method. the first one is the atena software [16, 17] developed for specific applications in concrete structures. the second one is the abaqus software [18]. the results from the compression test provide an average value of 32 mpa for the cylindrical compressive strength, which corresponds to a cubic compressive strength of 37 mpa. according to table 7 from european standard en 206-1 (page 20), the concrete mixture was classified as c 30/37. a cubic compressive strength of 37 mpa was used as input value for the material model of concrete (sbeta) and after that the values of tensile strength and young’s modulus, etc. are calculated from empirical equations implemented in the atena software. the characteristic input parameters of steel and concrete used in both cases of numerical simulations in atena and abaqus are listed in tab. 2, where: t n a. fernández-canteli et al., frattura ed integrità strutturale, 30 (2014) 383-393; doi: 10.3221/igf-esis.30.46 386 e: young’s modulus [mpa], ν: poisson coefficient [-], fc: compressive strength of the concrete [mpa] and ft: tensile strength of the concrete [mpa]. figure 3: specimen set up into the servohydraulic mts bionix 25 kn machine. e [mpa] ν [-] fc [mpa] ft [mpa] steel 210000 0.3 concrete 33010 0.2 31.45 2.665 table 2: mechanical input parameters for the material used in the atena and abaqus calculations. in order to propitiate the factual non-symmetry behavior of the crack initiation at the notch and further propagation in the real specimen due to the non-uniformity of the aggregate, symmetry is disregarded so that the whole specimen is considered in the computations. 2d-model 1 using atena code an adaptation from the model of holušová et al. [19] is performed for the new dimensions adopted as presented in tab. 1, using the same commercial software atena 2d. the material is identified in atena as the model for concrete 3d non linear cementitious 2 working under plain stress or plain strain conditions and sbeta that works only under plain strain condition, see [20,21]. steel bars are there modeled as ideal lines, which simulate the pulling load axis of the testing machine. the mesh and boundary conditions are shown in fig. 4. the size of elements is, typically, 2 mm with a refinement up to 1 mm around the starting notch. 2d-model 2 using abaqus code with rigid bars this model, created in abaqus, is based on the same premises as model 1, i.e. assuming the bars maintain a fixed pulling axis orientation during the test. this implies impeding any deviation or relative transversal displacement of the bars that unavoidably occurs during the real test as a consequence of the necessary compatibility between displacements of a. fernández-canteli et al., frattura ed integrità strutturale, 30 (2014) 383-393; doi: 10.3221/igf-esis.30.46 387 both concrete specimen and pulling bars during the notch opening process thus provoking reactions and bending of the pulling bars. in this case, the bar is assumed to be perfectly rigid, so that the prescribed displacement in the pulling axis direction suffices to define the loading process. the material is modeled according to the so called “concrete damaged plasticity” model [22]. the mesh, load and boundary conditions are shown in fig. 5. in this case, the size of the mesh is 5 mm, with a refinement in the ligament length up to 1 mm. figure 4: mesh and boundary conditions used for model 1. figure 5: mesh and boundary conditions for model 2. 3d-model 3 using abaqus with free elastic lineal bars this model, see fig. 6, once more developed in abaqus code, represents loads and boundary conditions in a closer manner to the real modified compact tension test than the former two handled. a displacement in the longitudinal xdirection is prescribed at the end of the bars thus restricting the movement (displacement or rotation) in any other direction. modeling as 3d geometry implies considering a larger amount of elements. due to non-symmetry reasons related to crack forming, as already exposed, no consideration of double symmetry, i.e. of a specimen quarter, is considered that would allow a significant reduction of the computational time. exemplary, the element size is taken as 5 mm with a refinement up to 1 mm size in the ligament area and up to 3 mm in the perimeter of the hole where the bars are inserted. prescribed displacement ( x ) prescribed displacement () linear support quasi-brittle material a. fernández-canteli et al., frattura ed integrità strutturale, 30 (2014) 383-393; doi: 10.3221/igf-esis.30.46 388 figure 6: mesh and boundary conditions for model 3. 3d-model 4 using abaqus intermediate in this model, the transversal displacement is prescribed only at the bar ends, identified with the machine clamps, but the transversal displacement of the notch mouth, uy, is impeded. the model can be understood as a mixture between model 2 and model 3, see fig. 7. figure 7: mesh and boundary conditions for model 4. prescribed displacement ( x ) xy symmetry xy symmetry prescribed displacement ( x ) uy=0 prescribed displacement () a. fernández-canteli et al., frattura ed integrità strutturale, 30 (2014) 383-393; doi: 10.3221/igf-esis.30.46 389 results and discussion he load-cod curves for every model are generated. the following graphs, see figs. 8-9, show the numerical results obtained for the different numerical models and those from the experimental test for comparison. 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 2.2 2.4 2.6 2.8 3 0 1 2 3 4 5 6 cod (mm) l o ad ( kn ) experimental 2d-model 1. atena 2d-model 2. rigid bars 3d-model 3. free bars el 3d-model 4. intermediate 0 0.2 0.4 0.6 0.8 1 1.2 1.4 0 0.5 1 1.5 2 2.5 3 cod (mm) l o ad ( kn ) experimental 3d-model 3. free bars el 3d-model 4. intermediate a) b) figure 8: load-cod curves for specimen 1: a) all modes including 2d model, and b) zoom detailing only 3d models and experimental results. 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 0 1 2 3 4 5 6 7 cod (mm) l o ad ( kn ) experimental 2d-model 1. atena 2d-model 2. rigid bars 3d-model 3. free bars el 3d-model 4. intermediate 0 0.2 0.4 0.6 0.8 1 1.2 1.4 0 0.5 1 1.5 2 2.5 3 3.5 4 cod (mm) l o ad ( kn ) experimental 3d-model 3. free bars el 3d-model 4. intermediate a) b) figure 9: load-cod curves for specimen 2: a) all modes including 2d model, and b) zoom detailing only 3d models and experimental results. the theoretical difference between the cohesive model adopted in the atena code [16] and the smeared crack model used in abaqus [18] has not noticeable influence on the numerical results obtained.  opening mechanisms there are two different forms in the evolution of the load-cod curves obtained from models 1, 2, 3 and 4. these differences are related to the boundary conditions applied in the bars. curves with higher maximum load emanate from models in which the transversal displacement is impeded along the total length of the bar. otherwise, models with lower maximum load are only restricted at the ends of the bar. in consequence, models behavior is influenced by the enforced perpendicularity of the bars to the notch plane. as a result, two different notch opening mechanisms, parallel and angular ones, appear, see fig. 10.  influence of the transversal displacement in the fracture energy the first analysis of the model of mct proposed by holušová et al. [19], points out that the determinant factor explaining differences among the load-displacement curves is the restriction of the transversal y-displacement of the model. that’s why model 4 has been developed, changing from 2d to 3d and from a restriction in the length of the bars to a restriction in the notch mouth. t a. fernández-canteli et al., frattura ed integrità strutturale, 30 (2014) 383-393; doi: 10.3221/igf-esis.30.46 390 the results for this model, however, approaches the load-displacement curves of models 3 and 4 (see figs. 8 and 9), especially in the initial ascending part of the curve. the maximum load is about the same, and the same applies for the initial region of the softening curve. then, a new rise in the load happens, due to the difficulty of continuing crack opening. a) b) c) figure 10: schematic representation of the opening mechanism of the notch: a) parallel opening, b) angular opening and c) transversal displacement of the specimen during testing by parallel opening. models 1 and 2 correspond to a parallel opening, whilst models 3 and 4 generate an angular opening.  correction of the load-displacement curves some problems appear in describing the softening part of the load-cod curves in both experimental and simulation results. in most cases, the last part of the softening curve has an asymptotic behavior tending to a certain value of the load different from zero, instead of approaching gradually to null load, as it would be expected in a real case. accordingly, a correction in the ordinate is introduced using the following equations, see fig. 11:   tany x x   (3)      correctedy x y x y x  (4) where: θ = angle between abscissa axis and the slope line y’. line y’ is formed by connecting the origin of the θ coordinate system with a far point, or eventually, the last point of the curve y. tan θ = slope of the line y’. figure 11: scheme for the correction of the y axis. a. fernández-canteli et al., frattura ed integrità strutturale, 30 (2014) 383-393; doi: 10.3221/igf-esis.30.46 391 figures 12-13 show a) the experimental and b) the numerical load-cod curves for model 3 before and after introducing the correction, respectively, for specimen 1 and specimen 2, while fig. 14 presents a direct comparison for the experimental and numerical energy curves for specimens 1 and 2 once corrected. 0 0.5 1 1.5 2 2.5 3 0 0.5 1 1.5 2 2.5 cod (mm) l o ad ( kn ) without correction with correction 0 0.5 1 1.5 2 2.5 3 0 0.5 1 1.5 2 2.5 3 cod (mm) l o ad ( kn ) without correction with correction a) b) figure 12: original and corrected fracture energy curves for specimen 1: a) experimental and b) numerical results. 0 0.5 1 1.5 2 0 0.5 1 1.5 2 2.5 3 3.5 cod (mm) l o ad ( kn ) without correction with correction 0 0.5 1 1.5 2 0 0.5 1 1.5 2 2.5 3 3.5 cod (mm) l o ad ( kn ) without correction with correction a) b) figure 13: original and corrected fracture energy curves for specimen 2: a) experimental and b) numerical results.  relationship between experimental test and numerical model results the results and estimated errors for the former numerical calculations, referred to work energy and fracture energy, and the tests performed are summarized in tab. 3. wf [j] gf [j/m2] error [%] specimen 1 experimental 475.4 98.3 0.96 simulation 480 99.2 specimen 2 experimental 710.4 127.3 24.2 simulation 538.1 96.4 table 3. summary of the numerical and test results. a. fernández-canteli et al., frattura ed integrità strutturale, 30 (2014) 383-393; doi: 10.3221/igf-esis.30.46 392 0 0.5 1 1.5 2 2.5 3 0 0.5 1 1.5 2 2.5 3 cod (mm) l o ad ( kn ) experimental numerical simulation 0 0.5 1 1.5 2 0 0.5 1 1.5 2 2.5 3 3.5 cod (mm) l o ad ( kn ) experimental numerical simulation a) b) figure 14: direct comparison for the experimental and numerical energy curves once corrected. (a) specimen 1; (b) specimen 2. conclusions he principal conclusions derived from this work are the following: the 2d simulation implies considering hypothetical bars in which the opening process during testing is achieved by means of prescribing a progressive horizontal displacement of the pulling bars. as a matter of fact, the calculations do not facilitate a reliable reproduction of the real pulling bars bending during testing. as a consequence of the inadequate boundary conditions imposed, two effects not occurring during execution of the real test are introduced: a) a parallel opening of the notch lips is enforced so that the factual bending of the pulling bars during testing is not adequately modeled, and b) the transversal free movement of the specimen, necessary for maintaining the geometrical compatibility notch-bar under equilibrium conditions during testing is impeded. both effects implying stiffer solutions lead to an overestimation of the fracture energy in the test simulation compared to the experimental results the first effect having greater influence on the result of the fracture energy. accordingly, 3d calculations are unavoidable to an adequate numerical simulation of the real testing conditions is intended aiming at to facilitate a true value of the fracture energy of the concrete. a reasonable agreement between the experimental results and the numerical simulation of the fracture curve is achieved. a conversion between the modified compact tension test (mct) and the standard procedures, i.e. wedge-splitting (wst) and three point (3pb) or four point bending test (4pb) can be now envisaged and justified numerically. acknowledgements he investigation reported in this paper was supported by grants m100411204, cz. 107/2.3.00/20.0214 and fasts-14-2532 and projects bia2010-19920 of the spanish ministry of science and innovation micinn and sv-pa11-012 of the dept. of education and sciences of the asturias regional government. references [1] karihaloo, b.l., fracture mechanics & structural concrete, longman scientific & technical, new york (1995). [2] cifuentes, h., alcalde, m., medina, f., comparison of the size-independent fracture energy of concrete obtained by two test methods. viii international conference on fracture mechanics of concrete and concrete structures. framcos-8. toledo (2013) 1–6. [3] cifuentes, h., alcalde, m., medina, f., measuring the size-independent fracture energy of concrete. strain: an international journal for experimental mechanics. 49(1) (2013) 54–59. t t a. fernández-canteli et al., frattura ed integrità strutturale, 30 (2014) 383-393; doi: 10.3221/igf-esis.30.46 393 [4] rilem report 5 fracture mechanics test methods for concrete (s. p. shah & a. carpinteri eds.), chapman and hall, london (1991). [5] rilem tc-50 fmc recommendation determination of the fracture energy of mortar and concrete by means of three-point bend test on notched beams, materials & structures (1985). [6] brühwiler, e . , wittmann, f . h . , the wedge splitting test, a new method of performing stable fracture mechanics tests, engineering fracture mechanics, 35 (1990) 117-125. [7] korte, s., boel, v., de corte, w., de schutter, g., static and fatigue fracture mechanics properties of self-compacting concrete using three-point bending tests and wedge-splitting tests, construction and buildings materials, 57 (2014) 1– 8. [8] korte, s., boel, v., de corte, w., de schutter, g., vibrated concrete vs. self-compacting concrete: comparison of fracture mechanics properties, key engineering materials, 601 (2014) 199–202. [9] merta, i., tschegg, e.k., fracture energy of natural fibre reinforced concrete, construction and building materials, 40 (2013) 991-997. [10] merta, i., tschegg, e.k., uniaxial fracture energy of waste tyre rubber concrete, viii international conference on fracture mechanics of concrete and concrete structures, framcos-8, toledo (2013) 1–5. [11] astm e399-90, standard test method for plane-strain fracture toughness of metallic materials, annual book of astm standards, vol. 03.01, astm international, (2002) 443–473. [12] astm international standard e399-06 (2006), standard test method for linear-elastic method of plane-strain fracture toughness kic of metallic materials, (2006) 1–32. [13] wagoner, m.p., buttlar, w.g., paulino, g.h., disk-shaped compact tension test for asphalt concrete fracture, experimental mechanics, 45 (2005) 270–277. [14] linsbauer, h.n., tschegg, e.k.., fracture energy determination of concrete with cube-shaped specimens, zement und beton, 31 (1986) 38–40. [15] cifuentes, h., medina f., fracture mechanics applied to concrete (in spanish), servicio de publicaciones, universidad de sevilla, sevilla, (2013). [16] červenka consulting, http://www.cervenka.cz atena program documentation, theory and user manual [17] cervenka, v., cervenka, j., pukl, r., atena – a tool for engineering analysis of fracture in concrete, sadhamaacademy proceedings in engineering sciences, 27(4) (2002) 485–492. [18] abaqus/cae documentation. analysis user’s manual: materials. [19] holušová, t., seitl, s., fernández-canteli, a., numerical support of experimental compact tension test on concrete cylindric specimens, transactions of the všb – technical university of ostrava, civil engineering series, no. 1 vol. xiv, (2014). [20] holušová, t., seitl, s., fernández-canteli, a., numerical simulation of modified compact tension test depicting of experimental measurement by aramis, key engineering materials (2015). [21] holušová, t., seitl, s., fernández-canteli, a., comparison of fracture energy values obtained from 3pb, wst and ct test configurations, advanced material research journal, 969 (2014) 89–92. [22] hillerborg, a., modeer, m., petersson, p.e. analysis of crack formation and crack growth in concrete by means of fracture mechanics and finite elements, cem concr res, 6 (1976) 773–782. microsoft word numero_33_art_18 m. mokhtari et alii, frattura ed integrità strutturale, 33 (2015) 143-150; doi: 10.3221/igf-esis.33.18 143 focussed on characterization of crack tip fields some experimental observations of crack-tip mechanics with displacement data m. mokhtari, p. lopez-crespo, b. moreno department of civil and materials engineering, university of malaga, c/dr. ortiz ramos s/n, 29071 malaga, spain plopezcrespo@uma.es m. zanganeh orau, oak ridge, tn, usa mohammad.zanganehgheshlaghi@nasa.gov abstract. in the past two decades, crack-tip mechanics has been increasingly studied with full-field techniques. within these techniques, digital image correlation (dic) has been most widely used due to its many advantages, to extract important crack-tip information, including stress intensity factor (sif), crack opening displacement, j-integral, t-stress, closure level, plastic zone size, etc. however, little information is given in the literature about the experimental setup that provides best estimations for the different parameters. the current work aims at understanding how the experimental conditions used in dic influence the crack-tip information extracted experimentally. the influence of parameters such as magnification factor, size of the images, position of the images with respect the crack-tip and size of the subset used in the correlation is studied. the influence is studied in terms of sif and t-stress by using williams’ model. the concept of determination of the k-dominance zone from experimental data has also explored. in this regard, cyclic loading on a fatigue crack in a compact tension (ct) specimen, made of aluminium 2024-t351 alloy, has been applied and the surface deformation ahead of the crack tip has been examined. the comparison between theoretical and experimental values of ki showed that the effect of subset size on the measured ki is negligible compared to the effect of size of the image. keywords. digital image correlation; stress intensity factor; t-stress; crack tip displacement field. introduction ince 1980s in which a group of researchers at the university of south carolina [1-3] developed the digital image correlation (dic) method for obtaining the full-field in-plain deformation of an object directly, a growing number of researches has been done to modify the method and its parameters. in brief, dic compromises of three sequences including 1) sample preparation, 2) taking images before and after loading from the surface of the specimen, and finally 3) calculating displacement and strain information by image processing [4]. dic is a straight forward, low cost and simple method to measure experimentally surface deformation data with few advantages compared to other full-field s m. mokhtari et alii, frattura ed integrità strutturale, 33 (2015) 143-150; doi: 10.3221/igf-esis.33.18 144 techniques such as moiré interferometry, photoelasticity and thermoelasticity [4-8]. experimentally, dic measurement accuracy can be affected by several factors, such as sub-pixel optimization algorithm, subset size, image quality, etc.[4]. it should be noted here that “subset” refers to an area in the image in which the displacement between images is tracking. some of the errors introduced by dic measurements have been estimated by researchers. for example, fazzini et al. [9] have studied the errors caused by different bit depths of the image, image saturation in respect with subset size, speckle pattern and subset shape function on synthetic images. they found that decreasing the encoding of the images and overexpose of the speckle deteriorate the measurements by a factor of 2 and 10 respectively. in addition, systematic errors due to intensity interpolation, under-matched subset shape function and over-matched subset shape functions have been calculated by shreier et al. [10, 11] and yu et al. [12] respectively. since the initial works on dic, algorithms for displacement and strain measurement have been improved and so have the different methods for estimating sif from dic data. most works estimate sif by fitting numerical functions (such as westergaard’s, willialms’ or muskhilishvili’s series developements) to experimental data [8, 13-15]. earlier works developed in 1980s used a least-square error analysis procedure in order to estimate the sif [1, 16]. subsequently sif were estimated for fatigue cracks grown in steel by introducing an enriched crack kinematics in cyclic fatigue based on conventional and integrated dic techniques [17]. later, a similar methodology was used to evaluate mixed-mode sif on a crack emanating form a fastener hole [18]. in addition, other more comprehensive models have been proposed to account driving and retarding forces on the crack-tip [19]. vanladuit et al. [20] introduced a post-processing method for measuring the crack length, crack tip position and stress intensity factors automatically from displacement field. they have validated their methodology by performing a fatigue crack propagation test on an aluminum u-profile. however, it is well known that there is a small region quite close to crack tip, called k-dominance zone, where stress field can be effectively described by stress intensity factor merely. beyond this annular region, to characterize the crack tip field, the higher order terms (non-singular part of stress field) must be considered. sun et al. [17], has evaluated the size of k-dominance for a plexiglass. they considered not only the singular but also the nonsingular part of stress fields in order to predict the fracture of the material precisely. in spite of all these efforts for optimizing dic and related post processing procedures, it seems that the effect of the size of the dic image fitted to the analytical model has been neglected. in optic literature, the size of the dic image is studied through the field of view (fov) and is defined as the angular extent for a given scene imaged by a camera [21]. since the fov determines the number and position of data points for a constant subset size, the fov must be taken into consideration as key parameter for sif evaluation from dic data. finally, the the k-dominance zone has been studied experimentally with the help of higher orders in williams’ series. materials and methods xperiments were conducted on a 2024-t351 aluminum plate. this was machined to obtain a ct specimen according to astm e-647 standards [22]. fig. 1 illustrates the specimen geometry and dimensions. the mechanical properties of the material are summarised in tab. 1. the sample surface was scratched by abrasive 240, 380 and 800 grit sic grinding paper to achieve the a random grey intensity distribution required by dic technique. cyclic loading was applied with a 100kn instron servo-hydraulic testing machine. the specimen was fatigue pre-cracked under mode i at a frequency of 10 hz, load ratio (r) 0.1 and constant stress intensity range (kmin/kmax) of 10.1 mpa√m. after 980,000 cycles the measured crack length was 28.6 mm (a/w = 0.57). an 8-bit 2452×2052 pixels ccd camera coupled with navitar lens with magnification ranging from 7x to 0.35x and a ring light illumination was used to take images for dic (fig. 2). higher magnification images were acquired with a questar qm-100 lens (magnification of 9x). in order to achieve larger field of view, macro images were also taken using a macro lens 0.25x. a questar 3-axis stage was also used to mount and adjust the camera position precisely. the different lenses combinations were used to obtain fovs ranging from 0.5×0.5 mm2 to 20×20 mm2. in order to acquire sufficient number of images, the loading rate was reduced to 0.1 hz while capturing the images. young modulus yield stress uts elongation brinell hardness 73 gpa 325 mpa 470 mpa 20% 137 table 1: mechanical properties of 2024-t351 aluminium alloy. e m. mokhtari et alii, frattura ed integrità strutturale, 33 (2015) 143-150; doi: 10.3221/igf-esis.33.18 145 figure 1: geometry of the test ct specimen [19]. figure 2.imaging set up and selected aois for a constant field of view. the white point highlights the crack tip location. in this way, 48 images were acquired each cycle during the loading and unloading of the cycle. images were captured in seven different magnifications. subsequently the images were processed with vic-2d software to obtain the displacement fields. each image was compared to the initial reference image at pmin. the subset centre distance (step size) was set to 1/4 of the subset size in order to achieve independent and non-repetitive data. a high-order interpolation scheme of optimized 8-tap spline was used to achieve sub-pixel accuracy. the correlation criterion was set to zero-normalized sum of squared differences which is insensitive to offset and scale in lighting [21]. the standard deviation confidence interval (e), the confidence interval for matching the points in subsets, was confined lower than 4%. to study the effect of the area of interest (aoi) on the sif, six different aois in a constant fov were analysed (fig. 2). displacement fields obtained by dic were then substituted into williams’ series [8]: m. mokhtari et alii, frattura ed integrità strutturale, 33 (2015) 143-150; doi: 10.3221/igf-esis.33.18 146                                               1 2 1 2 2 )4( sin 22 sin)1( 22 2 )4( cos 22 cos)1( 22 n n n n i n n n n i nnnn a r v nnnn a r u modei       (1) and                                               1 2 1 2 2 )4( cos 22 cos)1( 22 2 )4( sin 22 sin)1( 22 n n n n ii n n n n ii nnnn b r v nnnn b r u modeii       (2) where u and v are horizontal and vertical displacements in mode i,  is the shear modus and )1/()3(   for plane stress and  43  for plane strain condition,  is the poisson’s ratio, r and θ are radial and phase distance from the crack, a and b are constant. eq. 1 and 2 can be written in terms of the stress intensity factors and t-stress as follows:           cos)1( 8 ) 2 cos21( 2 sin 22 ) 2 sin21( 2 cos 22 22  r trkrk u iii (3)           sin)3( 8 ) 2 cos21( 2 cos 22 ) 2 cos21( 2 sin 22 22  r trkrk v iii (4) by using 21ak i  , 21bk ii  , 24at  (5) where ki and kii are mode i and ii of stress intensity factor respectively and t represents t-stress. the effects of addition of non-singular terms of williams’ solution on the experimental and numerical data fitting was also explored. the number of terms increased until the best displacement fit reach and the value of sifs become stable. in order to compare the experimental results with the theoretical estimations, the theoretical value of ki for ct specimen was calculated with the following equations [23]: ),(. 1 2 1 f tw p k i  w a  (6) 2/3 432 1 )1( 6.572.1432.1364.4886.0)(2( )(      f (7) where a and t are crack length and thickness of sample respectively. the accuracy of experimental results was then examined by introducing a parameter, δ, which is the difference between experimental and theoretical measurements: δ = | ki experimental – ki theoretical | (8) lower δ will be indicative of more accurate estimations of ki. results and discussion ig. 3 illustrates how the standard deviation confidence interval (e) and δ are change with increasing the subset size. it can be seen that although e is reduced by increasing the subset size, no considerable change is observed in δ. this behaviour can be attributed to the surface pattern. in other words, scratching the surface by different grades of abrasive paper, provides sufficient intensity gradients in each subset, even for the smallest one, 19 pixel. however, caution must be taken in subset size selection especially in case of using speckle patterns. although the large subset size f m. mokhtari et alii, frattura ed integrità strutturale, 33 (2015) 143-150; doi: 10.3221/igf-esis.33.18 147 leads to lower displacement uncertainty, underlying deformation field undergoes incorrect estimation. on the other hand, heterogeneity of displacement fields requires small subset size [17]. too small subsets, however, increase the random errors [24]. hild et al. [13], showed that there is a reverse power law relation between e and subset size. therefore, it has been stated that there is a trade-off between using large and small subset size [4]. nevertheless, subset sizes ranging from 19 to 151 pixel (equal to the displacement vectors of 39 to 311 micron) have not had significant effect on sifs measurements in this study. the effect of considering different number of williams’ solution terms on the quality of fitted data to the experimental displacement for a fov of 8×8 mm2 is shown in fig. 4. figs. 4e and 4f show that after 10 terms not only the sifs and tstress values have converged, but the data also are fitted very well to the analytical model. figure 3. δ as a function of subset size in the magnification of 0.75x. to have a better understanding of the effect of the number of considered terms on sifs estimations, the value of δ has been plotted as a function of fov (fig. 5). there are two main points in this figure. first, the addition of the second term, t-stress, has not considerable effect on the estimated sif. in addition, the 10-terms solution provides more accurate estimation of ki than the 1 or 2-terms solutions. this is more significant for fields of view larger than 8×8 mm2. in fact, while the average difference between the 1 and 10-terms estimation of ki in small fields of view (0.5×0.5 and 1.2×1.2 mm2) are 0.22 mpa√m, it increases to the average value of 0.98 mpa√m for fovs larger than 8×8 mm2. this can be inferred by recalling the fact that the area in the immediate vicinity of the crack-tip is a singular area, where asymptotic singular solutions, k and t terms, can represent the stress state alone [24, 25]. increasing the size of the field of view and thereby using data points far from the crack-tip, means that higher order terms need to be considered to characterise the crack-tip fields. this idea can be used to estimate experimentally the kdominance zone from dic data. in this study, at least 10 terms of williams’ solution need to be considered in fovs larger than 8×8 mm2 to obtain accuracy smaller than 0.5 mpa√m. different aois can be selected for each fov. since aoi determines the number and location of data points as well as fov, the aoi directly affects the sif’s measurements. hence, the effect of aoi on sif is investigated in fig. 6. the aim is to find out if the same sized fovs and aois will result in a similar estimation of sifs or not. in this regard, fig. 6 shows the value of δ as a function of the different fovs and corresponding aois which have been shown in fig. 2. the interesting point in this figure is that the same-sized fov and aoi leads to almost the same sifs estimation. therefore, one can measure the sif by selecting a small aoi in an image with low magnification (large fov). in this way, not only there is no need for high magnifying lenses, but the number of data points that needs to be analysed can also be reduced. conclusion he displacement field analysis ahead of a fatigue crack illustrates that the fov is an effective parameter in measuring the sif from displacement fields derived from dic and thus should be reported in test procedures. it was highlighted that subset sizes ranging from 19 to 151 pixel have no considerable effect on measured sifs in the fov ranging from 2×2mm2 to 20×20 mm2. it also was observed that the same-sized fov and aoi leads to almost the t m. mokhtari et alii, frattura ed integrità strutturale, 33 (2015) 143-150; doi: 10.3221/igf-esis.33.18 148 same estimation of ki. therefore, in order to obtain a reliable experimental estimation of sif (accuracy less than 0.5 mpa√m) from displacement data measured by dic of aluminium 2014-t351 alloy, one can choose the fov ranging from 8×8 to 20×20 mm2 with an arbitrary subset size ranging from 19 to 151 pixel for a scratched surface of a fatigue cracked ct specimen. 1 term 2 terms 10 terms figure 4. analysed displacement field, a) vertical displacement, b) horizontal displacement. fitting of displacement data to williams’ solution with one (c), two (d) and 10 terms (e) and stability of calculated sif and t-stress for the first 20 terms of williams’ series (f). a b c d f e m. mokhtari et alii, frattura ed integrità strutturale, 33 (2015) 143-150; doi: 10.3221/igf-esis.33.18 149 figure 5. difference between theoretical and experimental sif, δ, as a function of fov for different number of williams’ terms. figure 6. comparison between the effect of the aoi and fov on δ acknowledgements inancial support of junta de andalucía through proyectos de excelencia grant reference tep-3244; spanish ministerio de economía y competitividad through grant reference dpi2012-33382; and university of malaga through campus de excelencia internacional del mar (ceimar) through líneas emergentes program and for providing phd excahnge scholarship is greatly acknowledged. references [1] peters, w.h., ranson, w.f., kalthoff, j.f., winkler, s.r., a study of dynamic near-crack-tip fracture parameters by digital image analysis, le journal de physique colloques, 46(c5) (1985) c5-631-c635-638. [2] sutton, m.a., mingqi, c., peters, w.h., chao, y.j., mcneill, s.r., application of an optimized digital correlation method to planar deformation analysis, image and vision computing, 4(3) (1986) 143-150. f m. mokhtari et alii, frattura ed integrità strutturale, 33 (2015) 143-150; doi: 10.3221/igf-esis.33.18 150 [3] sutton, m.a., wolters, w.j., peters, w.h., ranson, w.f., mcneill, s.r., determination of displacements using an improved digital correlation method, image and vision computing, 1(3) (1983) 133-139. [4] pan, b., qian, k., xie, h., asundi, a., two-dimensional digital image correlation for in-plane displacement and strain measurement: a review, measurement science and technology, 20(6) (2009) 062001. [5] pan, b., xie, h., wang, z., qian, k., wang, z., study on subset size selection in digital image correlation for speckle patterns, optics express, 16(10) (2008) 7037-7048. [6] roux, s., réthoré, j., hild, f., digital image correlation and fracture: an advanced technique for estimating stress intensity factors of 2d and 3d cracks, journal of physics d: applied physics, 42(21) (2009) 214004. [7] lopez-crespo, p., shterenlikht, a., yates, j.r., patterson, e.a., withers, p.j., some experimental observations on crack closure and crack-tip plasticity, fatigue and fracture of engineering materials and structures, 32 (2009) 418-429. [8] yates, j.r., zanganeh, m., tai, y.h., quantifying crack tip displacement fields with dic, engineering fracture mechanics, 77(11) (2010) 2063-2076. [9] fazzini, m., mistou, s., dalverny, o., robert, l., study of image characteristics on digital image correlation error assessment, optics and lasers in engineering, 48(3) (2010) 335-339. [10] schreier, h., sutton, m., systematic errors in digital image correlation due to undermatched subset shape functions, experimental mechanics, 42(3) (2002) 303-310. [11] schreier, h.w., braasch, j.r., sutton, m.a., systematic errors in digital image correlation caused by intensity interpolation, optical engineering, 39(11) (2000) 2915-2921. [12] yu, l., pan, b., the errors in digital image correlation due to overmatched shape functions, measurement science and technology, 26 (2015) 045202-045202. [13] hild, f., roux, s., digital image correlation: from displacement measurement to identification of elastic properties–a review, strain, 42(2) (2006) 69-80. [14] yoneyama, s., ogawa, t., kobayashi, y., evaluating mixed-mode stress intensity factors from full-field displacement fields obtained by optical methods, engineering fracture mechanics, 74 (2007) 1399-1412. [15] lopez-crespo, p., shterenlikht, a., patterson, e.a., withers, p.j., yates, j.r., the stress intensity of mixed mode cracks determined by digital image correlation, journal of strain analysis for engineering design, (2008) 43. [16] mcneill, s.r., peters, w.h., sutton, m.a., estimation of stress intensity factor by digital image correlation, engineering fracture mechanics, 28(1) (1987) 101-112. [17] hamam, r., hild, f., roux, s., stress intensity factor gauging by digital image correlation: application in cyclic fatigue, strain, 43(3) (2007) 181-192. [18] lopez-crespo, p., burguete, r.l., patterson, e.a., shterenlikht, a., withers, p.j., yates, j.r., study of a crack at a fastener hole by digital image correlation, experimental mechanics, 49 (2009) 551-559. [19] vasco-olmo, j.m., díaz, f.a., garcía-collado, a., dorado-vicente, r., experimental evaluation of crack shielding during fatigue crack growth using digital image correlation, fatigue and fracture of engineering materials and structures, 38 (2015) 223-237. [20] vanlanduit, s., vanherzeele, j., longo, r., guillaume, p., a digital image correlation method for fatigue test experiments, optics and lasers in engineering, 47(3-4) (2009) 371-378. [21] sutton, m.a., orteu, j.j., schreier, h., image correlation for shape, motion and deformation measurements, (2009). [22] american society of t, materials, standard methods for the measurement of fatigue crack growth rates e647-95a, 03.01,1999. annual book of standards, e647-95a. 1999;03.01. [23] murakami, y., stress intensity factors handbook. oxford: pergamon press, (1987). [24] sun, c.-t., jin, z.h., fracture mechanics. academic press, (2012). [25] soboyejo, w., mechanical properties of engineered materials. crc press, (2002). microsoft word numero_56_art_12_3038 s. melais et alii, frattura ed integrità strutturale, 56 (2021) 151-159; doi: 10.3221/igf-esis.56.12 151 effects of coarse sand dosage on the physic-mechanical behavior of sand concrete saloua melais, meriem fakhreddine bouali, ahmed melaikia, amine amirat department of civil engineering, faculty of sciences & technology, university of mohamad cherif messaadia, souk ahras, 41000, algeria s.melais@univ-soukahras.dz, m.bouali@univ-soukahras.dz b.meriemfakhreddine@gmail.com,http://orcid.org/0000-0002-6986-980x hamdi.10mel@gmail.com, amine.amirat1623@gmail.com abstract. the development and research of a new formulation of concrete integrating natural resources such as sands (from dunes and/or quarries) as well as waste from steel factories in the form of granulated slag from blast furnaces lead to the development of new sand concretes for which the improvement of specific properties will lead to a search for an agreement between production cost and performance. the objective of this research is to study the influence of the dosage of the size of the largest aggregate on the workability of sand concretes as well as on the compressive strength at 7 days, 14 days and 28 days. five types of concrete are made by substituting aggregates (dune sand and quarry sand) with each other and with different percentages (100%, 75%, 50%, 25% and 0%). the results show that the workability of fresh concrete is considerably influenced by the nature of the sand; the richer the sand in coarse elements, the fineness modulus increases and the more handling improves. in the hardened state, the results show that optimization of the compressive strength is achieved when a good homogeneity of the concrete is achieved and when a large percentage of coarse sand is mixed with a small percentage of fine sand. keywords. sand concrete; extended granular; workability; mechanical behavior. citation: melais, s. bouali, m.f., melaikia, a., amirat, a., effects of coarse sand dosage on the physic-mechanical behavior of sand concrete, frattura ed integrità strutturale, 56 (2021) 151-159. received: 09.03.2021 accepted: 13.03.2021 published: 01.04.2021 copyright: © 2021 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. introduction n a country like algeria rich in sand of different granulometry (more than two million km2 with a very vast desert) and poor in stony materials, reinforced concrete constructions become a little expensive, the modification of local resources in terms of materials can at least partially solve the problem of the growing demand for housing [1]. sand concretes (henceforth sc) are a new line of building materials that can replace traditional concrete for economic reasons and for its specific qualities [2-5]. i https://youtu.be/qxpvkrocbi8 s. melais et alii, frattura ed integrità strutturale, 56 (2021) 151-159; doi: 10.3221/igf-esis.56.12 152 in addition to its richness in sand, algeria has an "el-hadjar" iron and steel complex which produces enormous quantities of waste and by-products each year, in particular crushed slag and granulated slag. these quantities are estimated at 500,000 tons per year. these slags can be used in the manufacture of concrete and mortars in the form of sand, gravel and fine additions or mineral additions. granulated slag as a mineral or fines additions or as a cement substitute is widely used in the formulation of different types of mortars, concrete and innovative concretes. several countries around the world have started using bs (sand concrete). in france, a national program called sablocrete has been launched. this project has largely introduced and developed the technique of sand concrete [2]. russia, a rich country in sand, but poor in gravel and massive rocks, has not ceased since 1941 to use bs in various fields of civil engineering [2, 6]. several studies and research have been carried out in algeria in order to develop this material [7,8]. in tunisia, research has led to very encouraging results [9,10] with a view to the use of sand concrete compacted into bodies of pavement, this material remains ignored in the building industry. sand concretes can hence be used for the prefabrication of low or non-bearing elements, or structural elements. it can be poured in place for the construction of horizontal or vertical elements [2]. this material also presents a good alternative for sprayed concrete which eliminates complex formwork and allows various shapes [11]. several studies have been conducted in order to minimize the drawbacks of sand concrete and improve mechanical performance by correcting the granular extent, the type and dosage of addition fines, addition of admixtures, addition of fibers, etc. the aim of this essentially experimental research is to study the influence of the dosage of the size of the largest aggregate on the workability of sand concretes as well as on the compressive strength. the main purpose of this work is also to find the optimal mixture possible between dune sand and quarry sand in order to obtain satisfactory mechanical characteristics and plastic sand concrete. many works have been carried out for the use of dune sand as a substitute for quarry sand. [12,13] and they have shown that the incorporation of desert sand into the crushing sand improves the mechanical strengths, as long as the percentage of replaced dune sand is less than 15%, an excess of fines will be observed beyond this percentage. on the other hand [12,14], they have also shown that the best mechanical strengths were obtained for a substitution of 30% river sand and 70% of crushed sand. this was explained by the decrease in the volume of voids following the incorporation of river sand. thus [15], it has been found that the best resistances are obtained with the mixture of coarse quarry sand fine siliceous sand with the same volume which show the best granular spread with a 23% cladding, then quarry sand and crystallized slag sand with gains of 15% and 12% respectively. this was explained by the improvement in the compactness of sand concretes and consequently the increase in density and mechanical resistance thanks to the good grain size distribution of quarry sand and the mixture of silica sand quarry sand, which is confirmed by [16], that showed that the behavior of concrete is influenced by the type of sand, the rate of fines and the shape of sand particles. other researchers have shown that aggregates with their shapes have a significant influence on the rheological properties of cement mortars as well as on the physical properties [17]. it is in this context that our study falls under the use of two types of fine and coarse sand, the aim of which is to obtain results that can improve the state of knowledge of the mechanical performance of sand concrete. finally, the comparison of the experimental results of compressive strengths and workability between the different formulations will complete this study. materials and formulation of study concretes materials o formulate a sand concrete one must respect the standard nfp 18-101 which limits the size of the largest grains of sand to 5 mm. the selected constituents are represented in fig. 1 and are as follows: aggregates: two types of sand are used: dune sand (ds) with a granular extent of 0/1.25 with a fineness modulus of 2.1, quarry sand (qs) with a granular extent of 1.25/5 and a fineness modulus from 3.22. the mean values of the sand equivalents show that the study sands are slightly clayey with an acceptable cleanliness for concrete of current quality and shrinkage is not particularly feared. cement the cement used is a composite portland cement (cpj-cem ii / a 42.5) (nf en197-1) from a single delivery from the cement plant (gica) in the town of chlef. the chemical and mineralogical compositions are given in tabs. 1 and 2 respectively. t s. melais et alii, frattura ed integrità strutturale, 56 (2021) 151-159; doi: 10.3221/igf-esis.56.12 153 elements cao sio2 al2o3 p.a.f fe2o3 so3 mgo residue content (%) 61.69 20.34 5.37 5.03 3.00 2.20 1.80 1.12 table 1: chemical composition of cement. elements c3s c2s c3a c4af content (%) 58.3 14.6 8.7 11.26 table 2: mineralogical composition of the used cement. filler the used additive fines are granulated slag fillers obtained by grinding the by-products of the iron and steel industry with a granular extent of <80μm. (standard xp p 18-540). the chemical composition is shown in tab. 3. elements cao sio2 al2o3 fe2o3 s mgo mno content (%) 43.0 40.8 5.2 0.50 0.8 6.4 3.0 table 3: chemical composition of slag. super plasticizer sika viscocrete tempo 12 is the super plasticizer chosen for the formulation of sand concrete. it has a liquid form and a light brown color. it complies with standard nf en 934-2. its properties are shown in tab. 4. p.h density content in na2o content in ions cl dosage 6  1 1.06  0.01  1%  0.1% 0.2 to 3% of diluent weight or that of cement table 4: property of the sika viscocrete tempo 12. mixing water according to nfp 18-303, drinking water is always suitable. the used water is that of the tap. formulation of study concretes the retained method for the sand concrete formulation will be a theoretical approach of sablocrete formulation adjusted experimentally. the different formulations of study sand concretes are distinct in terms of the dosage of the two mixtures of dune sand (fine) and quarry sand (coarse), the aim of which is to seek the optimal type of concrete that gives the best physico-mechanical characteristics.: five types of sand concrete are tested: sc1 100% dune sand, 0% quarry sand; sc2 75% dune sand, 25% quarry sand; sc3 50% dune sand, 50% quarry sand; sc4 25% dune sand, 75% quarry sand); sc5 0% dune sand, 100% quarry sand. all the retained formulations are given in tab. 5. s. melais et alii, frattura ed integrità strutturale, 56 (2021) 151-159; doi: 10.3221/igf-esis.56.12 154 figure 1: constituents of the study sand concrete. concrete references dune sand (ds) (kg) quarry sand (qs) (kg) cement (kg) filler (kg) water (liters) super plasticizer 2% (kg) sc1 sc2 sc3 sc4 sc5 1472.8 1183 789 394.5 0 0 408 816 1224 1932 397.92 362.49 362.49 362.49 362.49 195.32 145.13 145.13 145.13 145.13 207.5 182.33 182.33 182.33 182.33 11.86 10.15 10.15 10.15 10.15 table 5: formulation and properties of sand concretes. experimental procedure he mixing of the concrete is carried out according to the nf p18-404 standard in a concrete mixer with a capacity of 30 liters, with a total mixing time of 5 minutes. the vibration of the concrete is carried out on a vibrating table for 30 + 30s. after storing the molds in air for 24 hours, the test pieces are stored in saturated humidity (rh = 100%) and at a room temperature. for each type of concrete, the average compressive and flexural tensile strengths were determined at a time period of 7, 14 and 28 days. the three-point bending tensile test is carried out on prismatic specimens with dimensions (4×4×16 cm) according to nfp18-406 (fig. 2), the half obtained specimens after the tensile test were tested by the test compression according to en 196-1 the resulting half-test pieces are therefore fitted between the two plates of the hydraulic press (fig. 3) figure 2: tensile machine, three point bending test. figure 3: machine for compresiion test. t s. melais et alii, frattura ed integrità strutturale, 56 (2021) 151-159; doi: 10.3221/igf-esis.56.12 155 results and discussion effect of varying the dosage of dune sand and quarry sand on the sag test of sand concrete he results of the influence of the dosage of dune and quarry sand are grouped together in tab. 6. fig. 4 shows clearly that the fine sand dosage influences considerably the workability of the concretes tested, for a constant dosage of water and cement and with use of a super plasticizer. tests show that the richer the sand is in coarse elements (in the case of sc4 and sc5, it becomes more porous and very absorbent, the fineness modulus increases and the more the workability improves, on the other hand the increase in the fin content ( case of sc1, sc2) decreases the fineness modulus and results in poorer handling, the abrams cone sag is of the order of 2cm which corresponds to firm concretes. conversely, for sc3 and sc4 the mixture binary with the same dosage of coarse sand and fine sand or with a high dosage of coarse sand compared to fine sand gave the best maneuverability with subsidence of the order of 5 and 7cm (according to the nfp18-451 standard) which reflects the plasticity of the study concrete thanks to the good granulometry of the granular extent. the sc5 is a very plastic concrete. during the test it was noted that before the vibration the water penetrates into the pores (observation of dry concrete) and during the vibration, a film of water is observed on the surface concrete (the water in the pores). in general, the variation in the workability of sand concretes depends on the dosage of coarse sand, the mineralogical nature and the morphology (surface condition, types and shapes of the pores) of the used sands. fig. 5 presents an example of workability test carried out by the abrams' cone on plastic concrete (sc3 and sc4). type of concrete sc1 sc2 sc3 sc4 sc5 sagging (cm) 2 2 5 7 12 table 6: evolution of the subsidence value of the 5 types of sand concrete. figure 4: influence of the dosage of the size of the largest aggragate on the sagging of sand concrete. figure 5: sagging of plastic concrete (sc3, sc4). influence of the dosage of the size of the largest aggregate on the resistance on the mechanical resistance tensile strength by three-point bending (at 7 days, 14 days and 28 days) fig. 6 shows that the granulometry, shape and surface condition of aggregates can play an important role in the tensile strength by bending of the studied concrete and that the coarse sand dosage influences the tensile strength by bending. it can be seen that sand is the material which controls the tensile strength for sand concrete, and that increasing the dosage of the size of the larger aggregate has a positive effect on the tensile strength. it is clearly visible in fig. 6 that, each time the percentage of quarry sand is increased, the tensile strength improves as a function of the age of the concrete for each type of concrete. the lowest three-point flexural tensile strength was recorded at 7 days of time; the minimum is reached by sc1 composed of 100% dune sand and the maximum was reported by sc3 composed of 50% ds and 50% qs, this t s. melais et alii, frattura ed integrità strutturale, 56 (2021) 151-159; doi: 10.3221/igf-esis.56.12 156 increase is of the order of 26.60% compared to sc1. for sc4, we noticed a decrease in resistance then it increases again for the sc5 but they always remain slightly lower than that given by the sc3. the rate of increase of sc5 over sc1 is in the order of 21.13%. at 14 days and 28 days, it was observed that the best strengths are obtained with sc5, which presents the best granular extent with a sheath of the order of 63.88% and 89.72% respectively compared to sc1, then the mixture composed of 75% coarse quarry sand + 25% fine siliceous sand. the gain in strength compared to sc1 concrete with silica sand is mainly due to the good grain size, the rough surface state and the mineralogical nature of the coarse sand which gives good adhesion between the grains of this sand and the cement matrix and consequently the increase in resistance, which confirms the research results found by [15,16], which showed that the behavior of concrete is influenced by the type of sand, the level of fines and the shape of the particles of the sand. the highest flexural tensile strengths are obtained with quarry sands and the mixture of quarry sand-silica sand. figure 6: tensile strength by bending of the study sc at 7 days, 14 days and 28 days. compressive strength (at 7 days, 14 days and 28 days) the results grouped together in tab. 7 and illustrated in fig. 7 show that the size of the largest aggregate has a favorable effect on the compressive strength of the study sand concrete for the various maturities. the best results obtained compared to sc1 are those of sc4 (25% ds and 75% qs). at 7 days, the increase in compressive strength of sc2, sc3, sc4 and sc5 was on the order of 30.43% and 75.21% and 90.65% and 79.78% respectively. going from sc4 to sc5, we observed a drop in resistance of around 12%. at 14 days, a gain in resistance of sc2, sc3, sc4 and sc5 is to be reported in the order of 4% and 40.56% and 71.04% and 54.19% respectively. a decrease in resistance is recorded going from sc4 to sc5 of around 23.72%. the same finding was observed at 28 days, the compressive strength of sc2, sc3, sc4 and sc5 increases by the order of 3.46%, 51.54%, 80.21% and 73.53% respectively. going from sc4 to sc5, we observed a drop in resistance of around 8.33%. we can say that to have a good compressive strength, it is necessary to use a large percentage of coarse sand with a small percentage of fine sand. the essential effect of quarry sand is the improvement of the mechanical behavior such as the compressive strength and the addition of a dune sand (which occupies 25% of the amount of aggregates) has the role of closing the voids and the pores, thus avoiding porosity and achieving good homogeneity and workability for concrete, as well as good compressive strength. various researchers [12,14,15] agree that mixing coarse sand with fine sand significantly improves the mechanical behavior of study sand concretes. it can be concluded that the best results obtained in compression are those with a strong dosage of coarse sand (sc) and other weak of fine sand (sd); one can consider sc4 as an optimal dosage. the compressive and flexural tensile strength is influenced by the mineralogical nature and the surface condition of the used sands. s. melais et alii, frattura ed integrità strutturale, 56 (2021) 151-159; doi: 10.3221/igf-esis.56.12 157 concrete type average compressive strength (acs) 7days 14days 28days sc1 sc2 sc3 sc4 sc5 18.60 24.26 32.59 35.46 33.44 25.52 26.54 35.87 43.65 39.35 26.33 27.24 39.90 47.45 45.69 table 7: average compressive strengths of the study sand concrete at 7days, 14days and 28days on half of the specimen (4x4x16)cm3. figure 7: compressive strength of study sc at 7 days, 14 days and 28 days. conclusion ifferent types of concrete are produced in all structures that exist around the world. each type of concrete has mechanical and physical characteristics depending on their material compositions and formulations. sand concrete has advantages such as improved workability to facilitate the pouring of heavily scrapped elements and in places with difficult access, as well as cost savings (especially in desert countries).mechanical performances remain one of the most widely used criteria for judging the quality of these concretes and for their classifications. several studies have been carried out in order to minimize the disadvantages of sand concrete and improve mechanical performance such as correcting the granular extent, adding fibers, etc. this study has highlighted the influence of the dosage of the size of the largest aggregate on the mechanical behavior of hardened sand concretes while maintaining the rheology in the fresh state necessary for their placement. sand concrete composed of a high dosage of coarse sand and other weak of fine sand exhibits improvements in compressive strength and sagging which classifies this concrete (sc4) in the range of plastic concrete. the drawn conclusions from the study are the following:  in a fresh state; the richer the sand in coarse elements, the fineness modulus increases the better the workability improves, on the other hand, increasing the fineness content decreases the fineness modulus and results in poorer handling.  to ensure great sagging and therefore good workability, it is always necessary to substitute the small aggregate by the large aggregate, the latter forming the granular skeleton of the sand concrete.  a sand concrete which contains 100% or 75% dune sand of the mass of aggregates (sc1 and sc2) is a firm concrete, because of the fineness of the dune sand which contributes to the closing of the pores and voids and also the absorption of mixing water. d s. melais et alii, frattura ed integrità strutturale, 56 (2021) 151-159; doi: 10.3221/igf-esis.56.12 158  the use of quarry sand with percentages of 50% and 75% of the granular mass have obtained a plastic concrete thanks to the reduction of dune sand which absorbs water and occupies the pores that exist in the body of the concrete. as well as sc5 concrete which contains a percentage of 100% quarry sand is classified as very plastic concrete based on its slump value (12cm).  in the hardened state; using 100% and 75% sdd (case of sc1 and sc2) gave us low compressive and bending tensile strengths when compared to those of sc3, sc4 and sc5.  the sc4 gave a gain in compressive stress of around 90.69%; 71.04% and 80.21% at different ages 7 days, 14 days and 28 days respectively compared to a control concrete without coarse sand sc1.  to achieve good compressive strength, it is necessary to ensure good homogeneity of the concrete and it is strongly recommended to use a large percentage of coarse sand with a small percentage of fine sand.  the increase in the dosage of coarse sand in the composition of sand concretes improves the tensile strength by bending, optimization is achieved for a sc5 composed only of quarry sand. the rate of increase of sc5 over sc1 over 7 days, 14 days and 28 days is of the order of 21.13%, 63.88% and 89.72% respectively over sc1. according to the findings, we can conclude that the optimization of the study sand concretes is ensured by the sc4 because it offers to the new sand concrete not only an improvement of the mechanical behavior (tension by bending and compression) but also a plastic grade sand concrete p. nomenclature sc: sand concrete sd: sand dune qs: quarry sand sc1: sand concrete type 1 sc2: sand concrete type 2 sc3: sand concrete type 3 sc4: sand concrete type 4 sc5: sand concrete type 5 references [1] tavana amlashi, a., alidoust, p., pazhouhi, m., pourrostami niavol, k., khabiri, s., & ghanizadeh, a. r. (2021). aibased formulation for mechanical and workability properties of eco-friendly concrete made by waste foundry sand. journal of materials in civil engineering, 33(4), 04021038. doi: 10.1061/(asce)mt.1943-5533.0003645 [2] sablocrete, bétons de sable. (1994). caractéristiques et pratiques d’utilisation. presses de l’école nationale des ponts et chaussées (france), 230 p. [3] melais, g. f. z., melais, s., achoura, d., & jauberthie, r. (2015). valorisation des sous-produits de hauts fourneaux dans la fabrication d‟ une nouvelle gamme de béton de sable (valorisation of underproducts of blast furnaces in the manufacture of a new sandcrete range). j. mater. environ. sci, 6(3), pp. 735-742. [4] mani, m., bouali, m. f., kriker, a., & hima, a. (2021). experimental characterization of a new sustainable sand concrete in an aggressive environment. frattura ed integrità strutturale, 15(55), pp. 50-64. doi: 10.3221/igf-esis.55.04 [5] melais, s., & bouali, m. f. (2020). experimental study of flexural tensile strength of sand concrete plates reinforced with metallic fibers. in key engineering materials, 857, pp. 74-82. trans tech publications ltd. doi: 10.4028/www.scientific.net/kem.857.74 [6] l’vovich, k. i. (2004). the sand concrete is a russian construction material for the xxi century. construction materials, the equipment and technologies of xxi century, russia, 61(2), pp. 16-19. [7] bédérina, m., khenfer, m. m., dheilly, r. m., & quéneudec, m. (2005). reuse of local sand: effect of limestone filler proportion on the rheological and mechanical properties of different sand concretes. cement and concrete research, 35(6), pp. 1172-1179. doi: 10.1016/j.cemconres.2004.07.006 s. melais et alii, frattura ed integrità strutturale, 56 (2021) 151-159; doi: 10.3221/igf-esis.56.12 159 [8] guettala, a., mezghiche, b., & chebili, r. (1999). strength comparisons between rolled sand concrete and dune sand concrete. in concrete durability and repair technology: proceedings of the international conference held at the university of dundee, scotland, uk on 8-10 september 1999 (p. 55). thomas telford. [9] el euch khay, s., neji, j., & loulizi, a. (2010). compacted sand concrete in pavement construction: an economical and environmental solution. aci materials journal, 107(2). [10] khay, s. e. e., neji, j., & loulizi, a. (2010). shrinkage properties of compacted sand concrete used in pavements. construction and building materials, 24(9), pp. 1790-1795. [11] benaissa, a., kamen, a., chouicha, k., & malab, s. (2008). panneau 3d au béton de sable. materials and structures, 41(8), pp. 1377-1391. doi: 10.1617/s11527-007-9336-8 [12] rmili, a., ouezdou, m. b., added, m., & ghorbel, e. (2009). incorporation of crushed sands and tunisian desert sands in the composition of selfcompacting concretes part ii: scc fresh and hardened states characteristics. international journal of concrete structures and materials, 3(1), pp. 11-14. doi: 10.4334/ijcsm.2009.3.1.011 [13] bederina, m., makhloufi, z., bounoua, a., bouziani, t., & quéneudec, m. (2013). effect of partial and total replacement of siliceous river sand with limestone crushed sand on the durability of mortars exposed to chemical solutions. construction and building materials, 47, pp. 146-158. doi: 10.1016/j.conbuildmat.2013.05.037 [14] balapgol, b., kulkarni, s. a., & bajoria, k. m. (2002, august). strength and durability of concrete with crushed sand. in 27th conf. our world concr. struct, pp. 29-30. [15] melais, f. z. (2016). durabilité des bétons de sable fibres dans les différents milieux agressifs effets de la nature des fines d’ajouts et fibres, doctoral dissertation, université badji mokhtar, annaba. [16] khouadjia, m. l. k., mezghiche, b., & drissi, m. (2015). experimental evaluation of workability and compressive strength of concrete with several local sand and mineral additions. construction and building materials, 98, pp. 194203. [17] reddy, t. s. s., & dadapeer, a. b. s. (2018). an experimental analysis on the effects of manufactured sand on the compressive strength of concrete. international journal of scientific research in science and technology (ijsrst), 4(2), pp. 54-60. microsoft word 2276 l. romanin et alii, frattura ed integrità strutturale, 48 (2019) 116-124; doi: 10.3221/igf-esis.48.14 116 focussed on “crack paths” a novel algorithm for crack path identification based on infrared images luca romanin university of padua, italy luca.romanin@phd.unipd.it alexei vinogradov, filippo berto norwegian university of science and technology, norway alexei.vinogradov@ntnu.no filippo.berto@ntnu.no paolo ferro university of padua, italy paolo.ferro@unipd.it abstract. the present work aims at developing a new approach towards the analysis of the crack path through the access to the information from the infrared (ir) video imaging of the steady fatigue crack growth. we first test some commonly available infrared image filtering techniques, and then we introduce a new robust algorithm to identify the position of the dynamic crack. the proposed procedure performs the local analysis of the temperature distribution around the fatigue crack tip in the 316l stainless steel. the developed matlab framework simplifies the routine processing and permits analyzing multiple experiments reasonably easily. two filtering procedures gaussian and wavelet shrinkage were implemented and applied successively to denoise the ir images. both filters produce comparable and good quality results. the new algorithm capable of automatically locating the crack tip position from consecutive filtered ir images is proposed. remarkably successful results are demonstrated with only small errors caused by materials distortion. keywords. image denoising; crack tip; infrared imaging; wavelet shrinkage. citation: romanin, l., vinogradov, a., berto, f., ferro, p., a novel algorithm for crack path identification based on infrared images, frattura ed integrità strutturale, 48 (2019) 116-124. received: 24.11.2018 accepted: 03.02.2019 published: 01.04.2019 copyright: © 2019 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. http://www.gruppofrattura.it/va/48/2276.mp4 l. romanin et alii, frattura ed integrità strutturale, 48 (2019) 116-124; doi: 10.3221/igf-esis.48.14 117 introduction n recent years, numerous energy-based approaches have gained considerable interest in attempts to characterize the fatigue crack growth. the consensus exists that failure is a dissipative process involving competing mechanisms of accumulation and dissipation of elastic energy at the crack tip. a large portion of the dissipated energy is irradiated as heat which is, nowadays, measurable by high-speed ir-cameras. already in 1920, griffith hypothesized that: “the “theorem of minimum potential energy” may be extended so as to be capable of predicting the breaking loads of elastic solids, if account is taken of the increase of surface energy which occurs during the formation of cracks”. later, in 1950, freudenthal concluded that: “the study of mechanical behavior and properties at different levels of aggregation is possible only in terms of a concept which on all levels has the same meaning. this concept is energy.” multiple energy criteria for fatigue life estimation based on the hysteresis energy loss [1–4] or stored energy [4,5] have been proposed in the literature. a general assumption that plastic-strain hysteresis is a measure of fatigue damage is neither able to provide a satisfactory fit for experimental data [1] nor able to account for different stress ratios r [4]. as an alternative, the energy-based approaches, e.g. the volume-based strain energy density (sed) method [6], have been proved capable of accurate predicting fatigue life, thus illustrating the power of local energy-based concepts in application to the fatigue life characterization. several experimental attempts have been made to measure the dissipated energy in situ [7,8]. in this context, the work of bannikov and plekhov [5] is particularly worth noticing. using thermal camera images of a growing crack and calculating the plastic work at the fatigue crack tip from the hutchinson, rice and rosengren solution, a local parameter of stored energy was defined. it was clearly demonstrated that shortly before fracture, stored elastic energy reduced while the heat dissipation energy increased and reached the value of the plastic work as the material at fracture was no longer able to store the mechanical energy in nice agreement with the orowan energy criterion of ductile fracture [9]. at that time, the rate of the plastic work accumulation was lesser than the rate of the heat dissipation energy. this indicated that the stored energy nullified. it was assumed by the authors that the damage accumulation mechanism changed as a harbinger of the imminent fracture where the role of macroscopic displacements was essential, and where the energy dissipation increased significantly. they proposed the value of the stored energy in the material to be a failure criterion based on the thermodynamic principles. meneghetti and ricotta [8] quantified the energy generated in the small area surrounding the crack tip and found an empiric correlation between the crack growth rate and the specific heat energy. the exponential relation between these two parameters remained even beyond the applicability of lefm in the final crack growth stage. figure 1: crack path determination from experiments using the temperature distribution t(x,y,t) exploiting the capacity of modern ir cameras, we performed a series of systematic fatigue crack growth tests with different loading ratios. the temperature distribution around the crack tip was continuously monitored by means of an infrared (ir) camera. the necessity of analysing a huge array of stored data and of improving image quality motivated us to develop a versatile data processing framework in the matlab environment. this work is focused on automatic pre-processing filtering/smoothing procedures required to reach the necessary image quality before the position of the crack tip can be i l. romanin et alii, frattura ed integrità strutturale, 48 (2019) 116-124; doi: 10.3221/igf-esis.48.14 118 located along the crack path. results of the tests revealing the energy associated with the crack growth under varying loading conditions (loading ratio and amplitude) are beyond the scope of the present paper centred around methodological aspects of crack path determination. the obtained ir images were processed aiming at obtaining the heat source function defined in the next session. for this purpose, the noise from the images must be removed. in fact, experimental data are contaminated by electronic noise, material and surfaces inhomogeneity, surface vibrations, etc. two filtering procedures were tested. the first one applied an anisotropic three-dimensional gaussian filter to reduce the time-dependent noise. the second approach was based on the wavelet shrinkage denoising strategy. a novel algorithm has been finally developed to follow the evolution of the crack path and to locate the crack tip on the basis of the temperature distribution in function of time t(x,y,t), as is illustrated in fig. 1. the crack length is assumed to be constant during every recording. finally, the crack tip position and the path are reconstructed after denoising. heat source definition btaining a 3d temperature map is challenging. the thermal vision cameras provide a 2d distribution map of the temperature at the surface of the tested specimen. knowledge of the 2d temperature field assumes an obvious simplification, reducing an actual 3d situation to a two-dimensional diffusion problem and neglecting the temperature through the thickness gradients [10,11]. the temperature distribution appears in response to the energy dissipation in the bulk due to a variety of interrelated irreversible processes involving, first of all, plastic deformation (mechanical work done in the plastic zone) and crack jumps (elastic energy release due to a new surface opening). thus, although the temperature provides access to the thermodynamics of the dissipative processes of the crack growth, it is only indirectly related to the material’s behaviour. to get a better understanding of the thermodynamics of underlying processes, it is necessary to recover the properties of the heat sources. this is commonly achieved by solving the heat equation for the heat source function  , ,q x y t [8,12]. the general structure of this equation in cartesian (x,y) coordinates reads as        2 2 2 2 , , , , , , , , t x y t t x y t t x y t q x y t c k t x y              (1)   where is the material density, c is the specific heat capacity, and k is the heat transfer coefficient. thereafter, thermo-elastic coupling and dissipative phenomena can be evaluated [13] and correlated with the stress fields. since the solution of this equation requires both spatial and temporal derivation, the noise-induced fluctuations of the temperature function  , ,t x y t are of crucial importance and have to be alleviated. since eqn.(1) is a differential equation for  , ,t x y t , obtaining the smooth (“denoised”) form of  , ,t x y t is of key importance for the overall success in the further evaluation of  , ,q x y t and for any next steps of the analysis including monitoring of the crack tip position. two effective fileting methods are presented in the following sections. both the heat source function over the whole specimen and its temporal evolution in the crack tip affected zone are presented in what follows. since the aim is to obtain the heat source function characterizing the irradiated heat, comparisons are made between these differently evaluated quantities instead of the directly measured temperature. experiment set-up atigue crack growth tests were performed on sen(t) specimens shaped by waterjet from the cold-rolled 316l lowcarbon stainless steel. the specimen surface was coated with the high emissivity black coating. cyclic load with a maximum of 6500n and fatigue ratio r=0.1 was applied using electrodynamic machine instron electropuls10000. sine wave control signal was set at 10 hz frequency. a larger set of load amplitude and fatigue ratio was tested, but the results are outside the scope of this work. the telops infrared camera ts-ir mw (noise equivalent temperature difference –netd is of 20 mk) with 25 mm lens was used after 1h warming up and stabilization. a spatial resolution was 15 m with the 400x512 pixels. the exposure time o f l. romanin et alii, frattura ed integrità strutturale, 48 (2019) 116-124; doi: 10.3221/igf-esis.48.14 119 has been fixed to 2500 μs to increase the frame rate to 190 hz. the telops’ cameralink acquisition card was used to perform continuous testing and data streaming from the camera to the personal computer (pc). recorded data was continually transferred to the pc hard drive. special care was exercised to minimize a possible thermal noise contribution. three main sources of errors are known:  the electronic noise which can only be corrected including time in filtering  inhomogeneities of the high emissivity paint which is easily solved with a spatial filter  thermal reflections. various precautions are suggested in the literature to overcome these problems and reduce these detrimental factors. the electronic noise is dependent on the camera parameters and settings. the thermal reflections were minimized by a slight rotation of the camera with respect of the surface normal. the experiments were conducted in a dark room with the ambient temperature kept constant throughout the testing [14]. it is believed, admittedly with caution, that most metals can be considered adiabatic for frequencies above 2 hz, but other factors such as the coating and system electronics might introduce concern below 10 hz [15]. in fact, the energy emitted per frame might be of the same order of magnitude as the noise level. image filtering he importance of noise removal is particularly acute for high-speed imaging when the exposure time is low. one possible method is to subtract the “baseline” reference image from the acquired sequence of frames to erase thermal reflections [16]. this method experiences considerable difficulties in the final stage of the crack growth where the material’s deformation is not negligible. the motion compensation technique (“lock-in”), of course, helps to improve the results [17]. admittedly the most common method of the noise smoothing is the median filtering and its variations, which are used to remove the spiky noise before applying a gaussian filter. this method cannot be regarded as noise-specific as it does not consider any particular properties of the noise. to account for the local features of the noise and improve the filtering results, vandone tried to use the wavelet decomposition [18]. this method is quite flexible as it allows for many tuning strategies including optimization of the mother wavelet shape and judicious ways of choosing threshold coefficients. at the first stage, defective pixels are removed. then the filtering method is adopted. hereafter is presented a comparison of the standard method with the new filtering proposals for infrared images. defective pixel removal defective pixels can be defined as those being significantly deviating from the average behaviour of their neighbours. two types of defective pixels are commonly identified in the literature: “dead” pixels having very little sensitivity and “hot” pixels, which retain a very high level of energy. defective pixels do not cause any problem for gaussian filtering. however, due to their locality, they may affect the performance of wavelet-based functions. it is therefore convenient to filter them out. the algorithm is based on the work of giron and correa [19] who defined a unique value of the threshold for the whole image frame. instead of using the median of all the pixels of the frame, we found that the mean value produces more accurate results for our application. the image is sectioned into square 50 pixels wide areas, where the filtering applies. a smaller area size increases the computational time without obtaining notably better results. figure 2: example of a raw frame with the rainbow color-coded temperature (left) and its fourier spectrum (middle). red colors indicate the higher temperature points. on the right-hand image, the fft spectrum derived from the gaussian filter. t l. romanin et alii, frattura ed integrità strutturale, 48 (2019) 116-124; doi: 10.3221/igf-esis.48.14 120 for every area, a threshold is defined as three times the standard deviation of the temperature values. then, every defective pixel being outside the three-sigma interval is marked, and for each one a small neighbouring area 8 pixels wide is considered. finally, the mean of this new area is calculated (defective pixels exclusive), and the corresponding value is substituted to the corrupted pixel. standard method: gaussian filtering all the above methods as well as the standard procedures such as two-dimensional gaussian filtering produce good results for the naked eye. fig. 2 shows a typical fourier spectrum after filtering of the raw frame. however, to solve the heat equation (eqn. 1) and to obtain a smooth q(x,y,t) heat source function, we employed a more elaborated solution. simply increasing the smoothing parameter of the gaussian filter is not sufficient since it does not remove the spatial irregularities as can be seen in fig. 3. the comparisons below are made in terms of the generated heat generation per unit volume q and the integration in a finite area region to obtain a time varying function, the main objective of our energetic approach. it is therefore convenient to treat all relevant data for q as dimensionless, considering the scope of the present work is to find the crack tip position and to compare different denoising methods. the high emissivity paint is the source of the error that causes apparent thermal gradients. fig. 3 shows irregularities in the heat field, and in the crack tip area where the shape should be sinusoidal as the load. time irregularities are due to electronic noise. all the sequences utilized for comparison comes from a test performed with fatigue ratio r=0.3 and fmax=6500n starting from around δk = 30 mpa√m. every 750 cycles a 1s sequence has been recorded, this is a good compromise between hard disk space and discretization of crack growth. as it can be seen in fig.6b quite reasonable points have been obtained with this procedure. to enhance the anisotropic three-dimensional gaussian filtering capabilities for motion compensation, a sequence in the unstable stage iii for crack propagation has been chosen. the sequence has been recorded at 108000 cycles, just 2000 cycles before fracture, when a = 20.05 mm and δk = 123.5 mpa√m. figure 3: the heat source function ahead of the fatigue crack after the standard gaussian filtering (left) and the total irradiated heat in the process zone (right). here and in the following figures the values for the heat function are normalized and dimensionless; therefore, only the shape is important. the red circle corresponds to the frame plotted on the left. first method: anisotropic three-dimensional gaussian filtering the limit of using a common gaussian filter is that it works only in the space coordinates while electronic noise is time dependent. having decreased the exposure time, electronic noise has an energy comparable with the signal deriving from the environment. a more sophisticated filtering technique is needed. the simple solution is build up on the threedimensional gaussian filter, where smoothing in the time domain can be performed too. anisotropic gaussian smoothing is achieved using the following kernel [20]:       22 2 2 2 2 22 2 3 2  1 x, y, t e 2π     x y t yx t x y t g           (2) the filtered result is achieved by convolving the  x, y, tg gaussian distribution function with the image sequence. ,,   x y t   are the values of sigma (smoothing parameter) for respective spatial variables and time. this method permits l. romanin et alii, frattura ed integrità strutturale, 48 (2019) 116-124; doi: 10.3221/igf-esis.48.14 121 smoothing in the time domain with the adjusted t , which is independent of ,and   x y  and can be arbitrarily smaller than for the space dimensions. fig. 4 illustrates the results which are apparently better smoothed and are better following the load function behaviour than those displayed in fig. 3. figure 4: results of the heat source function with the three-dimensional gaussian filtering applied (σx,y=8.8 σt=0.88) (left). the generated energy is shown in the neighbourhood of the crack tip area (right). second method: wavelet shrinkage wavelet coefficients are obtained from a single prototype wavelet ψ called mother wavelet by scaling and translation. various kernel pairs can be chosen. we choose daubechies-10 (db10) as a wavelet family which has a good compromise between filtering and valuable information preservation. a level 5 decomposition has been utilized in the filtering procedures. under besov norms, the magnitudes of wavelet coefficients are directly proportional to the irregularity of a given image. when noise is present, such irregularity grows in the wavelet coefficients. because coefficients at finer scales tend to be the primary carriers of edge information, we set discrete wavelet transformation (dwt) coefficients at zero if their values are below a certain threshold tr. these coefficients are mostly corresponding to noise. the performance of the denoising algorithm relies heavily on the optimal value of the threshold. we noted that for the particular type of thermographs, as opposed to conventional light photography, the method for estimating the threshold is not too influencing. the computational speed and easiness of implementation are however of major concern. we choose universal thresholding as the preferred method whereby a threshold value is uniquely chosen for all wavelet coefficients. the threshold tr for the coefficients is defined as follows: 2 logt n 2 logtr n (3) where n is the image size, and σ is the noise variance taken at unity. a soft thresholding function has been applied. fig. 5 shows the results for the heat source function q after wavelet filtering. figure 5: results for the heat source function using a wavelet decomposition level of 5 and db10 (left). results are very similar to those obtained with 3d gaussian filtering in terms of smoothness in the space dimension. temporal filtering is not implemented in this processing scheme and therefore the time dependence of the q-function is not perfectly sinusoidal and is not following the load well (right). l. romanin et alii, frattura ed integrità strutturale, 48 (2019) 116-124; doi: 10.3221/igf-esis.48.14 122 crack tip location o determine and visualize the crack path, one has to spot the position of the crack tip in every recorded sequence as in fig. 1. during the stable crack growth, every recorded sequence 1 s long corresponds to a certain position of the crack tip; at this small time scale, the crack length can be considered constant. the thermo-elastic effect causes a positive heat generation during unloading, and a negative one during loading. temperature is thus increasing in the unloading phase, especially at stress singularity points such as the crack tip.  the simplest idea is to find the maximum temperature in every frame and to calculate the mean of the maxima positions. this is of course not sufficient to obtain an accurate estimate of the position of the crack tip. the motion of the specimen during testing, friction on the crack edges and plasticity ahead of the crack tip distort the results and create additional errors, which should be compensated in separate procedures. besides, outliers must be excluded for the sake of accuracy. for the scope of calculating δk and locating a region around the crack tip, the procedure has proven itself valuable and economical to analyse large quantity of data. the proposed workflow is as follows:  the temperature and the size of the frame are normalized to unity.  only the values in the 0.2 to 0.8 temperature range are kept for the analysis. in this way, the crack surface friction affecting the mean values because of the increased temperature, and the frames containing the highest deformation of the specimen are excluded. at the same time, as the crack closure is approached in the unloading part of the cycle, the peak temperature point moves from the crack tip to the centre of the plastic zone as has been noted also by meneghetti et al. [8]. the limit of 0.8 has been found empirically to take into account this phenomenon as well as the friction effects.  in the spatial domain, the values outside the 0.01-0.99 interval for the horizontal dimension and 0.2-0.8 for the vertical dimension are ignored. this eliminates the border effects which can be quite significant.  points where the temperature decreases are excluded. this is the most important filter. it has been observed that during the loading phase, due to the thermo-elastic effect, the temperature can decrease below the mean value. the concept for which the maximum corresponds to maximum temperature would not be applicable anymore.   the plot of maximum temperature against the frame number (time) is shown in fig. 6, and is self-explanatory of the process adopted. blue circles correspond to the frames along the ascending half-cycle curve, which were kept for the analysis.  figure 6: maximum temperature in the frame versus the frame number in a sequence. circle marks are the points used to calculate the crack tip position. on the right figure, the crack length is plotted as a function of the number of cycles. blue lines correspond to the calculated points; black circles are obtained from a high degree polynomial fitting. inaccuracies occur in derivative calculations. comparing sequence frames with the calculated crack tip point, it resulted that the fatigue crack tip position can be determined with an error lower than 10 pixels related to the camera resolution. this error also can be noticed in fig. 7, highlighting the difference between the actual crack tip position and the calculated crack path. the method proves to be particularly efficient and accurate during the steady paris stage of the crack propagation whereas the error approaches the upper limit of 10 pixels in the crack initiation stage and final critical crack growth stage. in fact, the blunt notch for crack initiation does not create a sharp temperature profile where the maximum is precisely detectable, while large surface displacements occur in the final rupture stage, and the mean value for the crack tip position has less significance. fig. 6 shows the calculated crack length against the number of loading cycles. results are reasonable and can be used for the location of the crack tip position. however, they are not recommended for calculations of the crack growth rate da/dn before additional smoothing. a regression to high order polynomial has been tested and shown efficient. t l. romanin et alii, frattura ed integrità strutturale, 48 (2019) 116-124; doi: 10.3221/igf-esis.48.14 123 figure 7: crack path determined for the test specimen from ir images (cropped from a 640x512 px, 9.6x7.7 mm). cross points represents the crack tip position located after 3d gaussian filtering and q-function calculation. diamond marks are calculated with the wavelet shrinkage procedure. conclusions urther study should be conducted to compare the calculated crack length and the crack growth rate with independent measurements by optical observations, crack gage or crack tip opening displacement data. at the current state of research, the proposed algorithm is accurate enough to locate the crack tip in order to integrate the heat source function q over a finite area as a proof of concept. however, due to chosen computationally cheap measurement strategy when the thousand of cycles occurred between every ir–recorded sequence, the crack growth rate da/dn cannot be measured satisfactory from the thermographic data in the present test. nevertheless, the method itself does have this capacity, provided the records are performed continuously. in addition, we have shown that both three-dimensional anisotropic gaussian filtering and wavelet shrinkage-based filtering perform appreciably better than the conventional 2d gaussian filtering in obtaining the heat source field. in fact, due to their flexibility and tenability, they offer a good compromise between information preservation and noise filtering. fig. 7 shows that nearly coincident crack path is predicted with both procedures. the gaussian filtering method has the advantage of being more straightforward to implement and providing a more accurate time representation. wavelets are a bit more complex to handle. they however have a hood potential for removal specific noise features. overall, the anisotropic gaussian filtering appears to be a viable tool for this type of application. in conclusion, a versatile and fully functional framework for automatic ir data processing is presented. it has been successively applied to a large set of experiments. future development of methodological tools (besides calibration tools) should be based on precise motion compensation algorithms. references [1] feltner, c.e., morrow, j.d. (1961). microplastic strain hysteresis energy as a criterion for fatigue fracture, j. basic eng., 83(1), pp. 15, doi: 10.1115/1.3658884. [2] korsunsky, a.m., dini, d., dunne, f.p.e., walsh, m.j. (2007). comparative assessment of dissipated energy and other fatigue criteria, int. j. fatigue, 29(9–11), pp. 1990–1995, doi: 10.1016/j.ijfatigue.2007.01.007. [3] stowell, e.z. (1966). a study of the energy criterion for fatigue, nucl. eng. des., 3, pp. 32–40. doi: 10.1016/0029-5493(66)90146-4. [4] klingbeil, n.w. (2003). a total dissipated energy theory of fatigue crack growth in ductile solids, int. j. fatigue, 25(2), pp. 117–128, doi: 10.1016/s0142-1123(02)00073-7. [5] bannikov, m. v., plekhov, o.a. (2013). a study of the stored energy in titanium under deformation and failure using infrared data, 24, pp. 81–88, doi: 10.3221/igf-esis.24.08. [6] lazzarin, p., livieri, p., berto, f., zappalorto, m. (2008). local strain energy density and fatigue strength of welded joints under uniaxial and multiaxial loading, eng. fract. mech., 75(7), pp. 1875–1889. doi: 10.1016/j.engfracmech.2006.10.019. [7] vshivkov, a., iziumova, a., plekhov, o. (2016). experimental study of heat dissipation at the crack tip during fatigue crack propagation, 35, pp. 57–63, doi: 10.3221/igf-esis.35.07. [8] meneghetti, g., ricotta, m. (2016). evaluating the heat energy dissipated in a small volume surrounding the tip of a f l. romanin et alii, frattura ed integrità strutturale, 48 (2019) 116-124; doi: 10.3221/igf-esis.48.14 124 fatigue crack, int. j. fatigue, 92, pp. 605–615, doi: 10.1016/j.ijfatigue.2016.04.001. [9] orowan, e. (1954). energy criteria of fracture, welding j., 84, 157-160. [10] louche, h., chrysochoos, a. (2001). thermal and dissipative effects of accompanying lüders band propagation, mater. sci. eng. a, 307(1–2), pp. 15–22, doi: 10.1016/s0921-5093(00)01975-4. [11] boulanger, t., chrysochoos, a., mabru, c., galtier, a. (2004). calorimetric analysis of dissipative and thermoelastic effects associated with the fatigue behavior of steels, int. j. fatigue, 26(3), pp. 221–229. doi: 10.1016/s0142-1123(03)00171-3. [12] iziumova, a., vshivkov, a., prokhorov, a., kostina, a., plekhov, o. (2016). the study of energy balance in metals under deformation and failure process, quant. infrared thermogr. j., 13(2), pp. 242–256. doi: 10.1080/17686733.2016.1212527. [13] berthel, b., chrysochoos, a., wattrisse, b., galtier, a. (2008). infrared image processing for the calorimetric analysis of fatigue phenomena, exp. mech., 48(1), pp. 79–90, doi: 10.1007/s11340-007-9092-2. [14] bodelot, l., sabatier, l., charkaluk, e., dufrénoy, p. (2009). experimental setup for fully coupled kinematic and thermal measurements at the microstructure scale of an aisi 316l steel, 501, pp. 52–60, doi: 10.1016/j.msea.2008.09.053. [15] chasiotis, i. (2008). springer handbook of experimental solid mechanics. springer handbook of experimental solid mechanics. [16] seelan, p.j., dulieu-barton, j.m., pierron, f. (2017).the effect of microstructure on energy dissipation in 316l stainless steel., pp. 15–19. [17] bannikov, m. v., plekhov, o.a., plekhova, e. v. (2012). infrared thermography study of the fatigue crack propagation, 21, pp. 46–53, doi: 10.3221/igf-esis.21.06. [18] vandone, a. (2011). algorithms for infrared image processing, thesis, politecnico di milano. [19] david, a., girón, r., correa, h.l., david, a., girón, r., correa, h.l. (2010). nuevo algoritmo de detección y corrección de píxeles anómalos en imágenes a new algorithm for detecting and correcting bad pixels in infrared images, 30(2), pp. 197–207. [20] law, m.w.k., chung, a.c.s. 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/hrv (za stvaranje adobe pdf dokumenata najpogodnijih za visokokvalitetni ispis prije tiskanja koristite ove postavke. stvoreni pdf dokumenti mogu se otvoriti acrobat i adobe reader 5.0 i kasnijim verzijama.) /hun 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can be opened with acrobat and adobe reader 5.0 and later.) >> /namespace [ (adobe) (common) (1.0) ] /othernamespaces [ << /asreaderspreads false /cropimagestoframes true /errorcontrol /warnandcontinue /flattenerignorespreadoverrides false /includeguidesgrids false /includenonprinting false /includeslug false /namespace [ (adobe) (indesign) (4.0) ] /omitplacedbitmaps false /omitplacedeps false /omitplacedpdf false /simulateoverprint /legacy >> << /addbleedmarks false /addcolorbars false /addcropmarks false /addpageinfo false /addregmarks false /convertcolors /converttocmyk /destinationprofilename () /destinationprofileselector /documentcmyk /downsample16bitimages true /flattenerpreset << /presetselector /mediumresolution >> /formelements false /generatestructure false /includebookmarks false /includehyperlinks false /includeinteractive false /includelayers false /includeprofiles false /multimediahandling /useobjectsettings /namespace [ (adobe) (creativesuite) (2.0) ] /pdfxoutputintentprofileselector /documentcmyk /preserveediting true /untaggedcmykhandling /leaveuntagged /untaggedrgbhandling /usedocumentprofile /usedocumentbleed false >> ] >> setdistillerparams << /hwresolution [2400 2400] /pagesize [612.000 792.000] >> setpagedevice microsoft word numero_57_art_10_3122 r. fincato et alii, frattura ed integrità strutturale, 57 (2021) 114-126; doi: 10.3221/igf-esis.57.10 114 fully implicit numerical integration of the yoshida-uemori two-surface plasticity model with isotropic hardening stagnation riccardo fincato, seiichiro tsutsumi university of osaka, jwri, japan fincato@jwri.osaka-u.ac.jp, http://orcid.org/0000-0003-4058-0460 tsutsumi@jwri.osaka-u.ac.jp alex zilio, gianluca mazzucco, valentina salomoni university of padova, dicea, italy alex.zilio@studenti.unipd.it, gianluca.mazzucco@dicea.unipd.it, valentina.salomoni@dicea.unipd.it abstract. the paper deals with the numerical investigation and implementation of the two-surface plasticity model (or bounding surface model). this plasticity theory allows to describe the deformation behavior under large strain cyclic plasticity and the material stress-strain responses at small-scale re-yielding after large pre-straining. a novel strategy to model the isotropic hardening stagnation is developed within a fully implicit integration scheme in order to speed up the computation and to improve the material description. keywords. bounding surface model; return mapping; workhardening stagnation; finite strain; finite element analyses. citation: fincato, r., tsutsumi, s., zilio, a., mazzucco, g., salomoni, v., implicit numerical integration of the yoshida-uemori two-surface plasticity model with isotropic hardening stagnation, frattura ed integrità strutturale, 57 (2021) 114-126. received: 19.05.2021 accepted: 03.06.2021 published: 01.07.2021 copyright: © 2021 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. introduction lastic deformation on metallic materials represents an important aspect in civil engineering and in several industrial sectors (automotive, construction, naval, etc.). an underestimation of the material capability of bearing loads, or an incorrect design of components can lead to a catastrophic outcome with severe consequences in terms of lives or economic impact. this problem has been deeply investigated by many authors, resulting in a high number of analytical and numerical models that try to catch a realistic description of irreversible deformation in structural analyses and design processes. this phenomenon also occurs in sheet metal forming: the shape of a part changes during removal from the tooling due to the recovery of elastic deformation. in this case, it is important to predict accurately the springback and to compensate it correctly during the die design. in cyclic mobility problems, for example in the field of sheet metal forming, the bauschinger p https://youtu.be/ajprgy6tby4 r. fincato et alii, frattura ed integrità strutturale, 57 (2021) 114-126; doi: 10.3221/igf-esis.57.10 115 effect should be taken into account for a better prediction of springback (uemori et al. [1])). in many typical large strain applications, the springback is a process of small-scale re-yielding after a large pre-strain. therefore, it is necessary to define a constitutive model able to describe both the deformation behavior in large strain plasticity and the stress-strain response at small-scale re-yielding. yoshida and uemori [2] formulated an elastoplastic model for the description of metals behavior under cyclic loading conditions based on experimental observations on mild and high strength steels [3]. among others constitutive theories (e.g. [4–8]) the yoshida and uemori approach appears to be the most consistent and capable to model the transient bauschinger effect, permanent softening and the workhardening stagnation under large elastoplastic deformation. on the other hand, the increase of the computational power incentivized the research on mechanical models. the great interest around numerical simulations derives from the possibility of conducting parametric studies on components, varying geometrical features or loading conditions without additional experimental costs. numerical codes can be applied for the simulation of service life of large structures such as bridges, skyscrapers, ships, for which full-scale experimental approaches would be unfeasible or too costly. in particular, the recurs to implicit integration schemes of material constitutive equations allows to furtherly improve the computation time, without loss of accuracy. ghaei and green [9] and ghaei et al. [10] proposed a fully implicit and a semi-implicit algorithms for the integration of the two-surface model, investigating the predictive ability of the constitutive model in metal forming processes. moreover, they enriched the formulation of the yoshida-uemori model by taking into account an anisotropic yield criterion, the yld20002d yield function [11]. an interesting aspect in [9] and [10] is the resolution strategy for the implicit update of the workhardening stagnation, necessary to model the stress plateau observed in metals sheets subjected to cyclic loading conditions. the same numerical scheme for the workhardening stagnation was also adopted by jia [12] to simulate the metal behavior under cyclic loading and large plastic strain. a brief description of the algorithm proposed by ghaei and green is presented in the following section 3.2, highlighting the main aspects and assumptions. in detail, it will be shown in section 4 that the aforementioned strategy is characterized by a non-negligible inaccuracy in the update of the workhardening stagnation surface that accumulates during loading cycles, leading to an imprecise description of the material behavior. the goal of this work is to develop a fully implicit integration scheme of the two-surface plasticity model proposed by yoshida and uemori, formulating a novel algorithm for the evaluation of the workhardening stagnation with an accuracy imposed by the user. the paper is organized as follows. section 2 deals with some preliminary aspects, defining the kinematic framework accounting for large plastic deformation in metals and introducing the two-surface model. section 3 is dedicated to describe the fully implicit integration scheme, focusing on the numerical strategy for the update of the workhardening stagnation. both the ghaei and green and the proposed algorithms are presented. section 4 reports the results obtained in the finite element analyses (fea), showing the advantages of adopting the novel integration strategy. the limitations and future works are discussed in section 5. lastly, conclusions are reported in section 6. preliminaries he two-surface model with non-isotropic hardening memory surface has been widely used to perform numerical simulation on cyclic mobility and metal forming problems [9, 10, 12, 13]. some limitations were pointed out by [14] in case of large plastic strains (> 20%). in the original formulation, yoshida and uemori expressed the constitutive model under hypoelastic-based plasticity, adopting the jaumann spin for the definition of the co-rotational framework. this choice has been often criticized since it leads to abnormal oscillatory stress in classical shear tests (e.g. in [15], among others). the aforementioned shortcoming is discussed in the following subsection 2.1. on the other hand, the adoption of a hypobased-plasticity framework has the benefit that the constitutive equations developed for small deformation material models can be reused for large deformation simply defining a co-rotational framework. therefore, the use of a different corotational spin does not alter the two-surface model constitutive equations, briefly recalled in subsection 2.2. kinematic framework two recent works from jiao and fish [16, 17] investigated extensively the role of the co-rotational framework, pointing out the drawbacks of the most common objective stress rates (i.e. jaumann, green-naghdi and logarithmic). in addition, jiao and fish proposed a new co-rotational spin, the kinetic logarithmic spin, demonstrating that this new co-rotational spin can bridge multiplicative hyper-elasto-plasticity and additive hypo-elasto-plasticity models. t r. fincato et alii, frattura ed integrità strutturale, 57 (2021) 114-126; doi: 10.3221/igf-esis.57.10 116 the current formulation of the two-surface model adopts an additive decomposition of the strain rate d into elastic de and plastic dp parts. the expression of the co-rotational rate of the cauchy stress σ (plastic incompressibility is assumed ,σ σ τ kirchhoff stress) can be written as follows:                   log log log log , k k k p k k p p p σ σ ω σ σω ω w w w b σ d w σd d σ (1) where σ is the co-rotational kinetic logarithmic stress rate, logkω is the kinetic logarithmic spin, w is the continuum spin, wp is the plastic spin tensor defined by means of the material constant  according to zbib and aifantis [18]. logkw is a skew-symmetric second-order tensor valued function dependent on the total strain rate d as well as on the kinetic left cauchy-green deformation tensor kb . this work does not consider plastic anisotropy, therefore, the contribution of the plastic spin tensor is neglected by imposing   0 . future works will consider this aspect. the yoshida-uemori model yoshida et al. [3] conducted a series of in-plane cyclic tension-compression tests on steel sheets in order to characterize the material deformation at large strain. based on the observation in the experimental campaign, they formulated a constitutive model (yoshida and uemori [2]) to point out and to correct the shortcomings of classical models with mix isotropic and kinematic hardening. the main features of the two-surface model address three main aspects: • the reverse deformation is characterized by an initial early yielding and smooth elastoplastic transition with a rapid change of the workhardening rate followed by a softening region. • in case of mild steel sheets, the shape of the reversed stress-strain curve needs an ad hoc modeling. • the cyclic stress amplitude strongly depends on cyclic strain ranges and mean strains. the model was formulated accounting for two separate surfaces: the yield surface f (eqn. (2)1), that considers only kinematic hardening (eqn. (2)8), and the bounding surface f (eqn. (2)2), characterized by both isotropic and kinematic hardening (eqs. (2)9 and (2)7). additionally, the workhardening stagnation can be described by adopting a third surface, the non-isotropic hardening surface g (non-ih hereafter) (eqn. (2)3). a novel algorithm for the numerical definition of the non-ih surface is the object of this work. briefly, the constitutive equation of the two-surface model are presented in eqn. (2), referring to fig. 1. figure 1: sketch of the two-surface model.                                              * * * * * * * * * ( ) 3 2 ; 3 2 ( ) 3 2 2 3 ; 3 2 ; ; 2 3 ; ; 1 ; 2 3mhsat f y f b r g r ca a a b r y f f m b r r e h dt σ α σ β β q α n n α σ α n n σ α β n β α α β (2) where the symbol ‘°’ indicates the co-rotational rate, σ is the deviatoric part of the cauchy stress, r is the isotropic hardening function of the bounding surface, α and β are the back stress of the yield and bounding surface. b, y, m, b, c r. fincato et alii, frattura ed integrità strutturale, 57 (2021) 114-126; doi: 10.3221/igf-esis.57.10 117 and rsat are material parameters,  is the plastic multiplier and h is the cumulative plastic strain. a detailed explanation of the model can be found in yoshida and uemori [2]. as it can be seen in eqs. (2)1 and (2)2 the original model considers a classical von mises plastic potential. moreover, yoshida and uemori considered an empirical approach for the reduction of the elastic modulus e in relation to the generation of plastic deformation.         0 0 1 h ae e e e e (3) where e0 and ea are the young’s modulus of the virgin and infinitely large pre-strained material, respectively, and  is a material constant. the same approach has been used in this work; however, the reduction of the elastic stiffness could be better described within the continuum damage mechanics framework [19–21]. one of the main features of the two-surface model is the possibility of describing the stress plateau observed after the reverse loading or re-loading in the experiments. from a physical point of view, the phenomenon is related to the dissolution of dislocation cell walls during a reverse deformation. to model this behavior, yoshida and uemori introduced an additional surface in the stress space (see eqn. (2)3) that can translate and expand by means of the evolution of the back stress tensor q and the radius r. in detail, the isotropic expansion of the bounding surface is allowed only if the following conditions are satisfied simultaneously:                    2 2, , 3 2 0 , , : : 0 g r r g r β q β q β q β β q β β (4) the first condition in eqn. (4)1 is fulfilled whenever the back stress of the bounding surface lies on g ,whereas the second in eqn. (4)2 is satisfied when the co-rotational rate of β is directed outside the non-ih surface. if both eqs. (4)1 and (4)2 are true, the bounding surface expands (i.e.,  0r ) following the evolution law in eqn. (2)9 and the back stress q and the radius r are updated according to the following formulas: a) b) figure 2: sketch of the non-ih surface a) in case of non isotropic hardening (  0r ), b) in case of isotropic hardening (  0r ).                    2 3 : , 2 3 : 2 r rr r h r β q β q β q β q β (5) therefore, the co-rotational rate of the back stress can be re-written as: r. fincato et alii, frattura ed integrità strutturale, 57 (2021) 114-126; doi: 10.3221/igf-esis.57.10 118        3 :1 2 h r r β q β q (6) where h (  0 1h ) is a material constant set by the user. briefly, larger values of h give a rapid expansion of the non-ih surface with the consequent smaller cyclic hardening of the material. eqn. (5)1 is obtained directly from the consistency condition eqn. (2)1. on the contrary, in case one or both the requirements are not satisfied, the isotropic hardening term of the bounding surface is not updated (i.e.,  0r ). only the back stress q is updated through eqn. (6), while  0r . numerical integration onsidering an equilibrium state at the generic time   0,nt t the aim of the integration algorithm is the computation of the unknowns at the subsequent time    1n nt t t with   1 0,nt t , given the total strain increment d . in detail, the set of the unknowns can be expressed as:   *, , , , , ,h rx σ α β q (7) where the back stress of the yield surface α can be simply obtained by means of eqn. (2)8 once the terms *α and β are computed at the n+1 time step. in [2] the constitutive equations of the two-surface model are integrated by means of an explicit scheme, that requires to proceed with small time increments t to fulfill the convergence and to obtain accurate solutions. in this work the set of equations in eqn. (2) is integrated with a fully implicit return map algorithm in the form of the closest point projection method [22,23] (cppm). for sake of simplicity, the following subsection 3.1 shows the integration algorithm without accounting for the evolution of the non-ih surface. the workhardening stagnation requires an additional numerical scheme that is described in subsection 3.3. lastly, subsection 3.4 summarizes the complete cppm used for the update of all the unknowns in eqn. (2). cppm without stagnation of the isotropic hardening firstly, the trial elastic is performed by computing the new stress state:    1 : trial n nσ σ e d (8) the trial elastic stress state is used to judge if a plastic correction is required or not. in case the trial stress state is not an admissible stress state for the material (i.e.,  0f ) a plastic correction is performed through a series of k sub-iterations (starting by k = 0 and assigning the internal variable, except the stress state, as       0 1 k n n ). if the evolution of the non-ih surface is not considered, the set of the unknows in eqn. (2) can be reduced to the following set of five unknowns:   *, , , , hx σ α β (9) it is therefore possible to write a system of five equations associated with the variables as in eqn. (10) and to compute the solution at the k+1 sub-iteration by means of eqn. (11). c r. fincato et alii, frattura ed integrità strutturale, 57 (2021) 114-126; doi: 10.3221/igf-esis.57.10 119                                                             1 1 1 1 1 *, 1 1 *, 1 *, 1 *, 1 1 1 1 1 3 2 3 2 ( ) 2 3 2 3 2 3 k k n n k k k n n n k nk k k k n n n n n k k k n n n n k n n f y f b r ca a m b h h σ α σ β b α α n n β β n β (10)               11 1 1 1 1 1 1 1 k k k k k k n n n n n nx x a b x x (11) where a is the matrix of the partial derivatives of the equations in b against the unknowns. the idea is to perform a multiequation newton-raphson scheme that guarantees a quadratic rate of convergence, speeding up the computation time compared to an explicit integration scheme. moreover, the algorithm is stable and accurate for large d inputs. the subiterations k stop whenever the following condition is fulfilled:    1 1 1 k n tolb (12) where tol1 is a threshold imposed by the user, usually 10-8, as in the present work. another benefit of the current approach consists in the possibility of computing the consistent tangent operator to directly after the local equilibrium is fulfilled (i.e., eqn. (12) is satisfied) as:      1( 1) 1 12 :to kna e (13) where     11 1 12 k na is a matrix with the same dimensions as elastic constant matrix e and the first term is located in the first row and second column of     11 1 k na . a detailed explanation of the algorithm, together with iso-error maps for the evaluation of the finite step accuracy, can be found in [24,25]. ghaei and green algorithm for the definition of the workhardening stagnation in large finite steps integration, the conditions in eqn. (4) can be rewritten as the condition in eqn. (14), which implies that the update of the workhardening stagnation has to be performed whenever the back stress  1 1 k nβ lies outside the non-ih estimated at the n step. ghaei and green proposed a single scalar equation for the update of g . assuming to know the back stress  1 1 k nβ of the bounding surface, the radius of the non-ih surface at the n+1 step is approximated with a taylor expansion as:           2 21 1 1 1, , 3 2 0 k k n n n n n ng r rβ q β q (14)                                              2 2 2 1 1 1 1 1 1 1 1 1 1 1 1 3 : 1 1 k n n n n n n k k n n n n nk n n n n r r r r h χ β β β β β qχ χ β q (15) r. fincato et alii, frattura ed integrità strutturale, 57 (2021) 114-126; doi: 10.3221/igf-esis.57.10 120 the only unknown in eqn. (15) is represented by the term  that can be obtained substituting the expressions in eqn. (15) into the consistency condition of eqn. (4)1. after mathematical manipulations (details can be found in [9])  can be computed as follows:                   21 1 2 1 1 2 3 3 : 3 : 4 : 2 1 2 k k n n n n n n n n h h r r χ β χ β χ χ (16) lastly, the back stress 1nq and the radius rn+1 are updated by substituting the computed  into eqn. (15)3 and then 1nχ in eqn. (15)1. novel algorithm for the definition of the workhardening stagnation the novel approach consists in the observation that, if the condition in eqn. (14) is fulfilled, the back stress of the bounding surface 1nβ , computed at the k+1 sub-iteration of the cppm, should lies on the non-ih surface. therefore, it is possible to estimate the updated g by means of a series of additional sub-iteration j within the same k+1 sub-step. in particular,    1 , 1 j ng can be obtained from the previous  , 1 j ng by a taylor expansion that neglects the quadratic terms: figure 3: schematic representation of the evolution of the non-ih surface.                                  1 1 1 , 1 , 1 1 1 11 , 1 , 1 1 with for 0 j j j j j j n n n n nn j n n j n n j n n g g g g r r g g j r r q q q q (17) the only terms that need to be estimated are the increments of the back stress  1 1 j nq and of the radius   1 1 j nr . to compute those terms the following variable  is introduced:                 1 1 1 1 1 11 1 2, 1 1 3 : 2 k j k n n nj n j nr β q β (18) from eqs. (5) and (6) it is possible to write:                          1 1 1 1 1 1 1 1 1 1 1 1 1j j k jn n n n j j j n n n h r h r q β q (19) r. fincato et alii, frattura ed integrità strutturale, 57 (2021) 114-126; doi: 10.3221/igf-esis.57.10 121 at this point the only unknown of the problem is represented by   1 1 j n that can be obtained by substituting eqn. (19)1 and 2 into the linear expansion of eqn. (17). after manipulations it is possible to write:                         , 11 1 1 1 1 1 11 1 : j nj n j j k j j n n n nn g g g h h r r β q q (20) once computed   1 1 j n , function of all the variables at the j sub-iteration, the values of   1 1 j nq and   1 1 j nr are updated through eqn. (19). the algorithm stops whenever the following conditions is fulfilled:     1 , 1 2 j ng tol (21) from a theoretical point of view, the scheme for the update of the non-ih surface can be seen as a sort of return mapping where, instead of correcting the back stress  1 1 k nβ , the values of the radius and the back stress of g are updated (see fig. 3). it is important to highlight that the condition in eqn. (21) expresses exactly the updated non-ih surface that passes through the current value of  1 1 k nβ . moreover, the threshold tol2 can be set independently form tol1, depending on the accuracy required. in this work both tol1 and tol2 were both set equal to 10-8. cppm with stagnation of the isotropic hardening this section summarizes the steps necessary for the computation of all the variables in eqn. (7) from the step n to the subsequent step n+1. the procedure is reported in the flow chart of fig. 4. figure 4: flow chart of the cppm with isotropic hardening stagnation. 1. perform the trial elastic. 2. in case the plastic correction of the stress is needed, the scheme applies the procedure explained in subsection 3.1 through a series of k sub-iterations. 3. within the same k sub-iteration and after the computation of the unknowns in eqn. (11), the fulfillment of the condition in eqn. (14) is verified. 4. the condition in eqn. (14) is true, the algorithm updates the non-ih surface with a series of j sub-iterations by means of the procedure explained in sub-section 3.3 until eqn. (21) is verified. subsequently, the isotropic hardening term r for the bounding surface is updated. instead, in case the condition in eqn. (14) is false, the non-ih surface is not updated and  0r . only 1nq is updated,  1n nr r . 5. lastly, the fulfillment of the local convergence at the n+1 step and k+1 subiterations is checked with eqn. (12). if eqn. (12) is true the algorithm proceeds to the next time step, otherwise it is necessary to repeat the procedure from point 2. r. fincato et alii, frattura ed integrità strutturale, 57 (2021) 114-126; doi: 10.3221/igf-esis.57.10 122 numerical analyses he constitutive equations presented in the previous subsections 3.1and 3.3 were implemented via user subroutine for the commercial code abaqus (ver. 6.14-4). the present section deals with the results of the numerical analyses divided into two parts. the first part aims to show the benefit of the novel approach for the update of the non-ih surface compared with the ghaei and green algorithm. the second part shows the ability of the model to reproduce the experimental results carried out by yoshida et al. [3] on a mild (i.e., spcc) and high strength (i.e., spfc) steel sheets. the material parameters are reported in tab. 1, while the geometry of the sample and the sketch of the mesh and boundary conditions are reported in fig. 5a and b, respectively. the fea were carried out considering 1695 hexahedral elements with reduced integration (i.e., abaqus element c3d8r) and applying fully reversed displacement conditions on the top of the sample. to reduce the computation time only 1/8 of the sample was considered (see red dashed line in fig. 5a). moreover, to reproduce the experimental set up, the loading condition was controlled by a sensor positioned to simulate the strain gauge on the specimen. whenever the nominal strain on the sensor exceeded the ±5% axial strain the direction of the load was inverted (e.g., from tensile to compressive and vice versa). material spcc spfc e0 [gpa] 206 206 ea [gpa] 152 159 υ 0.3 0.3 ξ 30.8 61 y [mpa] 124 360 rsat [mpa] 190 143 c 500 300 b [mpa] 9 66 m 12 26 b [mpa] 168 478 table 1: material constants for the spcc and spfc steels. a) b) figure 5: a) geometry of the sample, the red dashed line indicates the portion modeled in the fea (dimensions in mm). b) boundary conditions, mesh and sensor location for the control of the loading conditions. t r. fincato et alii, frattura ed integrità strutturale, 57 (2021) 114-126; doi: 10.3221/igf-esis.57.10 123 ghaei and green algorithm vs novel approach the purpose of this section is to compare the ghaei and green formulation against the proposed approach. the sample in fig. 5b is subjected to three fully reversed loading cycles; the material parameters correspond to the spcc steel and the parameter h is set to 0.9 to enhance the expansion of the radius r over the back stress q. the results by the explicit integration in yoshida and uemori [2] are indicated with black solid lines, the fea carried out with the ghaei and green algorithm with blue markers while the current approach is displayed with red markers. as it can be seen in fig. 6a, the proposed approach gives a better description of the material behavior catching a realistic stress plateau during the first reverse loading. the ghaei and green formulation overestimates the stress plateau resulting in a less accurate description of the stress-strain curves in the remaining cycles. the performance of the two formulations can be better observed in the graphs of fig. 6b and c, reporting the evolution of q and r against the nominal strain. while the current approach is able to describe the evolution of the back stress and the radius with good approximation. the algorithm by ghaei and green suffers from an underestimation of the back stress evolution and an initial overestimation of the radius. this results can be explained by the fact that r in eqn. (15)1 is evaluated with a taylor expansion that neglects the contributions of  2r . moreover, the condition in eqn. (4)1 is not checked after performing the update of q and r. on the contrary, the novel approach computes simultaneously the back stress and the radius through an iterative procedure that guarantees that the final non-ih surface passes through the current back stress of the bounding surface. a) b) c) figure 6: a) nominal stress vs nominal strain curves. back stress q and radius r evolution carried out with b) proposed approach, c) ghaei and green formulation. r. fincato et alii, frattura ed integrità strutturale, 57 (2021) 114-126; doi: 10.3221/igf-esis.57.10 124 numerical results on spcc and spfc steel sheets the aim of this section is to show the performance of the fully implicit integration scheme against the experimental results carried out by yoshida et al. [2]. fig. 7a and b report with black solid lines the stress-strain responses during cyclic loading with total strain ranges of 4% and 10% for the mild and high strength steel, respectively. the red lines show the stress-strain curves obtained with the numerical model. as it can be seen the fe simulations can catch quite well the material response, especially the workhardening stagnation during the reverse loading, proving the correct implementation of the proposed approach. in general, the stress plateau is observed in the mild steel, whereas the high strength steel gives a hardening response. the elastic stiffness seems slightly underestimated in the numerical analyses, probably due to the use of the sensor for the control of the loading conditions. overall, the numerical results are in good agreement with the experimental data. a) b) c) d) figure 7: numerical vs experimental results on a) spcc steel and b) spfc steel. c) local convergence of the cppm, d) convergence of the proposed algorithm for the update of the non-ih surface. discussion he benefit of the ghaei and green formulation lies on the use of a single scalar equation for the update of the nonih surface. on the other hand, the proposed algorithm requires an iterative procedure for modeling of the workhardening stagnation. however, it has been shown how the ghaei and green algorithm is characterized by less accuracy due to the lack of control on the mutual position between the final non-ih surface and the bounding surface back stress. the novel approach can guarantee the fulfillment of the consistency condition for the non-ih with an accuracy set by the user. moreover, fig. 7c and d report the convergence graphs of the cppm and of the update algorithm for the workhardening stagnation, respectively. the data are reported for the quadrature point of the element experiencing the largest amount of cumulative plastic strain h (the curves are reported at 10-50-100% cumulative plastic strain values). as it can be seen the t r. fincato et alii, frattura ed integrità strutturale, 57 (2021) 114-126; doi: 10.3221/igf-esis.57.10 125 novel approach does not require a large amount of sub-iteration j (fig. 7d) and it does not influence the convergence rate of the k sub-iterations (fig. 7c). conclusions he work presented a novel algorithm for the computation of the evolution of the workhardening stagnation surface in the yoshida-uemori model. the numerical scheme guarantees a quadratic rate of convergence for the local and global equilibrium without loss of accuracy even at large integration steps. the current implementation does not consider an anisotropic yield criterion, but it assumes a classical von mises plastic potential. in case of hot-rolled or cold-rolled metals sheets, anisotropy plays a fundamental role in the material behavior and therefore a j2 plasticity might lead to inaccurate results. future works will consider this aspect. a recent work from xie et al. [26] formulated the workhardening stagnation phenomenon with a non-ih defined in the strain space rather than in the stress space, with an additional recovery term. xie’s model showed a better description of the hysteresis loops under various amplitudes compared with the original two-surface model. future works will investigate this aspect. it is worth mentioning that a definition of the workhardening stagnation in the strain space does not invalidate the proposed approach, that can be still adopted. lastly, it should be pointed out that the level of deformation in the current work is quite limited. the results carried out with the jaumann co-rotational rate and the kinetic logarithmic spin showed negligible differences. future works will consider higher deformation regimes. references [1] uemori, t., okada, t., yoshida, f. (2000). fe analysis of springback in hat-bending with consideration of initial anisotropy and the bauschinger effect, key eng. mater., 177–180, pp. 497–502, doi: 10.4028/www.scientific.net/kem.177-180.497. [2] yoshida, f., uemori, t. (2002). a model of large-strain cyclic plasticity describing the bauschinger effect and workhardening stagnation, int. j. plast., 18(5–6), pp. 661–686, doi: 10.1016/s0749-6419(01)00050-x. [3] yoshida, f., uemori, t., fujiwara, k. (2002). elastic–plastic behavior of steel sheets under in-plane cyclic tension– compression at large strain, int. j. plast., 18(5–6), pp. 633–659, doi: 10.1016/s0749-6419(01)00049-3. [4] sanchez, l.r. (2010). modeling of springback, strain rate and bauschinger effects for two-dimensional steady state cyclic flow of sheet metal subjected to bending under tension, int. j. mech. sci., 52(3), pp. 429–439, doi: 10.1016/j.ijmecsci.2009.11.002. [5] li, k.p., carden, w.p., wagoner, r.h. (2002). simulation of springback, int. j. mech. sci., 44(1), pp. 103–122, doi: 10.1016/s0020-7403(01)00083-2. [6] chun, b.k., jinn, j.t., lee, j.k. (2002). modeling the bauschinger effect for sheet metals, part i: theory, int. j. plast., 18(5–6), pp. 571–595, doi: 10.1016/s0749-6419(01)00046-8. [7] chun, b.k., kim, h.y., lee, j.k. (2002). modeling the bauschinger effect for sheet metals, part ii: applications, int. j. plast., 18(5–6), pp. 597–616, doi: 10.1016/s0749-6419(01)00047-x. [8] gau, j.-t., kinzel, g.l. (2001). a new model for springback prediction in which the bauschinger effect is considered, int. j. mech. sci., 43(8), pp. 1813–1832, doi: 10.1016/s0020-7403(01)00012-1. [9] ghaei, a., green, d.e. (2010). numerical implementation of yoshida–uemori two-surface plasticity model using a fully implicit integration scheme, comput. mater. sci., 48(1), pp. 195–205, doi: 10.1016/j.commatsci.2009.12.028. [10] ghaei, a., green, d.e., taherizadeh, a. (2010). semi-implicit numerical integration of yoshida–uemori two-surface plasticity model, int. j. mech. sci., 52(4), pp. 531–540, doi: 10.1016/j.ijmecsci.2009.11.018. [11] barlat, f., brem, j.c., yoon, j.w., chung, k., dick, r.e., lege, d.j., pourboghrat, f., choi, s.-h., chu, e. (2003). plane stress yield function for aluminum alloy sheets—part 1: theory, int. j. plast., 19(9), pp. 1297–1319, doi: 10.1016/s0749-6419(02)00019-0. [12] jia, l.-j. (2014). integration algorithm for a modified yoshida–uemori model to simulate cyclic plasticity in extremely large plastic strain ranges up to fracture, comput. struct., 145, pp. 36–46, doi: 10.1016/j.compstruc.2014.08.010. [13] eggertsen, p.-a., mattiasson, k. (2011). on the identification of kinematic hardening material parameters for accurate springback predictions, int. j. mater. form., 4(2), pp. 103–120, doi: 10.1007/s12289-010-1014-7. t r. fincato et alii, frattura ed integrità strutturale, 57 (2021) 114-126; doi: 10.3221/igf-esis.57.10 126 [14] jia, l.-j., kuwamura, h. (2014). prediction of cyclic behaviors of mild steel at large plastic strain using coupon test results, j. struct. eng., 140(2), pp. 04013056, doi: 10.1061/(asce)st.1943-541x.0000848. [15] perić, d. (1992). on consistent stress rates in solid mechanics: computational implications, int. j. numer. methods eng., 33(4), pp. 799–817, doi: 10.1002/nme.1620330409. [16] jiao, y., fish, j. (2017). is an additive decomposition of a rate of deformation and objective stress rates passé?, comput. methods appl. mech. eng., 327, pp. 196–225, doi: 10.1016/j.cma.2017.07.021. [17] jiao, y., fish, j. (2018). on the equivalence between the multiplicative hyper-elasto-plasticity and the additive hypoelasto-plasticity based on the modified kinetic logarithmic stress rate, comput. methods appl. mech. eng., 340, pp. 824–63, doi: 10.1016/j.cma.2018.06.017. [18] zbib, h.m., aifantis, e.c. (1988). on the concept of relative and plastic spins and its implications to large deformation theories. part i: hypoelasticity and vertex-type plasticity, acta mech., 75(1–4), pp. 15–33, doi: 10.1007/bf01174625. [19] tsutsumi, s., kitamura, t., fincato, r. (2020). ductile behaviour of carbon steel for welded structures: experiments and numerical simulations, j. constr. steel res., 172, doi: 10.1016/j.jcsr.2020.106185. [20] gurson, a.l. (1977). continuum theory of ductile rupture by void nucleation and growth: part i—yield criteria and flow rules for porous ductile media, j. eng. mater. technol., 99(1), pp. 2, doi: 10.1115/1.3443401. [21] lemaitre, j. (1985). coupled elasto-plasticity and damage constitutive equations, comput. methods appl. mech. eng., 51(1–3), pp. 31–49, doi: 10.1016/0045-7825(85)90026-x. [22] de souza neto, e.a., peric, d., owen, d.r.j. (2008). computational methods for plasticity, 55. [23] simo, j.c., hughes, t.j.r. (1998). computational inelasticity, vol. 7, new york, springer-verlag. [24] fincato, r., tsutsumi, s. (2017). closest-point projection method for the extended subloading surface model, acta mech., 228(12), pp. 4213–4233, doi: 10.1007/s00707-017-1926-0. [25] fincato, r., tsutsumi, s. (2018). a numerical study of the return mapping application for the subloading surface model, eng. comput., 35(3), pp. 1314–1343, doi: 10.1108/ec-12-2016-0446. [26] xie, x., jiang, w., chen, j., zhang, x., tu, s.-t. (2019). cyclic hardening/softening behavior of 316l stainless steel at elevated temperature including strain-rate and strain-range dependence: experimental and damage-coupled constitutive modeling, int. j. plast., 114, pp. 196–214, doi: 10.1016/j.ijplas.2018.11.001. microsoft word numero_57_art_19_3081 m. t. nawar et alii, frattura ed integrità strutturale, 57 (2021) 259-280; doi: 10.3221/igf-esis.57.19 259 enhancement of blast resistance of r.c beams using micro/nano silica in the presence of steel fibers mahmoud t. nawar, kareem a. el-awady, hamdy k. shehab, ahmed s. eisa zagazig university, department of structural engineering, egypt. mn6w8@mail.missouri.edu, k_ahmed2012@hotmail.com abstract. the study investigates the effect of micro/nano silica and steel fibers on improving the dynamic response of r.c beams, using the abaqus/explicit dynamic analysis. according to the results of magnusson and hallgren's experimental investigation, the fe model has been wellverified and calibrated. the fe test program has further been extended to study the effect of tensile reinforcement ratios 𝝁 of 0.5%, 0.78%, and 1.13%, in comparison with the enhancement of concrete’s material properties, on the behavior of tested beams under blast loading. the results were compared in terms of changes in the max deflection at mid-span and flexural toughness values. the results showed that the flexural toughness of beams decreases when the tensile reinforcement ratio increases due to an increase in the moment of inertia (ieffective).r.c beams incorporating smcs (10%ms+1%ns) with different volume fractions (0%, 1%, 2%) of steel fibers showed that the concrete mixes with higher compressive strength values lead to an increase in the last beam deflection, producing a considerable rise in the flexural toughness by 18.2%, 27% and 31.8% for 𝝁 (0.50%) and 15%, 19.9% and 23.6% for 𝝁 (0.78%) and 6.6%, 13.7% and 19.6% for 𝝁 (1.13%) respectively in comparison with the reference beam. keywords. reinforced concrete; micro silica; nano silica; blast load; flexural toughness; steel fibers. citation: nawar, m., el-awady, k., shehab, h., eisa, a., enhancement of blast resistance of r.c beams using micro/nano silica in the presence of steel fibers , frattura ed integrità strutturale, 57 (2021) 259-280. received: 20.04.2021 accepted: 10.06.2021 published: 01.07.2021 copyright: © 2021 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. introduction last loads are considered one of the severe loads impacting structures, and even a small amount of blast may cause significant damage to the structure, baker et al. [1].enhancement of the ductility and flexural toughness of concrete material plays an important role in absorbing much more energy of r.c structural elements, not only under static loads but also dynamic loads such as "blast" . ductility refers to the ability of material to undergo plastic deformation without failure. on the other hand, toughness refers to the energy required to deform a material to failure. tough materials tend to have both high strength and significant deformation before failure. in case of a blast pressure b https://youtu.be/pr08othgbbm m. t. nawar et alii, frattura ed integrità strutturale, 57 (2021) 259-280; doi: 10.3221/igf-esis.57.19 260 resulting from an explosion, the equation of motion under dynamic loads can be generalized as shown in eqn. 1. the dynamic response in terms of deflection y can be predicted by various numerical procedures (biggs 1964) [2]. f(t) =m y''+r (1) where, the mass (m), the static resistance (r), and the applied load function of time (f(t)) are the parameters for the equation of motion. therefore, the static resistance of the structural system has a main role in predicting the dynamic response to blast loads. the challenge is to expand the static response limit and increase the limits of ductility. according to magnusson [3], ductility and structural stiffness have a significant impact on the failure mode of r.c beams under blast loading. that is, when r.c beams with various reinforcement ratios are exposed to blast loads, only beams with the low reinforcement ratio fail in flexure; and when the reinforcement ratio increases, the failure mode changes into a brittle shear failure. therefore, the sudden shear failures can be avoided by designing structural components that are less stiff and, hence, more ductile. several codes such as ufc [4] and fkr [5] indicate that the ratio of longitudinal reinforcement and the yield strength of a structure should be representative of its capacity to withstand a blast load. when considering extreme dynamic loads, it is important to design ductile elements that can withstand significant plastic deformations, and brittle modes of failure must be avoided [4]. fig. 1 shows the typical behavior of a brittle and ductile failure mode. figure 1: schematic illustration of a brittle and ductile structural response. in the ductile mode of response, the element may attain large inelastic deflections without complete collapse in general. the present paper focuses on introducing many ways to improve the structural element’s efficiency and energy absorption against blast loads. adding a steel plate shear wall to a dual moment-resisting frame system, this has many advantages, including high energy absorption and suitable ductility against blast loadings. increasing stiffness and decreasing displacement have made the steel plate shear wall a proper system for retrofitting existing structures [6]. on the other hand, for r.c structures at the far design range, the applied blast load has a fairly uniform distribution, the deflections needed to absorb the loading are comparatively small, and the single leg stirrups are used as shear reinforcement in slabs and walls. this form of reinforcement will provide shear resistance [4]. for the close-in design range, the applied blast load has a non-uniform distribution, with high strength and extremely high-pressure concentrations. this, in turn, can produce a local punching failure of an element. the use of lacing reinforcement improves the ductility of the structural element significantly, protecting the concrete between the two layers of flexural reinforcement and maintaining it despite the massive cracking. moreover, it prevents the local shear failure caused by the high intensity of the blast pressures [4]. ductile structural elements and proper shear capacities that prevent shear failure before flexural failure are the most efficient ways to avoid progressive collapse due to the development of blast loads. so, it is an issue of high priority to enhance the ductility and flexural toughness of concrete material for r.c structural elements by developing material technologies that can meet the highest levels of the structural performance requirements. micro and nano silica have remained the most valuable and commonly used mineral admixture of pozzolanic materials in the concrete and cement technology [7-9]. on the other hand, addition of steel fibers with supplementing cementitious materials (scms) improves the flexural toughness of concrete [10-15]. m. t. nawar et alii, frattura ed integrità strutturale, 57 (2021) 259-280; doi: 10.3221/igf-esis.57.19 261 based on previous experimental work investigated by authors [16] to study the effect of using micro/nano silica in the presence of steel fibers with different volumetric fractions (0%, 1%, 2%) on the enhancement of the static response of r.c beams. the results showed that replacing cement with 1% ns and 10% ms provides the optimum mixture, which improves the mechanical properties and response of r.c beams under static loads significantly [16]. furthermore, addition of steel fibers with different volume fractions has a major influence on the flexural toughness of concrete mixes. the main objective of this research is to enhance the blast resistance of r.c structural element under blast loading, depending upon the mechanical properties of the concrete material constructed from 1% ns and 10% ms in the presence of steel fibers with different volume fractions. furthermore, an extensive parametric study will be conducted to investigate the effect of enhanced concrete materials with different steel reinforcement ratios 𝝁 (0.5%, 0.78%, and 1.13%) on the flexural toughness behavior of r.c element under blast loading. blast loading n explosion is described as a large-scale release of energy in a short period of time caused by chemical reactions. this rapid release of energy raises the temperature and pressure of the surrounding air. the distance available between the blast source and the target is called "stand-off distance". since all blast parameters are dependent on the amount of energy emitted by the explosion and the distance available to a specific target from the explosion's source, a scaled distance in evaluates of explosion effects [4]. this is illustrated in cube root scaling: z=       1 3 r w (2) where z is the scaled distance, r is the range from the center of the charge (stand-off distance), w is the mass of the spherical tnt charge equivalent. figure 2: overpressuretime profile. pressure variation at a particular point after the explosion with time is described in the overpressure time profile as shown in fig. 2. it consists of a positive phase followed by a negative phase with different time durations [4]. the area under the curve represents the related impulse caused. a simplification of the blast wave profile is made and preserved the positive phase linear variation as shown in fig. 3. the relationship is presented as follows: p(t)=po+pso(1 o t t ) (3) where p(t) is the pressure at time t, pso is the peak side-on overpressure, t is the time measured from the instant that the blast wave arrives (at time = ta), to is the duration of the positive phase of the blast. a m. t. nawar et alii, frattura ed integrità strutturale, 57 (2021) 259-280; doi: 10.3221/igf-esis.57.19 262 this simple formula is sufficient to forecast the blast pressure as the positive phase is significant in determining the structural response. numerical values for these parameters can be obtained from various sources in respect to the required scaled distance, (z). figure 3: simplified blast wave overpressure profile. dynamic analysis (sdof) heoretical studies of the response of blast-loaded structures are sometimes difficult and highly intricate , so some simplified approaches are used for practical design objectives. fig. 4 shows how simple structures like slabs and beams can be simplified to an equivalent single degree of freedom (sdof) system that behaves similarly to the real element. the transformation factors are used to transform the analyzed structure to an equivalent sdof system. figure 4: beam idealized as sdof mass and spring system. deflection time history tab. 1 shows the transformation factors for converting a simply supported beam under uniform loads to an equivalent sdof system in accordance with ufc [4]. eqn. 4 can be used to measure the corresponding sdof elastic stiffness of a simply supported beam under a uniform load. range of behavior mass factor (km) load factor (kf) load-mass factor (kmf) elastic 0.5 0.64 0.78 plastic 0.33 0.5 0.66 average 0.42 0.57 0.72 table 1: transformation factors for a simply supported beam under uniform loads [4]. k= 3 384 ei 5l (4) as the r.c beam deflects in response to a dynamic load, it goes through several stages before coming to a rest. the stiffness of the beam varies significantly across the stages as shown in fig. 5. magnusson [17] defines state (1) as the elastic t m. t. nawar et alii, frattura ed integrità strutturale, 57 (2021) 259-280; doi: 10.3221/igf-esis.57.19 263 stage and state (2) as a cracked beam. according to ufc [4], an approximate formula of flexural stiffness is calculated as follows: ei = 0.5 ec 3 384 ei ( 5l +αηρbd3) (5) where αηρ is a factor that is affected by the configuration and amount of the reinforcement as well as the steel to concrete modulus of elasticity ratio [4]. figure5: schematic of the reduction in stiffness at an increasing cracking of the r.c beam with a modified stiffness [17]. the circular frequency and natural period of this equivalent sdof system can be obtained using the eqn. 6. the equation of motion of the undamped sdof system subjected to an applied force p(t) is represented by eqn. 7. t =   2 = 2π  . mfk m k (6) p(t) = (kmf. m) ÿ + kу (7) to consider the plastic deformations that occur after the structure's initial elastic response, fig. 6a shows how an elasticperfectly plastic resistance function can be used to simplify the element's resistance function. fig. 6b shows how a simple triangle pulse load can be used to approximate the air blast load on a structure with reasonable accuracy. (a) (b) figure 6: (a) simplified equivalent triangular load, (b) linear elastic-perfectly plastic resistance function of sdof system. as shown in fig. 6, by using the resistance functions and simplified load, the duhamel's integral can be used to solve eqn. 7, chopra [18]. thus, the following equations can represent the deflection time history of the sdof system up to the peak:  the elastic stage's response, (0 ≤ t ≤tel) is: m. t. nawar et alii, frattura ed integrità strutturale, 57 (2021) 259-280; doi: 10.3221/igf-esis.57.19 264 у = 1 p k (1-cos(ωt)) + 1 . d p k t (    sin t -1) (8)  the plastic range response up to the peak, (tel ≤ t ≤ tm) is: у = 1 6   mf d p m k t (t tel)3 +   11 1( 2   2   el mf d mf t pp r m k t m k ) (t tel)2 + ' ely (t tel)+уel (9) several diagrams for the maximum response of sdof systems exposed to different types of simple load functions have been developed for practical design purposes as presented in fig. 7. the peak response can be calculated, using the ratio (td/t) and the internal resistance to the applied load ratio (r1/p1). eqn. 10 calculates the ultimate static pressure load over a simply supported beam based on the ultimate moment capacity (mp). the ultimate moment capacity can be determined using the corresponding design code: qu = 2 8 pm bl (10) figure 7: max deflection of elasto-plastic, one-degree-of-freedom system for triangular load [4]. figure 8: the dynamic reactions for a simply supported beam. m. t. nawar et alii, frattura ed integrità strutturale, 57 (2021) 259-280; doi: 10.3221/igf-esis.57.19 265 dynamic reaction force the dynamic reaction forces are so important in shear design and can be estimated by taking into account the dynamic equilibrium of the real element. fig. 8 shows a simply supported r.c beam under a uniformly distributed dynamic load. the inertia of the beam with a uniformly distributed mass follows the same pattern as the assumed deflected form as follows: v(t) = xr r(t) + xp p(t) (11) numerical simulations he deflection capacity and the dynamic flexural toughness values of r.c beams under blast loading were evaluated, using a nonlinear explicit fe model. this research used an explicit dynamic analysis based on the central difference integration rule. the explicit analysis has a major advantage over the implicit one in terms of the absence of a global tangent stiffness matrix and convergence problems [19]. verification of fe model the fe model has been validated using the results of magnusson and hallgren's experimental investigation [3]. the results of the fe model were compared to the deflection and dynamic reaction force time histories during the verification process. it has been also important to see if the results obtained in the numerical analysis are the same as in the experiment. figs. 9 and 10 show the experimental setup of the shock tube test in addition to the geometry and reinforcement details of the tested r.c beam. a shock tube was used to create the air blast at (swedish defense research agency) foi´s testing ground in märsta, which simulates blast waves. an r.c beam was bolted and nutted to the supports to keep them in place during the tests. because of the bolts' low flexural strength, the beams were assumed to be simply supported. furthermore, the bolt holes near the beam ends were rectangular to allow for beam movement and rotation [3]. figure 9: experimental air blast test set up [3]. the material properties and reinforcement of the tested beam are summarized in tab. 2. the reinforcement ratio of stirrups and spacing has been configured to prevent the shear failure. the beam was loaded with a transient uniform pressure caused by the explosive charge as showed in fig. 9. tab. 3 contains a summary of the air blast test results. figures 10: geometry and reinforcement details of the tested beam. (a) plan; (b) elevation; (c) cross section [3]. t m. t. nawar et alii, frattura ed integrità strutturale, 57 (2021) 259-280; doi: 10.3221/igf-esis.57.19 266 beam type d (m) fc,cub (mpa) fsp (mpa) dmax (mm) fy (mpa) ρf (%) av/s (mm) s (m) s/d b40 0.13 53.8 4.6 25 604 2.5 0.54 0.2 1.5 table 2: material properties and reinforcement of tested beam. beam type q (kg) p (kpa) i (kpa) f tot,u (kn) ym (mm) b40-d4 2.5 1249 6.4 348 17.5 table 3: results of blast tests. approximation of pressure loads the pressure-time function of the air blast test was approximated with the linear piecewise pressure-time function. fig. 11 shows the pressure time history approximation obtained from the beam (b40-d4) test. the linear piecewise function fits the registered pressure curve well, whereas up to a period of about 10 ms, which is the point of time corresponding to maximum deflection. tab. 4 shows data for approximated linear piecewise pressure loads, while tab. 5 shows data for approximated triangular pressure loads for the beam (b40-d4) analysis. t (ms) 0 .07 1.97 2.87 4.77 5.42 7.47 8.17 9.47 15 20 25 p (kpa) 0 1170 610 710 410 500 250 380 210 100 45 0 table 4: approximated linear piecewise pressure. t (ms) 0 12 p (kpa) 870 0 table 5: triangular pressure. figures 11: piecewise linear approximation of the pressure time history of the tested beam. the r.c beams were modeled using abaqus/explicit version 6.14[19]. fig. 12 shows the model's geometry, stirrup configuration, longitudinal reinforcement, and boundary conditions. an 8-node solid element (c3d8) was used to mesh the concrete and plates. both stirrups and longitudinal reinforcement were discretized by a 2-node, three-dimensional truss element (t3d2). as shown in fig. 13, the whole model was discretized with a 12.5 by 12.5 mm uniform mesh. the element sizes were chosen to be small enough to achieve convergence in the results [20]. m. t. nawar et alii, frattura ed integrità strutturale, 57 (2021) 259-280; doi: 10.3221/igf-esis.57.19 267 figure 12: geometry of a modeled beam and applied boundary conditions. figure 13: meshing of r.c beam model. to simulate the concrete behavior of beams, the concrete damage plasticity (cdp) model was used according to abaqus theory manual 6.14 [19]. the cdp model is intended to analyze the overall behavior of concrete structures exposed to dynamic loads. the main failure mechanism of concrete is thought to be tension cracking and compression crushing. figs. 14 show the simulated response of concrete to uniaxial loading in tension and compression. a) stress-strain due to tension b) stress-strain due to compression figure 14: response of concrete to uniaxial loading. the material model cdp requires the different constants to be defined in all stages: the elasticity stage (modulus of elasticity and poisson's ratio), the plasticity stage (plasticity parameters, compressive behavior, tension behavior).as mentioned in the abaqus theory manual 6.14 [19] the definitions of other parameters can be outlined as follows: the dilation angle equals 30° in the present study; and ψ describes the performance of concrete under compound stress. the eccentricity is recommended to be assumed as 0.1, the ratio between tensile and compressive strength. the ratio between the strength in the biaxial state and that in the uniaxial state fb0/fc0 equals 1.16 as a default value according to abaqus user’s manual. k is equal to 2/3 as it is typical for concrete, the ratio of the distances between the hydrostatic axis and respectively the compression meridian and the tension meridian in the deviatoric cross section. the viscosity parameter equals 0 as a default value, and it indicates the relaxation time of the viscoplastic system. the reinforcement element was assumed to be an elastic perfectly plastic material. the interface between the reinforcement and the concrete was simulated by the embedded constraint. the embedded element was steel reinforcement, and the host element was concrete. tabs. 6 and 7 show the properties of the steel and concrete material used in the fe model respectively. the values in these tables are derived from material test results. tab. 7 shows the increased values due to the strain rate effect, which was calculated using malvar and crawford's equations [21]. figure 15 shows the input compressive stress-inelastic strain curves for concrete damage plasticity model (cdp). the scale of the time increment in the explicit dynamic analysis has a significant impact on the results. all analyses in the current simulations were carried out within a fixed time increment equal to ∆t = 10-8. the time increment was chosen to be small enough to ensure stability in the results. m. t. nawar et alii, frattura ed integrità strutturale, 57 (2021) 259-280; doi: 10.3221/igf-esis.57.19 268 mechanical properties longitudinal rein. stirrups elastic modulus (gpa) 210 205 poisson´s ratio 0.3 density (t/m3 ) 7.85 yield stress (mpa) 604 501 ultimate stress (mpa) 703 597 table 6: material properties of reinforcing steel for the fe model. mechanical properties static dynamic* elastic modulus (gpa) 34.5 46 poisson´s ratio 0.2 density (t/m3 ) 2.40 compressive cylinder strength (mpa) 44.5 56.5 tensile strength (mpa) 4.1 6.0 * strain rate ≈ 1 (1/sec) table 7: static and dynamic properties of concrete material for the fe model figure 15: input compressive stress-inelastic strain curves for concrete under different strain rates. verification results of the tested beam (b40-d4) the results were compared with the calculated deflection and dynamic reaction force time histories obtained from the experimental test to determine the fe model's confidence. as previously stated, due to the simplification of support modeling, the structure's response is only accurate up to the rebound stage. ductile failure occurred, and the steel reinforcement stress reached yielding stress first then the concrete crushes at the compression zone as illustrated by concrete compressive stress contours in fig. 16. fig. 17shows the concrete strain contours. m. t. nawar et alii, frattura ed integrità strutturale, 57 (2021) 259-280; doi: 10.3221/igf-esis.57.19 269 figure 16: concrete stress contours. figure 17: concrete strain contours. deflection time history fig. 18 shows the experiment's mid-span deflection time history, and the calibrated fe model in addition to the sdof calculation, up to the peak response. the fe model curve has good agreement with the experimental result. the peak values of deflection obtained from the analysis and experiment are shown in tab. 8. according to the findings, the fe model predicts the deflection response better than the sdof calculation. figure 18: mid span deflection time history of (b40-d4) beam m. t. nawar et alii, frattura ed integrità strutturale, 57 (2021) 259-280; doi: 10.3221/igf-esis.57.19 270 test ym (mm) tm (ms) sdof analysis 16.5 6.8 exp test 17.5 7.8 fe model 16.3 7.2 exp/fem 1.07 1.08 table 8: max.mid-span deflection and peak time. reaction force time history fig. 19 shows the time histories of dynamic reaction force obtained from the experiment and fe analysis. according to the findings, the trends of time histories have good agreement up to the rebound stage. the maximum reaction force and peak response time values obtained from fe analysis and experiments are shown in tab. 9. figure 19: dynamic reaction force time history of (b40-d4) beam. test dynamic reactions (kn) tm (ms) exp-test 348 3.5 fe-model 364 4.1 exp/fem 0.95 0.85 table 9: maximum dynamic reactions and peak time values. effect of blast loading on studied r.c beams n the present study, the finite element results using abaqus/explicit are used to investigate the behavior of tested r.c beams with and without smcs (10%ms+1%ns) in the presence of sfs with different volumetric fractions under blast loading. tab. 10 shows a summary of mechanical properties results of tested concrete mixtures obtained from previous experimental work conducted by authors [16]. fig. 20 shows stress-strain relationship curves for tested mixtures. i m. t. nawar et alii, frattura ed integrità strutturale, 57 (2021) 259-280; doi: 10.3221/igf-esis.57.19 271 b ea m n o . concrete mix compressive strength (fc’) (mpa) maxstrain modulus of elasticity (mpa) tensile strength (mpa) b1 scms0%+sfs0% 33.3 0.0031 28297 2.7 b2 scms0%+sfs1% 40.3 0.0041 30961 6.3 b3 scms0%+sfs2% 44.6 0.0052 33584 8.0 b4 ms10%+ns1%+sfs0% 48.9 0.0031 33220 4.2 b5 ms10%+ns1%+sfs1% 53.5 0.0045 35666 7.9 b6 ms10%+ns1%+sfs2% 57.3 0.0059 37540 9.3 table 10: test results of mechanical properties. figure 20: stress-strain relationship curves for tested mixtures. the dynamic mechanical properties of concrete material and steel reinforcement models used in the fe model were calculated according to us-army design approach ufc [4]. tab. 11 shows the values of difs for the far design range. type of stress reinforcement concrete yield ultimate bending 1.17 1.05 1.19 diagonal tension 1 --1 direct shear 1.1 1 1.1 bond 1.17 1.05 1 compression 1.1 --1.12 table 11: difs for the far design range of r.c members [4]. as shown in fig. 21, all beams were reinforced with two 10 mm diameter deformed reinforcements made of high-grade steel (st fy=400/fu=600), as a main reinforcement and with an 8 mm diameter non-deformed reinforcement made of mild steel (st fy=280/ fu=450) , as hooks hangers . hooks with a diameter of 8 mm were spaced at a distance of 150 mm from one another in the major bending plane. clear cover to reinforcement was maintained at 25 mm. m. t. nawar et alii, frattura ed integrità strutturale, 57 (2021) 259-280; doi: 10.3221/igf-esis.57.19 272 figure 21: typical beam reinforcement details. all r.c beams were exposed to the same air blast pressure as the verified r.c beam (b40-d4). the following results were obtained for each beam model:  max deflection at mid-span.  mode of failure.  flexural toughness (energy absorption). time-deflection relationship deflection was measured at mid-span of the tested beams. time-deflection curves were developed. figs. 22 show loaddeflection curves for tested beams, reflecting the effect of adding smcs and revealing the effect of the presence of steel fibers with different volume fraction content. figures 22: time-deflection curves for tested beams. modes of failure igs. 23 and 24 show the tensile stress s11 for reinforcement steel and compressive stress s33 results for the tested r.c beams obtained by a numerical simulation. figures show that ductile failure has occurred in all tested beams. the steel reinforcement stress reached yielding stress first then the concrete crushes at the compression zone after experiencing large deflections. figs. 25 show the failure shapes expected by strain contours and indicates how all beams suffer flexural deformations and bending failure. flexural toughness (energy absorption) a ductile structure can withstand much more energy (toughness) than a brittle structure of the same static strength. the area under the dynamic reactions-deflection curve (limited up to concrete reaching the maximum compressive stress) was taken into consideration as flexural toughness of tested beams as illustrated in figs. 26. tab. 12 shows the max deflection and flexural toughness results of tested beams. fig. 27 shows the percentage of increase in flexural toughness of tested beams under blast loading in comparison with the compared to reference beam (b1). f m. t. nawar et alii, frattura ed integrità strutturale, 57 (2021) 259-280; doi: 10.3221/igf-esis.57.19 273 figures 23: time-tensile stress (s11) curves for tested beams. figures 24: time-compressive stress (s33) curves for tested beams. m. t. nawar et alii, frattura ed integrità strutturale, 57 (2021) 259-280; doi: 10.3221/igf-esis.57.19 274 r.c (b1) r.c (b4) r.c (b2) r.c (b5) r.c (b3) r.c (b6) figures 25: mode of failure for tested beams. beam model concrete mix failure time (ms) max. deflection (mm) flexural toughness (joule) b1 scms0%+sfs0% 3.6 8.5 626.2 b2 scms0%+sfs1% 3.75 7.7 676.4 b3 scms0%+sfs2% 3.75 7.5 705.3 b4 ms10%+ns1%+sfs0% 4.2 9.3 720.3 b5 ms10%+ns1%+sfs1% 4.8 8.8 750.7 b6 ms10%+ns1%+sfs2% 6 8.2 774.0 table 12: flexural toughness results of tested beams. figures 26: dynamic reaction-deflection curves (limited) for tested beams. m. t. nawar et alii, frattura ed integrità strutturale, 57 (2021) 259-280; doi: 10.3221/igf-esis.57.19 275 figure 27: the increase in flexural toughness of r.c beams under blast loading. parametric study he finite element test program was further extended to investigate the impact of the tensile reinforcement ratio on the behavior of tested r.c beams under blast loading with and without smcs (10%ms+1%ns) in the presence of sfs with different volume fractions. three reinforcement ratios were selected. these ratios are 0.5% (using 2bars with diameter of 8 mm), 0.78% (using 2 bars with diameter of 10 mm), and 1.13% (using 2 bars with diameter of 12 mm). tab. 13 shows a summary of the calculated results for fe r.c beam models under blast loading. the following results were obtained for each beam model:  max deflection at mid-span.  flexural toughness values (energy absorption). beam model 𝝁 % max. deflection(mm) failure time (ms) flexural toughness (joule) failure mode b1 0.5 9.13 3.6 587 ductile failure 0.78 8.5 3.6 626.2 1.13 7.88 3.6 631.7 b2 0.5 8.03 3.75 627.4 ductile failure 0.78 7.7 3.75 676.4 1.13 7.08 3.75 649.1 b3 0.5 7.67 3.75 644.1 ductile failure 0.78 7.6 3.75 705.3 1.13 6.52 3.75 602 b4 0.5 10.7 4.2 693.88 ductile failure 0.78 9.35 4.2 720.3 1.13 8.08 4.2 673.1 b5 0.5 8.72 4.2 745.6 ductile failure 0.78 8.21 4.8 750.7 1.13 7.46 4.8 718 b6 0.5 8.39 4.2 773.5 ductile failure 0.78 8.22 6 774 1.13 7.25 4.8 755.6 table 13: finite element results for r.c beams models using different reinforcement ratios. t m. t. nawar et alii, frattura ed integrità strutturale, 57 (2021) 259-280; doi: 10.3221/igf-esis.57.19 276 steel reinforcement ratio (𝜇) effect on the time-deflection relationship of tested beams under blast loading for all tested r.c beams it can be noted that the maximum dynamic reaction capacity of beams increases when the amount of the steel reinforcement increases. in all cases, however, the higher amount of steel reinforcement reduces the deflection of beams. it is noted that concrete with high strength values, for the same reinforcement ratio, leads to an increase in the last beam deflection value and a decrease in the last dynamic reaction value. for the same concrete mixture, the mid-span deflection of the beam decreases as the steel reinforcement ratio increases. due to the increase of steel reinforcement ratio, the neutral axis’s depth increases and as a consequence, the moment of inertia ieffective will increase, producing a decrease in deflection of r.c beam as shown in figs. 28. by reducing the amount of longitudinal reinforcement, the ductility of r.c elements will significantly increase in general. figures 28: time-deflection curves for tested beam models using different reinforcement ratios steel reinforcement ratio (𝜇) effect on the flexural toughness results for tested beams under blast loading figs. 29 show the dynamic reaction-deflection relationship of tested r.c beams with different reinforcement ratios. flexural toughness results are obtained from the area under the dynamic reactions deflection curves. it can be observed, m. t. nawar et alii, frattura ed integrità strutturale, 57 (2021) 259-280; doi: 10.3221/igf-esis.57.19 277 in the figs. 29, that beams with ductile behavior carry a lower dynamic reaction force under same load value. fig. 30 shows the flexural toughness results for tested beams models under blast loading. figures 29: dynamic reaction-deflection curves for tested beam models using different reinforcement ratios. when the reinforcement ratio decreases from 0.78% to 0.5%, the results show an increase in the flexural toughness by 6.9% and 9.7% for reinforced concrete beams (b2) and (b3) in comparison with reference beam (b1), reflecting the effect of sfs with volume fractions 1% and 2% respectively. for r.c beams with smcs (10%ms+1%ns), the results show an increase in the flexural toughness by 18.2%, 27% and 31.8% respectively in comparison with (b1). fig. 31 illustrates the significant increase in the beam ductility within decreasing the tensile reinforcement ratio. m. t. nawar et alii, frattura ed integrità strutturale, 57 (2021) 259-280; doi: 10.3221/igf-esis.57.19 278 figure 30: flexural toughness values for tested beam models using different reinforcement ratios. figure 31: percentages of increase/decrease in flexural toughness when the reinforcement ratio decreases from 0.78% to 0.5%. for the reinforcement ratio of 0.78%, the results show an increase in the flexural toughness by 8% and 12.6% for reinforced concrete beams (b2) and (b3) in comparison with reference beam (b1), reflecting the effect of sfs with volume fractions 1% and 2% respectively. for r.c beams with smcs (10%ms+1%ns), the results show an increase in the flexural toughness by 15%, 19.9% and 23.6% respectively in comparison with (b1) as shown in fig. 32. it is observed that the percentage of increase in flexural toughness for reinforcement ratio 𝝁 0.78% is smaller than 𝝁 0.5% due to an increase in the moment of inertia (ieffective), leading to a decrease in the deflection of r.c beam and producing a smaller area under dynamic reactions-deflection curves as shown in figs. 29. figure 32: percentages of increase/decrease in flexural toughness with reinforcement ratio 0.78% m. t. nawar et alii, frattura ed integrità strutturale, 57 (2021) 259-280; doi: 10.3221/igf-esis.57.19 279 when the reinforcement ratio increases from 0.78% to 1.13%, the results show an increase in the flexural toughness by 2.8% and a decrease by 4.7% for reinforced concrete beams (b2) and (b3) in comparison with reference beam (b1), reflecting the effect of sfs with volume fractions 1% and 2% respectively as shown in fig. 33. due to the increase of the steel reinforcement ratio (𝜇) to be 1.13%, in the presence of sfs with 1% and 2% volume fractions which had a high modulus of rupture value on concrete according to the experimental flexural test on tested prisms [16], the neutral axis depth of cross section increases, leading to an increase in the moment of inertia ieffective and resulting in a reduction in the deflection and flexural toughness capacity of r.c beams as shown in figs. 29. figure 33: percentages of increase/decrease in flexural toughness of tested beams when the reinforcement ratio increased from 0.78% to 1.13%. r.c beams with smcs (10%ms+1%ns) showed an increase in the flexural toughness by 6.6%, 13.7% and 19.6% respectively in comparison with (b1). accordingly, smcs play an important role in enhancing the flexural toughness of tested beams due to their high compressive strength value in general. for the same steel reinforcement ratio (𝜇), the neutral axis depth decreases for concretes with high strength values. this behavior produces an increase in the last beam deflection, leading to an increase in the flexural toughness value of r.c beams. this behavior indicates that combining compressive and flexure characteristics of concrete in case of a high steel reinforcement ratio (𝜇) is necessary for reducing the brittle behavior of the r.c structure in general. conclusion ccording to the numerical analysis of tested r.c beams, the fe model effectively simulates the dynamic responses of displacement and dynamic reaction force time histories. the specific conclusions of the present study can be outlined as follows:  improvement in the flexural toughness of the reinforcement ratio 𝝁 0.78% is smaller than that of 𝝁 0.5% due to the increasing moment of inertia (ieffective). concretes with high strength values lead to an increase in the last beam deflection value, producing a considerable rise in the ductility and flexural toughness of the r.c element.  when the reinforcement ratio increases from 0.78% to 1.13%, in the presence of sfs with 0%, 1% and 2% volumetric fractions, the flexural toughness increases only by 2.8% and decreases by 4.7% respectively in comparison with reference beam. the results reflect the negative impact of the high modulus of rupture value of the steel fiber reinforced concrete, and the high ratio of steel reinforcement 𝝁 in r.c beams. by adding smcs (10%ms+1%ns), the flexural toughness increases by 6.6%, 13.7% and 19.6% respectively in comparison with the reference beam.  combination between the compressive and flexural characteristic of concrete is necessary in case of high steel reinforcement ratios to reduce the brittle behavior of the r.c structure element, especially when the r.c elements are exposed to a high strain rate loading due to the added value of (difs) for steel reinforcement’s mechanical properties, which make the element stiffer than usual. it is recommended to study the dynamic response of these concrete mixtures experimentally in future works to investigate the exact values of (difs) for concrete materials with scms in the presence of steel fibers in order to show the enhancement in the response of concrete under blast loads in comparison with the (difs) values mentioned in the a m. t. nawar et alii, frattura ed integrità strutturale, 57 (2021) 259-280; doi: 10.3221/igf-esis.57.19 280 unified facilities criteria ufc [4]. in addition, the plastic hardening of materials should be highly considered in the sdof calculations. this leads to a real improvement in the response of the element to the blast loads as a result of the enhancement in the ductility and flexural toughness of the r.c structural elements behavior. references [1] baker, w.e., cox, p.a., westine, p.s., kulesz, j.j., strehlow, r.a. (1983). explosion hazards and evaluation. amsterdam; elsevier. [2] biggs, j.m., (1964). introduction to structural dynamics, mcgraw-hill, new york. [3] magnusson, j., hallgren, m. (2000). high performance concrete beams subjected to shock waves from air blast, swedish defense research establishment (foa), report r--00-01586-311--se, tumba, sweden. [4] ufc 3-340-02unified facilities criteria (ufc) structures to resist the effects of accidental explosions, department of the defense, (2008), usa. [5] fkr, (2011). fortskydd. bilaga till fortifikationsverketskonstruktionsregler fkr, dnr 4535/2011, försvarsmakten. [6] khizab, b., sadeghi, a., hashemi, s., mehdizadeh, k., nasseri, h. (2020). investigation the performance of dual systems moment-resisting frame with steel plate shear wall subjected to blast loading. journal of structural and construction engineering. doi: 10.22065/jsce.2020.177510.1820. [7] ahmadi, h., kamran, m. and tafaroj, n. (2011). lightweight nano concrete. journal of technology and arts, construction engineering organization, gilan province, 52, pp. 8 -13. [8] sharaky, i. a., megahed, f. a., seleem, m. h. and badawy, a. m. (2019). the influence of silica fume, nano silica and mixing method on the strength and durability of concrete. sn applied sciences, 1(6). doi: 10.1007/s42452-019-0621-2. [9] barbhuiya, g. h., moiz, m. a., hasan, s. d. and zaheer, m. m. (2020). effects of the nanosilica addition on cement concrete: a review. materials today: proceedings, 32, pp. 560–566. doi: 10.1016/j.matpr.2020.02.143. [10] taher, m. j., hassan, m. s. and al-azawi, z. m. (2015). combined effect of silica fume and steel fiber on modulus of elasticity of high performance concrete. engineering and technology journal, 33(4 part (a) engineering), 868-876. [11] ghazy, a., bassuoni, m. t., maguire, e. and o’loan, m. (2016). properties of fiber-reinforced mortars incorporating nano-silica. fibers, 4(1), 6. doi: 10.3390/fib4010006. [12] fawzy, y. a. e. and metwally, k. a. (2017). impact of steel fiber or nano silica on properties of concrete containing various cement types. life science journal, 14(12). doi: 10.7537/marslsj141217.06. [13] hasan-nattaj, f. and nematzadeh, m. (2017). the effect of forta-ferro and steel fibers on mechanical properties of high-strength concrete with and without silica fume and nano-silica. construction and building materials, 137, pp. 557-572. doi: 10.1016/j.conbuildmat.2017.01.078. [14] sharma, r. and bansal, p. p. (2019). efficacy of supplementary cementitious material and hybrid fiber to develop the ultra-high-performance hybrid fiber reinforced concrete. advances in concrete construction, 8(1), pp. 21-31. doi: 10.12989/acc.2019.8.1.021. [15] murthy, a. r. and ganesh, p. (2019). effect of steel fibers and nano silica on fractions properties of medium strength concrete. advances in concrete construction, 7(3), pp. 143-150. doi: 10.12989/acc.2019.7.3.143. [16] eisa, a. s., shehab, h. k., el-awady, k. a. and nawar, m. t. (2021). improving the flexural toughness behavior of rc beams using micro/nano silica and steel fibers. advances in concrete construction, 11(1), pp. 45-58. doi: 10.12989/acc.2021.11.1.045. [17] magnusson, j. (2007). structural concrete elements subjected to air blast loading, licentiate thesis, royal institute of technology, division of concrete structures, stockholm, sweden. [18] chopra, a. k. (2007). dynamics of structures, 3rd edition. pearson education, inc. [19] abaqus 6.14, abaqus analysis user's guide, release 14.0 documentation, (2014). [20] zukas, j. a. and scheffler, d. r. (2000). practical aspects of numerical simulations of dynamic events: effects of meshing. international journal of impact engineering, 24(9), pp. 925–945. doi: 10.1016/s0734-743x(00)00012-9. [21] malvar, l.j., crawford, j.e., (1998). dynamic increase factors for concrete, department of defense explosives safety seminar (ddesb), orlando fl, usa. microsoft word numero_49_art_22_2485 n. burago et alii, frattura ed integrità strutturale, 49 (2019) 212-224; doi: 10.3221/igf-esis.49.22 212 focused on russian mechanics contributions for structural integrity algorithms for calculation damage processes nikolay g. burago ishlinsky institute for problems in mechanics of the ras, moscow, russia burago@ipmnet.ru, http://orcid.org/0000-0002-1806-9386 ilia s. nikitin, alexander d. nikitin, boris a. stratula institute of computer aided design of ras, moscow, russia i_nikitin@list.ru, http://orcid.org/0000-0003-3499-6910 nikitin_alex@bk.ru, http://orcid.org/0000-0002-2916-758x stratula@matway.net abstract. the paper reviews the existing approaches to calculating the destruction of solids. the main attention is paid to algorithms using a unified approach to the calculation of deformation both for nondestructive and for the destroyed states of the material. the thermodynamic derivation of constitutive relations for solids with elastic, viscous and plastic properties accounting possible destruction is presented. explicit and implicit non-matrix algorithms for calculating the evolution of deformation and fracture development are presented. implicit schemes are implemented using iterations of the conjugate gradient method, with the calculation of each iteration exactly coinciding with the calculation of the time step for two-layer explicit schemes. therefore the solution algorithms are very simple. the results of solving typical problems of destruction of solid deformable bodies for slow (quasistatic) and fast (dynamic) deformation processes are presented. recommendations are given for modeling the processes of destruction and ensuring the reliability of numerical solutions. keywords. fracture; damage; elasticity; plasticity; thermodynamics; softening; grid methods; through calculations. citation: burago, n.g., nikitin, i.s., nikitin, a.d., stratula, b.a., algorithms for calculation damage processes, frattura ed integrità strutturale, 49 (2019) 212-224. received: 15.04.2019 accepted: 22.05.2019 published: 01.07.2019 copyright: © 2019 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. introduction umerical computations for destruction processes have been conducted since computers and numerical algorithms appeared, i.e. more than 50 years. there are a lot of various approaches to obtain answers to such questions as which types of destruction processes are possible, when and where microdamages are going to originate, how long artificial and natural constructions can perform satisfying operational and safe conditions. in cases when a large margin of n http://www.gruppofrattura.it/va/49/2485.mp4 n. burago et alii, frattura ed integrità strutturale, 49 (2019) 212-224; doi: 10.3221/igf-esis.49.22 213 safety is required, for example in operation of buildings, it is enough to identify places with the highest possible stress levels and to take care that such stresses are several times smaller than the destructive ones for building materials. such recommendations are formulated in the so-called theories of strength in the theory of resistance of materials. the next level of studying the processes of destruction is the study of the distribution of individual cracks to predict the possibility and time to continue the safe operation of structures in cases where the mentioned defects have already been found. such problems are solved by analytical and numerical-analytical methods of brittle fracture mechanics [1]. throughout the history of the application of numerical methods in this direction a very large amount of research has been performed. it is to admit that even for a single crack, the formulation of its propagation conditions and taking into account conditions (possibly contact) on newly formed free surfaces during its development is a very difficult mathematical task, which is practically impossible to implement in the case of multiple cracks. the number of subdomains between cracks is catastrophically increasing and their location is unpredictable in advance. it seems that the way to get out of this difficulty for fracture mechanics as well as for gas dynamics with multiple shock waves is to use through calculation methods with trapping narrow zones of large solution gradients. it may be done using zones for deformations localization that simulate cracks in solids, shock wave zones and contact discontinuities in gas dynamics. for the first time, through calculation methods for fracture modeling were described in maenchen-sack’s paper half a century ago [2]. however, for a long time, the insufficient performance of computers did not make it possible to effectively use such methods of through calculations. now, when the performance of computers increased up by 3-4 orders of magnitude, the through calculation methods begin to dominate and allow not only to significantly expand the range of actual tasks to be solved but also to simplify the solution processes. maenchen and sack in their work considered the case in which material in an infinitely small volume was destroyed instantly when a certain criterion of destruction was fulfilled. the destruction was mathematically expressed in the replacement of the usual bond of stresses and strains in the framework of the theory of elasticity and plasticity by a bond describing the behavior of the destroyed material. in the principle axes of the stress tensor a new bond ensured the absence of resistance to tensile strength while maintaining the resistance to compression. it is important to notice that the solution algorithms, regardless of the loading rate beyond the yield point, are stepwise in time since the properties of materials depend on the loading history. in boundary value problems in the formulation of maenchen and sack, an important property of positive definiteness of the linearized operator of the problem is preserved for increments of the sought functions at each time step. here, the criterion of correctness of hadamard boundary value problems is satisfied [3]. this criterion ensures the existence, uniqueness and continuous dependence of the solution on the input data. unlike the maenchen-sack approach (brittle destruction), in reality materials lose the ability to resist deformation not instantaneously but gradually so there is a long stage of softening. in the case of softening, step-by-step operators for solving the problems of elastoplasticity in increments use explicitly or implicitly the so-called tangential modules of elasticity (stress derivatives by strain). when softening, the tangent modules of elasticity become negative. because of this at the time step the operators of the elastic-plasticity problems lose the property of positive definiteness, so the boundary problem becomes incorrect according to hadamard, the numerical solutions become physically meaningless and the calculation ends abnormally. in continuum mechanics this phenomenon is known as a violation of the material resistance criterion according to the drucker [4]. thus classical theories of elastoplasticity are not suitable for describing gradual softening. a way out of this difficulty was found in [5, 6] where the experimentally observed drop in stresses with increasing deformations was due to degradation (decrease) of elastic modules and yield strength due to an increase in the density of microcracks, called damage. this meant that the areas of weakening did not reflect the properties of the material in alternating stresses elastoplastic deformations, but were due to external causes (the growth of microdamages). so the use of negative tangent moduli of elasticity which violates the correctness of boundary value problems is not required. the introduction of damage allowed computing the processes of softening without violating the conditions of hadamard and drucker. to implement damage models in through calculation algorithms, the enhanced formulation of the constitutive relations for damage processes in deformable solids is required, that is suitable for describing the behavior of both the original intact and destroyed materials including the transition process of softening. variants of the such constitutive relations may be found in [5, 7 – 14]. in the problems of calculating the fatigue failure of structural elements along with the proposing of the multi-axial fracture criteria under cyclic loading (see the review [15]) also proposed models that take into account the damage accumulation process with an increase in the number of loading cycles [16]. for example the corresponding differential equations for the damage function are formulated in [17]. the accuracy of through calculation methods for damage modeling may be significantly improved by the use of adaptive movable computational grids in order to minimize approximation errors in areas of large gradients of solutions (reviews and descriptions are in [18 – 20]). n. burago et alii, frattura ed integrità strutturale, 49 (2019) 212-224; doi: 10.3221/igf-esis.49.22 214 in this paper we consider the above components of the formulation and numerical solution of problems on the destruction of solids, show how to implement the corresponding algorithms and give examples of solutions to typical problems on the destruction of solids. statement of a general problem he system of equations describing the behavior of a thermoelastoplastic damageable medium is used here in the variant described in [9]. the system of equations contains the laws of conservation of mass, momentum and energy, as well as the kinematic relations: 1 0 1 0 0 0 1 1 ( ) ( ) 2 2 , t t t d d du r dt dt dt d d dt dt                                            u e i e q f x ε i f f e l l ε x e ε l l ε l u u (1) and also the constitutive relations that deserve a more detailed consideration given below. the following traditional notation is used:  is density, u is a velocity, t is a time, x is an euler radius vector (actual configuration), 0x is a lagrangian radius vector (initial configuration), f is a deformation gradient, l is a velocity gradient, ε is an almansi strain tensor, e is an eulerian strain rate tensor, σ is a cauchy stress tensor, u is an internal energy per mass unit, q is a heat flux vector, t is a temperature, r is a mass heat source, /d dt is a material time derivative,  is a spatial differentiation operator in the current configuration and i is a unit tensor. constitutive equations represent the relations between the characteristics of the state of an infinitely small volume of material, imposed by the laws of thermodynamics. let’s arrange a minimal set of mutually independent state parameters of an infinitely small volume of the continuum: 0 0 0 0 ddtt t dt dt       χ ε χ e , where 0( )p  χ ε are structural parameters namely 0pε is a plastic strain tensor and  is a damage and is defined further. they change the internal structure of the continuum, so they are responsible for the development of dislocations and microcracks. marked with zeros are material tensors associated with spatial tensors by the ratios 0 0 0 1 t t t           ε f ε f e f e f σ f σ f the law of entropy increasing  from the first law of thermodynamics, which asserts the law of conservation of energy, and the second law of thermodynamics 0 d r dt t t           q whence the inequality of dissipation rate is 0 0 0 ,0 0 0t dt t d t dt t                                 σ e χ q ε χ here u t   is free energy per mass unit. free energy and dissipation rate are t n. burago et alii, frattura ed integrità strutturale, 49 (2019) 212-224; doi: 10.3221/igf-esis.49.22 215   2 0 0 0 ( )) ( ) ( ) 2 p p tk ln t t                    ε ε ε ε 2 ( ) ( ) q p p p p kd d h k h k t t dt t                   e e where h is the heaviside's function. it is assumed that the elastic components of the strain deviator are small compared to unity. the effect of thermal expansion is taken into account by a member with a coefficient  . the component of the dissipation rate, which is responsible for the plastic flow, is assumed to be a homogeneous function of the first order of the rate of plastic deformation, which corresponds to the case of an elastoplastic medium. plastic deformation increases when active loading condition 0 0( ) 0p pt      ε ε e is satisfied. it is also assumed that the material is plastically incompressible i.e. the dissipation rate depends only on the plastic strain rate deviator, which is usually well performed for metals. the resistence of the medium is represented by the modules of elasticity and yield strength. in addition to temperature, deformation and plastic deformation it also depends on the additional structural parameter of the state  . this parameter is called damage. following relations utilize the damage parameter: 0 ( )g   , 0 ( )kk k g  , 0 ( )p p pk k g  , where 0 and 0k are elastic modules and 0pk is a yield strength for intact material. the functions g , kg and pg are decreasing from 1 to 0 while   . they provide a decrease in the resistance of the medium with an increase in the damage that occurs when the condition of destruction 0 0( ) 0pt      ε ε e is fulfilled. the kinetics of the destruction process is determined by the dependence of the dissipation rate on the growth rate of damage. non-negative functions 0 , 0k , 0pk , k and qk depend on 0t ε and 0pε . so the constitutive relations take the following form: 0 0 0 1 2 ( ) ( ) ( ) ( ) q p p p p p p u t k t p t t p k ln t t d h k h k dt                                                               q σ i σ σ ε ε e e e (2) boundary conditions are 0 0 ( ) 0 0 ( ) 0 0 ( ) un n un n u u t t n s t u s \ s t p s t u s \ s t p s t t t s \ s t q                                                    x u n x σ n n x u x σ n x x q n (3) where 1, 2  . initial conditions are 0 0 00 0 0px v t t t             x x u u ε (4) thus it is required to solve the initial-boundary problem for the system of equations (1), (2) with the boundary (3) and initial (4) conditions. n. burago et alii, frattura ed integrità strutturale, 49 (2019) 212-224; doi: 10.3221/igf-esis.49.22 216 appendix to section 2 the purpose of this appendix is to clarify the meaning of the introduction of the damage parameter. let us consider the system of equations of the prandtl-reuss classical nonlinear elastic-plastic model: / : ( )pd dt     u σ σ e ε ε 0( ( )) /s d dt     ε x x x u / ( ) : ( ) 0p p p pd dt h     pε λ σ ε ε where ( ) ( ) 2ts   a a a is a symmetrization operator. for increments of stresses and strains at a time step the following relations take place :t  σ e ε where fourth order tensor te depends on full and plastic deformations as well as on the loading mode (active or unloading). let’s rewrite the stress increments in the following form : ( )t s    σ e x for velocities at each time step we have the following equation / ( : ( ) )sd dt t      tu σ e u the correctness of this equation is determined either by the hadamard condition 0te   σ or by its physical equivalent known as drucker condition 0t t  σ ε destruction is accompanied by weakening 0te  and leads in the framework of the considered classical theory to the loss of correctness of the problem (unlimited exponential increase in speed, loss of continuous dependence of the solution on the input data, instability). let’s consider the phenomenon of destruction using the following one-dimensional problem of tensile rod. rod’s material is elastic with young’s modulus e . let’s assume that there is a small area of weakened resistance (“fracture zone”) with a small young's modulus 1e e in the middle of the rod. it may be shown by an elementary solution that there is a surge of deformations in the “fracture zone” (fig. 1a) and the displacements (and velocities) change almost by jump (fig. 1b). the question arises about possibility to construct a physically and mathematically correct model of an elastoplastic material that describes the appearance of zones of reduced material resistance similar to the “fracture zone” from the considered model elastic problem. the affirmative answer is obtained from the theories of damage [5, 6]. indeed, with the introduction of the additional soughtfor damage parameter  the system of elastoplasticity equations takes the following form: / ( ) : ( )pd dt e     u σ σ ε ε n. burago et alii, frattura ed integrità strutturale, 49 (2019) 212-224; doi: 10.3221/igf-esis.49.22 217 0( ( )) /s d dt     ε x x x u / ( ) : ( ) 0p p p p pd dt h       pε λ σ ε ε / ( ) ( ) 0 ( )p pd dt h                 ε ε ε ε where h is the heaviside's function. for increments of stress at the time step we get: : ( ) ( ) : ( ) 0p p            σ e ε ε e ε ε e e a) b) figure 1: an exact solution for a stretchable rod with a weakened central part: qualitative graphs of the distribution of deformation (a) and displacement (b) along the rod. the drop in stresses regardless of the change in strain is provided by the second term in the above expression for stress increments. the coefficient 0e  is negative, which reflects the fact that the modules of elasticity ( ) 0e   and stress decrease with increasing damage. fig. 2 may serve as illustration of this process. the positivity of the elastic modulus ensures the fulfillment of the necessary conditions for the correctness of the initial-boundary problems according to hadamard and drucker. it should be noted that, together with the elastic moduli, the yield strength also decreases with increasing damage. the left-hand image in fig. 2 shows the experimentally observed dependence in stress-strain variables. the right-hand image in fig. 2 shows the same process in the extended stress-strain-damage coordinates. one may see that for any fixed value of damage, there are no areas of weakening in the stress-strain diagrams. figure 2: the effect of damage on the deformation diagrams. in the theory of damage the responsibility for softening is no longer on the condition of plasticity but is on the equation of damage. мore of that the damage may take place independently of plastic deformation the softening or, more generally, the destruction is considered as the loss of the ability of the material to resist elastic deformation, expressed in a decrease in the values of elastic modules and yield strength due to breaking of elastic bonds or, equivalently, due to an increase in the n. burago et alii, frattura ed integrità strutturale, 49 (2019) 212-224; doi: 10.3221/igf-esis.49.22 218 number of microcracks per unit volume. destruction is described as a process independent of deformation (exactly independent). therefore, the fracture characteristic called the damage parameter is related to deformation, temperature, and other state parameters only to the extent that they all participate in the general system of equations and initial-boundary conditions of thermomechanics. in fact, the destruction can happen without any deformation at all, for example due to chemical reactions or laser radiation and other external influences of a non-mechanical nature. it is important to note that the areas of weakening of experimental diagrams of material deformation cannot be used to determine the properties of elastoplastic materials since in these areas the deformation processes are controlled by increasing damage through the change of elasticity coefficients of the material and yield strength. the formulation of theories and reasoning were deliberately simplified in this commentary. in particular, temperature, hardening parameters and hardening dependence on strain rate were not considered; members related to large deformations were neglected. the goal was to more clearly describe the basic idea of damage theories. it has to be noticed that these simplifications are not used further as the basis for our numerical calculations. for describing the elastic properties of material the simplified form of hooke's law is used, obtained under the assumption of the initial isotropy of the properties of the material: ( ) : 2 ( )p p         i i where the stiffness constants of lame and the yield point, which determines the boundaries of the elastic behavior of material, depend on damage as follows: 1000 0e    , 10000e    , 10000p p e    . values for the intact material are marked by index "0". we assume that the damage grows if the maximum principal deformation reaches the positive critical value. so the maximum principal deformation should be a tensile deformation. destruction condition takes the form:  1/22 21 ( ) ( ) 4 0 2 d x y x y xy df m                where the dimensionless scale factor is introduced max min max min min( , ) max[( ),( )] x yh h m x x y y    it represents the well known feature, inherent in the concentration of deformations in the tip of crack in the elastic material, which makes it possible to treat this local criterion as the approximation of the usual criterion of destroying the mechanics of brittle failure using of the coefficients of stress-strain concentration. the criterion of destruction with the scale factor ensures the convergence of the numerical values of the integral critical loads of destruction under the mesh refinement. otherwise since the concentration of deformations is described increasingly better on the finer grid, the critical deformation of destruction is reached increasingly earlier, with the smaller values of the applied load, that tends to zero with grid refinement. certainly, calculated critical loads depend on grid permission, but this dependence must demonstrate the convergence of calculated critical loads to a certain nonzero limiting value. such behavior of nymerical model ensures the introduced above scale factor. the introduction of such coefficient is not the final solution of the problem of the convergence of the calculated critical loads of destruction, but it is possible that this is step to the side of the possible solution of described problem. it can be, someone will devise the best regularization of the criterion of destruction. under the conditions of the absence of the information about the kinetics of damage, we accept the kinetic equation for the damage in the simplest form: 1000 ( )t dh f  where h is the heaviside's function. large magnitude coefficient in the right side is introduced for guaranteeing the rapid growth of damage in order to provide the lost of material resistance for several temporal steps. this makes it possible to n. burago et alii, frattura ed integrità strutturale, 49 (2019) 212-224; doi: 10.3221/igf-esis.49.22 219 consider mathematical model of damage used here as regularized and, simultaneously, the simplified version of maenchensack model [2], in whom the stress-strained state due to the destruction is corrected instantly by jump. the instantaneous correction of stresses leads to the appearance in the numerical solution of the nonphysical oscillations and requires smoothing of sought functions is required. numerical method he solution algorithm is based on the modification of an implicit finite element scheme built in [20] and implemented as part of the astra application package. the main features of the algorithm are as follows. the initial equations of the problem including the constitutive and kinematic differential relations are applied in the integral variational form of bubnov – galerkin. a simple piecewise linear finite element approximation is introduced by spatial variables on a moving grid containing triangular and quadrilateral cells in the two-dimensional geometry and tetrahedra, prisms and parallelepipeds in three-dimensional geometry. piecewise linear approximation is applied to all desired functions, including displacements, velocities, temperature, heat fluxes, deformations, plastic deformations, stresses, hardening parameters and damage, the discrete values of which are represented by nodal values. the set of basic functions contains displacement, velocity, temperature, plastic deformation and damage parameter. the rest of unknowns can be determined by basic functions using spacial differentiation and non-differential relations. numerical integration points are located at the nodes of the grid, so the mass matrix is diagonal. at each time step the nonlinear terms of the equations are linearized by the newton method with respect to small increments of the basic functions. to solve auxiliary linearized problems iterative method of conjugate gradients is used. it is implemented without matrix operations and working on each iteration as an explicit two-layer central-difference scheme. as the time step decreases, the number of iterations of the conjugate gradient method for solving linearized equations decreases (due to better initial approximation) and for time steps within the courant constraint the implicit scheme works asymptotically as fast as usual explicit schemes. under the least successful initial approximation no more than n iterations are required to determine the solution, where n is the number of unknowns. since physical splitting is applied, the velocities, temperature, plastic deformation, damage and coordinates of the moving grid nodes are determined in turn and the number of discrete variables is not too large. the time step is chosen in implicit schemes from the accuracy conditions in order either to limit the maximum deformation increment to about one tenth of the deformation corresponding to the yield strength or, for elastic materials, to a value much less than one. in explicit schemes the usual stability conditions are applied for the cases of hyperbolic and parabolic equations. for preconditioning of the algebraic problems (multiplication of the system of equations by an approximate inverse matrix) diagonal approximations of stiffness matrices are used that corresponds to scaling of unknowns. this is quite enough to ensure the stability of conjugate gradients iterations, even if penalty terms are used to account contact or incompressibility conditions. the conditions of approximation, stability, and convergence of numerical solutions are justified on the level of simplified model equations. therefore, even a stable numerical solution may contain unwanted non-physical oscillations. the wavelength and period of such oscillations coincides with the length of the steps of the computational grid in space and time. a large number of various approaches are known to eliminate such disturbances. usually the introduction of explicit or scheme viscosities makes the solution monotonous. for problems of destruction such smoothing methods should be introduced very carefully, because the physical phenomenon of destruction is very sensitive to small disturbances. too coarse smoothing procedure (such as averaging in the lax method) or, conversely, its absence can strongly distort the solution. localization of deformations does not take place if the non-physical viscosity of the scheme is large, or, conversely, the location of the fracture zones will be strongly and obviously dependent on the grid steps in time and space if the smoothing is insufficient. in the present work, the following method of monotonizing numerical solutions is recommended and utilized. at the end of each time step the function f that is to be monotonized is twice differentiated in each of the spatial independent variables. smoothing process is performed in a coordinate-wise manner although the grid may contain cells with arbitrarily spaced edges. when using a piecewise linear approximation, the values of the second derivatives xxf are calculated as generalized solution from the variational equation: ( ) 0xxxx xx v ff f f dv x x        t n. burago et alii, frattura ed integrità strutturale, 49 (2019) 212-224; doi: 10.3221/igf-esis.49.22 220 since it is assumed that at the boundary points the first or second derivatives are negligible, in the equation for the second derivatives the integrals over the boundary of the solution domain are rejected. then for each node of the grid the averaged value f of the monotonized function is calculated. this value also depends on the coordinate direction (to put it simply, it is the average of the function values at points of intersection of the border of the neighborhood of a node with a given coordinate line). finally the old values f are substituted with new ones ( ) 2f f  only in those few grid nodes (points of non-monotonicity) in which the second derivative xxf changes the sign at the nodes of one edge. we want to emphasize an important fact that the old value is not replaced by the average, as in the lax method, but is shifted only at half towards the average value. unlike most other methods the described monotonization procedure does not work in all grid nodes, but changes the solution only at non-monotonic points. acting more selectively it can even turn an unstable scheme into a stable and converging to the right solution one. it well regularizes standard two-layer central-difference explicit schemes not only for problems of the dynamics of solid deformable bodies, but also for problems of euler mechanics of fluid and gas. of course, when constructing such schemes, the elementary requirements for the description of dissipative processes at jumps must be taken into account i.e. destabilizing terms with negative viscosity coefficients found in the first differential approximations of such difference schemes must be balanced by adequate artificial viscosity. in this case this method of monotonization works fine as a supplementary one. here the monotonization procedure is used in conjunction with an implicit scheme as a control of the monotony of the solution. the procedure does nothing if the solution is monotonous but immediately eliminates any non-physical oscillations if they occur. it should be mentioned that described monotonization procedure is not conservative. that is why additional conservation control and correction procedure is desirable. results elow we examine the task about the development of the zones of destruction in the stretchable flat square plates with the round and elliptical macro-pores or rigid inclusions. the two-dimensional spatial domain can be seen in fig. 3-5. we use the grid of triangular finite elements is usual almost uniform grid, generated automatically. on the vertical boundaries of the square region of the solution horizontal displacements is relied by equal to zero. lower boundary has zero vertical displacement. upper boundary slowly moves up (with the speed that is much less than speed of sound in the material) and provides quasi-static extension of the body in question. shearing stresses on the boundaries are relied by equal to zero. on the surface of the macro-pore external forces are absent. rigid inclusions are filled with the absolutely rigid material, completely coupled with the material of the body in question. finite elements in region of rigid inclusions have huge values of the elastic moduli and yield point (100 times more than for the plate material). calculated diagrams of deformation depict the dependence of the stress averaged over the upper horizontal section on the monotonically increasing assigned vertical displacement of upper boundary. in the dimensionless coordinates in the solution domain are: 6.0 6.0x   и 6.0 6.0y   , the diameter of circular pore and rigid inclusion is equal to 1.0, the semiaxes ratio of elliptical pores and inclusion is equal to 0.5, angle of rotation is equal 30 . young's modulus is equal to 1000, poisson ratio is equal to 0.2, the speed of sound is equal to 1.0, the speed of the motion of upper boundary yv grows from zero for 0t  to the value 0.001 for 510t  . in the calculations according to the model of ideally-plastic material the yield point is equal to one. the deformation of destruction is equal to 0.02. the results for the elastic plate with the circular rigid inclusion are shown in figure 3. black narrow zones correspond to the developing macrofissures, darkening answers the amount of maximum principal deformation. right graph depicts the calculated diagram of deformation. the case with one circular pore is demonstrated in figure 4. a difference in the pictures of destruction for inclusion and pore is explained by the different nature of the concentration of deformations near the pore and near the rigid inclusion (fig. 5). in the case of the pore the destruction begins from the points in the horizontal direction outermost from the center of the pore, and for the rigid inclusion destruction earlier begins at the points in the vertical direction outermost from the center of inclusion. solution for the elliptical pore, oriented at the angle, in the elastic-plastic material it is shown in figure 6, where are depicted the zone of destruction (a), the calculated diagram of deformation (b), the distribution of plastic work and vertical b n. burago et alii, frattura ed integrità strutturale, 49 (2019) 212-224; doi: 10.3221/igf-esis.49.22 221 displacement. the splash of the values of plastic work in the zone of destruction and an jump like change of the displacement is distinctly visible. a) b) figure 3: circular rigid inclusion in the elastic material: the zone of destruction and the distribution of the maximum principal deformations of (a) and the calculated diagram of deformation (b). a) b) figure 4: destruction of elastic material with the presence of the circular pore: the zone of destruction and the distribution of the stress y (a); calculated stress-strain diagram (b). a) b) figure 5: maximum principal deformations near the pore (a) and the rigid inclusion (b) in the elastic material n. burago et alii, frattura ed integrità strutturale, 49 (2019) 212-224; doi: 10.3221/igf-esis.49.22 222 a) b) c) d) figure 6: destruction of ideal elastic-plastic material with the presence of one large oval pore: the zone of destruction (a); the calculated diagram of deformation (b); the distribution of plastic work (c); vertical displacement (d) in figures 7 and 8 the zones of destruction and the calculated diagrams of deformation for the idealelastic-plastic models with the large and small elliptical pores are compared. result is obvious: with an equal quantity of pores the sample with small pores has greater strength. a) b) figure 7: destruction of ideal-elasticplastic material with the group of the large oval pores, oriented at the angle 30o , in the absence the horizontal displacements of the lateral boundaries: the zone of destruction (a); the calculated diagram of deformation (b). in the parametric analyses the influence of the characteristics of discreteness is investigated. depending on the size of timespatial steps and on the form of mesh the local picture of destruction is different in details. however, the integral averaged characteristics of process (represented by diagrams of the deformation) are practically the same. n. burago et alii, frattura ed integrità strutturale, 49 (2019) 212-224; doi: 10.3221/igf-esis.49.22 223 below we present results for cracking of massif near drill-hole. the continuum model of stochastically inhomogeneous rock massif destruction was implemented for modeling the formation and development of fractal fracture structures in the vicinity of a cylindrical hole under the excessive internal hydrostatic pressure (fig. 9). a) b) figure 8: destruction of ideal-elastic-plastic material with the group of the small oval pores, oriented at the angle 30o , in the absence the horizontal displacements of the lateral boundaries: the zone of destruction (a); the calculated diagram of deformation (b). a) b) figure 9: formation and development of fractal fracture structures in the vicinity of a cylindrical drill-hole under the excessive internal hydrostatic pressure. the range of random strength limit values 5% (a), and 20% (b) the criterion of fracture based on the limit values of principal deformation is used. the stochastic heterogeneity of the strength properties of the massif was provided by an artificially limited spread of the values of the parameters of the damage criterion using a random number generator. stochasticity ensures the formation and development of multiple zones of fracture, forming fractal structures. the introduction of the initial spread of the strength properties of the medium is quite capable of reproducing the cracking of rocks with the formation of fractal fracture structures. with the same loading programs, the damage patterns are quite different due to difference in the level of stochasticity of the strength properties (fig. 9-a, b). conclusions umerical experiments have shown that fracture criteria for ultimate deformations for elastoplastic materials work better than criteria for ultimate stresses. the following properties of the theoretical model also play an important role to obtain localization zones in the form of narrow crack-like bands:  an abrupt decrease in material’s resistance with increasing damage;  the accuracy of calculation controlled by increments of deformations;  accounting for inertia forces (natural regularization of the problem); n n. burago et alii, frattura ed integrità strutturale, 49 (2019) 212-224; doi: 10.3221/igf-esis.49.22 224  minimum smoothing (especially in areas of destruction);  resistance of the fractured material to compression (to ensure the nondegeneracy of the law of motion). due to the above properties, the usual model of a damaged elastoplastic medium describes well the sharp localization of deformations along thin bands of large gradients of displacements and deformation and supports the convergence of the solution in the process of developing narrow fracture zones. the issues of bringing the model of a damaged elastoplastic medium in accordance with the data of physical experiments remain open and relevant. by using astra application package as it was done here one is able to confidently carry out such calculations. the number of calculated examples, as well as the degree of detail of the description of the results can be easily increased. acknowledgments he work was supported by rsf, grant № 19-19-00705. references [1] cherepanov, g.p. (1979). mechanics of brittle fracture, new york, mcgraw hill. [2] maenchen, g., sack, s. (1964). the tensor code, in: methods in computational physics, v.3, fundamental methods in hydrodynamics, new york, academic press. [3] hadamard, j. (1902). sur les problèmes aux dérivées partielles et leur signification physique, princeton university bulletin, pp. 49-52. [4] drucker, d.c. (1964). on the postulate of stability of material in the mechanics of continua, mekhanika. period. sbornik perevodov inostr. statei, 3, pp. 115-128. [5] kachanov, l.m. (1986). introduction to continuum damage mechanics, kluwer, acad. publ. [6] rabotnov, yu. n. (1959). mekhanizm dlitelnogo razrusheniya, sbornik “voprosy prochnosti materialov i konstruktsii”, pp. 5-7. [7] lemaitre, j. (1996). a course on damage mechanics, 2nd ed., berlin, heidelberg, new york, springer. [8] fomin, v.m., gulidov, a.i., sapozhnikov, g.a. et al. (1999). vysokoskorostnoe vzaimodeistvie tel, novosibirsk, izdatelstvo so ran. [9] burago, n.g., glushko a.i., kovshov a.n. (2000). termodinamicheskii metod polucheniya opredelyayuschih uravnenii dlya modelei sploshnykh sred, izvestiya ran. mekhanika tverdogo tela, 6, pp. 4-15. [10] bazant, z.p. (2002). reminiscences on four decades of struggle and progress in softening damage and size effect, concr. j. (japan concr. inst.), 40, pp. 16-28. [11] kondauro,v v.i., fortov, v.e. (2002). osnovy termodinamiki kondensirovannoi sredy, moscow, mfti. [12] krajcinovic, d. (1996). damage mechanics, amsterdam, elsevier science. [13] oliver, j. (1999). continuum modeling of strong discontinuities in solid mechanics using damage models, comput. mech., 17, pp. 49-61. [14] voyiadjis, g.z., kattan, p.i. (1999) advances in damage mechanics: metals and metal matrix composites, amsterdam, elsevier. [15] burago, n.g., zhuravlev, a.b., nikitin i.s. (2011). models of multiaxial fatigue fracture and service life estimation of structural elements, mechanics of solids, 46, pp. 828-838. [16] lemaitre, j., desmorat, r. (2005). engineering damage mechanics, berlin, heidelberg, springer. [17] marmi, a.k., habraken, a.m., duchene, l. (2009). multiaxial fatigue damage modeling at macro scale of ti6al4v alloy, int. j. of fatigue, 31, pp. 2031-2040. [18] ortiz, m., quigly, j.j. (1991). adaptive mesh refinement in strain localization problems, comput. meth. appl. mech. engng., 90, pp. 781-804. [19] liseikin, v.d. (2010). grid generation methods, springer. [20] burago, n.g., nikitin, i.s., yakushev, v.l. (2016). hybrid numerical method for unsteady problems of continuum mechanics using arbitrary moving adaptive overlap grids, computational mathematics and mathematical physics, 56, pp. 1064-1074. t << /ascii85encodepages false /allowtransparency false /autopositionepsfiles true /autorotatepages /none /binding /left /calgrayprofile (dot gain 20%) /calrgbprofile (srgb iec61966-2.1) /calcmykprofile (u.s. web coated \050swop\051 v2) /srgbprofile (srgb iec61966-2.1) /cannotembedfontpolicy /error /compatibilitylevel 1.4 /compressobjects /tags /compresspages true /convertimagestoindexed true /passthroughjpegimages true /createjobticket false /defaultrenderingintent /default /detectblends true /detectcurves 0.0000 /colorconversionstrategy /cmyk /dothumbnails false /embedallfonts true /embedopentype false /parseiccprofilesincomments true /embedjoboptions true /dscreportinglevel 0 /emitdscwarnings false /endpage -1 /imagememory 1048576 /lockdistillerparams false /maxsubsetpct 100 /optimize true 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/hrv (za stvaranje adobe pdf dokumenata najpogodnijih za visokokvalitetni ispis prije tiskanja koristite ove postavke. stvoreni pdf dokumenti mogu se otvoriti acrobat i adobe reader 5.0 i kasnijim verzijama.) /hun 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/pdfxoutputintentprofileselector /documentcmyk /preserveediting true /untaggedcmykhandling /leaveuntagged /untaggedrgbhandling /usedocumentprofile /usedocumentbleed false >> ] >> setdistillerparams << /hwresolution [2400 2400] /pagesize [612.000 792.000] >> setpagedevice microsoft word numero_56_art_04_3002 d. pilone et alii, frattura ed integrità strutturale, 56 (2021) 56-64; doi: 10.3221/igf-esis.56.04 56 haynes 242 alloy for lares 2 satellite d. pilone, a. brotzu, f. felli dicma, sapienza università di roma, via eudossiana 18, 00184 roma, italy daniela.pilone@uniroma1.it, andrea.brotzu@uniroma1.it, ferdinando.felli@uniroma1.it i. ciufolini dipartimento di ingegneria dell’innovazione, università del salento, via per monteroni, 73100 lecce, italy ignazio.ciufolini@gmail.com b. negri agenzia spaziale italiana, italy barbara.negri@asi.it c. paris centro ricerche enrico fermi, via panisperna 89/a, 00184 roma, italy claudio.paris@cref.it abstract. the satellite lares 2 is designed to test dragging of inertial frames, or frame-dragging, predicted by einstein’s theory of general relativity, with accuracy of a few parts in a thousand. for this purpose, besides the typical requirements for a space construction, a high density alloy must be used. in this paper are reported the studies performed on a nickel alloy, the haynes 242, that is considered a possible candidate for manufacturing all the metallic parts of lares 2 and other passive geodetic satellites. haynes 242 density and mechanical properties are compliant with the requirements of the mission. three different casting with the nominal composition of the alloy have been prepared and tested along with a commercial bar of haynes 242. the results of tensile and hardness tests on several specimens with different aging time are reported, along with the relevant metallographic analysis. furthermore, a test on the machinability, performed on a screw, which is the most demanding item from the manufacturing point of view, is reported. keywords. haynes 242; lares 2; mechanical properties; passive satellite. citation: pilone, d., brotsu, a., felli, f., ciufolini, i., negri. b., paris, c., haynes 242 alloy for lares 2 satellite, frattura ed integrità strutturale, 56 (2021) 56-64. received: 08.01.2021 accepted: 07.02.2021 published: 01.04.2021 copyright: © 2021 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. introduction ares 2 is a satellite of the italian space agency (asi), designed to test the dragging of inertial frames [1], or framedragging, an intriguing phenomenon predicted by einstein’s theory of general relativity, with accuracy of a few parts in a thousand [2]. frame-dragging has important implications in high energy astrophysics, the physics of black l https://youtu.be/magbl8ln7oo d. pilone et alii, frattura ed integrità strutturale, 56 (2021) 56-64; doi: 10.3221/igf-esis.56.04 57 holes and gravitational waves detection. the satellite will also contribute to space geodesy and global climate monitoring similarly to what has been done with lares satellite [3]. the main body of the satellite is made of one single piece of bulk metal. this type of design has been experimented the first time with lares satellite [4]. the single piece design was chosen to reduce thermal gradients on the satellite and consequently the thermal thrust, a small but not negligible perturbation [5]. the satellite is completely passive, and it behaves as a test particle in the gravitational field of the earth. it is covered with cube corner reflectors (ccrs) that reflect the laser pulses sent from the network of ground stations of the international laser ranging service (ilrs). the ccrs used for lares 2 are smaller than the ones used for lares and are commercial off the shelf (cots). by reconstructing its orbit with the laser ranging technique [6] it is possible to reach accuracies at the centimeter level or less. the lares 2 mission has been designed aiming to an accuracy of one order of magnitude better than the one of lares satellite. this goal can be achieved because of the special design of the satellite, its orbit, that must be supplementary to the one of the lageos satellite, and the use of an updated gravitational field of earth from grace and grace follow-on missions [7-9]. the launch of lares 2 is scheduled for 2021 with the qualification launch of vega c, an enhanced version of the vega launcher of the european space agency (esa), and manufactured by an avio-asi joint venture. the main requirements for the structural material of the satellite are:  physical: density of about 9000 kg/m3, low sensitivity to heating by irradiation, non-magnetic properties, high thermal conductivity.  technological: good castability, good workability.  mechanical: hardness higher than 28 hrc (285 hv), yield strength higher than 517 mpa and elastic modulus greater than 200 gpa. the first requirement is a compromise between the radius of the satellite, that cannot be smaller than 0.2 m, and the need to have the smallest surface-to-mass ratio. in fact, a radius smaller than 0.2 m would have not allowed to accommodate the 303 ccrs which have been considered an acceptable threshold for the strength of the reflected signal from the satellite. the non-gravitational perturbations are proportional to the surface-to-mass ratio, that therefore must be minimized. the non-gravitational perturbations cannot be modeled with the required accuracy and degrade the accuracy of the framedragging measurement. the second requirement is related to the manufacturing of the satellite. the third requirement concerns the contact between the four hemispherical heads of the arms of the separation system and the corresponding four hemispherical cavities manufactured at the equator of the satellite. in fig. 1 two hemispherical cavities are indicated with the arrows while the darker cavity is manufactured to allow handling and transportation of the satellite. figure 1: rendered image of lares 2 satellite and sketch of preliminary separation system [10]. the second and third requirements are induced by the pressure of the separation system on the satellite that is defined as a pre-load. this one is required to maintain the satellite in place during all the launch phases [11]. based on these requirements, some copper and nickel-based alloys have been developed and analyzed. these alloys meet the above-mentioned physical requirements, but they have advantages and disadvantages. d. pilone et alii, frattura ed integrità strutturale, 56 (2021) 56-64; doi: 10.3221/igf-esis.56.04 58 the copper-based alloys better meet the physical and the technological requirements but hardly reach the limit of the required mechanical properties; moreover, they change surface color due to oxidation during exposure to the air. the nickelbased alloys are more difficult to produce, have lower thermal conductivity, are more expensive but with significantly higher mechanical properties. different alloys of various compositions [12-14] have been produced and studied by analyzing microstructures, heat treatments, mechanical characteristics and workability. important preliminary indications were obtained for a final choice of the alloy for the satellite, also bearing in mind all the problems related to the certifications required for new alloys to be used for a satellite to be launched with a rocket [15,16]. the construction of the satellite involves the production of a spherical component of about 0.40 m in diameter. it is therefore necessary to evaluate the possible technologies that can be used (casting, forging, sintering, etc.). in particular, it is important to study which technology can be usefully applied to the different candidate alloys. among the alloys having mechanical properties close to the requirements the haynes® 242 ™ alloy is one of the most interesting [17-22]. this alloy was originally developed for applications in gas turbines. it is an alloy with very low thermal expansion and high resistance, even at high temperatures. it maintains good mechanical performances up to 760 °c. the traditional heat treatment of the alloy leads to the formation of ni2 (mo, cr) precipitates having a size of about 10 nm. due to the formation of a large volumetric fraction of this phase, a great increase in the mechanical strength of the alloy is obtained. literature data suggest that the standard thermal treatment is aging at 650 °c for 24 h. a study was therefore carried out producing some demonstrative castings. forging tests, machinability tests and mechanical tests were carried out on these castings to evaluate their potential, their characteristics and to verify whether they could be usefully used for the satellite production. samples of commercial haynes 242 alloy were also tested for comparison. experimental or the production of the specimens a vacuum induction melting furnace (vim) was used. the first casting was produced by melting the alloy under vacuum and by casting the molten metal in a metallic mold. the second casting made under vacuum was poured into a ceramic mold and was characterized by the presence of big shrinkage cavities. for that reason, the metallic mold was preferred in this experimental work. the third casting was obtained by casting the molten metal, after fusion in air, in a metallic mold. the production of the castings under vacuum is divided into two phases. first, nickel was inserted into the crucible and molten inside the furnace at about 1455 °c. after about 7 minutes, a temperature of 1480 °c was reached and the alloying elements were added: molybdenum, chromium, silicon, manganese and aluminum. about 10 minutes were required to obtain the complete fusion of all elements. when the temperature reached 1420 °c the alloy was cast. the production of the casting in air required the same procedure. in addition to the three ingots described above, a commercial hot rolled bar was purchased from haynes international. the solubilization treatment conducted on the specimens produced from the three ingots and the rolled bar, as well as on the forged material, that will be discussed below, is the standard treatment [17,20]. the solubilization treatment was carried out at 1100 °c for 1 hour and the subsequent cooling was carried out in air. the aging of the specimens was performed at 650 °c for 24 h, 48 h, 120 h and 144 h. the specimens were subjected to metallographic characterization and to mechanical tests to observe the variations induced by the heat treatment. metallographic analyses were performed after electrochemical etching carried out at 6 v by using a solution of 1 g of oxalic acid in 20 ml of hydrochloric acid. some specimens were produced from the ingot poured under vacuum, cast in a ceramic mold and subjected to hot forging. forging was performed after bringing the casting to a temperature of 1150 ° c for 2h: the obtained deformation was about 15%. tensile tests were carried out for determining tensile strength, yield stress and elongation. tensile test specimens were cut from the three ingots, the commercial bar and the forged material described above; they were 8 mm large, 3 mm thick and they had a gauge length of 30 mm. machinability tests have been carried out by producing screws. results and discussion he compositional characterization of the samples by means of sem-eds allowed the determination of the composition of the specimens produced. tests were carried out on various samples taken from the three produced castings (tab. 1). the alloy density was measured by using several specimens and the resulting mean value was 9,1 g/cm3. f t d. pilone et alii, frattura ed integrità strutturale, 56 (2021) 56-64; doi: 10.3221/igf-esis.56.04 59 the electrochemical etching revealed the dendritic structure of the alloy (fig 1). optical images in fig. 2 highlights the presence of fine precipitates in the interdendritic areas. these precipitates are ni2mo e ni2cr. samples subjected to forging and aging have been also analyzed to identify their microstructure. as it can be seen in fig. 3 the dendritic structure disappeared and a fine microstructure formed. ni mo cr fe co si al nom. comp. bal. 25 8 2 max 1 max 0.8 max 0.5 max casting 1 64.75 26.63 7.75 0.46 0 0.27 0.15 casting 2 65.39 26.15 8.05 0.38 0 0 0 casting 3 65.1 25.9 8 0.5 0.12 0 0 table 1: mean composition of the 3 castings. casting 1 was cast in vacuum in a metallic mould. casting 2 was cast in vacuum in a ceramic mould. casting 3 was cast in air in a metallic mould. figure 2: optical micrographs showing the alloy microstructure in the as-cast condition (a) and after solubilization (b). figure 3: optical image showing the alloy microstructure after forging and aging at 650 °c for 24 h. considering that the mechanical properties of these alloys can be increased by performing aging treatment, aging tests have been performed on the as-cast, on the forged and on the commercial alloys. fig. 4 shows the obtained results. in all the considered cases the mechanical properties increase is due to the precipitation of fine and dispersed particles of ni2mo e ni2cr. (a) (b) d. pilone et alii, frattura ed integrità strutturale, 56 (2021) 56-64; doi: 10.3221/igf-esis.56.04 60 the results show that in the solubilized state the commercial alloy has a slightly higher hardness. by performing aging treatment at 650 °c the as-cast alloy increases its hardness, reaches a maximum after 48 h and then there is an overaging phenomenon. the forged alloy behavior is characterized by a hardness increase with time and it reaches 387 hv10 after 120 h. this is probably due to the formation of fine grains that allows a more dispersed precipitate distribution. the commercial alloy shows a hardness that is slightly higher in comparison with the others; this may be ascribable to a structure that is more homogeneous in comparison with that of the as-cast material. figure 4: aging curves showing the hardness of the as-cast, forged and commercial alloys as a function of aging time. vickers hardness (hv10) rockwell hardness (hrc) yield stress (mpa) ultimate tensile strength (mpa) elongation (%) cast under vacuum as-cast 270 26 340 522 26 solubilized 228 20 320 625 46 aged 24h 308 32 450 596 16 aged 48h 360 38 490 630 12 aged 120h 336 35 532 855 25 forged solubilized 232 21 345 638 31 aged 24h 350 37 580 907 22 aged 48h 360 38 570 761 11 aged 144h 387 40 641 913 16 commercial alloy aged 24h 309 32 720 1190 33 aged 48h 383 40 747 1210 31 cast in air aged 24h 297 30 520 593 10 aged 120h 336 35 610 704 11 table 2: mechanical properties of the tested specimens. d. pilone et alii, frattura ed integrità strutturale, 56 (2021) 56-64; doi: 10.3221/igf-esis.56.04 61 the results of the tensile tests are summarized in tab. 2 for various castings both in the as-cast and in the forged state after heat treatment. the results obtained for the commercial alloy are also reported for comparison. for all the castings, even in the forged state, the obtained mechanical properties are lower than the ones characterizing the commercial alloy, but they abundantly meet the design requirements. as far as the differences with the commercial alloy are concerned, we can make the following considerations. the commercial alloy has been forged and drawn in the form of a bar, undergoing significant plastic deformations, while for the satellite we need to produce a sphere. it is being assessed whether to produce it by casting or by casting and forging, but with low deformations. our study considered different types of castings whose properties meet the physical and mechanical requirements. it is apparent that forging treatment with a 15% reduction improves the mechanical properties of the alloy and that casting mechanical behavior is affected by the presence of microshrinkage cavities that decrease strength and toughness of the alloy as well as its density. by examining the behavior of the samples, we can observe that as the aging time increases, the mechanical strength increases and the ductility decreases and then increases again after 120 hours treatment. the alloy cast in air is generally less ductile. some significant σ-ε curves characterizing the forged alloy (fig. 5) are reported and compared with the one of the commercial alloy (fig. 6). for all the tested specimens the plastic behavior is tendentially linear with a work hardening exponent of about 0.24. figure 5: stress-strain curves of the forged haynes 242 alloy after solubilization and heat treatment. figure 6: stress-strain curve of the commercial haynes 242 alloy aged for 48 h. d. pilone et alii, frattura ed integrità strutturale, 56 (2021) 56-64; doi: 10.3221/igf-esis.56.04 62 figure 7: sem micrograph showing the surface morphology of haynes 242 aged at 650 °c for 24 h. figure 8: sem micrograph showing the surface morphology of haynes 242 aged at 650 °c for 120 h. after carrying out several tensile tests, observations of the fracture surfaces were performed by means of sem. the observations were carried out on specimens aged for 24h and 120h. sem micrographs of the sample aged for 24h reveal at low magnifications that it is a ductile fracture (fig. 7), while at higher magnifications the coexistence of areas with dimples, typical of ductile fractures, and areas of cleavage fracture is apparent. d. pilone et alii, frattura ed integrità strutturale, 56 (2021) 56-64; doi: 10.3221/igf-esis.56.04 63 sem micrographs of the alloy aged for 120 h (fig. 8) highlight that, although the fracture appears prevalently ductile, the fracture morphology is a mixed mode fracture due to the presence of small areas characterized by a brittle behavior. after carrying out the mechanical tests, it was also necessary to evaluate the machinability of this alloy. this occurred through the production of screws. sem analyses allowed to inspect the screw surface in order to evaluate any presence of superficial defects. sem analyses showed that the alloy has a very good machinability even after aging. in fact, no defects are observable on the surface of the screws (fig. 9). figure 9: sem micrograph showing the surface of a screw produced with haynes 242 alloy aged for 24 h. conclusions n this work haynes 242 alloy has been considered as a possible candidate for the production of lares 2 and similar satellites that may be launched in the future. three different castings with the nominal composition of haynes 242 have been produced and tested along with a commercial bar of haynes 242. the results highlighted that the best results in terms of mechanical behavior were the ones relative to the commercial alloy that has been subjected to hot rolling. this thermomechanical treatment is not applicable to the satellite constituted by a metallic sphere, but it has been considered to substitute hot rolling with forging that will produce similar improvements to the mechanical characteristics. so on the ground of the obtained results the best process solution is casting, followed by forging that allows to optimize the alloy mechanical properties. however, the results show that even in absence of forging the aging is sufficient to fulfil the mechanical requirements. haynes 242, although considered the optimal solution, and in fact was considered the baseline for the project, could not be selected because the procuring time was not compatible with the launch date of lares 2. acknowledgment he authors acknowledge the italian space agency (asi) for supporting the lares and lares 2 missions under agreements n. 2020-7-hh.0 and n. 2017-23-h.0. i t d. pilone et alii, frattura ed integrità strutturale, 56 (2021) 56-64; doi: 10.3221/igf-esis.56.04 64 references [1] ciufolini, i. (2007). dragging of inertial frames. nature, 449 (7158), pp. 41-47. doi: 10.1038/nature06071. [2] ciufolini, i., paolozzi, a., pavlis, e.c. et al. (2017). a new laser-ranged satellite for general relativity and space geodesy: i. an introduction to the lares 2 space experiment. eur. phys. j. plus 132, 336. doi: 10.1140/epjp/i2017-11635-1. [3] sindoni, g., paris, c., vendittozzi, c., pavlis, e.c., ciufolini, i., paolozzi, a. (2015). the contribution of lares to global climate change studies with geodetic satellites, (2015) asme 2015 conference on smart materials, adaptive structures and intelligent systems, smasis 2015, 2. doi: 10.1115/smasis2015-8924. [4] paolozzi, a., ciufolini, i., paris, c., sindoni, g. (2015). lares: a new satellite specifically designed for testing general relativity. int j aerospace eng, 341384. doi: 10.1155/2015/341384. [5] ciufolini, i., paolozzi, a. paris, c., sindoni, g. (2014). the lares satellite and its minimization of the thermal forces, 2014 ieee international workshop on metrology for aerospace (metroaerospace), may 29-30, 2014, benevento, italy. [6] pavlis, e.c., paolozzi, a., paris, c., ciufolini, i., sindoni, g. (2015). quality assessment of lares satellite ranging data: lares contribution for improving the terrestrial reference frame (2015) 2nd ieee international workshop on metrology for aerospace, metroaerospace 2015 – proceedings, art. no. 7180616, 1-5. doi: 10.1109/metroaerospace.2015.7180616. [7] dahle, c., murböck, m., flechtner, f., dobslaw, h., michalak, g., neumayer, k.h., abrykosov, o., reinhold, a., könig, r., sulzbach, r., and förste, c. (2019). the gfz grace rl06 monthly gravity field time series: processing details and quality assessment. remote sensing, 11(18), 2116. doi:10.3390/rs11182116. [8] dahle, c., flechtner, f., gruber, c., könig, d., könig, r., michalak, g., and neumayer, k.-h. (2014). gfz rl05: an improved time-series of monthly grace gravity field solutions. in flechtner, f., sneeuw, n., and schuh, w.-d. (editors), observation of the system earth from space – champ, grace, goce and future missions, 29–40, springer, berlin, heidelberg. [9] kornfeld, r.p., arnold, b.w., gross, m.a., dahya, n.t., klipstein, w.m., gath, p.f., and bettadpur, s. (2019). grace-fo: the gravity recovery and climate experiment follow-on mission. j spacecraft rockets, 56(3), pp. 931– 951. doi: 10.2514/1.a34326. [10] ciufolini, i., paolozzi a., pavlis e.c., paris c., sindoni g. (2019). lares 2 an approved mission for testing general relativity, iac-19-a2.1.4, 70th international astronautical congress, 21-25 oct. 2019, washington, d.c. [11] paris, c. (2015). vibration tests on the preloaded lares satellite and separation system, aerosp sci technol, 42, pp. 470-476. [12] paolozzi, a., sindoni, g., felli, f., pilone, d., brotzu, a., ciufolini, i., pavlis, e.c., paris, c. (2019). studies on the materials of lares 2 satellite. j geodesy, 93 (11), pp. 2437-2446. doi: 10.1007/s00190-019-01316-z. [13] brotzu, a., felli, f., pilone, d., di cocco, v., sindoni, g., ciufolini, i. (2019). study of cucrzr alloy for the production of a passive satellite, procedia structural integrity, 18, pp. 742-748. doi: 10.1016/j.prostr.2019.08.222. [14] felli, f., brotzu, a., pilone, d., paolozzi, a., ciufolini, i. (2018). fracture behaviour of alloys for a new laser ranged satellite, procedia structural integrity, 9, pp. 295-302. doi: 10.1016/j.prostr.2018.06.026. [15] ecss-q-st-70-71c rev.1 – materials, processes and their data selection (15 october 2019), ecss secretariat, esaestec requirements & standards division, noordwijk, the netherlands [16] ecss-q-st-70c rev.2 – materials, mechanical parts and processes (15 october 2019), css secretariat, esa-estec requirements & standards division, noordwijk, the netherlands [17] gaurav, v., jacinto páramo kañetas, p., phanibhushana, m.v. (2018). hot deformation characterization of haynes242, mater today: proc, 5 (11), pp. 25389-25395. doi: 10.1016/j.matpr.2018.10.343. [18] stepniowska, e., dymek, s. (2012), structure-property relationship in a haynes® 242™ alloy subjected to long-term exposure at 650°c, sol st phen, 186, pp. 156-159. doi: 10.4028/www.scientific.net/ssp.186.156. [19] habeeb, h.h., kadirgama, k., noor, m.m., rahman, m.m., mohammad, b., bakar, r.a., abouel hossein, k.a. (2010). machining of nickel alloy 242 with cubic boron nitride tools, j appl sci, 10 (19), pp. 2322-2327. [20] dymek, s., wróbel, m., dollar, m., blicharski, m. (2006). influence of plastic deformation and prolonged ageing time on microstructure of a haynes 242 alloy, j microsc, 224 (1), pp. 24-26. [21] dymek, s., dollar, m., klarstrom, d.l. (1991). strain hardening mechanisms in a nimocr alloy, scripta metall mater, 25 (4), pp. 865-869. [22] rothman, m.f., srivastava, s.k. (1993). effect of cold work and aging upon the properties of a ni-io-cr fastener alloy, j eng gas turb power, 115 (1), pp. 160-164. microsoft word numero_49_art_16_2454 o. y. smetannikov et alii, frattura ed integrità strutturale, 49 (2019) 140-155; doi: 10.3221/igf-esis.49.16 140 focused on russian mechanics contributions for structural integrity numerical model of fracture growth in hydraulic re-fracturing oleg yurievich smetannikov, yuriy aleksandrovich kashnikov, sergey gennadievich ashikhmin, artem eduardovich kukhtinskiy perm national research polytechnic university, 614990, komsomolskiy av, 29, perm, russia sou2009@mail.ru, geotech@pstu.ru, a_s_g_perm@mail.ru, artyom@pstu.ru abstract. simulation of fracture propagation with fem method requires re-meshing to provide more accurate results. this raises a question about the determination of the direction and criterion for mesh modification. in the case of general-purpose cae-packages, we deal with a stationary mesh, and the fracture path is usually represented as a chain of elements with degraded properties. the algorithm proposed in this paper is based on the ansys mechanical apdl language for stepwise geometry reconstruction and mesh modification in accordance with the current configuration of a growing fracture and provides a more accurate description of its shape. the fracture propagation process is divided into stages. each subsequent stage differs from the previous one by the fracture shape modified due to the crack length increment in the calculated direction. to check the adequacy of the model, an experiment on fracture propagation in glass specimens with an initial notching under uniaxial compression was performed. the laboratory experiments were carried out to determine the fracture toughness of rocks. the developed numerical model has been used to solve the problem of refracturing for different stress anisotropy in the oil-bearing rock formation. keywords. fracture propagation; fem; stress anisotropy; fracture path; apdl. citation: smetannikov, o. y., . kashnikov, y. a, ashikhmin, s. g., kukhtinskiy, a. e., numerical model of fracture growth in hydraulic re-fracturing, frattura ed integrità strutturale, 49 (2019) 140-155. received: 03.04.2019 accepted: 22.05.2019 published: 01.07.2019 copyright: © 2019 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. introduction n the last few years the effect of the directional hydraulic refracturing (hf) on the stress-strain state of oil-bearing rock formations has been extensively discussed in the scientific and engineering literature. thus, as it was stated and verified by the specialists of ojsc “nk rosneft’ in [1, 2], the repeated hf leads to the formation of fracture, the direction of which differs from the direction of the primary hf. the fact of reorientation of the secondary hydraulic fracture with respect to the primary hf has been also supported by foreign specialists [3, 4]. the application of the directional hydraulic re-fracturing method offers much promise from the viewpoint of increasing the recovery of oil pools especially in the oil fields, in which the majority of wellbores has been already subject to primary hydraulic fracturing. as applied to these cases, it is of practical importance to analyze thoroughly an expected change in i http://www.gruppofrattura.it/va/49/2454.mp4 o. y. smetannikov et alii, frattura ed integrità strutturale, 49 (2019) 140-155; doi: 10.3221/igf-esis.49.16 141 the direction of the secondary hf and the prospects of using its positive effects for increasing the wellbore capacity. the practical implementation of the secondary hf method suggests the development of a new direction in the hydraulic fracturing technique. as a consequence, an essential improvement of the efficiency of oil wells and accordingly the growth of the oil recovery coefficient of the entire oil fields, which demonstrate a notable decrease in the production rate, is expected. the mathematical modeling of the process of fracture growth relies both on the analytical [5] and numerical [6] methods. the study, which is close to the present work with respect to the set of hypotheses used for problem consideration, is reported in paper [7] where the problem of hf growth was solved using author’s version of the hyper-singular boundary element method. at present, there is a series of customized commercial software packages for numerical simulation of fracture propagation allowing for mesh adaptation including the case of three-dimensional problem formulation. thus, work [8] offers a 3d model to describe the growth of a crack in machine elements, which was implemented numerically as a finite element zencrack program (developed by the company zentech international limited) applied in fracture mechanics. another example of adaptive remeshing to trace crack propagation is the franc3d program (fracture analysis code for 3d), which is based on the boundary element method. the possibilities of this package are demonstrated in work [9] in the context of the problem of crack growth in the gear wheel. both packages are intended for needs of mechanical engineering. the main constraint in finding the finite-element solution to the problem with the aid of generally recognized universal finite-element packages is the necessity of reconstructing the mesh to provide the desired accuracy in the evaluation of the fracture growth direction and fracture growth criterion. in the universal cae software, in which the mesh remains invariable, the fracture path is traditionally represented as a chain composed of the elements with degraded properties (see, for example [10]). this necessitates a search for an optimal mesh topology and essentially decreases the solution accuracy. the algorithm proposed in our work uses the facilities of ansys parametric design language in the framework of ansys mechanical package. it allows a step-wise reconstruction of the mesh according to the current configuration of the computational domain and provides the most accurate description of the shape of the growing fracture and the stress-strain state in its neighborhood. stress field after formation of the primary hf fracture and initiation of the secondary hf fracture in the orthogonal direction fter completion of the primary hf the properties of the rock formation in the neighborhood of the oil well change. the formation of the fracture improves the general picture of rock permeability causing a redistribution of internal loads, which essentially changes the stress-strain state (sss) of the rock formation. in view of this fact a series of computations have been done to get answers to the two main questions: how does the fracture pressure change under the conditions of the secondary hf and in what direction does the secondary hydraulic fracture propagate? the fracture geometry was described by the perkins-kern model [11, 12]. it was based on the assumption that the fracture cross section in the plane normal to the axis of the well is an ellipse and its maximum width is detected in the nearwellbore region. this is the area adjacent to the well where the filtering characteristics of the productive strata have changed as a result of physicochemical processes initiated by processing method and operating conditions. the general computational scheme and the system of coordinates are shown in fig. 1. then, we get a fracture of half-length 50fx  m, the direction of which coincides with the direction of the highest horizontal stresses h the stress state of the wellbore as a function of the fracture width w was analyzed at different ratios of maximum stress ( h ) to minimum stress values( h ). the problem was solved by the finite element based on the ansys package under the assumption that the mechanical properties of the proppant (the material used to secure the main hydraulic fracture) are similar to those of the rock formation. simulation of the existing hydraulic fracture involves a preset of fracture wing displacements according to a maximum opening width w and variation of w with a horizontal distance x according to the laws [13]: 1 4 ,0 3, 57 , f w q x w e       1 4 0 ,0( ) 1w f x w x w x       , (1) a o. y. smetannikov et alii, frattura ed integrità strutturale, 49 (2019) 140-155; doi: 10.3221/igf-esis.49.16 142 where  is the fracture liquid viscosity; q the rate of liquid pumping;  21e e    is the plane strain modulus of the rock ( e —is young’s modulus;  is poisson ratio). as one might expect the fem computations demonstrate the growth of tangential stresses  on the well walls with increase of the opening width of the primary hf. fig. 2 presents the results of six calculations for different values of maximum fracture opening. figure 1: computational scheme for the problem of secondary oriented hf in rock formation. figure 2: the incremental growth of incremental stresses  on the well walls depending on the value of the opening angle of the primary hydraulic fracture in the isotropic field of horizontal stresses ( h h   ) at different values of maximum opening w , mm: 3 (symbol ●); 5 (■);7,5 ();10 (♦); 15 (); 20 (□). o. y. smetannikov et alii, frattura ed integrità strutturale, 49 (2019) 140-155; doi: 10.3221/igf-esis.49.16 143 the maximum of incremental stresses  is located on the walls of the well. then, the stresses in the rock formation rapidly decrease in the radial direction until they are stabilized at a distance of 2-3 m from the wellbore, namely, at 20 30cr   , where  is the current radius and cr is the radius of the wellbore (fig. 3). figure 3: radial distribution of incremental stresses  in the isotropic field of horizontal stresses ( h h   ) at the width of opening of the primary hf 20w  mm. 1 — in the direction of h , 2 — in the direction of h . based on the characteristic features of the incremental stress distribution  we can conclude that in the isotropic field of horizontal stresses h h   it is more probable that re-fracturing will occur in the direction perpendicular to the primary hf, i.e., the secondary hf in the isotropic field of horizontal stresses is orthogonal to the primary fracture. in this case, the pressure increase can be observed at the moment of fracture initiation. thus, at the pressure of the primary fracture of 80.0 mpa and the width of the primary fracture opening near the wellbore equal to 20 mm the secondary fracture pressure is 92.2 mpa. essentially, the situation changes in the case when the minimum stress h is about 70–95% of the maximum stress 47h  mpa. irrespective of the appearance of incremental stresses  , in all examined cases the most likely direction of the secondary hf is the direction parallel to the primary fracture path. as in the first case, the pressure begins to grow at the time of initiation of the secondary fracture and the primary fracture opening increases. the degree of pressure growth depends on the anisotropy of the stress field. thus, the width of the primary fracture opening 20w  mm at 47h h    mpa is responsible for a maximal increase of the secondary fracture pressure by a factor of 1.15, whereas at 47h  mpa, 32.9h  mpa by a factor of 1.37. the deformation of porous liquid-saturated rocks is a complicated process, during which the deformation of the mineral matrix of rocks (under the action of varying effective stresses and fluid pressure gradients) occurs simultaneously with fluid filtration in pores (under the action of the fluid pressure gradients and bulk deformation of the skeleton). in the following, a drop of oil pressure due to extraction of fluid from the well with the primary hf causes a change in the stress state of the rock formation in the vicinity of the well. therefore, an adequate treatment of the processes accompanied the deformation of a porous liquid-saturated medium requires that the system of differential equations describing the deformation of the rock skeleton and fluid filtration should be considered simultaneously. the solution of this coupled problem was found numerically using the ansys software package. to simulate the process of liquid removal from the wellbore, we performed coupled calculations for sss and liquid filtration at the prescribed bottom-hole pressure. the finite element mesh was built using the cpt213 element, which makes it possible to implement numerically the filtration consolidation model [6]. by virtue of the problem symmetry we performed o. y. smetannikov et alii, frattura ed integrità strutturale, 49 (2019) 140-155; doi: 10.3221/igf-esis.49.16 144 computations only on a quarter of the computational domain shown in fig. 1. the computational 500 500 m domain reproduced the wellbore and the existing primary hf filled with proppant. the permeability of the proppant was taken to be equal to 200 d, the permeability of collector was 100 µd. these values are typical for the local oil fields. the problem was solved in two steps. at the first step we investigated the stress state of the rock formation after the occurrence of the primary hydraulic fracturing, which implies that the problem was solved at initial stresses 47h h    mpa and initial oil reservoir pressure of 20 mpa. the values for the problem under consideration were taken from field data. at the second stage a bottom-hole pressure of 12 mpa was applied and the operation of the well under such conditions was simulated within the period of three years. the time factor is accounted for explicitly in the coupled simulation in ansys. the calculated distribution of the oil bed pressure in the vicinity of the well was represented in the form of ellipse due to the influence of the primary hf. the simulation results show that the well exploitation is accompanied by a redistribution of the pore pressure, which in its turn leads to a change in the stress-strain state of the surrounding formation. near the fracture and well the full stresses are reduced to 44.5 mpa , that is, become smaller by 2.5 mpa against the initial 47 mpa. thus, pumping of liquid from the well with the primary hf leads to a reduction of horizontal stresses in the near-well region. however, in the present work the horizontal stresses were calculated taking no account of the above-mentioned incremental stresses, which are generated by the primary hf. the results of computation taking into account both of these factors are shown in fig. 4 in the form of curves of horizontal stresses x in the vertical cross-section over the well bore (the maximal opening of the primary hf near the well was set equal to 20 mm). figure 4: distribution of radial stresses along the trace of the plane crossing the well axis: taking into account liquid removal (solid line) and taking into account both the removal of liquid and opening of the primary fracture (dashed line) in the isotropic field of horizontal stresses: general picture (a) and its magnified fragment (b). as is evident from the plots, consideration of incremental stresses caused by opening of primary fracture leads to a growth of horizontal compressive stresses. the observed growth turns to be much greater than a reduction of stresses initiated by the drop of oil pore pressure caused by liquid pumping out. the growth of stresses is most pronounced in the vicinity of fracture but as the distance from the fracture increases the stresses decrease drastically and at a distance of 65 m from the fracture the stress curves practically merge together. the calculations show that in the vicinity of fracture the o. y. smetannikov et alii, frattura ed integrità strutturale, 49 (2019) 140-155; doi: 10.3221/igf-esis.49.16 145 horizontal stresses reach 60 mpa, but at a distance of 2 m their value does not exceed 48 mpa, which is by only 1 mpa higher than the initial values (47 mpa dashed line in fig. 4). these results show that after carrying out the directional hydraulic fracturing the main effect on the redistribution of stresses in the vicinity of well is produced by the deformation of rock formation caused by generation of the primary fracture rather than by the operation of the well. in this case, the main conclusion will be as follows: the growth of the secondary hf in the direction perpendicular to the path of the primary fracture is possible only in the presence of isotropic or sub-isotropic horizontal stresses. the stress–strain state of the priobskiy oilfield, in which the effect of reorientation of the secondary hf was recorded, is characterized by a rather small difference between the minimum and maximum horizontal stresses. in particular, the acoustic anisotropy does not exceed 5%. under the conditions of anisotropic horizontal stresses, the secondary hf is initiated by application of technical means allowing engineers to create a weakening surface at a certain depth [1] and in the desired direction. evolution of re-fracturing in the anisotropic stress field he computational scheme for this case is similar to that of the previous problem (see fig. 1). the only difference is that in the direction of the lowest horizontal stresses h the rock formation is subject to the condition of preweakening by the initial fracture of half -length 2fx  m, whereas in the direction of the highest horizontal stresses h the generation of fracture of halflength 50fx  m has been already completed. the value of the lowest horizontal stresses was prescribed as h a hk   , where ak is the coefficient of the sss (stress-strain state) anisotropy. the value of the anisotropy coefficient varied from 0.7 to 1.0 and the width of fracture opening in the vicinity of the well varied from 5 to 20 mm. the distribution of the liquid pressure in the primary hf in the course of its evolution was determined based on the perkinskern nordgren (pkn) model of hydraulic fracturing [11-13]. upon substituting the opening width eqn. (1) into the flow law with allowance made for the elliptical shape of the fracture and integrating the resultant expression we get the law of pressure distribution in the secondary fracture: 0 1 1 ,f f x p p a x               (2) where 0 (0, )hp p t    ;  30256 .fa x q hw   in formula (2) the time is taken into account implicitly, since the half-length fx changes with time. hence, by solving the flow equation at each instant of time we find the growing length of the secondary fracture and pressure distribution inside it. here we used the following assumptions:1) leakage of the fracture liquid into the oil bed is ignored; 2) the fracture remains rectilinear, since the pkn model provides for the existence of a straight fracture. in other words, the pressure distribution was taken from a model for a straight fracture although the fracture in this case was not straight. the version of the pkn model (originally 3d) used by the authors is based on the assumption that the profile of the average horizontal cross section remains invariable throughout the height of the fracture. this introduces a certain error in the computations, which decreases with increasing oil bed thickness. opening of the fracture (at most to a width of 20 mm) is significantly smaller than the height of the fractured oil bed (more than 2 m) and the length of the fracture (extending as long as 20 m) in this case, in the first approximation the computation error for 2d case can be considered acceptably small compared to the error in the 3d formulation. the obtained equations were solved for average parameters typical of the oilfields developed in the perm region (tab. 1). since the existence of the primary fracture changes the picture of the initial sss, the wellbore pressure is expressed as 0 h hp p      . the value of correction p is estimated by the independent calculation. by setting different values of pumping periods we can determine the parameters of the secondary hf – its length, opening width, well-head pressure, fracture pressure profile and also the parameters p , a . t o. y. smetannikov et alii, frattura ed integrità strutturale, 49 (2019) 140-155; doi: 10.3221/igf-esis.49.16 146 parameter value wellbore diameter,m 0.216 elasticity modulus of the rock gpa 40 poisson’s ratio 0.25 tensile strength 3.0 initial oil bed pressure – 0p , mpa 17 vertical rock formation pressure – v , mpa 47 lateral rock pressure h , mpa 47 rate of liquid feeding in the fracture, m3/min 3.0 viscosity of the liquid in the fracture, cps 100 fracture height – h , m 20 table 1: input data for simulation of the secondary hf. algorithm for numerical implementation of the secondary fracture growth model the proposed algorithm for numerical computation of the secondary fracture growth relies on the following hypotheses: hypothesis i. fracture initiation necessitates the fulfillment of the following criterion: [ ]par par , where par is the criterion of the fracture stability, where [ ]par is its critical value. for criteria we can take the principal stress at the fracture top 1 the stress intensity coefficient ik and the angle of fracture opening cr . hypothesis ii. the direction of fracture propagation coincides with the vector of the normal to the first principal stress at the fracture top directed at the smallest (in the absolute magnitude) angle (energyoptimal) to the current direction of the fracture. the process of the secondary hf growth is simulated in a step-wise manner. each subsequent step differs from the previous one by a changed topology of the secondary fracture caused by its extension in a specified direction to a specified length. the solution is sought for the problem of linear elasticity under the assumption of small strains the behavior of the fracture is described at each step by the system of standard equations of the stationary problem of elasticity ( ˆdiv 0  , vx ;   t1ˆ 2     u u , vx ; 4 ˆ ˆˆ c   ) with the following boundary conditions: u u , usx ; ̂  n p , sx . here,  ˆ , t x is the stress tensor,  , tu x is the displacement vector,  ˆ , t x is the total strain tensor, 4ĉ is the tensor of elastic constants, ,us s are the parts of the boundary with prescribed displacements and loads, respectively. for numerical implantation of the finite element model we used the ansys mechanical apdl consider the algorithm, which allows us to analyze the secondary fracture growth based on the limiting value of its opening: ( ) [ ].cr crl   (3) the simulation of fracture propagation at the k-th time step consists of the following steps: 1. calculate the stress-strain state for the current configuration of the computational domain, bearing in mind that the length-wise distribution of pressure is governed by law (2) 1 4 1( , ) 1 1 ,k w x p l x p a l             o. y. smetannikov et alii, frattura ed integrità strutturale, 49 (2019) 140-155; doi: 10.3221/igf-esis.49.16 147 where l is the current length of the fracture; w нр р    (where 47h  mpa); 0.2487 4.4611a l ; p is a variable quantity. verify the possibility of fracture growth by controlling the fulfillment of inequality (3). note that at the first step the initial value of 0kp is calculated as 0 0.2488 1 6.1873p l  and at subsequent steps as 0 0 1k kp p    . by the opening angle ( )cr l we mean the angle in the polar coordinate system with its origin lying at the top of the fracture, which is generated as a result of fracture opening under pressure between the lines connecting the fracture top with two adjacent nodes of the finite-element mesh on its wings (fig. 5). in the figure, the geometry of the fracture near the top in the unloaded state is shown by solid lines and dashed line denote its geometry in the loaded state; the circles denote the position of the mesh nodes. vector crx determines the current direction of the fracture. the opening angle due to smallness of the displacements is calculated by the formula cr r nr l nlu l u l   , where ru  , lu  are the circumferential components of the displacement vectors of nodes adjacent to the top and lying on the right and left wings of the fracture; nrl , nll are the distances from the top to the corresponding nodes. figure 5: the scheme of computation of the fracture opening angle. if condition (3) is not fulfilled to a specified accuracy, then the variable parameter kp is calculated by the chord method from expression (2) on the invariable mesh at the k-th time step according to the following integral scheme: 2.1. scale the value of the pressure increment for the next iteration using formula 1j jk kp a p    with a prescribed coefficient 1.5a  . here the subscript corresponds to the time step number and superscript to the iteration number. 2.2. solve the problem of determining the sss for modified boundary conditions and find the value of the fracture initiation parameter 1jcr  . 2.3. using jkp , 1j kp  , jcr , 1j cr  , determined in the previous iterations find the subsequent approximation 2jkp  : 1 2 1 1 1 j j j j jk k crk k j j cr cr p p p p                 , after which evaluate the stress-strain state and the corresponding value of the fracture initiation parameter 2jcr  . 2.4. in the case of non-fulfillment of condition 2 [ ] [ ] j cr cr cr       , where  is the prescribed accuracy, increase the iteration number by 1 and repeat the steps 2.1–2.4. o. y. smetannikov et alii, frattura ed integrità strutturale, 49 (2019) 140-155; doi: 10.3221/igf-esis.49.16 148 figure 6: computation of fracture growth direction. 3. specify the direction of the first principal stress at the fracture top node, at which the intensity of stresses is maximal. as an example, fig. 6 shows its direction at the top of the fracture and also the current orientation of the fracture (dot and dash vector) and possible paths of its growth (vectors 1crx and 2crx ). the ansys parametric design language macros contains following steps 3.1. determine 6 components of the tensor of stresses at the top using the function *get and load them in the six element comp file:  comp 11 22 33 12 23 13, , , , ,       . 3.2. determine the direction cosines of the vectors of principal stresses with respect to the global cartesian coordinate system using the function *vfun,dir,dircos, and locate them in the 9-elements dir file:  dir 11 12 13 21 22 23 31 32 33, , , , , , , ,c c c c c c c c c , ijc is the cosine of the angle between the i-th principal stress and the j-th coordinate vector. 3.3. determine possible directions of the fracture propagation vector (fig. 6):  1 12 11,cr c c x and its inverse  2 12 11,cr c c x . 3.4. determine the coordinates of the direction vector at the end of the currently existing fracture (fig. 6)  0 0 0 0 0,cr e b e bx x y y  x 3.5. calculate the angles 1 , 2 between the vectors 0crx and 1crx , 0crx and 2crx , respectively:  1 01 2 02 0arccosi cri cr cri crx x x x l     ( 1, 2i  ), where crijx is the j -th component of the vector crjx ( 0,1, 2i  ; 1, 2j  ); 2 2 0 01 02( ) ( )cr crl x x  is the length of the vector 0crx . 3.6. according to the hypothesis ii, select a directional vector of further advance of the fracture crx , lying at the smallest (in absolute magnitude) angle with the previous vector 0crx : 1 1 2 2 1 2 , ; , . cr cr cr         x x x in the example given in fig. 6 the fracture will grow in the direction 2cr crx x . 4. reconstruct the geometry of the sub-region around the fracture. here, it is necessary to exclude the region itself and its mesh (by means of commands aclear, adele), leaving only the boundary of the sub-region. extend the part of the o. y. smetannikov et alii, frattura ed integrità strutturale, 49 (2019) 140-155; doi: 10.3221/igf-esis.49.16 149 boundary adjacent to the fracture top. the increment of the fracture length at the k-th step is equal to kl and in the general case it can be a variable quantity. construct a sub-region within a newly generated closed contour, generate a mesh on its surface and set new boundary conditions. 5. calculate the stress-strain state of the rock formation, in which the fracture has a new configuration 6. repeat the algorithm item 1-4 n times the calculated total length of the growing fracture is 0 1 n k k l l l     meters in the case when the critical value of the stress intensity coefficient кi, is taken to be the fracture growth criterion, the generation of the finite element mesh suggests the usage of a special type of element arrangementsingular finite element meshing (fig. 7). experimental verification of the proposed algorithm to verify the adequacy of the accepted hypotheses we performed a fracture experiment to investigate the growth of fractures in glass specimens under uniaxial tension, by analogy with the experiment described in monograph [5]. the specimens were made of 200 100 mm window glass, 4 mm thick and had straight centrally located grooves 2.5 mm thick, which were cut by the abrasive water jet cutting machine at an angle of 30° to the horizontal axis of the specimens. actually, we repeated the experiment of hoek and brown in which the growth of fractures in rock formations under the action of compressive stresses was studied. the compression tests were performed in the lfm-50t test machine with grips 96 mm wide and acceptable load limit of 5 ton-force (fig. 8). to reduce inhomogeneities of the pressure distribution, we placed the polyurethane inserts 1 mm thick in the zones of sample contact with the grips. figure 7: types of finite element mesh with a singular block (cloud) for calculation of the secondary hf growth: general view and scaled up fragments. o. y. smetannikov et alii, frattura ed integrità strutturale, 49 (2019) 140-155; doi: 10.3221/igf-esis.49.16 150 figure 8: position of the sample during tests. the computations were done for the following glass properties and opening angle criterion 73e  gpa, 0.3  and 0.8  °. the size of the fracture length increment was a variable quantity and was equal to 0.5kl  mm for the first 10 steps of the algorithm and 1mm for all subsequent steps. the calculated and experimental configurations of the fracture are shown in fig. 9a. the fractures generated in almost all specimens are located both above and below the calculated fractures. in sample № 2 the lower fracture was initiated in the middle of the sample due to the presence of the local stress concentrator. first, in all cases the angle between the primary and secondary fractures remains unchanged and is equal to 85°. as the fracture grows further the opening angle first slightly decreases and then begins to increase. in this case the fracture shows the tendency to change its direction to a vertical one. the fracture paths were digitized and interpolated by the piece-wise linear functions (no less than 30 nodes for one fracture). owing to the specimen symmetry the fractures initiated at both ends of the initial cut were superimposed. then at each of 200 nodes of a thicker uniform mesh along the horizontal axis ix a mathematical expectation   8 1 1 8 ji i j y y    was determined (here i is the node number and j is the test number). as is evident from fig. 9b, the relative discrepancy between the calculated and actual fracture paths does not exceed 5%, which substantiates the adequacy of the proposed algorithm for computation of the growing fracture path. experimental determination of fracture toughness coefficients of rock formations to determine the value of the intensity coefficient к1с we tested the specimens 30 mm in diameter and 60 mm in length made from the core material extracted from the wellbore of the 118 enapaevskiy oilfield of “lukoil –perm” coltd from the terrigenous interval of 1538-1541 m. prior to tests of determining the critical coefficient of stress intensity we evaluated the static and dynamic elastic properties for some specimens in reservoir conditions. schematic diagram of testing cylindrical specimens with o-ring groove are presented in fig. 10. this testing scheme was chosen from [15] and adapted was rock samples. this type of test is convenient because core samples of standard size can be used. the size of a notch was 7 mm. tensile tests of rock specimens were carried out in the instron electropuls e10000 electrodynamic two-axis test system, which is designed for compression, tension, bending and torsion static tests; for dynamic fatigue tests at the frequency of 100 hz; for two-axis (tension-compression) static and dynamic tests under loads up to 10 kn/100 nm. testing specimens o. y. smetannikov et alii, frattura ed integrità strutturale, 49 (2019) 140-155; doi: 10.3221/igf-esis.49.16 151 of this type required the development and manufacture of special tooling for securing cylindrical specimens in the grips of testing machine during tensile tests. tensile tests were carried out at room temperature and at the prescribed speed of grips displacement, which was 0.2 mm/min. a b figure 9: comparison of experimental fractures in specimens and calculated fractures (thin solid lines) (a); the results of digitalization of fracture paths (b): line 1 – experiment; line 2 – experimental average, line 3 – calculation. the stress intensity factor к1с was calculated by the formulas presented in work [15] for a cylindrical specimen with a surface o-ring fracture subject to tensile stress. 12 ( )ic p k b f b     , o. y. smetannikov et alii, frattura ed integrità strutturale, 49 (2019) 140-155; doi: 10.3221/igf-esis.49.16 152 b r   , (4) 2 3 4 1 0, 5(1 0, 5 0, 375 0, 363 0, 731 ) 1f            here the notation corresponds to that of fig. 10. figure 10: diagram of loading of the rock specimen with o-ring fracture for estimating к1c [15] figure 11: correlation relationship between к1c and the static modulus of elasticity under the oil bed conditions we tested 25 specimens and based on the obtained results calculated the mean value of к1с, which was equal to 0.108 mpa·m1/2 at the maximum and minimum values of 0.044 mpa·m1/2 and 0.168 mpa·m1/2, respectively. the tensile o. y. smetannikov et alii, frattura ed integrità strutturale, 49 (2019) 140-155; doi: 10.3221/igf-esis.49.16 153 strength of the specimens р was found to vary from 0.55 mpa to 2.34 mpa, which are consistent with the values typical for the rocks of this kind. based on the results of our tests we determined the correlation relationship between the critical stress intensity coefficient and the static modulus of elasticity under the oil bed conditions (fig. 11). it is clear that further testing is needed to improve the correlation since the amount of tested samples was quite low. the obtained experimental data did not reveal the dependence of к1c and р on the porosity, velocity of longitudinal wave and dynamic elastic properties of specimens. figure 12: the calculated paths of the secondary hf at different widths of the primary hf opening and different values of the anisotropy coefficient of the initial stress field in the vicinity of the wellbore (a) ,0 20ww  mm; (b) ,0 5ww  mm. the results of simulation of the secondary hf growth in the anisotropic stress field he developed numerical model and the results of experimental investigation of к1c were used to solve the problem of the secondary fracture growth at the following values of the coefficient of the stress field anisotropy ak and the width of the primary fracture opening ,0ww . the calculations were done at ick =0.127, which is the mean of the tested rocks. the results of computation are shown in fig. 12. as it is seen from the figure, with increasing width of the primary fracture opening, the secondary hf practically does not change its direction towards the highest compressive stress even at large stress anisotropy and grows in the direction perpendicular to the primary fracture. the main reason of such behavior is that at large width of the primary fracture opening the level of the initial stress field anisotropy in the t o. y. smetannikov et alii, frattura ed integrità strutturale, 49 (2019) 140-155; doi: 10.3221/igf-esis.49.16 154 vicinity of fracture decreases. this causes an increase in the pressure minimum, at which the conditions for the primary fracture growth are generated. the direction of the secondary hf depends not only on the width of opening of the primary fracture, but also on the coefficient of stress anisotropy ak . the larger is the opening width of the primary fracture and the closer is the anisotropy coefficient to 1.0 the nearer is the path of the secondary hf to the normal to the primary fracture. thus, at the width of the primary fracture opening of 5 mm the direction of the secondary hf is close to the normal at 0.85ak  , and at the opening width of 20 mm this happens at 0.7ak  . conclusions he applications of the developed numerical model of the fracture growth under the conditions of hydraulic refracturing in the oil bed have shown that the following factors are responsible for the generation of the secondary fracture orthogonal to the primary fracture. 1. anisotropy of the medium, in which the fracture is propagating (the coefficient of stress anisotropy ak should be higher than 0.8) 2. an increase the pumping pressure of fracture liquid 3. an increase of the opening width of the primary fracture in the presence of all these factors the effect of the secondary hf will be maximal because its realization opens up the maximum of non-depleted zones of the oil pool. our calculations were carried out based on the assumption that during hydraulic re-fracturing the fracture liquid does not penetrate into the primary fracture, which means that it is necessary to provide isolation of the primary fracture while executing re-fracturing. otherwise, it is probable that its opening proceeds the conclusion that has been also arrived at by foreign researchers investigating the growth of the secondary hf in the framework of physical models [4]. furthermore, as was already mentioned, to resist the additional circumferential stresses caused by generation of the primary hf, it is necessary to create weakening surfaces at certain depth and in the certain direction. however, at equal components of the horizontal stresses the development of the secondary hf in the direction perpendicular to the primary hf is possible without artificial technical interference. references [1] latypov, i.d., borisov, g.a., haidar, a.m., gorin, a.n., nikitin, a.n., kardymon, d.v. (2011) reorientation refracturing on rn-yuganskneftegaz llc oilfields, neftyanoe khozyajstvo – oil industry, 6, pp. 34–38. [2] latypov, i.d., fedorov, a.i., nikitin, a.a. (2013). research of reorientation refracturing, neftyanoe khozyajstvo – oil industry, 10, pp. 74-78. [3] wright, c.a., conant, r.a., stewart, d.e. emanuel, m.a., wright, w.w. (1994). reorientation of propped refracture treatments, spe paper 28078 presented at the 1994 spe / ismr rock mechanics in petroleum engineering conference, delft, aug. 29-31. doi: 10.2118/28078-ms. [4] lan, zh., zhang, g., spe, hou, f., he, x., liu x. (2008). evaluation of refracture reorientation in both laboratory and field scales, spe international symposium and exhibition on formation damage control, 13-15 february, lafayette, louisiana, usa, spe-112445-ms. doi: 10.2118/112445-ms. [5] parton, v.z., morozov, e.m. (1985). mekhanika uprugoplasticheskogo razrusheniya [elastic-plastic fracture mechanics], nauka, moscow. [6] fadeev, a.b. (1987). metod konechnykh ehlementov v geomekhanike [finite element method in geomechanics], nedra, moscow. [7] zubkov, v.v., koshelev, v.f., lin'kov, a.m. (2007). numerical modeling of hydraulic fracture initiation and development, j. min. sci., 2007, vol. 43, no. 1, pp. 40-56. doi: 10.1007/s10913-007-0006-6 [8] timbrell, c., maligno, a., stevens, d. (2013). simulation of complex 3d non-planar crack propagation using robust adaptive re-meshing and radial basis functions. available at: http://www.zentech.co.uk/download/zentech-blos-nwc13.pdf. [9] kramberger, j., flasker, j. (2006). numerical simulation of 3-d crack growth in thin-rim gears. available at: http://www.gruppofrattura.it/ocs/index.php/esis/cp2006/paper/viewfile/9516/6139. t o. y. smetannikov et alii, frattura ed integrità strutturale, 49 (2019) 140-155; doi: 10.3221/igf-esis.49.16 155 [10] korolev, i.k., petinov, s.v., freidin, a.b. (2009). numerical simulation of damage accumulation and fatigue crack growth in elastic materials, vycisl. meh. splos. sred – computational continuum mechanics, 2(3), pp. 34-43. doi: 10.7242/1999-6691/2009.2.3.21 [11] perkins, t.k., kern, l.r. (1961). widths of hydraulic fractures, j. petrol. technol., 13(9), pp. 937-949. doi: 10.2118/89-pa. [12] nordgren, r.p. (1972). propagation of a vertical hydraulic fracture, soc. petrol. eng. j., 12(4), pp. 306-314. doi: 10.2118/3009-pa. [13] economides, m. j., oligney, r., valko, p. (2002). unified fracture design, orsa press, alvin, tx. [14] hoek, e. (1965). rock fracture under static stress conditions, phd thesis in philosophy and engineering, the faculty of engineering of the university of cape town. [15] murakami, yu. (1990). handbook of the stress intensity factors [spravochnik po koehfficientam intensivnosti napryazhenij], 1, mir, moscow. << /ascii85encodepages false /allowtransparency false /autopositionepsfiles true /autorotatepages /none /binding /left /calgrayprofile (dot gain 20%) /calrgbprofile (srgb iec61966-2.1) /calcmykprofile (u.s. web coated \050swop\051 v2) /srgbprofile (srgb iec61966-2.1) /cannotembedfontpolicy /error /compatibilitylevel 1.4 /compressobjects /tags /compresspages true /convertimagestoindexed true /passthroughjpegimages true /createjobticket false /defaultrenderingintent /default /detectblends true /detectcurves 0.0000 /colorconversionstrategy /cmyk /dothumbnails false /embedallfonts true /embedopentype false /parseiccprofilesincomments true /embedjoboptions true /dscreportinglevel 0 /emitdscwarnings false /endpage -1 /imagememory 1048576 /lockdistillerparams false /maxsubsetpct 100 /optimize true /opm 1 /parsedsccomments true /parsedsccommentsfordocinfo true 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/hrv (za stvaranje adobe pdf dokumenata najpogodnijih za visokokvalitetni ispis prije tiskanja koristite ove postavke. stvoreni pdf dokumenti mogu se otvoriti acrobat i adobe reader 5.0 i kasnijim verzijama.) /hun 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can be opened with acrobat and adobe reader 5.0 and later.) >> /namespace [ (adobe) (common) (1.0) ] /othernamespaces [ << /asreaderspreads false /cropimagestoframes true /errorcontrol /warnandcontinue /flattenerignorespreadoverrides false /includeguidesgrids false /includenonprinting false /includeslug false /namespace [ (adobe) (indesign) (4.0) ] /omitplacedbitmaps false /omitplacedeps false /omitplacedpdf false /simulateoverprint /legacy >> << /addbleedmarks false /addcolorbars false /addcropmarks false /addpageinfo false /addregmarks false /convertcolors /converttocmyk /destinationprofilename () /destinationprofileselector /documentcmyk /downsample16bitimages true /flattenerpreset << /presetselector /mediumresolution >> /formelements false /generatestructure false /includebookmarks false /includehyperlinks false /includeinteractive false /includelayers false /includeprofiles false /multimediahandling /useobjectsettings /namespace [ (adobe) (creativesuite) (2.0) ] /pdfxoutputintentprofileselector /documentcmyk /preserveediting true /untaggedcmykhandling /leaveuntagged /untaggedrgbhandling /usedocumentprofile /usedocumentbleed false >> ] >> setdistillerparams << /hwresolution [2400 2400] /pagesize [612.000 792.000] >> setpagedevice microsoft word numero_34_art_16 l.p. pook, frattura ed integrità strutturale, 34 (2015) 150-159; doi: 10.3221/igf-esis.34.16 150 focussed on crack paths crack paths and the linear elastic analysis of cracked bodies l. p. pook 21 woodside road, sevenoaks tn13 3hf, united kingdom abstract. the linear elastic analysis of cracked bodies is a twentieth century development, with the first papers appearing in 1907, but it was not until the introduction of the stress intensity factor concept in 1957 that widespread application to practical engineering problems became possible. linear elastic fracture mechanics (lefm) developed rapidly in the 1960s, with application to brittle fracture and fatigue crack growth. the first application of finite elements to the calculation of stress intensity factors for two dimensional cases was in 1969. finite element analysis had a significant influence on the development of lefm. corner point singularities were investigated in the late 1970s. it was soon found that the existence of corner point effects made interpretation of calculated stress intensity factors difficult and their validity questionable. in 1998 it was shown that the assumption that crack growth is in mode i leads to geometric constraints on permissible fatigue crack paths. current open questions are. the need for a new field parameter, probably a singularity, to describe the stresses at surfaces. how best to allow for the influence of corner point singularities in three dimensional numerical predictions of fatigue crack paths. adequate description of fatigue crack path stability. keywords. linear elastic analysis; stress intensity factors; corner point singularities; crack paths; finite element analysis. introduction he complete solution of a crack growth problem includes determination of the crack path. this review is a brief survey of the development of ideas on the linear elastic analyis of cracked bodies that are relevant to crack path determination. it is based on the author’s personal involvement over more than 50 years. the review is restricted to linear elastic, homogeneous, isotropic materials, with any yielding confined to a small region at a crack tip. the first relevant papers had been published 50 years earlier, but in the late 1950s theoretical understanding of crack growth due to fatigue and static loadings was limited. the situation changed dramatically in the 1960s with the development of fracture mechanics, which is the applied mechanics of crack growth [1]. it was realised that linear elastic fracture mechanics, based on linear elastic analyses, sufficed for the solution of many practical engineering problems. by the mid 1970s practical applications of fracture mechanics were well established. in considering practical aspects of linear elastic fracture mechanics, scales of observation need to be taken into account since the scale chosen can make a considerable difference to the appearance of an object in general, and a crack in particular [2]. scales of observation of 0.1 mm and above are usually described as macroscopic. the linear elastic concept of stress intensity factor describes the linear elastic stress field in the vicinity of a crack tip, and is a singularity. stress intensity factors may be used to characterise the mechanical properties of cracked test pieces in just the same way that stresses are used to characterise the mechanical properties of uncracked test pieces. the conventional notation for the position of a point relative to the crack tip, and for the stresses at t l.p. pook, frattura ed integrità strutturale, 34 (2015) 150-159; doi: 10.3221/igf-esis.34.16 151 this point, is shown in fig. 1. a point on the crack tip is the origin of the cartesian coordinate system and the z axis lies along the crack tip. displacements of points within the cracked body when the body is loaded are u, v, w in the x, y, z directions. a fundamental fracture mechanics concept is that of crack tip surface displacement [3]. there are three possible modes of crack tip surface displacement, as shown in fig. 2. these are: mode i where opposing crack surfaces move directly apart in directions parallel to the y axis; mode ii where crack surfaces move over each other in the xz plane in directions parallel to the x axis, that is perpendicular to the crack tip; and mode iii where crack surfaces move over each other in the xz plane in directions parallel to the z axis, that is parallel to the crack tip. by superimposing the three modes, it is possible to describe the most general case of crack tip surface displacement. where more precise description is needed volterra distorsioni can be used [1]. the term mixed mode means that at least one mode, other than mode i, is present. it is matter of observation that, when viewed on a macroscopic scale, and under essentially elastic conditions, cracks in metals tend to grow in mode i, so attention is largely confined to this mode. crack surfaces are assumed to be smooth, although on a microscopic scale they are generally very irregular. figure 1: notation for crack tip stress field. figure 2: notation for modes of crack tip surface displacement. stress analysis of cracks he philosophical basis for a fracture mechanics analysis is that for crack growth to take place two conditions need to be satisfied [4]. firstly, sufficient energy needs to be available to operate a crack growth mechanism (thermodynamic criterion). secondly crack tip stresses must be high enough to operate the mechanism (stress criterion). stress intensity factors the key concept of stress intensity factor, for mode i and for mode ii, arises from a two dimensional linear elastic analysis for a straight crack. mode iii is not possible in two dimensions, so for this mode a quasi two dimensional anti plane analysis is used. in 1957 it was shown by williams [5] that the stress field in the vicinity of a crack tip is dominated by the leading term of a series expansion of the stress field. this leading term is the stress intensity factor, k, which is a singularity. a particular type of elastic crack tip stress field is associated with each mode of crack tip surface displacement, and subscripts i, ii and iii are used to denote mode. other terms are non singular. individual stress components are proportional to k/r where r is the distance from the crack tip. displacements are non singular and proportional to kr. once k is known, stress and displacement fields in the vicinity of the crack tip are given by standard equations. for a mode i crack, the second term is a stress parallel to the crack, usually called the t-stress [6]. the t-stress is used in some linear elastic fracture mechanics analyses. the thermodynamic criterion implies that the energy needed to create new crack surfaces must be considered. stress intensity factors automatically satisfy the stress criterion. in 1957 irwin [7] showed that they also satisfy the thermodynamic criterion. in 1967 finite element stress analysis software was becoming generally available [8]. finite elements were first used for the calculation of mode i stress intensity factors in two dimensional geometries in 1969 [9]. a stress intensity factor provides a reasonable description of the crack tip stress field in a k – dominated region at the crack tip, radius r  a/10 where a is crack length, as shown in fig. 3. an apparent objection to the use of the stress intensity factor approach is the violation, in the immediate vicinity of the crack tip, of the initial linear elastic assumptions, in that strains and displacements are not small. however, as noted by williams in 1962 [10], if the assumptions are t l.p. pook, frattura ed integrità strutturale, 34 (2015) 150-159; doi: 10.3221/igf-esis.34.16 152 violated only in a small core region, radius << r, than the general character of the k-dominated region is, to a reasonable approximation, unaffected. similarly, by this small scale argument, small scale non-linear effects due to crack tip yielding, microstructural irregularities, internal stresses, irregularities in the crack surface, the actual fracture process, etc, may be regarded as within the core region. in the early 1960s there was scepticism about the validity and utility of stress intensity factors [8]. however, collaborative theoretical and experimental work in the late 1960s helped to establish confidence [11, 12]) and by 1974 their use for the solution of practical engineering problems was well established [13], nearly two decades after williams’ discovery of stress intensity factors. figure 3: k-dominated and core regions at a crack tip. figure 4: fracture surface of 19 mm thick aluminium alloy fracture toughness test piece. corner point singularities in three dimensional geometries, the derivation of stress intensity factors makes the implicit assumption that a crack front is continuous. this is correct for cracks growing from internal defects. it is not correct in the vicinity of a corner point where a crack front intersects a free surface. the nature of the crack tip singularity changes in the vicinity of a corner point, and these corner point singularities, sometimes called vertex singularities, are an important source of three dimensional effects [1]. many of the cracks observed in service, and in laboratory tests, have corner points, for example fig. 4. kinematic considerations for a crack surface intersection angle, γ, (fig. 5) of 90, and a crack front intersection angle, β, (fig. 6) of 90 show immediately that mode ii and mode iii crack tip surface displacements cannot exist in isolation in the vicinity of a corner point. the presence of one of these modes always induces the other, sometimes called a coupled mode, and indicated by a superscript c. thus mode ii induces mode iiic and mode iii induces mode iic. this has been demonstrated experimentally by foam plastic models [14]. hence, in the vicinity of a corner point there are two modes of crack tip surface displacement. one is the symmetric mode, which is mode i. the other is the antisymmetric mode, a combination of modes ii and iii. for corner point singularities, the polar coordinates in fig. 1 are replaced by spherical coordinates (r, , ) with origin at the corner point. the angle  is measured from the crack front. there do not appear to be any exact analytic solutions for corner point singularities. an approximate solution was obtained in 1977 by benthem [15] for the restricted case of a quarter infinite crack in a half space. a more general approximate solution, using essentially the same approach, was obtained in 1979 by bažant and estenssoro [16]. in their analysis they assumed that all three modes of crack tip surface displacement are proportional to rλf(θ, ). they then calculated λ numerically for a range of situations. the stress intensity measure, k, may be used to characterise corner point singularities, where  can be regarded as a parameter defining the corner point singularity. it follows from the initial assumption that stresses are proportional to k/r and displacements to kλr1-λ, where r is measured from the crack front. hence, stress and displacement plots are straight lines when plotted using logarithmic scales, and such plots obtained from finite element analyses can be used to determine values of λ. for a crack surface intersection angle, , of 90 and a crack front intersection angle, , of 90 there are two modes of stress intensity measure corresponding to the modes of crack tip surface displacement. for the symmetric mode the stress intensity measure is ks, and for the antisymmetric mode it is ka. for poisson’s ratio, ν = 0.3 λ = 0.452 for the symmetric mode and 0.598 for the antisymmetric mode. recent highly accurate finite element results for discs and plates under anti plane loading [17, 18, 19] do not confirm the latter value. bažant and estenssoro’s analysis shows that, for a crack surface intersection angle, , of 90,  is a function of poisson’s ratio, , and the crack front intersection angle. at a critical crack front intersection angle, c,  = 0.5 and stress intensity factors are recovered. ks becomes ki, and ka a combination of kii and kiii. for a growing crack the crack front l.p. pook, frattura ed integrità strutturale, 34 (2015) 150-159; doi: 10.3221/igf-esis.34.16 153 shape adjusts itself such that the crack front intersection angle tends to c. for the symmetric mode and  = 0.3, βc = 100.4 which, as predicted, is approximately the crack front intersection angle in fig. 4. for the antisymmetric mode and   0.3, c  67.0. crack front intersection angles of about this value have been observed [20]. figure 5: angle crack test piece, definition of crack figure 6: definition of crack front intersection angle, β. surface intersection angle, γ. crack paths crack front line tension crack has some analogies with a crystal dislocation. in particular, the elastic stress fields associated with a crack front and with a dislocation are both singularities. the associated energy means that a dislocation has a line tension, which controls its shape under an applied stress field. similarly [21], a crack front has a line tension which controls its shape, but with the important difference that a crack can grow, but in general cannot contract. at a corner point the corner point singularity provides a point force which balances the line tension in a direction corresponding to the crack front intersection angle. in consequence on a macroscopic scale, a crack front is smooth, and is usually curved as in fig. 4. any initial sharp corners rapidly disappear [22]. further in some circumstances, a growing fatigue crack tends to a particular stable shape [23, 24]. initial direction of crack growth in general, criteria are needed for the formation of a branch crack, its initial direction, and once formed, whether it will grow [25]. it is important to distinguish between criteria for formation of a branch crack and criteria for its growth. depending on circumstances, either can dominate behaviour [26, 27]. in two dimensions only modes i and ii are possible, the crack front is a point and the crack is a line. the direction of a mode i branch crack is given by the angle θ (fig. 7). related experimental work is usually carried out on plates or sheets of constant thickness, which are regarded as quasi two-dimensional. numerous criteria have been proposed for the initial direction of crack growth [28]. predicted initial branch crack directions are not sharply defined, so minor deviations from isotropy may have a significant influence on initial branch crack direction. in mixed modes i and ii fatigue testing measurement of the initial branch crack direction is of interest. however, the irregularity of actual fracture surfaces and, for curved branch crack paths, the need to estimate a tangent at the start of the branch crack make it difficult to measure crack directions accurately. the directions given in reference [29] are only repeatable to within 2 or 3 degrees. experimental results show that under fatigue loading initial crack directions vary widely [30]. the most widely used criterion for the initial crack growth direction, θ, is the maximum tensile stress (mts) criterion proposed by erdogan and sih in 1963 [31]. they considered a circle around the crack tip and took the direction of crack growth to be in the direction of the maximum tangential stress. this is a principal stress so the shear stress is zero, and leads to kisin = kii(3cos 1) (70.5…    -70.5…) where ki and kii are the modes i and ii initial crack stress intensity factors. an alternative approach is to find the value of θ for which the mode i branch crack stress intensity factor, ki, has its maximum value and the mode ii stress intensity, kii, is zero. calculation of ki and kii by comparison of stress field components leads to the same result [26, 27], so the two approaches are equivalent. several criteria have been proposed for the initial direction of crack growth in the general three dimensional case of mixed modes i, ii and iii loading [28]. in 2001 schöllmann et al [32] proposed a new criterion, which assumes that crack growth from a point on the crack front is perpendicular to the maximum principal stress. in two dimensions this is equivalent to the mts criterion. a complication is that, in the presence of mode iii on the initial crack, a mode i branch crack only intersects the initial crack front at one point [26, 27, 28]. what happens when a fatigue loading is applied in the presence of mode iii on the initial crack is illustrated by the fracture surface of the mild steel angle notch test piece shown in fig. 8 [33] (cf fig. 5). the rough area is static fracture where the test piece was broken open for examination. the expected a l.p. pook, frattura ed integrità strutturale, 34 (2015) 150-159; doi: 10.3221/igf-esis.34.16 154 tendency to mode i fatigue crack growth was observed on two distinct scales. on a scale of 1 mm crack the crack growth surface was smooth, crack fronts were approximately straight, and initially crack growth was mixed mode. as the fatigue crack grew the crack front rotated and crack growth eventually became mode i. rotation continued until the crack surface intersection angle was 90, and the crack front was curved. on a smaller scale of 0.1 mm the tendency to mode i fatigue crack growth results in the production of what is known as a twist crack [34]. a twist crack consists of narrow mode i facets usually connected by irregular, predominantly mode iii cliffs. the mode i facets gradually merged and the crack growth surface became smooth on this scale. figure 7: quasi two dimensional mixed modes i and ii initial figure 8: twist crack fracture surface of mild steel angle notch crack with a small mode i branch crack, crack growth angle, θ. test piece, fatigue loading. figure 9: directionally stable mode 1 fatigue crack growth. figure 10: mode i fatigue crack paths in a double cantilever beam specimen. crack path stability a fatigue crack growing in mode i is not necessarily directionally stable [28]. two dimensional linear elastic analyses are normally used in the consideration of crack path stability, with related experimental work on sheets or plates of constant thickness. a fatigue crack growing in mode i may be regarded as directionally stable if, after a small random deviation, perhaps due to microstructural irregularity, it returns to its expected ideal crack path, as shown in fig. 9. a directionally unstable crack does not return to the ideal path following a small random deviation; its path is a random walk. these ideas are not easily given rigorous mathematical form. for example, arbitrary limits have to be placed on what is regarded as returning to the ideal crack path. the direction stability of a mode i crack was analysed by cotterell [35] in 1966. he found that if the t-stress is compressive and there is a small random crack deviation, then the direction of mode i crack growth is towards the initial crack line. repeated random deviations mean that the crack follows a zigzag path about the ideal crack path, which is an attractor [28]. when the t-stress is tensile a crack is directionally unstable, and following a small random deviation, it does not return to the ideal crack path. a fatigue crack growing in a double cantilever beam specimen is directionally unstable in this sense. typical crack path behaviour is shown schematically in fig. 10. an initial random deviation can be either above or below the centre line, so there are two possible crack paths. these are shown as solid and dashed lines in the figure. the directional stability of a crack may change as it propagates, and a stable mode i crack may follow a curved path. cracks tend to be attracted by boundaries and are increasingly stable as a boundary is approached. the biaxiality ratio, b, is a nondimensional function of the t-stress. it is given by [6]: i t a b k   (1) l.p. pook, frattura ed integrità strutturale, 34 (2015) 150-159; doi: 10.3221/igf-esis.34.16 155 where a is the crack length (half crack length for an internal crack), and ki is the mode i stress intensity factor. it is sometimes found that cracks are directionally stable even when the t-stress is tensile (or b is positive). in particular, the tstress is tensile for the widely used compact tension test piece (fig. 11). this is specified in some fracture mechanics based mode i testing standards [12], and in practice cracks are usually directionally stable. an alternative approach, proposed by pook [36] in 1998, is to consider the direct stresses, on the crack line, and near the crack tip. that due to the t-stress is simply t. the stress, x, due to the mode i stress intensity factor, on the crack line and ahead of the crack, is given by: ix 2 k r    (2) where r is the distance from the crack tip. the t-stress ratio, tr, may now be defined as the ratio of the t-stress to x, given by eq. (2), at some characteristic value of r, rch. provided that rch is small tr is a point criterion which is within the k-dominated region. since the t-stress criterion is based on the idea of random crack path perturbations due to microstructural irregularities, rch should be of the same order of size as microstructural features. taking rch = 0.0159... mm leads, using mn-m units, to the convenient expression r 0.01b t a  (3) which implies that there is a size effect. for a particular material, there is a critical value of tr, trc, below which a fatigue crack path is directionally stable [28]. for fatigue tests on biaxially loaded waspaloy sheets trc = 0.022 and for static tests on biaxially loaded pmma sheets trc = 0.013. for a compact tension test piece with w = 50 mm trc < 0.22. it is unusual to carry out tests using compact tension test pieces with w < 50 mm so this value is consistent with the waspaloy result. figure 11: compact tension test piece. figure 12: crack fronts (solid lines) and trajectories (dashed lines) on a smoothly curved crack growth surface. geometric constraints on mode i crack paths in 1998 it was shown by pook [37] that the assumption that crack growth is in mode i leads to geometric constraints on permissible fatigue crack paths. consider a general, smoothly curved, crack growth surface, that is one that is differentiable at least three times. assume that on this surface there is an ordered family of smooth curves representing successive positions of the crack front, as shown by the numbered solid lines in fig. 12. crack growth must be in mode i for the surface to remain smooth. crack front line tension ensures that crack fronts are smooth curves. corresponding crack growth directions are given by the family of orthogonal trajectories. these are also smooth curves, and are shown by the dashed lines on the figure. in differential geometry terms these two families are an orthogonal net [38]. in general, there are two principal directions on the surface where the curvature is either a maximum or a minimum. for a given smooth surface the trajectories of these principal directions have zero torsion (twist in space), and are a unique orthogonal net [38]. geometric considerations show that, for mode i crack growth this orthogonal net defines permissible families of crack fronts and crack trajectories. on a crack growth surface either family of principal curvature trajectories can define a family of crack front positions. further, since a family of crack front positions is ordered, crack growth can be in either direction along the trajectories. hence, for a given crack growth surface there are four possible crack front families. there l.p. pook, frattura ed integrità strutturale, 34 (2015) 150-159; doi: 10.3221/igf-esis.34.16 156 is an important exception to the geometric constraint on permissible mode i crack front families. on a plane the curvature is zero in all directions, so principal directions cannot be defined, and there is no orthogonal net of principal curvature directions. therefore, for a flat mode i crack there is no geometric constraint on permissible crack front families, and a wide range of crack front families is possible and, indeed, observed [39, 40]. fatigue crack path prediction in general, fatigue crack paths are difficult to predict. in practice, fatigue crack paths in structures are often determined by large scale structural tests [23, 41]. theoretical predictions are carried out numerically using finite element analysis or boundary element analysis. the validity of the algorithms used is checked by comparison of predictions with experimental data. two dimensional mode i fatigue crack path predictions have been carried out by a number of authors, using the same general scheme including portela [42] in 1993. calculations are carried out using small increments of straight crack growth. the size of the increment is calculated using an appropriate fatigue crack growth equation. the direction taken by each increment is selected using the criterion that the increment is pure mode i. agreement between numerical predictions and experimental data obtained using thin sheets is variable [21]. the availability of increasingly powerful computers mean that two dimensional predictions have now largely been superseded by three dimensional predictions. for the special case of a flat mode i initial crack in a symmetrical configuration crack mode i fatigue crack growth is in the same plane as the initial crack, and in a direction perpendicular to the crack front. by definition the crack growth angle, θ, (fig. 7) is zero. it is implicitly assumed that the crack is directionally stable. increments of straight fatigue crack growth are calculated for a set of points along the crack front. the tips of these increments, connected by straight lines or a fitted curve, define a new crack front. in 1989 smith and cooper [22] carried out some finite element calculations for a flat irregular mode i crack and showed that irregularities rapidly disappeared. in 2005 dhondt [43] carried out some finite element calculations for a flat mode i fatigue crack path in a model containing geometric discontinuities. the results showed that the crack front intersection angle has a trend towards 100, which is close to the theoretical critical crack front intersection angle. when the crack crosses a geometric discontinuity there is a large, abrupt change in the crack front intersection angle, but it then converges to the critical crack front intersection angle. schöllmann et al’s criterion [32] for the initial direction of crack growth in the general three dimensional case of mixed modes i, ii and iii loading is evaluated on a curved cylinder with centre line along the crack front. the ends of the cylinder are perpendicular to its axis to avoid meshing difficulties. the resulting equations have to be evaluated numerically. the criterion also includes a method of calculating an equivalent mode i stress intensity factor for use in the calculation of fatigue crack growth increments. in the presence of mode iii the overall crack path increment is mixed mode. this is compatible with the idea of a twist crack where, on a scale of 1 mm, the crack path is mixed mode (fig. 8). a fully automatic finite element program incorporating the criterion was used to analyse fatigue crack growth in the frame of a hydraulic press that had failed in service [44]. the results showed good agreement with the observed crack path in the structure. however, there was considerable scatter in the predicted crack front intersection angles. a detailed description of a fully automatic finite element program for the calculation of fatigue crack paths in the general three dimensional case was given by dhondt [45] in 2014. a particular difficulty is meshing in the vicinity of a corner point when the crack front is not perpendicular to the surface. this is avoided by an approximation in which the surface is locally perpendicular to the crack front. the crack growth direction is determined iteratively using a principal stress criterion. the results obtained are justified by comparison with experimental data. differences arise where mode iii crack surface displacements lead to friction between opposing crack surfaces and to the development of twist cracks. neglecting friction leads to a conservative result. plane strain fracture toughness testing nterest in assessing the fracture toughness, or resistance to brittle fracture, of metals goes back to 1822 when tredgold commented on the assessment of cast iron [1]. by 1962 numerous empirical tests had been developed in order to determine whether a steel was brittle or ductile [1]. the best known test is the charpy impact test using notched test pieces. it is still in use, but it does not provide quantitative fracture toughness data that can be used in design [13]. the situation changed dramatically in the 1960s with the development of standards for plane strain fracture toughness (kic) testing. this was based on two empirical observations [1, 46]. first, that the sharpest possible machined notch may not adequately represent a crack. second, that in a test piece of constant thickness, the fracture toughness is a function of test piece thickness. however, if the test piece thickness is above a minimum value, which depends on the material, then the fracture toughness is a minimum, and it is a material constant [46]. this minimum value became known i l.p. pook, frattura ed integrità strutturale, 34 (2015) 150-159; doi: 10.3221/igf-esis.34.16 157 as kic. the minimum thickness depends on the yield stress, y, of the material, and is given by 2.5(ki/y)2. the factor 2.5 is empirical and is a compromise. it was also found that consistent values are obtained for kic if it is calculated from the load necessary to cause a significant amount of crack growth, defined as 2 per cent of the initial crack length. only two dimensional stress intensity factor solutions were available for test pieces of constant thickness, such as the compact tension test piece, shown in fig. 11 so a limit had to be based on permissible crack front curvature, and an appropriate through thickness average crack length defined. the empirical basis of some aspects of kic testing meant that extensive development work was needed to develop workable standards [8, 12]. it also means that standards contain very detailed requirements to ensure reproducibility between laboratories. discussion and conclusions he linear elastic analysis of cracked bodies, usually known as linear elastic fracture mechanics (lefm), is a twentieth century development. the first theoretical analysis appeared in 1907, but it was not until the introduction of the stress intensity factor concept in 1957 that widespread application to practical engineering problems became possible. lefm developed rapidly in the 1960s, with application to brittle fracture and fatigue crack growth, and the development of a standard for the plane strain fracture toughness testing of metals. the first application of finite elements to the calculation of stress intensity factors for two dimensional cases was in 1969. the 1970s were a period of consolidation. lefm was increasingly used in failure analysis. analyses were assisted by the publication of stress intensity factor handbooks. corner point singularities were investigated in the late 1970s. a key finding was that a corner point modes ii and iii cannot exist in isolation. hence, the presence of one of these modes always induces the other, and is sometimes called a coupled mode. by 1986 the increasing power of mainframe computers meant that three dimensional finite element analysis of cracked bodies became feasible. finite element analysis of cracked three dimensional configurations, which started in the late 1980s, confirmed the existence of coupled modes. it was soon found that the existence of corner point effects made interpretation of calculated stress intensity factors difficult, and their validity questionable. in a recent investigation a coupled mode generated by anti-plane loading of a straight through-the-thickness crack in linear elastic discs and plates was studied using accurate three dimensional finite element models. the results make it clear that bažant and estenssoro’s analysis of corner point singularities is incomplete. an open question is the need for a new field parameter, probably a singularity, to describe the stresses at surfaces. finite element analysis had a significant influence on this aspect of the development of lefm. numerical two dimensional mode i crack path predictions were carried out in the early 1990s. agreement between theoretical predictions and experimental data obtained using thin sheets is variable. the availability of increasingly powerful computers means that two dimensional predictions have now largely been superseded by three dimensional predictions. numerical three dimensional predictions of fatigue crack paths between 2003 and 2014 showed good agreement with observed fatigue crack paths. however, how best to allow for the influence of corner point singularities in three dimensional numerical predictions of fatigue crack paths is an open question. crack path prediction would not have been possible without the use of finite element analysis or boundary element analysis. in 1998 it was shown that the assumption that crack growth is in mode i leads to geometric constraints on permissible fatigue crack paths. line tension ensures that crack fronts are smooth curves. a necessary condition for crack growth to be in mode i is that the crack growth surface must be smooth. on a smoothly curved crack growth surface there is an ordered family of smooth curves representing successive positions of the crack front and a family of crack growth trajectories. these are an orthogonal net passing along directions of maximum and minimum curvature. on a plane the curvature is equal in all directions, there is no orthogonal net, and therefore no geometric constraint on permissible crack front families. the biaxiality ratio, a nondimensional function of the t-stress, is sometimes used as a crack path stability criterion, but it is not satisfactory. an alternative approach suggested in 1998, is to use the t-stress ratio, tr, which is a point criterion based on the t-stress. for a particular material, there appears to be a critical value of tr, trc, below which a fatigue crack path is directionally stable. however, adequate description of fatigue crack path stability is an open question. requirements for a valid kic fracture toughness test in the latest standard [47] and are essentially unchanged from those in the first standard published in 1970 [48]. in other words, 1960s technology is still being used. this would not matter if the latest standards were satisfactory in practice. however, in 2012 schijve pointed out that the transferability of fracture toughness test data to practical situations was restricted so structural testing was sometimes needed [49]. also in 2012 t l.p. pook, frattura ed integrità strutturale, 34 (2015) 150-159; doi: 10.3221/igf-esis.34.16 158 kotousov et al [50] remarked that current standards ignore three dimensional effects. development of an adequate plane strain fracture toughness testing standard is an open question. references [1] pook, l. p., a 50-year retrospective review of three-dimensional effects at cracks and sharp notches. fatigue fract. engng. mater. struct., 36 (2013) 699-723. [2] carpinteri, a., spagnoli, a., a fractal analysis of size effect on fatigue crack growth. int. j fatigue, 26 (2004) 125-133. [3] paris, p. c., sih, g. c., stress analysis of cracks. in fracture toughness testing and its applications. astm stp 381. american society for testing and materials, philadelphia, usa, (1965) 30-81. [4] cottrell, a. h., the mechanical properties of matter. london: john wiley and sons, (1964). [5] williams, m. l., on the stress distribution at the base of a stationary crack, j. appl. mech., 24 (1957) 109-114. [6] sherry, a. h., france, c. c., goldthorpe, m. r., compendium of t-stress solutions for two and three dimensional geometries. fatigue fract. engng. mater. struct., 18 (1995)141-155. [7] irwin, g. r., analysis of stresses and strains near the end of a crack traversing a plate. j. appl. mech., 24 (1957) 361364. [8] pook, l. p., an aircraft company, a government laboratory, and a university. in rossmanith h p (ed). fracture research in retrospect.: a balkema, rotterdam, the netherlands, (1997) 493-505. [9] dixon, j. r., pook, l. p., stress intensity factors calculated generally by the finite element technique. nature, 224 (1969) 166-167. [10] williams, m. l., some observations regarding the stress field near the point of a crack. in proc. crack propagation symposium, cranfield, (1961). the college of aeronautics, cranfield, uk, i (1962) 130-165. [11] cottrell, c. l. m., may, m. j., linear elastic fracture mechanics in the united kingdom: work of the bisra fracture toughness (high strength steels) committee. in dobson m o (ed). practical fracture mechanics for structural steel. risley, warrington: united kingdom atomic energy authority, (1969) b1-b12. [12] zhu, x. k., joyce, j. a., review of fracture toughness (g, k, j, ctod, ctoa) testing and standardization. eng. fract. mech., 85 (2012) 1-46. [13] frost, n. e., marsh, k. j., pook, l. p., metal fatigue. clarendon press, oxford, uk, (1974). [14] pook, l. p., crack profiles and corner point singularities, fatigue fract. engng. mater. struct., 23 (2000) 141-150. [15] benthem, j. p., state of stress at the vertex of a quarter-infinite crack in a half-space. int. j. solids struct., 13 (1977) 479-492. [16] bažant, z. p., estenssoro, l. f., surface singularity and crack propagation. int. j. solids struct., 15 (1979) 405-426. [17] pook, l. p., berto, f., campagnolo, a., lazzarin, p., coupled fracture mode of a cracked disc under anti-plane loading. eng. fract. mech., 128 (2014) 22-36. [18] pook, l. p., berto, f., campagnolo, a., lazzarin, p., coupled fracture mode of a cracked plate under anti-plane loading. eng. fract. mech., 134 (2015) 391-403. [19] campagnolo, a., berto, f., pook, l. p., three-dimensional effects on cracked discs and plates under nominal mode iii loading. presented at cp 2015. [20] pook, l. p., approximation of mixed mode stress intensity factors for part-through cracks in tubular welded joints. in salama m m, toyoda m, liu s, dos santos j f and williams j (ed). proc. 12th int. conf. on offshore mechanics and arctic engineering. american society of mechanical engineers, new york, usa, iiib (1993) 803-807. [21] pook, l. p., on fatigue crack paths. int. j. fatigue, 17 (1995) 5-13. [22] smith. r. a., cooper, j. f., a finite element model for the shape development of irregular planar cracks. int. j. pres. ves. & piping, 36 (1989) 315-326. [23] dover, w. d., dharmavasan, s., brennan, f. p., marsh, k. j. (ed), fatigue crack growth in offshore structures. engineering materials advisory services ltd, solihull, uk (1996). [24] lin, x. b., smith, r. a., finite element modelling of fatigue crack growth of surface cracks. part ii: crack shape change. eng. fract. mech., 63 (1999) 523-540. [25] pook, l. p., the role of crack growth in metal fatigue. london: metals society, (1983). [26] pook, l. p., mode i branch cracks and their implications for combined mode failure. nel report 667. east kilbride, glasgow: national engineering laboratory (1980). l.p. pook, frattura ed integrità strutturale, 34 (2015) 150-159; doi: 10.3221/igf-esis.34.16 159 [27] pook, l. p., the significance of mode i branch cracks for mixed mode fatigue crack growth threshold behaviour. in brown m w and miller k j (ed). biaxial and multiaxial fatigue. egf 3. london: mechanical engineering publications ltd. (1989) 247-263. [28] pook, l. p., crack paths. wit press, southampton, uk, (2002). [29] pook, l. p., the effect of crack angle on fracture toughness. eng. fract. mech., 3 (1971) 205-218. [30] lam, y. c., mixed mode fatigue crack growth with a sudden change in loading direction. theoretical and appl. fract. mech., 19 (1993) 69-74. [31] ton, uk, f., sih, g. c., on the crack extension in plates under plane loading and transverse shear. j. bas. engng., 85d (1963) 519-527. [32] schöllmann, m., kullmer, g., fulland, m., richard, h. a., a new criterion for 3d crack growth under mixed-mode (i+ii+iii) loading. in de freitas m (ed). proc. sixth int. conf. on biaxial/multiaxial fatigue & fracture. instituto superior técnico, lisbon, portugal, ii (2001) 589-596. [33] pook, l. p., the fatigue crack direction and threshold behaviour of mild steel under mixed mode i and iii loading. int. j. fatigue, 7 (1985) 21-30. [34] lawn, b. r., wilshaw, t. r., fracture of solids. cambridge university press, cambridge, uk (1975). [35] cotterell, b., on brittle fracture paths. int. j. fract. mech., 1 (1965) 96-103. [36] pook, l. p., an alternative crack path stability parameter. in brown m w, de los rios e r and miller k j (eds.). fracture from defects. ecf 12. cradley heath, west midlands: emas publishing, i (1998) 187-192. [37] pook, l. p., geometric constraints on fatigue crack paths in tubular welded joints. the archive of mechanical engineering, 45 (1998) 143-156. [38] kreyszig, e., differential geometry. university of toronto press, toronto, canada, (1963). [39] mahmoud, m. a., surface fatigue crack growth under combined tension and bending. eng. fract. mech., 36 (1990) 389-395. [40] barenblatt, g. i., botvina, l. r., self-oscillatory modes of fatigue fracture and the formation of self-similar structures at the fracture surface. proc. roy. soc. lond. a., 442 (1993) 489-494. [41] pook, l. p., metal fatigue: what it is, why it matters. springer, dordrecht, the netherlands, (2007). [42] portela, a., dual boundary element analysis of crack paths. southampton: computational mechanics publications (1993). [43] dhondt, g., cyclic crack propagation at corners and holes. fatigue fract. engng. mater. struct., 28 (2005) 25-30. [44] fulland, m., sander, m., kullmer, g., richard, h. a., analysis of fatigue crack propagation in the frame of a hydraulic press. eng. fract. mech., 75 (2008) 892-900. [45] dhondt, g., application of the finite element method to mixed-mode cyclic crack propagation calculations in specimens. eng. fract. mech., 58 (2014) 2-11. [46] brown, w. f., srawley, j. e., plane strain crack toughness testing of high strength metallic materials. astm stp 410. american society for testing and materials, philadelphia, usa, (1967). [47] astm e399-12e3. standard test method for linear-elastic plane-strain fracture toughness kic of metallic materials. american society for testing and materials, west conshohocken, usa, (2012). [48] tentative method of test for plane strain fracture toughness testing of metallic materials. e399-70 t. american society for testing and materials, philadelphia, usa, (1970). [49] schijve, j., some comments on the paper: review of fracture toughness and standards (efm, 2012, vol. 85, 1-46). eng. fract. mech., 96 (2012) 760-761. [50] kotousov, a., lazzarin, p., berto, f., pook, l. p. coupled fracture modes at sharp notches and cracks. in. carpinteri a, pook l p, iacoviello f and susmel l. (ed). proc. fourth international conference on crack paths. university of parma, parma, italy, (2012) 135-146. microsoft word numero_34_art_4 y. sumi, frattura ed integrità strutturale, 34 (2015) 42-58; doi: 10.3221/igf-esis.34.04 42 focussed on crack paths fracture morphology and its evolution a review on crack path stability and brittle fracture along butt-weld y. sumi yokohama national university, japan sumi@ynu.ac.jp abstract. considerations are made for the fracture morphology and its evolution in relation to the brittle fracture along butt-weld, where crack path stability may play important roles in various aspects. analyses of a kinked and curved crack are first reviewed in the present paper. having learned the solutions of a kinked and curved crack, several crack path criteria are compared for the crack path prediction. then, some aspects of stability of a crack path are examined as to whether it may propagate, keeping its original direction or not in a homogeneous material, and whether crack kinking in a material having inhomogeneous fracture toughness may be predicted by seeking the state which gives rise to an energetically stable one. having reviewed the morphology of brittle crack propagation along butt-weld, brittle fracture of extremely thick plates of high tensile steel is discussed for the fracture control of recently emerging large container ships. keywords. curved crack; kinked crack; crack path criteria; crack path stability; butt-weld; extremely thick plate. introduction nalyses of a kinked and curved crack are reviewed in the present paper focusing attention on the brittle crack propagation along butt-weld. the perturbation solutions of a slightly curved crack [1-8] are compared with analytical solutions [9, 10]. having learned the solutions of a kinked and curved crack, several crack path criteria are compared for the crack path prediction, where criteria may be derived from a stress state prior to the crack propagation [11], the geometrical continuity condition of crack surfaces [1-3], or an energetically favorable condition after crack growth [9]. then, some aspects of stability of a crack path are examined as to whether it may propagate, keeping its original direction or not in a homogeneous material [12], and whether crack kinking in a material having inhomogeneous fracture toughness may be predicted by energetic stability [7]. crack path stability in a symmetric homogeneous brittle solid is reviewed [13-15], where the geometry of the body is symmetric with respect to the initial straight-crack line, and where the presence of a small asymmetric loading or slight material inhomogeneity which may produce a small mode-ii stress-intensity factor kii at the original crack tip, leads to non-collinear crack growth. the crack path stability is then examined by taking into account the curved trajectory predicted by the local symmetry criterion [12]. lastly, having reviewed experimental and theoretical studies of brittle crack propagation paths along butt-weld [7, 16], the concept of fracture control applied to extremely thick plates of high tensile steel is discussed for the structural design of large container ships [17]. a y. sumi, frattura ed integrità strutturale, 34 (2015) 43-59; doi: 10.3221/igf-esis.34.04 43 solutions of a curved crack he problem of a slightly non-collinear, quasi-static crack growth is considered. problems of this kind have been treated by a first order perturbation method, in the context of muskhelishvili’s complex potentials [18], by banichuk [1] and goldstein and salganik [2,3]. cotterell and rice [4] employed the same method and obtained a rather simple first order expression for the stress intensity factors, which were used to examine the crack growth path of a semi-infinite crack in an infinitely extended domain. we shall consider the first and second order perturbation solutions which can take into account the effects of the geometry of the domain, i.e., finite outer boundaries as well as the finite crack length, sumi et al. [5], sumi [6,7]. for this purpose we first calculate the perturbation solution for a semi-infinite straight crack with a slightly kinked and curved extension, which will be used as the fundamental solution of the problem. we can establish the effect of the geometry of the domain by considering the far field behavior of the fundamental solution. second order perturbation solution consider a homogeneous linearly elastic brittle solid containing a straight crack of length a. the stress tensor and the displacement vector ij and ui are defined in the domain v occupied by the body. surface tractions, ti, are prescribed on the part of the outer boundary, st , and on the crack faces, sc± , while surface displacements, vi , are prescribed on the remaining part of the outer boundary, su (see fig. 1). the cartesian coordinate system (x1, x2) with the origin at the crack tip has its x1-axis along with the original crack line. in the following analysis this problem is referred to as the original problem.  figure 1: straight crack with slightly kinked and curved extension. for a slightly non-symmetric loading system, we may have a slightly kinked and curved crack extension, whose projected length on the x1-axis is h, and whose deviation from the x1-axis is (h). to investigate the detailed distribution of stresses ahead of the extended crack tip, we consider the second order perturbation solution of the semi-infinite straight crack with slightly kinked and curved extension, whose near tip field solution gives the stress intensity factors. then we account for the effect of the finite outer boundary by using the far field solution of the semi-infinite crack. in the following analysis we assume that the shape of the crack extension can be approximated by 3/2 2( ) ,1 1 1 1x x x x      (1) disregarding higher order terms. constants and  are considered as shape parameters of the crack extension. this expression has the appropriate asymptotic form associated with the stress field ahead of a preexisting crack tip. the crack profile may be determined based on an appropriate crack path criterion which will be discussed in the following section. as is shown in fig. 2, another linear orthogonal coordinate system (1, 2) is introduced, ,1 1x  (2) and the crack path deviation from the 1-axis is measured by t y. sumi, frattura ed integrità strutturale, 34 (2015) 42-58; doi: 10.3221/igf-esis.34.04 44 ( ) ( ) ( ),1 1 h      (3) following the same method as used by banichuk [1], goldstein and salganik [2, 3], and cotterell and rice [4], the perturbation solution of the stress field can be expressed by muskhelishvili’s analytic functions [18] given by figure 2: coordinate systems for a kinked and curved crack. 2[ '( ) '( )],11 22 2 2[( ) ''( ) ( ) '( )],22 11 12 z z i z z z z z                    (4) where z= x1+ix2. the analytic functions(z) and (z) are expanded in terms of (1) up to the second order in the following form: 3 0 1 2 3 0 1 2 '( ) ' ( ) ' ( ) ' ( ) ( ), ( ) ( ) ( ) ( ) ( ), z z z z o z z z z o                   (5) in which zand (z) are of the zero-th order, z and (z) are of the first order, and z and (z) are of the second order in . the boundary conditions on the crack surfaces, at z=1+i become 2'( ) '( ) [( ) ''( ) ( ) '( )] ( ),i n sz z e z z z z z t it             (6) where  is the angle of the slope on the crack line. it is assumed that the crack surfaces are subjected to normal and shear tractions tn and ts on the upper surface and -tn and -ts on the lower surface, respectively. we also assume that tractions on the crack surfaces, tn and ts are bounded and integrable in the defined range. approximate description of a slightly kinked and curved extension of a straight crack the second order approximation of the stress distribution in the vicinity of the original crack tip can be expressed by 1 2 3( , 0) ( , 0) ( , 0) ( ),1 ,2 1 ,22 12 x x x oij ij ij ij          (7) in which i 1( , 0) ( ),11 1 i 122 1 i 1( , 0) ( ),22 1 i 122 1 ii 1( , 0) ( ),12 1 ii 122 1 k x x t b o x x k x x b o x x k x x b o x x                 (8) where ki and kii are the stress intensity factors, and the coefficients t, bi, and bii are also determined from the solution of the boundary-value problem prior to the crack extension. the surface tractions on the extended crack surfaces, tn and ts y. sumi, frattura ed integrità strutturale, 34 (2015) 43-59; doi: 10.3221/igf-esis.34.04 45 can be calculated by using eq.(7), and the stress intensity factors at the extended crack tip in an infinite plane can be obtained as ( ) 2 2 1/2 2 i i ii ii i i ii ii 2 3/2 i 3 3 9 9 2 1 9 5 1 2 1 3 8 2 4 8 2 8 4 11 2 27 3 ( ), 2 32 2 k k k k k t h b k b t k h o h                                               (9) ( ) 2 1/2 2 ii ii i i ii ii i 2 3/2 i ii 7 1 3 2 21 2 1 27 1 2 1 8 2 4 8 2 8 3 63 2 5 2 ( ). 4 4 32 2 k k k k t k h b k b t k h o h                                                                 (10) as far as the terms obtained by wu [9], and amestoy and leblond [10] are concerned, eq. (9) represents the exact second order asymptotic behavior of the mode-i stress intensity factor, while the second order terms in eq. (10) are approximate. although being small, this slight numerical difference may arise from the interaction of stress singularities between the kinked corner and the crack tip. stress intensity factors for a finite body since the leading terms of the far-field stress and displacement are of the order of the crack extension length h [7], the finite body corrections of the stress intensity factors at the kinked and curved crack tip are given by     ( ) 2 2 i i ii 11 ii i 12 3/2 i ii 21 ii i 22 3 1 1 1 8 8 3 3 ( ), 2 2 fk k k k k k k k k k k k k h o h                                       (11)     ( ) 2 2 ii i ii 21 ii i 22 3/2 i ii 11 ii i 12 7 5 1 1 8 8 1 1 ( ), 2 2 fk k k k k k k k k k k k k h o h                                       (12) where 11k , 21k and 12k , 22k correspond to the stress intensity factors of mode-i and mode-ii for the mode-i and modeii fundamental fields [19], respectively, [5, 6,7]. the stress intensity factors ki and kii, at the kinked and curved crack tip are accordingly obtained by the sum of eqs. (9) and (11), and the sum of eqs. (10) and (12) given by, ( ) ( ) 3/2 i i i ( ), fk k k o h   (13) ( ) ( ) 3/2 ii ii ii ( ). fk k k o h   (14) if we only retain the first order terms with respect to (1), the solution is simplified as 1/2 i i i ii ii ii ii i 11 3/2 i 12 21 ii 12 ii 11 22 3 9 5 3 2 4 2 4 3 3 ( ), 2 2 b k k k k h b k k k k k k k k k k k h o h                                  (15) y. sumi, frattura ed integrità strutturale, 34 (2015) 42-58; doi: 10.3221/igf-esis.34.04 46 1/2 ii ii ii i i i i i 21 3/2 i 11 22 ii 22 ii 12 21 3 2 3 2 2 2 4 2 4 4 1 1 ( ). 2 2 b k k k k t h b t k k k k k k k k k k k h o h                                            (16) crack path criteria aving obtained the stress intensity factors of a slightly kinked and curved crack, investigations are made for possible crack paths along which fracture takes place. several aspects should be taken into account, such as the stress state prior to crack extension, geometrical continuity of a crack path, and the change of energy along different crack paths. the stress field ahead of a crack tip has been obtained for mode-i and mode-ii, respectively, and the corresponding hoop stress component of is expressed by 3 1 3 3 3 3i iicos cos sin sin . 4 2 4 2 4 2 4 22 2 k k r r                      (17) the solution of a straight kink of a finite kink angle was obtained by bilby and cardew [20], bilby et al. [21], hayashi and nemat-nasser [22], leblond [23], and amestoy and leblond [10], where the analytical expression of the stress intensity factors ahead of the kinked tip was obtained by amestoy and leblond [10] in the following form:      i 11 i 12 ii ,k f k f k    (18)      ii 21 i 22 ii ,k f k f k    (19) where ki and kii are the stress intensity factors at the original crack tip, and ki and kii are those at the extended crack tip, respectively. fpq (p,q=1,2) which are functions of the kink angle , are given by   2 4 6 811 2 4 2 3 1 5 1 11 119 1 ( ), 8 128 9 72 15360 f o                          (20)   3 5 712 2 4 2 3 10 1 2 133 59 ( ), 2 3 16 180 1280 f o                           (21)   3 5 721 2 4 2 1 4 1 2 13 59 ( ), 2 3 48 3 30 3840 f o                          (22)   2 4 6 822 2 4 2 6 4 2 4 3 8 29 5 32 4 1159 119 1 ( ). 8 3 18 128 15 9 7200 15360 f o                                       (23) using these equations, the energy release rate along the kink can be calculated by  2 2i ii 1 , 8 g k k      (24) in which is a function of poisson’s ratio andis the shear modulus. the crack path criterion based on the stress distribution prior to crack extension was proposed by erdogan and sih [11], where they assumed that a crack would propagate in the direction normal to the maximum hoop stress. by differentiating h y. sumi, frattura ed integrità strutturale, 34 (2015) 43-59; doi: 10.3221/igf-esis.34.04 47 eq. (17) with respect to , we can obtain the equation which gives rise to the direction as  sin 3cos 1 0,i iik k    (25) another criterion is the geometry-based one, the so-called local symmetry criterion proposed by banichuk [1] and goldstein and salganik [2, 3], where they assume that the crack extends under pure mode-i condition along the crack extension, i.e.      ii 21 i 22 ii 0.k f k f k     (26) in contrast to the condition (25), the stress intensity factor after crack extension is required for the crack path prediction. sometimes the explicit simplicity of the criterion (25) is in favor over the criterion (26), which may be consistent but numerically implicit. in order to examine whether the above two criteria are equivalent to each other or not, we calculate determinant, d1 of eqs. (25) and (26) with respect to ki and kii,      1 22 21 3 5 7 2 4 2 sin 3 cos 1 4 1 4 53 1 ( ), 3 4 90 32 d f f o                               (27) where f2q (q=1,2) are expanded in terms of . the result does not vanish so that these two criteria are independent with each other, and the difference appears in the third order term with respect to . a more fundamental question raised from this result is that since the crack path predicted by the maximum hoop-stress criterion certainly induces a finite mode-ii stress intensity factor at the crack tip after an infinitesimally small crack extension, we cannot expect a smooth trajectory of a crack path i.e., an infinitesimally small zig-zag crack path along the kink. the energy-based criterion is the one which maximizes the energy release rate so that the potential energy of the elastic body is minimized, wu [9]. using the energy release rate calculated by eq. (24), this condition is attained by i ii i ii 1 0, 4 dk dkdg k k d d d              (28) and 2 2 0. d g d  (29) suppose that the equivalence of the criteria (26) and (28) holds, then the second term of the right-hand side of eq. (28) vanishes so that i i 0. dk k d  (30) since ki can naturally be assumed to be positive during the fracturing process, we must have the stationary condition of ki, i.e.,    i 11 i 12 ii' ' 0, dk f k f k d       (31) in which prime denotes the differentiation with respect to and  1' qf  (q=1,2) are given by   3 5 711 2 4 2 3 4 5 2 11 119 ' ( ), 4 32 3 12 2560 f o                          (32) y. sumi, frattura ed integrità strutturale, 34 (2015) 42-58; doi: 10.3221/igf-esis.34.04 48   2 4 612 2 4 2 3 10 3 10 133 59 ' ( ). 2 16 36 256 f o                          (33) in order to examine the similarity of the criteria given by eqs. (31) and (26), we again calculate the determinant d2 of the coefficients of ki and kii, which is given by         5 72 21 12 11 21 2 2 ' ' ( ). 45 d f f f f o           (34) it is interesting to note that these two criteria are identical up to the 4th order with respect to the kink angle . also, from the above discussions, the direction which maximizes the mode-i stress intensity factor is another distinct criterion. in fig. 3, one may compare the difference or similarity of kink angles predicted by these criteria. it is rather difficult to numerically distinguish the difference of the local symmetry and maximum energy release rate criteria. we shall discuss the local symmetry criterion in the following discussions, because it may lead to slightly kinked and curved crack propagation in a relatively simple way by using the perturbation solution. figure 3: comparison of the kink angles under mixed mode conditions [16]. crack path prediction and its stability crack path prediction based on the local symmetry criterion ince a smooth path can be obtained by the local symmetry criterion and the equivalence of the maximum energy release rate may be expected within a small kink angle, discussions are made based on this criterion. we shall consider the prediction of a kinked and curved crack path based on the first order perturbation solution (15) and (16) at an arbitrarily extended crack tip from a straight crack, so that the crack path is obtained by substituting eq. (16) into the local symmetry criterion (26), and the shape parameters of the crack path are obtained as [6-8] ii i 2 , k k    (35) i 8 2 , 3 t k     (36) s y. sumi, frattura ed integrità strutturale, 34 (2015) 43-59; doi: 10.3221/igf-esis.34.04 49     2ii21 i 22 ii 22 11 i i i i i 1 1 1 2 4 / . 2 2 2 b k k k k k k k b t k k k                    (37) crack path stability based on the shape parameters obtained by the crack path prediction, crack path stability in a symmetric homogeneous brittle solid is considered, leevers et al. [13], broberg [14], pook [15]. we shall investigate the cases where the geometry of the body is symmetric with respect to the initial straight crack line, and where the presence of a small asymmetric loading or slight material inhomogeneity which may produce a small mode-ii stress-intensity factor kii at the original crack tip, leads to non-collinear crack growth with small, initial kink angle . the crack path stability is then examined by taking into account the second and third terms of eq. (1). let the crack growth profile be normalized by a representative length, ls, of the body. we set * * * 1 , h h h l l l s s s                                        (38) where * ** , , and .s s s l l l         (39) the crack path stability is determined by the quantity ds, given by * * 0 : stable 0 : unstable s h d s l                    , (40) where * i 8 2 / 3 s t l k     , (41) and     * 21 1 1ii/ 2 4 /21 i 22 ii 22 11 i i i2 2 2 2 ii i s b k k k k k k k b t k l k k                   . (42) the crack path stability for predominantly mode-i loading conditions can be determined from the values of */ and */. it has been confirmed that if the small imperfection parameter, kii, is considered to be independent on the crack length, sum of the first three terms in the right hand side of eq.(42) vanish, so that eqs. (36) and (42) are expressed only in terms of the quantities which do not depend on the small asymmetric loading condition. if we represent the stability condition (40) in terms of */ and */, we have     * * * * 2* * * * 2* * * * ( i ) / 0 and / 0 : stable (ii) / 0 and / 0 : unstable stable for 0 / / (iii) / 0 and / 0 : unstable for / / unstable (iv) / 0 and / 0 : s s h l h l                                       2* * 2* * for 0 / / stable for / / s s h l h l           (43) stable and unstable paths defined by (43) are illustrated in fig.4. y. sumi, frattura ed integrità strutturale, 34 (2015) 42-58; doi: 10.3221/igf-esis.34.04 50 figure 4: comparison of the crack path stability [12]. as can be seen from the condition (43), the present concept of crack path stability includes the length parameter h/ls and the stability may depend on the range of the crack growth length considered. an initially unstable crack growth path may recover its straight direction with increasing crack length under the condition (iv) in (43). on the other hand, if condition (iii) holds, the crack path may become unstable in the range h/ls>(*/*)2. the cotterell and rice theory [4] is based on the first term of the condition (40), leading to the following criterion for crack path stability: * 0 : stable / 0 : unstable      , (44) which is equivalent to 0 : stable 0 : unstable t    (45) this may be considered as a local stability criterion for the branched and curved crack extension, while the condition (43) may be regarded as an intermediate range of stability concept, in which the stability conditions change with increasing crack length. this theoretical prediction is borne out by experimental observations. a double-cantilever beam specimen is shown in fig. 5, where the length l equals 6b. the characteristic length is ls=b. the numerical values of */ and */ are given in fig. 6, which show the condition * */ 0 and / 0,     (46) except for an extremely long initial crack. in this case the value of ds, given by (40), is always positive, so that an unstable crack path is expected. on the contrary, when the initial crack is extremely long and the crack tip is very close to the righthand edge of the specimen, we have * */ 0 and / 0,     (47) where the intermediate range of stability may exist. the experimental results [12, 24], are shown in fig. 7, where sharp crack curving is observed and the final break-off of the specimen may occur at either the upper or the lower surfaces. however, if the initial straight crack is extremely long and its tip is close to the right-hand edge of the specimen, crack curving is stabilized after some crack extensions as predicted by the theory. y. sumi, frattura ed integrità strutturale, 34 (2015) 43-59; doi: 10.3221/igf-esis.34.04 51 figure 5: double-cantilever beam specimen [12, 24]. figure 6: stability parameters for a double-cantilever beam specimen [12, 24]. figure 7: crack paths observed in double-cantilever beam specimens [12, 24]. energy consideration of crack paths for inhomogeneous fracture toughness following bilby and cardew [20], the elastic energy release rate g due to the slightly kinked and curved crack extension can be calculated by eq.(24) for a homogeneous material, where ki and kii, are the stress intensity factors at the extended crack tip. substitution of eqs. (13) and (14) into eq. (24) leads to an expansion of g in an ascending order of h [7], and it is given by,    0 i ii; ,   og g k k h  (48) where 0g is obtained as   2 2 2 2 0 i ii i i ii ii 1 ; ,     1 2 1 8 2 2 g k k k k k k                             (49) the first and second variations of 0g with respect to are calculated as   2 20 i ii i ii1  2 8 g k k k k          (50) y. sumi, frattura ed integrità strutturale, 34 (2015) 42-58; doi: 10.3221/igf-esis.34.04 52  2 2 2 20 i ii 1   8 g k k        (51) as far as the condition i iik k holds, conditions (50) and (51) indicate that the kink angle  is given by i ii 3 i ii 2 2 ii ii i i 2 2 2k k k k o k k k k                 (52) which gives rise to the maximum elastic energy release rate of the body. this result together with eq. (35) in the previous section may designate equivalent crack paths by employing the conditions of local symmetry and maximum energy release rate in homogeneous materials within the second order approximation theory. considering material inhomogeneity such as a local degradation zone, a crack may be kinked and curved due to the spatial variation of the fracture toughness. the method presented here may be effective to obtain possible crack paths in materials with inhomogeneous fracture toughness. let us consider a crack under pure mode-i loading condition, whose tip intersects a line degradation zone oriented at angle * (see fig. 8), where the critical energy release rates for the base material and the degraded material are cg and * cg , respectively. if the crack extends in the base material, eq. (52) is applicable, which obviously leads to the straight crack extension. the stress intensity factor at the instance of fracture is calculated from eq. (49) and given by i 8 1 cgk     (53) in contrast, if the crack extends in the degraded zone, the kink angle is * , and the corresponding stress intensity factor at the instance of kinked propagation is also calculated by eq. (49) as   * * i * 2 8 1 1 2 cgk            (54) the crack may actually extend in the degraded zone under the condition *i ik k . substitution of eqs. (53) and (54) into this inequality leads to the following relationship between the angle of inclination and the material properties; * 2 * 1 2 c cg g        (55) which cannot be predicted by a conventional stress criterion. when one applies the inequality (55), the resulting inclination angle * should be less than 30–40°, where the second order perturbation solution of the stress intensity factors is practically applicable. brittle fracture along butt-weld morphological aspects of brittle fracture along butt-weld ne of the most hazardous failure modes of welded steel structures is an instantaneous fracture due to crack propagation along weldment, which may lead to the catastrophic failure of the total structure. typical crack paths along a welded joint are schematically illustrated in fig. 9, where the applied stress a and the welding residual stress r acting parallel to the weldment are also sketched, hall et al. [25], munse [26], wells [27]. o y. sumi, frattura ed integrità strutturale, 34 (2015) 43-59; doi: 10.3221/igf-esis.34.04 53 figure 8: a mode-i crack intersecting a line-degradation at angle . figure 9: a brittle crack propagating parallel to a welded joint; (a) crack propagation in the base metal; (b) crack propagation along butt-weld joint. early experimental results of the esso tests, which were performed by kihara et al. [28, 29] using welded mild steel plates, indicate that a brittle crack initiated along the welded joint turns off the welding line and propagates into the base metal as illustrated by the crack path (a) in fig.9. a brittle crack propagates in a region a finite distance away from the welding line, where the distance increases with decreasing the ratio of applied and residual stresses. these morphological characteristics of brittle fracture of welded mild steel plates had been confirmed later by more sophisticated dynamic crack propagation and crack arrest tests using middle and large size specimens, sr147 [30] and sr153 [31]. in the case of welded mild steel plates, since cracks are expected to turn off the welding line due to the high tensile welding residual stress acting parallel to the welding line [32], the localized decrease of fracture toughness in the heat-affected zone does not play an important role in relation to the crack arrest capability of a welded total structure. kihara and ikeda [33] observed crack paths of welded high tensile steel plates, which exhibited different behavior from what was observed in welded mild steel plates. these morphological aspects of brittle fracture of welded plates, which were made of high tensile steel for ship structural use, were later investigated in detail by the shipbuilding research association of japan, sr147 [30], and sr153 [31], and sr169 [34]. it is observed in these experiments that although in some cases cracks turn off the welding line and propagate in the base metal, they sometimes propagate along the welding line as is illustrated by the path (b) in fig. 9. since the ratio of applied stress a of high tensile steel plates and the maximum tensile residual stress is relatively high in comparison with that for the mild steel plates, and since the relatively large decrease of the fracture toughness may be expected near the bond zone, these effects could cause the brittle fracture along the butt-weld for high tensile steel plates. y. sumi, frattura ed integrità strutturale, 34 (2015) 42-58; doi: 10.3221/igf-esis.34.04 54 in this case, the conditions corresponding to the crack propagation in the base metal and along butt-weld should be clearly distinguished for the evaluation of the crack arrest capability of welded structures. we shall review some analytical studies in the following subsection. analytical model for crack path prediction investigations are made for a butt-weld joint under a uniaxial tensile stress a applied normal to the joint [7]. the longitudinal component of welding residual stress r is assumed to be constant in the region under consideration. as shown in fig. 10, the initial crack of length 2a is assumed to be parallel to the welding line. material deterioration is observed along the heat-affected zone, which is modeled as a line degradation being also parallel to the welding line at a distance sl from the initial crack line. the resistance forces of crack propagation are denoted by cg for base and weld metals, and *cg for the degradation zones, respectively. brittle crack propagation is assumed to occur from the right-hand side of the crack tip, at which we choose the origin of the cartesian coordinate system 1 2o x x . since a slightly kinked and curved crack extension may be expected, the crack intersects the degradation line at an angle * with *1x h . figure 10: a mathematical modeling of curved crack propagation along butt-weld. figure 11: crack path destabilizing factors * / αs  and *  / αs  [7, 16]. as far as the initial crack tip is embedded in a homogeneous material, a crack path can be determined by the local symmetry criterion by eqs.(35)-(37), using the stress field parameters such as ki, kii and etc. at the original crack tip. this will simply lead to 0     under the pure mode-i condition, but this straight crack extension could occur only for the perfect system, which means that the loading condition and the geometry have the perfect symmetry with respect to the crack line. we consider that non-collinear crack propagation is caused by some load-induced or material-induced y. sumi, frattura ed integrità strutturale, 34 (2015) 43-59; doi: 10.3221/igf-esis.34.04 55 disturbances in the system with a small initial kink angle at the original crack tip, which can be interpreted as the initial imperfection of the system. the crack path stability is then examined by taking into account the second and third terms of eq. (1). the crack path stability is determined by the condition (40). fig. 11 shows the crack path destabilizing factors, * / αs  and *  / αs  , for the present case, where the ratios of applied stress and maximum residual stress are chosen as 0.25 and 0.5. in the case where the applied stress level is relatively low, these parameters have high values, so that crack paths of low stress brittle fracture initiated from a small initial crack may be curved to the base metal. as the crack further extends, it begins to intersect the line degradation zone. at this point the question arises as to whether the crack intersects the zone and penetrates into the base metal, or it kinks to the degradation zone. in order to answer this question, we calculate the angle * formed by the crack and the degradation line, which will lead to condition of kinked crack extension along the degradation line by the inequality (55). effect of residual stress and toughness along butt-weld case-studies are shown for the initial half crack length a = 100, 200, 300, 400, 500 mm. since the distance, sl between the initial crack line and the degradation line is of the order of the bead-width, it is selected as 50 mm. the imperfection parameter is selected as 2.5   . based on the theory presented in the previous subsection, we can determine the critical curves which distinguish the crack propagation in the base metal and in the degraded zone, respectively. such curves are illustrated in fig. 12, in which if the ratio of the applied stress and the residual stress, /a r  , and the ratio of the toughness of degraded zone and the base metal, * /c cg g fall into the lower right-hand side of the respective curves, a brittle crack may propagate along the degradation zone. it can be quantitatively understood that if the tensile residual stress acting parallel to the welded joint is relatively low, and if the decrease of fracture toughness in the degraded zone is relatively large, cracks may propagate along the degradation zone. this result qualitatively explains the difference of brittle fracture behavior observed in welded mild steel plates and high tensile steel plates. as observed in fig. 12, brittle fracture initiating from a longer straight crack has a tendency to propagate along the degradation zone. this means that once a brittle crack has begun to propagate along a welded joint, it is hard to turn it into the base metal. figure 12: critical relations between the material degradation and the applied stress; cracks penetrate into the base metal for the conditions corresponding to the upper left regions with respect to the curves [7, 16]. fracture control of butt-weld of large container ships ith the rapid increase of the size of container ships, fracture control of extremely thick plates employed in the deck structure of large container ships has been studied in a project organized by japan ship technology research association (jstra) [17], which includes the crack arrest design of a brittle crack having unexpectedly started and propagating in the deck structure. possible scenarios to ensure the crack arrest performance in the hatch-side coaming and upper deck plates have been proposed by classnk [35] focusing attention on the practical w y. sumi, frattura ed integrità strutturale, 34 (2015) 42-58; doi: 10.3221/igf-esis.34.04 56 arrest design. as mentioned, brittle cracks propagating along the welded joint deviate their paths from the weld, and penetrate into the base plate possibly due to the effect of welding residual stress. the arrest toughness, cak , of a brittle crack in order to prevent the propagation of long brittle cracks was found to be within the range 4,000–6,000n/mm3/2 at the service temperature, sr147 [30], which were based on the tests of the steel plates with the thickness less than 35mm used for ship structures. since the thickness of the plates used for extremely large container ships is 50-80mm, investigations have been made by yamaguchi et al. [36]. for the brittle crack arrest design, certain brittle crack arrest toughness, cak , must be ensured for a steel plate used for the arrester, so that an efficient test method has been developed to evaluate brittle crack arrest toughness of extremely thick steel plates. the objective of the arrest design of a brittle crack is to arrest brittle crack propagation at specific locations so that a catastrophic failure of the hull structure is prevented in the event of an unexpected crack initiation. for this purpose, the following functional requirements are introduced; 1. brittle crack should be arrested at specific locations (see fig. 13), 2. hull girder stress after the arrest should be less than the specified yield stress of the applied steel plates, 3. consequently, a brittle crack initiation does not result in large-scale failure of the hull structure. in order to achieve these functional requirements, the following two methods of crack arrest are introduced; material arrest: to arrange materials of high resistance to brittle crack propagation to arrest brittle cracks, and structural arrest: to discontinue crack propagation paths by appropriate structural arrangements. figure 13: an example of brittle crack arrest in a deck structure. based on the large-scale crack arrest tests for the determination of minimum brittle crack arrest toughness, it has been found that the toughness 6, 000 cak  n/mm3/2 may be an upper limit for crack propagation in the ultra-wide duplex esso tests which can evaluate  cak without considering structural discontinuity, inoue et al. [37]. in order to ensure the crack arrest in the deck plate made of high-arrest steel plate, a minimum shift of butt-weld as illustrated in fig. 13 has also been recommended. conclusions erturbation analyses of a kinked and curved crack have been reviewed in the present paper focusing attention on the crack path criteria and crack path stability induced by local stress biaxiality or by inhomogeneous fracture toughness. having reviewed experimental and theoretical studies of brittle crack propagation paths along butt-weld, the concept of fracture control of extremely thick plates of high tensile steel, which are applied to the deck structures of recently developed large container ships, are presented. references [1] banichuk, n.v., determination of the form of a curvilinear crack by small parameter technique. mekhanika tverdogo tela, 7-2 (1970) 130–137. (in russian) [2] goldstein, r.v., salganik, r.l., plane problem of curvilinear cracks in an elastic solid. mekhanika tverdogo tela, 7-3 p y. sumi, frattura ed integrità strutturale, 34 (2015) 43-59; doi: 10.3221/igf-esis.34.04 57 (1970) 69–82. (in russian) [3] goldstein, r.v., salganik, r.l., brittle fracture of solids with arbitrary cracks, int j fract, 10 (1974) 507–523. [4] cotterell, b., rice. j.r., slightly curved or kinked cracks, int j fract, 16 (1980) 155–169. [5] sumi, y., nemat-nasser, s., keer, l.m., on crack branching and curving in a finite body, int j fract, 21 (1983) 67– 79; erratum, int j fract, 24 (1984) 159. [6] sumi, y., a note on the first order perturbation solution of a straight crack with slightly branched and curved extension under a general geometric and loading condition, eng fract mech, 24 (1986) 479–481. [7] sumi, y., a second order perturbation solution of a non-collinear crack and its application to crack path prediction of brittle fracture in weldment, naval architect ocean eng, 28 (1990) 143–156. [8] karihaloo, b.l., keer, l.m., nemat-nasser, s., oranratnachai, a., approximate description of crack kinking and curving. j appl mech, 48 (1981) 515–519. [9] wu, c.h., fracture under combined loads by maximum-energy-release-rate criterion, j appl mech 45 (1978) 553– 558. [10] amestoy, m., leblond, j.b., crack paths in plane situations-ii. detailed form of the expansion of the stress intensity factors. int j solids struct, 29 (1992) 465–501. [11] erdogan, f., sih, g.c., on crack extension in plates under plane loading and transverse shear, j basic eng, 85 (1963) 519–527. [12] sumi, y., nemat-nasser, s., keer, l.m., on crack path stability in a finite body, eng fract mech, 22 (1985) 759–771. [13] leevers, p.s., radon, j.c., culver, l.e., fracture trajectories in a biaxially stressed plate, j mech phys solids, 24 (1976) 381–395. [14] broberg, k.b., on crack paths, eng fract mech, 28 (1987) 663–679. [15] pook, l.p., crack paths, wit press, southampton, (2002). [16] sumi, y., mathematical and computational analyses of cracking formation, springer, tokyo, (2014). [17] sumi, y., et al., fracture control of extremely thick welded steel plates applied to the deck structure of large container ships, j mar sci tech, 18 (2013) 497–514. [18] muskhelishvili, n.i., some basic problems of the mathematical theory of elasticity, english ed. translated from the 3rd russian ed., noordhoff, groningen-holland, (1953). [19] bueckner, h.f., a novel principle for the computation of stress intensity factors, zamm, 59 (1970) 529–546. [20] bilby, b.a., cardew, g.e., the crack with a kinked tip, int j fract, 11 (1975) 708–712. [21] bilby, b.a., cardew, g.e., howard, i.c., stress intensity factors at the tips of kinked and forked cracks in: taplin dmr (ed.), fracture 1977, vol 3. pergamon press, oxford, (1978) 197–200. [22] hayashi, k., nemat-nasser, s., energy release rate and crack kinking, int j solids struct, 17 (1981) 107–114. [23] leblond, j.b., crack paths in plane situations-i, general form of the expansion of the stress intensity factors, int j solids struct, 25 (1989) 1311–1325. [24] sumi, y., kagohashi, y., a fundamental research on the growth pattern of cracks (second report), j soc naval architects jpn, 152 (1983) 397–404. (in japanese) [25] hall, w.j., kihara, h., soete, w., wells, a.a., brittle fracture of welded plate. prentice-hall, englewood cliffs, (1967). [26] munse, w.h., chapter 8 brittle fracture in weldments, in: liebowitz, h. (ed.), fracture: an advanced treatise iv engineering fracture design, academic press, new york, (1969) 371–438. [27] wells, a.a., chapter 7 effects of residual stress on brittle fracture, in: liebowitz, h. (ed.), fracture: an advanced treatise iv engineering fracture design, academic press, new york, (1969) 337–370. [28] kihara, h., yoshida, t., oba, h., initiation and propagation of brittle fracture in welded steel plate. international institute of welding (iiw) document no. x-217-59 (1959). [29] kihara, h., masubuchi, k., effect of residual stress on brittle fracture, weld j, 38 (1959) 159-s. [30] ship building research association of japan, report of research panel sr147: strength evaluation of brittle fracture of welded joints of high tensile steel plates with large heat-input in ship hull, http://www.jstra.jp/html/pdf/sr1435103.pdf , (1976). (in japanese) [31] ship building research association of japan, report of research panel sr153: research on brittle fracture and fatigue strength of welded joints of thick steel plates with large heat-input, http://www.jstra.jp/html/pdf/sr1535203-1.pdf , (1977). (in japanese) [32] sumi, y., computational crack path prediction for brittle fracture in welding residual stress fields, int j fract, 44 (1990) 189–207. [33] kihara, h., ikeda, k., on brittle fracture initiation (third report)brittle fracture initiation characteristics for welded joint of 80 and 60 kgf/mm2 high strength steels, j soc naval architects jpn 120 (1966) 207–220. (in japanese) y. sumi, frattura ed integrità strutturale, 34 (2015) 42-58; doi: 10.3221/igf-esis.34.04 58 [34] ship building research association of japan, report of research panel sr169: research on fracture control of ship structures, http://www.jstra.jp/html/pdf/sr169-5603.pdf (1981). (in japanese) [35] nippon kaiji kyokai (classnk), guidelines on brittle crack arrest design, tokyo, (2009). [36] yamaguchi, y., et al., development of guidelines on brittle crack arrest design brittle crack arrest design for large container ships -1 -, in: proc. 20th isope conference. beijing, 4 (2010) 71–79. [37] inoue, t., et al., required brittle crack arrest toughness kca value with actual scale model tests, in: proc. 20th isope conference. beijing, 4 (2010) 95–101. microsoft word numero_49_art_25_2499 a. baryakh et alii, frattura ed integrità strutturale, 49 (2019) 257-266; doi: 10.3221/igf-esis.49.25 257 focused on russian mechanics contributions for structural integrity on one approach to the numerical modeling of the strain-stress state of layered rock mass alexander baryakh perm federal research center of ural branch of russian academy of science, director, corresponding member of russian academy of science, russia bar@mi-perm.ru, http://www.permsc.ru/ sergey lobanov mining institute of the ural branch of the russian academy of science, russia lserg@mi-perm.ru, https://www.mi-perm.ru/ abstract. according to the principle of virtual work for a system of elastic layers, a semi-analytical scheme for constructing the finite-dimensional analog of the variational equation was developed based on the well-known analytical solution in the fourier series for a single layer. the solution of a test problem shows that the constructed numerical procedure of mathematical modeling ensures fairly accurate calculations and highly effective computer-aided realization. it was demonstrated that the proposed semi-analytical scheme for constructing the finite-dimensional analog of the variational equation can be effectively used for the assessment of safety conditions of the potash salt development within the upper kama salt deposit. keywords. mathematical modeling; finite elements; strains; stresses; rocks. citation: baryakh, a., lobanov., s., on one approach to the numerical modeling of the strain-stress state of layered rock mass, frattura ed integrità strutturale, 49 (2019) 257-266. received: 29.04.2019 accepted: 21.05.2019 published: 01.07.2019 copyright: © 2019 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. introduction edimentary rock masses, the interior of which often contains salt deposits, are characterized by a thin-layered structure. the analysis of their strain-stress state and failure as a result of mining operations is of considerable importance in ensuring the protection of mines against flooding [1,2]. in certain cases such rock masses can be represented as a system of plane-parallel layers. in solving the problems of this class, it is common practice to use both the traditional numerical finite and boundary element methods and special computational techniques, which are based on the "sequential stiffness" and "sequential compliance" procedures [3], the fourier series expansion [4], and combinations of various computational procedures [5.6]. these methods were thoroughly discussed and analyzed in work [7]. s http://www.gruppofrattura.it/va/49/2499.mp4 a. baryakh et alii, frattura ed integrità strutturale, 49 (2019) 257-266; doi: 10.3221/igf-esis.49.25 258 finite-dimensional analog construction method onsider a system of n plane-parallel elastic layers of arbitrary thickness 2 nh , which is under plane strain conditions (fig. 1). there are no mass forces. due to the fact that these forces are usually constant, they, if necessary, can be easily taken into account based on the usual superposition. let us assume that homogeneous conditions, for example, zero displacements, are preset at the distant side boundaries. in addition, for the sake of simplicity we will assume that cohesion between the contact layers is perfect. the displacement boundary conditions are as follows:   u u for s. here and in all following examples there is a line of symmetry at the left boundary. x y 0 u h hn -hn yn xn 0 figure 1: general computational scheme let us write down the principle of additional virtual work [8]:        t t v s dv t u ds    (1) where    ,  strain and stress vectors      tijt n  respectively, n cosine of the outer normal to s. as is known [8], this variational principle is true for arbitrary infinitely small stress variations that satisfy the equilibrium equations and the specified stress boundary conditions. for each layer in the local cartesian coordinate system х0у (the x axis runs across the middle line of a layer) stress at any point can be represented as a fourier series expansion:       1 1 ( , ) ( ) ( ) ( ) ( )c c a ak k k k k k x y t x y t x y                (2) where ( , ) ( , ) ( , ) ( , ) xx yy xy x y x y x y x y                , ( ) ( ) ( ) ( ) ( ) ( ) ( ) c a xxk c a c a k yyk c a xyk y y y                 cos 0 0 ( ) 0 cos 0 0 0 sin k c k k k x t x x x                , sin 0 0 ( ) 0 sin 0 0 0 cos k a k k k x t x x x                c a. baryakh et alii, frattura ed integrità strutturale, 49 (2019) 257-266; doi: 10.3221/igf-esis.49.25 259 ; 2k k l l  interval of expansion into the fourier series, upper indexes c and a denote, respectively, the values related to the symmetric and antisymmetric state of a layer in relation to the y axis. the fourier coefficients in expansion (2) can be expressed as constants within the layer of vectors  ckc and  akc [9]:     ( ) ( )c ck k ky r y c  ;     ( ) ( )a ak k ky r y c  , (3) where  ( )kr y the known matrix [6],   ( ) ( ) ( ) 2 ( ) ( ) 2 ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k sh y ch y y sh y ch y y ch y sh y r y sh y ch y y sh y y ch y ch y sh y y ch y sh y y sh y ch y                                                          . the representation of stresses in the form of expansion (2), with (3) taken into account, satisfies the equilibrium equations, which, as already noted, is an integral condition for the validity of the principle of virtual work. let us express constants ( )c akc in (3) in terms of the relevant coefficients of decomposition of force vectors ( )c a kp at the upper ( )c aktp and lower ( )c a kbp boundaries of a layer:      1( ) ( )0c a c ak k kc r p , (4) where    ( ) ( ) ( ),c a c a c ak kt kbp p p ;   ( ) ( ) ( ) ( ) ( ) c a yykc a kt c a xyk h p h            ;  ( ) ( ) ( ) ( ) ( ) c a yykc a kb c a xyk h p h            ;   * 0 * ( ) ( ) k k k r h r r h         ; * ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) k k k k k k k k k k k k k k k k k k k k sh y ch y y sh y y ch y r y ch y sh y y ch y sh y y sh y ch y                                          . then, the expression for stresses (2) can be represented as:       10 1 ( , ) ( ) ( )c ck k k k k x y t x r y r p             1 0 1 ( ) ( )a ak k k k k t x r y r p        , (5) and the strains will be determined by the following relation:         10 1 ( , ) ( ) ( )c ck k k k k x y c t x r y r p               1 0 1 ( ) ( )a ak k k k k c t x r y r p        , (6) where  c compliance matrix that is for an isotropic layer with young's modulus e and poisson's ratio  is written as: a. baryakh et alii, frattura ed integrità strutturale, 49 (2019) 257-266; doi: 10.3221/igf-esis.49.25 260   1 0 1 1 0 0 0 2 c e                  . based on the constructed relations for stresses (5) and strains (6), the left part of eqn. (1) determining the virtual work of strains can be represented as follows:    ( , ) ( ,t v x y x y dv                 1 10 0 1 1 ( ) ( ) ( ) ( ) t t ttc c c c k k k k m m m m k m v p r r y t x c t x r y dv r p                              1 10 0( ) ( ) ( ) ( ) tt ttc c a a k k k k m m m m v p r r y t x c t x r y dv r p                        1 10 0( ) ( ) ( ) ( ) tt tta a a a k k k k m m m m v p r r y t x c t x r y dv r p                        1 10 0( ) ( ) ( ) ( ) tt tta a c c k k k k m m m m v p r r y t x c t x r y dv r p              (7) if in eqn. (1):      * * 1 1 ( ) ( )c c a ak k k k k k t t x t x                where * cos 0 0 0 0 sin 0 0 0 0 cos 0 0 0 0 sin k kc k k k x x t x x                    , * sin 0 0 0 0 cos 0 0 0 0 sin 0 0 0 0 cos k ka k k k x x t x x                    then its right-hand part that determines the external virtual work is given as:             * * 1 ( ) ( ) ( ) ( ) t tt tt c c a a k k k k ks s s t u ds p t x u x ds p t x u x ds                   (8) substituting of (7), (8) into variational eqn. (1), makes it possible to use the standard procedures of the finite element method: integrating for the relevant areas and boundaries of a layer; constructing the local compliance matrices; proceeding to global coordinates; combining the generated matrices and, finally, forming the system of independent algebraic equations for the coefficients of the force vector decomposition at the boundary of each layer:     k k ks p f (9) where  ks is the global compliance matrix, which has a band structure,  kf is the k-th harmonic of a given displacement vector along the boundaries of the layers. a. baryakh et alii, frattura ed integrità strutturale, 49 (2019) 257-266; doi: 10.3221/igf-esis.49.25 261 the constructed finite element analog (9) of variational eqn. (1), owing to the use of nonlinear shape functions (as analytical solution of a stress problem for a single layer) in the fem (finite element method) semi-analytical scheme, allows us to considerably decrease the number of the unknown. when using this approach, the total number of the unknown in the elastic equilibrium problem for a system of plane-parallel layers is equal to 4 ( 1)k n  , where k is the number of terms in a fourier series retained in expansion (2), and n is the number of layers. symmetry about the yaxis, makes it possible to reduce the number of the unknowns by half. test example s a test example, we consider a massless plane, which is under the action of a distributed load. the computational scheme for the problem is presented in fig. 2. figure 2: the computational scheme of single layer test system the specified static boundary conditions are the following:     0, ; 0 0, ; 0 0; 0. xy y xy y x y h q x a y h q x a x x l u                    an analytical solution of this problem can be constructed with the use of the fourier series. according to [10], an equation for the airy stress function [11]: 4 4 4 4 2 2 4 2 0 x x y y             (10) will be identically satisfied if it is presented as follows:  sin m x f y l    (11) where m is any integer number, and function  f y is a solution of following equation:      4 22 0ivf y f y f y     (12) y h -h x 0 a b l q=-1 a a. baryakh et alii, frattura ed integrità strutturale, 49 (2019) 257-266; doi: 10.3221/igf-esis.49.25 262 where m l  . a general solution of this linear differential equation with constant coefficients takes the following form:   1 2 3 4( ) ( ) ( ) ( )f y c ch y c sh y c ych y c ysh y       (13) then a stress function is determined according to the following expression:  1 2 3 4sin ( ) ( ) ( ) ( )x c ch y c sh y c ych y c ysh y         (14) and the relevant stress components are calculated according to the following formulas:     2 2 2 1 2 3 42 sin ( ) ( ) 2 ( ) ( ) 2 ( ) ( )x x c ch y c sh y c sh y ych y c ch y ysh y y                            2 2 1 2 3 42 sin ( ) ( ) ( ) ( )y x c ch y c sh y c ych y c ysh y x                 (15)     2 1 2 3 4cos ( ) ( ) ( ) ( ) ( ) ( )xy x c sh y c ch y c ch y ysh y c sh y ych y x y                             where constants 1 2 3 4, , ,c c c c are determined by relevant stress boundary conditions. for the test problem (fig. 2), the boundary conditions can be represented in the form of symmetric expansion into a fourier series: 0 1 cosm m m x q a a l      (16) where the expansion coefficients are defined by the following expressions: 0 , qa a l  2 sin 1 cos a m a m a q m x la q dx l l m       (17) with account of the boundary conditions, the constants 1 2 3 4, , ,c c c c in expressions for stresses (15): 1 2 4 2 2 3 2 ( ) ( ) ( 2 ) 2cos 2 ( ) ( 2 ) 2cos 0 q sh h hch h c sh h ha q sh h c sh h ca c c                      (18) where qis determined by expression (16). the results of an analytical solution for middle line (y=0) on which only a normal stress takes place: a. baryakh et alii, frattura ed integrità strutturale, 49 (2019) 257-266; doi: 10.3221/igf-esis.49.25 263 1 sin ( ) ( ) 4 cos 2 ( ) 2 y m m a m h m h m h ch sh qa q m xl l l l m h m hl m lsh l l                        (19) are presented in tab. 1. x, m analytical solution, y /q numerical solution, y /q error,% 0.0 -0.69989 -0.70948 1.35169 1.0 -0.68535 -0.69497 1.38423 2.0 -0.64334 -0.65297 1.47480 3.0 -0.57850 -0.58792 1.60227 4.0 -0.49790 -0.50668 1.73285 5.0 -0.40988 -0.41746 1.81574 6.0 -0.32250 -0.32837 1.78762 7.0 -0.24219 -0.24603 1.56079 8.0 -0.17298 -0.17468 0.97321 9.0 -0.11649 -0.11617 0.27546 table 1: the results of calculation of a vertical stress along the middle line the calculations were performed for 20 , 4 , 2 18 ,l m а m h m е gpa    . tab. 1 also presents the results of the numerical solution, which was obtained based on the developed semi-analytical scheme of the finite element method. in the numerical implementation of the finite-dimensional analog, the force vector for the area consisting of three layers and the corresponding right-hand part of eqn. (9) are given as:                   3 3 3 3 yyk xyk yyk xyk k yyk xyk yyk xyk h h h h p h h h h                                         ,   0 0 cos 0 0 0 0 0 cos 0 m k m m x q a a l f m x q a a l                                   a comparative analysis of the results of the numerical and analytical solutions shows that the proposed approach for modeling the state of the system of plane-parallel layers ensures fairly accurate calculations. thus, the proposed scheme for the assessment of the strain-stress state of a layered rock mass, using the nonlinear shape functions as an analytical solution for a single layer, demonstrates its efficiency in solving the relevant problems with the aid of sufficiently accurate calculations. a. baryakh et alii, frattura ed integrità strutturale, 49 (2019) 257-266; doi: 10.3221/igf-esis.49.25 264 as an example problem, we consider the upper kama salt deposit russia, perm krai, which is a layered rock mass mined out by the room-and-pillar method. a computational scheme of the problem with account of symmetry about the y axis is given in fig. 3. the characteristics of the geological section and the mechanical properties of the examined layers are presented in tab. 2. figure 3: the computational scheme of multilayers system №. bed, stratum thickness of layer, m modulus of deformation e, gpa poisson's ratio  specific weight 3, /кн м 1 q 9.1 0.10 0.30 20 2 pts 18.3 0.70 0.30 23 3 tkt 50.0 1.20 0.30 24 4 smt 48.0 0.30 0.40 22 5 pp 0.80 0.30 22 6 pks 20.0 1.20 0.30 22 7 k, i-k 5.6 0.94 0.31 21.8 8 i, z-i 5.7 0.91 0.31 21.7 9 z, zh-z 5.1 0.89 0.31 21.6 10 zh, ezh 3.7 0.92 0.31 21.7 11 e 10.7 0.50 0.35 20 12 d-e 4.0 1.0 0.30 22 13 d 13.0 0.50 0.35 20 14 g-d 3.0 1.0 0.30 22 15 g 13.0 0.50 0.35 20 16 v-g 5. 1.0 0.30 22 17 v 10.0 0.60 0.30 22 18 b-v 4.5 1.0 0.30 22 table 2: physical and mechanical properties of rocks a. baryakh et alii, frattura ed integrità strutturale, 49 (2019) 257-266; doi: 10.3221/igf-esis.49.25 265 the boundary conditions are specified as follows: the upper boundary is free, at the side boundaries the horizontal displacements are equal to zero, the lower boundary has vertical displacements reflecting the deformation of the top of the upper mined bed as a result of mining operations (fig. 3.). it is very important that these displacements were obtained as the result of mine geodetic measurements and characterize the real deformation processes in the mined mass. the initial stress of the undisturbed mass was taken to be lithostatic. in this case , 0y h  ,   0 1x h     where  is the specific weight of rocks, h is the mining depth. additional stresses were determined by solving the initial problem. the stresses were expanded into a fourier series, in which 60 harmonics of their symmetric part were retained. the number of the unknowns in the algebraic analog of the problem was 2280. a specific feature of rocks, containing salt strata, is low values of ultimate tensile strains [12], which at the average is 0.10.2% and serve as the indicators of the formation of subvertical cracks in the salt beds [13]. the presence of the through tension zone with horizontal strains exceeding the threshold values for saliferous rocks is indicative of the risk of discontinuity in the waterproof stratum and ingress of fresh waters into mine openings. the distribution of horizontal tensile strains is illustrated in fig. 4. the obtained results are in good agreement with empirical data on the crack formation in the layers of mined rock strata [13]. figure 4: distribution of horizontal tension strains in the mined-out mass conclusions n this study, we demonstrated the efficiency of the proposed semi-analytical scheme of the finite element method for assessing the changes in the state of the layered rock mass under the conditions of underground mining based on a rather simple computational algorithm. at the same time, the degree of the impact of mining operations on the rock mass is determined by the boundary conditions and can be generally estimated using the field measurements. utilization of an actual survey data in geomechanical calculations provides higher validity of waterproof stratum stability estimations and is applied successfully for prompt analysis of mining safety. acknowledgments his work has been financed by the russian science foundation (grant no. 19-77-30008). references [1] baryakh, a.a., asanov, v.a., samodelkina, n.a., pankov, i.l., telegina, e.a. j. (2013). geomechanical provision of protection of potassium mines from flooding. gornyi zhurnal. 6, pp. 30-34. i t a. baryakh et alii, frattura ed integrità strutturale, 49 (2019) 257-266; doi: 10.3221/igf-esis.49.25 266 [2] baryakh, a.a., samodelkina, n.a. j. (2012). water-tight stratum rupture under large-scale mining. part ii. journal of mining science. 48(6), pp. 954-961. [3] maier, g., novatti, g. j. (1987). boundary element elastic analysis of layered soils by successive stiffness or compliance methods, int. j. numerical and analytical meth. in geomechanics, 11(5), pp. 435-447. [4] filippov, n.a. j. (1979). on calculating the strain-stress state of layered rock mass. physical and technical problems of mineral resource development, 2, pp. 3-10. [5] filippov, n.a. (1982). the fourier method in problems of mechanics of layered media under non-traditional contact conditions. in: problems in mechanics of solid deformable bodies, 14, pp. 221-229. [6] linkov, a.m., filippov, n.a., fot, k.k. (1989). on the solution of problems for layered media by means of the fourier series expansion. in: "studies of mechanics of building constructions and materials", lisi. [7] linkov, a.m., filippov, n.a., fot, k.k. (1988). difference equations in layered media problems. viniti, leningrad. [8] vasidzu k. (1987). variational methods in the theory of elasticity and plasticity. m.: mir. [9] petrishin, v.n., privarnikov, a.k. (1965). main boundary problems of the theory of elasticity for multilayered bases. in: applied mechanics, 4(1), pp. 58-66. [10] ribiere, m.c. (1898). compt. rend. 126, pp. 402-404, 1190-1192. [11] timoshenko, s.p., goodier, j. (1979). theory of elasticity: translated from english / edited by shapiro g.s. m.: nauka. main office of physical and mathematical literature. [12] baryakh, a.a., asanov, v.a., pankov, i.l. (2008). physical and mechanical properties of saliferous rocks of the upper kama potash deposit. perm. [13] baryakh, a.a. j. 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can be opened with acrobat and adobe reader 5.0 and later.) >> /namespace [ (adobe) (common) (1.0) ] /othernamespaces [ << /asreaderspreads false /cropimagestoframes true /errorcontrol /warnandcontinue /flattenerignorespreadoverrides false /includeguidesgrids false /includenonprinting false /includeslug false /namespace [ (adobe) (indesign) (4.0) ] /omitplacedbitmaps false /omitplacedeps false /omitplacedpdf false /simulateoverprint /legacy >> << /addbleedmarks false /addcolorbars false /addcropmarks false /addpageinfo false /addregmarks false /convertcolors /converttocmyk /destinationprofilename () /destinationprofileselector /documentcmyk /downsample16bitimages true /flattenerpreset << /presetselector /mediumresolution >> /formelements false /generatestructure false /includebookmarks false /includehyperlinks false /includeinteractive false /includelayers false /includeprofiles false /multimediahandling /useobjectsettings /namespace [ (adobe) (creativesuite) (2.0) ] /pdfxoutputintentprofileselector /documentcmyk /preserveediting true /untaggedcmykhandling /leaveuntagged /untaggedrgbhandling /usedocumentprofile /usedocumentbleed false >> ] >> setdistillerparams << /hwresolution [2400 2400] /pagesize [612.000 792.000] >> setpagedevice microsoft word 2335 h. s. patil et alii, frattura ed integrità strutturale, 48 (2019) 377-384; doi: 10.3221/igf-esis.48.36 377 characterizations of tig welded joints of unalloyed commercially pure titanium gr-2 for weld process parameters h. s. patil, d. c. patel mechanical department, gidc degree engineering college, abrama, gujarat, india hspatil28@gmail.com, pateldcp@gmail.com c. s. patil mechanical department, s. s. agrawal institute of engineering & technology, navsari, gujarat, india chetan27051985@gmail.com abstract. titanium and titanium alloys can be welded by gas tungsten arc, gas metal arc, plasma arc and electron beam welding processes. titanium material is a reactive metal and is sensitive to embrittlement by oxygen, nitrogen, and hydrogen gas at elevated temperatures. consequently, the metal must be protected from atmospheric contamination. this can be provided by shielding the metal with welding grade inert gas. the present work describes the application of tig arc welding to titanium and investigated the effect of welding parameters like weld current, weld gap and gas flow rate on mechanical properties of welded joints of unalloyed commercially pure titanium gr-2 materials. taguchi optimization method has been used to find out optimal setting of parameters for weld joints characterization. the welded joints showed maximum ultimate tensile strength of about 429mpa with percentage elongation of 23.33%. a significant grain coarsening has noticed in the fusion zone consisting of α-phase in different direction bounded by βphase. the hardness value at fusion zone and base metal are typically observed to be 235hv and 145hv respectively. keywords. tig welding; titanium gr-2; weld parameters; weld characterization. citation: patil, h. s., patel, d. c., patil, c. s., characterizations of tig welded joints of unalloyed commercially pure titanium gr-2 for weld process parameters, frattura ed integrità strutturale, 48 (2019) 377-384. received: 18.12.2018 accepted: 23.02.2019 published: 01.04.2019 copyright: © 2019 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. introduction he high strength, low weight ratio and outstanding corrosion resistance inherent to titanium and its alloys has led to a wide and diversified range of successful applications which demand high levels of reliable performance in surgery and medicine as well as in aerospace, automotive, chemical plant, power generation, oil and gas extraction, sports, and other major industries. t http://www.gruppofrattura.it/va/48/2335.mp4 h. s. patil et alii, frattura ed integrità strutturale, 48 (2019) 377-384; doi: 10.3221/igf-esis.48.36 378 in the majority of these and other engineering applications titanium has replaced heavier, less serviceable or less cost effective materials. designing with titanium taking all factors into account has resulted in reliable, economic and more durable systems and components, which in many situations have substantially exceeded performance and service life expectations. titanium is available in different grades, unalloyed or alloyed. unalloyed commercially pure (cp) titanium is available in four different grades, 1, 2, 3 and 4, which are used based on the corrosion resistance, ductility and strength requirements of the specific application. grade 1 has the highest formability, while grade 4 has the highest strength and moderate formability. cp titanium users utilize its excellent corrosion resistance, formability and weldable characteristics in many critical applications. titanium grade 2 is stronger than grade 1 and equally corrosion-resistant against most applications. titanium grade 2 is typically used for orthopedic applications, such as implants and prosthesis; airframe and aircraft engine parts; marine chemical parts; condenser tubing; heat exchangers. titanium grade 2 may be welded by a wide variety of conventional fusion and solid-state processes, although its chemical reactivity typically requires special measures and procedures. szymlek has reviewed joining methods for titanium and steel materials by means of explosive welding i.e.by tig and brazing process and also analyzed fsw analysis of titanium with the use of copper and tantalum or vanadium interlayer [1]. for welding of titanium and its alloys with precise and high quality weld, tungsten inert gas welding (tig) is ideally suitable. in improving the mechanical properties of the weld, high depth of penetration and low heat affected zone (haz) plays an important role [2]. however, the relatively shallow penetration capability and low productivity are the main limitations in the tig welding process. attaining full penetration of welds with superior mechanical properties in single pass weld the notable technique was to use activating flux with tig (a-tig) welding process [3]. wang has been used micro-plasma arc welding to weld ultra-thin titanium plates. it is widely used in manufacture of thin-walled titanium tubes, automobile parts, medical and other industrial fields, is an excellent structural material [4]. krishnanunni studied the effect of welding condition like shielding gas flow rate and numbers of weld passes on hardness of pure titanium material by butt tig welding [5]. ugur investigated the multi-response optimization of tungsten inert gas welding (tig) process for an optimal parametric combination to yield favorable bead geometry of welded joints using the grey relational analysis and taguchi method [6]. chen discussed the friction stir welding on commercially pure titanium with adc12 cast aluminum alloy using wc-co tool. defects arise due to insufficient flow of ti, causes inhomogeneous distribution. also due to lower heat input and low reaction time for ti and al, decrease in tensile strength was observed [7]. the modified butt joint configuration was employed into the fsw of ti-6al-4v alloy to al-6mg alloy with a special pin plunge setup by zhang [8]. the results reveal that the joint mechanical tensile strength can reach more than 92 % of the parent aluminium alloy strength. kato has stated that titanium (ti/ti) rods and titanium and stainless steel (ti/ss) rods has been joined by diffusion welding under phase transformation in an air atmosphere [9]. the effect of halide fluxes (nacl and cacl2) and welding parameters on welding of ti-6al-4v was investigated by pujari rao to find optimal setting of parameters for weld penetration and heat affected zone (haz). all the parameters on 2-way and 3-way interaction on penetration and interactions on haz were found to have significant effect [10]. zuhailawati has studied the shear strength and micro-structural characteristics of the spot brazed titanium and nickel base metal with and without addition of filler metal by spot resistance welding [11]. akman has studied about (ti-6al-4v) titanium alloys welded by laser welding and found that, the ratio between the pulse energy and pulse duration was the most important parameter in defining the depth of penetration also noted that variation of pulse duration at constant peak power has no influence on the depth of penetration [12]. materials & experimental methods nalloyed commercially pure titanium gr-2 sheets are used in this study. the chemical composition and mechanical properties of cp titanium is presented in table-1 and table-2. the dimension of each weld specimen was set 100 mm × 75 mm with thickness of 3 mm. c fe o n h ti <0.08% <0.3% <0.25% <0.03% <0.015% balance table 1 chemical specification of workpiece material. u h. s. patil et alii, frattura ed integrità strutturale, 48 (2019) 377-384; doi: 10.3221/igf-esis.48.36 379 yield strength ultimate tensile strength elongation reduction of area 275 mpa 345 mpa >20% >30% table 2 mechanical properties workpiece material. the tig welding operations were performed on the tig weld machine with argon of 99.99% purity used as shielding gas. for uniformity titanium filler rod with 2 mm diameter was selected, as its composition was same as the composition of workpiece material as shown in table 1. air-cooled torch with a titanium electrode rod with a 2 mm diameter was used. the electrode tip was of blunt point with a 45° angle. a direct-current, electrode-negative power supply device was used with a mechanized operation system in which the welding torch travelled at a constant speed. single-pass, manual tig welding was performed along the longitudinal centerline of the test specimen to produce a weld on a strip. the samples to be tig welded were polished with 400 grit (silicon carbide) flexible abrasive paper to remove surface impurities and then it was cleaned with acetone. the welding of c.p titanium are conducted using gta welding machine with air cooled torch head, as indicated in figure1(a). welded joints samples of cp titanium for different weld process parameters are shown in figure 1(b). figure1: experimental setup and tig welded joints for different parameters the welding parameters considered for this investigation were weld current, weld gap and gas flow rate on v-welding of cp titanium materials with 3 levels each as shown in table 3. welding parameters level 1 level 2 level 3 welding gap(mm) 0.5 0.75 1 gas flow rate(lit/min) 20 25 30 current(a) 90 95 100 table 3: control parameters and their levels taguchi method is a statistical method developed by taguchi and konishi which involves identification of proper control factors to obtain the optimum results of the process. orthogonal arrays (oa) are used to conduct a set of experiments and these experiments are used to analyze the data and predict the quality of weld joints produced. here, an attempt has been made to demonstrate the application of taguchi’s method to improve the weld quality and properties of weld components. welding quality also affects the life of titanium material joint and hence it is desirable to obtain higher quality of welding. the most suitable orthogonal array for experimentation is l9 array as shown in table-4. h. s. patil et alii, frattura ed integrità strutturale, 48 (2019) 377-384; doi: 10.3221/igf-esis.48.36 380 welding specimen welding current(a) voltage(v) welding gap(mm) gas flow rate(lit/min) 1 90 95 0.5 20 2 95 95 0.75 25 3 100 95 1 30 4 90 95 0.75 20 5 95 95 1 25 6 100 95 0.5 30 7 90 95 1 20 8 95 95 0.5 25 9 100 95 0.75 30 table 4: orthogonal array l9 result and discussion radiography analysis y using radiographic unit, x-ray radiographic inspection was carried out on weld samples as per radiography standard methods asme section-viii div-i. in radiographic test 30ci & iridium ir192 was used as radioactive source. the rt technique was s.w.s.i. with sensitivity of 2% and 5 minutes of developing time. the film used was agfa d-4 and the radiographs indicated welds with different defects. the table-5 indicated concluding radiography observations and remarks of the welded joints. weld specimen welding current gas flow rate welding gap observation remarks 1 90 20 0.5 porosity acceptable 2 90 25 0.75 porosity acceptable 3 90 30 1 lack of penetration rejected 4 95 20 0.75 lack of fusion acceptable 5 95 25 1 no significant defects acceptable 6 95 30 0.5 porosity/lack of penetration rejected 7 100 20 1 porosity acceptable 8 100 25 0.5 porosity acceptable 9 100 30 0.75 porosity/ lack of fusion reject table5: radiography observation/remarks of v-joints the presence of porosity, lack of penetration and fusion in tig welded joints was observed in ti-gr2. the low density of titanium alloys enables the in depth of penetration of radiation in welded structures, allowing for the observation of porosity. tensile properties analysis ensile tests have conducted on universal testing machine to determine the yield strength and ultimate tensile strength of the welded specimens. the specimens used for tensile testing were cut from welded samples using water jet machine. the dimension of tensile specimen as per astm-e8 has been represented by figure-2. b t h. s. patil et alii, frattura ed integrità strutturale, 48 (2019) 377-384; doi: 10.3221/igf-esis.48.36 381 figure 2: tensile test specimens for welded samples the tensile properties of welded titanium for different joints were measured at room temperature. the welded joints have mechanical properties like in the range of yielding strength of 190-339.23 mpa, ultimate tensile strength of 318.46429mpa and percentage elongation of 6.66 %-26.66%. the stress-strain curves for weld samples with various weld process parameters have been shown in figure-3. the weld sample-5 exhibited good mechanical properties than other weld samples. these results indicate that the ultimate tensile strength of welded joints is higher than the yield strength, which indicates a noticeable work hardening beyond the yielding. figure 3: tensile test specimens for welded samples weld microstructure analysis the samples for optical microscopy were cut into the size of 30mmx25mmx3mm and pieces were polished using 100, 150, 220, 400, 600 grit silicon carbide paper. etching procedures were used to expose the underlying microstructural features. solutions used for etching titanium include a fresh keller etchant with composition 5ml hno3, 3ml hcl, 2ml hf and 190ml distilled water. the polished metallographic mount was etched in the solution from 40 to 50 seconds to reveal the microstructural features. the variation of microstructures/grain structures of various welded samples and c.p titanium has been shown in figure 4. figure 5(a) shows the optical micrographs weld jointed commercially pure titanium moving from the base metal (bm) to the fusion zone (fz) through the heat affected zone (haz). it has observed from the figure-5(b) that the bm microstructure of commercial pure titanium consists of equi-axed α-phase grains with the presence of fine and disperses precipitation of β-phase. inside the grains structure and in the grain boundary, the fine and disperse precipitation of beta phase has noticed. the interface between the bm and the heat haz clearly indicates that the region from where the thermal cycles occurred during the welding process operate originally and usually on the change in microstructure. due to this complex thermal cycle, the equiaxed grains had grown in larger size in the haz and it has noticed in the figure-5(c). as a result of the welding thermal cycles with a peak temperature, a significant grain coarsening is noticed in the fz which consists of α-phase in different direction bounded by β-phase as depicted in figure 5(d). in comparison to the microstructure of the heat affected zone, an inhomogeneous growth of microstructure at the fusion zone has h. s. patil et alii, frattura ed integrità strutturale, 48 (2019) 377-384; doi: 10.3221/igf-esis.48.36 382 observed. based upon the cooling rate and stabilizing agent, the microstructures are grown at fusion zone. structural morphology of c.p. titanium sheet is altered with respect to heat input consisting of α-phase bounded by β-phase and it is evident in fig. 6. figure 4: microstructures structures of c.p titanium and various tig welded samples. figure 5: (a) optical micrographs of tig weld profile of titanium gr-2, and (b-d) optical micrographs showing grain structures in the bm, haz and fz figure 6: fusion zone microstructures for titanium welds. h. s. patil et alii, frattura ed integrità strutturale, 48 (2019) 377-384; doi: 10.3221/igf-esis.48.36 383 hardness properties analysis ig. 7 shows the hardness variations (across the weld) from the center of fusion zone to the base metal for various sample welded at different parameters for 3 mm thickness joints. these hardness values have some fluctuations along the fusion zone to base metal. this is due to the irregular grain growth and inherent variations of the alpha beta phases in the microstructure of the weldment of c.p titanium material. this behaviour is also due to the slow cooling rate of tig weld process. the maximum value of hardness at the fusion zone has found 235hv (for sample 5) and minimum value of 175 hv (for sample 9). as expected, the hardness value increased with increasing cooling rate i.e. low heat input due to the formation of an increasingly finer transformed structure. in addition, the hardness of the fusion zone increases with decrease in heat inputs. based on the micro-hardness test, it is evident that the weld provides good strength than the base metal due to the hardness in the fusion zone which is relatively higher than the hardness of the base metal. figure 7: hardness profile showing hardness in the bm, haz and fz conclusion ased on available literature and the results drawn from this investigation in tig welding of c.p titanium materials, the conclusions are: welding parameters like welding current, weld gap and gas flow rate are optimized and established from bead-on plate trials for full penetration v welds. in the fusion zone, a significant grain coarsening size is noticed consisting of alpha phase in different direction bounded by beta phase. in haz, equiaxed grains had grown larger in size compared to grains in base metal. as a result, the degree of grain coarsening decreases as one move from the fusion zone to the base metal. tensile test illustrates that the yield and ultimate strengths of the joints rises above the base metal and in actual fact all failures occurred in the base metal area. furthermore, percentage of elongation decreases in the order of fine grain microstructure due to the decreased heat input. it also seen that, hardness values are having some fluctuation because of variation in grain structures. the optimized weld sample 5 with weld parameterscurrent-95a, gas flow-25lit/min, wed gap-1mm has good mechanical properties with respect to other weld samples. references [1] szymlek, k. (2008). review of titanium and steel welding methods, advances in materials science, 8(1), pp. 186-194. [2] pal, s., pal, s.k., samantaray, a.k. (2010). determination of optimal pulse metal inert gas welding parameters with a neuro-ga technique, materials and manufacturing processes, 25, pp. 606615. f b h. s. patil et alii, frattura ed integrità strutturale, 48 (2019) 377-384; doi: 10.3221/igf-esis.48.36 384 [3] tseng, k.h., hsu, c.y. (2011). performance of activated tig process in austenitic stainless steel welds, journal of materials processing technology, 211, pp. 503–512. [4] xin wang, f., ping he, j., qiang fang, j., xiang, f., lei ren, l. (2012). study of titanium foil welding using microplasma arc welding, advanced materials research, 538 541, pp.1469-1472. [5] krishnanunni, (2011). effect of welding conditions on hardness of commercially pure titanium. int. j. technol., 3(2), pp. 19–24. [6] ugur esme, s. o., bayramoglu, m., kazancoglu, y. (2009). optimization of weld bead geometry in tig welding process using grey relational analysis and taguchi method, materials technology, 43(3), pp. 143–149. [7] chen, y.c., nakata, k. (2009). microstructural characterization and mechanical properties in friction stir welding of aluminum and titanium dissimilar alloys, materials and design, 30, pp. 469-474. [8] li b., zhang z., shen y., hub w., luo l., (2014). dissimilar friction stirs welding of ti–6al–4v alloy and aluminum alloy employing a modified butt joint configuration: influences of process variables on the weld interfaces and tensile properties, materials and design, 53, pp. 838-848. [9] h. kato, m. shibata, k. yoshikawa, (1986). diffusion welding of ti/ti and ti/stainless steel rods under phase transformation in air, materials science and technology, 2(4), pp. 405-409. [10] srinivasa rao, p., raju, p., kodanda rama rao, ch., priyangeli, s. p. (2016). effect of halide fluxes and welding parameters on penetration and haz of titanium alloy, jpe, 19(1), pp.81-86 [11] zuhailawati, h., saeed, a. m., ismail, a. b., samad, z., ariga, t. (2010). spot resistance welding of a titanium/nickel joint with filler metal, welding journal, 89, pp. 101-104 [12] akman, e., demir, a., canel, t., sınmazcelik, t. 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<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> /enu (use these settings to create adobe pdf documents best suited for high-quality prepress printing. created pdf documents can be opened with acrobat and adobe reader 5.0 and later.) >> /namespace [ (adobe) (common) (1.0) ] /othernamespaces [ << /asreaderspreads false /cropimagestoframes true /errorcontrol /warnandcontinue /flattenerignorespreadoverrides false /includeguidesgrids false /includenonprinting false /includeslug false /namespace [ (adobe) (indesign) (4.0) ] /omitplacedbitmaps false /omitplacedeps false /omitplacedpdf false /simulateoverprint /legacy >> << /addbleedmarks false /addcolorbars false /addcropmarks false /addpageinfo false /addregmarks false /convertcolors /converttocmyk /destinationprofilename () /destinationprofileselector /documentcmyk /downsample16bitimages true /flattenerpreset << /presetselector /mediumresolution >> /formelements false /generatestructure false /includebookmarks false /includehyperlinks false /includeinteractive false /includelayers false /includeprofiles false /multimediahandling /useobjectsettings /namespace [ (adobe) (creativesuite) (2.0) ] /pdfxoutputintentprofileselector /documentcmyk /preserveediting true /untaggedcmykhandling /leaveuntagged /untaggedrgbhandling /usedocumentprofile /usedocumentbleed false >> ] >> setdistillerparams << /hwresolution [2400 2400] /pagesize [612.000 792.000] >> setpagedevice microsoft word numero_33_art_43 m. cova et alii, frattura ed integrità strutturale, 33 (2015) 390-396; doi: 10.3221/igf-esis.33.43 390 focussed on multiaxial fatigue fast assessment of the critical principal stress direction for multiple separated multiaxial loadings m. cova, p. livieri, r. tovo university of ferrara, italy roberto.tovo@unife.it abstract. the critical plane calculation for multiaxial damage assessment is often a demanding task, particularly for large fem models of real components. anyway, in actual engineering requests, sometime, it is possible to take advantage of the specific properties of the investigated case. this paper deals with the problem of a mechanical component loaded by multiple, but “time-separated”, multiaxial external loads. the specific material damage is dependent from the max principal stress variation with a significant mean stress sensitivity too. a specifically fitted procedure was developed for a fast computation, at each node of a large fem model, of the direction undergoing the maximum fatigue damage; the procedure is defined according to an effective stress definition based on the max principal stress amplitude and mean value. the procedure is presented in a general form, applicable to the similar cases. keywords. multiaxial fatigue; principal stress directions; critical plane. introduction ulti-axial fatigue theories usually address problems characterized by different degrees of complexity. the simplest problems are typically the proportional loading conditions. in these situations, the principal stress directions are constant; they can be calculated at any time value and the variations (mean values, amplitudes or ranges) can be easily computed since, along each principal direction, principal stress is a known time-variable scalar. in this condition, many fatigue criteria based on principal stress value can be used; the most important is probably the sines criterion [1] which is actually based on octahedral shear stress and such a value requires the calculation of the principal stress direction. in a less specific way, under non-proportional loading, principal directions change in time; this variation is one of the most tricky problem in the investigation of the multi-axial fatigue damage, since there is not an intrinsic or natural frame of reference where defining the fundamental stress quantities. several research efforts, in multiaxial fatigue, deal with the definition and computation of critical plane direction or main principal frame of reference; for instance, just few examples can be found in [2-5]. specifically, the main principal stress directions can be used to evaluate the consequent shear based critical plane [2]. otherwise, the principal stress can be directly used for fatigue damage assessment [6], in this case the principal stress amplitudes and mean values are used in the criterion for equivalent stress amplitude definition. moreover, the variability of the principal directions, which is null under proportional loading, can be caused by several type of non-proportionalities. in the most complex cases, several independent time-variable component are superimposed. in these cases, the numerical iterative procedures are necessary. m m. cova et alii, frattura ed integrità strutturale, 33 (2015) 390-396; doi: 10.3221/igf-esis.33.43 391 more simple cases are given by a static loading combined with one time-variable component; in these cases, a proportional variability is combined with a non-proportional static loading; this is a generalization of the loading condition initially investigated in [7]. the overall stress condition is non-proportional, but it is less complex than previous general case. the presented research addresses this last case. it is explicitly established for fatigue damage assessment of materials dependent on principal stress variations. anyway, its application to more general cases is possible. more precisely, the following discussion deals with the problem of determining the direction of maximum damage in cases of an external static loading combined with one or several variable loading, ranging from null to a maximum value (in the following called pulsating loadings). in the first case, we will deal with the treatment of one single external pulsating loading combined with a static load. in the second case, superimposed to a static load, there will be the combination of two pulsating loading; the time variable loading shall act separately, i.e. disjoint in time. superposition of independent static and pulsating loading et us consider a point c of a structural component, loaded, in a period 0-t, by a static loading superimposed to an independent time-variable loading. the resulting stress tensor will be the sum of a constant value [σ]s and a time variable component. assuming that the time variable components ranges from zero to a value [σ]v, the overall stress tensor can be indicated as:         1s vt f t    (1) where, the function f1 varies continuously from zero to 1 and back to zero, in the time interval from t1 to t3; elsewhere f1 is null, see fig. 1. figure 1: qualitative trend of function f1, related to the case of a single time variable component. the versor “n” defines a generic direction at point c. the normal stress σn, acting on the plane defined by the versor “n”, is given by:           1t t tn s vt n t n n n n n f t      (2) due to the properties of the time variable function, the maxima and minima will necessarily occur at t1 and t2 alternatively. it is possible to evaluate the mean value and the amplitude of the normal stress:    ,max ,min, 1 2 2 n n t t n m s v n n n n          (3) l m. cova et alii, frattura ed integrità strutturale, 33 (2015) 390-396; doi: 10.3221/igf-esis.33.43 392       ,max ,min, 1 1 1max ,2 2 2 2n n t t tn a v v vn n n n n n            (4) where the max{} function identifies the maximum value among the values within the bracket. at this stage, it is clear that the simple amplitude of the normal stress is dependent only from the time-variable stress tensor. hence, the maximum value of normal stress amplitude is the half of the maximum eigenvalue of the [σ]v tensor; consequently, the direction “n” loaded by the maximum normal stress amplitude is the related eigenvector. the modulus is conveniently used in order to properly take into account even compressive loading.     , 1max max 2 a n n a v eigvl    (5) where eigvl[ ] function specifies the eigenvalues of the considered matrix. anyway, the problem turns out much more complex if, as usual, the consider material has any kind of sensibility to mean or hydrostatic stress components. let us consider a material showing a linear sensibility to mean value, i.e. the fatigue strength decreases linearly by increasing the mean stress value. this assumption is usually called “simplified goodman” relationship. in this case, it is possible to consider an effective value of the stress amplitude by combining the actual stress amplitude with a portion of the applied mean stress value. ,a eq a mb    (6) the constant “b” is dependent from the material, it is usually positive and lower than 1. the critical direction is no longer the direction previously identified, but the direction undergoing the maximum value of the equivalent amplitude. for a general direction n, the equivalent amplitude value turns out to be:                        , , , , 1 1 2 2 1 1 1 max , 2 2 2 1 1 max , 2 2 n a eq n a n m t t t v s v t t t t v v s v t t v s v s b n n b n n n n n n n n b n n n n b b n b n n b n                                                   (7) finally, it is necessary to find the direction with the maximum value of equivalent amplitude. the linear combination of tensors is itself a tensor; hence, the maximum value, by changing the direction n, is again the maximum eigenvalue of the considered tensors.          , , , 1 1 max max , 2 2 a eq n n a eq v s v s b b eigvl b eigvl b                       (8) applicative example let us consider a time variable tensile loading, ranging from 0 to 2s, so that its amplitude is s. the equivalent amplitude is simply (b+1)s. then, if the variable tensile loading is combined with a static torsional loading, the related tensors are:   0 0 0 0 0 0 0 s t t         ;   2 0 0 0 0 0 0 0 0 v s          (9) if we assume that the tensile loading is actually positive, the terms “b+1” are predominant and the resulting equivalent stress amplitude is: m. cova et alii, frattura ed integrità strutturale, 33 (2015) 390-396; doi: 10.3221/igf-esis.33.43 393   2 2 2 , 1 1 1 2 2 1 a eq b t b s b s                         (10) superposition of static and multiple independent pulsating loadings he procedure above described can be extended to multiple time variable components. it is relevant if such components are independent and separated, i.e. if each one is different from zero only when other components are null. let us consider, for instance, another time variable function [σ]v2, compared to the single one of eq. 1. with two separated time variable components, the resulting stress condition is:             1 21 2s v vt f t f t      (11) an example of two separated time-functions is given in fig. 2. if f1 is different from 0 between t1 and t3, then f2 will be different from 0 elsewhere, for instance from t3 to t5. figure 2: definition of two “separated” time functions. similarly to previous equations, the normal stress on the plane defined by tensor n is:            1 21 2 t t t n s v v t n n n n f t n n f t      (12) in this case relative maxima and minima will occur at t1 (or t3 or t5), t2 and t4. at these instants, necessarily an extreme occurs; generally, they could be local maxima or minima of σn. for fatigue strength assessment, the maximum amplitude shall be computed; such a maximum amplitude is defined by the largest difference between the values obtained at extremes. for instance, by investigating the extremes at t2 and t4, the mean value and relative amplitude shall be computed slightly differently from previous case:           , ,2 4 2 4 1 2 1 1 1 2 2 2 t t t n m n n s v v t t n n n n n n                            , ,2 4 2 4 1 2 1 2 1 2 1 1 2 2 1 1 max , 2 2 t t n a n n v v t t v v v v t t n n n n n n n n                          (13) according to previous considerations, the equivalent amplitude at a generic direction n, turns out: t m. cova et alii, frattura ed integrità strutturale, 33 (2015) 390-396; doi: 10.3221/igf-esis.33.43 394                            , , ,2 4 , , 1 2 1 2 1 2 1 2 1 2 1 1 max , 2 2 1 1 2 2 1 1 1 1 max , 2 2 2 2 n a eq n a n m t t v v v v t t t s v v t t v v s v v s b n n n n b n n n n n n b b b b n b n n b n                                                           (14) and the maximum value, by changing the direction n, is:               , ,2 4 , , 1 2 1 2 max 1 1 1 1 max , 2 2 2 2 a eq n n a eq v v s v v s b b b b eigvl b eigvl b                                (15) however, the relative amplitude between the extremes at t2 and t4 is only one of the possible critical amplitudes; the other possibilities are the differences between t1 and t2 and, finally, between t1 and t4. these two combination are similar to that investigated in the single pulsating loading case. then the relative equivalent amplitudes are:        , , ,1 2 1 1 1 1 max , 2 2 n a eq v s v s b b eigvl b eigvl b                     (16)                            svsveqan b b eigvlb b eigvl  2241,,, 2 1 , 2 1 max (17) the researched equivalent amplitude is, finally, the maximum of each computed amplitude; hence the maximum eigenvalue of the suggested six tensors:                                                                                        ; 2 1 ; 2 1 ; 2 1 ; 2 1 ; 2 1 2 1 ; 2 1 2 1 max 22 11 2121 ,, svsv svsv svvsvv eqan b b eigvlb b eigvl b b eigvlb b eigvl b bb eigvlb bb eigvl     (18) figure 3: stress distribution at minimum et maximum of fatigue loading. m. cova et alii, frattura ed integrità strutturale, 33 (2015) 390-396; doi: 10.3221/igf-esis.33.43 395 figure 4: safety factor and final result of the overall investigation. numerical application he proposed procedure is written in an algebraic form in order to use it in a computer-assisted procedure and to apply it in fatigue damage assessment in fe models. the method computes directly the equivalent stress amplitude, without time consuming iterative or recursive algorithms. this effectiveness is quite useful in large models where effective values shall be evaluated at each node; sometimes millions of nodes shall be processed. simply for instance, fig. 3 and 4 show an example of an industrial application. this groove is a detail of a machine component subjected to a fatigue load history, which has two relevant states. the maximum principal stresses in these load cases are reported. due to the complex 3d shape, the material is subjected to very different stress conditions, on a multi-axial fatigue perspective, from point to point. in these cases, it is crucial to have an automated multi-axial criterion to properly post-process the fem results in order to identify the critical locations and the relative safety margin. fig. 2 shows the safety factor plot according to the presented criterion. conclusions he paper suggests a procedure for explicit and direct assessment of an equivalent stress amplitude under multiaxial fatigue loading. the procedure is appropriate only for particular loading conditions, specifically under a static loading combined with one or several independent and separated pulsating loadings. moreover, the proposed procedure is suitable for materials where fatigue damage is mainly dependent from principal stress values, for instance cast irons or brittle materials. anyway, under these particular conditions, the procedure is effective and can be easily used in any fe software, by providing a fast and efficient assessment of an equivalent value for the direct valuation of fatigue damage all over a mechanical component. references [1] sines, g., behavior of metals under complex static and alternating stresses, in: metal fatigue. red. g. sines a j.l. waisman, new york, mcgraw hill (1959) 145-469 [2] carpinteri, a., macha, e., brighenti, r., expected principal stress directions under multiaxial random loading. part i: theoretical aspects of the weight function method, international journal of fatigue, 21(1) (1999) 83-88. t t m. cova et alii, frattura ed integrità strutturale, 33 (2015) 390-396; doi: 10.3221/igf-esis.33.43 396 [3] fatemi, a., socie, d. f., a critical plane approach to multiaxial fatigue damage including out-of-phase loading. fatigue fract. engng. mater. struct., 11(3) (1988) 149-165. [4] itoh, t., sakane, m., design criteria for multiaxial low cycle fatigue, journal of pressure equipment and systems, 6 (2008) 12-20. [5] papadopoulos, i. v., critical plane approaches in high-cycle fatigue: on the definition of the amplitude and mean value of the shear stress acting on the critical plane, fatigue fract. engng. mater. struct., 21(3) (1998) 269285. [6] tovo, r., lazzarin, p., berto, f., cova, m., maggiolini, e., experimental investigation of the multiaxial fatigue strength of ductile cast iron, theoretical and applied fracture mechanics, 73 (2014) 60-67. [7] kakuno, h., kawada, y., a new criterion of fatigue strength of a round bar subjected to combined static and repeated bending and torsion, fatigue & fracture of engineering materials & structures, 2(2) (1979) 229–236. shot peening processes to obtain nanocrystalline surfaces in metal alloys: m. ravikumar et alii, frattura ed integrità strutturale, 56 (2021) 160-170; doi: 10.3221/igf-esis.56.13 160 investigations on tensile fractography and wear characteristics of al7075-al2o3-sic hybrid metal matrix composites routed through liquid metallurgical techniques m. ravikumar department of mechanical engineering, r l jalappa institute of technology, bangalore (r), karnataka, india ravikumar.muk@gmail.com h. n. reddappa department of mechanical engineering, bangalore institute of technology, bangalore, karnataka, india reddyhn.phd@gmail.com r. suresh* department of mechanical and manufacturing engineering, msruas, bangalore, karnataka, india sureshchiru09@gmail.com y. s ram mohan department of aerospace engineering, b m s college of engineering, 560019, bangalore, india ysrmohan.mech@bmsce.ac.in c. r. nagaraja, e. r. babu department of mechanical engineering, bangalore institute of technology, bangalore, karnataka, india cnraaja@gmail.com, rajjbabu@gmail.com abstract. the al2o3-sic reinforced al7075 metal matrix composite (mmcs) is fabricated through liquid metallurgical technique. ceramic particulates were amalgamated into the aluminium alloy to achieve improved mechanical properties and wear resistance. al-7075/al2o3/sic hybrid mmcs were produced by reinforcing 2%, 3%, 4% and 5% of al2o3 and 3%, 5% and 7% of sic particles. microstructural analysis was carried out to evaluate the uniform dispersal of reinforcing particulates within the base matrix. the output results indicate that the mechanical properties of the hybrid mmcs are enhanced by increase the wt. % of ceramic particulates. tensile fractography results show the internal fracture structure of the tensile test specimens in which the particulates fracture and pullouts were observed. the wear characteristics of developed composites are studied using the pin-on-disc apparatus. the high wear resistance is observed at 5% al2o3 + 7% sic reinforced mmcs. citation: ravikumar, m., reddappa, h.n., suresh, r., ram mohan, y.s., nagaraja, c.r., babu, e.r., investigations on tensile fractography and wear characteristics of al7075-al2o3-sic hybrid metal matrix composites routed through liquid metallurgical techniques, frattura ed integrità strutturale, 56 (2021) 160-170. received: 22.01.2021 accepted: 14.03.2021 published: 01.04.2021 copyright: © 2021 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. https://youtu.be/4xt0zvgjsvm m. ravikumar et alii, frattura ed integrità strutturale, 56 (2021) 160-170; doi: 10.3221/igf-esis.56.13 161 keywords. al7075; mmcs; tensile; fractography analysis; hardness; wear loss. introduction etal composites find valuable to use as modern material in high temperature applications. al-based mmcs are being extensively used in various engineering industrial applications due to higher strength, higher thermal conductivity, & better wear resistance. the selection of ceramic reinforcements in the matrix material has played an important role in the manufacturing of mmcs but major challenges handled by metal matrix composite researchers to get optimized results from several alternatives of innovative organic and inorganic reinforcements [1]. generally, reinforcing materials used for these mmcs are sic, al2o3 and gr in the form of whiskers or particles [2]. the mechanical and wear behavior of metal matrix composites depend on their type of reinforcement, microstructure, weight percentage of reinforcement, size of the particulates, interfacial bonding, sliding distance, average load and sliding speed etc [3]. several composites with the incorporation of particulates were made by adding particulates, as in rheocasting, with the result that spherical primary particles were embedded in the matrix. aluminum composites are usually made by the stir casting (liquid casting) process. the stir-casting process can be carried out at a minimum cost [4 & 5]. in this process, the ceramic particulates are mixed at the melting temperature of the alloy. however, in others, for example compo casting, the particulates are added into the semisolid slurry alloy. continuously reinforced composites are highly expensive to manufacture compared to discontinuously reinforced composites. the performance of the base matrix is less expensive with particle reinforcement when compared with the fiber reinforcement [6 & 7]. ammcs which are reinforced by ceramic particulates show improvements in mechanical properties as compared to matrix alloy and they are most widely used in tribological applications due to the improved wear resistance, stroke density and high ratio of strength [8]. this is the inducement for increased focus on the use of the direction of particles reinforced al alloy mmcs for tribological applications [9]. furthermore, researchers had also studied the immense potential in their properties of al/sic/al2o3 based materials such as better machinability, superior weldability, formability, good castability and better corrosive resistance at high temperature and pressure [10]. based on the recent research survey, it can be considered that sic-al2o3 particulates reinforced composites are useful in automotive applications, for the manufacture of camshafts, pistons, bearing surfaces, braking systems and cylinder liners and also used in aerospace-applications, for the manufacture of wings of the aircraft structure, exhaust systems and engine components. from the literature studies, for al composites it was observed that by addition of hard reinforcements into the matrix increases the tensile strength, hardness and wear resistance of the mmcs. veeresh et al. [11] in their research on al 7075-al2o3 mmcs stated that the mechanical strength (tensile) of mmcs are found to be high compared to al7075 alloy. the hardness and wear resistance of the mmcs improved by increasing filler content [12]. radhika et al. [13] examined the wear characteristics of al-gr-al2o3 mmcs and observed that addition of the al2o3 particulates had a significant influence on the wear resistance of the mmcs. alaneme and bodunrin [14] investigated the mechanical properties of al6063-al2o3 composites. the obtained results indicated the mechanical properties enhanced by the addition of hard ceramic particulates. at the same time it was observed that the fracture toughness and strain to fracture also decreased by increasing wt. % of al2o3. al 2024/al2o3 composites produced by the vortex method showed an increase in mechanical properties and density when the al2o3 content was increased [15]. mahdavi et al. [16] investigated the effect of sicp reinforced mmcs and reported that, wear behavior improved by the addition of sic in the matrix. prashant et al. [17] observed that reinforcement of sic content reduces the wear behavior of the al 6061 composite. sharma et al [18] studied the effect of sicp reinforcement on the unlubricated wear characteristics of za27 alloy composites. experimentations were conducted by varying the sliding speeds and applied loads. the observed results indicated that al alloy exhibits a high wear rate when compared to reinforced mmcs and by increasing wt. % of reinforcing particles, the wear rate decreased. vedrtnam [19] studied the wear behavior of alsic-cu composites. they observed that the wear resistance of the mmcs was improved by increasing wt. % of the reinforcing particulates. komai and minoshima [20] examined the tensile strength of al/zn/mg reinforced by sic produced by a pm (powder metallurgy) method. it is revealed that the strength of the sic-al7075 composite was higher compared to unreinforced material. sourabh gargatte et al. [21] studied the wear behavior of al-sic composites. the sic particles enhance the hardness of mmcs and also increase the wear resistance. however, from the literature review it can be concluded that adequate data is not available on the tensile strength, hardness properties and wear behavior of al 7075 mmcs. therefore, the present research study aims at investigating wear behavior, hardness and tensile strength of the m m. ravikumar et alii, frattura ed integrità strutturale, 56 (2021) 160-170; doi: 10.3221/igf-esis.56.13 162 al7075+al2o3+sic hybrid mmcs having various wt. % of particulates. the output results of this research are adequate information about mechanical, wear behavior and fractography of the surface are analyzed through sem and edax analysis and also their results to inspire better and operative application based on the studies. raw materials and techniques reinforcements and instruments l7075 (bright extruded rod) was purchased from m/s perfect metal works, bengaluru, karnataka. al2o3 and sic were purchased from m/s the prince chemical co. bengaluru, karnataka. the casting facility was used from m/s aluminium fabrications, bengaluru. tensile strength was studied using a utm machine (load capacity of 400 kn) and a vickers hardness tester was used to measure the microhardness at m/s raghavendra spectro metallurgical laboratory, bengaluru, karnataka. tribological tests were evaluated by using pin and disc apparatus at bangalore institute of technology, bengaluru, india. the scanning electron micrographs (sem) were studied using hitachi s-3400 sem apparatus, manipal academy of higher education (mahe), udupi, karnataka. fabrication technique liquid metallurgical technique helps to improve the wettability of the metal matrix composites by avoiding the formation of gaseous and oxide layers on the surface of liquid metal and also avoids agglomeration of the particles in the matrix material. in this technique, the fluidity can be sustained, like cleaning the melt from suspended oxides, reducing the rate of heat transfer by mold material [22]. the composite was reinforced by 3%, 5% and 7% sic & 2%, 3%, 4% and 5% al2o3 of particle size: 100 meshes with ph value between 6.5 to 7.5 and sic particulates with mesh size of 220. it was fabricated by a stir-casting method. al7075 alloy was meltssed by using a coke furnace at 800ºc. the reinforcement (preheated) was mixed with al alloy. de-gassing tablets were used to eliminate gases from the molten melt. while adding reinforcements, stirring was done at 100 rpm for 5-6 min and later the melt was poured into the preheated mold box. the cast samples were removed from the mold box after the solidification. cast samples were prepared as test specimens by using the cnc machining process. the chemical composition of al 7075 and sic in wt. % is as in tab. 1 and 2. the wt. % of al 7075 and ceramic particulates used for the fabrication of composites is as in tab. 3. the hybrid composite test samples are depicted in fig. 1. content al cu mg si fe mn ni pb sn ti zn cr wt. % rem 1.480 2.306 0.059 0.256 0.052 0.052 0.023 0.012 0.052 5.424 0.280 table 1: the chemical composition of al 7075 in wt. %. content si p ca wt. % 99.41 0.32 0.26 table 2: the chemical composition of sic in wt. %. tensile behavior tensile testing was performed as per the astm standards e8. tensile tests were performed by subjecting the test specimen to axial or longitudinal load at a particular extension rate of increase of load till failure of the specimen occurred. test trials were carried out by using utm with a maximum load of 390-400 kn of capacity. hardness the hardness of composites was studied according to standards e92 using vickers-micro hardness testing equipment. the diamond indenter of 10 mm under the load condition of 0.5 kg with 15 seconds of duration was applied on the test specimens. hardness tests were carried out under the room temperature of 27ºc. the hardness of the composite was determined at 3 different places and the average of hardness values was recorded. a https://manipal.edu/mu.html https://manipal.edu/mu.html https://www.sciencedirect.com/topics/materials-science/molding-compound m. ravikumar et alii, frattura ed integrità strutturale, 56 (2021) 160-170; doi: 10.3221/igf-esis.56.13 163 wear behavior the pin on disc testing equipment was used for measuring the wear loss. the wear tests were performed as per the astm standards under the fixed sliding-speed of 1.66 m/s and the constant load of 3 kg against en-32 steel disc. for testing purposes, the specimens of length, 30 mm and 8 mm ϕ were prepared. the weights of the composite specimens were measured initially by using the digital weighing machine. the specimens were vertically rotated on a hardened steel disc. wear test was conducted when the specimen surfaces interface with the flat steel disc surface. after each test, specimens were removed from the fixture, and later acetone was used to clean the surface of the specimens. finally, the wear behavior was studied by considering the initial and final weight difference techniques. composite al7075 alloy (wt. %) sic (wt. %) al2o3 (wt. %) specimen 1 95 3 2 specimen 2 94 3 3 specimen 3 93 3 4 specimen 4 92 3 5 specimen 5 93 5 2 specimen 6 92 5 3 specimen 7 91 5 4 specimen 8 90 5 5 specimen 9 91 7 2 specimen 10 90 7 3 specimen 11 89 7 4 specimen 12 88 7 5 table 3: weight percentage of al7075 alloy and ceramic particulates for the developed composites. figure 1: (a) composite specimen for tensile test (b) composite specimen for hardness test and (c) composite specimen for the wear test m. ravikumar et alii, frattura ed integrità strutturale, 56 (2021) 160-170; doi: 10.3221/igf-esis.56.13 164 outcomes and discussions metallographic study he metallographic of fabricated mmcs are depicted in fig. 2. fig. 2(a) depicts the micrographic view of base material and fig. 2(b) depicts the micrographic view of al2o3 and sic reinforced al composite. from the metallographic study, uniform dispersal of particulates within the base matrix was observed. the reinforced particulates inhibited the dendritic development, which exhibited improved mechanical properties. micro-structure of composites showed the interface which specifies superior bonding of al2o3-sic particulates and base matrix. the uniform distributions of particulates are desired for obtaining enhanced mechanical properties and wear performance. the stirring of molten melt (slurry) affects extreme strain-rate and therefore resulted in uniform dispersal of the reinforcing particulates in melt alloy. as the reinforcement content increased, the decreased grain-size within the matrix was observed. the virtuous dense and cast defect-less microstructure generally produced excellent properties of the material. (a) (b) figure 2: microstructure images of composites: (a) 2%al2o3 + 3%sic (b) 5%al2o3 + 7%sic influence of reinforcements the influence of hard ceramic particulates (al2o3 and sicp) on the mechanical behavior of the mmcs obtained from tensile and hardness tests are depicted in figs. 3 and 6. the uts with varying al2o3 and sic is depicted in fig. 3. the obtained result indicates that the tensile strength is increased by increasing the wt. % of alumina content. it is due to the resistance to dislocations and hence the strength of hybrid composite increased by increasing wt. % al2o3 particulates. this type of observation conforms with the results of most hard particles reinforced in mmcs [23]. abhishek kumar et al. [24] studied the mechanical behavior of mmcs reinforced with al2o3 and sic particulates. they observed that the solidification process of mmcs increased by the amount of reinforcement in the matrix material. it is due to the intricacy in the addition of al2o3 and sic particulates that creates obstacles to the dislocation of movement through the matrix material. the evaluation of the stress v/s strain graph for the developed composite sample is as shown in fig. 4. one of the main reasons for the increase in stress is “direct strengthening outcomes from load transfer of matrix to reinforcement through shear stresses at an interface among the components”. from fig. 3 it is observed that composite with 5% al2o3 and 7% sic possesses better tensile strength as compared with other composition specimens. the combination of hard ceramic particulates (al2o3 and sic) makes the composite stronger so that it can withstand higher loads. from the graphical representation of the stress-strain curve depicted in fig. 4, it is also revealed that composite with 5% al2o3 and 7% sic withstands maximum stress. the stress-strain curve indicates the improved toughness apart from high tensile strength. this is significant. meanwhile, most strength improvement methods cause decreasing ductility. the fracture surface of composites test specimens is as depicted in fig. 5. from fig it is found that the fracture is mainly dimple rupture. generally, this is normally due to the overload failure and failure by merging of micro-voids process. from the composite (2% al2o3 + 3% sic) it is observed that, the size of dimples has reduced noticeably. fine dimples in the matrix region are present among the particulates. the numerous cuplike dimples are also observed in fractured image of 5% al2o3 + 7% sic composite material. formation and coalescence of micro-voids resulted in the dimples at localized strain regions (grain boundaries). fracture image of 5% al2o3 + 7% sic composite material shows that the number of dimples observed is more and in smaller sizes indicating the development of micro-voids. it specifies good bonding t m. ravikumar et alii, frattura ed integrità strutturale, 56 (2021) 160-170; doi: 10.3221/igf-esis.56.13 165 among the matrix and the reinforcements. generally, the grain size and shape of reinforcing particulates determine the bonding ability. generally, the dimple size shows the directly proportional relationship with composite strength. a fracture surface of tensile test specimens indicates the combination of hard ceramic particulates at the interface. a combination of particulates fracture and pullout was stated to be a fracture mechanism. the mode of fracture in the matrix alloy which has changed from ductile to cleavage nature was dominated by voids and micro-crack nucleation and propagation, as depicted in fig. 5. the fracture analysis of mmcs showed that, at higher wt. % of reinforcement content, nucleation of void took place at huge participates also of reinforcement into the matrix material whereas at lower wt. % of reinforcement, the fracture indicates the breakage of the particulates. figure 3: tensile strength with varying contents of al2o3 and sic. figure 4: stress-strain curve for all the composition. 0 20 40 60 80 100 120 140 160 180 200 0% 2% 4% 6% 8% 10% 12% 14% 16% s tr e ss ( m p a ) strain 2% al₂o₃ + 3% sic 3% al₂o₃ + 3% sic 4% al₂o₃ + 3% sic 5% al₂o₃ + 3% sic 2% al₂o₃ + 5% sic 3% al₂o₃ + 5% sic 4% al₂o₃ + 5% sic 5% al₂o₃ + 5% sic 2% al₂o₃ + 7% sic 3% al₂o₃ + 7% sic 4% al₂o₃ + 7% sic 5% al₂o₃ + 7% sic m. ravikumar et alii, frattura ed integrità strutturale, 56 (2021) 160-170; doi: 10.3221/igf-esis.56.13 166 figure 5: fracture images of the tensile specimen with different compositions . the variation of hardness with varying al2o3 and sic is as depicted in fig. 6. the hardness of the composite increased due to the addition of al2o3 and sic particulates. the improvement in the results is occurred due to the reinforcement of hard ceramics, which act as obstacles in the movement of dislocations [25]. the increased hardness of the mmcs can also be clarified based on dislodgment densities. by increasing the sic content in the matrix, the dislodgment density of mmcs increased which resisted the plastic deformation during sliding [26]. figure 6: vickers hardness of varying contents of al2o3 and sic. it was observed that the hardness value is maximum at 5 % al2o3 + 7 % sic reinforced mmcs. in many earlier research works on ceramic reinforced mmcs, it has been shown that there is an optimum range of reinforcement’s percentage for which the mechanical characteristics show maximum values. the piling up of the huge number of dislocations at the interface of particulates and matrix during the solidification because of the low coefficient of thermal expansion in sic al2o3 when compared with base alloy is the main reason for attaining better hardness in composites [27]. the hardness increased with increasing al2o3 and sic particulates and the maximum hardness was found at 5 % of al2o3 and 7 wt. % of sic reinforced composite. optimum values of uts and vickers hardness for the composite were obtained at 5 % of al2o3 + 7 wt. % of sic reinforced composite. as the number of particulates in the matrix increased, the corresponding matrix/particle interfacial areas also increased. it is observed that the ceramic particulates increase the mechanical properties of the mmcs. hence it is evident that tensile strength and hardness of al composite increased by adding of al2o3-sic particulates [28]. al7075 + 2% al2o3 + 3% sic cracks small dimples al7075 + 5% al2o3 + 7% sic particulate pullout large dimples m. ravikumar et alii, frattura ed integrità strutturale, 56 (2021) 160-170; doi: 10.3221/igf-esis.56.13 167 wear behavior of the mmcs wear loss of the mmcs (al7075/al2o3/sic) is depicted in fig. 7. the wear loss of hybrid composite decreased due to the addition of al2o3 and sic. from the results it is observed that high wear resistance was exhibited in 5 wt. % al2o3 7 wt. % sic reinforced hybrid composite. it is noticed that, the wear resistance of the mmcs would increase by increasing the wt. % of hard ceramic particulates [29, 30]. when the al2o3 particulates are intensely (strongly) bonded with the al matrix, they protect the composite surfaces against the destructive action of the counter face which results in less wear. the matrix and reinforcement particles interface is an extremely imperative constraint. meanwhile, inter-faces might be discreetly weak due to the interfacial reactions as well as poor wettability. better bonding among reinforcing particulates and the matrix increases the wear resistance of mmcs continuously due to an increase in the wt. % of reinforcements. in the case of al composites, the depth of dispersal by hard asperities of hard steel disc is generally directed by the protruding the hard ceramic reinforcements. the major part of the load applied is carried by sic particulates. the effect of reinforcing particulates is to withstand the contact-stresses and prevent high plastic deformation thereby reducing the amount of material worn out [26]. observation revealed that the al2o3 and sicp-reinforced mmcs increased the hardness and thus increased the wear resistance. similar outcomes have also been observed in the literature survey [15]. the wear loss of 2% al2o3 + 3% sic reinforced mmcs were higher than 5% al2o3 + 7% sic reinforced mmcs. this is due to the variation in the reinforcement properties. whereas the toughness of al2o3 is less than that of sicp and as a result of this fragmentation of al2o3 particulates occurred at an earlier phase than sicp, resulting in an improved in wear characteristics of al2o3 reinforced mmcs [27]. figure 7: wear rate of varying contents of al2o3 and sic morphological analysis a uniform dispersal of al2o3 and sic particulates in the mmcs has been detected. the uniform dispersal of the particles in the base alloy is essential to produce mmcs with better wear resistance and mechanical characteristics. the results reveal that the agglomeration of particulates was small. the worn surfaces of the composites led to the development of iron-rich layers [31]. scanning electron microscopy was done on composite samples as shown in fig. 8 and 9 which depicted the uniform distribution of reinforcements. here (fig. 9), al2o3 particles are seen as white (whitish phases) as well as sic particles are been observed in dark (black) phases within the base matrix structure. surface damages like detachments and de-cohesion of the material were also observed. the formation of grooves was noticeable in the path of sliding. fig. 9 shows the worn-out surfaces of al7075 with 5 % of al2o3 + 7 % sic reinforced mmcs. the plastic deformation was resisted in the base matrix due to the existence of hard ceramic particulates. grooves and minor patches are also noticed. due to the load applied, al2o3 and sic caused wrapping on the surface. these ceramic particulates acted like wrapping material on sliding surfaces and offered wear resistance. in the present investigation, al2o3-sic particulates were exposed to have valuable properties of the wear behavior of mmcs. al2o3-sic particles avoided the penetration of m. ravikumar et alii, frattura ed integrità strutturale, 56 (2021) 160-170; doi: 10.3221/igf-esis.56.13 168 steel disc into the mmcs and enhance the wear resistance. the al2o3-sic particulates may get crushed to powder form to maintain the wear resistance as detected in the results of wear rate [32, 33]. similar results have been noticed [5] and it is concluded that, from the analysis it is seen that, the sem analysis of worn-out surfaces of the mmcs (al7075 + 2%al2o3 + 3%sic) is different from that of al7075 + 5%al2o3 + 7%sic composite. figure 8: sem analysis of wornout surface composite sample (al 7075 + 2% al2o3 + 3% sic) figure 9: sem analysis of wornout surface composite sample (al 7075 + 5% al2o3 + 7% sic) figure 10: eds spectrum of composite specimen (al + 5% al2o3 + 7% sic). the composite with 2% al2o3 + 3% sic showed wide and also narrow grooves on the worn-out surfaces. whereas, fine grooves were observed in mmcs of 5% al2o3 + 7% sic. this remark supports the lower wear loss of mmcs. fig. 8 shows the material removed in the form of intensive plastic flow. it is witnessed that, the mmcs have been subjected to severe plastic deformation. though, the extent of the plastic deformation in 5%al2o3 + 7%sic composites seems to be less when compared to that of 2%al2o3 + 3%sic reinforced composite. further, it is noticed that the size of the grooves is high in 2%al2o3 + 3%sic reinforced composite, but no such morphologies are observed in 5%al2o3 + 7%sic reinforced composite, which shows the improved ability of mmcs to endure applied load during wear test. the eds (energy dispersive spectroscopy) analysis of al-al2o3-sic particles is depicted in fig. 10. the results reveal the existence of mg, al, si, zn, o and c in the interface layer. the small volume of oxygen was noticed in eds due to the development of the oxide layer [34]. from the results, it is inferred that oxygen (o) noticed in eds is probably due to the presence of oxide (al2o3) during sample preparation. also, the presence of a “si” peak was observed. this indicates that the presence of sic particulates in the composite. the peaks are shown in fig. 10, the eds configurations are indexed to a combination of different elements and other small peaks attributed to the impurity [27, 35, 36]. sliding direction plastic deformation sliding direction particulates ploughs m. ravikumar et alii, frattura ed integrità strutturale, 56 (2021) 160-170; doi: 10.3221/igf-esis.56.13 169 conclusions n the present investigation, the al 7075-al2o3-sicp hybrid mmcs were effectively produced using the liquid metallurgical technique. the effect of al2o3-sic reinforcement on mechanical properties and wear characteristics were studied and the outcome of the results is as follows: • the uts of the hybrid metal matrix composite was enhanced due to increasing of 5% of al2o3 and 7% of sic content. • the fractographic studies show that the changes in the mode of failure occurred from ductile to brittle due to an increase in the wt. % of hard ceramic particulates such as al2o3 & sic content. • maximum hardness of the produced composites was obtained at 5% of al2o3 and 7% of sic content. • the wear loss of the hybrid metal matrix composite decreased drastically with an increase in the content of al2o3 and sic particulates. • the sem images reveal that, the plastic deformation is resisted in the matrix due to the existence of hard ceramic particulates which acted as a barrier within the movement of dislocation, resulting in improved wear resistance. • eds spectrum indicates the existence of elements like al, mg, si, fe, and o. references [1] nikhilesh, s., belokar. r. m. and walia, r. s. (2020). a critical review on advanced reinforcements and base materials on hybrid metal matrix composites. silicon, doi: 10.1007/s12633-020-00853-z. [2] dharmalingam, s. and subramanian, r. (2010). analysis of dry sliding friction and wear behavior of aluminum alumina composites using taguchi’s techniques. journal of composite materials, pp. 1-17. [3] mulugundam, s. s. and gugulothu, s. k. (2021). fabrication, mechanical and wear characterization of silicon carbide reinforced aluminium 7075 metal matrix composite. silicon, doi: 10.1007/s12633-021-00992-x. [4] william, c. and harrigan. (1998). commercial processing of metal matrix composites. materials science and engineering. a244, pp. 75-79. [5] ramesh, c. s., keshavamurthy, r., channabasappa, b. h. and pramod, s. (2010). friction and wear behavior of ni– p coated si3n4 reinforced al6061composites. tribology international, 43, pp. 623-634. [6] deuis, r. l., subramanian, c. and yellup, j. m. (1997). dry sliding wear of aluminium composites-a review. composites science and technology, 57, pp. 415-435. [7] sannino, a. p. and rack, h. j. (1995). dry sliding wear of discontinuously reinforced aluminum composites: review and discussion. wear, 189, pp. 1-19. [8] dorward, r. c. and pritchett, t. r. (1988). advanced aluminium alloys for aircraft and aerospace applications. materials & design, 9, pp. 63-69. [9] chellman, d. j. and langebeck, s. l. (1992). aerospace application of advanced aluminum alloys. key engineering materials, 77, pp. 49-60. [10] reddy, p. v., kumar, g. s., krishnudu, d. m. and rao, h. r. (2020). mechanical and wear performances of aluminium-based metal matrix composites: a review. journal of bio-and tribocorrosion, 6(83), pp. 2-16. [11] veeresh kumar, g. b., rao, c. s. p., selvaraj, n. and bhagyashekar, m. s. (2010). studies on al6061-sic and al7075-al2o3 metal matrix composites. journal of minerals & materials characterization & engineering, 9, pp. 4355. [12] straffelini, g., bonollo, f., molinari, a. and tiziani, a. (1997.) influence of matrix hardness on the dry sliding behaviour of 20 vol. % al2o3-particulate-reinforced 6061 al metal matrix composite. wear, 211, pp. 192-197. [13] radhika, n., subramanian, r. venkat prasat, s. (2011). tribological behaviour of aluminium/alumina/graphite hybrid metal matrix composite using taguchi’s techniques. journal of minerals & materials characterization & engineering, 10, pp. 427-443. [14] alaneme, k. k. and bodunrin, m. o. (2013). mechanical behaviour of alumina reinforced aa (6063) metal matrix composites developed by two step stir casting process. acta technica corviniensis – bulletin of engineering, 4, pp. 105-110. [15] kok, m. (2005). production and mechanical properties of al2o3 particle-reinforced 2024 aluminium alloy composites. journal of materials processing technology, 161, pp. 381-387. i https://doi.org/10.1007/s12633-021-00992-x m. ravikumar et alii, frattura ed integrità strutturale, 56 (2021) 160-170; doi: 10.3221/igf-esis.56.13 170 [16] mahdavi, s. and akhlaghi, f. (2011). effect of the graphite content on the tribological behavior of al/gr and al/30sic/gr composites processed by in situ powder metallurgy (ipm) method. tribol lett, 44, pp. 1-12. [17] prashant, s. n., madev nagaral. and auradi, v. (2012). preparation and evaluation of mechanical and wear properties of al6061 reinforced with graphite and sic particulate metal matrix composites. int. j. mech. eng. & rob. res, 1, pp. 106-112. [18] sharma, s. c., girish, b. m., rathnakar kamath. and satish, b. m. (1997). effect of sic particle reinforcement on the unlubricated sliding wear behaviour of za-27 alloy composites. wear, 213, pp. 33-40. [19] ajitanshu vedrtnama. and anuj kumara. (2017). fabrication and wear characterization of silicon carbide and copper reinforced aluminium matrix composite. materials discovery, 9, pp. 16-22. [20] komai, k, and minoshima, k. (1993). tensile and fatigue fracture behavior and water-environment effects in a sicwhisker/7075-aluminum composite. composites science and technology, 46, pp. 59-66. [21] sourabh, g., rahul, r. u., venkatesh, s. d., srikanth, r. d. and bhimappa, s. w. (2013). preparation & characterization of al-5083 alloy composites. journal of minerals and materials characterization and engineering, 1, pp. 8-14. [22] sakthivelu, s., sethusundaram, p. p., ravichandran, m. and meignanamoorthy, m. (2020). experimental investigation and analysis of properties and dry sliding wear behavior of al-fe-si alloy matrix composites. silicon doi: 10.1007/s12633-020-00662-4. [23] shaik, m. q., murthy, b. s. and pinninti, r. r. (2016). processing and mechanical properties of al2o3 and red mud particle reinforced aa6061 hybrid composites. journal of minerals and materials characterization and engineering, 4, pp. 135-142. [24] abhishek kumar., shyam, l. and sudhir kumar. (2013). fabrication and characterization of a359/al2o3 metal matrix composite using electromagnetic stir casting method. journal of material research and technology, 2, pp. 250-254. [25] mehdi, r., nader, p. and naser, e. (2010). investigation of particle size and amount of alumina on microstructure and mechanical properties of al matrix composite made by powder metallurgy. materials science and engineering, a527, pp. 1031-1038. [26] padmavathi, k. r., ramakrishnan, r. and palanikumar, k. (2019). wear properties of sicp and tio2p reinforced aluminium metal matrix composites. indian journal of engineering & materials science, 26, pp. 51-58. [27] yogesh, k. s., rahul, c., hitesh, b. and anil, k. (2015). wear behavior of aluminum alloy 6061-based composites reinforced with sic, al2o3 and red mud: a comparative study. the journal of the minerals, metals & materials society, 67, 2160-2169. [28] pitchayyapillai, g., seenikannan, p., raja, k. and chandrasekaran, k. (2016). al6061 hybrid metal matrix composite reinforced with alumina and molybdenum disulphide. advances in materials science and engineering, pp. 1-9. [29] majid, h. and mahmood, m. (2005). tensile properties of in-situ aluminium-alumina composites. materials letters, 59, pp. 3414-3418. [30] karamıs, m. b., cerit, a. a., burhan, s. and fehmi, n. (2012). the effects of different ceramics size and volume fraction on wear behavior of al matrix composites (for automobile cam material). wear, 289, pp. 73-81. [31] rajesh, a. m., mohamed, k., saleemsab, d. and bharath, k. n. (2019). material characterization of sic and al2o3reinforced hybrid aluminum metal matrix composites on wear behavior. advanced composites letters, 28, pp. 1-10. [32] altinkok, n., ozsert, i. and findik, f. (2013). dry sliding wear behavior of al2o3/sic particle reinforced aluminium based mmcs fabricated by stir casting method. acta physica polonica, a124, pp. 11-19. [33] sekar, k. (2019). mechanical and tribological properties of al7475-sicp composites by stir casting method and wear rate modeling using rsm. sadhana, 44:129, pp. 1-8. [34] shorowordi, k. m., laoui, t., haseeb., celis, j. p. and froyen, l. (2003). microstructure and interface characteristics of b4c, sic and al2o3 reinforced al matrix composites: a comparative study. journal of materials processing technology, 142, pp. 738-743. [35] ravikumar, m., reddappa, h. n. and suresh, r. (2018). study on mechanical and tribological characterization of al2o3/sicp reinforced aluminum metal matrix composite. silicon, 10(6), pp. 2535-2545 doi: 10.1007/s12633-0189788-1. [36] ashokkumar, r and devaraju, a. (2020). modeling of mechanical properties and high temperature wear behavior of al7075/sic/crs composite using rsm. silicon, doi: 10.1007/s12633-020-00801-x. https://doi.org/10.1007/s12633-020-00662-4 https://doi.org/10.1007/s12633-018-9788-1 https://doi.org/10.1007/s12633-018-9788-1 https://doi.org/10.1007/s12633-020-00801-x microsoft word numero_57_art_20_3099 f. allaoua et alii, frattura ed integrità strutturale, 57 (2021) 281-290; doi: 10.3221/igf-esis.57.20 281 finite element analysis of stress state in the cement of total hip prosthesis with elastomeric stress barrier fadela allaoua, habib lebbal, abderrahmane belarbi department of mechanical engineering, university of science and technology, oran, algeria bouchamadila@gmail.com, https://orcid.org/0000-0002-1440-5768 lebbalh@yahoo.com, https://orcid.org/0000-0002-3514-857x belarbi_abd@yahoo.fr, https://orcid.org/0000-0002-0245-241x abstract. in the total hip prosthesis, according to different positions of the patient, there are a variety of loads acting on femoral head which generate stress concentration in the cement called polymethylmethacrylat (pmma) and consequently in interfaces stem/cement/bone. this load transfer can provoke loosening of the implant from the femoral bone. this paper focused on optimal stress distribution in the total hip prosthesis and devoted to the development of a redesigned prosthesis type in order to minimize stress concentration in the cement. this study investigated the effect of elastomeric stress barrier incorporated between the stem and femoral head using 3dfinite element analysis. the proposed model provided an acceptable solution for load transfer reduction to the cement. this investigation enabled an increase of the service life of total hip prosthesis avoiding the loosening. keywords. hip prosthesis; cement; stress concentration; stress barrier; finite element method (fem). citation: allaoua, f., lebbal, h., belarbi, a., finite element analysis of stress state in the cement of total hip prosthesis with elastomeric stress barrier., frattura ed integrità strutturale, 57 (2021) 281-290. received: 16.05.2021 accepted: 07.06.2021 published: 01.07.2021 copyright: © 2021 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. introduction any hip prostheses and fixation techniques have been introduced in orthopedics in recent years. recently, the cemented total hip replacement based on charnley low friction arthroplasty has proven outstandingly successful. the causes for long-term failure are characterized by the stem fracture, inadequate cementing or bad placement, but the introduction of high strength metal alloys and improved cemented techniques can increase their service lifetime. the stress patterns in the bone-prosthesis structure depend of the magnitudes and the orientations of the loads, the geometries of the structure, the mechanical properties of the materials and the physical conditions at material connections. during the polymethylmethacrylat (pmma) polymerization process, exothermic chemical reaction leads to a crack formation when its propagation depends to practiced exercise activity by the patients as described by charef and serier [1] in one hand and in another hand stress analysis on stem is analyzed as performed by colić et al. [2]. m https://youtu.be/n24158jtsos f. allaoua et alii, frattura ed integrità strutturale, 57 (2021) 281-290; doi: 10.3221/igf-esis.57.20 282 mahmoud et al. [3] analyzed revision of the well-fixed broken stem of cemented hemiarthroplasty using anterolateral proximal femoral window. also, the polished stems were predicted to induce a lower failure probability of cement mantle and higher integrity of the cement–stem interface when compared to the roughened stem and notable developments have included ceramic hip resurfacing and mini hip stems treated by [4]-[6] while topology and lattice in the optimized hip prosthesis design were performed to reduce stress shielding as shown by he et al. [7]. the finite element method (fem) is very suitable technique to interrelate these aspects quantitatively as shown by huiskes and chao [8] while huiskes and boeklagen [9] introduce a method of numerical shape optimization for prosthetic designs to minimize interface stresses. however, stress shielding of the femur is known to be a principal factor in aseptic loosening of hip replacements for that joshi et al. [10] present a study which explore the hypothesis that through redesign, a total hip prosthesis can be developed to substantially reduce stress shielding and fracture behavior has been investigated of different alloy materials used in total hip prosthesis replacement implants by sedmak et al. [11] and gross and abel [12] consider the use of a hollow stemmed hip implant for reducing the effects of stress shielding, while maintaining acceptably low levels of stress in the cement using finite element modeling. also, no relationship between residual stress and observed cracking of cement has yet been demonstrated. to investigate if any relationship exists, a physical model has been developed by lennon and prendergast [13] which allows direct observation of damage accumulation around cemented femoral components of total hip replacements. about the experimental part, a project is based on the clinical observation that higher subsidence (distal migration) correlates with early revision of hip prostheses to develop a pre-clinical testing platform for cemented femoral hip implants as measured by maher and prendergast [14]. the relationship between cement fatigue damage and implant surface finish in proximal femoral prostheses has been treated by lennon et al. [15] and has shown that, despite generally higher stresses in cement mantles of polished stems, the micro-damage does not apparently accumulate at a faster rate for those stems. a numerical study with four different stem shapes of varying curvatures for hip prosthesis was conducted by senalp et al. [16] to determine the fatigue endurance of cemented implant and to reduce sliding of the implant in the bonecement. the effect of the position and orientation of a crack in the cement mantle under various loads using the finite element method has been studied [17-19]. in this work, a three dimensional finite element method was employed to analyze both conventional and proposed prosthesis. in the second one, an elastomeric stress barrier is incorporated between the stem and the femoral head in order to reduce the force transfer to the cement developed by mehdi et al. [20]. the two models were modeled using solidworks cad sofware. materials and methods he total hip prosthesis with the principal components is presented in fig. 1 while fig. 2 shows two geometrical prosthesis models which are studied here: conventional model and redesigned model with an incorporated elastomer between the stem and the femoral head. figure 1: geometric model of the total hip prosthesis t cancelleous bone cement (pmma) femoral head cortical bone stem f. allaoua et alii, frattura ed integrità strutturale, 57 (2021) 281-290; doi: 10.3221/igf-esis.57.20 283 (a) (b) (c) figure 2: (a) full model, (b) detailed conventional model, (c) detailed proposed model. in reality, the femoral bone is an anisotropic material while the elastomer exhibits hyper-elastic behavior. for simplifying reasons, the mechanical behavior of all components was considered isotropic and linear elastic. tab. 1 provides their mechanical elastic properties. for the proposed model, an elastomeric material of 0.5 mm thickness was added between the femoral head and the stem. the both models were meshed with quadratic tetrahedral elements c3d10 chosen due to the model shape complexity, fig. 3a. the element size and type remain the same for the both models to avoid any influence of the mesh on the results. young modulus (mpa) poisson ratio cortical bone 17000 0,3 cancelleous bone 130 0,2 pmma 2300 0,3 stem 110000 0,3 femoral head 110000 0,3 elastomer 6 0,49 table 1: mechanical properties of the hip prosthesis components. three types of loading configurations were addressed: load 1, load 2 and load 3, depending on the high risk in the motion situations, are shown in tab. 2. the forces in the 3 directions as well as their resultant are given in percentage according to the weight of the body of the patient which is equal to 750 n. load movement % force weight load force components resulting force fx fy fz f load 1 walk quickly (5.3km/h or 1.47 m/s) -52 33 243 251 load 2 go down stairs (walking height : 17cm) -60 39 253 261 load 3 monopodal position -32 17 230 232 table 2: three loading situations with corresponding acting forces [13]. f. allaoua et alii, frattura ed integrità strutturale, 57 (2021) 281-290; doi: 10.3221/igf-esis.57.20 284 boundary conditions s shown in fig. 3b, the bottom of the femoral bone (cancelleous and cortical) is considered embedded: ux=uy=uz=urx=ury=urz=0, while that of the cement is blocked only along the axis (zz): uz=0. all interfaces are assumed fully bonded to ensure prosthesis stability. (a) (b) figure 3: (a) typical mesh, (b) loading and boundary conditions. loading conditions he loading is introduced for each situation according to the 3 directions with the values listed in tab. 2. acting forces are defined as 3 components applied on the femoral head: fx, fy and fz, fig. 3b. analysis and results umerical analysis of the two models under identical loading and boundary conditions was carried out using abaqus code based on finite element method (fem) [22]. in order to compare stress levels, choice was on the cement body (pmma), principal connexion between stem and bone ensures the stability of the prosthesis. fig. 4 presents the equivalent von mises stress distribution in the cement (pmma) in conventional and proposed models. it was observed that the high levels of stress values located in the stem/cement interface zone in the conventional model for the 3 situations are reduced in the proposed up to 35%. this is due to the presence of the elastomeric material which plays a stress barrier role while forces are transferring into the interface. stress distribution in the cement body (pmma) led to trajectories choice: external interface bone/cement ab-cd and internal interface stem/cement efg as indicated in fig. 5. fig. 6 shows the stress plot on the ab path for the three load cases. it is clear that point a is subjected to the highest levels of stress values for both models. nevertheless, it is observed that in point a stress level increases in the proposed prosthesis case compared to the conventional one. the difference of this increase for the largest values varies for the three load cases 13.2% (9.8 mpa to 11.1 mpa) 14.1% (9.9 mpa to 11.3 mpa) and 26.7% (10.1 mpa to 12.8 mpa) respectively. a t n f. allaoua et alii, frattura ed integrità strutturale, 57 (2021) 281-290; doi: 10.3221/igf-esis.57.20 285 figure 4: von mises stress in the cement of both conventional and proposed models f. allaoua et alii, frattura ed integrità strutturale, 57 (2021) 281-290; doi: 10.3221/igf-esis.57.20 286 figure 5: stress path in the cement. figure 6: von mises stress distribution along the cement path a-b for the three loading cases in the two models. -20 0 20 40 60 80 100 120 140 160 180 0 2 4 6 8 10 12 v on m is es s tr es s (m p a) path a-b (mm) load 1 conventional model proposed model -20 0 20 40 60 80 100 120 140 160 180 0 2 4 6 8 10 12 vo n m is es s tr es s (m p a) path a-b (mm) load 2 conventional model proposed model -20 0 20 40 60 80 100 120 140 160 180 0 2 4 6 8 10 12 vo n m is es s tr es s (m p a) path a-b (mm) load 3 conventional model proposed model f. allaoua et alii, frattura ed integrità strutturale, 57 (2021) 281-290; doi: 10.3221/igf-esis.57.20 287 in fig. 7 stresses are shown on the cd trajectory, indicating the concentrated stress in point c with a lower level than point a for the two models. in the proposed model, the stresses also increase with a percentage varying from 42.8% (6.3 mpa to 9.0 mpa), and 40.9% (6.6 mpa to 9.3 mpa) to 45.9% (6.1 mpa to 8.9 mpa). figure 7: von mises stress distribution along the cement path c-d for the three loading cases in the two models. the stress path in the efg interface is shown in fig. 8 for the three different loads. in the conventional model it is noted that in point e, stresses are greater compared to those observed throughout the cement body. contrary, in the proposed prosthesis the most concentrated zone observed a decrease in stress of 42.5% (15.5 mpa to 8.9 mpa), 42.0% (15.7 mpa to 9.1 mpa) and 42.4% (15, 8 mpa at 9.1 mpa) under load 1, load 2 and load 3 respectively. in particular, the case of the monopodal position seems to be the most dangerous. in the proposed prosthesis, it is noted that the stress levels decreased in this interface and in particular in the point e which was the most stressed area in the whole body of the cement in the conventional prosthesis. the reduction in these highest stresses in the stem/cement interface, which is the most sensitive, is estimated approximately 42% depending of the load. discussions inite element analysis has shown, that the most stressed area of the cement in the conventional hip prosthesis are in the vicinity of point e, in the internal cement/stem interface, being 15.5 mpa, 15.7 mpa and 15.8 mpa with the three load types respectively. this is due to the eccentric compression loads inducing a bending moment that tends to debond the stem from the cement. this interface stress level proves to be dangerous since it can initiate an interfacial -20 0 20 40 60 80 100 120 140 0 1 2 3 4 5 6 7 8 9 10 load 1 conventional model proposed model v on m is es s tr es s (m p a) path c-d (mm) -20 0 20 40 60 80 100 120 140 0 1 2 3 4 5 6 7 8 9 10 vo n m is es s tr es s (m p a) path c-d (mm) load 2 conventioal model proposed model -20 0 20 40 60 80 100 120 140 0 1 2 3 4 5 6 7 8 9 10 load 3 conventional model proposed model vo n m is es s tr es s (m p a) path c-d (mm) f f. allaoua et alii, frattura ed integrità strutturale, 57 (2021) 281-290; doi: 10.3221/igf-esis.57.20 288 crack propagating down the prosthesis causing the loosening. also, highest risk situations are those of walking down stairs and the monopodal position. however, the latter is not in common use while the descent of stairs can be frequent and cyclic if the patient lives in a building without elevator. a solution of stress deconcentration is proposed to solve this problem. this involves introducing an elastomeric material between the femoral head and the stem which made it possible to reduce the stress level in point e by redistributing stress field in the cement. this elastomer, through its deformation, reduced a force transfer rate to the prosthesis components allowing more even distribution of stress in the entire cement body. figure 8: von mises stress distribution along the cement path e-f-d for the three loading cases in the two models. in the proposed prosthesis, for all the applied loads, the presence of the elastomer reduced the stress concentration at the point e in the conventional prosthesis by more even distribution of the stress field at the stem/cement interface. these redistributed stresses in the cement have increased at point a, 11.1 mpa, 11.3 mpa and 12.8 mpa, and are the highest compared to those of the other points. consequently, the high stress levels in this concentrated interfacial zone stem/cement are reduced substantially while some other zones will increase their stress levels without reaching the peaks previously noted. however, the stress levels noted at points e and g which presented in important difference in the conventional prosthesis as 15.5 mpa~9.8 mpa, 15.7 mpa~10.1mpa and 15.8 mpa~9.5 mpa were not significantly different in this redesigned prosthesis 8.9 mpa~8.6 mpa, 9.1 mpa~7.7 mpa and 9.1 mpa~8.3 mpa. anyhow, the numerical models used in the study are based on some important limitations, notably those related to the constitutive laws of bone materials and to the characterization of the elastomer. 0 50 100 150 200 250 300 0 2 4 6 8 10 12 14 16 load 1 conventional model proposed model vo n m is es s tr es s (m p a) path e-f-g (mm) 0 50 100 150 200 250 300 0 2 4 6 8 10 12 14 16 vo n m is es s tr es s (m p a) path e-f-g (mm) load 2 conventional model proposed model 0 50 100 150 200 250 300 0 2 4 6 8 10 12 14 16 load 3 conventional model proposed model vo n m is es s tr es s (m p a) path e-f-g (mm) f. allaoua et alii, frattura ed integrità strutturale, 57 (2021) 281-290; doi: 10.3221/igf-esis.57.20 289 conclusions n this finite element analysis of both conventional and elastomeric prosthesis, it was concluded that: the obtained stresses in cement/stem interface using the new proposed prosthesis with elastomeric material are generally lower than those found with the conventional model. relative high stresses were observed at the cement/stem interface of the conventional model with the three load types. the use of soft and flexible elastomer positioned between the stem and the femoral head with low rigidity is able to reduce the load transfer to cement. the maximum stress concentration has moved from the cement/stem interface (in the conventional model) and reduced to the bone/cement interface (proposed model) because of the static equilibrium of forces in the new system. the stress levels reduction in the cement of the proposed prosthesis is estimated at 42%. in conclusion, the use of a shock absorbing elastomeric material appears to play a key role in the charge of transfer mechanism and the cement response. this stress absorber reduces the stress on the cement and thus increases its service life avoiding the loosening. acknowledgments he authors extend their appreciation to the director of scientific research at labps for funding the work through the biomechanics research group. references [1] charef, d., serier, b. (2017). prediction of crack propagation direction in the cemented total hip prosthesis, mechanics and mechanical engineering. 21(3), pp. 703-716. [2] colić, k., sedmak, a., grbovic a., tatic u., sedmak s., djordjevic b. (2016). finite element modeling of hip implant static loading, international conference on manufacturing engineering and materials, icmem 2016, procedia engineering, 149, pp. 257-262 [3] mahmoud, m.m.m., ibrahim, b., amr, a. a., and bayoumy, m.a. (2021). anterolateral bone window for revision broken cemented stem of unipolar hemiarthroplasty, adv. in orthopedics, pp. 1-5. [4] hung, j.p., bai, y.w., hung, c.q. and lee, t.e. (2019). biomechanical performance of the cemented hip stem with different surface finish, appl. sci., 9(19), pp. 1-16. [5] hoskins, w., van bavel , d., lorimer, m., de steiger, r.n. (2018). polished cemented femoral stems have a lower rate of revision than matt finished cemented stems in total hip arthroplasty: an analysis of 96,315 cemented femoral stems, j. arthroplasty, 33(5), pp. 1472–1476. [6] marsh, m. and newman, s. (2021). trends and developments in hip and knee arthroplasty technology, journal of rehabilitation and assistivetechnologies engineering, 8, pp. 1-9. [7] he, y., durocher, d., burkhalter, d., gilbert, j. m. (2018). solid-lattice hip prosthesis design: applying topology and lattice optimization to reduce stress shielding from hip implants, proceedings of design of medical devices conference, minneapolis, mn, usa, pp. 1-5, april 9-12. [8] huiskes, r. and chao, e.y-s. (1983). a survey of finite element methods in orthopaedic biomechanics: the first decade, j. biomechanics 16(6), pp. 385-409. doi: 10.1016/0021-9290(83)90072-6. [9] huiskes, r. and boeklagen, r. (1989). mathematical shape optimization oh hip prosthesis design. j. biomechanics 22(8-9), pp.796-804. doi: 10.1016/0021-9290(89)90063-8. [10] joshi, m.g., advani, s.g., miller, f., santare, m.h. (2000). analysis of a femoral hip prosthesis designed to reduce stress shielding. j. biomechanics 33(12), pp.1655-1662. doi: 10.1016/s0021-9290(00)00110-x. [11] sedmak, a., čolić, k., burzić, z., tadić, s. (2010). structural integrity assessment of hip implant made of cobaltchromium multiphase alloy, structural integrity and life, 10, pp.161-164 [12] gross, s. and abel, e.w. (2001). a finite element analysis of hollow stemmed hip prostheses as a means of reducing stress shielding of the femur. j. biomechanics, 34(8), pp.995-1003. i t f. allaoua et alii, frattura ed integrità strutturale, 57 (2021) 281-290; doi: 10.3221/igf-esis.57.20 290 [13] lennon, a.b. and prendergast, p.j. (2001). residual stress due to curing can initiate damage in porous bone cement: experimental and theoretical evidence. j. biomechanics 35(3), pp.311-321. doi: 10.1016/s0021-9290(01)00216-0. [14] maher, s.a. and prendergast, p.j. (2002). discriminating the loosening behaviour of cemented hip prostheses using measurements of migration and inducible displacement. j. biomechanics 35(2), pp.257-265. doi: 10.1016/s0021-9290(01)00181-6. [15] lennon, a.b., mccormack, b.a.o., prendergast, p.j. (2003). the relationship between cement fatigue damage and implant surface finish in proximal femoral prostheses. medical engineering & physics 25(10), pp.833-841. doi: 10.1016/s1350-4533(03)00120-6. [16] senalp, a. z., kayabasi, o., kurtaran, h. (2007). static, dynamic and fatigue behavior of newly designed stem shapes for hip prosthesis using finite element analysis. materials and design 28(5), pp.1577-1583. doi: 10.1016/j.matdes.2006.02.015. [17] bachir bouiadjra, b., belarbi, a., benbarek, s., achour, t., serier, b. (2007). fe analysis of the behaviour of microcracks in the cement mantle of reconstructed acetabulum in the total hip prosthesis. computational materials science 40(4), pp.485-491. doi: 10.1016/j.commatsci.2007.02.006. [18] ouinas, d., flliti, a., sahnoun, m., benbarek, s., taghezout, n. (2012). fracture behavior of the cement mantle of reconstructed acetabulum in the presence of a microcrack emanating from a microvoid. int j. of materials engineering, 2(6), pp.90-104. doi: 10.5923/j.ijme.20120206.04. [19] bounoua n., belarbi, a., belhouari m., bachir bouiadjra, b. (2014). stress intensity factors for micro-crack emanating from micro-cavity in cement of reconstructed acetabulum. mechanika, 20(6), pp.527-534. doi: 10.5755/j01.mech.20.6.9157. [20] mehdi, g., belarbi, a., mansouri, b., azari, z. (2015). numerical study of effect of elastomeric stress absorbers on stress reduction in bone-dental implant interface. j appl oral sci., 23(1), pp.87-93. doi: 10.1590/1678-775720140086. [21] foucat, d. (2003). effets de la présence d’un grillage métallique au sein du ciment de scellement des cupules des prothèses totales de hanche. etude mécanique et thermique. thèse de doctorat, université de strasbourg. laboratoire d’ingénierie des surfaces de strasbourg (l.i.s.s. ea 3435), i.n.s.a. de strasbourg. http://scd-theses.ustrasbg.fr/821/01/thèsefoucat.pdf. [22] abaqus/cae ver 6.9 (2007). user’s manual. hibbitt, karlsson & sorensen, inc. microsoft word numero_29_art_30 a. de rosis et alii, frattura ed integrità strutturale, 29 (2014) 343-350; doi: 10.3221/igf-esis.29.30 343 focussed on: computational mechanics and mechanics of materials in italy a numerical framework for simulating fluid-structure interaction phenomena a. de rosis department of agricultural sciences, university of bologna, viale giuseppe fanin 48, 40127 bologna alessandro.derosis@unibo.it s. de miranda, c. burrafato, f. ubertini department of civil, environmental, chemical and materials engineering, university of bologna stefano.demiranda@unibo.it, carlo.burrafato2@unibo.it, francesco.ubertini@unibo.it abstract. in this paper, a numerical tool able to solve fluid-structure interaction problems is proposed. the lattice boltzmann method is used to compute fluid dynamics, while the corotational finite element formulation together with the time discontinuous galerkin method are adopted to predict structure dynamics. the immersed boundary method is used to account for the presence of an immersed solid in the lattice fluid background and to handle fluid-structure interface conditions, while a volume-of-fluid-based method is adopted to take trace of the evolution of the free surface. these ingredients are combined through a partitioned staggered explicit strategy, according to an efficient and accurate algorithm recently developed by the authors. the effectiveness of the proposed methodology is tested against two different cases. the former investigates the dam break phenomenon, involving the modeling of the free surface. the latter involves the vibration regime experienced by two highly deformable flapping flags obstructing a flow. a wide numerical campaign is carried out by computing the error in terms of interface energy artificially introduced at the fluid-solid interface. moreover, the structure behavior is dissected by simulating scenarios characterized by different values of the reynolds number. present findings are compared to literature results, showing a very close agreement. keywords. fluid-structure interaction; lattice boltzmann method; immersed boundary method; volume-offluid method; dam break; flapping flags. introduction omputational fluid dynamics (cfd) represents a set of scientific methods whose aim is to solve problems, which involve fluids by adopting computers, algorithms and numerical methods. cfd can be studied and analyzed at three different levels. the “top” one is the so-called macroscopic level, consisting of the solution of the navierstokes equations, which govern flow behavior. the “bottom” one reduces a fluid flow problem to a microscopic one and it is solved by adopting laws arising from molecular dynamics. between these approaches, in the last decades the lattice boltzmann (lb) method [1,2] developed as a powerful alternative to standard approaches. it is characterized by a c a. de rosis et alii, frattura ed integrità strutturale, 29 (2014) 343-350; doi: 10.3221/igf-esis.29.30 344 mesoscopic point of view, where the flow behavior emerges by the space-time evolution of a function describing the density of a set of fictitious particles. these particles move upon an eulerian grid which is kept fixed during the overall analysis. among the possible advantages of the lb method over the macroscopic-based one, the most immediate is the greater computational efficiency, especially in interaction problems involving moving structures. it has been demonstrated that the solution given by the lb method is equivalent to the one of the navier-stokes equations for an incompressible flow with a second order of accuracy [3]. in order to account for the presence of a solid body immersed in the lattice fluid background, the immersed boundary (ib) method is adopted [4,5]. with respect to the well-consolidated bounce-back rule [6,7], such method is characterized by superior properties in terms of stability. according to a recent work carried out by the authors, it preserves a high level of accuracy and it leads to a quite general implementation of the numerical algorithm [8]. a volume-of-fluid-based approach (vof) [9,10] is used to take trace of the liquid-gas interface movements due to the mass advection. in particular, the model uses the vof to update the nodes fill levels (in terms of mass) and a pressure boundary to restore the missing distribution functions at the liquid-gas interface. when moving structures are considered, the non-linear structure dynamics is computed by adopting the time discontinuous galerkin (tdg) scheme. this choice over standard newmark algorithms is motivated by its superior properties in terms of stability, accuracy and convergence [11-13]. in this paper, the lb, vof, ib and tdg methods are combined within a staggered explicit coupling algorithm called felba (finite element lattice boltzmann analysis), which has been validated by the authors for different applications, including mechanics [14,15], industry [16], flapping flight [17,18], and even shallow waters [19], among the others. in particular, the above ingredients are combined together in order to predict the flow physics arising in two different cases: a dam break and two solid structures obstructing the development of a flow in a channel. structures are idealized by euler-bernoulli finite elements capable of undergoing large displacements, according to the corotational formulation [20,21]. the accuracy of the coupling algorithm is evaluated in terms of the energy that is artificially introduced in the system at the fluid-structure interface. here, scenarios characterized by different values of the reynolds number are investigated. findings in terms of the three components of the tip displacement are given for the above-mentioned configurations, together with considerations about the artificially introduced interface energy. as regards the simulation of the dam break phenomenon, findings from a numerical analysis are compared to literature results, showing the effectiveness of the proposed approach. problem statement he flow physics is computed by solving the lb equation, that is fi(x+ci t, t+t) = fi(x,t) + [fi(x,t)-fieq(x,t)] with i=0,…,8, (1) where fi are the particle distribution functions, x is the position, t is the time,  is the relaxation frequency, t is the time step and ci are the lattice vectors in the adopted d2q9 model [2]. notice that the relaxation frequency is strictly related to the fluid viscosity, i.e. =(1/-0.5)/3. the equilibrium distribution functions fieq are computed as a second-order expansion in the local mach number [2]. the presence of an immersed body is accounted for by adding at the right-hand side of eq. (1) the quantity 3ciwigi(x,t), where gi(x,t) is a term computed via an implicit velocity-correction based ib method [22]. once the corrected eq. (1) is solved, the macroscopic density  and fluid velocity v are computed as  = ifi, v=ifici/ (2) on the other hand, deformable solids are idealized as corotational beam finite elements. the resultant non-linear equation of the solid motion is integrated in time by adopting the tdg scheme according to the implementation proposed in [13]. as discussed in [16], the tdg scheme has shown superior properties with respect to the adoption of standard newmark algorithms for solving fluid-structure interaction problems. as mentioned above, in order to handle fluid-structure interface condition, the ib method is adopted. in this way, the solid body is represented by a set of lagrangian points, independent from the eulerian fluid mesh, thus allowing a quite general implementation of the algorithm of computation. if a free surface flow is considered, the difference in terms of density and viscosity between the two phases composing the system is usually very high. thus, it is possible to affirm that the behavior of the overall system is governed by the phase with the higher density [9]. the phase characterized by the lower density is considered only as a surface boundary condition, thus it is neglected in the rest of the domain. the adopted free surface model represents a combination of the lb and vof methods, the latter being responsible of the interface tracking. this method requires a particular treatment t a. de rosis et alii, frattura ed integrità strutturale, 29 (2014) 343-350; doi: 10.3221/igf-esis.29.30 345 of the interface lattice sites. since the part composed of the lower density is not affected by the solution of the lb equation, the missing values of the particle distribution functions should be computed by a pressure boundary, as sketched in fig. 1. the interested reader can refer to [9, 10] for further discussion about this approach. figure 1: handling of the missing distribution functions. red dotted arrows represent the distribution that need to be reconstructed. the present method, as a whole, is briefly described in the following steps: 1. initialize fluid and solid domain; 2. solve the fluid system, eq. (1) (lb); 3. compute mass fluxes (vof) and reconstruct a valid set of distribution functions at the interface (pressure boundary); 4. compute the fluid macroscopic variables and v, eq. (2); 5. enforce the no-slip condition at the fluid-structure interface via the iterative ib algorithm (compute gi(x,t) and compute the forces on the structure); 6. correct the populations with the term gi(x,t) and compute, again, the fluid macroscopic variables and v, eq. (2); 7. perform structure solution; 8. update nodes fill levels and re-initialize lattice state (i.e. emptied interface node become gas node, etc.); 9. advance in time going to step 2. results and discussion n this section, two cases are investigated. first, the dam break phenomenon is simulated. then, the dynamics of two slender deformable beams invested by a flow is examined. dam break making reference to fig. 2, a water column of height h=0.3m and width b=0.6m is placed in the right part of a tank of length l=1.61m, height d=6m. at t=0 the wall placed at x=0 is removed. the system described has been discretized using a relatively coarse grid, composed of 400 lattice nodes in x-direction and 150 in z-direction. during the test, the height of the water column is recorded at 4 checkpoints, h1, h2, h3 and h4. in the following, findings from a lb simulation are compared to the experimental data given in [2325]. in fig. 3, the time evolution of the simulated and experimental free-surface profiles are compared. moreover, in tab. 1, the simulated and experimental time instants at which the water column crosses the checkpoints h2, h3 and h4 and impacts the boundary are reported. as it is possible to observe, a very close agreement is experienced. finally, in fig. 4, the present findings in terms of water height are compared with literature results [23-25] at the above mentioned checkpoints. as it can be noted, also in this case a good agreement is obtained. i a. de rosis et alii, frattura ed integrità strutturale, 29 (2014) 343-350; doi: 10.3221/igf-esis.29.30 346 figure 2: dam break: sketch of the problem set-up [23]. figure 3: dam break: numerical and experimental [23] time evolution of the free-surface profile. checkpoint [23] present h2 159.9 181 h3 276.6 278.9 h4 373.3 364 boundary 449.9 441.2 table 1: dam break: time [ms] required to reach the checkpoints and impact the boundary. a. de rosis et alii, frattura ed integrità strutturale, 29 (2014) 343-350; doi: 10.3221/igf-esis.29.30 347 figure 4: water height evolution at the checkpoints h1, h2, h3, and h4 computed with the present method and compared with literature results [23-25]: checkpoint h1 (top-left); checkpoint h2 (top-right); checkpoint h3 (bottom-left); checkpoint h4 (bottomright). the gravity acceleration is denoted by g. two slender beams obstructing a flow making reference to fig. 5, two identical beams (blue lines) of length l=25 are placed in a channel of width w=200 and height h=60. figure 5: two slender beams obstructing a flow: sketch of the problem set-up. moreover, the distance d is set to 100 and it is chosen as the characteristic length of the problem. at the west-most section, a constant uniform rightward velocity profile v=0.01 is prescribed, whereas at the east-most section outflow boundary conditions are enforced. the fluid possesses density =1, viscosity  and is initially at rest. the zero-velocity condition imposed at the bottom and top walls complete the definition of the problem. notice that all the quantities are given in lb units. beams possess elastic modulus e=0.01, cross sectional area a=16 and inertia moment j=21.33, a. de rosis et alii, frattura ed integrità strutturale, 29 (2014) 343-350; doi: 10.3221/igf-esis.29.30 348 whereas the density is set to s=8. no structural damping is prescribed. beams are clamped at the walls of the channel. by varying the relaxation frequency, different reynolds number re are achieved, i.e. re=10, 25, 50. in fig. 6, the time history of the horizontal component of the tip displacement is depicted for the bottom beam. notice that the no symmetry breaking is experienced in the simulations. figure 6: two slender beams obstructing a flow: time history of the horizontal component of the tip displacement at different reynolds number, re=10 (red), 25 (green), 50 (blue). as it is possible to observe, as re grows, the amplitude of the displacement tends to reduce. such behavior has to be addressed to the fact that the viscous-dependent shear component of the stress induced by the flow upon the beam tends to vanish for progressively higher values of re. on the other hand, a more turbulent flow induces more complex oscillation for the beam. in order to assess the effectiveness of the coupling algorithm to properly enforce the interface conditions, the authors define an interface energy rate at the fluid–structure interface that is computed from both the fluid, jf, and the structure, js, sides as the product between forces and velocities computed from the fluid and solid sides, respectively. as shown in fig. 7, the two rates lie on the diagonal of the graph, thus showing values relatively close each other. only a part of the graph moves apart from the diagonal, which corresponds to the beginning of the simulation when the velocity profile suddenly impacts the beams. finally, some snapshots of the velocity field are given in fig. 8. figure 7: two slender beams obstructing a flow: jf vs js at different reynolds number, re=10 (red), 25 (green), 50 (blue). conclusions n this paper, a numerical framework able to simulate fluid-structure interaction problems has been presented. specifically, the fluid domain is solved by the lb method, whereas structure dynamics is predicted via the non-linear tdg method. the ib method is adopted to handle fluid-structure interface conditions. the moving free surface is treated by a vof-based method. all the ingredients described are coupled in a global algorithm that has been applied in the two different test cases presented. in the former, a dam break phenomenon is simulated by adopting a free surface model. present findings are compared to experimental data, showing a very close agreement. in the latter, a constant uniform rightward velocity profile invests two slender beams and scenarios characterized by different values of the reynolds number are dissected. the effectiveness and the accuracy of the proposed approach are assessed by computing the interface energy rates from the fluid and solid sides, which show very close values. based on numerical results, the i a. de rosis et alii, frattura ed integrità strutturale, 29 (2014) 343-350; doi: 10.3221/igf-esis.29.30 349 authors conclude that the proposed approach appears to be feasible and highly promising for simulating a wide range of fluid-structure interaction phenomena. figure 8: snapshots of the velocity field at re=10 (first row), 25 (second row), 50 (third row) for different time instants, t=150 (first column), 300 (second column), 400 (third column). references [1] benzi, r., succi, s., vergassola, m., the lattice boltzmann equation: theory and applications, physics reports, 222 (1992) 145-197. [2] succi, s., the lattice boltzmann equation for fluid dynamics and beyond, clarendon, oxford (2001). [3] chen, h., chen, s., matthaeus, w., recovery of the navier-stokes equations using a lattice-gas boltzmann method, physical review letters, 45 (1992) r5339-r5342. [4] peskin, c. s., the immersed boundary method, acta numerica, 11 (2002) 479-517. [5] fadlun, e., verzicco, r., orlandi, p., mohd-yusof, j., combined immersed-boundary finite-difference methods for three-dimensional complex flow simulations, journal of computational physics, 161 (2000) 35-60. [6] mei, r.., luo, l., shyy, w., an accurate curved boundary treatment in the lattice boltzmann method, journal of computational physics, 155 (1999) 307-330. [7] mei, r., yu, d., shyy, w., luo, l., force evaluation in the lattice boltzmann method involving curved geometry, physical review letters e, 65 (2002) 041203. [8] de rosis, a., ubertini, s., ubertini, f., a comparison between the interpolated bounce-back scheme and the immersed boundary method to treat solid boundary conditions for laminar flows in the lattice boltzmann framework, journal of scientific computing, (2014). [9] janßen, c., krafczyk, m., free surface flow simulations on gpgpus using the lbm, computers & mathematics with applications, 61 (2011) 3549-3563. [10] thürey, n., körner, c., rüde, u., interactive free surface fluids with the lattice boltzmann method, technical report, university of erlangen-nuremberg, germany (2005). [11] mancuso, m., ubertini, f., an efficient time discontinuous galerkin procedure for non-linear structural dynamics, computer methods in applied mechanics and engineering, 195 (2006) 6391-6406. [12] de miranda, s., mancuso, m., ubertini, f., time discontinuous galerkin methods with energy decaying correction for non-linear elastodynamics, international journal for numerical methods in engineering, 83 (2010) 323-346. [13] mancuso, m., ubertini, f., an efficient integration procedure for linear dynamics based on a time discontinuous galerkin formulation, computational mechanics, 32 (2003) 154-168. [14] de rosis, a., falcucci, g., ubertini, s., ubertini, f., a coupled lattice boltzmann-finite element approach for twodimensional fluid–structure interaction, computers & fluids, 86 (2013) 558-568. a. de rosis et alii, frattura ed integrità strutturale, 29 (2014) 343-350; doi: 10.3221/igf-esis.29.30 350 [15] de rosis, a., ubertini, s., ubertini, f., a partitioned approach for two-dimensional fluid-structure interaction problems by a coupled lattice boltzmann-finite element method with immersed boundary, journal of fluids and structures, 45 (2014) 202-215. [16] de rosis, a.; falcucci, g.; porfiri, m.; ubertini, f., ubertini, s., hydroelastic analysis of hull slamming coupling lattice boltzmann and finite element methods, computers & structures, 138 (2014) 24-35. [17] de rosis, a., falcucci, g. ubertini, s., ubertini, f. (2014), aeroelastic study of flexible flapping wings by a coupled lattice boltzmann-finite element approach with immersed boundary method, journal of fluids and structures, (2014) [18] de rosis, a., on the dynamics of a tandem of asynchronous flapping wings: lattice boltzmann-immersed boundary simulations, physica a: statistical mechanics and its applications, 410 (2014) 276-286 [19] de rosis, a., a lattice boltzmann-finite element model for two-dimensional fluid-structure interaction problems involving shallow waters, advances in water resources 65 (2014) 18-24. [20] felippa, c., haugen, b., a unified formulation of small-strain corotational finite elements: i. theory, computer methods in applied mechanics and engineering, 194 (2005) 2285-2335. [21] zagari, g., casciaro, r., de miranda, s., ubertini, f., koiter analysis of folded structures using a corotational approach, international journal of solids and structures, 50 (2013) 755-765. [22] wu, j., shu, c., implicit velocity correction-based immersed boundary-lattice boltzmann method and its applications, journal of computational physics 228 (2009), 1963-1979. [23] lobovský, l., botia-vera, e., castellana, f., mas-soler, j., souto-iglesias, a., experimental investigation of dynamic pressure loads during dam break, journal of fluids and structures, 48 (2014) 407-434. [24] bauchner, b., green water on ship-type off-shore structures, phd thesis, delft university of technology, (2002). [25] hang lee, t., zhou, z., cao, y., numerical simulations of hydraulic jumps in water sloshing and water impacting, journal of fluid engineering, 124 (2002) 215-226. microsoft word numero 1 notiziario.doc gruppo italiano frattura 2 notiziario i g f n. 18 luglio 2007 in questo numero 1) editoriale del presidente igf; 2) cariche sociali biennio 2005-2007; 3) verbale dell’assemblea annuale dei soci 2006; 4) verbali dei consigli di presidenza; 5) resoconti delle attività del 2006; 6) xix convegno nazionale igf – milano 2007; 7) convocazione assemblea annuale dei soci 2007; 8) calendario congressi internazionali ; 9) modulo di iscrizione igf-esis. presidente igf: giuseppe ferro, dipartimento di ingegneria strutturale e geotecnica, politecnico di torinocorso duca degli abruzzi, 24 10129 torino. tel. 0115644885, fax 011-5644899, e-mail: ferro@polito.it segretario igf curatore del notiziario: francesco iacoviello, di.m.s.a.t. università di cassino, via g. di biasio 43, 03043 cassino (fr). tel. 0776-2993681, fax 0776-2993733, e-mail: iacoviello@unicas.it (1) editoriale del presidente igf nel primo consiglio di presidenza svolto in via telematica (divertente esperienza iniziata con il sottoscritto connesso con abbondante ritardo e con firrao in veste di ascoltatore non microfonato che conferiva via sms, telefono e posta elettronica) è stata varata con molto entusiasmo da parte di tutti i membri del consiglio la rivista on-line del gruppo italiano frattura. la rivista si chiamerà frattura ed integrità strutturale. avrà una cadenza trimestrale e vedrà l’attuale segretario del gruppo nonché primo proponente, francesco iacoviello, nella veste di editor della rivista. questo editoriale inaugura il numero zero della nuova rivista. il comitato scientifico sarà costituito dai membri del consiglio di presidenza e dai più eminenti e autorevoli esperti di meccanica della frattura attivi in italia. la rivista sarà pubblicata facoltativamente in ltaliano o in inglese con sommario obbligatoriamente bilingua. cosa si può dire e augurare ad un progetto così ambizioso? sicuramente questa iniziativa darà l’opportunità a tutti i soci igf di poter pubblicare in un ambito molto indirizzato agli aspetti applicativi e industriali. usando un termine molto adoperato in questo periodo, la rivista aiuterà il trasferimento tecnologico nell’ambito dell’integrità strutturale in italia, dal momento che l’accesso alla rivista sarà libero e fortemente pubblicizzato per via telematica sfruttando gli importanti indirizzari telematici che siamo riusciti a costruirci nel corso di questi ultimi anni. il battesimo ufficiale della rivista avverrà nel corso del prossimo congresso nazionale che quest’anno si svolgerà a milano presso la sede del politecnico della bovisa. un concerto jazz presso il famoso locale blue note di milano rappresenterà l’aspetto mondano della festa. al congresso nazionale, molto ben organizzato da stefano beretta, le letture plenarie invitate saranno tenute da wolfgang brocks (recentemente insignito della griffth medal da parte dell’esis) e da hugo ernst. i due colleghi stranieri verranno nominati soci onorari del gruppo e si aggiungeranno ai precedenti soci onorari nominati nelle precedenti edizioni dei congressi nazionali (robert ritchie, yiu-wing may, david taplin, emmanuel gdoutos, george sih). un grosso lavoro è stato compiuto dal consiglio di presidenza in questi due anni di attività relativamente al nuovo sito igf (www.gruppo frattura.it) all’interno del quale sono stati inseriti gli atti dei congressi svolti nell’ultimo decennio (cassino 1997, trento 1998, bari 2000, catania 2002, bologna 2004, cosenza 2006) oltre al migliaio di paper presentati al congresso mondiale icf xi svoltosi a torino nel 2005, reperibili al sito www.icf11.com. entro il 2007 è nostra intenzione informatizzare tutti gli atti dei primi 12 congressi nazionali per rendere accessibili a tutti gli articoli che hanno fatto la storia della meccanica della frattura in italia, secondo lo spirito del nostro statuto. giuseppe ferro presidente igf e segretario esis gruppo italiano frattura 3 (2) cariche sociali biennio 2005-2007 presidente: • giuseppe ferro -politecnico di torino. consiglio di presidenza: • stefano beretta politecnico di milano; • francesco iacoviello università di cassino (segretario); • franco furgiuele università della calabria; • donato firrao politecnico di torino (vice presidente); • angelo finelli enea (tesoriere); • mario marchetti università di roma la sapienza (vice presidente); • lorenza barsanti – snam retegas; • roberto frassine politecnico di milano; revisori dei conti: • giuseppe demelio – politecnico di bari; • vincenzo sglavo università di trento; probiviri: • prof. alberto carpinteri politecnico di torino; • prof.sergio reale università di firenze; • prof. roberto roberti università di brescia. a norma di statuto il recapito dell'igf è presso il segretario: la quota annuale di iscrizione è di 30 euro (comprensiva di iscrizione esis), esente iva a norma dell'art.2 del dpr 26/10/72 e successive modifiche. la quota potrà essere versata a: gruppo italiano frattura mediante bonifico bancario su cc. n. 100940 del credito cooperativo bolognese, ag. via arcoveggio 56/22 bologna intestato al gruppo (abi 7082 cab 02402). (3) verbale dell’assemblea annuale dei soci verbale dell’assemblea ordinaria dei soci del 31 maggio 2006 l’assemblea ha inizio alle ore 18.00 del 31 maggio 2006 presso l’hotel san michele, cetraro (cs), sede del convegno nazionale igf xviii, con il seguente ordine del giorno: 1. approvazione verbale dell’assemblea dei soci di ferrara. 2. comunicazioni. 3. relazione revisore dei conti 4. presentazione bilancio consuntivo 2005 5. indirizzo attività per il biennio 2006-07 6. varie ed eventuali. 7. attribuzione “premio giovani” risultano presenti i seguenti consiglieri: ferro (presidente), barsanti, finelli, firrao, frassine, furgiuele, iacoviello. assenti giustificati: beretta, marchetti risultano presenti i seguenti soci: clubi vincenzo, colombo daniele, comino luca, esposito luca, fersini davide, gentile domenico, ghedini andrea, guagliano mario, iovani giuseppe, la vecchia marina, labanti martino, madia mauro, pasta antonino, peghini marco, piacente valentino, trentini elena punto 1 all’o.d.g.: approvazione verbale del consiglio di ferrara. il consiglio di presidenza approva il verbale. punto 2 all’o.d.g.: comunicazioni. il presidente comunica all’assemblea la recente scomparsa del prof. miller. l’assemblea osserva un minuto di silenzio. il presidente comunica che è attivo il sito internet all’indirizzo www.gruppofrattura.it e che, a breve, conterrà tutti i lavori presentati nei convegni nazionali e nelle giornate di studio. vengono distribuite a tutti i partecipanti le copie della relazione dei revisori dei conti e del bilancio consuntivo. punto 3 all’o.d.g.: relazione dei revisori dei conti. il revisore dei conti, sglavo, presenta all’assemblea la relazione dei revisori allegata al presente verbale, e ne propone l’approvazione. l’assemblea approva all’unanimità. punto 4 all’o.d.g.: presentazione bilancio consuntivo. il tesoriore, finelli, presenta all’assemblea il bilancio consuntivo, allegato al presente verbale, proponendone l’approvazione. l’assemblea approva all’unanimità. il presidente ricorda all’assemblea che la quota annuale ammonta a 30€, di cui 10€ vengono versati all’esis per l’iscrizione, e propone di mantenere la quota invariante anche nel prossimo anno. l’assemblea approva all’unanimità. punto 5 all’o.d.g.: indirizzo attività biennio 2006-2007. il presidente presenta all’assemblea l’attività svolta all’interno dell’esis, evidenziando il fatto che l’organizzazione igf è stata presa a modello da altri 16 paesi europei e sollecita l’assemblea per la proposta di attività da attivare nel prossimo biennio. barsanti propone l’organizzazione, in collaborazione con beretta, di una giornata di studio da svolgersi a milano ed avente come oggetto la gruppo italiano frattura c/o francesco iacoviello di.m.s.a.t. università di cassino via g. di biasio 43, 03043 cassino (fr). tel./fax 0776-2993681 e-mail: iacoviello@unicas.it gruppo italiano frattura 4 fatica e la frattura nelle strutture saldate da tenersi nella prima settimana di febbraio 2007. la giornata, in funzione del numero di partecipanti, si svolgerà nel centro ricerche di bolgiano (san donato milanese) oppure a piacenza. donzella e dogliano propongono un’altra giornata da organizzare a brescia a fine novembre – inizio dicembre 2006 ed avente come argomento l’integrità strutturale all’interfaccia ruota – rotaia. il presidente presenta da parte di beretta la candidatura della sede di milano ad organizzare il convegno nazionale igf xix nel mese di giugno 2007. l’assemblea approva all’unanimità tutte le attività proposte. punto 6 all’o.d.g.: varie ed eventuali. il presidente sollecita l’assemblea ad una discussione sulla missione del igf, ricordando all’assemblea l’importanza della partecipazione alle attività presenti nei tc – esis. inoltre propone che l’igf si presenti come autorevole interlocutore per contribuire alla stesura di normative. firrao interviene ricordando l’attività igf negli ultimi anni e propone all’assemblea una maggiore partecipazione alle attività a livello europeo. frassine propone un maggior legame con l’industria, proponendo che l’igf organizzi attività formative organizando scuole tematiche presso aziende interessate e partecipando a mostre. punto 7 all’o.d.g.: attribuzione “premio giovani” il cdp, dopo lunga ed approfondita discussione, decide di attribuire i due “premi giovani” ai seguenti autori: f. caimmi, autore del lavoro “sull’applicabilità della prova cens allo studio della tenacità interlaminare in modo ii di laminati in composito” e. trentini, autrice del lavoro “mechanical behaviour of a sicf/sic composite for nuclear applications at high temperature” il presidente scioglie l’assemblea alle ore 19.30. allegato a assemblea di bilancio 2005 relazione del tesoriere l’esercizio economico dell’anno 2005 mostra fra le uscite oltre ad un saldo di spesa relativo alla stampa di 1200 copie degli atti igf17, distribuite al convegno internazionale icf 11 di torino, le spese relative all’organizzazione della giornata sulla “fatica multiassiale” tenutasi presso la facoltà di ingegneria dell’università di ferrara nello scorso mese di giugno ed il contributo ad esis relativo all’iscrizione dei nostri soci. le entrate sono invece costituite dalle quote associative, dalle iscrizioni alla giornata su menzionata e da un nuovo prestito contratto con esis per un importo di 6000 €. e’ inoltre, secondo il mio parere, spiacevole dover notare come un evento importante come icf 11, nonostante una partecipazione elevata ed al di là delle più rosee previsioni, abbia garantito un introito pari solamente alla quota di partecipazione di 14 ospiti provenienti da paesi dell’est europeo. come si può notare dal rendiconto economico l’anno finanziario si chiude con un passivo di € 5.557,92, praticamente imputabili alla spesa per la stampa degli atti igf 17. l’andamento del mercato borsistico, ha, ancora una volta, sconsigliato il realizzo dei fondi investito in titoli, anche se, come già segnalato nella precedente assemblea, il suddetto mercato ha continuato a registrare un andamento positivo. su decisione dell’assemblea di catania del 2002, a bilancio viene comunque riportato il capitale inizialmente versato a cui viene detratto il valore di un prelievo effettuato nel 2003. il conto profitti o perdite verrà quantificato al momento di un eventuale completo realizzo. il capitale del gruppo passa pertanto da €. 50.802,07 a € 45.089,88 (11,2%). il giro di affari della gestione 2005, rilevabile dal bilancio consuntivo, è stato pari a € 80.898,43. il tesoriere: angelo finelli allegato b bilancio 2005 relazione dei revisori dei conti il bilancio 2005 chiude con entrate per € 13.086,72 e uscite per € 19.184,64. tenendo conto dell'avanzo di € 50.802,07 della gestione precedente, la presente gestione si chiude con un avanzo di € 45.089,88 che è stato iscritto alla voce bilancio del giornalmastro all'inizio dell'anno 2006. nel corso dell'anno 2005 abbiamo verificato che la contabilità del gruppo è stata tenuta regolarmente e che gli adempimenti fiscali del gruppo sono stati regolarmente ottemperati. riteniamo pertanto che il bilancio rifletta conti sinceri in accordo con la realtà dell'associazione e vi invitiamo ad approvarlo. i revisori dei conti: vincenzo m. sglavo e giuseppe demelio (4) verbali dei consigli di presidenza verbale del consiglio di presidenza del 20 marzo 2007 la riunione ha inizio alle ore 11.00 presso il politecnico di milano (sede bovisa), con il seguente ordine del giorno: 1. comunicazioni. 2. congresso nazionale igf 19 3. notiziario 4. sito web conosci i tc dell’esis ? www.esisweb.org gruppo italiano frattura 5 5. programmazione attività 07-08 6. varie ed eventuali. risultano presenti i seguenti consiglieri: ferro (presidente), beretta, frassine, finelli, firrao. sono inoltre presenti in audioconferenza iacoviello e furgiuele punto 1 all’o.d.g.: comunicazioni. ferro comunica che il convegno bilaterale italia russia previsto a san pietroburgo non avrà luogo a causa di problemi organizzativi presso il comitato russo. punto 2 all’o.d.g.: congresso nazionale igf 19 beretta riferisce che sono stati ricevuti fino al momento 33 abstract e che sono prevedibili circa una quarantina di lavori. il consiglio valuta l’opportunità di strutturare il convegno nazionale su due giorni pieni o lasciarne la calendarizzazione su tre giornate: la scelta finale sarà effettuata in base ai lavori presentati, considerando la durata di ogni presentazione pari a quindici minuti. beretta riferisce che le spese previste ammontano a circa 23 k€, parzialmente coperte dagli sponsor, comprensive delle spese relative al viaggio e soggiorno dei relatori delle memorie invitate, della cena sociale, della produzione dei cd contenenti gli atti e della stampa degli atti cartacei. a questo proposito, il consiglio richiede a furgiuele un preventivo del medesimo tipografo utilizzato per il precedente convegno nazionale, risultato in precedenza particolarmente conveniente. punto 3 all’o.d.g.: notiziario. il consiglio decide che il prossimo notiziario, oltre a contenere i verbali dei cdp e dell’ultima assemblea dei soci, dovrà contenere anche i resoconti dei tc esis cordinati da pavan, alberto carpinteri ed andrea carpinteri, delegando iacoviello (ed in subordine ferro) a contattare i colleghi per ottenere tale documentazione. punto 4 all’o.d.g.: sito web igf frassine rinuncia al ruolo di webmaster. il consiglio decide di delegare il presidente nell’identificazione di un gestore professionale, raccogliendo i preventivi dai candidati. il consiglio sottolinea la necessità di inserire sul sito almeno gli indici degli atti dei convegni nazionali e delle giornate disponibili solo in formato cartaceo. il consiglio discute quindi la proposta inviata nei giorni precedenti da iacoviello di inserire all’interno del sito una rivista on line, dotata di un comitato redazionale molto snello ed in grado di effettuare portare un lavoro in pubblicazione entro un mese dal primo invio (referaggio incluso). il consiglio ritiene tale proposta interessante, discutendo se dare a questa rivista un taglio maggiormente scientifico oppure divulgativo. il consiglio delega iacoviello alla preparazione di un paio di progetti da sottoporre al consiglio medesimo. punto 5 all’o.d.g.: programmazione attività 0708 ferro evidenzia il fatto che nell’ultimo periodo a causa di una serie di motivi contingenti sia diminuita l’attività igf tradizionalmente legata all’organizzazione di giornate seminariali, e propone l’organizzazione di una attività congiunta con l’associazione medici ortopedici italiani. il consiglio condivide la proposta. punto 6 all’o.d.g.: varie ed eventuali. non essendovi varie ed eventuali, il presidente scioglie il consiglio alle ore 16.00. verbale del consiglio di presidenza del 10 aprile 2007 la riunione ha inizio alle ore 10.00 in via telematica, con il seguente ordine del giorno: 1. rivista on line. 2. congresso nazionale 2007. 3. varie ed eventuali. risultano presenti i seguenti consiglieri: ferro (presidente), beretta, finelli, firrao, furgiuele, iacoviello. punto 1 all’o.d.g.: rivista on line. iacoviello espone al consiglio un resoconto delle procedure finalizzate alla attivazione di una rivista on-line. il consiglio dopo ampia ed approfondita discussione, decide unanimamente: di fondare una rivista on line dal titolo “frattura ed integrità strutturale – rivista ufficiale del gruppo italiano frattura”, con pubblicazione trimestrale; che la pubblicazione su questa rivista sia gratuita per tutti i membri igf ed esis; che la lingua ufficiale sia l’italiano, con abstract anche in inglese, e che siano accettati anche lavori in inglese; che il direttore editoriale sia iacoviello; che iacoviello sia delegato all’espletamento degli aspetti burocratico-amministrativi (attribuzione issn ed acquisto doi; accertamento delle eventuali procedure di registrazione della rivista, presso il tribunale, e del direttore, presso l’ordine dei giornalisti); su proposta di firrao, inoltre, il consiglio decide di verificare la possibilità di indicare all’interno del doi la dicitura italian group on fracture igf, member of esis; che il comitato editoriale sia costituito dal consiglio di presidenza e da una serie di personalità identificate dal consiglio medesimo; di delegare ferro a contattare le seguenti personalità per completare il comitato editoriale: carpinteri alberto, carpinteri andrea, firrao, fossati, gabetta, maier, pavan, rinaldi, roberti, sglavo, taylor. di produrre il primo numero in occasione del prossimo convegno nazionale (luglio 2007), producendo anche una cinquantina di copie gruppo italiano frattura 6 cartacee, contenente: un editoriale del presidente; un articolo elsevier (beretta si interesserà per i diritti e provvederà a trasmetterli a iacoviello); due articoli della esis newsletter (cui verranno attribuiti due doi igf; beretta provvederà a trasmetterli a iacoviello); le informazioni relative al convegno nazionale; i verbali dell’ultimo anno di attività del consiglio di presidenza. di utilizzare come formato della rivista quello trasmesso da iacoviello al consiglio con la denominazione “guida 3”. diversi consiglieri evidenziano l’importanza di un aggiornamento continuo e rapido del sito istituzionale dell’igf. ferro e iacoviello danno la loro disponibilità a recepire dei preventivi per una gestione professionale del sito dell’associazione. contestualmente ricercheranno la disponibilità di un grafico per la copertina della rivista da utilizzare anche per le comunicazioni via mail. punto 2 all’o.d.g.: convegno nazionale 2007. a seguito della proposta di iacoviello di procedere alla registrazione video del prossimo convegno nazionale ed alla loro pubblicazione in streaming sul sito, beretta propone di procedere comunque alla registrazione delle presentazioni invitate, previa autorizzazione dei relatori. il consiglio approva. per quanto riguarda la stampa degli atti cartaceo, furgiuele comunica che in giornata dovrebbe avere disponibile un preventivo dalla medesima tipografia utilizzata nel precedente convegno nazionale e provvederà a trasmetterlo al consiglio punto 3 all’o.d.g.: varie ed eventuali. non essendovi varie ed eventuali, il presidente scioglie il consiglio alle ore 12.00. (5) resoconti delle attività del 2006 esis (tc3) “fatigue of engineering materials and structures” chairmen: an. carpinteri, l.p.pook secretary: a. spagnoli activities during 2006 (a) professor cetin morris sonsino (darmstadt), professor h. zenner (clausthal-zellerfeld), professor andrea carpinteri (parma), professor les p. pook (london): guest editors of a special issue of the “international journal of fatigue (ijf)” (esis special technical publication), under the title “multiaxial fatigue and fracture”, with 26 papers selected from those presented at the 7th international conference on multiaxial fatigue and fracture (icbmff 7), held in berlin in june 2004. such a special issue of ijf has been published as issue nos 5-6, volume 28, 449-674, 2006. (b) professor andrea carpinteri (parma) and professor les p. pook (london): chairmen of the 2nd international conference on “crack paths (cp 2006)”, held in parma, italy, thursday 14th to saturday 16th september, 2006. present and future activities (a) professor andrea carpinteri (parma), professor les p. pook (london) and professor andrea spagnoli (parma) : guest editors of a special issue of the international journal “engineering fracture mechanics”, under the title “crack paths”, with papers selected from those presented at the international conference on “crack paths (cp 2006)”, held in parma, italy, thursday 14th to saturday 16th september, 2006. (b) dr upul fernando (sheffield hallam university, sheffield), professor mike w. brown (university of sheffield, sheffield), dr brian tomkins (aea technology plc): chairmen of the eighth international conference on multiaxial fatigue and fracture (icmff 8, http://www.icmff8.org.uk), to be held in sheffield, 10th to 14th june, 2007. (c) professor andrea carpinteri (parma) and professor les p. pook (london): chairmen of the 3rd international conference on “crack paths (cp 2009)”, september 2009. esis (tc4) “polymer and polymer composites” chairmen: j.g. williams, a. pavan. secretary: b.r.k. blackman. tc4 met twice during 2006, continuing their work on many of the existing project areas. in addition, polymer cutting and scratch testing have been proposed as new work areas for the committee. test protocols for these test methods are under development. ongoing work areas include mode i delamination at high test rates, quasi-static mode ii delamination in composites and structural adhesive joints, the peel testing of structural adhesives using 90 degree peel, t-peel and the mandrel test, j-crack growth resistance testing of polymers, high rate testing of polymers at greater than 1m/s, the essential work of fracture method, impact testing of short fibre composites and delamination fatigue. in 2007, the committee will meet on the following occasions: 23rd -25th may 2007 (regular tc4 committee meeting): les diablerets, switzerland. 17th-19th october 2007 (regular tc4 committee meeting): les diablerets, switzerland. the meetings are open to all. please contact the technical secretary for details and agenda. in 2008, the 5th international conference on fracture of polymers, composites and adhesives will be held in les diablerets, switzerland from 7th11th september 2008. www.tc4pca.elsevier.com (deadline for the submission of abstracts is 2nd november 2007). gruppo italiano frattura 7 esis (tc20) "role of defects and inclusions" chairmen: y. murakami, c.w. anderson secretary: s. beretta a meeting of tc20 was held on 13th september ’06 in politecnico di milano, dipartimento di meccanica (milan, italy) the participants of which were: y. murakami (kyushu university), s. beretta and f. benzoni (politecnico di milano), j. butler (corus group), d. girodin (snr roulements), e. henault (creas ascometal) f. cirilli (csm), e. paravicini (tenaris). round robin #1 (corus steel) murakami presents the results of measurements in his lab for the first round robin. beretta summarizes the results obtained in the first round robin by the different participants and the following discussion emphasizes the scatter of the results and the need of a confirmation by fatigue tests. it is then agreed to write a journal paper presenting the results of this round-robin on a suitable journal in order to have the widest circulation of results. some particpants (cirilli, henault) agree on carrying out a second series of measurements for estimating in-lab variability. round robin #2 (ascometal bearing steel) butler presents the results about automatical defect evaluation and the differences of corus measurements between 2005 and 2006 . girodin then presents some results obtained on a bearing steel and henault shows some interesting results obtained by simulations of measurements. the following discussion pin-point that there is a big difference in image analysis results and classification of the different inclusion types. it is agreed to circulate a cd containing the images by the different participants in order to have a direct comparison of measurements. future events cirilli briefly describes the evir+ project proposal presented at eccs. it is agreed to prepare a joint paper about rr#1 for spring 2007 esis (tc24) "integrity of railway structures” chairmen: e. smith, u. zerbst the annual meeting of tc24 was held in brescia (italy) on 29th november 06 with participants: u. zerbst – gkss (germany) r.a. smith – imperial college (uk) s. beretta – politecnico di milano (italy) l. drewitt – corus group (uk) g. donzella – università di brescia (italy) m. guagliano – politecnico di milano (italy) f. lombardo – lucchini sidermeccanica (italy) a. mazzu – università di brescia (italy) 1. future plans • zerbst proposes to hold next workshop/tc24 meeting in paris on spring 2007, in concomitance with the conclusion of a frenchgerman jointed research project on rails • beretta proposes a workshop/tc24 meeting in spring 2008 in milan, focussed on axles, summarizing the results of widem and deufrako projects; • smith proposes a future workshop/tc24 meeting in london entitled “load and infracstructure in railway application”, including several topics, like fatigue and fracture of rails, crashworthiness, structures (bridges), multiaxial fatigue of wheels, load spectra, climate changes, lightweighting, non-destructive controls. 2. proposals for reports from the committee it has been discussed about the best way to present the activities of the tc24 members, wich at the moment seems to be the special issues of elsevier journals. the space reserved by elsevier for esis could be used to announce these special issues and future tc24 meetings. 3. membership of the committee in the past, the requirement for tc24 membership was the esis membership, i.e. the participation to the correspondent national esis-related groups. anyway, a better definition of tc24 permanent membership is worthwhile. it would be usefull a revision of the tc24 mailing list, including people interested in the committee activities and people attending past meetings. workshop on the following day a workshop entitled “structural integrity of railway wheels and wheel/rail interface” was held at the university of brescia with an attendance of approx. 60 delegates. the following presentations were done: “railway wheels: the background” r.smith, imperial college “influence of the contact pressure distribution on the behavior of internally cracked railway wheels” m.guagliano, l.vergani , politecnico di milano “a numerical 3d model to study plastic ratchetting damage of a tramcar line” s.beretta, g.bucca, s.foletti, politecnico di milano “rcf-wear competition in railway wheel-rail interface” g.donzella, m.faccoli, a.mazzù, c.petrogalli, r.roberti, università di brescia “ultrasonic analysis of wheel-rail contact” b.leban, m.pau, università di cagliari “a simple approach to indirect control of railway vehicles rolling surfaces” r.ciuffi, f.piccioli, università di firenze “investigations on railway components some progress”, u.zerbst, gkss, geesthacht “innovative bainitic steel grade for solid wheels tested in artic heavy haul operations” gruppo italiano frattura 8 a.ghidini*, a.gianni*, a.ekberg**, lucchini sidermeccanica and chalmers university “photoelastic analysis of railway wheels in presence of cracks” c.colombo, m.guagliano, m. sangirardi, l.vergani, politecnico di milano tc24 members attendinding the workshop in brescia (from right): zerbst (chairman), drewitt, smith (chairman), guagliano, donzella, and beretta. (6) xix congresso nazionale igf – milano 2007 politecnico di milano, campus bovisa sud 2-4 luglio 2007 il gruppo italiano frattura (igf) organizza il prossimo convegno nazionale, giunto ormai alla sua xix edizione, al politecnico di milano, presso la nuovo campus bovisa sud (milano). il convegno nazionale rappresenta un’occasione per l’incontro, il dibattito e l’aggiornamento fra esperti provenienti dal mondo della ricerca e dell’industria. la finalità è quella di promuovere e diffondere studi ed applicazioni relativi alla meccanica della frattura e del danno in materiali, al calcolo e verifica di integrità strutturale, ai modelli computazionali avanzati. letture plenarie prof. wolfgang brocks is professor for mechanics of materials at the christianalbrechts-university, kiel (germany), where he teaches engineering mechanics and finite element method, and head of the department "modelling of solids and structures" at the institute of materials research in the gkss research centre, geesthacht. in 2002, professor brocks was awarded by esis the “griffith medal” for his outstanding research work in the field of deformation and fracture of metals and in the numerical modeling of ductile an brittle fracture. dr. hugo ernst has been: senior scientist, westinghouse r&d center pittsburgh, pa, usa; director of research fracture proof design corporation, st. louis; and full tenured professor at the georgia institute of technology, atlanta, georgia, usa. since february 1993, he works at the siderca r&d center. he is now head of the structural integrity department. dr. ernst has received the astm sam tour award, for the best paper in corrosion, published by the society in 1994; and the astm george irwin fracture mechanics medal in 1991. (7) convocazione assemblea annuale dei soci 2007 l’assemblea si riunirà in 1a convocazione lunedì 2 luglio 2007 alle ore 17.00 presso il politecnico di milano – campus bovisa sud. in mancanza del numero legale (metà dei soci), l’assemblea si riunirà in 2a convocazione, qualunque sia il numero dei soci presenti, alle ore 17.15 dello stesso giorno, nella stessa sede. ordine del giorno: 1 approvazione dell’ordine del giorno; 2approvazione del verbale dell’assemblea dei soci del 31 maggio 2006 3 comunicazioni del presidente; 4 relazione annuale del presidente; 5 relazione dei revisori dei conti; 6approvazione del bilancio consuntivo 2006; 7indirizzi dell’attività dell’associazione nell’anno 2007; 8previsione finanziaria e quota associativa 2008 9rinnovo delle cariche sociali; 10. varie ed eventuali. nuovo sito igf: www.igfweb.org www.gruppofrattura.it gruppo italiano frattura 9 ß (8) calendario congressi internazionali icmff8-2007 8th international conference on multiaxial fatigue and fracture 10th 14th june 2007 sheffield hallam university, sheffield, uk further details from: icmff8-2007 conference secretariat, sheffield hallam university, city campus, room 5503, surrey building, sheffield s1 1wb, uk. tel.: +44 114 225 5338; fax: +44 114 225 5337; e-mail: conference21@shu.ac.uk web: http://www.icmff8.org.uk/ framcos6-2007 6th international conference on fracture mechanics of concreteand concrete structures 17-22 june 2007 catania, italy further details from: web: http://www.icmff8.org.uk icem 13 international conference on experimental mechanics: experimental analysis of nano and engineering materials and structures 1–6 july 2007 alexandroupolis, greece further details from: professor e.e. gdoutos, school of engineering, democritus university of thrace, greece. e-mail: egdoutos@civil.duth.gr web: http://www.icem13.gr implast 2007 symposium on plasticity and impact mechanics 21–24 august 2007 bochum, germany further details from: professor dr. otto t. bruhns, lehrstuhl fu¨ r technische mechanik, fakulta¨t fu¨ r bauingenieurwesen, ruhr-universita¨ t bochum, d 44780 bochum, germany. tel.: +49 234 32 23080; fax: +49 234 32 14229; e-mail: implast07@tm.bi.rub.de complas 2007 9th international conference on computational plasticity 5–7 september 2007 barcelona, spain further details from: web: http://congress.cimne.upc.es/comp las07 semc 2007 the third international conference on structural engineering, mechanics and computation 10–12 september 2007 cape town, south africa further details from: professor a. zingoni, department of civil engineering, university of cape town, rondebosch 7701, cape town, south africa. e-mail: azingon@ebe.uct.ac.za web: http://www.semc2007.uct.ac.za dtas 2007 international conference on damage tolerance of aircraft structures () 25–28 september 2007 delft, the netherlands further details from: conference secretariat, d&g partners, ms. dineke heersma, ms. gemma van der windt tel: +31(0)6 27227520; fax: +31(0)10 5112119; e-mail: info@dtas2007.nl http://www.dtas2007.nl icfc4 fourth international conference on fatigue of composites 26–28 september 2007 kaiserslautern, germany further details from: conference secretariat, c/o dr n. himmel, institut fuer verbundwerkstoffe gmbh. fax: +49-631-2017-199; e-mail: icfc4@ivw.uni-kl.de www.ivw.uni-kl.de/icfc4 icmobt2 second international conference on mechanics of biomaterials and tissues 9–13 december 2007 lihue, kaua’i, hawaii, usa further details from: nina woods, icmobt conference secretariat, elsevier, the boulevard, langford lane, kidlington, oxford, ox5 1gb, u.k. tel.: +44 (0) 1865 843297 fax: +44 (0) 1865 843958 e-mail: n.woods@elsevier.com http://www.icmobt.elsevier.com dfe2008 international conference on design, fabrication and economy of welded structures 24–26 april, 2008 miskolc, hungary further details from: professor k. jarmai, university of miskolc, miskolc, hungary. e-mail: dfe2008@uni-miskolc.hu website: http://www.alt.unimiskolc. hu/dfe2008 ichmm–2008 second international conference on heterogeneous materials mechanics 3–8 june 2008 huangshan, china further details from: web: http://ichmm 2008.ustc.edu.cn/ichmm2008/ pcf 2008 11th portuguese conference on fracture 13 15 february 2008 lisbon, portugal further details from: rui fernando martins departamento de engenharia mecânica e industrial faculdade de ciências e tecnologia universidade nova de lisboa campus de caparica 2829-516 monte de caparica portugal e-mail: rfspm@fct.unl.pt web: http://eventos.fct.unl.pt/pcf2008 gruppo italiano frattura 10 esis procedures and documents (www.esisweb.org) two kinds of documents are produced by esis technical committees with the following designatory system: esis p2-92 or esis p4-92d, where: 1) p means "procedure", and 2 and 4 are the current numbers, while 92 is the year of issue. 2) d following the year (eg: 92d) means "draft", ie: not yet approved, while 3) d prior to the year (eg: d1-92) means "document" other than test methods. p1-92 esis recommendations for determining the fracture resistance of ductile materials. responsible body: tc1 subcommittee on fracture mechanics testing standards. p2-92 esis procedure for determining the fracture behaviour of materials. responsible body: tc1 subcommittee on fracture mechanics testing standards. p3-03d draft unified procedure for determining the fracture behaviour of material. responsible body: tc1 subcommittee on fracture mechanics testing standards (under preparation not available). p4-92d esis recommendations for stress corrosion testing using pre-cracked specimens. responsible body: tc10 committee on environmental-assisted cracking. p5-00/vamas procedure for determining the fracture toughness of ceramics using the sevnb method . responsible body: tc6 committee on ceramics. p6-98 esis procedure to measure and calculate material parameters for the local approach to fracture using notched tensile specimens. responsible body: tc8 committee on numerical methods. p7-00 esis procedure for dynamic tensile tests responsible body: tc5 subcommittee on dynamic testing at intermediate strain rates. p8-99d esis draft code of practice for the determination and interpretation of cyclic stress-strain data. responsible body: tc11 committee on high temperature mechanical testing. p9-02d guidance on local approach of rupture of metallic materials. (under preparation not available). p10-02 a code of practice for conducting notched bar creep rupture tests and interpreting the data. responsible body: tc11 high temperature mechanical testing committee. p11-02 technical recommandations for the extreme value analysis of data on large nonmetallic inclusions responsible body: tc20 committee on inclusions. d1-92 fracture control guidelines for stress corrosion cracking of high strength alloys. responsible body: tc10 committee on environmental assisted cracking. d2-99 fracture toughness of ceramics using the sevnb method; round robin, test programme. the esis tc6 and vamas twa3 developed a test method and conducted a round robin for its validation. d2-99 presents a detailed documentation of this activity. the final form of the test method has appeared as p5-00. responsible body: tc6 committee on ceramics. gruppo italiano frattura 11 (9) modulo di iscrizione igf-esis gruppo italiano frattura modulo di iscrizione 2007 la quota annuale di iscrizione è di 30 euro (comprensiva di iscrizione esis, european structural integrity society), esente iva a norma dell'art.2 del dpr 26/10/72 e successive modifiche. modalità di pagamento: bonifico bancario su cc. n. 100940 del credito cooperativo bolognese, ag. via arcoveggio 56/22, intestato al gruppo italiano frattura (abi 7082 cab 02402 cin k). paypal, dal sito www.gruppofrattura.it assegno non trasferibile, intestato a gruppo italiano frattura carta di credito. autorizzo il pagamento di 30 € mediante carta di credito eurocard master card visa american express scadenza cognome ……………………………….. nome ……………………. titolo ……… affiliazione ……………………………………………………………………………… indirizzo ………………………………………………………………………………… e-mail …………………………………….. tel …………………. fax ……………… firma ……………………………………… data ………………………………………: inviare il modulo a: segretario igf prof. francesco iacoviello di.m.s.a.t. università di cassino via g. di biasio 43, 03043 cassino (fr) tel./fax 0776-2993681 iacoviello@unicas.it(per cortesia, riempire in stampatello) n° sicurezza microsoft word numero_49_art_28_2386 m. abbadeni et alii, frattura ed integrità strutturale, 49 (2019) 282-290; doi: 10.3221/igf-esis.49.28 282 focused on fracture mechanics versus environment comparative study of conventional and hydromechanical deep drawing processes based on finite element analysis mohammed abbadeni, ibrahim zidane, hamou zahloul, zakaria madaoui university of chlef, rheology and mechanics laboratory, algeria mohamed.abbadeni@yahoo.fr, https://orcid.org/0000-0003-0681-9669 zidane_bra@hotmail.com zahloulh@yahoo.fr, https://orcid.org/0000-0003-2760-2872 zkrmadaoui@yahoo.fr, https://orcid.org/0000-0002-6653-0544 abstract. a two-dimensional finite element analysis has been performed to investigate hydromechanical and conventional deep drawing processes. the effects of the fluid structure interaction on the material formability, the strain and the thickness distributions are investigated. large plastic deformation is observed in the plank at the bottom and the corner of the punch. plastic deformation distribution results show a difference between the hydromechanical deep drawing process and the conventional deep drawing which is due to the friction effect. this latter represents one of the major features of the hydromechanical deep drawing process. concerning the formability of the blank, the obtained results show that the hydromechanical deep drawing process gives a better formability than the conventional deep drawing process. keywords. hydromechanical deep drawing; conventional deep drawing; finite element analysis; fluid pressure. citation: abbadeni, m., zidane, i., zahloul, h., madaoui, z., comparative study of conventional and hydromechanical deep drawing processes based on finite element analysis, frattura ed integrità strutturale, 49 (2019) 282-290. received: 13.02.2019 accepted: 30.04.2019 published: 01.07.2019 copyright: © 2019 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. introduction eep drawing is a manufacturing operation in which a thin sheet metal is deformed plastically to take the form of the punch or the die geometry. regarding its advantages, it is being used increasingly especially within the aerospace, aircraft and automotive industries [1-2]. each final product requires appropriate tools for being formed in deep drawing. classical forming processes have serious difficulties to fulfill the requirements of cost reduction, lightweight materials, low energy consumption and improved parts quality [2]. therefore, new manufacturing technologies have been developed and improved. one of the developed technologies and the most important formative processes is hydromechanical deep drawing (hdd). in this process, liquid is used as a pressurized medium to facilitate the deformation of a sheet (blank). d http://www.gruppofrattura.it/va/49/2386.mp4 m. abbadeni et alii, frattura ed integrità strutturale, 49 (2019) 282-290; doi: 10.3221/igf-esis.49.28 283 there are many advantages for this process, over conventional metal forming processes, such as better surface quality, increased drawing ratio, forming of complex shapes, cost-effective parts and lower tool costs [2]. hdd process, illustrated in fig. 1(b), is one type of sheet hydroforming. comparing the hdd process with conventional deep drawing process (cdd) (fig. 1(a)) it can be noticed some differences in tools, contact conditions and producing technology. the female die in the cdd process is replaced by a cavity filled with a fluid in the hdd process. the final form of the part is determined by the punch. in this process, when the punch penetrates in the die cavity, the liquid is pressurized and pushes the sheet onto the punch surface (fig. 2). the fluid pressure in the cavity can be controlled by a valve. the use of the fluid makes possible to reduce the friction and to prevent metal-to-metal contact at the blank-die interface which improve the possibilities of obtaining a better geometry of the final products [3-6]. warm pressurized fluid can be used to increase the formability of lightweight alloys [7,8]. the study of the hdd process and the effects of the fluid pressure were the subject of several research works. singh and kumar [9] studied the hdd process to show the influence of the fluid pressure in the cavity on the thickness distribution and the surface quality of the final products. they found that thinning of the sheet at the corner zone which exists in traditional sheet forming processes was reduced in the hdd process. they also noticed that the thickness distribution became more uniform with the increase in the maximum fluid pressure in the cavity. modanloo et al. [10] studied the effects of forming media on the hdd process experimentally and by simulation using a typical pressure path. water and oil were used as a forming media. they reported that by using oil, thinning decreases at the punch corner radius. in another work [11] they investigated, by experiments and simulation, the effects of forming parameters (fluid pressure, punch velocity, friction coefficients, punch and die corner radius…) on the thinning ratio of the deformed part. they found that a higher corner radius of the punch and the die lead to an increase in thickness reduction. moreover, an optimization method was presented to improve thinning ratio. in order to improve formability of the parts in hdd process, salahshoor et al. [12] investigated the effects of geometrical and process parameters on thickness distribution of cylindrical parts. the results showed that the pressure path has a great influence on the formability. by increasing the maximum fluid pressure, a reduction in thinning tendency is observed. furthermore, by decreasing the friction in the blank-blank holder contact region, a decrease in thinning and maximum punch force was observed. the effect of the initial pressurization during the hdd process was studied by lang et al. [13]. the obtained results showed that the use of an initial pressurization has a significant influence on the first stages of forming. the rise of the pressure increases the surface of contact between the part and the punch surface which avoid the rupture in the contact area. however, for excessive values of the pressure, the rupture will take place in the critical zones of the part. in another work [14], they studied the influence of the fluid pressure in the cavity on the deformation of the part. in this work, a uniform pressure was applied on the lower surface of the sheet. they found that a high pressure in the cavity can reduce the thickness of the formed part. hama et al. [5] established an experiment on the hdd process. the fluid pressure was measured in various positions (in the cavity, in the die corner and between the sheet and the die). from this experiment study, they showed that the drawing ratio in the hdd process is better compared to cdd process. figure 1: conventional and hydromechanical deep drawing processes. blank (sheet) die blank holder fluid cavity punch relief valve (a) conventional deep drawing (b) hydromechanical deep drawing m. abbadeni et alii, frattura ed integrità strutturale, 49 (2019) 282-290; doi: 10.3221/igf-esis.49.28 284 the previous work on modeling and simulating the hdd process of cylindrical parts by the authors [15] has established the reliability of the proposed approach in the modeling of process parameters. an analytical model was proposed to consider the non-uniform pressure distribution in the cavity and for the hydrodynamic pressure of the fluid film in the blank-die contact region. based on this previous work, this study focuses on the comparison of conventional and hydromechanical deep drawing processes by performing a finite element analysis. the fluid cavity pressure effect on the plastic strain and the thickness distribution has been investigated. numerical modeling finite element model inite elements simulations of conventional and hdd of a cylindrical cup are performed using the abaqus/explicit software. in the numerical modeling, the two processes (cdd and hdd) are involved at the same initial conditions: the same geometry of the instrument, the same boundary conditions, the same applied loads, etc. the deep drawing process involves a blank and an instrument consisting of three main parts: blank holder, punch and die (fig. 1 and fig. 2). in this case, considering the cylindrical symmetry, only one half of the blank and the instrument are analyzed in 2d. in the meshing of the blank the following initial conditions are used: continuum media; axial symmetry; and four node elements (cax4r). during the process, the punch, the blank holder and the die are considered as rigid, while the blank is deformable. the die is constrained fully and the punch can move only along the vertical direction. the punch motion is prescribed with a constant velocity. a constant blank holder force throughout the process is applied. uniform friction conditions are assumed for all contacting surfaces. the coulomb friction model is used to describe the contact between the blank and the tooling surfaces. the friction coefficients are adopted based on previous works in this field [17-19]. tab. 1 summarizes the friction coefficient values for different contacts. table 1: friction coefficient values. the fluid pressure variation in the die cavity is one of the most important parameters in the hdd process, because wrinkles appear if the pressure is not sufficiently high. in contrast, the blank is damaged by fracture if the pressure is too high [4]. during the simulation of this process, the modeling of the fluid-structure interaction is the principal difficulty. in a previous work [15], the authors give a detailed study of this problem. the fluid was represented by a non uniform pressure load applied on the lower surface of the blank. an analytical model was given to define the variation of the pressure in the cavity and the distribution of the pressure of the fluid between the blank and the die, this analytical model was implemented into the abaqus/explicit code using the user defined subroutine vdload. this developed program is used in the present work to take into account the fluid pressure in the cavity and the hydrodynamic pressure of the fluid film between the blank and the die. material parameters the blank thickness is 1.12 mm. the blank is made of an aluminum alloy (aa5086). elasto-plastic material behavior with isotropic hardening is supposed. hooke’s model with a young modulus e=67293 mpa and a poisson ratio ν = 0.3 is used to describe the elasticity. the von mises yield criteria is used for the plasticity to describe the isotropic characteristics of the blank material. the hardening behavior is described by following relation:     0 n k (1) f contact zone friction coefficient hdd cdd blank-die 0.05 (presence of fluid) 0.08 (boundary contact) blank-punch 0.1 (dry contact) 0.1 (dry contact) blank-blank holder 0.08 (boundary contact) 0.08 (boundary contact) m. abbadeni et alii, frattura ed integrità strutturale, 49 (2019) 282-290; doi: 10.3221/igf-esis.49.28 285 figure 2: schematic representation of: (a) conventional deep drawing process and (b) hydromechanical deep drawing process principle. where and  are the equivalent stress and the equivalent plastic strain, respectively, 0 =143.2 mpa is the yield stress, k = 296.9 mpa is the hardening coefficient and n = 0.40 is the strain hardening exponent. these material parameters are obtained from a bi-axial tensile test [16]. during the deep drawing, the blank is subjected to high plastic deformations. sometimes these deformations become excessive, so that necking begins to appear in critical regions of the part. this represents the limit of the formability and the beginning of the fracture. the term formability is generally used to describe the ability of a material to be plastically deformed without necking or fracture. to characterize a material formability, forming limit diagrams (fld) are widely used [20]. fld is a plot of the combination of the minor and major strains at the beginning of localized necking. it becomes an essential tool in metal forming industry and also during finite element analysis or forming simulation. in this work, in order to evaluate the severity and the feasibility of the forming operation for the two processes, the fld of the aa5086 aluminum alloy is used. this fld is obtained by a biaxial tensile test [16]. results and discussion ig. 3 shows the equivalent plastic strain distribution, for the two processes, after 15 mm of punch displacement. in cdd process, maximum plastic strain value of approximately 38% is observed. this value decreases to 25% in the hdd process. for the two processes, the blank undergoes maximum deformation on punch and die corners. in the hdd process, a strain concentration occurred at the die corner as a result of bending. for the same reason and because of excessive stretching, high strain concentration is present at the punch corner in the cdd process. this can be clearly observed in fig. 4 where the evolution of the plastic strain in the radial direction for a punch displacement of 15 mm is shown. we can see that the use of the fluid in the hdd process has a significant influence on the strain distribution. maximum strain values are observed at the punch and the die corner where the blank is exposed to bending. comparing the obtained results for the strain distribution, a large difference can be seen at the punch corner, at the die corner and at the blank-punch contact region. by contrast, a small difference is observed at the blank-blank holder contact zone (radial position is upper than 40 mm). the force exerted by the blank holder on the blank at this region supplies a restraining force which controls the metal flow and influences the strain distribution. in the hdd process, in addition to the blank holder force, there is high fluid pressure under the blank. the force generated by this pressure, which is opposite to the blank holder force, has also an influence on the strain distribution. this can explain the observed reverse behavior of the strain at this zone. according to the numerical results in fig. 3 and fig. 4, the resulting plastic strain distribution is more uniform and the maximum strain values are lower in the hdd process compared to cdd process. in cdd process, by the displacement of the punch, a radial traction force on the blank is produced. the absence of a fluid lubricating in the zone of contact blank-die causes a strong friction force in particular on the die corner. this implies a reduction in the slip of the blank under the blank holder. in this case, the force applied by the punch draws the blank and a plastic deformation dependent on this force is produced. consequently, a radial effort is created on the blank, thus a higher traction force is necessary for the deformation. drawing becomes significant producing an excessive thinning of the blank on the punch corner. as the traction force that the bank can resist is limited by the tensile strength of the used f (a) (b) m. abbadeni et alii, frattura ed integrità strutturale, 49 (2019) 282-290; doi: 10.3221/igf-esis.49.28 286 material, the fracture can appear with the advancement of the punch. it is possible to prevent the strain concentrations by using suitable process parameters such as a good lubrication and an appropriate blank holder force. figure 3: equivalent plastic strain distribution after 15 mm of punch displacement. figure 4: strain distribution in the radial position after 15 mm of punch displacement. m. abbadeni et alii, frattura ed integrità strutturale, 49 (2019) 282-290; doi: 10.3221/igf-esis.49.28 287 an evaluation of the forming severity for the two processes is obtained by comparing the numerical results for the strain distributions with the experimental fld of the used material. the fld is plotted in a principal strain reference. major strain which is the largest in algebraic value is on the ordinate. minor strain which is the smallest in algebraic value is on the abscissa. although the major strain is always positive because it is obtained by stretching, the minor strain is may be either positive in the case of stretching or negative in shrink drawing case. the upper region of the fld represents necking and fracture. the safe region in which no fracture is expected is the region under the fld. numerical major and minor strains distribution and experimental fld of the used blank material are presented in fig. 5. for the two processes, the material exhibits slightly different principal strains and the produced parts have not the same formability. the results prove that, until 15 mm of punch displacement, the parts can be formed without fracture. for cdd process, beyond this punch displacement (fig. 6), excessive thinning followed by a fracture can occur on the punch corner where the most dangerous points are located. from these results, it can be concluded that the use of the fluid pressure gives better formability and drawing ration. according to sadegh-yazdi et al. [21], formability can be improved using an optimum fluid pressure path for radial and cavity pressures in hdd process. figure 5: experimental fld and numerical results for principal strains distribution after 15 mm of punch displacement. the quality of the formed part not only depends on the formability but also depends on other factors such as thinning. to study the influence of the fluid pressure on the blank thickness distribution, a comparison of the blank thicknesses for the two processes is carried out and the result is shown in fig. 7. it can be shown that the thickness distribution is significantly influenced by the presence or not of the fluid in the cavity. as shown, there is a tendency of thinning at the punch corner in the cdd process with a minimum thickness of 0.81 mm. when compared with cdd process, less thinning is observed in hdd process. the decrease in thinning tendency in the hdd process is due to the presence of the pressurized fluid, as it acts as an effective lubrication which facilitates the flow of the blank. and also, the force generated by the fluid pressure in the cavity acts as uniform stress during the forming operation. as reported in the literature [22], the use of the pressure force, in the hdd process, reduces product defects like thinning. more uniformity of thickness distribution can be obtained by using the initial bulging of the blank [23]. conclusion n this paper, the hdd process and cdd process have been simulated by means of the fe software package abaqus/explicit. the plastic deformation distribution and the formability of the formed part were discussed. the obtained results indicate that the fluid pressure under the blank plays an important role in the lubrication effect, the i m. abbadeni et alii, frattura ed integrità strutturale, 49 (2019) 282-290; doi: 10.3221/igf-esis.49.28 288 plastic deformation and the thickness distributions. comparing the obtained results for the strain distribution, a large difference can be seen at the bottom and the corner of the punch. in hdd process, the plastic strain distribution is more uniform compared to cdd process and the maximum strain values are lower. figure 6: experimental fld and numerical results for principal strains distribution after 20 mm of punch displacement. figure 7: thickness distribution in the radial direction after 15 mm of punch displacement. m. abbadeni et alii, frattura ed integrità strutturale, 49 (2019) 282-290; doi: 10.3221/igf-esis.49.28 289 references [1] singh, h. (2003). fundamentals of hydroforming, society of manufacturing engineers (sme), usa. [2] koc, m. (2008). hydroforming for advanced manufacturing, crc press, usa. [3] hama, t., kurisu, k., matsushima, k., fujimoto, h., takuda, h. (2009). outflow characteristics of a pressure medium during sheet hydroforming, isij international, 49 (2), pp. 239–246. doi: 10.2355/isijinternational.49.239. [4] zhang, s.h., danckert, j. (1998). development of hydro-mechanical deep drawing, journal of materials processing technology 83, pp. 14–25. doi: 10.1016/s0924-0136(98)00039-9. [5] hama, t., matsushima, k., kitajima, t., fujimoto, h., takuda, h. (2009). correlation between sheet deformation and hydraulic pressure variation during sheet hydroforming, isij international, 49 (11), pp. 1736–1743. doi: 10.2355/isijinternational.49.1736. [6] alizad-kamran, m., hoseinpourgollo, m., hashemi, a., hossein seyedkashi, s.m. (2018). determination of critical pressure in analyzing of rupture instability for hydromechanical deep drawing using advanced yield criterion. archives of civil and mechanical engineering, 18, 103-113. doi.org/10.1016/j.acme.2017.05.008. [7] gaoshen, c., chuanyu, w., dongxing, z. (2018). investigation on the effect of type of cooling on the properties of aluminum alloy during warm/hot hydromechanical deep drawing. symmetry, 10, 362. doi:10.3390/sym10090362. [8] acara, d., türközb, m., gediklia, h., selçuk, h. h., necati, c. ö. (2017). warm hydromechanical deep drawing of aa 5754-o and optimization of process parameters. journal of engineering materials and technology, 140(1), doi:10.1115/1.4037524. [9] singh, s. k., ravi kumar, d. (2008). effect of process parameters on product surface finish and thickness variation in hydro-mechanical deep drawing, journal of materials processing technology, 204, pp. 169–178. doi: 10.1016/j.jmatprotec.2007.11.060. [10] modanloo, v., gorji, a., bakhshijooybari, m. (2016). effects of forming media on hydrodynamic deep drawing. journal of mechanical science and technology, 30(5), 2237-2242. doi 10.1007/s12206-016-0433-x. [11] modanloo, v., gorji, a., bakhshijooybari, m. (2018). a comprehensive thinning analysis for hydrodynamic deep drawing assisted by radial pressure. iran j sci technol trans mech eng, pp. 1-8. doi: 10.1007/s40997-018-0221-6. [12] salahshoor, m., gorji, h., bakhshi-jooybari, m. (2019). analysis of the effects of tool and process parameters in hydrodynamic deep drawing assisted by radial pressure. j braz soc mech sci eng, 41, 145. doi: 10.1007/s40430-019-1648-4. [13] lang, l., danckert, j., nielsen, k. b. (2004). investigation into the effect of pre-bulging during hydromechanical deep drawing with uniform pressure onto the blank, international journal of machine tools and manufacture, 44, pp. 649–657. doi: 10.1016/j.ijmachtools.2003.11.004. [14] lang, l., danckert, j., nielsen, k. b. (2004). study on hydromechanical deep drawing with uniform pressure onto the blank, international journal of machine tools and manufacture, 44, pp. 495–502. doi: 10.1016/j.ijmachtools.2003.10.028. [15] abbadeni, m., zidane, i., zahloul, h., fatu, a., hajjam, m. (2017). finite element analysis of fluid-structure interaction in the hydromechanical deep drawing process, journal of mechanical science and technology 31 (11), pp. 5485–5491. doi: 10.1007/s12206-017-1043-y. [16] zidane, i. (2009). développement d'un banc d'essai de traction biaxiale pour la caractérisation de la formabilité et du comportement élastoplastique de tôles métalliques, thèse de doctorat, insa rennes. [17] zhang, sh., jensen, mr., nielsen, kb., danckert, j., lang, lh., kang, dc. (2003). effect of anisotropy and prebulging on hydromechanical deep drawing of mild steel cups. j mater proc technol, 142, pp. 544–50. doi: 10.1016/s0924-0136(03)00656-3. [18] fazli, a., dariani, bm. (2006). theoretical and experimental analysis of the axisymmetric hydromechanical deep drawing process. proc inst mech eng b: j eng manuf, 220, pp. 1429–1437. doi: 10.1243/09544054jem472. [19] schuler gmbh, (1998). metal forming handbook, springer-verlag berlin heidelberg. [20] giuliano, g., bellini c., sorrentino, l., turchetta, s. (2018). forming process analysis of an aa6060 aluminum vessel. frattura ed integrità strutturale, 45, pp. 164-172. doi: 10.3221/igf-esis.45.14. [21] sadegh-yazdi, m., bakhshi-jooybari, m., shakeri, m., gorji, h., khademi, m. (2018). optimization of pressure paths in hydrodynamic deep drawing assisted by radial pressure with inward flowing liquid using a hybrid method. int j adv manuf technol, 97, 2587-2601. doi.org/10.1007/s00170-018-2023-9. m. abbadeni et alii, frattura ed integrità strutturale, 49 (2019) 282-290; doi: 10.3221/igf-esis.49.28 290 [22] atul, t. s., lenin babu, m. c. (2018). a review on effect of thinning, wrinkling and spring-back on deep drawing process. proc imeche part b: j engineering manufacture, 233:4, pp. 1011-1036. doi: 10.1177/0954405417752509. [23] desu, r. k., singh, s. k., gupta, a. k. (2016). comparative study of warm and hydromechanical deep drawing for low-carbon steel. int j adv manuf techno, 85, pp. 661-672. doi 10.1007/s00170-015-7819-2. shot peening processes to obtain nanocrystalline surfaces in metal alloys: k. benyahi et alii, frattura ed integrità strutturale, 58 (2021) 319-343; doi: 10.3221/igf-esis.58.24 319 periodic homogenization and damage evolution in rve composite material with inclusion karim benyahi, youcef bouafia, mohand said kachi, amel hamri department of civil engineering, mouloud mammeri university, 15000 tizi ouzou, algeria. karim.benyahi@ummto.dz, https://orcid.org/0000-0003-2033-6217 youcef.bouafia2012@yahoo.com, kachi_ms@yahoo.fr, hamri.a@hotmail.com sarah benakli laboratory lmssc, national conservatory of arts and crafts (cnam paris), france. benakli.s@gmail.com abstract. this work deals with the coupling between a periodic homogenization procedure, and a damage process occurring in a representative volume element (rve) of inclusion composite materials. we mainly seek, on the one hand to determine the effective mechanical properties according to the different volume fractions, and forms of inclusions for a composite with inclusions at the macroscopic level. on the other hand, to explore the rupture mechanisms that can take place at the microstructure level. to do this; the first step is to propose a periodic homogenization procedure, to predict the homogenized mechanical characteristics of an inclusion composite. this homogenization procedure is applied to the theory based on finite element analysis, by the abaqus calculation code. the inclusions are modeled by a random object modeler, and the periodic homogenization method is implemented by python scripts. it is then a matter of introducing the damage into the problem of homogenization, that is to say; once the homogenized characteristics are assessed in the absence of the damage initiated, by microcracks and micro cavitations. it is then possible to introduce damage models, by a subroutine (umat) in the abaqus calculation code. the verifications carried out focused on rve of composite materials with inclusions. keywords. periodic homogenization; elastic; modeling; inclusion; damage. citation: benyahi, k., bouafia, y., kachi, ms., benakli, s., hamri, a., periodic homogenization and damage evolution in rve composite material with inclusion, frattura ed integrità strutturale, 58 (2021) 319-343. received: 18.07.2021 accepted: 11.09.2021 published: 01.10.2021 copyright: © 2021 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. introduction he term "homogenization" is a process of calculating effective mechanical properties, and the term "localization" is used to determine stress and local strain (suquet [1]). the first idea when using a homogenization procedure, it is necessary to apply the law of mixtures. which postulates that the homogenized elastic modulus are the means of t k. benyahi et alii, frattura ed integrità strutturale, 58 (2021) 319-343; doi: 10.3221/igf-esis.58.24 320 the elastic modulus of different constituents, weighted by their volume fractions. this method is rather easy to use but not very rigorous, in order, to make an approach allowing to appreciate the effective mechanical properties. many analytical homogenization models, making it possible to predict the effective mechanical elasticity properties of a two-phase heterogeneous material. from those of its different constituents are proposed in the literature, those that have received the most attention are the diagrams diluted, mori-tanaka, self-consistent and eshelby's solution [2-4]. however, these analytical or semi-analytical homogenization models, did not make it possible to go back to the local properties of the desired solution. as the complexity of the various microscopic phenomena, gave rise to more recent resolution methods. nowadays, there are several micromechanical methods. the research having been carried out for the analysis, and prediction of the overall behavior of composite materials, and can be summarized as follows. michel et al. [5] proposed two different families of numerical methods to solve the problem. the first method is based on the finite element method, by implementing periodicity conditions either by a control of strains or of stresses. the second numerical method is based on fast fourier transforms (fft). which could be an alternative to the finite element method, for the micromechanical analyzes of representative solid elements with periodicity conditions. sun et al. [6] proposed a procedure for predicting the elastic constant of the composite from the rve, using the principles of strain energy equivalence. the average strain and stress for rve are defined using gauss's theorem and energy equivalence principles, and the full set of elastic constants for a unidirectional composite has been obtained. the appropriate stresses on the rve under various loads were determined from the conditions of symmetry and periodicity. xia et al. [7] proposed a method of micromechanical finite element method (fem) analysis applied to unidirectional, and right-angle laminates subjected to multiaxial loading conditions. on the basis of the general conditions of periodicity stated by suquet [1]. they presented an explicit form of boundary conditions suitable for finite element method (fem) analyzes, of parallelepipedic rve models subjected to multiaxial loads. several theoretical models have been proposed for determining the effective properties of composite materials. and the research that has been conducted to improve our understanding, of periodic homogenization is summarized below. yvonnet et al. [08] proposed a method for evaluating the higher-order tensors of an efficient general anisotropic straingradient (mindlin) model, by a homogenization technique to determine the effective parameters. this proposed method uses finite element calculations on rves based on the principle of superposition. jakabcin and seppecher [09] studied the applicability of these formulas for highly contrasted structures. the study is carried out on structures of which the limiting energy is already known and compares the energies given by the convergence results, the corrective formulas and by a direct numerical simulation of the complete structure. guinovart-díaz et al. [10] proposed an analytical method of asymptotic homogenization (ahm) to the calculation of the effective elastic stiffnesses of a composite reinforced with fibers, with an imperfect contact between the matrix, and the fibers for parallelogram-like arrangement of fibers. savvas et al. [11] proposed a simulation of the homogenization of random heterogeneous media with arbitrarily shaped inclusions. this study is carried out by modeling with the extended finite element method (xfem), coupled with monte carlo simulation (mcs). and where, the influence of the inclusion shape on the effective properties of random media was studied. tsalis et al. [12] proposed a method for the introduction of the admissible strain fields of materials, with generalized periodicity and present their properties. tsalis, et al. [13] presented an analytical homogenization technique of elastic composites, with generalized periodicity to explain the effect of microstructure nonlinearity on effective properties. wu et al. [14] used a method to reduce computational cost, and obtain more accurate approximations to predict the effective thermos-mechanical properties of random heterogeneous materials. by richardson's extrapolation technique using smaller cell domains, and without the need for calculations in a larger cell domain. godin [15] proposed an explicit formula to calculate the effective properties tensor of a periodic lattice of two-phase dielectric tubes embedded in a host matrix. dhimole et al. [16] used a method based on the minimum energy loss of the structural genome, to predict the mechanical properties of three-dimensional (3d) four-directional braided composites. beicha et al. [17] conducted a comparative study between the effective elastic properties of fiber-reinforced composites respectively built with a hexagonal, and random distribution of non-overlapping fibers. the results show that the observed constraints are higher for random distribution than for periodic distribution. bonfoh et al. [18] proposed a general formulation of the multicoated inclusion problem in the general case of ellipsoidal inclusions, and anisotropic elasticity. rodríguez-ramos et al. [19] used the asymptotic homogenization method (ahm), and eigenfunction expansion-variational method (eevm) to obtain the effective elastic moduli of two-phase fibrous periodic composites, for different types of parallelogram cells. nevertheless, the latter are more and more used for structures used at their limit, which prompts us to look for a method to predict the onset of damage and the resulting behavior. some analytical investigations directly related to this study are briefly reviewed. yang and misra [20] proposed a second gradient stress–strain theory for materials following damage elasticity based on the method of virtual power. this approach made it possible to develop the equations governing cohesive materials undergoing damage. khoroshun and shikula [21] described several mathematical models on the k. benyahi et alii, frattura ed integrità strutturale, 58 (2021) 319-343; doi: 10.3221/igf-esis.58.24 321 different coupled deformation, and long-term microdamage processes applied to linear elastic composites of stochastic structure. berthier et al. [22] developed a time-dependent nonlocal continuous damage model, which takes into account the transfer of elastic energy stored in fibers in breaking energy and viscous dissipation. dorhmi et al. [23] developed micromechanical model to describe the progressive loss of stiffness observed during plastic straining based on microstructure changes. the study is being carried out on ductile metal-matrix composites subjected to mechanical loadings. sorić et al. [24] proposed a numerical modelling of the responses to ductile damage in heterogeneous materials, by a second order homogenization approach. the evolution of ductile damage at the microlevel is taken into account, by using the gradient enhanced elastoplasticity. wu et al. [25] proposed an improved gradient homogenization procedure for fiber reinforced materials. in this model, the fiber is considered as transversely homogeneous isotropic and assumed to remain linear elastic. while the material of the matrix can be considered as homogeneous isotropic. it is modeled as elastoplastic coupled to a damage law described by a non-local constitutive model. the method has been validated by the simulation of a damage process, in unidirectional carbon fiber reinforced epoxy composites, subjected to different load conditions. devries et al. [26] developed the main results of the homogenization theory of periodic media, as well as the assessment and simulation of damage for composite materials. their applications focused on the simulation of the evolution of damage by fiber failure in a unidirectional composite, involving parameters defined at the microscopic scale. and the prediction of takeoff near a free edge in a layered structure, using asymptotic extensions of the boundary layer. xia et al. [27] developed a three-dimensional meso/micro-mechanical finite element multilayer model for the prediction of the overall mechanical behavior of glass fibers [0,903,0] t/epoxy laminate, and for the study of damage mechanisms in reinforced polymer laminates. the epoxy matrix is represented by a nonlinear viscoelastic constitutive model, and a criterion of damage to the epoxy matrix is introduced into the finite element model. the model prediction was in good agreement with the observation of experience, not only in the overall stress-strain response, but also in the initiation and propagation of damage to the transverse matrix. in this article, periodic boundary equations have been established and applied to the theory based on finite element analysis to predict macroscopic elasticity. while considering a microstructure composed by several inclusions with different shapes and orientations, and a random distribution of the latter. the use of the homogenization technique allows us to study various damage mechanisms, by introducing damaged medium models from a microscopic approach. while still utilizing the efficient mechanical properties of inclusion composites. this allowing us to take into account the damaging behavior that occurs in the material, specifically the matrix at the micro scale. this document is organized as follows. section 2 discusses a method of solving a periodic homogenization problem using the principles of strain energy equivalence, in a coordinated way with finite element analysis. it gives the modifications required in the abaqus calculation code by python srcipts, in order to introduce periodic boundary conditions at the micro scale. this procedure is performed by the introduction of additional degrees of freedom supporting the components of macroscopic strains. in section 3 are presented several damage models controlled by an equivalent strain tensor in the principal coordinate system. the inclusions are supposed to remain elastic, while the matrix is supposed to obey the actual behavior of the material constituting, it with damage at the micro level. section 4 presents detailed results obtained by several tests of this selected periodic homogenization method, which will be compared with an estimated homogenization method (mori-tanaka model). these results can be used to verify the implementation of the simplified approach proposed in the abaqus calculation code. finally, section 5 provides applications regarding the introduction of damage into the homogenization problem. it is a question of using a local formulation for the evolution of the damage at the level of the microstructure, using the subroutine (umat) implemented in the fortran language on the abaqus calculation code. this proposed method makes it possible to simulate the response of the matrix behavior, on several rves requested in uniaxial traction. periodic boundary condition onsider a periodic structure made up of a periodic network of repeated unit cells. in the case of a composite material with periodic microstructure, we can define a "basic cell" and also periodicity vectors (fig. 1). the field of displacement for a periodic structure, can be expressed as indicated by suquet [1]: = + ' ' ( ) . ( ) , iji i j i i iu x x u x u periodic (1) with: c k. benyahi et alii, frattura ed integrità strutturale, 58 (2021) 319-343; doi: 10.3221/igf-esis.58.24 322  . ij jx : represents a linear displacement field, ' ( )i iu x : is a periodic function representing a modification of the linear displacement field, because to the heterogeneity for the composite structure. figure 1: description of a different basic cells in periodic microstructure. for each unit base cell, its boundary surfaces should appear in parallel pairs, and displacements on a pair of opposite parallel boundary surfaces can be expressed as:  + + = + ( ) ( ) ' ij k k i j iu x u (2)  − − = + ( ) ( ) ' ij k k i j iu x u (3) + k and − k : the indices to identify the th k pair of two opposite parallel boundary surfaces of a representative volume element (rve). the periodic function ' ( )i iu x is considered to be the same for two parallel borders, the difference between the eqn. 2 and eqn. 3 is given as follows:   + − + − − = − =  ( ) ( ) ( ) ( ) ( ) k k k k k i i j ijij j ju u x x x (4) with:  k jx : the constants for each pair of parallel boundary surfaces, with  ij known,  ij : the tensor of the macroscopic strains of the periodic structure. the average tensors of stress and strain are obtained by an integration on the rve, as follows: ( ) ij ijv 1 = x, y, z dv v (5) ( ) ij ijv 1 = x, y, z dv v (6) the strain energy of a homogeneous composite material over the rve, is as follows:  = ij ij 1 2 u v (7) the stored strain energy of a heterogeneous composite material over the rve is as follows: k. benyahi et alii, frattura ed integrità strutturale, 58 (2021) 319-343; doi: 10.3221/igf-esis.58.24 323  =  * ij ij v 1 dv 2 u (8) ( )   += − * ij ijij ij v 1 dv 2 u (9) ( )    −= +  * ij ijij ij ij v v 1 1 dv dv 2 2 u (10) with:  ij : the strain tensor. from eqn. 7 and eqn. 10, we can therefore write the energy difference, as follows: ( ) ( )( )    − =      − − iij iij* ii v 1 + dv 2 j j u u u uu u x x (11) with: iu : the ith average displacement. and using the equilibrium equation:    = ij 0 jx (12) by replacing eqn. 12 with eqn. 11, we obtain: ( )( ) − =   −  iij i * v 1 dv 2 j u x u u u (13) using gauss's theorem, we can transform the integration on the volume into the integration on the surface, as follows: ( ) −− =  * iij i j s 1 d 2 j juu suu (14) then, at the level of the surface js , we have: = iiu u (15) we can conclude that: − = * 0u u (16) the above derivation shows that the homogenization, we have used ensures the equivalence between the heterogeneous and homogenized rve. to apply the periodic boundary conditions at the micro scale, there are three types of set of nodes: faces, edges and corners in the rve having been modeled in the form of a parallelepiped in 3d. the regions on the boundaries of the rve are selected and numbered as shown in fig. 2. additional equations should be introduced for periodic boundary conditions at the micro scale, where the macroscopic strain matrix has components  = ij with i, j = x, y, z. in order to include the macroscopic deformation of component k. benyahi et alii, frattura ed integrità strutturale, 58 (2021) 319-343; doi: 10.3221/igf-esis.58.24 324  ij , it is necessary to create six reference points (pr-1, pr-2, pr-3, pr-4, pr-5, pr-6). where their degree of freedom of displacement has a relation with      x xy xz y yz z, , , , , respectively as follows:      − − − − − −= = = = = = 1 1 1 1 1 1 x xy xz y yz z( 1) ( 2 ) ( 3) ( 4 ) ( 5 ) ( 6 ); ; ; ; ;pr pr pr pr pr pru u u u u u (17) figure 2: representation and periodic boundary conditions of an rve. we create the additional equations of all faces, edges and corners with the python command in order to apply the periodic boundary conditions in the abaqus calculation code. and we apply these periodic boundary conditions at the micro scale. finally, to solve the homogenization equations, we use the finite element method. equations for applying periodic boundary conditions at the corners:                    x yz xzg a x yz yxc e x yz xzd f x yz yxh b u -u = + + u -u = + u -u = u -u = + (18) equations for applying periodic boundary conditions at the faces:      xbcgf adhe fehg badc cdhg baef u -u = u -u =0 u -u =0 (19) equations for applying periodic boundary conditions at the edges:                        x xzfg ad x xzhe cb yx yzcg ae yx yzdh bf yx yzef dc yxhg ab yz u -u = + u -u = u -u = + u -u = u -u = + u -u = (20) k. benyahi et alii, frattura ed integrità strutturale, 58 (2021) 319-343; doi: 10.3221/igf-esis.58.24 325 the mean strain in eqn. 6 can be transformed as follows:  = −ij ( ) 1 ( ) j i j j i j s u n u n ds v (21) in order to evaluate the effective properties ijc , it is first necessary to evaluate the mean of the stress and the strain of eqns. 5 and 6 respectively, by the application of different outline conditions. then to introduce them into the constitutive relation as follows:   = ij ij ij c (22) with: ijc : the stiffness modulus corresponding to the application of the strain mode. from the relation between the flexibility matrix s, and the elastic property, we can calculate the effective elastic properties from the stiffness matrix of the rve.                                            3121 3311 22 12 32 11 22 33 13 23 33 11 22 12 13 23 1 00 0 ee e 1 0 0 0 e e e 1 0 0 0 e e es = 1 00 0 0 0 g 1 0 0 0 0 0 g 0 0 0 0 1 0 g (23) there are only five independent material constants ( ) 11 33 12 31 32, , , ,e e g for a transversely orthotropic / isotropic material. where 13 depends on ( ) 11 33 12 31, , ,e e and can be calculated by the following relation:  31 13 33 11 = e e (24) a material is isotropic when its property is the same in all three directions. in this case, ( )= = =11 22 33e e e e , ( )   = = =12 31 32 and ( )= = =12 31 32g g g g . there are only two independent material constants ( ),e for an isotropic material. however, anisotropic materials have non-zero values in the upper right and lower left parts of their flexibility and stiffness matrices. there exists a relation between the components of the flexibility matrix, with the components of the rigidity matrix, which is as continuation: ( ) ( ) 2 11 33 13 11 2 2 2 2 1133 11 11 13 12 33 12 13 c .c -c 1 s = = ec .c -2.c .c -c .c +2.c .c (25) k. benyahi et alii, frattura ed integrità strutturale, 58 (2021) 319-343; doi: 10.3221/igf-esis.58.24 326 ( ) ( )  2 12 33 13 21 12 2 2 2 2 2233 11 11 13 12 33 12 13 c .c -c s ==ec .c -2.c .c -c .c +2.c .c (26) ( ) 13 31 13 2 3311 33 13 12 33 c s ==ec .c -2.c +c .c (27) ( ) ( ) 11 12 33 2 3311 33 13 12 33 c +c 1 s = = ec .c -2.c +c .c (28) 44 44 12 1 1 s = = c g (29) 55 55 13 1 1 s = = c g (30) the determination of the effective elastic properties depends on the stress-state, and also on the property of the composite material (isotropic or orthotropic case) of the rve. for an isotropic case and a uniaxial stress-state according to the direction x-x, the effective elastic properties are determined:   eff eff 11 11 11 e =e = (31)    eff eff eff 12 13+= 2 (32) with:             eff 22 12 11 eff 33 13 11 == (33) for an orthotropic/isotropic case transversely and a uniaxial stress-state along the direction x-x, the effective elastic properties are determined:   eff 11 11 11 e = (34)    eff 22 12 11 = (35) general implementation flowchart on the abaqus calculation code he proposed periodic homogenization method has been implemented numerically using a python script, to invoke the solution in the abaqus finite element computational code. the iterative algorithm is presented in fig. 3. at each incremental step of the analysis, the material properties subroutine (umat), where the constitutive law was used to carry out the communication between the python code, and the abaqus solver. the python code modifies the boundary conditions to an abaqus input file, applied to the rve. t k. benyahi et alii, frattura ed integrità strutturale, 58 (2021) 319-343; doi: 10.3221/igf-esis.58.24 327 figure 3: periodic homogenization procedure implementation flowchart. damage problem nce the homogenized characteristics are appreciated in the absence of the damage initiated by microcracks and microcavitations. it is then possible to introduce models of damage by a subroutine (umat) in the abaqus calculation code. the materials are supposed to obey the criterion of von mises [28], which is based on the second invariant of the deviatoric stress tensor. it is then supposed that the plasticity of the composite, being governed by that of the matrix then the total plasticity criterion will be obtained from that of the matrix. to translate the real behavior of materials into nonlinear elasticity, relatively developed laws are introduced within the framework of damage mechanics. mazars damage model the mazars model ([29], [30]) was developed within the framework of damage mechanics (fig. 4). the stress is given by the following relation: ( )  e= 1-d e (36) the damage is controlled by the equivalent strain eq , which allows to translate a tri-axial state by an equivalence to a uniaxial state. the strain tensor in the principal coordinate system:     22 2 eq 1 2 3+ + + = + + (37) knowing that the positive part + is defined, such that if  i is the main strain in direction i:  i + =       i i i if 0 0 if 0 (38) eq is an indicator of the state of tension in the material, which generates the damage. this quantity defines the load surface f, such that: o import the rve generated in the format (.step) into the abaqus calculation code generate the microstructure (geometric generator of random objects) periodic homogenization by python scripts (imposition of periodic boundary conditions, introduction of elimination equations): read the rve file (.odb) calculate 𝜎 from the mean of the volume calculate the current jacobian 𝐶 start the simulation of the model under the abaqus calculation code determination of effective mechanical characteristics introduce the constitutive laws of the constituents of composite by the subroutine (umat) on the abaqus calculation code: read the macroscopic constraints read the current jacobian matrix submit to abaqus k. benyahi et alii, frattura ed integrità strutturale, 58 (2021) 319-343; doi: 10.3221/igf-esis.58.24 328 ( )eqf= -k d =0 (39) with: ( ) eqk d = d=0if (40) figure 4: behavior of concrete according to the mazars model ([29], [30]). the relation between these variables is given as follows:    t t c cd= d + d (41) usually the value of  is fixed at 1.06. the coefficients t and c carry out a link between the damage, and the state of traction or compression. when traction is activated  =t 1 while  =c 0 , and vice-versa in compression. the damage evolution laws td and cd are expressed only from the equivalent strain eq . ( ) ( )( )   t t t t eq d0 eq 1-a d =1-a exp -b (42) ( ) ( )( )   c c c c eq d0 eq 1-a d =1-a exp -b (43) with: d0 : the threshold strain of damage,  : coefficient which was introduced later to improve the shear behavior, t c t ca a b, , , band : material parameters to identify. damage model from bouafia et al. to describe the behavior of composites with cylindrical inclusions in tension. the relationships proposed by bouafia et al. ([31], [32]) within the framework of the theory of beams, with taking into account of the damage which was developed for k. benyahi et alii, frattura ed integrità strutturale, 58 (2021) 319-343; doi: 10.3221/igf-esis.58.24 329 the behavior of the concrete of fibers in tension (fig. 5). the fibers (cylindrical inclusions) are dispersed in the concrete at random, and the modeling is carried out considering a uniform distribution. figure 5: constitutive law (σ-ε) in traction of steel fiber concrete [31]. the variable of the damage in uni-axial traction, is given by: ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( )                       −     → = −             → = − −     6 u ft u 1 6 t t ft u 6 u u r 2 6 t r u 1 1 . 1 uc ftuc t ct ct uc t ct f d e e d e (44) the maximum ultimate stress of the composite (function of the characteristics of inclusions):      0 =c f u ul (45) the reference length is linked to the height h of the section: = hrl (46) the initial modulus of the composite in traction is given by: ( ) +0 01=ct be ne (47) the ultimate strain corresponding to the total mobilization of the inclusions-matrix adhesion, is given by:      + 2 = 3 u f u ft f l e h (48) when there is tearing of inclusions, the breaking strain of the composite, is given by:       + + 2 = 3 4 u f f rt ft f l l e h h (49) k. benyahi et alii, frattura ed integrità strutturale, 58 (2021) 319-343; doi: 10.3221/igf-esis.58.24 330 this strain is a consequence of opening the cracks too large. this fracture strain of the inclusions is limited as follows:  =rt ft (50) the damage is progressive in the field of strains. for a uni-axial state of tension, the equivalent strain ( )( )  1 2,t td d , in the nonlinear field is such that: ( ) ( ) ( ) ( ) ( ) ( )                → = =        → = =  ft u 1 1 1 u r 2 2 2 = 11= 11t ct t t t ct t t d e e d d d e e d d (51) and ( ) ( ) ( ) ( ) ( )         =       → =  1 1 ft ft 1 r 2 2 r f , 0 f , 0 t t t t t d d d d d (52) figure 6: damage model algorithm implementation diagram. the threshold function defines two limit states: an elastic state ( )ft . a breaking limit given by the value ( ) r . such as: ( )      =  = →   = → → ft 1 1 r 2 =0 f , 0 =0 t t t d d d (53) k. benyahi et alii, frattura ed integrità strutturale, 58 (2021) 319-343; doi: 10.3221/igf-esis.58.24 331 implementation of damage models in abaqus calculation code he model of mazars ([29], [30]), the model of bouafia et al. ([31], [32]) simulating an isotropic elastic-damageable behavior in tension, they are implemented in the abaqus calculation code. their algorithms thus obtain are presented in figs. 6a-6b respectively. damage search and introduction flowchart he flowchart for finding, and introducing damage into a periodic homogenization problem, is shown below (fig. 7): figure 7: damage search and introduction flowchart. numerical comparison of homogenization models to experience lightweight concrete composite n this example, the concrete used is hydraulic lightweight aggregates, the matrix is cementitious while the aggregates are expanded clay [33]. the elastic properties of the constituents of composite are presented in tab. 1. in this example, it is a question of comparing our numerical results obtained (by the semi-analytical method of homogenization (mori-tanaka model), and by the method of periodic homogenization (numerical model)), with the experimental results (experimental) [33]. these latter are obtained from compression tests carried out on cylindrical specimens (16 x 32 mm), for different volume fractions of light aggregates: 0.125, 0.25, 0.375 and 0.45. the width of the rve is taken on the order of the diameter of median grain of sand (0.08 mm) [33]. t t i yes breaking no yes ε̃ ≥ ε̃crit no 𝐢𝐧 𝐜 𝐫 = 𝐢𝐧 𝐜 𝐫 + 𝟏 periodic homogenization 𝐶0 𝑛, 𝐶 𝑛, 𝜎 𝑛, 𝐸𝑛 effective properties e, ν, g, k, incrmax ∆𝜀 imposed mazars model parameters at , ac , bt , bc , ε̃ crit bouafia et al. model parameters ϖ, θ0, lr , β, h, lf, ef, τu, ϕ, εrt , ε̃crit incr ≥ incrmax end of simulation k. benyahi et alii, frattura ed integrità strutturale, 58 (2021) 319-343; doi: 10.3221/igf-esis.58.24 332 lightweight concrete young's modulus (mpa) poisson coefficient matrix 23630 0.20 aggregates (expanded clay) 5679 0.15 table 1: the elastic properties of the constituents of lightweight concrete composite [33]. figure 8: variation of the equivalent young's modulus as a function of the percentage of aggregates. we notice in fig. 8 that the equivalent young's modulus values found by the semi-analytical homogenization method (mori-tanaka model) are close to the experimental values (experimental) [33], and that for very low volume fractions (less than 15%). on the other hand, the periodic homogenization model (numerical model) gives good results, which approach the experiment allowing a better prediction of the elastic characteristics, and that for different volume fractions. cementitious composite with grains of sand in this example, the heterogeneous material consists of a matrix and the spheroidal inclusions shown in fig. 9. the elastic properties of the constituents of composite are presented in tab. 2. lightweight concrete young's modulus (mpa) poisson coefficient matrix (cement paste) 7000 0.25 inclusion (sand) 107000 0.15 table 2: the elastic properties of the constituents of sand mortar composite [34]. the elastic modulus of sand grains [34] was taken to be equal to that of the siliceous aggregates, ie 107000 mpa, the poisson's ratio was taken to be 0.15. measurement of the elastic modulus of cement paste gave 6000 mpa. to improve the calibration of the curve between modulus and volume of sand [34], it was taken equal to 7000 mpa. the poisson's ratio was taken equal to 0.25. the width of the rve is taken on the order of the diameter of median grain of sand (0.02 mm) [34]. the rve used in this example is generated by a random object modeler, and this with a random distribution of spheroidal inclusions (with a number of 10 inclusions in the rve), and with different volume fractions. the inclusions of the rve are generated randomly, based on a sphere pattern. once the random generation of the inclusions of rve is carried out, we will integrate it into the abaqus calculation code. the size of the rve does not change, only the volume fraction k. benyahi et alii, frattura ed integrità strutturale, 58 (2021) 319-343; doi: 10.3221/igf-esis.58.24 333 which evolves. the objective of this study is to determine the effective behavior of a composite (matrix inclusion of spheroidal shape). a comparison of the mechanical characteristics between the semi-analytical homogenization model (mori-tanaka model), the periodic homogenization model (numerical model) and the experimental measurements [34] is shown in fig. 10. figure 9: modeling of the material with spheroidal inclusions on the abaqus calculation code. figure 10: elastic modulus of sand mortars. this involves comparing the results obtained by the semi-analytical homogenization model (mori-tanaka model), and by the periodic homogenization method (numerical model) with the experimental results (experimental) [34]. the elastic properties of isotropic materials (of the cement matrix and those of the sand) are average values, and they are obtained for different volume fractions of spheroidal shaped aggregates. we note that the estimations of the semi-analytical homogenization model (mori-tanaka model), the results obtained by the periodic homogenization method (numerical model), and the results from the experiment (experimental) are quite similar, and this for different volume fractions. estimation of the mechanical characteristics and taking into account the damage of an inclusion composite n this paragraph, we will deal with several examples in order to validate the periodic homogenization model, and this by varying the percentage and shape of inclusions for rve of composite materials. in this study, we will compare the results of our modeling by the periodic homogenization method which are represented by (numerical i k. benyahi et alii, frattura ed integrità strutturale, 58 (2021) 319-343; doi: 10.3221/igf-esis.58.24 334 homogenization), with the results of a semi-analytical method (mori-tanaka model) from the work of al kassem [35], which are represented by (mori-tanaka model). once the effective mechanical characteristics are assessed in the absence of damage, then we introduce damage models for the rve in composite materials, by a subroutine (umat) on the abaqus calculation code. determination of effective mechanical characteristics in this example the heterogeneous material consists of a matrix and inclusions. the elastic properties of the constituents are presented in tab. 3. materials young's modulus e (mpa) poisson coefficient ν matrix 2800 0.35 inclusion 72000 0.172 table 3: the elastic properties of the components of composite (matrix-inclusions) [35]. the representative volume element (rve) of the inclusion composite consists of two phases: the matrix and the inclusion which follow an isotropic behavior, this is a three-dimensional (3d) case in small perturbations. the matrix is modeled as an elementary cube and the inclusion is modeled in several forms (spheroidal, ellipsoidal and cylindrical), and as rigid bodies. the homogeneous boundary conditions introduced in our modeling do not give other stresses than in the direction of perturbation; therefore, they result in a uni-axial stress state under tensile loading. the inclusions of rve are generated at random (with a number of 10 inclusions in a rve), based on a pattern of inclusions in the form of a sphere, ellipse and cylinder. once the random generation of the inclusions of rve is carried out, we will integrate it into the abaqus calculation code. the size of rve does not change (size_rve_x= size_rve_y= size_rve_z=1) [35], only the volume fraction which evolves. the objective of this study is to determine the effective mechanical characteristics of a composite (matrix inclusions). figure 11: modeling of an inclusion composite. the results obtained in fig. 11, show that all the principal stresses of the microstructure are accumulated in the x direction, or at the level of the perturbation direction using periodic boundary conditions. a comparison of the effective mechanical characteristics between the mori-tanaka estimation method (mori-tanaka model) [35], and the periodic homogenization model developed in this study (numerical homogenization) is shown below (figs. 12-14). and this for different volume fractions of inclusions (spheroidal, ellipsoidal, cylindrical). this involves comparing the numerical results obtained by the periodic homogenization method (finite element model with periodic boundary conditions), with the results obtained by the mori-tanaka model [35]. the elastic properties of the materials (of the matrix and those of the inclusion) are average values, and they are obtained for different volume fractions of inclusions (spheroidal, ellipsoidal, cylindrical). we note that at low volume fractions, we observe a very small difference between our model (numerical homogenization), and the mori-tanaka model (mori-tanaka model) [35], while for large volume fractions, we observe a bigger difference. k. benyahi et alii, frattura ed integrità strutturale, 58 (2021) 319-343; doi: 10.3221/igf-esis.58.24 335 figure 12: homogenized mechanical characteristics for different volume fractions of spheroidal inclusions. figure 13: homogenized mechanical characteristics for different volume fractions of ellipsoidal inclusions. k. benyahi et alii, frattura ed integrità strutturale, 58 (2021) 319-343; doi: 10.3221/igf-esis.58.24 336 figure 14: homogenized mechanical characteristics for different volume fraction of cylindrical inclusions. it is also noted that the estimations of the semi-analytical model of mori-tanaka [35], and the results of the periodic homogenization method developed in this study are quite close. and that for very low volume fractions (less than 15%) caused by a weak interaction between the phases. on the other hand, for volume fractions greater than 15%, the effective mechanical properties are overestimated, a deviation is observed which can be caused by a phenomenon of interaction between the inclusions. we conclude, that the periodic homogenization method (pbc) gives mechanical characteristics more rigid, than those of the semi-analytical model (mori-tanaka model). introduction of damage into the problem of homogenization we implemented a mazars damage model ([29], [30]) for spheroidal and ellipsoidal shaped inclusions, and the model of bouafia et al. ([31], [32]) for cylindrical shaped inclusions in the abaqus calculation code by the use of a subroutine (umat). calculations on a rve containing 10 inclusions with type localization conditions (pbc), allowed us to study the k. benyahi et alii, frattura ed integrità strutturale, 58 (2021) 319-343; doi: 10.3221/igf-esis.58.24 337 influence of the variation of the volume fraction of inclusions on the mechanical characteristics. then, once the effective mechanical properties of the composite were known, a damage model was introduced to study the response of the microstructure. the effective mechanical properties of the representative volume element ( ),eff effe are those obtained from the periodic homogenization method, corresponding to each volume fraction. the volume element is stressed in pure tension. the loading is done with displacement imposed in three-dimensional strain. the characteristics of composite are defined in tab. 4: table 4: the effective properties and damage parameter of a composite. in a first case, we represent in figs. 15-16 the local stress-strain response and the evolution of the damage respectively, depending on the strain of a volume element loaded in pure tension, and under various volume fractions. we set the parameter ta and made the parameter tb varied. figure 15: influence of the variation of the volume fraction inclusions on the local stress-strain behavior. matrixspheroidal inclusions volume fraction (%) eh (mpa) νh ac bc at bt εd0 10 3440.43 0.333 1.4 240.83 0.8 2752.35 0.001 15 3764.60 0.335 1.4 263.52 0.8 3011.68 0.001 20 4264.90 0.326 1.4 298.54 0.8 3411.92 0.001 25 4779.03 0.316 1.4 334.53 0.8 3823.23 0.001 30 5324.70 0.312 1.4 372.73 0.8 4259.76 0.001 matrixellipsoidal inclusions volume fraction (%) eh (mpa) νh ac bc at bt εd0 10 3391.73 0.340 1.4 237.42 0.8 2713.39 0.001 15 3787.73 0.333 1.4 265.14 0.8 3030.19 0.001 20 4240.37 0.328 1.4 296.82 0.8 3392.30 0.001 25 4784.43 0.321 1.4 334.91 0.8 3827.55 0.001 30 5320.80 0.312 1.4 372.46 0.8 4256.64 0.001 matrixcylindrical inclusions 𝐅𝐜𝐣 (mpa) ftj (mpa) eh (mpa) νh ε0 (%) ϕ (mm) lf (mm) τu (mpa) ω (%) θ0 47.76 3.46 5247.08 0.342 0.21 0.04 0.8 7 5 0.405 47.76 3.46 7780.74 0.335 0.21 0.04 0.8 7 10 0.405 47.76 3.46 10360.73 0.327 0.21 0.04 0.8 7 15 0.405 47.76 3.46 13033.63 0.320 0.21 0.04 0.8 7 20 0.405 k. benyahi et alii, frattura ed integrità strutturale, 58 (2021) 319-343; doi: 10.3221/igf-esis.58.24 338 figure 16: influence of the variation of the volume fraction inclusions on the evolution of damage according to the strain. figs. 15-16 show us that the increase in the volume fraction of the inclusions (spheroidal, ellipsoidal), and of the parameter tb allows an improvement in the stiffness of composite. and it makes a change the shape of damage as a function of strain, or the composite becomes less ductile. in a second case, the influence of the parameter ta is given in figs. 17-18 with respect to the local stress-strain response, and the evolution of damage respectively, of a volume element loaded in pure tension. with an average volume fraction (taken equal to 20%), and a fixed value of the parameter tb corresponding to this percentage. figs. 17-18 show us that the increase in the volume fraction of shaped inclusions (spheroidal, ellipsoidal), and of the parameter ta results in a sudden drop in the strength of composite (very low residual stress). and it makes a change the shape of damage as a function of the strain, where the composite becomes more fragile. figure 17: influence of the parameter ta on the local behavior stress-strain. we represent the local stress-strain response and the evolution of damage respectively, as a function of the strain of a volume element stressed in pure tension, and under different volume fraction of cylindrical inclusions. figs. 19-20 show us that increasing the percentages of cylindrical inclusions increases elastic properties (the material becomes more rigid). and it causes a sudden drop in the strength of composite (low residual stress), and a ductility bearing having greater strain of the composite. what changes the rate of damage depending on the strain, where the resistance of the softening part of composite is very low. k. benyahi et alii, frattura ed integrità strutturale, 58 (2021) 319-343; doi: 10.3221/igf-esis.58.24 339 figure 18: influence of the parameter ta on the evolution of damage according to the strain. figure 19: local stress-strain behavior. figure 20: evolution of the damage according to the strain. the behavior of the composite follows an elastic phase until the appearance of the first cracks, then a sudden drop in stress results to a residual stress which activates the contribution of cylindrical inclusions to take up the forces developed. k. benyahi et alii, frattura ed integrità strutturale, 58 (2021) 319-343; doi: 10.3221/igf-esis.58.24 340 finally, this results in a level of ductility allowing greater strain of the composite. note that the stress corresponding to this level is a function of the percentage of inclusions. also, we notice, the more we increase the percentage of fibers, the shape of the local stress-strain behavior curve decreases, which corresponds to a less ductile behavior. conclusion he effective properties of heterogeneous materials (young's elastic modulus (e), poisson ratio (ν), shear modulus (g) and compressibility modulus (k)) were evaluated for different volume fractions (5 at 30%), taking into account the periodic displacement boundary conditions. for very low volume fractions (<15%), the comparison of the various results obtained by the numerical model of periodic homogenization (pbc), with the results of estimations of the mori-tanaka model [35] is satisfactory, caused by a weak interaction between phases. based analysis of the results, the following conclusions were drawn: on the other hand, for volume fractions greater than 15%, the effective mechanical properties obtained by our simulation are overestimated, they are more rigid than those of the semi-analytical model of mori-tanaka [35]. it is concluded that the percentage of inclusions as well as their shape, and orientation have an influence on the mechanical characteristics of the composite. the mazars damage model ([29], [30]) allowed us to introduce a non-local formulation for the evolution of damage at the microstructure level. and also makes it possible to reproduce the softening behavior of the material, which is gradually reduced as the microcracks develop until reaching zero. which corresponds to a visible macro-crack. regarding the parametric study, the following ascertainment were drawn: we set the parameter ta and we varied the parameter tb under different volume fraction, shows us that the variation of the volume fraction of shaped inclusions (spheroidal, ellipsoidal), and of the parameter tb increases the elastic properties of the composite (improvement of the stiffness). and, it slightly changes the shape of damage curve (the composite becomes a little less ductile). on the other hand for an average volume fraction (taken equal to 20%), and a fixed value of the parameter tb corresponding to this percentage. shows us that the variation of the parameter ta makes it possible to have a sudden drop in the resistance of the composite (no residual stress), as well as a very low contribution of inclusions in the softening part of the composite. and, it changes the shape of the composite damage curve (the composite becomes more fragile). the damage model of bouafia et al. ([31], [32]), allowed us to introduce the evolution of damage through a ductility plateau, which is a function of the characteristics of cylindrical inclusions (percentage, diameters, orientation and bond stress). acknowledgements he authors wish to thank the algerian ministry of higher education and scientific research for funding the university education research project (prfu – n° a01l02un150120180004) and tassili project (phc – 43940nj). declaration of interest statement n behalf of all authors, the corresponding author states that there is no conflict of interest. notation sj : the jth area, t t o k. benyahi et alii, frattura ed integrità strutturale, 58 (2021) 319-343; doi: 10.3221/igf-esis.58.24 341 nj : the unit normal, ui : the ith displacement, sj : the outer limit of the rve, e11, e22 and e33 : the moduli of elasticity of extensions along directions 1, 2 and 3, respectively, νij (i, j = 1, 2, 3) : poisson's ratios, g12, g13, and g23 : shear moduli, ui p : the nodal variable at the node p, of degree of freedom i, e : hooke's matrix, d : the damage variable, εe : elastic strain, eb0 : modulus of longitudinal elasticity of concrete, ϖ : percentage by volume of fibers, θ0 : fiber orientation coefficient, lr : reference length, β: model constant, h : composite cross section height, lf : fiber length, ef : elastic modulus of the fiber, n : fiber-concrete equivalence coefficient, τu : ultimate fiber-concrete bond stress, ϕ : diameter of a fiber, fft : composite tensile strength, εft : composite cracking strain, εrf : fiber breaking strain, εrt : breaking strain of the composite in tension. references [1] suquet, p. (1987). elements of homogenization theory for inelastic solid mechanics. sanchez-palencia, e., zaoui, a. (eds.), homogenization techniques for composite media. springer-verlag, berlin, pp. 194–275. doi: 10.1007/3-540-17616-0 [2] mori, t., tanaka, k. (1973). average stress in matrix and average elastic energy of materials with misfitting inclusions. acta metallurgica, 21(5), pp. 571-574. doi: 10.1016/0001-6160(73)90064-3. [3] hill, r. (1965). a self-consistent mechanics of composite materials. journal of the mechanics and physics of solids 13, pp. 213-222. doi: 10.1016/0022-5096(65)90010-4. [4] eshelby, j.d. (1957). the determination of the elastic field of an ellipsoidal inclusion and related problems. proceedings of the royal society of london. series a. mathematical and physical sciences, 241(1226), pp. 376-396. doi: 10.1098/rspa.1957.0133. [5] michel, jc., moulinec, h., suquet, p. effective properties of composite materials with periodic microstructure: a computational approach. computer methods in applied mechanics and engineering 172 (1-4), pp. 109-143. doi: 10.1016/s0045-7825(98)00227-8. [6] sun, c t., vaidya, r s. (1996). prediction of composite properties from a representative volume element. composites science and technology, 56(2), pp. 171-179. doi: 10.1016/0266-3538(95)00141-7. [7] xia, z., zhang, y., ellyin f. (2003). a unified periodical boundary conditions for representative volume elements of composites and applications. international journal of solids and structures 40, pp. 1907–1921. doi: 10.1016/s0020-7683(03)00024-6. [8] yvonnet, j., auffray, n., and monchiet, v. (2020). computational second-order homogenization of materials with effective anisotropic strain-gradient behavior. international journal of solids and structures, 191, pp. 434-448. doi: 10.1016/j.ijsolstr.2020.01.006. https://doi.org/10.1007/3-540-17616-0 https://doi.org/10.1016/0001-6160(73)90064-3 https://doi.org/10.1016/0022-5096(65)90010-4 https://doi.org/10.1098/rspa.1957.0133 https://doi.org/10.1016/s0045-7825(98)00227-8 https://doi.org/10.1016/0266-3538(95)00141-7 https://doi.org/10.1016/0266-3538(95)00141-7 k. benyahi et alii, frattura ed integrità strutturale, 58 (2021) 319-343; doi: 10.3221/igf-esis.58.24 342 [9] jakabcin, l. and seppecher, p. (2020). on periodic homogenization of highly contrasted elastic structures. journal of the mechanics and physics of solids, 144:104104. doi: 10.1016/j.jmps.2020.104104. [10] guinovart-díaz, r., rodríguez-ramos, r., bravo-castillero, j., lópez-realpozo, j., sabina, f., sevostianov, i. (2013). effective elastic properties of a periodic fiber reinforced composite with parallelogram-like arrangement of fibers and imperfect contact between matrix and fibers. international journal of solids and structures, 50(13), pp. 2022-2032. doi: 10.1016/j.ijsolstr.2013.02.019. [11] savvas, d., stefanou, g., papadrakakis, m. and deodatis, g. (2014). homogenization of random heterogeneous media with inclusions of arbitrary shape modeled by xfem. computational mechanics 54(5), pp. 1221–1235. doi: 10.1007/s00466-014-1053-x. [12] tsalis, d., baxevanis, t., chatzigeorgiou, g., charalambakis, n. (2013). homogenization of elastoplastic composites with generalized periodicity in the microstructure. international journal of plasticity, 51, pp. 161–187. doi: 10.1016/j.ijplas.2013.05.006. [13] tsalis, d., chatzigeorgiou, g., charalambakis, n. (2012). homogenization of structures with generalized periodicity. composites: part b, 43(6), pp. 2495–2512. doi: 10.1016/j.compositesb.2012.01.054. [14] wu, y., nie y., and yang z., (2014). prediction of effective properties for random heterogeneous materials with extrapolation. archive of applied mechanics 84(2), pp. 247–261. doi: 10.1007/s00419-013-0797-7. [15] godin, y.a. (2016). effective properties of periodic tubular structures. q. j. mech. appl. math., 69(2), pp. 181–193. doi: 10.1093/qjmam/hbw003. [16] dhimole, v.k., chen, y., cho, c. (2020). modeling and two-step homogenization of aperiodic heterogenous 3d four-directional braided composites. j. compos. sci., 4(4), 179. doi: 10.3390/jcs4040179. [17] beicha, d., kanit, t., brunet, y., imad, a., el moumen, a., khelfaoui, y. (2016). effective transverse elastic properties of unidirectional fiber reinforced composites. mech. mater. 102, pp. 47–53. doi: 10.1016/j.mechmat.2016.08.010. [18] bonfoh, n., coulibaly, m., sabar, h. (2014). effective properties of elastic composite materials with multi-coated reinforcements: a new micromechanical modelling and applications. compos. struct. 115, pp. 111–119. doi: 10.1016/j.compstruct.2014.04.011. [19] rodríguez-ramos, r., yan, p., lópez-realpozo, j.c., guinovart-díaz, r., bravo-castillero, j., sabina, f.j., jiang, c.p. (2011). two analytical models for the study of periodic fibrous elastic composite with different unit cells. compos. struct., 93(2), pp. 709–714. doi: 10.1016/j.compstruct.2010.08.008. [20] yang, y. and misra, a. (2012). micromechanics based second gradient continuum theory for shear band modeling in cohesive granular materials following damage elasticity. internat. j. solids structures 49(18), pp. 2500-2514. doi: 10.1016/j.ijsolstr.2012.05.024. [21] khoroshun, l. p. and shikula, e. n. (2012). deformation and damage of linear elastic homogeneous and composite materials (review). international applied mechanics, 48, pp. 131–175. doi: 10.1007/s10778-012-0512-3. [22] berthier, e., ponson, l., dascalu, c. (2014). quasi-brittle fracture of heterogeneous materials: a nonlocal damage model. procedia materials science, 3, pp. 1878-1883. doi: 10.1016/j.mspro.2014.06.303. [23] dorhmi, k., morin, l., derrien, k., hadjem-hamouche, z., chevalier, j.p. (2020). a homogenization-based damage model for stiffness loss in ductile metal-matrix composites. journal of the mechanics and physics of solids, 137, 103812. doi: 10.1016/j.jmps.2019.103812. [24] sorić, j., lesičar, t., tonković, z. (2021). on ductile damage modelling of heterogeneous material using secondorder homogenization approach. computer modeling in engineering and sciences,126 (3), pp. 915-934. doi: 10.32604/cmes.2021.014142. [25] wu, l., noels, l., adam, l., doghri, i. (2012). a multiscale mean-field homogenization method for fiber-reinforced composites with gradient-enhanced damage models. computer methods in applied mechanics and engineering 233, pp. 164-179. doi: 10.1016/j.cma.2012.04.011. [26] devries, f., dumontet, h., duvaut, g., and lene, f. (1989). homogenization and damage for composite structures. int. j. numer. meth. engrg., 27, pp. 285–298. doi: 10.1002/nme.1620270206. [27] xia, z., chen, y., ellyin, f. (2000). a meso/micro-mechanical model for damage progression in glass–fiber/epoxy cross-ply laminates by finite-element analysis. composite science and technology 60, pp. 1171–1179. doi: 10.1016/s0266-3538(00)00022-1. [28] mises, r v. (1913). mechanik der festen körper im plastisch-deformablen zustand. nachrichten von der gesellschaft der wissenschaften zu göttingen, mathematisch-physikalische klasse, pp. 582-592. [29] mazars, j. (1986). a description of micro-and macroscale damage of concrete structures. engineering fracture mechanics, 25(5-6), pp. 729-737. doi: 10.1016/0013-7944(86)90036-6. https://doi.org/10.1016/j.cma.2012.04.011 https://doi.org/10.1016/j.cma.2012.04.011 https://doi.org/10.1002/nme.1620270206 https://doi.org/10.1002/nme.1620270206 https://doi.org/10.1016/0013-7944(86)90036-6 https://doi.org/10.1016/0013-7944(86)90036-6 k. benyahi et alii, frattura ed integrità strutturale, 58 (2021) 319-343; doi: 10.3221/igf-esis.58.24 343 [30] mazars, j., hamon, f., grange, s. (2015). a new 3d damage model for concrete under monotonic, cyclic and dynamic loadings. materials and structures, 48(11), pp. 3779-3793. doi: 10.1617/s11527-014-0439-8. [31] bouafia, y., kachi, m s., fouré, b. (2002). stress-strain relationship in the case of reinforced steel fiber concrete. annals of btp. [32] belhadj, n., bouafia, y., smahi, r. (2015). modeling the behavior of the fiber reinforced concrete by damage mechanics. in: applied mechanics and materials. trans tech publications, pp. 386-390. doi: 10.4028/www.scientific.net/amm.749.386. [33] nguyen, hg. (2008). micromechanical approach for modeling the elastoplastic behavior of composites: application to resin mortars. doctoral thesis. university of cergy-pontoise, france. [34] duplan, f. (2014). cementitious composites with controlled elastic modulus: design, characterization and micromechanical modeling. doctoral thesis. university of toulouse iii paul sabatier, france. [35] al kassem, g., weichert, d. (2009). micromechanical material models for polymer composites through advanced numerical simulation techniques. in: pamm: proceedings in applied mathematics and mechanics. berlin: wiley‐vch verlag, pp. 413-414. doi: 10.1002/pamm.200910180. https://doi.org/10.1617/s11527-014-0439-8 https://doi.org/10.1617/s11527-014-0439-8 https://doi.org/10.4028/www.scientific.net/amm.749.386 https://doi.org/10.1002/pamm.200910180 https://doi.org/10.1002/pamm.200910180 microsoft word numero_33_art_9 m.-l. zhu et alii, frattura ed integrità strutturale, 33 (2015) 67-72; doi: 10.3221/igf-esis.33.09 67 focussed on characterization of crack tip fields near tip strain evolution of a growing fatigue crack m.-l. zhu university of portsmouth, uk east china university of science and technology, china y.-w. lu, c. lupton, j. tong university of portsmouth, uk jie.tong@port.ac.uk abstract. near tip full-field strains in a growing fatigue crack have been studied in situ using the digital image correlation (dic) technique in a compact tension specimen of stainless steel 316l under tension-tension cyclic loading. an error analysis of displacements and strains has been carried out, and the results show that the precision of displacements and strains in the wake of the crack is worse than that in front of the crack. a method for the determination of crack tip location is proposed for the dic analysis. strain ratchetting is observed ahead of the growing fatigue crack tip and found to be dependent on the distance to the crack tip; whilst normal strains appear to stabilise behind the crack tip. keywords. dic; crack tip; error analysis; fatigue crack growth; strain ratchetting. introduction lthough strain-based approaches have been proposed [1, 2] to deal with fatigue crack growth since the 60s, our interest in this line of enquiry began some 10 years ago, mainly using numerical simulations [3-7], where near-tip strain ratchetting was found to be common in several materials, regardless the constitutive laws used [3-5] or the numerical simulation strategies [4-6]. we hypothesise that if the normal strain near and ahead of the crack tip continues to accumulate with fatigue cycles, the material ahead of the crack tip will eventually fail thus prompting crack growth. although this concept has been successfully applied to rationalise fatigue crack growth in nickel-based superalloys [3], direct experimental validation was not possible until very recently, when the first experimental evidence of near-tip strain ratchetting was reported for stationary [8] and growing cracks [9] using in situ dic systems. the strain distribution near a fatigue crack tip obtained from the dic analysis may be influenced by data processing parameters used in the dic analysis. an accurate assessment of the near-tip strains based on the dic technique requires the knowledge of the errors in the measured displacements and strains; hence methods may be developed in the testing and analysis to minimize the errors. strain ratchetting behaviour has been observed for relatively straight cracks [8, 9], whilst evaluation of the strain evolution in a growing crack along a tortuous path is more challenging. determination of the exact location of the crack tip in such a situation is another challenge, which is important to a quantitative interpretation of crack tip micro-mechanical behaviour. in the present work, we report an error assessment of the displacements and strains measured using the dic system; and a method to determine the locations of the instantaneous crack tip with a tortuous path. the evolution of normal strain range with fatigue cycles was tracked and the critical strain values at incipient crack growth were obtained. a m.-l. zhu et alii, frattura ed integrità strutturale, 33 (2015) 67-72; doi: 10.3221/igf-esis.33.09 68 experimental methods he material studied is stainless steel 316l, which has yield strength of 280 mpa. an average grain size was measured as approximately 17 μm. a standard compact-tension specimen was used, with a width of 60 mm, a thickness of 7 mm and a machined notch size of 12 mm. pre-cracking was carried out under load-control using a load shedding scheme. the maximum load was decreased manually step-by-step from 10 kn to 6 kn, and the load was maintained constant at each step. the load ratio and loading frequency were 0.1 and 10 hz, respectively, during the entire pre-cracking process. crack growth was monitored by both the direct current potential-drop (dcpd) technique and surface replicas. the latter readings were taken as the true surface crack lengths whilst crack lengths from dcpd readings are indicative of the average crack lengths which were used to calculate the stress intensity factor k. the pre-cracking was terminated when the crack length reached 15 mm, after which a crack growth test was conducted for work reported in [9]. further crack growth was allowed to remove the influence of pre-history and the original crack length in this work was 24.15 mm (a/w ≈ 0.4). a random speckle pattern was applied on to one of the specimen surfaces with graphite powder deposited on a white paint background. the random speckle pattern generated from the current study may be described by its grey level intensity profile, which was a bell-shaped distribution and was deemed appropriate for image correlation purposes. the imaging system (lavision, gmbh) consists of a ccd camera (2456 × 2058 pixels) and a schneider kreuznach f2.8 50mm lens with 100mm extension tubes. a region of interest, a rectangle of 1.67  1.4 mm with the crack tip in the centre, was selected for imaging in order to capture the near-tip strain data ahead and behind the crack tip. a resolution of 0.68 µm/pixel was achieved. an increasing loading scheme was applied to grow the crack into a steady-state condition at a load ratio of 0.1, from pmax = 6 kn to 8.8 kn at a step about 10%. the loading waveform is trapezoidal with a 10 second loading/unloading and a 2 second hold at minimum and maximum loads. during the loading cycle, 23 images were collected during loading/unloading at a frequency of one image per second. optical microscopy (om) was used to monitor the crack in situ and verify the crack tip position and the crack growth morphology. determination of the crack tip n accurate determination of the crack tip position during crack growth is important in the dic analysis in order to capture accurately the strains near the crack tip. this is especially true when the resolution of the image is limited by the pixel size. in this work, we propose a method for locating the crack tip by a combination of information from om and the displacement distribution from dic analysis. fig. 1 presents a flow chart of the method. firstly, determine the horizontal position of the crack tip x0 (in pixel) from the reference image collected by the dic system and the image from the optical microscopy om. the value x0 may be determined from the reference image facilitated by the neighbouring speckles. secondly, calculate the average displacement value from the full data set of the displacement component in the y direction. the values of vy were obtained from image correlation between pmax and pmin. the value of y0 for the crack tip may be obtained when vy (x0, y0) is equal to . the crack tip location (x0, y0) is thus determined. the rigid body displacement was removed prior to this operation. in the case of stationary cracks, the crack tip location thus determined is fixed when the same reference image is used for subsequent correlation of deformed images. results and discussion o investigate the evolution of strain fields near the fatigue crack tips, a region of interest, centred at the crack tip, was imaged and analysed using the lavision software. the correlation procedure was carried out from images collected in situ during the fatigue crack growth tests. the ranges of deformation and strain for each cycle were determined by correlating the deformed image at maximum load relative to a reference image, which was taken at minimum load at the beginning of each test. in addition, dic analysis of several images collected under zero load was also carried out to assess the baseline errors for both displacement and strain. a subset size of 49 pixels by 49 pixels, or 33 µm × 33 µm, was chosen with a step size of 12 pixels, or 8.16 µm, in the dic analysis. t a t m.-l. zhu et alii, frattura ed integrità strutturale, 33 (2015) 67-72; doi: 10.3221/igf-esis.33.09 69 figure 1: schematic of the method used for locating the crack tip for dic analysis error analysis a baseline error analysis was carried out by post-processing the dic results under zero load. the precision of displacement and strain is defined as the standard deviation of selected data points within the region of interest. the assessment was made both in front of (front) and behind (wake) the crack tip, with a square area of 0.5  0.5 mm chosen on both sides, as shown in fig. 2a. fig. 2b shows that the standard deviation of the displacements in the x and the y directions, where the maximum error appears to be in the crack wake in the x direction, about 0.14 pixel, or 0.095 m, although the overall errors are between 0.064 and 0.1 m. the precision in the crack wake appears to be worse than that ahead of the crack, which is not unexpected. the strain errors are shown in fig. 2c, where the overall error band is between 0.22% and 0.41%, again the errors in the wake are worse than those ahead of the crack tip. a possible reason may be the discontinuity due to the presence of the crack, which may have affected the speckle distribution. the precision of yy is around 0.3%, which was deemed sufficient to give confidence in the measurement of near-tip strains in this work. strain evolution of a growing fatigue crack the near-tip strains were collected during the fatigue crack growth test at a maximum cyclic load of 8.8 kn, r=0.1 and k=33.5 mpam1/2. fig. 3 shows the crack growth morphology post testing. the crack deflected slowly at first, then followed a tortuous crack path, with a crack growth of about 106 m during the last 200 cycles. this last stage of crack growth was analysed and the normal strain evolution with the number of cycles was tracked. fig. 4 shows the range of normal strain yy distribution in the region of interest at the 200th cycle. selected points were used for tracking the strain evolution with the number of cycles. the tracking points were selected on the same plane, with varied distances to the initial crack tip. points 1, 3, 5 and 7 were chosen on the crack path, and the strain values at these points were assessed with respect to the incipient crack tip location during the crack growth process. the distance to the initial crack tip at points 3, 6 and 8 is double, 4 times and 6 times of the grain size, respectively. the strain values at m.-l. zhu et alii, frattura ed integrità strutturale, 33 (2015) 67-72; doi: 10.3221/igf-esis.33.09 70 the selected points were averaged over a square domain of 14  14 pixels (9.52  9.52 m), centred at each tracking point. this is illustrated in fig. 4, where the normal strain value at point 1 is obtained by averaging the strain data from the square. 0.00 0.02 0.04 0.06 0.08 0.10 vy, wake v y , front s ta n d a rd d e vi a tio n o f d is p la ce m e n t ( m ) v x , wake v x , front (b) 0.0 0.1 0.2 0.3 0.4  yy , wake  yy , front  xy , wake  xy , front s ta n d a rd d e vi a tio n o f st ra in ( % )  xx , wake  xx , front (c) figure 2: error analysis of displacements and strains for both ahead of (front) and behind (wake) the crack tip under zero load: (a) an image of the region of interest (1mm0.5mm) near the crack tip; (b) standard deviation of the displacement components and (c) standard deviation of the strain components. figure 3: a fatigue crack path with the initial and final crack tips indicated. the last stage of the crack growth was considered in the strain analysis using dic. m.-l. zhu et alii, frattura ed integrità strutturale, 33 (2015) 67-72; doi: 10.3221/igf-esis.33.09 71 the evolution of strain range with the number of cycles at the selected tracking points is shown in fig. 5. the normal strain range generally increases with the increase of fatigue cycles, clearly indicating strain ratchetting. similar strain evolution patterns may be observed at points 1-3; also at points 4-8. the reduced strains measured during early stages of crack growth may be due to the deflection of the crack growth path (fig. 3 and 4), thereafter the strains continue to increase. although no attempt was made to obtain the local normal strains along the tortuous crack path, the normal strains tracked at the selected points appear to behave similarly, indicating strain ratchetting is consistently observed near the crack tip. assuming the fatigue crack growth is steady state, the transient crack tip location is estimated to be at a, b, c and d for points 1, 3, 5 and 7, respectively. the normal strain range at these positions appears to be from around 8% (a) to 9.4% (d). a strain range of about 8% might be indicative of a critical value above which steady state fatigue crack growth occurred, consistent with our previous results [9]. it is of interest to note that the strain values from points 1-6 at the 200th cycle are similar, suggesting that the strains in the wake of the crack tend to stabilize. figure 4: the normal strain range distribution and the tracking points for strain measurement at n=200. points 3, 6, 8 were chosen to be 2, 4 and 6 times of the average grain size; points 1, 3, 5, 7 were chosen on the crack path. 0 50 100 150 200 -2 0 2 4 6 8 10 12 14 1 2 3 4 5 6 7 8   y y (% ) number of cycles figure 5: the evolution of the normal strain ranges at the selected tracking points as a function of number of cycles. the stars indicate the strains at which incipient crack growth occurred. m.-l. zhu et alii, frattura ed integrità strutturale, 33 (2015) 67-72; doi: 10.3221/igf-esis.33.09 72 conclusions he evolution of normal strain range with cycle has been captured in situ during the fatigue crack growth experiments using the dic technique in a compact tension specimen of stainless steel 316l. generally, the normal strain range measured is between 4% and 13% near the crack tip, hence the relative error in the measurements is no more than 7.5%. a method to determine the crack tip location is proposed for a crack with a tortuous crack path. strain ratchetting is observed in the near-tip field ahead of the crack tip, whilst normal strains behind the crack tip appear to be more stable. acknowledgements lz is supported by a visiting scholarship from china scholarship council. references [1] mcclintock, f.a., on the plasticity of the growth of fatigue cracks, john wiley & sons inc., new york, (1963). [2] haigh, j.r., skelton, r.p., a strain intensity approach to high temperature fatigue crack growth and failure, mater. sci. eng., 36 (1978) 133-137. [3] zhao, l.g., tong, j., byrne, j., the evolution of the stress – strain fields near a fatigue crack tip and plasticity-induced crack closure revisited, fatigue. fract. eng. mater. struct., 27 (2004) 19-29. [4] zhao, l., tong, j., a viscoplastic study of crack-tip deformation and crack growth in a nickel-based superalloy at elevated temperature, j. mech. phys. solids., 56 (2008) 3363-3378. [5] lin, b., zhao, l.g., tong, j., a crystal plasticity study of cyclic constitutive behaviour, crack-tip deformation and crack-growth path for a polycrystalline nickel-based superalloy, eng. fract. mech., 78 (2011) 2174-2192. [6] huang, m., tong, j., li, z., a study of fatigue crack tip characteristics using discrete dislocation dynamics, int. j. plast., 54 (2014) 229-246. [7] tong, j., zhao, l.g., lin, b., ratchetting strain as a driving force for fatigue crack growth, int. j. fatigue., 46 (2013) 49-57. [8] tong, j., lin, b., lu, y.w., madi, k., tai, y.h., yates, j.r., doquet, v., near-tip strain evolution under cyclic loading: in situ experimental observation and numerical modelling, int. j. fatigue., 71 (2015) 45-52. [9] lu y.-w., lupton, c., zhu, m.-l., tong, j., in situ experimental characterization of near-tip strain evolution of fatigue cracks, exp. mech., (2015) in press. t m microsoft word numero_34_art_29 k. nambu et alii, frattura ed integrità strutturale, 34 (2015) 271-279: doi: 10.3221/igf-esis.34.29 271 focussed on crack paths influence of vacuum carburizing treatment on fatigue crack growth characteristic in dsg2 k. nambu suzuka national college of technology, japan knambu@mech.suzuka-ct.ac.jp n. egami meijo university, japan egami@meijyo-u.ac.jp abstract. the aim of this research is to clarify the influence of vacuum carburizing on the fatigue-crack progress characteristics of dsg2 steel. the test specimen tempering material (qt material) and vacuum carburizing material (vc material) has been used. the fatigue-crack progress was examined by subjecting the samples to four-point bending. the loading-capacity fixed experiment was done using a maximum load of pmax = 4000– 7000 n. the δk fixed experiment was done using a load of δk = 18–36 mpa√m. the crack progress speed of vc material fell, after the high crack progress speed was shown, and after it showed the minimum, it showed the tendency to go up again. this is considered to be what is depended on the compressive residual stress given to the carburizing layer. from this, it is thinkable that there is a crack progress depression effect in a carburizing layer. in vc material, a carburizing layer has a crack progress depression effect from a plunger-helix bottom to about 2.6 mm, and it turned out that it is larger than an effective carburizing layer. moreover, in each δk, it was shown that depression effect revelation differs and the crack progress process accompanying it was able to be shown typically. keywords. vacuum carburizing; dsg2; fatigue-crack progress characteristics. introduction n recent years, longer life-span of the machine construction thing is called for from a viewpoint of earth environment. for longer life-span of a machine construction thing, the fatigue strength of material and wear-resistant improvement are especially required. in order to attain these, coexistence of a hardness and toughness becomes indispensable. the surface modification processing method is mentioned as an effective method for sharing these. it is a disposal method in which surface modification processing hardens the neighborhood of the surface of material, and an inside holds toughness. [1-3]. the surface modification processing methods include many processing methods including carburizing and a nitriding, such as a fine particle peening. [4-6]. the vacuum carburizing processing which is one of the surface modification disposal methods is a disposal method excellent in the improvement in fatigue characteristics, because oxygen is not included during carburizing atmosphere and i k. nambu et alii, frattura ed integrità strutturale, 34 (2015) 271-279: doi: 10.3221/igf-esis.34.29 272 an internal oxidation etc. do not occur. moreover, because this is pollution-free and there is little consumption of carburizing gas, it is saving resources and energy-saving technologies. [7-9]. there is gears as typical parts which perform carburizing processing. in recent years, also in the toothed wheels, a raise in a hardness and a miniaturization are strongly desired with low-fuel-consumption-izing and the weight saving of a motorcar, and also the engine higher power. the steel for dsg2 quantity hardness gears in which there were few internaloxidation layers which have on the fatigue strength of carburizing material, and they aimed at improvement in the toughness of a carburizing layer from this is developed. in old research, there are few measures of the research on the fatigue strength of vacuum carburizing material, and the research for dsg steel which is an exotic material is hardly found. it is the purpose that this research clarifies influence of vacuum carburizing processing on the fatigue strength of steel for dsg2 quantity hardness gears. test materials and test pieces est specimens were used for high strength gear steel dsg2. the chemical composition shown in tab. 1. first, thermal refining (primary quenching 1163k × 30min after holding oil cooling, secondary quenching 1113k × 30min after holding oil cold, tempering 463k × 1h after holding air cooling) is performed. the specimen was processed into the shape and size which are shown fig. 1, and were mirror-finished by polishing and water buffing. after creating these specimens, in order to remove the residual stress due to processing, vacuum annealing (873k 60 min) was performed. c si mn cu ni c r mo 0.21 0.19 0.72 0.12 0.06 0.99 0.16 table 1: chemical composition (mass.％). figure 1: shape and dimensions of specimen (in mm) vacuum carburizing treatment conditions pecimens were included in this study were two types. tempered material (qt material) and carburizing material (vc material) were prepared. vc material vacuum carburization process is performed at a heat pattern shown in fig. 2. in the vacuum carburization process of the present study were subjected to carburizing hardening rate is 38% in all specimens. fatigue crack propagation test method he fatigue-crack progress experiment was carried out with a four-point-bending fatigue-test system. the fatiguecrack progress experiment was carried out with a four-point-bending fatigue-test system. usually, when doing a crack progress experiment, after introducing a crack beforehand, it is common to perform the stress relieving t s t k. nambu et alii, frattura ed integrità strutturale, 34 (2015) 271-279: doi: 10.3221/igf-esis.34.29 273 anneal which removes the work-hardening region formed near the crack tip. however, in this research, because it was surface modification material, the vacuum anneal after crack generating was not performed. electro-hydraulic servo fatigue testing machine was used to test. the loading-capacity fixed experiment was done for qt and vc material under the conditions of maximum load pmax=4000 7000n. moreover, the δk fixed experiment was done under the conditions of δk=18~36 mpa√m. the experiment was done by the stress ratio r= 0.1 and the sine wave with a frequency of f= 20 hz. in addition, the crack measurements of length was performed by 100 times using the portable optical microscope. moreover, the measurement of crack opening stress was called for from the relationship between a loading capacity and a strain using the strain gauges. figure 2: heat pattern of carburizing residual stress, residual austenite and hardness measurement method he residual stress and the amount of retained austenites in the depth-of-cut direction were measured using the pspc/msf system. each measurement condition is shown in tab. 2 and 3. the hardness measurement was performed by the loading capacity of 2.94n using the micro vickers measuring machine. measurement principle counter method characteristic x-ray cr-kα diffraction 211 diffraction angle (deg) 156.4 stress constant k(mpa/deg) -318 slit diameter (mm) 4 tube voltage (kv) 30 tube current(ma) 20 incident angle (deg) 5, 25, 35, 45 analysis method half width method diffraction α-phase:(211) γ-phase:(220) diffraction angle (deg) α-phase:156.4 γ-phase:128.4 table 2: x-ray conditions for residual stress measurement. table 3:x-ray conditions for retained austenite measurements. residual stress, residual austenite and hardness measurement result he amount of retained austenites of the depth-of-cut direction of each processing material is shown in fig. 3. as shown in a figure, as compared with qt material, the retained austenite of vc material is increasing greatly. this is considered to be what is depended on austenite having been stabilized when the ms-point temperatures fell with the increase of value in the amount of carbon by vacuum carburizing. residual stress distribution of the depth-of-cut direction in each processing material is shown in fig. 4. as shown in a figure, vc material is about -100 mpa almost uniformly to 100 micrometers. t t k. nambu et alii, frattura ed integrità strutturale, 34 (2015) 271-279: doi: 10.3221/igf-esis.34.29 274 the depth-of-cut direction hardness distribution of each processing material is shown in fig. 5. as shown in a figure, vc material showed the maximum hardness of hv800 on the surface, and went up about 2.6 times as compared with hv400 of qt material. moreover, an effective hardening depth is 1.2 mm from the surface. figure 3: retained austenite distribution from surface figure 4: residual stress distribution from surface figure 5: vickers hardness distribution from surface relationship of crack growth rate da / dn and stress intensity factor width δk he relationship of crack progress speed da/dn and stress intensity factor width δk in the case of the conditions of pmax=7000 is shown in fig. 6. in the case of surface modification processing material, the progress behaviors of a surface crack and an internal crack differ, and it is thinkable that a crack entering edge curves greatly. about this, by report of egami et al [10], if the rate of internal crack pallet-length b to surface-crack length a is set to m, the following expressions of relations will be materialized among both. b=ma-c (1) t k. nambu et alii, frattura ed integrità strutturale, 34 (2015) 271-279: doi: 10.3221/igf-esis.34.29 275 in the case of nitriding processing material, this value is 0.92, and it is clear that there is no big difference in a surface crack and an internal crack length. it is thought that it is because progress of a crack is controlled by internal toughness rather than the surface modification layer as this reason. fig. 7 showed the observation state in that case typically. as shown in figure, the crack in case progresses in brittleness. however, crack progress is affected by the influence of base metal part, and progress is controlled. if only the hardened layer is observed, a crack progress speed will become early extremely by a brittle fracture, but because it is affected by the influence of a base metal part, it is thinkable to progress with configuration like illustration. therefore, the surface-crack length and internal crack length of the surface modification material which has a surface-hardening layer are considered to be an almost comparable length. therefore, it is thought that a stress intensity factor is computable using a surface-crack length. vc material showed bigger crack progress speed da/dn than qt material immediately after crack generating. then, after the crack growth rate of vc material became a low value and reached the local minimum rather than qt material, it showed the tendency to go up again. this reason is considered that crack progress was controlled because the opening of the crack was barred by the crack closure effect by the compressive residual stress given to the carburizing layer. moreover, as sugimoto et al.[11] is also described, when the retained austenite of a carburizing layer carries out a processing induction martensitic transformation with crack progress, a compression stress place is formed at the tip of a crack, and it is thought that crack progress was controlled. however, the area which has on crack progress is only a parts which has influence of a carburizing layer. the influence of a base metal part becomes large with progress of a crack. therefore, after a crack progress speed shows the local minimum, a crack growth rate rises and shows the same crack progress speed as a base metal. as mentioned above, it became clear that the carburizing layer has affected control of a crack progress speed. moreover, it is thinkable that the crack progressed in brittleness in the carburizing layer as a reason which showed the value with a big crack progress speed immediately after crack generating. figure 6: relation between da/dn and δk. figure 7: schematic diagram of crack propagation. δk constant test results n the loading-capacity fixed experiment shown for the preceding clause, because δk also increases with progress of a crack, it is difficult to consider the influence of a carburizing layer in detail. then, in order to consider the influence of a carburizing layer, the δk fixed experiment was done. the relationship of crack progress speed da/dn and crack length a in each δk was shown in fig. 8. the tendency to go up after a crack progress speed falls by the case of all the δ k in vc material like the case of a loadingcapacity fixed experiment, as shown in a figure. from this, the depth of a carburizing layer is presumed to be about 2.6 mm also from the crack length having been in agreement at about 2.6 mm. this shows that the carburizing layer has occurred until more deeply than an effective carburizing layer. (hv550). although the value up to 1.2 mm is shown by i k. nambu et alii, frattura ed integrità strutturale, 34 (2015) 271-279: doi: 10.3221/igf-esis.34.29 276 the hardness distribution mentioned above, the hardness of vc material decreases smooth and is in agreement with the hardness of qt material. the depth to converge is mostly in agreement with 2.6 mm of an above-mentioned carburizing layer. the position of the local minimum of the crack progress speed to δk=30 mpa√m is near a = 1.25mm. in δk=36 mpa√m, the position of the local minimum is near 1.6 mm to it. moreover, it became clear that a crack progress speed becomes fixed in a depth of 2.6 mm. in addition to it, it was also shown clearly the prohibitive power over crack progress of a carburizing layer and that δk followed on going up and had become weaker. the reason the position of the local minimum in high δk changes from the above thing is explained. in crack progress, the crack progress resistance accompanying a crack closure formation process decreases with crack progress, and a steady value is shown. it is expected to it that the crack shielding effect by the processing induction martensitic transformation by the crack progress in a carburizing layer is decided by the value of retained austenite and δk. in order that retained austenite may show the tendency which decreases in the depth-of-cut direction, the shielding effect accompanying it also becomes the same. because the assortment of these two effects serves as progress resistance, it is expected that the local minimum changes. therefore, in higher δk, after the high crack progress speed after crack generating is shown, a speed falls gradually, and after a crack progress speed falls to a= 2.6 mm, without showing the tendency to go up after that again, becoming fixed is guessed. figure 8: relation between crack length and crack propagation rate under constant δk. effects of δk that can be placed on each crack length ext, in order to see the influence of δk in each crack length, the relationship between crack progress speed da/dn in a crack length and δk shown in fig. 8 as a solid line was shown in fig. 9. moreover, it is thought that it is to 2.6 mm to have influence of a carburizing layer also from the 2.6-mm approximated curve and the gradual increase curve of qt material being in agreement. in addition, 0.5mm, 1.0mm, 1.25mm and δk do not match. this formation process of crack propagation mechanism or closing action which means different. on the other hand, because 0.5 mm, 1.0 mm, 1.25 mm, and δk are not in agreement, it is thinkable that the formation processes of a crack progress mechanism and a crack closure effect differ. then, in order to consider the influence of the crack closure effect by a carburizing layer, effective stress expansion coefficient width δkeff in fig. 8 was shown in fig. 10. as shown in a figure, in the case of a= 2.6 mm, it is thinkable that an crack closure effect and a progress mechanism are also almost the same. moreover, if it arranges by δkeff also in 1.25 mm, since an approximated curve is in agreement with qt material, it turns out that the crack progress speed was changing with the transitions of the crack opening loading capacity by the difference in the formation process of the crack closure by a carburizing layer. however, in a = 0.5 mm, since qt material and an approximated curve are not in agreement at all, it is guessed that the difference in a destructive configuration is a difference in a crack progress behavior. n k. nambu et alii, frattura ed integrità strutturale, 34 (2015) 271-279: doi: 10.3221/igf-esis.34.29 277 figure 9: relation between δk and da/dn at each points. figure 10: relation between δkeff and da/dn at each points. a study on the crack propagation behavior of carburized layer hen, the following conclusions were obtained from the result of fracture-surface observation. the crack progress process of vc material was classified into four stages from the crack progress behavior and the fracture-surface photograph. about each stage, the destructive configuration by the crack progress in vc material was shown. facture surface in fig. 11, schematic diagram is shown in fig. 12. each area is defined as follows. figure 11: change of fracture surface morphology with crack propagation.  stage a: in this stage, the influence of a crack closure effect is not shown by brittleness, but a quick crack progress speed is shown. also in a fracture surface, an intergranular fracture is mainly shown, and some transgranular fracture follows.  stage b: the influence of the compressive residual stress by a carburizing layer and a processing induction martensitic transformation is an area which appears most, a crack progress speed falls and the local minimum is shown. although t k. nambu et alii, frattura ed integrità strutturale, 34 (2015) 271-279: doi: 10.3221/igf-esis.34.29 278 the mixed fracture surface of transgranular fracture and an intergranular fracture is shown in a fracture surface, an intergranular fracture is a dominant fracture surface.  stage c: because the influence of a carburizing layer becomes weak, the influence of a plastic region appears and a crack progress speed rises gradually. in a fracture surface, it becomes a mixed fracture surface of a brittle fracture and a ductile rupture, and transgranular fracture is main.  stage d: because a crack progresses considerably and the influence of a carburizing layer is lost completely, a crack progress speed turns into a fixed speed like qt material. a fracture surface is only a ductile rupture. figure 12: change of fracture surface with applied stress intensity factor range and distance from notch root. as shown in the schematic diagram, in high delta k-value, stage area a continued to some extent, the stages b and c were short, and going to the stage d immediately was checked. moreover, the crack progress behavior which begins from a stage area b was shown by low delta k-value. thus, also from the fracture-surface configuration which changes with external load or crack progress parts being shown, it was suggested that the crack progress behavior is governed by external load and the crack progress part. if in other words the maximum-stress value which acts on the application part of material is decided, it will be thought possible to decide the rate of optimal effective carburizing as all the lifetime. moreover, about the point shown by fig. 8~12, even if materials differed, it was suggested that these things are applicable to steel material by performing vacuum carburizing processing. conclusion n this research, the surface modification effect over the fatigue-crack progress characteristic of dsg2 steel that vacuum carburizing processing was performed was examined, and the following results were obtained. 1. the maximum surface hardness of vc material showed one about 2.6 times the value of this as compared with qt material. moreover, the compressive residual stress was about -100mpa. 2. the crack progress speed of vc material fell, after the high crack progress speed was shown, and after it showed the minimum, it showed the tendency to go up again. this is considered to be what is depended on the compressive residual stress given to the carburizing layer. from this, it is thinkable that there is a crack progress depression effect in a carburizing layer. 3. in vc material, a carburizing layer has a crack progress depression effect from a plunger-helix bottom to about 2.6 mm, and it turned out that it is larger than an effective carburizing layer. moreover, in each δk, it was shown that depression effect revelation differs and the crack progress process accompanying it was able to be shown typically. references [1] yoshida, a., fujii, m., h. nakajima, influence of surface modification on rolling contact fatigue of steel rollers : in case of pure rolling contact condition, transactions of the japan society of mechanical engineers. c, j. soc. mat. sci., japan, 49(11) (2000), 1235-1241; 66 (2000) 275-282. i k. nambu et alii, frattura ed integrità strutturale, 34 (2015) 271-279: doi: 10.3221/igf-esis.34.29 279 [2] takakuwa, o., sanada, k., soyama, h., evaluation of fatigue crack propagation in surface modification layer by a load-controlled plate bending fatigue tester, transactions of the japan society of mechanical engineers, 80 (2014) 275-282. [3] naoe, t., konagawa, h., wakui, t., futakawa, m., takeuchi, h., bending fatigue strength of surface modified stainless steel with pitting damage, j. soc. mat. sci., japan., 57 (2008) 576-582. [4] ishigami, i., yokoyama, y., miura, k., uratani, f., hoshino, h., relationship between treating condition sand surface carbon concentration of low carbon steel vacuum –carburized with propane, j. soc. mat. sci., japan, 49(11) (2000) 1235-1241. [5] morimoto, t., umemoto, m., the effect of over-carburizing on the fatigue strength at edges of vacuumcarburized samples, tetsu-to-hagané, 96 (2010) 400-405. [6] egami, n., kagaya, c., inoue, n., takeshita, h., mizutani, h., hybrid surface modification of scm415 material by vacuum carburizing and fine particle peening, transactions of the japan society of mechanical engineers. a, 66 (2000) 1936-1942. [7] nambu, k., saruki, k., kondo, s., the influence that shot peening and micro straight notch give to rotary bending fatigue strength of the high si hard-drawn wire, transactions of the japan society of mechanical engineers, a, 76 (2010) 1936-1942. [8] kikuchi, s., nakahara, y., dobashi, k., komotori, j., effects of fpp/gas nitriding hybrid surface treatment on fatigue properties of austenitic stainless steel (sus316), j. soc. mat. sci., japan, 61 (2012) 680-685. [9] ochi, t., kozawa, s., kubota, m., crack propagation behavior and change of residual stress on the process of bending fatigue test of carburized steel tetsu-to-hagané, 97 (2011) 486-492. [10] egami, n., yamada, m., kagaya, c., fujii, k., effect of surface modification by tufftriding on fatigue strength behaviors of sm 490 a, transactions of the japan society of mechanical engineers. a, 63 (1997) 1829-1836. [11] sugimoto, k., sun, x., kobayashi, m., haga, t., shirasawa, h., fatigue properties of trip-aided dual-phase sheet steel, transactions of the japan society of mechanical engineers. a, 63 (1997) 717-724. microsoft word 2323 z. hu et alii, frattura ed integrità strutturale, 47 (2019) 383-393; doi: 10.3221/igf-esis.47.28 383 the strain energy density to estimate lifetime of notched components subjected to variable amplitude fatigue loading zheng hu science and technology on vehicle transmission laboratory, china north vehicle research institute, beijing, china, 100072 huzhengvip@126.com filippo berto norwegian university of science and technology, no-7491 trondheim, norway filippo.berto@ntnu.no, http://orcid.org/0000-0001-9676-9970 luca susmel department of civil and structural engineering, the university of sheffield, sheffield s1 3jd, uk l.susmel@sheffield.ac.uk, https://orcid.org/0000-0001-7753-9176 abstract. in the present paper, the approach based on the strain energy density (sed) averaged over a structural volume is reformulated to estimate the lifetime of notched components subjected to variable amplitude (va) uniaxial fatigue loading. the accuracy and reliability of the proposed reformulation of the sed approach was checked against a large number of data taken from the literature and generated, under two different load spectra, by testing specimens of carbon steel c40 containing notches of different sharpness. such a validation exercise allowed us to demonstrate that the extension of the sed approach as proposed in the present paper is capable of accurately estimating fatigue damage in notched components subjected to inservice va fatigue loading. keywords. strain energy density; notch; variable amplitude loading. citation: hu z, berto f, susmel l, the strain energy density to estimate lifetime of notched components subjected to variable amplitude fatigue loading, frattura ed integrità strutturale, 47 (2019) 383-393. received: 15.11.2018 accepted: 04.12.2018 published: 01.01.2019 copyright: © 2019 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. introduction ost components contain material defects or geometric discontinuities. examination of the state of the art demonstrate that the effect of stress concentrators on the fatigue strength of engineering materials has been investigated by considering mainly constant amplitude (ca) fatigue situations. however, most components experience variable amplitude (va) fatigue load histories which make the characteristics of the critical local stress/strain states more complex, with this affecting markedly fatigue strength. m http://www.gruppofrattura.it/va/47/2323.mp4 z. hu et alii, frattura ed integrità strutturale, 47 (2019) 383-393; doi: 10.3221/igf-esis.47.28 384 in order to predict in-service lifetime of notched components under va loading, it is important to make use of specific methods suitable for taking into account the way fatigue damage accumulates itself. palmgren [1] and miner [2] first formulated this concept in a mathematical form as: f ,( / )i id n n  (1) where d denotes the cumulative damage sum, and ni and nf,i are the applied cycles and the total number of cycles to failure under the ith constant amplitude stress level, respectively. when engineering metallic materials are damaged by va load histories, failure is supposed to occur as soon as the critical value of cumulative damage sum dcr is equal to unity. however, experimental evidence under va loading condition indicates that in situations of practical interest dcr varies in the range 0.02-5 [3, 4]. clearly, this fact can produce a remarkable discrepancy between estimated and actual lifetime, with this calculation resulting in non-conservative predictions. (a) (b) figure 1: (a) geometries of the tested notched samples (dimensions in millimetres). (b) fatigue results generated under ca uniaxial fatigue loading [3]. fatigue life estimation techniques based on local approaches require some detailed information about the stress-strain state around the notch tip [3, 5-9]. different sed-based approaches to deal with notch fatigue problems have been formulated since the beginning of the last century. recently, lazzarin et al. [8, 10, 11] developed a volume-based approach, in which the sed calculations are carried out in a material-related control volume. the averaged sed approach z. hu et alii, frattura ed integrità strutturale, 47 (2019) 383-393; doi: 10.3221/igf-esis.47.28 385 is based both on a precise definition of the control volume and on the fact that the critical energy does not depend on the notch sharpness. the control radius r0 of the volume is a material property, which involves the plain specimen’s fatigue limit and the threshold stress intensity factor range [10]. the approach was successfully used under both static and ca fatigue loading conditions to assess the strength of notched components subjected to uniaxial [12-14] as well as to multiaxial loading [15-19]. even if a lot of theoretical and experimental work has been carried out to check the accuracy and reliability of the sed approach, surprisingly, so far no systematic attempt has been made to extend the use of this powerful method to those situations involving va fatigue loading. accordingly, the ultimate goal of the research work summarized in the present paper was to reformulate the sed approach to make it suitable for assessing fatigue lifetime of notched components subjected to va uniaxial fatigue load histories, with this being done by using a suitable cycle counting method (i.e., the rain-flow method [20]) as well as a suitable cumulative damage model (i.e., palmgren and miner’s rule [1, 2]). experiment details n a recent work, susmel and taylor [3] tested under uniaxial va fatigue loading circumferentially notched specimens made of a medium-carbon steel c40 and containing three different geometrical features. the geometry of the tested specimens is reported in fig. 1a along with details of the notches that were characterized by three different values of the notch tip radius and opening angle. static tensile tests were performed in order to evaluate the mechanical properties according to the astm standard procedure. the yield stress, tensile stress and young’s modulus of the investigated materials were 672 mpa, 852 mpa and 209000 mpa, respectively. the net stress concentration factor, kt, was calculated by solving standard linear-elastic finite element (fe) models where the mesh density in the notch region was gradually increased until convergence occurred. this standard numerical procedure returned a kt value under tension equal to 4.42, 2.2 and 1.66 for the specimens with a root radius of 0.225, 1.2 and 3 mm, respectively. both ca and va fatigue tests were carried out in axial load control under a nominal load ratio, r=σmin/σmax, equal to -1 at a frequency of 4 hz. all the ca fatigue results are summarised in the wöhler diagrams of fig. 1b in terms of nominal stress amplitude evaluated onto the net cross-sectional area of the specimens. fig. 1b shows the fatigue data generated by testing both the un-notched specimens and the v-notched samples with root radius equal to 0.225 mm (kt = 4.42). the statistical analyses have been performed assuming a log-normal distribution of the number of cycles to failure for each stress amplitude. all data obtained from specimens characterized by a fatigue life between 104 and 2106 have been taken into account in the statistical analyses. it is worth observing here that the scatter bands plotted in the chart of fig. 1b were calculated for each stress level by assuming a confidence level equal to 95%. the results from the statistical re-analysis are summarised in tab. 1 in terms of: nominal stress amplitudes (σa for the plain specimens and σan for the notched samples) for a probability of survival ps =50% at a reference number of cycles to failure, na, equal to 106; inverse slope, k, of the wöhler curves and the scatter index tσ that provides the width of the scatter band between the curves with a probability of survival of 10% and 90% respectively (with a confidence level equal to 95%). specimen type rn(mm) dg(mm) dn(mm) (°) k σa, σan*(mpa) t kt plain 12 6 9.4 292.8 1.211 1.0 sharp 0.225 12 9.15 35 4.2 97.8 1.361 4.42 table 1: summary of the experimental results generated under fully-reversed ca loading [3]. as to the performed va tests, the specimens were tested under the two different random spectra (fig. 2) having sequence length, ntot =ʃni, equal to 1000 cycles. all the random spectra were repeated until failure of the specimens occurred. in particular, the concave upwards spectrum (cus) was derived from a conventional rayleigh distribution, whereas the concave downwards spectrum (cds) was defined so that we could have few cycles with high stress ranges combined with a relatively large number of cycles with low stress ranges [21]. the aim of two different spectra of tests was to determine the effect of spectrum shape on the fatigue lifetime of the notched material being investigated and to determinate the fatigue lifetime under random block loading. all the results generated by susmel and taylor [3] are summarized in tabs. 2-4, where the performed tests are described in terms of adopted spectrum, maximum force, fa,max, maximum amplitude in the spectrum of the axial, σa,max, load ratio, r, and experimental value of the number of cycles to failure, nf. for comparison, tab. 5 shows the fatigue results generated by testing plain samples under the two load spectra. tab. 5 also reports the corresponding experimental values of the critical damage sum, dcr,exp, calculated by using experimental ca plain wöhler curve. i z. hu et alii, frattura ed integrità strutturale, 47 (2019) 383-393; doi: 10.3221/igf-esis.47.28 386 (a) (b) figure 2: adopted load spectra (a) cus and (b) cds [3]. code spectrum fa,max(kn) σa,max(mpa) r nf(cycles) s2_va cus 34.2 520.1 -1 20975 s3_va cus 34.2 520.1 -1 21568 s4_va cus 18.4 279.8 -1 170155 s6_va cus 18.4 279.8 -1 182155 s7_va cus 25.6 389.3 -1 66703 s9_va cus 25.6 389.3 -1 61594 s10_va cds 65.8 1000.7 -1 8620 s12_va cds 49.3 749.7 -1 45620 s13_va cus 14.4 219.0 -1 391420 s14_va cds 65.8 1000.7 -1 7620 s15_va cds 49.3 749.7 -1 42620 s16_va cds 35.4 538.4 -1 179620 s17_va cus 14.4 219.0 -1 339763 s19_va cds 28.4 431.9 -1 367620 s20_va cds 35.4 538.4 -1 172620 s21_va cds 28.4 431.9 -1 376620 table 2: summary of the experimental results generated by testing the notched specimens with root radius equal to 0.225 mm under va fatigue loading [3]. code spectrum fa,max(kn) σa,max(mpa) r nf(cycles) i1_va cus 35.5 520.4 -1 37568 i2_va cus 29.5 432.4 -1 84463 i3_va cus 23.5 344.5 -1 170581 i4_va cus 35.5 520.4 -1 34044 i5_va cus 29.5 432.4 -1 83663 i6_va cus 23.5 344.5 -1 253927 i7_va cds 65.4 958.6 -1 10620 i8_va cds 48.5 710.9 -1 78620 i9_va cds 65.4 958.6 -1 11905 i10_va cus 20.5 300.5 -1 715859 i11_va cds 31.0 454.4 -1 732620 i12_va cds 31.0 454.4 -1 531620 i13_va cds 37.0 542.4 -1 285277 i14_va cus 20.5 300.5 -1 588009 i15_va cds 48.5 710.9 -1 76620 i16_va cds 37.0 542.4 -1 330620 table 3: summary of the experimental results generated by testing the notched specimens with root radius equal to 1.2 mm under va fatigue loading [3]. z. hu et alii, frattura ed integrità strutturale, 47 (2019) 383-393; doi: 10.3221/igf-esis.47.28 387 code spectrum fa,max(kn) σa,max(mpa) r nf(cycles) b1_va cus 42.0 631.8 -1 18736 b2_va cus 42.0 631.8 -1 15715 b3_va cus 33.0 496.4 -1 65733 b4_va cus 24.0 361.0 -1 274715 b5_va cus 27.5 413.7 -1 118044 b6_va cus 24.0 361.0 -1 300763 b7_va cus 33.0 496.4 -1 63450 b8_va cus 27.5 413.7 -1 138975 b9_va cds 65.0 977.8 -1 13620 b10_va cds 49.0 737.1 -1 85397 b11_va cds 39.0 586.7 -1 352620 b12_va cds 39.0 586.7 -1 300216 b13_va cds 65.0 977.8 -1 12620 b14_va cds 33.5 503.9 -1 665620 b15_va cds 33.5 503.9 -1 749620 b16_va cds 49.0 737.1 -1 78392 table 4: summary of the experimental results generated by testing the notched specimens with root radius equal to 3 mm under va fatigue loading [3]. spectrum σa-max(mpa) r nf(cycles) dexp cus 728.6 -1 14763 0.59 cus 728.6 -1 13525 0.54 cus 594.2 -1 49450 0.29 cus 512.8 -1 264594 0.38 cus 512.8 -1 219086 0.32 cds 891.3 -1 32620 1.31 cds 735.6 -1 136620 0.91 cds 618.9 -1 356620 0.47 cds 891.3 -1 23620 0.95 cds 618.9 -1 380085 0.50 average value= 0.63 table 5: summary of the experimental results generated by testing the plain samples under fully-reversed va loading and experimental values of the critical damage sum, dcr [3]. the sed to estimate lifetime of notched components under ca fatigue loading n recent years, the strain energy density (sed) has been widely used to estimate the fatigue lifetime of notched components subjected to ca fatigue loading [10, 12, 13, 22, 23]. the averaged sed approach states that failure occurs when the mean value of the strain energy density averaged over a control volume surrounding the notch tip is equal to a critical energy value. for rounded v-notches, the control volume is as depicted in fig. 3, where its radius r0 does not depend on the notch geometry. in more detail, r0 is the depth of the crescent shape as measured along the notch bisector line. the outer radius of the control volume equals r0+r0, where r0 is defined as a function of both the notch opening angle 2α and the notch root radius ρ, according to the following relationship: 0 2 2 2 r          (2) dealing with the fatigue assessment of notched components, the control radius, r0, can be defined by imposing the equality, with reference to the fatigue limit condition [24], between the averaged sed relevant to the plain specimens and that obtained from v-notched specimens with known geometry, i.e.: i z. hu et alii, frattura ed integrità strutturale, 47 (2019) 383-393; doi: 10.3221/igf-esis.47.28 388 2 a,p notch 0 plain 0 ( ) 2 ww r e     (3) where a,p is the fatigue strength of the plain sample at na cycles and e is the elastic modulus. by varying the control radius r0 around the notch tip in an fe model under the nominal stress σa,n, the corresponding values of strain energy density notchw averaged over the control volume can be determined. then the numerical value notch 0( )w r as a function of the control radius r0 is generated by a fitting equation. finally, the control radius r0 of the critical volume can be calculated since it is equal to the strain density energy of the plain sample, plain0w . due to the absence of experiment data related to stress intensity factor, the control radius can be easily evaluated by the procedure above. figure 3: definition of the control volume for specimens weakened by rounded v-notch. the averaged sed can also easily and quickly be calculated from fe analyses by summing the energy contributions welement,i for all the finite elements within the control volume v, i.e.: element ,v i w w w c v   (4) eq. (4) defines the so-called direct approach to evaluate the sed parameter. in order to consider the influence of the nominal load ratio r, the weighting parameter cw has to be adopted by using the following expressions [25, 26]: 2 2 2 2 1 for 0 (1 ) ( ) 1 for 0 1 for 0 1 (1 ) w r r r c r r r r r               (5) additionally, it is important to know that refined mesh in the control volume around the notch tip is not necessary to determine the value of the sed, because this parameter can be determined via the nodal displacements, without involving their derivatives. this means that the adopted fe meshes can be very coarse inside the control volume having radius r0 when accurately evaluating the value of the local sed [27]. the assumption of the sed as a damage parameter allows to summarize a large number of fatigue data obtained for notched specimens in a reasonable scatter band [10, 23, 28]. generally, it is important to understand the fatigue behaviour of notched components and to assess the fatigue strength without performing a large number of experiments. therefore, in order to predict the fatigue life of components having different geometrical features, the sed, w , versus the fatigue life, nf, relationship is calculated by considering the notched samples as sharp as possible. the averaged sed, w , can z. hu et alii, frattura ed integrità strutturale, 47 (2019) 383-393; doi: 10.3221/igf-esis.47.28 389 be obtained from the post-processing results by applying the value of nominal stress in the fe models. the relationship of the sed, w , and the fatigue life, nf, can be written as: f bw a n   (6) where a and b are material constants. keeping constant the material and the nominal load ratio, the fatigue life can be assessed by using eq. (6) for any geometrical configuration of the notch. the sed to estimate lifetime of notched components under va fatigue loading n the presence of va load histories, the value of the sed will change as the amplitudes of the applied load spectrum vary. this clearly implies that, to correctly extend the use of the sed to those situations involving va loadings, the procedure of the sed has to be redefined coherently according to the specific features of the assessed load spectrum. when the notched sample is subjected to the va fatigue loading, the va load spectrum can be counted by the rain-flow method [20]. such a spectrum is formed by j different stress levels that are characterized by a nominal stress amplitude equal to a-i as shown in fig. 4. the corresponding number of cycles is equal to ni(i=1,2,…,j), where: tot 1 j i i n n   . figure 4: estimation of the fatigue lifetime under va loading by sed. the different stress levels forming the above load spectrum can be treated as an independent ca loading, which can be applied in the fe model to obtain the value of the sed. then, the corresponding number of cycles to failure nf,i can directly be determined according to the relation of sed versus the fatigue life nf obtained by eq. (6). as formalized by palmgren and miner [1,2], the fatigue damage content associated with any stress level can be calculated as follows: f, i i i n d n  (7) the resulting total damage is equal to: w i z. hu et alii, frattura ed integrità strutturale, 47 (2019) 383-393; doi: 10.3221/igf-esis.47.28 390 j tot i 1 f, i i n d n   (8) finally, the number of cycles to failure, f,en , can be estimated from the predicted number of blocks to failure, b,en , i.e.: cr b,e f,e tot b,e tot d n n n n d     (9) where crd is the critical value of the damage sum. validation by experimental data he data used to validate the proposed extension of the sed approach are those generated by susmel and taylor by testing the notched samples of c40 under both the concave upwards spectrum (cus) and concave downwards spectrum (cds) [3]. as to the strain energy density analysis, the cylindrical samples were modelled by using axisymmetric bi-dimensional model with coarse meshes inside the volume. by applying the net nominal stress σan at 106 cycles to the fe model, the numerical values of notchw as a function of the critical radius r0 were obtained as shown in fig. 5. it is observed that the value of the critical radius r0 is about 0.11 mm when the value of the sed for the v-notched specimen equals to that of plain specimen, plain 0w . figure 5: numerical values of notchw as a function of the critical radius r0. the value of the sed averaged over the control volume was also calculated numerically by using the fe method. as shown in fig. 4, a set of stress levels are acquired after calculating the load spectrum by rain-flow method. then, the values of the sed of notched specimens with the sharpest radius are evaluated by applied above stress levels in the fe model. according to eq. (6), the relationship of the sed w versus fatigue life nf under ca fatigue loading is -0.5266 f=242.4w n (10) where the constants in eq. (10) are determined by a best fit to a series of calculated data. as to the critical value of the damage sum, dcr, initially the hypothesis was formed that it could be taken equal to its average value experimentally determined from the plain samples, dcr,exp=0.63. the obtained results with different notch t z. hu et alii, frattura ed integrità strutturale, 47 (2019) 383-393; doi: 10.3221/igf-esis.47.28 391 root radius are summarized in the experimental, nf, vs. estimated, nf,e, fatigue lifetime diagrams reported in fig. 6a. the predictions with small notch radius made using the sed are seen to fall always within the parent material scatter band. for the medium notch radius, the predicted results mostly fall within the patent material scatter band. the predictions with large notch radius nearly fall outside of the parent material scatter band, and on the non-conservative side. in this case, the accuracy of the predicted results is higher as the notch becomes sharper. as shown in fig. 6a, the novel formalization of the sed is seen to be capable of accurately assessing the fatigue lifetime of notched specimens under va loading by adopting simple palmgren-miner rule. using this approach can reduce the time and costs associated with the design process. figure 6: the accuracy of sed in estimating the fatigue lifetime of the notched samples under two critical value of the damage sum, dcr. (a) dcr=0.63. (b) dcr=1. the same analysis as above was performed also by taking, as suggested by the classical theory by palmgren and miner, a critical value for the damage sum equal to unity. the diagram reported in fig. 6b shows that for the damage sum equal to unity, the level of non-conservatism of increases, resulting in poor accurate estimates. the predictions with small notch radius have the highest accurate estimates, but on the non-conservative side. other predictions with medium and large notch radius mostly fall outside of the parent material scatter band and on the non-conservative side. it is also interesting to note that the estimated results under cus are higher accuracy than the results under cds, which shows that the loading shape has obvious effect on the fatigue behaviour. in the cds, the cycles of low stress levels take up the majority of the sequence length, which would make the prediction a little inaccurate. according to the experimental evidence (tab. 5), the critical value dcr of plain specimens varied as the shape of the load spectrum change. dcr under the cus spectrum is lower than the value of critical damage sum under the cds spectrum. such a high variability shows that the critical value of critical damage sum strongly affects the accuracy of predicted fatigue lifetime. so far, the only way to correctly obtained dcr is by running enough experiments. though many damage sum theories have also been developed [29-35], unfortunately, none of them enjoys universal acceptance due to the complexity of the problem, such as nonlinear damage, load sequence and small amplitude stress below fatigue limit. consequently, the palmgren-miner rule is still dominantly used in design, in spite of its major shortcomings. more efforts on the cumulative damage are needed in order to provide design engineers with a general and reliable fatigue damage analysis and life prediction approach. conclusions n the present work, the fatigue criterion based on the strain energy density (sed) has been applied to re-analyse some experimental results reported in the recent literature. the specimens being considered were characterized by three notch tip radius and tested under uniaxial loading. the relationship of the averaged sed and the number of cycles to failure was calculated by considering the sharper specimens. according to above the relationship and the rainflow method, the novel formalization of the sed proposed was seen to be accurate in estimating fatigue lifetime of 1000 10000 100000 1000000 1e7 1000 10000 100000 1000000 1e7 non-conservative cus,plain cds,plain cus,0.225 mm cds,0.225 mm cus,1.2 mm cds,1.2 mm cus,3 mm cds,3 mm n f( c y cl es ) nf,e(cycles) ps=90% ps=10% parent material scatter bandconservative dcr=0.63 sed 1000 10000 100000 1000000 1e7 1000 10000 100000 1000000 1e7 cus,plain cds,plain cus,0.225 mm cds,0.225 mm cus,1.2 mm cds,1.2 mm cus,3 mm cds,3 mm n f( c y cl es ) nf,e(cycles) non-conservative ps=90% ps=10% dcr=1 sed conservative parent material scatter band i z. hu et alii, frattura ed integrità strutturale, 47 (2019) 383-393; doi: 10.3221/igf-esis.47.28 392 notched components damaged by va uniaxial fatigue loading. it has also been observed that the critical value of damage sum has obvious effects on the accuracy of estimated fatigue life. acknowledgements he authors would like to acknowledge the support by the innovation program (237099000000170004) and the state key laboratory program (614221305020617) and also by the china scholarship council (grant no. 201705290009). references [1] palmgren a. (1924). durability of ball bearings, zvdi, 68(14), pp. 339-341. [2] miner m. (1945). cumulative damage in fatigue, j. appl. mech., 12, pp. a159-a164. [3] susmel l., taylor d. (2011). the theory of critical distances to estimate lifetime of notched components subjected to variable amplitude uniaxial fatigue loading, int. j. fatigue., 33(7), pp. 900-911. [4] susmel l, taylor d. (2012). a critical distance/plane method to estimate finite life of notched components under variable amplitude uniaxial/multiaxial fatigue loading, int. j. fatigue., 38, pp. 7-24. [5] neuber h. (1958). theory of notch stresses: principles for exact calculation of strength with reference to structural form and material, 2nd ed.. berlin: springer verlag. [6] molski k., glinka g. (1981). a method of elastic-plastic stress and strain calculation at a notch root, mater. sci. eng., 50(1), pp. 93-100. [7] ellyin f., kujawski d. (1989). generalization of notch analysis and its extension to cyclic loading, eng. fract. mech., 32(5), pp. 819-826. [8] lazzarin p., zambardi r. (2001). a finite-volume-energy based approach to predict the static and fatigue behavior of components with sharp v-shaped notches, int. j. fracture., 112(3), pp. 275-298. [9] taylor d. (1999). geometrical effects in fatigue: a unifying theoretical model, int. j. fatigue., 21(5), pp. 413-420. [10] lazzarin p., berto f. (2005). some expressions for the strain energy in a finite volume surrounding the root of blunt v-notches, int. j. fracture., 135(1-4), pp. 161-185. [11] lazzarin p., berto f. (2008). control volumes and strain energy density under small and large scale yielding due to tension and torsion loading, fatigue. fract. eng. m., 31(1), pp. 95-107. [12] berto f., lazzarin p. (2013). fatigue strength of al7075 notched plates based on the local sed averaged over a control volume, sci. china. phys. mech., 57(1), pp. 30-38. [13] berto f., gallo p., lazzarin p. (2014). high temperature fatigue tests of un-notched and notched specimens made of 40crmov13.9 steel, mater. design., 63, pp. 609-619. [14] negru r., șerban d., marșavina l., magda a. (2016). lifetime prediction in medium-cycle fatigue regime of notched specimens, theor. appl. fract. mec, 84, pp. 140-148. [15] berto f., lazzarin p., yates j.r. (2011). multiaxial fatigue of v-notched steel specimens: a non-conventional application of the local energy method, fatigue. fract. eng. m., 34(11), pp. 921-943. [16] berto f., lazzarin p. (2011). fatigue strength of structural components under multi-axial loading in terms of local energy density averaged on a control volume, int. j. fatigue., 33(8), pp. 1055-1065. [17] berto f., campagnolo a., lazzarin p. (2015). fatigue strength of severely notched specimens made of ti–6al–4v under multiaxial loading, fatigue. fract. eng. m., 38(5), pp. 503-517. [18] berto f., gagani a., aversa r., petrescu r.v.v., apicella a., petrescu f.i.t. (2016). multiaxial fatigue strength to notched specimens made of 40crmov13. 9, am. j. eng. appl. sci., 9(4), pp. 1269-1291. [19] berto f., lazzarin p., yates j. (2011). multiaxial fatigue of v‐notched steel specimens: a non‐conventional application of the local energy method, fatigue. fract. eng. m., 34(11), pp. 921-943. [20] matsuishi m., endo t. (1968). fatigue of metals subjected to varying stress, japan society of mechanical engineers, fukuoka, japan, 68(2), pp. 37-40. [21] gurney t.r. (2006). cumulative damage of welded joints, woodhead publishing. [22] lazzarin p., campagnolo a., berto f. (2014). a comparison among some recent energyand stress-based criteria for the fracture assessment of sharp v-notched components under mode i loading, theor. appl. fract. mec, 71, pp. 2130. t z. hu et alii, frattura ed integrità strutturale, 47 (2019) 383-393; doi: 10.3221/igf-esis.47.28 393 [23] berto f., lazzarin p. (2014). recent developments in brittle and quasi-brittle failure assessment of engineering materials by means of local approaches, materials science and engineering: r: reports, 75, pp. 1-48. [24] razavi s., ferro p., berto f., torgersen j. (2018). fatigue strength of blunt v-notched specimens produced by selective laser melting of ti-6al-4v, theor. appl. fract. mec, 97, pp. 376-384. [25] lazzarin p., livieri p., berto f., zappalorto m. (2008). local strain energy density and fatigue strength of welded joints under uniaxial and multiaxial loading, eng. fract. mech., 75(7), pp. 1875-1889. [26] lazzarin p., sonsino c., zambardi r. (2004). a notch stress intensity approach to assess the multiaxial fatigue strength of welded tube‐to‐flange joints subjected to combined loadings, fatigue. fract. eng. m., 27(2), pp. 127-140. [27] lazzarin p., berto f., zappalorto m. (2010). rapid calculations of notch stress intensity factors based on averaged strain energy density from coarse meshes: theoretical bases and applications, int. j. fatigue., 32(10), pp. 1559-1567. [28] berto f. (2016). fatigue and fracture assessment of notched components by means of the strain energy density, eng. fract. mech., 167, pp. 176-187. [29] manson s., halford g.r. (1981). practical implementation of the double linear damage rule and damage curve approach for treating cumulative fatigue damage, int. j. fracture., 17(2), pp. 169-192. [30] halford g.r. (1997). cumulative fatigue damage modeling—crack nucleation and early growth, int. j. fatigue., 19(93), pp. 253-260. [31] fatemi a., yang l. (1998). cumulative fatigue damage and life prediction theories: a survey of the state of the art for homogeneous materials, int. j. fatigue., 20(1), pp. 9-34. [32] socie d. (1987). multiaxial fatigue damage models, j. eng. mater. technol., 109(4), pp. 293-298. [33] łagoda t. (2001). energy models for fatigue life estimation under uniaxial random loading. part i: the model elaboration, int. j. fatigue., 23(6), pp. 467-480. [34] bui-quoc t. (1982). cumulative damage with interaction effect due to fatigue under torsion loading, exp. mech., 22(5), pp. 180-187. [35] aïd a., amrouche a., bouiadjra b.b., benguediab m., mesmacque g. (2011). fatigue life prediction under variable loading based on a new damage model, mater. design., 32(1), pp. 183-191. << /ascii85encodepages false /allowtransparency false /autopositionepsfiles true /autorotatepages /none /binding /left /calgrayprofile (dot gain 20%) /calrgbprofile (srgb iec61966-2.1) /calcmykprofile (u.s. web coated \050swop\051 v2) /srgbprofile (srgb iec61966-2.1) /cannotembedfontpolicy /error /compatibilitylevel 1.4 /compressobjects /tags /compresspages true /convertimagestoindexed true /passthroughjpegimages true /createjobticket false /defaultrenderingintent /default /detectblends true /detectcurves 0.0000 /colorconversionstrategy /cmyk /dothumbnails false /embedallfonts true /embedopentype false /parseiccprofilesincomments true /embedjoboptions true /dscreportinglevel 0 /emitdscwarnings false /endpage -1 /imagememory 1048576 /lockdistillerparams false /maxsubsetpct 100 /optimize true /opm 1 /parsedsccomments true /parsedsccommentsfordocinfo true 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can be opened with acrobat and adobe reader 5.0 and later.) >> /namespace [ (adobe) (common) (1.0) ] /othernamespaces [ << /asreaderspreads false /cropimagestoframes true /errorcontrol /warnandcontinue /flattenerignorespreadoverrides false /includeguidesgrids false /includenonprinting false /includeslug false /namespace [ (adobe) (indesign) (4.0) ] /omitplacedbitmaps false /omitplacedeps false /omitplacedpdf false /simulateoverprint /legacy >> << /addbleedmarks false /addcolorbars false /addcropmarks false /addpageinfo false /addregmarks false /convertcolors /converttocmyk /destinationprofilename () /destinationprofileselector /documentcmyk /downsample16bitimages true /flattenerpreset << /presetselector /mediumresolution >> /formelements false /generatestructure false /includebookmarks false /includehyperlinks false /includeinteractive false /includelayers false /includeprofiles false /multimediahandling /useobjectsettings /namespace [ (adobe) (creativesuite) (2.0) ] /pdfxoutputintentprofileselector /documentcmyk /preserveediting true /untaggedcmykhandling /leaveuntagged /untaggedrgbhandling /usedocumentprofile /usedocumentbleed false >> ] >> setdistillerparams << /hwresolution [2400 2400] /pagesize [612.000 792.000] >> setpagedevice microsoft word numero_55_art_08_2918 a. i. hassanin et alii, frattura ed integrità strutturale, 55 (2021) 110-118; doi: 10.3221/igf-esis.55.08 110 fatigue loading characteristic for the composite steel-concrete beams ahmed i. hassanin egyptian russian university, egypt ahmed_eng8028@yahoo.com, ahmed-ibrahim@eru.edu.eg, http://orcid.org/0000-0002-5606-3065 hesham m. fawzy zagazig university, egypt hmshaban@eng.zu.edu.eg ahmed i. elsheikh liverpool university, uk. ahmed.elsheikh@liverpool.ac.uk abstract. in the last few decades, composite beams, steel i beam, and concrete slab, have had a wide range of usage in bridges construction. this is due to its relatively low economic constructional cost compared to individual steel structures or reinforced concrete structures. this type of bridges in particular and many similar industrial structures in general are repeatedly subjected to fatigue loads, and that is frequently, as a result of the vehicles passing on these bridges or the vibrations caused by the machines in the industrial facilities. previous investigation of fatigue behavior of composite steel-concrete structures has become ever more important, specially, steel concrete composite beams. these studies focused mainly on the external structural behavior of these beams such as a load –deflection relation, observing of cracks appeared during the loading and failure stage, and the strain in the steel and concrete flanges. hence, in this study several factors affecting the mode of failure of these beams under the fatigue loads. ansys (workbench) software package was used to construct a finite element model subjected to cyclic loading, and obtain members’ cyclic behavior at a positive bending moment area. the results of the f.e. analysis were compared with experimental tests to obtain the validity of the finite element model and its accuracy. a parametric study was also conducted to investigate the effect of varying degrees of shear connection on the cyclic loading performance for each part of the composite section. keywords. composite beams; cyclic loading; fatigue loads; f.e.m.; shear connection. citation: hassanin, a.i., fawzy, h. m., elsheikh, a. i. fatigue loading characteristic for the composite steel-concrete beams, frattura ed integrità strutturale, 55 (2021) 110-118. received: 09.09.2020 accepted: 05.11.2020 published: 01.01.2021 copyright: © 2021 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. https://youtu.be/6vr0-woj00m a. i. hassanin et alii, frattura ed integrità strutturale, 55 (2021) 110-118; doi: 10.3221/igf-esis.55.08 111 introduction ecently, steelconcrete composite beams have been widely used in building and bridge construction. the advantages of these beams in comparison to traditional reinforced concrete girders can be clearly seen in their ability to bend and stiffness. this is due to the benefits of the composite action, which is achieved by connecting the concrete slab and steel section and utilizing the speed of manufacturing time. recently many steel-concrete composite structures failed to meet their functional and structural requirements, which was a result of corrosion and enlarged cracks resulting from fatigue caused by the dynamic loads of vehicles moving on bridges, and insufficient maintenance. the use of steel-concrete composite girders that were created in real building structures started in the 1950s, noting the phenomenon of fatigue failure, gained the attention of the designer and research community. the main member of the steel concrete composite girders is shear connectors and the type commonly type used is a shear stud. therefore, most of the research conducted on the cyclic and fatigue loading response of the steel-concrete composite girders had focused attention on the structural behavior of the shear connectors. slutter and fisher [1] performed fatigue loading tests on shear connectors and identified the welding surface between the steel top flange and shear connectors as the fatigue failure region. the tests led to a relationship between the shear stress acting on connectors and the number of loading cycles. furthermore, they proposed the “s–n” method as the most reliable for determining the shear connectors’ fatigue life. later, r.p. johnson [2] used experimental data on composite beam fatigue tests to predict the fatigue life of shear connectors:     lg n 8lg δτ 22.123 (1) where n is the number of cycles. this expression was later adopted by eurocode 4[3]. however, obtaining this equation was under the base of big experimental data’s number of and also under consideration of the guaranteed rate, so it was well suited for designers. paul geundy and geoff taplin [4] investigated the effect of cyclic load (monotonically) and fatigue load (reversely) on cumulative slippage at the surface between the steel top flange and concrete slab. they concluded that monotonic cyclic loading caused much slower growth in slippage than cyclic reversed fatigue loading. after 10 years, hanswille et al. [5], presented an equation to predict the growth in residual slippage with the number of loading cycles. follow-up research identified three stages, in which residual slip grows with loading cycles. the first stage involved fast growth in the residual slip followed by a stage of slow and stable growth before experiencing again fast growth in residual slip, which continued until failure [6–8]. in 2014 wang yu-hang et al. [7] performed fatigue analysis to study the performance of composite steel-concrete beams and shear connectors. seven beams were test to study the fatigue behavior of shear connectors in composite steel-concrete beams. shear fatigue failure of shear connectors was the failure mode for the tested beams. shear stress amplitude of shear connectors was a significant factor affecting the fatigue life of tested beams. then proposed mathematical calculations were presented to determine the deflection of the beams. so more than that, they decided to analyze more influence various parameters focused on the deflection of composite steel-concrete beams subjected to fatigue load. recently, hassanin et al.[9] conducted a numerical study on a large number of composite beams models under the influence of fatigue loads. during this study, they focused on several variables, the most important of which was changing the number of the shear studs, which results in changing the degree of shear connection of the concrete slab with the steel section. the study was also advanced in terms of interest in representing the welding region for studs. where a wild collar with a material similar to that reality. in this study, attention will be focused on two main points that most previous numerical studies have overlooked, namely the study of the form of failure at the weld region in the longitudinal section and the cross section of the stud. the second point is about the change in the shape of the failure in this region when changing the degree of shear connection between the concrete slab and the steel section. after these previous studies, the main objective of this study is to provide fem of nonlinear and material modeling of composite beams. these composite beams will be examined and studied under fatigue loads to observe failure patterns of the welding area between shear studs and the steel beam. also, these beams will be tested on different degrees of composite interaction starting from 40% to 100% (full shear interaction). the focus will be on specific results that were not taken into account in previous studies such as the mechanical performance of shear connector at failure and the ratio of stud forces to its relative position as a strong indicator of the degree of weld tolerance at the failure stage. fig. 1 shows a flow chart clarify the proposed numerical analysis work in this study. r a. i. hassanin et alii, frattura ed integrità strutturale, 55 (2021) 110-118; doi: 10.3221/igf-esis.55.08 112 figure 1: proposed numerical analysis work in this study numerical simulation non-linear analysis of 3d finite elements (fea) of composite beams was carried out using the software program ansys (workbench v.19.2). for the simulation of concrete, a 3d brick element with 8 nodes (solid65) was chosen, fig. 2. this element is suited for the representation of cracks, crush failures, and shear transfer of concrete after cracking. shell element (shell181) was used to model steel components with four nodes per node with six degrees of freedom. unlike most previous studies, that used single-line elements to model shear connectors, shear connectors in this study were simulated as a 3d body element (solid45) with two parts representing the stud body and the stud root and connected to a bonded connection (welding collar was assumed to be brittle)[9–11]. steel re-bars have been modeled using 3d link elements (link8-an element with two nodes and three degrees of freedom per node, which can model plasticity with large deflection). to represent the interface between the steel top flange and the concrete slab, node-to-node contact elements (contac52) and unidirectional spring elements (combine39) were chosen. the contact element will support tangential friction and compression to connect in the normal direction. the reason for using this element was to prevent surface penetration and ensure a physical separation of the steel and concrete components. figure 2: the finite element model used in the study. a a. i. hassanin et alii, frattura ed integrità strutturale, 55 (2021) 110-118; doi: 10.3221/igf-esis.55.08 113 model validation n this part, the validity of the fem was checked in comparison with the experimental results obtained from two previous studies. the results were included in the first study of a beam (fscb-2) tested by yu-hang et al. [7]. this was especially relied upon due to the availability of full details for this test. the model predictions were consistent with the experimental results, except that it was about 7% stiffer in the linear and nonlinear behavior stages. the reason for this difference is attributed to the assumption of complete bonding between concrete and steel reinforcement in the concrete slab. the second experimental study that was relied upon as one of the push-out tests performed by ovuoba and prinz [12] (slab 2 of specimen 1). it was taken into consideration during the verification process in order to assess the slip representation quality of the composite beam between the steel section and the concrete slab under fatigue loads. the results were consistent between the fe model and the experimental data, with the observation of greater stiffness in the linear model by about 9% in the linear phase. this stiffness may be attributed to the compatibility bonding between the shear studs and the steel section. this difference continued to grow until failure took place at 13×106 cycles. figure 3: details of validated models parametric study even models in terms of degree of shear connection divided into seven degrees (from 40% to full shear connection with 10% increment in the degree of interaction). in each type of these models, there were two loading intervals; interval 1: sinusoidal waveform fatigue loading with a constant amplitude [7]. the repeated load pr (which will be located in rang between (pmax. and pmin.)) will be determined using the beam initial cracking load (pcr=pmax. = pu/3). a residual static loading stage will be performed on models that did not suffer fatigue failure after repeated cycles of 2.5 × 105. interval 2: the residual static loading following fatigue failure of the beam will be reloaded with a static load to obtain its residual static capacity. fig. 4 shows the used cyclic loading pattern. i s a. i. hassanin et alii, frattura ed integrità strutturale, 55 (2021) 110-118; doi: 10.3221/igf-esis.55.08 114 the range of fatigue loads for shear connectors was obtained from the shear stress number of 118 mpa [13] and according to aashto specification [14] and european standards [15]. the average fatigue load was derived from the analyzed shear connector 's 30% static shear strength [16]. this can be considered a high cyclic fatigue load pattern with an average fatigue life over one million cycles. by adjusting the total number of shear connectors over the span length, we can control the degree of shear interaction [9,17]. for the effect of the shear interaction between the top flange of the steel beam and the concrete slab on the overall behavior of the composite beam, seven beams with seven different degrees of shear connection were evaluated under named sections ((hb-n) where n was the degree of interaction as a percentage from full shear interaction case). the parametric analysis was summarized in detail in tab. 1. figure 4: used cyclic loading pattern [9]. parameters cyclic load (kn) beams no. of studs shear studs spacing(mm) degree of interaction (%) upper limit (pmax.) lower limit (pmin.) amplitude hb-100 29 138 100 114 30 84 hb-90 26 153.8 90 hb-80 23 173.9 80 hb-70 20 200 70 hb-60 17 235.3 60 hb-50 15 266.7 50 hb-40 12 333.3 40 table 1: used models and analyzed parameters in this study. analysis of the obtained results mechanical performance of shear connector failure: hen the shear connector was finally broken, the crack shape had a crescent shape [11]. the simplification of the crack shape in the f.e. analysis as an even flat and the change rule in sectional geometry features of the shear connector was shown in fig. 5. it can be seen that at the beginning of the fatigue load, the crack is small and the sectional geometry feature displayed with small change, but after proceeding into a large number of cycles (more than 30×104 cycles) there were be a big change shown in increasing in deflection, small cracks noticed in concrete slab around shear connectors foot propagation and overall sectional composite action. at low degrees of shear connection models (hb60 and hb-40) there was a shear force redistribution in the interface from shear connectors with larger damage to those with smaller damage that occurred with a fast clang in every loading cycle. so, the conclusion about cumulative slippage, deflection, and composite action loss, controlled by the reduction in the interface bond or connection, and occurred due to the increasing of repeated load cycles [12]. w a. i. hassanin et alii, frattura ed integrità strutturale, 55 (2021) 110-118; doi: 10.3221/igf-esis.55.08 115 figure 5: the maximum principal shear stress distribution around stud root. strain changes at mid-span of beams: to assess the strain on the steel beam at various points in the steel beam section and to evaluate the incidence of a shearlag phenomenon in the contact region between the steel beams and shear connectors. for steel beam, strain values were detected, as shown in fig. 6. there was a linear strain distribution along the steel beam section but there also seems to be some irregularity of strain continuity at the interface between the top flange of the steel compression surface and the shear connectors. according to the last findings, the shear lag phenomenon had already occurred and had a strong impact on the welding region between the body of the shear connectors as a target element and the steel beam top flange. furthermore, it is the subject of future studies on strengthening this region for better performance of shear stud resistance. the indication of the assumption that plane sections remain plane [9, 10] was also agreed well with the used steel cross-section. a. i. hassanin et alii, frattura ed integrità strutturale, 55 (2021) 110-118; doi: 10.3221/igf-esis.55.08 116 figure 6: strain changes at mid-span of the tested beams. ratio of stud forces to its relative position from fig. 7, and based on the strength of the concrete slab, steel beam, and shear studs. by comparing the minimum and maximum bearing capacity of the studs along beam span (l), the following was noted: the slippage reaches its maximum value at the of the maximum shear force region (supporting points at this case), and these forces on the studs gradually decrease until they reach their lowest level at the zero points (between the two loading points (starting from 0.4 span length)). however, the value of the shear force affecting studs does not reach zero in this region, and the reason for this is due to the momentum resulting from the transmission of the shear force between studs along the length of the composite beam. on the other hand, a widening of the difference in the bearing capacity of the studs between the beams under different degrees of shear connection was noticed. the tested beams were divided into two groups according to the degree of shear connection. the first group from the lowest degree of shear connection value, from (40%) to (70%), and the value of the shear force was large on most studs along beam span, as a result of partial loss of composite action at the beginning of the loading stages, which ended with the loss of this composite action later before the failure occurred. the second group was from (80%) to (100%) degree of shear connection and the degree of influence on the studs was less severe, which gives the first impression that it is not allowed to reduce the shear connection degree in any way from 80% in the composite beams in order to avoid premature loss of composite action. figure 7: ratio of stud forces to its relative position. conclusions n this paper, the main purpose was to study the effect of fatigue loads on the failure shape in the weld region of the shear studs used in the composite beams. this study was carried out using nonlinear analysis of finite element modeling. by using the results of previous experimental tests, the validity and efficiency of the model used to extract results i a. i. hassanin et alii, frattura ed integrità strutturale, 55 (2021) 110-118; doi: 10.3221/igf-esis.55.08 117 consistent with the experimental results were verified. a study was also conducted on the effect of changing the degree of shear connection between the concrete slab and the steel beam, and some conclusions were reached: 1) a good compatibility has been reached between the model used by the finite element method and previous experimental test data, this compatibility ensures the validity of the model in predicting and analyzing the behavior of the composite beams under the influence of fatigue loading with different shear connection degrees. 2) based on the results obtained, it is preferable that the value of the degree of shear connection during fatigue loading is not less than 80% in order to avoid premature loss of composite action and thus reduce the fatigue life of the beam. 3) in cases of shear connection levels greater than 80%, the failure mode of the beam was fatigue cracking along the weld area when the upper fatigue limit equaled a value higher than 56% of the final load. 4) at shear connection levels below 80%, the mode of failure in the weld zone was more severe due to the premature loss of composite action. therefore, care should be taken to strengthen this area or be careful not to be loaded in low-levels of shear connection. 5) the distribution of shear forces resulting from loading is subject to the momentum created by the presence of the studs in a number that allows them to resist these forces. therefore, it is not possible to neglect the studs in the zero share areas. data availability statement ome or all data, models, or code that support the findings of this study are available from the corresponding author upon reasonable request. conflict of interest statement n behalf of all authors, the corresponding author states that there is no conflict of interest. references [1] slutter, r.g., fisher, j.w. (1966). fatigue strength of shear connectors, 45th annu. meet. highw. res. board, 315(147). [2] johnson, r.p. (2000). resistance of stud shear connectors to fatigue, j. constr. steel res. doi: 10.1016/s0143-974x(99)00082-6. [3] (2004). designers’ guide to en 1994-1-1: eurocode 4: design of composite steel and concrete structures, part 1-1 : general rules and rules for buildings, . [4] geoff t, p.g. (1997).incremental slip of stud shear connectors under repeated loading. composite constructionconventional and innovative, innsbruck, austria, pp. 145–50. [5] hanswille, g., porsch, m., ustundag, c. (2007). resistance of headed studs subjected to fatigue loading. part i: experimental study, j. constr. steel res., doi: 10.1016/j.jcsr.2006.06.035. [6] hanswille, g., porsch, m., ustundag, c. (2007). resistance of headed studs subjected to fatigue loading, j. constr. steel res., doi: 10.1016/j.jcsr.2006.06.035. [7] yu-hang, w., jian-guo, n., jian-jun, l. (2014). study on fatigue property of steel-concrete composite beams and studs, j. constr. steel res., doi: 10.1016/j.jcsr.2013.11.004. [8] wu, g., wang, h., wu, z., asce, m., liu, h., ren, y. (2012). experimental study on the fatigue behavior of steel beams strengthened with different fiber-reinforced composite plates, (may), pp. 127–137. doi: 10.1061/(asce)cc.1943-5614. [9] hassanin, a.i., shabaan, h.f., elsheikh, a.i. (2020). the effects of shear stud distribution on the fatigue behavior of steel – concrete composite beams, arab. j. sci. eng., doi: 10.1007/s13369-020-04702-4. [10] hamilton, r., tennyson, s., hamilton, w. (2001).analysis by the transformed-section method. asee annual conference proceedings. s o a. i. hassanin et alii, frattura ed integrità strutturale, 55 (2021) 110-118; doi: 10.3221/igf-esis.55.08 118 [11] wang, j., guo, j., jia, l., chen, s., dong, y. (2017). push-out tests of demountable headed stud shear connectors in steeluhpc composite structures, compos. struct., 170, pp. 69–79, doi: 10.1016/j.compstruct.2017.03.004. [12] ovuoba, b., prinz, g.s. (2018). investigation of residual fatigue life in shear studs of existing composite bridge girders following decades of traffic loading, eng. struct., doi: 10.1016/j.engstruct.2018.02.018. [13] ovuoba, b., prinz, g.s. (2016). fatigue capacity of headed shear studs in composite bridge girders, j. bridg. eng., doi: 10.1061/(asce)be.1943-5592.0000915. [14] aashto. (2012). aashto lrfd bridge, proquest diss. theses, , pp. 1661. [15] navr, j. (2014). eurocode design of composite concrete, (1), pp. 1–6. [16] xu, c., sugiura, k., su, q. (2018). fatigue behavior of the group stud shear connectors in steel-concrete composite bridges, j. bridg. eng., 23(8), doi: 10.1061/(asce)be.1943-5592.0001261. [17] el-zohairy, a., salim, h. (2017). parametric study for post-tensioned composite beams with external tendons. doi: 10.1177/1369433216684352. microsoft word numero 25 art 1 d. nowell et alii, frattura ed integrità strutturale, 25 (2013) 1-6; doi: 10.3221/igf-esis.25.01 1 special issue: characterization of crack tip stress field characterisation of crack tip fields under non-uniform fatigue loading d. nowell, m.e. kartal university of oxford, department of engineering science, parks road, oxford, ox1 3pj, uk. p.f.p. de matos u3is, unidade de investigação e internacionalização do isvouga, santa maria da feira, portugal. abstract. the paper analyses previously reported work, which uses digital image correlation to measure fatigue crack closure. as well as determining crack opening loads, the information on crack shape may be used to estimate the stress intensity factor, as well as other parameters in more complex models of crack tip fields. a number of specimens were subjected to single overload cycles, which produced a significant retardation in crack growth rate. the method previously applied to the analysis of constant amplitude loading is here used to analyse the single overload case. the stress intensity factor history is found to be very different in the two cases and the consequences of this observation for analysis of fatigue crack propagation are discussed. keywords. digital image correlation; displacement measurement; crack-tip fields; elastic-plastic fatigue crack. introduction he study of crack tip stress, strain, and displacement fields has a long history. one hundred years ago, inglis recognized that a sharp elastic crack would exhibit a stress (and strain) singularity [1]. twelve years later westergaard [2] produced a stress function solution for a crack in a biaxial stress field which formed the basis for the later concept of the stress intensity factor. an excellent compilation of seminal papers in the field has been provided by sanford [3,4]. the stress intensity factor has proved to be an extremely useful concept for the assessment of cracks and it has been widely used in industry. paul paris’ extension of the concept to its use in fatigue crack propagation [5] is particularly worthy of mention. however, it is clear that the stress intensity approach has many limitations. in particular, all fatigue cracks must exhibit some irreversibility at or close to the crack tip, otherwise they would not propagate. the stress intensity approach attempts to characterize this by a similitude argument, which depends on the assumption of small scale yielding (i.e. that the process zone of the crack tip is contained within a wider ‘k-dominant’ region). use of the stress intensity approach has particular limitations for the case of non-uniform loading, since load history effects are difficult to capture. hence, there has been increasing interest in improved characterization of crack tip fields. in parallel, new experimental techniques, such as digital image or volume correlation (dic/dvc); x-ray tomography; and large scale synchrotron facilities have provide tools which allow various models of crack tip behavior to be tested. a significant number of papers were presented at the first i.j. fatigue & ffems joint workshop on the characterisation of crack tip stress fields held in forni di sopra in 2011. this resulted in the publication of two special issues of the journals [6, 7], but the workshop showcased only a small proportion of the work in the field. on the experimental side, other recent papers of note include tomographic studies of cracked specimens under live loading [8] and in-situ sem t http://www.gruppofrattura.it http://dx.medra.org/10.3221/igf-esis.25.01&auth=true d. nowell et alii, frattura ed integrità strutturale, 25 (2013) 1-6; doi: 10.3221/igf-esis.25.01 2 studies of deformations in the crack tip region. the latter work has led to a suggested life prediction approach which obviates the need to characterize the number of cycles experienced by the crack [9]. despite the existence of rainflow and similar approaches, cycle counting can be a difficulty in non-uniform loading situations. the experimental work reported in the current paper springs from an investigation of crack closure originally carried out by de matos [10]. however, the data was later re-processed to compare with a two-parameter crack tip field model proposed by pommier and co-workers [11]. this work was reported at the forni di sopra workshop [12] and in the subsequent special issue [13]. however, the majority of the work reported was concerned with constant amplitude loading. a few experiments on simple overload cycles were carried out and the results of one of these experiments were presented in [13]. the displacement fields were converted into the two parameter description (k, ) and provided an interesting contrast to the results obtained from constant amplitude loading. the current paper therefore sets out to explore these results in more detail and to analyse a wider range of variable amplitude experiments. experimental work he fatigue experiments carried out by de matos have been reported elsewhere, but a brief summary is given here for clarity. fig. 1 shows the main experimental set-up, which employs a ct specimen manufactured from 6082 t6 aluminium alloy. the specimen is loaded in fatigue and the area along the crack flanks is monitored using a questar long range microscope and a digital camera (a low-cost usb webcam). a second camera is used to measure the crack length on the opposite side of the specimen, but this does not provide sufficient resolution for displacement measurement. the use of the microscope means that only a small area (approx. 600 x 400 m) close to the crack tip is imaged, but this permits high resolution and high accuracy evaluation of displacements. it should be noted that, because the primary focus of the investigation was crack closure, most of the image is along the crack wake, and there is very little information collected from the region ahead of the crack tip. figure 1: experimental configuration: side and top views. images were collected during fatigue loading at 30fps, whilst the specimen was loaded in a servo-hydraulic test machine at a frequency of 0.25 hz. a set of 360 images was collected over four loading cycles at a number of discrete points during crack propagation. the loading frequency was increased between these measurement steps in order to propagate the crack in a reasonable time interval. each set of images was analysed using a public domain matlab script [14]. rather than analyse a full displacement field, the relative displacement of five pairs of points along the crack flank was determined (fig. 2). this information proved useful in investigating crack closure directly, but may also be employed to determine crack tip loading history. the elastic model for a sharp crack predicts that the displacement along the crack faces is given by: t http://www.gruppofrattura.it http://dx.medra.org/10.3221/igf-esis.25.01&auth=true d. nowell et alii, frattura ed integrità strutturale, 25 (2013) 1-6; doi: 10.3221/igf-esis.25.01 3 4 ( ) 2 i i k r u r e    (1) so that a plot of log(relative displacement) against log(r) may be used to estimate the stress intensity factor at any particular time during the crack loading history. figure 2: typical image showing the crack tip, together with the five pairs of measurement points. results hilst the main experimental programme concerned the investigation of behaviour under constant amplitude loading, a small number of specimens were subjected to a single overload in an otherwise constant amplitude load history. analysis of this situation represents a useful first step towards a full theory which can be applied in any general loading case. fig. 3a shows the schematic loading history, whereas fig. 3b shows crack growth rate data (plotted against nominal k) for a number of 3mm thick specimens, including two (ctf6 and ctf8) which were subjected to an overload. the resulting retardation in crack growth rate can clearly be seen. figure 3: (a) schematic load history for single overload specimen; (b) variation of crack growth rate with nominal elastic k for 3mm thick specimens, including two with single overloads. w load time (a) (b) http://www.gruppofrattura.it http://dx.medra.org/10.3221/igf-esis.25.01&auth=true d. nowell et alii, frattura ed integrità strutturale, 25 (2013) 1-6; doi: 10.3221/igf-esis.25.01 4 the experimental data is processed as described above and used to determine the stress intensity factor history for the crack. in the case of specimen ctf6, the variation of k with load, just before the overload, is shown in fig. 4(a). it can be seen that the behaviour is quite similar to that predicted by an elastic analysis of the specimen geometry. however, there is an offset between the theoretical and experimental lines, caused by crack closure. alternatively, this phenomenon may be thought of as a residual (negative) k caused by the residual stress (and displacement) field present. the two lines have similar slope since, once the crack is fully open at a load of approximately 0.5 kn, the behaviour is predominantly elastic, with only a small zone of cyclic plasticity close to the crack tip. figure 4: variation of measured stress intensity factor with load for specimen ctf6 (a) before the overload and (b) immediately after the overload. fig. 4b shows equivalent data just after the overload. a cursory inspection suggests that the behaviour appears as expected. the slope of the curve remains approximately parallel to the elastic line, and the offset has increased (perhaps as a result of the increased magnitude of residual stress resulting from the overload). however, closer inspection reveals some unexpected features. the analysis yields negative stress intensity factors, which we would not expect to be physically admissible on their own. this must mean that the relative displacement between the crack flanks is varying as r, where  is a positive constant. further, this would imply that the stress field at the tip of the crack is compressive and reasonably well described by the singular westergaard solution. one possible explanation for these observations is that the crack is being held open by the additional crack opening displacement caused by the overload. investigation of the crack profile broadly confirms this view. as the crack propagates after the overload, the behaviour gradually returns to that which exists previously. fig. 5 shows a similar plot of load against k taken 23,500 cycles after the overload. the negative offset is substantially reduced, although negative stress intensity factor values still exist. moreover it is apparent that the variation is no longer linear over the range of load plotted. the deviation from linearity at lower load values is almost certainly caused by the onset of closure, which was absent immediately after the overload. the discussion above suggests that a single parameter, k, may be insufficient to fully characterize the crack tip environment, particularly under non-uniform loading conditions. an improvement can almost certainly be obtained by explicitly acknowledging the role of crack tip plasticity. a simple model has been proposed by pommier and hamam [11] which relies on partitioning the displacement field into elastic and plastic components. the elastic component, uel, is the usual field associated with k, whereas the plastic field, upl, is associated with crack tip opening. to a first approximation it may be taken as that given by a unit dislocation located at the crack tip. hence i el plu k u u  (2) as far as the relative displacements between the crack faces are concerned, this leads to 8 ( ) 2 i y k r u r e     (3) (a) (b) http://www.gruppofrattura.it http://dx.medra.org/10.3221/igf-esis.25.01&auth=true d. nowell et alii, frattura ed integrità strutturale, 25 (2013) 1-6; doi: 10.3221/igf-esis.25.01 5 hence, a plot of uy against √r should give a straight line with a gradient of 8ki/(e√(2)) and an intercept of , and values of k and  may be obtained from the experimental results in a similar manner to the purely elastic case. fig. 6 shows the variation of k with  for the cycle soon after the overload (i.e. corresponding to the elastic analysis shown in fig. 5b). this shows evidence of the hysteresis in of k/ space, which pommier and hamam suggest is associated with fatigue crack propagation. according to their hypothesis, absence of a cyclic variation in  corresponds to loading beneath the threshold value of k. figure 5: variation of measured stress intensity factor with load for specimen ctf6, 23,500 cycles after the overload. figure 6: variation of k with  when the elastic/plastic approach is used to analyse a cycle after the overload. conclusions he results presented here have demonstrated that displacement information collected in the crack wake can be analysed using digital image correlation in order to give reliable values of the stress intensity factor. for the case of constant amplitude loading, the results are broadly as expected and show a linear relationship of k with load, suggesting that the behaviour is predominantly elastic. there is, however, an offset to the experimental curve, compared with the linear elastic model, which can be attributed to the existence of crack closure. the situation when a non-uniform load history is examined appears more complex. here, a simple case of a single overload in an otherwise constant amplitude loading has been examined. even this relatively simple load history gives rise to some surprising results. for some time after the overload, negative stress intensity factors are measured when using a purely elastic model. normally it is only possible to obtain positive values, as the crack closes and allows transmission of compressive forces across the t http://www.gruppofrattura.it http://dx.medra.org/10.3221/igf-esis.25.01&auth=true d. nowell et alii, frattura ed integrità strutturale, 25 (2013) 1-6; doi: 10.3221/igf-esis.25.01 6 crack faces. the values measured here can only be possible when a significant crack tip opening displacement is also present. this suggests that a more sophisticated description of crack tip fields is necessary, perhaps including elastic and plastic terms as suggested by pommier and hammam [11]. future work will include the comparison of the measured results with strip yield and finite element models. further experiments are also planned, which will look at the region ahead of the crack tip as well as along the crack flanks. this should allow correlation of the results obtained in the crack wake with conditions in and around the process zone itself. acknowledgement .f.p. de matos would like to gratefully acknowledge the support of the portuguese fundação para a ciência e a tecnologia (fct) for providing a d.phil. scholarship (reference sfrh/bd/12989/2003, financed by posi). references [1] inglis, c.e., stresses in a plate due to the presence of cracks and sharp corners, trans of the institution of naval architects, 55 (1913) 219-230. [2] westergaard, h.m., bearing pressures and cracks, jnl appl. mech., 6 (1939) 49-53. [3] sanford, r.j., selected papers on foundations of linear elastic fracture mechanics, sem/spie, usa (1997). [4] sanford, r.j., selected papers on crack tip stress fields, sem/spie, usa (1997). [5] paris, p., erdogan, f., a critical analysis of crack propagation laws, jnl basic engineering, 85 (1963) 528-534. [6] james, m.n., yates, j.r., susmel, l., iacoviello, f., nowell, d., lazzarin, p., patterson, e.a., carpinteri, a., characterisation of crack tip stress fields, proceedings of the 1st joint international journal of fatigue/fatigue & fracture of engineering materials & structures conference, held in forni di sopra, ud, italy, 7-9 march, 2011, int. jnl fatigue, 46 (2013) 1-1. [7] james, m.n., yates, j.r., susmel, l., iacoviello, f., guest editorial: special issue on characterisation of crack tip stress fields, fatigue fract. engng mater. struct., 36 (2013) 1-2. [8] limodin, n., rethore, j., buffiere, j.y., influence of closure on the 3d propagation of fatigue cracks in a nodular cast iron investigated by x-ray tomography and 3d volume correlation, acta materiala, 58 (2010) 2957-2967. [9] zhang, w., liu, y., investigation of incremental fatigue crack growth mechanisms using in situ sem testing, int. jnl fatigue, 42 (2012) 14-23. [10] de matos, p.f.p., nowell, d., experimental and numerical investigation of thickness effects in plasticity-induced fatigue crack closure, int jnl fatigue, 31 (2009) 1795-1804. [11] pommier, s., hamam, r., incremental model for fatigue crack growth based on a displacement partitioning hypothesis of mode i elastic-plastic displacement fields, fatigue fract. engng mater. struct., 30 (2006) 582-598. [12] nowell, d., kartal, m.e., de matos, p.f.p., measurement and modelling of near-tip displacement fields for fatigue cracks in 6082 t6 aluminium, proc. first i.j. fatigue & ffems joint workshop, forni di sopra, italy, march 7-9, 2011, gruppo italiano frattura, 2011. [13] nowell, d., kartal, m.e., de matos, p.f.p., digital image correlation measurement of near-tip fatigue crack displacement fields: constant amplitude loading and load history effects, fatigue fract. engng mater. struct., 36 (2013) 3-13. [14] eberl, c. thompson, r., gianola, r., digital image correlation and tracking with matlab, matlab central file exchange (2006) http://www.mathworks.co.uk/matlabcentral/fileexchange/12413-digital-image-correlation-and-tracking. p http://www.gruppofrattura.it http://dx.medra.org/10.3221/igf-esis.25.01&auth=true microsoft word numero_58_art_05_3046 k. nabil et alii, frattura ed integrità strutturale, 58 (2021) 65-76; doi: 10.3221/igf-esis.58.05 65 evaluation of rheological performance of a local modified bitumen by styrene butadiene styrene polymer used in wearing course kebaili nabil departement of civil engineering and hydraulic, faculty of applied sciences, university kasdi merbah of ouargla, 30000, algeria kebailinabil69@gmail.com, https://orcid.org/0000-0001-6176-8919 mohamed djouhri laboratory of exploitation and valorization of natural resources in arid areas (evrnza), university of kasdi merbah, ouargla, 30000, algeria m.djouhri@yahoo.fr mohammed boucherba public works laboratory of the south, ghardaïa, 47000, algeria boucherbamohammed@yahoo.fr mustapha kebaili departement of civil engineering and hydraulic, faculty of applied sciences, university kasdi merbah of ouargla, 30000, algeria m_kebaili@yahoo.fr abstract. in road construction, bitumen is the binder that gathers the different aggregates of road pavements. bitumen, as a viscoelastic material, influences considerably the rheological behavior of bitumen concrete. the bitumen used in algeria, shows its limits in facing the traffic, which is increasing continuously. this research aims to valorize styrene-butadienestyrene sbs polymer in wearing course by modifying a pure 35/50 bitumen. the present paper aims to study the polymer derived from styrene and butadiene (sbs) the company kraton polymers international ltd for the modification of a bitumen to improve its mechanical characteristics. to this end, the incorporation of sbs polymer was carried out according to two contents: 5.0 and 7.5% (by weight of asphalt) to evaluate the influence of this type of polymer on the rheological properties of the bitumen ordinary road including viscosity and modulus. the results revealed that the bitumen modified with 7.5% of sbs has better mechanical performance on the rigidity and the elasticity compared to the conventional bitumen. recommendations have been made to implement a bitumen modification system to improve its quality and therefore the durability of bituminous pavements in the south of algeria. citation: nabil, k., djouhri, m., boucherba, m., kebaili, m., evaluation of rheological performance of a local modified bitumen by styrene butadiene styrene polymer used in wearing course, frattura ed integrità strutturale, 58 (2021) 65-76. received: 20.03.2021 accepted: 19.06.2021 published: 01.07.2021 copyright: © 2021 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. https://youtu.be/wumivo2bgcq k. nabil et alii, frattura ed integrità strutturale, 58 (2021) 65-76; doi: 10.3221/igf-esis.58.05 66 keywords. polymer modified bitumen; rigidity; sbs polymer; thermal susceptibility; dynamic mechanical analysis. introduction ccording to the european specification, bitumen is defined as a virtually nonvolatile, adhesive, and waterproofing material [1]; bitumen consists of viscous liquid, essentially made of mineral oil, hydrocarbon derivatives (such as asphaltenes, maltines), which are soluble in carbon di-sulphide, it is considerably non-volatile, and it gradually softens by heating. it is either black or brown in color [2,3,4] and its chemical structure, which depends on its origin and mode of derivation is not fully known [5]. bituminous binders are widely used by the paving industry [2,6,3,7] as currently produced in the various refineries, and they have limits in terms of mechanical performance necessary to withstand the constantly growing loads under the effect of heavy traffic [8,9]. this constraint requires algeria and other countries in the region to use bitumen improvement techniques. types of bitumen used in hot regions, such as the southern algeria region, are also subject to severe climatic constraints. indeed, the road sections located in southern algeria, where a hot and dry climate prevails in summer, are not spared from these obstacles, which represent another challenge that is added to the limits of the bitumen previously reported (fig. 1). in algeria, the traditional pure grade 35/50 bitumen used as a wearing course is relatively hard and rigid, which shortens its service life and affects its sensitivity to high summer temperatures. figure 1: ouargla weather data 2014-2017 [10] the most common solution to overcome this problem is the addition of polymers to the base bitumen to adapt its mechanical and rheological characteristics to the environmental constraints of climate and traffic as recommended by several authors [2,8,11,12]. to meet these constraints and to achieve better mechanical and rheological performance, it has become essential to switch to modified bitumen that has the advantage of being available and inexpensive as mentioned by many others [13,14,15,16]. one of the most common categories of bitumen modifiers is polymeric materials [17,18]. among these polymers, elastomers, and thermoplastics, due to their ability to enhance overall viscoelastic properties of bitumen, have a great impact on bitumen characteristics and their resistance to distresses [19]. bitumens modified with polymers (bmps) are bitumen binders whose properties are modified by the addition of a chemical agent. when the latter is introduced into the basic bitumen, modifies its chemical structure and the physical and mechanical structures [19,20,21]. they are generally used in the road sector. this modification of bitumen is done exclusively using polymers, which are macromolecules synthesized through a chemical reaction between smaller molecules (monomers) to form long chains. the physical properties of the resulting polymer are determined by the chemical structure of the monomers and by their sequence inside the polymer [22,23]. currently, the growing development and use of polymer materials in construction roads are observed [24,25]. in america and europe, bmp is commonly used; however, in algeria, using bmp dates back to ten years ago with the construction of the east-west highway. a k. nabil et alii, frattura ed integrità strutturale, 58 (2021) 65-76; doi: 10.3221/igf-esis.58.05 67 the modification of the bitumen by the polymer can be carried out according to two ways; by the so-called dry method, in which the polymer introduced is considered as an aggregate during mixing, or by the wet method, which consists in modifying the bitumen structure by the polymer before the operation of mixing with the aggregates. this last method is the most effective; it is adopted in the present study. to demonstrate the influence of this polymer, two dosages were tested; 5.0% (highly modified bitumen) and 7.5% (hyper modified bitumen). the viscosity of the modified bitumen is studied, in addition to other performances such as elasticity, plasticity index, and storage capacity. the present study constitutes a first experiment in characterizing of bitumen modified with a polymer of the styrenebutadiene-styrene (sbs) elastomer type produced by the company kraton corporation and intended for the road section d0234 (south of algeria). materials and methods he main materials used for this study are aggregates, bitumen and polymer in the form of granules. all the properties of the materials used were measured for the prior analysis. other tests were carried out to measure their properties. asphalt cement the asphalt cement used in this study was the bitumen 35/50 penetration grade obtained from the naftal refinery in alger, algeria. it is the most used bitumen. the identification tests carried out on bitumen are as follows:  penetration test en-1426: which is an empirical method to measure the consistency of the bitumen. penetration is defined as the distance a standard needle loaded with a 100g weight will penetrate a bitumen sample for 5sec at 25°c [26]. the penetration grade of the bitumen without and with sbs was investigating using the penetrometer in accordance with en 1426 specification, the device used is shown in fig.2. figure 2: penetration test apparatu.  softening point en-1427: it represents the temperature at which a material softens beyond some arbitrary softness. a ring and ball apparatus are used for the determination of the softening point of bituminous materials [12,27] the basic properties of this grade of the asphalt binder are given in tab. 1. modifier the modifier selected for the present study is the most used sbs polymer in bitumen modification. it confers to bitumen its properties of elasticity, creep stability, and durability. the used sbs polymer is called d0243 e, it comes in granules of millimeter dimensions and it was supplied by kraton polymers international ltd. tab. 2 gives its physical properties. sample preparation as mentioned previously, two types of bitumen modified at 5.0 and 7.5% (by weight of base asphalt) with the sbs polymer were produced; bmp5.0 and bmp7.5 [28]. fig. 3 shows the pure bitumen modification device. t k. nabil et alii, frattura ed integrità strutturale, 58 (2021) 65-76; doi: 10.3221/igf-esis.58.05 68 test standard value penetration at 25°c, 0.1(mm en-1426 37.9 softening point, °c en-1427 50.5 specific gravity en-1526 1.01 flash point en-12591 335 penetration index pfeiffer -1.7 pi lcpc* 2.320 table 1: basic characteristics of the 35/50 pen bitumen grade used [28]. *lcpc: laboratoire des travaux publics du sud, ouargla (algeria). propriety test method result polystyrene content (%) km 93 300% modulus (mpa) iso 37 1.0 tensile strength (mpa) iso 37 2.0 specific gravity iso 2781 0.94 hardness, shore a (10 sec) iso 868 79.0 table 2: physical characteristics of kraton d0243 e polymer used. figure 3: bitumen modifier apparatus. modification process: the bitumen-polymer mixing phase is critical and largely determines the success of the mixing, for this purpose special attention must be paid during all modification phases. the temperature, time and speed of mixing were chosen based on previous studies established by the researchers [12,28,29,30,31]. used equipment: electric propeller agitator (rotation speed = 2000 rpm), adjustable heating plate, digital thermometer. modification steeps: 1. preheat bitumen in the oven at 140 °c for 4hours. 2. placement of bitumen on the fitted heating plate (constant temperature). 3. switching on the mixer at a speed of 2000 rpm. 4. addition of the polymer during mixing for 1h until complete dissolution at 180°c. 5. reducing of the speed’s mix to 500 rpm for 2h (maturation phase). 6. end mixing by ensuring homogeneity. k. nabil et alii, frattura ed integrità strutturale, 58 (2021) 65-76; doi: 10.3221/igf-esis.58.05 69 the degree of dispersion of the polymer in the bituminous phase is shown by its microscopic structure in fig. 4, with the use of fluorescence microscopy scanning (fms) by simulated uv light. this technique gives the color contrast between the bitumen (no fluorescence) and the polymer used (greenish-yellow fluorescence). the fluorescent images show a change in the morphology of the pmbs as the polymer content increases. figure 4: fluorescent images of sbs modified bitumen. these two types of modified bitumen were subjected to the following tests: dynamic mechanical analysis, viscosity, storage stability. a) dynamic mechanical analysis: (abbreviated dma, also known as dynamic mechanical spectroscopy) is a technique used to study and characterize materials particularly polymers by studying their viscoelastic properties. for this purpose, a sinusoidal force (stress σ) is applied to a material and the resulting displacement (strain) is measured according to the en iso 6721 standard. the dynamic mechanical analysis (dma) was carried out at the leego research laboratory (usthb univ. algiers) using a metravib dma type device manufactured by dynatest as shown in fig.5. the samples were subjected to a frequency sweep between 1 and 10 hz, at a temperature of 30°c. after conservation of the cylindrical specimen ø10×h20mm for 30min, the shear module ||g*|| was measured by pull-compression over a frequency range of 1 to 10hz. figure 5: metravib apparatus used b) viscosity (en13302-2010): the brookfield viscometer developed by amtek was used, which makes it possible to measure the newtonian viscosity of the bitumen by measuring the speed of rotation and the torque applied following the application of shear stress [32]. c) storage stability (en13399): this test consists in measuring the softening temperature of the lower and upper parts of the bitumen samples subjected to storage conditions, after homogeneous dispersion of the polymer in the modified bitumen [33]. 5.0% 7.5% k. nabil et alii, frattura ed integrità strutturale, 58 (2021) 65-76; doi: 10.3221/igf-esis.58.05 70 results and discussion ig. 6 shows the evolution of the penetration considering the usual temperatures. according to fig. 6, it can be seen that the addition of the polymer to the bitumens increases its performances almost linearly; the modified bitumens become harder and less sensitive to temperature, this is in agreement with several author’s conclusions [34,35,36]. the penetration decreases by 39% and 41% respectively when 5.0 and 7.5% of a polymer are added. in this case, a certain superposition of the curves is recorded in the interval 20-25°c. beyond that, the sensitivity of bmp7.5 bitumen is more important. figure 6: penetration results according to the temperature likewise, it is possible to relate the penetrability to the thermal susceptibility of bitumen through the penetration index (pi) in the range of temperatures studied. penetration index is another way of looking at the temperature susceptibility of the bitumen as described by pfeiffer and van doormaal [37] fig. 7 shows the values of the penetration index calculated by the two methods; lcpc and pfeiffer [38] according to eqn. 1.            log    25º   80020 500                                          1 50  25º     º pen at c loga ip where a a c softening point c (1) figure 7: bar chart showing pi values calculated by two methods. ‐1,70 0,30 2,70 2,32 1,93 2,85 ‐2,0 ‐1,0 0,0 1,0 2,0 3,0 neat bit. bmp5.0 bmp 7.5p e n e tr a ti o n  i n d e x pi pfeiffer pi lcpc f k. nabil et alii, frattura ed integrità strutturale, 58 (2021) 65-76; doi: 10.3221/igf-esis.58.05 71 the penetration index represents a quantitative measure of the response of bitumen to variation in temperature. knowing the penetration index of particular bitumen, it is possible to predict its behavior in an application. effect of polymer on the softening in order to characterize the behavior of modified bitumens at high temperatures, the softening point was determining for modified bitumen using the ring and ball test in accordance with en 1427 specifications. the results are presented in fig. 8. figure 8: bar chart showing the effect of adding polymer on penetration value and recovery in terms of softening, a considerable change of more than 25% is recorded when changing from modified bitumen pmb5.0 to modified bitumen pmb7.5, which means that the consistency of the modified bitumens is very sensitive to the temperature. effect of polymer on elastic recovery & storage stability the elastic recovery is a good indicator that characterizes the ability of the binder to return to its original geometric shape following deformation. the values show that the sbs polymer makes the bitumen more elastic and therefore it has a positive influence on the elastic return. the recovery rate in the case of 7.5% modified bitumen is around 80%, which expresses very good reversibility after removal of the load. in order to evaluate the stability and compatibility of the modifier at high temperature in asphalt binder, the storage stability test was carried out according to the en 13399. tab. 3 gives the results obtained. we note, also, that the difference of softening point value between the top and bottom section is less than 1.0°c, this means that pmb is stable when stored at high temperature. test pure bitumen bmp 5.0 bmp 7.5 softening point (°c) 50.5 65.5 82.2 elastic recovery (%) 66.8 74.2 79.5 table 3: storage stability and elastic recovery results [30] effect of polymer on dynamic viscosity the viscosity of the bitumen was measured using the brookfield viscometer according to en-13702; the equipment was used to measure the newtonian viscosity characteristics of the polymer and modified bitumen pen 35/50. the sample, contained in a beaker with a cylinder, is stressed by the rotation of the rv-28 spindle. the objective is to determine the viscosity and the shear modulus of the modified bitumens. tab. 4 shows the results of the dynamic viscosity measured for the two types of modified bitumen (pmb5.0 and pmb7.5). 50,50 65,50 82,20 66,80 74,20 79,50 neat bit. pmb 5.0 pmb 7.5 softening (0,1mm) recovery (%) k. nabil et alii, frattura ed integrità strutturale, 58 (2021) 65-76; doi: 10.3221/igf-esis.58.05 72 table 4: rheological properties of pure and bmp. according to tab. 4, the dynamic viscosity of the bitumen is multiplied by 3 and 6 for the bitumen modified by 5.0 and 7.5% of the polymer, respectively. this increase is accompanied by an increase in the rate of torsion and the shear stress, which means that the modified bitumens require more stress to their mixing. dynamic mechanical analysis dynamic mechanical analysis (dma) is a measurement where sinusoidal stress or strain is given as the input, and the strain or stress, respectively, is measured as the output (fig. 5). because of damping, the strain in a viscoelastic material is observed with a phase delay φ from the stress. the stress and strain can be thus expressed as : the results of the dma test are presented in fig.s 9 and 10. the test measured the stiffness modulus ||e*||, the shear modulus ||g*|| was obtained by the following formula. ||e*|| = 3 ||g*|| (2) 10x20mm cylindrical specimens were tested in traction-compression mode under 30ºc at the frequencies: 1, 1.58, 2.51, 3.98, 6.31, and 10hz. in fig. 9, the values of the stiffness modulus e of the modified bitumen pmb7.5 are shown compared to the control bitumen, moreover, fig. 10 represents the evolution of the shear modulus g. figure 9: effect of sbs polymer on stiffness modulus for different frequencies. figure 10: effect of sbs polymer on shear modulus for different frequencies. 0 4000 8000 12000 16000 20000 1 1,58 2,51 3,98 6,31 10 e  ( k p a ) frequency (hz) neat bit. bmp 7.5 viscosity at 135 °c pure bitumen bmp 5.0 bmp 7.5 dynamic viscosity (cp) 1500 4500 9500 torsion ratio (%) 0.30 0.90 1.90 shear stress (pa) 0.42 1.26 2.66 k. nabil et alii, frattura ed integrità strutturale, 58 (2021) 65-76; doi: 10.3221/igf-esis.58.05 73 according to fig. 10, it is clear that the addition of sbs affects considerably the values of the stiffness modulus, which varies from more than 125% to 350% when moving from 1 to 10 hz in frequency in the case of 7.5% modified bitumen. we also note that the evolution of the rigidity, for pure bitumen, is almost linear with the increase in frequencies. however, for the modified bitumen, the evolution is rather exponential. the equations governing the module (e) according to the frequencies (f) are given in the two cases as follows:  neat bitumen: e= 152.3f² + 42.6f + 702 (3)  modified bitumen: e= 3937e0.27f (4) on the shear plane, the shear module g seems not to be very influenced by the sbs, since this evolution is from 49% at 1hz to -29% at the frequency 10hz. at 2.51 hz, the modified bitumen has the same shear modulus as the neat bitumen. conclusion n the context of improving the performance of road pavements to withstand the increasing traffic constraints and more severe climatic conditions, the present work aims to study a new bitumen improved by the styrene-butadienestyrene (sbs) "kraton polymer". the binder is the grade 35/50 bitumen frequently used in southern algeria. after characterization of the used bitumen from the point of view of penetrability and softening, the emphasis is put on the rheological characteristics; viscosity and modulus of bitumen after adding 5.0 and 7.5% of this polymer. in light of the laboratory results exposed throughout this study, the main conclusions is that the contribution of sbs in bitumen is very beneficial and acts positively on the mechanical and rheological performances of bitumen. indeed, in comparison with pure bitumen, bitumens after modification have the following performances: bitumen modified with 7.5% of sbs has better performance in terms of thermal sensitivity with a gain in penetration and softening temperature which exceeds 60%. storage stability is interesting for the different sbs contents and exceeds 80% in the case of modified bitumen 7.5%. on the other hand, the elastic recovery difference between the two sbs contents of the modified bitumen is relatively low. in terms of rheological behavior, the following remakes should be made; the dynamic viscosity of bitumen, at 135°c, is very sensitive to the polymer content; the viscosity is multiplied by 3 when the sbs content goes from zero (neat bitumen) to 5.0% and multiplied by 6 in the case of bitumen modified with 7.5% sbs. to this end, bitumen modified with polymers (bmps)are a good alternative in regions with a hot climate, as is the case in the region of southern algeria. the dynamic mechanical analysis (dma) tests showed that the addition of sbs increases the stiffness module significantly, while the shear moduli are little influenced. as shown above, the stiffness modulus, according to the frequencies tested, increases almost linearly for pure bitumen and exponentially for the modified bitumen. for the shear modulus, a slight difference is recorded between pure and modified bitumen in the range of frequencies studied. unlike low frequencies, the shear modulus of modified bitumen is lower than that of pure bitumen. these characteristics allow modified bitumens to withstand more dynamic loads caused by road traffic. finally, in order to make the most of it, it is important to continue this study project, by increasing the number of rheological tests such as bbr and dsr to assess the behavior of modified bitumen under different thermal conditions. following the success recorded at the performance level of bitumen modified by sbs, it is important to test the asphalt mixes based on bmp, to see their behavior once put on road surfaces. acknowledgments he authors of this article would like to express deep thanks to mr. haddadi smaïl the head of leggo laboratory for permitting carried out in his research laboratory and kraton polymers international company. i t k. nabil et alii, frattura ed integrità strutturale, 58 (2021) 65-76; doi: 10.3221/igf-esis.58.05 74 abbreviations a: thermal susceptibility bbr : bending beam rheometer bmps : bitumens modified with polymers dma : dynamic mechanical analysis dsr : dynamic shear rheometer e : stiffness modulus fms : florescent microscopy scanning g : shear modulus lcpc : laboratoire central des ponts et chaussées pen : penetrability pi : penetration index sbs : styrene-butadiene-styrene references [1] european committee for standardization. bitumen and bituminous binders-terminology., belgium. en 12597. [2] behzad, s. h. (2010). bitumen modification with polysulphide polymer prepared from heavy end waste. iranian polymer journal. (19(5), pp.363-373. [3] faridah, h., et al (2020). design and optimization of polyurethane modified bitumen (pumb) using response surface method, 2nd international conference on civil & environmental engineering, 476, pp. 1-7. doi:10.1088/1755-1315/476/1/012061. [4] gordon, a. (2002), rheological evaluation of ethylene vinyl acetate polymer modified bitumens, construction building mater, 16(8), pp. 473-487. doi:10.1016/s0950-0618(02)00103-4 [5] mehrdad, h., javad, t. and beiranvand, m. (2019). bitumen and its modifier for use in pavement engineering. sustainable construction and building materials, chapter 13. pp. 249-270. doi: 10.5772/intechopen.82489 [6] hunter, r., self, a., and read, j. (2014). the shell bitumen handbook. 6 ed. hardcover surrey, uk [7] noor, z. h., ibrahim, kamaruddin, m. n., and isa m. t. (2011). rheological properties of polyéthylene and polypropylene modified bitumen. word academy of science, international journal of civil and environmental engineering, 3(2), pp. 96-100. doi:10.5281/zenodo.1074737. [8] baha, v., et al (2018). effects of preparation conditions on the properties of crumb rubber modified binder, international journal of architectural, civil and construction sciences, 12(3), pp 289-294. doi:10.5281/zenodo.131610710.5281/z. [9] porto, m., caputo, p., et al (2019). bitumen and bitumen modification: a review on layest advances. applied sciences, 9(742), pp. 1-36. doi:10.3390/app9040742. [10] national office of meteorologie (2019). données statistiques météorologiques de la ville de ouargla, algeria. [11] strastna, j., zanzotto, l. and vacin o. j. (2003). viscosity functions in polymer-modified asphalts. journal of colloïd sciences, 259(1), pp. 200-207. doi: 10.1016/s0021-9797(02)00197-2. [12] munera, j. c., ossa, e. a. (2014). polymer modified bitumen: optimization and selection. materials and design, 62, pp. 91-97. doi: 10.1016/j.matdes.2014.05.009. [13] ghada, s. m., ashraf, a. r. and talaat, a. (2021). effect of nanoclay particles on the performance of high density polyethylene-modified asphalt concrete mixture, polymers, 13(434), pp.1-23. doi:10.3390/polym13030434. [14] jiang, z., et al (2017). evaluation of physical, rheological and structural properties of vulcanized eva/sbs modified bitumen. journal of polymers sciences. 134. doi:10.1002/app.44850. k. nabil et alii, frattura ed integrità strutturale, 58 (2021) 65-76; doi: 10.3221/igf-esis.58.05 75 [15] bala, n., napiah m., kamaruddin, i. (2018). effect of nanosilica particals on polypropylene polymer modified asphalt mixture performance. case studies in construction materials. 8, pp. 447-454. doi: 10.1016/j.cscm.2018.03.011 [16] xinyu, z., shifeng w., qiang w. and hongru, y. (2016). rheological and structural evolution of sbs modified asphalts under natural weathering. fuel 184, pp.242-247. doi: 10.1016/j.fuel.2016.07.018 [17] gordon, a. (2002). rheological evaluation of ethylene vinyl acetate polymer modified bitumens. construction and building materials, 16, pp. 473-487. doi: 10.1016/s0950-0618(02)00103-4 [18] brule, b., brion, y. and tanguy, a. (1988). paving asphalt polymer blends: relationship between composition, structure and properties. proc aapt, 57, pp. 41-64. [19] zhu, j., birgisson, b. and kringos, n. (2014). polymer modification of bitumen: advances and challenges. european polymer journal, 54, pp.18-38. doi: 10.1016/j.eurpolymj.2014.02.005 [20] word association of roads aipcr. (1999). use of modified bituminous binders, special bitumens and bitumens with additives in road pavements –technical guide-, technical committee of the flexible roads (c8), paris. [21] xiaohu, l. (1997). on polymer modified road bitumens [doctoral dissertation]. stockholm, kth royal institute of technology. [22] ameri, m., et al (2020). evaluating properties of asphalt mixtures containing polymers of styrene butadiene rubber (sbr) and recycled polyethylene terephthalate (rpet) against failures caused by rutting, moisture and fatigue, frattura ed integrità strutturale, 53, pp. 177-186. doi: 10.3221/igf-esis.53.15. [23] lesueur, d. (2002). rhéologie des bitumes: principes et modification. rhéologie. 2, pp 1-30. [24] ramadhansyah, p. j., et al (2019). effects of black rice husk ash on asphalt mixture under aging condition. eart and environment science, 220, pp. 1-6. doi:10.1088/1755-1315. [25] romastarika, r., et al (2017). effect of black rice husk ash on the physical and rheological properties of bitumen. construction and building materials 24, pp. 2145-2150. doi:10.1063/1.4998383 [26] european standards. bitumen and bituminous binders determination of needle penetration. 1426:2007. [27] european standards. bitumen and bituminous binders determination of the softening point ring and ball method. 1427:2007 [28] kebaili, n. (2015). l’asphalte caoutchouc valorisation de la poudrette de caoutchouc en domaine routier. thèse de doctorat en génie civil, université ouargla, 130 pp. [29] kebaili, n., benabdelouahab, f. and zerzour, a. (2013). valorization of asphalt rubber fine powder in road field. key engineering materials, 550 pp. 85-90. doi: 10.4028/www.scientific.net/kem.550.85 [30] kemassi, n., boucherba, m., and kebaili, n. (2019). bitumes hautement modifiés par polymère (hima): influence des polymères sur la viscosité des liants -etude de cas : d0234. mémoire de master en génie civil, fsa. université de ouargla. [31] farazmand, p., hayati, p., shaker, h. and rezaci, s. (2021). relationship between microscopic analysis and quantitative and qualitative indicators of moisture susceptibility evaluation of warmmix asphalt mixtures containing modifiers. frattura ed integrità strutturale, 51, pp.215-224. doi: 10.3221/igf-esis.51.17 [32] european standards. bitumen and bituminous binders determination of dynamic viscosity of bituminous binder using a rotating spindle apparatus 13302:2010 [33] european standards. bitumen and bituminous binders determination of storage stability of modified bitumen 13399:2018 [34] damadi, s. m., edrisi, a., fakhri, m., rezaei, s. and worya, m. k. (2020). fatigue analysis of bitumen modified with composite of nano-sio2 and styrene butadiene styrene polymer. frattura ed integrità strutturale, 53, pp.202-209. doi: 10.3221/igf-esis.53.17 [35] ming, l., et al (2015). thermo-rhological behavior and compatibility of modified asphalt with various styrenebutadiene structures in sbs copolymers. materials and design, 88, pp.177-185. doi:10.1016/j.matdes.2015.09.002 [36] karakas, a. s., kuloglu, n., kök, b. v. and yilmaz, m. (2015). the evaluation of the field performance of the neat and sbs modified hot mixture asphalt. construction and building materials, 98, pp. 678-684. doi: 10.1016/j.conbuildmat.2015.08.140. k. nabil et alii, frattura ed integrità strutturale, 58 (2021) 65-76; doi: 10.3221/igf-esis.58.05 76 [37] olugbenga, a. e., olugbenga, a. f., and jonathan, g. (2012). softening point and penetration index of bitumen from parts of southwestern nigeria. nafta zaghreb, 63 (9-10), pp. 319-323. [38] boucherba, m., kriker, a., and kebaili, n. (2017). the valorization of the plastic waste to the rheological characteristics of bituminous mixtures. aip conference proceeding, 1814, pp. 1-11. doi: 10.10631/1.4976244. microsoft word numero_57_art_14_3075 m. chaib et alii, frattura ed integrità strutturale, 57 (2021) 169-181; doi: 10.3221/igf-esis.57.14 169 optimization of ultimate tensile strength with doe approach for application fsw process in the aluminum alloys aa6061-t651 and aa7075 -t651 mohammed chaib institut des sciences et techniques appliquées, université ahmed ben bella es senia oran 1 b.p. 1524-el m’naoeur, oran, algeria, smart structures laboratory/dgrsdt. chaib.mohammed@univ-oran1.dz, pro19moh@hotmail.com, https://orcid.org/0000-0002-0493-1764 abdelkader slimane laboratoire de mécanique appliquée, département de génie mécanique, université des sciences et de la technologie d’oran mohamed boudiaf, usto-mb, bp 1505, el m’naouer, 31000 oran, algerie. laboratory of materials and reactive systems (lmsr), department of mechanical engineering, university of sidi-bel-abbes, bp 89, cité ben m'hidisidibel-abbes 22000-algeria. aek.slimane@univ-usto.dz, https://orcid.org/0000-0003-4409-2077 sid ahmed slimane centre of satellite development (cds), bp.: 4065 ibn rochd usto, oran, algeria. sslimane@cds.asal.dz, https://orcid.org/0000-0001-7110-1704 abdelkader ziadi smart structures laboratory/dgrsdt, university of ain temouchent, n101, ain temouchent 46000, algeria. aekziadi@hotmail.com, https://orcid.org/0000-0002-0452-9361 benattou bouchouicha laboratory of materials and reactive systems (lmsr), department of mechanical engineering, university of sidi-bel-abbes, bp 89, cité ben m'hidisidibel-abbes 22000-algeria. benattou.bouchouicha@gmail.com, https://orcid.org/0000-0002-6051-5108 abstract. friction stir welding process is increasingly used to connect metal structures for industrial applications as shipbuilding and offshore, aerospace, automotive, rolling stock for railways and robotics, friction stir welding makes it much easier for us to fusion the aluminum alloys like aa6061-t651 and aa7075 -t651. it is essential to carefully study to contain many parameters such as the welding speed, the rotation speed and the type of pin used during the operation to optimize mechanical properties and in particular to obtain high rupture strength with the tensile test. citation: chaib, m., slimane, a., slimane, s., ziadi, a., m., bouchouicha, b., optimization of ultimate tensile strength with doe approach for application fsw process in the aluminum alloys aa6061-t651 & aa7075 t651, frattura ed integrità strutturale, 57 (2021) 169-181. received: 16.04.2021 https://youtu.be/1m2kemz4pma ² m. chaib et alii, frattura ed integrità strutturale, 57 (2021) 169-181; doi: 10.3221/igf-esis.57.14 170 in this paper we aim to treat carefully this process by using the design of experiment method which is an original approach that resides in the possibility of interpretation of experimental results with a minimal effort on the experimental level whichever generates the minimization of the necessary number of experiments and allows a saving in time and in financial cost. for each parameter, the effect of interaction with the rotation speed, the welding speed and the choice of the pin, were determined. a mathematical model between the response and the parameters are modeled, which represents the analytical part of this optimization. keywords. fsw welding; rupture strength; design of experiment; optimization uts. accepted: 07.06.2021 published: 01.07.2021 copyright: © 2021 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. introduction he welding process goes back to the discovery of metals, and since the latter has not stopped evolving as technologically, but also on the methods and working conditions. in 1991 the british institute (the welding institute) invented a new ecological and efficient process especially for aluminum alloys as well as other alloys complicated to weld by conventional methods, this process known as friction stir welding fsw[1-3]. this technique, which is currently used in many sectors, consists of assembling two metal sheets by friction and local mixing, using a tool. the latter is placed between the two sheets to create the weld joint, by significant rotational action and a force exerted underneath, causing plastic deformation, we can create an effective weld without ever reaching the melting temperature of the base metal[4-7]. figure 1: schematic representation of fsw principle [8]. t advanced welding weld zone apparence pin joint m. chaib et alii, frattura ed integrità strutturale, 57 (2021) 169-181; doi: 10.3221/igf-esis.57.14 171 this process allowed us to use more and more the alloys of non-ferrous metals which offer important mechanical characteristics[9, 10], it also contributed to reduce the manufacturing costs[11, 12], that is why we find so important, to focus our research on how to optimize the operation at low cost, while controlling the parameters, with the best plausible configuration, which will play a crucial role in the maintenance of structures, like the speed of the tool and welding, but also the tool geometry (fig. 2). figure 2: friction stir welding tools with different pin profiles [13]. in industrial processes, it is useful to explore the relationships between the key variables (or factors) of the input process and the output performance characteristics (or quality characteristics) [14]. for example, in a metal shotpeening operation, the impact velocity, the processing time that induces the coverage rate, the shot’s hardness, can be treated as input variables and the quality of the surface will been considered as performance characteristic so an answer[15]. design of experiment (doe) is a robust technique used to explore new processes, gain insights into existing processes, and optimize these processes to achieve world-class performance [16, 17]. many researchers have been involved in the use of doe since the mid-1990s to promote mathematical and statistical skills[17, 18], yunus et al [19] also reported how genetic programming can be applied to the fsw process to derive precise relationships between the output and input parameters in order to obtain a generalized prediction model. though the welding is a controlled process, we aim in this article to get more knowledge and skills by using the doe, that helps to supervise much more the operation at a lower cost. optimization by the design of experiment method n this paper, an experimental design method was used on the fsw friction stir welding process, basically using parameters that effect the process, such as rotational speed, welding speed, and profile. pin which carries a surface ratio (ss / sd) representing the type of the pin, where ss / sd represents the ratio between the area occupied by the pin in static state and the area occupied by the pin in dynamic state. for example, in the case of a round pin, the surface ratio is equal to 1 and in the case where the pin is square, the ratio 1.57 is found. we focused on the welding area, which consists of two different materials, the aa6061-t651 and the aa7075-t651 elaborated by the friction stir welding method, with decrypting the parameters which are the speed of rotation and welding through the pin profiles on tensile strength of joints. two types of h13 steel tools have been used to fabricate welded joints with different pin profiles. we have based on the results of ravikumar [18], which studied the influence of welding parameter variation on the rupture strength. however, we have well expolited this data by the doe method to highlight such a deep and profound analysis. tab. 1 shows the fsw welding parameters and their working ranges of aa6061-t651 and aa7075 -t651. n° parameters symbol unit level low (-1) high (+1) 1 rotational speed (rpm) r rpm 800 1000 2 welding speed (mm/min) s mm/min 90 100 3 pin profile p cylindrical (1) square (1,57) table 1: process parameters with different levels i ² m. chaib et alii, frattura ed integrità strutturale, 57 (2021) 169-181; doi: 10.3221/igf-esis.57.14 172 matrix designs he purpose of the experimental design can be defined as a means of reducing the number of trials with maximum precision. we can use a unique coding relation defined from the bijective transformation defining the value xi from relation (1), which deals also the plans to study the response surface [20]:            max min max min 2 2 i i i i i i u u u x u u (1) ui max and ui min being the limits defined by the experimenter and ui the real level given to factor i. the coded factor x, has values in the bounded interval between [-1; 1]. we obtain a complete factorial plan with k factors at two levels by the combination of each two levels of this factor[21]. our matrix of experiences of three factors is represented by tab. 2. the fig. 7 represents the experimental points located at the vertices of a hyper cube which forms a named space, the experimental field of study. the effects and the interaction of the factors given in a matrix of experiences of type 2k on a well determined response, can be estimated by the values of the coefficients of a mathematical model of the polynomial type of the first degree, which translates the relation between the answer y and the factors xi. the response y, of a mathematical model in the case of a plane 23 is defined by the relation:       0 1 1 2 2 3 3 12 12 13 13 23 2. . . . . .y a a x a x a x a i a i a i (2) a0: the general average. a1, a2, a3: effect of the rotational speed, the welding speed and the profile of the pin respectively. a12: effect of the interaction of the rotation speed and the welding speed. a13: effect of the interaction of the rotation speed and the pin profile. a23: effect of the interaction of the welding speed and the pin profile. i12, i13eti23: interaction between the different variables. n° test rotation speed (rpm) (r) ≡ (x1) welding speed (mm/min) (s) ≡ (x2) pin profile (ss/sd) (p) ≡ (x3) rupture strength -uts (mpa) (y) 01 800 90 1 174 02 1000 90 1 184 03 800 100 1 186 04 1000 100 1 188 05 800 90 1.57 150 06 1000 90 1.57 172 07 800 100 1.57 160 08 1000 100 1.57 175 table 2: experimental matrix. a system of 8 equations with 8 unknowns is generated by the mathematical model resulting in a set of results from a plane of 23, if we neglect the experimental errors. we can form this system in a matrix form according to the relation (3): t m. chaib et alii, frattura ed integrità strutturale, 57 (2021) 169-181; doi: 10.3221/igf-esis.57.14 173  .y x a (3) with: y: vector of responses represented by a column matrix (2k, 1), a: vector of the effects of the factors and all the interactions, represented by a column matrix (2k, 1); these components are the unknowns that we are trying to determine, x: square matrix (2k, 2k) composed of 1 and + 1 according to the values of the levels xi. the relation (10) represents the matrix form of our plane 23 system:                                                                             1 0 2 1 3 2 4 3 5 12 6 13 7 23 8 123 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 y a y a y a y a y a y a y a y a         the orthogonality of our matrix is a very important property because the inverse of x is equal to the transpose of x divided by the number of lines n [22]. indeed, according to hadamard, we have the relation (4):  .tx x n i (4) with i represents the unit matrix and xt: is the transposed matrix of x. i: the identity matrix. n: the number of experiments performed (n must be a multiple of 4). from relation (4) and taking account of relation (5), we can calculate the unknown a:          . . . 1 t t t t x y x x a x y n i a a x y n (5) the elements of a are calculated in the following form:       1 2 3 1 i na y y y y n (6) tab. 3 is used which defines the calculation matrix to gather all the tests carried out. it is made up of several columns; the first column represents the average of the different tests, the other parameters express the state of the coded factors, each column represents a factor. the responses obtained are indicated by the last column [23]. we obtain the following adjusted mathematical model using the least squares method: y= 173.625 + 6.125 x1 + 3.625 x2 9.375 x3 1.875 i12 + 3.125 i13 0.375 i23 + 0.128 i123 uts=173.625 + 6.125 r+ 3.625 s9.375 p1.875 rs+ 3.125 rp 0.375 ps +0.128 rsp ² m. chaib et alii, frattura ed integrità strutturale, 57 (2021) 169-181; doi: 10.3221/igf-esis.57.14 174 fig. 3 shows the geometric state of the experimental design. n° test average x1 x2 x3 i12 i13 i23 i123 uts (mpa) (y) 01 1 -1 -1 -1 1 1 1 -1 174 02 1 1 -1 -1 -1 -1 1 1 184 03 1 -1 1 -1 -1 1 -1 1 186 04 1 1 1 -1 1 -1 -1 -1 188 05 1 -1 -1 1 1 -1 -1 1 150 06 1 1 -1 1 -1 1 -1 -1 172 07 1 -1 1 1 -1 -1 1 -1 160 08 1 1 1 1 1 1 1 1 175 effects and interactions a0 a1 a2 a3 a12 a13 a23 a123 173.625 6.125 3.625 -9.375 -1.875 3.125 -0.375 0.128 level – 800 90 cylindrical level + 1000 100 square table 3: calculation matrix. figure 3: geometric representation of a plane 23. effects analysis principal effect for each factor e are basing on complete factorial plan at two levels; we studied in a first case the effect of each factor separately from each other on the rupture strength, with a simultaneous variation and in an ordered manner balanced (fig. 4). w m. chaib et alii, frattura ed integrità strutturale, 57 (2021) 169-181; doi: 10.3221/igf-esis.57.14 175 fig. 4 shows the evolution of the rupture strength considered as a response (uts), influenced by the change of the three parameters, rotation speed (x1), welding speed (x2) and the type of pin profile ( x3), implied from his low to the high level. we can say that the rupture strength increases during the increase of the factors in the welding operation 800 rpm to 1000 rpm, regarding the rotation speed 90 mm / min to 100 mm / min, in addition the circular pin profile shows a significant advantage compared to the square pin, this manifests including the value of the breaking strength which is included between 183 mpa and 164.25 mpa respectively. otherwise, we observe in fig. 8 that the main effect of the speed of rotation corresponds to approximately 13 units of rupture strength from 167.5 mpa to 179.75 mpa, and 8 units from 170 mpa at 177.25 mpa. figure 4: illustration of the principal effect with three factors. interaction effect for two factors to better understand this effect, we have created specific interaction graphs (fig. 5). figure 5: interaction between rotational speed and welding speed. fig. 5-left shows us that the rupture strength increases with the increase of the rotation speed. however, a higher influence of the rotation speed during a higher welding speed compared to the low level. in other words, the effect of the speed of rotation depends on the level of the welding speed and especially if the rotation speed has the smallest value. we also see in fig. 5-right that the influence of the welding speed is greater when the rotation speed is fixed at its higher level. in an identical way, it can be seen in figs. 6 and 7 on the left side, that the rupture strength is improved with highest welding speed and higher rotational speed in the case where the round pin’s ratio (ss / sd) equal to 1 compared with the ratio of 1.57. ² m. chaib et alii, frattura ed integrità strutturale, 57 (2021) 169-181; doi: 10.3221/igf-esis.57.14 176 we can clearly see from figs. 6 and 7 on the right side, that the resistance is low for a square pin with high rotation and welding speed values, it remains greater with a round pin. we also observe that the resistance is modest for a large area ratio. figure 6: interaction between the speed of rotation and the profile of the pin. figure 7: interaction between the welding speed and the pin profile. model validation calculation of residuals ccording to the calculations made, we can calculate the estimated expenses based on the mathematical model found, we collect all the results in the table indicated below: to calculate the difference between the experimental response and the predicted (estimated) response, it suffices to use the relation (14) which represents the residue of each experiment.  exp estimatedie y y (14) when adjusting a regression model, the most important diagnostic tool consists of two companion parameters r2 and q2. the r2 parameter is called the quality of the fit, it is a way of measuring where the regression model can be brought to fit the raw data. when r2 is equal to 1, all the points are located on the diagonal of fig. 9. consequently, r2 alone, is not a sufficient indicator to probe the validity of a model. a m. chaib et alii, frattura ed integrità strutturale, 57 (2021) 169-181; doi: 10.3221/igf-esis.57.14 177 also a determination of the parameter of the prediction quality was very important to validate the outcomes of doe method. fig. 8 show value of 0.996 which is a more realistic performance indicator, as it reflects the objective of modeling forecasts for new experiences. yi applied model of each experiment ypredicted y1 190.194.69 (-1)91.53(-1)+ 144.03(-1)+ 2 (1)3.35(1)69.48(1) 71.56 y2 190.194.69 (1)91.53(-1)+ 144.03(-1)+ 2 (-1)3.35(-1)69.48(1) 64.86 y3 190.194.69 (-1)91.53(1)+ 144.03(-1)+ 2 (-1)3.35(1)69.48(-1) 23.44 y4 190.194.69 (1)91.53(1)+ 144.03(-1)+ 2 (1)3.35(-1)69.48(-1) 24.78 y5 190.194.69 (-1)91.53(-1)+ 144.03(1)+ 2 (1)3.35(-1)69.48(-1) 505.29 y6 190.194.69 (1)91.53(-1)+ 144.03(1)+ 2 (-1)3.35(1)69.48(-1) 485.21 y7 190.194.69 (-1)91.53(1)+ 144.03(1)+ 2 (-1)3.35(-1)69.48(1) 179.24 y8 190.194.69 (1)91.53(1)+ 144.03(1)+ 2 (1)3.35(1)69.48(1) 167.17 table 4: calculation of estimated responses. yexp yestimated ei 70.17 71.56 -1.39 66.25 64.86 1.39 24.83 23.44 1.39 23.39 24.78 -1.39 506.68 505.29 1.39 483.82 485.21 -1.39 177.85 179.24 -1.39 168.56 167.17 1.39 table 5: calculation of residues. figure 8: adjustment parameters. we can say that the fit is excellent, because all the points are located near the line according to fig. 09. however, the estimate of the small deviations between the calculated and measured response values is given by the residual standard deviation. ² m. chaib et alii, frattura ed integrità strutturale, 57 (2021) 169-181; doi: 10.3221/igf-esis.57.14 178 figure 9: the relationship between the calculated and observed responses of fsw welding. signification of effects we use the student test given by relation (7) to determine the influence of each variable and each interaction for a chosen risk of 5%. for a given risk, if an effect is different from 0, it can be considered significant on the studied response.  i i i a t (7) in order to use the student table, it is necessary to calculate the degree of freedom as follows:  = n p(ddl) with: n: is the number of experiments carried out, p: is the number of effects including the constant (the average). to find the signification of an effect:  if ti>tcrit(), the effect is significant.  if ti<tcrit (), the effect is not significant. experimental variance in order to estimate the common variance of the residuals, it is imperative to neglect at least one effect. without this action, we cannot calculate the common variance of the residuals for a complete plan n = p. it will be useful to pass over the high-order interactions (3 or more) [24]. the estimator of the common variance of the residuals is given by the relation (8):     2 21 ie n p (8) under these conditions, we can show that all the effects have the same variance given by the relation (9):    2 2 i n (9) we collect the residuals and the variances corresponding to each effect in tab. 6: m. chaib et alii, frattura ed integrità strutturale, 57 (2021) 169-181; doi: 10.3221/igf-esis.57.14 179 yi estimated 2 ie  i 71.56 1.39 1.179 64.86 1.39 1.179 23.44 1.39 1.179 24.78 1.39 1.179 505.29 1.39 1.179 485.21 1.39 1.179 179.24 1.39 1.179 71.56 1.39 1.179 table 6: calculation of residuals and variances. ti results observation t 0 =161.318 > 12.71 significant the effect of the constant (average) value is significant t 1 = 3.977 < 12.71 not significant the effect of vibration amplitude (a) is not significant t 2 = 77.639 > 12.71 significant the effect of tool rotation speed (s) is significant t 3 = 122.166 > 12.71 significant the effect of feedrate (fr) is significant t 12 = 1.702 < 12.71 not significant the effect of the interaction between vibration amplitude (a) and tool rotation speed (s) is not significant t 13 = 2.840 < 12.71 not significant the effect of the interaction between vibration amplitude and the feedraten is not significant t 23 = 58.937 > 12.71 significant the effect of the interaction between tool rotation speed and feedrate (fr) is significant table 7: signification of effects. the calculation of the common variance of the residuals is given as follows:        2 21 1 8 * 1.39 11.12 8 7 ie n p and the common variance of each effect:      2 2 11.12 1.39 8 i n the calculation of the student test "t" for each effect is given as follows:   ii i a t ² m. chaib et alii, frattura ed integrità strutturale, 57 (2021) 169-181; doi: 10.3221/igf-esis.57.14 180 the student test table gives, for a risk of 5 % with  = n p= 8-7 = 1ddl : t() = t(0,05;1) = 12.706 where "ti" is higher than 12.706. it is found that effect will therefore be significant with 5% risk. tab. 7 is obtained: it is observed from tab. 7 that the results are significant only with variables x2, x3 and the interaction i23. therefore, we should retain a model of the following form: y= 190.1991.53x2 + 144.03x3 69.48i23 f= 190.1991.53s+ 144.03fr 69.48s fr conclusion his research paper described the application of design of experiment based desirability analysis for parametric design of fsw process. in order to show the influence of the three parameters studied and their effects on the tensile strength for the fsw welding process according to the experimental plan method, we find a mathematical model which represents the analytical part of this optimization. our optimization model allows us to better understand the process, the following outcomes were disclosed:  the doe technique was very convenient for predicting the parametric design of input process parameter;  the influence of the parameters is quantified;  this process improves the quality characteristics in term of the best output responses.  the parameters are prioritized;  the optimum welding condition found as rotation speed 1000 rpm, welding speed 90 (mm/min) and the round pin which takes the ratio (ss / sd) equal to 1 which mean the circular pin profile show a significant advantage compared to the square pin;  their direction of variation is known;  interactions are highlighted;  the responses are modeled;  the difference between the experimental response and the predicted (estimated) response were calculated taking into account the parameter of the prediction quality estimated equal to 0.996. we can therefore conclude that the choice of the type of pin is very important in an fsw welding operation, the interaction of the latter with the rotation speed has more influence than the interaction with the welding speed, knowing that the choice of the pin is the most influential (dominant) factor than the effect of the rotational speed and the welding speed. the effect of the welding speed is less significant when the rotation speed takes on greater values and this is manifested in the slight slope. conflict of interests he authors declare that there is no conflict of interests regarding the publication of this paper. references [1] thomas, w. (1991). friction stir butt welding, int. patent., pct/gb92/02203. [2] murr, l, liu, g. and mcclure, j. (1997). dynamic recrystallization in friction-stir welding of aluminium alloy 1100, journal of materials science letters, 16, pp. 1801-1803. doi: 10.1023/a:1018556332357. t t m. chaib et alii, frattura ed integrità strutturale, 57 (2021) 169-181; doi: 10.3221/igf-esis.57.14 181 [3] mishra, r. s. and ma, z.y. (2005). friction stir welding and processing, materials science and engineering:r: reports., 50(1-2), pp. 1-78. doi:10.1016/j.mser.2005.07.001. [4] mahoney, m. w., rhodes, c. g., flintoff, j.g., bingel, w.h and spurling, r.a. (1998). properties of friction-stir-welded 7075 t651 aluminum, j. metallurgical and materials transactions a., 29, pp. 1955-1964. doi: 10.1007/s11661-998-0021-5. [5] nicholas ,e. (1998). developments in the friction stir welding of metals, proc. of icaa-6, conference on papers 6th int. conf. aluminum alloys, toyohashi, japan., 1, pp. 139-151. [6] prado, r. a., murr, l., shindo, d.j and soto , k. (2001). tool wear in the friction-stir welding of aluminum alloy 6061+ 20% al2o3: a preliminary study, scripta materialia., 45 (1), pp. 75-80. doi: 10.1016/s1359-6462(01)00994-0. [7] slimane, a., bouchouicha, b., benguediab, m and slimane, s. a. (2015). contribution to the study of fatigue and rupture of welded structures in carbon steel-a48 ap: experimental and numerical study, transactions of the indian institute of metals., 68(3), pp. 465-477. doi: 10.1007/s12666-014-0477-5. [8] zimmer, s., laye, j., guyomard, c., langlois, l., bigot, r and martin, p. (2009). fsw: un procédé de soudage pour les alliages d’aluminium de fonderie. conference on papers 11ème colloque national aip primeca, la plagne, pp. 2224. [9] bocchi, s., cabrini m., d’urso, g., giardini, c., lorenzi, s and pastore,.t. (2018). the influence of process parameters on mechanical properties and corrosion behavior of friction stir welded aluminum joints. journal of manufacturing processes., 35, pp. 1-15. doi: 10.1016/j.jmapro.2018.07.012. [10] hou, w., shah, l. h. a., huang, g., shen, y., and gerlich, a. (2020). the role of tool offset on the microstructure and mechanical properties of al/cu friction stir welded joints. journal of alloys and compounds., 825(0925-8388). pp. 130. doi: 10.1016/j.jallcom.2020.154045. [11] rai, a., de, a., bhadeshia, h. k. d. h and debroy, t. (2011). review: friction stir welding tools, science and technology of welding and joining., 16(4), pp. 325-342. doi: 10.1179/1362171811y.0000000023. [12] slimane, a., kebdani, s., bouchouicha, b., benguediab, m., slimane, s., bahram, k., chaib, m and sardi, n . (2018). an interactive method for predicting industrial equipment defects, the international journal of advanced manufacturing technology, 95 (9), pp. 4341-4351. doi: 10.1007/s00170-017-1416-5. [13] goyal, a and garg r. k.. (2018). selection of fsw tool parameters for joining al-mg4. 2 alloy: an experimental approach, metallography, microstructure, and analysis, 7(5), pp. 524-532. doi: 10.1007/s13632-018-0468-8. [14] slimane, a., slimane, s., kebdani, s., chaib, m., dahmane, s., bouchouicha.b. (2019). parameters effects analysis of rotary ultrasonic machining on carbon fiber reinforced plastic (cfrp) composite using an interactive rsm method, international journal on interactive design and manufacturing (ijidem), 13(2), pp. 521-529. doi: 10.1007/s12008-018-0518-0. [15] chaib, m., megueni, a., ziadi, a., guagliano, m and belzunce f. j. v. (2016). experimental study of the shot peening treatment effect on austenitic stainless steel. international journal of materials and product technology, 53(3-4), pp. 298-314. doi: 10.1504/ijmpt.2016.079197. [16] ayad, m. and barka, y. (2014). modélisation des betons ordinaires par des plans d’experiences. available at: http://dspace.univ-tlemcen.dz/bitstream/112/3998/1/memoire%202013.pdf. [17] goupy, j and creighton, l.. (2013). introduction aux plans d'expériences, 5e éd. toutes les techniques nécessaires à la conduite d'une étude: dunod. [18] [18] ravikumar, s., rao v. s and pranesh, r. (2014). effect of process parameters on mechanical properties of friction stir welded dissimilar materials between aa6061-t651 and aa7075-t651 alloys, int. j. adv. mech. eng., 5(1), pp. 101114. [19] yunus, m and alsoufi, m. s. (2018). mathematical modelling of a friction stir welding process to predict the joint strength of two dissimilar aluminium alloys using experimental data and genetic programming. modelling and simulation in engineering., 2018. doi: 10.1155/2018/4183816. [20] goupy, j. (1999). plans d'expériences pour surfaces de réponse. dunod. paris. pp. 409. isbn 2 10 003993 8. [21] kamoun, a., chaabouni, m.m and ayedi, h. f. (2011). plans d’expériences et traitements de surface-méthodologie des surfaces de réponses (msr). techniques de l’ingénieur, doc. m 1429, 1-24. [22] goupy, j. (1992). plans d'expériences. techniques de l'ingénieur. traité analyse chimique et caractérisation, p230. 1. [23] box, g. e. p., william, g. hunter, j.s., wiley. j and sons. (1978). statistics for experimenters, 664. john wiley and sons new york. doi: 10.1002/aic.690250233. [24] gendre l., soulier, b and savary, a. (2009). les plans d'expérience, sciences de l'ingénieur. microsoft word numero_33_art_28 j. toribio et alii, frattura ed integrità strutturale, 33 (2015) 221-228; doi: 10.3221/igf-esis.33.28 221 focussed on characterization of crack tip fields crack tip fields and mixed mode fracture behaviour of progressively drawn pearlitic steel j. toribio, b. gonzález, j.c. matos university of salamanca toribio@usal.es abstract. this paper deals with the influence of the cold drawing process on the fracture behaviour of pearlitic steels. to this end, fracture tests under axial loading were performed on steel wires with different drawing degree (from a hot rolled bar to a commercial prestressing steel wire), transversely pre-cracked by fatigue, analyzing in detail the changes in fracture micromechanisms. the deflection angles of the fracture path were measured by longitudinal metallographic sections and the characteristic parameters of the loaddisplacement plot were related to different fracture events. results allowed a calculation of critical stress intensity factors for different fracture angles and drawing degrees, thus evaluating the strength anisotropy and obtaining a sort of directional toughness. keywords. progressively drawn pearlitic steel; strength anisotropy; crack path deflection; mixed mode fracture; directional toughness. introduction he micro-mechanisms taking place during the fracture process of metals and alloys, as well as the fracture toughness, change with the temperature, the loading rate, and the cold work [1-3]. in the particular case of pearlitic steel used to produce high-strength cold-drawn prestressing wires, the cold drawing process affects the phenomenon of the fracture, so that the most heavily drawn steels (undergoing severe plastic deformation) exhibit strength anisotropy, and a change in the crack propagation direction, which approaches the wire axis or drawing direction [4]. this leads to the calculation of two values of the angular fracture toughness, one in the radial direction and the other in the axial one, the first being much greater than the second for steels with severe plastic deformation [5-7]. in wires with axisymmetric notches, the degree of the fracture anisotropy also depends on the notch geometry [8]. the fracture surface of pearlitic steel presents a change in the fracture mechanism as the wire is drawn [6]. in the hot rolled wire the fracture is produced through cleavage, while in the early stages of cold drawing there appears fracture caused by growth and coalescence of microvoid and then cleavage. on the other hand, the heavily drawn steels exhibit, after the propagation of microvoids in mode i, a step at about 90º followed by a mixed propagation of microvoids and cleavage [4]. the fracture behaviour of pearlitic steel mainly depends on the size of the prior austenite grain [9-11]: the smaller the size of the grain, the greater the fracture toughness. if the pearlitic steel is cold drawn, then the pearlite colony, rather than the prior austenite grain, is the critical fracture unit determining the size of the cleavage facet [12]. this paper deals with the anisotropic fracture behaviour of eutectoid pearlitic steel wires with different degree of cold drawing (distinct level of strain hardening and diverse microstructural arrangements) exhibiting strength anisotropy. the analysis is focused on the crack path deflection angle and the directional toughness. t j. toribio et alii, frattura ed integrità strutturale, 33 (2015) 221-228; doi: 10.3221/igf-esis.33.28 222 experimental procedure progressively drawn pearlitic steel, eutectoid chemical composition (tab. 1), was used in this work: from the hotrolled bar (not cold drawn at all) to the cold drawn wire (obtained after seven cold drawing steps and a stressrelieving treatment), as well as the intermediate steps. the code used to designate the steel consists of the letter b followed by a digit indicating the number of drawing steps applied to each one. %c %mn %si %p %cr %v 0.789 0.681 0.210 0.010 0.218 0.061 table 1: chemical composition (wt %) of the steels. the degree of cold drawing is characterized by means of the cumulative plastic strain εp as a function of the diameter reduction according to the following expression, p 0 i ln d d   (1) where di is the diameter of the wire after i drawing steps and d0 that corresponding to the initial steel wire. the stress-strain curves (fig. 1) and the conventional mechanical properties were obtained by means of a standard tension test. the cold drawing process does not modify the young’s modulus e (~200 gpa), and produces a clear improvement of material strength in the form of increase of both yield strength σy and ultimate tensile strength (uts) σr (fig. 2). 0.0 0.5 1.0 1.5 2.0 0.00 0.02 0.04 0.06 0.08 b7 b6 b5 b4 b3 b2 b1 b0  ( g p a )  0.0 0.5 1.0 1.5 2.0 0.0 0.2 0.4 0.6 0.8 1.0 1.2  r  y  ( g p a )  figure 1: stress-strain curves σ-ε (standard tension tests). figure 2: mechanical properties as a function of the strain hardening level. to evaluate the fracture toughness, a standard measurement procedure could not be applied because of the scarcity of the material (supplied in either bar or wire form with different diameters). the method applied in this paper is based in the calculation (from experimental measurements) of a critical stress intensity factor (sif) and the use of a local fracture criterion, as explained elsewhere [13]. to perform the fracture tests, samples of 300 mm were taken from the wires, with diameters of 12 mm in the hot rolled bar and 7 mm in the cold drawn wire. samples were precracked by means of axial tensile fatigue with a sinusoidal wave (at a frequency of 10 hz and r-ratio equal to 0) under load control and decreasing loading steps. the maximum value of the stress intensity factor at the end of precracking was 25-30 mpam1/2. after this fatigue precracking, specimens were subjected to monotonic tensile loading under displacement control up to fracture, the crosshead speed being 3 mm/min. an extensometer was placed in front of the crack mouth (symmetrically in relation to the crack faces), so that both the load applied on the sample (f) and the relative displacement by the extensometer (u) were recorded to plot the loaddisplacement curve f-u. a j. toribio et alii, frattura ed integrità strutturale, 33 (2015) 221-228; doi: 10.3221/igf-esis.33.28 223 experimental results microstructural analysis igure 3 shows the microstructure of hot rolled bar and prestressing steel wire, longitudinal section, where the horizontal size of the micrograph corresponds to the radial direction and the vertical size is associated with the axial direction in the longitudinal cut. the drawing process produces important microstructural changes in the steel at the two basic microstructural levels of pearlitic colonies and lamellae. the colonies become progressively enlarged and oriented in axial direction with cold drawing. with regard to the lamellae, they are also axially oriented after drawing and, at the same time, the pearlite interlamellar spacing decreases with the level of cumulative plastic strain. therefore, the microstructure becomes progressively packed and oriented with cold drawing. figure 3: microstructure, longitudinal section, b0 (left) and b7 (right). fracture surface fig. 4 shows the fracture surface for the different steels, where the fatigue surface, starting from a small mechanical cut (on the left side of the photographs), appears with a semi-elliptical final front from which the fracture initiates. macroscopically, the fracture surfaces of the slightly drawn steels propagate perpendicularly to the applied stress, following the fatigue crack. on the contrary, in heavily drawn steels, the fracture is very anisotropic, with abundant deflections and longitudinal cracking. symmetrical longitudinal cuts were made in the fracture-tested specimens, they were photographed (fig. 5), and the fracture angle was measured. in these photographs the fatigue growth is shown on the left, with a flatter profile, in addition to the fracture appearing after such a fatigue growth. as the plastic deformation increases with the number of drawing steps, so does the roughness of the fracture surface, as well as the fracture angle θ (in relation to the cross section of the wire), which implies the occurrence of a fracture in mixed mode. furthermore, in heavily-drawn steels, the existence of a step oriented with an angle of 90º (in relation to the cross section of the wire) can be observed at the beginning of the fracture event. figure 4: fracture surfaces, b0 to b7. f j. toribio et alii, frattura ed integrità strutturale, 33 (2015) 221-228; doi: 10.3221/igf-esis.33.28 224 figure 5: longitudinal section of the fracture, b0 to b7. crack fronts are characterized by a semi-elliptical geometry centred on the surface of the wire. in slightly-drawn steels, a micro-void coalescence (mvc) zone appears at the fracture surface after fatigue crack, with an extension of a few tenths of a micron, whose surface increases with the cold-drawing process. then the fracture propagates by cleavage and ends with a small external ring of mvc. the initial mvc zone is not taken into account in the calculations (due to its small size); instead of it, the crack front used in the calculations is that created by fatigue. it is modelled as a part of an ellipse of semiaxes af and bf, with af coincident with the crack depth. in heavily drawn steels, the main fracture micro-mechanisms are mvc and vertical walls consisting of elongated cleavage. such walls appear surrounding the fatigue crack in the form of abundant secondary radial cracking, and their sizes increase in extension with cold drawing. the final external ring of mvc has a greater surface than in slightly drawn steels. the crack growth area prior to the first propagation step (oriented with an angle of 90º) has a size on the order of hundreds of microns, and is taken into account in the calculations, resulting in the appearance of two critical crack sizes during the fracture: the fatigue crack (with semiaxes af and bf), and the crack existing at the time of growth of the afore-said 90º crack propagation step (with semiaxes ae and be). load-displacement curve the records obtained for the load-displacement curve f-u are different for slightlyand heavily-drawn steels (fig. 6). both have an initial linear zone that becomes a curve, with this curvature being generally greater as the drawing process increases, although it could also depend on other factors. the curves were characterized from two parameters: the load at the end of the linear behaviour portion of the curve (fe) and the maximum load (fmax). in heavily drawn steels, a characteristic load (fy) also appears that can be associated with a micro-tearing phenomenon called pop-in [14], which is accompanied by a characteristic tearing noise. by performing interrupted tests [15], it has been observed that the phenomenon of pop-in is physically associated with the occurrence of vertical cracking. u f f e f max u f f e f max f y figure 6: load-displacement curve, b0 (left) and b7 (right). fracture toughness the value of the critical sif, obtained for cracked cylindrical specimens, is the fracture toughness of the material, being independent of the wire’s diameter and of the crack size. once the fracture tests were carried out, the critical sif j. toribio et alii, frattura ed integrità strutturale, 33 (2015) 221-228; doi: 10.3221/igf-esis.33.28 225 corresponding to the macroscopic angle of the fracture surface (kcθ) was calculated, as well as the critical sif associated with the pop-in phenomenon (kc90º) for those steels where a vertical step existed. to calculate these characteristic values, the maximum sif was considered over practically the whole crack front in which plane strain conditions occur (the points at the wire surface were not taken into account in the calculations of the characteristic sif). on the basis of previous research [16], the dimensionless sif y used in the computations is that proposed by shin and cai [17] in the form of a three-parameter expression as a function of the relative crack depth a/d, the crack aspect ratio a/b and the position along of the crack front x/h: i0º i0º ( , , ) , , a a x k k f a b y a d b h         (2) to obtain the sif of a secondary crack with angle θ from the main one (fig. 7), it has been considered that the local sifs at the tip of a secondary crack ( *1k , * 2k ) are related with the global sifs from the main crack (ki, kii) for the case in which the secondary crack length tends to zero [18]. the expression of the local sifs, for the crack tip in deflection, is given by: i ii * 11 121 * 21 222 k k kk k k kk               (3) where the coefficients kij only depend on the value of the deflection angle θ. for the calculations, the coefficients obtained by amestoy [18] were used, fitted to third-order polynomial expressions with high regression coefficients.  da 0 ,k ki ii * * 1 2,k k figure 7: crack tip deflection. the energy release rate value satisfies the following expression [18, 19]: *2 *2 1 2( )k kg e    (4) where e'=e/(1-2) in plane strain and e'=e in plane stress. in the matter of the materials that exhibit an anisotropic fracture behaviour, the fracture specific energy depends on the angle of propagation, θ, with respect to the crack plane (contained in the wire cross section). the directional energy release rate, g(θ), can be related to the energy release rate at 0º, g(0º), and similarly their critical values: 2 211 21( ) ( ) (0º )g k k g   (5) for the slightly drawn steels, eq. 6 allows the calculation of the directional fracture toughness, keeping in mind the maximum load and the size of the fatigue crack: c i0º f f 2 2 11 21 max( , , )k k k k f a b   (6) in heavily drawn steels, the critical sif was calculated in mode i at 90º, from the pop-in load. in the fracture step, corresponding to the vertical cleavage burst (fig. 8), the relationship between the energy release rate in the axial direction (for the 90º angle) and in the radial direction (for 0º) [18] permits the calculation of the critical sif at 90º. 90º da 0 figure 8: crack tip deflection towards 90º. the critical sif at 90º can be obtained as follows [6, 7]: j. toribio et alii, frattura ed integrità strutturale, 33 (2015) 221-228; doi: 10.3221/igf-esis.33.28 226 c90º i0º y e e0.2615 ( , , )k k f a b (7) in the crack propagation from the vertical cleavage wall, which appears in the heavily drawn steels, the energy release rate for crack growth in the fracture plane oriented with an angle θ can be obtained after simplification by neglecting the vertical deflection length (fig. 9). 90º a 0 da 0    da 0 figure 9: crack tip deflection towards θ. thus, the critical sif at θ can be calculated as: c i0º e e 2 2 11 21 max( , , )k k k k f a b   (8) fig. 10 shows the results related to the critical sif in mode i for the fracture angle θ of each drawing step, as well as those linked with the critical sif in mode i for the fracture angle 90º in those steels where the anisotropy takes place in the form of vertical cracking. both directional toughness values increase with the drawing process, but the increase of critical sif associated with the θ angle is much more pronounced than that related to the 90º angle, the former reaching values as high as 110 mpam1/2. to assure the adequacy of using the sif as the key parameter governing the fracture process (through its critical value at the fracture instant), an estimation was performed of the plastic zone size in the vicinity of the crack tip at such a moment in the cases in which the fracture process develops in mode i (precisely the most brittle fracture events) or with a negligible component of mode ii. in those cases crack tip plasticity is confined in the near tip region, because the plastic zone size never exceeds 10% of the uncracked ligament, thereby indicating that the critical sif is adequate as a key parameter governing fracture. for heavily drawn steels the situation is not so clear, because mixed mode propagation appears and thus the plastic zone size cannot be easily estimated. however, even in these more ductile cases the sif can be considered as an adequate parameter due to the global constraint (triaxiality) provided by the plane strain stress state in the inner points of the crack front. 0 20 40 60 80 100 120 0.0 0.2 0.4 0.6 0.8 1.0 1.2 k c k c90º k c ( m p a m 1 /2 ) p figure 10: fracture toughness, kc and kc90º. discussion old drawing is an effective process for increasing the strength of pearlitic steel, resulting in a considerable improvement in the matter of fracture behaviour (this is very important from the practical engineering viewpoint) while at the same time a strong anisotropy appears during fracture, it being related to microstructural anisotropy produced by plastic deformation as a consequence of cold drawing. similar results were obtained in a fully pearlitic rail steel subjected to large shear strains by equal channel angular pressing (ecap) [3] and by high-pressure torsion (hpt) [20]. c j. toribio et alii, frattura ed integrità strutturale, 33 (2015) 221-228; doi: 10.3221/igf-esis.33.28 227 with regard to the relationship between the macroscopic fracture behaviour of the wires and the microstructure of the progressively drawn pearlitic steels, fig. 11 represents the fracture angle θ (macroscopic) and the pearlite lamellae angle θm (microscopic), both measured in relation to the cross section of the wire, and plotted as a function of the cumulative plastic strain (a measure of the strain hardening level or cold drawing degree in the steel wires). it is seen in fig. 11 shows how both macroand micro-angles increase with plastic deformation, thereby showing how the cumulative plastic strain (and its associated microstructural orientation inside the material) affects the fracture performance of the wires in the form of strength anisotropy, crack path deflection and mixed mode propagation. 0 5 10 15 20 25 30 35 40 45 45 50 55 60 65 70 75 0.0 0.2 0.4 0.6 0.8 1.0 1.2   m  (º )  m (º) p 0 20 40 60 80 100 120 140 160 0.0 0.2 0.4 0.6 0.8 1.0 1.2 k c0º k c90º k c ( m p a m 1 /2 ) p figure 11: fracture angle. figure 12: fracture toughness, kc0º and kc90º. the calculation of the critical sif in mode i at 0º was carried out in a linear way when values were available for both angles. when only the critical sif for an angle different from 0º was available, the slope was not considered, because it was small. results show that the steel becomes more anisotropic in its fracture behaviour as the number of wire drawing steps increases (fig. 12). furthermore, kc0º markedly increases with plastic deformation, tripling itself, while kc90º only slightly increases. for high deformations, kc90º is significantly lower than kc0º, which explains the presence of vertical cleavage walls on the fracture surfaces (and specially the first propagation step oriented 90º in relation to transverse section). this phenomenon can be related to the existence of a rounded crack tip causing a cleavage stress in the horizontal direction, tending to open a vertical cleavage crack [15], in addition to the microstructural anisotropy caused by the wire drawing itself. conclusions old drawing in pearlitic steel induces strength anisotropy associated with a deflection angle in the crack path, changing from being transversal to the wire (in the non-drawn steel) to producing crack deflection with an ever increasing angle as the degree of cold drawing increases during manufacture. the directional toughness (or directional critical stress intensity factor, sif) depends on the deflection angle (macroscopic) of the fracture crack path, such an angle being in turn a function of the microstructural orientation angle of the pearlite lamellae (which tend to be oriented in the wire axis or cold drawing direction). the cold drawing process improves the fracture behavior in mode i for a 0º angle in pearlitic steel (by increasing the fracture toughness and improving the engineering performance), but it induces a marked anisotropy in its fracture behaviour (strength anisotropy, greater with increasing amount of plastic deformation after drawing) due to the strong microstructural anisotropy. acknowledgements he authors wish to acknowledge the financial support provided by the following spanish institutions: ministry for science and technology (micyt; grant mat2002-01831), ministry for education and science (mec; grant bia2005-08965), ministry for science and innovation (micinn; grants bia2008-06810 and bia2011-27870) c t j. toribio et alii, frattura ed integrità strutturale, 33 (2015) 221-228; doi: 10.3221/igf-esis.33.28 228 and junta de castilla y león (jcyl; grants sa067a05, sa111a07 and sa039a08) and the steel supplied by emesa trefilería (la corun ̃a, spain). references [1] juhas, m.c., bernstein, i.m., effect of prestrain on the mechanical properties of eutectoid steel, metall. trans. a, 14 (1983) 1379–1388. [2] yu, s.r., yan, z.g., cao, r., chen, j.h., on the change of fracture mechanism with test temperature, eng. fract. mech., 73 (2006) 331–347. [3] wetscher, f., stock, r., pippan, r., changes in the mechanical properties of a pearlitic steel due to large shear deformation, mater. sci. eng. a, 445–446 (2007) 237–243. [4] toribio, j., toledano, m., fatigue and fracture performance of cold drawn wires for prestressed concrete, constr. build. mater., 14 (2000) 47–53. [5] astiz, m.a., valiente, a., elices, m., bui, h.d., anisotropic fracture behaviour of prestressing steels, in: l.o. faria (ed.), life assessment of dynamically loaded materials and structures ecf5, emas, portugal, (1985) 385–396. [6] toribio, j., valiente, a., approximate evaluation of directional toughness in heavily drawn pearlitic steels, mater. lett., 58 (2004) 3514–3517. [7] toribio, j., valiente, a., failure analysis of cold drawn eutectoid steel wires for prestressed concrete, eng. fail. anal., 13 (2006) 301–311. [8] toribio, j., ayaso, f.j., fracture performance of progressively drawn pearlitic steel under triaxial stress states, mater. sci., 37 (2001) 707–717. [9] alexander, d.j., bernstein, i.m., the cleavage plane of pearlite, metall. trans. a, 13 (1982) 1865–1868. [10] park, y.j., bernstein, i.m., the process of crack initiation and effective grain size for cleavage fracture in pearlitic eutectoid steel, metall. trans. a, 10 (1979) 1653–1664. [11] fernández-vicente, a., carsí, m., peñalba, f., taleff, e., ruano, o.a., toughness dependence on the microstructural parameters for an ultrahigh carbon steel (1.3 wt.% c), mater. sci. eng. a, 335 (2002) 175–185. [12] toribio, j., ayaso, f.j., anisotropic fracture behaviour of cold drawn steel: a materials science approach, mater. sci. eng. a, 343 (2003) 265–272. [13] toribio, j., a fracture criterion for high-strength steel cracked bars, struct. eng. mech., 14 (2002) 209–222. [14] singh, u.p., banerjee, s., on the origin of pop-in crack extension, acta metall. mater., 39 (1991) 1073–1084. [15] toribio, j., gonzález, b., matos, j.c., cleavage stress required to produce fracture path deflection in cold-drawn prestressing steel wires, int. j. fract., 144 (2007) 189–196. [16] toribio, j., álvarez, n., gonzález, b., matos, j.c., a critical review of stress intensity factor solutions for surface cracks in round bars subjected to tension loading, eng. fail. anal., 16 (2009) 794–809. [17] shin, c.s., cai, c.q., experimental and finite element analyses on stress intensity factors of an elliptical surface crack in a circular shaft under tension and bending, int. j. fract., 129 (2004) 239–264. [18] amestoy, m., bui, h.d., dang-van, k., analytic asymptotic solution of the kinked crack problem, in: d. francois (ed.), advances in fracture research ecf5, pergamon press, france, (1981) 107–113. [19] wu, c.h., fracture under combined loads by maximum-energy-release-rate criterion, j. app. mech., 45 (1978) 553– 558. [20] hohenwarter, a., taylor, a., stock, r., pippan, r., effect of large shear deformations on the fracture behavior of a fully pearlitic steel, metall. mater. trans. a, 42 (2011) 1609–1618. microsoft word numero_33_art_19 p.j. whithers et alii, frattura ed integrità strutturale, 33 (2015) 151-158; doi: 10.3221/igf-esis.33.19 151 focussed on characterization of crack tip fields 2d mapping of plane stress crack-tip fields following an overload p. j. withers school of materials, grosvenor st, university of manchester, manchester m13 9pl, uk and the research complex at harwell, rutherford appleton laboratory, didcot, oxfordshire ox11 0fa, uk philip.withers@manchester.ac.uk p. lopez-crespo department of civil and materials engineering, university of malaga, c/ doctor ortiz ramos, s/n, 29071, malaga, spain plopezcrespo@uma.es m. mostafavi department of mechanical engineering, university of sheffield, sir frederick mappin building, mappin street, sheffield s1 3jd, uk m.mostafavi@sheffield.ac.uk a. steuwer nelson mandela metropolitan university, gardham av., 6031 port elizabeth, south africa axel.steuwer@gmail.com j. f. kelleher isis, science and technology facilities council, rutherford appleton laboratory, didcot, oxfordshire ox11 0qx, uk joe.kelleher@stfc.ac.uk t. buslaps esrf, 6 rue j horowitz, 38000, grenoble, france buslaps@esrf.fr abstract. the evolution of crack-tip strain fields in a thin (plane stress) compact tension sample following an overload (ol) event has been studied using two different experimental techniques. surface behaviour has been characterised by digital image correlation (dic), while the bulk behaviour has been characterised by means of synchrotron x-ray diffraction (xrd). the combination of both surface and bulk information allowed us to visualise the through-thickness evolution of the strain fields before the ol event, during the overload event, just after ol and at various stages after it. unlike previous work, complete 2d maps of strains around the crack-tip were acquired at 60m spatial resolution by xrd. the dic shows less crack opening after overload and the xrd a lower crack-tip peak stress after ol until the crack has grown past the compressive crack-tip residual stress introduced by the overload after which the behaviour returned to that for the baseline fatigue response. while the peak crack-tip stress is supressed by the compressive residual stress, the crack-tip stress field changes over each cycle are nevertheless the same for all kmax cycles except at ol. p.j. whithers et alii, frattura ed integrità strutturale, 33 (2015) 151-158; doi: 10.3221/igf-esis.33.19 152 keywords. linear elastic fracture mechanics; closure; plastic strain; bainitic steel; effective stress intensity factor. introduction any crack retardation effects occurring during the fatigue of materials have been explained by the concept of crack closure [1]. closure of the crack-faces either near to, or distant from, the crack-tip means that the cracktip does not experience the full crack-opening fatigue cycle. such effects have been held to be responsible for the immediate acceleration and then subsequent retardation of the crack growth rate observed following an overload during fatigue cycling. diffraction peak shifts are predominantly sensitive to the elastic strain and a number of studies have mapped the strain ahead of, and behind, the crack-tip using neutron [2, 3] or synchrotron x-ray [4, 5] beams. the problem with linescans along the crack plane is that there is a danger that the location of the peak stress may be missed. steuwer et al. [6] were the first to map the stresses in thick (plane strain) samples in 2d at high (25m) resolution, but in this case the plastic zone was small and the crack-tip stress fields dominated largely by elastic behaviour. in this paper, we employ digital image correlation (dic), a non-contact full-field measurement technique, to measure the total (elastic plus plastic) strain on the surface of the specimen. the accuracy of dic to measure elastic strain is debateable, but its capability to measure total strain (considering that plastic strains are orders of magnitude bigger than elastic strains) is unrivalled. the combination of the two techniques provides both elastic (from xrd) and total (dic) strains if the measurements are carried out on the same gauge volume. therefore, we selected a thin (i.e. plane stress) specimen so that the variation of the strain field on the surface, where dic measures the total strain, and the elastic strain averaged through thickness as measured by xrd, is minimised. dic has found increasing application for the study of crack-tip strain fields [7] and it has been possible to extract fracture mechanics information such as closure stresses [8, 9], plastic zone sizes [10], crack-tip opening displacements (ctod) and effective stress intensity factors at the crack-tip, keff [10-14]. lopez-crespo et al. have already combined these complementary methods to examine the strain fields local to a crack-tip in a plane stress (thin) stainless steel compact tension sample prior and subsequent to an overload event [15]. even under plane stress where the surface and bulk states might be expected to be the same, important differences were observed between dic and xrd. surface dic measurements suggested that under fatigue cycling the cracks faces appear to be in contact for around 50% of the cycle supporting a traditional plasticity-induced closure interpretation. indeed they observed a knee in the closure response for baseline fatigue prior to overload, an absence of closure in the accelerated growth regime followed by accentuated closure in the retardation regime. by contrast, measurement of the mid-thickness elastic strain field behind and ahead of the crack made by synchrotron x-ray diffraction showed no evidence of significant crack-face contact stresses immediately behind the crack-tip on approaching minimum loading. though the results were affected by point-to-point scatter due to an insufficiently small grain size, the changes during loading and overloading could mostly be explained by a simple elastic plastic analysis using a value of the yield stress intermediate between the initial yield stress and the uts. this showed very significant compressive plastic strains ahead of the crack that start to form early during unloading. here we revisit this topic by studying a bainitic rather than stainless steel. this has an inherently much finer grain size allowing us to achieve much higher spatial resolution in the x-ray diffraction data with much reduced point to point scatter [16]. further the steel has sufficient toughness that a large plastic zone can be introduced in contrast to the al-li studied by steuwer et al. [6]. this has enabled us to study the elastic strain field and the effect of plasticity on closure in unparalleled detail. material and specimen compact tension (ct) fatigue specimen was machined from quenched and tempered bainitic steel similar to q1n (hy80) [17]. its chemical composition is summarised in tab. 1. the tensile properties are as follows: yield stress (y) = 570 mpa and ultimate tensile stress, uts= 663 mpa. the ct specimen had a width (w) of 60 mm and thickness (b) of 3.3mm. m a p.j. whithers et alii, frattura ed integrità strutturale, 33 (2015) 151-158; doi: 10.3221/igf-esis.33.19 153 alloy c si mn p s cr ni mo cu q1n 0.16 0.25 0.31 0.010 0.008 1.42 2.71 0.41 0.10 table 1: chemical composition in weight % of q1n steel. the balance is fe. experimental setup the crack-tip elastic strain fields were measured on the id15 beamline at the european synchrotron radiation facility (esrf), using the same arrangement as that described in [6] and shown schematically in fig. 1a. the incident beam slits were opened to 60 × 60 µm giving a lateral resolution (x,y) of 60m and a nominal gauge length through-thickness (z) of around 1.4 mm (diamond shaped centred on the mid-plane (z = 0)). this allowed a 10 times greater resolution than in previous elastic strain field mapping experiments for plastically extended crack-tips [15]. such a good resolution was possible because of the small grain size of the bainitic steel used here. the dic was undertaken simultaneously using a single camera set-up [9] taking contrast from the speckle paint as shown in fig 1. the slightly oblique view of the sample was corrected for before the analysis of the data. commercial dic analysis software (la vision gmbh, gottingen, germany) was used to analyse the results and details of the approach are provided in [18]. in this experiment great care was taken to correct for the slight sample movements that took place when the sample was fatigued and when it was statically loaded to kmax (= 35 mpa√m) and kmin (= 1.2 mpa√m) to ensure that all of the strain maps were recorded with respect to the sample coordinates and not the lab coordinates. to this end both shifts recorded by dic analysis and by edge scans by xrd were used. it is estimated that we were able to correct the sample location to ± 50m.  a) b) figure 1: schematics showing a) the diffraction geometry with two detectors so as to measure two in-plane directions of strain; note the coordinate system for xx and yy. for very low  these strains can be taken as representative of those in the loading (y) and crack growth (x) directions, b) the dic arrangement [9]. in actual fact the camera viewed the sample at a slight angle to allow the x-ray beam unimpeded access to the sample. fatigue experiment he specimen was fatigue pre-cracked for 3000 cycles at a frequency of 10 hz, stress intensity range δk = 35 mpa√m and load ratio kmin/kmax = 0.03. plane stress conditions were met at the mid-plane through the thickness for all loads applied during the experiment [19]. the crack length was measured perpendicularly to the loading direction from the centre of the loading holes [20]. once the fatigue crack had grown to a length of 12.75 mm, a 67 % overload (ol) was applied. strain measurements were made at a number of fatigue stages, namely during the cycle just before the overload (ol 1), during the overload (ol), 40 cycles after the overload (ol + 40), 2040 cycles after the overload (ol + 2k), 8040 cycles after the overload (ol + 8k) and 37540 cycles after the overload (ol+37k). in addition to t x y p.j. whithers et alii, frattura ed integrità strutturale, 33 (2015) 151-158; doi: 10.3221/igf-esis.33.19 154 2d maps, a profile of the evolution of strain behind and ahead of the crack-tip was produced for each of the fatigue stages studied by measuring around 50 strain points along the crack plane (y = 0) at different distances from the location of the crack at overload. crack growth in the specimen was measured from the overload location using xrd line scans: 0.08 mm for ol + 40, 0.22 mm for ol+2k, 0.27 mm for ol+8k and 2.05 mm for ol+37k cycles. these values were used for correcting the current location of the crack tip at each loading stage in the following results. results and discussion he elastic strains were measured directly from the diffraction profiles using a rietveld-style refinement to obtain the lattice spacing representative of the diffraction peaks as a whole. elastic strain maps were obtained showing very little point-to-point scatter. the elastic strains parallel to the loading direction (yy) and parallel to the crack growth direction (xx) are shown in fig. 2 at the overload. the elastic strain fields are broadly similar in shape and magnitude to those recorded by steuwer et al. [6]. the images taken from the surface of the sample were analysed using lavision davis v6.4 employing a least square algorithm with subset size 31 (patch size) and step size 8 pixels (75 % overlap). the corresponding total (elastic plus plastic) strains recorded at 1.7 kmax were obtained from dic and are also shown in fig 2. unsurprisingly, the elastic strains are 5-10 times smaller than the total strains local to the crack due to plastic deformation. a simple irwin analysis would predict a plastic zone of around 3.5mm for the overload event (60 mpa√m). the dic shows clearly the characteristic plastic lobes. a) b) c) d) figure 2: strain maps at overload (ol) showing the elastic strains measured by xrd in the a) loading direction yy (%) and b) parallel to the crack growth direction xx (%) and the total strain measured by dic in the c) loading direction tot yy (%) and d) parallel the crack growth direction totxx (%). the xrd measurements were performed while the sample was loaded at the maximum load (1.7 kmax); the dic strains were calculated from full-field displacements measured by comparing the images of the surface of the sample taken at maximum load (1.7 kmax) and minimum load (kmin) in the cycle just before the overload. t p.j. whithers et alii, frattura ed integrità strutturale, 33 (2015) 151-158; doi: 10.3221/igf-esis.33.19 155 a) b) figure 3: mid-plane maps of stress in the loading direction yy (in mpa) calculated from the elastic xx and yy measured by synchrotron xrd a) at ol (1.7 kmax) b) immediately after ol at minimum load (kmin). note the different colours scales used. unfortunately it is not possible to measure the through-thickness elastic strain zz with the same spatial definition as the two in-plane strains, however the stresses can be inferred using the relation for plane stress ( 0zz  ) using the diffraction elastic constants representative of the polycrystal because all the diffraction peaks were used in the refinement. 21 xx xx yy e         the crack-tip stress in the loading direction is shown in fig. 3a), which clearly shows the classical butterfly stress field (hrr field) formed around the crack-tip. the 2d elastic stress field within the plastic zone has not been mapped in previous studies. the dic data allow the crack opening displacement to be mapped in the vicinity of the crack (fig. 4a). it is clear from the dic (fig. 2) that the plastic zone extends 3-4 mm ahead of the crack tip although its magnitude falls away quickly. the residual stress field shows a slight tensile hump around 2.5 mm ahead of the crack (see later discussion). a) b) figure 4: dic analysis showing the a) vertical displacement field vy (in mm) between 1.7kmax (ol) and at kmin prior to ol, b) change in crack opening displacement (cod) profiles at maximum load using the state at kmin prior to ol as the reference state. the effect of the compressive residual stress field, which has been generated at the crack-tip by the overload, on the peak stress in the loading direction after (ol + 40) compared with that measured before the (ol 1) overload is evident in fig. 5a. an approximately 50% decrease is observed in the maximum stress in the crack loading direction near the crack-tip before and after the overload. the magnitude of the residual stress induced by the overload can be estimated by comparing the peak compressive stress just ahead of the crack-tip before and after the overload (see fig. 5b). as can be seen in the figure the maximum compressive stress at kmin just before the overload is approximately 550 mpa which increases to almost 1000 mpa immediately after the overload. it is clear from fig. 5c that the elastic change in stress in the crack-tip region upon loading to kmax is essentially the same as that for the baseline fatigue cycle (ol 1) for all the post overload cycles, it is just that post ol the cycles are displaced by the compressive residual stress field introduced by the ol event. this is consistent with the observations of lopez-crespo et al. [16] for a thick (plane strain) ct sample of the same steel. p.j. whithers et alii, frattura ed integrità strutturale, 33 (2015) 151-158; doi: 10.3221/igf-esis.33.19 156 the change in crack opening displacement (cod) between minimum and maximum load with distance behind the crack tip is shown in fig. 4b. unsurprisingly the crack opening is much greater at ol than prior to it (ol 1). after ol the crack opening displacement appears to be reduced (by around 30 %) at kmax relative to ol 1 for the first 8k cycles returning to a level similar to that for ol 1 after 37k cycles. the reduction in the change in crack opening (i.e. crack opening displacement between first kmin before ol and kmax at each loading state) displacement can be interpreted as 54% reduction in the effective stress intensity factor range and is consistent with plasticity-induced crack closure. given the resolution of the dic system, the crack can be assumed to be closed if cod < 2.5m. accordingly, the crack length can be fictitiously reduced by 1mm for ol 1 and ol + 37k and by 2mm for ol + 40, ol + 2k and ol + 8k. this may be because of the closure effects, which might be expected to be most prominent on the surface where the dic measurements are made and does not allow the crack to open beyond the resolution of the dic and therefore gives the impression of a shorter crack. there are a number of other interesting features relating to the stress profiles shown in fig. 5. most importantly, it is evident that only when the crack has grown through the compressive residual stress field introduced by the ol, does the cod or the peak crack-tip elastic strain field revert to that representative of the original baseline fatigue response (ol 1). secondly, the ‘hump’ in the stress in the crack-opening direction which is generated 2.5 mm ahead of the crack when the overload is applied is retained for the ol + 40, +2k and +8k cycles but is not present for the baseline fatigue or for the last increment. because the unload curves are elastic the ‘hump’ is also evident in the unloaded profiles too. both these observations are almost certainly connected to the fact that only after 37k cycles has the crack-tip grown sufficiently (by 2.05 mm) to have emerged from the plastic zone introduced by the overload. a) b) c) figure 5: xrd line profiles along y = 0 showing the crack loading stress yy (mpa) a) at maximum load b) at minimum load and c) the difference between the stresses at maximum and minimum load at each stage in the fatigue crack growth response. conclusions x-ray diffraction and digital image correlation techniques were simultaneously used to successfully measure the change in the elastic and plastic strain fields around a fatigue crack after an overload p.j. whithers et alii, frattura ed integrità strutturale, 33 (2015) 151-158; doi: 10.3221/igf-esis.33.19 157 the dic surface strain measurements are consistent with a plastic zone extending some 3-4 mm ahead of the cracktip; while the stresses recorded by diffraction show a slight tensile hump 2.5 mm ahead of the crack-tip. both the elastic strain field measured by xrd and the crack opening displacement measured by dic showed a reduction in their peak values as a result of the compressive residual stress field induced around the crack-tip after the overload once the crack had grown through the sufficiently to have essentially both the change in crack opening displacement and the peak tensile crack-tip stress field returned to levels similar to that prior to the overload event. acknowledgements he authors are grateful to the esrf for id15 beam-time awarded under ma1483. references [1] elber, w., fatigue crack closure under cyclic tension, eng. fract. mech., 2 (1970) 37-45. [2] hutchings, m.t., hippsley, c.a., rainey, v., neutron diffraction measurement of the stress field during fatigue cycling of a cracked test specimen, mat. res. soc. symp. proc., 166 (1990) 317. [3] lee, s.y., liaw, p.k., choo, h., rogge, r.b., a study on fatigue crack growth behavior subjected to a single tensile overload part i. an overload-induced transient crack growth micromechanism, acta materialia, 59 (2011) 485-494. [4] steuwer, a., santisteban, j.r., turski, m., withers, p.j., buslaps, t., high-resolution strain mapping in bulk samples using full-profile analysis of energy dispersive synchrotron x-ray diffraction data, nucl. instr. meth. physics research b, 238b (2005) 200-204. [5] croft, m., zhong, z., jisrawi, n., zakharchenko, i., holtz, r.l., skaritka, j., fast, t., sadananda, k., lakshmipathy, m., tsakalakos, t., strain profiling of fatigue crack overload effects using energy dispersive x-ray diffraction, international journal of fatigue, 27 (2005) 1408-1419. [6] steuwer, a., rahman, m., shterenlikht, a., fitzpatrick, m.e., edwards, l., withers, p.j., the evolution of crack-tip stresses during a fatigue overload event, acta. mater., 58 (2010) 4039-4052. [7] sutton, m.a., mcneill, s.r., helm, j.d., boone, m.l., measurement of crack tip opening displacement and full-field deformations during fracture of aerospace materials using 2d and 3d image correlation methods, iutam symposium on advanced optical methods and applications in solid mechanics, 82 (2000) 571-580. [8] nowell, d., de matos, p.f.p., application of digital image correlation to the investigation of crack closure following overloads, in: p. lukas (ed.) fatigue 2010, (2010) 1035-1043. [9] yusof, f., lopez-crespo, p. p.j. withers, effect of overload on crack closure in thick and thin specimens via digital image correlation, international journal of fatigue, 56 (2013) 17-24. [10] lopez-crespo, p., shterenlikht, a., yates, j.r., patterson, e.a., withers, p.j., some experimental observations on crack closure and crack-tip plasticity, fat. fract. eng. mater, struct., 32 (2009) 418-429 [11] shterenlikht, a., garrido, f.a.d., crespo, p.l., withers, p.j., patterson, e.a., mixed mode (ki + kii) stress intensity factor measurement with espi and image correlation, adv. in exp. mech., 1-2 (2004) 107-112. [12] shterenlikht, a., lopez-crespo, p., patterson, e.a., withers, p.j., yates, j.r., determining stress and stress intensity from displacement fields using muskhelishvili’s approach, i. j. fatigue, (2007). [13] lopez-crespo, p., shterenlikht, a., patterson, e.a., yates, j.r., withers, p.j., the stress intensity of mixed mode cracks determined by digital image correlation j. strain anal. by eng. design, 43 (2008) 769-780. [14] lópez-crespo, p., patterson, e.a., shterenlikht, a., withers, p.j., yates, j.r., study of a crack at a fastener hole by image correlation, exp. mech., 49 (2009) 551-559. [15] lopez-crespo, p., withers, p.j., yusof, f., dai, h., steuwer, a., kelleher, j.f., buslaps, t., overload effects on fatigue crack-tip fields under plane stress conditions: surface and bulk analysis, fatigue and fracture of engineering materials and structures, 36 (2013) 75-84. [16] lopez-crespo, p., steuwer, a., buslaps, t., tai, y.h., lopez-moreno, a., yates, j.r., withers, p.j., measuring overload effects during fatigue crack growth in bainitic steel by synchrotron x-ray diffraction, international journal of fatigue, 71 (2015) 11-16. t p.j. whithers et alii, frattura ed integrità strutturale, 33 (2015) 151-158; doi: 10.3221/igf-esis.33.19 158 [17] robertson, i.m., measurement of the effects of stress ratio and changes of stress ratio on fatigue crack growth rate in a quenched and tempered steel. , int. j. fatigue, 16 (1994) 216-220. [18] quinta da fonseca, j., mummery, p.m., withers, p.j., full-field strain mapping by optical correlation of micrographs acquired during deformation, j. micros., 218 (2005) 9-21. [19] anderson, t.l., fracture mechanics, fundamentals and applications, 3rd edition ed., crc press, (2005). [20] murakami, y., stress intensity factors handbook, oxford: pergamon press, (1987). microsoft word numero_34_art_48 m. goto et alii, frattura ed integrità strutturale, 34 (2015) 427-436; doi: 10.3221/igf-esis.34.48 427 focussed on crack paths growth behavior of fatigue cracks in ultrafine grained cu smooth specimens with a small hole masahiro goto, kakeru morita, junichi kitamura, takaei yamamoto, masataka baba department of mechanical engineering, oita university, japan. masagoto@oita-u.ac.jp, v14e1035@oita-u.ac.jp, junichi@oita-u.ac.jp, tyama@oita-u.ac.jp, v14e1025@oita-u.ac.jp seung-zeon han materials engineering department, korea institute of materials science, republic of korea. szhan@kims.re.kr sangshik kim department of metallurgical and materials engineering, gyeongsang national university, republic of korea. sang@gnu.ac.kr abstract. in order to study the growth mechanism of fatigue cracks in ultrafine grained copper, stresscontrolled fatigue tests of round-bar specimens with a small blind hole as a crack starter were conducted. the hole was drilled on the surface where an intersection between the shear plane of the final ecap processing and the specimen surface makes an angle of 45° or 90° with respect to the loading axis. at a low stress (a = 90 mpa), the direction of crack paths was nearly perpendicular to the loading direction regardless of the location of the hole. profile of crack face was examined, showing the aspect ratio (b/a) of b/a = 0.82. at a high stress (a = 240 mpa), although the growth directions inclined 45° and 90° to the loading-axis were observed depending on the location of the drilling hole, crack faces in these cracks were extended along one set of maximum shear stress planes, corresponding to the final ecap shear plane. the value of aspect ratios was b/a = 0.38 and 1.10 for the cracks with 45° and 90° inclined path directions, respectively. the role of deformation mode at the crack tip areas on crack growth behavior were discussed in terms of the mixed-mode stress intensity factor. the crack path formation at high stress amplitudes was affected by the in-plane shear-mode deformation at the crack tip. keywords. fatigue; ultrafine grain; copper; crack propagation; grain coarsening; stress intensity factor. introduction qual channel angular pressing (ecap) is currently used to obtain grains down to the submicron level, which are tenfold to hundredfold finer than conventional materials. until recently, most studies have focused on optimizing processing conditions, underlying microstructural mechanisms, or attainable post-ecap strength levels [1-4]. for e m. goto et alii, frattura ed integrità strutturale, 34 (2015) 427-436; doi: 10.3221/igf-esis.34.48 428 envisaged structural applications of ultrafine grained (ufg) metals, attention has been paid to fatigue performance. studies of fatigue on ufg materials processed by ecap has been focused mainly on cyclic deformation, s-n plots, formation of shear bands (sbs) and underlying microstructural mechanisms [5-11]. since the fatigue life of machine components and structures is mainly controlled by the growth life of a fatigue crack, the crack growth behavior should be clarified for the design of safe machine components and structures. recently, in the high-cycle fatigue (hcf) tests, the growth behaviors of long (millimeter-range) cracks in ufg metals [12-16] were studied for compact-tension, single edge-notched, single edge bend and center-cracked tensile specimens. with regard to the growth characteristics of long fatigue cracks in ufg materials, the higher growth rates in low and medium values of the stress intensity factor (sif) range and the lower growth thresholds have been reported. these phenomena appear to be attributed to the weakened roughness-induced crack closure caused by the much smoother fracture surface and lower deflection of the crack path. the smoother crack-path/fracture-surface is caused by decreased grain sizes and limited crack tip plasticity. it has been shown that the crack growth life from an initial size to 1 mm accounted for about 70% of the fatigue life of plain specimens of many conventional grain-sized metals [17, 18]. therefore, the growth behavior of small cracks must be clarified to estimate the fatigue life of smooth members. regarding the crack growth in strain-controlled low-cycle fatigue (lcf) tests and stress-controlled fatigue tests at high stress amplitudes corresponding to lcf regime, study on fatigue crack growth mechanism has been relatively rare, and only a few reports can be found [19, 20]. meanwhile, for ecaped samples, the yz-, zx-, and xy-planes are defined by three mutually orthogonal sectioning planes that are perpendicular to the longitudinal axis of the pressed sample, parallel to the sample side, and parallel to the sample top faces at the point of exit from the die, respectively. in strain-controlled lcf tests, sbs in the zx-plane were oriented at 45° to the loading axis parallel to the longitudinal axis of the pressed samples, while those in the xy-plane were nearly perpendicular to the loading axis [21]. the sbs appear on the zx-plane at 45° to the loading direction mainly because it is the plane of maximum resolved shear stress [22]. fatigue cracks were initiated in and propagated along these sbs. consequently, the lcf crack on the zx-plane grew along the direction inclined at 45° to the loading axis. up to now, lcf crack growth behavior of ufg materials have been mainly discussed from the viewpoints of microstructure and morphological features of surface damage. on the other hand, the discussion from the mechanical viewpoints should be done for a better understanding of the fatigue damage of ufg materials. however, such studies are few and certain questions remain unanswered. the objective of this study is to investigate the physical background of the formation mechanism of crack growth paths in the hcf and lcf regimes in terms of the mixed-mode deformation at the crack tip. experimental procedures ure oxygen-free copper (99.99 wt% cu) was used in the experiment. prior to ecap processing, the samples were annealed at 500°c for 1 h (average grain size: 100 m). the ecap die had a 90° angle between intersecting channels. the angles at the inner and outer corners of the channel intersection in the die were 90° and 45°, respectively. repetitive ecap was accomplished according to the bc route (after each pressing, the billet bar was rotated 90° around its longitudinal axis). eight extrusion passes resulted in an equivalent shear strain of approximately 7.8. the microstructure of an ecap rod obtained using a transmission electron microscope showed fine equiaxed grains of approximately 300-nm diameter and large elongated grains. fatigue specimens 5 mm in diameter were machined from their respective processed bars. although the specimens had shallow circumferential notches (20-mm notch radius and 0.25-mm notch depth), the fatigue strength reduction factor for this geometry was close to 1, meaning that they could be considered plain. the fatigue specimens were electrolytically polished (approximately ≈25 m from the surface layer) prior to mechanical testing to remove any preparation-affected surface layer. polishing was carried out at 25°c using an electrolyte consisting of 600 ml of phosphoric acid, 300 ml of distilled water, and 100 ml of sulfuric acid. prior to testing, a small blind hole (both diameter and depth of 0.1 mm) was drilled as a crack starter on the middle surfaces of the plain specimens. fig. 1 shows the location of the drilling hole. a hole was drilled on the surface where an intersection between the shear plane of the final pressing and the specimen surface makes an angle of 45° (zx-plane) or 90° (xy-plane) with respect to the loading axis. all fatigue tests were performed at room temperature using a rotating-bending fatigue machine (constant bending-moment type) operating at 50 hz. the fatigue damage on the specimen surface was observed using an optical microscope (om) and a scanning electron microscope (sem). the crack length, l, was measured along the circumferential direction of the surface. the p m. goto et alii, frattura ed integrità strutturale, 34 (2015) 427-436; doi: 10.3221/igf-esis.34.48 429 crack length was measured using a plastic replication technique. the stress value referred to is that of the nominal stress amplitude, a, at the minimum cross-section (5-mm diameter). figure 1: illustration showing the location of the drilled hole as a crack starter, and the shear plane of the final ecap pressing. the distribution of the grain sizes and grain boundary misorientation were determined by electron backscatter diffraction (ebsd) analysis. the specimens were ground using silicon carbide papers and polished with polycrystalline 3and 1-m diamond suspension. final polishing was performed using a 0.04-m colloidal silica suspension for 30–60 min. ebsd mappings were executed using a tescan mira ii sem incorporating an edax-tsl hikari ebsd detector. each hexagonally shaped pixel was 40 nm for the ufg copper samples and 1.0 m for the conventional grain-sized copper samples. orientation imaging microscopy analysis software version 5.3 was used to analyze the orientation characteristics and misorientation distributions. experimental results ig. 2 show the crack growth paths in the zxand xy-planes under high and low stress amplitudes (a = 240 and 90 mpa). the surface-cracks within the zxand xy-planes are referred to hereafter as the “zx-plane crack” and “xyplane crack”, respectively. at a = 240 mpa, the zx-plane crack that initiated from the hole created a 45° incline to the loading axis and this crack path direction was parallel to the shear direction of the final ecap processing (fig. 1). the 45° inclined crack growth direction has been commonly observed in the zx-plane of lcf ufg metals [20, 21, 23]. however, the xy-plane crack grew nearly perpendicular to the loading axis like crack paths in conventional grain-sized materials. at a = 90 mpa, on the other hand, the macroscale growth direction was perpendicular to the loading axis regardless of the plane where the crack initiated; nevertheless, the crack propagated in a zigzag manner at the microscale. figure 2: effect of stress amplitudes on crack growth paths in the zxand xy planes: (a, and b) the zx-plane crack at a = 240 and 90 mpa; (c and d) the xy-plane crack at a = 240 and 90 mpa. f m. goto et alii, frattura ed integrità strutturale, 34 (2015) 427-436; doi: 10.3221/igf-esis.34.48 430 the sem micrograph in fig. 3a shows the post-fatigued surface at repeated stressing of a = 240 mpa. a high population of sbs was observed over the whole surface of the specimen. the sbs initiated along the shear plane of the final ecap processing, and their lengths were less than ten micrometers. on the other hand, the post-fatigued surface formed under a = 90 mpa (fig. 3b) had slip-band like traces greater than a few tens of micrometers. the difference in formation mechanism of surface damage between high and low stress amplitudes should affect the formation mechanisms of crack paths under high and low stresses. figure 3: sem micrographs of damaged traces in the post-fatigued specimens: (a) sbs at a = 240 mpa (nf =1.95×105); (b) slip band like traces at a = 90 mpa (nf =1.33×107) . to study the crack growth path inside the specimen fatigued at high and low stress amplitudes, the specimens were sectioned in the longitudinal direction (parallel to the x-axis), at specific crack lengths (figs. 4 and 5), followed by etching of the sectioned planes. figs. 4b and 4d show the crack growth path formed at a = 240 mpa in the sectioned plane for the zxand xy-plane crack, respectively. the inner growth direction of the zx-plane crack was perpendicular to the specimen surface (zx-plane). for the xy-plane crack, although the inner growth direction just after the initiation was nearly perpendicular to the loading axis, the crack gradually changed its direction to the plane inclined 45° to the specimen surface (xy-plane). although the inclination direction of the crack path to the loading axis was different between the zx and xy-plane cracks, the paths for both cracks were parallel to the shear plane of the final ecap pressing (fig. 1), except for the initial growth path in the xy-plane crack. figs. 5b and 5d show the crack growth path formed at a = 90 mpa in the sectioned plane for the zxand xy-plane crack, respectively. the crack growth paths for both planes were vertical to the specimen surface. the vertical growth path was commonly observed in the conventional grain-sized materials. figure 4: crack paths at a = 240 mpa: (a and c) sectioning position described in the crack paths of the zxand xy-planes; (b and d) crack paths in the sectioned plane for the zxand xy-plane cracks. m. goto et alii, frattura ed integrità strutturale, 34 (2015) 427-436; doi: 10.3221/igf-esis.34.48 431 figure 5: crack paths at a = 90 mpa: (a and c) sectioning position described in the crack paths of the zxand xy-planes; (b and d) crack paths in the sectioned plane for the zxand xy-plane cracks. fig. 6 shows the profile of the crack face, y/l or z/l versus t/l relationship. dashed lines in fig. 6a are the crack face profile at a = 240 mpa represented in terms of t/l, where, l and l are the crack length measured along the circumferential direction at the specimen surface, and along the crack path direction, respectively, and t and t are the crack depth measured along the vertical direction to the specimen surface, and along the crack face direction, respectively (figs. 7a and 7b). here, for the xy-plane crack, the flat crack face/path illustrated in fig. 7b was assumed, whereas the actual path was slightly curved, especially in the initial growth stage. the values of t/l and t/l at the deepest point were figure 6: profile of the crack face in terms of dimensionless sizes: (a) a = 240 mpa; (b) a = 90 mpa. figure 7: definition of the crack length/depth for inclined cracks: (a) the zx-plane crack; (b) the xy-plane crack. m. goto et alii, frattura ed integrità strutturale, 34 (2015) 427-436; doi: 10.3221/igf-esis.34.48 432 0.266 and 0.189 for the zx-plane crack, and 0.389 and 0.550 for the xy-plane crack, respectively. fig. 6b shows the crack face profile at a = 90 mpa. there was no significant difference in the crack face shape between the zxand xy-plane cracks. the value of t/l (= t/l) at the deepest point was 0.41 for both planes. discussion fg materials processed by spd techniques have non-equilibrium microstructures [24, 25] with limited thermal and mechanical stability. such non-equilibrium microstructures can easily change properties under applied cyclic stressing at a certain temperature. remarkable levels of grain coarsening as the result of dynamic recrystallization have generally occurred in post-fatigued high-purity ufg copper [26, 27], whereas it has been shown that no grain coarsening occurred in cyclically deformed ufg copper [23, 28]. to study the grain growth as a result of cyclic stressing, ebsd analysis of the post-fatigued specimens was conducted. in order to conduct ebsd analysis of the post-fatigued microstructure just under the specimen surfaces, 0.15 mm surface layers of the post-fatigued round bar specimens were polished off to make a flat surface for ebsd analysis. the procedure for making the flat surface and the area analysed by ebsd are shown in a previous work [20]. fig. 8a shows inverse pole figure (ipf) maps and grain boundary (gb) map of a post-ecap sample (pre-fatigue) in the zx-plane. figs. 8b and 8c show the microstructure after a constant stressing of a = 240 and 90 mpa, respectively. the gbs in the gb maps are denoted either by red lines corresponding to low angle gbs (lagbs) where the misorientation, , is between 2˚ and 15˚ or by black lines corresponding to high angle gbs (hagbs) with  > 15˚. the ipf maps for the post-fatigued sample indicates the development of subgrains within elongated grains, isolated with lagbs. image quality maps [27] showed that the microstructure in post-ecap copper has enhanced strain energy due to the redundant defect structure, and the microstructure was therefore in the process of evolving to equiaxed grains isolated with hagbs. the post-fatigue microstructure subjected to the constant stressing experienced grain coarsening, but the coarse grain sizes depended on the applied stress amplitudes. at high stress amplitude of a = 240 mpa, coarse grains evolved from 1 to a few m (figs. 8b). no significant difference in coarse grain sizes between the zx and xy-planes was observed. at a = 90 mpa, long-term repetitions produced large coarse grains in excess of several tens of micrometres (fig. 8c). like the zx--plane, large coarse grains were observed in the xy-plane fatigued at a = 90 mpa. accordingly, it should be concluded that the damaged traces greater than a few tens of micrometers initiated at a low stress (fig. 3b) were slip-bands formed in the coarse grains generated as a result of dynamic recrystallization. regarding sb formation in the lcf regime, many investigators have observed morphological features and microstructure of sbs, discussing the formation mechanism of sbs in conjunction with the grain coarsening. however, clear evidence for an sb formation in ufg copper is still lacking, there are opposite views; for example, i) in ref.[26], the mechanism responsible for the sb formation was found to be the interaction of cyclically induced cell/grain coarsening, which led to strain localization, and ii) no grain coarsening occurred in cyclically deformed ufg copper (99.9% cu [23]), and the coordinating gb sliding along the shear plane of the last ecap pass could be the decisive mechanism in sb formation. the role of grain coarsening on the formation of sbs have been under discussion for a long time and are still awaiting final answers. regarding the crack paths, at low stress amplitudes (hcf regime), the growth direction of fatigue cracks in ufg copper was perpendicular to both the surface and loading direction regardless of the initiation site of cracks. there was no effect of microstructural inhomogeneity resulted from ecap processing on the crack growth direction. this was because of the grain coarsening. as a result of generation of dynamically recrystallized coarse grains, the inhomogeneity of matrix caused by the ecap processing is likely to disappear, giving rise to the macroscale growth-path perpendicular to both the specimen surface and loading direction. accordingly, like conventional grain-sized materials, the crack at low stresses propagates via the striation formation mechanism [27], which is associated with crack tip retardation and blunting. however, the crack growth direction in the lcf regime (high stress amplitudes) was different from that in the hcf regime. in order to investigate the physical background of the unique crack growth directions at high stress amplitudes from the viewpoints of the deformation mode at the crack tip, the sif values were evaluated, by assuming a semi-infinite body with inclined semi-elliptical surface cracks, subjected to tension stress in the x-direction at infinity. the applied tension stress is resolved into two stress components perpendicular and tangential to the crack face. accordingly, a 45° inclined surface crack is subjected to both normal,  (= 1), and shear stress,  (= 1), as illustrated in figs. 9a and 9b. noda et al. [29] analysed the sifs of a semi-elliptical surface-crack subjected to modes i, ii and iii loading. the values of dimensionless sif (dl-sif), fi, fii, fiii, for the current surface-crack were taken from noda’s solution calculated for poisson’s ratio:  = 0.3. the dl-sif, fi(), fii(), fiii(), were defined as; u m. goto et alii, frattura ed integrità strutturale, 34 (2015) 427-436; doi: 10.3221/igf-esis.34.48 433 figure 8: orientation imaging microscopy orientation for sub-surface microstructure in the zx-plane: (a) original microstructure before stressing; (b) after constant stressing at a = 240 mpa; (c) after constant stressing at a = 90 mpa fi(α) = ki(α)/kie(α) i = i, ii, iii (1) where, ki() is sif along the crack front and kie() is sif of an elliptical crack [29]. the location along a crack front was defined by the eccentric angle of the ellipse, , defined as the angle for mapping a semi-circle illustrated with a dashed line in fig. 9c. namely, the actual position of a semi-elliptical crack at a given value in fig. 9c is indicated by a point a for the zx-plane crack (b < a), and point b for the xy-plane crack (a < b). here, a and b are the half lengths and depth of a semi-elliptical crack measured along the crack face, respectively (fig. 9c). the crack front at the surface and the deepest point are shown by = 0 and 90°, respectively. however, the dl-sif values at the surface were evaluated by the values figure 9: inclined semi-elliptical surface-cracks in a semi-infinite body subjected to tension load in the x-direction at infinity: (a and b) a model for crack on the zxand xy-planes; (c) the definition of , and actual position for the zxand xy-plane crack fronts. at  = 1° instead of  = 0°, because in 3-dimensional surface cracks, the point where the crack front intersects a free surface is known as a corner point. the stress singularity at this point is different from that of an ordinary crack [30]. generally, it has been difficult to obtain smooth distributions of sifs along the crack front accurately. m. goto et alii, frattura ed integrità strutturale, 34 (2015) 427-436; doi: 10.3221/igf-esis.34.48 434 tabs. 1 and 2 show the dl-sif values of cracks with the aspect ratio, b/a = 0.38 (t/l = 0.189) for the zx-plane crack, and 1.1 (t/l = 0.550) for the xy-plane crack, which are given from fig. 6a. the value of fi for the zx-plane crack is larger at the crack bottom ( = 90°), than at the surface ( = 1°). therefore, it is natural to consider that the crack growth rate toward the inner direction should be larger than that toward the crack length direction in the surface, giving rise to an aspect ratio larger than 1. however, the actual aspect ratio was much smaller than 1. regarding the value of fii, it was 0.77 at the surface, but it was 0 at the bottom. the large fii value at the surface promotes in-plane shear-mode crack growth. at the bottom, fiii takes a value of 0.83, but it seems reasonable to assume that anti-plane shear-mode deformation at the deepest point is negligible for the inward crack growth. consequently, the zx-plane crack predominantly propagated at the surface due to in-plane shear-mode deformation, which brings the generation of new sbs and extension of pre-existent sbs around the crack tip areas, producing the aspect ratio much smaller than 1. the tensile-mode deformation reflected by large fi values should play the role of crack growth. however, by considering a shallow semi-elliptical shape of crack face, it can be expected that the tensile-mode crack growth has negligible effect on the formation of shallow crack face shape. rather, the tensile-mode deformation might assist shear-mode growth, through the de-bonding of sbs around the crack tip. it was shown that in stress-controlled fatigue tests of ufg cu corresponding to an lcf regime [20], the crack grows along the direction at an incline of 45° to the loading axis, because of the shear banding induced by the maximum shear stress and sb decohesion process. under frictionless condition, the growth resistance to shear-mode crack is likely to be smaller than that to tensile-mode crack. it was shown that in conventional grain sized cu alloys [31], the growth rate of the shear-mode crack is larger than that of the tensile-mode crack, with the same crack length and same stress amplitude. type of crack (deg) fⅰ fⅱ fⅲ zx-plane crack b/a = 0.38 1 0.68 0.77 0.31 90 0.93 0 0.83 table 1: dimensionless stress intensity factors for the zx-plane crack (b/a = 0.38, a = l/2). type of crack (deg) fⅰ fⅱ fⅲ xy-plane crack b/a = 1.1 1 0.74 -0.08 0.09 90 0.60 0.53 0 table 2: dimensionless stress intensity factors for the xy-plane crack (b/a = 1.10, a = l/2). for the xy-plane crack (tab. 2), the fi value at the surface was 0.74, which is larger than 0.60 at the bottom. this should lead to a superior extension of crack length, compared to the crack depth (b/a < 1), if the crack growth was dominantly controlled by the tensile-mode. however, the actual crack extension was accelerated at the bottom, rather than the surface. on the other hand, the fii value was higher at the bottom (0.53) than the surface (-0.08), suggesting that the deep semi-elliptical shape of the xy-plane crack was attributable to the crack extension due to in-plane shear-mode deformation at the bottom. at the surface, mode i crack growth appeared to be predominant, because of negligible values of fii and fiii. in addition, the de-bonding of pre-existent sbs in the heavily deformed zone around crack tips occurred due to the tensile-mode deformation, forming a zigzag crack path, as the result of joining the crack and de-bonded sbs. such a growth path may be convenient for roughness-induced crack closure, which contributes to a decrease in cgr at the surface. it can be concluded, therefore, that mode ii crack growth plays an important role in determining the crack face shape of ecaped ufg copper in lcf regime. it has been shown that the sbs appear on the zx-plane at 45° to the loading direction, mainly because it is the plane of maximum resolved shear stress. however, as innumerable planes of maximum shear stress exist, why does only one set of sbs form? to answer this question regarding the formation of only one “family” (one plane and shear direction), agnew et al. [22] suggested the action of a small sample misalignment. during the full tension-compression of such small samples (2×2 mm cross section), alignment is critical and any deviation would increase the likelihood of the nucleation one type of sbs. goto et al. [32] monitored the surface of ecaped copper fatigued by a rotating-bending fatigue machine that has no structural misalignment relating to the nucleation of one type of sbs, showing that sbs were oriented along one set of m. goto et alii, frattura ed integrità strutturale, 34 (2015) 427-436; doi: 10.3221/igf-esis.34.48 435 maximum shear planes which correspond to the shear plane of the final pressing. therefore, questions regarding why one type of sbs nucleates, as observed, are still unanswered. conclusions he main findings of this study can be summarized as follows: the direction of the crack growth paths strongly depended on both stress amplitudes and crack initiation sites along the circumferential direction of the round-bar specimen. at low stress amplitudes, like conventional grainsized materials, the cracks grew perpendicular to both the loading direction and specimen surface regardless of the crack initiation sites. at high stress amplitudes, the inclination of crack paths were observed. on the specimen surface, the inclination of the crack paths to the loading direction was 45° in the zx-plane and 90° in the xy-plane, whereas the inner crack path was inclined 90°and 45°to the specimen surface in the zxand xy-plane crack, respectively. profile of crack at low stress amplitudes showed the aspect ratio of b/a = 0.82 for both plane cracks. at high stress amplitudes, the values of aspect ratios was b/a = 0.38 and 1.10 for the zxand xy-plane crack, respectively. the crack at low stress amplitudes propagated via the striation formation mechanism, which is associated with crack tip retardation and blunting. at high stress amplitudes, however, the formation of crack paths was strongly affected by the in-plane shear-mode deformation and the sb decohesion process around the crack tip areas. acknowledgments his study was supported by a grant-in-aid for scientific research (c) (kakenhi: no. 26420021) from the ministry of education, science and culture of japan, as well as a national research foundation of korea (nrf) grant funded by the korean government (msip) (no.2011-0030058), and by a grant from the global frontier r&d program (2013m3a6b1078874) on global frontier hybrid interface materials r&d center funded by the ministry of science, ict and future planning. the authors are very grateful to the members of the strength of materials laboratory of oita university for their excellent experimental assistance. thanks are also extended to the members of the korea institute of materials science, for performing the ecap processing of our copper rods. references [1] valiev, r.z., kozlov, e.v., ivanov, yu. f., lian, j., nazarov, a.a., baudelet, b., deformation behaviour of ultra-fine grained copper, acta metal.l mater., 42 (1994) 2467-2475. [2] valiev, r.z., structure and mechanical properties of ultrafine-grained metals, mater. sci. eng., a234-236 (1997) 5966. [3] iwahashi, y., horita, z., nemoto, m., langdon, t.g., the process of grain refinement in equal-channel angular pressing, acta mater., 46 (1998) 3317-3331. [4] zhu, y.t., lowe, t.c., observations and issues on mechanisms of grain refinement during ecap process, mater. sci. eng., a291 (2000) 46-53. [5] agnew, s.r., weertman, j.r., cyclic softening of ultrafine grain copper. mater. sci. eng., a244 (1998) 145-153. [6] hashimoto, s., kaneko, y., kitagawa, k., vinogradov, a., valiev, r.z., on the cyclic behavior of ultra-fine grained copper produced by equi-channel angular pressing, mater. sci. forum, 312-314 (1999) 593-598. [7] vinogradov, a., hashimoto, s., multiscale phenomena in fatigue of ultra-fine grain materials-an overview, mater. trans., 42 (2001) 74-84. [8] patlan, v., vinogradov, a., higashi, k., kitagawa, k., overview of fatigue properties of fine grain 5056 al-mg alloy processed by equal-channel angular pressing, mater. sci. eng., a300 (2001) 171-182. [9] höppel, h.w., zhou, z.m., mughrabi, h., valiev, r.z., microstructural study of the parameters governing coarsening and cyclic softening in fatigued ultrafine-grained copper, philos. mag. a, 82 (2002) 1781-1794. [10] wu, s.d., wang, z.g., jiang, c.b., li, g.y., alexandrov, i.v., valiev, r.z., the formation of psb-like shear bands in cyclically deformed ultrafine grained copper processed by ecap, scr. mater., 48 (2003) 1605-1609. [11] mughrabi, h., höppel, h.w., kautz, m., fatigue and microstructure of ultrafine-grained metals produced by severe plastic deformation, scr. mater., 51 (2004) 807-812. t t m. goto et alii, frattura ed integrità strutturale, 34 (2015) 427-436; doi: 10.3221/igf-esis.34.48 436 [12] vinogradov, a., nagasaki, s., patlan, v., kitagawa, k., kawazoe, m., fatigue properties of 5056 al-mg alloy produced by equal-channel angular pressing, nanostruct. mater., 11 (1999) 925-934. [13] chung, c.s., kim, j.k., kim, h.n., kim, w.j., improvement of high-cycle fatigue life in a 6061 al alloy produced by equal channel angular pressing, mater. sci. eng., a337 (2002) 39-44. [14] pao, p.s., jones, h.n., cheng, s.f., feng, c.r., fatigue crack propagation in ultrafine grained al-mg alloy, inter. j. fatigue, 27 (2005) 1164-1169. [15] collini, l., fatigue crack growth resistance of ecaped ufg copper, eng. fract. mech., 77 (2010) 1001-1011. [16] meyer, l.w., sommer, k., halle, t., hockauf m. crack growth in ultrafine-grained aa6063 produced by equalchannel angular pressing, j. mater. sci., 43 (2008) 7426-7431. [17] nisitani, h., goto, m., kawagoishi, n., a small-crack growth law and its related phenomena, eng. fract. mech., 41 (1992) 499-513. [18] goto, m., nisitani, h., fatigue life prediction of heat-treated carbon steels and low alloy steels based on a small crack growth law, fatigue fract. eng. mater. struct., 17 (1994) 171-185. [19] zhang, j.z., a shear band decohesion model for small fatigue crack growth in an ultra-fine grain aluminium alloy, eng. fract. mech., 65 (2000) 665-681. [20] goto, m., kamil, k., han, s.z., euh, k., kim, s.s., lee, j., fatigue-induced grain coarsening and crack growth behavior in ultrafine grained copper under different loading histories, int. j. fatigue, 51 (2013) 57-67. [21] zhang, z.f., wu, d.s., li, y.j., liu, s.m., wang, z.g., cyclic deformation and fatigue properties of al–0.7 wt.% cu alloy produced by equal channel angular pressing, mater. sci. eng., a412 (2005) 279-286. [22] agnew, s.r., vinogradov, a., hashimoto, s., weetman, j.r., overview of fatigue performance of cu processed by severe plastic deformation, j. electronic mater., 28 (1999) 1038-1044. [23] kunz, l., lukáš, p., svpboda, m., fatigue strength, microstructural stability and strain localization in ultrafine-grained copper, mater. sci. eng., a434 (2006) 97-104. [24] valiev, r.z., kozlov, e.v., ivanov, yu. f., lian, j., nazarov, a.a., baudelet, b., deformation behaviour of ultra-fine grained copper, acta metall. mater., 42 (1994) 2467-2475. [25] goto, m., han, s.z., kim, s.s., kawagoishi, n., lim, c.y., significance of non-equilibrium grain boundaries in surface damage formation of ultrafine-grained copper in high-cycle fatigue, scripta mater., 57 (2007) 293-296. [26] mughrabi, h., höppel, h.w., cyclic deformation and fatigue properties of ultrafine grain size materials: current status and some criteria for improvement of the fatigue resistance, mater. sci. res. symp. proc., (eds. farkas, d., kung, h., mayo, m., swygenhoven, h.v., mughrabi, h., and weertman, j.), usa, 634 (2001) b2.1.1-12. [27] goto, m., han, s.z., euh, k., kang, j-h., kim, s.s., kawagoishi, n., formation of a high-cycle fatigue fracture surface and a crack growth mechanism of ultrafine grained copper with different stages of microstructural evolution, acta mater., 58 (2010) 6294-6305. [28] xu, c., wang, q., zheng, m., li, j., huang, m., jia, q., zhu, j., kunz, l., buksa, m., fatigue behavior and damage characteristics of ultra-fine grain low-purity copper processed by equal-channel angular pressing (ecap), mater. sci. eng., a475 (2008) 249-256. [29] noda, n-a., kagita, m., variations of stress intensity factors of a semi-elliptical surface crack subjected to mode i, ii, iii loading, inter. j. pressure vessels piping, 81 (2004) 635-644. [30] benthem, j.p., state of stress at the vertex of crack in a half-space, int. j. solids struct., 13 (1977) 479–492. [31] goto, m., han, s.z., kim, c.j., yamamoto, t., kawagoishi, n., crack initiation and small crack growth behavior of age-hardened cu-6ni-2mn-2sn-2al alloys, j. soc. mater. sci. jpn., 53 (2004) 223-229. (in japanese) [32] goto, m., han, s.z., yakushiji, t., lim, c.y., kim, s.s., formation process of shear bands and protrusions in ultrafine grained copper under cyclic stresses, scripta mater., 54 (2006) 2101-2106. microsoft word 2283 s.c.s.p. kumar krovvidi et alii, frattura ed integrità strutturale, 48 (2019) 577-584; doi: 10.3221/igf-esis.48.56 577 focused on “showcasing structural integrity research in india” low cycle fatigue and creep-fatigue response of the 316ti stainless steel s.c.s.p. kumar krovvidi, sunil goyal, a. k. bhaduri indira gandhi centre for atomic research, kalpakkam603102, india krovvidi@igcar.gov.in, goyal@igcar.gov.in, bhaduri@igcar.gov.in abstract. ss 316ti is widely used in bellows industry and is a good candidate material for high temperature bellows in sodium cooled fast reactor (sfr) systems. typical operating temperature experienced by sfr systems is around 823k. design of bellows for nuclear applications need to be in compliance with the standard design codes such as asme section-iii and rcc-mr. the fatigue data and cyclic stress strain curve of ss316ti are not available in design codes such as rcc-mr or asme section-iii/nh. hence, the material data required for high temperature design of bellows are generated experimentally. initially, the basic tensile data such as yield strength, ultimate tensile strength and % elongation of the material were obtained from tensile testing at 823k. low cycle fatigue tests were carried out in strain controlled mode on ss316ti at 823k different strain ranges in air and variation of number of cycles with strain range was obtained. creep-fatigue interaction (cfi) experiment was also conducted at 823k and strain amplitude of ± 0.4% with 1 minute hold time in peak tensile strain. the stress response (peak stress variation with number of cycles) of the material showed continuous hardening up to saturation followed by crack nucleation and final failure. the fatigue life was found to decrease with increase in strain range. the fatigue life decreased in presence of hold period in tension. the design fatigue curve for ss316ti at 823k has been generated using the lcf data by incorporating factors of safety on strain and number of cycles. cyclic stress strain curve was generated for the material at 823k. the tensile, lcf and cfi data generated will be useful in design of ss316ti bellows for sfr systems. keywords. ss 316ti; bellows; low cycle fatigue; creep-fatigue interaction. citation: kumar krovvidi, s.c.s.p., goyal, s., bhaduri, a. k., low cycle fatigue and creepfatigue response of the 316ti stainless steel, frattura ed integrità strutturale, 48 (2019) 577-584. received: 27.11.2018 accepted: 28.02.2019 published: 01.04.2019 copyright: © 2019 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. introduction 16ti stainless steel is a titanium-stabilized grade of type 316 austenitic stainless steel. type 316 stainless steels are generally susceptible to sensitization in the temperature range of 500ºc to 850ºc due to the formation of grain boundary chromium carbides resulting in reduction in corrosion resistance [1]. resistance to sensitization is achieved 3 http://www.gruppofrattura.it/va/48/2283.mp4 s.c.s.p. kumar krovvidi et alii, frattura ed integrità strutturale, 48 (2019) 577-584; doi: 10.3221/igf-esis.48.56 578 in type 316ti with titanium additions by the formation of titanium carbide against chromium carbide precipitation [1]. ss 316ti is widely used in bellows industry and is a candidate material for the bellows operating at high temperature in sodium cooled fast reactor (sfr) systems [2]. bellows are generally used in piping system to absorb the differential thermal expansions and in bellow-sealed valves to prevent the entry of the process fluid to external environment. typical applications of the bellows are given in fig. 1. bellows are subjected to pressure and movements (axial, lateral and angular). bellows are specified mainly with their design pressure and fatigue life for the rated movements. thickness of the bellows ply is decided based on the design pressure. however, the remaining design parameters such as pitch, depth of convolution, and number of convolutions are decided based on the fatigue life expectancy of the bellows. design of the bellows in conventional system is carried out by using standards of expansion joints manufacturer’s association (ejma) [3]. however, design methodology of the bellows sfr systems shall comply with standard design codes for nuclear systems such as rcc-mr or asme boiler and pressure vessel code, section-iii [4,5]. a typical operating temperature in sfr systems is around 550oc. design of the bellows against fatigue as per rcc-mr requires material properties such as cyclic stress-strain curve, design fatigue curve (strain range versus number of cycles). the material properties of ss316ti are not available in rcc-mr. creep-fatigue interaction (cfi) testing is generally carried out by imposing strain hold in continuous cycle fatigue either in tension or compression or both. the presence of hold time results in stress relaxation which in turn leads to creep damage in the material. the response of materials to application of hold depends upon the microstructure, duration of hold, location of hold, environment and temperature. more deleterious effects of tensile hold compared to equal compressive hold have been observed in many materials such as austenitic stainless steels (ss 304, ss 316 and their modified grades) and some superalloys [6-11]. very limited data exist on the mechanical properties of 316ti ss in open literature. the present investigation has been carried out to evaluate the mechanical properties such as tensile, low cycle fatigue, and creep-fatigue interaction of the material. figure 1: typical applications of bellows in sfr systems (a) bellows sealed sodium valve and (b) bellows in piping system to absorb thermal expansions. experimental he 316ti austenitic stainless steel (ss) has been used for the present investigation. the chemical composition of the material is shown in tab. 1. the plate was received in solution annealed condition, with the chemical and the mechanical properties confirming to astm a240. the plate was heated to a temperature of 1311 k followed by water quenching. tensile test was carried out at 823 k and at a strain rate of 3×10-3 s-1 in air environment. the low cycle fatigue experiments were carried out on 316ti ss at different strain amplitudes ranging from ± 0.25% to ± 0.8% in air environment at a strain rate of 3×10-3 s-1 and 823 k. the gauge length and diameter of the specimen were 15 mm and 6 mm, respectively. the schematic of specimen is shown in fig. 2. all the tests were carried out in air under fully reversed, total axial strain control mode employing a symmetrical triangular strain-time waveform using dartec servo hydraulic t s.c.s.p. kumar krovvidi et alii, frattura ed integrità strutturale, 48 (2019) 577-584; doi: 10.3221/igf-esis.48.56 579 fatigue testing system. the creep-fatigue interaction test was also conducted at total strain amplitude of ± 0.4 % with 1 minute hold at peak tensile strain. element c mn si ni ti cr mo s p fe wt.% 0.018 1.89 0.27 10.81 0.19 16.9 2.14 0.001 0.04 bal. table 1: chemical composition of 316ti stainless steel (wt. %) figure 2: the schematic of specimen used for lcf and cfi testing. results and discussion ensile test was carried out at 823 k and at a strain rate of 3×10-3 s-1. the engineering stress-strain curve obtained from the tensile test is shown in fig. 3. the tensile properties evaluated for the steel are given in tab. 2. dynamic strain ageing (dsa) during tensile deformation is generally manifested as serrated yielding in the stress– strain curve, fig. 1. the dsa occurs at certain strain rate and temperature ranges and is a characteristic of the material and its microstructure [12]. generally, the dsa occurs due to the interaction between solute atoms and dislocations at temperature where the mobility of solute is sufficient to lock mobile dislocations [13]. the serrations in the tensile curve or hysteresis loops in fatigue associated with the repeated locking and unlocking of dislocations in solute atmospheres. ganesan et al. studied the effect of nitrogen on dsa behaviour of 316 ln ss during tensile test [13]. serrated flow was observed in the stress-strain curve for tensile tests in the intermediate temperature range of 773–973 k. figure 3: the engineering stress-strain curve of the steel obtained from tensile test at 823 k. elastic modulus, mpa yield stress, mpa ultimate tensile strength, mpa uniform elongation, % total elongation, % 154000 151 394 25.8 32.1 table 2: tensile properties of the material at 823 k t s.c.s.p. kumar krovvidi et alii, frattura ed integrità strutturale, 48 (2019) 577-584; doi: 10.3221/igf-esis.48.56 580 pure fatigue tests were carried out on ss316ti specimens at 823 k at different total strain amplitudes. the cyclic stress response of the alloy is shown in fig. 4. the material showed continuous hardening followed by saturation for a brief time period and the decrease in peak stress due to the formation of macro-cracks. ss 316 and other grades of stainless steels are used in solution annealed condition; an initial hardening is quite expected during fatigue cycling in this material [6,7,14]. the initial hardening in this material generally occurs due to the dislocation generation and their mutual interactions as well as interactions between mobile dislocations and the solute atoms present in the matrix. dsa during cyclic deformation is observed in the form of serrations in the hysteresis loops, fig. 5. various other manifestations include pronounced cyclic hardening, increase in stress response with increase in temperature, decrease in plastic strain with increasing temperature or decreasing strain rate (negative strain rate sensitivity) [15]. the influence of dsa on dislocation substructure in austenitic stainless steels has been studied by rao et al. [16]. at room temperature, well developed dislocation cell structure was observed. however, in the dsa range, the tendency from cell to planar slip bands was observed [16,17]. it is interesting to note that the serrations in the hysteresis loop disappear slowly with cycling, fig. 5. similar observation has been reported by goyal et al. on 316 ln ss at 873 k [18]. sarkar et al. observed the dsa during lcf of 316 ln ss in the temperature range of 823-923 k [19]. figure 4: the cyclic stress response of 316ti ss at 823 k under total strain controlled cycling. figure 5: occurrence of dynamic strain ageing during low cycle fatigue testing at 823 k and at strain amplitude of ± 0.5%. the influence of total strain amplitude on fatigue life of the material is shown in fig. 6. the fatigue life decreased with increase in total strain amplitude. the variation of low cycle fatigue life with total, plastic and elastic strain amplitudes has been analyzed on the basis of strain-life relationship, which is defined by the following equation:    2 2 2 f b ct f f fn n e      (1) s.c.s.p. kumar krovvidi et alii, frattura ed integrità strutturale, 48 (2019) 577-584; doi: 10.3221/igf-esis.48.56 581 where, t, nf, e, f, f, b, c are total strain range, fatigue life, young’s modulus, fatigue strength coefficient, fatigue ductility coefficient, fatigue strength exponent and fatigue ductility exponent respectively. the elastic and plastic strain amplitudes were obtained from the stabilized hysteresis loops at respective total strain amplitudes. the values for the coefficients for 316ti ss determined from least square fit are given in tab. 3. hardening characteristics exhibited by the material are reflected in the cyclic stress-strain behavior as shown in fig. 7. from the locus of the stress-strain maxima of the stable hysteresis loops of different strain amplitudes, cyclic stress-strain curve can be represented by a power law equation as follows:  / 2 2 npk     (2) where, , p, k, n are stress range, plastic strain range, cyclic strain hardening coefficient, cyclic strain hardening exponent, respectively. the value of k and n obtained by least square method is given in tab. 3. cyclic stress strain curve coefficients basquin relation coefficients coffin-manson relation coefficients k n f b f c 1326 mpa 0.259 1052 mpa -0.147 0.13 -0.51 table 3: values of coefficients of strain-life relation for 316ti ss figure 6: strainlife plots for ss 316ti at 823 k. figure 7: the cyclic stress-strain curve of ss 316ti at 823 k. fractographic studies conducted on failed fatigue tested samples revealed the crack initiation and propagation as transgranular, figs. 8(a) and (b). crack initiation occurred at surface connected slip bands and crack propagation is reflected by fatigue striations on fracture surface, figs. 8(a) and (b), respectively. transgranular crack propagation was observed for 1 minute tensile hold test also. since the lcf damage is mainly due to the accumulation of plastic strain, the hysteresis loop energy approach can provide accurate estimation of fatigue life of the material [20,21]. the relationship between fatigue life and hysteresis loop energy follows linear relationship on log-log plot and can be represented as power law relation  2 bt fw a n  (3) where, tw is the strain energy density at half life, 2nf is the number of reversals to failure and a and b are material constants. the energy was calculated from the integration of hysteresis loop area at stabilization. the plot is shown in fig. 9. the value of constants a and b were found to be 454.78 and -0.689 respectively. s.c.s.p. kumar krovvidi et alii, frattura ed integrità strutturale, 48 (2019) 577-584; doi: 10.3221/igf-esis.48.56 582 figure 8: the fracture appearance of the fatigue tested specimen at ± 0.8 % strain amplitude (a) crack initiation sites and (b) transgranular crack propagation in the material. figure 9: variation of hysteresis loop energy as a function of number of reversals for 316ti ss. creep-fatigue interaction test was conducted at strain amplitude of ± 0.4% with hold time of 1 minute in peak tensile strain. the stabilized hysteresis loops for continuous cycling with and without hold time are shown in fig. 10. the fatigue life of the material decreased in presence of tensile hold compared to the continuous cycling at same strain amplitude (± 0.4%) and temperature (823 k), tab. 4. the introduction of the hold time at maximum tensile strain allows for the conversion of elastic strain to plastic strain and results in the stress relaxation. the stress relaxation results from the creep deformation in the specimen resulting in creep cavitation on the grain boundaries. the amount of stress relaxation was found to be significantly lower than that of ferritic steels and superalloys, tab. 4 [11,22]. the stress relaxation is generally found to occur from the creep deformation in the specimen interior that can result in cavities on grain boundaries. these internal grain boundary cavities interact with a propagating fatigue crack to result in an enhanced crack growth rate. the material properties generated in these experiments are useful for design of bellows made of ss316ti as per rcc-mr design code for sfr applications. s.c.s.p. kumar krovvidi et alii, frattura ed integrità strutturale, 48 (2019) 577-584; doi: 10.3221/igf-esis.48.56 583 figure 10: the stabilized hysteresis loop for ± 0.4% strain amplitude with and without hold. nf (continuous cycling: ± 0.4%) nf (1 minute tensile hold: ± 0.4%) amount of stress relaxed at half life 2060 1735 9 mpa table 4: comparison of creep-fatigue life with continuous cycling conclusions ased on the investigation of low cycle fatigue and creep-fatigue interaction tests on ss316ti at 823 k, following conclusions can be drawn: 1. the material showed significant cyclic hardening followed by saturation and final fracture during cyclic loading. 2. the fatigue life decreased with increase in strain amplitude. 3. dynamic strain ageing was observed in the material during initial cycles which disappeared with further cycling. 4. the creep-fatigue interaction life was found to be lower than that in pure fatigue experiment. 5. the tensile and fatigue data generated will be useful for the design of ss316ti bellows. references [1] fontana m. g. (1987). corrosion engineering, mcgraw hill book company, singapore. [2] kumar krovvidi s.c.s.p., padmakumar g. and bhaduri a.k. (2017). experience of various materials for design and manufacture of bellows for nuclear industry, j. advance mater. proc., 2 pp. 156-161. doi: 10.5185/amp.2017/305. [3] standards of expansion joint manufacturer’s association (ejma) – 10th edition, 2016. [4] design and construction rules for mechanical components for nuclear installations rcc-mrx, 2012. [5] asme boiler and pressure vessel code, section-iii, 2017. [6] srinivasan v.s., valsan m., rao k.b.s., mannan s.l. and raj b. (2003). low cycle fatigue and creep–fatigue interaction behavior of 316l(n) stainless steel and life prediction by artificial neural network approach, int. j. fatigue, 25 pp. 13271338. doi: 10.1016/s0142-1123(03)00064-1. [7] rao k.b.s., sandhya r. and mannan s.l. (1993). creep-fatigue interaction behaviour of type 308 stainless steel weld metal and type 304 stainless steel base metal, int. j. fatigue 15 pp. 221-229. doi: 10.1016/0142-1123(93)90180-x. b s.c.s.p. kumar krovvidi et alii, frattura ed integrità strutturale, 48 (2019) 577-584; doi: 10.3221/igf-esis.48.56 584 [8] sandhya r., rao k.b.s. and mannan s.l. (2005). creep–fatigue interaction behaviour of a 15cr–15ni, ti modified austenitic stainless steel as a function of ti/c ratio and microstructure, mater. sci. engg. a 392 pp. 326-334. doi: 10.1016/j.msea.2004.09.040. [9] zhang x., tu s.t. and xuan f. (2014). creep–fatigue endurance of 304 stainless steels, theo. appl. fract. mech. 71 pp. 51-66. doi: 10.1016/j.tafmec.2014.05.001. [10] goswami t. and hanninen h. (2001). dwell effects on high temperature fatigue damage mechanisms: part ii, mater. des. 22 pp. 217-236. doi: 10.1016/s0261-3069(00)00061-3. [11] goyal s., mariappan k., shankar v, sandhya r., laha k. and bhaduri a.k. (2018). studies on creep-fatigue interaction behaviour of alloy 617m, mater. sci. engg. a 730 pp. 16-23. doi: 10.1016/j.msea.2018.05.037. [12] rodriguez p. (1984). serrated plastic flow, bull. mater. sci. 6 pp. 653-663. [13] ganesan v., laha k., nandagopal m., parameswaran p. and mathew m.d. (2014). effect of nitrogen content on dynamic strain ageing behaviour of type 316ln austenitic stainless steel during tensile deformation, mater. high temp. 31 pp. 162-170. doi: 10.1179/1878641314y.0000000009. [14] goyal s., sandhya r., valsan m. and rao k.b.s. (2009). the effect of thermal ageing on low cycle fatigue behaviour of 316 stainless steel welds, int. j. fatigue 31 pp. 447454. doi: 10.1016/j.ijfatigue.2008.07.006. [15] mannan s.l. (1993). role of dynamic strain ageing in low cycle fatigue, bull. mater. sci. 16 pp. 561-582. doi: 10.1007/bf02757656. [16] rao k.b.s., valsan m., sandhya r., mannan s.l. and rodriguez p. (1990). manifestations of dynamic strain ageing during low cycle fatigue of type 304 stainless steel, met. mater. proc. 2 pp. 17-36. [17] srinivasan v.s., sandhya r., rao k.b.s., mannan s.l. and raghavan k.s. (1991). effects of temperature on the low cycle fatigue behaviour of nitrogen alloyed type 316l stainless steel, int. j. fatigue 13 pp. 471-478. doi: 10.1016/0142-1123(91)90482-e. [18] goyal s., mandal s., parameswaran p., sandhya r., athreya c.n. and laha k. (2017). a comparative assessment of fatigue deformation behavior of 316 ln ss at ambient and high temperature, mater. sci. engg. a 696 pp. 407415. doi: 10.1016/j.msea.2017.04.102. [19] sarkar a., nagesha a., sandhya r., laha k. and okazaki m. (2018). manifestations of dynamic strain aging under low and high cycle fatigue in a type 316ln stainless steel, mater. high temp. 35 pp. 523528. doi: 10.1080/09603409.2017.1404684. [20] kujawski d. (1989). fatigue failure criterion based on strain energy density, theoretical appl. mech. 7 pp. 15-22. [21] roy s.c., goyal s., sandhya r. and ray s.k. (2012). low cycle fatigue life prediction of 316 l(n) stainless steel based on cyclic elasto-plastic response, nucl. eng. des. 253 pp. 219225. doi: 10.1016/j.nucengdes.2012.08.024. [22] shankar v., mariappan k., sandhya r., laha k., jayakumar t. and kumar r.e. (2015). effect of w and ta on creep– fatigue interaction behavior of reduced activation ferritic–martensitic (rafm) steels, fusion eng. des. 100 pp. 314320. doi: 10.1016/j.fusengdes.2015.06.191. << /ascii85encodepages false /allowtransparency false /autopositionepsfiles true /autorotatepages /none /binding /left /calgrayprofile (dot gain 20%) /calrgbprofile (srgb iec61966-2.1) /calcmykprofile (u.s. web coated \050swop\051 v2) /srgbprofile (srgb iec61966-2.1) /cannotembedfontpolicy /error /compatibilitylevel 1.4 /compressobjects /tags /compresspages true /convertimagestoindexed true /passthroughjpegimages true /createjobticket false /defaultrenderingintent /default /detectblends true /detectcurves 0.0000 /colorconversionstrategy /cmyk /dothumbnails false /embedallfonts true /embedopentype false /parseiccprofilesincomments true /embedjoboptions true /dscreportinglevel 0 /emitdscwarnings false /endpage -1 /imagememory 1048576 /lockdistillerparams false /maxsubsetpct 100 /optimize true 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/hrv (za stvaranje adobe pdf dokumenata najpogodnijih za visokokvalitetni ispis prije tiskanja koristite ove postavke. stvoreni pdf dokumenti mogu se otvoriti acrobat i adobe reader 5.0 i kasnijim verzijama.) /hun 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can be opened with acrobat and adobe reader 5.0 and later.) >> /namespace [ (adobe) (common) (1.0) ] /othernamespaces [ << /asreaderspreads false /cropimagestoframes true /errorcontrol /warnandcontinue /flattenerignorespreadoverrides false /includeguidesgrids false /includenonprinting false /includeslug false /namespace [ (adobe) (indesign) (4.0) ] /omitplacedbitmaps false /omitplacedeps false /omitplacedpdf false /simulateoverprint /legacy >> << /addbleedmarks false /addcolorbars false /addcropmarks false /addpageinfo false /addregmarks false /convertcolors /converttocmyk /destinationprofilename () /destinationprofileselector /documentcmyk /downsample16bitimages true /flattenerpreset << /presetselector /mediumresolution >> /formelements false /generatestructure false /includebookmarks false /includehyperlinks false /includeinteractive false /includelayers false /includeprofiles false /multimediahandling /useobjectsettings /namespace [ (adobe) (creativesuite) (2.0) ] /pdfxoutputintentprofileselector /documentcmyk /preserveediting true /untaggedcmykhandling /leaveuntagged /untaggedrgbhandling /usedocumentprofile /usedocumentbleed false >> ] >> setdistillerparams << /hwresolution [2400 2400] /pagesize [612.000 792.000] >> setpagedevice shot peening processes to obtain nanocrystalline surfaces in metal alloys: k. singh et alii, frattura ed integrità strutturale, 50 (2019) 319-330; doi: 10.3221/igf-esis.50.27 319 focused on showcasing structural integrity research in india brittle fracture model parameter estimation for irradiated bcc material through dislocation based crystal plasticity model kulbir singh indira gandhi centre for atomic research, hbni, kalpakkam, india – 603 102 kulbir@igcar.gov.in c. robertson den-service de recherches metallurgiques appliquees, cea, universite paris-saclay, gif-sur-yvette, france christian.robertson@cea.fr a.k. bhaduri indira gandhi centre for atomic research, hbni, kalpakkam, india – 603 102. bhaduri@igcar.gov.in abstract. radiation effects lead to a significant reduction in ductility during the life of the components used in nuclear reactors. a sharp change in fracture toughness at a lower temperature in body centered cubic (bcc) materials as compared to face centered cubic (fcc) materials is a major concern restricting their application in nuclear reactors in spite of having better thermal properties, excellent resistance to helium embrittlement and void swelling under higher dpa levels. in the present paper, such a strong temperature dependence of strain rate and flow stress in bcc materials is investigated numerically for both non-irradiated and irradiated conditions. the bcc materials subjected to radiation would undergo embrittlement, which raises the ductile to brittle transition (dbt) temperature up to or above the room temperature. in view of dislocations mobility being a fundamental property to determine the plastic behavior, the dislocations based material model is proposed, which has the physical rather than phenomenological basis. this material model accounts for both thermally activated and athermal regime dislocation mobilities in bcc materials and is capable of predicting the effect of irradiation-induced defects on the mobility of the dislocations which in turn directly affect the behavior of such materials. the relative change in the stress field due to the presence of irradiation defects in comparison to the nonirradiated case provides valuable input for brittle fracture model to develop advanced materials for nuclear application. keywords. irradiation defects; crystal plasticity; dislocation mobility. citation: singh, kulbir, robertson, c, bhaduri, a.k, brittle fracture model parameter estimation for irradiated bcc material through dislocation based crystal plasticity model, frattura ed integrità strutturale, 50 (2019) 319-330. received: 30.11.2018 accepted: 12.05.2019 published: 01.07.2019 copyright: © 2019 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. http://www.gruppofrattura.it/va/50/2306.mp4 k. singh et alii, frattura ed integrità strutturale, 50 (2019) 319-330; doi: 10.3221/igf-esis.50.27 320 introduction efect clusters (interstitial & vacancies) produced during irradiation strongly affects the mechanical properties of the structural materials. in irradiated bcc materials, it has been observed that dislocation-loops (interstitial type) are primary defects produced [1]. the interaction of these defects with dislocations controls the material hardening and embrittlement behavior. for the given material, chemical composition and irradiation flux, the number of dislocationloops ( irrn ) formed, and their diameter ( irrd ) is majorly dependent upon the irradiation dose and temperature respectively [2, 3]. furthermore, in bcc materials, plasticity is strongly temperature dependent and could be defined according to low and high temperature regimes named as a thermal and athermal regime, respectively [4, 5]. in thermal regime, the plasticity in bcc materials is temperature dependent (kink pair formation) whereas in athermal regime it is mostly independent of temperature. to study such behavior, crystal plasticity models within the finite element methods have become an important tool for material development and continuum mechanics based evaluation of materials [6]. development of suitable model based on the available experimental data could facilitate in simulating irradiation effects, which otherwise involve considerable time and cost to conduct an experiment in a controlled environment. dislocation based crystal plasticity can be used at the continuum scale to model the evolution of various crystallographic variables on each slip system to account for heterogeneous plastic strain development in crystal. this will allow to include the physical definition of different plasticity mechanisms depending upon the wide range of temperature and strain rates along with dislocations and dislocation-loops interaction. crystal plasticity models are developed with dislocation density as internal state variable to investigate the plasticity in bcc materials by zerilli et al. [7], armstrong et al. [8], kubin et al. [9], stainier et al. [10], ma et al. [11], alankar et al. [12], monnet at al. [13] and cereceda et al. [14]. also, attempts have been made to account for irradiation effects on the plasticity of bcc materials. dispersed barrier hardening model has been used to describe the irradiation dose and temperature effect on the yield stress of the materials [15]. dislocation multiplication due to their pinning with irradiation-induced defects [16] and assuming the irradiation defects as shearable obstacles for fcc materials [17] is used to study the irradiation defects. in the current work, dislocation density based crystal plasticity material model for bcc material is used to account for temperature dependent plasticity in non-irradiated and irradiated materials. the radiation induced defects are considered by incorporating strength based defect interaction with dislocations and also their impact on the mobile dislocation density in addition to total dislocation density. the developed dislocation based material model takes into account the irradiation defects along with temperature dependent plasticity behavior of bcc materials [7-9]. constitutive equations adapted (discussed in subsequent sections) to define thermal and as well as athermal regime assist in determining the plasticity behavior for a wide range of temperature and strain rates. the radiation induced defects are accounted by incorporating strength based defect interaction with dislocations and also their impact on the mobile dislocation density in addition to total dislocation density. the model can be used to analyze the effect of irradiation-induced dislocation-loop size and number density on the bcc material, which indirectly simulates the various irradiation conditions on single-crystal. in the present work, the different irradiation conditions are investigated, and results are post-processed to estimate the relative change in the sub-crystalline stress distribution in the form of the weibull parameters. these parameters will serve as valuable input for the microstructure informed brittle fracture (mibf) model to study the effect of various irradiation condition on the fracture response of the bcc materials. the mibf model is based on a local approach and accounts for microstructural aspects of material along with behavioral law and fracture mechanics [10]. it relies on crystal plasticity results in terms of heterogeneity of the stress field at the microstructure scale to study the compact tension (ct) specimen behavior under applied loading. an elementary volume (zone near the crack tip) consists of cleavage triggering sites like carbides having specific size distribution depending upon materials composition. each carbide is a potential site for the cleavage and taken as the point of nucleation. the rupture (propagation) will be triggered at such sites according to the griffith criterion (local stress and critical stress). finally, the mibf model provides the failure/rupture probability based on the carbide size distribution and local stress distribution obtained from crystal plasticity. these results are transformed to estimate the variation in toughness as the function of temperature. the dislocation based material model, simulation results, and the effect of various irradiation conditions on the weibull parameters to be subsequently used in the mibf model are highlighted and discussed in the following sections. d k. singh et alii, frattura ed integrità strutturale, 50 (2019) 319-330; doi: 10.3221/igf-esis.50.27 321 material model he dislocation based material model is developed for bcc materials accounting for 12 slips systems ({110} 1/2<111>). this material model accounts for temperature dependent plasticity along with the influence of irradiation-induced defects in the form of interstitials loops. the following subsections discuss the various constitutive equations used in the material model. temperature dependent plasticity the temperature dependence of plasticity in bcc materials is accounted by two independent formulations meant for thermal and athermal regimes. dislocation velocity in thermal regime is governed by kink pair nucleation [7-9] and is taken as a function of effective shear stress and temperature value. subsequently, using orowan’s relation  = mbv to relate mobile dislocation density ( m ) and dislocation velocity ( v ) with strain rate (  ), the thermal regime strain rate is expressed as 2 0 0 8 δ 1 q p eff eff thermal m s b h b exp l b k t            = − −         (1) where p & q are material constants. eqn. 1 gives the dependence of strain rate on temperature, effective resolved shear stress and, an average length of screw dislocation segment. athermal regime’s dislocation mobility is controlled by the velocity of edge dislocations, which leads to effective resolved shear stress dependence. however, a minor thermal component is observed due to the presence of thermally activated jog drag. for the athermal regime, the following expression is adapted for strain rate to ensure the accurate coupling between strain rate sensitive macroscopic response and rate sensitive microscopic evolution of critical shear stress [9]. 2 0 0 8 δ 1 q p eff eff athermal m b h b exp x b k t             = − −         (2) x represents the distance swept by a kink pair before its annihilation with another kink pair along with an infinitely long screw dislocation. various terms in eqn. (2) are defined as: 2 k v x j = , /k effv b b= and 2 0 0 8 δ 1 q p eff eff b h j exp bh k t          = − −         based on time spent in each regime, the harmonic mean is calculated from individual strain rates representing each regime to obtain the generalized expression for the strain rate [9, 11]. 1 1 1 total thermal athermal   = + or s total s l x l x    = + (3) this expression represents the flow rule for the material model. at lower temperature range (thermal regime), the value of sl is smaller than x which makes total strain rate dependent upon the sl , whereas in athermal regime x reduces as compared to sl , making total strain rate as x dependent. hardening and obstacles strengthening hardening in the material is considered, which arises due to resistance to dislocation motion provided by the obstacles cutting the slip planes. these obstacles in the form of forest dislocation can multiply during plastic deformation and increase t k. singh et alii, frattura ed integrità strutturale, 50 (2019) 319-330; doi: 10.3221/igf-esis.50.27 322 slip resistance. the shear stress must reach a critical value called critical resolved shear stress ( c ) for overcoming the opposition to dislocation motion, hence effective shear stress eff which is the stress required to impart velocity v to the screw dislocation segment and can be expressed as: eff rss c  = − (4) the c is defined as 2 2 2 c self lt  = + , self is stress due to an interaction between all dislocations present on the same slip system, and lt is line tension resistance on dislocation. critical stress on any slip system is dependent upon the dislocation density and strength of interaction of all systems with respect to the reference system [13, 14]. based on relative strength between each slip system, the matrix form of interaction coefficients [ af ] is adapted [15 -17]. [ af ] is an interaction matrix with size dependent upon the number of interacting slip systems considered, and each coefficient represents the strength of the interaction. in current work, 12 slip systems are considered, which can be defined with interaction matrix (size [ af ] = 12×12) having six independent coefficients. the value of self is determined based on the interaction strength between the same slip system self and is expressed as self self selfb   = . the average length of screw dislocation (in eqn. 1) is directly dependent upon the distance between forest obstacles encountered by it. these forest obstacles can be in the form of dislocations, particles, or irradiation defects. the average length of a screw dislocation is estimated based on the line tension model using obstacle spacing, obstacle strength, and corresponding obstacle number density [7-9, 11]. following are the equations used to estimate the average length of screw dislocation when it encounters an obstacle: obstacle spacing ( ) 1 ; 2 a a obs s obs d min r d    = −  +    (5) the average length of screw dislocation  2 ;s s minl max r l = − (6) average obstacle strength f af a obs     =  (7) a minimum value of the average length of screw dislocation min c cl f l= (fc is constant, estimated to be six based on fitting with experimental results for activation volume) (8) radius of curvature 2s eff b r   = (9) the lt value becomes significant and contributes to eqn. 4 for smaller obstacle spacing [11]. this is defined based on the radius of curvature as: 2 2 lt c s b b r r    = − (10) where / 2cr  = and α depend upon the forest and obstacle dislocation densities. effect of irradiation defects is taken appropriately based on their strength and number density in calculation of the above internal variables in the constitutive model [9]. irradiation defects are treated as obstacles to dislocation motion and hence induce irradiation hardening. because of the generation of distinct internal stress due to complex structure generation in dislocation-irradiation defect interaction, a k. singh et alii, frattura ed integrità strutturale, 50 (2019) 319-330; doi: 10.3221/igf-esis.50.27 323 correction factor lf is introduced [9]. this factor scales with average spacing due to the presence of irradiation defects and is multiplied with total strain rate value given in eqn. 3 (accounting an effect on velocity). , 1 2 s m l min irr irr l f min l n d    =        (11) dislocations and dislocation-loops density evolution strain dependence is used to define the dislocation density evolution based on storage (leads to an increase in flow stress) and annihilation (leads to dynamic recovery) phenomenon of dislocation as [11, 18]: 1 1 λ d y d b      = −     (12) λ is dislocation mean free path defined as 0 1 1 λ a a a a selfeff obs self forestk k         = − +    and y is temperature dependent material parameter accounting for dynamic recovery expressed as 21 1 eff propy y b   = + . temperature dependence of y is accounted by using a harmonic average of critical distance in thermal ( 2 eff b  ) and athermal regime ( propy ). for irradiated materials, the current investigation focuses on dislocation loops (sessile), which are primary irradiationinduced defects. it is assumed that the material has pre-known dislocation loops density ( irr irr irrn d = ) due to radiation exposure. further, these defects will interact with the dissociations to induce strain hardening. a gradual reduction in the irradiation defect density on the active slip plane due to their interaction with mobile dislocations is accounted. rate of change of irr [8] is defined as: irr irr  = − (13) with  as a loop annihilation parameter. increase in the value of tot (accounted in eqn. 12) and m is generally observed due to the presence of irradiation defects in the material [12, 19]. the increase in m may be attributed to the interaction of irradiation defects with screw dislocation lines. the rate of increase of mobile dislocations due to interaction with irradiation defects is expressed as: ( ) 0 m irrr t r    = (14) where  is the number of screw-loop interaction which produces dislocation source before irradiation loop’s removal from lath and 0r is an initial ratio of irr over m . the resistance against the dislocation motion is dependent upon the size (increases for higher defect size) of the defects (loops) along with their number density. size effect of irradiation defects is incorporated by introducing size factor sizef [9] defined as: , 1irrsize r r d f max s d   =     with ( ) , 1irr irrr irr irr lim n d s min n d   =       (15) k. singh et alii, frattura ed integrità strutturale, 50 (2019) 319-330; doi: 10.3221/igf-esis.50.27 324 rd is the reference diameter (taken as 2 nm), ( )irr irr limn d is the material parameter defining its saturated value for increasing dose. the factor sizef is multiplied with eqn. 14, this incorporates the defect size dependence of the dislocation velocity. the various material parameters [7-9, 11] used in the material model are listed in tab. i. parameter value parameter value b 0.2481 nm bk 8.6173×10 -5 ev/k e 236.4-0.0459t gpa cf 6  0.35 . af coll 0.7 p 0.593 . af non coll − 0.1 q 1.223 selfk 100 0δh 0.76 ev forestk 2 3, 1 300 selfk min t   +    0 360 mpa c 1 d 10 nm irr 0.3 b 10.5×10 -11 mpa.s-1  4 propy 2 nm  4 initial  4×10 12 m-2 rd 2 nm initial m = initial  ( )irr irr limn d 150×10 6 m-2 table i: various material parameters considered in material model. figure 1: validation of a material model with experimental results: resolved shear stress variation as a function of temperature. finite element formulation the constitutive equations discussed in previous sections encompass the behavior of bcc materials under both nonirradiated and irradiated conditions. flow rule is defined by eqn. 1, 2 & 3, eqn. 4 to 10 define the hardening behavior, eqn. 12 defines the evolution of dislocation density and eqn. 13 and eqn. 14 defines the evolution of irradiation defects and mobile dislocation density, respectively. these equations are solved at each increment for 12 slip systems to estimate the plasticity behavior. the constitutive equations are formulated with finite strain formulation using the mfront interface [20] and subsequently solved with finite element solver. the results are validated with available experimental data in terms of resolved shear stress [21-23]. the material model predicts satisfactorily the temperature dependence of plasticity in bcc materials (shown in fig. 1). for irradiated material, it is also capable of predicting the effect of irradiation defects for different size and number densities, highlighting the influence on hardening and strain localization [9]. k. singh et alii, frattura ed integrità strutturale, 50 (2019) 319-330; doi: 10.3221/igf-esis.50.27 325 application of the material model in the present work, a relative change in local stress at the microstructure level is predicted, and the same will be used as input to the mibf model. predicted stress field would assist in estimating the rupture probability based on a local approach. mibf model relies on crystal plasticity results in terms of heterogeneity of the stress field at the microstructure scale [10]. the concept, theory, and application of mibf model are discussed in detail elsewhere [10, 24-27]. generally, a compact tension (ct) specimen is modeled in the fea framework to apply the mibf. an elementary volume (zone near the crack tip) consists of cleavage triggering sites like carbides having specific size distribution depending upon materials composition. each carbide is a potential site for the cleavage and taken as the point of nucleation. the rupture (propagation) will be triggered at such sites according to the griffith criterion (local stress and critical stress). finally, the mibf model provides the failure/rupture probability based on the carbide size distribution and local stress distribution obtained from crystal plasticity. mibf model is capable of reproducing the variation in toughness with temperature and irradiation without arbitrarily introducing a change in cleavage critical stress. to assess the effect of various irradiation conditions at the microstructure level, a unit cell model is analyzed at 300 k for non-irradiated and irradiated material cases. in the unit cell, the small inclusion of radius 2µm (with and without crack) present at the center of the unit cell is envisaged (unit cell with inclusion case, shown in the fig. 2). this is to account for fracture behavior dependency upon the defects present at the microscale. mostly, inclusions (sulphides, oxides, nitrides, etc.) which act as a crack initiator are harder than the surrounding material. in the present study, the inclusion is assumed to be elastic and have e value ~ 300 gpa. the direction of loading is oriented such that it inclines with [-149] direction of the crystallographic axis. the displacement controlled loading in the form of 10 % global strain is applied at one face of the unit cell, while the opposite face is restricted. figure 2: unit cell model with inclusion, the meshed model with a highlighted area of consideration for weibull distribution’s parameter estimation results and discussion he various irradiation conditions are analyzed corresponding to different defect size and number density. each set of defect size (2 nm, 5 nm, 10 nm, 15 nm, 25 nm, 50 nm) and their number density ( 12 3 1 10 mm −  , 12 3 2 10 mm −  , 12 3 4 10 mm −  12 3 6 10 mm −  , 12 3 8 10 mm −  , 12 3 10 10 mm −  , 12 3 12 10 mm −  , 12 3 14 10 mm −  ) represents the particular irradiation condition in terms of irradiation temperature and dose. the simulation results obtained are further post-processed to get the frequency distribution of the equivalent stress value in the unit cell. this is used in the mibf model in the form of weibull distribution to calculate the failure probability of toughness specimen. further, an effect of irradiation on local stress distribution is estimated in terms of relative change in parameters of weibull distribution with respect to the non-irradiated case. this relative change in parameters as a function of irradiation defect size and number density assist in estimating the fracture toughness of irradiated materials. the rate of change of parameters of weibull distribution due to irradiation corresponds to the rate of change of the local stress distribution in the elementary volume due to the respective irradiation condition. the purpose of the current work is to solely provide an effect of t k. singh et alii, frattura ed integrità strutturale, 50 (2019) 319-330; doi: 10.3221/igf-esis.50.27 326 irradiation conditions relative to non-irradiated conditions. the elemental area normalization is carried out for calculation of frequency distribution of the equivalent stress in the zone highlighted in fig. 2. the frequency data is extracted for each case, and weibull distribution is fitted which is represented by: ( ) 1 w wf exp         − − −     −  =     (16) where  is the shape parameter,  is the scale parameter, and w is the position parameter (zero in this case). figure 3: probability density of equivalent stress for both irradiated and non-irradiated conditions at 300 k, with corresponding fitted weibull distribution: results of irradiation condition with a) irrn =2.0×10 12 mm-3 and irrd =15 nm, b) irrn =10.0×10 12 mm-3 and irrd =15 nm, c) irrn =2.0×10 12 mm-3 and irrd =25 nm and d) irrn =10.0×10 12 mm-3 and irrd =25 nm. (c) (d) (a) (b) σvm σvm σvm σvm k. singh et alii, frattura ed integrità strutturale, 50 (2019) 319-330; doi: 10.3221/igf-esis.50.27 327 the stress field (for equivalent stress) in the unit cell is transformed into probability density for the non-irradiated and irradiated case. the probability density of the local stress field in the unit cell and the corresponding weibull distribution of the stress field in the unit cell are plotted against the equivalent stress for various irradiation conditions in fig. 3. it shows the results for different irradiation conditions (irradiation flux and temperature). the irradiation temperature defines the size of the dislocation loop ( )irrd , whereas the flux controls the irradiation defect number density ( irrn ) of irradiation defects. similar defect size (say 15 nm in fig. 3a and 3b) with different irradiation defect number density ( irrn ) represents the material exposed to different flux levels but at the same temperature during irradiation. in the case of fig. 3a and 3c, the irradiation defect density is same but differ in defect size; this depicts the material irradiated at different temperature values but same flux. presence of irradiation defects shifts the mean stress value towards higher magnitude relative to the nonirradiated case representing the irradiation hardening. it is observed that there is a significant shift in equivalent stress towards higher magnitude for all cases of irradiated material. the direct dose dependence of the local stress field (represented by the change in weibull distribution) due to irradiation defects is evident from the reported results. based on the fea results, it is found that the influence of inclusion (with or without crack) is negligible in estimating the relative change in the stress field due to the presence of irradiation defects. moreover, the stress raising effect of the local defects like inclusion is explicitly handled by mibf model by having the probabilistic distribution of the carbides with a crack like defects. the weibull parameters (  shape and  scale) estimated for each irradiation conditions are presented in the form of the relative change in their value with respect to the non-irradiation case. this relative change in weibull parameter is plotted as a function of irradiation defect number density for each defect size (shown in fig. 4). through this curve, it is possible to estimate the relative change in the stress field at the microstructure level for the material exposed to irradiation conditions at a specific temperature and flux level. knowing the value of the weibull parameters for the non-irradiated case, the parameters for irradiated material can be estimated. through these parameters, it is viable to determine the change in local stress distribution at microstructure level for desired irradiation conditions (flux and irradiation temperature) and finally lead to predicting the fracture response under irradiated condition using mibf model. figure 4: relative change in weibull distribution parameters for different irradiation defect size and number density. subscript ‘rl’ represents the relative value of the corresponding parameter. for example, the relative change in the shape parameter is defined as (βirr – βnon-irr) / βnon-irr. conclusions he material model developed for bcc materials to define the temperature dependent plasticity along with irradiation modeling is discussed. the two different constitutive equations representing thermal and athermal regime can describe the plasticity behavior satisfactorily, which is confirmed with experimental validation. the irradiation defects are treated as barriers to the motion of the dislocation, and the evolution of various irradiation related parameters is incorporated. presence of irradiation defects in the form of interstitial loops affects the local stress field for different irradiation conditions is presented for the unit cell model (with and without inclusion). shifting of equivalent stress towards higher magnitude for irradiated material signifies the irradiation hardening in the material. different irradiation conditions t k. singh et alii, frattura ed integrità strutturale, 50 (2019) 319-330; doi: 10.3221/igf-esis.50.27 328 are simulated, and results are post-processed to fit the weibull distribution, which quantifies a relative change in the local stress distribution at the microstructure level due to irradiation. estimation of relative change in weibull distribution parameters for irradiated material with respect to the non-irradiated case would be used in the mibf model to predict the toughness behavior of the ct specimen of bcc material to get fracture response. acknowledgment he present research work was jointly supported by indira gandhi centre for atomic research-dae, india and jules horowitz reactor-cea, france. we wish to thank vincent ludovic, helfer thomas, pierre forget, p.puthiyavinayagam, k. velusamy, s. jalaldeen and r. suresh kumar for their kind help and technical support. references [1] zinkle, s.j. and matsukawa, y. observation and analysis of defect cluster production and interactions with dislocations, journal of nuclear materials, 329-333 (2004), pp. 88–96. doi: 10.1016/j.jnucmat.2004.04.298. [2] larson b. c., young, f. (1977). effect of temperature on irradiation-induced dislocation loops in copper, journal of applied physics, 48, pp. 880–886. doi: 10.1063/1.323750. [3] hardie, christopher d., williams, ceri a., xu, s., roberts, steve g. (2013). effects of irradiation temperature and dose rate on the mechanical properties of self-ion implanted fe and fe–cr alloys, journal of nuclear materials, 439, pp. 33– 40. doi: 10.1016/j.jnucmat.2013.03.052. [4] balasubramanian, n. (1969). the temperature dependence of the dislocation velocity-stress exponent, scripta metallurgica, 3, pp. 21-24. doi: 10.1016/0036-9748(69)90171-9. [5] kubin, l., devincre, b., tang, m. (1998). mesoscopic modelling and simulation of plasticity in fcc and bcc crystals: dislocation intersections and mobility, journal of computer-aided materials design, 5, pp. 31-54. doi: 10.1023/a:1008648120261. [6] roters, f., eisenlohr, p., hantcherli, l., tjahjanto, d., bieler, t., raabe, d. (2010). overview of constitutive laws, kinematics, homogenization and multiscale methods in crystal plasticity finite-element modeling: theory, experiments, applications, acta materialia, 58, pp. 1152–1211. doi: 10.1016/j.actamat.2009.10.058. [7] singh, k., robertson, c., bhaduri, a.k. (2017). assessing the irradiation defect induced changes using dislocation based crystal plasticity model for bcc materials, procedia structural integrity, 5, pp. 294–301. doi: 10.1016/j.prostr.2017.07.136. [8] singh, k., robertson, c., bhaduri, a.k., irradiation in bcc materials: defect-induced changes of the effective dislocation mobility and their relation with the dose-dependent fracture response, manuscript submitted for publication. [9] singh, k., robertson, c., bhaduri, a.k., irradiation dose and temperature effects on bcc material with dislocation based crystal plasticity, manuscript submitted for publication. [10] forget, p., marini, b., vincent, l. (2016). application of local approach to fracture of an rpv steel: effect of the crystal plasticity on the critical carbide size, procedia structural integrity, 2, pp. 1660-1667. doi: 10.1016/j.prostr.2016.06.210. [11] monnet, g., vincent, l., devincre, b. (2013). dislocation-dynamics based crystal plasticity law for the low and hightemperature deformation regimes, acta materialia, 61, pp. 6178-6190. doi: 10.1016/j.actamat.2013.07.002 [12] li, y., robertson, c. (2018). irradiation defect dispersions and effective dislocation mobility in strained ferritic grains: a statistical analysis based on 3d dislocation dynamics simulations, journal of nuclear materials, 504, pp. 84-93. doi: 10.1016/j.jnucmat.2018.03.026. [13] taylor, g. (1934). the mechanism of plastic deformation of crystals. part i – theoretical', proc. of the royal society of landon. series a, containing papers of mathematical and physical character, 145, pp. 362–387. doi: 10.1098/rspa.1934.0106. [14] besinski, z. (1974). forest hardening in face centred cubic metals, scripta metallurgica, 8, pp. 1301-1308. [15] franciosi, p., berveiller, m., zaoui, a (1980). latent hardening in copper and aluminium single crystals, acta metallurgica, 28, pp. 273-283. doi: 10.1016/0001-6160(80)90162-5. [16] peirce, d., asaro, r., needleman, a. (1981). an analysis of nonuniform and localized deformation in ductile single crystals, division of engineering,brown university, providence. ri 02912. u.s.a. [17] devincre, b., hoc, t., kubin, l. p. (2005). collinear interaction of dislocation and slip systems, materials science and engineering a, vol 400-401, pp. 182-185. doi: 10.1016/j.msea.2005.02.071 t k. singh et alii, frattura ed integrità strutturale, 50 (2019) 319-330; doi: 10.3221/igf-esis.50.27 329 [18] estrin, y., mecking, h. (1984). a unified phenomenological description of work hardening and creep based on oneparameter model, acta metallurgica, vol 32, pp. 57-70. doi: 10.1016/0001-6160(84)90202-5. [19] gururaj, k., robertson, c., fivel, m. (2015). post-irradiation plastic deformation in bcc fe grains investigated by means of 3d dislocation simulations, journal of nuclear materials, 459, pp. 194-204. doi: 10.1016/j.jnucmat.2015.01.031. [20] thomas, h., bruno, m., jean-michel, p., maxime, s., jerome, s., michel, c. (2015). introducing the open-source mfront code generator: application to mechanical behaviours and material knowledge management within the pleiades fuel element modelling platform, computers & mathematics with applications, 70, pp. 994–1023. doi: 10.1016/j.camwa.2015.06.027 [21] spitzig, w. (1973). the effect of orientation, temperature and strain rate on deformation of fe-0.16 wt.% ti single crystals, material science and engineering, 12, pp. 191–202. doi: 10.1016/0025-5416(73)90010-4. [22] quesnel, d., sato, a., meshii, m. (1975). solution softening and hardening in the iron-carbon system, material science and engineering, 18, pp. 199–208. doi: 10.1016/0025-5416(75)90170-6. [23] kuramoto, e., aono, y., kitajima, k. (1979). thermally activated slip deformation of high purity iron single crystals between 4.2 k and 300 k, scripta metallurgica, 13, pp. 1039–1042. doi: 10.1016/0036-9748(79)90199-6. [24] vincent, l., libert, m., marini, b., rey, c. (2010). towards a modelling of rpv steel brittle fracture using crystal plasticity computations on polycrystalline aggregates, journal of nuclear materials, 406, pp. 91-96. doi: 10.1016/j.jnucmat.2010.07.022. [25] vincent, l., gelebart, l., dakhlaoui, r., marini, b. (2011). stress localization in bcc polycrystals and its implications on the probability of brittle fracture, materials science and engineering a, 528, pp. 5861-5870. doi: 10.1016/j.msea.2011.04.003. [26] libert, m., rey, c., vincent, l., marini, b. (2011). temperature dependant polycrystal model application to bainitic steel behavior under tri-axial loading in the ductile–brittle transition, international journal of solids and structures, 48, pp. 2196-2208. doi: 10.1016/j.ijsolstr.2011.03.026. [27] n’guyen, c.n., barbe, f., osipov, n., cailletaud, g., marini, b., petry, c. (2012). micromechanical local approach to brittle failure in bainite high resolution polycrystals: a short presentation, computational materials science, 64, pp. 6265. doi: 10.1016/j.commatsci.2012.03.034. nomenclature t absolute temperature m mobile dislocation density (m-2) obs total obstacles (forest dislocation and irradiation loops) self dislocation density on same slip system f  forest dislocation density irr irradiation defect density  strain rate on slip system af  interaction coefficient of system a with obstacle system f  average obstacle strength based on a quadratic average rule self obstacle strength between same slip system b magnitude of burger’s vector h distance between peierls valleys b phonon/viscous drag coefficient  average obstacle spacing 0 peirels shear stress at 0 k eff effective resolved shear stress on the slip plane rss resolved shear stress on the slip plane c critical resolved shear stress self same slip system’s dislocations induced stress lt line tension resistance  shear modulus 0h pair activation enthalpy at 0 k bk boltzmann constant irrn irradiation defects (interstitial loop) number density irrd irradiation defects (interstitial loop) diameter x distance swept by kink pair before its annihilation y dynamic recovery parameter k. singh et alii, frattura ed integrità strutturale, 50 (2019) 319-330; doi: 10.3221/igf-esis.50.27 330 cr critical radius of curvature of dislocation to bypass the obstacle sr dislocation curvature radius near obstacle on slip systems sl average length of screw dislocation segment on slip system s d obstacle diameter cl critical length of kink pair minl minimum/limiting value of the average length of screw dislocation segment kv velocity of kink  dislocation-loop annihilation parameter  screw-loop interaction to produce dislocations  shape parameter of weibull distribution  scale parameter of weibull distribution w position parameter of weibull distribution λ dislocation mean free path microsoft word numero_33_art_38 y. wang et alii, frattura ed integrità strutturale, 33 (2015) 345-356; doi: 10.3221/igf-esis.33.38 345 focussed on multiaxial fatigue critical plane approach to multiaxial variable amplitude fatigue loading yingyu wang key laboratory of fundamental science for national defense-advanced design technology of flight vehicle, nanjing university of aeronautics and astronautics, nanjing, 210016, china yywang@nuaa.edu.cn luca susmel department of civil and structural engineering, the university of sheffield, sheffield s1 3jd, uk l.susmel@sheffield.ac.uk abstract. a new critical plane approach based on the modified manson-coffin curve method (mmccm) is presented in this paper for predicting fatigue lifetime under variable amplitude (va) multiaxial fatigue loading. the critical plane is assumed to coincide with that material plane experiencing the maximum variance of the resolved shear strain. fatigue damage is hypothesized to be a function of both the amplitude of the resolved shear strain and the so-called critical plane stress ratio. the latter quantity depends on the mean value and the variance of the stress perpendicular to the critical plane as well as on the variance of the shear stress resolved along the direction experiencing the maximum variance of the resolved shear strain. load cycles are counted from the resolved shear strain time history by using the classic rain flow counting method. palmgren-miner’s linear damage rule is applied to estimate cumulative fatigue damage. the accuracy and reliability of the proposed approach is checked by using several experimental data taken from the literature. the estimated fatigue lives based on the new approach are seen to be in sound agreement with the experimental results. keywords. multiaxial fatigue; variable amplitude loading; critical plane; fatigue life prediction. introduction atigue life prediction approaches based on the concept of the critical plane are generally considered to be accurate enough to estimate fatigue lifetime under multiaxial load histories. the critical plane concept is based on the physical observation that cracks initiate and grow on some specific material planes. we believe there are three key aspects needed to be considered when applying the critical plane approach to estimate fatigue lifetime under multiaxial variable amplitude loading, i.e.: (i) determining the orientation of the critical plane, (ii) counting the fatigue cycles and (iii) calculating the amplitude and mean value of the stress/strain components relative to the critical plane. as to the available critical plane approaches, findley [1] determined the critical plane by maximizing a linear combination of the shear stress amplitude and the maximum normal stress. brown and miller [2] defined the critical plane as the plane experiencing the maximum shear strain amplitude. wang and brown [3] have also proposed a modified version of their criterion by defining the critical plane as the one experiencing not only the maximum shear strain range, but also the largest value of the normal strain excursion. fatemi and socie [4] assumed that the critical plane is the plane of maximum shear strain amplitude when the crack initiation process is mode ii governed. from the brief review presented above, it f y. wang et alii, frattura ed integrità strutturale, 33 (2015) 345-356; doi: 10.3221/igf-esis.33.38 346 becomes clear that there are different ways to define the critical plane itself. however, it is not an easy task to determine the orientation of the critical plane when the applied multiaxial load history varies randomly. several investigations [5-9] have been published by focusing attention on the determination of the critical plane under multiaxial random loading. susmel [9] have recently formalized a novel technique, the shear stress-maximum variance method (-mvm). the maximum variance method (mvm) postulates that the critical plane can be defined as that plane containing the direction (passing through the assumed critical point) that experiences the maximum variance of the resolved shear stress. the peculiarity of the mvm is that it is not necessary to calculate the stress/strain components relative to any plane passing through the assumed critical point to determine the critical plane itself. therefore, from a computational point of view, it is more efficient than the other existing methods. in order to take into account cyclic hardening or softening in the fatigue failure criteria, both stress and strain components are recommended to be used to estimate the fatigue damage extent. as to the in-field usage of the available va multiaxial fatigue life estimation techniques, correctly performing the cycle counting under such complex loading conditions is one of the trickiest aspects [10]. even though there are a few methods suitable for counting the cycles under uniaxial loading, among these the rainflow cycle counting method [11] has been most widely and successfully used. the number of published papers dealing with va multiaxial loading histories is small [12]. bannantine and socie [13] proposed a method based on the critical plane concept and the rainflow cycle counting. wang and brown [14] proposed a cycle counting method based on the rainflow and a modified von mises equivalent strain. the accuracy of the results predicted by using the critical plane approach to a great extent relies on the determination of the amplitude and mean value of the normal and shear stresses and strains acting on a particular plane [15]. for a particular plane under complex loading, the direction of the normal stress/strain does not change over time, since just the magnitude of the normal stress/strain vector varies. however, in the most general case, the shear stress/strain vector on this particular plane changes in both magnitude and direction. therefore, the tip of the shear stress/strain vector draws an imaginary curve on that plane. in this situation, it is not an easy task to calculate the amplitude and mean value of the shear stress/strain on a given plane. there are several techniques proposed to address this problem, namely the longest chord method, the longest projection method, the minimum circumscribed circle concept, and the minimum circumscribed ellipse method. these methods have been discussed in the refs [9, 15]. the present paper summarizes an attempt of extending the use of the modified manson-coffin curve method (mmccm) to those situations where complex variable amplitude loadings are involved. by making the most of our previous experience [10, 16-18], now we intend to use the stain-based mvm in conjunction with mmccm to predict fatigue lifetime under va multiaxial fatigue loading. in more detail, the mmccm is suggested here as being applied in conjunction with the maximum variance method (mvm) to estimate fatigue lifetime by directly post-processing the strain state relative to that material plane containing the direction along which the variance of the resolved shear strain is maximized. since, by definition, the resolved shear strain is a monodimensional quantity, the rainflow method can directly be used to count the loading cycles. after counting the cycles and estimating the fatigue damage for each counted cycle, fatigue lifetime can be predicted directly by using the palmgren-miner’s linear damage rule. finally, the validation of the new approach is presented. the shear strain_maximum variance method (-mvm) he shear strain-maximum variance method (mvm) assumes that the critical plane can be defined as that plane containing the direction experiencing the maximum variance of the resolved shear strain. in order to calculate the shear strain relative to a generic material plane,  , and resolved along a generic direction, q, consider a body subjected to an external system of forces resulting in a triaxial strain state at point o (fig. 1a). point o is taken as the center of the absolute system of coordinates, oxyz. the time-variable strain state at point o is defined through the following strain tensor:   x xy xz x xy xz yx y yz xy y yz zx zy z xz yz z 1 1 ε (t ) (t ) (t ) 2 2ε (t ) ε (t ) ε (t ) 1 1 ε t ε (t ) ε (t ) ε (t ) γ (t ) ε (t ) γ (t ) 2 2 ε (t ) ε (t ) ε (t ) 1 1 γ (t ) γ (t ) ε (t ) 2 2                              (1) t y. wang et alii, frattura ed integrità strutturale, 33 (2015) 345-356; doi: 10.3221/igf-esis.33.38 347 where x , y and z are the three normal strains, and xy , xz and yz are the total shear strains. the orientation of a generic material plane,  , having normal unit vector n can be defined through angles  and  (fig. 1b).  is the angle between axis x and the projection of unit vector n on plane x-y.  is the angle between n and axis z. a new system of coordinates, onab, can now be defined. the unit vectors defining the orientation of axes n, a and b can be expressed as follows:           sin cos sin sin cos x y z n n n                        n ;     sin cos 0 x y z a a a                      a ;           cos cos cos sin sin x y z b b b                        b (2) figure 1: generic plane and shear strain resolved along one generic direction in a body subjected to an external system of forces. consider now a generic direction q lying on plane  and passing through point o. α is the angle between direction q and axis a. the unit vector defining the orientation of q can be calculated as follows:                         cos sin sin cos cos cos cos sin cos sin sin sin x y z q q q                                 q (3) according to the definition reported above, the instantaneous value of the shear strain resolved along direction q, q ( )t , can then be calculated as: x xy xz q y xy y yz xz yz z 1 1 ε (t ) (t ) (t ) 2 2 γ ( ) 1 1 γ (t ) ε (t ) γ (t ) 2 2 2 1 1 γ (t ) γ (t ) ε (t ) 2 2 x x z y z n t q q q n n                         (4) in order to make the calculation easier, it is useful to express q ( )t through the following scalar product:  q γ ( ) 2 t t d s (5) where d is the vector of direction cosines, that is: y. wang et alii, frattura ed integrità strutturale, 33 (2015) 345-356; doi: 10.3221/igf-esis.33.38 348                                 2 1 2 2 3 4 5 6 1 sin θ sin 2φ cos α sin 2θ cos φ sin α 2 d 1 sin θ sin 2φ cos α sin 2θ sin φ sin α d 2 1d sin 2θ sin α 2d 1d sin 2θ sin 2φ s 2d x x y y z z x y y x x z z x y z z y n q n q n q n q n q n q n q n q n q                                                    d                                 in α sin θ cos 2φ cos α cos 2θ cos φ sin α cos θ sin φ cos α cos 2θ sin φ sin α cos θ cos φ cos α                                       (6) and s(t) is a six-dimensional vector process depending on  [ε ]t and defined as: x y z xy xz yz 1 1 1 ( ) ε (t ) ε (t ) ε (t ) (t ) (t ) γ (t ) 2 2 2 t       s (7) according to the quantities defined above, the variance of the shear strain, q ( )t , resolved along direction q can then be calculated directly as:      var var ( ) cov , ( ) 2 q t k k i j i j k i j t d s t d d s t s t c                   d d (8) where [c] is a symmetric square matrix of order six, and the terms of the covariace matrix are defined as    cov ,  ij i jc s t s t    (9) where, when i j then      cov ,   vari j is t s t s t       , whereas when i j then        cov ,   cov ,  i j j is t s t s t s t       . now [c] can be rewritten in explicit form by using both the variance and covariance terms:   x x , y x ,z x ,xy x ,xz x , yz x , y y y ,z y ,xy y ,xz y , yz x ,z y ,z z z,xy z,xz z, yz x ,xy y ,xy z ,xy xy xy ,xz xy , yz x ,xz y ,xz z,xz xy ,xz xz xz, yz x , yz y , yz z, yz xy , yz xz, yz yz v c c c c c c v c c c c c c v c c c c c c c v c c c c c c v c c c c c c v                     (10) where  var     for  ,  ,  ,  ,  , i iv t i x y z xy xz yz    (11)    ,  covar ,       for  ,  ,  ,  ,  , i j i jc t t i x y z xy xz yz     (12) then eq. (8) can be rewritten in the following simple form:    var tq t c    d d (13) eq. (13) makes it evident that the determination of the direction experiencing the maximum variance of the resolved shear strain is a conventional multi-variable optimization problem. it can be solved satisfactorily by simply using the so-called gradient ascent method [19]. fig. 2 reports the flowchart summarising the algorithm which was proposed in ref. [9] to be used to determine the orientation of the critical plane. y. wang et alii, frattura ed integrità strutturale, 33 (2015) 345-356; doi: 10.3221/igf-esis.33.38 349 after determining the direction of the maximum variance, the shear strain resolved along this direction, mv ( )t , can directly be evaluated, at any instant, t, of the load history, through the following relationship:   x xy xz mv xy y yz xz yz z 1 1 ε (t ) (t ) ( t ) 2 2 1 1 γ ( t ) ε ( t ) γ (t ) 2 2 2 1 1 γ (t ) γ (t ) ε (t ) 2 2 x x y z y z n t q q q n n                             (14)                                                              nnn nnn nnn n n n n n n t t t k                ,, )(var ,, )(var ,, )(var q q q 1 1 1 figure 2: flowchart summarizing the algorithm for the determination of the critical plane orientation. the shear stress resolved along the maximum variance direction, mv ( )t , and the stress normal to the plane experiencing the maximum variance of resolved shear strain, n ( )t , can be evaluated, at any instant, t, of the load history, through the following relationships:   x xy xz mv xy y yz xz yz z (t ) (t ) (t ) (t ) (t ) (t ) (t ) (t ) (t ) x x y z y z n t q q q n n                            (15) y. wang et alii, frattura ed integrità strutturale, 33 (2015) 345-356; doi: 10.3221/igf-esis.33.38 350   x xy xz n xy y yz xz yz z (t ) (t ) (t ) (t ) (t ) (t ) (t ) (t ) (t ) x x y z y z n t n n n n n                            (16) evaluation of strain and stress components relative to the critical plane onsider the body subjected to a complex system of time variable forces shown in fig. 3. the applied load history is defined in the time interval [0, t ] and it is assumed to result in a va multiaxial strain state at point o. by using the -mvm, the orientation of the potential critical plane can be determined through that direction which experiences the maximum variance of the resolved shear strain. after determining the direction of maximum variance (mv), the shear strain resolved along this direction, mv ( )t , the shear stress resolved along the maximum variance direction, mv ( )t , and the stress normal to the plane experiencing the maximum variance of the resolved shear strain, n ( )t , can be evaluated, at any instant, t, of the load history, through eq. (14) to (16). attention can initially be focused on stress component, n ( )t , which is defined in the time interval [0, t]. the mean value of this stress component is equal to t n , m n 0 1 σ σ ( ) t t dt  (17) the equivalent amplitude of n ( )t is suggested here as being calculated as follows:  n ,a nσ 2 var[σ ]t  (18) where var[ n ( )t ] is the variance of stress component n ( )t , i.e. t 2 n n n ,m 0 1 var[σ ( )] [σ ( ) σ ] t t t dt  (19) consider now the shear stress, mv ( )t , resolved along direction mv. owing to the fact that also mv ( )t is a monodimensional stress quantity defined in the time interval [0, t], its mean value and its equivalent amplitude can directly be determined by following a strategy similar to the one adopted above to calculate n ,m and n ,a . in particular, m is equal to t m mv 0 1 τ τ ( ) t t dt  (20) whereas the equivalent amplitude of the shear stress resolved along direction mv takes on the following value:  a mvτ 2 var[τ ]t  (21) where t 2 mv mv m 0 1 var[τ ( )] [τ ( ) τ ] t t t dt  (22) then a stress ratio  ρ , which will be used to adapt the manson-coffin curve to the degree of multi-axiality and nonproportionality of the stress/strain state at the assumed crack initiation site can be defined as follows: n , m n , a a σ σ ρ τ   (23) c y. wang et alii, frattura ed integrità strutturale, 33 (2015) 345-356; doi: 10.3221/igf-esis.33.38 351 to conclude the present section it is important to highlight that, in general, there exist two or more different directions which experience the maximum variance of the resolved shear strain, so that, it is always possible to locate, at least, two potential critical planes: amongst all the potential critical planes, the one which has to be used to estimate fatigue lifetime is that experiencing the largest value of ρ . the mmccm to address the variable amplitude problem the use of the mmccm in those situations involving va multiaxial load histories is based on the following assumptions: (i) initiation and initial propagation of stage  cracks occur on that material plane containing the direction experiencing the maximum variance of the resolved strain, mv ( )t ; (ii) the fatigue damage depends also on the stress ratio ρ which is defined in the previous section. fig. 3 summarizes the approach proposed in the present paper to be followed to estimate fatigue lifetime of engineering materials subjected to in-field va multiaxial fatigue loading. in more detail, consider a body subjected to a complex system of time variable forces resulting in a va multiaxial strain state at the assumed crack initiation site (i.e. point o in fig. 3a). initially, by making use of the shear -mvm, the orientation of the candidate critical planes can directly be determined through that direction, mv, experiencing the maximum variance of the resolved shear strain (fig. 3b). after determining the direction of maximum variance of the shear strain, the shear strain resolved along this direction, mv ( )t , the shear stress resolved along the maximum variance direction, mv ( )t , and the stress normal to the critical planes, n ( )t , can be evaluated, at any instant, t, of the load history, through eq. (14) to (16) (figs 3c and d). subsequently, the calculated values for n ,m (eq. 17), n ,a (eq. 18) and a (eq. 21) have to be used to estimate, according to eq. (23), critical plane stress ratio ρ . according to the determined value for ρ , the profile of the corresponding modified manson-coffin curve can be described by using the following general relationship [18]:     ' ( )f ( ) ' a f f f( 2 ) ( ) 2 cbn n g       (24) where 'f ( )  , ' f ( )  , ( )b  , ( )c  are material functions, which can be determined through the following equations [18]:     0 0 b b b b b b       (25)     a , ref' f ( ) a ( ) 2 b n       (26)       0 ' 'f a , ref a f a2 (1 ) 2 2 b b n n         (27)    ' ' 'f p f f1 ν (1 )          (28)     0 0 c ρ c c c c c     (29) where p is poisson’s ratio for plastic strain, na is the reference number of cycles to failure. after determining the appropriate reference fatigue curve as above, by post-processing the shear strain resolved along direction mv, the classical rain-flow method allows the corresponding shear strain spectrum to be built directly (figs 3g and h). finally, from such spectrum fatigue strength under va multiaxial fatigue loading can be predicted according to palmgren-miner’s rule (fig. 3i). here it is assumed that breakage takes place when the damage sum equals unity. y. wang et alii, frattura ed integrità strutturale, 33 (2015) 345-356; doi: 10.3221/igf-esis.33.38 352 validation by experimental data n order to check the accuracy of the proposed approach in estimating fatigue lifetime under va multiaxial fatigue loading, a number of experimental data were selected from the technical literature [12, 20-22]. the summary of the static and fatigue properties of the considered materials is reported in tab. 1 and 2. when the torsional material constants listed in the above tables were not directly available in the original sources, they were calculated as follows [23]: 2(1 ) e g    ' '3f f  ' ' 3 f f    0b b 0c c figure 3: in-field use of the mmccm to estimate fatigue lifetime under va multiaxial fatigue loading. the investigated materials’ non-proportional hardening was taken into account by making the following assumption [23]: i y. wang et alii, frattura ed integrità strutturale, 33 (2015) 345-356; doi: 10.3221/igf-esis.33.38 353 ' 'np 1.25k k  ' ' npn n both the strain loading history and the stress loading history at the assumed crack initiation site are needed. if the stress loading histories were not given in the original sources, they were calculated by using the model proposed by jiang and sehitoglu [24]. in fig. 4, the predicted fatigue lives are compared with the experimental ones for s45c steel and sncm630 steel under va multiaxial fatigue loading. fig. 4 also shows the loading paths applied to specimens made of s45c steel and sncm630 steel. as it can be seen from this figure, 81% of the data are within a scatter bands of 3. data points under loading blocks with a considerable portion of axial loading such as at, ta and av are outside of the target scatter band, being on the conservative side. material ref. e (mpa) g (mpa) ν s45c [20] 186,000 70,600 0.28 sncm630 [21] 196,000 77,000 0.273 1050 qt steel [12] 203,000 81,000 0.27 304l steel [12] 195,000 77,000 0.27 pure titanium [22] 112,000 40,000 0.4 titanium alloy bt9 [22] 118,000 43,000 0.37 table 1: elastic static constants for the considered materials. material ref. ’f ’f (mpa) b c ’f ’f (mpa) b0 c0 k’ (mpa) n’ k’np (mpa) n’np s45c [20] 0.359 923 0.099 0.519 0.198 685 -0.12 -0.36 1215 0.217 1519 0.217 sncm630 [21] 1.54 1272 0.073 0.823 1.51 858 -0.061 0.706 1056 0.054 1320 0.054 1050 qt st. [12] 2.01 1346 0.062 0.725 3.48 777 -0.062 0.725 1461 0.06 1420 0.113 304l st. [12] 0.122 1287 0.145 0.394 0.211 743 -0.145 0.394 680 0.214 5056 0.373 pure ti [22] 0.548 647 0.033 0.646 0.417 485 -0.069 0.523 bt9 [22] 0.278 1180 0.025 0.665 0.18 881 0.0082 -0.47 table 2: fatigue constants for the considered materials. figure 4: comparison of observed and predicted fatigue lives by the mmccm for s45c and sncm630. y. wang et alii, frattura ed integrità strutturale, 33 (2015) 345-356; doi: 10.3221/igf-esis.33.38 354 the predicted versus experimental fatigue lifetime diagram for 1050 qt steel and 304l steel under discriminating axialtorsion stain paths with random and incremental changes in straining direction is reported in fig. 5. as it can be seen from fig. 5, all the data are within scatter bands of 3 from predictions. fig. 6 shows the predicted versus experimental fatigue lifetime diagram for pure titanium and titanium alloy bt9 under step loading and block loading composed of different combinations of axial, torsion and 90°out-of-phase axial-torsion strain paths. as it can be seen from fig. 6, 90% of the data are within a scatter band of 3. figure 5: comparison of observed and predicted fatigue lives by the mmccm for 1045 qt steel and 304l steel. figure 6: comparison of observed and predicted fatigue lives by the mmccm fo pure titanium and titanium alloy bt9. conclusions (1) the mmccm originally proposed by susmel et al. [18] for multiaxial constant amplitude loading was reformulated to estimate fatigue lifetime of components subjected to va multiaxial fatigue loading. satisfactory fatigue life predictions were obtained by using the mmccm, when coupled with the rain-flow cycle counting method and palmgren-miner y. wang et alii, frattura ed integrità strutturale, 33 (2015) 345-356; doi: 10.3221/igf-esis.33.38 355 linear cumulative damage rule for different materials tested under va multiaxial fatigue loading. the critical plane was determined by using the -mvm. (2) the mvm is an efficient and valid method to determine the orientation of the critical plane when it is used to evaluate fatigue damage under complex variable amplitude multiaxial fatigue loading. (3) since the controlling parameter of the mmccm is just the shear strain resolved along the direction of maximum variance of the resolved shear strain, when the mmccm is used to estimate fatigue damage under variable amplitude multiaxial fatigue loading, cycles can directly be counted by using rainflow method. acknowledgements his work is partly supported by jiangsu oversea research & training program for university prominent young & middle-aged teachers and aviation science funds of china (no. 2013za52008). references [1] findley, w.n., modified theory of fatigue failure under combined stress, in: proc of the society of experimental stress analysis, 14 (1956) 35-46. [2] brown, m.w., miller, k.j., a theory for fatigue under multiaxial stress-strain conditions, in: proc institution of mechanical engineering, 187 (1973) 745-56. [3] wang, c.h., brown, m.w., a path-independant parameter for fatigue under proportional and non-proportional loading, fatigue of engineering materials and structures, 16 (1993)1285–1293. [4] fatemi, a., socie, d.f., a critical plane approach to multiaxial fatigue damage including out-of-phase loading, fatigue fract eng mater struct, 11 (1988) 149-65. [5] marciniak, z., rozumek, d., macha, e., verification of fatigue critical plane position according to variance and damage accumulation methods under multiaxial loading, int j fatigue, 58 (2014) 84-93. [6] bedkowski, w., macha, e., ohnami, m., sakane, m., fracture plane of cruciform specimen in biaxial low cycle fatigue-estimate by variance method and experimental verification, trans asme j eng mater technol, 117 (1995) 183–90. [7] carpinteri, a., macha, e., brighenti, r., spagnoli, a., expected principal stress directions under multiaxial random loading part i: theoretical aspects of the weight function method, int j fatigue, 21(1999) 83–88. [8] carpinteri, a., macha, e., brighenti, r., spagnoli, a., expected principal stress directions under multiaxial random loading part ii: numericalsimulation and experimentally assessment through the weight functionmethod, int. j. fatigue, 21(1999): 89–96. [9] susmel, l., a simple and efficient numerical algorithm to determine the orientation of the critical plane in multiaxial fatigue problems, int. j. fatigue, 32 (2010) 1875-1883. [10] susmel, l., tovo, r., estimating fatigue damage under variable amplitude multiaxial fatigue loading, fatigue & fracture of engineering materials & structures, 34 (2011) 1053-1077. [11] matsuishi, m., endo, t., fatigue of metals subjected to varying mar. stress, presented at japan society of mechanical engineers, fukuoka, japan, (1968). [12] shamsaei, n., fatemi, a., socie, d.f., multiaxial fatigue evaluation using discriminating strain paths. int. j. fatigue, 33 (2011) 597-609. [13] bannantine, j.a., socie, d.f., multiaxial fatigue life estimation technique, in: mitchel m, landgraf r, editors. astm symposium on advances in fatigue lifetime predictive techniques, astm stp 1122 (1991) 249–75. [14] wang, c.h., brown, m.w., life prediction techniques for variable amplitude multiaxial fatigue – part i: theories, j. eng. mater. technol. 118 (1996) 367–70. [15] papadopoulos, i.v., critical plane approaches in high-cycle fatigue: on the definition of the amplitude and mean value of the shear stress acting on the critical plane, fatigue fract. eng. mater. struct., 21 (1998) 269-285. [16] susmel, l., tovo, r., benasciutti, d., a novel engineering method based on the critical plane concept to estimate the lifetime of weldments subjected to variable amplitude multiaxial fatigue loading, fatigue & fracture of engineering materials & structures, 32 (2009) 441-459. [17] susmel, l., taylor, d., a critical distance/plane method to estimate finite life of notched components under variable t y. wang et alii, frattura ed integrità strutturale, 33 (2015) 345-356; doi: 10.3221/igf-esis.33.38 356 amplitude uniaxial/multiaxial fatigue loading, international journal of fatigue, 38 (2012) 7-24. [18] susmel, l., meneghetti, g., atzori, b., a simple and efficient reformulation of the classical manson-coffin curve to predict lifetime under multiaxial fatigue loading-part i: plain materials, journal of engineering materials and technology, 131 (2009) 021009-1-021009-9. [19] snyman, j.a., practical mathematical optimization: an introduction to basic optimizaion theory and classical and new gradient-based algorithms, springer publishing, (2005). [20] kim, k.s., park, j.c., lee, j.w., multiaxial fatigue under variable amplitude loads, trans asme j. eng. mater. technol., 121 (1999) 286-93. [21] han, c., chen, x., kim, k.s., evaluation of multiaxial fatigue criteria under irregular loading, int. j. fatigue, 24 (2002) 913-922. [22] shamsaei, n., gladskyi, m., panasovskyi, k., fatemi, a., multiaxial fatigue of titanium including step loading and load path alteration and sequence effects, int. j. fatigue, 32 (2010) 1862-1874. [23] socie, d.f., marquis, g.b., multiaxial fatigue, warrendale, usa, (1999). [24] jiang, y., sehitoglu, h., modeling of cyclic racheting plasticity, part : development of constitutive equations, journal of applied mechanics, 63 (1996) 720-725. microsoft word numero 1 art 3.doc v. tvergaard, frattura ed integrità strutturale, 1 (2007) 25-28 25 1 introduction many procedures for the analysis of crack propagation are based on using critical values of parameters characterising the crack-tip stress and strain fields, such as the stress intensity factor, the j-integral, the crack-tip opening displacement, or the crack-tip opening angle. alternatively, the prediction of crack growth may be directly based on the fracture mechanism operating on the microscale, either by incorporating the failure mechanism in the constitutive equations for the material, or by representing the failure mechanism through a cohesive zone model of the fracture process zone. the present paper will give a survey of a number of investigations where the prediction of crack growth has been based on models of the actual fracture mechanism. one of the most well known material models that accounts for the micromechanics of damage is the modified gurson model [1,2], which models the evolution of ductile fracture by the nucleation and growth of voids to coalescence. some of the analyses using this model to predict ductile crack growth will be discussed. also for creep failure in metals at high temperatures material models [3] have incorporated the micromechanisms of diffusive cavity growth in grain boundaries, leading to open micro-cracks at grain boundary facets at a rate strongly affected by grain boundary sliding. results on creep crack growth based on this failure model will be mentioned. the term continuum damage mechanics is used for constitutive relations, which are able to represent the effect of damage evolution on the macro level, by developing appropriate expressions in which free material parameters can be fitted to experiments, as in the case of low cycle fatigue [4]. as an example, predictions of micro-crack formation in a metal matrix composite, based on this material model, will be presented here. cohesive zone models have been used in recent years in a number of analyses of crack growth resistance in elasticplastic solids [5]. some of the predictions obtained in these studies will be briefly mentioned here. 2 material models with damage evolution when the failure mechanism is incorporated in in the constitutive relations, the crack growth follows directly from the predicted loss of stress carrying capacity in one or more integration points in an element. then it is natural to kill the failed elements, by using the element vanish technique [6]. this procedure has been used for the predictions of crack growth to be discussed in the following three subsections. crack growth by ductile failure much interest has been devoted to the development of elastic-plastic or viscoplastic constitutive equations that account for the effect of ductile damage development. the most well known model is that suggested by gurson [1], which makes use of an approximate yield condition ( , , ) 0ij fmσ σφ = for a material containing a volume fraction f of voids, where ijσ is the average macroscopic cauchy stress tensor and mσ is an equivalent tensile flow stress representing the actual microscopic stress-state in the matrix material. with some modifications to improve predictions of plastic flow localization numerical modelling in non linear fracture mechanics ( da esis newsletter 2005) viggo tvergaard dept. of mechanical engineering, solid mechanics, technical university of denmark, nils koppels allé, building 404, dk-2800 kgs. lyngby, denmark abstract: some numerical studies of crack propagation are based on using constitutive models that account for damage evolution in the material. when a critical damage value has been reached in a material point, it is natural to assume that this point has no more carrying capacity, as is done numerically in the element vanish technique. in the present review this procedure is illustrated for micromechanically based material models, such as a ductile failure model that accounts for the nucleation and growth of voids to coalescence, and a model for intergranular creep failure with diffusive growth of grain boundary cavities leading to micro-crack formation. the procedure is also illustrated for low cycle fatigue, based on continuum damage mechanics. in addition, the possibility of crack growth predictions for elastic-plastic solids using cohesive zone models to represent the fracture process is discussed. keywords: damage evolution, crack growth, coesive zone v. tvergaard., frattura ed integrità strutturale, 1 (2007) 25-28 26 ( ) ( ) ( ) ( ) i local 1 ˆˆ ˆyi i i i v f y f w y y dv w y = −∫& & [7] and of final failure by void coalescence [8] this yield condition is of the form ( ) 2 2* *2 1 12 2 cosh 1 02 k e k m m q q f q f σ σ σ σ ⎛ ⎞ ⎡ ⎤φ = + − + =⎜ ⎟ ⎢ ⎥⎣ ⎦⎝ ⎠ (1) where ( )½3 / 2ije ijs sσ = is the macroscopic effective mises stress, and / 3ij ij ij kks gσ σ= − is the stress deviator. this material model accounts for the growth of the void volume fraction f due to plastic flow of the material around voids and due to the nucleation of new voids, and final failure is directly predicted when f reaches the critical value, at which the yield surface has shrunk to a point. this material model has been applied in a number of numerical studies of crack growth, including some studies where two populations of void nucleating particles are modelled; large weak particles that nucleate voids at relatively small strains and small strong particles that nucleate voids at much larger strains. for an edge cracked specimen under dynamic loading [9] results of a plane strain analysis are shown in fig. 1, where contours of constant void volume fraction define the predicted crack growth path in a case of a random distribution of the larger inclusions ahead of the initial crack-tip. also a full three dimensional analysis has been used to analyse this type of specimen [10]. here the computer requirements were much larger, but the advantage is that more realistic spherical shapes of the larger inclusions can be accounted for, and that 3d modes of growth are accounted for, such as tunnelling and shear lip formation. continuations of the 3d fracture study have been carried out recently in analyses that do not directly focus on crack growth, e.g. the failure of a metal matrix composite [11] or of a charpy v-notch specimen cut through a weld [12]. some attempts to include a damage dependent material length scale in this constitutive model have been carried out by leblond et al. [13] and tvergaard and needleman [14], using an integral condition on the rate of increase of the void volume fraction. the expressions used in [14] are (2) (3) where 0l > is the material characteristic length, i j ijz g y y= , and 8p = , 2q = . the usual local formulation corresponds to the limit 0l → , and it has been shown, as for other non-local continuum models, that the mesh dependence of numerical solutions in a softening regime are removed by taking 0l > . this nonlocal damage model has been applied by needleman and tvergaard [15] to predict ductile crack growth in the edge cracked specimen under dynamic loading also analysed in [9,10]. figure 1: crack growth indicated by contours of constant void volume fraction, f , for random distribution of larger particles. (a) 1.5 ,t sμ= 0.09 mmaδ = ; (b) 1.6 ,t sμ= 0.27 mmaδ = . (from [9]). creep crack growth high temperature failure leading to crack growth has been modelled in terms of continuum damage mechanics (hayhurst et al. [16]), where damage parameters are fitted to material behaviour on the macro level. the micromechanisms of creep failure in polycrystalline metals involve the nucleation and growth of small voids to coalescence; but here diffusion plays an important role, and the cavities occur primarily on grain boundary facets perpendicular to the maximum principal tensile stress (e.g. ashby and dyson [17]), where a creep constraint on the rate of cavitation is often a dominant mechanism. cavity coalescence on a grain boundary facet leads to a microcrack, and final intergranular failure occurs as such micro-cracks link up. grain boundary sliding is an important mechanism that further complicates the analysis of creep failure. a micromechanically based constitutive model for creep failure in a polycrystalline metal has been proposed (tvergaard [3,18]), in which the macroscopic creep strain rate is given by the expression ( ) ( )0 0 3 1 * 2 n nijc c e ij e e s c f σ η ε ε σ σ ⎛ ⎞ ⎡ = + +⎜ ⎟ ⎢ ⎝ ⎠ ⎣ && 2* * * *3 1 2 2 1 1 ij n n ij e e e s s sn m n n σ σ ρ σ σ σ ⎤⎧ ⎫⎛ ⎞− −−⎪ ⎪⎥+⎨ ⎬⎜ ⎟ + + ⎥⎝ ⎠⎪ ⎪⎩ ⎭⎦ (4) here, n is the creep power, 0c > represents substructure induced acceleration of creep, and expressions for other parameters are determined by axisymmetric cell ( ) ( ) ( ) ( )1 ˆˆ, 1 / q i i i i p v w y w y w y y dv z l ⎡ ⎤ = = −⎢ ⎥ +⎢ ⎥⎣ ⎦ ∫ v. tvergaard., frattura ed integrità strutturale, 1 (2007) 25-28 27 model studies for a grain with a cavitating facet and sliding boundaries [3]. if there is no sliding, *f is unity, *ρ is the density of cavitating facets *ijm is a direction tensor for cavitating facets, and * ns σ− is the difference between the maximum principal stress and the normal stress on a cavitating facet. the material model has been used to predict crack growth [18], by applying the element vanish technique when cavity coalescence was predicted on a grain boundary. for a double edge cracked panel under tension fig. 2 shows the predicted damage near the crack-tip at two stages of time, where the damage parameter a/b is the cavity radius divided by the cavity half spacing on a facet, and vanished triangular elements are painted black. figure 2: distributions of creep damage ahead of a crack-tip. continuous cavity nucleation, no grain boundary sliding, and 40c = . (a) 0/ 0.064ft t = . (b) 0/ 0.686ft t = . (from [18]). plane strain multi-grain cell models for a polycrystalline aggregate have been used by van der giessen and tvergaard [19] to study the final creep fracture process, as microcracks formed at grain boundary facets link up. such analyses are however limited by the unrealistic grain geometry and the reduced constraint on sliding. but a great advantage is that large grain arrays can be analysed if a crude mesh is used within each grain, and this allows for direct modelling of intergranular crack growth in a plane strain multi-grain aggregate (onck and van der giessen [20]). fatigue cracking among the many applications of continuum damage mechanics [4], studies of failure by low cycle fatigue are an important example, where a material model directly based on the micro mechanics of failure has not been developed. as the development of fatigue fracture depends strongly on the plastic strain range in each cycle, an accurate cyclic plasticity model is needed (e.g. ohno and wang [21]), with damage mechanics incorporated. the scalar damage parameter d is taken to be zero initially, but when the accumulated plastic strain p reaches a threshold value dp , it is assumed that damage starts to develop according to the evolution law 1 , if ( ) , 0 , if d d p py d p p p ps α α ≥⎧ = = ⎨ <⎩ & & (5) here, s is a material parameter describing the energy strength of damage, the strain energy release rate is given by ( )( )22 / 2 1e vy r e dσ= − , and the expression for vr depends on the mean stress / 3 ,kkσ so that fatigue develops more rapidly under tensile stresses. when the damage parameter reaches a critical value cd , this is taken to represent such a high density of microcracks that coalescence into a macrocrack occurs. in a finite element analysis this failure event is represented in terms of the element vanish technique, such that the model can be used to predict the growth of a macroscopic crack. this type of numerical study has been carried out in [22] for a metal matrix composite, where the fatigue crack growth occurs in the metal matrix around short brittle fibres. 3 modelling by coesive zone as an alternative to the continuum models discussed above, a number of crack growth analyses describe the fracture process separately in terms of a traction separation law for the crack surface, while the inelastic deformations around the crack are accounted for by standard plasticity without damage. this gives an attractive possibility for separating effects of fracture process parameters from effects of the material parameters determining inelastic deformations, e.g. in relation to determining crack growth resistance curves. thus, analyses of this type determine directly the ratio between the remote fracture toughness and the local fracture toughness determined by the assumed cohesive model. in [5] a rather general case of crack growth along the interface between an elastic-plastic solid and a rigid solid was studied. here, a cohesive zone model was needed that accounts for both normal and tangential separation, or mixtures of these, not only in order to study effects of remote mixed mode loading, but also because of the oscillating elastic singularity resulting from the elastic mismatch across the interface, which gives varying mixtures of normal stress and shear stress along the interface. this work has been continued in a number of different studies of interface debonding, for different types of material systems. thus, in [23] resistance curves have been determined numerically for crack growth along an interface joining two elastic-plastic solids, or an elastic-plastic solid to an elastic substrate. the steady-state value ss k of the remote fracture toughness is found when the resistance curves reach their maximum, which depends on the local mode mixity 0ψ near the crack-tip. as an example fig. 3 shows such steady-state values for a case with an elastic substrate, where the elastic modulus 2e in the substrate is twice that in the elastic-plastic solid. the angular measure 0ψ is near o0 for mode i loading and would be near o90 or o90− for mode ii loading. the steady-state toughnesses are normalised by the value 0k corresponding to a purely elastic solid, for the separation v. tvergaard., frattura ed integrità strutturale, 1 (2007) 25-28 28 energy assumed in the traction separation law. the different curves correspond to different values of the peak stress σ̂ for the traction separation law, normalised by the initial yield stress. the curves show two typical features of such results, that the fracture toughness level is very sensitive to small increases of the peak stress, and that the curves have minima for near mode i conditions at the crack-tip. figure 3: steady-state interface toughness as a function of the local mixity measure 0ψ , for 1 1/ 0.003y eσ = and 2yσ ∞ , considering different values of 1/ ,yσ σ 2 1/ 2e e = . (from [23]). 4 references [1] a.l. gurson, engng. mater. technol., 99 (1977) 2. [2] v. tvergaard, advances in applied mechanics, academic press, inc., 27 (1990) 83. [3] v. tvergaard, acta metallurgica, 32 (1984) 1977. [4] j. lemaitre, a course on damage mechanics. springer-verlag, (1992). [5] v. tvergaard, j.w. hutchinson, j. mech. phys. solids, 41 (1993) 1119. [6] v. tvergaard, j. mech. phys. solids, 30 (1982) 399. [7] v. tvergaard, int. j. fracture, 17 (1981) 389. [8] v.tvergaard, a.needleman, acta metall., 32 (1984) 157. [9] v. tvergaard, a. needleman, j. mech. phys. solids, 40 (1992) 447. [10] k.k. mathur, a. needleman, v. tvergaard, j. mech. phys. solids, 44 (1996) 439. [11] v. tvergaard, modelling simul. mater. sci. eng., 9 (2001) 143. [12] v. tvergaard, a.needleman, 3d charpy specimen analyses for welds, to appear in proc. charpy centenery conf. (2001). [13] j.b. leblond, g. perrin, j. devaux, j. appl. mech. 61 (1994) 236. [14] v. tvergaard, a. needleman, int. j. solids structures 32 (1995) 1063. [15] a. needleman, v.tvergaard, eur. j. mech., a/solids, 17 (1998) 421. [16] d.r. hayhurst, p.r.brown, c.j. morrison, philosophical transactions, royal society london a311 (1984) 131. [17] m.f. ashby, b.f. dyson, national physical laboratory, report dma(a), (1984) 77. [18] v. tvergaard, int. j. fracture, 42 (1990) 145. [19] e. van der giessen, v. tvergaard, acta metall. mater., 42 (1994) 959. [20] p.r. onck, e. van der giessen, mech. mater, 26 (1997) 109. [21] n. ohno, j.-d. wang, int. j. of plasticity, 9 (1993) 375. [22] v. tvergaard, t.ø. pedersen, arch. mech., 52 (2000) 799. [23] v. tvergaard, j. mech. phys. solids, 49 (2001) 2689. microsoft word numero_55_art_22_2973 p. ferro et alii, frattura ed integrità strutturale, 55 (2021) 289-301; doi: 10.3221/igf-esis.55.22 289 microstructural and mechanical characterization of a stainless-steel wire mesh–reinforced al-matrix composite p. ferro, a. fabrizi, f. bonollo university of padova, italy paolo.ferro@unipd.it, https://orcid.org/0000-0001-8682-3486 alberto.fabrizi@unipd.it, https://orcid.org/0000-0002-7568-5804 franco.bonollo@unipd.it, https://orcid.org/0000-0002-7196-2886 f. berto norwegian university of science and technology ntnu, norway filippo.berto@ntnu.no, https://orcid.org/0000-0002-4207-0109 abstract. the microstructure and mechanical properties of stainless-steel aisi 304 wire mesh–reinforced alsi9cu-matrix composite specimens obtained by gravity casting were investigated. optical and scanning electron microscope analyses were carried out on samples in both as-cast and solution heat treated conditions. the obtained results showed the absence of intermetallic phases at the insert/al-matrix interface but even a significant fraction of lack-of-filling defects as well as lack-of-bonding areas that weekend the interface itself. the solution heat treatment, on the other hand, induced the precipitation of a thick and brittle intermetallic layer in the areas where a metallurgical bonding formed during casting. moreover, the silicon particle spheroidization, improved the ductility of the matrix. the resulting microstructure allowed to obtain a slight improvement of elongation at failure of the compound casting compared to that of the aluminum alloy. finally, basing on the obtained results, improvements are suggested that take into account both the preconditioning of the reinforcement surface and its geometry. keywords. al/fe bimetallic castings; interface; intermetallic compounds; microstructure; mechanical properties. citation: ferro, p., fabrizi, a., bonollo, f., berto, f. microstructural and mechanical characterization of a stainless steel wire meshreinforced al-matrix composite, frattura ed integrità strutturale, 55 (2021) 289-301. received: 29.11.2020 accepted: 24.12.2020 published: 01.01.2021 copyright: © 2021 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. introduction oday we are living in the era of advanced materials. all materials families have reached high levels of performances. so that even polymers and ceramics are today used in structural applications. for the same reason, it is difficult for each single material to be able to undergo new significant improvements quickly. a breakthrough can be possible t https://youtu.be/uf26rnay4mi p. ferro et alii, frattura ed integrità strutturale, 55 (2021) 289-301; doi: 10.3221/igf-esis.55.22 290 only combining different materials to each other hence designing multi-material components. this is particularly urgent in view of the huge challenge linked to the climate change. with the aim at reducing gas emissions, reducing weights of mechanical components is mandatory. thinking about the automotive and transport industry, lighter and lighter vehicles could be built by replacing steels with aluminum alloys [1]. these last in fact are characterized by a lower density, higher corrosion resistance and strength-to-weight ratio compared to steels. unfortunately, with respect to steels, they have a lower stiffness and creep resistance so that they alone are not able to meet the requirements of the automotive industry. in this scenario, aluminum-steel bimetals could be a solution worthy of investigation. different joining techniques are used to obtain such bimetallic components such as stir welding [2], friction welding [3], laser welding [4] and the most recent hybrid metal extrusion & bonding [5]. however, the most economical way to produce bimetallic components is pouring the liquid aluminum alloy into the mold cavity containing the steel reinforcement (compound casting). this allows also less geometrical restrictions compared to welding. examples can be found in the production of engine cylinder blocks [6], crankcases or pistons [7,8] that uses particular techiques to reach a sound metallurgical bonding between the two metals such as vibration assisted casting [9], expandable pattern casting [10] or the ‘al-fin’ process [11]. this is because in principle aluminum and iron are incompatible metals. different thermal expansion coefficients, low mutual diffusivity and easy-to-form oxide or brittle intermetallic phases at the interface make difficult to obtain sound mechanical and metallurgical bonding. in particular oxide films on the steel insert and liquid aluminum surface [12,13,14] reduce the wettability of the steel surfaces to liquid aluminum while the brittle and thick intermetallic layers promote interfacial brittle fractures [15], thus compromising the metallurgical bonding. despite these obstacles, the researchers were not discouraged and studied different strategies to obtain a good metallurgical bonding between the two metals. jiang et al. used a 0.1 wt% zn contained thin layer to protect the steel substrate from oxidation before pouring [16]. during pouring such thin layer completely dissolves into the liquid metal allowing a metallurgical bonding between the two materials and a significant increase of the shear stress of the bimetallic casting. the only issue is that zn seems to promote an increase in the intermetallic compound growth reducing the insert/alloy interface strength [17]. in another work, the same authors [18] found that a double surface treatment consisting of immersion of the steel insert into an ammonium chloride solution at 80 °c followed by aluminizing (780 °c for 200 s) improved the shear strength of the two alloys interface of 40% compared to that of the untreated casting. the dominant intermetallic phase induced by aluminizing was found to be al5fe2 characterized by a tongue-like morphology [2]. a good metallurgical bonding was also obtained by nitride coating on the steel insert [19]. in this case, the nitride coating was also found to slow dawn the growth of the brittle intermetallic layer with positive effects on the interface mechanical strength. it is worth noting that iron reached intermetallic phases such as feal or fe3al forms at higher temperatures compared to aluminum-reached ones like al5fe2, al2fe al3fe or al3fe3 and are even more desirable due to their better mechanical properties [20]. in this regard, with the aim at analyzing the mechanism of die soldering in aluminum die casting, han and viswanathan [21] measured a critical sticking temperature of 657 °c over which the intermetallic al3fe forms at the contact surface between pure aluminum and mild steel. the presence of a high concentration of silicon in the aluminum alloy promotes the formation of a thinner layer of al4.5fesi that is detrimental because of its platelet morphology causing internal stresses in the insert/alloy interface [22, 23]. in particular, it was found that the growth rates of the intermetallic layer decreased when the si content in the alloy was less than 1.5 wt%. on the opposite, the ternary fe-al-si intermetallic phases appeared and grew quickly as the si content in the molten metal increased to 2 wt% and 3 wt% [24,25]. the potential of cu coating to inhibiting the intermetallic layer during stainless steel 308/aluminum alloy a319 compound casting production was explored by khoonsari et al. [26]. they successfully found that cu coating was effective against the intermetallic layer formation and worked better than the zn protective layer. cast aluminum alloys undergo heat treatments such as solution followed by ageing to improve their mechanical properties. however, when dealing with aluminum-steel compound casting, such heat treatments could result very critical due to the metallurgical bonding alteration at the interface between the two coupled alloys. during solution treatment around 500 °c new intermetallic phases forms that according to their composition and thickness may increase or decrease the interface mechanical strength. viala et al. [27] studied the possibility to produce bimetallic automotive components, made out of an al–si light alloy reinforced with a cast iron insert, by gravity die molding. prior heat treatment, different kinds of intermetallic compounds were detected such as η(al5fe2), τ5(al7.4fe2si) and τ6(al4.5fesi) and after solution heat treatment at 520 °c for 12h τ2(al5fe2si2) and τ10(al12fe5si3) also appeared. in particular, the excessive growth of the intermetallic compound η during solution treatment with the consequent formation of kirkendall voids was attributed as the main cause of the insert/alloy interface bonding weakening. similar results were reached even by zhe et al. [28] after long-term (more than 40 hours!) solution treatments at 535 °c but in this case kirkendall voids were observed to form in the intermetallic compound τ6(al4.5fesi). the thickness (x) of the reaction layer was found to increase during time (t) fallowing a parabolic growth law, x2 = kt-b, where b is a constant and k meets the arrhenius type equation. the goal is to obtain a uniform intermetallic layer that doesn’t exceed a few micrometers in order to guarantee a strong and tough bond [29]. optimal heat treatment p. ferro et alii, frattura ed integrità strutturale, 55 (2021) 289-301; doi: 10.3221/igf-esis.55.22 291 process parameters were found by jiang et al. [30] who improved the shear strength of the aluminum/steel bimetal by 39%, compared to that measured in the as-cast conditions, by a solution heat treatment at 500 °c for 2 hours. this was mainly attributed to the obtained morphology and size of the intermetallic compound τ6(al4.5fesi) that showed a not excessive growth and absence of crack defects. in a recent work [31], the influence of galvanization and heat treatment on the reaction layer between al7simg and steel interface of a compound casting made out of low-pressure die casting was investigated. the authors found that a large amount of intermetallic phases form at the insert/alloy interface during casting with a prevalence of ternary al4.5fesi intermetallic particles (imp). the reaction layer thickness increased significantly (80 m) after heat treatment at 540 °c for 2h with cracks appearance that, de facto, weekend the interface bonding strength. the composition and microstructure of intermetallic compounds (imc) formed at the interface between aluminum alloy aa4343 and stainless steel sus316 upon annealing at 550 ◦c for 1h to 20h and at 610 ◦c for 15min to 10h were recently studied by zhang et al. [32]. the reaction layer after solution at 550 °c for 10h was constituted above all by τ10(al4fe1.7si) and η(al5fe2); its growth kinetics followed the rational equation x = (kt)n, where x is the layer thickness, t is the time and k and n are two constants. despite the great attention given by researchers to the steel/aluminum alloy interaction, only few works focused on the effective mechanical properties of such bimetallic materials. haga et al. [33] characterized the mechanical properties of aluminum/steel wire-inserted composite strip reporting an improvement of the tensile strength of about 20%-30% compared to that of the aluminum matrix. by using a new short-flow process based on twin-roll casting (trc) successfully developed to fabricate bimetallic laminated materials [34-36], huang et al. [37] investigated the mechanical properties of stainless-steel wire mesh–reinforced al-matrix composite plates. due to the rapid solidification time that characterizes the process, the reaction layer was only 5 m thick thus guarantying a good metallurgical bonding. despite this, the mechanical strength was mainly influenced by the wire square mesh orientation with respect to the applied load direction since it has a great influence on the deformation compatibility. they found that both the tensile strength (with an improvement of about 30%) and elongation rate are best when the orientation angle was 45°. the present study is useful to improve the mechanical properties in case of geometrical discontinuities [38-39] and can substantially impact on the final fatigue life at room [40-42] and high temperature [43] allowing to improve locally the strength to counterbalance local geometrical effects that can occur in a real 3d component [44-47]. starting from the results of huang et al. [37], the present work is aimed at studying metallurgical and static mechanical properties of a stainless-steel wire mesh–reinforced al-matrix composite samples obtained by gravity casting that compared to trc allows less geometrical restrictions. the effect of a solution heat treatment at 500 °c for 10 h was investigated, as well. materials and methods tainless steel wire mesh–reinforced al-matrix composite samples were obtained by gravity casting. the insert was constituted by a stainless steel aisi 304 square mesh grid, where the wire diameter and pitch were 0.6 mm and 2.3 mm, respectively. the aluminum alloy was the alsi9cu (en-ab 46400), which composition, measured with the optical emission spectrometer (foundry master pro oxford instrument) prior and after pouring, is collected in tab. 1. alsi9cu al si cu zn fe mg mn ti cr pb ni before pouring bal. 9.25 1.05 0.624 0.502 0.439 0.292 0.135 0.0353 0.0291 0.0238 after pouring bal. 8.85 1.04 0.664 0.483 0.446 0.301 0.132 0.0364 0.0286 0.0218 table 1: chemical composition (wt%) of the aluminum alloy before and after pouring. fig. 1 shows the steel mold with the mesh and filter located inside before pouring. following a similar procedure by huang et al. [37], the wire mesh has been degreased using ultrasonic cleaning in acetone and then placed inside the mold cavity with an orientation angle () of 0° relative to the load direction [37]. a thermocouple was also placed on mold surface in order to monitor and control the mold preheating temperature (350 ± 5°c). 12 samples were casted of which 6 without the steel insert. the alloy pouring temperature was 730 °c while the maximum mold temperature reached during all castings was 395.3 ± 3.4°c. the steel mesh positioning and eventual presence of macro defects in the obtained samples were first investigated by a non-destructive x-ray radiography testing (rt). the metallurgical investigations were carried out on both transversal and longitudinal sections (fig. 2) using the standard metallographic sample preparation. optical (leica lm2500) and scanning electron microscope (sem, model quanta feg-250 of fei©) were used for the microstructural characterization with particular attention to the bonding interface as well as the intersection between the longitudinal and latitudinal wires of the mesh. as shown in fig. 2(a,b), two different transversal sections planes were prepared. image s p. ferro et alii, frattura ed integrità strutturale, 55 (2021) 289-301; doi: 10.3221/igf-esis.55.22 292 analyses aimed at measuring the volume of lack of filling closed to the wire mesh and the secondary dendrite arms spacing (sdas) were carried out with the las software. figure 1: mold geometry with insert and filter positioning figure 2: transversal (a,b) and longitudinal (c) sections used for the metallurgical investigations. the obtained castings underwent to machining to reach the target geometry for tensile tests schematized in fig. 3. tensile tests were performed using an mts machine with an elongation rate equal to 4 mm/min. finally, the effect of a solution heat treatment at 500 °c for 10 h on metallurgical and mechanical properties of the reinforced specimens were investigated. p. ferro et alii, frattura ed integrità strutturale, 55 (2021) 289-301; doi: 10.3221/igf-esis.55.22 293 figure 3: geometry of tensile specimens (mm) and picture of a sample before and after machining. results bi-material integrity and metallurgy he rt was used to check the wire mesh has not be moved during pouring as well as the presence of macro-porosities. fig. 4 shows an example of the obtained results. in most cases the wire meshes maintained their good centered position while residual voids were detected above all at wires intersections. figure 4: results of radiography testing showing the wire mesh position and lack of filling at the wires intersection. with the attempt to estimate the amount of residual voids, two zones were investigated close to the ends of the sample practical length. for each zone two transversal sections were observed, as shown in fig. 2(a,b). it has to point out that large black zones as shown in the longitudinal section (fig. 2(c)) were not taken into account since they are due to errors in sample preparations. the area fractions occupied by voids in the transversal and longitudinal sections were found to be 7.86% and (0.76±0.38)%, respectively. the lack of filling of matrix could be reduced or even avoided by improving the wettability between the molten aluminum alloy and steel wire or rising the casting temperature. t p. ferro et alii, frattura ed integrità strutturale, 55 (2021) 289-301; doi: 10.3221/igf-esis.55.22 294 from 15 to 20 sdas measurements were performed in order to obtain a good statistical value of such parameter. it was found a little decrease of the sdas value of the aluminum matrix with the steel insert (22.10±1.89 m) compared to that of the aluminum matrix without the reinforcement (25.71±1.85 m). fig. 5 shows the microstructure of the aluminum matrix and reveals also some features of the interface steel/al. some phases are well detectable such as fe-rich precipitates (-al15fes) and a quite low amount of cu-rich phases. the optical micrograph in fig. 5(a) reveals an interface with zones characterized by a metallurgical bonding and zones with a possible gap between the steel and the matrix. fig. 5(b) shows at high magnifications the zone with a quite good contact between the two alloys where both the -al and the eutectic silicon are bonded to the stainless-steel wire. figure 5: optical micrographs of the two alloys and their coupling interface in the as-cast condition at different magnifications. using the scanning electron microscope, it was possible to better investigate the interface morphology of the as-cast sample (fig. 6). in addition to the iron-rich precipitates visible in the aluminum matrix, using different magnifications it is possible to observe both lack-of-contact and good contact zones between the two alloys. after the solution heat treatment at 500 °c for 10 h, the insert/al-matrix interface was partially decorated with an intermetallic substrate (fig. 7). it is also observed how the eutectic silicon modified its morphology after the heat treatment from plate-like to almost equiaxed shape. p. ferro et alii, frattura ed integrità strutturale, 55 (2021) 289-301; doi: 10.3221/igf-esis.55.22 295 figure 6: sem micrographs of the two alloys and their coupling interface in the as-cast condition. figure 7: optical micrographs of the two alloys and their coupling interface after solution treatment (500 °c, 10h). tensile tests for the sake of simplicity, only one representative nominal stress-strain curve is shown in fig. 8 for each condition. it is easy to observe that the steel wire mesh improved neither the mechanical strength (yield strength (ys) and ultimate tensile strength (uts)) nor the elongation at fracture (a%) of the aluminum alloy in the as-cast condition. only a little improvement of the young’s modulus (e) is obtained. on the contrary, the reinforcement slightly increases the uts as well as the p. ferro et alii, frattura ed integrità strutturale, 55 (2021) 289-301; doi: 10.3221/igf-esis.55.22 296 elongation at fracture of the aluminum alloy in the solution heat treated condition. moreover, the solution heat treatment decreases the mechanical strength but increases the ductility compared to those of the samples in the as-casting conditions. tab. 2 summarizes the results of the tensile tests. it worth mentioning that all the tensile tests stopped as soon as the aluminum matrix broke. figure 8: stress-strain curves of the compound castings and al alloy in different conditions. e [gpa] ys [mpa] uts [mpa] a [%] al matrix, as-cast 72.00±1.20 127.00±1.41 202.32±1.57 1.46±0.11 al matrix + insert, as-cast 76.33±1.53 126.33±1.52 184.32±4.04 1.01±0.05 al matrix, heat treated 74.50±0.71 122.50±0.76 191.00±1.41 1.89±0.03 al matrix + insert, heat treated 74.67±1.48 122.67±1.03 194.68±1.52 2.34±0.05 table 2: comparison between the mechanical properties of the compound casting and the aluminum alloy. discussion tainless steel wire mesh–reinforced al-matrix composite specimens were obtained. the first issue is related to the significant percentage of residual voids at the v-shape narrow space at the intersection of steel wires and due to lack of filling. they in fact can easily trigger the crack propagation and above all the wire/matrix debonding. at the same time, they could be drastically reduced by increasing the casting temperature. the steel wire mesh was found to influence the al-matrix microstructure. as a matter of fact, it increased the grain refinement by increasing the cooling rate, as suggested by the sdas measurements. unfortunately, this grain refinement was not significant to obtain an increment of the mechanical strength in the as-cast condition, except for a slight increase in the yield stress that could be attribute to both the matrix refinement by grain refinement and the steel insert. the compound castings in the as-cast condition showed only a partial contact surface between the steel wire and the aluminum alloy (fig. 5). since the solidification and cooling times were short, no intermetallic phases were formed in those zones. on the other hand, according to the work of huang et al. [37], al-fe interdiffusion is supposed to be occurred, promoting a metallurgical bonding. however, compared to huang et al. [37] results, the metallurgical bonding didn’t occur in all the wire surface probably because, using a gravity casting process instead of solid-liquid cast-roll bonding, the solidification front was more complicated resulting in complex shrinkages that could have generated same gaps between the wire and the aluminum alloy. moreover, the presence of needle or plate shaped phases at the steel/al interface (fig. 5b) could further reduce the bonding strength [48]. the presence of lack-of-bonding areas in the as-cast condition is also confirmed by the intermetallic layer that formed during the solution heat treatment around the steel wires but obviously only at the prior s p. ferro et alii, frattura ed integrità strutturale, 55 (2021) 289-301; doi: 10.3221/igf-esis.55.22 297 steel/aluminum contact zones (fig. 7). the intermetallic layer does not cover the entire wire surface, in fact. its high thickness (about 200 m) is due to the long holding time at an elevate temperature during solution treatment, which allows new intermetallic layers to form through solid state diffusion. kirkendall voids were also observed to form in the intermetallic compound as also reported by zhe et al. [27] (fig. 9). with reference to the work of bakke et al. [30], the two intermetallic compounds were supposed to be β-al4.5fesi and/or τ10-al4fe1.7si. finally, different cracks were observed in the intermetallic layer (fig. 9) that confirm its brittle nature. they were attributed to the build-up of thermal stress at the interface during quenching due to the different thermal expansion coefficients of aluminum, steel and interfacial intermetallic phases, which results in cracks formation and propagation through the brittle intermetallic phases [49,50]. in such conditions, the steel/aluminum bonding is expected to be poor, as also reported in literature and confirmed by tensile tests. figure 9: sem micrographs of the intermetallic layer after solution treatment (500 °c, 10h). despite the different casting technology used, the present mechanical results are in good agreement with those found by huang et al. [37]. as expected from metallurgical analyses, specimens fracture occurred only in the aluminum matrix (fig. 10), proving an easy debonding and sliding of the steel wire mesh during the tensile test. however, the solution heat treatment, by increasing the ductility of the matrix through a silicon particles spheroidization, allows delaying the cracks initiation at the wire/al interface therefore increasing the elongation at fracture of the al/steel compound casting compared to that of the aluminum alloy (tab. 2). it is interesting to observe the brittle fracture morphology of intermetallic layer. fragments of the intermetallic layer are visible both in the steel and al matrix surfaces (fig. 10). the results obtained in this investigation suggest different possible improvements. process parameters, such as pouring and mold temperatures, should be optimized in order to eliminate voids due to lack of fusion. in this regard, also the kinetics of the solidification front could be investigated (say, through numerical simulation) and controlled in order to avoid debonding during the alloy solidification [51]. as a matter of fact, by controlling the solidification front is should be possible in principle to improve both the metallurgical and mechanical bonding [51]. the steel surface preconditioning is another design aspect to care about. according to literature [26], a cu coating will result more effective, compared to zn, against the intermetallic layer formation. finally, another parameter worthy of investigation and improvement is the insert geometry. in fact, by optimizing the roughness and shape of the mesh, it will be possible to improve the al/steel mechanical bonding, eliminate difficult-to-fill zones and above all, to design an insert stiffness closer to that of the alloy:             insert insert matrix matrix e a e a l l (1) p. ferro et alii, frattura ed integrità strutturale, 55 (2021) 289-301; doi: 10.3221/igf-esis.55.22 298 in eqn. (1) e is the young’s modulus, a is the cross section and l is the practical length. figure 10: broken sample in the as-cast condition and sem micrographs of the steel/al interface after heat treated specimen failure. this last effect (eq. 1) was already highlighted by huang et al. [37] who found improvements by simply rotating the steel wire mesh by 45° relative to the rolling direction. however, authors think that even better results could be obtained by further improving the insert design, taking advantage of additive manufacturing technologies and process simulation [], as well. conclusions he microstructure and mechanical properties of stainless-steel wire mesh–reinforced al-matrix composite specimens obtained by gravity casting were investigated. moreover, the effect on metallurgical transformations and mechanical properties of a solution heat treatment at 500 °c for 10 hours were studied. metallurgical investigations carried out on the as cast samples showed the absence of intermetallic phases at the insert/al-matrix interface but even a significant fraction of lack-of-filling defects and lack-of-bonding areas. this compromised the interface strength that wasn’t able to transfer the load from the matrix to the reinforcement. the solution heat treatment, on the other hand, induced the precipitation of a thick and brittle intermetallic layer in the areas where a metallurgical bonding formed during casting. moreover, the silicon particle spheroidization, improved the ductility of the matrix. the resulting microstructure allowed to obtain a slight improvement of elongation at failure of the compound casting compared to that of the aluminum alloy. t p. ferro et alii, frattura ed integrità strutturale, 55 (2021) 289-301; doi: 10.3221/igf-esis.55.22 299 finally, basing on the results of the present work, possible improvements were suggested that take into account not only the insert surface preconditioning but also its geometry aimed at improving the alloy filling, the mechanical bonding and its stiffness that should be comparable with that of the matrix. acknowledgements uthors would like to thank mr. giacomo mazzacavallo for his precious support during metallurgical investigations as well as tensile tests. references [1] miller, w., zhuang, l., bottema, j., wittebrood, a., de smet, p., haszler, a., vieregge, a. (2000). recent development in aluminum alloys for the automotive industry, mater. sci. eng. a 280, pp. 37-49. doi: 10.1016/s09215093(99)00653-x. [2] springer, h., kostka, a., dos santos, j.f., raabe, d. (2011). influence of intermetallic phases and kirkendall-porosity on the mechanical properties of joints between steel and aluminium alloys, mater. sci. eng. a 528, pp. 4630-4642. doi: 10.1016/j.msea.2011.02.057. [3] herbst, s., aengeneyndt, h., maier, h.j., nürnberger, f. (2017). microstructure and mechanical properties of friction welded steel-aluminum hybrid components after t6 heat treatment, mater. sci. eng. a 696, pp. 33-41. doi: 10.1016/j.msea.2017.04.052. [4] jia, l., shichun, j., yan, s., cong, n., junke, c., genzhe, h. (2015). effects of zinc on the laser welding of an aluminum alloy and galvanized steel, j. mater. process. technol. 224, pp. 49-59. doi: 10.1016/j.jmatprotec.2015.04.017. [5] berto, f., torgersen, j., grong, ø., sandness, l. and ferro, p. (2018). characterization of hybrid metal extrusion & bonding (hyb) joints of aa6082-t6 aluminium alloy and s355 steel. proceedings of 22nd european conference on fracture, ecf22, belgrade, serbia, 26-31 august. [6] miyamoto, n. et al. (2007). insert casting component, cylinder block, method for forming coating on insert casting component and method for manufacturing cylinder block, u.s. patent wo2007007826, 18 jan 2007. [7] nunney, m.j. (2006). light and heavy vehicle technology, 4th ed., butterworth-heinemann. [8] bennett, s. (2009). modern diesel technology: diesel engines, 4th ed., thomson delmar learning, division of thomson learning. [9] pan, j., yoshida, m., sasaki, g., fukunaga, h., fujimura, h. and matsuura, m. (2000). ultrasonic insert casting of aluminum alloy, scripta mater., 43(2), pp. 155-159. [10] choe, k.h., park, k.s., kang, b.h., kim, k.y., lee, k.w. and kim, m.h. (2008). study of the interface between steel insert and aluminum casting in epc, j. mater. sci. technol. (shenyang, china), 24(1), pp. 60-64. [11] guertler, g. (1969). compound casting, aluminium (isernhagen, germany), 45(6), pp. 368-373. [12] aylward, g., findlay, t. (2002) si chemical data, fifth ed., john wiley & sons australia, milton. [13] papis, k.j.m., loeffler, j.f., uggowitzer, p.j. (2009). light metal compound casting, sci. china, ser. a 52, pp. 46-51. [14] papis, k.j.m., hallstedt, b., lo€ffler, j.f., uggowitzer, p.j. (2008). interface formation in aluminum-aluminum compound casting, acta mater. 56, pp. 3036-3043. doi: 10.1016/j.actamat.2008.02.042. [15] springer, h., kostka, a., payton, e.j., raabe, d., kaysser-pyzalla, a., eggeler, g. (2011). on the formation and growth of intermetallic phases during interdiffusion between low-carbon steel and aluminum alloys, acta mater. 59, pp. 15861600. doi: 10.1016/j.actamat.2010.11.023. [16] jiang, w., fan, z., li, g., li, c. (2016). effects of zinc coating on interfacial microstructures and mechanical properties of aluminum / steel bimetallic composites, j. alloys compd. 678, pp. 249-257. [17] springer, h., szczepaniak, a., raabe, d. (2015). on the role of zinc on the formation and growth of intermetallic phases during interdiffusion between steel and aluminum alloys, acta mater. 96, pp. 203-211. doi: 10.1016/j.actamat.2015.06.028 [18] jiang, w., fan, z., li, g., li, c. (2015). improved steel/aluminum bonding in bimetallic castings by a compound casting process. journal of materials processing technology, 226, pp. 25–31. [19] nazari, k.a., shabestari, s.g. (2009). effect of micro alloying elements on the interfacial reactions between molten aluminum alloy and tool steel, j. alloys compd. 478, pp. 523-530. doi: 10.1016/j.jallcom.2008.11.127. a p. ferro et alii, frattura ed integrità strutturale, 55 (2021) 289-301; doi: 10.3221/igf-esis.55.22 300 [20] kobayashi, s., yakou, t. (2002). control of intermetallic compound layers at interface between steel and aluminum by diffusion-treatment, mater. sci. eng. a 338, pp. 44-53. doi: 10.1016/s0921-5093(02)00053-9. [21] han, q., viswanathan, s. (2003). analysis of the mechanism of die soldering in aluminum die casting. metallurgical and materials transactions a 34(1), pp. 139-146. doi: 10.1007/s11661-003-0215-9. [22] cheng, w.-j., wang, c.-j. (2011). effect of silicon on the formation of intermetallic phases in aluminide coating on mild steel, intermetallics 19, pp. 1455-1460. doi: 10.1016/j.intermet.2011.05.013. [23] seifeddine, s., johansson, s., svensson, i.l. (2008). the influence of cooling rate and manganese content on the bal5fesi phase formation and mechanical properties of al-si-based alloys, mater. sci. eng. a, 490, pp. 385-390. doi: 10.1016/j.msea.2008.01.056. [24] yin, f.c, zhao, m.x., liu, y.x., et al. (2013). effect of si on growth kinetics of intermetallic compounds during reaction between solid iron and molten aluminum, j. transactions of nonferrous metals society of china, 23, p. 556-561. doi: 10.1016/s1003-6326(13)62499-1 [25] wei, h., fu-cheng, y., xu-ping, s. et al. influence of silicon on growth kinetics of fe2al5 during reactive diffusion between solid iron and aluminum, j. transactions of materials and heat treatment, 31, pp. 28-32. [26] viala, j.c., peronnet, m., barbeau, f., bosselet, f., bouix, j. (2002). interface chemistry in aluminium alloy castings reinforced with iron base inserts, compos. part a appl. sci. manuf. 33, pp. 1417-1420. doi: 10.1016/s1359835x(02)00158-6. [27] zhe, m., dezellus, o., gardiola, b., braccini, m., viala, j.c. (2011). chemical changes at the interface between low carbon steel and an al-si alloy during solution heat treatment, j. phase equilibria diffus. 32(6), pp. 486-497. doi: 10.1007/s11669-011-9949-z. [28] durrant, g., gallerneault, m. and cantor, b. (1996). squeeze cast aluminium reinforced with mild steel inserts, j. mater. sci., 31(3), pp. 589-602. [29] jiang, w., li, g., wu, y., liu, x., fan, z. (2018). effect of heat treatment on bonding strength of aluminum/steel bimetal produced by compound casting, j. mater. process. technol. 258, pp. 239-250. doi: 10.1016/j.jmatprotec.2018.04.006. [30] bakke, a.o., arnberg, l., løland, j.-o., jørgensen, s., kvinge, j., li, y. (2020). formation and evolution of the interfacial structure in al/steel compound castings during solidification and heat treatment. journal of alloys and compounds 849, 156685. doi: 10.1016/j.jallcom.2020.156685. [31] zang, x., gao, k., hu, x., ding, y., wang, g., wu, x., nie, z. (2020). growth kinetics of interfacial intermetallic compound in al(aa4343)/steel(sus316) clad strip. materials science forum, 993, pp 447-456. [32] khoonsari, e.m., jalilian, f., paray, f., emadi, f., drew, r.a.l. (2010). interaction of 308 stainless steel insert with a319 aluminium casting alloy. materials science and technology, 26, pp. 833-841. [33] haga, t., takahashi, k., watari, h., et al. (2007). casting of wire-inserted composite aluminum alloy strip using a twin roll caster. j. mater. process tech., 192–193, pp. 108–113. [34] huang, h.g., chen, p. and ji, c. (2017). solid-liquid cast-rolling bonding (slcrb) and annealing of ti/al cladding strip. mater. design. 118, pp. 233–244. [35] bae, j.h., rao, a.k.p., kim, k.h., et al. (2011). cladding of mg alloy with al by twin-roll casting. scripta mater. 64, pp. 836–839. [36] grydin, o., gerstein, g., nurnberger, f. et al. (2013). twin-roll casting of aluminum–steel clad strips. j. manuf. process. 15, pp. 501–507. [37] huang, h., wang, j., liu, w. (2017). mechanical properties and reinforced mechanism of the stainless steel wire mesh– reinforced al-matrix composite plate fabricated by twin-roll casting. advances in mechanical engineering, 9(6), pp. 1– 9. [38] ayatollahi, m.r., rashidi moghaddam, m., razavi, s.m.j., berto, f. (2016). geometry effects on fracture trajectory of pmma samples under pure mode-i loading, engineering fracture mechanics, 163, pp. 449–461. doi: 10.1016/j.engfracmech.2016.05.014. [39] torabi, a.r., campagnolo, a., berto, f. (2015). local strain energy density to predict mode ii brittle fracture in brazilian disk specimens weakened by v-notches with end holes materials and design, 69, pp. 22–29. doi: 10.1016/j.matdes.2014.12.037. [40] zhu, s-p., yu, z-y, correia, j., de jesus, a., berto, f. (2018). evaluation and comparison of critical plane criteria for multiaxial fatigue analysis of ductile and brittle materials, international journal of fatigue, 112, pp. 279-288. doi: 10.1016/j.ijfatigue.2018.03.028. p. ferro et alii, frattura ed integrità strutturale, 55 (2021) 289-301; doi: 10.3221/igf-esis.55.22 301 [41] correia, j., apetre, n., arcari, a., de jesus, a., muñiz-calvente, m., calçada, r., berto, f., fernández-canteli, a. (2017). generalized probabilistic model allowing for various fatigue damage variables, international journal of fatigue volume 100, pp. 187-194. doi: 10.1016/j.ijfatigue.2017.03.031. [42] ferro, p., lazzarin, p., berto, f. (2012). fatigue properties of ductile cast iron containing chunky graphite, materials science and engineering a, 554, pp. 122–128. doi: 10.1016/j.msea.2012.06.024. [43] berto, f., gallo, p., lazzarin, p. (2014). high temperature fatigue tests of un-notched and notched specimens made of 40crmov13.9 steel. materials and design, 63(1), pp. 609–619. doi: 10.1016/j.matdes.2014.06.048 [44] berto, f., lazzarin, p., wang, c.h. (2004). three-dimensional linear elastic distributions of stress and strain energy density ahead of v-shaped notches in plates of arbitrary thickness. int. j. fracture, 127(3), pp. 265–282. doi: 10.1023/b:frac.0000036846.23180.4d [45] berto, f., lazzarin, p., kotousov, a. (2011). on higher order terms and out-of-plane singular mode. mechanics of materials, 43(6), pp. 332–341. doi: 10.1016/j.mechmat.2011.03.004. [46] berto, f., lazzarin, p. (2013). multiparametric full-field representations of the in-plane stress fields ahead of cracked components under mixed mode loading, international journal of fatigue, 46, pp. 16–26. doi: 10.1016/j.ijfatigue.2011.12.004. [47] wu, w., hu, w., qian, g., liao, h., xu, x., berto, f. (2019). mechanical design and multifunctional applications of chiral mechanical metamaterials: a review, materials and design, 180, 107950. doi: 10.1016/j.matdes.2019.107950 [48] seifeddine, s., johansson, s., svensson, i.l. (2008). the influence of cooling rate and manganese content on the bal5fesi phase formation and mechanical properties of al-si-based alloys, mater. sci. eng. a 490, pp. 385-390. doi: 10.1016/j.msea.2008.01.056. [49] jin, y., hong, s.i. (2014). effect of heat treatment on tensile deformation characteristics and properties of al3003/sts439 clad composite, mater. sci. eng., a 596, pp. 1-8, https://doi.org/10.1016/j.msea.2013.12.019. [50] wang, q., leng, x.-s., yang, t.-h., yan, j.-c. (2014). effects of fedal intermetallic compounds on interfacial bonding of clad materials, trans. nonferrous metals soc. china 24, pp. 279-284. doi: 10.1016/s1003-6326(14)63058-2. [51] soderhjelm, c., appelian, d. (2018). multi-material casting: practical foundry guidelines. modern casting, june, pp. 40-43. [52] ferro, p., berto, f. and romanin, l. (2020). understanding powder bed fusion additive manufacturing phenomena via numerical simulation. frattura ed integrità strutturale, 14(53), pp. 252-284. doi: 10.3221/igf-esis.53.21. microsoft word numero_49_art_11_2503 t. profant et alii, frattura ed integrità strutturale, 49 (2019) 107-114; doi: 10.3221/igf-esis.49.11 107 focused on crack tip fields the ab-initio aided strain gradient elasticity theory: a new concept for fracture nanomechanics tomáš profant, jaroslav pokluda brno university of technology, technická 2896/2, 616 69 brno, czech republic profant@fme.vutbr.cz, pokluda@fme.vutbr.cz abstract. when the width of cracked nanocomponents made of brittle or quasi-brittle materials is less than approximately 10 nm , the size of the k dominance zone becomes smaller than 2 3nm and comparable to the fracture process zone ( 0.4 0.6 nm). the fracture process starts to be dominated by far-stress field terms and the critical stress intensity factor can no more represent the total fracture driving force. this means a breakdown of a classical linear elastic fracture mechanics suffering from the undesirable crack-tip stress singularity. the contribution presents a new concept expected to properly predict the critical crack driving force for nano-components: the ab-initio aided strain gradient elasticity theory (ai-sget). in contrast to the barenblatt cohesive model, the strain gradient elasticity theory does not require to prescribe a suitable field of cohesive tractions along the crack faces in order to eliminate the stress singularity and to exhibit cusp-like profiles of crack flanks close to the crack front in accordance with atomistic models. the only unknown and necessary quantity is the material length scale parameter which can be, e.g., determined by best strain gradient elasticity fits of ab-initio computed phonon-dispersions and near-dislocation displacement fields. atomistic approaches can also be employed to determine fracture mechanical parameters (crack driving force, crack tip opening displacement) related to the moment of crack instability in a given material. such ai-sget codes can then be utilized to a successful prediction of fracture of cracked nanocomponents made of brittle or quasi-brittle materials. keywords. strain gradient elasticity; ab-initio adjustment; stress singularity; cusp-like crack profile; cracked nanopanel. citation: profant, t., pokluda., j., the abinitio aided strain gradient elasticity theory: a new concept for fracture nanomechanics, frattura ed integrità strutturale, 49 (2019) 107-114. received: 30.04.2019 accepted: 25.05.2019 published: 01.07.2019 copyright: © 2019 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. introduction he basic hypothesis of linear fracture mechanics says that the size of the k dominant region must be much higher than the fracture process zone incorporating inelastic deformations near the crack-tip. this gives rise to a question regarding the sufficiency of the stress intensity factor to predict the fracture toughness of nanostructures. shimada et al. in [1] indeed showed that beyond a certain critical size of a nano-component (the specimen t http://www.gruppofrattura.it/va/49/2503.mp4 t. profant et alii, frattura ed integrità strutturale, 49 (2019) 107-114; doi: 10.3221/igf-esis.49.11 108 width below approximately 10 15 nm), the classical continuum approach breaks down and the k dominance zone smaller than 2 3nmbecomes comparable to the fracture process zone of a constant size of about 0.5 nm where, according to atomistic models, a highly localized discrete motion of atoms takes place. the fracture process then starts to be dominated by far-stress field terms, the stress intensity factor becomes size dependent and can no more be used for characterizing the fracture toughness of cracked nano-structures. similar behavior also exhibits the griffith energy release rate (err). there are attempts in literature to capture the size dependency of the critical stress intensity factor ck using a two parameter model based on williams’s expansion but the size dependency of both ck and the critical err contradicts the constant critical err obtained from atomistic simulations [2]. it was proved in [3] that mindlin’s strain gradient elasticity theory (sget, [4]) allows the continuum assumption to be extended beyond the limit of the classical fracture mechanics. in contrast to the barenblatt cohesive model, the strain gradient elasticity theory does not require to prescribe a suitable field of cohesive tractions along the crack faces in order to eliminate the undesirable stress singularity and to produce cusp-like profiles of near-tip crack faces in accordance with atomistic models even when the simplest form of the sget is used containing elastic constants and one length material parameter only. the crucial point is to identify this internal length scale parameter. this length parameter can be determined by fitting the ab initio solutions for (i) the displacement field near a screw dislocation, (ii) the critical crack tip opening displacement and (iii) the phonon dispersions using a finite element code based on the sget. it is worth to note that all the three methods should give equivalent results. atomistic approaches can also be employed to determine fracture mechanical parameters (crack driving force, crack tip opening displacement) related to the moment of crack instability in a given material. coupling of these calibration procedures with the sget-based finite element (fe) code then leads to a multi-scale approach we call the abinitio aided strain gradient elasticity theory (ai-sget). this article is focused on a comparison of barenblatt and sget solutions of the stress-strain crack tip field to demonstrate a usefulness of the ai-sget as well as its capability to remove the stress singularity and to exhibit the neartip cusp-like profile of crack flanks. classical vs. strain gradient elasticity solution he classical elasticity is not able to describe the process region at the crack tip by simply applying the equilibrium and boundary conditions prevailing at the crack front. a special model has to be used to describe the mechanical behavior inside the process region. probably the most popular known is the barenblatt model, see fig. 1a. it is assumed that the barenblatt region is developed in an isotropic elastic surrounding to be subjected to the classical linear elasticity laws. if the cohesive stress density ( )yy xs¢ is given, then the displacements in the process region in the range 0 px r< < for semi-infinite solid 0y ³ are evaluated as the superposition of displacements ahead and behind the crack tip, respectively, 1 2 3/2 0 ( )2 (1 ) ( ) d 3 yy p p y p p p r r k u r r r s a m e e a p a + ¢ »ò for 1. p p r x r e =  (1) the detailed derivation of (1) can be found in [5]. the exponent of the non-dimensional coordinate 3/2e in (1) provides a smooth cusp-like opening of the crack face. although the stress density yys¢ is unknown, from the condition 1 0 ( ) d 0 yy p pr rs a a a ¢ <ò (2) follows a decreasing character of the cohesion-decohesion curve as depicted in fig. 1 in terms of stress density yys¢ and displacement of the upper crack face +yu . the barenblatt model confirms the fact that the classical theories can be applicable in a multi-scale range and even in the nano-scale regime. although the smooth opening of the crack tip is estimated in (1), the stress conditions prevailing at the crack tip can be evaluated only when the cohesion-decohesion t t. profant et alii, frattura ed integrità strutturale, 49 (2019) 107-114; doi: 10.3221/igf-esis.49.11 109 relations are known. these relations are hidden in the unknown stress density yys¢ and their creation is the topic of many works, e.g. [6, 7]. (a) (b) figure 1: the comparison of the (a) barenblatt model of the process zone and (b) the process zone in sget. the cohesiondecohesion stress at the point as the superposition of the monopolar stress differentials is symbolically depicted in the barenblatt model (a). the boundary condition of the stress free crack faces as well as the asymptotic and full-filed total stresses ahead of the crack tip are visualised in the sget model (b). a second way how to avoid the break-down of the classical fracture mechanics at the nanoscale is an application of the sget model introduced by mindlin. a detailed presentation of the form ii of the mindlin’s theory can be found in [811]. here the strain energy density ( , )ij k ijw w e e= ¶ is a function of the linear strain tensor 1/ 2( )ij j i i ju ue = ¶ +¶ and its gradient k ije¶ . the monopolar stress tensor ijs and the so-called dipolar (or double) stress tensor kijm are then defined as ,ij ij w s e ¶ = ¶ . ( ) kij k ij w m e ¶ = ¶ ¶ (3) the simplest possible linear form of the strain energy density with a single length-scale parameter is 21 1 , 2 2 ijkl ij kl ijkl r ij r klw c c le e e e= + ¶ ¶ (4) *x dyy  yyt t. profant et alii, frattura ed integrità strutturale, 49 (2019) 107-114; doi: 10.3221/igf-esis.49.11 110 where l is the internal length scale parameter. along the plane const.y = , i.e., for the plane with the normal unit vector defined as (0, 1)= n , the so-called total stresses yxt and yyt can be defined. these stresses result from the monopolar traction conditions and have a form ( ) ( ) , . yx yx x xyx y yyx x yxx yy yy x xyy y yyy x yxy t m m m t m m m t t =  -¶ -¶ -¶ =  -¶ -¶ -¶ (5) the mode i crack tip dominant displacement field ( ),r qu which determines the near crack tip opening displacement is of the form 3/2 1 1 2 2( / ) ( ; ) ( ; ) ,ijkl ijkll r l a c a cq qé ù= +ê úë ûu u u (6) where 1a , 2a are the amplitude factors and r , q are polar coordinates. these constants are unspecified by the asymptotic analysis and must be determined by a complete solution of the boundary value problem. it should be noted that (6) is derived under the condition of the stress-free crack faces (fig. 1b) contrary to the barenblatt model in which the nonzero stress density yys¢ along the crack faces is prescribed (fig. 1a). the vectors 1( ; )ijklcqu and 2 ( ; )ijklcqu have a complicated form but, for an isotropic material, they can be found in [8]. similarly to the barenblatt solution (1) the 3/2r variation in (6) shows a cusp-like profile of crack faces. the modelling of the process zone is the size-depended phenomena and it requires the theory taking a material length scale l into account. this length scale enters both the constitutive and the equilibrium equations and appends the dependency of the strain energy function on the gradients of the strains as one can see in (4). the consequence of this fact is a particular role of the total stress (5) in the fracture process. its normal component yyt is depicted in fig. 1b, where it appeares as the full-field and the asymptotic solution ahead of the crack tip having a strong singularity 3/2r - . the total stress takes on negative values thus exhibiting a cohesive-traction character along the prospective fracture zone. as shown in [8], the asymptotic solution for the total stress yyt derived from (6) is a good approximation of the full-field solution in a very small distance from the crack tip ( 110 l- ). it appreciably deviates from the full-field solution for the larger distances and quickly tends to zero. however, the full-field solution for the total stress yyt takes on positive values for 0.5x l> and tends asymptotically to the limit of the classical elasticity [8]. the weakness of the sget is the identification of the material internal length scale parameter l in (4) and (6). this crucial point can be solved by three different approaches. the first one employs the fitting of displacement fields near the crew dislocation as obtained by ab-initio (ai) approaches by the analytical sget solution, the second one compares the critical crack tip opening displacement in the sget fe model and the ai-aided molecular statics (ms) and the third one utilizes the fitting of the ab initio calculated phonon dispersion relations by the sget dispersion solution. all the three methods give equivalent results, i.e., they provide identical values of the material length parameter l [12, 13]. numerical results he fe model of a center cracked nano-panel consisting of a tungsten with elastic coefficients of the cubic structure 11 523gpac = , 12 205 gpac = and 44 161 gpac = is introduced as the numerical example to illustrate the cohesion relation at the crack tip. the scheme of the specimen is shown in fig. 2. a mixed formulation of fe solution of the gradient elasticity 4th-order equations was used where instead of the 1c displacement field it utilizes ordinary 0c -continuous finite elements, see [14, 15]. except the available software [17], an original novel method for fe solution of the gradient elasticity 4th-order equations was developed in [16]. detailed fe calculations of the cracked nanopanel subjected to mod i loading in terms of the sget were carried out under the plane strain conditions. only a quarter of the nanopanel under the remote loading 312 10 mpas = ´ , corresponding to the moment of unstable fracture as t t. profant et alii, frattura ed integrità strutturale, 49 (2019) 107-114; doi: 10.3221/igf-esis.49.11 111 predicted by atomistic simulations [13], and the crack length 5.25 nmca = were employed in the analysis. the material length scale parameter assessed from the ai-sget analyses based on the screw dislocation and the phonon dispersions was 0.25 nml = [13]. a fine mesh and opening of the upper face of the crack is depicted in fig. 3. the scaled-up detail shows the cusp like opening of the near-tip crack faces. figure 2: the dimensions of the cracked fe nano-panel and a local polar coordinate system at the crack tip. the normal and shear strains yye and xye , respectively, along the crack upper face and in the near distances ahead of the crack tip ( 24 40l x l< < ) are depicted in fig. 4. the crack face extends along the negative axis 0x < . one can observe that the normal strains yye take a finite value at the crack tip 0x = contrary to the well-known classical solution, where the normal strain exhibits a square root singularity. it is also evident, that the effect of microstructure (stress gradients) is distinct only in the zone 5x l< , according to [8]. outside this zone the normal strains yye and xye tend to classical ones. the shear strain xye ahead of the crack tip ( 0x > ) is zero due to the model symmetry and mode i loading, but it is non zero along the crack face ( 0x < ). this is contrary to the classical linear elasticity result but in accordance with the cjp model taking the nonlinear effects near the crack tip into account [18]. one can suppose the pointwise convergence of xye to the singular classical linear elasticity solution for the length scale parameter l tending to zero. figure 3: upper crack face opening in sget fe model. t. profant et alii, frattura ed integrità strutturale, 49 (2019) 107-114; doi: 10.3221/igf-esis.49.11 112 (a) (b) figure 4: the respective shear and normal strains xye and yye along the upper crack face 0x < and ahead of the crack tip 0x > . (a) (b) yu  (c) figure 5: (a) the normal monopolar stress , (b) the displacement along the upper crack face and ahead of the crack tip , (c) the total stress in front of the crack tip and its components appearing in (5)1. the bold part of the monopolar stress in (a) corresponds to the monopolar component of the total stress in (c). yy 0x  0x  yyt yy yyt t. profant et alii, frattura ed integrità strutturale, 49 (2019) 107-114; doi: 10.3221/igf-esis.49.11 113 the distribution of the monopolar normal stress yys along the upper crack face as well as ahead of the crack tip is also interesting from the point of view of the cohesion-decohesion relation. fig. 5a shows the normal stress yys with finite value at the crack tip ( 0x = ) copying the distribution of the normal strain yye from fig. 4b. the curve of yys for 0x < obeys the barenblatt´s condition (2) and converges to the zero value and hence to the classical elasticity solution for 4x l<. ahead of the crack tip ( 0x > ) the convergence of yys to the classical elasticity solution is slightly slower. the upper crack face opening is depicted in fig. 5b, where the “closing” effect of the crack tip is obvious for 0l x< < . it should be emphasized that both the monopolar normal stress yys and the displacement yu + depicted in fig. 5 well correspond to the results obtained by ab-initio adjusted molecular static codes for cracked tungsten nanoplates [13]. contrary to the classical elasticity, the monopolar normal stress yys is only a partial component of the total stress yyt , which is responsible for the exhibiting of cohesive tractions along the crack faces. the full-filed total stress yyt distribution is displayed in fig. 5c. one can deduce the strong singular character 3/2x - of yyt and a fast degreasing influence of the stress gradients for the increasing distance x from the crack tip. for x l> the total stress yyt tends to the classical linear elasticity monopolar stress distribution yys ahead of the crack tip. conclusions he classical linear elastic fracture mechanics, suffering from the undesirable crack-tip stress singularity, breaks down when the size of cracked components becomes less than several nanometers. the article presents a new concept of coupling methods based on atomistic and continuum mechanics approaches: the ab-initio aided strain gradient elasticity theory (ai-sget). this method is expected to properly predict both the critical crack driving force and the critical crack tip opening displacement also for cracked nano-components. similarly to the barenblatt model, the sget removes the stress singularity at the crack tip and produces a cusp-like profile of crack faces near the crack tip in accordance with atomistic models. even the simplest form of the ai-sget involving only one unknown material lengthscale parameter l provides a reasonable form of the cohesion-decohesion stress distribution. the length-scale parameter can be determined by ab-initio methods applied to the displacement field near the screw dislocation, critical crack tip opening displacement or acoustic phonon dispersions. an important message is the fact that all these methods provide identical results. the capability of the ai-sget method to remove the stress singularity and to exhibit a plausible near-tip cusp-like profile of crack flanks is demonstrated by the results obtained on cracked tungsten nanopanels. acknowledgments he authors acknowledge a financial support of the czech science foundation (the project no. 17-18566s). references [1] shimada, t., ouchi, k., chihara, y., kitamura, t. (2015). breakdown of continuum fracture mechanics at the nanoscale, sci. rep., 8596(5), doi: 10.1038/srep08596. [2] sun, c.t., qian, h. (2009). brittle fracture beyond the stress intensity factor, j. mech. mater. struct., 4(4), pp. 743– 753, doi: 10.2140/jomms.2009.4.743. [3] kotoul, m., skalka, p. (2017). applicability of the critical energy release rate for predicting the growth of a crack in nanoscale materials applying the strain gradient elasticity theory, key eng. mater., 754, pp. 185–188, doi: 10.4028/www.scientific.net/kem.754.185. [4] mindlin, r.d., eshel, n.n. (1968). on first strain-gradient theories in linear elasticity, int. j. solids struct., 4(1), pp. 109–124, doi: 10.1016/0020-7683(68)90036-x. t t t. profant et alii, frattura ed integrità strutturale, 49 (2019) 107-114; doi: 10.3221/igf-esis.49.11 114 [5] broberg, k.b. (1999). crack and fracture, academic press. [6] park, k., paulino, g.h. (2013). cohesive zone models: a critical review of traction-separation relationships across fracture surfaces, asme. appl. mech. rev., 64(6), pp. 060802-1-060802-20, doi: 10.1115/1.4023110. [7] elices, m., guinea, g.v., gómez, j., planas, j. (2002). the cohesive zone model: advantages, limitations and challenges, eng. fract. mech., 69(2), pp. 137–163, doi: 10.1016/s0013-7944(01)00083-2. [8] gourgiotis, p.a., georgiadis, h.g. (2009). plane-strain crack problems in microstructured solids governed by dipolar gradient elasticity, j. mech. phys. [9] aravas, n., giannakopoulos, a.e. (2009). plane asymptotic crack-tip solutions in gradient elasticity, int. j. solids struct., 46(25–26), pp. 4478–4503, doi: 10.1016/j.ijsolstr.2009.09.009. [10] georgiadis, h.g., grentzelou, c.g. (2006). energy theorems and the j-integral in dipolar gradient elasticity, int. j. solids struct., 43(18–19), pp. 5690–5712, doi: 10.1016/j.ijsolstr.2005.08.009. [11] grentzelou, c.g., georgiadis, h.g. (2008). balance laws and energy release rates for cracks in dipolar gradient elasticity, int. j. solids struct., 45(2), pp. 551–567, doi: 10.1016/j.ijsolstr.2007.08.007. [12] friák, m., šesták, p., řehák, p., profant, t., skalka, p., kotoul, m. (2018). prediction of the critical energy release rate of nanostructured solids using the laplacian version of the strain gradient elasticity theory, key eng. mater., 774, pp. 447–452, doi: 10.4028/www.scientific.net/kem.774.447. [13] kotoul m., skalka p., profant t., friák m., řehák, p., šesták, p., černý m., pokluda j. (2019). prediction of the critical energy release rate of nanostructured solids using the ab-initio aided strain gradient elasticity theory (submitted for publication). [14] shu, j.y., king, w.e., fleck, n.a. (1999). finite elements for materials with strain gradient effects, int. j. numer. methods eng., 44(3), pp. 373–91, doi: 10.1002/(sici)1097-0207(19990130)44:3<373::aid-nme508>3.0.co;2-7. [15] phunpeng, v., baiz, p.m. (2015). mixed finite element formulations for strain-gradient elasticity problems using the fenics environment, finite elem. anal. des., 96, pp. 23–40, doi: 10.1016/j.finel.2014.11.002. [16] skalka, p., navrátil, p., kotoul, m. (2016). novel approach to fe solution of crack problems in the laplacian-based gradient elasticity, mech. mater., 95, pp. 28–48, doi: 10.1016/j.mechmat.2015.12.007. [17] alnæs, m., blechta, j., hake, j., johansson, a., kehlet, b., logg, a., richardson, c., ring, j., rognes, m.e., wells, g.n. (2015). the fenics project version 1.5, arch. numer. softw., 3(100), pp. 9–23, doi: 10.11588/ans.2015.100.20553. [18] james m.n., christopher c.j., lu y., patterson e.a. 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/hrv (za stvaranje adobe pdf dokumenata najpogodnijih za visokokvalitetni ispis prije tiskanja koristite ove postavke. stvoreni pdf dokumenti mogu se otvoriti acrobat i adobe reader 5.0 i kasnijim verzijama.) /hun 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can be opened with acrobat and adobe reader 5.0 and later.) >> /namespace [ (adobe) (common) (1.0) ] /othernamespaces [ << /asreaderspreads false /cropimagestoframes true /errorcontrol /warnandcontinue /flattenerignorespreadoverrides false /includeguidesgrids false /includenonprinting false /includeslug false /namespace [ (adobe) (indesign) (4.0) ] /omitplacedbitmaps false /omitplacedeps false /omitplacedpdf false /simulateoverprint /legacy >> << /addbleedmarks false /addcolorbars false /addcropmarks false /addpageinfo false /addregmarks false /convertcolors /converttocmyk /destinationprofilename () /destinationprofileselector /documentcmyk /downsample16bitimages true /flattenerpreset << /presetselector /mediumresolution >> /formelements false /generatestructure false /includebookmarks false /includehyperlinks false /includeinteractive false /includelayers false /includeprofiles false /multimediahandling /useobjectsettings /namespace [ (adobe) (creativesuite) (2.0) ] /pdfxoutputintentprofileselector /documentcmyk /preserveediting true /untaggedcmykhandling /leaveuntagged /untaggedrgbhandling /usedocumentprofile /usedocumentbleed false >> ] >> setdistillerparams << /hwresolution [2400 2400] /pagesize [612.000 792.000] >> setpagedevice microsoft word numero_56_art_10_3004 k. fawzy et al, frattura ed integrità strutturale, 56 (2021) 123-136; doi: 10.3221/igf-esis.56.10 123 experimental and analytical investigations of reinforced concrete beams strengthened by different cfrp sheet schemes khaled fawzy, hilal hassan, m. madqour university of zagazig, egypt khaled_lashen1@yahoo.com, https://orcid.org/0000-0003-2275-4025 hilalcivil@yahoo.com madqour42@gmail.com, https://orcid.org/0000-0002-0994-2884 abstract. the use of reinforced fibre polymers to strengthen and repair structural elements is widely spreading. however, there is lack of knowledge of the actual behavior of strengthened structures with frp sheets. this paper discusses the experimental results of the flexural strengthening of reinforced concrete (rc) beams by carbon fibrereinforced polymer (cfrp) sheets bonded by epoxy adhesive to the tensile surface of the beams. using a four-point bending load system over an effective span of 1800 mm, a total of ten beams with an overall dimension of 150 mm * 200 mm * 2000 mm with different degrees of strengthening schemes were tested. the number of layers, strengthening scheme (side and u-shape bonding) and reinforcement ratio are the major parameters of the experimental study. the research indicates that the flexural strength of the beams was substantially improved as the layers of laminate increased (between 31.80 and 71.50 %) and using u shape in ends that delay or prevent debonding failure. the experimental results compared to that analytically obtained by using ansys model showing acceptable agreement with deviations varying no more than 10 % for all specimens. keywords. strengthening; carbon fibre reinforced polymer; deflection; ansys; ultimate strength; ductility. citation: fawzi., f., hassan, h., madqour., m. experimental and analytical investigations of reinforced concrete beams strengthened by different cfrp sheet schemes, frattura ed integrità strutturale, 56 (2021) 123-136. received: 31.01.2021 accepted: 08.03.2021 published: 01.04.2021 copyright: © 2021 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. introduction he external bonding of high-strength cfrp to structural concrete components has gained widespread significance in recent years, particularly in rehabilitation works. due to the various benefits of the use of cfrp as reinforcement, such as corrosion resistance, lightweight, and high strength. the need for bridges, buildings, and other structural elements to be rehabilitated or strengthened may occur due to one or a combination of several reasons including but not limited to construction or design deficiencies, increased load carrying demands, damage to the structural components, and seismic rehabilitation. cfrp was commonly used for strengthening reinforced concrete, masonry, and steel structures. several studies have shown the suitability of cfrp material for structures made up of different materials, stiffness, and t https://youtu.be/6maz7ecy9nc k. fawzy et al, frattura ed integrità strutturale, 56 (2021) 123-136; doi: 10.3221/igf-esis.56.10 124 ductility [1-4]. by following the proper technique of retrofitting, cfrp greatly improves the shear and flexure strength of concrete structures compared to the standard concrete structure. the epoxy resin which is the adhesive that allows the bond between the concrete surface and cfrp a key parameter for the control for the ultimate strength because it often fails first. flexure, shear, and compression cracks can be minimized with the help of cfrp technology in rc beams. the use of cfrp compared to other fibre-reinforced polymer (frp) materials for retrofitting results from its low density, its resistance to elevated tensile forces, fatigue, and corrosion. hasnat el al [5] performed research on simply supported rc beams reinforced by cfrp wrap. a cfrp wrap withstood the premature debonding of the cover and acted as a u-clip resulting in an improvement in the capacity of the ultimate moment. mostafa and razaqpur [6] carried out an experiment on t-section reinforced concrete beams. the load was applied and the deflection was calculated for each beam. the full post-peak load/softening response of each beam also was obtained. fu et al. research on the effectiveness of the u-jacket system in preventing or delaying debonding failure has been published. nine largerange rc beams were studied in their experimental analysis to study and examine the effects of different frp u-jacket modes on debonding failure. abid and al-lami [7] also performed a detailed analysis of previous studies that highlight the strength and durability of concrete beams that have been externally bonded to frp reinforcement. the study focused on bond behavior, testing approaches, and models used to determine bond strength. flexure, shear, and fatigue behaviors of multiple reinforcement techniques have been reviewed and discussed in detail. benaoum el al [2] in this study, 3d-fem is analyzed in reinforced concrete beams on the basis of a load-deflection reaction analysis. the value of loading magnitude, crack initiation and geometric parameters has been shown. a cracked concrete beam supported by externally bonding cfrp and a concrete beam strengthened by steel bars. however, the debonding process of collapse, structural ductility, and long-term durability are the major challenges facing cfrp due to weak bonding and decreased vapor pressure [8-12]. flexural strength, failure behavior, and structural ductility are the most important parameters to be considered in structural design, especially when the structure is in high earthquake zone. cfrp is a substance that is brittle and collapses suddenly, and has a linear elastic effect up to failure, i.e., its failure strain in tension varies from 2% to 4% [6]. once the strain of failure has been achieved, cfrp gives no warning signs, it separates suddenly and causes loss of strength. these retrofitted reinforced concrete systems are not ideal because they do not have any sort of early warning before the collapse, resulting in the system collapsing. however, these systems would sustain large loads due to the high strength of the cfrp besides in large deformation/ deflection of the structural member.in this paper the effect of using various layers of cfrp sheets with different u-shape and side bonding schemes is experimentally studied. in addition, a finite element numerical model is performed and the obtained results are compared to the experimental behavior of rc beams in terms of ultimate load, crack patterns, and failure modes. experimental program and setup test specimens en reinforced concrete beams under a monotonical four-point loading scheme were tested in this research work. all the ten beam specimens have the same cross-section 200 mm height and 150 mm width, and a length of 2000 mm (fig.1). the beams were simply supported with 1800 mm of clear span. the lower longitudinal reinforcement for beams b00 to b07 was two 10 mm bars. two 12 mm bars were used for b09, and 16 mm for b08. the upper longitudinal reinforcement of all specimens consisted of two 8 mm bars. the stirrups were 6 mm diameter placed at intervals of 125 mm. the thickness of cfrp laminates was 0.129 mm, while their ultimate strain and elasticity module was 1.55% and 230 gpa, respectively. figure. 1. details of the tested beams (in mm). t k. fawzy et al, frattura ed integrità strutturale, 56 (2021) 123-136; doi: 10.3221/igf-esis.56.10 125 material properties cfrp: the fibre used in the experimental work is longitudinal, unidirectional wrap of carbon fibre (fig. 2). tab. 3 displays the main features of the manufactured cfrp strengthening material used for the tests. epoxy adhesive: the epoxy adhesive consists of two-part; resin (component a) and hardener (component b). tab. 3 shows a summary of the mechanical and physical characteristics of cfrp impregnation resin used. concrete and steel: to achieve concrete mix constituents with a strength of 32 n/mm2, the concrete mixture was designed using the aci method. for each casting process, three standard concrete cubes (150 mm x 150 mm x 150 mm) and three standard concrete cylinders (150 mm x 300 mm) were cast and cured in water for 28 days. the average of compressive strength after 28 days was 32 mpa (tab. 1). standard tension tests were performed on steel specimens according to astm using mts 200 tons universal testing machine. three steel specimens were tested for each bar diameter and the average value was considered. the average steel yield stress was 525 mpa for the longitudinal reinforcement and 400 mpa for the stirrups (tab. 2). properties values found in the laboratory compressive strength (mpa) 32 modulus of elasticity (gpa) 30.6 modulus of rupture (mpa) 3.4 table 1: concrete properties. reinforcement type yield strength (mpa) modulus of elasticity (gpa) tension (10 mm) 525 200 compression (8mm) 525 200 shear (6 mm) 400 195 table 2: steel properties. materials properties values (gpa) cfrp laminates modulus of elasticity (gpa) 230 elongation at ultimate (%) 1.70 design thickness (mm/ply) 0.129 tensile strength (mpa) 4000 density (g/cm3) 1.82 epoxy (the mix) modulus of elasticity (gpa) 4.50 elongation at ultimate (%) tensile strength (mpa) 0.90 30 table 3: cfrp laminates and epoxy adhesive properties. figure 2: cfrp sheet used in this study. k. fawzy et al, frattura ed integrità strutturale, 56 (2021) 123-136; doi: 10.3221/igf-esis.56.10 126 strengthening and instrumentation concrete was poured into the moulds in three layers by using the vibrator to eliminate the appearance of voids. to achieve a smooth surface, the extra concrete was removed. at ambient temperature for 24 hours, the beams, cubes, and cylinders were coated with plastic sheets, then separated from the moulds and numbered. the curing process for the beams was carried out by using a wet sackcloth for 28 days, while the concrete cubes and cylinders were submerged in clean water. the surface of the concrete beams was cleaned to remove the weak strip of dry cement paste and then the dust was removed by air nozzle to achieve perfect bonding. the bonding onto the concrete surface of one or more layers of cfrp was carried out according to the following procedure. firstly, concrete surfaces were covered with a continuously thick adhesive layer for even surface impregnation, the fabric was cut at the desired size, the adhesive penetrates completely into the fabric's open spaces by using flexible roller. subsequently, the second layer of adhesive was immediately applied to create a uniform layer of bonded surface reinforcement on top of the fabric. the second adhesive layer was applied in the direction of the fibres with a trowel without excessive pressure and movements. the process was repeated as additional layers of fabric in fig. 3. figure 3: beam after the installation of cfrp. beam strengthening included different layers of cfrp and different schemes reported as in tab. 4. the beams were subjected to a monotonic load up to failure using a 200 kn hydraulic jack. by using linear variable displacement transducers lvdt, the deflection of all specimens was measured at the mid span as in fig. 4. figure 4: test set-up. k. fawzy et al, frattura ed integrità strutturale, 56 (2021) 123-136; doi: 10.3221/igf-esis.56.10 127 table 4. strengthening scheme. deflection and failure modes the mechanisms of failure can be categorized in global failure and local failure [13-15].  global failure involves compression failure of concrete in bending before or after yielding of steel, rupture of frp layer in tension, and shear failure of concrete. beam no. strengthening schemes type of strengthening b 00 control beam b 01 one layer with length 1700 mm b 02 two layers with length 1700 & 1400 mm b 03 three layers with length 1700 & 1400 & 1100 mm b 04 one layer and on sides above bottom edge by 20 mm with length 1700 mm b 05 one layer and 6 u shapes b 06 two layers and 6 u shape b 07 three layers and 6-u shape b 08 one layer with length 1700 mm with lower longitudinal reinforcement 16 mm diameter b 09 one layer with length 1700 mm with lower longitudinal reinforcement 12 mm diameter k. fawzy et al, frattura ed integrità strutturale, 56 (2021) 123-136; doi: 10.3221/igf-esis.56.10 128  local failure is characterized in some places with high interfacial peeling or shear stresses, which may cause the debonding of the composite layer from the concrete beam. various failure modes, controlled by the mechanical properties of the materials and the strengthening configuration was founded in the tested specimens. experimental results control beam he reference beam b00 had a yield load of 39.9 kn and a maximum load of 51.20 kn. the beam failure began with the yield of steel, then very high ductility values were observed, steel tension failure was observed at mid-span. the ultimate deflection was 32.01 mm (see also tab. 5). one layer strengthening of beams beam b01 was strengthened with a single layer parallel to the bottom surface of the beam. the beam reinforcement reached its yield at a load of 59.70 kn and supported a maximum load of 69.44 kn with strength gain of 135 % compared with the control beam, while its deflection at failure reached 27.72 mm. beam b01 showed higher initial stiffness. at mid-span, flexure cracks started, followed by debonding of the cfrp as in fig. 8. specimen b04 with strengthened with one layer on the soffit of the specimen and on sides. the ultimate load was 75.66 kn with a strength increase of 148%. the final failure occurred by rupture of cfrp in the lower chord and then on sides of the beam after concrete crushing in compression at mid-span at a deflection of 31.74 mm. beam b05 had one sheet with a width of 100 mm attached on the bottom chord and 6 u shape sheets with a width of 50 mm wrapped on the bottom and on the sides to prevent cfrp debonding. the ultimate load was 73.76 kn with a strength increase of 144%. the failure was ductile because the deflection at failure was approximately twice the deflection at the yield of steel reinforcement. at the mid-span, flexure cracks occurred, followed by cfrp sheet rupture at the bottom chord. figure 5: load-deflection curve for one-layer beams. two and three layers strengthening of beams beam b02 was reinforced with two layers of cfrp. the strengthening was applied on the bottom of the beam with unequal lengths (1700 mm and 1400 mm). the yield load was 62.72 kn and the ultimate load was 75.10 kn, which represents a gain in strength of 147 %. the beam failure was sudden and brittle due to the rupture of the reinforcing composite material. the beam failure was sudden and brittle in form of rupture of the reinforcing composite material. several flexural cracks occurred t 0 10 20 30 40 50 60 70 80 0 10 20 30 40 50 60 70 80 l o ad ( k n ) mid-span deflection (mm) b00 b01 b04 b05 k. fawzy et al, frattura ed integrità strutturale, 56 (2021) 123-136; doi: 10.3221/igf-esis.56.10 129 in the central span of the beam before the composite material failed. the maximum deflection at failure was 27.58 mm as in (fig. 8). the strengthening of beam b06 was similar to beam b05, except for the number of layers, which is two rather than one. the rupture started with the cfrp wrapped sheets and then the cfrp bottom chord, at the final load of 87.85 kn and the ultimate deflection of 36.96 mm. beam b03 was strengthened with 3 layers of cfrp, and the failure occurred in the concrete compression zone, followed by the rupture of cfrp. the maximum load was 79.39 kn, which is higher than b00 by 155%, and the maximum deflection was 23.33 mm. specimen b06 with two strengthening layers and 6 u-shape sheets had a maximum load of 87.85 kn with a strength gain of 172 % compared with b00. at mid-span, more cracks started, followed by debonding of the cfrp (fig. 8). beam b07 with three layers and 6u-shape sheets showed that had a maximum load of 88.78 kn with approximately 2% strength gain compared with b06, the deflection was 30.97. figure 6: comparison of the load vs. mid-span deflection of: (a) beams strengthened by two layers cfrp, (b) beams strengthened by three layers cfrp. different reinforcement strengthening of beams specimens b08 and b09 were strengthened by one layer of cfrp with different reinforcement ratio. their ultimate loads increased by 43 % and 16 % compared with b01, respectively. for b08 large shear cracks with almost 45° from supports. the beam failed completely at the load of 99.08 kn due to failure in the shear region. but for b09, the failure occurs firstly in concrete compression zone, then rupture of the cfrp sheet at a load of 80.38 kn as in fig. 8. ductility characteristics in the seismic regions, ductility is a significant parameter for the design of concrete structures. the ductility can be evaluated in terms of energy or deflection. for comparison purposes, thomsen et al. [16] use ductility depended on the concept of energy, µe, described as the ratio of the system's energy at failure, eu, to that of the first steel yield, ey. the concept of deformation is based on the deflection ductility index (displacement at failure divided by displacement at yield) while the energy ductility is measured as the ratio of the area under the load deflection curve at ultimate failure to the area under the 0 10 20 30 40 50 60 70 80 0 10 20 30 40 50 60 70 lo a d  ( k n ) mid‐span deflection (mm)  b00 b02 b06 0 10 20 30 40 50 60 70 80 90 0 10 20 30 40 50 60 70 lo a d  ( k n ) mid‐span deflection (mm)  b00 b03 b07 (a) (b) k. fawzy et al, frattura ed integrità strutturale, 56 (2021) 123-136; doi: 10.3221/igf-esis.56.10 130 load deflection curve at yielding of tension steel. oudah and hash [17] recently published a new definition of ductility, a model based on beam deflection and energy. the ductility indexes can be described as: deflection ductility: μ∆=∆u/∆y (1) energy ductility: μe = eu/ey (2) tab. 6 displays the energy and deflection ductility of the prepared rc beams reinforced by using different combinations of cfrp. it was also found that the beam without strengthening displayed greater displacement or ductility relative to concrete beams of different cfrp configurations. figure 7: load-deflection curve for one layer with different reinforcement. beam no. at first crack at steel yield at failure load (kn) deflection (mm) load (kn) deflection δy (mm) max load (kn) deflection δu (mm) b 00 11.80 1.98 39.9 8.35 51.20 32.01 b 01 16.73 2.1 59.7 14.10 69.44 27.72 b 02 26.32 6.45 62.72 14.32 75.1 26.13 b 03 25.59 3.45 63.88 14.88 79.39 23.33 b 04 21.88 1.51 60.25 14.51 75.66 31.74 b 05 13.68 1.54 60.15 16.83 73.76 32.96 b 06 17.47 2.56 80.50 25.61 87.85 36.96 b 07 23.99 2.17 71.55 20.44 88.78 30.97 b 08 15.58 1.09 88.8 23.77 99.06 33.76 b 09 12.17 1.46 53.07 14.27 80.38 36.56 table 5: tested specimen data. k. fawzy et al, frattura ed integrità strutturale, 56 (2021) 123-136; doi: 10.3221/igf-esis.56.10 131 figure 8: failure mode of the tested beams. beam no. ductility ductility ratios in terms of deflection µ in terms of energy µ in terms of deflection µ in terms of energy µ b 00 3.83 5.96 1 1 b 01 1.97 2.64 0.51 0.44 b 02 1.54 1.92 0.40 0.32 b 03 1.57 2.08 0.41 0.35 b 04 1.68 2.09 0.44 0.35 b 05 1.96 2.66 0.514 0.45 b 06 1.49 1.64 0.39 0.28 b 07 1.51 2.06 0.39 0.34 b 08 1.42 1.49 0.37 0.25 b 09 2.56 3.70 0.67 0.62 table 6: ductility index. k. fawzy et al, frattura ed integrità strutturale, 56 (2021) 123-136; doi: 10.3221/igf-esis.56.10 132 verification study he finite element (fe) models were calibrated with the experimental results. the purpose of this comparison is to verify the validity of the analysis and model. as in the (fig. 10), there is a really very good correlation between the experimental and numerical load-deflection curves for all loading stages. the fe models were able to predict the load-carrying capacity of rc beams. the validity and reliability of the fe models established to simulate the experimental performance. the concrete is modelled using the form of element solid65 [18]. this element has eight nodes with three degrees of freedom at each node; translations in the global reference directions x, y, and z. this element is capable of plastic deformation, cracking and crushing in three orthogonal directions. the nonlinear behavior of geometry and properties of materials for concrete structures was considered in this research according to several sources [2, 19-22], the mechanical properties of concrete, frp plate and adhesive are selected and are given in tab. 7. material elastic modulus (gpa) poisson’s ratio compressive strength (mpa) yield strength (mpa) tensile strength (mpa) concrete 32 0.20 32 3.02 steel bars 30.6 0.30 500 cfrp 230 0.30 epoxy 4.50 0.30 table 7: mechanical properties of concrete, steel and cfrp reinforcement. figure 9: (a) sample representation of developed fe models., (b) different element of the beam modeled. tab. 8 summarizes the comparison of experimental and numerical results achieved for all specimens studied and demonstrates that the analytical approach discussed here can be used to model strengthened beam behavior in a satisfactory way when there is no premature delamination of the strengthened composite material. the proposed ansys [23] model results showed acceptable agreement with the experimental results, with deviations of less than 10 %. t (b) (a) k. fawzy et al, frattura ed integrità strutturale, 56 (2021) 123-136; doi: 10.3221/igf-esis.56.10 133 0 10 20 30 40 50 60 70 80 0 20 40 60 lo a d  ( k n ) mid‐span deflection (mm)  b02 exp b02 ansys boo exp boo ansys 0 10 20 30 40 50 60 70 80 0 20 40 60 lo a d  ( k n ) mid‐span deflection (mm)  b01 exp b01 ansys b03 exp b03 ansys 0 10 20 30 40 50 60 70 80 90 0 10 20 30 40 50 60 70 lo a d  ( k n ) mid‐span deflection (mm)  b07 exp b07 ansys b06 exp b06 ansys 0 10 20 30 40 50 60 70 80 0 20 40 60 lo a d  ( k n ) mid‐span deflection (mm)  b04 exp b05 exp b04 ansys b05 ansys k. fawzy et al, frattura ed integrità strutturale, 56 (2021) 123-136; doi: 10.3221/igf-esis.56.10 134 figure 10: comparison between experimental and numerical load deflection curve for b00 to b09. beam no. theoretical (ansys) experimental 𝑃 𝑃 failure mode (experimental) load (kn) deflection δu (mm) load (kn) deflection δu (mm) b 00 51.39 30 51.20 32.01 1 concrete crushing b 01 75.21 23.92 69.44 27.72 1.08 debonding of the cfrp b 02 77.67 23.82 75.1 26.13 1.03 rupture of the cfrp b 03 76.39 23.69 79.39 23.33 0.96 rupture of the cfrp and concrete crushing b 04 72.43 31.76 75.66 31.74 1 rupture of the cfrp and concrete crushing b 05 78.43 24.79 73.76 32.96 1.06 rupture of the cfrp b 06 88.03 24.53 87.85 36.96 1 rupture of the cfrp b 07 86.43 26.48 88.78 30.97 0.97 rupture of the cfrp b 08 100.15 24.3 99.06 33.76 1.01 local shear rupture b 09 82.25 22.56 80.38 36.56 1.02 debonding of the cfrp table 8: comparison between experimental and theoretical results. conclusions he aim of this analysis is to investigate the influence of different parameters on the flexural behavior of repaired concrete beams, such as the number of layers, strengthening scheme (side and u-shape bonding), and reinforcement ratio. based on these experimental and numerical results, we can deduce the following:  the outcome of the experimental program shows that externally bonded cfrp may be used to support reinforced concrete beams effectively. with the increase in cfrp layers, an increase in stiffness and flexural strength was observed. t 0 20 40 60 80 100 0 10 20 30 40 lo a d  ( k n ) mid‐span deflection (mm)  b08 exp b09 exp b08 ansys b09 ansys k. fawzy et al, frattura ed integrità strutturale, 56 (2021) 123-136; doi: 10.3221/igf-esis.56.10 135  the ultimate load of the beam was increased as the length of the frp reinforcement was increased.  the u-shape used to anchor longitudinal cfrp helped to avoid damage due to debonding ends of cfrp and increased flexural strength. this scheme has the best results with strength gain of 174 % compared with control beam.  using the cfrp on sides of beams was just more successful than the u-shape.  fe model showing acceptable agreement with deviations varying no more than 10 % for all specimens. references [1] ahmed, e., sobuz, h. r. and sutan, p. s. (2011). flexural performance of cfrp strengthened rc beams with different degrees of strengthening schemes, international journal of the physical sciences, 6(9), pp. 2229-2238. [2] benaoum, f., khelil, f. and benhamena, a. (2020). numerical analysis of reinforced concrete beams pre cracked reinforced by composite materials, frattura ed integrità strutturale, 14(54), pp. 282-296. [3] fawzy, k. (2018). upgraded the performance of the fortifying rc beam by cfrp in flexural, osr journal of mechanical and civil engineering (iosr-jmce). [4] shardakov, i., shestakov, a. and bykov, i. s. (2016). "delamination of carbon-fiber strengthening layer from concrete beam during deformation (infrared thermography), frattura ed integrità strutturale, 10(38), pp. 331-338. [5] hasnat, a., islam, m. and amin, a. j. j. (2016). enhancing the debonding strain limit for cfrp-strengthened rc beams using u-clamps: identification of design parameters, the journal of composites for construction, asce, 20(1), p. 04015039. [6] mostafa, a. a., razaqpur, a. g. j. c. (2017). finite element model for predicting post delamination behaviour in frpretrofitted beams in flexure, construction and building materials, 131, pp. 195-204. [7] abid, s. r. and al-lami, k. (2018). critical review of strength and durability of concrete beams externally bonded with frp, cogent engineering, 5(1), p. 1525015. [8] triantafillou, t. c. and plevris, n. (1992). strengthening of rc beams with epoxy-bonded fibre-composite materials, materials and structures, 25(4), pp. 201-211. [9] wu, z., li, w. and sakuma, n. (20069. innovative externally bonded frp/concrete hybrid flexural members, composite structures, 72(3), pp. 289-300. [10] uomoto, t. (2001). durability of frp reinforcement as concrete reinforcement, in frp composites in civil engineering. proceedings of the international conference on frp composites in civil engineeringhong kong institution of engineers, hong kong institution of steel construction, 1. [11] ibrahim, y. e., fawzy, k. and farouk, m. a. (in press). effect of steel fiber on the shear behavior of reinforced recycled aggregate concrete beams, structural concrete. [12] fu, b., chen, g. and teng, j. j. c. s. (2017). mitigation of intermediate crack debonding in frp-plated rc beams using frp u-jackets, composite structures, 176, pp. 883-897. [13] saadatmanesh, h. and ehsani, m. r. (1991). rc beams strengthened with gfrp plates. i: experimental study, journal of structural engineering, 117(11), pp. 3417-3433. [14] chen j. f. and teng, j. g. (2003). shear capacity of frp-strengthened rc beams: frp debonding, construction and building materials, 17(1), pp. 27-41. [15] mahmoud t. e.-m. and joseph, w. t. (2001). prediction of anchorage failure for reinforced concrete beams strengthened with fiber-reinforced polymer plates, aci structural journal, 98(3). [16] thomsen, h., spacone, e., limkatanyu, s. and camata, g. j. (2004). failure mode analyses of reinforced concrete beams strengthened in flexure with externally bonded fiber-reinforced polymers, structural concrete, 8(2), pp. 123-131, 2004. [17] oudah, f. and el-hacha, r. (2012). a new ductility model of reinforced concrete beams strengthened using fiber reinforced polymer reinforcement, composites part b: engineering, 43(8), pp. 3338-3347, 2012/12/01/ 2012. [18] schesnyak, l. (2019). modeling of the conjugation of vortex flows with downstream in ansys, in iop conference series: materials science and engineering, 675(1), p. 012026. [19] bennegadi, m., sereir, z. and amziane, s. (2013). 3d nonlinear finite element model for the volume optimization of a rc beam externally reinforced with a hfrp plate," construction and building materials, 38, pp. 1152-1160. [20] bennati, s., dardano, n. and valvo, p. s. (2012). a mechanical model for frp-strengthened beams in bending, frattura ed integrità strutturale, 6(22), pp. 39-55. k. fawzy et al, frattura ed integrità strutturale, 56 (2021) 123-136; doi: 10.3221/igf-esis.56.10 136 [21] boulebd, a., noureddine, f., mohcene, b. and mesbah, h. (2020). modeling of cfrp strengthened rc beams using the snsm technique, proposed as an alternative to nsm and ebr techniques, frattura ed integrità strutturale, 54, pp. 21-35. [22] hawileh, r. j. m. (2015). finite element modeling of reinforced concrete beams with a hybrid combination of steel and aramid reinforcement, materials and design, 65, pp. 831-839. [23] a. r. j. c. version, pa, 12.1. 0, a finite element computer software and user manual for nonlinear structural analysis, ansys inc, (2009). microsoft word numero_58_art_27_3234.docx m. słowik, frattura ed integrità strutturale, 58 (2021) 376-385; doi: 10.3221/igf-esis.58.27 376 focussed on steels and composites for engineering structures the role of aggregate granulation on testing fracture properties of concrete m. słowik lublin university of technology, poland m.slowik@pollub.pl, http://orcid.org/0000-0001-9627-3625 abstract. concrete is a porous material containing aggregate of different sizes, hardened cement matrix with air pores, microcracks and water. concrete internal structure is different from that of other engineering materials. furthermore concrete is described as quazi-brittle material. fracture processes in it form in a way that does not fit within classical theories. therefore, to describe failure of concrete structures nonlinear fracture mechanics is often applied with success. basic concrete parameters, like compressive and tensile strength, and modulus of elasticity, are not enough to analyze fracture processes in concrete structures. additional fracture properties should be tested, among them fracture energy, complete diagram of stress-deformation under axial tension and the width of fracture process zone. recognizing and testing fracture parameters is of paramount importance when analysing fracture process in concrete structures. the correct data of material’s properties and the adequate fracture model applied in numerical simulations influence final results. in the paper the findings reported in the professional literature are summarized and obtained results of the own numerical simulation are reported in order to give a deeper knowledge on the role of aggregate on fracture properties of concrete. keywords. concrete; fracture process; aggregate. citation: słowik, m., the role of aggregate granulation on testing fracture properties of concrete, frattura ed integrità strutturale, 58 (2021) 376-385. received: 18.08.2021 accepted: 29.08.2021 published: 01.10.2021 copyright: © 2021 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. introduction oncrete is a porous material containing aggregates, hardened cement paste and water. its internal structure is entirely different from that of other engineering materials. the maximum size of the aggregate can fall between 10 to 32 mm for structural applications and thus, the dimensions of the areas where fracture processes nucleate and develop are comparable with the size of normal structures. aggregates constitute the bulk of the concrete. they comprise 60-80% of the volume of the concrete and have to be so graded that the whole mass of concrete acts as a relatively solid, homogeneous, dense combination, with the smaller sizes acting as an inert filler of the voids that exist between the large particles. however, the concrete, as a structural material, c https://youtu.be/b6r57sd6gi4 m. słowik, frattura ed integrità strutturale, 58 (2021) 376-385; doi: 10.3221/igf-esis.58.27 377 has not a closed structure. besides of entrained air porosity, concrete is intensely micro-cracked before loading. all these facts significantly influence concrete properties. concrete is usually described as a quasi-brittle material. for most of structural engineering applications, concrete needs to be reinforced because its tensile strength is only around one tenth of its compressive strength. in order to obtain the basic characteristic of concrete as a constructional material the following parameters should be known: compressive strength of the concrete (fc ), tensile strength of the concrete (fct ), modulus of elasticity (ecm ), poisson’s ratio, coefficient of thermal expansion. however these parameters are not enough to deeper analyze failure in concrete structures. fracture processes in concrete form in a way that does not fit within classical theories. therefore to describe crack propagation in concrete, nonlinear fracture mechanics can be applied with success. several models of concrete cracking were developed based on nonlinear fracture mechanics. one of them is a crack band model of tensile concrete which was proposed by hillerborg, modeer, petersson [1] – see fig. 1. the crack starts to propagate when the stress at the crack tip reaches the tensile strength fctm. the stress does not fall to zero at once but it decreases with increasing crack width and it reaches zero when crack width is w1. for that part of the crack where w < w1, there is a fracture process zone with some remaining ligaments, which allow to transfer stress. as these ligaments are to be overcome during opening the crack, energy is absorbed. figure 1: the essence of crack band model of tensile concrete. in a crack bend model additional concrete fracture parameters should be determined. these parameters are: uniaxial tensile strength limit (fct ), fracture energy (gf ), the shape of the stress-deformation diagram ( ). the stress-deformation properties of concrete are given by two curves: stress-strain () and stress-crack opening curve (wbecause after reaching the tensile strength, stress starts to decrease whereas deformation increases within the damage zone and decreases in the remaining part of a member – see fig. 2. the value of the energy gf corresponds to the area under the curve -w. figure 2: stress-deformation diagram for concrete in tension.   f   w g w = + ct f fct ct f m. słowik, frattura ed integrità strutturale, 58 (2021) 376-385; doi: 10.3221/igf-esis.58.27 378 the decrease in stress under increasing deformation is called strain softening and it takes place in the narrow zone where the progressive microcracking appears – see fig. 3. the width of the active microcracking band, which is called the width of fracture process zone (wc), is the additional parameter taken into account when fracture in concrete is modelled as a smeared crack band. figure 3: fracture process zone width. recognizing and testing fracture parameters is of paramount importance when analyzing fracture process in concrete structures. the correct data of material’s properties and adequate fracture model applied in numerical simulations influence final results. in the paper the findings reported in professional literature are summarized and obtained results of the own numerical simulation are reported in order to give a deeper knowledge on the role of aggregate on fracture processes in concrete structures. in particular the problem how the choice of the width of the fracture process zone influences the results of numerical calculations is discussed. methods of testing concrete fracture properties aterial property values shall be determined from standardized tests performed under specified conditions. a conversion factor shall be applied where it is necessary to convert the test results into values which can be assumed to represent the behaviour of the material or product in the structure or the ground. the procedure of making specimens for testing hardened concrete and the shape and dimensions of standardized specimens are described in the codes [2,3]. the general rule says that the size of specimen for testing concrete property should not be less than four times the maximum aggregate size. therefore cubes 150/150/150 mm and cylinders 150/300 mm are recommended for concrete with the aggregate size up to 32 mm. cubes 100/100/100 mm can be used for testing concrete with the maximum aggregate size 16 mm and cubes 200/200/200 mm when the aggregate size is up to 63 mm. the specimens which are used in testing concrete properties are shown in fig. 4. figure 4: specimens for testing concrete properties (dimensions in cm). the test procedure for determining the main concrete property – compressive strength is well known [4]. the compressive strength of concrete is tested in an axial compression test on standardized cylindrical or cubic specimens. the fact that a shape and sizes od specimens influence the compressive strength of concrete is well known. the parameter taken in design of concrete structure is characteristic compressive strength derived from values tested on cylinders 150/300 mm. therefore, conversion factors should be applied when compression strength is tested on other specimens: w c m m. słowik, frattura ed integrità strutturale, 58 (2021) 376-385; doi: 10.3221/igf-esis.58.27 379   , 15 , 10 , 20 , 15/300.9 1.05 1.25c cube c cube c cube c cylf f f f (1) the tensile strength of concrete should be tested in an axial tensile test. as it is not easy to perform a stable tension test, therefore the tensile strength of concrete is usually determined in a splitting tensile test and this test is described in the code [5] as a standardized test. for testing the splitting tensile strength of concrete, cylindrical specimens 150/300 mm are recommended, but cubic specimens are also available. it is pointed in [5] that the value of the splitting tensile strength also depends on the shape and dimensions of tested specimens. the tensile splitting strength tested on cubic specimens 150/150/150 mm is approximately 10% higher compering to the strength obtained on cylinders 150/300 mm and lower than strength tested on cubes 100/100/100 mm. the uniaxial tensile strength of concrete should be calculated on the basis of the splitting tensile strength fct = 0.9fct,sp, as it is written in eurocode 2 [6]. main fracture parameters of tensile concrete should be determined in a deformation-controlled tensile test. unfortunately, such a test is difficult to perform. for measurements of energy absorption, a three point bend test on a beam with a central notch has been proposed by rilem technical committee 50 [7]. such a test is recommended for testing fracture energy because it is much easier to perform it than a stable tensile test. also some alternative methods of testing fracture energy can be found in the literature, for example the wedge-splitting test [8, 9], as yet they have not been standardized. the sizes of standard specimens recommended by rilem [7] for testing fracture energy depend on a maximum aggregate size dmax, according to tab. 1. taking into account a significant effect of specimen’s size on fracture energy values, the new recommendation as to fracture energy testing was proposed by rilem [10]. in the modified method it is assumed to determine fracture energy on at least three different sizes beams with the notch. the dimensions of specimens also depend on aggregate granulation. the width b and the depth d of the tested beams must not be less than three times of maximum aggregate size whereas the notch width should not exceed 0.5 times the maximum aggregate size . dmax[mm] depth d [mm] width b [mm] length l [mm] span l [mm] 1  16 100  5 100  5 840  10 800  5 16.1  32 200  5 100  5 1190  10 1130  5 32.1  48 300  5 150  5 1450  10 1385  5 48.1  64 400  5 200  5 1640  10 1600  5 table 1: sizes of specimens for testing fracture energy [7]. in experimental investigation on fracture energy of concrete which were performed on different size specimens for concretes with different maximum size of aggregate it has been found that fracture energy increases with an increase of the maximum aggregate size and with an increase of the specimen size. for example, in kleinschrodt and winkler experiment [11] the doubling of the maximum gravel aggregate from dmax=8 mm to dmax=16 mm caused an increase of the gf value by 25%. whereas 60% higher fracture energy was obtained in concretes with limestone aggregate size up to 16 mm than up to 8 mm in tests performed by golewski [12]. these findings have been applied not only in rilem recommendations according to sizes of beams for fracture energy tests but they are also reflected in analytic formulas for estimating fracture energy. for example, the formula (2) proposed by bažant and oh [13] can be mentioned.    6 2 max3.1 10 2.57f ct ct c d g f f e , (2) where gf is given in [nm/m2], fct and ec in [pa], and dmax in [m]. in case of the lack of testing values of fracture energy, gf can be calculated according to ceb-fip model code [14] where the maximum aggregate size was also taken into account in the formula (3).  0.7f f cg f [nm/m2], (3) m. słowik, frattura ed integrità strutturale, 58 (2021) 376-385; doi: 10.3221/igf-esis.58.27 380 where f depends on dmax and is equal f = 4; 6; 10 when dmax = 8; 16; 32 mm, fc is compressive strength of concrete in [mpa]. the determination of the width and the length of the fracture process zone is even more difficult experimental problem and there are no standard methods of their measurement. the findings which have been reported in several scientific papers suggests that the ratio wc/dmax ranges from 1 to 5. mostly the relation wc =3 dmax is recommended as a good approximation in numerical analyses, for example by bažant and oh [13], and zhang and wu [15]. interesting experiments were performed by otsuka and date [16]. to investigate the behavior of the fracture process zone in concrete, they used x-rays with contrast medium and three-dimensional acoustic emission techniques. experiments were carried out on differently-sized specimens made by concrete with different maximum aggregate size 5, 10, 15 mm. when comparing fracture process zone traced from x-ray films, the researchers have found that width and the length of fracture process zone are closely related each to the other. with the increase of maximum aggregate size, the width of fracture process zone increases whereas the length of fracture process zone decreases see fig. 5. figure 5: fracture process zone traced from x-rays films [16]. the influence of aggregate granulation on testing methods according to compressive and tensile strength, as well as fracture energy is deeply recognized. as already pointed out, there are no standard methods to determine the width of fracture process zone experimentally. the experimental finding suggest that the width of fracture process zone is affected by maximum aggregate size but there are no consensus how. the question arises on how to model the width of fracture process zone when performing numerical simulations of concrete structures. numerical investigation o analyze how the choice of the width of the fracture process zone influences the results of numerical calculations in the case of concrete beams, the numerical simulation has been performed using the commercial program algor, which is based on finite element method (fem). then, the obtained results of calculations have been compared with the authors’ own experimental data. when performing the experimental investigation, three concrete beams were tested. the beams had a rectangular cross section of the width b = 0.15 m and the height h = 0.30 m. the total length of the beams was l = 3.00 m whereas the span was l = 2.70 m. the beams were tested in four-point bend test, but the reversed type of loading was used. beams were loaded symmetrically by two concentrated forces, which were applied from bottom towards the top by hydraulic t m. słowik, frattura ed integrità strutturale, 58 (2021) 376-385; doi: 10.3221/igf-esis.58.27 381 jacks. the procedure of controlling displacement was used during the test in order to slow down the cracking process. beam geometry and the static scheme of the test specimen are shown in fig. 6. figure 6: static scheme of a tested beam. the basic mechanical properties of concrete were tested by standard methods and evaluated statistically. they are listed below: the tensile strength fctm = 1.5 mpa, the compressive strength fcm = 20.5 mpa, the modulus of elasticity ecm = 22 gpa, the fracture energy gf = 83 nm/m2. when preparing the concrete mixture, a gravel aggregate was used with the maximum size dmax = 32 mm. during the test, concrete strains were recorded on two levels in tension and compression zone of the beam, by huggenberger’s gauge. the measured concrete strains were than used to compare them with numerical findings. the wider description of performed experiments has been presented in [17]. the fem-analysis was performed on one half of the concrete beam corresponding to the test specimen since the fourpoint test is symmetrical. the brick and truss elements were used in beam modelling, brick elements for bulk material and truss element for concrete in the fracture process zone. the bulk material of the beam was chosen as linear elastic one and only in the region of fracture zone the concrete was modelled as nonlinear material. the fracture process zone was modeled in the region where the force was applied as it was the cross section of the biggest bending moment due to reversed static scheme and the influence of a self-weight. to analyze the influence of the width of the fracture process zone on the results of numerical calculations different widths were taken at modelling this zone: wc = 5; 10; 20; 26.5; 50 and 100 mm. the finite element mesh for the analyzed beam with the width of fracture process zone wc = 10 mm is shown in fig. 7. the numerical simulation was performed to analyze other scientific problems as well [18,19]. figure 7: the mesh used in a fem simulation [18]. m. słowik, frattura ed integrità strutturale, 58 (2021) 376-385; doi: 10.3221/igf-esis.58.27 382 the same material properties as those obtained during the experiment were used in numerical simulation. the crack band model was applied. the stress-deformation diagrams were simplified by bilinear relations according to the proposition given in ceb-fip model code [20] – see fig. 8. figure 8: model of tensile concrete recommended by ceb-fip: stress-strain diagram for uncracked concrete (a), stress-crack opening for cracked concrete (b) [20]. when performing the numerical simulations, the dislocations of nodes and stress components along three axes of the global coordinate system were obtained. in order to verify the model of tensile concrete applied in the numerical simulation, experimental results were compared with the results of numerical calculations. the elongations measured in the concrete beams on the base 250 mm long by huggenberger’s gauge in tension and compression zone were juxtaposed with the adequate elongation from the numerical simulation. the bases were situated in the middle of the beam’s span, in the region outside the fracture process zone. from the comparison which is presented in fig. 9, a satisfactory agreement between experimental measurements and numerical results can be observed. it confirms that concrete in the bulk material outside the active fracture zone can be described by bilinear stress-strain relation presented in fig 8.a. figure 9: elongation in compression zone (left) and tension zone (right) comparison of experimental measurements and numerical results. furthermore, diagrams of normal stress distribution along the fracture process zone for analyzed beams have been made. to compare the obtained diagrams for concrete beams with different wc, they have been juxtaposed at the same level of loading (fig. 10). when analyzing the diagrams presented in fig. 10, some differences in numerical results can be seen in -0.04 -0.03 -0.02 -0.01 0.00 contraction [mm] 2.0 3.0 4.0 5.0 6.0 7.0 p [ k n ] a) 0.00 0.01 0.02 0.03 0.04 elongation 2.0 3.0 4.0 5.0 6.0 7.0 p [ kn ] b) m. słowik, frattura ed integrità strutturale, 58 (2021) 376-385; doi: 10.3221/igf-esis.58.27 383 dependence of the width of fracture process zone. we can observe that at applied load f = 6 kn in the simulation with fracture process zone wc = 50 and 100 mm, normal stress at upper stage of tension zone reaches the tensile stress whereas in case of width of fracture process zone 5, 10, 20 and 26.5 the normal stress start to decrease and the tensile strength was reached at a lower loading stage. it can be concluded that the greater the width of fracture zone, taken in femcalculation, the less intensive strain softening of tension concrete. figure 10: comparison of normal stress distribution in the cross section of crack band in the simulated beam with different fracture process zone width wc at the load stage f = 6 kn (note that tension zone is in a upper part of a cross section). the performed numerical simulation has confirmed that nonlinear model for tensile concrete should be used when analyzing failure of concrete structures. microcracks in the region of a cross section with the highest internal forces tend to join leading to formation and propagation of the failure crack. but the crack does not appear in the moment when stress reaches the tensile strength of concrete. there are still some ligaments which cause a slower crack formation and we can observe the descending branch in stress distribution diagram obtained in numerical simulation – see fig 10. but the numerical analysis has clearly showed the differences in calculation results resulting by the width of the fracture process zone taken in fem-calculations. the energy which is necessary for crack formation is cumulated in the narrow region of fracture process zone. the performed numerical simulation has given the evidence how important is to apply correct fracture parameters, in particular the width of fracture process zone, in numerical calculations. conclusions n the basis of the review of scientific works presented in the paper, it may be concluded that the influence of aggregate granulation on fracture parameters of concrete exists. in case of tensile strength and fracture energy of concrete this problem has been wider described. there are no definite conclusions as far as the influence of aggregate size on the width of the fracture process zone is concerned. the performed numerical analysis confirms that the width of the fracture process zone has an influence on the fem results. the proper choice of this parameter during the numerical calculation is a condition of obtaining correct results performed by finite element method. when explaining the influence of aggregate graining on fracture parameters of concrete, in particular fracture energy and the width of fracture process zone, the non-homogeneous internal structure of hardened concrete should be considered. concrete is intensively microcracked before loading in so called virgin state. additionally, several air pores and water is left in concrete matrix. all these facts cause a non-uniform distribution of local fracture energy. furthermore, the presence of large size aggregate grains prevents the crack from opening and results in wider fracture process zone. in normal strength -2000 -1500 -1000 -500 0 500 1000 1500 xx [kpa] 0.03 0.06 0.09 0.12 0.15 0.18 0.21 0.24 0.27 0.30 z [m ] the beam with wc=5.0 mm the beam with wc=10.0 mm the beam with wc=20.0 mm the beam with wc=26.5 mm the beam with wc=50.0 mm the beam with wc=100.0 mm o m. słowik, frattura ed integrità strutturale, 58 (2021) 376-385; doi: 10.3221/igf-esis.58.27 384 concrete the crack surrounds aggregate grains during the process of crack formation and propagation. this phenomenon can be observed when analyzing a crack path obtained in splitting tensile test see fig. 11. figure 11: crack’s path obtained during the splitting tensile test [21]. it would be valuable to find general standard rules for determining all fracture parameters of concrete. in particular the influence of the maximum aggregate size on the width of fracture process zone requires systematic investigations. in further works, the analysis of cracking mechanisms in concrete should be performed on both microand macro-level. acknowledgments his work was supported by lublin university of technology. references [1] hillerborg, a., modeer, m., petersson, p. e. (1976) analysis of crack formation and crack growth in concrete by means of fracture mechanics and finite elements. cement and concrete research, 6, pp. 773-782 . [2] en 12390 testing hardened concrete. part 1: shape, dimensions and other requirements of specimens and moulds. cen, brussels. [3] en 12390: 2019, (2019). testing hardened concrete. part 2: making and curing specimens for strength tests. cen, brussels. [4] en 12390: 2019, (2019). testing hardened concrete. part 3: compressive strength of test specimens. cen, brussels. [5] en 12390: 2019, (2019). testing hardened concrete. part 6: tensile splitting strength of test specimens. cen, brussels. [6] en 1992-1-1: 2004, (2004). eurocode 2. design of concrete structures – general rules and rules for buildings. cen, brussels. [7] rilem draft recommendation, (1985). determination of the fracture energy of mortar and concrete by means of three-point bent tests on notched beams. matériaux et constructions. 18(106), pp. 258-290. [8] fernández-canteli, a. et al., (2014). determining fracture energy parameters of concrete from the modified compact tension test. frattura ed integrità strutturale, 30, pp. 383-393. doi: 10.3221/igf-esis.30.46 [9] korte, s., et al. (2014). static and fatigue fracture mechanics properties of self-compacting concrete using three-point bending tests and wedge-splitting tests. construction and buildings materials, 57, pp. 1-8. doi: 10.1016/j.conbuildmat.2014.01.090 [10] rilem draft recommendation, (1990). size-effect method for determining fracture energy and process zone size of concrete. matériaux et constructions. 23(138), pp. 461-465. t m. słowik, frattura ed integrità strutturale, 58 (2021) 376-385; doi: 10.3221/igf-esis.58.27 385 [11] kleinschrodt, h. d. and winkler, h. (1986). the influence of the maximum aggregate size and the size of specimen on fracture mechanics parameters. fracture toughness and fracture energy of concrete, edited by f. h. wittmann, elsevier science publishers b. v., amsterdam, pp. 391-402. [12] golewski, g. j. (2007). influence of dmax on fracture mechanics parameters of concrete made of limestone aggregate at three point bending (in polish). budownictwo i architektura, 1, pp. 5-16. [13] bažant, z. p. and oh, b. h. (1983). crack band theory for fracture of concrete. matériaux et constructions, 16(193), pp. 155-177. [14] ceb-fip model code 1990 bulletin d’information no. 19. [15] zhang, d., wu, k. (1999) fracture process zone of notched three-point-bending concrete beams. cement and concrete research, 29, pp. 1887-1892. doi: 10.1016/s0008-8846(99)00186-6. [16] otsuka, k., date, h. (2000). fracture process zone in concrete tension specimen. engineering fracture mechanics. 63, pp. 111-131. doi: 10.1016/s0013-7944(99)00111-3. [17] słowik, m. (2019). the analysis of failure in concrete and reinforced concrete beams with different reinforcement ratio. archive of applied mechanics, 89, pp. 885-895. doi: 10.1007/s00419-018-1476-5. [18] słowik, m. (2010). numerical analysis of the width of fracture process zone in concrete beams. computational materials science, 50, pp.1347-1352. doi: 10.1016/j.commatsci.2010.05.013 [19] słowik, m., stroeven, p., akram, a. (2020). crack mechanism in concrete from micro to macro scale. budownictwo i architektura, 19(4), pp. 55-65. doi: 10.35784/bud-arch.2147. [20] ceb-fip model code 1990. bulletins d’information. no 196. [21] benkemoun, n., et al. (2017). 3-d mesoscale simulation of crack-permeability coupling in the brazilian splitting test. international journal for numerical and analytical methods in geomechanics 42(1), pp. 1-20. microsoft word numero_50_art_25_2467 p. qiu, frattura ed integrità strutturale, 50 (2019) 300-309; doi: 10.3221/igf-esis.50.25 300 experimental research on fracture behavior of concrete after high temperature peng qiu college of architecture and civil engineering, jiangsu city vocational college nantong campus, nantong, 226006, china qiupengrt@163.com abstract. high-strength concrete has been widely used in various complex buildings. the fracture and mechanical properties of high-strength concrete after fire have great research value. based on the double k fracture model, the fracture properties of c70 strength grade concrete after being processed by high temperature of 25 °c ~ 800 °c were studied by three-point bending beam test. the change rules of fracture toughness kic and fracture energy under different temperatures after being processed by high temperature were analyzed. the results showed that the initial crack toughness and instability toughness of c70 concrete decreased with the increase of temperature; the fracture energy first decreased rapidly and then decreased slowly with the development of temperature. keywords. high temperature; concrete; fracture toughness; fracture energy. citation: qiu, p., experimental research on fracture behavior of concrete after high temperature, frattura ed integrità strutturale, 50 (2019) 300-309. received: 08.04.2019 accepted: 21.08.2019 published: 01.10.2019 copyright: © 2019 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. introduction n today’s construction industry, concrete as the most important engineering material has been widely used; high-rise buildings, bridges, channels will use a lot of concrete materials and there will be some small cracks in the use process of concrete. these cracks may be formed in the process of concrete forming, or may be formed by the external environment (high temperature, man-made) [1-3]. cracks will expand in a very strong pressure state, leading to gradual increase of crack width and length and decrease of bearing capacity, which will ultimately cause the breakage of structure, and crack is one of the main factors leading to the decrease of bearing capacity of concrete structures [4,5]. therefore, many researchers have concerned about the problem of concrete cracks and tried to find out why cracks generate, how cracks expand and how to prevent cracks [6]. however, the fracture mechanism of concrete is very complex as the uneven distribution of coarse aggregate and fine aggregate results in internal multi-level system. fracture mechanics is a discipline that studies the law of crack generation and propagation in materials or structures by using elasticity and plasticity mechanics, starting from the point that macro cracks exist in materials or components. its task is to obtain the fracture parameters of component materials and study the fracture problems of components under different external environments (high temperature, freeze thawing, external load, etc.). i http://www.gruppofrattura.it/va/50/2467.mp4 p. qiu, frattura ed integrità strutturale, 50 (2019) 300-309; doi: 10.3221/igf-esis.50.25 301 as the intrinsic characteristics of materials, scholars from all over the world have studied the fracture properties of concrete at room temperature extensively and have formulated standard test methods for mode i fracture related fracture parameters [7,8]. however, there are few studies on fracture properties after high temperature in china and abroad, and the research results of scholars are slightly different. a study [9] shows that the chemical composition, physical properties and mechanical properties of concrete have changed greatly at high temperature or after high temperature. in real society, besides buildings damaged by fire, there are many concrete structures affected by high temperature, such as cooling towers of power plants, prestressing nuclear reactor containers, etc. therefore, it is of far-reaching significance to understand the high temperature fracture properties of concrete for the design, identification and strengthening of such structures. based on the double k fracture toughness criterion, yu et al. [10] carried out the experimental study on mode i fracture behavior of concrete after high temperature. the results showed that the initial fracture toughness qick decreased gradually with the increase of temperature, while the instability toughness sick , fracture energy gf and characteristic length lch all showed the trend of “unchanged-risingfalling” with the increase of temperature, which indicated that the three parameters could be used as ductility indicators of concrete after high temperature. baker [11] studied the fracture energy of concrete under different cooling regimes. the results showed that the fracture energy of concrete increases first and then decreased with the increase of test temperature, the maximum value of fracture energy appeared near 300 °c, which showed that the toughness of concrete was the best at about 300 °c and the influence of different cooling regimes on fracture energy was very small. menou et al. [12] pointed out that the value of fracture energy of concrete after high temperature was higher than that at normal temperature before reaching a certain temperature and the value of fracture energy decreased rapidly when the temperature exceeded that value. in this study, the fracture behavior of high strength concrete after high temperature processing was studied through the test of three-point bending beams with initial cracks. comparative experiment was carried out using c70 concrete and five temperature gradients. based on the double k fracture theory, the law of fracture toughness and fracture energy of high strength concrete varying with temperature was analyzed to obtain the relationship between relevant fracture parameters and temperature, so as to provide a reliable basis for damage assessment of building structures after disaster. overview of test he standard three-point bending beam specimens with a span-height ratio (s/h) of 4 proposed by international union of laboratories and experts in construction materials, systems and structures were used in this test. a notch which was 30 mm deep were reserved at the middle and lower part. the basic shape of the three-point bending beam is shown in fig. 1. figure 1: schematic diagram of the three-point bending beam specimen (mm). the highest temperature endured was 25, 200, 400, 600 and 800 °c respectively. considering the discreteness of the fracture test, five specimens were set up at each temperature, and another one was prepared for standby application. the specimen number was expressed as plain concrete strength the maximum temperature endured, for example, 70-25 indicates that strength of the specimen was c70 and the maximum temperature that could endure was 25 °c. the mix proportion of the concrete specimen is shown in tab. 1. conch po52.5 portland cement was used. the maximum diameter of coarse aggregate was 10 mm, and medium sand with the diameter of 0.25-0.5 mm was used as the fine aggregate. after 28 days of sprinkling water curing, the compressive strength of the concrete cube reached 88.2 mpa, respectively. t p. qiu, frattura ed integrità strutturale, 50 (2019) 300-309; doi: 10.3221/igf-esis.50.25 302 strength grade water/ (kg·m-3) cement /(kg·m-3) water cement ratio river sand/ (kg·m-3) gravel / (kg·m-3) silica fume/ (kg·m-3) water reducing agent/(kg·m-3) unit weight/ (kg·m-3) c70 150.00 441.27 0.31 615.32 1194.44 39.21 6.74 2446.97 table 1: the mixing proportion of the concrete specimen an electric furnace with a furnace size of 500 mm × 500 mm × 1200 mm was used as the heating device, and an ai-518 (v7.1) programmed intelligent temperature regulator was used for temperature regulation and constant temperature control. the heating curve adopted the standard heating system, and the heating time was controlled according to the rate of 200 °c rising every half hour. when the heating temperature reached the predetermined temperature, it was switched to the constant temperature mode and kept for 3 hours. finally, the samples were taken out after the power-off of the electric furnace and 24 h of natural cooling [13]. test procedures waw-1000b microprocessor-controlled electro-hydraulic servo universal testing machine was used in this test. the computer was controlled manually and the testing machine starting testing automatically. the test device is shown in fig. 2. the test steps are as follows. 1. the support of the universal testing machine was adjusted to keep a distance of 300 mm between the central lines of the two supports. the screw was tightened to keep the two supports fixed. moreover, the loading shaft was adjusted parallel to the two supports. 2. after the support was adjusted, the specimen was slowly placed between the two supports, so that the two handdrawn lines of the specimen were aligned with the center of the two supports, and the notch of the three-point bending beam was aligned with the loading axes on the testing machine. 3. the computer system was connected. the load sensor and displacement sensor of the computer were calibrated, and the bending parameters of the computer were set. then the load, midspan displacement and notch displacement were adjusted to zero, and the initial position was adjusted. 4. the distance between the two load-bearing sheets of the electronic extensometer was adjusted to the shortest (10 mm) by holding them by hand. because of its good elasticity, the two pieces of the electronic extensometer were stuck between the two steel sheets at the crack opening. the load-opening displacement curve of the specimen was measured by the extensometer, and the load-span displacement curve was also be measured by the testing machine to obtain fracture parameters. 5. continuous loading method was adopted in this test. the loading speed was 0.08 kn/s. it was loaded directly until the specimen failed, and the control system automatically saved the data. 6. in the process of the experiment, the test machine was unloaded to prevent the oil pump from rising too high and damaging the test machine after the testing of five test specimens. the concrete blocks which needed to be processed by 200 °c and 400 °c were directly heated to the preset temperatures. the concrete blocks which needed to be processed by 600 °c and 800 °c were pre-heated to 200 °c, keeping for 24 h, and then heated to the preset temperature from 200 °c. figure 2: the testing device. p. qiu, frattura ed integrità strutturale, 50 (2019) 300-309; doi: 10.3221/igf-esis.50.25 303 the concrete fracture test was carried out on a 2000 kn electro-hydraulic servo universal testing machine. the whole test process was controlled by displacement, and the loading velocity was 0.02 mm/min to achieve stable splitting test. the average loading time of specimens which were processed with temperature lower than 400 °c was 20 minutes, while that of specimens which were processed with temperature higher than 400 °c was 40 minutes due to the long time spent in the descending section of the load-crack opening displacement curve. as shown in fig. 2, the crack opening displacement (cmod) and the crack tip opening displacement (ctod) of the specimens were measured with a clamp extensometer, and the deflection of the middle position of the specimens was measured with two displacement meters. experimental observations the experimental phenomena of the three-point bending beams after high temperature processing are shown in fig. 3. when the temperature that the concrete specimen ensured did not exceed 400 °c, the crack was vertical and downward, and there was no split crack. the splitting surface was relatively flat, and there was aggregate breaking on the fracture surface. when the load has not reached its peak value, visible cracks did not appear at the tip of the specimens; but once there were visible cracks, the load of the specimens suddenly dropped and then steadily decreased. when the temperature of the concrete specimen was 600 or 800 °c, the cracks bent downward; at the beginning, several small cracks appeared on the surface of specimens, and with the increase of the load, a main crack and several split cracks appeared. with the increase of temperature, the splitting surface became more tortuous, and the phenomenon of cracks passing through aggregates decreased obviously, instead, it went around between aggregates. when the load did not reach the peak value, visible cracks appeared at the tip of the prefabricated crack; when the load reached the peak value, the crack opening became larger and the length expanded, but then they slowly decreased, and the descending section lasted longer with the increase of the temperature of the specimen. for the specimens which were processed by 400 °c, 600 °c and 800 °c, obvious cracks detoured between the aggregate. figure 3: the pictures of test phenomenon. test results and analysis measurement of ignition loss of specimens after high temperature he loss of free water and bound water occurred in the concrete specimens at high temperature, and the weight of the concrete specimens decreased significantly compared with that before heating. in order to prevent water vapor from entering after heating, the specimen was wrapped by plastic bags. by measuring the mass change of the t p. qiu, frattura ed integrità strutturale, 50 (2019) 300-309; doi: 10.3221/igf-esis.50.25 304 concrete specimens before and after high temperature, the burning loss curves of concrete with different strengths at different temperatures were obtained (fig. 4). it was seen that the burning loss of general concrete basically presented three stages [14, 15]. the first stage was a physical change process. when the temperature did not exceed 200 °c, the main reason for the increase of the burning loss was the rapid evaporation of free water in the specimens. the second stage was a physical-chemical change process. when the temperature that the test specimen ensured was between 200 and 400 °c, the growth rate of the loss of ignition was slower than that in the first stage. in this stage, the free water has been exhausted and the bound water was difficult to separate. the third stage was a chemical change process, in which the temperature of the specimen was between 400 and 800 °c, and the loss of ignition was mainly caused by the decomposition of chemical components of concrete mortar and aggregate at high temperature, which was manifested as the dehydration of c-s-h gel crystal water and the dehydration of ca(oh)2. overall, the loss of ignition showed a law of increasing with the improvement of temperature. figure 4: relationship between ignition loss and elevated temperature. for concrete of different strength grades, the physical and chemical effects were dominant respectively due to the large difference of water-cement ratio. for c50 concrete, the water-cement ratio was large, and the fast increasing stage of ignition loss was 0 °c ~ 400 °c, in which free water loss was the main phenomenon. the loss caused by the physical effect was more obvious than that caused by the chemical effect. for c70 concrete, the water-cement ratio was moderate, the physical and chemical effects were equal, and the ignition loss remained stable as a whole. overall, the loss of ignition presented a law of decreasing first and then increasing with the increase of the strength. load-displacement curve of specimens after high temperature complete load-displacement curves including load-crack mouth opening displacement (p-cmod) curve and loaddeflection (p-δ) curve can represent a series of important results, such as initial stiffness, ultimate bearing capacity, opening displacement corresponding to cracking load and instability load and hardening and softening characteristics, and the geometric shape of the curve can also reflect the toughness and brittleness of the material to a certain extent. therefore, the full load-displacement curve plays a key role in the calculation of concrete fracture parameters. figure 5: the curve of p-cmod of the test specimens under different temperatures. p. qiu, frattura ed integrità strutturale, 50 (2019) 300-309; doi: 10.3221/igf-esis.50.25 305 figure 6: the curve of p-δ of the test specimens under different temperatures. fig. 5 and 6 are the typical p-cmod curve and p-δ curve of c70 concrete specimen at different temperatures. it was found that both types of curves showed a trend of shortening and fattening with the increase of temperature. the peak load decreased with the increase of temperature, and the corresponding critical cmod and deflection increased. linear regression was made on a part of the ascending section of p-cmod curve that was approximately straight line, and the coincidence degree between them was observed. the point where the curve began to deviate from the fitting straight line was found, and the corresponding load was the initial cracking load pini, t. details are shown in tab. 2. temperature/°c p ini, t/kn pmax, t/kn comd corresponding to pmax, t/mm c70 c70 c70 25 3.80 5.78 46.88 200 3.86 5.65 50.31 400 2.33 3.66 79.13 600 1.11 2.40 141.62 800 0.25 0.73 368.36 table 2: calculated results of fracture parameters (average values). calculation of fracture toughness fracture toughness of concrete is the ability of material to resist crack propagation. initial fracture toughness qick represents the resistance to crack propagation when the crack is about to crack and the instability toughness sick represents the resistance to external forces when the material is in critical instability state. crack initial fracture toughness qick and instability toughness sick can be calculated by the formula given in the norm for fracture test of hydraulic concrete [16]: 2 3 1/2 int, 0 02 mg 1.5( 10 ) 10 2 ( ) t q ic p sa k f th       (1) where 0( )f  stands for a function related to the value of 0 /a h , and its expression is:     0 2 0 0 0 0 0 03/2 0 0 1.99 (1 ) 2.15 3.93 2.7 ( ) , 1 2 1a f h                (2) p. qiu, frattura ed integrità strutturale, 50 (2019) 300-309; doi: 10.3221/igf-esis.50.25 306 2 3 1/2 max,t 2 mg 1.5( 10 ) 10 2 ( ) c s ic c p sa k f th       (3) where ( )cf  is a function related to the value of /ca h , and its expression is:      2 3/2 1.99 (1 ) 2.15 3.93 2.7 ( ) , 1 2 1c c c c c c c c c a f h                (4) where the calculation formula of ca is: 1/20 0 max, 2 ( )arctan( 0.1135) 32.6 c c t tecmod a h h h p     (5) where pini, t stands for the initial crack load, m stands for the weight between the supports of the specimens, which is converted using the total mass of the specimens according to s/l ratio, g is the acceleration of gravity, 9.81 m/s2 here, s is the span between the two supports of the specimens, 0a stands for the depth of the notch reserved at the middle and lower parts, t is the thickness of the specimens, h is the height of the specimens, pmax, t is the maximum load, ca stands for the effective crack length, 0h stands for the thickness of the sheet steel plate at the notch, e is the elastic modulus, and cmodc is the critical value of cmod. relationship between fracture toughness and temperature fig. 7a and b show the relationships of qick and s ick with temperature. it was seen from fig. 7 that the general change trend of qick and s ick decreased with the increase of temperature. a) b) c) figure 7: relationship between fracture toughness and elevated temperature. a) the change of initial fracture toughness with the maximum temperature; b) the change of instability toughness with the maximum temperature; c) the change of the ratio of initial fracture toughness to instability toughness with the maximum temperature. p. qiu, frattura ed integrità strutturale, 50 (2019) 300-309; doi: 10.3221/igf-esis.50.25 307 the relationship between the average values of qick and s ick of the concrete with different strength grades at different temperatures and temperature could be expressed by the following regression equations (25 °c≤ mt ≤800 °c). -0.001 0.8392, 0.9532qic mk t r   (6) -0.0022 2.2086, 0.9901sic mk t r   (7) as shown in fig. 7(a), qick of the concrete of both strength grades decreased with the increase of temperature (c70 is abnormal at 200 °c). the slope of the regression fitting curve was 0.001. the variation law of sick with temperature was similar with qick , as shown in fig. 7(b). as shown in fig. 7(c), with the increase of the maximum temperature, the qick / s ick of the concrete decreased (except 200 °c), indicating that qick decreased faster than s ick with the increase of the temperature, i.e., the sensitivity of q ick to temperature was higher than that of sick . calculation of fracture energy fracture energy is defined as the energy consumed to form a unit fracture surface, usually expressed by gf [17]. the fracture energy of concrete can be directly obtained from the load-midspan displacement curve (i.e. p-δ curve) obtained from the fracture test. in the fracture test, the work on concrete specimens consists of two parts, i.e., the work done by the loading axis applied on the beam and the work done by the gravity of the beam itself. in the calculation, according to the principle of equal bending moment acting on the notch section, the beam weight was equivalent transformed into the concentrated external force wp acting on the loading point, 2 w mg p  . the deadweight equivalent force of the beam wp was applied to the beam together with the applied load ap , so that the total load became w ap p . the displacement at the time of 0ap  was denoted as 0 , the area under the total load-displacement curve could be divided into three parts, 0w , 1w and 2w , as shown in fig. 8. 0w is the area under the curve of 0ap  , 1 0ww p  , and 2w represents the area of the curve after point 0 . reference [18] analyzed the value of 2w and approximately considered 1 2w w . therefore, the total work done by the external force was: 0 1 2 0 0 0 02 ww w w w w p w mg        (8) mid-span displacement p p ow wp 1w 0 2w   figure 8: the diagram for the analysis of fracture energy calculated based on the load-midspan displacement. it was assumed that all the work done by external forces flew into the fracture zone for fracture development, then the expression of fracture energy per unit area was: p. qiu, frattura ed integrità strutturale, 50 (2019) 300-309; doi: 10.3221/igf-esis.50.25 308 0 0 0( ) f lig w mgw g a t h a     (9) where 0w stands for external work, 0 stands for the cmpd when the specimen is damaged, liga stands for the ligament area of the specimen, and 0a stands for the height of the prefabricated crack of the specimen. relationship between fracture energy and temperature the relationship between the average fracture energy of concrete with different strength grades at different temperatures and temperature can be expressed by the following regression equations. 0.095470.32 , 0.8766fg t r   (10) it was noticed from fig. 9 that for c70 concrete specimens, the fracture energy decreased sharply with temperature when the temperature was lower than 200 °c. when the temperature was higher than 200 °c, temperature had little effect on fracture energy, the fracture energy showed a trend of slow decreasing, and the fracture energy was basically maintained at 297 n/m. the small variation of the fracture energy was because that the water-cement ratio of high-strength concrete was small, the proportion of cementitious material was large, and the crack development was relatively uniform. overall, the fracture energy showed a law of decreasing rapidly first and then decreasing slowly with the development of temperature. the development law of fracture energy of concrete specimens with different strength grades with temperature was comprehensively analyzed. when the concrete strength was c50, the fracture energy increased first and then decreased. when the concrete strength was c70, the fracture energy decreased rapidly first and then slowly with the development of temperature. figure 9: relationship between fracture energy of concrete with different strength grades and elevated temperature conclusions he fracture behavior of high strength concrete after high temperature was studied by the experiment of three-point bending beam with initial cracks. comparative experiment was carried out by using c70 concrete. the load-midspan displacement curve and load-cmod curve of concrete of different strength grades before and after high temperature were obtained. the fracture parameters such as initial cracking load, maximum load, critical value of cmod, initial fracture toughness and instability toughness were calculated based on the load-cmod. the fracture energy of the concrete was calculated based on the load-midspan displacement curve. the relationship of fracture parameters and fracture energy of concrete with temperature was analyzed and studied. the main contents and conclusions are as follows. 1. the ignition loss of the high-strength concrete decreased first and then increased with the increase of strength at high temperatures. 2. the initial fracture toughness qick and instability toughness s ick decreased with the increase of temperature, and the sensitivity of qick to temperature was higher than that of s ick . t p. qiu, frattura ed integrità strutturale, 50 (2019) 300-309; doi: 10.3221/igf-esis.50.25 309 3. fracture energy fg decreased rapidly first and then slowly with the development of temperature. references [1] caggiano, a., cremona, m., faella c., lima c. and martinelli e. (2012). fracture behavior of concrete beams reinforced with mixed long/short steel fibers, construction & building materials, 37(3), pp. 832-840. doi: 10.1016/j.conbuildmat.2012.07.060 [2] akcay, b., agar-ozbek, a.s. and bayramov, f. (2012). interpretation of aggregate volume fraction effects on fracture behavior of concrete, construction & building materials, 28(1), pp. 437-443. [3] zhang, c., yang, x. and hu, g. (2018). effect of randomness of interfacial properties on fracture behavior of concrete under uniaxial tension, acta mechanica solida sinica, 31(2), pp. 1-13. [4] arezoumandi, m. and volz, j.s. (2013). effect of fly ash replacement level on the fracture behavior of concrete, frontiers of structural and civil engineering, 7(4), pp. 411-418. [5] corr, d., accardi, m., graham-brady, l. and shah, sh. (2016). digital image correlation analysis of interfacial debonding properties and fracture behavior in concrete, engineering fracture mechanics, 74(1), pp. 109-121. [6] zhai, c., wang, x. and kong, j. (2017). a sophisticated simulation for the fracture behavior of concrete material using xfem, earthquake engineering & engineering vibration, 16(4), pp. 1-23. [7] simonin, f., olagnon, c. and maximilien, s. (2010). room temperature quasi-brittle behaviour of an aluminous refractory concrete after firing, journal of the european ceramic society, 22(2), pp. 165-172. [8] basamant, z.p. and becq-giraudon, e. (2002). statistical prediction of fracture parameters of concrete and implications for selection of test standard, cement & concrete research, 32(4), pp. 529-556. [9] gawin, d., majorana, c.e. and schrefler, b.a. (2015). digital analysis of hygro thermal behaviour and damage of concrete at high temperature, international journal for digital & analytical methods in geomechanics, 4(1), pp. 37-74. [10] lu, z.d., yu, k.q., su, l., lin, c.l. (2012) residual fracture behaviors of concrete subjected to elevated temperatures, journal of building materials, 15(6), pp. 836-840. [11] baker, g. (1996). the effect of exposure to elevated temperatures on the fracture energy of plain concrete, rilem materials and structures, 29(190), pp. 383-388. [12] menou, a., mounajed, g., boussa, h., pineaud, a. and carre, h. (2006). residual fracture energy of cement paste, mortar and concrete subject to high temperature, theoretical & applied fracture mechanics, 45(1), pp. 64-71. [13] general office of the national development and reform commission. (2005). dl/t 5332-2005, norm for fracture test of hydraulic concrete. [14] yan, l., xing, y.m. and hao, y.h. (2012). high temperature mechanical properties and microscopic analysis of hybrid fiber reinforced high performance concrete (hfhpc), concrete, (1), pp. 24-28. [15] wang, b.s. and li, z. (2011). experiment study on ascertaining the burning degree of the concrete components, concrete, 27(2), pp. 162-167. [16] xu, s.l., zhou, h.g., gao, h.b. and zhao, s.y. (2006). an experimental study on double-k fracture parameters of concrete for dam construction with various grading aggregates, china civil engineering journal, 39(11), pp. 50-62. [17] carloni, c., santandrea, m. and wendner, r. (2017). an investigation on the “width and size effect” in the evaluation of the fracture energy of concrete, procedia structural integrity, 3, pp. 450-458. [18] swartz, s.e. and yap, s.t. 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can be opened with acrobat and adobe reader 5.0 and later.) >> /namespace [ (adobe) (common) (1.0) ] /othernamespaces [ << /asreaderspreads false /cropimagestoframes true /errorcontrol /warnandcontinue /flattenerignorespreadoverrides false /includeguidesgrids false /includenonprinting false /includeslug false /namespace [ (adobe) (indesign) (4.0) ] /omitplacedbitmaps false /omitplacedeps false /omitplacedpdf false /simulateoverprint /legacy >> << /addbleedmarks false /addcolorbars false /addcropmarks false /addpageinfo false /addregmarks false /convertcolors /converttocmyk /destinationprofilename () /destinationprofileselector /documentcmyk /downsample16bitimages true /flattenerpreset << /presetselector /mediumresolution >> /formelements false /generatestructure false /includebookmarks false /includehyperlinks false /includeinteractive false /includelayers false /includeprofiles false /multimediahandling /useobjectsettings /namespace [ (adobe) (creativesuite) (2.0) ] /pdfxoutputintentprofileselector /documentcmyk /preserveediting true /untaggedcmykhandling /leaveuntagged /untaggedrgbhandling /usedocumentprofile /usedocumentbleed false >> ] >> setdistillerparams << /hwresolution [2400 2400] /pagesize [612.000 792.000] >> setpagedevice microsoft word numero_56_art_14_3039 s. i. eleonsky et alii, frattura ed integrità strutturale, 56 (2021) 171-186; doi: 10.3221/igf-esis.56.14 171 residual stresses near cold-expanded hole at different stages of highcycle fatigue by crack compliance data s. i. eleonsky, v.s. pisarev, m.d. zajtsev, m.ch. zichenkov central aero-hydrodynamics institute named after prof. n.e. zhukovsky (tsagi). 1 zhukovsky street, zhukovsky 140180 moscow region, russia. juzzepka@mail.ru, https://orcid.org/0000-0003-4345-067x vsp5335@mail.ru, https://orcid.org/0000-0002-5378-609x zaytcev@list.ru, zichenkov@tsagi.ru m.r. abdullin public joint-stock company «tupolev». 1 dementiev street, kazan 420127, russia. maratabdullin@mail.ru abstract. experimental method for a characterization of high-cycle fatigue evolution of residual stress near cold-expanded hole is developed and implemented. the technique is based on simultaneous measurements of deformation response to narrow notch, inserted in residual stress field, on opposite specimen’s faces by electronic speckle-pattern interferometry (espi). two-side measurements of through notch opening displacements are performed when a single notch, emanating from cold-expanded hole edge, is inserted. the transition from in-plane displacement component to residual stress intensity factor (sif) values follows from the relationships of modified version of the crack compliance method. the approach provides a difference in residual stress values referred to mandrel entrance and exit surface. notches are inserted at different stages of high-cycle fatigue without applying external load. the results obtained describe fine nuances of residual stress evolution, which cannot be considered as monotonic relaxation. keywords. high-cycle fatigue; cold hole expansion; residual stress intensity factor; residual stress evolution. citation: eleonsky, s. i., pisarev, v.s., zajtsev, m.d., zichenkov, m.ch., abdullin, m.r., residual stresses near cold-expanded hole at different stages of high-cycle fatigue by crack compliance data, frattura ed integrità strutturale, 56 (2021) 171-186. received: 11.03.2021 accepted: 18.03.2021 published: 01.04.2021 copyright: © 2021 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. introduction old hole expansion process is widely used to improve the fatigue life of aerospace structures [1]. the cold working of holes introduces a zone of compressive residual stresses around the hole, which, firstly, attenuates the initial crack appearance that eventually leads to an increase in damage tolerance life. secondly, residual stress influence c https://youtu.be/ojl4_o4yt6e s. i. eleonsky et alii, frattura ed integrità strutturale, 56 (2021) 171-186; doi: 10.3221/igf-esis.56.14 172 reduces the effective range of sif thus decreasing fatigue crack growth rates [2]. circumferential compressive residual stresses are especially beneficial at resisting fatigue when the plate with fastener holes is subjected to a tensile load. the skin of lower wing surface is the most characteristic example of tensile-dominate airplane structure. thus, information related to initial residual stress level as well as residual stress evolution is of considerable importance for reliable lifetime estimation. naturally, estimation of the fatigue life without considering the residual stress evolution might lead to inaccurate results. numerous numerical and experimental methods have been developed and implemented to solve the first from above problems [3–10]. a set of both experimental and numerical works concerns residual stress evolution [11–18]. required data are available for restricted spectrum of loading cycle parameters. deriving additional information, which is related to residual stress redistribution near cold-expanded holes in plane rectangular specimens under high-cycle fatigue on a base of two-side measurements, is the main goal of this paper. plane specimens of dimensions 200×70×10 mm with centred cold-expanded hole serve as investigated objects. specimen’s thickness corresponds to the thickness of real wing panel skin. the degree of cold expansion is 0.5 per cent. initial experimental information follows from a measurement of deformation response to narrow notch inserting in terms of notch opening displacements by espi. a sequence of narrow notches is used for residual stress energy release at different stages of fatigue loading with stress range δσ = 162 mpa and stress ratio r = 0.01. the original point of the first non-symmetrical notch is located at the intersection of the hole boundary and the transverse symmetry axis of the specimen. required residual sif values are derived from the relationships developed for modified version of the crack compliance method [19]. in previous papers modified version of the crack compliance method has been implemented for residual stress characterization near cold-expanded holes [17, 18]. the objects of investigations were plane rectangular specimens measuring 180×30×5 mm with centred cold-expanded holes of diameter 2𝑟 = 4.0 mm. interference value was equal to 5%. so high degree of cold expansion leads to circumferential residual stress of order 300 mpa at the hole vicinity [6, 7]. this means that a direct implementation of narrow notch inserting to quantitatively reveal residual stress level is quite difficult due to very high fringe density along the notch borders. to overcome this problem, specimens were subjected to constant tensile loading before a notch inserting [17, 18]. this approach has two drawbacks. first, deriving sif values, related to pure residual stress influence, needs using superposition principal. relatively low interference level provides reason enough to obtain residual sif values as a result of direct measurements of notch opening displacements. second, measurements of deformation response to local material removing can be performed on only one from two external faces of the specimen. chosen surface was mandrel entrance side. but a significant difference in the magnitude of compressive residual stress has been established between the mandrel entry side and exit side. these data follow from both experimental and numerical analysis [10, 11–14, 20, 21]. the stress value has a lower value at the entry face compared to the exit face. the residual tangential stress value varies gradually, due to the material flow in axial direction caused by the mandrel, reaching maximum value at exit side. thus, simultaneous evaluation of residual stress level on two opposite sides of the specimen is of great both applied and scientific interest. specimens and cold expansion technique atigue specimens were made from thick 1163t aluminium alloy plate to the dimensions 200×70×10 mm as it is shown in fig. 1. russian 1163t aluminium alloy is analogous to 2024 alloy. the specimens were cut from a 1200×800×15 mm plate by the same technology so that their longitudinal axes were aligned with the plate rolling direction. full set of rsh specimens includes 7 units. absence of residual stresses in all specimens has been established by data of probe hole drilling and further optical interferometric measurements of deformation response to local material removing [22]. mechanical properties such as elasticity modulus e = 74,000 mpa, yield stress y = 330 mpa and poisson’s ratio µ = 0.33 follow from standard tensile tests. each specimen contains centred open hole of nominal diameter 2 0r = 10.0 mm. pilot holes of 9.82 mm in diameter were drilled, followed by a 10.0 mm final reaming. cold expansion process was performed by special steel tool (mandrel) of dimensions shown in fig. 2. narrow external mandrel ring provides a possibility of quite gradual application of loading pressure. before carrying out cold expansion, contacting surfaces of the pin and the hole were lubricated. the forcing load has been applied by using 50 kn capacity testing machine with a speed equal to 1 mm/min. maximal load value reached 14 kn. the degree of cold expansion is equal to 0.5%. it is defined as relative ratio of external pin diameter to the hole diameter. a split sleeve is not introduced because of a small interference value. the same pin was used for all cold expanded holes. specimen thickness, hole diameter and interference value correspond to real manufacturing conditions. f s. i. eleonsky et alii, frattura ed integrità strutturale, 56 (2021) 171-186; doi: 10.3221/igf-esis.56.14 173 figure 1: drawing of specimens of rsh type. figure 2: cold expansion tool. the first specimen rsh_1 is used for lifetime estimation. the second specimen rsh_2 serves for a proper choice of the first and the second notch length proceeding from fringe resolution limit. the third specimen rsh_3 gives residual stress characterization before fatigue loading. other specimens are subjected to uniaxial pull-push sinusoidal loads with stress range δσ = 162 mpa and stress ratio r = 0.01. the fatigue tests were carried out with a load frequency of 3 hz in mts250 servo hydraulic testing machine. fracture of the reference specimen occurred after nf = 110,000 cycles. the number of loading cycles for each investigated specimen is listed in tab. 1. specimen rsh_3 rsh_4 rsh_5 rsh_6 rsh_7 rsh_1 number of cycles, n 0 20,000 40,000 60,000 80,000 110,000 lifetime, % 0 18.2 36.4 54.6 72.7 100 table 1: nomenclature of rsh specimens and fatigue loading program. practical realization of two-side measurements imposes heavy demands to design of experiment. namely, a notch location as well as configuration should be carefully chosen. the point is that a specimen with gross dimensions in plane equal to 200×70 mm can be only tested on a base of interferometer equipped with videoscan usb-285 ccd camera. using videoscan usb-285 ccd camera (1200x800 pixels) with a micro-nikkor lens for image recording gives us an observation field of whole dimensions 28×20 mm (1 pixel = 0.0185 mm). this means that symmetrical notches, original points of which are located at the intersection of the hole boundary and the short symmetry axis of the specimen, cannot be implemented for two-side measurements. that is why non-symmetrical notch is used for residual stress energy release as a result of local material removing. a kinematically designed mount (kdm) serves for two-side measurements of deformation response to narrow notch inserting [23]. the upper and lower part of kdm is shown in fig. 3. each specimen is placed on the upper part of kdm s. i. eleonsky et alii, frattura ed integrità strutturale, 56 (2021) 171-186; doi: 10.3221/igf-esis.56.14 174 so that initial notch point belonging to the hole edge coincides with the centre of both kdm parts. assembly of the upper part of kdm with clamped specimen and the lower part of kdm are shown in fig. 4.              a b figure 3: the upper (a) and lower (b) part of kinematically designed mount. a b figure 4: real view of specimen with non-symmetrical notch clamped in the upper part of kinematically designed mount: measurements on side a (a) and side b (b). the main subject of present research resides in a determination of pure residual sif values proceeding from notch opening displacement measurement. this means that only one from two in-plane displacement components, namely v-component, has to be derived from interference fringe pattern. optical set-up essential for v-component measurement is shown in fig.5. when projection of illumination directions onto the plane surface of the investigated object coincides with y-direction, interference fringe pattern is described as [19]: 2sinψ vv n   (1) where v is in-plane displacement component in y-direction; vn = ± 1; ±2; ±3, . . . are the absolute fringe orders; λ is the wavelength of laser illumination; ψ / 4 is the angle between inclined illumination and normal observation directions. s. i. eleonsky et alii, frattura ed integrità strutturale, 56 (2021) 171-186; doi: 10.3221/igf-esis.56.14 175 figure 5: general scheme of obtaining interference fringe patterns for deriving in-plane displacement component v by espi; (1) a specimen with a notch; (2) illuminating wave of laser light; (3) a ccd camera. a sequence of narrow notches is used for crack modelling at different stages of fatigue loading. step-by-step procedure of notch length increasing is performed by narrow jewellery saw of width δb = 0.25 mm. the original point of the first nonsymmetrical notch is located at the intersection of the hole boundary and the short symmetry axis of the specimen. details of experimental procedure are described in works [17, 19]. only short description relevant to sif extraction from interference fringe pattern, based on notations shown in fig. 6, follows below. the experimental procedure includes the following steps. the first exposure is made for a notch of initial length 1na  (see fig. 6). then the initial notch length is increased by a small increment δ na so that the new total notch length becomes equal to 1δ δn n na a a  and the second exposure is conducted. interference fringe patterns required for further interpretation are visualized by numerical subtraction of two images recorded for two surface states. figure 6: polar co-ordinate system connected with the notch tip and notation used for sif determination; n-1 and n-0.5 are the initial and final points of crack length increment δ na . formula for sif determination has the following form [19]:  1 0.5 0.522 2 2δ δ 8 δ n n i n n n e k a v v a       , (2) s. i. eleonsky et alii, frattura ed integrità strutturale, 56 (2021) 171-186; doi: 10.3221/igf-esis.56.14 176 where e is the elasticity modulus of the material; δ  na is the notch length increment. two parameters in relationship (2), notch mouth opening displacement at point n-1 denoted as 1δ nv  and notch opening displacement at point n-0.5 denoted as 0.5δ nv  , must be obtained from experimental data. these points are shown in fig. 7. figure 7: typical interference fringe pattern obtained in terms of in-plane displacement component v as the result of narrow notch prolongation, δ𝑁 = 29.0. measurement procedure includes a determination of notch opening displacements in two points n-1 and n-0.5 with coordinates ( δ ,nr a    ) and ( δ / 2,nr a    ), respectively (see fig. 6 and 7). the point n-1 can be reliably identified in any interference fringe pattern of type shown in fig. 7 as the interface between the dark and bright parts of the crack line. the point n-0.5 is located in the middle of the bright segment of the notch line. the value of the notch opening at points n-1, denoted as 1 1 1δ n n nv v v       , can be derived in the following way. first, the absolute fringe orders in the upper and the lower notch borders, which correspond to displacement components 1nv   and 1nv   , respectively, must be calculated starting from zero order fringe. after this displacement component values 1nv   and 1nv   , are derived by formula (1): 1 1 2sinψ v n nv n     , 1 1 2sinψ v n nv n     , (3) 1 v nn   and 1 v nn   are the absolute fringe orders related to the upper and the lower crack borders, respectively;  is the wavelength of laser illumination;  = π/4 is the sensitivity angle (fig. 5). we should keep in mind that 1nv   and 1nv   as well as 1 v nn   and 1 v nn   have opposite physical signs (fig. 6). the notch mouth opening displacement (nmod) in the point n1 follows from (3):  1 1 1 1 1 1δ δ 2sinψ 2sinψ v v v n n n n n nv v v n n n                , (4) where 1δ v nn  is the fringe order difference referred to the point n-1. this value is counted over the single fringe pattern, as it is shown in fig. 7, between two points, belonging to the upper and the lower crack borders. interference images of large scale are used for this purpose. the value of the notch opening displacement (nod) at the point n-0.5 (fig. 6), denoted as 0.5 0.5 0.5δ n n nv v v       , can be determined in the same way. thus, two experimentally measured parameters, namely nmod s. i. eleonsky et alii, frattura ed integrità strutturale, 56 (2021) 171-186; doi: 10.3221/igf-esis.56.14 177 1δ nv  (4) and nod 0.5δ nv  , are available, and required sif value n ik for the notch of na length can be determined through the use of formula (2). experimental technique and initial information he upper part of kdm includes six symmetrical v-shaped cuts separated by  / 3 in angular direction (fig. 3b). three steel balls are symmetrically arranged in the lower part of kdm divided by 2 / 3 angular distance (fig. 3a). this design feature provides a way of performing two-side measurements. the experimental procedure developed includes following steps: • the specimen is initially mounted so that contact between three balls and cuts numbered by 1, 3 and 5 enables illumination of side a. • the first exposure of specimen in initial state is performed to obtain information essential for determining component v on side a; • the specimen is turned about so that contact between three balls and cuts numbered by 2, 4 and 6 enables illumination of side b; • the first exposure of specimen in initial state is performed to obtain information essential for determining component v on side b; • the specimen is removed out of the optical setup; • narrow notch is inserted through the specimen thickness at the surface area of interest; • the specimen with inserted notch is replaced into interferometer system so that contact between three balls and cuts numbered by 2, 4 and 6 enables illumination of side b; • the second exposure of the specimen with inserted notch is performed to complete determining component v on side b; • the specimen is turned about so that contact between three balls and cuts numbered by 1, 3 and 5 enables illumination of side a; • the second exposure of the specimen with inserted notch is performed to complete determining component v on side a. above procedure has been completed for five successive notch prolongations in each from five first specimens listed in tab. 1. thus, 2×5×5 = 50 interference fringe patterns, caused by local material removing, have been recorded. interferograms obtained for the first and the second notch length increments in specimen rsh_3 are shown in fig. 8 and 9, respectively. interference fringe patterns obtained for three last notch length increments in specimen rsh_3 on side a and side b are presented in fig. 10. a b figure 8: specimen rsh_3. interference fringe patterns obtained in terms of in-plane displacement component v on side a (a) and side b (b) as the result of narrow notch inserting. initial notch length 0a = 0 with increment 1δ aa = 1.70 mm and 1δ ba = 1.70 mm. t s. i. eleonsky et alii, frattura ed integrità strutturale, 56 (2021) 171-186; doi: 10.3221/igf-esis.56.14 178 a b figure 9: specimen rsh_3. interference fringe patterns obtained in terms of in-plane displacement component v on side a (a) and side b (b) as the result of narrow notch inserting. initial notch length 0 aa 1.7 mm with increment 2δ aa = 2.04 mm; initial notch length 0 ba 1.7 mm with increment 2δ ba = 2.15 mm. a b c d e f figure 10: specimen rsh_3. interference fringe patterns obtained in terms of in-plane displacement component v on side a: (a)3δ aa , (b)4 δ aa , (c)5 δ aa and side b: (d)3δ ba , (e)4 δ ba , (f)5 δ ba . s. i. eleonsky et alii, frattura ed integrità strutturale, 56 (2021) 171-186; doi: 10.3221/igf-esis.56.14 179 interferograms obtained for the first and the second notch length increments in specimen rsh_7 are shown in fig. 11 and 12, respectively. interference fringe patterns obtained for three last notch length increments in specimen rsh_7 on side a and side b are presented in fig. 13. a b figure 11: specimen rsh_7. interference fringe patterns obtained in terms of in-plane displacement component v on side a (a) and side b (b) as the result of narrow notch inserting. initial notch length 0a = 0 with increment 1δ aa = 1.81 mm and 1δ ba = 1.81 mm. a b figure 12: specimen rsh_7. interference fringe patterns obtained in terms of in-plane displacement component v on side a (a) and side b (b) as the result of narrow notch inserting. initial notch length 0 aa 1.81 mm with increment 2δ aa = 1.85 mm; initial notch length 0 ba 1.81 mm with increment 2δ ba = 1.81 mm. the results of interpretation of fringe patterns, obtained for specimen rsh_3 in terms of in-plane displacement component v, are listed in tab. 2. this table also includes sif values, calculated by formula (2). the results of interpretation of fringe patterns, obtained for specimen rsh_7 in terms of in-plane displacement component v, are listed in tab. 3. this table also includes sif values, calculated by formula (2). the same data are also available for specimen rsh_4, specimen rsh_4 and specimen rsh_6. s. i. eleonsky et alii, frattura ed integrità strutturale, 56 (2021) 171-186; doi: 10.3221/igf-esis.56.14 180 a b c d e f figure 13: specimen rsh_7. interference fringe patterns obtained in terms of in-plane displacement component v on side a: (a)3δ aa , (b)4 δ aa , (c)5 δ aa and side b: (d)3δ ba , (e)4 δ ba , (f)5 δ ba . notch number 1 2 3 4 5 side a  na , mm 1.70 2.04 1.96 2.96 3.74 na , mm 1.70 3.74 5.7 8.66 12.4  1 v nn , fringes –21.0 –21.5 –13.0 –10.0 –5.5  1nv , μm –7.98 –8.17 –4.94 –3.8 –2.09  0.5 v nn , fringes –14.0 –15.0 –11.0 –8.0 –5.0  0.5nv , μm –5.32 –5.7 –4.18 –3.04 –1.9 , mpa mnik –4.0 –4.1 –3.6 –2.0 –1.2 side b  na , mm 1.70 2.15 1.96 3.33 3.81 na , mm 1.70 3.85 5.81 9.14 12.95  1 v nn , fringes –61.0 –59.0 –32.0 –22.0 –6.0  1nv , μm –23.18 –22.42 –12.16 –8.36 –2.28  0.5 v nn , fringes –41.0 –51.0 –28.0 –15.0 –4.5  0.5nv , μm –15.58 –19.38 –10.64 –5.7 –1.71 , mpa mnik –11.8 –16.2 –9.4 –3.1 –1.0 table 2: the results of fringe patterns interpretation for specimen rsh_3. s. i. eleonsky et alii, frattura ed integrità strutturale, 56 (2021) 171-186; doi: 10.3221/igf-esis.56.14 181 notch number 1 2 3 4 5 side a  na , mm 1.81 1.85 1.85 2.81 5.00 na , mm 1.81 3.66 5.51 8.32 13.32  1 v nn , fringes –40.0 –36.0 –19.0 –13.5 –8.0  1nv , μm –15.2 –13.68 –7.22 –5.13 –3.04  0.5 v nn , fringes –31.0 –27.0 –13.5 –10.0 –6.5  0.5nv , μm –11.78 –10.26 –5.13 –3.8 –2.47 , mpa mnik –9.9 –8.3 –3.9 –2.5 –1.3 side b  na , mm 1.81 1.81 1.85 2.96 4.81 na , mm 1.81 3.62 5.47 8.43 13.24  1 v nn , fringes –50.0 –34.0 –25.0 –17.5 –10.0  1nv , μm –19.0 –12.92 –9.5 –6.65 –3.8  0.5 v nn , fringes –37.0 –28.5 –20.5 –14.5 –8.0  0.5nv , μm –14.06 –10.83 –7.79 –5.51 –3.04 , mpa mnik –11.3 –9.7 –6.8 –3.8 –1.6 table 3: the results of fringe patterns interpretation for specimen rsh_7. results and discussion xperimental data of type presented in tab. 2 and 3 offer distributions of sif values along total crack length for specimens attributed to different loading cycles number. these dependencies are shown in fig.14. dependencies, presented in fig. 14, display considerable difference in residual sif values, which are referred to side a and side b for first three notch length increments. obtained data reliably confirm an availability of remarkable disparity between the residual stress field at the mandrel entry and exit faces. it is of crucial importance that experimental information follows from two-side measurements of deformation response to single through notch inserting, which are simultaneously performed on opposite specimen’s faces. this response has a form of notch opening displacements. that is why data thus obtained is of considerable interest for refining various numerical models used for quantifying the crack tip surface displacements in the area where the corner point of the crack front intersects a free surface [24, 25]. minimal discrepancy between residual sif values referred to side a and side b is observed for specimen rsh_7 after applying 80,000 loading cycles. a difference in residual sif values on opposite specimen’s faces is decreased starting from the third notch length. this point lies at the distance 5.5  3a 6.2 mm from the hole edge. residual sif values for the fifth notch length increment  5a practically coincide for all tested specimens. experimental data reveal negative sif values for all investigated notch length increments. this means that an influence of compressive circumferential residual stress runs to a distance equals to 5 0r from the hole edge, as minimum, nevertheless to low interference level (0.5%) inherent in cold expansion process. fig. 14 reflects residual sif values as a function of total crack length related to different stages of high-cycle fatigue. obtained information can be reconstructed to receive dependencies of residual sif values for notches of fixed length against of loading cycle number. required distributions are shown in fig.15a and 15b for the first and the second notch length, respectively. plots, presented in fig.15, indicate initial level of residual sif 1ik and 2 ik values, which are related to different distances from cold-expanded hole boundary and their evolution due to high-cycle fatigue. this evolution cannot be characterized as monotonic relaxation. moreover, curves obtained for side a reveal a contrary process. naturally, initial negative sif values are monotonically decreased when cycle number is increased. e s. i. eleonsky et alii, frattura ed integrità strutturale, 56 (2021) 171-186; doi: 10.3221/igf-esis.56.14 182 a b c d e figure 14: residual sif nik values as a function of notch length na at different stages of high-cycle fatigue: n = 0 (a); n= 20,000 cycles (b); n = 40,000 cycles (c); n = 60,000 cycles (d); n = 80,000 cycles (e). similar, but more complex situation, takes place for sif redistribution on side b (fig. 15a). negative 1ik -values demonstrate a monotonic decrease instead of relaxation up to n = 40,000 cycles. this stage of high-cycle fatigue corresponds to the reverse «anti-relaxation» point, after which sif increase occurs, reaching initial value at n = 80,000 cycles. maximal relative increase is equal to:                 1 1 1 _ 5 _ 3 21.9 11.8 0.461 21.9_ 5 i i b i k rsh k rsh r k rsh . (5) s. i. eleonsky et alii, frattura ed integrità strutturale, 56 (2021) 171-186; doi: 10.3221/igf-esis.56.14 183 thus, an increase of 46 per cent in 1ik -value corresponds to 36.4 per cent of lifetime. 1 ik -values at the initial state (specimen rsh_3) and at 72.7% of lifetime (specimen rsh_7) coincide within 4.2 per cent (see tab. 2 and 3). obtained results clearly evidence that there is no «classical relaxation» of circumferential residual stress referred to side b. a b figure 15: residual sif values as a function of loading cycle number n for the first 1a (a) and second 2a (b) notch length increment. the same statement is true for side a. maximal relative increase in 1ik -value inherent in «anti-relaxation» process equals to:                 1 1 1 _ 7 _ 3 9.9 4.0 0.596 9.9_ 7 i i a i k rsh k rsh r k rsh . (6) it should be noted that a difference in 1ik -values, corresponding to 72.7% of lifetime on side a and side b, lies within 12.4 per cent (see tab. 3). residual sif values can be accurately converted into residual stress values based on the approach developed in a set of famous works [26–28]. but this procedure lies out of the scope of present paper, because main subject concerns residual stress evolution. that is why the analytical results presented in the handbook of murakami [29] are involved for residual stress estimation in the cold-expanded hole vicinity. these data follow from the solution for the through non-symmetrical crack starting from the hole boundary in the infinite plane under uniform two-axes compression (section 5.2 of handbook [29]). the main feature of this approach resides in normalizing residual sif values obtained for different specimens by  12 a . this procedure serves for smoothing slight differences in experimental sif values caused by minor deviations in the first notch length. dependencies of principal residual stress component for the first notch against of loading cycle number are shown in fig. 16. obtained results should be considered as minimal possible values of circumferential residual stress component at the vicinity of cold-expanded hole edge. but evolution parameters (5) and (6) are valid for residual stress curves shown in fig. (16). plots, presented in fig. 15 and 16, confirm very interesting conclusion deals with residual stress relaxation, presented in work [30]. the author declared that «the relaxation mechanism is not clear from the physical point of view, except for the case of loads that cause macroscopic plastic deformations». moreover, the results obtained are in direct contradiction to the opinion of authors of work [12]. they said: «cyclic loading causes these compressive residual stresses to relax, thus reducing their beneficial effect». we can see that in the case considered residual stress evolution demonstrates «anti-relax» character thus strengthening their beneficial effect. data concerning residual stress evolution in aluminium (7075-t73 alloy) plane specimens of 2.3 mm thickness with coldexpanded hole of 4.83 mm diameter are presented in work [14]: «to investigate the possible relaxation of residual stresses in cold expanded holes, specific tests were carried out. some split sleeve cold expanded specimens were fatigue tested at δσ=160 mpa, r= 0.1, up to prefixed number of cycles, in the range from 20% to 95% of the mean fatigue life. preliminary fem simulations ensured that the residual stress field was not altered by the application of the external fatigue load. subsequently, round plates were machined from the fatigued specimens, to be used for sachs’ method residual stress s. i. eleonsky et alii, frattura ed integrità strutturale, 56 (2021) 171-186; doi: 10.3221/igf-esis.56.14 184 measurement. the results obtained show that no relaxation was present». it is of interest that fatigue loading parameters used in present paper and work [14] practically coincide. figure 16: values of circumferential residual stress component 2 rs as a function of loading cycle number n obtained for the first notch length 1a . revealed mechanism of residual stress redistribution is of great importance for deep understanding of the technological process used here for cold hole expansion. this process is relatively simple but leads to appropriate lifetime enhance. evident drawback of the technology resides in low level of initial residual stress arising on side a. but, quite unexpectedly, fatigue loading tends to an increase in negative residual stress value referred to side a. this fact slows down fatigue crack initiation thus explaining lifetime increase inherent in cold expansion technology used. accurate detection of surface crack appearance was not carefully arranged. small, but reliably visible crack (of length 𝑎 1.2 mm), displayed on side a after n= 95,000 cycles. a crack of the same length was observed on side b after 100,000 cycles. the approach developed has two major areas of application. the first of them is connected with residual stress investigation near cold-expanded holes in thick specimens, which correspond to real thickness of aircraft components. the main advantage resides in the capability of two-side measurements thus quantifying a difference in residual sif values referred to mandrel entrance and exit face. it is of importance that this difference considerably increases with a rise of specimen’s thickness. the second field of use resides in investigations of stress range/ratio influence on residual stress evolution at the vicinity of cold-expanded holes. note, however, that practical implementation of the experimental technique is restricted to low expansion degree. it seems that interference value must be less that one per cent. future developments of the approach include two directions. the first of them assumes an upgrade of interferometer optical system. the key point of this procedure resides in a decrease of interferometer sensitivity with respect to notch opening displacement. this modification will eventually lead to a gain in cold-expansion degree range, for which through notch technique might be implemented. damage accumulation analysis related to cold-expanded hole vicinity proceeding from notch sif evolution is the second way of further progress. conclusion ovel experimental method of residual stress characterization near cold-expanded hole is developed and implemented. the technique is based on two-side measurements of deformation response to narrow notch, which is simultaneously inserted on opposite specimen’s faces. deformation response has a form of notch opening displacements, which are measured by espi. the transition from in-plane displacement component to residual sif values follows from the relationships of modified version of the crack compliance method. two-side measurements are performed on opposite specimen’s faces for a single through notch, emanating from the edge of cold-expanded hole. thus, the approach is capable of quantifying a difference in residual stress values referred to mandrel entrance and exit surface. notches are inserted without applying external tensile load. this means that residual sif values are determined directly. n s. i. eleonsky et alii, frattura ed integrità strutturale, 56 (2021) 171-186; doi: 10.3221/igf-esis.56.14 185 realization of developed procedure at different stages of high-cycle fatigue offers quantitative description of residual stress evolution inherent in both specimen faces. specimens of measuring 200x70x10 mm with centred cold-expanded holes of pilot diameter 2 0r = 10.0 mm and the interference value equals to 0.5% are used to describe residual sif evolution. highcycle fatigue with stress range δσ = 162 mpa and stress ratio r = 0.01 is considered. it is established that residual stress evolution cannot be characterised as monotonic relaxation. initial level of negative residual stress on mandrel entrance surface reveals monotonic growth of negative values up to 72.7% of lifetime. negative residual 1ik -values, related to mandrel exit surface, demonstrate a monotonic decrease instead of relaxation up to n = 40,000 cycles. this stage of highcycle fatigue corresponds to the reverse «anti-relaxation» point, after which sif values increase occurs, reaching initial value at 72.7% of lifetime. a difference in 1ik -values, corresponding to 72.7% of lifetime on opposite specimen faces, lies within 12.4 per cent. the approach developed has demonstrated remarkable capabilities for revealing fine nuances of residual stress evolution near cold-expanded holes. information thus obtained is of considerable importance for development and verification of numerical methods related to residual stress analysis near cold-expanded holes. references [1] reid, l. (2014). hole cold expansion – the fatigue mitigation game changer of the past 50 years, advanced materials research, 891–892, pp. 679-684. doi: 10.4028/www.scientific.net/amr.891-892.679. [2] stefanescu, d. (2004). measurement and prediction of fatigue crack growth from cold expanded holes, part 1: the effect of fatigue crack growth on cold expansion residual stresses, j. of str. analysis, 39(1), pp. 25-39. doi: 10.1177/030932470403900103. [3] ball, d.l. (1995). elastic-plastic stress analysis of cold expanded fastener holes, fatigue and fract. of eng. mat. and struct., 18(1), pp. 47-63. [4] zhang, y., fitzpatrick, m.e., edwards, l. (2005). analysis of the residual stress around a cold-expanded fastener hole in a finite plate, strain, 41(2), pp. 59-70. doi: 10.1111/j.1475-1305.2005.00181.x. [5] pavier, m.j., poussard, c.g.c., smith d.j. (1999). effect of residual stress around cold worked holes on fracture under superimposed mechanical load, eng. fract. mechanics, 63(6), pp.751-773. doi: 10.1016/s0013-7944(99)00050-8. [6] moreira, p.m.g.p., de matos, p.f.p., pinho, s.t., pastrama, s.d., camanho, p.p., de castro, p.m.s.t. (2004). the residual stress intensity factors for cold-worked cracked holes: a technical note, fatig. & fract. of eng. mat. & struct., (27), pp. 879-886. doi: 10.1111/j.1460-2695.2004.00768.x. [7] yongshou, l., xiaojun, s., jun, l., yue zhufeng. (2010). finite element method and experimental investigation on the residual stress fields and fatigue performance of cold expansion hole, materials and design, 31(3), pp. 1208-1215. doi: 10.1016/j.matdes.2009.09.031. [8] garcia-granada, a.a., pavier, m.j., smith, d.j. (2001). a new procedure based on sachs’ boring for measuring nonaxisymmetric residual stresses: experimental application, int. j. of mech. sciences, 43(12), pp. 2753-2768. doi: 10.1016/s0020-7403(01)00071-6. [9] özdemir, a.t., edwards, l. (2004). through-thickness residual stress distribution after the cold expansion of fastener holes and its effects on fracturing, j. eng. mater. technol., 126, pp. 129-135. doi: 10.1115/1.1634278. [10] zuccarello, b., di franco, g. (2013). numerical-experimental method for the analysis of residual stresses in coldexpanded holes, exp. mechanics; 53(4), pp. 673-686. doi: 10.1007/s11340-012-9669-2. [11] ozdemir, a. t., edwards, l. (1997). relaxation of residual stresses at cold worked fastener holes due to fatigue loading, fatigue fract. eng. mater. struct. 20(10), pp. 1443–51. doi: 10.1111/j.1460-2695.1997.tb01501.x. [12] chakherlou t. n., yaghoobi, a. (2010). numerical simulation of residual stress relaxation around a cold-expanded fastener hole under longitudinal cyclic loading using different kinematic hardening models, fatigue & fracture of engineering materials & structures, 33(11), pp. 740–751. doi: 10.1111/j.1460-2695.2010.01485.x. [13] backman, d., cowal, c., patterson, e.a. (2010). analysis of the effects of cold expansion of holes using thermoelasticity and image correlation, fat. & fract. of eng. mat. & struct., 33(12), pp. 859–870. doi: 10.1111/j.1460-2695.2010.01472.x. [14] boni, l., fanteria, d., lanciotti, a., polese, c. (2013). experimental and analytical assessment of fatigue and crack propagation in cold worked open hole specimens, fatigue fract. engng. mater struct., 36(9), pp. 930–941. doi: 10.1111/ffe.12050. [15] keith, w.j., ralph, w.b. (2017). investigation of residual stress relaxation in cold expanded holes by the slitting method, eng. fract. mech., 179, pp. 213-224. doi: 10.1016/j.engfracmech.2017.05.004. s. i. eleonsky et alii, frattura ed integrità strutturale, 56 (2021) 171-186; doi: 10.3221/igf-esis.56.14 186 [16] matvienko, y.g., pisarev, v.s., eleonsky, s.i. (2019). residual stress/strain evolution due to low-cycle fatigue by removing local material volume and optical interferometric data, fat. & fract. of eng. mat. & struct., 42, pp. 2061– 2078. doi: 10.1111/ffe.13083. [17] matvienko, y.g., pisarev, v.s., eleonsky, s.i. (2019). the effect of low-cycle fatigue on evolution of fracture mechanics parameters in residual stress field caused by cold hole expansion, fratt. ed int. str., 13(47), pp. 303-320. doi: 10.3221/igf-esis.47.23. [18] chernov, a.v., eleonsky, s.i., pisarev, v.s. (2021). influence of stress ratio on residual stress evolution near coldexpanded hole due to low-cycle fatigue by crack compliance data, fratt. ed int. str., 55, pp. 174-186; doi: 10.3221/igf-esis.55.13. [19] pisarev, v.s., matvienko, y.g., eleonsky, s.i., odintsev, i.n. (2017). combining the crack compliance method and speckle interferometry data for determination of stress intensity factors and t-stresses, eng. fract. mech., 179, pp. 348374. doi: 10.1016/j.engfracmech.2017.04.029. [20] pavier, m. j., poussard, c. g. c., smith, d. j. (1997). finite element simulation of the cold working process for fastener holes, j. strain anal. eng. des., 32, pp. 287–300. [21] zhang, x., wang, z. (2003). fatigue life improvement in fatigue-aged fastener holes using the cold expansion technique. int. j. fatigue, 25(9-11), pp. 1249–1257. doi: 10.1016/s0142-1123(03)00152-x. [22] pisarev, v.s., odintsev, i.n., eleonsky, s.i., apalkov, a.a. (2018). residual stress determination by optical interferometric measurements of hole diameter increments, optics and lasers in engineering, 110, pp. 437–456, doi: 10.1016/j.optlaseng.2018.06.022. [23] maclead, n. (1973). a kinematically designed mount for the precise location of specimen for holographic interferometry, j. of physics e: scien. inst., 6, pp. 423-424. [24] pook, l. p., campagnolo, a., berto, f. (2016). coupled fracture modes of discs and plates under anti-plane loading and a disc under in-plane shear loading, fat. & fract. of eng. mat. & struct., 39(8), pp. 924–938. doi:10.1111/ffe.12389. [25] pook, l. p., berto, f., campagnolo, a. (2016). coupled fracture modes under anti-plane loading, fratt. ed int. str., 10(37), pp. 108-113. doi: 10.3221/igf-esis.37.15. [26] schindler, h.-j. (1995). determination of residual stress distributions from measured stress intensity factors, int. j. of fract., 74(2): r23-r30. doi: 10.1007/bf00036266. [27] schindler, h.-j., cheng, w., finnie, i. (1997). experimental determination of stress intensity factors due to residual stresses, exp. mech., 37(3), pp. 272-277. doi: 10.1007/bf02317418. [28] prime, m.b. (1999). residual stress measurement by successive extension of a slot: the crack compliance method, app. mech. rev, 52(2), pp. 75-96. doi: 10.1115/1.3098926. [29] murakami, y. (1987). stress intensity factors handbook, oxford: pergamon. [30] mcclung, r. c. (2007). a literature survey on the stability and significance of residual stresses during fatigue, fatigue fract. eng. mater. struct., 30(3), 173–205. doi: 10.1111/j.1460-2695.2007.01102.x. shot peening processes to obtain nanocrystalline surfaces in metal alloys: b. wang, et alii, frattura ed integrità strutturale, 57 (2021) 291-299; doi: 10.3221/igf-esis.57.21 291 dynamic strength analysis of the key components of the beam-type pumping unit with dynamic tracking balance bo wang, de-chun chen school of petroleum engineering, china university of petroleum (east china), qingdao, 266580, china. s20060010@s.upc.edu.cn abstract. aiming at the shortages of large reversing impact, high energy consumption and poor balance effect of conventional beam-type pumping unit, the design scheme of beam-type pumping unit with dynamic tracking balance is proposed. the load-displacement curves from on-site trial shows that the pumping with dynamic tracking balance has a better effect of load balance, and a high production and power efficiency. according to the designed structure, the dynamic responses of the beam and connecting rods are analyzed. the results show that the maximum von mises stresses in the beam and connecting rods are 36.96 mpa and 27.83 mpa, respectively. the key components of designed beam-type pumping unit with dynamic tracking balance meet the requirement of strength. keywords. dynamic tracking balance; load balance; power efficiency; dynamic response; strength. citation: wang, b., chen, d. c., dynamic strength analysis of the key components of the beam-type pumping unit with dynamic tracking balance, frattura ed integrità strutturale, 57 (2021) 291-299. received: 24.04.2021 accepted: 10.06.2021 published: 01.07.2021 copyright: © 2021 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. introduction il extraction with sucker rod is the most important way of oil production in china and even all over the world. according to the statistics, more than 80 % of the total crude oil in china is extracted by sucker rod pumping system, which accounts for nearly 90 % output of the total oil wells in service [1]. the sucker rod pumping system is mainly composed of ground oil pumping unit, downhole pump and sucker rod, among which the oil pumping unit is the core lifting element. according to the structural characteristics, pumping units can be divided into beam pumping and non-beam pumping types. the main feature of the beam-type pumping unit is to change the reciprocating swing of beam into the reciprocating linear motion of suspension point by the arc surface of horse-head. the conventional beam-type pumping unit has the advantages of simple structure, convenient operation, high reliability and good adaptability to various working conditions. therefore, it is always the dominated rod pumping unit in onshore oilfields, and will still be the preferred pumping unit for a long time in the future. however, the conventional beam-type pumping unit also has the deficiencies such as poor balance effect, large fluctuation of net torque of crank shaft, low efficiency and high energy consumption [2]. the statistics show that the average system efficiency of pumping wells in the oilfields of china is less than 25 %, the annual power consumption of oil production is about 9 billion kwh, accounting for about o https://youtu.be/nu3_g72ddz8 b. wang, et alii, frattura ed integrità strutturale, 57 (2021) 291-299; doi: 10.3221/igf-esis.57.21 292 45% of the total energy consumption of oilfields. therefore, reducing energy consumption has become one of the important topics in front of the oilfield development [3, 4]. at present, three approaches are commonly adopted on energy savings in oil-gas extraction. first one is the improvement of pumping unit structure. for example, double-horsehead pumping unit [5, 6], pumping unit balanced with phased crank [7], and pump-stroke optimization [8] have been adopted to improve the structure of pumping unit. the second one is employing the specially designed motor, such as high-slip motor, super-high-slip motor, and permanent-magnet motor, to improve the motor efficiency [9, 10]. the third approach is to control the motor speed properly according to the operating condition of the oil well through power electronic devices, such as multifunction energy-saving device, frequency converter, and energy feedback device [11-16]. although the former two approaches have positive effect on the overall efficiency, it is not economically justifiable to replace the old pumping units with new ones while they are still functioning. since it only inserts another device in a pumping system without altering the overall structure, the third approach is a favorable solution from the practical application. figure 1: the conventional beam pumping unit figure 2: beam-type pumping unit with dynamic tracking balance the beam-type pumping unit with dynamic tracking balance is a typical front-mounted pumping unit, with the structure shown in figure 2. when compared with the conventional beam pumping unit, the swing angle of the front-mounted beam is small, which effectively reduces the change rate of load and ensures the stability during the up-down strokes. in order to improve the motion characteristics of the pumping unit, the dynamic tracking balance is designed to improve the effect of load balance by assembling a moving pulley, which can automatically adjust the arm of force on the beam from the balance of moment according to the loads from suspension point and connecting rod at different positions. compared with the moment balance of the beam by the rear-mounted crank in the traditional pumping unit, as shown in figure 1, the moment balance of the beam with dynamic tracking balance can be accomplished by a lifting weight, which can eliminate the negative torque reduce the peak torque from the rear-mounted crank simultaneously. the movable pulley can generate the force twice the lifting weight, and the moment from the lifting weight can adjust directly from the movement of pulley, to balance the moment from the suspended load automatically. meanwhile, the lifting weight can be also changed to achieve the close even equal peak powers in the up and down strokes, and to reduce the power fluctuation of motor. so the dynamic tracking balance can effectively reduce the matching power capacity of the pump and improve the mechanical efficiency in terms of energy saving effect [17]. now the preliminary industrial application of the beamtype pumping unit with dynamic tracking balance has been promoted in yanchang oilfield in western china, and the result shows that the energy saving effect of dynamic tracking balance is remarkable. however, the fact is that the developed small-scale pumping unit cannot meet the increasing requirements of large liquid extraction and deep well pumping. therefore, a large-scale beam-type pumping unit with dynamic tracking balance as well as its supporting intelligent control system have been put on the agenda since 2016. as a new type of pumping unit, its technical features and dynamic strength of the key components are worthy of attentions. so far, the kinematic and stress analysis of the key components of beam-type pumping unit are available [18-20]. however, these work are mainly focus on the high-slip motors and double horse-head pumping units [21-23]. no previous research crank horse-head sucker-rod lifting weight beam crank lifting pulley system bracket connecting rod motor base movable pulley b. wang, et alii, frattura ed integrità strutturale, 57 (2021) 291-299; doi: 10.3221/igf-esis.57.21 293 work has been done to study the dynamic behavior of beam-type pumping unit with dynamic tracking balance. to make up this deficiency and provide the guidance of the structural design, in this paper, the working principle and efficiency of beam-type pumping unit with dynamic tracking balance are investigated, and the dynamic strength analysis of the key components are analyzed by the finite element method. technical features of dynamic tracking balance working principle he beam-type pumping unit with dynamic tracking balance is composed of base, bracket, front-mounted beam, horse-head, lifting pulley system, crank, connecting rod, motor and other parts, as shown in figure 2. the frontmounted beam is hinged on the bracket, and is driven to swing up and down by the crank-connecting rod system. the steel wire rope connected with the balance weight is fixed on the bracket, which can apply the force to the beam through a group of pulleys, to balance with the moment to the bracket caused by the suspension load from the sucker rod. the crank-connecting rod mechanism changes the rotation of crank wheel driven by motor into the up and down swing of the traveling beam through the reciprocating push-pull motion of the connecting rod. when the beam swings up, the lifting moment from the gravity of the lifting weight is applied to the beam assisting the oil pumping, when the beam swings down, the lifting block is raised to accumulate the potential energy. the main technical features of the developed beam pumping unit with dynamic tracking balance are listed as follows: (1) the support and the bracket can bear all the pumping load and counterweight load, and the operation safety is excellent. (2) the designed pulley block mechanism can generate the balance moment with less lifting blocks and it is convenient to increase or decrease the balance weight. (3) the swing angle of the front traveling beam is small, so the mechanism can run smoothly. (4) the hanging rope is in good neutral position, and the service life of the pump rod ban be extended. (5) the forces of the driving parts is smaller than those in the conventional beam pumping unit. (6) the motor power can be reduced and the situation of negative torque can be prevented, which greatly improves the service life of the motor. benefited from the above design, the beam-type pumping unit with dynamic tracking balance can better adapt to different well conditions. at the same time, the motion characteristics are completely controllable, and the pumping unit exhibits the performance of high efficiency and energy saving, safe and convenient management. type of bumping balance (%) effective power (%) system efficiency (%) electricity consumption per ton liquid lifting 100 meter (kwh/100m·t) beam-type pumping with dynamic tracking balance 113.12 1.09 13.54 2.01 102.01 1.09 11.71 2.32 107.57 1.09 12.63 2.17 traditional beam-type pumping 134.54 1.09 12.55 2.17 69.17 0.78 9.52 2.86 73.13 0.78 9.28 2.93 72.38 0.81 9.75 2.79 87.31 0.87 10.28 2.69 table 1: comparison of balance and power efficiency between the traditional beam-type pumping and beam-type pumping with dynamic tracking balance. t b. wang, et alii, frattura ed integrità strutturale, 57 (2021) 291-299; doi: 10.3221/igf-esis.57.21 294 balance effect and production efficiency at present, the conventional large-scale beam-type pumping unit has been replaced by the dynamic tracking balanced one in shuai 5-17 oil well in the huadong oilfield of china. the differences of load balance and operational efficiency between the conventional beam pumping unit and dynamic tracking balanced one are listed in table 1. it can be seen that the overall performance of beam-type pumping unit with dynamic tracking balance outweighs that of the conventional one, which attributes to the fact that the dynamic tracking balance can effectively improve the effect of load balance and reduce the power loss. figure 3: the comparison of load-displacement curves (a. traditional beam-type pumping; b. beam-type pumping with dynamic tracking balance). the load-displacement curves of the traditional beam-type pumping unit and dynamic tracking balanced one are compared in figure 3. the load-displacement curve of the beam-type pumping unit with dynamic tracking balance is more regular than that of the conventional one. the included area of the load-displacement curve of the pumping unit with dynamic tracking balance is smaller, which means that less power is needed during the oil extraction. the curve fluctuation of the dynamic tracking balance is also small, this fact indicates the vibration of suspension load is small and the whole pumping unit runs more smoothly. in addition, the down-stroke (in green) in load-displacement curve mainly reflects the load fluctuation and the storage of potential energy during the lifting of balance weight. the curve of dynamic tracking balanced one in the down-stroke is much stable than that of the conventional unit and the efficiency of load balance is better. dynamic analysis of the key components analysis of suspension load he mechanism diagram of the beam-type pumping with dynamic tracking balance is shown in figure 4. the crank, the horse-head and beam are subjected to the torque m from the motor, the suspension load p1 and the balance weight p2. in the up-stroke and down-stroke processed, the suspension loads can be expressed as [2, 24] + + +  − −  −   1u 1d = = ju iu vu u jd id vu d p w f w f w w p w w （1） where wju, wiu, wvu and fu are the static load, inertial load, vibration load and friction load in the up-stroke, respectively, and wjd, wid, wvd and fd are the static load, inertial load, vibration load and friction load in the down-stroke, respectively. when the bottom of the oil tubing is anchored, the vibration load could be ignored, then equation (1) can be rewritten as         + +      −+ − + + − − − −  1u 1d ( g g )= ( ( ) g g ( g g ) ( = ) g )l p r u r r r r p p l m p r l r r r p p l m p rl p r d a a p a l l gh p a a f a a f a w w a a l l gh a w （2） displacement/ m l o a d / k n a l o a d ( k n ) displacement (m) l o a d / k n displacement/ m b displacement (m) l o a d ( k n ) t b. wang, et alii, frattura ed integrità strutturale, 57 (2021) 291-299; doi: 10.3221/igf-esis.57.21 295 where ρr and ar are the density and cross-section area of sucker rod, g is the acceleration of gravity, lp is the length of sucker rod string, ρl is the density of liquid in the well, ap the cross-section area of plunger, hm is the submergence depth, wr and wl are the weights of sucker rod and liquid column, ε is the correction coefficient of acceleration, and ar is the acceleration of sucker rod. figure 4: mechanism diagram of beam-type pumping with dynamic tracking balance. the balance weight p2 can be determined by the balance of the beam. the moment balance of the rotating center of the beam yields:   + + − = 1 a l l z z c b 2 cos 2 cos y y p p l g l g l f l p l （3） where g1 is the weight of the horse-head, gy is the weight of the beam, fz is the reaction force from connecting rod,θz is the angle between connecting rod force and horizontal line, θp is the angle between steel wire rope of upper moving pulley on the beam and horizontal line, and la is the distance from suspension point to rotation center of the beam, lb is the distance from moving pulley center to rotation center of the beam, lc is the distance between the bearing center of connecting rod and beam to the rotation center of the beam. in this work, the external loads except the gravity to the pumping unit are listed in table 2, and the stroke distance is 4.5 m. parameter stroke period suspension load p1 (kn) torque m at the crank (kn.m) weight of balance p2 (kn) 4 min 140 37.26 80 5 min 140 43.72 78 6 min 140 49.88 77 table 2: loads of beam-type pumping with dynamic tracking balance at different stroke periods. m 1 p 2 p center of rotation of beam p z b. wang, et alii, frattura ed integrità strutturale, 57 (2021) 291-299; doi: 10.3221/igf-esis.57.21 296 dynamic simulation for key components of beam-type pumping with dynamic trscking balance finite element model he finite element of crank-connecting rod-beam is shown in figure 5. the degrees of freedom of the left end of the beam and the center of crank wheel are constrained by the pin. the crank wheel is applied the angular velocity, and the beam is applied the suspension load at the horse-head. according to the moving track and the center line of the lifting pulley system, a user subroutine is programmed in the abaqus to accomplish the location variations of loading p2 according to the dynamic tracking balance. (a) geometric model (b) finite element model figure 5: the finite element model of the beam-type pumping with dynamic tracking balance. dynamic response of the key components figure 6 demonstrates the variations of displacement, velocity and acceleration of the suspension point. the displacement curve of the suspension point is close to a cosine curve, and its stroke length is close to the design value 4.5 m. according to the speed curve of the suspension point, the speed change of the pumping unit is relatively stable, and there is no speed mutation. when the suspension point is close to the top of the up-stroke and down-stroke, the speed reaches the maximum, and the beam is in the horizontal position, which is very consistent with the motion of a four-bar structure. through the acceleration curve of the suspension point, it can be seen that when the horse head of the pumping unit reaches the upper and lower dead points, the displacement of the suspension point is the largest. at this time, the speed almost approaches to zero, and the acceleration reaches its maximum at the same time. figure 7 shows the von mises stress distribution of the beam and connecting rod under the static maximum load. a cross brace is welded at the bottom of the beam to support the connecting rods. the maximum stress of the beam occurs at the junction of the beam and the cross brace, and the maximum stress is 25.05 mpa, as shown point a in figure 7(a). the cross brace and connecting rod are connected by pin, and the maximum stress on both sides appears at the bottom of the joint, and the maximum stress is 21.87 mpa, as shown in figure 7(b). figure 8 shows the dynamic von mises stress variations of points a and b in the oil extraction process. it can be seen that the dynamic stress variations exhibit a good periodicity, which is consistent with the actual stroke cycle. the maximum von mises stresses of points a and b are 36.96 mpa and 27.83 mpa. it can be concluded that dynamic load factors of the beam and connecting rod are 1.48 and 1.27, respectively. the pumping unit is made of 45 carbon steel with yield stress 425 mpa. therefore, the key components of the designed beam-type pumping with dynamic tracking balance can meet the requirement of strength. t b. wang, et alii, frattura ed integrità strutturale, 57 (2021) 291-299; doi: 10.3221/igf-esis.57.21 297 (a) displacement (b) velocity and acceleration figure 6: motion response of the suspension point. (a) beam (b) connecting rod figure 7: the von mises stress of the beam and the connecting rods under the static maximum load -6 -4 -2 0 2 4 6 0 60 120 180 240 300 360 420 480 d is p lc a m e n t o f su se n si o n p o in t (m ) time (s) displacement -0.04 -0.03 -0.02 -0.01 0 0.01 0.02 0.03 0.04 0.05 -0.1 -0.08 -0.06 -0.04 -0.02 0 0.02 0.04 0.06 0.08 0.1 0 60 120 180 240 300 360 420 480 v e le c it y ( m /s ) time (s) velocity acceleration 2 a c c e le ra ti o n ( m /s ) point a point b b. wang, et alii, frattura ed integrità strutturale, 57 (2021) 291-299; doi: 10.3221/igf-esis.57.21 298 figure 8: the von mises stress variation with time at points a and b (stroke period: 4 min). conclusion n the present study, the technical feature of beam-type pumping unit with dynamic tracking balance is analyzed. when compared with the conventional beam-type pumping unit, the pumping unit with dynamic tracking balance has a better balance effect and production efficiency. benefit from the dynamic tracking balance design, it has a more regular load-displacement curve and effectively reduce the load fluctuation in the operation process. according to the dynamic analysis, the dynamic stress variations of the key components of the beam-type pumping unit with dynamic tracking balance are obtained. the results show that the maximum in the beam and connecting rod are 36.96 mpa and 27.83 mpa, and the structural design of the pumping unit with dynamic tracking balance is reasonable and efficient. acknowledgments he research work is supported by the natural science foundation of shandong province (no. zr2020me092), the national natural science foundation of china (no.51404286), and the fundamental research funds for the central universities of china (no.20cx02308a). references [1] feng, z.m., guo, c.h., zhang, d.s., cui, w., tan, c.d., xu, x.f., zhang, y. (2020). variable speed drive optimization model and analysis of comprehensive performance of beam pumping unit. journal of petroleum science and engineering, 191, pp.107155. doi: 10.1016/j.petrol.2020.107155. [2] lu, j. m, he, j.p, mao, c.x, wu, w.w., wang, d., lee, w.j. (2014). design and implementation of a dual pwm frequency converter used in beam pumping unit for energy saving. ieee transactions on industry applications, 50(5), pp.2948–2956. doi: 10.1109/tia.2014.2304621. [3] langbauer c. (2018). sucker rod pumping system optimisation based on a novel finite elements analysis. spe-192475ms, spe middle east artificial lift conference and exhibition, pp.1–13. doi: 10.2118/192475-ms. [4] kochtik, d., langbauer, c. (2018). volumetric efficiency evaluation of sucker-rod-pumping applications performed on a pump testing facility. spe-192454-ms. spe middle east artificial lift conference and exhibition, pp.1–11. doi: 10.2118/192454-ms. 0 10 20 30 40 50 0 40 80 120 160 200 240 280 320 360 400 440 480 m is e s st re ss ( m p a ) time (s) point a point b i t https://onepetro.org/search-results?f_allauthors=langbauer+clemens https://onepetro.org/spemeal/proceedings/18meal/1-18meal/d011s003r003/214648?searchresult=1 https://doi.org/10.2118/192475-ms https://onepetro.org/search-results?f_allauthors=langbauer+clemens https://doi.org/10.2118/192454-ms https://doi.org/10.2118/192454-ms b. wang, et alii, frattura ed integrità strutturale, 57 (2021) 291-299; doi: 10.3221/igf-esis.57.21 299 [5] long, q. z., gui, j. c., zhang, x., fu, h.l. (2016). study on mechanical performance simulation method of key components in double horse head pumping unit. ieee international conference on ubiquitous robots & ambient intelligence, pp.152–156. doi: 10.1109/urai.2016.7734044. [6] wu, w., xu, t., he, p.f. (2019). development of analysis and optimization software for dual horse head pumping unit with single arc back horse head based on gui editor. iop conference series: earth and environmental science 242, pp.022052. doi: 10.1088/1755-1315/242/2/022052. [7] feng, z.m, zhang, j.d., gu, h.b., luan, y.w. (2013). research on energy-saving technology of crank balanced pumping unit. research journal of applied sciences engineering and technology, 6(22), pp.4152–4157. doi: 10.19026/rjaset. 6.3525. [8] elmer, w.g., elmer, j.b. (2018). pump-stroke optimization: case study of twenty-well pilot. spe production & operations, 33, pp.419–436. doi: 10.2118/181228-ms. [9] leng, x.m., liu, h. t. (2007). design on the high-efficiency pm synchronous motor with high start torque in purpose of drawing out oil. electrical machinery technology, 3, pp. 5–7. (in chinese) [10] feng, z., ma, q.y., liu, x.l., cui, w., tan, c.d., liu, y. (2020). dynamic coupling modelling and application case analysis of high-slip motors and pumping units. plos one, 15(1), pp. e0227827. doi: 10.1371/journal.pone.0227827. [11] luo, y. l., cui, x. s., zhao, h. s. (2011). a multifunction energy-saving device with a novel power-off control strategy for beam pumping motors. ieee industry applications society 56th annual petroleum and chemical industry conference, anaheim, ca, usa, pp. 1606–1611. doi: 10.1109/pcicon.2009.5297164. [12] gogolyuk, p., lysiak, v., grinberg, i. (2008). influence of a frequency control strategies on induction motor-centrifugal pump unit and its modes. ieee international symposium on industrial electronics, pp. 656–661. doi: 10.1109/isie. 2008.4676893. [13] he, j.p., ji, k., xu, m., mei, g.z., lin, d.r., xia, h.j. (2018). analysis of variable frequency energy-saving operation of beam pumping unit. iop conference series: materials science and engineering, 452, 4, pp.042185. doi: 10.1088/1757-899x/452/4/042185. [14] lv, h.q., liu, j., han, j.q., an, j. (2016). an energy saving system for a beam pumping unit. sensors, 16(5), pp.685. doi: 10.3390/s16050685. [15] abdullah, a., luis, v.r., antonio, a.m., angus, m., haytham, r., khalid, s., dimas, l.p., amur, h., khadija, s., shehu, a. kevin, d.a. (2017). self optimizing thermal field using beam pumps with variable speed drive. spe-188137-ms. spe kingdom of saudi arabia annual technical symposium and exhibition, pp. 1–11. doi: 10.2118/188137-ms. [16] napoles, j., leon, j.i., portillo, r., franquelo, l.g., aguirre, m.a. (2010). selective harmonic mitigation technique for high-power converters. ieee transactions on industrial electronics, 57(7), pp.2315–2323. doi: 10.1109/tie.2009. 2026759. [17] liu, l.h. (2019). calculation and study of balance performance of oil pumping unit with dynamic balance. machinery, 11(45), pp.27–30. (in chinese) [18] chang, z.y., yu, y.q., qi, y.g. (2017). study on dynamic characteristics of hydraulic pumping unit on offshore platform. china ocean engineering, 31(006), pp.693–699. doi:10.1007/s13344-017-0079-1. [19] larrainzar, c., korin, i., ipiña, j. p. (2010). analysis of fatigue crack growth and estimation of residual life of the walking beam of an oilfield pumping unit. engineering failure analysis, 17(5), pp.1038–1050. doi:10.1016/j.engfailanal. 2009.12.003. [20] carpenter, c. (2015). reliability improvement in beam pumps by use of a unique methodology. journal of petroleum technology, 67, pp.96–98. doi: 10.2118/0715-0096-jpt. [21] bhagavatula, r., fashesan, o. a., heinze, l. r., lea, j.f. a computational method for planar kinematic analysis of beam pumping units. journal of energy resources technology, 2007, 129(4), pp.300. doi: 10.1115/1.2790981. [22] ding, h., xie, j.f., bai, z.q., li, y., li, h.b. (2019). fracture analysis of a connecting rod for oil pumping unit in china western oilfield. engineering failure analysis, 105, pp.313-320. doi:10.1016/j.engfailanal.2019.07.021. [23] hansen, b., tolbert, b., vernon, c., hedengren, j.d. (2019). model predictive automatic control of sucker rod pump system with simulation case study. computers & chemical engineering, 121, pp.265–284. doi: 10.1016/j.compchemeng. 2018.08.018. [24] gibbs, s.g. (1975). computing gearbox torque and motor loading for beam pumping units with consideration of inertia effects. journal of petroleum technology, 27 (9), pp.1153–1159. doi: 10.2118/5149-pa. https://doi.org/10.1109/urai.2016.7734044 https://doi.org/10.1109/pcicon.2009.5297164 https://xueshu.baidu.com/s?wd=author%3a%28lg%20franquelo%29%20&tn=se_baiduxueshu_c1gjeupa&ie=utf-8&sc_f_para=sc_hilight%3dperson https://xueshu.baidu.com/s?wd=author%3a%28ma%20aguirre%29%20&tn=se_baiduxueshu_c1gjeupa&ie=utf-8&sc_f_para=sc_hilight%3dperson https://www.sciencedirect.com/science/article/pii/s135063070900288x#! microsoft word numero_34_art_17 b. žužek et alii, frattura ed integrità strutturale, 34 (2015) 160-168; doi: 10.3221/igf-esis.34.17 160 focussed on crack paths effect of segregations on mechanical properties and crack propagation in spring steel b. žužek, m. sedlaček, b. podgornik institute of metals and technology, lepi pot 11, si-1000 ljubljana, slovenia borut.zuzek@imt.si abstract. considerable efforts have been made over the last decades to improve performance of spring steels, which would increase the service time of springs and also allow vehicles weight reduction. there are different possibilities of improving properties of spring steels, from modifying the chemical composition of steels to optimizing the deformation process and changing the heat treatment parameters. another way of improving steel properties is through refining the microstructure and reducing amount of inclusions. therefore, the focus of the current investigation was to determine the effect of more uniform and cleaner microstructure obtained through electro-slag remelting (esr) of steel on the mechanical and dynamic properties of spring steel, with special focus on the resistance to fatigue crack propagation. effect of the microstructure refinement was evaluated in terms of tensile strength, elongation, fracture and impact toughness, and fatigue resistance under bending and tensile loading. after the mechanical tests the fracture surfaces of samples were analyzed using scanning electron microscope (sem) and the influence of microstructure properties on the crack propagation and crack propagation resistance was studied. investigation was performed on hot rolled, soft annealed and vacuum heat treated 51crv4 spring steel produced by conventional continuous casting and compared with steel additional refined through esr. results shows that elimination of segregations and microstructure refinement using additional esr process gives some improvement in terms of better repeatability and reduced scattering, but on the other hand it has negative effect on crack propagation resistance and fatigue properties of the spring steel. keywords. spring steel; crack propagation; electro-slag remelting; segregations; fracture toughness. introduction ncreasing demands of industry, especial automotive industry on performance improvement of steels put a lot of pressure on the steel and steel parts producers. the pressure is in weight reduction and cost savings what governs the producers in new design concepts and further material development. weight reduction is very important because it reduces costs and even more importantly it reduces fuel consumption and co2 pollution in automotive industry. one of the biggest fuel consumers and polluters are trucks, where redesign and use of lighter high strength leaf springs can bring considerable benefits. beside lower weight of springs, reduced dimensions also allow increased flexibility in design, enabling more room for additional safety components. traditional parabolic leaf springs used in suspension systems of truck front axles are usually made of two leafs, and serve two main purposes: support the weight of the trailer and also i b. žužek et alii, frattura ed integrità strutturale, 34 (2015) 160-168; doi: 10.3221/igf-esis.34.17 161 provide the spring function in the suspension system. with the new spring designs, eventually aiming at a single leaf solution, savings of over 20% of the total weight of the spring can be expected. however, this would also lead to about 10-15% increase in spring maximum stress, which requires better spring steel with ultimate tensile strength of over 2.000 mpa [1,2]. considerable efforts have been made over the last decades to develop high strength spring steels to meet the needs for weight and cost savings in the automotive industry [3]. improved properties of spring steel can be achieved through precise control of chemical composition of steel, optimum heat treatment, micro-alloying, thermomechanical treatment and shot-peening [3-12]. for the martensitic steels the best possibility for strength improvement are achievable trough lowering the austenizing and tempering temperature, which leads to the increase of ultimate tensile strength but on the other hand it reduces the steel ductility and toughness [8,13]. however, in the case of springs improvement in strength should not degrade other spring steel properties such as formability and fatigue resistance [6]. another way of improving spring steel strength is through grain refinement [5,6,14], mainly based on micro-alloying and thermomechanical treatment. the addition of certain alloying elements has been reported to effectively improve spring steel strength as well as sag resistance [3]. si of up to 2% was found to improve properties through the refinement of tempered carbides obtained by retardation of ε-carbide conversion to cementite during tempering [3,15]. the addition of nb and v, has also been reported beneficial due to the precipitation and dispersion of fine micro-alloyed carbonitrides [9]. further improvement in tensile properties can be obtained through deformation of austenite prior to quenching [8]. improvement is related to refined austenite grains and to the austenite grain substructure. those conditions reflect into finer structured martensite, i.e. refined block size, with no or refined carbides at the prior austenite grain boundaries. most commercial steels, including spring steels contain impurities that significantly influence the ductility and toughness, with the loss in properties being dependent on the impurity element concentration [16]. the well-known embrittlement phenomena observed around 350°c is such an example where grain boundary segregation of impurity element together with carbide films at grain boundaries deteriorate the mechanical properties of the steel [17]. however, there are also nonmetallic inclusions, which depending on the type and size, may further degrade spring steel properties [18-20]. in the case of tool steels microstructure refinement and properties improvement can be achieved through utilization of electro-slag remelting (esr) [21]. uniform, relatively rapid solidification in esr with highly reactive slag leads to an improvement in the chemical uniformity and uniformity of macrostructure, greatly improved cleanliness and reduced segregation tendency, removal of exogenous oxide inclusions and substantial sulphur reduction [21]. microstructural features such as the eutectic cell size and the eutectic carbide particle size are also reduced. these features, beside other, result in improved hot workability and better ductility and fatigue properties of tool steels [22]. it has been shown, that the surface defects and inclusions have a huge effect on the fatigue life and on the fracture surface appearance, and it can also change the s-n property from duplex to single one or vice versa [23]. the condition of the surface of spring steel specimens, for instance just the grinding direction can change the fracture of the specimen from the surface-induced failure to the interior-induced failure [24]. the aim of the presented research work was to investigate the possibility of refining spring steel microstructure using electro-slag remelting and to determine its effect on the mechanical and dynamic properties of commercial 51crv4 spring steel, with the focus on the resistance to fatigue crack propagation. experimental material and heat treatment aterial used in this investigation was commercial 51crv4 spring steel produced by a conventional casting process used for the research in [25]. two charges of steel (chemical composition of both charges is given in tab. 1) were cast in a billets (180x180 mm). one charge, used as a reference and denoted ccc was directly hot rolled in strips (25x90 mm) and soft annealed, while the other, denoted esr was first electro-slag remelted and then hot rolled and soft annealed under the same conditions as the first charge (ccc). for each charge adequate specimens were taken from hot rolled and soft annealed stripes in the rolling direction and vacuum heat treated in a vacuum furnace with uniform high-pressure gas-quenching using nitrogen gas at a pressure of 5 bar. after heating (10°c/min) to the austenitizing temperature of 870°c, specimens were soaked for 10 min, gas quenched to a temperature of 60°c, and then single tempered for 1h at 300, 375 and 475°c, respectively. m b. žužek et alii, frattura ed integrità strutturale, 34 (2015) 160-168; doi: 10.3221/igf-esis.34.17 162 charge c si mn p s cr al cu v esr 0.53 0.29 0.94 0.010 0.003 1.07 0.025 0.18 0.16 ccc 0.54 0.33 0.97 0.012 0.007 1.10 0.006 0.17 0.17 table 1: chemical composition of ccc and esr spring steel charges (mas. %). mechanical testing mechanical properties involved tensile test, hardness measurement, as well as fracture and impact toughness analysis. tensile test according to en iso 6892-1 a224 was performed on standard b10x50 mm specimens using universal testing machine instron 8802, and all standard tensile test parameters were determined. fracture toughness measurement were performed on non-standard circumferentially notched and fatigue-precracked tensile-bar specimens (fig. 1), designated cnptb specimens [26]. fatigue pre-crack of about 0.5 mm was created under rotating-bending loading before the final heat treatment [27]. using instron 8802 tensile-test machine and cross-head speed of 1.0 mm/min load at fracture was measured and fracture toughness kic calculated using eq. 1 [28]: 3 2 1.27 1.72ic p d k d d          (1) where p is the load at failure, d the outside non-notched diameter (10 mm), and d the diameter of the instantly fractured area. eqn. (1) is valid for 0.5 < d/d < 0.8 and linearly elastic behavior, as displayed by all investigated specimens. figure 1: a) cnptb specimen, circumferentially notched and fatigue-precracked (units in mm), b) detail on notch marked on fig.1a. impact toughness was determined on charpy v-notch specimens (kv2) according to standard en iso 148-1 using 300 j pendulum. tests were performed at room and sub-zero temperatures of 0°c, -20°c and -40°c in order to reveal ductile to brittle transition temperature (dbtt), carried out for specimens tempered at 475°c. finally, the rockwell hardness measurements (hrc) were performed on each cylindrical specimen using an instron b2000 hardness testing machine. dynamic testing fatigue properties were determined under bending as well as tensile-compression loading. bending fatigue testing was performed on a rumul cracktronic resonant machine using standard 10x10x55 mm charpy v-notch test specimens. the testing resonant stress frequency was 175 hz using a sinusoidal waveform at a stress ratio r of 0.1. a constant amplitude bending stress, ranging between 275 mpa and 430 mpa was used. a criterion of specimen failure was a drop of inherent oscillation for more than 3%, where fatigue cracks occurred in a depth of up to 3 mm. fatigue testing under tension-compression loading were conducted in servo hydraulic instron 8802 dynamic test machine under the conditions of r = -1 and sine wave of 30 hz. tests were performed on polished hourglass-shaped fatigue specimens with a gauge length of 38 mm and neck diameter of 7.5 mm. maximum tensile stresses were in the range between 500 and 780 mpa. p p l0 d d 60° detail 1 8 1 0 7 ,1 1 2 15 l = 120t 10 l = 60v l = 500 a b b. žužek et alii, frattura ed integrità strutturale, 34 (2015) 160-168; doi: 10.3221/igf-esis.34.17 163 figure 2: microstructures of ccc specimens (a), (c) and (e) and esr specimens (b), (d) and (f) of investigated spring steel in a longitudinal direction. all microstructures were revealed by nital etching, with figs. (e) and (f) over-etched to show the segregation phenomenon. results and discussion microstructure icrostructure of examined spring steel was investigated using light microscope (lm) as well as scanning electron microscope (sem). microstructure of conventionally cast (ccc) and electro-slag remelted (esr) spring steel after hot rolling and soft annealing is shown in fig. 2. microstructure for both charges of steel consists of fine m a b c d e f b. žužek et alii, frattura ed integrità strutturale, 34 (2015) 160-168; doi: 10.3221/igf-esis.34.17 164 carbides in ferrite phase (fig. 2a and 2b). carbides are mainly distributed along previous martensitic laths, with some of the carbides being slightly coarsened, mostly those along primary ferrite grain boundaries (fig. 2c and 2d). no obvious difference in size and distribution of carbides between ccc and esr specimens can be noticed. nevertheless, in the case of esr specimens more homogeneous microstructure was obtained without distinctive segregations and reduced number of non-metallic inclusions (fig. 2e and 2f). additional remelting of steel trough esr also slightly reduced the grain size, according to standard en iso 643 from g10 for ccc specimens to g11 for esr specimens (fig. 2c and 2d). beside these, as indicated in tab. 1, concentration of p and s, as well as other alloying elements has been slightly reduced by esr. on one hand esr resulted in refined microstructure of spring steel, but on the other hand esr also caused the appearance of some al2o3 inclusions [27], otherwise absent in ccc specimens. all three different tempering temperatures during heat treatment resulted in the martensitic microstructure, with very distinctive segregations being observed only in the case of ccc specimens. mechanical and toughness properties after vacuum heat treatment hardness of both ccc and esr spring steel specimens was more or less the same. more uniform microstructure of esr specimens with reduced number of inclusions increased yield and tensile strength. at the lowest tempering temperature (300°c) yield strength has been increased from 1735 mpa to 1755 mpa and tensile strength from 1960 mpa to 1990 mpa. for the highest tempering temperature (475°c) yield strength has been increased from 1410 mpa to 1420 mpa and tensile strength from 1480 mpa to 1485 mpa when using esr refining method. however, the increase was less than 1.5%. on the other hand esr greatly reduced scattering of results, and increased contraction for up to 40%, especially for the lowest tempering temperature. more pronounced effect of esr refinement was observed in the case of impact toughness. for ccc spring steel, tempered at 475°c impact toughness at 20°c was 20.6 j. by decreasing testing temperature to 0°c impact toughness of ccc spring steel dropped to 19.9 j and below -20°c even to 16.0 j. on the other hand, impact toughness for esr specimens at 20°c increased to 22.0 j, which even at the lowest testing temperature of -40°c didn't dropped below 21.5 j, thus showing much better resistance to low temperature brittleness. additional esr refinement of investigated spring steel had practically no influence on the steel fracture toughness level. however, through more uniform microstructure and reduced number of inclusions scattering was reduced and fractured surfaces differs significantly (fig. 3). in the case of ccc spring steel specimens fracture toughness after tempering at 300°c was 25.8±1 mpa m1/2 and increased with higher tempering temperature at 375°c to 29.2±0 mpa m1/2 and finally increased to 92.3±1 mpa m1/2 at 475°c. on the other hand, for esr specimens fracture toughness improvement was only marginal, increasing to 25.9±7 mpa m1/2, 31.0±0 mpa m1/2 and 92.8±1.8 mpa m1/2 when tempered at 300°c, 375°c and 475°c, respectively. figure 3: fractured surface of kic-test specimens tempered at 475°c (a) ccc and (b) esr. fatigue resistance microstructure refinement through esr, in contrast to static mechanical properties, didn't had any positive effect on fatigue properties of the investigated spring steel. both ccc and esr spring steel specimens showed the same level of scattering and confidence at dynamic bending testing. nevertheless, results of the performed tests show, that conventional continuous cast spring steel (ccc) has better fatigue resistance (fig. 4). for ccc spring steel specimens tempered at a b b. žužek et alii, frattura ed integrità strutturale, 34 (2015) 160-168; doi: 10.3221/igf-esis.34.17 165 300°c fatigue failure at bending stress level of 330, 380 and 430 mpa occurred after approximately 120.000, 50.000 and 30.000 cycles, respectively. at the highest tempering temperature of 475°c fatigue life at given bending stress levels increased to approx. 170.000, 75.000 and 45.000 cycles. the number of bending cycles till failure at the same stress levels has been shortened for 10-15% when using esr refinement, as clearly shown in fig. 4. figure 4: effect of esr refinement and segregations removal on bending fatigue resistance. effect of esr process shown in microstructure refinement and segregations removal has even more negative effect on fatigue properties of spring steel under tensile-compression loading mode. however, these tests were carried out only for tempering temperature of 475°c. for the esr test specimens tempered at 475°c fatigue failure at 660, 720 and 780 mpa stress level occurred after 29.000, 43.000 and 54.000 cycles, respectively. on the other hand, classical ccc specimens tempered at 475°c showed between 5 to 20% longer lifetime, lower scattering and about 5% higher tensile fatigue limit of 650 mpa, as shown in fig. 5. these results indicate positive effect of elongated segregations being present in ccc spring steel on its fatigue resistance. however, this positive effect of segregations can be expected only when segregations are oriented perpendicular to the crack propagation direction. on the other hand, presence of some al inclusions after esr, as revealed by sem microstructure analysis has further negative effect on the fatigue resistance of esr refined spring steel, representing critical locations for crack initiation. figure 5: tensile-compression fatigue properties of ccc and esr spring steel, tempered at 475°c. fractographic analysis macrographic investigation of the fractured surfaces reveals positive effect of segregations on the crack propagation resistance. it is assumed that combination of softer sulphide-type non-metallic inclusions in positive segregations (fully martensitic) and harder negative segregations (martensite and bainite) in ccc specimens retard propagation of transversal crack, thus improving spring steel fatigue resistance. fractured surfaces of both ccc and esr samples are shown in fig. b. žužek et alii, frattura ed integrità strutturale, 34 (2015) 160-168; doi: 10.3221/igf-esis.34.17 166 6, where image a presents ccc specimen with more smoother surface in the crack propagation zone and image b presents esr specimen with rougher and sharper fractured surface. the region of crack propagation zone is marked with black dot (fig. 6). figure 6: macrographic image of fractured surfaces (a) ccc specimen, (b) esr specimen. figure 7: sem observation of fractured surfaces (a and c) ccc specimen, (b and d) esr specimen. dc ba b. žužek et alii, frattura ed integrità strutturale, 34 (2015) 160-168; doi: 10.3221/igf-esis.34.17 167 fractured surfaces of specimens exposed to tensile-compression testing were analyzed using sem and fatigue quasiductile fractured surfaces are shown in fig. 7. the images of fractured surface are from the crack propagation zone, where obvious difference between fractured surface of ccc (fig. 7a and 7c) and esr (fig. 7b and 7d) can be seen. in the case of ccc specimens fractured surface is smoother and consist of large number of separated short micro cracks being oriented perpendicular to the main crack patch through the specimen. it can be concluded that those micro cracks are formed during propagation of the main crack trough the specimen, when it reaches the softer negative segregation region in the material, containing sulphide-type non-metallic inclusions. at those inclusions the main crack changes its direction from transversal to longitudinal, thus retarding crack propagation rate. energy needed for changes in the crack propagation direction coupled with longer crack propagation path also results in better fatigue resistance of ccc specimens. in the case of fractured surface of esr specimens (fig. 7b and 7d) very distinctive regions of fracture can be found, with staircase-like fracture regions being clearly visible. fatigue test results show, that the absence of segregations, which leads to vivid larger staircase-like fracture regions and faster crack propagation result in reduced fatigue strength of the material, corresponding to reduced lifetimes of the spring steel. conclusions dditional process of electro-slag remelting contributes to more uniform and refined microstructure of spring steel as well as elimination of segregations. more uniform and refined microstructure mostly results in better repeatability and smaller scattering in mechanical and fatigue properties of examined spring steel. results of this investigation revealed that esr process increase mechanical properties of hot rolled and heat treated spring steel. it contributes to considerable increase in impact toughness, especially at sub-zero temperatures, while increase in hardness, tensile strength and fracture toughness is less pronounced. on the other hand, esr results in reduced fatigue resistance and fatigue limit of the spring steel investigated. for both, tensile-compressive and bending loading conditions elimination of segregations and presence of some al non-metallic inclusions contributes to reduced cracking resistance and deteriorated fatigue properties of spring steel. in the examined fractured surfaces additional esr process leads to formation of staircase-like fracture regions with reduced crack propagation resistance and consequently to reduced fatigue properties of spring steel. in the case of the ccc specimens crack patch is changed at softer inclusions in the positive segregations, thus leading to formation of a large number of smaller cracks perpendiculars to the main crack direction. acknowledgments uthors would like to thanks štore steel company for the financial support and to slovenian research agency (arrs) for the support through research program p2-0050. references [1] perrard, f., charvieux, f., languillaume, j., a new spring steel with improved ductility dedicated for high strength parabolic leaf springs, 2nd int. conference super-high strength steels, peschiera del garda, italy, (2010). [2] choi, s., optimization of microstructure and properties of high strength spring steel, ph.d. thesis, posco, korea, (2011). [3] nam, w.j., lee, c.s., ban, d.y., effects of alloy additions and tempering temperature on the sag resistance of si–cr spring steels, materials science and engineering, a289 (2000) 8-17. [4] ona, h., cold roll forming for high tensile strength steel sheet proposition on forming of thin spring steel sheet pipe, journal of materials processing technology, 153–154 (2004) 247-252. [5] ai, j.h., zhao, t.c., gao, h.j., hu, y.h., xie, x.s., effect of controlled rolling and cooling on the microstructure and mechanical properties of 60si2mna spring steel, journal of materials processing technology, 160 (2005) 390-395. [6] ardehali barani, a., ponge, d., raabe, d., refinement of grain boundary carbides in a si–cr spring steel by thermomechanical treatment, materials science and engineering, a426 (2006) 194-201. [7] nie, y.-h., hui, w.-j., fu, w.-t., weng, y.-q., effect of boron on delayed fracture resistance of medium-carbon high strength spring steel, journal of iron and steel research, international, 14 (2007) 53-59. a a b. žužek et alii, frattura ed integrità strutturale, 34 (2015) 160-168; doi: 10.3221/igf-esis.34.17 168 [8] ardehali barani, a., li, f., romano, p., ponge, d., raabe, d., design of high-strength steels by microalloying and thermomechanical treatment, materials science and engineering, a463 (2007) 138-146. [9] zhang, c.-l., liu, y.-z., jiang, c., xiao, j.-f., effects of niobium and vanadium on hydrogen-induced delayed fracture in high strength spring steel, journal of iron and steel research, international, 18 (2011) 49-53. [10] zhang, c.-l., liu, y.-z., zhou, l.-y., jiang, c., secondary hardening, austenite grain coarsening and surface decarburization phenomenon in nb-bearing spring steel, journal of iron and steel research, international, 19 (2012) 47-52. [11] ganesh, p., sundar, r., kumar, h., kaul, r., ranganathan, k., hedaoo, p., tiwari, pragya, kukreja, l.m., oak, s.m., dasari, s., raghavendra, g., studies on laser peening of spring steel for automotive applications, optics and lasers in engineering, 50 (2012) 678-686. [12] li, w., sakai, t., wakita, m., mimura, s., effect of surface finishing and loading condition on competing failure mode of clean spring steel in very high cycle fatigue regime, materials science and engineering, a552 (2012) 301-309. [13] dziemballa, h., manke, l., steel, future for the automotive industry, verlag stahleisen gmbh, dusseldorf, (2005) 341-348. [14] ardehali barani, a., ponge, d., optimized thermomechanical treatment for strong and ductile martensitic steels, materials science forum, 539-543 (2007) 4526-4531. [15] assefpour-dezfuly, m., brownrigg, a., parameters affecting sag resistance in spring steels, metallurgical and materials transactions a, 20 (1989) 1951-1959. [16] shin, j.-c., lee, s., hwa ryu, j., correlation of microstructure and fatigue properties of two high-strength spring steels, international journal of fatigue, 21 (1999) 571-579. [17] krauss, g., mcmahon, c.j., martensite, asm international, materials park, (1992). [18] bytyqi, a., puksic, n., jenko, m., godec, m., characterization of the inclusions in spring steel using light microscopy and scanning electron microscopy, materials and technology, 45 (2011) 55-59. [19] wang, x.h., jiang, m., chen, b., li, h.b., study on formation of non-metallic inclusions with lower melting temperatures in extra low oxygen special steels, science china technological sciences, 55 (2012) 1863-1872. [20] senčič, b., leskovšek, v., fracture toughness of vacuum heat treated spring steel 51crv4. materials and technology, 45 (2011) 67-73. [21] roberts, g., kraus, g., kennedy, r., tool steels. 5th edition, asm international, materials park, (1998). [22] tang, w., wu, x., min, y., xu, l., effect of microstructural homogeneity on mechanical and thermal fatigue behavior of a hot-work tool steel, proceedings of 6th international tooling conference, karlstad university, sweden, (2002) 755-765. [23] li, w., sakai, t., wakita, m., mimura, s., influence of microstructure and surface defect on very high cycle fatigue properties of clean spring steel, international journal of fatigue, 60 (2014) 48–56. [24] li, w., sakai, t., wakita, m., mimura, s., effect of surface finishing and loading condition on competing failure mode of clean spring steel in very high cycle fatigue regime, materials science and engineering: a, 552 (2012) 301–309. [25] podgornik, b., leskovšek, v., godec, m., senčič, b., microstructure refinement and its effect on properties of spring steel, materials science and engineering: a, 599 (2014) 81–86. [26] podgornik, b., žužek, b., leskovšek, v., experimental evaluation of tool steel fracture toughness using circumferentially notched and precracked tension bar specimen, materials performance and characterization, 3 (2014) 1-17. [27] wei, s., tingshi, z., daxing, g., dunkang, l., poliang, l., xiaoyun, q., fracture toughness measurement by cylindrical specimen with ring-shaped crack, eng. fract. mech. 16 (1982) 69-82. [28] gdoutos, e.e., fracture mechanics criteria and applications, kluwer academic publishers, london, (1990). microsoft word numero_33_art_42 d. g. hattingh et alii, frattura ed integrità strutturale, 33 (2015) 382-389; doi: 10.3221/igf-esis.33.42 382 focussed on multiaxial fatigue multiaxial fatigue of aluminium friction stir welded joints: preliminary results d. g. hattingh nelson mandela metropolitan university, private bag x6011, port elizabeth 6000, south africa danie.hattingh@nmmu.ac.za m. n. james university of plymouth, drake circus, devon pl4 8aa, england, united kingdom m.james@plymouth.ac.uk l. susmel the university of sheffield, sheffield s1 3jd, united kingdom l.susmel@sheffield.ac.uk r. tovo university of ferrara, via saragat 1, 44100 ferrara, italy roberto.tovo@unife.it abstract. the aim of the present research is to check the accuracy of the modified wöhler curve method (mwcm) in estimating the fatigue strength of friction stir (fs) welded tubular joints of al 6082-t6 subjected to in-phase and out-of-phase multiaxial fatigue loading. the welded samples being investigated were manufactured by equipping an mts i-stir process development system with a retracting tool that was specifically designed and optimised for this purpose. these specimens were tested under proportional and non-proportional tension and torsion, the effect of non-zero mean stresses being also investigated. the validation exercise carried out by using the generated experimental results allowed us to prove that the mwcm (applied in terms of nominal stresses) is highly accurate in predicting the fatigue strength of the tested fs welded joints, its usage resulting in estimates falling with the uniaxial and torsional calibration scatter bands. keywords. friction stir welding; multiaxial fatigue; critical plane. introduction riction stir (fs) welding is a solid-state joining process that results, if applied correctly, in connections characterised by high mechanical performance. the large plastic deformations induced in the weld zone produce dynamically recrystallized fine grains (i.e. in the weld nugget), the low heat input limiting local distortions and the magnitude of residual stresses. these effects are generally beneficial to the dynamic performance of welds. alongside these advantages, f http://www.gruppofrattura.it/pdf/rivista/numero33/audioslides/susmel2/susmel2.html d. g. hattingh et alii, frattura ed integrità strutturale, 33 (2015) 382-389; doi: 10.3221/igf-esis.33.42 383 the process can also be used to join dissimilar metals and alloys that are difficult to be welded metallurgically. there has therefore been a substantial take-up of fs welding in structural manufacturing across a wide range of industrial sectors [1] including ship building [2], transportation [3], and aircraft [4]. in the case of the aircraft industry both the american welding society and nasa have recently published technical standards for friction stir welding of aerospace hardware fabricated from aluminium alloys [5, 6]. whilst the fatigue behaviour of aluminium fs welded joints subjected to uniaxial cyclic loading has been studied in depth over the last two decades (see, for instance, ref. [7] and references reported therein), examination of the state of the art suggests that no systematic theoretical/experimental work has been carried out so far in order to formalise and validate specific criteria suitable for performing the multiaxial fatigue assessment of this type of welded connections. in this complex scenario, this paper summarises a part of a large programme of work on the issue of multiaxial fatigue design for fw welded tubular structures. figure 1: schematic of the tube welding system and final setup on the mts i-stirtm platform. figure 2: retractable tool shoulder (10mm) and pin. figure 3: al 6082-t6 fs welded tubular specimen. pipe welding system for fsw of tubes riction stir welding of tubes presented particular challenges in terms of pin plunge depth, support for the material during welding and arranging tool retraction as not to leave the typical plunge pin hole in the joint line after retracting the tool. an mts i-stir™ process development system (pds) provided the foundation for this work, which involved incorporating a helical sew worm gear motor with a tube support system for the welding process. this drive system control was integrated with that of the i-stir platform to ensure optimal process control. fig. 1 shows a schematic of the worm gear drive and actual integration into the i-stir platform. an important consideration was the development of a small diameter shoulder retracting tool to match the small diameter thin wall tube samples. the retractable pin tool differs from the fixed pin tool in that the pin length can be adjusted during welding. this adjustability allows the welder to compensate for variable plate or component thicknesses, ensuring that the correct ligament between the tool tip and the backing plate is maintained. in addition, the tool tip can be retracted towards the end of the weld thus eliminating the pin exit hole. the elimination of the pin exit hole cannot be realized in all f flange coupling sew helical worm gear motor bearing supports with integrated clamping d. g. hattingh et alii, frattura ed integrità strutturale, 33 (2015) 382-389; doi: 10.3221/igf-esis.33.42 384 applications as the pin must be retracted over a minimum distance or at a rate that prevents the formation of defects. fig. 2 shows the final tool being developed and optimised with a 10 mm shoulder and threaded pin configuration. control of this additional fixture was integrated with that of the i-stir platform. via an iterative optimisation process the optimum values for the manufacturing process variables were determined. this allowed fs welds of high quality to be made in small diameter aluminium tubes. fig. 3 shows a typical al 6082-t6 specimen manufactured by using this innovative fs welding technology. the fs welded tubular samples used to generate the necessary experimental results had outer nominal diameter equal to 38 mm and inner nominal diameter to 31 mm. both the static and fatigue results were determined by testing samples in the as-welded condition. this new fs welding technology was developed and optimised at the nelson mandela metropolitan university (nmmu), south africa. br=0, r=-1 nf=1664764 cycles to failure br= 3 , r=-1, =0° nf=369237 cycles to failure br=1, r=-1, =0° nf=650684 cycles to failure br= 3 , r=-1, =90° nf=173954 cycles to failure br=0, r=0 nf=1071840 cycles to failure br= 3 , r=0, =0° nf=501988 cycles to failure br=1, r=0, =0° nf=857370 cycles to failure br= 3 , r=0, =90° nf=224230 cycles to failure figure 4: examples of the observed macroscopic cracking behavior under biaxial fatigue loading (br=nom,a/nom,a, r=nom,min/nom,max=nom,min/nom,max, = out-of-phase angle). experimental details ince welded joints’ mechanical properties are a suitable indicator of the overall weld quality, several static tests were run by testing the manufactured tubular joints under pure tension as well as under pure torsion. irrespective of the type of applied loading, cracks were seen to initiate at the tip of the undercut resulting from the fs welding process. as a further check of the tensile strength, the axial strength was also determined at the university of plymouth, uk, via microtensile quasi-flat specimens tested by using a gatan microtest 2000ew device. such a systematic experimental investigation resulted in an average value of the ultimate tensile strength for fs welded al 6082-t6 equal to 152 mpa, the axial static strength of the parent material being equal to 303 mpa. this allowed us to prove that the average efficiency of the manufactured welded joints (which is defined as the ratio of weld over parent plate tensile strength) approaches 0.5; this value compares well with the figure of 0.49 which is usually reported for fs welds in 3 mm thick plates of 6082-t6 [8]. the average static strength under torsion was seen to be equal to about 120 mpa. the axial tests were performed at the university of ferrara, italy, by using an mts 810 mod. 318.25 servo-hydraulic axial testing machine. the samples were tested under a load ratio (r=nom,min/nom,max) equal to 0.1 as well as equal to -1. the fatigue behaviour of the al 6082-t6 fs welded specimens under biaxial loading was investigated at the university of sheffield, uk, by using a schenck servo-hydraulic axial/torsional testing machine equipped with two mts hydraulic grips. both the torsional and the biaxial tests were carried out under nominal load ratios equal to -1 and 0. the force/moment controlled tests were run under in-phase and 90° out-of-phase constant amplitude sinusoidal load histories. the pictures seen in fig. 4 show some examples of the typical cracking behaviours displayed by the al 6082-t6 fs welded joints tested under biaxial loading. s d. g. hattingh et alii, frattura ed integrità strutturale, 33 (2015) 382-389; doi: 10.3221/igf-esis.33.42 385 the generated experimental data were post-processed under the hypothesis of a log-normal distribution of the number of cycles to failure for each stress level with a confidence level equal to 95% [9]. the results of the statistical reanalysis are summarised in tab. 1 in terms of sn curves. in particular, br=nom,a/nom,a is the ratio between the amplitudes of the axial and torsional nominal stress, r is the nominal load ratio (r=nom,min/nom,max=nom,min/nom,max),  is the out-of-phase angle, k is the negative inverse slope, a and a are the amplitudes of the axial and torsional endurance limits extrapolated at na=2106 cycles to failure, and, finally, t is the scatter ratio of the amplitude of the endurance limit for 90% and 10% probabilities of survival. to conclude, it is worth observing that the fatigue curves summarised in tab. 1 are determined in terms of nominal stresses referred to the annular section of the parent tube. br r  n. of data k a a t [°] [mpa] [mpa]  -1 9 6.5 33.5 1.58  0.1 10 4.4 18.6 1.82 0 -1 11 10.8 38.9 1.49 0 0 10 9.5 32.9 1.52 3 -1 0 8 5.3 26.2 15.1 1.54 1 -1 0 7 5.3 23.1 23.1 2.13 3 0 0 7 4.2 17.2 9.9 1.74 1 0 0 7 3.2 12.8 12.8 2.00 3 -1 90 7 3.7 18.5 10.7 2.25 3 0 90 7 10.4 23.4 13.5 1.38 table 1: summary of the generated experimental results. fundamentals of the modified wöhler curve method he mwcm is a critical plane approach which predicts the number of cycles to failure via the maximum shear stress amplitude, a, as well as via the mean value, n,m, and the amplitude, n,a, of the stress normal to the critical plane. in this setting, the critical plane is defined as that material plane experiencing the maximum shear stress amplitude, a [10]. the combined effect of the relevant stress components relative to the critical plane is taken into account by means of stress index eff which is defined as follows [11]: , ,n m n aeff a m        (1) in definition (1), m is the so-called mean stress sensitivity index [10]. this index is a material property ranging in between 0 and 1 whose value has to be determined by running appropriate experiments [11]. ratio eff is a stress quantity which is sensitive not only to the presence of superimposed static stresses, but also to the degree of non-proportionality of the applied loading path [10]. the way the mwcm estimates fatigue lifetime under multiaxial fatigue loading is schematically shown via the modified wöhler diagram sketched in fig. 5. this log-log diagram plots the shear stress amplitude relative to the critical plane, a, against the number of cycles to failure, nf. by performing a systematic investigation based on numerous experimental results generated under multiaxial fatigue loading [12-14], it was observed that fatigue damage tends to increase as eff increases. this results in the fact that the corresponding fatigue curve tends to shift downward in the modified wöhler diagram with increasing of eff (fig. 5). by taking full advantage of the classic log-log schematisation which is commonly adopted to summarise stress based fatigue data, the position and the negative inverse slope of any modified wöhler curve can unambiguously be defined via the following linear laws [10, 12-14]: t d. g. hattingh et alii, frattura ed integrità strutturale, 33 (2015) 382-389; doi: 10.3221/igf-esis.33.42 386  eff effk       (2)  re f eff effa b     (3) in relationships (2) and (3), k(eff) is the negative inverse slope, while ref(eff) is the reference shear stress amplitude extrapolated at na cycles to failure (see fig. 5). constants, , a and b are material parameters to be determined experimentally. in particular, by recalling that eff is equal to unity under fully-reversed uniaxial fatigue loading and to zero under torsional cyclic loading [10], the constants in the mwcm’s calibration functions can directly be calculated as follows [10, 14]:        1 0 0eff eff eff eff effk k k k              (4)  ,re 2 a a f eff a eff a              (5) figure 5: modified wöhler diagram. in eq. (4) k(eff=1) and k(eff=0) are the negative inverse slope of the uniaxial and torsional fatigue curve, respectively; in eq. (5) a and a are instead the endurance limits extrapolated at na cycles to failure under fully-reversed uniaxial and torsional fatigue loading, respectively. it is worth pointing out here that the reference shear stress, a,ref(eff), and the negative inverse slope, k(eff), to be used to estimate lifetime under multiaxial fatigue loading are assumed to be constant and equal to a,ref(lim) and to k(lim), respectively, for eff values larger than an intrinsic threshold denoted as lim [10, 11]. this correction, which plays a role of primary importance in determining the overall accuracy of the mwcm, was introduced to take into account the fact that, under large values of ratio eff, the use of the mwcm is seen to results in conservative estimates [15, 16]. according to the experimental results due to kaufman and topper [17], such a high level of conservatism can be ascribed to the fact that, when micro/meso cracks are fully open, an increase of the normal mean stress does not result in a further increase of the associated fatigue damage. this important finding is taken into account by the mwcm via lim that represents the upper bound for stress ratio eff [10, 16]. according to the theoretical framework briefly summarised above, the mwcm can be used to estimate fatigue lifetime by following the simple procedure described in what follows. initially, the maximum shear stress amplitude, a, and the effective critical plane stress ratio, eff, have to be determined at the assumed critical location [18, 19]. subsequently, according to the calculated value for eff, the corresponding modified wöhler curve can directly be estimated from eqs (4) and (5). finally, the number of cycles to failure under the investigated loading path is predicted via the following trivial relationship [10, 14]: log nf log a 1 1 k(eff=0) k(eff=1) na a,ref(eff=0)=a a,ref(eff=1)=a/2 1 k(0<eff<1) a,ref(0<eff<1) 1 k(eff>1) a,ref(eff>1) increasing eff d. g. hattingh et alii, frattura ed integrità strutturale, 33 (2015) 382-389; doi: 10.3221/igf-esis.33.42 387 ( ) , ( ) t effk a ref eff f a a n n            (6) to conclude, it is worth observing that the mwcm has proven to be highly accurate in performing the multiaxial fatigue assessment of conventional welded joints when it is applied not only in terms of nominal [20-22] and hot-spot stresses [23, 24], but also along with the reference radius concept [24-27] as well as the theory of critical distances [26-30]. 1000 10000 100000 1000000 10000000 100000000 1000 10000 100000 1000000 10000000100000000 nf [cycles] nf,e [cycles] axial loading, r=-1 axial loading, r=0.1 torsion, r=-1 torsion, r=0 =0°, =√3, r=-1 =0°, =√3, r=0 =90°, =√3, r=-1 =90°, =√3, r=0 =0°, =1, r=-1 =0°, =1, r=0 ps=90% ps=10% non-conservative conservative torsional scatter band uniaxial scatter band fsw aluminium tubes  br  br  br  br  br  br run out figure 6: accuracy of the mwcm in estimating the fatigue lifetime of the tested al 6082-t6 fs welded joints. validation by experimental data n order to check the accuracy of the mwcm in estimating the fatigue lifetime of the tested fs welded joints, initially the calibration constants in eqs (2) and (3) were determined, according to eqs (4) and (5), by using the fatigue curves generated under fully-reversed uniaxial and torsional fatigue loading (see tab. 1), i.e.:   4.3 10.8eff effk      (7)  re 21.2 38.9f eff eff      [mpa] (8) as proven by the uniaxial fatigue curves summarised in tab. 1, the axial fatigue strength of the investigated fs welded joints was seen to be sensitive to presence of non-zero mean stresses, this holding true even though the specimens were tested in the as-welded condition. as to this aspect, it is interesting to observe that a similar behaviour has been observed also in conventional welded joints tested, in the as-welded condition, under uniaxial fatigue loading (see, for instance, refs [31, 32] and references reported therein). according to this experimental evidence, in this initial investigation the mean stress sensitivity index, m, was simply taken equal to unity [10]. further, owing to the fact that the mwcm was aimed to be applied in terms of nominal stresses, the limit value for stress ratio eff was set equal to 1.3 (i.e., lim=1.3) [10, 20]. after calibrating the mwcm, multiaxial fatigue software multi-feast (www.multi-feast.com) was used to systematically post-process all the experimental results that have been generated so far. the experimental, nf, vs. estimated, nf,e, number of cycles to failure diagram reported in fig. 6 summarises the overall accuracy which was obtained by using the mwcm to predict the lifetime of the fs welded tubular samples being tested. i d. g. hattingh et alii, frattura ed integrità strutturale, 33 (2015) 382-389; doi: 10.3221/igf-esis.33.42 388 the chart of fig. 6 makes it evident that the use of the mwcm resulted in estimates falling within the wider scatter band between the two characterising the fully-reversed uniaxial and torsional fatigue curve used to calibrate the constants in the mwcm’s governing equations. it is possible to conclude by observing that the obtained level of accuracy is certainly satisfactory, since, from a statistical point of view, we cannot ask a predictive method to be more accurate than the experimental information used to calibrate the method itself. conclusions  the novel fs welding process developed via this project is seen to be capable of producing high quality fs welds in aluminium tubular joints. such an advance in joining technology is anticipated to have high industrial impact.  the mwcm applied in terms of nominal stresses is a powerful design tool suitable for performing multiaxial fatigue assessment of fs welded connections.  more work needs to be done in order to formalise a comprehensive design approach suitable for designing fs welded joints against multiaxial fatigue loading by directly post-processing the local linear-elastic stress fields acting on the material in the vicinity of the crack initiation locations. acknowledgements he leverhulme trust (www.leverhulme.ac.uk) is acknowledged for fully supporting the present research investigation (project’s reference number: in-2012-107). references [1] shah, s., tosunoglu, s., friction stir welding: current state of the art and future prospects, in: 16th world multiconference on systemics, cybernetics and informatics, orlando, florida, (2012). (available at www.eng.fiu.edu). [2] colligan, k. j., friction stir welding for ship construction, contract n0014-06-d-0048 for the office of naval research, concurrent technologies corporation, harrisburg, pa, (2004) (available at www.nmc.ctc.com). [3] thomas, w. m. , nicholas, e. d., friction stir welding for the transportation industries, mater. design, 18(4/6) (1997) 269-273. [4] burford, d., widener, c., tweedy, b., advances in friction stir welding for aerospace applications, in: 6th aiaa aviation technology, integration and operations conference, (2006), american institute for aviation and astronautics. doi: 10.2514/6.2006-7730 [5] american national standards institute, aws d17.3/d17.3m:2010, specification for friction stir welding of aluminum alloys for aerospace hardware, american welding society, (2010). [6] msfc technical standard em 30, msfc-spec-3679, process specification – welding aerospace hardware, national space and aeronautics administration, (2012). [7] lomolino, s., tovo, r., dos santos, j., on the fatigue behaviour and design curves of friction stir butt-welded al alloys, int. j. fatigue, 27(3) (2005) 305-316. [8] moreira, p. m. g. p., santos, t., tavares, s. m. o., richter-trummer, v., vilaça, p., de castro, p. m. s. t., mechanical and metallurgical characterization of friction stir welding joints of aa6061-t6 with aa6082-t6, mater. design, 30 (2009) 180-187. [9] spindel, j. e., haibach, e., some considerations in the statistical determination of the shape of s-n cruves, in: r. e. little and j. c. ekvall (eds.), statistical analysis of fatigue data, astm stp 744, (1981) 89–113. [10] susmel, l., multiaxial notch fatigue: from nominal to local stress-strain quantities, woodhead & crc, cambridge, uk, isbn: 1 84569 582 8, (2009). [11] susmel, l., multiaxial fatigue limits and material sensitivity to non-zero mean stresses normal to the critical planes, fatigue fract. eng. mat. struct., 31 (2008) 295-309. [12] susmel, l., lazzarin, p., a bi-parametric modified wöhler curve for high cycle multiaxial fatigue assessment, fatigue fract. eng. mat. struct., 25 (2002) 63-78. t d. g. hattingh et alii, frattura ed integrità strutturale, 33 (2015) 382-389; doi: 10.3221/igf-esis.33.42 389 [13] susmel, l., petrone, n., multiaxial fatigue life estimations for 6082-t6 cylindrical specimens under in-phase and outof-phase biaxial loadings, in: a. carpinteri, m. de freitas and a. spagnoli (eds.), biaxial and multiaxial fatigue and fracture, elsevier and esis, (2003) 83-104. [14] lazzarin, p., susmel, l., a stress-based method to predict lifetime under multiaxial fatigue loadings, fatigue fract. eng. mat. struct., 26 (2003) 1171-1187. [15] susmel, l., tovo, r., lazzarin, p., the mean stress effect on the high-cycle fatigue strength from a multiaxial fatigue point of view, int. j. fatigue, 27 (2005) 928-943. [16] susmel, l., taylor, d., the modified wöhler curve method applied along with the theory of critical distances to estimate finite life of notched components subjected to complex multiaxial loading paths, fatigue fract. eng. mat. struct., 31(12) (2008) 1047-1064. [17] kaufman, r. p., topper, t., the influence of static mean stresses applied normal to the maximum shear planes in multiaxial fatigue, in: a. carpinteri, m. de freitas and a. spagnoli (eds.), biaxial and multiaxial fatigue and fracture, elsevier and esis, (2003) 123-143. [18] susmel, l., a simple and efficient numerical algorithm to determine the orientation of the critical plane in multiaxial fatigue problems, int. j. fatigue, 32 (2010) 1875–1883. [19] susmel, l., tovo, r., socie, d. f., estimating the orientation of stage i crack paths through the direction of maximum variance of the resolved shear stress, int. j. fatigue, 58 (2014) 94–101. [20] susmel, l., tovo, r., on the use of nominal stresses to predict the fatigue strength of welded joints under biaxial cyclic loadings, fatigue fract. engng. mater. struct., 27 (2004) 1005-1024. [21] susmel, l., nominal stresses and modified wöhler curve method to perform the fatigue assessment of uniaxiallyloaded inclined welds, p. i. mech. eng. c-j. mec., 228 16 (2014) 2871-2880. [22] susmel, l., tovo, r., benasciutti, d., a novel engineering method based on the critical plane concept to estimate the lifetime of weldments subjected to variable amplitude multiaxial fatigue loading, fatigue fract. engng. mater. struct., 32 (2009) 441–459. [23] susmel, l., tovo, r., local and structural multiaxial stress states in welded joints under fatigue loading, int. j. fatigue, 28 (2006) 564-575. [24] susmel, l., three different ways of using the modified wöhler curve method to perform the multiaxial fatigue assessment of steel and aluminium welded joints, eng. fail. anal., 16 (2009) 1074–1089. [25] susmel l., sonsino c. m., tovo r., accuracy of the modified wöhler curve method applied along with the rref=1 mm concept in estimating lifetime of welded joints subjected to multiaxial fatigue loading, int. j. fatigue, 33 (2011) 1075-1091. [26] susmel, l., askes, h., modified wöhler curve method and multiaxial fatigue assessment of thin welded joints, int. j. fatigue, 43 (2012) 30–42. [27] susmel, l., four stress analysis strategies to use the modified wöhler curve method to perform the fatigue assessment of weldments subjected to constant and variable amplitude multiaxial fatigue loading, int. j. fatigue, 64 (2014) 38-54. [28] susmel, l., modified wöhler curve method, theory of critical distances and eurocode 3: a novel engineering procedure to predict the lifetime of steel welded joints subjected to both uniaxial and multiaxial fatigue loading, int. j. fatigue, 30 (2008) 888-907. [29] susmel, l., the modified wöhler curve method calibrated by using standard fatigue curves and applied in conjunction with the theory of critical distances to estimate fatigue lifetime of aluminium weldments, int. j. fatigue, 31 (2009) 197-212. [30] susmel, l., estimating fatigue lifetime of steel weldments locally damaged by variable amplitude multiaxial stress fields, int. j. fatigue, 32 (2010) 1057–1080. [31] brandt, u., lawrence, f. v., sonsino, c. m., fatigue crack initiation and growth in almg4.5mn but weldments, fatigue fract. engng. mater. struct., 24 (2001) 117-126. [32] morgenstern, c., sonsino, c. m., hobbacher, a., sorbo, f., fatigue design of aluminium welded joints by the local stress concept with the fictitious notch radius of rf=1mm, int. j. fatigue, 28 (2006) 881-890. microsoft word numero_34_art_5 r. brighenti et alii, frattura ed integrità strutturale, 34 (2015) 59-68; doi: 10.3221/igf-esis.34.05 59 focussed on crack paths effect of fibre arrangement on the multiaxial fatigue of fibrous composites: a micromechanical computational model roberto brighenti, andrea carpinteri, daniela scorza university of parma, italy brigh@unipr.it, andrea.carpinteri@unipr.it, daniela.scorza@nemo.unipr.it abstract. structural components made of fibre-reinforced materials are frequently used in engineering applications. fibre-reinforced composites are multiphase materials, and complex mechanical phenomena take place at limit conditions but also during normal service situations, especially under fatigue loading, causing a progressive deterioration and damage. under repeated loading, the degradation mainly occurs in the matrix material and at the fibre-matrix interface, and such a degradation has to be quantified for design structural assessment purposes. to this end, damage mechanics and fracture mechanics theories can be suitably applied to examine such a problem. damage concepts can be applied to the matrix mechanical characteristics and, by adopting a 3-d mixed mode fracture description of the fibre-matrix detachment, fatigue fracture mechanics concepts can be used to determine the progressive fibre debonding responsible for the loss of load bearing capacity of the reinforcing phase. in the present paper, a micromechanical model is used to evaluate the unixial or multiaxial fatigue behaviour of structures with equi-oriented or randomly distributed fibres. the spatial fibre arrangement is taken into account through a statistical description of their orientation angles for which a gaussian-like distribution is assumed, whereas the mechanical effect of the fibres on the composite is accounted for by a homogenization approach aimed at obtaining the macroscopic elastic constants of the material. the composite material behaves as an isotropic one for randomly distributed fibres, while it is transversally isotropic for unidirectional fibres. the fibre arrangement in the structural component influences the fatigue life with respect to the biaxiality ratio for multiaxial constant amplitude fatigue loading. one representative parametric example is discussed. keywords. fibres; composites; debonding, multiaxial fatigue. introduction omposite materials are obtained mixing two or more constituents combined at a macroscopic level: typically a matrix material (made with polymers, metals or ceramics) and a dispersed reinforcing phase (fibres, particles or flakes) are used to get very high-quality mechanical properties (such as improved tensile strength, fracture resistance, durability, corrosion resistance, enhanced wear and fatigue strength) of the resulting material. among the numerous composite materials, the fibre-reinforced ones are commonly used in several engineering applications where traditional materials cannot be conveniently employed [1, 2]. the mechanical characteristics of composite materials obviously depend on those of their constituents, i.e. matrix material and reinforcing phase (such as fibres), and on their reciprocal interaction. c r. brighenti et alii, frattura ed integrità strutturale, 34 (2015) 59-68; doi: 10.3221/igf-esis.34.05 60 the reliability and durability of composite structural components must be assessed through the evaluation of the damage phenomena taking place in such a class of materials due to in-service loading, especially when the external actions act cyclically on the structure. the degrading effects caused by repeated loading are responsible for a significant loss of the mechanical performances, and can be related to the fibre-matrix delamination (debonding), fibre breaking, fibre buckling, matrix plastic deformation or cracking, matrix damage [3, 4]. the present research aims at developing a micromechanical approach for the assessment of the fatigue behaviour of short-fibre-reinforced composites under cyclic loading causing a multiaxial stress state. the assessment of the degrading effects in such non-homogeneous materials under fatigue loading is complex, and requires a reliable mechanics-based model for their quantitative evaluation. damages in the matrix and in the fibres are quantified by a damage mechanics approach, whereas the loss of fibre-matrix bonding is examined through fracture and fatigue mechanics. all these degrading phenomena are taken into account and quantified by analysis at micro-scale level. finally, the behaviour of a fibre-reinforced material under multiaxial fatigue conditions is examined and compared with experimental data. multiaxial fatigue of materials he safety evaluation of engineering structures under variable loading is a key aspect of the material reliability [5-7]. fatigue damage is a mechanical phenomenon affected by several factors such as stress values, stress gradients, size of structural components, surface roughness. moreover, the load variability with time (cyclic or random) and the type of stress field in the material (uniaxial or multiaxial) play a crucial role in fatigue assessment. many approaches have been formulated to analyse fatigue problems: empirical models based on the experimental wöhler curves [8, 9], power laws for propagating cracks such as the paris law [10], the critical plane approach [11-13], the average stress criterion and the stress invariant approach [14-16], the energy approach [17], the damage mechanics approach [18, 19], the fatigue fractal approach in the framework of the wöhler approach [20]. the above problem becomes even more awkward in presence of relevant stress gradients, such as in structural components with notches (holes, fillets, welding, etc.), or geometrical irregularities. as is well-known, the cyclic loading reduces the mechanical properties of materials also if the stresses are below the yielding stress value, due to the irreversible rearrangement of the lattice structure at the microscopic level. in composite materials, the cyclic loadings are responsible for the decreasing mechanical properties of the matrix and for the reduction of the fibre-matrix bond effectiveness. further, a fibre-matrix detachment can also take place, leading to a reduction of the useful fibre length for the load bearing purpose. multiaxial fatigue assessment of the reinforced matrix material in fibre-reinforced composite materials, the fatigue assessment must take into account the matrix damage as well as the fibre-matrix interface. since the local mechanical behaviour of a material containing a straight cylindrical fibre can be supposed to be transversally isotropic (fig. 1a), the presence of a multiaxial stress state can be represented only by the stresses acting along the transversally isotropic axes, i.e. the radial axis and the axial one. according to such simplification, the multiaxial fatigue damage can be assessed by considering only the variability of such stresses. figure 1: (a) cylindrical fibre surrounded by a cylindrical portion of matrix material; (b) partially detached fibre under radial and axial stresses. t (b)(a) r. brighenti et alii, frattura ed integrità strutturale, 34 (2015) 59-68; doi: 10.3221/igf-esis.34.05 61 in the present paper, the damage taking place in the matrix and at the fibre-matrix interface is assumed to be non interacting, i.e. each of them can be assessed independently of the other. moreover, the effect of the cyclic loading on the fibres is completely neglected. finally, as far as the matrix damage is concerned, the hypothesis of no crack formation and propagation in the bulk material is adopted, since the matrix is assumed to be ductile. the multiaxial fatigue strength determination in the case of biaxial tension-torsion cyclic stress state is typically tackled by empirical approaches. in particular, for normal and shear cyclic stresses (with amplitudes a and a , respectively), a suitable relationship to identify the fatigue limit is [13]: 2 2, 1 , 1( / ) ( / ) 1a af a af      (1) that can be determined once different values of biaxiality ratio, /a ar   , and phase shift angles have been fixed. typically the stress amplitudes a , a are stresses measured in a particular plane, called critical plane. in the case of a reinforced material, the relevant cyclic stress amplitudes for the material interface can be assumed to be equal to ,r a and ,z a , i.e. the radial and the axial one. in fig. 2a, the effective radial and axial (in phase) cyclic stresses amplitudes against time are shown. as can be noted, they are evaluated by neglecting the compressive portion of the cyclic stress diagrams, having assumed no damage when the material is compressed. equation (1) can be rewritten as follows (fig.1a, b): 2 2, , 1 , , 1( / ) ( / ) 1z a af r a af      (2) which represents a circle in the , ,z a r a  plane (fig. 3a) related to a given number of loading cycles to failure, fn ( fn is the number of loading cycles to failure for an uniaxial fatigue stress with the amplitude ,z a or ,r a ). then, the normalized amplitudes are defined as follows: , , 0, , , 0,' / , ' /z a z a ref r a r a ref       (3) with 0,ref = reference remote applied stress amplitude. the fatigue domain (2) can be rewritten through the above dimensionless stress amplitudes: 2 2 , 0, , 0 , , 1 , 1 ' ' 1 z a ref r a ref af af                         (4) such a biaxial fatigue stress domain can conveniently be applied to assess the damage degradation of the fibre-matrix interface layer, as is discussed later. in fig. 2b, the radial and axial stresses for a generic fibre are represented in the case of a reinforced body under remote uniaxial cyclic stress. a multiaxial fatigue-related parameter can be defined as follows: , ( ) / ( )f n f id n n n s (5) where n is the current number of cycles characterising the stress state a and , ( )f nn a is the number of cycles to failure under the uniaxial cyclic stress with amplitude 2 2 1/2, ,( ) , 1, 2, 3, ....n r a z as n    , while its dimensionless amplitude is 2 2 1/2, , , 1 1 ' ( ) , 1, 2, 3, ....n r a z a af s n       (fig. 3a). the wöhler curve (fig. 3b) is generally a continuously decreasing function of the number of loading cycles, since a well defined horizontal asymptote cannot easily be identified from experiments for many materials. in this context, the so-called fatigue limit loses its original meaning because experimental results classified as ‘run out’ simply represent the achievement of a number of cycles beyond that of interest for the applications being considered. r. brighenti et alii, frattura ed integrità strutturale, 34 (2015) 59-68; doi: 10.3221/igf-esis.34.05 62 0 2 4 6 8 10 dimensionless time, t / t -0.4 -0.2 0.0 0.2 0.4 0.6 0.8 1.0 d im e n si o n le s s c y c lic s tr e ss e s ,  ' r,  ' z  ' r ,a  ' z ,a 'r 'z (a) figure 2: (a) radial and axial cyclic dimensionless stresses vs time: definition of the effective stress amplitudes. (b) scheme of the radial and axial matrix stresses near a cylindrical fibre. figure 3: (a) z r  fatigue domains that identifies conventional fatigue life for a biaxial normal stress state. (b) the wöhler curve for a uniaxial cyclic stress history. a generic mechanical parameter can be reduced by using the above damage variable as follows: ,0 ,( ) 1 ( )m m f np n p d n     (6) where ,0mp is the initial value of the generic parameter, and ( )mp n is its fatigue affected counterpart. a suitable choice for modeling the matrix material under fatigue is to impose 0 0m mp e , where 0me is the undamaged young modulus, whereas its damaged counterpart is equal to the modulus ( )me n , with * * 0( ) 1 ( , , )m m cme n e d r n     , where * *( , , )cmd r n is the damage parameter obtained according to eq. (5) evaluated by assuming 1, , ,max( , )n a r a z as     , i.e. the equivalent uniaxial cyclic stress is identified by the maximum principal stress amplitude at the point under consideration. fracture mechanics approach to examine the fibre detachment he problem of the fibre-matrix detachment can be solved through a fracture mechanics approach. as a matter of fact, a partially debonded cylindrical fibre can be represented by a three-dimensional crack lying between two different materials [21, 22]. such a problem is the spatial counterpart of the case related to an elastic bi-material t (a) (b) (b) (a) r. brighenti et alii, frattura ed integrità strutturale, 34 (2015) 59-68; doi: 10.3221/igf-esis.34.05 63 plane with an interface crack [23, 24]. according to the above assumption, the debonded zone corresponds to a 3d cylindrical crack lying between two different materials [21] (fig. 1b). typically, the fibre-matrix stress interaction is analysed through the well-known shear lag model [25, 26], even if such an approach presents some limitations due to the inability of examining a complex stress state around the fibre. the generic fibre, embedded in an elastic matrix (fig 1b) under remote axial ( z  ) and radial ( r  ) stresses, is characterised by an energetically equivalent sif (along the circular crack front) defined as follows [27]: 22 ( ) ( ) ( ) 0 ( ) 0 i r ii r ii z r i ii z r k k k k k                       (7) the generic dimensionless mode m sif ( ,m i ii ), due to the remote stress w  ( ,w r z ), can be defined as * ( ) / mw m w wk k l     with ( )mw m wk k   . all the above sifs , ( ), ( ), ( )i i r ii r ii zk k k k      are independent of the angular co-ordinate  due to the axial symmetry of the examined configuration. an application of the above fracture mechanics problem concerns the dimensionless mode ii sifs, *iizk and *iirk , due to remote longitudinal ( z  ) and radial ( r  ) stresses. in fig. 4, such quantities are represented for different values of the material young modulus ratio, f me e , and two values of the relative fibre detached length, / fl l  . as can be noted, the sif is an increasing function of the modulus ratio, while its value decreases by increasing the aspect ratio of the fibre, 2 f fl  , i.e. the sif is much more severe for short fibre-matrix detached length. the remote axial stress approximately produces only a mode ii sif, whereas the remote radial positive stress is mainly responsible for both mode i and mainly mode ii sifs. the last cited stress-intensity factor arises due to the different elastic properties of the two joined materials. in fig. 5, the dimensionless mode i sif due to a remote radial stress is displayed against the relative debonded length (fig. 5a) and against the fibre aspect ratio (fig. 5b). such a sif decreases by increasing the detached fibre length and by increasing the fibre aspect ratio, i.e. it is lower for longer fibres in the case of a given relative detached length. the equivalent sif at the fibre-matrix interface crack front is suitable to define the condition of unstable crack propagation (leading to a complete fibre-matrix separation), according to the energy-based griffith approach: 2 plane stress plane strain 1 i i ic i i e k k e           ic ic g g (8) where icg is the critical interface fracture energy, ick is the corresponding fracture toughness, and ie and i are the young modulus and the poisson ratio at the interface, respectively. multiaxial fibre-matrix interface damage under cyclic loading the fracture mechanics approach to examine the fibre detachment has the benefit to allow us the use of the well-known crack growth approach to fatigue. as a matter of fact, if the total fatigue life is assumed to be the sum of the initiation and the propagation number of loading cycles, and the propagation stage prevails over the first one as in pre-cracked components or in presence of high stress concentration effects, the crack growth evaluation can lead to a proper expected fatigue life. in the present case, the pre-existing crack can be considered to be always present due to the unavoidable fibre-matrix detachment at the fibre extremities. moreover, irrespective of the stress state in the material surrounding the fibre, the crack path is always well defined, since it corresponds to the outer fibre surface. the crack propagation assessment can be performed through the debonding length rate law, or the crack growth velocity cgv quantified with respect to the number of loading cycles, evaluated through standard power laws such as the classical paris law: r. brighenti et alii, frattura ed integrità strutturale, 34 (2015) 59-68; doi: 10.3221/igf-esis.34.05 64 1 40 young modulus ratio, ef /em 0.0 0.1 0.2 0.3 0.4 0.5 0.6 d im en si on le ss s if s, k * i ir (a) l / lf=0.1 num. data2lf /f 20 40 80 5 10 15 20 25 30 35 l / lf=0.7 1 40 young modulus ratio, ef /em 0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 d im en si on le ss s if s, k * i iz num. data2lf /f 20 40 80 5 10 15 20 25 30 35 l / lf=0.1 l / lf=0.7 (b) figure 4: dimensionless radial and longitudinal mode ii sif, (a) ,ii rk and (b) ,ii zk , vs young modulus ratio, f me e , for different values of fibre aspect ratio, 2 f fl  , and relative debonded length equal to 0.1 and 0.7. 0 0.2 0.4 0.6 0.8 1 relative crack length, l/lf 0.0 0.1 0.2 0.3 0.4 d im e n si o n le ss s if s, k * ir (a) lf / f = 80 num. datainterpol. ef /em 1 10 25 40 0 20 40 60 80 100 fiber aspect ratio, 2lf /f 0.0 0.1 0.2 0.3 0.4 d im e n si o n le ss s if s, k * ir (b) ef / em=10 num. datainterpol. l /lf 0.05 0.20 0.50 0.90 figure 5: dimensionless radial and longitudinal mode ii sif, (a) ,ii rk and (b) ,ii zk , vs young modulus ratio, f me e , for different values of fibre aspect ratio, 2 f fl  , and relative debonded length equal to 0.1 and 0.7. / ,imcg i i th i icv dl dn c k k k k       (9) in eq. (9), ,i ic m are the paris constants of the interface, l is the debonded length (fig. 1b), and ik is the equivalent stress intensity factor range produced by the cyclic remote stresses. the above crack growth rate takes place in a thin weak layer placed between two different materials. such a layer can be considered as a third material whose properties are themselves affected by the fatigue process. for the above reason, the interface crack propagates in such a degraded material, and a suitable evaluation of the damage can be done by using eqs. (4) to (6). in the present study, the above biaxial damage evaluation is applied to the paris constant ic : 0 ,( ) / (1 )i i f ic n c d  , where 0ic is the undamaged initial constant value. the critical detached length, cl , and the corresponding number of loading cycles, cn , leading to such an ultimate condition can be evaluated as follows: (b)(a) (a) (b) r. brighenti et alii, frattura ed integrità strutturale, 34 (2015) 59-68; doi: 10.3221/igf-esis.34.05 65 0 ( ) , c i n m c c i il n l c k dn   such that ( , , )i c z r ick l k    (10) ( ) ( ) / 0i cd n l n l  where the interface equivalent sif is indicated as ( , , )i z rk l     since it depends on the remote stress field and on the current debonded length for the given composite material. the current detached length can be used to quantify a debonding-related damage id which is assumed to be equal to the ratio between the current debonded length l and the critical length cl corresponding to the condition of unstable crack propagation, that is, to the condition of complete fibre detachment from the matrix material for which the damage is complete, i.e. ( ) 1i cd n  . on the other hand, it has been shown that ( , , )i z rk l     is a decreasing function of l [27], i.e. the sif decreases as the detached length increases, and the critical condition cannot be reached during crack propagation. the fibre-matrix debonding-related damage id can also be defined as follows: 0 / 1i fd l l   (11) and measures the effectiveness of the fibre in the bearing mechanism of the composite material. on the other hand, the detachment phenomenon could synthetically be quantified also through a so-called sliding scalar function ( )mfs  [26] (and the interface damage can thus be measured as follows: 1 ( ) m i fd s   ). the sliding scalar function can approximately be estimated as follows: ( ) ( ) /mf f fs l l l   . by means of the current debonded fibre length determined above, the sliding function parameter ( ) /m mf f fs ε   (given by the ratio of the fibre strain to matrix strain measured in the fibre direction) can be evaluated, and the tangent elastic tensor 'eqc of the homogenized material can be obtained [27]: ( ) ' ' ' ( ) ( ) ( ) m fm m eq m f f f m f ds ε e s ε p p d dε                          c c f f (12) where ,  are the fibre and matrix volume fractions, respectively; ' , 'm fec are the tangent elastic tensor of the matrix material and the fibre tangent elastic modulus, respectively; ( )p  and ( )p  are the probability distribution functions describing the fibres arrangement in 3d space; f is the second-order tensor defined as follows:  f k k , where k is the unit vector identifying the fibre axis [27]. such a homogenization procedure is carried out as the fibre progressively detaches due to fatigue loading. numerical simulations ow the fatigue behaviour of a 13% glass fibre-reinforced polyamide specimen (with fibres oriented parallel, i.e. with 0º  , or inclined by an angle 30º  with respect to the load direction) under constant amplitude uniaxial cyclic stress is examined [28]. the materials constituting the specimen are characterised by the following mechanical properties: matrix young modulus 2.2me gpa , poisson’s ratio 0.4m  , fibres young modulus 72.45fe gpa , poisson’s ratio 0.23f  , fibre diameter equal to 10f m  and length 42 5.5 10fl m   . the paris constants of the interface are 98.7 10ic   and 13.9im  ( /dl dn in mm/cycle, ik in mpa m ), i.e. those of the matrix material, whereas the wöhler constants are 0 10mpa  , 6 0 2 10n   (fatigue limit and corresponding conventional number of loading cycles), 0.133b  . n r. brighenti et alii, frattura ed integrità strutturale, 34 (2015) 59-68; doi: 10.3221/igf-esis.34.05 66 (a) 1e+003 1e+004 1e+005 1e+006 1e+007 number of cycles to failure, nf 25 30 35 40 45 50 55 60 65 70 s tr e ss a m p lit u d e ,  * ( m p a) (b) f =13%  exp. res. [28] fem, present res. 0º 30º figure 6: (a) geometrical dimensions, expressed in (mm), and fem model of the specimen; (b) the wöhler curves of the glass fibrereinforced polyamide specimen: experimental [28] and present results. 1e+003 1e+004 1e+005 1e+006 1e+007 number of cycles to failure, nf 0.0 0.2 0.4 0.6 0.8 1.0 m a tr ix d a m a g e p a ra m e te r, d e ( -) 0.000 0.010 0.020 m a tr ix s tr a in ,  m ( -) (a) * = 45 mpa  0º 30º de m 1e+003 1e+004 1e+005 1e+006 1e+007 number of cycles to failure, nf 0.0 0.2 0.4 0.6 0.8 1.0 d im e n si o n le ss d e b o n d e d le n g th ,  ( -) 0.0 0.2 0.4 0.6 0.8 1.0 s lid in g fu n c tio n , s ( -) (b) * = 45 mpa  0º 30º  s figure 7: (a) damage and strain evolution in the matrix (at point p) vs the number of stress cycles; (b) dimensionless fibre debonded length  , and sliding parameter s, (at point p) vs the number of stress cycles. the fatigue failure of the material is assumed to occur when the maximum matrix strain reaches a given admissible value that has been assumed equal to 10% in the present case. in figure 6, the experimental s-n curves for the two considered fibre arrangements are reported. it can be observed that the fibres aligned with the fatigue loading direction are most effective and, for a given stress amplitude, a greater number of loading cycles can be reached before the material failure for such fibre arrangement. the numerical evaluation of the number of loading cycles to failure is in accordance with the above observation, providing results that are in acceptable agreement with the experimental outcomes [28]. in figure 7a, the damage parameter ed , applied to the young modulus of the matrix, is plotted together with the matrix strain against the number of loading cycles. in figure 7b, the dimensionless fibre debonded length and the sliding function are plotted against the number of loading cycles n : the function ( )s n decreases with n , indicating a decreasing of the fibre capability to carry the applied load transferred from the matrix as the number of cycles increases. as a consequence, the stress fraction sustained by the matrix increases with n (being constant the maximum applied stress during fatigue), and the damage in the bulk material increases. (b) (a) (b) r. brighenti et alii, frattura ed integrità strutturale, 34 (2015) 59-68; doi: 10.3221/igf-esis.34.05 67 in the case of fibres aligned with the loading direction ( 0º  ), the sliding parameter stabilises after a certain number of loading cycles, and the maximum strain in the matrix appears to increase very slightly with n . conclusions n the present paper, a micromechanical model for the evaluation of the unixial or multiaxial fatigue behaviour of fibre-reinforced structural elements having equi-oriented or randomly distributed fibres has been presented. the effective spatial arrangement of the fibres is statistically taken into account by adopting a gaussian-like distribution function, whereas the mechanical effect of the fibre on the composite is accounted for by a homogenization approach aimed at obtaining the macroscopic elastic constants of the material. the fatigue fibre-matrix debonding is evaluated by using a fracture mechanics approach. matrix damage under fatigue is determined by considering the local anisotropy of the material due to the fibres, i.e. a multiaxial fatigue criterion for constant amplitude loading is proposed. finally, the micromechanical model is employed to assess the fatigue behaviour of a representative unidirectional-reinforced polymeric samples, providing results in line with the experimental data. references [1] jones, rma., mechanics of composite materials, second ed., taylor & francis group, (1999). [2] cheng, qg., fiber reinforced composites. nova science publishers, inc., hauppauge, ny, (2012). isbn: 978-162081-559-5. [3] brighenti, r., numerical modelling of the fatigue behaviour of fiber reinforced composites. comp part b, 35(3) (2004) 197–210. doi: 10.1016/j.compositesb.2003.10.003 [4] guo, lp., carpinteri, a., spagnoli, a., sun w., experimental and numerical investigations on fatigue damage propagation and life prediction of high-performance concrete containing reactive mineral admixtures. j fat., 32 (2010) 227–37. doi: 10.1016/j.ijfatigue.2009.05.009 [5] pook, lp., the role of crack growth in metal fatigue, metals society, london, uk, (1983). [6] carpinteri, a., (ed.) handbook of fatigue crack propagation in metallic structures, elsevier science bv, amsterdam, (1994). [7] pook, lp., crack paths, wit press, southampton, uk (2002). [8] wöhler, a., versucheüber die festiykeit eisenbahnwagenuchsen, z bauwesen, 10 (1860). [9] basquin, oh., the exponential law of endurance tests, proc astm, 10 (1910) 625–630. [10] paris, p., erdogan, f., a critical analysis of crack propagation laws, j. basic engng, trans am soc mech eng, 85 (1963) 528–534. doi: 10.1115/1.3656900 [11] brown, mw., miller, kj., a theory for fatigue failure under multiaxial stress-strain condition, proc inst mech engrs, 187 (1973) 745–755. doi: 10.1243/pime_proc_1973_187_161_02 [12] carpinteri, a., macha, e., brighenti, r., spagnoli, a., expected principal stress directions for multiaxial random loading part i: theoretical aspects of the weight function method, int. j. fat., 21 (1999) 83–88. doi: 10.1016/s0142-1123(98)00046-2 [13] carpinteri, a., spagnoli, a., multiaxial high-cycle fatigue criterion for hard metals, int. j. fat., 23 (2001) 135–145. doi: 10.1016/s0142-1123(00)00075-x [14] sines, g., failure of materials under combined repeated stresses with superimposed static stresses, tech. rep. technical note 3495, nat. adv. coun. aeronaut., washington d.c., usa (1955). [15] cristofori, a., susmel, l., tovo, r., a stress invariant based criterion to estimate fatigue damage under multiaxial loading, int. j. fat., 30 (2007) 1646–1658. doi: 10.1016/j.ijfatigue.2007.11.006 [16] smith, k.n., watson, p., topper, th., a stress-strain function for the fatigue of metals, j. mater jmlsa, 5 (1970) 767–778. [17] macha, e., sonsino, cm., energy criteria of multiaxial fatigue failure, fat. fract. engng mater. struct., 22 (1999) 1053–1070. doi: 10.1046/j.1460-2695.1999.00220.x [18] ottosen, n.s., stenstrom, r., ristinmaa, m., continuum approach to high-cycle fatigue modelling, int. j. fat., 30 (2008) 996–1006. doi: 10.1016/j.ijfatigue.2007.08.009 [19] brighenti, r., carpinteri, a., a notch multiaxial-fatigue approach based on damage mechanics, int. j. fat., 39 (2012) 122-133. doi: 10.1016/j.ijfatigue.2011.02.003 i r. brighenti et alii, frattura ed integrità strutturale, 34 (2015) 59-68; doi: 10.3221/igf-esis.34.05 68 [20] carpinteri, a., spagnoli, a., vantatori, s., an approach to size effect in fatigue of metals using fractal theories, fat. fract. engng mater. struct., 25 (2002) 619–627. doi: 10.1046/j.1460-2695.2002.00506.x [21] wüthrich, c., stress intensity factors for cylindrical cracks in long cylinders, engng fract mech., 13 (1980) 987–990. doi: 10.1016/0013-7944(80)90028-4 [22] zbib, h.m., hirth, j.p., demir, i., the stress intensity factor of cylindrical cracks, int j engng sci., 33 (1995) 247–253. doi: 10.1016/0020-7225(94)e0051-j [23] rice, jc., elastic fracture mechanics concepts for interfacial cracks, j appl mech., 55 (1988) 98–103. doi: 10.1115/1.3173668 [24] hutchinson, j.w., mear, m.e., rice, j.c., crack paralleling an interface between dissimilar materials, j appl mech., 54 (1987) 828–832. doi: 10.1115/1.3173124 [25] cox, h.l., the elasticity and strength of paper and other fibrous materials, british journal of applied physics, 3 (1952) 72–79. doi: 10.1088/0508-3443/3/3/302 [26] brighenti, r., scorza, d., a micro-mechanical model for statistically unidirectional and randomly distributed fibrereinforced solids, mathem mech. sol., 18 (2012) 876–893. doi: 10.1177/1081286512454447 [27] brighenti, r., carpinteri, a., scorza, d., fracture mechanics approach for a partially debonded cylindrical fibre, compos. part b: engineering, 53 (2013) 169-178. doi: 10.1016/j.compositesb.2013.03.042 [28] bernasconi, a., davoli, p., basile, a., filippi, a., effect of fibre orientation on the fatigue behaviour on a short glass fibre reinforced polyamide, int. j. fat., 29 (2007) 199–208. doi: 10.1016/j.ijfatigue.2006.04.001 microsoft word numero_33_art_10 g.p. nikishkov et alii, frattura ed integrità strutturale, 33 (2015) 73-79; doi: 10.3221/igf-esis.33.10 73 focussed on characterization of crack tip fields specimen thickness effect on elastic-plastic constraint parameter a g.p. nikishkov, yu.g. matvienko mechanical engineering research institute russian academy of sciences, moscow, russia nikishkov@imash.ru, ygmatvienko@gmail.com abstract. three-dimensional elastic-plastic problems for a power-law hardening material are solved using the finite element method. distributions of the j-integral and constraint parameter a along the crack front for varying specimen thickness and crack depth are determined for edge cracked plate, center cracked plate, three point bend and compact tension specimens. the constraint parameter a is a measure of stress field deviation from the hrr field. higher a values signify lower specimen constraint. results of finite element analyses show that the constraint parameter a significantly decreases when specimen thickness changes from 0.1 to 0.5 of the specimen width. then it has more or less stable value. among four specimen the highest constraint is demonstrated by the compact tension specimen which has the constraint parameter a lower than its small scale yielding value. keywords. elastic-plastic crack tip field; three-term elastic-plastic asymptotic expansion; constraint parameter; finite element method. introduction he j -integral [1, 2] is the most used fracture mechanics parameter for structural integrity analysis of elastic-plastic cracked structures. however, fracture criterion based on the j -integral alone correctly works when the near crack tip stress fields are described by the one-term hrr asymptotic solution [3, 4]. in many cases (for example, short and inner cracks) a one-parameter approach is not suitable for fracture prediction. finite element modeling shows that the one-term asymptotic expansion is unable to produce satisfactory description of near-tip stress fields in the microstructurally significant region. even for the small scale yielding conditions the deviation of actual stress field from hrr-field is noticeable. it is natural to assume that fracture in a structure occurs when a stress field in some region near the crack tip approaches the same value as in a test specimen under fracture load. since the j -integral that controls the hrr-field cannot describe stresses in the crack-tip region under different load conditions it is necessary to utilize additional parameters and construct better equations for stress fields. betegon and hancock [5] used elastic t -stress for studying effects on crack-tip triaxiality. while the t -stress can distinguish states with high and low constraint it cannot serve as a constraint parameter for elastic-plastic bodies because of its elastic nature. o’dowd and shih [6] introduced a second fracture parameter in the form of a dimensionless stress q which is defined as the difference between normal stresses in the near-tip region determined by a numerical analyses and the hrr stress field. t g.p. nikishkov et alii, frattura ed integrità strutturale, 33 (2015) 73-79; doi: 10.3221/igf-esis.33.10 74 main drawback of q is its considerable dependence on radial and angular coordinates of a point selected for its determination. a mathematical approach to the introduction of a second fracture parameter is based on higher order elastic-plastic asymptotic expansions of the stress field in the near crack tip region. three-term asymptotic solutions have been reported by yang, chao and sutton [7] and by nikishkov [8, 9]. it was found that for mode i plane strain crack the three terms of the asymptotic expansion are enough for representing the stresses in the crack tip region with sufficient accuracy. it appeared that the three-term expansion is controlled by just two parameters the j -integral and an additional amplitude parameter a . amplitude a can be used as a constraint parameter in elastic-plastic fracture. two-parameter j a fracture criterion has wider range of applicability than the criterion based on j -integral alone. here we present finite element three-dimensional elastic-plastic solutions for cracked specimens. stress fields near the crack front are used for calculation of the constraint parameter a . distributions of a along crack front are found for specimens of different thickness. three-term asymptotic expansion uppose that the deformation behavior of an elastic-plastic material can be described with the ramberg-osgood uniaxial strain-stress curve: 0 0 0 n                (1) where 0 is the yield stress, is the hardening coefficient, n is the hardening exponent ( 1n  ), 0 / e  , e is young's modulus. the three-term asymptotic expansion for the stress field near the tip of mode i crack in an elastic-plastic body can be presented in the following form [9]: 2 ( 0 ) ( 1) 2 ( 2 ) 0 0 0 ( ) ( ) ( ) ij s t t s ij ij ij a a a a                 (2) here ij are stress components r ,  and r in the polar coordinate system r with origin at the crack tip, ( )k ij are dimensionless angular stress functions obtained from the solution of asymptotic problems of order (0), (1) and (2). angular stress functions ( 0 )ij and ( 1) ij are scaled in such a way that maximal equivalent mises stress is equal to unity. power t is a numerically computed eigenvalue that depends on hardening exponent n . power s is expressed as 1/ ( 1)s n   . dimensionless radius  is defined by formula 0/ r j    (3) where j is the energy integral computed along small contour  1 1 i ij j u j wn n d x             (4) here w is the density of work done by stresses on mechanical strains, ij are stresses, iu are displacements, jn and are components of external normal to the contour. coefficient 0a is given by expression 0 0( ) s na i (5) where ni is a scaling integral [3, 4]. s g.p. nikishkov et alii, frattura ed integrità strutturale, 33 (2015) 73-79; doi: 10.3221/igf-esis.33.10 75 while asymptotic series (2) contain three terms, the expression depends on two parameters the j -integral which is hidden in radius  and the amplitude (or constraint) parameter a . the parameter a is a measure of stress field deviation from the hrr field. fracture criterion based on two parameters j and a compares j -integral values in a structure and in a test specimen that correspond to the same value of the constraint parameter a ( )| ( )a cj p j a (6) first, the j -integral value is computed for a structure subjected to load p . then the constraint parameter a is estimated for the structure. computed j -integral is compared to experimental fracture toughness corresponding to the same value of a . calculation of j-integral and parameter a he equivalent domain integral method [10-12] is used for calculation of the j -integral values. this method replaces small contour integral by domain integral over large region. 1 1 1 i ij jv v uq q j w dv f x x x                (7) integration domain v v around the crack segment is a difference between large cylinder v and small cylinderv . weight function q is selected in such a way that it is equal to zero on external and side surfaces of the integration domain. area f under q -function on the inner surface of the integration domain is computed as 3f q dx  (8) an evident method for the determination of parameter a is solution of the quadratic eq. (2) for any point near the crack front using finite element results for some stress component. since finite element results are characterized by some scatter different points produce different a values. scattered data can be smoothed by the least squares fitting. the value of a for a set of points is determined by fitting of expression (2) to the finite element stress data at reduced integration points 2×2×2 in the near-crack front region which is significant for the local fracture process. minimization of sum of squared differences between the finite element stresses and three-term asymptotic stresses leads to a cubic equation that can be solved by the direct method or by newton’s iteration. numerical results lastic-plastic problems for a power-law hardening material are solved using the finite element method for the following specimens shown in fig. 1: edge cracked plate (ecp), center cracked plate (ccp), three-point bend specimen (3pb) and compact tension specimen (ct). a typical finite element mesh for a quarter of an edge cracked plate / 0.3a w  is shown in fig. 2. it consists of 3008 quadratic 20-node elements and 13827 nodes. the crack front is surrounded by a polar mesh with 15 elements in angular direction. the radial size of the smallest element is 41 / 0.5·10r w  . elements with smaller thickness are placed near the specimen surface. limit loads for rigid-plastic bodies are used to normalize the applied loads [13]: ecp: 2 01.455 1 1l a w a w a               t e g.p. nikishkov et alii, frattura ed integrità strutturale, 33 (2015) 73-79; doi: 10.3221/igf-esis.33.10 76 ccp: 0 2 3 l w a w     (9) 3pb: 2 0 ( ) 1.455 2 l w a p h    ct: 2 01.455 1 2 2l a a p w w w               where 0 is yield stress, a is crack length, w and h are specimen width and semi-height. limit loads for the edge cracked plate and center cracked plate l are given if the form of remote stress. limit load lp for three point bend and compact specimens is a load per unit thickness. figure 1: specimens: edge cracked plate (ecp), center cracked plate (ccp), three-point bend specimen (3pb), compact tension specimen (ct). figure 2: finite element mesh for an edge cracked plate / 0.3a w  . values of the j -integral are calculated with the domain decomposition method for node locations at the crack front. results for the j -integral are presented as normalized elastic-plastic stress intensity factors 2 0 1 (1 ) ep je k w     (10) g.p. nikishkov et alii, frattura ed integrità strutturale, 33 (2015) 73-79; doi: 10.3221/igf-esis.33.10 77 figure 3: distribution of elastic-plastic stress intensity factor epk and constraint parameter a along the crack front of the edge cracked plate ( 5n  , / 0.5a w  , / 0.4t w  ) values of the amplitude a are determined by the least squares fitting procedure using circumferential stress  at integration points 2 2 2  inside area 1 4  , 0 45   . according to the definition (2), the a values are dimensionless and normalized by a yield stress 0 . normalization of the constraint parameter a is done with its small scale yielding value ssya . this value can be determined from solution of an elastic-plastic problem for any specimen under plane strain conditions loaded by infinitely small load. another way (which is more efficient) is a solution of elastic-plastic plane strain crack problem with boundary conditions as stresses or displacements from elastic asymptotic distributions near the crack tip. for considered materials with hardening coefficient 1  and hardening power 5, 10n  the small scale yielding values of the constraint parameter are ( 5) 0.380ssya n  and ( 10) 0.184ssya n  . a series of elastic-plastic finite element solutions has been performed with variation of the following parameters: specimens: ecp, ccp, 3pb, ct; hardening power: 5, 10n  ; thickness: /t w from 0.1 to 1.0; crack depth: /a w from 0.1 to 0.7. typical results obtained after solution of an elastic-plastic problem are presented in fig. 3 where elastic-plastic stress intensity factor epk and constraint parameter a along the crack front of the edge cracked plate for material with hardening power 5n  , relative crack depth / 0.5a w  and relative thickness / 0.4t w  are given for load levels / l  from 0.25 to 1.3. coordinate z is counted from a free specimen surface. while epk has its highest value at the specimen midplane the constraint parameter a considerably increases to the specimen surface. higher values of a indicate lower constraint at the surface. dependencies of the constraint parameter a on specimen thickness /t w at the center of the crack front for all four specimens (ecp, ccp, 3pb, ct), hardening power 10n  and load level / 1.0lp p  are shown in fig. 4. general tendency is that the magnitude of the constraint parameter a decreases (higher constraint) with the increase of relative specimen thickness /t w . in most cases stabilization of the constraint parameter occurs for thickness / 0.5t w  . change of the constraint parameter a with crack depth /a w at the center of the crack front for different specimens is presented in fig. 5 for combination of parameters 10n  , / 0.5t w  , / 0.75lp p  . the center cracked plate shows low constraint for all crack depths. for the edge cracked plate constraint parameter a decreases with the increase of the crack depth and reaches its small scale yielding value for crack / 0.7a w  . the three-point bend specimen has / 1ssya a  for crack depth around / 0.5a w  and less than unity for deeper cracks. unique behavior is demonstrated by the g.p. nikishkov et alii, frattura ed integrità strutturale, 33 (2015) 73-79; doi: 10.3221/igf-esis.33.10 78 compact tension specimen – the constraint parameter a is considerably lower ssya for all crack depths that are used for fracture toughness determination. figure 4: dependence of constraint parameter a on specimen thickness /t w at the center of the crack front for ecp, ccp, tpb and ct specimens ( 10n  , / 1.0lp p  ) figure 5: dependence of constraint parameter a on crack depth /a w at the center of the crack front for different specimens ( 10n  , / 0.5t w  , / 0.75lp p  ). g.p. nikishkov et alii, frattura ed integrità strutturale, 33 (2015) 73-79; doi: 10.3221/igf-esis.33.10 79 conclusions istributions of the constraint parameter a along the crack front were studied for specimens of different thickness. the constraint parameter a is amplitude for the second and third terms in the three-term elasticplastic asymptotic expansion for the near-crack tip stress field. three-dimensional elastic-plastic stress analyses of four specimens edge cracked plate, center cracked plate, three point bend and compact tension specimens were performed using the finite element method with variation of specimen thickness and crack depth. values of the constraint parameter a were determined by fitting stresses in the three-term asymptotic expansion to finite element results at integration points near the crack front. higher values of the constraint parameter a show that the stress field is considerably deviates from the small scale yielding stress field that is usually called low constraint. typical distribution of the constraint parameter a is characterized by two features: minimal a is at the specimen midplane, magnitude of a considerably increases to the specimen free surface. the constraint parameter a at the specimen midplane diminishes when relative thickness /t w changes from 0.1 to 0.5 and has more or less stable value after that. comparison of different specimens show that the center cracked plate specimen has highest values of the constraint parameter a for all crack depths. the compact tension specimen demonstrates lowest values of a that are even less than its small scale yielding value. acknowledgements he author acknowledges the support of the russian science foundation (project n 14-19-00383). references [1] cherepanov, g.p., the propagation of cracks in a continuous medium, j. appl. math. mech., 31 (1967) 503-512. [2] rice, j.r., a path independent integral and the approximate analysis of strain concentration by notches and cracks, j. appl. mech. asme, 35 (1968) 379-386. [3] hutchinson, j.w., singular behavior at the end of a tensile crack in a hardening material, j. mech. phys. solids, 16 (1968) 13-31. [4] rice, j.r., rosengren, g.f., plane strain deformation near a crack tip in a power law hardening material, j. mech. phys. solids, 16 (1968) 1-12. [5] betegon, c., hancock, j.w., two-parameter characterization of elastic-plastic crack-tip fields, j, appl, mech., 58 (1991) 104-110. [6] o'dowd, n.p., shih, c.f., family of crack-tip fields characterized by a triaxiality parameter. i. structure of fields, j. mech. phys. solids, 39 (1991) 989-1015. [7] yang, s., chao, y.j., sutton, m.a., higher-order asymptotic fields in a power-law hardening material, eng. fract. mech., 45 (1993) 1-20. [8] nikishkov, g.p., an algorithm and a computer program for the three-term asymptotic expansion of elastic–plastic crack tip stress and displacement fields, eng. fract. mech. 50 (1995) 65-83. [9] nikishkov, g.p., bruckner-foit, a., munz, d., calculation of the second fracture parameter for finite cracked bodies using a three-term elastic-plastic asymptotic expansion, eng. fract. mech., 52 (1995) 685-701. [10] delorenzi, h.g., energy release rate calculations by the finite element methods, eng. fract. mech., 21 (1985) 129-143. [11] li, f.z., shih, c.f., needleman, a., a comparison of methods for calculating energy release rates, eng. fract. mech., 21 (1985) 405-421. [12] nikishkov, g.p., atluri, s.n., calculation of fracture mechanics parameters for an arbitrary three-dimensional crack by the equivalent domain integral method, int. j. numer. meth. eng., 24 (1987) 1801-1821. [13] anderson, t.l., fracture mechanics: fundamentals and applications, crc press, boca raton, (2005). d t microsoft word numero_59_art_04_3123.docx zb. xia et alii, frattura ed integrità strutturale, 59 (2022) 49-61; doi: 10.3221/igf-esis.59.04 49 analysis of the bond-slip performance of steel bars and steel fiber recycled concrete based on the constitutive relationship model xia zhengbing, duan xiaofang college of architecture and civil engineering, jiangsu city vocational college nantong campus, nantong, 226006, china zhengbxia@163.com abstract. in order to promote the application of steel fiber recycled concrete in road and bridge construction, 25 groups of steel fiber recycled concrete with different mix proportions were designed, taking the replacement rate of recycled aggregates and the volume fraction of steel fibers as experimental parameters, and 77 steel bars and steel fiber recycled concrete bonded specimens were made and pasted with strain gauges for the pull-out test. the research results showed that the greater the replacement rate of recycled aggregates was, the lower the bond strength between steel bars and steel fiber recycled concrete was; in the range of 0~1.2%, the higher the mixing amount of steel fibers was, the greater the bond strength of the specimen was; in the range of 0~1.6%, the higher the mixing amount of steel fibers was, the greater the slip value of the specimen under the peak load was; the addition of steel fibers improved the failure behavior of the recycled concrete pull-out specimens; the test specimens mainly had pull-out failure when the mixing amount of steel fibers was 1.2% and 1.6%. finally, this study modified the bond-slip constitutive relationship model of steel and steel fiber recycled concrete, analyzed the influence of the replacement rate of recycled aggregates and the mix proportion of steel fibers on its bonding performance, and compared the results with the test results. the results demonstrate that the test curve is in good agreement with the fitted curve, which can provide theoretical support for engineering applications. keywords. steel bar; steel fiber recycled concrete; bonding performance; constitutive model. citation: xia, z.b., duan, x.f., analysis of the bond-slip performance of steel bars and steel fiber recycled concrete based on the constitutive relationship model, frattura ed integrità strutturale, 59 (2022) 49-61. received: 03.06.2021 accepted: 01.10.2021 published: 01.01.2022 copyright: © 2022 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. introduction ith the rapid development of highway construction in china, the demolition, maintenance and reinforcement of existing roads and bridges have produced an astonishing amount of abandoned concrete construction waste, causing extremely serious damages to the environment [1]. therefore, it is imperative to realize the green and sustainable development of the construction industry, and the processing of waste concrete into recycled aggregates is an important trend in the development of civil engineering materials today, which w https://youtu.be/wiovobs5bjo zb. xia et alii, frattura ed integrità strutturale, 59 (2022) 49-61; doi: 10.3221/igf-esis.59.04 50 is of great significance for saving sand aggregate resources and maintaining ecological balance [2]. due to the presence of defects such as initial microcracks and micropores in recycled aggregates, the performance of recycled aggregate concrete is poor than natural aggregate concrete. studies have shown that the addition of steel fibers to recycled concrete can optimize the internal defects of recycled concrete, improve its various properties, further enhance its ductility and strength, and inhibit the development of cracks [3, 4]. the above studies provide new ideas for the promotion and application of recycled concrete in reinforced concrete structures. in recent years, steel fiber recycled concrete has developed extremely fast and has been widely used in high-rise building engineering, bridge engineering, pipeline engineering, and maintenance and reinforcement engineering [5]. in the reinforced concrete structure, the good bonding between steel bars and concrete ensures that they can work normally and bear the load; thus, it is of great significance to study the bonding between steel bars and concrete. the bonding of steel bars and concrete is affected by many factors, such as the composition of concrete, the performance of steel bars, the restraint effect of steel bars or concrete, and the anchorage length. in recent years, chinese and foreign scholars have analyzed the influence of factors such as the replacement rate and size of recycled aggregates, direction and position of steel bars, and concrete age on the bonding performance of steel bars and recycled concrete through a series of experiments [6]. jau et al. [7] conducted a bond test and found that the bond strength between recycled concrete and steel bars varied greatly, but was lower than that between steel bars and ordinary concrete. cao et al. [8] found that when the concrete coarse aggregate was 100% recycled aggregates, the bond strength between steel bars and concrete decreased significantly, which was significantly lower than that when the replacement rate of recycled coarse aggregate was 33% ~ 66%, and the bond strength when using deformed steel bars was higher than when using plain round steel bars. the test results of li et al. [9] showed that when the relative anchorage length was five times the diameter of steel bars, the bond strength between deformed steel bars and high-strength ceramsite concrete was about 25% higher than that of ordinary concrete of the same strength level. the core issue of the current bond-anchorage experimental research is the bond-slip constitutive relationship between steel bars and concrete. the slip here refers to the relative displacement between steel bars and concrete interface under the action of external force. in reinforced concrete structures, the bond-slip constitutive relationship curve is an indispensable basis in nonlinear calculations, and it is as important as the stress-strain relationship curve of concrete. so far, the research on the bond characteristics and bond-slip constitutive model between steel bars and ordinary concrete and between steel bars and steel fiber concrete have been relatively sufficient. li et al. [10] have studied the bond-anchorage performance of high-strength steel bars and concrete. through the pull-out experiment, the basic bond-slip relationship and position function have been established, and the bond-slip constitutive relationship of high-strength steel bars in concrete structures has been determined. the bonding between mediumand high-strength recycled concrete and reinforcement [8], the bonding between rusted reinforcement and recycled concrete [11] and the stress distribution in the bonded section of reinforcement and recycled concrete [12] have also been discussed. however, scholars in china and abroad studied little about the bond-slip performance of steel bars and steel fiber recycled concrete. in this paper, the center pull-out test was conducted to systematically study the bond-slip properties of steel and steel-fiber recycled concrete under the influence factors, including the replacement rate of recycled aggregates and the volume fraction of steel fibers, and the constitutive relationship model of bond-slip was modified. the objective of this study is to confirm that changing the replacement rate of recycled aggregates and the mix proportion of steel fibers can affect the bonding and slipping performance of steel bars and steel fiber recycled concrete through experiments. however, through the experimental analysis and summary, it was found that there were still shortcomings in the experimental process to be improved. the bond-slip performance of steel bars and concrete is usually studied through the center pull-out test. due to the limited test conditions, there are errors in the measurement process; therefore, the test equipment has an important influence on the study of the bond-slip performance of steel bars and concrete. test overview test materials he materials used in the experiment mainly included cement, natural coarse aggregate, natural fine aggregate, recycled coarse aggregate, mixing water, water reducing agent, steel fiber, etc. p.o 42.5 grade ordinary portland cement (zhengzhou tianrui group, china) with a density of 3.02 g/cm3, a t zb. xia et alii, frattura ed integrità strutturale, 59 (2022) 49-61; doi: 10.3221/igf-esis.59.04 51 specific surface area of 328 m2/kg, a mortar fluidity of 192 mm, a normal consistency water demand of 29.8%, an initial setting time of 126 min, and a final setting time of 208 min was used. the raw material of recycled coarse aggregate was waste concrete (xuchang jinke resource recycling co., ltd., china), and its performance indicators are shown in tab. 1. the fine aggregate was natural river sand, and the coarse aggregate was natural gravel. sika viscocrete 530 pc high-efficiency water-reducing agent (nanjing sitai trading co., ltd., china) with high water-reducing rate and high plasticity retention was used. the milled shaped wave-steel fiber (shengze building materials co., ltd., china) was used, and its performance indicators are shown in tab. 2. hrb400 hot-rolled ribbed steel bars with a diameter of 18 mm were used. particle size/mm apparent density/(kg/m3) bulk density/(kg/m3) water absorption/% moisture content/% 5~25 2550 1460 4.1 1.8 table 1: the performance indicators of coarse aggregate equivalent diameter/mm aspect ratio tensile strength/mpa density (g/cm3) 0.600 45 ≥ 600 7.86 table 2: the performance indicators of steel fibers design of the mix proportion the basic mix proportion of c40 concrete was used, as shown in tab. 3. ρ represents the replacement rate of recycled aggregates. ρ/% cement/ (kg/m3) sand/ (kg/m3) water/(kg/m3) coarse aggregate/(kg/m3) free water added water natural recycled 0 430 675 194 0 1102.1 0 30 430 675 194 7.61 771.3 330.5 50 430 675 194 12.68 551.0 551.0 70 430 675 194 17.73 330.5 771.3 100 430 675 194 25.35 0 1102.1 table 3: the mix proportion of recycled concrete specimen design and production a total of 25 sets of pull-out specimens were designed for the center pull-out test, and each set included three specimens. the design parameters of the test specimens are shown in tab. 4, and n-0-0 was defined as the baseline group. the test specimen was a concrete test cube with a side length of 150 mm, and a 18 mm hrb400 steel bar with a diameter of d was inserted in the middle of the cube. the effective bonding length of the steel bars was 5 d. the non-bonding section was embedded with a polyvinyl chloride (pvc) casing with a length of 60 mm and painted with glass glue to prevent the relative sliding of the steel bar. the design dimensions of the test specimens are shown in fig. 1. zb. xia et alii, frattura ed integrità strutturale, 59 (2022) 49-61; doi: 10.3221/igf-esis.59.04 52 figure 1. the design dimensions of the test specimen (unit: mm) no. of test specimen ρ/% volume fraction of steel fibers/% splitting tensile strength/mpa compressive strength/mpa n-0-0 0 0 2.27 43.21 dc-30 30 0 2.00 40.81 dc-50 50 0 1.94 35.70 dc-70 70 0 1.43 36.52 dc-100 100 0 1.31 32.33 sfc-0.4 0 0.4 2.40 50.98 sfc-0.8 0 0.8 2.65 54.82 sfc-1.2 0 1.2 2.96 55.70 sfc-.16 0 1.6 3.25 57.18 sfdc-30-0.4 30 0.4 2.08 45.23 sfdc-30-0.8 30 0.8 2.15 47.40 sfdc-30-1.2 30 1.2 2.54 51.70 sfdc-30-1.6 30 1.6 2.58 53.22 sfdc-50-0.4 50 0.4 1.80 44.01 sfdc-50-0.8 50 0.8 1.93 44.69 sfdc-50-1.2 50 1.2 2.20 49.31 sfdc-50-1.6 50 1.6 2.25 47.14 sfdc-70-0.4 70 0.4 1.45 40.36 sfdc-70-0.8 70 0.8 1.81 40.18 sfdc-70-1.2 70 1.2 2.02 41.29 sfdc-70-1.6 70 1.6 1.99 39.69 sfdc-100-0.4 100 0.4 1.40 32.68 sfdc-100-0.8 100 0.8 1.68 34.73 sfdc-100-1.2 100 1.2 1.29 39.70 sfdc-100-1.6 100 1.6 1.71 38.85 table 4: the design parameters of the test specimen (dc: recycled concrete; sfc: steel fiber concrete; sfdc: steel fiber recycled concrete) zb. xia et alii, frattura ed integrità strutturale, 59 (2022) 49-61; doi: 10.3221/igf-esis.59.04 53 loading system in the pull-out test a waw-600c electro-hydraulic servo universal testing machine was used for loading. the loading speed was controlled no more than 0.4 kn/s. the loading device is shown in fig. 2. figure 2. the layout drawing of the loading device a displacement meter with a measuring range of 50 mm was set at the free end of the steel bar to measure the free-end slip. the slip at the loading end was measured by two displacement meters with a measuring range of 50 mm, which was the difference between the mean value of the two displacement meters and the elastic elongation of the steel bar. the free-end slip was defined as the relative slip between the steel bar and the concrete. the calculation method of the average bond stress between the steel bar and the concrete is:    1000 d e p l (1) where  stands for the average bonding stress between the steel bar and the concrete, p stands for the pull-out load value, d stands for the diameter of the steel bar, and el stands for the effective bonding length of the steel bar. analysis of test results failure behavior fter analysis of the test phenomenon, the failure behaviors of the test specimens in the bond-slip performance test mainly included splitting failure, splitting pull-out failure, and pull-out failure, as shown in fig. 3. (a) splitting failure (b) splitting pull-out failure (c) pull-out failure figure 3. the failure behaviors of the test specimens splitting failure mainly occurs in the pull-out specimen without steel fibers, and its failure behavior is shown in fig. 3(a). at the beginning of the test, when the pull-out load was small, the relative slip between the steel bar and the concrete mainly occurred at the loading end; at that time, the free end had no obvious slip, and the specimen had no obvious cracks. with the further increase of the load, the slip of the loading end gradually expanded to the free end, a zb. xia et alii, frattura ed integrità strutturale, 59 (2022) 49-61; doi: 10.3221/igf-esis.59.04 54 and the main cracks that penetrated the surface of the specimen began to appear. when the load rose to the limit, the specimen suddenly cracked, the load dropped sharply, the slip values of the free end and the loading end no longer increased, the steel bar completely separated from the main body of the concrete specimen, the specimen split into two or three pieces, and it was seen from the split surface that the concrete was sheared by the steel bar rib. splitting pull-out failure mainly occurred in the pull-out specimen with a low content of steel fibers. the failure behavior is shown in fig. 3(b). there was no obvious slip at the free end of the specimen at the beginning of loading. with the further increase of the load, when the bonding stress reached the split bond strength of the specimen, the internal cracks of the specimen developed slowly because of the cracking resistance effect of steel fibers. when the cracks further increased, the relative slip between the steel bar and the concrete gradually expanded to the free end, and the concrete on the surface of the steel bar was sheared by the ribs. after the failure, there were obvious transverse cracks on the surface of the test specimen, and the steel bar and the concrete were partially separated, but the test specimen was not completely split; there was a friction resistance and mechanical interaction between the steel bar and the concrete. no. of test specimen ultimate load pu/kn) ultimate strength u /mpa the slip value sui of the free end/mm the slip value suz of the loading end/mm average slip value su/mm failure behavior n-0-0 112.85 22.19 1.95 3.39 2.67 splitting failure dc-30 109.05 21.41 1.38 2.36 1.87 splitting failure dc-50 108.97 21.40 1.39 2.11 1.75 splitting failure dc-70 96.08 18.87 1.50 1.92 1.71 splitting failure dc-100 86.87 17.08 1.25 2.23 3.48 splitting failure sfc-0.4 117.18 23.01 1.26 3.40 2.33 splitting pull-out failure sfc-0.8 117.90 23.15 1.45 2.69 2.07 splitting pull-out failure sfc-1.2 121.28 23.84 1.54 2.92 2.43 pull-out failure sfc-.16 117.32 23.05 1.91 2.99 2.45 pull-out failure sfdc-30-0.4 109.43 21.50 1.58 2.18 1.88 splitting pull-out failure sfdc-30-0.8 111.05 21.81 1.26 2.70 3.96 splitting pull-out failure sfdc-30-1.2 113.17 22.23 0.94 3.12 2.03 pull-out failure sfdc-30-1.6 116.45 22.87 1.16 3.50 2.33 pull-out failure sfdc-50-0.4 108.95 21.40 1.42 1.50 1.46 splitting pull-out failure sfdc-50-0.8 109.33 21.49 1.08 2.68 1.88 splitting pull-out failure sfdc-50-1.2 112.28 22.05 1.21 2.33 1.77 pull-out failure sfdc-50-1.6 113.13 22.23 1.28 2.90 2.09 pull-out failure sfdc-70-0.4 98.36 19.31 1.48 1.66 1.57 splitting pull-out failure sfdc-70-0.8 102.75 20.20 1.63 1.75 1.69 splitting pull-out failure sfdc-70-1.2 101.18 19.88 1.62 1.84 1.73 splitting pull-out failure sfdc-70-1.6 101.43 19.92 2.04 2.86 2.45 pull-out failure sfdc-100-0.4 97.30 19.13 1.50 2.10 1.80 splitting pull-out failure sfdc-100-0.8 102.41 20.11 0.78 3.02 1.90 splitting pull-out failure sfdc-100-1.2 106.33 20.89 1.55 2.49 2.02 splitting pull-out failure sfdc-100-1.6 101.22 19.88 0.73 4.95 2.84 pull-out failure table 5: the results of the pull-out test zb. xia et alii, frattura ed integrità strutturale, 59 (2022) 49-61; doi: 10.3221/igf-esis.59.04 55 pull-out failure mainly occurred in the pull-out specimen with a large content of steel fibers. the failure behavior is shown in fig. 3(c). with the increase of the load, the slip value of the steel bar continued to increase, and there were micro cracks penetrating the surface of the test specimen at the loading site. as the load increased further, the steel bar slowly separated from the main body of the concrete specimen, and the specimen began to fail; at that time, the slip value continued to rise and the load gradually decreased. due to the crack resistance of the steel fibers, there were only fine and concentrated cracks on the surface of the specimen when it was destroyed; at that moment, the integrity of the specimen was good, and there was a degree of bonding ductility. a) the mix proportion of steel fibers is 0%. b)the mix proportion of steel fibers is 0.4%. c) the mix proportion of steel fibers is 0.8%. d) the mix proportion of steel fibers is 1.2%. e) the mix proportion of steel fibers is 1.6% figure 4: the bond stress-slip relationship curve under different replacement rates of recycled aggregates. bond-slip performance: characteristic value the bond-slip performance test was performed using a waw-600c universal testing machine and donghua strain testing system. the measured characteristic values are shown in tab. 5. zb. xia et alii, frattura ed integrità strutturale, 59 (2022) 49-61; doi: 10.3221/igf-esis.59.04 56 it was seen from tab. 5 that the pull-out specimens mainly underwent splitting failure when steel fibers were not mixed, the specimens mainly underwent splitting failure when the content of steel fibers was 0.4% and 0.8%, and the specimens mainly underwent pull-out failure when the content of steel fibers was 1.2% and 1.6%. effects of the replacement rate of recycled aggregates on the bond-slip performance when the mix proportion of steel fibers was 0, 0.4%, 0.8%, 1.2%, and 1.6%, the bond stress-slip relationship under different replacement rates of recycled aggregates is shown in fig. 4. the following results were seen from fig. 4. (1) when the mix proportion of the steel fiber content was 0%, the pull-out specimens and recycled concrete pull-out specimens in the baseline group immediately were destroyed immediately after reaching the ultimate strength because of the lack of the restraining effect of steel fibers, and the bond stress dropped rapidly. the slip value further increased in the initial stage of loading, and the curve had an obvious linear rising relationship. when the load reached the limit, the slip value increased slowly, and there was only a small slip. (2) when the mix proportion of steel fibers was not 0%, the peak bond stress of the curve decreased with the increase of the replacement rate of recycled aggregates under different mix proportions of steel fibers, i.e., recycled aggregates weakened the bond strength of the pull-out specimens. when the mix proportion of steel fibers was fixed, the slope of the curve had no obvious change law under different replacement rates of recycled aggregates, i.e., although the change of the replacement rate of recycled aggregates had a significant influence on the bond strength of the specimens, it had no significant influence on the bond stress-slip relationship. (3) when the replacement rate of recycled aggregates was 100%, the strength in the descending section of the bond stress-slip curve under different mix proportions of steel fibers changed rapidly, but the slip value did not change significantly. the reason for the above result was because the internal mechanical properties of the specimen had relatively large defects when the replacement rate of recycled aggregates was 100%, and the incorporation of steel fibers had a weak effect in improving the bond-slip performance of the specimen. effects of the mix proportion of steel fibers on the bond-slip performance when the replacement rate of recycled aggregates was 0%, 30%, 50%, 70%, and 100%, the bond stress-slip relationship under different mix proportions of steel fibers is shown in fig. 5. the following results were seen from fig. 5. (1) the bond stress-slip curve of the pull-out specimens under the influence of the mix proportion of steel fibers was mainly divided into an ascending section, a slip failure section, and a descending section. (2) in the initial stage of loading, the bond stress-slip curve was nearly in a linear rising relationship. when the replacement rate of recycled aggregates was 0%, 30%, 50%, and 70%, within the range of 0.4% ~ 1.2%, the larger the mix proportion of steel fibers was, the steeper the bond stress-slip curve was, and the larger the ultimate bond strength of the specimen was. the reasons for the above result was that the cracking resistance and energy dissipation effects of steel fibers further restrain the relative displacement of steel bars, and the larger the mix proportion of steel fibers, the more significant the restraint effect was, the smaller the change of the slip value was, and the faster the development of the bond strength was. (3) when the load reached about 95% of the ultimate load, the bond stress-slip curve entered the slip failure section. in this period, the load rose slowly, the slip values of the free end and the loading end continued to increase, microcracks began to appear on the surface of the specimen, and the specimen began to fail. (4) when the load reached the limit, the bond stress-slip curve began to enter the descending section. as the steel fibers formed a fiber space network structure inside the test specimen, the descending section of the bond stress-slip curve of the pull-out specimen was more complete, and the descending speed of the bond strength was smaller than that of the pull-out specimen without steel fibers. steel fibers improved the bond-slip failure process of the pull-out specimen and made the bond stress-slip curve more complete when the specimen failed. (5) the comparison of the bonding strength between sfdc-100-1.6 and sfdc-100-1.2 found that the bonding strength declined when the mix proportion of steel fibers was 1.2% and 1.6%, which was because the steel fibers dispersed unevenly in the mixing process of the concrete with the increase of the mix proportion of the steel fibers, forming weak layers. zb. xia et alii, frattura ed integrità strutturale, 59 (2022) 49-61; doi: 10.3221/igf-esis.59.04 57 (a) ρ=0 (b) ρ=30% (c) ρ=50% (d) ρ=70% (e) ρ=100% figure 5: the bond stress-slip curve under different mix proportions of steel fibers. design of the bond-slip constitutive model for steel and steel fiber recycled concrete commonly used bond-slip constitutive relationship models t present, a large number of studies have been carried out on the bond-slip constitutive relationship between steel bars and concrete in china and abroad, and some research results have been obtained. this article summarizes the bond-slip constitutive relationship models for steel bars and concrete. (1) houde model through a pull-out test, houde [13] proposed an expression for the bond stress-slip constitutive relationship that a zb. xia et alii, frattura ed integrità strutturale, 59 (2022) 49-61; doi: 10.3221/igf-esis.59.04 58 considers compressive strength of concrete:        2 4 2 3 6 4(5.29 10 2.51 10 5.84 5.46 10 ) 40.7 cfs s s s (2) where cf stands for the compressive strength of concrete and s stands for a slip value. (2) nilson model nilson [14] further studied the pull-out test results of some scholars and proposed a constitutive relationship expression of the average bond stress and the slip at the end of steel bars:       2 4 2 5 39.78 10 5.72 10 8.35 10s s s (3) (3) haraji model haraji [15] obtained the bond-slip constitutive relationship through study. the ascending section is expressed as:    ( )a u u s s (4) where a is a constant and u and us represent the maximum bond strength and corresponding slip respectively. (4) teng zhiming’s model teng zhiming [16] proposed an equation of bond-slip relationship after comprehensively studying the influence of the tensile strength of concrete, the thickness of protective layer of steel bars, the diameter of anchor bars, and anchor position on the bond stress:          3 3 3 4 4(61.5 693 3.14 10 0.478 10 ) 4 (1 )ts c x x s s s s f d l l (5) where tsf stands for the tensile strength of concrete, c d stands for the relative thickness of the protective layer of concrete, x stands for the transverse distance to the nearest crack, and l stands for the spacing of cracks. the modified bond-slip constitutive relationship model the failure behaviors of the test specimens in this test mainly included splitting failure, splitting pull-out failure, and pull-out failure. for the pull-out specimens whose failure behavior was splitting failure, the bond-slip curve only had an ascending section but had no obvious descending section. for the specimens with splitting pull-out failure and pull-out failure, the bond-slip curves had complete ascending and descending sections. therefore, this paper divided the bond-slip constitutive relationship into an ascending section and a descending section. as the main research subject of this experiment was the steel fiber recycled concrete, and the bond-slip relationship of recycled concrete was similar to that of ordinary concrete, the ascending section of bond-slip can be fitted with eqn. (4) proposed by haraji. the descending section was fitted by the curve model of the concrete tension descending section proposed by guo zhenhai. the stress and strain of the concrete under tension were respectively equivalent to the bond stress and slip value between the steel bar and the concrete, and the peak stress and strain were equivalent to the peak bond strength and the corresponding peak slip. see eqn. 6 for details:     2 / ( / 1) / u u u u s s b s s s s (6) according to the test data, 1stopt software was used for curve fitting, and the parameter a of the ascending section and the parameter b of the descending section of the bond-slip constitutive relationship were obtained. the constitutive relationship model when ρ = 30% the comparison between the test results and fitted curves and the test results when the replacement rate of recycled aggregates was 30% are shown in fig. 6 and tab. 6. zb. xia et alii, frattura ed integrità strutturale, 59 (2022) 49-61; doi: 10.3221/igf-esis.59.04 59 (a) sfdc-30-0.4 (b) sfdc-30-0.8 (c) sfdc-30-1.2 (d) sfdc-30-1.6 figure 6: the test curves and fitted curves. number of test specimen parameter of ascent stage a correlation coefficient parameter of descent stage b correlation coefficient sfdc-30-0.4 1.57 0.998 44.68 0.999 sfdc-30-0.8 1.11 0.999 16.73 0.999 sfdc-30-1.2 0.75 0.998 24.88 0.997 sfdc-30-1.6 0.76 0.974 34.65 0.998 table 6: comparison of values obtained from fitting. the constitutive relationship model when ρ = 50% the comparison between the test results and fitted curves and the test results when the replacement rate of recycled aggregates was 50% is shown in fig. 7 and tab. 7. number of test specimen parameter of ascent stage a correlation coefficient parameter of descent stage b correlation coefficient sfdc-50-0.4 1.72 0.997 / / sfdc-50-0.8 1.27 0.999 176.2 0.999 sfdc-50-1.2 0.86 0.984 65.54 0.999 table 7: comparison of values obtained from fitting. zb. xia et alii, frattura ed integrità strutturale, 59 (2022) 49-61; doi: 10.3221/igf-esis.59.04 60 (a) sfdc-50-0.4 (b) sfdc-50-0.8 (c) sfdc-50-1.2 (d) sfdc-50-1.6 figure 7. the test curves and fitted curves. it was seen from fig. 7 and tab. 7 that when the replacement rate of recycled aggregates was 30% and 50%, the measured bond stress-slip curve of the pull-out specimens was fitted well with the fitted curve under different volume fractions of steel fibers, and the correlation coefficient was kept between 0.974 and 0.999. the relevant parameters obtained from the fitting could be regarded as a good reference basis of the bond-slip constitutive relationship. conclusions he purpose of this paper is to study the bond-slip performance between steel bars and steel fiber recycled concrete. by varying two factors, namely recycled aggregate replacement rate and the mix proportion of steel fibers, the data analysis was carried out on the steel fiber recycled concrete center pull-out test. the following conclusions were obtained. (1) the addition of steel fibers improved the failure state of the pull-out specimens. the main failure form of ordinary concrete pull-out specimens and recycled concrete pull-out specimens was splitting damage. splitting pull-out failure and pull-out failure mainly occurred in steel fiber recycled concrete specimens. the cracks of concrete pull-out specimens without addition of steel fibers developed rapidly and damaged abruptly. in the steel fiber-added pull-out specimens, the cracks developed relatively slowly, the amount of cracks was large, the width of cracks was small, and the integrity of the specimens was good. (2) based on the measured bond-slip test results, the influence of two factors, namely, the replacement rate of recycled aggregates and the mix proportion of steel fibers, on the bond-slip performance was summarized: with the increase of the replacement rate of recycled aggregates, the bond strength of the pull-out specimens showed a decreasing trend, and the maximum decrease reached 36.64%; the steel fiber improved the bond-slip performance of the recycled concrete; after the steel fiber was incorporated, the maximum increase of the bond strength of the pull-out specimens was 16.52%, and the slip value under the peak load also increased; the bond-slip performance was t zb. xia et alii, frattura ed integrità strutturale, 59 (2022) 49-61; doi: 10.3221/igf-esis.59.04 61 better when the mix proportion of steel fibers was 1.2%. (3) based on the measured bond stress-slip curve and the existing bond-slip constitutive relations, the actual curve and the fitted curve were compared and analyzed, and the results showed that the test curve and the fitted curve were in good agreement. references [1] xie, z.h., xie, j.h., huang, p.y., guo, y.c. (2016). effects of high temperature damage on compressive and flexural behavior of high strength recycled aggregate concrete with steel fiber and crumb rubber, china journal of highway and transport, 29(3), pp. 17-24. [2] yang, y., zhao, p., chen, m.l. (2017). research on the evaluation of construction and demolition waste utilization models, industrial safety and environmental protection, 43(7), pp. 102-106. [3] yang, r.n., yin, j.r., xiao, h.m., liu, q.f. (2016). experimental study of steel fiber reinforced regenerated concrete's mechanical properties, concrete, (1), pp. 27-30. [4] zhang, l.j., gao, d.y., wang, l. (2017). experiments on shear behavior of steel fiber recycled concrete, journal of civil engineering and management, 3(2), pp. 104-107. [5] wang, x.y., tong, l.w. (2009). research status of concrete-filled steel tubular joints and problems to be solved, low temperature architecture technology, 31(8), pp. 45-47. [6] prince, m.j.r., uaurav, u., sinuh, b. (2018). splice strength of steel reinforcement embedded in recycled aggregate concrete, construction and building materials, 160, pp. 156-168. [7] jau, w.c., fu, c.w. (2004). study of feasibility and mechanical properties for producing high-flowing concrete with recycled coarse aggregates, proceedings of the international workshop on sustainable development and concrete technology. beijing, china, pp. 89-102. [8] cao, w.l., lin, d.z., qiao, q.y., chen, g.l., jiang, w., peng, s.y. (2017). experimental study on bond-slip properties and influence factors between rebars and recycled concrete, journal of natural disasters, 26(5), pp. 38-46. [9] li, y.j., ye, l.p., chen, z.j., wang, x.f., ding, j.t. (2006). bond strength between high-strength lightweight aggregate concrete and deformed bar, building science, 22(4), pp. 51-55. [10] li, y.y., li, x.q., su, h.b. (2017). experimental analysis of bond-anchorage properties between 600 mpa high strength reinforcement and concrete, journal of chongqing jianzhu university, 39(2), pp. 19-25. [11] yang, h.f., deng, z.h., qin, y.h. (2015). experimental study on bond-slip relationship between corroded rebar and recycled concrete, engineering mechanics 32(10), pp. 114-122. [12] wang, b., bai, g.l., dai, h.j., wu, s.h. (2013). experimental and mechanical analysis of bond-slip performance between recycled concrete and rebar, engineering mechanics 30(10), pp. 54-64. [13] mirza, s.m. (1979). study of bond stress-slip relationships in reinforced concrete, aci, 76(1), pp. 19-46. [14] nilson, a,h. (1972). internal measurement of bond-slip, aci, 69, pp. 439-441. [15] haraji, m.h. (1994). development/splice strength of reinforcing bars embedded in pail and fiber reinforced concrete, aci structural journal, 91(5), pp. 511-520. [16] teng, z.m., zhu, j.m., concrete structures and masonry structures, beijing: china building industry press, 1. s. pereira et alii, frattura ed integrità strutturale, 49 (2019) 450-462; doi: 10.3221/igf-esis.49.43 450 focused on new trends in fatigue and fracture characterisation and evaluation of the mechanical behaviour of endodontic-grade niti wires samuel pereira instituto superior técnico, universidade de lisboa, av. rovisco pais 1, 1049-001, lisboa, portugal samuel.p.pereira@tecnico.ulisboa.pt andré carvalho cimosm isel/ipl, instituto superior de engenharia de lisboa, av. conselheiro emídio navarro 1, 1959-007 lisboa, portugal idmec – instituto superior técnico, universidade de lisboa, av. rovisco pais 1, 1049-001, lisboa, portugal adcarvalho@dem.isel.pt luís reis, manuel freitas idmec – instituto superior técnico, universidade de lisboa, av. rovisco pais 1, 1049-001, lisboa, portugal luis.g.reis@tecnico.ulisboa.pt, manuel.freitas@tecnico.ulisboa.pt diogo montalvão department of design and engineering, faculty of science and technology, bournemouth university, poole house, talbot campus, fern barrow, bh12 5bb, uk dmontalvao@bournemouth.ac.uk abstract. with the introduction of new materials and advances in medical science, the endodontic files have changed since the early days of root canal treatments. in the late days, we have seen an increasing use of nickel-titanium (niti) alloys. at body temperature, niti alloys present a superelastic behaviour, which allows to be more effective in the removal of the tooth pulp tissue, and in the protection of the tooth structure. anyhow, these niti instruments will eventually fracture, usually without any visual signal of degradation. thus, there is a need of studying these alloys, as they present a high hysteresis cycle and non-linearities in the elastic domain. currently, there is no international standard to test niti endodontic files, so various authors have attempted to design systems that can test them under fatigue loads, usually based on empirical setups. following a systematic approach, this work presents the results of rotary fatigue tests for two alfa aesar® nitinol wires with different diameters (0.58mm and 0.25mm).the formulation is presented, where the material strength reduction can be quantified from the determination of the strain and the number of cycles until failure, as well numerical fem simulation to verify the analytical model predictions. citation: pereira, s., carvalho, a., reis, l., freitas, m., montalvão, d. characterisation and evaluation of the mechanical behaviour of endodontic-grade niti wires, frattura ed integrità strutturale, 49 (2019) 450-462. received: 20.12.2018 accepted: 10.05.2019 published: 01.07.2019 copyright: © 2019 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. mailto:samuel.p.pereira@tecnico.ulisboa.pt mailto:adcarvalho@dem.isel.pt mailto:luis.g.reis@tecnico.ulisboa.pt mailto:manuel.freitas@tecnico.ulisboa.pt mailto:dmontalvao@bournemouth.ac.uk http://www.gruppofrattura.it/va/49/2338.mp4 s. pereira et alii, frattura ed integrità strutturale, 49 (2019) 450-462; doi: 10.3221/igf-esis.49.43 451 keywords. fatigue; superelastic alloys; niti wires; life evaluation introduction ndodontic files have been used in dentistry since the middle ages and, as so, the shape, material and operation mode have changed since those days. these files are used in root canal procedures to remove the inflamed pulp and nerve endings in a tooth. in the past, endodontic files used in this procedure were made from highly flexible steel alloys. however, steel alloy files, while being flexible, are still too rigid to avoid damaging the walls of the root canals. [1-4] in order to minimise these adverse effects, nickel-titanium (niti) alloys are used in the design of endodontic files. this change in the material allowed the use of rotary systems to be used to prepare root canals more safely and predictably. [5] niti alloys are superelastic metal alloys able to fully recover from large deformations (up to strains of 10% [6]). the niti alloys, as others superelastic alloys, that are included in shape memory alloys family, present a particular behaviour for the stress vs strain plot, both on loading and unloading. on loading, the alloys start to present a linear phase, where the alloy presents a stable crystalline phase, known as austenite. after this first part, a second region of the plot shows a phase, also linear but with a much smaller slope and where occurs the transition from the austenitic phase to the martensitic phase. this transition phase is often referred as r-phase [7, 8], and a large strain is produced with a small variation of the stress. the third phase, in which the material presents a fully martensitic phase, is again linear and presents a greater slope than in the second region. during the unloading, the plot also presents three different parts, yet the stress plateau of the transition phase is much lower comparing to the loading. [9] these alloys, however, have a drawback: when compared to steel files their fatigue life is relatively shorter than steel and, seen in commercial endodontic files, they break without a previous mechanical warning (such as visible plastic deformation), increasing the risk of the file failing inside the teeth. [10] to prevent these accidents the niti files are used only once, which leads to an increase of cost, making this material not that viable. in order to increase the viability of the use of niti alloys in dentistry, some studies were made to determine the fatigue life of these alloys, usually through traditional uniaxial fatigue tests and rotary bending fatigue tests [11]. although rotary bending tests are the tests that most accurately replicate the kind of loads and deformation a file is subjected to when inside a root canal, the great majority of the existing machines in the literature only perform the fatigue test with a predetermined set of shapes. however, most of the imposed deformations are far from the complex shapes of the root canals [12]. to workaround this problem, cheung and darvell in 2007 [12] and carvalho et al. in 2015 [10] developed machines with a variable set shape, being able to evaluate the fatigue life of files and specimens in a more versatile way [13-16]. however, even with the efforts to characterise this material, the mechanical properties of niti change with the manufacturing process and, consequently, the mechanical behaviour during the endodontic procedure is highly variable. this variability creates the need to study niti alloys from different suppliers. in this work, the mechanical properties of endodontic-grade niti wires, from alfa aesar®, will be studied both by experimental tests and numerical simulations. this paper is part of a research project that aimed to study the fatigue life of endodontic files. since there is a plethora of different geometries and alloys (of which the manufactures do not disclose de composition), there is a need to compartmentalize the study. studying a specimen with simple geometry, the results of the fatigue life can be directly correlated with the fatigue properties of the material itself. from this point forward, the study can be taken to the actual files, where the differences in fatigue life can then be corelated with the complex geometry of the files(the fatigue properties of the material are known). for this, it is of special interest the rotary fatigue machine designed by carvalho et al. (2015) [10], as this is the machine used to perform the fatigue test presented herewith. this machine consists of three pins that can be positioned precisely through numerical control to deform the test specimen with a degree of bending that can range from simple point bending to more complex multi-point bending, depending on the need of the user. the file/wire is then put into rotation using a brushless dc motor with variable speed, until failure is detected. material and methodology material o perform the rotating fatigue four-point bending tests two niti alloy wires (alfa aesar® nitinol wire) are used, with a composition of 55.75% nickel and 44.25% titanium. one with a diameter of 0.58mm and the other with a diameter of 0.25 mm, both straight annealed and with an oxide surface. [17] e t s. pereira et alii, frattura ed integrità strutturale, 49 (2019) 450-462; doi: 10.3221/igf-esis.49.43 452 beam model to model the beam, one uses the euler-bernoulli beam theory, according to eqn. (1) ( ) 4 4 d w ei q x dx = (1) where q(x) is the distributed transverse load, e is the young’s modulus, i is the second moment of area of the cross section of the beam, x is the dimension across the length of the beam and w is the beam’s deflection. since there are no distributed transverse loads (only point loads due to the imposed displacement), (1) becomes: 4 4 0 d w dx = (2) with the homogenous solution given by (3): ( ) 3 21 2 3 4w x c x c x c x c= + + + (3) due to the discontinuous nature of the displacement application system, the beam must be divided into four sections, as seen in fig. 3. figure 3: beam model of the specimen, where x0 is the clamped end of the specimen; x1, x2 and x3 are the positioning pins; and x4 is the free end of the specimen [9]. section 2 is the constant curvature section. figure 1: test machine with an endodontic file [10]. figure 2: test machine with the tree pins in a testing configuration [10]. s. pereira et alii, frattura ed integrità strutturale, 49 (2019) 450-462; doi: 10.3221/igf-esis.49.43 453 using the boundary conditions (2), one can solve the equation for given pin displacements (w1, w2 and w3). ( ) ( ) 1 0 ' 1 0 0 0 w x w x =  = (2a) ( ) ( ) ( ) ( ) ( ) ( ) 1 1 2 1 ' ' 1 1 2 1 '' '' 1 1 2 1 1 w x w x w w x w x w x w x = =  =  = (2b) ( ) ( ) ( ) ( ) ( ) ( ) 2 2 3 2 ' ' 2 2 3 2 '' '' 2 2 3 2 2 w x w x w w x w x w x w x = =  =  = (2c) ( ) ( ) ( ) ( ) ( ) ( ) 3 3 4 3 ' ' 3 3 4 3 '' '' 3 3 4 3 3 w x w x w w x w x w x w x = =  =  = (2d) ( ) ( ) '' 4 4 ''' 4 4 0 0 w x w x  =  = (2e) knowing the shape of the deformed beam, the axial strain at any point can be determined by (3): 2 2x d w z dx  = − (3) where x is the axial strain, and z is the radial coordinate of the point. if z is the radius of the wire, the resulting strain will be the surface strain (which has the highest absolute value, at each cross-section). with (3), one can reverse the computations and find what pin displacements are needed in order to obtain a constant strain in section 2, [10]. instead of using the strain, one can also use the radius of curvature of the beam (  ), which can be obtained by: 2 2 1 d w dx = (4) uniaxial tension test the uniaxial tension tests, with or without a hysteresis cycle, were performed with a nominal strain rate of 1 0.1 min − = and the measurement on the extension, which later was converted to nominal strain, were obtained using a clip gauge. only the wire of 0.58mm was used in this testing due to the slenderness of the thinner one with 0.25mm. besides the uniaxial tension test until rupture, the specimen was also subjected to one hysteresis cycle in order to determine their superelastic properties. the full hysteresis cycle can be obtained from loading the specimen in the elastic domain until the full transformation from austenite into martensite, and then reversing the process by unloading the specimen rotary bending test the rotary fatigue bending tests were performed in the machine mentioned above and with a rotational speed of 500rpm (8.33 hz). as it is a rotary fatigue test, the average stress is 0m = and the fatigue ratio is 1 min max r   = = − . s. pereira et alii, frattura ed integrità strutturale, 49 (2019) 450-462; doi: 10.3221/igf-esis.49.43 454 these tests were conducted up to 5% maximum strain for the 0.58mm wire and up to 3% for the 0.25mm wire, using the pin positions given by tab. 1. strain 0.58mm wire 0.25mm wire  (mm) pin 1 (mm) pin 2 (mm) pin 3 (mm)  (mm) pin 1 (mm) pin 2 (mm) pin 3 (mm) 0.6% 48.3 -0.66 -0.479 0.516 20.83 -1.53 -1.097 1.155 0.8% 36.25 -0.88 -0.636 0.68 15.63 -2.03 -1.449 1.507 1% 29 -1.1 -0.792 0.84 12.5 -2.53 -1.794 1.846 2% 14.5 -2.19 -1.547 1.589 6.25 -5.02 -3.433 3.403 3% 9.67 -3.26 -2.266 2.271 4.17 -7.47 -4.973 4.843 4% 7.25 -4.33 -2.953 2.906 5% 5.8 -5.39 -3.615 3.512 table 1: pin positions and radius of curvature for the used strain levels. finite element analysis a static structural finite element analysis (fea) was conducted in ansys 19.0 workbench with the model shown in fig. 4 to replicate the experiments conducted in the testing machine. the 0.58mm diameter wire was modelled with 10810 elements, and the 0.25mm diameter wire was modelled with 10850 elements, both with superelastic material properties showed in tab. 1. the wire was clamped at one end and it was deformed under bending using three steel actuator pins that moved in the y direction based on the constant curvature formulation earlier presented. the movement of the actuators was simulated as being gradual, in an explicit iterative way. contact properties were added between the actuator pins and the wire, with a considered frictional coefficient of 0.2, in order to mimic the experimental procedure [18]. results for niti wire uniaxial tension and uniaxial fatigue test efore the rotary fatigue tests, the 0.58 specimen was tested under a uniaxial tension test and the results can be seen in fig. 5, as well as the results, under the same conditions, for two other niti alloys [19]. also, the specimen was subjected to one hysteresis cycle, fig. 6, and the material properties obtained can be seen in tab. 2. b figure 4: the fea model with the clamp and the pins. s. pereira et alii, frattura ed integrità strutturale, 49 (2019) 450-462; doi: 10.3221/igf-esis.49.43 455 figure 5: uni-axial tension test results. material property alfa aesar® isotropic elasticity young's modulus (gpa) 60 poisson’s ratio 0.33 superelasticity starting stress value for the forward (austenite to martensite) phase transformation σ as s (mpa) 522 final stress value for the forward (austenite to martensite) phase transformation as f (mpa) 555 starting stress value for the reverse (martensite to austenite) phase transformation sa s (mpa) 280 final stress value for the reverse (martensite to austenite) phase transformation sa f (mpa) 235 maximum residual strains l (mm/mm) 0.0645 table 2: list of material properties to alfa aesar® nitinol. from fig. 5, it can be seen that, while having the same overall behaviour with an elastic plateau (which is typical of niti alloys), there is a large variation in the ultimate tensile strength and phase transformation stress/strain necessary to start the phase transition, but not as such with regards to the overall strain and the “length” of the phase transformation region (i.e., the quasi-horizontal plateau). fatigue tests the results for the strain vs number of cycles for the fatigue tests under different levels of strain induced in the 0.58mm and 0.25mm niti wires are presented in fig. 7. in this figure it is also possible to see the fatigue results for two others different niti alloys tested in the same apparatus [19]. for the wire of 0.58mm diameter, the fatigue tests were conducted on a range of maximum extension from 0.6% to 5%. where the specimens were subjected to strains under 1%, i.e., where the crystallography of the niti alloy still is austenitic, the material showed a large fatigue life, when compared with tests where specimens were subjected to larger levels of strain. more specifically, the 0.6% strain specimens, showed an infinite fatigue life (i.e., above 6 10 cycles). the specimens with strains equal to and above 1% show a fatigue life nearly constant, in the order of magnitude of 2 10 to 3 10 , as expected for superelastic alloys [20, 21]. the specimen with the shortest life time failed after 145 cycles. s. pereira et alii, frattura ed integrità strutturale, 49 (2019) 450-462; doi: 10.3221/igf-esis.49.43 456 for the specimens with 0.25mm diameter, the fatigue tests were conducted with a strain ranging from 0.6% to 3%. the specimens with strain under 1%, that correspond to the austenitic region, show a large fatigue life, when compared with the rest of points with some specimens showing an infinite fatigue life. the specimens with strains equal to and above 1% show a decreasing fatigue life as the maximum imposed strain increases. the specimen with the shortest life time failed after 1989 cycles. figure 6: uni-axial tension test with one hysteresis cycle, with the starting and final stress values for the forward and reverse transformations (the 𝜎𝑓 𝐴𝑆 is not reached in this test, because it marks the beginning of the plastic deformation regions). figure 7: surface strain vs number of cycles. the surface strain is estimated using eqn. (3). it is also possible to see from fig. 7 that all the alloys present an infinite life only when in austenitic phase, but not when under all strains during this phase. for a finite life time, the alloys tend to increase the life time with a decreasing diameter. this life time increase can be explained as a result of the energy absorption experienced by the material during the deformation. the energy per volume is given, for a uniaxial tension test, by the eqn. (4) and, as the material is under the same strain, the energy absorption will increase with the volume. s. pereira et alii, frattura ed integrità strutturale, 49 (2019) 450-462; doi: 10.3221/igf-esis.49.43 457 0 m energy d volume   =  (4) where m is the maximum strain for the differential volume of material, and  is the stress. this behaviour is in line with the results found on the literature, as the niti alloys tend to increase the life time with a decreasing diameter. [22] fracture surface the fracture surfaces of the rotary bending tests were subjected to a closer look on a sem (scanning electron microscope). in fig. 8, one can see that the surface shows some porosities that act like locations of stress concentrations where crack initiation can occur. this feature is not uncommon in other niti alloys but is not present in all of them. also, after the rupture, the material presents a well-seen granular surface through which the fatigue fracture grew. figure 8: detail of the porosities found in the alloy (2000x magnification). the observation of the crack propagation zones showed, for the 0.58mm diameter wire, a similar size of crack propagation zone before the final rupture, for specimens obtained in the lcf zone, fig. 9(a)-9(d). in fig. 9(b), it can be seen a detail of a specimen tested under 5% of strain showing a small crack propagation zone near the surface. for lower strain (greater fatigue life time), the crack propagation zone size gets bigger as the strain levels decrease, resulting that the fracture propagates slower, fig. 9(e). in fig. 9(f), it can be seen a detail of a specimen tested under 1% of strain showing a greater crack propagation zone. for the 0.25mm diameter wire, the analysis in the sem showed that the crack propagation zone increases as the strain levels decrease. in figs. 9(h) and 9(i) can be seen a detail of the crack initiation zone for a specimen tested under 2% of strain and 1% of strain, respectively, where this increase can be observed. fea results normal stress the results obtained for the normal stress on the x direction, between pin 1 and pin 2, for the different strain levels, are presented in fig. 10, for both wires. the maximum compression stress (identified as min, coloured in blue) occurs near the first actuator pin and is slightly greater than the maximum tension stress (identified as max, coloured in red). the reason for this phenomenon is presumed to be the frictional contact friction between the pins and the wire, in order to mimic the real experiment. the maximum stress randomly floats through the section 2, appearing near the first pin, but without a fixed location. being a “constant strain region” according to the theoretical deformation model, the floating of the maximum tension stress location can only be attributed numerical error. therefore, it is expected that the wires will fracture near the pin 1 due to friction s. pereira et alii, frattura ed integrità strutturale, 49 (2019) 450-462; doi: 10.3221/igf-esis.49.43 458 figure 9: fracture surfaces for several specimens. the maximum value for the normal stress is being determined to be near the clamping region according to the fea results. this should not be a surprise, because the clamping is modelled as being infinitely rigid. this leads to a stress concentration at this location, reason why the values can be quite significant. since the true clamping region is very difficult to be modelled -accurately and the wires failed between the first two pins during the experiments, the analysis neglects the clamping location. fea results normal strain the finite element model presents a maximum strain slightly lower than the theoretical euler-bernoulli beam model. for strains under and equal 1%, the relative error is small, but it increases with the deformation of the wire. this increase of error is among the expectations as the euler-bernoulli beam theory assumes the specimen to follow an isotropic elastic behaviour and small deformations, which happens for low strains than 1%; and does not provide accurate results to superelastic behaviour, which happens for greater strains. b: ε5% ø0.58mm (x300 magnification) a: ε5% ø0.58mm (x140 magnification) c: ε5% ø0.58mm (x140 magnification) d: ε2% ø0.58mm (x140 magnification) e: ε1% ø0.58mm (x140 magnification) g: ε2% ø0.25mm (x300 magnification) h: ε2% ø0.25mm (x1000 magnification) i: ε1% ø0.25mm (x1000 magnification) f: ε1% ø0.58mm (x300 magnification) s. pereira et alii, frattura ed integrità strutturale, 49 (2019) 450-462; doi: 10.3221/igf-esis.49.43 459 in the charts of fig. 11, can be seen the fea strain vs the maximum theoretical strain (mts) for the 0.58mm diameter wire and the 0.25mm diameter wire, for both tension and compression, as the strain slightly differ. figure 10: stress distribution in the wires between pins 1 and 2 figure 11: comparison between theoretical and fea strains fea results stress in the cross section of the specimen the stress along the cross section of the specimen shows the amount of material which is in the austenitic phase or already in the austenite to martensite transformation phase. a: ø0.58mm, 𝜀𝑑 = 0.6% b: ø0.58mm, 𝜀𝑑 = 2% c: ø0.58mm, 𝜀𝑑 = 5% d: ø0.25mm, 𝜀𝑑 = 0.6% e: ø0.25mm, 𝜀𝑑 = 1% f: ø0.25mm, 𝜀𝑑 = 3% a: ø0.58mm wire b: ø0.25mm wire s. pereira et alii, frattura ed integrità strutturale, 49 (2019) 450-462; doi: 10.3221/igf-esis.49.43 460 it can be seen in fig. 12, for the region between pin 1 and pin 2, that some specimens, with low strain levels, show a linear change of stress along the cross section, suggesting that are still fully austenitic. in the other hand, the remaining specimens, under greater strain levels, show an inverted ‘s’ profile, meaning that they are partially austenitic (in the central zone, showing a straight line) and partially in the transformation phase (in the outer part, which is approximately flat) [6, 8, 23, 24]. comparing the information obtained in these charts with the uniaxial tension results, the results converge as the 1% strain specimens present a fully austenitic cross section, as obtained in these tests. for strains above 1%, the wire starts to exhibit the transformation phase from austenite to martensite across the cross-section from the outer circle of the wire’s crosssection towards its centre axis. final results after comparing the fea results and the theoretical approach, as the results in terms of strain slightly differ, the combination of these two is imposed in order to improve the accuracy of the fatigue results presented. conclusions and future work he work developed and presented in this paper show the results obtained in the rotating bending machine developed by carvalho et. al [10] and, later, the analysis and validation of both theoretical model and method used for that purpose. the method used, as well as the machine used, allow to address a range of different issues and is able to analyse them based on sound engineering foundations and materials science. the versatility of the machine allows one to perform tests for different ranges of strains in a simple and intuitive way. a series of fatigue tests were conducted using alfa aesar® nitinol wires of two different diameters, one of 0.58mm and the other of 0.25mm diameter. the wires, when under strain levels in the elastic isotropic austenitic phase corresponding to strains of 0.6% and 0.8% for the 0.58mm and 0.25mm diameter wires, respectively, showed infinite (above 〖10〗^6 cycles) life time. when under strain levels in the transformation phase condition, both wires showed a reduced fatigue life that is almost constant during this phase: between 145 and around 1000 cycles for the thicker wire with 0.58mm; and between 1989 and around 15000 cycles for the thinner wire with 0.25mm. this happens due to the stress-strain relation during this phase being t a: ø0.58mm wire b: ø0.25mm wire figure 12: stress profile along the beam cross section. figure 13 stress vs life time concerning fea and laboratorial results. a – stress vs life time b – strain vs life time s. pereira et alii, frattura ed integrità strutturale, 49 (2019) 450-462; doi: 10.3221/igf-esis.49.43 461 an almost constant plateau concerning to the stress. this is in line with the known behaviour of the niti alloys, in which the life time will be smaller than the one observed in this plateau only when it is tested under strains on the fully martensitic phase. it can also be seen that, comparing the results of the two wires, the fatigue life of the thinner wire is always greater than the life time of the thicker one. this is in line with the literature, as for each different niti alloy, set of process parameters, and shape must be individually tested and analysed to provide accurate fatigue life data. the analyses of the fracture surfaces allow to confirm the surfaces resulting from low cycle fatigue, showing a small crack propagation zone and a rough surface in the rest of the fracture surface, as the crack propagates fast and through the grain boundaries, as expected. as we move into the high cycle fatigue, the crack propagation zone increases, while the rest of the surface, where the crack propagates fast and through the grain boundaries, showed the same rough appearance. concerning the fea, the results met the expectations and were validated from the theoretical model, showing an approximately constant strain zone between the first two pins. the specimens tend to present the highest value for the stress near the first pin, which statistically happened in the laboratory tests as that was the location where fracture occurred. still concerning the fea, the stress across the beam showed that, as predicted, specimens up to 1% of strain are fully austenitic, while specimens with greater strain levels have the central part still in austenitic phase, while the outer part is already in the austenite to martensite transformation phase (r-phase). the comparison of fea results with the theoretical model suggests that the models are suitable when the specimens are still in the isotropic elastic region. however, when the specimens start the austenite to martensite transformation, there is a slight loss in accuracy, although this is not significant to invalidate the fea prediction of the fatigue life of the alloys tested. for future work, other niti alloys used in endodontic files should be tested, as well as other alloys used in dentistry or other applications. also, a greater range of rotary speeds should be tested to study the influence of this parameter in the fatigue life of these alloys. in order to improve the quality of the results, in special to improve the accuracy of the fea, the thermal expansion coefficient of the materials studied should be considered, as well as the thermal energy dissipated during the rotary fatigue tests. acknowledgments his work was supported by fct, through idmec, under laeta, project uid/ems/50022/2019. references [1] craig, r. g., mcilwain, e. d., and peyton, f. a. (1968). bending and torsion properties of endodontic instruments. oral surgery, oral medicine, oral pathology, 25(2), pp. 239–254. doi: 10.1016/0030-4220(68)90286-7. [2] thompson, s. a. (2000). an overview of nickel-titanium alloys used in dentistry. international endodontic journal, 33(4), pp. 297–310. doi: 10.1046/j.1365-2591.2000.00339.x. [3] civjan, s., huget, e. f., and desimon, l. b. (1975). potential applications of certain nickel-titanium (nitinol) alloys. journal of dental research, 54(1), pp. 89–96. doi:10.1177/00220345750540014301. [4] schafer, e. (2002) metallurgie und eigenschaften von nickel-titan-instrumenten zur maschinellen wurzelkanalaufbereitung. in: hulsmann, m., editor. wurzelkanalaufbereitung mit nickel-titan-instrumenten. ein handbuch. berlin: quintessenz, pp. 35–46 [5] krupp, d., brantley, j., and gerstein, h. (1984). an investigation of the torsional and bending properties of seven brands of endodontic files. journal of endodontics, 10(8), pp. 372–380. doi: 10.1016/s0099-2399(84)80157-0. [6] montalvão, d., alçada, f. s., braz fernandes, f. m., and de vilaverde-correia, s. (2014). structural characterisation and mechanical fe analysis of conventional and m-wire ni-ti alloys used in endodontic rotary instruments. the scientific world journal, pp. 1–8. doi: 10.1155/2014/976459. [7] nagasawa, a., (1970). a new phase transformation in the niti alloy. journal of the physical society of japan, 29(5), pp.1386-1386. [8] ling, h. c., and kaplow, r. (1981). macroscopic length changes during the b2 ⇆ r and m → b2 transitions in equiatomic ni-ti alloys. materials science and engineering, 51(2), pp. 193–201. doi: 10.1016/0025-5416(81)90195-6. t s. pereira et alii, frattura ed integrità strutturale, 49 (2019) 450-462; doi: 10.3221/igf-esis.49.43 462 [9] montalvão, d., shengwen, q., and freitas, m. (2014). a study on the influence of ni–ti m-wire in the flexural fatigue life of endodontic rotary files by using finite element analysis. materials science and engineering: c, 40, pp. 172–179. doi: 10.1016/j.msec.2014.03.061. [10] carvalho, a., freitas, m., reis, l., montalvão, d., and fonte, m. (2015). rotary fatigue testing machine to determine the fatigue life of niti alloy wires and endondontic files. procedia engineering, 114, pp. 500–505. doi: 10.1016/j.proeng.2015.08.098. [11] plotino, g., grande, n. m., cordaro, m., testarelli, l., and gambarini, g. (2009). a review of cyclic fatigue testing of nickel-titanium rotary instruments. journal of endodontics, 35(11), pp. 1469–1476. doi: 10.1016/j.joen.2009.06.015. [12] cheung, g. s. p., and darvell, b. w. (2007). fatigue testing of a niti rotary instrument. part 1: strain-life relationship. international endodontic journal, 40(8), pp. 612–618. doi: 10.1111/j.1365-2591.2007.01262.x. [13] plotino, g., grande, n. m., melo, m. c., bahia, m. g., testarelli, l., and gambarini, g. (2010). cyclic fatigue of niti rotary instruments in a simulated apical abrupt curvature. international endodontic journal, 43(3), pp. 226–230. doi: 10.1111/j.1365-2591.2009.01668.x. [14] lopes, h. p., britto, i. m. o., elias, c. n., machado de oliveira, j. c., neves, m. a. s., moreira, e. j. l., and siqueira, j. f. (2010). cyclic fatigue resistance of protaper universal instruments when subjected to static and dynamic tests. oral surgery, oral medicine, oral pathology, oral radiology, and endodontology, 110(3), pp. 401–404. doi: 10.1016/j.tripleo.2010.05.013. [15] gambarini, g., gergi, r., naaman, a., osta, n., and al sudani, d. (2012). cyclic fatigue analysis of twisted file rotary niti instruments used in reciprocating motion. international endodontic journal, 45(9), pp. 802–806. doi: 10.1111/j.1365-2591.2012.02036.x [16] de-deus, g., moreira, e. j. l., lopes, h. p., and elias, c. n. (2010). extended cyclic fatigue life of f2 protaper instruments used in reciprocating movement. international endodontic journal, 43(12), 1063–1068. doi: 10.1111/j.1365-2591.2010.01756.x [17] alfa aesar by thermo fisher scientific (2018) https://www.alfa.com/pt/nitinol-nickel-titanium-shape-memory-alloys/ [18] zhao, h., liu, l., hu, w., and shen, b. (2007). friction and wear behavior of ni-graphite composites prepared by electroforming. materials and design, 28(4), pp. 1374-1378. doi: 10.1016/j.matdes.2006.01.001. [19] carvalho, a., freitas, m., reis, l., montalvão, d., and fonte, m. (2016). rotary fatigue testing to determine the fatigue life of niti alloy wires: an experimental and numerical analisys. procedia structural integrity, 1, pp. 34–41. doi: 10.1016/j.prostr.2016.02.006. [20] ueland, s. m., and schuh, c. a. (2012). superelasticity and fatigue in oligocrystalline shape memory alloy microwires. acta materialia, 60(1), pp. 282–292. doi: 10.1016/j.actamat.2011.09.054. [21] mahtabi, m. j., shamsaei, n., and mitchell, m. r. (2015). fatigue of nitinol: the state-of-the-art and ongoing challenges. journal of the mechanical behavior of biomedical materials, 50, pp. 228–254. doi: 10.1016/j.jmbbm.2015.06.010. [22] norwich, d. w., and fasching, a. (2009). a study of the effect of diameter on the fatigue properties of niti wire. journal of materials engineering and performance, 18(5-6), pp. 558–562. doi:10.1007/s11665-009-9415-9. [23] nagasawa, a. (1970). a new phase transformation in the niti alloy. journal of the physical society of japan, 29(5), pp. 1386–1386. doi: 10.1143/jpsj.29.1386. [24] paula, a. s., mahesh, k. k., dos santos, c. m. l., canejo, j. p. h. g., and fernandes, f. m. (2006). one-and two-step phase transformation in ti-rich niti shape memory alloy. international journal of applied electromagnetics and mechanics, 23(1, 2), pp. 25-32. https://www.alfa.com/pt/nitinol-nickel-titanium-shape-memory-alloys/ shot peening processes to obtain nanocrystalline surfaces in metal alloys: b. chen et alii, frattura ed integrità strutturale, 48 (2019) 385-399; doi: 10.3221/igf-esis.48.37 385 fatigue strength analysis of bogie frame in consideration of parameter uncertainty bingzhi chen, pengpeng zhi school of mechanical engineering, dalian jiaotong university, dalian 116028, china, chenbingzhi06@hotmail.com, zhipeng17@yeah.net yonghua li school of locomotive and rolling stock engineering, dalian jiaotong university, dalian 116028, china, yonghuali@163.com abstract. in this paper, a fatigue strength analysis approach based on goodman-smith fatigue limit diagram （gsfld） and reliability theory is proposed to solve the problem that the traditional fatigue strength analysis of bogie frame is too conservative, considering the parameter uncertainty in engineering practice. firstly, according to uic615-4, en13749 standard and gsfld, the fatigue strength of the frame is calculated. the experimental results are compared with the simulation data to determine the location of the maximum fatigue strength as the control point for the strength evaluation. secondly, the parametric model of the frame is established by ansys parametric design language (apdl) language, and the d-optimal experiment design of uncertainty parameters is carried out. the polynomial response surface function with the mean stress and stress amplitude of the control point as the objective is established. the control points under the influence of uncertainty parameters are obtained by importance sampling method. finally, the functional expression of gsfld without considering the safety factor is derived, and the fatigue strength reliability of control point is calculated. the results of this study not only reveal the influence of parameter uncertainty on fatigue strength, but also demonstrate a need of developing new evaluation methods to accommodate fatigue analysis. keywords. bogie frame; fatigue strength; goodman-smith fatigue limit diagram; response surface; fatigue reliability. citation: chen, b., zhi, p., li, y., fatigue strength analysis of bogie frame in consideration of parameter uncertainty, frattura ed integrità strutturale, 48 (2019) 385-399. received: 23.01.2019 accepted: 26.02.2019 published: 01.04.2019 copyright: © 2019 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. introduction ogie frame is the base of carrying and transferring forces of many structural parts in the running gear of train. its reliability plays an important role in the safety and stability of train operation. however, as a large plate welding member, the evaluation of its structural reliability is essentially to check the structural strength and fatigue strength b mailto:chenbingzhi06@hotmail.com mailto:zhipeng17@yeah.net mailto:yonghuali@163.com http://www.gruppofrattura.it/va/48/2363.mp4 b. chen et alii, frattura ed integrità strutturale, 48 (2019) 385-399; doi: 10.3221/igf-esis.48.37 386 after welding. with the continuous improvement of train operation speed, the fatigue failure of the structure is particularly prominent. in the fracture accidents of the frame, most of them are caused by fatigue failure. therefore, it is more important to accurately evaluate the fatigue strength of the frame than the structural strength. at present, the research on fatigue strength of bogie frame is mainly based on two aspects: dynamics and statics. dynamics-based research, the dynamic model of multi-rigid-body system of vehicle body is established by analyzing the irregularity of track line, and the load history of vehicle suspension system is obtained. on this basis, the dynamic analysis and stress evaluation of the bogie are carried out, and the fatigue life of the bogie is predicted according to the cumulative damage theory. the difference lies in that different scholars consider different contents in the construction of dynamic model and fatigue life evaluation [1-4]. statics-based research, researchers mainly use finite element method (fem) to simulate the load of bogie frame in operational condition and determine the location to be evaluated. then, the fatigue strength is evaluated based on fatigue limit diagram [5-8]. the difference between the two methods is that the static fatigue strength assessment is based on the fatigue limit diagram and standard loads. the dynamic fatigue strength assessment is based on the measured stress spectrum, and the fatigue life of the frame is predicted by calculating cumulative damage. the results of the former are conservative, while the latter are less accurate because the stress spectrum is difficult to deal with [9]. in view of the above reasons, static method is usually used in the design stage to check the fatigue strength of the frame and the accuracy of calculation is verified by comparison of experimental and simulation results, so as to provide guidance for the design. currently, there are many reports about fatigue strength analysis of bogie frame at home and abroad. kim [10] proposed a method of evaluating bogie frame fatigue strength based on gsfld, which combines multi-body dynamics with structural strength simulation and verified the accuracy of the evaluation through experiments. different from kim's assessment method, wang et al [11] obtains the equivalent stress of key parts of the frame through simulation calculation and line measurement, and evaluates the static strength and fatigue strength according to jis e 4207 standard. although the methods of the two scholars are different, they are all based on the nominal stress method for fatigue strength assessment. in order to obtain more accurate calculation results, wang et al [12] employed hot spot stress method to analyze fatigue strength of bogie welded frame. however, the wang's method can only be applied to evaluate the welded joints with stress perpendicular to the toe and fatigue crack initiation at the toe. it can't be applied to evaluate the welded joints with fatigue cracks at the weld root and continuous welds subjected to longitudinal loads. compared with the above methods, lu et al [13] enhanced the efficiency of structural fatigue strength analysis by comparing the results of finite element analysis of fatigue strength of two different models. the above studies all take the deterministic model as the research object, without considering the uncertainty of design parameters in the process of machining and manufacturing. the results of fatigue strength assessment based on safety factor are conservative, which is not conducive to lightweight design of bogie frame. therefore, to further reduce the redundancy of fatigue strength analysis of bogie frame, this study modifies traditional approach. in the process of establishing finite element model, the uncertainty of design variables is taken into account. the response surface function of mean stress and stress amplitude are established, and the control points in consideration of uncertainty parameters are calculated. based on this, the expression of gsfld function without considering safety factor is derived, and the fatigue strength reliability of control point is calculated with reliability theory. (a) geometric model of bogie frame (b) finite element model of bogie frame figure 1: geometric model and finite element model of bogie frame b. chen et alii, frattura ed integrità strutturale, 48 (2019) 385-399; doi: 10.3221/igf-esis.48.37 387 fatigue strength analysis of bogie frame based on deterministic model fe model of the bogie frame n this paper, the analyzed bogie is a metro bogie (fig. 1(a)). the numerical analysis by the fem is performed to evaluate the fatigue strength of the bogie frame. a study conducted by lu shows that the calculation results of the shell model without considering weld details are more conservative than those of the shell model considering weld details. it is feasible to adopt the conservative method of seamless structure modeling in engineering design. [14]. therefore, the bogie which is modeled by shell and solid model, is given in fig. 1(b). the bogie frame is modeled using beam188, combin14, shell181 and solid185 elements. it is meshed to have 730,423 elements, including 123,755 triangular and quadrilateral shell elements and 606,659 tetrahedral and hexahedral solid elements. considering the boundary conditions of the bogie frame for the primary suspension, the spring elements combin14 are established and the stiffness of the elements is the same as the primary suspension. the material of the bogie frame is s355j2(h) and q345d (yield strength=355mpa and 355mpa). definition of the load conditions in conventional load cases, fatigue strength analysis is performed based on the uic standard. the main in-service load case is designed to verify the absence of any risk of fatigue cracks that could occur under the combined effect of the main forces encountered during service. therefore, in this study, six fatigue conditions are calculated according to uic615-4 and en13749 standard. tab. 1 and tab. 2 show the fatigue conditions for each load. the twisting loads of 1 and 2 working conditions are 11 mm, 3 and 4 working conditions are -11 mm. load case air spring vertical and right air spring vertical and left air spring horizontal lateral stop longitudinal gear box hanger front/after braking front/after 1 107.5 83.4 16.1 62.6 52.3 -23.8/23.8 -8.8/8.8 2 155 131.1 16.1 62.6 52.3 -23.8/23.8 -8.8/8.8 3 83.4 107.3 -16.1 -62.6 -52.3 23.8/-23.8 8.8/-8.8 4 131.2 155 -16.1 -62.6 -52.3 23.8/-23.8 8.8/-8.8 table 1: load cases for operational loads (kn) load case air spring vertical and right air spring vertical and left vertical inertia of motor transverse inertia of motor longitudinal inertia of motor gear box hanger front/after vertical inertia of brake transverse inertia of brake longitudinal inertia of brake 5 119.3 119.3 -20.8 -20.8 -20.8 -5.2/-5.2 -3.9 -3.9 -3.9 6 119.3 119.3 31.2 20.8 20.8 7.8/7.8 5.9 3.9 3.9 table 2: load cases for inertial load (kn) tab. 3 shows the mechanical properties of the materials used in the bogie frame. the material of steel plate and primary spring seat is s355j2(h) and the cross beam and traction seat are made from q345d. type material type yielding strength s=1 yielding strength s=1.1 yielding strength bogie frame steel plate s355j2(h) 355（≤16mm） 355 322 primary spring seat 345（>16mm） 345 313 cross beam q345d 345 345 313 traction seat table 3: material properties of the bogie frame (mpa) i b. chen et alii, frattura ed integrità strutturale, 48 (2019) 385-399; doi: 10.3221/igf-esis.48.37 388 fatigue strength analysis of bogie frame the equivalent stress occurring in the bogie frame on exceptional loads should be less than the yield strength of the used material and s=1.1 should be retained in the weld. under the normal service loads, the mean stress and stress amplitude are calculated on each load and they should be within the fatigue limit diagram. however, the bogie frame of railway vehicle bears vertical, transverse, longitudinal and oblique symmetrical loads during its service, which belongs to the typical multi-axle load state. for this purpose, this paper calculates the stress and amplitude according to the multi-axial stress state-uniaxial stress state transition method provided by ore b12/rp17. 1 2 （a） max   1 2 （b） max   min  n  figure 2: determination of maximum and minimum principal stresses the maximum principal stress direction of the structure under all load conditions is taken as the basic stress distribution direction, and its value is calculated as the maximum principal stress max , as shown in fig. 2(a). the principal stress under other loading conditions is projected to the determined direction of maximum principal stress, and the minimum principal stress is determined as the minimum principal stress min , as shown in fig. 2(b). by calculating the mean stress m and stress amplitude a or stress ratio r from the maximum and minimum principal stress values, the transformation from multi-axial stress state to uniaxial stress state is completed. the mean stress m and the stress amplitude a are defined as follows max min max min 2 2 m a       + − = = (1) according to tab. 1 and tab. 2, finite element analysis of bogie frame is conducted. fig. 3 displays the maximum utilization rate of all welds under fatigue conditions. the mean stress and stress amplitude are calculated under fatigue conditions, and the results of evaluating the fatigue limit diagram is obtained, as detailed in fig 4. figure 3: maximum utilization rate plot of fatigue conditions figure 4: fatigue analysis results of bogie frame b. chen et alii, frattura ed integrità strutturale, 48 (2019) 385-399; doi: 10.3221/igf-esis.48.37 389 it is seen from fig. 3 that the maximum utilization rate of all welds in the frame is 1.28, which occurs at the junction of the motor hanger and the cross beam, indicating that the welds in the frame do not meet the standard requirements. fig. 4 is the corresponding fatigue assessment results based on gsfld. the gsfld given in fig. 4 is a traditional gsfld, which is a fatigue strength diagram with comprehensive consideration of fatigue stress amplitude, average stress and mechanical property limitation of materials. it is often used in the fatigue design of railway vehicle structural components. for example, jis e4207-1992 (track frames for railway rolling stock-general rules for design) and uic ore b12/rp17 (tractive units-bogies and running gear–bogie frame structure strength tests) all take this diagram as design standard. this diagram is usually understood as "fatigue limit diagram", which mainly includes the gsfld of the base metal (outermost), butt weld (middle) and other weld (innermost). the corresponding limit values of turning points are shown in tab. 4. it can be observed from the fig.4 that some points have exceeded the weld evaluation area. it shows that under traditional gsfld, the over-standard points do not meet the standard requirements and the frame needs to be optimized. base metal butt welds other welds x y x y x y 240 240 220 220 220 220 152 240 188 220 200 220 -88 65 -110 22 -118 8 -240 -240 -240 -240 -240 -240 -85 -240 -108 -240 -116 -240 152 64 185 150 198 176 240 240 220 220 220 220 table 4: turning point value of gsfld of steel with tensile strength greater than 520mpa (a) strain gauge measuring point (b) rosette measuring point figure 5: platform and support mode of fatigue test figure 6: frame measuring point experimental verification the object of fatigue test that is performed based on the fatigue conditions specified in tab. 1 and tab. 2. it is to verify the fatigue strength of bogie frame experimentally and to study the reliability of the fatigue analysis results. fatigue test is carried out on the zjz (jp) 144 mts multi-channel fatigue test bed. the test loads are applied and distributed by the test tooling to the exact locations where these forces are generated in actual operation. the loading frequency is 5 hz, and the loading waveform refers to uic 615-4-2003 standard, which mainly includes the following three stages: (1) vertical and transverse loads  6 6 10 cycles, twisted loads  6 6 10 cycles; (2) vertical and transverse loads  6 2 10 cycles, static load remains unchanged, quasi-static and dynamic loads are multiplied by 1.2. twist load is multiplied by 1.2 and cycle  6 0.2 10 times; (3) vertical and transverse loads cycles  6 2 10 times while static load remains unchanged. quasi-static and b. chen et alii, frattura ed integrità strutturale, 48 (2019) 385-399; doi: 10.3221/igf-esis.48.37 390 dynamic loads are multiplied by 1.4 and cycle  6 0.2 10 times. the equipment and specimen for fatigue test are shown in fig. 5. fig. 6 describes the strain gauge type at the welding of bogie frame. base metal butt welds other welds x y x y x y 170 170 155 155 155 155 84 170 88 155 101 155 -50 78 -58 60 -66 45 -170 -170 -170 -170 -170 -170 -50 -170 -58 -170 -66 -170 84 -2 88 21 101 47 170 170 155 155 155 155 table 5: turning point value of gsfld of steel with tensile strength greater than 420mpa figure 7: schematic diagram of bogie frame patch layout figure 8: fatigue analysis results of bogie frame fig. 7 presents part of the strain gauge position of the bogie frame. it can be seen that the location of the patch is mostly the weld, which indicates that the evaluation of fatigue strength of the weld is more important. then, compared with the position of the weld shown in fig. 3, there are fewer test points in the experiment, which can't reflect the fatigue situation of all welds. hence, the combination of finite element simulation and experiment can more accurately evaluate the fatigue strength of the bogie frame. figure 8 displays the fatigue strength analysis results of the frame based on gsfld of ore b12/rp17. the gsfld given in fig. 8 are basically similar to those in fig. 4, which include gsfld of base metal, butt weld and other weld. the difference is that the limit values of the turning points of gsfld in fig. 4 are based on steel with tensile strength greater than 520 mpa, while those in fig. 8 are based on steel with tensile strength greater than 420 mpa. however, because the maximum yield strength of bogie frame is 355 mpa, which is less than the steel used in gsfld, therefore, both types of gsfld can be used as standard to judge whether the fatigue strength of the frame meets the requirements. in order to increase the evaluation range of fatigue strength, the gsfld of steel with tensile strength greater than 520 mp is generally selected in the actual simulation analysis tab. 5 shows the limit value of the turning point corresponding to the gsfld in fig. 8. it can be seen that the fatigue strength analysis results of each test point are basically in the gsfld of the weld, which meets the standard requirements. however, some of the test points are beyond or near the gsfld, which is more dangerous to the fatigue design of the frame. as can be seen from the comparison between fig. 4 and fig. 5, the results of experiment and simulation are basically the same. since the simulation calculation has continuity in extracting the fatigue strength analysis results of welds, there are more over-standard points. it can be seen that it is feasible to analyze the fatigue strength of bogie frame with simulation analysis in the design stage, and the calculation results are more accurate and reasonable. it can provide some guidance for the anti-fatigue design of bogie frame in detail design stage. b. chen et alii, frattura ed integrità strutturale, 48 (2019) 385-399; doi: 10.3221/igf-esis.48.37 391 fatigue strength analysis of bogie frame in consideration of parameters uncertainty establishment of polynomial response surface function raditional fatigue strength analysis based on deterministic model can't reflect the influence of uncertainty factors such as size and shape on fatigue strength. therefore, taking the maximum fatigue strength as the control point and analyzing its fluctuation under the influence of uncertainty factors can effectively characterize the fatigue strength reliability of the frame and provide a basis for lightweight design. in view of this, this study chooses the parameters which have a large impact on fatigue strength of control point as uncertainty variables, and uses apdl language to establish a parametric finite element model. in order to improve the computational efficiency, the d-optimal experimental design is used to select sample points, and the polynomial response surface surrogate model is adopted to characterize the functional relationship between variables and responses [15-17]. according to the fatigue strength analysis results of fig. 3 and fig. 4, the node number 287745 is taken as the control point, and the influence of uncertainties on it is calculated. tab. 6 and tab. 7 show the range of variables and the d-optimal experimental design process, respectively. design parameters sign unit lower limit mean value upper limit cross beam t1 mm 15 16 17 vertical inertia f1 kn -21.84 -20.8 -19.76 transverse inertia f2 kn -21.84 -20.8 -19.76 longitudinal inertia f3 kn -21.84 -20.8 -19.76 vertical inertia f4 kn 29.64 31.2 32.76 transverse inertia f5 kn 19.76 20.8 21.84 longitudinal inertia f6 kn 19.76 20.8 21.84 table 6: uncertainty design parameters. run number factors response t1 (mm) f1 (kn) f2 (kn) f3 (kn) f4 (kn) f5 (kn) f6 (kn) x y 1 15 -19.76 -19.76 -19.76 31.1844 21.84 19.76 12.4326 118.454 2 15 -19.76 -21.7568 -21.84 30.108 20.9917 21.84 14.3174 121.604 3 15 -21.84 -21.84 -19.76 29.64 19.76 19.76 11.2513 117.517 … … … … … … … … … … 44 17 -19.76 -21.84 -19.76 29.64 19.76 19.76 7.86325 112.135 45 17 -21.84 -19.76 -21.84 29.64 19.76 21.84 8.02718 113.298 46 17 -21.84 -21.84 -19.76 29.64 19.76 21.84 6.61196 113.293 table 7: d-optimal experimental design and response value. the polynomial response function with cross-terms is obtained by fitting the sample points obtained by experiment design with the least square method and the basic equation is given by 2 0 1 1 n n n ii i ij i j i i i i j i y c x c x x c x c =  = = + + +   (2) where n is the number of uncertain variables, 0c is the constant, and ic , iic , and ijc are the polynomial coefficients, respectively. according to eqn. (2), the experimental data in tab. 7 are fitted to obtain the response surface function of the control point coordinates, in which x represents the mean stress and y represents the stress amplitude. t b. chen et alii, frattura ed integrità strutturale, 48 (2019) 385-399; doi: 10.3221/igf-esis.48.37 392 1 1 2 3 4 5 6 -3 -3 -3 -3 -3 1 1 1 2 1 3 1 4 -3 -3 1 5 1 6 1 2 5.272 0.267 0.844 0.958 0.184 0.536 1.131 0.129 2.828 10 6.505 10 4.691 10 4.041 10 3.900 10 3.205 10 1.383 10 1.838 10 x t f f f f f f t f t f t f t f t f t f f f = + +  +  +  +  +  +  −  +    +    +    +    +    +    +    +  3 -4 1 3 1 4 -3 -4 -4 -4 -4 1 5 1 6 2 3 2 4 -3 -4 -3 -4 2 5 2 6 3 4 3 5 3 6 -4 4 5 3.826 10 1.659 10 8.623 10 1.752 10 2.331 10 1.265 10 1.067 10 6.201 10 1.710 10 2.139 10 3.634 10 7.699 f f f f f f f f f f f f f f f f f f f f f f f f   +    −    +    +    +    −    −    +    +    −    +    + -4 -3 -3 2 -3 4 6 5 6 1 2 -3 2 -4 2 -3 2 -3 2 -3 2 1 2 3 4 5 6 10 1.938 10 6.660 10 1.367 10 1.380 10 2.712 10 4.437 10 5.182 10 8.601 10 f f f f t f f f f f f    −    −   −   +   −   +   −   +   (3) 1 1 2 3 4 5 6 -3 -3 -3 -3 1 1 1 2 1 3 1 4 -3 -3 -3 1 5 1 6 1 2 66.695 4.045 0.118 1.758 0.617 2.631 5.914 4.453 2.828 10 6.505 10 4.691 10 4.041 10 3.900 10 3.205 10 1.383 10 1.838 10 y t f f f f f f t f t f t f t f t f t f f f = + +  +  +  −  −  + −  +    +    +    +    +    +    +    +  3 -4 1 3 -3 -4 -4 -4 1 4 1 5 1 6 2 3 2 -4 -3 -4 -3 4 2 5 2 6 3 4 3 5 -4 -4 3 6 4 5 3.826 10 1.659 10 8.623 10 1.752 10 2.331 10 1.265 10 1.067 10 6.201 10 1.710 10 2.139 10 3.634 10 7.699 f f f f f f f f f f f f f f f f f f f f f f f f   +    −    +    +    +    −    −    +    +    −    +    + -4 -3 4 6 5 6 -3 2 -3 2 -3 2 -4 2 -3 2 1 1 2 3 4 -3 2 -3 2 5 6 10 1.938 10 6.660 10 1.367 10 1.380 10 2.712 10 4.437 10 5.182 10 8.601 10 f f f f t f f f f f f    −    −   −   +   −   +   −   +   (4) the accuracy of response surface is the basis for ensuring the validity of experimental design and response surface function, and the premise of further analysis by using this model. the accuracy of response surface function and the significance of choosing design parameters can be obtained by checking the accuracy of response surface function, which is helpful to determine whether the selected design parameters are reasonable or not. in this paper, anova is used to analyze the model. some results are shown in tab. 8 and tab. 9. in order to better observe the fitting accuracy of response surface, the correlation diagrams of experimental and predicted values are given in fig. 9, in which actual represents the results of finite element calculation and predicted represents the results of response surface calculation. the f and p values in the table represent the significance of correlation coefficients. the larger of the f value, the more significant of the correlation coefficients is. on the contrary, the smaller of the p value, the more significant of the correlation coefficient is. as can be seen from tab. 8, the response surface model is significant, and the sensitivity of each design parameter to the response is significant, as well. it shows that the fitting accuracy of response surface is high and the selection of design parameters is reasonable. because of space, the interaction among design parameters can't be given. through analysis, it is found that the interaction among design parameters in response surface function is relatively low, which indicates that the interaction between design parameters has less influence on response. similarly, tab. 9 shows that although the sensitivity of each design parameter to response is not all significant, the response surface model is generally significant. combining tab. 8 and tab. 9, we can see that although the significance of design parameters to x and y is different, the control points (x, y) composed of x and y still show significant characteristics, which indicates that the selected design variables have a greater impact on the control points, and further proves the rationality of the selection of design variables. it can be observed from fig. 9 that all design points are near the 45 diagonal line, and the residual is small, which shows that the predicted values of response surface functions x and y are quite close to the actual values. (a) fitting accuracy of response surface x (b) fitting accuracy of response surface y figure 9: fitting accuracy of control points b. chen et alii, frattura ed integrità strutturale, 48 (2019) 385-399; doi: 10.3221/igf-esis.48.37 393 source model sum of squares df mean square f value p-value prob > f model 230.04 35 6.57 6.873e+5 < 0.0001 significant t1 0.036 1 0.036 3735.32 < 0.0001 significant f1 17.85 1 17.85 1.867e+6 < 0.0001 significant f2 26.41 1 26.41 2.762e+5 < 0.0001 significant f3 1.91 1 1.91 2.0e+5 < 0.0001 significant f4 51.34 1 51.34 5.369e+6 < 0.0001 significant f5 24.41 1 24.41 2.552e+6 < 0.0001 significant f6 2.37 1 2.37 2.48e+5 < 0.0001 significant … … … … … … … residual 9.562e-5 10 9.562e-5 lack of fit 9.562e-5 5 1.912e-5 1.125e6+5 < 0.0001 significant pure error 8.500e-10 5 1.700e-10 cor total 230.04 45 table 8: anova for response surface x quadratic model. source model sum of squares df mean square f value p-value prob > f model 498.34 35 14.24 9191.84 < 0.0001 significant t1 9.08 1 9.08 5860.00 < 0.0001 significant f1 1.326e-3 1 1.326e-3 0.86 0.3766 non-significant f2 0.026 1 0.026 16.82 0.0021 non-significant f3 0.041 1 0.041 26.19 0.0005 non-significant f4 206.54 1 206.54 1.33e+5 < 0.0001 significant f5 94.29 1 94.29 60871.61 < 0.0001 significant f6 9.65 1 9.65 6229.75 < 0.0001 significant … … … … … … … residual 0.015 10 1.549e-5 lack of fit 0.015 5 3.098e-3 pure error 0.000 5 0.000 cor total 498.36 45 table 9: anova for response surface y quadratic model the control points value in consideration of parameter uncertainty in order to calculate the mean stress and stress amplitude of control points more accurately, this study uses the important sampling method to select the sample points of uncertainty parameters. important sampling method is one of the most effective monte carlo techniques, the basic principle is that it doesn't from a given probability distribution function of sampling, but modifies the given probability distribution so as to shift the sampling center towards the failure region to gain information more efficiently [18]. probability of structural failure can be expressed in the following form [ ( )] ( ) [ ( )] ( ) ( ) = ( ) ( ) x x x x f v v v i g v f v i g v f v p p v dv e p v p v + −   =      (5) b. chen et alii, frattura ed integrità strutturale, 48 (2019) 385-399; doi: 10.3221/igf-esis.48.37 394 where v denotes basic input variables, ( )g v is the performance function, ( )xf v is the joint probability density function of a random variables, ( )vp v is the assumed importance sampling density(isd). obviously, the success of importance sampling relies on the proper choice of isd. the optimal isd can be drawn through theoretical analysis [19]. [ ( )] ( ) ( ) x x opt f i g v f v p v p = (6) in order to illustrate the influence of uncertainties in design parameters on control points, 46 experimental design control points are given based on tab. 7. comparing fig. 3 and fig. 10 it is seen that due to the uncertainty of design parameters, the control points show a large degree of discreteness, which greatly exceeds the evaluation range of fatigue limit of bogie frame. fig. 11 plots the distribution of control points based on importance sampling method. it can be clearly seen from the figure that the fluctuation of design parameters leads to a greater dispersion of control points. comparing fig. 10 and fig. 11 shows that the distribution of the control points in the dense area is reasonable, which can reflect the influence of the fluctuation of the over-standard points near the fatigue limit diagram on the fatigue strength analysis results well. compared with the deterministic model, the results of uncertainty analysis are more in line with engineering practice. figure 10: the fluctuation of control points under uncertain factors figure 11: importance sampling results of control points functional expression of goodman-smith fatigue limit diagram gsfld is widely used in fatigue strength checking of materials in the world. at present, most railway rolling stock adopt modified gsfld to design fatigue strength of its parts. the modified goodman curves are generally divided into two forms: haigh graphics and smith graphics. in this paper, the modified gsfld is used to evaluate the fatigue strength of the frame [20]. the determination of the modified gsfld requires three limit values, i.e. strength limit  b and yield limit yt  of materials and fatigue limit  −1n of frame. according to tab. 3, the yield strength of the material is 345 mpa. the ultimate strength of s355j2(h) material is 520 mpa. in the traditional gsfld, when calculating the fatigue limit  −1n of frame, factors such as size, shape and surface machining quality are involved in the calculation in the form of safety factor. -1 -1 1 1 = =38+0.43 n f b k       − − (7) where -1  is the surface machining factor,  is the size factor, fk is the stress concentration factor. as can be seen from eqn. (7), the calculation of fatigue limit -1n  based on safety factor is too conservative, resulting in high redundancy of fatigue strength, which is not conducive to the lightweight design of the frame. therefore, gsfld b. chen et alii, frattura ed integrità strutturale, 48 (2019) 385-399; doi: 10.3221/igf-esis.48.37 395 without safety factor is adopted to more accurately evaluate the fatigue strength of the frame. since the cause of stress concentration factor is complex, it is taken as a fixed value. f k =1.1 is selected according to the stress concentration coefficient factors diagram provided by bs7608 standard (guide to fatigue design and assessment of steel structures) and the s-n curve of steel under different stress concentration factors given in the book of fatigue life prediction of structural. the fatigue limit -1n  of the frame and the fatigue limit -1  of the material are calculated to be 237.8mpa and 261.6mpa, respectively. tab. 10 shows the turning point coordinates of the gsfld. in tab. 10, the closed 8-sided region formed by abcdefgha is a gsfld, with turning points at each point. among them, a and e are the symmetrical cyclic fatigue strength under given fatigue life n; c and g are the turning points of the tensile yield limit and the compressive yield limit in transverse and longitudinal coordinates, which are equal for general metal materials. b, f, d and h are turning points to control the limit state when goodman correction is carried out considering the average stress. in the coordinates of each point,  −1n is the symmetrical cyclic fatigue strength under given fatigue life n;  b is the ultimate tensile strength; yt  is the yield tensile strength;  yc is the ultimate tensile strength. combined with tab. 10 and mechanical properties of the frame material, a new goodman-smith fatigue limit diagram (ngsfld) is obtained, as listed in fig. 12 and fig. 13. turning point mean stress  m stress amplitude  a turning point mean stress  m stress amplitude  a a 0 −1n e 0 −− 1n b      − − − − 1 1 yt n b b n  yt f  − −1n yc − yc c  yt  yt g − yc − yc d      − − − − 1 1 yt n b b n ( )       − − − + − − 1 1 1 2 b n yt b n b n h  − −1n yc  − −12 n yc table 10: goodman-smith plot of turning point coordinates figure 12: comparison of goodman-smith fatigue limit diagrams figure 13: goodman-smith fatigue limit diagram without considering the safety factor the black line in fig. 12 is gsfld without safety factors, and the red line is the fatigue limit diagram specified in ore b12/rp17 standard. fig. 12 shows that the newly defined gsfld is broader than the ore b12/rp17 standard definition, that is, it is more conservative to use the gsfld defined by ore b12/rp17 standard to evaluate the fatigue strength of bogie frame. it is not only simple and universal to evaluate the fatigue strength of the frame conservatively in engineering practice, but also to ensure the reliability of the product. however, conservative anti-fatigue design can no longer meet the requirements of rail vehicles which are increasingly pursuing lightweight. therefore, the redundancy of design can be reduced by using the ngsfld drawn in fig. 13 for fatigue strength analysis. fig. 13 contains the types of b. chen et alii, frattura ed integrità strutturale, 48 (2019) 385-399; doi: 10.3221/igf-esis.48.37 396 fatigue strength assessments for base metal, butt weld and other weld forms. in order to evaluate the fatigue strength reliability of the frame, the function expressions of ngsfld are given in eqn. (8), eqn. (9) and eqn. (10). ( ) ( ) ( ) ( ) ( ) ( ) =    = + −     = + −   −  = − −   −  = − −    = −   345 197.5 345 0.68 206 107.2 197.5 2 345 345 107.2 345 345 107.2 1.30 206 107.2 197.5 2.2 345 197.5 345 y x y x x y x x y x y x x y x x (8) ( ) ( ) ( ) ( ) ( ) ( ) =    = + −     = + −   −  = − −   −  = − −    = −   316.3 243.7 316.3 0.68 148 150.5 243.7 2 345 345 150.5 345 345 150.5 1.30 148.2 150.5 243.7 2.2 318.9 243.7 316.3 y x y x x y x x y x y x x y x x (9) ( ) ( ) ( ) ( ) ( ) ( ) =    = + −     = + −   −  = − −   −  = − −    = −   316.3 269.7 316.3 0.68 133.68 160.5 269.7 2 345 345 160.5 345 345 160.5 1.30 137.75 160.5 269.7 2.2 401.8 269.7 316.3 y x y x x y x x y x y x x y x x (10) fatigue strength reliability calculation of control point control point as the maximum point of fatigue strength in the deterministic model, its fluctuation under uncertainty variables directly reflects the minimum fatigue strength reliability of the frame. therefore, the accuracy of fatigue strength reliability analysis of control point provides theoretical support for ensuring the overall fatigue reliability of the frame, reducing design redundancy and lightweight. traditional fatigue strength analysis of bogie frame is based on observing whether the evaluation points are within the gsfld or not, and for the evaluation points beyond the ngsfld, if the stress amplitude does not exceed 20% of the corresponding yield stress, the fatigue strength design requirements are considered to be satisfied. because of the excessive security redundancy, this method allows the existence of evaluation points exceeding the standard. however, the excessive safety redundancy makes the bogie frame designed meet the standard requirements, but it is too bulky and does not meet the current goal and demand of lightweight structure. based on this, the reliability-based fatigue strength analysis method proposed in this paper perfectly solves the above problem. the control points are calculated by eqn. (3) and (4), and the probability of control points within the fatigue limit diagram is calculated by combining the function expression of gsfld. the limited state equation of bogie frame can be defined as = − ( ) x z y f x (11) the fatigue strength reliability of bogie frame is given by = n r n (12) where y is the y value of the control point obtained from the important sampling, ( )xf x is the ngsfld function corresponding to the x value of the control point, n is the number of control points at  0z and n is the total number of control points. b. chen et alii, frattura ed integrità strutturale, 48 (2019) 385-399; doi: 10.3221/igf-esis.48.37 397 since the control point is located at the weld and the weld is t-shaped, the gsfld corresponding to eqn. (10) should be selected as the standard for evaluating the fatigue strength of the control point. in order to compare the results of two fatigue strength evaluation standard, the fatigue strength of control points is calculated based on eqn. (10) and traditional method, respectively, as illustrated in fig. 14. figure 14: comparison of fatigue strength analysis results of control points. figure 15: comparison of safety factor of fatigue strength at control points. from fig. 14, it can be seen that the fatigue strength analysis results based on the ngsfld are higher than the importance sampling results. although the control points fluctuate to a certain extent due to the uncertainty of design parameters, the fatigue strength is still within the fatigue limit diagram, indicating that the fatigue strength of bogie frame basically meet the requirements. however, the results of fatigue strength analysis based on traditional method are lower than those of importance sampling. the reason is that the control point is beyond the scope of fatigue limit diagram when it is selected. although the uncertainty of design parameters leads to the fluctuation of control points, all the results are still out of the fatigue limit diagram, indicating that the fatigue strength of bogie frame does not meet the requirements. in order to further analyze whether the fatigue strength meets the requirements or not, fig. 15 plots the results of safety factor under two evaluation standards. it can be observed from the figure that the safety factors of the ngsfld are all greater than 1.1, and basically remain at about 1.2. it meets the requirement of safety factor for fatigue strength analysis of bogie frame. on the contrary, the safety factors obtained by traditional method are less than 1, which does not meet the b. chen et alii, frattura ed integrità strutturale, 48 (2019) 385-399; doi: 10.3221/igf-esis.48.37 398 standard requirements, and the bogie frame needs to be redesigned and optimized. according to eqn. (12), the reliability of bogie frame under the two evaluation standard is 1 and 0, respectively. it shows that the fatigue limit diagram without considering safety factor can also be used to evaluate the bogie frame, and the traditional method has excessive safety factor, which is too conservative in design. conclusions his paper presents a fatigue strength analysis method by considering uncertainty of design parameters based on gsfld and reliability theory, and the practicability of the method is verified by employing ngsfld for bogie frame. the proposed method solves the problem of conservatism in traditional fatigue strength analysis from two aspects: on the one hand, considering the uncertainty of design parameters, a parameterized model is established, and the fluctuation of control points under the uncertainty parameters is calculated. compared with deterministic analysis, it can reflect the discreteness of analysis results caused by uncertainties such as design, manufacturing and working conditions. on the other hand, the fatigue limit diagram without considering safety factor is established. compared with the fatigue limit diagram provided in ore b12/rp17 standard, the excessive redundancy and conservative of the design scheme are solved. the fatigue strength reliability analysis results of the two methods are 1 and 0, respectively. it shows that the traditional method is too conservative to evaluate the design scheme, which results in that the reliability of the original qualified design is 0 due to the high safety factor of the evaluation standard, which does not meet the requirements. it not only wastes resources, but also is not conducive to the lightweight design of railway vehicles. in general, in order to ensure the safety of structural design and achieve the purpose of lightweight design, the parameter uncertainty considered in the design stage is more consistent with the actual needs of the project. acknowledgments his research is supported by the national natural science foundation of china under contract no. 51875073, the education project of liaoning provincial department under contract no. jdl2017022, liaoning provincial natural science foundation of china under contract no. 20170540129. references [1] claus, h. and schiehlen, w. (2007). modeling and simulation of railway bogie structural vibrations, veh. syst. dyn., 29(1), pp. 538-552. doi: 10.1080/00423119808969585. [2] stichel, s. and knothe, k. (2007). fatigue life prediction for an s-train bogie, veh. syst. dyn., 29(1), pp. 390-403. doi: 10.1080/00423119808969573. [3] ren, z.s. and xie, j.l. (2008). influence on axle load to the service life of the crossbar set of railway freight car with equivalent load, j. mech. eng., 44(3), pp. 16-21. doi: 10.3321/j.issn:0577-6686.2008.03.003. [4] zhu, n., sun, s.g., li, q. and zou, h. (2016). theoretical research and experimental validation of elastic dynamic load spectra on bogie frame of high-speed train, chin. j. mech. eng., 29(3), pp. 498-506. doi: 10.3901/cjme.2016.0308.027. [5] park, b.h. and lee, k.y. (2006). bogie frame design in consideration of fatigue strength and weight reduction, proceedings of the institution of mechanical engineers, part f: journal of rail and rapid transit, 220(3), pp. 201–206. doi:10.1243/09544097f01405. [6] han, j.w., kim, j.d. and song, s.y. (2013). fatigue strength evaluation of a bogie frame for urban maglev train with fatigue test on full-scale test rig, eng. fail. anal., 31, pp. 412–420. doi:10.1016/j.engfailanal.2013.01.009. [7] hwa, p.b., po, k.n., seok, k.j. and yong, l.k. (2006). optimum design of tilting bogie frame in consideration of fatigue strength and weight, veh. syst. dyn., 44(12), pp. 887–901. doi:10.1080/00423110600737106. [8] seo, j.w., hur, h.m., jun, h.k., kwon, s.j. and lee, d.h. (2017). fatigue design evaluation of railway bogie with full-scale fatigue test, adv. mater. sci. eng., 2017, pp. 1–11. doi:10.1155/2017/5656497. [9] li, f.s., wu, p.b., zeng, j. and wang, j.b. (2014). study on the differences between the three common fatigue strength, j. mech. eng., 50(14), pp. 170-176. doi: 10.3901/jme.2014.14.170. t t b. chen et alii, frattura ed integrità strutturale, 48 (2019) 385-399; doi: 10.3221/igf-esis.48.37 399 [10] kim, j.s. (2006). fatigue assessment of tilting bogie frame for korean tilting train: analysis and static tests, eng. fail. anal., 13(8), pp. 1326–1337. doi: 10.1016/j.engfailanal.2005.10.007. [11] wang, w.j., li, z.m., li, q. and miao, l.x. (2009). fatigue strength analysis of crh2 motor bogie frame, journal of beijing jiaotong university, 33(1), pp. 5-9. doi: 10.3969/j.issn.1673-0291.2009.01.002. [12] wang, h., liu, w.x. and shang, y.j. (2013). fatigue strength analysis on welded frame of domestic y25 bogie based on hot spot stress, china railway science, 34(4), pp. 66-70. doi: 10.3969/j.issn.1001-4632.2013.04.11. [13] lu, y.h., feng, z., chen, t.l., zeng, j. and wu, p.b. (2014). finite element analysis of multi-axial fatigue strength for railway vehicle bogie frame, journal of beijing jiaotong university, 38(4), pp. 26-31. doi: 10.11860/j.issn.1673-0291.2014.04.005. [14] lu, y.h., xiang, p.l., zeng, j. and chen, t.z. (2016). evaluation method of fatigue strength for welding bogie frame on railway vehicle, journal beijing jiaotong university, 40(6), pp. 83-88. doi: 10.11860/j.issn.1673-0291.2016.06.014. [15] elgendy, n.s., ali, b.a. and amr, s.s.a. (2016), application of d-optimal design and rsm to optimize the transesterification of waste cooking oil using natural and chemical heterogeneous catalyst, energy sources, part a: recovery, utilization, and environmental effects, 38(13), pp. 1852-1866. doi: 10.1080/15567036.2014.967417. [16] olofsson, u. and sundvall, k. (2004). influence of leaf, humidity and applied lubrication on friction in the wheel-rail contact: pin-on-disc experiments, proceedings of the institution of mechanical engineers, part f: journal of rail and rapid transit, 218(3), pp. 235–242. doi: 10.1243/0954409042389364. [17] zhi, p.p., li y.h. and chen, b.z. (2019). structural strength analysis of bogie frames considering parameter uncertainty, chin. mech. eng., 30(1), pp. 22-29. doi: 10.3969/j.issn.1004-132x.2019.01.004. [18] zhao, h., yue, z., liu, y., gao, z., and zhang, y. (2015). an efficient reliability method combining adaptive importance sampling and kriging metamodel, appl. math. modell., 39(7), pp. 1853–1866. doi:10.1016/j.apm.2014.10.015. [19] lee, s., and kim, j.h. (2017). an adaptive importance sampling method with a kriging metamodel to calculate failure probability, j. mech. sci. technol., 31(12), pp. 5769–5778. doi: 10.1007/s12206-017-1119-8. [20] diao, y., shi, c., and tian, h. (2016). effect of multi-repair welding on fatigue performance of aluminum alloy profile welded joint, mater. sci. eng., a, 2016, pp. 521-528. doi: 10.1142/9789813141612_0071. microsoft word numero_58_art_13_3100.docx a. talhi et alii, frattura ed integrità strutturale, 58 (2021) 179-190; doi: 10.3221/igf-esis.58.13 179 effect of gaseous carburizing thermochemical treatment on tribological behavior of ti–6al–4v alloy amar talhi, mohamed zine touhami metallurgy and materials engineering, foundry laboratory, badji mokhtar university annaba, algeria talhiamaryacine@gmail.com kamel fedaoui university of constantine 1, constantine, algeria kamel.fedaoui@umc.edu.dz, https://orcid.org/0000-0003-0885-6914 abstract. this study concerns the improvement of performance of resistance to wear phenomena of the ti-6al-4v alloy surface by means of gaseous carburizing thermochemical treatment. three-thermochemical treatment durations (2h, 4h, and 6h) were chosen for investigation of the effect of such treatment on this alloy. the hardness test under an indentation load of 0.05 kgf with a vickers pyramidal indenter revealed that the surface hardness is 335 hv for the untreated samples. the hardness reaches approximately 1500 hv during gas cementation at 930 °c for variable times (2h, 4h, 6h) followed by quenching at 840 °c in an oil medium, which was accompanied by a significant improvement in wear resistance. the characterization of the modified surface layers was studied by means of a microscopic analysis and by x-ray diffraction. the case-hardening made it possible to obtain a wear resistance greater than that of the alloy not treated, minimal loss of mass by dry friction and an improvement in roughness as well as a good coefficient of friction. keywords.ti-6al-4v; tribological behavior; carburizing; wear; hardness. citation: a. talhi, mz. touhami, k. fedaoui, effect of gaseous carburizing thermochemical treatment on tribological behavior of ti–6al– 4v alloy, frattura ed integrità strutturale, 58 (2021) 179-190. received: 16.05.2021 accepted: 08.08.2021 published: 01.10.2021 copyright: © 2021 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. introduction itanium-aluminum-vanadium ti-6al-4v alloy is one of the most used alloy in industrial application .these properties include better corrosion resistance, biocompatibility and the possibility of working in a wide temperature range. these specific characteristics make this alloy a product used in 50% of the industrial market [1]. titanium alloys are materials of choice in aeronautics in particular because of their low densities (4.5 g/cm3 for titanium and 4.4 g/cm3 for ti-6al-4v). t https://youtu.be/pzsd_gdimhe a. talhi et alii, frattura ed integrità strutturale, 58 (2021) 179-190; doi: 10.3221/igf-esis.58.13 180 ti-6al-4v alloy offers excellent properties, which are advantageous after doing the casehardening. we note the increases of mechanical characteristics such as hardness, better resistance to fatigue and the borne of new complex phases resultants of diffusion of carbon during the interaction with the basic elements. due to its low tribological property, ti-6al-4v is known to have poor wear and friction behavior. for this reason, it is rarely used in industrial applications where the parts are often subjected to movements causing friction or sliding. therefore, various techniques of surface modification by thermochemical processes such as carburization or carburizing [24], nitriding [5-6] and carbonitriding [7] have been used to improve wear resistance of titanium alloys. as the results, carbides and nitrides newly formed with carbon and nitrogen are difficult and stable at high temperatures, which will improve the wear resistance and surface hardness of this alloy [8-9]. the damage to the material gradually leads to the establishment of three areas of research carried out respectively by: the mechanics who deal with the influence of fretting on cracking use for this purpose fretting tests [10]. researchers in materials sciences are developing new surface treatments and coatings, which allow high surface hardening and an improvement in tribological properties [11]. tribologists try to understand the mechanisms of action of the interfacial layers or debris which in turn increases friction, field [12], zahavi [13] and daoud [14], studied the influence of roughness on the fatigue strength and demonstrated that the fatigue strength increases when the surface roughness decreases. our work can be classified in the research of a new treatment to improve of the tribological properties of such alloy. we focused our experimental investigation to study the role of treatment on the mechanical, tribological and structural properties of the titanium-aluminum-vanadium ti-6al-4v alloy. in this paper, we present an experimental investigation of the effect of time of material hardening on the mechanical and microstructural properties of the surface and sub-layers for untreated and carburizing state. titanium-aluminum-vanadium ti-6al-4v alloy is the subject of this study. the techniques used to study the tribological behavior of this alloy are the mass losse, the surface roughness, the coefficient of friction; therefore, we have also shown by sem the morphology of the friction tracks created by the ball, as well as the hardness as a function of time hardening. material studied and experimental techniques he alloy used in this study is titanium-aluminum-vanadium ti-6al-4v alloy, which was delivered in the form of a plate of dimensions (100x60x5 mm). this alloy has undergone hot rolling and the structure of which is completely recrystallized. it is a two-phase alloy of alpha + beta type (α + β). compared to others designation of titanium alloys, this alloy has the highest mechanical strengths [15]. as long as parts made of ti6al4v alloy are exposed to high conditions (temperature, oxidation medium, friction ...), can undergo rapid degradation and to improve it we must proceed with a casehardening to be able to give a better tribological behavior. it is found that in a situation of friction, the ti-6al-4v shows poor wear resistance behavior, thus causing a loss of material following its degradation. the chemical composition of the titanium alloy is shown in tab. 1: elements o c fe al v h n ti mass (%) 0.13 0.08 0.25 6 4 0.02 0.05 bal. table 1: chemical compositions of the titanium alloy ti-6al-4v studied [16]. the aim of this study is carrying out a gas carburizing treatment with a view to improving the tribological behavior of the titanium alloy "ti6al4v", known for its low resistance to wear. carburizing is one of the most used surface treatments and more widespread. it improves certain properties of materials, notably their hardness, wear resistance and their corrosion resistance. surface hardening treatment by quenching after carburizing was done in an aichelein-type oven at the level of the thermochemical treatment workshop of the epe / spa etrag company in constantinealgeria. the properties of carburizing gas are:  gas components: ch4nh3  air / gas ratio: 2.8  flow rate: 0.2 0.3 m3nh-1 t a. talhi et alii, frattura ed integrità strutturale, 58 (2021) 179-190; doi: 10.3221/igf-esis.58.13 181  dew point ± 2 °  carbon potential: 0.8%  cracking temperature: 1040°c the treatment was carried out according to the operating conditions set for the needs of the company's thermochemical treatment workshop: a treatment temperature of 930°c, for three variable times (2h, 4h, 6h) followed by a soaking at 840°c in an oil medium. scanning electron microscope is used to visualize the layers formed on the surface of the alloy after gas carburization. the same surface preparation described above was carried out. to estimate the hardness of ti-6al-4v, we performed the vickers micro-hardness tests before and after the cementation treatment, using a micro vickers hardness tester zwick roell zhv. the hardness tests of ti-6al-4v are carried out by applying a load of 0.05 kgf for 15 seconds. wear or loss of mass test was done at the metallography laboratory (metallurgy department of university of annaba-algeria). the device used is composed of a sample holder system fixed on a variable speed polisher. the load applied to the parallelepiped sample (10x7x5) mm is fixed to 5n for 1 minute. the sample rotate with angular speed of 65 rpm and the grade of silicon carbide paper is 800. weight loss is measured after each minute using an electronic microbalance whose measurement accuracy is around 10-3 g. note that the samples are cleaned with acetone before each weight gain. x-ray diffraction (xrd) is one of the techniques commonly used to identify the crystal structures present in a metal sample. from the diffraction diagram, it is possible to determine the nature, the mesh parameters or even the quantity of each of the phases present in a multi-phase alloy for example. x-ray diffraction (xrd) can also inform us about possible states of stress and crystallographic textures. the principle of this technique is based on the measurement of the inter-reticular distances relative to the different families of crystalline planes (in agreement with the bragg relation). the diffractograms are recorded with the radiation (cukα = 1.5406 å), in the case of a simple identification of the phases, a range from 0° to 100° (in 2θ). all the diffraction spectra were performed on a panalytical 'x'pert pro "type diffract-meter at the university of bejaiaalgeria. the surface roughness was carried out on the surface of the samples before and after treatments using a mitutoyo type roughness tester. the effect of the cementation conditions on the surface roughness was measured according to the average roughness values (ra). for the tribology test and according to previous work [16-17] that treated the same material, the following parameters were chosen, see tab. 2. all the tests are carried out without lubrication and in air. course 40 m rotation diameter 6 mm the applied load 10 n the material of the ball alumina (al2o3). ball diameter 10 mm the rotation speed 3 cm/s table 2. parameters of tribology test. results and discussions n this section, results from different technics of characterization of material used to study the effect of treatment on the mechanical and structural properties of ti-6al -4v alloy were presented. microstructures of the ti 6al 4v alloy the sample alloys were cut, with a precision chainsaw, coated in section and polished. a chemical attack was made with the attack reagent consisting of 5% hf, 5% hno3 and 90% distilled water. the microstructures were observed under an optical microscope and the sem. we observe on the (fig.1) untreated state, an alpha + beta type structure (α + β) and cemented layers according to the carburizing time (fig.2). i a. talhi et alii, frattura ed integrità strutturale, 58 (2021) 179-190; doi: 10.3221/igf-esis.58.13 182 figure 1: structures by optical microscope (untreated ti6al4v, a-b). figure 2: microstructures of ti 6al 4v carburizing at 930 °c a) for 2h, b) for 4h and c) for 6h. we note that the carburizing depths is about: for 2h = 71.98 µm, 4h = 123.66 µm and for 6h = 160.04 µm. from the figures, we see that the effect of the treatment times is clearly visible, the saturation of the cemented area with the presence of carbon and other elements give birth to hard and complex phases such as titanium carbide and carbide of vanadium (tic, vic ...) confirmed by hailiang du et all [18]. x-ray diffraction -ray diffraction will remain, for a long time, one of the techniques used to the identification of crystallographic structures and the phases formed. the microstructures show the presence of layers of mixed and complex carbides and nitrides (tin + tinx, tic, alc, vc, alti, ...). a) x a. talhi et alii, frattura ed integrità strutturale, 58 (2021) 179-190; doi: 10.3221/igf-esis.58.13 183 b) c) d) a. talhi et alii, frattura ed integrità strutturale, 58 (2021) 179-190; doi: 10.3221/igf-esis.58.13 184 e) figure 3: xrd of a) untreated statereference and carburizing state 930°c – b) for 2h, c) 4h, d) 6h and e) for all the cases. we note that the effect of the carburizing after decomposition of the carrier gas during the diffusion and under the action of the dissolution of the elements (carbon, nitrogen and oxygen) have an affinity to be dissolved with the whole elements (titanium, aluminum and vanadium). we observe that the peaks of titanium are the most dominant from the point of view of quantity. note: for the superposition of the xrd cannot be identical since the untreated sample and the three other samples are not realized with the same parameters such as the scanning step. we can clearly see in the figure that the reference sample the main peak (αti) is shifted with respect to the three others at the angle 2θ = 38 °. tribological behavior weight loss of ti-6al-4v alloy or each sample, we weigh its mass before and after the tribological test using a precision balance up to 10-3 g. we note that the loss of mass by degradation of the surfaces by friction of the treated sample for 6 h have a constant mass loss over 300 m. the sample with 4 h present an increase in weight loss after the 200 m. the same observation is valid for the sample of 2 hours where an increase in mass loss from 120 m is recorded. the original sample without treatment, presented a linear and remarkable degradation. by comparison, to the other samples, a gain in mass was observed for the cemented samples unlike the original sample without treatment. several slip regimes and different wear mechanisms have been observed depending on the applied load [19-21]. abrasion phenomenon was observed at different case hardening times for the applied load. the wear mechanism by delamination and by fatigue appears during the hardening times (2h, 4h and 6h). in fact, the increase in the loss of mass in the wear track results from a dissipation of the friction energy in the contact zone [22]. roughness he effect of the cementation conditions on the surface roughness was explored according to the average roughness values (ra) after seven tests for each sample. we note here that cementation technic is a good technique for improving roughness surfaces (fig.5). f t a. talhi et alii, frattura ed integrità strutturale, 58 (2021) 179-190; doi: 10.3221/igf-esis.58.13 185 0 200 400 600 800 1000 0,00 0,01 0,02 0,03 0,04 0,05 ti6al4v 930°c: 6 h ti6al4v 930°c: 4 h ti6al4v 930°c: 2 h ti6al4v reference lo s s o f m a s s ( g ) distance (m) figure 4: variation in mass loss (untreated state -reference and carburizing 930°c : 2h, 4h, 6h). figure 5: roughness evolution (ra : arithmetic mean height, rp: maximum height of peaks,rz : maximum height of the profile and rv: maximum depth of the valleys). wear resistance (coefficient of friction) n order to have an idea of the behavior in the face of wear, we carry out, on each case hardened samples, a tribological test with identical conditions. a first analysis of these results (fig.6) shows that the coefficient of friction increases from the first cycles of friction; this is defined as the transition or running-in period observed during the test. friction can be classified into three characteristic periods of the evolution of friction as a function of time. for the first one, it represents the incubation time, which corresponds to the adaptation of the two surfaces by elimination of the surface oxides to give rise to the ceramic metal interaction, hence a rapid increase in the coefficient of friction. the second is a period of modification of the friction properties of surfaces, which corresponds to the transition from friction to the stabilized state with formation of the 3 rd body; the last one corresponds to the stabilized condition of friction. at room temperature, the coefficient of friction of the ti-6al-4v alloy and the alloy coating varied with the wear time for different loads [24 23]. when the load was 3 n, the coefficient of friction of ti-6al-4v alloy increased with test time in the first 15 min, then stabilized after 15 min and the coefficient of friction was kept between 0.47 and 0.53. when the load was 6 n, the pre-grinding period was reduced to 10 min, then stabilized, and the coefficient of friction was kept in the range of 0.40 ~ 0.47. when the load increases to 9n, there was no pre-grinding period; it was directly in the stable period. here coefficient of friction decreased and maintained in the range of 0.39-0.44. finally, this observation confirms our parameters i a. talhi et alii, frattura ed integrità strutturale, 58 (2021) 179-190; doi: 10.3221/igf-esis.58.13 186 and our results as the 10n load and the al2o3 ball under the same conditions at ambient temperature without lubrication and with air. this achieved a good improvement in the coefficient of friction by addition of the thermochemical-hardened layer (gaseous cementation). figure 6: coefficient of friction (untreated and carburizing 930°c 2h , 4h , 6h ). a) b) c) d) figure 7: morphological state of the samples after wear test using a scanning electron microscope. a) untreated; b) carburized at 930°c – 2h; c) carburized at 930°c – 4h; d) carburized at 930°c – 6h. a. talhi et alii, frattura ed integrità strutturale, 58 (2021) 179-190; doi: 10.3221/igf-esis.58.13 187 from all these results, we note that the improvement in the coefficient of friction depend on the quantity of carbon diffused in the alloy; we observe that the tribological performances for (6h) are superior to those of the other samples (fig.7). the sliding of the ball on the surfaces of the hardened samples is carried out under a load of 10n in order to quantify the wear and the coefficient of friction. a streaks observed on the facies, on the friction track, scratches and / or streaks are caused by the hard particles of the third body which indicates a real deterioration of the surfaces as well in width which is very clear in fig. 7, (reference = 762.3 µm, 2h = 652.9µm, 4h = 529.7µm and for 6h = 410µm). noting therefore that the sample of fig. 7-d, presents a better behavior from the point of view of resistance to wear, hardness and depth of cementation. we previously knew that oxygen was mainly found on the surface of the sample layer (titanium oxide tio) without it forming crystalline precipitates. we can assume that oxygen impairs good tribological behavior by causing a three-body wear regime more quickly (fig.8). the diffusion of carbon in the titanium alloy by gas carburizing makes it possible to significantly improve both the hardness and the tribological performance of ti-6al-4v, see work of j.c. sánchez-lópez et al [24]. observation by scanning electron microscope (fig.7-8) shows the presence of plowing grooves corresponds to the same abrasive wear mechanism. the width of the passage of the ball for the untreated state is greater compared to the other case-hardened samples, (the values are respectively: untreated state = 762.3 µm , 2h = 652.9 µm , 4h = 529.7µm and for 6h = 410µm). figure 8: appearance of the asperities of the third body (white). depending on the number of cycles, the particles detached from the surface participate in the kinetics of wear in the contact. in fact the type of contact passes each time from a two-body contact; al2o3 -ti 6al 4v to that with three bodies; debris al2o3 ti 6al 4v; (fig.8), which brings us to have the same phenomenon which are in agreement with those of [19, 2526]. hardness profile o study the effect of cementation on the mechanical properties of samples, vickers microdurometer with a 0.05 kgf of load is used. vickers method (hv) is simple and can provide some information’s on the hardness property of samples and their depths. the presence of complex phases in the case hardened layers improves the fatigue strength of the treated titanium alloy. therefore, it is often necessary to carry out a surface treatment on titanium alloys in order to improve their behavior in friction according to [27]. the hardened layers have a high surface hardness, close to 1500 hv for the sample of the 6 hours of cementation while the hardness of the sample without treatment is 335 hv. we note here a great increase of 5 times in surface hardness implies a high resistance to wear, friction, abrasion and seizure. we assume that the diffusion distance is only determined by two factors (one is the speed of diffusion, and the other is the driving force of diffusion), (see fig 9). we deduce that the role played by the cementation time on the increase of hardness can be important in specific cases, but other factors such as mechanical, microstructural and contact surface characteristics (material / ball) have an influencing role, see [28-30]. t the third body a. talhi et alii, frattura ed integrità strutturale, 58 (2021) 179-190; doi: 10.3221/igf-esis.58.13 188 figure 9: micro hardness profile for different carburizing durations (2h, 4h, 6h). the variation of surface hardness as a function of the carburizing time depends on the growth of the carburizing time relative to the surface hardness, which increases at the same time, (see fig.10). figure 10: surface hardness (untreated state -reference and carburizing 930°c 2h, 4h, 6h) conclusions his study was carried out with the aim of having a global vision on the effects of gas carburizing at high temperature and by the diffusion of carbon after decomposition of the carrier gas with variation of treatment durations. the microstructural study taught us that these improvements were due not only to the presence of a layer of titanium carbide but also to the formation of phase clusters. the samples of the cemented titanium alloy were characterized by optical microscope, sem and xrd, which allowed us to delimit the cemented layers and showed that the depth of the cementation layer depended on the diffusion time. studies have revealed that the cementation layer has simple and complex phases with a mixed microstructure of (tic, α-ti, al2o3, vc, ti3al2c2, ...). t a. talhi et alii, frattura ed integrità strutturale, 58 (2021) 179-190; doi: 10.3221/igf-esis.58.13 189 improving tribological performance has therefore answered many questions, but it has also opened the way to new areas of investigation like corrosion tests. indeed, according to the results from the literature and with others surface treatment processes intended for titanium alloys; the origins of the improvements in corrosion resistance are the same as the increase in tribological performance. from the microstructural view, the wear resistance behavior study of the ti-6al-4v alloy before and after treatment by hardness, friction and wear tests, resulted in a significant improvement in the hardness and wear behavior of the alloy. all this confirms the effectiveness of the treatment carried out according to the conditions presented. references [1] peters, m., hemptenmacher, j., kumpfert, j., leyens, c., peters, m. (2003). structure and properties of titanium and titanium alloys. in:. titanium and titanium alloys. weinheim: wiley-vch. doi: 10.1002/3527602119.ch1 [2] kim, t.s., park, y. g., wey, m. y. (2003). characterization of ti-6al-4v alloy modified by plasma carburizing process. mater. sci. eng. a, 361, pp. 275-280. doi: 10.1016/s0921-5093(03)00559-8 [3] moriya, a., li, j.f., watanabe, r., (2004). fatigue property of functionally graded plasma-carburized ti and ti-alloy. j. jpn. soc. powder metall., 51, pp. 255-259 (in japanese). doi: 10.2497/jjspm.51.255 [4] ji, s., li, z., du, j. (2010). analysis of hydrogen-free carburized coating on ti6al4v substrate. rare met. mater. eng., 39(2), pp. 152-156 (in chinese). [5] zhecheva, a., sha, w., malinov, s. (2005). enhancing the microstructure and properties of titanium alloys through nitriding and other surface engineering methods. surf. coat. technol., 200, pp. 192-207. doi: 10.1016/j.surfcoat.2004.07.115 [6] hosseini, s.r., ashrafizadeh, f. (2011). compositional depth profile investigation of plasma nitriding by multiple analyses techniques. vacuum, 85, pp. 920-926. doi: 10.1016/j.vacuum.2011.01.011 [7] zhang, g., zhang, p., pan, j., (2005). research of tribological characteristics of double glow plasma hydrogen-free carbonitriding on titanium alloys. rare met. mater. eng., 34, pp. 646-649 (in chinese). [8] yilbas, b.s., sahin, a.z., al-garni, a.z. (1996), plasma nitriding of ti6al-4v alloy to improve some tribological properties . surf. coat.technol. 80, pp. 287-292. doi:10.1016/0257-8972(95)02472-7 [9] tsuji, n., tanaka, s., takasugi, t. (2009). effects of combined plasmacarburizing and shot peening on fatigue and wear properties of ti-6al-4v alloy. surf .coat. technol., 203, pp. 1400-1405. doi: 10.1016/j.surfcoat.2008.11.013 [10] beaa (bureau d’enquête sur les accidents d’avion), (2003). rapport final concernant l’accident de l’hélicoptère sa 330 puma hb – xvi, département fédéral de l’environnement, des transports, de l’énergie et de la communication, n° 1780, 17. [11] matsuura, k., kudon, m. (2002). surface modification of titanium by a diffusion carbonitriding method, acta materialia, 50, pp. 2693-2700. doi: 10.1016/s1359-6454(02)00102-7 [12] field, m. (1970). machining of high strength steel with emphasis on surface integrity. air force machinability data center, metcut research association, pp. 1-229. [13] zahavi, e., torbilo, v. (1996). in fatigue design: life expectancy of machine parts, 1st ed. boca raton, florida: crc press, pp. 185-195. [14] daoud, a. (2007). influence croisée de la rugosité et de l’anodisation chromique sur la tenue en fatigue de l’alliage 7010, rapport d’étude, isae-ensica, toulouse. [15] zhongping, y., zhaohua, j, shigang,. x, xuetong, s., xiaohong. w. (2005). electrochemical impedance spectroscopy of ceramic coatings on ti–6al–4v by micro-plasma oxidation. electrochemica acta, 50, pp. 3273-3279. doi: 10.1016/j.electacta.2004.12.001 [16] fellah, m., aissani, l., iost, a., zairi, a., montagne, a., mejias, a. (2018). comportement à l’usure et au frottement de deux biomatériaux aisi 316l et ti-6al-7nb pour prothèse totale de hanche. matériaux & techniques 106, 402. doi: 10.1051/mattech/2018051. [17] jibin, t. p., mathew, j., kuriachen, b. (2019): tribology of ti6al4v: friction 7(6), pp. 497-536. doi: 10.1007/s40544-0338-7. [18] hailing, d., ning, t., li, f., zhuang, j., zhichao, q., yanhua, l. (2019). formation mechanism of aluminide diffusion coatings on ti and ti-6al-4v alloy at the early stages of deposition by pack cementation: materials, 12, 3097. doi: 10.3390/ma12193097. [19] yu, s. m., liu, d. x., zhang, x. h., liu .c. s. (2016). a comparison study of wear and fretting fatigue behavior between cralloyed layer and cr-ti solid-solution layer, acta metall. sin. (english letters) 29(8), pp. 782–792. doi:10.1007/s40195-016-0449-3. a. talhi et alii, frattura ed integrità strutturale, 58 (2021) 179-190; doi: 10.3221/igf-esis.58.13 190 [20] zivić, f., babić, m., grujovic, n., mitrović, s. (2013). influence of loose pmma bone cement particles on the corrosion assisted wear of the orthopedic aisi 316lvm stainless steel during reciprocating sliding, wear 300, 65, pp. 65-77. doi: 10.1016/j.wear.2013.01.109. [21] iijima, d., yoneyama, t., doi, h., hamanaka, h. (2003). wear properties of ti and ti-6al-7nb castings for dental prostheses, biomater. 24, 1519. doi: 10.1016/s0142-9612(02)00533-1. [22] fellah, m., aissani, l., abdul samad, m., purnama, a., djbaili, h., montagne, a., iost, a., nouveau, c. (2018). effect of zr content on friction and wear behavior of cr-zr-n coating system, int. j. appl. ceram. technol. 15(3), pp. 701715. doi: 10.1111/ijac.12833. [23] chen, q., zhang, j., huang, a., wei, p. (2021). study on wear resistance of ti-6al-4v alloy composite coating prepared by laser alloying, appl .sci.11, 446. doi: 10.3390/ app11010446. [24] sánchez-lópez, j. c., martínez-martínez, d., lópez-cartes, c., fernández, a. (2008). tribological behaviour of titanium carbide / amorphous carbon nanocomposite coatings: from macro to the micro-scale, surface & coatings technology 202, pp. 4011–4018. doi: 10.1016/j.surfcoat.2008.02.012. [25] baccouch, z., mnif, r., elleuch, r., richard, c. (2017). the effect of tribolayers on the behavior friction of x40crmov5/fe360b steel couple in an open sliding contact, j. mater. res. 32(13), pp. 2594 2600. doi: 10.1557/jmr.2017.81 [26] li, y., yang, c., zhao, h., qu, s., li, x., li, y. (2014). new developments of ti-based alloys for biomedical applications, mater. 7, pp. 1709-1800. doi: 10.3390/ma7031709. [27] mohan, l., anandan, c., william grips, v. k. (2013). investigation of electrochemical behavior of nitrogen implanted ti-15mo-3nb-γal alloy in hank’s solution, journal of materials science, mat. med., 24, pp. 623-633. doi: 10.1007/s10856-012-4835-8. [28] hutchings, i., shipway, p. (2017). friction and wear of engineering materials. 2nd ed. oxford (uk): butterworth heinemann, tribology, isbn: 9780081009512. [29] hadke, s., khatirkar, r.k., shekhawat, s.k., jain, s., sapate, s .g. (2015). microstructure evolution and abrasive wear behavior of ti-6al-4v alloy. j mater eng perform 24 (10), pp. 39693981. doi: 10.1007/s11665-015-1667-y. [30] feng, c., khan, t.i. (2008). the effect of quenching medium on the wear behavior of a ti-6al-4v alloy. j mater sci 43 (2), pp. 788-792. doi: 10.1007/s10853-007-2298-y. microsoft word numero_29_art_31 g. maurelli et alii, frattura ed integrità strutturale, 29 (2014) 351-363; doi: 10.3221/igf-esis.29.31 351 focussed on: computational mechanics and mechanics of materials in italy mixed methods for viscoelastodynamics and topology optimization giacomo maurelli, nadia maini, paolo venini department of civil engineering and architecture, university of pavia, via ferrata 3, 27100 pavia, italy paolo.venini@unipv.it abstract. a truly-mixed approach for the analysis of viscoelastic structures and continua is presented. an additive decomposition of the stress state into a viscoelastic part and a purely elastic one is introduced along with an hellinger-reissner variational principle wherein the stress represents the main variable of the formulation whereas the kinematic descriptor (that in the case at hand is the velocity field) acts as lagrange multiplier. the resulting problem is a differential algebraic equation (dae) because of the need to introduce static lagrange multipliers to comply with the cauchy boundary condition on the stress. the associated eigenvalue problem is known in the literature as constrained eigenvalue problem and poses several difficulties for its solution that are addressed in the paper. the second part of the paper proposes a topology optimization approach for the rationale design of viscoelastic structures and continua. details concerning density interpolation, compliance problems and eigenvalue-based objectives are given. worked numerical examples are presented concerning both the dynamic analysis of viscoelastic structures and their topology optimization. keywords. viscoelasticity; mixed finite elements; topology optimization. introduction iscoelasticity is a constitutive feature of materials that finds applications in several areas such as structural engineering (concrete), biomedics (soft tissues) and also synthetic materials and polymers fabrication [1]. from a modeling viewpoint, the most classic approach to viscoelasticity is based on hereditary integral formulations that rely on the interpretation of viscoelastic materials as materials with memory: the current stress is based on a time integral of the strain history. given such a complex constitutive response, the design of viscoelastic structures is quite a challenging task that calls for a robust numerical model and a rationale design approach. within this scenario, object of this paper is the proposal of a truly-mixed finite element method for the analysis of viscoelastic structures coupled to a topology optimization approach with the ultimate goal of the development of an integrated analysis-design tool for viscoelastic systems. for this paper's sake, eigenvalue-based objectives shall be pursued within a few numerical applications that are based on the purely elastic cases discussed in [2]. as to the mixed finite-element formulation, the truly-mixed setting in a general hellinger-reissner framework has been selected mainly because of the need to pursue an accurate approximation of the stress field, feature that is not shared by any standard displacement-based approach. furthermore, such a formulation is well known to pass the inf-sup condition [3] even in the limiting case of incompressible materials with no further tricks or enrichments and this could represent a v g. maurelli et alii, frattura ed integrità strutturale, 29 (2014) 351-363; doi: 10.3221/igf-esis.29.31 352 key issue when modeling and designing rubber devices such as base isolators. the adopted formulation resembles the one presented in [4] in that an additive decomposition of the stress field is considered that finds its motivation if the adoption of a maxwell-type phenomenological model. however, a weak enforcement of the stress tensor symmetry is considered in [4] as opposed to a strong approach adopted herein. the arnold-winther finite element is used as to the discretization of the stress field [5]. to the author's knowledge, it has never been used for the analysis of viscoelastic structures whereas a few applications in a purely elastic framework are available in the literature [6]. optimal design with respect to eigenvalues is a topic that has received much attention in the last decades and [7, 8] and [9] may be cited among the most interesting contributions in this respect. however, optimal design of nonclassically damped viscoelastic structures is far from being a mature topic and further research seems to be in order. to gain insight into such a complex problem, a viscoelastic thin-beam truly-mixed formulation is introduced that has the merit to allow a deep understanding of the spectral properties of the discretized structure so as to end up with convincing optimal topologies. the first three eigenvalues shall be object of optimization and a strict relation between the optimal density distribution and the relevant eigenmode shapes clearly determined. though preliminary, not many such results are available in the literature and should open the way to more complex results concerning two-dimensional systems. formulation and discretization (continuum case) oal of this section is the definition of a truly-mixed variational formulation for two-dimensional viscoelastic continua. based on a parallel phenomenological model, compatibility, equilibrium and viscoelastic laws are written in strong form so as to allow the definition of a truly mixed variational formulation of hellinger-reissner type. eventually, the arnold-winther finite-element is introduced along with some technical details concerning its implementation. figure 1: standard solid phenomenological model. strong form reference is made to fig. 1 for the standard viscoelastic solid model that is the basis for the continuum and thin-beam models to be developed hereafter. as usual when adopting hellinger-reissner variational principles, compliance tensors relating strains to stresses are introduced that allow one to write 0 0 0 0 1 1 ( ) ( ) e v e a a v a v               (1) where 0ea and 0 va are the elastic and viscous compliance tensors of the viscoelastic component, 1 ea is the elastic compliance tensor that is in parallel to the viscoelastic one and v is the velocity field. one should notice that a stressvelocity formulation is being used that presents several advantages over more classical stress-displacement approaches, including the ease with which dynamic effects may be considered in the analysis. therefore, compatibility relations are written in terms of strain velocities as g g. maurelli et alii, frattura ed integrità strutturale, 29 (2014) 351-363; doi: 10.3221/igf-esis.29.31 353   1 ( ) 2 s tv v v v       (2) whereas the dynamic equilibrium reads div v g      (3) truly-mixed variational formulation by observing that the total stress  may be additively decomposed as 0 1    , the continuous variational formulation of the problem at hand may be obtained by eliminating the strain tensor  in eq. (1) and (2) testing the resulting equation by two virtual stress fields 0 1,  and the equilibrium eq. (3) by a virtual velocity field w so as to write: find 20 1( , , ) (div, ) (div, ) ( )v h h l        such that 0 0 0 0 0 0 0 1 1 1 1 0 1 , , , div  0 , , div  0 , div  , div  , , e v e a a v a v v w w w g w                                                (4) 2 0 1(div, ), (div, ), ( ).h h w l          in more compact form eq. (4) may be rewritten as . 0 0 0 0 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 t e v t e a a b a b m v b b v g                                                  (5) it should be emphasized that static and dynamic models differ only in that the mass matrix m may be neglected or considered in statics or dynamics, respectively. eq. (5) amounts to a system of ordinary algebraic-differential equations (ade) in the former case, of differential equations in the latter. imposing dirichlet and neumann boundary conditions within the adopted truly mixed formulations, dirichlet boundary conditions on the velocity field , on uv v  (6) are imposed weakly thanks to the line integral   u n v ds    (7) that appears on the right hand side of eq. (4)1 and (4)2, and in fact, taking no action on a boundary amounts to imposing a homogeneous condition 0, on uv   . conversely, neumann traction boundary conditions n t   are to be imposed strongly. however, when an additive stress decomposition is adopted, as is the case herein, i.e. 0 1    , neither 0 nor 1 are known but their sum. therefore a lagrange multiplier approach is adopted to enforce weakly a condition of type 0 1( ) n t    . therefore, the resulting linear algebraic-differential system takes the form . 0 0 0 2 0 1 1 12 2 2 0 0 0 0 0 00 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 t t e v t t e a a b b a b b v v gm b b tb b                                                                 (8) g. maurelli et alii, frattura ed integrità strutturale, 29 (2014) 351-363; doi: 10.3221/igf-esis.29.31 354 that may be compactly rewritten as 1 0d y d y f  (9) with an obvious definition of vectors and matrices. the arnold-winther finite element the triangular arnold-winther finite element used in this paper is the lowest-order of the family of finite elements introduced in the pioneering paper [5]. fig. 2 shows the relevant degrees of freedom that may be listed as follows. arnold-winter stress dofs dispacement dofs figure 2: degrees-of-freedom of the arnold-winther stress element. as to the stresses, one should notice that the symmetry of the stress tensor is imposed strongly so that the components to be approximated are 11 22 12, ,   and one ends up with 24 degrees-of-freedom:  the three components of the stress tensor 11 22 12, ,   at each vertex of the triangle (9 dofs),  the moments of order zero and one of the traction vector n  along each edge of the triangle (12 dofs),  the averages of the components of the stress tensor over the triangle, i.e. 11 22 12, , t t t      (3 dofs). as to the displacements, the two components xu and yu are linear on each element and globally discontinuous. implementation details no doubt that implementing the arnold-winther finite element represents a severe challenge, especially if the goal of minimizing the memory storage is pursued as it should if one recalls that this element is far more expensive than more conventional ( , )u p elements and other ( )h div elements such as the johnson-mercier element [10]. a possible implementation of the arnold-winther element is proposed in [6] that exploits indirect evaluations of the relevant stiffness matrices. within the present paper, a different semi-analytical approach has been followed inspired by classical isoparametric elements according to which stress shape functions are first computed analytically on a parent triangular domain. though not being isoparametric, the arnold-winther element enjoys the well-known piola transformation property ˆ ˆ( ) ( ) tx b x b  (10) where b is the jacobian of the affine transformation between the reference and actual configuration. this allows to compute the stiffness matrix in any actual deformed configuration. g. maurelli et alii, frattura ed integrità strutturale, 29 (2014) 351-363; doi: 10.3221/igf-esis.29.31 355 formulation and discretization (thin beam case) he present section mimics the content of previous one but for the fact that it focuses on a bernoulli viscoelastic beam. truly mixed variational form and fem discretization the phenomenological model of fig. 1 is now used to express the adopted viscoelastic behavior in terms of bending moments m and dual curvatures  . eq. (1) is then rewritten in the form 0 00 0 11 1 1 1 e v e m m ej ej m ej           (11) and coupled to the equilibrium equation '' m q  (12) to arrive at the following hellinger-reissner truly-mixed formulation: find 2 2 20 1( , , ) ( )m m v h h l   such that: * * * 0 0 0 0 00 0 0 0 0 * * 1 1 10 0 0 0 1 0 0 0 0 1 1 0 1 0 e v e m m m m v m ej ej m m v m ej vw m w m w qw                                              (13) * 2 * 2 2 0 1, ,m h m h w l      , which is apparently the thin beam counterpart to eq. (4). as to the finite element discretization, the bending moment is approximated by means of cubic hermite polynomials so that each node has two degrees of freedom, i.e. the bending moment itself and its first spatial derivative, i.e. the shear value. by analogy with the continuum case, the velocities are interpolated by elementwise linear, globally discontinuous polynomials. for later use, eq. (14) is rewritten in compact form as 1 0d y d y f  (15) where 1 * * * 0 0 0 0 00 0 0 0 0 * 1 * 1 1 1 00 0 0 0 0 0 0 1 1 0 0 0 1 0 0 , 0 0 0 0 0 e v e m m m m v m ej ej d m m d v m ej vw m w m w                                                                 (16) and 0 1 0 , 0 m y m f v q                    t g. maurelli et alii, frattura ed integrità strutturale, 29 (2014) 351-363; doi: 10.3221/igf-esis.29.31 356 eigenvalue-based topology optimization and solution of the differential-algebraic problem eigenvalue based topology optimization he abstract unforced equation of motion for the two systems intriduced above reads 1 0 0d y d y  (18) that, by considering a vector solution of type ( ) sty t ye , gives rise to the classical generalized eigenproblem 0 1[ ] 0.d sd y  (19) the class of eigenvalue based optimal design problems considered herein may be written as 0 1 0 max ( ) s.t. [ ] 0 0 f s d sd y v                 (20) where ( )f s is a scalar-valued objective function depending on the eigenvalues s of the problem, (20)2 is the eigenproblem that enters the optimization procedure as a constraint and (20)3 and (20)4 are global and local material density bounds, respectively. a classical simp model relating elastic and viscoelastic moduli to the third power of the material density is considered whereas a linear dependence between the mass density and the material density is adopted, i.e. the two densities coincide as a matter of fact. the solution of the topology optimization problem is sought by means of a sequential quadratic programming approach that has been implemented in matlab in a self-consistent code that include the finite-element analysis part as well. numerical solution of the algebraic-differential problem the solution of the (forced) algebraic-differential equation that governs the dynamics of the viscoelastic problem 1 0d y d y f  (22) is far from being trivial, especially in the 2d case wherein the algebraic part of the system has considerable dimension because of the need to impose several cauchy boundary conditions on all the unconstrained sides of the domain. for this paper’s sake, a second-order accurate numerical approximation consisting of a trapezoidal rule followed by a 2-step backward difference scheme, as suggested in [4], has been adopted: 1 1 1 2 2 2 1 0 11 1 1 12 1 0 1 2 2 3 1 2 2 2 2 n n nn n n nn n n n t d y y f f d y y t d y y y d y f                                            (23) numerical studies analysis and topology optimization of a clamped/simply-supported beam clamped/simply-supported beam of length 8l  is investigated first. the initial design consists of a uniform cross-section and density. if x denotes the local density of the beam (that may be interpolated element wise or the node level), the following simp-like interpolations are adopted: t a g. maurelli et alii, frattura ed integrità strutturale, 29 (2014) 351-363; doi: 10.3221/igf-esis.29.31 357 0 0 0 0 min max min 1 1 1 1 min max min 0 0 0 0 min max min min max min ( ) ( ) ( ( ) ( )) ( ) ( ) ( ( ) ( )) ( ) ( ) ( ( ) ( )) ( ) ( ) ( ( ) ( )) p e e e e p e e e e p v v v v ej x ej x x ej x ej x ej x ej x x ej x ej x ej x ej x x ej x ej x x x x x x                       (24) where 3p  and the minimum and maximum values adopted in the numerical simulations are respectively given in tab. 1 and 2. 0 min( )eej x 1 min( )eej x 0 min( )vej x min( )x min values 0.1 0.05 0.005 0.02 max values 10 5 0.5 3 table 1: simp interpolation: minimum and maximum values. before introducing a few choices for ( )f s to be tested numerically, a few comments on the spectral properties of the problem at hand are in order. notice in fact that neither is the system classically damped, nor enjoys the classical structure of state-space structural dynamics whose eigenproperties are well known. reference is made to the doubly-clamped beam but similar considerations apply to all constraint cases as well. if numel denotes the number of elements, the total dimension n of the problem may be written and decomposed as velocity dofsmoment dofs viscoleastic law dofs 2 ( 1) 2 2 ( 1)n numel numel numel           (21) the 2 numel constitutive laws (two devices in parallel per element) bring into the formulation an equal number of purely real eigenvalues, whereas moments and velocities dofs, globally amounting to 4 2numel  , are associated to 2 numel pairs of complex and conjugate eigenvalues and 2 null eigenvalues (that become 3 in the case of a clampedsupported beam). as to the objective function ( )f s in eq. (20), the following three cases are considered:        1 1 1 2 2 2 2 1 2 2 3 3 3 2 2 1 ( ) im( ) ( ) im( ) im(s ) ( ) im( ) im(s ) im( ) im(s ) f s s f s s f s s s              (25) where 4 6 31 2 310 , 10 , 10     . the first objective is very classical and aims to the maximization (of the imaginary part of) the lowest eigenvalue. the second objective aims to maximize the spectral band between the first two adjacent eigenvalues to avoid dangerous mode superpositions. the third function follows the same streamline as the second but involves the third eigenvalue as well. for the three optimal design problems with objectives 1 2 3, ,f f f , fig. 3, 4 and 5 respectively present the convergence path (on the left) and the optimal density distribution along the beam axis (on the right). fig. 6 and 7 show the first three velocity and moment eigenmodes, respectively, and demonstrate the strict correlation between the optimal density at convergence and the spectral properties of the beam. tab. 3 shows a few values for the three design cases. the three objective functions 1 2 3, ,f f f are respectively dominated by the first, second and third eigenmode and therefore each design maximizes its own objective (boldface values on the diagonal in tab. 3) but, with no surprise, happen to lead to small values when tested on a different objective than the one used in the optimization (first three columns in tab. 3). g. maurelli et alii, frattura ed integrità strutturale, 29 (2014) 351-363; doi: 10.3221/igf-esis.29.31 358 0 200 400 600 800 1000 1200 1400 1600 1800 −200 −180 −160 −140 −120 −100 −80 −60 −40 −20 number of iterations o b je ct iv e f u n ct io n f 1 (s ) 0 1 2 3 4 5 6 7 8 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 beam axis o p tim a l m a ss d e n si ty figure 3: objective function 1: path to convergence and optimal density. 0 500 1000 1500 2000 2500 −2500 −2000 −1500 −1000 −500 0 number of iterations o b je ct iv e f u n ct io n f 2 (s ) 0 1 2 3 4 5 6 7 8 0 0.2 0.4 0.6 0.8 1 1.2 1.4 beam axis o p tim a l m a ss d e n si ty figure 4: objective function 2: path to convergence and optimal density. 0 500 1000 1500 2000 2500 −7000 −6000 −5000 −4000 −3000 −2000 −1000 0 number of iterations o b je ct iv e f u n ct io n f 3 (s ) 0 1 2 3 4 5 6 7 8 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 beam axis o p tim a l m a ss d e n si ty figure 5: objective function 3: path to convergence and optimal density. g. maurelli et alii, frattura ed integrità strutturale, 29 (2014) 351-363; doi: 10.3221/igf-esis.29.31 359 0 1 2 3 4 5 6 7 8 −0.2 0 0.2 0.4 0.6 0.8 1 1.2 beam axis d is p la ce m e n t e ig e n m o d e 1 0 1 2 3 4 5 6 7 8 −0.2 0 0.2 0.4 0.6 0.8 1 1.2 beam axis d is p la ce m e n t e ig e n m o d e 2 0 1 2 3 4 5 6 7 8 −1 −0.8 −0.6 −0.4 −0.2 0 0.2 0.4 beam axis d is p la ce m e n t e ig e n m o d e 3 figure 6: first three velocity eigenmodes. 0 1 2 3 4 5 6 7 8 −4 −3.5 −3 −2.5 −2 −1.5 −1 −0.5 0 0.5 x 10 −5 beam axis b e n d in g m o m e n t e ig e n m o d e i 0 1 2 3 4 5 6 7 8 −12 −10 −8 −6 −4 −2 0 2 x 10 −5 beam axis b e n d in g m o m e n t e ig e n m o d e i i 0 1 2 3 4 5 6 7 8 −6 −4 −2 0 2 4 6 8 10 x 10 −5 beam axis b e n d in g m o m e n t e ig e n m o d e i ii figure 7: first three moment eigenmodes. design objective 1 ( )f s 2 ( )f s 3( )f s 1im( )s 2im( )s 3im( )s 1( )f s 0.019 0.198 1.67 0.019 0.034 0.072 2 ( )f s 0.0065 2.432 2.945 0.0065 0.0558 0.0785 3( )f s 0.0055 0.189 6.261 0.0055 0.0192 0.097 table 3: numerical results. to assess accuracy and convergence of the proposed approach reference is made to fig. 8, 9 and 10 that, for the objectives 1 2 3, ,f f f respectively, show the optimal values taken on by the objective functions versus the number of elements used for the discretization (on the left) and relevant optimal designs (on the right). the method is clearly robust in that optimal solutions are clearly mesh insensitive and even using a coarse mesh of 8 elements a good approximation to the exact optimal solution (that is of course analytically unknown and is herein assumed to coincide with the numerical one computed with a mesh of 64 elements) is found. of course, the higher the mode number that dominates the objective function the finer the mesh needed to find an accurate solution: one may in fact see that the solution using 8 elements (fig. 8 on the right) nearly coincides with the exact one when the objective function is 1f that depends on the first eigenmode only, whereas the accuracy decreases when solving the optimal design problems governed by 2f and 3f that involve higher eigenmodes. however, this should not be seen as a limitation of the proposed optimization approach in that when a coarse mesh is not capable to approximate accurately the eigenmodes for a given material density, the solution of the optimization procedure cannot be any better. g. maurelli et alii, frattura ed integrità strutturale, 29 (2014) 351-363; doi: 10.3221/igf-esis.29.31 360 0 10 20 30 40 50 60 70 0.0165 0.017 0.0175 0.018 0.0185 0.019 0.0195 0.02 number of elements f 1 (s ) 0 1 2 3 4 5 6 7 8 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 beam axis o p tim a l d e n si ty − f 1 (s ) 23 elements 24 elements 25 elements 26 elements figure 8: 1 sf : convergence vs number of elements (left) – optimal densities vs number of elements (right). 0 10 20 30 40 50 60 70 −2.45 −2.4 −2.35 −2.3 −2.25 −2.2 −2.15 −2.1 −2.05 −2 −1.95 number of elements f 2 (s ) 0 1 2 3 4 5 6 7 8 0 0.2 0.4 0.6 0.8 1 1.2 1.4 beam axis o p tim a l d e n si ty − f 2 (s ) 23 elements 24 elements 25 elements 26 elements figure 9: 2 sf : convergence vs number of elements (left) – optimal densities vs number of elements (right). 0 10 20 30 40 50 60 70 −7 −6 −5 −4 −3 −2 −1 number of elements f 3 (s ) 0 1 2 3 4 5 6 7 8 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 beam axis o p tim a l d e n si ty − f 3 (s ) 23 elements 24 elements 25 elements 26 elements figure 10: 3 sf : convergence vs number of elements (left) – optimal densities vs number of elements (right). g. maurelli et alii, frattura ed integrità strutturale, 29 (2014) 351-363; doi: 10.3221/igf-esis.29.31 361 analysis of a plane cantilever the plane cantilever of fig. 11, uniformly loaded on the right side is considered. the spatially uniform load is modulated in time by means of the function 1 1 sin 2 ( ) 0 t t t tf t else     (26) where 1 2t s and [0,10] .t s as to the physical properties of the structure the following values are adopted as to the isotropic elastic and viscous compliance tensors that are defined in terms of lamé constants: 0 1 0 100 80 100 75 90 30 e e v a a a         (27) a uniform mass density 0.5  is further considered. fig. 12, 13 and 14 show the maps of the stress components , ,xx xy yy   at final time 10t s . figure 11: plane viscoelastic cantilever under investigation. figure 12: xx (normal stress). g. maurelli et alii, frattura ed integrità strutturale, 29 (2014) 351-363; doi: 10.3221/igf-esis.29.31 362 figure 13: xy (shear stress) figure 14: yy (vertical stress) to appreciate the diffusion of the stress components with time, fig. 15 and 16 show a few snapshots that display the variation of the stress component ,xx xy  at regularly spaced time stations. figure 15: evolution of xx (normal stress) with time. figure 16: evolution of xy (shear stress) with time. finally, fig. 17 shows the time-variation of the stress xx at the upper-left corner of the cantilever. conclusions truly-mixed variational formulation for the analysis of viscoelastic continua and thin beams has been presented that uses stresses (moments) as primary variables and velocities (instead of displacements) as lagrange multipliers. a topology optimization method for viscoelastic devices has then been developed and applied to thin beams within a few representative numerical simulations. ongoing extensions include applications to two dimensional viscoelastic devices with respect to eigenvalue-based design objectives. a g. maurelli et alii, frattura ed integrità strutturale, 29 (2014) 351-363; doi: 10.3221/igf-esis.29.31 363 figure 17: evolution of xx (normal stress) with time at the upper left corner of the cantilever. references [1] phan-thien, n., understanding viscoelasticity, advanced texts in physics, springer-verlag, berlin, (2002). [2] bruggi, m., venini, p., eigenvalue-based optimization of incompressible media using mixed finite elements with application to isolation devices, computer methods in applied mechanics and engineering, 197(13-16) (2008) 12621279. [3] brezzi, f., fortin, m., mixed and hybrid finite element methods, springer series in computational mathematics. springer-verlag, new york, 15 (1991). [4] rognes, m.e., winther, r., mixed finite element methods for linear viscoelasticity using weak symmetry', math. models & methods in applied sciences, 20(6) (2010) 955-985. [5] arnold, d., winther, r., mixed finite elements for elasticity, numer. math., 92 (2002) 401-419. [6] carstensen, c., gunther, d., reininghaus, j., thiele, j., the arnold-winther mixed fem in linear elasticity. part i: implementation and numerical verification, computer methods in applied mechanics and engineering, 197 (2008) 3014-3023. [7] diaz, a., kikuchi, n., solution to shape and topology eigenvalue optimization problems using a homogenization method, int. j. numer. methods engrg. 35(3) (1992) 1487–1502. [8] krog, l.a., olhoff, n., topology optimization of plate and shell structures with multiple eigenfrequencies, in: n. olhoff, g.i.n. rozvany, proceed. wcsmo-1 first world congress of structural and multidisciplinary optimization, 675–682, (1995). [9] pedersen, n.l., maximization of eigenvalue using topology optimization, struct. multidiscip. optim. 20 (2000) 2–11. [10] johnson c., mercier, b., some equilibrium finite elements methods for two dimensional elasticity problems, numer. math., 30 (1978) 103–116. [11] bruggi, m., venini, p., a mixed fem approach to stress-constrained topology optimization, int. j. numer. methods engrg., 73 (2008) 1693–1714. shot peening processes to obtain nanocrystalline surfaces in metal alloys: g. deng et alii, frattura ed integrità strutturale, 46 (2018) 45-53; doi: 10.3221/igf-esis.46.05 45 developments in the fracture and fatigue assessment of materials and structures bending fatigue strength design method for machine components with complex geometries gang deng, tsutomu nakanishi department of mechanical design systems engineering, faculty of engineering, university of miyazaki, 1-1 gakuen kibanadai-nishi, miyazaki shi, miyazaki 889-2192, japan t0d114u@cc.miyazaki-u.ac.jp, t0d115u@cc.miyazaki-u.ac.jp abstract. the purpose of this study is to devise a bending fatigue strength evaluation method that can be widely used for any machine component under the consideration that bending fatigue breakage depends on the initiation of a surface fatigue crack, namely, the conditions for the initiation of a fatigue crack can be used as the criteria for bending fatigue strength design. the specially designed and manufactured three-point bending specimens with crowned round notches are used in bending fatigue experiments. the obtained bending fatigue strengths are expressed as the maximum actual stress at the critical point, which increases with decreasing notch radius. considering the effects of the stress distribution on the bending fatigue strength, we present a method for estimating the tension fatigue strength of a smooth specimen, which is shape-independent fatigue strength and can be applied to bending fatigue strength design for machine components with complex geometries. keywords. bending fatigue strength; fatigue crack initiation; stress distribution; shape-independent fatigue strength citation: deng, g., nakanishi, t., bending fatigue strength design method for the machine components with complex geometries, frattura ed integrità strutturale, 46 (2018) 45-53. received: 07.03.2018 accepted: 15.04.2018 published: 01.10.2018. copyright: © 2018 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. introduction lthough the bending fatigue strength design of machine elements such as gears and shafts can be performed in accordance with design documents, there are still no practical methods applicable to other machine elements with different shapes. many accidents have occurred owing to the fatigue of machine component with a wide range of geometries, such as the fatigue breakage of the tire hub of heavy-duty truck. since the bending fatigue strength is expressed as the nominal stress calculated on the basis of material mechanics with many simplifications of the shapes and loading conditions, it varies even among machine components with the same material qualities [1,2]. consequently, the bending fatigue strength design of machine components with a wide range of geometries cannot be performed using the methods shown in the design documents. to avoid accidents owing to the bending fatigue breakage of machine components, a general bending fatigue strength evaluation method applicable to a wide range of geometries is required. bending fatigue breakage is a result of surface crack initiation and propagation. nisitani [3] and ohba [4] indicated that a fatigue crack will not stop growing unless an extremely high stress concentration occurs at the critical point where the fatigue crack is initiated. deng [5] and hammouda [6] showed that the fatigue initiation life accounts for a large proportion of the a http://www.gruppofrattura.it/va/46/5.mp4 g. deng et alii, frattura ed integrità strutturale, 46 (2018) 45-53; doi: 10.3221/igf-esis.46.05 46 fatigue life when the stress level is near to the bending fatigue strength. on the basis of fracture mechanics and the research of nisitani [7], the mechanical factors determining fatigue breakage are not only the actual stress but also its distribution. at present, the actual stress and its distribution can be easily and accurately calculated for any machine component, but they have not yet been used in bending fatigue strength design. to develop a general bending fatigue strength evaluation method applicable to machine components with a wide range of geometries, the actual stress and its distribution should be considered as very important factors. nisitani [3,7] and tanaka [8] carried out many studies on bending fatigue strength evaluation, where the strengths were defined on the basis of the criteria of crack initiation or the arrest of crack propagation, and they presented a method of obtaining the fatigue strength from the threshold stress intensity factor. because of the difficulty of determining the threshold stress intensity factor and because fatigue strength design allowing the existence of a non-propagating crack is unrealistic considering safety, their method is not practically used. kato [9] introduced the use of the initial crack length to evaluate the qualities of a surface and presented a fatigue life simulation method under the assumption that the progress of fatigue involves only the progress of crack propagation. however, many problems remain in deciding the initial crack length, which is very sensitive to the simulation conditions. the purpose of this study is to search for a general method for bending fatigue strength design applicable to machine components with a wide range of geometries that considers the effects of the actual stress and its distribution on fatigue crack initiation. as the first stage of this study, three-point bending specimens with notches of different shapes are used to obtain bending fatigue limit stresses, which are expressed as the maximum stress at the critical point on the notch surface, and an approach to estimating the tension fatigue strength of a smooth specimen is presented, which will be the basic material property used in general bending fatigue design. consideration of the strength and criteria for bending fatigue bending fatigue limit stress and bending fatigue load capacity hanges in the shape of a machine element, such as the introduction of a notch, a hole, or a corner, will decrease the bending fatigue strength expressed by the nominal stress as, stated in fatigue design documents, and this phenomenon is evaluated using the fatigue stress concentration factor. however, if the actual stress at the critical point is used in fatigue strength evaluation, the limit stress for bending fatigue breakage will increase owing to the existence of a feature such as a notch or stress concentration [10]. to avoid introducing the misunderstanding that the stress concentration increases the fatigue strength of a machine element, the bending fatigue limit stress and bending load capacity are used to indicate the maximum actual stress and the bending load without fatigue breakage, respectively. thus, the stress concentration due to the introduction of such notches, holes, or corners will increase the bending fatigue limit stress but decrease the bending load capacity. factors affecting the initiation of a fatigue crack many studies have shown that the fatigue crack initiation life accounts for a large proportion of the fatigue life, particularly when the stress level is close to the fatigue strength, and that a fatigue crack will not stop growing unless the shape around the critical point is very sharp [3]. thus, fatigue crack initiation may be a sufficient condition for bending fatigue breakage, which means that whether or not bending fatigue breakage occurs depends on the initiation of a surface fatigue crack, and the criteria for the initiation of a fatigue crack can be used for bending fatigue strength design. fatigue crack initiation and growth depend on the stress intensity factor in fracture mechanics [11,12]. on the basis of linear elastic fracture mechanics, the stress intensity factor is related to the potential energy release rate and elastic properties of the material. the potential energy release rate is also strongly related to the distribution of the stress around the tip of the crack or the critical point. consequently, the initiation of a fatigue crack depends not only on the actual surface stress but also on its distribution. fig. 1 shows images of the stress distributions around notches with small and large radii that have sharp and gentle stress gradients, respectively. the change in the potential energy release rate owing to the initiation is related to the hatched area. if the threshold value of the potential energy release rate for fatigue crack initiation is constant (e1=e2), a larger surface stress with a high gradient will exist on the surface of the notch with the smaller radius, and a smaller stress with a gentle stress gradient will exist on the surface of the notch with the larger radius. this is considered to be the main reason why the fatigue strength expressed by the actual stress at the critical point varies for different shapes. in the evaluation of the effect of the stress distribution on bending fatigue crack initiation, we think that only a very small region around the critical point should be considered since the length of the initiated crack is only micrometer order; and on the basis of the linear-elastic analysis results of stress distributions in depth direction for the typical shapes such as that c g. deng et alii, frattura ed integrità strutturale, 46 (2018) 45-53; doi: 10.3221/igf-esis.46.05 47 shown in fig.1 as well as our test specimens, the stress distribution form the critical point can in practice be approximated by a linear distribution under several tens of micrometer. thus, the stress gradient at the critical point can be used to characterize the stress distribution. in this research, three directions at the critical point are considered as shown in fig. 2. however, if the shape around the critical point is not sharply notched and the critical point is located at the bottom of the notch, owing to the symmetrical shape very close to the notch bottom, the stress gradients along the y and z directions on the surface will be zero. thus, as the first step, the effect of the stress distribution on bending fatigue crack initiation is evaluated using the stress gradient in the depth direction. in addition, if we use the requirement for surface fatigue crack initiation as the criteria for bending fatigue breakage, our noticing spot in fatigue design will be a very small area around the critical point instead of the geometry of the machine component. fig. 3 shows a magnified view around initiated cracks (microcracks) of 10, 5, and 1m on an edge with a radius of 1mm. since the just-initiated fatigue crack is extremely short compared the dimensions around the critical point, except for in the case of a sharp notch, the geometries of the critical points of many machine components can be simplified as a semi-infinite surface in comparison with the length of the initiated fatigue crack. thus, only the maximum stress at the critical point and the stress gradient should be considered in the bending strength design for machine components with a wide range of geometries. a) b) figure 1: different stress distributions for an identical potential energy release. a) sharp stress gradient; b) gentle stress gradient. figure 2: stress directions at the critical point. figure 3: microcrack on a circular surface of radius 1.0mm. three-point bending fatigue test and specimens o investigate the effects of the stress distribution on the bending fatigue limit stress, three-point bending specimens were used in fatigue tests on a hydroelectric servo pulsating fatigue test rig. the loading frequency was 30hz and the load ratio (pmin/pmax) was about 0.05. the loading method and a view of a specimen in the test rig are shown in fig. 4. in general, standard three-point bending specimens are used to investigate fatigue crack growth characteristics, where u notches or v notches are introduced so that a crack easily initiates. however, in this research, the three-point bending specimens are used to estimate the fatigue strength determined by the crack initiation and crack propagation process. to t g. deng et alii, frattura ed integrità strutturale, 46 (2018) 45-53; doi: 10.3221/igf-esis.46.05 48 prevent crack initiation from the sharp corner of a notch and consider the situation that a crack initiates from the fillet of a machine element, notches with a crowned round shape are introduced in the specimens. the dimensions of the specimens are shown in fig. 5; the length, thickness, and height of each specimen were 100, 10, and 20mm, respectively, and the supporting span in the test was 80mm. the depth of the notch t was about 5mm and the crowning radius r was from 5.8mm to 6.2mm. the stress distributions around the notches were changed by changing the radius of the round notch to 2.5, 3.0, 4.0, 5.0, and 6.0mm. figure 4: three-point fatigue test rig. figure 5: three-point bending specimen. figure 6: notch shapes and surface features. the specimens were made of carbon steel (s55c jis, c0.55%, si0.25%, mn0.75%) from a bar of 110mm diameter. since the purpose of this research is to estimate the shape-independent fatigue strength of a material, the surfaces were treated to g. deng et alii, frattura ed integrità strutturale, 46 (2018) 45-53; doi: 10.3221/igf-esis.46.05 49 minimize the effects of surface roughness and work hardening around the notches, which influence the crack initiation process, as follows. after the machining of the notch, the notch surfaces were mirror-polished using abrasive papers, and then vacuum normalization was carried out to minimize the effects of machining on the notch surface. the hardness of the specimens was approximately 219hbs (0.2>390mpa). the very thin oxide layer that formed during the normalization was removed using a #2000 emery paper. the calculated average roughness ra and maximum height roughness ry of the specimens were approximately 0.03mra and 0.15mry, respectively. photographs of the final notch surfaces are shown in fig. 6, and the realization of mirror-polished notch surfaces was confirmed. bending fatigue limit stresses and bending load capacities he staircase method recommended by little [13] is used to estimate the bending fatigue strength evaluated by the actual stress at the critical point. distinguishing the bending fatigue strength evaluated by the nominal stress from that evaluated by the actual stress at the critical point, the bending fatigue limit stress is used in this research. on the basis of little’s method, the bending fatigue limit stress w was estimated as 0+･d, where 0 is the stress level for the first specimen,  is a coefficient depending on the permutation of fatigue test results, and d is the increment of the stress level in the fatigue tests. the permutations of the fatigue test results are shown by o and x, where o denotes that fatigue breakage did not occur up to 1×107 load cycles and x denotes that fatigue breakage occurred before 1×107 load cycles. five fatigue tests were performed for each type of specimen. the stress level 0 for the first specimen was determined by pretests. the increment of the stress level d in the staircase method was set to 30mpa, referring to the standard deviation in the work of jeong [14]. a sinusoidal pulsating load was applied to each specimen. the maximum actual stress (the maximum principal stress 1) at the critical point of the notch in the length direction of the specimen, calculated using fem analysis software, was used to represent the stress level and the bending fatigue limit stress. table 1: fatigue test results and estimated bending fatigue limit stresses. the permutations of o and x, coefficient  determined on the basis of the relationship between  and the permutation recommended by little [13] and the estimated bending fatigue limit stresses w for the five types of specimens are shown in tab. 1 and fig. 7. the estimated bending fatigue limit stresses w for the specimens with notch radii of 2.5, 3.0, 4.0, 5.0, and 6.0mm are 787, 765, 753, 735, and 697mpa, respectively. since the bending fatigue limit stresses are expressed as the actual stresses at the critical point, they increased with decreasing notch radius with a more severe stress concentration. therefore, although the bending fatigue limit stress increased with decreasing notch radius, as shown in fig. 7. it does not mean that a sharper notch will increase the strength of the specimen. fig. 8 shows the load pw corresponding to the results in fig. 7, which indicates the load capacity of the specimen, and the nominal bending fatigue strengths wn given by the bending stress of the smooth specimen with the same section as the minimum section shape of the notched specimens under a load of pw. t g. deng et alii, frattura ed integrità strutturale, 46 (2018) 45-53; doi: 10.3221/igf-esis.46.05 50 as shown in fig. 8, a smaller radius or sharper notch with a more severe stress concentration decreases the bending load capacity. this corresponds to the common knowledge that the stress concentration reduces the fatigue strength of machine elements. figure 7: bending fatigue limit stresses of the specimens with different notch radii. figure 8: nominal bending fatigue strengths and bending load capacities. estimation of the tension fatigue strength of a smooth specimen actual stress and its distribution in the depth direction from the critical point s mentioned above, assuming that whether or not bending fatigue breakage occurs depends on the initiation of a surface fatigue crack, the criteria for the initiation of a fatigue crack can be used for bending fatigue strength design. considering that the initiated fatigue crack is very small, the region affecting the crack initiation should be restricted within a very small area; thus, the stress gradient at the critical point can be used as the main factor characterizing the distribution of the stress around the critical point. consequently, the effect of the stress distribution on the bending fatigue strength may be evaluated by the stress gradient at the critical point. referring to the research of siebel [10], we focus on the gradient of the normal stress distribution in the depth direction at the critical point, as shown in fig. 9, where the color bands show the stress distribution. the stress gradient g [mm-1] along the depth direction (x direction) is defined by the following expressions: 　　 dx d g ,      == 0 (1) where  is the normal stress, namely the actual bending stress, perpendicular to the critical section, 0 is  at the critical point, ' is the dimensionless stress, and x is the depth below the critical point. the gradients at the critical point g0 [mm-1] are shown in fig. 10, from which it is clear that a smaller notch radius, namely a more severe stress distribution, is accompanied by a higher gradient. the gradients were 0.848, 0.800, 0.688, 0.598, and 0.491mm-1 for notch radii of 2.5, 3.0, 4.0, 5.0, and 6.0mm, respectively. estimation of the tension fatigue strength of the smooth specimen we consider that the fatigue strength should be a shape-independent mechanical property that depends on the properties of the material such as the yield stress and hardness, and the surface qualities such as the roughness and texture at the critical point. here, we call this fatigue strength the material fatigue strength. this material fatigue strength should be obtained for the smooth specimen (no stress concentration) and have no stress gradient (uniformly distributed stress, g=0). siebel [10] compared the bending fatigue strength of a notched specimen w with the tension-compression (push-pull) fatigue strength w0 of a smooth specimen. we also consider that the fatigue strength of a smooth specimen under a uniformly distributed stress may be used as the material fatigue strength for bending fatigue strength design. a g. deng et alii, frattura ed integrità strutturale, 46 (2018) 45-53; doi: 10.3221/igf-esis.46.05 51 figure 9: stress distribution around the notch of a specimen. figure 10: stress gradient at the critical point. figure 11: extrapolation for tension fatigue strength figure 12: gradient factor vs. stress gradient fig. 11 shows the relationship between the bending fatigue limit stress w and the stress gradient g0, which indicates that the bending fatigue limit stress decreases almost linearly with decreasing stress gradient in the depth direction at the critical point. along the horizontal axis in fig. 11, a smaller gradient corresponds to a smoother specimen. thus, g0=0 corresponds to a smooth specimen under a pulsating tension load. the tension fatigue strength w0 was estimated by extrapolation using the experimental results of the notched specimens, and we obtained the value of 592mpa in fig. 11 using the experimental results in fig. 7. however, the appropriateness of the estimation of the tension fatigue strength should be investigated and discussed on the basis of many experiments. here we only present an approach for the determination of the tension fatigue strength, which can used as the material fatigue strength for bending fatigue strength design. through the use of the tension fatigue strength w0 as the material fatigue strength for bending fatigue strength design, the gradient factor , which is used to evaluate the effect of the stress distribution on the bending fatigue strength, can be defined as the ratio of the bending fatigue limit stress w to the tension fatigue strength w0 (=w/w0). the gradient factors for the specimens used in this research increase progressively according to the increased gradients as shown in fig. 12. conceivable approach for general bending fatigue strength design many further bending fatigue tests should be conducted using specimens with different shapes to confirm that the tension fatigue strength depends on the material properties and to clarify the relationship between the gradient factor and the stress gradient for different materials. a conceivable approach for general bending fatigue strength design applicable to machine components with a wide range of geometries is shown in fig. 13. first, the actual stress max and its gradient at the critical point g0 are calculated by fem analysis, then the gradient factor  is determined from the relationship between the gradient factor and the stress gradient. next, the tension fatigue strength w0 is estimated for the material. the allowable actual stress a, which is the limit bending stress for the designed machine component, is calculated as the product of the tension fatigue g. deng et alii, frattura ed integrità strutturale, 46 (2018) 45-53; doi: 10.3221/igf-esis.46.05 52 strength w0 and the gradient factor  the fatigue strength design is performed while ensuring that max<a. in addition, the tension fatigue strength w0 depends not only on the material properties but also on the surface qualities as mentioned above. since we used mirror-polished notches, this research does not deal with the effects of surface qualities on the tension fatigue strength, namely the material fatigue strength. figure 13: conceivable general bending fatigue strength design method. conclusions nder the consideration that bending fatigue breakage depends on the initiation of a surface fatigue crack, the conditions for the initiation of a fatigue crack can be used as the criteria for bending fatigue strength design; whether or not the fatigue crack initiation depends on the maximum actual stress and its distribution at the critical point on the basis of fracture mechanics. in this study, the maximum stress and its gradient in the depth direction at the critical point were taken as the predominant factors affecting fatigue crack initiation. three-point bending test pieces with crowned and round notches were used in fatigue experiments to obtain bending fatigue limit stresses, and we presented an approach to estimating the tension fatigue strength of a smooth specimen, which is the material fatigue strength used in general bending fatigue design. the main results obtained in this research are as follows. 1) if the fatigue strength is expressed as the actual stress at the critical point, the bending fatigue limit stress will be higher for a more severe stress concentration. in our experiments, a higher bending fatigue limit stress was obtained for a smaller notch radius. 2) the tension fatigue strength of a smooth specimen, which is the material fatigue strength used in bending fatigue strength design, was estimated by extrapolation using the experimental results of notched specimens. 3) a conceivable approach to general bending fatigue strength design applicable to machine components with a wide range of geometries is presented that uses the actual stress, stress gradient factor, and tension fatigue strength of a smooth specimen. references [1] jsme, (1991). strength design for gears (in japanese), technical document, pp. 86-99. [2] jsme, (1992). fatigue strength design for metals ii (in japanese), technical document, pp. 66-141． [3] nisitani h., (1968). size effect on fatigue limit and the diverge point on the rotating bending tests for carbon steel, transactions of the jsme (in japanese), 34-259, pp. 371-382. [4] ohba, h., murakami, y. and endo, t., (1983). effects of an artificial small defect on the fatigue strength of notched u g. deng et alii, frattura ed integrità strutturale, 46 (2018) 45-53; doi: 10.3221/igf-esis.46.05 53 specimen, transactions of the jsme a (in japanese), 49-444, pp. 901-910. [5] deng, g., sakanashi, y. and nakanishi, t., (2009). a practical method for fatigue crack initiation detection using an ionsputtered film, transaction of the asme, journal of engineering materials and technology, 131-1 pp. 011007-1011007-6. [6] hammouda, m. m. and miller, k. j., (1980). prediction of fatigue lifetime of notched members, fatigue of engineering materials and structures, pp. 377-386. [7] nisitani h., (1977). non-propagating crack (notched surface), materials (in japanese), 26-282, pp. 296-306. [8] tanaka, k. and akiniwa, y., (1987). a method for the prediction of fatigue limits of notched members, transactions of the jsme a (in japanese), 53-488, pp. 709-717. [9] kato, m., deng, g., inoue, k. and takatsu, n., (1993). evaluation of the strength of carburized spur gear teeth based on fracture mechanics, jsme international journal, series c, 36-2, pp. 233-240. [10] siebel, e. and stieler, m., (1955). ungleichformige spannungsverteilung bei schwingender beanspruchung, verein deutscher ingenieure, dusseldorf (in german), vdi-z, 97-5, pp. 121-126. [11] inoue, k., deng, g. and kato, m., (1989). evaluation of the strength of carburized spur gear teeth based on fracture mechanics (1st report, stress intensity factor considering the effect of residual stress distribution in the case), transactions of the jsme c (in japanese), 55-514, pp. 1488-1493. [12] akiniwa, y., tanaka, k. and kinefuchi, m., (1989). effect of microstructure on propagation and non-propagation of short fatigue cracks at notches, materials (in japanese), 38-434, pp. 1275-1281. [13] little, r. e., (1972). astm spec. tech. publ., 5-11, p. 29. [14] jeong, b., kato, m., inoue, k. and takatsu, n., (1992). the bending strength of carburized fine module gear teeth: carburizing conditions and their effects on the fatigue strength, jsme international journal, 35-1, pp. 136-141. microsoft word 2395 c.m.s. vincente et alii, frattura ed integrità strutturale, 48 (2019) 748-756; doi: 10.3221/igf-esis.48.68 748 effect of protective coatings on the water absorption and mechanical properties of 3d printed pla carlos m. s. vicente, joão fernandes, luís reis* idmec, instituto superior técnico, universidade de lisboa, av. rovisco pais, 1049–001 lisboa, portugal carlos.vicente@tecnico.ulisboa.pt, https://orcid.org/0000-0003-0701-190 joaofranciscomirandafernandes@gmail.com *luis.g.reis@tecnico.ulisboa.pt, http://orcid.org/0000-0001-9848-9569 augusto moita de deus, m.f. vaz idmec, instituto superior técnico, universidade de lisboa, av. rovisco pais, 1049–001 lisboa, portugal and cefema, instituto superior técnico, universidade de lisboa, 1049–001 lisboa, portugal amd@tecnico.ulisboa.pt, http://orcid.org/0000-0002-0451-6245 fatima.vaz@tecnico.ulisboa.pt, http://orcid.org/0000-0003-1629-523x marco leite unidemi, departamento de engenharia mecânica e industrial, faculty of science and technology, new university of lisbon, campus da faculdade de ciência e tecnologia, 2829–516 caparica, portugal marcoleite@tecnico.ulisboa.pt, http://orcid.org/0000-0002-0319-4475 abstract. this work aims to study the influence of protective coatings on the water absorption and mechanical properties of 3d printed poly–lactic acid (pla) parts. the pla parts were fabricated with different levels of the 3d printing process parameters, aiming to define samples with distinct strength and ductility/toughness characteristics. water absorption tests following the standard astm d570–98 were performed on uncoated and coated pla specimens. the effectiveness of two protective coatings based on acrylic and polyurethane varnish on reducing water absorption was evaluated. both protective coatings have shown being effective on preventing water absorption by the pla, with polyurethane presenting the best performance reducing water absorption by 38%. tensile tests were carried out to determine the ultimate tensile strength, elastic modulus, yield tensile strength, fracture strain and toughness of specimens, before and after the application of protective coatings. the polyurethane protective coating also benefits the tensile properties of pla parts, increasing the strength and ductility/toughness characteristics of specimens up to 24%. citation: vincente, c.m.s., fernandes, j., reis, l., de deus, a. m. vaz, m. f., leite, m., effect of protective coatings on the water absorption and mechanical properties of 3d printed pla, frattura ed integrità strutturale, 48 (2019) 748-756. received: 13.02.2019 accepted: 13.03.2019 published: 15.04.2019 copyright: © 2019 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. http://www.gruppofrattura.it/va/48/2395.mp4 c.m.s. vincente et alii, frattura ed integrità strutturale, 48 (2019) 748-756; doi: 10.3221/igf-esis.48.68 749 keywords. 3d printing; pla; mechanical properties; water absorption; printing parameters introduction n recent years the use of 3d printing technologies has increased significantly and this rapid growth it is expected to remain in a near future. the 3d printers are now commonly used for the manufacture of a broad array of products, ranging from leisure articles to medical components [1]. from all available 3d printing technologies, one of the most popular to the public is fused deposition modelling (fdm) due to the vast number of companies that develop and market 3d printers based on this technology, at relatively low cost [2]. fdm printed materials include among others : acrylonitrile butadiene styrene (abs), poly–lactic acid (pla), polycarbonate, nylon and polyamide, which are now available for building mechanical parts with diversified characteristics, on demand [3]. from the listed materials pla, a biodegradable thermoplastic polymerized from lactic acid from natural sources such as corn [4], was one of the materials that attracted most attention due to their unique properties for 3d printing. the main advantages of pla are low printing temperature, smoother appearance, high geometric resolution, low warping effect and biodegradability. on the other hand, the comparative disadvantages with other thermoplastics relies on his brittleness and low thermal stability. as 3d printing technology spreads into more domestic users or at industrial level, pla emerge as a valid sustainable thermoplastic alternative to non–biodegradable polymers, able to address the problem of residues derived from manufacturing processes, which impacts the environment of our planet. in this context, the characterization and improvement of the mechanical properties of pla parts produced by fdm it is a topic of great interest, so that this material can be used on a reliable way. on the past several studies stablished a relation between fdm parameters and their combinations on the mechanical properties of 3d printed pla [5–11]. these studies allow the designer to define the 3d printing conditions (so that they can meet mechanical design requirements) by controlling the strength and ductility of materials, or assigning variable mechanical properties to parts, according to their final application. from the literature it’s well know that the higher strength of pla parts produced by fdm is linked to higher extrusion temperatures [12–14], raster angles aligned with the direction of the applied force [7,9,15] and smaller layer thicknesses [7,8,16], while the ductility follows the inverse trend. these trends of the fdm process provide guidelines for the definition of processing parameters of pla parts regarding his application in elements of strength or ductility/toughness, depending on the project requirements. another important issue that also must be considered on the project of pla components by fdm is water absorption, especially when exists direct contact with fluids, such as in the case of underwater [17], biomedical [18], or microfluidic devices [19]. water absorption can arise due to the porosity of the printed part or from the pla material itself. it is known that the polar bonds in pla can make it susceptible to water absorption, which can cause partial breakdown the pla polymer chains and change mechanical properties, turning pla even more brittle. moreover, after the 3d printing process pla becomes more chemically reactive, increasing the susceptibility of pla to water,[20] which will tend to decompose the material over time [21,22]. a classical, simple and inexpensive way to protect a water reactive material is by applying a protective coating using the painting method. this method was successful applied on surface modification of abs reducing water absorption (from 1.6 to 0.4 % in weight) [23] and on the protection of a pla hull with a polyurethane (pu) coating, reducing water absorption from 3.8 to 1.5% in weight [17]. despite the significance of this topic, there is also a lack of studies evaluating the impact of surface treatments on mechanical properties of fdm parts made with pla, with most works mainly focused on evaluating the staircase effect reduction [24–27]. the few reported works evaluating the impact of surface treatments on mechanical properties of pla parts produced by fdm, are until now limited to blow cold vapor surface treatments [28]. on our work, pla specimens were fabricated by fdm with different levels for the 3d printing parameters: layer thickness, raster angle and extrusion temperature, aiming to define distinct levels of strength (improved ultimate tensile stress, modulus of elasticity and yield strength) and ductility/toughness (improved fracture strain and toughness). the 3d printing conditions of specimens were replicated on cubic samples that were subjected to water absorption tests. the water absorption was estimated for uncoated and coated samples with acrylic or polyurethane (pu) protective coatings. the influence of protective coatings on mechanical properties were also evaluated trough tensile tests. the use of protective coatings for watertight applications of pla 3d printed parts, will enable new designs where both sealing and the preservation of mechanical properties are critical aspects. to the best of our knowledge the water absorption i c.m.s. vincente et alii, frattura ed integrità strutturale, 48 (2019) 748-756; doi: 10.3221/igf-esis.48.68 750 and the mechanical behavior of 3d printed pla parts (before and after protective coatings application), was not previously systematically investigated. materials and methods 3d printing and protective coatings ultimaker 2™ machine was used to print all the samples from the same white pla filament roll. the 3d models were modelled in solidworks® and exported in a stereolithographic (stl) file to the slicing software cura®, to generate the g–code file. for the constant printing parameters, the recommended standard profile by cura® was adopted. the infill density as set to 60% for all samples. the extrusion was performed with a nozzle diameter of 0.4 mm. the temperature of the platform was set to 60 oc. the printing speed was 40 mm.s–1 for the first layer, external layers (top and bottom) and contours. the printing speed chosen for internal contours and filling layers was 60 and 80 mm.s–1, respectively. the thickness of the contours is 0.4 mm, while for tops and bottoms is equal to 0.8 mm. the thickness of initial layer as set to 0.3 mm. two kind of samples (lvl1 and lvl2) were printed with the levels of printing parameters, displayed on tab. 1. for each sample three repetitions were considered. parameters samples layer thickness (mm) raster angle (o) extrusion temperature (ºc) levels lvl1 0.1 (0o/90o) 220 lvl2 0.2 (–45o/45o) 200 table 1: fdm process parameters and its levels. the tensile tests specimens were printed on the flat direction, with the geometry and dimensions displayed on fig. 1. figure 1: geometry and dimensions of tensile tests specimens. water absorption samples consists on coated and uncoated cubes with dimensions of approximately 10 mm, which were fabricated with the printing parameters of tab. 1. two different protective coatings were selected: a pu wood sealant (lakeone™) and an acrylic aqueous varnish (luxens™). before the application of protective coatings and water immersion tests, the samples were placed in an oven during 24 hours, in order to ensure that the water content was minimum and equal for all samples. after the application of coatings, the pla coated samples were dried at room temperature, for complete solvent removal. tensile tests tensile tests were performed using a universal testing machine (instron 3369) with a load cell of 50 kn and a strain rate of 2 mm.min–1. at least three tests were made for each sample manufacturing conditions. stress-strain curves were obtained for each test from the load vs. displacement curves. the toughness of each specimen was calculated from the integration of the stress–strain curve [29]. a c.m.s. vincente et alii, frattura ed integrità strutturale, 48 (2019) 748-756; doi: 10.3221/igf-esis.48.68 751 water absorption tests water absorption was analysed according to the astm d570–98 standard with both uncoated and coated specimens. the specimens were weighted before water immersion and his dry mass was recorded. the number of tests repetitions for each pair sample/coating was three. the samples immersion was done by covering half of the specimen’s height with water on a glass container. to guarantee that water reaches the bottom part of the samples, an absorbing filter paper was placed on the bottom of the specimens. in each defined time interval, the cubes were taken from the container, the excessive water was removed with paper and were posteriorly weighted. the weighing of the cubes was done in intervals of 30 minutes, for the first 4 hours, in intervals of 1 hour, for the next 4 hours, and in intervals of 24 hours, for the next 4 days. in total, the cubes spent 104 hours inside water. some properties can be obtained from this type of test, namely: weight gain (wg) and open porosity (p), calculated by eq. (1) and eq. (2): 100%   sat dry dry m m wg m (1)   2 / 100%    sat dry h om m p v (2) where msat is the saturated mass (the mass at the end of the experiment), mdry is the dry mass (the mass at the beginning of the experiment), ρh2o is the density of water (1 g.cm–3) and v is the volume of the cube (1 cm3). the absorption coefficient (k) was calculated graphically as the initial slope of the graph where x axis is the square root of the immersion time, and the y axis is the weight gain per unit of area of the cube. the weight gain per area is calculated by eq. (3):    m mwetwg dry area a m dry (3) where mwet is the mass of the cube in a certain instant of time, and a is the area of one of the faces of the cube. morphological characterization the external surface surfaces of pla specimens were inspected by scanning electron microscopy (sem). the sem images were obtained with a field emission type microscope (hitachi®–s2400) operating at 20.0 kv, in a secondary electron emission mode. the surface of specimens was fixed on the sem sample holder with a conductive adhesive and the sample surface was cleaned with an air flux before coating process on a sputtering system (quorum–q150tes). the conductive coating was performed with au–pt alloy using a current of 40 ma and evaporation time of 60 s. figure 2: mechanical properties of samples lvl1 and lvl2. c.m.s. vincente et alii, frattura ed integrità strutturale, 48 (2019) 748-756; doi: 10.3221/igf-esis.48.68 752 results and discussion mechanical properties of pla uncoated samples he tensile tests average response values for each different specimen according with the experimental parameters defined on tab. 1 are presented on fig. 2. the best conditions for maximizing strength correspond to sample lvl1, with a layer thickness of 0.1 mm, raster angle of (0o/90o) and extrusion temperature of 220 oc. the level of parameters that lead to a maximum ductility they correspond to sample lvl2, with a layer thickness of 0.2 mm, raster angle of (–45o/45o) and extrusion temperature of 200 oc. the obtained results represent a variation in strength (more than 15%) and ductility (more than 20%) between samples, by simply changing the levels of the fdm process parameters. these results are consistent with the previous reported trends of the fdm process for strength and ductility of pla parts [7,9,12,14–16]. taking in account the mechanical design specifications, these mechanical properties for pla, reinforces the idea that adapting the levels of parameters could lead to a reduction of raw materials and energy costs of the fdm process. water absorption tests on fig. 3a are shown the results obtained from the experiments of water absorption tests for pla samples lvl1 and lvl2. figure 3: (a) evolution of the wg per area of samples lvl1 and lvl2 (uncoated, coated with acrylic and coated with pu) as a function of the square root of the immersion time (grey shadowed areas correspond to the statistical errors). sem images evidencing the roughness of samples with a layer thickness of (b) 0.2 and (c) 0.1 mm. solid lines are auxiliary visual guidelines. the maximum weight gain per area of the cubes was reduced in average from 2.98×10–3 g.cm–2 (uncoated) to 2.50×10–3 g.cm–2 (acrylic coated) and 1.84×10–3 g.cm–2 (pu coated), meaning that adding protective coatings of acrylic or pu on pla helps on preventing the absorption of water by pla, tab. 2. the variation from uncoated to acrylic coated samples represents a reduction of water absorption of 16%, while the pu coating allow reduce water absorption by 38%. it was also observed that sample lvl1 absorbs more water per area than sample lvl2, with or without protective coatings. the open porosity follows the same trend as the weight gain per area in all samples meaning that it is one important mechanism for water absorption in pla parts produced by fdm. the values of water absorption coefficient also reveal that the time needed to absorb a volume unit of water (proportional to k–1), increases when samples are coated, reaching its maximum with the pu coating. sample lvl1 possess the lowest layer thickness (0.1 mm) and higher extrusion temperature (220 oc). the lower the layer thickness, the rougher the surface is expected to be [30], as it can be verified by the comparison of fig. 3b and 3c. t c.m.s. vincente et alii, frattura ed integrità strutturale, 48 (2019) 748-756; doi: 10.3221/igf-esis.48.68 753 samples wg (%) p (%) k (g.cm2.min1/2) lvl1 uncoated 0.316 ± 0.023 0.315 ± 0.020 (1.23 ± 0.05) × 10–4 acrylic coated 0.266 ± 0.006 0.264 ± 0.006 (1.04 ± 0.10) × 10–4 pu coated 0.208 ± 0.013 0.205 ± 0.013 (7.25 ± 0.08) × 10–5 uncoated 0.281 ± 0.016 0.277 ± 0.013 (3.26 ± 0.03) × 10–4 lvl2 acrylic coated 0.236 ± 0.008 0.234 ± 0.006 (8.96 ± 0.08) × 10–4 pu coated 0.163 ± 0.011 0.161 ± 0.011 (5.34 ± 0.02) × 10–5 table 2: weight gain, open porosity and water absorption coefficient of samples lvl1 and lvl2. the effect of the surface roughness on wettability was described on the earlier work of wenzel [31], concluding that the presence of roughness on a surface will contribute to enhance his natural hydrophilic or hydrophobic behaviour. pla surfaces are described as intermediate surfaces between hydrophilic and hydrophobic, presenting a contact angle with water of approximately 73o. the effect studied by wenzel was demonstrated on a pla surface in the work of jordá–vilaplana [32], showing that the contact angle with water of pla sheets is reduced from 73.4o to 27o, when the root mean square roughness values vary from 12 to 55 nm. from these findings we can expect that the surface of sample lvl1 will be more hydrophilic than sample lvl2, promoting thus water absorption. another important mechanism for water absorption in polymers is the diffusion of water molecules in the micro voids between polymeric chains [33]. it is also known that the processing temperature of the polymer is responsible for the creation of these micro–cracks. an increase in micro–cracks leads to an increase of water absorption [34]. this fact is linked to the porosity of the material. in our work, the extrusion temperature of 220 oc was responsible for the highest porosity, and consequently the highest amount of water absorbed, on sample lvl1. after verifying that the application of pu coating was efficient on protecting the pla parts from water absorption, it’s now important to know which will be the impact of the pu coating on the mechanical properties of pla parts. effect of the pu coating on mechanical properties on fig. 4 are displayed the mechanical properties of samples lvl1 and lvl2, estimated from tensile tests, before and after the application pu coating on specimens. figure 4: mechanical properties of specimens lvl1 and lvl2, before and after the application pu coating. from the results presented on fig. 4, we can observe that the application of pu coating improve the strength and ductility/toughness of samples. the best mechanical properties maximizing strength (uts=36.4 mpa, σy=22.8 mpa and e=1.40 gpa), were obtained for pu coated lvl1 specimens, while the best values for ductility/toughness (εf =7.14 % and t=1.33 j/cm2) were found on pu coated lvl2 specimens. in average the mechanical properties related with strength were improved by 17 % (uts), 13% (σy) and 8.0 % (e), while the mechanical properties related with ductility increases 24 % (εf) and 16 % (t), with the application of the pu coating. the beneficial effect of the pu coating on the mechanical properties c.m.s. vincente et alii, frattura ed integrità strutturale, 48 (2019) 748-756; doi: 10.3221/igf-esis.48.68 754 can be explained by the fact that the pu coating will fill the air gaps of pla left by the fdm process (which will reduce the roughness), helping to distribute the applied load and preventing the process of crack propagation. in fact, a similar effect was also reported on the work of leite et al, where the application of an acrylic varnish on abs parts fabricated by fdm, behind prevent water absorption was led to a strong increase of σy (> 30%) for samples printed in the flat direction [23]. the benefits and simplicity of the use of protective coatings on pla parts are a potential alternative to other chemical treatments that were proposed to sealing fdm components, but with negative consequences on some mechanical properties [26,28,35] especially when thin sections are present on parts [36]. conclusions his work describes the fabrication and characterization of pla parts produced by fdm, with and without protective coatings. the relationships between processing and properties that were determined allow to provide guidelines for obtain pla parts with tailored properties depending on the final application. the 3d printing studied parameters levels and protective coatings influence strength and ductility/toughness of pla parts. the application of acrylic and pu based coatings reduces water absorption of pla produced by fdm. the pu protective coating demonstrated to be the most effective, reducing the water absorption by 38%, when compared with uncoated samples. the mechanical properties of pla parts were also improved from 8 to 24 %, when samples are coated with pu. the presented results contribute to fulfill the lack of data which users of fdm printers face when projecting with pla, contributing to stablish a better balance between strength and ductility/toughness on fdm pla parts and broadening the scope of application of this environment– friendly material. acknowledgments his work was supported by fundação para a ciência e tecnologia (fct), through idmec, under laeta project, uid/ems/50022/2019. the authors also gratefully acknowledge the funding of fibr3d project, reference saictpac/0036/2015, financed by european structural and investment funds (esifs) through the lisbon regional operational programme 2020 and by fct national funds, poci-01-0145-feder-016414. marco leite acknowledges the fct funding through unidemi project uid/ems/00667/2019. carlos m.s. vicente acknowledge the fibr3d project, reference saictpac/0036/2015, for the post-doctoral research grant. references [1] gibson, i., rosen, d., stucker, b. (2015).introduction and basic principles. additive manufacturing technologies, new york, springer, pp. 1–18. [2] gibson, i., rosen, d., stucker, b. (2015).the impact of low-cost am systems. additive manufacturing technologies, new york, springer, pp. 293–301. [3] ligon, s.c., liska, r., stampfl, j., gurr, m., mülhaupt, r. (2017). polymers for 3d printing and customized additive manufacturing, chem. rev., 117(15), pp. 10212–10290, doi: 10.1021/acs.chemrev.7b00074. [4] nampoothiri, k.m., nair, n.r., john, r.p. (2010). an overview of the recent developments in polylactide (pla) research, bioresour. technol., 101(22), pp. 8493–8501, doi: 10.1016/j.biortech.2010.05.092. [5] torres, j., cole, m., owji, a., demastry, z., gordon, a.p. (2016). an approach for mechanical property optimization of fused deposition modeling with polylactic acid via design of experiments, rapid prototyp. j., 22(2), pp. 387–404, doi: 10.1108/rpj-07-2014-0083. [6] bayraktar, ö., uzun, g., çakiroğlu, r., guldas, a. (2017). experimental study on the 3d-printed plastic parts and predicting the mechanical properties using artificial neural networks, polym. adv. technol., 28(8), pp. 1044–1051, doi: 10.1002/pat.3960. [7] lanzotti, a., grasso, m., staiano, g., martorelli, m. (2015). the impact of process parameters on mechanical properties of parts fabricated in pla with an open-source 3-d printer, rapid prototyp. j., 21(5), pp. 604–617, doi: 10.1108/rpj-09-2014-0135. [8] liu, x., zhang, m., li, s., si, l., peng, j., hu, y. (2017). mechanical property parametric appraisal of fused deposition t t c.m.s. vincente et alii, frattura ed integrità strutturale, 48 (2019) 748-756; doi: 10.3221/igf-esis.48.68 755 modeling parts based on the gray taguchi method, int. j. adv. manuf. technol., 89(5–8), pp. 2387–2397, doi: 10.1007/s00170-016-9263-3. [9] casavola, c., cazzato, a., moramarco, v., pappalettere, c. (2016). orthotropic mechanical properties of fused deposition modelling parts described by classical laminate theory, mater. des., 90, pp. 453–458, doi: 10.1016/j.matdes.2015.11.009. [10] song, y., li, y., song, w., yee, k., lee, k.-y., tagarielli, v.l. (2017). measurements of the mechanical response of unidirectional 3d-printed pla, mater. des., 123, pp. 154–64, doi: 10.1016/j.matdes.2017.03.051. [11] spoerk, m., arbeiter, f., cajner, h., sapkota, j., holzer, c. (2017). parametric optimization of intraand inter-layer strengths in parts produced by extrusion-based additive manufacturing of poly(lactic acid), j. appl. polym. sci., 134(41), pp. 45401, doi: 10.1002/app.45401. [12] sood, a.k., ohdar, r.k., mahapatra, s.s. (2012). experimental investigation and empirical modelling of fdm process for compressive strength improvement, j. adv. res., 3(1), pp. 81–90, doi: 10.1016/j.jare.2011.05.001. [13] sun, q., rizvi, g.m., bellehumeur, c.t., gu, p. (2008). effect of processing conditions on the bonding quality of fdm polymer filaments, rapid prototyp. j., 14(2), pp. 72–80, doi: 10.1108/13552540810862028. [14] ehrenstein, g.w., theriault, r.p. (2001). polymeric materials: structure, properties, applications, munich, carl hanser verlag gmbh & co. kg. [15] rajpurohit, s.r., dave, h.k. (2017).effect of raster angle on tensile properties of pla part fabricated using fused deposition modeling process. proceedings of 10th international conference on precision, meso, micro and nano engineering, chennai, india, iit madras, pp. 103–106. [16] li, h., wang, t., sun, j., yu, z. (2018). the effect of process parameters in fused deposition modelling on bonding degree and mechanical properties, rapid prototyp. j., 24(1), pp. 80–92, doi: 10.1108/rpj-06-2016-0090. [17] griffiths, a., dikarev, a., green, p.r., lennox, b., poteau, x., watson, s. (2016). avexis-aqua vehicle explorer for in-situ sensing, ieee robot. autom. lett., 1(1), pp. 282–287, doi: 10.1109/lra.2016.2519947. [18] serra, t., mateos-timoneda, m.a., planell, j.a., navarro, m. (2013). 3d printed pla-based scaffolds: a versatile tool in regenerative medicine., organogenesis, 9(4), pp. 239–244, doi: 10.4161/org.26048. [19] morgan, a.j.l., hidalgo san jose, l., jamieson, w.d., wymant, j.m., song, b., stephens, p., barrow, d.a., castell, o.k. (2016). simple and versatile 3d printed microfluidics using fused filament fabrication, plos one, 11(4), pp. e0152023, doi: 10.1371/journal.pone.0152023. [20] cuiffo, m.a., snyder, j., elliott, a.m., romero, n., kannan, s., halada, g.p. (2017). impact of the fused deposition (fdm) printing process on polylactic acid (pla) chemistry and structure, appl. sci., 7(6), pp. 579, doi: 10.3390/app7060579. [21] li, s., mccarthy, s. (1999). further investigations on the hydrolytic degradation of poly (dl-lactide), biomaterials, 20(1), pp. 35–44, doi: 10.1016/s0142-9612(97)00226-3. [22] de jong, s.j., arias, e.r., rijkers, d.t.s., van nostrum, c.f., kettenes-van den bosch, j.j., hennink, w.e. (2001). new insights into the hydrolytic degradation of poly(lactic acid): participation of the alcohol terminus, polymer (guildf)., 42(7), pp. 2795–2802, doi: 10.1016/s0032-3861(00)00646-7. [23] leite, m., varanda, a., ribeiro, a.r., silva, a., vaz, m.f. (2018). mechanical properties and water absorption of surface modified abs 3d printed by fused deposition modelling, rapid prototyp. j., 24(1), pp. 195–203, doi: 10.1108/rpj-04-2016-0057. [24] haidiezul, a.h.m., aiman, a.f., bakar, b. (2018). surface finish effects using coating method on 3d printing (fdm) parts, iop conf. ser. mater. sci. eng., 318(1), pp. 12065, doi: 10.1088/1757-899x/318/1/012065. [25] adel, m., abdelaal, o., gad, a., nasr, a.b., khalil, a. (2018). polishing of fused deposition modeling products by hot air jet: evaluation of surface roughness, j. mater. process. technol., 251, pp. 73–82, doi: 10.1016/j.jmatprotec.2017.07.019. [26] jin, y., wan, y., zhang, b., liu, z. (2017). modeling of the chemical finishing process for polylactic acid parts in fused deposition modeling and investigation of its tensile properties, j. mater. process. technol., 240, pp. 233–239, doi: 10.1016/j.jmatprotec.2016.10.003. [27] chai, y., li, r.w., perriman, d.m., chen, s., qin, q.-h., smith, p.n. (2018). laser polishing of thermoplastics fabricated using fused deposition modelling, int. j. adv. manuf. technol., 96(9–12), pp. 4295–4302, doi: 10.1007/s00170-018-1901-5. [28] mazlan, s.n.h., alkahari, m.r., ramli, f.r., maidin, n.a., mohd., sudin, n., zolkaply, a.r. (2018). surface finish and mechanical properties of fdm part after blow cold vapor treatment, j. adv. res. fluid mech. therm. sci., 48(2), pp. 148–55. [29] davis, j.r. (2004). tensile testing, ohio, oh, asm international. c.m.s. vincente et alii, frattura ed integrità strutturale, 48 (2019) 748-756; doi: 10.3221/igf-esis.48.68 756 [30] anitha, r., arunachalam, s., radhakrishnan, p. (2001). critical parameters influencing the quality of prototypes in fused deposition modelling, j. mater. process. technol., 118(1–3), pp. 385–388, doi: 10.1016/s0924-0136(01)00980-3. [31] wenzel, r.n. (1936). resistance of solid surfaces to wetting by water, ind. eng. chem., 28(8), pp. 988–994, doi: 10.1021/ie50320a024. [32] jordá-vilaplana, a., fombuena, v., garcía-garcía, d., samper, m.d., sánchez-nácher, l. (2014). surface modification of polylactic acid (pla) by air atmospheric plasma treatment, eur. polym. j., 58, pp. 23–33, doi: 10.1016/j.eurpolymj.2014.06.002. [33] espert, a., vilaplana, f., karlsson, s. (2004). comparison of water absorption in natural cellulosic fibres from wood and one-year crops in polypropylene composites and its influence on their mechanical properties, compos. part a appl. sci. manuf., 35(11), pp. 1267–1276, doi: 10.1016/j.compositesa.2004.04.004. [34] dhakal, h.n., zhang, z.y., richardson, m.o.w. (2007). effect of water absorption on the mechanical properties of hemp fibre reinforced unsaturated polyester composites, compos. sci. technol., 67(7–8), pp. 1674–1683, doi: 10.1016/j.compscitech.2006.06.019. [35] galantucci, l.m., lavecchia, f., percoco, g. (2010). quantitative analysis of a chemical treatment to reduce roughness of parts fabricated using fused deposition modeling, cirp ann., 59(1), pp. 247–50, doi: 10.1016/j.cirp.2010.03.074. [36] neff, c., trapuzzano, m., crane, n. 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/hrv (za stvaranje adobe pdf dokumenata najpogodnijih za visokokvalitetni ispis prije tiskanja koristite ove postavke. stvoreni pdf dokumenti mogu se otvoriti acrobat i adobe reader 5.0 i kasnijim verzijama.) /hun 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can be opened with acrobat and adobe reader 5.0 and later.) >> /namespace [ (adobe) (common) (1.0) ] /othernamespaces [ << /asreaderspreads false /cropimagestoframes true /errorcontrol /warnandcontinue /flattenerignorespreadoverrides false /includeguidesgrids false /includenonprinting false /includeslug false /namespace [ (adobe) (indesign) (4.0) ] /omitplacedbitmaps false /omitplacedeps false /omitplacedpdf false /simulateoverprint /legacy >> << /addbleedmarks false /addcolorbars false /addcropmarks false /addpageinfo false /addregmarks false /convertcolors /converttocmyk /destinationprofilename () /destinationprofileselector /documentcmyk /downsample16bitimages true /flattenerpreset << /presetselector /mediumresolution >> /formelements false /generatestructure false /includebookmarks false /includehyperlinks false /includeinteractive false /includelayers false /includeprofiles false /multimediahandling /useobjectsettings /namespace [ (adobe) (creativesuite) (2.0) ] /pdfxoutputintentprofileselector /documentcmyk /preserveediting true /untaggedcmykhandling /leaveuntagged /untaggedrgbhandling /usedocumentprofile /usedocumentbleed false >> ] >> setdistillerparams << /hwresolution [2400 2400] /pagesize [612.000 792.000] >> setpagedevice microsoft word numero_34_art_34 m. kikuchi et alii, frattura ed integrità strutturale, 34 (2015) 318-325; doi: 10.3221/igf-esis.34.34 318 focussed on crack paths crack growth simulation in heterogeneous material by s-fem and comparison with experiments masanori kikuchi tokyo university of science, 2641 yamazaki, noda, chiba, 278-8510, japan kik@rs.noda.tus.ac.jp yoshitaka wada 3-4-1, kowakae, higashi-oosaka, oosaka, 577-0818, japan wada@mech.kindai.ac.jp yulong li northwestern polytechnical university, 127 youyi xilu, xian 710072 shaanxi, p.r.china liyulong@nwpu.edu.cn abstract. fully automatic fatigue crack growth simulation system is developed using s-version fem (sfem). this system is extended to fracture in heterogeneous material. in the heterogeneous material, crack tip stress field becomes mixed mode condition, and crack growth path is affected by inhomogeneous materials and mixed mode conditions. stress intensity factors (sif) in mixed mode condition are evaluated using virtual crack closure method (vccm). criteria for crack growth amount and crack growth path are used based on these sifs, and growing crack configurations are obtained. three crack growth problems are simulated. one is crack growth in bi-materila made of cfrp plate and aluminum alloy. initial crack is located in cfrp plate, and grows toward aluminum alloy. crack growing direction changes and results are compared with experimental one. second problem is crack growth in bimaterial made of pmma and aluminum alloy. initial crack is located in pmma plate and parallel to phase boundary. by cahnging loading conditions, several cases are simulated and compared with experimental ones. in the experiment, crack grows into pahse boundary and grow along it. this case is simulated precisely, and the effect of pahse boundary is discussed. last case is stress corrosion cracking (scc) at hot-leg safe-end of pressurized water rreactor. this location is made of many kinds of steels by welding. in some steel, scc does not occur and in other steel, scc is accelerated. as a result, small surface crack grows in complicated manner. keywords. heterogeneous material; s-fem; fatigue; scc; vccm. introduction atigue crack growth is important problem for the integrity of structures. to avoid catastrophic accident, predictions of crack growth path and fatigue life are key technologies. as fatigue crack growth occurs in complicated structures, these predictions have met serious difficulties. fem is usually used for these predictions, f m. kikuchi et alii, frattura ed integrità strutturale, 34 (2015) 318-325; doi: 10.3221/igf-esis.34.34 319 but re-meshing process is needed for modeling of growing crack configurations, it has been a bottleneck for the application of fem to fatigue crack growth problems, especially in three-dimensional field. recently, several new techniques have been developed to overcome these difficulties. element free galerkin method [1], x-fem [2] and superposion-fem(s-fem[3]) have been developed to make re-meshing processes easy, and predict complicated crack paths. authors have developed fully automatic fatigue crack growth simulation system[4], and applied it to three-dimensional surface crack problem, interaction evaluation of multiple surface cracks[5] and evaluation of crack closure effect of surface crack[6]. this system is developed for residual stress field problem, and stress corrosion cracking process is simulated [7]. residual stress field is generated by welding, and evaluation of crack growth in heat affected zone (haz) is another important problem. in haz, grain size is different from other area, and mechanical properties are different from those of base metals. for the evaluation of scc in such areas, changes of material properties should be considered. in s-fem, local mesh is re-meshed for each step of crack growth, and local area changes its’ shape in each step. it seems difficult to change material properties of local mesh following the change of local mesh shape. in this paper, this problem is solved, and crack growth simulation system in heterogeneous material is developed. in the following, this new method is explained briefly, and example problem is simulated and compared with previous works to verify this method. several practical problems are simulated and effect of existence of interface and changes of material properties are studied and discussed. application of s-fem to heterogeneous material. -fem is originally proposed by j. fish [3]. as shown in fig.1, a structure with a crack is modeled by global mesh and local mesh. global area, g , does not include a crack, and course mesh is used for the modeling of global area. a crack is modeled in local area, l , using fine mesh around crack tip. local area is superimposed on global area and full model is made. in each area, displacement function is defined independently. in overlapped area, displacement is expressed by the summation of displacement of each area. to keep the continuity at the boundary between global and local area, gl , displacement of local area is assumed to be zero as shown in the following equation.            0 g g l i g l l i i i l gl i u i u u u i u i (1) figure 1: concept of s-fem. the derivatives of displacements can be written in the same way. these displacement functions are applied to virtual work principle, as shown in eq. (2), and .the final matrix form of s-fem is obtained as shown in eq. (3) , , , , , , , , g l l l t g g g l i j ijkl k l i j ijkl k l l g l l g tg i j ijkl k l i j ijkl k l i i u d u d u d u d u d u d u d u d u t d                         (2)       0 gg gl g g lg ll l k k u t k k u                                    (3) s m. kikuchi et alii, frattura ed integrità strutturale, 34 (2015) 318-325; doi: 10.3221/igf-esis.34.34 320 where g tgg g gg gk b d b d                l tgl g ll lk b d b d                (4) l tll l ll lk b d b d                gb   and lb   are displacementstrain matirces defined in global and local area, respectively. ggd   and lld   are stress-strain matices which are described using young’s modulus and poisson’s ratio. these are material constants which may change in heterogenous material in each material. in eq. (3), t tlg glk k       , and the stiffness matrix is symmetric. glk   expresses the relationship between local and global areas. by calculating this term with high accuracy, accurate fem results are obtained. by solving eq.(3), both displacement fields of local and global areas are obtained simultaneously. the detail of the theory was presented in the literature of one of the author [8]. this method is applied to crack growth in heterogeneous material. as shown in fig.2, global model is made of two materials, and it is easy to define phase bounday in global model. material properties are different from each other in material 1 and 2. but in local area, it is seen that it is difficult to arrange mesh in local area along phase boundary of global model. local mesh is overlapped on global mesh. glk   and llk   are calculated by eq.(4), and lld   , material properties in each material, are needed for these calculations. as shown in fig.2, integrations are conducted using gaussian numerical integration method in each local element, and material properties at these gaussian points are needed for integration. in s-fem analysis, all gaussian points in local elements belong to some global element. then, material properties of each gaussian point is same as those of global element in which gaussian point is located. for this meaning, local mesh needs not to have material properties, and it becomes easy to calculate eqs.(4) using material properties of global element. by this method, it becomes possible to apply s-fem methodology to crack growth simulation in heterogeneous material. + = global mesh global mesh local mesh local mesh interfaceinterface figure 2: global mesh and local mesh in heterogeneous material. crack growth in bi-material of cfrp and aluminum alloy ig. 3 shows test specimen made of aluminum alloy, a2017 and cfrp. as shown in fig. 4, fiber orientation of cfrp plate is 90 degree to loading direction. initial notch is introduced in cfrp plate and grows toward to a2017. phase boundary of two material is inclined about 80 degree to horizontal axis. tensile load is subjected along x axis in fig. 4. mechanical properties of these two materials are shown in tab. 1. young’s modulus of a2017 is much larger than that of cfrp. fig. 5(a) shows experimental result. initial crack grows toward to phase boundary, and it changes growing direction a little to upper ward. this is the effect of mismatch of mechanical properties between two materials. as the young’s modulus of a2017 is larger than that of cfrp, crack prefers to stay in cfrp side. finally it reaches to the phase boundary, and separation occurred between two materials. fig. 5 (b) shows result of numerical simulation. in this paper, crack growing direction is determined using the maximum tangential stress (mts) criterion [9], which determines the crack growth direction, , to satisfy the following equation, f m. kikuchi et alii, frattura ed integrità strutturale, 34 (2015) 318-325; doi: 10.3221/igf-esis.34.34 321  sin 3 cos 1 0i iik k           (5) where ki and kii are stress intensity factors (sif) in mode i and ii, respectively. fig. 5 (c) shows overlapped result of experiment and numerical simulation. it is noticed that both results agree very well. it also means that mts criterion is available to predict crack growing direction under mixed mode loading condition. figure 3: specimen of composite material (cfrp & a2017). a2017 cfrp x y z shape of the test specimen fiber direction notch surface figure 4: overview of specimen and direction of fiber. material constant young’s modulus e (gpa) poisson’s ratio  a2017 70.6 0.30 cfrp (perpendicular direction of fiber 9.53 0.49 table 1: material constants. (a) experimental result. (b) numerical simulation (c) overlapping of both results. figure 5: comparison of crack path in bi-material. crack growth in a bi-material of pmma and a6061 ee and krishnaswamy [10] conducted experiment of crack growth in bi-material made of pmma and aluminum alloy al6061. as shown in fig.6, pmma and al6061 were pasted, and initial crack is introduced in pmma. three loading conditions are tested, as shown in fig. 6 (a)-(c), and crack growing paths are obtained. in case (a), l m. kikuchi et alii, frattura ed integrità strutturale, 34 (2015) 318-325; doi: 10.3221/igf-esis.34.34 322 nearly symmetrical loading condition is subjected. in case (b), loading condition is not symmetric, and supporting load in pmma is near to initial crack. in case (c), supporting load becomes much nearer to the initial crack. the distance between initial crack and phase boundary is 10mm in case1 and case 3, and 16mm in case 2. in all cases, stress field at initial crack tip becomes under mixed mode loading condition, and crack grows by changing the growing direction. table 2 shows material constants of two materials. in this case, young’s modulus of pmma is much smaller than that of aluminum alloy. experimental results are shown in fig. 7 (a)-(c) with those of numerical simulation where experimental results are shown by yellow lines, and numerical results are expressed by red line. in case 1, crack grows toward inside of pmma and goes far from phase boundary. numerical simulation well predicts the crack growth path, and agrees very well with experimental one. in case 2, crack grows nearly straight forward in numerical simulation and experiment. in this case agreement of numerical prediction and experiment is well. in case 3, difference between experiment and numerical simulation becomes clear. by the experiment, crack grows into the phase boundary and grows along the phase boundary. but numerical simulation predicts that crack grows once nearer to the phase boundary, but after some amount of crack growth, it goes far from the phase boundary. this difference is due to the numerical model in which phase boundary is not modelled correctly. numerical model assumes that two materials are bonded tightly and there is no phase boundary thickness. but in the real structure, phase boundary has some small thickness and has its’ own strength. then phase boundary is modelled in s-fem simulation. fig. 8 shows mesh pattern around phase boundary. the thickness of the phase boundary is assumed to be 0.5mm, and three layered finite element mesh is used. material constants of the phase boundary are also shown in tab. 2. it is assumed that phase boundary has very small stiffness comparing with other materials. it is because two materials are bonded using some bond, and it is reasonable to assume that it has very low stiffness. numerical result is shown in fig. 9 (a). by assuming phase boundary layer, crack grows into the phase boundary and grows along it. it is similar to experimental result, but path does not agree completely. this may be due to the phase boundary model. in this simulation, the thickness of phase boundary is assumed to be 0.5mm, which may be much larger than the real structure. also, material constants in the phase boundary are assumed to be very small value, without any verification. by studying in detail on the effects of phase boundary thickness and material constants, better phase boundary model may be proposed in future. fig. 9 (b) shows detailed crack path in the phase boundary. it grows in the phase boundary layer in zig-zag manner. as the crack grows in the phase boundary, and does not grow along the border line between different materials, it is easy to evaluate stress intensity factors by the conventional vccm method [11]. in many composite materials, for example, cfrp, crack growth along phase boundary is observed. the strength of phase boundary is key parameter for the discussion on the strength of composite material. experimental studies have been done by many authors [12-14], but it has been very difficult to discuss this problem based on numerical simulation. through these simulations, it is shown that crack growth process along phase boundary becomes possible, if the phase boundary is properly modelled. (a) case 1 (b) case 2 (c) case 3 figure 6: initial carack location and loading conditions of bi-material of pmma and a6061. pmma a6061 phase boundary e [gpa] 3.24 69 0.15  0.35 0.3 0.35 table 2: material constants. 156mm94mm 150m 150m150m 30m 150mm50mm pmma a6061 m. kikuchi et alii, frattura ed integrità strutturale, 34 (2015) 318-325; doi: 10.3221/igf-esis.34.34 323 (a) case 1 (b) case 2 (c) case 3 figure 7: crack growth path in experiment and numeircal simulation. (a) (b) figure 8: fem model of phase bourdary. figure 9: crack growth in the phase boudary. (a) crack path (b) detail in phase boundary. stress corrosion cracking in hot leg of nuclear plant due to welding thermal stress tress corrosion cracking (scc) frequently occurs in nuclear plant by welding thermal residual stress. fig. 10 shows half of hot leg of a pipe at nuclear pressure vessel. it is welded to pressure vessel using several kinds of welding metals. fig. 10 shows circumferentioal residual stress field by welding, which is obtained by numerical welding simulation. residual stress field is generated in the cross section of hot leg, which triggers the crack initiation and growth by stress corrosion. detailed cross section of this hot leg is shown in fig.11. hot leg is made of three materials. they are low carbon steel, stainless steel and ni-based alloy. material constants of them are shown in tab. 3. crack growth rate by stress corrosion is expressed by eq. (6), where  and  are material constants [15], and are shown in tab. 2. scc does not occur in law carbon steel and stainless steel, and occurs only in ni-based alloy.  / eqda dt k   (6) initial crack is assumed in ni-based alloy, in green area in fig.11, and crack growth simulation is conducted. figs. 12 (a)(e) show crack growing processes. initial crack is located inside of hot leg pipe, where residual hoop stress is very large. this initial carck grows gradually and goes near to phase boundary between low carbon steel and stainless steel. it terminates at the phase boundary, and crack continues growing inside ni-based alloy. after 30 years, crack grows nearly s m. kikuchi et alii, frattura ed integrità strutturale, 34 (2015) 318-325; doi: 10.3221/igf-esis.34.34 324 half of the plate thickness. fig. 14 shows change of crack depth and crack length along inner sursface with time (year). in the first several years, crack grows very rapidly, but growth rate decreases in low residual stress area. after 27 years, crack depth increases again very fast. if the crack depth exceeds 75% of plate thickness, this crack is treated to be fixed immediately. this crack reaches to this limit depth after 27 years, as shown in fig.13. it is enoughly long time for the usual operation of nuclear power plant. by using this method, similar estimation of scc process is possible. it enables to evaluate correctly the integrity of nuclear components. figure 10: residual stress distribution in hot leg. figure 11: cross section of hot leg and materials. table 3: material constants of hot leg materials. (a) initial crack (0 year). (b) 1.95 years. (c) 15.4 years. (d) 22.8 years. (e) 30.2 years. figure 12: scc growing process in the hot leg. material e[gpa] ν α β low carbon steel 176.0 0.3 0.0 1.00 stainless steel 174.5 0.3 0.0 1.00 ni-based alloy 198.3 0.3 6.73×10-14 2.42 m. kikuchi et alii, frattura ed integrità strutturale, 34 (2015) 318-325; doi: 10.3221/igf-esis.34.34 325 figure 13: crack growth rates. summary hree crack growth problems in heterogenous material are simulated using s-version fem. in two cases, results are compared with experimental ones, and good agreements are obtained. it is verified that s-fem is powerful tool for these compicated problems. it is also shows that fracture process along phase boundary is also simulated by this method. by careful modeling of phase boundary layer, realistic fracture process in cfrp plate becomes possible. references [1] belytchko, t,. lu, y.y., gu, l.,element free galerkin method, international journal for numerical methods in engineering, 37 (1994) 229-256. [2] belytschko, t., black, t., elastic crack growth in finite elements with minimal remeshing, international journal for numerical methods in engineering, 45 (1999) 601-620. [3] fish, j., markolefas, s., guttal, r., nayak, p., on adaptive multilevel superposition of finite element meshes, applied numerical mathematics, 14 (1994) 135-164. [4] kikuchi, m., wada, y., takahashi, m., li, y., fatigue crack growth simulation using s-version fem, proc. asme pvp2008, pvp2008-61900. [5] kikuchi, m., interacation evaluation between two surface cracks by fatigue, proc. asme pvp2009, pvp200977073. [6] kikuchi, m., maigefeireti, m., sano, h., closure effect on interaction of two surface cracks under cyclic bending, proc. asme pvp2010, pvp2010-25241. [7] kikuchi, m., wada, y., shimizu, y., li, y., crack growth analysis in a weld-heat-affected zone using s-version fem, int. j. pvp, 90-91 (2012) 2-8. [8] okada, h., endo, s., kikuchi, m., on fracture analysis using an element overlay technique, engng. fracture mech., 72 (2005) 773-789. [9] paris, p.c., erdogan, f., a critical analysis of crack propagation of laws, trans. asme ser. d, (1963) 528-533. [10] lee, h., krishnaswamy, s., quasi-static propagation of subinterfacial cracks, asme journal of applied mechanics, 67(3) (2000) 444-452. [11] rybicki, e. f., kaninen, m.f., a finite element calculation of stress intensity factors by a modified crack closure integral, engng. fracture mech., 9 (1977) 931. [12] konur, o., matthews, f.l., effect of the properties of the constituents on the fatigue performance of composites: a review, composites, 20-4 (1989) 317-328. [13] wu, c.m.l., thermal and mechanical fatigue analysis of cfrp laminates, composite structures, 25 (1993) 339-344. [14] kawai, m., morishita, m., fuzi, k., sakurai, t., kemmochi, k., effect of matrix ductility and progressive damage on fatigue strength of unnotched and notched carbon fiber plain woven roving fabric laminates, composites: part a, 27a (1996) 493-502. [15] jsme s nal-2004, codes for nuclear power generation facilities, (2004), (in japanese). t microsoft word numero 22 articolo 4.doc a. namdar, frattura ed integrità strutturale, 22 (2012) 26-30; doi: 10.3221/igf-esis.22.04 26 natural minerals mixture for enhancing concrete compressive strength abdoullah namdar faculty of civil engineering & earth resources, universiti malaysia pahang, malaysia ab_namdar@yahoo.com abstract. the construction material quality is required to be improved in order to enhancing structure stability, optimizing construction cost and quality. the kaolin and bentonite have been mixed in equal quantity and treated by heat for 1 hour under 600 ºc, 800 ºc and 1000 ºc to create new minerals under high temperature condition to introduce an acceptable concrete additive for achieving concrete compressive strength in early age. to study micro properties of additive-cement mixture, x-ray and fesem experiments have been used. the results indicate that acceptable proportion of unheated kaolin-bentonite is improving the concrete compressive response. but if kaolin-bentonite mixture treated by heat under 800 ºc and in quantity of 12 % has been used in concrete mixed design, then the concrete compressive strength of 7 days shows the best result. the result is due to the development of new minerals under high temperature condition in mineral mixture and also kaolinbentonite additive change cement past crystal and lead to enhancement of nano structural cement bonding. keywords. concrete additive; kaolin; bentonite; heat treatment; new minerals. introduction he use of high-fast strength concrete has many applications, both technical and economical. over last decade, the high strength concrete in short time was very important issue for researcher. the reconnaissance on economically and feasibility concrete additive is highly significant in construction industry. a high strength concrete is introduced by using large volumes of low calcium as an additive and compressive strength of 80 mpa was for 28 days [1]. the various chemical and supplementary cementitious materials are investigated on improvement concrete compressive strength [2-3]. and also fly ash, bottom ash and coarse aggregate mechanical properties and quality are evaluated for enhancement of concrete compressive strength [4-7]. the natural minerals are shown good results among other techniques. the investigation show natural minerals are improved concrete compressive strength and cement geopolymer [8-11]. from other view of point the investigation on materials macroscopic quality and minerals in concrete mix design is important topic for construction industry [12-13]. for example geopolymers can be synthesized from aluminosilicate powders including natural pozzolans [14-15]. the replacing cement by mineral additions resulted in lower early age strength and low cement quantity consumption [16]. the modern construction projects are trust to high strength concrete [17]. to optimize admixture cost and better improvement concrete characteristics many methods have been introduced [18-20]. the natural minerals mixture treatment by heat to develop new minerals based on kaolin-benonite interaction minerals in high temperature for produced new materials which can be useful as a concrete additive in concrete mixed design process have been investigated in order to improve concrete compressive strength in short term for minimizing construction time and cost. t http://dx.medra.org/10.3221/igf-esis.22.04&auth=true http://www.gruppofrattura.it a. namdar, frattura ed integrità strutturale, 22 (2012) 26-30; doi: 10.3221/igf-esis.22.04 27 methodology he natural minerals have ability in producing new material or modifying characteristics of materials. in this research work the kaolin and bentonite have been selected for improve concrete compressive strength. the kaolin and bentonite have been mixed in equal weight and subjected to the heat for 1 hour for 600 ºc, 800 ºc and 1000 ºc. the main propose for mixing kaolin and bentonite before submitting to heat is to analysis minerals of kaolin and bentonite interaction in high temperatures. the unheated and new produced materials have been mixed with concrete for 6% and 12% of cement weight (tab. 1). the compressive strength of concrete for 7 days and 14 days has been tested. to study macro properties of additive-cement mixture x-ray experiment and fesem have been used. result and discussion n figs. 1-3 the image of fesem shows nano particles of cement past without additive and, when 6% and 12% additive have been used in concrete mixed design. in fig. 1 the nano particle have almost plane shape and in fig. 2 the shape is convert to the lengthy shape and in fig. 3 this process is increased, and subsequently resulted in improving concrete compressive strength. the additive creates new crystal structure in cement past. the result is indicated that 6% proportion of unheated kaolin-bentonite is improving concrete compressive. and if kaolin-bentonite mixture treated by heat under 800 ºc and in quantity of 12 % of cement weight has been used in concrete mixed design the concrete compressive strength of 7 days is resulted in improving concrete compressive strength in maximum level. it is due to develop new crystal morphology under high temperature condition in bentonite-kaolin-cement mixture and also considerably enhancement bonding of cement. if quantity of bentonite-kaolin mixture treated by heat increased in concrete mixed design resulted in better enhancement compressive strength, and it is not for unheated bentonite-kaolin mixture. figure 3: image fesem of cement mixed with 12% additive. t i figure 1: image fesem of cement. figure 2: image fesem of cement mixed with 6% additive. http://dx.medra.org/10.3221/igf-esis.22.04&auth=true http://www.gruppofrattura.it a. namdar, frattura ed integrità strutturale, 22 (2012) 26-30; doi: 10.3221/igf-esis.22.04 28 the fig. 4 is highlighted xrd pattern of cement, and cementkaolin-bentonite mixture, the kaolin-bentonite was submitted to 800 ºc heat for 1 hour. the xrd pattern shown that ca(od) is converted to ca(oh)2 but no significant change in xrd pattern in increasing kaolin-bentonite mixture from 6% to 12% in concrete mixed design. the tab. 2 and fig. 5 show the result of different mixed design for compressive strength of concrete. the result is indicated appropriate proportion of natural minerals mixture can improve concrete compressive strength without and treatment process. sl no con type unheated additive (%) additive produced by 600 ºc (%) additive produced by 800 ºc (%) additive produced by 1000 ºc (%) 1 40 2 40 6 3 40 12 4 40 6 5 40 12 6 40 6 7 40 12 8 40 6 9 40 12 table 1: concrete-additive mixture ratio. sl no type of concrete additive (%) 7 days 14 days stress (n/mm2) stress (n/mm2) 1 without additive 25.77 30.48 2 natural additive 6 33.65 34.50 3 natural additive 12 21.87 28.44 4 additive produced under 600 ºc heat 6 18.70 33.07 5 additive produced under 600 ºc heat 12 25.14 40.19 6 additive produced under 800 ºc heat 6 30.95 35.15 7 additive produced under 800 ºc heat 12 40.32 42.39 8 additive produced under 1000 ºc heat 6 27.05 31.70 9 additive produced under 1000 ºc heat 12 31.97 33.44 table 2: concrete compression strength. http://dx.medra.org/10.3221/igf-esis.22.04&auth=true http://www.gruppofrattura.it a. namdar, frattura ed integrità strutturale, 22 (2012) 26-30; doi: 10.3221/igf-esis.22.04 29 figure 4: xrd pattern of cement, and cement-kaolin-bentonite mixture, the kaolin-bentonite was submitted to 800 ºc heat for 1 hour. figure 5: concrete compressive strength. conclusion  the fesem image indicated changing crystal structure of cement past is responsible for enhancing concrete compressive strength.  the proportion of additive before subjected to heat has different effect on concrete compressive strength compare to when additive is modified under high level of heat.  the quantity of 12% additive produced by 800 ºc heat has shown best result in improving concrete compressive strength.  the amount of 6% additive not subjected to the heat has shown acceptable result in improving concrete compressive strength.  increasing bentonite-kaolin mixture which was treated by heat in concrete mixed design resulted in better enhancement compressive strength. http://dx.medra.org/10.3221/igf-esis.22.04&auth=true http://www.gruppofrattura.it a. namdar, frattura ed integrità strutturale, 22 (2012) 26-30; doi: 10.3221/igf-esis.22.04 30 references [1] c.s. poon, l. lam, y.l. wong, cement and concrete research, 30 (2000) 447. [2] u. s. yilmaz, h. turken, civil engineering, 55(2) (2011) 107. [3] m.a. megat johari, j.j. brooks, s. kabir, p. rivard, construction and building materials,; 25, (2011) 2639. [4] h. beshr, a.a. almusallam, m. maslehuddin, construction and building materials, 17 (2003) 97. [5] a. kilic, c. d. atiş, a. teymen, o. karahan, f. özcan, c. bilim, m. özdemir, cement & concrete composites, 30 (2008) 290. [6] h.k. kim, h.k. lee, construction and building materials, 25 (2011) 1115. [7] u. atici, expert systems with applications, 38 (2011) 9609. [8] a. behnood, h. ziari, cement & concrete composites, 30 (2008) 106. [9] h. yazici, building and environment, 42 (2007) 2083. [10] d. bondar, alkali activation of iranian natural pozzolans for producing geopolymer cement and concrete. ph.d. thesis, university of sheffield, uk (2009). [11] h. xu, j.s.j. van deventer, int j mineral process, 59 (2000) 247. [12] p. folino, g. etse, int. j. of solids and structures, 49 (2012) 701. [13] dali bondar, c.j. lynsdale, n.b. milestone, n. hassani, a.a. ramezanianpour, construction and building materials, 25 (2011) 2906. [14] j. davidovits, j. therm. anal., 37 (1991) 1663. [15] j. davidovits, j. mater. educ., 16 (1994) 91. [16] m. i. a. khokhar, e. roziere, p. turcry, f. grondin, a. loukili, cement & concrete composites, 32 (2010) 377. [17] k. kovler, o. jensen, concr int, 27(9) (2005) 39. [18] s. shah, j. weiss, w. yang, concr. int., 20(4) (1998) 51. [19] d. bentz, cementitious barriers partnership, (2009) cbp-tr-2009-002-c3. [20] aci-231. report on early-age cracking: causes, measurement and mitigation. farmington hills (mi): american concrete institute; (2010). http://dx.medra.org/10.3221/igf-esis.22.04&auth=true http://www.gruppofrattura.it microsoft word numero_49_art_30_2460 a. kostina et alii, frattura ed integrità strutturale, 49 (2019) 302-313; doi: 10.3221/igf-esis.49.30 302 focused on russian mechanics contributions for structural integrity numerical analysis of a caprock integrity during oil production by steam-assisted gravity drainage method anastasiia kostina, maxim zhelnin, oleg plekhov institute of continuous media mechanics of the ural branch of russian academy of sciences, perm, russia kostina@icmm.ru, http://orcid.org/0000-0002-5721-3301 zhelnin.m@icmm.ru, http://orcid.org/0000-0003-4498-450x poa@icmm.ru, http://orcid.org/0000-0002-0378-8249 abstract. the work is devoted to the investigation of a caprock integrity during oil production by steam-assisted gravity drainage method. an originally proposed thermo-hydro-mechanical model was used for the evaluation of mechanical loading acting on the over-burden. the model includes mass conservation laws, the energy conservation law and the linear momentum balance. filtration of each phase of the three-phase flow (steam, oil and water) is described by darcy’s law. effective stress concept is used to take into account the effect of pore pressure on the stress-strain state. inelastic deformations are described by the phenomenological viscoplastic model based on drucker-prager yield criterion. two qualitatively and quantitatively different scenarios of porosity evolution are considered. the first scenario corresponds to the case of the pore compression while the second one describes increase in porosity induced by the volumetric strains. the obtained stress-strain state in the reservoir was used for the assessment of the caprock integrity for both cases of porosity evolution. in addition, the effect of the porosity evolution on the oil production rate is studied. it has been shown that the oil production rate strongly depends on the prevailing physical mechanism of the porosity evolution. keywords. coupled problems; steam-assisted gravity drainage; caprock integrity; rock failure. citation: kostina, a., zhelnin, m., plekhov, o., numerical analysis of a caprock integrity during oil production by steam-assisted gravity drainage method, frattura ed integrità strutturale, 49 (2019) 302-313. received: 04.04.2019 accepted: 04.06.2019 published: 01.07.2019 copyright: © 2019 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. introduction epletion of conventional oil resources requires the development of advanced techniques for crude oil recovery. thermal methods are an effective way to reduce viscosity and enhance oil production rate. steam-assisted gravity drainage (sagd) method is characterized by a very high recovery factor (from 0.6 up to 0.8) [1]. this technique includes a number of horizontal parallel wells located one above the other. steam injection into the upper wells d http://www.gruppofrattura.it/va/49/2460.mp4 a. kostina et alii, frattura ed integrità strutturale, 49 (2019) 302-313; doi: 10.3221/igf-esis.49.30 303 leads to the formation of a high-temperature steam chamber. increase in the temperature reduces oil viscosity and enhances oil mobility. oil together with the pore water and the condensed steam flow downwards into the production wells under the gravity. optimization of sagd requires formulation of mathematical models which takes into account multiphase flow, filtration, phase change processes and alteration of the stress-strain state due to the thermal and mechanical loading of the reservoir. injection of the hot steam under the high pressure leads to the various geomechanical phenomena. for example, dilation and fracture significantly increase the porosity whereas compaction of soil grains and its thermal expansion reduces it [2]. moreover, excessive stresses in the reservoir can break the integrity of the steam chamber. loss of the caprock integrity is a serious problem for human safety and the environment which leads to the water and air pollution. usually, numerical models of sagd include momentum, mass and energy conservation laws which are supplemented by state and constitutive equations [3-6]. to describe the effect of fluid flow on a stress-strain state of porous media poroelastic biot’s theory is used. to provide a full coupling between fluid flow and the stress-strain state of the reservoir it is necessary to include a constitutive equation for porosity evolution into the model. the porous media is a complicated system which deformational behavior and properties are strongly depend on the level of the applied load, initial heterogeneity, anisotropy and many other factors. therefore, there is a wide variety in the choice of relations for the description of the porosity evolution. in the simplest case, the porosity can be related to the pore pressure using the pore compressibility coefficient [7-8]. in [9-10] the incremental relation between the porosity and the mean stress with the coefficient which is linearly dependent on the current porosity value has been obtained. in case of the low compressibility, the porosity can be associated with the mean effective stresses using the composition of the linear fractional function and the exponent [11]. another exponential dependence of the porosity on the mean effective stresses has been obtained in [12]. the incremental equation relating porosity to the linear combination of the volumetric strains and pore pressure has been proposed in [13-14]. in case of the low compressibility the dependence between the porosity and volumetric strains is also expressed as the exponential function [15-16]. at the same time, a linear fractional dependence of the porosity on volumetric strains has been proposed in [17-19]. as regards to the viscous oil production, the main mechanisms affecting the value of porosity is the shear dilation. in [1] it has been mentioned that propagation of the thermal front within the reservoir leads to the rise in the horizontal compressive stresses and substantial reduction of the vertical stresses. such changes cause a significant shear dilation which enhances permeability and increases porosity of the soil. this effect can be described by the models which relate porosity to volumetric strains [4], [15-19]. however, when the effective confining pressures are high the shear dilation can be suppressed. in this case, the pore compression leads to the squeezing of the oil out of the pore space which can be described by relating of the porosity to the effective stresses [9-12]. alteration of porosity during thermal oil production can significantly affect mechanical state of the reservoir near the caprock. analysis of the existing works have shown that only few works are devoted to the study of the caprock integrity during sagd. rahmati et al. [20] investigated effect of the intrinsic anisotropy of caprock on maximum operating pressure of sagd. for this purpose, they combined anisotropic mohr-coloumb failure criterion with transversely isotropic elastic model. they have shown that isotropic model gives a little bit higher values of maximum operating pressure than anisotropic. mclellan et al. [21] took into account statistical distribution of the natural fractures in caprock. khan et al. [22] proposed an integrated geomechanics approach to evaluate caprock integrity which is based on the construction of the real three-dimensional formation taking into account petrophysical properties of the reservoir, strength parameters of the caprock and the results of mini-frac or leak-off tests. the obtained geological model is integrated with the coupled reservoir simulator which allows one to obtain stress-strain state of the considered formation. these results can be used for estimation of the caprock failure on the base of mohr-coulomb fracture criterion. walters et al. [23] confirmed that the key factors determining maximum operating pressure in sagd are the knowledge of the initial stress-strain state of the reservoir and its material properties. they have conducted analytical and numerical analysis of the stress change during sagd. analytical method was based on the theory of poro-thermo-elasticity and the mohr-circle analysis for evaluation of the shear failure. numerical assessment included a coupled reservoir and geomechanical simulator. tensile and shear stress ratios were used as failure indicators. uwiera-gartner et al. [24] have analyzed caprock integrity of sagd project in northeast alberta (canada) using geological and geomechanical parameters. the drawback of this method is existence of the uncertainties in geomechanical parameters of the caprock. the key uncertainties affecting the analysis are heterogeneity, anisotropy, delamination and large fractures, which can reduce rock strength. this work is devoted to the investigation of sagd operating parameters (the temperature and the pressure of the injected steam) on the caprock integrity near its base. the following algorithm has been used in order to estimate the integrity. firstly, the coupled thermo-hydro-mechanical problem is solved to obtain mechanical state of the reservoir. an originally proposed model is applied to this purpose. according to the model, the process of steam injection is governed by mass a. kostina et alii, frattura ed integrità strutturale, 49 (2019) 302-313; doi: 10.3221/igf-esis.49.30 304 conservation law, energy conservation law, darcy’s law for oil, steam and water filtration. water-vapor phase change is determined by the additional heat source proposed in [25]. inelastic deformations of the reservoir induced by propagation of the thermal front are described by the phenomenological viscoplastic model. on the second step of the algorithm, the values of mechanical stresses near the top of the reservoir are determined. the last step is the assessment of the caprock failure according to drucker-prager criterion. the specific feature of this work is that two qualitatively different scenarios of porosity evolution is considered. the first scenario corresponds to the case of the pore compression which can be described by the model [10]. the second scenario demonstrates increase in porosity induced by the volumetric strains. this effect can be described by the model [11] which is widely used in sagd simulation. mathematical model he developed model of sagd is based on the following assumptions. fluid within the pore space consists of the three immiscible components (water, steam and oil). the flow of each component is slow and obeyed to darcy’s law. capillary pressure is negligible due to relatively high porosity. the change in the oil viscosity is the result of the change in the temperature only. the deformations of porous media are small. elastic behavior of solid skeleton is described by hook’s law. effective stress concept is used to take into account the effect of pore pressure on the stressstrain state. viscoplastic behavior of the reservoir is described by perzyna’s theory and drucker-prager yield criterion [2627]. therefore, the complete system of equations can be written as:           w w w w w n s q t v , (1)           s s s s s n s q t v , (2)           0o o o o n s t v , (3)    1w s os s s , (4)        rw w w w kk pv g , (5)        rs s s s kk pv g , (6)        ro o o o kk pv g , (7)                                    , , , , 1 r r i i i eff i i i i i w o s i w o s t n c n s c t s c nt q t v , (8)    effσ g 0 , (9)        0: vpt bt t pσ c ε e ε e , (10) t a. kostina et alii, frattura ed integrità strutturale, 49 (2019) 302-313; doi: 10.3221/igf-esis.49.30 305    vp f f a b ε σ , (11)     1 2 tε u u , (12)             , , sat s s sat sat s w sat w w sat sat t t rns t t t q q t t rns t t t , (13) where subscript i takes values s , w , o , r and denotes steam, water, oil and solid skeleton respectively; n is the porosity; i is the density; t is the time; ws is the water saturation; ss is the steam saturation; os is the oil saturation; iv is darcy’s velocity; k is the absolute permeability; rik is the relative permeability; i is the dynamic viscosity; p is the pressure; g is the gravity; t is the temperature; ic is the heat capacity;         , , 1eff i i r i w o s ns n is the effective thermal conductivity;  wq lq is the heat source due to the phase change; l is the latent heat; σ is the stress tensor;         , , 1eff i i r i w o s ns n is the effective density; c is the stiffness tensor which has two components in case of linear isotropic elasticity (young’s modulus and poisson’s ratio); ε is the strain tensor; t is the thermal expansion coefficient; 0t is the initial temperature; e is the unity tensor; vpε is the viscoplastic strain tensor; b is the biot coefficient; a is the viscoplastic rate coefficient;  denotes mccayley brackets;   2 1f j ai b ; 2j is the second invariant of the deviatoric part of the stress tensor; 1i is the first invariant of the stress tensor; a , b are material parameters; u is the displacement vector; r is the mass transfer intensity factor; satt is the phase change temperature. the following functions were used to define relative phase permeabilities [28]:              1 1 , 1 1 0, m w rw rw w rw rw ro w rw s s a s s k s s s s , (14)               2 2 , 1 1 0, m s rs rs s rs rs rw ro s rs s s a s s k s s s s s , (15)              3 3 , 1 1 0, m o ro ro o ro rw ro o ro s s a s s k s s s s , (16) where 1a , 2a , 3a , 1m , 2m , 3m are the empirical parameters; rws , rss , ros are the residual values of water steam and oil saturations. in this work the effect of volumetric strains and effective stresses on the porosity evolution of the reservoir is investigated. for this purpose two qualitatively and quantitatively different models are considered. the first model [10] relates porosity to mean effective stresses by means of the coefficient which is linearly dependent on the current value of porosity: a. kostina et alii, frattura ed integrità strutturale, 49 (2019) 302-313; doi: 10.3221/igf-esis.49.30 306      (1 ) 'p rdn c n c d , (17) where pc is the pore compressibility; rc is the rock compressibility;    ' m b p ;         / 3m xx yy zz ;  xx ,  yy ,  zz are the diagonal stress tensor components. this model can be applied in case of the high confining pressure when the effect of shear dilation is small. the second model [11] uses exponential dependence of volumetric strain on porosity:     01 (1 ) exp voln n , (18) where 0n is the initial porosity; vol is the volumetric strain. this model can be applied to the cases when the prevailing mechanism of deformation is the increase in volumetric strains. the following boundary and initial conditions were used to close the developed system of equations for sagd simulation:    00p t p , (19)    00t t t , (20)    00w ws t s , (21)   0 0ss t , (22)  1w rws s , (23)    1 1s rw ros s s , (24)  1 bp p , (25)  2 wp p , (26)  1 bt t , (27)   2' 0n q , (28)         1s s s sn v n v , (29)         1w w w wn v n v , (30)   3 4, 0xu , (31)   5 6, 0yu , (32) a. kostina et alii, frattura ed integrità strutturale, 49 (2019) 302-313; doi: 10.3221/igf-esis.49.30 307 where 0p is the initial pressure; 0 ws is the initial water saturation; 1 denotes the boundary of the injection well; bp is the injection pressure; 2 denotes the boundary of the production well; wp is the pressure in the production well; n is the unit normal vector; 'q is the heat flux vector; 3 , 4 denote left and right boundaries of the rectangular domain; 5 , 6 denote upper and lower boundary of the rectangular domain. results and discussions he system of eqns. (1)-(18) together with the initial and boundary conditions (19)-(32) was solved numerically using finite-element software comsol multiphysics®. for this purpose, the following algorithm has been proposed. firstly, eqns. (1)-(7) were reformulated using the total velocity of the three-phase flow. after this, the obtained equations were represented in the weak form. each of the equations was multiplied by the test function. then, the integration by parts was applied to reduce the order of differentiation. in the considered equations, the convective term prevails over the diffusive one. to smooth the oscillations caused by the convective terms the artificial diffusion was added to each equation. the resulting equations were implemented to comsol multiphysics® by weak form pde interface. to solve the eqns. (8)-(12) heat transfer and structural mechanics modules were used. the more detailed description of the algorithm can be found in [29]. the developed numerical algorithm has been applied to the three-dimensional numerical simulation of the rectangular reservoir containing two horizontal wells (injection and production). schematic representation of the simulated domain is given in fig. 1 (a). the thickness of the considered area is 1 m. dimensions in the x and z directions are equal to 30 m and 24 m. the wells have diameter of 0.178 m. the production well is located at a distance of 10 m from the bottom of the reservoir. the distance between the wells is 5 m. the considered area has been discretized by triangular prismatic finite elements with the minimal element size of 0.03 m (near the wells) and the maximum element size of 1 m (near the boundary of the simulated domain). the reservoir and oil properties correspond to yarega oil deposit (russian crude oil deposit in komi republic). physical and mechanical properties of water, steam, oil and reservoir are given in tabs. 1-2. fig. 1 (b) describes the temperature dependence of oil dynamic viscosity used in simulation. the main focus of this work is the assessment of the caprock integrity during oil production by sagd with two sets of operational parameters: pb=2.5 mpa, tb=213 k and pb=3.5 mpa, tb=220 k. values of other initial and boundary conditions are given in tab. 3. the loads acting on a caprock are fully determined by the stress-strain state of the reservoir which depends on the structural changes induced by propagation of the steam chamber. property value unit young’s modulus 3·109 pa poisson’s ratio 0.25 thermal expansion coefficient 5·10-6 1/k biot coefficient 0.44 material parameter a 0.19 material parameter b 475725 pa table 1: mechanical properties of reservoir. fig. 2 shows the form of the steam chamber after 100 days of the heating with two different regimes. steam injection with operational parameters pb=2.5 mpa, tb=213 k results in the vertical growth of the steam chamber while operational parameters pb=3.5 mpa, tb=220 k give a completely different shape with substantial sideway growth. it is noticeable that fig. 2(a) corresponds to the early stage of the steam chamber growth whereas fig. 2(b) illustrates the spreading phase. therefore, the second regime of the heating is characterized by the very high values of the steam propagation within the reservoir. t a. kostina et alii, frattura ed integrità strutturale, 49 (2019) 302-313; doi: 10.3221/igf-esis.49.30 308 property value unit initial value of absolute permeability 5·10-12 m2 dynamic viscosity of water 10-3 pa·s dynamic viscosity of steam 1.6·10-5 pa·s residual oil saturation 0.68 residual water saturation 0 oil density 933 kg/m3 water density 1012 kg/m3 reservoir density 2100 kg/m3 steam density 0.3 kg/m3 thermal conductivity of oil 0.14 w/(m·k) thermal conductivity of water 0.58 w/(m·k) thermal conductivity of steam 0.23 w/(m·k) thermal conductivity of reservoir 2.325 w/(m·k) heat capacity of oil 2090 j/(kg·k) heat capacity of steam 2000 j/(kg·k) heat capacity of water 4200 j/(kg·k) heat capacity of reservoir 1050 j/(kg·k) initial value of porosity 0.27 empirical parameter a1 0.75 empirical parameter a2 0.04 empirical parameter a3 0.012 empirical parameter m1 3.45 empirical parameter m2 3 empirical parameter m3 2.1 table 2: thermophysical properties. property value unit initial value of oil saturation 0.88 initial value of water saturation 0.12 initial pressure 2·106 pa initial temperature of the reservoir 281.15 k residual oil saturation 0.68 residual water saturation 0 pressure in the production well 1.7·106 pa table 3: initial and boundary conditions. a. kostina et alii, frattura ed integrità strutturale, 49 (2019) 302-313; doi: 10.3221/igf-esis.49.30 309 (a) (b) figure 1: (a) schematic representation of the simulated domain ( 1 is the boundary of the injection well, 2 is the boundary of the production well, 3 is the left boundary, 4 is the right boundary, 5 is the upper boundary, 6 is the lower boundary). all sizes are in mm. (b) dependence of the dynamic oil viscosity on the temperature [30]. (a) (b) figure 2: steam chamber distribution after 100 days of heating: (a) pb=2.5 mpa, tb=213 k; (b) pb=3.5 mpa, tb=220k. the effect of volumetric strains and effective stresses on the porosity evolution is shown in fig. 3. it can be seen that the considered models (17) and (18) give a qualitatively and quantitatively different distribution of the porosity. the porosity eqn. (17) describes compression of the soil in the process of sagd (fig. 3(a)). pore compression leads to the decrease in pore pressure and increase in effective compressive stresses in such a way that all domain is in the compressive state. the highest contraction is observed within the area which corresponds to the spreading steam chamber. by contrast, the model (18) demonstrates pore expansion due to the influence of the pore pressure and temperature. according to this model, the porosity changes only in the heating zone and does not affect the rest of the domain. thus, the first model is more sensitive to the applied mechanical and thermal loading than the second one. to choose the more appropriate model of the porosity for the specific reservoir it is necessary to determine the prevailing mechanism of its evolution because the obtained results can significantly affect the oil production rate. the effect of porosity evolution on the oil production rate is studied using the kozeny-carman model which is widely applied to the problems of petroleum engineering. the model relates absolute permeability to the porosity and can be written in the following form [31]:        23 0 23 0 0 1 1 n nk k n n , (33) where 0k is the initial value of an absolute permeability; 0n is the initial value of porosity. fig. 4 shows specific oil production rate obtained by the proposed sagd model after the establishment of the interwell communication using models (17)-(18) and two abovementioned sets of operational parameters. the first case of the operational parameters gives an upward trend of the production rate while the second case shows a stable production rate corresponding to the spreading phase of the steam chamber. as the one would expect, the highest value of the production a. kostina et alii, frattura ed integrità strutturale, 49 (2019) 302-313; doi: 10.3221/igf-esis.49.30 310 rate predicts the eqn. (18) and the second set of operational parameters. the first set of the parameters for the same porosity model gives almost threefold smaller rate. the eqn. (17) predicts moderate value of the oil production rate due to the pore compression. in this case, the second set of the parameters are also preferable to the first. the high values of injection pressure and temperature result in a faster development of the steam chamber, so the more oil becomes mobile. however, there is a possibility to change the structure of the reservoir in such a way that there will be little pore space available for the oil filtration and the reservoir can become almost impermeable. thus, if the prevailing physical mechanism of the porosity evolution for the specific formation is the pore compaction, the increase in the values of the operational parameter can lead to the drop in the oil production rate instead of its rise. (a) (b) figure 3: typical distribution of porosity according to: (a) model (17), (b) model (18). figure 4: oil production rate obtained under the following conditions: (1)-porosity model (18), pb=3.5 mpa, t=220 k; (2)-porosity model (18), pb=2.5 mpa, tb=213 k; (3)-porosity model (17), pb=3.5 mpa, t=220 k; (4)-porosity model (17), pb=2.5 mpa, t=213 k. the main criteria for the optimal choice of the operational parameters is to ensure the safe conditions which will not lead to the caprock failure. loss of a caprock integrity is the serious problem for a human safety and the environment. the overburden provides isolation of the injected material from penetration of it into the water. fig. 5 shows assessment of the caprock integrity according to the drucker-prager fracture criterion for two sets of operational parameters. the strength parameters a and b are equal to 0.19 and 243623 pa. the following cases have been considered. the first and the second cases correspond to the solution to the thermo-poroelastic problem (neglecting of the visco-plastic strains defined by eqn. (11)) obtained for both sets of operational parameters (fig. 5, (a)-(b)). in all other cases, visco-plastic strains were taken into account. the second and the third case describe porosity evolution according to the eqn. (17) (fig. 5, (c)-(d)). as regards to the fourth and the fifth, the eqn. (18) was used (fig. 5 (e)-(f)). the obtained results show that neglecting of the plastic strains in the reservoir leads to the high values of mechanical stresses which induce caprock failure for both a. kostina et alii, frattura ed integrità strutturale, 49 (2019) 302-313; doi: 10.3221/igf-esis.49.30 311 sets of operational parameters (fig. 5, (a)-(b)). on the contrary, the more sophisticated model which takes into account plastic strains in the reservoir predicts integrity of the caprock for all considered cases (fig. 5, (c)-(f)). therefore, neglecting of the inelastic strains leads to the overestimation of the caprock strength even for the small values of the operational parameters. the potentially dangerous zones are located over the steam chamber which produces a gaussian-type loading acting on the base of the caprock. it is interesting to note that higher values of operational parameters predict safer condition than lower in case of the porosity model (17). this effect can be attributed to the drucker-prager model which is a pressure-dependent fracture criterion. according to this criterion, stress state with the lower value of the hydrostatic pressure is closer to the fracture surface than the state with the higher value under the same value of the equivalent (von mises) stress. (a) (b) (с) (d) (e) (f) figure 5: drucker-prager yield (fracture) surface (contour lines denote effective plastic strains): (a)-solution to thermo-poroelastic problem, pb=2.5 mpa, t=213 k; (b)-solution to thermo-poroelastic problem, pb=3.5 mpa, t=220 k; (c)-solution to thermoporoinelastic problem with porosity model (17), pb=2.5 mpa, t=213 k; (d)-solution to thermo-poroinelastic problem with porosity model (17), pb=3.5 mpa, t=220 k; (e)-solution to thermo-poroinelastic problem with porosity model (18), pb=2.5 mpa, t=213 k, (f) solution to thermo-poroinelastic problem with porosity model (18), pb=3.5 mpa, t=220 k. conclusion n this study, an assessment of the caprock integrity during oil production by sagd is carried out. the evaluation of the loadings acting on a base of the caprock was calculated with the use of the originally proposed thermo-hydromechanical model of steam injection into the porous media. the model describes convective heat transfer, phase change process, thermal expansion of solid grains and influence of the pore pressure on the stress-strain state of the reservoir. the process of steam injection is governed by mass conservation law, energy conservation law, darcy’s law for oil, steam and water filtration. water-vapor phase change is determined by the additional heat source. inelastic deformations of the reservoir induced by propagation of the thermal front are described by the phenomenological viscoplastic model. two qualitatively and quantitatively different scenarios of porosity evolution is considered. the first i a. kostina et alii, frattura ed integrità strutturale, 49 (2019) 302-313; doi: 10.3221/igf-esis.49.30 312 scenario corresponds to the case of the pore compression while the second one describes increase in porosity induced by the volumetric strains. the following conclusions can be made:  operational parameters pb=3.6 mpa, tb=220 k substantially accelerate steam propagation within the reservoir compared to the values pb=2.5 mpa, tb=213 k.  the oil production rate strongly depends on the prevailing physical mechanism of the porosity evolution. pore compression impairs oil production. the operational parameters pb=2.5 mpa, tb=213 k give almost threefold smaller oil production rate for both porosity models.  the considered values of operational parameters do not induce caprock failure if plastic strains in the reservoir is taking into account. therefore, neglecting of the inelastic strains leads to the overestimation of the caprock strength even for the small values of the operational parameters. acknowledgments his work was supported by the grant of the president of russian federation for support of young russian scientists and leading scientific schools [mk-4174.2018.1]. references [1] shafiei, a., dusseault, m. b. (2013). geomechanics of thermal viscous oil production in sandstones, j. pet. sci. eng., 103, pp. 121–139. doi: 10.1016/j.petrol.2013.02.001 [2] uribe-patino, j.a., alzate-espinosa, g.a., arbelaez-londono, a. (2017). geomechanical aspects of reservoir thermal alteration: a literature review, j. pet. sci. eng., 152, pp. 250-266. doi: 10.1016/j.petrol.2017.03.012. [3] yin, y., li, y. (2015). fem analysis of fluid-structure interaction in thermal heavy oil recovery operations, sustainability, 7, pp. 4035-4048. [4] lin, b., chen, s., jin, y. (2017). evaluation of reservoir deformation induced by water injection in sagd wells considering formation anisotropy, heterogeneity and thermal effect, j. pet. sci. eng., 157, pp. 767-779. [5] pao, w. k. s., lewis, r. w., masters, i. (2001). a fully coupled hydro‐thermo‐poro‐mechanical model for .black oil reservoir simulation, int. j. numer. anal. meth. geomech., 25 (12), pp. 1229-1256. doi: 10.1002/nag.174 [6] chen, w., tan, x., yu, h., wu, g., jia, s. (2009). a fully coupled thermo-hydro-mechanical model for unsaturated porous media, j. rock mech. geotech. eng., 1, pp. 31–40. doi: 10.3724/sp.j.1235.2009.00031. [7] zandi, s., renard, g., nauroy, j.-f., guy, n., tijani, m. (2010). numerical coupling of geomechanics and fluid flow during steam injection in sagd, spe improved oil recovery symposium, 24-28 april, tulsa, usa, spe-129739-ms. doi: 10.2523/129739-ms. [8] settari, a. (1992). physics and modeling of thermal flow and soil mechanics in unconsolidated porous media, spe production engineering, 7(1), pp. 47-55. doi: 10.2118/18420-pa. [9] zimmerman, r. w., somerton w. h., king m. s. (1986). compressibility of porous rocks, j. geophys. res.-sol. ea., 91, pp. 12765-12777. doi: 10.1029/jb091ib12p12765. [10] osorio, j. g., chen, h-y., teufel, l.w. (1997). numerical simulation of coupled fluid-flow/geomechanical behavior of tight gas reservoirs with stress sensitive permeability, latin american and caribbean petroleum engineering conference, 30 august 3 september, rio de janeiro, spe-39055-ms. doi: 10.2118/39055-ms. [11] mckee, c. r., bumb, a. c., koenig, r. a. (1988). stress-dependent permeability and porosity of coal and other geologic formations, spe formation evaluation, 3(1), pp. 81-91. doi: 10.2118/12858-pa. [12] rutqvist, j., wu, y.-s., tsang, c.-f., bodvarsson, g. a. (2002). modeling approach for analysis of coupled multiphase fluid flow, heat transfer, and deformation in fractured porous rock, int. j. rock mech. min. sci., 39(4), pp. 429-442. doi: 10.1016/s1365-1609(02)00022-9. [13] wang y., dusseault m. b. (1991). the effect of quadratic gradient terms on the borehole solution in poroelastic media, water resour. res., 27 (12), pp. 3215-3223. doi: 10.1029/91wr01552. t a. kostina et alii, frattura ed integrità strutturale, 49 (2019) 302-313; doi: 10.3221/igf-esis.49.30 313 [14] wang y., lu b. a. (2001). coupled reservoir-geomechanics model and applications to wellbore stability and sand prediction, spe international thermal operations and heavy oil symposium, 12 14 march, porlamar, venezuela, spe-69718-ms. doi: 10.2118/69718-ms. [15] minkoff, s. e., stoneb, c. m., bryantc, s., peszynskac, m., wheeler, m. f. (2003). coupled fluid flow and geomechanical deformation modeling, j. pet. sci. eng., 38(1-2), pp. 37-56. doi: 10.1016/s0920-4105(03)00021-4. [16] du j., wong r. c. k. (2009). coupled geomechanics reservoir simulation of utf phase a project using a full permeability tensor, j. can. pet. tech., 48 (7), pp. 66-73. doi: 10.2118/09-07-66. [17] lin b., chen s., jin y. (2017). evaluation of reservoir deformation induced by water injection in sagd wells considering formation anisotropy, heterogeneity and thermal effect, j. pet. sci. eng., 157, pp. 767-779. doi: 10.1016/j.petrol.2017.07.067. [18] li, p., chalaturnyk, r.j., tan, t.b. (2006). coupled reservoir geomechanical simulations for the sagd process, j. can. pet. tech., 45(1), pp. 33-40. doi: 10.2118/2003-08.3 [19] azad, a., chalaturnyk, r. j. (2009). geomechanical coupling simulation in sagd process; a linear geometry model, 3rd canus rock mechanics symposium. toronto, paper 4153. [20] rahmati, e., nouri, a., fattahpour, v. (2017). numerical assessment of the maximum operating pressure for sagd projects considering the effects of anisotropy and natural fractures, j. pet. sci. eng., 157, pp. 196-206. doi: 10.1016/j.petrol.2017.07.005. [21] mclellan, p., read, r., gillen, k. (2000). assessing caprock integrity for steam-assisted gravity-drainage projects in heavy-oil reservoirs, spe/petroleum society of cim international conference on horizontal well technology, 6-8 november, calgary, canada, spe 65521. [22] khan, s., han, h., ansari, s., vishteh, m., khosravi, n. (2011). caprock integrity analysis in thermal operations: an integrated geomechanics approach, world heavy oil congress, 14-17 march, edmonton, canada, paper 11-609. [23] walters, d. a., wang, j., settari, a. (2012). a geomechanical methodology for determining maximum operating pressure in sagd reservoirs, spe heavy oil conference canada, 12-14 june, calgary, canada, spe-157855-ms. doi: 10.2118/157855-ms. [24] uwiera-gartner, m.m.e., carlson, m. r. (2011). evaluation of the clearwater formation caprock for a proposed, low pressure, steam-assisted gravity-drainage pilot project in northeast alberta, spe annual technical conference and exhibition, 30 october – 2 november, denver, usa, spe 147302-pp. doi: 10.2118/147302-ms. [25] lee, h., kharangte, c. r., mascarenhas, n. (2015). experimental and computational investigation of vertical downflow condensation, int. j. heat mass transfer, 85, pp. 865-879. doi:10.1016/j.ijheatmasstransfer.2015.02.037. [26] debernardi, d., barla, g. (2009). new viscoplastic model for design analysis of tunnels in squeezing conditions, rock mech. rock engng, 42(2). – pp. 259-288. doi: 10.1007/s00603-009-0174-6. [27] grujicic, m., he, t., pandurangan, b., bell, w.c., cheeseman, b.a., roy, w. n., skaggs r. r. (2009). development, parameterization, and validation of a visco-plastic material model for sand with different levels of water saturation, proc. imeche part l: j. materials: design and applications, 223, pp. 63-81. doi:10.1243/14644207jmda237. [28] lake, l.w. (1989). enhanced oil recovery, englewood cliffs, prentice-hall inc. [29] kostina, a. a., zhelnin, m. s., plekhov, o. a. (2018). study of oil filtration during steam-assisted gravity drainage process, bulletin of perm scientific center, 3, pp. 6-16. doi: 10.7242/1998-2097/2018.3.1. [30] konoplev, yu. p. (2004). scientific and methodological foundations of design and analysis of thermomine oil field development, phd thesis, vniineft, moscow. (in russian). [31] du, j., wong, c.k. (2007). coupled geomechanics-reservoir simulation of utf phase a project using a full permeability tensor, canadian international petroleum conference, 12-14 june, calgary, canada, paper 2007-152. doi: 10.2118/09-07-66. << /ascii85encodepages false /allowtransparency false /autopositionepsfiles true /autorotatepages /none /binding /left /calgrayprofile (dot gain 20%) /calrgbprofile (srgb iec61966-2.1) /calcmykprofile (u.s. web coated \050swop\051 v2) /srgbprofile (srgb iec61966-2.1) /cannotembedfontpolicy /error /compatibilitylevel 1.4 /compressobjects /tags /compresspages true /convertimagestoindexed true /passthroughjpegimages true /createjobticket false /defaultrenderingintent /default /detectblends true /detectcurves 0.0000 /colorconversionstrategy /cmyk /dothumbnails false /embedallfonts true /embedopentype false /parseiccprofilesincomments true /embedjoboptions true /dscreportinglevel 0 /emitdscwarnings false /endpage -1 /imagememory 1048576 /lockdistillerparams false 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/hrv (za stvaranje adobe pdf dokumenata najpogodnijih za visokokvalitetni ispis prije tiskanja koristite ove postavke. stvoreni pdf dokumenti mogu se otvoriti acrobat i adobe reader 5.0 i kasnijim verzijama.) /hun 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/pdfxoutputintentprofileselector /documentcmyk /preserveediting true /untaggedcmykhandling /leaveuntagged /untaggedrgbhandling /usedocumentprofile /usedocumentbleed false >> ] >> setdistillerparams << /hwresolution [2400 2400] /pagesize [612.000 792.000] >> setpagedevice microsoft word 2324 v. shlyannikov et alii, frattura ed integrità strutturale, 48 (2019) 77-86; doi: 10.3221/igf-esis.48.10 77 focussed on “crack paths” the effect of creep damage model formulation on crack path prediction valery shlyannikov, andrey tumanov institute of power engineering and advanced technologies, frc kazan scientific center, russian academy of sciences, russia. shlyannikov@mail.ru, https://orcid.org/0000-0003-2468-9300 tymanoff@rambler.ru abstract. the stress, strain rate and process zone with respect to the creepcrack growth are analyzed by employing damage-evolution equations. the damage models for the fracture of the process zone are represented using a stress and ductility based formulation. special attention has been addressed in the present study to the influence of the creep damage model formulation on the crack path prediction. to evaluate the significance of dominating fracture mechanism a comparison of the cases for pure mode ii is considered. it was observed that in the case of stress based model one side of the notch, dominated by tensile stresses, blunts, while the other side, dominated by shear strains, sharpens. in the case of ductility based model, there is a tendency for creep damage to localize only at the blunted part of the notch. this because the highest tensile hydrostatic stress and crack-tip constraint always occur near the blunted part of the notch. in this region, the crack growth direction and general creep damage zone deviate from the initial crack plane. as a result of numerical calculations the consequence of the crack deviation angle values, crack length increments and finally crack path were determined. keywords. creep damage; limit stresses and strains; crack path. citation: shlyannikov v., tumanov a., the effect of creep damage model formulation on crack path prediction, frattura ed integrità strutturale, 48 (2019) 77-86. received: 03.12.2019 accepted: 10.02.2019 published: 01.04.2019 copyright: © 2019 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. introduction n the past, the continuum damage mechanics (cdm) was used as a complementary approach in high-temperature fracture mechanics to analyze the damage and fracture process at different scales with respect to the changing material structure from the initiation of micro-cracks to the final fracture resulting from the macro-cracks [1, 2]. the cdm covered several microscopic mechanisms in the area near the macroscopic creep crack including void nucleation and growth on the grain-boundary facets, cavities coalescing to form a grain-size micro-crack, coalescing of micro-cracks, which finally lead to the propagation of creep macro-cracks. i http://www.gruppofrattura.it/va/48/2324.mp4 v. shlyannikov et alii, frattura ed integrità strutturale, 48 (2019) 77-86; doi: 10.3221/igf-esis.48.10 78 in the present study the continuum damage mechanics is applied to assess the creep damage behavior. special attention has been addressed to the influence of the creep damage model formulation on the on crack path prediction. to evaluate the significance of dominating fracture mechanism a comparison of the case for pure mode ii is considered. the crack tip damage zones for extensive creep conditions are compared for stress and ductility based models. the crack growth direction and general creep damage zone deviate from the initial crack plane. as a result the consequence of the crack deviation angle values, crack length increments and finally crack path were determined. stress based model et  denote in eq.(1) the measure of damage with  = 0 denoting the undamaged state and  = 1 the fully damaged state. the creep strain rate accumulation constitutive equation is generalized by the authors [1, 2] to multi-axial state of stress using j2 flow theory as follows          13 1 2 1 n eqv n eqv ij d b s dt (1) where b and n are constants of the norton power law equation. the simplest creep damage rate model, which is introduced by kachanov [1], is a function of applied nominal stress and current accumulated damage has the following form              1 m fd c dt (2) where c and m are material constants. similarly eq.(2), shlyannikov and tumanov [3] introduced a model for the rate of accumulation of stress-based creep damage as a function of multi-axial stress function   f   described by eqs.(3,4) in the generalized form      /1f kk mp e        (3)        1 2 3 3kk m ,        1 2 3 2 e ij ijs s ,    ij ij m ijs . (4) where  is the experimental material constant that is determined as the ratio of uniaxial tensile to compression strength = t /c. according to [16] the equivalent stresses can be present by the following equation      1 int1eqv (5) for  = 0 brittle fracture is occurred and the equivalent stresses corresponds to maximum tensile stresses (maximum tensile stress theory), while for ductile fracture  = 1 and   inteqv (von mises-hencky’s theory). ductility based model he crack size is assumed to increase when the local accumulated creep strain at the crack tip reaches the critical creep ductility. in this case the damage evolution law is given by simple relationship * cr f d dt        , (6) where  and cr  are the damage rate and the creep strain rate, respectively. term * f  denotes the multi-axial creep failure strain, which normally differs from the uniaxial creep ductility. using the general critical-stress criterion in the form of pisarenko-lebedev [4] criterion, shlyannikov [5] proposed a multi-axial failure strain equations: l t v. shlyannikov et alii, frattura ed integrità strutturale, 48 (2019) 77-86; doi: 10.3221/igf-esis.48.10 79 * 0 1 1 n f i f i i b                   (7) 22 1 3 i b     ;         2 2 1 1 1 1                ;   221 1 1 i            (8) where 0f is uniaxial failure strain, 2 1   is the principal stress ratio,  is posson's ratio. the basic relationship between the secondary creep rate cr and creep rate in the tertiary range is given by bendick [6]  1 cr g        (9) where n cr e b  is modified norton's law. using this expression and substituting eq.(9) into eq.(6) one finds  * *(1 ) 1 n cr e gm f f bd dt            . (10) for uniaxial tension bendick [6] proposed relation between the secondary creep rate ,0cr and failure strain 0f based on the approximation of the experimental data for many different materials ,0 0 0 n cr f f f f t b t        or 0 n f f b t    (11) where tf is time to fracture and  is experimental constant. substitution of eqs. (7) and (8) into eq. (10) leads to the expression for ductile creep damage rate under multi-axial stress-strain state  1 1 (1 ) n n i i e g f bd dt t                  (12) going back to eq.(3) it should be noted that in eq.(2) d dt is assumed to be implicit function of the hydrostatic stress m and the von mises equivalent stress e. the governing parameter in the form of the material constant  helps in describing the effect of the multi-axial state of the stress-strain behavior of the material. crack path prediction procedure tructural integrity prediction under mixed mode fracture generally includes two issues. the first is the crack path determination, while the second is the crack growth rate prediction along definite curvilinear trajectory. crack path prediction for mixed mode loading carried out making use the following scheme (fig.1). crack was assumed to growth in a number of discrete steps. the principal feature of such modeling is determination of the crack growth direction and definition of crack length increment in this direction. after the crack is initiated with kinking, the stress and creep strain fields around the crack tip changes. in our computations the predicted initial crack angle i coincides with the position of maximum value of the creep damage parameter  (eqs. (2) and (12)) after corresponding loading history. the virtual crack extension amount ai =(ai+1 ai) is the sum of linear sizes for fe number in which the creep damage exceed  > 0.6. such finite elements are excluded from the global finite element mesh creating new free surfaces of the crack. the continuum damage formulation (eqs.(1) and (6)) combined with the stress and ductility based models eqs. (2) and (12) has been implemented in ansys via the user element subroutine. s v. shlyannikov et alii, frattura ed integrità strutturale, 48 (2019) 77-86; doi: 10.3221/igf-esis.48.10 80 figure 1: crack path model. results and discussion he geometry considered in this study is a biaxially loaded plate containing the inclined central crack (fig.2,a). the panel is subjected to two perpendicular loads: one parallel to the y-axis  and another parallel to the x-axis . the combination of inclination crack angle  =45and nominal stress biaxial ratio at equi-biaxial tensioncompression  = -1 corresponds to pure mode ii fracture. the center-cracked plate (ccp) contains an internal crack of length 2a=20mm (a/w=0.01, where w is plate width) and loaded to a uniform biaxial stress of magnitude  = 50 mpa. the 2d plane strain eight-node isoparametric elements were applied to ccp geometry. to consider the details of large deformation and blunting of the crack tip, a typical fe-mesh (fig.2,b) was used with the initial notch root radius /a =0.001. computations were performed in ansys, in which the solid 186 element was employed, together with the user-defined creep damage law. we define the reference time tt as the time corresponding to the transition from the small-scale creep to the extensive creep conditions. the considered material is power steam turbine rotor steel r2m. the creep properties of analyzed material at the elevated temperature of 550c are summarized in table 1. in our case the transition time for given nominal stress  =50 mpa and crack length a =10mm is tt = 21.88 hrs. a) b) figure 2: biaxially loaded plate with inclined crack. e [gpa]  0 [mpa] b [1/(mpa^nhr)] n c [1/(mpa^mhr)] m g 200 0.3 100 110-14 5.0 110-10 3.0 5.0 table 1: the creep properties of material. a fracture-damage zone (fdz) or fracture-process zone (fpz) local with respect to the crack tip is defined as the core where the microstructure damage accumulates until the crack growth occurs at the macroscopic scale level. after t v. shlyannikov et alii, frattura ed integrità strutturale, 48 (2019) 77-86; doi: 10.3221/igf-esis.48.10 81 determining these stress invariants in the fem procedure, the creep-damage distribution or the fpz shape and size are obtained by integrating eqs.(2) and (11) for stress and ductility models, respectively. the crack tip damage zones under pure mode ii for extensive creep conditions t/tt =45.7 are shown in fig.3 for stress (a) and ductility (b) based models. a) b) figure 3: mode ii crack tip creep damage zones for stress (a,  =1.0) and ductility (b,  =0.6) models at t/tt =45.7. it can be observed in fig. 3 non-uniform deformation and damage fields near an initially smooth notch tip under mode ii loading conditions. in the case of stress based model (fig.3,a) one side of the notch, dominated by tensile stresses, blunts, while the other side, dominated by shear strains, sharpens. thus, two competing fracture mechanisms occur at the blunted and the sharpened part of the notch respectively. as the result the general creep damage zone is approximately symmetrical with respect to the initial crack plane. in the contrary, in the case of ductility based model (fig.3,b), there is a tendency for creep damage to localize only at the blunted part of the notch. this because the highest tensile hydrostatic stress and crack-tip constraint always occur near the blunted part of the notch. in this region, crack initiation and propagation takes place due to microvoid coalescence. the crack growth direction and general creep damage zone in fig.3,b deviate from the initial crack plane. a) b) figure 4: creep damage zone as a function of creep time for (a) stress and (b) ductility based models. the contours, shown in fig. 4, demonstrated the process of the crack-tip stress and ductility damage accumulation under the biaxial loading as a function of the creep time. the finite element calculations have been presented for material cases wherein the multi-axial stress formulation (eqs. (5) and (6)) is a function of the hydrostatic or principal stresses. note that, stress (a) and ductility (b) based creep damage contours do not coincide with each other at the same creep time. based on the comparison the stress and ductility creep damage models for pure mode ii, it can be seen that at equibiaxial tensioncompression  = −1.0 in fig.4(a) for the stress model, the maximum distance of the damage contour boundary from the crack tip is located along the crack line for any creep time. however in fig.4(b) for the ductility model, the maximum size of the creep-damage zone deviated sufficiently from the crack line to directly ahead of the crack tip (0 °direction) as a function of the multi-axial stress material constant . v. shlyannikov et alii, frattura ed integrità strutturale, 48 (2019) 77-86; doi: 10.3221/igf-esis.48.10 82 creep crack path prediction y employing the constitutive eq. (1), as well as damage models eqs.(2) and (12) directly into the fem ratedependent formulation and using an explicit time integration procedure, we obtain a standard runge–kutta integration scheme wherein the finite-element stiffness matrix is derived from the elastic moduli. thus, to determine the numerical stress/strain-rate fields, we need to first determine the damage-rate function by substituting the stress obtained in the initial iteration into eqs.(2) and (12) for stress and ductility based models, respectively. after determining the damage function  using numerical integration and by substituting the creep strain rate ij of eq. (1) obtained from the resulting damage function  into the ansys, the damage stress/strain rate fields are found. finally, after obtaining the solution to the nonlinear problem, the ansys output file is used as an input data for the special code developed to determine the dimensionless stress-strain angular distributions, damage contour, and creep-stress intensity factor. we shall remind that on the plate containing the inclined central crack (fig.2,a) subjected to biaxial tension-compression loads the pure mode ii takes place when the load biaxiality ratio is  = -1 and  =45. fig. 5 shows several computational crack paths as a function of the creep holding time. it is evident that, the crack propagates no longer in the initial direction. from comparison of our computations for pure mode ii obtained on both the compact tension-shear and cruciform specimens with appropriate experimental data [7] which was obtained using the steel and aluminum alloy follows that the crack initiation directions predicted from the numerical prediction and analytical solution are in good agreement. as is seen in fig.5, inclusion in eqs.(2) and (12) the creep damage functions allows one to take into account the influence constitutive equation formulation on a creep crack path prediction. figure 5: creep crack path prediction for pure mode ii. considering the crack-growth interpretation, in particularly creep crack path prediction, it should be noted that the effect of the creep-damage accumulation on the creep-crack growth rate might be scaled through the corresponding value of the creep-stress intensity factor (sif) introduced by the authors [8, 9]. in addition, an inherent property of the creep sif is the dependence on the multi-axial stress state through the equation for the damage functions (eqs. 3 and 7). furthermore, current value of the creep sif is sensitive to the class of using creep damage models, i.e. stress or ductility based models. creep stress intensity factor ccording to approach [8] kcr is amplitude of singularity in the form of creep stress intensity factor. for extensive creep conditions the relation between the c-integral and creep sif is introduced by the authors [8] as follows: b a v. shlyannikov et alii, frattura ed integrità strutturale, 48 (2019) 77-86; doi: 10.3221/igf-esis.48.10 83 1 * 1 0 1 crn cr cr n c k bi l        (13)    10 cr n cr cr nc k bi l   (14) where c* is the c-integral. the value of this line integral corresponding secondary creep deformation used in [10] as the relevant loading parameter to characterize the local stress-strain rate fields at any instant around the crack front in a cracked body subjected to extensive creep conditions            ds x u ndxwc ijij 1 2*   (15) where the first term in eq.(15) is the strain energy rate density (serd) for power-law hardening creep [11,12] 0 1 kl cr cr cr crcr cr ij ij e e cr n w d n            (16) and  is an arbitrary counterclockwise path around the crack tip and the cartesian coordinate system xi is centered at the crack tip. substitution of eq. (16) into eq. (15) leads to the expression for c*-integral   1* cos sin cos 1 cr cr crcr cr ncr cr cr cr crcr r r e rr r rr r cr n u uu u c br d r d n r r                                                       (17) similarly to the plastic problem, eqn. (13) for the creep stress intensity factor include a governing parameter for powerlaw nonlinear viscous materials in the form of crni -integral which can be obtained using the numerical method elaborated by the authors [8]. this method was extended by shlyannikov and tumanov [13] to analyze the fracture resistance characteristics of creep-damaged material. according to this method, the crni -integral value can be determined directly from the fea distributions of the displacement rate criu and dimensionless angular stress  cr ij functions    , , , , , ,cr femn cr cr cri t n t n d            (18)       1 , , , cos sin 1 1 cos 1 cr crcr nfem cr cr cr cr crcr r cr cr e rr r r cr cr cr cr cr rr r r cr n dudu t n u u n d d u u n                                                      (19)   1 0 0 0 0 1 cr crcr cr cr cr n nn ncr cr cr cr cr cr cr ncr i i e i e i e i n cr cr cr e e ecr u u u du u r l l dt lbl k                                         (20) where t is creep time, e is the von mises equivalent stress and    0 cr cr e e . in eqs.(19,20) a dot over a displacement quantity denotes a time differentiations. the -variation angular functions of the suitably normalized functions  ij and iu and correspondingly governing parameter crni -integral depend on the damage function  and creep exponent n. in the traditional models for creep or creep-fatigue crack growth rate prediction the in-integral is a function only the creep v. shlyannikov et alii, frattura ed integrità strutturale, 48 (2019) 77-86; doi: 10.3221/igf-esis.48.10 84 exponent. in the present work it will be demonstrated that these governing parameters are different for elastic-plastic f ni and creep crni problems. generally, they depend on the loading conditions including creep holding time and applied load, specified cracked body geometry, the elastic-plastic and creeping crack tip stress-strain fields, crack front curvature and size. figure 6: in-factor distributions for plastic and creep problems as a function of relative crack length. figure 7: plastic and creep sifs behavior as a function of relative crack length. fig. 6 shows for the c(t) specimen the behavior of the governing parameter of elastic-plastic and creep crack-front fields in the form of the normalizing plastic and creep in-integrals ( ,f crn ni i ) as a function of relative crack length a/w at the midplane z/b = 0.5 and a crack front distance of 31.5 10r   . it can be seen that the plastic and creep in-integral values do not coincide at the same loading conditions and crack length. furthermore, in terms of the continuum damage mechanics formulation, as shown by the authors [13], the cr ni -integral distributions as functions of the creep times for undamaged and defective materials differ. based on eqs. (18-20), these distributions of the in-integral are used to calculate the plastic and creep sifs in the c(t) specimen. fig. 7 illustrates the corresponding numerical results for the plastic and creep stress intensity factors behavior in the midplane of the c(t) specimen as a function of relative crack length. in this figure the finite element nonlinear sifs variations correspond to the crack tip distance 31.384 10r   . fig. 7 shows the comparison of the plastic sif behavior for power law cyclic strain hardening material and the creep sif distribution for damaged elastic-nonlinear-viscous material with the damage parameter  and constitutive law obtained using eq. (12). as observed in fig. 7, the plastic and creep sif distributions as a function of relative crack length differ, and these distinctions depend on the number of loading cycles or creep time. based on the comparison in fig. 7, we can conclude that in the case of creep and fatigue interaction the dimensionless nonlinear stress intensity factors provide a more convenient representation of the fracture resistance characteristics of structural materials as parameters of the same scale. in order to interpretation of test results and theoretical predictions for creep crack growth rate test results obtained on the c(t) specimen used c*-integral and the creep stress intensity factor crk values based on experimentally determined forceline deflection (fld) rate [14,15] * gc s g fpv c b w f          (21)  1 1n gc cr cr n s g fvp k bi b wl f              (22) where cv  is the force-line displacement rate, fg is geometry dependent correction factor,  gf  is its derivative. in the case of theoretical prediction for creep crack growth rate in extensive creep conditions used the steady-state values of c*integral and corresponding expression for creep stress intensity factor crk for c(t) specimen in the following form [14,15] v. shlyannikov et alii, frattura ed integrità strutturale, 48 (2019) 77-86; doi: 10.3221/igf-esis.48.10 85      1 * 1 1 crn s p c b w a h q b w a          (23)     1 1 1 1 0 crn cr cr n s w a h p k i l q b w a               (24) where 2 1 2 2 2 2 2 1 a a a w a w a w a                           ; q = 1.455 plane strain, q = 1.071plane stress, h1 is tabulated in ref.[10]. in the general form, the creep sif is a function of the cracked body configuration and their loading conditions, current crack length, holding time, damage, constraint parameters, and creep and multi-axial material properties. under certain circumstances, this numerical solution may also have application to creeping solids that undergo damage near the crack tip. thus, the creep sif may by identified as a damage-sensitive high-temperature fracture parameter for correlating the crack growth under multi-axial stress/strain conditions. the fracture mechanics in terms of the creep-stress intensity factor provides a useful framework for correlating the data, for the design, and for remaining-life prediction. conclusions he consequence of the crack deviation angle values, crack length increments and finally crack path were determined by local creep damage accumulation model. the effect of the creep-damage accumulation on the creep-crack growth rate might be scaled through the corresponding value of the creep-stress intensity factor. thus, the creep sif may by identified as a damage-sensitive high-temperature fracture parameter for correlating the crack growth under multi-axial stress/strain conditions. acknowledgment he authors gratefully acknowledge the financial support of the russian science foundation under the project 1719-01614. references [1] kachanov, l.m. (1986), introduction to continuum damage mechanics, martinus-nijhoff, dordrecht. [2] lemaitre, j. (1996). a course on damage mechanics, springer-verlag, berlin, . [3] shlyannikov, v.n., tumanov, a.v. (2018). creep fracture resistance parameters determination based on stress and ductility damage model, fatigue fract. eng. mater. struct., 41, pp. 2110-2129. [4] pisarenko, g.s., lebedev, a.a. (1976). deformation and strength of materials under complex state of stress, naukova dumka, kiev. [5] shlyannikov, v.n. (2003). elastic-plastic mixed-mode fracture criteria and parameters, springer verlag, berlin, . [6] bendick, w. (1991). analysis of material exhaustion and damage by creep, int. j. pres. vess. piping, 47, pp. 57–78. [7] shlyannikov, v.n., tumanov, a.v. (2014). characterization of crack tip stress fields in test specimens using mode mixity parameters, int. j. fract. 185, pp. 49–76. [8] shlyannikov, v.n., tumanov, a.v., boychenko, n.v. (2015). a creep stress intensity factor approach to creep-fatigue crack growth, engng. fract. mech. 142, pp. 201–219. [9] shlyannikov, v.n., tumanov, a.v., boychenko, n.v., tartygasheva, a.m. (2016). loading history effect on creepfatigue crack growth in pipe bend, int. j. press. vess. piping 139-140, pp. 86–95. [10] saxena, a. (1998). nonlinear fracture mechanics for engineers. crc press lcc, 472p. [11] hutchinson, j.w. (1983). constitutive behavior and crack tip fields for materials undergoing creep-constrained grain boundary cavitation, acta metall, 31, pp. 1079-1088. t t v. shlyannikov et alii, frattura ed integrità strutturale, 48 (2019) 77-86; doi: 10.3221/igf-esis.48.10 86 [12] yun-jae, k. (2001). contour integral calculations for generalized creep laws within abaqus, int j press vess piping. 78, pp. 661-666. [13] shlyannikov, v.n., tumanov, a.v. (2018). creep damage and stress intensity factor assessment for plane multi-axial and three-dimensional problems, int. j. solids struct. 150, pp. 166–183. [14] shlyannikov, v.n., tumanov, a.v., boychenko, n.v. (2018). creep-fatigue crack growth rate assessment using ductility damage model, int. j. fatigue 116, pp. 448–461. [15] astm e2760–10, (2010). standard test method for creep-fatigue crack growth testing. annual book of astm standards. philadelphia (pa): american society for testing and materials. [16] pisarenko, g.s. and lebedev, a.a. 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can be opened with acrobat and adobe reader 5.0 and later.) >> /namespace [ (adobe) (common) (1.0) ] /othernamespaces [ << /asreaderspreads false /cropimagestoframes true /errorcontrol /warnandcontinue /flattenerignorespreadoverrides false /includeguidesgrids false /includenonprinting false /includeslug false /namespace [ (adobe) (indesign) (4.0) ] /omitplacedbitmaps false /omitplacedeps false /omitplacedpdf false /simulateoverprint /legacy >> << /addbleedmarks false /addcolorbars false /addcropmarks false /addpageinfo false /addregmarks false /convertcolors /converttocmyk /destinationprofilename () /destinationprofileselector /documentcmyk /downsample16bitimages true /flattenerpreset << /presetselector /mediumresolution >> /formelements false /generatestructure false /includebookmarks false /includehyperlinks false /includeinteractive false /includelayers false /includeprofiles false /multimediahandling /useobjectsettings /namespace [ (adobe) (creativesuite) (2.0) ] /pdfxoutputintentprofileselector /documentcmyk /preserveediting true /untaggedcmykhandling /leaveuntagged /untaggedrgbhandling /usedocumentprofile /usedocumentbleed false >> ] >> setdistillerparams << /hwresolution [2400 2400] /pagesize [612.000 792.000] >> setpagedevice http://www.gruppofrattura.it http://www.gruppofrattura.it http://dx.medra.org/10.3221/igf-esis.06.01&auth=true d n shot peening processes to obtain nanocrystalline surfaces in metal alloys: m. el habiri et alii, frattura ed integrità strutturale, 46 (2018) 34-44; doi: 10.3221/igf-esis.46.04 34 developments in the fracture and fatigue assessment of materials and structures effect of cold expansion on improving of fatigue initiation life in aluminium alloy mohamed el habiri, mustapha benachour*, nadjia benachour university of tlemcen, ingeniery of mechanical systems and materials laboratory, tlemcen, algeria faculty of technology, mechanical engineering department yacine2704@gmail.com, bmf_12002@yahoo.fr, nbenachour2005@yahoo.fr abstract. in this paper, numerical investigation was carried out to quantify the effect of the cold expansion on fatigue crack initiation in aluminium alloy. the improvement in fatigue initiation life of specimen after the cold expansion process was investigated with the drilled hole of 2024 t351 aluminium alloy plate. the applied degree of expansion (dce%=100 (dd)/d) is 4.6% where the effect of friction (µ=0.2) is considered. residual stress field is determined using 3d finite element analysis and shows the presence of compressive residual stress around the hole. the results showed a high compressive residual stress near the hole in exit face of the hole and at middle of the plate thickness around the hole. local strain approach is applied in evaluation of fatigue initiation lives under afgrow environment code. fatigue initiation lives are improved by the presence of the compressive residual stresses comparatively to the drilled hole without of compressive residual stresses. also, the fatigue initiation lives are increased with the increase in stress ratio for drilled hole and expanded hole keywords. fatigue crack initiation; cold expansion; compressive residual stress; stress ratio; aluminium alloy. citation: el habiri, med., benachour, m., benachour, n., effect of cold expansion on improving of fatigue initiation life of aluminium alloy, frattura ed integrità strutturale, 46 (2018) 34-44. received: 07.03.2018 accepted: 09.04.2018 published: 01.10.2018 copyright: © 2018 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. introduction reventing fatigue failures in aircraft structures is a principle aiming of aircraft designers and maintainers. the need to prevent fatigue failures and extended the fatigue life, improvement methodologies are necessaries. fatigue phenomenon presents an essential failure mode in aircraft structures. the percentage of failure varies from 55 to 61% [1] in aeronautic components. in aircraft structures, the joints are carried out by mechanically fastened joints, adhesively and bonded joints. in fastened joints is necessary to improve the quality of holes by introducing compressive residuals stresses. the method to introduce the compressive residuals stress are such as shot peening [2, 3] laser shock [4, 5], and cold expansion [6-9]. p http://www.gruppofrattura.it/va/46/4.mp4 m. el habiri et alii, frattura ed integrità strutturale, 46 (2018) 34-44; doi: 10.3221/igf-esis.46.04 35 fatigue phenomenon undergoes several stages and from an engineering point of view it is convenient to divide the fatigue life of a structure into three stages [10]: fatigue crack initiation, stable of crack growth and unstable crack growth. fatigue crack initiation presents the main stage in fatigue life which has been extensively studied [11, 12]. different approaches will be used for estimation of fatigue crack initiation life has been applied by many researchers [13, 14], which is based essentially on stress concentration factor and local stress-strain concepts. others researchers have used the equivalent strain-energy density method to predict fatigue crack initiation [12, 15]. these works assumed that crack growth part of fatigue life is small comparatively to the initiation fatigue life. in initiation phase, fatigue life is linked strongly to metallurgical, geometrical, loading parameters and stress state without external loading (presence of residual stress). the main loading parameter under constant applied load is stress ratio (mean stress effect) investigated by several researchers, principally in stable crack propagations on some materials [16, 17]. effect of stress ratio on fatigue crack initiation from hole without residual stress was investigated by fujczak [18]. it is noticed that an increase in the r-ratio decreases the number of cycles to initiate a fatigue crack. in study conducted by ranganathan et al [19], crack initiation phase has been considered in the estimation of total fatigue life when short crack growth approach has been applied. the results on fatigue crack initiation of 2024 t351 al-alloy shows an increasing in initiation life with increasing in stress ratio and maximum remote stress in absence of residuals stresses. fatigue life depends essentially on zone of compressive residuals stresses around the hole. these stresses decrease the effect of external applied stress field and tend to delay crack growth rate and increase the fatigue life. to quantify cold expansion effects on fatigue crack initiation and propagation, amrouche et al. [20] have conducted experimental and numerical investigation on 6005 al-alloy plate. it was found that the compressive residual stresses induced by the cold expansion process are the important parameter for the improvement of fatigue initiation life. also, it was shown that the fatigue initiation life increases with increasing in the degree of cold expansion and depend on compressive residuals stress zones [20, 21]. in study conducted by gopalakrishna et al. [22], two cold expansion techniques were applied to generate compressive residuals stress around hole, as split-sleeve with taper pin and split-sleeve with ball. it was concluded that split-sleeve with tapered pin technique gives higher compressive residuals stress comparatively to split-sleeve with ball technique. the improvement in fatigue life was also found to be maximal at 5% degree of expansion, at which the fatigue life is 5.3 times higher than the non-expanded holes. the same tendency was confirmed by others researchers [22-25]. in experimental fatigue investigation of chandawanich and sharpe [23] of cold worked hole in 7075 t6 al-alloy plate, they consider initiation stage corresponded to crack approximately 0.1 mm long. the fatigue initiation lives are too large comparatively to the non-cold-worked hole for all level of applied external load. additionally to the changes of compressive residuals stress along the plate thickness from entrance face to exit face in cold expansion process, distribution of compressive residuals stress and fatigue lifetime is affected also by variation of plate thickness [26]. in combined numerical/experimental study, chakherlou and vogwell [27] have investigated the effect of residual stress induced by cold expansion process of hole on fatigue life failure of 7075 t6 al-alloy plate. a 3d finite element model was used to simulate cold expansion. in fe modelling, 8-node linear isoparametric cubic elements were used for the pin and the plate. the fatigue results show the improvement in fatigue life in cold expanded hole of specimens comparatively to the drilled specimens. the improvement in fatigue life is almost 10 times. liu et al [28] have used cold expansion with a split sleeve to produce residuals stress fields. they have performed numerical simulations using 3d finite element modelling. the friction effect was included in this investigation by using the elastic coulomb friction with a friction coefficient =0.1 also primary included by chakherlou and vogwell [27]. also, liu et al. [28] have studied the effect of cold expansion on prediction of fatigue life using respectively swt model [29] and wb model [30]. it was concluded that wb model give a better result than the swt model. kurhade et al. [31] conducted 3d finite element analysis for plane stress, where the effect of strain hardening was investigated on the distribution of residuals stress induced by new method called “cssmpcx process: sleeve with split mandrel and pilot cold expansion” on 7050-t7451 aluminium alloy. from this process the residual stresses along the plate front and back edges decreases with some rise in the tensile stresses away from the hole edge. as for the increase in fatigue amelioration of hole with cold expansion process, liu et al. [32] reported that, the fatigue life was improved by a factor from 1.5 to 5.0 witch depend on the expansion level. also, in work of semari et al. [6], the effects of residuals stresses induced by ball in cold expansion process on fatigue life of 6082 t6 are given by experimentally and numerically investigation (3d finite element analysis). improvement in fatigue life by expansion was shown under increasing of degree of expansion. the aiming of this paper is to evaluate the residual stress field induced by cold expansion process around hole in the first hand. on the other hand, we investigate the effects of compressive residuals stresses around the hole on improving of fatigue crack initiation life using local strain approach in 2024 t351 of al-alloy plate. also, the effect of stress ratio is highlighted. m. el habiri et alii, frattura ed integrità strutturale, 46 (2018) 34-44; doi: 10.3221/igf-esis.46.04 36 finite element modeling 3d finite element model was used to simulate cold expansion process using ansys code [33]. tetrahedral element with four nodes was used for the mesh of the holed plate. it is a common practice in the industry to use automatic tetrahedral mesh generators to discretize complex three-dimensional structural components. this type of mesh generators can handle very complex geometries with a minimum of human intervention (as compared to, e.g., the manual generation of a mesh of hexahedral elements) [34, 35]. oñate et al [36] have used linear tetrahedral element in finite element analysis for evaluation of pressure and plastic strain distribution where numerical solution is improved [36]. the linear tetrahedral element is robust in contact analysis, the element matrices are inexpensive to calculate, and the resulting global stiffness matrix has a relatively small bandwidth [37, 38]. the applied of a large and complex analysis model with hexahedral finite elements is a much more difficult task than with tetrahedral elements [39]. also, for tapered pin, eight-node structural solid elements (solid 185) were used with reduced integration. less computation time presents required advantage of these elements. additionally, eight node surface-to-surface contact (conta174) and (targe170) elements were generated to model the surface-to-surface contact. these contact elements allow the pressure to be transferred between the contacting surfaces and prevents them from penetrating each other [27]. due to double symmetry with respect to the x-z and y-z planes, a quarter of the plate and pin were modelled. in addition to the boundary constraints along the planes of symmetry, the plate was constrained in the z direction at the exit face nodes. the dimension of the plate are 6.32 mm in thick, 25 mm wide and 40 mm long witch corresponds to the central part of the fatigue specimens (fig. 1). the hole diameter “d” is 5 mm and the largest diameter of the tapered pin “d” is 5.23 mm which produces a 4.6% degree of expansion ( )( )d/dd100%dce −= . in published paper, several researchers have ignored friction in cold expansion process [9, 40], although introduced by others [27, 41]. the friction effect was included in this work using elastic coulomb fraction with µ=0.2. an elastic–plastic material relationship was used to represent the aluminium alloy 2024 t351 with isotropic hardening. the stress-strain curve is shown on fig. 2 and mechanical properties are summarised in table 1. a linear elastic material relationship was assumed for the steel pin with young’s modulus of 210 gpa and poisson’s ratio of 0.3. figure 1: geometrical model of fatigue specimen 0 100 200 300 400 500 0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 strain (mm/mm) s tr e s s ( m p a ) figure 2: true strain-stress curve of 2024 t351 al-alloy. a m. el habiri et alii, frattura ed integrità strutturale, 46 (2018) 34-44; doi: 10.3221/igf-esis.46.04 37 e (gpa) e (mpa) uts (mpa)  74.08 363 477 0.33 table 1: mechanical properties of 2024 t351 al-alloy. the tapered pin as shown in fig 3a was positioned near the hole at the entrance face (fig 3b). the simulation of cold expansion was carried out by incrementing the position of the nodes in the pin upper face in the -z direction. fig. 3b shows the meshed model with fixed and symmetric boundary conditions. the inner surface of the hole was then subjected to incremental pressure loading since the tapered mandrel was considered in this study. (a) (b) figure 3: cold expansion process a) detail of tapered pin used for cold expansion, b) mesh using 3d finite element model. residuals stresses distribution dues to cold expansion he cold-expansion simulation shows the hoop stress evolution around the hole during the loading and unloading steps (entrance and exit of mandrel through the hole). during the loading phase, the level of the compressive residual stress is achieved with few steps witch the mandrel improves the plastic radius up to a maximum value generated at a maximum nominal interference. in unloading phase, the elastic–plastic release of the plate generates the reverse-yielding zone. identification of the accurate residual stress profile around a cold expanded hole is critical due to related of the level and distribution of the residual stress on fatigue performance of the hole. it is recognized that magnitude and distribution of the residual stress is directly related to the fatigue performance of the hole. so, the residual compressive stress generated around the hole has the effect of reducing the stress concentration after the application of tensile cyclic loads to the fastener hole (maximum stress at hole) and therefore reduces the effective stress intensity factors for growth of cracks emanating from the hole [42]. the residual stress field with 4.6% in the degree of cold expansion is presented in fig. 4 respectively in entrance, mild and exit faces of the hole. the path of these residual stress profiles extends from the edge of the hole to the free edge of the plate, along the x-axis shown in fig. 1. this is the critical plane for fatigue crack growth assuming the plate is axially loaded in the longitudinal direction (y-axis). the curves in fig. 4 show compressive residuals stresses within about 2.8 mm from the hole edge at the entrance face location, but in midplane position is about 2.4 mm. so, at exit face, the length of compressive residuals from hole is about 3.8 mm. also it is noticed that maximum compressive residuals stresses at entrance face is about 100 mpa. these stresses increase in midplane and exit face positions and are respectively 390 mpa and 410 mpa which is greater than the yield stress of 363 mpa [42]. after 4 mm position, the residuals stresses are tensile for all position through thickness. additionally to the effect of cold expansion on circumferential residuals stresses, fig. 5 shows also, the effect of cold expansion on von mises t m. el habiri et alii, frattura ed integrità strutturale, 46 (2018) 34-44; doi: 10.3221/igf-esis.46.04 38 equivalents stresses sqv. the figure reveals the significant difference between the equivalent stress at exit and entry surfaces. these stresses decrease and present constants variations from 6 mm to the expanded hole. also, the equivalent stress field at the exit surface is dramatically increased witch is shown after the exit of the pin (fig. 6.c). -500 -400 -300 -200 -100 0 100 200 0 2 4 6 8 10 12 distance from hole (mm) t a n g e n ti a l r e s id u a ls s tr e s s e s ( m p a ) exit face mid-plane position entrance face figure 4: tangential residual stress at different through-thickness positions for 6.32 mm in thick of plate. 0 60 120 180 240 300 360 420 0 2 4 6 8 10 12 distance from hole (mm) e q u iv a le n t v o n m is e s s tr e s s e s ( m p a ) exit face mid-plane position entrance face figure 5: von-mises equivalent stress along the path of growth. tangential residual stress distribution established from the finite element analysis shows that it not uniform throughout the thickness of a cold expanded hole of finite plate (fig. 7). significant compressive tangential residual stress is produced between tapered pin and hole. this shows beneficial effect of induced friction between aluminium alloy plate and steel pin at free surface of hole. the evolution of tangential residuals stresses throughout thickness can be described by a polynomial equation shown above. 2 15.55 148.45 99.1a a =  −  − (1) “a” present parameter variation of the thickness from the entrance face to the exit face m. el habiri et alii, frattura ed integrità strutturale, 46 (2018) 34-44; doi: 10.3221/igf-esis.46.04 39 figure 6: distribution of von-mises equivalent stress around the hole. -500 -400 -300 -200 -100 0 0 1 2 3 4 5 6 7 distance from hole (mm) t a n g e n ti a l re s id u a ls s tr e s s e s ( m p a ) figure 7: tangential residual stress throughout thickness of plate influence of compressive residual stress on fatigue crack initiation n order to evaluate the fatigue crack initiation life, local strain approach was applied by several researchers cited above. in fatigue case and at the notch tip, local strains are obtained by using the neuber’s rule or glinka [43] expressed in following form: ( ) 2 . . 4 2 f ak e      = (2) where “a” is the applied stress and “” and “” are the resulting local stress and strain values corrected for the notch effect. the fatigue notch factor, (kf), is essentially the kt value corrected to account for the notch sensitivity for the given material [44]. it is determined as follows: i (a) (b) (c) m. el habiri et alii, frattura ed integrità strutturale, 46 (2018) 34-44; doi: 10.3221/igf-esis.46.04 40 ( ) 1.0 1.0 1.0 f f k k r −  = +   +  (3) where “” is an empirically determined material constant [45] and r is the notch root radius. in glinka’s approach the local strains and stresses should represent energy equivalence as compared the remote loading conditions, leading to the following equation: ( ) 2 1 2. 2 4 1 2 nf ak e e n k          = +    +   (4) in this equation “ k ” and “ n ” correspond to the material’s cyclic hardening law. the local strains were determined by coupling equation (2) and (4), given local strain range in function of local stress range named cyclic stress-strain (equation 5). 1 2 2 2 n e k        = +     (5) in 1910, basquin [46] observed that stress-life (s-n) data could be plotted linearly on a log-log scale and expressed by: ( ) ' 2 2 2 2 bfe fn e e    = = (6) manson and coffin [47] [41], working independently, found that plastic strain-life data (p-n) could be linearized in loglog co-ordinates. ( ) 1 ' 2 2 2 cnp f fn k       = =    (7) the relationship between total strain amplitude, 2 and life to failure, 2 fn , can be expressed in the form [25]: ( ) ( )2 2 2 2 f b c f f fn n e    = + (8) where “ f ” is the fatigue strength coefficient; “ b ” is the fatigue strength exponent, “ f ” is the fatigue ductility, “ c ” is the fatigue ductility exponent. the strain-life based crack initiation analysis method to predict crack initiation life is incorporated in afgrow code [48]. cyclic strain-life parameters used in fatigue crack initiation analysis for investigated material are given in table 2. f  f b c fk k n 1013.53 0.21 -0.21 -0.52 0.510-4 786 0.09 table 2: cyclic strain life properties of 2024 t351 aluminium alloy. the effect of expansion is illustrated in fig. 8. the 4.6% degree of expansion is applied to a hole. the applied spectrum is with constant amplitude loading considering four stress ratios are applied varying from 0.1 to 0.54. the maximum stress used in this investigation was 240 mpa. the initiation lives are predicted for crack initiation length equal to 0.5 mm. others researchers have taken the initiation of the crack is equivalent to 105 cycles [6, 49-51]. it is noticed from fig. 5 that the expansion process improves initiation fatigue life due to the existence of compressive residual stresses on the side of m. el habiri et alii, frattura ed integrità strutturale, 46 (2018) 34-44; doi: 10.3221/igf-esis.46.04 41 the hole. the mean residual stress field is applied. this field of stresses tends to increase the initiation fatigue life as shown in fig. 8 comparatively to drilled hole in plate without residual stress field. indeed, the increase in the hole diameter reduces the stresses concentration factor tk [44]. the concentration factor is equal to 3 for drilled hole and decreases to 1.75 where “kt” is defined as ( )maxt res nomk   = + . the ratio of initiation life ( )re re/i s i w sri n n− − −= depends on stress ratio. this ratio increases with increasing of stress ratio and vary from 3.22 to 3.85. also, the increasing in stress ratio increases the initiation life [19] that is attributed to reduction in amplitude loading. the predicted results have exponential evolution and are given by equation 9 and 10 respectively for expanded hole and drilled hole (without residual stress). it concluded that initiation life is improved by the presence of compressive residual around the hole. ( )4_ re 3.07 10 . 5.75i sn exp r=   (9) ( )4_ 1.01 10 . 5.38i w esn exp r− =   (10) 0.0e+00 2.0e+05 4.0e+05 6.0e+05 8.0e+05 0 0.1 0.2 0.3 0.4 0.5 0.6 stress ratio "r" in it ia ti o n l if e ( c y c le s ) "drilled hole" "cold expansion hole" figure 8: effect of cold expansion of hole on initiation fatigue life conclusion he aim of this work is to investigate the effect of residual stress induced by cold expansion in drilled hole on the crack initiation of 2024 t351 al-alloy plate. also the following conclusions can be drawn from the analysis: • a 3d finite element simulation of cold expansion using a tapered pin has shown that the tangential residual stress is not uniform at the hole edge through the plate thickness. • the maximum compressive tangential residual stress occurs at the hole edge near exit face and the mid-plane. also the smallest compressive residual stress occurs at the entrance face. • in the present investigation we have considered that crack is initiated with the same length through the thickness, so the mean residual stress field due to cold expansion is applied. • fatigue initiation life is improved by the presence of compressive residual stress around the hole comparatively to drilled hole without residual stress. the percentage in this improving varies from 3.22 to 3.85. additionally, the effect of stress ratio on initiation life is highlighted. t m. el habiri et alii, frattura ed integrità strutturale, 46 (2018) 34-44; doi: 10.3221/igf-esis.46.04 42 references [1] wanhill, r., barter, s. and molent, l. (2014). fatigue crack growth failure analyses in metallic aircraft components. 11th international fatigue congress 2014, pp. 2-7, melbourne, australia. [2] rodopoulos, c.a., curtis, s.a., de los rios, e.r. and solis romero, j. (2004), optimisation of the fatigue resistance of 2024-t351 aluminium alloys by controlled shot peening-methodology, results and analysis. international journal of fatigue 26(8), pp. 849–856. doi: 10.1016/j.ijfatigue.2004.01.003. [3] huang, s., zhou, j.z. , sheng, j. , luo, k.y. , lu, j.z., xu, z.c. and meng, x.k. (2013). effects of laser peening with different cover age areas on fatigue crack growth properties of 6061-6 aluminum alloy, international journal of fatigue 47, pp. 292–299. doi: 10.1016/j.ijfatigue.2012.09.010. [4] sheng, j., huang, s., zhou, j.z., lu, j.z., xu, s.q. and zhang, h.f. (2016). effect of laser peening with different energies on fatigue fracture evolution of 6061-t6 aluminum alloy. optics & laser technology, 77, pp. 169–176. doi: 10.1016/j.optlastec.2015.09.008 [5] ren, x.d., zhan, q.b., yang, h.m., daic, f.z., cui, y., sun, g.f. and ruan, l. (2013). the effects of residual stress on fatigue behavior and crack propagation from laser shock processing-worked hole, materials & design 44, pp. 149154. doi: 10.1016/j.matdes.2012.07.024 [6] semari, z., aid, a. and benhamena, a. (2013). effect of residual stresses induced by cold expansion on the crack growth in 6082 aluminum alloy. engineering fracture mechanics, 99, pp. 159-68. doi:10.1016/j.engfracmech.2012.12.003 [7] yucan, f., ende, g., honghua, s., jiuhua, x. and renzheng, l. (2015). cold expansion technology of connection holes in aircraft structures: a review and prospect. chinese journal of aeronautics, 28(4), pp. 961–973. doi:10.1016/j.cja.2015.05.006 [8] chakherlou, t.n., taghizadeh, h. and aghdam, a.b. (2013). experimental and numerical comparison of cold expansion and interference fit methods in improving fatigue life of holed plate in double shear lap joints. aerospace science technology, 29(1), pp. 351–362. doi: 10.1016/j.ast.2013.04.006. [9] yongshou, l., jun, l. and zhufeng, y. (2010). finite element method and experimental investigation on the residual stress fields and fatigue performance of cold expansion hole. materials & design, 31(3), pp. 1208-1215. doi: 10.1016/j.matdes.2009.09.031. [10] glinka, g. (1987). residual stress in fatigue and fracture: theoretical analyses and experiments. in niku-lari a., editor, advances in surfaces treatments, pp. 413-454. pergamon press, residual stresses, 4. [11] topper, t. h., wetzel, r. m. and morrow, j. (1969). neuber’s rule applied to fatigue of notched specimens, journal of materials, 4(1), pp. 200-209. [12] glinka, g. (1985). a notch stress-strain analysis approach to fracture crack growth, engineering fracture mechanics, 21(2), pp. 245-261. doi: 10.1016/0013-7944(85)90014-1. [13] truchon, m. (1982). application of low-cycle fatigue test results to crack initiation from notches, low-cycle fatigue and life prediction. astm stp 770, c. amzallag, b. n. leis, and p. rabbe, (eds.), american society for testing and materials, pp. 254-268. [14] zheng, x. (2001). on some basic problems of fatigue research in engineering, international journal of fatigue, 23, pp. 751–766. doi: 10.1016/s0142-1123(01)00040-8. [15] zheng, m., niemi, e. and zheng, x. (1997). an energetic approach for predict fatigue crack initiation life of ly 12 cz aluminum and 16 mn steel, theoretical applied fracture mechanics, 26, pp. 23-38. doi: 10.1016/s0167-8442(96)00030-4. [16] mcmaster, f.j. and smith, d.j. (2001). predictions of fatigue crack growth in aluminium alloy 2024–t351 using constraint factors. international journal of fatigue, 23, pp. 93-101. doi: 10.1016/s0142-1123(01)00134-7. [17] rodopoulos, c.a., choi, j.h., de los rios, e.r. and yates, j.r. (2004). stress ratio and the fatigue damage map-part ii: the 2024-t351 al-alloy, international journal of fatigue, 26, pp. 747-752. doi:10.1016/j.ijfatigue.2003.10.018 [18] fujczak, r.r. (1984). effects of r-ratio on crack initiation at external discontinuities in auto frettaged cylinders, experimental mechanics, 9, pp. 122-128. doi: 10.1007/bf02324994. [19] ranganathan, n., aldroe, h., lacroix, f., chalon, f., leroy, r. and tougui, a. (2011). fatigue crack initiation at a notch. international journal of fatigue, 33, pp. 492–499. doi: 10.1016/j.ijfatigue.2010.09.007l. [20] amrouche, a., mesmacque, g. and garcia, s. (2003). cold expansion effect on the initiation and the propagation of the fatigue crack. international journal of fatigue, 25(9-11), pp. 949–954. doi: 10.1016/s0142-1123(03)00127-0. https://doi.org/10.1016/j.ijfatigue.2012.09.010 https://doi.org/10.1016/j.optlastec.2015.09.008 https://www.sciencedirect.com/science/article/pii/s0261306912004761#%21 https://www.sciencedirect.com/science/article/pii/s0261306912004761#%21 https://www.sciencedirect.com/science/article/pii/s0261306912004761#%21 https://www.sciencedirect.com/science/article/pii/s0261306912004761#%21 https://doi.org/10.1016/j.matdes.2012.07.024 https://doi.org/10.1016/j.engfracmech.2012.12.003 https://doi.org/10.1016/j.cja.2015.05.006 https://doi.org/10.1016/j.ast.2013.04.006 https://www.sciencedirect.com/science/article/pii/s0261306909005160#! https://www.sciencedirect.com/science/article/pii/s0261306909005160#! https://www.sciencedirect.com/science/article/pii/s0261306909005160#! https://doi.org/10.1016/j.matdes.2009.09.031 https://doi.org/10.1016/0013-7944%2885%2990014-1 https://doi.org/10.1016/s0142-1123%2801%2900040-8 https://doi.org/10.1016/s0167-8442%2896%2900030-4 https://www.sciencedirect.com/science/article/pii/s0142112301001347 https://www.sciencedirect.com/science/article/pii/s0142112301001347 https://doi.org/10.1016/s0142-1123%2801%2900134-7 https://doi.org/10.1016/j.ijfatigue.2003.10.018 https://doi.org/10.1016/j.ijfatigue.2010.09.007 https://doi.org/10.1016/s0142-1123%2803%2900127-0 m. el habiri et alii, frattura ed integrità strutturale, 46 (2018) 34-44; doi: 10.3221/igf-esis.46.04 43 [21] zhao, q., liu, f. and huang, h. (2014). study on the residual stress and fatigue performance of cold expansion hole on 7050-t7451. advanced materials research, 1004-1005, pp. 1299-1304. doi: 10.4028/www.scientific.net/amr.1004-1005.1299. [22] gopalakrishna, h.d., narasimha murthy, h.n., krishna, m., vinod, m.s. and suresh, a.v. (2010). cold expansion of holes and resulting fatigue life enhancement and residual stresses in al 2024 t3 alloy – an experimental study. engineering failure analysis, 17, pp. 361-368. doi: 10.1016/j.engfailanal.2009.08.002. [23] chandawanich n. and sharpe w. (1979). an experimental study of fatigue crack growth initiation and growth from cold worked holes, engineering fracture mechanics, 11, pp. 609-920. doi: 10.1016/0013-7944(79)90122-x. [24] su, m., amrouche, a., mesmacque, g. and benseddiq, n. (2008). numerical study of double cold expansion of the hole at crack tip and the influence on the residual stresses field. computational materials sciences, 41, pp. 350-355. doi: 10.1016/j.commatsci.2007.04.022. [25] warner, j.j., clark, p.n. and hoeppner, d.w. (2014). cold expansion effects on cracked fastener holes under constant amplitude and spectrum loading in the 2024-t351 aluminum alloy. international journal of fatigue, 68, pp. 209-216. doi: 10.1016/j.ijfatigue.2014.05.002. [26] liu, y.s, gou, b.w., shao, x.j, jiang, z.f. and yue z.f. (2010). effect of thickness on residual stress fields of cold expansion hole. advanced materials research, 97-101, pp. 601-604. doi: 10.4028/www.scientific.net/amr.97-101.601. [27] chakherlou, t.n. and vogwell, j. (2003). the effect of cold expansion on improving the fatigue life of fastener holes. engineering failure analysis, 10, pp. 13-24. doi: 10.1016/s1350-6307(02)00028-6. [28] liu, j., wu, h., yang, j. and yue, z. (2013). effect of edge distance ratio on residual stresses induced by cold expansion and fatigue life of tc4 plates. engineering fracture mechanics, 109, pp. 130–137. doi:10.1016/j.engfracmech.2013.05.012. [29] smith, k.n., watson, p. and topper, t.h. (1970). a stress-strain function for the fatigue of metals. journal materials, 15, pp. 767-778. available at: https://www.researchgate.net/publication/269929853_14_ smith_k_n_watson_p_and_topper_t_h_'a_stressstrain_function_for_the_fatigue_of_metals_nl_of_marls_1m lsa_5_4_767-778_dee_1070. [30] wang, c.h. and brown, m.w. (1993). a path-independent parameter for fatigue under proportional and nonproportional loading. fracture of engineering materials & structures, 16(12), pp. 1285-1297. doi: 10.1111/j.1460-2695.1993.tb00739.x. [31] kurhade, r.s., wadegaonkar, a.p. and pradhan, b. (2004). finite element analysis of effects of strain hardening rate on cold expansion of fastener holes. available at : www.ansys.com/-/media/ansys/.../2004-int-ansys-conf-164.pdf [32] liu, j., shao, x.j., liu, y.s. and yue, z.f. (2009). effect of cold expansion on fatigue performance of open holes. engineering fracture mechanics, 477, pp. 271-276. doi: 10.1016/j.msea.2007.05.034. [33] ansys release 11.0 documentation, ansys inc., 2008. [34] brandts, j., korotov, s. and krızek, m. (2011). a geometric toolbox for tetrahedral finite element partitions. in book: efficient preconditioned solution methods for elliptic pdes (2011), pp. 103-122. doi:10.2174/978160805291211101010103. [35] duarte, c.a., babuska, i. and oden, j.t. (2000). generalized finite element methods for three dimensional structural mechanics problems. computers & structures, 77(2), pp. 215-232. doi: 10.1016/s0045-7949(99)00211-4. [36] oñate, e., rojek, j., taylor, r.l. and zienkiewicz, o.c. (2004). finite calculus formulation for incompressible solids using linear triangles and tetrahedral. int. j. numer. meth. engng, 59, pp. 1473-1500. doi: 10.1002/nme.922. [37] persson, p.o. and peraire, j., curved mesh generation and mesh refinement using lagrangian solid mechanics. american institute of aeronautics and astronautics. proc. of the 47th aiaa aerospace sciences meeting and exhibit, 2009. available at: https://pubarchive.lbl.gov/islandora/object/ir%3a152677. [38] payen, d. j. and bathe, k.-j. (2011). improved stresses for the 4-node tetrahedral element. computers and structures, 89, pp. 1265-1273. doi: 10.1016/j.compstruc.2011.02.009. [39] okada, h. and kamibeppu, t. (2005). a virtual crack closure-integral method (vccm) for three-dimensional crack problems using linear tetrahedral finite elements. cmes, 10(3), pp. 229-238, tech science press. available at: https://www.techscience.com/doi/10.3970/cmes.2005.010.229.pdf [40] farhangdoost, kh. and hosseini, a. (2011). the effect of mandrel speed upon the residual stress distribution around cold expanded hole. procedia engineering, 10, pp. 2184–2189. doi: 10.1016/j.proeng.2011.04.360. [41] nigrelli, v. and pasta, s. (2008). finite-element simulation of residual stress induced by split-sleeve cold-expansion process of holes. journal of materials processing technology, 205, pp. 290-296. doi:10.1016/j.jmatprotec.2007.11.207. https://doi.org/10.1016/j.engfailanal.2009.08.002 https://doi.org/10.1016/0013-7944%2879%2990122-x https://doi.org/10.1016/j.commatsci.2007.04.022 https://doi.org/10.1016/j.ijfatigue.2014.05.002 https://doi.org/10.1016/s1350-6307%2802%2900028-6 https://doi.org/10.1016/j.engfracmech.2013.05.012 http://www.ansys.com/-/media/ansys/.../2004-int-ansys-conf-164.pdf https://doi.org/10.1016/j.msea.2007.05.034 https://www.sciencedirect.com/science/journal/00457949 https://www.sciencedirect.com/science/journal/00457949/77/2 https://doi.org/10.1016/s0045-7949(99)00211-4 https://pubarchive.lbl.gov/islandora/object/ir%3a152677 https://doi.org/10.1016/j.compstruc.2011.02.009 https://doi.org/10.1016/j.proeng.2011.04.360 https://doi.org/10.1016/j.jmatprotec.2007.11.207 m. el habiri et alii, frattura ed integrità strutturale, 46 (2018) 34-44; doi: 10.3221/igf-esis.46.04 44 [42] houghton, s.j. (2010). finite analysis of the cold expansion of aircraft fastner holes, dta report 295. [43] neuber, h. (1960). theory of stress concentration for shear-strained prismatical bodies with arbitrary nonlinear stress-strain law. trans. asme, journal of applied mechanics, pp. 544-550. [44] peterson, r.e. (1974). stress concentration factors, john wiley and sons. [45] hall, l.r., shah, r.c. and engstorn, w.l. (1974). fracture and fatigue crack growth behavior of surface flaws originating at fastener holes. affdl-tr-74-47, air force flight dynamics lab, ohio. [46] basquin, o.h. (1910). the exponential law of endurance tests, proceedings of american society of testing and materials, 10 part ii, pp. 625-630. [47] coffin, l.f. (1954). a study of effects of cyclic thermal stresses on a ductile metal, transactions of the asme, 76, pp. 931-950. [48] harter, j.a. (2006). afgrow users guide and technical manual: afgrow for windows 2k/xp. version 4.0011.14, air force research laboratory. [49] man, s. (2005). etude de l’influence et de l’optimisation du degré d’expansion à froid dans les mécanismes de réamorçage d’une fissure: étude numérique et expérimentale. doctoral thesis. university of sciences and technologies of lille; france. [50] todoroki, a. and kobayashi h. (1991). prediction of fatigue crack growth rate in residual stress fields. key engineering materials: fracture strength, 367, pp. 51–62. doi:10.4028/www.scientific.net/kem.51-52.367. [51] nigrelli, v. and pasta, s. (2008). finite-element simulation of residual stress induced by split-sleeve cold expansion process of holes. journal of materials processing technology, 205, pp. 290–296. doi:10.1016/j.jmatprotec.2007.11.207. https://www.journals.elsevier.com/journal-of-materials-processing-technology https://doi.org/10.1016/j.jmatprotec.2007.11.207 microsoft word numero_33_art_29 f. berto et alii, frattura ed integrità strutturale, 33 (2015) 229-237; doi: 10.3221/igf-esis.33.29 229 focussed on multiaxial fatigue multiaxial fatigue strength of severely notched titanium grade 5 alloy f. berto, a. campagnolo university of padua, italy berto@gest.unipd.it, campagnolo@gest.unipd.it abstract. the multiaxial fatigue strength of severely notched titanium grade 5 alloy (ti-6al-4v) is investigated. experimental tests under combined tension and torsion loading, both in-phase and out-of-phase, have been carried out on axisymmetric v-notched specimens considering different nominal load ratios (r = -1, 0). all specimens are characterized by a notch tip radius less than 0.1 mm, a notch depth of 6 mm and a notch opening angle equal to 90 degrees. the experimental data from multiaxial tests are compared with those from pure tension and pure torsion tests on un-notched and notched specimens, carried out at load ratio ranging from r = -3 to r = 0.5. in total, more than 160 new fatigue data are examined, first in terms of nominal stress amplitudes referred to the net area and then in terms of the local strain energy density averaged over a control volume surrounding the v-notch tip. the dependence of the control radius on the loading mode is analysed showing a very different notch sensitivity for tension and torsion. for the titanium alloy ti-6al-4v, the control volume is found to be strongly dependent on the loading mode. keywords. titanium alloy; ti-6al-4v; multiaxial fatigue; v-notch; control volume; strain energy density. introduction ultiaxial fatigue of metallic materials is a topic of active research. for a comparison between different criteria we mention here a recent overview [1] and the report [2] based on a large body of experimental data from notched specimens. a central position is occupied by the critical plane approach [3, 4] and by some interesting variants [5-7]. in this ambit, energy-based criteria find important applications [8]. recently it has been proposed a multiaxial fatigue criterion based on a frequency-domain formulation of a stress invariant, called “projection by projection” (pbp) approach [9]. a frequency-domain formulation of the critical plane-based c-s criterion has recently been presented in [10]. in 1923 jasper [11] first used an energy-based parameter to analyse fatigue strength under tension–compression loadings. afterwards dealing with multiaxial fatigue loading ellyin proposed an approach based on the combination of both the plastic and elastic strain work [12-13]. a wide review of energy-based multiaxial fatigue life formulations was carried out in [14]. theoretical and experimental problems tied to multiaxial fatigue were discussed by several researchers [15-22]. the present work deals with multiaxial fatigue strength of severely notched titanium grade 5 alloy (ti-6al-4v). this titanium alloy is widely used for advanced military, civil aerospace and naval applications. the in-service conditions are usually characterized by a complex stress state combined with aggressive environments. the ti-6al-4v titanium alloy has m f. berto et alii, frattura ed integrità strutturale, 33 (2015) 229-237; doi: 10.3221/igf-esis.33.29 230 very good static and fatigue properties, an high strength-to-mass ratio, with an excellent wear resistance, also at high temperature and in corrosive environments. the uniaxial fatigue resistance of smooth and notched specimens made of ti6al-4v has been extensively investigated in the recent literature. a complete set of data from sharply v-notched specimens under torsion and combined tension and torsion loadings, both in-phase and out-of-phase, is not available in the literature for ti-6al-4v. with the aim to fill this lack, a complete set of experimental data from a severely notched titanium alloy under multiaxial loading is provided. circumferentially v-notched specimens are tested under combined tension and torsion loading, both in-phase and out-ofphase, with two nominal load ratios, r = -1 and r = 0. all axisymmetric specimens are characterized by a notch tip radius less than 0.1 mm, a notch depth of 6 mm and a v-notch angle equal to 90 degrees. the experimental data from multiaxial tests are discussed together with those from pure tension and pure torsion tests on un-notched and notched specimens, carried out at a load ratio ranging from r = -3 to r = 0.5. altogether more than 160 new fatigue data (15 wöhler curves) are analyzed in terms of nominal stress amplitudes referred to the net area. the application of a multiaxial loading reduces the fatigue life compared to the pure tension loading case, with reference to the same normal stress amplitude, but the reduction results to be quite limited for the specific value of the biaxiality ratio (= 0.6). stronger is the reduction of the multiaxial fatigue strength due to the nominal load ratio r. the phase angle effect is found to be weak for r = -1, being the mean values of the normal stress amplitude about the same at 2·106 cycles. more clear is the effect of the phase angle when r = 0: the out-of-phase loading is slightly beneficial with respect to in-phase loading at high cycle fatigue regime whereas the fatigue strength is almost the same at low cycle regime. the sensitivity of this titanium alloy under multiaxial fatigue loading to the phase angle effect results to be quite limited, being lower than +15 percent for the r = 0 case and negligible for the r = -1 case. the fracture surfaces of the specimens tested under multiaxial conditions have been analyzed. the fracture surface morphology seem to be affected by the phase angle. some signs of micro abrasions could be observed on all fracture surfaces and the extent to which the rubbing occurred depends on phase angle. generally, a limited but distinguishable quantity of debris and powder was emanated from the notch tip when a visible crack started to propagate. afterwards, all fatigue strength data are summarized in terms of the local strain energy density (sed) averaged over a material-dependent control volume surrounding the v-notch tip [23-30]. the dependence of the control volume size on the loading mode is investigated showing the need to use for the titanium alloy ti-6al-4v a different size of the control volume under tension and under torsion, due to a very different notch sensitivity for tension and torsion. the expressions for estimating the control radii, thought of as material properties, are obtained imposing at 2·106 cycles the constancy of the sed from smooth and v-notched specimens, which depends on the notch stress intensity factors and the radius of the control volume. in particular, a control volume of radius r1c are used to evaluate the averaged contribution to local stress and strains due to tensile loading, whereas a radius r3c are used to assess the averaged contribution due to torsion loading. the control radii result to be r1c = 0.051 mm and r3c = 0.837 mm. the size of r3c radius is highly influenced by the presence of larger plasticity under torsion loading with respect to tensile loading and by friction and rubbing between the crack surfaces, as discussed extensively for different materials [31]. the sed is called ‘apparent linear elastic sed’ to remember that the evaluation of the strain energy in two different volumes (for tension and torsion, as determined from experimental data) allows us to overcome the problem tied to shielding mechanisms maintaining a linear elastic model. the unifying capacity of the sed approach is highlighted, in fact the synthesis based on the local strain energy density allows to obtain a quite narrow scatter-band, which has an equivalent stress-based scatter index t equal to 1.58, considering all the data from v-notched and smooth specimens under pure tension, pure torsion and multiaxial loading, independent of the load ratio and the phase angle. the results of the synthesis in terms of sed are also compared with those from other materials already reported in the literature by the same authors. material properties and geometry of the specimens he material under investigation is a grade 5 titanium alloy, also known as ti-6al-4v. the geometries of the unnotched and v-notched specimens are shown in fig. 1 together with some details of the notch tip. the hourglass un-notched specimens (fig. 1) were characterized by a diameter of the net transverse area equal to 12 mm and by a connecting radius ( = 100 mm) between the net and gross sections large enough to avoid any effect of stress concentration. the cylindrical notched specimens (fig. 1) were characterized by a v-notch depth d = 6 mm and an opening angle equal to 90 degrees, whereas the notch root radius, , was always lower than 0.1 mm. the experimental measurements of the notch tip radius, carried out by means of an optical microscope and the dedicate software las t f. berto et alii, frattura ed integrità strutturale, 33 (2015) 229-237; doi: 10.3221/igf-esis.33.29 231 (leica application suite), have provided a mean value equal to 0.09 mm with a very reduced scatter. the precision ensured by the employed procedure is ± 5% of the measured quantity. the typical notch geometry constituted by two rectilinear flanks tangent to the notch tip radius is shown in fig. 1b, for one of the v-notched specimens. the experimental tests have been performed on a mts 809 servo-hydraulic bi-axial testing device (± 100 kn, ± 1100 nm, ± 75mm/± 55°) under load control. a mts load cell with ± 0.5 % error at full scale has been used to measure the applied load. altogether 15 different fatigue test series have been performed according to the parameters described below: -four series of tests on un-notched and v-notched specimens under pure tension and pure torsion fatigue loading at the nominal load ratio r = -1; -four series of tests on un-notched and v-notched specimens under pure torsion fatigue loading at the nominal load ratios r = 0 and 0.5; -three series of tests on un-notched specimens under pure torsion fatigue loading at the nominal load ratios r = 0.25, -2 and -3; -four series of tests on v-notched specimens under combined tension and torsion loading, with a constant biaxiality ratio = 0.6. two nominal load ratios, r = 0 and r = -1 (referred separately to the normal and shear stress components), and two phase angles, = 0° (in-phase loading) and = 90° (out-of-phase loading), have been adopted in these tests. (a) (b) figure 1: geometry of un-notched and v-notched specimens (a) and details of the notch tip (b). results from fatigue tests ll specimens have been polished with the aim of removing surface scratches and processing marks, before performing the tests. a mts 809 servo-hydraulic biaxial machine with a 100 kn axial load cell and a torsion load cell of 1100 nm has been used for fatigue tests. all tests have been conducted under load control at a frequency between 10 and 15 hz as a function of the applied load. the statistical analyses have been performed assuming a log-normal distribution. all data obtained from specimens characterized by fatigue life between 104 and 2·106 have been taken into account in the statistical analyses, excluding the run-outs. the nominal stress amplitudes for a probability of survival ps = 50% at different number of loading cycles, na = 106 and 2·106, the inverse slope k of wöhler curves and the scatter index t, which provides the width of the scatterband between the curves with 10% and 90% probabilities of survival (with a confidence level equal to 95%) are shown in tab. 1. the plot of the fatigue curves are reported in [31]. synthesis by means of the local sed ith regard to smooth specimens, all the experimental data are summarised here in terms of the strain energy density, which can be expressed under linear elastic hypothesis according to beltrami’s expression. under pure tension one obtains: 2 2 nomw e    (1) a w f. berto et alii, frattura ed integrità strutturale, 33 (2015) 229-237; doi: 10.3221/igf-esis.33.29 232 table 1: results from fatigue tests. mean values, ps=50%. stresses referred to the net area. while under pure torsion it results:   2 1 nomw e       (2) where nom and nom represent the range of the nominal stress components. for ti-6al-4v titanium alloy the young’s modulus e is equal to 110 gpa while the poisson’s ratio ν is 0.3. also the experimental data related to v-notched specimens will be summarised here in terms of linear elastic strain energy density, but in this case the sed calculation is based on the local stress and strain state in a control volume surrounding series load n k tσ or tτ σa or τa 106 2 · 106 1 tension r = -1 12 σ 9.25 1.120 512.76 475.74 2 torsion r = -1 16 τ 22.13 1.205 400.60 388.25 3 torsion r = 0 9 τ 15.03 1.322 300.78 287.22 4 tension r = -1, v-notch 2α = 90° 15 σ 6.26 1.133 112.70 100.89 5 torsion r = -1, v-notch 2α = 90° 9 τ 14.59 1.229 303.39 289.31 6 torsion r = 0, v-notch 2α = 90° 11 τ 13.82 1.159 259.87 247.16 7 torsion r = 0.5, v-notch 2α = 90° 7 τ 19.91 1.080 175.91 169.89 8 multiaxial r = -1, = 0°, = 0.6, v-notch 2α = 90° 13 σ 6.82 1.197 104.03 93.89 τ 62.42 56.39 9 multiaxial r = -1, = 90°, = 0.6, v-notch 2α = 90° 10 σ 7.84 1.124 104.99 96.11 τ 63.00 57.67 10 multiaxial r = 0, = 0°, = 0.6, v-notch 2α = 90° 12 σ 8.09 1.159 73.80 67.74 τ 44.28 40.64 11 multiaxial r = 0, = 90°, = 0.6, v-notch 2α = 90° 12 σ 10.43 1.158 85.12 79.65 τ 51.07 47.79 12 torsion r = 0.5 12 τ 21.19 1.134 186.74 180.73 13 torsion r = 0.25 8 τ 25.67 1.078 275.46 268.12 14 torsion r = -3 7 τ 16.25 1.178 373.13 357.55 15 torsion r = -2 8 τ 21.32 1.042 422.53 409.01 f. berto et alii, frattura ed integrità strutturale, 33 (2015) 229-237; doi: 10.3221/igf-esis.33.29 233 the notch tip. being the radius at the notch tip very small ( less than 0.1 mm), the mode 1 and mode 3 notch stress intensity factors k1 and k3 can be used to re-analyse the fatigue strength data related to v-notched specimens in terms of the sed. these field parameters were calculated by means of linear elastic fe analysis considering a sharp v-notch with = 0, see fig. 2. in particular, considering a cylindrical coordinate system (r, θ, z) centered at the notch apex, where r is the radial coordinate,  is the angle between a particular point and the notch bisector line while z is the longitudinal axis of the specimens, the mode 1 and mode 3 notch stress intensity factors (nsifs) can be defined according to the following expressions: 111 02 lim ( , 0)rk r r         (3) 313 02 lim ( , 0)zrk r r         (4) in the case of a v-notch opening angle equal to 90 degrees, the eigenvalues 1 and 3 are equal to 0.545 and 0.667 respectively. on the other hand in conditions of linear elasticity the nsifs can be linked to the nominal stress components according to the following expression: 111 1 nomk k d     (5a) 313 3 nomk k d     (5b) where d is the notch depth (d = 6.0 mm) while k1 and k3 are non-dimensional factors derived from fe analysis. they simply represent the shape factors, in analogy with the representation of linear elastic fracture mechanics. the harmonic element solid plane 83 of the ansys code was used in the finite element analysis. taking advantage of the geometric and loading symmetry, it was possible to model only one quarter of the specimen. fe models gave k1 = 1.000 and k3 = 1.154. the stress field is controlled by the first singular term (nsif) up to a distance from the notch tip about equal to 1.0 mm. substituting the notch depth of the specimens examined here, d = 6 mm, in eqs. (5a) and (5b), one can obtain: 1 2.260 nomk    (in mpa ·mm0.445) (6a) 3 2.096 nomk    (in mpa ·mm0.333) (6b) taking into account the range of the nominal stresses at na = 2·106 cycles relating to v-notched specimens tested under pure tension and pure torsion with a nominal load ratio r = -1 (tab. 1) and substituting them into the eq. (6a) and (6b), it can be obtained: 0.4451 2.260 200 452ak mpa mm     (7a) 0.3333 2.096 580 1216ak mpa mm     (7b) in the case of a component weakened by a sharp v-notch and in conditions of linear elasticity, the sed averaged over a control volume, which embraces the notch tip, can be calculated by means of the following expression:    1 3 22 31 1 32 1 2 1 1c 3c 1 kk w e e e r r              (8) where k1 and k3 represent the mode i and mode iii nsif ranges, r1c and r3c are the radii of the control volume related to mode i and mode iii loadings while e1 and e3 are two parameters that summarize the dependence from the vnotch geometry. these parameters are directly linked to the integrals of the angular functions over the control volume and they can be determined a priori by means of closed-form expressions once known the v-notch opening angle. since the specimens examined here are characterized by a notch opening angle 2 equal to 90 degrees, e1 and e3 are equal 0.146 and 0.310 respectively, with the poisson’s ratio  = 0.3. the use of refined meshes in the close neighborhood of the stress singularity is necessary in the calculation of nsifs. on the other hand the sed averaged over a control volume is insensitive to the mesh refinement, it can be accurately evaluated also by means of coarse meshes because it directly depends on nodal displacements. some of the advantages linked to the use of the averaged sed are described in details in ref. [30]. f. berto et alii, frattura ed integrità strutturale, 33 (2015) 229-237; doi: 10.3221/igf-esis.33.29 234 it is possible to estimate the control volume radii described in fig. 2, r1c and r3c, considering separately the loading conditions of mode i and mode iii. these radii are functions of the high cycle fatigue strength of smooth specimens, 1a = 950 mpa,3a = 776 mpa, and of the mean values of the nsifs, k1a andk3a, all referred to the same number of cycles, na = 2·106: 1 1 1 1 1c 1 1 2 a a k r e          (9a) 3 1 1 3 3 3c 31 a a e k r            (9b) eq. 9a and 9b provide as a result: r1c = 0.051 mm and r3c = 0.837 mm. the obtained values will be used to summarise all fatigue strength data by means of the averaged sed. the expressions for estimating the control radii, thought of as material properties, have been obtained imposing at na cycles the constancy of the sed from smooth and v-notched specimens, which depends on the notch stress intensity factors and the radius of the control volume. considering instead cracked specimens, the critical nsifs should be replaced by the threshold values of the stress intensity factors. figure 2: control volumes for v-shaped notches under tension and torsion loading. in particular, a control volume of radius r1c will be used to evaluate the averaged contribution to local stress and strains due to tensile loading, whereas a radius r3c will be used to assess the averaged contribution due to torsion loading. the size of r3c radius is highly influenced by the presence of larger plasticity under torsion loading with respect to tensile loading and by friction and rubbing between the crack surfaces, as discussed extensively for different materials [31]. with the aim to unify in a single diagram the fatigue data related to different values of the nominal load ratio r, it is necessary to introduce a weighting factor cw on the basis of mere algebraic considerations. the result of these observations [24], provides as master cases cw = 1.0 for r = 0 and cw = 0.5 for r = -1. the expression of cw as a function of the nominal load ratio r is:     2 2 2 2 1 0 1 1 0 1 0 1 1 r for r r for r r for r r                (10) by applying the weighting factor cw, the expressions for calculating the strain energy density under linear elasticity, for unnotched specimens (eqs. (1, 2)) and for v-notched ones (eq. (8)), become: f. berto et alii, frattura ed integrità strutturale, 33 (2015) 229-237; doi: 10.3221/igf-esis.33.29 235      1 3 2 2 22 31 1 32 1 2 1 1c 3c 2 1 nom w nom w w c un notched specimens pure tension e sed c un notched specimens pure torsion e c kk e e v notched specimens multiaxial loading e r r                                (11) fig. 3 shows the synthesis in terms of sed of all the fatigue strength data presented in this contribution is shown. again two different control radii equal to r1c = 0.051 mm and r3c = 0.837 mm respectively have been adopted. the scatterband includes all the data from un-notched and v-notched specimens under pure tension, pure torsion and multiaxial loading, regardless of the load ratio and the phase angle. it is also characterized by an inverse slope k equal to 5.90, a scatter index tw = 2.5 and a value of the strain energy density at the reference number of cycles, na = 2·106, that equals 3.08 mj/m3. the equivalent stress-based scatter index t results to be 1.58, that is comparable with that observed in the haibach scatterband (t= 1.50). figure 3: synthesis by means of local sed of un-notched and v-notched specimens data. conclusions large bulk of fatigue strength data referred to cylindrical v-notched specimens made of titanium grade 5 alloy (ti-6al-4v) and tested under combined tension and torsion loading, both in-phase and out-of-phase, have been analysed together with those obtained from un-notched and v-notched specimens under pure tension and pure torsion loading. a total of over 160 new fatigue data (15 wöhler curves) have been summarised in the present work. all fatigue strength data from uniaxial and multiaxial tests have been presented first in terms of nominal stress amplitudes referred to the net area and then reanalysed in terms of the local strain energy density averaged over a control volume that embraces the vnotch tip. the dependence of the control radius by the loading mode is analysed showing the need to use, for the titanium alloy ti-6al-4v, a different size of the control volume under tension and under torsion. the synthesis based on the local strain energy density allows us to obtain a quite narrow scatter-band, which has a scatter index equal to 2.50, considering all the data from v-notched and smooth specimens under pure tension, pure torsion and multiaxial loading, independent of the load ratio and the phase angle. a f. berto et alii, frattura ed integrità strutturale, 33 (2015) 229-237; doi: 10.3221/igf-esis.33.29 236 references [1] fatemi, a., shamsaei, n., multiaxial fatigue: an overview and some approximation models for life estimation, int j fatigue, 33 (2011) 948-958. [2] nieslony, a., sonsino, c.m., comparison of some selected multiaxial fatigue assessment criteria, lbf report 2008; no. fb-234. [3] fatemi, a., socie, d.f., a critical plane approach to multiaxial fatigue damage including out-of-phase loading, fatigue fract eng mater struct, 11 (1988) 149-165. [4] fatemi, a., kurath, p. p., multiaxial fatigue life prediction under the influence of mean stresses, asme j eng mater techn, 110 (1988) 380-388. [5] łagoda, t., macha, e., bedkowski, w., a critical plane approach based on energy concepts: application to biaxial random tension-compression high-cycle fatigue regime, int j fatigue, 21 (1999) 431-443. [6] carpinteri, a., spagnoli, a., multiaxial high-cycle fatigue criterion for hard metals, int j fatigue, 23 (2001) 135-145. [7] carpinteri, a., spagnoli, a., vantadori, s., bagni, c., structural integrity assessment of metallic components under multiaxial fatigue: the c-s criterion and its evolution, fatigue fract eng mater, 36 (2013) 870-883. [8] ye, d., hertel, o., vormwald, m., a unified expression of elastic–plastic notch stress–strain calculation in bodies subjected to multiaxial cyclic loading, int j solids struct, 45 (2008) 6177-6189. [9] cristofori, a., benasciutti, d., tovo, r., a stress invariant based spectral method to estimate fatigue life under multiaxial random loading, int j fatigue, 33 (2011) 887–899. [10] carpinteri, a., spagnoli, a., vantadori, s., reformulation in the frequency domain of a critical plane-based multiaxial fatigue criterion, int. j. fatigue, 67 (2014) 55-61. [11] jasper, t.m., the value of the energy relation in the testing of ferrous metals at varying ranges and at intermediate and high temperature, philos mag, 46 (1923) 609–627. [12] ellyin, f., cyclic strain energy density as a criterion for multiaxial fatigue failure, brown, miller, editors. biaxial and multiaxial fatigue, 3. london: egf publication; (1989) 571–83. [13] ellyin, f., fatigue damage, crack growth and life prediction. edmonton: chapman and hall, (1997). [14] macha, e., sonsino, c.m., energy criteria of multiaxial fatigue failure, fatigue fract engng mater struct, 22 (1999) 1053–1070. [15] pook, l.p., sharples, j.k., the mode iii fatigue crack growth threshold for mild steel, int j fract, 15 (1979) r223r226. [16] pook, l.p., the fatigue crack direction and threshold behaviour of mild steel under mixed mode i and iii loading, int j fatigue, 7 (1985) 21-30. [17] tong, j., yates, j.r., brown, m.w., some aspects of fatigue thresholds under mode iii and mixed mode and i loadings, int j fatigue, 18 (1986) 279-285. [18] yu, h.c., tanaka, k., akiniwa, y., estimation of torsional fatigue strength of medium carbon steel bars with circumferential crack by the cyclic resistance-curve method, fatigue fract eng mater, 21 (1998) 1067-1076. [19] tanaka, k., akiniwa, y., yu, h., the propagation of a circumferential fatigue crack in medium-carbon steel bars under combined torsional and axial loadings, in: mixed-mode crack behaviour, astm 1359 (eds kj miller and dl mcdowell), west conshohocked, pa, (1999) 295-311. [20] pippan, r., zelger, c., gach, e., bichler, c., weinhandl, h., on the mechanism of fatigue crack propagation in ductile metallic materials, fatigue fract engng mat struct, 34 (2011) 1-16. [21] christopher, c.j., james, m.n., patterson, e.a., tee, k.f., towards a new model of crack tip stress fields, int j fracture, 148 (2007) 361–371. [22] christopher, c.j., james, m.n., patterson, e.a., tee, k.f., a quantitative evaluation of fatigue crack shielding forces using photoelasticity, eng fract mech, 75 (2008) 4190-4199. [23] berto, f., lazzarin, p., yates, j., multiaxial fatigue of v-notched steel specimens: a non-conventional application of the local energy method, fatigue fract engng mater struct, 34 (2011) 921–943. [24] lazzarin, p., sonsino, c.m., zambardi, r., a notch stress intensity approach to assess the multiaxial fatigue strength of welded tube-to-flange joints subjected to combined loadings, fatigue fract engng mater struct, 27 (2004) 127140. [25] berto, f., lazzarin, p., fatigue strength of structural components under multi-axial loading in terms of local energy density averaged on a control volume, int j fatigue, 33 (2011) 1055-1065. f. berto et alii, frattura ed integrità strutturale, 33 (2015) 229-237; doi: 10.3221/igf-esis.33.29 237 [26] berto, f., lazzarin, p., marangon, c., fatigue strength of notched specimens made of 40crmov13.9 under multiaxial loading, materials and design, 54 (2014) 57-66. [27] berto, f., lazzarin, p., tovo, r., multiaxial fatigue strength of severely notched cast iron specimens, international journal of fatigue, 67 (2014) 15-27. [28] berto, f., lazzarin, p., marangon, c., brittle fracture of u-notched graphite plates under mixed mode loading, mater des, 41 (2012) 421-432. [29] lazzarin, p., campagnolo, a., berto, f., a comparison among some recent energyand stress-based criteria for the fracture assessment of sharp v-notched components under mode i loading, theoretical and applied fracture mechanics, 71 (2014) 21-30. [30] berto, f., lazzarin, p., recent developments in brittle and quasi-brittle failure assessment of engineering materials by means of local approaches, mater sci eng r, 75 (2014) 1-48. [31] berto, f., campagnolo, a., lazzarin, p., fatigue strength of severely notched specimens made of ti-6al-4v under multiaxial loading, fatigue fract eng mater struct, 38(5) (2015) 503-517. microsoft word numero_33_art_20 c. montebello et alii, frattura ed integrità strutturale, 33 (2015) 159-166; doi: 10.3221/igf-esis.33.20 159 focussed on characterization of crack tip fields multi-scale approach for the analysis of the stress fields at a contact edge in fretting fatigue conditions with a crack analogue approach c. montebello, s. pommier lmt (ens cachan / cnrs / université paris saclay) claudio.montebello@ens-cachan.fr, sylvie.pommier@ens-cachan.fr k. demmou, j. leroux, j. mériaux snecma villaroche karim.demmou@snecma.fr, julien.leroux@snecma.fr, jean.meriaux@snecma.fr abstract. this paper describes a novel method to model the stress gradient effect in fretting-fatigue. the analysis of the mechanical fields in the proximity of the contact edges allows to extract nonlocal intensity factors that take into account the stress gradient evolution. for this purpose, the kinetic field around the contact ends is partitioned into a summation of multiple terms, each one expressed as the product between nonlocal intensity factors, is, ia, ic, depending on the macroscopic loads applied to the mechanical assembly, and spatial reference fields, ds, da, dc, depending on the local geometry of the part. this description is obtained through nonintrusive post-processing of fe computation and is conceived in order to be easily implementable in the industrial context. by using as input the macroscopic load, the procedure consists in computing a set of nonlocal stress intensity factors, which are an index of the severity of the stress field in the proximity of the contact edges. this description has two main advantages. first, the nonlocal stress intensity factors are independent from the geometry used. secondly, the procedure is easily applicable to industrial scale fe model.. keywords. fretting fatigue; contact; fatigue. introduction omputational models for fatigue damage analysis in presence of a steep stress gradient still remain poorly effective. this is the case of fretting-fatigue where a local stress concentration is introduced by contacting components experiencing small amplitude relative motion. this phenomenon is a major concern for the aerospace industry, in particular for aircraft engine applications where there are several components that may suffer fretting-fatigue failure like the dovetail blade-root connections. in the last years several fatigue criteria have been developed aiming at improving the accuracy of the fatigue life prediction in the presence of a severe stress gradient. almost all of them can be divided into two major families. on the one hand, the nonlocal stress fatigue models [1, 2] employ an averaged quantity as input for the prediction criterion in order to c c. montebello et alii, frattura ed integrità strutturale, 33 (2015) 159-166; doi: 10.3221/igf-esis.33.20 160 mitigate the effect of the strong stress gradient. on the other hand, a different approach consists in computing the evolution of the stress intensity factors, ∆k, as a function of the crack length to analyse whether the crack will stop or not [3, 4]. even though both the approaches show good results in terms of life prediction accuracy some important limitations make them difficult to implement in the industrial context. for instance, the analysis of the ∆k evolution at the crack tip implies to set up a computational strategy to determine the crack path resulting from the macroscopic load application. this operation is heavily time-consuming. on the other hand, the methods based on an averaged quantity over a critical distance require an accurate description of the stress gradient evolution that is obtainable only by using a really fine mesh (micron size range), condition difficult to reproduce in industrial fem models. model background retting-fatigue is a special damage process that occurs at the contact area between two materials under load and subject to minute relative motion by vibration or some other force. one of the main peculiarities of this phenomenon is the fact that the contact introduces a severe and extremely localized stress gradient in the vicinity of the contact edge. the feature presented above is the same that characterizes cracks or notches where a steep stress gradient is present as well. as a consequence the mechanical fields generated close to the contact edge and the ones arising at the crack tip are comparable. this analogy can be exploited to apply the mathematical tools already developed for fracture mechanics to fretting fatigue. giannakopoulos has been the first author to quantify from an analytical point of view this analogy [5, 6]. two different contact configuration are studied: (i) flat punch over a planar surface which creates a stress singularity at the contact tip (crack analogue) and (ii) round punch over a planar surface characterized by a smooth transition to zero pressure at the contact area edges (notch analogue). among the different approaches available in fracture mechanics one in particular can be really useful to describe the stress gradient effect in fretting-fatigue. an original model has been proposed by pommier [7, 8] aiming at describing mixedmode cyclic elastic-plastic behavior of the crack tip at the global scale. the purpose was to establish a reasonably precise model but condensed into a set of partial differential equations so as to avoid huge elastic-plastic fe computations. the model proposed hereunder exploits the results obtained by giannakopoulos [5, 6] and pommier [7, 8]. a description of fretting-fatigue using nonlocal quantities has been developed. the tools employed to describe the elastic-plastic behavior of the crack tip at the global scale are redefine and adapted to fretting fatigue contact problem via the crack analogue approach. field partitioning the model presented here, is based on the post-treatment of the velocity field generated by fretting-fatigue close to the contact edges. the velocity field is partitioned into a summation of multiple terms, each one expressed as the product between nonlocal intensity factors, is, ia, ic, depending on the macroscopic loads applied to the mechanical assembly, and spatial reference fields, ds, da, dc, depending on the local geometry of the part,              ,     s s a a c cv x t i t d x i t d x i t d x (1) from the practical point of view, the velocity field is obtained through a finite element computation. in fig. 1 an example of a fe model used in the analysis, is presented. a cylinder-plain contact configuration is employed. this choice is driven by the fact that the numerical procedure is validated by comparing it with experimental tests [9-11], carried out with a cylinder-plain apparatus. in other word the fe model needs to be as close as possible to the experimental setting. concerning the main parameters used in the fe model definition, it consists in an elastic quasi-static computation and plane strain linear elastic quadrilateral elements are employed. to handle the contact at the interface, the technique employed is the lagrange multipliers, which assures the best accuracy. to modelling the friction, coulomb’s friction law is employed. with regard to the mesh used, it is a structured mesh characterized by an average length of 5-10 microns. the loads applied to the pad to reproduce fretting-fatigue consist in a constant normal load (p) and a cyclic tangential load (q). a cyclic bulk load (σfa) is applied to the specimen to reproduce the fatigue effect. once the velocity field is computed, the following step is to partition it in order to extract the nonlocal intensity factors. since the most critical zone in fretting-fatigue is situated close to the contact edge, only the value of the velocity field inside a circular region ω, of radius r, centered at the contact tip is retained. f c. montebello et alii, frattura ed integrità strutturale, 33 (2015) 159-166; doi: 10.3221/igf-esis.33.20 161 figure 1: fe model and fretting-fatigue loading variation. to obtain the partition presented in eq. (1), the first step is the determination of the reference fields (da and ds). ds is selected as the field generated by a δp, while da as the one produced by a δq in a situation where all the contact surface is in a stick condition. further details of the procedure followed can be found in [9]. by expressing the reference fields in polar coordinates, their radial and tangential evolution with respect to the crack tip can be obtained.        ,  s s s sd x d r f r g (2)        ,  a a a ad x d r f r g (3) to express the reference fields as a product between two functions depending separately on r and θ, the karhunen-loeve decomposition [10] is employed. figure 2: radial and tangential evolution of ds. in fig. 2 and 3 the radial and tangential evolution of ds and da are presented. clearly the analogy between crack and contact problems is justified. furthermore, both reference fields are normalized in order to correspond to the displacement field obtained at the crack tip during an elastic loading phase with either δki or δkii equal to 1mpa. c. montebello et alii, frattura ed integrità strutturale, 33 (2015) 159-166; doi: 10.3221/igf-esis.33.20 162 figure 3: radial and tangential evolution of da. the projection of the reference fields on the velocity field allows us to extract is and ia as follows:   ˙ ,         ω ω  ns ss i t is i t n s ss s i ii v d v d i t i d dd d (4)   ˙ ,         ω ω  na aa i t ia i t n a aa a i ii v d v d i t i d dd d (5) a first approximation of the velocity field is therefore obtained:          ,   e s s a av x t i t d x i t d x (6) ve is the elastic approximation of the velocity field. since the friction between the contacting bodies introduces a nonlinearity in the system a third term, vc, has to be added to the approximation presented in eq. (6),      , , , c ev x t v x t v x t (7) here, the karhumen-loeve decomposition is used twice: the first time to partition the residual velocity field in a product between two functions depending separately on time and space,            ,   c c c c c cv x t i t d x i t f r g (7) and the second time to analyze the evolution of dc with respect to r and θ, as presented in fig. 4. also in this case the field is normalized in order to assure that fc(r=0) is equal to 1. by contrast with the elastic reference fields, here the intensity decreases quickly far from the contact confirming the extremely localized effect of friction. the error introduced by the approximation can be defined as follows:         2 2 , , ,      ω ω e e v x t v x t ξ t v x t (8)           2 2 , , , ,       ω ω e c t v x t v x t v x t ξ t v x t (9) where e is the error introduced considering just the elastic approximation while in t all the terms presented in eq. (1) are taken into account. in fig. 5 the evolution of the error during a fretting-simulation is shown. it is worth noting that the total error falls below 5 %. c. montebello et alii, frattura ed integrità strutturale, 33 (2015) 159-166; doi: 10.3221/igf-esis.33.20 163 figure 4: radial and tangential evolution of dc. figure 5: error evolution during fretting-fatigue simulation. the maximum of the cumulative integral of the intensity factors rate is computed in order to obtain, ia, is, ic. to resume for any given macroscopic load combination (p, q, σfa), a univocal set of nonlocal intensity factors (ia, is, ic) is found which characterizes completely the stress field close to the contact edge. experimental validation he procedure described in the previous section has been validated by comparing it to the experimental results coming from the work of fouvry [2]. the author performs several plain fretting tests using a cylinder-plain apparatus in order to determine different crack initiation frontiers as a function of the pad radius used. the material employed in the experimental campaign is 35 ni cr mo 16 low-alloyed steel with the following properties: o young’s modulus = 205000 mpa o poisson’s ratio = 0.3 o yeld stress (0.2%) = 950 mpa o ultimate stress= 1130 mpa o traction compression fatigue limit (r=-1, 107 cycles) = 575 mpa o shear fatigue limit (r=-1, 107 cycles) = 386 mpa o long crack threshold, δk0 = 3.2 concerning the test apparatus, the plain fretting tests are carried out using a tension-compression hydraulic system as presented in fig. 6. the normal force (p) is kept constant, while a purely alternating cyclic displacement (δ) is imposed. as a consequence, a cyclic tangential load (q) is generated at the contact surface. after a certain number of cycles, usually 105 or 106, the test is stopped and the specimen is cut along the median axis of the fretting scar in order to verify whether the crack is initiated or not. this procedure is repeated several times to find the tangential load amplitudes (q∗) that provokes crack initiation for a given normal load. here, the crack is considered “initiated” if its projected length is higher than 10 μm. t c. montebello et alii, frattura ed integrità strutturale, 33 (2015) 159-166; doi: 10.3221/igf-esis.33.20 164 to highlight the stress gradient effect, this process is reiterated for different cylinder radii. varying the normal force, the normal pressure (p0) at the contact surface is kept constant and, therefore, the eventual difference in the initiation threshold needs to be caused by different stress gradients generated by the change in geometry. figure 6: schematic representation of a plain fretting apparatus. in fig. 7, the experimental crack initiation frontiers are presented. it is clear that the gradient effect plays an important role. in particular it is evident that the biggest is the pad radius the worst is the effect in term of crack initiation threshold. to interpret this tendency, it is important to notice that two factors influence crack nucleation; (i) the maximum stress at the hot spot and (ii) the material process volume over which the maximum stress operates. the increase in pad dimension extends the influence of contact stress below the surface, and therefore increases the process volume. figure 7: crack initiation frontier for 35nicrmo16 low-alloyed steel. application of the methodology. the steps followed in the application of the numerical algorithm presented above are the followings (fig. 8): 1. the experimental data highlight different crack initiation frontiers expressed in (qmax-p0) coordinates. for each point belonging to these frontiers the macroscopic load to apply in the fe model are computed. for cylinderplain contact configuration, analytical expressions linking qmax-p0 to p and q are available. 2. a fe computation is run and the velocity field is computed. the forces used as input to load the structure are the ones found in the previous step. 3. the velocity field is partitioned as presented in eq. (1). 4. the nonlocal stress intensity factors are extracted and a nonlocal crack initiation map is defined. before to comment the results shown in fig. 8, it is worth noting that only the elastic nonlocal stress intensity factors (iais) are used in the description of the crack initiation frontiers for two reasons. the third term, ic, describe the nonlinear effect of friction, which is extremely localized as confirmed by fig. 4. as a consequence the elastic nonlocal intensity c. montebello et alii, frattura ed integrità strutturale, 33 (2015) 159-166; doi: 10.3221/igf-esis.33.20 165 factors, is and ia, are sufficient to univocally characterize the contact edge stress condition. this approach is analogue to the one followed in fracture mechanics where the hypothesis of small scale yielding permits to use an elastic stress intensity factor, k, to describe the mechanical field close to the crack tip. on the other hand, all the test data are obtained assuring that the contact is in a partial slip regime. as explained by vinsdbo and sodemberg in [11], in this condition the wear rate due to friction is negligible. the outcome of the application of the numerical algorithm to extract nonlocal intensity factors (fig. 8), shows clearly how these quantities are objective quantities through which is possible to take into account the gradient effect efficiently. the different crack initiation frontiers displayed in a classical qmax-p0 crack initiation map, merge into a single one if the nonlocal intensity factors are used. figure 8: different steps in the application of the numerical algorithm. conclusions and prospects n order to apply the methodology described above, it is useful to remember the main challenges that the industrial sector has to handle when the structures are interested by fretting fatigue problems. the first main problem is related to the fact that fretting-fatigue introduces a severe stress gradient at the contact interface that depends on the local geometry of the part. the fatigue life of the part depends on the stress gradient, which in turn depends on the local geometry. as a consequence, if the example of an aircraft engine is considered, the manufacturer has to certify experimentally several parts to show that no catastrophic failures occur. the limitation here is that the certification performed for a given part cannot be used for another part sharing the same properties except for the geometry. this is a big limitation because it forces the manufacturer to multiply the experimental tests to certify all the different components. with the methodology introduced here, we propose a possible solution to this problem. if the nonlocal stress intensity factors are used to describe the mechanical field arising close to the contact edges, the gradient effect is taken into account and the change in geometry is no more a problem. a second important complication is due to the fact that the few multi-axial fatigue criteria suited to be used for fretting fatigue [14], need a really precise description of the stress gradient evolution. the only way to obtain it is by using fe computations characterized by extremely fine meshes. this requirement is not compatible with industrial constraints. the methodology presented here is well-suited for a multi-scale approach. the nonlocal stress intensity factors can be extracted from rough meshes. in addition, since the procedure is not intrusive, it can be easily implemented in industrial procedures. i c. montebello et alii, frattura ed integrità strutturale, 33 (2015) 159-166; doi: 10.3221/igf-esis.33.20 166 the future works will focus on the development of a fatigue criterion that take as input the nonlocal stress intensity factors extracted from the post-treatment of the velocity field. in this way it should be possible to place the position of the crack initiation frontier easily. the second main objective is to apply the procedure to an industrial part. in particular the disc-blade root attachment will be analyzed. the authors acknowledge snecma (safran group) for its financial support, within the irg cognac project framework. references [1] araújo, j., susmel, l., taylor, d., ferro, j., mamiya, e., on the use of the theory of critical distances and the modified wöhler curve method to estimate fretting fatigue strength of cylindrical contacts, international journal of fatigue, 29 (1) (2007) 95-107. [2] fouvry, s., gallien, h., berthel, b., from unito multi-axial fretting-fatigue crack nucleation: development of a stress-gradient-dependent critical distance approach, international journal of fatigue, 62(0) (2014) 194-209. [3] fouvry, s., nowell, d., kubiak, k., hills, d., prediction of fretting crack propagation based on a short crack methodology, engineering fracture mechanics, 75 (6) (2008) 1605-1622. [4] dini, d., nowell, d., dyson, i. n., the use of notch and short crack approaches to fretting fatigue threshold prediction: theory and experimental validation, tribology international, 39(10) (2006) 1158-1165. [5] giannakopoulos, a., lindley, t., suresh, s., aspects of equivalence between contact mechanics and fracture mechanics: theoretical connections and a life-prediction methodology for fretting-fatigue, acta mater, 46(9) (1998) 2955-68. [6] giannakopoulos, a., suresh, s., chenut, s., similarities of stress concentrations in contact at round punches and fatigue at notches: implication to fretting fatigue crack initiation, fatigue fract eng mater struct, 23(7) (2000) 561-71. [7] pommier, s., hamam, r., incremental model for fatigue crack growth based on a displacement partitioning hypothesis of mode i elastic-plastic displacement fields, fatigue & fracture of engineering materials & structures, 30 (7) (2007) 582-598. [8] pommier, s., lopez-crespo, p., decreuse, p.y., a multi-scale approach to condense the cyclic elastic-plastic behaviour of the crack tip region into an extended constitutive model, fatigue & fracture of engineering materials & structures, 32(11) (2009) 899-915. [9] montebello, c., pommier, s., demmou, k., leroux, j., meriaux, j., analysis of the stress gradient effect in frettingfatigue through nonlocal intensity factors, internation journal of fatigue, (2015). [10] loéve, m., probability theory, van nostrand, new york, (1955). [11] vingsbo, o., söderberg, s., on fretting maps, wear, 126(2) (1988) 131-147. microsoft word numero_49_art_41_2309 l. suchý et alii, frattura ed integrità strutturale, 49 (2019) 429-434; doi: 10.3221/igf-esis.49.41 429 focused on new trends in fatigue and fracture fatigue strength of inner knurled interference fit joined by forming and cutting methods l. suchý chemnitz university of technology, institute of design engineering and drive technology, germany reichenhainer straße 70, 09126 chemnitz, germany lukas.suchy@mb.tu-chemnitz.de e. leidich, a. hasse chemnitz university of technology, institute of design engineering and drive technology, germany erhard.leidich@mb.tu-chemnitz.de, alexander.hasse@mb.tu-chemnitz.de t. gerstmann, b. awiszus chemnitz university of technology, institute for machine tools and production processes, germany thoralf.gerstmann@mb.tu-chemnitz.de, birgit.awiszus@mb.tu-chemnitz.de abstract. the joining of machine parts by plastic forming is a common method for transmitting forces and torque. in drive trains, the ‘knurled interference fit’ has a high transmission capacity through the combination of frictional connection and form fit. in the present study, the shaft specimen made of c45 steel is joined with an inner knurled hub made of 16mncr5 casehardened steel. the influence of the joining process parameters on the torsional fatigue strength of the shaft-hub connection is experimentally investigated in this paper. the most important parameter is the chamfer angle of the knurled hub, which determines the rate of strain hardening in the material and differs between the cutting and forming joining processes. this study shows that knurled interference fit connections, joined by forming, achieve a higher fatigue strength and a higher maximum static torque than connections joined by cutting. keywords. inversed knurled interference fit; notch fatigue; joining by plastic forming; high-cycle fatigue testing; torque transmission. citation: suchý, l., leidich, e., hasse, a., gerstmann, t., awiszus, b., fatigue strength of inner knurled interference fit joined by forming and cutting methods, frattura ed integrità strutturale, 49 (2019) 429-434. received: 30.11.2019 accepted: 17.06.2019 published: 01.07.2019 copyright: © 2019 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. introduction knurled interference fit (kif) is a component connection that can be used in various applications, such as torque transmission connections. it combines the friction fit and form fit and creates a permanent part connection with a high power density of transmittable drive torques and axial forces. the connection of the components is established a http://www.gruppofrattura.it/va/49/2309.mp4 l. suchý et alii, frattura ed integrità strutturale, 49 (2019) 429-434; doi: 10.3221/igf-esis.49.41 430 through the axial joining of a harder knurled component into a softer undersized component. while joining, a counter profile is incised by performing a plastic deformation on the surface of the softer component. for decades, the principle of self-forming connections has already been used for joining parts in fine mechanics [1]. thomas [2] investigated a similar component connection back in the late 60s. he estimated the fundamental joining of torque characteristics of the so-called “press fit with discontinuous groove” [2]. not until 8 years ago, various approaches have been proposed to describe the static and cyclic torque and bending load capacity of the kif. bader reported the minimal hardness ratio of 1.8 [3] and developed empirical calculations for several material combinations. further calculations of the static load capacity in studies reviewed by the authors are predicated on the shear failure or equivalent stress of the counter profile [3–6]. some of these studies regard the strain hardening in relation to the shaft chamfer angle φ, which divides the joining process into cutting and forming joining [7]. similar to chip removing processes, a sharp edge (φ = 90°, figure 1b) of the harder knurled machine part cuts a groove into the softer part, forming a chip. in contrast, a chamfered edge (φ < 60°) generates a smooth radial forming process, which leads to a massive local plastic strain and an additional elastic radial pressure due to the young’s-modulus-related spring-back effect. depending on the contact pressure, axial loads can also be transmitted due to friction between the components. concerning the high-cycle fatigue, the calculation approach in [5] is based on the local stress gradient according to the guideline analytical strength assessment (fkm-guideline) [8] in combination with the criterion of maximum shear strain. in [9], the authors of the industrial application of kif in differential gear emphasize the high power density of the connection with simultaneous cost efficiency. in contrast to the introductory literature, the tool part in the present study is a harder hub with an inner-knurled bore hole (fig. 1). the counter-profile formation is carried out on the shaft surface. subsequently, the softer shaft component of the inversed knurled interference fit (i-kif) is subjected to a more advantageous pressure stress state in contrast to the tensile stress portion of the softer component of the kif (radial hub expansion). only the authors in [10] investigated the load capacity and assembling characteristics of i-kif. knurled interference fit with ductile hub knurled interference fit with hardened hub figure 1: geometry and material reversion of knurled interference fit nevertheless, determining the fatigue strength of the kif is challenging and has not yet been fully explored. in the present study, the high-cycle fatigue life of an inversed knurled interference fit (i-kif) is investigated by means of experimental torque fatigue tests. regarding the forming and cutting joining process, existing studies on fatigue strength of pre-strained specimen [11, 12] suggest a higher fatigue strength of the investigated materials. experimental setup he aim of the experimental investigations is to estimate the fatigue limit of the i-kif with steel-steel pairing, distinguishing between the two different joining processes. specimen specification and testing procedure figure 1a-d shows the geometry of the investigated hub specimen made of 16mncr5 case-hardened steel. due to the pulsing axial forming procedure, the knurling is created prior to the heat treatment as described in [6]. the hardness of the shaft specimen made of c45 untreated steel was 233 hv. the connection interference is adjusted by the shaft diameter dos. the slightly oversized shaft shoulder (figure 1c) defines the supporting length of the connection by the parameter lj. table 1 t l. suchý et alii, frattura ed integrità strutturale, 49 (2019) 429-434; doi: 10.3221/igf-esis.49.41 431 summarizes all parameters used in the present study. table 2 lists the material properties of the investigated specimens. according to [13] and [14], cyclic properties for torsion were determined by a standardized tensile test at room temperature figure 1d illustrates the assembled i-kif connection. the joining of the shaft and hub was performed at a joining velocity of vj = 0.5 mm/s. the coaxiality of the parts was guaranteed by the use of a tight tolerated guiding appliance during the joining process. additionally, the diameter of the end shaft section was adjusted for guiding purposes. similar to the conventional kif, the type of joining process was determined by the chamfer angle of the harder joining part. in [10], different hub chamfer angles in ranges of φ = 5° to 90° were examined with the aim of developing an empirical calculation algorithm for the estimation of the joining forces and the torque capacity of i-kif. analogous to the shaft chamfer angle of external knurling, higher hub chamfer angle of i-kif leads to lower joining forces, lower axially transmittable forces and lower maximal torque [10]. a) b) c) d) figure 1: geometry parameters of inner knurled kif, a)-b) hub parameter, c) shaft parameter, d) assembled shaft-hub-specimen after a rest period of 24 hours, the assembled specimen (figure 2b) was mounted on a fatigue test bench and exposed to an alternating harmonic torsional load ( 1r   ) powered by a hydraulic drive (figure 2a). in order to determine the torsional fatigue, the staircase method [15] with the logarithmic load gradation was used. the maximum number of load changes was defined as 107 cycles due to the late fatigue break point of contact-based specimens. a typical thin-walled specimen geometry cannot be implemented because of application related specimen. therefore, the switch-off criterion during testing was the defined loss of torsional stiffness resulting in a turning angle of 2°. afterwards, magnetic crack detection was performed with the aim of reviewing the failure mechanism. only specimen without visible cracks (figure 4c) were rated as a “run out”. a) b) figure 2: a) test bench, b) assembled specimen the fatigue limit estimated according to the method of hück [16] corresponds to 50% reliability. / 0 a f a a d   in this relation, a is the fatigue limit, 0a is the lowest level of the load staircase, and d is the logarithmic interval depending on the standard deviation. values f and a correspond to the sum of events at evaluated staircase levels as well as the multiplication with its ordinal numeral according to [15], [16]. l. suchý et alii, frattura ed integrità strutturale, 49 (2019) 429-434; doi: 10.3221/igf-esis.49.41 432 parameter symbol value hub diameter dih 45 mm hub outer diameter doh 95 mm joining length lj 5 mm hub chamfer angle φ 15°, 90° geometric interference igeo 0.4 mm shaft diameter dos 45.4 mm table 1: geometry parameters of investigated inner knurled interference fit connection yield stress, mpa tensile strength, mpa strain to rapture, % hardness 16mncr5 426 (untreated) 632 (untreated) 26.9 (untreated) 785 hv (case hardened) c45 387 (untreated) 664 (untreated) 25.7 (untreated) 233 hv (untreated) table 2: material properties. results in comparison to the presented references, the maximum joining force (figure 3a) of connections joined by cutting (φ = 90°) is also lower than the one of the formed connection (φ = 15°). in contrast to the cutting method, where material is separated through chip formation, forming methods generate a higher friction force due to higher deflected radial forces. characteristic curve features of the joining forces can be extracted as well as described in [14]. compared to forming joining, for cutting i-kif a higher slope can be determined at the beginning of the joining process (figure 3a). the bend at approx. 1 mm of the stroke represents the pure cutting force. the following increase of the force can be linked to the increasing friction force due to the passive cutting force and growing contact area. (a) (b) figure 3: a) joining forces of cutting and forming i-kifs, b) fatigue test results related to smooth surface of ø45 according to the coulomb friction and the pressure-force-area-expression, the frictional force will grow with stroke. the last section of the joining curve (φ = 90°) corresponds to the pure friction force at fully shaped joining length lj. this force level also corresponds to the maximal axially transmittable force of the connection. l. suchý et alii, frattura ed integrità strutturale, 49 (2019) 429-434; doi: 10.3221/igf-esis.49.41 433 at the end of the joining section at joining length lj the chip folds over (figure 4) and remains a part of the shaft. the lower joining forces of cutting i-kif indicate a lower local plastic strain at the groove root, which leads to lower strain hardening (figure 3a). as reported by lätzer [4], cutting joining of a kif leads to a lower static torsional capacity. it is therefore assumed that both, the lower plastic strain and lower radial residual pressure, affect the cyclic properties of the cutting ikif. a) b) c) figure 4: detected fatigue cracks at the shaft notch, material c45, igeo = 0.4 mm, a) φ =90°, b) φ =15°, c) global cracks. figure 3b compares the results from fatigue testing, where the stress values are related to the smooth shaft surface of ø45 mm. the arrow points represent a run-out specimen related to 107 cycles. below this cycle limit, the depicted points correspond to a failure in the low-cycle fatigue region. the results of the magnetic crack detection show a typical crack propagation of 45° for the applied torsional load (figure 4c). an approximately 14% higher fatigue limit of the strain-hardened test samples (φ = 15°) is observed in comparison to the broaching type (φ = 90°). this is similar to the static torque transmissibility of the i-kif. referring to the fatigue limit of the smooth shaft net area, the estimated high-cycle limits result in a fatigue notch factor of 1.7 for the cutting i-kif, compared to 1.4 for a formed connection according to the german standard for load capacity calculation of shafts and axles din 743 [14]. although a positive effect of plastic pre-strain on fatigue strength was observed in basic research [11], [12] the grain structure evaluation in figure 5 shows similar grain refinement on the surface near the area of both, cutting and forming joining process. therefore, the increase of fatigue limit rather has to be linked to the higher groove pressure of formed knurling. in [14], higher residual pressure stresses were estimated for the presented connection. additionally in figure 5b, the grain structure underneath the surface of the formed shaft knurling shows a stretched pattern, which can also be associated with higher radial pressure. a) b) c) figure 5: grain structure of a) the cut shaft knurling (φ =90°), b) the formed shaft knurling (φ =15°). c) location of grain evaluation conclusion he present work has introduced the experimental investigations of the inversed knurled interference fit, which is a novel connection type for transmitting torque with high power density. by moving away from the pairing conditions of the well-known knurled interference fit (knurled and harder shaft) to the connection of the inner-knurled hardened hub with the softer smooth shaft, beneficial residual compression stresses are achieved in the shaft. the presented results also show the influence of the hub chamfer angle on the high-cycle fatigue of the connection. concerning forming joining, a 14% higher endurance limit was achieved by using a hub chamfer angle of φ = 15° due to higher radial residual t l. suchý et alii, frattura ed integrità strutturale, 49 (2019) 429-434; doi: 10.3221/igf-esis.49.41 434 stresses achieved during the joining process. as a result, not only a higher fatigue limit is achieved but also a higher capacity of axial forces in forming i-kif is reached. despite the limitations of the cutting i-kif, some applications with thin-walled hubs require a small radial expansion, which a forming i-kif cannot perform. in addition, the designing of a hub chamfer angle above φ =15° can lead to less radial stresses due to a better cutting edge. appropriate geometry parameters can therefore be chosen depending on the requirements of the component connection. acknowledgement he authors would like to thank the dfg (german research foundation) , which made the research project no. 249500173 possible. references [1] hildebrand, s. (1980). feinmechanische elemente. berlin: veb verlag technik. [2] thomas, k. (1969). die presspassung mit unterbrochener fuge“, phd-thesis, technische universität hannover. [3] bader, m. (2009). das übertragungsverhalten von pressverbänden und die daraus abgeleitete optimierung einer formschlüssigen welle-nabe-verbindung“, phd-thesis, technische universität graz, graz. [4] lätzer, m. (2016). joining and transmission behaviour of torsional stressed steel-aluminum knurled interference fits“, phd-thesis, technische universität chemnitz, chemnitz, germany. [5] mänz, t., auslegung von pressverbindungen mit gerändelter welle, phd-thesis, technische universität clausthal, clausthal. [6] suchý, l., leidich, e., gerstmann, t. and awiszus, b. (2018). influence of hub parameters on joining forces and torque transmission output of plastically-joined shaft-hub-connections with a knurled contact surface, machines, 6(2). [7] kleditzsch, s., awiszus, b., leidich, e. and lätzer, m. (2015). numerical and analytical investigation of steel– aluminum knurled interference fits: joining process and load characteristics, journal of materials processing technology, 219, pp. 286–294. [8] rennert, r., kullig, e., vormwald, m. and siegele, d. (2012). analytical strength assessment 6.th edition, 6. aufl. forschungskuratorium maschinenbau (fkm), 2012. [9] coban, h., silva, k. m. d., and harrison, d. k. (2009). mill-knurling as an alternative to laser welding for automotive drivetrain assembly, cirp annals, 58(1), pp. 41–44. [10] suchý, l., leidich, e., hasse, a., gerstmann, t. and awiszus, b. (2018). inner knurled interference fit as a further development of the conventional knurled interference fit, in vdi-berichte 2337, stuttgart. [11] ruffing c. et alii (2015). fatigue behavior of ultrafine-grained medium carbon steel with different carbide morphologies processed by high pressure torsion, metals, 5(2), pp. 891–909. [12] kang, m., aono, y. and noguchi, h. (2007). effect of pre-strain on and prediction of fatigue limit in carbon steel“, international journal of fatigue, 29(9), pp. 1855–1862. [13] iso 6892-1, metallic materials—tensile testing—part 1: method of test at room temperature,. geneva: international organization for standardization, (2017). [14] din 743, calculation of load capacity of shafts and axles. din deutsches institut für normung e. v., (2012). [15] din 50100, load controlled fatigue testing execution and evaluation of cyclic tests at constant load amplitudes on metallic specimens and components. (2016). [16] hück, m. (1983). an improved procedure for the evaluation of staircase step tests (german: ein verbessertes verfahren fur die auswertung von treppenstufenversuchen)“, zeitschrift werkstofftechnik, 14, pp. 406–417. t << /ascii85encodepages false /allowtransparency false /autopositionepsfiles true /autorotatepages /none /binding /left /calgrayprofile (dot gain 20%) /calrgbprofile (srgb iec61966-2.1) /calcmykprofile (u.s. web coated \050swop\051 v2) /srgbprofile (srgb iec61966-2.1) /cannotembedfontpolicy /error /compatibilitylevel 1.4 /compressobjects /tags /compresspages true /convertimagestoindexed true /passthroughjpegimages true /createjobticket false /defaultrenderingintent /default /detectblends true /detectcurves 0.0000 /colorconversionstrategy /cmyk /dothumbnails false /embedallfonts true /embedopentype false /parseiccprofilesincomments true /embedjoboptions true /dscreportinglevel 0 /emitdscwarnings false /endpage -1 /imagememory 1048576 /lockdistillerparams false /maxsubsetpct 100 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/hrv (za stvaranje adobe pdf dokumenata najpogodnijih za visokokvalitetni ispis prije tiskanja koristite ove postavke. stvoreni pdf dokumenti mogu se otvoriti acrobat i adobe reader 5.0 i kasnijim verzijama.) /hun 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can be opened with acrobat and adobe reader 5.0 and later.) >> /namespace [ (adobe) (common) (1.0) ] /othernamespaces [ << /asreaderspreads false /cropimagestoframes true /errorcontrol /warnandcontinue /flattenerignorespreadoverrides false /includeguidesgrids false /includenonprinting false /includeslug false /namespace [ (adobe) (indesign) (4.0) ] /omitplacedbitmaps false /omitplacedeps false /omitplacedpdf false /simulateoverprint /legacy >> << /addbleedmarks false /addcolorbars false /addcropmarks false /addpageinfo false /addregmarks false /convertcolors /converttocmyk /destinationprofilename () /destinationprofileselector /documentcmyk /downsample16bitimages true /flattenerpreset << /presetselector /mediumresolution >> /formelements false /generatestructure false /includebookmarks false /includehyperlinks false /includeinteractive false /includelayers false /includeprofiles false /multimediahandling /useobjectsettings /namespace [ (adobe) (creativesuite) (2.0) ] /pdfxoutputintentprofileselector /documentcmyk /preserveediting true /untaggedcmykhandling /leaveuntagged /untaggedrgbhandling /usedocumentprofile /usedocumentbleed false >> ] >> setdistillerparams << /hwresolution [2400 2400] /pagesize [612.000 792.000] >> setpagedevice microsoft word numero 23 articolo 3 g. scirè mammano et alii, frattura ed integrità strutturale, 23 (2013) 25-33; doi: 10.3221/igf-esis.23.03 25 scilla 2012 the italian research on smart materials and mems functional fatigue of niti shape memory wires for a range of end loadings and constraints g. scirè mammano, e. dragoni department of engineering sciences and methods, university of modena and reggio emilia – reggio emilia – italy giovanni.sciremammano@unimore.it abstract. the availability of engineering strength data on shape memory alloys (smas) under cyclic thermal activation (functional fatigue) is central to the rational design of smart actuators based on these materials. test results on smas under functional fatigue are scarce in the technical literature and the few data available are mainly limited to constant-stress loading. since the sma elements used within actuators are normally biased by elastic springs or by another sma element, their stress state is far from constant in operation. the mismatch between actual working conditions and laboratory arrangements leads to suboptimal designs and undermines the prediction of the actuator lifetime. this paper aims at bridging the gap between experiment and reality. four test procedures are planned, covering most of the typical situations occurring in practice: constant-stress, constant-strain, constant-stress with limited maximum strain and linear stress-strain variation with limited maximum strain. the paper describes the experimental apparatus specifically designed to implement the four loading conditions and presents fatigue results obtained from commercial niti wires tested under all those protocols. keywords. sma wires; functional fatigue; constant-stress; constant-strain; limited maximum strain; linear stress-strain variation. introduction hape memory alloys (smas) are increasingly employed to build solid state actuators, characterized by sleek design and outstanding power density. for the rational design of shape memory actuators, a thorough knowledge of the fatigue behaviour of the alloy is needed [1]. since the actuation is always provided by thermal activation of the alloy, the fatigue incurred by the material is called “thermomechanical” or “functional”, implying that material performs mechanical work against the external applied load when heated during the actuation cycle. although the purely mechanical fatigue (i.e. at constant temperature) of shape memory alloys is well established in the technical literature [2], only scanty data exist on the response of these materials to functional fatigue. furthermore, the few papers available on functional fatigue of shape memory alloys are limited to the constant-stress loading condition and cover a very limited number of cycles [3-5]. test methods different from the constant-stress concept were carried out in [6] and [7]. mertmann et al. [6] investigated the stability of the shape memory effect under constant-strain conditions. they observe that memory effect is quickly lost under these conditions accompanied by a general elongation of the specimen. demers et al. [7] tested the functional fatigue of a niti alloy after various thermomechanical training processes based on three steps: “stress-free shape recovery”, “constrained recovery” (constant-strain) and “constant-stress recovery” (assisted-two-way-shape-memoryeffect). the authors have lately started a systematic test campaign on sma wires undergoing realistic functional fatigue cycles [8, 9]. a specific testing machine has been designed and built to implement a variety of loading conditions likely to be s http://www.gruppofrattura.it http://dx.medra.org/10.3221/igf-esis.23.03&auth=true g. scirè mammano et alii, frattura ed integrità strutturale, 23 (2013) 25-33; doi: 10.3221/igf-esis.23.03 26 encountered in practice. test results have been published for three arrangements: constant-stress, constant-strain and constant-stress cycle with limited maximum strain [8, 9]. this paper reviews those results and presents a new experimental set-up to test sma wires under a linear variation of stress and strain. preliminary experimental data obtained under this loading condition are also presented and discussed in comparison with the outcomes of the previous tests. materials and methods characteristic stress-strain tests ypically, a shape memory actuator comprises an active sma element (for example a wire) and a backup element (for example a spring) used to restore the reference position when the sma element is deactivated. the particular load acting on the active element strongly depends on the backup element and on the external load applied to the actuator. fig. 1 illustrates four test conditions in which the stress and the strain in the sma element vary along specific paths representative of what can occur in operation. (a) (b) (c) (d) figure 1: specific tests proposed to characterize the sma wires under functional fatigue: a) constant-stress; b) constant-strain; c) constant-stress with limited maximum strain; d) linear stress-strain cycle. fig. 1a describes the classical constant-stress test, in which the sma element undergoes variable strain under prescribed stress, provided for example by an applied constant load. this test reproduces the situation occurring in an actuator backed up by a constant force and operated under no external load (positioning device). given the material, this test is fully defined by the stress applied to the sma element. fig. 1b describes the constant-strain test, in which the sma element undergoes variable stress under prescribed strain, provided for example by rigid restraints fixing the ends of the sample. this test reproduces the situation in which the actuator is operated in a locked position. given the material, this test is fully defined by the strain imposed to the sma element. fig. 1c describes a constant-stress test with limited maximum strain, in which the sma element undergoes variable strain under prescribed stress but the maximum strain achievable is limited by an external restraint. this test reproduces the t http://www.gruppofrattura.it http://dx.medra.org/10.3221/igf-esis.23.03&auth=true g. scirè mammano et alii, frattura ed integrità strutturale, 23 (2013) 25-33; doi: 10.3221/igf-esis.23.03 27 situation in which an actuator backed up by a constant force works between hard stops. given the material, this test is fully defined by two parameters: the applied stress and the maximum strain. fig. 1d describes a cyclic-stress test, in which the sma element undergoes a linear variation of stress and strain, with the stress level increasing during strain recovery and the maximum strain limited by an external restraint. this test reproduces the situation in which the sma element of an actuator is backed up by a spring (or another sma element) and works between hard stops. given the material, this test is defined by three parameters: the stress-strain slope, the maximum strain, the initial stress at the maximum strain. properties of the tested shape memory alloy to the aim of gathering fatigue data on shape memory materials readily available to the designer, the niti wire smartflex® 150 marketed by saes getters was used throughout the experimental campaign. the wire has a diameter of 0.150 mm, a ni content of 54% by weight and the following transformation temperatures: as = 86°c, af = 94°c, ms = 65°c, mf = 57°c. the stress-strain tensile properties of the wire in the martensitic and austenitic states are presented in [8]. experimental equipment the custom test machine used to apply the stress-strain conditions of fig. 1 is described in detail in [8]. basically, the machine comprises a c-shaped aluminium chassis to which a secondary plastic frame is attached. the upper part of the plastic frame holds the primary load cell to which one end of the sma wire under test is attached through a rigid clamp. the lower end of the sma wire is loaded or constrained as shown in fig. 2, according to the test to be performed. heating of the wire is provided by electric current supplied by an electronic power board. a fan maintains a constant air flow across the wire [8] with the double purpose of reducing the cycle time during cooling (electric power switched off) and improving the uniformity of the temperature along the wire during heating. although the temperature was not measured directly during the tests, a numerical simulation (not reported here) has shown that under the adopted conditions of forced convection the temperature is fairly constant over the wire length. the only regions of significant temperature deviation are the short portions of the wire close to the end crimps in contact with the cooler frame [9]. (a) (b) (c) (d) figure 2: details of the apparatus used to apply the four test conditions of fig. 1: (a) constant-stress; (b) constant-strain; (c) constantstress with limited maximum strain; (d) linear stress-strain cycle. the supplied current and the signals from the sensors (load cell and displacement transducer) are picked up, processed and controlled by a daq board (national instruments usb 6251). the operating parameters are displayed on the graphical user interface developed in labview®, and the sensors signals are stored continuously on disk. in the configuration detailed in fig. 2a, with a loading basked appended to the wire, the machine performs the constantstress test of fig. 1a. by removing the basket and locking the bottom end of the rod as in fig. 2b, the constant-strain test condition of fig. 1b is achieved. by placing a polymer spacer on top of the displacement sensor to function as a hard stop for the loading basket (fig. 2c), the test condition in fig. 1c (constant-stress with limited maximum strain) is performed. the implementation of the test condition “linear stress-strain cycle” (fig. 1d) is shown in fig. 2d. a traditional compression spring, mounted between the frame and an adjusting nut on the sliding rod, provides the backup force on http://www.gruppofrattura.it http://dx.medra.org/10.3221/igf-esis.23.03&auth=true g. scirè mammano et alii, frattura ed integrità strutturale, 23 (2013) 25-33; doi: 10.3221/igf-esis.23.03 28 the wire according to a linear stress-strain variation. the spring rate of the spring controls the slope of the stress-strain path. the equipment accepts springs with internal diameters from 6 mm and free lengths up to 60 mm. the limit maximum strain is adjustable by a flange nut which functions as a hard stop for the rod. another nut provides the desired preload of the spring. the exact preload of the spring is verified by the instrumented aluminum plate, which functions as secondary load cell. it should be noted that in the constant stress test with limited strain and in the linear stress-strain cycle, the stress is strictly constant and, respectively, linearly variable only as long as the moving end of the wire is not in contact with the bottom restraint (hard stop) used to limit the strain. when contact occurs during the cooling phase (power switched off), the stress in the wire decreases with respect to the nominal value because part of the load exerted by the dead load or the spring is partly sustained by the hard stop. no adjustment on the supply current is made to avoid this stress decrease because these test conditions are typical of what actually happens in real-world actuators where the limit positions of the output port are mostly determined by hard-stops. tests under "constant-stress" and "constant-stress with limited max strain" for the tests in constant-stress (both free and with limited maximum strain) the wire coupons were cut from the coil and electrical-type cord end ferrules (http://www.partex.co.uk/cefs.html) were crimped to both ends giving a net test length of 100 mm. each wire was loaded by filling the basket with lead beads until the desired stress in the wire (read by the primary load cell) was achieved. the heating of the wire was provided by sinusoidal current oscillating from zero to a peak value capable of producing the full transformation of the alloy under the cooling conditions adopted. the maximum achievable frequency was limited by the force ripples in the wire produced by the inertia of the moving basket and by full transformation of the alloy (m→a, a→m). the maximum strain rate measured during the constantstress tests ranged between 0.150 s-1 and 0.300 s-1 during activation and between 0.065 s-1 and 0.150 s-1 during relaxation. the tests were terminated automatically at fracture of the sma wire (no current flowing in the sample) or when the sample survived a prescribed number of cycles (5x105). the constant-stress tests with limited maximum strain were carried out for two levels of limit strain: lim = 3%, 4%. further information on the testing procedure is available from [10]. tests under "constant-strain" the constant-strain tests were performed on wire lengths of 100 mm cut from the same coil as the constant-stress tests and mounted on the machine using the same end crimping technique. the prescribed strain (read by the position transducer in fig. 2) was applied to the wire by lowering the restraining cross-head in fig. 2b. the heating of the wire was provided by sinusoidal current oscillating from zero to a peak value capable of producing the full transformation of the alloy under the cooling conditions adopted. the test was terminated automatically at fracture of the sma wire (no current flowing in the sample) or when a prescribed number of cycles (5x105) was endured with no failure. the experimental plan adopted in the test campaign included five strain values (1, 2, 3, 4 and 5%) with three samples per level. more details on the testing procedure are available from [10]. tests under "linear stress-strain variation" using the set-up in fig. 2d, the tests under linear stress-strain variations were carried out by choosing the following three characteristic parameters for each test: the stress-strain slope (controlled by the stiffness of the backup spring), the limit maximum strain (3% and 4% were the selected values) and the pre-stress in the wire before start (controlled by the spring preload). the stress-strain slope and the limit maximum strain remained constant for an entire test run, with each run involving a set of single tests performed for different pre-stresses. the pre-stress in the wire was used as control variable much in the same way as the stress level in the constant-stress tests or the strain level in the constant-strain tests described above. this is not the only way to perform the tests under linear stress-strain variations but it is by far the simplest choice from an experimental point of view and the most realistic from a practical standpoint. experimentally, this procedure allowed the entire set of results for given maximum strain and given stress-strain slope (single backup spring) to be easily collected and readily elaborated with standard statistical methods (see results and discussion). in practical terms, this procedure fits well with the normal stress-strain conditions occurring in real-life actuators where a given backup spring with a particular spring rate fixes the stress-strain slope in the active sma element for its entire life. the tests performed so far derive from a single backup spring (with spring rate kb = 0.62 n/mm) and a limit maximum strain lim = 4%. the pre-stress levels were chosen so as to coincide with the stress levels of the constant-stress tests with the maximum strain (section tests under "constant-stress" and "constant-stress with limited max strain") limited to the same value http://www.gruppofrattura.it http://dx.medra.org/10.3221/igf-esis.23.03&auth=true g. scirè mammano et alii, frattura ed integrità strutturale, 23 (2013) 25-33; doi: 10.3221/igf-esis.23.03 29 lim = 4%. starting from the maximum applied stress in the first test, the stress level was lowered stepwise in the next tests until no fracture in the wire was observed after a life of 5x105 cycles. after accomplishment of the first runout, the staircase method was performed according to the method described in [10]. also in this test, the heating of the wire was provided by a sinusoidal current oscillating from zero to a peak value capable of producing the full transformation of the alloy under the cooling conditions adopted. results and discussion he data of applied stress () and cycles to failure (nf) obtained from the test campaign under constant stress (circles) and constant stress with limited maximum strain (triangles and diamonds for limit strains of 3% and 4%, respectively) are plotted in the semi-log woehler diagram of fig. 3 together with the bilinear interpolation (solid line for constant stress, dotted and dashed lines for limit strains of 3% and 4%, respectively). the interpolations were obtained through statistical treatment of the results according to the accelerated staircase method [11] developed by the japanese society of mechanical engineers (jsme). fig. 3 shows that the inclined part of the woehler’s curves is well represented by straight lines. the slope of the interpolating line is  /log(nf) =101 mpa for the constant-stress test and higher for the constant-stress test with limited maximum strain, which have a common slope  /log(nf) = 245 mpa, regardless of the specific strain limit. these results show that putting a limit, however small, to the maximum strain during constant-stress tests is extremely beneficial to the fatigue life. it is worth noting that limiting the maximum strain to 3% does not produce further advantages because the sloped legs of the woehler's curves in fig. 3 for 3% (dashed line) and 4% maximum strain (dotted line) are very close to each other. this occurrence suggests that a threshold limit strain does exist above which the described life increase is definitely obtained with respect to constant-stress tests with unlimited strain. figure 3: woehler’s diagram with the fatigue results for the constant-stress tests and the tests at constant stress with limited maximum strain (3% and 4%). the distribution of the experimental points in fig. 3 along the horizontal part of the woehler’s curve suggests the existence of a true fatigue limit of the material under constant-stress conditions, both for limited and unlimited maximum strains. this conclusion is supported by the fact that a sample wire which had survived the staircase method (5x105 cycles) was mounted on the machine and cycled again up to one million cycles without any sign of failure. the fatigue limit for the constant-stress tests calculated from fig. 3 for the chosen life (5x105 cycles) is w=101.8mpa. for constant-stress tests with limited maximum strain the fatigue limits estimated by the jsme elaboration is greater here than for the constant-stress conditions and takes up for decreasing limit strain (108.7 and 127.3 mpa for limit strains of 4% and t http://www.gruppofrattura.it http://dx.medra.org/10.3221/igf-esis.23.03&auth=true g. scirè mammano et alii, frattura ed integrità strutturale, 23 (2013) 25-33; doi: 10.3221/igf-esis.23.03 30 3%, respectively). all these fatigue limits are calculated with a confidence level of 50%. quantitatively, the difference between the fatigue limits with limited strain and the fatigue limit at constant-stress is proportional to the difference in strains achieved in the tests under those stresses. fitting the fatigue data for the constant-stress tests with coffin-manson equation, we obtain a fatigue ductility exponent c = 0.4894. this result is very similar to that obtained by laogoudas (0.47÷0.49) in [5] for an niticu alloy. the strength-life (woehler’s) curve in fig. 4 (semi-log diagram) for the constant-strain tests features only the inclined part (the wire failed for all strain levels tested between 1% and 5%) and there is no indication of a strain threshold (strain fatigue limit). the slope of the interpolating line is  /log(nf)=8.28 ( expressed in percent). the functional life can be as low as 7000 cycles (for applied strain of 5%) and never exceeds 19 000 cycles (applied strain of 1%) in the strain range investigated. this outcome confirms that the constant-strain loading condition is much more demanding on the material than the constant-stress test, even though the maximum strains induced in the alloy are of the same order of magnitude in the two tests. fig. 5 shows that the stress induced in the wire during constant-strain cycles decreases exponentially with the number of cycles. the residual stress just before failure falls in the range 400-500 mpa, regardless of the strain applied. dropping of the maximum stress into this range could be adopted as a predictor of incipient fracture of the material undergoing constant-strain functional cycling of whatever amplitude. figure 4: woehler’s diagram with the fatigue results for the constant-strain tests. figure 5: evolution of the maximum stress in the wire under constant-strain loading. tab. 1 compares the preliminary results obtained from the tests under linear stress-strain variation (lines 1, 3, 5, 7, 9, 11, 13, and 15) with the results for the constant-stress test with limited strain (lines 2, 4, 6, 8, 10, 12, 14, and 16). for each line, tab. 1 reports the number of cycles to failure, nf , and, separately for the second cycle after start and for the last cycle before termination, the maximum stress achieved, max, together with the actual minimum (min a), maximum (max m) and differential (sme  = max min) strains measured in the wire. from tab. 1 it is seen that the reference life of 5x105 cycles is achieved only for test 15 under a stress of 82.8 mpa. for the highest stress levels (300, 235 and 170 mpa) the number of cycles to failure is almost the same for both test conditions. the stress-life data from tab. 1 are plotted in fig. 6 as woehler's curves. the dashed line is the same as in fig. 3 for the constant-stress test with maximum strain limited to 4%, while the solid line represents the linear interpolation of the data available so far for the linear stress-strain variation. the inclined legs of both woehler's curves are nearly perfectly superimposed, suggesting that the linear stress-strain variation does not change the fatigue life, for the particular stiffness of the backup spring adopted, with respect to the test under purely constant stress. this behaviour is similar to what was observed from fig. 3 in relation to the negligible effect of the limit strain for the constant-stress tests with limited maximum strain. the ongoing tests will show whether the fatigue limit for the linear stress-strain variation will be different from the constant-stress test for the same limit strain of 4%. http://www.gruppofrattura.it http://dx.medra.org/10.3221/igf-esis.23.03&auth=true g. scirè mammano et alii, frattura ed integrità strutturale, 23 (2013) 25-33; doi: 10.3221/igf-esis.23.03 31 second cycle after start last cycle before termination line test lim (%) p (mpa) nf max (mpa) min a (%) max m (%)  sme (%) max (mpa) min a (%) max m (%)  sme (%) 1 linear stress-strain 4.0 300 4 728 425 0.96 4.03 2.27 370 2.62 3.97 1.35 2 constant-stress 4.0 300 3 579 311 0.57 4.099 23.03 310 2.08 4.08 2.00 3 linear stress-strain 4.0 300 4 597 416 0.97 3.91 2.54 359 2.53 3.93 1.40 4 constant-stress 4.0 300 3 301 311 0.53 4.048 23.07 312 1.99 4.05 1.26 5 linear stress-strain 4.0 235 8193 367 0.76 4.03 2.47 328 1.86 4.02 1.36 6 constant-stress 4.0 235 8 899 241 0.35 4.00 3.25 243 1.15 4.00 2.45 7 linear stress-strain 4.0 235 8 000 380 0.80 4.00 2.40 339 1.91 3.99 2.08 8 constant-stress 4.0 235 6 972 242 0.39 4.03 3.24 243 1.24 4.05 2.41 9 linear stress-strain 4.0 170 18 723 293 0.60 4.00 3.00 267 1.30 3.88 2.58 10 constant-stress 4.0 170 17 693 188 0.35 4.00 3.25 174 0.81 4.00 2.39 11 linear stress-strain 4.0 170 14 673 320 0.61 4.03 3.02 288 1.42 4.02 2.20 12 constant-stress 4.0 170 15 665 178 0.28 4.036 23.32 177 0.80 4.04 2.44 13 linear stress-strain 4.0 105 21 678 248 0.50 4.00 3.10 228 0.94 3.98 3.04 14 constant-stress 4.0 105 500 000 110 0.22 4.00 3.38 109 0.70 4.00 2.50 15 linear stress-strain 4.0 82.8 500 000 221 0.42 3.96 3.54 196 1.08 3.95 3.27 16 constant-stress 4.0 82.8 500 000 85 0.08 3.95 4.27 85 0.39 3.97 3.58 table 1: comparison of fatigue results between the tests under linear stress-strain variation (39 mpa for each percent of strain) with maximum strain limited to 4% and the constant-stress tests with limited maximum strain of 4%. figure 6: woehler’s diagram with the fatigue results for the tests under linear stress-strain variation and maximum strain of 4%. woehler’s curve for the constant stress tests with maximum strain limited to 4% is shown for comparison (dashed line). http://www.gruppofrattura.it http://dx.medra.org/10.3221/igf-esis.23.03&auth=true g. scirè mammano et alii, frattura ed integrità strutturale, 23 (2013) 25-33; doi: 10.3221/igf-esis.23.03 32 conclusions his paper proposes four types of tests to characterize shape memory wires under functional fatigue loading: constant-stress test, constant-strain test, constant-stress test with limited maximum strain, linear stress-strain variation with limited maximum strain. tests carried out on commercial niti wires (0.15 mm saes getters smartflex®) under all four loading conditions have produced interesting results. for the conditions of “constant-stress” and “constant-stress with limited max strain” the stress-life curve on a semi-log diagram is similar to the ordinary metals, with an initial inclined line followed by a final horizontal line that identifies a fatigue limit (at 5x105 cycles). in the “constant-stress with limited max strain test”, the increase of the fatigue limit with respect to the regular constant-stress test is proportional to the difference between the maximum strains. exposure to constant-strain conditions due to overrestraint of the wire promoted by dynamic loading is very detrimental to the fatigue life and should be avoided. preliminary tests under linear stress-strain variation (39 mpa for each percent strain) with limited maximum strain (4%) show a marked reduction of the fatigue limit with respect to constant-stress tests with the same limit maximum strain. interestingly, although the data available so far suggest that the fatigue limit is higher for the constant-stress test, the slope of the inclined part of woehler's curve is almost the same for both test conditions. references [1] spinella, e. dragoni, proc instn mech engrs, part c: j. of mechanical engineering science, 223 (2009) 531. [2] g. eggeler, e. hornbogen, a. yawny, a. heckmann, m. wagner, materials science and engineering a, 378 (2004) 24. [3] l. fumagalli, f. butera, a. coda, j. of materials engineering and performance, 18 (2009) 691. [4] m. mertmann, g. vergani, eur. phys. j. special topics, 158 (2008) 221. [5] d. c. lagoudas, d. a. miller, l. rong, p. k. kumar, smart materials and structures, 18 (2009) 085021. [6] m. mertmann, a. bracke, e. hornbogen, j. de physique, iv c8 (1995) 1259. [7] v. demers, v. brailovski, s. d. prokoshkinb, k. e. inaekyana, materials science and engineering a, 513-514 (2009) 185. [8] g. scirè mammano, e. dragoni, engineering procedia, 10 (2011) 3962. [9] s. j. furst, j. h. crews, s. seelecke, continuum mechanics and thermodynamics, 24 (2012) 485. [10] g. scirè mammano, e. dragoni, functional fatigue of ni–ti shape memory wires under various loading conditions. int. j. fatigue 2012 (in press) http://dx.doi.org/10.1016/j.ijfatigue.2012.03.004 [11] h. nakazawa, s. kodama, statistical research on fatigue and fracture, (1987) 59. appendix 1 nomenclature af austenite finish temperature as austenite start temperature c empirical constants in coffin-manson equation kb spring rate of the backup spring in the test with linear stress-strain variation mf martensite finish temperature ms martensite start temperature nf number of cycles to failure sme shape memory effect (   m  a) s0 initial stress level in the jsme fatigue test method  wire strain a amplitude of total strain cycle a wire strain in the austenitic state lim maximum wire strain in the constant-stress test and in linear stress-strain cycle with limited maximum strain m wire strain in the martensitic state t http://www.gruppofrattura.it http://dx.medra.org/10.3221/igf-esis.23.03&auth=true g. scirè mammano et alii, frattura ed integrità strutturale, 23 (2013) 25-33; doi: 10.3221/igf-esis.23.03 33 max maximum wire strain recorded in the cycle (m) min minimum wire strain recorded in the cycle (a)  shape memory effect ( sme = m  a)  nominal stress applied to the wire max maximum wire stress recorded in the cycle p pre-stress in the wire under the maximum strain in the linear stress-strain cycle w fatigue limit http://www.gruppofrattura.it http://dx.medra.org/10.3221/igf-esis.23.03&auth=true shot peening processes to obtain nanocrystalline surfaces in metal alloys: y. yamakazi, frattura ed integrità strutturale, 48 (2019) 26-33; doi: 10.3221/igf-esis.48.04 26 focussed on “crack paths” isothermal and thermomechanical fatigue interaction in fatigue crack propagation behavior of a low-carbon nitrogen-controlled 316 stainless steel yasuhiro yamazaki chiba university, japan y.yamazaki@chiba-u.jp abstract. in this work, the effect of superimposing of isothermal low cycle fatigue (lcf) loading to the thermomechanical (tmf) fatigue loading on the short crack propagation behavior of low-carbon nitrogen-controlled 316 stainless steel is investigated. the experimental results indicate that the crack propagation path depends on the loading condition; cracks initiate and propagate at grain boundary perpendicular to the loading axis (intergranular mode), which is a relatively weak region, under the in-phase tmf loading and the lcf loading at high temperature. on the other hand, cracks initiate by the transgranular mode under the out-of-phase tmf loading and the lcf loading at middle temperature. the crack growth rate is also affected by the microstructure, i.e., the intergranular crack exhibits higher crack growth rate compared with the transgranular crack. in addition, the crack growth rate is accelerated by the superimposing of the isothermal lcf loading to the tmf loading. the crack growth rate can be predicted according to the summation law of crack growth behavior based on the fatigue j-integral approach taking into account the crack propagation path. keywords. crack growth behavior; short fatigue crack; thermomechanical fatigue, low cycle fatigue citation: yamazaki, y., isothermal and thermomechanical fatigue interaction in fatigue crack propagation behavior of a lowcarbon nitrogen-controlled 316 stainless steel, frattura ed integrità strutturale, 48 (2019) 2633. received: 27.11.2018 accepted: 07.01.2019 published: 01.04.2019 copyright: © 2019 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. introduction ow-carbon nitrogen-controlled 316 stainless steel (316fr) was developed as a structural material for a fast breeder reactor (fbr) plant [1–3]. the characteristics of high-temperature strength, such as the creep strength, have been investigated to apply 316fr to the fbr with high reliability [2-4]. in addition, failure due to creep-fatigue and thermomechanical fatigue (tmf) are critical issues that affect the design and reliability of the primary cooling piping because it undergoes cyclic thermal stress due to the start-up and shut-down of the reactor. since the major part of the component life consists of the crack propagation process in lcf situations, an assessment of the naturally initiated fatigue l y. yamakazi, frattura ed integrità strutturale, 48 (2019) 26-33; doi: 10.3221/igf-esis.48.04 27 crack growth is required for the design of components at high-temperature. therefore, the fatigue crack propagation behaviors and the fatigue strength have been widely investigated under lcf, creep-fatigue and tmf conditions [5–15]. in the high-temperature components, the high-cycle fatigue (hcf) and the low-cycle fatigue (lcf) loadings are often superimposed on tmf loading. the superimposition of hcf or lcf loadings on the tmf loading may lead to lifetime reduction, as recently reported in refs. [16–20]. the large value of tmf (and also lcf) leads to early fatigue crack nucleation compared with that of hcf. therefore, the lifetime of components subjected to tmf is mainly controlled by the propagation process of the naturally-initiated small cracks. the fatigue crack generated by the main tmf loading might be accelerated by hcf/lcf loading even if the amplitude of hcf/lcf loading is smaller than that of tmf loading. based on the abovementioned background, this study deals with how naturally-initiated cracks on smooth specimen surfaces (made of 316fr) propagate under tmf loading combined with isothermal lcf loading. the influence of superimposition of lcf loading on the tmf loading is discussed using the j-integral approach, taking into account the crack propagation path. experimental procedures he material tested in this study is a low-carbon nitrogen-controlled 316 stainless steel (316fr) plate manufactured by hot-rolling. the chemical composition of the tested material is 0.009c-0.55si-0.84mn-0.024p-0.007s-11.25ni17.0cr-2.11mo-0.0751n (mass %). the solution heat treatment was given by keeping the plate at 1050 ˚c for 30 min followed by water quenching. additional heat treatment was applied at 1250°c for 16 h before the hot-rolling process to suppress carbide precipitation by homogenizing the chromium distribution. a solid cylindrical smooth specimen with a diameter of 6 mm and gage section with a length of 16mm was used to study the crack propagation behavior. the surfaces of all specimens were mechanically polished to mirror surface using alumina powders before and after the tests to remove machining marks and the oxide film. the observations and measurements of crack growth behavior were conducted by periodically replicating the specimen surface by using an acetyl cellulose film after cooling to room temperature. the crack growth tests were performed under the following conditions. tmf loading (ip, op): in-phase (ip) and out-of-phase tmf loading. combined in-phase tmf and lcf loading (ipc02, ipc04): 10 cycles of the isothermal-lcf loadings were superimposed on the primary ip cycle at the maximum temperature. the mechanical strain ranges of the superimposed lcf loading were 0.2% (ipc02) or 0.4% (ipc04). isothermal lcf loading (cc1, cc2, pp): the isothermal-lcf loading at the maximum temperature (cc2, cc1) or the middle temperature (pp) of the tmf. the test conditions are summarized in table 1. op ip ipc02 ipc04 cc2 cc1 pp main cycle temperature [°c] max.: 650, min.: 290 650 470 strain range [-] 0.6% strain rate [1/s] 0.0025% 0.01% strain ratio [-] -1 phase angle [°] 180 0 superimposed cycle temperature [°c] 650 strain range [-] 0.2% 0.4% strain rate [1/s] 0.025% strain ratio [-] 1/3 -1/3 table 1: test conditions employed in the experimental campaign t y. yamakazi, frattura ed integrità strutturale, 48 (2019) 26-33; doi: 10.3221/igf-esis.48.04 28 all tests were performed under strain-controlled conditions by means of the tmf testing machine. a triangle waveform was used for both mechanical and thermal cycling. the total strain as the control signal was calculated by adding thermal strain (recorded previously as a function of temperature) to the mechanical strain. results and discussions macroscopic stress-strain response ig. 1 shows typical hysteresis loops observed during the experimental tests. as shown in fig. 1(a) and (d), the ip and op hysteresis loops were asymmetric as a result of temperature dependence on the deformation resistance of 316fr steel. the magnitudes of mean stress were less than 10% of the maximum stress although the mean stresses were negative in ip and positive in op. the stress amplitude was comparable in both hysteresis loops for ip and op, and both loops were symmetrical about the origin. in contrast, hysteresis loops were symmetric under the lcf conditions, as shown in figs. 1(e), (f) and (g). figs. 1(b) and (c) show that the main tmf loops of ipc02 and ipc04 were also asymmetric, and had almost the same shape as the ip loop. however, their stress ranges were smaller than those of ip and were almost comparable to those of cc1 and cc2 conditions. these results suggest that the stress-strain response of the main tmf cycle can be affected by the sub-lcf cycles. the sub-lcf loop of ipc04 had almost the same shape as the cc1 and cc2 loops. inelastic deformation occurred during the sub-lcf cycle of ipc04 (fig. 1(c)). no inelastic deformation occurred in the sub-lcf loop of ipc02, as shown in fig. 1(b). figure 1: stress–strain hysteresis loops observed during different test conditions: (a) ip, (b) ipc02, (c) ipc04, (d) op, (e) cc1, (f) cc2 and (g) pp. crack propagation behavior typical fatigue cracks initiated by means of tmf and isothermal lcf loadings are shown in fig. 2 and the mode of crack propagation is summarized in table 2. the results indicate that the initiation and propagation morphologies of naturally initiated fatigue crack are sensitive to the microstructure and the test temperature. under ip, ipc02, ipc04, cc1 and cc2 conditions, where the tensile loading is applied at high temperature, the cracks initiated and propagated at grain boundary perpendicular to the loading axis. the grain boundary might be a relatively weak region at elevated temperature. on the other hand, under op and pp conditions, where the tensile loading is applied at a lower temperature, the cracks initiated and propagated by the transgranular mode. fig. 3 shows the fatigue crack growth rates under the isothermal lcf loading correlated with the fatigue j-integral range, ∆jf. in particular, the value of ∆jf for surface short crack is evaluated from the following equation [21, 22]: ( ) 2f e f pj f f n a     =   +   (1) -0.2 0 0.2 -200 0 200 (e) cc1 s tr e ss [ m p a ] -0.2 0 0.2 mechanical strain [%] (f) cc2 (b) ipc02 -200 0 200 (a) ip (c) ipc04 -0.2 0 0.2 (g) pp -0.2 0 0.2 (d) op f y. yamakazi, frattura ed integrità strutturale, 48 (2019) 26-33; doi: 10.3221/igf-esis.48.04 29 where ∆σ is the stress range, ∆εe and ∆εp are the elastic and plastic strain range, respectively, and a is the half crack length. in this study, the total crack length, 2a, is defined as the crack length projected on the plane perpendicular to the load axis. morever nf is the cyclic hardening exponent (nf = 0.304 for isothermal lcf loading). f and f(nf) are given by: ( )1.65 1.12 1 1.47 f   = + and ( ) ( )3.85 1 f f f f n f n n n − = + , (2) where λ is the ratio of the crack depth and the surface crack half-length (λ = 0.84 obtained from the fracture surface). for comparison, the fatigue crack growth curve of physically long crack obtained by using compact-tension (ct) and centercracked-tension (cct) specimens is also shown in fig. 3 [5]. the growth rates of naturally initiated short cracks are higher than those of the physically long cracks at a given ∆jf. this experimental evidence indicates the importance of the investigation of naturally initiated short crack growth behavior since the information on the basis of a physically long crack growth rate provides a dangerous evaluation of the reliability to real components. (a) ip (b) op (c) cc1 (d) pp figure 2: typical fatigue cracks on the specimen surface: (a) ip, (b) op, (c) cc1 and (d) pp. ip ipc02 ipc04 cc1 cc2 op pp intergranular mode transgranular mode table 2: propagation modes of fatigue cracks initiated on the specimen surface. figure 3: fatigue crack growth rates under isothermal-lcf conditions correlated with the fatigue j-integral range; the shaded band indicates the fatigue crack growth curve of physically long crack obtained by using ct and cct specimens in ref. [5]. 10 -1 10 0 10 1 10 -8 10 -7 10 -6 10 -5 fatigue j-integral range, δjf [kn/m] c ra c k g ro w th r a te , d a /d n [ m /c y c le ] : pp : cc1 : cc2 ln y=a + b ln x a=-1.54531359e+01 b=1.23241744e+00 9.34146072e-02 |r|=9.93720155e-01 ln y=a + b ln x a=-1.48552481e+01 b=1.08770312e+00 2.90591114e-01 |r|=9.62104128e-01 long crack (ct&cct)* : 550℃ : 600℃ : 650℃ * ref. [5] y. yamakazi, frattura ed integrità strutturale, 48 (2019) 26-33; doi: 10.3221/igf-esis.48.04 30 it can be also found in fig. 3 that the fatigue crack growth rate under the isothermal lcf loading depends on the test temperature; the growth rates at 650°c where the crack exhibits the intergranular propagation mode (cc1 and cc2) are higher than those at 470°c of which the crack growth modes is transgranular (pp). however, the strain rate dependence on the crack growth rate at 650°c is negligible. the crack growth rate at 650°c might be accelerated by the creep effect. when the 316fr is subjected to the creep superimposed fatigue loading, so-called creep-fatigue loading, the creep damages such as cavity nucleation and growth, which are accumulated at the grain boundaries perpendicular to the loading axis, cause the intergranular failure [23]. however, the crack propagates by transgranular mode under pure fatigue condition [24]. empirically, it is well known that the crack growth rate under the creep-fatigue condition can be estimated by the linear summation law consisting of fatigue and creep terms as follows [25, 26]: f c m m f f c c fatigue creep da da da c j c j dn dn dn     = + =  +         (3) where cf, mf, cc and mc are fatigue and creep material constants, respectively, ∆jc is the creep j-integral range, evaluated from following equation for surface short crack [27]; ( )2c c max cj f f n a  =  (4) where σmax is the maximum stress in each cycle, nc is the creep exponent, and ∆ε c is the creep strain range. f and f(nc) are obtained by means of eq. (2). ∆εc can be evaluated from the comparison between the hysteresis loop of creep-fatigue condition and that of fatigue dominant one as shown in fig. 4. it was reviled from the cyclic deformation tests at the various strain rates that the creep deformation was negligible when the strain rate was higher than 0.1%/s. therefore, the hysteresis loop of fatigue dominant condition was obtained at 0.1%/s in this study. fig. 5 shows the comparison between the crack growth rate predicted by using eq. (3) and the experimental data for cc1 and cc2. in the prediction, cf and mf of fatigue terms are obtained from the experimental data under pp condition, and cc and mc of creep terms are obtained from the static creep crack growth test reported in ref. [28]. as shown in fig. 5, the crack growth rates are overestimated when the predictions are made by using eq. (3). takahashi et al. also reported that the static creep crack showed higher growth rates compared with the creep-fatigue one in 316 fr [29]. figure 4: evaluation of the creep strain range from hysteresis loops. figure 5: comparison between the predicted (see eq. (3)) and the measured crack propagation rate for isothermal lcf tests at 650 °c; the dashed lines indicate the range of a factor of 10. fig. 6 shows the fatigue crack growth behaviors under the tmf conditions as a function of ∆jf evaluated by eq. (1), where nf for tmf loadings is 0.426. in fig. 6, the ∆jf for ipc02, ipc04 was calculated by using eq. (1) with ∆σ, ∆εe and ∆εp evaluated from the main tmf hysteresis loop. in this paper, the fatigue crack growth rate for the combined tmf and lcf loadings (ipc02 and ipc04) is defined by crack growth rate per main tmf cycle. for comparison, the fatigue crack -0.2 0 0.2 -200 -100 0 100 200 mechanical strain [%] s tr e ss [ m p a ] : cc1 : cc2 : fatigue dominant condition (rapid loading at 0.1%/s) : cc1 : rapid loading at 0.1%/s 10 -8 10 -7 10 -6 10 -5 10 -4 10 -8 10 -7 10 -6 10 -5 10 -4 predicted crack growth rate [m/cycle]m e a su re d f a ti g u e c ra c k g ro w th r a te , d a /d n [ m /c y c le ] : cc1 : cc2 δεc y. yamakazi, frattura ed integrità strutturale, 48 (2019) 26-33; doi: 10.3221/igf-esis.48.04 31 growth curves related to the isothermal lcf loading are also shown in fig. 6. as shown in fig. 6, scatters of data points are relatively large. however, it can be found that the fatigue crack growth rate under ip condition is almost comparable to those under cc1 and cc2 conditions. also, the growth rate under op condition is nearly the same of pp condition. it can be concluded from these results that the fatigue crack growth rate under simple tmf condition can be estimated from the fatigue crack growth curve under the isothermal lcf condition, taking into account the crack propagation path even if the thermal cycle is applied synchronizing with the strain cycle. it is found in fig. 6 that the growth rate is accelerated by superimposing of the isothermal lcf loading to the main cycle of tmf loading. the effect of such a superimposing on the fatigue crack growth rate will be discussed in the next section. figure 6: fatigue crack growth rates under tmf and combined tmf and lcf conditions correlated with the fatigue j-integral range. estimation of crack growth rate under simple tmf and combined tmf-lcf conditions as shown in fig. 5, the crack growth rates under cc1 and cc2 conditions were overestimated when the predictions are made by using the linear summation law, eq. (3). in the case of tmf cracks, it is more difficult to apply the summation law because the loading rate of the tmf test can not be increased sufficiently due to the limitation of the heating rate synchronizing with the strain rate. therefore, in this study, the crack growth rates are correlated with the fatigue j-integral range, ∆jf, taking into account the crack growth modes. from fig. 3, the following equations may be employed to express the growth rate for the transgranular crack-propagation (pp) or the intergranular one (cc1 and cc2): 7 1.23 7 1.09 1.94 10 for the transgranular crack propagation 3.54 10 for the intergranular crack propagation f fm f f f jda c j dn j − −    =  =    (5) it is also revealed from fig.6 that eq. (5) is applicable to the fatigue crack which propagates under op and ip tmf conditions. the fatigue crack growth rates under combined tmf and lcf conditions are predicted according to the following summation law: ( ) ( ), , f fm m f f main sub f f sub main tmf cycle sub lcf cycle da da da c j n c j dn dn dn     = + =  +         (6) where ∆jf,main and ∆jf,sub are the fatigue j-integral range for the main-tmf cycle and the sub-lcf cycle, respectively, and nsub is the number of sub lcf cycle per main tmf cycle (nsub =10 cycles in this study). the material constants cf and mf are the experimental values depending on the crack propagation modes (see eq. (5)). the prediction results for the combined tmf-lcf loadings as well as for the tmf loadings are shown in fig. 7. it is revealed in fig. 7 that the fatigue crack growth rate under the above test conditions can be predicted by using eqs. (5) and (6) according to the crack propagation modes. 10 -2 10 -1 10 0 10 1 10 -8 10 -7 10 -6 10 -5 fatigue j-integral range, δjf [kn/m] c ra c k g ro w th r a te , d a /d n [ m /c y c le ] : ip : ipc02 : ipc04 : op : measured crack growth curve under cc1 and cc2 conditions : measured crack growth curve under pp condition y. yamakazi, frattura ed integrità strutturale, 48 (2019) 26-33; doi: 10.3221/igf-esis.48.04 32 figure 7: comparison between the predicted (see eq. (5) and (6)) and the measured crack propagation rate for tmf and combined tmf and lcf tests; the dashed lines indicate the range of a factor of 2. conclusions n this paper, the effect of superimposing of sub-cycles under isothermal low cycle fatigue (lcf) loading to a main cycle under thermomechanical fatigue (tmf) loading on the crack propagation behavior of 316fr stainless steel was investigated. the main conclusions obtained are summarized as follows. 1) the stress range of main tmf cycle was affected by the superimposition of sub-cycles of lcf; the stress range for the combined tmf and lcf loading was decreased compared with that for the pure tmf condition at the given strain range. 2) the crack propagation path depends on the loading condition. under the isothermal lcf loading at high temperature and in-phase tmf loading (where the tensile loading is applied at high temperature) the cracks appear to be initiated and propagated at grain boundary perpendicular to the loading axis. on the other hand, under the isothermal lcf loading at the middle temperature and the out-of-phase tmf loading (where the tensile loading is applied at low temperature) the cracks initiated and propagated by means of the transgranular mode. 3) the fatigue crack growth rate was accelerated by superimposing of the isothermal lcf loading to the tmf loading. the crack growth rates could be predicted according to the summation law of crack growth behavior based on the jintegral approach, according to the crack propagation path. references [1] miura, n., nakayama, y., takahashi, y., (2002). development of flaw evaluation guideline for fbr component, nuclear eng. and design, 212, pp. 13-19. [2] nakazawa, t., kimura, h., kimura, k., kaguchi, k. (2003). advanced type stainless 316fr for fast breeder reactor structures, j. of mat. processing tech., 143-144, pp. 905–909. [3] ekaputra, i.m., kim, w.g., park, j-y., kim, e-s. (2016). characterization of the q* parameter for evaluation creep crack growth rate for type 316ln stainless steel, j. of mech. sci. and tech., 30, pp. 3151-3158. [4] takahashi, y., shibamoto, h., inoue, k. (2008). long-term creep rupture behavior of smoothed and notched bar specimens of low-carbon nitrogen-controlled 316 stainless steel (316fr) and their evaluation, nuclear eng. and design, 238, pp. 310–321. [5] fujioka, t., shimakawa, t., miura, n., kashima, k. (1995). development and verification of an evaluation method for creep-fatigue crack propagation in fbr components, asme pvp, 305, pp. 395-402. [6] ueta, m., nishida, t., koto, h., sukekawa, m., taguchi, k. (1995). creep-fatigue properties of advanced 316-steel for fbr structures, asme pvp, 313, pp. 423–428. 10 -8 10 -7 10 -6 10 -5 10 -8 10 -7 10 -6 10 -5 predicted crack growth rate [m/cycle] e x p e ri m e n ta l re su lt , d a /d n [ m /c y c le ] : ip : ipc02 : ipc04 : op i y. yamakazi, frattura ed integrità strutturale, 48 (2019) 26-33; doi: 10.3221/igf-esis.48.04 33 [7] okazaki, m., yamazaki, y. (1999). creep-fatigue small crack propagation in a single crystal ni-base superalloy, cmsx-2: microstructural influences and environmental effects, int. j. of fatigue 21, pp. s79–s86 [8] yoshihisa, e., raman, s.g.s. (2000). thermomechanical and isothermal fatigue behavior of type 316 stainless steel base metal, weld metal, and joint, sci. and tech. of welding and joining, 5, pp. 174-182. [9] takahashi, y., shibamoto, h., inoue, k. (2008). study on creep-fatigue life prediction methods for low-carbon nitrogen-controlled 316 stainless steel (316fr), nuclear eng. and design, 238, pp. 322–335. [10] samuel, k.g., sasikala, g., ray, s.k. (2011). on r ration dependence of threshold stress intensity factor range for fatigue crack growth in type 316(n) stainless steel, mat. sci. and tech., 27, pp. 371-376. [11] babu, m.n., dutt, b.s., venugopal, s., sasikara, g., albert, s.k., bhaduri, a.k. jayakumar, t. (2013). fatigue crack growth behavior 316ln stainless steel with different nitrogen contents, procedia eng., 55, pp. 716-721. [12] hormozi, r., biglari, f., nikbin, k. (2015). experimental and numerical creep-fatigue study of type 316 stainless steel failure under high temperature lcf loading condition with different hold time, eng. fracture mech., 141, pp. 19-43. [13] buss, t.m., hyde, c.j. (2015). cyclic thermomechanical testing of 316 stainless steel, mat. at high temp. 32, pp. 276279. [14] prasad reddy, g.v., nagesha, a. (2017). kannan, r., sandhya, r., laha, k., thermomechanical fatigue behavior of nitrogen enhanced 316ln stainless steel: effect of cyclic strain, int. j. fatigue, 103, pp. 176-184. [15] zhao, l., xu, l., nikbin, k. (2017). predicting failure modes in creep and creep-fatigue crack growth using random grain/grain boundary idealized microstructure meshing system, mat. sci. & eng. a, 704, pp. 274-286 [16] metzger, m., nieweg, b., schweizer, c., seifert, t. (2013). lifetime prediction of cast iron materials under combined thermomechanical fatigue and high cycle fatigue loading using a mechanism-based model, int. j. of fatigue, 53, pp. 58–66. [17] hormozi, r., biglari, f., nikbin, k. (2015). experimental study of type 316 stainless steel failure under lcf/tmf loading conditions, int. j. of fatigue, 75, pp. 153-169. [18] norman, v., skoglund, p., leidermark, d., moverare, k. (2016). the effect of superimposed high-cycle fatigue on thermo-mechanical fatigue in cast iron, int. j. of fatigue, 88, pp. 121–131. [19] fedelich, b., kühn, h.-j., rehmer, b. skrotzki, b. (2016). modeling the lifetime reduction due to the superposition of tmf and hcf loadings in cast iron alloys, procedia structural integrity, 2, pp. 2190–2197. [20] sarkr, a., nagasha, a., parameswaran, p. sandhya, r., laha, k., okazaki, m. (2017). evolution of damage under combined low and high cycle fatigue loading in a type 316ln stainless steel at different temperatures, int. j. of fatigue, 103 28-38. [21] shih, c.f., hutchinson, j.w. (1976), fully plastic solutions and large scale yielding estimates for plane stress crack problems, j. of eng. mat. and tech., 98, pp. 289–295. [22] dowling, n.e. (1977). crack growth during low-cycle fatigue of smooth axial specimens, cyclic stress-strain and plastic deformation aspects of fatigue crack growth, astm stp, 637, pp. 97–121. [23] wada, y., aoto, k. ueno, f. (1997). creep-fatigue evaluation method for type 304 and 316fr ss, international atomic energy agency, 282, pp. 75–86. [24] kato, s., furukawa, t., yoshida, e. (2010) high-cycle fatigue properties of fbr grade type 316ss at elevated temperatures, jaea-research-2010-022. doi: 10.11484/jaea-research-2010-022 (in japanese). [25] taira, s., ohtani, r., kitamura, t., yamada, k. (1979). j-integral approach to crack propagation under combined creep and fatigue condition, j. soc. mat. sci., japan, 28, pp. 414-420 (in japanese). [26] ohtani, r., kitamura, t., abe, m., kuriyama, y., miki (1990). h., surface small crack initiation and growth of heat resisting alloys in creep-fatigue, j. soc. of mat. sci., japan, pp.529-535 (in japanese). [27] ohtani, r., kitamura (1985). on the fatigue life law for smooth specimens at elevated temperatures derived from fracture mechanics law of crack propagation, j. soc. of mat. sci., japan, pp.843-849 (in japanese). [28] koto, h., kaneko, h., takanabe, k., wada, y. (1989). creep-fatigue strength of modified 316 steel, proc. of the 27th symposium on strength of materials at high temperatures, soc. of mat. sci., japan, pp. 51-55 (in japanese). [29] takahashi, h., uno, t., tanaka, k. (2000). evaluation of creep-fatigue crack propagation for 316fr stainless steel welded joints, j. soc. mat. sci., japan, 49, pp. 322-326 (in japanese). microsoft word numero_34_art_6 d. scorza et alii, frattura ed integrità strutturale, 34 (2015) 70-73; doi: 10.3221/igf-esis.34.06 69 focussed on crack paths investigation of mode i fracture toughness of red verona marble after thermal treatment daniela scorza, andrea carpinteri, giovanni fortese, sabrina vantadori, daniele ferretti, roberto brighenti department of civil-environmental engineering and architecture university of parma parco area delle scienze, 181/a, 43124 parma, italy daniela.scorza@nemo.unipr.it abstract. the present paper aims to assess the effect of freeze/thaw cycles on fracture behaviour of a natural stone: the red verona marble. a wide variety of specimen types and methods to determine mode i fracture toughness of natural stones are available in the literature and, in this context, the model originally proposed for plain concrete, i.e. the two-parameter model (tpm), is adopted. such a method is able to take into account the slow nonlinear crack growth occurring before the peak load, typical of quasi-brittle materials, with the advantage of easy specimen preparation and simple test configuration. in the present paper, the atmospheric ageing is simulated by means of thermal pre-treatments consisting of freeze/thaw cycles. experimental tests are carried out using three-point bending single-edge notched (sen) specimens, according to the tpm procedure. the effects of thermal treatment on both mechanical and fracture parameters are examined in terms of elastic modulus and fracture toughness, respectively. keywords. mode i fracture toughness; red verona marble; thermal treatment; two-parameter model. introduction xterior building panelling made in natural stone was widely employed in the past, but it is used even today. one of the materials for such a panelling is the red verona marble, a natural sedimentary stone, composed of limekilns and fine grains, with a colour variation from red to pink. due to its formation, it contains defects such as inclusions and cracks. for such a reason, the evaluation of its mechanical properties is needed in order to ensure suitable safety of marble panelling in service. in particular, fracture toughness is able to describe the material behaviour related to fracture failure [1, 2]. while a singlevalue measure of such a mechanical parameter is appropriate for brittle materials, a resistance-curve (r-curve) is required in the case of quasi-brittle materials, as the red verona marble is, to take into account that fracture resistance increases with crack extension, promoting stable crack growth before the load peak. moreover, the above panelling is directly subjected to atmospheric agents during service life, of both chemical and physical nature, able to produce an ageing of the marble. among the physical atmospheric agents, the temperature variations induced by seasonal range are also included. e d. scorza et alii, frattura ed integrità strutturale, 34 (2015) 70-73; doi: 10.3221/igf-esis.34.06 70 in the present paper, the fracture behaviour of the red verona marble is experimentally examined, focusing the attention on the effects caused by a thermal pre-treatment, consisting in freeze/thaw cycles, on peak failure load and critical stressintensity factor. more precisely, the specimens employed in the experimental campaign are extracted from plates panelling the auditorium of the university campus in parma. such an investigation is here developed in order to understand the parting of a marble plate occurring from the auditorium panelling. a possible cause seems to be the material ageing produced by temperature variations induced by seasonal range. (a) (b) figure 1: (a) specimen geometry mean values and variations; (b) experimental set up of the instron testing machine. the investigations found in the literature are mainly aimed at analysing the influence of thermal pre-treatments, carried out at constant temperature, on fracture failure and toughness of natural stones [3-7] but, to the best knowledge of the present authors, no experimental data regarding the effects of such pre-treatments on the red verona marble fracture parameters are available. recently, the two-parameter fracture model, originally proposed for concrete, has efficiently been employed to determine the critical stress intensity factor of a no-thermally-pre-treated carrara marble [8]. therefore, also for the easiness in specimens preparation and the simplicity of loading configuration, such a model is herein used to evaluate the fracture behaviour of both thermal pre-treated and as-received red verona marble specimens. specimen description and experimental procedure or the experimental tests, we have used 14 red verona marble specimens obtained from the same panel of stone and prepared in the same direction in order to minimize the errors generated due to the sampling. the prismatic specimens, having the geometry shown in fig. 1a, have a notch in the middle cross-section with depth equal to about 9.54mm ± 8%. we consider two cases (as-received and thermal pre-treated specimens) and, therefore, the minimum number of samples according to the indications contained in the uni en 12371 [9] is 14, since at least 7 specimens are needed for each test condition. the specimens tested are as follows: 7 as-received specimens (signed as c0-x), and 7 specimens subjected to 32 thermal cycles (signed as c32-x). the thermal treatments, consisting in freeze/thaw cycles, are regulated by uni 11186 [10]. the specimens are immersed in water at room temperature for 48 hours, in order to ensure a proper imbibition. then, they are subjected to daily thermal cycles, each one to maintain the specimens at a temperature of -28°c for 6 hours and to spend the remaining 18 hours in water at room temperature. according to the uni en 12371 [9], periodic visual analysis of the specimen surface integrity are performed during the thermal cycles in order to assess possible damages caused by the thermal treatments. in the present study, this control has been made every 4 cycles and, on the scale from 0 (undamaged specimen) to 4 (specimen broken into two or more parts), the worst result obtained from our treated specimens is 2, i.e. small crack (<1mm) or detachment of small fragments (<30mm2) have occurred. the specimens are subjected to three-point bending by using an instrom testing machine (fig. 1b). the tests are performed under crack mouth opening displacement (cmod) control by employing a clip gauge with an average speed of 0.05 mm/h and, according to the two-parameter model (tpm) [7], the specimen is unloaded when the load is about 95% of the peak load along the post-peak branch, and subsequently reloaded in order to determine the unloading compliance. f d. scorza et alii, frattura ed integrità strutturale, 34 (2015) 70-73; doi: 10.3221/igf-esis.34.06 71 experimental results rom the analyses of the fracture surfaces of the as-received as well as the thermally pre-treated specimens, we can observe two different types of specimen: (a) the first type, named a-type and related to the as-received specimens (c0-2, c0-4, c0-5, c0-6) and the thermally pre-treated ones (c32-3, c32-4, c32-6), shows wide portion of fe-hydroxides (represented by black crust coating the bioclasts or by refilling of stylolites) embedded in the matrix with allochemical grains on such failure surfaces; (a) the second type, named b-type and related to the as-received specimens (c0-1, c0-3, c0-7) and the thermal pretreated ones (c32-1 and c32-7), shows wide portion of matrix with a packstone texture, with compacted thin-shelled bivalves and interstitial micritic matrix on such failure surfaces. such types have different fracture behaviours, as can be observed from the graphs reported in the figures below, resulting from a statistical analysis of the data of each specimen type. the experimental results regarding the specimens c32-2 and c32-5 are not plotted in the following graphs, since their failure is reached when the material behaves again elastically and, consequently, we are not able to determine the correct value of the peak load and of the corresponding critical stress intensity factor (sif). from fig. 2a, referred to the case of as-received specimens, we can observe that: (i) for small values of the relative crack extension (lower than 10%), the peak load values are greater. this happens for the b-type: the mean value of the peak load is equal to 567.77 n, and its variation is about 3.38%; (ii) for high values of the relative crack extension (greater than 10%), the peak loads obtained from the tests are smaller than the previous ones. this happens for the a-type: the peak load mean value is equal to 310.63 n and its variation is about 24.38%. we can observe that the reduction of the peak load mean value with respect to the first type is about 83%. also the experimental data related to the case of thermally pre-treated specimens are plotted in fig. 2b: in this case, the difference between a-type and b-type is less significant, with a peak load mean value equal to 311.31 n and a variation of about 18.20%. in the case of as-received specimens, fig. 3a shows that: (i) for b-type, the variation of the initial compliance is very small and, therefore, the mean value of the young modulus is equal to 50.02 gpa with ±7.55%; (ii) for a-type, instead, the variation of the initial compliance is more significant and, therefore, the mean value of the young modulus is equal to 46.18 gpa with ±29.44%. in fig. 3b, analogous results are reported for the thermally pre-treated specimens. we can observe that, also in this case, the difference between the two types is less significant than that for the as-received specimens. fig. 3b also shows a sensible variation of the initial compliance and, consequently, the mean value of the young modulus is equal to 34.07 gpa with ±44%. 0 10 20 30 40 relative crack length increment, % 0 200 400 600 800 p e a k l o a d , p m ax [ n ] a-type b-type as-received 567.77 n 310.63 n (a) 0 15 30 45 60 relative crack length increment, % ther. treatment 323.25 n 303.35 n (b) a-type b-type figure 2: peak load against relative crack length increment for: (a) the as-received and (b) the thermal pre-treated specimens. f (a) (b) d. scorza et alii, frattura ed integrità strutturale, 34 (2015) 70-73; doi: 10.3221/igf-esis.34.06 72 1e-005 2e-005 3e-005 4e-005 initial compliance, ci [mm/n] 0 200 400 600 800 p e a k l o a d , p m ax [ n ] 567.77 n 310.63 n as-received (a) a-type b-type 1e-005 4e-005 7e-005 initial compliance, ci [mm/n] 323.25 n 303.35 n ther. treatment (b) a-type b-type figure 3: peak load against initial compliance for: (a) the as-received and (b) the thermal pre-treated specimens. 0 10 20 30 40 relative crack length increment, % 0.0 0.5 1.0 1.5 2.0 c ri tic a l s if , k s ic [ m p a m 1 /2 ] 1.45mpam1/2 0.99mpam1/2 as-received (a) 0 15 30 45 60 relative crack length increment, % 1.22mpam1/2 0.85mpam1/2 ther. treatment (b) figure 4: critical sif against relative crack length increment for: (a) the as-received and (b) the thermal pre-treated specimens. the different mechanical behaviour of the two specimen types can also be observed in terms of critical stress intensity factor (sif) values. for the as-received specimens, fig. 4a shows that: (i) in the case of b-type, the critical sif, sick , reaches higher values with a small scatter of data. the critical sif mean value is equal to 1.454 mpa m , and its variation is about 7.02%; (ii) in the case of a-type, the critical sif, sick , reaches values significantly smaller than the previous ones, and the scatter of data is greater. the critical sif mean value is equal to 0.990 mpa m , and its variation is about 22.27%. the reduction of the critical sif with respect to the first specimen type is about 32%. in fig. 4b, analogous results are plotted for thermally pre-treated specimens, and we can observe that: (i) for b-type, the critical sif, sick , reaches again higher values, but with a larger variation of the corresponding relative crack extension. the critical sif mean value is equal to 1.223 mpa m , and its variation is about 2.58%; (ii) for a-type, the critical sif, sick , reaches values significantly smaller than the previous ones. the critical sif mean value is equal to 0.848 mpa m , and its variation is about 21.52%. the reduction of the critical sif with respect to the first specimen type is about 38.8%. (a) (a) (b) (b) d. scorza et alii, frattura ed integrità strutturale, 34 (2015) 70-73; doi: 10.3221/igf-esis.34.06 73 conclusions rom the above tests on as-received specimens, we have obtained a peak load equal to 420.84 ± 147.93 n, a young modulus equal to 47.83 ± 10 gpa, and a fracture toughness equal to 1.189 ± 0.299 mpa m . then, from the tests on the thermal pre-treated specimens, we have obtained a peak load equal to 311.31 ± 56.67 n, a young modulus equal to 34.07 ± 15.27 gpa, and a fracture toughness equal to 0.998 ± 0.243 mpa m . the degradation of the red verona marble mechanical properties due to the thermal cycles is evident, and can be quantified in terms of mean values: the peak load reduction is equal to about 26%, the young modulus reduction is equal to about 28.77%, and the fracture toughness reduction is about 16%. moreover, for the first specimen type (a-type), the presence of wide portion of fe-hydroxides: (i) eases the stable crack growth behaviour related to its petrographic nature; (ii) induces dispersion of results in terms of initial compliance and, therefore, of elastic modulus, such a behaviour being connected to its chaotic dispersion inside the matrix. on the other hand, the second specimen type (b-type) is characterised by wide portions of material with allochemical grains. such portions: (i) partially inhibit the stable crack propagation, such a behaviour being related to its petrographic nature; (ii) produce a mechanical behaviour rather constant in terms of initial values of compliance and, therefore, of elastic modulus, such an attitude being connected to its rather homogeneous distribution inside the matrix. references [1] astm e 399-90 (reapproved 1997). annual book of astm standards, vol. 03.01: metals-mechanical testing; elevated and low-temperature tests; metallography (astm, west conshohocken, pennsylvania, usa, 2001). [2] zuo, j., xie, h., dai, f., ju, y., three point bending test investigation of the fracture behaviour of siltstone after thermal treatment, int. j. rock mech. min. sci., 70 (2014) 133–143. [3] ouchterlony, f., review of fracture toughness testing of rock, sm arch., 7 (1982) 131–211. [4] whittaker, b.n., singh, r.n., sun, g., rock fracture mechanics: principles, design and applications. elsevier science ltd, oxford, uk, (1992). [5] isrm testing commission (co-ordinator: ouchterlony, f.) suggested methods for determining the fracture toughness of rock, int. j. rock mech. min. sci. geomech. abstr., 25 (1988) 71–96. [6] isrm testing commission (co-ordinator: fowell, r.j.) suggested methods for determining mode i fracture toughness using cracked chevron notched brazilian disc specimens. int. j. rock mech. min. sci. geomech. abstr., 32 (1995) 57–64. [7] jenq, y., shah, s., two parameter fracture model for concrete, j. eng. mech., 111 (1985) 1227–1241. [8] spagnoli, a., ferrero, a.m., migliazza, m., a micromechanical model to describe thermal fatigue and bowing of marble, int. j. solids struct., 48 (2011) 2557–2564. [9] uni en 12371:2010, from en 12371: natural stone test methods: determination of frost resistance, (2010). [10] uni 11186:2008: beni culturali materiali lapidei naturali ed artificiali metodologia per l'esposizione a cicli di gelo e disgelo, (2008). f microsoft word numero_33_art_41 a. carpinteri et alii, frattura ed integrità strutturale, 33 (2015) 376-381; doi: 10.3221/igf-esis.33.41 376 focussed on multiaxial fatigue time and frequency domain models for multiaxial fatigue life estimation under random loading andrea carpinteri, andrea spagnoli, camilla ronchei, sabrina vantadori dipartimento di ingegneria civile, dell’ambiente del territorio e architettura, università di parma spagnoli@unipr.it abstract. engineering structures and components are often subjected to random fatigue loading produced, for example, by wind turbulences, marine waves and vibrations. the methods available in the literature for fatigue assessment under random loading are formulated in time domain or, alternatively, in frequency domain. the former methods require the knowledge of the loading time history, and a large number of experimental tests/numerical simulations is needed to obtain statistically reliable results. the latter methods are generally more advantageous with respect to the time domain ones, allowing a rapid fatigue damage evaluation. in the present paper, a multiaxial criterion formulated in the frequency-domain is presented to estimate the fatigue lives of smooth metallic structures subjected to combined bending and torsion random loading. a comparison in terms of fatigue life prediction by employing a time domain methods, previously proposed by the authors, is also performed. keywords. multiaxial fatigue. critical plane approach. random loading. frequency-domain. winde-band spectrum. introduction he design of engineering structures subjected to cyclic loading characterized by randomly varying amplitudes is a complex and critical issue, which becomes even more complex in the case of multiaxial loading. in such a case, the procedures usually employed in the fatigue assessment of structural components are formulated in time domain or, alternatively, in frequency domain. the former procedures usually represent a generalisation of their counterparts for constant amplitude loading, by introducing a cycle counting method (e.g. rainflow method) and a damage model (e.g. the miner rule) [1-5]. some criteria present specific cycle counting methods to resolve multiaxial loading histories into individual cycles (e.g. see refs [2, 6]). the knowledge of the time histories of the local stress or strain tensor components, experimentally measured on the structural component, is required, and many records are needed in order to obtain reliable statistical parameters of the loading process. frequency-based procedures, instead, require the knowledge of cycle distribution of random loading from a statistical point of view: as a matter of fact, starting from the (psd) power spectral density function of local stress or strain tensor components, an estimation of damage is directly obtained [7-10]. in the present paper, a stress-based critical plane criterion formulated in the frequency-domain is proposed to evaluate the fatigue lives of smooth metallic structures subjected to multiaxial random loading. it consists of the following three steps: (i) definition of the critical plane; (ii) psd evaluation of an equivalent normal stress; (iii) determination of fatigue life. more precisely: (i) the critical plane is proposed to be dependent on the psd matrix of the stress tensor; (ii) on such a verification plane, the psd of an equivalent stress is defined by a linear combination of the psd functions of both the t http://www.gruppofrattura.it/pdf/rivista/numero33/audioslides/spagnoli2/sp2.html a. carpinteri et alii, frattura ed integrità strutturale, 33 (2015) 376-381; doi: 10.3221/igf-esis.33.41 377 normal stress and shear stress, the latter projected along the direction that maximises the variance of such a stress; (iii) the psd of the above equivalent stress is used to estimate damage, and hence to determine fatigue life of the structural component via the tovo-benasciutti method [11]. the frequency-based criterion being presented is applied to combined bending and torsion random fatigue test data [12], which are also compared with the results determined by employing the time-domain criterion proposed in refs [4,5]. critical (verification) plane orientation he verification plane orientation, named critical plane, is here assumed to be dependent on the psd matrix of the stress vector [13], as is explained in the following. let us assume that: (i) the random features of the stress tensor,  xyz 1 2 3 4 5 6( ) t t s , s , s , s , s , ss , defined with respect to the fixed frame pxyz (being p a point of the structural component), can be described by a six-dimensional ergodic stationary gaussian stochastic process with zero mean values; (ii) the corresponding psd functions are known. the coefficients of the psd matrix, xyz ( )s , are given by: , , 1 ( ) ( ) 2 i i j i js r e d          , 1, 6i j   (1) where , ( )i jr  are the autoand cross-correlation functions and  is the angular frequency. the psd matrix with respect to a rotated coordinate system px'y'z' can be defined by employing the xyz ( )s matrix and a rotation matrix c depending on the three rotation euler angles , ,   . in such a coordinate system, the corresponding stress tensor components and psd coefficients are indicated as 'is and ', ' ( )i js  , with ', ' 1, 6i j   . the above axes are made to vary as follows: the direction z' (defined by the angles ,  ) is such that 3's experiences the maximum in a statistical sense, according to davenport [14]: 3' 0 0 0 0 0.5772 max ( ) 2 ln( ) 2 ln( )t t e s t t t             (2) being 0 the spectral moment of order 0 of the psd function 3',3's , 0  the expected rate of mean zero-upcrossings of 3's and t the observation time interval. the y' axis (defined by the angle  ) is made to vary in order to maximize the variance of 6 's : 26 ',6 ' 6 ',6 ' 0 2 0 2 ( , )max max s d                          (3) the directions z' and y' are regarded as the averaged principal directions 1̂ and 3̂ , respectively. then, the normal to the critical plane, w , is defined in the 1̂ 3̂ plane by the off-angle  (clockwise rotation), function of the ratio between fully reversed shear fatigue limit and normal stress fatigue limit: 2 , 1 , 1 3 1 8 af af                 (4) psd evaluation of the equivalent normal stress et us define the psd matrix with respect to a coordinate system puvw , where u and v belong to the critical plane and w is the normal to the critical plane. in such a coordinate system, the corresponding stress tensor components and psd coefficients are indicated as is  and , ( )i js   , with '', '' 1, 6i j   . the axes u and v are made to vary in the critical plane in order to maximize the variance of 6s  : t l a. carpinteri et alii, frattura ed integrità strutturale, 33 (2015) 376-381; doi: 10.3221/igf-esis.33.41 378 26 '',6 '' 6 '',6 '' 0 2 0 2 ( , )max max s d                          (5) being  a counterclockwise rotation about the w -axis. in order to reduce the multiaxial stress state to an equivalent unixial stress state, we propose to determine an equivalent psd function through the following linear combination: , 1 3 ,3 6 ,6 , 1 af eq af s s s                  (6) fatigue life evaluation for random loading et us consider the equivalent psd function related to an equivalent unixial stress state, that is, to a onedimensional stochastic process. in such a case, the expected fatigue damage per unit time,  e d , may be evaluated by employing the following linear cumulative damage rule:   1 0 ( )ka ae d c s p s ds   (7) being a and ( )ap s the expected rate of occurrence and the marginal amplitude distribution of the counted equivalent stress cycles, respectively, whereas k and c are the parameters of the normal stress s-n curve. note that damage estimation depends on the algorithm used to count loading cycles, that is, it is related to the method adopted to estimate the marginal density ( )ap s . let us consider the rain-flow counting (rfc) procedure [15]. for rfc methods, an analytical solution for ( )ap s is not available in the literature and, therefore, tovo and benasciutti [11] addressed the problem of the rfc damage estimation as the search for the proper intermediate value between the lower and the upper bounds of  rfce d . by taking as counting variable an equivalent uniaxial stress having the psd function eqs proposed in eq.(6), the expected fatigue damage  rfce d and the fatigue life calt are hereafter evaluated. in particular, by considering a critical damage equal to the unity, the calculated fatigue life, calt , is:   1 cal rfc t e d  (8) experimental applications he criterion proposed is hereafter applied to some results of fatigue tests on round specimens made of 10hnap steel, subjected to a combination of random proportional bending and torsion [12]. such a steel presents a finegrained ferritic-pearlitic structure, and its mechanical properties are as follows: tensile strength mr = 566 mpa, yield stress er = 418 mpa, young modulus e = 215 gpa, poisson ratio  = 0.29. the adopted fatigue properties are: normal stress fatigue limit (under fully reversed bending) af = 358.0 mpa at 6 0 1.282 10n   cycles [12], shear stress fatigue limit (under fully reversed torsion) af = 182.0 mpa at 6 0 1.282 10n   cycles [12], inverse slope of normal stress s-n curve (under push-pull) k = 9.82 [4] (for af = 358.0 mpa at 6 0 1.282 10n   cycles c = 1.54(10)31 mpa9.82. ). stationary and ergodic random loading applied to the above specimens presents zero expected value, normal probability distribution and wide-band frequency spectrum (0-60 hz). the high-cycle fatigue tests here examined are related to two combinations of proportional torsional, ( )tm t , and bending, ( )bm t , moments, namely: 21 specimens for / 8  , and 14 specimens for / 4  (fig. 1). for each specimen, the fatigue life texp is experimentally determined. l t a. carpinteri et alii, frattura ed integrità strutturale, 33 (2015) 376-381; doi: 10.3221/igf-esis.33.41 379 m mb  mt 8 90 30 r 45 12.7 30 figure 1: fatigue tests on round specimens (10hnap steel): torsion and bending. the 35 specimens tested under multiaxial loading are analysed in the following by employing the actual experimental loading histories, which are characterised by a sampling frequency of 266.67 hz and a total duration of 184.32 s [12]. then, the theoretical procedure presented in the previous sections is applied to such experimental data, and the fatigue life calt is computed. the comparisons between experimental data and theoretical evaluations are illustrated in figs 2 and 3, where the solid line indicates calt = texp , the dashed lines correspond to /cal ext t p equal to 0.5 and 2 , and the dashdot lines correspond to /cal ext t p equal to 0.3 and 3. a good agreement for the fatigue loading examined can be observed. t ca l , [c y c le s ] texp , [cycles] 105104102 106 107 102 103 104 105 106 = 8 103 107 t ca l , [c yc le s] texp , [cycles] 105104102 106 107 102 103 104 105 106 = 4 103 107 figure 2: comparison between experimental and theoretical fatigue lives ( / 8  ). figure 3: comparison between experimental and theoretical fatigue lives ( / 4  ). the comparisons presented in figs 2 and 3 seem to be quite satisfactory, with 63% of the fatigue life calculation results included into the scatter band with coefficient 2, whereas 66% of such results are included into the scatter band with coefficient 3. the theoretical results based on the frequency domain approach are also compared with those determined by the timedomain criterion proposed in ref. [4] (figs 4-5). note that the results here presented based on the time-domain criterion (based on a non-linear damage accumulation rule) are slightly different from those shown in ref. [4], due to the different value adopted for the normal stress fatigue limit (in ref. [4], af = 225.0 mpa related to push-pull loading was adopted). a. carpinteri et alii, frattura ed integrità strutturale, 33 (2015) 376-381; doi: 10.3221/igf-esis.33.41 380 it can be observed that better results are derived by applying the new formulation, which has also the capability to be more computationally-efficient than that based on the time domain. t ca l , [c y c le s] texp , [cycles] 105104102 106 107 102 103 104 105 106 = 8 103 107 time frequency t ca l , [c yc le s] texp , [cycles] 105104102 106 107 102 103 104 105 106 = 4 103 107 time frequency figure 4: comparison between experimental and theoretical fatigue lives ( / 8  ), the latter determined by employing: the frequency domain criterion here proposed (see solid symbols) and the time domain criterion reported in ref. [4] (see hollow symbols). figure 5: comparison between experimental and theoretical fatigue lives ( / 4  ), the latter determined by employing: the frequency domain criterion here proposed (see solid symbols) and the time domain criterion reported in ref. [4] (see hollow symbols). conclusions frequency domain criterion is presented to evaluate the fatigue life of a smooth metallic structure subjected to multiaxial random loading. the critical plane orientation is determined through the psd matrix of the stress tensor. then, an equivalent psd function is defined and processed through a damage model in order to determine the fatigue life of the structural component being examined. the comparison between theoretical and experimental results appears to be quite satisfactory for the cases analysed. references [1] lagoda, t., macha, e., estimated and experimental fatigue lives of 30crnimo8 steel under in-phase and out-of-phase combined bending and torsion with variable amplitudes, fatigue fract. engng mater. struct., 17 (1994) 1307-1318. [2] wang, c.h., brown, m.w., life prediction techniques for variable amplitude multiaxial fatigue part 1: theories, j. eng. mater. technol., 118 (1996) 367-370. [3] lagoda, t., macha, e., nieslony, a., muller, a., comparison of calculation and experimental fatigue lives of some chosen cast irons under combined tension and torsion, in: m. fuentes et al. (eds.), proceedings of ecf13 application and challenges, elsevier, san sebastian, spain, (2000) 6 pages. [4] carpinteri, a., spagnoli, a., vantadori, s., a multiaxial fatigue criterion for random loading, fatigue fract. engng mater. struct., 26 (2003) 515-522. [5] carpinteri, a., spagnoli, a., vantadori, s., fatigue life estimation under multiaxial random loading using a critical plane-based criterion, in: proceedings of the 2nd int. conference on material and component performance under variable amplitude loading, darmstadt, germany, (2009) 475-484. a a. carpinteri et alii, frattura ed integrità strutturale, 33 (2015) 376-381; doi: 10.3221/igf-esis.33.41 381 [6] bannantine, j.a., socie, d.f., a variable amplitude multiaxial fatigue life prediction method, in: k.f. kussmaul, d.l. mcdiarmid, d.f. socie (eds.), fatigue under biaxial and multiaxial loading, esis publication 10, london, (1991) 3551. [7] pitoiset, x., preumont, a., spectral methods for multiaxial random fatigue analysis of metallic structures, int. j. fatigue, 22 (2000) 541–550. [8] lagoda, t., macha, e., nieslony, a., fatigue life calculation by means of the cycle counting and spectral methods under multiaxial random loading, fatigue fract. engng mater. struct., 28 (2005) 409–420. [9] cristofori, a., benasciutti, d., tovo, r., a stress invariant based spectral method to estimate fatigue life under multiaxial random loading, int. j. fatigue, 33 (2011) 887–899. [10] carpinteri, a., spagnoli, a., vantadori, s., reformulation in the frequency domain of a critical plane-based multiaxial fatigue criterion, int. j. fatigue, 67 (2014) 55-61. [11] benasciutti, d., tovo, r., comparison of spectral methods for fatigue analysis in broad-band gaussian random processes, probab. eng. mech., 21 (2006) 287-299. [12] achtelik, h., bedkowski, w., grzelak, j., macha, e., fatigue life of 10hnap steel under synchronous random bending and torsion, in: proceedings 4th int. conference on biaxial/ multiaxial fatigue, esis publication, paris, (1994) 421-434. [13] pitoiset, x., rychlik, i., preumont, a., spectral methods to estimate local multiaxialfatigue failure for structures undergoing random vibrations, fatigue fract. engng. mater. struct., 24 (2001) 715-727. [14] davenport, a.g., note on the distribution of the largest value of a random function with application to gust loading, in: proceedings institution of civil engineers, 28 (1964) 187-196. [15] anthes, r.j., modified rainflow counting keeping the load sequence, int. j. fatigue, 19 (1997) 529-535. microsoft word numero_55_art_20_2960 b. sunil et alii, frattura ed integrità strutturale, 55 (2021) 271-277; doi: 10.3221/igf-esis.55.20 271 effect of the intermediate quenching on fracture toughness of ferritemartensite dual phase steels b. sunil department of mechanical engineering, siddaganga institute of technology,tumakuru, vtu-belagavi, india sunilb@sit.ac.in s. rajanna department of mechanical engineering, government engineering college, kushalnagar, vtu-belagavi, india rajanna.cit@gmail.com abstract. the main aim of the research work is to examine the fracture toughness of the dual phase steels prepared using the intermediate quenching method. the ferrite-martensite dual phase (dp) steel is produced using low carbon micro alloyed steel by the heat treatment and intercritical quenching technique using various intercritical temperatures such as 740,760,780,800 and 820oc. the samples of the produced dual phase steel are analyzed for their microstructure using optical microscope. the fracture toughness investigations for the dual phase steel have been carried out using astm standard testing procedure. from the results it is observed that the fine distribution and equal volume fraction of ferrite and martensite phases at 780oc. the effect of which, the a780 steel has demonstrated excellent fracture toughness which is the result of intermediate quenching technique. the fractography analysis it is clear that the ductile initiated brittle fracture is occurred which is due to the increased hard martensite phase and the increment in the stress accumulation at the ferrite which also leads to the higher elongation. keywords. martensite; ferrite; intercritical temperature; volume fraction; dual phase steel; fracture toughness. citation: sunil, b., rajanna, s., thermal effect of the intermediate quenching on fracture toughness of ferrite-martensite dual phase steels, frattura ed integrità strutturale, 55 (2021) 271-277. received: 03.12.2020 accepted: 18.12.2020 published: 01.01.2021 copyright: © 2021 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. introduction he steel grades of properties such as high strength, strong, safe, economic and reliable are used as the steel structures for automobile, aerospace components. from last two decades many researchers have developed many grades of steel such as high strength steels (hss) [1] to fulfill the demands of the automobile industries on safety and reduced weight. the high strength steels are the new interested and exploring area for research for many of the researchers for its advanced capabilities. because of cost effectiveness and light weight of hss, these are used for the manufacture of automobile body and chassis. hence, extensive research has to be carried out to develop its optimized microstructure for improved structural integrity and mechanical performance. by utilizing the suitable characterization methods, it is possible to optimize and comprehend the micro-structural constituents on the fracture behavior and its performance. the limited t https://youtu.be/k24shmryuyw b. sunil et alii, frattura ed integrità strutturale, 55 (2021) 271-277; doi: 10.3221/igf-esis.55.20 272 ductility of high strength steel in contrast with the mild steel has increased the cracking issues were not possible to characterize using the conventional uniaxial tensile test experimentation. in this perspective, fracture mechanics based evaluation of the hss will give the more understanding of the fracture behavior of the material related the crack initiation and resistance to crack propagation [2]. from the works of yoon et al. [2] and casellas et al. [3] worked on the high strength steel sheets and observed that the correlation between the edge crack resistance and fracture toughness of the material. the same methodology has been further investigated for the edge formability of dual phase and complex phase steel [4-5] for their resistance to crack propagation. such high strength steel, which is fulfill the requirements of increased ductility, high initial strain hardening rate, high strength with high formability attributes [6] is the dual phase (dp) steel. dp steel suits the strength and ductility requirements as its phases consists of ferrite and martensite. research also shows, dual phase steels are considered as metallic composite due to its composite microstructure, have the special characteristics like high strength and ductility properties, excellent formability [7], light weight [8-9], continuous yielding behavior, uniform plastic deformation, better work hardenability, ease of welding [10-11]. with these properties, dual phase steels are considered to be attractive and potential material for the use in automobile and structural industries. dual phase steels are produced, in a simple and easy way, by the intercritical heat treatment method also referred as intermediate quenching (iq) method [12-13] from the low carbon micro alloy steels. the low carbon micro alloyed steels were heated to the austenization temperature followed by the rapid quenching where it forms the martensite phase. the quenched samples were further intercritically annealed [14] for the shorter period and quenched to obtain the required volume fraction of the ferrite-martensite phases. rajanna s et al [15-18] studied the microstructure and mechanical properties of the rail steel. sunil b et al [19] studied the effect of carbon on the microstructure of the dp steels. from results obtained it is clear that the as martensite content increases hardness of the dp steels. jiecen zhang et al [21] studied two different morphologies of martensite in dp steels viz., intermediate quenching (iq) and cold rolled intercritical annealing (cr-ia). for both the cases inter-critical temperature varied from 750oc to 850oc to obtain the different martensite volume fraction. from the results it is observed that, in both samples, with the increment in the inter-critical temperature, the existing fibrous martensite is converted into blocky martensite eventually increasing the martensite cracking. on the other hand, there is decrement in the martensite cracking was observed in the iq samples with the increment in the martensite fraction. the investigations on different advanced high strength steels such as complex phase steel, dual phase steel, trip-aided bainitic ferritic steel and quenching and partitioning steel [22] was carried out to access the crack initiation and propagation resistance by means of different assessments. among the different parameters adopted, specimen geometry, testing method were found independent parameters which doesn’t affect the crack initiation resistance. shengci li et al [23] used the compact tension (ct) specimen to evaluate the fracture behavior of the dp780 dual phase steel. also the effect of loading [24], elevated temperature [25], inclusions [26], ferrite morphology and of ferrite volume fraction [27] of the ferritic/martensitic stainless steel was studied by the various authors. from the results it is recommended that the volume fraction of the produced ferrite/martensite influence the fracture toughness of the material. the fracture toughness testing using ct specimens is the most widely used one [28]. the fracture toughness of as-cast and annealed medium carbon steel was investigated using the round notched tensile specimen for different notch diameters and angles [29] and found that higher notch angle and lower notch diameter demonstrate higher value of fracture toughness. fracture toughness of medium carbon steel using circumferential notched tensile (cnt) specimens [30] was carried out and found that the results obtained were in close relation with the literature [29]. in the present work, the main aim is to brief review on the fracture toughness of the dual phase steel produced through intermediate quenching (iq) [31] technique. the motivation to use the iq samples is that, as the martensite fraction increases the martensite cracking decreases [21] in the dual phase steels. it is aimed to provide the better understanding of the fracture behavior of the dp steels, as the literature survey shows the few authors worked on the fracture characterization. for the same, the advanced high strength steel like dual phase steel, which commonly used in the automobile sectors, is used to investigate the fracture toughness using the lefm based techniques. material and preparation he material used in the present work is the hot rolled low carbon micro alloyed steel plate of 8mm thick. in its chemical composition, it observed that the major alloying elements are ni-0.4%, mn-1.32%, c-0.16%, si-0.42% [31]. the some of the minor elements include s, p, mo, v, b and cr, which are also influence the performance of the dp steel. the concentration of the alloying elements was measured by utilizing the optical emission spectrometer. t b. sunil et alii, frattura ed integrità strutturale, 55 (2021) 271-277; doi: 10.3221/igf-esis.55.20 273 the intercritical heat treatment process has been carried out in a laboratory thermocouple controlled muffle furnace. the lower critical (ac1) and upper critical (ac3) temperatures [31] were determined. the heat treatment procedure followed is as mentioned by the sunil b et al [31]. experimentation rom the prepared dp steels, samples are machined to the requisite thickness and width to fulfill the plain strain condition. the prepared samples of the dp steel are machined to the requisite dimensions as per the american society for testing and materials (astm) standard [20]. the specimen used for the fracture toughness testing is, the compact tension (ct) specimen, as per astm e399 standard as shown in fig.1. the requisite specimens have a notch of size 2mm x 12mm and were prepared using wire-cut edm at an accuracy of 0.1mm. in the servo hydraulic testing machine, the fatigue crack of 1mm is introduced for the crack length to width (a/w) ratio of 0.45, at the end of the notch. the displacement rate of 1mm/min is maintained [28] in the conducted fracture toughness tests. the specimens tested were subjected to load ratio of 0.1 and cyclic load at the frequency 5hz. all the ct specimens of dp steels of thickness (b) = 6mm are tested to find the fracture toughness using a universal testing machine (utm) as per astm standard testing procedure. figure 1 (a): ct specimen with 780oc iq temperature figure 1 (b): experimental setup for the each specimen tested, the value of the critical load pq and the crack opening displacement is measured and using those values the fracture toughness (kic) is determined using the empirical equation available in the literatures [20, 26]. results and discussion he fracture load and the calculated value of the fracture toughness of all the specimens of dual phase steel for the different iq temperatures have been listed in the tab. 1. from the table, it can be observed that the increment in the iq temperatures leads to increment in the fracture toughness up to the 780oc. later, the decrement in the values of the fracture toughness is observed. the increment and decrement in the fracture toughness of the dual phase steel is mainly due to the volume fraction of the ferrite-martensite phase formed during the processing. it is seen that the dp steel developed from hot rolled low carbon micro alloyed steel exhibits better fracture toughness values in comparison with the dual phase steels produced with medium carbon steel [30]. the fracture toughness of the a780 steel is yielding the maximum fracture toughness i.e. kic of 54.89 mpa√m with dp800 yielded a fracture toughness of 52.70 mpa√m (reduction of 4% in contrast with the a780). the a820 yielded the lesser fracture toughness of 49.10 mpa√m (a further reduction of 10% in contrast with the a780). this further decrement in the fracture toughness with the a820 specimen is a result of the high volume fraction of martensite (60%). f t b. sunil et alii, frattura ed integrità strutturale, 55 (2021) 271-277; doi: 10.3221/igf-esis.55.20 274 the fig 2 shows the variation of the fracture toughness of the dual phase steel with the increment in the intermediate quenching temperature. from the fig it is observed that as the increment in iq temperature leads to increase in the fracture toughness up to the 780oc, later fracture toughness decreases. the increased fracture toughness of a780 is characterized by the hard martensite and soft ferrite phase, which assist in the increment in the material resistance to crack initiation and propagation. from the literature [29-30], the fracture toughness of the above said materials is in close agreement with the dp steels produced from medium carbon steels using the similar intercritical temperatures. the dual phase steel prepared by the intermediate quenching method maintains the appreciable ductility and thus gives the better resistance to the crack propagation. the facture toughness test was conducted using the cnt [29] and ct specimens are in good agreement with each other. however, the steep stress induced by the notch, the fracture toughness values obtained from the cnt specimens is lower than the ct specimens. specimen thickness (b) mm width (w) mm fracture load (pq) kn f (a/w) kic mpa√m a740 08 40 8.79 8.34 45.82 a760 08 40 9.48 8.34 49.41 a780 08 40 10.53 8.34 54.89 a800 08 40 10.11 8.34 52.70 a820 08 40 9.42 8.34 49.10 table 1: kic of dual phase steel at different iq temepratures figure 2: variation of fracture toughness with respect to iq temperature in the fig 3, the fractography of the tested samples shows both ductile and brittle fracture. the dp steels produced using the intermediate quenching technique at 740, 760 and 780oc shows the ductile fracture under the tensile loading whereas the dp steels at 800 and 820oc shows the ductile initiated brittle fracture. the increment in the fracture toughness up to the 780oc, is the sign of increasing the hard martensite phase and availability of soft ferrite phase. due to which the ductile fracture has occurred. the ductile initiated brittle fracture is due to the increased hard martensite phase and the increment in the stress accumulation at the ferrite. since there is no sign of sudden transition of ductile to brittle in the fractographs, there is a higher percentage of elongation. b. sunil et alii, frattura ed integrità strutturale, 55 (2021) 271-277; doi: 10.3221/igf-esis.55.20 275 (a) a740 (b) a760 (c) a780 (d) a800 (e) a820 figure 3: microstructure of fractured surfaces for dp steels conclusions he low carbon micro alloyed steel is used to prepare the dual phase steels and fracture toughness of the same has been evaluated. from the outcomes of the experiments following conclusions were drawn. i. dual phase steels can be produced successfully from the hot rolled low carbon micro alloy by using the intermediate quenching techniques which forms the different volume fractions of the ferrite-martensite phases. t b. sunil et alii, frattura ed integrità strutturale, 55 (2021) 271-277; doi: 10.3221/igf-esis.55.20 276 ii. the obtained equal volume fraction and fine distribution of ferrite and martensite phases, exhibits the better fracture toughness. the equal volume fraction of the ferrite-martensite phases helps to maintain the appreciable ductility and thus gives the greater resistance to crack initiation and propagation. iii. from the comparison of ct specimens and cnt specimens (from literatures), it is clear that, the geometry of the specimens will not affect majorly on the fracture toughness of the material. however the fracture toughness of the dp steels produced from low carbon micro alloy steels exhibits better results as compared to the dp steels produced from the medium carbon steels. iv. from the fractography tests it is clear that the ductile initiated brittle fracture is observed which is due to the increased hard martensite phase and the increment in the stress accumulation at the ferrite which also leads to the higher elongation. funding his research received no specific grant from any funding agency in the public, commercial, or not-for-profit sectors. conflict of interest he authors declare that they have no conflict of interest. references [1] movaheda, p., kolahgara, s., marashia, s.p.h., pouranvari, m, parvin, n. (2009). the effect of intercritical heat treatment temperature on the tensile properties and work hardening behavior of ferrite–martensite dual phase steel sheets. materials science and engineering a 518, pp. 1–6. doi: 10.1016/j.msea.2009.05.046 [2] yoon, j.i., jung, j., joo, s.h., song, t.j., chin, k.g., seo, m.h. (2016). correlation between fracture toughness and stretch-flangeability of advanced high strength steels. matter lett, 180, pp. 322–326. [3] casellas, d., lara, a., frómeta, d., gutiérrez, d., molas, s., pérez, ll. (2017). fracture toughness to understand stretchflangeability and edge cracking resistance in ahss. metall mat trans a, 48, pp.86–94. [4] frómeta, d., tedesco, m., calvo, j., lara, a., molas, s., casellas, d., (2017). assessing edge cracking resistance in ahss automotive parts by the essential work of fracture methodology. j phys: conf ser, 896, 012102. [5] frómeta, d., lara, a., parareda, s., casellas, d. (2019). evaluation of edge formability in high strength sheets through a fracture mechanics approach. aip conf proc 2113, 160007. [6] debdulal, d., partha protim, c., (2009). influence of martensite morphology on the work-hardening behavior of high strength ferrite–martensite dual-phase steel. j mater sci 44, pp. 2957–2965. doi:10.1007/s10853-009-3392-0. [7] saaia, o.s., hopperstad, y., granbomc, o.-g. (2014). influence of volume fraction and distribution of martensite phase on the strain localization in dual phase steels. procedia materials science, 3, pp. 900 – 905. [8] ahmad, e., manzoor, t., ziai, m.m.a., hussain, n. (2012). effect of martensite morphology on tensile deformation of dual-phase steel. journal of materials engineering and performance 21, pp. 382–387. [9] adamczyk, j., grajcar, a. (2007). heat treatment and mechanical properties of low-carbon steel with dual-phase microstructure. journal of achievements in materials and manufacturing engineering 22.1. [10] rajanna, s., shivanand, h.k., akash deep, b.n. (2009). improvement in mechanical behaviour of expulsion with heat treated thermite welded rail steel. proc. of world academy of science, engineering and technology. 60, pp. 558-562. [11] poole, m., mazinani, w.j. (2007). effect of martensite plasticity on the deformation behavior of a low-carbon dualphase steel. metallurgical and materials transactions a, pp. 328-339. t t b. sunil et alii, frattura ed integrità strutturale, 55 (2021) 271-277; doi: 10.3221/igf-esis.55.20 277 [12] sharma, p. (2017). study of the effect of quenched and inter critical heat treatment on mechanical properties of plain low carbon steel (0.09% c, 0.5% mn, 0.05% s). international journal of current engineering and technology 7(1), pp. 2347 – 5161. [13] rudnizki, j., prahl, u. and bleck, w. (2012). phase-field modelling of microstructure evolution during processing of cold-rolled dual phase steels. integrating materials and manufacturing innovation, pp-1-3. doi: 10.1186/2193-9772-1-3 [14] bello, k.a., hassan s.b. and aponbiede, o. (2011). effects of austenitising conditions on the microstructures and mechanical properties of martensitic steel with dual matrix structure. journal of minerals & materials characterization & engineering 11(1), pp. 69-83. doi: 10.4236/jmmce.2012.111006 [15] rajanna, s., shivanand, h.k., deep, b.n. (2009). improvement in mechanical behavior of expulsion with heat treated thermite welded rail steel, proceedings of world academy of science, engineering and technology, 60, pp. 558-562. [16] rajanna, s. and shivanand, h.k. (2009). improvement in mechanical response of thermite welded rail steel using expulsion with heat treatment, international journal of materials science, 4(3), pp. 313-322. [17] shantharaja, m., rajanna, s., shivanand, h.k. and keshavamurthy, y.c. (2009). characterization of mechanical properties of postweld heat-treated shielded manual metallic arc welded rails, international journal of recent trends in engineering, 1(5), 153. [18] rajanna, s. and shivanand, h.k. (2008). microstructure and mechanical characterization of post weld heat treated thermite welded rails, indian welding journal, 41(1), 44. [19] sunil, b., rajanna, s. (2018). influence of carbon percentage on the microstructure of dual phase steel, international journal of advanced research methodology in engineering & technology, 2(1), pp.108-112. [20] astm standards (2017). standard test method for plane-strain fracture toughness of metallic materials, astm international, e 399-17. [21] jiecen, z., hongshuang, d., yonggang, d., misra, r.d.k. (2015). effect of martensite morphology and volume fraction on strain hardening and fracture behavior of martensite–ferrite dual phase steel. materials science & engineering a, 627, pp. 230–240. doi: 10.1016/j.msea.2015.01.006. [22] frómeta, d., parareda, s., lara, a., molas, s., casellas, d., jonsén, p., calvo, j. (2020). identification of fracture toughness parameters to understand the fracture resistance of advanced high strength sheet steels. engineering fracture mechanics, 229, 106949. doi: 10.1016/j.engfracmech.2020.106949. [23] shengci, l., yinghui, z., liang, q., yonglin, k. (2018). effect of single tensile overload on fatigue crack growth behavior in dp780 dual phase steel, international journal of fatigue, 106, pp. 49–55. doi: 10.1016/j.ijfatigue.2017.09.018. [24] huaxin, l., jones, r.h., hirth, j.p., gelles, d.s. (1994). effect of loading mode on the fracture toughness of a reducedactivation ferritic/martensitic stainless steel, journal of nuclear materials, 212-215, pp. 741-745. [25] dubey, j.s., wadekar, s.l., chakravartty, j.k. (1998). elevated temperature fracture toughness of aisi 403 martensitic stainless steel, journal of nuclear materials, 254, pp. 271–274. [26] pouranvari, m. (2017). fracture toughness of martensitic stainless steel resistance spot welds, materials science & engineering a, 680, pp. 97-107. doi: 10.1016/j.msea.2016.10.088. [27] ulu, s., aytekin, h., said, g. (2013). an alternative approach to the fracture toughness of dual phase steels, strength of materials, 45(5). doi: 10.1007/s11223-013-9498-2. [28] doddamani, s. and kaleemulla, m. (2018). effect of graphite on fracture toughness of 6061al-graphite, strength, fracture and complexity, 11(4), pp 295-308. doi:10.3233/sfc-180230. [29] nath, s. k. and kr das, u. (2006). effect of microstructure and notches on the fracture toughness of medium carbon steel, journal of naval architecture and marine engineering, 3, pp 15-22. [30] kanayo alaneme, k. (2011). fracture toughness (k1c) evaluation for dual phase medium carbon low alloy steels using circumferential notched tensile (cnt) specimens, materials research, 14(2), pp. 155-160. [31] sunil, b., rajanna, s. (2020). evaluation of mechanical properties of ferrite-martensite dp steels produced through intermediate quenching technique. sn appl. sci. 2, 1461. doi: 10.1007/s42452-020-03246-4. microsoft word numero_50_art_6_2509 i. g. f. silva et alii, frattura ed integrità strutturale, 50 (2019) 46-53; doi: 10.3221/igf-esis.50.06 46 leak-before-break methodology applied to different piping materials: a performance evaluation israel gleybson ferreira da silva navy technological center in são paulo, brazil rael_gfs@hotmail.com arnaldo homobono paes de andrade, waldemar alfredo monteiro nuclear and energy research institute, brazil arnaldo.homobono@gmail.com wamontei@ipen.br abstract. this paper presents a study of the application of leak-beforebreak (lbb) to nuclear piping using three different materials. although had been introduced more than three decades ago, through a fundamentally technical justification, the lbb concept currently has been widely applied in nuclear installations projects in several countries. based on the fracture mechanics, the lbb concept considers that a leakage from a crack can be detected before it reaches a critical size that implies the pipe failure, that is, the lbb analysis demonstrates through a technical justification that the probability of pipe rupture is extremely low. among the aspects that involve the application of lbb, the main ones are: the definition of the material properties, which are obtained through tensile and fracture tests; the leakage analysis, which determines the rate of leakage due to the presence of a through-wall crack; and the analysis that verifies if the crack is stable considering the failure modes by ductile tear and plastic collapse. the materials sa-508 cl. 3, sa-106 gr. b and sa-376-tp304 were evaluated in relation to their performances for lbb. data obtained from literature cases were used for the materials properties, and for the geometry and loadings of the pipe, all corresponding to the primary circuit of a pwr reactor. after application of the lbb, it was verified that all three materials met the limits established in the methodology. sa-508 cl. 3 and sa-376-tp304 steels showed the best performance for ductile tear failure and plastic collapse failure, respectively, and sa-106 gr. b steel had the lowest performance in both. all three materials presented plastic collapse as the most likely failure mode. in general, sa-376-tp304 steel presented the best performance for the lbb among the three materials evaluated in this work. citation: silva, i. g. f, andrade, a. h. p., monteiro, w. a., performance evaluation of different piping materials for application of leak-before-break (lbb), frattura ed integrità strutturale, 50 (2019) 46-53. received: 02.05.2019 accepted: 09.07.2019 published: 01.10.2019 copyright: © 2019 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. http://www.gruppofrattura.it/va/50/2509.mp4 i. g. f. silva et alii, frattura ed integrità strutturale, 50 (2019) 46-53; doi: 10.3221/igf-esis.50.06 47 keywords. leak-before-break; lbb; piping material; material performance; pwr reactor; fracture mechanics. introduction uclear power plants use nuclear fission as a source of heat for energy production. currently, 450 nuclear reactors are in operation in the world, producing about 400 gw of electrical capacity; of these units in operation, 298 are pwr (pressurized water reactor). in addition, 55 nuclear reactors are under construction, 45 of them being pwr [1]. the operating principle of a pwr nuclear plant is based on the removal of heat from the reactor core through a closed circuit of high pressure water, called the primary circuit. the water heated under high pressure in the primary circuit passes through a steam generator where it heats and turns into steam the water of the secondary circuit. this steam moves a turbine that drives an electric generator. the electricity generated reaches final consumers through distribution networks. pipes that are part of the pwr reactors are commonly manufactured from stainless steels or high toughness low alloy steels that are resistant to unstable defect growth. a crack in the piping should cause a leakage in a considerable amount, allowing its identification and quantification, before a growth can occur that would lead to a sudden rupture of the pipe. this is the essence of the leak-before-break (lbb) concept. a fundamental step in the application of the lbb concept is the evaluation of the stability of postulated through-wall crack in a given pipe system. because they are built using ductile materials, this evaluation is made through the concepts of elastic-plastic fracture mechanics (epfm). through a fundamentally technical justification, the lbb concept has been widely applied in nuclear installation projects in several countries [2, 3, 4, 5]. lbb concept ccording to the united states atomic energy commission [6], the gdc (general design criterion) 4 requires that structures, systems, and components important for safety be designed to accommodate the environmental and dynamic effects associated with normal operation, and even with postulated accidents. it indicates that dynamic loading from the effects of these conditions, including missiles, pipe whipping, and discharging fluids must be verified in the designs. in the case of primary circuit piping, the regulators of nuclear activity required, in the early 1970s, that nuclear plant designs take into account the hypothesis of a sudden rupture of the complete transversal section of a pipe (degb double-ended guillotine break), causing a loss of coolant (loca-loss-of-coolant accident). this requirement, when applied to a high energy system, as the primary circuit of the reactor, demanded the consideration of two dynamic effects caused by sudden pipe rupture, whipping and jet effects. thus, to protect the essential safety equipment of a nuclear plant, it was necessary the use of devices as pipe whip restraints and jet impingement shield. for about a decade, the nuclear industry has sought solutions to disconsider the dynamic effects of a degb. so, the lbb methodology emerged as a technically justifiable approach to remove such analysis of the design bases of nuclear plants, leading to the realization of several studies between the 1970s and 1980s and acceptance by the regulators of nuclear activity [7]. the usnrc (united states nuclear regulatory commission) established in the early 1980's the pipe break task group whose work culminated in the publication nureg-1061 [8], which outlined the feasibility of applying the lbb concept. based on this document, the document nureg-0800-srp 3.6.3 [9] was elaborated, where is characterized the deterministic evaluation procedure for application of the lbb concept proposed by the usnrc. these documents became a basic reference for the implementation of the criteria associated to the lbb concept in the american plants and, by extension, in other countries. since lbb is demonstrated, such ruptures can be excluded from the design bases, and the dynamic efforts resulting from loca are not considered in the structural analysis of the plant systems. as a result, it is no longer necessary to design components, equipment or piping supports of primary circuit to cope with such dynamic loads. another advantage of the application of lbb is that pipe whip restraints and jet impingement shield, both required to protect important equipment n a i. g. f. silva et alii, frattura ed integrità strutturale, 50 (2019) 46-53; doi: 10.3221/igf-esis.50.06 48 from the dynamic effects of postulated rupture, can be removed. as the costs of these protection elements are high, and in some cases their existence makes it difficult or even impossible the in-service inspection of components, the withdrawal of the devices is desirable, not only for economic reasons, but also to reduce the dose of radiation received by maintenance staff [10]. among the several points that involves the application of lbb, it is considered that its main aspects are the definition of the materials properties, leakage analysis, and stability analysis of the crack. materials and methods evaluated materials mong the materials that have been used as base metal in primary circuits piping of pwr reactor sa-508 cl. 3 (low alloy steel), sa-106 gr. b (carbon steel) and sa-376-tp304 (stainless steel), were chosen to be evaluated due their different characteristics and chemical compositions according to the asme [11]. applied methodology as established in nureg-1061 [8] and nureg-0800-srp 3.6.3 [9], the methodology for applying lbb for each of the evaluated materials consisted basically of the following steps: 1) the tensile and fracture properties of the material were obtained from the stress versus strain curve and j-integral versus crack extension curves (j-r curve), both according to the results of the literature cases that performed experiments with these materials. 2) the pipe loading considered was that in the section of the pipe where the combinations of stress and material properties are most unfavorable. this loading and piping geometry were extracted from the primary circuit of a pwr reactor described in a literature case. 3) a circumferential through-wall crack was postulated in this section. 4) the leakage detected by the plant monitoring system was multiplied by 10. in this work, it was considered that the plant has a leakage detection system of 1.0 gpm (gallon per minute) where 1.0 gpm = 3.8 liters/minute. 5) the leakage analysis was performed for the cracks subjected to the normal operation loading to determine the crack size (lq) that causes the leakage of 10 gpm (38 liters/minute). this analysis was done with the help of picep software [12]. 6) case 1: the elastic-plastic j-integral analysis was applied to verify the stability of 2 times the leakage crack size (2lq) under normal operation loading plus sse (safe shutdown earthquake). then it was possible to calculate its safety margin (m1 = jic/j1), and m1 ≥ 1.0. 7) case 2: the elastic-plastic j-integral analysis was applied to verify the stability of the leakage crack size (lq) under excessive loading, which is 1.414 times the normal operation loading plus sse. then it was possible to calculate its safety margin (m2 = jic/j2), and m2 ≥ 1.0. 8) case 3: the limit load analysis was applied to obtain the critical crack size (lcr3) under normal operation loading plus sse. this was done with the help of picep software [12]. then it was possible to calculate its safety margin (m3 = lcr3/lq), and m3 ≥ 2.0. 9) case 4: the limit load analysis was applied to obtain the critical crack size (lcr4) under excessive loading. this was done with the help of picep software [12]. then it was possible to calculate its safety margin (m4 = lcr4/lq), and m4 ≥ 1.0. after this application with each of the three materials, it was possible to evaluate their performances for lbb. this was done based on the lower safety margin (among the four calculated) presented by these materials, considering the ductile tear failure (elastic-plastic j-integral analysis) and the plastic collapse failure (limit load analysis). thus, this margin corresponds to the most critical case, and to the most likely failure mode. materials properties in this paper, the tensile and fracture properties of the evaluated materials are presented in tab. 1, according to those referred cases. the same heat of material contemplates the tensile and fracture tests; the tests were performed at a temperature of 300 °c (±25 °c); and the fracture test the pipe had a circumferential through-wall crack under bending moment loading. a i. g. f. silva et alii, frattura ed integrità strutturale, 50 (2019) 46-53; doi: 10.3221/igf-esis.50.06 49 applied loadings the applied loadings used to apply the lbb in this paper correspond to the primary circuit of a pwr reactor. this information was obtained from jong [13]. the reactor cooling system of this plant operates with internal pressure of 13 mpa and temperature of 300 °c, where the maximum stresses occurred in the pipe of nps 10 sch 160s, being therefore, this piping geometry used in this work. based on this case of the literature, the applied loadings which were considered for the application of lbb are presented in tab. 2. material experiment number e [gpa] σ0 [mpa] σu [mpa] α n jic [kj/m2] c [kj/m2] m ref. sa-508 cl. 3 sfb2 188 410 579 1.26 8.98 652 724 0.51 [14] sa-106 gr. b ipirg-2 1.8 193 216 506 1.38 5.05 305 88 1.00 [15] sa-376-tp304 dp3-ii 4131-1 183 131 459 9.58 3.21 745 255 0.86 [15] table 1: tensile and fracture properties. loading axial force [n] bending moment [nm] internal pressure [mpa] total equivalent moment [nm] normal operation 15146 23769 13.0 51012 normal operation plus sse 22455 28293 13.0 55942 excessive 31751 40006 18.4 79102 table 2: applied loadings [13]. crack description the description of the postulated crack considered in this paper is presented in tab. 3. this information was required for leakage analysis, which was done with the help of picep software [12]. orientation of through-wall crack crack crosssectional shape ratio of the crack exit to inlet areas entrance loss coefficient surface roughness [mm] circumferential elliptical 1 for straight crack channel 0.61 for sharp-edged entrance 0.025 table 3: crack description. results leakage analysis he leakage analysis using picep software [12] determined the leakage rate curves versus crack size. according to the lbb methodology, the normal operating loading was considered in this step. the information of the materials properties and crack description were also used as input data for this software. the corresponding curve for each material is presented in fig. 1. this paper considered that the plant has a leakage detection system of 1.0 gpm. according to the lbb methodology, this leakage must be multiplied by 10 to determine the leakage crack size (lq). the size and angle of the leakage crack to 10 gpm for the evaluated materials are presented in tab. 4. material leakage crack size lq [mm] leakage crack angle [°] sa-508 cl. 3 206.23 96.7 sa-106 gr. b 207.17 97.1 sa-376-tp304 149.82 70.2 table 4: size and angle of the leakage crack to 10 gpm. t i. g. f. silva et alii, frattura ed integrità strutturale, 50 (2019) 46-53; doi: 10.3221/igf-esis.50.06 50 figure 1: leakage rate curves versus crack size. elastic-plastic j-integral analysis after defining the leakage crack size (lq), the elastic-plastic j-integral analysis was applied to verify the stability of the crack. initially, this check consisted of the calculation of applied j-integral according to eq. 1 [16]. when it is smaller than jic, the crack growth does not occur, but if it is equal to or greater than jic, the tearing is initiated. n 122 b 0 0 13 2 0 f m θ m j  ασ ε πr 1 h π mr t e              (1) two applications of the elastic-plastic j-integral analysis were performed for each of the evaluated materials, called case 1 and case 2, defined according to the lbb application methodology. in case 1, the verification considered the crack size of 2lq and normal operation loading plus sse. in case 2, the verification considered the crack size of lq and excessive loading. tabs. 5 and 6 present the details of the calculation for case 1 and 2, respectively. material θ [rad] t [m] r [m] m [nm] m0 [nm] fb h1 j1 [j/m2] sa-508 cl. 3 1.6871 0.02857 0.12224 55942 117760 3.4603 0.6792 38672 sa-106 gr. b 1.6948 0.02857 0.12224 55942 61148 3.7450 1.0480 57352 sa-376-tp304 1.2256 0.02857 0.12224 55942 77742 1.5553 1.4880 65616 table 5: details of the calculation of applied j-integral for case 1. material θ [rad] t [m] r [m] m [nm] m0 [nm] fb h1 j2 [j/m2] sa-508 cl. 3 0.8435 0.02857 0.12224 79102 377275 0.6041 0.6500 13486 sa-106 gr. b 0.8474 0.02857 0.12224 79102 197998 0.6465 0.9410 14308 sa-376-tp304 0.6128 0.02857 0.12224 79102 148949 0.3647 1.0560 24803 table 6: details of the calculation of applied j-integral for case 2. the safety margin was defined as the ratio between jic and applied j-integral, where m1 corresponds to the safety margin for case 1, and m2 corresponds to the safety margin for case 2. the performance evaluation of materials for elastic-plastic j-integral analysis was based on the values of these safety margins. figs. 2 and 3 present the safety margin m1 and m2, respectively, for each of the evaluated materials. i. g. f. silva et alii, frattura ed integrità strutturale, 50 (2019) 46-53; doi: 10.3221/igf-esis.50.06 51 figure 2: safety margin m1. figure 3: safety margin m2. limit load analysis the limit load analysis must also be applied to check for failure by plastic collapse. this application was performed with the help of picep software [12] to calculate the critical crack size (lcr). two applications of the limit load analysis were performed for each of the evaluated materials, called case 3 and case 4, defined according to the lbb methodology. in case 3, the verification considered the normal operation loading plus sse. in case 4, the verification considered the excessive loading. tab. 7 presents the calculated values for case 3 and 4, respectively. material critical crack size for case 3 lcr3 [mm] critical crack size for case 4 lcr4 [mm] sa-508 cl. 3 452.29 415.62 sa-106 gr. b 421.73 378.94 sa-376-tp304 415.62 378.94 table 7: critical crack size for cases 3 and 4. the safety margin was defined as the ratio between lcr and lq, where m3 corresponds to the safety margin for case 3, and m4 corresponds to the safety margin for case 4. the performance evaluation of materials for limit load analysis was based on the values of these safety margins. figs. 4 and 5 present the safety margin m3 and m4, respectively, for each of the evaluated materials. i. g. f. silva et alii, frattura ed integrità strutturale, 50 (2019) 46-53; doi: 10.3221/igf-esis.50.06 52 figure 4: safety margin m3. figure 5: safety margin m4. conclusions n the four cases, the safety margins of the evaluated materials have met the limits established in the methodology, that is, any of the three meets the minimum required and benefits from the advantages that the application of lbb can provide. among the materials evaluated and considering the two approached failure modes in the lbb methodology, sa-508 cl. 3 and sa-376-tp304 steels showed the best performance for ductile tear failure and plastic collapse failure, respectively. in these two failure modes, sa-106 gr. b steel showed the lowest performance of the three materials. in all three materials, the most critical case and the most likely failure mode was case 4. this case considers excessive loading, and evaluates failure by plastic collapse. as sa-376-tp304 steel had the highest safety margin for this case, it was considered that this obtained the best performance for lbb among the three evaluated materials. references [1] iaea (2019). pris database, reactor status report. available at: https://www.iaea.org/pris/worldstatistics/operationalreactorsbytype.aspx [2] bourga, r., moore, p., janin, y. j., wang, b., sharples, j. (2015). leak-before-break: global perspectives and procedures. international journal of pressure vessels and piping, 129-130, pp. 43-49. doi: 10.1016/j.ijpvp.2015.02.004. i i. g. f. silva et alii, frattura ed integrità strutturale, 50 (2019) 46-53; doi: 10.3221/igf-esis.50.06 53 [3] heckmann, k., sievers, j. (2018). leak-before-break analyses of pwr and bwr piping concerning size effects. nuclear engineering and design, 326, pp. 383-391. doi: 10.1016/j.nucengdes.2017.11.027. [4] deschanels, h., gilles, p., kayser, y., pignol, m., lacroix, r. (2017). improvement of leak-before-break methodology for sodium fast reactors. smirt 24, busan, korea. [5] liu, j., wang, y. (2017). leak before break (lbb) technology and application in china experimental fast reactor (cefr). mechanics and materials science, pp. 29-36. doi: 10.1142/9789813228177_0004. [6] united states atomic energy commission (1971). 10 cfr part 50 appendix a general design criteria for nuclear power plants. [7] iaea (1993). applicability of the leak before break concept, iaea, vienna, issn 1011-4289. [8] nureg-1061 (1984). report of the u.s nuclear regulatory commission piping review committee, evaluation of potential for pipe breaks, volume 3. usnrc. [9] nureg-0800-srp 3.6.3 (1987). leak-before-break evaluation procedures. usnrc. [10] maneschy, j. e., miranda, c. a. j. (2014). fracture mechanics in nuclear industry. lithos (in portuguese). [11] asme (2013). asme boiler and pressure vessel code, section ii, part a, ferrous materials specifications. [12] norris, d. m., chexal, b. (1987). picep: pipe crack evaluation program. epri np-3596-sr, revision 1. [13] jong, r. p. (2004). structural integrity assessment of cracked pwr piping systems. m.sc. dissertation, nuclear technology program, university of são paulo (in portuguese). [14] koyama, k.; muroya, i.; tanaka, t.; nakamura, t. (1999). low alloy steel piping test for fracture criteria of leak before break. nuclear engineering and design, 191, pp. 147-156. [15] miura, n. (1999). approximate evaluation method for ductile fracture analysis of a circumferentially through-wallcracked pipe subjected to combined bending and tension. nuclear engineering and design, 191, pp. 177-194. [16] zahoor, a. (1989). ductile fracture handbook. np-6301-d research project, electronic power research institute. nomenclature e young’s modulus σ0 yield strength σu tensile strength ε0 strain for σ0 α strain hardening coefficient (parameter of ramberg-osgood’s law) n strain hardening exponent (parameter of ramberg-osgood’s law) jic j-integral associated with the beginning of crack growth c constant of the j-r curve m exponent of the j-r curve lq leakage crack size j1 applied j-integral for case 1 j2 applied j-integral for case 2 lcr critical crack size (limit load analysis) lcr3 critical crack size for case 3 lcr4 critical crack size for case 4 m1 safety margin for case 1 m2 safety margin for case 2 m3 safety margin for case 3 m4 safety margin for case 4 m applied moment m0 reference moment calculated according to ref. [16] fb correction factor calculated according to ref. [16] h1 influence function calculated according to ref. 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can be opened with acrobat and adobe reader 5.0 and later.) >> /namespace [ (adobe) (common) (1.0) ] /othernamespaces [ << /asreaderspreads false /cropimagestoframes true /errorcontrol /warnandcontinue /flattenerignorespreadoverrides false /includeguidesgrids false /includenonprinting false /includeslug false /namespace [ (adobe) (indesign) (4.0) ] /omitplacedbitmaps false /omitplacedeps false /omitplacedpdf false /simulateoverprint /legacy >> << /addbleedmarks false /addcolorbars false /addcropmarks false /addpageinfo false /addregmarks false /convertcolors /converttocmyk /destinationprofilename () /destinationprofileselector /documentcmyk /downsample16bitimages true /flattenerpreset << /presetselector /mediumresolution >> /formelements false /generatestructure false /includebookmarks false /includehyperlinks false /includeinteractive false /includelayers false /includeprofiles false /multimediahandling /useobjectsettings /namespace [ (adobe) (creativesuite) (2.0) ] /pdfxoutputintentprofileselector /documentcmyk /preserveediting true /untaggedcmykhandling /leaveuntagged /untaggedrgbhandling /usedocumentprofile /usedocumentbleed false >> ] >> setdistillerparams << /hwresolution [2400 2400] /pagesize [612.000 792.000] >> setpagedevice microsoft word numero_56_art_07_3006 s. a. rizvi et alii, frattura ed integrità strutturale, 56 (2021) 84-93; doi: 10.3221/igf-esis.56.07 84 development of mathematical model and optimization of gma welding parameters of is 2062 grade a steel weldments saadat ali rizvi university polytechnic, jamia millia islamia, new delhi india saritbhu@gmail.com, http://orcid.org/0000-0001-2345-6789 wajahat ali scriet, ccs university meerut, india wajahatali@rediffmail.com abstract. in this experimental work, the effects of gas metal arc (gma) welding process parameters, such as arc voltage, wire feed speed, and gas flow rate on the mechanical quality of is 2062 structural steel of grade a have been studied. process parameters play an important role in determining the weld quality. in this research work the response surface methodology (rsm) via the design expert version 12 (doe) software was applied to determine the weld quality, for 3d plot, maximize desirability for all response, and also to develop a mathematical model that can predict the main effect of the listed parameters on weld quality i.e. toughness and hardness. a set of experiments has been conducted to collect the response data using a central composite design and anova was used to predict the impact of welding parameters on toughness and hardness. the obtained and predicated results were compared and it was verified that toughness and hardness of weldments are significantly affected by arc voltage and wire feed speed while gas flow rate has a minor effect. keywords. response surface methodology (rsm); centre composite design (ccd); modeling; optimization; gma welding; mechanical quality. citation: rizvi, s. a., ali., w., development of mathematical model and optimization of gma welding parameters of is 2062 grade a steel weldments, frattura ed integrità strutturale, 56 (2021) 84-93. received: 31.01.2021 accepted: 17.02.2021 published: 01.04.2021 copyright: © 2021 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. introduction s 2062 structural steel is frequently used in fabrication industries due to its good weldability, good tensile strength (uts), toughness, easy availability, economical etc. in this work, gas metal arc (gma) welding process was used to join this grade a steel. now a day’s gas metal arc welding process is frequently used to weld various materials as it is a semi automatic joining process and can even be used as automatic. in gma welding process a copper coated mild steel i https://youtu.be/xexqflyx8lg s. a. rizvi et alii, frattura ed integrità strutturale, 56 (2021) 84-93; doi: 10.3221/igf-esis.56.07 85 wire is used as a filler wire [1]. several statistical and computational techniques such as response surface methodology, ann, and taguchi [2] techniques were applied to develop the mathematical modeling and process parameters optimization. response surface methodology (rsm) is a powerful mathematical tool used to optimize the process parameters in processes such as machining, welding, and casting etc [3-5] and also used to develop a mathematical model [6] and it minimize the number of experiments. muralimohan cheepu et al [7] developed a mathematical model and optimize the welding process parameters during the laser welding of titanium alloys and compared the obtained results from response surface methodology with experimental results. shekhar srivastava and r.k. garg[8] developed a mathematical model and optimized gma welding process parameters during the welding of is2062 via rsm approach . they verified that the wire feed speed has a significant effect, followed by arc voltage and travel speed. sanjay a. swami et al [9] investigated the effect of gma welding parameters on the mechanical properties of mild steel by designing the experiments using central composite matrix. they concluded that on increasing the co2 gas percentage in ar gas ultimate tensile strength (uts) increase up to some extend and then decreases. a g kamble and r venkata rao [10] studied the effect of gma welding process parameters on aisi 202 steel weldments and developed a model for mechanical properties and they showed in their results that higher the arc voltage decreases the hardness and mechanical quality but increases with increasing in welding speed. in the present experimental research work the effect of gma welding process parameters on the toughness and hardness of is2062 structural steel of grade a weldments were investigated and a mathematical model was developed by response surface methodology. scanning electron microscopy (sem) micromorphology fracture surface of toughness test samples was studied to determine the ductile or brittle fracture. experimental procedure n this research work, is 2062 structural work of grade a in form of plate of size 300 mm x 60 mm x10 mm was used as parent metal. gas metal arc (gma) welding process was used to weld the parent metal in the shielding environment of 75% ar+25% co2 gas mixture. er70s-6 of ø 2 mm is used as filler wire to join the parent metal. chemical composition of parent metal and filler wire is mentioned in tab. 1. material c mn s p si fe is 2062 0.22 1.5 0.049 0.05 0.37 bal. er70s-6 0.20 1.61 0.025 0.025 0.98 bal. table 1: chemical composition of parent metal and filler wire (wt.%) tab. 2 illustrates the different selected input parameters of gma welding with their corresponding level, their notation, and unit in actual form. the proposed experimental design involves the variation of three factors (arc voltage, wire feed speed, and gas flow rate) at three levels. welding trials were completely conducted based on central composite design of experiments associated with twenty numbers runs. factors notation unit level -1 0 +1 arc voltage v v 25 26 27 wire feed speed wf ipm 300 350 400 gas flow rate gf lpm 10 15 20 table 2: process parameters and their level design matrix is shown in tab. 3. toughness test samples before fracture and after fracture are showed in fig. 1. i s. a. rizvi et alii, frattura ed integrità strutturale, 56 (2021) 84-93; doi: 10.3221/igf-esis.56.07 86 std run experimental run arc voltage (v) wire feed speed (ipm) gas flow rate (lpm) toughness (j) hardness (vhn) 9 1 24 350 15 200 178 6 2 27 300 20 156 181 16 3 26 350 15 266 161 5 4 25 300 20 188 186 13 5 26 350 6 258 199 20 6 26 350 15 261 159 3 7 25 400 10 186 165 1 8 25 300 10 242 171 15 9 26 350 15 274 165 19 10 26 350 15 255 162 12 11 26 434 15 188 182 2 12 27 300 10 214 196 8 13 27 400 20 190 180 10 14 28 350 15 208 206 18 15 26 350 15 268 150 4 16 27 400 10 192 181 14 17 26 350 23 194 186 17 18 26 350 15 260 155 11 19 26 266 15 156 189 7 20 25 400 20 202 175 table 3: doe table with responses figure 1: toughness test samples. result and discussion development of mathematical model n this work arc voltage (v), wire feed speed (f), and gas flow rate (l) were selected as welding process parameters. mechanical properties, i.e. toughness and hardness of welded joints, are significantly affected by welding parameters and it is very clear from previous research work that toughness and hardness of is 2062 steel weldments is i s. a. rizvi et alii, frattura ed integrità strutturale, 56 (2021) 84-93; doi: 10.3221/igf-esis.56.07 87 considerably influenced by arc voltage and wire feed speed [11]. in regression analysis [12] as expressed by eq. (1), an experimental mathematical model was generated in between the toughness, hardness, and independents variable [13] and check for its adequacy. response surface methodology is also used based on central composite design (ccd) to develop a model to predict the mechanical quality and checked by anova for its adequacy [14]. the mechanical properties dimensions response function can be expressed as eqn. (1): ytrans=f (x1,x2, x3, x4,...............xn) (1) where ytrans is the power transformation of the welding parameters and xn represent the input parameters. x1=arc voltage, x2=wire feed speed, and x3=gas flow rate selected as welding input parameters in this experimental work. usually 2nd order eqn. (2) can be expressed [15] as:          k k k k o i i ii i ij i ji j i i y d d x d x d x x 2 1 1 (2) where y is the response (toughness and hardness) variable,xi is the uncoated level of the variables, ε is the fitting error, the coefficient do is the constant value or intercept, and coefficients di,dii, and dij represent the linear, quadratic, and interaction terms of the variable, respectively. figure 2: response surface plot showing the interation effect of (a) wfs vs v,(b) gfr vs and v and (c) gfr vs wfs on toughness. effect of welding parameters on mechanical properties (toughness) from the tab. 4 it is very clear that quadratic is the best possible fit for toughness. as the main interaction and quadratic factors that contribute significant to toughness include arc voltage (a), gas flow rate (b), wire feed speed (c), arc voltage (a) (b) (c) s. a. rizvi et alii, frattura ed integrità strutturale, 56 (2021) 84-93; doi: 10.3221/igf-esis.56.07 88 and gas flow rate (ab), arc voltage and wire feed speed (ac), gas flow rate and wire feed speed(bc),current (a2),gas flow rate (b2),and wire fed speed (c2). model for toughness developed mathematical model for toughness is represented by eq.3             14402.13068 1066.54705 * 4.72138 * 5.50615 0.135000 * * 0.550000 * * 0.063000 * * 21.33451 * ² 0.013059 * ² 0.542253 * ²     toughness a b c a b a c b c a b c (3) from fig. 2 (a) and (b) it is very clear that as on increasing the wire feed speed toughness of weldment increases up to 350 ipm after that toughness start to reduce where as on increasing the voltage toughness tends to increases and it is obtained maximum at point 26v after that toughness tends to decreases it is due to increasing in the heat input. fig.3 (a) & (b) repersent the normal probalility curve for toughness and hardness and this plot is used to check the adquancy of model. as all points are in a straight line,it can concluded that model is adequate[16-18]. figure 3: residuals plot for the developed model (a) toughness (b) hardness. design expert12 version software was used in this experimental work to develop and choose the suggented model that described the response factor in regression analysis and sequential f test was performed to test the significence of the regression model and determine the significent model terms of developed model. data of tab. 4 and 5 indicate that a quadratic model is statstically significant for the weldments mechancial quality i.e. toughness and hardness and can be used for further analysis in this investigation. source sequential p-value lack of fit p-value adjusted r² predicted r² linear 0.5587 0.0002 -0.0476 -0.2908 2fi 0.7135 0.0001 -0.1650 -1.0345 quadratic < 0.0001 0.0505 0.9088 0.6829 suggested cubic 0.0162 0.8845 0.9746 0.9803 aliased table 4: statistics model for toughness test source sum of squares df mean square f-value p-value mean vs total 9.496e+05 1 9.496e+05 linear vs mean 3340.00 3 1113.33 0.7125 0.5587 2fi vs linear 2409.50 3 803.17 0.4622 0.7135 quadratic vs 2fi 21231.24 3 7077.08 52.00 < 0.0001 suggested cubic vs quadratic 1134.00 4 283.50 7.49 0.0162 aliased residual 227.06 6 37.84 total 9.780e+05 20 48897.50 table 5: sequential model sum of square for toughness model. s. a. rizvi et alii, frattura ed integrità strutturale, 56 (2021) 84-93; doi: 10.3221/igf-esis.56.07 89 analysis of variance (anova) anova is a power full statically tool to determine which factor influence the response [19]. a model or model term is significant when p value is less than 0.05. in anova p-term represent the probability of importance for each control parameters and higher signifies the use fullness of that parameters. importance of design or control parameters can be determined and confirmed by anova [20]. tabs. 6 and 7 shows the anova table for toughness and hardness of weldment. for both cases quadratic model was suggested. for both cases, as the value of r2 is closer to 1 hence model is accepted. model 26980.75 9 2997.86 22.03 < 0.0001 significant a-voltage 202.17 1 202.17 1.49 0.2509 b-wire feed speed 41.54 1 41.54 0.3052 0.5928 c-gas flow rate 3096.29 1 3096.29 22.75 0.0008 ab 364.50 1 364.50 2.68 0.1328 ac 60.50 1 60.50 0.4445 0.5200 bc 1984.50 1 1984.50 14.58 0.0034 a² 6559.46 1 6559.46 48.19 < 0.0001 b² 15361.09 1 15361.09 112.86 < 0.0001 c² 2648.42 1 2648.42 19.46 0.0013 residual 1361.05 10 136.11 lack of fit 1135.05 5 227.01 5.02 0.0505 not significant pure error 226.00 5 45.20 cor total 28341.80 std. dev. 11.67 r² 0.9520 mean 217.90 adjusted r² 0.9088 c.v. % 5.35 predicted r² 0.6829 adeq precision 13.7511 table 6: anova table for toughness. model 3574.75 9 397.19 4.83 0.0108 significant a-voltage 568.20 1 568.20 6.91 0.0252 b-wire feed speed 146.78 1 146.78 1.79 0.2110 c-gas flow rate 12.12 1 12.12 0.1474 0.7090 ab 0.1250 1 0.1250 0.0015 0.9697 ac 210.13 1 210.13 2.56 0.1409 bc 10.13 1 10.13 0.1232 0.7329 a² 1204.41 1 1204.41 14.66 0.0033 b² 674.99 1 674.99 8.21 0.0168 c² 1251.44 1 1251.44 15.23 0.0029 residual 821.80 10 82.18 lack of fit 676.47 5 135.29 4.65 0.0584 not significant pure error 145.33 5 29.07 cor total 4396.55 std. dev. 9.07 r² 0.8131 mean 176.35 adjusted r² 0.6449 c.v. % 5.14 predicted r² -0.2269 adeq precision 6.5677 table 7: anova table for hardness s. a. rizvi et alii, frattura ed integrità strutturale, 56 (2021) 84-93; doi: 10.3221/igf-esis.56.07 90 effect of welding parameters on mechanical properties (hardness) the moderate fit for hardness (vhn) also highlighted the quadratic relation as the possible best fit. from anova table it is clear that as the main interaction and quadratic factors that contribute significant to hardness include arc voltage (a), gas flow rate (b), wire feed speed (c), arc voltage and gas flow rate (ab), arc voltage and wire feed speed (ac), gas flow rate and wire feed speed (bc), current (a2), gas flow rate (b2), and wire fed speed (c2).reduced anova is tabulated in tab. 7. developed mathematical model for hardness is represented by eq.4.            6262.89689 454.42813 * 2.11433 * 13.70422 * 0.002500 * * 1.02500 * * 0.004500 * * 9.14189 * ² 0.002738 * ² 0.372747 * ² hv a b c a b a c b c a b c (4) from fig. 4 (a) and (b) it is very clear that as on increasing the arc voltage there is increment in the hardness of weldment where as on increasing the wire feed speed and gas flow rate there is little increment in the hardness. but from fig. 4 (c) it is very clear on increasing the amount of gas flow rate hardness of weldment first increases and then decreases. figure 4: response surface plot showing the interation effect of (a) wfs vs v,(b) gfr vs and v and (c) gfr vs wfs on hardness. fig. 5 shows the effect of all the three welding process parameters on the weldment hardness at the centre point in the dsign space. fractographic analysis toughness test samples of is 2062 steel weldments were tested for mode of fracture with the support of scanning electron microscope (sem) to determine the nature of fracture i.e. ductile fracture of brittle fracture and it was observed that from fig. 6 ab having quasi-cleavage fracture [21] that consist a river patter and shows a brittle fracture but from fig. 6 c it is very clear as there are a large number of dimples on fracture surface hence representing a ductile fracture. s. a. rizvi et alii, frattura ed integrità strutturale, 56 (2021) 84-93; doi: 10.3221/igf-esis.56.07 91 figure 5: perturbation plot showing the effect of all factor on the hardness of weldment. figure 6: sem image of fracture surface of samples. conclusion his experimental work focuses on the gma welding of is 2062 structural steel of grade a. this study was carried out in order to determine the effect of gma welding process parameters on the mechanical quality of weldments i.e. toughness and hardness. in addition, the interactions between the welding parameters were determined via 3d response plot and a mathematical model was proposed to predict the mechanical behavior of the weldments using response surface methodology (rsm). the following conclusions have achieved.  response surface methodology approach can be effectively applied to determine the effect of process parameters on response i.e. on output.  rsm method is also used to plot the contour graph for various responses to show the interaction between the different process parameters.  the effective of both models i.e. toughness and hardness was checked according to r2 terms. as the r2 value in model is near to unity hence developed model represent good accuracy.  ductile fracture was observed on sem fractrography of toughness test samples t s. a. rizvi et alii, frattura ed integrità strutturale, 56 (2021) 84-93; doi: 10.3221/igf-esis.56.07 92  wire feed speed and arc voltage having the significant effect on toughness and hardness. gas flow rate is least effective parameters. references [1] rizvi, s. a., ali, w. (2009). a text book of advanced welding technology, kataria & sons (p) ltd new delhi, 55. [2] rizvi, s. a., ali, w. (2020). multi attribute decision making parametric optimization in weld bead by gas metal arc welding through grey relation analysis: a case study, international journal of engineering, science and technology,12(2) 2020, pp. 59-66. doi:10.4314/ijest.v12i2.7. [3] kuntoğlu, m., aslan, a., pimenov, d. y., giasin, k., mikolajczyk, t., sharma, s. (2020). modeling of cutting parameters and tool geometry for multi-criteria optimization of surface roughness and vibration via response surface methodology in turning of aisi 5140 steel, materials (basel), 13(19) 4242, pp. 1-21. doi: 10.3390/ma13194242. [4] safeen, w., hussain, s. wasim, a., jahanzaib, m., aziz, h., abdalla, h. (2016). predicting the tensile strength, impact toughness, and hardness of friction stir-welded aa6061-t6 using response surface methodology, international journal of advanced manufacturing technology, 87, pp. 1765–1781. doi 10.1007/s00170-016-8565-9. [5] aliemeke, b.n.g., oladeinde, m. h. (2020). box-behnken design optimization of sand casting orocess parameters, international journal of engineering technologies, 6(2), pp. 25–36. doi:10.19072/ijet.714473 [6] zhao, d., bezgans, y., vdonin, n., du, w. (2021). the use of topsis-based-desirability function approach to optimize the balances among mechanical performances, energy consumption, and production efficiency of the arc welding process, international journal of advanced manufacturing technology, pp. 1-15. doi: 10.1007/s00170-021-06601-w. [7] cheepu, m., venkateswarlu, d., nageswara rao, p., senthil kumaran, s., srinivasan, n. (2019). optimization of process parameters using surface response methodology for laser welding of titanium alloy, materials science forum, 969, pp. 539-545. doi:10.4028/www.scientific.net/msf.969.539 [8] srivastava, s., garg, r.k. (2017). process parameter optimization of gas metal arc welding on is: 2062 mild steel using response surface methodology, journal of manufacturing processes 25, pp. 296-305. doi: 10.1016/j.jmapro.2016.12.016. [9] swami, s. a., jadhav, s. m., deshpande, a. (2016). influence of mig welding process parameters on tensile properties of mild steel, jers, european journal of engineering research and science 1(2), pp. 1-5. [10] kamble, a. g., venkata rao, r, (2017). effects of process parameters of gmaw on bead geometry, tensile strength, hardness, microstructure and thermo-mechanical simulation of aisi 202 steel, indian journal of engineering & materials sciences, 24(6), pp. 413-428. [11] rizvi, s. a., ali, w. (2016). application of taguchi technique to optimize the process parameters of mig wedging on is2062 steel, international journal on emerging trends in mechanical & production engineering, 2(2), pp. 1-11. [12] kumar, a., sharma, r. (2020). multi-response optimization of magnetic field assisted edm through desirability function using response surface methodology, journal of the mechanical behavior of materials 29, pp. 19–35. doi:10.1515/jmbm-2020-0003 [13] choudhary, a., kumar, m., rajen.dra unune, d. (2019). experimental optimization of weld bead characteristics during submerged arc welding of aisi 1023 steel, defence technology 15, pp. 72—82. doi:10.1016/j.dt.2018.08.004. [14] xu, w. h., lin, s. b., fan, c. l., yang, c. l. (2015). prediction and optimization of weld bead geometry in oscillating arc narrow gap all-position gma welding, international journal of advanced manufacturing technology 79, pp. 183– 196. doi:10.1007/s00170-015-6818-7. [15] xu, j., yan, f., li , y., yang, z., li, l. (2020). multiobjective optimization of milling parameters for ultrahigh-strength steel af1410 based on the nsga-ii method, advances in materials science and engineering 3, pp. 1-11. doi:10.1155/2020/8796738. [16] sada, s. o. (2018). optimization of weld strength properties of tungsten inert gas mild steel welds using the response surface methodology, nigerian journal of technology (nijotech), 37(2), pp. 407 – 415. doi:10.4314/njt.v37i2.15. [17] nakhaei, m. r., mostafa arab, n. b., naderi, g. (2013). application of response surface methodology for weld strength prediction in laser welding of polypropylene/clay nanocomposite, iran polymer journal 22, pp. 351–360. doi 10.1007/s13726-013-0134-6. [18] aslantas, k., danish, m., hasçelik, a., mia, m., gupta, m., ginta, t., ijaz, h. (2020). investigations on surface roughness and tool wear characteristics in micro-turning of ti-6al-4v alloy, materials, 13(13), pp. 1-20. s. a. rizvi et alii, frattura ed integrità strutturale, 56 (2021) 84-93; doi: 10.3221/igf-esis.56.07 93 doi:10.3390/ma13132998 [19] rizvi, s. a. (2018). application of taguchi technique to optimize the gma welding parameters and study of fracture mode characterization of aisi 304h welded joints, int. rev. appl. sci. eng. 9 (1), pp. 9–16. doi: 10.1556/1848.2018.9.1.2 [20] mia, m., dey, p.r., hossain, m.s., arafat, md. t., asaduzzaman, md., shoriat ullah, md., zobaer, s.m.t. (2018). taguchi s/n based optimization of machining parameters for surface roughness, tool wear and material removal rate in hard turning under mql cutting condition, measurement, 122, pp. 380-391. doi: 10.1016/j.measurement.2018.02.016. [21] juan, w., yajiang, l., peng, l. (2003). effect of weld heat input on toughness and structure of haz of a new superhigh strength steel, bull. mater. sci., 26(3), pp. 301–305. microsoft word numero 1 art 2.doc r..l. colombo et al., frattura ed integrità strutturale, 1 (2007) 19-24 19 1 introduzione che l'uomo primitivo avesse nozione dell'esistenza dei gas è altamente dubbio. al contrario, egli certamente conosceva la differenza fra liquidi e solidi. per lui, i liquidi non offrivano praticamente nessuna resistenza alla deformazione, mentre i solidi la offrivano. la ragione di questa differenza di comportamento per molto tempo eluse la sua capacità di riflessione. nell'antica grecia, democrito (460-370 a.c.) ed epicuro (341-270 a.c.) tentarono di risolvere il problema. poichè la maggior parte dei loro lavori è andata perduta, noi sapremmo ben poco di quel che scrissero se non fosse stato per lucrezio (94-50 a.c.), un grande poeta latino mancante tuttavia di qualsiasi originalità scientifica, che riferì il pensiero di epicuro nel suo "de rerum natura": i solidi sono così resistenti perchè gli atomi che li costituiscono sono legati da uncini o "ami" [1]. ciò può sembrare piuttosto ingenuo all'uomo moderno, ma fino a questo secolo ben poco progresso venne fatto in questo campo: nei fatti, la teoria della coesione nei solidi, così come la conosciamo oggi, è parte della fisica dei solidi e necessita di concetti di meccanica quantistica. 2 leonardo tutti sanno che la fisica sperimentale, almeno ai suoi inizi, è una conquista del rinascimento italiano. crediamo che il primo uomo ad occuparsi della resistenza dei solidi agli sforzi sia stato leonardo da vinci (1453-1519), che certamente trasse profitto da molte visite agli arsenali italiani, tra i quali quello di venezia ebbe la più alta reputazione che gli meritò una citazione da parte di dante nella sua commedia. nel folio 325 del "codex atlanticus" [2] si legge: sperienza della forza che può fare un filo di ferro di varie lunghezze ricordo come tu debbi fare sperienzia del reggere, o vero quanto peso po sostenere uno filo di ferro; alla quale sperienzia terrai questo modo: appicca uno filo di ferro di lunghezza di 2 braccia, o circa, in loco che stia forte; di poi li appicca uno cavagno, o sporta, o quello che a te pare, nel quale, per uno picciolo buso, verserai una tramoggia di minuta rena; e quando esso filo di ferro non potrà più sostenere, si rompa, adatta una molletta che subito el buso della tramoggia si riserri, acciò che più rena non caggi in esso cavagno, il quale caderà in piè, perchè ½ dito caderà da alto; e nota quanto peso fu quello che esso filo spezzò, e nota in che parte di sè detto filo si rompe, e fa più volte questa pruova, per confermare se sempre ‘n un medesimo loco si rompe. di poi fa esso filo più corto la metà di prima, e nota quanto peso sostiene di più; e poi lo fa 1/4 della prima lunghezza, e così di mano in mano farai in diverse lunghezze, notansulla storia degli studi di frattura in italia roberto l. colombo consulente, pino torinese (to) donato firrao politecnico di torino, dipartimento di scienza dei materiali ed ingegneria chimica, corso duca degli abruzzi 24, 10129 torino riassunto: la storia degli studi sulla frattura è inestricabilmente connessa con il progresso della tecnologia. all'inizio pochissimo fu scritto. dobbiamo riconoscere a leonardo e galileo il merito di essere stati fra i primi a scrivere su questo problema e sui modi di misurare e prevedere carichi di rottura. più tardi, scienziati italiani si distinsero nel tentativo di stabilire leggi sulla resistenza dei materiali e sui criteri di rottura sotto sforzi multipli. in questa memoria si descrivono i lavori degli scienziati italiani dei secoli scorsi e si confrontano con i lavori di altri scienziati europei del passato. abstract. history of studies of fracture is inherently intermingled with the history of technology developments. in the beginning very little was written about. we must credit leonardo and galileo as the first ones that wrote about the problem and on how to measure and foresee rupture loads. later, nineteenth century italian scientists distinguished themselves in attempting to establish material laws and multiple stresses rupture criteria. a review of the works of past centuries italian scientists is presented, along with a critical comparison with the work of other past european scientists. parole chiave: leonardo, galileo, cavalli, curioni, beltrami, storia degli studi di frattura, criteri di frattura. r. l. colombo et al., frattura ed integrità strutturale, 1 (2007) 19-24 20 do il peso che ciascuno rompe e ‘l loco dove si rompe... ci vorranno secoli prima che un esperimento così accurato con una apparecchiatura così sofisticata venga fatto o almeno progettato (non sappiamo se leonardo lo eseguì mai davvero). in ogni modo è sorprendente che tanta attenzione venga dedicata alla lunghezza del filo, che noi sappiano irrilevante, piuttosto che al suo diametro. possiamo offrire solamente due spiegazioni: una è che ai tempi di leonardo la misura del diametro di un filo sottile di una data lunghezza fosse molto difficoltosa, l'altra che i fili fossero sovente difettosi per insufficienze tecnologiche e che la probabilità di avere difetti di dimensioni rilevanti fosse più alta in una certa lunghezza di filo e più bassa in fili di lunghezza inferiore, i quali quindi raggiungerebbero carichi di rottura più elevati. se questa seconda interpretazione fosse quella valida, potremmo considerare leonardo un diretto precursore delle teorie probabilistiche di frattura. in un' altra parte del codex leonardo si dilunga sulle resistenze relative di colonne di forma differente e sulla posizione delle rotture. leggendo leonardo bisogna por mente al fatto che egli non è a rigore nè uno scienziato, nè un filosofo, ma bensì un uomo dotato di una straordinaria curiosità per i fatti della natura, che egli riferisce in una serie di aforismi piuttosto che in trattati accademici, come avrebbe fatto galileo, e che molto spesso non si preoccupò di giustificare teoricamente [3]. secondo paolo rossi [4] la sua indagine, sempre oscillante fra l’esperimento e l’annotazione, non ha alcun interesse a lavorare ad un corpus sistematico di conoscenze; per tale ragione le sue intuizioni spesso incredibili ai nostri occhi sono qualche volta accompagnate da ciò che noi giudichiamo errori. 3 galileo galileo galilei (1564-1642) è universalmente considerato il fondatore della fisica sperimentale, che egli perseguì attivamente, quasi devotamente, in contrasto con l'aristotelismo imperante ai suoi tempi. il problema della rottura fu uno di quelli che attrassero la sua attenzione. egli ne trattò nel suo "discorsi e dimostrazioni matematiche intorno a due nuove scienze" [5], libro scritto nel medesimo stile del più famoso "dialogo sopra i due massimi sistemi del mondo" [6]: cioè una conversazione immaginaria tra tre persone, salviati, sagredo e simplicio, le prime due scienziati-filosofi morti giovani poco prima l'apparire dei due trattati, l'ultimo avente il nome, ovviamente significativo, di un filosofo aristotelico del vi secolo d.c., si ignora se attribuito realmente a qualche contemporaneo o semplicemente fantastico. la conversazione va avanti per tre giorni, dei quali quello che ci interessa è il secondo. simplicio incomincia pretendendo che la resistenza di una fune o di una trave dipenda dalla sua lunghezza, un' affermazione condivisa a quei tempi da molte persone intelligenti, tra cui, come abbiamo visto, leonardo. salvati non ha difficoltà a mostrarne l'infondatezza. in seguito egli si dimostra sorpreso dal fatto che, se si sospende la trave in qualche posto con un peso all'estremità (fig. 1), essa si romperà con un carico molto superiore a quello che causerà la rottura nel caso in cui fosse stata incastrata orizzontalmente in un muro di mattoni (fig. 2). figura 1. prova di trazione di una colonna (galilei [5], p.7). figura 2. prova di flessione di una trave (galilei [5], p. 128) queste sono evidentemente le condizioni che oggi chiamiamo di trazione e di flessione. sembra ovvio che galileo non avesse una chiara comprensione delle sollecitazioni che si manifestano sotto differenti condizioni di r. l. colombo et al., frattura ed integrità strutturale, 1 (2007) 19-24 21 carico. in ogni modo, usando brillanti analogie, egli viene alla conclusione che il carico (non la tensione) di rottura è inversamente proporzionale alla lunghezza l della trave e direttamente proporzionale al cubo del raggio della sua sezione (se cilindrica, altrimenti egli sarebbe bene in grado di distinguere fra il ruolo dell'altezza e quello della larghezza). ora, consideriamo un campione cilindrico di raggio r ed un prisma parallepipedo avente una sezione di altezza h e larghezza b. sappiamo dalla teoria dell'elasticità che al limite elastico, σ0, il carico è p = (r3/2l) σ0 (cilindro) (1) e p = (bh2/6l) σ0 (prisma) (2) così che noi siamo subito colpiti dalla somiglianza di queste espressioni (che, non dimentichiamolo, sono valide solo in campo elastico, certamente non fino allo snervamento e men che meno alla rottura torneremo su questi concetti in seguito) con le proporzionalità di galileo. ma galileo non si preoccupava nè del carico al limite elastico, nè dello snervamento. prima di tutto, egli non sapeva nulla dell'elasticità, che è la proprietà per cui se un carico agisce su di un corpo, il corpo da parte sua agisce sul carico. in più, come abbiamo visto, non aveva alcuna chiara visione delle tensioni. si deve ricordare, come abbiamo detto, che ciò che lo preoccupava era il calcolo del carico di rottura ed in questo proposito egli fallì completamente, seppure scusabilmente. gordon [7] spiega che gli scienziati del passato erano confusi dall'analogia col comportamento degli animali (inclusi gli uomini). se uno sostiene un peso di qualche sorta, generalmente non si vedono deformazioni nel suo corpo (per quanto naturalmente qualche deformazione avrà luogo nel suo scheletro). ma uno allora reagisce al peso mettendo i suoi muscoli in tensione, e questo lo stanca e produce un certo lavoro, sicchè alla fine deve smettere e deporre il peso. d'altro canto dobbiamo far credito a galileo della prima osservazione scritta (primo giorno) del fatto che sotto trazione travi più grandi sostengono carichi più elevati e col primo disegno di una prova di trazione su di un corpo di grande sezione (fig. 1). tuttavia egli non riuscì a trasferire questo concetto alla flessione, perchè oltre tutto gli mancava il concetto di asse neutro. certamente ci ha dato anche le prime immagini di quanto può essere considerata una prova di flessione su tre punti (fig. 3). una notazione curiosa ci viene dall’esame del volume originale di galileo. i suoi editori in leyda, dove il suo manoscritto arrivò in maniera probabilmente avventurosa e ufficialmente a sua insaputa [4] (probabilmente solo ufficialmente; non possiamo essere in contrasto con quanto in maniera provocatoria illustra brecht nella “vita di galileo”1), sono gli elfevirii, i quali ancora oggi continuano 1brecht, nella scena quattordicesima, riporta il dialogo fra galileo ed il suo discepolo, andrea sarti, figlio della serva, il quale si prepara a partire per a pubblicare di frattura sotto la traslitterazione moderna di elsevier. fra l’altro sono gli editori degli atti dei congressi quadriennali sulla frattura. figura 3. modi di rottura sotto flessione (galilei [5], p. 133). 4 hooke, newton e young non possiamo passare a prendere in considerazione scienziati italiani in secoli posteriori senza riferire di altri grandi scienziati che diedero inizio al lavoro che condusse alla scoperta dell'elasticità. l'elasticità non è altro che un aspetto del principio di azione e reazione di isacco newton (1642-1727), per quanto questi apparentemente non se ne accorgesse: il carico agisce su un solido deformandolo ed il solido reagisce opponendovisi. l'uomo che se ne accorse fu robert hooke (1635-1702), che per questo è considerato il padre della teoria dell'elasticità. nel 1660, riflettendo sull'opera di un amico che era un famoso orologiaio, egli annunciò i suoi risultati nel seguente anagramma: ceiiinosssttvv fortunatamente, nel 1676 (!) in un trattato intitolato "de potentia restitutiva" egli risolse così l'anagramma: vt tensio sic vis certamente e. mariotte (1620-1684) disse qualcosa sull'elasticità lineare entro il 1676, ma non prima del 1660, inoltre non tentò di risolvere l'anagramma dello hooke. per questo noi consideriamo costui, e non il mariotte, padre (forse sarebbe meglio dire nonno) della teoria dell'elasticità. tuttavia lo hooke con la parola "tensio" non intese quello che oggi intendiamo noi, ma piuttosto "estensione", cioè, in parole povere, "allungamento". nei fatti, egli comprese l'elasticità, ma non quello che noi intendiamo per tensione. questo perchè egli si disinteressò della forma e delle dimensioni del solido di cui andava occupandosi. inoltre egli non si accorse che la sua legge era valida solamente nel campo che noi chiamiamo elastico. ci ritorneremo su. l’olanda con il manoscritto dei “discorsi” sotto il mantello. andrea sarti non sembra essere una figura storica, ma introdotta perché nel populismo brechtiano il messaggero doveva essere, appunto, “figlio della serva”. r. l. colombo et al., frattura ed integrità strutturale, 1 (2007) 19-24 22 thomas young (1773-1829) ebbe senza alcun dubbio una chiara comprensione delle tensioni. nel 1807 era stato appena licenziato dalla royal society perchè il suo lavoro non era considerato abbastanza pratico (per fortuna fu presto assunto dal bureau des longitudes). in quell'anno egli annunziò la legge che porta il suo nome, cioè: σ / ε = e (3) dove σ e and ε sono ciò che noi chiamiamo tensione e deformazione. il coefficiente di proporzionalità e prende il nome di modulo di young o di elasticità. l'invenzione del modulo di young fu un fatto rivoluzionario ed il primo anello di una catena che in una ventina d'anni consentì di sviluppare la scienza dell'elasticità su basi rigidamente matematiche. come abbiamo suggerito, la legge di hooke è valida soltanto nel campo elastico, cioè fino al cosiddetto limite elastico o di proporzionalità. in seguito la deformazione cresce più rapidamente, cioè il materiale si snerva. alla fine si raggiunge un massimo nella tensione ingegneristica ed il solido incomincia a rompersi. 5 cavalli mentre gli scienziati si occupavano di sviluppare la matematica della teoria dell'elasticità usando l'analisi differenziale, introdotta dal newton e da gottfried wilhelm leibniz (1646-1716), l'interesse per lo snervamento e la rottura andava scemando. chi tentò di affrontare il problema, sebbene in maniera un po' rozza, fu giovanni cavalli (1807-1879). quando era capitano di artiglieria nell'esercito del re di sardegna, egli inventò un cannone a retrocarica e soprattutto il cannone a canna rigata, ed oggi è ricordato solo per questo, il che è francamente ingiusto. sebbene egli si occupò soprattutto di problemi di carattere militare (in seguito raggiunse il grado di generale nell'esercito italiano, divenne direttore della scuola di artiglieria, fu deputato al parlamento ed infine senatore del regno), condusse importanti studi di ingegneria e di meccanica fondamentale: per esempio, con federigo menabrea e carlo mosca fu membro del comitato di consulenza per la geologia creato dal ministro dei lavori pubblici pietro paleocapa per il traforo del frejus. in tre memorie [8, 9, 10] egli esprime il dubbio che la legge di proporzionalità dello hooke possa non esser mai interamente valida, specialmente per certi materiali, tra i quali egli cita la ghisa ed il ferro, ed in ogni modo sicuramente non oltre una certa tensione, cioè il limite elastico, al di là della quale hanno luogo deformazioni permanenti. nell'insieme egli esprime diverse leggi: 1 la proporzionalità fra carico e deformazione non esiste in maniera assoluta per la ghisa ed il ferro dolce, se non al massimo per tensioni fra 0 e la metà del carico di rottura. 2 un allungamento permanente ha luogo già sotto i carichi più bassi; il punto in cui la deformazione cresce molto più rapidamente che secondo la legge di hooke è altamente variabile anche in ferri della stessa provenienza. in conseguenza, il limite elastico, se esiste, perde qualsiasi rilevanza pratica. 3 omissis 4 omissis 5 ferro e ghisa non sottoposti ad urti e vibrazioni sopportano indefinitamente tensioni vicine alla tensione di rottura istantanea. 6 le formule di resistenza in uso devono essere emendate. nel 1846 il cavalli costruì una macchina di flessione, che sotto molti aspetti sembrava una macchina di rilassamento tipo denyson, eccetto che il carico veniva applicato deponendo gentilmente dei pesi crescenti, e munita di un sistema di registrazione. nei suoi esperimenti egli credette di poter distinguere due parti della deformazione, una elastica e reversibile, l'altra irreversibile dalla partenza e poi fino alla rottura: entrambe seguono leggi differenti, ma uniformemente regolari. tra i pesi deposti, egli ne scopre uno, che la provetta non può sopportare stabilmente perchè al di sopra di esso incomincia un rilassamento, che poi accelera man mano che si avvicina la rottura, e questo anche se la durata della prova è breve. come oggi sappiamo, questo rilassamento è una conseguenza dello snervamento, ma il cavalli, cui va anche il merito di aver posto attenzione a un fenomeno come l'incrudimento, credette di aver scoperto una legge di natura. egli propose che al carico intermedio che abbiamo appena descritto venisse dato il nome di limite di stabilità e che esso venisse usato nei calcoli di ingegneria al posto del limite elastico. 6 curioni molti tentarono di estendere la formula che fornisce il limite elastico alla tensione di rottura σr , scrivendo: σr = αpl/(bh2) (4) dove α è una costante numerica. galileo la pose uguale a 2, baumgarten a 2,5, hodkinson & fairbain a 2,63, leibniz a 3 ed infine navier a 6, cioè quest’ultimo trascurò completamente l'influenza della plasticizzazione. a molti sembrava possibile eliminare le incongruenze ammettendo semplicemente che al di sopra del limite elastico l'asse neutro non fosse più baricentrico, cioè che le caratteristiche meccaniche in trazione e compressione non fossero più uguali. presto si scoprì negli stati uniti che α non era per nulla una costante, il che significava che o la teoria era sbagliata o gli esperimenti in difetto. giovanni curioni (1831-1887) incominciò la sua carriera come allievo del mosca, che abbiamo già incontrato come membro del comitato di consulenza per il traforo del frejus e che progettò il ponte in muratura sulla dora r. l. colombo et al., frattura ed integrità strutturale, 1 (2007) 19-24 23 riparia a torino: a quel tempo, era considerata un'impresa rischiosa, così il mosca rimase sotto il ponte durante le prove di carico, per mostrare la sua fiducia nei suoi calcoli. a tempo debito, il curioni divenne professore della scuola di applicazione per gli ingegneri e del politecnico di torino e poi direttore di quest’ultimo e scrisse un libro col titolo: "resistenza dei materiali e stabilità delle costruzioni" [11]. marchis e jarre [12] ricordano che costruì un buon numero di macchine di prova differenti fino al 1880. il curioni definisce accuratamente le tensioni di snervamento e di rottura: "lo snervamento ha luogo nei corpi soggetti a forze esterne quando queste, crescendo al di sopra di un certo limite, hanno prodotto un tale spostamento molecolare che non è più possibile che le molecole spostate, mentre restano sotto l'azione delle dette forze, si riaggreghino in un nuovo stato di equilibrio stabile, il che quindi col tempo produce una disaggregazione totale, cioè la rottura. la rottura può aver luogo pressocchè immediatamente all'applicazione delle forze esterne, se sono abbastanza grandi." il curioni fece anche delle osservazioni interessanti sull'influenza del tempo, dichiarando: a) una forza esterna, che non produce snervamento in un corpo in cui è applicata, può farlo se la sua azione si prolunga per un tempo abbastanza grande; b) una forza esterna, che non può rompere un corpo dopo aver agito su di esso per breve tempo, può romperlo dopo un tempo supplementare; c) forze esterne intermittenti ripetute abbastanza frequentemente possono produrre lo stesso effetto di un'azione continua. oggi chiamiamo questi effetti rilassamento meccanico, frattura ritardata e fatica. e' interessante notare che due degli studiosi che abbiamo già nominato a proposito della tensione di rottura, e cioè e.a. hodkinson [13] e w. fairbain [14], sono fra i pionieri nello studio di quella che diventerà la scienza della fatica. 7 beltrami quando un corpo sottoposto ad un certo sistema di forze si snerva o si rompe (nei fatti, quando inizia lo snervamento massiccio, la rottura finisce col seguirne)? l'idea più semplice apparve ritenere che ciò succede quando la tensione di trazione raggiunge un certo valore, che è il carico di snervamento. al di fuori della trazione pura, questo non è vero. così sono stati introdotti numerosi criteri [15]. fra questi il criterio di tresca (in verità inventato dal coulomb) suggerisce che lo snervamento ha luogo quando la tensione tangenziale risolta raggiunge un certo valore. nel caso della torsione pura, cioè quando delle sei componenti della tensione soltanto τxy è diversa da 0, si trova: σs = 2τs (5) cioè: τs = 0,5σs (6) di solito sperimentalmente si trova un valore più alto (0,58). tuttavia il criterio di tresca è ancora usato in ragione della sua semplicità. eugenio beltrami (1835-1900) fu professore di algebra complementare e geometria analitica nell'università di bologna, poi di geodesia a pisa, quindi di meccanica razionale ancora a bologna e poi a roma con l'incarico ulteriore di analisi superiore, di fisica matematica e meccanica superiore a pavia, infine di meccanica e fisica matematica di nuovo a roma. nel suo peregrinare scientifico oltre che accademico, partendo dalla geometria analitica, si avvicinò progressivamente alla teoria dell’elasticità sulla scia di lamé, de saint-venant e neumann [16]. sulla scorta dei suoi studi sulle funzioni potenziali, beltrami si occupò a fondo del potenziale d’elasticità in una serie serrata di studi [17, 18, 19, 20]. egli arrivò così ad ipotizzare che, allorchè l'energia potenziale di deformazione raggiunge un massimo, si perviene ad un equilibrio instabile che comporta uno snervamento generalizzato a cui segue la rottura. l'energia potenziale volumica ϕ è: ϕ = (1/2e)(σid2) = [(1+1/m)/e]τxy2 (7) dove m è il modulo di poisson, approssimativamente uguale a 10/3. di qui: τs = 0,62σs (8) questo fattore non è ancora soddisfacente, ma il criterio di beltrami (nel mondo anglo-sassone individuato come criterio di haig) è importante perchè è il primo basato sul concetto di energia piuttosto che su quello di tensione o deformazione. oggi esso è sostituito da quello dovuto a richard von mises, che notò come una pressione puramente idrostatica, per quanto elevata, non conduca allo snervamento, e quindi adottò un criterio analogo a quello di beltrami, ma prendendo in considerazione solo quella parte delle tensioni che producono distorsione e non dilatazione (o contrazione). il criterio di von mises fornisce il valore corretto per il rapporto τs/σs = 0,58. 8 dal 900 ad oggi da quei tempi ormai remoti, il lavoro sulla frattura ha fatto progressi in italia come in qualsiasi altro paese. poichè un corpo completo di cognizioni teoriche come quello sviluppato da g.r. irwin sulla meccanica della frattura statica doveva attendere i tardi anni '50, molto dello sforzo compiuto nella prima metà di questo secolo fu de r. l. colombo et al., frattura ed integrità strutturale, 1 (2007) 19-24 24 dicato alla fatica, che venne presto riconosciuta come la causa della rottura della maggior parte dei pezzi meccanici. la rapida crescita della fiat auto spinse la ricerca in questo campo nei suoi laboratori centrali sotto la guida di l. locati, scomparso pochi anni fa. più tardi, un certo lavoro sulla meccanica della frattura iniziò da qualche luogo senza tuttavia essere inserito in uno sforzo coordinato. per esempio, s. venzi & a.h. priest [21] scoprirono che nei primi stadi delle prove di resilienza l'influenza dell' inerzia è tanto importante quanto la reazione delle incudini, di modo che la significatività dei risultati per solidi molto fragili finisce per scemare grandemente. la ricerca post-irwin iniziò al centro sperimentale metallurgico a roma ad opera di un gruppo di giovani ricercatori, principalmente s. venzi, m. mirabile, g. buzzichelli e m. castagna, sotto la direzione di p. brozzo. nel 1982 gli autori della presente memoria con numerosi compagni e per impulso di g. caglioti, fondarono a torino il gruppo italiano frattura come foro per la circolazione di idee ed applicazioni e come punto di incontro per scienziati di tutte le nazioni, che sono affluiti numerosi ai suoi congressi e giornate di lavoro. 9 conclusioni il contributo degli scienziati italiani all'insieme della ricerca sulla frattura risale ai tempi di roma antica: parole come "duttile" e "fragile" si trovano già nella "naturalis historia" di plinio il vecchio (23-79 d.c.) e riflettono quell'abitudine all'osservazione che aprì la strada, dopo la rivoluzione culturale dell'umanesimo, ai grandi scienziati del rinascimento e del principio dell'età moderna. nel secolo scorso sono emersi contributi importanti da quella culla della scienza ingegneristica che fu a quei tempi l'accademia delle scienze di torino, dove gli scienziati poterono anche condurre esperimenti sfruttando i progressi tecnologici dell'arsenale locale. abbiamo cercato di illustrare questi successi storici del nostro paese, dedicando minore attenzione agli sviluppi più recenti. abbiamo pensato infatti che il nostro contributo di storici autodidatti potesse giovare ai giovani ricercatori per fornire un senso dello sviluppo storico che li ha portati alle moderne teorie della meccanica della frattura, iniziate con g.r. irwin a metà di questo secolo. 10 bibliografia [1] lucretius t. caro, “de rerum natura“ (57 a.c.). testo latino con trad. ital. di e. cetrangolo, sansoni, firenze, 1978. [2] l. da vinci, , “codex atlanticus” (1483-1518) biblioteca ambrosiana milano. pinnati, milano, 1894-1904. [3] j. recupero, , “selezione di scritti di leonardo da vinci”, editrice italiana di cultura, roma (1966). [4] p. rossi “la nascita della scienza moderna in europa”, laterza, bari (1997). [5] g. galilei, , “discorsi e dimostrazioni sopra due nuove scienze attenenti alla mecanica & i movimenti locali”, elsevirii, leida (1638). [6] g. galilei, “dialogo sui due massimi sistemi del mondo”, 1632, einaudi, torino (1990). [7] j.e. gordon, “the new science of strong materials”, penguin book, harmondsworth (1971). [8] g. cavalli, , “memoria su vari perfezionamenti militari”. mem. acc. sci. torino, xvii, serie ii (1858) 1. [9] g. cavalli, “memoria sul delineamento equilibrato degli archi in muratura ed in armatura”, mem. acc. sci. torino, xix, serie ii (1859) 143. [10] g. cavalli, “mémoire sur la théorie de la resistance statique e dinamique des solides (surtout aux impressions comme celle du tir des canons)”, mem. acc. sci. torino, xxii, serie ii (1863) 157. [11] g. curioni, “resistenza dei materiali e stabilità delle strutture”, augusto federico negro, torino (1874). [12] v. marchis, g. jarre, “accademici o tecnologi?”, in: società e scienza. 200 anni di storia dell'accademia delle scienze di torino, allemandi & c., p.92, torino (1988). [13] w. fairbairn, phil., trans. roy. soc., (1864) 311 [14] e.a. hodkinson, ponts et chaussées, (1851) 193. [15] c. brutti, “costruzioni di macchine”, parte i (resistenza dei materiali). dispense ciclostilate dalle lezioni universitarie, roma (1947). [16] e. beltrami, “sulle equazioni generali dell’elasticità”, ann. mat. pura appl., x, serie ii (188082) 188. [17] e. beltrami, , “sulla rappresentazione delle forze newtoniane per mezzo di forze elastiche”, rend. r. ist. lombardo, xvii, serie ii (1884) 581. [18] e. beltrami, “sull’uso delle coordinate curvilinee nelle teorie del potenziale e dell’elasticità”, mem. r. acc. sc. ist. bologna, vi, serie iv (1884) 401. [19] e. beltrami, “sulle condizioni di resistenza dei corpi elastici“, rend. r. ist. lombardo, xviii, serie ii (1885) 704. [20] e. beltrami, “sull’interpretazione meccanica delle formole di maxwell”, mem. r. acc. sc. ist. bologna, vii, serie iv (1886) 1. [21] s. venzi, a.h. priest, “influence of inertial load on instrumented impact test”, bisra rep. mg/c/61/68, (1968). microsoft word numero_58_art_04_3076 m. emara et alii, frattura ed integrità strutturale, 58 (2021) 48-64; doi: 10.3221/igf-esis.58.04 48 numerical assessment of reinforced concrete beams strengthened with cfrp sheets under impact loading mohamed emara, nada elkomy, hilal hassan structural engineering dept., faculty of engineering, zagazig university, zagazig, 44519, egypt mremara@eng.zu.edu.eg, http://orcid.org/0000-0003-4936-5257 nadaelkomy16@gmail.com habdelkader@zu.edu.eg, http://orcid.org/0000-0001-5486-5497 abstract. this paper investigates numerically the behavior of reinforced concrete (rc) beams, strengthened using carbon fiber reinforced polymers (cfrp) sheets, subjected to impact loading. three-dimensional finite element analysis was performed and its results were verified against experimental ones available in the literature showing good agreement. then, a comprehensive parametric study was performed to investigate the effect of studied parameters on the strengthened rc beams. the main studied parameters were the type and size of reinforcing bars, geometric characteristics of externally bonded cfrp sheets (width, length, and thickness), impact velocity, and the position of the impactor with respect to the beam. results showed that the use of externally bonded cfrp sheets enhanced the beam capacity and failure mode, and reduced the mid-span deflection. on the other hand, increasing the impact velocity increased the mid-span displacement, however, the use of cfrp bars as internal reinforcement could reduce the increase in the deflection. moreover, changing the position of the impact load application showed a significant effect on the mid-span displacement as well as the failure mode of tested beams. keywords. concrete; rc beams; finite element; carbon fiber reinforced polymers; impact. citation: emara, m., elkomy, n., hassan, h., numerical assessment of reinforced concrete beams strengthened with cfrp sheets under impact loading, frattura ed integrità strutturale, 58 (2021) 48-64. received: 16.04.2021 accepted: 11.07.2021 published: 01.10.2021 copyright: © 2021 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. introduction mpact loading research has significant civil engineering applications, such as crash barrier design, structural impact resistance design toward military and terrorist attack, rock fall, vehicle collision, inadvertently dropping heavy objects on buildings, marine buildings impact resistance design, and blonde fence design. nowadays, fiber reinforced polymers (frp) materials are being widely used in strengthening and retrofitting reinforced concrete (rc) structures due i https://youtu.be/mi9dpggvt6u m. emara et alii, frattura ed integrità strutturale, 58 (2021) 48-64; doi: 10.3221/igf-esis.58.04 49 to several advantages they provide over the traditional steel plates, such as high tensile strength, high corrosion resistance, ease of use and low cost [1-3]. the utility of using frp for strength beams subjected to static loads has been extensively studied, although minimal studies have been identified to strengthen carbon frp (cfrp) for beams subjected to impact loads [4-6]. many studies had investigated experimentally and analytically the dynamic response of rc beams under impact load. the dynamic response to the impact load of rc beams was tested experimentally and analytically by fujikake et al. [7]. twelve rc beams had been tested under the drop weight induced impact load. the influence of the weight drop height and the amount of longitudinal reinforcing steel in the beam on the dynamic response of rc beams were the main parameters of the study. the results showed that the local failure was minimized by raising the longitudinal steel reinforcement. moreover, the amount of bottom longitudinal steel reinforcement influenced the local damage close to the impact point. for rc beams failing in flexure, a strong agreement between experimental and analytical results was observed. the impact behavior of frp-strengthened rc beams without stirrups was studied by pham and hao [8]. the author performed dropweight testing on thirteen beams that had been wrapped in different ways to strengthen them in shear. experimental results showed the possibility of estimating the frp contribution to shear strength with fair precision by the method recommended by aci 440.2r-08 [9]. however, under impact loads, the frp debonding strain is significantly lower than that under quasistatic loads. therefore, to achieve better estimations, actual debonding strains of frp were recommended for impact loads. kantar et al. [10] performed an experimental and theoretical analysis investigating the influence of concrete compressive strength on the impact behavior of rc beams. testing of two sets of five beams manufactured with normal and high concrete compressive strength was part of the experimental program. under impact loading, all beams were tested, using a drop hammer from five various heights. the results indicated that the compressive strength of concrete influenced the mode of failure of rc beams. a greater number of drops were also expected for beams with high compressive strength than those with normal compressive strength. more energy was also consumed by normal compressive strength concrete beams compared to high-strength beams. numerical analysis was performed to simulate the tested beams under impact loading. the verification contrasted the results of the finite element model with those of experimental tests. the observations indicated a good agreement between both the finite elements and the experimental results. in order to improve the flexural capacity of rc beams, erki and meier [11] conducted experimental tests on four externally reinforced rc beams under impact loading. two beams were strengthened using cfrp laminates, while the other two beams were strengthened using steel plates. the impact load was created by lifting and dropping a weight on simply supported beams from the height provided. results have shown that the energy absorption of cfrp laminate beams is lower than that of external steel plate reinforced beams. tang and saadatmanesh[12] conducted an experimental study to investigate the impact behavior of rc beams externally reinforced using frp sheets. the results indicated that the bending strength and stiffness of retrofitted rc beams can be greatly improved by the composite sheets. esfahani et al. [13] studied the flexural strength of rc beams strengthened with cfrp sheets. steel reinforcement ratio, length, width and number of cfrp layers were the experimental variables. twelve rc beams and three different steel reinforcement ratios were used. three beams were regarded as control beams, while nine rc beams were externally strengthened using cfrp laminates. the results showed an improvement in flexural strength of rc beams strengthened with cfrp laminates over that of control beams. compared with the maximum longitudinal reinforcement steel ratio, the improvement in flexural strength is overestimated when using small steel reinforcement ratios. the proportion of the increase in flexural strength of the strengthened beams was influenced by the steel bar size. increasing the bar size decreased the carrying capacity of the load, which increased even as the number of cfrp layers increased due to the debonding of cfrp laminate in strengthened beams. in beams with large steel bars, the cfrp debonding occurs faster than in beams with small steel bar sizes. high bending load resisted the wide bar size steel bars beams and this caused high tensile stresses in the steel bars. the behavior of rc beams under quasi-static and impact loading conditions has been investigated by banthia and mindess [14]. twelve specimens of reinforced concrete beams had been tested, two of them under quasi-static loading and the others under impact loading. one rc beam was strengthened with gfrp sheets for quasi-static and impact loading. the results indicated that the capacity of the beam under quasi-static load is greater than that of beams under dynamic loading. watstein [15] carried out dynamic experiments on rc beams, the results showed that under dynamic loads the compressive strength of concrete increased 85 to 100 percent compared to that of static conditions. experimental research on concrete beams strengthened with gfrp bars under static and impact loading was conducted by goldston et al.[16]. they conducted experimental experiments on twelve rc beams with the aim of investigating the effect of gfrp reinforcement on the strength of the concrete beam subjected to static and dynamic loading. they showed that under static loading conditions, the higher gfrp reinforcement ratio resulted in a higher cracking rate and less ductility. on the other hand, the strength of the beams was 15-20% percent higher than the strength obtained by the static loading conditions under dynamic loads. the bond between frp and concrete under quasi-static and impact loadings was studied by khalighi[17]. they carried out experimental studies on frp reinforced concrete beams and showed an improvement in the beams' bearing capacity. a new heavy-drop weight impact test machine was designed and produced m. emara et alii, frattura ed integrità strutturale, 58 (2021) 48-64; doi: 10.3221/igf-esis.58.04 50 by al-farttoosi, mahdi [18] to perform the experimental work to study the impact behavior of the cfrp strengthened concrete beams. to strengthen the rc beams, externally bonded reinforcement (ebr) was used. the width and height of the beams measured were 150 mm and 200 mm respectively and 3150mm long with a clear span of 3000 mm. the results indicated that the force of impact encountered by the strengthened beams was lower than that of the control beam. cfrp increased the beam stiffness in strengthened beams, decreased the width of the cracks and their propagation, and decreased both the deformation of the beam and the number of cracks. under impact loading, the cfrp significantly reduced the residual deflection and maximum deflection of the reinforced beams. the use of cfrp to strengthen the beams diminished the beams' ductility and increased the risk of their sudden failure. pham and hao [19] investigated the behavior of reinforced concrete beams strengthened with fiber-reinforced polymers under impact loads. the experimental program included a control beam (rb) and strengthened one (nl1b) tested under impact loads. longitudinal fiber-reinforced polymer strips were used to strengthen the beam. the experimental results showed that the strengthened beam with cfrp layer is better than the control beam against impact loads. from the analysis of the available literature, it can be concluded that the finite element analysis (fea) can be considered as a reliable alternative to the expensive and time-consuming experimental approach. moreover, more research still required to investigate the behavior of rc beams strengthened with frp materials. for this, this paper investigates numerically the flexural response of rc beams strengthened using cfrp sheets under impact loading. a three-dimensional finite element model (fem) was developed, and the obtained results were validated against experimental results available in the literature. then a parametric study was performed considering the flexural reinforcement type, the diameter of reinforcing steel rebars, cfrp sheet width, and the bonded length of the cfrp. (a) (b) figure 1: details of cfrp strengthened rc beam specimens [19]: (a) longitudinal section, and (b) cross-sections. experimental work n experimental study available in the literature [19] was used to verify and validate the numerical model. in this study, a series of cfrp strengthened rc beams were tested under impact load. the rectangular beam had dimensions of 150 mm, 250 mm and 2200 mm for the width, height and total length, respectively, with a clear span of 1900 mm between supports as shown in fig. 1. at 28 days of age, the concrete compressive strength was 46 mpa. two steel bars with a diameter of 12 mm were used at the top of the beam, while two steel bars with a diameter of 10 mm were used to reinforce the bottom of the beam. for shear reinforcement, 10 mm steel bars were used. for the total beam length, a m. emara et alii, frattura ed integrità strutturale, 58 (2021) 48-64; doi: 10.3221/igf-esis.58.04 51 the distance between the stirrups was 125 mm. steel reinforcement yield strengths (d12, d10) were 500 and 250 mpa, respectively. the beam was strengthened in flexure by an externally bonded cfrp sheet, with a nominal thickness of 0.45 mm, the width of the cfrp layer used in the experiments was 75 mm. the tensile strength and elastic modulus of the cfrp sheets were 1548 mpa and 89 gpa, respectively. in this analysis, two samples were selected to be simulated and verified. the two samples were an un-strengthened sample (control beam (rb)), and a strengthened sample (nl1b) with cfrp sheet in the longitudinal direction. the impact experiments were conducted out by dropping a mass from a particular height onto the mid-span of the beams. a solid cylinder, of 203.5 kg weight, was lowered from a vertical height of 2 m at mid-span to achieve a velocity of 6.3 m/sec. numerical modeling materials constitutive models nown geometry and mechanical properties of materials are needed for abaqus inputs, particularly for concrete materials. typically, concrete parameters are based on empirical equations linking stress to their corresponding strains. in this research, the principles of the concrete damage plasticity model (cdp) [20-23] were used to link stresses to strains. due to their versatile utility, the cdp model has been used in various types of loading conditions for instance: static, dynamic or monotonic and cyclic loadings. compressive and tensile stress-strain under its damage states is considered by the model. for the cdp model available in abaqus, fig. 2 is used to identify the post-failure stress-strain interaction of concrete. young's modulus (εo), stress (σt), cracking strain (εck) and the damage parameter values (dt and dc) for the specific concrete grade were the input parameters. the cracking strain (εck) can be determined by eqn. (1).  ck t elε ε ε (1) where the elastic-strain referring to the undamaged material is εel= σt/ εo, and εt is the total tensile strain. furthermore, the plastic strain (εpl) for concrete tensile behavior can be defined as shown in eqn. (2):    t t pl ck t d σ ε ε d e01 (2) a generic diagram of the relationship between compressive stress-strain with damage properties is shown in fig. 2 (a). the inputs are stresses (σc) that lead to stress values and damage properties (dc) with inelastic in tabular format, inelastic strains (εin). it should be noted that using eqn. (3), the total strain values should be translated into inelastic strains.  in c elε ε ε (3) where εel refers to the strain of undamaged material, and εc is the total compressive strain. moreover, using eqn. (4), the plastic strain values in compression (εpl) can be calculated as follows:    pl c ε ε 01 c c c d d e (4) tab. 1 presents the parameters used to define the cdp model. steel was modeled as elastic-perfectly plastic material with similar behaviors in tension and compression as shown in fig. 3. the material properties for the steel reinforcement are as follows: elastic modulus (es=200,000) mpa, poisson’s ratio (0.3). cfrp material was defined using a lamina model in which the elastic moduli, shear moduli in two directions and poisson's ratio, and cfrp's linear elastic response were defined. abaqus/explicit offers hashin 's failure criteria[24], widely used to describe the damage in composite materials, in order to implement the damage in the cfrp in this model. in addition to longitudinal and transverse shear strengths, this damage model is identified by supplying cfrp's longitudinal and transverse tensile and compression strengths as presented in tab. 2. k m. emara et alii, frattura ed integrità strutturale, 58 (2021) 48-64; doi: 10.3221/igf-esis.58.04 52 (a) (b) figure 2: concrete damage plasticity model: (a) compression, and (b) tension figure 3: stress-strain relationship for steel reinforcement parameter value description ψ 30 dilation angle  0.1 eccentricity fb fc0 0/ 1.16 the ratio of initial equibiaxial compressive yield stress to initial uniaxial compressive yield stress. μ 0.0001 viscosity parameter k 0.667 kc, the ratio of the second stress invariant on the tensile meridian table 1: material parameters of concrete, based on abaqus recommendations. property description unit value ρ density kg/ 3m 1600 1e elastic modulus in longitudinal (fiber) direction gpa 89 2e elastic modulus in transverse (matrix) direction gpa 17 12g in-plane shear modulus gpa 6 1tσ longitudinal tensile strength mpa 1548 1cσ longitudinal compressive strength mpa 1200 2tσ transverse tensile strength mpa 50 2cσ transverse compressive strength mpa 250 12τ in-plane shear strength mpa 70 table 2: cfrp material properties. σ + σ fy fy εy εy es compression tension m. emara et alii, frattura ed integrità strutturale, 58 (2021) 48-64; doi: 10.3221/igf-esis.58.04 53 model built-up, boundary conditions, and interaction properties. solid elements (c3d8r) available in the abaqus / explicit element library with three degrees of freedom (8-nodes) were used to model the reinforced concrete beams studied in this paper. the concrete parameters in tab. 1 are needed to completely describe the cdp model, and their numerical parameters were chosen based on simulia [25] recommendations. a two-node linear displacement beam element (b31) was chosen to reflect the internal reinforcement (main reinforcement and stirrups). using a discrete rigid body as a reference point, the impactor was modelled to provide the hammer's mass. the discrete rigid body was selected as no deformation occurred in the experimental investigation [18]. in order to simulate the cfrp, shell elements (s4r) were employed. cfrp mechanical properties used in the current study are shown in tab. 2 [19, 26]. to represent the bond between longitudinal and transverse reinforcements with concrete, embedded region coupling was used. this coupling allows one region to be identified by the user as the host and another as embedded. reinforcements reflected the embedded region in this model, and the host region was the concrete beam [27]. cohesive elements, six degrees of freedom per node (coh3d8), have been used to model the contact region between cfrp and the concrete beam. this type of element has been commonly used to identify this type of contact zone [28]. by using the contact pair possible choice in abaqus/explicit, the interaction between the impactor and the tested beams was established. to implement the abaqus/explicit contact pair algorithm, it is important to define the master and slave surfaces. in order to describe these surfaces, a few rules should be followed. among these guidelines, the softer underlying material should be the slave surface. the impactor was therefore viewed as a master surface, while the impacted member (rc beam) was selected to be a slave surface [28, 29]. coupling restriction was made to prevent the scattering of results. a reference point (rp) placed at the center of the support on the bottom of the projectile creates this coupling restriction. the loading is exercised at the mid-span of the beam via a hammer for impact, and a surface-to-surface constraint was used. consequently, at one point, one might obtain force-displacement results with minimal errors. as the beams were simply supported, the degrees of freedom of u1, u2, and u3 were set to zero. several mesh sizes were used to calibrate the fe model, and finally, a mesh size equal to 20 mm was selected for providing acceptable results while keeping lower computational time. fig. 4 demonstrates the arrangement of reinforcing bars, rc beams, supports, and hammer in the abaqus program [27]. figure 4: details of fe model. results and verifications igs. 5-7 and tabs. 3 and 4 verify the comparison between abaqus modeling and the experimental tests of pham and hao [19]. fig. 5 shows the impact force-time history (f-t) curves for the two specimens chosen from pham and hao [19], comparing fe predictions and experimental data. the comparison demonstrates the capability of the developed fe model to predict the (f-t) curves of rc beams strengthened in flexure under impact load, with reasonable f m. emara et alii, frattura ed integrità strutturale, 58 (2021) 48-64; doi: 10.3221/igf-esis.58.04 54 accuracy. in addition to the general response, the model must be able to accurately predict the key points within the curve, which are: (1) the maximum impact force (fmax), (2) maximum displacement (δmax); (3) residual displacement (δr); (4) and impact duration (d)[30]. the fe predictions for fmax, δmax, and δr agreed very well with the experimental data, with a percentage difference of 2.35-7.99% for fmax, 1.74-7.62% for δmax, and 6.6-16% for δr. tab. 3 shows that the percentage of difference between fe and test for impact period predictions (d) varied between 16 to 18 %. this may be due to a variety of fixity conditions in the actual test that can't be numerically captured, the damping force generated by the testing rig, model limitations in terms of material idealization and mesh, or a combination of these factors. however, the observed difference in d is within the acceptable maximum range found in the literature [31] and doesn’t affect the overall accuracy of the model's results. fig. 6 shows the displacement-time histories (d-t) for the modelled beams. it can be shown in this figure that the overall displacement of strengthened beams is usually less than that of un-strengthened beams, with different values depending on the cfrp configuration. in addition, the comparison between the experimental and fe (δ-t) history confirmed the capability of developed models in capturing these curves very well, for both, the un-strengthened samples, and this strengthened by longitudinal cfrp sheet. furthermore, cfrp strengthening can be considered an effective method to reduce impact and blast loads. fig. 7 shows that the reaction forces began as negatives due to the rayleigh wave as described above, then increased to maximum values in the positive region due to the global equilibrium of the beam against impact loadings, before returning to negatives due to free vibrations of the beam. the first maximum negative reaction forces associated with beam-free vibrations were greater than their second counterparts. another way to validate the accuracy of a developed model is the concrete crack pattern. in most cases, the cracking patterns in abaqus are visualized by plotting the concrete principal strains[32]; but in this analysis, a more precise methodology is used by enabling and plotting the tensile damage parameter (dt) in the cdp model. tab. 4 shows the experimental and fe predicted cracks patterns for two beams from the experiment set [19]. the crack patterns from the model were almost identical to those occurring in the experimental tests. sample peak impact force  maxf (kn) maximum displacement  max (mm) residual displacement ( r ) (mm) duration (d) (ms) exp fem diff% exp fem diff% exp fem diff% exp fem diff % rb 453 442.4 2.4 % 52.3 51.4 1.7 % 41.6 49.5 16% 39 32 18% nl1b 470 510.9 8 % 41.1 38 7.6 % 31.2 33.4 6.6% 38 32 16% table 3: comparison between experimental and fe results. (a) (b) figure 5: fe versus experimental impact force-time histories: (a) beam rb, and (b) beam nl1b. m. emara et alii, frattura ed integrità strutturale, 58 (2021) 48-64; doi: 10.3221/igf-esis.58.04 55 (a) (b) figure 6: fe versus experimental displacement-time histories: (a) beam rb, and (b) beam nl1b. (a) (b) figure 7: fe versus experimental reactions-time histories: (a) beam rb, and (b) beam nl1b. parametric study ue to the scarcity of studies on rc beams strengthened in flexure and subjected to impact loading, the optimized fe model presents a great opportunity to investigate the behavior of these members in depth and to perform a detailed parametric study on the effects of several variables that are designed to affect the member's capacity. the following sections discuss the parametric analysis carried out concerning the type and diameter of reinforcement bars, geometric parameters of cfrp layer of externally bond reinforcement ebr (width, length and thickness), impact velocity and position of the impactor in relation to the length of the beam. as shown in tab. 5, fourteen specimens were strengthened using cfrp sheets. the length and width of cfrp sheet varied in different specimens. two specimens were kept without change in cfrp length or width, but reinforcement changed only. specimens are named as follows; ba-bdcld. the letters a, b, c, and d refer to beam number, tensile bar diameter, the width of layer and length of cfrp sheet, respectively. d m. emara et alii, frattura ed integrità strutturale, 58 (2021) 48-64; doi: 10.3221/igf-esis.58.04 56 beam exp/fem comparison rb exp fem nl1b exp fem table 4: fe versus experimental failure modes. samples parameters reinforcement width of cfrp sheet (mm) length of cfrp sheet (mm) b1-8d ph 8 75 full length b2-10d ph 10 75 full length b3-12d-75l600 ph 12 75 600 b4-12d-75l1200 1200 b5-12d-75l full full length b6-12d-150l600 150 600 b7-12d-150l1200 1200 b8-12d-150l full full length b9-cbd-75l600 cfrp bars 75 600 b10-cbd75l1200 1200 b11-cbd-75l full full length b12-cbd-150l600 150 600 b13-cbd-150l1200 1200 b14-cbd-150l full full length table 5: parametric study specimens. in order to reduce the displacement of beams showed in the experimental study of pham and hao and the proposed fe model, some adjustments were made to the model. figs. 8 and tab. 6 show the effect of reinforcement changes on displacement-time (d-t), impact force-time (f-t) curves, and failure modes. three different diameters were used to reinforce rc beams (8,10 and 12mm), moreover reinforcing steel bars were replaced by cfrp bars. these beams are represented as (b1-8d, b2-10d, b5-12d-75l full and b11-cbd-75l full). from these changes, it is noted that the deflection had reduced by (6.6, 14.8, 29.1 %) when using gradually change in diameters from d8 to cfrp bars. m. emara et alii, frattura ed integrità strutturale, 58 (2021) 48-64; doi: 10.3221/igf-esis.58.04 57 (a) (b) figure 8: effect of reinforcement type and diameter: (a) displacement-time histories, and (b) impact force-time histories. sample comparison b1-8d b2-10d b5-12d-75l full b11-cbd-75l full table 6: various reinforcement types and diameters (failure modes). to increase the bending resistance of the reinforced concrete beams, it’s suggested to strength beams with one layer of cfrp with different lengths (600mm,1200mm and full beam length) as shown in beams (b3-12d-75l600, b4-12d75l1200, b5-12d-75l full) (b6-12d-150l600, b7-12d-150l1200, b8-12d-150l full) (b9-cbd-75l600, b10-cbd75l1200, b11-cbd-75l full) (b12-cbd-150l600, b13-cbd-150l1200, b14-cbd-150l full). when using steel bars (ph 12) in reinforcement there was a significant change in displacement results by (2.1, 7.3 %), (8.4, 10.8 %) and impact forces results by (1.7, 4.3 %), (2.2, 4.2 %) as shown in figs. 9 and 10 (a) for 75 mm width of cfrp layer and (b) for 150 mm width of cfrp layer, respectively. whereas, when using cfrp bars for reinforce beams, there was a slight change in the results when changing the length of the strengthening layer as shown in figs. 9 and 10 (c) and (d). m. emara et alii, frattura ed integrità strutturale, 58 (2021) 48-64; doi: 10.3221/igf-esis.58.04 58 (a) (b) (c) (d) figure 9: effect of the length of cfrp layer for strengthening on the displacement-time histories. (a) (b) (c) (d) figure 10: effect of the length of cfrp layer for strengthening on impact force-time histories. m. emara et alii, frattura ed integrità strutturale, 58 (2021) 48-64; doi: 10.3221/igf-esis.58.04 59 according to tab. 5 and fig. 11, for beams (b4-12d-75l1200, b7-12d-150l1200, b10-cbd75l1200, and b13-cbd150l1200), there was a change in the width of the cfrp strengthening layer (75 mm and 150 mm) when using ph 12 and cfrp bars for reinforcement at 1200 mm length of strengthening layer. these changes leading to reduce deflection by 6.5 and 1.7 % and impact load by 2.7 and 0.3 % for ph 12 and cfrp bars reinforcement, respectively. (a) (b) figure 11: time-deflection curve samples parameters reinforcement impact velocity (v) m/s position of impactor (l) mm thickness of cfrp layer (th) mm c1 steel bars 5.2 1100 0.45 c2 0.9 c3 1.8 c4 6.3 1100 0.45 c5 0.9 c6 1.8 c7 6.3 550 0.45 c8 0.9 c9 1.8 c10 8.5 1100 0.45 c11 0.9 c12 1.8 c13 cfrp bars 5.2 1100 0.45 c14 0.9 c15 1.8 c16 6.3 1100 0.45 c17 0.9 c18 1.8 c19 6.3 550 0.45 c20 0.9 c21 1.8 c22 8.5 1100 0.45 c23 0.9 c24 1.8 table 7: additional parametric study samples. m. emara et alii, frattura ed integrità strutturale, 58 (2021) 48-64; doi: 10.3221/igf-esis.58.04 60 models (b8-12d-150l full and b14-cbd-150l full), which are shown in tab. 5 and discussed in the previous section, were selected to perform the following parameters: impact velocity (v) m/s, the position of impactor from the left support at distance (l) mm and thickness of cfrp layer (th) mm as shown in tab. 7. the effects of impact velocity (v) on the behavior of rc beam strengthened with cfrp against impact loading were investigated by using three values for v (5.2, 6.3, and 8.5 m/s). fig. 12 plots (d-t) histories for strengthened beams with a 0.45mm thickness of cfrp layer for reinforced beams with ph 12mm in (a) and cfrp bars in (b), for the three selected velocities; while fig. 13 shows the relation between δmax and v for the same samples. comparing the strengthened beam with 0.45 mm cfrp layer for ph 12 and cfrp bars reinforcement, δmax increased for v = 5.2, 6.3, and 8.5 m/s, respectively. this shows that cfrp reinforcement can significantly improve the beam’s resistance to impact, at various impact energy values. (a) (b) figure 12: strengthened rc beams with various impact velocities (displacement-time histories) figure 13: comparing beams reinforcement models (maximum displacement vs. impact velocity) additional numerical models were generated to study the effects of important geometrical parameter related to the cfrp strengthen; thickness (th) of cfrp sheets. fig. 14 shows the effects of (th) on the (d-t) histories, by comparing the response of three models, strengthened with th =0.45, strengthened with th=0.9 mm, and strengthened with th=1.8mm, for variable impact velocity (5.2 in fig. 14 (a) and (d), 6.3 in fig. 14 (b) and (e), and 8.5 in fig. 14 (c) and (f) m/s) when using ph 12 in fig. 14 (a), (b) and (c), and cfrp bars in fig. 14 (d), (e) and (f) for reinforcement beams. the deflection decreased by (7.9, 13.9) %, (3.9, 14.2) %, (8.5, 15.2) %, (1.6, 5.8) %, (4.2, 8.8) % and (7.5, 9.9) % as shown in fig. 14 (a), (b), (c), (d), (e) and (f), respectively. because the effects of impact location on the behavior of cfrp-strengthened rc members under impact loads have not been investigated yet, they are included in the current parametric study. this factor was investigated by varying the impact position. the impactor's distance from the left side to half the beam's span length. values were chosen for 550 mm and 0,0 10,0 20,0 30,0 40,0 50,0 60,0 70,0 80,0 0,0 4,0 8,0 12,0 ∆  m a x  (m m ) velocity (m/s) ph 12 reinforcement cfrp bars m. emara et alii, frattura ed integrità strutturale, 58 (2021) 48-64; doi: 10.3221/igf-esis.58.04 61 1100 mm. tab. 8 shows the crack patterns for the strengthened models with 0.45 mm thickness of cfrp layer under 6.3 m/s impact velocity for both types of beams reinforced with ph 12 and cfrp bars, with different values of impactor positions. fig. 15 plots the displacementtime (d-t) histories to compare the displacement at midspan of the beam for variable impactor position. sample position of impactor (l) (mm) comparison c4 1100 c7 550 c16 1100 c19 550 table 8: cracking patterns for different impact location. (a) (b) (c) (d) m. emara et alii, frattura ed integrità strutturale, 58 (2021) 48-64; doi: 10.3221/igf-esis.58.04 62 (e) (f) figure 14: effect of cfrp sheet thickness on displacement-time histories. (a) (b) (c) (d) (e) (f) figure 15: effect of impact location on the displacement-time histories. m. emara et alii, frattura ed integrità strutturale, 58 (2021) 48-64; doi: 10.3221/igf-esis.58.04 63 conclusions and recommendations his study investigates numerically the behavior of rc beams strengthened with externally bonded cfrp sheets and subjected to impact load. the main parameters of the study were the reinforcing bars type and size, cfrp width, length, and thickness, impact velocity, and the position of the impactor. based on the results obtained, the following conclusions can be drawn:  the general behavior of the finite element models represented by time-deflection at midspan, time-load and failure mode curves showed good agreement with the test data from the full-scale beam tests.  the finite element models showed a slight difference from the test data in both the linear and nonlinear ranges. this is most probably due to ignorance of the effect of concrete toughening mechanisms.  the load-carrying capacity of the rc beams strengthened in flexural is higher than that of the control beam by 13.4%.  the failure modes obtained through the finite element models correspond well with the observed failure modes of the experimentally tested beams.  using cfrp bars as internal reinforcement reduced the mid-span deflection of rc beams by 29.1% compared to steel bars. moreover, increasing the bar diameter decreased the mid-span deflection by 6.6 to 14.8 %.  in the case of impact loadings, the load capacity of specimens reinforced with cfrp bars was much higher than that of steel.  increasing the length of the cfrp layer (600 mm, 1200 mm and full beam length) decreased the midpoint deflection by (2.1, 7.3 %), and impact forces by (1.7, 4.3 %) for beams (b3, b4 and b5).  increasing the cfrp layer width from 75 mm to 150 mm decreased the midpoint deflection of rc beams subjected to impact loading by 6.5% for beams (b4 and b7).  increasing impact velocity from 5.2 to 6.3 then 8.5 m/s increased the deflection of rc beams by 26.6, 38.1 and 71.9 mm, respectively.  the displacement decreased from 7.9 to 13.9 % for beams (c1, c2 and c3) due to increasing the thickness of the cfrp strengthening layer (0.45, 0.9 and 1.8 mm).  the change of impactor position from 550 mm to 1100 mm concerning the left side to half beam length increased the displacement values from 31.2 mm to 71.9 mm and changed the failure modes of tested beams. references [1] bakis, c.e., bank, l.c., brown, v.l., cosenza, e., davalos, j.f., lesko, j.j., machida, a., rizkalla, s.h., triantafillou, t.c. (2003). fiber-reinforced polymer composites for construction state-of-the-art review, perspect. civ. eng. commem. 150th anniv. am. soc. civ. eng., 6(may), pp. 369–383, doi: 10.1061/(asce)1090-0268(2002)6:2(73). [2] wight, j.k., barth, f.g., becker, r.j., bondy, k.b., breen, j.e., cagley, j.r., collins, m.p., corley, w.g., dolan, c.w., fiorato, a.e., french, c.e., garcia, l.e., griffis, l.g., gustafson, d.p., harman, d.k., harris, j.r., hawkins, n.m., holland, t.c., iverson, p.j., jirsa, j.o., kelly, d.j., klein, g.j., kopczynski, c.s., martin, l.d., mast, r.f., mccabe, s.l., mccall, w.c., moehle, j.p., murray, m.a., ramirez, j.a., stark, r., tolles, e.m., wood, s.l., aschheim, m.a. (2005). aci committee 318,"building code requirements for structural concrete (aci 318-05) and commentary (aci 318r05)", am. concr. institute, farmingt. hills, mi, 2003, pp. 430. [3] emara, m., barris, c., baena, m., torres, l., barros, j. (2018). bond behavior of nsm cfrp laminates in concrete under sustained loading, constr. build. mater., 177, pp. 237–246, doi: 10.1016/j.conbuildmat.2018.05.050. [4] kadhim, m.m.a. (2012). effect of cfrp sheet length on the behavior of hsc continuous beam, j. thermoplast. compos. mater., 25(1), pp. 33–44, doi: 10.1177/0892705711401847. [5] quantrill, r.j., hollaway, l.c., thorne, a.m. (1996). experimental and analytical investigation of frp strengthened beam response: part i, mag. concr. res., 48(4), pp. 331–42, doi: 10.1680/macr.1996.48.177.331. [6] kadhim, m.m.a.;mohammed, m. j.; abid, a.j. (2012). effect of prestressed cfrp plate location on behavior of rc beam strengthened with prestressed cfrp plate, babylon university, 20(1), pp. 105–113, available at: https://www.researchgate.net/publication/333056468_effect_of_prestressed_cfrp_plate_location_on_behavior_ of_rc_beam_strengthened_with_prestressed_cfrp_plate. [7] fujikake, k., li, b., soeun, s. (2009). impact response of reinforced concrete beam and its analytical evaluation, j. t m. emara et alii, frattura ed integrità strutturale, 58 (2021) 48-64; doi: 10.3221/igf-esis.58.04 64 struct. eng., 135(8), pp. 938–950, doi: 10.1061/(asce)st.1943-541x.0000039. [8] pham, t.m., hao, h. (2016). impact behavior of frp-strengthened rc beams without stirrups, j. compos. constr., 20(4), pp. 04016011, doi: 10.1061/(asce)cc.1943-5614.0000671. [9] soudki, k., alkhrdaji, t. (2005). guide for the design and construction of externally bonded frp systems for strengthening concrete structures (aci 440.2r-02), proc. struct. congr. expo., pp. 1627–1633, doi: 10.1061/40753(171)159. [10] kantar, e., erdem, r. t., anıl, ö. (2011). nonlinear finite element analysis of impact behavior of concrete beam, mathematical and computational applications, 16(1), pp. 183–193. [11] erki, m.a., meier, u. (1999). impact loading of concrete beams externally strengthened with cfrp laminates, j. compos. constr., 3(3), pp. 117–124, doi: 10.1061/(asce)1090-0268(1999)3:3(117). [12] tang, t., saadatmanesh, h. (2003). behavior of concrete beams strengthened with fiber-reinforced polymer laminates under impact loading, j. compos. constr., 7(3), pp. 209–218, doi: 10.1061/(asce)1090-0268(2003)7:3(209). [13] esfahani, m.r., kianoush, m.r., tajari, a.r. (2007). flexural behaviour of reinforced concrete beams strengthened by cfrp sheets, eng. struct., 29(10), pp. 2428–2444, doi: 10.1016/j.engstruct.2006.12.008. [14] soleimani, s., banthia, n., mindess, s. (2007). behavior of rc beams under impact loading: some new findings. in proceedings of the 6th int. conference on fracture mechanics of concrete and concrete structures, catania, italy. [15] watstein, d. (1953). effect of straining rate on the compressive strength and elastic properties of concrete, j. proc., 49(4), pp. 729–44, doi: 10.14359/11850. [16] goldston, m., remennikov, a., sheikh, m.n. (2016). experimental investigation of the behaviour of concrete beams reinforced with gfrp bars under static and impact loading, eng. struct., 113, pp. 220–232, doi: 10.1016/j.engstruct.2016.01.044. [17] khalighi, y. (2009). a study of bond between fibre reinforced polymer and concrete under quasi static and impact loading, phd dissertation, university of british columbia library, doi: 10.14288/1.0063162. [18] al-farttoosi, m. (2016). impact behaviour of reinforced concrete beams strengthened or repaired with carbon fibre reinforced polymer (cfrp), phd dissertation, university of plymouth. [19] pham, t.m., hao, h. (2017). behavior of fiber-reinforced polymer-strengthened reinforced concrete beams under static and impact loads, int. j. prot. struct., 8(1), pp. 3–24, doi: 10.1177/2041419616658730. [20] abulebdeh, t.m., voyiadjis, g.z. (1993). plasticitydamage model for concrete under cyclic multiaxial loading, j. eng. mech., 119(7), pp. 1465–1484, doi: 10.1061/(asce)0733-9399(1993)119:7(1465). [21] jankowiak, t., and, lodygowski, t. (2005). identification of parameters of concrete damage plasticity constitutive model, foundations of civil and environmental engineering, 6(1), pp. 53–69. [22] voyiadjis, g.z., abu-lebdeh, t.m. (1994). plasticity model for concrete using the bounding surface concept, int. j. plast., 10(1), pp. 1–21, doi: 10.1016/0749-6419(94)90051-5. [23] emara, m., hamoda, a. (2019). numerical modeling of time-displacement response ofrc slab subjected to impact loading ., 16(5), pp. 11–20, doi: 10.9790/1684-1605031120www.iosrjournals.org. [24] hashin, z. (1981). fatigue failure criteria for unidirectional fiber composites, j. appl. mech., 48(4), pp. 846–852, doi: 10.1115/1.3157744. [25] dauphin, j.-c., jean-christophe. (2016). guide du chercheur américaniste à brown university, providence, rhode island, usa, http://journals.openedition.org/nuevomundo, , doi: 10.4000/nuevomundo.70083. [26] hashin, z. (1980). failure criteria for unidirectional fiber composites, j. appl. mech., 47(2), pp. 329–334, doi: 10.1115/1.3153664. [27] soleimani, s., sayyar, r. s. (2019). analytical study of reinforced concrete beams tested under quasi-static and impact loadings, j. appl. sci., 9(14), pp. 2838, doi: 10.3390/app9142838. [28] al-zubaidy, h., al-mahaidi, r., zhao, x.l. (2013). finite element modelling of cfrp/steel double strap joints subjected to dynamic tensile loadings, compos. struct., 99, pp. 48–61, doi: 10.1016/j.compstruct.2012.12.003. [29] kadhim, m., wu, z. j., cunningham, l. (2016). fe modelling of cfrp strengthened steel members under impact loads, in proceedings of the 24th uk conference of the association for computional mechanics in engineering, uk. [30] kadhim, m.m.a., wu, z., cunningham, l.s. (2018). experimental study of cfrp strengthened steel columns subject to lateral impact loads, compos. struct., 185, pp. 94–104, doi: 10.1016/j.compstruct.2017.10.089. [31] zeinoddini, m., harding, j.e., parke, g.a.r. (2008). axially pre-loaded steel tubes subjected to lateral impacts (a numerical simulation), int. j. impact eng., 35(11), pp. 1267–1279, doi: 10.1016/j.ijimpeng.2007.08.002. [32] genikomsou, a.s., polak, m.a. (2017). finite element analysis of rc flat slabs with different amount and placement of shear bolts, spec. publ., 321, pp. 6.1-6.20. microsoft word numero_52_art_03_2468 w. xiangming et alii, frattura ed integrità strutturale, 52 (2020) 25-32; doi: 10.3221/igf-esis.52.03 25 numerical analysis and verification of residual stress in t joint of s355 steel wang xiangming, guo erfu school of mechanical and electrical engineering, shijiazhuang university of applied technology, shijiazhuang, 050081 wangxmxming@163.com abstract. t joint is a widely used welding form. the welding deformation and residual stress produced during the welding process affect the integrity and reliability of the resultant structure. in this study, s355 low alloy steel was used as test material, and the thermal-mechanical coupling characteristics of multi-layer welding were combined with sysweld finite element software to calculate the residual welding stress of t joint. the residual welding stress of multi-layer welding t joint with tangent tube and sheet was measured using x-ray diffraction method. the results showed that the numerical simulation was in good agreement with the experimental findings. with respect to the transverse residual stress, the maximum residual stress appeared near the weld toe. the transverse stress perpendicular to the weld direction represented the tensile stress at the weld center as well as the tensile stress at the tube surface far from the weld. regarding longitudinal residual stress, the maximum residual stress also appeared near the weld toe, and its value was highest at the center of the weld, but decreased along the direction perpendicular to the weld. these results can serve as useful guide for actual welding design. keywords. t joint; residual stress; welding deformation; finite element method. citation: wang, xm., guo, ef., numerical analysis and verification of residual stress in t joint of s355 steel, frattura ed integrità strutturale, 52 (2020) 25-32. received: 04.08.2020 accepted: 21.04.2020 published: 01.04.2020 copyright: © 2020 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. introduction he main connection mode in steel structure engineering in china is welding connection. this connection method is economical and flexible: it simplifies the structural details, saves materials and improves production efficiency [1]. welding connection has been widely used in ship, locomotive, vehicle, bridge, boiler and other industrial fields, and also in energy engineering, marine engineering, aerospace engineering, petrochemical engineering, large plants and high-rise buildings [2-5]. t joint is a common joint in welding. residual stress and welding deformation are important factors that affect the accuracy and performance of welding products [6,7]. welding deformation and residual stress affect mechanical properties such as resistance to corrosion and crack growth, and fatigue strength [8,9]. moreover, they have tremendous impact on the physical and mechanical properties of materials. t joint is one of main structures of bogie beam components, and its welding residual stress affects the load-carrying capacity, fatigue strength, structural stiffness and dimensional precision of bogie beam. in recent years, a large number of scholars in china and elsewhere have studied the prediction and control of post-weld deformation and residual stress. wudi et al. [10] tested the residual stress in q345 steel welded with mag, and compared t https://youtu.be/wqcaqqyhqjq w. xiangming et alii, frattura ed integrità strutturale, 52 (2020) 25-32; doi: 10.3221/igf-esis.52.03 26 and analyzed the residual stress in the fusion zone and heat affected zone. in another study, mato peridic et al. [11] simulated and tested the residual welding stress and defects in t joint, and proved that the peak value of residual stress appeared near the weld toe. inoue et al. [12] studied the effect of coupling of temperature, phase transition and thermal stress in the process of temperature change accompanying phase transition, and proposed a general form of constitutive equation under the coupling condition. however, reports on the welding simulation of t joint of s355 steel are scanty. based on the finite element numerical simulation method, the residual stress of t joint of steel s355 after wielding was calculated as a function of the thermo-mechanical coupling characteristics of multi-layer welding. then the residual stress of t joint with tangent tube and sheet was measured with x-ray diffraction test. the transient stress changes and the distribution of residual stresses during welding were simulated. the results of the numerical simulation laid a foundation for the subsequent optimization of welding process parameters and the realization of residual stress control based on numerical simulation. establishment of finite element model establishment of finite element mesh model inite element meshing was accomplished with hypermesh software. the total number of meshes was 488910, with 452741 nodes. the maximum mesh element size was 5 mm × 3 mm × 0.8 mm, while the minimum mesh element size was 5 mm × 1 mm × 0.8 mm (fig. 1 and 2). in order to ensure the convergence of the calculation results, the base grids of the weld and immediate vicinity of the weld were divided tightly in the mesh generation process, while the mesh far from the weld was sparsely divided [10]. figure 1: network model. figure 2: the finite element model of t joint. at the end of mesh partitioning, visual-mesh was imported for grouping, and constraints were imposed. the constraints are shown in fig. 3, i.e., exerting clamping on the node along the axes pointed by the arrow to ensure arrest of the rigid motion. figure 3: constraints. establishment of material model considering the effect of phase change on residual stress and deformation during welding, the main phases of materials such as ferrite, pearlite and martensite were loaded in the simulation process. their thermophysical properties are shown in fig. 4. f w. xiangming et alii, frattura ed integrità strutturale, 52 (2020) 25-32; doi: 10.3221/igf-esis.52.03 27  (a) specific heat capacity (b) thermal conductivity figure 4: thermophysical properties of s355 material. double ellipsoid heat source model the double ellipsoid heat source model was used as the heat source for deformation simulation. double ellipsoid heat source is a kind of volume-distributed heat source [14]. its heat source model shows three-dimensional distribution in space. it considers not only the plane distribution of heat flow on the action surface, but also the distribution of heat energy along the direction of thickness of the plate. at present, the double ellipsoidal heat source model proposed by goldak is effective since it takes full account of the asynchronism of the temperature changes at the front and back ends of the heat source in the welding process. moreover, it provides a more accurate description of heat source than the hemispherical and ellipsoidal heat sources. the double ellipsoid heat source model is shown in fig. 5. 2c o 1c x b ay figure 5: double ellipsoid heat source model. different expressions are used for the front and back parts of the double ellipsoid heat source model. the expression for the heat source distribution in the front part of the ellipsoid is: 2 22 1 2 2 2 1 2 6 3 ( , , ) exp 3 exp 3 exp 3 a f q y zx q x y z bc a b c                            (1) the expression of the heat source distribution in the back part of the ellipsoid is: w. xiangming et alii, frattura ed integrità strutturale, 52 (2020) 25-32; doi: 10.3221/igf-esis.52.03 28 2 22 2 2 2 2 2 2 6 3 ( , , ) exp 3 exp 3 exp 3 a f q y zx q x y z bc a b c                            (2) where q = ηui (η is heat source efficiency), u is arc voltage, v, i is welding current, a; a, b and c are ellipsoidal parameters, and f1 and f2 are the heat distribution functions of the front and back parts of the ellipsoid, f1 + f2 = 2. in order to obtain an accurate heat source model, it was necessary to check its heat source. firstly, the initial values of the heat source parameters of the double ellipsoid heat source model were given, and the calculated results were compared with the actual weld pool shape. constant adjustment made the simulation results consistent with the shape of weld pool, and the correct heat source model was obtained. finally, the parameters obtained were: a1=2.5, a2=5, b=2, c=3. sysweld software provides the solution method of average thermal cycle curve. fig. 6 shows the average thermal cycle curve obtained using sysweld software. t / ℃ t/s figure 6: average thermal cycle curve of welding. calculation of residual stress ulti-layer welding was used in the welding process. the welding sequence is shown in fig. 7. the heat input was 0.74, 1.05 and 1.48 j/mm, respectively. the welding process was simulated based on sysweld and the coupling characteristics of multi-layer welding. figure 7: welding sequence. after the welding simulation process of heating, cooling and stress annealing, the transverse and longitudinal stress distribution nephograms were obtained (fig. 8). it can be seen intuitively from fig. 8 that the post-weld peak values of transverse and longitudinal residual stresses appeared at the re-striking arc on the surface of the weld center. this phenomenon was due to the fact that an unstable arc at the superimposed arc could lead to decrease in the fusion ratio between the filler material and the base metal of the previous weld [15], thereby resulting in the concentration of residual stress at the re-striking arc of the weld. moreover, it is clearly shown in fig. 8 that the longitudinal (z direction) peak residual stress and the transverse (x direction) peak residual stress m w. xiangming et alii, frattura ed integrità strutturale, 52 (2020) 25-32; doi: 10.3221/igf-esis.52.03 29 appeared at the weld. when the welding pool was melting the base metal and filler material, the surrounding non-melting low-temperature base metal produced compressive stress and compressive plastic deformation due to temperature difference, while the metal of the weld produced tensile residual stress under the tensile action of the surrounding base metal during cooling. however, the tensile plastic stress induced by the tensile residual stress was unable to offset the compressive plastic stress produced previously. thus, to balance the residual thermal plastic strain at the weld during cooling, large tensile stress occurred at the weld. that was why the longitudinal peak residual stress and the transverse peak residual stress appeared at the weld. moreover, in order to balance the tensile stress of the system at the weld on both sides of the base metal, compressive stress was displayed on both sides far from the center of the weld. the compressive stress prevented large bending deformation of the specimens and maintained the overall stress balance in the specimens. (a) nephogram of transverse residual stress distribution (b) nephogram of longitudinal residual stress distribution figure 8: residual stress distribution nephogram it can be seen intuitively from fig. 8 that the post-weld peak values of transverse and longitudinal residual stresses appeared at the re-striking arc on the surface of the weld center. this phenomenon was due to the fact that an unstable arc at the superimposed arc could lead to decrease in the fusion ratio between the filler material and the base metal of the previous weld [15], thereby resulting in the concentration of residual stress at the re-striking arc of the weld. moreover, it is clearly shown in fig. 8 that the longitudinal (z direction) peak residual stress and the transverse (x direction) peak residual stress appeared at the weld. when the welding pool was melting the base metal and filler material, the surrounding non-melting low-temperature base metal produced compressive stress and compressive plastic deformation due to temperature difference, while the metal of the weld produced tensile residual stress under the tensile action of the surrounding base metal during cooling. however, the tensile plastic stress induced by the tensile residual stress was unable to offset the compressive plastic stress produced previously. thus, to balance the residual thermal plastic strain at the weld during cooling, large tensile stress occurred at the weld. that was why the longitudinal peak residual stress and the transverse peak residual stress appeared at the weld. moreover, in order to balance the tensile stress of the system at the weld on both sides of the base metal, compressive stress was displayed on both sides far from the center of the weld. the compressive stress prevented large bending deformation of the specimens and maintained the overall stress balance in the specimens. measurement and comparative analysis of residual stress measurement of residual stress using x-ray he test specimen was a t joint with tube and sheet in tangential orientation. the size of the test sheet was 350 mm × 150 mm × 12 mm, and the tube was circular, with an inner diameter of 80 mm, a 100-mm outer diameter and a length of 350 mm. the test followed gb/t 2008-7704 standard for x-ray non-destructive stress detection. the testing instrument used was i xrd x-ray diffraction stress meter, and cr target was the target material. the residual stresses of the center of the weld and the sites were 2, 5, 12, 15 and 25 mm away from the surface of the weld toe tested. the testing position is shown in fig. 9. t w. xiangming et alii, frattura ed integrità strutturale, 52 (2020) 25-32; doi: 10.3221/igf-esis.52.03 30 figure 9: the testing position of the residual stress of the weld. comparison and analysis of simulation results and experimental results with reference to the test range, the longitudinal and transverse residual stresses of the weld were extracted from the simulation results. the residual stress obtained in the test and simulations were compared, and the residual stress curve was drawn, as shown in fig. 10. (a) comparison of transverse residual stress. simulation value actual measurement value weld toe distance with weld toe/mm l o n gi tu d in al r es id u al s tr es s/ m p a (b) comparison of longitudinal residual stress figure 10: comparison of measured and simulated residual stress fig. 10 shows clearly that the trends in variation in the transverse residual stress and longitudinal residual stress were quite close, and the maximum residual stress also appeared near the weld toe. moreover, it could be seen from the trend of the whole curve that the residual stress at the weld was very large, showing a state of tensile stress, and the tube surface far from w. xiangming et alii, frattura ed integrità strutturale, 52 (2020) 25-32; doi: 10.3221/igf-esis.52.03 31 the weld showed a state of compressive stress as a function of distance. with respect to longitudinal residual stress, the tensile stress was applied at the center of the weld, and the compressive stress appeared when it moved away from the center of the weld to both sides [16,17]. fig. 10a is a comparison of transverse residual stresses. it could be seen clearly from the figure that the maximum simulation value of 203 mpa appeared at the weld which was 5 mm away from the weld toe. the maximum measured value (179 mpa) appeared at the tube surface side which was 5 mm away from the weld toe. the difference between the two peak values was 24 mpa, suggesting high coincidence. fig. 10b shows comparison of longitudinal residual stresses. it can be seen from the figure that the maximum simulation value of 517 mpa appeared at the weld 5 mm away from the weld toe, while the maximum measured value of 422 mpa appeared at the tube surface which was 2 mm away from the weld toe. the difference between the two peak values was 95 mpa, again suggesting high coincidence. it should be pointed out that the center of the weld experienced two thermal cycle processes, since the welding was continuous, thereby avoiding the problem of re-striking arc, and every layer was calculated in two sections in the simulation process. therefore, the simulated peak values of both transverse and longitudinal residual stresses were slightly higher than the experimental peak values. conclusions hrough the numerical simulation calculation and analysis of sysweld, changes in transient stress and the distribution of post-weld residual stress were analyzed in detail. the concrete conclusions are as follows: (1) the maximum residual stress of multi-layer welding of s355 low-alloy steel appeared on the surface of the weld, indicating that the current weld was obtained after performing post-weld thermal treatment on the last weld. therefore, the residual welding stress of the last weld was greatly reduced. however, the last weld, i.e. the weld surface in the test, did not experience the effect of post-weld heat treatment. thus, the residual stress was relatively prominent. therefore, the residual stress on the surface of the weld was largest, followed by residual stress at the middle of the weld, and residual stress at the weld. (2) for t joint with tangent sheet and tube, the curves of simulation and test values were similar, with small difference in peak stress. the transverse residual stress perpendicular to the weld surface along one tube side showed tensile stress at the center of the weld, while the transverse residual stress far from the weld center showed compressive stress. the longitudinal residual stress also showed peak tensile stress at the weld center, and there was tensile stress when it moved towards the tube surface. in addition, it is important to point out that the simulated longitudinal peak residual stress was 538 mpa and the test longitudinal peak residual stress was 421 mpa. these values exceeded the yield limit of s355 low alloy steel (355 mpa), which would affect the fatigue life of the weldment to some extent. therefore, in the actual welding process in the future, special attention should be paid to the control of inter-channel temperature and welding speed to prevent excessive peak residual stress after welding caused by excessive heat input. references [1] chen, l.m. (2012). the influence of temperature control in welding process on the qualification rate of welded parts, china packaging industry, (13), pp. 43. [2] alyakrinskiy, o.n., logachev, p.v. and semenov, y.i. (2017). investigation of the process of electronic beam welding in an external magnetic field, welding international, 31(8), pp. 1-4. [3] hu, w.h., wang, g.y. and yang, x.h. (2018). study on the residual stress of truck frame welding of high speed train, welding technology, 47(3), pp. 19-22. [4] cong, s., zhang, w.w., wang, y.s., wen, z.j. and tian, y.h. (2018). effect of heat input on failure mode and connection mechanism of parallel micro-gap resistance welding for copper wire, international journal of advanced manufacturing technology, 96(1), pp. 299-306. [5] jin, s.w., ohmori, h. and lee, s.j. (2017). optimal design of steel structures considering welding cost and constructability of beam-column connections, journal of constructional steel research, 135(673), pp. 292-301. [6] shanmugam, n.s., buvanashekaran, g., sankaranarayanasamy, k. and kumar, s.r. (2010). a transient finite element simulation of the temperature and bead profiles of t-joint laser welds, international journal of modelling & simulation, 30(1), pp. 108-122. t w. xiangming et alii, frattura ed integrità strutturale, 52 (2020) 25-32; doi: 10.3221/igf-esis.52.03 32 [7] huang, j., liu, y.g., zhang, t. and xie, f. (2009). experimental study on residual stress of thick plate welding, chinese ship research, 4(5), pp. 33-37. [8] jia, k.n., wang, h.d. and jiang, q.y. (2012). study on welded cold cracking susceptibility of high-strength bridge steel, electric welding machine, 42(2), pp. 23-25. [9] katsuyama, j., tobita, t., itoh, h. and onizawa, k. (2012). effect of welding conditions on residual stress and stress corrosion cracking behavior at butt-welding joints of stainless steel pipes, journal of pressure vessel technology, 134(2), pp. 021403. doi: 10.1115/1.4005391 [10] wu, d., zhang, c., zhu, h.r. and han, s. (2016). weld residual stress test for welded q345 steel, construction machinery, (11), pp. 86-88. [11] peric, m., tonkovic, z., rodic, a., surjak, m., garasic, i. and boras, i. (2014). numerical analysis and experimental investigation of welding residual stresses and distortions in a t-joint fillet weld, materials & design, 53(1), pp. 10521063. [12] inoue, t. (1996). metllo-thermo-mechanics application to phase transformation incorporated processes, trans. jwri, 25(2), pp. 69-87. [13] feng, x.n., liu, y.l., yang, x.h. and he, x.l. (2017). numerical simulation and test of multi-layer multi-weld residuall stress of q345e steel, welding technology, 46(11), pp. 5-9. [14] du, b.s., ma, x.z., zhang, z.w. and xu, g.x. (2014). numerical simulation of residual stress in multipass weld joint of ultrafine-grained q460 steel, transactions of the china welding institution, 35(2), pp. 42-46. [15] zhang, g.d. and zhou, c.y. (2006). finite element analysis of pipe discontinuous and continuous butt welding, transactions of the china welding institution, 27(12), pp. 85-88. [16] li, z.z., zhou, j.p., xu, y. and li, b.r. (2016). numerical simulation analysis on t-shaped pipe weldments temperature and stress-strain field based on sysweld, transactions of the china welding institution, 37(4), pp. 77. [17] jiang, k.b., xiao, y.t. and guo, y.t. 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/pdfxoutputintentprofileselector /documentcmyk /preserveediting true /untaggedcmykhandling /leaveuntagged /untaggedrgbhandling /usedocumentprofile /usedocumentbleed false >> ] >> setdistillerparams << /hwresolution [2400 2400] /pagesize [612.000 792.000] >> setpagedevice microsoft word numero_58_art_03_3050 a. arbaoui et alii, frattura ed integrità strutturale, 58 (2021) 33-47; doi: 10.3221/igf-esis.58.03 33 wavelet-based multiresolution analysis coupled with deep learning to efficiently monitor cracks in concrete ahcene arbaoui university of bouira, department of civil engineering, bouira, algeria a.arbaoui@univ-bouira.dz abdeldjalil ouahabi umr 1253, ibrain, université de tours, inserm, tours, france university of bouira, department of computer science, limpaf, bouira, algeria ouahabi@univ-tours.fr sébastien jacques university of tours, greman umr 7347, cnrs, insa centre val-de-loire, tours, france sebastien.jacques@univ-tours.fr madina hamiane college of engineering, royal university for women, bahrain mhamiane@ruw.edu.bh abstract. this paper proposes an efficient methodology to monitor the formation of cracks in concrete after non-destructive ultrasonic testing of a structure. the objective is to be able to automatically detect the initiation of cracks early enough, i.e. well before they are visible on the concrete surface, in order to implement adequate maintenance actions on civil engineering structures. the key element of this original approach is the wavelet-based multiresolution analysis of the ultrasonic signal received from a sample or a specimen of the studied material subjected to several types of solicitation. this analysis is finally coupled to an automatic identification scheme of the types of cracks based on artificial neural networks (anns), and in particular deep learning by convolutional neural networks (cnns); a technology today at the cutting edge of machine learning, in particular for all applications of pattern recognition. wavelet-based multiresolution analysis does not add any value in detecting fractures in concrete visible by optical inspection. however, the results of its implementation coupled with different cnn architectures show cracks in concrete can be identified at an early stage with a very high accuracy, i.e. around 98%, and a loss function of less than 0.1, regardless of the implemented learning architecture. citation: arbaoui, a., ouahabi, a., jacques, s. and hamiane, m., wavelet-based multiresolution analysis coupled with deep learning to efficiently monitor cracks in concrete, frattura ed integrità strutturale, 58 (2021) 33-47. received: 26.03.2021 accepted: 01.07.2021 published: 01.10.2021 copyright: © 2021 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. https://youtu.be/5ddjphwe_no a. arbaoui et alii, frattura ed integrità strutturale, 58 (2021) 33-47; doi: 10.3221/igf-esis.58.03 34 keywords. crack monitoring; concrete; non-destructive ultrasonic testing; wavelet-based multiresolution analysis; deep learning. introduction ince its creation, concrete, the flagship material of civil engineering structures, has been the basis of construction techniques, whether industrial (factories, warehouses, ...) or hydraulic (dams, dikes, ...), but also of infrastructures such as transportation (bridges, tunnels, ...) or urban infrastructure (aqueducts, ...). this success is due to several factors: concrete is an economical material, easy to work with, resistant to compressive stress, durable, sound and heat insulating, and it contributes to architecture through the shapes, textures and colors it provides [1]. coupled with a reinforcement usually made of steel, reinforced concrete can compensate for the low tensile strength of concrete. the service life of reinforced concrete structures is conditioned by the response to chemical (e.g. carbonation, corrosion, etc.), physical (e.g. freeze-thaw cycle) and mechanical (e.g. overloading) aggressions of the environment, as well as by the capacity of the constituent materials to protect themselves against these aggressions. in this work, we are interested in the corrosion of reinforcement which is one of the main causes of degradation of reinforced concrete structures [2]. this corrosion induces a modification of the steel-concrete bond, a reduction in section of the steel bars, a decrease of the ductility of the steel as well as a peripheral damage of the concrete due to the pressure of the corrosion products. more precisely, bhaskar et al. showed that when the porous zone at the interface between steel and concrete (a zone whose volume depends on the surface of the reinforcement, the water/cement mass ratio and the degree of hydration) is completely filled by the corrosion products, pressures are exerted on the concrete cover and can generate cracks [3]. as shown in figure 1, monitoring the propagation of these cracks is therefore essential to stop them from reaching critical sizes that could lead to the reduction of the bearing capacity of the concrete or reinforced concrete structure or even to its failure [4–8]. this research topic is still of great interest and recent studies have shown that it is possible to limit interfacial micro-cracks in concrete and its composites subjected to dynamic loads, for instance by adding fly ash and/or silica fume at a rate of a few thenths of the weight of the cement [7, 8]. figure 1: examples of cracks in reinforced concrete structures [provided by the authors]. s a. arbaoui et alii, frattura ed integrità strutturale, 58 (2021) 33-47; doi: 10.3221/igf-esis.58.03 35 visual inspection of civil engineering structures is now complemented by high-performance, high-definition scanner or photogrammetry surveys, and artificial intelligence (ai), in particular deep neural networks, can detect defects, classify them and propose a diagnosis. the internet of things (iot) and new generations of sensors (e.g. fissurometers, inclinometers) make it possible to instrument infrastructure and continuously monitor a number of structural health indicators from 24/7 control centers [6]. there are many methods to evaluate the detection of anomalies in materials or components of a civil engineering structure. non-destructive testing (ndt), which is a long-standing, common and mandatory practice in many industries such as aeronautics or aerospace, is an important category [10]. ndt methods consist in causing a disturbance in the material to be studied, here of an ultrasonic nature, and recording its response. this response to the ultrasonic excitation is a function of the state of the material or the component of the structure to be controlled. these techniques are therefore important tools to help detect cracks, characterize the degree of corrosion of reinforcement in reinforced concrete, determine the thickness of concrete slabs, etc. [11, 12]. however, a critical point of this type of method is the extraction of relevant information on the state of the material from its response. multiresolution analysis (mra) is the original method implemented in this work to extract this key information by decomposing the signals at different levels of resolution. in particular, we will use wavelets, i.e. an extension of fourier analysis, as an analytical tool to mathematically describe the increment of information required to move from a coarser approximation of the material response to a higher resolution approximation. wavelet-based multiresolution analysis, which has received significant attention in recent years in various fields, is therefore a powerful tool for efficiently representing signals and images at multiple levels of detail [13, 14]. the last key point of the work described in this paper is to build a classifier to detect cracks from the images obtained at the spatial scale. in this regard, an automatic crack type identification scheme, based on artificial neural networks (anns), is proposed. crack detection techniques based on deep anns, i.e. deep learning, are currently under active research due to their renowned outstanding performance [15]. in particular, some authors have recently proposed improved convolutional neural networks (cnns) that can extract crack patches in an image with 99% accuracy [16]. the structure of this article is as follows. first, we will point out the fundamental concepts, as well as the experimental procedures, associated with each of the three key points of the method proposed here: non-destructive ultrasonic testing to obtain an ultrasonic signal identifying the defect; multiresolution wavelet-based analysis to preserve the important elements of the signal, i.e. the cracks, at high resolution and produce a scalogram localizing the defect; and finally classification by cnns. the results obtained will then be analyzed and discussed. finally, we will emphasize the originality of this work, namely the multiresolution analysis based on wavelets, as input to the deep neural network, which allows us to obtain a high level of classification accuracy, independently of the chosen cnn architecture. research significance and proposed methodology research signification his work solves the important problem of detecting the onset of cracks inside concrete structures. these cracks are optically invisible from the outside and may propagate unexpectedly until structure failure. in some sensitive infrastructures, such as nuclear power plants, dams or bridges, a concrete failure can lead to very serious disasters. although this type of disaster remains unusual, each occurrence can generate serious human, environmental and technical consequences. this is why it is important to have a protocol for detecting and monitoring cracks in their early stages in order to secure structures of vital interest. what is interesting is to know the cost of our proposed protocol to practically evaluate its implementation in the field. the cost of our investigations is low since all that is required is an on-site portable ultrasonic device and an ordinary processor, either a dsp card or a laptop computer since we are implementing an architecture that has already learned to detect and track possible internal cracks or the beginnings of cracks. to quantify the hardware implementation of our approach, we recall the instruments used: the instrument used is the pundit pl-200. it allows first class ultrasonic pulse velocity tests to examine the quality of concrete: to estimate the compressive strength of concrete or to measure the surface velocity and the depth of cracks. our software supports settings directly accessible in real time from the measurement screen. the developed software is implemented on an electronic board with dsp or directly implemented in a laptop. the global cost of all this instrumentation is about $5,000.00. t a. arbaoui et alii, frattura ed integrità strutturale, 58 (2021) 33-47; doi: 10.3221/igf-esis.58.03 36 methodology the methodology implemented in this paper is composed of three main steps (see figure 2) that we will detail in the rest of this section. the objective of the proposed methodology is the detection and monitoring of internal cracks in concrete structures. such cracks will be detected by ultrasonic ndt and analyzed by the wavelet transform providing a spatially scaled image allowing to localize the crack in space and at each resolution. the resulting multi-resolution image is then subjected to a deep learning-based crack/non-crack classification process (alexnet, vgg16). this methodology comprises three steps: the first step consists of performing a non-destructive ultrasonic test (ndt) on aging concrete samples of different compositions. the objective is to collect the ultrasonic signal received. in the second step, a wavelet-based multiresolution analysis is conducted on the received ultrasound signal. this is the key step of the work presented in this article since it will allow to highlight the initiation of cracks within the material. from the multi-resolution analysis, a b-scan mapping will then be obtained. finally, the obtained image will be the input of a deep learning algorithm based on convolutional neural networks (cnns). two well-known architectures in the literature, namely alexnet and vgg16, will be tested. alexnet won the imagenet competition in 2012, and vgg16 won the same competition in 2014. these are the two networks that were used in our experiments due to the fact that they are behind the explosive emergence of deep learning. they will be the basis for evaluating the performance of our approach for crack detection in concrete structures. other neural networks exist, as powerful as alexnet and vgg16 and maybe more, which are used in pattern recognition. however, the goal of this work is not to find the network that will give the best accuracy in detecting an internal crack in concrete from optical images. indeed, the aim is to demonstrate that with wavelet-based multiresolution analysis, the detection of a crack in concrete at an early stage will be very accurate independently of the type of deep learning architecture used. figure 2: methodology for effective monitoring of cracks in concrete after non-destructive ultrasonic testing. a. arbaoui et alii, frattura ed integrità strutturale, 58 (2021) 33-47; doi: 10.3221/igf-esis.58.03 37 experimental procedure preparation of concrete specimens n this section, the four main steps in the preparation of concrete specimens will be detailed, i.e. fabrication, casting, curing and end grinding. as shown in figure 3 a, the following raw materials were used to manufacture the concrete specimens:  cement (sour el-ghozlane cement plant in algeria) dosed at 350 kg/m3;  sand (bou-sâada sand in algeria) characterized by a grain size between 200 µm and 500 µm;  three types of gravel i.e., grain size 3/8 mm, grain size 8/15 mm and grain size 15/25 mm. five batches of standardized size specimens, corresponding to five different concrete mixes (see table 1), were made. each batch is composed of one cubic specimen of 150 mm side and six cylindrical specimens of 160 mm diameter and 320 mm height. each of the thirty-five specimens dedicated to this study was cast in a galvanized steel mold on a vibrating table (see figure 3 b. the final mass of a concrete specimen is 15 kg. as shown in figure 3 c, each specimen was stored at 20 °c and 98% humidity in a curing chamber for 28 days to simulate the fabrication of concrete columns. finally, as shown in figure 3 d, a “deluxe hi-kenma tsuru-tsuru” type end grinding machine from the manufacturer marui & co., ltd. was then used so that each concrete specimen had a perfect surface, i.e., low roughness after machining. figure 3: main steps in the manufacture of concrete specimens: a) raw materials; b) casting; c) curing; d) end grinding [provided by the authors]. batch no. characteristic strength [mpa] water/cement ratio cement [kg.m-3] sand [kg.m-3] gravel [kg.m-3] 1 10 1.20 150 1,016 1.11 2 15 0.80 225 954 1.11 3 20 0.65 277 911 1.11 4 25 0.62 290 900 1.11 5 30 0.55 327 870 1.11 table 1: proportion of constituents of the five batches of concrete mixtures and associated characteristic compressive strengths. i a. arbaoui et alii, frattura ed integrità strutturale, 58 (2021) 33-47; doi: 10.3221/igf-esis.58.03 38 ultrasonic tests on concrete specimens there are many standardized processes related to ndt that can be classified into two categories: the first allowing to evaluate the strength and its variation in time; the second to evaluate characteristics other than strength (e.g. dimensions of structural elements, corrosion, dampness etc.) [10], [17–20]. in the first category, we find sclerometric methods [21] (whether static or dynamic), acoustic methods [22, 23] (e.g. ultrasound) or pull-off methods [24] which are semi-destructive. in the second category, the techniques are much more numerous: we can mention, among others, acoustic methods [25, 26] (e.g. acoustic emission, echo, ultrasonic, impact echo), electromagnetic methods [27] (e.g. continuous wave eddy current testing), physical methods [28] (e.g. methods based on measuring thermal properties, electric methods such as linear polarization resistance) or radiological methods [29] (e.g. techniques based on x-rays). unfortunately, civil engineering cannot benefit from all the technical advances of ndt in the mechanical industries because the nature of the materials used and the concerns differ. unlike metals, concrete is a composite material that originally contains a large number of defects in the form of small cavities, pores and gaps. it is also a material whose mechanical properties are not rigorously reproducible, even under the best conditions. moreover, these properties degrade more or less rapidly over time due to increased service loads, climatic conditions, alkaliaggregate reaction, etc. therefore, only acoustic techniques, infrared thermography, penetrant testing and corrosion rate measurement (e.g. linear polarization) methods are generally used in civil and mechanical engineering. many authors have designated acoustic ndt methods, used individually (e.g. ultrasonic tomography or impact-echo, both used individually) or in combination (e.g. impulse response combined with impact-echo), as particularly well suited for testing structures or building materials, especially concrete. in this article, we have implemented an acoustic method based on the measurement of the ultrasonic pulse velocity. this type of method is only suitable for the study of concrete consistency, discontinuities, cracks and crack depth but is not reliable for strength determination, except for the determination of poisson's ratio and young's modulus with reasonable accuracy [30]. by correlating ultrasonic pulse velocity and the concrete compressive strength, this latter can also be determined. the equipment used to perform the tests is the pundit® pl-200 from proceq (see figure 4). figure 4: experimental procedure for ultrasonic pulse velocity tests. two p-wave ultrasonic pulse velocity transducers with a frequency of 54 khz are used. the ultrasonic pulse velocities are between 100 vpp and 400 vpp. the pulse echo range is from 0.1 µs to 1,200 µs. a 7 inch 800 × 480 pixel touch screen with very high resolution is available with the equipment to analyze the measured waveforms. to determine the compressive strength, a 2,000-3,000 kn one-piece compression testing machine from 3r is used (see figure 5). according to table 1, with the five batches of concrete mixtures made, the estimated values of compressive strength are 10 mpa, 15 mpa, 20 mpa, 30 mpa and 35 mpa. the cylindrical specimens were first tested ultrasonically, using 54 khz longitudinal and transverse wave transducers. this method consists in measuring the transit time of an ultrasonic pulse passing through the concrete sample under test. the a. arbaoui et alii, frattura ed integrità strutturale, 58 (2021) 33-47; doi: 10.3221/igf-esis.58.03 39 higher the speed, the better the quality of the concrete in terms of density, uniformity, homogeneity, etc. the axial compression tests were performed immediately after the ultrasonic tests. figure 5: experimental procedure for compressive tests. wavelet-based multiresolution analysis wavelets are an interesting analytical tool to describe mathematically the increase in information required to go from a coarse approximation to a higher resolution approximation. through a multiresolution analysis (mra), a signal can be decomposed and reconstructed as a series of approximations of decreasing scale, completed by a series of details [13]. to illustrate this concept, let us consider an image built from a succession of approximations; the details enrich this image. thus, thanks to the mra based on wavelets, the coarse vision becomes finer and more precise. engineers, practitioners and researchers are confronted daily with increasingly difficult technological problems at multiple scales of analysis, in terms of classification, segmentation, detection of contours or parameters of interest, noise reduction or elimination, compression for transmission or storage, synthesis or reconstruction, etc. this concerns many fields such as astrophysics [31], finance [32], fluid mechanics [33], thermodynamics [34], medicine and biology [35–37], multimedia [38], telecommunications [39, 40], signal and image processing, and of course, the monitoring of cracks and detection of fractures in materials [41–46]. mra based on wavelets can thus become an essential tool for solving the difficulties encountered in the above-mentioned fields. this tool, sometimes described as miraculous, produces an immediate, easily interpretable and exploitable result. however, for specific applications requiring the extraction of targeted information, it is clear that advanced methods will have to be developed and “merged” in order to effectively utilize existing techniques or to optimize the analyses (for example in compression) by taking into account edges or contours, using 2nd and 3rd generation wavelets such as peaks, curves [47], contours [48], bands [49], etc. indeed, these anisotropic wavelets are automatically oriented and extended by unifying the geometry of a given edge or contour. this conceptualization of mra is comparable to a camera that moves closer to a subject or uses a zoom lens to distinguish details, and further away to capture larger features– the famous concept of the mathematical microscope. the principle of wavelet-based mra is illustrated in figure 6. three levels of resolution are considered here. at the first level of resolution, the signal s is decomposed into an approximation 1a and a detail 1d . at the second level of resolution, the 1a approximation is decomposed into an 2a approximation and a 2d detail. finally, at the third level of resolution, the 1a approximation is in turn decomposed into an 3a approximation and a 3d detail. thus, the signal s can be expressed as shown in (1).    3 3 2 1s a d d d (1) let   t denote a reference pattern called the mother wavelet. it is generally requested that   t has jointly highly concentrated time and frequency supports.   t satisfies (2), when n controls the number of oscillations of   t . this relation means that   t is orthogonal to polynomial components of degree less than n . a. arbaoui et alii, frattura ed integrità strutturale, 58 (2021) 33-47; doi: 10.3221/igf-esis.58.03 40 figure 6: principle of wavelet-based multiresolution analysis with three levels of resolution.        0,    0pt t dt p n (2) the wavelet transform  ,xw u s of a signal x at time u and scale s is defined by (3), where  * denotes the complex conjugate of  .           *,x t u w u s x t dt s (3) looking closely at equations (2) and (3), it is clear that  ,xw u s will be insensitive to the most regular behaviors of the signal assimilated to a polynomial of degree less than n (the number of vanishing moments of  ). conversely,  ,xw u s takes into account the irregular behavior of polynomial tendencies. this important property plays a central role in the detection of signal singularities, especially in the detection and tracking of cracks. the discrete wavelet transform (dwt) is given by (4).            , 2 , 2 ,    ,j jx xd j k w u k s j k (4) clearly, to reduce or eliminate redundancy, the family      2, ,j k j k must be an orthonormal basis of   2 , where   2 denotes the vector space of one-dimensional measurable, square-integrable functions. this property of the wavelet makes it possible to obtain a fast wavelet transform. the fast wavelet transformation is calculated by a cascade of low-pass filtering by h and high-pass filtering by g followed by a downsampling (or decimation) by a factor of 2 (see figure 7). in figure 7, ja (or  ,xa j k , where k is time) and jd (or  ,xd j k , where k is time) are referred to as approximation coefficients and wavelet coefficients (or details) of the signal at level j , respectively. moreover, the symbol represents the decimation by a factor of 2, i.e., keeping every other sample. the impulse response of the mirror low-pass filter is     h k h k and that of the mirror high-pass filter is     g k g k . these two impulse responses are linked by        1 1kg k h k whose coefficients are obtained directly from the chosen wavelet  [13]. figure 8 shows an example of signal decomposition over three levels of resolution using matlab. note that the original signal has 1,000 samples while the detail (and approximation) signals have been decimated by a factor of 2 at each resolution a. arbaoui et alii, frattura ed integrità strutturale, 58 (2021) 33-47; doi: 10.3221/igf-esis.58.03 41 level. thus, after 3 levels of resolution, from a signal of 1,000 samples, we arrive at the 3a approximation and the 3d detail, which each have only 125 samples. figure 7: principle of fast wavelet transform or multiresolution analysis. in this study, the investigative ultrasonic signal scalogram will be used to determine and analyze cracks in concrete. the scalogram of the signal  x t can be defined using (5).          2, ,       ,x xs j k d j k j k (5) figure 9 shows an example of scalogram of a signal representing three cracks in a concrete specimen, one of which (the central crack) is in an advanced state that could lead to an imminent rupture. figure 8: example of decomposition of a signal on three levels of resolution using matlab. detecting cracks in concrete using deep neural networks in recent years, artificial intelligence has become a necessity because of its groundbreaking innovations in many areas, including pattern recognition in construction and structural engineering [50]. deep learning methods, which use consecutive hidden layers of information processing organized in a hierarchical manner, have become essential for representation, learning and classification. considered today in the top 10 of the most efficient and flexible deep learning techniques, a. arbaoui et alii, frattura ed integrità strutturale, 58 (2021) 33-47; doi: 10.3221/igf-esis.58.03 42 convolutional neural networks (cnns) are particularly well suited for tasks such as image recognition, image analysis, image segmentation, video analysis or natural language processing [51, 52]. however, this type of machine learning requires the use of sufficiently large input database for training and testing to ensure the highest possible accuracy of the recognition process [53]. a cnn architecture is typically characterized by the presence of multiple convolutional blocks–each consisting of a convolution layer, an activation function and a pooling layer– and a fully connected layer [54]. a convolutional layer, which is a key element of the method, performs a convolution operation on the output of the previous layers using a set of filters, also called kernels, to extract the features that are important for classification, i.e. in this case the “crack” and “non-crack” classes. figure 9: example of scalogram of a signal representing three cracks in a concrete specimen. a cnn architecture is typically characterized by the presence of multiple convolutional blocks–each consisting of a convolution layer, an activation function and a pooling layer– and a fully connected layer [54]. a convolutional layer, which is a key element of the method, performs a convolution operation on the output of the previous layers using a set of filters, also called kernels, to extract the features that are important for classification, i.e. in this case the “crack” and “non-crack” classes. there are many cnn architectures, including alexnet, vgg16, inception and resnet, and their performances are regularly compared by many authors [55, 56]. in this article, two different pre-trained cnn models, i.e. alexnet and vgg16, are experimented. the objective is to demonstrate that the wavelet-based mra is the key component of the proposed approach which guarantees a very high level of accuracy in the classification, independently of the type of cnn architecture used. since its introduction in 2012, in the framework of the imagenet large scale visual recognition challenge (ilsvrc 2012), the alexnet architecture has already become a very popular cnn architecture and has obtained good results in many applications such as computer vision [51], [57]. alexnet is not a complex architecture when compared to other major cnn architectures, such as resnet, that have emerged in recent years [58]. it is also easy to implement with tensorflow and keras. as shown in figure 2, alexnet consists of five convolutional layers that use kernels to scan the input image by performing convolution operations. the first two convolution layers use a (11 × 11) and (5 × 5) size filter, respectively; the last three layers each use a (3 × 3) kernel. some of these convolutional layers (i.e., the first two layers and the last layer) are followed by max-pooling (i.e., a subsampling operation usually applied after a convolutional layer, where the maximum values are taken). at this stage, the model is composed of more than 1.7 million parameters. each convolution layer uses the rectifier linear unit (relu) activation function. unlike the sigmoid activation function, which is frequently used for a binary classification network, relu increases the non-linear properties of the decision function and the global network without affecting the receiver fields of the convolution layers. at the output of the convolutional layers, a flattening step is necessary to create a single vector containing the main characteristics of the crack to be identified. initially intended to classify 1,000 categories, we have modified the alexnet architecture so it handles only two possible classes, i.e. images with and without cracks. this architecture ends with three fully connected layers (the first two layers are composed of 4,096 a. arbaoui et alii, frattura ed integrità strutturale, 58 (2021) 33-47; doi: 10.3221/igf-esis.58.03 43 outputs, and the last layer has only two) with a softmax classifier, which is reduced in our work to a simple logistic regression, composed of the two possible labels. the three fully connected layers alone account for more than 18.8 million parameters. therefore, the network, having more than 20 million parameters, can then be trained. the adam optimizer was used. however, in case of dropout, a neuron is removed from the network with a probability of 0.5. even if dropout increases the number of iterations by 2, this step is essential to prevent oversizing of alexnet. vgg16 (the number 16 meaning that the architecture is composed of 16 layers) is a convolutional neural network model proposed by simonyan and zisserman [59] to achieve 92.7% accuracy in the famous imagenet top-5 test, which is a dataset of over 15 million labeled high-resolution images belonging to roughly 22,000 categories. this architecture improves alexnet by replacing the large kernel filters (11 and 5 in the first and second convolutional layers, respectively) with multiple 3 × 3 kernel filters, one after another. as shown in figure 2, the image to be classified goes through a stack of convolutional layers, where filters of size 3 × 3. the spatial padding of the input to the convolution layers is such that the spatial resolution is preserved after convolution. the spatial pooling is performed by five max-pooling layers, which follow some of the convolution layers (not all convolution layers are followed by max-pooling). as for the alexnet architecture, the relu activation function is used in the convolution steps. three fully connected layers follow the convolutional layer stack. the last layer is a softmax layer used to classify each pixel into “crack” or “non-crack” classes. although the vgg16 architecture is very large and requires nearly eight times more parameters to be trained compared to the alexnet architecture, it is easy to implement in current open-source software libraries for artificial neural networks. to conduct this study, we used two computers connected in parallel; each of the two being equipped with a 9th generation intel core i7 hexa core microprocessor. each computer is equipped with a high-end nvidia geforce rtx 2080 graphics processing unit (gpu) with the following main memory features: gddr6 type; 8 gigabyte (gb) capacity; 14 gb/s speed; 448 gb/s bandwidth; and a speed of 60 tops (tera operations per second) to process the very large number of operations (up to a few billion for each image) required to compute neural networks. as for software tools, the open source machine learning tool tensorflow, developed by the google brain team, was used. this is now an essential tool for machine learning applications, such as neural networks [60]. the implementation of the convolutional neural network algorithms was done with the keras library, using the python programming language. keras, which is used here as an interface for tensorflow, was chosen for the ease of its implementation of many functions and procedures, its modularity, and its extension capabilities. main results and discussion irst, we tested the methodology on available image datasets of visually or optically observable cracks on the surface of concrete samples. for this purpose, we used a public database containing 4,800 manually labeled images of cracked and non-cracked concrete bridge decks [61]. 80% of these images were allocated to the training phase and 20% for validation. it is noted that regardless of the deep learning architectures implemented, the wavelet-based mra does not add anything at this stage as the accuracy levels obtained are those found in the literature. we then sought to demonstrate the relevance of wavelet-based multiresolution analysis to identify the initiation of cracks in concrete, i.e. well before the fracture is visible on the surface of the material. for this purpose, a private database of bscan mappings obtained by wavelet-based mra was constructed from the 35 concrete specimens we fabricated and aged by the compression tests. for each concrete specimen, this database contains 40 images without cracks, and 100 images representing several stages of aging, i.e. from the initiation of cracks in the core of the material, then to their propagation, to the fracture of the specimen itself. in total, 4,900 images are available, each with dimensions of 120 pixels × 120 pixels × 3 color channels. for each of the two classes, i.e. “crack” and “non-crack”, 80% of the images are assigned to the training phase and 20% to the validation. before training and validation, the images are normalized by subtracting their mean in order to have centered data. this ensures similar image characteristics to avoid uncontrollable gradients in the loss function with respect to the neural network weights during backpropagation. figure 10 gives an illustrative example of the impact of wavelet-based multiresolution analysis combined with a simple deep learning architecture to automatically detect cracks in concrete long before they are visible by optical inspection. we have of course tested both architectures in figure 2 (i.e., alexnet and vgg16), as well as a more advanced architecture such as resnet-50 (i.e., composed of 50 layers with over 23 million trainable parameters). with a cnn architecture composed of about 20 million of parameters, and the equipment used, the training phase lasted about 25 hours, or about 30 minutes per epoch (i.e. the number of cycles through the full training dataset). similar results can be obtained regardless of the deep learning architecture implemented. f a. arbaoui et alii, frattura ed integrità strutturale, 58 (2021) 33-47; doi: 10.3221/igf-esis.58.03 44 in figure 10, the graph on the left shows the smoothed accuracy of the recognition of a crack as a function of the epochs. the graph on the right shows the evolution of the associated cost function. the cross-entropy loss function, also known as the logarithmic loss function, is one of the most commonly used cost functions when adjusting model weights during training. we have used the binary cross-entropy loss function is implemented. it consists of comparing each predicted class probability with the desired 0 or 1 output, identifying “crack” or “non-crack” respectively, for the actual class. a score is then computed, penalizing the probability according to the distance between it and the expected real value. in the case that we have implemented, the penalty function is logarithmic, which gives a high score for large differences close to 1 and a low score for small differences tending towards 0. for both training and validation, the results in figure 10 show that fewer than 25 epochs are required for the smoothed accuracy and loss function to converge. more precisely, the smoothed accuracy reaches a maximum of 97% during the training phase and 98% during the validation phase, thus confirming the great importance of the wavelet-based multiresolution analysis. the loss function, on the other hand, reaches a minimum lower than 0.1 during both training and validation, which means that the model is adequately fine-tuned. figure 10: wavelet-based multiresolution analysis coupled with a simple deep learning architecture for automatic detection of crack formation in concrete: examples of smoothed accuracy and loss function (binary cross-entropy model). conclusions his paper reports on an original methodology that was implemented to efficiently detect crack initiation using nondestructive ultrasonic testing of elements of a concrete civil engineering structure. compared to existing related studies in the literature, our main contributions are as follows:  proposal of a detection method at an early stage, i.e. well before the concrete fracture is visible on the surface, in order to implement appropriate maintenance actions and thus avoid the failure of the structure.  a key element of this method is the wavelet-based multi-resolution analysis (mra) of the ultrasonic signal received from a sample or a concrete specimen subjected to several types of solicitation. the received ultrasonic signal is analyzed at each resolution (or scale) by wavelet transformation.  the resulting image is squared to serve as input to an automatic crack type identification system based on deep learning by convolutional neural networks (cnns). two architectures, chosen both for their ease of implementation in open-source platforms and libraries dedicated to machine learning and to limit the computational load, were tested. the purpose was not to optimize cnn architectures. if this were the case, then we would have chosen modular structures (e.g. resnext, xception, channel boosted cnn, etc.) based on auxiliary learners that utilize either spatial or feature map information or input channels to improve classification performance. the objective was to rather show that with a multiresolution analysis based on wavelets, it is possible to detect crack initiations in concrete and that the accuracy of this detection is independent of the chosen cnn architecture. after aging concrete specimens in compression tests, we built a database containing nearly 5,000 b-scan mappings from wavelet-based mra of specimens with and without crack initiation and propagation. regardless of the two architectures implemented, the results show that the accuracy is greater than 98%. the loss function reaches values less than 0.1, which t a. arbaoui et alii, frattura ed integrità strutturale, 58 (2021) 33-47; doi: 10.3221/igf-esis.58.03 45 means that both models are finely tuned. all these results prove the relevance and efficiency of the approach described in this paper. it would be interesting if the non-destructive methodology proposed in this paper could be implemented on all or part of civil engineering structures, such as suspension bridges, reinforced concrete bridges with central cantilever spans or masonry railway viaducts, that require permanent remote monitoring in order to prevent the occurrence of failures that would jeopardize the safety and performance of the structure itself. remote monitoring should not in any case replace visual or optical surveillance of structures, which remains the basis of monitoring. however, deep learning algorithms are of undisputable relevance for remote monitoring, especially when many images or videos showcasing structures’ state of health are captured, because any cracks can in this case be detected very quickly and automatically. references [1] mani, m., bouali, m. f., kriker, a. and hima a. (2021). experimental characterization of a new sustainable sand concrete in an aggressive environment, frattura ed integrità strutturale, 55, pp. 231–251. doi: 10.3221/igf-esis.55.0. [2] vasco, m. c., polydoropoulou, p., chamos, a. n. and pantelakis s. g. (2017). experimental characterization of a new sustainable sand concrete in an aggressive environment, frattura ed integrità strutturale, 42, pp. 9–22. doi: 10.3221/igf-esis.42.02. [3] bhaskar, s., gettu, r., bharatkumar, b. h. and neelamegam m. (2011). studies on chloride induced corrosion of reinforcement steel in cracked concrete, sdhm structural durability and health monitoring, 7(4), pp. 231–251. doi: 10.3970/sdhm.2011.007.231. [4] golewski, g. l. (2019). new principles for implementation and operation of foundations for machines: a review of recent advances. structural engineering and mechanics, 71(3), 317–327. doi: 10.12989/sem.2019.71.3.317. [5] wang, d., dong, y., zhang, d., wang, w. and lu x. (2020). monitoring and analysis of reinforced concrete plate-column structures under room temperature and fire based on acoustic emission, frattura ed integrità strutturale, 53, pp. 9–22. doi: 10.3221/igf-esis.53.20. [6] golewski, g. l. (2020). changes in the fracture toughness under mode ii loading of low calcium fly ash (lcfa) concrete depending on ages. materials, 13, 5241. doi: 10.3390/ma13225241. [7] golewski, g. l.; gil, d. m. (2021). studies of fracture toughness in concretes containing fly ash and silica fume in the first 28 days of curing. materials, 14, 319. doi: 10.3390/ma14020319. [8] golewski, g. l. (2021). the beneficial effect of the addition of fly ash on reduction of the size of microcracks in the itz of concrete composites under dynamic loading. energies, 14, 668. doi: 10.3390/en14030668. [9] lamonaca, f., sciammarella, p. f., scuro, c., carnì, d. l. and olivito, r. s. (2018). internet of things for structural health monitoring. 2018 ieee international workshop on metrology for industry 4.0 and iot, brescia, italy, 16–18 april, pp. 95–100. doi: 10.1109/metroi4.2018.8439038. [10] schabowicz, k. (2019). non-destructive testing of materials in civil engineering, materials, 12, 3237. doi: 10.3390/ma12193237. [11] kogbara, r. b., iyengar, s. r., grasley, z. c., masad, e. a. and zollinger, d. g. (2015). non-destructive evaluation of concrete mixtures for direct lng containment, materials & design, 82, pp. 260-272. doi: 10.1016/j.matdes.2015.05.084. [12] wiggenhauser, h., köpp, c., timofeev, j. et al. (2018). controlled creating of cracks in concrete for non-destructive testing, journal of nondestructive evaluation, 37(67). doi: 10.1007/s10921-018-0517-x. [13] ouahabi, a. (2013). signal and image multiresolution analysis, wiley-iste ltd, london (uk) and hoboken (new jersey, usa). isbn: 978-1-118-56866-8. [14] he, w.-y., zhu, s. and chen, z.-w. (2017). wavelet-based multi-scale finite element modeling and modal identification for structural damage detection, advances in structural engineering, 20(8), pp. 1185–1195. doi: 10.1177/1369433216687566. [15] kim, j. j., kim, a.-r. and lee, s.-w. (2020). artificial neural network-based automated crack detection and analysis for the inspection of concrete structures, applied sciences, 10, 8105. doi: 10.3390/app10228105. [16] li, s. and zhao, x. (2019). image-based concrete crack detection using convolutional neural network and exhaustive search technique, advances in civil engineering, 2019, pp. 1–12. doi: 10.1155/2019/6520620. [17] bulatovic, s., aleksic, v. and milovic l. (2013). failure of steam line causes determined by ndt testing in power and heating plants, frattura ed integrità strutturale, 26, pp. 41–48. doi: 10.3221/igf-esis.26.05. a. arbaoui et alii, frattura ed integrità strutturale, 58 (2021) 33-47; doi: 10.3221/igf-esis.58.03 46 [18] prakash, r. v. and john m. (2019). post-impact fatigue damage analysis of quasi isotropic cfrp laminates through infrared thermography, 49, pp. 536–546. doi: 10.3221/igf-esis.49.50. [19] akgul, f. (2020). inspection and evaluation of a network of concrete bridges based on multiple ndt techniques, structure and infrastructure engineering. doi: 10.1080/15732479.2020.1790016. [20] lee, t., lee, j. and choi, h. (2020). assessment of strength development at hardened stage on high-strength concrete using ndt, applied sciences, 10(18), 6261. doi: 10.3390/app10186261. [21] jaskowska-lemańska, j. and sagan, j. (2019). non-destructive testing methods as a main tool supporting effective waste management in construction processes, archives of civil engineering, 65(4), pp. 263–276. doi: 10.2478/ace-2019-0059. [22] girault, j.-m., ossant, f., ouahabi, a., kouamé, d. and patat, f. (1998). time-varying autoregressive spectral estimation for ultrasound attenuation in tissue characterization, ieee transactions on ultrasonics, ferroelectrics, and frequency control, 45(3), pp. 650–659. doi: 10.1109/58.677609. [23] labat, v., remenieras, j.-p., matar, o. b., ouahabi, a. and patat, f. (2000). harmonic propagation of finite amplitude sound beams: experimental determination of the nonlinearity parameter b/a, ultrasonics, 38(1–8), pp. 292–296. doi: 10.1016/s0041-624x(99)00113-4. [24] sadowski, ł., hoła, j., czarnecki, s. and wang, d. (2018). pull-off adhesion prediction of variable thick overlay to the substrate, automation in construction, 85, pp. 10–23. doi: 10.1016/j.autcon.2017.10.001. [25] louhi kasahara, j. y., yamashita, a. and asama, h. (2020). acoustic inspection of concrete structures using active weak supervision and visual information, sensors, 20(3), 629. doi: 10.3390/s20030629. [26] ouahabi, y. r., bensadok, k. and ouahabi, a. (2021). optimization of the biomethane production process by anaerobic digestion of wheat straw using chemical pretreatments coupled with ultrasonic desintegration, sustainability, 13(13), 7202. doi: 10.3390/su13137202. [27] yuan, f., yu, y., li, l. and tian, g. (2021). investigation of dc electromagnetic-based motion induced eddy current on ndt for crack detection, ieee sensors journal, 21(6), pp. 7449–7457. doi: 10.1109/jsen.2021.3049551. [28] rodrigues, r., gaboreau, s., gance, j., ignatiadis, i. and betelu, s. (2021). reinforced concrete structures: a review of corrosion mechanisms and advances in electrical methods for corrosion monitoring, construction and building materials, 269, 121240. doi: 10.1016/j.conbuildmat.2020.121240. [29] moosavi, r., grunwald, m. and redmer, b. (2020). crack detection in reinforced concrete, ndt & e international, 109, 102190. doi: 10.1016/j.ndteint.2019.102190. [30] levitt, m. (2004). precast concrete: materials, manufacture, properties and usage, applied science publishers, london (uk) and new jersey (usa). isbn: 0-203-49057-6. [31] de moortel, i. and hood, a. w. (2000). wavelet analysis and the determination of coronal plasma properties, astronomy and astrophysics, 363, pp. 269–278. [32] ramsey, j. b. (2002). wavelets in economics and finance: past and future, studies in nonlinear dynamics and econometrics, 6(3). doi: 10.2202/1558-3708.1090. [33] shiralashetti, s. c. and deshi, a. b. (2017). numerical solution of differential equations arising in fluid dynamics using legendre wavelet collocation method, international journal of computational materials science and engineering, 6(2), 1750014. doi: 10.1142/s2047684117500142. [34] su, t., li, z. and kahn, r. (2020). a new method to retrieve the diurnal variability of planetary boundary layer height from lidar under different thermodynamic stability conditions, remote sensing of environment, 237, 111519. doi: 10.1016/j.rse.2019.111519. [35] guetbi, c., kouamé, d., ouahabi, a. and remenieras, j.-p. (1997). new emboli detection methods [doppler ultrasound], 1997 ieee ultrasonics symposium proceedings, an international symposium (cat. no.97ch36118), toronto, on, canada, 5–8 october, pp. 1119–1122. doi: 10.1109/ultsym.1997.661775. [36] ouahabi, a. (2010). multifractal analysis for texture characterization: a new approach based on dwt, proceedings of the 10th international conference on information science, signal processing and their applications (ieee/isspa), kuala lumpur, malaysia, 10–13 may, pp. 698–703. doi: 10.1109/isspa.2010.5605576. [37] djeddi, m., ouahabi, a., batatia, h., basarab, a. and kouamé, d. (2010). discrete wavelet transform for multifractal texture classification: application to ultrasound imaging, proceedings of the 17th ieee international conference on image processing (icip), hong kong, china, 26–29 september, pp. 637–640. doi: 10.1109/icip.2010.5650017. [38] sui, k. and kim, h.-g. (2019). research on application of multimedia image processing technology based on wavelet transform, eurasip journal on image and video processing, 24. doi: 10.1186/s13640-018-0396-1. [39] haneche, h., ouahabi, a. and boudraa, b. (2019). new mobile communication system design for rayleigh environments based on compressed sensing-source coding, iet communications, 13(15), pp. 2375–2385. a. arbaoui et alii, frattura ed integrità strutturale, 58 (2021) 33-47; doi: 10.3221/igf-esis.58.03 47 doi: 10.1049/iet-com.2018.5348. [40] haneche, h., boudraa, b. and ouahabi, a. (2020). a new way to enhance speech signal based on compressed sensing, measurement, 151, pp. 107–117. doi: 10.1016/j.measurement.2019.107117. [41] ait aouit, d. and ouahabi a. (2008). monitoring crack growth using thermography, comptes rendus mécanique, 336, pp. 677–683. doi: 10.1016/j.crme.2008.06.001. [42] girault, j.-m., kouamé, d. and ouahabi, a. (2010). analytical formulation of the fractal dimension of filtered stochastic signal, signal processing, 90(9), pp. 2690–2697. doi: 10.1016/j.sigpro.2010.03.019. [43] ait aoui, d. and ouahabi, a. (2011). nonlinear fracture signal analysis using multifractal approach combined with wavelet, fractals complex geometry, patterns, and scaling in nature and society, 19(18), pp. 175–183. doi: 10.1142/s0218348x11005270. [44] ouahabi, a. and femmam, s. (2011). wavelet-based multifractal analysis of 1-d and 2-d signals: new results, analog integrated circuits and signal processing, 69(1), pp. 3–15. doi: 10.1007/s10470-011-9620-y. [45] jacques, s., caldeira, a., batut, n., schellmanns, a., leroy, r. and gonthier, l. (2012). lifetime prediction modeling of non-insulated to-220ab packages with lead-based solder joints during power cycling, microelectronics reliability, 52(1), pp. 212–216. doi: 10.1016/j.microrel.2011.08.017. [46] calvez, d., roqueta, f., jacques, s., béchou, l., ousten, y. and ducret, s. (2014). crack propagation modeling in silicon: a comprehensive thermo-mechanical fem approach for power devices, ieee transactions on components packaging manufacturing technologies, 4(2), pp. 360–366. doi: 10.1109/tcpmt.2013.2293094. [47] alzubi, s., islam, n. and abbod, m. (2011). multiresolution analysis using wavelet, ridgelet, and curvelet transforms for medical image segmentation, international journal of biomedical imaging, 2011. doi: 10.1155/2011/136034. [48] anila, s., sivaraju, s.s. and devarajan, n. (2017). a new contourlet based multiresolution approximation for mri image noise removal. national academy science letters, 40, pp. 39–41. doi: 10.1007/s40009-016-0498-1. [49] kafieh, r., rabbani, h. and g. unal. (2019). bandlets on oriented graphs: application to medical image enhancement, ieee access, 7, pp. 32589–32601. doi: 10.1109/access.2019.2903467. [50] pan, y. and zhang, l. (2021). roles of artificial intelligence in construction engineering and management: a critical review and future trends, automation in construction, 122, 103517. doi: 10.1016/j.autcon.2020.103517. [51] adjabi, i., ouahabi, a., benzaoui, a. and taleb-ahmed, a. (2020). past, present, and future of face recognition: a review, electronics, 9(8), 1188. doi: 10.3390/electronics9081188. [52] ouahabi, a. and taleb-ahmed, a. (2021). deep learning for real-time semantic segmentation: application in ultrasound imaging, pattern recognition letters, 144, pp. 27–34. doi: 10.1016/j.patrec.2021.01.010. [53] mimouna, a., alouani, i., ben khalifa, a., el hillali, y., taleb-ahmed, a., menhaj, a., ouahabi, a. and ben amara, n. e. (2020). olimp: a heterogeneous multimodal dataset for advanced environment perception. electronics, 9, 560. doi: 10.3390/electronics9040560. [54] dung, c. v. and anh, l. d. (2019). autonomous concrete crack detection using deep fully convolutional neural network, automation in construction, 99, pp. 52–58. doi: 10.1016/j.autcon.2018.11.028. [55] adjabi, i., ouahabi, a., benzaoui, a. and jacques, s. (2021). multi-block color-binarized statistical images for singlesample face recognition, sensors, 21(3), 728. doi: 10.3390/s21030728. [56] wu, x. and liu, x. (2021). building crack identification and total quality management method based on deep learning, pattern recognition letters, 145, pp. 225–231. doi: 10.1016/j.patrec.2021.01.034. [57] khan, a., sohail, a., zahoora, u. and qureshi, a. s. (2020). a survey of the recent architectures of deep convolutional neural networks, articial intelligence review, 53(8), pp. 5455–5516. doi: 10.1007/s10462-020-09825-6. [58] abbas, q., ibrahim m. e. a. and jaffar, m. a. (2019). a comprehensive review of recent advances on deep vision systems, artificial intelligence review, 52(1), pp. 39–76. doi: 10.1007/s10462-018-9633-3. [59] simonyan, k. and zisserman, a. (2015). very deep convolutional networks for large-scale image recognition. proceedings of the 3rd international conference on learning representations, iclr 2015, san diego, ca, usa, may 7–9. [60] yuan, l., qu, z., zhao, y., zhang, h. and nian, q. (2017). a convolutional neural network based on tensorflow for face recognition. 2017 ieee 2nd advanced information technology, electronic and automation control conference (iaeac), chongqing, china, 25–26 march, pp. 525–529. doi: 10.1109/iaeac.2017.8054070. [61] maguire, m., dorafshan, s. and thomas, r. j. (2018). sdnet2018: a concrete crack image dataset for machine learning applications, utah state university, logan. doi: 10.15142/t3td19. microsoft word numero_41_art_57.docx p. gallo et alii, frattura ed integrità strutturale, 41 (2017) 456-463; doi: 10.3221/igf-esis.41.57 456 creep behavior of v-notched components p. gallo department of mechanical engineering, aalto university, marine technology, puumiehenkuja 5a, espoo 02150, finland. s.m.j. razavi, m. peron, j. torgersen, f. berto department of mechanical and industrial engineering, norwegian university of science and technology (ntnu), norway javad.razavi@ntnu.no, mirco.peron@ntnu.no, jan.torgersen@ntnu.no, filippo.berto@ntnu.no abstract. geometrical discontinues such as notches play a significant rule in structural integrity of the components, especially when the component is subjected to very severe conditions, such as the high temperature fatigue or creep. in this paper, a generalized form of the existing notch tip creep stressstrain analysis method developed by nuñez and glinka, is developed and extended to a wide variety of blunt v-notches. assuming the generalized lazzarin-tovo solution that allows a unified approach to the evaluation of linear elastic stress fields in the vicinity of both cracks and notches is the key in getting the extension to blunt v-notches. numerous cases have been analysed and the stress fields obtained according to the proposed method were compared with proper finite element data, showing a very good agreement. keywords. creep; v-notches; stress fields; stress evaluation; strain energy density. citation: gallo, p., razavi, s.m.j., peron, m., torgersen, j., berto, f., creep behavior of vnotched components, frattura ed integrità strutturale, 41 (2017) 456-463. received: 12.05.2017 accepted: 23.07.2017 published: 01.07.2017 copyright: © 2017 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. introduction ue to the complexities of the geometry and loading conditions in modern structural components, it is essential to be able to predict the behavior of components including geometrical discontinuities that generate localized high stress concentration zones [1,7]. they become even more important when, in operating conditions, the component is subjected to very demanding conditions such as high temperature fatigue or creep loading. various methods have been proposed by researchers to evaluate the behavior of structural components under various loading conditions [812]. the structural components show a nonlinear stress-strain response such as creep (visco-plasticity) under applied load in a high temperature environment. in presence of geometric discontinuities such as notches, localized-creep takes place in a small region near the notch root. on the other hand, non-localized (or gross) creep condition refers to situations in which the far stress field also experiences some creep which may lead to more intense creeping in the vicinity of the notch tip. d p. gallo et alii, frattura ed integrità strutturale, 41 (2017) 456-463; doi: 10.3221/igf-esis.41.57 457 to the best of the authors’ knowledge only a few solutions related to the localized time-dependent creep-plasticity problems are available in literature. nuñez and glinka [13] proposed a solution for non-localized creep strains/stresses at the notch root, based on the linear-elastic behavior of the material, the constitutive law and the material creep model. the formulation was derived by using the total strain energy density rule proposed by neuber [14]. considering the u-notched specimens (2α=0 and ρ≠0) very good results were obtained using this method. the main aim of the current paper is to extend the method proposed by nuñez and glinka to blunt v-notches. for this aim, the creager and paris [15] equations were substituted with the lazzarin and tovo [16] equations. finally an approach for fast evaluation of the stresses/strains at notches under non-localized creeping condition is proposed which doesn’t require any complex and time-consuming fe non-linear analyses. output of the proposed approach can be used as input for creep life prediction models based on local approaches. evaluation of stresses and strains under non-localized creeping condition for blunt vnotches uñez and glinka [13] presented a method for the estimation of stress and strain at u-notch tip, subjected to non-localized creep. the method was based on the neuber [14] concept extended to time dependent plane stress problems and on the introduction of kω parameter introduced by moftakhar et al. [17]. it can be assumed in fact that the total strain energy density changes occurring in the far field produce magnified effects at the notch tip. for this reason, the total strain energy density concentration factor is introduced in order to magnify the energy at the notch tip. the introduction of this parameter and of the far field stress and strain contribution in the neuber’s time dependent formulation is the main difference within the non-localized and localized creep formulation that, instead, can be easily derived directly by extending the neuber’s rule. details about the original formulation can be found in the original works nuñez and glinka [13] and in gallo et al. [18]. the key to extend the nuñez-glinka method to blunt vnotches is the assumption of the lazzarin and tovo [16] equations to describe the early elastic state of the system. (a) (b) figure 1: (a) coordinate system and symbols used for the stress field components in lazzarin-tovo equations; (b) coordinate system and symbols used for the elastic stress field redistribution for blunt v-notches. the lazzarin-tovo equations, in the presence of a traction loading, along the bisector (x axis), can be expressed as follows, as a function of the maximum stress (see fig. 1):                 1 1 1 1 1 1 1 1 1 1 1 1 0 0 1 1 1 1 1 1 0 1 1 3 1 4 3 1 3 1 max r r rr r r r                                                                         (1) n p. gallo et alii, frattura ed integrità strutturale, 41 (2017) 456-463; doi: 10.3221/igf-esis.41.57 458 where σmax can be expressed as a function of stress concentration factor kt (evaluated through linear elastic finite element analysis) and the applied load σnom, max t nom k  (2) employing the more general conformal mapping of neuber [19] that permit a unified analysis of sharp and blunt notches, the notch radius, ρ, and the origin of the coordinate system, r0, are related by the following equation on the basis of trigonometric considerations: 0 1 q r q     (3) where 2 2 q      . the main steps to extend the method to blunt v-notches can be summarised as follows:  assumption of lazzarin-tovo equations to describe the stress distribution ahead the notch tip instead of creager-paris equations;  calculation of the origin of the coordinate system, r0, as a function of the opening angle and notch radius, as described by eq. (3);  re-definition of the plastic zone correction factor cp that is a function of plastic zone size rp and plastic zone increment δrp; the definition of the parameters cp, rp, δrp is very similar to that clearly reported by glinka [20], except for the assumption of different elastic stress distribution equations. definition of these variables is briefly reported hereafter. referring to fig. 2, considering the von mises [21] yield criterion in polar coordinate: 2 2 ys r r         (4) and introducing eqs. (1) into eq. (4), a first approximation of rp that can be solved numerically is obtained. once rp is known, the force f1 can be evaluated as follows:                  0 1 1 1 1 1 1 1 1 0 1 0 1 1 1 1 0 0 0 1 1 1 1 0 1 1 1 0 0 0 1 1 1 1 3 4 1 1 1 (3 ) pr p p r p p pt nom p p p p p f dr r r r r r rk r r r r r r r r r r r r r                                                                                                    1 1             (5) the stress σy (rp) is considered to be constant inside the plastic zone, which means elastic-perfectly plastic behavior is assumed. the lower integration limit is r0, which depends on the opening angle and notch tip radius. due to the plastic yielding at the notch tip, the force f1 cannot be carried through by the material in the plastic zone rp. but in order to satisfy the equilibrium conditions of the notched body, the force f1 has to be carried through by the material beyond the plastic zone rp. as a result, stress redistribution occurs, increasing the plastic zone rp by an increment ∆rp. if the plastic zone is small in comparison to the surrounding elastic stress field, the redistribution is not significant, and it can be interpreted as a shift of the elastic field over the distance ∆rp away from the notch tip. therefore the force f1 is mainly carried through the material over the distance ∆rp, and therefore the force f2 (represented by the area depicted in the fig. p. gallo et alii, frattura ed integrità strutturale, 41 (2017) 456-463; doi: 10.3221/igf-esis.41.57 459 1-b) must be equal to f1. for this reasons, f1 = f2 = σθ(rp)δrp, and the plastic zone increment can be expressed as the ratio between f1 and σθ evaluated (through lazzarin-tovo equations [16]) at a distance equal to the previously calculated rp:   1 p p f r r   (6) substituting in eq. (6) the formula given by eq. (5) for f1 and the explicit form of σθ, the expression for the evaluation of δrp is obtained:                 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 0 0 0 0 1 1 1 1 1 0 1 1 1 0 0 0 1 1 1 1 3 1 1 1 3 p p p p p p p p p p r r r r r r r r r r r r r r r r r r r                                                                                                                      1 1 1 1 1 1 1 1 1 0 0 / 1 1 1 3 p pr r r r                                           (7) the last step consists in the definition of the plastic zone correction factor cp, which is according to glinka [20] but introducing the lazzarin-tovo equations:                 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 0 0 0 0 1 1 1 1 1 0 1 1 1 0 0 0 1 δ 1 1 1 1 1 3 1 1 1 3 p p p p p p p p p p p p r r r r r c r r r r r r r r r r r r r r r                                                                                                               1 1 1 1 1 1 1 1 1 0 0 / 1 1 1 3 p p p r r r r r                                                    (8) at this point, the general stepwise procedure to be followed to generate a solution is identical to that proposed by nuñez and glinka [13]: 1. determine the notch tip stress, 22 e , and strain, 22 e , using the linear-elastic analysis. 2. determine the elastic-plastic stress, 022 , and strain, 0 22 , using the neuber [14] rule (or other methods e.g. esed by molski and glinka [22], finite element analysis). 3. begin the creep analysis by calculating the increment of creep strain, 22δ n c , for a given time increment δtn. the selected creep hardening rule has to be followed.  22 22δ δ ;nc cnt t    (9) 4. determine the decrement of stress, 22δ n t , from eq. (10), due to the previously determined increment of creep strain, 22δ nc : p. gallo et alii, frattura ed integrità strutturale, 41 (2017) 456-463; doi: 10.3221/igf-esis.41.57 460 1 1 0 22 22 22 22 22 0 22 22 ( ) δ δ δ 2 n n n n n n cf t cf pt t cp k c e               (10) 5. for a given time increment δtn, determine from eq. (11) the increment of the total strain at the notch tip, 22δ nt : 22 22 22 δ δ δ n n n t t c e     (11) 6. repeat steps from 3 to 5 over the required time period. results he proposed new method has been applied to a hypothetical plate weakened by lateral symmetric v-notches, under mode i loading; see fig 1b. the notch tip radius ρ and the opening angle 2α have been varied, while for the notch depth a, a constant value equal to 10 mm has been assumed. three values of the opening angle 2α have been considered: 60°, 120° and 135°. the notch tip radius assumes for every opening angle three values: 0.5, 1 and 6 mm. the plate has a constant height, h, equal to 192 mm and a width, w, equal to 100 mm. the numerical results have been obtained thanks to the implementation of the new developed method and its equations in matlab®. in the same time, a 2d finite element analysis has been carried out through ansys. the solid 8 node 183 element has been employed and plane stress condition is assumed. the material elastic (e, ν, σys) and norton creep power law (n, b) properties are reported in tab. 1. for the sake of brevity, only few examples are reported in fig. 2 (a-b). all the other cases present the same trend of fig. 2. the theoretical results are in good agreement with the numerical fe values. all the stresses and strains as a function of time have been predicted with acceptable errors. in detail, maximum discrepancy in modulus of 20% has been found for both quantities, with a medium error about 10%. considering the examples of the strain prediction depicted in fig. 2(b), the discrepancy within numerical and predicted solution of the strain is most likely due to different approximations introduced in the theoretical formulation, such as the assumption of the elastic-perfectly plastic behavior of the material inside the plastic zone and the employment of the irwin’s method to estimate the plastic radius. e (mpa) ν σys (mpa) n b (mpa-n/h) 191000 0.3 275.8 5 1.8 table 1: mechanical properties. (a) (b) 0 0.01 0.02 0.03 0.04 0 500 1000 1500 2000 2500 0 4 8 12 16 20 ε θ θ cr ee p σ θθ [m p a] t [h] fem theoretical solution 2α = 120° ρ = 0.5 mm a = 10 mm cp = 1.57 kω = 103 stress strain 0.000 0.010 0.020 0.030 0.040 0 4 8 12 16 20 ε θ θ cr ee p t [h] fem theoretical solution 2α = 135° a = 10 mm cp = 1.41 kω = 10.10 ρ = 0.5 mm ρ = 1 mm ρ = 6 mm figure 2: comparison between theoretical and fem evolution of stress and strain as a function of time for v-notch geometry: (a) ρ = 0.5 mm, 2α = 120°; (b) 2α = 135° and ρ = 0.5, 1, 6 mm. t p. gallo et alii, frattura ed integrità strutturale, 41 (2017) 456-463; doi: 10.3221/igf-esis.41.57 461 conclusions he present paper proposed an extension of the method presented by nuñez and glinka [13] for blunt u-notches, to a blunt v-notches. the key to getting the extension to blunt v-notches is the substitution of the creager and paris [15] equations with the more general lazzarin and tovo [16] equations that allow an unified approach to the evaluation of linear elastic stress fields in the neighbourhood of crack and notches. the main advantage of the new formulation is that it permits a fast evaluation of the stresses and strains at notches under creep conditions, without the use of complex and time-consuming fe non-linear analyses. it is presented for blunt v-notches but also valid for unotches. moreover, the localized creep formulation can be easily derived neglecting the contribution of the far field. the results have shown a good agreement between numerical and theoretical results. thanks to the extension to blunt vnotches, all geometries can be easily treated with the aim of the numerical method developed. although lazzarin and tovo equations are valid also in case of sharp v-notches (i.e. for a notch radius that tends to be zero), the values of stress and strain are no longer suitable as characteristic parameters governing failure. as well known, in fact, these local approaches failed when the stress fields tends toward infinity (such as for crack or sharp notches), and the development of alternative solutions becomes crucial. the evaluation of stress and strain at some points ahead of the notch tip may be a possible way to address the problem. different methods are available in literature dealing with this matter, for example based on energy local approaches such as strain energy density [23-25]. this parameter could be useful also to characterize creeping conditions if combined with the present model, giving the possibility to include in the analysis also cracks and sharp v-notches. however, some points remain open: -order singularity variation with time: when considering creeping conditions, the singularity order does not assume a constant value, but varies with time. -evolution against time from elastic to elastic-plastic or fully plastic state of the system, especially when dealing with high temperature. because of the promising results showed in the preliminary analyses, the authors still devoting effort to overcome the problems cited previously and to combine successfully the proposed model for the prediction of stresses and strain with the sed averaged over a control volume, in order to give a useful and more general tool when dealing with notches subjected to creep, regardless of the specimen geometries. references [1] cui, l., wang, p., crack initiation behavior of notched specimens on heat resistant steel under service type loading at high temperature, frattura ed integrita strutturale, 10(38) (2016) 26-35. [2] gallo, p., berto, f., high temperature fatigue tests and crack growth in 40crmov13.9 notched components, frattura ed integrita strutturale, 9(34) (2015) 180-189. [3] kotousov, a., berto, f., lazzarin, p., pegorin, f., three dimensional finite element mixed fracture mode under antiplane loading of a crack, theor. appl. fract. mech., 62(1) (2012) 26-33. [4] radaj, d., berto, f., lazzarin, p., local fatigue strength parameters for welded joints based on strain energy density with inclusion of small-size notches, eng. fract. mech., 76(8) (2009) 1109-1130. [5] berto, f., campagnolo, a., gallo, p., brittle failure of graphite weakened by v-notches: a review of some recent results under different loading modes, strength mater., 47 (2015) 488–506. [6] he, z., kotousov, a., berto, f., effect of vertex singularities on stress intensities near plate free surfaces, fatigue fract. eng. mater. struct., 38 (2015) 860–869. [7] sih, g.c., redemption of the formalism of segmented linearity: multiscaling of non-equilibrium and nonhomogeneity applied to fatigue crack growth, fatigue fract. eng. mater. struct. 38 (2015) 621–628. [8] ayatollahi, m.r., razavi, s.m.j., rashidi moghadam, m., berto, f., mode i fracture analysis of polymethylmetacrylate using modified energy—based models, phys. mesomech. 18(5) (2015) 53-62. [9] ayatollahi, m.r., rashidi moghaddam, m., razavi, s.m.j., berto, f., geometry effects on fracture trajectory of pmma samples under pure mode-i loading, eng. fract. mech., 163 (2016) 449–461. [10] ayatollahi, m.r., razavi, s.m.j., sommitsch, c., moser, c., fatigue life extension by crack repair using double stophole technique, mater. sci. forum, 879 (2017) 3-8. [11] razavi, s.m.j., ayatollahi, m.r., sommitsch, c., moser, c., retardation of fatigue crack growth in high strength steel s690 using a modified stop-hole technique, eng. fract. mech., 169 (2017) 226–237. t p. gallo et alii, frattura ed integrità strutturale, 41 (2017) 456-463; doi: 10.3221/igf-esis.41.57 462 [12] rashidi moghadam, m., ayatollahi, m.r., razavi, s.m.j., berto, f., mode ii brittle fracture assessment using an energy based criterion, phys. mesomech., (in press). [13] nuñez, j., glinka, g., analysis of non-localized creep induced strains and stresses in notches, eng. fract. mech. 71 (2004) 1791–1803. [14] neuber, h., theory of stress concentration for shear-strained prismatical bodies with arbitrary nonlinear stressstrain law, j. appl. mech., 28 (1961) 544-550. [15] creager, m., paris, p., elastic field equations for blunt cracks with reference to stress corrosion cracking, int. j. fract. mech., 3 (1967) 247–252. [16] lazzarin, p., tovo, r., a unified approach to the evaluation of linear elastic stress fields in the neighborhood of cracks and notches, int. j. fract., 78 (1996) 3–19. [17] moftakhar, a.a., glinka, g., scarth, d., kawa, d., multiaxial stress-strain creep analysis for notches. in: astm special technical publication. astm (1994) 230–243. [18] gallo, p., berto, f., glinka, g., generalized approach to estimation of strains and stresses at blunt v-notches under non-localized creep, fatigue fract. eng. mater. struct. 39 (2016) 292–306. [19] neuber, h., 1958. theory of notch stresses. springer-verlag, berlin. [20] glinka, g., calculation of inelastic notch-tip strain-stress histories under cyclic loading, eng. fract. mech., 22 (1985) 839–854. [21] von mises, r., mechanik der festen körper im plastischdeformablen zustand, j. math. phys., 1 (1913) 582–592. [22] molski, k., glinka, g., a method of elastic-plastic stress and strain calculation at a notch root, mater. sci. eng., 50 (1981) 93–100. [23] berto, f., gallo, p., extension of linear elastic strain energy density approach to high temperature fatigue and a synthesis of cu-be alloy experimental tests, eng. solid mech. 3 (2015) 111–116. [24] gallo, p., berto, f., high temperature fatigue tests and crack growth in 40crmov13.9 notched components, frattura ed integrita strutturale, 9 (2015) 180–189. [25] gallo, p., berto, f., advanced materials for applications at high temperature: fatigue assessment by means of local strain energy density, adv. eng. mater., 18 (2015) 2010-2017. nomenclature a notch depth cp plastic zone correction factor d distance from the coordinate system origin at which the far field contribution is evaluated e young’s modulus kω strain energy concentration factor kt stress concentration factor ki mode i stress intensity factor r radial coordinate r0 distance within notch tip and coordinate system origin rp plastic zone radius t time 2α notch opening angle 22 nc creep strain increment at the notch tip at step n 22 fnc incremental far field creep strain 22 nt increment of total strain δrp plastic zone increment 22 nt stress decrement at the notch tip at step n δtn time increment εp0 plastic strain at time t = 0 22 fc creep strain at the far field 22 nc creep strain at the notch tip 22 t time dependent notch tip strain p. gallo et alii, frattura ed integrità strutturale, 41 (2017) 456-463; doi: 10.3221/igf-esis.41.57 463 0 ij actual elastic-plastic strain e ij hypothetical strain components obtained from linear elastic analysis θ angular coordinate λ1 mode i eigenvalue μ1 mode i second order eigenvalue ρ notch tip radius σmax maximum stress at the notch tip σnom applied nominal stress 22 f far field stress 0 22 f far field stress, t = 0 22 t time dependent notch tip stress 0 ij actual elastic-plastic stress e ij hypothetical stress components obtained from the linear elastic analysis χ1 mode i associated constant << /ascii85encodepages false /allowtransparency false /autopositionepsfiles true /autorotatepages /none /binding /left /calgrayprofile (dot gain 20%) /calrgbprofile (srgb iec61966-2.1) /calcmykprofile (u.s. web coated \050swop\051 v2) /srgbprofile (srgb iec61966-2.1) /cannotembedfontpolicy /error /compatibilitylevel 1.4 /compressobjects /tags /compresspages true /convertimagestoindexed true /passthroughjpegimages 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/hrv (za stvaranje adobe pdf dokumenata najpogodnijih za visokokvalitetni ispis prije tiskanja koristite ove postavke. stvoreni pdf dokumenti mogu se otvoriti acrobat i adobe reader 5.0 i kasnijim verzijama.) /hun 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can be opened with acrobat and adobe reader 5.0 and later.) >> /namespace [ (adobe) (common) (1.0) ] /othernamespaces [ << /asreaderspreads false /cropimagestoframes true /errorcontrol /warnandcontinue /flattenerignorespreadoverrides false /includeguidesgrids false /includenonprinting false /includeslug false /namespace [ (adobe) (indesign) (4.0) ] /omitplacedbitmaps false /omitplacedeps false /omitplacedpdf false /simulateoverprint /legacy >> << /addbleedmarks false /addcolorbars false /addcropmarks false /addpageinfo false /addregmarks false /convertcolors /converttocmyk /destinationprofilename () /destinationprofileselector /documentcmyk /downsample16bitimages true /flattenerpreset << /presetselector /mediumresolution >> /formelements false /generatestructure false /includebookmarks false /includehyperlinks false /includeinteractive false /includelayers false /includeprofiles false /multimediahandling /useobjectsettings /namespace [ (adobe) (creativesuite) (2.0) ] /pdfxoutputintentprofileselector /documentcmyk /preserveediting true /untaggedcmykhandling /leaveuntagged /untaggedrgbhandling /usedocumentprofile /usedocumentbleed false >> ] >> setdistillerparams << /hwresolution [2400 2400] /pagesize [612.000 792.000] >> setpagedevice microsoft word numero_34_art_36 t. makino et alii, frattura ed integrità strutturale, 34 (2015) 334-340; doi: 10.3221/igf-esis.34.36 334 focussed on crack paths effect of defect length on rolling contact fatigue crack propagation in high strength steel t. makino, y. neishi nippon steel & sumitomo metal corporation, japan makino.hb3.taizo@jp.nssmc.com, neishi.58e.yutaka@jp.nssmc.com d. shiozawa, s. kikuchi, s. okada kobe university, japan shiozawa@mech.kobe-u.ac.jp, kikuchi@mech.kobe-u.ac.jp k. kajiwara japan synchrotron radiation research institute, japan kajiwara@spring8.or.jp y. nakai kobe university, japan nakai@mech.kobe-u.ac.jp abstract. the objective of the present paper is to clarify the effect of defect length in depth direction on rolling contact fatigue (rcf) crack propagation in high strength steel. rcf test and synchrotron radiation micro computed tomography (sr micro ct) imaging were conducted. in the case of the defect with the 15 m diameter, flaking life decreased with increasing defect length. in a comparison of the ct image and the sem view, the shapes of defects and the locations of the horizontal cracks were almost the same respectively. the mechanism of rcf crack propagation was discussed by finite element (fe) analysis. defects led to higher tensile residual stress than that without defects in the region where the defect exists. the shear stress range at 0.1 mm in depth on the middle line of the defect and the range of mode ii stress intensity factor at the bottom of a vertical crack increased with increasing defect length. keywords. rolling contact fatigue; artificial defect; crack propagation; high strength steel; synchrotron radiation micro computed tomography imaging; stress intensity factor. introduction olling contact fatigue (rcf) tests for evaluation of bearing steel are commonly conducted under pure rolling contact with oil lubrication. non-metallic inclusions in internal region cause fatigue cracks [1-2]. cracks propagate and eventually form typical rcf damage called flaking. the refinement of sphere-type inclusions like oxides has r t. makino et alii, frattura ed integrità strutturale, 34 (2015) 334-340; doi: 10.3221/igf-esis.34.36 335 been applied to increase flaking life. recently it was indicated that stringer-type inclusions can be the origin of rcf cracks and flaking[3], and the inclusion length influenced the rcf life[4]. in the present paper, to discuss the mechanism of the above phenomena, rcf test was conducted using specimens with artificial defects that simulate stringer-type inclusions. the effect of defect length on flaking life was evaluated using specimens with different-length defects. synchrotron radiation micro computed tomography (sr micro ct) imaging and microscope observation were performed for rcf cracks and their fracture surface. the morphology of rcf cracks before flaking was investigated. the experimental result was discussed in terms of stress states and fracture mechanics based on the analytical result by finite element (fe) analysis. materials, specimens, and test methods materials and specimens all-on-disc type rcf tests were conducted under oil lubrication. disc specimens were made of two steels: high carbon–chromium bearing steel jis suj2 and induction-hardened 0.55% carbon steel jis s55c. both steels were received as rolled bars. suj2 bar was spheroidizing-annealed, and then quenched and tempered. s55c bar was normalized and was then machined to disc shape. the ring-shaped region of the ball rolling track surface was inductionhardened and tempered. the disc specimen was 60 mm in diameter and 5 mm in thickness. the diameter of ball rolling track was 38.5 mm, the region in the vicinity of the track had a vicker’s hardness of 700–750 hv in both specimens of suj2 and s55c. artificial defects of 15 or 50 m diameter and 30–300 m length from surface in depth direction were introduced on the ball rolling track of the disc specimen by electro-discharge machining. the above length of defect is referred to as defect length in this paper. ball specimens are commercial products made of suj2. the ball diameter was 9.525 mm. test methods three balls were rolled on one side of a disc specimen surface under oil lubrication. a vertical contact force was set so that the hertzian stress pmax was 5.22 gpa. the half-width of the contact patch a was then calculated as 0.346 mm. tests were continued until a preset number of cycles or automatically stopped by detecting the vibration due to flaking. rolling contact fatigue test result ig. 1 presents the relationship between defect length and flaking life obtained from rcf test of suj2 disc specimen. in the case of the defect with the 15 m diameter, flaking life decreased with increasing defect length. in the case of the defect with the 50 m diameter, flaking life was almost constant from 50 to 300 m of defect length and shorter than the shortest life in the case of the 15-m-diameter defect. 10 15 20 25 30 35 40 45 50 1.0e+02 1.0e+03 1.0e+04 1.0e+05 1.0e+06 1.0e+07 s ur fa ce c ra ck le ng th 2 c [μ m ] number of cycles n [cycle] jis suj2, 15 m dia. defect l =  200 m l = 50 m l = 100 m figure 1: relationship between defect length and flaking life obtained from rcf test of suj2. figure 2: changes in surface length of vertical crack including defect during rcf test. b f t. makino et alii, frattura ed integrità strutturale, 34 (2015) 334-340; doi: 10.3221/igf-esis.34.36 336 cracks were initiated at the edges of 15-m-diameter defect in radial direction on rolling contact surface. according to the following investigation, they propagated not only in radial direction but also in depth direction along defect. these cracks are referred to as vertical cracks in this paper. the surface length of vertical crack including defect 2c was measured during rcf test. fig. 2 shows changes in 2c during rcf test. vertical cracks initiated at longer defects propagated faster. sr micro ct imaging of crack initiation and propagation behaviour inspection samples n order to discuss the mechanism of the rcf damage described in the previous section, it is of great importance to clear how the cracks observed on surface propagate in internal region and form flaking. in this section, the morphology of internal cracks initiated in disc specimens of s55c inspected by sr micro ct imaging at spring-8 is discussed. artificial defects introduced in disc specimens were 15 m in diameter and 50, 100, and 200 m in defect length. the rcf test stopped at an arbitrary number of cycles. inspection samples having a square cross section of 0.5 mm × 0.5 mm with the defect were taken from the disc specimens. the dimension is regulated by the penetrative thickness for the present x-ray energy for fe material. ct imaging method ct imaging was performed at the bl19b2 beam line of spring-8, the most powerful synchrotron radiation facility in japan. the measurement conditions were as follows: x-ray energy of 37 kev and sample-detector distance of 0.7 m [5]. the effective pixel size of the detector was from 0.74 to 2.8 m depending on the magnification of the beam monitor. for a 3-d reconstruction, a set of 900 radiographs of a sample were recorded at rotations over 180°, where each rotation angle was 0.2°. slice images were reconstructed from the series of the projection images by a filtered-back projection algorithm. 20μｍ (a)l=50 μｍ, n=1×104 20μｍ (b)l=50 μｍ, n=1×106 25μｍ (c)l=100 μｍ, n=1×106 50μｍ 50μｍ (d)l=200 μｍ, n=1×106 y x z defect vertical crack horizontal crack figure 3: ct images and sem view of artificial defect and cracks (defect diameter: 15 μm, left: ct image, and right: sem view). ct imaging result images of the artificial defect and cracks shown in the left-hand side of fig. 3 were obtained by ct scanning. several samples were broken at liquid nitrogen temperature to observe the fracture surface of the vertical crack. sem views of the fracture surfaces are also shown in right-hand side of fig. 3. shapes of rcf cracks identified from fractography were also i t. makino et alii, frattura ed integrità strutturale, 34 (2015) 334-340; doi: 10.3221/igf-esis.34.36 337 indicated by lines on the sem views of fig. 3. cracks parallel to the surface and perpendicular to the defect were observed. the cracks are referred to as horizontal crack in this paper. in a comparison of the ct image and the sem view, the shapes of defects and the locations of the horizontal cracks were almost the same respectively, but the shapes of vertical cracks in ct images (fig. 3 (b), (d)) were smaller in the deeper region than those in sem views. these results provide the validity of ct imaging and future task for optimizing imaging condition. crack shapes and sizes between different number of cycles and defect lengths were compared from sem views. fig. 4 summarizes the comparison result in the same scale. a vertical crack initiated from a defect of 50m length propagated in x and z (depth) direction from n = 1×104 to 1×106. in comparison under the same cycles, horizontal cracks initiated from longer defects propagated longer. 50μｍ 1×106 l=50μｍ n= 1×104 l=100μｍ l=200μｍ yx z :front line of vertical crack :horizontal crack diameter of defect : 15μm rolling contact surface defect figure 4: comparison of crack shape and size between different number of cycles and defect lengths. finite element analysis of stress states under rolling contact e analysis was conducted using models with a circular hole and/or a crack to evaluate the effect of defect length on the stress states around the defect and the stress intensity factors (sifs) of the rcf cracks. abaqus ver. 6.12 was used for the fe analysis. fe modelling and analytical condition a numerical fe model for the rcf test was developed as shown in fig. 5. the fe model comprises a rectangular block for the disc specimen and a hemisphere for the ball specimen taking symmetry into account. a circular hole of the same size as the artificial defect, whose diameter was 15 m, in the experiment was modeled in a small rectangular section. the section was tied at the centre of the disc specimen model. models are classified into three types (i.e., defect without crack, vertical crack without defect, and defect and vertical crack; fig. 5(b–d)). the defect model (fig. 5(b)) comprises a hole with depth l = 0 (plane, no defect), 50, 100, 150, and 200 m. the vertical crack model (fig. 5(c)) comprises a vertical crack with the surface half length c of 15 m and depth of 50 m. the crack size was determined from the ct imaging result. the defect and vertical crack model (fig. 5(d)) comprises a hole with the various depths mentioned above and a vertical crack with the above size. a fine mesh was applied to the region around the crack tip; the minimum length between nodes was 0.0005 mm at crack tip and 0.00125 mm on the internal surface of the hole. the number of elements was 242,093 and 32,914 in the rectangular model and hemisphere model, respectively. friction coefficients between the ball and disc specimen model and between crack faces were zero with the consideration of the oil lubrication. the elastic modulus and poisson’s ratio were 205.8 gpa and 0.3, respectively. in the case of elastic– plastic fe analysis, an experimentally measured stress–strain curve was applied in the disc specimen model. a vertical force was applied to obtain the same hertzian stress pmax (5.22 gpa) as the experiment, then the half-width of the contact f t. makino et alii, frattura ed integrità strutturale, 34 (2015) 334-340; doi: 10.3221/igf-esis.34.36 338 patch a was 0.346 mm. the ball specimen model moved 8 mm across the circular hole and cracks on the disc specimen model along the symmetric surface. in the case of elastic-plastic analysis, stress states after four repeats of above cycle were evaluated. (a) (b) ball disc circular hole defect (ϕ15×l) vertical crack infinite element symmetry surface 50 μm 50 μm l l l=0-200μm (c) (d) y x z figure 5: fe models for the rcf test. (a) entire model. (b) magnification of defect (without crack). (c) vertical crack (l=0 μm). (d) defect & vertical crack. fe analysis result in order to clarify the stress state at the artificial defect with different defect length during the passage of ball before crack initiation, the defect model shown in fig. 5(b) was calculated by elastic–plastic fe analysis. fig. 6 shows the residual stress in y-direction distributions on the middle line of the hole (in z-direction). remarkably high tensile residual stress was generated at the surface edge of the defect. the residual stress distribution exhibited a peak value below the surface and a decrease from the depth of the peak to the bottom of the defect. furthermore, it shifted to the distribution of residual stress, which was in compression side, in the plane model (l = 0 m, without defect). defects led to higher residual stress to tension side than that without defects in the region where the defect exists. fig. 7 presents the variation in shear stress τyz at 0.1 mm in depth on the middle line of the hole during rolling contact obtained from elastic-plastic fe analyses. the shear stress had a peak and a valley before and after rolling contact. the shear stress range, derived from the peak and the valley of the shear stress, was the smallest in the case without defect, larger in the case of l = 100 m (l coincides with the stress evaluation point), and the largest in the cases of l = 150 and 200 m. ‐1500  ‐1000  ‐500  0  500  1000  1500  2000  0.00  0.10  0.20  0.30  0.40  r e si d u a l s tr e ss  in  y  d ir e ct io n          σ y ,r e s [m p a ] location in depth direction z [mm] plane (w/o defect) l=100μm l=150μm l=200μm bottom of defect figure 6: residual stress distributions along defect obtained from elastic–plastic fe analyses. sifs for vertical cracks with and without defects were evaluated from elastic fe analysis. the size of the crack was constant, but the defect length (hole depth in the model) l varied from 0 to 200 m. the mode i sif ki at the surface edge of vertical crack and the mode ii sif kii at the bottom of vertical crack were calculated from the displacement distribution on the crack face near the crack tip. the ranges of sif δki and δkii were derived from the variation in ki and kii respectively during rolling contact. δki (v-s) and δkii (v-b) were compared between different defect lengths in fig. 8. t. makino et alii, frattura ed integrità strutturale, 34 (2015) 334-340; doi: 10.3221/igf-esis.34.36 339 δkii increased with increasing l, but δki slightly decreased simultaneously. a case of l = 50 m implies that the vertical crack tip reaches the bottom of the defect. on the other hand, a case of l > 50 m implies that the vertical crack tip is before reaching the bottom of the defect. δkii at l = 50 m was larger than that at l = 100 m. this result suggests that when the vertical crack tip reaches the bottom of the defect, the increase of δkii due to crack propagation exhibits slowdown or decrease; the propagation of the vertical crack is retarded. -1500 -1000 -500 0 500 1000 1500 -3 -2 -1 0 1 2 3 s h e a r  st re ss  τ ｙ z [m p a] y/a plane (w/o defect) l=100μm l=150μm l=200μm z=0.1mm figure 7: variation in shear stress at 0.1 mm depth during rolling contact obtained from elastic–plastic fe analyses. 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 0 50 100 150 200 250 s if [m p a√ m ] defect length in depth direction l [μm] v-s, ki v-b, kii(plane stress) v-b, kii(plane strain) figure 8: comparison of δki at the surface edge of vertical crack and δkii at the bottom of vertical crack between different defect lengths (v:vertical crack, s:surface, and b:bottom). discussion ynthesizing the above experimental and analytical results, the authors believe that the degradation of flaking life due to the longer length of defect with the diameter of 15 m is caused by the following mechanism. vertical cracks are likely to form at surface edge of defects because a remarkably large tensile residual stress is generated and tension– compression and alternate shear stresses vary widely during rolling contact. vertical cracks propagate in depth direction along defects, later, when the vertical crack tip reaches the bottom of the defect, the propagation of the vertical crack is retarded. therefore, longer defects lead to rapid propagation of vertical crack. the authors’ previous study [6] revealed that the existence of vertical cracks accelerates the propagation of horizontal cracks causing flaking. above process implies that longer defects shorten the flaking life. on the other hand, flaking life in the case including a defect with the diameter of 50 m does not change regardless of the difference of the defect lengths. this is probably because the horizontal cracks form and propagate before vertical cracks grow to the effective size. s t. makino et alii, frattura ed integrità strutturale, 34 (2015) 334-340; doi: 10.3221/igf-esis.34.36 340 conclusion cf test was conducted using specimens with artificial defects which simulate stringer-type inclusions. the effect of defect length on flaking life was evaluated using specimens with different-length defects. the following results were obtained. (1) in the case of the defect with the 15 m diameter, flaking life decreased with increasing defect length. in the case of the defect with the 50 m diameter, flaking life was almost constant from 50 to 300 m of defect length and shorter than the shortest life in the case of the 15-m-diameter defect. (2) in a comparison of the ct image and the sem view, the shapes of defects and the locations of the horizontal cracks were almost the same respectively, but the shapes of vertical cracks in ct images were smaller in the deeper region than those in sem views. (3) stress states around a circular hole during rolling contact were calculated by elastic-plastic fe analysis. remarkably high tensile residual stress was generated at the surface edge of the defect. defects led to higher tensile residual stress than that without defects in the region where the defect exists. the shear stress range at 0.1 mm depth on the middle line of the hole increased with increasing defect length. (4) the sifs of the rcf cracks were calculated by elastic fe analysis. the range of mode ii sif δkii at the bottom of a vertical crack increased with increasing defect length. (5) above analytical results described in (3), (4) provided valuable information for understanding the mechanism of the experimental results described in (1), (2). acknowledgements he synchrotron radiation experiments were performed at bl19b2 in spring-8 with the approval of the japan synchrotron radiation research institute (jasri) under proposal numbers 2011a1787, 2011b1955, 2012a1596, 2012b1306, and 2013a1307. references [1] chen, q., shao, e., zhao, d., guo, j., fan, z., measurement of the critical size of inclusions initiating contact fatigue cracks and its application in bearing steel, wear, 147 (1991) 285–294. [2] lewis, m. w. j., tomkins, b., a fracture mechanics interpretation of rolling bearing fatigue, proceedings of the institution of mechanical engineers, part j. j eng. tribol., 226(5) (2012) 389–405. [3] nagao, m., hiraoka, k., unigame, y., influence of nonmetallic inclusion size on rolling contact fatigue life in bearing steel, sanyo tech report, 12(1) (2005) 38–45 (in japanese). [4] neishi, y., makino, t., matsui, n., matsumoto, h., higashida, m., ambai, h., influence of the inclusion shape on the rolling contact fatigue life of carburized steels, metall. mater. trans. a, 44(5) (2013) 2131–2140. [5] nakai, y., shiozawa, d., fukuda, y., neishi, y., makino, t., observation of cracks in carbon steel under contact rolling fatigue by micro ct imaging using ultrabright synchrotron radiation, 15th international conference on experimental mechanic, paper ref:2635, (2012) [6] makino, t., neishi, y., shiozawa, d., fukuda, y., kajiwara, k., nakai, y., evaluation of rolling contact fatigue crack path in high strength steel with artificial defects, int. j. of fatigue, 68 (2014) 168–177． r t microsoft word numero_34_art_18 f. berto, frattura ed integrità strutturale, 34 (2015) 169-179; doi: 10.3221/igf-esis.34.18 169 focussed on crack paths crack initiation at v-notch tip subjected to in-plane mixed mode loading: an application of the fictitious notch rounding concept f. berto university of padova, italy berto@gest.unipd.it abstract. the fictitious notch rounding concept is applied for the first time to v-notches with root hole subjected to in-plane mixed mode loading. out-of-bisector crack propagation is taken into account. the fictitious notch radius is determined as a function of the real notch radius the microstructural support length and the notch opening angle. due to the complexity of the problem, a method based on the simple normal stress failure criterion has been used. it is combined with the maximum tangential stress criterion to determine the crack propagation angle. an analytical method based on neuber's procedure has been developed. the method provides the values of the microstructural support factor as a function of the mode ratio and the notch opening angle. the support factor is considered to be independent of the microstructural support length. finally, for comparison, the support factor is determined on a purely numerical basis by iterative analysis of fe models. keywords. fictitious notch rounding; mixed mode loading; v-notches with root hole; microstructural support. introduction ll previous publications on the fictitious notch rounding (fnr) concept deal with the pure loading modes 1, 2 and 3. the difficulty of considering mixed mode loading conditions is due to the fact that the most critical direction, in which cracks might provisionally initiate and propagate, varies as a function of the mode ratio. this direction varies from the notch bisector line in the case of pure mode 1 loading, to a direction substantially out of the notch bisector line in the case of pure mode 2 loading. the present work extends the fnr concept to mixed mode 1 and 2 loading conditions for the first time and provides a solution to the problem as a function of the mode ratio. the fnr concept [1-3] refers to the fact that the theoretical maximum notch stress does not characterise the static strength or fatigue strength of pointed or sharply rounded notches. the notch stress averaged over a short radial distance at pointed notches or over a small distance normal to the notch edge at rounded notches (real notch radius ) is the key parameter of the method. the mentioned distance * is usually called ‘microstructural support length’. in the high-cycle fatigue regime, notch stress averaging should take a path which coincides with the point and direction of fatigue crack initiation and propagation. the basic idea of the fnr concept is to determine the fatigue-effective averaged notch stress directly (i.e. without actual notch stress averaging) by performing the notch stress analysis with a fictitiously enlarged notch radius f given by a f. berto, frattura ed integrità strutturale, 34 (2015) 169-179; doi: 10.3221/igf-esis.34.18 170  f = + s * (1) by taking advantage of the analytical frame provided by filippi et al. [4] and neuber [1], the fnr approach has been applied to v-notches under mode 1 and mode 3 loading, respectively [5, 6]. the support factor s was found to be highly dependent on the notch opening angle 2. a satisfactory agreement was found between the theoretical stress concentration factor kt(f) evaluated at the fictitiously rounded notch and the averaging stress concentration factor k t obtained by integrating the relevant stress over the distance * in the bisector line of the pointed v-notch. it is worth mentioning that the notch stress averaging method was originally proposed for brittle fracture problems by wiegardt [7] and later extended by weiss [8]. the fnr concept was mathematically formalised by neuber [1, 3, 9], who provided a general theoretical frame of the method. the application of the concept to strength assessments was demonstrated in ref. [2]. there is also a correspondence of the concept with the ‘critical distance approach’ proposed and successfully applied by peterson [10]. it was also applied many years later to notched thin plates subjected to fatigue loading [11, 12] using the characteristic length a0 derived by el-haddad, topper and smith [13] from the conventional endurance limit and the threshold stress intensity factor range. referring to neuber’s concept, radaj [14-17] proposed to apply the fnr method to assess the high-cycle fatigue strength of welded joints (toe or root failures). a worst case assessment for welded low-strength steels, notch radius  = 0 mm, microstructural support length * = 0.4 mm and support factor s = 2.5, resulted in f = 1.0 mm. this reference radius was found to be generally applicable to fatigue strength assessments of welded joints in structural steels and aluminium alloys and has become a standardised procedure within the design recommendations of the international institute of welding (iiw) [18]. a recent work has been devoted to the application of the fnr approach to notches with root hole subjected to pure mode 1 loading [19, 20]. some analytical expressions have been derived for the fictitious notch radius f and the support factor s taking advantage of some closed form expressions specifically derived for v-notches with root hole [21]. an extension to pure mode 3 loading has been carried out in [22] on the basis of the same set of equations [21]. the case of in-plane shear loading (mode 2) is more complex to analyse than mode 1 and mode 3 loading. the reason for the higher complexity is the fact that out-of-bisector crack propagation is observed, because the maximum notch stress occurs outside the notch bisector line. the mode 2 problem was considered from a theoretical point of view resulting in closed-form solutions for elliptical notches and in numerical solutions for keyhole notches [23]. in a recent paper, pointed v-notches subjected to pure mode 2 loading were investigated [24]. due to the complexity of the analytical developments, the support factor s was determined numerically using the fe method. the key problem was the choice of the crack path direction for stress averaging over the microstructural support length. two criteria available from the literature were used to determine the angle of most probable crack propagation, the maximum tangential stress (mts) criterion according to erdogan-sih [25] and the minimum strain energy density (msed) criterion according to sih [26]. taking advantage of the closed form equations provided in ref. [21] for v-notches with root hole, the fnr concept has been mathematically formalised for this notch shape in the case of in-plane shear loading [27]. two analytical methods and one numerical method have been proposed in the quoted contribution for determining the fictitious notch radius f and therefrom the support factor s dependent on the notch opening angle 2 . in all three methods, the crack propagation angle has been determined based on the mts criterion. a state-of-the art review of the fnr approach comprising also the recent developments just mentioned has been carried out in refs [28, 29]. while the application of the fnr approach to the pure loading modes is well developed, in-plane mixed mode loading remains an open problem which is difficult to solve for various reasons. the main difficulty is that the most probable crack propagation angle depends on the mode ratio ranging from pure mode 1 to pure mode 2 loading. the aim of the present paper is to provide a theoretically founded basis for the application of the fnr approach to inplane mixed mode loading. using the newly developed analytical frame [21], the values of the support factor s as a function of the mode ratio m and the notch opening angle 2 are obtained. as implied by eq. (1), the support factor s is considered to be independent of the microstructural support length *, which is only approximately the case. but all the s values reported in the present contribution are on the safe side when used for strength assessments. the analytical procedure given by neuber [1, 3] for determining the factor s is applied in edge-normal directions outside the bisector line. this is an extension of what has been done by the authors [5, 6] in the cases of pure mode 1, mode 2 and mode 3 loading. by this method, v-notches with root hole, both in the real and in the fictitious configuration, are considered. pointed notches are the limit case obtained when the real notch root radius tends to zero. the proposed method requires a numerical solution of the rather complex governing equation to determine the values of s, but easy-tosurvey tables and diagrams present these values as a function of the mode ratio m for various notch opening angles 2 in f. berto, frattura ed integrità strutturale, 34 (2015) 169-179; doi: 10.3221/igf-esis.34.18 171 order to provide a simple tool for the engineering application of the fnr approach in the case of mixed mode loading. finally, for verification of the method, the factor s is also determined on a purely numerical basis by iteration of fe models. analytical frame for v-notches with root hole subjected to mixed mode loading conditions sing the normal stress criterion in combination with the mts criterion (for the crack propagation angle), an analytical method has been developed for evaluating the fictitious notch radius f and the support factor s therefrom as a function of the mode ratio m defined below. the method refers to fig. 1 where the real root radius  is substituted by the fictitious notch radius f. the v-notch with root hole subjected to mode 1 loading is considered. taking the relevant boundary conditions into account, the stress components for the symmetric mode result from ref. [21]:   1 11 1 1 2 2 11 1 1 1 11 12 11 1 1 2 2( 1) 1 1 1 1 cos(1 ) (1 ) ( ) ( ) ( ) (1 ) ( )2 ( )cos(1 ) 1 (1 ) 2 k r r r r r                                                                                (2.1)   1 11 1 1 2 2 11 1 1 1 11 12 11 1 1 2 2( 1) 1 1 1 1 cos(1 ) (3 ) ( ) ( ) ( ) (1 ) ( )2 ( )cos(1 ) (3 ) 1 2 rr k r r r r r                                                                               (2.2)   1 11 1 1 2 2 11 1 1 1 11 12 12 1 1 2 2( 1) 1 1 1 1 sin(1 ) (1 ) ( ) ( ) ( ) (1 ) ( )2 ( )sin(1 ) (1 ) 1 2 r k r r r r r                                                                                (2.3) figure 1: fictitious notch rounding concept applied to mixed mode loading (mode 1+2): real root hole notch with stress averaged over * in direction of crack propagation (a) and substitute root hole notch with fictitious notch radius f producing max = (b). the parameter 1 is williams’ [30] mode 1 eigenvalue, which is dependent on the notch opening angle 2 the generalised mode 1 notch stress intensity factor k1 can be expressed as follows: u * y a 2 x 2 a  f =s max(f) =  (a)  (b)   *ρρ ρ th d * 1 xσ ρ σ r  f. berto, frattura ed integrità strutturale, 34 (2015) 169-179; doi: 10.3221/igf-esis.34.18 172  1 1 1 1 1 1 1 1 2 2 1 2 2 1 2 3 4 2 ( , 0) (1 ) ( )r r k g g g g r r r                                             (3) when the notch radius  tends to zero, k1 tends to the mode 1 notch stress intensity factor k1 defined according to gross and mendelson [31]: 111 02 lim rk r      (4) considering the v-notch with root hole under mode 2 loading, the stress components for the antisymmetric mode result also from ref. [21]:   2 22 2 2 2 2 11 2 2 2 21 22 22 2 2 2 2( 1) 2 2 2 2 sin(1 ) ( 1) ( ) ( ) ( ) (1 ) ( )2 ( )sin(1 ) 1 (1 ) 2 k r r r r r                                                                                 (5.1)   2 22 2 2 2 2 11 2 2 2 21 22 22 2 2 2 2( 1) 2 2 2 2 sin(1 ) (3 ) ( ) ( ) ( ) (1 ) ( )2 ( )sin(1 ) 1 (3 ) 2 rr k r r r r r                                                                                (5.2)   2 22 2 2 2 2 11 2 2 2 21 22 21 2 2 2 2( 1) 2 2 2 2 cos(1 ) (1 ) ( ) ( ) ( ) (1 ) ( )2 ( )cos(1 ) 1 (1 ) 2 r k r r r r r                                                                                 (5.3) the parameter 2 is williams’ [30] mode 2 eigenvalue, which is dependent on the notch opening angle  the generalised mode 2 notch stress intensity factor k2 can be expressed as follows: 2 2 2 2 1 2 2 2 1 2 2 1 2 3 2 ( , 0) 1 rr rk h h h r r r                                      (6) when the notch root radius tends to zero, k2 tends to the mode 2 notch stress intensity factor k2 defined according to the following expression: 212 02 lim r rk r      (7) it is important to underline that the property of k to converge to the stress intensity factor of the pointed v-notch, k2, when the notch root radius tends to zero, is a characteristic of the set of equations provided in ref. [21] for v-notches with root hole. other sets of equations [32, 33] applicable to rounded v-notches of different shape do not have this property as discussed in ref. [34]. in that paper it was also documented the stable trend of the generalized notch stress f. berto, frattura ed integrità strutturale, 34 (2015) 169-179; doi: 10.3221/igf-esis.34.18 173 intensity factors given in eqs (4) and (8) as a function of the distance r. the problem of the oscillating trend of kand kdescribed in [33] for blunt v-notches with flanks tangent to the notch root radius is overcome by employing the set of equations reported in [21]. fictitious notch rounding is considered for v-notches with root hole subjected to mode 1 and mode 2 loading based on eqs. (2.1) and (5.1). based on the mts criterion, the crack propagation angle 0 is obtained from the following condition d/d = 0 (8) the hoop stress field  depends on the position variables r and  in such a way the condition d/d = 0 does not determine the angle of crack propagation unless a value of r is specified. the angle 0 increases by increasing the distance r due to the higher contribution of mode 2 with respect to mode 1 loading at greater distances from the notch tip. in this paper the values of =0 (worst case configuration) and r=0.005 mm (early crack propagation) have been set to evaluate the crack initiation angle 0. it will be shown in the following that the specific value of r allows us to match the values of s obtained for pure mode 1 [20] and pure mode 2 [27]. the normal stress criterion is now introduced for the averaged stress  and the mts criterion for the crack propagation angle 0. based on eqs. (2.1) and (5.1) the maximum theoretical notch stress th(r, 0) is obtained and the averaged stress in the direction of 0 is determined:   * 0 1 σ σ , dr ρ * th r        (9) the determinate integral in eq. (9) has first been solved in its indeterminate form separated into mode 1 and mode 2 components (termed ii1 and ii2), and only then in its determinate form (termed di1 and di2). �he determinate integrals referring to mode 1 and mode 2, respectively, result in the following form: 0 0 01( , *, ) 1( *, ) 1( , )di ii ii          (10) 0 0 02( , *, ) 2( *, ) 2( , )di ii ii          (11) for the sake of brevity of presentation and due to the length of the final expressions, the explicit forms of di1 and di2 are omitted here. the limit value of the average stress for *0 (and f) is:     1 1 1 1 0 1 1 0 1 12 0 11 0 11 0 * 0 0 1 1 4 cos 1 cos 1 (1 ( ) ( ) ( )) lim 1( , *, ) 2 (1 )f f k di                                              (12)     2 1 2 2 0 2 2 0 2 22 0 22 0 21 0 * 0 0 2 2 4 sin 1 sin 1 (1 ( ) ( ) ( )) lim 2( , *, ) 2 ( 1)f f k di                                               (13) the equation * 0( , *) lim ( )    , according to the procedure given by neuber [1,3], results in the following equation with di10) and di20) according to eqs. (10-11):           1 2 0 0 1 1 1 0 1 1 0 1 12 0 11 0 11 0 1 1 1 2 2 0 2 2 0 2 22 0 22 0 21 0 2 2 1( , *, ) 2( , *, ) 4 cos 1 cos 1 (1 ( ) ( ) ( )) 2 (1 ) 4 sin 1 sin 1 (1 ( ) ( ) ( )) 2 ( 1) f f di di k k                                                                                   (14) f. berto, frattura ed integrità strutturale, 34 (2015) 169-179; doi: 10.3221/igf-esis.34.18 174 solving eq. (14), with k1=k1 and k2=k2, it is possible to determine the fictitious radius f and therefrom the support factor s by using the following expression derived from eq. (1): * fρ s     (15) the factor s under mixed mode loading results as a function of the mode 1 and mode 2 stress intensity factors and of the crack propagation angle 0. eq. (14) can be solved in general terms for any ratio k2/k1 of the notch stress intensity factors, the crack propagation angle 0 being dependent on this ratio. the mode ratio is defined as follows based on the ratio  of the notch stress intensity factors k2 and k1: 2 arctanm    (16) 2 12 1 f k k        (17) pure mode 1 loading results in m = 0 and pure mode 2 loading in m = 1. the dimension of the notch stress intensity factors being dependent on the relevant eigenvalues 2 or 1, which are not identical in general, a length parameter ℓf is introduced in eq. (17) with the condition ℓf=1. in the case of pointed notches,  = 0, eq. (14) can be applied by replacing kby k1 and k by k2 while 0 remains the angle of crack propagation. pointed notches are relevant in worst case considerations of strength assessments. the following expression is valid for , updating eq. (17): 2 12 1 f k k     (18) the simplified hypothesis, k1=k1and k2=k2 which has been inherently assumed for the analytical calculations, avoids an iterative procedure for the determination of s and then of f. this is the hypothesis implicitly used by neuber without the explicit introduction of the stress intensity factors [1], but is approximately true only when the fictitiously enlarged notch root radius is sufficiently small. in the reality, for large f, k1 and k2 do not match k1 and k2 [20,34]. evaluation of the support factor under mixed mode loading conditions y considering eq. (14) and solving it for different values of the mode ratio m, it is possible to obtain the support factor s as a function of the mode ratio m. to evaluate the values of s, the condition ≈ 0 approximating pointed notches has been used. this choice was made for two specific reasons. the first reason is that pointed notches are the most critical ones in strength assessments. in many practical cases, the real notch radius is not equal to zero, but it is very small and it can be approximated in the safe direction by the worst case condition  = 0. the second reason is that by considering pointed notches, it is possible to define the mode ratio m uniquely. the mode ratio m is evaluated here by using k = k1 and k = k2. eq. (8) has been employed here to determine the crack propagation angle 0 by applying the mts criterion to pointed v-notches . due to the fact that eq. (14) has been expressed in terms of the real notch radius this radius has to remain finite. in this contribution, = 0.001 mm has been introduced in order to model quasi-pointed v-notches. the values of s have been evaluated by solving eq. (14) numerically for different values of the mode ratio m and keeping constant *=0.1 mm together with =0.001 mm. the data are plotted in fig. 2. the support factor s rises with the mode ratio m varying from m = 0 (pure mode 1) to m = 1 (pure mode 2). whereas the rise is rather weak for the keyhole (2 = 0), it is rather strong b f. berto, frattura ed integrità strutturale, 34 (2015) 169-179; doi: 10.3221/igf-esis.34.18 175 for larger notch opening angles (2 = 60°). it has to be noted that large values of s mean large fictitious notch radii f, i.e. uncritical strength conditions. 0 5 10 15 20 25 30 35 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 mode ratio, m s u p p o rt f ac to r, s 2α = 60° 2α = 45° 2α = 30° 2α = 0° figure 2: support factor s as a function of the mode ratio m for different values of the notch opening angle 2 validation of the proposed fnr approach for mixed mode loading conditions he fnr approach applied to in-plane mixed mode loading is validated by comparisons based on the fe method considering inclined v-notches with end holes (notch radius f=s*) characterized by different notch opening angles 2. geometry and dimensions of the double-v-notched plate are shown in fig. 3 together with the applied remote boundary conditions. the values of the notch stress intensity factors k1 and k2 found by fe analysis for the corresponding pointed v-notches (=0) are presented in tab. 1 for different notch opening angles 2 and notch inclination angles . tab. 2 also summarises the mode ratio m, the crack propagation angle 0 and the support factor s determined by solving eq. (14) for the specific parameters. the following parameters are considered in the numerical investigation by fe analysis: – the notch opening angle 2= 0, 30, 45 and 60°, – the notch inclination angle = 15, 30, 45 and 60° corresponding to a value of m varying between 0.16 and 0.73, – the microstructural support length * varying between 0.05 and 0.3 mm, – the notch depth 2a = 10 2 mm combined with the plate width w = 100 mm. the averaged stress has been obtained by numerical integration over the length * of the hoop stress component (th=) along the direction 0 evaluated by using eq. (8).   * 0 0 1 σ σ , dr ρ * th r    (19) the stress concentration factor characterising the averaged notch stress over * in pointed v-notches is defined in eq. (20) with reference to the nominal stress n. * 0 1 k σ dr ρ* t th n n       (20) the stress concentration factor kt(f) of the fictitiously rounded notch is defined as follows: t f. berto, frattura ed integrità strutturale, 34 (2015) 169-179; doi: 10.3221/igf-esis.34.18 176   max ( *, )k t f n s     (21) the relative deviation can be defined as follows:     t f t t f δ k k k     (22) figure 3: geometry and dimensions of the double-v-notched quadratic plate specimen considered in the fe analyses; remote loading by prescribed nominal stress n; dimensions w = 100 mm and 2a = 14.14 mm; real pointed versus fictitiously rounded (root hole) vnotch. 2 (°)  (°) k1 (mpa mm1-1) k2 (mpa mm1-2) 1 2 0 (°)  m s 45 15 472 128 0.550 0.660 –13.49 0.272 0.169 2.56 30 376 222 0.550 0.660 –25.73 0.592 0.340 3.16 45 244 257 0.550 0.660 –36.52 1.053 0.516 4.24 60 112 223 0.550 0.660 –46.70 1.993 0.704 6.08 table 1: notch stress intensity factors k1 and k2 and crack propagation angle0 for different mode ratios m resulting in support factors s. comparison with fe results he maximum stress max(*,s) has been determined in this section directly by means of finite element analyses modeling the plate shown in fig. 3 with f=s*, while  values are those evaluated analytically. the finite element analyses (fea) were carried out by using ansys (release 13.0). in total 2000 models have been analysed, each model characterized by the specific values of 2 and f. the results from some models exhibiting relative deviations less than or equal to 10% are listed in tab. 2 as example. the errors are due not only to the adopted simplified hypothesis, k1=k1 and k2=k2, but also to the fact that the maximum stress component max takes place outside the notch bisector, t f 2a w w n  f. berto, frattura ed integrità strutturale, 34 (2015) 169-179; doi: 10.3221/igf-esis.34.18 177 creating an additional stress concentration effect linked to the nominal stress component parallel to the notch inclination angle . finally it is worth mentioning that another consistent approach for mixed-mode loading is based on the strain energy density (sed) averaged on a defined control volume [35]. this approach has been successfully used to assess the static behaviour of notched plates made of brittle material as well as the high-cycle fatigue strength of welded joints. in the presence of pointed notches subjected to mixed mode 1–2 loading conditions, the control volume (a semicircular sector under plane strain or plane stress conditions) is introduced as constant, at first for mode 1 loading conditions. in the case of blunt uor v-notches, the crescent shape control volume is rigidly rotated with respect to the notch bisector line and centred in the point of maximum tangential stress (or maximum strain energy density) on the notch edge resulting in an ‘equivalent’ mode 1 loading condition. one of the main advantages of the average sed approach is that it can be applied using coarse meshes. 2α (°) β (°)  m 0 (°) s ρ* (mm) ρf (mm) tk eq.(28) kt(ρf) fem δ (%) 45 15 0.272 0.169 –13.50 2.56 0.05 0.128 16.90 16.93 0.17 0.1 0.256 12.06 12.57 4.07 0.2 0.511 8.61 9.24 6.86 0.3 0.767 7.07 7.81 9.47 30 0.592 0.340 –25.73 3.16 0.05 0.158 14.62 14.73 0.75 0.1 0.316 10.58 10.92 3.11 0.2 0.631 7.67 8.18 6.28 0.3 0.947 6.36 6.97 8.79 45 1.053 0.516 –36.52 4.24 0.05 0.212 11.08 11.19 0.99 0.1 0.424 8.18 8.56 4.48 0.2 0.848 6.05 6.65 9.03 table 2: fnr results for mixed mode loading conditions; normal stress failure criterion combined with the mts criterion for 0; different values of the microstructural support length * and the mode ratio m. conclusions ased on fnr concept used in combination with the normal stress criterion for the averaged notch stress and the maximum tangential stress criterion for the crack propagation angle, the support factor has been analytically and numerically determined for v-notches with root hole subjected to in-plane mixed mode loading. a suitable definition and quantification of the mode ratio for pointed v-notches has been found. taking advantage of a recently conceived analytical frame for v-notches with root hole, the original neuber procedure for determining the fictitious notch radius and the support factor has been applied to out-of-bisector crack propagation, the propagation direction being determined by the maximum tangential stress criterion as a function of the mode ratio and the notch opening angle. different values of this length, of the notch depth and of the notch opening angle have been considered as well as different mode ratios. the obtained values of the support factor are well suited for engineering usage in structural strength assessments. the relative deviations have been found variable from case to case. a large set of cases have been found to be characterized by relative deviations less than 10%, directly using the original neuber’s procedure. references [1] neuber, h., kerbspannungslehre, 2nd edn, springer-verlag, berlin, (1958). [2] neuber, h., űber die berücksichtigung der spannungskonzentration bei festigkeitsberechnungen. konstruktion, 20 (1968) 245-251. b f. berto, frattura ed integrità strutturale, 34 (2015) 169-179; doi: 10.3221/igf-esis.34.18 178 [3] neuber, h., kerbspannungslehre, 3rd edn, springer-verlag, berlin, (1985). isbn-10: 3540676570. [4] filippi, s., lazzarin, p. tovo, r., developments of some explicit formulas useful to describe elastic stress fields ahead of notches in plates. int. j. solids struct., 39 (2002) 4543-4565. doi: 10.1016/s0020-7683(02)00342-6 [5] berto, f., lazzarin, p., radaj, d., fictitious notch rounding concept applied to sharp v-notches: evaluation of the microstructural support factor for different failure hypotheses. part i: basic stress equations, eng. fract. mech., 75 (2008) 3060-3072. doi: 10.1016/j.engfracmech.2007.12.011 [6] berto, f., lazzarin, p., radaj, r., fictitious notch rounding concept applied to sharp v-notches: evaluation of the microstructural support factor for different failure hypotheses. part ii: microstructural support analysis. eng. fract. mech., 76 (2009) 1151-1175. doi: 10.1016/j.engfracmech.2008.01.015 [7] wieghardt, k., über das spalten und zerreiβen elastischer körper, z. mathematik u. physik, 55 (1907) 60-103. [8] weiss, v., eine bruchmechanik fűr kerben, schweiz arch angew wiss techn, 37 (1971) 1-7. [9] neuber, h., zur theorie der technischen formzahl, forsch. ing. wes., 7 (1936) 271-274. [10] peterson, r.e., relation between stress analysis and fatigue of metals. proc. sesa, 11 (1950) 199-206. [11] atzori, b., lazzarin, p., tovo, r., evaluation of the fatigue strength of a deep drawing steel, österr ing. arch. z., 137 (1992) 556-561. [12] lazzarin, p., tovo, r., meneghetti, g., fatigue crack initiation and propagation phases near notches in metals with low notch sensitivity, int j fatigue, 19 (1997) 647-657. doi:10.1016/s0142-1123(97)00091-1. [13] el haddad, m.h., topper, t.h., smith, k.n., prediction of non-propagating cracks, eng. fract. mech., 11 (1979) 573-584. doi: 10.1016/0013-7944(79)90081-x. [14] radaj, d., näherungsweise berechnung der formzahl von schweiβnähten, schw. schn., 21 (1969) 97-105, and 21 (1969) 151-158. [15] radaj, d., design and analysis of fatigue resistant welded structures. abington publishing, cambridge, (1990). isbn-9781855730045 [16] radaj, d., ermüdungsfestigkeit, 2nd ed., springer verlag, berlin, (2003). isbn 978-3-662-07107-6 [17] radaj d., sonsino c.m., fricke w., fatigue assessment of welded joints by local approaches, 2nd ed. woodhead publishing, boca raton, fl: crc press, cambridge, (2006). isbn:9781855739482. [18] hobbacher, a. (ed.) fatigue design of welded joints and components. abington publishing, cambridge, uk, 1996 (iiw doc. xiii-1539/xv-845-96) and update 2008 (iiw doc. xiii-2151-07/xv-1254-07). weld res coun, new york, bull 520, 2009. [19] berto, f., zappalorto, m., fictitious notch rounding concept applied to v-notches with end holes under mode 1 loading, int. j. fract., 171 (2011) 91–98. doi: 10.1007/s10704-011-9626-6. [20] berto, f., zappalorto, m., the fictitious notch rounding approach applied to v-notches with root holes subjected to mode 1 loading, j. strain anal., 47 (2012) 176–186. doi: 10.1177/0309324712437106. [21] zappalorto, m., lazzarin, p., in-plane and out-of-plane stress field solutions for v-notches with end holes, int. j. fract., 168 (2011)167-180. doi: 10.1007/s10704-010-9567-5. [22] berto, f., fictitious notch rounding concept applied to v-notches with end holes under mode 3 loading, int. j. fatigue, 38 (2012) 188–193. doi: 10.1016/j.ijfatigue.2011.12.008. [23] radaj, d., zhang, s., on the relations between notch stress and crack stress intensity in plane shear and mixed mode loading, eng. fract. mech., 44 (1993) 691-704. doi: 10.1016/0013-7944(93)90198-2. [24] berto, f., lazzarin, p., fictitious notch rounding approach of pointed v-notch under in-plane shear, theor. appl. fract. mech., 53 (2010) 127-135. doi: 10.1016/j.tafmec.2010.03.003. [25] erdogan, f., sih, c.g., on the crack extension in plates under plane loading and transverse shear. j. basic eng. (1963) 519-525. doi: 10.1115/1.3656897 [26] sih, g.c., strain-energy-density factor applied to mixed mode crack problems. int. j. fracture, 10 (1974) 305-321. doi: 10.1007/bf00035493 [27] berto, f., lazzarin, p., radaj, d., fictitious notch rounding concept applied to v-notches with root holes subjected to in-plane shear loading, engng fract. mech., 79 (2012) 281-294. doi: 10.1016/j.engfracmech.2011.11.007. [28] radaj, d., lazzarin, p., berto, f., generalised neuber concept of fictitious notch rounding, int. j. fatigue, 51 (2013) 105-115. doi: 10.1016/j.ijfatigue.2013.01.005. [29] radaj, d., vormwald, m., advanced methods of fatigue assessment, springer-verlag, berlin (2013). doi: 10.1007/978-3-642-30740-9. [30] williams, m.l., stress singularities resulting from various boundary conditions in angular corners on plates in tension, j. appl. mech., 19 (1952), 526-528. f. berto, frattura ed integrità strutturale, 34 (2015) 169-179; doi: 10.3221/igf-esis.34.18 179 [31] gross, r., mendelson, a., plane elastostatic analysis of v-notched plates, int. j. fract. mech., 8 (1972), 267-27. doi 10.1007/bf00186126. [32] lazzarin, p., tovo, r., a unified approach to the evaluation of linear elastic fields in the neighbourhood of cracks and notches, int. j. fract., 78 (1996) 3-19. doi: 10.1007/bf00018497. [33] lazzarin, p., filippi, s., a generalised stress intensity factor to be applied to rounded v-shaped notches, int. j. solids struct., 43 (2006) 2461-2478. doi: 10.1016/j.ijsolstr.2005.03.007. [34] lazzarin, p., zappalorto, m., berto, f., generalised stress intensity factors for rounded notches in plates under inplane shear loading, int. j. fract., 170 (2011)123-144. doi: 10.1007/s10704-011-9613-y. [35] berto, f., lazzarin, p., recent developments in brittle and quasi-brittle failure assessment of engineering materials by means of local approaches, 75 (2014) 1-48. doi: 10.1016/j.mser.2013.11.001. microsoft word numero_33_art_12 r.c.o. góes et alii, frattura ed integrità strutturale, 33 (2015) 89-96; doi: 10.3221/igf-esis.33.12 89 focussed on characterization of crack tip fields 3d thickness effects around notch and crack tip stress/strain fields r.c.o. góes, j.t.p. castro, m.a. meggiolaro pontifical catholic university of rio de janeiro cesarafael@gmail.com, jtcastro@puc-rio.br, meggi@puc-rio.br abstract. notches and cracks are usually approximately modeled as two-dimensional problems using solutions from plane elasticity to quantify localized stress/strain concentration effects around their tips. however, they may be associated with high gradients that can severely restrict local poisson-induced transversal strains and cause important 3d stress fields around those tips. fatigue crack initiation and growth, plastic zone sizes and shapes, and localized constraint effects that affect toughness are typical problems associated with such 3d effects, which may lead to non-conservative damage and life predictions if neglected. to quantify how important they can be, first finite element techniques are used to simulate thickness and notch-tip radius effects in the fields around such tips, and to evaluate their importance from the structural design point of view. then, versatile sub-modeling techniques are used to study similar effects along the fronts of short and long cracks, and a stepwise re-meshing routine is used to show how an initially straight crack must slightly curve its front during its propagation by fatigue, due to the unavoidable 3d effects that always surround real crack tips. keywords. 3d notch and crack tip fields, 3d stress concentration, fatigue crack front curvature, stress gradient effects. introduction or design purposes, the maximum stresses max that act at notch tips are usually calculated using a linear elastic (le) stress concentration factor (scf) kt to multiply the nominal stress n that would act there if the notch had no effect on the stress and strain fields that surround it: max  ktn (1) since kirsch and inglis studied circular and elliptical notches in infinite plates, a few analytical and many numerical and experimental scf have been obtained for many other notch geometries from their 2d approximations, assuming idealized plane stress (pl-σ), plane strain (pl-ε), or axisymmetric conditions [1-2]. creager and paris [3] estimated scf from stress intensity factors (sif) of similar cracks, but most sif assume planar geometries as well [4]. however, 2d models of notched components have limitations, even in simple cases like a notched plate loaded by a uniform nominal stress. indeed, in such cases the material works under pl- far from the notch tips, but the stress/strain fields that surround the tips are in fact 3d, due to the poisson restriction induced by the stress/strain gradients that act there. if  is the poisson ratio, a transversal constraint factor tz can be defined to quantify this transversal restriction at any point by 0, , z z x y pl t pl            (2) since very few analytical solutions are available for 3d fields around notches [5-6], numerical tools are needed to study most 3d scf problems. using finite element (fe) to model many notches, guo et al. [7-10] and yang et al. [11] f http://www.gruppofrattura.it/pdf/rivista/numero33/audioslides/megg2/index.html r.c.o. góes et alii, frattura ed integrità strutturale, 33 (2015) 89-96; doi: 10.3221/igf-esis.33.12 90 investigated 3d le fields on tensioned plates, concluding that scf along 3d notch tips depend on their shape and thickness-to-tip-radius ratio b/. although the stresses along the notch front y0 may vary significantly, the stress ratio distributions ahead of the notch tips at any given z’ plane y(x, z’)/y0(z’) are almost z-independent. particularly, the ymp(x)/y0mp ratio along the notched plate mid-plane z  0 is almost insensitive to the plate thickness b and to the notch shape up to x/  0.75, and can be approximated by its 2d solution. moreover, the 3d affected zone is almost independent of the notch shape for notches with a/ρ ≥ 1, and it is limited to a distance of about 3b/8 from the notch tip. the transversal constraint along the notch tip tz0 is maximal at the notch mid-plane and decreases to zero close to the plate free surface. the through-thickness variation of the transversal constraint along the notch tip tz0(z)/tz0mp is also nearly independent of the notch shape, and the constraint level decays with the distance from the notch tip. unlike cracks, notches have finite tip radii and cannot provide enough constraint to reach limit pl- conditions along the notch tip thickness. so, instead of the single scf value traditionally used in 2d analyses kt  max/n max/n, independent stress and strain concentration factors k  max/n and k max/n must be used to analyze 3d notch problems, even in le cases. the constraint gradient along the x-direction at the mid-plane (z  0) of notched plates tzmp(x)/tz0mp is almost independent of the notch tip radius and depth, and can be well fitted by     0 2 4 ( ) 1 4.35 1 0.686 1 0.686z mp z mpt x t x b x b         (3) 3d crack solutions are scarce as well. bazant and estenssoro [12] related the stress field singularity of ideal crack tips at the free surface with the angle  with which the crack intersects it. for pure mode i cracks they showed that the sif ki must be zero on the free surface for   /2. for the crack to achieve a r1/2 singularity, the   /2 value solely depends on . nakamura and parks [13-14] studied 3d le fields around ideally straight crack fronts in thick plates within the sifdominated zone, modeling that region as a disk of radius r centered at the tip, assuming the crack size a long compared to the cracked plate thickness (a >> b). the disk boundary (r  r) was assumed loaded by the displacement field generated by the 2d sif ki and kii applied on the plate, the so-called boundary layer (bl) model. strong 3d effects were observed within a distance r  b/2 from the crack tip, with a 3d-2d transition occurring within b/2 < r < 3b/2. the sif was shown to significantly vary along the crack front when compared with 2d predictions. however, albeit ingenious, 3d bl models have some limitations. they assume that the cracks are much longer than the thickness, thus they do not model well small cracks, with size a  b or smaller, an important problem for fatigue predictions. in addition, the cracked plate stress field is obtained assuming that the plate is far-field loaded by the 2d stresses induced by the sif applied on it. hence, all k-field assumptions are incorporated by bl models. for instance, kdescription for the (assumed le) stress fields in cracked components is strictly valid only very close to the crack tips, exactly where plasticity-induced perturbations tend to invalidate it. such assumptions also fail to describe the situation where the 3d affected zone surpasses the k-dominated region. moreover, since k-fields do not reproduce the nominal stresses far from the crack tips [15], non-negligible effects induced by high n cannot be accounted for by them. furthermore, ideally straight cracks are just a convenient mathematical hypothesis, as tests show that they propagate with slightly curved fronts, a phenomenon known as crack tunneling. extensive research on this phenomenon shows that the curved front shape in a through-cracked plate can present a tunneling depth (amax  asurf) up to 0.05 b [16]. this slight curvature brings considerable impact on 3d sif calculations along the crack front. this work first revisits the literature on 3d le stress analysis around notch tips and discusses the importance of 3d effects on notch design issues. then it uses powerful sub-modeling techniques, which eliminate the k-field domination and long crack hypothesis limitations, to numerically simulate 3d sif distributions for large single-edge cracked plates with several b/a ratios, and to evaluate their influence on the ki distribution. to illustrate how 3d issues can be important to explain practical problems, the growth of an initially straight-front crack with initial length a0, assuming it can be described by the classical paris rule, is simulated to evaluate how the crack front shape and the local sif distribution along the crack tip front change as the crack grows until achieving a stable slightly curved front. 3d effects on stress fields around notch tips o evaluate typical notch-induced 3d stress concentration effects around notch tips, several elliptical holes (eh) and semi-elliptical (se) notches with semi-axes a and b in large tensioned plates of width w and height h were simulated in abaqus, using finite sizes w/a  h/a  60 to avoid boundary effects within 1% error. to verify similar previously published results, e  200gpa and   0.33 are used, although   0.29 would better match the chosen t r.c.o. góes et alii, frattura ed integrità strutturale, 33 (2015) 89-96; doi: 10.3221/igf-esis.33.12 91 modulus, a typical value for steels. the models were built with symmetry with respect to the xy plane at the plate midthickness and to the xz plane. the eh models received additional symmetry with respect to the yz plane. the uniform load is applied in the model as a uniform tensile stress on the upper plate face y  h. the notch tip region is described by structured meshes with a maximum element size of 0.1 at the notch tip, where   b2/a is the notch tip radius. the dimensions of the analyzed notches are listed in tab. 1. notch b/a /a b/ elliptical 1 1 0.1, 0.2, 0.4, 0.6, 1, 1.5, 2, 3, 4, 6, 8, 10, 20 0.5 0.25 0.4, 0.8, 2, 2.8, 4, 6, 8, 12, 16, 32, 48 0.2 0.04 3, 6, 10, 15, 20, 30, 50, 75, 100 0.1 0.01 0.4, 0.6, 1, 2, 4, 6, 10, 20, 40, 60, 100 semi elliptical 1 1 0.2, 0.3, 0.5, 0.7, 1, 2, 3, 5, 7, 10, 20, 30 0.5 0.25 0.16, 0.24, 0.4, 0.8, 2, 4, 8, 12, 16 0.2 0.04 0.5, 1, 3, 10, 20, 30 0.1 0.01 0.6, 6, 10, 20, 40, 60, 100, 200, 400 table 1: elliptical and semi-elliptical notch parameters analyzed in the present fe models. figure 1: k/kt distribution along the notch tip front, for a large plate with an elliptical hole with b/a = 0.5 and /a = 0.25. figure 2: k/kt distribution along the notch tip front, for a large plate with an elliptical hole with b/a = 0.5 and /a = 0.25. fig. 1-2 shows typical k/kt and k/kt distributions along the notch tips of eh with b/a  0.5 and /a  0.25. note that k  k, and that their maximum values occur close to the surface of thick plates (with b >> ), whereas for thinner plates they occur at the plate center. k/kt ratios depend on b/, see fig. 3. for relatively blunt notches (those with low b/ ratios), the maximum values of the stresses and strains along the notch tip max and εmax occur on the middle plane of the plate, but for sharper notches these values dislocate towards the plate free surfaces (located at z/b  0.5), in a slightly decoupled way. k and k can differ up to 15% in such plates. the maximum scf at the notch tip kmax can be up to about 8% higher than the 2d scf kt, a non-negligible difference. therefore, even experimental kt values, measured as usual at the notched component free surfaces, may underestimate the actual value of max at such notch tips, so 3d effects on stress/strain fields along notch tips may indeed be relevant for some practical applications. r.c.o. góes et alii, frattura ed integrità strutturale, 33 (2015) 89-96; doi: 10.3221/igf-esis.33.12 92 figure 3: variation of kmax/kt, kmp/kt, and ksurf/kt with the thickness to notch tip radius ratio b/ for elliptical holes in large plates. maximum stress and/or strain points indicate preferred locations for crack initiation along the notch front, whereas the stress gradients ahead of such critical points affect how short cracks propagates from them [17-19]. if cracks prefer to start at maxima stress or strain points, as reasonably assumed in most damage models, they should do so at the center of thinner notched plates (z/b  0) and closer to the free surfaces (z/b  0.5) of the thicker ones, but the growth of such initially small surface cracks is strongly dependent on the stress gradient around the notch tip, as discussed elsewhere [14]. since the studied notches have much stronger stress gradients in the x than in the z-direction, the short crack driving force decrease is sharper ahead than along the notch tip direction. therefore, cracks initiated at notch tips should prefer to advance first along them trying to become a passing crack, then along the x-direction, inwards the specimen. however, although reasonable, such speculations certainly need further investigation, see góes et al. for further details [16]. fe models for cracks at the border of large plates he influence of the thickness-to-crack-size b/a ratio on the crack tip fields of large edge-cracked plates under uniaxial loads was investigated through several le fe 3d analyses, using sub-modeling techniques to take advantage that the major part of such plates is expected to work under pl-, with 3d stress effects limited to the proximities of the crack tip. a large global model for the plates was built using plane elements, with overall dimensions wglobal/a  hglobal/a  1000, while several 3d sub-models of the region surrounding their cracks were built with b/a ratios varying from 0.1 to 100. in-plane displacement fields (ux,uy) from the global model solution were applied to every node of the sub-models boundary surfaces, while their out-of-plane displacements uz were left free. to maintain kinematic compatibility between global and local solutions, the sub-model dimensions wsub/a, and hsub/a were chosen so that tz  0 within the sub-model limits. since the size of the 3d affected zone for an arbitrary b/a value was not known beforehand, the sub-models were built with both wsub/a and hsub/a > 5b/a. the results presented following show that such limits were adequately chosen. besides numerically efficient, this procedure has some non-negligible advantages over the bl modeling approach. its crack tip fields are calculated considering all the load characteristics, since they are not restricted by sif-based hypotheses. it recognizes as well nominal stress effects far from the crack tips, which are ignored when k-conditions are assumed valid in the entire plate, even far from the crack tips. so, contrary to the bl models, it allows analyses of relatively shallow cracks with high b/a ratios. the behavior of such cracks is usually much more important for fatigue life estimations than the behavior of long cracks. the sub-models were built assuming symmetry with respect to xy and xz crack planes, using 15 elements along their thickness (the z-direction) with sizes varying in geometric progression from the middle-plane (coarser) to the free surface (finer), with a progression ratio q  1.3. the circumferential direction is divided into 24 elements. in the radial direction, the elements are built with size 0.003b at the very crack tip, coarsening in geometric progression with ratio q  1.15. this refinement is enough to guarantee convergence of the numerical simulations. a 2d solution can properly model such cracked plates’ far-field conditions because it is possible to establish 3 distinct domains for their (le) stress/strain fields: (i) very far from the crack tip the crack is irrelevant, thus if the plate is large enough this domain works under constant nominal plane stress field conditions, which may be used to model it and thus the contour conditions of the sub-models; (ii) in the intermediate domain around the crack tip but not within its t r.c.o. góes et alii, frattura ed integrità strutturale, 33 (2015) 89-96; doi: 10.3221/igf-esis.33.12 93 dominance zone, the crack affects the stress/strain fields but they remain 2d, since there is no restriction to force them to vary along the z direction; (iii) close to the crack tip within its dominance zone such a restriction exists and 3d effects are clearly present, hence the stresses and strains vary along z. the main intent here is to investigate how such restriction affects short cracks. 3d fe are strictly needed only in this third zone, but it is not possible to precisely model its size prior to its simulation. even so, sub-modeling allows the 3d model frontier to be reduced and located somewhere within the 2nd domain without the need to assume a (questionable, to say the least) k-dominance there, recognizing the nominal stress effects that are not accounted for by the sif fields and significantly saving computational effort at the same time. therefore, the simulation results obtained from the sub-models can furnish more information than would be possible to get from assuming a k-field around the crack tip. fig. 4 shows how much normalized sif distributions along idealized straight crack fronts ki/ki,2d deviate from standard 2d solutions, for a wide range of b/a values including short and long cracks. for long cracks with small b/a, the ki distribution along the crack front gets closer to standard sif-dominated far field conditions as expected, but shallow cracks behave differently. their sif distribution tends to the 2d solution along most of the crack front, but it shows a peak close to the plate free surface, which does not appear for the long cracks. this difference may affect how they grow by fatigue, thus should not be neglected. note that “long cracks” mean “cracks large in comparison to the plate thickness b”, not compared to the plate width w. the analysis of very deep cracks, those with large a/w ratios, which must include the influence of the back face plane on the le fields ahead of the crack tip, is considered beyond the scope of this work. figure 4: ki/ki,2d distribution along the front of short and long cracks. figure 5: kimax/ki,2d and kimp/ki,2d variation with the crack size in large plates. fig. 4 also shows that the sif drops near the free surface (z/b  0.5). as the crack front is assumed straight and perpendicular to it in such 3d analyses, ki should be null at that surface, as already mentioned above, but such a limit could not be achieved with any reasonable mesh refinement. anyway, its importance is to force real cracks to slightly curve their fronts during their propagation, as studied next. fig. 5 shows how the ratios kimax/ki,2d and kimp/ki,2d vary with b/a, and compares them with the long crack sif-dominated limit solution from she and guo [20]. the maxima sif tend to the long crack solution for cracks with very low b/a, and the middle plate sif kimp tend to the limit 2d solution ki,2d as b/a becomes large and the cracks get shorter. moreover, the separation of the kimax/ki,2d curve from the kimp/ki,2d curve of the short cracks shows that their kimax value is higher than the reference ki,2d value, about 3% higher for the poisson coefficient   0.3 used in these numerical simulations, see góes et al. [16] for details. growth of edge cracks with initially straight fronts in large plates he specialized franc3d code [21] was used to simulate the growth of large and small edge cracks with an idealized initially straight front in large plates, supposing lefm conditions. since the solution of le problems is unique and proportional to the imposed load p, the calculated sif kcal along the crack front can be interpreted as a shape function, hence kmax  pkcal, kmin  prkcal, r  kmin/kmax, and k  kmax – kmin. without loss of generality, the analyses developed here considered r  0 and p  1, thus in the propagation cases described below k  kmax  kcal. t r.c.o. góes et alii, frattura ed integrità strutturale, 33 (2015) 89-96; doi: 10.3221/igf-esis.33.12 94 moreover, it is assumed that the local crack advance at any specific point of the crack front follows paris’ fatigue crack growth (fcg) rule. since the material is assumed isotropic and homogeneous, its fcg behavior along the crack front is also assumed as so, and to depend only on the local crack driving force k, since kmax, the other fcg driving force, is fixed. from the kcal values at the crack front nodes in any given step, a crack growth vector a  is obtained by a local increment a multiplied by a unitary vector p  in the local crack growth direction, which must be parallel to the crack plane (xz in this work notation) and normal to the crack front at each point, as the model is symmetric with respect to the xz plane. since fcg increments are assumed to follow paris’ rule, they can be described for any given node i at every j-th growth step by  nji jmean ji jmeana a k k     (4) the sif distribution along the crack front k(z) calculated using such (reasonable) hypotheses, and the ratios between the sif increments at each crack front node and the mean sif increment at each load step, δkji/δkjmean, are all a function of ai(z), the crack length at each node in that given step. hence, δajmean is an arbitrary analysis parameter, dissociated from the number of load cycles. the crack length at the plate free surface, asurf, is adopted as a descriptive parameter of its overall length, as it can be measured by optical methods. after solving each particular fcg step, the crack front increment is smoothed and fitted by a 7th degree polynomial to minimize the unavoidable numerical noise associated with the ki(z) solution. such high order polynomial was chosen to capture the odd ki distributions typical of shallow cracks. the simulated edge-cracked plates are built with the same overall dimensions h, b, and w. the initial edge cracks are introduced with idealized straight fronts, but with different depths a0. values of δajmean between 0.002b and 0.05b are used along the fcg simulation, to deal with convergence issues in the calculation of the crack front in step j  1. the plate models assume symmetric boundary condition at the plate mid-plane z  0 and are supposed tensioned by a unitary uniformly distributed load at their upper and lower boundaries. tab. 2 shows the parameters used in the various models. poisson’s ratio ν  0.3 young’s modulus e  200gpa plate thickness b  5 plate width w 4b plate height h 2.5b crack initial length a0 0.02b, 0.2b, and b paris’ rule exponent n  2.0 and 4.0 table 2: parameters used to model the edge-cracked plates. fig. 6 shows how the 3d-to-2d sif ratio ki(z)/ki,2d varies along the crack front with increasing values of asurf for a0/b  0.02 and a paris’ exponent n  2, and the crack front shape evolution along the plate thickness for the same crack growth stages, quantified by the (a(z) – amin)/b ratio. the shapes assumed by the crack front while it grows from the initially straight profile with a0/b  0.02 show first an anti-tunneling and then a tunneling effect, driven by the non-uniform ki(z) distribution along the crack front at each crack increment. this non-intuitive behavior occurs because the crack front naturally curves itself looking for a more uniform sif distribution along it. the non-uniform sif distribution along the initially straight crack front tends to disappear after the crack propagates for a while and gradually assumes its characteristic slight curved front. for other similar results see góes et al. [16]. such results deserve some comments. even though to assume that fcg rates are primarily controlled by sif is an uncontested hypothesis, there is some dispute on which are the actual fcg driving forces. some prefer k for the cyclic and kmax for the static damage mechanisms, while others defend the use of keff  kmax – kop based on elber’s plasticityinduced crack closure arguments [22], but this point is irrelevant for this work. assuming fixed loading conditions, paris’ r.c.o. góes et alii, frattura ed integrità strutturale, 33 (2015) 89-96; doi: 10.3221/igf-esis.33.12 95 rule usually fits well the phase ii of the fcg curves of many structural alloys. it has been successfully used for a long time to model 1d fcg assuming that the crack growth is controlled by k, and that it is uniform along the crack front in that phase, neglecting that the fatigue damage process may (and usually does) locally vary along such fronts due to microscopic non-homogeneities. even when 2d corner and surface cracks are analyzed, they can be modeled in the same way, if it is recognized that their sif values vary along their fronts. such macroscopic procedures are acceptable if the cracks are large enough because the specimens used to measure fcg properties generate da/dn curves that are obtained by fitting the average behavior of their entire crack front. figure 6: evolution of the 3d to 2d sif ratio along the crack front ki/ki2d and of the crack front shape as the crack grows from an initially straight front, for a0/b  0.02 and n  2. the original results presented in this paper show how such classical assumptions can explain as well why fatigue cracks like to propagate with a slightly curved crack front: they do so as a consequence of their attempt to achieve an iso-ki regime along their fronts. in this sense, such results quantitatively explain why real cracks do not grow by fatigue maintaining a straight front. hence, albeit in a microscopic scale it is not possible to simulate what is actually happening at every instant along a real crack front by using the same paris’ constants for every node along the modeled crack front, it certainly can be properly evaluated where this (macroscopically reasonable) assumption leads to. in this way, the results obtained here also demonstrate that deeper tunneling effects along the crack front should be associated with further details not included in this model, like plasticity-induced crack closure, for example. indeed, if as expected closure effects vary significantly along the crack front inducing non-negligible variations on the keff values along it, and if keff is the actual driving force for fcg as assumed by the many supporters of the classical elberian model, then more pronounced tunneling effects could be expected in such cases. however, such a fascinating argument cannot be further pursued here due to space limitations. conclusions e analyses were used to simulate 3d effects on stress/strain fields close to notch and crack tips. it was observed that the stress and strain concentration along the notch tips is variable, but the y gradient ahead of it can be obtained from the planar 2d solution, although it causes an out-of-plane restriction on the material that tends to lead the notch tip to plane-strain conditions as the tip radius grows sharper ( → 0). further on, sub-modeling techniques were used to examine 3d effects present in cracks on the edge of tensioned large plates with different thickness-to-cracklength (b/a) ratios. crack-tip le stress/strain fields were obtained taking into account the full load description, not restricted to k-field limitations and long crack assumptions, intrinsically considering t-stress and nominal stress effects. sif were observed to vary along the crack front, presenting maximum ki values always higher than the 2d solution. the influence of the b/a ratio on the ki,mp was obtained, which describes a smooth transient from the long crack solution presented before in the literature (for b/a  0.1) and the planar 2d solution (for b/a  100). it was observed that ki,max is always higher than the 2d predictions. several fcg calculations were performed, showing that initially straight cracks progressively curved their front during propagation, simultaneously flattening the ki distribution along the front. after some transient propagation, all cracks converged to the crack propagation front with same regime, with tunneling depth close to 2.5% of b. f r.c.o. góes et alii, frattura ed integrità strutturale, 33 (2015) 89-96; doi: 10.3221/igf-esis.33.12 96 references [1] pilkey, w., pilkey, d., peterson, r., peterson’s stress concentration factors, wiley (2008). [2] savin, g.n., stress distribution around holes, nasa technical translation (1968). [3] creager, m., paris, p.c., elastic field equations for blunt cracks with reference to stress corrosion cracking, int j fract, 3 (1967) 247-252. [4] tada, h., paris, p.c., irwin, g.r., the stress analysis of cracks handbook, 3rd ed. asm (2000). [5] sadowsky, m.a., sternberg, e., stress concentration around a triaxial ellipsoidal cavity, j applied mechanics, 16 (1949) 149-157. [6] youngdahl, c.k., sternberg, e., three-dimensional stress concentration around a cylindrical hole in a semi-infinite elastic body, j app mech, 33 (1966) 855-865. [7] li, z., guo, w., kuang, w., three-dimensional elastic stress fields near notches in finite thickness plates, int j solids and structures, 37 (2000) 7617-7631. [8] guo, w., li, z., three-dimensional elastic stress fields ahead of blunt v-notches in finite thickness plates, int j fracture, 107 (2001) 53-71. [9] guo, w., she, c., three-dimensional stress concentrations at elliptic holes in elastic isotropic plates subjected to tensile stressm int j fatigue, 29 (2007) 330-335. [10] yu, p., guo, w., she, c., zhao, j., the influence of poissons ratio on thickness-dependent stress concentration at elliptic holes in elastic plates, int j fatigue, 30 (2008) 165-171. [11] yang, z., kim, c.b., cho, c., beom, h.g., the concentration of stress and strain in finite thickness elastic plate containing a circular hole, int j solids and structures, 45 (2008) 713-731. [12] bazant, z.p., estenssoro, l.f., surface singularity and crack propagation, int j solids struct, 15 (1979) 405-426. [13] nakamura, t., parks, d.m., three-dimensional stress field near the crack front of a thin elastic plate, j app mech, 55 (1988) 805-813. [14] nakamura, t., parks, d.m., three-dimensional crack front fields in thin ductile plate, j mech phys sol, 38 (1990) 787812. [15] souza, r.a., castro, j.t.p., lopes, a.a.o., martha, l.f., on improved crack tip plastic zone estimates based on tstress and on complete stress fields, fatigue fract eng mater struct, 36 (2013) 25-38. [16] góes, r.c.o., castro, j.t.p., martha, l.f., 3d effects around notch and crack tips, int j fatigue, 62 (2014) 159-170. [17] meggiolaro, m.a., miranda, a.c.o., castro, j.t.p., short crack threshold estimates to predict notch sensitivity factors in fatigue, int j fatigue, 29 (2007) 2022–2031. [18] castro, j.t.p., meggiolaro, m.a., miranda, a.c.o., wu, h., imad, a., nouredine, b., prediction of fatigue crack initiation lives at elongated notch roots using short crack concepts, int j fatigue, 42 (2012) 172-182. [19] castro, j.t.p., landim, r.v., leite, j.c.c., meggiolaro, m.a., prediction of notch sensitivity effects in fatigue and eac, fatigue fract eng mater struct, (2014). doi: 10.1111/ ffe.12156. [20] she, c., guo, w., the out-of-plane constraint of mixed-mode cracks in thin elastic plates, int j solid struct, 44 (2007) 3021-3034. [21] carter, b.j., wawrzynek, p.a., ingraffea, a.r., automated 3-d crack growth simulation, int j num methods eng, 47 (2000) 229-253. [22] castro, j.t.p., meggiolaro, m.a., miranda, a.c.o., singular and non-singular approaches for predicting fatigue crack growth behavior, int j fatigue, 27 (2005) 1366-1388. microsoft word numero_57_art_11_3103 j. r. chandrashekar et alii, frattura ed integrità strutturale, 57 (2021) 127-137; doi: 10.3221/igf-esis.57.11 127 microstructure and mechanical properties of aluminum cast alloy a356 reinforced with dual-size b4c particles j. r. chandrashekar department of mechanical engineering, government polytechnic, kgf, kolar, karnataka, india. chandrujramanna@gmail.com m. h. annaiah department of mechanical engineering, sapthagiri college of engineering, bangalore, karnataka, india drannaiahmh@gmail.com r. chandrashekar department of mechanical engineering, sambhram institute of technology, bangalore, karnataka, india rajchandras@gmail.com abstract. the paper details the studies carried out on a dual-size particulate composite prepared by stir casting using a 356 aluminum alloy and b4c powders. three composite compositions, viz., a356 plus 2% b4c (44µm size and 105µm size in 1:1 ratio), 4% b4c (3:1 ratio), and 6% b4c (1:3 ratio) were cast in finger molds, from which test specimens were prepared for hardness and tensile tests as well as for metallography. vickers hardness tests, tensile tests and microstructure analysis using an optical microscope were conducted. the results obtained indicated that the b4c particles were evenly distributed in the alloy matrix. eds also revealed the presence of b4c in all the three composites. in general, the hardness and tensile strengths increased with increase in concentration b4c powders. while the increase in hardness was increases less than 15%, there was significant increase (more than 35 %) in tensile strength. however, the ductility represented by % elongation, which was already very low in a 356 cast alloy (24.2%,), further decreased in composites. tensile fractography results shows inter crystalline fracture where the breakage in the b4c particle instead of deboning were observed. keywords. a356 aluminum alloy; dual-size composites; microstructure; mechanical tests; fractrography analysis. citation: chandrashekar, j. r., annaiah, m. h., chandrashekar, r., microstructure and mechanical properties of aluminum cast alloy a356 reinforced with dual-size b4c particles, frattura ed integrità strutturale, 57 (2021) 127-137. received: 17.05.2021 accepted: 05.06.2021 published: 01.07.2021 copyright: © 2021 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. introduction luminum alloys find application in diverse fields owing to their high strength-to-weight ratio, low cost, and ease of fabrication [1-3]. substituting the base aluminum alloys with particulate composites has the advantage of improving the mechanical strength parameters without seriously disturbing the thermal and electrical conductivities and other properties a https://youtu.be/xzvyg_y6wks j. r. chandrashekar et alii, frattura ed integrità strutturale, 57 (2021) 127-137; doi: 10.3221/igf-esis.57.11 128 [4-7]. the common reinforcement particles used in ammcs are graphite, sio2, sic, al2o3 and b4c used in small percentages of about 2 to 8% [8-12]. some researchers have used hybrid reinforcement, i.e., using two types of particulates [13-14], while some others have employed dual or treble sizes of same particulate [15-16]. the automaker honda uses a hybrid ammc for some of its engine blocks [17]. of the reinforcement particulates available, b4c is perhaps the hardest. hence an ammc with b4c particles may be expected to have higher strengths than other ammcs. the work presented here, which is part of a larger comprehensive study, is based on aluminum alloy particulate composites with b4c particles. in this study, two sizes of b4c particles (44 µm, and 105 µm) in different ratios were employed to obtain three ammcs in the as-cast condition. these were evaluated for their microstructural features and mechanical properties using standard testing procedures. materials and methods he cast aluminum alloys a 356 was selected for the study. the chemical composition of the alloy as tested and as required by standard is given in tab. 1. two sizes of b4c powder, one fine and the other coarse, viz., 44 µm and 105µm were procured from reputed suppliers. the chemical assay of b4c powders is given in tab. 2. the physical properties of aluminum, which is the major component of a 356 alloy, and b4c are compared in tab. 3. elements si mg fe cu mn ni zinc others al weight % 7.18 0.34 0.13 0.05 0.027 0.03 0.01 0.15 balance table 1: chemical composition analysis of a356. element / component weight % fe 0.2 si 0.1 b2o3 0.5 b4c balance b 79 c 20 table 2: chemical composition assay of b4c particles. property a356 b4c melting point, oc 750 2363 boiling point, oc 2425 3500 density, kg/m3 2670 2420 crystal structure fcc rhombohedral hardness, vpn 65.8 94-97 tensile strength, mpa 143 350 table 3: comparison of physical properties of a356 and b4c particles. t j. r. chandrashekar et alii, frattura ed integrità strutturale, 57 (2021) 127-137; doi: 10.3221/igf-esis.57.11 129 preparation of materials the ammcs were prepared by the well-established stir casting method. pieces of a 356 alloy cut from ingots were placed in a graphite crucible and melted in an electric resistance furnace (schematic diagram of stir casting is shown in fig.1). the melt was degassed using hexachloromethane tablet, and held at above 8000c, and stirring started. when a nice vortex was formed, pre-weighed quantities of b4c powders were introduced, and stirring continued. after about three minutes, the melt was skimmed and the liquid metal poured into preheated finger molds. the three compositions of the ammc, viz., 2% b4c (44µ size and 105µ size in 1:1 ratio), 4% b4c (3:1 ratio), and 6% b4c (1:3 ratio), as shown in tab. 4, were prepared as detailed above. from these cast fingers, test specimens for hardness, microstructure and tensile tests were machined as per astm standards figure 1: schematic diagram of stir equipment. sl no a356 wt% b4c wt% ratio of fine and coarse b4c particle 1 100 2 98 2 1fine:1coarse 3 96 4 3fine:1coarse 4 94 6 1fine:3coarse table 4: material composition with different ratios of fine and coarse size b4c particle. microstructural examination the test specimens were polished to 6-0 smoothness and etched with keller’s reagent. an optical microscope (model nikon lv-150, fig.2) was used for the purpose. hardness tests hardness tests were performed on specimens polished to 5-0 smoothness with a vickers micro hardness tester (model vhm-102, fig. 3(a)). the applied load was 100 g for 10 s. fig. 3(b) shows the schematic of hardness specimen. j. r. chandrashekar et alii, frattura ed integrità strutturale, 57 (2021) 127-137; doi: 10.3221/igf-esis.57.11 130 figure 2: optical microscope. figure 3: (a) mitutoyo vickers hardness testing machine (b) schematic of hardness specimen tensile tests the tensile test specimens were of 6.35 mm diameter and gauge length of 26 mm, conforming to astm e8 standard. the tensile tests were accomplished using a hounsfield-type testing machine (model tue-c-400, fig. 4(a)) at a strain rate of 0.2 mm/s, at room temperature. fig 4(b) shows schematic of tensile specimen. figure 4: tensile testing (a) tensile testing machine (b) schematic of tensile specimen. j. r. chandrashekar et alii, frattura ed integrità strutturale, 57 (2021) 127-137; doi: 10.3221/igf-esis.57.11 131 results and discussions microstructure he photomicrographs of the as-cast structures of base a 356 alloy, and ammcs with a 356 and 2% b4c, 4% b4c, and 6% b4c respectively is shown in the fig.5.(a to d), from fig. 5(a), it is seen that the cast structure of the base a 356 alloy is dendritic or semi-dendritic. the al-si eutectic phase forms the dendritic structure with in a matrix of primary α-al phase. figs. 5 (b), (c)and (d), being the microstructures of cast 2%b4c, 4% b4c, and 6% b4c respectively, indicate that the structures of all three cat composites are similar. there is nearly uniform distribution of b4c particles in all three composite castings. this is true for the fine b4c particles, as well as for the coarse b4c particles. the microstructural examination reveals simple primary α-al phase as matrix in which there are dendrites of the intermetallic al-si phase. in the composites, there is distribution of the b4c particles, which are mostly spheroidal in shape. [18]. figure 5: photomicrographs of (a) base a 356 alloy, (b) a356+2%b4c, (c) a356+4%b4c, (d) a356+6%b4c, energy dispersive spectroscopy (eds) spectrum energy dispersive spectroscopy (eds) permits researcher to identify what those particular elements are and also their comparative proportions in the selected area. this technique is one of the influential and convenient type of elemental t (a) (b) (c) (d) j. r. chandrashekar et alii, frattura ed integrità strutturale, 57 (2021) 127-137; doi: 10.3221/igf-esis.57.11 132 investigation. the graphical depiction of eds analysis of a356 aluminum alloy, a356+2% b4c, a356+4% b4c and a356+6% b4c composites is shown in figs. 6(a to d) respectively. from fig. 6 (a) is the eds spectrograph of a356 aluminum alloy. the spectrum confirms the existence of aluminum as the uppermost element followed by silicon and magnesium alloys. from fig. 6(b to d) is the eds spectrograph of a356 and b4c composites spectrum which evidence the existence of boron (b), carbide (c), in the carbon form. figure 6: (a) shows the eds spectrum of a356 alloy figure 6: (b) shows the eds spectrum of a356+2%b4c composite. j. r. chandrashekar et alii, frattura ed integrità strutturale, 57 (2021) 127-137; doi: 10.3221/igf-esis.57.11 133 figure 6: (c) shows the eds spectrum of a356+4%b4c composite. figure 6: (d) shows the eds spectrum of a356+6%b4c composite. hardness fig. 7 is a bar graph of the hardness values of the a 356 alloy and the three composites, hardness being measured in vhn. it is seen from fig.7 that while the composites seem to have higher hardness than the base a 356 alloy, the increase in hardness is being 6%, 3.4% and 14.14% respectively for the composites with 2%, 4% and 6% b4c. among the dual size particle composites, the composite with 6%b4c of the ratio 1fine and 3coarse size particles shows marginally higher hardness. this may be due to the higher ratio of coarse size b4c particle. the higher amount of coarse j. r. chandrashekar et alii, frattura ed integrità strutturale, 57 (2021) 127-137; doi: 10.3221/igf-esis.57.11 134 particle in ammc shields the finer particles, additionally coarse particles helps to carry a extra portion of the applied load in comparison with the finer size particles [19]. the composite with 4% b4c of the ratio 3 fine: 1coarse particle particles shows slightly lower hardness. this may be due to the higher amount of fine size b4c particle. the higher amount of the fine size is more prone to the particle clustering hence the dispersion of fine size particle is very difficult [20-21]. figure 7: hardness values of as-cast a356 alloy and composites. tensile strength fig. 8 plots the uts of the base alloy and three composites in their as-cast condition. while there is no significant increase in uts by adding 2% or 4% b4c (increase in uts by 3.8% and 7.5% respectively), there is a significant increase achieved by adding 6% b4c with the ratio of 1fine and 3coarse size. (an increase of 38.8%). the b4c ceramic particle acts as a barrier against the plastic deformation in the a356 matrix material to counter the tensile load. the composite with 6% b4c of the ratio 1fine:3 coarse size particle exhibits higher uts this may be due to the increase in the wt% of b4c reinforced particle [22-23]. and also a significant increase due to the higher ratio of coarse size b4c particle in the composites. higher ratio of coarse size b4c particle acts as an effective stress carrier between reinforcement and matrix material. [24] figure 8: uts of as-cast a 356 alloy and composites ductility (% of elongation) fig. 9 is a plot showing the ductility (represented by % elongation) of the base a356 alloy and the three composites. it is evident from fig. 7 that there is a significant loss in ductility in composites as compared with the a356 alloy. the loss in ductility, as calculated by the reduction in % elongation is found to be 24.2%, 27.1%, and 28.6% respectively for the 2%, 4%, and 6% b4c composites. it is further evident that the % elongation decreases as the b4c particulate quantity increases [25] irrespective of the sizes of the b4c particle. (though initially there is a drastic drop in % elongation from the base a 356 alloy and 2% b4c.this is due to the presence of needles like of silicon in the α-al matrix (silicon is the second highest constituent of a356 alloy) is responsible for the reduction in ductility [26-27]. j. r. chandrashekar et alii, frattura ed integrità strutturale, 57 (2021) 127-137; doi: 10.3221/igf-esis.57.11 135 figure 9: bar chart of % elongation for as-cast a 356 alloy and composites tensile fracture analysis fig.10 shows the sem images of a356alloy, 2wt%,4 wt% and 6wt% of b4c composites after the tensile test. the a356 alloy shows an inter crystalline fracture, fig 10(a) this is due to the existence of dendritic shrinkage porosity. the reason is that the crack nucleation at the inter-dendritic region and propagation along these dendrites is the primary mechanism for failure of a356 alloys. all the a356 composites exhibited brittle failure along with quasi-cleavage feature, as shown in fig. 10 (b to d). the micro cracks and quasi-cleavage feature is common feature of materials with lower elongation. this may be due to the detachment of coarse size b4c particle. a small dimple was also absorbed on fracture area of the composite, fracture of coarse size b4c causes pullout due to the decrease in ductility as compared to the a356 alloy. from all this observation it is considered that as the load increase b4c particle of both size, breaks instead of debonding hence the nature of fracture in the composites is brittle & quasi cleavage type. [28-29]. figure 10: fractographs of (a) base a 356 alloy, (b) a356+2%b4c, (c) a356+4%b4c, (d) a356+6%b4c, in the figure, 1 represents -al grains, 2 represents micro cracks and voids 3 represents small dimples 4 represents shrinkage porosity. j. r. chandrashekar et alii, frattura ed integrità strutturale, 57 (2021) 127-137; doi: 10.3221/igf-esis.57.11 136 conclusions he following conclusions / inferences could be drawn from the present study on as-cast a 356 alloy and its composites with 2%, 4% and 6% b4c particulates with dual size. 1. stir casting can be used to successfully prepare a 356 – b4c composites up to 6% b4c particulates without any problem. uniform distribution of b4c particles, fine or coarse, can be achieved. 2. the microstructural examination reveals simple primary α-al phase as matrix in which there are dendrites of the intermetallic al-si phase. in the composites material, there is distribution of the b4c particles, which are mostly spheroidal in shape. 3. eds spectrograph of a356 and b4c composites spectrum which evidence the presence of boron (b), carbide (c), in the carbon form. 4. while there is an increase in hardness values by addition of 6wt% of b4c at the ratio of 1 fine and 3 coarse size, (increased by 14.14%) this is due to the higher ratio of coarse particle in composites shields the finer sized particles, but there is a decrease in hardness values by addition of 4wt% of at the ratio of 3 fine and 1 coarse size b4c particle, (decreased by 3.4%) this is due to clustering of higher amount of fine size particle. 5. there is significant increase in uts (nearly an increase of 40%). in the composite of 6wt% of b4c with a ratio of 1 fine and 3 coarse size b4c particle when compared to the other two composites, this is due to the higher ratio of coarse size b4c particle acts as an effective stress carrier between reinforcement and matrix material. 6. there is a decrease in ductility in composites, which may be expected. however, with increased amount of b4c particulates (2wt%,4wt% & 6wt%), ductility loss is minimal. it is evidence that the % of elongation decreases with the increase in wt% of b4c particle in the composites irrespective of the sizes of the b4c particle. 7. the fractographic studies reveals that as the load increase b4c particle of both size, breaks instead of debonding hence the nature of fracture in the composites is brittle & quasi cleavage type. references [1] rama koteswara rao, v., rangaraya chowdary, j. and balaji, a. (2016). a review on properties of aluminium based metal matrix composites via stir casting, international journal of scientific & engineering research, 7(2), pp. 742-749. issn 2229-5518, [2] dwivedi, s. p., sharma, s., raghavendra kumara mishra (2014). a356 aluminium alloy and applications a review advanced materials manufacturing & characterization, advanced materials manufacturing & characterization, 4(2), pp. 81-86. doi:10.11127/ijammc.2014.08.01. [3] singh, r. and rai, r. n. (2018). characterization of b4c-composite reinforced minimum alloy composites, aip conference proceedings, pp. 020073-11. doi:10.1063/1.5029649. [4] frank czerwinski. (2020). review thermal stability of aluminum alloys, canmet materials, natural resources canada materials, 13(15), pp. 1-49. doi:10.3390/ma13153441. [5] summers, p.t. chen, y. rippe, c.m and ben allen. (2015). overview of aluminum alloy mechanical properties during and after fires, fire science reviews, doi 10.1186/s40038-015-0007-5. [6] omotoyinbo, j.a. oladele, i.o. and shokoya, w. (2014). effect of the degree of plastic deformation on the electrical resistance and thermal conductivity of al-mg-si alloy leonardo electronic, journal of practices and technologies, 13(24), pp. 37-50. [7] mamala, a. and sciezor, w. (2014). evaluation of the effect of selected alloying elements on the mechanical and electrical aluminium properties, archives of metallurgy and material, 59(1), pp. 413-417. doi: 10.2478/amm-2014-0069. [8] sridhar raja, k. and bupesh raja, s. (2013). production and characteristic of boron carbide reinforced aluminum a356 composites, international journal on design and manufacturing technology, 7(2), pp. 29-32. doi: /10.18000/ijodam.70131. [9] vencl, a., bobic, i. and arostegui, s. (2010). structural mechanical and tribological properties of a356 aluminium alloy reinforced with sic, al2o3 particles, journal of alloys and compounds, 506(2), pp. 631-639. doi: 10.1016/j.jallcom.2010.07.028. [10] vanarotti, m., shrishail, p., sridhar, b.r., venkateswarlu, k. and kori, s.a., (2014). surface modification of sic reinforcements & reinforcements & its effects on mechanical properties of aluminum based mmc, applied mechanics and materials, 446(447), pp. 93-97. doi: 10.4028/www.scientific.net/amm.446-447.93. t j. r. chandrashekar et alii, frattura ed integrità strutturale, 57 (2021) 127-137; doi: 10.3221/igf-esis.57.11 137 [11] hu, q., zhao, h. and li, f. (2016). effects of manufacturing processes on microstructure and properties of al/a356– b4c composites, materials and manufacturing processes, 31(10), pp. 1292-1300. doi: 10.1080/10426914.2016.1151049. [12] nirala. a., soren, s., kumar, n.and kaushal, d.r. (2019). a comprehensive review on mechanical properties of alb4c stir casting fabricated, composite materials today proceedings, 21(3), pp. 1432-1435. doi: 10.1016/j.matpr.2019.09.172. [13] sukesha, v., ranjan, r., nagesh, g. and sekar, k. (2014). fabrication and study on mechanical and tribological properties of nanoal2o3 and micro b4c particles reinforced a356 hybrid composites, (aimtdr). [14] rajmohan, t., palanikumar, k. and ranganathan, s. (2013). evaluation of mechanical and wear properties of hybrid aluminum matrix composites, transactions of nonferrous metals society of china, 23(9), pp. 2509-2517. doi: 10.1016/s1003-6326(13)62762-4. [15] nanda kumar, n. and muthukumaran, n. (2019). experimental investigation on microstructural and wear behaviour of dual reinforced particles (drp) aluminium alloy composites, advanced materials research, 1159(1), pp. 42-53. doi: 10.4028/www.scientific.net/amr.1159.42. [16] bindumadhavan, p.n., keng wah, h. and prabhakar, o. (2001). dual particle size (dps) composites: effect on wear and mechanical properties of particulate metal matrix composites, wear, 248(1), pp.112-120. doi: 10.1016/s0043-1648(00)00546-9. [17] stojanovic, b. and ivanovic, l. (2015). application of aluminium hybrid composites in automotive industry, research gate, article in tehnicki vjesnik, 22(1), pp. 247-251. doi: 10.17559/tv-20130905094303. [18] islam, s. k., das, t.,das. p. (2015). deformation behaviour of rheocast a356 al alloy at microlevel considering approximated rves, metals and materials international, 21(2), pp.311-323. doi: 10.1007/s12540-015-4234 [19] kumar, s., sharma, v., panwar, r.s. (2012). wear behavior of dual particle size (dps) zircon sand reinforced aluminum alloy. tribol lett, 47(3), pp.231–251. doi: 10.1007/s11249-012-9983. [20] montoya-davilaa, m., pech-canul, m.a, pech-canul, m.i. (2007). effect of bimodal and tri-size distribution on thesuperficial hardness of al/sicp composites prepared by pressure less infiltration. powder technology, 176(2), pp. 66-71. doi: 10.1016/j.powtec.2007.02.008. [21] lakshmikanthan, a., bontha, s., krishna, m., praveennath, g. and koppad ramprabhu., t. (2019). microstructure, mechanical and wear properties of the a357 composites reinforced with dual sized sic particles, journal of alloys and compounds, 786(8), pp. 570-580. doi: 10.1016/j.jallcom.2019.01.382. [22] beigi khosroshahi, n., taherzadeh mousavian, r., azari khorsoshahi, r. and brabazon, d. (2015). mechanical properties of rolled a356 based composites reinforced by cu coated bimodal ceramic particles, material &design, 83(5), pp.678-688. doi: 10.1016/j.matdes.2015.06.027. [23] venkat kishore, n. and venkata rao, k. (2016). mechanical properties in mmc of aluminum alloy (a356/lm25) matrix and boron carbide (b4c) reinforcement, international journal of engineering research & technology (ijert), 5(2), pp.683-689. [24] fu, s.-y., feng, x.-q., lauke, b. and mai, y. w. (2008). effects of particle size, particle/matrix interface adhesion and particle loading on mechanical properties of particulate, polymer composites composites part b, 39(6), pp.933–961. doi: 10.1016/j. compositesb.2008.01.002. [25] kanta das, d., chandra mishra, p., singh, s. and kumar thakur, r. (2014). properties of ceramic-reinforced aluminium matrix composites a review, international journal of mechanical and materials engineering, 9(12), pp.116. doi:10.1186/s40712-014-0012-9. [26] kori, s.a. and chandrashekharaiah, t.m. (2007). studies on the dry sliding wear behavior of hypoeutectic and eutectic al-sic alloys, wear, 263(1), pp. 745-755. doi: 10.1016/j.wear.2006,11,026. [27] karabulut, s., karakoc, h. and cıtak, r. (2016). influence of b4c particle reinforcement on mechanical and machining properties of al6061/b4c composites, composites part b, 101(15), pp. 87-98. doi: 10.1016/j.compositesb.2016.07.006. [28] chen, z., hao, x., wang, y.and zhao, k. (2014). in-situ observation of tensile fracture in a357 casting alloys, j. mater. sci.technol, 30(6), pp. 139-145. doi: 10.1016/j.jmst.2013.04.014. [29] jiang, w., fan, z., dai, y. and li, c. (2014). effects of rare earth elements addition on microstructures, tensile properties and fractography of a357 alloy, mater. sci.eng, a 597(12), pp.237-244. doi: 10.1016/j.msea.2014.01.009. microsoft word numero_33_art_21 g. laboviciute et alii, frattura ed integrità strutturale, 33 (2015) 167-173; doi: 10.3221/igf-esis.33.21 167 focussed on characterization of crack tip fields growth of inclined fatigue cracks using the biaxial cjp model g. laboviciute, c. j. christopher, m. n. james university of plymouth mjames@plymouth.ac.uk e. a. patterson university of liverpool e.a.patterson@liverpool.ac.uk abstract. the cjp model of crack tip stresses is a modified version of the williams crack tip stress field which takes account of simplified stress distributions that arise from the presence of a zone of plastic deformation associated with the crack flanks and crack tip, and that act on the elastic field responsible for driving crack growth. the elastic stress field responsible for crack growth is therefore controlled by the applied loading and by the induced boundary stresses at the interface with the plastic zone. this meso-scale model of crack tip stresses leads to a modified set of crack tip stress intensity factors that include the resultant influence of plastic wake-induced crack tip shielding, and which therefore have the potential to help resolve some longstanding controversies associated with plasticity-induced closure. a full-field approach has now been developed for stress using photoelasticity and also for displacement using digital image correlation. this paper considers the characterisation of crack growth rate data with the biaxial cjp model, using compact tension specimens that contain inclined cracks at the notch tip with initial angles of 30°, 45° and 60° to the horizontal axis. significant experimental difficulties are experienced in growing cracks in a biaxial field under uniaxial tensile loading, as the natural tendency of the crack is to turn so that it becomes perpendicular to the maximum principal stress direction. however, crack angle is not an issue in the cjp model which calculates the stress field parallel with, and perpendicular to, the crack plane. these stress components can be rotated into directions comparable with the usual ki and kii directions and used to calculate stress intensity parameters that should be directly comparable with the standard stress intensity formulations. another difficulty arises, however, in finding published expressions for ki and kii for ct specimens with curved or kinked cracks. the cjp model has been successful in achieving a sensible rationalisation of crack growth rate data for the specimens considered in this work, although some observations are not easily explained. nonetheless, considering the complexity of characterising crack growth rates for cracks with an initial orientation of 30°, 45° or 60° to the horizontal and which subsequently change angle during growth, the results found so far indicate that there is value in further pursuing the cjp approach. the paper introduces future research directions for the cjp model. keywords. biaxial crack tip displacement field; cjp model; william’s model; compact tension specimen; digital image correlation; fatigue crack growth rate. g. laboviciute et alii, frattura ed integrità strutturale, 33 (2015) 167-173; doi: 10.3221/igf-esis.33.21 168 introduction he cjp model of crack tip stresses is a modified version of the williams crack tip stress field which takes account of simplified stress distributions that arise from the presence of a zone of plastic deformation associated with the crack flanks and crack tip, and that act on the elastic field that drives crack growth [1]. the elastic stress field responsible for crack growth is therefore controlled by the applied loading and by the induced boundary stresses at the interface with the plastic zone. the cjp model is essentially an extension of the crack tip stress model which underpins the use of the classic stress intensity factor k and that uses a ‘plastic inclusion’ approach for dealing with the stresses induced by local plasticity which is concomitant with a growing fatigue crack [1]. a localised zone of plasticity arises from crack growth mechanisms and essentially blunts the crack and creates a reversed cyclic plastic zone. in addition the compatibility requirement for displacements at the elastic-plastic boundary induces interfacial shear stresses along the crack flanks, along with the possible generation of wake contact stresses. these induced stresses act on the applied elastic stress field at the boundary of the elastic-plastic enclave surrounding the crack. this meso-scale model of crack tip stresses leads to a modified set of crack tip stress intensity factors that include the resultant influence of plastic wakeinduced crack tip shielding, and which therefore have the potential to help resolve some long-standing controversies associated with plasticity-induced closure. this full-field approach has been developed for stress using photoelasticity [1] and also for displacement using digital image correlation [2]. the cjp model was initially derived for a uniaxial stress field and was then extended to deal with biaxial loading; the appropriate equations being presented at the malaga crack tip fields conference in 2013 [2]. it is worth noting that tada and paris [3] used a similar approach in considering the influence that additional terms in the westergaard stress function might have on fatigue crack growth when the crack surfaces are not stress-free. their examples were focussed on specific cases of applied forces, e.g. an internal crack subject to concentrated mode 1 splitting forces. they did not consider plastic constraint effects and were not focussing on crack tip shielding, but did give some attention to the possible presence of terms which cannot be included in the series expansion of the form given below:   2 0 1 2     2 n nk k z k z k zz z z      (1) in the period between the malaga and urbino crack tip fields conferences, an internet-mediated research group has been established between research groups at plymouth (james, christopher) and liverpool (patterson) in the uk and jaen (díaz garrido) in spain. the intention has been to characterise the plastic zone size and shape using sophisticated experimental techniques (e.g. thermoelastic stress analysis, electronic speckle pattern interferometry, and digital image correlation) and materials with several strain hardening exponents, and to compare this data with the predictions of the williams crack tip stress model and the cjp model. as the cjp model contains five terms, the williams crack tip stress expansion is considered with two terms and with five terms. preliminary results from this work have indicated that the cjp model gives a closer correlation to the size and shape of the experimentally obtained plastic zones than the williams model. the part of the work that will be presented in this paper has been aimed at exploring the characterisation of crack growth rate data with the biaxial cjp model. crack growth rates have been measured with compact tension specimens that contain inclined cracks at the notch tip with initial angles of 30°, 45° and 60° to the horizontal axis. significant experimental difficulties are experienced in growing cracks in a biaxial field under uniaxial tensile loading, as the natural tendency of the crack is to turn so that it becomes perpendicular to the maximum principal stress direction. coupled with this tendency, the tension, bending and buckling stress field in thin compact tension (ct) specimens also lead to changes in crack direction as the crack extends. the cjp model resolves the displacement field around the crack tip to obtain stresses and hence stress intensity factors (kf, kr and ks) parallel with, and perpendicular to, the crack plane. kf represents the total driving force on the crack, kr the retarding influences arising from the plastic enclave and ks reflects the compatibility-induced shear stresses at the elastic-plastic interface along the complete plastic boundary. in the cjp model crack angle is not an issue, and the stress components can be rotated into directions comparable with the usual ki and kii directions and used to calculate stress intensity parameters that should be directly comparable with the standard stress intensity formulations. another difficulty arises, however, in finding published expressions for ki and kii for ct specimens with curved or kinked cracks. this paper will present experimental crack growth rate data obtained from testing inclined notch specimens at r=0.1 and characterised using the three stress intensity factors derived from the biaxial cjp model, which is given in eq. (2) [2]: t g. laboviciute et alii, frattura ed integrità strutturale, 33 (2015) 167-173; doi: 10.3221/igf-esis.33.21 169 1 3 1 3 02 2 2 22 ( 3 ) )( ln( l) n( )y x xy r i r ii a i b z ib z z cz dzb z z ze z              (2) this five parameter model, where the coefficients a and b are complex and the following assumptions are made 3biara i , b bbr i i  , 0d e  can be solved in terms of stresses or displacements [2]. the work reported in this paper was obtained using digital image correlation (dic) and the displacement solution is more useful: 1 1 2 2 1 1 2 2 1 1 1 2 2 2 2 2 ln(( ) 2( ) 4 ( 2 ) ln( ) 4 ( 3 ) ln( ) 2 2 )x y r i r i r i c u iu b ib z z c z b ib e z z z c a i b z z z ez dz z e d z                                     (3) where xu and yu are the horizontal and vertical displacements respectively, 2(1 ) e     ; 3 4   (plane strain) or 3 1       (plane stress). xu and yu are shown explicitly below with the assumption 0d e  . 1 1 1 2 2 2 1 1 2 2 2 ( ( 2 ( 2 )cos sin ln 3 2 2 )cos 3 )sin 2 2 2 3 3 3 (1 2 )cos sin (1 2 )sin 2 2 ( ) cos 2 2 2 (1 )cos 4 x r r i i r i u r b e r b r r r c r a b b e b e r                                             (4) 1 1 1 2 2 2 1 1 2 2 2 ( 2 ( ( 2 )sin cos ln 3 3 )cos 2 2 )sin 2 2 2 3 3 3 sin (1 2 )sin (1 2 )cos 2 2 2 2 2 ( ) co n s (3 )si 4 i i y i r r ru r b r b e r r r b a b e b r e r c                                              (5) crack growth rate testing ompact tension (ct) specimens were machined from 2mm thick 2024-t6 aluminium ct specimen with nonstandard dimensions [2]. a jeweller’s saw with blade thickness of 0.15 mm was used to extend the notch tip into slits some 5 mm long at angles of 30°, 45° or 60° to the original horizontal notch plane; fig. 1 shows typical ct specimens used in this work. a fatigue crack some 2 mm long was then grown in mode i collinear with this slit. this was achieved by starting with a larger dimension ct specimen with additional loading holes in a similar fashion to the diskshaped compact specimen described by ding et al [4]. the specimen was then machined to final dimensions and the inclined fatigue crack extended under vertical uniaxial loading, giving a combination of mixed mode i and mode ii crack tip stresses. the applied load ratio was r = 0.1 and the peak load was 1.2 kn. a dantec digital image correlation (dic) system operating in 2d mode was used to measure the crack tip displacement field and to compare the predictions of the cjp model with the measured displacement field data. a facet size of 17 pixels with a centre-line pitch of 17 pixels was used with a magnification of 107 pixels per millimetre. digital image correlation requires a fine speckle pattern to be sprayed onto the side of the specimen on which displacement is being measured. increments in crack length during a period of fatigue cycling were monitored using acetate surface replicas taken on the opposite side of the specimen, which was polished to improve the visibility of the crack. the acetate replicas could then be inspected at magnifications up to 1,000x using an optical microscope and the c g. laboviciute et alii, frattura ed integrità strutturale, 33 (2015) 167-173; doi: 10.3221/igf-esis.33.21 170 crack increments accurately measured. in calculating da/dn, the total increment in crack length was used, taken account of any local deviations in path during the incremental growth. figure 1: typical aluminium ct specimens used in this work. in these specimens the initial inclined slit has been extended by fatigue crack growth. once a crack of sufficient size had been grown under biaxial stress conditions, sequential series of images were acquired from which the kmin and kmax values could be obtained after incremental amounts of crack growth. the experimental procedure followed in acquiring these images for analysis was the same for every specimen and is outlined in fig. 2. figure 2: illustration of the test procedure followed during the digital image correlation procedure. step 1 the pmin load of 150 n load is applied; step 2 load cycling of the specimen between pmax = 1,500 n and pmin = 150 n; step 3 the specimen is ramped up to the maximum load of 1,500 n; step 4 maximum load was held for a period of time (30s in this instance) whilst step 5 a signal is sent to the dantec system to take an image; step 6 the load was decreased to the pmin value of 150 n; step 7 the minimum load was held for a period of time (30s in this instance) whilst step 8 a signal is sent to the dantec system to take an image; finally, a surface replica was taken to measure the crack length increment during the applied number of cycles. the complexities in this process due to the change in crack angle with growth can be illustrated through the crack path shown in fig. 3 for the sp5a specimen that contained an initial 45° slit. in each case the angle is measured from the load line and the angle was then used to rotate the data for input into the cjp model. figure 3: illustration of the varying crack path angle on an acetate surface replica for specimen sp5a with an initial 45° slit. the arrow indicates the direction of the applied load during the crack growth under biaxial stresses. 30° 45° 60° g. laboviciute et alii, frattura ed integrità strutturale, 33 (2015) 167-173; doi: 10.3221/igf-esis.33.21 171 results he biaxial cjp model provides values for kf, kr, ks, kii and the t-stress. the values determined for kf and kr are shown in fig. 4 and 5. several points can be observed from this data; firstly, in the cjp model negative stress intensity values of kr and ks can occur and this is reasonable and sensible for stress intensity factors that may act to either retard or accelerate crack advance. secondly, there is considerable scatter between stress intensity factors obtained with nominally similar initial slit angles; part of this is likely to arise from the rather large variations in actual crack angle that occur during fatigue crack growth under mixed mode loading conditions, while another influence may be that fact that crack length is being measured on only a single surface. this later problem is not easy to resolve as potential drop techniques will also be subject to influence by crack angle variation. it was also the case that the crack growth data was subject to considerable point-to-point scatter and in further analysis of the results a 3-point sliding average technique was used to smooth the growth rate data. this approach is believed to be justified as many of the lower growth rate data points are bounded by much higher growth rates immediately before and after the lower value, but it does lead to a lower overall range of crack growth rate. figure 4: fatigue crack growth rate data for all inclined crack specimens plotted against kf. figure 5: fatigue crack growth rate data for all inclined crack specimens plotted against kr. a significant reduction in scatter can be achieved by considering the vector sum of the two stress intensity factors that the cjp model assumes are driving crack growth, kf and kii and the vector sum of the two retarding stress intensity factors kr and ks, and then finding the vector sum of the net driving force as shown in eq. (6):     2 2 2 2 2 2 f ii r snet driving force   k k k k    (6) the data obtained by using this equation is shown in fig. 6 and is difficult to interpret in classical da/dn versus stress intensity factor terms, as while the resulting curve is reasonably bilinear for the data obtained thus far in the work, it appears to indicate an almost constant growth rate for specimens with slits at initial angles of 30° and 60° over the complete range of net stress intensity factor considered in this work. only the data for the two specimens with initial 45° t g. laboviciute et alii, frattura ed integrità strutturale, 33 (2015) 167-173; doi: 10.3221/igf-esis.33.21 172 slits show a trend of increasing growth rate with increasing net driving force. the correlation between the 30° and 60° crack growth rate data is reassuring in the sense that, for a crack growing with a biaxial crack tip stress state under uniaxial loading, one would expect that the vector sum driving force in the two cases would be the same and hence deliver the same growth rate at equivalent values. however, this does not explain the reason underlying the approximately constant growth rate observed. figure 6: reduction in scatter obtained by using the net vector sum driving force, expressed as a stress intensity factor. conclusions he work completed since the malaga crack tip fields conference in 2013 has demonstrated that the cjp model is better able to characterise experimentally determined crack tip plastic zone size and shape that the original williams model for crack tip stresses, irrespective of whether two terms or five terms are used in the williams expansion [1]. work on characterising the growth of inclined cracks in compact tension specimens under uniaxial loading (which therefore experience biaxial crack tip stress fields), using stress intensity parameters obtained from the cjp model, has been successful in achieving a sensible rationalisation of crack growth rate data, although some observations are not easily explained. nonetheless, considering the complexity of characterising crack growth rates for cracks with an initial orientation of 30°, 45° or 60° to the horizontal and which subsequently change angle during growth, the results found so far indicate that there is value in further pursuing the cjp approach. the present authors are taking several approaches to further refinement of the cjp model, by considering whether an energy-based approach to crack tip fields would be more useful for complex crack path situations, and by exploring the mathematical solution for an interfacial stresses around a plastic inclusion embedded in an elastic body. alongside this work, further crack growth data will be acquired from ct specimens with horizontal cracks while the size and shape of plastic zones around growing fatigue cracks remains under active consideration. t g. laboviciute et alii, frattura ed integrità strutturale, 33 (2015) 167-173; doi: 10.3221/igf-esis.33.21 173 references [1] james, m.n., christopher, c.j., lu, yanwei, patterson, e.a., local crack plasticity and its influences on the global elastic stress field, int. j. fatigue, 46 (2013) 4-15. [2] christopher, c.j., laboviciute, c., james, m.n., patterson, e.a., extension of the cjp model to mixed mode i and mode ii, frattura ed integrita strutturale, 7 (2013) 161-166. [3] tada, h., paris, p.c., secondary elastic crack tip stresses which may influence very slow fatigue crack growth— additional results, int. j. fatigue, 27 (2005) 1307–1313. [4] ding, f, zhao, t., jiang, y., a study of fatigue crack growth with changing load direction, engng fract. mech., 74 (2007) 2014-2029. shot peening processes to obtain nanocrystalline surfaces in metal alloys: y.h. shao et alii, frattura ed integrità strutturale, 48 (2019) 757-767; doi: 10.3221/igf-esis.48.69 757 fatigue reliability assessment of small sample excavator working devices based on bootstrap method yuhong shao, pengmin lu, binhua wang, qingyi xiang key laboratory of road construction technology and equipment, ministry of education, chang’an university, xi’an 710064, china shaoyh@chd.edu.cn, lpmin@chd.edu.cn, wangbh@chd.edu.cn, 383393093@qq.com abstract. to evaluate the fatigue reliability of the excavator working device, the fatigue tests of 2 sets of moving arm and bucket rod of medium-sized excavators with self-weight of 26000 kgwere carried out. the virtual augmented sample method (vasm) combined with bootstrap method was used to analyze the reliability of the excavator working device under extreme small samples, and the interval and point estimations of life parameters were obtained. based on the lognormal distribution of the excavator working device, the reliability evaluation model of the excavator working device was established, and reliability indexes, such as reliability function, failure distribution function, inefficiency function, reliable life and so on, were obtained. and the results of fatigue safety life under different confidence and reliability were calculated. the evaluation results show that the average failure time of the excavator working device is 6124 hours under the confidence of 75%, which provides an important reference for the design, the safety inspection and maintenance decision of the excavator working device. keywords. fatigue reliability; small sample; bootstrap; excavator working device; f test. citation: shao y.h., lu p.m., wang b.h., xiang q.y., fatigue reliability assessment of small sample excavator working devices based on bootstrap method, frattura ed integrità strutturale, 48 (2019) 757-767. received: 24.01.2019 accepted: 21.03.2019 published: 01.04.2019 copyright: © 2019 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. introduction he working device of the excavator is the direct actuator of the excavator operation, and the reliability of the working device is one of the key indexes of the excavator's quality. therefore, it is of great significance to study the reliability of the excavator's working device [1]. due to the high cost of the excavator working device and the limitation of the test cost and time, the fatigue life test can only be carried out by using 2~3 test pieces rather than the large sample size test data to meet the statistical requirements. as a result, the fatigue reliability evaluation of excavator working device is a problem of very small sample. t http://www.gruppofrattura.it/va/48/2364.mp4 y.h. shao et alii, frattura ed integrità strutturale, 48 (2019) 757-767; doi: 10.3221/igf-esis.48.69 758 the existing reliability assessment methods include semi-empirical method [2], bayes method [3], student-t distribution method [4], bootstrap method [5] and so on. under the condition of no empirical data, the student-t distribution method can be used in the case of the small sample with the unknown parent variance to deduce the interval estimation of the overall mean of the set confidence level. however, the confidence interval estimated by this method is often wider. the bootstrap method is a statistical method that only relies on sample information proposed by efron.b in 1979 [6]. there is no need to make any assumptions and restrictions on the parent distribution. after the simulated samples are sampled, the unknown parameters can be estimated through statistical prediction, which is suitable for small sample test data processing [7, 8]. bootstrap can be used in statistical fields such as parameter estimation, regression analysis, interval estimation, hypothesis testing and cross validation, and has been widely used in weaponry and aerospace products [9, 10]. the bootstrap method is not applicable to the reliability evaluation of the sample number 1, 2n = , feng yunwen et al [11] proposed a minimal subsample test evaluation method for the virtual augmented regenerative subsample and obtained the related reliability estimation. the bootstrap method has also been applied to the interval estimation of parameters with a small sample on mechanical engineering field, i.e., the tank roadarm [12], the gearbox [13] and the production processing [14]. however, for the excavator working device, there is a lack of fatigue life reliability test and evaluation research. based on the test on site and the load spectrum of the excavator working devices, the full-scale fatigue life tests of the excavator's moving arm and the bucket rod were carried out. according to the results of the small sample fatigue test, the bootstrap method combined with vasm was used to evaluate the actual fatigue reliability of the medium-sized excavator working devices. bootstrap method t is assumed that the independent random sample 1 2( , , )nx x x=x comes from the unknown parent distribution f , and ( )f = is the unknown parameter in the parent distribution. the basic idea of the bootstrap method is to use the sample empirical distribution function nf to replace the unknown parent distribution function f . the unknown parent parameter  is deduced by sufficient statistics of the resampling statistics, and the steps are as follows: step 1: for independent and identically distributed sample 1 2( , , )nx x x=x , the order statistics of (1) ( 2 ) ( )nx x x   is obtained by sorting from small to large. the empirical cumulative distribution function ( )nf x of samples, as demonstrated in eqn. (1), is constructed. the estimation of  is ˆ ˆ( )nf = and the estimated error is ˆ( ) ( )nr f f = − . 1 1 0 ( ) 1 n i i n x x i f x x x x n x x +    =     （ ） （ ） （ ） （ ） (1) step 2: a sample * 1 2( , , )nx x x    =x with a random capacity of n is resampled randomly from empirical distribution function nf , which is called bootstrap subsample. nf  is an empirical distribution function of * x . * ˆ ˆ( ) ( )n nr f f   = − was identified as bootstrap statistics r . step 3: by repeating steps (2) n times (usually 1000n  ), the n bootstrap samples of ( 1, 2, )j j n  =x can be obtained. the estimated ( 1, 2, )j j n  =r of each bootstrap sample statistic are calculated, and the distribution of r is simulated by the distribution of j  r , as a result, the samples 1 2 ˆ ˆ ˆˆ ( , , , )n       =θ of ( )f are determined. step 4: the optimal distribution fitting, the parameter estimating and the hypothesis testing for ˆ  θ are carried out successively, and the distribution function of the parent parameter  is replaced by ˆ( )nf θ . step 5: the percentile method or the corrected percentile method are commonly used to perform the interval estimation on parameter  . the bootstrap sample estimated value of 1 2 ˆ ˆ ˆˆ ( , , , )n       =θ is arranged in ascending order. if the i y.h. shao et alii, frattura ed integrità strutturale, 48 (2019) 757-767; doi: 10.3221/igf-esis.48.69 759 percentile method is adopted, the interval containing ( ) ˆ1100%  θ is equal to the confidence interval of parameter  at ( )1- confidence level. that is, the confidence interval of parameter  is 2 1 2,k k −   , where 2k and 1 2k − are the empirical quantiles of parameter  . due to the shortcomings of the percentile method in the convergence of probability, the corrected percentile method is used to perform interval estimation on the unknown parameter  , then the correction of b is defined as follows: 1 1 1 ˆ( ) n j j b i n  −  =   =        (2) where 1 ( ) −  is defined as the inverse function of standard normal distribution and ( )i is the indicative function, as follows: ˆ ˆ1 , ( ) ˆ ˆ0 , j j j i          =   (3) after correcting the parameter  , the confidence interval with confidence level ( )1- is ( , )pl puk k . where plk and puk are the quantiles of parameter  , and /2( 2 )pl z b=  + , 1 /2( 2 )pu z b−=  + and z are the standard normal quantiles. fatigue testing procedure and results n this paper, the questionnaire surveys were conducted about the material types and material proportions for medium-sized excavators (self-weight is about 26000 kg) in china. a total of 405 valid questionnaires were collected. the survey included the following excavator manufacturers: xugong, sunward, sany, hitachi, komatsu, doosan, cat, hyundai and liugong. according to the statistical analysis on the survey data and the material conditions of the load spectrum test site, the type and proportion of the materials for the medium-sized excavator were determined with reference to standard for engineering classification of soil [ 15], which were as follows: loose soil (24.6%), sub clay (22.6%), clay (24.1%), and heavy clay containing clay (28.7%). finally, the load spectrum tests of excavators were completed on the test site, and the load spectrums of the excavator working devices were obtained. due to the changing of the attitude of the excavator working devices (moving arm and bucket rod) in the actual operation, the fatigue loading schemes on the platform under the local coordinates of the moving arm and the bucket rod were put forward. for the complex loads on moving arm and bucket rod, a load equivalent method (lem) based on the maximum bending moment cross section was proposed. in order to verify equivalent loads, the stress histories of major stress points on moving arm and bucket rod were calculated by finite element analysis, and the stress histories were compared with the measured stress histories obtained by testing onsite. the location of the measuring points is shown in fig. 2, and the comparison results are shown in fig. 3. using the corrcoef function in matlab software, it is concluded that the correlation between the measured points and the measured stress histories under the 95% confidence level is 88.6%~97.21%. the damage equivalent criterion [16] was used to correct the equivalent vertical load of moving arm and bucket rod, and the fatigue test load spectrums of moving arm and bucket rod on medium-sized excavators were obtained. the schematic diagrams of fatigue test are shown in fig. 1. eqf and keqf are fatigue test loads for moving arm and bucket rod respectively. for details, see the previous paper [17]. the full-scale fatigue tests of 2 sets of excavators' moving arm and bucket rod were completed, as shown in fig. 2. in order to ensure uniformity of the manufacturing quality of the moving arm and bucket rod, the robotized welding is mainly used. during the experiment, the loading frequency is 1-2 hz, and the penetration crack or crack propagation to about 5cm is the criterion of stopping. the fatigue test results are illustrated in tab. 1 and the fatigue failures are shown in fig. 4 and fig. 5. in addition, according to the experience of the industry, the life target of the excavator working device is about 8000~10000 hours. thus, during the fatigue test, the testing machine will be stopped when the fatigue life is over i y.h. shao et alii, frattura ed integrità strutturale, 48 (2019) 757-767; doi: 10.3221/igf-esis.48.69 760 11000 hours for the members without fatigue crack. the shorter fatigue life of the moving arm and bucket rod is identified as the fatigue life of the excavator. therefore, the fatigue life of the 2 sets of excavators is 1 9870ht = and 2 4179ht = respectively. e d f g k f keq x2 x z z2 o (a) moving arm of excavator (b) bucket rod of excavator figure 1: schematic diagrams of the loading scheme during fatigue testing. and are the fatigue test loads of moving arm and bucket rod on platform frame respectively, and o1, b, e and d are hinged points. the link of bc is used to support moving arm. no. moving arm bucket rod fatigue life for working devices of excavator /h fatigue life /h failure location fatigue life /h failure location 1 10470 the front end of welding toe at the supporting plate on the upper flange plate of the moving arm, as shown in fig. 4(a). 9870 the front end of welding toe at the supporting plate on the upper flange plate of the bucket rod, as shown fig. 4(b). 9870 2 4179 the front end of welding toe at the supporting plate on the upper flange plate of the moving arm, as shown in fig. 5. >11000 no failure 4179 mean value 7024.5 table 1: fatigue test results of excavator working devices. (a) moving arm (b) bucket rod figure 2: fatigue test photo of working device of medium-sized excavator. y.h. shao et alii, frattura ed integrità strutturale, 48 (2019) 757-767; doi: 10.3221/igf-esis.48.69 761 790 810 830 850 870 890 910 -100 -70 -40 -10 20 50 80 110 应 力 /m p a 采样时刻 (s) 计算应力 实测应力 (a) no.1 measuring point on moving arm 350 400 450 500 -40 -20 0 20 40 60 80 100 120 应 力 （ m p a ） 采样时刻（s） 当量垂向载荷计算应力 实测应力 (b) no.2 measuring point on bucket rod figure 3: comparisons of calculated stress and measured stress at measuring points (i) (ii) enlarged view (a) fatigue failures on moving arm (i) (ii) enlarged view (b) fatigue failures on bucket rod figure 4: fatigue failures on no.1 excavator figure 5: fatigue failures on moving arm of no.2 excavator, which is the same as failure position of no.1 excavator fatigue crack fatigue crack fatigue crack s tr e s s / m p a sampling time / s sampling time / s s tr e s s / m p a y.h. shao et alii, frattura ed integrità strutturale, 48 (2019) 757-767; doi: 10.3221/igf-esis.48.69 762 reliability evaluation on small-size sample of excavator working devices he statistical distribution of fatigue life of structural parts is generally considered to obey lognormal distribution or weibull distribution. in this study, the fatigue life of the excavator working device is assumed to be logarithmic normal distribution, and then the logarithmic fatigue life lgy t= obeys the normal distribution. its mean value is y , and the standard deviation is y . under certain reliability r , the logarithmic safety life ry of the excavator working device is defined as: ( ) ( ) r r y p y y f y dy r   = = (4) where ( )f y is the probability density function of the logarithmic life. the logarithmic safety life r y r yy u = + can be obtained according to eqn. (4), and its estimated value is as follows: ˆ ˆˆ r y r yy u = + (5) where: ˆ y is the mean value of the parent; ˆ y is the estimated standard deviation of the parent; ru is a standard normal deviation corresponding to reliability r , that is ( )-1= 1-ru r . the bootstrap method is usually applied to small sample test evaluation with sample size of 10n  . as the test sample of the excavator working device was only 2 sets in this study, the vasm was used to augment the original sample 2n = to the sample 12n  = . the basic principle of the vasm is that the average value and the standard deviation of the augmented sample should be equal to those of the original test. the recommended virtual augmented empirical formula is [11]: ( ) 3 , 2 0.017 1 1 2 2i i my y i i m +  =   − + =  ， ，， (6) where: y is an augmented sample value; y is the mean life mean of the test sample;  is a standard deviation of the subsample of a similar part; m is an augmented sample number;  is the undetermined coefficient. an augmented sample obtained by the eqn. (6) was: 1 2 3 3 3 4 3 5 6 3 7 8 3 3 9 10 11 12 , (0.017 ) , (0.017 2 ) , (0.017 3 ) , (0.017 4 ) , , (0.017 ) , (0.017 2 ) , (0.017 3 ) , (0.017 4 ) , lg 4197, lg 9870 y y y y y y y y y y y y y y y y y y y y y y                   = − = − + = −  + = −  + = −  + = + = + + = +  + = +  + = +  + = = from the fatigue test results of the excavator working device, the mean value of logarithmic fatigue life 1 1 lg =3.8077 n i i y t n = =  and standard deviation 0.2639y = of the sample were achieved. according to the basic principle of vasm, the equations were as follows: t y.h. shao et alii, frattura ed integrità strutturale, 48 (2019) 757-767; doi: 10.3221/igf-esis.48.69 763 12 0 12 2 2 0 1 12 1 ( ) 11 j j j y j y y y y  = =  =    − =     (7) the augmented sample 1 12y y was substituted to the eqn. (7), and 0.5727 = was obtained. the augmented samples arranged in order were y = {3.3694，3.5354，3.6207，3.6211，3.6521，3.6566，3.9588，3.9633，3.9943，3.9947， 4.0800，4.2460}. the empirical cumulative distribution function * ( ) n f y of the augmented sample was set up, as shown in fig. 6. montecarlo method was used to resample the n groups of bootstrap samples from the empirical cumulative distribution function * ( ) n f y , that is 1 2 * ( )( ) ( ) ( ) ( , , ), kk k k n y y y y= ( 1, 2, )k n= . the mean value of bootstrap sample mean value and the mean value of bootstrap sample standard deviation with sampling number were illustrated in fig. 7. the results showed that when the number of bootstrap samples was 01000n  , the mean values of bootstrap sample mean value and bootstrap sample standard deviation reached a stable state. therefore, the number of bootstrap sampling number was 10000n = . the mean value and standard deviation of 10000 sets of bootstrap samples were statistically analyzed, and the distribution characteristics of logarithmic life mean y and standard deviation y were estimated. k-s test results showed that the logarithmic life mean and standard deviation followed normal distribution, and ( )23.8120, 0.0645y n , ( ) 2 0.2221, 0.0305y n . the frequency distribution histograms and normal distribution fitting curves of bootstrap sample mean value and its standard deviation were shown in fig. 8 and 9 respectively. figure 6: empirical distribution function of augmented logarithmic life sample y . figure 7: logarithmic life parameter estimation varies with bootstrap simulations. figure 8: the frequency distribution histogram and curve fitting of bootstrap sample mean value figure 9: the frequency distribution histogram and curve fitting of bootstrap sample standard deviation y.h. shao et alii, frattura ed integrità strutturale, 48 (2019) 757-767; doi: 10.3221/igf-esis.48.69 764 referring to the international fatigue strength design standard for welded structures [18], the general reliability is 75%. therefore, the confidence interval of the 75% confidence level of the mean logarithmic life was estimated to be [3.7311, 3.8793] using the bootstrap corrected percentile method. according to the student-t distribution theory, the confidence interval of the logarithmic life expectancy at the 75% confidence level was [3.3571, 4.2582] . by comparing the two results, the average confidence interval obtained by bootstrap method was narrow, and the accuracy of interval estimation was improved. in practice, the confidence lower limit of the percentile value of the parent is often used to estimate the true value of logarithmic safety life. thus, the lower confidence limit of percentile value of the logarithmic life expectancy at the 75% confidence level was 3.7311y = . estimated value of bootstrap sample standard deviation 0.2221y = was adopted as the standard deviation of the parent logarithmic life. the above estimated values were substituted in the eqn. (5), and the reliability indexes of the working device of the excavator were calculated as follows: reliably function ( )r t is lg 3.7311 ( ) 1 0.2221 t r t −  = −     (8) the reliability function curve of excavator working device under 75% confidence level was shown in fig. 10. as the working hours increasing, the reliability of working devices will be decreased. when the working time reaches 0~2300 hours, the reliability is gradually reduced. the working time is 2300~7000 hours, and the reliability is rapidly reduced. but when the working time is 7000 hours, the reliability decreases slowly. the working hours is closing to 15000 hours, and the reliability tends to 0. figure 10: reliability function curve of excavator working device (2) the failure distribution function ( )f t and the probability density function ( )f t are lg 3.7311 ( ) 1 ( ) 0.2221 t f t r t −  = − =     (9) 2 2 lg lg 3.73111 1 1 1 ( ) exp exp 2 2 0.22212 ln 10 0.2221 2 ln 10 y yy t t f t t t         − −   = − = −              (10) the failure probability density function curve of the excavator working device was shown in fig. 11. it can be seen that the failure probability is − =  4 max ( ) 1.6586 10f t when  4400t h. this indicates that when the working device test sample runs to 4400h, the failure samples account for about 0.0166% of the total sample size. y.h. shao et alii, frattura ed integrità strutturale, 48 (2019) 757-767; doi: 10.3221/igf-esis.48.69 765 figure 11: failure probability function curve of excavator working device （3）inefficiency function is lg 3.7311 ln 10 ( ) 0.2221 ( ) lg 3.7311( ) 1 0.2221 t t f t t tr t   −      = = −  −     (11) the failure rate function curve of the excavator working device was shown in fig. 12. without preventive maintenance, the failure rate function of the excavator working device is incremental, and the increasing speed is faster, then slows down, and finally tends to be stable. when the working time is 0~1800 hours, the failure probability is increased slowly. this stage is an occasional failure stage. at this stage, we should do a good job in maintenance of the excavator work device, so that the working time of the product can be prolonged as long as possible. when the working time is 1800~4800 hours, the failure probability is increased rapidly. this stage is mainly caused by the fatigue damage and abrasion of the excavator working device. if the preventive maintenance or updating parts are to be applied at this time, the failure rate can be reduced to ensure the reliable operation of the excavator working device. figure 12: failure rate curve of excavator working device y.h. shao et alii, frattura ed integrità strutturale, 48 (2019) 757-767; doi: 10.3221/igf-esis.48.69 766 （4）reliablelife is    − − +  − = = 1 ( ) [ 3.7311 0.2221 (1 )] 10 10y y r rt (12) by using the above method, the fatigue life evaluation results of the excavator working device under different confidences and reliabilities are calculated, as shown in tab. 2. confidence level reliability average fatigue life 36.8% 50% 75% 90% 95% 99% 75% 6384 5372 3803 2787 2314 1633 6124 90% 5909 4974 3525 2585 2147 1516 5667 95% 5647 4753 3367 2469 2051 1448 5416 table 2: fatigue life evaluation results of excavator working device (h) conclusions (1) according to the load characteristics of the excavator working devices, i.e., the moving arm and the bucket rod, the equivalent load models under fixed attitude were established based on the load equivalent method (lem). the schemes for fatigue test of excavator working devices in a local coordinate system were designed to overcome the contradiction between the variable posture during working and the fixed attitude during fatigue testing. the full-scale fatigue life tests of 2 sets of medium-sized excavators' moving arm and bucket rod were carried out respectively. (2) according to the data of the minimum sample fatigue life test of the excavator working device, the reliability evaluation of the excavator working device was carried out by the bootstrap method combined with virtual augmented sample method (vasm). by this way, the reliability function, the failure distribution function, the failure rate function and the reliable life were obtained. the evaluation results show that the reliability of the excavator working device varying with time is basically consistent with the performance degradation rule of mechanical products. the analysis results can provide a reference for the detection and maintenance of the excavator working devices. (3) the fatigue lives of excavator working device under different confidence and reliability were obtained. under the 75% confidence level, the average working time of the excavator working device is 6124 hours, which is far from the expected 8000-10000 hours in the line. fatigue design method and fatigue tests should be adopted to optimize the structures and gradually improve the fatigue lives of excavator structural parts. acknowledgements his work is supported by the national science-technology support program project (no. 2015baf07b02), the shanxi national science foundation project (no. 2017jm5040) and the fundamental research funds for the central universities (no. 300102258508). references [1] illera, d., pugliese, v., mesa, j., et al. (2018). failure assessment of a weld-cracked mining excavator boom, eng. failure anal., 90(8), pp. 47-63. doi: 10.1016/j.engfailanal.2018.03.022 [2] zheng, g., yang, x., zhou, h., et al. (2018). a simplified prediction method for evaluating tunnel displacement t y.h. shao et alii, frattura ed integrità strutturale, 48 (2019) 757-767; doi: 10.3221/igf-esis.48.69 767 induced by laterally adjacent excavations, comput. geotech., 95, pp. 119-128. doi: 10.1016/j.compgeo.2017.10.006 [3] gran, b. a., and helminen, a. (2001). a bayesian belief network for reliability assessment, computer safety, reliability and security, springer berlin heidelberg, pp. 35-45. [4] ahsanullah, m., kibria, b. m. g., shakil, m. (2014). characterizations of student’s t distribution. atlantis press, pp. 129-141. [5] saberi, m. r., rahai, a. r., sanayei, m., et al. (2017). steel bridge service life prediction using bootstrap method, int. j. civ. struct. eng., 15(1), pp.1-11. doi: 10.1007/s40999-016-0036-z [6] efron, b. (1992). bootstrap methods: another look at the jackknife, breakthroughs in statistics. springer new york, pp. 1-26. [7] šeruga, d., nagode, m. (2015). a method for long-term creep–rupture strength prediction based on a small sample of experimental results, smoothed bootstrapping and time–temperature parameters, mater. des., 67, pp. 180-187. doi: 10.1016/j.matdes.2014.11.011 [8] wang, y., zhou, w., dong, d., et al. (2017). estimation of random vibration signals with small samples using bootstrap maximum entropy method, meas, 105, pp. 45-55. doi: 10.1016/j.measurement.2017.04.003 [9] peng, w., fang, y. w., zhan, r., et al. (2016). weapon systems accuracy evaluation using the error spectrum, aerosp. sci. technol., 58, pp. 369-379. doi: 10.1016/j.ast.2016.08.032 [10] muller, l., roche, j. m., hurmane, a., et al. (2018). experimental monitoring of the self-heating properties of thermoplastic composite materials, procedia eng., 213, pp. 183-191. doi: 10.1051/matecconf/201816507003 [11] hung, w.，feng, y.，lu, z. (2005). virtually expanded sample estimation method for extremely small-scale sample test, j. northwest. polytech. univ., 23(3), pp. 384-387. doi: 10.3969/j.issn.1000-2758.2005.03.024 (in chinese) [12] noh, y., choi, k. k., lee, i., et al. (2010). reliability-based design optimization with confidence level for nongaussian distributions using bootstrap method, j. mech. des., 133(9), pp. 1065-1076. doi: 10.1115/1.4004545 [13] wang, h., deng, x., li, j., et al. (2015). dynamic assessment of vibration of tooth modification gearbox using grey bootstrap method, shock vib., 4, pp. 1-8. doi: 10.1155/2015/204609 [14] niaki, s. t., abbasi, b. (2007). bootstrap method approach in designing multi-attribute control charts, int. j. adv. manuf. technol., 35(56), pp. 434-442. doi: 10.1007/s00170-006-0728-7 [15] “standard for engineering classification of soil”, gb/t 50145-2007, national standards of the people's republic of china, pp. 8-10. (in chinese) [16] zhang, s. g. (2008). research on load spectrum test and establishment method of high speed train bogie, sci. china, 38(11), pp. 1805-1814. doi: 10.3321/j.issn:1006-9275.2008.11.002 (in chinese) [17] xiang, q. y., lu, p. m., wang, b. h., et al. (2017). load spectrum test method of hydraulic excavator working device, china j. highw. transp., 30(9), pp. 151-158. doi: 10.3969/j.issn.1001-7372.2017.09.019 (in chinese) [18] hobbacher, a., f. (2016). recommendations for fatigue design of welded joints and components. springer international publishing. microsoft word numero_58_art_11_3204.doc e.s.m.m. soliman, frattura ed integrità strutturale, 58 (2021) 151-165; doi: 10.3221/igf-esis.58.11 151 damage severity for cracked simply supported beams ehab samir mohamed mohamed soliman mechatronics and robotics department, faculty of engineering, egyptian russian university, badr city, cairo, 11829, egypt. swgezumo@yahoo.com, http://orcid.org/0000-0001-6427-3022 abstract. this paper investigated the static and dynamic behaviors of isotropic cracked simply supported beam using finite element analysis (fea), ansys software. modal and harmonic vibration analysis of intact and damaged beam were performed in order to extract mode shapes of bending vibration, natural frequencies and obtain frequency response diagram. static finite element analysis of undamaged and damaged simply supported beam was carried out to determine static deflection, then stiffness of intact and cracked beam was computed using conventional formula. crack damage severity of damaged beam was calculated and it is noticed that as crack position is increased from left hand support of beam up to central point and crack depth is increased, then crack damage severity increases. the effect of mode shape pattern is investigated and it is found that the amount of decreasing of natural frequency is proportional to the normalized mode shape at position of crack. the exhibited correlation between results for damaged beam revealed that crack damage severity is proportional to static deflection and inversely proportional to first mode frequency. keywords. isotropic; damaged simply supported beam; crack damage severity; mode shape; static deflection. citation: soliman, e.s.m.m., damage severity for cracked simply supported beams, frattura ed integrità strutturale, 58 (2021) 151-165. received: 26.07.2021 accepted: 21.08.2021 published: 01.10.2021 copyright: © 2021 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. introduction tructures must work in safety during service life but the initiation of a breakdown period on it is due to damages as cracks [1]. crack may be caused by manufacturing and material defects and furthermore, fatigue cracks in structures are easily triggered under periodical alternating loads in operating conditions [2]. the mass and stiffness distributions of the structure are to be an effective on the dynamic behavior of the structure, i.e., dynamic response, natural frequencies and mode shapes of a structure [3]. vibration-based inspection methodology is one of the modern approaches to non-destructive testing and evaluation (nde) [4]. a noticeable shift in the natural frequencies is revealed by plotting the deformation responses in the y-direction for the intact and cracked cantilever beams [5]. the effects of the developed damage in the structure are the reduction of the rigidity of the structure and altering the associated dynamic and static properties to some extent [6]. for monitoring the crack, mostly modal frequencies are used where modal frequencies are properties of the whole component [7]. a change in model parameters i.e. model frequencies, model damping values and mode shapes associated with each model frequencies characterizes the change in dynamic characteristics of damaged structures [8]. the reduction of natural frequency of the component occurs as a result of crack s https://youtu.be/li-4znau3ha e.s.m.m. soliman, frattura ed integrità strutturale, 58 (2021) 151-165; doi: 10.3221/igf-esis.58.11 152 and by measuring the change in the natural frequencies of the component due to crack, many methods have been developed to identify the crack [7]. the complex structures are decomposed into simple elements such as beams, columns and plates using the structural elements during the machine design process and the functioning of the whole machine may stop due to failure of any small component [9]. khalkar and ramachandran [10] carried out static and modal analyses for intact and cracked cantilever beam by ansys software to get static deflection and natural frequency. they determined stiffness of intact and various cracked cases of a cantilever beam based on results of ansys static deflection. through this research study [10], it is found that when the crack position is kept constant and crack depth is increased, then stiffness of the beam decreases and when the crack depth is kept constant and crack position is varied from the fixed end, then stiffness of the beam increases. in this work, the damaged simply supported beam with single edge crack is investigated for its natural frequencies of bending vibration modes, mode shape pattern of bending vibration, static deflection and stiffness to study crack damage severity. also, the correlation between results of crack damage severity and results of dynamic and static parameters are investigated. methodology n this study, the cracked simply supported beam is considered as an euler–bernoulli beam. the crack is uniformly extending along the damaged beam width and the crack is considered as fully open edge. the material of damaged and undamaged beams used in the analysis is considered as isotropic and homogeneous. the governing differential equation of the free transverse vibration of an undamaged euler-bernoulli beam without crack which is uniform, isotropic and homogeneous can be written as [11]:          4 2, , 0 4 2 y x t y x ta eix t (1) where the origin of x and y is at left end of the beam, y(x, t) is the function of the transverse displacements, e is modulus of elasticity, i is the area moment of inertia, ρ is mass density, a is the cross-sectional area and t is time. according to [12], for solution eqn. (1), assume that:     , j ty x t y x e (2) where  1j , ω is natural frequency of the beam. by substituting eqn. (2) into eqn. (1), then eqn. (3) can be expressed as [12]:            4 4 0 4 y y x (3)            1 42 4al ei (4) where ζ = x / l is normalized location, x is the coordinate and its origin at left end of beam and λ is non-dimensional frequency parameter. according to [12], the general solution of eqn. (3) can be written as the following:                 cos sin cosh sinhy a b c d (5) the damaged beam can be simulated as two uniform beam segments, joined by a torsional spring at the position of crack [13]. the modes of harmonic vibration for these two beam segments can be written as [12]: i e.s.m.m. soliman, frattura ed integrità strutturale, 58 (2021) 151-165; doi: 10.3221/igf-esis.58.11 153                 cos sin cosh sinh1 1 1 1 1y a b c d (6)                 cos sin cosh sinh2 2 2 2 2y a b c d (7) where ai and bi, i=1, 2, 3, 4, are coefficients can be obtained from the boundary conditions. the boundary conditions for the simply supported beam at the supports are [12] at the supports no displacement and no moments:   01 0y (8)   02 1y (9)     2 1 0 2 0 d y d (10)     2 2 0 2 1 d y d (11) if ζ = µ = lc / l is the normalized crack position, lc is the crack distance from left hand support, the continuity conditions at the crack position are [12]: displacement:     1 2y y (12) moment:         2 2 1 2 2 2 d y d y ei ei d d (13) shear force:         3 3 1 2 3 3 d y d y ei ei d d (14) compatibility condition i.e., jump in the slope at the crack location due to rotational flexibility can be defined as [14]:             2 1 1 2 2 dy d y dy e ktd dd (15) kt is the bending spring constant at cracked section and it is, originally calculated by [15] and can be written as [14]:  1k ct (16)     5.346c h ei f s h (17) e.s.m.m. soliman, frattura ed integrità strutturale, 58 (2021) 151-165; doi: 10.3221/igf-esis.58.11 154                              2 3 4 5 1.8624 3.95 16.3754 37.226 6 7 8 9 10 76.81 126.9 172 143.97 66.562 f s h s h s h s h s h s h s h s h s h s h (18) where c is compliance, f (s/h) is dimensionless local compliance function, s, is depth of crack and h, is height of beam. according to elementary beam theory, sayyad and kumar [13] are expressed the relationship between the changes in eigen frequency and the crack location and stiffness of crack for a simply supported beam as the following:    2sinf f n x ei k ln n t (19) where δfn is the difference of eigen frequencies between un-cracked and cracked beams and n is number of bending mode. from eqns. (16), (17), (18) and (19) the following equation can be extracted as [13]:             22 29.9563.sin . . 1 2 . f fn ns h h n l (20) single characteristic equation for simply supported beam with a single crack can be expressed as [16]:                      cos 2 cos 2 0 2 2sin 2 ch ch k sh (21)  0k k l eit (22) where k0 is non-dimensional stiffness of the rotational spring. if f is zero frequency applied load at midpoint of beam, the deflection at the center point of simply supported beam can be written as [17]:   3 48 fl ei (23) figure 1: model of damaged simply supported beam. e.s.m.m. soliman, frattura ed integrità strutturale, 58 (2021) 151-165; doi: 10.3221/igf-esis.58.11 155 model of damaged beam n this study, an aluminum damaged simply supported beam model with single open edge crack of depth (s) at distance (lc) from left hand support of beam as shown in figure 1 is used to determine crack damage severity and modal parameters for cracked beam. the geometry properties of the undamaged and damaged beam are length (l) = 0.44 m, and cross-sectional area (a) = 0.026×0.026 m2. the crack location ratio µ is defined as µ = lc / l and crack depth ratio ψ is defined as ψ = s / h, where (h) is height of beam. the material properties of the undamaged and damaged beam are young’s modulus of elasticity (e) = 70 gpa, poisson’s ratio (ν) = 0.346 and density (ρ) = 2710 kg/m3. in order to consider different damage scenarios of the beam in the analysis, crack location ratio 0.1, 0.3 and 0.4 are chosen and for each crack location ratio crack depth ratio is varied as 0.2, 0.3 and 0.4. figure 2: fea results of frequency of first mode validation n order to validate the developed model used in this study, the results of fea frequency of the first mode of bending vibration for different three scenarios of cracked simply supported beam used by khalkar [17] is obtained (see figure 2), comparing it with those available in the literature as shown in fig. 3. the following beam and crack parameters are given in table 1 [17]. the solid 186 element is adopted for meshing the 3d model of cracked simply supported beam in the finite element analysis. in the analysis for the three scenarios of cracked beam, the location of crack is measured from left hand support of beam (lhs) as considered in [17]. from figure 3, it is found that fea results meet with excellent agreement with the results already published by khalkar [17] and thus verifies the precise of results of finite element analysis (fea) used in this study. i i e.s.m.m. soliman, frattura ed integrità strutturale, 58 (2021) 151-165; doi: 10.3221/igf-esis.58.11 156 parameter value elastic modulus 2.104×1011 n/m2 density 7820 kg/m3 poisson’s ratio 0.3 beam length 0.36 m beam cross sectional area 0.02×0.02 m2 table 1: beam and crack parameters [17] figure 3: comparison of the results of first mode frequency figure 4: finite element model of damaged simply supported beam: µ = 0.3, ψ = 0.4 numerical analysis he numerical analysis is carried out for both undamaged and damaged beams using finite element analysis (fea), ansys. in the analysis, modal and static analysis respectively are used to obtain mode shapes of bending vibration and static deflection, respectively. harmonic analysis is carried out to see difference between frequencies of undamaged and damaged beams in the frequency response diagram. in the static and harmonic analysis load of 300 n is applied at the central point of the simply supported beam. a 20 node structural solid element (solid 186) was adopted in the analysis to model the beam. a special mesh around the crack tip was established with singular elements surrounding the crack apex (see figure 4). t e.s.m.m. soliman, frattura ed integrità strutturale, 58 (2021) 151-165; doi: 10.3221/igf-esis.58.11 157 mode extraction and harmonic frequency n modal analysis, the block lanczos method was used to estimate frequencies of first two mode shapes of bending vibration for undamaged and damaged beams. the first natural frequencies of damaged beams are calculated analytically using eq. 20 [13] and compared with those of fea. as depicted in table 2, it is found that analytical results have been met with good agreement with the fea results and thus validates the precise of developed model used in this study. crack location ratio (µ) crack depth ratio (ψ) first natural frequency (hz) variation (%) analytical fea 0.1 0.2 302.39 303.648 -0.4 0.1 0.3 294.13 302.708 -2.9 0.1 0.4 283.3 301.155 -6.3 0.2 0.2 302.9 302 0.3 0.2 0.3 295.2 298.82 -1.2 0.2 0.4 285.1 293.71 -3 0.3 0.2 303.66 299.978 1.2 0.3 0.3 296.87 294.298 0.9 0.3 0.4 287.8 285.407 0.8 0.4 0.2 304.6 298.418 2 0.4 0.3 298.97 290.861 2.7 0.4 0.4 291.39 279.35 4.1 0.5 0.2 305.7 297.85 2.6 0.5 0.3 301.4 289.63 3.9 0.5 0.4 295.4 277.23 6.2 healthy un-damaged beam 309.34 304.34 1.6 table 2: comparison between analytical and numerical results finite element analysis (fea) results for the first two mode of bending vibration for some scenarios of damaged beam are depicted in figures 5, 6 and 7. figures 8 and 9 show the plotted of first two frequencies of bending mode as a function of crack location ratio for varying crack depth ratio. the influence of crack location ratio and crack depth ratio on first two frequencies of bending mode is indicated in figures 10 and 11. from figures 8, 9, 10 and 11 it is observed the following: 1when the crack depth ratio is kept constant and crack location ratio is increased from the left hand support of the simply supported beam, then first frequency of bending mode decreases up to central point of the beam. 2when the crack depth ratio is kept constant and crack location ratio is increased from the beam midpoint towards the right hand support of the beam, then first frequency of bending mode increases. 3for the second mode of bending vibration, when the crack depth ratio is kept constant the decreasing of frequency is the following ways: (a) at µ = 0.1, it is moderate decreasing, (b) at µ = 0.3, it is maximum decreasing, and (c) at µ = 0.4, it is minimum decreasing. the amount of decreasing frequencies for damaged beam is showed as shift between frequencies of damaged and undamaged beams in frequency response diagram as indicated in figures 12 and 13. the shift between frequencies of damaged and undamaged beams can be expressed as:   f f f n n cn (24) where n is number of bending mode, f is un-damaged beam frequency and fc is damaged beam frequency. i e.s.m.m. soliman, frattura ed integrità strutturale, 58 (2021) 151-165; doi: 10.3221/igf-esis.58.11 158 figure 5: fea results of first two mode shapes of bending vibration for damaged beam: µ = 0.1, ψ = 0.4 figure 6: fea results of first two mode shapes of bending vibration for damaged beam: µ = 0.3, ψ = 0.4 e.s.m.m. soliman, frattura ed integrità strutturale, 58 (2021) 151-165; doi: 10.3221/igf-esis.58.11 159 figure 7: fea results of first two mode shapes of bending vibration for damaged beam: µ = 0.4, ψ = 0.4 figure 8: variation of first bending mode frequency vs. crack location ratio. figure 9: variation of second bending mode frequency vs. crack location ratio. crack damage severity n this study, similar to khalkar [17], static finite element analysis is carried out and static deflection at the midpoint of undamaged and damaged beams is obtained. fea static deflection plots for some scenarios of damaged beam are shown in figure 14. figure 15 shows the variation of static deflection versus crack location ratio and crack depth ratio. from figure 15, it is observed that when the crack location ratio is increased from the left hand support of the simply supported beam up to midpoint of the beam and crack depth ratio is increased, then static deflection increases. stiffness of undamaged and damaged beams is computed using the following conventional formula [18]: i e.s.m.m. soliman, frattura ed integrità strutturale, 58 (2021) 151-165; doi: 10.3221/igf-esis.58.11 160   f k (25) where k is stiffness of beam, f is load and δ is static deflection or zero frequency deflection. in this study, the severity of crack can be expressed as crack damage severity (%) which is estimated using the following equation:    100 k kundamaged damaged k kundamaged (26) where δk is crack damage severity, kundamaged is stiffness of undamaged beam and kdamaged is stiffness of damaged beam. figure 10: variation of first bending mode frequency vs. µ and ψ. figure 11: variation of second bending mode frequency vs. µ and ψ. e.s.m.m. soliman, frattura ed integrità strutturale, 58 (2021) 151-165; doi: 10.3221/igf-esis.58.11 161 figure 12: harmonic response for the damaged beam; ψ = 0.4 in the range of 250-350 hz figure 13: harmonic response for the damaged beam; ψ = 0.4 in the range of 1070-1170 hz the variation of crack damage severity versus crack location ratio and crack depth ratio is depicted in figure 16. from figure 16, it is found that when the crack location ratio is increased from the left hand support of the simply supported beam up to midpoint of the beam and crack depth ratio is increased, then crack damage severity of the beam increases. figure 14: static deflection for damaged beam; ψ = 0.4: (a) µ = 0.1, (b) µ = 0.3, (c) µ = 0.4 e.s.m.m. soliman, frattura ed integrità strutturale, 58 (2021) 151-165; doi: 10.3221/igf-esis.58.11 162 figure 15: variation of static deflection vs. µ and ψ figure 16: variation of crack damage severity vs. µ and ψ. discussion of results n this section, the correlation between the outcomes of the analysis, i.e., results for the damaged simply supported beam are discussed. when zero frequency deflection is increased, then crack damage severity of the damaged beam increases as shown in figure 17. as frequency of first mode of bending vibration is decreased, then crack damage severity of the damaged beam increases as shown in figure 18. for the first two modes of bending vibration, when normalized mode shape at location of crack is increased, then shift between frequencies of damaged and undamaged i e.s.m.m. soliman, frattura ed integrità strutturale, 58 (2021) 151-165; doi: 10.3221/igf-esis.58.11 163 beams increases as depicted in figures 19 and 20, i.e., ∂f1 is proportional to uy1 and ∂f2 is proportional to uy2. on the other hand, it is found that the normalized mode shape at location of crack depends on the pattern of mode shape. figure 17: variation of crack damage severity vs. static deflection figure 18: variation of crack damage severity vs. first mode frequency figure 19: plot of uy1 vs. ∂f1 e.s.m.m. soliman, frattura ed integrità strutturale, 58 (2021) 151-165; doi: 10.3221/igf-esis.58.11 164 figure 20: plot of uy2 vs. ∂f2 conclusion n this study, the finite element analysis (fea) is applied for un-cracked and cracked simply supported beams to investigate crack damage severity and its correlation to static and dynamic parameters. for first two mode shape of bending vibration for undamaged and damaged beams, frequencies are calculated and also mode shape pattern is obtained. furthermore, frequency response diagram is obtained to determine the shift in frequencies between undamaged and damaged beams. it is observed that the pattern of mode shape seems to be an effective in the determining the value of normalized mode shape at location of crack. any decrease in the frequency is largest, i.e. maximum shift between undamaged and damaged beams in frequency response diagram is due to largest value of normalized mode shape at location of crack. based on fea static deflection, stiffness of damaged beam was computed and crack damage severity is estimated. from the results, it is found that when static deflection is increased and first mode frequency is decreased, then crack damage severity (%) increases. furthermore, in this study, pattern of mode shape played a vital role for interpreting decreasing or increasing natural frequencies for damaged beam. references [1] orhan, s. (2007). analysis of free and forced vibration of a cracked cantilever beam. ndt e int., 40, pp. 443–450, doi: 10.1016/j.ndteint.2007.01.010. [2] zeng, j., ma, h., zhang, w., wen, b. (2017). dynamic characteristic analysis of cracked cantilever beams under different crack types. eng. fail. anal. 74, pp. 80–94, doi: 10.1016/j.engfailanal.2017.01.005. [3] rezaee, m., hassannejad, r. (2011). a new approach to free vibration analysis of a beam with a breathing crack based on mechanical energy balance method. acta mech. solida sin. 24 (2), pp. 185-194, doi: 10.1016/s0894-9166(11)60020-7. [4] owolabi, g.m., swamidas, a.s.j., seshadri, r. (2003). crack detection in beams using changes in frequencies and amplitudes of frequency response functions. j. sound vib. 265(1), pp. 1–22, doi: 10.1016/s0022-460x(02)01264-6. [5] soliman, e.s.m.m. (2019). investigation of crack effects on isotropic cantilever beam. j. fail. anal. prev. 19(6), pp. 1866–1884. doi: 10.1007/s11668-019-00796-7. [6] andreaus, u., casini, p. (2016). identification of multiple open and fatigue cracks in beam-like structures using wavelets on deflection signals. contin. mech. thermodyn. 28, pp. 361–378, doi: 10.1007/s00161-015-0435-4. [7] sayyad, f.b., kumar, b., khan, s.a. (2012). approximate analytical method for damage detection in free–free beam by measurement of axial vibrations. int. j. damage mech. 22(1), pp. 133–142, doi: 10.1177/1056789512440897. [8] sayyad, f.b., kumar, b. (2010). theoretical and experimental study for identification of crack in cantilever beam by measurement of natural frequencies. j. vib. control 17(8), pp. 1235–1240, doi: 10.1177/1077546310384005. [9] bhaurkar, v.p., thakur, a.g. (2019). investigation of crack in beams using anti-resonance technique and fea approach. j. eng. des. technol. 17(6), pp. 1266–1284, doi: 10.1108/jedt-10-2018-0179. i e.s.m.m. soliman, frattura ed integrità strutturale, 58 (2021) 151-165; doi: 10.3221/igf-esis.58.11 165 [10] khalkar, v., ramachandran, s. (2017). paradigm for natural frequency of an un-cracked cantilever beam and its application to cracked beam. arpn j. eng. appl. sci. 12(6), pp. 1714–1729 [11] barad, k.h., sharma, d.s., vyas, v. (2013). crack detection in cantilever beam by frequency based method. procedia eng. 51, pp. 770–775, doi: 10.1016/j.proeng.2013.01.110. [12] mungla, m.j., sharma, d.s., trivedi, r.r. (2016). identification of a crack in clamped-clamped beam using frequencybased method and genetic algorithm. procedia eng. 144, pp. 1426–1434, doi: 10.1016/j.proeng.2016.05.174. [13] sayyad, f.b., kumar, b. (2011). identification of crack location and crack size in a simply supported beam by measurement of natural frequencies. j. vib. control 18(2), pp. 183–190, doi: 10.1177/1077546310395979. [14] rizos, p.f., aspragathos, n., dimarogonas, a.d. (1990). identification of crack location and magnitude in a cantilever beam from the vibration modes. j. sound vib. 138(3), pp. 381–388, doi: 10.1016/0022-460x(90)90593-o. [15] dimarogonas, a.d. and paipetis, s.a. (1983). analytical methods in rotor dynamics, london, elsevier applied science. [16] petrova, d.k. (2014). vibration-based methods for detecting a crack in a simply supported beam. j. theor. appl. mech. 44(4), pp. 69-82, doi: 10.2478/jtam-2014-0023. [17] khalkar, v. (2018). paradigm for natural frequency of an un-cracked simply supported beam and its application to single-edged and multi-edged cracked beam. vib. phys. syst. 29, 2018028 [18] khalkar, v., ramachandran, s. (2018). the effect of crack geometry on stiffness of spring steel cantilever beam. j. low freq. noise vib. act. control 0, pp. 1–13, doi: 10.1177/1461348418765959. microsoft word numero_57_art_17_3130 r. andreotti et alii, frattura ed integrità strutturale, 57 (2021) 223-245; doi: 10.3221/igf-esis.57.17 223 a simplified ale model for finite element simulation of ballistic impacts with bullet splash – development and experimental validation riccardo andreotti callens® area3 via merini 37 21100 varese, italy dipartimento di meccanica, politecnico di milano, via la masa 1, 20156 milano, italy riccardo.andreotti@callens.it sergio abate reparto investigazioni scientifiche, ris-roma, viale tor di quinto 151, 00191 roma, italy sergio.abate@carabinieri.it andrea casaroli dipartimento di meccanica, politecnico di milano, via la masa 1, 20156 milano, italy andrea.casaroli@polimi.it mauro quercia callens® area3 via merini 37 21100 varese, italy mauro.quercia@area3.it riccardo fossati rtm breda, via po 84, 20032 cormano (mi), italy riccardo.fossati@rtmbreda.it marco v. boniardi dipartimento di meccanica, politecnico di milano, via la masa 1, 20156 milano, italy marco.boniardi@polimi.it abstract. an original simplified finite element model is proposed to simulate the effects of non-penetrating ballistic impacts causing the so-called bullet splash phenomenon (complete bullet fragmentation), while no fragmentation is caused to the target. the model is based on the arbitrary lagrangian eulerian formulation (ale) and it simulates the impact as a fluidstructure interaction. the bullet splash phenomenon has been tested by experimental analyses of aisi 304l plates impacted by 9x21 fmj (full metal jacket) bullets. the model has been developed with the aim of creating a simplified approach to be used in the industry and forensic sciences to simulate the non-penetrating interaction of soft impactors with hard targets. comparisons between evidence and simulation results lead to the conclusion citation: andreotti r., abate s., casaroli a., quercia m., fossati r., boniardi m.v., a simplified ale model for finite element simulation of ballistic impacts with bullet splash – development and experimental validation, frattura ed integrità strutturale, xx (2021) 223-245. received: 01.06.2021 accepted: 10.06.2021 published: 01.07.2021 https://youtu.be/bqbwadbyne8 r. andreotti et alii, frattura ed integrità strutturale, 57 (2021) 223-245; doi: 10.3221/igf-esis.57.17 224 that the proposed approach can be used in a conservative way to estimate both local and global effects of bullet-splash phenomena. keywords. ballistic impact; bullet splash; stainless steel plate; arbitrary lagrangian eulerian (ale); finite element simulation (fem); explicit solver. copyright: © 2021 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. introduction any applications, particularly in aerospace and defense industry, involve the assessment of the structural consequences of impacts such as bird strike (heimbs, 2012 [1]), hail strike (anghileri et al., 2005 [2]), or ballistic impacts against structures, with the aim of optimizing their response in terms of protective capabilities. in industry, the optimization of protective capabilities of a structural system is mainly done by means of finite element simulations. this paper aims at proposing and discussing the effectiveness of an easy-to-use model for finite element simulations in the field of terminal ballistics for industrial and forensic applications, conceived for the assessment of protective structures impacted by splashing bullets. the typical bullet splash phenomenon [3] was brilliantly captured by photographer harold edgerton in 1938 [4], and is due to the low stiffness and strength of the impactor compared to the strength, stiffness, and inertia of the target, causing the high fragmentation of the bullet and the deflection of its fragment’s trajectory. bullet splash is what generally happens when the bullet hits the target at impact angles near to 90 degrees and is unable either to penetrate nor to cause fragmentation of the target; the bullet itself, instead, undergoes large deformations and eventually a complete fragmentation into small debris, which are subsequently deflected and projected around the epicenter of the impact by the target surface. this phenomenon is relevant for industrial applications in the field of protective functionality of structures because it represents what generally happens when a solid protective structure works properly, being able to locally withstand the pressure field caused by the impact and maintaining its continuity. consequently, the impact forces locally generated are transmitted to the surrounding structures. in this framework, the optimization of an effective protective structural system thus passes through the verification of the response of the overall system to a vast range of impact tests in all the possible locations at various incidence angles, to assure that the entire structure can safely withstand all the possible impact scenarios, not only locally, but globally. the possibility of simulating a vast range of load cases in a consistent and stable manner is nowadays fundamental to save time and costs in the process of developing a structural system with multiple safety requirements. but developing finite element simulations in the field of protective functionalities against ballistic impacts is still a challenging problem for the industry, with high costs due to the material characterization and model development and validation. most of the literature available on ballistic impacts simulation is focused on analyzing and simulating the effects of rigid projectiles impacting on deformable targets, with the aim of estimating the ballistic limit velocity and the modes of failure of the target. rajput & iqbal (2017) [5] showed both experimentally and numerically the effects of rigid projectiles of different nose shapes impacting on thin aluminum plates at different speed. in 2014, yunfei et al. [6] demonstrated and simulated the effectiveness of impactors of different strengths and deformability on penetrating single and multilayered metallic plates. early studies about numerical strategies for the simulation of three-dimensional fragmentation phenomena during impacts, involving simplified geometries and brittle materials, has been carried out by camacho & ortiz in 1996 [7]. pandolfi and ortiz (2002) [8] were able to reproduce the dynamic crack propagation of notched specimens during three point bend dynamic tests and their work was taken as a reference for a more recent study by bresciani et al. (2016) [9] on the simulation of the interaction between projectile and target involving the fragmentation of both, using the adaptive solid mesh to sph technique. no studies have been found focused on the analysis and simulation of soft bullets interacting with much harder targets causing the bullets-splash phenomenon, which is also common in the forensic investigation of crime scenes and is typically observed in the aerospace and defense industry when a hard solid protective structure is subjected to non-penetrating impacts. to investigate the phenomenon, we propose the experimental analysis of aisi 304 steel plates (4mm thick) impacted by 9x21mm fmj bullets, causing the typical bullets-splash phenomena at different incidence angle. the analysis of the residual deformation of the plates, the local state of hardening around the impact area, and the evidence of complete bullet m r. andreotti et alii, frattura ed integrità strutturale, 57 (2021) 223-245; doi: 10.3221/igf-esis.57.17 225 fragmentation has been used to conceive and validate a simplified simulation model that, under the given assumptions, does not require any complex characterization of the impactor and can be implemented easily on all the most popular finite element explicit simulation platforms commercially available. the model is based on the observation that during the bullet splash phenomena the change in shape of the impactor and its subsequent fragmentation makes the impactor act like a fluid mass rather than a proper solid. the modelling approach has been inspired from the simulation techniques commonly used for the numerical assessment of airframe structures against bird-impacts (heimbs, 2012 [1]). in fact, the softness of the 9x21mm fmj bullet, compared to the target, makes the observed phenomena qualitatively comparable with what happens during bird-strikes: the compact heterogeneous mass of skin, flesh, bones, and biological fluids hits a much harder surface at severe speed, encountering a complete loss of integrity. the high fragmentation of the impactor causes then the mass of debris to act like a fluid flow deflected by the target surface. bird strike is the most frequent cause of accident in aviation, and the industry has developed standard tests to assess the safety of the aircraft and its occupants against this risk. since the early 90s modern aerospace engineering procedures include the use of simulation to predict the response of the airframe structures under bird-strike tests to optimize the structural design in advance. the scientific literature on the modelling of the impactor for bird-strike simulation (heimbs, 2012) shows that the models commonly used to simulate bird strikes use few different formulations, all having in common the extreme simplification of the impactor, always represented as a homogeneous volume of soft or pre-fragmented matter, characterized by an initial simplified geometry to represent the main dimensions of the real impactor, associated with equivalent mass and speed (heimbs, 2012 [1]). this paper introduces a similar strategy to simplify the bullet and simulate ballistic impacts once the hardness of the impactor is significantly lower than the one of the target. even though 9x21fmj bullets are conceptually very simple, a rigorous characterization and modelling of their mechanical behavior during the impacts would have been extremely difficult and unpractical for industrial use. therefore, to model the phenomenon, a simplified approach has been hypothesized, based on the assumption that the structural effects of these impacts on the target are mostly due to the inertial forces needed to deviate the mass of the bullet debris from their initial trajectory, and the internal forces needed to stretch and break the impactor during the interaction with the target can be considered neglectable. this strong assumption allowed us to avoid the characterization and modelling of the deviatoric component of the constitutive laws governing the bullet’s behavior, therefore modelling it like a volume of compressible inviscid fluid with initial shape, linear compressibility, mass and velocity being the only few physical parameters to mechanically describe the impactor. to implement these hypotheses into a simulation that can be of practical use in the industry, we chose to model the interaction between impactor and target using the arbitrary lagrangian-eulerian formulation (ale) [10], which, during the last two decades, has been successfully used for several industrial applications to investigate the mechanical interaction between soft and hard continua like fluid-structure interaction, bird-strike [11], and impacts involving soft materials [12], guaranteeing strong stability of the calculation even in case of extremely large deformation fields. this technique, despite some intrinsic and well-known drawbacks [1], minimizes the risk of local instabilities, which are particularly negative inconveniences when encountered in the industry, where engineers frequently need to process several batch analyses with multiple load cases and sensitivity tests on tight deadlines. section 2 of the article illustrates the experimental evidence collected to quantify the effects of the bullet-splash phenomena used to develop and validate the model. the effects of the impacts are quantified in terms of microhardness distribution in the impact area and residual deformation of the plates depending on the impact angle. section 3 introduces the simulation model and the main phases of its development. in section 4 the simulation results are discussed and validated based on the comparison with experimental data in terms of equivalent plastic strain and residual deformation of the plates. to compare the microhardness measurements taken on the impact area of the samples with the equivalent plastic strain field estimated by the simulations, an empirical linear relation by qiao et al. [13] was applied. a discussion on the accuracy of the results and some practical indications to overcome the drawbacks of the technique are then introduced to conclude the section, with the aim of giving the reader a practical guide to the use of the model always in a conservative way, depending on the scope. in section 5 we summarize the conclusions and discuss the possible improvements and developments to the research. experimental analysis of the bullet splash phenomenon ullet splash is an expression coming from the terminal ballistics and legal jargon (oxford university press, 2020) [14] defined as “the particles sprayed from a bullet on its impact against metal or other hard material”. to verify and measure the effects of bullet splash on the target, we tested the response of 4-millimeter aisi 304 plates impacted b r. andreotti et alii, frattura ed integrità strutturale, 57 (2021) 223-245; doi: 10.3221/igf-esis.57.17 226 by 9x21 fmj bullets, with the scope of guaranteeing the non-penetration of the bullet and a significant ductile response of the plate. this way the field of plastic strain and plastic deformation of the plates have been treated as a measure of the severeness of the impacts. the visual analysis of the impact point and a debris collection screen allowed the investigation of the bullet fragmentation. ballistic test procedures the ballistic tests were conducted at the experimental shooting range of the reparto investigazioni scientifiche (ris) of carabinieri in rome (fig. 1). the bullets were shot by an automatic handgun beretta storm d px4 actuated by a pneumatic shooting machine which allows the control and reproducibility of the shots in terms of position and direction (fig. 2). the projectile speed was measured by means of a magnetic speed detector (fig. 3) positioned at 2.5 m from the muzzle of the gun to avoid the detonation gases to interfere with the measurements. the samples were positioned 14.3 meters far from the shooting machine according to the shooting area scheme represented in fig. 4. the speed measured was consistently 320-330 meters per second. figure 1: the experimental shooting range of the reparto investigazioni scientifiche (ris) of carabinieri in rome, italy, 2016. figure 2: the pneumatic shooting machine allowing the control and reproducibility of the shots. figure 3: the magnetic speed detector used to control the projectile speed at 2.5 m from the gun muzzle. r. andreotti et alii, frattura ed integrità strutturale, 57 (2021) 223-245; doi: 10.3221/igf-esis.57.17 227 figure 4: general scheme of the shooting area. target samples positioning the tested samples were 4mm x 500mm x 500mm plates, kept in position by means of a plate holder to which they were clamped as shown in fig. 5. the 4mm thick aisi 304 plates were chosen to guarantee that the targets would stand the impacts without allowing any penetration or fragmentation, being able to collect enough plastic strain to allow to experimentally catch the residual deformation of the plates as well as the local hardening in the impact areas. a polystyrene witness screen to collect bullets debris was also positioned sideways depending on the orientation of the sample with respect to the shooting machine. the angular position of the sample was changed manually by the operator. figure 5: the tested samples plates (4mm x 500mm x 500mm), kept in position by means of a support frame to which they were clamped at the angles. sideways to the sample plate a polystyrene screen was positioned in order to collect debris. chemical characterization of aisi 304l inox steel the tested samples were made of austenitic stainless steel x2 cr ni 18-9, commercially known as aisi 304l, where “l” stands for “low-carbon”, which improves the weldability and ductility i.e. formability and high energy absorption under impulsive loading conditions (toughness). the exact composition of the alloy was verified quantometer measurements, whose results are resumed in tab. 1. c si mn p s cr ni mo cu fe 0.023 0.351 1.46 0.0291 0.0017 18.11 8.11 0.25 0.46 70.809 table 1: chemical composition (weight %) of x2 cr ni 18-9 samples. r. andreotti et alii, frattura ed integrità strutturale, 57 (2021) 223-245; doi: 10.3221/igf-esis.57.17 228 quasi-static tensile characterization of aisi 304l plates to test the effective static strength of the material, two tensile samples were cut using a waterjet machine according to the uni en iso 6892-1-2009 standard (see fig. 6) and tested. this characterization work on the undeformed material is useful for allowing both the numerical characterization of the material and significant comparisons between pre and post impact properties. the engineering stress strain curve of the aisi 304l is shown in fig. 7; the standard mechanical characterization is resumed in tab. 2. figure 6: tensile characterization sample design according to uni en iso 6892-1-2009 standard. material x2 cr ni 18-9 e [mpa] 205000 rp0,2 [mpa] 297 rm [mpa] 673 a [%] 63 z [%] 61 table 2: mechanical proprieties of aisi 304l. figure 7: aisi 304l’s engineering stress – strain curve. ammunition and projectile the impactor of 9x21 fmj cartridges is composed by a core, made of lead, and the thin brass jacket, aimed to prevent the erosion of the soft core with a thickness of around 0.04 mm. the mass of the bullet is 8g and the expected velocity is between 320-330 m/s. r. andreotti et alii, frattura ed integrità strutturale, 57 (2021) 223-245; doi: 10.3221/igf-esis.57.17 229 figure 8: 9x21 mm fmj scheme (length scale in millimeters). the ball length is 15mm. experimental results each 500x500mm plate was shot four times, one time for each quarter, thanks to the laser pointing system of the shooting machine. the large dimensions of the plates compared to the expected extension of the local effects of each single shot allowed us to exclude any interference among different shot-altered areas. the aisi 304l plates were tested at four different incidence angles (90°, 85°, 60°, 45°) with 2 replicates. as expected, none of the tested samples show any sign of penetration. the observation of all different samples shows how the projectile has been almost completely pulverized because of the impacts, especially at higher angles. traces of the bullet debris are clearly visible, with the epicenter characterized by the significant presence of residuals of the projectile (the brown/orange brass jacket of the bullet is particularly evident) accumulated in the curved surface of the plates. fig. 9 shows the aspect of the samples impacted at different angles impact angle. figure 9: impacted surface of the eight samples tested: left to right the four impact angle values: 90°, 85°, 60°, 45°. the two rows represent the two replicates of the shots. according to the evidence available from the debris collection screen positioned sideways to the plates, the rebound angle of the debris is practically neglectable compared to the incidence angle. all the samples show traces of the debris (fig. 9), clearly visible around the epicenter of the impact, for a radial distance of about 50 millimeters. the epicenter shows significant presence of residuals of the projectile accumulated in the curved surface of the plates. it is also evident how the angle affects the deflection of the debris. the number of visible traces is around 102. the measurement has been carried out using a borletti mechanical comparator (with a sensibility of 10 micron) and a calibrated workbench. the results are collected in fig. 10. r. andreotti et alii, frattura ed integrità strutturale, 57 (2021) 223-245; doi: 10.3221/igf-esis.57.17 230 figure 10: maximum back-plate residual displacements in millimeters. micrographic analyses micrographic analyses were conducted to verify the microstructural condition of the permanently deformed plates near the impacts epicenter. for this characterization work, the samples were sectioned to check the cross section of the projectiletarget interaction zone, the cut was performed along the lamination direction. the micrographic analysis (fig. 12) shows that neither signs of penetration nor cracks are present in the section of the impacted samples. they also show no evident grain size or shape changes (fig. 14). no strain concentration zones can be observed, but a smooth and continuous deformation field. these results confirm the visual examination and the insufficient penetration capability of the chosen projectile associated with the 4 mm-thick aisi 304l plate under investigation. figure 11: sample cut for micrographic analysis. figure 12: 90° (50x magnification). the deformation field appears smooth all along the section without any relevant spall phenomenon even at the epicenter. the epicenter shows the residue of the brass jacket of the projectile. 1,2 1,8 3,1 3,3 3,9 4,1 4,4 4,8 0,0 1,0 2,0 3,0 4,0 5,0 6,0 45° 45° 60° 60° 85° 85° 90° 90° r e si d u a l  d is p la ce m e n t  [m m ] impact angle [deg] r. andreotti et alii, frattura ed integrità strutturale, 57 (2021) 223-245; doi: 10.3221/igf-esis.57.17 231 figure 13: 90° (200x magnification). at the epicenter, the residue of the brass jacket of the projectile is clearly visible. figure 14: 90° (1000x magnification). the grain size and shape at the epicenter of the impact does not show any variation compared to the original state of the material. micro-hardness analyses micro-hardness measurements were performed along the section of the plate across the impact zone; this can be considered an indicator of the amount of plastic strain collected by the samples. hardness is an empirical and punctual measure of the mechanical properties of the material and its value grows with the amount of plastic deformation locally collected by the hardening material. we defined a path all along the impact zone (fig. 15), at 200 micrometres depth from the impact surface to avoid the boundary effect and conducted forty measures along the path. five control measures were also taken in the undeformed zone (fig. 15). the micro-hardness profile of the 90-degrees impacted sample (fig. 16) is characterized by two peaks well over 300hv which are almost symmetrical with respect to the local minimum at 270hv, located in correspondence to the epicentre of the impact. the two peaks are 1.7 millimetres far from the epicentre. at farther distances from the epicentre the hv profile decreases gradually until the hv level reaches the values of the undeformed plate, which happens at around 15 millimetres far from the epicentre of the impact. analog hv profile characterizes the plate impacted at 85 degrees, with two peaks at around 300hv and a local minimum at the epicentre (fig. 17). the hv profiles of the plates impacted at 60and 45-degrees angle do not show evident peaks but a maximum value located at the epicentre (fig. 18 and fig. 19). it is evident how the peaks of hardness decrease as impact angle decreases. r. andreotti et alii, frattura ed integrità strutturale, 57 (2021) 223-245; doi: 10.3221/igf-esis.57.17 232 figure 15: path (blue line) all along which the micro hardness measures were taken. undeformed zone is marked orange. figure 16: micro-hardness profile for 90° impacts. two peaks well over 300hv are located symmetrically with respect to the relative minimum at 270hv, corresponding to the epicentre of the impact. these features give the hv distribution an m-shaped profile. figure 17: micro-hardness profile for 85° impacts. two peaks at around 300hv are located symmetrically with respect to the relative minimum at 230hv, corresponding to the epicentre of the impact. these features give the hv distribution an m-shaped profile. r. andreotti et alii, frattura ed integrità strutturale, 57 (2021) 223-245; doi: 10.3221/igf-esis.57.17 233 figure 18: micro-hardness profile for 60° impacts. no significant peaks are measured. the maximum value is 275hv, located at the epicentre of the impact. figure 19: micro-hardness profile for 45° impacts. no significant peaks are observed. the maximum value is 224hv, located at the epicentre of the impact. development of the numerical model he numerical models were developed according to the experimental evidence, characterized by high fragmentation of the bullet and a reasonably continuous field of plastic strain of the target as demonstrated by the micro-hardness measures. the simulations were conducted by means of the well-established explicit solver ls-dyna. a simplified finite element model for the splashing impactor the bullet is defined as a volume fraction of an 50x50x40 millimeter eulerian material reference system. the position and geometry of the impactor is initialized by means of a shell container representing the external faces of the bullet. the portion t r. andreotti et alii, frattura ed integrità strutturale, 57 (2021) 223-245; doi: 10.3221/igf-esis.57.17 234 of the eulerian mesh internal to the container is initialized with the material associated with the bullet, while the external volume is associated with void (fig. 20). figure 20: initial void mesh (yellow) and bullet geometry container (red) to initialize the position and shape of the impactor with ale formulation. the ale formulation allows the entire eulerian reference system to follow the center of mass of the bullet. the interaction between the impactor and the target is guaranteed by means of a penalty algorithm [10] (fig. 21). the material associated with the bullet is a homogeneous inviscid fluid defined as *mat_null [15] with a density value ρ0= 10090 kg/m3 to guarantee that the total mass associated to the bullet would equal the actual mass of the impactor (8 g). the compressibility of the fluid is regulated by a linear polynomial equation of state (*eos_linear_polynomial [15]) with all the coefficients being associated with zero value except for the elastic bulk modulus imposed equal to β = 45.8 gpa, a value representative of solid lead [16]. so that the pressure 𝑝 depends linearly on the variation of density as stated in eqn. (1). 0 1p           (1) figure 21: 60° impact. arbitrary lagrangian eulerian interaction between bullet (red) and solid mesh plate (green). finite element model of the plate the plates have been discretized as a 3d structured finite elements mesh, which motion field is described according to a lagrangian specification. being interested in the detailed analysis of the through-thickness stress and strain fields in the surroundings of the impact zone, we opted for a local model characterized by a highly structured 3d solid mesh composed by 6-nodes fully integrated hexahedral elements with homogeneous size, extended to include the entire impactor-target interaction zone (60mm x 60mm extension). the rest of the plate was instead simplified with shell elements. the structural continuity of the plate was then ensured by rigid connections between solid nodes and the corresponding shell nodes. to reduce the computational cost, a symmetry plane boundary condition was associated with the plane containing the bullet velocity direction and the direction normal to the sample surface. the shell plate boundary nodes are also constrained in the direction normal to the plate (fig. 22). r. andreotti et alii, frattura ed integrità strutturale, 57 (2021) 223-245; doi: 10.3221/igf-esis.57.17 235 figure 22: 3d representation of the finite element model of the plate. the blue surface represents the shell mesh, in green is represented the 3d solid mesh. red marks represent the rigid link to connect shell nodes to solid nodes at the interface between shell and solid meshes. constitutive model associated with aisi 304l the plates are associated with an elastic plastic material model implementing rate effect and damage (*mat_plasticity_with_damage [15]). the static parameters of the model are set as: density ρ = 7800 kg/m3, young modulus e = 200000mpa, poisson ratio ν =0.33, hardening modulus etan = 1508.4mpa, damage initiation strain eppf = 68.8%, numerical strain at break eppfr = 140% (for mesh size 0.2mm). the rate effect is implemented by means of the two empirical constants (d, q) that parameterize the cowper-symonds model (eqn. 2) that introduces the rate effect as a dimensionless coefficient acting on the static yield stress of the material (σ0) scaling it to the corresponding value (σ) at a generic strain-rate έ. the values of the parameters d = 100/s and q = 10 were taken from literature [17]. 1/ 0 1 q d                (2) convergency of the equivalent plastic strain field with increasing nodal density the mesh size of the 3d solid elements representing the interaction zone of the plate was set at 0.2 millimeters after a sensitivity study of the equivalent plastic strain peaks estimated with 90-degree impacts simulated with models of increasing nodal density (fig. 23). the sensitivity study showed a stabilization of the peak of equivalent plastic strain at the value of 0.4 with a nodal density of 5 nodes per millimeter. the impactor mesh size was then set to 0.5 millimeters to guarantee the convergence of the penalty contact between impactor and target. figure 23: sensitivity of the peak of equivalent plastic strain (ordinate) calculated with increasing nodal density (abscissa in nodes/mm). r. andreotti et alii, frattura ed integrità strutturale, 57 (2021) 223-245; doi: 10.3221/igf-esis.57.17 236 numerical simulation results and validation o verify the effectiveness of the model in predicting the effects of the impacts on the target, the simulation results have been compared to the experimental evidence in terms of maximum residual displacement and plastic strain. the plastic strain field collected by the real samples have been calculated from the micro-hardness profiles of the samples thanks to an empirical linear correlation (eq.3) between plastic strain and microhardness established by qiao et al. [13] for aisi 304l: 304 382 152l phv    (3) from which, by reversing the correlation: 304 152 382 l p hv    (4) where εp is the plastic strain and hv304l is the measure of vickers micro-hardness. 90-degree impact the simulation of the 90-degree impact shows the progressive deformation of the impactor (fig. 24: ), with the mass of fluid representing the debris of the bullet flowing radially from the impact point. at the end of the simulation time, a small part of the impactor mass is accumulated at the epicenter of the impact, compatibly with the experimental evidence. the equivalent plastic strain field predicted by the simulation is characterized by a peak of plastic deformation at around 2 millimeters from the epicenter. the calculated equivalent plastic strain field (fig. 26 and fig. 27) to the plastic strain extrapolated from the experimental micro-hardness values shows good adherence of the results with a slight overestimation of the peaks and a slight underestimation of the plastic strain field in the peripherical area. the residual displacement of the plate is estimated as 3.6 millimeters (fig. 25), about 22% underestimated with respect to the average value of the displacements measured on the two experimental replicates (fig. 10). figure 24: dynamic interaction between bullet and plate. from left to right four frames showing the progressive deformation of the impactor and target from initial contact time at 0.0045 milliseconds to the stabilization of the plate at 0.2 milliseconds (time scale in seconds). t r. andreotti et alii, frattura ed integrità strutturale, 57 (2021) 223-245; doi: 10.3221/igf-esis.57.17 237 figure 25: field of residual resultant displacement of the plate at the end of the 90-degree impact. figure 26: field of equivalent plastic strain at the end of the 90-degree impact simulation. figure 27: equivalent plastic strain field at 0.2 millimeters beneath the impact surface as calculated by means of simulation (continuous line) compared with the plastic strain values calculated form micro-hardness measures by means of the linear correlation taken from qiao et al. [13]. abscissa values represent the coordinate along the section of the plate in millimeters. ‐0,050 0,000 0,050 0,100 0,150 0,200 0,250 0,300 0,350 0,400 0,450 0,0 5,0 10,0 15,0 20,0 25,0 30,0 35,0 fe_eqplstrain_90deg plstrain_90deg r. andreotti et alii, frattura ed integrità strutturale, 57 (2021) 223-245; doi: 10.3221/igf-esis.57.17 238 85-degree impact similarly, the simulation results of the 85-degree impact show an equivalent plastic strain show two peaks of plastic deformation at around 2 millimeters from the epicenter. the calculated equivalent plastic strain field (fig. 30 and fig. 31 ) compared to the plastic strain values extrapolated from the experimental micro-hardness profile shows good adherence of the results with an overestimation of the peaks and a slight underestimation of the plastic strain field in the peripherical area. the residual displacement of the plate (fig. 29) is estimated as 3.5 millimeters, about 13% underestimated with respect to the average value of the displacements measured on the two experimental replicates (fig. 10). figure 28: dynamic interaction between bullet and plate. from left to right four frames showing the progressive deformation of the impactor and target from initial contact time at 0.005 milliseconds to the stabilization of the plate at 0.2 milliseconds (time scale in seconds). figure 29: field of residual resultant displacement of the plate at the end of the 85-degree impact. r. andreotti et alii, frattura ed integrità strutturale, 57 (2021) 223-245; doi: 10.3221/igf-esis.57.17 239 figure 30: field of equivalent plastic strain at the end of the 85-degree impact simulation. figure 31: equivalent plastic strain field at 0.2 millimeters beneath the impact surface as calculated by means of simulation (continuous line) compared with the plastic strain values calculated form micro-hardness measures by means of the linear correlation taken from qiao et al. [13]. abscissa values represent the coordinate along the section of the plate in millimeters. 60-degree impact at 60-degree impact angle, the simulation still shows two peaks of plastic deformation at around 1.5 millimeters from the epicenter whereas the experimental curve appears smooth, without any significant peak, with maximum values around 23%, i.e. about 30% lower than the maximum peak estimated by the simulation (fig. 34 and fig. 35). still, the simulation slightly underestimates the plastic deformation in the peripherical area. the residual displacement of the plate (fig. 33) is estimated as 2.6 millimeters, about 20% underestimated with respect to the average value of the displacements measured on the two experimental replicates (fig. 10). ‐0,050 0,000 0,050 0,100 0,150 0,200 0,250 0,300 0,350 0,400 0,450 0,500 0,0 5,0 10,0 15,0 20,0 25,0 30,0 35,0 fe_eqplstrain_85deg plstrain_85deg r. andreotti et alii, frattura ed integrità strutturale, 57 (2021) 223-245; doi: 10.3221/igf-esis.57.17 240 figure 32: dynamic interaction between bullet and plate. from left to right four frames showing the progressive deformation of the impactor and target from initial contact time at 0.003 milliseconds to the stabilization of the plate at 0.2 milliseconds (time scale in seconds). figure 33: field of residual resultant displacement of the plate at the end of the 60-degree impact. figure 34: field of equivalent plastic strain at the end of the 60-degree impact simulation. r. andreotti et alii, frattura ed integrità strutturale, 57 (2021) 223-245; doi: 10.3221/igf-esis.57.17 241 figure 35: equivalent plastic strain field at 0.2 millimeters beneath the impact surface as calculated by means of simulation (continuous line) compared with the plastic strain values calculated form micro-hardness measures by means of the linear correlation taken from qiao et al. [13]. abscissa values represent the coordinate along the section of the plate in millimeters. 45-degree impact the 45-degree impact the simulation still predicts two peaks of plastic deformation at around 2.0 millimeters from the epicenter whereas the experimental curve is smooth without showing any significant peak. the maximum peak estimated by the simulation reaches 33.4%, whereas the maximum experimental value is around 11.4%. thus, in the 45-degree case, the plastic strain profile estimated by the simulation is much more severe than the real one in the surroundings of the epicenter but still underestimated in the peripherical area (fig. 38 and fig. 39). the residual displacement of the plate is estimated as 1.6 millimeters (fig. 37), about 8% overestimated with respect to the average value of the displacements measured on the two sample replicates (fig. 10). figure 36: dynamic interaction between bullet and plate. from left to right four frames showing the progressive deformation of the impactor and target from initial contact time at 0.003 milliseconds to the stabilization of the plate at 0.2 milliseconds (time scale in seconds). spurious energy erosion and velocity correction the ale formulation is characterized by a well-known intrinsic drawback, which consists in a spurious dissipation of the kinetic energy of the ale material while encountering movements through the reference mesh[10]. this is due to the systematic error of the so-called advection algorithm that updates the velocity of the material moving through the ale ‐0,050 0,000 0,050 0,100 0,150 0,200 0,250 0,300 0,350 0,400 0,0 5,0 10,0 15,0 20,0 25,0 30,0 fe_eqplstrain_60deg plstrain_60deg r. andreotti et alii, frattura ed integrità strutturale, 57 (2021) 223-245; doi: 10.3221/igf-esis.57.17 242 mesh. this causes the reduction of the available impact energy during the interaction phase between impactor and target as much as the material associated with the bullet encounters deformation. anyway, this intrinsic problem can be easily quantified and overtook by analyzing the decay of the total energy during the interaction time of the impact, while the impactor transfers momentum to the target. for a soft impactor, the characteristic interaction time can be estimated as the time needed for the impactor to travel a distance equal to its length in the direction of movement. in the considered case the bullet is 15 millimeters long and travels at 322 m/s, therefore the interaction time is 46.6 microseconds. during this time, the total energy of the simulation encounters a reduction of 37% (fig. 40), which is only due to the progressive reduction of velocity of the impactor during its deformation. the average kinetic energy available to the impactor during the interaction time is then reduced by 18.5%. figure 37: field of residual resultant displacement of the plate at the end of the 60-degree impact. figure 38: field of equivalent plastic strain at the end of the 85-degree impact simulation. therefore, this phenomenon can be quantified and corrected by means of an increase of the initial speed of the impactor. in our case the initial energy must be increased by a factor 1/0.815 = 1.226 which can be done by correcting the initial speed of the impactor by a factor 1.11. this way the energy effectively available to the impactor during the interaction phase will be correct even if slightly higher in the first half of the interaction phase and slightly lower in the second half. the results of the simulations with the corrected initial speed of the impactor show a clear improvement in the prediction of the residual displacements, as displayed in fig. 41. r. andreotti et alii, frattura ed integrità strutturale, 57 (2021) 223-245; doi: 10.3221/igf-esis.57.17 243 figure 39: equivalent plastic strain field at 0.2 millimeters beneath the impact surface as calculated by means of simulation (continuous line) compared with the plastic strain values calculated form micro-hardness measures by means of the linear correlation taken from qiao et al. [13]. abscissa values represent the coordinate along the section of the plate in millimeters. figure 40: decrease of the total energy of the simulation during the interaction time (in seconds). figure 41: comparison between experimental and numerical residual displacements. light blue and orange lines represent the minimum and maximum experimental displacements. the grey line represents the average of the experimental results. the yellow line represents the results of the simulations without initial velocity correction. the dark blue line represents the simulation results with initial velocity corrected. ‐0,050 0,000 0,050 0,100 0,150 0,200 0,250 0,300 0,350 0,400 0,0 5,0 10,0 15,0 20,0 25,0 30,0 35,0 fe_eqplstrain_45deg plstrain_45deg 1,63 2,54 3,45 3,56 2,12 3,30 4,49 4,63 0 1 2 3 4 5 6 45° 60° 85° 90° m a xi m u m  r e si d u a l d is p la ce m e n t  [m m ] impact angle [deg] inox 1 inox 2 inox avg fem fem vcorrected r. andreotti et alii, frattura ed integrità strutturale, 57 (2021) 223-245; doi: 10.3221/igf-esis.57.17 244 conclusions he study investigated the effects of bullet splash phenomena with the aim of developing and validating a simplified finite element model to be of practical use in the industry to simulate and optimize the response of protective structural systems subjected to splash bullet impacts. the ballistic tests were conducted on 4-millimeter thick aisi 304l plates, shot by 9x21 fmj bullets at various incidence angles (90°, 85°, 60°, and 45°). the visual analysis of the impact surface and the debris collection screen confirmed the complete fragmentation of the bullets with most of its mass being separated in small fragments and deflected by the target surface. according to the traces visible on the target and the number of holes reported by the collection screen, the number of fragments was estimated in the order of 102. the residual displacements measured on the plates range from 4.6mm at 90° to 1.5mm at 45°. the micrographic analyses of the plates section near the impact epicenter show a smooth deformation field with no evident signs of grain distortion. to catch the plastic strain field across the section of the plates subjected to the impacts, forty microhardness measures were taken at 0.2mm depth from the impact surface. the microhardness profiles show two different shapes depending on the acuteness of the impact angle. at 90° and 85° the microhardness distributions show an m-shaped profile, with of two peaks at a reciprocal distance of about 3 mm, with a relative minimum in the middle, corresponding to the position of the epicenter of the impact. at 60° and 45° angles the microhardness profiles are smoother, like bell curves, with no evident peaks and the maximum value located at the epicenter of the impacts. based on these observations, the simplified numerical model was conceived on the assumption that the effects of the splashing impacts on the target are mostly due to the initial shape, inertia, and compressibility of the impactor, so that the impacts can be simulated as a fluid structure interaction, similarly to what is already being done in the industry to simulate ‘soft’ impacts like bird strikes or hail strikes. the simulation model was created based on the arbitrary lagrangian eulerian (ale) formulation, which allows to simulate very effectively the large deformation of the impactor with good stability of the calculation. the results of the simulations in terms of plastic strain showed a good adhesion with the microhardness profiles of the plates. the simulation was able to predict the m-shaped plastic strain curve across the impact area, and the linear correlation between microhardness measures and plastic strain field allowed to quantitatively compare the predicted and experimental plastic strain fields, showing a very good prediction at 90° and a progressively growing overestimation of the plastic strain peaks as the impact angles decrease. on the contrary, the simulation tends to slightly underestimate the effects of the impacts in the area exceeding the diameter of the bullet, where the samples show local peaks of plastic deformation due to the impacts and deflection of the fragments of the lead core and brass jacket. the residual displacement estimated by the simulations compared to the measurements show an underestimation of the displacements filed of about 20% at higher angles. this is due to the spurious energy erosion intrinsic to the ale formulation. this problem can be effectively solved by introducing a correction coefficient to the initial velocity of the bullet. all the above confirm that the major simplifications introduced to model the bullet splash phenomenon are compatible with a reasonably accurate prediction of both local and global effects of the impacts. provided that the hypotheses of bullet splash are verified and the energy loss due to the advection algorithm is kept under control, the model can be effectively used in a conservative way to estimate the global effects of ballistic impacts on protective structural systems. the validation of the results shows that the model overestimates the local effects of the impacts at low angle, probably since the impactor is modelled as a mass of inviscid fluid, so it underestimates the actual energy dissipations due to the bullet fragmentation and deformation. possible improvements and developments to the model can be put in place by testing a simplified pre-fragmented formulation to overcome the spurious energy loss and repeating the same experimentation with other types of real impactors and targets. acknowledgements his paper resumes some of the results of the research project started in 2016 and led by marco v. boniardi (politecnico di milano) in collaboration with reparto investigazioni scientifiche (ris) of carabinieri in rome, italy and callens® area3. all the ballistic tests took place at ris’s shooting gallery in rome and were conducted by the carabinieri technicians. riccardo andreotti and mauro quercia were responsible for all the modelling and numerical simulation activities. andrea casaroli has conducted all the experimental, chemical, and metallurgical analyses. riccardo t t r. andreotti et alii, frattura ed integrità strutturale, 57 (2021) 223-245; doi: 10.3221/igf-esis.57.17 245 fossati collaborated to the experimental activities between 2016 and 2017 and developed his master’s degree thesis on the subject. references [1] heimbs, s. (2011). computational methods for bird strike simulations: a review, comput. struct., 89(23–24), pp. 2093– 112, doi: 10.1016/j.compstruc.2011.08.007. [2] anghileri, m., castelletti, l.m.l., invernizzi, f., mascheroni, m. (2005). a survey of numerical models for hail impact analysis using explicit finite element codes, int. j. impact eng., 31(8), pp. 929–44, doi: 10.1016/j.ijimpeng.2004.06.009. [3] parker, s.p. (2003). bullet splash. available at: https://encyclopedia2.thefreedictionary.com/bullet+splash. [accessed may 29, 2021]. [4] edgerton, h.e., jussim, e., kayafas, g. (1987). stopping time: the photographs of harold edgerton, new york, h.n. abrams. [5] iqbal, m.a., diwakar, a., rajput, a., gupta, n.k. (2012). influence of projectile shape and incidence angle on the ballistic limit and failure mechanism of thick steel plates, theor. appl. fract. mech., 62(1), pp. 40–53, doi: 10.1016/j.tafmec.2013.01.005. [6] yunfei, d., wei, z., guanghui, q., gang, w., yonggang, y., peng, h. (2014). the ballistic performance of metal plates subjected to impact by blunt-nosed projectiles of different strength, mater. des., 54, pp. 1056–1067, doi: 10.1016/j.matdes.2013.09.023. [7] camacho, g.t., ortiz, m. (1996). computational modelling of impact damage in brittle materials, int. j. solids struct., 33(20–22), pp. 2899–2938, doi: 10.1016/0020-7683(95)00255-3. [8] pandolfi, a., ortiz, m. (2002). an efficient adaptive procedure for three-dimensional fragmentation simulations, eng. comput., 18(2), pp. 148–59, doi: 10.1007/s003660200013. [9] bresciani, l.m., manes, a., romano, t.a., iavarone, p., giglio, m. (2016). numerical modelling to reproduce fragmentation of a tungsten heavy alloy projectile impacting a ceramic tile: adaptive solid mesh to the sph technique and the cohesive law, int. j. impact eng., 87, pp. 3–13, doi: 10.1016/j.ijimpeng.2015.10.003. [10] day, j. (2009). guidelines for ale modeling in ls-dyna, . [11] smojver, i., ivančević, d. (2011). bird strike damage analysis in aircraft structures using abaqus/explicit and coupled eulerian lagrangian approach, compos. sci. technol., 71(4), pp. 489–98, doi: 10.1016/j.compscitech.2010.12.024. [12] gabrys, j., schatz, j. (2004).the use of ls-dyna in the columbia accident investigation and return to flight activities. 8th international ls-dyna users conference, detroit, lstc, pp. 1–10. [13] qiao, d., zhang, w., pan, t.y., crooker, p., david, s., feng, z. (2013). evaluation of residual plastic strain distribution in dissimilar metal weld by hardness mapping, sci. technol. weld. join., 18(7), pp. 624–630, doi: 10.1179/1362171813y.0000000144. [14] gooch, g., williams, m. (2014). bullet splash. available at: https://www.oxfordreference.com/view/10.1093/oi/authority.20110803095534946. [accessed may 29, 2021]. [15] lstc. (2015). ls-dyna r8.0 keyword user’s manual volume ii material models, vol. ii. [16] gale, w.f., totemeier, t.c. (2004).15 elastic properties, damping capacity and shape memory alloys. smithells metals reference book (eighth edition) eighth edition, oxford, butterworth-heinemann, pp. 15–45. [17] nordberg, h. (2004). note on the sensitivity of stainless steels to strain rate, avestapolarit res. found., 1(04), pp. 1– 10. microsoft word numero_55_art_23_2974 p. mendes et alii, frattura ed integrità strutturale, 55 (2021) 302-315; doi: 10.3221/igf-esis.55.23 302 a brief review of fatigue design criteria on offshore wind turbine support structures p. mendes, j.a.f.o. correia, a.m.p. de jesus construct & inegi, university of porto, faculty of engineering, portugal pjmendes@fe.up.pt, https://orcid.org/0000-0002-8588-4807 jacorreia@fe.up.pt, https://orcid.org/0000-0002-4148-9426 ajesus@fe.up.pt, https://orcid.org/0000-0002-1059-715x b. ávila, h. carvalho federal university of minas gerais, brazil biancavieiraavila@gmail.com, http://orcid.org/0000-0003-0630-7487 hermes@dees.ufmg.br, https://orcid.org/0000-0002-4652-8068 f. berto ntnu – norwegian university of science and technology, department of mechanical and industrial engineering, norway filippo.berto@ntnu.no, https://orcid.org/0000-0001-9676-9970 abstract. in this paper, a brief review of the main fatigue design criteria and some advanced fatigue approaches applied to offshore structures (e.g. offshore wind turbines) are presented. it is extremely important to understand the fatigue phenomenon and how it affects structures since offshore structures are constantly submitted to cyclic loading and corrosive attacks that aggravate the problem. all the influencing factors and approaches used during the design phase are also discussed. keywords. fatigue; life extension; design codes; offshore wind turbines; support structures. citation: mendes, p., correia, j.a.f.o., de jesus, a.m.p., ávila, b., carvalho, h., berto, f. a brief review of fatigue design criteria on offshore wind turbine support structures, frattura ed integrità strutturale, 55 (2021) 302-315. received: 02.12.2020 accepted: 24.12.2020 published: 01.01.2021 copyright: © 2021 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. introduction espite taking into consideration the effect of environmental loads, as wind loads, wave loads, current loads, and water levels in the design of offshore wind turbines, the structural breakdown will probably occur due to fatigue damage before its extreme failure from loads [1]. in these structures, fatigue is related to cyclic loading and continuous dynamic loading, environmental factors such as corrosion can also contribute to a faster collapse. therefore, the fatigue design of offshore structures is based on the assessment of each individual member, so a fatigue reliability design d https://youtu.be/rczerf5-khm p. mendes et alii, frattura ed integrità strutturale, 55 (2021) 302-315; doi: 10.3221/igf-esis.55.23 303 becomes mandatory in offshore tubular joints due to the concentration of stress in the connection region [2]. this analysis should be applied in order to minimize the costs in the useful life of an onor off-shore tubular member, considering inspections, maintenance, and repairs [3]. currently, there are many design recommendations, such as the dnvgl [4] and api [5] recommendations, which present estimation methods to assess the damage and estimate the service life due to the fatigue of an offshore tubular member. dong et al. [6,7] carried out a fatigue study on multiplanar welded tubular joints on an offshore wind turbine of the jacket type and the dynamic response of the structure due to wind and wave loads was also evaluated. dong et al. [7] normalize load histories to ensure that the fatigue design requirements are based on the sn-palmgren-miner approach. an important point identified in this work is that the authors also considered an increased rate of corrosion-induced crack growth. alati et al. [8] presented a comparative study of the fatigue performance in offshore wind turbines (owt) structures of the jackets type in waters of intermediate depth. the fatigue behaviour was evaluated in the time domain under a combined stochastic load of wind and wave loads. yeter et al. [9] performed an analysis of the structural integrity of the support structure in various loading scenarios for different operational modes. the authors used the weibull distribution of two parameters to adjust the long-term statistical distribution of voltage ranges for critical points of representative environmental conditions in the operating conditions of the wind turbine. colone et al. [10] investigated the impact of turbulence-induced loads and kinematic wave models in the assessment of fatigue reliability on offshore monopile wind turbines. this research focused on the study of the effects of uncertain marine environments on the distribution of the fatigue load. biswal and mehmanparast [11] performed an estimation of the fatigue life in monopile structures and the fatigue damage analysis was performed on the weld joints, using the finite element method. the s-n fatigue design approach and the maximum stress range in the weld were used to determine the fatigue crack life in monopiles. a study of fatigue assessments in the time domain was carried out by chian et al. [12], using the monte carlo sampling method, in addition to stochastic processes that were considered to simulate wind and wave loads. peeringa [13], demonstrated that the wave-current interaction must be taken into account for the load calculations of the fatigue project of owt structures. teixeira et al. [14] evaluated statistics data on the extrapolation of fatigue loads to the tower and the influence of environmental parameters on short-term damage, a sensitivity analysis was conducted to assess which of the five environmental variables evaluated were most prominent in quantifying the damage uncertainty of the turbine. horn and leira [15] investigated the impact on the estimated life of an offshore wind turbine through the introduction of a stochastic model. an incremental damage model of two scales was proposed by rocher [16], in order to follow the temporal evolution of the damage caused by fatigue. fatigue assessments of offshore wind turbine support structures have also been proposed in the literature considering realistic environmental conditions [17], economic-tracking nmpc [18], and a parallel scheme [19]. offshore structure types ffshore structures are divided into fixed and floating structures. inside these two types of structures, there is a different wide of models for platforms. determining which type of structure fits the best depends on various factors as water depth, role, and functionality [2,20]. floating structures the floating structures may be grouped as neutrally buoyant and positively buoyant (buoyant is the ability of something to float). the neutrally buoyant structures include spars, semi-submersible modus (mobile offshore drilling unit), and fpss (floating production systems), ship-shaped fpsos (floating production and storage systems) and drill-ships. positively buoyant structures, such as the tension leg platforms (tlps) and tethered buoyant towers (tbts) or buoyant leg structures (bls) are tethered to the seabed and are heavy-restrained. the sizing of floating structures is dominated by considerations of buoyancy and stability. topside weight for these structures is more critical than it is for a bottom-founded structure [21]. some of the examples of floating structures can be seen in fig. 1. fixed structures loads in fixed offshore structures are directly transmitted to the foundation members and these elements are, generally, welded steel tubular members. these platforms have rigid behaviour and must withstand all the dynamic environmental forces. of the most commonly known types of fixed structures, there are gravity base structures that use their own weight to remain stable when subjected to stresses on the structure, guyed towers but the most common type of offshore platform o p. mendes et alii, frattura ed integrità strutturale, 55 (2021) 302-315; doi: 10.3221/igf-esis.55.23 304 is fixed, pile-supported steel template platform, often called a jacket. for wind turbines, the supporting structures are composed of limbs deep-immersed steel or concrete pipes filled with high-density materials [21]. monopiles are the most commonly used type of support for wind turbines due to their design simplicity and suitability for shallow waters. also, they are composed by tubular steel members with huge diameter and thickness. jacket type structures are usually composed of tubular members interconnected, shaping a tridimensional spacial structure allowing the application of them in higher water depths. since there are joints in these structures, it is necessary to deepen the studies in this area during the design phase because most of the failures are due to fatigue. [21,23]. examples of fixed offshore structures are shown in fig. 2. figure 1: types of offshore wind turbine foundations [22]. figure 2: examples of fixed offshore structures [5]. the design of offshore structures is based on the conditions and environmental aspects in which the structure is submitted. for the static analysis, an offshore structure can be submitted to permanent loads as dead weight and equipments, gravity loads, live loads, and hydrostatic loads. dynamic loads are, generally, originated by environmental loads: wind loads, wave loads, current loads, ice loads, snow loads, earthquake loads, and other environmental loads. environmental loads are studied with more detail since the evolution of cracks in these structures are due to then [2,20,21,23]. wind wind-induced loads are often treated as time-invariant and wind acts in a direction normal to the surface of the structure. in cases of large windswept surface, the frictional forces due to tangential drag must also be considered [24]. the strength of wind, in a circular structural member, acting normal to the member surface is calculated by: p. mendes et alii, frattura ed integrità strutturale, 55 (2021) 302-315; doi: 10.3221/igf-esis.55.23 305   2 1 sin 2 w d wf c au (1) where:  is the mass density of air;    wu is the wind velocity averaged over a time interval t at a height z meter above the mean water level or onshore ground; dc is the shape coefficient; a is the projected area of the member normal to the direction of the force; and  is the angle between the direction of the wind and the axis of the exposed member or surface. the aerodynamic study in offshore wind turbine structures is of great importance because the marine environment provides winds of greater speed and consistency, less turbulence and less shear which, in addition, are used in this study to evaluate aerodynamic damping, since they are slender structures and, as said, subjected to high wind loads [25]. liu et al. [26], present an analysis of a model of aerodynamic damping for wind turbine blades and wind turbine blades have been found to undergo significant vibrations and deflections during operation so the aerodynamic damping considerably affects the structural response of the blades. liu et al. [25] also carried out an analysis that combines aerodynamics, hydrodynamics and structural dynamics of the structure and includes the effects of aerodynamic damping, but this time for the entire wind tower, with the aim for a better understanding of the role of aerodynamic damping during interaction of wind and waves in the structure. in addition, the influence of different methods to calculate aerodynamic damping on the prediction of fatigue loads is studied. li et al. [27] investigated the effect of the wind field on power generation and the aerodynamic performance of offshore floating wind turbines and for this purpose, three types of wind fields were studied: a uniform wind field, a constant wind field with shear and a turbulent wind field. it was observed that the final structural and fatigue loads at the blade root were increased by the turbulence of the flow and by the wind shear. waves due to the random nature of ocean waves, in height, shape, direction, length, and speed of propagation, the state of the sea is best described in a random wave model. however, waves can take the form of a regular wave. these waves have the characteristics of a period such that each cycle has exactly the same shape. several theories have been developed to simplify the use of wave calculations. the wave conditions considered in the design of the offshore structures, can be described using deterministic methods or by stochastic methods. in structures with the quasi-static response the use of deterministic regular waves is sufficient but structures with significant dynamic response need more accurate studies, so in this way, stochastic modelling of the sea is more appropriate [21,24]. the linear model, developed by airy, is the simplest theory of waves and, currently, the most precise for waves of small amplitude [28] (skjelbreia and hendrickson, 2011). it is considered that the height of the wave is much shorter than the wave length and the depth of the water. for the airy wave theory, the waves have sinusoidal shapes, where the free surface profile is described by the formula:    cos 2 h kx t (2) where: h is the height of the wave; k=2π/l is the wave number; l is the wave length; x is the position of the wave; ω=2π/t is the wave frequency; t is the wave period; and, t is the instant of a duration of the wave. in cases where the wave amplitude is not small or for high values of wave inclination, and linear theories do not reach an adequate degree of precision, nonlinear theories are adopted as the theories of stokes, cnoidal or solitary. stokes' theory assumes that any variation in the x-direction can be represented by the fourier series, which can be written as disturbance expansions that increase with the wave height [29]. in this way, the wave velocity potential and the wave surface profile can be represented respectively, by the following equations:           1 , ,  sin   m n n n b h t d n kx t (3)          1 , ,  cos   m n n n a f h t d n kx t (4) p. mendes et alii, frattura ed integrità strutturale, 55 (2021) 302-315; doi: 10.3221/igf-esis.55.23 306 where: m is the considered order; bn and an are initially unknown functions that depend on the boundary conditions. using these series, any order of approximation for stokes' theory can be obtained, and this one used in the first order is identical to a linear wave [24]. for example, the wave surface profile in second-order theory can be obtained from the equation:                   2 3 cosh cos   2 cosh 2 cos 2 2 8 sinh kdh h kx t kd kx t l kd (6) selecting the wave theory applicable to an offshore structure model is an essential step in a hydrodynamic analysis. the nonlinearity of the waves and the depth of the water are two keywords in the hydrodynamic analysis for fixed and floating wind turbines since offshore wind farms are generally implanted in areas of relatively shallow water, where the waves become more non-linear and lead to a considerable increase in hydrodynamic loads [30]. cheng et al. [31] analysed a numerical model with second-order wave effects for aero-hydrodynamic analysis of floating offshore wind turbines. marino et al. [32] evaluated the structural response of an offshore wind turbine subjected to two wave models: linear and non-linear, and observed that when the turbine is parked, the linear wave modelling approach significantly underestimates fatigue loads. stokes' fifth-order model has been used due to good results regarding the actual representation of water particles. chen et al. [33] used stoke's fifth-order nonlinear theory to represent regular waves in an analysis of static and dynamic loading behaviour in offshore wind turbines. li et al. [34] verified the influence of different water depths on the structural behaviour induced by non-linear waves. the effect of wave non-linearity due to the kinematics of non-linear waves was quantified by xu et al. [30]. the structural responses of the floating wind turbine were compared when exposed to irregular linear aerial waves and totally non-linear waves. morison’s equation morison's equation is applied when it's needed to transform wave kinematics into hydrodynamic forces. morison's load formula is applied when the λ>5d ratio is met, λ is the wave length, and d is the cross-sectional dimension of the member [24]. for fixed structures in waves and currents the hydrodynamic force is calculated according to the equation:          1 1 2 n a df t c av c dv v (6) where:  v is the fluid particle (waves and/or current) velocity (m/s); v is the fluid particle acceleration (m/s2); a is the cross-sectional area in (m2); d is the diameter or typical cross-sectional dimension (m);  is the mass density of the fluid (kg/m3); ac is the added mass coefficient; and dc is the drag coefficient. both coefficients, ac and dc , vary with the reynolds number and the keulegan-carpenter number. other types of loads other environmental loads can be studied according to the occurrence and necessity as, current loads due to tides, storms, and atmospheric variations. in places like the artic, where it's expected the presence and formation of ice, the distribution and concentration of ice must be considered. earthquakes should also be considered if platforms are located in a seismically active zone [24]. environmental effects on fatigue projects arine environments provide immersed steel structures corrosive attacks that influence directly the performance and the fatigue design of a tubular member. when corrosion appears in a structure, there is a reduction in the effective section area that consequently raises the applied stress levels and decreases the lifespan of the whole structure. the interaction between the corrosive environment and the cyclic mechanical loading generally results in a m p. mendes et alii, frattura ed integrità strutturale, 55 (2021) 302-315; doi: 10.3221/igf-esis.55.23 307 significant increase in the rate of crack growth, as compared to a non-corrosive environment, which further reduces the overall fatigue life [35]. there are two mechanisms associated with the corrosion effects that when started aggravate the initiation process of cracks. in the first mechanism, there is localized corrosion -pitting-, which constitutes the formation of corrosion pits that act as micro-notches locally increasing the stress level. in the second mechanism, corrosive environments may introduce hydrogen into the metal by the dissociation of hydrogen molecules into atomic hydrogen. under cyclic loading conditions, the resulting hydrogen embrittlement of the material may accelerate the initiation of surface flaws [35,36,37]. fig. 3 shows the common pit shapes. figure 3: common pit shapes [37]. fatigue design criteria present ifferent approaches can be used in the fatigue analysis but the decision of which method suits better depends on which structural details need to be considered. the fatigue life evaluation is based on the linear damage hypothesis (palmgren-miner’s rule) and in the s-n curves presented in the fatigue design recommendations as in dnvglrp-c203 [4], api [5], etc. [2,20]. an extensive study in a more considerable portion of the structure or a fracture mechanic approach analysis must be done when the crack is going to be fatal and if estimating the fatigue life based on the data of sn curves becomes insufficient or inappropriate [4]. in this section, the damage accumulation law and global fatigue design s-n curves are presented. the damage accumulation law called palmgren-miner [38] is a common method to estimate the fatigue life of structures submitted to a history of variable loads based on a series of fatigue stresses with constant amplitudes. palmgren-miner's rule [38] can be translated into eqn. 7:           1 1 1k k mi i ii i i n d n n a (7) where: d is the cumulative fatigue damage; ni is the number of cycles the structural detail endures at stress range,  i ; ni is the number of cycles to failure at stress range,  i ; i is the number of considered stress range intervals; k is the number of considered stress range intervals;  a is the intercept of the design s-n curve with the log 𝑁; m is the negative inverse slope of the s-n curve; and η is the usage factor given by the eqn. (8). it's possible to find in the literature several modifications of the palmgren-miner rule that have been suggested related to the damage rate and to the strength limits [39].   1 dff (8) where: dff is the design fatigue factor that can be found in section 6 of the dnvgl-os-c101 standard [40]. code's approach the s-n curves found in the technical recommendations are expressed in a bi-logarithmic scale, in which the fatigue strength is given by the number of cycles until failure (n) in function with the stress range (  ). wohler s-n curves consider a global approach and are used in the fatigue design of tubular joints. the fatigue strength in welded joints depends on the member thickness due to local geometric discontinuity in the weld toe in relation to the thickness of the adjacent plates [4]. d p. mendes et alii, frattura ed integrità strutturale, 55 (2021) 302-315; doi: 10.3221/igf-esis.55.23 308 the thickness effect in the fatigue resistance can also be explained with the modification of the stress range in a way that for a higher thickness compared with the referenced thickness, the s-n curve can be obtained through eqn. (9):                log log log k ref t n a m t (9) where: m is the negative inverse slope of s-n curve; log a is the interception of the log n-axis; tref is reference thickness equal to 25mm for welded connections other than tubular joints. for tubular joints the reference thickness is 32 mm; t is the thickness through which a crack will most likely grow, t=tref is used for thickness less than tref; k is the thickness exponent on a fatigue strength, where k is considered 0.1 for tubular butt welds made from one side and 0.25 for threaded bolts subjected to stress variation in the axial direction. the s-n curves for the tubular joints considering different environmental conditions are presented in fig. 4. figure 4: s-n curves for tubular joints in air environment, seawater with cathodic protection and free corrosion [4]. simplified approach the fatigue evaluation in tubular joints is essential to the design of offshore structures. the fatigue results will influence the structure reliability in various aspects but more precisely the residual stresses on a partially damaged structural system [39]. some principal methodologies will be approached to estimate the fatigue accumulated damage using s-n curves. the deterministic analysis is based on a limited number of waves with a specified height and period to all fatigue states. the selection of waves is based on the contribution of each sea state in the wave length dispersion diagram. these waves are assessed discretely and are combined such that they have the highest impact on fatigue damage. each of these specific waves is considered at various wave crest states. these crest wave states are combined in such a way that the maximum and minimum values of stress and consequently the range of stress in the members and joints of the structure are achieved. the fatigue damage ratio can be estimated after evaluating the hot-spot stress according to the number of occurrences of the waves for each period of time and using the palmgren-miner rule [41]. to the fatigue damage evaluation, the weibull distribution of two-parameters is used to analyse the distribution of stresses around the tubular joints. this methodology also uses the palmgren-miner rule allied to the s-n curves [4,42]. for continuous stress spectrum cases, the long-term stress range distribution might be defined applying the weibull distributions for the different load conditions and can be estimated using the following equation:                                 1 2 1 1 2 1 0 1 2 γ 1 ; γ 1 ; h hm m d q m s q m s d v t a h q a h q (10) p. mendes et alii, frattura ed integrità strutturale, 55 (2021) 302-315; doi: 10.3221/igf-esis.55.23 309 where:   dt is the design life in seconds; 0v is the average zero up-crossing frequency; n is the weibull stress range shape parameters; q is the weibull scale distribution parameters; 1s is the stress range for which change of slope of s-n curve occur; 1a and 1m are the s-n fatigue parameters for n<107 cycles (air conditions); 2a and 2m are the s-n fatigue parameters for n>107 cycles (air conditions); and, γ() and γ() are the incomplete gamma functions. in the long run, the stress distribution in the stress spectrum can be presented as a weibull distribution of two-parameters:                h q exp q (11) where: q is the probability of failure in the stress spectrum; h is the weibull shape parameter; q is the weibull scale parameter defined from the stress spectrum that can be estimated through:     0 1/ 0ln h q n (12) spectral fatigue analysis is used to evaluate the dynamic response of the structure to the wave height range and to the frequencies corresponding to the dispersion diagram. this structural response considerably includes all states of the influence of the waves in the damage caused by fatigue. the spectral dynamic analysis is based on the spectral (wave spectrum) density function in each sea state. sea waves are then modelled according to the wave dispersion diagram model as a set of sea states. therefore, in order to create a transfer function for spectral analysis, the expression for the nonlinear drag force in the morrison equation should be linearized with one of the proposed methods of the regulation such as the use of the steepness of the continuous wave [41]. spectral approach in the simplified fatigue approach, fatigue damage is estimated assuming that the stress follows a weibull distribution for a long-term response. due to the sensitivity of the estimated damage to fatigue in the weibull parameters, the spectral assessment of fatigue has become more popular in offshore structural analysis [39]. the spectral fatigue analysis method recognizes the stochastic nature of the marine environment to which the offshore structures are inserted. the spectral fatigue calculations start from the assumption that there is a relationship between the direction and frequency of the wave and the voltage response at a specific location. the function that performs this correlation is called the transfer function [39]. this technique is complex and numerically intensive, so there is more than one variant of the method that can be validly applied in a specific case. the method is appropriate when there is a linear relationship between the height of the wave and the loads compelled to the structure by the wave. adaptations were made to the basic method to supply the non-linearities, in these cases, the "time-domain analysis methods" is used in the evaluation of fatigue due to the limitations of the spectral method [5,39]. when the direction of the wave is considered in the definition of sea states, using the rayleigh distribution, the accumulated damage for all sea states can be calculated using eqn. (13).                  0 0 1,  1  γ 1 2 2 2 all seastates all headings m d ij ij i j v t m d r m a (13) where: rij is the relative number of stress cycles in short-term condition i, j; v0 is long-term average response zero-crossingfrequency; and, m0ij is zero spectral moment of the stress response process. advanced fatigue approaches several fatigue approaches based on local criteria, multiaxial criteria, static toughness, strain energy density, etc. have been proposed [43-56]. mourão et al. [43] proposed a global-local methodology based on a local approach using the strain fatigue damage parameter to assessing the fatigue damage accumulation. in his scientific work, the proposed methodology was applied for an offshore jacket-type platform [43]. other approaches has been used to evaluate the fatigue damage p. mendes et alii, frattura ed integrità strutturale, 55 (2021) 302-315; doi: 10.3221/igf-esis.55.23 310 accumulation based on isodamage curves through the exhaustion of static toughness as suggested by xia [44], as well as the strain energy density approach applied to ocean systems as proposed by zarandi and skallerud [45]. additionally, a generalized probabilistic model for various fatigue damage variables proposed by correia et al. [46] can also be used to assessing the fatigue damage accumulation [47]. analysis and stress concentration factors nominal, notch and hot-spot approach n welded joints, the fatigue strength is estimated through cyclic stress in the point of interest. there are several methods and approaches to determine the s-n curves: nominal, notch, and hot-spot approaches. in the nominal stress approach, the stresses are estimated without considering any stress concentration due to the local structural detail or due to the weld. this approach has some disadvantages primarily since it is impossible to establish reasonable nominal stress due to complex geometry and to the applied load, and secondly because fatigue strength tests aren't usually available for these types of complex joints in offshore structures [4]. the nominal stress can be determined using elementary theories of structural mechanics based on linear-elastic behaviour:   nom p m y a i (14) where: p is the force acting on cross-section; a is the cross-section area; m is applied bending moment; i is section inertia; and, y is the position of the extreme fibre. the hot-spot stress approach, different from the nominal stress approach, considers the stress raising effect due to structural discontinuity except the stress concentration due to weld toe, this means without considering the localized weld notch stress [57]. hot-spot is defined as the region in the joint where fatigue cracks are more susceptible to appear due to cyclic loading, meaning that hot-spot stress is the value of the stress in the surface of the hot-spot. radaj [58] demonstrated that the hotspot stress corresponds to the sum of the membrane and bending stresses at the weld toe, which can be determined through extrapolation [57,59]. according to dnvgl recommendations, notch stresses must be considered in special cases in which is hard to evaluate with assurance the fatigue strength using other methods. radaj [58] also demonstrated that the notch stress components can be divided from the non-linear stress: membrane stress (𝜎𝑚𝑒𝑚), bending stress (𝜎𝑏𝑒𝑛) and non-linear stress part (𝜎𝑛𝑙𝑝). the stress distribution through the thickness of the weld plate and its components are shown in fig. 5. figure 5: stress distribution through the thickness of the weld plate and its components [57]. stress concentration factor in tubular welded joints when geometry discontinuities are considered, consequently, there are changes in the stress field of these elements. this way, with higher points of stress, the structure is more suitable to fail. therefore, the stress concentration factor is used to evaluate this concentration ratio and it is defined as the ratio between the hot-spot stress (𝜎hot-spot), and the nominal stress (𝜎nom) [4].    hot spot nom scf (15) the dnvgl recommendations [4] present different parametric equations to obtain the scf based on efthymiou's researches, calculated in different points of the joint connection, taking into consideration different geometrical parameters. the stress concentration factor can be obtained analytically, numerically using the fe method and experimentally [4]. i p. mendes et alii, frattura ed integrità strutturale, 55 (2021) 302-315; doi: 10.3221/igf-esis.55.23 311 fracture mechanics approach crack growth due to fatigue he fracture mechanics approaches assume that all structural elements have defects and cracks, and, consequently, the design is based on the tolerance to these defects. thus, fracture mechanics is focused on calculating the number of cycles that a certain critical crack takes to achieve the final failure, in order to evaluate how long a structure or component can operate without having to be fixed [3,60,61]. there are three basic modes of fracture: mode i is the tensile opening mode and is characterized by the separation of crack faces in the direction perpendicular to the crack plane, mode ii is the in-plane shear mode and is the mode in which the crack faces are sheared in the direction parallel to the crack front face, mode iii is the transverse shear mode and, similarly to mode ii, in this mode, the crack faces are sheared, but this time in the direction perpendicular to the crack front face. the three basic modes of fracture are displayed below, respectively [3,60,62]. figure 6: (a) mode i; (b) mode ii; (c) mode iii [60]. it is assumed that compression doesn't influence crack propagation but since welded joints contain residual stresses, all the stress spectrums must be considered [4]. the crack propagation can be divided into three stages: the first is characterized by considerable low crack growth rates and in this region can be identified a value, known as the threshold, above which there is no crack growth; the second stage is the region known as "paris region", because the crack growth as a function of stress intensity can be defined by the following expression, which was proposed by paul paris:      mda c k dn (16) where: da/dn is the fatigue crack growth rate; c and m are constants obtained through experimental tests; and δk is the stress intensity factor range (δκ=kmax–kmin). the stress intensity factor, k, can be expressed as:  k g a (17) where: σ is the nominal stress on the normal member to the crack; g is the factor depending on the member geometry, weld, and crack geometry; and, a is the depth of the crack. the third phase is the last phase and is characterized by an unstable crack growth until the total failure. several studies to characterize the fatigue crack propagation behaviour considering corrosion [63], variable amplitude loading [64], crack closure effects [65], mixicity conditions [66], as well as, using local approaches [67,68, have been suggested. evaluation of the residual lifetime of structural components the availability of accurate fatigue crack propagation laws is the key to reliable fatigue life predictions of mechanical components or structural details. the most common use of the fracture mechanics based on fatigue crack propagation relations consists of residual fatigue life assessment of mechanical components or structural details containing initial known defects acting like cracks. this can be accomplished by integrating the crack propagation law, according to the following expression: t p. mendes et alii, frattura ed integrità strutturale, 55 (2021) 302-315; doi: 10.3221/igf-esis.55.23 312           , , , , f i a f a da da f k r n dn f k r (18) the main difficulty implied in this approach is the determination of the initial crack size for the crack growth analysis. one practical solution is using an empirically assumed crack length, such as 0.15–1 mm for metals whereby the assumption of such macro-crack could underestimate the fatigue life of the component. aeran et al. [69] suggested a framework to assess structural integrity of ageing offshore jacket structures for fatigue life extension. for situations in which crack growth near the threshold is significant, a less conservative form of paris law based on the effective value of k ,  effk , may be justified. in these circumstances, the relevant equation is the following:      m eff da c k dn (19)       0 1 eff k k k r (20)                 1 f i m a a r da c n k g a (21) where, c and 𝑚 are constants which depend on the material and the applied conditions, including environment and cyclic frequency. for k ≤  0k , /da dn is assumed to be zero. conclusion n offshore wind turbine support structure can be exposed to various factors that carry fatigue damage. the phenomenon of fatigue is one of the main causes of structural failure, which consists of the loss of strength due to the appearance of cracks in an element subjected to cyclic or dynamic loading. understanding the fatigue design phases, criteria and existing approaches is, therefore, of extreme importance for an effective and clear design of an offshore wind turbine support structure. in this paper, a brief overview of the fatigue design criteria and some advanced approaches that have been used in the assessment and analysis of support structures for oceanic systems are presented. acknowledgements his work was financially supported by: base funding uidb/04708/2020 and programmatic funding uidp/04708/2020 of the construct instituto de i&d em estruturas e construções funded by national funds through the fct/mctes (piddac). additionally, this research was also supported by the project grant (uta-expl/iet/0111/2019) sos-windenergy sustainable reuse of decommissioned offshore jacket platforms for offshore wind energy by national funds (piddac) through the portuguese science foundation (fct/mctes). this research study was also supported by the capes – print program (coordination for the improvement of personnel of graduation) and ufmg (universidade federal de minas gerais). references [1] ju, s.h., su, f.c., ke, y.p., xie m.h. (2019). fatigue design of offshore wind turbine jacket-type structures using a parallel scheme. renewable energy, 136, pp. 69-78. a t p. mendes et alii, frattura ed integrità strutturale, 55 (2021) 302-315; doi: 10.3221/igf-esis.55.23 313 [2] mendes, p., correia, j.a.f.o., mourão, a., pereira, r., fantuzzi, n., de jesus, a. and calçada, r. (2021). fatigue assessments of a jacket-type offshore structure based on static and dynamic analyses. practice periodical on structural design and construction, 26(1), 04020054. [3] dantas, r.g. (2019). fatigue life estimation of steel half-pipes bolted connections for onshore wind towers applications. msc thesis, university of porto, porto, portugal, 183 p. [4] dnv gl group. dnvgl-rp-c203 (2016). fatigue design of offshore steel structures. [5] api. recommended practice for geotechnical and foundation design considerations. rp 2geo. washington, d.c.: american petroleum institute; (2011). [6] dong, w.b., moan, t., gao, z. (2011). long-term fatigue analysis of multi-planar tubular joints for jacket-type offshore wind turbine in time domain. engineering structures, 33, pp. 2002-2014. [7] dong, w.b., moan, t., gao, z. (2012). fatigue reliability analysis of the jacket support structure for offshore wind turbine considering the effect of corrosion and inspection. reliability engineering and system safety, 106, pp. 11-27. [8] alati, n., nava, v., failla, g., arena, f., santini, a. (2014). on the fatigue behavior of support structures for offshore wind turbines. wind and structures, 18, pp. 117-134. [9] yeter, b., garbatov y., guedes soares, c. (2014). fatigue damage analysis of a fixed offshore wind turbine supporting structure. book: developments in maritime transportation and exploitation of sea resources, pp. 415-424. [10] colone, l., natarajan, a., dimitrov, n. (2018). impact of turbulence induced loads and wave kinematic models on fatigue reliability estimates of offshore wind turbine monopiles. ocean engineering, 155, pp. 295-309. [11] biswal, r., mehmanparast, a. (2019). fatigue damage analysis of offshore wind turbine monopile weldments. procedia structural integrity, 17, pp. 643-650. [12] chian, c.y., zhao, y.q., lin, t.y., nelson, b., huang h.h. (2018). comparative study of time-domain fatigue assessments for an offshore wind turbine jacket substructure by using conventional grid-based and monte carlo sampling methods. energies, 11, p.3112. [13] peeringa, j.m. (2014). fatigue loading on a 5mw offshore wind turbine due to the combined action of waves and current. journal of physics: conference series, 524. [14] teixeira, r., o’connor, a., nogal, m., krishnan, n., nichols, j. (2017). analysis of the design of experiments of offshore wind turbine fatigue reliability design with kriging surfaces. procedia structural integrity, 5, pp. 951-958. [15] horn, j.t., leira b.j. (2019). fatigue reliability assessment of offshore wind turbines with stochastic availability. reliability engineering and system safety, 191, 106550. [16] rocher, b., schoefs, f., françois, m., salou, a., caouissin, a.l. (2020). a two-scale probabilistic time-dependent fatigue model for offshore steel wind turbines. international journal of fatigue, 136, 105620. [17] li, x. and zhang, w. (2020). long-term fatigue damage assessment for a floating offshore wind turbine under realistic environmental conditions. renewable energy, 159, pp. 570-584. [18] luna, j., falkenberg, o., gros, s. and schild, a. (2020). wind turbine fatigue reduction based on economic-tracking nmpc with direct ann fatigue estimation. renewable energy, 147, pp. 1632-1641. [19] ju, s., su, f., ke, y. and xie, m. (2019). fatigue design of offshore wind turbine jacket-type structures using a parallel scheme. renewable energy, 136, pp. 69-78. [20] pereira, r.r. b. dynamic analysis and fatigue assessment of a jacket-type offshore platform. msc thesis, university of bologna, italy, 112 p. [21] chakrabarti, s. handbook of offshore engineering. elsevier, (2005). [22] european wind energy association: deep water: the next step for offshore wind energy. brussels, belgium: a report by the european wind energy association; (2013). [23] mendes, p. (2018). stress concentration factor evaluation in offshore tubular kt-joints for fatigue design. msc thesis, university of porto, porto, portugal, 120 p. [24] dnv gl group. dnv-rp-c205 (2010). environmental conditions and environmental loads. [25] liu, x., lu, c., li, g., godbole, a., chen, y. (2017). effects of aerodynamic damping on the tower load of offshore horizontal axis wind turbines. applied energy, 204, pp. 1101-1114. [26] liu, x., zhang, x., li, g., chen, y., ye, z. (2010). dynamic response analysis of the rotating blade of horizontal axis wind turbine, wind engineering, 34, pp. 543-560. [27] li, l; liu y; yuan, z; gao, y. (2018) wind field effect on the power generation and aerodynamic performance of offshore floating wind turbines. energy, 157, pp. 379-390. [28] skjelbreia, l; hendrickson, j. (2011) fifth order gravity wave theory. engineering proceedings, 7. [29] fenton, j. (1990). nonlinear wave theories. the sea, 9, pp. 3-25. p. mendes et alii, frattura ed integrità strutturale, 55 (2021) 302-315; doi: 10.3221/igf-esis.55.23 314 [30] xu, k., zhang, m., shao, y., gao, z., moana, t. (2019). effect of wave nonlinearity on fatigue damage and extreme responses of a semi-submersible floating wind turbine. applied ocean research, 91, 101879. [31] cheng, d., gao, p., huang, s., li, c., yu, x. (2020). static and dynamic loading behavior of a hybrid foundation for offshore wind turbines. marine structures, 71, 102727. [32] marino, e., giusti, a., manuel, l. (2017). offshore wind turbine fatigue loads: the influence of alternative wave modeling for different turbulent and mean winds. renewable energy, 102, pp. 157-169. [33] chen, p., huang, y., wan, d. (2019). a numerical model for fully coupled aero-hydrodynamic analysis of floating. ocean engineering, 173, pp. 183-196. [34] li, h., du, j., wang, s., sun, m., chang, a. (2016). investigation on the probabilistic distribution of mooring line tension for fatigue damage assessment. ocean engineering, 124, pp. 204–214. [35] bmt fleet technology, (2013). fatigue design review of offshore wind turbine generator structures. [36] prabhakar, s., goswami g. (2019). design, management and key success factors of an offshore cathodic protection system for corrosion control. international journal of engineering and management, 9, pp. 171-179. [37] bhandari, j., khan f., abbassi r., garaniya v., ojeda r (2015). modelling of pitting corrosion in marine and offshore steel structures a technical review. journal of loss prevention in the process industries, 37, pp. 39-62. [38] miner m.a. (1945). cumulative damage in fatigue. transactions of the asme. series e. j. appl. mech., 12, pp.159– 164. [39] bai y. (2003) marine structural design, elsevier, 634 p. [40] dnv gl group. dnvgl-os-c101 (2015). design of offshore steel structures, general lrfd method. [41] havigh s.n., askar m.b. (2017). the process of fatigue analysis on fixed metal offshore platforms. scientifc & academic 7, pp. 10-16. [42] mourão a. (2018). fatigue analysis of a jacket-type offshore platform based on local approaches. msc thesis, university of porto, porto, portugal, 139 pages. [43] mourão, a., correia, j.a.f.o., ávila, b.v., de oliveira, c.c., ferradosa, t., carvalho, h., castro, j.m. and de jesus, a.m.p. (2020). a fatigue damage evaluation using local damage parameters for an offshore structure. proceedings of the institution of civil engineers: maritime engineering, 173(2), pp. 43-57. [44] xia, f.-., zhu, s.-., liao, d., dantas, r., correia, j.a.f.o. and de jesus, a.m.p. (2020). isodamage curve-based fatigue damage accumulation model considering the exhaustion of static toughness. engineering failure analysis, 115, 104575. [45] zarandi, e.p. and skallerud, b.h. (2020). cyclic behavior and strain energy-based fatigue damage analysis of mooring chains high strength steel. marine structures, 70, 102703. [46] correia, j., apetre, n., arcari, a., de jesus, a., muñiz-calvente, m., calçada, r., berto, f. and fernández-canteli, a. (2017). generalized probabilistic model allowing for various fatigue damage variables. international journal of fatigue, 100, pp. 187-194. [47] fernández-canteli, a., blasón, s., correia, j.a.f.o. and de jesus, a.m.p. (2014). a probabilistic interpretation of the miner number for fatigue life prediction. frattura ed integrita strutturale, 30, pp. 327-339. [48] ayatollahi, m.r., rashidi moghaddam, m., razavi, s.m.j. and berto, f. (2016). geometry effects on fracture trajectory of pmma samples under pure mode-i loading. engineering fracture mechanics, 163, pp. 449-461. [49] berto, f. and lazzarin, p. (2013). multiparametric full-field representations of the in-plane stress fields ahead of cracked components under mixed mode loading, international journal of fatigue, 46, pp. 16-26. [50] ferro, p., lazzarin, p. and berto, f. (2012). fatigue properties of ductile cast iron containing chunky graphite, materials science and engineering a, 554, pp. 122-128. [51] zhu, s.-., yu, z.-., correia, j., de jesus, a. and berto, f. (2018). evaluation and comparison of critical plane criteria for multiaxial fatigue analysis of ductile and brittle materials, international journal of fatigue, 112, pp. 279-288. [52] torabi, a.r., campagnolo, a. and berto, f. (2015). local strain energy density to predict mode ii brittle fracture in brazilian disk specimens weakened by v-notches with end holes, materials and design, 69, pp. 22-29. [53] berto, f., gallo, p. and lazzarin, p. (2014). high temperature fatigue tests of un-notched and notched specimens made of 40crmov13.9 steel, materials and design, 63(1), pp. 609-619. [54] berto, f., lazzarin, p. and kotousov, a. (2011). on higher order terms and out-of-plane singular mode, mechanics of materials, 43(6), pp. 332-341. [55] berto, f., lazzarin, p. and wang, c.h. (2004). three-dimensional linear elastic distributions of stress and strain energy density ahead of v-shaped notches in plates of arbitrary thickness, international journal of fracture, 127(3), pp. 265282. [56] wu, w., hu, w., qian, g., liao, h., xu, x. and berto, f. (2019). mechanical design and multifunctional applications of chiral mechanical metamaterials: a review, materials and design, 180, 107950. p. mendes et alii, frattura ed integrità strutturale, 55 (2021) 302-315; doi: 10.3221/igf-esis.55.23 315 [57] saini, d. s., karmakar, d., ray-chaudhuri, s. (2016). a review of stress concentration factors in tubular and nontubular joints for design of offshore installations. journal of ocean engineering and science 3, 186-202. [58] radaj, d. (1990). design and analysis of fatigue resistant welded structures, cambridge: abington publisher. [59] shabakhty, n., haselibozchaloee, d., correia, j.a.f.o. (2021). investigation on fatigue damage calibration factors of steel members in offshore structures. proceedings of the institution of civil engineers: maritime engineering, doi: 10.1680/jmaen.2020.17 [60] suresh, s. (1998). fatigue of materials. cambridge university press, new york. [61] xin, h., correia, j.a.f.o., veljkovic, m. (2021). three-dimensional fatigue crack propagation simulation using extended finite element methods for steel grades s355 and s690 considering mean stress effects. engineering structures, 227, 111414. [62] fernandes, a., de castro, p., moura branco, c. (1999). fadiga de estruturas soldadas. fundacão calouste gulbenkian, lisboa (in portuguese). [63] jacob, a., mehmanparast, a. (2021). crack growth direction effects on corrosion-fatigue behaviour of offshore wind turbine steel weldments. marine structures, 75, 102881. [64] correia, j., carvalho, h., lesiuk, g., mourão, a., grilo, l.f., de jesus, a., calçada, r. (2020) fatigue crack growth modelling of fão bridge puddle iron under variable amplitude loading. international journal of fatigue, 136, 105588. [65] correia, j.a.f.o., blasón, s., arcari, a., calvente, m., apetre, n., moreira, p.m.g.p., de jesus, a.m.p., canteli, a.f. (2016). modified ccs fatigue crack growth model for the aa2019-t851 based on plasticity-induced crack-closure. theoretical and applied fracture mechanics, 85, pp. 26-36. [66] silva, a.l.l., de jesus, a.m.p., xavier, j., correia, j.a.f.o., fernandes, a.a. (2017). combined analytical-numerical methodologies for the evaluation of mixed-mode (i+ii) fatigue crack growth rates in structural steels. engineering fracture mechanics, 185, pp. 124-138. [67] correia, j.a.f.o., de jesus, a.m.p., fernández-canteli, a. and calçada, r.a.b. (2015). modelling probabilistic fatigue crack propagation rates for a mild structural steel. frattura ed integrita strutturale, 31, pp. 80-96. [68] huffman, p.j., ferreira, j., correia, j.a.f.o., de jesus, a.m.p., lesiuk, g., berto, f., fernández-canteli, a. and glinka, g. (2017). fatigue crack propagation prediction of a pressure vessel mild steel based on a strain energy density model. frattura ed integrita strutturale, 11(42), pp. 74-84. [69] aeran, a., siriwardane, s.c., mikkelsen, o. and langen, i. (2017). a framework to assess structural integrity of ageing offshore jacket structures for life extension. marine structures, 56, pp. 237-259. microsoft word numero_49_art_68_2518 h. chbani et alii, frattura ed integrità strutturale, 49 (2019) 763-774; doi: 10.3221/igf-esis.49.68 763 determination of fracture toughness in plain concrete specimens by r curve chbani hamza, saadouki bouchra laboratory of control and mechanical characterization of materials and structures, national higher school of electricity and mechanics, bp 8118 oasis, hassan ii, morocco boudlal mostapha, barakat mohamed laboratory of mechanics higher institute of maritimes ‘studies (isem), km 7 road el jadida casablanca, morocco abstract. experimental tests and computational algorithm are implemented to investigate crack growth phenomena in c0.7 concrete. firstly, three point bending tests are carried out on normalized prismatic specimens notched laterally (senb), then, computational calculation was developed to calculate the concrete toughness on the basis of r-curve method. the r-curve was obtained from the curve connecting the crack mouth opening displacement (cmod) to the applied load. during loading, elastic deformation followed by a significant plastic deformation were observed. therefore, the crack growth in c0.7 concrete is defining by three stages: crack initiation, stable crack propagation and an unstable fracture. the average value of the critical stress intensity factor for the c0.7 concrete is 1.05 mpa.m1/2. keywords. toughness, r-curve, cmod, senb, three-point bending citation: chbani, h., saadouki, b., boudlal, m., barakat, m., determination of fracture toughness in plain concrete specimens by r curve, frattura ed integrità strutturale, 49 (2019) 763-774. received: 13.05.2019 accepted: 19.06.2019 published: 01.07.2019 copyright: © 2019 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. introduction oncrete is one of the most used construction materials in morocco, just like in the rest of the world. the main benefits of this material are the low cost of production compared to other civil engineering materials, its secular durability and its elaboration which is relatively simple as it gives the availability of primary natural materials. it is therefore for economic and technical reasons that concrete has become irreplaceable in the construction domain. much of immense structures such as nuclear center, dams and bridges undergoes an aging and requires particular attention to ensure their maintenance and safety. innovative and large sizes structures are built of concrete such as nuclear power plants, dams and bridges, which encourages researchers to focus more on investigations related to this material. structural calculations performed by technical offices are based on the classical mechanical characteristics (yield strength, compressive strength, bending strength...); the builder chooses the type of concrete to realize its structure from the data provided by the technical office. under certain stress conditions a defect even of very small dimensions can lead to sudden failure. faced with the impossibility of structures calculating from the results of the brittle failure [1], it seemed fundamental to predict the critical dimensions of the defects that, under given stress conditions, caused catastrophic failures. this led to the introduction of c http://www.gruppofrattura.it/va/49/2518.mp4 h. chbani et alii, frattura ed integrità strutturale, 49 (2019) 763-774; doi: 10.3221/igf-esis.49.68 764 a certain characteristic of the material toughness « fracture toughness » characterizing the ability of a material to resist the sudden crack propagation. however, concrete structures are complex systems that can represent significant damage. the fracture mechanism of concrete can be similar to that produced in composite systems [2-4], these studies have used analytical formulation and developed computational methods based on fem approach in order to predict crack growth and failure scenarios in structural and mechanical systems. in the current work, concrete was considered as a homogeneous material but a calculation algorithm by computational tool was required besides experimental tests to determine the concrete toughness. the stress intensity factor kic is an important parameter for the characterization of brittle and quasibrittle materials when they contain cracks. in order to perform an accurate analysis of materials fracture, the measurement of strength at failure by laboratory tests is essential. several tests have been adopted in this sense, we quote the most used: single edge pre-cracked beam (sepb), chevron notched beam (cnb) and surface crack in flexure and indentation methods [5–8]. these prototypes are all based on three or four point bending test, but they use different forms of notches, with different adjustment and calculation of stress intensity factor methods. the study of the cracking mechanism in the case of brittle and quasibrittle materials has been investigated in several studies research. the common aim of all this work is to determine the r curve; the test used is often the three-point bending test, but the employed techniques for tenacity determination change from one paper research to another. graziani et al [9] determined the curve r of material clay using the digital image correlation technique (dic), they confirmed the effectiveness of the optical technique in the acquisition of experimental parameters cmod, ctod, and delta (a). another technique based on the analytical resolution of the euler equation was also adopted in [10], this technique does not require the measurement of the crack length and uses only the initial and the failure concrete energies. the finite element method was also developed by alam et al [11] for the concrete toughness calculation; they concluded that the toughness value is affected by the aggregate change. kumar et al [12] used the 3-parameter r curve to predict the critical load of concrete. however, the experimental measurement of cmod remains the most common technique for concrete toughness measurement; the r-curve is established directly from the experimental load-cmod curve. thus, the toughness is defined by the asymptotic limit of the r-curve [13, 14]. shilang xu et al [15, 16] have investigated crack growth in concrete using double-k criterion. in their work, laser speckle interferometry on small size three-point bending notched beams was used in order to predict the crack propagation during the fracture process in quasi-brittle materials. their investigation defined the critical stress intensity factor for each crack propagation stage. in this work, we have been interested in the b25 concrete study, for this reason we have used the single edge pre-cracked beam (sepb) as it gives reliable kic values, especially in the case of a brittle material in which the linear mechanic of fracture can be applied [14], this method is summarized in a prismatic specimen with a notch, mounted on a three-point bending test bench. an adequate assembly was put in place to measure the crack opening each moment of the test until the material failure. this allows us to predict the crack evolution the: stopping the propagation, stable propagation, or unstable propagation and specimen failure. indeed, we obtained the r-curve in which the strength failure is measured according to the crack length using the cmod. material and methods material he standard nf en 206-1 specifies five types of reference concretes, defined by the maximum size of aggregates and the proportions of the mixture. the reference concrete is chosen according to the type of product, the system of protection and repair of concrete structures, and also according to the standards of associated test methods. given the importance of concrete in the construction domain, we have chosen for this study the most used concrete type which is the ordinary concrete of the reference c 0.7 known by the trade name b25. the studied concrete is formulated for 28 days to have a simple compressive strength of the order of 25 mpa for cylindrical specimens and 30 mpa for cubic specimens. about the workability of this concrete type in the fresh state which is characterized, inter alia, by the cone of abrams slump value, the formulation is established for a plastic concrete with the slump of the order of 18 cm. tab. 1 gives the different constituents dosage (aggregates, cement, water and admixture) of the c 0.7 type concrete. material characterization several experimental techniques allow to characterize physically and mechanically the concrete. in this study we measured slump, porosity, density, compressive strength and bending strength. tab. 2 represent the different results found at the age of 28 days. t h. chbani et alii, frattura ed integrità strutturale, 49 (2019) 763-774; doi: 10.3221/igf-esis.49.68 765 concrete constituents weight in kg/m3 sand 0/4 1026 aggregate 1 4/10 611 aggregate 2 12/16 335 water 192 cement cpj 55 mpa 275 admixture 2.475 table 1: c 0.7concrete constituents slump porosity volume weight young's modulus e compressive strength for cylindrical specimens compressive strength for cubic specimens 3 points bending strength 181 mm 7.43 % 2447 kg/m3 32 gpa 25.37 mpa 32.35 mpa 6.31 mpa table 2: c 0.7 concrete characteristics specimen manufacturing in order to determine the toughness of c0.7 concrete, prismatic specimens were notched laterally (senb). fig. 1 shows the geometry and dimensions for used specimens ( s 4 w , w 2b ) normalized by the astm e399 [17, 18]. fig. 2 offered details of the shape and geometry of notch. tab. 3 shows the dimensional characteristics of senb concrete specimens. notation description dimension in mm l specimen length 440 ±0.1 s distance between supports 440 ±0.1 w specimen width 100 ±0.1 b specimen thickness 50 ±0.1 a0 notch length 30,40,50,60 table 3: dimensional characteristics of senb concrete specimens. (a) (b) figure 1: senb specimen standardized by astm e399 (a) geometry, (b) dimensions and three point bending test principle. h. chbani et alii, frattura ed integrità strutturale, 49 (2019) 763-774; doi: 10.3221/igf-esis.49.68 766 (a) (b) figure 2: notch details (a) photo of notched concrete specimen, (b) notch geometry sixteen senb specimens were manufactured. dimensionless notch length ratio α = a0/w is included between 0.3 and 0.6 (0.3 α 0.6) .for each notch length, four specimens are manufactured; the notch length incrementation is of 10 mm. the specimens spent 28 days in a pool of water (fig. 3) at a temperature (20 ± 2 ° c), this 28 day period is called cure age of concrete corresponding to the time at which concrete reaches 90% of its maximum compressive strength. this strength is called the concrete characteristic strength. figure 3: conservation of concrete specimen in water pool at a temperature of 20 ° c ± 2 °c features and tests assembly in order to measure the crack mouth opening displacement for the senb specimens during the three-point bending test, we have used the assembly presented by fig. 4. with: 1 : applied load support 2 : reaction support 3: displacement sensor with 1 μm precision used to measure the crack mouth opening displacement cmod (fig. 5) 4: support-sensor with two circular magnets in its base serves to hold the sensor on a rectangular metal plate 3 mm thick (fig. 6). 5: l-shaped metal plate in contact with the probe, it allows the sensor to follow the gap between the notch lips. h. chbani et alii, frattura ed integrità strutturale, 49 (2019) 763-774; doi: 10.3221/igf-esis.49.68 767 figure 4: test assembly for the three points bending test on senb concrete specimens figure 5: displacement sensor figure 6: sensor support tests progress three-point bending tests are performed using a uniaxial press “controls” (fig. 7) with maximum capacity of 10 kn. the specimen surfaces must be smooth and perfectly parallel, hence the need to rectify or pre-plan them. before placing the test specimen in the machine, we have pasted the two metal plates (rectangular and l) with a special glue, then, we placed the magnetic displacement support -sensor on the rectangular plate. a slight compression was applied on the sensor stem before positioning it on the l-plate. to obtain a better cmod measurement, we placed the sensor in the same basic plane of the specimen, such that the axis of the sensor rod is in the plane direction of the specimen opening notch. h. chbani et alii, frattura ed integrità strutturale, 49 (2019) 763-774; doi: 10.3221/igf-esis.49.68 768 the tests were carried out with imposed displacement. the axial cylinder is moved until the sample failure, which allows to better apprehending the post-peak phase of the mechanical behavior. in order to compare the tests results for different notch lengths, tests have all been carried out with an identical displacement velocity of 30 μm/min. the press acquisition system has two measurement channels, and allows to recording data (load sensor and displacement sensors (lvdt)) at a sampling frequency of 5 hz. figure 7: uniaxial press “controls” determination of the stress intensity factor using the r curve in the case of three-point bending test with s/w=4, we used the approach developing by tada [19] and adopted in [12] 19, 12]. the stress intensity factor expression is given by the eqn. (1).  i nk w k  (1)         2 3 2 1, 99 1 2,15 3, 93 2, 7 1 2 1 k                (2) where k(α) is a geometric factor, α= a/w and σn is the nominal stress in the beam due to external load p and self weight of the structure which is given by : 2 3 2 4 n mgs p s lbw       (3) the r curve plot requires the definition, at each moment, of the propagated crack length a and the corresponding load p. in practice, the measuring of instantaneous crack length is very difficult. for this reason, effective crack length is determined by the following equations [12]:   6ps cmod v ebw   (4)   2 3 2 0, 66 0, 76 2, 28 3, 87 2, 04 (1 ) v            (5) in order to search the ratio α which verifies eqn. (4), we used the dichotomy method; the principle of this method is based on the intermediate value theorem: if f (a) · f (b) < 0, then it exists c ∈ [a, b] such as f (c) = 0 h. chbani et alii, frattura ed integrità strutturale, 49 (2019) 763-774; doi: 10.3221/igf-esis.49.68 769 the condition f (a). f (b) <0 means that f (a) and f (b) have opposite signs (or that one of them is zero). the hypothesis of continuity is essential. to translate the dichotomy algorithm into a program, we used the vba as a programming language. after solving eqn. (4), we have placed the α found in relation (1), which allowed us to plot the r curve. results and dicussions ab. 4 shows all the results found for the 16 concrete specimens. concrete is a material with a very complex structure, for the notchs of 70 mm, a large part of the test pieces break during demolding or in tests. it should also be noted that a remarkable dispersion has been found in the cmod values for the same notch, which may be due to the nature and the distribution of aggregates in the material. specimen number a0 (mm) p (kn) cmodc (µm) δac (mm) kic (mpa. m1/2) 1 30 1.435 53.8 18 1.25 2 30 1.601 56 30 1.2 3 30 2.2 46 13 0.78 4 30 1.7 25 28 1.5 average 1.734 45.200 20 1.183 5 40 1.17 47.8 10 1.17 6 40 1.572 34.8 9 1.01 7 40 1.473 57 28 0.937 8 40 1.3 33 16 0.948 average 1.38 43.15 15.8 1.016 9 50 1.135 33.7 9 0.86 10 50 1.174 39.3 10 1.16 11 50 1.26 39 11 0.96 12 50 0.938 52 8 1.05 average 1.13 41.00 9.5 1.008 13 60 0.805 38 4.4 0.81 14 60 0.601 30 6 0.82 15 60 0.6 46 9 1.37 16 60 0.618 30 7 1.03 average 0.66 36.00 6.6 1.008 table 4: summary of found results fig. 8 show the load evolution as function of the cmod for four different notch lengths. we note that the results obtained on these notched specimens show similar evolutions. each of these curves begins with an elastic linear part, followed by a continuous remoteness of the real curve to the ideal line load-displacement. this non-linearity is mainly due on the one hand to a plasticization of the area in the immediate crack tip vicinity, and on the other hand to the fact that the crack tends to propagate slowly and disproportionately to the applied load until the specimen failure. figs. 9, 10 and 11 show respectively regrouped charge / cmod curves, evolution of the maximum load as function of different lengths notch and the evolution of cmodc as function of different lengths notch. we can observe that the maximum load and the cmodc decrease as the length notch increases. the crack propagation occurs in a zone strongly damaged by the plasticization. the size of this zone increases when the notch length decreases. the cmod technique and the numerical tools allowed us to plot the r-curves as a function of the crack propagation δa (fig..13), according to a preliminary analysis of these curves, we note well that the evolution of cracking goes always through three stages:  if δa = 0: the crack propagation is stopped .  if the δa ranges between 0 and δac we can say that the crack propagation is stable.  if the δa is higher than δac , the crack propagation is unstable t h. chbani et alii, frattura ed integrità strutturale, 49 (2019) 763-774; doi: 10.3221/igf-esis.49.68 770 figure 8: evolution of the applied load as function of the cmod for various notch lengths. a) a0=30 mm, b) a0=40mm, c) a0=50mm and d) a0=60mm. figure 9: load evolution as function of cmod for the four studied notch lengths. figure 10: load evolution as function of notch lengths. figure 11: cmodc evolution as function of notch lengths figure 12: δac evolution as function of notch length. h. chbani et alii, frattura ed integrità strutturale, 49 (2019) 763-774; doi: 10.3221/igf-esis.49.68 771 fig. 12 demonstrates the evolution of δac as function of notch length. therefore, we may observe that crack propagation decreases almost linearly and disproportionately with a0. figure 13: kr curve as function of δa for various notch lengths a) a0=30 mm, b) a0=40mm, c) a0=50mm and d) a0=60mm it was demonstrated that the crack propagation zone does not exceed 90 mm for the various initial notches a0 [20]. for our case, this is means that the specimen failure occur at αmax = 0.9 (fig. 14). figure 14: representation of the crack propagation zone [15] the critical stress intensity factor kic corresponding to δac and pmax is respectively equal to 1.18, 1.02, 1.01, and 1.01 mpa.m1/2 for a0 = 30, 40.50, and 60 mm (fig.. 14). from the found results, kic has an average value of 1.05 mpa.m1/2 and a standard deviation of 0.04 mpa.m1/2. h. chbani et alii, frattura ed integrità strutturale, 49 (2019) 763-774; doi: 10.3221/igf-esis.49.68 772 figure 15: kic values as function of notch length fig. 16 groups the kr curves as function of δa for the different studied notch lengths. we observe that the curves are practically confounded in the unstable propagation stage, which confirms that the r-curve is a unique curve independent of the notch length. figure 16: regrouped kr curves as function of δa conclusions n this paper, three point bending tests were carried out on notched specimens made from c0.7 concrete in order to understand the mechanical behavior and the crack propagation mechanism of this quasi-brittle material. therefore, many conclusions were made:  the crack propagates mechanism consists of two propagation stages: 1-stable propagation stage while the load is lower than pmax, 2-unstable propagation stage. the stage of unstable propagation is more important than the stable propagation stage.  the stable propagation stage decreases disproportionately to the notch length.  the opening displacement mechanism of the critical notch lips occurs in a perpendicular direction to the applied load direction; this opening displacement is even higher than the notch length is small. i h. chbani et alii, frattura ed integrità strutturale, 49 (2019) 763-774; doi: 10.3221/igf-esis.49.68 773  the load / cmod curve is a useful and effective technique for determining the length propagated crack during loading, thus the r curve plot with good accuracy.  the r curves give almost the same kic and the same maximum crack length for the various notch lengths.  our study confirms that the r curve is unique and independent of the notch length, this curve represents an intrinsic parameter of concrete material, it allows to determine the critical stress intensity factor and to describe the crack evolution in quasi-fragile materials cases, so the r curve is a mechanical characteristic. nomenclature a a0 ac b e w s l senb cmod cmodc p pmax crack length notch length critical crack length specimen thickness young’s modulus specimen width distance between supports specimen length specimen for three-point bending crack mouth opening displacement critical crack mouth opening displacement applied load maximal load σn kr fpz δa δac δamax α0 α αc αmax ki kic nominal stress r-curve in function of stress intensity factor fracture process zone crack extension critical crack extension maximal crack extension α0= a0/w initial crack length ratio α= (a0+δa)/w crack extension ratio αc= (a0+δac)/w critical crack extension ratio αmax= (a0+δamax)/w maximal crack extension ratio stress intensity factor in mode i critical stress intensity factor in mode i references [1] sanz, g. (1974). la rupture des aciers – première partie : la rupture fragile – collection irsid-otua. [2] funari, m.f., greco, f., lonetti, p., luciano, r., penna, r. (2018) an interface approach based on moving mesh and cohesive modeling in z-pinned composite laminates. composites part b: engineering; 135, pp. 207-217, doi: 10.1016/j.compositesb.2017.10.018. [3] funari, m.f., lonetti, p., spadea, s. (2019) a crack growth strategy based on moving mesh method and fracture mechanics. theoretical and applied fracture mechanics; 102, pp. 103-115, doi: 10.1016/j.tafmec.2019.03.007. [4] funari, m.f., greco, f., lonetti, p. (2019) a numerical model based on ale formulation to predict crack propagation in sandwich structures. frattura ed integrità strutturale, 47, pp. 277-293. doi: 10.3221/igf-esis.47.21. [5] broek, d. (1984). elementary engineering fracture mechanics. boston: kluwer academic publisher [6] broek, d. (1988).the practical use of fracture mechanics. boston: kluwer academic publisher [7] zhu, x.-k., joyce, j.a. (2012) review of fracture toughness (g, k, j, ctod, ctoa) testing and standardization. engng. fract. mech. 85, pp. 1–46. , doi: 10.1016/j.engfracmech.2012.02.001. [8] kailer, a. marc, s. (2016). on the feasibility of the chevron notch beam method to measure fracture toughness of fine-grained zirconia ceramics. 32(10), pp. 1256-1262 , doi: 10.1016/j.dental.2016.07.011. [9] graziani, l. (2014). measurement of r-curve in clay brick blocks using optical measuring technique, engineering fracture mechanics, 121, pp. 1-10. doi: 10.1016/j.engfracmech.2014.04.007. [10] yanhua, z., jianmei, c., hangab, h.g. (2015). a three-parameter r-curve of concrete-like quasi-brittle materials, construction and building materials. 78(1), pp. 243-249. doi: 10.1016/j.conbuildmat.2015.01.029. [11] alam, m.r. (2010). fracture toughness of plain concrete specimens made with industry-brunt brick aggregates. 38(1), pp. 81-94. [12] kumar, s., rajendra, k.c. (2015). further observations on the three-parameter r-curve of concrete-like quasi-brittle materials, construction and building materials, 93, pp. 857-868. doi: 10.1016/j.conbuildmat.2015.05.079. [13] ferreiraa, l.e.t. bittencourt, t.n. sousa, j..l.a.o . gettu.r. (2002). r-curve behavior in notched beam tests of rocks, engineering fracture mechanics.69(17): 1845-1852 , doi: 10.1016/s0013-7944(02)00064-4 [14] jisun, c., goangseup, z., shinichi, h., kohei, y., soye, k. (2014). influence of fiber reinforcement on strength and toughness of all-lightweight concrete, construction and building materials. 69, pp. 381-389 doi: 10.1016/j.conbuildmat.2014.07.074. h. chbani et alii, frattura ed integrità strutturale, 49 (2019) 763-774; doi: 10.3221/igf-esis.49.68 774 [15] shilang, x., reinhardt, h.w. (1999) determination of double-k criterion for crack propagation in quasi-brittle materials, part i: experimental investigation of crack propagation, international journal of fracture, 98(2), pp. 111-149 doi: 10.1023/a:1018668929989 [16] shilang, x., reinhardt, h.w. (1999) determination of double-k criterion for crack propagation in quasi-brittle materials, part ii: analytical evaluating and practical measuring methods for three-point bending notched beams, international journal of fracture, 98(2), pp. 151-177. doi: 10.1023/a:1018740728458 [17] astm international standard e399-72. standard method of test for plane strain fracture toughness of metallic materials. (1972). [18] astm international standard e399-06. standard test method for linear elastic method plane strain fracture toughness test kic of metallic materials. (2006), pp. 1-32. [19] tada, h., paris, p.c., irwin, g., (1985). the stress analysis of cracks handbook. st. louis, mo, usa: paris productions incorporated; [20] chen, h.h., su, r.k.l. 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/hrv (za stvaranje adobe pdf dokumenata najpogodnijih za visokokvalitetni ispis prije tiskanja koristite ove postavke. stvoreni pdf dokumenti mogu se otvoriti acrobat i adobe reader 5.0 i kasnijim verzijama.) /hun 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can be opened with acrobat and adobe reader 5.0 and later.) >> /namespace [ (adobe) (common) (1.0) ] /othernamespaces [ << /asreaderspreads false /cropimagestoframes true /errorcontrol /warnandcontinue /flattenerignorespreadoverrides false /includeguidesgrids false /includenonprinting false /includeslug false /namespace [ (adobe) (indesign) (4.0) ] /omitplacedbitmaps false /omitplacedeps false /omitplacedpdf false /simulateoverprint /legacy >> << /addbleedmarks false /addcolorbars false /addcropmarks false /addpageinfo false /addregmarks false /convertcolors /converttocmyk /destinationprofilename () /destinationprofileselector /documentcmyk /downsample16bitimages true /flattenerpreset << /presetselector /mediumresolution >> /formelements false /generatestructure false /includebookmarks false /includehyperlinks false /includeinteractive false /includelayers false /includeprofiles false /multimediahandling /useobjectsettings /namespace [ (adobe) (creativesuite) (2.0) ] /pdfxoutputintentprofileselector /documentcmyk /preserveediting true /untaggedcmykhandling /leaveuntagged /untaggedrgbhandling /usedocumentprofile /usedocumentbleed false >> ] >> setdistillerparams << /hwresolution [2400 2400] /pagesize [612.000 792.000] >> setpagedevice microsoft word numero_58_art_30_3235.docx s. khatir et alii, frattura ed integrità strutturale, 58 (2021) 416-433; doi: 10.3221/igf-esis.58.30 416 focussed on steels and composites for engineering structures damage identification in steel plate using frf and inverse analysis samir khatir, magd abdel wahab soete laboratory, faculty of engineering and architecture, ghent university, technologiepark zwijnaarde 903, b-9052, zwijnaarde, belgium khatir_samir@hotmail.fr, https://orcid.org/0000-0002-8101-3633 magd.abdelwahab@ugent.be, https://orcid.org/0000-0002-3610-865x samir tiachacht laboratory of mechanics, structure and energetics (lmse), mouloud mammeri university of tizi-ouzou, b.p.n°17 rp, 15000, algeria cuong le thanh ho chi minh city open university, ho chi minh city, viet nam roberto capozucca, erica magagnini università politecnica delle marche, ancona, italy brahim benaissa toyota technological institute, department of mechanical systems engineering, design engineering lab, 468-8511 aichi, nagoya, tempaku ward, hisakata, 2 chome−12−1, japan https://orcid.org/0000-0002-9472-9331 abstract. metaheuristic algorithms have known vast development in recent years. and their applicability in engineering projects is constantly growing; however, their deferent exploration and exploitation techniques cause the engineering problems to favor some algorithms over others. this paper studies damage identification in steel plates using frequency response function (frf) damage indicator to detect and localize the healthy and damaged structure. the study is formulated as an inverse analysis, investigating the performance of three new metaheuristic algorithms of wild horse optimizer (who), harris hawks optimization (hho), and arithmetic optimization algorithm (aoa). the objective function is based on measured and calculated frf damage indicators. the results showed that the case of four damages with different damage severity levels presented a good challenge where the hwo algorithm was shown to have the best performance. both in convergence speed and cpu time. citation: khatir, s., wahab, m.a., tiachacht, s., le thanh, c., capozucca, r., magagnini, e., benaissa, b., damage identification in steel plate using frf and inverse analysis, frattura ed integrità strutturale, 58 (2021) 416-433. received: 18.08.2021 accepted: 30.08.2021 published: 01.10.2021 copyright: © 2021 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. https://youtu.be/owc0ypizgqi s. khatir et alii, frattura ed integrità strutturale, 58 (2021) 416-433; doi: 10.3221/igf-esis.58.30 417 keywords. metaheuristic algorithms; frequency response function; damage indicator; damage identificaion. introduction etaheuristic optimization algorithms are very robust tools that help solve almost any problem with the inputoutput relationship. they require a limited number of control parameters, depending on the algorithm strategy [1]. some require several parameters, while other algorithms need just the population size and the search parameters. these are the search boundaries of design variables and the search stopping criteria; most studies use a maximum number of iterations [2]. the population size is the number of potential solutions considered in every iteration; following the structure of early evolutionary algorithms, the strategy of the population is adopted in most metaheuristic algorithms because of its efficiency. each potential solution is a set of values for the problem parameter; the algorithm suggests them within the earlier set boundaries. depending on the performance of each set, the new sets for the population are calculated according to the algorithm's design [3]. the performance of the potential solutions is compared based on their fitness value. in a minimization problem, the set of variables corresponding to the minimum fitness are considered to be the best solution. the algorithm tries to reach a better solution in each iteration by generating new solutions based on the earlier knowledge. most metaheuristics have two strategies; the first strategy is exploration, when the algorithm is looking to find solutions in different areas of the design space. this feature makes metaheuristics algorithms a powerful tool against non-convex problems and problems with many local minima. the other strategy is called exploitation, which is when the algorithm locks on a small area and looks deeper to find better solutions that are very close. this strategy allows these algorithms to find precise solutions and compete for accuracy with classical methods like the gradient descent method [2, 3]. the application of metaheuristic algorithms in structural health monitoring is widely adopted due to their good performance in such methods. due to the complexity of structural behavior, most research projects are formulated as ill-posed inverse problems, both in the behavior nonlinearity of the material and in the behavioral characteristics of the structures. classical methods cannot solve such ill-posed problems, and they often require complex analytical methodologies. tiachacht et al. [4] investigated genetic algorithm (ga) for crack identification in 3d. zenzen et al. [5, 6] suggested bat optimization algorithm in damage detection in truss structures. cuong-le et al. [7] suggested a pso and support vector machine (svm) method for structural health monitoring. khatir et al. used jaya algorithm to predict crack size and orientation in steel plates [8]. chen et al. [9] presented a hybrid nelder–mead algorithm (nm) ant lion optimizer (alo) for the estimation of multiple damages. livani et al. [10] proposed an enhanced particle swarm optimization (pso) with a strategy called active/inactive flaw (aif) of damage identification in an aluminum plate. in [11] the cuckoo search (cs) algorithm merged with pso was suggested to predict structural damages under temperature variation. several metaheuristic algorithms exist, and although they all offer better performance in ill-posed problems, each engineering problem is unique in how output varies according to the change in the design variables. therefore, some metaheuristic methods perform better than others in different areas. this is because each optimization method has a different way to calculate the variables of every iteration and different ways to change from exploration to exploitation. which can make some inverse problems favor some strategies over others. benaissa et al. [12-14] compared several optimization algorithms for the suggested method of fast crack identification in steel plates. mishra et al. [15] compared the performance of 10 optimization algorithms in damage detection in trusses. ding et al. compared the jaya and tree seeds algorithm [16] in the case of experimental and simulation-based damage estimation. moezi et al. [17] proposed an improved cs algorithm. its performance is compared to well-established optimization algorithms. the aoa [18] is a method based on mathematical primes, using a math optimizer accelerated strategy, a function that helps explore the search space. it uses another technique called the math optimizer probability, which is a function that helps guide the search. the hho [19] uses a strategy inspired by the harris' hawks. namely, the hunting behavior, as wait to detect a prey based on two systems. the soft besiege and the hard besiege, in combination with the rapid dive. these techniques are modeled mathematically, and each potential solution is considered a hawk in this algorithm, looking to find better solutions in every iteration by reimplementing the search techniques. the who optimization algorithm is a metaheuristic presented by iraj et al. [20] inspired by the social life of wild horses. it models the hierarchical characteristics for selecting and changing the leader. this method is led by what is called grazing behavior. it guides the horse herd members to search in different radiuses around the leader. m s. khatir et alii, frattura ed integrità strutturale, 58 (2021) 416-433; doi: 10.3221/igf-esis.58.30 418 frf is a damage indicator based on the vibrational response of the structure and calculated from its mass and stiffness matrices [21]. this paper compares the performance of who, hho, and aoa algorithms in damage identification in a cccc rectangular plate. based on the frf indicator. the plate is discretized into 100 elements, and the goal for the algorithm is to predict what element is damaged and to what degree it is damaged. the algorithms are subjected to the same search conditions, run on the same computer, and using the same search parameters. the second section discusses the rfr damage indicator theory and how it is calculated; this indicator will be used later by the optimization algorithms for the fitness evaluation. the third section presents the details of each optimization algorithm. section 4 shows the considered damage scenarios and discusses the results obtained using each algorithm. we compare their performance in the case of limited damage element and damage severity variables and a final case with four damaged elements with different damage severity. and evaluating their computational cost. the results show that there is one metaheuristic algorithm that performs better than the others in all cases. frf for damage index he following formulation present frf for the healthy and damaged structure:                                    1 2 1 2 a a a t t t m k m k (1) where  m and  k are mass and stiffness matrices, the symbol    ,a t are undamaged and damaged cases, respectively. as a result of the damage, the stiffness changes as follows:        a tk k k (2) where  ak ,  tk denotes the stiffness healthy and damaged structure, respectively by combining eqns. (1) and (2), we can write:                       1 1a t k (3)  denote values for the position of damage considering the degree of freedom and position of elements and by using the first row of the global frf matrix are defined as:                          1 :,1 :, 1, t a in i i i (4) in order to be able to develop the new formulation-based damage index, you should first learn how to write a formula, then the dimensions of the vector to the dimension of total degrees of freedom (dofs) should be increased, including the boundary conditions. the damage index can be written as follows [22]:     n i i j i dof (5) optimization or the purposes of quantification of localized damages by the frequency response function (frf) damage index method, we present in this section three optimization methods that we are going to use, namely: harris hawks t f s. khatir et alii, frattura ed integrità strutturale, 58 (2021) 416-433; doi: 10.3221/igf-esis.58.30 419 optimization (hho) [19], arithmetic optimization algorithm (aoa) [18] and horse herd optimization algorithm [20]. harris hawks optimization (hho) [19]  exploration phase in hho [19], the harris' hawks perch randomly on some locations and wait to detect the prey based on two strategies.                            1 2 3 4 2 0.5 1 <0.5 rand rand rabbit m x t r x t r x t q x t x t x t r lb r ub lb q (6) where   1x t is the position vector of hawks in the next iteration t ,  rabbitx t is the position of rabbit,  x t is the current position vector of hawks, 1 2 3 4, , ,r r r r and q are random numbers inside (0,1), which are updated in each iteration, lb and ub show the upper and lower bounds of variables,  randx t is a randomly selected hawk from the current population, and mx is the average position of the current population of hawks. the average position of hawks is attained using eqn. (7):        1 1 hn m i ih x t x t n (7)  ix t indicates the location of each hawk in iteration t and hn denotes the total number of hawks.  transition from exploration to exploitation to model this step, the energy of a rabbit is modeled as:       02 1 t w w t (8) w indicates the escaping energy of the prey, t is the maximum number of iterations and 0w is the initial state of its energy.  exploitation phase this behavior is modeled by the following rules:            1 rabbitx t x t w jx t x t (9)        rabbitx t x t x t (10) where  x t is the difference between the position vector of the rabbit and the current location in iteration t , 5r is a random number inside (0,1), and    52 1j r represents the random jump strength of the rabbit throughout the escaping procedure. the j value changes randomly in each iteration to simulate the nature of rabbit motions. in this situation, the current positions are updated using eqn. (11):         1 rabbitx t x t w x t (11) to perform a soft besiege, we supposed that the hawks can evaluate (decide) their next move based on the following rule in eqn. (12):        rabbit rabbity x t w jx t x t (12) s. khatir et alii, frattura ed integrità strutturale, 58 (2021) 416-433; doi: 10.3221/igf-esis.58.30 420 we supposed that they dive based on the lf-based patterns using the following rule:    z y s lf d (13) where d is the dimension of the problem and s is a random vector by size 1 d and lf is the levy flight function, which is calculated using eqn. (14):                                           1 1 1 2 1 sin 2 0.01 , 1 2 2 u lf x v (14) where ,u v are random values inside (0,1),  is a default constant set to 1.5. hence, the final strategy for updating the positions of hawks in the soft besiege phase can be performed by eqn. (15):                   1 y if f y f x t x t z if f z f x t (15) where y and z are obtained using eqns. (12) and (13). the following rule is performed in hard besiege condition by eqn. (15); where y and z are obtained using new rules in eqns. (16) and (17).        rabbit rabbit my x t w jx t x t (16)    z y s lf d (17) where  mx t is obtained using eqn. (7). arithmetic optimization algorithm (aoa) [18] as presented in the following formulation eqn. 18, the optimization process begins with a collection of candidate solutions ( 𝑋) which would be created at random, and in each iteration, the best candidate solution is assumed the best-obtained solution or approximately the optimum so far.                                 1,1 1, 1, 1 1, 2,1 2, 2, 1,1 1, 1, ,1 , , 1 , j n n j n n n j n n n n j n n n n x x x x x x x x x x x x x x x (18) eqn. (19) compute the math optimizer accelerated (moa) feature used in the main search phrases.           iter iter iter max min moa c min c m (19) s. khatir et alii, frattura ed integrità strutturale, 58 (2021) 416-433; doi: 10.3221/igf-esis.58.30 421 where  itermoa c presents the function value at the tth iteration, which is figured out by eqn. (19). iterc indicates the current iteration, which is between  1 iterm . min and max the accelerated function's minimum and maximum values, respectively. the most straightforward rule, which can simulate the action of arithmetic operators, has been presented. the following position updating calculations for the exploration sections are shown in the following formulation:                                   2 , 0.5 1 otherwise j j j j i j iter j j j j best x mop ub lb lb r x c best x mop ub lb lb (20) where   1i iterx c denotes the ith solution in the next iteration,  ,i j iterx c represents the jth position of the ith solution at the current iteration, and  jbest x is the jth position in the best-obtained solution so far.  is a small integer number, jub and jlb represents the upper and lower values of the jth position, respectively.  indicates a control parameter to adapt the search process, can be presented by 0.5 based on the analyzed problem.      1 1 1 iteriter iter c mop c m (21) math optimizer probability is used as a coefficient, represents the function value at the tth iteration,  iterc indicates the current iteration, and  iterm indicates the maximum number of iterations. 𝛼 denotes a sensitive parameter and defines the exploitation accuracy over the iterations, which is fixed equal to 5. the moa function value conditions this phase of searching for the condition of r1 is not greater than the current  itermop c value (see eqn. (18)). in aoa, the exploitation operators (subtraction (s) and addition (a)) of aoa explore the search field in-depth on many dense regions and use two fundamental search techniques to come up with a better solution that is modeled.                               3 , 0.5 1 otherwise j j j j i j iter j j j j best x mop ub lb lb r x c best x mop ub lb lb (22) the aoa is a relatively new algorithm, and this work is one of the early attempts to test its performance in damage quantification. horse herd optimization algorithm [20] iraj and farshid [20] present a new optimizer algorithm called the wild horse optimizer (who), inspired by the social life behavior of wild horses. the wild horse optimizer consists of five main steps as follows:  creating an initial population and forming horse groups, and selecting leaders; the basic framework of all optimization algorithms is the same. the algorithm starts with       1 2, , , nx x x x an initial random population. the target function repeatedly evaluates this random population, and a target value is determined      1 2, , , no o o o . it is also improved by a set of rules that are the core of an optimization technique.  grazing and mating of horses; eqn. (23) simulates grazing behavior. eqn. (23) causes group members to move and search around the leader with a different radius. s. khatir et alii, frattura ed integrità strutturale, 58 (2021) 416-433; doi: 10.3221/igf-esis.58.30 422       , ,2 cos 2j j j ji g i gx z rz stallion x stallion (23) , j i gx is the current position of the group member (foal or mare), jstallion is the position of the stallion (group leader), z is an adaptive mechanism calculated by eqn. (24), r is a uniform random number in the range  2, 2 that causes the grazing of horses at different angles (360 degrees) of the group leader, and finally , j i gx is the new position of the group member when grazing.                1 2 3 0 p r tdr idx p z r idx r idx (24) p is a vector consisting of 0 and 1 equal to the dimensions of the problem,  1r and  3r are random vectors with uniform distribution in the range  0,1 , 2r is a random number with uniform distribution in the range  0,1 , idx indexes of the random vector  1r returns that satisfy the condition   0p . application n this section, we consider a fully clamped (cccc) square plate (side a ) with a thickness-to-side ratio  0.01h a . the non-dimensional natural frequency is given by    mn a g (25) frequency [23] [24] [25] 20 × 20 q4 actual 10 × 10 q4 damage case 1 2 3 1 1.594 1.5582 1.5955 1.6216 1.6140 1.6101 1.5849 2 3.039 3.0182 3.0662 3.1893 3.1603 3.1329 3.0609 3 3.039 3.0182 3.0662 3.1893 3.1814 3.1778 3.0888 4 4.265 4.1711 4.2924 4.4458 4.4287 4.3580 4.2329 5 5.035 5.1218 5.1232 5.5280 5.4499 5.4643 5.3480 6 5.078 5.1594 5.1730 5.5848 5.5682 5.5230 5.4264 table 1: natural frequencies of a cccc plate. where  is the material density, g the shear modulus    2 1g e , e the modulus of elasticity and  the poisson's coefficient. indices m and n are the vibration half-waves in axes x and y , and we use a shear correction factor  0.8601k tab. 1 presents the natural frequencies of the cccc plate, along with the frequencies of the three damages scenarios. we show the details of the damages cases in tab. 2. starting with single damage, then double damage, and multiple damages with variable severity in the last case. in the first two cases, we considered the same levels of damage severity. these scenarios are chosen in this manner to create a challenge for the optimization algorithms regarding two variables, first the location, then the severity. then finally, the last case challenges the combination of variables simultaneously, with the complexity of i s. khatir et alii, frattura ed integrità strutturale, 58 (2021) 416-433; doi: 10.3221/igf-esis.58.30 423 multiple damages, which makes the last scenario the hardest from an inverse problem perspective. this creates a problem with multiple local optima due to the similarity of the frequencies corresponding to the possible variable combinations. case 1 2 3 element (severity %) 15 (15%) 23 (20%) 33 (10%) element (severity %) – 87 (20%) 37 (15%) element (severity %) – – 62 (20%) element (severity %) – – 78 (5%) table 2: damage case. fig. 1 shows the frequency modes of the cccc plate, along with the discretization considered for the study. the plate has 100 elements. higher modes 3 and 4 show unsymmetrical behavior. mode 1 mode 2 mode 3 mode 4 figure 1: modes of vibration for a cccc plate. damage detection the first case considers a single damaged element positioned near the side and on the centerline. element number 15, coordinates (5,9). in this case, this element had 15% damage severity on the damage index. more details are shown in fig. 2(a) and fig. 2(b). fig. 2(c) is the plot of log(frf) vs. the frequency in the case of healthy and damaged plates. it shows a shift in the natural frequencies, noticing a relatively large shift for the second natural frequency, with major variation in the last two natural frequencies. the second case considers a double damaged plate; the two damaged elements are positioned near the side as well, closer to the plate corners, namely the element number 23 and the element number 78 with coordinates (3,8) and (7,2), respectively. in this case, both elements have 20% damage severity on the damage index. the details are shown in fig. 3(a) and fig. 3(b). fig. 3(c) is the plot of log(frf) vs. the frequency in the case of healthy and damaged plates. it shows a slight shift in the natural frequencies in the first four natural frequencies, with significant variation in the last two natural frequencies, similar to the first case. in the last case, the considered plate has four damaged elements, with two damages closer to the sides and two elements closer to the center of the plate, namely the element numbers 33, 37, 62, and 78, with coordinates (3,7), (2,4), (7,7) and (8,3) respectively. in this case, elements have different damage severity of 10%, 5%, 15%, and 20 %, respectively. the details are shown in fig. 4(a) and fig. 4(b). in this case, fig. 4(c) shows a more significant shift in most natural frequencies with a s. khatir et alii, frattura ed integrità strutturale, 58 (2021) 416-433; doi: 10.3221/igf-esis.58.30 424 minor shift in the first and second peaks. we notice that multiple damages do not affect the first natural frequencies the same way the single damage case does. there is a similarity between the natural frequencies affected in double damages and multiple damages, with the difference in the magnitude of the shift. (a) (b) (c) figure 2: damage case 1 – cccc plate. (a) element mesh numbers, (b) damage index, and (c) comparison of  4,8h before and after damage. optimization: severity of damage detection in this section, we compare the performance of damage identification results of three metaheuristic algorithms, namely the wild horse optimizer (who), harris hawks optimization (hho), and arithmetic optimization algorithm (aoa), coupled with the frequency response function (frf) damage index. the fitness function is defined as the error between and , and is calculated from the following equation:  measuredi  calculated i s. khatir et alii, frattura ed integrità strutturale, 58 (2021) 416-433; doi: 10.3221/igf-esis.58.30 425 (26) where is extracted from eqn. 5 for a fair comparison, we used a population of 50 solutions and a maximum number of iterations equal to 100. fig. 5 depicts the fitness convergence for the three damages cases. the who algorithm presents an obvious better performance in all cases, converging toward a value of 1e-10 in the first and second case, 1e-5 in the last case. we also notice that the convergence speed is much higher in the case of single damage than in the cases where there are multiple damages. the case of four damages corresponds to the highest computational time. on the other hand, the hho algorithm presents a good result in the single damage case, but it is outperformed in the other cases. lastly, aoa algorithm presents the weakest performance on the three algorithms in these cases of damage detection. (a) (b) (c) figure 3: damage case 2 – cccc plate. (a) element mesh numbers, (b) damage index, and (c) comparison of  4,8h before and after damage.      1 n measured calculated i i i of  calculatedi s. khatir et alii, frattura ed integrità strutturale, 58 (2021) 416-433; doi: 10.3221/igf-esis.58.30 426 (a) (b) (c) figure 4: damage case 3 – cccc plate. (a) element mesh numbers, (b) damage index, and (c) comparison of  4,8h before and after damage. tab. 3 shows the fitness values for all cases in some iteration pints. in this table, the performance of who algorithm is better from the earliest stage of the search, while the other two algorithms make progress but in a much slower manner. fig. 6 presents the damage index convergence in the first case, comparing the performance of the three algorithms. this figure shows that all algorithms are efficient for this variable; as shown in tab. 4, the three algorithms converge toward the actual damage severity, but the who algorithm accuracy is higher. s. khatir et alii, frattura ed integrità strutturale, 58 (2021) 416-433; doi: 10.3221/igf-esis.58.30 427 figure 5: fitness for all damage case – cccc plate: (a) case 1, (b) case 2 and (c) case 3. iteration case 1 case 2 case 3 who hho aoa who hho aoa who hho aoa 1 0.00403 0.003507 0.06316 0.032108 0.08396 0.14573 0.302640 0.229766 0.221604 10 1.12e-05 0.000120 0.00333 0.000387 0.00187 0.14573 0.029882 0.124371 0.178281 20 1.04e-08 0.000120 0.00333 3.32e-05 0.00173 0.14573 0.005921 0.121648 0.131715 30 9.63e-11 5.51e-05 0.00333 2.90e-07 0.00159 0.11978 0.001183 0.112177 0.113453 40 2.95e-13 5.51e-05 0.00333 1.36e-08 0.00157 0.09393 0.000386 0.109543 0.101677 50 2.22e-16 8.13e-06 0.00333 6.84e-10 0.00157 0.07503 0.000195 0.069667 0.087802 60 2.22e-16 1.17e-06 0.00333 1.03e-12 0.00077 0.05913 0.000136 0.066543 0.050043 70 2.22e-16 9.57e-07 0.00333 1.74e-14 0.00064 0.04168 4.41e-05 0.064518 0.050043 80 0 5.05e-09 0.00333 3.39e-15 0.00058 0.02033 1.28e-05 0.062890 0.050043 90 0 4.13e-14 0.00333 2.29e-15 0.00055 0.01958 8.08e-07 0.062193 0.045408 100 0 6.66e-16 0.00041 9.16e-16 0.00055 0.01958 1.13e-07 0.023583 0.045408 table 3: variation of fitness for all damage cases – cccc plate: case 3. f it n es s f it n es s f it n es s s. khatir et alii, frattura ed integrità strutturale, 58 (2021) 416-433; doi: 10.3221/igf-esis.58.30 428 figure 6: damage index – cccc plate: case 1. iteration element 15 who hho aoa 1 14.78 15.19 11.68 10 15.00 14.99 15.18 20 15.00 14.99 15.18 30 15.00 15.00 15.18 40 15 15.00 15.18 50 15 15.00 15.18 60 15 15.00 15.18 70 15 15.00 15.18 80 15 15.00 15.18 90 15 15 15.18 100 15 15 14.98 actual 15% table 4: variation of damage index – cccc plate: case 1. fig. 7 presents the damage index identification in the second case, comparing the performance of the three algorithms as this case has two damages. fig. 7(a) is dedicated to the severity of the damage in the first damaged element, and fig. 7(b) is for the second element. this figure shows that all algorithms are efficient; as shown in tab. 5, the three algorithms converge toward the actual damage severity. who algorithm accuracy is higher in this case as well, with noticeable fluctuation in the prediction of aoa algorithm; this is due to its exploitation technique; in this particular case, this method does not allow the algorithm to converge quickly. the details in tab. 5, suggest that the who algorithm performance is apparent in the early iterations. and the fluctuation in the aoa algorithm gets smaller by the progress of iterations. but it this algorithm is not able to find the actual damage severity with high accuracy within the 100 iteration limit. d am ag e in d ex [ % ] s. khatir et alii, frattura ed integrità strutturale, 58 (2021) 416-433; doi: 10.3221/igf-esis.58.30 429 figure 7: damage index – cccc plate: case 2. iteration element 23 element 87 who hho aoa who hho aoa 1 19.57 24.88 15.00 21.83 23.78 27.73 10 19.98 19.93 15.00 19.98 20.09 27.73 20 20.00 19.90 15.00 20.00 20.06 27.73 30 20.00 19.89 26.87 20.00 20.04 15.87 40 20.00 19.90 25.72 20.00 20.05 17.02 50 20.00 19.90 18.51 20.00 20.05 24.23 60 20 19.95 19.31 20 20.02 23.42 70 20 19.96 16.58 20 20.02 19.28 80 20 19.96 21.42 20 20.02 19.53 90 20 19.96 19.82 20 20.01 21.12 100 20 19.96 19.82 20 20.01 21.12 actual 20% 20% table 5: variation of damage index – cccc plate: case 2. fig. 8 presents the damage index identification in the last case, comparing the performance of the three algorithms of four damages. fig. 8(a) is dedicated to the severity of the damage in the first damaged element, and fig. 8(b) is for the second element, and fig. 8(c) and fig. 8(d) for the third and fourth elements, respectively. this figure shows that this case presents a challenge in the first 20 iterations; the who algorithm converges toward the correct damage severities in all four elements. the aoa and hho algorithms are efficient in only two cases separately, with aoa algorithm corresponding to the highest error. the fluctuation technique is irregular in this case. hho algorithm is noticed to have a less smooth convergence than the earlier cases. tab. 6 shows that the three algorithms converge toward the actual damage severity with different error levels. the who algorithm is the most accurate in this case, and the aoa algorithm corresponds to the most significant error rate. d am ag e in d ex [ % ] d am ag e in d ex [ % ] s. khatir et alii, frattura ed integrità strutturale, 58 (2021) 416-433; doi: 10.3221/igf-esis.58.30 430 figure 8: damage index – cccc plate: case 3. iteration element 33 element 37 element 62 element 78 who hho aoa who hho aoa who hho aoa who hho aoa 1 29.77 11.76 0.00 16.05 20.02 0.00 47.71 0.00 23.52 17.88 8.68 0.00 10 6.70 8.08 20.09 12.34 15.93 20.09 17.87 8.39 31.08 4.46 8.08 0.00 20 10.60 7.56 0.75 15.41 15.54 3.95 20.19 7.78 14.93 5.44 6.91 0.00 30 9.93 9.39 0.00 15.02 16.29 4.59 19.99 9.48 15.58 5.04 7.48 0.00 40 10.02 10.29 1.33 15.03 15.71 5.92 20.03 10.44 16.91 5.02 8.34 0.00 50 10.03 15.80 3.21 15.01 15.74 7.81 20.02 16.92 17.65 5.01 6.48 0.00 60 10.02 16.94 9.50 15.01 16.90 14.09 20.01 18.23 23.94 5.01 6.65 6.29 70 10.00 16.87 9.50 15.00 17.04 14.09 20.00 18.41 23.94 5.00 6.58 6.29 80 10.00 16.32 9.50 15.00 16.65 14.09 20.00 18.02 23.94 5.00 6.50 6.29 90 10.00 16.35 10.54 15.00 16.76 15.14 20.00 18.12 22.90 5.00 6.77 7.33 100 10.00 7.67 10.54 15.00 15.18 15.14 20.00 18.59 22.90 5.00 4.30 7.33 actual 10% 15% 20% 5% table 6: variation of damage index – cccc plate: case 3. d am ag e in d ex [ % ] d am ag e in d ex [ % ] d am ag e in d ex [ % ] d am ag e in d ex [ % ] s. khatir et alii, frattura ed integrità strutturale, 58 (2021) 416-433; doi: 10.3221/igf-esis.58.30 431 fig. 9 presents the estimated severity of all damage cases compared to the actual severity level in the blue bar. the accuracy is highest for the first two cases. the considerable difference is shown in the case of four damages, shown in fig. 9(c). figure 9: the estimated severity of all damage cases – cccc plate. tab. 7. compares the computations time in seconds, showing that the aoa and the who algorithm correspond to the lowest cpu time, with a slight advantage to the who algorithm. hho has the highest cpu time in all cases. case who hho aoa 1 4781.614611 11627.064433 4916.620988 2 4826.606647 11703.876201 4854.762505 3 4806.776610 11664.881398 4888.876639 table 7: cpu times. conclusion n this paper, we studied the performance of three metaheuristic algorithms in the case of a cccc plate; the problem is formulated as minimization of rfr damage indicator difference as an inverse problem. the plate is a square shape with 100 quadratic elements discretization, and the goal is to identify the damaged element and its damage severity level. the optimization algorithms showed acceptable performance within the considered search condition, with who algorithm corresponding to the best outcome in all cases and in terms of computational time. hho and aoa algorithms presented relatively comparable performance, with aoa algorithm having an advantage in cpu time. the single and double damage cases presented a moderate challenge compared to the third case, with four damages with different damage severity. showing that the frf indicator coupled with metaheuristic algorithms can easily handle the isolated variables, namely the element position and damage severity. while the case of multi variables with a higher number of damaged elements highlighted the good performance of who algorithm in the considerably limited number of iterations. element 23 element 87 0 5 10 15 20 25 30 d am ag e in d ex [ % ] actual who hho aoa element 15 0 5 10 15 20 25 30 d am ag e in d ex [ % ] element 33 element 37 element 62 element 78 0 5 10 15 20 25 30 d am ag e in d ex [ % ] (c) (a) (b) i s. khatir et alii, frattura ed integrità strutturale, 58 (2021) 416-433; doi: 10.3221/igf-esis.58.30 432 references [1] dokeroglu, t., sevinc, e., kucukyilmaz, t., cosar, a. (2019). a survey on new generation metaheuristic algorithms, computers & industrial engineering, 137, pp. 106040. [2] gandomi, a.h., yang, x.-s., talatahari, s., alavi, a.h. (2013). metaheuristic algorithms in modeling and optimization, metaheuristic applications in structures and infrastructures, pp. 1-24. [3] abdel-basset, m., abdel-fatah, l., sangaiah, a.k. (2018). metaheuristic algorithms: a comprehensive review, computational intelligence for multimedia big data on the cloud with engineering applications, pp. 185-231. [4] tiachacht, s., bouazzouni, a., khatir, s., behtani, a., zhou, y.-l.-m., wahab, m.a. (2018). structural health monitoring of 3d frame structures using finite element modal analysis and genetic algorithm, journal of vibroengineering, 20(1), pp. 202-214. [5] zenzen, r., belaidi, i., khatir, s., wahab, m.a. (2018). a damage identification technique for beam-like and truss structures based on frf and bat algorithm, comptes rendus mécanique, 346(12) pp. 1253-1266. [6] zenzen, r., khatir, s., belaidi, i., le thanh, c., wahab, m.a. (2020). a modified transmissibility indicator and artificial neural network for damage identification and quantification in laminated composite structures, composite structures, 248 pp. 112497. [7] cuong-le, t., nghia-nguyen, t., khatir, s., trong-nguyen, p., mirjalili, s., nguyen, k.d. (2021). an efficient approach for damage identification based on improved machine learning using pso-svm, engineering with computers, pp. 1-16. [8] khatir, s., boutchicha, d., le thanh, c., tran-ngoc, h., nguyen, t., abdel-wahab, m. (2020). improved ann technique combined with jaya algorithm for crack identification in plates using xiga and experimental analysis, theoretical and applied fracture mechanics, 107, pp. 102554. [9] chen, c., yu, l. (2020). a hybrid ant lion optimizer with improved nelder–mead algorithm for structural damage detection by improving weighted trace lasso regularization, advances in structural engineering, 23(3) pp. 468-484. [10] livani, m., khaji, n., zakian, p. (2018). identification of multiple flaws in 2d structures using dynamic extended spectral finite element method with a universally enhanced meta-heuristic optimizer, structural and multidisciplinary optimization, 57(2), pp. 605-623. [11] huang, m., cheng, s., zhang, h., gul, m., lu, h. (2019). structural damage identification under temperature variations based on pso–cs hybrid algorithm, international journal of structural stability and dynamics, 19(11) pp. 1950139. [12] benaissa, b., hocine, n.a., belaidi, i., hamrani, a., pettarin, v. (2016). crack identification using model reduction based on proper orthogonal decomposition coupled with radial basis functions, structural and multidisciplinary optimization, pp. 1-10. [13] benaissa, b., köppen, m., wahab, m.a., khatir, s. (2017). application of proper orthogonal decomposition and radial basis functions for crack size estimation using particle swarm optimization. in journal of physics: conference series. : iop publishing 012014. [14] samir, k., brahim, b., capozucca, r., wahab, m.a. (2018). damage detection in cfrp composite beams based on vibration analysis using proper orthogonal decomposition method with radial basis functions and cuckoo search algorithm, composite structures, 187, pp. 344-353. [15] mishra, m., barman, s.k., maity, d., maiti, d.k. (2020). performance studies of 10 metaheuristic techniques in determination of damages for large-scale spatial trusses from changes in vibration responses, journal of computing in civil engineering, 34(2), pp. 04019052. [16] ding, z., li, j., hao, h.(2020). non-probabilistic method to consider uncertainties in structural damage identification based on hybrid jaya and tree seeds algorithm, engineering structures, 220, pp. 110925. [17] moezi, s.a., zakeri, e., zare, a. (2018). a generally modified cuckoo optimization algorithm for crack detection in cantilever euler-bernoulli beams, precision engineering, 52, pp. 227-241. [18] abualigah, l., diabat, a., mirjalili, s., abd elaziz, m., gandomi, a.h. (2021). the arithmetic optimization algorithm, computer methods in applied mechanics and engineering, 376, pp. 113609. doi: 10.1016/j.cma.2020.113609. [19] heidari, a.a., mirjalili, s., faris, h., aljarah, i., mafarja, m., chen, h. (2019). harris hawks optimization: algorithm and applications, future generation computer systems, 97, pp. 849-872. doi: 10.1016/j.future.2019.02.028. [20] naruei, i., keynia, f. (2021). wild horse optimizer: a new meta-heuristic algorithm for solving engineering optimization problems, engineering with computers, doi:10.1007/s00366-021-01438-z. [21] wang, z., lin, r., lim, m. (1997). structural damage detection using measured frf data, computer methods in applied mechanics and engineering, 147(1-2), pp. 187-197. s. khatir et alii, frattura ed integrità strutturale, 58 (2021) 416-433; doi: 10.3221/igf-esis.58.30 433 [22] khatir, s., tiachacht, s., le thanh, c., ghandourah, e., mirjalili, s., abdel wahab, m. (2021). an improved artificial neural network using arithmetic optimization algorithm for damage assessment in fgm composite plates, compos. struct., 273, pp. 114287. doi: 10.1016/j.compstruct.2021.114287. [23] dawe, d.j., roufaeil, o.l. (1980). rayleigh-ritz vibration analysis of mindlin plates, j. sound vibrat., 69(3), pp. 345359. doi: 10.1016/0022-460x(80)90477-0. [24] liew, k.m., wang, j., ng, t.y., tan, m.j. (2004). free vibration and buckling analyses of shear-deformable plates based on fsdt meshfree method, j. sound vibrat., 276(3), pp. 997-1017. doi: 10.1016/j.jsv.2003.08.026. [25] ferreira, a.j. (2009). matlab codes for finite element analysis. springer. microsoft word numero_34_art_7 c. ronchei et alii, frattura ed integrità strutturale, 34 (2015) 74-79; doi: 10.3221/igf-esis.34.07 74 focussed on crack paths life estimation by varying the critical plane orientation in the modified carpinteri-spagnoli criterion camilla ronchei, andrea carpinteri, giovanni fortese, andrea spagnoli, sabrina vantadori department of civil-environmental engineering and architecture, university of parma parma, italy camilla.ronchei@nemo.unipr.it marta kurek, tadeusz łagoda department of mechanics and machine design, opole university of technology opole, poland abstract. the modified carpinteri-spagnoli (c-s) criterion is a multiaxial high-cycle fatigue criterion based on the critical plane approach. according to such a criterion, the orientation of the critical plane is linked to both the averaged directions of the principal stress axes and the fatigue properties of the material. the latter dependence is taken into account through a rotational angle, . then, the multiaxial fatigue strength estimation is performed by computing an equivalent stress amplitude on the critical plane. in the present paper, some modifications of the original  expression are implemented in the modified c-s criterion. more precisely, such modified expressions of  depend on the ratio between the fatigue limit under fully reversed shear stress and that under fully reversed normal stress (in accordance with the original expression), and can be employed for metals ranging from mild to very hard fatigue behaviour. some experimental data available in the literature are compared with the theoretical results in order to verify if the modified expressions are able to improve the fatigue strength estimation capability of the modified c-s criterion. keywords. constant amplitude loading; fatigue lifetime prediction; modified c-s criterion; multiaxial highcycle fatigue; critical plane. introduction n the high-cycle fatigue related to a linear-elastic material, several criteria available in the literature to assess fatigue strength are based on the so-called critical plane approach. this approach takes into account the crack nucleation and early growth mechanisms experimentally observed during cyclic loading. according to such criteria, fatigue failure assessment is performed on a specific plane (the critical plane) within the test specimen or component. the above criteria are characterized by different rules suitable to define the orientation of the critical plane but, for all these criteria, the fatigue life assessment is carried out by employing a combination of stresses acting on the critical plane itself [1] (see also the review on the critical plane and other approaches to multiaxial fatigue, published in ref. [2]). for instance, several researchers define the critical plane as the plane where amplitude or some stress component or a combination of them exhibits a maximum value [3-6]. alternatively, the position of the critical plane may be correlated with that of the principal stress directions by using appropriate weight functions [7]. i c. ronchei et alii, frattura ed integrità strutturale, 34 (2015) 74-79; doi: 10.3221/igf-esis.34.07 75 it is important to highlight that the above definitions represent just some of those reported in the literature (a general account on the critical plane orientation is given in ref. [8]). among the critical plane fatigue criteria, the modified carpinteri-spagnoli (c-s) criterion [9], a simplified version of the original c-s criterion [10], correlates the critical plane orientation with the weighted mean directions of the principal stress through an off-angle,  (which is regarded to be dependent on the ratio between the fatigue limit under fully reversed shear and that under fully reversed normal stress, , 1 , 1af af   ). then, the multiaxial fatigue assessment is performed by using a nonlinear combination of the equivalent normal stress amplitude and the shear stress amplitude acting on the critical plane (see ref. [11] for a general account of the criterion). in accordance with the original idea developed by carpinteri et al. [9, 10], łagoda et al. [12] have recently proposed some modifications to the original  expression which, in limit conditions, are pertinent to both mild and very hard metals. the goal of the present paper is to implement the different expressions of the rotational angle  in the modified c-s criterion. in order to verify whether the above expressions are able to improve the fatigue lifetime estimation capability of the criterion, some experimental data available in the literature [13-17] are examined. critical plane orientation and fatigue life evaluation he high-cycle multiaxial fatigue criterion, known as the modified carpinteri-spagnoli (c-s) criterion [9], is a simplified version of the original one proposed in ref. [10]. in particular, the modifications are related to a simplified weighting procedure to determine the averaged principal stress axes, and to the effect of the non-zero normal mean stress on the fatigue limit. fig. 1 summarizes how to use the modified c-s criterion to estimate fatigue lifetime of structural components failing in high-cycle fatigue regime. figure 1: graphical representation of the modified c-s criterion. in particular, from the stress state at a material point p, the averaged directions of principal stress axes can be determined on the basis of their instantaneous directions by means of the averaged values of the principal euler angles. the orientation of the critical plane is linked to the above averaged directions through the rotational angle :   2 1 , 1 , 13 2 1 45af af         (1) t c. ronchei et alii, frattura ed integrità strutturale, 34 (2015) 74-79; doi: 10.3221/igf-esis.34.07 76 then, the fatigue strength is assessed through an equivalent stress amplitude expressed by a quadratic combination of the equivalent normal stress amplitude ( ' ,a eqn ) and the shear stress amplitude ( ac ) acting on the critical plane. finally, the number of loading cycles to failure, fn , can be found by solving the following equation through an iterative procedure:     2 2 *2 2 2, 1' 0 , , 1 , 1 0 0 mm m af f f a eq a af af f n nn n c n n n                               (2) where 0n is the reference number of loading cycles (for example 6 0 2 10n   ), and m and *m are the slopes of s-n curve for fully reversed normal and shear stress, respectively. recently, łagoda et al. [12] have proposed some modifications to the original  expression. in accordance with the idea originally developed by carpinteri et al. [9-10] to assume that  is function of the ratio , 1 , 1af af   (such an expression can be employed for metals ranging from mild to very hard fatigue behaviour), the relationships reported in ref. [12] are the following:   4 2 , 1 , 1 9 1 45 8 af af         (3)   3 3 , 1 , 1 3 3 1 45 3 3 1 af af         (4)  4 , 1 , 1 3 3 1 45 3 3 3 af af        (5)     2 5 , 1 , 12 3 1 45 3 1 af af         (6) experimental validation n the present paper, the different relationships of the rotational angle  previously described are implemented in the modified c-s criterion in order to verify whether they are able to improve the above criterion in terms of lifetime estimation of some experimental test results available in the literature. the examined data are related to samples made of 30crnimo8 steel [13,14], 6082-t6 aluminum alloy [15,16] and s335j0 alloy steel [17] subjected to synchronous, sinusoidal, in-phase loading (with zero and non-zero mean value). the relevant mechanical properties for each examined material are reported in tab. 1. material u [mpa] , 1af  [mpa] m [-] , 1af  [mpa] *m [-] 30crnimo8 steel 1014 427.37 -0.13 371.52 -0.04 6082 t6 aluminium alloy 290 152.83 -0.11 87.90 -0.15 s355j0 alloy steel 611 276.58 -0.15 183.70 -0.09 table 1: static and fatigue properties for each examined material. i c. ronchei et alii, frattura ed integrità strutturale, 34 (2015) 74-79; doi: 10.3221/igf-esis.34.07 77 the mean square-root error method [12] is applied to the statistical analysis of the fatigue lifetime results determined by using the modified c-s criterion. in particular, the value of the root mean square logarithmic error is computed as follows:  2 ,exp , 1 log n f f cal i rms n n e n   (7) where n is the total number of data, ,expfn is the experimental multiaxial fatigue life, and ,f caln is the theoretical multiaxial fatigue life determined by considering eqs (1; 3-6) . the mean square error rmst is given by: 10 rmse rmst  . for the different examined materials, fig. 2 (a), (b) and (c) represents the mean square error obtained for the five expressions of angle  (from 1 to 5 ). 0 0.5 1 1.5 2 2.5 t r m s a) 30crnimo8 steel 1 = 16.49° 2 = 21.71° 3 = 19.12° 4 = 13.91° 5 = 4.30° 1.5 1.75 2 t r m s (b) 6082-t6 aluminium alloy 1 = 45.17° 2 = 45.09° 3 = 45.12° 4 = 45.24° 5 = 45.47° 0 0.5 1 1.5 2 2.5 3 t r m s (c) s355j0 alloy steel 1 = 37.72° 2 = 40.77° 3 = 39.40° 4 = 35.76° 5 = 28.41° figure 2: mean square error related to: (a) 30crnimo8 steel; (b) 6082 t6 aluminum alloy ; (c) s335j0 alloy steel. (a) (b) (c) c. ronchei et alii, frattura ed integrità strutturale, 34 (2015) 74-79; doi: 10.3221/igf-esis.34.07 78 a good agreement between experimental and theoretical results is in general observed, since the value of rmst is lower than 3 (note that if all the calculated results fell within the scatter band 2, the value of rmst would be equal to 2). moreover, the analysis of the results in terms of the mean square error for the examined materials indicates that: a) for 30crnimo8 steel, higher accuracy is gained for the orientation of the critical plane computed by means of 4 . note that, by implementing eq.(5) in the modified c-s criterion, the value of rmst decreases to 6% in comparison to that determined by applying the 1 expression; b) for 6082 t6 aluminum alloy, the same accuracy is deduced by using the five different  expressions, since the value of  is essentially the same; c) for s335j0 alloy steel, the most accurate result is provided by using the 5 expression to determine the critical plane, with a decrease of the rmst value up to 20.4% with respect to that deduced by computing the critical plane orientation through eq.(1). therefore, the implementation of the  relationships (proposed by łagoda) in the modified c-s criterion yields, only for materials characterized by fatigue limit ratio typical of hard and very hard metals, fatigue lifetime results different from those determined through the original  expression. in particular, the 4 and 5 expressions, respectively for 30crnimo8 steel and for s335j0 alloy steel, provide better results than those deduced by employing the other relationships. conclusions n the present paper, the orientation of the critical plane, linked to the averaged principal stress directions, is computed by taking into account different expressions of the rotation angle . in particular, such relationships have been implemented in the modified c-s criterion in order to estimate the fatigue lifetime by varying the critical plane orientation. the comparison with some experimental data related to stress-controlled fatigue tests of specimens under biaxial loading appears to be satisfactory. in particular, better estimations in terms of fatigue life are obtained for experimental data related to hard metals by using some of the modified  expressions (instead of the original one). references [1] socie, d.f., marquis, g.b., multiaxial fatigue, society of automative engineers, warrendale, usa (1999). [2] marquis, g.b., karjalainen-roikonen, p., long-life multiaxial fatigue of a nodular graphite cast iron, in: a. carpinteri, m. de freitas, a. spagnoli (eds.), biaxial/multiaxial fatigue and fracture, elsevier, amsterdam, (2003) 383-400. [3] susmel, l., lazzarin, p., a stress-based method to predict lifetime under multiaxial fatigue loadings, fatigue fract. engng mater. struct., 26 (2003), 1171-1187. doi: 10.1046/j.1460-2695.2003.00723.x. [4] łagoda, t, ogonowski, p., criteria of multiaxial random fatigue based on stress, strain and energy parameters of damage in the critical plane, mat. wiss. u. werkstofftech, 36 (2005) 429–37. [5] anes, v., reis, l., li, b, freitas, m., crack path evaluation on hc and bcc microstructures under multiaxial cyclic loading, int. j. fatigue, 58 (2014) 102-113, doi: 10.1016/j.ijfatigue.2013.03.014. [6] wang, c., shang, d.g., wang, x.w., a new multiaxial high-cycle fatigue criterion based on the critical plane for ductile and brittle materials, j. mater. eng. perform., 24 (2015) 816-824. doi: 10.1007/s11665-014-1335-7. [7] carpinteri, a., karolczuk, a., macha, e., vantadori, s., expected position of the fatigue fracture plane by using the weighted mean principal euler angles, int. j. fracture, 115 (2002), 87–99. doi: 10.1023/a:1015737800962. [8] karolczuk, a., macha, e., a review of critical plane orientations in multiaxial fatigue failure criteria of metallic materials, int. j. fracture, 134 (2005) 267-304. doi: 10.1007/s10704-005-1088-2. [9] carpinteri, a., spagnoli, a., vantadori, s., multiaxial fatigue assessment using a simplified critical plane-based criterion, int. j. fatigue, 33 (2011) 969-76. doi: 10.1016/j.ijfatigue.2011.01.004 [10] carpinteri, a., spagnoli, a., multiaxial high-cycle fatigue criterion for hard metals, int. j. fatigue, 23 (2001) 135-45. doi: 10.1016/s0142-1123(00)00075-x. i c. ronchei et alii, frattura ed integrità strutturale, 34 (2015) 74-79; doi: 10.3221/igf-esis.34.07 79 [11] carpinteri, a., spagnoli, a., vantadori, s., bagni, c., structural integrity assessment of metallic components under multiaxial fatigue: the c–s criterion and its evolution, fatigue fract. engng. mater. struct., 36 (2013) 870-883. doi: 10.1111/ffe.12037 [12] walat, k., łagoda, t., lifetime of semi-ductile materials through the critical plane approach, int. j. fatigue 67 (2014) 73-77. doi: 10.1016/j.ijfatigue.2013.11.019. [13] sanetra, c., untersuchungen zum fetigkeitsvwrhalten bei mehrachsiger randombeanspruchung unter biegung und torsion, dissertation, technische universitat clausthal (1991). [14] łagoda, t., macha, e., estimated and experimental fatigue lives of 30crnimo8 steel under in-and out-of-phase combined bending and torsion with variable amplitudes, fatigue fract. engng. mater. struct., 17 (1994) 1307-1318. doi: 10.1111/j.1460-2695.1994.tb00218.x [15] niesłony, a., łagoda, t., walat, k., kurek, m., multiaxial fatigue behaviour of selected aluminium alloys under bending with torsion loading condition, mat.-wiss. u. werkstofftech., 45 (10) (2014) 947-952. [16] kurek, m., łagoda, t., including of ratio of fatigue limits from bending and torsion for estimation fatigue life under cyclic loading, 6th new methods of damage and failure analysis of structural parts (mdfa), ostrava, czech republic (2014). [17] krzysztof, k., łagoda, t., new energy model for fatigue life determination under multiaxial loading with different mean values, int. j. fatigue, 66 (2014) 229-245. doi: 10.1016/j.ijfatigue.2014.04.008. microsoft word numero_49_art_59_2396 a. bendada et alii, frattura ed integrità strutturale, 49 (2019) 655-665; doi: 10.3221/igf-esis.49.59 655 focused on fracture mechanics versus environment numerical-experimental characterization of honeycomb sandwich panel and numerical modal analysis of implemented delamination aya bendada, djilali boutchicha, adel chouiter, mokhtaria miri université des sciences et de la technologie d’oran mohamed boudiaf, usto-mb, algérie. aya19-23-05@hotmail.fr(aya.bendada@univ-usto.dz), boutchicha@hotmail.com, achouiter25@gmail.com, m_miri31@yahoo.fr abstract. in this paper, a numerical characterization of aluminum honeycomb sandwich panel and experimental validation are proposed. firstly, numerical homogenization approach to predict the elastic properties of the core only are performed using initial finite element model of representative volume element (rve) which does not take into account the double thickness wall existing in aluminum core structure. according to these initial parameters, finite element model of sandwich composite plate is constructed to extract its elasto-dynamic characteristics. in order to validate the numerical achievements, experimental modal analysis of sandwich plate was carried out. secondly, the double thickness wall is selected to be introduced in the rve because of important error between results, new comparative study validates the improved elastic parameters and illustrate that the double thickness wall play an important role in the homogenization procedure. furthermore, the influence of the delamination defect on the vibration behavior of the composite panel is investigated using the validated 3-d finite element model. keywords. homogenization; honeycomb sandwich; frequency; mode shape; experimental modal analysis; delamination. citation: bendada, a., boutchicha, d., chouiter, a., miri, m., numericalexperimental characterization of honeycomb sandwich panel and numerical modal analysis of implemented delamination, frattura ed integrità strutturale, 49 (2019) 655-665. received: 06.03.2019 accepted: 15.06.2019 published: 01.07.2019 copyright: © 2019 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. introduction oneycomb sandwich panels are finding its use in many fields such as thermal and structural applications. these panels are extensively used in structural applications due to their properties such as high strength to weight ratio, high energy absorbing capacity, bending stiffness etc. due to such properties honeycomb panels are used for design and construction of lightweight transportation systems such as satellites, aircrafts, rocket fins, high speed trains, fast ferries where structural weight reduction is of prime importance. in order to use these materials in different applications, the knowledge of their mechanical behaviour is required. this calls for the development of rigorous mathematical and experimental methods capable of characterizing, modelling, designing and optimizing of the composite under any given set of conditions. numerical simulation of these structures requires, firstly, a proper experimental h http://www.gruppofrattura.it/va/49/2396.mp4 a. bendada et alii, frattura ed integrità strutturale, 49 (2019) 655-665; doi: 10.3221/igf-esis.49.59 656 identification of the core and the skins material behaviours, and secondly an adequate kinematic model to obtain a reasonable computational cost. for reasons of characterizing the honeycomb core, the cellular core is replaced by a quasihomogeneous medium, and the sandwich theory can be adopted to analyze the sandwich structure [1], in 1958 kelsey first provided a set of equations for xzg and yzg based on energy methods applied on the honeycomb cell walls[2]. gibson and ashby extended this analytical approach to drive all the nine orthotropic parameters [3]. other improvement of theorical model proposed by masters and evans for predicting the in-plane elastic stiffness of honeycomb cores based on deformation of honeycomb cells [4]. xu et al presented another investing approach [5]. chen and davalos improved an analytical model to calculate the modulus and interface constraints for extension problems [6]. a new analytical method to analyze the out-of-plane stiffness of honeycomb cores based on the modified laminate theory proposed by meraghni et al [7]. hu and al presented a complete review of the various kinematics and theories concerning the sandwich composite modeling [8] experimental methods on testing the elastic properties of honeycomb core have been developed. young’s moduli in the thickness direction were determined by compression tests [9]. cunningham et al proposed a new measurement technique for estimating the shear strain in a totally enclosed core [10]. saito et al considered an aluminium honeycomb sandwich panel as an orthotropic timoshenko beam for identifying the corresponding parameters by solving the least squares problems by a non-linear optimization method [11]. finite element model of e representative volume element (rve) of more complicated honeycomb sandwich cores [12] can be constructed to predict the elastic equivalent properties [13, 14]. in the past decades, many researchers have studied the vibration of sandwich structures. kerwin proposed a new theoretical model which is developed for the damping in sandwich structure [15]. by varying the thickness and materials of the skins, it’s possible to obtain a desired performance, particularly high strength and stiffnessto-mass ratio [16-18]. the objective of present paper is to carry out a comparative study on numerical and experimental techniques capable of predicting the mechanical parameters of honeycomb core. for initial prediction; the analytical gibson and ashby formulations are used for determining the constants parameters that will be compared with numerical homogenization results. once the honeycomb core is homogenized, the whole sandwich panel constituted of three elastic layers: isotropic/orthotropic/isotropic was created using the finite element code ansys and numerical modal analysis was performed. in order to validate the accuracy of the numerical approach, experimental modal analysis was carried out. according to the important error between numerical-experimental results, the inaccurate initial elastic constants need to be improved. in reality, the aluminum honeycomb core contains the double cell wall which is not taken into account in the initial rve. so, the in-plane parameter xyg and out-of plane parameters ze , yzg were selected to be estimated again by a new rve which takes into consideration the double thickness wall. comparison between the measured and the new computed eigenvalues and the corresponding eigenmodes shows the good agreement and minimized error which confirms the improved properties and the 3d model of panel that will be used for the next numerical analysis to predict the influence of the delamination on the structure rigidity. homogenization procedure the classical gibson method he analytical expressions (tab. 1) used for the elastic properties prediction of honeycomb core which is assimilated to an orthotropic material, are based on the important research of [3] where se and s  present the young modulus and poisson’s ratio of the cell material. the unit cell of the honeycomb core is a regular hexagon (fig.1) of dimensions: 0.08t mm , 11.085h mm , 030  , density of 329 /mkg and w-oriented configuration. figure 1: unit regular hexagon cell of honeycomb with simple wall. t a. bendada et alii, frattura ed integrità strutturale, 49 (2019) 655-665; doi: 10.3221/igf-esis.49.59 657 in-plane (x, y) parameters out-of-plane parameters xe :young modulus in x direction 3 3 sin cos s h t l e l              ze :young modulus in z direction 2 2 sin cos s h t l e hl l                   ye :young modulus in y direction 3 2 cos sin sin s t e hl l               yzg :shear modulus in yz plane cos sin s t g hl l          xyg :shear modulus in xy plane 3 2 sin 2 1 cos s h t l e l h h l l                         xzg shear modulus in xz plane sin 2 1 cos s h t lg ll h               poisson’s ratio xy 2 sin sin cos h l         poisson’s ratio yz y s z e e  poisson’s ratio yx 2cos sin sin h l        poisson’s ratio xz x s z e e  table 1: equivalent elastic properties of honeycomb core of gibson. numerical approach in this study, an elaborated ansys program makes it possible to build the rve model consisting of 40 cells of dimensions 166.27xl mm , 86.4yl mm , 8.8zl mm , as shown in fig. 2, the material properties of the core are presented in tab. 2. the numerical homogenization method consists of series of simulations carried out on the rve. density () 2700 3/kg m poisson’s ratio 0.34 young modulus 69000 mpa figure 2: initial rve model. table 2: material properties. the rve model is meshed using shell element. three extension simulations in the directions x, y, z were applied on the rve to estimate young’s moduli xe , ye , ze and poisson’s ratios xy , yz , xz . young’s moduli are determined using the tensile behavior relations ships of uniaxial linear elasticity with simple transformations: i i i i i f e s    (1) a. bendada et alii, frattura ed integrità strutturale, 49 (2019) 655-665; doi: 10.3221/igf-esis.49.59 658 where if is the applied force on the rve when the displacement iu is imposed, si is the perpendicular surface to the displacement. poisson’s ratios are determined by the following equation: j ij i      with i j , , ,i j x y z (2) where the deformations   i , j are given by the following equations: i i i u l    and jj j u l    (3) with ,   i jl represents the length, thickness and width of the rve. the boundary conditions applied in each case for identifying the young’s moduli are given in tab. 3, tab. 4 presents the deformation of the rve in each extension numerical simulation. x direction y direction z direction 0x  0.0xu mm 0y  0.0yu mm 0z  0.0zu mm xx l 1.0xu mm yy l 1.0yu mm zz l 0.1yu mm / 2yy l 0.0yu mm / 2xx l 0.0xu mm / 2xx l 0.0xu mm / 2zz l 0.0zu mm / 2zz l 0.0zu mm / 2yy l 0.0yu mm table 3: extension boundary conditions. x direction y direction z direction (a) (b) (c) table 4: rve0 undeformed shape, rve1 deformed shape, in each case of extension simulation. shear moduli xyg , xzg , yzg are determined by the equation: i i ij ik i i f g s u  , i j k  , ik i ks l l  (4) if is the resulting shear forces in direction i by applying the displacement iu along the directions x ,y, z . the boundary conditions and deformation shape are given in tab. 5-6. a. bendada et alii, frattura ed integrità strutturale, 49 (2019) 655-665; doi: 10.3221/igf-esis.49.59 659 xyg xzg yzg 0y  0.0xu mm 0z  0.0xu mm 0z  0.0xu mm 0.0yu mm 0.0yu mm 0.0yu mm 0.0zu mm 0.0zu mm 0.0zu mm yy l 1.0xu mm zz l 1.0xu mm zz l 0.0xu mm 0.0yu mm 0.0yu mm 1.0yu mm 0.0zu mm 0.0zu mm 0.0zu mm table 5: shear boundary conditions. xyg xzg yzg table 6: rve0 undeformed shape, rve1 deformed shape in each case of shear simulation. analytical and numerical results in tab. 7, comparison between analytical and numerical results. it’s clearly seen that the obtained numerical equivalent parameters give a good agreement. constant parameters gibson ansys error (%) xe (mpa) 25.989 10 25.99 10 0.016 ye (mpa) 25.989 10 25.96 10 0.484 ze (mpa) 575.006 594.167 3.33 xyg (mpa) 21.497 10 21.475 10 1.46 xzg (mpa) 107.277 113.223 5.54 yzg (mpa) 107.277 105.645 1.52 xy 1 1 0.00 yz 53.54 10 53.33 10 5.93 xz 53.54 10 53.36 10 5.08 table 7: equivalent elastic properties of honeycomb core. numerical modal analysis o study the vibrational behavior of completely free honeycomb sandwich plate, 3-d model of panel is built and consists of thick core which is homogenized to orthotropic volume in the previous section, and thin face sheets joined with a core (fig. 3). it is meshed using solid element (solid185, brick 8node185) and consisted of 4620 t a. bendada et alii, frattura ed integrità strutturale, 49 (2019) 655-665; doi: 10.3221/igf-esis.49.59 660 nodes and 2592 elements. geometric dimensions of the panel are shown in tab. 8. the skins and the core are made of an aluminum alloy (tab. 2). table 8: geometric dimensions of the panel. figure 3: numerical model of honeycomb sandwich panel. experimental validation he non-destructive testing (ndt) is crucially important for composite structures during manufacturing, as well as in-service maintenance and repair and it play a fundamental role in the characterization of composite materials [19-21]. in this study, for the experimental modal procedure, the honeycomb sandwich plate surface is marked by 5 5 parallel grid points with the size of each element is 62.5 52.5mm mm . to avoid the boundary effects and presence of any other errors in free-free boundary condition experimental study, the structure is vertically suspended by flexible strings. fig. 4 shows the modal testing setup which is executed by exciting all marked points of the panel using a pcb086c03 impulse hammer whose sensitivity is 2.25 mv. consequently, a pcb356a15 accelerometer is fixed inside the structure at marked point number 1. a frequency response analyzer, national instruments (ni) cdaq-9184 executed the signal acquisition and conditioning. finally, the frequency response functions (frf) measurements (fig.5) and associated mode shape are obtained. figure 4: experimental set-up. figure 5: frf measurements at 25 different grid points. frequenc y hz a m pl it ud e g /n 500 2k1.5k1k 0 80 60 40 20 length (mm) width (mm) thick (mm) core 250 210 8.8 skin 250 210 0.6 t a. bendada et alii, frattura ed integrità strutturale, 49 (2019) 655-665; doi: 10.3221/igf-esis.49.59 661 initial comparative study tab. 9 shows the mode shapes achieved via experimental modal analysis and finite element analysis. mode experimental modal analysis finite element analysis 1st : torsion 2nd: bending 3rd: bending 4th: coupling 5th: coupling table 9: experimental and numerical mode shapes for a completely free honeycomb sandwich panel. a. bendada et alii, frattura ed integrità strutturale, 49 (2019) 655-665; doi: 10.3221/igf-esis.49.59 662 mode order experimental results (hz) numerical results (hz) error % 1 680.82 712.29 4.60 2 1081.42 1095.30 1.20 3 1393.90 1506.00 8.00 4 1511.35 1526.10 0.97 5 1638.42 1747.30 6.64 table 10: comparison between experimental and numerical results for simple thickness wall. it can be observed from tab. 9 that the mode shapes measured by experimental and numerical modal analysis are very much alike from the visual inspection, comparison between frequencies is shown in tab. 10, the maximum error is 8.00 %, and the mean error is 4.28%, results show that the equivalent elastic properties are not so efficient for reflecting the macro-mechanical parameters of the honeycomb core, this discrepancy can be explained by the neglect of the double thickness wall existing in aluminum honeycomb core (fig. 6) in the analytical and numerical homogenization procedure. figure 6: double thickness wall location. precise constant parameters n this step, we have modified the program by introducing the double thickness wall (fig. 7) to recalculate ze , xyg , yzg which influenced the results [14]. tab. 11 represents the improved elastic parameters. ze (mpa) 796.196 xyg (mpa) -21.169 10 yzg (mpa) 88.81 figure 7: rve with double wall. table 11: improved parameters. comparison between experimental frequencies and new identified results is presented in tab. 12. the maximum error is no more than 4.5%, results show that the improved orthotropic elastic properties determined on taking into account the double cell wall are appropriate. mode order experimental results (hz) new numerical results (hz) error % 1 680.82 702.04 3.2 2 1081.42 1091.20 0.9 3 1393.90 1456.70 4.5 4 1511.35 1497.50 0.9 5 1638.42 1692.00 3.2 table 12: comparison between experimental modal frequencies and new computational results. i a. bendada et alii, frattura ed integrità strutturale, 49 (2019) 655-665; doi: 10.3221/igf-esis.49.59 663 delamination size mode 1 mode 2 mode 3 mode 4 30 mm 131.9 hz 265.67 hz 305.99 hz 350.42 hz 60 mm 105.71 hz 241.90 hz 268.77 hz 279.13 hz 90 mm 85.65 hz 154.86 hz 164.99 hz 228.58 hz 120 mm 67.60 hz 94.90 hz 104.86 hz 219.45 hz table 13: frequencies and corresponding mode shapes of damaged composite plate. a. bendada et alii, frattura ed integrità strutturale, 49 (2019) 655-665; doi: 10.3221/igf-esis.49.59 664 effect of delamination continuous effort was addressing to study the vibrational behaviour of damaged composite plate using the numerically predicted parameters. the damages are inevitable in structures [22-23]; delamination is a common type of the honeycomb sandwich panel damage. in this work the detection of modal parameters of damaged honeycomb sandwich panel was carried out. we created a delamination of different size in one face only of sandwich panel. the natural frequencies and the mode shapes of a damaged model structure are obtained and presented in tab. 13. the results show that the natural frequencies are very influenced by this defect (reduced rigidity) and new mode shapes appear in each delamination size. conclusion rediction study for determining the accurate orthotropic parameters of honeycomb aluminum core were investigated. according to the numerical equivalent properties a finite element model of honeycomb sandwich panel was created to extract the dynamical characteristic (frequencies and mode shapes), experimental modal analysis was carried out to validate the numerical achievements. the important error between the computational results and experimental modal analysis led to introduce the double thickness wall in the representative volume elements for determining the precise properties. the good agreement of frequencies and also corresponding mode shapes between numerical and experimental results after introducing the double thickness walls shows that:  the neglect of double wall in the characterization of pure core gives not efficient elastic properties which affects the mechanical analysis results of honeycomb sandwich panel.  the numerical homogenization method using rve can provide accurate equivalent elastic constants of honeycomb core.  non-destructive experimental method based on a precise contact free–free measurement system is very effective to validate the numerical achievements. according to the efficient parameters, a numerical study of damaged panel model is carried out to examine the influence of delamination on the modal parameters of the structure. the results show that the natural frequencies became lower which can be explained by the degradation of structural rigidity due to delamination. references [1] hohe, j., becker, w. (2002). effective stress-strain relations for two-dimensional cellular sandwich cores: homogenization, materials models and properties, appl. mech, 55(1), 61. [2] kelsey, s., gellatly, r a., clark, b w. (1958). the shear modulus of foil honeycomb cores, aircraft engineering, 30, pp.294–302. [3] gibson, l., ashby, m f. 2nd éd., (1999). cellular solids: structure and properties, cambridge: cambrige solid state series. [4] masters, i g., evans, k e. (1996). models for the elastic deformation of honeycombs, composite structure, 35, pp. 403–422. [5] xu, x f., qiao, p. (2002). homogenized elastic properties of honeycomb sandwich panels with skin effect, journal solids and structures, 39, pp.2153–2188. [6] chen, a., davalos, j. (2005). solution including skin effect for stiffness and stress field of sandwich honeycomb core, j solids and structures, 42, pp. 2711–2739. [7] meraghni, f., desrumaux, f., benzeggagh, m l. (1999). mechanical behavior of cellular core for structural sandwich panels, composites: part a, 30, pp. 767–779. [8] hu, h., belouettar, s., daya, e m. (2006). evaluation of kinematic formulations for viscoelastically damped sandwich beam modeling, j sandwich struct master, 8, pp.477–495. [9] mujika, f., pujana, j., olave, m. (2011). on the determination of out-of-plane elastic properties of honeycomb sandwich panels, polymer testing, 30(2), pp.222–228. a p a. bendada et alii, frattura ed integrità strutturale, 49 (2019) 655-665; doi: 10.3221/igf-esis.49.59 665 [10] cunningham, p r., white, r g. (2001). a new measurement technique for the estimation of core shear strain in closed sandwich structures, composites structures, 51(3), pp.319–334. [11] saito, t., parbey, r d., kuno, s. o and al. (1997). parameter identification for aluminum honeycomb sandwich panels based on orthotropic timoshenko beam theory, journal sound vibration, 208 (2), pp.271–287. [12] nilsson, e., nilson, a c. (2002). prediction and measurement of some dynamic properties of sandwich structures with honeycomb and foam cores, journal of sound and vibration, 251(3), pp.409–430. [13] hohe, j., becker, w. (2001). a rafined analysis of the effective elasticity tenser for general cellular sandwich cores, international journal of solids and structures,38, pp.3689–3717. [14] keskes, b: compotement en fatigue des composites type sandwich nid d’abeille. dissertation. universté ferhat abbas algeria (2007). [15] kerwin, e m. (1959). damping of flexural waves by a constrained viscoelastic layer, journal of acoustical society of america., 31(7), pp. 952–962. [16] boudjemai, a., bekhti, m., bouanane, m h., si mohammed, a m., cooper, g and richardson, g.(2005). small satellite computer-aided design and manufacturing, proceedings of the european conference on spacecraft structures, materials and mechanical testing, pp.181-188, sp-581. [17] boudjemai, a., bouanane, m h., si mohammed, a m. (2007). structural modeling and small satellite optimization, page 51, second international congress design and modeling of mechanical systems, proceeding, pp. 12–21 march, monastir tunisia. [18] boudjemai, a., amri, r., mankour, a., salem, h., bouanane, m.h., boutchicha, d. (2011). modal analysis and [19] testing of hexagonal honeycomb plates used for satellite structural design, [quick edit] materials and design doi:10.1016. [20] hardik, p., jamadar n i. (2016). modal analysis of composite structure, international journal of advancement in engineering technology, management and applied sciences, 3(1), pp.71–82. [21] asif, m., khan, m a., khan, s., choudhry, r z. (2018). identification of an effective nondestructive technique for bond defect determination in laminate compositea technical review, journal of composite materials, pp.1-11. [22] sandeep, k. d., akhilesh, s. (2018). advances and researches on non-destructine testing: a review, materials today:proceedings, 5(2), pp. 3690–3698. [23] keskes, b., abbadi, a., azari, z., bouaouadja, n. (2015). static and fatigue characterization of nomex honeycomb sandwich panels, international review of civil engineering, 6(4), pp. 81–87. [24] keskes, b., menger, y., abbadi, a., gilgert, j., bouaouadja, n., azari, z. (2007). a fatigue characterization of honeycomb sandwich panels with a defect, materials and technology, 41(4), pp. 157–161. << /ascii85encodepages false /allowtransparency false /autopositionepsfiles true /autorotatepages /none /binding /left /calgrayprofile (dot gain 20%) /calrgbprofile (srgb iec61966-2.1) /calcmykprofile (u.s. web coated \050swop\051 v2) /srgbprofile (srgb iec61966-2.1) /cannotembedfontpolicy /error /compatibilitylevel 1.4 /compressobjects /tags /compresspages true /convertimagestoindexed true /passthroughjpegimages true /createjobticket false /defaultrenderingintent /default /detectblends true /detectcurves 0.0000 /colorconversionstrategy /cmyk /dothumbnails false /embedallfonts true /embedopentype false /parseiccprofilesincomments true /embedjoboptions true /dscreportinglevel 0 /emitdscwarnings false /endpage -1 /imagememory 1048576 /lockdistillerparams false /maxsubsetpct 100 /optimize true /opm 1 /parsedsccomments true /parsedsccommentsfordocinfo true 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/hrv (za stvaranje adobe pdf dokumenata najpogodnijih za visokokvalitetni ispis prije tiskanja koristite ove postavke. stvoreni pdf dokumenti mogu se otvoriti acrobat i adobe reader 5.0 i kasnijim verzijama.) /hun 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can be opened with acrobat and adobe reader 5.0 and later.) >> /namespace [ (adobe) (common) (1.0) ] /othernamespaces [ << /asreaderspreads false /cropimagestoframes true /errorcontrol /warnandcontinue /flattenerignorespreadoverrides false /includeguidesgrids false /includenonprinting false /includeslug false /namespace [ (adobe) (indesign) (4.0) ] /omitplacedbitmaps false /omitplacedeps false /omitplacedpdf false /simulateoverprint /legacy >> << /addbleedmarks false /addcolorbars false /addcropmarks false /addpageinfo false /addregmarks false /convertcolors /converttocmyk /destinationprofilename () /destinationprofileselector /documentcmyk /downsample16bitimages true /flattenerpreset << /presetselector /mediumresolution >> /formelements false /generatestructure false /includebookmarks false /includehyperlinks false /includeinteractive false /includelayers false /includeprofiles false /multimediahandling /useobjectsettings /namespace [ (adobe) (creativesuite) (2.0) ] /pdfxoutputintentprofileselector /documentcmyk /preserveediting true /untaggedcmykhandling /leaveuntagged /untaggedrgbhandling /usedocumentprofile /usedocumentbleed false >> ] >> setdistillerparams << /hwresolution [2400 2400] /pagesize [612.000 792.000] >> setpagedevice 404 not found microsoft word numero_46_art_3 n. hiyoshi et alii, frattura ed integrità strutturale, 46 (2018) 25-33; doi: 10.3221/igf-esis.46.03 25 developments in the fracture and fatigue assessment of materials and structures effect of additive elements bi/ni/ge on crack initiation and propagation for low-ag solders noritake hiyoshi university of fukui, japan hiyoshin@u-fukui.ac.jp mitsuo yamashita tohoku university, japan mitsuo-yamashita@jcom.home.ne.jp hiroaki hokazono fuji electric co., ltd., japan hokazono-hiroaki@fujielectric.com abstract. this study discusses an effect of additive elements on crack propagation behaviour for low-ag contain sn1.0ag0.7cu lead-free solders at high temperature. a cyclic push-pull loading tests for four kinds of sn1.0ag0.7cu solders were conducted at 313 k with a single hole specimen. stress amplitude of solders containing additive element bi were bigger than that of bi-free solders. crack initiation cycle of solders containing bi were earlier than that of bi-free solders. low-ag solders containing bi had shorter crack propagation cycles than that of bi-free solders. these results indicate that the additive element bi have the effects on the crack initiation and propagation cycles, that is, bi accelerates the crack propagation rate. we also discuss the adaptation of j-integral range parameter to the crack propagation rate evaluation for solders. j-integral range parameter evaluates the crack propagation rate for low-ag solders independent of the additive elements. keywords. additive elements; crack initiation; crack propagation; leadfree solder; low-ag. citation: hiyoshi, n., yamashita, m., hokazono, h., effect of additive elements bi/ni/ge on crack initiation and propagation for low-ag solders, frattura ed integrità strutturale, 46 (2018) 25-33. received: 07.03.2018 accepted: 15.04.2018 published: 01.10.2018 copyright: © 2018 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. introduction oldering is an important and a fundamental technique for electronic device mounting. it is well known that sn-pb solders are not allowed to use because it contains pb which is a harmful element to the earth environment and human bodies. there are many kinds of candidate lead (pb)-free solders and it is needed to investigate their s http://www.gruppofrattura.it/va/46/3.mp4 n. hiyoshi et alii, frattura ed integrità strutturale, 46 (2018) 25-33; doi: 10.3221/igf-esis.46.03 26 mechanical properties and fatigue life [1]-[6]. solder joints in electronic devices undergo cyclic fatigue damage caused by not only mechanical loading but also thermal loading due to the mismatch of thermal expansion coefficient of different connecting parts. the solder joints also have lots of stress concentration parts, so that it is useful for fatigue life estimation of electronic devices to make clear the cyclic crack initiation and propagation behaviour of solders from the stress concentration part at commercial operating temperature. although sn-3.0ag-0.5cu lead-free solder is widely used solder all over the world, there are some issues for the solder. one of these issues is that high material cost due to it contains ag element. there are lots of candidate lead-free solders substitute for sn-3.0ag-0.5cu solder in order to reduce the material cost. sn-low-ag-cu solders which is one of the candidate solders have a lower material cost than that of sn-3.0ag-0.5cu solder as reducing ag element, so that the snlow-ag-cu solders are useful material for industrial use. the melting point temperature of sn-low-ag-cu solders is 500 k and the material cost is about 4,800jpy (japanese yen) per 1kg while sn-3.0ag-0.5cu solder costs about 7,500jpy. although it is important for commercial safety products design to clarify not only tensile strength and mechanical properties but also fatigue life of the electronic materials, there is little experimental research paper on sn-low-ag-cu solders. there is also little research paper on crack initiation and propagation behaviour of the solders at commercial operating temperatures. the reason for little research paper on the crack investigation of solders might be a difficulty of testing technique for solders which have low strength and small hardness. this study discusses the crack initiation and propagation behaviour of sn-low-ag-cu solders at high temperature. a cyclic push-pull loading tests with a single hole specimen were conducted to investigate the crack initiation and propagation behaviour of the solders. this study also discusses the adaptation of j-integral range parameter for the crack propagation rate evaluation. experimental procedure he materials tested in this study are four kinds of low-ag solders of which chemical composition are listed in tab. 1. sn1.0ag0.7cu solder (snagcu) contains lower ag element in order to reduce the coarse intermetallic compound forming and to reduce the materials costs. the melting point temperature of snagcu is 500 k. sn1.0ag0.7cunige solder (snagcu+nige) is the solder which is added 0.07% ni and 0.01% ge to snagcu. sn1.0ag0.7cu2.0bi solder (snagcu+bi) is the solder which is added 2.0% bi to snagcu. sn1.0ag0.7cu2.0binige solder (snagcu+binige) is the solder which is added 2.0% bi, 0.07% ni and 0.01% ge to snagcu. a cyclic push-pull loading tests were conducted with a single hole specimen. fig, 1 shows shape and dimensions of the specimen, which has a single through hole with 1mm in diameter at a center of the specimen as a stress concentration part. the specimen has a stress concentration factor of kt=2.72, which is calculated by using eqn. (1) [7]. 2 3 3.00 3.13 3.66 1.53t d d d k w w w                     (1) where, d and w is diameter of the center thorough hole and specimen width, respectively. the specimen is produced by a mechanical procedure from a low-ag solders ingot which were casted under controlled temperature and controlled instruction. figure 1: shape and dimensions of the specimen (mm). fig, 2 is a photograph of an electric hydraulic cyclic push-pull loading apparatus for solders. a 10kn small capacity actuator and a 10kn capacity load cell are adapted in order to conduct the fatigue test for solders. the cyclic push-pull t n. hiyoshi et alii, frattura ed integrità strutturale, 46 (2018) 25-33; doi: 10.3221/igf-esis.46.03 27 loading tests were conducted under strain control mode with fully reversed symmetrical triangle waveform. the applied strain ratio was r=-1. the rapid strain rate of 0.1%/s was used in order to eliminate a creep damage during the cyclic loading. an axial extensometer with linear variable differential transformer was used to measure the axial total strains of 10mm gage part. to avoid unexpected bending deformation of the specimen or unexpected cracking at the location of the extensometer rod tips, two small bumps of epoxy resin with grooves were formed on the specimen surface and the tips of the extensometer rods were placed on the grooves [8]. (a) general view (b) enlarged view of gage part of the specimen figure 2: cyclic push-pull loading apparatus with crack observation system. the specimen was heated up to 313 k with rubber heaters which are attached to both upper and lower connecting rods. we had confirmed in advance that temperature distribution and variation of the specimen during the tests were satisfied with the testing standard for solders [8]. crack initiation and propagation behaviour was observed with a ccd camera and a lcd monitor. crack length (2a), which is defined as the length from one end to another end of the crack in a horizontal direction including the center through hole, was also measured with the ccd camera view. crack initiation cycle (ni) was defined as the cycle of a newly 0.01mm in crack length were observed at the center through hole. the number of cycles to failure (nf) was defined as the cycle of 25 percent tensile stress amplitude drop from that at a midlife of nf. low-ag solders sn ag cu bi ni ge sn1.0ag0.7cu bal. 1.0 0.7 ------ sn1.0ag0.7cunige bal. 1.0 0.7 --0.07 0.01 sn1.0ag0.7cu2.0bi bal. 1.0 0.7 2.0 ---- sn1.0ag0.7cu2.0binige bal. 1.0 0.7 2.0 0.07 0.01 table 1: chemical composition of material tested (mass%). experimental results and discussion stress-strain relationship and crack propagation direction ig. 3 shows stress-strain relationship for four kinds of low-ag solders at 100th cycle. there is stress amplitude difference between snagcu / snagcu+nige bi-free solders and snagcu+bi / snagcu+binige solders containing bi. bigger stress amplitude of snagcu+bi / snagcu+binige solders indicates that bi element increase the stress amplitude for cyclic loading. fig, 4 is a photograph of surface crack observation results after the tests. main crack initiated from edge of the center through hole and propagated in the maximum shear direction for snagcu (photo (a) and (b)). crack propagation direction of snagcu+nige were also the maximum shear direction (photo (c) and (d)). on the other hand, crack f n. hiyoshi et alii, frattura ed integrità strutturale, 46 (2018) 25-33; doi: 10.3221/igf-esis.46.03 28 propagation direction of solders containing bi were complicated. one side crack propagated in the principal direction and a propagation direction of another crack changed from the maximum shear direction to the principal direction for snagcu+bi (photo (e) and (f)). crack propagated in the maximum shear direction for snagcu+binige in the smaller strain range (photo (g)), but crack propagation direction of one side for snagcu+binige in the larger strain range was changed from the principal direction to the maximum shear direction (photo (h)). the crack propagation direction difference and the direction changing behaviour among the low-ag solders might depend on the existence of bi element. the detailed crack propagation mechanism and effect of bi element on the crack propagation direction are still unknown, we need more sufficient crack observations and data analysis. -0.2 0 0.2 0.4 -40 -20 0 20 40 strain  s tr e s s  , m p a sac107 solders, 313k snagcu snagcu+nige snagcu+bi snagcu+binige =0.4% -0.4 figure 3: hysteresis loop at 100th cycle. =0.3% =0.4% snagcu snagcu +nige snagcu +bi snagcu +binige figure 4: crack propagation observations after the tests. (a) (b) (c) (d) (e) (f) (g) (h) 1mm l o ad in g di re ct io n n. hiyoshi et alii, frattura ed integrità strutturale, 46 (2018) 25-33; doi: 10.3221/igf-esis.46.03 29 crack initiation and propagation behaviour crack initiation cycle (ni) are summarized in tab. 2. crack initiation cycle ratio (ni/ni-sac) which is calculated as division by crack initiation cycle of snagcu at same strain range are shown in fig. 5. although crack initiation cycle of bi-free solders were over 1900 cycles, crack initiation cycle of solders containing bi were below 800 cycles. crack initiation cycle of solders containing bi were smaller than that of bi-free solders because the bigger stress amplitude was occurred for solders containing bi. larger crack initiation cycle of snagcu+nige as twice or three times as snagcu may indicates that ni and ge elements are useful for the long-life improving crack initiation cycle. but there is no crack initiation cycle ratio difference between snagcu+bi and snagcu+binige. these results indicate that effect of bi element as decreasing crack initiation cycle is more significant than effect of ni and ge elements as long-life improving crack initiation cycle. low-ag solders =0.3% =0.4% ni nf n2a=5mm ni nf n2a=5mm sn1.0ag0.7cu 1,910 14,200 19,870 1,950 12,000 17,450 sn1.0ag0.7cunige 5,990 12,850 28,250 3,600 18,350 18,350 sn1.0ag0.7cu2.0bi 500 3,220 5,400 500 4,800 4,800 sn1.0ag0.7cu2.0binige 800 2,040 2,040 150 3,180 3,200 table 2: crack initiation cycle (ni), number of cycles to failure (nf) and 5mm in crack length (n2a=5mm). 0 1 2 3 4 c ra c k in iti a tio n c y cl e r a tio , n i / n is a c sac107 solders, 313k snagcu +nige +bi +binige  =0.3%  =0.4% figure 5: effect of additive elements on crack initiation cycle. fig, 6 shows relationship between fatigue life ratio (n/nf) and crack length for the four kinds of low-ag solders at 313 k. the fatigue life ratio is the cycle number divided by the failure cycle which are listed in tab. 2. solid line in fig. 6 is an average data, which is lined based on all the experimental crack length data obtained. this figure depicts that crack initiated at early stage of the fatigue cycle for all the low-ag solders. crack initiated at the early stage and almost all the life period was crack propagation process for the four kinds of low-ag solders. the fatigue life ratio parameter also correlates with the crack length within a factor of 2 scatter band independent of the additive elements. these results also imply that it is important for establishing the accurate fatigue life estimation method to evaluate the crack initiation and propagation behaviour. the accurate evaluation of the crack propagation behaviour leads to the accurate fatigue life estimation. as we mentioned above crack initiation cycles of the four kinds of low-ag solders depend on the existence of bi element, but effect of ni and ge additive elements were smaller than that of bi element. since it is useful to investigate the crack propagation behaviour separately from the crack initiation phenomena, crack propagation cycle (np) was considered in n. hiyoshi et alii, frattura ed integrità strutturale, 46 (2018) 25-33; doi: 10.3221/igf-esis.46.03 30 this study as a new evaluation parameter. crack propagation cycle was calculated as subtract the crack initiation cycle (ni) from the total number of cycles (n). fig, 7 depicts crack propagation curves of the low-ag solders, crack initiation cycle was replaced into a first cycle of the crack propagation cycle. the crack propagation of snagcu (colored in black) and snagcu+nige (colored in blue) seem to have a slower crack propagation rate than that of snagcu+bi (colored in red) and snagcu+binige (colored in green). these results indicate that additive element bi increase the crack propagation rate, but effect of additive elements ni and ge on the crack propagation rate are small. 0.5 1.0 1.5 2.0 2.5 10 -1 10 0 10 1 10 2 fatigue life ratio n/nf h o ri zo n ta l cr a c k le n g th 2a , m m sac107 solders, 313k factor of 2  =0.3% snagcu snagcu+nige snagcu+bi snagcu+binige  =0.4% figure 6: crack length as a function of fatigue life ratio. 10000 20000 30000 0 2 4 6 number of propagation cycle np h o ri zo n ta l cr a ck l e n g th 2a , m m sac107 solders, 313k snagcu 1 snagcu+nige snagcu+bi snagcu+binige  =0.3%  =0.4% figure 7: crack propagation curve of sn-low-ag-cu solders at 313 k. fig, 8 shows the number of crack propagation cycles which crack length reached to 5mm for comparing the crack propagation rate. snagcu and snagcu+nige have almost same crack propagation cycles for both 0.3% and 0.4% strain n. hiyoshi et alii, frattura ed integrità strutturale, 46 (2018) 25-33; doi: 10.3221/igf-esis.46.03 31 range. snagcu+bi and snagcu+binige also have same crack propagation cycles at same strain range. there is no effect of additive elements ni and ge on the crack propagation rate, but there is bi element effect on the crack propagation rate as shown in fig. 8. the number of crack propagation cycle of solders containing bi were less than half of bi-free solders. 0 10000 20000 30000 n u m b e r o f c ra c k p ro p a g a ti o n c yc le sac107 solders, 313k snagcu +nige +bi +binige  =0.3%n 2 a = 5 m m 1  =0.4% figure 8: effect of additive elements on crack propagation cycle. crack propagation rate evaluation because of a small proof stress and a small proportional limit for solders, almost all the total strain range is equivalent to inelastic strain range [4]. the adaptation of j-integral range parameter which is usually used for crack propagation rate evaluation of conventional steel was discussed in this study in order to evaluate the crack propagation rate of low-ag solders. j-integral range value is calculated with dowling method which uses an experimental data and is expressed as eqn. (2) [9].  2*k s j e bb     (2) where, k*, e, bb is stress intensity factor range, young’s modulus and ligament of crack-initiated specimen, respectively. s is a tensile going energy calculated as hysteresis loop area of experimental load-displacement diagram. since a crack closer phenome was observed in the load-displacement diagram, tensile side area of a crack closer point was used for the tensile going energy calculation. fig, 9 shows correlation results of the crack propagation rate with j-integral range parameter. crack propagation data of bi-free solders are plotted in the left side of the graph, on the other hand the crack propagation data of solders containing bi are plotted in the right side in the same graph. this data grouping trend indicates that low-ag solders containing bi have faster crack propagation rate and larger j-integral range value than that of the bi-free solders. the approximation line equation which is lined based on the experimental data at steady crack propagation stage for each low-ag solder is expressed as follows, for snagcu, 3 0.852.27 10 da j dn    (3) for snagcu+nige, 4 0.518.72 10 da j dn    (4) n. hiyoshi et alii, frattura ed integrità strutturale, 46 (2018) 25-33; doi: 10.3221/igf-esis.46.03 32 for snagcu+bi, 3 0.731.75 10 da j dn    (5) for snagcu+binige, 3 0.723.29 10 da j dn    (6) slope of the approximation line equations are almost same although there are data grouping due to bi containing. this result indicates that j-integral range parameter evaluates the crack propagation rate of low-ag solders independent of a small quantity of additive elements. solid line colored in orange in fig. 9 is lined based on all the low-ag solders experimental data. approximation line correlates almost all the experimental data within a factor of 2 scatter band. crack propagation rate of the steady crack propagation stage is evaluated in the narrow band with j-integral range parameter and is expressed as following equation, 3 0.821.09 10 da j dn    (7) 10 -2 10 -1 10 0 10 1 10 -6 10 -5 10 -4 10 -3 10 -2 10 -1 j, n/mm d a /d n , m m /c y c le sac107 solders, 313k snagcu snagcu+nige snagcu+bi snagcu+binige  =0.3%  =0.4% 0.82 figure 9: relationship between crack propagation rate and j. conclusions ffect of additive elements on the crack initiation and propagation behaviour of sn-low-ag-cu solders were discussed in this study. (1) crack initiation cycle of solders containing bi were earlier than that of bi-free solders. bi element hastened the crack initiation from a stress concentration part. (2) crack propagation rate of solders containing bi were faster than that of bi-free solders. bi element also hastened the crack propagation rate during cycle fatigue process. (3) fatigue life ratio parameter correlates with the crack length within a factor of 2 scatter independent of the additive elements. (4) j-integral range parameter evaluates the crack propagation rate with grouping the solders containing bi and bi-free solders. slope of the approximation line equation in the j-integral range evaluation are almost same independent of the additive elements. e n. hiyoshi et alii, frattura ed integrità strutturale, 46 (2018) 25-33; doi: 10.3221/igf-esis.46.03 33 references [1] zhu, y., li, x., gao, r. and wang, c. (2014). low-cycle fatigue failure behavior and life evaluation of lead-free solder joint under high temperature, microelectronics reliability 54(12), pp. 2922–2928. [2] kawano, k., naka, y., tanie, h., kimoto, r. and yamamoto, k. (2012). fatigue life evaluation of sn3ag0.5cu solder joints after high temperature holding, transactions of the japan society of mechanical engineers, series a, 78(793), pp. 1314–1324. [3] yamamoto, t., itoh, t., sakane, m. and tsukada, y. (2012). creep-fatigue life of sn-8zn-3bi solder under multiaxial loading, international journal of fatigue, 43, pp. 235–241. [4] hiyoshi, n., katoh, a., sakane, m. and tsukada, y. (2009). low cycle fatigue lives of sn-37pb and sn-3.5ag solders at low temperatures, journal of the society of materials science, 58(2), pp. 155–161. [5] hiyoshi, n., itoh, t. and sakane, m. (2009). development of thermal mechanical fatigue testing machine for solders, journal of the society of materials science, 58(2), pp. 162–167. [6] the society of materials science, japan, factual database on tensile, creep, low cycle fatigue and creep-fatigue of lead and lead-free solders, the society of materials science, japan (2013). [7] pilkey, w. d., pilkey, d. f. (2007). peterson’s stress concentration factors. [8] the society of materials science, japan, standard low cycle fatigue testing for solders, the society of materials science, japan (2000). [9] dowling n. e. 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can be opened with acrobat and adobe reader 5.0 and later.) >> /namespace [ (adobe) (common) (1.0) ] /othernamespaces [ << /asreaderspreads false /cropimagestoframes true /errorcontrol /warnandcontinue /flattenerignorespreadoverrides false /includeguidesgrids false /includenonprinting false /includeslug false /namespace [ (adobe) (indesign) (4.0) ] /omitplacedbitmaps false /omitplacedeps false /omitplacedpdf false /simulateoverprint /legacy >> << /addbleedmarks false /addcolorbars false /addcropmarks false /addpageinfo false /addregmarks false /convertcolors /converttocmyk /destinationprofilename () /destinationprofileselector /documentcmyk /downsample16bitimages true /flattenerpreset << /presetselector /mediumresolution >> /formelements false /generatestructure false /includebookmarks false /includehyperlinks false /includeinteractive false /includelayers false /includeprofiles false /multimediahandling /useobjectsettings /namespace [ (adobe) (creativesuite) (2.0) ] /pdfxoutputintentprofileselector /documentcmyk /preserveediting true /untaggedcmykhandling /leaveuntagged /untaggedrgbhandling /usedocumentprofile /usedocumentbleed false >> ] >> setdistillerparams << /hwresolution [2400 2400] /pagesize [612.000 792.000] >> setpagedevice microsoft word numero_33_art_3 f. berto et alii, frattura ed integrità strutturale, 33 (2015) 17-24; doi: 10.3221/igf-esis.33.03 17 focussed on characterization of crack tip fields three-dimensional effects on cracked components under anti-plane loading f. berto, a. campagnolo university of padova, department of management and engineering, stradella s. nicola 3, 36100, vicenza (italy) berto@gest.unipd.it, campagnolo@gest.unipd.it l. p. pook woodside road 21, sevenoaks tn13 3hf (united kingdom) les.pook@tesco.net abstract. the existence of three-dimensional effects at cracks has been known for many years, but understanding has been limited, and for some situations still is. understanding improved when the existence of corner point singularities and their implications became known. increasingly powerful computers made it possible to investigate three-dimensional effects numerically in detail. despite increased understanding, threedimensional effects are sometimes ignored in situations where they may be important. the purpose of the present investigation is to study by means of accurate 3d finite element (fe) models a coupled fracture mode generated by anti-plane loading of a straight through-the-thickness crack in linear elastic plates. an extended version of the present work has recently been published in the literature. the results obtained from the highly accurate finite element analyses have improved understanding of the behaviour of through cracked components under anti-plane loading. the influence of plate bending is increasingly important as the thickness decreases. it appears that a new field parameter, probably a singularity, is needed to describe the stresses at the free surfaces. discussion on whether kiii tends to zero or infinity as a corner point is approached is futile because kiii is meaningless at a corner point. the intensity of the local stress and strain state through the thickness of the cracked components has been evaluated by using the strain energy density (sed) averaged over a control volume embracing the crack tip. the sed has been considered as a parameter able to control fracture in some previous contributions and can easily take into account also coupled three-dimensional effects. calculation of the sed shows that the position of the maximum sed is independent of plate thickness. both for thin plates and for thick ones the maximum sed is close to the lateral surface, where the maximum intensity of the coupled mode ii takes place. keywords. fracture mechanics; finite element analysis; anti-plane loading; stress intensity factor; corner point effects. introduction rack tip surface displacements in the vicinity of a corner point in which a crack front intersects a surface are often of practical interest. assuming that poisson’s ratio, v > 0, then kinematics considerations for an antisymmetric loading [1-2] show that modes ii and iii crack tip surface displacements cannot exist in isolation. mode ii c f. berto et alii, frattura ed integrità strutturale, 33 (2015) 17-24; doi: 10.3221/igf-esis.33.03 18 induces mode iiic and mode iii induces mode iic. these induced modes are sometimes called coupled modes, indicated by the superscript c. the existence of three-dimensional effects at cracks has been known for many years [3,4], but understanding has been limited, and for some situations still is. understanding improved when the existence of corner point singularities [5] and their implications became known [6]. despite increased understanding, three-dimensional effects are sometimes ignored in situations where they may be important. within the framework of linear elastic fracture mechanics [7] the stress field in the vicinity of a crack tip is dominated by the leading term of a series expansion of the stress field [8]. this leading term is the stress intensity factor, k. in three dimensional geometries, the derivation of stress intensity factors makes the implicit assumption that a crack front is continuous. this is not the case in the vicinity of a corner point, and the nature of the crack tip singularity changes. the resulting corner point singularities were described in detail in 1979 by bažant and estenssoro [5]. some additional results were given by benthem in 1980 [9]. for corner point singularities, the polar coordinates in fig. 1 are replaced by spherical coordinates (r, , ) with origin at the corner point. the angle  is measured from the crack front. there do not appear to be any exact analytic solutions for corner point singularities. in their analysis bažant and estenssoro [5] assumed that all three modes of crack tip surface displacement are of the form rλρpf(θ, ), where ρ is distance from the crack tip, and p is a given constant. they then calculated λ numerically for a range of situations: λ is a function of poisson’s ratio, υ. for the antisymmetric mode, λ = 0.598 for υ = 0.3. benthem [9] made an equivalent assumption but used a different numerical method to calculate . the stress intensity measure, k, may be used to characterise corner point singularities, where  can be regarded as a parameter defining the corner point singularity. however, expressions for numerical values of k, and associated stress and displacement fields, do not appear to be available. at the present state of the art the extent of a corner point singularity dominated region has to be determined numerically. at a corner point stresses are a singularity. they must be either infinite or zero,  is indeterminate, and it is reasonable to speak of stress intensity factors in an asymptotic sense [3]. in the limit, as a crack front is approached, displacement fields must be those of a stress intensity factor [9]. hence, there is an infinitesimal k-dominated region within the core region of a corner point singularity. the stress intensity factors are proportional to s0.5 λ where s is the distance from the surface along the z axis [9]. hence, for the antisymmetric mode kii and kiii both tend to infinity as a corner point is approached. further, as a corner point the ratio kiii/kii tends to a limiting value which is a function of v. for v = 0.3 the limiting ratio is 0.5 [9]. benthem points out that kii and kiii lose their meaning at a corner point [9]. dhondt suggests that modes iic and iiic might not be singular [10]. the predicted tendency to infinity is reasonable for kii since relevant stresses are in plane and disclinations are zero [3]. from a linear elastic viewpoint the predicted tendency of kiii to infinity cannot be correct [4]. at a surface shear stresses perpendicular to the surface are zero, which implies that kiii tends to zero as the surface is approached. mode iii is a torsion problem [11]. under mode iii (anti-plane) loading initially plane cross sections, including the surface at a corner point, do not remain plane under load [4] and disclinations appear. it is well known that serious error can arise if warping of non-circular cross sections under torsion is not taken into account in stress analyses [12]. warping of the surface under mode iii means that τyz at the surface does not have to be zero, and finite values of kiii are possible. the implication is that the non linearities cannot be regarded as being in a core region within a corner point singularity dominated region and that bažant and estenssoro’s prediction that kiii tends to infinity as a corner point is correct. the alternative view, which is supported by a large body of evidence [4], is that apparent values of kiii decrease towards the surface in the z direction. this implies that kiii tends to zero as a corner point is approached, which is intuitively correct. it also implies that non linearities can be regarded as being within a core region, but does not explain why bažant and estenssoro’s analysis does not give the correct limit. nevertheless, this alternative view may well be adequate when considering practical implications. this paradox needs to be resolved so that the results of finite element analysis can be interpreted correctly. there does not appear to have been a systematic investigation of the extent to which bažant and estenssoro’s initial assumption is justified. their assumption does appear to be satisfactory for the symmetric mode (mode i) in that their analysis leads to useful results [4]. the purpose of the present investigation is to study a coupled fracture mode generated by anti-plane loading of a straight through-the-thickness crack in linear elastic plates by means of accurate threedimensional finite element (fe) models. an extended version of the present work has recently been published in the literature [3]. the material is assumed to be a homogeneous isotropic continuum, and its behaviour is assumed to be linearly elastic. due to the uncertainties in the definition of the stress intensity factors on the free surfaces, as stated above, the strain energy averaged in a control volume (sed) has been employed in the present contribution to quantify the stress intensity through the thickness of the plate. for a review of the sed the reader can refer to [13]. this parameter has been f. berto et alii, frattura ed integrità strutturale, 33 (2015) 17-24; doi: 10.3221/igf-esis.33.03 19 successfully used by lazzarin and co-authors to assess the fracture strength of a large bulk of materials, characterized by different control volumes, subjected to wide combinations of static loading [14 16] and the fatigue strength of notched components [17, 18]. as described in [13, 19] an intrinsic advantage of the sed approach is that it permits automatically to take into account higher order terms and three-dimensional effects. the parameter is easy to calculate in comparison with other well-defined and suitable 3d parameters [20, 21] and can be directly obtained by using coarse meshes [13, 19]. another advantage of the sed is that it is possible to easily understand whether the through-the-thickness effects are important or not in the fracture assessment for a specific material characterized by a control volume depending on the material properties. some brittle materials are characterized by very small values of the control radius and are very sensitive to stress gradients also in a small volume of material [13]. on the other hand more ductile materials have the capability of stress averaging in a larger volume and for this reason are less sensitive to the variations of the stress field through the thickness of the plate. the sed, once the control volume is properly modeled through the thickness of the plate, is able to quantify the 3d effects in comparison with the sensitivity of the specific material so providing precious information for the fracture assessment. finite element modelling n the present calculations, stresses, stress intensity factors and displacements are examined in detail for 100 mm square plates of various thicknesses under anti-plane (nominal mode iii) loading. one half of the plate geometry used is shown in fig. 2. the thickness is t. a through thickness crack has its tip at the centre of the plate, so its length, a, is 50 mm. calculations are carried out using ansys 11 for t/a = 0.25, 0.5, 0.75, 1, 1.25, 1.5, 1.75, 2, 2.25, 2.5, 2.75 and 3. poisson’s ratio is taken as 0.3 and young’s modulus as 200 gpa. a displacement of 10-3 mm is applied to the edge of the plate. stress intensity factors are calculated from stresses on the crack surface near the crack tip using standard equations [7, 11]. the strain energy density is calculated from a control volume at the crack tip. one quarter of the plate is modelled. an overall view of the finite element mesh is shown in fig. 3. details of the mesh at the outer surface and crack tip are shown in the figure. figure 1: notation for crack tip stress field. figure 2: plate geometry. figure 3: overall view of finite element mesh. detail of finite element mesh at outer surface and at crack tip. i f. berto et alii, frattura ed integrità strutturale, 33 (2015) 17-24; doi: 10.3221/igf-esis.33.03 20 results rack surface stresses, τyz and τxy (fig. 1) were extracted from the finite element results at distances, s, from the plate surfaces of 0 mm, 0.25 mm, 1 mm and 2 mm. results for t/a = 1, plotted on logarithmic scales, are shown in figs. 4-6. results for other values of t/a are generally similar, but with some differences in detail. when the plot is a straight line its slope is -λ. values of λ taken from straight line plots are shown in tab. 1 and 2. where no value is shown the plot could not be regarded as a straight line. for s = 0.25 mm, 1 mm and 2 mm λ calculated from τxy is close to the theoretical value of 0.5 for a stress intensity factor singularity (tab. 1). hence, realistic values of kii can be calculated. for s = 0 mm the value of λ has a maximum for t/a = 0.25, and decreases as t/a increases. the values of λ are all significantly less than the theoretical value of 0.598 for a corner point singularity. realistic values of kii can probably be calculated for t/a > 2. realistic values of kiii can be calculated from τyz for s = 1 mm and 2 mm. the results for s = 0 mm (fig. 4) show that τyz is slightly lower than τxy for small x, and decreases as x increases. realistic values of kiii cannot be calculated. the presence of finite values of τyz, linked to finite values of kiii, appears because of the appearance of mode i disclinations, which are rotations about the y axis. differentiating the expression for the displacement uz gives the amount of this rotation which increases towards the crack tip, with a concomitant increase in τyz at a surface. this accounts qualitatively for the observed distributions of τyz at a surface. t/a s = 0 mm s = 0.25 mm s = 1 mm s = 2 mm 0.25 0.538 0.498 0.497 0.497 0.5 0.527 0.498 0.497 0.497 0.75 0.523 0.498 0.497 0.497 1 0.520 0.498 0.497 0.497 1.25 0.517 0.498 0.497 0.497 1.5 0.515 0.498 0.497 0.497 1.75 0.513 0.498 0.497 0.497 2. 0.512 0.498 0.497 0.497 2.25 0.510 0.498 0.497 0.497 2.5 0.510 0.498 0.497 0.497 2.75 0.509 0.498 0.497 0.497 3 0.508 0.498 0.497 0.497 table 1: values of λ for τxy, s is the distance from the free surface in the z direction. t/a s = 0 mm s = 0.25 mm s = 1 mm s = 2 mm 0.25 0.507 0.504 0.5 0.506 0.503 0.75 0.506 0.502 1 0.506 0.502 1.25 0.506 0.502 1.5 0.506 0.502 1.75 0.506 0.502 2 0.506 0.502 2.25 0.506 0.502 2.5 0.505 0.502 2.75 0.506 0.502 3 0.506 0.502 table 2: values of λ for τyz, s is the distance from the free surface in the z direction. c f. berto et alii, frattura ed integrità strutturale, 33 (2015) 17-24; doi: 10.3221/igf-esis.33.03 21 figure 4: stresses τyz and τxy on crack surface at s = 0 mm from plate surface, t/a =1. figure 5: stresses τyz and τxy on crack surface at s = 0.25 mm from plate surface, t/a =1. figure 6: stresses τyz and τxy on crack surface at s = 2 mm from plate surface, t/a =1. figure 7: through thickness distribution of kii and kiii for: t/a = 1, x = 0.05 mm. through-the-thickness distributions of kii and kiii for t/a = 1 is shown in fig. 7. from tab. 1 and 2 the values of kii are not realistic for s < 0.25 mm and the values of kiii are not realistic for s < 1 mm. the distribution of kiii presents a maximum at the centre line, but kiii then remains nearly constant for about half the distance to the plate surface. the influence of plate bending means that maxima steadily decrease as t/a decreases. as a surface is approached kiii first decreases slightly then increases to a maximum at about 0.15 mm from the surface. there is then an abrupt drop which is within the region where realistic values of kiii cannot be calculated. plate bending theory [2] suggests that kii should be zero on the centre line, with a linear increase towards a surface. kii does indeed increase linearly for much of the thickness with a greater increase as the surface is approached. this is within the region where realistic values of kii cannot be calculated. the extent of the linear portion, in terms of plate thickness, decreases as t/a increases but is still present when t/a = 3. maximum values of kii are at the surface. this is within the region where calculated kii values are not realistic so caution is needed in the interpretation of results. discussion here has been a lot of discussion on whether kiii tends to zero or infinity as a corner point is approached [3]. when apparent kiii values are calculated from stresses at a constant distance from the crack tip then kiii appears to tend to zero as the model surface is approached (fig. 7), in accordance with the linear elastic prediction. however, apparent values of kiii at the surface, linked to finite values of τyz (fig. 4), increase strongly as the distance from the crack tip at which they are calculated decreases. these results can be interpreted as indicating that kiii tends to infinity at a corner point in accordance with bažant and estenssoro’s prediction. the results in fig. 7 also show that kii does t f. berto et alii, frattura ed integrità strutturale, 33 (2015) 17-24; doi: 10.3221/igf-esis.33.03 22 appear to tend to infinity as the surface is approached, in accordance with bažant and estenssoro’s prediction. the discussion is futile because, as pointed out by benthem [9], kiii is meaningless at a corner point and there is no paradox. for s ≥ 0.2 mm λ calculated from τxy is close to the theoretical value of 0.5 for a stress intensity factor singularity so kii provides a reasonable description of the crack tip stress field. similarly, kiii provides a reasonable description of the crack tip stress field for s ≥ 1 mm. at the surface values of λ obtained from τxy are always less than the theoretical value for a corner point singularity, and decrease with increasing plate thickness. the distribution of τyz at the surface (fig. 4) cannot be accounted for on the basis of bažant and estenssoro’s analysis. there is clear evidence of a boundary layer effect whose extent is independent of plate thickness. the only available characteristic dimension controlling the boundary layer thickness is the crack length, a. strain energy density through the plate thickness he intensity of the local stress and strain state through the plate thickness can be easily evaluated by using the strain energy density (sed) averaged over a control volume embracing the crack tip (see ref. [13] for a review of the sed approach). the main advantage with respect to the local stress-based parameters is that it does not need very refined meshes in the close neighbourhood of the stress singularity [19]. furthermore the sed has been considered as a parameter able to control fracture and fatigue in some previous contributions [14-16] and can easily take into account also coupled three-dimensional effects [4, 22]. with the aim to provide some numerical assessment of the contribution of the three-dimensional effects, specifically the coupled fracture mode, kii, the local energy density through the plate thickness is evaluated and discussed in this section. fig. 8 shows the local sed variation across the plate averaged over a cylindrical volume having radius r0 and height h, with h about equal to r0. in refs [13-18] r0 was thought of as a material property which varies under static and fatigue loading but here, for the sake of simplicity, r0 and h are simply set equal to 1.0 mm, only to quantify the three-dimensional effects through the disc thickness. the influence of the applied mode iii loading combined with the induced singular mode ii loading is shown in fig. 8. it is evident that the position of the maximum sed is the same in all cases. it is close to the lateral surface, where the maximum intensity of the coupled mode ii takes place, both for thin plates, t/a = 0.5 and 1.0, and for thick ones, t/a = 2 and 3. in fact, as can be seen from fig. 7, the maximum contribution of the coupled mode ii, at the lateral surface, is significantly higher (about 4 times) compared to the maximum contribution of the applied mode iii, at the mid plane. figure 8: through the thickness sed distribution for t/a = 0.50, 1, 2, 3. control radius r0 = 1.00 mm. conclusions 1) the results obtained from the highly accurate finite element analyses have improved understanding of the behaviour of through cracked plates under anti-plane loading. in particular, it is confirmed that mode iii does induce coupled mode iic. t f. berto et alii, frattura ed integrità strutturale, 33 (2015) 17-24; doi: 10.3221/igf-esis.33.03 23 2) the influence of plate bending is increasingly important as plate thickness decreases. the anti-plane loading used is a nominal mode iii loading. for thin plate it is a mixed modes iii and ii loading, in which mode iii induces mode iic and vice versa. at the present state of the art it is not possible to separate the coupled modes from the applied modes. 3) bažant and estenssoro’s analysis works well for the symmetric mode (mode i), but it is incomplete for the asymmetric mode (a combination of modes ii and iii). 4) discussion on whether kiii tends to zero or infinity as a corner point is approached is futile because, as pointed out by benthem, kiii is meaningless at a corner point. 5) the present results do not confirm the existence of a corner point singularity dominated region within a k-dominated region. it appears that a new field parameter, probably a singularity, is needed to describe the stresses at the plate surfaces. 6) calculation of the strain energy density (sed) in a control volume at the crack tip shows that the position of the maximum sed is independent of plate thickness. both for thin plates and for thick ones the maximum sed is close to the lateral surface, where the maximum intensity of the coupled mode ii takes place. 7) under the anti-plane loading used theoretical understanding of the stress field in the vicinity of a corner point is still incomplete. references [1] kotousov, a., lazzarin, p., berto, f., harding, s., effect of the thickness on elastic deformation and quasi-brittle fracture of plate components, eng. fract. mech., 77 (2010) 1665-1681. [2] kotousov, a., lazzarin, p., berto, f., pook, l. p., three-dimensional stress states at crack tip induced by shear and anti-plane loading, eng. fract. mech., 108 (2013) 65-74. [3] pook, l. p., campagnolo, a., berto, f., lazzarin, p., coupled fracture mode of a cracked plate under anti-plane loading, eng. fract. mech., 134 (2015) 391-403. [4] pook, l. p., a 50-year retrospective review of three-dimensional effects at cracks and sharp notches, fatigue fract. engng. mater. struct., 36 (2013) 699-723. [5] bažant, z. p., estenssoro, l. f., surface singularity and crack propagation, int. j. solids struct., 15 (1979) 405-426. [6] pook, l. p., some implications of corner point singularities, eng. fract. mech., 48 (1994) 367-378. [7] pook, l. p., linear elastic fracture mechanics for engineers. theory and applications, wit press, southampton (uk), (2000). [8] williams, m. l., on the stress distribution at the base of a stationary crack, j. appl. mech., 24 (1957) 109-114. [9] benthem, j. p., the quarter-infinite crack in a half-space; alternative and additional solutions, int. j. solids struct., 16(2) (1980) 119-130. [10] dhondt, g., on corner point singularities along a quarter circular crack subject to shear loading, int. j. fract., 89 (1998) l13-l18. [11] paris, p. c., sih, g. c., stress analysis of cracks, in: fracture toughness testing and its applications, astm stp 381, american society for testing and materials, philadelphia (usa), (1965) 30-81. [12] timoshenko, s. p., goodier, j. n., theory of elasticity, third ed., mcgraw-hill book company, new york (usa), (1970). [13] berto, f., lazzarin, p., recent developments in brittle and quasi-brittle failure assessment of engineering materials by means of local approaches, mater. sci. eng. r, 75 (2014) 1-48. [14] lazzarin, p., berto, f., elices, m., gómez, j., brittle failures from uand v-notches in mode i and mixed, i+ii, mode. a synthesis based on the strain energy density averaged on finite size volumes, fatigue fract. engng mater. struct., 32 (2009) 671–684. [15] torabi, a. r., campagnolo, a., berto, f., mode ii brittle fracture assessment of key-hole notches by means of the local energy, j. test. eval., 44 (2016) doi: 10.1520/jte20140295. [16] torabi, a. r., campagnolo, a., berto, f., local strain energy density to predict mode ii brittle fracture in brazilian disk specimens weakened by v-notches with end holes, mater. design, 69 (2015) 22-29. [17] berto, f., lazzarin, p., yates, j. r., multiaxial fatigue of v-notched steel specimens: a non-conventional application of the local energy method, fatigue fract. engng. mater. struct., 34 (2011) 921-943. [18] berto, f., campagnolo, a., lazzarin, p., fatigue strength of severely notched specimens made of ti-6al-4vunder multiaxial loading, fatigue fract. engng. mater. struct., 38 (2015) 503-517.   f. berto et alii, frattura ed integrità strutturale, 33 (2015) 17-24; doi: 10.3221/igf-esis.33.03 24 [19] lazzarin, p., berto, f., zappalorto, m., rapid calculations of notch stress intensity factors based on averaged strain energy density from coarse meshes: theoretical bases and applications, int. j. fatigue, 32 (2010) 1559-1567. [20] yosibash, z., shannon, s., computing edge stress intensity functions (esifs) along circular 3-d edges, eng. fract. mech., 117 (2014) 127-151. [21] omer, n., yosibash, z., on the path independency of the point-wise j integral in three dimensions, int. j. fracture, 136 (2005) 1-36. [22] campagnolo, a., berto, f., lazzarin, p., the effects of different boundary conditions on three-dimensional cracked discs under anti-plane loading, eur. j. mech. – a/solids, 50 (2015) 76-86. microsoft word numero 20 articolo 2 p. rezakhani, frattura ed integrità strutturale, 20 (2012) 17-21; doi: 10.3221/igf-esis.20.02 17 current state of existing project risk modeling and analysis methods with focus on fuzzy risk assessment – literature review pejman rezakhani kyungpook national university, school of civil and architectural engineering, 1370 sankyuk-dong, buk-gu, daegu 702-701, korea rezakhani@knu.ac.kr abstract. risk modeling and analysis is one of the most important stages in project success. there are many approaches for risk assessment and an investigation of existing methods helps in developing new models . this paper is an extensive literature survey in risk modeling and analysis methods with main focus on fuzzy risk assessment. keywords. risk modelling; fuzzy risk assessment; project risk. risk is defined as the potential for complications and problems with respect to the completion of a project and the achievement of a project goal [1] and as an uncertain future event or condition with the occurrence rate of greater than 0% but less than 100% that has an effect on at least one of project objectives (i.e., scope, schedule, cost, or quality, etc). in addition, the impact or consequences of this future event must be unexpected or unplanned [2]. it is well accepted that risk can be effectively managed to mitigate its’ adverse impacts on project objectives, even if it is inevitable in all project undertakings. the source of risk includes inherent uncertainties and issues relative to company’s fluctuating profit margin, competitive bidding process, weather change, jobsite productivity, the political situations, inflation, contractual rights, and market competition, etc [3]. it is important for the construction companies to face these uncertain risks by assessing their effects on the project objectives because a risk quantitative method allows deciding which of the project is more risky, planning for the potential sources of risk in each project, and managing each source during construction [4]. it is noteworthy that risk is distinguished from uncertainty. the one is measurable uncertainty; the other is immeasurable risk [3, 5, 6]. therefore, managing risks is involved in identifying, assessing and prioritizing risks by monitoring, controlling, and applying managerial resources with a coordinated and economical effort so as to minimize the probability and/or impact of unfortunate events and so as to maximize the realization of project objectives [7]. project risk management, which has been practiced since the mid-1980s, is one of the nine main knowledge areas of the project management institute’s project management body of knowledge [8]. effective risk management may lead the project manager to several benefits such as identification of favorable alternative course of action, increased confidence in achieving project objective, improved chances of success, reduced surprises, more precise estimates (through reduced uncertainty), reduced duplication of effort (through team awareness of risk control actions), etc [9]. systemic project risk management has an effect on the project success. it is found that there is a strong relationship between the amount of risk management efforts undertaken in a project and the level of the project success [10]. several project risk management approaches are proposed as follows; i.e., pram [11], ramp [12], pmbok [13], rms [14], etc [15]. existing approaches may be summarized into a four phase process for effective project risk management, i.e., identifying risks, assessing risks, responding risks, and monitoring and/or reviewing risks. identifying risks is the first step which determines which risk components may adversely affect which project objectives and documents their characteristics [3]. construction risks are classified in many ways by risk types (i.e., natures, and magnitudes, etc), the sources and/or origins, or project phase [16-19]. some of the existing researchers propose a hierarchical structure of risks which classifies the risks according to their origin and the location which the risk impacts to the project [20, 21]. a http://dx.medra.org/10.3221/igf-esis.20.02&auth=true http://www.gruppofrattura.it p. rezakhani, frattura ed integrità strutturale, 20 (2012) 17-21; doi: 10.3221/igf-esis.20.02 18 assessing risks is the step which prioritizes the risks for further analysis by quantifying their occurrence rates. risk assessment method is an essential component for this step. the existing methods are classified into (1) simple classical methods, and (2) advanced mathematical models [3]. the existing risk assessment methods are either qualitative or quantitative which require different information and the level of detail [22]. the simple classical methods integrate deterministic risk modeling and analysis into cpm scheduling. the deterministic methods include sensitivity analysis [23], critical path method [24], fault tree analysis [25], event tree analysis [26], failure mode, and effects and criticality analysis, etc [27]. other advanced approaches were proposed as follows; a monte carlo simulation [23] for stochastic quantitative modeling and analysis; scenario analysis [28], and fuzzy set theory for qualitative judgment [28]. there are many factors which should be considered when a project risk manager selects a risk assessment method as follows; i.e., the cost of employing the technique, the level of external party`s approval, organizational structure, agreement, adoptability, complexity, completeness, level of risk, organizational size, organizational security philosophy, consistency, usability, feasibility, validity, and credibility and automation [29]. it is essential for the risk manager to have high quality data in order to effectively apply the quantitative methods, even if it is not easy to obtain such high quality data relative to risk items in the construction industry. the difficulty is attributed to address the uncertainties and subjectivities associated with construction activities [30]. beside the lack of collectability, the uniqueness, and non-repetitive nature of construction projects impedes using probabilistic risk quantification approaches [31]. responding risks is involved in developing options and/or actions to enhance opportunities to achieve the project objectives. finally, monitoring and reviewing risks is to implement a risk response plan, to keep tracking of the risks identified, to monitor residual risks, to identify new risks, and to evaluates the effectiveness of the project risk management process [15]. for this step, each engineering expertise should use specialized risk management tool as shown in table 1 for risk analysis depending on project phase. discipline planning/ programming preliminary engineering final design construction planning environmental funding approval project management engineering civil, structural, systems cost estimating scheduling budgeting controls real estate/right of way construction management/oversight constructability/contractor other technical (e.g. legal, permitting, procurement) risk facilitation table 1: key expertise for risk analysis by project phase (adapted from [32]). highly desirable; desirable but optional depending upon circumstances. fuzzy risk assessment fter zadeh [33] introduced the concept of fuzzy sets, and fuzzy set theory, several researchers such as kangari [34], kangari and riggs [35], peak et al. [36], tah and mccaffer [20], wirba et al. [21], , cho et al. [38], choi et al. [39], lyons and skitmore [40], baker and zeng [41], dikmen et al. [42], zeng et al. [30], wang and elang [43], karimiazar et al. [3], and nieto et al. [15] -introduced fuzzy set theory(fst)-based risk modeling and analysis methods that deal with ill-defined, vague, imprecise, and complex risk analysis problems. for example, kangari [34] proposes the application of fuzzy theory in risk analysis method using linguistic terms. the fuzzy theory-based risk analysis method was implemented as a part of construction project risk management system which consists of five steps (i.e., risk identification, policy definition, risk sharing and allocation, risk analysis, and risk minimization and response planning, etc). the fourth component, risk analysis, consists of three steps as follows; natural language computation, fuzzy set risk evaluation, and linguistic approximation. a http://dx.medra.org/10.3221/igf-esis.20.02&auth=true http://www.gruppofrattura.it p. rezakhani, frattura ed integrità strutturale, 20 (2012) 17-21; doi: 10.3221/igf-esis.20.02 19 kangari and riggs [35] presents a risk analysis model, which makes use of fuzzy set theory (fst) as a risk assessment tools, consists of three modess follows; natural language computation, fuzzy set evaluation of risk, and linguistic approximation [44]. specifically, the linguistic approximation method handle subjectivity issues in construction risk assessment by finding the nearest natural language expression for the estimated fuzziest using euclidean distance in order to. peak et al. [36] propose a risk pricing model that en determines the bid price of a construction project. the model estimates the risk-associated consequence as fuzzy numbers that represent risk consequences to reflect the uncertainty involved in determining the bid price. the fuzzy numbers are assumed by two intervals; i.e., the most likely and the largest likely intervals which are obtained from either historical data or expert opinions. the model applies fuzzy arithmetic operation to compute the risk contingency value and . a ranking method to calculate the value of risk contingency in terms of monetary cost by transferring the fuzzy number into crisp value. the method was verified by applying it to a real construction project. tah and mccaffer [20] introduced a computer tool which approximates the amount of contingency cost in pascal programming. the system determines the risk level in linguistic terms to be used as the basis of the contingency allocation for tender preparation. . it proposes a new risk breakdown structure called a hierarchical riskbreakdown structure (hrbs) which presents contractor’s risk. wirba et al. [21] presented a fuzzy set theory-based risk assessment approach which identifies risks, checks for dependencies amongst them, and assesses risk likelihood of occurrence by using linguistic variables. carr and tah [37] presented a fuzzy set based qualitative risk assessment model which implements hierarchical risk breakdown structure. the model allows to define the risk descriptions and their consequences using linguistic variables and to formulate the rules using the relationship between the likelihood of occurrence (l), the severity (v), and the effect of risk factor (e), i.e., “if l and v then e”. fuzzy approximation and composition were performed to identify and quantify the relationship between risk sources and the consequences on project performance measures. it evaluates the risk exposure by assessing the consequences relative to project performance measures (i.e., time, cost, quality and safety, etc) using the fuzzy estimates of the risk components. cho, et al. [38] proposed an uncertainty range estimate method which incorporates uncertainties using fuzzy concepts. the method introduces some forms of fuzzy membership functions that that represents the degree of uncertainties involved in both probabilistic parameter estimates and subjective judgments. the method uses linguistic variables (i.e., “close to any value” or “higher/lower than analyzed value”, etc) which include some quantification with giving specific value by defining three membership functions(i.e., “close to”, “lower than”, and “higher than” curves). choi, et al. [39] presented a fuzzybased uncertainty assessment system which considers uncertainty as objective probabilities and subjective judgment by incorporating probabilistic or linguistic variables. the system was under rigorous tests with underground construction. it implements four steps, i.e., identifying, analyzing, evaluating and managing the risks inherent in construction projects. it was confirmed that the system accommodate both probabilistic data obtained from historical data and subjective data obtained from expert group. an et al. [44] proposed risk assessment or risk management system for construction project. this system has also proposed a risk analysis method as a part of the risk management system developed. dikmen et al. [42] propose a fuzzy risk rating method which rates the risk involved in cost overrun in international construction projects. the model introduces “controllability” or “manageability” concepts into the contractor’s decision making which determines if the contractor enters into international market. it allows assessing the contractor’s decision using four categories, i.e., internationalization, market selection, project selection, and markup selection. the system identifies risks, models the risks using influence diagrams, selects membership function of each variable, captures the experts’ opinion using aggregation rules, aggregates fuzzy rules into a fuzzy cost overrun risk rating, carries out fuzzy operations, and determine the risk level of an international project by quantifying the final risk rating. zeng et al. [30] hybridized fuzzy reasoning and ahp approach to to handle subjective assessments and to prioritize diverse risk factors, respectively [44]. the model quantifies the risk magnitude (rm) of risks a by integrating a risk parameter called factor index (fi) which evaluate the magnitude of possible risk and combine it with risk likelihood (rl) and risk severity (rs) into the fuzzy inference system. the system utilized a modified fuzzy ahp to capture and convert expert’s fuzzy information and subjective judgment. wang and elang [46] proposed a fuzzy multi criteria and multi participant decision making approach which allows decision makers to rapidly and effectively evaluate multiple fuzzy risk factors using linguistic terms by aggregating the assessments of multiple risk factors. zhang and zou [45] proposed a methodology which produces the appraisal vector of risky conditions of the construction project by aggregating the weight coefficient of risk groups, and fuzzy risk factors obtained from experts using the ap technique, a hierarchical structure of risks, and the fuzzy evaluation matrixes of risk factors. nieto et al. [15] proposed an algorithm to handle the inconsistency in the fuzzy preference relation when pair-wise comparison judgments are necessary. karimiazari et al. [3] proposed an extended version of technique for order preference by similarity to ideal solution (topsis) which solve the multi criteria risk assessment model under a fuzzy environment. lyons and skitmore [40] describes the common procedure that all fuzzy risk assessment methods retain as follows; the first step, definition and measurement of parameters, is to define the risk http://dx.medra.org/10.3221/igf-esis.20.02&auth=true http://www.gruppofrattura.it p. rezakhani, frattura ed integrità strutturale, 20 (2012) 17-21; doi: 10.3221/igf-esis.20.02 20 probability and the risk severity with which a project are assessed. in linguistic terms and to convert them into corresponding fuzzy numbers. second step, definition of fuzzy inference, is to define the relations between input parameters and output parameters in “if-then” rules or mathematical functions using an appropriate fuzzy arithmetic operator. final step, defuzzification, is to convert the fuzzy result into an exact numerical value. these and other researchers recommend taking into account the imprecise, vagueness, and fuzziness of the risk factors in a construction project to appropriately deal with a contractor’s project risks by using fuzzy set theory (fst). it is well accepted that fuzzy set theory (fst) provides a useful way to deal with ill-defined and complex problems in a decision making by quantifying imprecise information, incorporating vagueness, and making decisions based on the imprecise and vague data. the method allows translating the subjective judgment given in linguistic expressions (i.e., “low”, “high” etc) into mathematical measures. dikmen et al. [42] mentions that fst is commendable to project-based industries because it is almost impossible to use probabilistic methods due to the unique nature of construction undertakings. the rational to use fst in project risk assessment are as follows; first, the modeling of vague input is successfully done with the use of membership functions. second, the inherent ability of fst to explain its reasoning ensures that the modeling process is understood and could also be intuitively verified. third, the parallel nature in which rules are activated in a fuzzy system ensures that all factors are considered in a harmonized manner. fourth, the results of fuzzy systems can naturally be scaled to be comparable with each other, with the use of the scaling membership functions. finally, fuzzy logic’s use of linguistic sets and rules ensures that the terminology of the user interface and modeling structure can be tailored toward the specific environments. references [1] w. mark, p. e. cohen, r. p. glen, project risk identification and management. aace international transaction. int.01.1-5.s (2004). [2] e. chia, risk assessment framework for project management. ieee, (2006) 376. [3] karimiazari et al., expert systems with applications, 38 (2011) 9105. [4] t. zayed, m. amer, j. pan, international journal of project management, 26 (4) (2008) 408. [5] d. hillson, effective opportunity management for projects – exploiting positive risk. new york: marcel dekker (2004) [6] r. olsson, international journal of project management, 25 (2007) 745. [7] h. douglas,. the failure of risk management: why it`s broken and how to fix it. john wiley and sons, (2009) 46. [8] tuysuz, kahreman, international journal of intelligent systems, 21 (2006) 559. [9] p. l. bannerman, the journal of systems and software, 81(12) (2008) 2118. [10] p. elkington, c. smallman, international journal of project management, 20 (2002) 49. [11] c. chapman, international journal of project management, 15 (1997) 273. [12] risk analysis and management for projects (ramp). institution of civil engineers and faculty and institute of actuaries. thomas telford, london (2002). [13] project management institute,. a guide to the project management body of knowledge. project management institute standards committee (2008). [14] institute of risk management,. a risk management. standard institute of risk management (2002). [15] a. nieto-morote, f. ruz-vila, international journal of project management, 29 (2011) 220. [16] d. f. cooper, c. b. champan, risk analysis for large project.wiley, chichester (1987). [17] p. j. edwards, p. a. bowen, engineering, construction and architectural management, 5(4) (1998) 339. [18] a. klemetti, risk management in construction project networks. report 2006/ 2. finland: laboratory of industrial management, helsinki university of technology (2006). [19] l. zhou, a. vasconcelos, m. numes, information management & computer security, 16 (2008) 166. [20] j. h. m. tah, a. thorpe, r. mccaffer, computing system in engineering, 4 (1993) 281. [21] e. n. wirba, j. h. m.tah, r. howes, journal of engineering, construction and architectural management, 3 (1996) 251. [22] j. c. bennett, g. a. bohoris, e. m. aspinwall, r.c. hall, european journal of operation research, 95 (1996) 467. [23] d. white, management decision, 3(10) (1995) 35. [24] a. kaufmann, m. m. gupta, fuzzy mathematical models in engineering and management science. amsterdam: north-holland (1988). [25] t. terano, k. asai, m. sugeno, fuzzy systems theory and its applications. san diego, ca: academic press (1992). http://dx.medra.org/10.3221/igf-esis.20.02&auth=true http://www.gruppofrattura.it p. rezakhani, frattura ed integrità strutturale, 20 (2012) 17-21; doi: 10.3221/igf-esis.20.02 21 [26] d. huang, t. chen, m. -j. wang, fuzzy sets and systems, 118 (2001) 153. [27] j. b. bowles, c. e. pelaez, reliability engineering and system safety, 50, (1995) 203. [28] r. k. j. r. rainer, c. a. snyder, h. h. carr, journal of management information systems, 8 (1) (1991) 129. [29] sh. lichtenstein, information management and computer security, 4 (1996) 20. [30] j. zeng, m. an, n. j. smith, international journal of project management, 25, (2007) 589. [31] d. baloi, a. d. f. price, international journal of project management, 21, (2003) 261. [32] nchrp 8-60: guidebook on risk analysis tools and management, (2009). [33] l. a. zadeh, information control, 8 (1965) 338. [34] r. kangari, civil engineering system, 5 (1988). [35] r. kangari, l. s. riggs, ieee transaction on engineering management, 36(2) (1989) 126. [36] j. h. paek, y. w. lee, j. h. ock, journal of construction engineering and management, 119(4) (1993) 743. [37] v. carr, j. h. m. tah, advances in engineering software, 32 (2001), 847–857. [38] h. n. cho, h. h. choi, y. b. kim, reliability engineering and system safety, 78 (2002) 173. [39] h. choi, h. cho, j. w. seo, journal of construction engineering and management, 130(2) (2004) 258. [40] t. lyons, m. skitmore, international journal of project management, 22 (2004) 51. [41] m. an, c. baker, j. zeng, world journal of engineering, 2 (2005) 1. [42] i. dikmen, m. birgonul, s. han, international journal of project management, 25 (2007) 494. [43] y. m. wang, t.m.-s. elhag, computers and industrial engineering, 53 (2007) 137. [44] a. taroun, j. b. yang, d. lowe, the built and human environment review, 4(1) (2011). [45] g. zhang, p. x. w. zou, journal of construction engineering and management, 133 (2007) 771. http://dx.medra.org/10.3221/igf-esis.20.02&auth=true http://www.gruppofrattura.it microsoft word numero 22 articolo 6.doc s. bennati et alii, frattura ed integrità strutturale, 22 (2012) 39-55; doi: 10.3221/igf-esis.22.06 39 a mechanical model for frp-strengthened beams in bending s. bennati, n. dardano, p. s. valvo università di pisa, dipartimento di ingegneria civile – strutture, largo lucio lazzarino, 56126 pisa s.bennati@ing.unipi.it, p.valvo@ing.unipi.it abstract. we analyse the problem of a simply supported beam, strengthened with a fibre-reinforced polymer (frp) strip bonded to its intrados and subjected to bending couples applied to its end sections. a mechanical model is proposed, whereby the beam and frp strip are modelled according to classical beam theory, while the adhesive and its neighbouring layers are modelled as an interface having a piecewise linear constitutive law defined over three intervals (elastic response – softening response – debonding). the model is described by a set of differential equations with appropriate boundary conditions. an analytical solution to the problem is determined, including explicit expressions for the internal forces, displacements and interfacial stresses. the model predicts an overall non-linear mechanical response for the strengthened beam, ranging over several stages: from linearly elastic behaviour to damage, until the complete detachment of the frp reinforcement. sommario. nel presente lavoro affrontiamo il problema di una trave semplicemente appoggiata, rinforzata con una striscia di materiale fibro-rinforzato a matrice polimerica (frp) incollata all’intradosso, e soggetta a coppie flettenti applicate alle sue estremità. nel modello meccanico proposto, la trave e la striscia di rinforzo sono modellate secondo la teoria delle travi classica, mentre l’adesivo e gli strati adiacenti sono modellati come un’interfaccia avente una legge costitutiva lineare a tratti definita su tre intervalli (risposta elastica – risposta softening – debonding). il modello è descritto da un sistema di equazioni differenziali, completato da opportune condizioni al contorno, che viene risolto analiticamente ricavando espressioni esplicite per le principali grandezze di interesse (spostamenti, caratteristiche della sollecitazione, sforzi d’interfaccia). il modello prevede per la trave rinforzata una risposta meccanica complessiva non lineare, articolata in più fasi: da quella elastica lineare a quella danneggiata, fino ad arrivare al completo distacco del rinforzo di frp. keywords. frp strengthening; adhesive; beam theory; interface. introduction ibre-reinforced polymers (frp) are currently used in civil engineering to carry out strengthening and repair operations on existing constructions. the pre-existing structural elements (made of traditional materials such as, for instance, masonry, wood, concrete, steel etc.) are strengthened by gluing frp reinforcement sheets or strips on their external surface. the shape and thickness of the external reinforcement obviously vary according to the type of element and the level of structural performance desired [1–4]. in order to evaluate the effectiveness of such operations, however, it is necessary to take in account the possible emergence of phenomena of delamination or detachment of the frp reinforcement, which can seriously jeopardize the outcome of the strengthening operations. moreover, delamination and detachment phenomena may manifest themselves in various and complex ways. in the case of concrete structures, for instance, delamination may occur at different levels involving the frp strips themselves, the adhesive and/or the superficial layers of the concrete. delamination is caused f http://dx.medra.org/10.3221/igf-esis.22.06&auth=true http://www.gruppofrattura.it s. bennati et alii, frattura ed integrità strutturale, 22 (2012) 39-55; doi: 10.3221/igf-esis.22.06 40 mainly by the stresses that develop on the interface between the bonded elements. in order to account for these possible effects, various theoretical models have been developed that enable evaluating such stresses. moreover, a number of special laboratory tests have been studied to evaluate the strength of the bonding under different loading conditions. one very commonly adopted test procedure is to glue an frp strip to a block of concrete and then subject it to tension until it detaches completely [5, 6]. various theoretical models have been proposed for this test and differ mainly in the constitutive law assumed for the interface between the concrete and frp. in general, the different models assume an initially linear elastic response, in which the stresses tangential to the interface are proportional to the corresponding relative displacements. subsequently, the models assume a softening response, which is meant to represent the progressive damage occurring prior to complete detachment of the reinforcement. cottone and giambanco [7] have formulated a linear decreasing law for the softening phase, while cornetti and carpinteri [8] propose an exponential decreasing one. in the present work we address the problem of a simply supported beam, strengthened with an frp strip bonded to its intrados and subjected to bending couples applied to its end sections. a similar problem, though with the concentrated load applied to the mid-span section, has been considered by carpinteri et al. [9] and by de lorenzis and zavarise [10]. in the mechanical model proposed here, the beam and reinforcement strip are bonded by a zero-thickness interface representing the adhesive layer and the superficial layers of the bonded elements. the interface transfers tangential stresses only from one element to the other. furthermore, the following simplifying hypotheses are adopted: a) the beam is flexible, but inextensible, and exhibits indefinitely elastic behaviour; b) the reinforcement strip is extensible, but completely lacking flexural rigidity, hence it is subject to solely axial stresses; c) the tangential stresses transferred by the interface are functions of the relative displacements between the beam and the strip through a piecewise linear function defined over three intervals (elastic response − softening response − debonding). the mechanical model is described by a set of differential equations, supplemented by appropriate boundary conditions. the resulting mathematical problem is solved analytically and explicit expressions for the main quantities of interest (displacements, internal forces, interface stresses) are determined. the model predicts an overall non-linear mechanical response for the frp-strengthened beam, which passes through various distinct, recognisable stages of behaviour as the intensity of the applied bending couples is increased. in the first stage, the entire system exhibits a linearly elastic response and the beam can be divided into two parts: the portion initially lacking reinforcement and that connected to the reinforcement through the interface, which is still completely in the elastic field. the first stage of behaviour ends when the tangential interfacial stresses at the extremities of the reinforcement reach the elastic limit. in the second stage, the interface portions near the reinforcement extremities enter the softening response domain and the beam is thus divided into three parts: the portion initially lacking reinforcement and those portions connected to the reinforcement through the interface, which is now partly damaged and partly still in the elastic field. the second stage of behaviour ends when the relative displacements at the extremities of the reinforcement reach their ultimate value, corresponding to interface debonding. in the third stage, the reinforcement strip progressively detaches from the beam, beginning at the extremities, and the beam can be thought of as still divided into three parts: an unreinforced portion made up of the area initially lacking reinforcement plus the area with the now detached strip, a portion whose reinforcement is connected via the damaged interface and the portion with reinforcement still connected by an elastic interface. as the loads increase, the damaged and debonded interface portions extend to involve the entire length of the beam. upon complete detachment, the overall response of the system reduces to that of the beam lacking any reinforcement. it is interesting to note that this last stage is however only reached asymptotically with infinite growth of the couples applied to the beam. mechanical model et us consider a beam ab of length 2l l , simply supported at its ends, where it is loaded by two equal and opposite couples of magnitude m (fig. 1). a strip of frp reinforcement is bonded along the centre of the beam intrados for a length 02 b . we indicate h as the height of the cross section of the beam and h the distance of the section’s centre from its intrados (for a rectangular cross section, / 2h h ). thanks to the symmetry of the problem, it is possible to limit the study to the left half alone by introducing appropriate constraints in correspondence to the axis of symmetry (fig. 2). the positions of the beam and strip cross sections are given by an abscissa s , whose origin is placed at the left-hand extremity of the active (not detached) portion of the reinforcement strip. this choice helps obtaining simpler expressions for the integration constants characterising the analytical solution. with 0 0 a l b the length of the initially unreinforced segment of the beam, we indicate by ( )v s and l http://dx.medra.org/10.3221/igf-esis.22.06&auth=true http://www.gruppofrattura.it s. bennati et alii, frattura ed integrità strutturale, 22 (2012) 39-55; doi: 10.3221/igf-esis.22.06 41 ( ) s the transverse displacement and rotation (positive if clockwise) of the cross section of the beam, respectively, and by ( )w s the axial displacement of the cross section of the reinforcement. figure 1: frp-strengthened beam in bending. figure 2: mechanical model of the strengthened beam. figure 3: constitutive law of the interface. in the proposed mechanical model, the beam is flexible, but inextensible, while the reinforcement strip is extensible only. we denote e and j as the young’s modulus and moment of inertia of the cross section of the beam, respectively, and fe and fa as the young’s modulus and area of the cross section of the frp strip, respectively. with fb the width of the reinforcement strip, and ft its thickness, we have f f fa b t . the beam and reinforcement are connected to each other by an interface of negligible thickness. since the reinforcement is subject to axial stresses alone, the interface transmits only tangential stresses, ( ) s , which we assume are functions of the relative displacement between beam and reinforcement in correspondence to the interface, http://dx.medra.org/10.3221/igf-esis.22.06&auth=true http://www.gruppofrattura.it s. bennati et alii, frattura ed integrità strutturale, 22 (2012) 39-55; doi: 10.3221/igf-esis.22.06 42 ( ) ( ) ( )  w s w s h s (1) in particular, we assume the following piecewise linear constitutive law (fig. 3): 0 0 , 0 ( ) ( ), 0, (elastic response) (softening response) (debonding)                      s u u u k w w w w k w w w w w w w (2) where k and sk are the interface elastic constants for the fields of elastic and softening response, respectively, and 0w and  uw are the relative displacements corresponding, respectively, to the elastic limit and debonding of the interface. differential problem he behaviour of the frp-strengthened beam varies according to the response field in which the interface is found. the adopted piecewise linear constitutive law enables distinguishing three cases, for which the differential problem is appropriately formulated and solved in the following. the resulting solutions will then be employed to reconstruct the overall response of the system in the different stages of behaviour. case a) interface with elastic response in the case of the interface response in the elastic field, from the equilibrium equations and the constitutive law we formulate the following set of governing differential equations (here and henceforth, primes indicate derivation with respect to the abscissa s ; the quantities in this case are indicated with the subscript e elastic ): 2 ''''( ) ''( ) '( ) 0 ''( ) ( ) '( ) 0            f f e e e f f e e e f f f f kb h kb h v s v s w s ej ej kb kb h w s w s v s e a e a (3) by solving eqs. (3), we obtain the general solution for the transverse displacement of the beam, 3 2 1 2 3 4 5 6( ) cosh sinh      ev s a s a s a s a s a s a (4) and for the axial displacement of the reinforcement, 2 1 2 3 4 3 5( ) ( sinh cosh ) 3 2 6        f f e f f f e a hej w s a s a s a hs a hs a a h e a h kb (5) where 2 2(1 / / )  f f fkb e a h ej . thus, we can obtain the rotation of the beam cross section, 2 1 2 3 4 5( ) '( ) ( sinh cosh ) 3 2        e es v s a s a s a s a s a (6) the relative displacement at the interface, 3 1 2 3( ) ( ) ( ) ( sinh cosh ) 6         f f e e e f f e a hej w s w s h s a s a s a kb h kb (7) the tangential stress at the interface, 3 1 2 3( ) ( ) ( sinh cosh ) 6        f f e e f f e a hej s k w s a s a s a b h b (8) the bending moment in the beam, t http://dx.medra.org/10.3221/igf-esis.22.06&auth=true http://www.gruppofrattura.it s. bennati et alii, frattura ed integrità strutturale, 22 (2012) 39-55; doi: 10.3221/igf-esis.22.06 43 2 1 2 3 4( ) ''( ) [ ( cosh sinh ) 6 2 ]        e em s ejv s ej a s a s a s a (9) the shear force in the beam, 2 3( ) '''( ) ( ) 6 ( )     e e f e f ft s ejv s hb s a ej e a h (10) and, lastly, the axial force in the reinforcement, 2 1 2 3 4( ) '( ) ( cosh sinh ) 2 (3 )      e e f f ej n s eaw s a s a s e a h a s a h (11) in eqs. (4)–(11), 1 2 6, , ,a a a are integration constants to be determined by imposing boundary conditions. case b) interface with softening response in the case of the interface response in the softening field of behaviour, the equilibrium equations and the constitutive law enable us to formulate the following set of governing differential equations (the quantities in this case are indicated by the subscript s softening ): 2 ''''( ) ''( ) '( ) 0 ''( ) ( ) '( ) 0              s f s f s s s s f s f s f s s s u f f f f f f k b h k b h v s v s w s ej ej k b k b h k b w s w s v s w e a e a e a (12) solving eqs. (12) yields the general solution for the transverse displacement of the beam, 3 2 1 2 3 4 5 6( ) cos sin      sv s b s b s b s b s b s b (13) and the axial displacement of the reinforcement, 2 1 2 3 4 3 5( ) ( sin cos ) 3 2 6           f f s u f f s f e a hej w s b s b s b hs b hs b b h w e a h k b (14) where 2 2(1 / / )  s f f fk b e a h ej . thus, we can now obtain the rotation of the beam cross section, 2 1 2 3 4 5( ) '( ) ( sin cos ) 3 2         s ss v s b s b s b s b s b (15) the relative displacement at the interface, 3 1 2 3( ) ( ) ( ) ( sin cos ) 6            f f s s s u s f s f e a hej w s w s h s b s b s b w k b h k b (16) the tangential stress at the interface, 3 1 2 3( ) [ ( )] ( sin cos ) 6          f f s s u s f f e a hej s k w w s b s b s b b h b (17) the bending moment in the beam, 2 1 2 3 4( ) ''( ) [ ( cos sin ) 6 2 ]       s sm s ejv s ej b s b s b s b (18) the shear force in the beam, 2 3( ) '''( ) ( ) 6 ( )     s s f s f ft s ejv s hb s b ej e a h (19) and, lastly, the axial force in the reinforcement, http://dx.medra.org/10.3221/igf-esis.22.06&auth=true http://www.gruppofrattura.it s. bennati et alii, frattura ed integrità strutturale, 22 (2012) 39-55; doi: 10.3221/igf-esis.22.06 44 2 1 2 3 4( ) '( ) ( cos sin ) 2 (3 )       s s f f ej n s eaw s b s b s e a h b s b h (20) in eqs. (13)–(20), 1 2 6, , ,b b b are integration constants to be determined by imposing boundary conditions. case c) debonded interface (or lacking reinforcement) in the case that the interface is debonded (or the reinforcement is absent right from the start), the differential equation for the beam is simply (the quantities in this case are indicated by the subscript d debonding ): ''''( ) 0dejv s (21) the transverse displacement of the beam has the following expression 3 2 1 2 3 4( )    dv s c s c s c s c (22) thus, we can obtain the rotation of the beam cross section, 2 1 2 3( ) '( ) 3 2    d ds v s c s c s c (23) the bending moment in the beam, 1 2( ) ''( ) (6 2 )    d dm s ejv s ej c s c (24) and lastly, the shear force in the beam, 1( ) '''( ) 6   d dt s ejv s c ej (25) in eqs. (22)–(25), 1 2 3 4, , ,c c c c are integration constants to be determined by imposing boundary conditions. solution for the frp-strengthened beam in the different stages of behaviour stage 1) entirely elastic interface or small values of the applied couple m , the system exhibits a linearly elastic response. in particular, the entire interface is within the initial stage of elastic behaviour. the strengthened beam can be divided into two parts: the portion lacking reinforcement, of length 0a , and that with the reinforcement, of length 0 0 b l a (fig. 4). in these two distinct regions, the solution to the problem is given by eqs. (22)–(25) and eqs. (4)–(11), respectively. now, imposing the boundary conditions, 0 0 0 0 0 ( ) 0, ( ) (0) (0), (0) (0), (0) (0), (0) (0), (0) 0 ( ) 0, ( ) 0, ( ) 0               d d d e d e d e d e e e e e v a m a m v v m m t t n b t b w b (26) yields the integration constants for stage 1, whose analytical expressions are given in the appendix. figure 4: stage 1) entirely elastic interface. f http://dx.medra.org/10.3221/igf-esis.22.06&auth=true http://www.gruppofrattura.it s. bennati et alii, frattura ed integrità strutturale, 22 (2012) 39-55; doi: 10.3221/igf-esis.22.06 45 stage 1 takes place for values of the applied couple m between 0 and 0m . to determine the latter value, it is sufficient to consider that stage 1 ends when the (maximum) relative displacement at the extremity of the frp strip reaches the elastic limit value, that is, when 0(0)  w w (27) by substituting the solution obtained for the relative displacement, w , into eq. (27), after some simplifications, we get 0 0 0coth   ej m w b h (28) which is the value of the applied couple corresponding to the end of stage 1. for current applications, the argument of the hyperbolic function appearing in eq. (28) is quite large, so that the following approximate expression can be used: 0 0  ej m w h (29) stage 2) elastic−damaged interface as the intensity of the applied couple m grows beyond the value 0m , the frp-strengthened beam enters stage 2 of behaviour. the interface response is partly still in the elastic field (elastic interface) and partly in the softening field (damaged interface). the strengthened beam can be divided into three parts: the portion lacking reinforcement, of length 0a , the portion with the damaged interface, of length c (to be determined), and the portion with the elastic interface, of length 0 d b c (fig. 5). in these three distinct regions, the solution to the problem is respectively given by eqs. (22)– (25), eqs. (13)–(20) and eqs. (4)–(11). imposing the boundary conditions, 0 0 0 0 0 ( ) 0, ( ) (0) (0), (0) (0), (0) (0), (0) (0), (0) 0 ( ) ( ), ( ) ( ), ( ) ( ), ( ) ( ), ( ) ( ), ( ) ( ) ( ) 0, ( ) 0, ( ) 0                        d d d s d s d s d s s s e s e s e s e s e s e e e e v a m a m v v m m t t n v c v c c c m c m c t c t c w c w c n c n c b t b w b (30) yields the integration constants for stage 2, whose analytical expressions are given in the appendix. figure 5: stage 2) elastic–damaged interface. the unknown length c can be determined by requiring that the relative displacement in the transition section between the damaged and elastic interface portions be equal to the value corresponding to the elastic limit: 0( )  w c w (31) rendering eq. (31) explicit and taking into account the expressions for the integration constants listed in the appendix, we obtain the value of the applied couple corresponding to any given value of c : http://dx.medra.org/10.3221/igf-esis.22.06&auth=true http://www.gruppofrattura.it s. bennati et alii, frattura ed integrità strutturale, 22 (2012) 39-55; doi: 10.3221/igf-esis.22.06 46 0 0 0[cos coth ( ) sin ] tanh         m m c b c c b (32) vice versa, by (numerically) solving eq. (32), we can determine the length c as a function of m . it can thus be seen that c grows with m throughout the entire stage 2. the value of the applied couple, um , at the end of this stage of behaviour is determined by imposing that the (maximum) relative displacement at the extremity of the frp strip be equal to the value corresponding to interface debonding: (0)   uw w (33) by rendering eq. (33) explicit and simplifying, we obtain 0tanh ( ) tan    u ub c c (34) eq. (34) can be solved numerically to determine the maximum value of c , indicated by uc , corresponding to the end of stage 2. to this purpose, noting that since the first member of eq. (34) is always positive, the second must be likewise, hence the following condition must hold, 2    u cc c (35) where cc is a characteristic length. the system’s response is different in the three cases corresponding to a reinforcement length, 0b , respectively, less than, equal to, or greater than cc . an analogous result has been found by cottone and giambanco [7] for the problem of a stretched strip. for our problem, however, considering current parameter values, it is likely that 0  cb c , so that we will focus on this case only in what follows. furthermore, the hyperbolic tangent in eq. (34) takes on values very near unity. therefore, instead of solving eq. (34) numerically, it is also possible to use the approximate expression 1 arctan    uc (36) by substituting the calculated value of uc into eq. (32), we finally obtain the value of the couple, um , applied at the end of stage 2. in particular, from the approximate value given by eq. (36), we get 2 0 0 02 0 1 1          u u s wk m m m m k w (37) stage 3) elastic–damaged–debonded interface as the intensity of the applied couple m increases beyond the value um , the frp-strengthened beam enters stage 3 of behaviour. the interface portions near the reinforcement extremities become debonded and the reinforcement progressively detaches from the beam. in this stage, the beam can once again be divided into three parts: the total unreinforced portion (made up of the part initially lacking reinforcement and the part whose reinforcement has detached), of length a (to be determined), the damaged interface portion, of length c (also to be determined), and the still elastic interface portion, of length   d l a c (fig. 6). in these three distinct regions, the solution to the problem is given respectively by eqs. (22)–(25), eqs. (13)–(20) and eqs. (4)–(11). imposing the boundary conditions, ( ) 0, ( ) (0) (0), (0) (0), (0) (0), (0) (0), (0) 0 ( ) ( ), ( ) ( ), ( ) ( ), ( ) ( ), ( ) ( ), ( ) ( ) ( ) 0, ( ) 0, ( ) 0                           d d d s d s d s d s s s e s e s e s e s e s e e e e v a m a m v v m m t t n v c v c c c m c m c t c t c w c w c n c n c l a t l a w l a (38) yields the integration constants for stage 3, whose analytical expressions are given in the appendix. http://dx.medra.org/10.3221/igf-esis.22.06&auth=true http://www.gruppofrattura.it s. bennati et alii, frattura ed integrità strutturale, 22 (2012) 39-55; doi: 10.3221/igf-esis.22.06 47 figure 6: stage 3) elastic–damaged–deboned interface. the unknown lengths a and c can both be determined by requiring that the value of the relative displacement at the reinforcement strip’s extremity be that corresponding to incipient debonding of the interface and that the relative displacement in the transition section between the damaged and the elastic interface portions be equal to the value corresponding to the elastic limit, or in other terms, that 0(0) ( )and     uw w w c w (39) by substituting the expressions for the relative displacements into eqs. (39), with the expressions for the integration constants listed in the appendix, after some simplifications, we obtain the following equation set: 2 00 2 2 00sin cos tanh ( )] ( ) tanh 0 tanh ( ) [ sin tanh ( ) cos ] tanh 0 [                                  c c l a c b l a c c l a c c b m m m m (40) by solving the first of eqs. (40) for tanh ( )  l a c and substituting into the second equation, we get a quadratic equation for m : 2 2 2 2 2 0 0 0 02 2 1 (1 ) sin ] tanh (1 ) tanh 0[ sin               c mm m b m b c (41) eq. (41) has two possible solutions, one of which is however to be discarded, as it leads to physically unacceptable values of length a . consistently, we find 0 0 1 tanh sin      b c m m (42) and 1 arctanh( tan )       a l c c (43) since, for physical reasons, length a can only increase, we may consider its derivative with respect to c . thus, it can be seen that as long as a is increasing, during stage 3 of behaviour c must necessarily decrease from the value uc to 0 . at the same time, a grows from the value 0a to l , that is, until complete detachment of the reinforcement. actually, such situation is arrived at only asymptotically. in fact, from eqs. (42) and (43) it can be seen that as c falls towards 0 , length a tends to l and the applied couple m increases boundlessly. stage 4) entirely debonded interface in stage 4 of behaviour, which is however reached only asymptotically for  m , the interface is entirely debonded and the reinforcement is completely detached from the beam except for the mid-span section where, for reasons of symmetry, http://dx.medra.org/10.3221/igf-esis.22.06&auth=true http://www.gruppofrattura.it s. bennati et alii, frattura ed integrità strutturale, 22 (2012) 39-55; doi: 10.3221/igf-esis.22.06 48 the relative displacement at the interface and the corresponding tangential stress are always null. the system thus behaves as a beam lacking any reinforcement (fig. 7). the solution to the problem in this case is given by eqs. (22)–(25). by imposing the boundary conditions, ( ) 0, ( ) (0) 0, (0) 0       d d d d v l m l m t (44) we deduce the integration constants for this stage: 1 2 3 40, , , 0 2      m ml c c c c ej ej (45) figure 7: stage 4) entirely debonded interface. numerical application y way of example, let us consider a concrete beam of length 6 ml with rectangular cross section of dimensions 30 cmb and 40 cmh . the width and thickness of the frp reinforcement are respectively 25 cmfb and 0.5 cmft . a segment of length 0 50 cma is initially devoid of any reinforcement. the other relevant lengths are / 2 300 cm l l and 0 0 250 cm  b l a . the young’s modulus of the beam and frp strip are respectively 30000 mpae and 256000 mpafe , and the constants defining the interface constitutive law are 48 3n/mk , 0 4.2 mpa  , and 0.53 mm uw [7]. from these values, we also deduce 0 0 / 0.0875 mm  w k and 0 0/ ( ) 9.49 2n/mm    s uk w w . using eq. (28), we determine the value of the applied couple at the elastic limit, 0 144.73 kn mm , corresponding to the end of stage 1. eq. (35) furnishes the value of the characteristic length of the damaged region, 51.3 cmcc . for the problem in question, the condition 0  cb c is thus clearly verified. numerical solution of eq. (34) gives the length of the damaged region at the end of stage 2, 37.6 cmuc (fig. 8). from this latter value, through eq. (32), we calculate the value of the applied couple at the end of stage 2, 356.21 kn mum . in practice, the same results could have been obtained using the approximate expressions given in eqs. (29), (36), and (37). in order to show the trends of the computed quantities (displacements, internal forces and interfacial stresses) along the beam, we define a new abscissa, z , measuring the distance of the generic cross section from the left-hand support of the beam. the abscissa z , different from the abscissa s used to deduce the analytical solution, turns out to be more effective to present the obtained results. fig. 9 shows a plot of the beam transverse displacement, v , as a function of z , for four values of the applied couple, m , corresponding to the four stages of behaviour described in the previous section. b http://dx.medra.org/10.3221/igf-esis.22.06&auth=true http://www.gruppofrattura.it s. bennati et alii, frattura ed integrità strutturale, 22 (2012) 39-55; doi: 10.3221/igf-esis.22.06 49 figure 8: determination of cu. a) b) c) d) figure 9: transverse displacement v(z): a) stage 1: 0m m ; b) stage 2: 0.9 um m ; c) stage 3: 1.01 um m ; d) stage 4: 1.01 um m . fig. 10 shows a plot of the interfacial relative displacement, w , and tangential stress,  , as functions of the abscissa, z , for three values of the applied couple, m , corresponding to the first three stages of behaviour described in the previous section. as can be observed, as m increases, the relative displacement in the end section of the reinforcement increases: http://dx.medra.org/10.3221/igf-esis.22.06&auth=true http://www.gruppofrattura.it s. bennati et alii, frattura ed integrità strutturale, 22 (2012) 39-55; doi: 10.3221/igf-esis.22.06 50 the instants such displacement exceeds the values 0w and  uw respectively mark the beginning of interface softening and debonding behaviour. a) b) c) figure 10: relative displacement w(z) and tangential stress (z): a) stage 1: 0m m ; b) stage 2: 0.9 um m ; c) stage 3: 1.01 um m . fig. 11 shows a plot of the bending moment in the beam, m , as a function of the abscissa, z , for four values of the applied couple, m , corresponding to the four stages of behaviour described in the previous section. note that with increasing m and the consequent progressive detachment of the reinforcement, the strengthened beam’s response tends towards that of a beam lacking any reinforcement. http://dx.medra.org/10.3221/igf-esis.22.06&auth=true http://www.gruppofrattura.it s. bennati et alii, frattura ed integrità strutturale, 22 (2012) 39-55; doi: 10.3221/igf-esis.22.06 51 a) b) c) d) figure 11: bending moment m(z): a) stage 1: 0m m ; b) stage 2: 0.9 um m ; c) stage 3: 1.01 um m ; d) stage 4: 1.01 um m . the shear force in the beam, t , is instead null everywhere. this follows from obvious reasons of equilibrium, considering moreover that by virtue of the hypotheses adopted, the frp reinforcement strip is only able to bear axial stresses. fig. 12 shows a plot of the axial force, n , on the reinforcement strip as a function of the abscissa, z , for three values of the applied couple, m , corresponding to the first three stages of behaviour described in the previous section. note that with growing m and the consequent progressive detachment of the reinforcement, the length of the active part of the reinforcement is progressively reduced (falling to zero at the limit for  m ). fig. 13 shows the length of the damaged region, c , as a function of the length of the region lacking reinforcement, a . during stage 2, c increases from 0 to uc , while the applied couple goes from 0m to um . during stage 3, the length c decreases from uc to 0 , while a increases from its initial value, 0a , up to the half-length of the beam, l (complete detachment of the reinforcement). fig. 14 sums up the mechanical response of the frp-strengthened beam as predicted by the proposed mechanical model. in particular, it shows a plot of the applied couple, m , as a function of the transverse displacement in the mid-span section,  . the different stages of behaviour are clearly distinguishable. in stage 1 ( 00  m m ), the strengthened beam exhibits a linearly elastic response, while in stage 2 ( 0   um m m ), the system’s response takes on a weakly non-linear quality, due to the fact that a part of the interface has entered the field of softening response (though the non-linearity of such response is not clearly evidenced in the graph of the considered numerical example, it is however evident in the equations describing the model). in stage 3 ( um m ), the response becomes strongly non-linear, due to the fact that increasing portions of the interface enter the debonding range, and the reinforcement accordingly detaches from the beam. in particular, at the beginning of stage 3, an abrupt increase in the mid-span transverse displacement can be observed to occur with almost constant applied load. subsequently, the behaviour of the system tends asymptotically (  m ) to that of a beam lacking reinforcement, represented in the figure by the dashed blue line (stage 4). http://dx.medra.org/10.3221/igf-esis.22.06&auth=true http://www.gruppofrattura.it s. bennati et alii, frattura ed integrità strutturale, 22 (2012) 39-55; doi: 10.3221/igf-esis.22.06 52 a) b) c) figure 12: axial force n(z): a) stage 1: 0m m ; b) stage 2: 0.9 um m ; c) stage 3: 1.01 um m . figure 13 length of damaged region c as a function of the length, a, of the region lacking reinforcement. http://dx.medra.org/10.3221/igf-esis.22.06&auth=true http://www.gruppofrattura.it s. bennati et alii, frattura ed integrità strutturale, 22 (2012) 39-55; doi: 10.3221/igf-esis.22.06 53 figure 14: applied couple m as a function of the transverse displacement,  of the mid-span section. considering the above, it is reasonable to conclude that the value of the applied couple, um , corresponding to the end of stage 2 and the beginning of stage 3, represents a limit load for the frp-strengthened beam. although the model provides for the possibility of reaching equilibrium at higher load values, this comes at the cost of very large displacements and deformations, together with undesirable dynamic effects, which may not be compatible with the structure’s bearing capacity. moreover, the fact that the stage 2 response may exhibit an only weakly non-linear trend represents a further hazard, as structural failure may come about suddenly without any warning signs. conclusions he problem of a simply supported beam strengthened with a strip of frp glued to the intrados and subject to concentrated couples applied to its ends has been analysed. a mechanical model has been developed whereby the beam and reinforcement strip are modelled according to classical beam theory, while the adhesive and adjacent layers are modelled as a zero-thickness interface having a piecewise linear constitutive law defined over three distinct intervals (elastic response – softening response – debonding). the differential problem which describes the model has been solved analytically, and explicit expressions for the main variables of interest (displacements, internal forces, interfacial stresses) have been determined. for such a strengthened beam the model predicts an overall non-linear mechanical response divided into several stages: from a linearly elastic to a non-linear (damaged) response, up to complete detachment of the frp reinforcement. the values of the applied couple corresponding to the beginning and end of each stage of behaviour have been determined. in particular, approximate, yet effective, analytical expressions for 0m and um have been given. these values correspond respectively to the end of the linearly elastic response (end of stage 1) and to incipient detachment of the frp reinforcement (beginning of stage 3). um has been recognised as a limit load for such an frp-strengthened beam. in fact, higher values of the applied couple produce very large displacements and deformations, potentially incompatible with the structure’s bearing capacity. moreover, it has been noted that these large displacements may occur suddenly, without warning, together with undesired dynamic effects, which could represent a further hazard in implementing strengthening operations of this type. acknowledgements financial support from miur (prin 2008 – prot. n. 20089rjkyn_002) is gratefully acknowledged. t http://dx.medra.org/10.3221/igf-esis.22.06&auth=true http://www.gruppofrattura.it s. bennati et alii, frattura ed integrità strutturale, 22 (2012) 39-55; doi: 10.3221/igf-esis.22.06 54 references [1] l. hollaway, m. leeming, strengthening of reinforced concrete structures, woodhead publishing, uk (1999). [2] v. zerbo, a. di tommaso, l. ceriolo, in: proceedings of structural analysis of historical constructions, balkema (2004). [3] l. c. bank, composites for construction, john wiley & sons, new jersey (2006). [4] cnr-dt 200/2004, istruzioni per la progettazione, l’esecuzione ed il controllo di interventi di consolidamento statico mediante l’utilizzo di compositi fibrorinforzati, rev. 7 (2008). [5] j. yao, j. g. teng, j. f. chen, compos. part b-eng., 36 (2005) 99. [6] c. mazzotti, m. savoia, b. ferracuti, constr. build. mater., 23 (2009) 1529. [7] a. cottone, g. giambanco, eng. fract. mech., 76 (2009) 1957. [8] p. cornetti, a. carpinteri, eng. struct., 33 (2011) 1988. [9] a. carpinteri, p. cornetti, n. pugno, eng. struct., 31 (2009) 2436. [10] l. de lorenzis, g. zavarise, int. j. solids struct., 46 (2009) 4181. appendix stage 1) entirely elastic interface imposing the boundary conditions given in eqs. (26) yields the following expressions for the integration constants characterising the analytical solution in stage 1: 2 2 1 2 0 34 4 0 4 52 2 2 6 02 1 2 2 0 0 2 0 0 0 3 2 0 0 0 2 2 4 0 0 , tanh , 0 1 , 2 [ tanh + 0, 2 tanh 1 ( + )+ ( + ( )] 2 2 2 ) [ (                             f f f f f f f f f f f f f f f f f a a a a b kb kbh m h m a a b a ej ej ej ej kb kbbm m a a e a ej e a ej kb h m a b e a ej m c c ej kb b bh m c e a ej ej kb a a c b e a ej 22 0 0 0) ( tanh )] 2     a ah m b ej ej (a1) stages 2) elastic−damaged interface and 3) elastic–damaged–debonded interface imposing the boundary conditions given in eqs. (30) yields the following expressions for the integration constants characterising the analytical solution in stage 2: 2 2 0 2 0 1 4 2 2 0 2 0 2 4 3 4 52 2 ( ) tanh sin cos tanh sin ( ) tanh sin tanh cos tanh sin 1 0, , 2 f f f f f f f f mm b ckb h ej eja ej c d c mm b ckb h ej eja d ej c d c kb kbm d m a a a e a ej e a ej                                       http://dx.medra.org/10.3221/igf-esis.22.06&auth=true http://www.gruppofrattura.it s. bennati et alii, frattura ed integrità strutturale, 22 (2012) 39-55; doi: 10.3221/igf-esis.22.06 55 2 22 0 6 4 3 2 2 2 2 0 02 2 2 2 3 2 2 0 0 0 0 ( sin tanh cos ) cos tanh sin 1 ( ) ( )( ) 2 2 ( ) sin ( )[ ( ) ] tanh cos tanh sin 1 f f f kb a c d ch m a ej c d c ej m a a c l d m ej e a h a c m a c b c d c ej                                                           2 2 0 2 0 1 3 2 2 2 0 2 0 2 3 3 4 2 2 2 2 03 2 2 2 2 0 5 ( ) tanh sin cos tanh sin tanh ( ) tanh cos cos tanh sin 0, 2 [ ( ) tan 1 h ]                                             f f f f f f f f mm b ckb h ej ejb ej c d c mm d b ckb h ej ejb ej c d c kb m b b e a ej kb mm h b d e b e a j ej e j b6 1 6 1  a a b (a2) 1 2 2 2 3 1 2 3 4 5 1 2 3 2 4 0 1 0 2 0 3 0, 2 sin cos 3 2 3 2 ( ) ( ) ( )                     m c c ej c b c b c b c b c b c c c c c a c c a c c a c c the integration constants for the solution in stage 3 are given again by eqs. (a2), provided that the current lengths a and   d l a c are considered in place of 0a and 0 d b c , respectively. http://dx.medra.org/10.3221/igf-esis.22.06&auth=true http://www.gruppofrattura.it microsoft word numero_41_art_23.docx j.m. vasco-olmo et alii, frattura ed integrità strutturale, 41 (2017) 166-174; doi: 10.3221/igf-esis.41.23 166 focused on crack tip fields experimental methodology for the quantification of crack tip plastic zone and shape from the analysis of displacement fields j.m. vasco-olmo, f.a. díaz university of jaén, spain jvasco@ujaen.es fdiaz@ujaen.es m.n. james, c.j. christopher university of plymouth, uk m.james@plymouth.ac.uk c.christopher@plymouth.ac.uk e.a. patterson university of liverpool, uk eann.patterson@liverpool.ac.uk abstract. the current work presents a novel methodology for the experimental quantification of the crack tip plastic zone during fatigue crack growth. this methodology is based on the application of yield criteria to estimate the area and the shape of the plastic zone at the crack tip. the implementation of the proposed methodology requires the use of strain maps calculated from the differentiation of the displacement fields obtained by digital image correlation (dic). stress maps can subsequently be inferred from both von mises and tresca yield criteria. fatigue tests and associated measurements of plastic zone size and shape were conducted on a compacttension specimen made from commercially pure titanium at r ratio of 0.6. in addition, the ability to predict the shape and size of the experimentally observed crack tip plastic zone has been explored using three different analytical elastic crack tip models [westergaard, williams and christopherjames-patterson (cjp)]. this analysis indicated that the cjp model provided the most accurate prediction of the plastic zone and shape. keywords. crack tip plastic zone; fatigue; crack tip fields; crack shielding; stress intensity factor, dic. citation: vasco-olmo, j.m., díaz, f.a., james, m.n., christopher, c.j., patterson, e.a., experimental methodology for the quantification of crack tip plastic zone and shape from the analysis of displacement fields, frattura ed integrità strutturale, 41 (2017) 166-174. received: 28.02.2017 accepted: 15.04.2017 published: 01.07.2017 copyright: © 2017 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. j.m. vasco-olmo et alii, frattura ed integrità strutturale, 41 (2017) 166-174; doi: 10.3221/igf-esis.41.23 167 introduction t has long been recognised in the fracture mechanics community that identifying plastic zone shape and size, and any influences of the plastic zone on a growing fatigue crack is relatively complex whether attempted by simulation or experiment. in simulation work, predictions are usually based on a purely elastic theoretical modelling of crack tip stress fields. experimentally, determination of the plastically deformed region surrounding a growing fatigue crack has been pursued using a variety of techniques to identify the dimensions of crack tip plastic zones. uguz and martin [1] provide a useful review of the early experimental work on characterising the crack tip plastic zone; this includes techniques based on microhardness measurements, etching, optical interference, micro-strain gauge and electron microscopy. modern numerical modelling techniques and advanced experimental techniques, including synchrotron diffraction and tomography [2], digital image correlation (dic) [3], thermography [4] and electron backscatter diffraction (ebsd) [5] have started to unlock the potential of full-field measurements in determining crack tip stress intensity factors, residual stresses, strains and hence plastic zone dimensions. most of the reported works to predict plastic zone size and shape at the crack tip employ approaches based on linear elastic fracture mechanics (lefm), such as irwin’ [6] or dugdale’s [7] estimates, or the model based on westergaard equations [8], among others. however, these are simplistic approaches and, therefore there is a clear application field consisting in combining full field measurement techniques with an improved model of the crack tip stress field that attempts to better incorporate the influence on the elastic stress field driving growth, of any stresses induced by the plastically deformed region that surrounds a growing fatigue crack. the objective of the current work is the experimental determination of the plastic zone size and shape by using dic in titanium compact tension specimens, and then to evaluate the capability of three crack tip field models to characterise stress or displacement and hence to predict plastic zone size and shape. the three models considered in this work are the westergaard crack tip stress equations, williams’ expansion series for crack tip stresses and the recently developed cjp model [9] for crack tip displacement fields. description of the models for the characterisation of crack tip fields westergaard equations ccording to the westergaard equations, the stress field around the crack tip [8] is described using the stress intensity factors (sifs), ki and kii, the t-stress (t) and a polar coordinate system with its origin at the crack tip. crack tip stress fields are then defined as:                                                                          0 0 2 3 2 1 2 2 3 22 2 3 2 2 2 2 2 3 2 2 3 2 1 2 3 2 1 22 t sinsincos sincossin coscossin r k cossin sinsin sinsin cos r k iii xy y x             (1) in a similar way, crack tip displacement fields [8] are described as:                                                                                        sin cos r g t sincos cossin r g k cossin sincos r g k v u iii 3 1 8 2 21 2 2 21 2 22 2 21 2 2 21 2 22 2 2 2 2 (2) where g = e/2(1+ν) is the shear modulus, e and ν are the young’s modulus and poisson’s ratio of the material respectively, and к = (3-ν)/(1+ν) for plane stress or к = 3-4ν for strain plain. i a j.m. vasco-olmo et alii, frattura ed integrità strutturale, 41 (2017) 166-174; doi: 10.3221/igf-esis.41.23 168 williams’ crack tip stress expansion n the williams’ series expansion, crack tip stress fields [10] are expressed as a function of a number of terms in the series, the series coefficients and a polar coordinate system with its origin at the crack tip:                                                                                                                                                                                                                        3 2 1 2 1 22 1 3 2 1 2 1 22 12 3 2 1 2 1 22 12 2 3 2 1 2 1 22 1 3 2 1 2 1 22 12 3 2 1 2 1 22 12 2 1 2 2 1 2 2 n cos nn cos n n sin nn sin n n sin nn sin n ra n n sin nn sin n n cos nn cos n n cos nn cos n ra n n n n n` n iin n n n n n in xy y x (3) where ai1 = ki/√2π, aii1 = -kii/√2π and ai2 = -t/4. in addition, crack tip displacement fields [11] are defined as:                                                                              2 4 22 1 2 2 4 22 1 2 2 2 4 22 1 2 2 4 22 1 2 2 1 2 1 2         n cos nn cos n n sin nn sin n b g r n sin nn sin n n cos nn cos n a g r v u n n n n n n n n n n (4) where a1 = ki/√2π, b1 = -kii/√2π and a2 = t/4. cjp model he cjp model is a novel mathematical model developed by christopher, james and patterson [9] based on muskhelishvili complex potentials [12]. the authors postulated that the plastic enclave which exists around the tip of a fatigue crack and along its flanks will shield the crack from the full influence of the applied elastic stress field and that crack tip shielding includes the effect of crack flank contact forces (so-called crack closure) as well as a compatibility-induced interfacial shear stress at the elastic-plastic boundary. in the original formulation of this model, crack tip fields [9] were characterised as:                                                               2 3 2 3 2 5 22 1 2 5 2 5 2 5 2 5 2 1 2 5 2 1 2 84 2 1 2 3 2 5 2 3 2 5 2 1 2 5 2 1 2 84 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1               sincosrlnsinfrsinbsinar sinsincoscosrlnfrhcosbrcosrfba sinsincoscosrlnfrccosbrcosrfba xy y x (5) five coefficients (a, b, c, f, h) are therefore used to define the stress fields around the crack tip. on the other hand, crack tip displacement fields [9] were characterised according to expression (6). in the mathematical analysis, the i t j.m. vasco-olmo et alii, frattura ed integrità strutturale, 41 (2017) 166-174; doi: 10.3221/igf-esis.41.23 169 assumption d+f=0 must be made in order to give an appropriate asymptotic behaviour of the stress along the crack flank. therefore, crack tip displacement fields are also defined from the same five coefficients. (6) the cjp model provides three stress intensity factors to characterise the stress and displacement fields around the crack tip; an opening mode stress intensity factor kf, a retardation stress intensity factor kr, a shear stress intensity factor ks and also gives the t-stress. kf is defined from the applied remote load, traditionally characterized by ki, but is modified by force components derived from the stresses acting across the elastic-plastic boundary and which therefore influence the driving force for crack growth. thus, kf is defined by evaluating the stress component σy:     fbarlnfrrlimk y r f 83 2 22 2 1 0      (7) kr characterises forces applied in the plane of the crack and which provide a retarding effect on fatigue crack growth. thus, kr is evaluated from σx:     frlimk x r r 2 3 22 0    (8) besides the two previous sifs, the cjp model proposes that a shear term arises from the requirement of compatibility at the elastic-plastic boundary of the plastically deformed crack wake. therefore, this shear stress intensity factor (ks) characterises compatibility-induced shear stress along the plane of the crack at the interface between the plastic enclave and the surrounding elastic field. according to this, ks is defined from the shear stress component σxy:    barlimk xy r s   2 2 0    (9) the t-stress is defined from its components in the x and y directions: tx = -c; ty = -h. experimental work compact tension (ct) specimen (dimensions shown in fig. 1a) was manufactured from a 1 mm thick sheet of commercially pure titanium and subjected to constant amplitude fatigue loading at a r ratio of 0.6 (pmin = 450 n, pmax = 750 n). figure 1: (a) dimensions (mm) of the ct specimen tested. (b) experimental set-up used to measure dic data during fatigue testing. a (b) (a)                            z hc zdzlnzdza hc zlnzfzfbzz hc zlnfzfzzfbivug 2 2 4 2 4 24222 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1  j.m. vasco-olmo et alii, frattura ed integrità strutturale, 41 (2017) 166-174; doi: 10.3221/igf-esis.41.23 170 the two faces of the specimen were prepared for experimental observations in two different ways. the surface to be used for digital image correlation (dic) was treated by spraying a black speckle with an airbrush over a white background, while the other face was polished to assist in tracking the crack tip with a zoom lens. fatigue test was conducted on an electropuls e3000 electric machine (fig. 1b) at a frequency of 10 hz. a ccd camera fitted with a macro-zoom lens (mlh-10x eo) to increase the spatial resolution at the region around the crack tip, was placed perpendicular to each face of the specimen. during fatigue testing, the cycling was periodically paused to allow acquisition of a sequence of images at uniform increments through a complete loading and unloading cycle. the ccd camera viewing the speckled face of the specimen was set up so that the field of view was 17.3 x 13 mm (resolution of 13.5 μm/pix) with the crack path located at the centre of the image. illumination of the surface was provided by a fibre optic ring placed around the zoom lens (shown in fig. 1b). experimental methodology n this section, the two methodologies developed to evaluate the plastic zone size and shape are described. the first methodology is a direct method in which the plastic zone is estimated from the displacement fields determined by experiment, while the second one is an indirect method in which data from experiments is employed in the models to determine the plastic zone size and shape. direct method for estimating the plastic zone this method is based on the application of a yield criterion and consists in identifying the plastic stress field by differentiating the experimentally measured displacement fields. in this work, 2d-dic has been employed to make experimental displacement measurements. then, the procedure for implementing this method is described. the first step in the methodology consists in obtaining the horizontal and vertical displacement fields around the crack tip. in fig. 2 typical examples of displacement maps are shown for a crack length of 9.40 mm and a load level of 750 n. the developed process will be illustrated using these displacement maps. figure 2: horizontal (a) and vertical (b) displacement fields measured with dic for a crack length of 9.40 mm and a load level of 750 n, and data point collection employed for the calculation of stress intensity factors. the next step in the process involves determining the strain fields at the crack tip by differentiation of the displacement fields. for this purpose, the green-lagrange strain tensor [13] is employed because it considers the second order terms and is more accurate than those using only first order terms. thus, this strain tensor is given by the following expressions: (10) i                                                                                                        y v x v y u x u x v y v x u y u y v y u y v x u x v y u y v x u xy yy xx 00 00 2 1    j.m. vasco-olmo et alii, frattura ed integrità strutturale, 41 (2017) 166-174; doi: 10.3221/igf-esis.41.23 171 once the strain fields have been calculated, the next step is to determine the stress fields using hooke’s law. the equivalent stress is calculated from the stress tensor either using the second invariant of the stress deviator (von mises), or the difference of the maximum and minimum principal stress (tresca). an estimate of the size and shape of the plastic zone is obtained by connecting all points where the yield criterion is met, i.e., where the equivalent stress is equal to the yield stress. figs. 3a and 3b show the region of equivalent stress where the value exceeds the yield stress for both the von mises and tresca yield criteria. thus, the plastic zone area can be easily identified from the surrounding elastic field. figure 3: equivalent stress maps above the yield stress corresponding to von mises (a) and tresca (b) criteria for a crack length of 9.40 mm at a load level of 750 n. in this paper, the area of the plastic zone has been considered as a variable that contains information on both size and shape and which can therefore provide an efficient and powerful technique for making quantitative measurements. once the plastic zone has been identified, the next step is to characterise its size by quantifying its area at the crack tip. initially, a set of data points that define the equivalent yield stress contour of the plastic zone must be detected (fig. 4a). next, a triangulation function is applied to define the area enclosed by these data points (fig. 4b). finally, the plastic zone area can be calculated as the sum of the areas of all the triangles previously defined in the triangulation process. figure 4: (a) detection of the data points defining the contour of the plastic zone. (b) triangulation of the enclosed area for the selected contour. indirect method for estimating the plastic zone the plastic zone estimated from experimental data will be compared with that predicted by the analytical models defining crack tip fields to validate the proposed methodology. in the literature, the two most popular methods used to estimate the plastic zone size are the irwin and dugdale approaches. both approaches lead to simple estimates for crack tip plastic zone size based on elastic solutions. therefore, it is more useful to estimate the size and shape of the plastic zone at all angles around the crack tip by applying a yield criterion to an analytical model that describes crack tip stress field. in this work, the three models described in the second will be used to find the plastic zone shape. the first step in this indirect method consists in determining the stress intensity factors in each crack tip stress model from analysis of the experimental displacement fields. the multi-point over-deterministic method developed by sanford (b) (a) j.m. vasco-olmo et alii, frattura ed integrità strutturale, 41 (2017) 166-174; doi: 10.3221/igf-esis.41.23 172 and dally [14] forms the basis for this process. the models are valid only for the elastic field near the crack tip singularity and hence it was necessary to identify the near-tip zone where valid experimental data could be obtained. an annular mesh (fig. 2) was defined to establish the region from which determining the sifs. two parameters are fundamentals for defining the annular mesh: inner and outer radii. the inner radius was defined with sufficient extent to avoid including plastic deformation at the crack tip, while the outer radius was defined to be within the singularity dominated zone. from the calculation of the stress intensity factors, the coefficients defining the crack tip fields in the analytical models can be extracted to found the plastic zone contour. crack tip stress fields in the analytical models depend on a set of coefficients and the coordinates of the analysed data points. therefore, an expression as a function of the above parameters for the equivalent stress according to a yield criterion can be obtained. from this expression, an error function is defined as the difference between the equivalent stress and the yield stress of the material. thus, plastic zone contour is found from the evaluation of the error function by analysing angle values between 0º and 360º to estimate the radius of the plastic zone. hence the size and shape of the experimentally determined plastic zone can be compared with that found using the three different theoretical models that describe the crack tip stress and displacement fields. results and discussion ig. 5 shows size and shape data obtained for the plastic zone at maximum load using the von mises yield criterion for two different crack lengths (6.42 and 9.20 mm). the white area represents the experimental plastic zone estimated from the direct method, while the dotted contours correspond to the plastic zone found for the three models by implementing the indirect method using the model coefficients. it is clear that the plastic zone size and shape predicted by the cjp model is an excellent fit to the experimental data, while the westergaard and williams models predict somewhat larger dimensions. therefore, from a qualitative point of view, the cjp model seems that shows a great potential to predict the plastic zone at the crack tip. figure 5: comparison between the experimental plastic zone shape and that predicted by the models using the von mises criterion for two crack lengths, (a) 6.42 and (b) 9.20 mm at maximum load. moreover, as indicated above the plastic zone area is evaluated for its quantification. fig. 7 shows the evolution of both experimental and predicted plastic zone area with the crack length using the von mises yield criterion. again, the experimental data is in close agreement with the plastic zone area calculated from the cjp model at all crack lengths, while the predicted area using the westergaard and williams models is higher than the experimental results. the westergaard model shows a progressively larger error as the crack length increases while the error in the williams solution remains fairly constant. it can be concluded that the cjp model provides an improved prediction of the crack tip plastic zone area and shape compared with either the westergaard or williams models. fig. 6 illustrates the difference that choice of yield criterion (von mises or tresca) would make to the experimental and cjp predictions of plastic zone area. as expected, sizes predicted using the tresca criterion are higher, but close agreement is still observed between the experimental predictions and those provided by the cjp model. f (a) (b) green (westergaard) cyan (williams) yellow (cjp) j.m. vasco-olmo et alii, frattura ed integrità strutturale, 41 (2017) 166-174; doi: 10.3221/igf-esis.41.23 173 figure 6: (a) comparison between the experimental and model predictions of plastic zone area at maximum applied load as a function of the crack length using the von mises criterion. (b) comparison between the experimental and cjp model predictions of plastic zone size at maximum load using both the von mises and tresca yield criteria. conclusions n the present paper a novel experimental methodology for the quantitative evaluation of the crack tip plastic zone size during fatigue crack growth has been presented. this methodology uses differentiation of the measured displacement fields to obtain strain maps that can be combined with a yield criterion to estimate the shape and size of the crack tip plastic zone. these predictions can be compared with estimates of the plastic zone size obtained from analytical models that describe crack tip displacement fields. this work indicates that the cjp model provides the best prediction of the crack tip plastic zone shape and size. it is proposed that this agreement supports the fact that the cjp model, through its basic assumptions regarding the influences of plasticity on the elastic stress fields ahead of the crack tip, is better at defining the real size of the plastic zone. acknowledgements he current work has been conducted with the financial support from gobierno de españa through the project ‘proyecto de investigación de excelencia del ministerio de economía y competitividad mat2016-76951-c2-1-p’. references [1] uguz, a., martin, j.w., plastic zone size measurement techniques for metallic materials, materials characterization, 37 (1996) 105–118. [2] steuwer, a., edwards, l., pratihar, s., ganguly, s., peel, m., fitzpatrick, e.m., marrow, t.j., withers, p.j., sinclair, i., singh, k.d., gao, n., buslaps, t., buffière, j.y., in situ analysis of cracks in structural materials using synchrotron xray tomography and diffraction, nuclear instruments and methods, in physics research section b: beam interactions with materials and atoms, 246 (2006) 217–225. [3] nowell, d., kartal, m.e., de matos, p.f.p., digital image correlation measurement of near-tip fatigue crack displacement fields: constant amplitude loading and load history effects, fatigue and fracture of engineering materials and structures, 36(1) (2013) 3–13. [4] díaz, f.a., patterson, e.a., yates, j.r., assessment of effective stress intensity factors using thermoelastic stress analysis, the journal of strain analysis for engineering design, 44 (2009) 621–631. [5] wright, s.i., nowell, m.m., field, d.p., a review of strain analysis using electron backscatter diffraction, microscopy and microanalysis, 17 (2011) 316–329. [6] irwin, g.r., analysis of stresses and strains near the end of a crack traversing a plate, journal of applied mechanics, 24 (1957) 361–364. 0 1 2 3 4 5 6 7 8 9 10 11 12 5,0 5,5 6,0 6,5 7,0 7,5 8,0 8,5 9,0 9,5 p la st ic z o n e ar ea ( m m 2 ) crack length (mm) experimental cjp westergaard williams 0 1 2 3 4 5 6 7 8 9 5,0 5,5 6,0 6,5 7,0 7,5 8,0 8,5 9,0 9,5 p la st ic z o n e ar ea ( m m 2 ) crack length (mm) experimental (von mises) cjp (von mises) experimental (tresca) cjp (tresca) i t (a) (b) j.m. vasco-olmo et alii, frattura ed integrità strutturale, 41 (2017) 166-174; doi: 10.3221/igf-esis.41.23 174 [7] dugdale, d.s., yielding in steel sheets containing slits, journal of the mechanics and physics of solids, 8 (1960) 100– 104. [8] janssen, m., zuidema, j., wanhill, r.j.h., fracture mechanics, spon press, (2006). [9] james, m.n., christopher, c.j., lu, y., patterson, e.a., local crack plasticity and its influence on the global elastic field, international journal of fatigue, 46 (2013) 4–15. [10] ramesh, k., gupta, s., kelkar, a.a., evaluation of stress field parameters in fracture mechanics by photoelasticity– revisited, engineering fracture mechanics, 56 (1997) 25–45. [11] yates, j.r., zanganeh, m., tai, y.h., quantifying crack tip displacement fields with dic, engineering fracture mechanics, 77 (2010) 2063–2076. [12] muskhelishvili, n.i., some basic problems of the mathematical theory of elasticity, nordhoff international publishing, (1977). [13] singh, a.k., mechanics of solids, prentice-hall of india private limited, (2010). 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can be opened with acrobat and adobe reader 5.0 and later.) >> /namespace [ (adobe) (common) (1.0) ] /othernamespaces [ << /asreaderspreads false /cropimagestoframes true /errorcontrol /warnandcontinue /flattenerignorespreadoverrides false /includeguidesgrids false /includenonprinting false /includeslug false /namespace [ (adobe) (indesign) (4.0) ] /omitplacedbitmaps false /omitplacedeps false /omitplacedpdf false /simulateoverprint /legacy >> << /addbleedmarks false /addcolorbars false /addcropmarks false /addpageinfo false /addregmarks false /convertcolors /converttocmyk /destinationprofilename () /destinationprofileselector /documentcmyk /downsample16bitimages true /flattenerpreset << /presetselector /mediumresolution >> /formelements false /generatestructure false /includebookmarks false /includehyperlinks false /includeinteractive false /includelayers false /includeprofiles false /multimediahandling /useobjectsettings /namespace [ (adobe) (creativesuite) (2.0) ] /pdfxoutputintentprofileselector /documentcmyk /preserveediting true /untaggedcmykhandling /leaveuntagged /untaggedrgbhandling /usedocumentprofile /usedocumentbleed false >> ] >> setdistillerparams << /hwresolution [2400 2400] /pagesize [612.000 792.000] >> setpagedevice microsoft word 2326 a. zakharovet alii, frattura ed integrità strutturale, 48 (2019) 87-96; doi: 10.3221/igf-esis.48.11 87 focussed on “crack paths” the crack path in fuselage panel under mixed mode biaxial loading alexander zakharov, valery shlyannikov, andrey tumanov institute of power engineering and advanced technologies, frc kazan scientific center, russian academy of sciences, russia alex.zakharov88@mail.ru, https://orcid.org/0000-0003-3568-1427 shlyannikov@mail.ru, https://orcid.org/0000-0003-2468-9300 tymanoff@rambler.ru abstract. this paper provides the background for practical applications of nonlinear fracture resistance parameters for structural integrity assessment of aviation structures with initial cracks. the subject of this numerical study is a fragment of airplane fuselage panel, with an initial central crack under biaxial loading. the plastic stress intensity factor (sif) concept is here applied to estimate the critical crack size in fuselage panel under biaxial loading. the fracture damage zone influence on crack tip stress state in airplane fuselage panel under biaxial loading is evaluated. the values of plastic stress intensity factor kp, obtained from both elastic-plastic solution for isotropic body and elastic-plastic solution with cohesive zone, are compared to the critical values of nonlinear fracture resistance parameter, for fuselage panel under biaxial loading. the curvilinear crack path in the considered fuselage panel under mixed mode biaxial loading is finally evaluated. keywords. crack path; mixed mode; fuselage panel; biaxial loading; plastic stress intensity factor; cohesive zone. citation: zakharov a., shlyannikov v.., tumanov a., crack path in fuselage panel under mixed mode biaxial loading, frattura ed integrità strutturale, 48 (2019) 87-96. received: 04.12.2018 accepted: 19.02.2019 published: 01.04.2019 copyright: © 2019 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. introduction n recent years, significant advances have been made in stress analyses of the cracked aircraft components, especially in the prediction of fatigue live and crack propagation [1]. in particular, it is important to analyze the critical crack size to prevent catastrophic failure in the presence of small initial defects and cyclic loading. repeated pressurization/depressurization cycles during airplane takeoff and landing may lead to fatigue crack in the fuselage panels. prediction of crack growth in the aircraft fuselage panels is one of the key problems in aircraft structural integrity assessment. advanced methods of fracture and damage mechanics are widely used to investigate crack initiation and propagation in curved and stiffened fuselage panel. citarella et al. [2] used the dual boundary element method (dbem) to examine the crack propagation of a repaired aeronautic panel. experimental tests and numerical dbem simulations of the multiaxial static and fatigue strength of a flat stiffened fuselage panel with central initial crack were made by armentani et al. [3]. the i http://www.gruppofrattura.it/va/48/2326.mp4 a. zakharovet alii, frattura ed integrità strutturale, 48 (2019) 87-96; doi: 10.3221/igf-esis.48.11 88 elastic sif for a longitudinal crack between the two frames in fuselage panel under the pressurization was calculated using linear elastic fracture mechanics assumptions and the modified virtual crack closure technique [4]. a significant success has been achieved in the modeling of the fracture process zone at the crack tip by using special cohesive elements. all microstructural mechanisms of the fracture process can be described by two cohesive parameters, i.e., the maximum traction or cohesive strength (t0) and critical separation (δ0). for the practical application of the cohesive model in modeling of crack initiation and propagation cornec et al. [5] proposed the procedure for traction-separation law material parameters determination. scheider and brocks [6] introduced a cohesive interface element for ductile tearing of thinwalled metal sheets. cornec et al. have used a cohesive model for the residual strength prediction of a large curved and stiffened fuselage panel containing a two-bay crack [7]. it is a common practice to use elastic sif to characterize the stress state at the crack tip. shlyannikov et al. suggested to use plastic sif in residual life prediction for the structural components with cracks [8, 9]. it has been shown that the application of the plastic sif concept in the residual life assessment for turbine disk allows to obtain more reliable estimations [10]. in this study, nonlinear fracture resistance parameter in the form of plastic sif was suggested to estimate the critical values of the crack length in fuselage panel under biaxial loading. based on the numerical results of the governing parameter of the elastic-plastic stress field in the form of the in-integral, the plastic sif is computed for the considered cracked fuselage panel and operation loading conditions. the comparison of the results of calculation of fracture resistance characteristics for fuselage panel by means of elastic solution, traditional elastic-plastic solution and elasticplastic solution with cohesive elements is presented. on the basis of the strain energy density (sed) and cohesive zone concepts, the curvilinear crack path in the fuselage panel under biaxial loading was predicted. subject of study and material properties he subject of the present study is a stiffened fuselage panel with central straight-fronted crack under biaxial loading. the prototype of fe model was a fuselage panel from airbus a-330 [11]. the fuselage panel was made of the d16t aluminum alloy that is an analogue of the al2024 alloy. detailed analysis of the stress-strain state in the fuselage panel with central crack is performed for the fragment of the full-scale finite element model with the following sizes: width w=440mm; height h=220mm; thickness t=2mm. the fe model of the fragment of fuselage panel with central crack is shown in fig.1. the submodeling displacements determined from the numerical analysis of the full-scale model under biaxial loading were utilized as the boundary conditions to the fragment of the fuselage panel. at operation, fuselage panel is subjected to biaxial loading. three types of biaxial loading conditions are considered in the numerical study: internal pressure p=0.05 mpa, internal pressure p=0.1 mpa and combination of internal pressure p=0.05mpa with longitudinal forces f=50mpa. figure 1: finite element model of the stiffened fuselage panel. the numerical calculations in the present study were performed in the following sequence. in the first case, the elastic and elastic–plastic finite element analyses (fea) were carried out. the fuselage panel with the mathematical notch-type crack was considered. the 3d, 20-node, quadrilateral brick, isoparametric solid elements were used to model the biaxially loaded cracked fuselage panel. the typical finite element mesh of the fuselage panel with central crack is illustrated in fig. t a. zakharovet alii, frattura ed integrità strutturale, 48 (2019) 87-96; doi: 10.3221/igf-esis.48.11 89 1. since the crack-tip region contains steep displacement and high stress gradients, the mesh needs to be very refined at the crack tip. for this purpose, a corresponding mesh topology having a focused ring of elements surrounding the crack front was used to enhance convergence of the numerical solutions. for each type of loading conditions of cracked fuselage panel at the crack-tip area in the circumferential direction, 40 equally sized elements are defined in the angular region from 0 to π. to model the 3d stress field in curvilinear fuselage panel correctly and because of the strong variations of the stress gradients, the thicknesses of the successive element layers were gradually reduced toward the inner and outer surface of the fuselage panel with respect to the crack-front line. the elastic–plastic parameters for the bilinear isotropic hardening model were determined through experimental studies. the main mechanical properties for d16t alloy have been determined by standard tension tests. stress-strain curve is described by the well-known ramberg-osgood equation. elastic-plastic material properties for d16t alloy are listed in tab. 1. material young’s modulus, e (mpa) poisson’s ratio, ν yield stress, σ0 (mpa) ultimate stress, σf (mpa) tangent modulus, gt (mрa) strain hardening exponent, n strain hardening coefficient, α d16t 73262 0.33 310 529 1430 5.6839 1.6667 table 1: elastic-plastic properties for d16t alloy. the second series of numerical calculations of the cracked fuselage panel was performed using special cohesive elements in the ansys finite element code on the base of the bilinear cohesive zone model [12]. in accordance [13] the tractionseparation law can be expressed in the following form: cttd c   0 0 0 2 1   (1) where γ0 – cohesive energy, t0 – cohesive stresses and δc – cohesive separation. the parameters for the traction–separation law should be determined before using the cohesive elements in the numerical analysis of the stress fields around the crack tip. for d16t aluminum alloy that is an analogue of the al2024 alloy was used numerical and experimental method for determination of parameters for traction-separation law, proposed in [5]. the layer of special cohesive elements was integrated to fe model with the mathematical notch-type crack, generated for elastic-plastic solution mentioned above. cohesive elements were located in the region of the crack tip in the plane of the further crack propagation. in this study, for the elastic-plastic analysis of the cracked fuselage panel with cohesive elements were used the following parameters of the constitutive equation of the bilinear traction-separation law: gcn=8.641 kj/m2, t0 = 484 mpa, 03571.0cn mm for the d16t aluminum alloy. to estimate the critical crack size in structures, it is necessary to know fracture resistance parameters for the considered material. traditionally, elastic fracture resistance characteristic in the form of the fracture toughness k1c was used. the special fracture toughness tests for compact tension (ct) specimens from aluminum alloy d16t have been carried out according by astm e1820. as a result, the critical value of the elastic fracture resistance parameter for d16t aluminum alloy is equal to kq = 28 mpa√m. in this study, the nonlinear fracture resistance parameter in the form of plastic sif is applied to estimate critical crack size in fuselage panel. the critical value of the plastic sif for d16t alloy under mode i conditions can be expressed in terms of elastic sif using rice’s j-integral:   1 2 0 2 1  npn ki ee k j  and 1 1 2 0 2            n fem q p wi k k n (2) the critical value of plastic sif was calculated on the base of experimentally determined critical elastic sif (kq) and inintegral obtained by fea of ct specimen. on the basis of experimental data of the fracture toughness tests, numerical calculations related to the ct specimens have been carried out to determine the governing parameter for the stresses fields at the crack tip in-integral. shlyannikov and tumanov [14] suggested a numerical procedure for calculating in-integral for different cracked bodies by means of the a. zakharovet alii, frattura ed integrità strutturale, 48 (2019) 87-96; doi: 10.3221/igf-esis.48.11 90 elastic–plastic fe-analysis of the near crack-tip stress-strain fields. in this case, in-integral in eq. (2) is a function a material property and configurations of the cracked body and loading conditions:                  d uu n d ud u d ud u n n i fem r fem r femfem rr fem fem r fem r fem rfemfem rr femn e fem n                                                         cos~~~~ 1 1 sin ~ ~~ ~ ~~ cos~ 1 1 (3) dimensionless functions of stresses and displacements in eq. (3) were determined by numerical analysis. as a result, the critical value of the elastic-plastic fracture resistance parameter for d16t aluminum alloy is equal to kp = 0.57. elastic and elastic-plastic fracture resistance characteristics of the considered aluminum alloy, obtained from experimental tests and numerical studies, are used for the assessment of the critical crack size in the fuselage panel under biaxial loading. critical crack size assessment in the fuselage panel s it mentioned before, this study mainly focused on numerical analysis of stress-strain state in cracked fuselage panel. the fe-analysis of the nominal stress–strain state of the investigated fuselage panel without crack was performed by shlyannikov et al. [15]. as a result the equivalent stress distributions were obtained for considered fuselage panel along the longitudinal direction, ox-axis, transverse direction, oy-axis, and thickness direction, oz-axis. stress distributions along the transverse direction in fuselage panel are presented in fig.2.a. a) b) a figure 2: equivalent stress distributions along the thickness of the fuselage panel. notably, stress distributions along the thickness of the panel have significant gradients, while stress distributions along longitudinal direction more uniform. so, results of the numerical calculations for the cracked fuselage panel will be presented in outer surface and inner surface of the panel as it shown in fig. 2,b. critical size of the crack in the fuselage panel under biaxial loading was determined in both outer and inner surfaces from the fracture initiation point of view. in this study numerical analysis of critical crack size in the considered fuselage panel under biaxial loading is performed for mode і conditions on the base of elastic solution, traditional elastic-plastic solution and elastic-plastic solution with cohesive elements. three values of the crack length in the fuselage panel were examined: 100, 200 and 300mm. in the case of elastic and elastic–plastic fe-analyses, the fuselage panel with the mathematical notch-type crack was considered. the young’s modulus (e = 73262 mpa) and poisson’s ratio (ν = 0.33) were used as the elastic properties of the investigated d16t alloy, whereas yield stress (σ0 = 310 mpa) and tangent modulus (gt = 1430 mpa) were utilized for the bilinear isotropic hardening model. the third series of numerical calculations of the cracked fuselage panel was performed using special cohesive elements in the ansys fe code [12] of the bilinear cohesive zone model. in addition, a a. zakharovet alii, frattura ed integrità strutturale, 48 (2019) 87-96; doi: 10.3221/igf-esis.48.11 91 the cohesive energy (gcn = 8.641 kj/m2), cohesive stress (t0 = 484 mpa), and critical cohesive separation ( 03571.0cn mm) were employed for the constitutive equation of the bilinear traction–separation law. fig.3. represent the results of elastic solution and traditional elastic-plastic solution for the cracked fuselage panel. figure 3: elastic and plastic sif as a function of relative crack length in fuselage panel: (a) elastic sif under internal pressure p=0.05 mpa, (b) elastic sif under internal pressure p=0.1 mpa, (c) plastic sif under internal pressure p=0.1 mpa. results of the numerical solution for the cracked fuselage panel is presented for both types of biaxial loading, namely, internal pressure p=0.05 mpa and internal pressure p=0.1 mpa. elastic and plastic sif are presented as a function of the dimensionless crack length normalized by the width of the considered fragment of fuselage panel. as follows from results of elastic solution (fig.3.a,b) the critical value of the relative crack length on the outer surface of the fuselage panel under internal pressure р=0.05 mpa is equal to (a/w)cr =0.24. in the case of internal pressure р=0.1 mpa, the current values of elastic sif on the outer surface of the fuselage panel exceed the critical values of elastic solution in the full range of considered crack lengths. results of the elastic-plastic solution show that internal pressure р=0,05 mpa does not lead to initial crack propagation, because the current values of the plastic sif on both outer surface and inner surface of the fuselage panel do not exceed the critical value of plastic sif. the plastic sif as a function of relative crack length in the fuselage panel under internal pressure р=0.1 mpa is presented in fig.3.c. in this case, the critical value of the relative crack length on the outer surface of the fuselage panel under internal pressure р=0.1 mpa is equal to (a/w)cr=0.34. the values of plastic sif kp obtained by both elastic-plastic solutions for isotropic body and elastic-plastic solution with cohesive elements are compared to the critical values of nonlinear fracture resistance parameter for fuselage panel under biaxial loading in the range of crack sizes (see fig.4). figure 4: comparison of the elastic-plastic solution and the elastic-plastic solution with cohesive elements: (a) plastic sif distributions on outer surface of the fuselage panel, (b) plastic sif distributions on inner surface of the fuselage panel. a. zakharovet alii, frattura ed integrità strutturale, 48 (2019) 87-96; doi: 10.3221/igf-esis.48.11 92 elastic-plastic solution with cohesive elements gives lower values of the critical crack size (a/w)cr=0.3 in comparison to results of the traditional elastic-plastic solution, where the critical crack size is (a/w)cr=0.34. this value is slightly lower than the critical crack size obtained by using the traditional elastic–plastic solution, but it is remarkably differ from the results of the elastic solution. the results of the traditional elastic–plastic solution (i.e., (a/w)cr = 0.34) and elastic–plastic solution with cohesive elements (i.e., (a/w)cr = 0.3) are close to each other. it means that structural integrity assessment of cracked bodies should be performed on the basis of a nonlinear analysis. curvilinear crack path prediction in fuselage panel n this work, prediction of the curvilinear crack path in considered fuselage panel under biaxial loading is presented. the fragment of the fuselage panel with initial straight-fronted crack equal to 100 mm is considered. the crack path in the fuselage panel is calculated for combination of the internal pressure p=0.05mpa and longitudinal stresses f=50mpa. the crack angle deviation in the fuselage panel is calculated on the basis of the sed concept. shlyannikov et. al. used sed criterion in the application to the mixed mode crack path and growth prediction. [16-18]. according to the sed concept, fracture process is initiated at the local area near the crack tip where (dw/dv) reaches a critical value (dw/dv)c which is a material property. the critical value of sed is the area under the true stress-strain curve, and can be expressed as follows:             12 0 2 0 12 1 n ffff c n n e d dv dw f       (4) where 0/ ff  – true ultimate tensile stress. for elastic-plastic material’s behavior, current value of sed can be determined on the base of normalized hydrostatic stress, m , and equivalent stress, e , as:                 122 0 2 0 16 21 3 1 n emeijij n n e d dv dw ij         (5) the total sed may be divided into an elastic part, (dw/dv)e, and plastic part, (dw/dv)p:                         pe dv wd dv wd dv wd (6) where w is equal 20/ew . for linear elastic material behavior the sed function can be written as curve, and can be expressed as follows:       t e g g t rg kbkb rg kakakkaka dv dw 16 1 224 222111 2 333 2 2222112 2 111              (7) where k1, k2 and k3 are elastic stress intensity factors. plastic part of the total strain energy density can be expressed by:   p nn e n n p s areiw a ar kk n n edv dw )/( 1~ )/()1( 2 1 2 2 2 1 2                  (8) where k1, k2 and k3 are elastic stress intensity factors. i a. zakharovet alii, frattura ed integrità strutturale, 48 (2019) 87-96; doi: 10.3221/igf-esis.48.11 93 more details of the application of sed concept for predictions of crack path under mixed mode biaxial loading are given in ref. [16-17]. calculation of the curvilinear crack propagation in fuselage panel under biaxial loading was given in discrete steps. it should be noted that, at each step, both elastic-plastic solution and elastic-plastic solution with cohesive elements were performed. the sequence of the numerical calculations was as follows: the crack angle deviation was determined on the basis of the sed distributions using the elastic–plastic solution. the crack length increment in the crack angle deviation was calculated using the elastic–plastic solution with cohesive elements. the step-by-step procedure of the crack growth trajectory calculation in fuselage panel is schematically shown in fig.5. in the first step, the fuselage panel with initial mode i crack of 100 mm was considered. on the basis of traditional elasticplastic solution, the sed distributions and hence the crack angle deviation in the fuselage panel were calculated. in the present work, the third hypothesis of the sed criterion was used to determine the angle of crack propagation, θ*. thus, a line drawn from each point on the crack front in the normal plane at the angle, θ*, with respect to the crack plane indicates the directions where the strain energy density has its minimal value. it is assumed that the crack will be propagating in this direction. hence, a layer of cohesive elements was inserted into the cracked fuselage panel fe model at the crack tip in the plane of the proposed crack angle deviation. the crack length increment was calculated using the elastic–plastic solution with cohesive elements. on the each iteration new crack-tip position on the curvilinear crack path is determined in combination with the crack angle deviation and crack length increment. on the following step fe model of the fuselage panel with new crack tip position was generated and the second iteration of the crack path prediction was carrying out. the results of the previous step were used for generating a new fe model of the fuselage panel for next crack tip position. figure 5: crack growth trajectory calculation procedure. sed distributions around the crack tip as a function of crack length in the fuselage panel are given in fig.6. these results illustrate the difference in the stress distributions around the crack tip in fuselage panel as a function of the constitutive model of the material behavior. it should be noted that sed extremum values calculated by both elastic-plastic solution and elastic-plastic solution with cohesive elements are different. it means that different values of the crack angle deviation in fuselage panel can be obtained depending on type of solution. in this study, based on the sed distributions obtained on the base of traditional elastic-plastic solution displayed in fig.6, crack angle deviation of the further crack growth trajectory was computed. as it mentioned above, the crack length increments are determined by elastic-plastic analysis with cohesive elements. the crack angle deviation and crack length increments determined at each step are used to model general curvilinear crack path in the fuselage panel under biaxial loading. results of the crack angle deviation and the crack length increments for the fuselage panel with curvilinear crack under operational loading conditions are listed in tab. 2. the fe analysis of the stress–strain state for the fuselage panel with straight-fronted and curvilinear cracks by using the traditional elastic–plastic and elastic–plastic solutions with cohesive elements showed the possibility of predicting the crack path and crack growth rate for actual structural components and operational loading conditions. a. zakharovet alii, frattura ed integrità strutturale, 48 (2019) 87-96; doi: 10.3221/igf-esis.48.11 94 figure 6: strain energy density distributions at the crack tip: (a) for initial crack with of 100 mm, (b-f) for the subsequent crack tip position with projection of the crack length on the ox-axis in the range of 200 – 360 mm. crack length 2аx,i [mm] crack angle deviation δθi [°] total crack angle deviation σδθi [°] crack length increments δаmax,i [mm] 100 0 0 0.00 200 3 3 0.49 240 7 10 1.30 280 14 24 1.48 320 0 24 4.29 360 12 36 2.59 table 2: crack angle deviation and crack length increments calculations. conclusions he assessment of the critical crack size in a fuselage panel under biaxial loading is performed on the basis of plastic sif concept. the values of stress intensity factors in fuselage panel with a central crack, obtained by elastic and elastic-plastic solution for isotropic body and elastic-plastic solution with cohesive zone, are compared to the critical values of fracture resistance parameters. as follows from this comparison, the structural integrity assessment of cracked bodies should be carried out on the basis of nonlinear fracture mechanics concepts. it is shown that cohesive zone model and nonlinear fracture resistance parameter in the form of plastic stress intensity factor can be effectively applied in the residual life predictions. t a. zakharovet alii, frattura ed integrità strutturale, 48 (2019) 87-96; doi: 10.3221/igf-esis.48.11 95 the curvilinear crack path in the fuselage panel is calculated. it is demonstrated the effectiveness of the proposed numerical procedure based on advanced fracture mechanics concepts such as strain energy density concept and cohesive zone model, for curvilinear crack growth trajectory calculation in the fuselage panel under mixed mode biaxial loading. acknowledgment he authors gratefully acknowledge the financial support of the russian science foundation under the project 1879-00279. references [1] newman, j.c. (2000) advances in fatigue and fracture mechanics analyses for metallic aircraft structures, nasa tm. [2] citarella, r., apicella, a. (2006) advanced design concepts and maintenance by integrated risk evaluation for aerostructures, sdhm, 2, pp. 183-196. [3] armentani, e., citarella, r., sepe, r. (2011) fml full scale aeronautics panel under multiaxial fatigue: experimnetal test and dbem simulation // engineering fracture mechanics, 78, pp. 1717-1728. [4] tavares, s., castro, p. (2011). stress intensity factor calibration for a longitudinal crack in a fuselage barrel and the bulging effect influence // engineering fracture mechanics, 78, pp. 2907-2918. [5] cornec, a., scheider, i., schwalbe, k.-h. (2003). on the practical application of the cohesive model // engineering fracture mechanics, 70, pp. 1963-1987. [6] scheider, i., brocks, w. (2006). cohesive elements for thin-walled structures // computational materials science, 37, pp. 101-109. [7] cornec a., schönfeld w., schwalbe k.-h., scheider i., (2009) application of the cohesive model for predicting the residual strength of a large scale fuselage structure with a two-bay crack, engineering failure analysis, 16, pp. 25412558. doi: 10.1016/j.engfailanal.2008.10.014 [8] shlyannikov, v.n., tumanov, a.v., zakharov, a.p., gerasimenko, a.a. (2016). surface flaw behavior under tension, bending and biaxial cyclic loading // international journal of fatigue, 92, pp. 557–576. doi: 10.1016/j.ijfatigue.2016.05.003. [9] shlyannikov, v.n., (2016) nonlinear stress intensity factors in fracture mechanics and their applications, procedia structural integrity, 2, pp. 744-752. doi: 10.1016/j.prostr.2016.06.096. [10] shlyannikov v.n., zakharov a.p., r.r. yarullin., (2016) structural integrity assessment of turbine disk on a plastic stress intensity factor basis, international journal of fatigue, 92, pp. 234–245. doi: 10.1016/j.ijfatigue.2016.07.016. [11] armentani e., citarella r., sepe r., (2011) fml full scale aeronautics panel under multiaxial fatigue: experimnetal test and dbem simulation, engineering fracture mechanics, 78, pp. 1717-1728. doi: 10.1016/j.engfracmech.2011.02.020. [12] ansys mechanical apdl theory reference, release 14.5 // ansys inc., southpointe, 275 technology drive, canonburg, pa, (2012). [13] tvergaard, v., needleman, a. (1984). analysis of the cup-cone fracture in a round tensile bar, acta metallurgica, 32(1), pp. 157-169. [14] shlyannikov v.n., tumanov a.v., (2014) characterization of crack tip stress fields in test specimens using mode mixity parameters, international journal of fracture, pp. 49-76. [15] shlyannikov, v.n., tumanov a., tartygasheva a. (2015) damage growth in fuselage panels under biaxial loading, transactions of academenergo, 4, pp. 54-71. [16] shlyannikov, v.n. (2003). elastic–plastic mixed-mode fracture criteria and parameters, springer-verlag, berlin. [17] shlyannikov, v.n., yu, s., kislova, a.v., tumanov (2010) inclined semi-elliptical crack for predicting crack growth direction based on apparent stress intensity factors, theoretical and applied fracture mechanics, 53, pp. 185-193. doi: 10.1016/j.tafmec.2010.06.003. [18] shlyannikov, v., boychenko, n., fernández-canteli, a., muñiz-calvente, m. (2015) elastic and plastic parts of strain energy density in critical distance determination, engineering fracture mechanics, 147, pp. 100-118. doi: 10.1016/j.engfracmech.2015.08.024. t a. zakharovet alii, frattura ed integrità strutturale, 48 (2019) 87-96; doi: 10.3221/igf-esis.48.11 96 nomenclature ε strain σ stress σ0 yield stress e young’s modulus n strain hardening exponent α strain hardening coefficient ν poisson’s ratio σf ultimate stress gt tangent modulus γ0 cohesive energy t0 cohesive stresses c n normal cohesive separation defining fracture k1, k2, k3 elastic stress intensity factors in governing parameter at the crack tip w width of the specimen kq critical value of the elastic stress intensity factor θ polar angle ijiu  ~,~ dimensionless angular functions of stresses and displacements σe equivalent stresses σm hydrostatic stresses 0/ ff  true ultimate stress normalized by yield stress dv dw strain energy density r distance from the crack tip η biaxial stress ratio << 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/hrv (za stvaranje adobe pdf dokumenata najpogodnijih za visokokvalitetni ispis prije tiskanja koristite ove postavke. stvoreni pdf dokumenti mogu se otvoriti acrobat i adobe reader 5.0 i kasnijim verzijama.) /hun 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can be opened with acrobat and adobe reader 5.0 and later.) >> /namespace [ (adobe) (common) (1.0) ] /othernamespaces [ << /asreaderspreads false /cropimagestoframes true /errorcontrol /warnandcontinue /flattenerignorespreadoverrides false /includeguidesgrids false /includenonprinting false /includeslug false /namespace [ (adobe) (indesign) (4.0) ] /omitplacedbitmaps false /omitplacedeps false /omitplacedpdf false /simulateoverprint /legacy >> << /addbleedmarks false /addcolorbars false /addcropmarks false /addpageinfo false /addregmarks false /convertcolors /converttocmyk /destinationprofilename () /destinationprofileselector /documentcmyk /downsample16bitimages true /flattenerpreset << /presetselector /mediumresolution >> /formelements false /generatestructure false /includebookmarks false /includehyperlinks false /includeinteractive false /includelayers false /includeprofiles false /multimediahandling /useobjectsettings /namespace [ (adobe) (creativesuite) (2.0) ] /pdfxoutputintentprofileselector /documentcmyk /preserveediting true /untaggedcmykhandling /leaveuntagged /untaggedrgbhandling /usedocumentprofile /usedocumentbleed false >> ] >> setdistillerparams << /hwresolution [2400 2400] /pagesize [612.000 792.000] >> setpagedevice microsoft word numero_37_art_21 j. kramberger et alii, frattura ed integrità strutturale, 37 (2016) 153-159; doi: 10.3221/igf-esis.37.21 153 focussed on multiaxial fatigue and fracture computational simulation of biaxial fatigue behaviour of lotus-type porous material j. kramberger, m. šori university of maribor, faculty of mechanical engineering, smetanova 17, 2000 maribor, slovenia janez.kramberger@um.si marko.sori@um.si m. šraml university of maribor, faculty of civil engineering, transportation engineering and architecture, smetanova 17, 2000 maribor, slovenia matjaz.sraml@um.si s. glodež university of maribor, faculty of mechanical engineering, smetanova 17, 2000 maribor, slovenia srecko.glodez@um.si abstract. a computational simulation of low-cycle fatigue behaviour of lotus-type porous material, subjected to biaxial in-phase loading cycles is presented in this paper. fatigue properties of porous materials are less frequently published in the literature. this paper evaluates computational analyses, where different pore distribution and biaxial loading conditions in relation to the pore orientations is considered in each simulation. the fatigue analysis is performed by using a damage initiation and evolution law based on the inelastic strain energy. the computational results are subjected to the appropriate statistical analysis, because of different pore topology a different fatigue lives are obtained on the same loading level. results of computational simulations show also a qualitative understanding of porosity influence on low-cycle fatigue failures of lotus-type porous material under biaxial loading conditions. keywords. lotus-type porous material; low-cycle fatigue; damage; finite element analysis. introduction orous materials are relatively new class of materials, which offer potential for lightweight structures, energy absorption and other applications [1-3]. current manufacturing methods enable to create various porous materials, either open-celled or closed-celled porous structures with varying pore morphology. a new type of porous material with unidirectional cylindrical pores is lotus-type porous material, which is often used in lightweight structures, medicine, automotive engineering, sports equipment, etc. [4]. the porosity of lotus materials is usually lower than porosity of some conventional porous metals [5]. p j. kramberger et alii, frattura ed integrità strutturale, 37 (2016) 153-159; doi: 10.3221/igf-esis.37.21 154 when porous material is used for a structural component, the fatigue behavior should be taken into account. some investigations presented in [6-8] cannot be used to describe the fatigue behavior of lotus-type porous materials due to different pore shapes and orientations. the experimental research of the fatigue behavior of copper and magnesium lotustype porous structures presented by seki et al [9, 10] has shown that, for the fatigue loading parallel to the longitudinal axis of pores, the stress field in the matrix is homogeneous, and slip bands appear all over the specimen surface. this is not the case for transverse loading, where stress field is inhomogeneous, and slip bands are formed only around pores due to of high stress concentration in this region. some existing researches show that the most common method to determine structural properties of porous materials is the experimental investigation [11-14] determined mechanical property is usually only compressive yield strength or plateau strength while fatigue properties have less frequently been published in details, especially for lotus-type porous materials. this paper discusses the low-cycle fatigue (lcf) behavior of lotus-type porous material, and evaluates the fatigue damage initiation and propagation through computational simulations using the direct cyclic analysis procedure in the framework of abaqus/standard software [15]. it is shown that in displacement controlled regime, cracks are easily detectable via reaction forces. methodology omputational simulations allow us a better insight into analyzed structure behavior, and can provide information, which is sometimes very difficult or even impossible to determine with experimental measurements. the direct cyclic analysis procedure, implemented in abaqus/standard [15], is used in this work to compute the stabilized response of the structure directly, without having to compute a number of sequential cycles that would lead to such a stabilized cycle in the traditional approach. abaqus/standard offers a general capability for modelling the progressive damage and failure of ductile materials due to stress reversals and the accumulation of inelastic strain energy when the material is subjected to sub-critical cyclic loadings. damage initiation and evolution criteria are adopted to determine the low-cycle fatigue damage. these two criteria are based on the stabilized accumulated inelastic hysteresis strain energy per cycle, δw, as is illustrated in fig. 1. figure 1: inelastic hysteresis energy for the stabilized stress cycle material failures refer to the complete loss of load-carrying capacity which results from progressive degradation of the material stiffness. the stiffness degradation process is modelled using a damage mechanics theory, which takes into account the process of material degradation due to the initiation, growth and coalescence of micro-cracks/voids in a material element under applied fatigue loading. for low-cycle fatigue analysis, the direct cyclic procedure can be used to directly obtain the stabilized cyclic response of the model. the direct cyclic procedure combines a fourier series approximation with time integration of the nonlinear material behaviour in order to obtain the stabilized solution iteratively using the modified σ ε 3 2 1 1 2 δw δε = const c j. kramberger et alii, frattura ed integrità strutturale, 37 (2016) 153-159; doi: 10.3221/igf-esis.37.21 155 newton method. the number of fourier terms, the number of iterations and the incrementation during the cyclic time period can be controlled to improve the accuracy [15]. the damage initiation criterion is a phenomenological model for predicting the onset of damage due to stress reversals and the accumulation of inelastic strain in a low-cycle fatigue analysis. it is characterized by the accumulated inelastic hysteresis energy per cycle, δw, in a material point when the structure response is stabilized in the cycle. the number of stress cycles n0, corresponding to the damage initiation, is given by [15]:   20 1 cn c w (1) where c1 and c2 are material constants. the damage evolution law describes the rate of the material stiffness degradation per cycle once the corresponding damage initiation condition has been reached. for damage in ductile materials, abaqus/standard assumes that the degradation of the stiffness can be modelled using a scalar damage variable d where the stress tensor at any given loading cycle during the numerical analysis can be expressed as follows [15]:    1 d (2) where  is the effective (or undamaged) stress tensor that would exist in the material in the absence of damage computed in the current increment. once the damage criterion is satisfied at the material integration point, the damage state is calculated and updated based on the inelastic hysteresis energy for the stabilized cycle. the rate of damage per cycle is given by:  4 3δ cc wdd dn l (3) where c3 and c4 are material constants, and l is the characteristic length referred to the material point and based on the finite element geometry. it is assumed that material loses its load capacity when d = 1. when this condition is satisfied in a certain finite element, such an element can be removed from the mesh. in such a way, the damage (crack) propagation can be monitored in the proposed computational model. computational model general structure of lotus-type porous material is simplified in the computational model and represented by a square with random pore sizes and patterns, as is shown in fig. 2. the size of the model is 3.3 × 3.3 mm [16]. five computational models with different pore topologies and the same porosity, equal to 0.234, are generated and examined. the 2d numerical analysis is performed under plane strain loading conditions. all models are discretized with linear plane strain finite elements (cpe4r and cpe3 type of elements). the global size of finite elements 0.03 mm is chosen. the geometric structure, shown in fig. 2a, is used as a basis for fem analysis. fig. 2b shows the applied boundary conditions with bi-axial loading. the load is applied to the top and bottom edge under displacement rate control. the displacement load vary sinusoidal in-phase, in such a way that the global deformation corresponds to values, given by eq. (4) and (5):     0 siny t (4)         01 sinxy t (5) where ε0 is a global deformation in y-direction. selected maximum value of global deformation is ε0 = 0.1%. the load is applied in the low-cycle fatigue step with a time period of 1 second. in the numerical analyses, the linear kinematic hardening model with linearized monotonic stress-plastic strain behaviour presented in tab. 1 is used. furthermore, the young’s modulus e = 200 gpa and the poisson’s ratio ν = 0.33 is assumed. a j. kramberger et alii, frattura ed integrità strutturale, 37 (2016) 153-159; doi: 10.3221/igf-esis.37.21 156 figure 2: (a) computational model and (b) applied boundary conditions stress (mpa) plastic strain 400 0 800 24 table 1: linearized stress-plastic behavior of the base material [15] the mechanical properties considered in the damage analysis for the studied porous structure have been obtained from the literature [15]. it should be noted that the values of material parameters c1 and c3 in tab. 2 depend on the system of units in which the model is applied. c1       22 2 cycle n mmc c c2 c3         24 4 cmm cycle( n mm )c c c4 100 24 2.7∙10-5 1.27 table 2: material parameters for damage initiation and evolution [15] results and discussion ig. 3 shows the state of all five models at different states through the analysis. after one cycle, there is no damage in any of the models, while after 20 cycles some cracks occur between large adjacent pores. f j. kramberger et alii, frattura ed integrità strutturale, 37 (2016) 153-159; doi: 10.3221/igf-esis.37.21 157 model 1 model 2 model 3 model 4 model 5 n um b er o f cy cl es 1 20 40 60 80 100 150 200 figure 3: crack propagation in models with the same porosity and different topology. after 60 cycles, cracks between the pores and pores themselves form a larger coalesced crack, which is almost completely formed at 100 cycles. some miniscule crack growth occurs between 100 and 200 cycles, but due to drop of macro-rigidity, the crack growth rate stops near 200 cycles and although the calculation runs until 500 cycles, no further crack growth is detected. j. kramberger et alii, frattura ed integrità strutturale, 37 (2016) 153-159; doi: 10.3221/igf-esis.37.21 158 fig. 4 gives correlation between reaction forces in tension/compression (y-axis) and shear (x-axis). at the 1st cycle, the magnitude force in tension/compression direction is around 300 n and around 100 n in shear direction. in the first 100 cycles, reaction forces in both directions are dropping linearly, but near zero point, tension/compression component drops to zero, while the shear component remains near 30 n even after 500 cycles – long after crack growth has stopped. apparently, this is a consequence of local bend-like conditions around the pore, where relatively large pore radius prevents crack initiation. figure 4: reaction force shares for different pore morphologies as seen in fig. 3, the majority of crack growth occurs in first 100 load cycles, which is also evident from diagram in fig. 5, where dependence of the reaction force magnitude versus number of load cycles is plotted. there is also some drop between 100 and 200 cycles, but afterwards, reaction force magnitude remains constant. data even suggests that higher reaction forces at the initiation of damage result lower reaction forces after crack growth, but this fact needs a deeper investigation. figure 4: drop of reaction force magnitude between 1 and 100 cycles j. kramberger et alii, frattura ed integrità strutturale, 37 (2016) 153-159; doi: 10.3221/igf-esis.37.21 159 conclusions n this paper, the response of lotus-type porous material is investigated to biaxial loading that is applied with displacements rate control. it is shown that different pore morphology has some effect on multiaxial lcf-life, but only in form of statistical scatter band. it is shown that adjacent large pores are critical areas for crack formation and growth under given boundary conditions. furthermore, it is shown, that with increase of crack length reaction force magnitude decreases towards zero. the tension/compression reaction force drops almost to zero, but shear reaction force remains at 0.3% of the initial shear reaction force. possible explanation for this phenomenon are local bending-like conditions, which appear near large pores. large pore radii then serve as stress relaxation areas. presented numerical approach for low-cycle multiaxial fatigue failure study based on direct cyclic algorithm and inelastic strain energy is general and efficient. however, further research on modelling other general porous structures will be our tendency in this field. references [1] banhart, j., manufacture, characterisation and application of cellular metals and metal foams, progress in materials science, 46 (2001) 559-632, doi: 10.1016/s0079-6425(00)00002-5. [2] smith, b., szyniszewski, s., hajjar, j., schafer, b., arwade, s., steel foam for structures: a review of applications, manufacturing and material properties, journal of constructional steel research, 71 (2012) 1-10, doi: 10.1016/j.jcsr.2011.10.028. [3] lefebvre, l., banhart, j., dunand, d., porous metals and metallic foams: current status and recent developments, advanced engineering materials, 10 (2008) 775-787, doi: 10.1002/adem.200800241. [4] vesenjak, m., kovacic, a., tane, m., borovinsek, m., nakajima, h., ren, z., c ompressive properties of lotus-type porous iron, computational materials science, 65 (2012) 37-43, doi: 10.1016/j.commatsci.2012.07.004. [5] seki, h., tane, m., nakajima, h., fatigue crack initiation and propagation in lotus-type porous copper, materials transactions, 49 (2008) 144-150, doi: 10.2320/matertrans.mra2007623. [6] amsterdam, e., de hosson, j., onck, p., failure mechanisms of closed-cell aluminum foam under monotonic and cyclic loading, acta materialia, 54 (2006) 4465-4472, doi: 10.1016/j.actamat.2006.05.033. [7] olurin, o., mccullough, k., fleck, n., ashby, m., fatigue crack propagation in aluminium alloy foams, international journal of fatigue, 23 (2001) 375-382, doi: 10.1016/s0142-1123(01)00010-x. [8] zhou, j., gao, z., cuitino, a., soboyejo, w., effects of heat treatment on the compressive deformation behavior of open cell aluminum foams, materials science and engineering a-structural materials properties microstructure and processing, 386 (2004) 118-128, doi: 10.1016/j.msea.2004.07.042. [9] seki, h., tane, m., nakajima, h., effects of anisotropic pore structure and fiber texture on fatigue properties of lotustype porous magnesium, journal of materials research, 22 (2007) 3120-3129, doi: 10.1557/jmr.2007.0385. [10] seki, h., tane, m., otsuka, m., nakajima, h., effects of pore morphology on fatigue strength and fracture surface of lotus-type porous copper, journal of materials research, 22 (2007) 1331-1338, doi: 10.1557/jmr.2007.0164. [11] vesenjak, m., borovinšek, m., fiedler, t., higa, y., ren, z., structural characterisation of advanced pore morphology (apm) foam elements, materials letters, 110 (2013) 201-203, doi: 10.1016/j.matlet.2013.08.026. [12] vesenjak, m., ren, z., ochsner, a., dynamic behaviour of regular closed-cell porous metals – computational study, international journal of materials engineering innovation, 1 (2009) 175-196, doi: 10.1504/ijmatei.2009.029363. [13] ingraham, m., demaria, c., issen, k., morrison, d., low cycle fatigue of aluminum foam, materials science and engineering a-structural materials properties microstructure and processing, 504 (2009) 150-156, doi: 10.1016/j.msea.2008.10.045 [14] allison, p.g., hammi, y., jordon, j.b., horstemeyer, m.f., modelling and experimental study of fatigue of powder metal steel (fc-0205), powder metallurgy, 56 (2014) 388-396, doi: 10.1179/1743290113y.0000000063. [15] abaqus/cae user's manual (ver. 6.12), dassaults systemes inc, 2011. [16] kramberger, j., šraml, m., glodež, s., computational study of low-cycle fatigue behaviour of lotus-type porous material, international journal of fatigue, in press (2016), doi: 10.1016/j.ijfatigue.2016.02.037. i << /ascii85encodepages false /allowtransparency false /autopositionepsfiles true /autorotatepages /none /binding /left /calgrayprofile (dot gain 20%) /calrgbprofile (srgb iec61966-2.1) /calcmykprofile (u.s. web coated \050swop\051 v2) /srgbprofile (srgb iec61966-2.1) /cannotembedfontpolicy /error /compatibilitylevel 1.4 /compressobjects /tags /compresspages true /convertimagestoindexed true /passthroughjpegimages true /createjobticket false /defaultrenderingintent /default /detectblends true /detectcurves 0.0000 /colorconversionstrategy /cmyk /dothumbnails false /embedallfonts true /embedopentype false /parseiccprofilesincomments true /embedjoboptions true /dscreportinglevel 0 /emitdscwarnings false /endpage -1 /imagememory 1048576 /lockdistillerparams false /maxsubsetpct 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/hrv (za stvaranje adobe pdf dokumenata najpogodnijih za visokokvalitetni ispis prije tiskanja koristite ove postavke. stvoreni pdf dokumenti mogu se otvoriti acrobat i adobe reader 5.0 i kasnijim verzijama.) /hun 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can be opened with acrobat and adobe reader 5.0 and later.) >> /namespace [ (adobe) (common) (1.0) ] /othernamespaces [ << /asreaderspreads false /cropimagestoframes true /errorcontrol /warnandcontinue /flattenerignorespreadoverrides false /includeguidesgrids false /includenonprinting false /includeslug false /namespace [ (adobe) (indesign) (4.0) ] /omitplacedbitmaps false /omitplacedeps false /omitplacedpdf false /simulateoverprint /legacy >> << /addbleedmarks false /addcolorbars false /addcropmarks false /addpageinfo false /addregmarks false /convertcolors /converttocmyk /destinationprofilename () /destinationprofileselector /documentcmyk /downsample16bitimages true /flattenerpreset << /presetselector /mediumresolution >> /formelements false /generatestructure false /includebookmarks false /includehyperlinks false /includeinteractive false /includelayers false /includeprofiles false /multimediahandling /useobjectsettings /namespace [ (adobe) (creativesuite) (2.0) ] /pdfxoutputintentprofileselector /documentcmyk /preserveediting true /untaggedcmykhandling /leaveuntagged /untaggedrgbhandling /usedocumentprofile /usedocumentbleed false >> ] >> setdistillerparams << /hwresolution [2400 2400] /pagesize [612.000 792.000] >> setpagedevice microsoft word 2342 a. s. bouchikhi et al., frattura ed integrità strutturale, 48 (2019) 174-192; doi: 10.3221/igf-esis.48.20 174 finite element analysis of interactions between two cracks in fgm notched plate under mechanical loading aboubakar seddik bouchikhi, abdelkader lousdad, khalfi yassine, nasser eddine bouida, sadek gouasmi, abdelkader megueni department of mechanics, bp 89, cité ben m’hidi sidi bel abbes (22000), university of sidi bel abbès, sidi bel abbes, algeria bouida24@gmail.com, as_bouchikhi@univ-sba.dz abstract. the investigation of multiple crack interactions in fracture mechanics is important to predict the safety and reliability of structures. this paper introduces a 2d numerical investigation used to calculate the j-integral of the main crack behavior emanating from a semicircular notch and double semicircular notch and its interaction with another crack which may occur in various positions in titanium /titanium boride functionally graded material (tib/ti fgm) plate subjected to tensile mechanical load. young’s modulus of the functionally graded material plate varies along the specimen width (notch radius direction r-fgm) with exponential-law (e-fgm) function. further, the poisson’s ratio is taken as a constant in normal direction. for this purpose the variations of the material properties are applied at the integration points and at the nodes by implementing a subroutine usdfld in the abaqus software. the variation of the j-integral according to the position, the length, and the angle of rotation of cracks are examined; also the effect of different parameters for double notch fgm plate is investigated as well as the effect of band of fgm within the ceramic plate to reduce jintegral. according to the numerical analysis, all parameters above played an important role in determining the j-integral. keywords. functionally graded material (fgm); finite element method (fem); crack; j integral; mode i; interaction. citation: bouida, n., bouchikhi, a.s., lousdad, a., gouasmi, s., megueni, a., finite element analysis of interactions of between two cracks in fgm notched plate under mechanical loading, frattura ed integrità strutturale, 48 (2019) 174-192. received: 29.12.2018 accepted: 17.02.2019 published: 01.04.2019 copyright: © 2019 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. introduction he formations of cracks are strongly depending on the type of materials, loading, environmental aggression and design condition of mechanical components. in general, crack grows perpendicularly to the axis of loading. however under circumstances, a crack also propagates obliquely especially as a result of hydrogen induced cold crack after the metal welding. in this case, most cracks appeared not in a single crack but in the form of multiple cracks. tremendous amount of works can be found in analyzing the growth crack in open literature [1-3]. for examples matsumto et al. [1] evaluated the stress intensity factor of growth crack along two different materials using an interaction t http://www.gruppofrattura.it/va/48/2342.mp4 a. s. bouchikhi et al., frattura ed integrità strutturale, 48 (2019) 174-192; doi: 10.3221/igf-esis.48.20 175 energy release rate and boundary element method. in order to indicate the reliability of their method, some numerical models are used and compared. the present method capable to produce more accurate results with a coarse mesh than the method based on the displacement extrapolation which is based on the boundary element method. hammond and fawaz [2] reviewed stress intensity factors of various size single edge-cracked tension specimens. finite element method is used to calculate the stress intensity factors for wide ranges of crack and sample geometries. comparison is also performed between the existing and their results generally satisfactory correlation and large differences about 12.7% is observed for short cracks in small plate aspect ratio. ismail et al. [3] investigated stress intensity factors of double edge cracks in large groove plate under mode i tension. they used finite element method to determine the stress intensity factor via domain integral method. it is found numerically that the stress intensity factor (sifs) are strongly affected by the relative crack depth and the groove geometries. it is also found that the large groove is capable of reducing the sifs in comparison with the circular notched due to lower stress concentration factors. several works discussed on the multiple normal cracks can also be found in [4-8]. for examples yan and miao [4] studied the interaction of multiple cracks in a rectangular plate using boundary element method. they reported that the boundary element method is simple yet accurate for determining the stress intensity factors of multiple crack problems. while, yang and soh [5] developed finite element method using complex potential and the conformal mapping technique to study the multiple crack problems. it is found that the method developed useful for modelling the crack interactions between many cracks and defects. shu et al. [6] studied the problems of three cracks on both edges of finite width sheet under mode i loading. they modeled the multiple cracks using finite element method and due to symmetrical effect only half of model is developed. they found that when there are several cracks co-existed, the flexibility of the plate increased and the stress intensity factors at the crack tips decreased. ismail [7] studied the stress intensity factors of three parallel edge cracks under bending moments. cracks are modeled using finite element method and different relative crack length and spacing between cracks are used. it is found that due to the presence of multiple crack edge cracks, the stress distribution is relaxed and therefore, the stress intensity factors for all cracks decreased and when the distance between the cracks is increased, interaction is seemed to be diminished and it is can be neglected especially for shallow cracks. the behavior of offset crack under mixed mode loading can also be found in [8]. in term of slanted cracks, several works are found such as [9-11]. kuang and chen [9] used a displacement extrapolation method to investigate the mixed mode crack problems under mode i loading. there are two important parameters are used such as crack length and size of element at the crack tip. however, when the crack is only slanted at limited angle, it is hard to understand the role of angles on the stress intensity factors. albinmousa et al. [10] provided solution of stress intensity factors for mixed mode i-ii single edge notched tension specimen. wide range of crack geometries and inclined angles are used and stress intensity factors are determined based on such parameters. then, curve fitting is performed to simplify the stress intensity factors for prediction purposes. they found that their model can be used to predict the stress intensity factors very well. another study on the slanted crack can be found in [11-13]. however, this work focused on the 2d two dimensional cracks. the present study consists in investigating the 2d simulation used to calculate the j-integral of the main crack behavior emanating from a semicircular notch and double semicircular notch and its interaction with another crack which may occur in various positions in (tib/ti) fgm plate under mode i. the j-integral is determined for various load applied. the cracked plate is joined by bonding a fgm layer to tib plate on its double side. the determination of the gain on jintegral by using fgm layer is highlighted. the calculation of j integral of fgm’s involves the direction of the radius of the notch in order to reduce the j integral. the graded finite elements are implemented in the fe software abaqus 6.9 to verify the usdfld used subroutine given in appendix1. fracture analysis the interaction integral he interaction integral is derived from the path-independent j-integral [14] for two admissible states of a cracked elastic fgm. the standard j-integral is given by [14]:        1 ,10lim ( )ss j ij i jj w u n d (1) t a. s. bouchikhi et al., frattura ed integrità strutturale, 48 (2019) 174-192; doi: 10.3221/igf-esis.48.20 176 where w is the strain energy density, σij denotes the stress, ui denotes the displacements, and nj is the outward normal vector to the contour γ, as shown in fig. 1. figure 1: schematic of a cracked body and notation. j-integral when a crack grows at the constant displacement the energy release rate (serr) is determined by the following relationship [15]:   du g da (2) g, u and a respectively are the strain energy release rate, energy and area of the crack face. for the plane strain case the stress intensity factor (sif) is achieved eq. 3. [15]:    2 21 tip i ge k (3) in which, etip is young’s modulus at the crack tip. in the homogeneous materials, the serr is equal to the j-integral, which is obtained through equation [14]:       1 1 ( ) j ij u j wn ds x (4) where ds a is the area inside the contour. for 2d cracked plates г is a favorite path begins from the lowest edge and ends at the highest edge of the crack .w, uj, and nj are the serr, displacement component and the component of the unit vector normal to the г path respectively. neglecting the body forces, crack face tractions (crack surface assumed to be traction free) and thermal strains, the jintegral is path independent for homogeneous materials. for these materials, the serr, g, and the j-integral are similar. independent j-integral for the nonhomogeneous case, the serr in addition to strain is dependent on x (w(x) = w (ε(x), x)). for this reason, to obtain the contour independent j-integral, an extra term needs to be subtracted from the classical j-integral as follows [14]:        1 ,11 ( ) j ij a u j wn ds w qda x (5) where q is the weight function chosen such that it has a value of unity at the crack tip the strain energy density. in which, г is a favorite path begins from the lowest edge and ends at the highest edge of crack and a is the area surrounded by the contour. w,1 denotes partial differentiation of w with respect to the x variable. the j-integral gives null magnitude for a closed contour in the homogeneous and nonhomogeneous materials. a. s. bouchikhi et al., frattura ed integrità strutturale, 48 (2019) 174-192; doi: 10.3221/igf-esis.48.20 177 hence, in fracture problems, it is permanently independent of path as it was analytically proved by honein and herrmann [14]. ignoring the crack surface tractions and thermal stresses, the fem formulation of the independent contour integral j is constructed using the following discredited form as suggested by li et al. [16]:               ,1 1, ,1 11 1 ( ) det n k ij i i q pa p x j u w q w (6) where: wp is the weight function of the corresponding gaussian integration points and w,1 is partial differentiation of w with respect to x when the young's modulus e is an explicit function of x ( e = e(x) ). for the specified material property variation, analytically drive of the expression is simple. meanwhile, in the accolade, all of the quantities are considered at the integration points for any element with the opted contour. n is defined the number of integration points of element and q1 is a parameter, employed to simplify the calculation of a contour integral in the fem. in overall, a nodal value of 0 or 1 is given to q1, while q1 is defined by the following relation [16]:    4 1 11 i ii q n q (7) in which ni represents the interpolation functions. finite element analysis this section details the finite-element formulation of enriched crack tip elements for mode i fracture analyses of 2dimensional cracks in fgms. similar to many other studies in the literature, the form of material property gradient functions is selected to be exponential. for the fgm domain shown in fig. 1 containing an inclined embedded crack, the modulus of elasticity varies according to:  1( ) re x e e (8)   1 2 1 ( ) e ln h e (9) where β is a material constant and r is the coordinate by which the material property changes along the notch radius (rfgm) [17, 18]. h is the thickness of the plate and e is the young modulus, e1 is the young modulus at r=r, e1 and e2 young modulus for ceramic and metal respectively tab. 1. indicates the scale of length over variations of the properties for validation of the fe model. materials young’s modulus (gpa) poisson’s ratio ti e1=110 ʋ1=0.34 tib e2=375 ʋ2=0.14 table 1: material properties of ti and tib. as shown in fig 2, a cracked rectangular fgm plate (ti-tib) plate with a semicircular notch at side under uniform loading (σ0=100 mpa ) is numerically simulated in the abaqus commercial fem code version 6.9.126 [19]. the geometrical characteristics of the fgm plate are the width w=200 mm; the length h=2w=400 mm. to analyze the fracture behavior, a crack of length (c) is supposed to be initiated at the notch root with radius (r). meshing an unstructured triangular mesh is automatically generated by employing the advancing front method. the singular elements have to be constructed correctly to get a proper field of singularity around the crack tip as shown in fig. 3. the number of elements depends on the distributed nodes around the crack tip, which can be set by the user as shown in fig. 4. a. s. bouchikhi et al., frattura ed integrità strutturale, 48 (2019) 174-192; doi: 10.3221/igf-esis.48.20 178 figure 2: geometrical model of notched fgm plate. figure 3: the cut and patch procedure of generating singular elements around a crack tip. figure 4: a typical arrangement of the natural triangle quarter-point elements around a crack tip. in fact, the natural triangular quarter point elements are used [20] instead of the collapsed quadrilateral element, which is proposed by barsoum [21]. the success of the adaptively in general depends to a large extent on the efficient coupling between the error estimator, refinement scheme and automatic mesh generator. the importance of these adaptive techniques in practical applications has led to a considerable research on fully automatic mesh generators that require only the specification of the boundary and mesh size distribution over the domain. moreover, several comprehensive numerical tools have been developed to enhance the accuracy at the crack tip. in this work, the unstructured triangle mesh is automatically generated by employing the advancing front method. many researchers applied the fem with remeshing to study the fracture propagation and its j-integral analysis ([22]; and [23]), though it is not an easy task. in contrast, it is almost impossible to automatically remesh finite elements of an arbitrarily growing crack [24]. one of the advantages of the advancing front method is that the new triangle element formation is coinstantaneous with new node generation, and this advantage makes it possible to control the shape and size of the element through the adjustment of the location of the node [25]. however, a lot of intersection checking between the new generated triangular elements and the existing elements must be computed in order to ensure that the triangular elements are valid. accordingly, an observation was stated that the algorithm for the advancing front method has been shown to be robust in two-dimensional mesh generation of triangles and could be extended easily to generate quadrilaterals [26]. a. s. bouchikhi et al., frattura ed integrità strutturale, 48 (2019) 174-192; doi: 10.3221/igf-esis.48.20 179 figure 5: meshing model of fgm plate. (a) of the plate and (b) near the crack tip. adaptive refinement mesh in general, the smaller mesh size gives more accurate finite element approximate solution. however, reduction in the mesh size leads to greater computational effort. the adaptive mesh refinement is employed as the optimization scheme. this scheme bases on a posteriori error estimator which is obtained from the solution from the previous mesh. basically, the success of the adaptively in overall is depends to a large extent on the efficient coupling between the error estimator, refinement scheme and automatic mesh generator. the importance of these adaptive techniques in practical applications has led to a considerable research on fully automatic mesh generators that require only the specification of the boundary and mesh size distribution over the domain. convergence study the % error in j-integral obtained is plotted for various nodal discretizations in fig.6. notably, the fe method incorporates enrichment functions to model the crack-tip stress field [27]. the visibility and diffraction method involves modified weight functions around the crack tip. their details are given in [28]. this plot shows that the present method decreases the % error in j-integral with increasing nodal density. 50 100 150 200 250 300 -2,0 -1,8 -1,6 -1,4 -1,2 -1,0 -0,8 -0,6 -0,4 -0,2 0,0 j -i n te g ra l % e rr o r nodal density fe method figure 6: j-integral % error with nodal density. fig. 7 shows the convergence of j-integral using a coarser nodal discretization of 66297, and the present fe method with various refinements in the region around the crack tip. it is observed that even with the usage of very low refinement, the (a) (b) a. s. bouchikhi et al., frattura ed integrità strutturale, 48 (2019) 174-192; doi: 10.3221/igf-esis.48.20 180 j-integral % error becomes less than 2%. as the refinement increases, the error decreases and the result converges to the exact solution. this is advantageous especially for modeling the crack propagation through non-homogenous materials because this eliminates the need of enrichment functions. 1000 2000 3000 4000 5000 6000 7000 8000 -2,5 -2,0 -1,5 -1,0 -0,5 0,0 j -i n te g ra l % e rr o r reffinement fem-reffinement figure 7: % error in j-integral with refinement in the region around the crack tip, using the proposed method. results and discussions n this study the numerical calculation is based on fe using abaqus software. the direction of variation of the young's modulus of the fgm is according to r-fgm [17, 18]. effect of crack-crack interaction according to their position on j-integral in this section, we studied the influence of the interaction between two cracks ab et cd according to their position on the j-integral. figure 8: interaction between two cracks for different positions. five different geometric configurations between two cracks ab and cd are studied, their interaction effects are analyzed and compared. fig. 8 shows the details and designation of the geometrical shapes under consideration (a) two cracks (ab) and (cd) are parallel (it is perpendicular to the applied load), and the transversal interdistance l between is assumed variable of these two cracks. (b) two cracks (ab) and (cd) are parallel (it is perpendicular to the applied load), and the longitudinal interdistance d between is assumed variable of these two cracks. i a. s. bouchikhi et al., frattura ed integrità strutturale, 48 (2019) 174-192; doi: 10.3221/igf-esis.48.20 181 (c) two cracks (ab) and (cd) collinear (ported by the same horizontal line and perpendicular to the applied load) and the longitudinal interdistance d between is assumed variable of these two cracks. (d) horizontal crack (cd) at notch with fixed orientation and an inclined orientation crack (ab) is assumed variable. the orientation of the inter notch-cracks (ab) and (cd) varies; in this case the two cracks sizes are assumed invariable. case (1): the objective of this investigation is an analysis of the effect of the distance l separating two cracks ab and cd. the two cracks are considered constant in size and have the same length; the crack cd at notch is parallel to crack ab and located near it as shown in fig. 8.a. the fig.9 represents the variations of the j-integral at the crack tip d of the crack cd with respect to the distance l. it can be observed that the j-integral at crack tip becomes greater with the transversal distance. it has a maximum value at l=24 mm after which it stabilizer and the interaction effect of these cracks disappears completely. 0 4 8 12 16 20 24 28 32 3,0 3,2 3,4 3,6 3,8 4,0 4,2 4,4 4,6 4,8 5,0 j -i n te g ra l (j /m 2 ) l(mm) figure 9: variation of the j-integral at crack tip d versus distance l. the behavior is proved by results shown in fig.10 representing the variation of the j-integral at tips a and b of the crack ab. the j-integral becomes smaller at tip a when it gets away from the cd crack and stabilized for a distance l>24 mm after which the j-integral becomes independent for a distance l less than 24mm, the j-integral value has an exponential evolution with decreasing distance l. it is observed that the j-integral value at tip a is greater than at tip b. the effect of interaction vanishes when the distance between the cracks approaches 24mm at which j-integral values at tip a and b are similar. 0 4 8 12 16 20 24 28 0,0 0,2 0,4 0,6 0,8 1,0 1,2 1,4 1,6 1,8 2,0 2,2 jin te g ra l (j /m 2 ) l(mm) crack tip a crack tip b figure 10: variation of the j-integral at crack tip crack tip a and b versus distance l. a. s. bouchikhi et al., frattura ed integrità strutturale, 48 (2019) 174-192; doi: 10.3221/igf-esis.48.20 182 case (2): in the following part, the ab crack is moved transversally near the notch of the crack cd see in fig.8.b.this displacement has an effect on the j-integral as presented in fig.11. it is observed it value at tip d is maximum when the transversal distance d=8 mm and the minimum value when d=0 mm; when d>0mm or d<8mm the effect of interaction vanishes completely and the j-integral at tips of cd crack is stabilized and becomes independent. -16 -12 -8 -4 0 4 8 12 16 20 4,0 4,2 4,4 4,6 4,8 5,0 5,2 5,4 5,6 j -i n te g ra l (j /m 2 ) d(mm) figure 11: variation of the j-integral at crack tip d versus distance d. the effect of transversal distance is also investigated for ab crack tips. this is illustrated in fig 12. from this figure the maximum j-integral values at tips a and b are attained when d tends to 2 mm. the minimum is obtained for d=-12mm and d=16mm at which the effect of interaction vanishes. form fig.11 we can see that the j-integral is critical at d=2mm where the effect is significant. -16 -12 -8 -4 0 4 8 12 16 20 0,0 0,5 1,0 1,5 2,0 j in te g ra l (j /m 2 ) d(mm) crack tip a crack tip b figure 12: variation of the j-integral at crack tip a and b versus distance d. case (3): from the preceding studies treating the effect due the longitudinal displacement represented in fig.8.c, the obtained results represented in fig.13. the figure shows the j-integral variations with respect to the distance d between the crack tips. it is noticed the interaction effect is dependent on the distance d. when crack tip b approaches crack tip d. the j-integral at crack tip d increases exponentially. it is also observed a critical distance at d=16mm after which the j-integral is not stable. the interaction effect disappears completely. the effect of these cracks is determinant when they are closer to each other. a. s. bouchikhi et al., frattura ed integrità strutturale, 48 (2019) 174-192; doi: 10.3221/igf-esis.48.20 183 since crack tip b lies in the direction of propagation of the cd crack the j-integral value is grater at tip a than at tip b. for a distance d>12mm the values of j-integral at tip a and b are similar. 4 8 12 16 20 24 28 1 2 3 4 5 6 j -i n te g ra l (j /m 2 ) d(mm) crack tip d crack tip b crack tip a figure 13: variation of the j-integral at crack tip versus distance d. case (4): in the following subsection, the orientation of crack ab is varied near the crack notch cd as shown in fig.8.d the effect of the orientation of the crack ab on the j-integral at crack tip d is represented in fig.14. it can be observed the j-integral is maximum when the crack ab is parallel to the loading to a low stress and strain fields at it tips. regarding the effect of orientation of the ab crack on the j-integral variations at tips a and b, the results show that the maximum is observed for a parallel orientation i.e (angle θ=0° and angle θ=180°) with respect to the cd crack notch. for these positions, the ab crack is an opening mode and its tips are closer to the cd crack tip. the minimum of jintegral is reached for angle (θ = 90 °) orientation to the ab crack. in this position the load is parallel to the ab crack and its tips a and b are practically notch under stress and strain fields. figure 14: variation of the j integral at crack tip d versus angle θ. figure 15: variation of the j integral at crack tip a and b versus angle θ. case (5): in order to analyze their effects on the j-integral at the tip of notch cracks in fgm plate, let us consider the same structure, the orientation between the cracks at notch is varied. the length of notch cracks has same length (fig.8.e). the fig.16 represents the variation of the j-integral in mode i as a function of the variation of the inclination angle between the crack ab and cd at notch. a. s. bouchikhi et al., frattura ed integrità strutturale, 48 (2019) 174-192; doi: 10.3221/igf-esis.48.20 184 it is noted that the j-integral is the same for θ = 0 between to two cracks (when the two cracks is parallel to loading). as θ increases, the j-integral at crack tip a increases asymptotically and it decreases at crack tip d. at crack tip a the resistance to the crack propagation increases as θ increases and inversely this resistance increases at crack tip d (when the two cracks is perpendicular between them). 0 10 20 30 40 50 60 70 80 90 0,0 0,5 1,0 1,5 2,0 2,5 3,0 3,5 4,0 4,5 5,0 j -i n te g ra l (j /m 2 ) angle ° crack tip a crack tip d figure 16: variation of the j-integral at crack tip a and d versus angle θ. interaction between two cracks with the same orientation and different size crack (c/c0) on the j-integral for two-crack interactions, the j-integral of each crack is evaluated through varying the crack length ratio for the same angle inclination. first, the ratio of the 2nd crack length to the 1st crack length (c/c0) ranges from 0.2 to 1.5 (fig.8.e). figs. 17and .18 describes the evolution of j-integral in different ratios of crack lengths size (c/c0) emanating from notch at angle θ. it is the fact that the j-integral exhibit an asymptotic behavior as the crack length increases whatever the position of the crack in the fgm plate. it can be noted that the j-integral at crack tip a increases with the crack length. an opposite behavior is observed for the j-integral at crack tip d. when two-crack lengths are almost similar (e.g., c/c0 = 1.5), the magnitude of j-integral is similar. the result shows also, that the interaction vanishes with higher angle (θ = 80 °), at this point the value of j is maximum for crack a and inverse at angle (θ = 20 °) .the size ratio affects the value of j proportionally at crack a, and inversely at crack d. on the other hand, the difference in the j-integral becomes increasingly important with decreasing crack length and increasing in crack inclination. figure 17: variation of the j-integral at crack tip a versus c/c0 crack length ratio for different changing orientation θ. figure 18: variation of the j-integral at crack tip d versus c/c0 crack length ratio for different changing orientation θ. a. s. bouchikhi et al., frattura ed integrità strutturale, 48 (2019) 174-192; doi: 10.3221/igf-esis.48.20 185 thus, the maximum reduction of the j-integral is obtained when the cracks are parallel to the applied load direction. it can be said that the importance of j-integral reduction is strongly dependent on crack size. the larger the crack length, the relatively more important the reduction is. this is explained by the fact that the small cracks are requested in the stress field generated by the semicircular notch. the reduction in the j-integral influences directly the kinetics of the crack. effect of notch radius and material gradient β on j-integral the maximum stress is localized in the notch root which allows to characterize the notch by a j-integral that depends only of the notch geometry. fig. 19 presents the as a function of the normalized radius (r/w) ratio of the lateral semicircular notches. it can be observed also that the j-integral becomes larger by increasing the control radius. when the notches’ normalized radius lies between 0.1 and 0.3, the j-integral lies between 5 and 24 j/m2 for circular notches for semicircular notches. 0,10 0,15 0,20 0,25 0,30 5 10 15 20 25 j in te g ra l (j /m 2 ) r/w figure 19: variation of the j-integral versus normalized r/w ratio with (c/w=0.1, c0/w=0.1) the young’s modulus may vary exponentially through the fgm plate width. in this case, for example, the young’s modulus varies from 70 to 140 gpa. the poisson’s ratio assumed to be constant and equal to 0.3. the variation of the jintegral versus values of β is plotted in fig. 20. it should be noted again that β = 0 may represent the homogenous material. for high material gradient (the exponent β) the j-integral is negligible, it may be concluded that the material gradient (the exponent β) has larger effect on the j-integral (fig.20). 0 2 4 6 8 10 12 14 16 6,8 7,0 7,2 7,4 7,6 7,8 8,0 j i n e g ra le ( j /m 2 ) (m -1 ) figure 20: variation of j-integral versus material gradient β(c/w=0.1, c0/w=0.1). a. s. bouchikhi et al., frattura ed integrità strutturale, 48 (2019) 174-192; doi: 10.3221/igf-esis.48.20 186 behavior of a fixed and oblique cracks emanating from double notched fgm plate under tension effect of interaction of the orientation between two inter notch-cracks with equal lengths emanating from each semicircular notch root in double notched plate are studied in this part; in fig. 21, one considers the geometrical model of the fgm plate, to ensure the opening of cracks, we let the plate be under constant unidirectional loadings σ_0 at the farfield. the influence of the orientation of the second crack ab is highlighted while maintaining the angle of the first crack cd constant (crack cd is fixed, whereas the orientation of crack ab is changed.). figure 21: geometrical model of fgm plate with fixed and oblique crack at notches. the fig.22 illustrates the variation of the j-integral at crack tip b and d in mode i as a function of the variation of the inclination angle of the crack ab at semicircular notch root. one shows respectively the effect of the main crack ab rotation located at notch with the angle for various values between 60° and -60°. because of symmetry, the j-integral possesses the same curve for the positive and negative angles of inclination; this shows that it is independent of the sense of orientation of the existing crack ab. in the case of the negative angles, the j-integral takes positive values and the curve is asymmetric with regard to the y-axis. the results show also that the crack the rotation of the crack ab has relatively great effect on j-integral when the crack angle is relatively small. for this case that the crack inclined angle is smaller, the traction on the crack is larger and the stresses near the crack are larger. so the crack ab has greater effect on the crack cd in the case. fig. 22 shows that the effect of right cracks on crack tip d is illustrate in this case the j-integral for both crack tips are identical as (θ = 0) because of the symmetry. at this angle, the value of j-integral is maximum. the angle of crack tip b is inversely influenced at crack tip d. the j integral of crack tip d is minimum when θ increases. -60 -40 -20 0 20 40 60 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 j i n te g ra l (j /m 2 ) ngle crack tip d crack tip b figure 22: variation of j integral at crack tips versus angle inclination θ oblique crack at crack tip b and d. a. s. bouchikhi et al., frattura ed integrità strutturale, 48 (2019) 174-192; doi: 10.3221/igf-esis.48.20 187 behavior of two oblique cracks with same angle inclination emanating from double notched fgm plate under tension in this part the interaction of two cracks emanating from notches in a plate is investigated. as fig. 23 indicates, we present the geometrical model of the double notched plate in the presence of two cracks located at each notch emanating from the notch root. the plate considered is subjected to the same boundary conditions. fig. 23 (a) shows the fgm plate geometry, fig. 23 (a) shows the complete mesh configuration, fig. 23 (b) shows mesh detail of two cracks and fig. 23 (c) shows a zoom of the left crack tip region showing mesh. figure 23: fgm plate with two cracks emanating from notches:(a) geometry and complete finite element mesh; (b) mesh details of two crack tips; (c) zoom of the right crack tip for two-crack interactions, the j-integral of each crack is evaluated through varying the crack angle inclination which is the same of the two cracks for the same length ratio. the fig. 24 shows the variation of the j-integral as a function of the variation of the inclination angle of the two crack. the results are respectively obtained for seven positions of the two cracks emanating from the semicircular notch with which have the same angle rotation between (θ = -60°and 60° ). the angle is positive following the application of the principle of local symmetry. it is clear that the j-integral curves are symmetric with regard to the ligament of the plate. the curves take the importance when the angle θ decreases. one notices that function j-integral (θ) passes by a maximum corresponding to the angle θ = 0 of the two existing cracks (i.e. the preexisting cracks is perpendicularly oriented with respect the applied load). figure 24: variation of j-integral versus angle inclination θ of two cracks. new techniques to reduce the j-integral with fgm materials effect of fgms layers jointed on ceramic plate (tib) to reduce the j-integral he real structures are of complex geometrical forms containing numerous zones of stress concentrations. these sites are characterized by weak sections due to the presence of notches which are the main causes of cracks initiation. the knowledge of the distribution of the stress field in the neighborhood of a notch is of an extreme t a. s. bouchikhi et al., frattura ed integrità strutturale, 48 (2019) 174-192; doi: 10.3221/igf-esis.48.20 188 importance for the analysis of the variation of the j-integral. this section has been made to determine the performance of the (ti-tib) fgm materials to reduce the j-integral calculated for the crack tip emanating from the semicircular notch root in mode i, when the crack is propagated from the notch root. two-crack interactions in a double notched fgm plate are investigated with remote tension (𝜎0). the geometry of a notched plate with two cracks is shown in fig. 25. for two cracks of ab and cd, the lengths of two cracks are c and c0. in order to analyze the effect of a fgm layer jointed on ceramic plate (tib) for reducing the integral j on the repair of the cracks emanating from the notch subjected to unidirectional tensile load was studied (fig. 25.c), we consider the geometric model of a tib ceramic plate containing two fgm layers (r1-fgm, (ti-tib)) around a circular notch of radius r, the layer is of width w0 (w0 = r1-r) as shown in fig. (25.b). figure 25: geometric model of a ceramic plate (tib) jointed with two fgms layers at notches. for a better illustration of the beneficial effect of the fgm materials to reduce the j-integral, it is plotted in fig. 26 , the variation of the asymptotic j-integral according to the fgm layer w0 defined as w0=r1-r for a double notched jointed to tib plate for various load applied. 0,2 0,3 0,4 0,5 0,6 0 5 10 15 20 25 30 35 40 jin té gr al ( j/ m 2 ) w0/w  = 40 mpa  = 80 mpa  = 200 mpa  =300 mpa  = 400 mpa figure 26: variation of the j integral versus (w0/w) ratio. (c/w=c0/w=0.1, θ=45°). a. s. bouchikhi et al., frattura ed integrità strutturale, 48 (2019) 174-192; doi: 10.3221/igf-esis.48.20 189 on one hand, the j-integral is affected by the fgm layer jointed. the increase in the width leads to the increase in the jintegral. the j-integral is stabilized when fgm layer jointed width exceeds w0/w = 0.4. this effect is due to the fact that the increase in the size of the fgm layer jointed width involves an increase in the stress field at the crack tip, which leads to a saturation of the stresses transfer. this saturation involves a stabilization of the increase of the j integral according to the crack size, an optimization of the fgm layer width is recommended. on the other hand, the j-integral increases proportionally with the increment in the applied loads. the use of a fgm layer of size w0/w = 0.2 results in a significant decrease of the j-integral with a gain of (69%). the maximum of j is almost at the level of w0/w = 0.4 with gain of (52%). effect of the radius of notched fgm layer for reduce j-integral the influence of the geometry plate is very important, in order to determine the effect of the notch radius on the performance of the bonded tib plate repair by fgm layer jointed in mode i, the orientation of notched crack is θ =45° for fgm layer width of w0/w =0.125 maintained constant. fig. 27 presents the variation of the j-integral as a function of the notch radii for various subject loads. from it is noted that the j-integral increased such that the important factor (r/w) in fgms layers w0/w =0.125, the difference of the jintegral becomes larger and more important with the increase of the notch radius and important load. 0,10 0,15 0,20 0,25 0,30 0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36  = 40 mpa  = 80 mpa  = 200 mpa  = 300 mpa j -i n te g ra l (j /m 2 ) r/w figure 27: variation of the j-integral versus r/w (w0/w=0.125, c/w=c0/w=0.1, θ=45°) conclusion he primary goal of a designer is to predict whether a crack in a component is likely to grow under the given loading conditions. he can either obtain the critical j-integral at crack tip to determine it. the objective of this work is to describe the effect of interaction between two cracks in notched and double-notched (tib/ti) fgm plate. the plate is numerically simulated using the finite element method (fem). the obtained results allow us to deduce the following conclusions:  the transversal (l) and longitudinal (d) displacement and the angle of orientation (θ) characterizing the interaction effect between two cracks plays an important role on the level and distribution of j-integral.  for the transversal displacement (l) and longitudinal (d); the j-integral increases dramatically and reaches its maximum value. for a far displacement, the interaction effect disappears completely; it results in a stabilization of the j-integral at a constant value.  the effect of between two cracks interaction depends not only on their interdistance but also the orientation angle of between these two cracks. the j integral reaches its maximum when the crack is directly parallel to the t a. s. bouchikhi et al., frattura ed integrità strutturale, 48 (2019) 174-192; doi: 10.3221/igf-esis.48.20 190 load. this orientation leads to the crack opening. a perpendicular orientation causes the closing of the crack leading to negligible j-integral.  a normal crack to load leads to a highest j-integral at the crack tip. this energy decreases gradually as the orientation angle decreases.  the j-integral at the crack tip depend both on the crack length and its position,  the increase of the crack length causes an increase in the j-integral. the crack propagation leads to an increase of fracture energy.  in case of two cracks emanating from notch in a fgm plate under tension, the interaction and their effect on the j-integral is important when value of θ is maximum  effect of the orientation with different crack sizes is remarkable ; the maximum of j-integral is obtained when the angle increases corresponding obtained when the crack is parallel to loading and higher size, and the minimum value is obtained for the crack perpendicular to loading.  for the case of two cracks emanating from double notched fgm plate under tension, the j integral for both crack tips are identical as (θ = 0) due to symmetry. at this angle, the j-integral value is maximum. the angle of crack b is inversely influenced at crack a. the j integral of crack a is minimum when θ increases.  the effect of the loading and the notch radius ratio (σ0, r/w) on the j-integral was highlighted; the interaction grows for high value of the loading and notch radius.  the good choice of the fgms layers at the notches in ceramic plate (tib) and notch radius must be optimized; because it is the best means for decreasing the j-integral considerably and improves the fracture strength.  the decrease of the j-integral becomes more and more important with the importance of the semicircular fgm layer radius around the notch. the use of a fgm layer of size w0/w = 0.2 results in a significant decrease of the j integral with a gain of (69%). the maximum of j is almost at the level of w0/w = 0.4 with gain of (52%). these results are helpful to analyze the fracture or fatigue behaviors of the materials. references [1] matsumto, t.,tanaka, m. and obara, r. (2000). computation of stress intensity factors of interface cracks based on interaction energy release rates and bem sensitivity analysis, eng. fract. mech., 65(6), pp. 683–702. doi: 10.1016/s0013-7944(00)00005-9. [2] hammond, m., and fawaz, s. (2016). stress intensity factors of various size single edge-cracked tension specimens: a review and new solutions, eng. fract. mech. 153, pp. 25-34. doi: 10.1016/j.engfracmech.2015.12.022. [3] ismail, a.e., azlan, ma. , mohd tobi, al. , ahmad, mh. (2016). mode i stress intensity factors of slanted cracks in plates iop conf. series: mat. sci. and eng. 152, pp. 012-049. [4] yan, x., miao. c. (2012). interaction of multiple cracks in a rectangular plate. appl. math. mod. 36, pp. 5727-5740. doi: 10.1016/j.apm.2011.12.060. [5] yang, c.h. and soh, a.k. (2002), modeling of voids/cracks and their interactions. theo. and appl. frac. mech., 38, pp.81–101. doi: 10.1016/s0167-8442(02)00083-6. [6] shu, h. m. petit, j. jiang, z. d. and bezine, g. (1993). stress intensity factors and interaction of three cracks on both edges of finite width sheet, eng. frac. mech., 45(3), pp. 407–414. doi: 10.1016/0013-7944(93)90026-o. [7] ismail, a.e. (2013). stress intensity factors of three parallel edge cracks under bending moments. iop conf. series: mat. sci. and eng. 50, pp. 12-20. [8] ismail, a.e. ariffin, a. abdullah, k .ghazali , m.j. (2013). stress intensity factors under mode iii loadings. inter. rev. of mech. eng. 7(3) , pp. 578-582. [9] chen, l. s. kuang, j. h. (1992). a displacement extrapolation method for determining the stress intensity factors along flaw border, inter. jour. of frac., 57 (4), pp. r51-r58. doi: 10.1007/bf00013064. [10] albinmousa, j. merah , n. and khan, sma. (2011). a model for calculating geometrical factors for a mixed-mode iii single edge notched tension specimen .eng. frac. mech. 78, pp. 3300-3307. doi: 10.1016/j.engfracmech.2011.09.005. [11] ismail, a.e. (2013). development of j-integral prediction model for surface cracks in rounds bars under combined loadings. appl. mech. and mat. 315, pp. 665-669. doi: 10.4028/www.scientific.net/amm.315.665. a. s. bouchikhi et al., frattura ed integrità strutturale, 48 (2019) 174-192; doi: 10.3221/igf-esis.48.20 191 [12] murakami, y. (1987). stress intensity factors handbook volume 1, pergamon press. stress intensity factors handbook. (1990) vol.1, ed y. murakami, pergamon press. murakami, y. (1986) two semi-infinite solids bonded by a bond of arbitrary shape subjected to tensile load. in: stress intensity factor handbook. japan: soc. of mat. sci. doi: 10.1115/1.2900983. [13] ismail, a.e. ariffin , a.k. abdullah, s. ghazali. m.j (2014). j-integral evaluation of surface cracks in round bar under mode iii loadings. research journal of applied sciences, engineering and technology 7 (10) 1985-1993. doi:10.19026/rjaset.7.490. [14] honein, t. and herrmann, g., (1997). conservation laws in nonhomogeneous plane elastostatics, journal of the mech. and phy. of sol., 45( 5), pp. 789805. doi: 10.1016/s0022-5096(96)00087-7. [15] jin, z. h. and batra, r., (1996).some basic fracture mechanics concepts in functionally graded materials, journal of the mechanics and physics of solids, 44(8), pp. 1221-1235. [16] li, f. z., shih, c. f. and needleman, a., (1985). a comparison of methods for calculating energy release rates, engineering fracture mechanics, 21( 2), pp. 405-421. doi: 10.1016/0013-7944(85)90029-3. [17] ismail, a.e, mohd tobi, al. and mohd nor, n.h. (2015) stress intensity factors of slanted cracks in round bars subjected to mode i tension loading aip conference proceedings 1660 070027. [18] bouida, n. bouchikhi, a.s. megueni, a. and gouasmi, s. (2018). a finite element analysis for evaluation of jintegral in plates made of functionally graded materials with a semicircular notch. j fail. anal. and preven. 18, pp. 15-33. doi: 10.1007/s11668-018-0558-6. [19] abaqus finite element program. (2008) abaqus/standard 6.9.1. hibbit, karlsson and sorensen, inc. pawtuket, usa. [20] freese, c.e., tracey, d.m . (1976). the natural triangle versus collapsed quadrilateral for elastic crack analysis. int. j. of fract. 12, pp. 767-770. doi: 10.1007/bf00037924. [21] barsoum, r. s. (1976).on the use of isoparametric finite elements in linear fracture mechanics. int. j. for num. meth. in eng., 10, pp. 25-37. doi: 10.1002/nme.1620100103 [22] xie, m., gerstle, w.h., rahulkumar, p. (1995). energy-based automatic mixed-mode crack-propagation modeling. j. of eng. mech. asce. 121, pp. 914–923. doi: 10.1061/(asce)0733-9399(1995)121:8(914). [23] bittencourt, t. wawrzynek, p.a., ingraffea, a.r., sousa, j.l. (1996). quasi-automatic simulation of crack propagation for 2d lefm problems, eng. fract. mech., 55, pp. 321–334. [24] chiou, y.j., lee, y.m., jowtsay, r. (2002). mixed mode fracture propagation by manifold method. int. j. of fract. 114, pp. 327–347. [25] guan, z.q., song, c., gu, y.x. (2003). recent advances of research on finite element mesh generation methods. j. of comp. aided design and comp. graph. 15 (1), pp. 1–14. doi: 10.1023/a:1015713428989 [26] zienkiewicz, o., taylor, r., zhu, j. elsevier ed.(2005).the finite element method: its basis and fundamentals. sixth publisher. [27] muthu, n. maiti, s.k. falzon, b.g. guiamatsia, i. (2013). a comparison of stress intensity 28 factors through crack closure integral and other approaches using extended element-free galerkin method. computational mechanics, 52, pp. 587-605. doi: 10.1007/s00466-013-0834-y. [28] muthu, n. maiti, s.k. falzon, b.g. khoddam, s. (2014). modified crack closure integral for extraction of sifs in meshfree methods. finite element in analysis and design, 78, pp. 25-39. doi: 10.1016/j.finel.2013.09.005. appendix user subroutine usdfld for fgms **user subroutine subroutine usdfld(field,statev,pnewdt,direct,t,celent, 1 time,dtime,cmname,orname,nfield,nstatv,noel,npt,layer, 2 kspt,kstep,kinc,ndi,nshr,coord,jmac,jmatyp,matlayo,laccfla) c include 'aba_param.inc' c character*80 cmname,orname character*3 flgray(15) dimension field(nfield),statev(nstatv),direct(3,3), 1 t(3,3),time(2) dimension array(15),jarray(15),jmac(*),jmatyp(*),coord(*) c dimension intv(1),realv(1) a. s. bouchikhi et al., frattura ed integrità strutturale, 48 (2019) 174-192; doi: 10.3221/igf-esis.48.20 192 x=coord(1) y=coord(2) z=coord(3) l=20*(2**0.5) r=((((x)**2)+((y)**2))**0.5) field(1)=exp((1.22/l)*(r-3)) return end << /ascii85encodepages false /allowtransparency false /autopositionepsfiles true /autorotatepages /none /binding /left /calgrayprofile 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/pdfxoutputintentprofileselector /documentcmyk /preserveediting true /untaggedcmykhandling /leaveuntagged /untaggedrgbhandling /usedocumentprofile /usedocumentbleed false >> ] >> setdistillerparams << /hwresolution [2400 2400] /pagesize [612.000 792.000] >> setpagedevice microsoft word numero_57_art_04_3053 t. salem et alii, frattura ed integrità strutturale, 57 (2021) 40-49; doi: 10.3221/igf-esis.57.04 40 analysis of above-ground steel storage tanks resting over piles or stone columns tarek salem, hassan maaly, ahmed abdelbaset zagazig university, department of structural engineering, egypt. nageeb2@yahoo.com, dr_h_maaly@yahoo.com, ahmed_mohammed_1281@yahoo.com abstract. static and dynamic behavior of above-ground steel storage oil tanks resting on end bearing piles or stone columns are studied and analyzed using adina (2019) program. the studied soil profile is an upper soft clay soil layer, followed by an extended dense sand layer. the main purpose of this research is to explore to what extent stone columns can be used as an effective alternative to concrete piles under steel storage tanks. therefore, many three-dimensional numerical models are conducted to analyze and study the performance of such tanks in both static and dynamic cases. ten of the studied cases are steel tanks resting over stone columns with different numbers and properties. on other hand, one model studied the behavior of steel tank resting on large diameter concrete piles. results indicate that stone columns can be used instead of end bearing piles as long as the computed settlements are safe. in addition, stone columns are behaving better than concrete piles in decreasing of hoop stress in tank shell. it is also noticed that stone columns with high elastic modulus are effective in reducing the sloshing height of the oil surface during earthquakes. keywords. steel tanks; stone column; piles; soft clay; adina. citation: salem, t., maaly, h., abdelbaset, a., analysis of above-ground steel storage tanks resting over piles or stone columns, frattura ed integrità strutturale, xx (2021) 4049. received: 30.03.2021 accepted: 11.05.2021 published: 01.07.2021 copyright: © 2021 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. introduction oastal areas in many countries suffer from soft clay soils which cause a lot of problems to structures. in egypt, many regions are covered with surface layers of soft clay such as zones in alexandria, port said, damietta and eastern sinai. two problems are associated with soft clays; high compressibility and low shear strength so that constructions over these soils cause problems to structures. steel storage tanks resting on soft clay soil is a challenge for engineers because of their relatively higher loads, sensitivity for total and differential settlements, and containing high risk fluids. there are a lot of techniques which can be used to improve and reinforce soft clay soil. concrete piled-raft foundations are the most popular solution for this situation because of their capacity in transmitting high loads. end bearing concrete piles carry the tank surface loads to the competent bearing soil layer. however, friction piles may be used for relatively light weight structures, where there is no hard layer to reach where the piles resist loads by their skin friction with the surrounding soil with slight end bearing values. although concrete piled-raft foundations are mostly used to support steel storage tanks under both static and dynamic cases, there is another economic alternative which is granular columns. stone (granular) columns are one of the effective c https://youtu.be/2qugnpv-mx0 t. salem et alii, frattura ed integrità strutturale, 57 (2021) 40-49; doi: 10.3221/igf-esis.57.04 41 ground improvement techniques used to enhance saturated soft clay properties because of their relatively high capacity. in addition, their high permeability leads the columns to act as vertical drains to accelerate consolidation process of soft clay soil around stone columns [1]. stone column is constructed by boring the ground and pouring gravel or stones into the pit to enhance the surrounding soft soil. therefore, stone columns carry the largest part of load than surrounding weak soil because of their higher elastic modulus and stiffness [1, 2, 3, 4, 5]. the behavior of steel storage tanks under static and dynamic loads is concerned by researchers because of damage which occur in both static and dynamic stages. many tanks contained hazardous materials which may spill from tanks under dynamic excitations which lead to catastrophes. other tanks contained petroleum materials which may cause fires and explosion and lead to kill a lot of people and plants and also affect human health. for example, niigata and alaska earthquakes in 1964 caused spillage of toxic and led to destructive fires. there were many types of failure were detected in steel storage tanks during past earthquakes like imperial valley (1979) and northridge (1994). the main three types of failure of steel storage tanks were anchorage system failure, buckling in tank shell and foundation failure [6]. many studies concentrated on the failure of tank itself such as anchorage failure, settlement and shell buckling however there is another essential problem occurs during earthquake. this problem is the sloshing or leakage of hazardous materials from the tank which may causes fires and environmental damage. therefore, studies should introduce procedures to design steel storage tanks not only for strength condition but also for serviceability condition to prevent buckling, sloshing and uplift [7]. this study is an initial survey of the issue and focused on the nonlinear dynamic behavior of cylindrical above-ground steel oil tanks resting on piled-raft foundation (prf) or stone columns foundation (scf). comparison between prf and scf are conducted in both static and dynamic analyses to explore the extent that scf can be an effective alternative to prf. nonlinear time-history analysis using adina software are conducted to investigate the purpose of this research. results of settlements; hydrostatic pressure, dynamic settlement, sloshing and hoop stresses are presented. numerical modeling n this section, three dimensional tank and soil models are established using nonlinear fem analysis (adina software, 2019) to study the behavior of steel liquid storage tanks resting on piled-raft and stone column foundations. soft clay soil is represented by cam-clay nonlinear soil model and the extended sand layer and stone columns are represented by mohr-coulomb soil model. soil properties used in the analysis are presented in tab. 1. tank shell and its base are modeled as elastic isotropic material with properties of astm a516 steel grade 70. the shell required thickness is designed by variable-design-point method and the 1-foot method as presented by api-650 (2014). in addition, elastic isotropic material model is used again to model the raft and piles with properties of reinforced concrete material. tank content (oil) is modeled by 3-d fluid linear potential based element with free surface, with capability to consider fluidstructure interaction and applied acceleration. the specific gravity of the liquid (oil) included in the tank is supposed to be 0.9. properties of concrete and steel used in this paper are presented in tab. 2. soil properties soft clay soil sand soil poisson’s ratio (ν) 0.48 0.35 elastic modulus (e), mpa 2.00 50.0 unit weight, kn/m³ 16.00 19.0 lambda (λ) 0.25 table 1: properties of soft clay and extended sand layers the studied tanks are selected to have a typical diameter, d = 16.0 m and height, h = 10.0 m with an aspect ratio (h/d, height to diameter of the tank) equal to 0.625. tank diameter and height are chosen due to its commonness in the petroleum fields. raft thickness is considered to be 1.20 m resting on circular concrete piles or stone columns. each pile or stone column has diameter of 1.20 m and length of 16.0 m. tanks are open-top with no attached roof. thickness of the tank shell and base plate is considered to be 8.0 and 6.0 mm, according to api standards, respectively. fig. 1 shows the finite element model used in the studied cases. i t. salem et alii, frattura ed integrità strutturale, 57 (2021) 40-49; doi: 10.3221/igf-esis.57.04 42 material properties concrete steel poissonʼs ratio (ν) 0.20 0.30 elastic modulus (e), mpa 20,000 200,000 unit weight, kn/m³ 25.00 78.00 table 2: properties of concrete and steel used in this research figure 1: 3-d finite element model for above-ground open top oil storage tank. steps of finite element analysis static and nonlinear dynamic time-history analyses are employed in order to study the behavior of the tanks. static analysis: this stage included defining materials and tank model, soil, foundation, liquid, and boundary conditions. hydrostatic pressure and static hoop stresses could be obtained after this stage. time-history analysis: the seismic analysis is performed using loma prieta (1989) earthquake record in terms of horizontal component acting at the lower boundary of the soil domain. acceleration-time history of the earthquake record for loma prieta earthquake is presented in fig. 2. figure 2: acceleration-time history of the loma prieta earthquake, (1989) comparison between prf and scf n this section, the behavior of steel storage above-ground tanks founded on either prf or scf are studied and analyzed to investigate the extent of stone columns effectiveness as an alternative to supporting the tanks constructed over soft clay soil. tab. 3 presents the cases studied in this research. the elastic modulus of stone columns can be controlled (either increased or decreased) by controlling the compaction effort and energy utilized in i t. salem et alii, frattura ed integrità strutturale, 57 (2021) 40-49; doi: 10.3221/igf-esis.57.04 43 compacting the stone columns. in addition, the materials of stone columns (sand, gravel or crushed stone) can also control the elastic modulus values. case material of piles or stone columns elastic modulus, e (mpa) number of piles or stone columns unit weight, γ (kn/m³) angle of friction (φ) 1 concrete, prf 20,000 13 25.00 2 stone, scf2-13 50 13 19.00 36 3 stone, scf3-13 75 13 19.50 38 4 stone, scf4-13 100 13 20.00 40 5 stone, scf5-13 125 13 20.50 42 6 stone, scf6-13 150 13 21.00 44 7 stone, scf7-19 50 19 19.00 36 8 stone, scf8-19 75 19 19.50 38 9 stone, scf9-19 100 19 20.00 40 10 stone, scf10-19 125 19 20.50 42 11 stone, scf11-19 150 19 21.00 44 table 3: properties of stone columns and piles used in this research. static settlement settlement due to static loads (weight of raft, tank and fluid) is very important factor in designing tanks or any building resting on weak soils because of local codes total and differential settlement limits. for example, egyptian code recommended a raft total settlement not exceeding 15 cm for buildings and tanks constructed in clay soil. the authors own opinion is that more strict total settlement limits should be applied for such strategic structures. therefore, studying the settlement of steel storage tanks resting on soft clay soil is one of the main targets because the settlement controls the static design procedures in most cases. in this study, the calculated settlements of tanks due to static loads for all studied cases are presented in fig. 3. it is noticed that end bearing concrete piles are the most effective method in reducing static settlements of tanks with a total settlement value of 1.76 cm. on the other hand, minimal number of stone columns (13 stone columns) having the lowest elastic modulus resulted in the maximum computed settlement in all cases with 12.80 cm. results also indicated that 19 stone columns with relatively high elastic modulus, e.g., (e) = 150 mpa are the best effective alternative to concrete piles with total settlement value of 7.30 cm. thus, whenever increasing the number and the elastic modulus of stone columns, static settlement values consequently decrease. in all the studied cases, the computed settlement values do not exceed the allowable upper limit value. hydrostatic pressure color contour shading of the hydrostatic pressure for case (3) is presented in fig. 4. results indicated that the maximum stresses occurred near the tank bottom. results of the stone columns cases seem to have consistent small increase in the hydrostatic pressure where the maximum difference between stone columns cases and concrete piles case is not exceeding 1%, as shown in fig. 5. therefore, using of stone columns with different number and elastic modulus instead of concrete piles do not cause a significant effect on hydrostatic pressure values, but rather tend to reduce the computed hydrostatic pressure values. t. salem et alii, frattura ed integrità strutturale, 57 (2021) 40-49; doi: 10.3221/igf-esis.57.04 44 figure 3: comparison of static settlements for all the studied cases. figure 4: color contour shading of hydrostatic pressure for case (3). settlement during the dynamic event as stated earlier, settlement is a major factor that controls the behavior of all structures in both static and dynamic stages. in this section, maximum settlement of tanks due to earthquake loads are studied and analyzed. fig. 6 shows the settlement-time history due to dynamic excitation for case 1 (concrete piles) and case 10. results indicate that end bearing concrete piles resist the settlement due to earthquake excitations better than stone columns models. for concrete piles (case 1), the dynamic settlements oscillate around zero with a maximum value of settlement equals to 1.35 cm at 28.6 sec. however, for stone column case scf10-19, the dynamic settlements oscillate around -1.00 cm and the maximum settlement value is equal to 3.38 cm at 38.5 sec for (case 10). moreover, for stone columns also, small value of permanent settlement is noticed after the dynamic event calms down. it is also found that decreasing the number of stone columns t. salem et alii, frattura ed integrità strutturale, 57 (2021) 40-49; doi: 10.3221/igf-esis.57.04 45 resulted in decreasing the dynamic settlement as shown in fig. 7. however concrete piles are better than stone columns in reducing dynamic settlement, but the values of dynamic settlement of stone columns models are still within reason. figure 5: comparison of hydrostatic pressures for the studied cases. figure 6: variation of dynamic settlements with time during the dynamic event for cases (1) and (10) hoop stresses in tank shell elephant-foot buckling is defined as outward bulge above the tank base. it always occurs at the lower third of the tank shell at the location of maximum hoop stresses. therefore, studying of hoop stresses generated in tank shell is very important to make sure that shell buckling is under control. it is noticed that stone columns are effective than concrete piles in reducing maximum hoop stresses in the tank shell, as shown in fig. 8. the figure shows that the maximum hoop stresses decreased from 92.5 to 88.0 mpa, by about 5%, when concrete piles (case 1) are replaced by 13 stone columns with elastic modulus = 150 mpa (case 6). therefore, stone columns are effective than concrete piles in this regard because of their low elastic modulus when compared with concrete piles. slightly higher settlements under the tank center tend to reduce such stresses. it is also noticed that the maximum hoop stresses for all cases are found at about 1.0 m above the tank base. fig. 9 presents the variation of hoop stresses with time during the dynamic excitation for case 1 (concrete piles) and case 8. for concrete piles (case 1), the hoop stress oscillates around 80.9 mpa and the maximum value of hoop stress reach 92.5 mpa at 39.4 sec. however the hoop stress oscillates around 80.3 mpa and the maximum t. salem et alii, frattura ed integrità strutturale, 57 (2021) 40-49; doi: 10.3221/igf-esis.57.04 46 value of settlement touches 89.18 mpa at 16.3 sec for (case 8). in general, lower stone column modulus resulted in relatively lower hoop stresses within the tank shell, as previously noted in the static analysis. figure 7: comparison of dynamic settlements for the studied cases. figure 8: comparison of hoop stresses values between all the studied cases. t. salem et alii, frattura ed integrità strutturale, 57 (2021) 40-49; doi: 10.3221/igf-esis.57.04 47 figure 9: variation of total hoop stresses in the tank shell with time during the dynamic event for cases (1) and (8). sloshing sloshing of liquid surface out of tank causes an enormous trouble such as fires and explosion because most ground tanks are used in storing chemical or hazardous materials. therefore this research focuses on studying sloshing of fluids contained in tanks. it is noticed that sloshing height value decreased from 44.8 to 27.0 cm (by about 40%) when concrete piles case (case 1) is replaced by 19 stone columns with e = 150 mpa (case 11), as shown in fig. 10. therefore, stone columns, especially with high elastic modulus, are better than concrete piles in reducing sloshing height values during earthquakes, and tend to dampen and soothe earthquake excitation. fig. 11 presents variation of sloshing height with time due to dynamic excitation for case 1 (concrete piles) and case 11, which is 19 stone columns having the highest modulus. it is not just the maximum sloshing value, but the amplitude of variation of sloshing height along the whole earthquake excitation period in case of piles is clearly higher than those computed in the stone column case. figure 10: comparison between sloshing heights for all the studied cases t. salem et alii, frattura ed integrità strutturale, 57 (2021) 40-49; doi: 10.3221/igf-esis.57.04 48 figure 11: variation of fluid sloshing height with time during the dynamic event for cases (1) and (11) conclusions ased on the results of the current research, the following conclusions are drawn: 1. using stone columns instead of reinforced concrete piles under above-ground steel tanks proves to be a good economic alternative. 2. using reinforced concrete columns as tank foundations is more effective in reducing the static and dynamic settlements under such tanks. however, stone columns are behaving better than concrete piles regarding hoop stresses within the tank shell during static analysis and sloshing during the dynamic analysis for their ability to dampen (absorb) the earthquake excitation. 3. calculated static settlements for concrete piles are equal to 1.76 cm for 13 concrete piles supporting the tank. however, this value becomes equal to 7.30 cm when using 19 stone columns, with relatively high modulus. in all cases, the static settlement values are safe and within the code limits. 4. the maximum settlement occurred during earthquake increases from 1.35 cm to 3.5 cm and 2.75 cm when the concrete piles replaced by cases (2) and (6) stone columns, with about 1.0 cm permanent settlement for the stone column cases. 5. using high elastic modulus stone columns instead of concrete piles has a significant effect in decreasing the sloshing height of liquid surface during the dynamic analysis. sloshing height decreases by 40% when concrete piles are replaced by stone columns of larger number (from 13 rc to 19 sc), with e = 150 mpa. 6. replacement of thirteen concrete piles by thirteen or nineteen stone columns caused a reduction in hoop stresses by small values of about 5%. however, this change is only about 1% when calculating the hydrostatic pressure within the tank shell. references [1] dash, s.k. and bora, m.c. (2013). improved performance of soft clay foundations using stone columns and geocellsand mattress, geotextiles and geomembranes, 41, pp. 26-35. [2] hugher, j.m.o. and withers, n.j. (1974). reinforcing of soft cohesive soils with stone columns, ground engineering, 7(3). [3] juran, i. and guermazi, a. (1988). settlement response of soft soils reinforced by compacted sand columns, journal of geotechnical engineering, 114(8), pp. 930-943. [4] wood, d., hu, w. and nash, d.f. (2000). group effects in stone column foundations: model tests, geotechnique, 50(6), pp. 689-698. [5] mckelvey, d., sivakumar, v., bell, a. and graham, j. (2004). modelling vibrated stone columns in soft clay, proceedings of the institution of civil engineers-geotechnical engineering, 157(3), pp. 137-149. b t. salem et alii, frattura ed integrità strutturale, 57 (2021) 40-49; doi: 10.3221/igf-esis.57.04 49 [6] roopkumdee, w. (2017). buckling of liquid-filled steel storage tanks under earthquake loading, dissertation, university of north dakota, grand forks, north dakota. [7] hafez, a. (2012). seismic response of ground-supported circular concrete tanks, dissertation, civil engineering department, ryerson university, canada. [8] api standard (2014). welded tanks for oil storage, washington dc, american petroleum institute, usa. microsoft word numero 2 art 4.doc m. guagliano, frattura ed integrità strutturale, 2 (2007) 25-35; doi: 10.3221/igf-esis.02.04 25 1 introduzione la diffrattometria dei raggi x (xrd) è una tecnica di misura usata in molti settori scientifici ed industriali per misurare differenti proprietà dei materiali. la tecnica può essere utilizzata su materiali mono o policristallini e consiste nel misurare l’angolo di massima diffrazione di un fascio incidente di raggi x su una superficie. nel campo dell’ingegneria e delle costruzioni meccaniche, la diffrattometria dei raggi x è utilizzata per la misura degli sforzi residui nei componenti meccanici [1, 2]. le informazioni che si ottengono da una misura diffrattometrica sono essenzialmente due: l’angolo per il quale si verifica il picco di diffrazione di un fascio di raggi x incidenti sulla superficie e l’ampiezza del picco di diffrazione (generalmente misurata ad ½ dell’altezza del picco e chiamata fwhm, full width at half maximum). l’angolo di diffrazione è direttamente legato al valore degli sforzi residui nella zona di misura, mentre la fwhm può essere messa in relazione alla distorsione dei grani cristallini, alla densità delle dislocazioni e ai cosiddetti micro-sforzi residui di tipo ii [1,3]. queste informazioni possono essere usate anche in sede di analisi di un cedimento. infatti le misure xrd condotte su superfici di frattura possono fornire importanti indicazioni per interpretare i cedimenti e per determinare le cause che li hanno indotti. ciò è possibile applicando i concetti propri della meccanica della frattura elastica ed elastoplastica insieme ai risultati ottenuti con misure xrd. i primi tentativi in tal senso sono stati eseguiti durante gli anni ’70 del xx secolo [4, 5]. ogura et al. [6-7] hanno usato la xrd per studiare gli sforzi residui lasciati sulla superficie di frattura di provini compact–tension (ct) in acciaio dalla propagazione di una cricca di fatica ed hanno confrontato i risultati ottenuti con quelli di analisi a elementi finiti: si è trovato che i valori sono positivi (trazione) sulla superficie di frattura e decrescono in profondità. un altro risultato del loro studio è stato quello di trovare una relazione tra la variazione ciclica del fattore di intensificazione degli sforzi (δk) e il suo massimo valore (kmax) e l’andamento di fwhm in profondità. e’ stata poi valutata l’estensione della zona plastica per mezzo della distribuzione degli sforzi residui. kodama et al. [8-9] hanno analizzato superfici di frattura sottolineando l’effetto di rapporti di ciclo r sull’andamento degli sforzi residui sulla superficie di frattura e negli strati di materiale sub-superfciali: è stato trovato che valori di r inferiori a -3 ed elevati carichi applicati inducono valori di sforzi residui di compressione in superficie. in [9] si descrive un modello per la previsione della distribuzione degli sforzi residui nella frattografia xrd. bignonnet et al. [10], lebrun et al. [11], dias et al. [12] hanno posto l’attenzione sulla relazione che intercorre tra l’estensione delle zone di plasticizzazione monotona e ciclica, rpm e rpc, i valori di kmax e δk, la misura degli sforzi residui e del fwhm: essi hanno trovato risultati originali, specialmente in relazione ad un modello per la stima della zona di plasticizzazione ciclica basato sulla distribuzione in profondità dell’fwhm ed applicabile a materiali che addolciscono ciclicamente. altri studi considerano matel’applicazione della diffrattometria dei raggi x per l’analisi del cedimento dei componenti meccanici mario guagliano politecnico di milano, dipartimento di meccanica, via la masa 34, 20156 milano riassunto. la diffrattometria dei raggi x è una tecnica sperimentale utilizzata per la misura degli sforzi residui nei materiali metallici. se applicata alla superficie di un elemento rotto può divenire uno strumento di indagine frattografica, il che vuol dire che è possibile mettere in relazione i risultati delle misure ottenute con le condizioni di carico che hanno indotto il cedimento. in questa memoria, dopo una parte introduttiva relativa ai principi di diffrattometria dei raggi x ed alla sua applicazione in sede frattografica, la si utilizza per l’analisi del cedimento di un albero a gomiti, evidenziando alcuni aspetti originali relativi all’applicazione di questa tecnica a componenti reali. abstract. x-ray diffraction is a well-known experimental technique for measuring residual stresses in metallic materials. if xrd is applied to the fracture surface of a broken part it becomes a fractographical technique, that is to say that it is possible to relate the results of the measures to the loading condition that lead a component to fail. in this paper, after an introduction about the technique, xrd fractography is applied to a fatigue failed diesel engine crankshaft. it was possible to determine the load that lead the crankshaft to fail and to evidence some original aspects about the application of this technique to real machine parts. parole chiave. xrd; fatica; alberi a gomito. http://www.gruppofrattura.it http://www.gruppofrattura.it http://dx.medra.org/10.3221/igf-esis.02.04&auth=true m. guagliano, frattura ed integrità strutturale, 2 (2007) 25-35 26 riali differenti ed hanno contribuito allo sviluppo di questa tecnica: suzuki et al. [13] hanno eseguito uno studio xrd sulla superficie di frattura di un pezzo in ghisa duttile considerando la misura dell’austenite residua. mori et al. [14] hanno applicato questa tecnica alla frattografia di compositi sinterizzati considerando solo situazioni statiche. rajianna et al. [15-17] hanno eseguito analisi frattografiche xrd su un acciaio c45 considerando differenti temperature di frattura. la maggior parte degli studi condotti si riferiscono, tuttavia, a provini standard, tipicamente provini ct. ci sono pochi articoli che considerano l’analisi di cedimenti su elementi di macchine o componenti strutturali. in [18] viene descritta la frattografia xrd di una biella di un solenoide rotta per fatica. in [18] si considera una giunzione tubolare saldata di una struttura off-shore, mentre in [19] si analizza la rottura della testa di una rotaia per mezzo di provini di laboratorio. in [20] si ricercano le cause del cedimento dell’albero di una turbina a vapore per mezzo della xrd. lo studio di veri e propri elementi di macchine con la diffrattometria dei raggi x, presenta differenze non trascurabili rispetto ad analisi condotte su provini di laboratorio: ciò è dovuto al fatto che le effettive condizioni di lavoro non sono sempre note e possono variare durante la durata operativa della macchina, rendendo più difficile l’analisi dei dati sperimentali. in questa memoria si considera un albero a gomiti utilizzato in un motore diesel veloce per applicazioni navali. l’albero si è rotto durante prove di fatica flessionale (r=1) [21]. dopo aver caratterizzato il materiale con cui l’albero a gomiti era costruito per mezzo di prove sperimentali e di misure xrd condotte su provini standard, si è analizzata la superficie di frattura dell’albero a gomiti con la xrd, considerando diversi punti sulla superficie per differenti stati di propagazione della cricca. la finalità di queste analisi è verificare la possibilità di utilizzare convenientemente questa tecnica di misura per analizzare cedimenti avvenuti in esercizio. i risultati ottenuti sono stati confrontati con dati relativi ad una albero a gomiti molto simile a quello considerato; il confronto è stato più che soddisfacente. nella memoria alcuni aspetti relativi all’utilizzo del xrd e alla misura degli sforzi residui e del fwhm per l’analisi dei cedimenti sono discussi alla luce dell’attuale stato dell’arte. 2 principi di diffrattometria dei raggi x nel presente paragrafo si espongono i principi che sono alla base della diffrattometria dei raggi x per la misura degli sforzi residui e il suo utilizzo in sede di analisi frattografica di cedimenti per fatica. ulteriori dettagli possono essere reperiti in letteratura, ad esempio in [1,2] e in [11,12]. 2.1 la diffrattometria dei raggi x per la misura degli sforzi residui la misura degli sforzi residui con la diffrazione dei raggi x in materiali policristallini si fonda sull’applicazione della legge di bragg. se un fascio di raggi x colpisce un cristallo, ci sarà interferenza costruttiva, o diffrazione, quando (1) dove λ è la lunghezza d’onda della radiazione incidente, d è la distanza tra due piani cristallini consecutivi con indici hkl di miller assegnati, θ è l’angolo di incidenza del fascio di raggi x rispetto ai piani cristallini di interesse, n=1, 2, 3, con l’unica limitazione che sen θ<1. in fig. 1 è illustrata graficamente la condizione di diffrazione dei raggi x. se il cristallo è deformato, come nel caso di sforzi residui indotti da precedenti trattamenti o dall’applicazione di carichi elevati, la distanza d cambia, e, con essa, varierà anche l’angolo θ di diffrazione. misurando la variazione dell’angolo di diffrazione si è in grado di mettere in relazione la variazione della distanza tra i grani cristallini con la deformazione del reticolo cristallino: (2) con l’applicazione delle formule della teoria dell’elasticità lineare è poi possibile mettere in relazione le deformazioni con gli sforzi presenti nel materiale. tuttavia, i metalli e le leghe metalliche sono caratterizzati da una struttura policristallina, con i grani cristallini orientati casualmente rispetto alla superficie dei pezzi. ciò implica che avremo piani caratterizzati dai medesimi indici di miller diversamente orientati rispetto alla superficie, in quanto appartenenti a differenti grani cristallini. in fig. 2 è illustrato il sistema di coordinate definito dalle direzioni principali. in tale figura si assume che lo sforzo normale alla superficie (σ33) sia nullo; inoltre si definiscono gli angoli ψ e φ. variando l’angolo ψ di incidenza tra il fascio di raggi x e la superficie oggetto della misura, si interessano alla misura differenti grani cristallini. si ottiene: θλ dsenn 2= θθε δ−= δ = cot d d figura 1. diffrazione dei raggi x rispetto a un reticolo cristallino. m. guagliano, frattura ed integrità strutturale, 2 (2007) 25-35 27 (3) in cui dψ è la distanza tra i piani cristallini oggetto della diffrazione quando l’angolo di incidenza rispetto alla superficie è ψ, mentre do è la distanza interplanare del materiale indeformato (privo di sforzi residui). se si vuole conoscere il valore dello sforzo σφ è necessario ripetere la misura cambiando l’angolo di incidenza ψ. la teoria dell’elasticità insegna che la deformazione εφψ lungo una direzione inclinata di un angolo ψ rispetto alla superficie è legata agli sforzi principali σ1 e σ2 dalla seguente equazione: (4) con semplici trasformazioni che considerano il legame tra gli sforzi principali e σφ [1] si arriva a scrivere (5) (e è il modulo elastico del materiale, υ il coefficiente di poisson). e’ immediato dedurre che sussiste una relazione lineare tra εφψ e sen2ψ e che σφ è la pendenza della retta divisa per (1+υ)/e. ciò significa che è possibile determinare il valore di σφ eseguendo più misure con differenti angoli di incidenza ψ. questa è la procedura più comunemente eseguita per la misura degli sforzi residui con la xrd. nella applicazioni pratiche, la relazione tra εφψ e sen2ψ non è perfettamente lineare ed è necessario eseguire la regressione lineare dei risultati delle misure (in altri casi la relazione è sistematicamente non lineare, ellittica, ma ciò è dovuto alla presenza di un elevato gradiente degli sforzi nel sottile strato di materiale interessato dalla misura). un altro aspetto da considerare è che, data la natura policristallina dei materiali metallici, si avrà diffrazione più o meno marcata in un range angolare attorno il picco di diffrazione come illustrato in fig. 3. ciò richiede che il picco debba essere elaborato utilizzando qualche funzione matematica (gaussiana, parabola, cross correlation…) per trovare la massima intensità di diffrazione e la sua posizione angolare θ. analizzando la larghezza del picco è possibile avere informazioni relative alla deformazione plastica subita dal materiale e relative alla densità di dislocazioni presenti: la grandezza che è usualmente considerato a tal fine è l’ampiezza del picco a metà altezza del ciclo medesimo (fwhm). 2.2 la diffrazione dei raggi x per le analisi frattografiche i dati ottenuti con le misure xrd possono essere utilizzati per l’analisi del cedimento dei pezzi sollecitati fatica. infatti durante la propagazione si hanno, lungo il fronte di propagazione, deformazioni plastiche che lasciano deformazioni e sforzi residui sulla superficie di frattura, le quali influenzeranno le misure xrd. per mezzo di un numero sufficiente di misure superficiali e subsuperficiali è possibile determinare la profondità di materiale interessato dal passaggio della cricca e mettere quest’ultimo in relazione con i parametri della meccanica della frattura e, quindi, con le condizioni di carico che hanno causato la rottura. andamenti tipici sono illustrati in fig. 4. si nota che sia considerando l’andamento del fwhm che quello degli sforzi residui è possibile determinare l’estensione della zona plastica. nella stessa figura si può notare l’andamento di fwhm sotto l’azione di carichi affaticanti che inducono plasticizzazione ciclica e, conseguentemente, la formazione di una zona di plasticità ciclica. l’estensione di questa zona può essere determinata con la xrd solo per materiali addolcenti. un volta che rpm e rpc sono determinati è possibile metterli in relazione alle grandezze proprie della meccanica della frattura. infatti: (6) ( ) ( )2122221 cos 1 σσ υ ψφσφσ υ εφψ +−+ + = e sensen e ( )212 1 σσ υ ψσ υ ε φφψ +− + = e sen e 2 max ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ = ys pm k r σ α 2 '2 ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ δ = ys pc k r σ α figura 2. definizione di: (a) piani hkl per grani differenti, (b) sistemi di riferimento principale 1, 2, 3 e degli angoli φ e ψ. figura 3. tipico aspetto di un picco di diffrazione. o o d dd − = ψφψε m. guagliano, frattura ed integrità strutturale, 2 (2007) 25-35 28 dove kmax e δk sono il valor massimo e l’ampiezza in un ciclo del fattore di intensificazione degli sforzi, σys e σ’ys sono valori degli sforzi di snervamento monotono e ciclico, rispettivamente, e α è un coefficiente funzione del materiale. quest’ultimo coefficiente può essere determinato sperimentalmente con prove sperimentali con carichi e provini noti. fattori che possono contribuire a modificare i tipici andamenti ora illustrati sono la rugosità superficiale, l’effetto di chiusura della cricca (crack closure) e deformazioni di compressione (dovute al contatto tra le facce della cricca, per esempio) [22]. se le condizioni affaticanti rendono non trascurabili questi ultimi fattori, gli andamenti prima illustrati saranno modificati: in fig. 4b si illustra la sovrapposizione degli andamenti dovuti alla deformazione plastica e alla rugosità superficiale: il risultato è un andamento complessivo crescente-decrescente con un massimo sotto la superficie. 3 analisi xrd del cedimento di un albero a gomiti l’albero a gomiti oggetto dell’analisi è utilizzato su un motore diesel veloce che equipaggia imbarcazioni marine. in fig. 5 sono illustrati i principali rapporti geometrici. la geometria è del tutto analoga a quella degli alberi considerati in [21]. sezioni singole dell’albero a gomiti sono stati sottoposti a cicli di fatica flessionale (r=-1) con un momento flettente applicato sul perno di manovella pari a ±220 knm. dopo circa 600.000 cicli di carico è stata notata una cricca di fatica lungo il raccordo interno tra fianco e perno di manovella:la prova è proseguita fino a che la cricca è divenuta passante lungo la sezione minima dell’albero. in fig. 6 è mostrata la superficie di frattura dell’albero; le linee di spiaggia corrispondono ad arresti temporanei della prova. l’analisi xrd della superficie di frattura ha richiesto prove preliminari di caratterizzazione del materiale, sia per ciò che riguarda la resistenza statica che per le caratteristiche cicliche. 3.1 caratterizzazione del materiale il materiale dell’albero a gomiti è l’acciaio basso legato 39nicrmo3, bonificato. alcuni provini sono stati ricavati da una barra dello stesso diametro dell’albero. sono state seguite tre prove di trazione in accordo con la norma astm e8m: le differenze tra le tre prove sono risultate del tutto trascurabili. i risultati ottenuti sono i seguenti: uts=907mpa, σys = 733 mpa, e=210.000 mpa, a%=18%. la rottura è di aspetto duttile. le prove cicliche sono state eseguite seguendo la norma astm e606 ed utilizzando un provino per ogni livello di deformazione considerato. figura 4. andamento qualitativo di fwhm (a) e degli sforzi residui (b) dovuti alle deformazioni plastiche in prossimità del fronte della frattura su una superficie di rottura a fatica di un materiale ciclicamente addolcente. figura 5. definizione dei rapporti geometrici caratterizzanti l’albero a gomiti: r=0.05,s=0.35, t=0.27, b=1.58, δ=0.038. figura 6. superficie di frattura dell’albero a gomiti. m. guagliano, frattura ed integrità strutturale, 2 (2007) 25-35 29 la curva ciclica, descritta con l’equazione di rambergosgood è risultata la seguente: (7) con e=210.000mpa, k’=1114.3, n=0.124. lo snervamento ciclico è pari a σ’ys = 513 mpa. in fig. 7 sono mostrate la curva monotona e la curva ciclica ricavate dalle prove eseguite. sono state eseguite anche prove di propagazione di cricche per fatica, in accordo con quanto previsto dalla norma e647-05. provini “disk compact tension”(dct) sono stati tagliati da una barra (w=50.8mm, b=12.7mm, a0=13.2mm, h=3mm, in accordo con la nomenclatura della norma). la lunghezza della cricca è stata monitorizzata con un “clip-gage”che misura l’effettiva deformabilità del provino. il provino è stato precriccato fino a raggiungere una lunghezza complessiva della cricca pari a 16.5 mm. dopodichè le prove sono state eseguite mantenendo δk costante. tre sono i valori di δk impostati (13mpam1/2, 22mpam1/2, 30 mpam1/2) con lo scopo di evidenziare eventuali differenze nelle frattografie xrd e di confrontare i risultati con quelli dell’albero a gomiti, provato con cicli di sforzo ad ampiezza costante e, quindi, con δk crescente. i rapporti di ciclo considerati sono r=0.1 e r=0.35. in fig. 8 sono illustrate le superficie di frattura di due provini: si nota la differente rugosità superficiale. 3.2 misure diffrattometriche sui provini dct le misure diffrattometriche sulle superfici di frattura dei provini dct sono state eseguite con un diffrattometro stresstech xstress 3000 (radiazione cr α, area irradiata 3mm2, metodo del sen2ψ, 11 differenti valori di ψ equispaziati in termini di sen2ψ). le misure sono state seguite lungo 3 direzioni in modo da calcolare le direzioni e gli sforzi principali e verificare la loro corrispondenza con la direzione di propagazione e quella a quest’ultima perpendicolare. le misure sono state eseguite seguendo le raccomandazioni npl [23]. le misure in profondità sono state eseguite asportando per via elettrochimica il materiale superficiale. in fig. 9 è mostrato l’andamento degli sforzi misurato sui diversi provini dct: si nota che l’andamento è quello atteso, gli sforzi residui sono sempre di trazione. per r=0.1 e δk=13mpam1/2 r=0.1 e δk=30mpam1/2 gli sforzi residui decrescono fino ad annullarsi, ad una profondità di 015mm e 0.22 mm rispettivamente. in fig. 10 è mostrato l’andamento del fwhm in profondità: per r=0.1 e δk=13mpam1/2 si ha un massimo subsuperficiale, mentre in tutti gli altri casi l’andamento è decrescente-crescente-decrescente, con un minimo ed un massimo più profondo. e’ interessante confrontare i dati ottenuti per r=0.1 e δk=13mpam1/2 con quelli relativi a r=0.35 e δk=13mpam1/2 : nel secondo caso il più elevato valore massimo del fattore di intensificazione degli sforzi causa un incremento del raggio di plasticità ciclica e una zona plastica più profonda. ciò differisce dalle osservazioni riportate in bibliografia [12], in cui l’andamento decrescente-crescente e decrescente è legato unicamente a δk e non a r. in tab. 1 sono riassunti i risultati ottenuti dalle misure. da questi, applicando la (5) si è calcolato il valore di α c he d ipende solo dal materiale, come valor medio tra i valori sperimentali. il valore risultante è stato 0.157, e tale valore è stato adottato per l’analisi dell’albero a gomiti. 3.3 frattografia xrd dell’albero a gomiti dopo aver terminato la caratterizzazione del materiale si è analizzata la sezione di rottura dell’albero a gomiti, vedi fig. 6: si nota il punto di innesco della cricca di fatica, n tot e k ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ δ + δ δ = ' σ σ ε (a) (b) figura 7. curve ciclica e curva monotona ricavate dalle prove: si nota chiaramente l’addolcimento ciclico. figura 8. superfici di frattura di provini dct provati in differenti condizioni: (a) δk=13.5 mpam1/2 r=0.1, (b) δk=30.0 mpam1/2 r=0.1. m. guagliano, frattura ed integrità strutturale, 2 (2007) 25-35 30 il fronte semiellittico e la presenza di alcune linee di spiaggia. si nota anche che la superficie di frattura è a tratti rovinata e non permette analisi quantitative sulla velocità di propagazione. anche la rugosità appare maggiore rispetto a quella dei provini dct. le misure diffrattometriche sono state eseguite in quattro punti differenti, posizionati sul piano di simmetria longitudinale dell’albero a gomiti (sul punto più profondo del fronte della frattura). tali punti sono illustrati in fig. 11, dove sono indicati come a, b, c e d. il punto a è posizionato a 3mm, il punto b a 9 mm, il punto c a 18mm ed il punto d a 28mm dalla superficie del raccordo dell’albero. le misure sono state eseguite utilizzando gli stessi parametri usati per le misure condotte sui provini dct. prov. r δk (mpam1/2) σys (mpa) σ∋ys (mpa) rpm (mm) rpc (mm) 1 0.1 13 733 513 0.1 0.025 2 0.1 30 733 513 0.33 0.11 3 0.35 13 733 513 0.16 0.05 4 0.35 22 733 513 0.37 0.09 5 0.35 30 733 513 0.65 0.2 tabella 1 – risultati delle misure condotte sui provini dct in fig. 12 si mostrano gli sforzi residui misurati nella direzione di propagazione della cricca: si nota come essi tendono ad incrementarsi all’aumentare della profondità della cricca e che nei punti a e b sono di compressione: figura 9. andamento in profondità degli sforzi residui sulle superfici di frattura dei provini dct: (a) r=0.1, (b) r=0.35. (a) (b) m. guagliano, frattura ed integrità strutturale, 2 (2007) 25-35 31 ciò non è comune e raramente evidenziato in letteratura. infatti, nella maggior parte dei casi, gli sforzi residui che si trovano su una superficie di un pezzo rotto per fatica sono di trazione, a causa del rilassamento che si ha al passaggio della cricca. tenendo presenti gli andamenti di fig. 4 e l’aspetto della superficie di frattura è possibile giustificare questo risultato come dovuto all’effetto di chiusura plastica della cricca ed alla rugosità della superficie, che modificano il trend atteso, causando sforzi residui di compressione in superficie. un’altra possibile ragione è legata al valore di r (=-1), che causa il contatto tra le facce della cricca ed il loro danneggiamento, con conseguente modifica degli sforzi residui attesi. ciò può anche spiegare perché gli sforzi siano di compressione solo in corrispondenza dei punti a e b, dove la cricca è più corta e soggetta per un maggior numero di cicli: l’andamento è chiaro e l’effetto diviene sempre meno evidente fino ad annullarsi per cricche profonde più di 18mm. (a) (b) figura 10. andamento in profondità di fwhm sulle superfici di frattura dei provini dct: (a) r=0.1, (b) r=0.35. figura 11. definizione dei punti a, b, c e d lungo i quali sono state eseguite le misure diffrattometriche. m. guagliano, frattura ed integrità strutturale, 2 (2007) 25-35 32 questo trend anomalo non ha impedito di determinare il valore di rpm, in quanto l’andamento in profondità non è stato modificato. in fig. 13 è illustrato l’andamento di fwhm in profondità, il trend è simile nei quattro punti e si differenzia nettamente da quello misurato sui provini dct: infatti è continuamente decrescente e non si osservano né massimi né minimi. le ragioni che permettono di interpretare un simile risultato sono le medesime prima figura 12. andamento in profondità degli forzi residui nei punti a (a),b(b), c (c) e d (d). (a) (b) (c) (d) m. guagliano, frattura ed integrità strutturale, 2 (2007) 25-35 33 descritte e discusse: il valore di r (=-1), il contatto tra le facce della cricca, la rugosità superficiale. solo al punto d, il più profondo, è osservabile un leggero massimo, che può essere considerato il raggio plastico ciclico. in tab.2 è riportata la sintesi dei risultati ottenuti elaborando le misure in profondità: i valori di k sono determinati utilizzando le (5) ed assumendo α=0.157. figura 13. andamento in profondità di fwhm nei punti a (a), b(b), c (c) e d (d). (a) (b) (c) (d) m. guagliano, frattura ed integrità strutturale, 2 (2007) 25-35 34 se si focalizza l’attenzione sui valori di kmax è possibile trovare una conferma delle analisi eseguite confrontando i risultati riportati in [21], relativi a calcoli a elementi finiti elastiche lineari di un albero a gomiti criccato del tutto analogo a quello qui considerato. l’unico punto in cui si nota una marcata differenza è d, il più profondo, dove la zona plastica è più pronunciata e giustifica le differenze trovate (i calcoli fem sono elastici lineari). punto a (mm) α rpm (mm) kmax (mpam1/2) kmax ([22] (mpam1/2) a 3.5 0.157 0.3 32.0 30.9 b 9 0.157 0.5 43,4 34.1 c 18 0.157 0.75 50.7 46.3 d 28 0.157 1.1 61.3 67.6 tabella 2. risultati delle misure condotte sull’albero a gomiti e confronto con risultati di [21]. 4 conclusioni si è analizzato un albero a gomiti rotto per fatica flessionale per mezzo della diffrattometria dei raggi x. ciò ha richiesto la preliminare esecuzione di prove meccaniche e di misure diffrattometriche su provini standard. i risultati sono stati discussi criticamente alla luce dei riferimenti bibliografici e si possono tracciare le seguenti conclusioni: le prove e le misure xrd condotte sui provini standard hanno mostrato un buon accordo con gli andamenti attesi secondo quanto presente in letteratura. in particolare, gli sforzi residui e il fwhm hanno consentito di determinare il valore di α; l’andamento di fwhm in profondità è, per i provini dct, generalmente decrescente-crescente-decrescente e dipende sia sa r che da δk; le analisi xrd condotte sulla superficie di frattura di un albero a gomiti hanno permesso di determinare il valore del valore del fattore di intensificazione degli sforzi per differenti profondità di propagazione. il confronto con dati di bibliografia ha convalidato i risultati trovati; i risultati delle misure xrd condotte sull’albero a gomiti mostrano sostanziali differenze rispetto ai provini dct: in particolare, si sono misurati sforzi residui di compressione sulla superficie di frattura, per le cricche meno profonde. il risultato è stato imputato all’effetto di chiusura della cricca, alla rugosità delle superfici di frattura ed al rapporto di ciclo r=-1, che induce contatto tra le facce della cricca, causando la modifica degli sforzi residui residenti ed impedendo la determinazione del raggio di plasticità ciclica. il favorevole confronto con risultati a elementi finiti incoraggia l’applicazione della procedura come complementare alle osservazioni al microscopio elettronico, oppure come sostituto a queste ultime, nel caso in cui le superfici di frattura siano rovinate e le osservazioni al sem risultino, quindi, impedite. 5 bibliografia [1] c. noyan, j.b. cohen (1987) residual stressmeasurement by diffraction and interpretation”, springerverlag, new york. [2] e. macherauch, k.h: kloos (1987). origin, measurement and evaluation of residual stresses. in: residual stresses in science and technology (edited by e. macherauch and v. hauck), dgm informationsgesellschaft, pp. 3-26. [3] g.h. farrahi, j.l. lebrun, d. courtain (1995) effect of shot peening and residual stress and fatigue life of a spring steel; fatigue fract. engng mater struct., 18, 211220. [4] t. matsumoto, h. kitagawa (1971) x-ray investigation of fatigue crack growth in: proc. int. conf. on mechanical behavior of mat., kyoto (japan), 59-66. [5] a. komine, e. nakanishi, k. komine (1978); residual stress at fatigue fracture surface of heat treated high strength steels. j. soc. mat. sci. (japan). 31, 245-250. [6] k. ogura, y. miyoshi and m. kayama (1985); a study of x-ray analysis of fatigue fracture surface. engng fracture mech. 22, 123-133. [7] k. ogura, y. miyoshi, i. nishikawa (1990); new developments in fracture surface analysis using x-ray and laser. jsme international journal (japan),series i, 33, 119-127. [8] s. kodama, h. mìsawa and k. ohsumi (1989); compressive residual stress on fatigue fracture surface. in: proc. of international conference on residual stresses, icrs2 (edited by g. beck, s. denis and a. simon), elsevier applied science, nancy, france, 858-863. [9] s. kodama, k. akita. h. misawa and s. tobe (1991); a model for residual stress distribution in x-ray fractography. in: residual stresses—iii, science and technology, icrs3 (edited by h. fujiwara, t. abe and k. tanaka), vol. ii, elsevier applied science, tokushima. japan, 1421-1428. [10] a. bignonnet, a. dias and j. l. lebrun (1989); fatigue failure analysis of x-ray fractography. in: advances in fracture research, icf7 (edited by k. salama, [11] k. ravi-chandar, d. m. r. taplin and p. rama rao). pergamon press, houston, usa, 3457-3463. [11] j. l. lebrun, a. dias and a. bignonnet (1988); xray fractography of the plastic zones of fatigue cracks. in: proc. of the international conference on residual stresses, icrs2 (edited by g. beck, s. denis and a. simon), elsevier applied science, nancy, france, pp. 526-832. [12] a. dias, j.l. lebrun and a. bignonnet (1999); xray diffraction studies on fatigue crack plastic zones developed under plane strain state conditions. fatigue fract. engng mater struct., 22, 133-144. m. guagliano, frattura ed integrità strutturale, 2 (2007) 25-35 35 [13] a. suzuki, y. kishi, z. yajima, y. hirose (1994); x-ray fractographic study on fatigue fracture surface of ductile cast iron. advances in x-ray analysis, 37, 327334. [14] t. mori, m. kawasaki, t. sasaki and y. hirose (2000); an x-ray fractography study of a sintered composites system of al2o3/sic (wiskers). advances in xray analysis, 43, 376-381. [15] k. rajanna, b. pathiraj and b. h. kolster (1997); duplex stainless steel fracture surface analysis using xray fractography. j. mater. engng perform., 6, 35-40. [16] k. rajanna, b. pathiraj and b. h. kolster (1991); fatigue fracture surface analysis in c45 specimens using x-ray fractography. engng fracture mech., 39, 147-157. [17] k. rajanna, b. pathiraj and b. h. kolster (1996); some studies on the influence of stress ratio and test temperature on x-ray fractography observations in c45 steel specimens. engng fracture mech., 54, 457-470. [18] k. matsui, k. tanaka (1991); x-ray fractographic study on fracture of a machine part. in: residual stresses—iii, science and technology, icrs3 (edited by h. fujiwara, t. abe and k. tanaka), vol. ii, elsevier applied science, tokushima. japan, 833-838. [19] c. maillard-salin, a. nhari, j. l. lebrun, h. p. lieurade, b. prasie and r. y. deroche (1986); analysis of 'kidney-shape' fatigue crack development in rail head using laboratory specimen. in: measurements and fatigue, eis 86 (edited by j. m. tunna), emas, birmingham, uk, 255-268. [20] s. bayard and j. l. lebrun (1986); application ot x-ray fractography to a cracked steam turbine shaft. in: residual stresses in science and technology, icrs1 (edited by e. macherauch and v. hauk), vol. ii, dgm, garmisch partenkirchen. germany, 935-942. [21] m. guagliano, l. vergani (1994) a simplified model to crack growth prediction in a crankshaft. fatigue fract engng mater struct, 17, 1295-1306. [22] y. hirose and k. tanaka (1986) x-ray measurement of residual stress near fatigue fracture surfaces of high strength steel. adv. x-ray anal., 29, 265-270. [23] e. fitzpatrick, a.t. fry, p.holdway, f.a. kandlin, j. shackelton and l. suominen (2002) determination of residual stresses by x-ray diffraction; measurement good practice guide n. 52, national physical laboratory, teddington (uk). 6 nomenclatura parametro definizione d distanza interatomica di una famiglia di paini cristallografici con dai indici di miller hkl kmax massimo valore del fattore di intensificazione degli sforzi e modulo elastico fwhm ampiezza del picco di diffrazione a metà altezza r rapporto di fatica rpc estensione della zona soggetta a plasticità ciclica rpm estensione della zona soggetta a plasticità monotona uts carico di rottura a trazione α coefficiente che lega la dimensione della zona plastica al fattore di intensificazione degli sforzi δk ampiezza del ciclo di fatica in termini di fattore di intensificazione degli sforzi ε deformazione ψ angolo di incidenza del fascio di raggi x rispetto alla superficie oggetto della misura θ angolo di bragg σys sforzo di snervamento monotono σ’ys sforzo di snervamento ciclico microsoft word numero_33_art_30 a. bolchoun et alii, frattura ed integrità strutturale, 33 (2015) 238-252; doi: 10.3221/igf-esis.33.30 238 focussed on multiaxial fatigue numerical measures of the degree of non-proportionality of multiaxial fatigue loadings a. bolchoun technische universität darmstadt, chair of system reliability and machine acoustics (szm), darmstadt, germany h. kaufmann, c. m. sonsino fraunhofer institute for structural durability and system reliability lbf, darmstadt, germany abstract. the influence of the non-proportional loadings on the fatigue life depends on the material ductility. ductile materials react with a shortening of lifetime compared to proportional loading conditions. for a semiductile material there is almost no difference between proportional and non-proportional loadings with respect to the fatigue life. brittle materials show an increase of the lifetime under non-proportional loadings. if fatigue life assessment is performed using stress-based hypotheses, it is a rather difficult task to take into account material ductility correctly, especially the fatigue life reduction as displayed by ductile materials. most stress-based hypotheses will compute a longer fatigue life under non-proportional loading conditions. there are also hypotheses, which already include quantitative evaluation of the non-proportionality (e.g. eesh, ssch and mwcm). anyway in order to improve assessment for ductile materials, some sort of numerical measure for the degree of non-proportionality of the fatigue loading is required. a number of measures of this kind (or non-proportionality factors) were proposed in the literature and are discussed here: the factor used in eesh is a quotient of stress amplitudes integrals, the factor according to gaier, which works with a discrete stress tensor values in a scaled stress space, the factor according to kanazawa, which makes use of plane-based stress values, the factor used in mwcm, which exploits stress values in the plane with the highest shear stress amplitude, a new non-proportionality factor, which is based on the correlation between individual stress tensor components, is proposed. general requirements imposed on the non-proportionality factors are discussed and each of the factors is evaluated with respect to these requirements. also application with the stress-based hypotheses is discussed and illustrated using the experimental data for aluminum and magnesium welded joints under constant and variable amplitude loadings. keywords. multiaxial fatigue; non-proportional loadings; non-proportionality measures; welded joints; stress-based criteria. introduction aterials and structural components subjected to multiaxial fatigue loadings can react differently depending on the non-proportionality of the loading. some materials (brittle material state) exhibit a longer fatigue lifetime under non-proportional loadings compared to the proportional ones. other materials (ductile material state) m a. bolchoun et alii, frattura ed integrità strutturale, 33 (2015) 238-252; doi: 10.3221/igf-esis.33.30 239 react with a shorter fatigue life to non-proportional loadings [1]. this behavior is also exhibited by welded joints of steel, aluminum and magnesium [2-6]. if fatigue life evaluation is performed using stress-based hypotheses, taking nonproportionality into account in a correct manner is a rather difficult task. most of the stress-based hypotheses compute a longer fatigue life under non-proportional loadings unless there is some explicit non-proportionality measure ‘built in’ into the hypothesis. examples of such hypotheses are essh [7], ssch [3, 5], mwcm [8]. for other stress-based hypotheses an external non-proportionality factor can be introduced and so improve fatigue assessment under non-proportional loadings. such non-proportionality factors similarly to the stress-based hypotheses can be subdivided into two large families: the integral and the critical plane based factors. to the first family belong the non-proportionality factors introduced by bishop [9], gaier [10], sonsino [7] and the new non-proportionality factor based on the statistical correlation of stress components [11], which is presented in the current paper. these factors make use of integral stress values. the nonproportionality factors by susmel (mwcm) [8] and kanazawa [12] are critical plane based values. for factors of this type a critical plane (in both cases plane with the highest shear stress amplitude) is determined and then certain stress relations, which belong to the critical plane are computed and used as a non-proportionality measure. the non-proportionality factors introduced by gaier and bishop are an improvement over the factor introduced by chu et al. [13], which does depend on the choice of coordinate system. most of the non-proportionality factors under discussion attend values between 0 and 1 also evaluation of variable amplitude loadings can be performed using all the factors. other important features are independence on material properties (only the time-dependent stress tensor path is used for evaluation of the non-proportionality) as well as independence on the choice of the coordinate system. as an illustration for the application of the non-proportionality factors the findley criterion is used to evaluate fatigue life of aluminum and magnesium welded joints. non-proportionality factors of integral type his class of non-proportionality factors involves some form of integral evaluation of stresses in different planes. depending on the situation those can be planes orthogonal to the specimen surface (plane stress state) or arbitrary oriented planes (general stress state). computation of these factors to variable amplitude loadings can require a sufficiently fine sampling of the time-dependent loading path and/or a sophisticated integration procedure. with the only exception all factors discussed in this section yield values between 0 and 1, with 0 being the value for the proportional loading and 1 being ascribed to the ‘most non-proportional case’. exact definition of the ‘most non-proportional case’ is different for each factor. non-proportionality factors due to bishop and gaier bishop proposed two measures of the non-proportionality or, more precisely, out-of-phase measures [9]. nonproportionality obtained due to the presence of mean stresses in the case of in-phase time-dependent parts is neglected. the measures are based on the notion of the principal axes of a tensor path. a stress tensor   x xy xz xy y yz xz yz z                    σ (1) is mapped to the vector  ,   2 ,   ,   2 ,   2 ,  x xy y xz yz z     σ x (2) the scaling factor 2 for the shear stresses results in the identity: 1 2 1 2: x x σ σ (3) for any two vectors 1x and 2x , on which the tensors 1σ and 2σ respectively are mapped. the identity (3) in turn results in the independence of the choice of the coordinate system for the values introduced below. a tensor path is defined if t a. bolchoun et alii, frattura ed integrità strutturale, 33 (2015) 238-252; doi: 10.3221/igf-esis.33.30 240 the tensor ( )tσ is time-dependent with  ,t a b for finite real values a and b . the respective time-dependent vector ( )tx will be also called tensor path. first of all the length of the tensor path ( )tx computes to   b a l t dt  x and the mean value (or centroid) of the time-dependent vector ( )tx is given by the integral    1 b a t t dt l   x x x with    t t y x x the rectangular moment-of-inertia tensor can be defined:          b a t t t dt  i y y y or componentwise     ;     , 1, 2, , 6 b ij i j a i y y t dt i j   y spherical moment of inertia tensor is given by   s idtr  i i i i where  tr i is the trace of the tensor i and idi is the identity tensor. if the tensor path is given in the form of discrete sample points      1 2 11 2 1,   , ,   nt t t    nσ σ σ σ σ σ or the respective vector values 1 2 1, , ,  nx x x , the path is assumed to be linear between the samples and the following approximation formulas hold: 1 n k k l l    (4) 1 1 1 ( ) 2 n k k k k l l    x x x (5) 1 1  1 1 1 1 ( ( )( )) 6 n k k k k k k k k k ij i j i j i i j j k i l y y y y y y y y          (6) with 1k k kl  x x and k k y x x . the formulas (4)-(6) can be used in order to compute the tensor i for a variable amplitude loading. the rectangular moment-of-inertia tensor i is symmetric and hence has 6 real eigenvalues 1 2 6     and its respective eigendirections 1 2 6, , ,p p p comprise an orthonormal coordinate system. these eigendirections are the principle directions of the tensor path ( )tx . two non-proportionality measures can be defined now:          1 , 1 , max max ,  2, , 6 t a b t a b m i       i p x t p x t (7) 2 2 1 m    (8) the value 1m lies between 0 and  , if it is close to zero, the tensor path ( )tx is nearly in-phase (fig. 1), if the tensor path contains narrow long spikes (fig. 2), it results in 1 1m  . the value 2m lies between 0 and 1, however values near 0 can be attained if the tensor path ( )tx have some short significantly non-proportional parts (narrow spikes). a. bolchoun et alii, frattura ed integrità strutturale, 33 (2015) 238-252; doi: 10.3221/igf-esis.33.30 241 figure 1: a nearly proportional time-dependent tensor path (plane stress): 1 2, , 0m  m  d . figure 2: a non-proportional time-dependent tensor path (plane stress). non-proportionality due to a narrow spike: 1 1,m 2 , 0m  d . gaier et al. [10] employ an idea, which is very similar to bishop’s. for a tensor path given by discrete samples 1 2 1, , ,  nx x x they construct a tensor-of-inertia, which is similar to the tensor si defined above. the individual components siji for , 1, .., 6i j  are given by the formulas:   1 6 2 1, 1 n s k ii j jk j i i x      (9) 1 1 ,  n s k k ij i j k i x x i j       (10) figure 3: a non-proportional time-dependent tensor path (plane stress): 1 2, , 1m  m  d . a. bolchoun et alii, frattura ed integrità strutturale, 33 (2015) 238-252; doi: 10.3221/igf-esis.33.30 242 if 1 2 6     are the eigenvalues of the tensor si , components of which are given by the eq. (9) and (10), then the non-proportionality measure of stresses is given by: 6 5 npd    (11) the formula (11) is the ratio of the second largest axis to the largest axis of the moment-of-inertia ellipsoid of the points 1 2 1, , ,  nx x x , if a unit mass is assigned to each of them. the measure npd attends values between 0 and 1 and similar to the non-proportionality measure 2m (eq. (8)) does not account for short but highly non-proportional pieces in a mostly proportional tensor path. a major difference between the values 1 2, m m and the value npd is, that no subtraction of the mean stresses x occurs as npd is computed. all the non-proportionality measures 1 2, m m and npd yield the value 1 e.g. for the loading of the type: 2 cos ,  sin  x xya t a t     with all other stress components being equal to 0 (cf. fig. 3). also all three factors can be computed for a plane stress state with vector path ( )tx restricted to three components only. in this case the moment-of-inertia tensors will have the 3 3 instead of the 6 6 shape. correlation-based non-proportionality factor this factor was briefly introduced in [11], here it is presented and discussed in a greater detail. the non-proportionality of the loading implies, that time-dependent normal and shear stress components in different planes are essentially of different shapes. statistical correlation ( , )cor f g of two functions ,f g provides a numerical measure for how ‘similar’ the shapes of the functions are. in particular  , 1cor f g   means that the functions differ by a scaling factor and  , 0cor f g  means that f and g are ‘fully uncorrelated’. in order to give the precise definition for  ,cor f g some notions from statistics are required. in what follows the functions f and g are considered to be dependent on a time variable t , which belongs to a finite interval [ , ]a b . the mean value (or expected value)  e f of f and its variance  var f on the interval [ , ]a b are given by [14]:   1 ( ) b a e f f t dt b a    (12)              22 2 2 a 1 ( ) b a b var f e f e f f t e f dt e f e f        (13) the covariance ( , )cov f g of two functions is defined by:                        a a a , 1 1 b a b b b cov f g e f e f g e g e f g e f e g f t g t dt f t dt g t dt b a                 (14) using the notions introduced above, the correlation coefficient of f and g can be defined:         , , . cov f g cor f g var f var g   (15) this value is bounded  1   , 1cor f g   also if f and g are trigonometric functions of the same frequency with zero mean and a phase-shift  between them, i.e.: a. bolchoun et alii, frattura ed integrità strutturale, 33 (2015) 238-252; doi: 10.3221/igf-esis.33.30 243      1 2sin ,   sinf t a t g t a t    with 1a and 2a being the respective amplitudes, the correlation coefficient  ,cor f g over the full period [0, 2 ] computes to:  , coscor f g  that is the correlation coefficient can be used to generalize the notion of phase-shift for arbitrary functions. now let the stress tensor be defined by the matrix 11 12 13 12 22 23 31 32 33 s                    with respect to a coordinate system xyz and 11 12 13 21 22 23 31 32 33 q q q q q q q q q            a coordinate transformation matrix into the coordinate system ' ' 'x y z , such that the stress tensor admits with respect to this coordinate system the form: ' ts q sq consider two components 'ij and ' kl of 's , they can be expressed in terms of the components of s and q as follows: 3 3 ' 1 1 ij im jn mn m n q q      3 3 ' 1 1 kl km ln mn m n q q      if the components of s are functions and their covariances can be calculated, then the convariance of 'ij and ' kl computes to   3 3 3 3 3 3 3 3 ' ' 1 1 1 1 1 1 1 1 ,  ,  ( , ).ij kl im jn mn km ln mn im jn ks lt mn st m n m n m n s t cov cov q q q q q q q q cov                        that is covariances of the components of 's can be computed, if the covariances of the components of s and the matrix q are known. the same applies to the variances, since  ' ' '( ,  )mn mn mnvar cov   . therefore the correlation coeffcients of any two components of the stress tensor with respect to the coordinate system ' ' 'x y z can be expressed using the covariances of the components with respect to the coordinate system xyz and the components of the coordinate transformation matrix. that is only six variances and 15 covariances of the components must be computed explicitly for a stress tensor representing a general stress state in order to be able to compute variances and covariances of the components with respect to any coordinate system. similar considerations hold true of course for a plane stress state. now consider a plane stress state given by the stress tensor x xy xy y s            (16) with the time-dependent components ,  , x y xy   . the tensor s defined above can be transformed (rotated) into another coordinate system by means of the transformation matrix a. bolchoun et alii, frattura ed integrità strutturale, 33 (2015) 238-252; doi: 10.3221/igf-esis.33.30 244 cos sin sin cos t            the transformed tensor computes to ' ' ' ' ' x xyt xy y s t st              with the components equal to ' cos 2 sin 2 2 2 x y x y x xy              ' cos 2 sin 2 2 2 x y y x y xy              ' sin 2 cos 2 2 y x xy xy          now a measure for non-proportionality of the time-dependent stress tensor s , which does not depend on a coordinate system, can be introduced. the mean of the square of the correlation  2 ' ', x xycor   over all coordinate systems, i.e. over all angles [ 0,  ]   2 ' ' 0 1 ,x xym cor d        provides such a measure. it is equal to 1 for a proportional time-dependent stress tensor and it is equal to 0 for a stress tensor of the form sin cos 2 2 2 . cos sin 2 2 2 i ii i ii i ii i ii i ii i ii t t s t t                                a tensor of this shape results in unchanging principal values , i ii  , but constantly rotating principle directions (fig. 4). that means especially, that each plane experiences the same shear stress amplitude. figure 4: mohr-circle, which does not change its shape, but rotates constantly: 1npf . finally the non-proportionality factor, which can be used in further fatigue life evaluations, is defined using the value m :  2 ' ' 0 1 1 1 , .np x xyf m cor d           (17) a. bolchoun et alii, frattura ed integrità strutturale, 33 (2015) 238-252; doi: 10.3221/igf-esis.33.30 245 in the eq. (17) the value  2 ' ',x xycor   is used instead of  ' ',x xycor   since this way the sign (direction) of the phaseshift is ignored. for a general stress state the value m is computed as follows:   22 2 ' ' 2[ 0, ) 0 2 1 min    ,  2 x xym cor d d               and the non-proportionality factor analogous to eq. (16):     22 2 ' ' 20, 0 2 1 1 min    ,  2 np x xyf m cor d d                 (18) the minimization over the angle  leads to a compatibility with the factor defined by the eq. (17). for a plane stress state the eq. (18) will always yield the same or higher value npf as the eq. (17). all the integration and minimization operations employed in the eq. (17), (18) can be computed numerically in an efficient manner. non-proportionality factor employed by the eesh the effective equivalent stress hypothesis (eesh) [7] is designed specifically for evaluation of a time-dependent plane stress state. the non-proportionality factor is based on the integral of the shear stress amplitude taken over all planes, which are orthogonal to the component surface. if the x and xy components of the stress tensor defined by the eq. (16) have a phase-shift  between them, the value ( )arith  can be defined:     0 1 .arith a d          (19) using the eq. (19) the non-proportionality factor can be defined:    0 arith essh arith f        (20) which is known to admit values between 1 ( 0   ) and approx. 1.1 ( 90 )   . in case of variable amplitude loading the rainflow-counting is used in each plane given by the angle  in order to obtain the value ( )a  . subsequently the arithmetic mean of the amplitudes of all the rainflow-cycles in the given plane is computed. critical-plane-based non-proportionality measures he non-proportionality measures of this type make use of the stress values related to a certain plane, known as the critical plane, in order to evaluate the non-proportionality of a time-dependent stress tensor. two values of this type are considered: the non-proportionality factor according to kanazawa [12] and the multiaxiality factor used in the mwcm [8]. for both factors critical plane is defined to be the one with the highest shear stress amplitude. so the first step is to identify the critical plane, which can be done by a direct computation for a constant amplitude loading and methods like the maximum variance method [15] can be used for a constant amplitude loading. the non-proportionality factor according to kanazawa in kanazawas original paper [12] the factor is defined for a plane stress state as follows: ,45 , a kanazawa a crit f    (21) in the eq. (21) ,a crit denotes the shear stress amplitude in the critical plane and ,45a  the shear stress amplitude in the plane, which has the angle of 45° to the critical plane. this definition is straight-forward in the case of a planar loading t a. bolchoun et alii, frattura ed integrità strutturale, 33 (2015) 238-252; doi: 10.3221/igf-esis.33.30 246 and there is no obvious extension to the general 3d stress case, since there is an infinite number of planes, which enclose the angle of 45° with the critical plane. it can be proposed to minimize the value (21) over all such planes: ,45 , ( ) min akanazawa a crit f      (22) with [0, 2 )  being the angle, which defines the orientation of the plane. the value according to the eq. (22) can be computed numerically. the multiaxiality factor according to susmel in [8] the multiaxiality factor  is used to take the effects of multiaxiality including non-proportionality of the load into account. , ,   n max a crit     (23) with ,  a crit being as before and , n max being the maximal normal stress occurring in the critical plane. it can be split into the amplitude and the mean stress component: , , ,n max n a n m    , this in turn allows to decompose the multiaxiality factor  : , , ,   ,   n a n m a crit a crit        and to introduce a mean stress sensitivity parameter m as follows: , , ,   ,   n a n m a crit a crit m        (24) the factor defined by the eq. (23) or (24) was introduced in order to be used with the modified wöhler curve method (mwcm) [8], but can be seen as a method-independent measure for non-proportionality. however it can attend values from  to  , which make require additional work in order to use it with some other criterion. in this paper it is used for evaluation with mwcm only. evaluation of fatigue life results for aluminum and magnesium welded joints atigue life test results under constant and variable amplitude loading for aluminum thin-walled laserbeam welded joints are presented in the thesis [5]. fe-modelling was carried out in order to obtain linear elastic local stresses according to the notch stress concept with fictitious radius rref = 0.05 mm [16]. for magnesium laserbeam welded joints the results for constant amplitudes are provided in the thesis [6] and variable amplitude loadings are the subject of an ongoing research project funded by the dfg (german research foundation). fatigue life evaluations were performed using two well-known methods: the findley-criterion [17] and sih (shear stress intensity hypothesis) [18]. the nonproportionality factor proposed within eesh is used also within eesh and the multiaxiality factor proposed within the mwcm is also applied with the mwcm only. some proposals to adapt the two latter non-proportionality factors are provided in the previous section, however a further investigation is required if these factors are going to be applied outside of their respective hypotheses. in general the following way to apply the non-proportionality factors together with the stress-based hypotheses is proposed:   * 1 1a aw f    (25) with a a shear stress amplitude value involved in the respective hypothesis, w a hypothesis-dependent material parameter, f is the non-proportionality factor and *a the shear stress amplitude corrected with respect to the nonproportionality of the loading. in order to apply the eq. (25) it is an important assumption, that 0    1f  . for the nonf a. bolchoun et alii, frattura ed integrità strutturale, 33 (2015) 238-252; doi: 10.3221/igf-esis.33.30 247 proportionality measure 1m given by eq. (7) an exception is made, since for the evaluated tensor paths it is always 10 1m  . experimental results the experimental results were obtained in a tension-torsion testing rig using the specimen geometry as shown in fig. 5. for both magnesium and aluminum welded joints the same specimen geometry was used. the tested aluminum alloys are en aw 5042 and en aw 6082 t6, the magnesium alloys are az31 and az61. the type of alloy does not show a significant influence of the fatigue strength of the welded joints. figure 5: specimen geometry. the wöhlerlines for the aluminum alloy en aw 5042 (cf. [5]) and for magnesium alloy az31 (cf. [6]) are shown in fig. 6 and fig. 7 respectively. figure 6: experimental results for aluminum alloy en aw 6082 t6 under constant amplitudes figure 7: experimental results for magnesium alloy az31 under constant amplitudes. a. bolchoun et alii, frattura ed integrità strutturale, 33 (2015) 238-252; doi: 10.3221/igf-esis.33.30 248 both materials show a fatigue life decrease under non-proportional loadings in the finite fatigue life region. the magnesium alloy az31 shows this behavior below the knee point of the wöhlerlines as well. as can be seen in the tab. 16 the non-proportionality factors computed using different methods lie in a narrow interval between 0.6 and 0.75. if in the eq. (25) it is assumed 2w  . results as shown in fig. 8 and fig. 9 can be obtained using the correlation-based factor and the hypotheses findley [17] and sih [18]. other factors will lead to similar (slightly more conservative) results. figure 8: experimental and computational gassner-lines for aluminum alloy en aw 6082 t6 with the application of nonproportionality factors. figure 9: experimental and computational gassne-rlines magnesium alloy az31 t6 with the application of non-proportionality factors. both figures show conservative estimates for high number of cycles. the inverse slope of the gassner-lines is not correctly computed using the hypotheses (especially the palmgren-miner damage accumulation rule, which is used for the fatigue life computations in this case). aluminium magnesium cal, 90   val, 90   cal, 90   val, 90   0.659 0.658 0.677 0.675 table 1: non-proportionality factor according to kanazawa, plane stress state. a. bolchoun et alii, frattura ed integrità strutturale, 33 (2015) 238-252; doi: 10.3221/igf-esis.33.30 249 aluminium magnesium cal, 90   val, 90   cal, 90   val, 90   0.610 0.609 0.623 0.622 table 2: non-proportionality factor according to kanazawa, generalized for spatial stress state aluminium magnesium cal, 90   val, 90   cal, 90   val, 90   0.689 0.685 0.679 0.675 table 3: non-proportionality factor according to bishop, 1m aluminium magnesium cal, 90   val, 90   cal, 90   val, 90   0.755 0.750 0.746 0.742 table 4: non-proportionality factor according to bishop, 2m aluminium magnesium cal, 90   val, 90   cal, 90   val, 90   0.689 0.687 0.679 0,677 table 5: non-proportionality factor according to gaier, d aluminium magnesium cal, 90   val, 90   cal, 90   val, 90   0.590 0.590 0.590 0.590 table 6: correlation-based non-proportionality factor, npf results obtained using the mwcm according to susmel for this hypothesis only the results for aluminum alloy under constant amplitudes are shown. evaluation of fatigue life of welded joint using the notch stress concept for thick-walled structures is discussed in [19]. here mwcm is applied along with the notch stress concept for thin-walled structures. aluminium cal, 90   1.97 table 7: multiaxiality factor according to susmel,  the value of the non-proportionality factor  is shown in tab. 7. if the value lim as it is described in [9] is taken into account, the results as they are shown in fig. 10 can be obtained. in the region of finite fatigue life the results lie in a narrow scatter band around the line exp calcn n and towards the knee point of the wöhlercurves change on the non a. bolchoun et alii, frattura ed integrità strutturale, 33 (2015) 238-252; doi: 10.3221/igf-esis.33.30 250 conservative side. it can also be noted, that results under non-proportional loading are evaluated in a slightly more nonconservative way than the results for the proportional one. figure 10: experimental results for the en aw 6082 t6 alloy. experimental vs. calculated (mwcm) fatigue life. results obtained using eesh according to sonsino evaluations using eesh for aluminum welded joints were performed in the doctoral thesis [5]. there good agreement of experimental and computational results could be observed. computations for magnesium welded joints under constant amplitude loadings were performed in the thesis [6]. eesh shows there non-conservative computational results. the same behavior is observed under variable amplitude loadings (fig. 11). figure 11: experimental gassner-curves and gassner-curves computed using eesh. according to the computed value of the non-proportionality measure (cf. eq. (20), tab. 8) eesh computes a 10% fatigue strength decrease for the non-proportional loading. magnesium val, 90   1.104 table 8: non-proportionality factor used in eesh (sonsino), eeshf a. bolchoun et alii, frattura ed integrità strutturale, 33 (2015) 238-252; doi: 10.3221/igf-esis.33.30 251 conclusion number of measures for the non-proportionality of the loadings were presented and used for evaluation of fatigue life of aluminum and magnesium welded joints. in general if a non-proportionality measure yields values between 0 and 1 it can be applied with any stress-based fatigue life hypothesis. the eq. (25) can be used to modify a suitable stress value and hence take the non-proportionality into account. so it is a plausible requirement for a non-proportional measure to yield values between 0 and 1. there are also measures such as the factor  used in mwcm (eq. (23)), which is required to interpolate between axial and torsion wöhler-lines and cannot be easily interchanged with any other non-proportionality measure discussed in this paper. also the non-proportionality measures are subdivided into integral and critical-plane-based ones. the latter group contains two measures discussed in this paper: the measure according to kanazawa (eq. (21), (22)) and the measure  used in mwcm according to susmel (eq. (23)). the value of this measures can rapidly change due to a small change in the loading, since such a change can lead to a change in the position of the critical plane. as a result two very similar loads can get very different non-proportionality evaluation. this problem can be avoided if an integral measure of nonproportionality is used. in order to use non-proportionality measures safely for arbitrary loadings, experimental results under loadings with different degrees of non-proportionality are required. in particular this can mean different phase-shifts between axial and torsion loadings and different amplitude ratios. all non-proportional measures presented in this paper are “global” i.e. they deliver information on the nonproportionality of a loading path as a whole. the question arises, whether these measures still work in an adequate manner, if a loading path consists of a number of pieces with different degrees of non-proportionality. is it possible to provide some “local” measure of non-proportionality? as can be observed for the magnesium welded joints taking into account non-proportionality does improve the evaluation, however it can be further improved for variable amplitude loadings if the slopes of the gassner-lines are taken into account correctly by the hypotheses. references [1] sonsino, c.m., influence of material’s ductility and local deformation mode on multiaxial fatigue response, int. j. fatigue, 33(8) (2011) 930-947. [2] sonsino, c. m., küppers, m., eibl, m., zhang, g., fatigue strength of laser welded thin steel structures under multiaxial loading, int. j. fatigue, 28 (5-6) (2006) 657-62. [3] störzel, k., wiebesiek, j., bruder, t., hanselka, h., betriebsfeste bemessung von mehrachsig belasteten laserstrahlschweißverbindungen aus stahlfeinblechen des karroseriebaus. fraunhofer-institut für betriebsfestigkeit und systemzuverlässigkeit lbf, lbf-bericht nr. fb-235, darmstadt (2008). [4] küppers, m., betriebsfestigkeit von aluminiumschweißverbindungen unter mehrachsigen spannungszuständen mit konstanten und veränderlichen hauptspannungsrichtungen. dissertation: fachbereich maschinenbau, fachgebiet szm, tu darmstadt (2006), lbf-bericht nr. fb-233 [5] wiebesiek, j., festigkeitshypothesen zum schwingfestigkeitsverhalten von dünnwandigen laserstrahlschweißverbindungen aus aluminium unter mehrachsigen beanspruchungen mit konstanten und veränderlichen hauptspannungsrichtungen, dissertation, shaker verlag, aachen (2012). [6] exel, n., schwingfestigkeit laserstrahlgeschweißter magnesiumlegierungen unter mehrachsigen proportionalen und nichtproportionalen beanspruchungen, dissertation., shaker verlag, aachen (2013). [7] sonsino, c. m., multiaxial fatigue of welded joints under in-phase and out-of-phase local strains and stresses, int. j. fatigue, 17(1) (1995) 55-70. [8] susmel, l., multiaxial notch fatigue, woodhead, cambridge (2009). [9] bishop, j. e.. characterizing the non-proportional and out-of-phase extent of tensor paths, fatigue fract. engng. mater. struct. 23 (2000) 1019-1032. [10] gaier, c., lukacs, a., hofwimmer, k., investigations on a statistical measure of non-proportionality of stresses, int. j. fatigue, 26 (2004) 331-337. a a. bolchoun et alii, frattura ed integrità strutturale, 33 (2015) 238-252; doi: 10.3221/igf-esis.33.30 252 [11] bolchoun, a., sonsino, c.m., kaufmann, h., melz, t., multiaxial random fatigue of magnesium laserbeam-welded joints – experimental results and numerical fatigue life evaluation, proc. engng., 101 (2015) 61-68. [12] kanazawa, k., miller, k.j., brown, m. w., cyclic deformation of 1% cr-mo-v steel under out-of-phase loads, fatigue engng. mater. struct., 2 (1979) 217-228. [13] chu, c.c., conle, f.a., hübner, a., an integrated uniaxial and multiaxial fatigue life prediction method, vdi-verlag, düsseldorf, vdi-bericht 1283, (1996) 337-348. [14] capasso, v., backstein, d., an introduction to continuous-time stochastic processes, birkhäuser, boston (2005). [15] susmel, l., a simple and efficient numerical algorithm to determine the orientation of the critical plane in multiaxial fatigue problems, int. j. fatigue, 32 (2010) 1875-1883. [16] radaj, d., sonsino, c.m., fricke, w., fatigue assessment of welded joints by local approaches, 2n ed., woodhead, cambridge, (2006). [17] findley, w.n., a theory of the effect of mean stress on fatigue of metals under combined torsion and axial loading or bending, j. eng. ind. (asme), 81 (1959) 301-306. [18] zenner, h., richter, i., eine festigkeitshypothese für die dauerfestigkeit bei beliebigen beanspruchungskombinationen, konstruktion, 29 (1) (1977) 11-18. [19] susmel, l., sonsino, c.m., tovo, r., accuracy of the modified wöhler curve method applied along with the rref = 1 mm concept in estimating lifetime of welded joints subjected to multiaxial fatigue loading, int. j. fatigue, 33 (2011) 1075-1091. microsoft word numero_51_art_4_2511 n. benachour et alii, frattura ed integrità strutturale, 51 (2020) 45-51; doi: 10.3221/igf-esis.51.04 45 focussed on structural integrity and safety: experimental and numerical perspectives experimental investigation of fatigue crack initiation from notches in 2024 t351 al-alloy nadjia benachour, mustapha benachour* university of tlemcen, ingeniery of mechanical systems and materials laboratory, tlemcen, algeria faculty of technology, mechanical engineering department nbenachour2005@yahoo.fr, bmf_12002@yahoo.fr mohamed benguediab university of sidi bel abbes, lmpm laboratory, sidi bel abbes (algeria), mechanical engineering department benguediab_m@yahoo.fr abstract. in this investigation, fatigue crack initiation criterion was established from notches in aged hardening aluminum alloy. this criterion was used to predict the residual lifetime in aeronautical structures subjected to constant amplitude loading using concept of local stress at notch. charpy vnotch specimens were taken from sheet plate and the notch radius accurately machined at value of 0.2mm. the local stresses were determined numerically and validated analytically. in experimental investigation, the v-notched specimens were loaded in four point bending fatigue with a stress ratio r=0.1 and variation in amplitude loading. keywords. fatigue crack initiation; notch; finite element method; stress field; aluminum alloy. citation: benachour, n., benachour, m., benguediab, m., experimental investigation of fatigue crack initiation from notches in 2024 t351 al-alloy, frattura ed integrità strutturale, 51 (2020) 45-51. received: 04.05.2019 accepted: 12.10.2019 published: 01.01.2020 copyright: © 2020 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. introduction enerally, aeronautical structures are subjected to cyclic loading. discontinuities and notches in mechanical components and structures present a site of stress concentration resulting of external load that could be sites of crack initiation. the fatigue life of structural components is determined by the sum of the numbers cycles required to initiate a fatigue crack and to propagate this crack up to the critical dimension. many approaches may be classified in different manner to analyses fatigue crack initiation from notch. the global elastic analysis, it takes into account linear fracture mechanics. firstly, this approach was sued by heckel et al. [1] by introducing the loading parameter (k/1/2). k is the amplitude loading of stress intensity factor and  is the radius of the tip of notch. this approach was used by some researchers. suresh and ritchie [2] have applied this approach for some alloys (steel and al-alloy). also bauss [3] and duquesnay [4] have used this approach respectively for high strength steel, 2024 t351 al-alloy and sae 1045 steel. these authors noted that this correlation for small numbers of cycles at radius notch les than critical value does g http://www.gruppofrattura.it/va/51/2511.mp4 n. benachour et alii et alii, frattura ed integrità strutturale, 51 (2020) 45-51; doi: 10.3221/igf-esis.51.04 46 not give good satisfactory results. a non local fatigue criterion has been proposed by schwob et al. [5], with a single additional parameter compared to traditional criteria, by averaging a classical criterion over a damaged area. the analyzed domain by the global approach is between 102 and 105 cycles [6]. in experimental investigation, hammouda and el-batanony [7] have established a criterion in estimation of fatigue crack initiation life for notched plate under amplitude loading, stress ratio and radius at notch tip effects. the local elastic analysis was takes into the local stress amplitude  at a distance “d” from the tip of the notch. this approach was applied by devaux et al. [8] in establishment a fatigue crack initiation criterion for low fatigue cycle. the established criterion was given by the curve ( , in ). this method was applied successfully by batise at al. [9] in predicting of fatigue crack initiation of x65 pipeline steel. in neuber’s analysis [10], a number of authors noted that this analysis overestimates the notch effect on fatigue crack initiation [11-13]. in study conducted by ranganathan et al. [14] a short crack approach has been developed to determine the fatigue crack initiation life at notch tip. this approach is compared to conventional local-strain approach and it is shown that the short crack approach gives acceptable predictions as compared to experiments, in the 2024 t351 alloy. in the investigation of agbessi et al. [20] an analysis of high cycle multi-axial fatigue crack initiation modes based on sem observations is conducted. also it is concluded that different modes of high cycle fatigue micro cracks initiation were observed under complex loading conditions at stress levels close to the median fatigue limit of the material at 106 cycles. a physics-based multi scale approach was developed by zhang et al. [21] to predict the fatigue life of crystalline metallic materials. an energy-based damage and slip-based damage criterion is developed to model two important stages of fatigue crack initiation: the nucleation and the coalescence of micro cracks. in the present study, elastic analysis based on the knowledge of the local stresses amplitude at a distance from the tip of the notch presents best approach and is applied in 2024 t351 al-alloy. local’s stresses amplitude at distance “d” are determined numerically by finite element analysis and validated analytically using creager approach. evaluation of distribution of stress near the notch root inite element n order to shown the effect of stresses concentrations on fatigue crack initiation, distribution of stress fields near the notch was determined analytically and numerically. this study was applied in aged hardening al-alloy in four bend specimen with v-notch. the analytical calculations was made using the formulation of creager approach [19] which gives the stress field near the tip of a hyperbolic notch loaded in tension (fig. 1). figure 1: system coordinate applied in the calculation of stresses in the notch root in opening mode, creager equations are given by: 3 3 cos 1 sin sin . cos 2 2 2 2. 22 . 2 . 3 3 cos 1 sin sin . cos 2 2 2 2. 22 . 2 . 3 3 sin cos cos . sin 2 2 2 2. 22 . 2 . i i xx i i yy i i xx k k rr r k k rr r k k rr r                                             (1) in eqn. 1, ik is the stress intensity factor given by murakami [22] considering notch as a crack. the radius r and  are cylindrical coordinates shifted by /2 with respect the notch root. we are interested in the component xx given by eqn. 2 (stress opening in cracking plane). i n. benachour et alii, frattura ed integrità strutturale, 51 (2020) 45-51; doi: 10.3221/igf-esis.51.04 47     1 2 / 22 / 2 i xx k dd             (2) numerical calculations of stresses at notch root are led by finite element ansys code. some researches were applied finite element analysis to determine the stress distribution at notch root, stress intensity factor, crack opening stress, …etc. [23-25]. half of the sample is considered taking into account geometric symmetry and applied loading. the mesh, the boundary conditions and loading are shown in fig. 2. at specified boundaries conditions and according to the direction x, displacement ux is equal to zero. the modelling was done by two-dimensional finite element (plane 82) in plane strain condition. plane82 is a higher order version of the two-dimensional, four-node element (plane42). it provides more accurate results for automatic meshes and can tolerate irregular shapes without as much loss of accuracy. the 8-node elements have compatible displacement shapes and are well suited to model curved boundaries. the 8-node element is defined by eight nodes having two degrees of freedom at each node: translations in the nodal x and y directions (fig. 3). the element may be used as a plane element or as an axisymmetric element. the element has supplementary capabilities as plasticity and large strain. automatic mesh option was used with refined meshing at notch where the number of element is 363 elements. the number of gauss integration point per element is equal to 4. the studied material is 2024 t351 al-alloy, quenched and tempered at room temperature. based on elastic local stress concept approach at notch, elastic isotropic material model is used. the mechanical properties are given in tab. 1 in t orientation. this study is conducted for radius at notch equal to 0.2 mm. figure 2: mesh of v-notch specimen: applied load and boundary conditions figure 3: eight node isoparametric element: plane82 e (gpa) y0.2 (mpa) uts (mpa) a(%)  74.0 363 465 22.1 0.33   table 1: mechanical properties of 2024 t351 al-alloy n. benachour et alii et alii, frattura ed integrità strutturale, 51 (2020) 45-51; doi: 10.3221/igf-esis.51.04 48 fig. 3 shows the effect of applied loading on the concentration and the stress distribution near the notch for notch radius =0.2 mm using analytical solution. an important difference at notch root is found. for p=3.99 kn, the developed stress represents 1.45 times the stresses in applied loading of 2.755 kn. the variation in the opening stress obtained numerically xx  in the plane of the slot depending on the distance to the tip there of to a radius  = 0.2 and a variable loading p, is shown in fig. 4. the same tendency is obtained with respect to analytical results by application of creager formulation (fig. 3), where the gap is important in stress at the tip of the notch (high stress concentration). a good correlation was found between the numerical results and analytical results. the high difference is found at the tip of the notch where the difference not exceeds 7.4%. 0 200 400 600 800 1000 1200 1400 0 0.2 0.4 0.6 0.8 1 1.2 distance from the notch root (mm) o p e n in g s tr e s s ( m p a ) p = 2.755 kn p = 3.310 kn p = 3.990 kn figure 3: analytical results of applied loading effect on stresses near the notch root 0 200 400 600 800 1000 1200 1400 0 0.2 0.4 0.6 0.8 1 distance from the notch root (mm) o p e n in g s tr e s s ( m p a ) p = 2.755 kn p = 3.310 kn p = 3.990 kn figure 4: numerical results of applied loading effect on stresses near the notch root experimental procedures atigue crack growth tests were conducted on v-notch four points bending specimen in t-s orientation. the notch is machined in short direction (s). to detect the starting and monitoring of crack, a polishing was performed to remove surface scratches. the geometrical model and dimension of specimens are represented in fig. 5. fatigue tests were conducted at constant amplitude loading at room temperature (23 °c) with a frequency of 10 hz on a servof n. benachour et alii, frattura ed integrità strutturale, 51 (2020) 45-51; doi: 10.3221/igf-esis.51.04 49 hydraulic machine "mts 810" with capacity 100 kn. fatigue tests were conducted at r-ratio (r = 0.1) with variation of the levels of amplitude loading (pmax=2.755 ; 3.31 ; 3.99 kn). figure 5: v-notch specimen in four points bending tests in 2024 t351 al-alloy results and discussion he effect of mean stress on fatigue crack is characterized either by variation of r-ratio or amplitude of loading. this work presents the effect of the amplitude loading on fatigue crack initiation in 2024 t351aluminum alloy. tab. 2 summarizes the lifetimes of initiation crack for a crack initiation length between 170 and 180 m. the considered lengths are in the order of the average grain size of studied material. the applied cyclic loading p is characterized by the amplitude loading where the maximal amplitude loading for the three tests are respectively pmax=3.99 kn, 3.31 kn and 2.755 kn. it should be noted that the lifetime of the crack initiation decreases with increasing in the amplitude loading for the same order of magnitude of the detected length. the transition in the amplitude loading p from 2.48 to 2.98 kn has reduced the number of cycles of 22.000 cycles to 12,800 cycles. this represents a decrease of 1.72 times. according to the high applied load, the lifetimes in crack initiation are negligible comparatively to fatigue life in crack growth stage where the percentage in lifetime varies from 3% to 6.6% [26]. the greatness in results was confirmed by ranganathan et al. [14] under a high load (3%). fatigue tests pmax (kn) p (kn) ai (m) ni (cycles) s1 2.755 2.480 175 22000 s2 3.310 2.980 170 12800 s3 3.990 3.591 180 3000   table 2: effect of amplitude loading on fatigue initiation life at r=0.1 for 2024 t351 al-alloy in order to establish fatigue criterion to predict crack-initiation at the tip of a notch in aged hardening aluminum alloy from experimental results, an attempt is conducted for critical length from notch tip “d=175 m” where the evolution in opening stress xx  for three amplitude loading determined analytically and numerically (figs 3 and 4). analytical results of opening stress xx  are used for curves given the fatigue initiation criterion. the curve giving the opening stress versus number of initiation cycles at critical distance d=175 m is shown in fig. 6. the criterion for fatigue crack initiation thus obtained is given by eqn. 2 where “ xx  ” is expressed in mpa and “ni” in cycles. this criterion remains valid for cycle numbers between 103 and 3104 cycles.  0.2092761.1xx in  (3) t n. benachour et alii et alii, frattura ed integrità strutturale, 51 (2020) 45-51; doi: 10.3221/igf-esis.51.04 50 the obtained results are in good agreement with those in the literature [15-18] for the same material and remain in the validity domain of the results in endurance tests for the same material (al-alloy 2024 t351). y = 2761.1x-0.209 r2 = 0.97 100 200 300 400 500 600 700 1.0e+03 1.0e+06 number of crack initiation cycles ni o p e n in g s tr e s s e s ( m p a ) actual criterion pompetzki et al, [18] jurcevic et al. [17] zheng [15] ngiau & kujawski [16] figure 6: crack initiation criterion. conclusion he present investigation is conducted in order to evaluate the of fatigue crack initiation criterion in the 2024 t351 al-alloy. numerical and analytical approaches were applied to evaluate the stress distribution in four v-notched specimens. from this investigation, we can conclude that:  the fatigue crack initiation lifetime increases in decreasing of the amplitude loading (i.e. mean loading).  the opening stresses determined numerically are validated analytically and depends on the level of applied load  a fatigue crack initiation criterion at notch root for 2024 t351 al-alloy showed the advantages in many applications. this criterion gives a satisfactory in prediction of fatigue crack initiation lifetimes comparatively to others published results. acknowledgments he authors gratefully acknowledge the technical support from the: centre des matériaux d’evry – ecole des mines de paris, france. authors also with to express their gratitude to professor emeritus andré pineau for fruitful discussions on fatigue crack growth and assistance in fatigue crack growth tests. references [1] heckel, f., warner, r., (1975), the tensile fatigue behavior of ct specimens with small notch root radius. international journal of fracture mechanics 11, pp. 135-140. doi : 10.1007/bf00034720. [2] suresh, s., ritchie, r.o. (2013). propagation of short fatigue cracks. international metals reviews, 29(6), pp. 446475, doi: 10.1179/imtr.1984.29.1.445. t t n. benachour et alii, frattura ed integrità strutturale, 51 (2020) 45-51; doi: 10.3221/igf-esis.51.04 51 [3] bauss, h.p., lieurade, g., sanz, m.t. (1977). correlation between the fatigue crack initiation at the root of notch and low-cycle fatigue date: flaw growth and fracture. astm stp 631, pp. 96-111. doi: 10.1520/stp35534s. [4] duquesnay, d.l., topper, t.h., yu, m.t., (1986), the effect of notch radius on the fatigue notch factor and the propagation of short cracks: the behavior of short fatigue cracks, egf pub, edited by k.j. miller and e.r. de los rios, mechanical engineering publications, london, pp. 323-335. [5] schwob, c., chambon, l., ronde-oustau, f. (2006). fatigue crack initiation in stress concentration areas. in proceedings of the 16th european conference of fracture, gdoutos, e.e. (ed.), alexandroupolis, greece. [6] jack, j.r., price, a.t., the initiation of fatigue cracks from notches in mild steel plates, international journal of fracture mechanics, 6(4), pp. 401-409. doi: 10.1007/bf00182628. [7] hammouda, m.m.i., el-batanony, i.g., (2010), notch fci life under constant amplitude uniaxial loads, international journal of structural integrity 1, pp. 12-19. doi: 10.1108/17579861011023766 . [8] devaux, j.c., d’escatha, y., rabbe, p., pellissier-tanon, a. (1979). a criterion for analysing fatigue crack initiation in geometrical singularities. transaction of the 5th international conference on structural mechanics in reactor technology, berlin. [9] batisse, r., meziere, y., mokhdani, c., pineau, a. (1995). a fatigue crack initiation criterion for the assessment of the residual life of gas transmission pipelines with gouge only or gouge in dent defects. eprg/prc 10th biannual joint. technical meeting on pipelines research proceeding, cambridge, uk, 1, pp. 1-11. [10] neuber, h. (1961). theory of stress concentration for shear-strained prismatical bodies with arbitrary nonlinear stress-strain law. journal of applied mechanis 28(4), pp. 544-551. doi: 10.1115/1.3641780. [11] molski, k., glinka, g. (1981). method of elastic plastic stress and strain calculation at a notch root. materials sciences engineering 50, pp. 93-100. doi: 10.1016/0025-5416(81)90089-6 [12] rice, j.r., (1968), mathematical analysis in the mechanics of fracture. fracture ii. liebowitz pp 255-264. [13] topper, t.h., wetzel, r.m., morrow, j. (1967). neuber's rule applied to fatigue of notched specimens. report no, naec-asl-1114 june 1967, u.s. naval air engineering center philadelphia. pennsylvania, usa. [14] ranganathan, n., aldroe, h., lacroix, f., chalon, f., leroy, r., tougui, a. (2011). fatigue crack initiation at a notch. international journal of fatigue 33(3), pp. 492–499. doi: 10.1016/j.ijfatigue.2010.09.007 [15] xiulin, z. (1986), a further study on fatigue crack initiation life mechanical model for fatigue crack initiation, international journal of fatigue 8(1), pp 17-21. doi: 10.1016/0142-1123(86)90042-3 [16] ngiau, c., kujawski, d. (2001). sequence effects of small amplitude cycles on fatigue crack initiation and propagation in 2024-t351 aluminum. international journal of fatigue 23, pp. 807–815. doi: 10.1016/s0142-1123(01)00033-0 [17] jurcevic, r., duquesnay, d.l., topper, t.h., pompetzki, m.a. (1990). fatigue damage accumulation in 2024-t351 aluminium subjected to periodic reversed overloads. international journal of fatigue 12(4), pp 259-266. doi: 10.1016/0142-1123(90)90453-l [18] pompetzki, m.a., topper, t.h., duquesnay, d.l., yu, m.t. (1990). effect of compressive underloads and tensile overloads on fatigue damage accumulation in 2024-t351 aluminum. journal of testing and evaluation, 18(1), pp. 53-61. doi: 10.1520/jte12451j [19] creager, m., paris, p.c. (1967). the elastic field near tip for blunt crack. international journal of fracture 3, p. 247. doi: 10.1007/bf00182890 [20] agbessi, k., saintier, n., palin-luc, t., (2013), high cycle multiaxial fatigue crack initiation: experimental observations and microstructure simulations. 21ème congrès français de mécanique, bordeaux. [21] zhang, j., johnston, j., chattopadhyay, a. (2017). physics-based multiscale damage criterion for fatigue crack prediction in aluminium alloy. fatigue & fracture of engineering materials & structures 37(2), pp. 119-131. doi: 10.1111/ffe.12090 [22] murakami, y. (1987). stress intensity factors handbook, pergamon press, oxford, 1, pp. 9-17. [23] náhlík, l., huta, p. and štegnerová, k. (2014). critical applied stresses for a crack initiation from a sharp vnotch, frattura ed integrità strutturale, 8(30), pp. 55-61. doi: 10.3221/igf-esis.30.08 [24] han, q., yaruwang, y., yin, y., wang, d. (2015). determination of stress intensity factor for mode i fatigue crack based on finite element analysis. engineering fracture mechanics, 138, pp. 118-126. doi: 10.1016/j.engfracmech.2015.02.019 [25] ricardo, l. c. (2017). crack propagation by finite element method, frattura ed integrità strutturale, 12(43), pp. 57-78. doi: 10.3221/igf-esis.43.04 [26] benachour, m., hadjoui, a., benguediab, m., benachour, n. 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can be opened with acrobat and adobe reader 5.0 and later.) >> /namespace [ (adobe) (common) (1.0) ] /othernamespaces [ << /asreaderspreads false /cropimagestoframes true /errorcontrol /warnandcontinue /flattenerignorespreadoverrides false /includeguidesgrids false /includenonprinting false /includeslug false /namespace [ (adobe) (indesign) (4.0) ] /omitplacedbitmaps false /omitplacedeps false /omitplacedpdf false /simulateoverprint /legacy >> << /addbleedmarks false /addcolorbars false /addcropmarks false /addpageinfo false /addregmarks false /convertcolors /converttocmyk /destinationprofilename () /destinationprofileselector /documentcmyk /downsample16bitimages true /flattenerpreset << /presetselector /mediumresolution >> /formelements false /generatestructure false /includebookmarks false /includehyperlinks false /includeinteractive false /includelayers false /includeprofiles false /multimediahandling /useobjectsettings /namespace [ (adobe) (creativesuite) (2.0) ] /pdfxoutputintentprofileselector /documentcmyk /preserveediting true /untaggedcmykhandling /leaveuntagged /untaggedrgbhandling /usedocumentprofile /usedocumentbleed false >> ] >> setdistillerparams << /hwresolution [2400 2400] /pagesize [612.000 792.000] >> setpagedevice microsoft word numero_57_art_15_3077 m. bentahar et alii, frattura ed integrità strutturale, 57 (2021) 182-194; doi: 10.3221/igf-esis.57.15 182 numerical modeling of the contact effect on the parameters of cracking in a 2d fatigue fretting model mohammed bentahar faculty of technology, university tahar moulay, saida, laboratoire labab, enp maurice audin, oran, algeria bentahae@yahoo.fr habib benzaama national polytechnic school of oran m.a., enpo, laboratoire labab, enp maurice audin, oran, algeria habenza@yahoo.fr mahmoudi noureddin faculty of technology, university tahar moulay, saida, laboratory gidd, university of relisane, algeria mahmoudi.noureddine@yahoo.fr abstract.the objective of this work is to study the effects of contact parameters on the cracking parameters of a specimen and a pad assembly. these parameters have been studied and evaluated by the finite element method analysis in two dimensions fretting fatigue model through the abaqus calculation code. different values of the coefficient of friction of 0.1, 0.3 and 0.6 were applied on the various lengths in contact for a = 0.1, 0.5 and 1mm. thus, on the various values of angle of orientation of the crack equal to 15 °, 30 ° and 45 °. in addition, elements of the type (cpe4r) and the criterion of maximum tangential stress were applied. the curves of the crack parameters such as the sif coefficients and the integral j were obtained and discussed. keywords: 2d crack; fem; fretting fatigue; stress intensity factor (sif); coefficient of friction (cof). citation: bentahar, m., benzaama, h., mahmoudi, n., numerical modeling of the contact effect on the parameters of cracking in a 2d fatigue fretting model,frattura ed integrità strutturale, 57 (2021) 182-194. received: 16.04.2021 accepted: 05.06.2021 published: 01.07.2021 copyright: © 2021 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. introduction retting fatigue is a mechanical phenomenon of damage that occurs between two assembled parts (a test tube and a pad), under a contact load and in the presence of repeated oscillatory or relative surface movement. indeed, several studies have been proposed in the literature to model the problems in fretting fatigue, among these studies we cite the work of kyvia et al [1] treated the different aspects related to the modeling of fretting fatigue by the fem method, to present common experimental setups and analytical solutions for thecylindrical contact. another numerical method used by hojjati et al [2] to predict both sides the initiation phase and the crack propagation. thus, to estimate the fracture life by fretting fatigue under a conforming contact configuration. julien et al [3] studied the propagation of fretting fatigue cracks by the use of f https://youtu.be/t1pivc3kgqu m. bentahar et alii, frattura ed integrità strutturale, 57 (2021) 182-194; doi: 10.3221/igf-esis.57.15 183 the fem method, to simulate and deduce the distributions of the stress intensity factor (sif) in the length of the crack front. thanh et al [4] proposed a new approach based on the evaluation of nucleation, and the lifetime of deterioration due to fretting fatigue, to measure the change of the central point of the power spectral density (cp -psd). in addition, nadeem ali bhatti, and abdel wahab [5] used three numerical models in fretting fatigue, to model the effect of in-phase and out-of-phase loads on contact stresses and damage initiation locations. qingmingetal [6] used the finite element method (fem), for different sizes, shapes and properties of inclusions, to study and analyze the effects of randomly distributed micro-inclusions on the fretting fatigue behavior of heterogeneous materials. antti et al [7] presented a robust wear simulation method, based on the finite element method, and adapted to contact friction. tongyan and abdel wahab [8] used the finite element method (fem) to study the evolution of contact variables and wear scars during the wear process by friction. antti et al [9] to assess the risk of friction in the large end performed a detailed contact analysis of a large connecting rod. jouko et al [10] studied the role of wear particle movements under axisymmetric loading conditions, of a flat on flat annular contact in a self-coupled hardened and tempered steel material. wijesuriya and mallikarachchi [11] evaluated finite element models and analytical techniques for fatigue fretting crack propagation. wang and abdel wahab [12] analyzed the wear characteristics in partial slip regime on the effects of loading conditions in fretting fatigue. chen et al [13] studied by the finite element method the initiation and growth of fretting fatigue cracks, in addition, they calculated the contact stress, to know the crack initiation angle by the criterion (mts). nitikornet al [14] carried out finite element fatigue fretting experiments, to study the influence of cylindrical contact on plate and on crack nucleation. the goal of this study is to model the effect of the variation of the coefficient of friction, on the parameters of cracking. more precisely, on the evaluation of the stress intensity factor in mode i and the contour integral j for a model in homogeneous material with linear and isotropic elastic behavior.this problem is studied in fretting fatigue, two cases of crack were studied with different positions, one of horizontal crack of angle α = 0 ° and another case of an inclined crack of α = 15, 30 and 45 °. crack modelization maximum tangential stress criterion his criterion, introduced by erdogan and sih [15] for elastic materials, indicates that the crack propagates in the direction for which the circumferential stress σθθ is maximum, it is a local approach since the direction of the crack growth is directly determined by the local stress field. according to this criterion, the growth of the crack follows the direction of (θ = θ0) which is perpendicular to the tangent of maximum stress. the angle of deviation of the crack θ0 can be obtained by:                       0 0 0 2 2 0, 0 0and (1)               1 3 3 (cos cos ) 3 (sin sin ) 2 2 2 24 2 i iik k (2) we can deduce:    sin (3cos 1) 0i iik k (3) so, we have: t m. bentahar et alii, frattura ed integrità strutturale, 57 (2021) 182-194; doi: 10.3221/igf-esis.57.15 184    2 1 1 tan( ) ( ) ( ) 8 2 4 4 i i ii ii k k k k (4) θ gives the direction of the maximum of the circumferential stress which determines the angle of bifurcation. different parameters to characterize the singular zone the characterization of the singular zone subjected to several essential parameters, which makes it possible to study this zone such as, the stress intensity factor k and the integral of the contour j. figure 1: singular zone meshing stress intensity factor saverio [16] defined the stress intensity factor k, which is the only significant parameter, which allows to know the state of stress and strain at any crack point.  ik f a (5) where, f is the geometric correction factor of the model used.          2 3 41.12 0.23( / ) 10.6 / w 21.7 / w 30.4 / wf a w a a a (6) where the stress intensity factor kii is calculated by the relation.    sin (3cos 1) 0i iik k (7) contour integral j several authors in fracture mechanics have allowed to model the problem of the presence of a crack in an indepth way and have developed the calculation methods. among these authors rice [17] and bui [18] with contour integrals (j), nguyen [19] and destuynder [20] by introducing an arbitrary field in the formulation of the integral they have approached. indeed, work has been developed on the basis of elasticity in small displacements and mainly addresses the first phase of the cracking process. relation betweenk and jparameters in the fracture mechanics, we have two eqns. (8) and (9) which allow to assemble the two parameters one obtains according to tran [21]:     2 1 i i dp j k da e (8)    2 2 1 ii ii dp j k da e (9) m. bentahar et alii, frattura ed integrità strutturale, 57 (2021) 182-194; doi: 10.3221/igf-esis.57.15 185 stress field in the crack front vicinity the stress field in 2d in the vicinity of the crack front, were proposed by tada et al. [22] by the general equation:        ,,,j ,, 2 i i iiiii i j k r f r (10) fig.2 shows the stress field near a crack point with the polar coordinates (r, θ). in addition, eqn. (11) which is illustrates the constraints on the two axes (x and y). figure 2: stress field in the crack front vicinity                             3 cos 1 sin sin 2 2 22 3 cos 1 sin sin 2 2 22 3 sin cos cos 2 2 22 i xx i yy i xy k r k r k r (11) singularity zone in modeling we have chosen cpe4r type elements for the modeling by abaqus. this type of element is used for 2d models. a reduced integration element (cpe4r) two-dimensional plane strain quadrilateral at 4 nodes (bilinear). this type of element is well suited for simulation. thus, one uses singular elements around the front of the crack. the types of these singular "quarter point" elements are collapsed quadratic elements. the mesh around the zone of singularity is refined according to the number of the contour, thus according to the size of the crack front. (a) (b) figure 3: collapsed quadrilateral element to obtain a triangular element b)the elements chosen types for modeling around of tow cracks tips. cpe4r m. bentahar et alii, frattura ed integrità strutturale, 57 (2021) 182-194; doi: 10.3221/igf-esis.57.15 186 fretting fatigue different geometric configurations used in fatigue fretting o apply the contact stress, three types of counter-body are generally used (fig. 4). the sphere/plane contact is preferred in the study of wear because it is easy to implement and facilitates the comparison with the pion-disc contact. the cylinder/plane contact is more often linked to the study of cracking because we can then formalize the loading in two dimensions and model it by finite elements. the plane/plane contact is used more and more. by varying the radius of curvature of the edges of the counter-body (zero for a straight edge), the contact pressure profile can be adjusted and thus more easily approach a real situation. sphere-plane cylinder-plane plane-plane figure 4: different geometric configurations used for fretting tests. coefficient of friction (cof) the coefficient of friction, µ, is a measure of the amount of friction that exists between two surfaces. a low value of the coefficient of friction indicates that the force required for sliding to occur is less than the force required when the coefficient of friction is high. the value of the coefficient of friction is given by:     frictional force normal force (12) the transposition gives: friction force = µ × normal force. the friction coefficient is the ratio of a force to a force and therefore has no units bird and chivers [23]. (a) (b) figure 5: model to model fretting fatigue and initial cracking; a) slave-master model of fretting fatigue; b) boundary conditions and dimensions of model. numerical model for modeling n our model, the dimensions of the mesh are: height b = 8mm and width c = d = 7mm, the length of the horizontal crack has dimensions a = 0.1, 0.5, and 1mm. a 4-node (bilinear) two-dimensional plane strain quadrilateral reduced integration element (cpe4r) was used around the contact zone (fretting fatigue). the number of elements t i m. bentahar et alii, frattura ed integrità strutturale, 57 (2021) 182-194; doi: 10.3221/igf-esis.57.15 187 of this model is 180436 and the number of nodes is 183916. coefficients of friction (cof) of 0.1, 0.3 and 0.6, were used in this study. the steel structure, the elastic material parameters are e = 72.10 gpa and ν = 0.3. the structure is subjected to uniform tensile stress, normal load, the pressure load were considered σ = 100 mpa, 50n and 50n, respectively, the fixed support was applied to the lower surface of the structure. the crack is inclined by the angle α = 15 °, 30 ° and 45 °. results and discussions he variation of the stress intensity factor as a function of (a/w) is shown in (fig. 6). from this comparison, we show that the value of ki is much higher than that of kii. for the modeling of the problems in fretting fatigue, these comparisons are confirmed by numerous studies kimura and sato [24], cho [25], giner et al [1] and as a function of the crack length have been presented by pitta et al [26], hojjati et al [27] and ackiel et al [28]. thus, these results were confirmed by nandish et al [29] on crack propagation. indeed, kimura and sato [24] obtained that the stress intensity factor ki in fatigue by fretting has higher values compared to the study without fretting. a) b) figure 6: the variation of the sif factor along the ratio (a/w) a); and b)the variation of the (j) in function of crack length. fretting fatigue from a horizontal crack the figure below presents the model in contact with fretting fatigue in detail, in precision the contact surface. thus, the boundary conditions of a horizontal crack of α = 0°. figure7: fem model and contact zone in the case α = 0°. t m. bentahar et alii, frattura ed integrità strutturale, 57 (2021) 182-194; doi: 10.3221/igf-esis.57.15 188 a) b) c) figure 8: the evolution of the fic as a function of time increment with cof a) 0.1, b) 0.3 and c) 0.6α = 0°. the variation of the stress intensity factor as a function of the increment of the cracking time in fretting fatigue, for the model studied is presented on fig. 8. one uses the various crack lengths (a) = 0.1, 0.5 and 1.0 mm and coefficient of friction 0.6 for the problem of fritting fatigue. indeed, we notice that the increase in the time increment causes an increase in ki, and a decrease in kii of the same length and the same coefficient of friction. in addition, the increase in the coefficient of friction in the studied case α = 0 ° causes a decrease in ki and kii. these results were obtained by sallam et al [30] in the case of the effects of the coefficient of friction on the stress intensity factor concerning the ki. the rate of increase of kii is small compared to ki. fig. 9 shows the evolution of the integral of the contour (j) as a function of the time increment for the cases of cof = 0.1, 0.3 and 0.6 between the three cases of lengths a = 0.1, 0.5 and 01mm, at from this comparison. the first three values are almost zero and linear. it can also be observed that, with the increase of the time increment, there is an increase in (j) of the same length and the same coefficient of friction from the third time increment. however, there is a decrease in the results of (j) for different friction coefficients between them. fretting fatigue from an inclined crack the following model shows the fatigue fretting of two parts in contact with each other and contains a crack inclined by the angle α = 15 °, 30 ° and 45 ° with a coefficient of friction 0.6. the sif evolution as a function of the time increment with a friction coefficient 0.6 is indicated in (fig.11). this comparison is carried out on the different crack lengths for a = 0.1, 0.5 and 01mm and the angle inclination α = 15 ° (fig.11a), α = 30 ° (fig.11b) and α = 45 ° (fig.11c) for the fretting fatigue model. in addition, the increase in the increment time causes a decrease in ki and an increase in kii on the contrary for the comparison of the results obtained m. bentahar et alii, frattura ed integrità strutturale, 57 (2021) 182-194; doi: 10.3221/igf-esis.57.15 189 for α = 0 °.however, the value of kii is almost linear is equal to 0 in the case of (a = 0.1mm) with (α = 15 °), but kii less than (0) in the case of a = 0.5mm with (α =45 °).moreover, the results obtained from fic are proportional to the crack length. a) b) c) figure 9: the evolution of the integral of the contour (j) as a function of time increment with cof a) 0.1, b) 0.3 and c) 0.6α =0°. figure10: fretting fatigue model with an initial inclined crack α = 15°, 30° and 45°. m. bentahar et alii, frattura ed integrità strutturale, 57 (2021) 182-194; doi: 10.3221/igf-esis.57.15 190 a) b) c) fig. 11: the evolution of the fic as a function of time increment with cof 0.6 and α = 15°, 30° and 45°. a) b) m. bentahar et alii, frattura ed integrità strutturale, 57 (2021) 182-194; doi: 10.3221/igf-esis.57.15 191 c) figure 12: the evolution of the integral of the contour(j) as a function of time increment with cof 0.6 and α = 15°, 30° and 45°. fig. 12 shows the evolution of the fic as a function of time increment with a friction coefficient 0.6 and the angle of inclination α = 15° (fig. 12a), α = 30° (fig. 12b) and α= 45° (fig.12c), the values of (j) are proportional to the crack length.however, increasing the time of the increment causes an increase in (j) in all three cases of the crack length.the value of (j) is increased by increasing the time increment and the tilt angle α. the tables below explain the different results of comparison between the angles of inclination and the crack length concerning the sif (tab. 1). tab. 2 shows the results of the integral of the contour (j). α=0° α=15° α=30° α=45° 𝑎 ki kii ki kii ki kii ki kii 0.1 51.96 -15.83 51.74 -1.654 50.85 11.39 41.04 14.04 0.5 136.7 -20.12 135.3 9.121 122.4 32.90 69.98 48.97 1.0 216.1 -24.35 215.8 21.21 184.4 54.39 138.2 70.03 table1: the different results of sif comparisons between tilt angles and crack length. α=0° α=15° α=30° α=45° 𝑎 j j j j 0.1 3.9551e-08 3.7222e-08 3.7717e-08 2.6127e-08 0.5 2.5744e-07 2.5544e-07 2.2318e-07 6.9398e-08 1.0 6.2125e-07 6.5278e-07 5.1345e-07 3.3319e-07 table2:different results of comparison of the integral of the contour (j) between the angles of inclinationand the crack length. m. bentahar et alii, frattura ed integrità strutturale, 57 (2021) 182-194; doi: 10.3221/igf-esis.57.15 192 a) b) figure 13: sif evolution: a)as a function of the crack length (a);b) as a function of the angle (α) fig. 13 shows the evolution of the stress intensity factor (sif) as a function of the length of the crack in fig. (13a) and as a function of the angle (α) in fig. (13b).in addition, the angle of the crack α increases ki decreases for the same α as the length of the crack increases.fayed [31] justified that ki increases for higher crack tilt angles, i.e. α> 60° and the rate of increase of kii is relatively low when the ratio (a/w) increases. a) b) figure 14: the evolution of the integral of the contour j: a)as a function of the crack length (a);b) as a function of the angle (α). fig. 14 shows the integral of the contour (j) as a function of the crack length in fig. (14a) and as a function of the angle (α) in fig. (14b) for different crack lengths (a).the increase in crack length causes an increase in (j), these forms of results were obtained by margi et al [32].in addition, the results obtained are proportional, and the increase in the angle (α) fig. (14b) causes a decrease in (j) in all cases of the crack length.the low rate of decrease of (j) for the low crack length a = 0.1mm is high for a = 0.5mm and 1.0mm. especially from α> 20°. conclusion wo cases of fretting fatigue were studied, firstly the contact in fretting fatigue concerning a horizontal crack and the other study based on an inclined crack for different values of angles α = 15 °, 30 ° and 45 °. the finite element method was used to model the contact between the two parts. it is observed that with the increase of the time increment of the load the integral of the contour j increases, for the different cases of the angle of inclination of the crack. t m. bentahar et alii, frattura ed integrità strutturale, 57 (2021) 182-194; doi: 10.3221/igf-esis.57.15 193 the results obtained in our work justified, that the effects of contact to influence important on the parameters of crack. thus, the low value of (cof) gives results of stress intensity factor (ki) in mode i higher in fretting fatigue. the results obtained show that the coefficient of friction of a low value causes a time is higher compared to a higher coefficient of friction for the case of a rectilinear crack of α = 0°. there is a proportionality between the results obtained from fic and the integral of the contour (j) as a function of the time increment of the load in fretting fatigue. references [1] pereira, k. libardo v. vanegas-useche and m. a. wahab, (2020). aspects of fretting fatigue finite element modelling computers, materials & continua cmc, 64(1), pp.97-144. [2] hojjati-talemi, r., wahab, m. a.,giner, e.,sabsabi, m. (2013). numerical estimation of fretting fatigue lifetime using damage and fracture mechanicsv 52, pp. 11–25.doi:10.1007/s11249-013-0189-8. [3] julien, s., siegfried, f., georges, c., christine, y.and fikri, h. (2020). shear driven crack arrest investigation under compressive state prediction of fretting fatigue failure of aluminium strands, international journal of fatigue, 136, 105589. doi: 10.1016/j.ijfatigue.2020.105589. [4] thanh, q. n., hieu, c.d., luan. c. v., nguyen, h. x. and nhi, k.n. (2020). fretting fatigue damage nucleation and propagation lifetime using a central point movement of power spectral density, shock and vibration, 4985134, doi: 10.1155/2020/4985134 [5] nadeem, a. b. and magd, a.w. (2017). finite element analysis of fretting fatigue under out of phase loading conditions,materials science, doi:10.1016/j.triboint.2017.01.022 [6] qingming, d., nadeem, b., xiaochun, y. and magd, a.w. (2018). numerical modeling of the effect of randomly distributed inclusions on fretting fatigue-induced stress in metals, metals, 8, 836. doi:10.3390/met8100836. [7] antti, m., janne, j., jouko, h., tero, f. and arto, l.(2020). fem-based wear simulation for fretting contacts, rakenteiden mekaniikka, journal of structural mechanics, 53(1), pp.20-27, doi: 10.23998/rm.76261. [8] tongyan, y. and magd, a. w.(2017). finite element analysis of fretting wear under variable coefficient of friction and different contact regimes, tribology international, 107, pp. 274-282. doi: 10.1016/j.triboint.2016.11.044. [9] antti, m., jussi, g., anton, l. and tero, f. (2017). arge bore engine connecting rod fretting analysis rakenteidenmekaniikka, journal of structural mechanics, 50(3), pp.239-243. doi: 10.23998/rm.64914. [10] jouko, h., arto l. and antti, m. (2016).third particle ejection effects on wear with quenched and tempered steel fretting contact, journaltribology transactions, 60(11), pp. 70-78. doi: 10.1080/10402004.2016.1146813. [11] wijesuriya, h.s. and mallikarachchi, h.m.y.c. (2018). predicting fretting fatigue crack propagation using finite element analysis,moratuwa engineering research conference (mercon). doi: 10.1109/mercon.2018.84218862018. [12] wang, s.and abdel wahab, m. (2020) effect of loading conditions in fretting fatigue on wear characteristics, proceedings of the 13th international conference on damage assessment of structures. [13] chen, h., dasheng, w., yanrong, w. and xianghua, j. (2019). introduction of fretting-contact-induced crack closure: numerical simulation of crack initiation and growth path in disk/blade attachment, chinese journal of aeronautics, 32,(8), pp 1923-1932. doi: 10.1016/j.cja.2019.04.011. [14] nitikorn, n., anchalee, m. and chaosuan, k. (2017). fretting fatigue with cylindrical-on-flat contact: crack nucleation, crack path and fatigue life, materials(basel), 10(2). doi: 10.3390/ma10020155. [15] erdogan, f. and sih, g.c. (1963).on the crack extension in plates under plane loading and transverse shear, journal of basic engineering, 85, 19-527. [16] saverio, f. (2014) modélisation tridimensionnelle de la fermeture induite par plasticité lors de la propagation d’une fissure de fatigue dans l’acier 304l thèse de doctorat, l’école nationale supérieure de mécanique et d’aérotechnique. [17] rice, j.r. (1968). a path independent integral and the approximate analysis of strain concentrations by notches and cracks. j. of appl. mech., 35, pp.379-386. [18] bui, h.d. (1973). dualité entre les intégrales de contour. compte rendu acad. sciences, t. 276, paris. [19] nguyen, q.s. (1980). méthodes énergétiques en mécanique de la rupture. j. de méca.,19(2), pp. 363-386. [20] destuynder, ph. and djaoua, m. (1981). sur une interprétation mathématique de l’intégrale de rice en théorie de la rupture fragile, math. meth. in the appl. sci., 3, pp. 70-87. [21] tran, a. t. (2011). etude du delaminage en mode ii de composites unidirectionnels soumis a des sollications rapides, approche globale et approche locale, ph.d. thesis, ecole doctorale n˚432 : sciences des métiers de l’ingénieur paris. m. bentahar et alii, frattura ed integrità strutturale, 57 (2021) 182-194; doi: 10.3221/igf-esis.57.15 194 [22] tada, h.p., paris, p.c. and irwin, g.r. (2000). the stress analysis of cracks handbook, american society of mechanical engineering. [23] bird, j. o., chivers, p. j . (1993). friction, newnes engineering and physical science pocket book, pp. 235-237. [24] kimura, t. and sato, k. (1999) stress intensity factors for oblique cracks in fretting fatigue transactions on engineering sciences, 24. [25] cho, j.r. (2014). stress intensity factor calculation for 2-d cracked bodies by petrov-galerkin natural element method advences in civil en vironmental, and materiels research (acem14) busan, korea. [26] pitta, s.,rojas,j. i. and crespo,d. (2017). comparison of fatigue crack growth of riveted and bonded aircraftlap joints made of aluminium alloy 2024-t3 substrates – a numerical study, 6th international conference on fracture fatigue and wear, iop conf. series: journal of physics: conf. series 843012035. [27] hojjati, t.r.and abdel wahab, m. (2012). xfem for fretting fatigue: straight vs mixed mode crack propagation journal carpinteri a, iacoviello f, pook lp, susmel l, eds proceedings of the 4th international conference on crack paths, gaeta, italy, pp. 351-358. [28] mohamed, m.a. manurung, y.h.p., ghazali,f.a. and karim,a.a. (2015).finite element-based fatigue life prediction of a loadcarrying cruciform joint, journal of mechanical engineering and sciences (jmes) 8, pp. 1414-1425. doi: 10.15282/jmes.8.2015.16.0138. [29] nandish, r. v., niranjanpattar, raja reddy, c v., vizhian, s. p. and ramachandra, s. (2013).computational analysis of stressintensity factors for a single-edgenotch tension specimen by astress function int. j. mech. eng. &rob. res. 2(4). [30] sallam, h.e.m., sisi, a.e.a. el. and matar, e.b. (2011). effect of clamping force and friction coefficient on stress intensity factorof cracked lapped joints, engineering failure analysis, 18, pp. 1550–1558. [31] fayed, a. s. (2017). numerical analysis of mixed mode i/ii stress intensity factors of edge slant cracked plates engineering solid mechanics pp. 61-70. [32] margi, g., himanshu, p. and sachin, k. (2020). elasto-plastic fracture modeling for crack interaction with xfemtransactions of the indian institute of metals 73, pp. 1679–1687. microsoft word 2236 a. spagnoli et alii, frattura ed integrità strutturale, 47 (2019) 401-407; doi: 10.3221/igf-esis.47.30 401 focussed on “crack paths” size effect on the fracture resistance of rough and frictional cracks andrea spagnoli, andrea carpinteri, michele terzano department of engineering and architecture, university of parma, parco area delle scienze 181/a, 43124 parma, italy spagnoli@unipr.it abstract. elastic fracture mechanics commonly defines the fracture resistance of brittle materials within an idealized picture of planar and traction-free cracks. an efficient approach to describe the interface conditions in real cracks, such as those occurring in concrete, ceramics or stones, is to include the effect of both roughness and friction by means of a constitutive relationship between opposite points on the interface. in the present paper, we use a numerical technique, based on the solution of singular integral equations, to derive the near-tip stress field with various interface conditions. then, the technique is applied to investigate the size effect of the interface roughness, where such an effect is related to the ratio between the characteristic length of the roughness and the nominal length of the crack. it is found that the resulting near-tip stresses can be profoundly influenced by the crack path, particularly for short cracks. keywords. interface models; friction; roughness; distributed dislocation technique; size effect. citation: spagnoli, a., carpinteri, a., terzano, m., n., size effect on the fracture resistance of rough and frictional cracks, frattura ed integrità strutturale, 47 (2019) 401-407. received: 26.10.2018 accepted: 08.11.2018 published: 01.01.2018 copyright: © 2019 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. introduction n linear elastic fracture mechanics (lefm), the stress field in proximity of the tip of a crack is described by a single parameter, the stress intensity factor (sif), which is consequently used to give a measure of the fracture resistance of a certain material. such an approach is based on the assumption of small-scale yielding, and considers a crack with flat and smooth interfaces, neglecting any interaction between its surfaces. this rather idealised picture might be satisfactory for mode i crack growth, because the surface interaction is somehow limited; however, when the fracture surfaces are displaced relative to one another in shear, the interaction cannot be neglected. observations on the failure of quasi-brittle and brittle materials, such as concrete, ceramics, rocks or glass, revealed that crack growth does not proceed planarly, but on the contrary tortuous topologies of the crack paths are noticed. a combination of different factors is used to explain the observed behaviour, including the effect of far field multi-axial stresses, residual stresses, microstructural inhomogeneities, and material properties dispersion [1–5]. in many polycrystalline and aggregate materials, the crack surfaces are not macroscopically flat, instead they consist of several asperities, with peculiar size, which interact in a complex combination of sliding, sticking, climbing and deforming [6]. as a consequence, the fracture strength can be strongly altered, particularly in the presence of mixed-mode loading as a result i http://www.gruppofrattura.it/va/47/2236.mp4 a. spagnoli et alii, frattura ed integrità strutturale, 47 (2019) 401-407; doi: 10.3221/igf-esis.47.30 402 of far field stresses, or geometrical and material discontinuities. specifically, ballarini and plesha [7] noticed that a pure mode i crack growth occurs in very few cases, since the mode mixity is often a result of the crack tortuosity. the same authors presented an interface model, previously proposed by plesha [8], to deal with the effect of roughness and friction along the crack surfaces in a simplified way, and included such a model in a numerical algorithm based on the solution of singular integral equations. the same effect, appropriately defined ‘sliding mode crack closure’, was observed by tong et al. [9] in the analysis of cracks under shear fatigue loading. on the other hand, the interaction of the crack surfaces through the asperities generates a mode i component, even if the remote loading is purely mode ii. this phenomenon is generally known as dilatancy, that is, an opening displacement caused by the coupling between normal and tangential directions along the nominal crack line. in the present paper, we adopt an interface model to account for the effects of friction and roughness, which follows from the work of plesha [8], and whose complete formulation has been firstly presented by the authors in [10]. frictional effects are described with the classical coulomb’s law, while the roughness is exemplified by a uniform distribution of rigid saw-tooth asperities. the solution technique follows an analytical method derived from the application of the complex function theory, generally known as the distributed dislocation technique (ddt), which has been applied successfully in the solution of crack problems with different geometric configurations [11]. we have previously showed its potential in characterising the near-tip stress fields of cracks under mixed mode loading, specifically the effect of the interface interaction with respect to the onset of crack propagation under monotonic loading [12]. the aim of this study is to further explore the effects of interface interaction, by exploring the possible influence on the fracture resistance of a size effect, introduced by a characteristic length of the material roughness. it is well known that the strength of materials, both the fracture resistance and the fatigue limit, is generally affected by the size of the specimen or its microstructural properties. studies have tried to explain this phenomenon by adopting a fractal description of the microstructure of brittle and disordered materials, and noticed that the fatigue crack growth rate depends not only on a fractal dimension but also, in an explicit fashion, on the crack length [13–16]. for sinusoidally-patterned surfaces, the size effect on the critical load has been related to the ratio between the amplitude and the wave length [17]. in this work, the size effect is related to the ratio between the crack roughness period and the length of the crack. specifically, we explore the influence of both the height and the length of the saw-tooth asperities on the mode ii stress intensity factor, under a mixed-mode loading condition. the paper is structured in two main sections. we start with a formulation section where we review the interface model and give some details on the numerical algorithm that we have used to compute the stress intensity factor; following, we present the results, obtained by an application of the method to a simple edge-cracked geometry, and discuss the implications of the interface asperities and the size effect. figure 1: a) the saw-tooth asperity model, showing the local and global reference systems adopted in the formulation, eqns. (1)-(4). b) schematic model of the geometry with an edge crack of length c. a. spagnoli et alii, frattura ed integrità strutturale, 47 (2019) 401-407; doi: 10.3221/igf-esis.47.30 403 formulation description of the model n order to account for the effects of friction and roughness, we make use of an interface model formulated as a constitutive relationship between opposing points along the crack, written in the form of a classic elastic-plastic law of small strain plasticity. globally, the crack is smooth and frictionless and the surface interference is modelled by means of bridging stresses between the crack surfaces. in this fashion, we can obtain a straightforward implementation within the distributed dislocation technique, as the bridging stresses, computed at a discrete number of points, are simply added to the stress distribution resulting from the remote loads. let us define the relative displacement (increments) between two opposing points of the crack as composed of a recoverable elastic part dwie, related to the remote stress field, and a non-recoverable plastic part dwip, which accounts for frictional sliding and dilatancy. the stresses on the crack interface are related to the displacement increments by means of interface stiffnesses eijep: , , ep i ij j nd d i j te w   (1) where t,n denote, respectively, the tangential and normal directions with respect to the nominally flat crack surface (fig. 1a). in order to compute the interface stiffness, we need to introduce a slip function f and a slip potential g. it can be noticed that, since coulomb’s friction law is non-associated, f and g do not coincide, and the direction of slip is given by the gradient of g. therefore, we can express the non-recoverable displacement increment as: 0 if f 0 or df=0 if f= df=0 p p i i i dw dw g        (2) while the interface stiffness eijep is computed according to the following equation: if f 0 or df=0 if f=df=0 iq pj p qep ep ij ij ij pq p q f g e e e e e e f g e                 (3) eij is the elastic interface stiffness, which is taken two to four orders of magnitude greater than the elastic modulus of the medium itself, in order to assure the impenetrability between the crack surfaces and ensure good numerical compatibility. the surface roughness is described through a saw-tooth model, characterised by a constant angle , a mean length of the asperities equal to 2l and a height h. the coefficient of coulomb’s friction f is kept constant. with the previous assumptions, we obtain the following formulation of f and g: 1 2 1 sin cos ( cos sin ) sin cos n t n t n t f f f g                         (4) we can define a crack size parameter by considering the ratio c/l, where ideally c/2l approaching the unity identifies the case of a short crack. the parameters used to describe the surface roughness are somehow related to the specific material, and the scale length might differ of several orders of magnitude. for instance, the fracture process in concrete is influenced by particles and voids whose sizes are in the order of few nanometres, but if the aggregate is particularly coarse the size of the irregularities can go up to some millimetres [18]. it is also common to evaluate roughness through a digitalisation of the crack profiles, and consider it as a high-frequency shortwave length component of the measured surface, characterised through average measures or peak-to-valley heights [19]. the numerical algorithm in this sub-section, we briefly summarise the numerical algorithm used in the present work, which is based on the application of the distributed dislocation technique, combined with the interface model introduced above. we begin by i a. spagnoli et alii, frattura ed integrità strutturale, 47 (2019) 401-407; doi: 10.3221/igf-esis.47.30 404 introducing a suitable distribution of dislocations along the crack surface: dislocations are commonly used in the theory of elasticity as kernel of integral equations, to describe the singular stress state occurring near a source of discontinuity, such as the tip of a crack. the stresses thereby obtained, known as the corrective term, assume the following formulation (refer to fig.1b for an explanation of the variables): 0 ( )2 ( ) ( ) ( , ) ( 1) c i i j ij b x b f x d x                    (5) where  is the elastic shear modulus and  is the kolosov constant of the material. fij are influence functions, whose expression for the case considered here can be found in the literature [11] and bi() is the dislocation density, which yields the relative displacement between the crack surfaces by integration. applying the superposition principle, we obtain the stress state along the crack surface, adding the stresses generated by the remote loads (x) to the corrective term in (5). if we assumed a traction-free crack, the overall stress state on the surfaces would have to be null; here, on the contrary, we need to add the bridging stresses  b(x) resulting from the surface interaction, so that the integral formulation takes the following form: 0 ( )2 ( ) ( ) ( , ) ( ) ( 1) c bi j ij b x b f x d x x                   (6) the standard method of solution for integral equations of this kind consists in normalising the interval between [-1,1], so that the variables x, are replaced by u and v. we can also express the unknown dislocation densities as follows: 1 ( ) ( ) ( ) ( ) , , 1 j j j u b u u u u j x y u         (7) where 𝜔(u) is the fundamental singular function while 𝜙j(u) are the unknowns. here we have assumed the dislocation densities to be square root singular at the tip of the crack (u=+1) and bounded to zero at the crack mouth (u=-1). using gauss-chebyshev numerical quadrature, the integral eqn. (6) is converted in a set of non-linear algebraic equations: 1 ( )2 ( ) ( ) ( , ) ( ) ( ) ( 1) n bi k k j k ij k l i l i l k l k u w u u f u v v v v u                   (8) where w(uk) are weight functions. we recall that the integration points uk are the points at which the displacements are computed, whereas the collocation points vl are those at which we evaluate the stresses. in the usual applications of the dislocation methods, the right-side of eqn. (8) is known, often null in the case of open cracks or of separating contacts, so that the system of algebraic equations is linear. instead, in our case the bridging stresses are function of the relative displacements, through the constitutive relationship of eqns. (1)-(5). the displacements can be obtained from the dislocation densities through the following integration: 1 ( ) ( )i i u w u b u du  (9) the resulting system is therefore non-linear. an efficient technique of solution is achieved if we introduce a compliance matrix, which directly connects stresses and displacements so that we eliminate the need to integrate the dislocation densities at each step of the incremental solution. for each increment of the external loads, the stiffness matrix eijep in (5) needs to be updated, using the configuration of stresses and displacements at the beginning of the increment. details of the technique are provided in [12]. the stress intensity factors at the crack tip are computed from the unknown functions (j), through an extrapolation to the singular point u=+1: a. spagnoli et alii, frattura ed integrità strutturale, 47 (2019) 401-407; doi: 10.3221/igf-esis.47.30 405 2 2 2 ( 1), 2 ( 1) ( 1) ( 1) i n ii tk c k c                 (10) results n this section we summarise the results that we have obtained, applying the method to a simple geometry, consisting of an edge crack in a half-plane. the material is linear elastic and a state of plain strain is assumed. compressive and tangential stresses are applied remotely, such that uniform normal and shear stresses, p and q respectively, act along the crack line (see fig. 1b). in order to explore the influence of the roughness ratio, we have performed several analyses, varying the ratio c/l and computed the mode ii sif at the crack tip. all the results presented in this section are normalised with respect to the crack length c and the mean normal pressure p. in fig.2 we show the variation of the normalised sif during the increment of external loads, considering two different values of the asperity angle 𝛼. we observe that kii is null until the stress ratio q/p reaches 0.5, which is the value of the coefficient of friction f chosen in the simulation: this was expected, since the stress distribution due to the external loads is constant. for q/p>0.5, we notice an increase, which is more pronounced for shorter cracks, i.e. for c/l tending to 1. in fig.3 we show the variation of the sif, evaluated at q/p =1, with the angle of roughness, for three different values of c/l. we can appreciate the effect of the roughness angle, which causes a decrease of the mode ii sif: as already noticed in [12],the reason for this is that the surface roughness generates a resistance to sliding, which is added to the one due to friction. however, while the decrease is almost linear for short cracks, for bigger c/l ratios we observe a greater reduction, although it appears to attenuate at bigger roughness angles. figure 2: the normalised stress intensity factor kii versus the applied load ratio q/p. different relative crack lengths c/l are considered. f =0.5. (a) angle of the surface asperity =2° and (b) angle of the surface asperity =5°. the inset shows the loading history. finally, we explore the effect of the ratio c/l, considering two different cases: in fig.4a, we keep the angle 𝛼 constant, while in fig.4b we keep constant the height h of the asperities. indeed, throughout the other simulations, we have always kept the asperity angle constant: as a consequence, a change in the ratio c/l implies also a change in the height h of the saw-tooth. conclusions he crack tip stress fields in brittle and quasi-brittle material can be highly influenced by the surface interaction due to microscopic asperities. as a result, the stress intensity factor might differ from the theoretical values computed according to the relationships of lefm, which assumes a crack with flat and smooth surfaces. i t a. spagnoli et alii, frattura ed integrità strutturale, 47 (2019) 401-407; doi: 10.3221/igf-esis.47.30 406 in the present paper a numerical algorithm, based on the distributed dislocation technique, is used in combination with a non-linear interface model to characterise the near-tip stress field of rough and frictional cracks. the interface roughness and the frictional effects are included through a rigid-plastic constitutive relationship between stresses and relative displacements along the crack. the stress intensity factors are computed through a numerical solution of singular integral equations, adopting an iterative algorithm developed by the authors, which has proved to be effective in different geometries and loading scenarios. specifically, the model is used here to examine the influence of a size effect parameter, related to the ratio between the crack roughness period and the length of the crack. the results confirm a crack shielding effect due to roughness and friction, that is, a reduction in the mode ii stress intensity factor for increasing roughness (notably, the asperity angle). moreover, we show that the crack shielding is more pronounced for longer cracks. figure 3: variation of the normalised sif kii with respect to the roughness angle, for q/p=1. figure 4: (a) variation of the normalised sif kii with respect to the relative crack length c/l, for q/p =1. the angle of the surface asperity is kept constant. (b) variation of the normalised sif kii with respect to the relative crack length c/l, for q/p =1. the height of the surface asperity is kept constant. the coefficient of friction is equal to 0.5 in all the simulations. a. spagnoli et alii, frattura ed integrità strutturale, 47 (2019) 401-407; doi: 10.3221/igf-esis.47.30 407 references [1] kitagawa, h., yuuki, r., and ohira, t. (1975). crack-morphological aspects in fracture mechanics, eng. fract. mech., 7(3), pp. 515–529, doi: 10.1016/0013-7944(75)90052-1. [2] suresh, s. (1983). crack deflection: implications for the growth of long and short fatigue cracks, metall. trans. a, 14(11), pp. 2375–2385, doi: 10.1007/bf02663313. [3] evans, a.g. and hutchinson, j.w. (1989). effects of non-planarity on the mixed mode fracture resistance of bimaterial interfaces, acta metall., 37(3), pp. 909–916, doi: 10.1016/0001-6160(89)90017-5. [4] shah, s.p., swartz, s.e., and ouyang, c. (1995).fracture mechanics and compressive failure. fracture mechanics of concrete: applications of fracture mechanics to concrete, rock and other quasi-brittle materials, wiley, pp. [5] brighenti, r., carpinteri, a., and spagnoli, a. (2014). influence of material microvoids and heterogeneities on fatigue crack propagation, acta mech., 225(11), pp. 3123–3135, doi: 10.1007/s00707-014-1111-7. [6] bian, l.-c., fawaz, z., and behdinan, k. (2006). a mixed mode crack growth model taking account of fracture surface contact and friction, int. j. fract., 139(1), pp. 39–58, doi: 10.1007/s10704-006-6633-0. [7] ballarini, r. and plesha, m.e. (1987). the effects of crack surface friction and roughness on crack tip stress fields, int. j. fract., 34(3), pp. 195–207, doi: 10.1007/bf00019717. [8] plesha, m.e. (1987). constitutive models for rock discontinuities with dilatancy and surface degradation, int. j. numer. anal. methods geomech., 11(4), pp. 345–362, doi: 10.1002/nag.1610110404. [9] tong, j., yates, j.r., and brown, m.w. (1995). a model for sliding mode crack closure part ii: mixed mode i and ii loading and application, eng. fract. mech., 52(4), pp. 613–623, doi: 10.1016/0013-7944(95)00045-w. [10] carpinteri, a., spagnoli, a., terzano, m., and vantadori, s. (2017). fracture toughness of rough and frictional cracks emanating from a re-entrant corner, frat. ed integrita strutt., 41, pp. 175–182, doi: 10.3221/igf-esis.41.24. [11] hills, d.a., kelly, p.a., dai, d.n., and korsunsky, a.m. (2013). solution of crack problems: the distributed dislocation technique, springer netherlands. [12] spagnoli, a., carpinteri, a., and terzano, m. (2018). near-tip stress fields of rough and frictional cracks under mixedmode loading, fatigue fract. eng. mater. struct., 41(4), pp. 2099–2109, doi: 10.1111/ffe.12765. [13] carpinteri, a. (1994). fractal nature of material microstructure and size effects on apparent mechanical properties, mech. mater., 18(2), pp. 89–101, doi: 10.1016/0167-6636(94)00008-5. [14] carpinteri, a. and spagnoli, a. (2004). a fractal analysis of size effect on fatigue crack growth, int. j. fatigue, 26(2), pp. 125–133, doi: 10.1016/s0142-1123(03)00142-7. [15] carpinteri, a., spagnoli, a., vantadori, s., and viappiani, d. (2008). influence of the crack morphology on the fatigue crack growth rate: a continuously-kinked crack model based on fractals, eng. fract. mech., 75, pp. 579–589, doi: 10.1016/j.engfracmech.2007.05.007. [16] carpinteri, a., spagnoli, a., and vantadori, s. (2010). a multifractal analysis of fatigue crack growth and its application to concrete, eng. fract. mech., 77(6), pp. 974–984, doi: 10.1016/j.engfracmech.2010.01.019. [17] cordisco, f.a., zavattieri, p.d., hector, l.g., and carlson, b.e. (2016). mode i fracture along adhesively bonded sinusoidal interfaces, int. j. solids struct., 83, pp. 45–64, doi: 10.1016/j.ijsolstr.2015.12.028. [18] shah, s.p. and ouyang, c. (1994). fracture mechanics for failure of concrete, annu. rev. mater. sci., 24(1), pp. 293– 320. [19] xie, h.b., jiang, z.y., and yuen, w.y.d. (2011). analysis of friction and surface roughness effects on edge crack evolution of thin strip during cold rolling, tribol. int., 44(9), pp. 971–979, doi: 10.1016/j.triboint.2011.03.029. << /ascii85encodepages false /allowtransparency false /autopositionepsfiles true /autorotatepages /none /binding /left /calgrayprofile (dot gain 20%) /calrgbprofile (srgb iec61966-2.1) /calcmykprofile (u.s. web coated \050swop\051 v2) /srgbprofile (srgb iec61966-2.1) /cannotembedfontpolicy /error /compatibilitylevel 1.4 /compressobjects /tags /compresspages true /convertimagestoindexed true /passthroughjpegimages true /createjobticket false /defaultrenderingintent /default /detectblends true /detectcurves 0.0000 /colorconversionstrategy /cmyk /dothumbnails false /embedallfonts true /embedopentype false /parseiccprofilesincomments true /embedjoboptions true /dscreportinglevel 0 /emitdscwarnings false /endpage -1 /imagememory 1048576 /lockdistillerparams false /maxsubsetpct 100 /optimize true /opm 1 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/hrv (za stvaranje adobe pdf dokumenata najpogodnijih za visokokvalitetni ispis prije tiskanja koristite ove postavke. stvoreni pdf dokumenti mogu se otvoriti acrobat i adobe reader 5.0 i kasnijim verzijama.) /hun 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/pdfxoutputintentprofileselector /documentcmyk /preserveediting true /untaggedcmykhandling /leaveuntagged /untaggedrgbhandling /usedocumentprofile /usedocumentbleed false >> ] >> setdistillerparams << /hwresolution [2400 2400] /pagesize [612.000 792.000] >> setpagedevice microsoft word numero_33_art_23 e. maggiolini et alii, frattura ed integrità strutturale, 33 (2015) 183-190; doi: 10.3221/igf-esis.33.23 183 focussed on characterization of crack tip fields effective stress assessment at rectangular rounded lateral notches enrico maggiolini, roberto tovo, paolo livieri university of ferrara enrico.maggiolini@unife.it, roberto.tovo@unife.it, paolo.livieri@unife.it abstract rectangular lateral notches are not common engineering components, thus little research attention has been directed towards the investigation of their stress field properties. indeed, no in-depth investigations have been conducted to date to assess their effective stress distributions according to the effective stress definitions provided by more recent non-local approaches (i.e. critical distance, average values, implicit gradient values, etc.). in fact, the potential applications of this kind of investigation are not even particularly relevant. however, rectangular notches could provide an interesting theoretical and experimental benchmark or reference case in order to validate the effective stress definitions. the aim of this paper is to investigate the linear elastic stress field at edges, corners and in the surrounding material of rectangular, sharp or rounded lateral notches. the consequent effective values of these notches are evaluated in relation to brittle fracture or their predicted fatigue strength values. the main goal of this paper is to investigate the relationship between geometrical proportions and the location of critical failure points according to the definitions of effective stress proposed in the literature. keywords. fillet radius; shoulder fillet; notches; equivalent stress; local field; implicit gradient. introduction n practice, shoulder fillets (a shaft is a typical example) and u-notches (for example in relation to keyways) are commonly used and much researcher is being performed worldwide to understand the mechanisms underlying the geometry irregularity and the material behaviour in their near fields. shoulder fillets are more frequently used than unotches for reducing the weight and the volume of material; especially in high performance structures, where designers tend to introduce sudden reductions in section and thickness. a well-known problem associated with the use of notches regards their stress concentration factors. in the worst case scenario, notches can even result in a stress singularity with all its associated problems . neuber [1] and peterson [2] are highly renowned in the field of ... because, more than 50 years ago, they provided the first solutions (in relation to just a few simple cases) for u-notches of different shapes. since then, a great deal of research has been directed towards these kinds of notches, characterising them according to the depth and radius of the notch [3, 4], because because for how they are made it is mostly impossible to have a sharp edge instead of a notch radius. over the years, the precision of mechanical tools has increased dramatically, resulting in very small notch radii that often result in geometry singularities (considering the very high stress concentration factors that can increase the local stress to a negligible value for the application of a local study). for this reason, energy based criteria (strain energy densities [5]) and average stress field approaches (implicit gradient [6]) are becoming more important. u-notches of various shapes and under different load directions have been studied over recent years [7, 8], nevertheless the brazilian disk has become one i e. maggiolini et alii, frattura ed integrità strutturale, 33 (2015) 183-190; doi: 10.3221/igf-esis.33.23 184 of the most useful tools for studying this kind of problem in a simple way. ever since the 1970’s, the brazilian disk has been commonly used for mixed-mode fracture testing of a cracked component [9, 10]; 30 years later, torabi started to use a modified version of the original brazilian disk, the u-notched brazilian disc specimen, to understand the triaxial stress state around u-notches under mixed-mode loading [11, 12]. in the present article, the authors investigate the geometries of different shaped u-notches, maintaining the same depth and only changing the angle of the notch axis (perpendicular to the applied force and at 45° to the applied force) and the height of the u-notch (from 0 to a height where the middle point of the notch tip is not affected by the proximity of the notch edge). in a subsequent step, another set of geometries were created by adding a fillet radius. u-notches characterised by these differing geometries were subjected to pure tensile load, and the notch tip was studied according to implicit gradient (ig) theory. focusing on the position of the point of maximum first principal stress, and later ig, we investigated how its location changed with changing notch height. it is clear that the location of the point of maximum first principal stress is always in the notch tip due to the presence of a stress singularity; the situation is different for rounded notches, where it moves from the beginning of the fillet to the inside of the rounded part of the fillet. theoretical framework he authors present an approach capable of estimating the fatigue life of notched structures and welded joints based on an effective stress value computed numerically by solving the helmholtz differential equation linked to the implicit gradient method [13]. implicit gradient (ig) was originally formulated by neuber in the 1930’s [14]. the concept is that when it is not possible to use the local value of stress (due to the infinite value of the stress given by fem in the crack tip, for example), the better way to calculate an effective local stress is to use the near stress field with a proper averaging function. the implicit gradient method supports the idea that the damage should be related to an average value of the stress components exerted on the body; when calculating this average, the stress values near to the critical point have a greater impact than the distant field (this suggests the possible use of a weight function). in other words, with a non-local approach we can determine the local effective stress and then compare it with the reference resistance. this theory is based on a differential equation resulting from the helmholtz equation that includes a constant representing the characteristic length “c” for a weldable structure equal to 0.2 mm. 2 2, ,ceff ig eff ig eq     (1) 2 , n = 0eff ig  (2) the gradient parameter “c” is a squared length; an internal length scale is therefore present in the gradient formulation (the set-up of this parameter is explained in [15]). as shown in eq. (1), the only variable of this equation is the equivalent stress σeq, which in our case is the first principal stress. as a result, we obtained the ig effective stress σeff,ig. eq. (2) is the natural boundary condition [16, 17]. it is important to consider that if the first principal stress is taken as σeq, the entire study field is around the point of maximum tension, but that does not mean that the result (maximum value of σeff,ig) is necessarily in the same location. however, as will be shown below, the maximum σeff,ig does not always match the location of maximum first principal stress, but it remains in the very near field. the fe software comsol multiphysics admits the implementation of this kind of equation. geometries and model properties wo macrosets of notch geometry were created with variable notch height. the first set is based on a horizontal notch with a fixed depth, and the second set is based on a notch of the same depth, but with the orientation of the notch set at 45 degrees. the origin is taken in the notch upper tip. the half notch height h varies between 0 and 4. a vertical tensile unitary load is applied to the top 25mm side, while the bottom 25mm side is fixed. to make a proper model, we created a mesh with triangular elements and a mapped mesh zone over the notch tip. for the horizontal notch, the model was created with symmetry constraints in the mid-section of the notch. t t e. maggiolini et alii, frattura ed integrità strutturale, 33 (2015) 183-190; doi: 10.3221/igf-esis.33.23 185 figure 1: first two sets of notch geometries. the spotted line is a symmetry axis. size in mm. figure 2: mesh detail: element size=0.01 mm, h=0.4 mm. results he first principal stress (σ1) in notched geometries is maximum in the tip of the notch. as can be seen in this example, the maximum value of σeff,ig is located in an unexpected position, and its location moves as h changes. as concerns the horizontal notch, the maximum value of σeff,ig is clearly located in the mid-section of the notch until h/c=1.5. in the inclined notch, the location of maximum tension is always near the upper tip. t e. maggiolini et alii, frattura ed integrità strutturale, 33 (2015) 183-190; doi: 10.3221/igf-esis.33.23 186 figure 3: an isoline graph depicting first principal stress (100 lines). figure 4: example of σeff,ig plot with isolines graph (100 lines). max σeff,ig horizontal inclined h/c x y x y 0 -0.05 0.00 -0.01 -0.06 0.1 -0.02 -0.02 0.01 -0.05 0.25 0.00 -0.05 0.00 -0.09 0.5 0.00 -0.10 0.00 -0.15 1 0.00 -0.20 0.00 -0.27 2 0.00 -0.14 0.00 -0.72 4 0.00 -0.08 0.00 -1.56 6 0.00 -0.06 0.00 -0.11 10 0.00 -0.06 0.00 -0.10 20 0.00 -0.05 0.00 -0.20 table 1: position of the max σeff,ig related to h/c. we can easily create a coordinate system to locate the point of maximum stress and graph its position (curvilineal coordinate dimension d). figure 5: coordinate systems for the max tension point location. e. maggiolini et alii, frattura ed integrità strutturale, 33 (2015) 183-190; doi: 10.3221/igf-esis.33.23 187 graph 1: tendency of the position in the horizontal notch. graph 2: tendency of the position in the inclined notch with regards to the trend of the maximum value of σeff,ig as a function of h/c, a trend very similar to that reported in [18] is seen, whereby it does not depend on the notch height, but on the lateral v-notch opening angle. graph 3: trend of σeff,ig depending on the opening angle in [18] (left) and on h/c (right) in both cases, σeff,ig rises until it reaches its maximum level (located at 2α=60° and h/c=0.05), before falling back down to the minimum. second set of geometries as concerns the notched geometries with radius, σ1 does not reach its maximum in the point where the fillet starts, but it moves in the curvilinear part of the notch as shown in fig. 7. figure 6: coordinate system for the max tension point location. 0 2 4 6 8 10 12 0 30 60 90 120 150 180 σ e ff ,i g /σ n o m 2α [°] 0 1 2 3 4 5 6 7 0 1 2 3 4 5 σ e ff ,i g /σ n o m h/c e. maggiolini et alii, frattura ed integrità strutturale, 33 (2015) 183-190; doi: 10.3221/igf-esis.33.23 188 figure 7: example of first principal stress plot in rounded notch. even σeff,ig moves around the curvilinear part of the notch, always remaining in the first half of the rounded part. max. σ1 max. σeff,ig (h-r)/c x y x y 0 0.0000 0.0000 -0.0416 0.0000 0.05 0.0009 0.0040 -0.0157 -0.0100 0.45 0.0015 0.0053 0.0000 -0.0900 0.95 0.0018 0.0057 0.0000 -0.1900 1.45 0.0019 0.0058 0.0000 -0.2225 1.95 0.0019 0.0058 0.0000 -0.1263 3.95 0.0021 0.0061 0.0000 -0.0710 5.95 0.0021 0.0061 0.0000 -0.0595 9.95 0.0022 0.0062 0.0000 -0.0442 19.95 0.0022 0.0062 0.0000 -0.0443 table 2: position of the max. σeff,ig and σ1 related to (h-r)/c for r=c/20. graph 4: tendency of the position as a function of r/c and (h-r)/c e. maggiolini et alii, frattura ed integrità strutturale, 33 (2015) 183-190; doi: 10.3221/igf-esis.33.23 189 graph 5: zooms of the graph 4. it is extremely difficult to consider the fillet radius in inclined notches due to the different opening angles of the two notch tips: the lower tip has an opening angle of 135° and can support almost any radius, whereas the upper tip has a very sharp angle of 45° and cannot support large radii for the lower values of h. conclusions he aim of this work was to investigate how the location of maximal σeff,ig changes with varying notch geometries as estimated using implicit gradient theory. to confirm the findings, specimens should be made and tensile tests performed to verify whether fracture initiation occurs in the same points as highlighted by this paper. with regard to the inclined notch: as h increases, the location of maximum σeff,ig moves up towards the sharper notch angle; for large values of h, the locations of maximal σeff,ig concentrate in the notch tip. for the horizontal notch, on the other hand, both notch tips have the same opening angle. graph 5 shows how the location of maximum σeff,ig moves from the middle of the notch towards the notch tip: i.e. the rising parts after the first 45° straight line. it increases until d/c=0; this means that, in the fillet notch, the maximum tension point moves to the curvilinear parts of the notch. in a future study, a material should be chosen, the constant “c” calculated, and a fillet radius selected; using these data and graph 5, it will be clear how big h should be in order to have the fracture initiation point in the notch wall or in the notch tip. however, since notch size and radius are very small, it may not be clear or easy to locate the starting point of the cracks. if identification of the fraction initiation points proves to be possible, we will be able to ascertain whether the initiation point follows the implicit gradient rules, the first principal rules or neither of the two. references [1] neuber h., kerbspannungslehre, springer, berlin (1957). [2] walter d., deborah f., peterson's stress concentration, 3rd edition, john wiley & sons, inc. (2008). [3] noda, n.-a., takase y., monda, k., stress concentration factors for shoulder fillets in round and flat bars under various loads, int. j. fatigue, 19(1) (1997) 75-84. [4] waldman, w., heller, m., chen, g.x., optimal free-form shapes for shoulder fillets in flat plates under tension and bending, international journal of fatigue, 23 (2001) 509–523. [5] torabi, a.r., berto, f., strain energy density to assess mode ii fracture in u-notched disk-type graphite plates, int. journal of damage mechanics, 23(7) (2014) 917-930. [6] maggiolini, e., livieri, p., tovo, r., implicit gradient and integral average effective stresses: relationships and numerical approximations, fatigue and fracture of engineering materials and structures, in press, (2014). [7] zappalorto, m., lazzarin, p., stress fields due to inclined notches and shoulder fillets in shafts under torsion, journal of strain analysis for engineering design, 46 (2011). t e. maggiolini et alii, frattura ed integrità strutturale, 33 (2015) 183-190; doi: 10.3221/igf-esis.33.23 190 [8] majima, t., tobita, t., kimizuka, y., experimental investigation on interference effect of notch on strength of notched bar with double u-notches of unequal depth and radius, zairyo/journal of the society of materials science, japan, 36(407) (1987) 871-877. [9] awaji, h., sato, s. combined mode fracture toughness measurement by the disc test, j. engng. mater. tech., 100 (1978) 175–182. [10] awaji, h., kato, t., griffith criterion for mode ii fracture of ceramics, experimental mechanics, alison, balkema, rotterdam, (1978) 1199–1204. [11] torabi, a.r., fakoor, m., pirhadi, e., fracture analysis of u-notched disc-type graphite specimens under mixed mode loading, international journal of solids and structures, manuscript draft, ijss-d-13-00336. [12] torabi, a.r., berto, f., strain energy density to assess mode ii fracture in u-notched disk-type graphite plates, international journal of damage mechanics, 23(7) (2014) 917–930. [13] tovo, r., livieri, p., an implicit gradient application to fatigue of sharp notches and weldments, engineering fracture mechanics, 74 (2007) 515–526. [14] neuber: theory of notch stresses, springer-verlag, berlin (1958). [15] tovo, r., livieri, p., an implicit gradient application to fatigue of sharp notches and weldments, engineering fracture mechanics, 74 (2007) 515–526 [16] lasry, d., belytschko, t., localization limiters in transient problems, inf. j. solids struct., 24 (1988) 581–597. [17] miihlhaus, h.-b., aifantis, e. c., a variational principle for gradient plasticity, int. j. solids struct., 28 (1991) 845–857. [18] maggiolini, e., livieri, p., tovo, r., on numerical integration for effective stress assessment at notches, frattura ed integrità strutturale, 25 (2013) 117-123; doi: 10.3221/igf-esis.25.17. microsoft word 2289 m. k. hussain et alii, frattura ed integrità strutturale, 48 (2019) 599-610; doi: 10.3221/igf-esis.48.58 599 focused on “showcasing structural integrity research in india” evaluation of mixed mode (i/ii) notch stress intensity factors of sharp v-notches using point substitution displacement technique mirzaul karim hussain, k.s.r.k. murthy department of mechanical engineering, indian institute of technology guwahati, guwahati-781039, india mirzaul@iitg.ac.in, https://orcid.org/0000-0003-4300-360x ksrkm@iitg.ac.in, https://orcid.org/0000-0002-9112-8557 abstract. in this paper, determination of the accurate notch stress intensity factors (nsifs) have been demonstrated using a recently proposed technique: the point substitution displacement technique (psdt) for the sharp vnotched configurations. in this technique, certain optimal point(s) on the notch flanks are obtained where the displacements are found to be highly accurate. using the psdt, the nsifs are determined from the finite element (fe) displacements at these optimal point(s). the nsifs of two pure mode i and two mixed mode (i/ii) examples have been determined and excellent agreement of the present results with the published results is observed. the psdt is efficient, robust and easy to be implemented in the available fe code. keywords. v-notch; nsif; stress intensity; finite element; mixed mode citation: hussain, m. k., murthy, k. s. r. k., evaluation of mixed mode (i/ii) notch stress intensity factors of sharp v-notches using point substitution displacement technique, frattura ed integrità strutturale, 48 (2019) 599-610. received: 30.11.2018 accepted: 25.02.2019 published: 01.04.2019 copyright: © 2019 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. introduction harp v-notches are frequently encountered in many engineering applications and structures. due to the presence of these notches, a very high local stresses and stress gradient is observed close to the notch tip. the presence of notch drastically decreases the load-bearing capacity of the component and may cause damage to structures subjected to both static and variable loads. therefore, a very accurate assessment of the strength of the singularity is desired near the notch tip. williams [1] investigated plane v-notched configurations. in linear elastic fracture mechanics (lefm), notch stress intensity factors (nsifs) are widely used to characterize the singular stress field in the vicinity of the notch tip. the singularity stress field in the vicinity of the notch tip can be stated in the form of   1 ijkr f here k is the notch stress intensity factor, r is the radial distance from the notch tip,   1 is the order of stress singularity and  ijf are the angular stress components [1]. due to the widespread use of the nsifs in brittle [2-7] and fatigue [8, 9] fracture criteria, many efforts have been put forward to develop various post-processing techniques [10-29] to calculate nsifs. gross and mendelson [10] and carpenter [11] determined nsifs of sharp v-notches using the boundary collocation method. chen [12] proposed a body force method to evaluate the nsifs for problems under tensile and in-plane bending loadings. noda et al. [13] also used body force method to calculate the nsifs. ju and chung [14] and liu et al. [15] used s http://www.gruppofrattura.it/va/48/2289.mp4 m. k. hussain et alii, frattura ed integrità strutturale, 48 (2019) 599-610; doi: 10.3221/igf-esis.48.58 600 the least-squares method for determining the nsifs using the stresses obtained from finite element method (fem). as these least-squares methods [14, 15] use the stress field, they require either very fine meshes at the notch tip or higher order williams coefficients to attain the accurate nsifs. triefi et al. [16] developed a strain energy method to determine the mixed mode nsifs of sharp v-notches. in another research, lazzarin et al. [17] proposed a strain energy density technique for the rapid evaluation of nsifs. many researchers used fractral-like finite element method [18-20] and extended finite element method [21, 22] to calculate the nsifs. other researchers employed various path independent integrals [23-26] to estimate the nsifs of sharp v-notches. apart from these methods, ayatollahi and nejati [27] determined the nsifs along with the higher order terms of williams coefficients using an overdeterministic method utilizing fe displacements. recently, hussain and murthy [28, 29] developed a collocation technique and a point substitute displacement technique (psdt) to obtain the mixed mode (i/ii) nsifs using the fe displacements along the notch flank. in their method [29], certain optimal point(s) of the notch tip element along the notch flanks have been identified by minimizing the error in displacements, and interestingly, the displacements and its slope are found to be more accurate at those points. the psdt utilizes the displacements on the notch flanks at these optimal point(s) to calculate nsifs accurately. this method is efficient, simple and straightforward to be implemented in the available fe code and can be employed to find the nsifs using manual calculations. it is worth noting here that, unlike the availability of well-known quarter point elements [30, 31] in the crack problems, no such popular singular elements are currently available for use in the sharp v-notched configurations. consequently, any post-processing techniques for the determination of the nsifs should be capable enough to determine the accurate nsifs yet using the conventional elements at the notch tip and concurrently it should be simple enough to implement in the existing code. the main thrust of the present work is to demonstrate further the efficacy of the above technique, psdt proposed by hussain and murthy [29] in terms accurate estimation of the nsifs of the specimens having straight and curved boundaries under mode i and mixed mode (i/ii) loading conditions. theoretical background short description of the formulations for psdt is presented in this section. however, for more details, one may refer to ref. [29]. for a homogeneous elastic 2d problems containing sharp v-notch (in fig. (1)), the displacement field at any nearby point  ,p r under any arbitrary in-plane loading can be given as [14]                                                           1 1 re cos 2 cos 2 cos cos 2 2 re cos 2 cos 2 sin sin 2 2 2 for i n ii n i i i i i in n n n n n r n ii ii ii ii ii iin n n n n n r n n a u r u g b r u g n b (1)                                                         1 1 re cos 2 cos 2 sin sin 2 2 re cos 2 cos 2 cos cos 2 2 2 for i n ii n i i i i in n n n n n n ii ii ii ii ii iin n n n n n r n n a v r g b r v g n b (2) where na and nb are williams’ coefficients corresponding to n -th term for mode i and mode ii, respectively,  ,r denotes the polar coordinate components,  re denotes real part of the variables, kolosov constant  is equal to      3 1 for plane stress and 3 4 for plane strain conditions,   ( 180 2 ) is the notch angle (fig. (1)),   2 1g e is the shear modulus,  and e are the poisson’s ratio and young’s modulus, respectively. in and  iin are the mode i and mode ii eigenvalues, respectively, and can be obtained by solving the following characteristic eqn. (3). the constants displacements i ru , ii ru and ii rv can be shown in eqn. (4) [27]. a m. k. hussain et alii, frattura ed integrità strutturale, 48 (2019) 599-610; doi: 10.3221/igf-esis.48.58 601             sin 2 sin 2 0 sin 2 sin 2 0 i i n n ii ii n n (3)             0 2 0 2 1 1 1 ; sin ; ( cos ) 2 2 2 i ii ii r r ru a u b r v b b r g g g (4) where 0a and 0b are williams’ coefficients corresponding to the rigid body translation and 2b is williams’ coefficient corresponding to the rigid body rotations. figure 1: a notch geometry with a local coordinate system. mode i and mode ii nsifs can be defined as [10]                                                  1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 0 lim 2 0 2 1 cos 2 cos 2 lim 2 0 2 1 cos 2 cos 2 i ii i i i i i y r ii ii ii ii ii xy r k r a k r b (5) considering only the singular terms and constant displacement terms, the displacement field at any nearby point  ,p r under any arbitrary in-plane loading can be given as [14]                                                 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 2 1 cos 2 cos 2 cos cos 2 2 2 1 cos 2 cos 2 sin sin 2 sin 2 2 i ii i i i i i ii ii ii ii ii a u a r g g b r b r g g (6)                                                1 1 1 1 1 1 1 0 1 1 1 1 1 1 2 1 cos 2 cos 2 sin sin 2 2 2 1 cos 2 cos 2 cos cos 2 cos 2 2 i ii i i i i i n ii ii ii ii ii a v r b g g b r b r g g (7) where 1a and 1b are williams coefficients for the singular terms for mode i and mode ii, respectively. it can be shown that the notch opening displacement (nod) can be written as [29]                                       1 1 1 1 1 1 1 1 1 1 cos 2 cos 2 sin 2 2 2 2 sin 2 i i i i i i i i i i a v v v v r a c r g (8) m. k. hussain et alii, frattura ed integrità strutturale, 48 (2019) 599-610; doi: 10.3221/igf-esis.48.58 602 similarly, the notch sliding displacement (nsd) can be obtained as [29]                                             1 1 1 1 1 1 1 1 2 1 2 2 3 cos 2 cos 2 sin 2 sin 2 1 sin ii ii ii ii ii ii ii ii ii ii b u u u u r g b r b c r b c r g (9) where 1c , 2c and 3c are constants which depend upon eigenvalues,  and  . thus, using eqn. (8) the coefficient 1a can be calculated and 1b can be calculated from the nsd (eqn. (9)) under all loading conditions (pure mode i, pure mode ii and mixed mode (i/ii)). assuming the isoparametric quadratic quadrilateral elements are deployed at the notch tip, the fe displacement along notch flank nodes 1–2–4 (fig. (2)) can be written with r being the distance from the notch tip as [29]     2fev a r br (10) where the constants a and b are constants and can be obtained from the fe displacements using the following equation                  12 2 2 2 2 4 4 4 fe fe a r r v b r r v (11) where 2 fev and 4 fev are fe displacements at nodes 2 and 4, respectively, and 2r and 4r are distances of nodes 2 and 4, respectively, from notch tip 1. the fe nod can be expressed as   22 2fev ar br (12) figure 2: a notch flank finite elements around a notch tip. the residual  between the analytical nod (eqn. (8)) and fe nod (eqn. (12)) can be written as          1 22 2 1 12 2 2 ifev v a c r ar br (13) m. k. hussain et alii, frattura ed integrità strutturale, 48 (2019) 599-610; doi: 10.3221/igf-esis.48.58 603 by minimizing the function  with respect to r and after some algebraic manipulations, r and 1a can be obtained as [29]            1 1 1 2 i op i b r r a (14)       1 1 2 1 1 1 op i i fe r rop op op op var br a c r c r (15) thus, by using the notch opening displacement  fev at opr , 1a can be obtained using the eqn. (15) and hence ik using the eqn. (5). taking logarithm on both sides of eqn. (8), one can write  1 1 1ln ln ln iv r a c (16) it can be seen that, eqn. (16) is a straight line equation whose slope is equal to 1 i . it can be shown that the slope of the plot of     ln fev versus  ln / nr l (eqn. (10)) becomes equal to 1 i at the optimal point optr (refer [29] for more details). here nl is the notch tip element length as shown in fig. (2). similar to the mode i problems, estimation of the opr or optr from u -displacement for mode ii is not possible as   feu (or   feu ) contains the term iiru (eqn. (9)). therefore, to calculate the mode ii nsifs, it is presumed that the mode ii u displacements are also accurate at the optimal points obtained for the mode i problems using eq. (14). to calculate both the constants 1b and 2b , two nearby points  op opt nr r l and    op op opt nr r r l are considered [29]. therefore, from the fe u -displacements at the two close points opr and opr , the williams’ coefficient 1b can be obtained as [29]            1 1 1 1 1 2 op op ii ii fe fe r op r op op op op op u r u r b c r r r r (17) again, by substituting fe nsd  op fe ru and  op fe ru at opr and opr , 1b can be obtained using the eqn. (17) and hence iik using the eqn. (5). finally, the nsifs can be normalized as       ( ) 11 ( ) ( ) ( ) i ii i ii i iif k a and  ( ) 1 ( ) ( ) i ii i ii i iif k r f for the rectangular and circular plates, respectively. numerical examples his section presents a numerical examination of the psdt for the evaluation of the nsifs under mode i and mixed mode (i/ii) loading conditions. the fe analysis is carried out in ansys® [32]. throughout the domain conventional eight noded quadratic elements are used and no singular elements are utilized at the notch tip. at the notch tip, they are collapsed to form a spider web pattern. four problems viz. (a) mode i example of a single edge notched plate under uniform tension (sent), (b) mode i example of a single edge notched plate under in-plane bending (senb), (c) mixed mode problem of an angled single edge notched plate under uniform tension (asent) and (d) mixed mode problem of a sharp v-notched brazilian disc (sv-bd) are considered for the demonstration of the efficacy of the psdt. the notch length to width ratio  0.5a w is considered for the single edged notch plates and the notch length to radius ratio  0.5a r is considered for the brazilian disc. it is assumed that all the specimens are under plane stress condition. consistent units are employed in all the examples. the thickness of all the specimens is considered as unity. t m. k. hussain et alii, frattura ed integrità strutturale, 48 (2019) 599-610; doi: 10.3221/igf-esis.48.58 604 example 1: mode i problems the first set of examples considered are single edge notched plate under uniform tension (sent) and single edge notched plate under in-plane bending (senb) as pure mode i examples (as shown in fig. (3)). the geometrical parameters considered for the sent and senb are as follows:  1.0w and  1.2h as shown in fig. (3). the uniform tensile loading  (=1.0) and a bending loading 3 .2 /h w (=7.2) are considered for the sent and senb specimens, respectively (fig. (3a) and 3(b)). the notch angles   0°, 15°, 30°, 45°, 60°, 75°, 90, 105° and 120° are considered for validating the present method. young’s modulus  1e and poisson’s ratio   0.25 are considered. one-half (shaded portion in fig. (3a) and fig. (3b)) of the geometries is modeled due to the symmetry with appropriate boundary conditions. the typical mesh with 211 number of elements (ne) and 702 number of nodes (nn) used for both the specimens is shown in fig. (3c). the notch tip element to notch length ratio is considered as  0.025nl a for both the specimens. the optimum points  opt op nr r l obtained using eq. (14) are found to be centered around 0.79 for all the notch angles in the present examples (for a detailed description, one may refer to ref. [29]). it has been observed that  fev at the optimal points optr obtained using eqn. (14) are very accurate. the mode i nsifs calculated at the respective optimal points and are listed in tab. (1) and tab. (2) for the sent and senb specimens, respectively. figure 3: (a) single edge notched plate under uniform tension (sent), (b) single edge notched plate under in-plane bending (senb) and (c) typical fe mesh used for both sent and senb specimens (ne=211, nn=702).    if present gross and mendelson [10] zhan and hahn [33] chen [12] 0 2.7856 2.8237 2.8301 – 15 2.8019 – – – 30 2.8279 2.8448 2.8408 2.8440 45 2.8775 – – – 60 2.9620 2.9716 2.9937 2.9700 75 3.1005 – – – 90 3.3191 3.3244 3.3716 3.3220 105 3.6532 – – – 120 4.1578 4.1458 4.0133 – table 1: normalized nsif if for the sent specimen (  0.5a w ). m. k. hussain et alii, frattura ed integrità strutturale, 48 (2019) 599-610; doi: 10.3221/igf-esis.48.58 605    i f present chen [12] 0 1.4881 – 15 1.4922 – 30 1.5000 1.5010 45 1.5185 – 60 1.5537 1.5530 75 1.6153 – 90 1.7164 1.7140 105 1.8749 – 120 2.1185 – table 2: normalized nsif if for the senb specimen (  0.5a w ). it can be observed that the nsifs calculated from the present technique are in excellent agreement with the available results (% relative error is less than 1% with respect to chen [12] results). due to the implementation of the nod, very accurate values of nsifs can be attained with coarse meshes. example 2: mixed mode example of an angled single edge notched plate under uniform tension (asent) the third example considered is a mixed mode example of an angled single edge notched plate under uniform tension (asent) to analyze the efficiency of the psdt under mixed mode loading. the geometry and loading for asent are as follows:  1.0w ,  3.5h and   1.0 as shown in fig. (4a). the notch inclination angles  =15°, 30° and 45° and notch angles   0°, 30°, 60°, and 90° are considered for determining the mixed mode nsifs. a poisson’s ratio   0.25 and young’s modulus  1e are considered. a typical fe mesh for the asent is shown in fig. (4b) for   30 and   30 with 531 number of elements and 1723 number of nodes. fig. (4c) shows the enlarged portion near the notch tip with  0.025nl a . figure 4: (a) angled single edge notched plate under uniform tension (asent), (b) typical fe mesh used for the asent specimen (ne=531, nn=1723) and (c) mesh arrangement near the notch tip portion. m. k. hussain et alii, frattura ed integrità strutturale, 48 (2019) 599-610; doi: 10.3221/igf-esis.48.58 606 similar to the pure mode i problem 1a can be obtained from  fev at optr using eqn. (14). 1b can be obtained from  feu at two radii (  op opt nr r l and    op op op nr r r l ) using eqn. (17).  opr can be considered as 0.002 for calculating the mode ii nsifs [29]. the normalized mixed mode (i/ii) nsifs obtained using the psdt are listed in tab. (3). once again, the results obtained from the present method show a good agreement with the published results for various  and  . the results in tab. (3) show that using psdt by the mere substitution of fe nod and nsd at the optimal points accurate values of mixed mode (i/ii) nsifs can be obtained.       i f iif present chen [12] present chen [12] 15 0 2.7108 – 0.3970 – 30 2.7507 2.7670 0.5468 0.5410 60 2.8790 2.8870 0.7764 0.7660 90 3.2257 3.2300 1.1220 1.1160 30 0 2.0399 – 0.7122 – 30 2.5315 2.5460 1.0190 1.0100 60 2.6447 2.6530 1.4619 1.4280 90 2.9587 2.9640 2.0576 2.0950 45 0 2.1792 – 1.0078 – 30 2.2039 2.2170 1.3615 1.3520 60 2.2937 2.3040 1.9383 1.9110 table 3: normalized nsifs if and iif for the asent specimen (  0.5a w ). example 3: mixed mode example of a sharp v-notched brazilian disc (sv-bd) a sharp v-notched brazilian disc (sv-bd) as shown in fig. (5) is considered as the fourth example for analyzing mixed mode (i/ii) problem. the radius of the sv-bd is taken as  60r and a compressive loading 1.0f is applied as shown in fig. (5). the notch length to radius ratio  0.5a r , notch inclination angles   0º, 10º, 20° and 30° and notch angles   30°, 60°, and 90° are considered for determining the mixed mode nsifs for the sv-bd. a poisson’s ratio   0.25 and young’s modulus  1e are considered. the boundary conditions used for the fe analysis are shown in fig. (5a). fig. (5b) shows the typical mesh used for the sv-bd (ne=1833 and nn=5643). fig. (5c) shows the enlarged portion near the notch tip. figure 5: (a) sharp v-notched brazilian disc (sv-bd), (b) typical fe mesh used for the sv-bd specimen (ne=1833, nn=5643) and (c) mesh arrangement near the notch tip portion. m. k. hussain et alii, frattura ed integrità strutturale, 48 (2019) 599-610; doi: 10.3221/igf-esis.48.58 607 the mode i and mode ii nsifs are also calculated in a similar way to that of the asent specimen. tab. (4) lists the results of mode i and mode ii nsifs obtained using the psdt. for comparison, the numerical and experimental results of ayatollahi and nejati [34] are also presented in tab. (4) and it has been noticed that the present results are in good agreement with the published results. thus, the results in all the examples indicate that the psdt is simple and robust. the fe displacements at the optimal points are more accurate than the other points on the notch tip element. the psdt can provide very good results with coarse mesh even with convention elements at the notch tip.       if iif present ayatollahi and nejati [34] (fem) ayatollahi and nejati [34] (experimental) present ayatollahi and nejati [34] (fem) ayatollahi and nejati [34] (experimental) 0 30 0.7213 0.7100 0.7400 0.0027 0.0000 0.0200 60 1.1530 1.1300 1.1700 0.0000 0.0000 0.0500 90 2.3108 2.2900 2.2900 0.0000 0.0000 0.0600 10 30 0.5727 0.5600 0.6000 0.7470 0.7200 0.7200 60 0.9599 0.9400 0.9900 1.2619 1.1700 1.1100 90 2.0187 2.0000 1.9500 2.1169 2.0200 2.1300 20 30 0.2148 0.2000 0.2200 1.2006 1.1800 1.1800 60 0.4940 0.4800 0.4800 1.9260 1.8600 1.8900 90 1.3013 1.2900 1.2700 3.0792 3.1200 3.0300 30 30 0.1980 – – 1.3447 – – 60 0.0555 -0.0100 0.0900 2.0788 2.0200 1.9200 90 0.4395 – – 3.2716 – – table 4: comparison of the normalized nsifs if and iif for the sv-bd specimen ( a w 0.5). conclusions n this paper, the efficacy of an fe based nsif extraction technique: the point substitution displacement technique (psdt) has been demonstrated by determining the nsifs of various configurations under mode i and mixed mode (i/ii) loading conditions. the nsifs are determined from the fe notch flank displacements at the optimum point(s) in the notch tip elements. the efficacy of the present method is examined with two mode i and two mixed mode (i/ii) problems. the results obtained using the present method is validated with the available results. the results show that the psdt is simple, robust and easy to be implemented in the available fe code. further, accurate values of mode i and ii nsifs can be obtained using coarse meshes. references [1] williams, m.l. (1952). stress singularities resulting from various boundary conditions in angular corners of plates in extension, j. appl. mechs., 19, pp. 526–528. [2] dunn, m.l. and suwito, w. (1997). fracture initiation at sharp notches: correlation using critical stress intensities, int. j. solids struct., 34(29), pp. 3873–3883. doi: 10.1016/s0020-7683(96)00236-3 [3] seweryn, a. (1994). brittle fracture criterion for structures with sharp notches, eng. fract. mech., 47, pp. 673–81. doi: 10.1016/0013-7944(94)90158-9 i m. k. hussain et alii, frattura ed integrità strutturale, 48 (2019) 599-610; doi: 10.3221/igf-esis.48.58 608 [4] berto, f. and lazzarin, p. (2014). recent developments in brittle and quasi-brittle failure assessment of engineering materials by means of local approaches, mater. sci. eng. r. rep., 75, pp. 1–48. doi: 10.1016/j.mser.2013.11.001. [5] dunn, m.l., suwito, w., cunningham, s. and may, c.w. (1997). fracture initiation at sharp notches under mode i, mode ii, and mild mixed mode loading, int. j. fract., 84, pp. 67–381. doi: 10.1023/a:1007346203407. [6] ayatollahi, m.r., torabi, a.r. and azizi, p. (2011). experimental and theoretical assessment of brittle fracture in engineering components containing a sharp v-notch, exp. mech., 51, pp. 919–932. doi: 10.1007/s11340-010-9401z. [7] ayatollahi, m.r. and torabi, a.r. (2011). failure assessment of notched polycrystalline graphite under tensile-shear loading, mater sci. eng. a., 528, pp. 5685–5695. doi: 10.1016/j.msea.2011.04.066. [8] lazzarin, p. and livieri, p. (2001). notch stress intensity factors and fatigue strength of aluminium and steel welded joints, int. j. fatigue, 23, pp. 225–232. doi: 10.1016/s0142-1123(00)00086-4. [9] fischer, c., fricke, w. and rizzo, c.m. (2016). review of the fatigue strength of welded joints based on the notch stress intensity factor and sed approaches, int. j. fatigue, 84, pp. 59–66. doi: 10.1016/j.ijfatigue.2015.11.015. [10] gross, b. and mendelson, a. (1972). plane elastostatic analysis of v-notched plates, int. j. fract. mech., 8 (3), pp. 267–276. doi: 10.1007/bf00186126. [11] carpenter, w.c. (1984). a collocation procedure for determining fracture mechanics parameters at a corner, int. j. fract., 24, pp. 255–266. doi: 10.1007/bf00020740. [12] chen, d.h. (1995). stress intensity factors for v-notched strip under tension or in-plane bending, int. j. fract., 70, pp. 81–97, 1995. doi: 10.1007/bf00018137. [13] noda, n.a., oda, k. and inoue, t. (1996). analysis of newly-defined stress intensity factors for angular corners using singular integral equations of the body force method, int. j. fract., 76, pp. 243–261. doi: 10.1007/bf00048289. [14] ju, s.h. and chung, h.y. (2007). accuracy and limit of a least-squares method to calculate 3d notch sifs, int. j. fract., 148 (2), pp. 169–183. doi: 10.1007/s10704-008-9193-7. [15] liu, y., wu, z., liang, y. and liu, x. (2008). numerical methods for determination of stress intensity factors of singular stress field, eng. fract. mech. 75 (16), pp. 4793–4803. doi: 10.1016/j.engfracmech.2008.06.007. [16] treifi, m. and oyadiji, s.o. (2013). strain energy approach to compute stress intensity factors for isotropic homogeneous and bi-material v-notches, int. j. solids struct., 50(14–15), pp. 2196–2212. doi: 10.1016/j.ijsolstr.2013.03.011 [17] lazzarin, p., berto, f. and zappalorto, m. (2010). rapid calculations of notch stress intensity factors based on averaged strain energy density from coarse meshes: theoretical bases and applications, int. j. fatigue., 32(10), pp. 1559–1567. doi: 10.1016/j.ijfatigue.2010.02.017. [18] treifi, m., oyadiji, s.o. and tsang, d.k.l. (2009). computation of the stress intensity factors of sharp notched plates by the fractal-like finite element method, int. j. numer. meth. engng., 77, pp. 558–580. doi: 10.1002/nme.2425. [19] treifi, m., oyadiji, s.o. and tsang, d.k.l. (2008). computations of modes i and ii stress intensity factors of sharp notched plates under in-plane shear and bending loading by the fractal-like finite element method, int. j. solids struct., 45(25–26), pp. 6468–6484. doi: 10.1016/j.ijsolstr.2008.08.013. [20] treifi, m., oyadiji, s.o. and tsang, d.k.l. (2009). computations of the stress intensity factors of double-edge and centre v-notched plates under tension and anti-plane shear by the fractal-like finite element method, eng. fract. mech., 76, pp. 2091–2108. doi: 10.1016/j.engfracmech.2009.05.018. [21] yu, t. and shi, l. (2012). determination of sharp v-notch stress intensity factors using the extended finite element method, j. strain anal. eng. des., 47, pp. 95–103. doi: 10.1177/0309324711433981. [22] yi, g., yu, t., quoc, t., ma, c. and hirose, s. (2017). sifs evaluation of sharp v-notched fracture by xfem and strain energy approach, theor. appl. fract. mec., 89, pp. 35–44. doi: 10.1016/j.tafmec.2017.01.005. [23] sinclair, g.b., okajima, m. and griffin j.h. (1984). path independent integrals for computing stress intensity factors at sharp notches in elastic plates, int. j. numer. meth. eng., 20(6), pp. 999–1008. doi: 10.1002/nme.1620200603. [24] labossiere, p.e.w. and dunn, k.l. (1998). calculation of stress intensities at sharp notches in anisotropic media, eng. fract. mech., 61(5–6), pp. 635–654. doi: 10.1016/s0013-7944(98)00039-3. [25] chang, j.h. and kang, l.k. (2002). evaluation of the stress field around a notch tip using contour integrals, int. j. eng. sci., 40(5), pp. 569–586. doi: 10.1016/s0020-7225(01)00078-7. [26] kim, j.k. and cho, s.b. (2009). effect of second non-singular term of mode i near the tip of a v-notched crack, fatigue fract. eng. mater. struct., 32(4), pp. 346–356. doi: 10.1111/j.1460-2695.2009.01336.x. [27] ayatollahi, m.r. and nejati, m. (2011). determination of nsifs and coefficients of higher order terms for sharp notches using finite element method, int. j. mech. sci., 53(3), pp. 164–177. doi: 10.1016/j.ijmecsci.2010.12.005. m. k. hussain et alii, frattura ed integrità strutturale, 48 (2019) 599-610; doi: 10.3221/igf-esis.48.58 609 [28] hussain, m.k. and murthy, k.s.r.k. (2019). calculation of mixed mode (i/ii) stress intensities at sharp v-notches using finite element notch opening and sliding displacements, fatigue fract. eng. mater. struct. pp. 1–18. doi: 10.1111/ffe.12977. [29] hussain, m.k. and murthy, k.s.r.k. (2018). a point substitution displacement technique for estimation of elastic notch stress intensities of sharp v-notched bodies, theor. appl. fract. mec., 97, pp. 87–97. doi: 10.1016/j.tafmec.2018.07.010. [30] henshel, r.d. and shaw, k.g. (1976). crack tip finite elements are unnecessary, int. j. numer. meth. eng., 9, pp. 495–507. doi: 10.1002/nme.1620090302. [31] barsoum, r.s. (1976). on the use of isoparametric finite elements in linear fracture mechanics, int. j. numer. meth. eng., 10, pp. 25–27. doi: 10.1002/nme.1620100103. [32] ansys. theory reference manual. release 11. swanson analysis systems, inc., 2007. [33] zhao, z. and hahn, h.g. (1992). determining the sif of a v-notch from the results of a mixed-mode crack, eng. fract. mech., 43(4), pp. 511–518. doi: 10.1016/0013-7944(92)90195-k. [34] ayatollahi, m.r. and nejati, m. (2011). experimental evaluation of stress field around the sharp notches using photoelasticity, mater. des., 32, pp. 561–569. doi: 10.1016/j.matdes.2010.08.024. nomenclature a notch length ,a b parameters related to finite element displacements 0 0 2, ,a b b parameters related to rigid body motion  1, 2, 3,...na n williams coefficients for mode i  1, 3, 4,...nb n williams coefficients for mode ii e young’s modulus ,i iif f modes i and ii normalized notch stress intensity factors f compressive point load on the sharp v-notched brazilian disc g shear modulus h semi-height of the notched plate nl notch tip element length ,i iik k modes i and ii notch stress intensity factors r radius of the sharp v-notched brazilian disc  residual  ,r polar coordinate components optr optimum point opr optimum radius ,u v notch field displacement w plate width  parameter related to notch angle  notch inclination angle  notch opening angle  kolosov constant  1 1, i ii modes i and ii 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can be opened with acrobat and adobe reader 5.0 and later.) >> /namespace [ (adobe) (common) (1.0) ] /othernamespaces [ << /asreaderspreads false /cropimagestoframes true /errorcontrol /warnandcontinue /flattenerignorespreadoverrides false /includeguidesgrids false /includenonprinting false /includeslug false /namespace [ (adobe) (indesign) (4.0) ] /omitplacedbitmaps false /omitplacedeps false /omitplacedpdf false /simulateoverprint /legacy >> << /addbleedmarks false /addcolorbars false /addcropmarks false /addpageinfo false /addregmarks false /convertcolors /converttocmyk /destinationprofilename () /destinationprofileselector /documentcmyk /downsample16bitimages true /flattenerpreset << /presetselector /mediumresolution >> /formelements false /generatestructure false /includebookmarks false /includehyperlinks false /includeinteractive false /includelayers false /includeprofiles false /multimediahandling /useobjectsettings /namespace [ (adobe) (creativesuite) (2.0) ] /pdfxoutputintentprofileselector /documentcmyk /preserveediting true /untaggedcmykhandling /leaveuntagged /untaggedrgbhandling /usedocumentprofile /usedocumentbleed false >> ] >> setdistillerparams << /hwresolution [2400 2400] /pagesize [612.000 792.000] >> setpagedevice microsoft word numero_34_art_20 a. campagnolo et alii, frattura ed integrità strutturale, 34 (2015) 190-199; doi: 10.3221/igf-esis.34.20 190 focussed on crack paths three-dimensional effects on cracked discs and plates under nominal mode iii loading a. campagnolo, f. berto university of padova, department of management and engineering, stradella s. nicola 3, 36100, vicenza (italy) campagnolo@gest.unipd.it, berto@gest.unipd.it l. p. pook 21 woodside road, sevenoaks tn13 3hf (united kingdom) les.pook@tesco.net abstract. the existence of three-dimensional effects at cracks has been known for many years, but understanding has been limited, and for some situations still is. understanding improved when the existence of corner point singularities and their implications became known. increasingly powerful computers made it possible to investigate three-dimensional effects numerically in detail. despite increased understanding, threedimensional effects are sometimes ignored in situations where they may be important. the purpose of the present contribution is to review the study carried out by the same authors in some recent investigations, in which a coupled fracture mode generated by anti-plane loading of a straight through-the-thickness crack in linear elastic discs and plates has been analysed by means of accurate 3d finite element (fe) models. the results obtained from the highly accurate finite element analyses have improved understanding of the behaviour of through cracked components under anti-plane loading. the influence of plate bending is increasingly important as the thickness decreases. it appears that a new field parameter, probably a singularity, is needed to describe the stresses at the free surfaces. discussion on whether kiii tends to zero or infinity as a corner point is approached is futile because kiii is meaningless at a corner point. the intensity of the local stress and strain state through the thickness of the cracked components has been evaluated by using the strain energy density (sed) averaged over a control volume embracing the crack tip. the sed has been considered as a parameter able to control fracture in some previous contributions and can easily take into account also coupled three-dimensional effects. calculation of the sed shows that the position of the maximum sed in the discs case is a function of the thickness. in the plates case instead the position of the maximum sed is independent of plate thickness, contrary to disc results. keywords. fracture mechanics; finite element analysis; anti-plane loading; stress intensity factor; corner point effects. introduction rack tip surface displacements in the vicinity of a corner point in which a crack front intersects a surface are often of practical interest. assuming that poisson’s ratio, v > 0, then kinematics considerations for an antisymmetric loading [1] show that modes ii and iii crack tip surface displacements cannot exist in isolation. mode ii induces c a. campagnolo et alii, frattura ed integrità strutturale, 34 (2015) 190-199; doi: 10.3221/igf-esis.34.20 191 mode iiic and mode iii induces mode iic. these induced modes are sometimes called coupled modes, indicated by the superscript c. the existence of three-dimensional effects at cracks has been known for many years [2-4], but understanding has been limited, and for some situations still is. understanding improved when the existence of corner point singularities [5] and their implications became known [6]. despite increased understanding, three-dimensional effects are sometimes ignored in situations where they may be important. within the framework of linear elastic fracture mechanics [7] the stress field in the vicinity of a crack tip is dominated by the leading term of a series expansion of the stress field [8]. this leading term is the stress intensity factor, k. in three dimensional geometries, the derivation of stress intensity factors makes the implicit assumption that a crack front is continuous. this is not the case in the vicinity of a corner point, and the nature of the crack tip singularity changes. the resulting corner point singularities were described in detail in 1979 by bažant and estenssoro [5]. some additional results were given by benthem in 1980 [9]. for corner point singularities, the polar coordinates are replaced by spherical coordinates (r, , ) with origin at the corner point. the angle  is measured from the crack front. there do not appear to be any exact analytic solutions for corner point singularities. in their analysis bažant and estenssoro [5] assumed that all three modes of crack tip surface displacement are of the form rλρpf(θ, ), where ρ is distance from the crack tip, and p is a given constant. they then calculated λ numerically for a range of situations: λ is a function of poisson’s ratio, υ. for the antisymmetric mode, λ = 0.598 for υ = 0.3. benthem [9] made an equivalent assumption but used a different numerical method to calculate . the stress intensity measure, k, may be used to characterise corner point singularities, where  can be regarded as a parameter defining the corner point singularity. however, expressions for numerical values of k, and associated stress and displacement fields, do not appear to be available. at the present state of the art the extent of a corner point singularity dominated region has to be determined numerically. at a corner point stresses are a singularity. they must be either infinite or zero,  is indeterminate, and it is reasonable to speak of stress intensity factors in an asymptotic sense [2,3]. in the limit, as a crack front is approached, displacement fields must be those of a stress intensity factor [9]. hence, there is an infinitesimal k-dominated region within the core region of a corner point singularity. the stress intensity factors are proportional to s0.5 λ where s is the distance from the surface along the z axis [9]. hence, for the antisymmetric mode kii and kiii both tend to infinity as a corner point is approached. further, as a corner point the ratio kiii/kii tends to a limiting value which is a function of v. for v = 0.3 the limiting ratio is 0.5 [9]. benthem points out that kii and kiii lose their meaning at a corner point [9]. dhondt suggests that modes iic and iiic might not be singular [10]. the predicted tendency to infinity is reasonable for kii since relevant stresses are in plane and disclinations are zero [2,3]. from a linear elastic viewpoint the predicted tendency of kiii to infinity cannot be correct [4]. at a surface shear stresses perpendicular to the surface are zero, which implies that kiii tends to zero as the surface is approached. mode iii is a torsion problem [11]. under mode iii (anti-plane) loading initially plane cross sections, including the surface at a corner point, do not remain plane under load [4] and disclinations appear. it is well known that serious error can arise if warping of non-circular cross sections under torsion is not taken into account in stress analyses [12]. warping of the surface under mode iii means that τyz at the surface does not have to be zero, and finite values of kiii are possible. the implication is that the non linearities cannot be regarded as being in a core region within a corner point singularity dominated region and that bažant and estenssoro’s prediction that kiii tends to infinity as a corner point is correct. the alternative view, which is supported by a large body of evidence [4], is that apparent values of kiii decrease towards the surface in the z direction. this implies that kiii tends to zero as a corner point is approached, which is intuitively correct. it also implies that non linearities can be regarded as being within a core region, but does not explain why bažant and estenssoro’s analysis does not give the correct limit. nevertheless, this alternative view may well be adequate when considering practical implications. this paradox needs to be resolved so that the results of finite element analysis can be interpreted correctly. there does not appear to have been a systematic investigation of the extent to which bažant and estenssoro’s initial assumption is justified. their assumption does appear to be satisfactory for the symmetric mode (mode i) in that their analysis leads to useful results [4]. the purpose of the present contribution is to review the study carried out by the same authors in some recent investigations [2,3], in which a coupled fracture mode generated by anti-plane loading of a straight through-the-thickness crack in linear elastic discs and plates has been analysed by means of accurate 3d finite element (fe) models. due to the uncertainties in the definition of the stress intensity factors on the free surfaces, as stated above, the strain energy density averaged in a control volume (sed) has been employed to quantify the stress intensity through the thickness of the discs [2] and plates [3]. for a review of the sed the reader can refer to [13]. this parameter has been successfully used by lazzarin and co-authors to assess the fracture strength of a large bulk of materials, characterized by a. campagnolo et alii, frattura ed integrità strutturale, 34 (2015) 190-199; doi: 10.3221/igf-esis.34.20 192 different control volumes, subjected to wide combinations of static loading [14 16] and the fatigue strength of notched components [17, 18]. as described in [13, 19] an intrinsic advantage of the sed approach is that it permits automatically to take into account higher order terms and three-dimensional effects. the parameter is easy to calculate in comparison with other well-defined and suitable 3d parameters [20, 21] and can be directly obtained by using coarse meshes [13, 19]. another advantage of the sed is that it is possible to easily understand whether the through-the-thickness effects are important or not in the fracture assessment for a specific material characterized by a control volume depending on the material properties. some brittle materials are characterized by very small values of the control radius and are very sensitive to stress gradients also in a small volume of material [13]. on the other hand more ductile materials have the capability of stress averaging in a larger volume and for this reason are less sensitive to the variations of the stress field through the thickness of the component. the sed, once the control volume is properly modeled through the thickness of the disc or plate, is able to quantify the 3d effects in comparison with the sensitivity of the specific material so providing precious information for the fracture assessment. finite element modelling tresses and stress intensity factors have been examined in detail for 100 mm diameter discs [2] and 100 mm square plates [3] of various thicknesses under anti-plane (nominal mode iii) loading. the thickness is t for both components while in the discs case the radius, r, is 50 mm. a through thickness crack has its tip at the centre of the component, so its length, a, is 50 mm. calculations have been carried out using ansys 11 for t/a = 0.25, 0.5, 0.75, 1, 1.25, 1.5, 1.75, 2, 2.25, 2.5, 2.75 and 3. poisson’s ratio is taken as 0.3 and young’s modulus as 200 gpa. in the discs case, displacements corresponding to kiii = 1 mpam0.5 (31.62 n·mm0.5) have been applied to the cylindrical surface, while in the plates case a displacement of 10-3 mm has been applied to the edge of the plate. stress intensity factors have been calculated from stresses on the crack surface near the crack tip using standard equations [7,11]. the strain energy density has been calculated from a control volume at the crack tip. one quarter of the cracked component has been modelled. an overall view of the finite element meshes is shown in fig. 1a for the discs case and in fig. 1b for the plates one. figure 1: overall view of finite element meshes. (a) disc and (b) plate. results rack surface stresses, τyz and τxy have been extracted from the finite element results at distances, s, from the disc and plate surfaces of 0 mm, 0.25 mm and 1 mm. results for t/a = 1 and s = 0 mm and 1 mm, plotted on logarithmic scales, are shown in figs. 2-3 with reference only to discs case for the sake of brevity. results for other values of t/a and with reference to plates case are generally similar, but with some differences in detail. when the plot is a straight line its slope is -λ. values of λ taken from straight line plots, related to both discs and plates, are shown in tabs.1 and 2. where no value is shown the plot could not be regarded as a straight line. s c a. campagnolo et alii, frattura ed integrità strutturale, 34 (2015) 190-199; doi: 10.3221/igf-esis.34.20 193 for s ≥ 0.25 mm the value of λ calculated from τxy is close to the theoretical value of 0.5 for a stress intensity factor singularity (tab. 1). hence, realistic values of kii can be calculated. for s = 0 mm, in the discs case λ increases as t/a increases, this is in contrast to the plate results where the value of λ has a maximum for t/a = 0.25, and decreases as t/a increases. the values of λ are all significantly less than the theoretical value of 0.598 for a corner point singularity. realistic values of kii can probably be calculated for t/a ≥ 0.25 mm. realistic values of kiii can be calculated from τyz for s ≥ 1 mm. the results for s = 0 mm (fig. 2) show that τyz is slightly lower than τxy for small x, and decreases as x increases. realistic values of kiii cannot be calculated. the presence of finite values of τyz, linked to finite values of kiii (fig. 4), appears because of the appearance of mode i disclinations, which are rotations about the y axis. differentiating the expression for the displacement uz gives the amount of this rotation which increases towards the crack tip, with a concomitant increase in τyz at a surface. this accounts qualitatively for the observed distributions of τyz at a surface. t/a s = 0 mm s = 0.25 mm s = 1 mm disc plate disc plate disc plate 0.25 0.505 0.538 0.497 0.498 0.497 0.497 0.50 0.520 0.527 0.497 0.498 0.497 0.497 0.75 0.530 0.523 0.497 0.498 0.497 0.497 1.00 0.538 0.520 0.497 0.498 0.497 0.497 1.25 0.544 0.517 0.497 0.498 0.497 0.497 1.50 0.549 0.515 0.497 0.498 0.497 0.497 1.75 0.553 0.513 0.497 0.498 0.497 0.497 2.00 0.556 0.512 0.497 0.498 0.497 0.497 2.25 0.559 0.510 0.497 0.498 0.497 0.497 2.50 0.542 0.510 0.497 0.498 0.497 0.497 2.75 0.545 0.509 0.497 0.498 0.497 0.497 3.00 0.547 0.508 0.497 0.498 0.497 0.497 table 1: values of λ for τxy, s is the distance from the surface in the z direction. t/a s = 0 mm s = 0.25 mm s = 1 mm disc plate disc plate disc plate 0.25 0.508 0.507 0.5 0.506 0.506 0.75 0.507 0.506 1.00 0.507 0.506 1.25 0.506 0.506 1.50 0.506 0.506 1.75 0.506 0.506 2.00 0.506 0.506 2.25 0.507 0.506 2.50 0.506 0.505 2.75 0.506 0.506 3.00 0.507 0.506 table 2: values of λ for τyz, s is the distance from the surface in the z direction. a. campagnolo et alii, frattura ed integrità strutturale, 34 (2015) 190-199; doi: 10.3221/igf-esis.34.20 194 figure 2: discs case: stresses τyz and τxy on crack surface at s = 0 mm from disc surface, t/a =1. figure 3: discs case: stresses τyz and τxy on crack surface at s = 1 mm from disc surface, t/a =1. figure 4: discs case: kii and kiii at s = 0 mm from disc surface, t/a = 1. a. campagnolo et alii, frattura ed integrità strutturale, 34 (2015) 190-199; doi: 10.3221/igf-esis.34.20 195 figure 5: discs case: through thickness distribution of kii and kiii for: t/a = 1, x = 0.05 mm. figure 6: plates case: through thickness distribution of kii and kiii for: t/a = 1, x = 0.05 mm. through-the-thickness distributions of kii and kiii for t/a = 1 are shown in figs. 5-6. from tabs. 1 and 2 the values of kii are not realistic for s < 0.25 mm and the values of kiii are not realistic for s < 1 mm. for the discs results (fig. 5) maximum values of kiii are at the centreline. the influence of plate bending means that maxima steadily decrease as t/a decreases. maximum values of kiii tend to zero as t/a tends to zero. this is to be expected because kiii is not possible in two dimensions. for the thicker discs kiii is nearly constant for s > 50 mm [2], and then decreases steadily towards the surface, with an abrupt drop close to the surface. for thinner discs behaviour is similar except that there is no constant kiii region [2]. hence, there is clear evidence of an end effect. for the plates results (fig. 6) the distributions of kiii are significantly different from those for discs results. there are maxima at the centre line but kiii then remains nearly constant for about half the distance to the plate surface. the influence of plate bending again means that maxima steadily decrease as t/a decreases. as a surface is approached kiii first decreases slightly then increases to a maximum at about 0.15 mm from the surface. there is then an abrupt drop which is within the region where realistic values of kiii cannot be calculated. plate bending theory [1] suggests that kii should be zero on the centre line, with a linear increase towards a surface. kii does indeed increase linearly for much of the thickness with a greater increase as the surface is approached. this is within a. campagnolo et alii, frattura ed integrità strutturale, 34 (2015) 190-199; doi: 10.3221/igf-esis.34.20 196 the region where realistic values of kii cannot be calculated. the extent of the linear portion, in terms of plate thickness, decreases as t/a increases but is still present when t/a = 3 [3]. this is in contrast with the discs results [2] where linear portions are less extensive and kii becomes essentially zero for s > 40 mm. maximum values of kii are at the surface. this is within the region where calculated kii values are not realistic so caution is needed in the interpretation of results. discussion here has been a lot of discussion on whether kiii tends to zero or infinity as a corner point is approached [2,3]. when apparent kiii values are calculated from stresses at a constant distance from the crack tip then kiii appears to tend to zero as the model surface is approached (fig. 5-6), in accordance with the linear elastic prediction. however, apparent values of kiii at the surface (fig. 4) increase strongly as the distance from the crack tip at which they are calculated decreases. these results can be interpreted as indicating that kiii tends to infinity at a corner point in accordance with bažant and estenssoro’s prediction. the results in figs. 5-6 also show that kii does appear to tend to infinity as the surface is approached, in accordance with bažant and estenssoro’s prediction. the discussion is futile because, as pointed out by benthem [9], kiii is meaningless at a corner point and there is no paradox. for s ≥ 0.25 mm the value of λ calculated from τxy is close to the theoretical value of 0.5 for a stress intensity factor singularity so kii provides a reasonable description of the crack tip stress field. similarly, kiii provides a reasonable description of the crack tip stress field for s ≥ 1 mm. at the surface, values of λ obtained from τxy are always less than the theoretical value for a corner point singularity. the distribution of τyz at the surface (fig. 2) cannot be accounted for on the basis of bažant and estenssoro’s analysis. there is clear evidence of a boundary layer effect whose extent is independent of the thickness. the only available characteristic dimension controlling the boundary layer thickness is the crack length, a. strain energy density through the disc and plate thickness he intensity of the local stress and strain state through the disc and plate thickness can be easily evaluated by using the strain energy density (sed) averaged over a control volume embracing the crack tip (see ref. [13] for a review of the sed approach). the main advantage with respect to the local stress-based parameters is that it does not need very refined meshes in the close neighbourhood of the stress singularity [19]. furthermore the sed has been considered as a parameter able to control fracture and fatigue in some previous contributions [14-18, 22] and can easily take into account also coupled three-dimensional effects [2, 3, 23, 24]. with the aim to provide some numerical assessment of the contribution of the three-dimensional effects, specifically the coupled fracture mode, kii, the local energy density through the disc and plate thickness has been evaluated and discussed in this section. figure 7: discs case: through the thickness sed distribution for t/a = 0.50, 1, 2, 3. control radius r0 = 1.00 mm. t t a. campagnolo et alii, frattura ed integrità strutturale, 34 (2015) 190-199; doi: 10.3221/igf-esis.34.20 197 figs. 7-8 show the local sed variation respectively across the disc and the plate averaged over a cylindrical volume having radius r0 and height h, with h about equal to r0. in refs [13, 14-16, 17-18] r0 was thought of as a material property which varies under static and fatigue loading but here, for the sake of simplicity, r0 and h are simply set equal to 1.0 mm, only to quantify the three-dimensional effects through the disc and plate thickness. the influence of the applied mode iii loading combined with the induced singular mode ii loading is shown in figs. 7-8. for the discs results the ratio between the maximum values of kii and kiii is quite low (about 2) as can be seen from fig. 5, so that the maximum contributions are not significantly different and the position of the maximum sed results to be a function of disc thickness [2]. for thin discs it is close to the lateral surface, but for thick discs the maximum sed is at the mid-plane and its value is about 1.5 times the value at the lateral surface. for the plate results (fig. 6), indeed, the maximum contribution of the coupled mode ii is significantly higher (about 4 times) compared to the maximum contribution of the applied mode iii. it is evident that the position of the maximum sed is the same in all cases. it is close to the lateral surface, where the maximum intensity of the coupled mode ii takes place, both for thin plates, t/a = 0.5 and 1.0, and for thick ones, t/a = 2 and 3. figure 8: plates case: through the thickness sed distribution for t/a = 0.50, 1, 2, 3. control radius r0 = 1.00 mm. conclusions (1) the results obtained from the highly accurate finite element analyses have improved understanding of the behaviour of through cracked discs and plates under anti-plane loading. in particular, it is confirmed that mode iii does induce coupled mode iic. (2) the influence of plate bending is increasingly important as thickness decreases. the anti-plane loading used is a nominal mode iii loading. for thin discs and plates it is a mixed modes iii and ii loading, in which mode iii induces mode iic and vice versa. at the present state of the art it is not possible to separate the coupled modes from the applied modes. (3) bažant and estenssoro’s analysis works well for the symmetric mode (mode i), but it is incomplete for the asymmetric mode (a combination of modes ii and iii). (4) discussion on whether kiii tends to zero or infinity as a corner point is approached is futile because, as pointed out by benthem, kiii is meaningless at a corner point. (5) the present results do not confirm the existence of a corner point singularity dominated region within a k-dominated region. it appears that a new field parameter, probably a singularity, is needed to describe the stresses at the free surfaces. (6) calculation of the strain energy density (sed) in a control volume at the crack tip shows that the position of the maximum sed in the discs case is a function of the thickness. in the plates case instead the position of the maximum sed is independent of plate thickness, contrary to discs results. a. campagnolo et alii, frattura ed integrità strutturale, 34 (2015) 190-199; doi: 10.3221/igf-esis.34.20 198 (7) under the anti-plane loading used theoretical understanding of the stress field in the vicinity of a corner point is still incomplete. references [1] kotousov, a., lazzarin, p., berto, f., pook, l. p., three-dimensional stress states at crack tip induced by shear and anti-plane loading, eng. fract. mech., 108 (2013) 65-74. doi:10.1016/j.engfracmech.2013.04.010. [2] pook, l. p., berto, f., campagnolo, a., lazzarin, p., coupled fracture mode of a cracked disc under anti-plane loading, eng. fract. mech., 128 (2014) 22-36. doi:10.1016/j.engfracmech.2014.07.001. [3] pook, l. p., campagnolo, a., berto, f., lazzarin, p., coupled fracture mode of a cracked plate under anti-plane loading, eng. fract. mech., (2015). doi:10.1016/j.engfracmech.2014.12.021. [4] pook, l. p., a 50-year retrospective review of three-dimensional effects at cracks and sharp notches, fatigue fract. engng. mater. struct., 36 (2013) 699-723. doi: 10.1111/ffe.12074. [5] bažant, z. p., estenssoro, l. f., surface singularity and crack propagation, int. j. solids struct., 15 (1979) 405-426. [6] pook, l. p., some implications of corner point singularities, eng. fract. mech., 48 (1994) 367-378. [7] pook, l. p., linear elastic fracture mechanics for engineers. theory and applications, wit press, southampton (uk), (2000). [8] williams, m. l., on the stress distribution at the base of a stationary crack, j. appl. mech., 24 (1957) 109-114. [9] benthem, j. p., the quarter-infinite crack in a half-space; alternative and additional solutions, int. j. solids struct., 16(2) (1980) 119-130. doi:10.1016/0020-7683(80)90029-3. [10] dhondt, g., on corner point singularities along a quarter circular crack subject to shear loading, int. j. fract., 89 (1998) l13-l18. [11] paris, p. c., sih, g. c., stress analysis of cracks, in: fracture toughness testing and its applications, astm stp 381, american society for testing and materials, philadelphia (usa), (1965) 30-81. [12] timoshenko, s. p., goodier, j. n., theory of elasticity, third ed., mcgraw-hill book company, new york (usa), (1970). [13] berto, f., lazzarin, p., recent developments in brittle and quasi-brittle failure assessment of engineering materials by means of local approaches, mater. sci. eng. r, 75 (2014) 1-48. doi:10.1016/j.mser.2013.11.001. [14] lazzarin, p., berto, f., elices, m., gómez, j., brittle failures from uand v-notches in mode i and mixed, i+ii, mode. a synthesis based on the strain energy density averaged on finite size volumes, fatigue fract. engng mater. struct., 32 (2009) 671–684. doi: 10.1111/j.1460-2695.2009.01373.x [15] torabi, a. r., campagnolo, a., berto, f., mode ii brittle fracture assessment of key-hole notches by means of the local energy, j. test. eval., 44 (2016). doi: 10.1520/jte20140295. [16] torabi, a. r., campagnolo, a., berto, f., local strain energy density to predict mode ii brittle fracture in brazilian disk specimens weakened by v-notches with end holes, mater. design, 69 (2015) 22-29. doi:10.1016/j.matdes.2014.12.037. [17] berto, f., lazzarin, p., yates, j. r., multiaxial fatigue of v-notched steel specimens: a non-conventional application of the local energy method, fatigue fract. engng. mater. struct., 34 (2011) 921-943. doi: 10.1111/j.1460-2695.2011.01585.x. [18] berto, f., campagnolo, a., lazzarin, p., fatigue strength of severely notched specimens made of ti-6al-4vunder multiaxial loading, fatigue fract. engng. mater. struct., (2015). doi: 10.1111/ffe.12272. [19] lazzarin, p., berto, f., zappalorto, m., rapid calculations of notch stress intensity factors based on averaged strain energy density from coarse meshes: theoretical bases and applications, int. j. fatigue, 32 (2010) 1559-1567. [20] yosibash, z., shannon, s., computing edge stress intensity functions (esifs) along circular 3-d edges, eng. fract. mech., 117 (2014) 127-151. doi:10.1016/j.engfracmech.2014.01.013. [21] omer, n., yosibash, z., on the path independency of the point-wise j integral in three dimensions, int. j. fracture, 136 (2005) 1-36. doi: 10.1007/s10704-005-3934-7. [22] torabi, a. r., campagnolo, a., berto, f., experimental and theoretical investigation of brittle fracture in key-hole notches under mixed mode i/ii loading, acta mech., 226 (2015) 2313-2322. doi: 10.1007/s00707-015-1323-5. [23] campagnolo, a., berto, f., lazzarin, p., the effects of different boundary conditions on three-dimensional cracked discs under anti-plane loading, eur. j. mech. – a/solids, 50 (2015) 76-86. doi:10.1016/j.euromechsol.2014.11.001. [24] marangon, c., campagnolo, a. berto, f., three-dimensional effects at the tip of rounded notches subjected to modei loading under cyclic plasticity, j. strain anal. eng., 50 (2015) 299-313. doi: 10.1177/0309324715581964. microsoft word numero_49_art_26_2519 n. s. popova et alii, frattura ed integrità strutturale, 49 (2019) 267-271; doi: 10.3221/igf-esis.49.26 267 focused on russian mechanics contributions for structural integrity predicting the crack path in a wedge under a concentrated tensile force by means of variational principle nataliya s. popova, evgeny m. morozov national research nuclear university mephi (moscow engineering physics institute), russia pakhalina0990@gmail.com, evgeny.morozof@gmail.com yury g. matvienko mechanical engineering research institute of the russian academy of sciences, russia ygmatvienko@gmail.com, http://orcid.org/0000-0003-2367-0966 abstract. variational principle of brittle fracture mechanics is employed to predict the crack path in an infinite wedge under a concentrated tensile force. the weight function in basic equation of variational problem is assumed to be proportional to the maximum strain in the uncracked wedge. obtained equation for solving the variational problem allowed predicting the crack path in general. the predicted crack path is in agreement with experimental results obtained in the case of the truncated wedge. keywords. crack path; variational principle; wedge; concentrated tensile force. citation: popova, n. s., morozov, e. m., matvienko, y, g., predicting the crack path in a wedge under a concentrated tensile force by means of variational principle, frattura ed integrità strutturale, 49 (2019) 267-271. received: 14.05.2019 accepted: 25.05.2019 published: 01.07.2019 copyright: © 2019 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. introduction search of the crack path is one of important problems in the field of brittle and elastic-plastic fracture mechanics. this problem can be solved by means two basic approaches of fracture mechanics, namely, incremental and integral approaches. first approach is based on incremental methods which are widely spread and associated with local criterion. local criteria allow estimating a fracture angle between directions of the initial crack propagation and succeeding crack increment. basically, local criteria for determining the crack path under complex mixed mode loading conditions employ an analysis of energy and stress (strain) fields in the vicinity of the crack tip. possible local criteria can be based on the maximum tangential stress criterion, the maximum tangential strain criterion, the maximum energy release rate criterion, criterion of the minimum energy consumption for fracture, criterion of the strain energy density, the jintegral concept and etc. the details of modern criteria for predicting the crack path can be found in refs. (e.g. [1-6]). integral approach allows predicting the crack path in general and can be based on a variational principle of fracture mechanics [7-9]. the minimum of the certain functional in this principle is assumed to interpret the crack propagation line as a geodesic line on the surface of solids. it should be noted that the functional contains the weight function depending a http://www.gruppofrattura.it/va/49/2519.mp4 n. s. popova et alii, frattura ed integrità strutturale, 49 (2019) 267-271; doi: 10.3221/igf-esis.49.26 268 on the stress and strain field of the uncracked solid and search functions. in this case, the crack path on the surface is described by means of search functions. the present paper deals with a variational principle of fracture mechanics to predict the crack path in a wedge under a concentrated tensile force. the variational principle in a search of the crack path he crack tip is assumed to be a material particle which has some effective mass [7]. in this case, the crack propagates due to movement of this effective mass at the crack tip. the above-mentioned assumption leads to the variational problem for predicting crack paths and can be given by the following equation  l 0 . (1) the functional l should be determined to solve the variational problem for predicting the crack path in a solid under considered loading conditions. the functional l in the case of a flat plate can be written as follows    b a l x, y ds ,   2ds 1 y dx . (2) the weight function in eq. (1) is denoted as φ(x,y). this function is dependent on stresses (or strains) in the uncracked solid. the crack path on the solid surface can be described by the following equation r=r(x,y), where r is the radius-vector. a point belonging to the crack path has cartesian coordinates x and y. equation of the crack path is assumed to be an extremal that should be calculated from basic eqn. (1). a formulation of the variational problem, taking into account the euler-lagrange equation, the minimum of the functional l and the transversally condition, gives well-defined boundary conditions for ends of the crack path, i.e. the crack path should be perpendicular to the free surface of a solid [9]. according to the variational principle, the crack path is interpreted as a geodesic line which is the shortest possible line between two points a and b on the surface of a solid. in this case, the crack propagation line has to satisfy the following condition   b a ds 0 . the crack increment is also assumed to be deviated from the initial direction of crack growth by the stress state. therefore, a metric of the generalized geodesic line is also determined by the stress state of the untracked body and can be written by the following expression  *ds ds , i.e.   b * a ds 0 [7, 8]. it was shown [7-9] that the function  in brittle fracture mechanics is connected with the maximum principal stress or strain in solids without cracks. to illustrate predicting the crack path by means of variational principle, an infinite wedge under concentrated tensile force p is analyzed (fig. 1). the angle between the wedge axis and the lateral surface is marked as α. in this case, the function  in eq. (2) is assumed to be proportional to the maximum strain 1 [9]        1 2 2 2p x x, y e x y (3) where ν is poisson’s ratio and e is young’s modulus. taking into account the above-mentioned statement, the minimum of the functional l can be written in the following form   2 1 x 2 2 2 x 2νp x δ 1+ y' dx = 0 πe x + y (4) this relationship leads to equation for solving the variational problem in a search of the crack path t n. s. popova et alii, frattura ed integrità strutturale, 49 (2019) 267-271; doi: 10.3221/igf-esis.49.26 269             2 2 2 2 2 y '' x y x y ' y x 2xy 0 1 y ' (5) figure 1: the scheme of an infinite wedge under concentrated tensile force p. eqn. (5) can be solved related to y as a function of x to predict the crack path in an infinite wedge under concentrated tensile force p. it should be also noted, the crack path is in agreement with the minimum value of the energy lost accompanied by creating a new surface of the crack. in this case, the radius-vector r is constant for the crack path in an infinite wedge under concentrated tensile force p [7]. the results of numerical solution of eq. (5) are presented in fig. 2 for two angles α and the radius-vector r0. it can be seen that the crack paths have arc shapes and are perpendicular to the free surface of the truncated wedge as it was expected according the variational principle. figure 2: predicted crack paths in an infinite wedge under concentrated tensile force p: (a) 2α = 400, (b) 2α = 600. n. s. popova et alii, frattura ed integrità strutturale, 49 (2019) 267-271; doi: 10.3221/igf-esis.49.26 270 validation of the variational principle o validate the variational principle for a search of the crack path, the truncated wedge (having 3 mm thickness) (fig. 3) is tested under concentrated tensile force p at room temperature. the angle between the truncated wedge axis and the lateral surface is 20o. the specimen is made from the organic glass. mechanical properties of the material are the following: young’s modulus e = 3000 mpa, ultimate strength σu=70 mpa and poisson’s ratio ν = 0.36. figure 3: the scheme of the truncated wedge which is tested under concentrated tensile force. to initiate the crack propagation under concentrated tensile force, the initial notch perpendicular to the lateral surface of the truncated wedge was created. the notch length is 5 mm. the specimen was painted for better visualization of the crack propagation. it can be seen that the predicted crack path is in agreement with the experimental crack path (fig. 4). moreover, the crack propagates perpendicular to free surface of the truncated wedge. this result confirms correctness of the employed model and the variational principle to predict the crack path in the wedge under concentrated tensile load. figure 4: comparison of the experimental crack path (a) with the predicted crack path (b) in the truncated wedge under concentrated tensile load. t n. s. popova et alii, frattura ed integrità strutturale, 49 (2019) 267-271; doi: 10.3221/igf-esis.49.26 271 conclusions he paper deals with the variational principle of brittle fracture mechanics which is applied to predict the crack path in the case of the wedge under concentrated tensile load. the basic equations of the variational principle are presented. the following conclusions can be made. the weight function in basic equations, which is assumed to be proportional to the maximum strain in an infinite wedge under concentrated tensile load, allows predicting crack path in general. to validate the variational principle for a search of the crack path in the case of a wedge under concentrated tensile force p, the truncated wedge is tested at room temperature. the crack paths have arc shapes and are perpendicular to the lateral surface of the truncated wedge as it was expected according the variational principle. the predicted crack path is in agreement with experimental results. acknowledgements rofessor matvienko acknowledges the support of the russian science foundation (project n 18-19-00351). references [1] aliha, m.r.m., ayatollahi, m.r., smith, d.j. and pavier, m.j. (2010). geometry and size effects on fracture trajectory in a limestone rock under mixed mode loading, engng. fract. mech., 77, pp. 2200-2212. [2] sajjadi, s. h., ostad ahmad ghorabi, m. j. and salimi-majd, d. (2015). a novel mixed-mode brittle fracture criterion for crack growth path prediction under static and fatigue loading, fatigue fract. eng. mater. struct., 38, pp. 1372– 1382. [3] mirsayar, m.m., berto, f., aliha, m.r.m. and park, p. (2016). strain-based criteria for mixed-mode fracture of polycrystalline graphite, engng. fract. mech., 156, pp. 114-123. [4] pook, l.p. (2016). the linear elastic analysis of cracked bodies, crack paths and some practical crack path examples, eng. fract. mech., 167, pp. 2-19. [5] berto, f. and gomez, j. (2017). notched plates in mixed mode loading (i+ ii): a review based on the local strain energy density and the cohesive zone mode, engineering solid mechanics, 5, pp. 1-8. [6] matvienko, yu.g. (2012). maximum average tangential stress criterion for prediction of the crack path, int. j. fract., 176, pp. 113-118. [7] parton, v.z. and morozov, e.m. (1989). mechanics of elastic-plastic fracture, hemisphere publ.: n.y. [8] morozov, e.m. (1998) some heuristic models of propageting cracks. in fracture: a topical encyclopedia of current knowledge (cherepanov, g.p., ed.), krieger publ. comp.: florida. [9] matvienko, y.g., morozov, e.m. (2017). two basic approaches in a search of the crack propagation angle, fatigue fract. eng. mater. struct., 40, pp. 1191-1200. t p << /ascii85encodepages false /allowtransparency false /autopositionepsfiles true /autorotatepages /none /binding /left /calgrayprofile (dot gain 20%) /calrgbprofile (srgb iec61966-2.1) /calcmykprofile (u.s. web coated \050swop\051 v2) /srgbprofile (srgb iec61966-2.1) /cannotembedfontpolicy /error /compatibilitylevel 1.4 /compressobjects /tags /compresspages true /convertimagestoindexed true /passthroughjpegimages true /createjobticket false /defaultrenderingintent /default /detectblends true /detectcurves 0.0000 /colorconversionstrategy /cmyk /dothumbnails false /embedallfonts true /embedopentype false /parseiccprofilesincomments true /embedjoboptions true /dscreportinglevel 0 /emitdscwarnings false /endpage -1 /imagememory 1048576 /lockdistillerparams false /maxsubsetpct 100 /optimize true /opm 1 /parsedsccomments true /parsedsccommentsfordocinfo true 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can be opened with acrobat and adobe reader 5.0 and later.) >> /namespace [ (adobe) (common) (1.0) ] /othernamespaces [ << /asreaderspreads false /cropimagestoframes true /errorcontrol /warnandcontinue /flattenerignorespreadoverrides false /includeguidesgrids false /includenonprinting false /includeslug false /namespace [ (adobe) (indesign) (4.0) ] /omitplacedbitmaps false /omitplacedeps false /omitplacedpdf false /simulateoverprint /legacy >> << /addbleedmarks false /addcolorbars false /addcropmarks false /addpageinfo false /addregmarks false /convertcolors /converttocmyk /destinationprofilename () /destinationprofileselector /documentcmyk /downsample16bitimages true /flattenerpreset << /presetselector /mediumresolution >> /formelements false /generatestructure false /includebookmarks false /includehyperlinks false /includeinteractive false /includelayers false /includeprofiles false /multimediahandling /useobjectsettings /namespace [ (adobe) (creativesuite) (2.0) ] /pdfxoutputintentprofileselector /documentcmyk /preserveediting true /untaggedcmykhandling /leaveuntagged /untaggedrgbhandling /usedocumentprofile /usedocumentbleed false >> ] >> setdistillerparams << /hwresolution [2400 2400] /pagesize [612.000 792.000] >> setpagedevice microsoft word numero_49_art_19_2471 v. matveenko et alii, frattura ed integrità strutturale, 49 (2019) 177-189; doi: 10.3221/igf-esis.49.19 177 russian mechanics contributions for structural integrity numerical analysis of the strain values obtained by fbg embedded in a composite material using assumptions about uniaxial stress state of the optical fiber and capillary on the bragg grating. valerii p. matveenko institute of continuous media mechanics ub ras mvp@icmm.ru, http://orcid.org/0000-0003-2787-6558 natalia a. kosheleva perm national research polytechnic university nataly.kosheleva@gmail.com, http://orcid.org/0000-0002-8760-2957 grigorii s. serovaev, andrey yu. fedorov institute of continuous media mechanics ub ras serovaev@icmm.ru, http://orcid.org/0000-0003-0312-8088 fedorov@icmm.ru, http://orcid.org/0000-0001-8239-3386 abstract. one of the issues in the strain measurement with the help of fiber-optic sensors based on bragg gratings is the calculation of the strain based on the information from the sensor and its correspondence to the material strain. relationships between the data measured by the sensor and the strain in the bragg grating have a unique solution under the condition of uniaxial stress state of the fiber, which are not fulfilled when the fiber is embedded in the material. the paper presents the results of numerical simulations with an example of a model problem for a polymer composite material with an embedded optical fiber, which can be surrounded by a resin pocket. the presented results allow to estimate the error of the strain values calculated on the basis of uniaxial stress state assumption of the optical fiber. based on numerical calculations, parameters of a capillary on an optical fiber in the bragg grating zone are estimated, ensuring uniaxial stress state of the fiber in the bragg grating zone. to ensure these conditions, the cross section of the capillary in an isotropic material is a circle, and in an anisotropic material, good results can be obtained with an elliptical cross section. keywords. single-mode optical fiber; fbg; polymer composite material; sensor embedded in the material; capillary. citation: matveenko, v., kosheleva, n., serovaev, g., fedorov, a., numerical analysis of the strain values obtained by fbg measurements embedded in a composite material using assumptions about uniaxial stress state of the optical fiber and capillary on the bragg grating, frattura ed integrità strutturale, 49 (2019) 177-189. received: 09.04.2019 accepted: 16.05.2019 published: 01.07.2019 copyright: © 2019 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. http://www.gruppofrattura.it/va/49/2471.mp4 v. matveenko et alii, frattura ed integrità strutturale, 49 (2019) 177-189; doi: 10.3221/igf-esis.49.19 178 introduction owadays fiber-optic sensors successfully compete and in some cases displace piezoelectric, acoustic, thermal, electromagnetic, electrical devices for measuring physical quantities. this is a consequence of the unique properties of fiber-optic sensors: insensitivity to electromagnetic effects and to radiation; no need for power supply near the sensor; ability to work in a wide temperature range. the fiber is both a sensor and information transmission channels, which makes it possible to use fiber-optic systems for objects of large size successfully. fiber optic sensors are based on the use of various physical effects. in this paper, the widely used fiber optic sensors based on bragg gratings written in a standard single-mode optical fiber for strain measurements are considered. examples of their successful applications in various structures and industries are contained in the refs. [1–6]. for structural health monitoring one of the most demanded are products made of polymer composite materials (pcm). the known methods do not provide a guaranteed solution to the corresponding issues while the range and areas of application of pcm are constantly expanding. the small dimensions of the optical fiber and the manufacturing process of pcm products make it possible to embed optical fibers into pcm structure. the use of fiber-optic strain sensors (foss) embedded into material discovers fundamentally new possibilities for structural health monitoring of constructions during their operation, including the stage of manufacturing process of material. optical fibers can be embedded between different layers of the composite material, thereby forming a network of optical fibers inside material. a number of problems arise when foss based on bragg gratings embedded into pcm are used. one of the most difficult tasks is related to the evaluation and search for options to ensure the reliability of strain values calculated on the basis of a physical quantity recorded by a sensor. great opportunities to solve this problem are associated with mathematical modeling. a significant number of works are devoted to this area. the main essence of the problem is that the wellknown relations between the physical quantity recorded by the sensor and the components of the strain tensor in the zone of bragg gratings [7] have a unique solution only under the condition of uniaxial stress state in an optical fiber. optical fiber embedded in a material, as a rule, operates under complex stress state. it should also be noted that in order to make reasonable use of foss, it is necessary to ensure the coincidence of strains along the fiber in the material and in the bragg grating zone of the optical fiber. in the given in ref. [8], it is noted that the embedded fiber bragg grating (fbg) operates under complex stress state and, therefore, for the fbg it is necessary to introduce calibration coefficients for the corresponding strains. in this case, studies have shown that the calibration of the transverse strains is difficult to control. calibration problems are discussed in detail in refs. [9,10]. in ref. [11], it is noted that large radial strains lead to a large deviation of the measured strain by embedded fbgs. it is noted that after embedding into the material, each sensor must be calibrated or, for the embedded sensor, the strain tensor must have a dominant component along the fiber axis. as a constructive solutions to obtain reliable information about the axial components of the strain tensor, it is proposed in refs. [12,13] to use a pair of micro-structured fbgs that are precisely oriented relative to each other. a sensor model is proposed that is experimentally tested on layered composites. in ref. [14], it is proposed to introduce a transfer matrix based on numerical modeling, the components of which establish the connection of strains in the material and fiber and are calculated based on consideration of three loading options: tension along the optical fiber, out of plane transverse load and transverse load in the plane of the specimen. in ref. [15], the problem of estimating the strain transfer from the host material to the embedded sensor is also considered. experimental data show that under certain types of loading strong birefringent effects are present. in order to eliminate the effect of transverse strains on the embedded optical fiber measurements, the authors use a capillary in the region of the bragg grating. such scheme leads to uniaxial stress state of the grating and the relationship between the longitudinal and transverse components of the strain tensor through the poisson coefficient. in order to ensure the sensitivity of the bragg grating to compressive strain, a preliminary tension of the optical fiber is carried out. encapsulation of the bragg grating in the capillary ensures the single peak on the reflected spectrum after the implementation of the technological process of composite material production. the results of fairly accurate measurements of the strain field in carbon-fiber specimens are demonstrated. another example of the use of a capillary in the region of the bragg grating is given in ref. [16], in which the use of a capillary is aimed at increasing the temperature sensitivity of a fiber-optic sensor. the authors demonstrate the applicability of the proposed approach to various fbgs enclosed in a zinc capillary and various binder materials. an example of the use of a transfer matrix is discussed in ref. [17], where the results based on numerical and experimental data are given. the importance of converting measured strains into real strains, which can differ significantly from each other, is demonstrated. this paper proposes a method for the numerical estimation of the error of strain values determined by formulas based on the assumption of uniaxial stress state of an optical fiber. the results are presented when the pcm is represented by a n v. matveenko et alii, frattura ed integrità strutturale, 49 (2019) 177-189; doi: 10.3221/igf-esis.49.19 179 layered model and a homogeneous medium model. a variant of the embedded optical fiber in the presence and absence of a resin pocket is considered. the use of a capillary in the area of the bragg grating is proposed as a constructive solution to ensure the use of the embedded foss on bragg gratings for various types of loading. based on numerical calculations, the capillary parameters are estimated, which ensure uniaxial stress state of the fiber in the bragg grating zone and the correspondence of the strains in the material and the strains calculated on the basis of the physical quantity measured by the fbg. numerical analysis of strains, calculated based on embedded fbg measurements he measurement of strain by sensors based on bragg gratings written in a standard single-mode optical fiber is implemented according to the diagram presented in fig. 1. figure 1: the principle of fbg operation. the interrogator sends a broadband optical signal over an optical fiber in a given wavelength range. part of this signal is reflected on the bragg grating. the main part of the reflected signal determines the resonant wavelength of the reflected spectrum. this wavelength λ* is proportional to the effective refractive index n of the optical fiber in the area of the grating and the geometric length of the period of the bragg grating l [8]: * 2nl  (1) the scheme of strain measurement by a fbg sensor embedded into pcm is shown in fig. 2. figure 2: the scheme of strain measurement by a fbg sensor. t v. matveenko et alii, frattura ed integrità strutturale, 49 (2019) 177-189; doi: 10.3221/igf-esis.49.19 180 when foss interacts with a deformable material, a change in the bragg grating length occurs. this leads to a change in the wavelength of the reflected spectrum δλ, which is recorded by the interrogator. the relationship between the changes in the bragg wavelength and the strain of the fiber in the bragg grating zone is determined by the relations [8]: 21 3 11 1 12 2 3* 22 3 11 2 12 1 3* 1 ( ( )) 2 1 ( ( )) 2 n p p n p p                     (2) where 3 – is the strain along the fiber, 1 2,  – are the principle strains in the plane perpendicular to the optical fiber, * * 1 1 2 2,          – are the differences in the values of the resonant wavelengths of the reflected spectrum at the current 1 2,  and initial * moments of time, 11 12,p p – are the pockels coefficients. under uniaxial stress state of an optical fiber, which is free from interaction with the environment, the relation between strain components can be expressed as 1 2 3     , where  is the poisson's ratio of the optical fiber. in this case 1 2     and   2 12 11 12 3* 1 ( ) 2 n p p p             (3) or 3 * 1 k      (4) for quartz optical fiber with parameters 11 0.113p  , 12 0.252p  , 1.5n  , 0.17  , the coefficient k ~0.79. when the fiber-optic sensor is embedded in a polymer composite material or even connected in some way with the surface of the material, for example, by gluing, a complex-stressed state in the sensor as a result of the interaction with the material, will be realized. there will be strains 1 2 3, ,   that need to be identified on the basis of experimental information, namely the values of 1 *   and 2 *   . from eq. (2) it follows that if 1 2   , we have two equations with three unknowns, and when 1 2   one equation with two unknowns. figure 3: the reflected spectrum with two peaks of foss embedded in pcm. v. matveenko et alii, frattura ed integrità strutturale, 49 (2019) 177-189; doi: 10.3221/igf-esis.49.19 181 the presence in the reflected spectrum of two resonant wavelengths as a result of the interaction of the bragg grating with the surrounding material is noted as an experimental result, for example, in refs. [8,18]. the following result can be presented as an example. the foss with a bragg wavelength of 1565 nm was embedded in the middle part of the specimen (a plate with a size of 502005 mm), manufactured by an autoclave method and consisting of 20 layers of fiberglass prepreg (vps-48). after the sample is manufactured, the process-induced strains take place in it [19]. as a result, the embedded fbg is under the influence of these strains, and two peaks are observed in the reflected spectrum (fig. 3). thus, a direct relation between the experimental information *  and the strain component 3 along the fiber takes place only under the uniaxial stress state of the bragg grating. numerical simulations allow to estimate the limits of applicability of eq. (4). as a model object, parallelepiped with integrated optical fiber (fig. 4) was considered with different loading options (normal displacements along the side faces x ou u ; y ou u ; z ou u ). figure 4: the calculation scheme for material with embedded foss. the parameters of the polymer composite material related to the , ,x y z axes and optical fiber are shown in tab. 1 and tab. 2. the fiber has a diameter of 0.124 mm and a protective polyimide coating of 0.012 mm thick. material x e , gpa ye , gpa ze , gpa xy  yz zx xyg , gpa yzg , gpa zxg , gpa unidirectional prepreg 158.5 8.96 8.96 0.32 0.45 0.32 4.6 3.0 4.6 effective mechanical characteristics of the layer stacking 84.1 84.1 10.7 0.035 0.45 0.45 4.3 3.5 3.5 table 1: mechanical properties of the unidirectional prepreg and effective mechanical characteristics of the layer stacking. material e, gpa  quartz 71.4 0.17 polyimide 2.5 0.35 epoxy 2.9 0.36 table 2: mechanical characteristics of optical fiber and epoxy. in numerical experiments, pcm was considered on the basis of a layered and homogeneous models (fig. 5). v. matveenko et alii, frattura ed integrità strutturale, 49 (2019) 177-189; doi: 10.3221/igf-esis.49.19 182 figure 5: variants of composite material models: layered (a) and homogeneous (b). in a layered model, the pcm is represented as a layer stacking, each of which is a homogeneous anisotropic body. this model allows to take into account the different orientation of the layers. pcm in the framework of a homogeneous model is represented as a homogeneous anisotropic elastic body with effective mechanical characteristics. the optical fiber embedded between the pcm layers, retains its geometry. wherein the prepreg layers in the vicinity of the fiber can be bent, which leads to the pocket formation filled with polymer matrix. this sub-area is a technological defect called a resin pocket. the geometry of a resin pocket significantly depends on the type of prepregs and their stacking options. for unidirectional prepregs, there may be various options associated with the formation of a resin pocket. in particular, if there are two layers [0/0] in the layer stacking and the fiber is laid between these layers then for this variant the resin pocket is not formed. the option of having two layers [90/90] in a laminated composite material and an optical fiber embedded between these layers leads to the formation of the maximum resin pocket, with all other factors equal. the geometry of the resin pocket (fig. 6) obtained by experimental and numerical methods is shown in ref. [20]. figure 6: polymer composite material with optical fiber and resin pocket: optical fiber (1); optical fiber coating (2); a resin pocket (3); polymer composite layer (4). in this paper, the variants of a layered model without a resin pocket when the optical fiber is placed between the [0/0] layers and with resin pocket when the fiber is placed between the [90/90] layers are considered. also, variants with and without a resin pocket are considered for a homogeneous model. cross-sections of the corresponding model objects are shown in fig. 7. following the conclusions given in ref. [21], the following size of the resin pocket is taken 18b r . the calculations were carried out by the finite element method in a three-dimensional formulation using mesh that is refined in the zone of stress concentration. fig. 8 shows the finite element discretization of the cross section of the model. the accuracy of calculations was estimated on the basis of an analysis of the convergence of solutions with an increase in the number of elements. v. matveenko et alii, frattura ed integrità strutturale, 49 (2019) 177-189; doi: 10.3221/igf-esis.49.19 183 figure 7: variants of the representation of a polymer composite material with embedded optical fiber. figure 8: finite element mesh of the model with embedded optical fiber and resin pocket. the purpose of numerical experiments is to calculate the strains 1 2 3, ,   in the optical fiber under different loading options, and to calculate the values *1  and * 2  according to eq. (2). wherein, the coincidence of the strain 3 v. matveenko et alii, frattura ed integrità strutturale, 49 (2019) 177-189; doi: 10.3221/igf-esis.49.19 184 and the corresponding strain in the material in the vicinity of the fiber is controlled in the calculations. further, the values * 1  and * 2  are taken as experimental data to calculate the strain 3 exp along the fiber based on the eq. (4). then the error between the strain 3 and 3 exp is estimated. in tab. 3 the values 1 2 3 * * *, ,   ,  **1  ,   ** 2  and the magnitude of the errors 1 and 2 are shown. here 1 * 1 ou   , 2 * 2 ou   , 3 * 3 ou   ; * * 1 1 2 2 ,/ /o ou u                               . the error in the calculation of strain based on the eq. (4) is determined as follows:  11 3 3 3 100%exp       ,  2exp2 3 3 3 100%       , where 1exp 13 * 1 k      , 2exp 23 * 1 k      . tab. 3 also shows the values of 1k and 2k , which, according to the formulas * 1 1 3k    , * 2 2 3k    , provide reliable strain values. layered model with the formation of a resin pocket [90/90] 1 * 2 * 3 *  **1    ** 2  1k 1 % 2k 2 % 0xu u -74.01 -94.32 500.00 389.88 393.09 0.78 0.03 0.79 0.79 0yu u 106.31 -84.90 -22.26 -35.46 -5.18 1.59 104.22 0.23 70.16 0zu u 113.62 10.08 -35.27 -42.65 -59.05 1.21 55.05 1.67 114.66 homogeneous model with the formation of a resin pocket 1 * 2 * 3 *  **1    ** 2  1k 1 % 2k 2 % 0xu u -74.15 -94.17 500.00 389.90 393.07 0.78 0.02 0.79 0.79 0yu u 91.54 -53.13 -20.02 -35.96 -13.04 1.80 130.28 0.65 16.46 0zu u 108.86 10.29 -30.49 -43.47 -59.08 1.43 82.76 1.94 148.40 layered model without the formation of a resin pocket [0/0] 1 * 2 * 3 *  **1    ** 2  1k 1 % 2k 2 % 0xu u -64.57 -96.30 500.00 387.43 392.45 0.77 0.66 0.78 0.63 0yu u 86.79 -27.76 -14.02 -31.33 -13.19 2.23 186.51 0.94 20.64 0zu u 92.21 7.86 -23.99 -31.22 -44.58 1.30 66.83 1.86 138.22 homogeneous model without the formation of a resin pocket 1 * 2 * 3 *  **1    ** 2  1k 1 % 2k 2 % 0xu u -74.30 -94.93 500.00 390.04 393.31 0.78 0.01 0.79 0.85 0yu u 403.99 -147.25 -18.58 -105.69 -18.39 5.69 629.14 0.99 26.85 0zu u 104.11 -13.96 -28.63 -25.16 -43.86 0.88 12.65 1.53 96.38 table 3: the results of the evaluation of the limits of applicability of relations (4) on a model of a cube with integrated optical fiber. v. matveenko et alii, frattura ed integrità strutturale, 49 (2019) 177-189; doi: 10.3221/igf-esis.49.19 185 for clarity, the dependences of 1k and 2k with respect to the plane 0.78k  by varying  2 3ln   ,  1 3ln   are presented in fig. 9. figure 9: dependences of 1k and 2k on the components of the strain tensor. the obtained results allow us to conclude that the use of bragg gratings written in a single-mode optical fiber provides acceptable information about the component of the strain tensor along the fiber, only in case when the sensor is located in the material zone, where this component of strain is predominant. the dependences given in fig. 9 allow us to estimate the error in the calculation of the strain for different ratios of the strain values 1 and 2 . simulation of foss embedded in pcm with a capillary on the bragg grating ne of the directions for obtaining reliable information about the strains measured by fbg sensors embedded into pcm is associated with a change in the conditions of interaction with the material of the optical fiber section with the bragg grating. in a constructive implementation, this can be achieved by using an additional coating around the fiber in the bragg grating zone (fig. 10). figure 10: cross-section of the sample with foss based on the bragg grating and capillary. o v. matveenko et alii, frattura ed integrità strutturale, 49 (2019) 177-189; doi: 10.3221/igf-esis.49.19 186 the geometrical dimensions of such a coating are determined by the thickness t and the length l. within the framework of the problem statement under consideration, an additional coating must ensure the fulfillment of two conditions: the realization of a uniaxial stress state in the bragg grating section and the coincidence of the longitudinal strain component in the fiber and in the material zone adjacent to the fiber. numerical simulation allows us to estimate the possibility of achieving the goal and determine the parameters of an additional coating for the corresponding pcm and optical fiber. a problem of stress-strain state evaluation on a model of a cube with embedded optical fiber with additional coating is considered (fig. 11). a variant of the calculation scheme with resin pocket is not presented, since its consideration does not affect the magnitude of the strain tensor component along the optical fiber. figure 11: cube with embedded optical fiber and additional coating. dimensions of the cube significantly exceed the length of the additional coating. based on the results of the previous chapter, the most unfavorable loading option is considered, in which external forces operate in the plane of maximum stiffness of the pcm and the direction perpendicular to the fiber. in order to estimate the parameters of the coating that ensure the fulfillment of the condition of a uniaxial stress state in the zone of the bragg grating of the optical fiber, calculations were performed for various combinations of poisson’s ratio and the ratio of the elastic moduli of the optical fiber and the additional coating. calculations have shown that the goal can be achieved only if there is a cavity between the pcm and the optical fiber. technologically, this means using a capillary in the bragg grating zone [15]. with the considered mechanical characteristics of pcm, it is not possible to ensure the coincidence of the corresponding strain in the material and the fiber. so, with a capillary thickness and its length equal to 0.3 and 10 fiber diameters, respectively, the difference between the corresponding strains in the pcm and the optical fiber in the middle cross section along the length of the capillary is 4-5 times. the change in the mechanical characteristics of the pcm showed that it is possible to achieve the conditions of coincidence of the strains when using a capillary with a circular cross section with the isotropic properties of the material. for anisotropic materials, these conditions can be achieved by using a capillary with an elliptical cross section (fig. 12). the results of calculations of the strains /x yu , /y yu , /z yu in an optical fiber, in the middle across the length cross section of the capillary for various relations between the ellipse’s semi axes a ( 0.16a  mm), b and ratios of the capillary length l to the optical fiber diameter d are presented in tab. 4 for materials whose properties are given in tabs. 1 and 2. the analysis of these results should be carried out taking into account the strain value x in pcm equal to 34.37 10 . for the data in the table, it should be noted that the condition y z x     , where ν is the poisson's ratio of the optical fiber material is fulfilled up to 0.22%. the results show that if / 0.6a b  , it is possible to achieve an acceptable coincidence of the strain along the fiber in the pcm and the optical fiber. the obtained values of l show that when using such a capillary, its length should be 20-40 diameters larger than the bragg grating length to ensure that the strain in the material and the fiber coincides along the entire bragg grating length. the v. matveenko et alii, frattura ed integrità strutturale, 49 (2019) 177-189; doi: 10.3221/igf-esis.49.19 187 performed calculations show the possibility of determining by the methods of numerical simulation for specific characteristics of pcm and optical fiber of the capillary sizes that ensure the fulfillment of the set conditions. technological aspects of the implementation of the results obtained in this paper are not considered. figure 12: the scheme of a polymer composite material with an embedded optical fiber and a cavity with an elliptical cross section: optical fiber (1); protective polyimide coating of optical fiber (2); cavity (3); composite material (4). /x yu /y yu /z yu /a b /k l d -0.002653 0.000452 0.000452 1 10 -0.001943 0.000330 0.000330 2 10 -0.005044 0.000858 0.000858 0.5 10 -0.004837 0.000822 0.000822 0.5 20 -0.00399 0.000678 0.000678 0.75 10 -0.00419 0.000712 0.000712 0.6 10 -0.004348 0.000739 0.000739 0.6 20 -0.004372 0.000743 0.000743 0.6 40 table 4: the results of the calculation of strains in the optical fiber with different capillary geometries. conclusions he analysis of the possibility of obtaining reliable strain values in the pcm based on the use of fbg sensor written in a single-mode optical fiber and embedded in the material is carried out. it is noted that for this type of sensors direct relation between the longitudinal strain of the fbg, which with good contact of the sensor with the pcm coincides with the corresponding strain in the material, and the physical quantity recorded by the sensor takes place only with a uniaxial stress state in the fiber. a numerical experimental technique is presented. using the assumption about the nature of stresses in a fiber, it is possible to estimate the error in calculating the strain values of an optical fiber in the fbg zone based on the change in the wavelength of the reflected spectrum measured by the sensor. for the model object of pcm with embedded foss, an analysis of the strain fields in the fiber and material under different loading options is performed. calculations based on the finite element method were carried out for two pcm models: a layered model and a homogeneous medium model. the model takes into account the possibility of a resin pocket in the vicinity of the fiber. different options for the optical fiber location between the layers [0/0], when the resin pocket is absent, and between the layers [90/90], when the resin pocket is formed, were analyzed. t v. matveenko et alii, frattura ed integrità strutturale, 49 (2019) 177-189; doi: 10.3221/igf-esis.49.19 188 obtained results make it possible to estimate the error of the values of the strain tensor component in the fiber along its length based on the values of the physical quantity measured by the sensor, which is the result of numerical calculations within the framework of the considered technique. the combination of the achieved numerical results makes it possible to conclude that for obtaining, with an acceptable error, the values of the measured strains, it is necessary that the sensors should be located in the material zone, where the strain component along the fiber is predominant. a numerical simulation was performed to determine the parameters of the coating around the fbg, which provides a uniaxial stress state in the fbg and the coincidence of the strain values along the fiber directly in the fiber and in the material zone adjacent to the fiber. it is established that the uniaxial stress state is reached only in the presence of a capillary (cavity) between the pcm and the optical fiber. the condition of coincidence of the corresponding strains in the material and the fiber at the circular cross-section of the capillary is ensured only with the isotropic properties of pcm. it is shown that for anisotropic pcm the fulfillment of the condition of coincidence of strains can be achieved with an elliptical capillary cross section. the specific dimensions of the capillary are found by numerical analysis for the corresponding characteristics of the pcm and the optical fiber. acknowledgements his study was supported by russian science foundation (project no.15-19-00243). references [1] gebremichael, y.m., li, w., boyle, w.j.o., meggitt, b.t., grattan, k.t. v., mckinley, b., fernando, g.f., kister, g., winter, d., canning, l., luke, s. (2005). integration and assessment of fibre bragg grating sensors in an all-fibre reinforced polymer composite road bridge, sensors actuators, a phys., 118(1), pp. 78–85, doi: 10.1016/j.sna.2004.08.005. [2] lee, j.-r., ryu, c.-y., koo, b.-y., kang, s.-g., hong, c.-s., kim, c.-g. (2003). in-flight health monitoring of a subscale wing using a fiber bragg grating sensor system, smart mater. struct., 12, pp. 147–155, doi: 10.1088/0964-1726/12/1/317. [3] ghoshal, a., ayers, j., gurvich, m., urban, m., bordick, n. (2015). experimental investigations in embedded sensing of composite components in aerospace vehicles, compos. part b eng., 71, pp. 52–62, doi: 10.1016/j.compositesb.2014.10.050. [4] wymore, m.l., van dam, j.e., ceylan, h., qiao, d. (2015). a survey of health monitoring systems for wind turbines, renew. sustain. energy rev., 52(1069283), pp. 976–990, doi: 10.1016/j.rser.2015.07.110. [5] sierra-pérez, j., torres-arredondo, m.a., güemes, a. (2016). damage and nonlinearities detection in wind turbine blades based on strain field pattern recognition. fbgs, obr and strain gauges comparison, compos. struct., 135, pp. 156–166, doi: 10.1016/j.compstruct.2015.08.137. [6] hong, c.y., zhang, y.f., zhang, m.x., leung, l.m.g., liu, l.q. (2016). application of fbg sensors for geotechnical health monitoring, a review of sensor design, implementation methods and packaging techniques, sensors actuators, a phys., , pp. 184–197, doi: 10.1016/j.sna.2016.04.033. [7] kersey, a.d., davis, m.a., patrick, h.j., leblanc, m., koo, k.p., askins, c.g., putnam, m.a., friebele, e.j. (1997). fiber grating sensors, j. light. technol., 15(8), pp. 1442–1463, doi: 10.1109/50.618377. [8] luyckx, g., voet, e., lammens, n., degrieck, j. (2010). strain measurements of composite laminates with embedded fibre bragg gratings: criticism and opportunities for research, sensors, 11(1), pp. 384–408, doi: 10.3390/s110100384. [9] di sante, r. (2015). fibre optic sensors for structural health monitoring of aircraft composite structures: recent advances and applications, sensors, 15(8), pp. 18666–18713, doi: 10.3390/s150818666. [10] majumder, m., gangopadhyay, t.k., chakraborty, a.k., dasgupta, k., bhattacharya, d.k. (2008). fibre bragg gratings in structural health monitoring present status and applications, sensors and actuators a-physical, 147(1), pp. 150–164, doi: 10.1016/j.sna.2008.04.008. [11] fan, y., kahrizi, m. (2005). characterization of a fbg strain gage array embedded in composite structure, sensors actuators, a phys., 121(2), pp. 297–305, doi: 10.1016/j.sna.2005.01.021. t v. matveenko et alii, frattura ed integrità strutturale, 49 (2019) 177-189; doi: 10.3221/igf-esis.49.19 189 [12] sonnenfeld, c., luyckx, g., sulejmani, s., geernaert, t., eve, s., gomina, m., chah, k., mergo, p., urbanczyk, w., thienpont, h., degrieck, j., berghmans, f. (2015). microstructured optical fiber bragg grating as an internal threedimensional strain sensor for composite laminates, smart mater. struct., 24(5), pp. 055003, doi: 10.1088/0964-1726/24/5/055003. [13] sonnenfeld, c., sulejmani, s., geernaert, t., eve, s., lammens, n., luyckx, g., voet, e., degrieck, j., urbanczyk, w., mergo, p., becker, m., bartelt, h., berghmans, f., thienpont, h. (2011). microstructured optical fiber sensors embedded in a laminate composite for smart material applications, sensors, 11(3), pp. 2566–2579, doi: 10.3390/s110302566. [14] luyckx, g., voet, e., dewaele, w., degrieck, j. (2010). multi-axial strain transfer from laminated cfrp composites to embedded bragg sensor: i. parametric study, smart mater. struct., 19(10), doi: 10.1088/0964-1726/19/10/105017. [15] voet, e., luyckx, g., de waele, w., degrieck, j. (2010). multi-axial strain transfer from laminated cfrp composites to embedded bragg sensor: ii. experimental validation, smart mater. struct., 19(10), pp. 105018, doi: 10.1088/0964-1726/19/10/105018. [16] li, y., wen, c., sun, y., feng, y., zhang, h. (2014). capillary encapsulating of fiber bragg grating and the associated sensing model, opt. commun., 333, pp. 92–8, doi: 10.1016/j.optcom.2014.07.068. [17] lammens, n., luyckx, g., degrieck, j., de waele, w. (2011). experimental determination of the multi-axial strain transfer from cfrp-laminates to embedded bragg sensor, smart struct. mater. 5th eccomas themat. conf. proc., pp. 482–485. [18] wagreich, r.b., atia, w.a., singh, h., sirkis, j.s. (1996). effects of diametric load on fibre bragg gratings fabricated in low birefringent fibre, electron. lett., 32(13), pp. 1223, doi: 10.1049/el:19960806. [19] matveenko, v.p., kosheleva, n.a., shardakov, i.n., voronkov, a.a. (2018). temperature and strain registration by fibre-optic strain sensor in the polymer composite materials manufacturing, int. j. smart nano mater., 9(2), pp. 99– 110, doi: 10.1080/19475411.2018.1450791. [20] lammens, n., luyckx, g., voet, e., van paepegem, w., degrieck, j. (2015). finite element prediction of resin pocket geometry around embedded optical fiber sensors in prepreg composites, compos. struct., 132, pp. 825–832, doi: 10.1016/j.compstruct.2015.07.003. [21] shivakumar, k., bhargava, a. 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can be opened with acrobat and adobe reader 5.0 and later.) >> /namespace [ (adobe) (common) (1.0) ] /othernamespaces [ << /asreaderspreads false /cropimagestoframes true /errorcontrol /warnandcontinue /flattenerignorespreadoverrides false /includeguidesgrids false /includenonprinting false /includeslug false /namespace [ (adobe) (indesign) (4.0) ] /omitplacedbitmaps false /omitplacedeps false /omitplacedpdf false /simulateoverprint /legacy >> << /addbleedmarks false /addcolorbars false /addcropmarks false /addpageinfo false /addregmarks false /convertcolors /converttocmyk /destinationprofilename () /destinationprofileselector /documentcmyk /downsample16bitimages true /flattenerpreset << /presetselector /mediumresolution >> /formelements false /generatestructure false /includebookmarks false /includehyperlinks false /includeinteractive false /includelayers false /includeprofiles false /multimediahandling /useobjectsettings /namespace [ (adobe) (creativesuite) (2.0) ] /pdfxoutputintentprofileselector /documentcmyk /preserveediting true /untaggedcmykhandling /leaveuntagged /untaggedrgbhandling /usedocumentprofile /usedocumentbleed false >> ] >> setdistillerparams << /hwresolution [2400 2400] /pagesize [612.000 792.000] >> setpagedevice microsoft word numero_57_art_24_3104 a. kusch et alii, frattura ed integrità strutturale, 57 (2021) 331-349; doi: 10.3221/igf-esis.57.24 331 strain energy density criterion as failure assessment for quasi-static uni-axial tensile load andrea kusch, simone salamina, daniele crivelli university of applied sciences and arts of southern switzerland, lugano, switzerland andrea.kusch@student.supsi.ch, simone.salamina@supsi.ch, daniele.crivelli@supsi.ch filippo berto norwegian university of science and technology, norway filippo.berto@ntnu.no abstract. strain energy density is successfully used as criterion for failure assessment of brittle and quasi-brittle material behavior. this work investigates the possibility to use this method to predict the strength of vnotched specimens made of pmma under static uniaxial tensile load. samples are characterized by a variability of notch root radii and notch opening angles. notched specimens fail with a quasi-brittle behavior, albeit pmma has a nonlinear stress strain curve at room temperature. the notch root radius has most influence on the strength of the specimen, whereas the angle is less relevant. the value of the strain energy density is computed by means of finite element analysis, the material is considered as linear elastic. failure predictions, based on the critical value of the strain energy density in a well-defined volume surrounding the notch tip, show very good agreement (error <15%) with experimental data. keywords. strain energy density; quasi-brittle material; pmma; failure assessment. citation: kusch, a., salamina, s., crivelli, d., berto. f., strain energy density criterion as failure assessment for quasi-static uni-axial tensile load, frattura ed integrità strutturale, 57 (2021) 331-349. received: 17.05.2021 accepted: 16.06.2021 published: 01.07.2021 copyright: © 2021 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. introduction eal life application components are often characterized by shapes which produce a stress concentration, that are frequently in the form of notches, holes and re-entrant corners. these weak points act as crack starter, leading to usually brittle failures for both static and fatigue loads. traditionally, to predict the failure of weakened components, generalized stress intensify factors are used, which are difficult to obtain and depend on the weakening feature. to assess the strength of notched components it is useful to have a parameter which depends not on geometry, but rather on the material, and also to make use of numerical methods which can provide reliable results in a convenient time. there are three fundamental ways in which a load enables the crack to propagate, called mode i, ii and iii. real components are often subjected to mixed mode loading, but mode i has most practical interest because it is predominant [1]. r https://youtu.be/uxm9ixb7zsy a. kusch et alii, frattura ed integrità strutturale, 57 (2021) 331-349; doi: 10.3221/igf-esis.57.24 332 strain energy density strain energy is the energy stored in a component undergoing deformation, both elastic and plastic. it can be computed as: 1 2 v w dv  (1) strain energy density (sed) is the average strain energy evaluated over a defined volume: w w v  (2) for perfectly linear elastic brittle materials: 2 2 w d e      (3) finite element analysis is the tool used to numerically compute the sed in the present work. the total strain energy in a finite element is directly computed from the nodal displacement [2]: 1 2 tw k d d (4) where:  d is the vector of nodal displacements;  k is the stiffness matrix. the same is obviously true for the strain energy density, which is computed by the strain energy divided by the volume. literature review he average strain energy density failure criterion was firstly introduced by lazzarin and zambardi [3, 4] and it is validated as failure criterion for brittle and quasi-brittle behavior [5]. failure occurs if the average value of strain energy density, computed over a defined control volume surrounding the point of singularity, exceeds the critical value. for ideally brittle materials, the critical value of the strain energy density can be easily determined by eqn. 3: 2 2 ut cw e   (5) the biggest advantage is that this method does not require very fine mesh for finite elements analysis, contrary to other failure assessment methods [2], because the elastic strain energy can directly be determined by nodal displacement (eq. 4), whereas stress and strain are computed with derivatives of the displacement. this property allows to get sufficiently accurate results with coarse mesh finite elements analysis, which can be solved in much less time. for this reason, it is considered a powerful tool to assess failure of notched and welded components [6, 7]. sed approach has been widely tested on brittle and quasi-brittle behavior, on both static and fatigue failures [8] both in simple and mixed mode loading [9, 10, 11, 12]. this should cover the majority of applications, because both fatigue and the presence of a notch in ductile materials frequently induce a brittle behavior [13]. the sed approach has been proposed also as an alternative method to determine notch stress intensify factors (nsifs) with relatively coarse meshes using simple closed form expressions [6, 2]. t a. kusch et alii, frattura ed integrità strutturale, 57 (2021) 331-349; doi: 10.3221/igf-esis.57.24 333 figure 1: control volume geometry for sharp and blunt v-notches. planar problems can be treated as two-dimensional, where the control volume assumes the shape of a circular segment. the center of the control volume corresponds to the edge of the notch for sharp v-notches, and is shifted towards the center of the notch root radius for blunt v-notches, as shown in fig. 1. in the latter case, the control radius r0 is the width of the volume measured along the notch bisector line. for mode i loading, control radius can be evaluated for plane strain condition with the formula from [14]:    2 0, 5 8 1 4 ic pn ut k r             (6) and for plane stress [15]:   2 0, 5 3 4 ic ps ut k r           (7) the distance of the center of the control volume, according to fig. 1 is defined as [16]: 0 2 2 2 r          (8) this distance is then dependent on both the notch root radius and the opening angle, decreasing with increasing angles. methods he present work follows an experimental approach to analyze the problem. in practice, what has been found in previous studies is being applied to a new set of data to validate the sed approach in static uniaxial load case, and to investigate the possibility to extend the presented failure assessment to nonlinear elastic materials. poly(methyl methacrylate) (pmma) plane dog bone specimens are subjected to static tensile test to characterize the properties of the material, in particular its elastic modulus e and its ultimate tensile strength ut. then, plane specimens weakened by a double symmetric v-notch are subjected to static tensile test to measure the force needed to break them. this value of force is then applied to a finite element model of the corresponding specimen. after finite element analysis is performed, the strain energy density is valuated over a range of control volumes, which depend on the control radius r0. the values are compared to find the critical value of the strain energy density and the control radius r0 for which this critical value is reached inside the control volume. both plane strain and plane stress condition are considered and the respective results are used to evaluate which approach fits best. a validation set of notched specimens is then considered to blindly predict the failure loads using this information. t a. kusch et alii, frattura ed integrità strutturale, 57 (2021) 331-349; doi: 10.3221/igf-esis.57.24 334 specimen geometry control group (i.e. unnotched straight specimens) geometry is derived from iso 527 [17]. three different notch opening angles are considered (2=45°, 60°, 90°) and two different notch root radii =1 and 0 mm (the minimal radius achievable with the capability of the manufacturing process). figure 2: specimens geometry (2 . =45°,60°,90°). series of specimens are labeled according to the opening angle and radius: v45r0, v60r0, v90r0, v45r1, v60r1, v90r1 and str being the unnotched set. for each series 5 specimens are produced. manufacturing tolerances are checked using measurements from a leica dm ml (leica camera ag, wetzlar, de) optical microscope image data. three other types of blunt notched specimen are considered as validation set, with 2=90° and =0.5,2,3 mm. for =0.5 mm, a geometry similar to the one proposed by campagnolo and berto [9] is examined. figure 3: specimens geometry for validation. a. kusch et alii, frattura ed integrità strutturale, 57 (2021) 331-349; doi: 10.3221/igf-esis.57.24 335 manufacturing and conditioning specimens, made from industrial grade pmma 5 mm thick sheet, were manufactured by milling. all the specimens belonging to the same series were machined jointly. the surface of the raw sheet was not finished. specimens were not further conditioned. experimental testing tensile tests were performed on a zwick roell z050 universal testing machine (zwick roell group, ulm, de), with a 5 kn load cell, ±0.5% error at full scale, at room temperature. tests were performed in a random order according to iso 527 [17], with 25 n pre-load and test speed 5 mm/min. elastic modulus is evaluated using regression, computed in strain ranging from 0.05% to 0.25%, at test speed 0.5 mm/min. finite elements analysis finite element models are created with nx 12.0 (siemens plm software, plano, usa). analysis are performed using nastran solver (msc software corporation, newport beach, usa). the necessary material properties not derived from the tensile test are obtained from relevant literature. finite element models of the specimens were defined according to the dimensions of the notch root radius obtained with microscope images. linear elastic simulations are performed using the value of the failure load normalized for a0=50 mm2, so that the differences in cross-sectional area are considered: 0 50 n cf f a   (9) quarter specimens are modeled with a 2d mesh with ctria(6) triangular parabolic elements, taking advantage of the double symmetry, with the appropriate boundary condition, to reduce model size and computational time. sectors of the control volume according to fig. 2 with radii varying from 0.005 to 0.05 mm are defined to evaluate the average value of the strain energy density. mesh refinement up to size 0.002 mm is applied in the control volume to precisely compute the value, whereas the rest of the model is divided into elements of size 0.5 mm, with a transition region to smoothly increase elements size. material properties, typical for pmma at room temperature [16], are reported in tab. 1. property value unit density 1.18 g/cm3 elastic modulus 3’000 mpa poisson’s ratio 0.4 table 1: pmma properties for fea. the average value of the strain energy value is calculated as the total strain energy, computed within the control radius, divided by the undeformed volume, considering negligible displacement. results manufacturing o particular problems were encountered during manufacturing. specimens were measured with a caliper and pictures of a random specimen for each series were taken to evaluate the geometry of the notch. the width at the notch was tested to be within ±3% of the nominal value (±0.3 mm). specimens are within the dimensional tolerances for notch opening angle, thickness and minimal width, with a smooth surface finish. sharp notched samples, except those with angle 90°, are characterized by a small root radius. v90r0 are treated in fea as ideally sharp, while v60r0 are modeled with a fillet radius of =0.045 mm and v45r0 with =0.075 mm, both being the lower bound of the measured values. specimens with 45° sharp notch show a small crack at the notch tip (fig. 4a). n a. kusch et alii, frattura ed integrità strutturale, 57 (2021) 331-349; doi: 10.3221/igf-esis.57.24 336 a b c d e f figure 4: sharp v-notch specimens dimension. a. kusch et alii, frattura ed integrità strutturale, 57 (2021) 331-349; doi: 10.3221/igf-esis.57.24 337 a b c d e f figure 5: blunt v-notch specimens dimension. a. kusch et alii, frattura ed integrità strutturale, 57 (2021) 331-349; doi: 10.3221/igf-esis.57.24 338 a b c d e f figure 6: validation specimens dimension. specimens for validation are also within tolerances (fig. 6), with the width being ±3% of the nominal value. on a side note, specimen with notch end hole are easier to manufacture. tensile tests all specimens broke with a flat smooth fracture surface perpendicular to the load axis without fragmentation, as fig. 7 shows. a b figure 7: failed unnotched (a) and notched (b) samples. a. kusch et alii, frattura ed integrità strutturale, 57 (2021) 331-349; doi: 10.3221/igf-esis.57.24 339 results from the tensile tests are reported in tabs. 2 and 3 and figs. 8, 9 and 10. unnotched specimen behavior is nonlinear with high and sparse strain values at break, which vary from 5.5% to 10.7%, but very consistent in stress-strain trend (fig. 12). the average value of the elastic module of 3’000 mpa is consistent with what found in literature for pmma at room temperature [18, 16]. given that straight smooth specimen should have constant strain energy density across their section, this can be directly computed as the area under the stress-strain curve giving a mean value of 4.9 nmm/mm3, a maximum of 6.8 nmm/mm3 and a minimum of 2.9 nmm/mm3. 0a [mm2] ut [mpa] e [mpa] r [%] cf [n] cw [nmm/mm3] str_01 49.4 75.7 2870 5.5 3738 2.9 str_02 50.6 75.5 2960 8.2 3820 5.0 str_03 50.3 75.7 3090 8.5 3807 5.3 str_04 49.0 75.7 3140 10.7 3708 6.8 str_05 50.3 75.7 2940 7.3 3807 4.3 avg 49.9 75.7 3000 8.0 3777 4.9 sd 0.62 0.08 99.8 1.7 44.5 1.3 table 2: pmma properties, results from tensile tests. cf [n] v45r0 v45r1 v60r0 v60r1 v90r0 v90r1 v90r2 v90r3 v90r05 675 3005 843 2713 1103 2993 3306 3668 2008 722 2972 975 2840 1022 2739 3781 4012 1977 702 2823 983 2818 1015 3019 3767 3937 1956 754 2849 919 2845 1011 2986 3794 4154 1974 825 2791 915 2908 1062 3017 3734 3988 2086 avg 735 2888 927 2825 1042 2951 3676 3952 2000 sd 52 85 51 63 35 107 186 159 46 table 3: failure loads, results from tensile tests. there is a very low scatter within series with no outliers. specimens showed no evident permanent deformation, suggesting an elastic behavior. whilst unnotched specimens showed a strongly nonlinear behavior (fig. 8), notched ones failed in a quasi-brittle manner (figs. 9 and 10). it is worth noting that the slope of the load-displacement curve is similar for all the notched specimens, i.e. the apparent specimen rigidity is independent from notch parameters. a. kusch et alii, frattura ed integrità strutturale, 57 (2021) 331-349; doi: 10.3221/igf-esis.57.24 340 figure 8: stress-strain curves for unnotched specimens. a (v45r0) b (v45r1) c (v60r0) d (v60r1) e (v90r0) f (v90r1) figure 9: load-displacement curve of notched specimen. a. kusch et alii, frattura ed integrità strutturale, 57 (2021) 331-349; doi: 10.3221/igf-esis.57.24 341 whilst specimens with end hole at the notch tip maintain a brittle behavior, those characterized by a bigger notch root radius begin to have a nonlinear trend before failure. a (v90r2) b (v90r3) c (v90r05) figure 10: load-displacement curve of validation samples. figure 11: comparison of the load-displacement curves for all specimens (for each series the most representative is shown). finite element analysis for every series of specimens, the mean, maximum and minimum value of the failure load are considered to compute the strain energy density. for the sake of clarity, only the mean values are considered in this section. fig. 12 shows the value of the average strain energy density as a function of the control radius. blunt notch samples show a nearly constant sed, with imperceptible difference between notch opening angles, whereas the mean sed decays with a likely exponential trend for sharp v-notches. v90r0 and v60r0 samples cross the other curves at r0=0.02 mm and r0=0.015 mm, respectively. v45r0 samples have a lower average value of sed in the range of control radii considered here. a. kusch et alii, frattura ed integrità strutturale, 57 (2021) 331-349; doi: 10.3221/igf-esis.57.24 342 figure 12: average sed in function of the control radius (fea under plane strain condition). in general, what observed for plane strain condition holds true for plane stress, only with higher values of the average sed, as shown in fig. 13. in this case, the crossing point for v90r0 specimens occurs near r0=0.025 mm. for both plane strain and plane stress conditions, v45r0 samples seem to be outliers with lower average strain energy density than the other specimens. for this series a crack was observed at the notch tip (fig. 4a), which could be the cause for a premature failure. modeling the crack is not possible because its dimension and shape are uncertain. these specimens are therefore excluded from the analysis. figure 13: average sed in function of the control radius (fea under plane stress condition). a. kusch et alii, frattura ed integrità strutturale, 57 (2021) 331-349; doi: 10.3221/igf-esis.57.24 343 discussion critical value of the sed and optimal control radius o find the optimal control radius, the variance of the average sed value of all the series of samples is computed, the optimal radius should be the one for which all the values have the least scatter. fig. 14 plots the variance and mean of the average sed for all the samples considered as a function of the control radius r0. for both plane stress and plane strain condition, among the radii investigated, r0=0.02 mm has the lowest variability. control radius for planar problems can be analytically evaluated with eqns. 7 and 6. using =0.4, kic=1.0 mpa·m1/2 [16] and ut=75.0 mpa, we obtain r0=0.054 mm for plane stress condition and r0=0.036 mm for plane strain condition, both being incorrect for the investigated experimental data, but there is an uncertainty on fracture toughness value. various values of r0 have been found in literature for the sed criterion using pmma at room temperature: r0=0.028 mm [19], r0=0.016 mm [14], r0=0.011 mm [16], r0=0.035 mm [16]. the control radius obtained in this work (r0=0.02 mm) remains in the range of results found by previous paper. tab. 4 lists the critical sed, evaluated for both plane stress and plane strain condition, and its boundary, being the highest and lowest value computed, considering all the samples. cw [nmm/mm3] min mean max plane stress 3.69 4.86 6.20 plane strain 2.87 3.85 4.46 table 4: maximum, mean and minimum values of the critical sed. under plane stress condition, the critical sed value has a higher scatter, but there is a better agreement with experimental results, being cw =4.9 nmm/mm3 the mean value measured for the smooth specimens. partly, the underestimated value of cw in plane strain condition is explained by the fact that the plane strain elastic modulus is e/(1- 2), scaling the results by 0.84 with the properties of the pmma considered in this work. albeit the higher discrepancy with experimental data, the plane strain condition is preferable because it better represent the tri-axial state of stress near the notch tip. nevertheless, both plane conditions are approximation for the situation here investigated, but these results confirm that it can be treated as planar problem with satisfactory accuracy. figure 14: mean sed and variance for the different series of specimen (fea under plane strain condition, excluding v45r0). t a. kusch et alii, frattura ed integrità strutturale, 57 (2021) 331-349; doi: 10.3221/igf-esis.57.24 344 figure 15: mean sed and variance for the different series of specimen (fea under plane stress condition, excluding v45r0). shape of the control volume the criterion is based on the average sed value, valuated in a small but finite volume around the notch tip, which has a circular shape. lazzarin and berto observed that the center of the strain energy density isocurves is located approximately at the midpoint between notch tip and root radius center when 2 = 0, and progressively approaches the tip with decreasing opening angle and root radius [16]. the control volume encloses a part of the rectilinear notch flanks when the root radius  is smaller than r0, but the shape of the curves remains circular. for ideally sharp v-notches, the curves assume a crescent shape in the direction perpendicular to the notch bisector line, as shown in fig. 16a. in this case, the circular control volume is clearly not well representing the trend of the sed, but the fea results still show good agreement with experimental data. in reality, all notches are blunt to some extent, this means that there is always a small volume near the notch tip where the sed isocurves have a circular shape. a (sharp v-notch, =0 mm) b (blunt v-notch, =1 mm) figure 16: strain energy distribution around the notch tip for 90° notch opening angle subjected to the critical load (fea under plane strain condition). a. kusch et alii, frattura ed integrità strutturale, 57 (2021) 331-349; doi: 10.3221/igf-esis.57.24 345 notch effect fig. 17 shows the failure loads, normalized to a0=50 mm2, as a function of notch opening angle. there is very low scatter for samples up to =1 mm. the root radius has a much higher influence than the angle, with the loads slightly decreasing with notch opening angle for sharp notches and with negligible difference for blunt specimens with root radius 1 mm. lazzarin and berto observed that the notch opening angle has no influence for r0/ ratios less than 0.2 [16], which means that, in this case, the notch opening angle should be irrelevant above =0.1 mm. for ≥2 mm the specimens withstand higher loads compared to smooth unnotched samples, suggesting a notch strengthening mechanism for pmma. however, the present data is insufficient to further investigate this behavior and, being temperature and humidity uncontrolled during storage and testing there is some uncertainty whether this could be the cause for such small variation, as some previous researches demonstrate [20]. moreover, these sets of specimens show wider scatter than the others and have a nonlinear behavior before failure. figure 17: normalized failure loads as a function of the notch opening angle. validation for linear elastic behavior, the value of the sed is directly proportional to the stress (eqn. 3), the same is obviously true for the applied load: 2w f (10) this relationship allows to estimate the failure load valuating the sed via fea with an arbitrary load: 2 2 c c ww f f  (11) thus: 2c c w f f w   (12) tab. 5 summarizes the prediction of the failure load for the validation samples. for the sake of simplicity, only the mean value is considered. the predicted loads are always within ±15% of the measured value, in most case the discrepancy is below 10%. in this case, the plane stress condition seems to be more representative. 0 0.5 1 1.5 2 2.5 3 m m 0 500 1000 1500 2000 2500 3000 3500 4000 4500 5000 n a. kusch et alii, frattura ed integrità strutturale, 57 (2021) 331-349; doi: 10.3221/igf-esis.57.24 346 the predicted values of the loads are also sufficiently accurate when a possible notch strengthening mechanism is observed. however, the value of the sed is underestimated when treating nonlinear behavior as linear elastic (fig. 18). this means that, in this case, the predicted loads are overestimated. again, more data is needed to better assess the problem. measured predicted, plane stress predicted, plane strain nf [n] n̂f [n] error [%] n̂f [n] error [%] v90r05 2139 2125 -0.7 2328 8.1 v90r2 3823 3789 -0.9 4251 10.1 v90r3 4104 4420 7.2 4826 15.0 table 5: predicted normalized failure loads. figure 18: comparison between real behavior of pmma and its linear elastic approximation. method evaluation being the sed proportional to the squared value of the load (eqn. 10), for practical purposes, it is meaningful to compare the squared values of the sed. fig. 19 and 20 plot the average value of the sed inside the control volume of r0=0.02 mm, normalized to the critical value for both plane stress and plane strain condition. for each series of specimens, the maximum, mean and minimum normalized load is considered. figure 19: scatter of the ratio of the sed over its critical value for all the specimens sampled in this work, considering mean, max and mean values from the tensile test (v45r0 specimens excluded), for plane strain condition. a. kusch et alii, frattura ed integrità strutturale, 57 (2021) 331-349; doi: 10.3221/igf-esis.57.24 347 figure 20: scatter of the ratio of the sed over its critical value for all the specimens sampled in this work, considering mean, max and mean values from the tensile test (v45r0 specimen excluded), for plane stress condition. in both cases, the scatter is very limited, with most series being under ±10% the critical value. under plane strain condition, predictions are generally more accurate. these results suggest that it is possible to compute the sed via fea under linear elastic hypothesis even if the material highlights a nonlinear behavior, as long as the behavior of the notched component is brittle or quasi-brittle, as already observed by lazzarin and zambardi [3]. conclusion n this work, the static failure in mode i loading has been investigated using a new set of experimental data obtained using smooth and notched specimens of pmma. in particular, a large variability of notch root radius and notch opening angle was considered. although pmma shows a strongly nonlinear behavior at room temperature, notched specimens fail in a brittle manner, with load-displacement slope independent from the notch dimensions. it has been observed that the notch root radius  has a much higher influence on the strength of the specimen than the opening angle of the notch, which becomes relevant only for  <0.1 mm. the criterion based on the average strain energy density in a finite volume surrounding the notch tip has been applied to the experimental data. finite element analysis’ have been computed to numerically evaluate the strain energy density of the specimens at failure, considering the material as ideally linear elastic and both plane stress and plane strain conditions were examined. the value of the control radius, has been determined to be r0=0.02 mm. the hypothesis of plane strain was more accurate to predict the failure load, but the critical strain energy density computed using finite elements analysis’ under plane stress condition ( cw =4.86 nmm/mm3) was closer to the value directly measured by means of tensile tests. a prediction based on a linear elastic material behavior showed very good agreement with experimental data, with an error that in most cases remains in the range of ±10%. a notch strengthening behavior has been observed for large values of the notch root radius, but it needs to be investigated with more experimental data, because with the present data samples there is some uncertainty about its relevance. i a. kusch et alii, frattura ed integrità strutturale, 57 (2021) 331-349; doi: 10.3221/igf-esis.57.24 348 nomenclature 2 notch opening angle cf failure load  engineering strain nf failure load normalized on nominal section r strain at break ick fracture toughness  engineering stress 0r control radius ut ultimate tensile stress 0r control volume center to notch tip distance  poisson’s ratio v volume  notch root radius w strain energy 0a initial section area w strain energy density e elastic modulus cw critical value of the strain energy density f force references [1] erdogan, f. and sih. g.c. (1963). on the crack extension in plates under plane loading and transverse shear, journal of basic engineering, 85(4), pp. 519–525. doi: 10.1115/1.3656897. [2] lazzarin, p., berto, f. and zappalorto, m. (2010). rapid calculations of notch stress intensity factors based on averaged strain energy density from coarse meshes: theoretical bases and applications, international journal of fatigue, 32(10), pp. 1559–1567. doi: 10.1016/j.ijfatigue.2010.02.017. [3] lazzarin, p. and zambardi, r. (2001). a finite-volume-energy based approach to predict the static and fatigue behavior of components with sharp v-shaped notches, international journal of fracture, 112(3), pp. 275–298. doi: 10.1023/a:1013595930617. [4] lazzarin, p. and zambardi, r. (2002). the equivalent strain energy density approach re-formulated and applied to sharp v-shaped notches under localized and generalized plasticity, fatigue & fracture of engineering materials & structures, 25(10), pp. 917–928. doi: 10.1046/j.1460-2695.2002.00543.x. [5] berto, f. and lazzarin, p. (2009). a review of the volume-based strain energy density approach applied to v-notches and welded structures, theoretical and applied fracture mechanics, 52(3), pp. 183–194. doi: 10.1016/j.tafmec.2009.10.001. [6] lazzarin, p., berto, f., gomez, f.j. and zappalorto, m. (2008). some advantages derived from the use of the strain energy density over a control volume in fatigue strength assessments of welded joints, international journal of fatigue, 30(8), pp. 1345–1357. doi: 10.1016/j.ijfatigue.2007.10.012. [7] radaj, d., berto, f. and lazzarin, p. (2009). local fatigue strength parameters for welded joints based on strain energy density with inclusion of small-size notches, engineering fracture mechanics, 76(8), pp. 1109–1130. doi: 10.1016/j.engfracmech.2009.01.009. [8] berto, f. and lazzarin, p. (2014). recent developments in brittle and quasi-brittle failure assessment of engineering materials by means of local approaches, materials science and engineering: r: reports, 75, pp. 1–48. doi: 10.1016/j.mser.2013.11.001. [9] campagnolo, a. and berto, f. (2015). tensile fracture analysis of blunt notched pmma specimens by means of the strain energy density, engineering solid mechanics, 3(1), pp. 35–42. [10] torabi, a.r., campagnolo, a. and berto, f. (2015). local strain energy density to predict mode ii brittle fracture in brazilian disk specimens weakened by v-notches with end holes, materials & design, 69, pp. 22–29. doi: 10.1016/j.matdes.2014.12.037. [11] ayatollahi, m.r., moghaddam, m.r., razavi, s.m.j. and berto, f. (2016). geometry effects on fracture trajectory of pmma samples under pure mode-i loading, engineering fracture mechanics, 163, pp. 449–461. doi: 10.1016/j.engfracmech.2016.05.014. [12] berto, f. and gomez, g. (2017). notched plates in mixed mode loading (i+ii): a review based on the local strain energy density and the cohesive zone mode, engineering solid mechanics, 5(1), pp. 1–8. doi: 10.5267/j.esm.2016.11.002. a. kusch et alii, frattura ed integrità strutturale, 57 (2021) 331-349; doi: 10.3221/igf-esis.57.24 349 [13] seweryn, a. (1994). brittle fracture criterion for structures with sharp notches, engineering fracture mechanics, 47(5), pp. 673–681. doi: 10.1016/0013-7944(94)90158-9. [14] yosibash, z., bussiba, a. and gilad, i. (2004). failure criteria for brittle elastic materials, international journal of fracture, 125, pp. 307–333. doi: 10.1023/b:frac.0000022244.31825.3b. [15] lazzarin, p. and berto, f. (2005). from neuber’s elementary volume to kitagawa and atzori’s diagrams: an interpretation based on local energy, international journal of fracture, 135(1-4): l33–l38. doi: 10.1007/s10704-005-4393-x. [16] lazzarin, p. and berto, f. (2005). some expressions for the strain energy in a finite volume surrounding the root of blunt v-notches, international journal of fracture, 135(1-4), pp. 161–185. doi: 10.1007/s10704-005-3943-6. [17] international organization for standardization (2019). iso 527:2019 plastics determination of tensile properties part 1: general principles, iso standard, geneva, ch. [18] johnson, j.a. and jones, d.w. (1994). the mechanical properties of pmma and its copolymers with ethyl methacrylate and butyl methacrylate, journal of materials science, 29(4), pp. 870–876. doi: 10.1007/bf00351404. [19] seweryn, a. and łukaszewicz, a. (2002). verification of brittle fracture criteria for elements with v-shaped notches, engineering fracture mechanics, 69(13), pp. 1487–1510. doi: 10.1016/s0013-7944(01)00138-2. [20] atkins, a.g., lee, c.s., and caddell, r.m. (1975). time-temperature dependent fracture toughness of pmma. journal of materials science, 10(8), pp. 1381–1393. doi: 10.1007/bf00540830. microsoft word numero_44_art_10 p.s. valvo, frattura ed integrità strutturale, 44 (2018) 123-139; doi: 10.3221/igf-esis.44.10 123 the effects of shear on mode ii delamination: a critical review paolo s. valvo department of civil and industrial engineering, university of pisa, italy p.valvo@ing.unipi.it, http://orcid.org/0000-0001-6439-1926 abstract. the paper focuses on the effects of shear deformation and shear forces on the mode ii contribution to the energy release rate in delaminated beams. a critical review of the relevant literature is presented, starting from the end-notched flexure test as the prototype of delaminated laminates subjected to pure mode ii fracture. several models of the literature are recalled from simple beam theory to more refined models. the role of first-order shear deformation in line with the timoshenko beam theory is investigated as distinct from the local crack-tip deformation related to the shear modulus of the material. then, attention is moved on to a general delaminated beam with an arbitrarily located through-the-width delamination, subjected to mixedmode fracture. several fracture mode partition methods of the literature are reviewed with specific attention on the effects of shear on the mode ii contribution to the energy release rate. keywords. delamination; mixed-mode fracture; mode ii fracture; beam theory; shear deformation; end-notched flexure test. citation: valvo, p.s., the effects of shear on mode ii delamination: a critical review, frattura ed integrità strutturale, 44 (2018) 123-139. received: 10.02.2018 accepted: 23.02.2018 published: 01.04.2018 copyright: © 2018 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. introduction elamination, or interlaminar fracture, is a major failure mode for composite laminates, which still attracts researchers’ attention despite the huge number of dedicated studies during the last decades [1–5]. since the earlier works, it has been recognised that the structural behaviour of a laminate affected by delamination can be analysed by schematising the laminate as an appropriate assemblage of sublaminates [6, 7]. these are in turn modelled as plates or beams, depending on the geometry, loads, and boundary conditions of the particular problem at hand. proper homogenisation techniques are used to obtain the overall laminate stiffnesses [8]. the euler-bernoulli beam theory – also referred to in the literature as classical or simple beam theory (sbt) – is the most elementary structural theory that can be used in this context. sbt assumes that the plane cross sections of a beam remain plane and orthogonal to the centreline after deformation. thus, sbt completely neglects shear deformation, which indeed can be relevant for composite laminates because of the orthotropic material behaviour. shear deformation is taken into account at first order by the timoshenko beam theory (tbt), which admits relative rotations between the plane cross sections and the centreline of a beam [9]. simple and timoshenko beam theories correspond to the kirchhoff-love and mindlin-reissner theories for thin and thick plates, respectively [10]. higher-order shear-deformation theories (hsdt) for d p.s. valvo, frattura ed integrità strutturale, 44 (2018) 123-139; doi: 10.3221/igf-esis.44.10 124 beams and plates assume that plane cross sections may not remain plane, which enables better agreement between the structural models and three-dimensional elastic analyses. after the pioneering work by reddy [11], several modified hsdts have been developed (see ref. [12] for a recent review), including specialised versions for the analysis of delaminated plates [13, 14]. besides the adoption of a more or less refined structural theory for the sublaminates, the connection between them has to be suitably described. to this aim, models of growing complexity can be chosen, ranging from rigid connections [15–24] to elastic interfaces [25–38] and cohesive zone models [39–47]. this choice is relevant not only for the accurate prediction of the laminate structural response – e.g. in terms of displacements, stresses, etc. – but also for the evaluation of crack growth. in fact, the type of connection model determines the type of description of the stress field at the delamination crack front. with a rigid connection, the stress field will be represented by concentrated forces and couples, whereas with deformable interfaces there will be a distribution of peeling and shearing stresses [23]. based on such quantities, typical fracture mechanics parameters can be evaluated. within linear elastic fracture mechanics (lefm), the energy release rate, g, is commonly considered to predict the initiation and growth of delamination cracks [48]. however, delamination cracks usually propagate under a mix of the three basic fracture modes (i or opening, ii or sliding, and iii or tearing). therefore, appropriate mixed-mode partition methods are adopted to decompose g into the sum of three modal contributions, gi, gii, and giii [49]. besides, suitable experimental procedures are used to characterise the delamination toughness in pure and mixed fracture mode conditions [50]. in particular, for pure mode ii, the end-notched flexure (enf) test is the current standard [51]. this paper focuses on delaminated laminates modelled according to simple or timoshenko beam theories with rigid connections or elastic interfaces. the aim is to shed light on the effects of shear deformation and shear forces on the mode ii contribution, gii, to the energy release rate. literature on this topic is contradictory with some authors asserting [19, 21, 31, 46] and others negating [16, 20, 24, 30, 36] this effect. as will be illustrated, the origin of this controversy can be dated back to a series of papers on the analysis of the enf test [52–65]. in particular, carlsson et al. [53] modelled the enf test by using the timoshenko beam theory and found correction terms depending on shear deformation for both the specimen compliance, c, and energy release rate, gii. their formulas have been widely used in the later literature for the interpretation of experimental results [66–68] and comparison purposes [69–71]. unfortunately, as pointed out by fan et al. [64], the derivation of such formulas was biased by a wrong boundary condition. actually, silva et al. [63] had obtained the correct expressions for c and gii according to the tbt: the compliance does have a term depending on shear deformation, which however does not depend on the crack length, a. hence, this term vanishes when differentiating c with respect to a to obtain gii according to the well-know irwin–kies formula [72]. notwithstanding the above, the wrong formulas from [53] are still used even in the more recent literature [73–77] and reported in the latest edition of an otherwise excellent book [50]. this paper extends some preliminary considerations by the author [75], also in the light of new findings in the recent literature. the outline is as follows. first, a review on the analysis of the enf test is given and some preliminary conclusions are drawn for laminates with symmetric – i.e. placed on the mid-plane – delamination. then, attention is moved on to a general delaminated beam with a through-the-width delamination arbitrarily located in the thickness. in this case, mixedmode fracture conditions generally occur with g = gi + gii. several mixed-mode partition methods of the literature are reviewed with specific attention on the effects of shear forces and shear deformation on gii. lastly, a quantitative comparison is pursued between the predictions for gi and gii stemming from (i) a rigid-connection model [24], (ii) an elastic-interface model [37], and (iii) a solution based on the theory of elasticity [21]. end-notched flexure test he end-notched flexure (enf) test has been recently standardised by astm international as the method for the characterisation of mode ii delamination toughness of unidirectional fibre-reinforced composite laminates [51]. in the test, a laminated specimen with rectangular cross section is loaded by a force p in a three-point bending configuration. let l = 2l denote the specimen length, b and h = 2h the cross-section width and thickness, respectively. specimens are prepared with a mid-plane delamination crack at one of their ends. let a be the delamination length. a cartesian reference system oxyz is fixed with the origin o at the centre of the crack-tip cross section, the x-axis aligned with the specimen’s longitudinal direction, the z-axis pointing downwards, and the y-axis completing the right-handed reference frame (fig. 1). the enf test specimen can be considered as subject to an antisymmetric loading condition with respect to its mid-plane (fig. 2). in this case, if also material properties have a symmetric distribution with respect to the mid-plane, then normal stresses on the delamination plane will be null. hence, pure mode ii fracture conditions will be attained. this is the case of t p.s. valvo, frattura ed integrità strutturale, 44 (2018) 123-139; doi: 10.3221/igf-esis.44.10 125 homogeneous and orthotropic specimens, as well as unidirectional laminated specimens and multidirectional laminated specimens with symmetric lay-ups. it is hardly necessary to remember that in the asymmetric end-notched flexure (aenf) test, the delamination crack will generally be subjected to mixed-mode fracture conditions [79–82]. in the following, focus will be on a homogeneous and orthotropic specimen. the elasticity moduli in the material reference will be denoted as ex, ez, gzx, and xz [8]. (a) (b) figure 1: scheme of the end-notched flexure (enf) test: (a) side view; (b) cross section. figure 2: free-body diagram of the enf test specimen. for the following analysis, it is useful to introduce the specimen compliance, c p   (1) defined as the ratio between the displacement,, of the load application poin and the load intensity, p. furthermore, the energy release rate, g, is defined as the decrease of potential energy of the system spent in the crack growth process, per unit area of new surface created. the energy release rate can be obtained by differentiating the compliance with respect to delamination length according to the irwin–kies formula [72]: 2 2 p dc g b da  (2) depending on the adopted structural model, various expressions for the specimen compliance have been obtained in the literature. correspondingly, various expressions for the energy release rate are deduced through eq. (2). simple and timoshenko beam-theory models the enf test was first used for composite materials by russell and street [52], who applied simple beam theory (sbt) to determine the specimen compliance, 3 3 sbt enf 3 2 3 8 x l a c e bh   (3) and energy release rate, 2 2 sbt enf 2 3 9 16 x p a g e b h  (4) p.s. valvo, frattura ed integrità strutturale, 44 (2018) 123-139; doi: 10.3221/igf-esis.44.10 126 to consider shear deformation, carlsson et al. [53] modelled the enf test via the timoshenko beam theory (tbt) [9] and obtained the following expressions: 3 3 carlsson,gillespie,pipes 2 enf 3 3 3 2 3 1.2 0.9 1 2 8 2 3 x zxx el a l a c h ge bh l a          (5) for the compliance, and 22 2 carlsson,gillespie,pipes enf 2 3 9 2 1 1016 x zxx ep a h g g ae b h           (6) for the energy release rate. however, whitney [55] promptly observed that «continuity of displacement at the crack tip is not attained with the approach that yields» eqs. (5) and (6). later, also fan et al. [64] realised that «a false assumption was made in the derivation», leading to «inconsistency (…) for the expressions that are used to calculate the energy release rate». actually, in ref. [53] the cross-section rotation at the crack tip is taken equal to the slope of the deflected beam, but this assumption manifestly contradicts the hypotheses on which timoshenko’s first-order shear-deformation beam theory is based. as a matter of fact, by applying the tbt without the above unnecessary approximations, silva et al. [63] obtained: 3 3 tbt sbt enf enf3 2 3 3 3 10 108 zx zxx l a l l c c g bh g bhe bh      (7) for the compliance, and 2 2 tbt sbt enf enf2 3 9 16 x p a g g e b h   (8) for the energy release rate. eq. (7) shows that shear deformation at first order modifies the compliance with an additional term with respect to simple beam theory. this correction terms is however constant with respect to a, hence it vanishes when applying eq. (2) to deduce the energy release rate. thus, as eq. (8) shows, gii turns out to have the same expression according to both sbt and tbt. to confirm this, it is instructive to examine qualitatively the deformed shapes due to shear only of two enf test specimens with shorter (fig. 3a) and longer (fig. 3b) delamination cracks. if the specimen is modelled as an assemblage of rigidly connected sublaminates, the deformed shape due to shear is clearly independent of the delamination length, a. (a) (b) figure 3: rigid-connection model of the enf test: deformed shapes due to shear for (a) shorter and (b) longer delamination cracks. in this respect, it can be mentioned that ozdil et al. [59] analysed the enf test using shear-deformation laminated plate theory and found that «there is no (…) contribution from shear deformation to the energy release rate for unidirectional (…) laminates with mid-plane cracks», while a «very small contribution» emerges for angle-ply laminates. also, chatterjee [56] used shear-deformation laminated plate theory to study the enf test and found that «the energy release rate (…) will not be affected if shear deformation effects (in the context of beam theory) are neglected». elasticity-theory models authors who modelled the enf test within the theory of elasticity generally obtained numerical results showing a dependence of the energy release rate on the shear modulus of the material [54, 56, 57]. p.s. valvo, frattura ed integrità strutturale, 44 (2018) 123-139; doi: 10.3221/igf-esis.44.10 127 chatterjee [56] suggested the following semi-empirical expression to match the elasticity theory solution: 2 2 2 chatterjee enf 2 3 9 1 0.13 16 x zxx ep a h g g ae b h          (9) wang and williams [57] used finite element analysis and found a dependence of both the compliance and energy release rate on the shear modulus of the material. they observed that their numerical results for the energy release rate could be approximated by introducing an increased delamination length into the sbt expression, eq. (4): 22 2 williams enf 2 3 9 ( ) 1 , where 3 2 and 1.18 63 116 x zx zx zxx e eep a h g g ge b h                 (10) a similar crack-length correction parameter, , was later adopted by many authors [36, 62]. today, it is also suggested in the standard method for the mixed-mode bending (mmb) test [83]. andrews and massabò [21], based on finite element analyses, gave the following expression for the energy release rate of an orthotropic enf test specimen:     22 2 andrews,massabò enf 1 2 1 22 3 9 1 2 1 12 916 n n vs vs x p a h h g a a a a a ae b h              (11) where 1 2 1 2, , , and n n vs vsa a a a are compliance coefficients given in a tabular form as functions of the material elastic moduli, including the shear modulus. andrews and massabò’s solution [21] highlights the fact that local deformation – in particular, deformation related to root rotations, i.e. the rotations of the sublaminate cross sections at the crack tip – plays a relevant role in delamination fracture problems. it is also noteworthy that for isotropic materials, eq. (11) degenerates into eq. (9). higher-order shear-deformation theory models whitney [55] used second-order shear-deformation beam theory (sobt) and obtained the following approximate polynomial solution for the energy release rate: 22 2 whitney enf 2 3 9 131 14 1 2 , where 4 75 516 zx xx gp a h h g a a ee b h                (12) pavan kumar and raghu prasad [61, 65] compared simple beam theory with first-order (i.e. tbt), second-order (sobt), and third-order shear-deformation beam theories (tobt). through numerical computation, they found that the simple and timoshenko beam theory models of the enf test yield the same values of the energy release rate, while the higher-order beam theory models furnish larger values. for short crack lengths, they reported that the tobt model gives corrections to gii up to 30% of sbt enfg for unidirectional laminated specimens and nearly 50% for multidirectional laminated specimens. they also found that tobt was in good agreement with the results of finite element analyses. elastic-interface models corleto and hogan [58] modelled the enf test by considering the upper half laminate as a timoshenko beam on a generalised elastic foundation consisting of extensional and rotational distributed springs. they found that the energy release rate is independent of the shear stiffness of the sublaminate, 5/6 gzxbh, but not of the shear modulus of the material, gzx, which enters the expressions of the elastic constants of the foundation. based on this result, ding and kortschot [60] used sbt to deduce a simplified model of the enf test, where the foundation consists of tangential springs only. wang and qiao [62] used tbt and considered an elastic foundation made of distributed tangential springs. by neglecting some numerically small terms in the solution, they obtained the following expression: p.s. valvo, frattura ed integrità strutturale, 44 (2018) 123-139; doi: 10.3221/igf-esis.44.10 128 23 3 wang,qiao enf 3 3 2 3 9 10 88 zx xx a l l a a c g bh e b h he bh                (13) for the compliance, and 2 2 wang,qiao enf 2 3 9 ( ) , where and 5 1216 x zxx ep a h g ge b h         (14) for the energy release rate. eq. (13) shows that the shear stiffness influences the specimen’s compliance, but not the energy release rate. the latter, however, is dependent on the shear modulus of the material through the crack-length correction parameter, . a similar result was obtained by bennati et al. [35, 36], who developed an enhanced beam-theory (ebt) model of the mmb test, where the sublaminates are flexible, extensible, and shear-deformable laminated beams, partly connected by an elastic interface consisting of normal and tangential springs. as a special case, they obtained the solution for an orthotropic enf test specimen in terms of compliance, 23 3 ebt 2 enf 3 3 2 3 9 2 2 4 exp 10 88 zx xx a l l a a l a l a c g bh e b h h h he bh                                  (15) and energy release rate, 2 2 ebt enf 2 3 9 ( ) , where 816 x xx ep a h g k he b h      (16) the third addend in eq. (15) comes from the deformability of the elastic interface. eq. (15) differs slightly from eq. (13), but furnishes quite similar numerical values. also according to the ebt model, the shear deformability does not influence the mode ii contribution to the energy release rate. however, it should be noted that, albeit the shear modulus, gzx, does not enter explicitly eq. (16), it is related to the elastic interface constant, kx [27]. as for models with rigidly connected sublaminates, this result is perfectly intuitive for elastic-interface models if the deformed shapes of two specimens with different delamination lengths are considered (fig. 4). (a) (b) figure 4: elastic-interface model of the enf test: deformed shapes due to shear for (a) shorter and (b) longer delamination cracks. preliminary conclusions from the above literature review, the following preliminary conclusions can be drawn with reference to the enf test: three-dimensional finite element analyses show that both the specimen compliance, c, and energy release rate, gii, exhibit a dependence on the shear modulus of the material, gzx; the timoshenko beam theory adds a correction term with respect to simple beam theory into the expression of c, depending on the (half) specimen shear stiffness, 5/6 gzxbh; the above correction term is constant with respect to delamination length, a; hence, it does not influence the energy release rate, gii, which turns out to be independent of shear deformation at first order; some widely used expressions of the literature for c and gii accounting for shear deformation turned out to be wrong; the dependence of gii on gzx seems to be related to local deformation occurring in the neighbourhood of the delamination front because of high stress concentration, e.g. strain in the laminate thickness direction, poisson’s effect, and root rotations; p.s. valvo, frattura ed integrità strutturale, 44 (2018) 123-139; doi: 10.3221/igf-esis.44.10 129 to catch such effects, it is necessary to use complex models, such as those based on the theory of elasticity or higherorder shear-deformation beam theories; alternatively, enhanced beam theory models with deformable – elastic or cohesive – interfaces between the delaminating sublaminates can be effectively used. the above considerations can be extended from the enf test to similar mode ii delamination tests – e.g. the end-loaded split (els) test, the four-point end-notched flexure (4enf) test, etc. [69] – where the specimen has a mid-plane delamination. in this case, fracture modes i and ii are related to the symmetric and antisymmetric external forces acting on the specimen, respectively. instead, the analysis of laminates with delamination cracks arbitrarily placed in the thickness requires the adoption of more complex mixed-mode partition methods. these will be the subject of the next section. general delaminated laminates ttention is now moved on to a general delaminated beam with an arbitrarily located through-the-width delamination. let l be the laminate length, b and h = 2h the cross-section width and height, respectively. a cartesian reference system oxyz is fixed with the origin o at the geometric centre of one of the end sections, the x-axis aligned with the laminate longitudinal direction, the yand z-axes aligned with the cross-section width and height directions, respectively (fig. 5a). the analysis can be limited to an infinitesimal beam segment included between two cross sections located immediately behind and ahead of the delamination front. the delamination is not necessarily placed on the mid-plane, but divides the laminate into two sublaminates with thicknesses h1 = 2h1 and h2 = 2h2 (fig. 5b) [24]. (a) (b) figure 5: (a) general delaminated beam and (b) crack-tip segment. rigid-connection models if the delaminated beam is modelled as an assemblage of rigidly connected sublaminates, the total energy release rate can be evaluated based on beam theory [21–24]. thus, an analytical expression for g is determined depending on the values of the internal forces acting on the crack-tip segment: the axial forces, ni, shear forces, qi, and bending moments, mi (i = 1, 2, 3). however, to distinguish the single contributions stemming from fracture modes, gi and gii, it is necessary to introduce additional assumptions. to this aim, several fracture mode partition methods have been proposed in the literature. williams’ global method [16] is based on the analysis of the external forces globally acting on the laminate. the method assumes that fracture mode i is produced when opposite bending moments act on the two sublaminates into which the laminate is split; besides, mode ii is obtained when the sublaminates have equal curvatures. as a consequence, the following expressions for the modal contributions to g can be obtained: 2 2 i i2 3 2 2 2 2 2 i 3 williams 2 i 1 1 2 3 williams 1 2 2 ii 2 1 2 i 11 i i2 2 1 6 1 1 10 1 1 2 1 , a 2 6 1 nd 18 x zx x x m q e b h g b h n m e b e h g h h h h h h g h h h hhb                                          (17) where a p.s. valvo, frattura ed integrità strutturale, 44 (2018) 123-139; doi: 10.3221/igf-esis.44.10 130   2 1 1 2ii 1 2 i 2 1 i ii, 1 , , and 1 1 1 m m m m n n n q q q m m                   (18) with 33 1 2 1 1 and 1 h h h h                  (19) according to eqs. (17)–(19), axial forces produce only mode ii, shear forces (and shear deformation) give only mode i, while bending moments contribute to both modes i and ii. schapery and davidson [18] observed that williams’ assumptions on the partition of fracture modes are not generally fulfilled if the delamination crack is not placed on the laminate mid-plane. hence, they proposed a method based on classical laminated plate theory, where the mode i and ii contributions to the energy release rate depend on the stress resultants – an axial force, nc, and a bending moment, mc – exchanged between the upper and lower sublaminates at the crack tip (fig. 6a, b). schapery and davidson did not consider shear forces and shear deformation in their method. (a) (b) (c) (d) figure 6: crack-tip forces on (a) a split crack-tip segment, according to (b) schapery and davidson [18], (c) wang and qiao [20], and (d) valvo [24]. wang and qiao [20] considered two perfectly bonded, shear-deformable laminated beams. they introduced a shear force at the crack tip, qc, but neglected the bending moment, mc (fig. 6c). their expressions for the modal contributions are: wang,qiao wang,qiao2 2 i ii 1 1 and 2 2 q c n cg q g n b b    (20) where, for orthotropic specimens, the coefficients take the following form: 1 2 1 2 6 1 1 4 1 1 and 5 q n zx xg b h h e b h h                  (21) according to eqs. (20) and (21), shear forces and shear deformation contribute only to mode i. valvo [24] extended williams’ method from homogeneous beams to general laminated beams. he determined the modal contributions to g based on a modified virtual crack closure technique. by considering all the three stress resultants – nc, qc, and mc – at the crack tip (fig. 6d), he obtained: p.s. valvo, frattura ed integrità strutturale, 44 (2018) 123-139; doi: 10.3221/igf-esis.44.10 131 valvo 2 2 valvo 2 i ii 1 1 1 and ( ) 2 2 un m um n c wq c un um cc un un f f f f g m f q g f n f m b f b f          (22) where, for orthotropic specimens, 2 2 1 2 1 21 2 3 3 1 2 4 1 1 6 1 1 6 1 1 , , , and 5 12 1 1 . un um n wq x x zx m x f f f f e b h h e b g b h hh h f e b h h                                (23) comparison of eqs. (22) and (23) with (20) and (21) shows that valvo’s method [24] reduces to wang and qiao’s method [20], if the crack-tip bending moment, mc, is disregarded. in general, however, mc gives a contribution to both modes i and ii. instead, shear forces and shear deformation contribute only to mode i. by substituting eqs. (23) into (22) and expressing the crack-tip forces in terms of the internal forces on the delaminated sublaminates, the expressions for the modal contributions to the energy release rate become   2 2 2 1 2 1 2 1 2 1 2 1 22 3 2 1 2 1 2 2 1 2 1 2 1 2 1 22 3 2 2 1 2 22 1 2 1 2 1 2 1 2 2 2 2 2 1 2 1 vval o i valv 2 o ii 3 3 8 5 3 and 33 2 1 9 8 2 x zx x x x h h n n h h q q h h h h h h hb e h b g h h h h h h m m b e h h h h h n n h h m m h h h hb e b e h g g h                                         (24) according to eqs. (24), axial forces may contribute also to mode i. this contribution – neglected by both williams’ [16] and wang and qiao’s [20] methods – passes through the crack-tip bending moment, mc, and depends on the contribution of axial forces on the moment balance on the laminate cross section [24]. elasticity-theory models as opposite to williams’ global method [16], suo and hutchinson [17] developed a local method based on the analysis of the singular stress field at the delamination crack tip. they analysed the problem of a semi-infinite crack between two homogeneous and isotropic elastic layers subjected to axial forces and bending moments. first, they computed the energy release rate based on simple beam theory. then, within linear elastic fracture mechanics, they solved numerically a plane elasticity problem to obtain the mode i and ii stress intensity factors, ki and kii [48]. li et al. [19] extended the local method to include the effects of shear forces. andrews and massabò [21] further extended the method to include the effects of root rotations. they computed the total energy release rate based on the j-integral and then determined the stress intensity factors. their analytical expressions depend on numerical coefficients obtained through finite element analyses and given in a tabular form. if no axial forces and bending moment are present, but only shear forces, their expression for the energy release rate takes the form  andrews,massabò 2 2 2 2shear 2 11 1 2 cosv d v s v v d s v vd s d s d s x g f v f v f f v v he b h            (25) and the stress intensity factors can be written as         1 43 8 andrews,massabò i,shear 1 1 41 8 andrews,massabò ii,shear 1 2 cos cos and 1 2 cos cos 1 v d v v s vd d s s v d v v s vd d s s k f v f v h k f v f v h                                    (26) p.s. valvo, frattura ed integrità strutturale, 44 (2018) 123-139; doi: 10.3221/igf-esis.44.10 132 where 1 2 2, , , and 2 x zz s d xz x zx e ee v q q v q e g           (27) the expressions for the parameters , , , , andv v v vd s d df f    are given in the cited paper [21]. the modal contributions to the energy release rate can then be computed as follows: 3 4 1 4andrews,massabò 2 andrews,massabò 2 i i ii ii 1 1 1 1 and 2 2x x g k g k e e          (28) inspection of eqs. (26)–(28) shows that, according to elasticity theory, shear forces and the material shear modulus will generally affect both modes i and ii. elastic-interface models bruno and greco [30] specifically addressed the influence of shear deformation on delamination in the setting of elasticinterface models. they considered a two-layer plate with an elastic interface consisting of normal and tangential distributed springs and obtained an analytical solution by treating the spring constants as penalty parameters approaching infinity. they concluded that, for symmetric delamination, shear forces influence only the mode i contribution. instead, for asymmetric delamination, shear forces are expected to affect both fracture modes. furthermore, they found an interaction between shear forces and normal stresses coming from axial forces and bending moments. qiao and wang [31] determined an analytical solution for a bilayer beam with an elastic interface. they computed the energy release rate through the j-integral [48] and determined the mode-mixity angle via an adaptation of suo and hutchinson’s method [17]. in general, they found an influence of shear forces and shear deformation on both fracture modes. wang et al. [46] compared several mixed-mode partition methods based on sbt and tbt with rigid and deformable interfaces. in general, they found that shear forces cause additional contributions to both modes i and ii. liu et al. [37] gave a general solution for adhesively bonded joints, where the adherends are modelled as timoshenko beams and the adhesive layer is represented as an elastic interface. the interface consists of a continuous distribution of linearly elastic springs with constants kz and kx, respectively acting in the normal and tangential directions with respect to the interface plane (fig. 7). their solution can be used also for the analysis of delamination in composite laminates, if the interface is interpreted as a conventional means to account for the laminate transverse deformability and not as representative of a physical layer of adhesive. figure 7: elastic-interface model of a delaminated beam. the modal contributions to the energy release rate can be expressed as [34]: p.s. valvo, frattura ed integrità strutturale, 44 (2018) 123-139; doi: 10.3221/igf-esis.44.10 133 2 2 interface interface0 0 i ii 1 1 and 2 2z x g g k k     (29) where 0 and 0 respectively are the values of the normal and tangential interfacial stresses at the crack tip. for a homogeneous delaminated beam, such stresses turn out to have the following expressions [37]: 4 7 0 0 1 5 andi i i i f f       (30) for symmetric delamination, i.e. when h1 = h2, and   70 6 6 0 0 1 1 2 3 and ix i i i i i k g g g            (31) for general asymmetric delamination. in eqs. (30) and (31), f1, f2, …, f7 and g1, g2, …, g7 are integration constants depending on the problem boundary conditions; furthermore, 0 32 2 1 21 2 46 1 1 1 1 and x x x k e e h hh h                  (32) are problem parameters, while 1,  2, …,  6 are the roots of the characteristic equation of the differential problem for the interfacial stresses [37]. inspection of eqs. (29) and (30) shows that, for symmetric delamination, it is possible to separate fracture modes, i.e. to give suitable boundary conditions producing f1 = f2 = f3 = f4 =0, hence gi = 0 (pure mode ii), or f5 = f6 = f7 =0, hence gii = 0 (pure mode i). in such cases, the analytical solution reported in ref. [37] also shows that the sublaminate shear stiffnesses influence only the mode i contribution to the energy release rate. instead, for asymmetric delamination, pure fracture modes cannot be obtained in general, since the normal and tangential stress components given by eqs. (31) depend on the same integration constants, g1, g2, …, g6 (the last constant, g7, corresponds to the jourawski shear stress occurring in a unbroken laminate and therefore is irrelevant in fracture problems). hence, for asymmetric delamination, mixed-mode fracture conditions are generally present. in this case, both the mode i and ii contributions to g depend on shear deformation and shear forces. numerical example to complete the above discussion with some quantitative results, a comparison will be made between the predictions for gi and gii stemming from (i) the rigid-connection model [24], (ii) the elastic-interface model [37], and (iii) the local method in the version by andrews and massabò [21]. the latter can be used for reference as it represents an exact solution obtained within the theory of elasticity. for illustration, a homogeneous and orthotropic laminate is considered with cross-section sizes b = 25 mm and h = 4 mm and elastic moduli ex = 100 gpa, ez = 10 gpa, gzx = 5 gpa, and xz = 0.3. such properties are intended to be representative of a typical laminated specimen used in delamination toughness tests. a beam segment at the delamination crack-tip is considered (fig. 8a), subjected to shear forces q1 and q2 on the delaminated sublaminates and q3 = q1 + q2 on the unbroken part. to investigate all possible load conditions, the acting forces are decomposed into the sum of a symmetric system (fig. 8b) and an antisymmetric system (fig. 8c) with 1 2 1 2and 2 2 s a q q q q q q     (33) with the above assumptions, for symmetric delamination, the symmetric and antisymmetric parts of the acting forces give rise to pure fracture modes i and ii, respectively. but, if the delamination is not placed on the mid-plane, mixed-mode fracture conditions are expected. p.s. valvo, frattura ed integrità strutturale, 44 (2018) 123-139; doi: 10.3221/igf-esis.44.10 134 (a) (b) (c) figure 8: decomposition of (a) the shear forces acting on a crack-tip segment into (b) symmetric and (c) antisymmetric systems. fig. 9 shows the mode i and ii contributions to the energy release rate produced by two symmetric shear forces of intensity qs = 100 n applied at the crack tip, as functions of the sublaminate thickness ratio, 1 2h h  . without loss of generality, attention is restricted to the case 1 2h h , corresponding to  0,1  . the limits 0  and 1  respectively correspond to thin-film debonding and symmetric delamination. continuous red lines represent the predictions of the rigidconnection model [24] as computed from eqs. (24). dashed orange lines correspond to the elastic-interface model [37], as per eqs. (29), for four increasing values (1, 10, 100, and 1000) of the dimensionless elastic-interface constants, / xx zxk h g  and / zz zk h e  . lastly, dotted blue lines correspond to the local method [21], as per eqs. (28). for the mode i contribution (fig. 9a), all compared methods predict similar qualitative trends. the predictions of the elasticinterface model approach those of the rigid-connection model as the values of the elastic-interface constants increase. for 10x z   , corresponding to 312500 n/ mmxk  and 325000 n/ mmzk  , there is good matching between the elastic-interface model and the local method. (a) (b) figure 9: (a) mode i and (b) mode ii contributions to the energy release rate due to symmetric shear forces. for the mode ii contribution (fig. 9b), the rigid-connection model predicts a null value over the whole range of thickness ratios. instead, the elastic-interface model and local method predict non-zero mode ii contributions. however, the computed gii values turn out to be two orders of magnitude lower than the corresponding gi values, as can be noticed p.s. valvo, frattura ed integrità strutturale, 44 (2018) 123-139; doi: 10.3221/igf-esis.44.10 135 from the different scales on the ordinate axes. thus, it can be concluded that the application of symmetric shear forces produces prevailing mode i fracture conditions, regardless of the asymmetry in the position of the delamination crack. for symmetric delamination ( 1  ), all compared methods predict ii 0g  , i.e. pure mode i fracture conditions. fig. 10 shows the mode i and ii contributions to the energy release rate produced by two antisymmetric shear forces of intensity qa = 100 n applied at the crack tip, as functions of the sublaminate thickness ratio. the same graphical conventions of fig. 9 are used to denote the predictions of the rigid-connection model [24], the elastic-interface model [37], and the local method [21]. also, similar comments apply. for the mode i contribution (fig. 10a), the elastic-interface model approaches the rigid-connection model as x and z increase. again, the predictions of the elastic-interface model match closely those of the local method for 10x z   . for the mode ii contribution (fig. 10b), the rigid-connection model predicts a null value over the whole range of thickness ratios. instead, the elastic-interface model and local method predict non-zero mode ii contributions. the computed gii values are lower than the corresponding gi values for smaller thickness ratios. mixed-mode fracture conditions generally occur, with the mode ii contribution increasing as  increases and gi correspondingly decreases. for symmetric delamination ( 1  ), all compared methods predict i 0g  , i.e. pure mode ii fracture conditions. lastly, it should be noticed that the above numerical results correspond to the application of only shear forces at the crack tip. in general, however, bending moments and axial forces will be present as well. indeed, their contributions to the energy release rate may be quite larger than that due to shear. however, a quantitative assessment of those effects requires referring to specific cases in terms of geometry, loads, boundary conditions, etc. this assessment is not pursued within this paper, as focus here is on shear forces and their effects on mode ii delamination. (a) (b) figure 10: (a) mode i and (b) mode ii contributions to the energy release rate due to antisymmetric shear forces. conclusions hear deformation is relevant for composite materials because of their anisotropic elastic behaviour, regardless of the slenderness of beam-like structural elements. as such, shear deformation increases the compliance of laminated beams affected by delamination and, consequently, may influence the energy release rate associated to delamination growth. in this paper, the effects of shear deformation and shear forces on the mode ii contribution to the energy release rate have been examined in the light of different structural theories and fracture mode partition methods of the literature. s p.s. valvo, frattura ed integrità strutturale, 44 (2018) 123-139; doi: 10.3221/igf-esis.44.10 136 first, attention has been devoted to the analysis of the enf test as the prototype of symmetrically delaminated laminates subjected to pure mode ii fracture conditions. comparison of the available models reveals that shear deformation as accounted for at first order by the timoshenko beam theory affects the specimen compliance, but not the mode ii energy release rate. the shear-deformation correction terms given in ref. [53] and used in much of the later literature turned out to be incorrect. hence, their use for experimental test interpretation and comparison of models should be avoided in the future. indeed, three-dimensional finite element analyses of the enf test show a dependence of the energy release rate on the shear modulus of the material. this behaviour may be related to local deformation occurring at the delamination crack tip because of high stress concentration, e.g. strain in the laminate thickness direction, poisson’s effect, and root rotations. such effects can be captured also with beam theory models, however based on higher-order shear-deformation theories or through the introduction of deformable interfaces connecting the delaminated sublaminates. similar considerations hold in general for laminates with symmetric, i.e. mid-plane, delamination. next, a general delaminated beam has been considered with an arbitrarily located through-the-width delamination. in this case, mixed-mode fracture conditions generally occur and gii is only a part of the total energy release rate. in the paper, several mixed-mode partition methods of the literature have been reviewed with specific attention on the effects of shear forces and shear deformation on gii. lastly, a quantitative comparison has been made between the predictions of the rigidconnection model [24], elastic-interface model [37], and local method [21] for a homogeneous and orthotropic laminate with shear forces applied at the crack tip. the results show a quite limited influence of the shear forces on the mode ii contribution to the energy release rate, except for nearly symmetric delamination and antisymmetric shear forces. for the sake of simplicity, in the paper, attention has been limited to homogeneous and orthotropic beams. further studies will be necessary to extend the above considerations to more complex structural elements, such as bi-material and multidirectional laminated beams and plates. references [1] garg, a.c., (1988). delamination-a damage mode in composite structures, eng. fract. mech., 29, pp. 557–584. doi: 10.1016/0013-7944(88)90181-6. [2] sela, n. and ishai, o., (1989). interlaminar fracture toughness and toughening of laminated composite materials: a review, composites, 20, pp. 423–435. doi: 10.1016/0010-4361(89)90211-5. [3] bolotin, v.v., (1996). delaminations in composite structures: its origin, buckling, growth and stability, compos. part b-eng., 27, pp. 129–145. doi: 10.1016/1359-8368(95)00035-6. [4] tay, t.e., (2003). characterization and analysis of delamination fracture in composites: an overview of developments from 1990 to 2001, appl. mech. rev., 56 1–31. doi: 10.1115/1.1504848. [5] senthil, k., arockiarajan, a., palaninathan, r., santhosh, b., usha, k.m., (2013). defects in composite structures: its effects and prediction methods – a comprehensive review, compos. struct., 106, pp. 139–149. doi: 10.1016/j.compstruct.2013.06.008. [6] chatterjee, s.n. and ramnath, v., (1988). modeling laminated composite structures as assemblage of sublaminates, int. j. solids struct., 24, pp. 439–458. doi: 10.1016/0020-7683(88)90001-7. [7] reid, s.r., zou, z., soden, p.d. and li, s., (2001). mode separation of energy release rate for delamination in composite laminates using sublaminates, int. j. solids struct., 38, pp. 2597–2613. doi: 10.1016/s0020-7683(00)00172-4. [8] jones, r.m., (1999). mechanics of composite materials, second ed., taylor & francis, philadelphia. [9] timoshenko, s.p., (1955).strength of materials, vol. 1: elementary theory and problems, third ed., d. van nostrand, new york. [10] timoshenko, s.p. and woinowsky-krieger, s., (1959). theory of plates and shells, second ed., mcgraw-hill, new york. [11] reddy, j.n., (1984). a simple higher-order theory for laminated composite plates, j. appl. mech., 51, pp. 745–752. doi: 10.1115/1.3167719. [12] adim, b., daouadji, t.h. and rabahi, (2016). a simple higher order shear deformation theory for mechanical behavior of laminated composite plates, int. j. adv. struct. eng., 8, pp. 103–117. doi: 10.1007/s40091-016-0109-x. [13] barbero, e.j. and reddy, j.n., (1991). modeling of delamination in composite laminates using a layer-wise plate theory, int. j. solids struct., 28, pp. 373–388. doi: 10.1016/0020-7683(91)90200-y. [14] williams, t.o. and addessio, f.l., (1997). a general theory for laminated plates with delaminations, int. j. solids struct., 34, pp. 2003–2024. doi: 10.1016/s0020-7683(96)00131-x. p.s. valvo, frattura ed integrità strutturale, 44 (2018) 123-139; doi: 10.3221/igf-esis.44.10 137 [15] pook, l.p., (1979). approximate stress intensity factors obtained from simple plate bending theory, eng. fract. mech., 12, pp. 505–522. doi: 10.1016/0013-7944(79)90093-6. [16] williams, j.g., (1988). on the calculation of energy release rates for cracked laminates, int. j. fract., 36, pp. 101–119. doi: 10.1007/bf00017790. [17] suo, z. and hutchinson, j.w., (1990). interface crack between two elastic layers, int. j. fract., 43, pp. 1–18. doi: 10.1007/bf00018123. [18] schapery, r.a. and davidson, b.d., (1990). prediction of energy release rate for mixed-mode delamination using classical plate theory, appl. mech. rev., 43, pp. s281–s287. doi: 10.1115/1.3120829. [19] li, s., wang, j. and thouless, m.d., (2004). the effects of shear on delamination in layered materials, j. mech. phys. solids, 52, pp. 193–214. doi: 10.1016/s0022-5096(03)00070-x. [20] wang, j. and qiao, p., (2005). mechanics of bimaterial interface: shear deformable split bilayer beam theory and fracture, j. appl. mech., 72, pp. 674–682. doi:10.1115/1.1978920. [21] andrews, m.g. and massabò, r., (2007). the effects of shear and near tip deformations on energy release rate and mode mixity of edge-cracked orthotropic layers, eng. fract. mech., 74, pp. 2700–2720. doi: 10.1016/j.engfracmech.2007.01.013. [22] harvey, c.m. and wang, s., (2012). mixed-mode partition theories for one-dimensional delamination in laminated composite beams, eng. fract. mech., 96, pp. 737–759. doi: 10.1016/j.engfracmech.2012.10.001. [23] li, w., cheng, g., wang, d. and wu, j., (2015). a mixed mode partition method for delaminated beam structure, eng. fract. mech., 148, pp. 15–26. doi: 10.1016/j.engfracmech.2015.09.005. [24] valvo, p.s., (2016). on the calculation of energy release rate and mode mixity in delaminated laminated beams, eng. fract. mech., 165, pp. 114–139. doi: 10.1016/j.engfracmech.2016.08.010. [25] kanninen, m.f., (1973). an augmented double cantilever beam model for studying crack propagation and arrest, int. j. fract., 9, pp. 83–92. doi: 10.1007/bf00035958. [26] allix, o. and ladeveze, p., (1992). interlaminar interface modelling for the prediction of delamination, compos. struct., 22, pp. 235–242. doi: 10.1016/0263-8223(92)90060-p. [27] corigliano, a., (1993). formulation, identification and use of interface models in the numerical analysis of composite delamination, int. j. solids struct., 30, pp. 2779–2811. doi: 10.1016/0020-7683(93)90154-y. [28] point, n. and sacco, e., (1996). a delamination model for laminated composites, int. j. solids struct., 33, pp. 483–509. doi: 10.1016/0020-7683(95)00043-a. [29] bruno, d., greco, f., (2001). mixed mode delamination in plates: a refined approach, int. j. solids struct., 38, pp. 9149–9177. doi: 10.1016/s0020-7683(01)00179-2. [30] bruno, d. and greco, f., (2001). delamination in composite plates: influence of shear deformability on interfacial debonding, cement concrete comp., 23, pp. 33–45. doi: 10.1016/s0958-9465(00)00068-8. [31] qiao, p. and wang, j., (2004). mechanics and fracture of crack tip deformable bi-material interface, int. j. solids struct., 41, pp. 7423–7444. doi: 10.1016/j.ijsolstr.2004.06.006. [32] bennati, s. and valvo, p.s., (2006). delamination growth in composite plates under compressive fatigue loads, compos. sci. technol., 66, pp. 248–254. doi: 10.1016/j.compscitech.2005.04.035. [33] szekrényes, a., (2007). improved analysis of unidirectional composite delamination specimens, mech. mater., 39, pp. 953–974. doi: 10.1016/j.mechmat.2007.04.002. [34] bennati, s., colleluori, m., corigliano, d. and valvo, p.s., (2009). an enhanced beam-theory model of the asymmetric double cantilever beam (adcb) test for composite laminates, compos. sci. technol., 69, pp. 1735–1745. doi: 10.1016/j.compscitech.2009.01.019. [35] bennati, s., fisicaro, p. and valvo, p.s., (2013). an enhanced beam-theory model of the mixed-mode bending (mmb) test – part i: literature review and mechanical model, meccanica, 48, pp. 443–462. doi: 10.1007/s11012-012-9686-3. [36] bennati, s., fisicaro, p. and valvo, p.s., (2013). an enhanced beam-theory model of the mixed-mode bending (mmb) test – part ii: applications and results, meccanica, 48, pp. 465–484. doi: 10.1007/s11012-012-9682-7. [37] liu, z., huang, y., yin, z., bennati, s. and valvo, p.s., (2014). a general solution for the two-dimensional stress analysis of balanced and unbalanced adhesively bonded joints, int. j. adhes. adhes., 54, pp. 112–123. doi: 10.1016/j.ijsolstr.2013.06.021. [38] dimitri, r., tornabene, f. and zavarise, g., (2018). analytical and numerical modeling of the mixed-mode delamination process for composite moment-loaded double cantilever beams, compos. struct., 187, pp. 535–553. doi: 10.1016/j.compstruct.2017.11.039. [39] borg, r., nilsson, l. and simonsson, k., (2001). simulation of delamination in fiber composites with a discrete cohesive failure model, compos. sci. technol. 61, pp. 667–677. doi: 10.1016/s0266-3538(00)00245-1. p.s. valvo, frattura ed integrità strutturale, 44 (2018) 123-139; doi: 10.3221/igf-esis.44.10 138 [40] camanho, p.p., dávila, c.g. and de moura, m.f., (2003). numerical simulation of mixed-mode progressive delamination in composite materials, j. compos. mater., 37, pp. 1415–1438. doi: 10.1177/0021998303034505. [41] yang, q. and cox, b., (2005). cohesive models for damage evolution in laminated composites, int. j. fract., 133, pp. 107–137. doi: 10.1007/s10704-005-4729-6. [42] parmigiani, j.p. and thouless, m.d., (2007). the effects of cohesive strength and toughness on mixed-mode delamination of beam-like geometries, eng. fract. mech., 74, pp. 2675–2699. doi: 10.1016/j.engfracmech.2007.02.005. [43] turon, a., dávila, c.g., camanho, p.p. and costa, j., (2007). an engineering solution for mesh size effects in the simulation of delamination using cohesive zone models, eng. fract. mech., 74, pp. 1665–1682. doi: 10.1016/j.engfracmech.2006.08.025. [44] harper, p.w. and hallett, s.r., (2008). cohesive zone length in numerical simulations of composite delamination, eng. fract. mech., 75, pp. 4774–4792. doi: 10.1016/j.engfracmech.2008.06.004. [45] sørensen, b.f. and jacobsen t.k., (2009). characterizing delamination of fibre composites by mixed mode cohesive laws, compos. sci. technol., 69, pp. 445–456. doi: 10.1016/j.compscitech.2008.11.025. [46] wang, s., harvey, c.m. and guan, l. (2013). partition of mixed modes in layered isotropic double cantilever beams with non-rigid cohesive interfaces, eng. fract. mech., 111, pp. 1–25. doi: 10.1016/j.engfracmech.2013.09.005. [47] dimitri, r., trullo, m., de lorenzis, l. and zavarise, g., (2015). coupled cohesive zone models for mixed-mode fracture: a comparative study, eng. fract. mech., 148, pp. 145–179. doi: 10.1016/j.engfracmech.2015.09.029. [48] friedrich, k. (ed.), (1989). application of fracture mechanics to composite materials, elsevier, amsterdam. [49] hutchinson, j.w. and suo, z., (1991). mixed mode cracking in layered materials, adv. appl. mech., 29, pp. 63–191. doi: 10.1016/s0065-2156(08)70164-9 [50] carlsson, l.a., adams, d.f. and pipes, r.b., (2014). experimental characterization of advanced composite materials, fourth ed., crc press, boca raton. [51] astm d7905/d7905m-14, standard test method for determination of the mode ii interlaminar fracture toughness of unidirectional fiber-reinforced polymer matrix composites, astm international, west conshohocken, (2014). doi: 10.1520/d7905_d7905m-14. [52] russell, a.j. and street, k.n., (1985). moisture and temperature effects on the mixed-mode delamination fracture of unidirectional graphite/epoxy, in: w.s. johnson (ed.), delamination and debonding of materials, astm stp 876, astm, philadelphia, pp. 349–370. doi: 10.1520/stp36314s. [53] carlsson, l.a., gillespie jr, j.w. and pipes, r.b., (1986). on the analysis and design of the end notched flexure (enf) specimen for mode ii testing, j. compos. mat., 20, pp. 594–604. doi: 10.1177/002199838602000606. [54] gillespie jr, j.m., carlsson, l.a. and pipes, r.b., (1986). finite element analysis of the end notched flexure specimen for measuring mode ii fracture toughness, compos. sci. technol., 27, pp. 177–197. doi: 10.1016/0266-3538(86)90031-x. [55] whitney, j.m., (1990). analysis of interlaminar mode ii bending specimens using a higher order beam theory, j. reinf. plast. compos., 9, pp. 522–536. doi: 10.1177/073168449000900601. [56] chatterjee, s.n., (1991). analysis of test specimens for interlaminar mode ii fracture toughness, part 1. elastic laminates, j. compos. mater., 25, pp. 470–493. doi: 10.1177/002199839102500501. [57] wang, y. and williams, j.g., (1992). corrections for mode ii fracture toughness specimens of composites materials, compos. sci. technol., 43, pp. 251–256. doi: 10.1016/0266-3538(92)90096-l. [58] corleto, c.r. and hogan, h.a., (1995). energy release rates for the enf specimen using a beam on an elastic foundation, j. compos. mat., 29, pp. 1420–1436. doi: 10.1177/002199839502901101. [59] ozdil, f., carlsson, l.a. and davies, p., (1998). beam analysis of angle-ply laminate end-notched flexure specimens, compos. sci. technol., 58, pp. 1929–1938. doi: 10.1016/s0266-3538(98)00018-9. [60] ding, w. and kortschot, m.t., (1999). a simplified beam analysis of the end notched flexure mode ii delamination specimen, compos. struct., 45, pp. 271–278. doi: 10.1016/s0263-8223(99)00030-6. [61] pavan kumar, d.v.t.g. and raghu prasad, b.k., (2003). higher-order beam theories for mode ii fracture of unidirectional composites, j. appl. mech., 70, pp. 840–852. doi: 10.1115/1.1607357. [62] wang, j. and qiao, p., (2004). novel beam analysis of end notched flexure specimen for mode-ii fracture, eng. fract. mech., 71, pp. 219–231. doi: 10.1016/s0013-7944(03)00096-1. [63] silva, m.a.l., de moura, m.f.s.f. and morais, j.j.l., (2006). numerical analysis of the enf test for mode ii wood fracture, compos. part a-appl. s., 37, pp. 1334–1344. doi: 10.1016/j.compositesa.2005.08.014. [64] fan, c., ben jar, p.-y. and cheng, j.-j.r., (2007). revisit the analysis of end-notched-flexure (enf) specimen, compos. sci. technol., 66, pp. 1497–1498. doi: 10.1016/j.compscitech.2006.01.016. p.s. valvo, frattura ed integrità strutturale, 44 (2018) 123-139; doi: 10.3221/igf-esis.44.10 139 [65] raghu prasad, b.k. and pavan kumar, d.v.t.g., (2008). analysis of composite enf specimen using higher order beam theories, thin wall. struct., 46, pp. 676–688. doi: 10.1016/j.tws.2007.11.004. [66] reeder, j.r. and crews jr, j.h., (1992). redesign of the mixed-mode bending delamination test to reduce nonlinear effects, j. compos. tech. res., 14, pp. 12–19. doi: 10.1520/ctr10078j. [67] ducept, f., davies, p. and gamby, d., (1997). an experimental study to validate tests used to determine mixed mode failure criteria of glass/epoxy composites, compos. part a-appl. s., 28, pp. 719–729. doi: 10.1016/s1359-835x(97)00012-2. [68] beghini, m., bertini, l. and forte, p., (2006). experimental investigation on the influence of crack front to fiber orientation on fatigue delamination growth rate under mode ii, compos. sci. technol., 66, pp. 240–247. doi: 10.1016/j.compscitech.2005.04.033. [69] davies, p., sims, g.d., blackman, b.r.k., brunner, a.j., kageyama, k., hojo, m., tanaka, k., murri, g., rousseau, c., gieseke, b. and martin, r.h., (1999). comparison of test configurations for determination of mode ii interlaminar fracture toughness results from international collaborative test programme, plast. rubber compos., 28, pp. 432–437. doi: 10.1179/146580199101540600. [70] agrawal, a. and ben jar, p.-y., (2003). analysis of specimen thickness effect on interlaminar fracture toughness of fibre composites using finite element models, compos. sci. technol., 63, pp. 1393–1402. doi: 10.1016/s0266-3538(03)00088-5. [71] theotokoglou, e.e. and vrettos, c.d., (2006). a finite element analysis of angle-ply laminate end-notched flexure specimens, compos. struct., 73, pp. 370–379. doi: 10.1016/j.compstruct.2005.02.010. [72] irwin, g.r. and kies, j.a., (1954). critical energy release rate analysis of fracture strength. weld. j. res. suppl., 33, pp. 193–198. [73] van der meer, f.p. and sluys, l.j., (2009). a phantom node formulation with mixed mode cohesive law for splitting in laminates, int. j. fract., 158, pp. 107–124. doi: 10.1007/s10704-009-9344-5. [74] thouless, m.d., (2009). the effects of transverse shear on the delamination of edge-notch flexure and 3-point bend geometries, compos. part b-eng., 40, pp. 305–312. doi: 10.1016/j.compositesb.2009.01.005. [75] wang, f., shao, z. and wu, y., (2013). mode ii interlaminar fracture properties of moso bamboo, compos. part beng., 44, pp. 242–247. doi: 10.1016/j.compositesb.2012.05.035. [76] liu, p.f., gu, z.p. and peng, x.q., (2016). a nonlinear cohesive/friction coupled model for shear induced delamination of adhesive composite joint, int. j. fract., 199, pp. 135–156. doi: 10.1007/s10704-016-0100-3. [77] li, y., stapleton, s.e., simon, j.-w. and reese, s., (2016). experimental and numerical study of paperboard interface properties, exp. mech., 56, pp. 1477–1488. doi: 10.1007/s11340-016-0184-8. [78] valvo, p.s., (2008). does shear deformability influence the mode ii delamination of laminated beams?, in: j. pokluda, p. lukáš, p. šandera, i. dlouhý (eds.), 17th european conference on fracture: multilevel approach to fracture of materials, components and structures, european structural integrity society (esis), brno, pp. 1470–1477. [79] sundararaman, v. and davidson, b., (1998). an unsymmetric end-notched flexure test for interfacial fracture toughness determination, eng. fract. mech., 60, pp. 361–377. doi: 10.1016/s0013-7944(98)00017-4. [80] yang, z. and sun, c.t., (2000). interlaminar fracture toughness of a graphite/epoxy multidirectional composite, j. eng. mater. technol., 122, pp. 428–433. doi: 10.1115/1.1289027. [81] samborski, s., (2017). analysis of the end-notched flexure test configuration applicability for mechanically coupled fiber reinforced composite laminates, compos. struct., 163, pp. 342-349. doi: 10.1016/j.compstruct.2016.12.051. [82] bieniaś, j., dadej, k. and surowska, b., (2017). interlaminar fracture toughness of glass and carbon reinforced multidirectional fiber metal laminates, eng. fract. mech., 175, pp. 127-145. doi: 10.1016/j.engfracmech.2017.02.007. [83] astm d6671/d6671m-13e1, standard test method for mixed mode i-mode ii interlaminar fracture toughness of unidirectional fiber reinforced polymer matrix composites, astm international, west conshohocken, (2013). doi: 10.1520/d6671_d6671m-13e01. << /ascii85encodepages false /allowtransparency false /autopositionepsfiles true /autorotatepages /none /binding /left /calgrayprofile (dot gain 20%) /calrgbprofile (srgb iec61966-2.1) /calcmykprofile (u.s. web coated \050swop\051 v2) /srgbprofile (srgb iec61966-2.1) /cannotembedfontpolicy /error /compatibilitylevel 1.4 /compressobjects /tags /compresspages true /convertimagestoindexed true /passthroughjpegimages true /createjobticket false /defaultrenderingintent /default /detectblends true /detectcurves 0.0000 /colorconversionstrategy /cmyk /dothumbnails false /embedallfonts true /embedopentype false /parseiccprofilesincomments true /embedjoboptions true /dscreportinglevel 0 /emitdscwarnings false /endpage -1 /imagememory 1048576 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can be opened with acrobat and adobe reader 5.0 and later.) >> /namespace [ (adobe) (common) (1.0) ] /othernamespaces [ << /asreaderspreads false /cropimagestoframes true /errorcontrol /warnandcontinue /flattenerignorespreadoverrides false /includeguidesgrids false /includenonprinting false /includeslug false /namespace [ (adobe) (indesign) (4.0) ] /omitplacedbitmaps false /omitplacedeps false /omitplacedpdf false /simulateoverprint /legacy >> << /addbleedmarks false /addcolorbars false /addcropmarks false /addpageinfo false /addregmarks false /convertcolors /converttocmyk /destinationprofilename () /destinationprofileselector /documentcmyk /downsample16bitimages true /flattenerpreset << /presetselector /mediumresolution >> /formelements false /generatestructure false /includebookmarks false /includehyperlinks false /includeinteractive false /includelayers false /includeprofiles false /multimediahandling /useobjectsettings /namespace [ (adobe) (creativesuite) (2.0) ] /pdfxoutputintentprofileselector /documentcmyk /preserveediting true /untaggedcmykhandling /leaveuntagged /untaggedrgbhandling /usedocumentprofile /usedocumentbleed false >> ] >> setdistillerparams << /hwresolution [2400 2400] /pagesize [612.000 792.000] >> setpagedevice microsoft word numero_30_art_18 a. namdar et alii, frattura ed integrità strutturale, 30 (2014) 138-144; doi: 10.3221/igf-esis.30.18 138 focussed on: fracture and structural integrity related issues evaluation of safe bearing capacity of soil foundation by using numerical analysis method abdoullah namdar, xiong feng western china earthquake and hazards mitigation research center, college of architecture and environment, sichuan university, chengdu, sichuan 610065, china fxiong@scu.edu.cn abstract. the soil mechanic laboratory results help in accurate soil foundation design and enhancement failure mitigation. the mixing soil design has been used in many geotechnical engineering for soil improvement. in this paper, several types of soil foundations have been made from mixed soil. the bearing capacity of soil foundations by using mixed soil parameters and change footing dimensions have been calculated. 180 footings, placed on 15 soil foundation types have been designed. it is assumed the underground water has not effect to bearing capacity of soil foundation. the results of numerical analysis and mixed soils technique have been combined. the numerical analysis has supported mixed soil design, and introduced an appropriate result for soil foundation design. the effects of mixed soil on depth and width of footing have been compared. the mixed soil design influenced numerical analysis result, and economically, soil foundation design helps to select the appropriate dimensions of footings. the result of numerical analysis supports geotechnical and structural engineering codes, predicts structural stability with different age, natural hazard and prevention as well as it is useful in understanding safe bearing capacity of soil foundation behavior. keywords. mixed soil; bearing capacity; failure mitigation; methodology; realistic simulation. introduction he mathematical modeling and numerical simulation have been used to understand tsunami behavior, and a mitigation technique has been proposed, based on bearing capacity of soil concept [1]. numerically safe bearing capacity of soil foundation is calculated and it is attempted to assess economical dimension of foundation as well as understanding of bearing capacity [2]. the numerical model ssifibo has been developed in matlab to study soilstructure interaction problems. the model allows computing structural forced-vibrations, as well as seismic responses [3]. there is a numerical analysis and theoretical attempt to evaluate interaction between sandy saturated soil foundation and embankment in presence of confined sandy dense column. in this work some confined sandy dense columns have been considered made up from sand-gravel mixture. the numerically wave theory concept has been applied in analyzing confined sandy dense columns, and the study indicated that the dense zone improves soil foundation bearing capacity [4]. the data relating to the design of foundation for improvement of structure at different layer of subsoil have been collected and, soil mechanical properties have been evaluated. the results of experiments were applied in evaluation of geotechnical characteristics of urban area for the development of a region with high level of structural stability. ultimately, a new method for calculation of liquefaction force numerically is suggested. it is applicable for improving geotechnical and structure codes and also for the reanalysis of structure and stability of previously constructed buildings [5]. to accurate soil foundation design the numerical computations, using flac code, are carried out to evaluate the soil bearing t a. namdar et alii, frattura ed integrità strutturale, 30 (2014) 138-144; doi: 10.3221/igf-esis.30.18 139 capacity factors. the computational results are presented in the form of tables and graphs, and compared with previous published results available in the literature [6]. the computational results predict the ultimate bearing capacity of shallow foundations on cohesionless soils. the neurofuzzy models combine the transparent, linguistic representation of a fuzzy system with the learning ability of artificial neural networks (anns) [7]. the vertical bearing capacity of spudcan foundations in strength anisotropic soils has been investigated numerically by using the mit-s1 model implemented in the afena finite element package. the model in afena is validated against existing laboratory test data of normally consolidated soil. the bearing capacities of spudcans in soils with isotropic and anisotropic strengths have been compared [8]. the zel method is employed to consider the stress level dependency of soil strength in the bearing capacity computation and load-displacement behavior of foundations, with a computer code was developed in matlab to solve zel equations [9]. the finite element analyses have been conducted to evaluate the combined horizontal-moment bearing capacities of tripod bucket foundations for offshore wind turbines in undrained clay [10]. to evaluate the safe bearing capacity of soil foundation and select appropriate dimensions of concrete foundation, when soil foundation is constructed from mixed soil, a numerical analysis has been made; ithas been attempted to appropriately improve stability of structures, to optimize application of mixed soil in soil foundation design, and to achieve realistic simulation of soil foundation design. methodology and experiment he footing or concrete foundation tasks are to transfer the structural load to soil foundation. the shallow concrete foundation has ration of /fd b ≤ 2.5, where the fd is the embedment depth and b is the width. the allowable bearing capacity or safe bearing capacity  fq is the maximum pressure on soil foundation, and it is margin of safety against the collapse due to shear failure. the 15 types of soil foundation have been produced from mixture of sand, gravel and six types of soils (table 1). the mechanical properties of mixed soils have been used in numerical analysis. total 180 types of footing have been designed. the substructure soil interaction behaviors have been depicted in form of graphs and tables. in numerical analysis the terzaghi method has been adopted. it is well known that the underground water changes safe bearing capacity of soil foundation; due to this reason, to simplify and improve the research output, it is assumed that the underground water has no effect to safe bearing capacity of soil foundation. formulas for calculation of safe bearing capacity are the following: 1) qf = 1.3c nc + γdnq + 0.4 γbnγ 2) qnf = qf qnf = qf -γd 3) qs = (qnf /f) + γd nq, nc and nγ are the general bearing capacity factors and depend upon 1) depth of footing 2) shape of footing 3) φ; they have been used from suggestion by the terzaghi calculation method [11]. mixed soil type % of red soil % of sand % of gravel 4.75 mm % of gravel 2 mm % of black soil % of green soil % of dark brown soil % of yellow soil % of light brown soil optimum moisture content (%)  (kn/m3) φ degree c (kn/m2) 1 100 0 0 0 0 0 0 0 0 11.20 21.94 38 21 2 55 45 0 0 0 0 0 0 0 10.61 21.83 39 12 3 55 0 45 0 0 0 0 0 0 10.72 23.46 39 46 4 55 0 0 45 0 0 0 0 0 12.15 23.82 36 28 5 55 0 0 0 45 0 0 0 0 22.39 20.09 32 20 6 55 0 0 0 0 45 0 0 0 18.86 20.95 32 26 7 55 0 0 0 0 0 45 0 0 14.56 23.35 18 44 8 55 0 0 0 0 0 0 45 0 14.23 20.96 30 28 9 55 0 0 0 0 0 0 0 45 14.56 21.61 28 26 10 90 0 0 0 2 2 2 2 2 16.83 21.61 36 22 11 80 0 0 0 4 4 4 4 4 18.27 21.56 15 47 12 70 0 0 0 6 6 6 6 6 16.76 21.07 22 49 13 60 0 0 0 8 8 8 8 8 20.21 21.83 21 33 14 50 0 0 0 10 10 10 10 10 18.68 21.18 27 38 15 55 15 15 15 0 0 0 0 0 9.58 23.02 40 8 table 1: the mixed soil design and characteristics [12]. t a. namdar et alii, frattura ed integrità strutturale, 30 (2014) 138-144; doi: 10.3221/igf-esis.30.18 140 results and discussion very foundation design requires satisfaction of safe bearing capacity [13]. the safe bearing capacity is governed by shearing strength of the soil and it is estimated by the theories of terzaghi [14], meyerhof [15], vesic [16] and others. the application of mixed soil in soil foundation design has been using in geotechnical engineering field for several years. the most of works has been performed basing on soil mechanics testing results and satisfying the theories of terzaghi, meyerhof, vesic and others. the application of numerical analysis in soil foundation design from soil mechanics result is a methodology that leads to reduce the gap between theoretical and realistic design. the 180 footings, rested on 15 types of soil foundation have been designed; from the results of these soils foundation designs (tab. 2-3), 2 major graphs (fig. 1-2) and 3 minor graphs (fig. 3-5) have been depicted. the interpretation of result of numerical analysis has been supporting to understand, role of soil morphology and mineralogy on safe bearing capacity of soil foundation and size of concrete foundation. the design of soil foundation and concrete foundation have been attempted to select suitable methodology and analysis, introduce appropriate materials produced from soil mixing technique. the mixed soil design has been responsible for numerical analysis result. in the numerical analysis of soil foundation the depth of footings have 1.00 (m), 1.30 (m), 1.60 (m), 1.90 (m), 2.20 (m) and 2.50 (m) been selected, and width of footings have been selected for 1.00 (m), 1.30 (m), 1.60 (m), 1.90 (m), 2.20 (m), 2.40 (m) and 2.50 (m). the results indicated (tab. 2-3 and fig. 1-2) the effect of mixed soil design on width and depth of concrete foundation size. and increase the footing width is economic compared to the increase of depth; it is suggested first to increase the width of concrete foundation for improve soil foundation safe bearing capacity. the increase width of square footing results in a more distributed transferred loads from structure to concrete and soil foundation, and subsequently, the bearing capacity of soil foundation is improved. the founding, from numerical analysis, has good coloration with theoretical concept and experimental results. the observations of mixed soil (in tab. 23 and fig. 1-2) have shown that the safe bearing capacity of mixed soil types 10, 11, 12, 13 and 14 have considerable fluctuation while the percentage of basic mixed soil have changed in increment of 2% only. it has been understood the best percentage of any soil in soil mixture depends on soil mineral interaction. combining mixed soil design with the numerical simulation results, it has been revealed the soil mineralogy effect to the design of concrete footing as well as the right selection type of soil foundation. the mixed soil type 3 with appropriate morphology has best been resulted in numerically design of soil foundation. the mixed soil deign can be introduced as an acceptable mitigation technique if its application has been simulated considering soil mineralogy and morphology. this work clearly shows the effect of soil mineralogy and morphology to select concrete foundation dimensions. the result indicate that failure mitigation of soil foundation is depending on soil mineralogy and morphology. micro and macro properties of soils have direct influence on footing size, and any modification of soil in soil mixture, reflects to the concrete foundation and soil foundation characteristics. sl. no  (kn/m3) φ degree c (kn/m2) d=1.00 (m) d=1.30 (m) d=1.60 (m) d=1.90 (m) d=2.20 (m) d=2.5 (m) 1 21.94 38 21 1577.81 1708.04 1838.28 1968.51 2098.75 2228.98 2 21.83 39 12 1470.57 1617.58 1764.58 1911.58 2058.59 2205.59 3 23.46 39 46 2735.73 2893.71 3051.69 3209.67 3367.65 3525.63 4 23.82 36 28 1382.55 1485.93 1589.31 1692.69 1796.07 1899.45 5 20.09 32 20 700.81 757.06 813.31 869.56 925.82 982.07 6 20.95 32 26 822.31 880.97 939.63 998.29 1056.95 1115.61 7 23.35 18 44 368.96 386.70 404.45 422.20 439.94 457.69 8 20.96 30 28 703.14 750.38 797.62 844.87 892.11 939.36 9 21.61 28 26 570.13 610.37 650.61 690.84 731.08 771.32 10 21.61 36 22 1169.07 1262.86 1356.64 1450.43 1544.22 1638.00 11 21.56 15 47 308.93 322.00 335.06 348.13 361.19 374.26 12 21.07 22 49 522.43 544.47 566.51 588.55 610.59 632.63 13 21.83 21 33 357.89 378.41 398.93 419.45 439.97 460.495 14 21.18 27 38 653.38 688.67 723.95 759.24 794.52 829.81 15 23.02 40 8 1564.83 1738.21 1911.60 2084.99 2258.37 2431.76 table 2: safe bearing capacity of soil foundation (kn/m2) when width of square footing is 2.5 m. e a. namdar et alii, frattura ed integrità strutturale, 30 (2014) 138-144; doi: 10.3221/igf-esis.30.18 141 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 0 500 1000 1500 2000 2500 3000 w= width of square footing = 2.5 d= depth of square footing the mixed soil type s af e be ar in g c ap ac it y of s oi l fo un da ti on ( kn /m 2 ) d=1.00 (m) d=1.30 (m) d=1.60 (m) d=1.90 (m) d=2.20 (m) d=2.50 (m) figure 1: safe bearing capacity of soil foundation (kn/m2) vs the mixed soil type. sl. no  (kn/m3) φ degree c (kn/m2) w=1.00 (m) w=1.30 (m) w=1.60 (m) w=1.90 (m) w=2.20 (m) w=2.50 (m) 1 21.94 38 21 1289.96 1347.53 1405.10 1462.67 1520.24 1577.81 2 21.83 39 12 1133.52 1200.93 1268.34 1335.76 1403.17 1470.58 3 23.46 39 46 2373.51 2445.96 2518.40 2590.84 2663.29 2735.73 4 23.82 36 28 1180.57 1220.96 1261.36 1301.76 1342.16 1382.56 5 20.09 32 20 606.29 625.19 644.10 663.00 681.91 700.81 6 20.95 32 26 723.74 743.46 763.17 782.89 802.60 822.31 7 23.35 18 44 352.62 355.89 359.16 362.43 365.69 368.96 8 20.96 30 28 628.94 643.78 658.62 673.46 688.30 703.14 9 21.61 28 26 510.92 522.77 534.61 546.45 558.29 570.14 10 21.61 36 22 985.82 1022.47 1059.12 1095.77 1132.42 1169.07 11 21.56 15 47 299.28 301.21 303.14 305.07 307.01 308.94 12 21.07 22 49 497.41 502.41 507.42 512.43 517.43 522.44 13 21.83 21 33 336.06 340.43 344.80 349.16 353.53 357.89 14 21.18 27 38 603.82 613.74 623.65 633.56 643.47 653.38 15 23.02 40 8 1155.99 1237.76 1319.53 1401.30 1483.06 1564.83 table 3: safe bearing capacity of soil foundation (kn/m2) when depth of square footings is 1.00 m. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 0 500 1000 1500 2000 2500 3000 the mixed soil type s af e be ar in g ca pa ci ty o f so il f ou nd at io n (k n m 2 ) w= width of square footing d= depth of square footing = 1.00 (m) w=1.00 (m) w=1.30 (m) w=1.60 (m) w=1.90 (m) w=2.20 (m) w=2.50 (m) figure 2: safe bearing capacity of soil foundation (kn/m2) vs the mixed soil type. a. namdar et alii, frattura ed integrità strutturale, 30 (2014) 138-144; doi: 10.3221/igf-esis.30.18 142 1 2 3 4 5 6 0 500 1000 1500 2000 2500 3000 3500 the mixed soil is 100% red soil s af e b ea ri n g c ap ac it y o f so il f o u n d at io n ( k n m 2 ) depth change from 1 to 2.5 (m) in increment of 0.3 (m) width change from 1 to 2.5 (m) in increment of 0.3 (m) figure 3: fluctuation of safe bearing capacity of soil foundation (kn/m2) vs the mixed soil type. 1 2 3 4 5 6 0 500 1000 1500 2000 2500 3000 3500 depth change from 1 to 2.5 (m) in increment of 0.3 (m) width change from 1 to 2.5 (m) in increment of 0.3 (m) the mixed soil is type 3 s af e be ar in g c ap ac it y of s oi l fo un da ti o n (k n m 2 ) figure 4: fluctuation of safe bearing capacity of soil foundation (kn/m2) vs the mixed soil type. 1 2 3 4 5 6 0 500 1000 1500 2000 2500 3000 3500 depth change from 1 to 2.5 (m) in increment of 0.3 (m) width change from 1 to 2.5 (m) in increment of 0.3 (m) the mixed soil is type 15 s af e b ea ri ng c ap ac it y o f so il f ou nd at io n (k n m 2 ) figure 5: fluctuation of safe bearing capacity of soil foundation (kn/m2) vs the mixed soil type. a. namdar et alii, frattura ed integrità strutturale, 30 (2014) 138-144; doi: 10.3221/igf-esis.30.18 143 fig. 3-5 shows the fluctuation of safe bearing capacity of soil foundation versus the mixed soil type. it has been reported higher safe bearing capacity with increasing depth, and in comparison of concrete used in construction of footing, the increase width is cost effective method. this research work is applicable in design of soil foundation and to minimize soil foundation failure. the result and interpretation of numerical analysis support the foundation design, it can be used to enhance structure stability, to improve geotechnical and structural engineering codes, to predict structural stability with different age and estimate structures stability while changing mechanical properties of soil foundation. one of the important factor that changes soil mechanical properties is the fluctuation of groundwater level; it occurs in many part of the world, due to many reasons like flood and etc. the numerical analysis helps in evaluation and application of geotechnical engineering map in construction industry, natural hazard prediction and prevention as well as soil foundation behavior. the founding may be required to be considered in data collection of site for understanding behavior of soil and concrete foundations. there is an experimental analysis. the shaking table has been used to generate dynamic force on embankment and embankment soil foundation. to improve system dynamic stability, dense zones have been installed in subsoil [17]. the seismic mechanical properties of soil mechanics are required in seismic numerical analysis, and seismic soil foundation design. it is important to use accurate data in seismic numerical analysis of soil foundation considering the changes of the soil characteristics. conclusion o accurate understanding failure mitigation of soil foundation, the numerical analyses of several soil foundations and results of mixed soil technique have been employed. 180 footings have been designed placing them on 15 soils foundation types. it has been observed that the mixed soil technique has the ability to predict soil foundation behavior. the results show soil parameters control footing dimensions. the effect of mixed soil on footing depth and width have been compared. the soil mineralogy and morphology govern safe bearing capacity of soil foundation and size of concrete foundation. the result of numerical analysis supports geotechnical and structural engineering codes, natural hazard prediction, prevention and understanding soil foundation behavior, predicts structural stability with different age.,. the methodology in this research work supports the application of mixed soil in designing soil foundation. to extent this research work , the role of mixed soil design in stress path can be investigated. reference [1] namdar, a., nusrath, a., tsunami numerical modeling and mitigation, frattura ed integrità strutturale, 12 (2010) 5762; doi: 10.3221/igf-esis.12.06. [2] namdar, a., pelkoo, m. k., numerical analysis of soil bearing capacity by changing soil characteristics, frattura ed integrità strutturale, 10 (2009) 37-41; doi: 10.3221/igf-esis.10.05. [3] galvín, p., romero, a., a matlab tool box for soil–structure interaction analysis with finite and boundary elements, soil dynamics and earthquake engineering, 57(2014) 10-14. [4] namdar, a., numerical simulation and pore water pressure from shaking table test results, scientific research and essays, 7(6) (2012) 636-646. [5] namdar, a., pelko, a. k., nusrath, a., liquefaction mathematical analysis for improvement structures stability, frattura ed integrità strutturale, 14(2010), 3-8; doi: 10.3221/igf-esis.14.08. [6] benmebarek, s., remadna, m.s., benmebarek, n., belounar, l., numerical evaluation of the bearing capacity factor n’γ of ring footings”, computers and geotechnics, 44 (2012) 132-138. [7] padmini, d., ilamparuthi, k., sudheer, k.p., ultimate bearing capacity prediction of shallow foundations on cohesionless soils using neurofuzzy models, computers and geotechnics, 35 (2008) 33-46. [8] liu, j., hu, y., the effect of strength anisotropy on the bearing capacity of spudcan foundations, computers and geotechnics, 36 (2009) 125-134. [9] veiskaramia, m., jahanandishb, m., ghahramanib, a., prediction of the bearing capacity and load–displacement behavior of shallow foundations by the stress-level-based zel method, scientia iranica a, 18 (1) (2011) 16–27. [10] hung, l. c., kim, s. r., evaluation of combined horizontal-moment bearing capacities of tripod bucket foundations in undrained clay, ocean engineering, 85 (2014) 100-109. [11] punmia, b. c., soil mechanics and foundations, madras, (1988). t a. namdar et alii, frattura ed integrità strutturale, 30 (2014) 138-144; doi: 10.3221/igf-esis.30.18 144 [12] namdar, a., pelkoo, m. k., bearing capacity of mixed soil model, frattura ed integrità strutturale, 7 (2009) 73-79; doi: 10.3221/igf-esis.07.06. [13] namdar, a., evaluation of seismic mitigation of embankment model, frattura ed integrità strutturale, 8(2009) 21-29; doi: 10.3221/igf-esis.08.02. [14] de beer, ee., bearing capacity and settlement of shallow foundations on sand, in: proceedings of symposium on bearing capacity and settlement of shallow foundations. duke university; (1965) 15-33. [15] terzaghi, k., theoretical soil mechanics, new york: john wiley & sons, (1943). [16] meyerhof, g.g., some recent research on the bearing capacity of foundations, can geotech j, 1(1) (1963) 16-26. [17] vesic, a.s., analysis of ultimate loads of shallow foundations, jsmfd, asce 99(1) (1973) 45-73. microsoft word numero_49_art_29_2399 s. djaballah et alii, frattura ed integrità strutturale, 49 (2019) 291-301; doi: 10.3221/igf-esis.49.29 291 focused on fracture mechanics versus environment detection and diagnosis of fault bearing using wavelet packet transform and neural network djaballah said, meftah kamel university of biskra, lgem laboratory, algeria said3988@gmail.com, https://orcid.org/0000-0002-8105-9199 meftah.kamel@gmail.com, http://orcid.org/0000-0002-5671-602x khelil khaled university of souk ahras, algeria k_khelil@yahoo.fr tedjini mohsein, sedira lakhdar university of biskra, lgm laboratory, algeria mohsein.tedjini@gmail.com, sedira.lakhdar@gmail.com, http://orcid.org/0000-0003-1735-2195 abstract. bearings, considered crucial components in rotating machinery, are widely used in the industry. bearing status monitoring has become an essential step in the deployment of preventive maintenance policy. this work is part of the diagnosis and classification of bearing defects by vibration analysis of signals from defective bearings using time domain and frequency analysis and wavelet packet transformations (wavelet packet transform wpt) with artificial neural networks (ann). wpt is used for extracting defect indicators to train the neural classifier. the main goal is the determination of the wavelet generating the most representative indicators of the state of the bearings for better detection and classification of defects. using the wpt-based neural classifier, the obtained simulation results showed that the db6 wavelet with level 3 decomposition is best suited for diagnosing and classifying bearing defects. keywords. conditional maintenance; bearing; the wavelet transform; neural networks. citation: djaballah, s., meftah, k., khelil, k., tedjini, m., sedira, l., detection and diagnosis of fault bearing using wavelet packet transform and neural network, frattura ed integrità strutturale, 49 (2019) 291-301. received: 16.02.2019 accepted: 07.04.2019 published: 01.07.2019 copyright: © 2019 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. introduction he goal of maintenance is to detect failures of rotating machinery before a critical failure occurs. practically, bearings are one of the most widely used elements in rotating equipment, and its failure is one of the main causes of breakdowns in this type of machines [1]. therefore, of course, the diagnosis of bearing defects has been the t http://www.gruppofrattura.it/va/49/2399.mp4 s. djaballah et alii, frattura ed integrità strutturale, 49 (2019) 291-301; doi: 10.3221/igf-esis.49.29 292 subject of several research studies. most research related to the diagnosis of bearing defects uses vibration signals because they contain valuable information about defects [2, 3]. in addition, vibration analysis is considered to be the most common and reliable method in this type of analysis [4]. however, ultrasound has also been used appropriately and precisely in the detection of bearing defects [5]. there are different vibration analysis tools to detect and diagnose the appearance of defects in rotating machinery. many publications synthesize these different methods or tools. they are generally classified into three main categories of vibration data analysis: time analysis, frequency analysis and time-scale analysis. the wavelets transform (to) be a timescale analysis technique suitable for both stationary and non-stationary signals [6]. the wavelet transform, offering a multiresolution analysis, is very suitable for fault diagnosis [7]. the wavelet packet transform (wpt) is an improvement of the multi-resolution mra [8] since it allows decomposition of all frequency sub-bands. in this work, we focus on the diagnosis of rolling defects, using an intelligent classification system based on artificial neural networks (ann) and wavelet packet transformation. the coefficients of the wpt will be used for the extraction of the indicators, in this case, the energy, and the kurtosis, which will drive the network of neurons [9]. thus, the main objective of our work is the determination of the wavelet generating the most representative indicators of the state of the bearings for better detection and a good diagnosis of the defects. wavelet transform wavelet packet transform he wavelet packet method is a generalization of wavelet decomposition that offers a range of possibilities for signal analysis in wavelet analysis; a signal is broken down into approximations and details. the approximation is then itself cut into approximation and second-level detail, and the process is repeated. for decomposition of "n" levels, there are (n + 1) possible ways to decompose or encode the signal [10]. in wavelet packet analysis, details, as well as approximations, can be decomposed. this yields more than (2n + 1) of different signal decompositions. the wavelet packet decomposition tree is shown in fig .1. in the case of the detection of bearing defects, this technique makes it possible to obtain the same analysis fineness regardless of the frequencies investigated. figure 1: representation in filter banks of the dwt at n = 3 level. the extraction of indicators due to the complex nature of the machines and the complexity of the associated parameters, it is generally difficult to evaluate the state of a machine directly from the time data. the advent of the wavelet transform has provided an efficient tool for feature extraction of various time signals. as an extension to the discrete wavelet transform, the dwpt, in comparison with the dwt, provides more flexibility in time-frequency decomposition, especially in the highfrequency region. in particular, the dwpt allows the extraction of the indicators (for example, energy or kurtosis) from the frequency sub-bands where the indicators are concentrated[11]. since the energy content of a signal provides a strong indicator of the signal but is not sensitive enough to incipient defects, kurtosis, on the other hand, is very sensitive to incipient defects but has low stability. therefore, these two t s. djaballah et alii, frattura ed integrità strutturale, 49 (2019) 291-301; doi: 10.3221/igf-esis.49.29 293 indicators, energy, and kurtosis can be combined, instead of using one, to better characterize the vibratory signal and improve fault detection [12]. bearing data center ibration signals (accelerations) are obtained by exploiting the data made available on the case western reserve university (cwru, bearing data center) site [13]. the signals are measured at a sampling frequency fe = 12 khz for 10 sec on a three-phase 1.5 kw (2 hp: horsepower) electric machine coupled to a load that determines its speed. the data were acquired from the rolling bearings under different loads (0, 1, 2 and 3 loads) and under different rolling conditions: normal condition, ball defect (bf), inner race defect (irf), and defect in the outer race (orf). as illustrated in fig 2. figure 2: bearing test stand the bearings used in this work are skf 6205 type ball bearings. internal ring, outer ring, and ball defects are introduced into the bearings by electrical discharge machining (edm). the defect diameters are 0.1778 mm (0.007 inches), 0.3556 mm (0.014 in), 0.5334 mm (0.021 in) and 0.7112 mm (0.028 in) corresponding to incipient, moderate, severe and very severe defects respectively. diagnosis of defects by methods of analysis using a classifier on neural networks detection of bearing defects by time analysis or temporal analysis, the input vector of the neural network is formed by the 7 temporal indicators already mentioned and are given by:  tpeak rms ku imf cf talaf thikat (1) two cases are considered according to the number of outputs. as shown in fig. 3, we have 4 output neural network and 10 output neural network is shown in fig. 4. the performance of the fault diagnosis is evaluated by the recognition rate which is defined as % 100 c r t n t n   (2) :cn number of correct decisions tn : total number of tests v f s. djaballah et alii, frattura ed integrità strutturale, 49 (2019) 291-301; doi: 10.3221/igf-esis.49.29 294 case 1: 4 output neural network figure 3: rna structure {7 10 4 } case 2: 10 output neural network figure 4: rna structure {7 10 10 } tab. 1 presents the classification performance of the single-layer hidden neural network with 10 neurons using time indicators for the two structures, 4 and 10 outputs: number of input neural network structure number of outputs performance rate % 7 4 91.10 7 10 85.34 table 1: classification performance of time indicators. feature rn feature rn s. djaballah et alii, frattura ed integrità strutturale, 49 (2019) 291-301; doi: 10.3221/igf-esis.49.29 295 diagnosis of defects by time and frequency analysis seven time indicators  tpeak rms ku imf cf talaf thikat three spectral descriptors t fouter finner fballx x x   (3) hence, the input vector of the rna, composed of 10 indicators, is given by                               t fouter finner fballpeak rms ku imf cf talaf thikat x x x   (4) case 1: 4 output neural network figure 5: rna structure {10 10 4 }. case 2: 10 output neural network figure 6: rna structure {10 10 10 }. feature rn feature rn s. djaballah et alii, frattura ed integrità strutturale, 49 (2019) 291-301; doi: 10.3221/igf-esis.49.29 296 number of input neural network structure number of outputs performance rate % 10 4 97.21 10 10 92.67 table 2: classification rate with time and frequency indicators. from the results shown in tab. 2, the neuronal classifiers {10 10 4 } and {10 10 10 } which is shown in fig. 5 and fig. 6 respectively, have classification rates of 97.21% and 92.67%, respectively. this confirms the contribution of frequency descriptors to the improvement of the classification rate and the diagnosis of defects. diagnosis of defects by the wavelet transform optimal choice of wavelet and decomposition level n practice, unfortunately, there is no wavelet that is better than the others for all cases; it all depends on the intended application. for vibratory analysis based on the wavelet transform, the selection of the mother wavelet depends on its properties or the similarity between the signal and the mother wavelet. based on the dwpt, this step consists of determining the best mother wavelet (type and order) and the optimal decomposition level best suited to our application. the wavelets chosen for this study are:  the wavelets of daubechies: db1, db2, db3, db20, db30, db40 and db44  coiflets: coif1, coif2, ..., coif5  symlets: sym2, ⋯, sym10 and sym15 for the search of the decomposition level by the wavelet packet transform, we have considered the levels j ={3, 4, 5, 6, 7}. these characteristics can be expressed in a vector such as: 1 2 2 1 2 2j j v j j j j j jf e e e k k k      (5) fig. 7 shows the classification is based on artificial neural networks. figure 7: classification scheme by rna-based dpwt with a level of decomposition j = 3, 4, 5, 6, 7 i s. djaballah et alii, frattura ed integrità strutturale, 49 (2019) 291-301; doi: 10.3221/igf-esis.49.29 297 configuration neural network the configuration chosen is the following: 3-layer network: 1 single hidden layer; 10 neurons in the hidden layer; performance error = 10-8. we have the database has 180 signals for each rolling condition among the 720 signals, 60% and 40% are exploited for learning the rna test respectively. the results showed in tab. 3, for the three families of wavelets, which the best classification rates are obtained with the classification rate, are obtained with the level 3 of decomposition. in addition, daubechies wavelets db1, db2, db3, db6, db7 and db8 have the best performance in terms of fault classification rates. using the wavelets db1, db2, db3, db6, db7 and db8, with which the best performances are obtained, were performed the neuron classification algorithm 100 times and the results obtained are reported in tab. 4. wavelet level 3 4 5 6 7 db1 99.21 98.17 97.91 90.88 79.68 db2 99.21 96.61 97.13 88.80 83.33 db3 99.21 97.39 98.17 89.84 86.45 db4 97.91 97.39 95.83 92.70 88.80 db5 98.17 97.13 97.39 90.88 79.94 db6 99.21 97.91 95.57 93.48 86.19 db7 99.21 96.87 96.61 90.62 89.58 db8 99.21 96.61 97.39 91.66 88.80 db9 96.87 98.17 97.39 90.36 76.04 db10 97.39 97.39 97.13 90.10 82.81 db11 98.43 96.61 96.61 92.18 80.20 db12 98.95 97.91 96.35 89.32 86.45 db13 98.43 97.65 97.91 91.40 85.93 db14 98.17 99.21 96.61 89.58 87.50 db15 97.65 98.69 97.39 91.92 89.84 db16 97.39 97.39 95.57 91.66 84.11 db17 98.17 97.91 98.17 90.36 82.81 db18 96.09 97.91 97.65 89.84 90.66 db19 98.69 97.39 97.31 92.96 75.00 db20 98.17 96.35 97.65 91.40 83.66 db30 98.17 97.39 97.65 90.88 87.50 db40 98.69 97.91 98.43 95.50 80.20 db44 98.17 98.17 97.39 96.09 85.84 coif 1 98.69 97.39 94.27 89.48 79.16 coif 2 98.17 97.13 97.13 91.66 84.63 coif 3 97.91 97.39 95.57 86.13 85.93 coif 4 98.17 96.09 94.01 85.15 82.81 coif 5 99.21 96.09 93.22 86.45 75.00 sym 2 98.43 97.13 97.39 89.06 76.04 sym 3 97.65 98.43 97.13 93.22 85.93 sym 4 98.95 98.43 97.39 90.62 87.50 sym 5 98.95 98.43 97.13 92.44 89.84 sym 6 98.17 97.65 95.57 90.62 83.07 sym 7 98.69 96.87 95.83 89.06 80.20 sym 8 98.17 96.09 96.61 91.92 84.11 sym 9 98.95 98.43 96.35 92.44 80.20 sym 10 98.17 96.61 94.27 82.03 75.00 sym 15 98.17 97.65 97.13 93.22 76.04 table 3: classification rates for different types of wavelet and different levels of decomposition s. djaballah et alii, frattura ed integrità strutturale, 49 (2019) 291-301; doi: 10.3221/igf-esis.49.29 298 wavelet db1 db2 db3 db6 db7 db8 performance % 98.95 98.95 99.21 99.47 98.69 99.21 table 4: classification rate with decomposition level n = 3 we conclude that the optimal wavelet most appropriate to fault diagnosis of bearings is the daubechies wavelet of order 6 "db6" with a level of decomposition, n = 3, has proven its performance in several works dealing with the diagnosis of defects [14,15,16]. reduction of the vector of indicators the application of the wavelet packet transform (dwpt) to the vibratory signal, using the wavelet db6 with decomposition level n = 3, generates 23 = 8 frequency sub-bands. recall that the 16 indicators used in this work are based on energy and kurtosis calculated for each frequency sub-band and are given by: 1 2 8 1 2 8 3 3 3 3 3 3vf e e e k k k     (6) in order to see which of the 16 indicators are sensitive to the state of rotation, the diagrams representing the energies and kurtosis of each sub-band are plotted and shown in fig. 8 and 9 respectively. from fig. 8, we can easily see that the two indicators, in this case, 5 63  3 and  e e are almost invariant. for kurtosis, represented by fig. 9, we can note that the 8 indicators 1 2 3 4 5 6 7 83 3 3 3 3 3 3 3  ,  ,  , ,  ,  ,  , and k k k k k k k k are sensitive to changing the state of the bearing. as a result, we have maintained the 14 most relevant indicators for the classification of bearing defects that are given by: 1 2 3 4 7 8 1 2 8 3 3 3 3 3 3 3 3 3vrf e e e e e e k k k    (7) figure 8: energy of each sub-band for the four states of the bearing: (a) no fault, (b) defect in the inner race, (c) defect in the outer race, (d) defect in the ball. 1 2 3 4 5 6 7 8 0 0.5 1 1.5 2 2.5 3 x 10 4 the frequency bands e n e rg y p e r fr e q u e n cy b a n d (a) 1 2 3 4 5 6 7 8 0 0.5 1 1.5 2 2.5 3 x 10 5 the frequency bands e n e rg y p e r fr e q u e n cy b a n d (b) 1 2 3 4 5 6 7 8 0 0.5 1 1.5 2 2.5 3 x 10 5 the frequency bands e n e rg y p e r fr e q u e n cy b a n d (c) 1 2 3 4 5 6 7 8 0 0.5 1 1.5 2 2.5 3 x 10 5 the frequency bands e n e rg y p e r fr e q u e n cy b a n d (d) s. djaballah et alii, frattura ed integrità strutturale, 49 (2019) 291-301; doi: 10.3221/igf-esis.49.29 299 diagnosis of defects by transform wavelet packets he diagnosis and classification of bearing defects are performed by an artificial neural network (ann) whose inputs are energy indicators and kurtosis calculated using coefficients derived from the decomposition level 3 transform wavelet packet ( dwpt) using the db6 wavelet. we kept the same configuration of the rna used before. thus, the structure of the rna takes the form:  3-layer network: 1 single hidden layer;  10 neurons in the hidden layer;  the number of nodes at the input is equal to the number of indicators that is 14;  the number of nodes in the output layer is: case 1: 4 outputs (see fig. 10) corresponding to the four bearing states. case 2: 10 outputs (see fig. 11) for detecting the severity of the fault. corresponding the different defects as well as their diameters:  normal.  fault in the inner race (0.007 and 0.014 and 0.021 inches).  fault in the inner race (0.007 and 0.014 and 0.021 inches).  fault in the ball (0.007 and 0.014 and 0.021 inches). figure 9: kurtosis of. each sub-band for the four states of the bearing: (a) no fault, (b) fault in the inner race, (c) fault in the outer race, (d) fault in the ball. tab. 5 shows the rna classification rates based on the wavelet packet transform for both the 4 and 10 output configurations. t 1 2 3 4 5 6 7 8 0 5 10 15 20 25 frequency bands k u rt o si s b y fr e q u e n cy b a n d (a) 1 2 3 4 5 6 7 80 5 10 15 20 25 frequency bands k u rt o si s b y fr e q u e n cy b a n d (b) 1 2 3 4 5 6 7 8 0 5 10 15 20 25 frequency bands k u rt o si s b y fr e q u e n cy b a n d (c) 1 2 3 4 5 6 7 80 5 10 15 20 25 frequency bands k u rt o si s b y fr e q u e n cy b a n d (d) s. djaballah et alii, frattura ed integrità strutturale, 49 (2019) 291-301; doi: 10.3221/igf-esis.49.29 300 number of input neural network structure number of outputs performance rate % 14 4 99.47 14 10 99.33 table 5: classification rate with indicators based on wavelet db6 figure 10: structure of rna classifier 4 outputs figure 11: structure of rna classifier 10 outputs the results shown in tab. 5 show a classification rate of 99.47% for the detection of the fault location (four outputs), and a rate of 99.33% for the detection of the diameter (severity) of the fault (ten outputs). these results confirm the efficiency of the use of the wavelet packet transform (with the db6 wavelet) for the extraction of indicators sensitive to the variations of the state of the bearing to be monitored. s. djaballah et alii, frattura ed integrità strutturale, 49 (2019) 291-301; doi: 10.3221/igf-esis.49.29 301 conclusions he work presented in this article is part of the preventive maintenance of rotating equipments and particularly the detection of defects bearings by vibration analysis. the temporal and frequency analysis is used to improve the classification rate and the diagnosis of bearing failure and the time and frequency analysis is used to determining its diameter and location. this objective was mostly achieved with a precision of about 92.67% when determining the diameter of the defect, and 97.21% when locating. next, we have tried to determine the optimal wavelet best suited to the diagnosis and classification of bearing defects using the wavelet packet transform and artificial neural networks (ann). the main objective was to determine the wavelet that generates indicators in this case energy and kurtosis best reflecting the state of the bearings. we could show that the wavelet db6 with decomposition level 3 is the most appropriate diagnosis and classification of bearing fault. this wavelet db6 and decomposition level 3 improve our result at 99.33 % when determining the diameter of the defect, and 99.47 % when locating references [1] gomez, m., castejon, c and garcía-prada, j. (2014) incipient fault detection in bearings through the use of wpt energy and neural networks, advances in condtion monitoring of machinery in non-stationary operations, springer, pp 63-72, doi: 10.1007/978-3-642-39348-8_4 [2] du q., yang, s. (2007) application of the emd method in the vibration analysis of ball bearings, mechsyst sig process 21, pp. 2634–2644, doi: 10.1016/j.ymssp.2007.01.006 [3] hu, q., he, z., zhang, z., zi, y. (2007) fault diagnosis of rotating machinery based on improved wavelet package transform and svms ensemble, mech syst sig process 21, pp668–705. doi: 10.1016/j.ymssp.2006.01.007 [4] aherwar, a., khalid, md s., hemaint, k n. (2012) vibration analysis of machine fault signature, national [5] conference on recent advances in mechanical engineering pp. 487-492 [6] amarnath, m., sugumaran, v., kumar, h. (2013) exploiting sound signals for fault diagnosis of bearings using decision tree, measurement. 2013 apr; 46(3), pp. 1250–1256, doi: 10.1016/j.measurement.2012.11.011 [7] rosani m. (1999). signal analysis in transient applying the wavelet technique, [master thesis], sao.paulo university [8] memon, a., khokhar, s., memon, z. (2014). discrete wavelet transform and multiresolution analysis algorithm with appropriate feedforward neural network classifier for power system transient disturbances, sci.int.(lahore), 26(5), pp. 2231-2238. [9] liu, b., ling, s. (1997) machinery diagnostic based on wavelet packets, vib control 3, pp. 5–17. doi: 10.1177/107754639700300102. [10] kafiey khan, a., azizur, r. (2010) wavelet based diagnosis and protection of electric motors, fault detection, wei zhang (ed.), intech, doi: 10.5772/9068. [11] michel, misiti., yves, misiti. (2003). les ondelettes et leurs applications, edition hermes, paris. [12] altmann, j., mathew, j. (2001). multiple band pass autoregressive demodulation for rolling element bearing fault diagnosis, mech syst signal process, 15, pp. 963-977, doi: 10.1006/mssp.2001.1410. [13] pandya, d_h., upadhyay, s_h., harsha, s p. (2013) fault diagnosis of rolling element bearing by using multinomial logistic regression and wavelet packet transform, doi: 10.1007/s00500-013-1055-1. [14] loparo, k. (2018). bearings vibration data set, case western reserve university. available online: http://csegroups.case.edu/bearingdatacenter/home (10 january 2018). [15] castejon, c., lara, o., garcía-prada, j. (2010) automated diagnosis of rolling bearings using mra and neural networks , mech syst sig process 24, pp. 289–299, doi: 10.1016/j.ymssp.2009.06.004. [16] lara, o., castejon, c., garcia-prada, j. (2006) bearing fault diagnosis based on neural network classification and wavelet transform, wseas trans. doi: 10.5555/1974867. [17] adewusi, s.a. (2001) wavelet analysis of vibration signals of an overhang rotor with a propagating transverse crack, j sound vib 5, pp. 777–793, doi: 10.1006/jsvi.2000.3611. t microsoft word numero_31_art_1 r.d.s.g. campilho et alii, frattura ed integrità strutturale, 31 (2015) 1-12; doi: 10.3221/igf-esis.31.01 1 advanced techniques for estimation of the tensile fracture toughness of adhesive joints r.d.s.g. campilho departamento de engenharia mecânica, instituto superior de engenharia do porto, instituto politécnico do porto, rua dr. antónio bernardino de almeida, 431, 4200-072 porto, portugal raulcampilho@gmail.com m.d. banea, l.f.m. da silva departamento de engenharia mecânica, faculdade de engenharia da universidade do porto, rua dr. roberto frias, s/n, 4200-465 porto, portugal abstract. adhesive bonding has become more efficient in the last few decades due to the adhesives developments, granting higher strength and ductility. as a result, adhesives are being increasingly used in industries such as the automotive, aerospace and construction. thus, it is highly important to predict the strength of bonded joints to assess the feasibility of joining during the fabrication process of components (e.g. due to complex geometries) or for repairing purposes. when using the finite element method with advanced propagation laws, the tensile (gnc) and shear (gsc) fracture toughness of adhesive joints must be determined with accuracy. several conventional methods to obtain gnc and gsc exist in the literature, mainly based on linear elastic fracture mechanics (lefm). the j-integral technique is accurate to measure these parameters for adhesives with high ductility. in this work, the j-integral is used to obtain gnc by the double-cantilever beam (dcb) test. an optical measurement method is developed for the evaluation of the crack tip opening and adherends rotation at the crack tip during the test, supported by a matlab® sub-routine for the automated extraction of these quantities. as output of this work, an optical method that allows an easier and quicker extraction of the parameters to obtain gnc than the available methods is proposed (by the j-integral technique) and some results are presented regarding joints with different geometry and adherend material. keywords. fibres; fracture toughness; damage mechanics; joining. introduction he developments in adhesives technology made possible the use of adhesive bonding in many fields of engineering, such as automotive and aeronautical [1]. however, stress concentrations exist in bonded joints along the bond length owing to the gradual transfer of load between adherends and also the adherends rotation in the presence of asymmetric loads [2]. a large amount of works addresses the critical factors affecting the integrity of adhesive joints, such as the parent structure thickness, adhesive thickness, bonding length and geometric modifications that reduce stress concentrations [3-5]. a large number of predictive techniques for bonded joints are currently available, ranging from analytical to numerical, using different criteria to infer the onset of material degradation, damage or even complete failure. initially, the prediction was performed by theoretical studies as those of volkersen [6], which had a lot of embedded simplifying assumptions, by t r.d.s.g. campilho et alii, frattura ed integrità strutturale, 31 (2015) 1-12; doi: 10.3221/igf-esis.31.01 2 comparing current stresses with the allowable material strengths. many improvements were then introduced, but these analyses usually suffered from the non-consideration of the material ductility. fracture mechanics-based methods took the fracture toughness of materials as the leading parameter. these methods included more simple energetic or stress-intensity fracture techniques that required the existence of an initial flaw in the materials [7]. more recent numerical techniques, such as cohesive zone models (czm), combine stress criteria to account for damage initiation with energetic, e.g. fracture toughness, data to estimate damage propagation [8]. this allows to consider the distinct ductility of adhesives and to gain accuracy in the predictions. all of these fracture toughness-dependent analyses rely on an accurate measurement of gnc and gsc. czm in particular can accurately predict damage growth if the fracture laws are correctly estimated [9]. these laws are based on the values of cohesive strength in tension and shear, tn0 and ts0, respectively, and also gnc and gsc. these parameters that cannot be directly related with the material properties measured as bulk, since they account for constraint effects (for adhesive joints, caused by the adherends). the estimation of these fracture parameters is generally accomplished by performing pure tension or shear tests. regarding gnc, the dcb test is the most suitable, due to the test simplicity and accuracy [10]. as described by suo et al. [11], in the presence of large-scale plasticity, j-integral solutions can also be employed for accurate results, in contrast to lefm-based solutions. the j-integral is a relatively straight-forward technique, provided that the analytical solution for a given test specimen exists for the determination of gnc or gsc. the most prominent example is the dcb specimen, for which j-integral solutions are available. it is also possible to estimate the tensile czm law. a few methods are available to estimate the cohesive parameters and the respective laws: the property identification and inverse methods consist on assuming a simplified shape (bilinear or trilinear) for the fracture laws and defining the respective parameters by standardized procedures, while the direct method estimates the precise law shape by computing it based on fracture characterization data [12]. this is accomplished by the differentiation of the strain energy release rate in tension (gn) or shear (gs) with respect to the relative opening (n for tension or s for shear). a few works addressed the j-integral method. carlberger and stigh [13] computed the czm laws of adhesive layers in tension and shear using the dcb and end-notched flexure (enf) tests, respectively, considering 0.1≤ta≤1.6 mm (ta is the adhesive thickness). the j-integral methodology and the direct method were used for measurement. the rotation of the adherends was measured by an incremental shaft encoder and the crack tip opening by two linear variable differential transducers (lvdt). the aforementioned techniques were considered accurate and enabled extracting the parameters with little noise during the full range of the tests. nonetheless, added difficulties were found because of the complicated test setup. the value of gnc revealed a monotonic increase from ta=0.1 to 1.0 mm. above this value, a slight reduction was found. under shear, the dependence of gsc with ta is not so significant, but an identical increasing trend is clear under ta=0.2 mm. in both cases, the observed behavior was explained in light of the increasing plastic zone size with the corresponding increase of ta. ji et al. [14] studied by the j-integral the influence of ta in dcb joints on tn0 and gnc for a brittle epoxy adhesive. gnc was measured by a direct technique. for the measurement of the adherends rotation, two digital inclinometers with a 0.01º precision were attached at the free end of each adherend. the normal displacement at the crack tip was measured by a charge-coupled device (ccd) camera. regarding the test setup, a step forward in terms of procedure was achieved by replacing the opening measurement system by a non-contact system. regarding the influence of ta on gnc, an increasing trend was found from 0.09≤ta≤1.0 mm, which was related to increasing plastic dissipations with the increase of ta. this work evaluates gnc of adhesive joints for different conditions: adhesive bonding for adhesive joints with natural fibre composite as adherends, adhesive bonding between aluminium adherends to study the effect of the adherends thickness (h) on gnc, and finally adhesive bonding between aluminium adherends considering varying values of ta. the j-integral is selected to measure gnc to account for the plasticity effects, together with the direct method to define the cohesive laws. an optical measurement method is used for the evaluation of crack tip opening and adherends rotation at the crack tip, supported by a matlab® routine for the automated extraction of these parameters. this technique provides a step forward in the available methods to extract the adherends rotation and crack opening at the crack tip, enabling a much easier test setup, without compromising the accuracy of the results. the data analysis is also automated to ease the data reduction process. experimental work characterization of the materials hree joint configurations were tested in this work, presented in tab. 1, considering the dcb test geometry. for configuration 1, typical properties of jute are as follows: density of 1.3-1.4 g/cm3, elongation at failure (f) of 1.51.8%, tensile strength (f) of 400-800 mpa and young’s modulus (e) of 15-30 gpa [15, 16]. epoxy was chosen t r.d.s.g. campilho et alii, frattura ed integrità strutturale, 31 (2015) 1-12; doi: 10.3221/igf-esis.31.01 3 for the matrix material on account of the good mechanical (strength and stiffness) and toughness properties, and also because of the superior wetting characteristics on natural fibres [17]. the epoxy resin type sr 1500 and sd 2505 hardener from sicomin epoxy systems were used. the matrix properties, as specified by the manufacturer, are as follows: e=3.1 gpa, f=74 mpa, strain at maximum load m=4.4% and f=6.0%. the jute-epoxy composite was composed by 30% of jute fabric (by weight) and gave the following properties in tensile testing: e=5.7 gpa and f=124.3 mpa. for configurations 2 and 3, the aluminium adherends were cut from a high strength aluminium alloy sheet (aa6082 t651). configuration adherends adhesive 1 jute-epoxy composite sikaforce® 7888 2 aluminium sikaforce® 7888 3 aluminium sikaforce® 7752-l60 table 1: configurations tested to measure gnc. this material was characterized in bulk tension in previous works by the authors [18] using dogbone specimens and the following mechanical properties were obtained: e=70.07±0.83 gpa, tensile yield stress (y) of 261.67±7.65 mpa, ultimate tensile stress (f) of 324±0.16 mpa and elongation (f) of 21.70±4.24%. configurations 1 and 2 used the polyurethane adhesive sikaforce® 7888, which was characterized in the work of neto et al. [19] by bulk tensile tests for the determination of e, f and f, and dcb and enf tests to define the values of gnc and gsc, respectively. the bulk characterization was performed as specified in the en iso 527-2 standard [20]. the obtained results gave e=1.89±0.81 gpa, f=28.60±2.0 mpa, f=43.0±0.6 %, gnc=0.7023±0.1233 n/mm and gsc=8.721±0.792 n/mm. configuration 3 used a novel polyurethane structural adhesive, sikaforce® 7752-l60. this is a two-part adhesive, and it consists of a filled polyol based resin and an isocyanate based hardener. it is characterized by a room temperature cure, high impact resistance and flexibility at low temperatures, having a tensile strength of approximately 10 mpa and tensile failure strain of 25% (manufacturer’s values). figure 1: geometry and characteristic dimensions of the dcb specimens. configuration l (mm) a0 (mm) h (mm) b (mm) ta (mm) 1 160 50 5 15 1 2 160 40 1, 2, 3 and 4 25 1 3 160 55 3 25 0.1, 0.2, 0.5, 1.0 and 2.0 table 2: dimensions of the three joint configurations. joint geometries the geometry of the dcb specimens is shown in fig. 1. the characteristic dimensions are the total length (l), initial crack length (a0), h, width (b) and ta. the chosen values for each joint configuration are presented in tab. 2. some dimensions differ between configurations, but these do not affect the gnc measurement. the joints for configuration 1 considered jute-epoxy composites as adherends, consisting of 8 stacked weave plies with a fibre volume fraction of approximately r.d.s.g. campilho et alii, frattura ed integrità strutturale, 31 (2015) 1-12; doi: 10.3221/igf-esis.31.01 4 30%. the plates were fabricated by hand lay-up and cured at room temperature in a vacuum bag. for the three joint configurations, for a uniform value of ta, calibrated spacers were inserted between the adherends. these spacers were inserted at both bonding edges between the adherends to control the value of ta. for the calibrated spacer at the crack tip, 3 plies were stacked and glued together, composed of a 0.1 mm thick razor blade between steel spacers to achieve the desired value of thickness, to create a pre-crack. for all specimens, stainless steel piano hinges were glued to both faces of the specimens at the cracked edge with a ductile adhesive, to provide a loading means in the testing machine grips. also, a metric scale was glued with cyanoacrylate in both adherends to allow measurement of the crack length (a) and of the input data for the extraction of the j-integral. six specimens of each configuration were tested at room temperature (≈20ºc), relative humidity of ≈40% and 2 mm/min in an electro-mechanical testing machine (shimadzu ag-x 100) with a load cell of 100 kn. data recording was carried out at 5 hz for the load (p) and testing machine grips displacement (), registered during the test as a function of the time elapsed since its initiation. pictures were recorded during the specimens testing with 5 s intervals using a 15 mpixel digital camera with no zoom and fixed focal distance to approximately 100 mm. j-integral technique to measure gn c n the proposed method, the czm law is measured by the direct method. under this scope, the path-independence of the j-integral can be used to extract relations between the specimen loads and the cohesive law of the crack path [21]. based on the fundamental expression for j defined by rice [22], it is possible to derive an expression for the value of gn applied to the dcb specimen from the concept of energetic force and also the beam theory for this particular geometry, as follows [23]:  u n u o n u p 2 3 12 or p a g p g p eh     (1) where pu represents the applied load per unit width at the adherends edges, o the relative rotation of the adherends at the crack tip andp the relative rotation of the adherends at the loading line (fig. 2). figure 2: dcb specimen under loading, with description of the analysis parameters. in this work, the first expression of (1) is considered, using o instead of p, due to a simpler extraction of the parameter by the optical method. the j-integral can be calculated along an arbitrary path encircling the start of the adhesive layer, giving [21]:   nc n n n n 0 dg t     (2) where nc is the end-opening at failure of the cohesive law (measured at the initial crack tip) and tn is the current normal traction. gnc can be considered the value of gn at the beginning of crack growth. thus, gnc is given by the steady-state value of gn, at a n value of nc [13]. the tn(n) curve can be easily obtained by differentiation of eq. (1) with respect to n   nn n n g t      (3) i r.d.s.g. campilho et alii, frattura ed integrità strutturale, 31 (2015) 1-12; doi: 10.3221/igf-esis.31.01 5 as a result, the procedure of an experiment is to measure the history of p, a, n and o. the cohesive law in tension can then be estimated by plotting gn in eq. (1) as a function of n, polynomial fitting of the obtained curve and differentiation [21]. optical method for the parameter measurement for calculating n and o for a given image, the optical method requires the identification of eight points (fig. 3): two points (p1, p2) for measuring the current ta value at the crack tip (tact) during loading in image units (pixels), two points (p3, p4) identifying a line segment in the image for which the length (d) is known in real world units (mm), two points (p5, p6) on the top specimen and two points (p7, p8) on the bottom specimen. figure 3: points taken by the optical method for measuring o and gn c. points identification all eight points are manually identified in the first picture of a trial using an in-house software tool. the identification of the points is aided by the ruler attached to the specimens. using the location of the points in the first picture, the points of the following pictures are automatically identified using a computer algorithm implemented in matlab®. basically, for each point pi, a rectangular region centred in pi is extracted from the first image forming a template (t). this template describes the image pattern that surrounds the point and is used for locating the point in the next image. this is done by finding the position (u,v) in the next image (i) that has the highest normalized cross-correlation with the template. the normalized cross-correlation is a measure of similarity between two grayscale images that is invariant to linear changes in illumination and that quantifies the correlation between the grayscale levels of two images/regions. the normalized cross-correlation () of template t with image i at the position (u,v) of image i is defined as:           , , 0.522 , ,, , . , , , . ,                            x y u v x y x yu v f x y f t x u y v t u v f x y f t x u y v t (4) r.d.s.g. campilho et alii, frattura ed integrità strutturale, 31 (2015) 1-12; doi: 10.3221/igf-esis.31.01 6 where f is the region of the image i with the same size as t centred in the position (u,v). calculating  for all the pixels of i results in a matrix, where the maximum absolute value yields the location of the region in i that has the highest correlation with t and, thus, the most likely location of pi in the next image. this is done for every one of the eight points identified in the first image. after successfully identifying all the points of the second image, new templates are computed from the second image to search for the eight points in the third image, and so on until processing all the images. computation of n the value of tact in real world units (mm) is calculated as follows 1 2cta 3 4    p p t d p p (5) for all trials, a region of length d=45 mm was used (fig. 3). the pixel size was on average 0.024 mm and, thus, the estimated maximum error of the image acquisition process is ±0.012 mm. finally, n can be defined as ctn a a  t t (6) where ta is the theoretical design value of 1 mm. since ta can show small variations due to the fabrication process, an adjustment to n is also applied to make n=0 at the beginning of the test. fig. 4 gives an example of the evolution of n for a selected test specimen of configuration 2 (with h=4 mm). shown in the graphic are the raw curve, the 6th degree fitting curve and the corrected polynomial and final curve, adjusted to make n (testing time=0)=0. this polynomial adjustment is required to smooth the raw data and remove experimental measurement scatter, but also to cancel any eventual misalignment between glued scales in both adherends. n = -4.2482e-17t6 + 3.5246e-13t5 1.5875e-10t4 + 2.3802e-08t3 7.1272e-07t2 + 1.3125e-04t 1.2653e-04 r² = 9.9307e-01 0.00 0.04 0.08 0.12 0.16 0 50 100 150 200 250 300  n [m m ] testing time, t [s] raw curve adjusted curve polinomial (raw curve)polynomial (raw curve) figure 4: evolution of n for one test specimen: raw curve obtained from the optical method, polynomial fitting curve and corrected polynomial curve. computation of o o is calculated as the angle between lines l1 and l2 (fig. 5). these lines could be directly calculated from points (p5, p6) and (p7, p8) respectively. however, for increasing robustness to small fluctuations of the point detection process, an image processing algorithm was used to extract the midline of the edge of the ruler that contains the pair of points in hand. in particular, a difference of gaussian filters was applied for enhancing the edges of the ruler, resulting in an image where pixels belonging to edges have high intensity values, while the remaining ones have low intensity (fig. 5). r.d.s.g. campilho et alii, frattura ed integrità strutturale, 31 (2015) 1-12; doi: 10.3221/igf-esis.31.01 7 figure 5: image after applying the difference of gaussian filters and the extracted lines (l1 and l2) that are used for measuring o. then, for the rows of the image between p5 and p6, the midpoint of the edge at each row is computed. the midpoint is first extracted for the row of p5 by (1) collecting all the pixels to the left and to the right of p5 that can be reached from p5 without dropping the pixel intensity bellow a given threshold (10% for all experiments), and (2) by averaging the position of all the collected pixels weighted by the pixels intensity value (so that pixels with higher intensities, i.e. pixels belonging to the edge, have a higher impact in the row’s midpoint calculation). this makes the process robust to blur in the images and to the point identification process because points p5 and p6 do not need to be identified exactly in the midline of the edge. this process is repeated for all the following rows until reaching p6, resulting in one point per row of the image between p5 and p6 that define the midline of the edge of the ruler. since these points are not necessarily collinear, a linear regression is used for obtaining l1. the same process is repeated with points (p7, p8) for obtaining l2 and, finally, o may be calculated as the angle between the two lines 1 20 1 2 arccos v v v v              (7) where 1v  and 2v  are the direction vectors of lines l1 and l2, respectively. fig. 6 shows the o-testing time plot for a specimen, more specifically the three curves of fig. 4. due to scaling difficulties, the raw curve in the figure is already translated such that o(testing time=0)=0. o = 1.0646e-11t4 4.6515e-09t3 + 8.0223e-07t2 + 7.7256e-05t + 8.6406e-03 r² = 9.9726e-01 0 0.02 0.04 0.06 0 50 100 150 200 250 300  o [r ad ] testing time, t [s] raw curve adjusted curve polinomial (raw curve) 0.06 0.04 0.02 0  o [r ad ] polynomial (raw curve) figure 6: evolution of o for one test specimen: raw curve obtained from the optical method, polynomial fitting curve and corrected polynomial curve. r.d.s.g. campilho et alii, frattura ed integrità strutturale, 31 (2015) 1-12; doi: 10.3221/igf-esis.31.01 8 results configuration 1 or the bonded specimens with jute-epoxy adherends, n and o were defined as specified previously. the values of gnc for the bonded joints were defined by plotting the gn-n curves, considering gnc as the steady-state value of gn in the gn-n curve [13]. fig. 7 plots the experimental gn-n law and the corresponding 6th degree polynomial fitting curve for a given specimen. at the beginning of the test, gn slowly increases with n, but the growth rate of gn rapidly increases up to nearly n=0.02-0.04 mm, and a steady-state value of gn is attained at approximately n = 0.09 mm. for this specimen, the measured value of gnc is 1.429 n/mm. for the six bonded specimens, the obtained data gave gnc=1.182±0.215 n/mm. fig. 8 shows the obtained experimental tn-n law, showing the ductile characteristics of the adhesive after the peak value of tn is attained. for this specimen, the following values were found: tn0=20.73 mpa and nc=0.0935 mm. for the complete batch of tested specimens, average values and deviations were as follows: tn0=23.18±3.57 mpa and nc=0.0843±0.156 mm. proposed triangular and trapezoidal simplified czm laws are also presented, allowing concluding that for the adhesive sikaforce® 7888 a trapezoidal law is particularly suited, since it accounts the best for the adhesive ductility. gn = 7.1158e+06n6 2.8985e+06n5 + 4.3017e+05n4 3.1299e+04n3 + 1.1496e+03n2 + 2.9621e-01n 6.2813e-04 r² = 9.9999e-01 0 0.4 0.8 1.2 1.6 2 0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 g n [n /m m ] n [mm] experimental law polinomial (experimental law) 0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 2 1.6 1.2 0.8 0.4 0 polynomial (experimental law) figure 7: experimental gn-n law for one test specimen and polynomial fitting curve (configuration 1). 0 5 10 15 20 25 0 0,02 0,04 0,06 0,08 0,1 0,12 0,14 t n [m p a] n [mm] exp erimental czm law triangular aprox. trap ezoidal ap rox. 25 20 15 10 5 0 0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 figure 8: experimental tn-n law for one test specimen. configuration 2 gnc was calculated by eq. (1). the experimental gn-n laws were identical in shape to fig. 7, and an example for h=3 mm is presented in fig. 9. the gnc results by applying this procedure for all tested specimens are shown in fig. 10 as a f r.d.s.g. campilho et alii, frattura ed integrità strutturale, 31 (2015) 1-12; doi: 10.3221/igf-esis.31.01 9 function of h. the deviation is somehow large, and whose justification lies on the experimental process to obtain gnc, which relies on a number of measured parameters and approximation functions, which are difficult to adjust to the experimental data [24]. while for the specimens with h=1 mm, a value of gnc=0.781±0.146 n/mm was obtained, improvements of 12.6, 37.7 and 40.2% were attained by increasing h up to 4 mm. these results show the stabilization of gnc for a given value of h (in this case between gnc=1.075±0.226 n/mm for h=3 mm and gnc=1.095±0.195 n/mm for h=4 mm a stabilization of gnc was found). y = 4.6496e+07x6 1.1350e+07x5 + 1.0422e+06x4 5.1126e+04x3 + 1.5765e+03x2 5.6343e+00x + 4.8466e-03 r² = 9.9994e-01 0 0.4 0.8 1.2 1.6 0 0.02 0.04 0.06 0.08 g i [n /m m ] n [mm] experimental law polinomial (experimental law) 0 0.02 0.04 0.06 0.08 1.6 1.2 0.8 0.4 0 polynomial (experimental law) figure 9: experimental gn-n law for one test specimen with h=3 mm and polynomial fitting curve (configuration 2). 0 0,4 0,8 1,2 1,6 0 1 2 3 4 g nc [n /m m ] h [mm] 1.6 1.2 0.8 0.4 0 figure 10: average values and deviation of gnc as a function of h by the j-integral. this increase of gnc is reported in the literature because of the stress field variations ahead of the crack tip being dependent on the joint geometry, which highly influences the shape and size of the damage zone, and the local yield stress as well [25]. as it was discussed in previous works [26], thicker adherends provide an elevation of peel stresses further within the joint, shifting the loading conditions from peeling to cleavage, and giving a larger length for the damage zone. these findings are corroborated in the work of azari et al. [27], regarding the adherend stiffness influence on the fatigue failure of bonded joints, which proved by finite elements that the plastic zone in adhesive joints between steel adherends was consistently higher than identical joints between aluminium adherends during the entire damage uptake process up to crack initiation. mangalgiri et al. [28] justified this tendency with the plastic zone and stress distributions ahead of the debond tip. actually, the plastic zone was bigger in length across the adhesive layer with increasing number of composite plies (and thus, increasing h). also, thicker adherends used a larger amount of the input energy to the specimen to develop a lengthier plastic zone, thus leaving less available energy for damage growth [29]. on account of this, higher values of gnc can be expected for joints with higher degrees of restraint (i.e., stiffer or thicker adherends). r.d.s.g. campilho et alii, frattura ed integrità strutturale, 31 (2015) 1-12; doi: 10.3221/igf-esis.31.01 10 configuration 3 following the method described in j-integral technique to measure gnc section, gnc was calculated identically to the previous cases, which considered o instead of p to obtain gn. the aforementioned method was applied to all tested specimens and the gnc results for each ta value and respective deviation are presented in fig. 11. for the specimens with ta=0.1 mm, the obtained results gave gnc=1.83±0.24 n/mm. the increase of gnc from this point was of 14.5% (ta=0.2 mm), 57.8% (ta=0.5 mm), 105.6% (ta=1.0 mm) and 195.9% (ta=2.0 mm). 0 1 2 3 4 5 6 0 0.5 1 1.5 2 2.5 g nc [n /m m ] ta [mm] figure 11: average values and deviation of gnc as a function of ta by the j-integral. regarding the available studies (for epoxy adhesives), yan et al. [30] studied the influence of ta on the fracture properties (gnc) of dcb and compact tension (ct) joints with aluminium adherends and a rubber-modified epoxy adhesive. using a large deformation finite element technique and the peak loads measured in the experiments, the critical value of the jintegral was calculated for different values of ta. a gnc increase was found up to ta=1 mm and a decrease afterwards. an identical conclusion was found by khoo and kim [31] for an epoxy adhesive between 0.2<ta<1.5 mm, with the maximum gnc being found for ta=1 mm. the increasing trend obtained in this work of gnc with ta is linear up to ta=2.0 mm, and this result is consistent with previous studies in this matter, except from a reduction of gnc for big values of ta that is common with less ductile epoxy adhesives. another exception is the work of marzi et al. [32], which attained a maximum gnc between ta=1 and 2 mm for the polyurethane sikapower 498tm, a modern crash resistant epoxy adhesive, without a reduction tendency of gnc up to ta=2 mm, due to its large ductility. an identical trend to this work regarding the gnc-ta law was found by banea et al. [33] with the high elongation polyurethane adhesive sikaforce® 7888, characterized with conventional fracture methods in the range of 0.2≤ta≤2 mm. in both this and the present work, the peak value of gnc is attained for a ta value bigger than 2 mm, but in this range of values the joints are more likely to have fabrication defects, and be more difficult to fabricate, which justifies its limited industrial applicability. discussion of results the proposed technique, applied to the 3 joint configurations, showed that the proposed j-integral methodology can be a valuable tool to estimate gnc of adhesive joints. moreover, with the measurement of n, the cohesive law of the adhesive layer can be obtained as well. by analyzing the obtained results between the three tested configurations, a direct analogy cannot be formed between configuration 3 and configurations 1 and 2, because a different adhesive was considered (although both tested adhesives are ductile polyurethanes). in the comparison between configurations 1 and 2, it should be noted that, as depicted in tab. 2, the value of h varied. this has a significant influence on the plastic zone size and, thus, also on the gnc measurements. the measured data for the bonded joint of configuration 1 gave gnc=1.182±0.215 n/mm (h=5 mm), while for configuration 2 and h=4 mm the value of gnc=1.095±0.195 n/mm was obtained. these values agree quite well, although the difference in bending stiffness of the adherends has to be considered: the values of h between these two configuration differ and, additionally, the value of e of the adherends for configuration 2 (aluminium) is much higher than that of configuration 1 (jute-epoxy composite). since the results of configuration 2 show that, for aluminium adherends, for h values above 3 mm the plastic zone effect ceases to affect the results, the gnc measurement theoretically should be identical between configurations 1 and 2. in view of this discussion, the 7.4% different between these two configurations is attributed to experimental scatter and related issues. r.d.s.g. campilho et alii, frattura ed integrità strutturale, 31 (2015) 1-12; doi: 10.3221/igf-esis.31.01 11 concluding remarks his work dealt with the determination of gnc of adhesive joints with different configurations, considering either the adhesive or adherend material. the j-integral was used to measure gnc, given the large adhesive plasticity. with this purpose, an optical measurement and data analysis method was built in matlab® to extract o to obtain gn, and n to build the czm laws. the complete tensile czm law of the adhesive was derived by the direct method in some cases, on account of the available gn-n curve that was differentiated to provide the tn-n (or czm) law. for configuration 1, an average value of gnc=1.182 n/mm was obtained for the adhesive sikaforce® 7888 between jute-epoxy composite adherends. this value can be compared to the average of gnc=1.095 n/mm estimated in configuration 2 for h=4 mm aluminium adherends. these values agree quite well, although it should be considered that both configurations differ in the values of h and e of the adherends. a direct analogy cannot be formed between configuration 3 and configurations 1 and 2, because a different adhesive was considered. as output of this work, gnc data was given for the strength prediction of bonded joints for different adhesives and joint conditions. additionally, a methodology was presented to accurately estimate gnc for ductile adhesives, as well as the czm law, which can be used for strength predictions of bonded structures by czm modelling. references [1] lee, m.j., cho, t.m., kim, w.s., lee, b.c., lee, j.j., determination of cohesive parameters for a mixed mode cohesive zone model, int. j. adhes. adhes., 30 (2010) 322-328. [2] pinto, a.m.g., magalhães, a.g., campilho, r.d.s.g., de moura, m.f.s.f., baptista, a.p.m., single-lap joints of similar and dissimilar adherends bonded with an acrylic adhesive, j. adhesion, 85 (2009) 351-376. [3] campilho, r.d.s.g., pinto, a.m.g., banea, m.d., silva, r.f., da silva, l.f.m., strength improvement of adhesivelybonded joints using a reverse-bent geometry, j. adh. sci. technol., 25 (2011) 2351-2368. [4] deng, j., lee, m.m.k., effect of plate end and adhesive spew geometries on stresses in retrofitted beams bonded with a cfrp plate, compos: part b, 39 (2008) 731-739. [5] kim, t.h., kweon, j.h., choi, j.h., an experimental study on the effect of overlap length on the failure of composite-to-aluminum single-lap bonded joints, j. reinf. plast. compos. 27 (2008) 1071-1081. [6] volkersen, o., die nietkraftoerteilung in zubeanspruchten nietverbindungen konstanten loschonquerschnitten, luftfahrtforschung, 15 (1938) 41-47. [7] chai, h., shear fracture, int. j. fract., 37 (1988) 137-159. [8] campilho, r.d.s.g., de moura, m.f.s.f., barreto, a.m.j.p., morais, j.j.l., domingues, j.j.m.s., fracture behaviour of damaged wood beams repaired with an adhesively-bonded composite patch, compos. part a 40 (2009) 852-859. [9] campilho, r.d.s.g., de moura, m.f.s.f., ramantani, d.a., morais, j.j.l., domingues, j.j.m.s., buckling behaviour of carbon-epoxy adhesively-bonded scarf repairs, j. adhes. sci. technol., 23 (2009) 1493-1513. [10] yoshihara, h., simple estimation of critical stress intensity factors of wood by tests with double cantilever beam and three-point end-notched flexure, holzforschung, 61 (2007) 182-189. [11] suo, z., bao, g., fan, b., delamination r-curve phenomena due to damage, j. mech. phys. solids, 40 (1992) 1-16. [12] campilho, r.d.s.g., de moura, m.f.s.f., pinto, a.m.g., morais, j.j.l., domingues, j.j.m.s., modelling the tensile fracture behaviour of cfrp scarf repairs. compos: part b, 40 (2009) 149-157. [13] carlberger, t., stigh, u., influence of layer thickness on cohesive properties of an epoxy-based adhesive-an experimental study, j. adhesion, 86 (2010) 814-833. [14] ji, g., ouyang, z., li, g., ibekwe, s., pang, s.s., effects of adhesive thickness on global and local mode-i interfacial fracture of bonded joints, int. j. solids struct., 47 (2010) 2445-2458. [15] wambua, p., ivens, j., verpoest, i., natural fibres: can they replace glass in fibre reinforced plastics?, compos. sci. technol., 63 (2003) 1259-1264. [16] ku, h., wang, h., pattarachaiyakoop, n., trada, m., a review on the tensile properties of natural fiber reinforced polymer composites, compos.: part b, 42 (2011) 856-873. [17] herrera-franco, p.j., valadez-gonzález, a., a study of the mechanical properties of short natural-fiber reinforced composites, compos: part b, 36 (2005) 597-608. [18] campilho, r.d.s.g., banea, m.d., pinto, a.m.g., da silva, l.f.m., de jesus, a.m.p., strength prediction of single and double-lap joints by standard and extended finite element modelling, int. j. adhes. adhes., 31 (2011) 363-372. t r.d.s.g. campilho et alii, frattura ed integrità strutturale, 31 (2015) 1-12; doi: 10.3221/igf-esis.31.01 12 [19] neto, j.a.b.p., campilho, r.d.s.g., da silva, l.f.m., parametric study of adhesive joints with composites, int. j. adhes. adhes., 37 (2012) 96-101. [20] iso 527-2 standard, plastics – determination of tensile properties – part 2: test conditions for moulding and extrusion plastics (2012). [21] stigh, u., alfredsson, k.s., andersson, t., biel, a., carlberger, t., salomonsson, k., some aspects of cohesive models and modelling with special application to strength of adhesive layers, int. j. fatigue, 165 (2010) 149-162. [22] rice, j.r., a path independent integral and the approximate analysis of strain concentration by notches and cracks, j. appl. mech., 35 (1968) 379-386. [23] banea, m.d., da silva, l.f.m., campilho, r.d.s.g., temperature dependence of the fracture toughness of adhesively bonded joints, j. adh. sci. technol. 24 (2010) 2011-2026. [24] campilho, r.d.s.g., moura, d.c., gonçalves, d.j.s., da silva, j.f.m.g., banea, m.d., da silva, l.f.m., fracture toughness determination of adhesive and co-cured joints in natural fibre composites, compos: part b, 50 (2013) 120126. [25] bell, a.j., kinloch, a.j., the effect of the substrate material on the value of the adhesive fracture energy, gc, j. mater. sci. lett., 16 (1997) 1450-1453. [26] blackman, b.r.k., kinloch, a.j., paraschi, m., the effect of the substrate material on the value of the adhesive fracture energy, gc: further considerations, j. mater. sci. lett., 20 (2001) 265-267. [27] azari, s., ameli, a., datla, n.v., papini, m., spelt, j.k., effect of substrate modulus on the fatigue behaviour of adhesively bonded joints, mater. sci. eng. a, 534 (2012) 594-602. [28] mangalgiri, p.d., johnson, w.s., everett jr., r.a., effect of adherend thickness and mixed mode loading on debond growth in adhesively bonded composite joints, j. adhesion, 23 (1987) 263-288. [29] azari, s., ameli, a., papini, m., spelt, j.k., adherend thickness influence on fatigue behaviour and fatigue failure prediction of adhesively bonded joints, compos: part a, 48 (2013) 181-191. [30] yan, c., mai, y.w., ye, l., effect of bond thickness on fracture behaviour in adhesive joints, j. adhesion, 75 (2001) 27–44. [31] khoo, t.t., kim, h., effect of bondline thickness on mixed-mode fracture of adhesively bonded joints, j. adhesion, 87 (2011) 989-1019. [32] marzi, s., biel, a., stigh, u., on experimental methods to investigate the effect of layer thickness on the fracture behavior of adhesively bonded joints, int. j. adhes. adhes. 31 (2011) 840-850. [33] banea, m.d., da silva, l.f.m., campilho, r.d.s.g., the effect of adhesive thickness on the mechanical behavior of a structural polyurethane adhesive, the journal of adhesion, in press. microsoft word numero_41_art_58.docx f. berto, frattura ed integrità strutturale, 41 (2017) 464-474; doi: 10.3221/igf-esis.41.58 464 v-notch tip subjected to in-plane mixed mode loading: overview of recent results and possible future outcomes f. berto norwegian university of science and technology ntnu, department of engineering design and materials, trondheim, 7491, norway abstract. the fictitious notch rounding concept is applied for the first time to v-notches with root hole subjected to in-plane mixed mode loading. outof-bisector crack propagation is taken into account. the fictitious notch radius is determined as a function of the real notch radius, the microstructural support length and the notch opening angle. due to the complexity of the problem, a method based on the simple normal stress failure criterion has been used. it is combined with the maximum tangential stress criterion to determine the crack propagation angle. an analytical method based on neuber's procedure has been developed. the method provides the values of the microstructural support factor as a function of the mode ratio and the notch opening angle. the support factor is considered to be independent of the microstructural support length. finally, for comparison, the support factor is determined on a purely numerical basis by iterative analysis of fe models. keywords. fictitious notch rounding; mixed mode loading; v-notches with root hole; microstructural support. citation: berto, f., v-notch tip subjected to in-plane mixed mode loading: overview of recent results and possible future outcomes, frattura ed integrità strutturale, 41 (2017) 464-474. received: 12.05.2017 accepted: 23.07.2017 published: 01.07.2017 copyright: © 2017 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. introduction ll previous publications on the fictitious notch rounding (fnr) concept deal with the pure loading modes 1, 2 and 3. the difficulty of considering mixed mode loading conditions is due to the fact that the most critical direction, in which cracks might provisionally initiate and propagate, varies as a function of the mode ratio. this direction varies from the notch bisector line in the case of pure mode 1 loading, to a direction substantially out of the notch bisector line in the case of pure mode 2 loading. the present work extends the fnr concept to mixed mode 1 and 2 loading conditions for the first time and provides a solution to the problem as a function of the mode ratio. the fnr concept [1-3] refers to the fact that the theoretical maximum notch stress does not characterise the static strength or fatigue strength of pointed or sharply rounded notches. the notch stress averaged over a short radial distance at pointed notches or over a small distance normal to the notch edge at rounded notches (real notch radius ) is the key parameter of the method. the mentioned distance * is usually called ‘microstructural support length’. in the high-cycle fatigue regime, notch stress averaging should take a path which coincides with the point and direction of fatigue crack initiation and propagation. the basic idea of the fnr concept is to determine the fatigue-effective averaged notch stress directly (i.e. a f. berto, frattura ed integrità strutturale, 41 (2017) 464-474; doi: 10.3221/igf-esis.41.58 465 without actual notch stress averaging) by performing the notch stress analysis with a fictitiously enlarged notch radius f given by  f = + s * (1) by taking advantage of the analytical frame provided by filippi et al. [4] and neuber [1], the fnr approach has been applied to v-notches under mode 1 and mode 3 loading, respectively [5, 6]. the support factor s was found to be highly dependent on the notch opening angle 2. a satisfactory agreement was found between the theoretical stress concentration factor kt(f) evaluated at the fictitiously rounded notch and the averaging stress concentration factor kt obtained by integrating the relevant stress over the distance * in the bisector line of the pointed v-notch. it is worth mentioning that the notch stress averaging method was originally proposed for brittle fracture problems by wiegardt [7] and later extended by weiss [8]. the fnr concept was mathematically formalised by neuber [1, 3, 9], who provided a general theoretical frame of the method. the application of the concept to strength assessments was demonstrated in ref. [2]. there is also a correspondence of the concept with the ‘critical distance approach’ proposed and successfully applied by peterson [10]. it was also applied many years later to notched thin plates subjected to fatigue loading [11, 12] using the characteristic length a0 derived by el-haddad, topper and smith [13] from the conventional endurance limit and the threshold stress intensity factor range. referring to neuber’s concept, radaj [14-17] proposed to apply the fnr method to assess the high-cycle fatigue strength of welded joints (toe or root failures). a worst case assessment for welded low-strength steels, notch radius  = 0 mm, microstructural support length * = 0.4 mm and support factor s = 2.5, resulted in f = 1.0 mm. this reference radius was found to be generally applicable to fatigue strength assessments of welded joints in structural steels and aluminium alloys and has become a standardised procedure within the design recommendations of the international institute of welding (iiw) [18]. a recent work has been devoted to the application of the fnr approach to notches with root hole subjected to pure mode 1 loading [19, 20]. some analytical expressions have been derived for the fictitious notch radius f and the support factor s taking advantage of some closed form expressions specifically derived for v-notches with root hole [21]. an extension to pure mode 3 loading has been carried out in [22] on the basis of the same set of equations [21]. the case of in-plane shear loading (mode 2) is more complex to analyse than mode 1 and mode 3 loading. the reason for the higher complexity is the fact that out-of-bisector crack propagation is observed, because the maximum notch stress occurs outside the notch bisector line. the mode 2 problem was considered from a theoretical point of view resulting in closed-form solutions for elliptical notches and in numerical solutions for keyhole notches [23]. in a recent paper, pointed v-notches subjected to pure mode 2 loading were investigated [24]. due to the complexity of the analytical developments, the support factor s was determined numerically using the fe method. the key problem was the choice of the crack path direction for stress averaging over the microstructural support length. two criteria available from the literature were used to determine the angle of most probable crack propagation, the maximum tangential stress (mts) criterion according to erdogan-sih [25] and the minimum strain energy density (msed) criterion according to sih [26]. taking advantage of the closed form equations provided in ref. [21] for v-notches with root hole, the fnr concept has been mathematically formalised for this notch shape in the case of in-plane shear loading [27]. two analytical methods and one numerical method have been proposed in the quoted contribution for determining the fictitious notch radius f and therefrom the support factor s dependent on the notch opening angle 2 . in all three methods, the crack propagation angle has been determined based on the mts criterion. a state-of-the art review of the fnr approach comprising also the recent developments just mentioned has been carried out in refs [28, 29]. while the application of the fnr approach to the pure loading modes is well developed, in-plane mixed mode loading remains an open problem which is difficult to solve for various reasons. the main difficulty is that the most probable crack propagation angle depends on the mode ratio ranging from pure mode 1 to pure mode 2 loading. the aim of the present paper is to provide a theoretically founded basis for the application of the fnr approach to in-plane mixed mode loading. using the newly developed analytical frame [21], the values of the support factor s as a function of the mode ratio m and the notch opening angle 2 are obtained. as implied by eq. (1), the support factor s is considered to be independent of the microstructural support length *, which is only approximately the case. but all the s values reported in the present contribution are on the safe side when used for strength assessments. the analytical procedure given by neuber [1, 3] for determining the factor s is applied in edge-normal directions outside the bisector line. this is an extension of what has been done by the authors [5, 6] in the cases of pure mode 1, mode 2 and mode 3 loading. by this method, v-notches with root hole, both in the real and in the fictitious configuration, are considered. f. berto, frattura ed integrità strutturale, 41 (2017) 464-474; doi: 10.3221/igf-esis.41.58 466 pointed notches are the limit case obtained when the real notch root radius tends to zero. the proposed method requires a numerical solution of the rather complex governing equation to determine the values of s, but easy-to-survey tables and diagrams present these values as a function of the mode ratio m for various notch opening angles 2 in order to provide a simple tool for the engineering application of the fnr approach in the case of mixed mode loading. finally, for verification of the method, the factor s is also determined on a purely numerical basis by iteration of fe models. analytical frame for v-notches with root hole subjected to mixed mode loading conditions sing the normal stress criterion in combination with the mts criterion (for the crack propagation angle), an analytical method has been developed for evaluating the fictitious notch radius f and the support factor s therefrom as a function of the mode ratio m defined below. the method refers to fig. 1 where the real root radius  is substituted by the fictitious notch radius f. the v-notch with root hole subjected to mode 1 loading is considered. taking the relevant boundary conditions into account, the stress components for the symmetric mode result from ref. [21]:   2 2 11 1 111 1 1 11 12 11 1 1 2 2( 1)1 1 1 1 1 1 cos(1 ) (1 ) ( ) ( ) ( ) (1 ) ( )2 ( )cos(1 ) 1 (1 ) 2 k r r r r r                                                                                (2.1)   2 2 11 1 111 1 1 11 12 11 1 1 2 2( 1)1 1 1 1 1 1 cos(1 ) (3 ) ( ) ( ) ( ) (1 ) ( )2 ( )cos(1 ) (3 ) 1 2 rr k r r r r r                                                                               (2.2)   2 2 11 1 111 1 1 11 12 12 1 1 2 2( 1)1 1 1 1 1 1 sin(1 ) (1 ) ( ) ( ) ( ) (1 ) ( )2 ( )sin(1 ) (1 ) 1 2 r k r r r r r                                                                                (2.3) figure 1: fictitious notch rounding concept applied to mixed mode loading (mode 1+2): real root hole notch with stress averaged over * in direction of crack propagation (a) and substitute root hole notch with fictitious notch radius f producing max = (b). the parameter 1 is williams’ [30] mode 1 eigenvalue, which is dependent on the notch opening angle 2 u * y a 2 x 2 a  f =s max(f) =  (a)  (b)   *ρρ ρ th d * 1 xσ ρ σ r  f. berto, frattura ed integrità strutturale, 41 (2017) 464-474; doi: 10.3221/igf-esis.41.58 467 the generalised mode 1 notch stress intensity factor k1 can be expressed as follows:  1 1 1 1 1 2 2 1 2 21 1 1 1 2 3 4 2 ( , 0) (1 ) ( )r r k g g g g r r r                                             (3) when the notch radius  tends to zero, k1 tends to the mode 1 notch stress intensity factor k1 defined according to gross and mendelson [31]: 1 11 02 limrk r      (4) considering the v-notch with root hole under mode 2 loading, the stress components for the antisymmetric mode result also from ref. [21]:   2 2 11 2 222 2 2 21 22 22 2 2 2 2( 1)2 2 2 2 2 2 sin(1 ) ( 1) ( ) ( ) ( ) (1 ) ( )2 ( )sin(1 ) 1 (1 ) 2 k r r r r r                                                                                 (5.1)   2 2 11 2 222 2 2 21 22 22 2 2 2 2( 1)2 2 2 2 2 2 sin(1 ) (3 ) ( ) ( ) ( ) (1 ) ( )2 ( )sin(1 ) 1 (3 ) 2 rr k r r r r r                                                                                (5.2)   2 2 11 2 222 2 2 21 22 21 2 2 2 2( 1)2 2 2 2 2 2 cos(1 ) (1 ) ( ) ( ) ( ) (1 ) ( )2 ( )cos(1 ) 1 (1 ) 2 r k r r r r r                                                                                 (5.3) the parameter 2 is williams’ [30] mode 2 eigenvalue, which is dependent on the notch opening angle  the generalised mode 2 notch stress intensity factor k2 can be expressed as follows: 1 2 2 2 2 1 2 22 2 2 1 2 3 2 ( , 0) 1 rr rk h h h r r r                                       (6) when the notch root radius tends to zero, k2 tends to the mode 2 notch stress intensity factor k2 defined according to the following expression: 1 22 02 limr rk r      (7) f. berto, frattura ed integrità strutturale, 41 (2017) 464-474; doi: 10.3221/igf-esis.41.58 468 it is important to underline that the property of k to converge to the stress intensity factor of the pointed v-notch, k2, when the notch root radius tends to zero, is a characteristic of the set of equations provided in ref. [21] for v-notches with root hole. other sets of equations [32, 33] applicable to rounded v-notches of different shape do not have this property as discussed in ref. [34]. in that paper it was also documented the stable trend of the generalized notch stress intensity factors given in eqs (4) and (8) as a function of the distance r. the problem of the oscillating trend of kand kdescribed in [33] for blunt v-notches with flanks tangent to the notch root radius is overcome by employing the set of equations reported in [21]. fictitious notch rounding is considered for v-notches with root hole subjected to mode 1 and mode 2 loading based on eqs. (2.1) and (5.1). based on the mts criterion, the crack propagation angle 0 is obtained from the following condition d/d = 0 (8) the hoop stress field  depends on the position variables r and  in such a way the condition d/d = 0 does not determine the angle of crack propagation unless a value of r is specified. the angle 0 increases by increasing the distance r due to the higher contribution of mode 2 with respect to mode 1 loading at greater distances from the notch tip. in this paper the values of =0 (worst case configuration) and r=0.005 mm (early crack propagation) have been set to evaluate the crack initiation angle 0. it will be shown in the following that the specific value of r allows us to match the values of s obtained for pure mode 1 [20] and pure mode 2 [27]. the normal stress criterion is now introduced for the averaged stress and the mts criterion for the crack propagation angle 0. based on eqs. (2.1) and (5.1) the maximum theoretical notch stress th(r, 0) is obtained and the averaged stress in the direction of 0 is determined:   * 0 1 σ σ , dr ρ * th r        (9) the determinate integral in eq. (9) has first been solved in its indeterminate form separated into mode 1 and mode 2 components (termed ii1 and ii2), and only then in its determinate form (termed di1 and di2). the determinate integrals referring to mode 1 and mode 2, respectively, result in the following form: 0 0 01( , *, ) 1( *, ) 1( , )di ii ii          (10) 0 0 02( , *, ) 2( *, ) 2( , )di ii ii          (11) for the sake of brevity of presentation and due to the length of the final expressions, the explicit forms of di1 and di2 are omitted here. the limit value of the average stress for *0 (and f) is:     11 1 1 0 1 1 0 1 12 0 11 0 11 0 * 0 0 1 1 4 cos 1 cos 1 (1 ( ) ( ) ( )) lim 1( , *, ) 2 (1 ) f f k di                                              (12)     12 2 2 0 2 2 0 2 22 0 22 0 21 0 * 0 0 2 2 4 sin 1 sin 1 (1 ( ) ( ) ( )) lim 2( , *, ) 2 ( 1) f f k di                                               (13) the equation * 0( , *) lim ( )    , according to the procedure given by neuber [1,3], results in the following equation with di10) and di20) according to eqs. (10-11):  f. berto, frattura ed integrità strutturale, 41 (2017) 464-474; doi: 10.3221/igf-esis.41.58 469           0 0 11 1 1 0 1 1 0 1 12 0 11 0 11 0 1 1 12 2 2 0 2 2 0 2 22 0 22 0 21 0 2 2 1( , *, ) 2( , *, ) 4 cos 1 cos 1 (1 ( ) ( ) ( )) 2 (1 ) 4 sin 1 sin 1 (1 ( ) ( ) ( )) 2 ( 1) f f di di k k                                                                                   (14) solving eq. (14), with k1=k1 and k2=k2, it is possible to determine the fictitious radius f and therefrom the support factor s by using the following expression derived from eq. (1): * fρ s     (15) the factor s under mixed mode loading results as a function of the mode 1 and mode 2 stress intensity factors and of the crack propagation angle 0. eq. (14) can be solved in general terms for any ratio k2/k1 of the notch stress intensity factors, the crack propagation angle 0 being dependent on this ratio. the mode ratio is defined as follows based on the ratio  of the notch stress intensity factors k2 and k1: 2 arctanm    (16) 2 2 1 1 f k k        (17) pure mode 1 loading results in m = 0 and pure mode 2 loading in m = 1. the dimension of the notch stress intensity factors being dependent on the relevant eigenvalues 2 or 1, which are not identical in general, a length parameter ℓf is introduced in eq. (17) with the condition ℓf=1. in the case of pointed notches,  = 0, eq. (14) can be applied by replacing kby k1 and k by k2 while 0 remains the angle of crack propagation. pointed notches are relevant in worst case considerations of strength assessments. the following expression is valid for , updating eq. (17): 2 2 1 1 f k k     (18) the simplified hypothesis, k1=k1and  which has been inherently assumed for the analytical calculations, avoids an iterative procedure for the determination of s and then of f. this is the hypothesis implicitly used by neuber without the explicit introduction of the stress intensity factors [1], but is approximately true only when the fictitiously enlarged notch root radius is sufficiently small. in the reality, for large f, k1 and k2 do not match k1 and k2 [20,34]. evaluation of the support factor under mixed mode loading conditions y considering eq. (14) and solving it for different values of the mode ratio m, it is possible to obtain the support factor s as a function of the mode ratio m. to evaluate the values of s, the condition ≈ 0 approximating pointed notches has been used. this choice was made for two specific reasons. the first reason is that pointed notches are the most critical ones in strength assessments. in many practical cases, the real notch radius is not equal to zero, but it is very small and it can be approximated in the safe direction by the worst case condition  = 0. the second reason is that by considering pointed notches, it is possible to define the mode ratio m uniquely. the mode ratio m is evaluated here by using k = k1 and k = k2. eq. (8) has been employed here to determine the crack propagation angle 0 by applying the mts criterion to pointed v-notches . due to the fact that eq. (14) has been expressed in terms of the real notch radius this radius has to remain finite. b f. berto, frattura ed integrità strutturale, 41 (2017) 464-474; doi: 10.3221/igf-esis.41.58 470 in this contribution, = 0.001 mm has been introduced in order to model quasi-pointed v-notches. the values of s have been evaluated by solving eq. (14) numerically for different values of the mode ratio m and keeping constant *=0.1 mm together with =0.001 mm. the data are plotted in fig. 2. the support factor s rises with the mode ratio m varying from m = 0 (pure mode 1) to m = 1 (pure mode 2). whereas the rise is rather weak for the keyhole (2 = 0), it is rather strong for larger notch opening angles (2 = 60°). it has to be noted that large values of s mean large fictitious notch radii f, i.e. uncritical strength conditions. figure 2: support factor s as a function of the mode ratio m for different values of the notch opening angle 2 validation of the proposed fnr approach for mixed mode loading conditions he fnr approach applied to in-plane mixed mode loading is validated by comparisons based on the fe method considering inclined v-notches with end holes (notch radius f=s*) characterized by different notch opening angles 2. geometry and dimensions of the double-v-notched plate are shown in fig. 3 together with the applied remote boundary conditions. the values of the notch stress intensity factors k1 and k2 found by fe analysis for the corresponding pointed v-notches (=0) are presented in tab. 1 for different notch opening angles 2 and notch inclination angles . tab. 2 also summarises the mode ratio m, the crack propagation angle 0 and the support factor s determined by solving eq. (14) for the specific parameters. the following parameters are considered in the numerical investigation by fe analysis: – the notch opening angle 2= 0, 30, 45 and 60°, – the notch inclination angle = 15, 30, 45 and 60° corresponding to a value of m varying between 0.16 and 0.73, – the microstructural support length * varying between 0.05 and 0.3 mm, – the notch depth 2a = 10 2 mm combined with the plate width w = 100 mm. the averaged stress has been obtained by numerical integration over the length * of the hoop stress component (th=) along the direction 0 evaluated by using eq. (8).   * 0 0 1 σ σ , dr ρ * th r    (19) the stress concentration factor characterising the averaged notch stress over * in pointed v-notches is defined in eq. (20) with reference to the nominal stress n. * 0 1 k σ dr ρ* t th n n       (20) 0 5 10 15 20 25 30 35 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 mode ratio, m s u p p o rt f ac to r, s 2α = 60° 2α = 45° 2α = 30° 2α = 0° t f. berto, frattura ed integrità strutturale, 41 (2017) 464-474; doi: 10.3221/igf-esis.41.58 471 the stress concentration factor kt(f) of the fictitiously rounded notch is defined as follows:   max ( *, )kt f n s     (21) the relative deviation can be defined as follows:     t f t t f δ k k k     (22) figure 3: geometry and dimensions of the double-v-notched quadratic plate specimen considered in the fe analyses; remote loading by prescribed nominal stress n; dimensions w = 100 mm and 2a = 14.14 mm; real pointed versus fictitiously rounded (root hole) vnotch 2 (°)  (°) k1 (mpa mm1-1) k2 (mpa mm1-2) 1 2 0 (°)  m s 45 15 472 128 0.550 0.660 –13.49 0.272 0.169 2.56 30 376 222 0.550 0.660 –25.73 0.592 0.340 3.16 45 244 257 0.550 0.660 –36.52 1.053 0.516 4.24 60 112 223 0.550 0.660 –46.70 1.993 0.704 6.08 table 1: notch stress intensity factors k1 and k2 and crack propagation angle0 for different mode ratios m resulting in support factors s. comparison with fe results he maximum stress max(*,s) has been determined in this section directly by means of finite element analyses modeling the plate shown in fig. 3 with f=s*, while  values are those evaluated analytically. the finite element analyses (fea) were carried out by using ansys (release 13.0). in total 2000 models have been analysed, each model t f 2a w w n  f. berto, frattura ed integrità strutturale, 41 (2017) 464-474; doi: 10.3221/igf-esis.41.58 472 characterized by the specific values of 2 and f. the results from some models exhibiting relative deviations less than or equal to 10% are listed in tab. 3 as example. the errors are due not only to the adopted simplified hypothesis, k1=k1 and k2=k2, but also to the fact that the maximum stress component max takes place outside the notch bisector, creating an additional stress concentration effect linked to the nominal stress component parallel to the notch inclination angle  (see table 2). finally it is worth mentioning that another consistent approach for mixed-mode loading is based on the strain energy density (sed) averaged on a defined control volume [35]. this approach has been successfully used to assess the static behaviour of notched plates made of brittle material as well as the high-cycle fatigue strength of welded joints. in the presence of pointed notches subjected to mixed mode 1–2 loading conditions, the control volume (a semicircular sector under plane strain or plane stress conditions) is introduced as constant, at first for mode 1 loading conditions. in the case of blunt uor v-notches, the crescent shape control volume is rigidly rotated with respect to the notch bisector line and centred in the point of maximum tangential stress (or maximum strain energy density) on the notch edge resulting in an ‘equivalent’ mode 1 loading condition. one of the main advantages of the average sed approach is that it can be applied using coarse meshes. 2α (°) β (°)  m 0 (°) s ρ* (mm) ρf (mm) tk eq.(28) kt(ρf) fem δ (%) 45 15 0.272 0.169 –13.50 2.56 0.05 0.128 16.90 16.93 0.17 0.1 0.256 12.06 12.57 4.07 0.2 0.511 8.61 9.24 6.86 0.3 0.767 7.07 7.81 9.47 30 0.592 0.340 –25.73 3.16 0.05 0.158 14.62 14.73 0.75 0.1 0.316 10.58 10.92 3.11 0.2 0.631 7.67 8.18 6.28 0.3 0.947 6.36 6.97 8.79 45 1.053 0.516 –36.52 4.24 0.05 0.212 11.08 11.19 0.99 0.1 0.424 8.18 8.56 4.48 0.2 0.848 6.05 6.65 9.03 table 2: fnr results for mixed mode loading conditions; normal stress failure criterion combined with the mts criterion for0; different values of the microstructural support length * and the mode ratio m; conclusions ased on fnr concept used in combination with the normal stress criterion for the averaged notch stress and the maximum tangential stress criterion for the crack propagation angle, the support factor has been analytically and numerically determined for v-notches with root hole subjected to in-plane mixed mode loading. a suitable definition and quantification of the mode ratio for pointed v-notches has been found. taking advantage of a recently conceived analytical frame for v-notches with root hole, the original neuber procedure for determining the fictitious notch radius and the support factor has been applied to out-of-bisector crack propagation, the propagation direction being determined by the maximum tangential stress criterion as a function of the mode ratio and the notch opening angle. different values of this length, of the notch depth and of the notch opening angle have been considered as well as different mode ratios. the obtained values of the support factor are well suited for engineering usage in structural strength assessments. the relative deviations have been found variable from case to case. a large set of cases have been found to be characterized by relative deviations less than 10%, directly using the original neuber’s procedure. references [1] neuber, h., kerbspannungslehre, 2nd ed. berlin: springer-verlag; (1958). b f. berto, frattura ed integrità strutturale, 41 (2017) 464-474; doi: 10.3221/igf-esis.41.58 473 [2] neuber, h., űber die berücksichtigung der spannungskonzentration bei festigkeitsberechnungen. konstruktion, 20 (1968) 245-251. [3] neuber, h., kerbspannungslehre, 3rd ed. berlin: springer-verlag; (1985). [4] filippi, s., lazzarin, p., tovo, r., developments of some explicit formulas useful to describe elastic stress fields ahead of notches in plates. int j solids struct, 39 (2002) 4543-4565. [5] berto, f., lazzarin, p., radaj, d., fictitious notch rounding concept applied to sharp v-notches: evaluation of the microstructural support factor for different failure hypotheses. part i: basic stress equations. eng fract mech, 75 (2008) 3060-3072. [6] berto, f., lazzarin, p., radaj, r., fictitious notch rounding concept applied to sharp v-notches: evaluation of the microstructural support factor for different failure hypotheses. part ii: microstructural support analysis. eng fract mech, 76 (2009) 1151-1175. [7] wieghardt, k., über das spalten und zerreiβen elastischer körper. z. mathematik u. physik 1907; 55: 60-103; translated in english by h.p. rossmanith, fatigue fract engng mater struct, 18 (1995) 1371-1405. [8] weiss, v., eine bruchmechanik fűr kerben. schweiz arch angew wiss techn, 37 (1971) 1-7. [9] neuber, h., zur theorie der technischen formzahl. forsch ing wes, 7 (1936) 271-274. [10] peterson, r.e., relation between stress analysis and fatigue of metals. proc. sesa, 11 (1950) 199-206. [11] atzori, b., lazzarin, p., tovo, r., evaluation of the fatigue strength of a deep drawing steel. österr ing arch z, 137 (1992) 556-561. [12] lazzarin, p., tovo, r., meneghetti, g., fatigue crack initiation and propagation phases near notches in metals with low notch sensitivity. int j fatigue, 19 (1997) 647-657. [13] el haddad, m.h., topper, t.h., smith, k.n., prediction of non-propagating cracks. eng fract mech, 11 (1979) 573584. [14] radaj, d., näherungsweise berechnung der formzahl von schweiβnähten. schw schn, 21 (1969) 97-105, 151-158. [15] radaj, d., design and analysis of fatigue resistant welded structures, cambridge: abington publishing; (1990). [16] radaj, d., ermüdungsfestigkeit, 2nd ed. berlin: springer verlag; (2003). [17] radaj, d., sonsino, c.m., fricke, w., fatigue assessment of welded joints by local approaches, 2nd ed. cambridge: woodhead publishing; boca raton, fl: crc press; (2006). [18] hobbacher, a., (ed.) fatigue design of welded joints and components. abington publishing, cambridge, uk, (1996) (iiw doc. xiii-1539/xv-845-96) and update 2008 (iiw doc. xiii-2151-07/xv-1254-07). weld res coun, new york, bull 520, (2009). [19] berto, f., zappalorto, m., fictitious notch rounding concept applied to v-notches with endholes under mode 1 loading. int j fract, 171 (2011) 91–98. [20] berto, f., zappalorto, m., the fictitious notch rounding approach applied to v-notches with root holes subjected to mode 1 loading. j strain anal, 47 (2012) 176–186. [21] zappalorto, m., lazzarin, p., in-plane and out-of-plane stress field solutions for v-notches with end holes. int j fract, 168 (2011) 167-180. [22] berto, f., fictitious notch rounding concept applied to v-notches with end holes under mode 3 loading. int j fatigue, 38 (2012) 188–193. [23] radaj, d., zhang, s., on the relations between notch stress and crack stress intensity in plane shear and mixed mode loading. eng fract mech, 44 (1993) 691-704. [24] berto, f., lazzarin, p., fictitious notch rounding approach of pointed v-notch under in-plane shear. theor appl fract mech, 53 (2010) 127-135. [25] erdogan, f., sih, c.g., on the crack extension in plates under plane loading and transverse shear. j basic eng, 85 (1963) 519-525. [26] sih, g.c., strain-energy-density factor applied to mixed mode crack problems. int j fract, 10 (1974) 305-321. [27] berto, f., lazzarin, p., radaj, d., fictitious notch rounding concept applied to v-notches with root holes subjected to in-plane shear loading. engng fract mech, 79 (2012) 281-294. [28] radaj, d., lazzarin, p., berto, f., generalised neuber concept of fictitious notch rounding. int j fatigue, 51 (2013) 105-115. [29] radaj, d., vormwald, m., advanced methods of fatigue assessment. berlin: springer-verlag (2013). [30] williams, m.l., stress singularities resulting from various boundary conditions in angular corners on plates in tension. j appl mech, 19 (1952) 526-528. [31] gross, r., mendelson, a., plane elastostatic analysis of v-notched plates. int j fract mech, 8 (1972) 267-276. f. berto, frattura ed integrità strutturale, 41 (2017) 464-474; doi: 10.3221/igf-esis.41.58 474 [32] lazzarin, p., tovo, r., a unified approach to the evaluation of linear elastic fields in the neighbourhood of cracks and notches. int j fract, 78 (1996) 3-19. [33] lazzarin, p., filippi, s., a generalized stress intensity factor to be applied to rounded v-shaped notches. int j solids struct, 43 (2006) 2461–2478. [34] lazzarin, p., zappalorto, m., berto, f., generalised stress intensity factors for rounded notches in plates under inplane shear loading. int j fract, 170 (2011) 123-144. [35] berto, f., lazzarin, p., recent developments in brittle and quasi-brittle failure assessment of engineering materials by means of local approaches. mater sci eng r, 75 (2014) 1-49. << /ascii85encodepages false /allowtransparency false /autopositionepsfiles true /autorotatepages /none /binding /left /calgrayprofile (dot gain 20%) /calrgbprofile (srgb iec61966-2.1) /calcmykprofile (u.s. web coated \050swop\051 v2) /srgbprofile (srgb iec61966-2.1) /cannotembedfontpolicy /error /compatibilitylevel 1.4 /compressobjects /tags /compresspages true /convertimagestoindexed true /passthroughjpegimages true /createjobticket false /defaultrenderingintent /default /detectblends true /detectcurves 0.0000 /colorconversionstrategy /cmyk /dothumbnails false /embedallfonts true /embedopentype false /parseiccprofilesincomments true /embedjoboptions true /dscreportinglevel 0 /emitdscwarnings false /endpage -1 /imagememory 1048576 /lockdistillerparams false /maxsubsetpct 100 /optimize true /opm 1 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can be opened with acrobat and adobe reader 5.0 and later.) >> /namespace [ (adobe) (common) (1.0) ] /othernamespaces [ << /asreaderspreads false /cropimagestoframes true /errorcontrol /warnandcontinue /flattenerignorespreadoverrides false /includeguidesgrids false /includenonprinting false /includeslug false /namespace [ (adobe) (indesign) (4.0) ] /omitplacedbitmaps false /omitplacedeps false /omitplacedpdf false /simulateoverprint /legacy >> << /addbleedmarks false /addcolorbars false /addcropmarks false /addpageinfo false /addregmarks false /convertcolors /converttocmyk /destinationprofilename () /destinationprofileselector /documentcmyk /downsample16bitimages true /flattenerpreset << /presetselector /mediumresolution >> /formelements false /generatestructure false /includebookmarks false /includehyperlinks false /includeinteractive false /includelayers false /includeprofiles false /multimediahandling /useobjectsettings /namespace [ (adobe) (creativesuite) (2.0) ] /pdfxoutputintentprofileselector /documentcmyk /preserveediting true /untaggedcmykhandling /leaveuntagged /untaggedrgbhandling /usedocumentprofile /usedocumentbleed false >> ] >> setdistillerparams << /hwresolution [2400 2400] /pagesize [612.000 792.000] >> setpagedevice shot peening processes to obtain nanocrystalline surfaces in metal alloys: v. barath et alii, frattura ed integrità strutturale, 57 (2021) 14-23; doi: 10.3221/igf-esis.57.02 14 fractographic characterization of al2o3p particulates reinforced al2014 alloy composites subjected to tensile loading v. bharath, v. auradi dept. of mechanical engineering, siddaganga institute of technology, tumkur, karnataka, india bharathv88@gmail.com, http://orcid.org/0000-0001-6765-4728 vsauradi@gmail.com, http://orcid.org/0000-0001-6549-6340 m. nagaral aircraft research and design centre, hindustan aeronautics limited, bangalore, karnataka, india madev.nagaral@gmail.com, http://orcid.org/0000-0002-8248-7603 abstract. in the current investigation, efforts are being made to produce an al2014-al2o3p composite with an average particle size of 88 m by liquid stir casting route. 9, 12 and 15 weight proportions of al2o3p were added to the al2014 base alloy. by using sem and eds testing, microstructural studies have been conducted. al2014-9, 12 and 15 weight proportion of al2o3p composites mechanical behavior is determined in line with astm standards. electron microscopic images showed that alumina (al2o3p) particles are dispersed uniformly within the al2014 composite matrix. eds study confirmed the proximity of al and o elements to composites reinforced by al2o3p. it is also found that al2014-al2o3p composite hardness, uts, and yield strength are improved by the addition of 9, 12 and 15 weight proportion of al2o3p. due to the addition of alumina particles in the al2014 matrix alloy, the ductility of the produced composites decreases. tensile fractography is performed using sem to consider the mechanisms for failure. keywords. al2014 alloy; al2o3p; mechanical behavior; fractography citation: bharath, v., auradi, v., nagaral, m., characterization and tensile fractography of 88 micron sized al2o3p particulates reinforced al2014 alloy composites, frattura ed integrità strutturale, 57 (2021) 14-23. received: 09.01.2021 accepted: 24.04.2021 published: 01.07.2021 copyright: © 2021 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. introduction etal–matrix composites (mmcs) attract attention for applications like packing, substrates and support structure for electronic equipment and a variety of automotive components because of their comprehensive features such as low density, high rigidity, low thermal expansion coefficient, high thermal conductivity, high strength m mailto:bharathv88@gmail.com http://www.orcid.org/0000-0001-6549-6340 mailto:madev.nagaral@gmail.com http://orcid.org/0000-0002-8248-7603 https://youtu.be/3-y-fkwla8q v. barath et alii, frattura ed integrità strutturale, 57 (2021) 14-23; doi: 10.3221/igf-esis.57.02 15 and high use resistance [1–4]. the processing of alumina reinforced aluminium composite by casting process is particularly complex. the main reason is poor wettability of the alumina particles and agglomeration mechanism and this may likely to result in a poor mechanical strength and non-homogeneous dispersion. for the vast majority of the applications, consistent particle dispersion is fundamental to enhance the mechanical and wear properties. stir casting (liquid metallurgy) has a number of significant points of interest. some of them are as follows; (i) good bonding between the matrix and reinforcement (ii) easy to control the structure of the matrix (iii) ease of handling (iv) highly economic (v) closer net shape and the wide selection of materials and (vi) suitable for the production of composites reinforced with higher volume fraction of the particulates [3, 5, 6, 7]. liquid state fabrication of mmc does comprise of two methods which rely upon the temperature at which the particles are brought into the melt. in melt stirring process, once the liquidus temperature of molten metal is accomplished the particles are infused into the melt, whereas in compo-casting strategy once the temperature of the base alloy reaches to semi solid state the particles are infused into it. in stir casting and compo-casting procedures, vortex produced is utilized for infuse the strengthening (reinforcing) particles. nonetheless, the procedure of melting has two-vital problems, the most part of the ceramic particles are not wetted with the liquid matrix material and besides the particles will in general float or sink as per their comparative (relative) density with the liquid metal. capacity of the melt to spread on a strong surface can be characterized as wettability. wettability also refers the degree of close contact between the solid-liquid phases [8]. if the ceramic particles are poorly dispersed, it might increases the porosity and reduces the composite mechanical properties. this signifies a big challenge to create metal matrix composites. low wettability implies the liquid matrix will not wet the surface of the strengthening particles subsequently they essentially drift on a superficial level attributable to surface tension, enormous surface space, maximum free energy of the surfaces at an interface and nearness of the oxide layer on the surface of the liquid metal. enhancement in the wettability somewhat can be accomplished by many techniques such as mechanical stirring, heating up of the particles to expel the adsorbed gases from the surface of the particles [3], the increasing of alloying elements, utilization of the surface coating on the strengthening particles, and so on [9]. one more issue is the distribution (here afterwards distribution is referred as dissemination) of the strengthened particles in liquid matrix. because of the density dissimilarity among the reinforcement and matrix, these particles in general drift or fix in the liquid matrix thus particles clustering/agglomeration take place [3]. it has been accounted for that infusion of particles with inert gas is useful in enhancing the dispersion [3]. m kok [10] in his investigation on aa2024-alumina composites with three different sizes of the particles and weight percentages have seen by using electron microscopy the dissemination of the larger sizes of alumina particles are uniformly distributed while small (finer) particles resulting to the porosity and particles agglomeration. hence, it is crucial to build up a strategy for creating aluminium metal matrix composites for the introduction and dispersion of strengthening particles in the liquid matrix and to accomplish a decent uniform dissemination of the particles in the matrix and the processing parameters relevant to the stir casting must be examined. keeping the above perceptions in mind the present work is taken up to synthesize and characterize al2014-alumina mmcs by varying weight percentages of the alumina particles by choosing optimized processing parameters such as stirring speed (250 rpm), stirring time (10 min) and preheating of reinforcing particles (250°c), pouring temperature 680°c and 2-stage addition of reinforcing particles by stir casting technique. nearly, the similar values of process parameters have been noticed in some previous studies [11-15]. typically, alumina particles tended to sink at a maximum pouring temperature, while at reduction in pouring temperature and speed of stirring, the higher rate of the addition of the particles into the molten metal leads to the agglomeration at the molten metal surface. meanwhile, increasing the speed of stirring few particles were expelled at the outer periphery (external end) of the molten metal of the crucible due to the impeller wind and hence, incorporation of the particle is difficult to accomplish. if the temperature of the mold is reduced, the composite mixture solidified quickly and it is then difficult to transfer into the mold and also the required pressure could not be applied. this results in increased porosity of the produced composites. suppose, if the mold temperature increased, alumina particles sunk to the bottom of the mold due to the low solidification rate and higher density of the alumina hence uniform dispersion of the particles is difficult to accomplish. therefore, the uniform distribution of alumina particles is only achieved under the optimum process conditions which are discussed above. the present study mainly deals with the preparation, characterization and evaluation of mechanical and fractographic properties of al2014 alloy reinforced with different weight percentages (0, 9, 12, and 15) of alumina particles by using above mentioned optimized process parameters. the above selected optimized parameters led to the improved wettability and distributions of the alumina particles in the aluminium melt thereby, it helps to improve the mechanical properties of the produced composites after the addition of alumina particles with increase in weight percentage of reinforcing alumina particles. v. barath et alii, frattura ed integrità strutturale, 57 (2021) 14-23; doi: 10.3221/igf-esis.57.02 16 experimental details he composites al2014-al2o3p, containing 9, 12 and 15 wt. % of al2o3p particulates, are synthesized in this research. the density of al2014 is 2.8 g/cm3 and that of al2o3p is 3.8 g/cm3 [16]. the density of composites decreases with the addition of al2o3p. the chemical composition, of al2014 and properties al2014 and al2o3p are shown in tab. 1 and tab. 2 respectively. for the present experiment, al2o3p with an average size of 88 μm are used (supplied by fenfee metallurgical pvt. ltd bangalore, karnataka, india). elements (wt. %) si fe cu mn mg cr zn ti others al al 2014 alloy 0.68 0.19 4.48 0.82 0.62 0.02 0.18 0.05 0.04 bal. table1: the chemical composition of al2014 alloy. table 2: properties of al2014 alloy and al2o3p [16]. al2014 alloy is charged into the heating furnace in order to liquidate the pre-calculated volume of al2014 alloy. normally, al2014 alloy melts at 630˚c; the melting furnace is superheated to 680˚c. for temperature measurements thermocouples are used. the molten metal in the crucible is then degassed upto 2 minutes with the help of a hexa-chloro-ethane (c2cl6) to extract the undesirable by-products. a ceramic material known as zirconia is coated (to avoid iron contamination) on the steel impeller used to stir the molten metal to form a vortex. the stirring process is conducted at a speed of 250 rpm and from the top of the melt; the impeller is plunged inside the melt of around sixty percent height of the molten metal. at the same time, the pre-calculated reinforcement quantity has been added into the vortex in two-stages to ensure a strong wet-ability agitation has been continued for up to ten minutes. the al2o3p reinforcing particles are pre-heated in the oven to 250°c, before being applied to the vortex of molten metal to extract the moisture content. now, al2014 alloy has been transferred into the solid cast iron mold along with 9 wt. % of al2o3p particles to get a composite after complete solidification. likewise, al2014-12 and 15 wt. % al2o3p composites are created for further experiments. using the sem instrument, the microstructural analysis is completed. casting samples were examined and properly cleaned and etched by using keller’s reagent. according to astm e92-17, micro-hardness tests are performed on the composite produced at fifteen various places with the similar specimen using micro-vickers hardness tester (zwick/roell-indent tester) with a load of hv 0.3 and a dwelling period 15 sec and an average of fifteen readings are considered. according to the astm e8 benchmark the tensile tests are carried out and for the tensile test the dimensions of the samples having a 9 mm gauge diameter and with a 45 mm gauge length. results and discussion characterization of the synthesized composites ig. 1 (a-d) depicts the microstructures of as-cast al2014 and al2014 with 9 weight percentage (fig.1 b), 12 weight percentages (fig.1 c) and 15 weight percentage (fig.1 d) of alumina particles. the composite microstructure includes eutectic silicon and primary -al dendrites and, whereas particles of alumina are isolated between eutectic silicon and territories of the dendrites. the stirring of the melt at 250 rpm when adding preheated alumina particles in two phases have leads to the breakdown of the dendrite-shape into an equiaxed structure, thus improving the wettability and incorporation of particles of alumina in the liquefy and as well as it leads to dissemination (dispersion) of the alumina particles more consistently in the matrix. fig. 1 (b-d) represents the dissemination of alumina particles in the produced composites at different weight percentage. additionally the electron microphotographs demonstrate the alumina particles continue to isolate (segregate) and grouped (cluster) enriched by eutectic silicon in inter-dendritic areas at very few places as the weight percentages of alumina increases and this is mainly because of the choice of optimized processing t properties density (g/cm3) hardness (hb500) uts (mpa) elastic modulus (gpa) al2014 2.8 135 483 70-80 al2o3p 3.8 1175 665 300 f v. barath et alii, frattura ed integrità strutturale, 57 (2021) 14-23; doi: 10.3221/igf-esis.57.02 17 parameters during stir casting. further, the electron microphotographs shows that the strengthened composite grain size (fig.1 b-d) is smaller contrasted to the base alloy without alumina particles (fig. 1 a) due to the introduction of the alumina particles into liquefy often serve as sites of heterogeneous nucleation throughout the solidification. eds analysis is carried out on as-cast al2014, al2014-9 and 15 wt. % of alumina reinforced specimens with a particle size of 88 µm which is demonstrated in fig. 2 (a-c). the energy dispersive spectrograph for al2014 as-cast (fig. 2 a) which contains major alloying elements like cu, mg, si, ti, mn, fe and zn and fig. 2 (b) al2014-9 wt. % of alumina composite clearly showed the presence of o, mg, si, fe, cu, ti, mn peaks in al matrix and fig. 2 (c) depicts the elemental analysis of al2014-15 wt. % of al2o3p composite which confirm the elements like o, mg, si, cu, ti and mn in al alloy matrix composite. dispersion of alumina in al2014 is confirmed by the existence of oxygen (o) peaks in fig. 2 (b-c). figure 1: sem images of al2014-alumina (a) as-cast al2014 alloy (b) al2014-9 wt. % al2o3p (c) al2014-12 wt. % al2o3p and (d) al2014-15 wt. % al2o3p. (a) v. barath et alii, frattura ed integrità strutturale, 57 (2021) 14-23; doi: 10.3221/igf-esis.57.02 18 figure 2: eds spectrum of al2014-alumina (a) as-cast al2014 (b) al2014-9 wt. % al2o3p and (c) al2014-15 wt. % al2o3p composites. hardness measurements in the present work, micro-hardness is examined on base alloy (al2014) and al2014 reinforced alumina particles with different weight percentages (0, 9, 12, and 15). for each composite sample three specimens are produced and average values (w.r.t standard deviation) are graphically shown in fig. 3. fig. 3 depicts the almost continuous increment in microhardness of the produced composite (al2014-9, 12 and 15 wt. % al2o3p) with increase in the weight percentage of alumina. the extent of improvement in the hardness of the produced composites is about 5.50, 13.17 and 19.20 percentages respectively as contrasted to al2014 alloy. enhancement in the matrix hardness is mainly because of existence of alumina [17, 18]. basically strengthening (reinforcing) particles are stronger and more rigid than the matrix and these strengthening particles always try to avoid the plastic deformation of the matrix throughout the testing [17, 19-20]. but avoiding the plastic deformation of the matrix relies on the dissemination of the alumina particulates throughout the matrix. if the dissemination of the particles is clustered in a specific area and absence in small places might leads to the remarkable change in the hardness value at various locations in the composite samples. among the above produced composite with different weight proportions, the composite (c) (b) v. barath et alii, frattura ed integrità strutturale, 57 (2021) 14-23; doi: 10.3221/igf-esis.57.02 19 reinforced with al2014-15 weight percentage of alumina particulate results in maximum hardness as compared to the ascast al2014 and composites produced with 9 and 12 weight percentage of alumina particulate composites. in addition, no major cracks are found across the indentation, the pyramidal indentations are not damaged and despite the difference in hardness between hard reinforcing phase and soft matrix (fig. 3). this suggests that the al2o3p are strongly formed a bond to the al matrix, that can play a key role in improving the composites mechanical properties. figure 3: micro-hardness values of al2014 and al2014 reinforced with alumina particles with different compositions evaluation of ultimate tensile strength (uts), yield strength (ys) and percentage elongation of synthesized composites for the evaluation of tensile behaviors each composite sample three trials are conducted and average values (w.r.t standard deviation) are graphically shown in fig. 4 (a-c). fig. 4 (a-b) depicts the almost continuous increment in the uts and ys of the produced composite with increase in the weight percentage of alumina. the extent of improvement in the uts and ys of the produced composites is about 12.46, 16.29 and 29.59 percentages and 5.45, 12.46 and 29.54 percentages respectively as contrasted to al2014 alloy. tab. 4 and fig. 4 (a) clearly reveals that improvements in uts are obtained in al2014 matrix after reinforcing with hard ceramic alumina particles. figure 4: (a-b) uts and ys values of al2014 and al2014 reinforced with alumina particles with different compositions (a) (b) v. barath et alii, frattura ed integrità strutturale, 57 (2021) 14-23; doi: 10.3221/igf-esis.57.02 20 figure 5: (a-d) stress-strain curves for al2014 and al2014 reinforced with alumina particles with different compositions. this enhancement is observed because of increasing the addition level of alumina particulates in the base alloy/ matrix (al2014). base alloy (matrix) strength is increased due to the incorporation of reinforcing particulates leading to higher resistance to the tensile stress and increases the overall tensile strength [21]. furthermore, since the alumina particles are stiffer than the al matrix, the alumina particles initially carry a large amount of stress. furthermore, due to geometric restrictions imposed by the presence of reinforcement, the inclusion of alumina particles in the matrix alloy contributes to an improvement in the work hardening of the composite. this increases the tensile strength of the composite [22] by the load necessary for void nucleation and its propagation is more. as several studies [23, 24] reported that the particle size of the reinforced phase is extremely low, so the chances of having strength limiting faults or failures in the composite is anticipated to be lower, contributing to an improvement in the uts. also, it is obvious that the existence of alumina particles substantially increases the yield strength. this may have been attributed to the following factors (i) good interface strength among alumina reinforcement and al2014 alloy as confirmed by electron microscopic images (i.e., fig. 1 b-d). the possible reason for this because of the lower pores in the interface, which contributes considerably less failures to serve as the initiating positions of a crack (ii) the presence of hard ceramic particles, a dislocation deficiency occurs, leading to pile up of dislocations as a result a back stress is generated [3], since, the plastic deformation of the matrix resisting elastically deformed particles, back stress arises [25] (iv) in addition to the trapping of dislocation of second phase alumina particle matrix during deformations, thermal mismatch between al matrix (23×10-6/°c) and ceramic al2o3p (8.2×10-6/°c) contributes to increased dislocation density [26]. fig. 5(a-d) shows the stress-strain relationship of the as cast al2014 alloy matrix and the produced composites with different weight fractions. as increase in weight fraction of al2o3p the fracture strain decreased and also the ductility of the produced composites was also decreased slowly due to the presence of alumina reinforcing particles which oppose the plastic flow of the matrix material. (a) (c) (d) (b) v. barath et alii, frattura ed integrità strutturale, 57 (2021) 14-23; doi: 10.3221/igf-esis.57.02 21 fig. 6 depicts the almost continuous decrements in the percentage elongation of the produced composite by increasing the weight percentage of alumina when contrasted with the cast al2014 matrix alloy. the decrease in ductility is because of the following reasons (i) void nucleation by increasing addition level of reinforcement. the specific explanation for this difference may be that alumina particle behaves like a stress concentrator ii) the solid interfacial strength with reinforcement and matrix is extremely high, leading to greater reinforcement load, thus fracturing at lower strains [27]. chandrasekhar and co-authors [28] have examined the tensile performance of al-al2o3p composite and decline in the ductility is noticed with addition of hard reinforcement. figure 6: percentage elongation values of al2014 and al2014 reinforced with alumina particles with different compositions fractography to find the cause of failure of the materials produced, a study on the broken surface of the alloys and their composites is essential. during study of fractography, there are two important points to recall: a ductile material when it fails to produce small dimples, such as structure, in broken areas, while transgranular (grain fractures) or intergranular (grain boundary fractures), fragmentations may be found in sem images taken out of a failed material, in case of fractured fractures. fig. 7 (a-d) illustrates the fractured surfaces of both as-cast al2014 alloy and al2014-9, 12 and 15 wt. % alumina particles. the base matrix displayed fine shallow and uniform dimples suggesting a ductile fracture, as is evident from fig 7a, while the composite showed a two-way dimple distribution i.e., the reinforcing particles were taken up by the bigger dimples, while the ductile breakdown of the matrix induced smaller dimples. in addition, the sem of the broken composite surface (fig. 7b and fig. 7d) showed hairline cracks on al2o3p, partial decohesion among matrix and reinforcement and also matrix fracture. in most cases, particles were smooth in fracture surfaces suggesting that the particles are broken and not de-cohered and that these composites are dominated by their high interface strengths. the fracture surfaces in al2014 matrix were divided between big dimples and while relatively smaller dimples were seen in composite reinforced with 12 and 15 wt % al2o3p (fig. 7 c-d), indicating the mechanism for failure resulting from ductile void growth, coalescence and failure. finally, the result is that the fracture behaviour of the al2014 matrix changed from the ductile to the fragile modes and then to intermediate ductile mode because of the incorporation of al2o3p. small dimples are seen with the matrix and hairline crack in the al2o3p particles. conclusions n the current work al2014-al2o3p composites were successfully synthesized with 9, 12 and 15 wt. % of al2o3p with an average particle size of 88 µm by the utilization of stir casting technology. astm criteria refer to the microstructural study and significant mechanical performance such as hardness, uts and ys, percentage elongation and fractography behaviour. as cast-alloy and equally distributed al2o3p in the prepared composite, the matrix is practically pores-free, as can be seen from sem micrographs. the eds analysis indicates that the al2014 alloy matrix includes al2o3p particles. the mechanical properties of al2014-9, 12 and 15 wt. % al2o3p composite are superior and improved i v. barath et alii, frattura ed integrità strutturale, 57 (2021) 14-23; doi: 10.3221/igf-esis.57.02 22 compared with unreinforced al2014 as-cast material. the fracture surface of the synthesized composite material comprises of tiny voids owing to strain localization. figure 7: (a-d) fractographs of images of (a) al2014 and (b) al2014-9 wt. % al2o3p (c) al2014-12 wt. % al2o3p and (d) al2014-15wt. % al2o3p. references [1] sajjadi, s.a., ezatpour, h.r. and torabi parizi, m. (2012). comparison of microstructure and mechanical properties of a356 aluminum alloy/al2o3p composites fabricated by stir and compo-casting processes. materials and design, 34, pp.106–111. [2] sajjadi, s.a., torabi parizi, m., ezatpour, h. r. and sedghi, a. (2012). fabrication of a356 composite reinforced with micro and nanoal2o3p particles by a developed compocasting method and study of its properties. journal of alloys and compounds, 511, pp. 226–231. [3] sajjadi, s.a., ezatpour, h.r. and beygi, h. (2011). microstructure and mechanical properties of al–al2o3p micro and nanocomposites fabricated by stir casting. materials science and engineering a, 528, pp. 8765–8771. [4] li, g.r., zhao, y.t., wang, h.m., chen, g., dai, q.x. and cheng, x.n. (2008). fabrication and properties of in situ (al3zr + al2o3p)p/a356 composites cast by permanent mould and squeeze casting. journal of alloys and compounds, 471, 04, 037. [5] alksandar, vencl., ilika, bobic., saioa, arostegui., biljana, bobic., aleksandar, marinkovic. and miroslav, babic. (2010). structural, mechanical and tribological properties of a356 aluminium alloy reinforced with al2o3, sic and sic+ graphite particles. journal of alloys compound, 506, pp. 631–639. [6] yung, c.k. and chan, s.l.i. (2004). tensile properties of nanometric al2o3 particulate reinforced aluminium matrix composites. journal of materials chemistry and physics, 85, pp. 438-443. [7] chawla, n. and shen, y.l. (2001). mechanical behavior of particle reinforced metal matrix composites. advanced engineering materials, 3, pp. 357-370. [8] kheder, a.r.i., marahleh, g.s. and al-jamea, d.m.k. (2011). strengthening of aluminum by sic, al2o3 and mgo. jordan journal of mechanical and industrial engineering, issn 1995-6665, pp. 533-541. [9] zhiqiang. y.u. (2005). microstructure and tensile properties of yttria coated-alumina particulates reinforced aluminum matrix composites. journal of material science and technology, vol. 21, no.1. v. barath et alii, frattura ed integrità strutturale, 57 (2021) 14-23; doi: 10.3221/igf-esis.57.02 23 [10] kok, m. (2005). production and mechanical properties of al2o3 particle-reinforced 2024 aluminium alloy composites. journal of materials processing technology, 161, pp. 381–387. [11] hanumanth, g.s. and irons, g.a. (1993). particle incorporation by melt stirring for the production of metal-matrix composites. journal of material science, 28, pp. 2459–2465. [12] seo, y.h. and kang, c.g. (1995).the effect of applied pressure on particle dispersion characteristics and mechanical properties in melt-stirring squeeze-cast sic/al composites. journal of material processing technology, 55, pp. 370– 379. [13] milliere, c. and suery, m. (1998). fabrication and properties of metal matrix composites based on sic fibre reinforced aluminium alloys. material science and technology, 4, pp. 41–51. [14] hung, n.p., boey, f.y.c., khor, k.a., oh, c.a. and lee, h.f. (1995). machinability of cast and powder-formed aluminum alloys reinforced with sic particles. journal of materials processing and technology, 48, pp. 291–297. [15] mclean, a., soda, h., xia, q., pramanick, a.k., ohno, a., motoyasu, g., shimizu, t., gedeon, s.a. and north, t. (1997). sic particulate-reinforced, aluminium-matrix composite rods and wires produced by a new continuous casting route. composites, part a, 28, pp. 153–162. [16] asm handbook. (1990). asm handbook committee, pp 62–122. doi: 10.1361/asmhb a0001 060. [17] bharath, v., nagaral, m., auradi, v. and kori, s, a. (2014). preparation of 6061al–al2o3p mmcs by stir casting and evaluation of mechanical and wear properties. procedia materials science, 6, pp. 1658–1667. [18] mittal, p. and dixit, g. (2016). dry sliding wear behaviour of 2014 aluminium alloy reinforced with sic composite. international journal of engineering research and technology, 5, pp. 147–153. [19] bharath, v., santrust, a., madeva, nagaral., auradi, v. and kori, s.a. (2018). characterization and mechanical properties of 2014 aluminum alloy reinforced with al2o3p composite produced by two-stage stir casting route. journal of the institution of engineers (india): series c, 100, pp. 277–282. [20] bharath, v., madeva, nagaral., auradi, v. and kori, s.a. (2020). experimental investigations on mechanical and wear behaviour of 2014al-al2o3p composites. journal of bio and tribo-corrosion, springer publication, pp. 1-10, doi: 10.1007/s40735-020-00341-2. [21] gupta, m. (1999). interrelationship between cumulative volume fraction of sic particulates and porosity with ductility of al/sic composites. aluminum transactions, 1, 1, pp. 33-39. [22] chawla, n. and shen, y, l. (2001). mechanical behavior of particle reinforced metal matrix composites. advanced engineering materials, 3, pp. 357-370. [23] lewandowski, j.j., liu, d.s. and liu, c. (1991). observations on the effects of particulate size and superposed pressure on deformation of mmcs. scr. metall., 25, pp 21-26. [24] kamat, s.v., hirth, j.p. and meharabian, r. (1989). mechanical properties of particulate-reinforced aluminum-matrix composites. acta metallurgica, 37, pp. 2395-2402. [25] vikram singh, gaharwar. and umashankar, v. (2014). the characterization and behavior of al2014 reinforced with al2o3p by powder metallurgy. material science and engineering a, 6, pp. 3272-3275. [26] modi, o.p. (2014). two-body abrasion of a cast al–cu (2014 al) alloy–al2o3p particle composite: influence of heat treatment and abrasion test parameters. wear. 248, pp. 100 2001. [27] mahon, g.j., jowe, j.m. and vasudevan, a.k. (1990). microstructural development and the effect of interfacial precipitation on the tensile properties of an aluminum/silicon-carbide composite. acta metallurgica et materialia, 38, 1503. doi: 10.1016/0956-7151(90)90118-z. [28] chandrashekar, a., ajaykumar, b.s. and reddappa, h.n. (2018). mechanical, structural and corrosion behavior of almg4.5-nano al2o3p metal matrix composites. materials today proceedings, 5, pp. 2811-2817. https://doi.org/10.1007/s40735-020-00341-2 https://doi.org/10.1016/0956-7151(90)90118-z microsoft word numero 25 art 17 e. maggiolini et alii, frattura ed integrità strutturale, 25 (2013) 117-123; doi: 10.3221/igf-esis.25.17 117 special issue: characterization of crack tip stress field on numerical integration for effective stress assessment at notches enrico maggiolini, paolo livieri university of ferrara (italy) roberto tovo university of ferrara (italy) abstract. this paper presents a numerical method for non-local stress assessment by means of a general fe tool and the local stress field. unlike usual calculations by means of a numerical pde solver, a more general numerical integration is used. different solutions are compared theoretically and numerically by evaluating the results obtained by two different fem commercial software. the application of the non-local tension field is applied to the strength assessment of notches, welded joints and cracks. keywords. implicit gradient; local tension field; notches; welding; fatigue. introduction n real applications, it is usual for an engineer to deal with strength assessment at stress raisers, i.e. notches, welding or cracks. there are several theories and approaches explaining how to tackle such problems, but, sometimes, the proposed approaches are difficult to use. in particular, it is often impossible to apply the “non-local” effective stress values without a particular software tool because many procedures require the integration of a specific partial differential equation to calculate the non-local stress field. the goal of this research is to find a method for the evaluation of the non-local field in a fast and simple way, by using the local stress field available in all fem software. for this purpose, both comsol multiphysics and ansys numerical software were used and compared. comsol has a pre-loaded module for an ordinary differential equation solution (helmholtz equation) that can be used to calculate stress for non-local resistance, and even has an integration procedure for a general user-defined integral evaluation all-over the investigated domain. alternatively, ansys only has the possibility to compute and export the nodal coordinates and nodal results turned out from a conventional local structural analysis. the final aim is to compute a non-local stress field by means of a sound conventional local stress analysis. implicit gradient method he authors recently presented a new way to estimate the fatigue life of notched structures and welded joints based on the implicit gradient [1, 2]. this method is particularly suitable for a numerical estimation of the component fatigue life dependent on their geometry. the idea is very simple and enables application of the average damage originally formulated in the 1930s by neuber [3], referred to as a geometry where fatigue crack propagation is on the bisector of the notch direction. this idea succeeds in attaining the fatigue limit of a plane component with notches by simple manual calculation [3,4]; on the other i t http://www.gruppofrattura.it http://dx.medra.org/10.3221/igf-esis.25.17&auth=true e. maggiolini et alii, frattura ed integrità strutturale, 25 (2013) 117-123; doi: 10.3221/igf-esis.25.17 118 hand, it is difficult and awkward when the maximum stress or the crack initiation and propagation is outside the bisector or generally when the component is three dimensional or geometrically complex. the implicit gradient method reinforces the idea that the damage should be related to the average of the stress components occurring on the body, where the values near to the critical point are more important than the far away field (by a weight function). the computed effective stress is representative of the overall damage in the process zone. the influence zone dimension is simply regulated by material properties and is indicated by the length c. in a uniaxial fatigue case, the authors proposed to only average the first principal stress; for multi-axial fatigue it is necessary to use a multiaxial criterion, for instance, by using stress invariants or critical plane approaches, it is possible to define the ratio ρ between the hydrostatic component and the deviatoric component in the tension field averaging [5]. mathematics of the problem n a body of volume v, it is possible to define a non-local effective tension σeff in a generic point x as an integral average of an equivalent local tension σeq, weighted by a gaussian function ψ (x,y) depending on the distance between points x and y of the body:         eq v eff ,int eq v v ψ x,y σ (y)dv1   ( x ) ψ x,y σ y  dy   vr(x) ψ x,y dv       in v (1) where ψ = 2 2 x y 2 l 2 e 2l   [mm-2] l c 2 [mm] (2) by approximating eq. (1), it is possible to define an effective stress σeff by the helmholtz equation [1, 2, 6] using neuman boundary conditions ( eff n 0   ) [6]. 2 2 eff ,ig eff ,ig eqc     in v (3) here σeq is the first principal stress and c is a material coefficient (for instance, it is 0.2 mm for weldable construction steel). figure 1: 2d geometry with a variable angle, size in mm. analysis by software with a built-in pde solver he initial investigated geometry is a simple 2d geometry (fig. 1), with the under linear elastic plane stress condition and remote tensile stress equal to one. the geometry has a notch-opening angle ranging from 0° to 180° and a notch tip radius varying from 0 to 1 mm, the initially investigated parameter being the null radius. i t http://www.gruppofrattura.it http://dx.medra.org/10.3221/igf-esis.25.17&auth=true e. maggiolini et alii, frattura ed integrità strutturale, 25 (2013) 117-123; doi: 10.3221/igf-esis.25.17 119 comsol has a built-in pde solver, including the helmholtz equation solver. the linear elastic stress solution provides the local stress field. the helmholtz equation (σeff,ig) can be directly solved on the same model. one of the obtained outputs is given in fig. 2. by changing the angle of the notch and plotting the results, it is possible to compare the differences at the tip (fig. 3). except for smaller angles, σeff,ig decreases by improving the opening angle of the notch. alternatively, by considering the integral value, the eq. (1) can also be evaluated by the comsol solver; fig. 3 also shows such type of result (σeff,int). figure 2: example of plot of the σeff,ig figure 3: trend of σeff,ig vs σeff,int 2α σeff,ig σeff,int difference [°] [mpa] [mpa] [%] 0 9.47 7.47 -21.1% 30 9.37 7.58 -19.1% 60 9.74 7.97 -18.2% 90 9.37 7.82 -16.5% 120 7.67 6.64 -13.4% 135 6.26 5.56 -11.1% 150 4.61 4.23 -8.2% 180 1.00 1.00 0.0% table 1: value of σeff,ig and σeff,int at any tested angle. 0 2 4 6 8 10 0 30 60 90 120 150 180 σ / σ n o m 2α [°] σ eff,ig σ eff,int http://www.gruppofrattura.it http://dx.medra.org/10.3221/igf-esis.25.17&auth=true e. maggiolini et alii, frattura ed integrità strutturale, 25 (2013) 117-123; doi: 10.3221/igf-esis.25.17 120 to achieve a sufficient approximation, it is not necessary to compute the integral across the whole domain, but it is faster to only make the integration in a subdomain (a circular subdomain with a radius equal to 5.5c has been verified as suitable). differences between these two estimations can be assumed to be the intrinsic scatter between the two methods so that if the “integral” value is available, the “ig effective” value can be computed by this correction (tab. 1). analysis by software without a built-in pde solver ost fem software does not have the pde solver or integration option; nevertheless, it is possible to have a reasonable approximation by means of the knowledge of nodal coordinates and nodal local stress. one possibility is to transform the integral into a summation, with a quadrature rules approximation [7]. for this calculation it is necessary to define a weight coefficient, called n, built on the distance between nodes:             v eff ,int eff ,sum v ψ x,y σeq(y)dv n x,y ψ x,y σeq(y)     n x,y ψ x,yψ x,y dv        in v (4) in a uniform mesh, i.e. with elements having the same dimension and constant distance between nodes, n should be constant. in any other case, n shall be computed depending on element dimension and actual node distances. this approach suggests using the nodal reaction (at each node constrained) as the n approximation, when the body is loaded by a uniform distributed load, such as the gravity load. consequently, the bigger the element, the bigger the reaction. fig. 4 shows the nodal reaction in a subdomain in the case of a fairly regular, but not uniform, mesh. figure 4: plot of reaction n in a subdomain for any kind of fe software, it is simply necessary to export coordinates of the node inside the subdomain, the first principal stress in each of those nodes, and the reaction of the same nodes. any mathematical tool (i.e. matlab or even a spreadsheet such as excel) can compute σeff,sum of eq. (4). figure 5: trend of σeff,int vs σeff,ig vs σeff,sum. 0 1 2 3 4 5 6 7 8 9 10 0 30 60 90 120 150 180 σ / σ n o m 2α [°] σ eff,ig σ eff,int σ eff,sum m http://www.gruppofrattura.it http://dx.medra.org/10.3221/igf-esis.25.17&auth=true e. maggiolini et alii, frattura ed integrità strutturale, 25 (2013) 117-123; doi: 10.3221/igf-esis.25.17 121 the σsum from the ansys structural analysis is not so far from the comsol integration for each opening angle taken into consideration (fig. 5), it is never higher than 4% as a maximum error (tab. 2). 2α σeff,ig σeff,int σeff,sum error [°] [mpa] [mpa] [mpa] [%] 0 9.47 7.47 7.22 -3.36 30 9.37 7.58 7.65 0.91 60 9.74 7.97 8.01 0.52 90 9.37 7.82 7.84 0.26 120 7.67 6.64 6.70 0.90 135 6.26 5.56 5.61 0.85 150 4.61 4.23 4.23 -0.13 180 1.00 1.00 1.00 0.00 table 2: value of σeff,ig, σeff,int and σeff,sum at any tested angle. ρ/c σeff,ig σeff,int difference σeff,sum error [mpa] [mpa] [%] [mpa] [%] 0 9.37 7.82 -16.5% 7.84 0.26 0.125 9.42 7.84 -16.8% 7.79 -0.60 0.25 9.47 7.87 -16.9% 7.87 -0.03 0.4 9.52 7.91 -16.9% 7.91 0.01 0.5 9.54 7.94 -16.8% 7.94 -0.05 1 9.55 8.06 -15.6% 8.06 0.00 2 9.32 8.18 -12.2% 8.18 0.00 3 8.99 8.16 -9.2% 8.16 0.00 5 8.31 7.84 -5.6% 7.84 0.04 table 3: value of σeff,ig, σeff,int and σeff,sum at any tested ratio. changing the filled radius y modifying the ratio of the filled radius over c; it is possible to compute effective stress in rounded geometries as well. results related to the opening-angle equal to 90° are given in tab. 3 and fig. 6. the scatter between the implicit gradient effective stress and the integral value decreases by increasing the notch tip radius. in any case, the error between the integral value and its numerical approximation is very low. hence, we can argue that the integral value of eq. (4) can be evaluated by means of generic fe software. the problem is the general relationship between the implicit gradient σeff,ig and integral value σeff,int by combining different values of the opening angle and notch tip radius. the ratio between σeff,ig and σeff,int is given in fig. 7. figure 6: trend of σeff,ig vs σeff,int vs σeff,sum on the filled radius. 0 2 4 6 8 10 0 0.2 0.4 0.6 0.8 1 σ / σ n o m ρ/c σ eff,ig σ eff,int σ eff,sum b http://www.gruppofrattura.it http://dx.medra.org/10.3221/igf-esis.25.17&auth=true e. maggiolini et alii, frattura ed integrità strutturale, 25 (2013) 117-123; doi: 10.3221/igf-esis.25.17 122 figure 7: σeff,ig/σeff,int function of filled radius and notch opening angle 2α. mesh influence further problem regarding the numerical assessment of non-local effective stress is the sensibility of results to the elements dimension. taking the 120° geometry and through mesh analysis, it is possible to look at the relationship between the maximum element size and errors that occur. tab. 4 d shows the dimension of the element at the notch tip. in this investigation “plane 42” elements in ansys and “quadrangular” elements in comsol, were used. mesh comsol ansys error d/c σeff,ig σeff,int σeff,sum σeff,int vs σeff,sum 4 7.44 6.66 7.39 10.93% 3 7.53 6.67 7.58 13.74% 2 7.57 6.66 6.84 2.73% 1 7.65 6.65 6.70 0.76% 0.5 7.67 6.64 6.70 0.90% 0.25 7.67 6.64 6.70 0.96% 0.1 7.67 6.64 6.70 0.97% table 4: error occurs in the mesh analysis. how to ccording to a previous theoretical framework, it is possible to sketch a procedure for effective non-local effective stress assessment by means of a general fe numerical tool. first of all, it is suitable to make a subdomain around the interested zone: this makes it easier to create a good quality mesh (element size close to c/2) and to export the needed results and no more. after that, it is only necessary to make an appropriate model and to export the nodal data: first principal stress of stress analysis, nodal coordinates, and reaction solutions under uniform loading. the eq. (2) defines “ψ” and the data are combined into the eq. (4), n is the reaction solution and σeq is the first principal stress. three-dimensional problem he applicability of the proposed approach was also verified for a three-dimensional component. the investigated structural detail is a welded joint depicted in fig. 9. the obtained results are reported in tab. 5. in this first application, the errors are slightly higher, however, it remains acceptable if used for design strength assessment. 1.00 1.05 1.10 1.15 1.20 1.25 1.30 1.35 0 1 2 3 4 5 6 7 8 9 10 σ e ff ,i g / σ e ff ,i n t ρ/c 0° 30° 60° 90° 120° 135° a a t http://www.gruppofrattura.it http://dx.medra.org/10.3221/igf-esis.25.17&auth=true e. maggiolini et alii, frattura ed integrità strutturale, 25 (2013) 117-123; doi: 10.3221/igf-esis.25.17 123 figure 9: three-dimensional geometry. dimension σeff,ig σeff,int σeff,sum error [mpa] [mpa] [mpa] [%] 2d 1.86 1.65 1.65 -0.24 3d 1.81 1.62 1.71 5.52 table 5: comparison between 2d-3d of the same geometry. conclusions he implicit gradient method has already been demonstrated to be effective particularly in fatigue strength assessment of notches or joints. what was not available was a sound procedure for the effective stress evaluation in most fem software, without integration or a pde solver. with this method, through the definition of proper weighted coefficients n, it is possible to determinate the integral approximation σeff,sum. this quantity is related to the implicit gradient effective value and their relations depends on local geometry; such relationship has been investigated in this paper. references [1] tovo, r. livieri, p., an implicit gradient application to fatigue of sharp notches and weldments, engineering fracture mechanics, 74 (2007) 515–526. [2] tovo, r., livieri, p., an implicit gradient application to fatigue of complex structures, engineering fracture mechanics, 75(7) (2008) 1804–1814. [3] tanaka, k., engineering formulae for fatigue strength reduction due to crack-like notches, international journal of fracture, 22 (1983) r39–r46. [4] livieri, p. tovo, r., fatigue limit evaluation of notches, small cracks and defects: an engineering approach, fatigue and fracture of engineering materials and structures, 27 (2004) 1037–1049. [5] cristofori, a., livieri, p., tovo, r., an application of the implicit gradient method to welded structures under multiaxial fatigue loadings, international journal of fatigue, 31(1) (2009) 12–19. [6] peerlings, r.h.j., de borst, r., brekelmans, w.a.m., de vree, j.h.p., gradient enhanced damage for quasi brittle material, international journal of numerical methods in engineering, 39 (1996) 3391–3403. [7] dalquist, g., björck, å., numerical methods in scientific computing, dover publications, inc., mineola, new york, 1 (1974). t http://www.gruppofrattura.it http://dx.medra.org/10.3221/igf-esis.25.17&auth=true microsoft word numero_49_art_42_2318 f.j.p. moreira et alii, frattura ed integrità strutturale, 49 (2019) 435-449; doi: 10.3221/igf-esis.49.42 435 focused on new trends in fatigue and fracture use of the xfem for the design of adhesively-bonded t-joints f.j.p. moreira departamento de engenharia mecânica, instituto superior de engenharia do porto, instituto politécnico do porto, portugal filipejpmoreira08@gmail.com r.d.s.g. campilho departamento de engenharia mecânica, instituto superior de engenharia do porto, instituto politécnico do porto, portugal inegi – pólo feup raulcampilho@gmail.com, https://orcid.org/0000-0003-4167-4434 abstract. the use of adhesive bonds greatly increased in industrial applications, as they have multiple advantages compared to other more traditional bonding methods (fastened, welded and riveted joints). the number of approaches to predict the strength of adhesive joints has increased over the years. the extended finite element method (xfem) is a recent variant of the (finite element method) fem to model damage growth in structures, although it is yet seldom studied within the context of bonded joints. this work consists of an experimental and xfem analysis of aluminium alloy t-joints, adhesively-bonded with three adhesive types. a parametric study is undertaken regarding the curved adherends’ thickness (tp2), with values between 1 and 4 mm. the adhesives araldite® av138 (strong but brittle), araldite® 2015 (less strong but moderately ductile) and the sikaforce® 7752 (with the smallest strength but highly ductile) were tested. a comparative analysis between the different joints conditions was undertaken by plotting peel (y) and shear (xy) stresses, and analysing the damage variable. the xfem predictive capabilities were tested with different damage initiation and propagation criteria. it was found that, provided that the modelling conditions are properly set, accurate numerical results can be found. keywords. fracture; finite element analysis; extended finite element method; bonded joint. citation: moreira, f.j.p., campilho, r.d.s.g., use of the xfem for the design of adhesively-bonded t-joints, frattura ed integrità strutturale, 49 (2019) 435-449. received: 30.11.2018 accepted: 14.05.2019 published: 01.07.2019 copyright: © 2019 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. introduction he use of adhesive bonds greatly increased in industrial applications, as they have multiple advantages compared to other more traditional bonding methods (fastened, welded and riveted joints). the aeronautical, naval, automotive and aerospace industries are good examples where adhesive joints are widely applied. more uniform distribution of t http://www.gruppofrattura.it/va/49/2318.mp4 f.j.p. moreira et alii, frattura ed integrità strutturale, 49 (2019) 435-449; doi: 10.3221/igf-esis.49.42 436 stresses, ease of manufacture, possibility of joining different materials and low cost are the main advantages of adhesive bonds. the main disadvantages are related to the requirement of surface preparation, low peel strength and difficulties in quality control and safety. the most common adhesive joint configurations are single-lap joints (slj), double-lap joints (dlj) and scarf joints [1]. slj are the most common. however, they develop major y peak stresses. dlj are more difficult to manufacture but, on the other hand, y stresses greatly diminish. scarf joints are highly efficient when compared to slj because of the reduction of stress concentrations [1]. although these types of joints are the most used in the industry, other types of joints have specific applications. stepped-lap configurations can be used in composite joining due to the easiness to make the step design during the materials’ fabrication process [2]. t-joints find application in the naval and aeronautical industries. in the naval industry, they allow joining panels with the hull [3] and the fiberglass hull with anti-flood panels [4]. in the aeronautical industry, they are used to join wing panels and fuselage sections [5]. several works were carried out to evaluate t-joints, using either analytical or numerical techniques [6, 7]. the number of approaches to predict the strength of adhesive joints has increased over the years. actually, analytical and numerical techniques have become more and more refined and with higher accuracy. numerical methods are typically founded on the fem. the fem allows modelling complex geometries with high precision, due to the computational advancements and computer aided engineering (cae) tools. within this scope, the use of continuum mechanics supposes using the obtained stresses or strains, whose maximum values are used in appropriate failure criteria to assess failure. however, this technique has limited applicability because of stress singularities (which make the predictions dependent on the applied mesh) and neglecting of fracture mechanics concepts [8]. actually, in a bonded joint fem analysis, stresses near the singular regions increase with the mesh refinement, making convergence impossible [9]. traditional fracture mechanicsbased techniques can be applied to the study of the behaviour of structures that contain defects, such as cracks. these cracks can result from stress concentrations, usually located in holes, notches or interfaces between different materials. however, it is not mandatory that the structures to be analysed already have cracks, which is a limitation of this method [10]. cohesive zone models (czm) were developed to describe damage under static loads in the cohesive process zone around the crack tip. they are based on cohesive elements, which allow connecting solid elements of two-dimensional (2d) and threedimensional (3d) structures, using pre-established traction-separation laws [11]. czm were tested and optimized to promote structural damage initiation and crack propagation simulations on cohesive and interfacial fracture problems, and delamination in composites. the use of czm to model structures enables to create one or more regions or interfaces in which damage nucleation and growth is made possible by the softening and release of homologous nodes of the cohesive elements [12]. fem simulations based on continuum mechanics wrongly consider that the solid elements undergo plasticization without taking damage. damage mechanics simulations work by inducing damage to the elements through the reduction of transmitted loads between solid elements. thus, it is possible to perform the simulation of crack growth, in which the cracks can assume a pre-defined trajectory or an arbitrary trajectory within a finite region [8]. in damage mechanics, a damage parameter is established to cause a change in the response of the constituent materials through the depreciation of the strength or stiffness, as occurs in adhesive layers, or in composite delaminations, to model damage during loading [13, 14]. the insertion of a damage variable in the constitutive law of the material enables simulating damage before and after crack nucleation. two types of damage variables can be introduced in the models: variables that empirically depreciate the properties of the materials, without any relation to the damage mechanism, and variables that have a physical significance, by directly relating to the observed type of damage (for example the size of porosities or micro-cavities) [15]. the growth of damage is usually ruled by the load function for static simulations [16] and as a function of the number of cycles for fatigue modelling [17, 18]. the xfem is a recent variant of the fem to model damage growth in structures, although it is yet seldom studied within the context of bonded joints. this method uses damage laws to predict fracture, based on strength concepts to infer damage initiation of damage and deformations for failure. comparing the xfem with czm, the xfem has the clear advantage of not requiring the crack to follow a predefined path by the user. this is because crack propagation occurs freely inside the material, without the geometry of the discontinuities being coincident with the mesh or the necessity to correct the mesh in the crack vicinity [19]. the xfem is based on the concept of partition of unity, and its implementation in the fem can be accomplished by introducing local enrichment functions for the displacements near the crack tip, allowing damage to grow and respective separation between the cracked faces [20]. mubashar et al. [21] carried out a study on the damage and failure modelling of adhesively-bonded slj with spew fillets at the overlap ends, combining two methods: xfem (to perform the modelling of the crack in the fillet region where the crack path is unknown) and czm (applied to model crack progression and damage along the adhesive bond interface). the numerical analysis was performed in abaqus®. aluminium alloy 2024 t3 adherends were bonded with the epoxy adhesive fm73-m, and the adhesive was modelled with elastoplastic properties, obtained in tensile tests. this work allowed to conclude that the xfem is capable of predicting, with a high degree of precision, the crack onset location and path within the spew fillet. moreover, it is possible to combine the xfem with czm to more accurately predict crack initiation and growth in bonded joints, f.j.p. moreira et alii, frattura ed integrità strutturale, 49 (2019) 435-449; doi: 10.3221/igf-esis.49.42 437 including at the interface. however, this technique is limited by the existence of a potential discontinuity in the crack at the xfem-czm transition. stuparu et al. [22] conducted a study on the combined use of czm and xfem for the strength prediction of bonded joints. the slj configuration was tested, with aluminium adherends and the adhesive araldite® av138. the following parameters were used: adherends’ thickness (tp) of 5 mm, adhesive thickness (ta) of 1, 3 and 5 mm, overlap length (lo) of 20 mm and sample width (b) of 25 mm. the numerical analysis was done in abaqus®. the xfem was used to simulate failure within the adhesive, considering a strain criterion (less mesh dependent than stress criteria) for crack onset prediction. thus, crack initiation/propagation will always take place orthogonally to the maximum principal strains. on the other hand, czm was equated to simulate an interfacial failure between the adhesive and adherends. different ta and the positions of initial bonding flaws were tested, resulting in modifications of the xfem crack trajectories, eventually attaining the interface. it was shown that the use of xfem is well complemented by czm to promote crack growth after the xfem crack attained the interface. this work consists of an experimental and xfem analysis of aluminium alloy t-joints, adhesively-bonded with three adhesive types. a parametric study is undertaken regarding tp2, with values between 1 and 4 mm. the adhesives araldite® av138 (strong but brittle), araldite® 2015 (less strong but moderately ductile) and the sikaforce® 7752 (with the smallest strength but highly ductile) were tested. a comparative analysis between the different joints conditions was undertaken by plotting y and xy stresses, and analysing the damage variable. the xfem predictive capabilities were tested with different damage initiation and propagation criteria. experimental work adherends and adhesives he t-joints are made of three aw6082 t651 aluminium alloy aluminium adherends bond together. this is a highstrength alloy, characterized in a previous work [23]. fig. 1 shows typical stress-strain (-) curves of this aluminium alloy, whose relevant properties in bulk tensile testing are: young’s modulus (e) of 70.1±0.8 gpa, tensile yield stress (y) of 261.7±7.7 mpa, tensile strength (f) of 324.0±0.2 mpa and tensile failure strain (f) of 21.7±4.2%. figure 1: experimental and numerical  curves of the aluminium. the following adhesives were tested in the t-joint configuration: araldite® av138 (brittle epoxy), araldite® 2015 (ductile epoxy) and the sikaforce® 7752 (high-elongation polyurethane). all adhesives were formerly tested and the respective properties detailed in references [23-25]. the tensile mechanical properties (e, y, f and f) resulted from bulk tests to dogbone specimens. the fabrication process for these specimens followed the indications stipulated in the nf t 76-142 french standard. the shear mechanical properties (shear modulus – g, shear yield stress – y, shear strength – f and shear failure strain – f) were estimated by thick adherend shear tests (tast). in this case, the 11003-2:1999 iso standard was considered for fabrication and testing protocols. the tast specimens were made with din ck 45 steel adherends, and curing was undertaken in a rigid mould to guarantee that the cured specimens are aligned [26]. the toughness properties of the adhesives were estimated with the double-cantilever beam (dcb) test (tensile fracture toughness or gic) and the endnotched flexure (enf) test (shear fracture toughness or giic). tab. 1 gives an overview of the obtained data, which will 0 50 100 150 200 250 300 350 0 0.05 0.1 0.15 0.2 0.25  [m p a]  experimental numerical approximation t f.j.p. moreira et alii, frattura ed integrità strutturale, 49 (2019) 435-449; doi: 10.3221/igf-esis.49.42 438 be used in this work for input in the numerical simulations. to be noted that the values of yield stress were defined considering a plastic strain of 0.2%. property av138 2015 7752 young’s modulus, e [gpa] 4.89±0.81 1.85±0.21 0.49±0.09 poisson’s ratio,  0.35 a 0.33 a 0.30 a tensile yield stress, y [mpa] 36.49±2.47 12.63±0.61 3.24±0.48 tensile failure strength, f [mpa] 39.45±3.18 21.63±1.61 11.48±0.25 tensile failure strain, f [%] 1.21±0.10 4.77±0.15 19.18±1.40 shear modulus, g [gpa] 1.81 b 0.70 b 0.19 b shear yield stress, y [mpa] 25.1±0.33 14.6±1.3 5.16±1.14 shear failure strength, f [mpa] 30.2±0.40 17.9±1.8 10.17±0.64 shear failure strain, f [%] 7.8±0.7 43.9±3.4 54.82±6.38 toughness in tension, gic [n/mm] 0.20 c 0.43±0.02 2.36±0.17 toughness in shear, giic [n/mm] 0.38 c 4.70±0.34 5.41±0.47 a manufacturer’s data b estimated from the hooke’s law using e and  c estimated in campilho et al. [23] table 1: properties of the adhesives araldite® av138, araldite® 2015 and sikaforce® 7752 [23-25]. experimental details fig. 2 represents the geometry and dimensions of the t-joints. the relevant dimensions are the following: lo=25 mm, b=25 mm, base length lt=80 mm, base thickness tp1=3 mm, tp2=1, 2, 3 and 4 mm, l-part length la=60 mm, l-part radius r=5 mm and ta=0.2 mm. specimen fabrication was initiated by cutting/bending the adherends to the respective shapes. the straight adherend, used as the specimen base, is obtained by cutting, in an automated cutter, a bar to the final dimensions. the l-parts were subjected to an identical procedure, but then they were manually bent in a press, such that the end surfaces were at an angle of 90º, and applying a tool with the chosen r, to produce the geometry depicted in fig. 2. the surface preparation before bonding consisted of manually increasing the roughness by sanding using emery paper with coarse grain (60 grit), followed by wiping with cleaning agent (acetone) to eliminate dust and oxides, thus achieving a strong bond. joining of the different parts was accomplished in a jig that positioned the three adherends in the layout of fig. 2 and enabled keeping this position throughout the entire adhesive hardening process. to assure the specified ta, steel spacers with identical thickness to ta were inserted at the edges of the bonded parts are removed after adhesive curing. before placing the spacers, they were initially coated with loctite® frekote 770nc demoulding agent, to guarantee easy removal after the adhesive has cured, which is essential to prevent damage to the cured adhesive layers. with the specimens in position after depositing the adhesive, and with the spacers providing the correct offset between adherends, grips were used to apply pressure to the set and enable curing to take place. this process was accomplished during a one-week period. the final step consisted of trimming the excess cured adhesive by milling. as a result of this set of operations, it was possible to obtain a good representation of the theoretical geometry of fig. 2, with emphasis to the bondline end geometry positioned at x/lo=0 (x is the horizontal coordinate initiating at the bondline end). the specimens were tested as depicted in fig. 2, i.e. by clamping the edges of the straight adherend and pulling in peel while transversely restraining the upper joint edge. this was done in a shimadzu ag-x 100 testing machine, equipped with a 100 kn load cell, at an approximate temperature of 20ºc and testing speed of 1 mm/min. five specimens were fabricated and tested for each joint type. a minimum of 4 valid tests was always assured for each joint type. f.j.p. moreira et alii, frattura ed integrità strutturale, 49 (2019) 435-449; doi: 10.3221/igf-esis.49.42 439 figure 2: representative geometry and dimensions of the t-joints. numerical work numerical simulation details he analysis performed in abaqus® was 2d, considering a geometrically non-linear fem formulation. the aluminium adherends (both base and l-parts) were modelled as solids with the plastic behaviour defined in a previous work for the same material [27]. the adhesive layer was also modelled with solid elements, but with enriched xfem formulation. the xfem model is presented in the next section. in all cases, 4-node solid elements with plane-strain conditions were used (with abaqus® reference cpe4). a perfect adhesion was considered in the models between the adherends and adhesive, since the models were built as a single part with different partitions and materials. two types of meshes were applied: a more refined mesh to perform a stress analysis in the elastic domain, such that the stress plots are accurate, and a less refined mesh to promote the xfem failure analysis. fig. 3 shows an example of mesh refinement for a t-joint with tp2=1 mm, with details at the loaded overlap edge for the stress and failure analyses. figure 3: mesh details at x/lo=0 for the joint with tp2=1 mm: stress analysis and xfem strength prediction analyses. t f.j.p. moreira et alii, frattura ed integrità strutturale, 49 (2019) 435-449; doi: 10.3221/igf-esis.49.42 440 mesh bias effects were employed in the models to grade the elements’ size, enabling to reduce the total number of elements but without compromising the accuracy. this was done by considering a more refined mesh near the adhesive layer and towards its edges, and a coarser mesh in the zones with less stress variations [28]. the elements’ side dimensions in the adhesive layer for the xfem simulations were 0.2×0.2 mm along the bondline, i.e., only one element through-thickness was considered. on the other hand, the models for the stress analysis were comprised of 0.02×0.02 mm elements at the overlap edges. the boundary conditions consisted of fixing the base edges to simulate gripping in the testing machine, applying symmetry at the middle of the specimen and pulling the curved adherends’ edges in peel. xfem formulation as an extension to the conventional fem, the xfem is based on the integration of enrichment functions in the fem formulation [29]. these functions allow modelling the displacement jump between crack faces that occur during the propagation of a crack. the abaqus® xfem formulation enables the user to create a pre-crack, or it can initiate cracks in un-cracked regions by using initiation criteria. in this last scenario, considered in this work, damage initiates and subsequently propagates during the simulation at regions experiencing stresses and/or strains higher than the corresponding limiting values. six crack initiation criteria are available in abaqus®. the maxps (maximum principal stress) and maxpe (maximum principal strain) criteria are based on the introduction of the following functions (by the respective order) 0 ormax max 0 max max f f                  (1) max and 0max represent the current and allowable maximum principal stress. the macaulay brackets indicate that a purely compressive stress state does not induce damage. max and 0max represent the current and allowable maximum principal strain. crack growth for the maxps and maxpe criteria is software defined as orthogonal to the maximum principal stress/strain direction. as a result of this, and due to the inherent mixed-mode loading of these joints, the crack grows fast towards the adherends. for these two criteria, the maximum load (pm) estimation was thus considered to take place at the time of first cracking in the adhesive layer. the maxs (maximum nominal stress) and maxe (maximum nominal strain) criteria are represented by the following functions, respectively 0 or n ns s 0 0 0 n s n s max , max , t t f f t t                  (2) tn and ts are the current normal and shear traction components to the cracked surface. tn0 and ts0 represent the respective limiting values. the strain parameters have identical significance. the quadratic nominal stress (quads) and quadratic nominal strain (quade) criteria are based on the introduction of the following functions, respectively or 2 22 2 n ns s 0 0 0 0 n s n s t t f f t t                              (3) for the maxs, maxe, quads and quade criteria the user can select between horizontal or vertical crack growth (in this work horizontal growth, i.e., along the adhesive layers’ length, was selected). all the six aforementioned criteria are fulfilled, and damage initiates, when f reaches unity. for damage growth, the fundamental expression of the displacement vector u, including the displacements enrichment, is written as [30]     1 n i i n x h x     u u ai i (4) ni(x) and ui relate to the conventional fem formulation, corresponding to the nodal shape functions and nodal displacement vector linked to the continuous part of the formulation, respectively. the second term between brackets, h(x)ai, is only active in the nodes for which any relating shape function is cut by the crack and can be expressed by the product of the nodal enriched degree of freedom vector including the mentioned nodes, ai, with the associated f.j.p. moreira et alii, frattura ed integrità strutturale, 49 (2019) 435-449; doi: 10.3221/igf-esis.49.42 441 discontinuous shape function, h(x), across the crack surfaces. the method is based on the establishment of phantom nodes that subdivide elements cut by a crack and simulate separation between the newly created sub-elements. propagation of a crack along an arbitrary path is made possible by the use of these phantom nodes that initially have exactly the same coordinates than the real nodes and that are completely constrained to the real nodes up to damage initiation. after being crossed by a crack, the element is partitioned in two sub-domains. the discontinuity in the displacements is made possible by adding phantom nodes superimposed to the original nodes. when an element cracks, each one of the two sub-elements will be formed by real nodes (the ones corresponding to the cracked part) and phantom nodes (the ones that no longer belong to the respective part of the original element). these two elements that have fully independent displacement fields replace the original one. thus, the crack size increment for a given crack orientation is equal to the distance between the cracked element’s edges. from this point, each pair of real/phantom node of the cracked element is allowed to separate according to a suitable damage law up to failure. at this stage, the real and phantom nodes are free to move unconstrained, simulating crack growth. tab. 2 summarizes the parameters introduced in abaqus®. a linear softening xfem law was initially considered with an energetic failure power law criterion of the type i ii ic iic 1, g g g g                (5) in which  is the damage law exponent (=1 for linear softening). property av138 2015 7752 e [gpa] 4.89 1.85 0.49 g [gpa] 1.81 0.70 0.19 0max [mpa] 39.45 21.63 11.48 0max [%] 1.21 4.77 19.18 tn0 [mpa] 39.45 21.63 11.48 ts0 [mpa] 30.2 17.9 10.17 n0 [%] 1.21 4.77 19.18 s0 [%] 7.8 43.9 54.82 gic [n/mm] 0.20 0.43 2.36 giic [n/mm] 0.38 4.70 5.41 table 2: parameters of the araldite® av138, araldite® 2015 and sikaforce® 7752 for xfem modelling. results experimental failure modes ll failures took place beginning with crack propagation at x/lo=0 and growing towards the other edge. after failure, the fracture surfaces were inspected and cohesive failures were found for all adhesives and tp2. however, in some cases, especially for the joints bonded with the araldite® av138, failure sometimes took place near to one of the adherend/adhesive interfaces (fig. 4 shows an example for the joints with tp2=2 mm), such that visually it resembled an adhesive failure. however, careful surface inspection including optical microscope observations revealed that the adherends that at first hand suffered form an adhesive failure actually were covered by a thin layer of adhesive. these findings are consistent with previous observations on this particular adhesive [27]. the fracture surfaces for the joints bonded with the araldite® 2015 and sikaforce® 7752 were smoother, indicative of ductile fractures, with a clearer evidence of cohesive failures. l-part adherend plasticization was detected in all joints bonded with the araldite® 2015 and tp2=1 mm, and also with the sikaforce® 7752 and tp2=1 and 2 mm, although for this last case it was under 0.1%. a f.j.p. moreira et alii, frattura ed integrità strutturale, 49 (2019) 435-449; doi: 10.3221/igf-esis.49.42 442     figure 4: fracture surfaces for the five sets of t-joints bonded with the araldite® av138 and with tp2=2 mm (for each set the l-parts are at the left and the base adherend to the right). stresses in the elastic domain this section briefly evaluates y and xy stresses along the adhesive during the initial stages of the elastic loading, such that the differences between adhesives and tp2 are properly accounted for. the graphics are represented as follows:  the x-axis represents the normalized distance along the adhesive length (x/lo), in which x is the horizontal coordinate beginning at the leftmost edge of the adhesive layer, i.e. the edge closest to the central portion of the joint;  the y-axis represents the normalized y and xy stresses (y/avg and xy/avg, respectively). avg is the average xy stress along the adhesive mid-thickness for the respective tp2. between the three adhesives, stresses in the elastic loading stage are identical, with the sole difference residing in the normalized peak values, since these increase in proportion with the adhesive stiffness (e values compared in tab. 1) [31]. thus, graphically, only the results for one adhesive are presented, in this case for the aradite® 2015 (fig. 5), which has the middle stiffness. it can be first observed that y stresses are prevalent over xy stresses, which was expected due to the expected peel loading, although xy of non-negligible magnitude also develop due to the sliding of the l-part over the base adherend. independently of tp2, peak stresses or at least stress perturbations exist at the vicinity of x/lo=0 and 1 mm, which consist of the stress singularity regions. a) b) figure 5: normalized y (a) and xy (b) stresses along the adhesive mid-thickness for the t-joints bonded with the araldite® 2015. y stresses were identical between the three adhesives, although with the aforementioned differences in magnitude of peak stresses. the curves depicted in fig. 5 (a), relating to the araldite® 2015, showed intermediate peak values between the other two adhesives. for the joints with tp2=1 mm, the critical region was undoubtedly x/lo=0, due to the small stiffness of the l-part, arising from its low thickness. for the other tp2, y stresses are either close to zero or compressive at this location. the increase of tp2 gradually reduces the harmful effect of y peak stresses at x/lo=0, but gradually loads the other edge (x/lo=1), which is deemed to occur because of the growing thickness and stiffness of the l-part. actually, this change in deformation pattern of the l-part, namely the significant reduction of its bending, works against the natural curvature -50 0 50 100 150 200 0 0.2 0.4 0.6 0.8 1  y / av g x/lo 1 mm 2 mm 3 mm 4 mm -100 -50 0 50 100 0 0.2 0.4 0.6 0.8 1  x y / av g x/lo 1 mm 2 mm 3 mm 4 mm f.j.p. moreira et alii, frattura ed integrità strutturale, 49 (2019) 435-449; doi: 10.3221/igf-esis.49.42 443 developing in the straight adherend due to the tensile pulling. this gives rise to tensile y peak stresses near x/lo=1, while the other edge tends to become lightly loaded. this effect can even be responsible by an alteration of the failure path if tp2 reaches a given limit. on the other hand, y stresses tend to span for a bigger region of the bonding length with the increase of tp2, which can be responsible for a pm improvement. identically to that found for y stresses, the behaviour of xy stresses has large similarities between adhesives, although with peak magnitude variation between adhesives due to their stiffness differences. the t-joints bonded with the araldite® 2015, whose curves are shown in fig. 5 (b), presented a middle behaviour between the three tested adhesives. the smallest xy peak stresses are those of the joints with tp2=1 mm and, for this joint, xy stresses peak close to x/lo=0, while being negligible for the remainder of the bonding portion. on the other hand, the increase of tp2 lightly increases xy peak stresses near x/lo=0, concurrently with a progressive increase of xy peak stresses near x/lo=1. this modification in the xy stress plots is related to the aforementioned behaviour of y stresses, i.e., due to the stiffening effect of the l-part, which is not accompanied by the transverse deformation of the base adherend, which subsequently leads to large adhesive strains near x/lo=1. moreover, the variation of xy stress plots can also influence the failure onset and growth, identically for that discussed for y stresses. study of the sdeg (damage) variable the stiffness degradation (sdeg variable) of the xfem damage laws along the bonded length is addressed in this section, with the objective of describing the extent of damage along the adhesive at the pm of the joints. the sdeg variable ranges from 0 to 1, in which 0 represents the absence of damage, i.e., the respective set of nodes are within the elastic loading phase, and 1 corresponds to full separation. sdeg values in-between indicate that the set of nodes is in the stress softening phase. fig. 6 shows the sdeg plots at pm along x/lo for the t-joints bonded with the araldite® av138 (a), araldite® 2015 (b) and sikaforce® 7752 (c). for each adhesive, the four joint geometries are analysed (tp2=1, 2, 3 and 4 mm). a) b) c) figure 6: sdeg variable at the pm instant for the t-joints bonded with the araldite® av138 (a), araldite® 2015 (b) and sikaforce® 7752 (c). the comparison between the three adhesives clearly shows different behaviours. the brittleness of the araldite® av138 reflects on a much localised portion of the adhesive layer under damage at the time pm is reached in the t-joints. this is visible by the steepness of the sdeg plot between sdeg=1 and 0. moreover, at pm some portion of the adhesive layer is already fully damaged, especially for bigger tp2. this could be indicative of brittle failure and a lesser performance of this 0 0.2 0.4 0.6 0.8 1 0 0.2 0.4 0.6 0.8 1 s d e g x/lo 1 mm 2 mm 3 mm 4 mm 0 0.2 0.4 0.6 0.8 1 0 0.2 0.4 0.6 0.8 1 s d e g x/lo 1 mm 2 mm 3 mm 4 mm 0 0.2 0.4 0.6 0.8 1 0 0.2 0.4 0.6 0.8 1 s d e g x/lo 1 mm 2 mm 3 mm 4 mm f.j.p. moreira et alii, frattura ed integrità strutturale, 49 (2019) 435-449; doi: 10.3221/igf-esis.49.42 444 adhesive in the t-joint configuration. the damage evolution is more gradual for the other adhesives, due to their inherent ductility, especially for the sikaforce® 7752. for the araldite® 2015, despite this modification in the failure process, it is clear that a damaged portion of adhesive of non-negligible dimensions is present which, in this particular loading case, can prove to have a positive effect on pm. this ductility effect is even more visible in the sikaforce® 7752. inclusively, for tp2=4 mm, a portion of adhesive in the vicinity of x/lo=1 also undergoes damage. for all adhesives, a modification of the sdeg and a clear tendency are found depending on tp2. irrespectively of the adhesive, the damage tends to extend further with the increase of tp2. at pm, the portion of adhesive under damage (sdeg between 0 and 1) for the araldite® av138 is 1.8; 2.6; 9.5 and 31.3% for tp2=1, 2, 3 and 4 mm, respectively. by the same sequence, these percentile values increase to 6.3; 9.5; 13.0 and 19.1% for the araldite® 2015 and further to 20.9; 33.9; 39.1 and 40.0% for the sikaforce® 7752. this evolution between adhesives is clearly due to the increasing ductility of the adhesives in the mentioned order, depicted in tab. 1 through the values of gic and giic. moreover, y and xy peak stresses reduce from the araldite® av138 to the araldite® 2015, and even further to the sikaforce® 7752, due to the differences in elastic stiffness (tab. 1), which helps in spreading the damage across the adhesive layer. higher damage zones should help in attaining higher pm in this particular joint configuration, which traditionally concentrates the load in a small portion of the adhesive. on the other hand, irrespectively of the adhesive, its damaged portion always increases with tp2, which can be explained by the corresponding reduction of l-part deformations due to a load scenario that gradually shifts from peeling to cleavage as tp2 increases. this shift should also bring a higher joint efficiency, because the adhesive region resisting pull-out increases. experimental strength the experimentally obtained pm for the t-joints bonded with the three adhesives are presented in this section. fig. 7 reports the average pm vs. tp2 curves, including the standard deviation of the experiments. figure 7: experimental pm vs. tp2 curves for the three adhesives. it can be found that pm always increases, and by a large amount, with tp2, irrespectively of the adhesive. the two araldite® adhesives show an increasing growth with tp2, while the sikaforce® 7752 has a marked linear evolution of the pm vs. tp2 curve. the percentile pm increase for the t-joints with tp2=2, 3 and 4 mm, over the t-joint with tp2=1 mm, was respectively of 75.0%, 173.8% and 419.3% (araldite® av138), 81.2%, 197.8% and 403.7% (araldite® 2015) and 110.9%, 227.1% and 358.6% (sikaforce® 7752). this marked pm improvement with tp2 is mainly due to the y stress levelling effect that is visible in fig. 5 (a) near x/lo=0, which corresponds to the stress initiation site. subsequently, this also reflects in a more widespread damage span (i.e., 0<sdeg<1) with the increase of tp2, as it is visible in fig. 6 for the three adhesives, although more clearly for the araldite® 2015 and sikaforce® 7752. between adhesives, the sikaforce® 7752 clearly outperforms the other two adhesives, despite being the less strong amongst the three adhesives (tab. 1). the pm improvement of the t-joints bonded with this adhesive, over those bonded with the araldite® av138, ranges between 213.8% (tp2=4 mm) and 328.0% (tp2=2 mm). on the other hand, compared against the joints bonded with the araldite® 2015, the pm improvement varies between 78.5% (tp2=4 mm) and 128.1% (tp2=2 mm). it is also visible in fig. 7 that pm for the joints bonded with the araldite® 2015 are higher than those with the araldite® av138. in fact, depending on tp2, pm may almost double that obtained with the araldite® av138 adhesive, although this adhesive has higher strengths. the improvement is minimum for tp2=4 mm (78.4%) and maximum for tp2=3 mm (97.2%). these results show that, in a test geometry that is mainly loaded in peel, and which 0 1 2 3 4 5 6 0 1 2 3 4 p m [k n ] tp2 [mm] av138 2015 7752 f.j.p. moreira et alii, frattura ed integrità strutturale, 49 (2019) 435-449; doi: 10.3221/igf-esis.49.42 445 promotes stresses to be concentrated in small areas, flexible and ductile adhesives behave best. in one hand, the flexibility tends to increase the area along which stresses are being transferred (fig. 5). on the other hand, the ductility permits plasticization of the adhesive at the stress concentration sites while the regions in the vicinity becomes loaded, resulting in an overall improved behaviour. numerical evaluation of the xfem initiation criterion the xfem initiation criteria described in section “xfem formulation” are evaluated against the experimental data, by directly comparing pm with the experiments. at this stage, the linear energetic criterion, considering =1 in eqn. (5), is considered in all simulations. as it was previously discussed, the use of the maxs, maxe, quads and quade criteria results in crack onset and growth parallel to the adhesive layer, while maxps and maxpe criteria leads to cracking perpendicular to the maximum principal stresses or strains, which subsequently makes the crack grow in the direction of the adherends. fig. 8 shows the pm comparison for all tp2 between the different xfem initiation criteria and the experiments for the adhesives araldite® av138 (a), araldite® 2015 (b) and sikaforce® 7752 (c). a) b) c) figure 8: experimental and numerical pm comparison, considering different xfem initiation criteria, for the t-joints bonded with the araldite® av138 (a), araldite® 2015 (b) and sikaforce® 7752 (c). for the araldite® av138, the quads and maxs criteria are closest to the experimental points, and the respective curves are practically overlapped in the figure. averaged over the experiments, the maximum relative deviations were +8.8% (tp2=2 mm) and +9.5% (tp2=2 mm), respectively, for these two criteria. the maxps criterion revealed to be unsuited, in the manner that it was used, since pm highly underestimates the tests (up to -82.5% for tp2=1 mm). oppositely to this behaviour, the strain-based criteria (quade, maxe and maxpe) overshoot the experimental data, with emphasis to the quade and maxe. the highest offsets for these criteria were +113.3% (quade), +117.3% (maxe) and +31.3% (maxpe), in all cases for tp2=2 mm. qualitatively, the pm predictions for the araldite® 2015 by the six criteria agree with those of the araldite® av138. thus, the quads and maxs criteria are quite close to the experimental values, with a negligible difference between them. the maximum pm deviations were, in both cases, obtained for tp2=4 mm, attaining -8.9% (quads) and -8.6% (maxs). the maxps criterion was offset up to -81.3% (tp2=1 mm), whilst the maximum deviations for the strain-based criteria attained maximums of +110.7% for both quade and maxe (tp2=1 mm), and +55.2% the maxpe criterion (tp2=2 mm). finally, the results for the sikaforce® 7752 were much alike those of the former adhesives although, in this case, even the quads and maxs criteria showed bigger variations to the experimental pm (up to -13.3% 0 1 2 3 0 1 2 3 4 p m [k n ] tp2 [mm] exp maxs quads quade maxe maxps maxpe 0 2 4 6 0 1 2 3 4 p m [k n ] tp2 [mm] exp maxs quads quade maxe maxps maxpe 0 4 8 12 16 20 0 1 2 3 4 p m [k n ] tp2 [mm] exp maxs quads quade maxe maxps maxpe f.j.p. moreira et alii, frattura ed integrità strutturale, 49 (2019) 435-449; doi: 10.3221/igf-esis.49.42 446 for the quads, considering tp2=4 mm, and +13.3% for the maxs, considering tp2=1 mm). identically, the curves for these two criteria overlap. due to the aforementioned approximations, the maxps criterion showed pm values much below the expected, with a maximum deviation of -85.8% (tp2=3 mm). the strain-based criteria significantly over predicted pm, in line with the previous adhesives. the maximum offsets, all by excess, were +197.8% for the quade (tp2=2 mm), +214.7% for the maxe (tp2=4 mm) and +160.5% for the maxpe (tp2=2 mm). it was shown in a previous work [23] that damage initiation is ruled by the adhesive layer’s stresses rather than the strains (which also vary by a large amount between adhesives). on the other hand, using strain-based criteria can result in major deviations to the real joint behaviour, with an over prediction tendency. this is why the quads and maxs criteria generally work very well. the quade and maxe criteria, being based on strains, naturally present wrong pm results and should not be considered in the design process of bonded joints. the maxps and maxpe criteria, due to its intrinsic formulation, are unable to promote a realistic damage growth path, since the crack growth direction is ruled by the maximum principal stresses or strains, in a sense that crack initiates and grows perpendicularly to the principal directions. as a result, adherend detaching by the adhesive through all the adhesive layer is rendered unfeasible because the mixed-mode loading induced in the adhesive results in short crack growth in the adhesive before the crack hits the adherend interface. since pm was assessed by the damage initiation load, i.e., at the time the first crack appears in the model, the results do not match the real joint behaviour. moreover, since stresses and strains in fem modelling are traditionally mesh dependent [11], the direct use of initiation criteria to assess failure, i.e., without failure criteria, should promote mesh-dependent pm. numerical evaluation of the xfem propagation criterion the study of the propagation criterion relied on the use of the quads initiation criterion, due to the consistency of results shown in the previous section, and consisted of changing the mixed-mode exponent  in expression (5) using the linear damage law, by considering =0.5, 1 and 2, and also testing an exponential damage law with =1. usually, from reported data [32], the triangular law manages to represent with accuracy the behaviour of the adhesive layer, but changing this parameter leads to different mixed-mode conditions for element failure, which may or not prove to have a noteworthy influence on the results. fig. 9 depicts the experimental and numerical pm comparison under the mentioned modelling conditions, for the t-joints bonded with the araldite® av138 (a), araldite® 2015 (b) and sikaforce® 7752 (c). a) b) c) figure 9: experimental and numerical pm comparison, considering different xfem propagation models, for the t-joints bonded with the araldite® av138 (a), araldite® 2015 (b) and sikaforce® 7752 (c). 0 1 2 3 4 0 1 2 3 4 p m [k n ] tp2 [mm] exp tri p1 tri p0.5 tri p2 expon p1 0 1 2 3 4 5 6 0 1 2 3 4 p m [k n ] tp2 [mm] exp tri p1 tri p0.5 tri p2 expon p1 0 4 8 12 16 0 1 2 3 4 p m [k n ] tp2 [mm] exp tri p1 tri p0.5 tri p2 expon p1 f.j.p. moreira et alii, frattura ed integrità strutturale, 49 (2019) 435-449; doi: 10.3221/igf-esis.49.42 447 in the case of joints bonded with the araldite® av138, the triangular propagation law with =1 presents the closest values to the experiments. compared against the test results, the relative deviations for these conditions ranged between -4.1% (tp2=1 mm) and +8.8% (tp2=2 mm). the results were much similar for =2, with a maximum deviation for tp2=3 mm of +12.5%. on the hand, =0.5 led to under predicted pm, up to -21.6% (tp2=1 mm). the exponential law proved to be unsuited for these joints by resulting in pm much above the experiments. the relative deviations showed a decreasing trend by increasing tp2, thus giving a maximum offset of +140.5% for tp2=1 mm and a minimum offset of +95.1% for tp2=4 mm. for this and the subsequent adhesives, this large difference is justified by the higher failure displacements resulting from the exponential damage laws, which artificially enlarge the damage length in the adhesive. analysis of the araldite® 2015 data denotes almost superimposed pm predictions between =1 and 2, and also good correlations to the experiments (maximum deviations of -8.9% for tp2=4 mm, considering =1, and -8.3% for tp2=4 mm, applying =2). identically to the former adhesive, the exponential propagation law presented much higher pm values than the experiments (up to +117.7% for tp2=1 mm, again showing an offset reduction tendency by increasing tp2). the effect of  on the xfem results for the sikaforce®7752 was the smallest between tested adhesives. it was found in a previous work [32] that this influence diminished by increasing the adhesive ductility, which also agrees with the results presented here. for this adhesive, the best results were again found with =1 and 2 mm, with the =0.5 values falling short over the former. nonetheless, compared against the experiments, there was a slightly higher under prediction tendency, which attained -19.4% for tp2=4 mm (=0.5), -13.3% for tp2=4 mm (=1) and -12.7% for tp2=4 mm (=2). the exponential promoted offsets up to +181.4% (tp2=2 mm), although here the reduction trend with tp2 is not clear. conclusions his work presented an experimental and numerical assessment of the behaviour of adhesively-bonded t-joints between aluminium adherends, considering different geometric conditions (tp2) and adhesives with different characteristics with respect to the strength and ductility. the experimental analysis showed that, for the particular joints conditions tested, i.e., a predominantly peel loading with major peak stresses, the most ductile although less strong sikaforce® 7752 is the one that presents better results for all tp2. increasing tp2 highly increased pm for all adhesives. the difference between adhesives was clarified by a y and xy stress analysis being performed to the adhesive layer, which showed that the y peak stresses ruling the failure process are inversely proportional to the adhesives’ stiffness. thus, the corresponding stress plots are more uniform and enable spreading the loads more evenly, which highly benefits pm. adding to this, the sikaforce® 7752 is highly ductile, thus permitting the adhesive to undergo plasticization at the highest stresses zones, whilst lightly loaded regions increase load transfer, before failure. the damage variable analysis also supported the experimental findings, showing an increasing portion of damaged length of adhesive at pm with the increase of tp2, for all adhesives. this tends to bring a higher joint efficiency because the adhesive region resisting pull-out increases. the comparison between the three adhesives showed that the brittleness of the araldite® av138 leads to a much localised portion of the adhesive layer under damage at the time pm is reached in the t-joints. the damage evolution was more gradual for the other adhesives, due to their inherent ductility, especially for the sikaforce® 7752. higher damage zones should help in attaining higher pm in this particular joint configuration that traditionally concentrates the load in a small portion of the adhesive. the xfem analysis applied to the initiation criterion enabled to conclude that, for all the adhesives, the quads and maxs criteria were the most adequate. the maxps criterion was inadequate, in view of the simplification taken to estimate pm. all strain-based criteria (quade, maxe and maxpe) overshot pm by a large amount for the three adhesives, and should not be considered as well. the xfem propagation law analysis showed good results for the triangular damage law for all adhesives, and the unsuitability of the exponential law. between the different  for the triangular law, =1 and 2 generally provided closer results than =0.5. references [1] petrie, e.m. handbook of adhesives and sealants. new york: mcgraw-hill; 2000. [2] akpinar, s. (2014). the strength of the adhesively bonded step-lap joints for different step numbers. compos: part b.67, pp. 170-178. doi: 10.1016/j.compositesb.2014.06.023. t f.j.p. moreira et alii, frattura ed integrità strutturale, 49 (2019) 435-449; doi: 10.3221/igf-esis.49.42 448 [3] di bella, g., borsellino, c., pollicino, e., ruisi, v.f. (2010). experimental and numerical study of composite t-joints for marine application. int j adhes adhes. 30, pp. 347-358. doi: 10.1016/j.ijadhadh.2010.03.002. [4] trask, r.s., hallett, s.r., helenon, f.m.m., wisnom, m.r. (2012). influence of process induced defects on the failure of composite t-joint specimens. composites part a: applied science and manufacturing. 43, pp. 748-757. doi: 10.1016/j.compositesa.2011.12.021. [5] bianchi, f., koh, t.m., zhang, x., partridge, i.k., mouritz, a.p. (2012). finite element modelling of z-pinned composite t-joints. compos sci technol. 73, pp. 48-56. doi: 10.1016/j.compscitech.2012.09.008. [6] burns, l.a., mouritz, a.p., pook, d., feih, s. (2012). bio-inspired design of aerospace composite joints for improved damage tolerance. compos struct.94, pp. 995-1004. doi: 10.1016/j.compstruct.2011.11.005. [7] yang, t., zhang, j., mouritz, a.p., wang, c.h. (2013). healing of carbon fibre–epoxy composite t-joints using mendable polymer fibre stitching. compos: part b.45, pp. 1499-1507. doi: 10.1016/j.compositesb.2012.08.022. [8] duan, k., hu, x., mai, y.-w. (2004). substrate constraint and adhesive thickness effects on fracture toughness of adhesive joints. j adhes sci technol.18, pp. 39-53. doi: 10.1163/156856104322746992. [9] panigrahi, s.k., pradhan, b. (2007). three dimensional failure analysis and damage propagation behavior of adhesively bonded single lap joints in laminated frp composites. journal of reinforced plastics and composites.26, pp. 183-201. doi: 10.1177/0731684407070026. [10] weißgraeber, p.a.w.b. crack initiation at weak stress singularities – finite fracture mechanics approach: procedia materials science; 2014. [11] da silva, l.f.m., campilho, r.d.s.g. advances in numerical modelling of adhesive joints. heidelberg: springer; 2012. [12] yang, q.d., thouless, m.d. (2001). mixed-mode fracture analyses of plastically-deforming adhesive joints. int j fract.110, pp. 175-187. doi: 10.1023/a:1010869706996. [13] khoramishad, h., crocombe, a.d., katnam, k.b., ashcroft, i.a. (2010). predicting fatigue damage in adhesively bonded joints using a cohesive zone model. international journal of fatigue 32, pp. 1146-1158. doi: 10.1016/j.ijfatigue.2009.12.013. [14] daudeville, l., ladevèze, p. (1993). a damage mechanics tool for laminate delamination. compos struct. 25, pp. 547555. doi: 10.1016/0263-8223(93)90203-3. [15] voyiadjis, g.z., kattan, p.i. damage mechanics. new york: marcell dekker; 2005. [16] raghavan, p., ghosh, s. (2005). a continuum damage mechanics model for unidirectional composites undergoing interfacial debonding. mechanics of materials. 37, pp. 955-979. doi: 10.1016/j.mechmat.2004.10.003. [17] imanaka, m., hamano, t., morimoto, a., ashino, r., kimoto, m. (2003). fatigue damage evaluation of adhesively bonded butt joints with a rubber-modified epoxy adhesive. j adhes sci technol. 17, pp. 981-994. doi: 10.1163/156856103322112888. [18] wahab, m.m.a., ashcroft, i.a., crocombe, a.d., shaw, s.j. (2001). prediction of fatigue thresholds in adhesively bonded joints using damage mechanics and fracture mechanics. j adhes sci technol.15, pp. 763-781. doi: 10.1163/15685610152540830. [19] mohammadi, s. extended finite element method for fracture analysis of structures. new jersey, usa: blackwell publishing; 2008. [20] moës, n., dolbow, j., belytschko, t. (1999). a finite element method for crack growth without remeshing. int j numer meth eng.46, pp. 131-150. doi: 10.1002/(sici)1097-0207(19990910)46:1<131::aid-nme726>3.0.co;2-j. [21] mubashar, a., ashcroft, i.a., crocombe, a.d. (2014). modelling damage and failure in adhesive joints using a combined xfem-cohesive element methodology. j adhesion.90, pp. 682-697. doi: 10.1080/00218464.2013.826580. [22] stuparu, f., constantinescu, d.m., apostol, d.a., sandu, m. (2016). a combined cohesive elements—xfem approach for analyzing crack propagation in bonded joints. j adhesion.92, pp. 535-552. doi: 10.1080/00218464.2015.1115355. [23] campilho, r.d.s.g., banea, m.d., pinto, a.m.g., da silva, l.f.m., de jesus, a.m.p. (2011). strength prediction of singleand double-lap joints by standard and extended finite element modelling. int j adhes adhes.31, pp. 363-372. doi: 10.1016/j.ijadhadh.2010.09.008. [24] campilho, r.d.s.g., banea, m.d., neto, j.a.b.p., da silva, l.f.m. (2013). modelling adhesive joints with cohesive zone models: effect of the cohesive law shape of the adhesive layer. int j adhes adhes.44, pp. 48-56. doi: 10.1016/j.ijadhadh.2013.02.006. [25] faneco, t., campilho, r., silva, f., lopes, r. (2017). strength and fracture characterization of a novel polyurethane adhesive for the automotive industry. j test eval.45, pp. 398-407. doi: 10.1520/jte20150335. [26] campilho, r.d.s.g., pinto, a.m.g., banea, m.d., silva, r.f., da silva, l.f.m. (2011). strength improvement of adhesively-bonded joints using a reverse-bent geometry. j adhes sci technol.25, pp. 2351-2368. f.j.p. moreira et alii, frattura ed integrità strutturale, 49 (2019) 435-449; doi: 10.3221/igf-esis.49.42 449 doi: 10.1163/016942411x580081. [27] nunes, s.l.s., campilho, r.d.s.g., da silva, f.j.g., de sousa, c.c.r.g., fernandes, t.a.b., banea, m.d., et al. (2016). comparative failure assessment of single and double-lap joints with varying adhesive systems. j adhesion.92, pp. 610634. doi: 10.1080/00218464.2015.1103227. [28] fernandes, t.a.b., campilho, r.d.s.g., banea, m.d., da silva, l.f.m. (2015). adhesive selection for single lap bonded joints: experimentation and advanced techniques for strength prediction. j adhesion.91, pp. 841-862. doi: 10.1080/00218464.2014.994703. [29] pike, m.g., oskay, c. (2015). xfem modeling of short microfiber reinforced composites with cohesive interfaces. finite elem anal des.106, pp. 16-31. doi: 10.1016/j.finel.2015.07.007. [30] abaqus®. documentation of the software abaqus®. dassault systèmes. vélizy-villacoublay 2013. [31] de sousa, c.c.r.g., campilho, r.d.s.g., marques, e.a.s., costa, m., da silva, l.f.m. (2017). overview of different strength prediction techniques for single-lap bonded joints. j mater des appl l.231, pp. 210-223. doi: 10.1177/1464420716675746. [32] xará, j.t.s., campilho, r.d.s.g. (2018). strength estimation of hybrid single-l bonded joints by the extended finite element method. compos struct.183, pp. 397-406. doi: 10.1016/j.compstruct.2017.04.009. << /ascii85encodepages false /allowtransparency false /autopositionepsfiles true /autorotatepages /none /binding /left /calgrayprofile (dot gain 20%) /calrgbprofile (srgb iec61966-2.1) /calcmykprofile (u.s. web coated \050swop\051 v2) /srgbprofile (srgb iec61966-2.1) /cannotembedfontpolicy /error /compatibilitylevel 1.4 /compressobjects /tags /compresspages true /convertimagestoindexed true /passthroughjpegimages true /createjobticket false /defaultrenderingintent /default /detectblends true /detectcurves 0.0000 /colorconversionstrategy /cmyk /dothumbnails false /embedallfonts true /embedopentype false /parseiccprofilesincomments true /embedjoboptions true /dscreportinglevel 0 /emitdscwarnings false /endpage -1 /imagememory 1048576 /lockdistillerparams false /maxsubsetpct 100 /optimize true /opm 1 /parsedsccomments 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/hrv (za stvaranje adobe pdf dokumenata najpogodnijih za visokokvalitetni ispis prije tiskanja koristite ove postavke. stvoreni pdf dokumenti mogu se otvoriti acrobat i adobe reader 5.0 i kasnijim verzijama.) /hun 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can be opened with acrobat and adobe reader 5.0 and later.) >> /namespace [ (adobe) (common) (1.0) ] /othernamespaces [ << /asreaderspreads false /cropimagestoframes true /errorcontrol /warnandcontinue /flattenerignorespreadoverrides false /includeguidesgrids false /includenonprinting false /includeslug false /namespace [ (adobe) (indesign) (4.0) ] /omitplacedbitmaps false /omitplacedeps false /omitplacedpdf false /simulateoverprint /legacy >> << /addbleedmarks false /addcolorbars false /addcropmarks false /addpageinfo false /addregmarks false /convertcolors /converttocmyk /destinationprofilename () /destinationprofileselector /documentcmyk /downsample16bitimages true /flattenerpreset << /presetselector /mediumresolution >> /formelements false /generatestructure false /includebookmarks false /includehyperlinks false /includeinteractive false /includelayers false /includeprofiles false /multimediahandling /useobjectsettings /namespace [ (adobe) (creativesuite) (2.0) ] /pdfxoutputintentprofileselector /documentcmyk /preserveediting true /untaggedcmykhandling /leaveuntagged /untaggedrgbhandling /usedocumentprofile /usedocumentbleed false >> ] >> setdistillerparams << /hwresolution [2400 2400] /pagesize [612.000 792.000] >> setpagedevice microsoft word numero_30_art_28 t. yin et alii, frattura ed integrità strutturale, 30 (2014) 220-225; doi: 10.3221/igf-esis.30.28 220 focussed on: fracture and structural integrity related issues on the use of the theory of critical distances to estimate the dynamic strength of notched 6063-t5 aluminium alloy t. yin, a. tyas department of civil and structural engineering, the university of sheffield, sheffield s1 3jd, united kingdom tyin4@sheffield.ac.uk, a.tyas@sheffield.ac.uk o. plekhov, a. terekhina institute of continuous media mechanics ub ras 1, ak. koroleva str., 614013 perm, russia poa@icmm.ru, tai_mm_90@mail.ru l. susmel department of civil and structural engineering, the university of sheffield, sheffield s1 3jd, united kingdom l.susmel@sheffield.ac.uk abstract. in this paper the so-called theory of critical distances is reformulated to make it suitable for estimating the strength of notched metals subjected to dynamic loading. the tcd takes as its starting point the assumption that engineering materials’ strength can accurately be predicted by directly post-processing the entire linear-elastic stress field acting on the material in the vicinity of the stress concentrator being assessed. in order to extend the used of the tcd to situations involving dynamic loading, the hypothesis is formed that the required critical distance (which is treated as a material property) varies as the loading rate increases. the accuracy and reliability of this novel reformulation of the tcd was checked against a number of experimental results generated by testing notched cylindrical bars of al6063-t5. this validation exercise allowed us to prove that the tcd (applied in the form of the point, line, and area method) is capable of estimates falling within an error interval of ±20%. this result is very promising especially in light of the fact that such a design method can be used in situations of practical interest without the need for explicitly modelling the non-linear stress vs. strain dynamic behaviour of metals. keywords. theory of critical distances; notches; dynamic fracture; al6063-t5. introduction t is well-known that, at room temperature, the mechanical behaviour of engineering materials under quasi-static loading is different from their behaviour under dynamic loading [1]. focussing attention on the material strength, it is seen from the experiments (see, for instance, refs [2-8] and references reported therein) that the failure stress, f, tends to increase as the loading/strain rate increases, this holding true both for steels and aluminium alloys. on the contrary, as far as the resistance to the propagation of cracks is concerned, examination of the state of the art [2, 8] suggests that the fracture toughness can either decrease, increase, or remain constant as the stress intensity factor (sif) i t. yin et alii, frattura ed integrità strutturale, 30 (2014) 220-225; doi: 10.3221/igf-esis.30.28 221 rate increases. tuning to finite radius stress concentrators, the few isolated investigations (see, for instance, ref. [9, 10]) which have been published in the technical literature so far make it evident that the problem of designing notched metals against dynamic loading has never been studied systematically. accordingly, there exists no universally accepted method which can be used in situations of practical interest to efficiently assess notched metallic components subjected to inservice dynamic loading. in this complex scenario, this paper reports on a attempt of reformulating the so-called theory of critical distances (tcd) [11] to make it suitable for estimating the dynamic strength of metals weakened by finite radius notches, the stress analysis being performed by accommodating the material non-linearities into a linear-elastic constitutive law. figure 1: definition of the local systems of coordinates (a) and effective stress, eff, calculated according to the point method (b), line method (c), and area method (d). reformulating the tcd to design notched metals against dynamic loading s far as notched materials subjected to quasi-static loading are concerned, the tcd postulates that static strength can accurately be estimated by directly post-processing the entire stress field acting on the material in the vicinity of the stress raiser being assessed [11]. the most important peculiarity of such a design method is that the required stress analysis can be performed by adopting a simple linear-elastic constitutive law, this holding true independently not only from the level of ductility characterising the mechanical behaviour of the material under investigation, but also from the degree of multiaxiality of the applied system of forces/moments [12-15]. according to the different formalisations of the tcd, the effective stress, eff, to be used to perform the static assessment can be calculated in terms of either the point, the line, or the area method as follows [11]:        2 l r,0yeff point method (pm) (1)    l2 0 yeff drr,0 l2 1 line method (lm) (2)       2 0 l 0 y2eff drdr, l 4 area method (am) (3) the meaning of the adopted symbols as well as of the effective stress determined according to these three different strategies is explained in fig. 1. in the definitions reported above, the critical distance, l, is a material property whose a nom nom  r x y y y eff eff r r eff point method line method area method (a) (b) (c) (d) l/2 l 2l t. yin et alii, frattura ed integrità strutturale, 30 (2014) 220-225; doi: 10.3221/igf-esis.30.28 222 value can directly be estimated by combining the plane strain fracture toughness, kic, with the so-called inherent material strength, 0, as follows [11-15]: 2 0 ick1l         (4) therefore, according to the tcd’s modus operandi, a notched engineering material subjected to in-service quasi-static loading does not fails as long as the effective stress, eff, is lower than the material inherent strength, 0 [11], i.e.: 0eff  (5) y 0 notch r linear-elastic stress distribution l/2 nom nom sharp notch blunt notch figure 2: determination of length scale parameter l and inherent strength 0 through experimental results generated by testing notches of different sharpness. eq. (4) and (5) make it evident that inherent material strength 0 plays a role of primary importance when the tcd is used to design notched components against static loading. as far as brittle materials are concerned, the inherent material strength is seen to be very close to the material ultimate tensile strength, uts [16]. on the contrary, when the fracture process zone experiences large scale plastic deformations, in general, 0 reaches a value which is somewhat larger than the ultimate tensile strength [11]. the latter consideration applies also to metallic materials, although, for certain metals, 0 is seen to be so close to uts [12] that the static assessment can accurately be performed by simply taking 0=uts. the considerations reported above clearly suggest that the only way to determine 0 is by testing notched specimens containing stress risers whose presence results in different stress distributions in the vicinity of the tested geometrical features [12-15]. such a procedure is summarised in fig. 2. in particular, according to the pm, the point at which the two linear-elastic stress-distance curves, plotted in the incipient failure condition, intersect each other allows both l and 0 to be estimated directly. as briefly mentioned above, the state of the art [1-7] shows that, in general, the mechanical response, the mechanical properties, and the cracking behaviour of metallic materials subjected to dynamic loading are different from the ones observed under quasi-static loading. having recalled this important aspect, the hypothesis can be formed that, similar to the dynamic failure stress, f, and the dynamic fracture toughness, kid, both the inherent material strength, 0, and the critical distance, l, may vary as the applied loading rate increases. therefore, according to definition (4), the critical distance under dynamic loading can be rewritten as follows: 2 0 id )f( )f(k1 )f(l            (6) where f is used to denote the loading rate. this new definition for critical distance l allows the effective stress to be determined under dynamic loading via the following definitions which are directly derived from eqs (1) to (3):        2 )f(l r,0)f( yeff   (pm) (7) t. yin et alii, frattura ed integrità strutturale, 30 (2014) 220-225; doi: 10.3221/igf-esis.30.28 223    )f(l2 0 yeff drr,0 )f(l2 1 )f(    (lm) (8)         2 2 )f(l 0 12eff drdrr, )f(l 2 )f(    (am) (9) therefore, a notched component is supposed to be able to withstand the applied dynamic loading as long as the following condition is assured: )f()f( 0eff   (10) owing to the complexity of the reasoning summarised in the present section, it is evident that a set of appropriate experimental results is required to check the validity of the formed hypotheses. this will be done in the next section. validation by experimental data n order to check the accuracy of the proposed reformulation of the tcd in predicting the strength of notched metals subjected to dynamic loading, an ad hoc experimental investigation was run in the testing laboratory of the sheffield university at harpur hill, buxton, uk. in more detail, twenty-six cylindrical samples of al6063-t5 were tested under both quasi-static and dynamic axial tensile loading. the loading was applied to the proximal end of the test sample, through a cross-head beam driven by pneumatic pressure. the distal end of the specimen was connected to a dynamic load cell which itself was connected to a stiff reaction frame. quasi-static loading was generated by slowly increasing the pneumatic driving load on the cross head, whilst dynamic loading was produced by storing pressurised air in a reservoir and releasing this suddenly to the cross-head by bursting a retaining diaphragm at the outlet of the reservoir. the un-notched specimens had net diameter, dn, equal to 5 mm and gross diameter, dg, to 10 mm. the bluntly notched specimens had dn=5 mm, dg=10 mm, and notch root radius rn equal to 4 mm, these resulting in a net stress concentration factor, kt, of 1.25. the samples containing both the intermediate and the sharp stress concentrators had dn=5.2 mm and dg=10 mm, the notch root radius being equal to 1.38 mm (kt=1.69) and to 0.38 (kt=2.93), respectively. the generated results are summarised in tab. 1 in terms of failure force, ff, time to failure, tf, and loading rate, f . in particular, the failure force, ff, was taken equal to the maximum force recorded during each test, the corresponding instant being used to define tf. accordingly, the loading rate, f , was directly estimated via the following trivial relationship: f f t f f  (11) the linear-elastic stress fields required to calculate the effective stress, eff, according to definitions (7) to (9) were determined by solving finite-element (fe) models done using commercial software ansys®. in these linear-elastic fe models the mesh in the vicinity of the notch apices was refined until convergence occurred. by assuming that 0( f ) could be taken equal to f( f ) [12], the results generated by testing both the plain and the sharply notched specimens were used, via a conventional best-fit procedure, to determine both material inherent strength 0( f ) and critical distance l( f ), by obtaining: 0118.0 f0 f9.209)f()f(   [mpa] (12) 0368.0f541.1)f(l   [mm] (13) tab. 1 summarises the accuracy of the tcd (applied in the form of the pm, lm, and am) in estimating the strength of the notched specimens we tested under both quasi-static and dynamic axial loading, the error being calculated as follows: )f( )f()f( error eff eff0      [%] (14) tab. 1 makes it evident that the use of the proposed reformulation of the tcd resulted in estimates falling within an error interval of ±20% (that is, in an accuracy level similar to the one which is usually obtained when the tcd is used in other i t. yin et alii, frattura ed integrità strutturale, 30 (2014) 220-225; doi: 10.3221/igf-esis.30.28 224 ambits of the structural integrity discipline [11]). such a high level of accuracy is certainly promising, especially in light of the fact that it was reached without the need for explicitly modelling the stress vs. strain dynamic behaviour of the tested aluminium alloy. accordingly, if the reliability and accuracy of the proposed approach were further confirmed by considering different metallic materials, this reformulation of the tcd could allow practitioners to perform the dynamic assessment of notched ductile components by remarkably reducing the time and costs of the design process. code dg dn rn kt ff tf f [mm] [mm] [mm] [kn] [s] [kn/s] s1 t1 10.0 5.0 plain 1.00 3.8 4.1 0.9268 s1 t2 10.0 5.0 plain 1.00 4.8 0.08 60.00 s1 t3 10.0 5.0 plain 1.00 4.1 35 0.1171 s1 t5 10.0 5.0 plain 1.00 4.6 0.05 92.00 s1 t6 10.0 5.0 plain 1.00 4 0.02 200.0 s1 t7 10.0 5.0 plain 1.00 4.4 0.006 733.3 s1 t8 10.0 5.0 plain 1.00 4.5 0.005 900.0 s1 t11 10.0 5.0 plain 1.00 4.1 0.004 1600 error [%] s1 t12 10.0 5.0 plain 1.00 4.7 0.01 470.0 pm lm am s1 t9 10.0 5.2 0.38 2.93 5.4 22 0.2455 -0.1 -2.2 4.4 s1 t10 10.0 5.2 0.38 2.93 6.7 0.004 1675 -1.4 3.0 3.9 s2 t1 10.0 5.2 0.38 2.93 6.8 0.007 971.4 1.4 5.4 6.9 s2 t2 10.0 5.2 0.38 2.93 6.7 0.007 957.1 0.0 3.9 5.3 s1 t17 10.0 5.2 1.38 1.69 4.6 29 0.1586 -1.5 -11.3 -3.0 s1 t18 10.0 5.2 1.38 1.69 6.2 0.003 2066.7 5.2 2.5 3.4 s2 t5 10.0 5.2 1.38 1.69 5.3 21 0.2524 12.2 1.2 10.5 s2 t6 10.0 5.2 1.38 1.69 5.1 16 0.3188 7.3 -3.0 5.7 s2 t7 10.0 5.2 1.38 1.69 6.7 0.007 957.1 15.9 11.8 13.8 s2 t9 10.0 5.2 1.38 1.69 6.2 0.009 688.9 8.1 3.9 6.2 s2 t10 10.0 5.2 1.38 1.69 6.9 0.007 985.7 19.3 15.1 17.1 s2 t11 10.0 5.2 1.38 1.69 4.9 11 0.4455 2.3 -7.4 0.7 s2 t12 10.0 5.2 1.38 1.69 5.2 16 0.3250 9.4 -1.1 7.7 s2 t13 10.0 5.2 1.38 1.69 6 0.007 857.1 4.1 0.2 2.2 s2 t14 10.0 5.2 1.38 1.69 5.9 0.009 655.6 3.0 -1.1 1.2 s1 t15 10.0 5.0 4.00 1.25 3.7 30 0.1233 -9.1 -16.4 -9.7 s1 t16 10.0 5.0 4.00 1.25 3.5 23 0.1522 -14.3 -21.2 -15.0 table 1: summary of the generated experimental results and accuracy of the proposed re-formulation of the tcd in estimating the quasi-static/dynamic strength of the tested notched samples of al6063-t5. conclusions 1) the proposed reformulation of the tcd was seen to be successful in estimating the strength of the notched specimens of al6063-t5 we tested under both quasi-static and dynamic axial loading. 2) thanks to its specific features, the proposed design methodology allows real notched components to be designed against dynamic loading by directly post-processing the relevant stress fields estimated via conventional linear-elastic fe models. this implies that an accurate assessment can be performed without the need for explicitly modelling the material response under dynamic loading. t. yin et alii, frattura ed integrità strutturale, 30 (2014) 220-225; doi: 10.3221/igf-esis.30.28 225 3) more work needs to be done in this area to further check the accuracy and reliability of the proposed design methodology against experimental results generated by testing, under dynamic loading, notched metallic materials characterised by different levels of ductility. acknowledgements he perm regional government № с-26/619, russia, is acknowledged for supporting the present research investigation. references [1] kolsky, h., an investigation of the mechanical properties of materials at very high rates of loading, in: proc. phys. soc. b, 62 (1949) 676-700. [2] wiesner, c.s., macgillivray, h., loading rate effects on tensile properties and fracture toughness of steel, in: 1999 tagsi seminar, cambridge, iom publication (1999). [3] lindholm, u.s., bessey, r.l., smith, g.v., effect of strain rate on yield strength, tensile strength, and elongation of three aluminium alloys, j mater., 6 (1971) 119-33. [4] oosterkamp, l.d., ivankovic, a., venizelos, g., high strain rate properties of selected aluminium alloys, materials science and engineering a, 278 (2000) 225-235. [5] lee, o.s., kim, m.s., dynamic material property characterization by using split hopkinson pressure bar (shpb) technique. nuclear engineering and design, 226 (2003) 119-125. [6] xm, z., et al., dynamic property evaluation of aluminum alloy 2519a by split hopkinson pressure bar, transactions of nonferrous metals society of china (english edition), 18 (2008) 1-5. [7] sakino, k., strain rate dependence of dynamic flow stress of 2017 aluminum alloy at very high strain rates. international journal of modern physics b, 22 (2008) 1209-1214. [8] yokoyama, t., kishida, k., a novel impact three-point bend test method for determining dynamic fracture-initiation toughness. experimental mechanics, 29 (1989) 188-94. [9] brisbane, a. w., the investigation of the effects of loading rate and stress concentration factors on the notch properties of three sheet alloy at subzero temperatures, technical documentary report no. asd-tdr-62-930, project no. 7351, task no. 735106, directorate of material and processes, wright-patterson air force base, ohio, usa (1963). [10] wang, g.z., wang, y.l., chen, j.h. effects of loading rate on the local cleavage fracture stress �f in notched specimens, engineering fracture mechanics, 72 (2005) 675–689. [11] taylor, d., the theory of critical distances: a new perspecive in fracture mechanics: elsevier science limited, oxford, uk, (2007). [12] susmel, l., taylor, d., on the use of the theory of critical distances to predict static failures in ductile metallic materials containing different geometrical features. engineering fracture mechanics, 75 (2008) 4410-4421. [13] susmel, l., taylor, d., the theory of critical distances to predict static strength of notched brittle components subjected to mixed-mode loading, eng. frac. mech., 75 (2008) 534-550. [14] susmel, l., taylor, d., the theory of critical distances to estimate the static strength of notched samples of al6082 loaded in combined tension and torsion. part i: material cracking behaviour, eng. frac. mech., 77 (2010) 452-69. [15] susmel, l., taylor, d., the theory of critical distances to estimate the static strength of notched samples of al6082 loaded in combined tension and torsion. part ii: multiaxial static assessment, eng. frac. mech., 77 (2010) 470-8. [16] taylor, d. predicting the fracture strength of ceramic materials using the theory of critical distances, engng. fract. mech., 71 (2004) 2407-2416. t microsoft word numero_30_art_58 a. de iorio et alii, frattura ed integrità strutturale, 30 (2014) 478-485; doi: 10.3221/igf-esis.30.58 478 transverse strength of railway tracks: part 1. planning and experimental setup antonio de iorio polytechnic school of basic sciences, federico ii university, naples, italy antdeior@unina.it marzio grasso, francesco penta, giovanni pio pucillo dii department of industrial engineering, federico ii university, naples, italy paolo pinto edge s.r.l., milan, italy stefano rossi, mario testa rfi italian state railways, rome, italy giuseppe farneti italcertifer, notified organism, florence, italy abstract. several studies have been carried out until now by various research agencies and railway administrations to quantify the effects of the track-bed geometrical characteristics on the transverse strength of the track. unfortunately, not all the possible scenarios in terms of track components, track-bed cross profile, operating conditions etc. have been investigated and not all the relevant variables have been directly measured. therefore data available from the literature have different degrees of reliability. with the aim of enlarging the knowledge on the track stability and covering much of the possible relevant scenarios, an experimental research program has been developed in the framework of a cooperation between rfi, italcertifer and dii. in order to perform the investigation under quite general conditions and to reduce the experimentation costs, n. 28 significant scenarios have been identified and reproduced on as many independent track segments. by applying on each track segment a transversal load, the strength of the ballast-sleeper interface has been determined. the results relative to the first four scenarios are presented in terms of applied load vs. lateral track displacement diagrams and in more synthetic numerical tables. keywords. ballast resistance; track stability; full scale test; cwr track; railway track. a. de iorio et alii, frattura ed integrità strutturale, 30 (2014) 478-485; doi: 10.3221/igf-esis.30.58 479 introduction rom the analysis of the technical literature concerning the continuous welded rail (cwr) problems, it can be inferred that together with the noteworthy advantages that it offers when compared to the traditional solution, in terms of both maintenance, comfort and performance, some essential precautions are needed. among these, the most important from the structural design point of view is related to the track buckling (usually in the horizontal plane, although the phenomenon can occur also in the vertical plane [1]) caused by the rail temperature increases due to sun irradiation or train induction brakes [2]. the phenomenon takes place especially in presence of eccentricity due to track misalignments, in the neighbourhood of bends, bridges and other track singularities or when the neutral temperature is decreased due to creep [3, 4]. this latter is an effect particularly important near tunnels, in correspondence of strong gradients or in bents [2]. also if the track neutral temperature can be restored to a safe value by periodic maintenance, very often the effects of local variability cannot be eliminated [4]. when rail temperature exceeds the maximum allowable value it is mandatory to reduce the rolling stock speed. furthermore, several authors have pointed out that loads (included the longitudinal ones) exerted on the track by trains can contribute to exceed the lateral strength limit [6], also due to the up-lift: design data for high speed trains and examples of horizontal track loads evaluation are also reported in [6]. in [6-8] it is demonstrated that track lateral strength offers a safety margin against lateral buckling and that most of the track strength is due to the friction between the sleepers base and the ballast; other important lateral strength contributions are given by the presence of ballast near the heads of the sleepers, the ballast parts included between successive sleepers and the ballast shoulders. the relative importance of these strength contributions depends on the track weight [6]. however, it is very difficult to trace a curve representative of the weight effect also because of the experimental data lack: until now direct measurements of track lateral strength have been carried out only with no more than two different weights of the track. other parameters that can affect the lateral strength are time, since the ballast mechanical properties degrade with time and, finally, the sleeper shape that affects the resultant friction force against the ballast. also the kind of fastening system between sleepers and rails can affect the track lateral strength [9]. when the track moves sideways, sleepers can remain parallel to each other or show a relative rotation [10, 11]. which of these behaviours predominates depends on the ballast strength and the primary and secondary twisting stiffness of the fasteners. however, it has not been possible to the authors finding in literature test data parameterized with fastener stiffness. in consequence of ballast maintenance operations, the lateral strength can be reduced up to the 40% of its full value. therefore, some operations cannot be carried out when the rail temperature is high, while some others are done imposing a reduced train speed until the ballast is consolidated [12]. a reliable solution to improve the track lateral stability is the adoption of sleeper anchors; unfortunately they involve additional costs. a related problem also very often examined is the track displacement in curves due to the thermal deformations of the cwr. it lays down precise limits to the cwr construction: curves having radius less than a given threshold value cannot be made by the continuous rail. several studies have been carried out on the contributions brought to the lateral strength by the geometrical details of the track [3, 6, 12]. most of them do not cover all the aspects involved: very often the scheduled experimental activities were not finished [6]. the tests usually were not repeated, when they were, the number of repetitions was quite low or however aprioristically fixed. sometimes, the reported experimental results are partially censored (see, f.e., [3]); in addition, data are referred to an uniform ballast also if generally the presence of water pockets [6] or other singularities can alter the ballast behaviour. on the basis of these data, that have limited and different reliability, several theoretical models and design software’s have been developed in order to make deterministic and probabilistic previsions about the cwr buckling behaviour (see, f.e., [3, 5, 7, 8, 11, 13, 14, 15]) and to establish an allowable buckling risk [1, 2, 5, 16], if the risk based approach is adopted. in addition to the buckling phenomenon probability, this latter approach takes account of the seriousness of its consequences [5]. in order to improve the reliability of the aforementioned tools adopted for the prediction of the ballast behaviour, an experimental activity wider and more realistic than those usually carried out till now by the institutions interested in this topic and in funding such research programs is needed. starting from this latter observation, rfi and dii have shown their interest in sharing resources and competences to develop a demanding research program. together with italcertifer, italian institute of railway research and certification, f a. de iorio et alii, frattura ed integrità strutturale, 30 (2014) 478-485; doi: 10.3221/igf-esis.30.58 480 they are partners in a research project whose main aim is a program of full scale tests on a great number of infrastructure archetypes simulating real scenarios of the track service conditions. experimental program rom the analysis of both data required to identify the critical service conditions for the type of tracks described in the technical specification (elaborated ad hoc by rfi [17]) and those gathered in literature, useful guidelines have been drawn in order to plan out the type of tests and their number. this information is necessary to define the range of variation of all the parameters on which the aforementioned critical situations depend. the parameters are:  type of sleeper (ai);  degree of ballast compaction (bi);  shoulder dimension (ci);  distance of the end of the sleeper from the ballast retaining wall (di);  height of the ballast in correspondence of the ends of the sleeper (ei);  type of the anchor of the sleepers (fi);  effect of the superelevation-cant (gi);  lowered ballast profile between two sleepers for a width of 2 m (1 m for each side in respect to the track axis) (hi);  height of ballast under the sleeper (ii);  applied vertical load (li);  type of ballast material (mi). the combinations of all these parameters would obviously lead to define an onerous number of scenarios to be reproduced in the experimentation if the subscript “i” assumes at least 3÷4 different values, therefore it is compelled to make a trade-off choice in order to realize a narrow number of tests, but sufficiently significant to make, on the basis of the results obtained from them, both numerical and mathematical models able to effectively simulate all the scenarios corresponding to the parameter values belonging to the predetermined fields of variation. on the basis of significance and representativeness considerations of the chosen track service conditions, as well as of economies of scale, 28 scenarios have been selected; they are summarized in tab. 1. m1, c2, h1, e1, a1, i1, b1, l1 m1, c2, h1, e1, a2, i1, b2, l2 m1, c2, h1, e1, a2, i3, b2, l1 m1, c2, h1, e1, a1, i3, g2, b1, l1 m1, c2, h1, e1, a1, i1, b1, l2 m1, c2, h1, e1, a1, i1, b2, l1 m1, c2, h1, e1, a2, i3, b2, l2 m1, c2, h1, e1, a1, i3, g2, b2, l1 m1, c2, h1, e1, a2, i1, b1, l2 m1, c2, h1, e1, a1, i1, b2, l2 m1, c2, h1, e1, a2, i3, b1, l1 m1, c2, h1, e1, a1, i3, g2, b2, l2 m1, c2, h1, e1, a2, i1, b1, l1 m1, c2, h1, e1, a1, i3, d3, b2, l1 m1, c2, h1, e1, a2, i3, b1, l2 m1, c2, h1, e1, a1, i3, f2, b2, l2 m1, c2, h1, e1, a2, i1, d3, b2, l2 m1, c2, h1, e1, a1, i3, d3, b2, l2 m1, c2, h1, e1, a1, i3, b1, l1 m1, c2, h1, e1, a1, i3, f2, b2, l1 m1, c2, h1, e1, a2, i1, d3, b2, l1 m1, c2, h1, e1, a1, i3, b2, l1 m1, c2, h1, e1, a1, i3, b1, l2 m1, c2, h1, e1, a1, i3, f1, b2, l1 m1, c2, h1, e1, a2, i1, b2, l1 m1, c2, h1, e1, a1, i3, b2, l2 m1, c2, h1, e1, a1, i3, g2, b1, l2 m1, c2, h1, e1, a1, i3, f1, b2, l2 a1 = rfi 230 pre-stressed concrete sleepers; a2 = rfi 240 pre-stressed concrete sleepers. b1 = de-consolidated ballast bed; b2 = dts consolidated ballast bed. c2 = 60 cm ballast shoulder. d3 = ballast retaining wall 60 cm apart from the sleeper end. e1 = regular ballast shoulder top profile. f1 = sleeper anchors at every 2nd sleeper; f2 = sleeper anchors at every sleeper. g2 = canted track. h1 = non lowered ballast profile. i1 = 30 cm ballast thickness; i3 = 60 cm ballast thickness. l1 = unloaded track; l2 = loaded track. m1 = regular ballast material. table 1: scenarios included in the testing plan: characterizing parameters. in order to establish a future correlation between test results and geometrical, mechanical and behavioural characteristics of all components and related materials used during testing, it has been decided to perform also a series of f a. de iorio et alii, frattura ed integrità strutturale, 30 (2014) 478-485; doi: 10.3221/igf-esis.30.58 481 characterization tests on the components and materials that were not already tested by the suppliers. on the basis of the choices made to define the scenarios, the ballast was the only material/component that needed a special investigative attention; for it both a geometrical characterization test program, to be carried out in the laboratory on the aggregate, and a series of loading and seismic tests in the service conditions (on the instrumented track) have been defined. in particular, the latter tests have been planned in order to evaluate those parameters that can affect the ballast capacity of constraining in the long run the displacements of the sleepers in their axial direction, under the action of the destabilizing forces acting on the rails. experimental methodologies and testing plan n the laboratory the following characterization tests, in accordance with the standard shown in brackets, have been planned for the rocks that compose the ballast:  granulometric properties of ballast grains (uni en 933-1 4/99);  shape index (uni en 933-4 4/01);  apparent particle density of ballast grains (uni en 1097-6 ann. b 2/02);  los angeles-test (uni en 1097-2); in order to characterize in situ the ballast, in other words on the instrumented permanent way, the following tests have been introduced in the plan:  dynamic plate load test;  seismic tests. the chosen kind of seismic test is the seismic refraction profile in p and s wave velocities and has an investigation depth of 1 m. it consists in positioning along a line-up (sub horizontal and straight – for instance parallel and external to the track) n. 12 seismic sensors (geophones), 0.5 m far-between them and fixed in the ballast; along this alignment, n. 5 explosion points for the p-wave are positioned, two of which placed outside the furthest geophones (g1 and g12 in fig. 1) at 0.25 m from them, one placed at the centre of the alignment and two in-between the furthest and the central explosion points. figure 1: arrangement layout of the geophones and the explosion points in the seismic tests. also, n. 2 explosion points for the s wave outside the furthest geophones (coincident to the first two for the p wave) will be realized by whacking with a hammer the vertical faces of a metallic plate having parallelepiped shape. to understand, then, the influence of other structural parameters of the tracks on the stability of the system, tests on track panels reproducing the planned scenarios have been scheduled. these tests consist in applying on the rails a load i a. de iorio et alii, frattura ed integrità strutturale, 30 (2014) 478-485; doi: 10.3221/igf-esis.30.58 482 orthogonal to them and parallel to the running plane, until extended flows in the ballast, corresponding to yielding of the ballast at the interface with the sleeper, occurs. track panels are composed of n. 4 sleepers at least and extracted from a continuous track built according to the prescriptions needed to reproduce in each of them a scenario different from all others. the use of the track panels allows to test several sleepers at the same time reducing the total time of the experimentation. moreover, the goodness of the results is not affected by this approach since the results, which are referred to a general sleeper belonging to a given scenario, are computed averaging the results of all sleepers of the scenario tested under the same conditions for the chosen series of geometrical configurations of the track and for one ballast material, by means of these tests, the strength offered by the ballast against the longitudinal displacement of the sleeper, crosswise the permanent way, under loading and unloading conditions, is determined. full-scale tests on railway sections have been carried out according to the following practice: 1. a structure for load-transfer (cluster) is constrained to the track in at least n. 8 points; 2. a tensile load, transversal to the track and parallel to the running plane, is applied on the aforementioned system, until a displacement greater than 30 mm is produced, acquiring both load and displacement values with a sampling rate high enough to plot the load-displacement curve; 3. the contiguous track is loaded, symmetrically to the load axis of the cluster system, by means of a 2 t mass/sleeper; 4. the test load is applied as in point 2 and the load-displacement curve is acquired. to carry out these tests in addition to, obviously, the hydraulic ram, the load cell, the displacement transducer and the high frequency data acquisition system the following equipments are needed: a constraining structure; block shaped masses, up to a total of 2 t/sleeper, laying on the track with the centre of mass in correspondence of the loading axis of the cluster system; an interface structure between rail/loading blocks that allows loading and centring of the masses. figure 2: schematic top view of the tested track segment (not in scale). to conduct the full-scale tests in the same place for the different scheduled scenarios, the testing plan on the track schematized in fig. 2 has been designed. in this figure different colours represent different zones. in particular, the green blocks represent the transition zones between two contiguous scenarios, while the blue one refer to canted track scenarios (only for rfi 230 sleepers). red and cyan blocks represent scenarios with ballast retaining wall and anchors mounted on ties, respectively, while the brown one represents “classical” scenarios, namely straight track without accessories (such as anchors). testing rig o implement the testing plan, an area of the naples campi flegrei railway station has been prepared for the experimental activities. from two old tracks two segments having length equal to about 200 m are removed. a new track is rebuilt in place of the old ones, in such a way to match the specifications for the 28 scheduled tests (fig. 3). the construction details of the testing plant and the procedure adopted to carry out the tests on all the selected scenarios will be published shortly together with the acquired results. in the present paper, some graphs related to the first results acquired during the transverse tests carried out on four of the most common scenarios are reported (see fig. 4). in particular, the curves depicted in the aforementioned graphs refer to the scenarios reported in the figures with the abbreviations lrs01, lrs04, lrs06, lrs07, which correspond to the following configurations, respectively:  lrs01: n. 4 rfi 230 sleepers, 60 cm ballast shoulder, 30 cm ballast thickness, de-consolidated ballast bed.  lrs04: n. 4 rfi 240 sleepers, 60 cm ballast shoulder, 30 cm ballast thickness, de-consolidated ballast bed.  lrs06: n. 4 rfi 240 sleepers, 60 cm ballast shoulder, 30 cm ballast thickness, dts consolidated ballast bed, ballast retaining wall.  lrs07: n. 4 rfi 240 sleepers, 60 cm ballast shoulder, 30 cm ballast thickness, dts consolidated ballast bed. t a. de iorio et alii, frattura ed integrità strutturale, 30 (2014) 478-485; doi: 10.3221/igf-esis.30.58 483 figure 3: photographic top view of the chosen testing field. figure 4: load vs. track displacement curves for some typical scenarios. the different components of the track panels are listed in tab. 2. the maximum values of the ballast resistance, corresponding to a single sleeper, together with the limit values which correspond to the sliding of the sleeper on the ballast due to pseudo plastic failure of this latter, are reported in tab. 3. the interpretation and the use of these results will be widely discussed in other papers, once the test campaign is completed. a. de iorio et alii, frattura ed integrità strutturale, 30 (2014) 478-485; doi: 10.3221/igf-esis.30.58 484 name type reference standards rail 60e1 en 13674-1 fastening system elastic type en 13481-2, en 13146-1÷7 concrete sleeper rfi 230 rfi 240 en 13230-2:2002 table 2: track components. scenario lrs 01 lrs 04 lrs 06 lrs 07 peak resistance [n] 5˙545 7˙715 10˙000 8˙840 limit resistance [n] 4˙370 7˙100 9˙100 8˙100 table 3: peak and limit values for scenarios of fig. 4. the presented experimental test program, besides being a collection of raw test data (obtained with a substantial funding) driven by the need to expand the field’s knowledge, will be a source of results directly useful for building up and validating a reliable cwr track model for a wide range of service conditions in terms of both scenarios and mechanical as well as environmentally induced loads that are able to produce the buckling phenomenon. conclusions relevant set of data concerning lateral track strength, directly useful for track design and maintenance, will be obtained through a series of full scale tests carried out on a number of different track layouts with various geometric configurations. in the present paper planning of the experimental activities as well as some details of the testing types and methodologies were described. as an example, the results of the first transverse tests carried out on four track panels corresponding to just as many scenarios were reported. the characterization of both materials and components used for the tested infrastructure will allow to identify a correlation between the parameters determining their mechanical behaviour and results obtained from full-scale testing. these latter will be used as starting point for the numerical modelling activity of the track system and for the final validation of a new track model, which is the true final aim of the present activity, offering to the railway technicians a more versatile and reliable tool for the design and management of the railway service. bibliography [1] sung, w., shih, m., lin, c., go, c.g., the critical loading for lateral buckling of continuous welded rail, journal of zehjiang university science, 6a (8) (2005) 878-885. [2] uic code 720 r, laying and maintenance of cwr track (2005). [3] improved knowledge of cwr track, coenraad esveld. [4] read, d.m., kish, a., clark, d. w., optimized readjustment length requirements for improved cwr neutral temperature management, in: arema conference, (2007) [5] kish, a., samavedam, g., risk analysis based cwr: track buckling safety evaluations, in: proceedings of the international conference on innovations in the design & assessment of railway, (1999). [6] erri dt202/dt363, improved knowledge of forces in tangential tracks including switches, determination of lateral and longitudinal ballast resistance of a railway track by experimental tests, utrecht, (1997) 2. [7] kish, a., samavedam, g., wormley, d., new track shift safety limits for high speed rail applications, in: proceedings of world congress on railway research, cologne, germany, (2001). a a. de iorio et alii, frattura ed integrità strutturale, 30 (2014) 478-485; doi: 10.3221/igf-esis.30.58 485 [8] analyses of track shift under high speed vehicle-track interaction, us department of transportation, dot/fra/ord-97/02, dot vntsc-fra-97-3 (1997). [9] lim, n. h., sung, i. h., thermal buckling behavior of continuous welded rail track, steel structures, 4 (2004) 111119. [10] poonia, r.s., understanding long welded rail, permanent rail bulletin, indian railways, 34 (1) (2007). [11] van, m.l., buckling analysis of continuous welded rail track, heron [0046-7316], 41 (1996) 3. [12] sussmann, t., kish, a., investigation on the influence of track maintenance on the lateral resistance of concrete tie track, trb annual meeting, (2004). [13] a new set of computer models for analyzing, cwr, coenraad esveld, esveld consulting services. [14] esveld, c., a better understanding of continuous welded rail track, rail engineering international edition, 4 (1996). [15] lim, n. y., parametric study on stability of continuous welded rail track-ballast resistance and track irregularity, steel structures, 8 (2008) 171-181. [16] kish, a., sussmann, t., trosino, m., effects of maintenance operations on track buckling potential, in: proceedings of international heavy haul association, (2003). [17] technical specification, rfi, rome, (2008). microsoft word numero_49_art_34_2418 a. guillalet alii, frattura ed integrità strutturale, 49 (2019) 341-349; doi: 10.3221/igf-esis.49.34 341 focused on fracture mechanics versus environment effect of shape factor on structural reliability analysis of a surface cracked pipeline-parametric study abdelkader guillal université m’hamed bougara de boumerdès guillal.abdelkader@univ-boumerdes.dz, https://orcid.org/0000-0001-7236-4928 noureddine abdelbaki université akli mohaned oulhadj de bouira abdelnor215@gmail.com, http://orcid.org/0000-0002-2345-6790 mohamed el amine bensghier, mourad betayeb université m’hamed bougara de boumerdès mohamed.el.amine.ben.seghier@gmail.com, https://orcid.org/0000-0002-5854-775x mouradbettayeb@gmail.com, https://orcid.org/0000-0002-7751-2034 bogdan kopei ivano-frankivsk national technical university of oil and gas kopeyb@ukr.net, http://orcid.org/0000-0002-5445-103x abstract. the variation of crack shape factor (a/c) during propagation has an important role on calculation of the stress intensity factor (sif), where imprecise estimation of this latter can lead us to an inaccurate prediction of failure probabilities. for the case of external cracked surface pipeline carried oil and gas products, such estimation can results undesired fault decisions like excessive repairs action or inspection planning. in this paper, the structural integrity analysis of pipeline with semi elliptical crack on the external surface is evaluated. reliability calculations expressed in term of reliability index β are carried out based on monte carlo simulation and first order reliability method (form). the crack shape factors are varied to cover a variety of geometries from shallow to deep cracks while fatigue crack growth is assumed in depth direction. for sif estimation, surface and deep point are considered. results of the analysis indicate that for a constant crack depth a/t, the reliability index is strongly affected by a/c ratio and the trend is not similar in deep and surface point for different crack shapes. keywords. crack, pipeline, reliability, failure index, monte carlo simulation. citation: guillal, a., abdelbaki, n., bensghier, m.e.a., kopei, b., effect of shape factor on structural reliability analysis of a surface cracked pipeline-parametric study, frattura ed integrità strutturale, 49 (2019) 341-349. received: 02.03.2019 accepted: 05.05.2019 published: 01.07.2019 copyright: © 2019 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. http://www.gruppofrattura.it/va/49/2418.mp4 a. guillalet alii, frattura ed integrità strutturale, 49 (2019) 341-349; doi: 10.3221/igf-esis.49.34 342 introduction ne of the strategic energy resources are oil and natural gaz. they have the advantage to ensure a continues and reliable energy supply with an acceptable cost. an important reason behind this success is the reliability of system transmission via pipeline from zone of production to market zone. pipes carrying such hazardous products are subject to different type of defects. crack growth in pipelines is an inevitable problem due to its nature. cracks in pipeline can have different origins such as pipe manufacturing defect, welding defect or external damage. crack growth may lead to a real concern about structural performance and failure of system production. the reliability and the fracture prediction of such piping systems are primordial given their impact on the economic plan and safety. several researchers studied the fracture behavior of pipes containing semi elliptical surface cracks and the change of crack shape during fatigue crack growth. zhang and ferguson [1] developed model to predict crack shape development, under fatigue. induced cyclic fatigue is due to service fluctuating pressure in pipeline based on api579 stress intensity factor calculation and paris law. for given initial a/c and a/t, final crack length with the crack propagation to through-wall thickness can be predicted. they found that crack shape development is strongly influenced by initial crack shape and depth ratios. the bs 9710 standard proposes an approximate integration method for fatigue life estimation. mahmoud [2] compared different methods used to predict crack shape development during fatigue crack growth in tension plate with experimental data. the used methods are based on analytical and empirical equations. the comparison shows that analytical method based on local sif (kloc) calculated according to newman and raju formula [3] and the assumption of cc=0.9ca (cc and ca are fatigue crack growth rate in surface and deep point) is the best solution over the full range of initial crack shape values compared to experimental data with standard deviation less than 0,07. boukharouba [4] reviewed proposed prediction model of crack shape factor evolution with depth ratio in fatigue cracking test for the following cases: tension plate, three point bending plates and tube under internal pressure. for the last case, they conclude that a/c ratio passes by maximum (growth in deep direction is more rapid comparing to surface direction) then remains steady following horizontal asymptote during crack growth. another important conclusion is that behavior of a/c evolution is similar in thick plate under tension and thick tube under internal pressure. this finding can be supported by the work of zhu and tao [5] where they found that stress distribution and stress intensity factor in plate and pipe are similar for the same magnification load. probabilistic methods are widely used when evaluating the structural performance due to theirs advantages. different mechanisms failure are studied using probabilistic methods such as corroded pipelines in [6-8] in comparing to deterministic methods or assessment again target reliability using calibration safely factor, it gives many advantages. the large number of input parameter involved in structural analysis, evaluation of failure probability can be optimized using probabilistic methods. use of worst case input parameters and very pessimistic estimations can be avoided. in probabilistic fatigue calculation many authors take into consideration crack growth in depth direction only for simplification purpose [9] or assume basic paris crack growth in depth and surface direction where crack growth rates are equal : ca=cc [10]. leander and al-emrani [11] published reliability fatigue assessment of steel bridge. they illustrated the effect of initial crack aspect ratio on fatigue lifetime. they found that for a target reliability of 3.1 and gumbel distribution of stress range, crack with initial a/c=1 had longer fatigue life then crack with initial a/c=0. however, the effect of shape factor variability on the estimation of reliability index is a point not well illustrated. the influence of random character of initial shape ratio on crack shape development, during probabilistic analysis has to be more clarified according to proposed crack shape prediction model. in this work, the effect of crack shape factor on reliability index calculation is considered. the aim is to show the lack of precision associated to inaccurate estimation of shape factor during crack growth. the variation of reliability index with crack shape factor is illustrated with plots at constant crack depths. this paper is structured as follow. probabilistic model based on liner elastic fracture mechanics was established. a developed reliability method called “importance sampling at the design point “was used to generate simples. this method is a simulation method based on crude monte carlo method. then a case study of pipeline with axially external defect is applied. probabilistic model liner elastic fracture mechanics iner elastic fracture mechanics (lefm) is widely used to evaluate structural reliability of onshore pipelines. early model of lefm simplify the relation modeled using triangle in fig. 1. therefore, three main parameters are involved as load, defect size and fracture toughness. in real situation, the problem is more complex; where many o l a. guillalet alii, frattura ed integrità strutturale, 49 (2019) 341-349; doi: 10.3221/igf-esis.49.34 343 parameters characterized by their uncertainties are involved and alter the three cited parameters such: fluctuating pressure, crack shape, constrain and other parameters. stress intensity factor (sif) is the most common parameter used to represent driving forces that allow surface crack to propagate. the early formula of irwin for stress intensity factor is developed by many researchers. closed form solution for sif where derived for many simple configurations. newman and raju have proposed an empirical stress intensity factor equation for sif estimation expressed by the following formula: ( )i t b a k s s f q     (1) where st represent remote uniform-tension stress, sb is the remote bending stress on outer fiber, q is the shape factor for elliptical crack and f is the stress-intensity boundary-correction factor. figure 1: stress-intensity boundary-correction factor uncertainties related to cracked surface in pipeline several uncertainties are related to fatigue life estimation of onshore pipeline. scatter in material proprieties, loading conditions, crack initial dimensions and pipeline geometrical configuration are input parameters for failure probability estimation, in which these parameters have large influence on calculation precision [12]. in probabilistic analysis, these parameters are presented as random variables. in practice, it is difficult to obtain an applicable representation of its randomness. when data are available from laboratory test or from service inspection, statistical representation can be derived easily. in other cases, the definition of scatter can be done by gathering variability of data from previous literature considering specification of the actual study. uncertainties related to loading parameters the applied load on oil and gas pipeline in case of axial surface crack is a circumferential stress due to internal pressure which is calculated via barlow equation presented in eqn. (1): * 2 * b p d s t      (2) where: ∆σ: applied pipeline wall stress range (mpa). d: pipeline diameter (mm). ∆p: fluctuating pressure range (mpa). t: pipeline wall thickness (mm). the uncertainties considered for load parameters are related to variation of all parameters involved in stress estimation, typically the geometrical (d, t) parameters and service pressure (∆p). during assessment of pipeline subjected to fatigue crack growth, both maximum operating pressure and actual operational characteristics should be considered. the first indicate the maximum cyclic stress experienced by the pipeline. the second gives information about increase and drop in operating pressure (∆p) and the frequency of cyclic stress. the direct way to quantify the cyclic pressure experienced during service time is pressure time history recording. the information gathered a. guillalet alii, frattura ed integrità strutturale, 49 (2019) 341-349; doi: 10.3221/igf-esis.49.34 344 by this record is the fluctuating pressure range and number of times that take place. to make this information useful as a constant amplitude pressure change events during time period, a cycle counting method as rain flow method can applied to obtain the pressure range histogram. to easily asses and compare the cyclic severity of a given pressure time history, stress severity indicator (ssi) is efficient tool. ssi is the number of cycles of a given pressure range required to grow a crack the same amount as the actual pressure time history over one year. an example is illustrated in fig. 2 where ssi of 150 mpa equivalent cycles is used. figure 2: spectrum severity indicator. limit state function of cracked pipeline reliability problem related to fatigue cracks in pipelines can be expressed using limit state function (lsf) that separate the failure region (lsf 0) (e.g. plastic collapse, fracture) and the safe region (lsf>0). the considered limit state in this work is based on lefm where it defines the failure as fracture that the crack growing force represented by stress intensity factor ki reaches a critical value equivalent to fracture toughness kic, therefore the limit state function can be represented as follow: iic lsf k k  (3) from above the considered problem is modeled as probability of failure estimation where the goal is to calculate failure probability of each crack configuration based on simulation or analytical methods such as the monte carlo simulation or form method. the eqn. (2) can be expressed as:   0f ic ip lsf k k   (4) 𝑃 𝐿𝑆𝐹 represents the failure probability and the results are expressed in term of reliability index. this later is related to the probability of failure according to eqn. 4:  1β φ fp  (5) where φ is the inverse of standardized normal distribution function. reliability methods robabilistic methods are widely used when evaluating the structural performance of pipeline due to theirs advantages[13, 14]. comparing to deterministic method or assessment again target reliability using calibration safely factor, it gives many advantages. due to the large number of input parameter involved in structural analysis, p a. guillalet alii, frattura ed integrità strutturale, 49 (2019) 341-349; doi: 10.3221/igf-esis.49.34 345 evaluation of failure probability can be optimized when using probabilistic methods. use of worst case input parameters can be avoided so on very pessimistic estimations. the reliability analyses were performed using importance sampling at the design point method. this method is based on crude monte carlo method, were the sampling is focused on important regions in order to save computational resources and time consuming. regions of importance during reliability analysis can be considered as failure domain precisely region with the highest probability density among all realizations in the failure region. fig. 3 shows the design point in the normal space witch accomplish the criterion of highest probability density. this point is situated on the limit state function and has the smallest distance to the origin of normal space [15]. the key aspect of the method is to define the design point using first order reliability method “form”. this design point is then used to have an importance sampling density function, the new density function is used to generate samples and calculate failure probability. figure 3: design point in the normal space application and results case of study a. material parameters he main design parameter involved in this study is fracture toughness where the considered material is api x 80 steel. this latter is a high strength steel characterized by high strength and toughness, guillal [16] made a review about development of high strength steel and the effect of local brittle zone on weld joints toughness. it was concluded that carbon content reduction and a better management of alloying elements, enhance mechanical properties in developed api 5l grade steel. estimation of fracture toughness is based on charpy v notch test from [17] and the used correlation to convert charpy data to facture toughness presented in eqn. (5) as fallow: 12 *ick cvn (6) b. geometrical parameters fig. 2 illustrate pipeline dimension with a crack on the surface where its geometries are dimension on pipeline. the scatter in diameter and thickness of pipe is due pipe manufacturing and fabrication process. cracks are generally characterized by ndt inspection tools. for purpose of our study, defect size is varied to cover a wide range of deep and shallow cracks. the used geometrical configuration is a pipeline with 1219.2 mm of diameter and 12.1 mm of wall-thickness. random distribution of diameter and thickness of pipeline are presented in tab. 1. c. loading parameters larger pipe diameters and high pressure are known to be the most economical solutions in oil and gas transportation. new constructed pipelines reach a diameter of 56” and service pressure of 11-12 mpa. in our case, an api grade x80 steel is chosen to reflect used api modern steel in many projects. maximum operating pressure and it random propriety are presented in tab. 1. t a. guillalet alii, frattura ed integrità strutturale, 49 (2019) 341-349; doi: 10.3221/igf-esis.49.34 346 figure 4: geometry of pipeline avec crack on the external surface variables description μ st distribution a crack depth (mm) 0.2t, 0.4t, 0.6t, 0.8t fixed c crack length (mm) a/c=0.125c-0.25c0,375-0,5-1-1,5-2 fixed d outside diameter (mm) 1219,2 0,0121 normal t pipe thickness (mm) 12,1 0,605 normal p maximum operating pressure (mpa) 8 0,08 normal kic fracture toughness (mpa.m1/2) 137 13,7 normal table 1: random variables and their statistical proprieties results and discussions aparametric study reliability index is calculated using different configuration of crack shape and depth ratio. the used reliability method is importance sampling at the design point method described in section 3. results of this study are presented in form of variation of reliability index. fig. 5 illustrates the variation of reliability index with different crack to depth ratio for three cases: deep crack (a/c=2), semicircular crack (a/c=1) and shallow crack (a/c=0.5). the calculations are made in deep point. the first observation is that reliability index decrease with increasing crack depth ratio. it seems that for all depth ratios shallow crack has reliability index lower then semicircular and deep crack. the difference is greater as depth ratio is increased. figure 5: variation of reliability index with depth ratio at different shape ratio. moreover, the variation of reliability index with different shape ratios at fixed crack depths is investigated. two cases are considered in fig. 6: case 1: reliability index estimated at deep point case 2: reliability index estimated at shallow point a. guillalet alii, frattura ed integrità strutturale, 49 (2019) 341-349; doi: 10.3221/igf-esis.49.34 347 in case 1, the letter a is used to refer to deep point. it is clear that reliability index is strongly influenced by shape factor. for the same depth ratio, reliability index decreases with increasing of the crack length. this trend is accentuated with increasing depth ratio from 0.2 to 0.8. a direct consequence is that a lack of precision during crack geometrical identification can lead to a considerable error in reliability estimation in advanced stage of growth (a/t = 0.8) comparing to initial stage (a/t = 0.2) in case 2, the letter c is used to refer to surface point. for (a/t ≤ 0.4), reliability index is approximately steady for the shape ratio (a/c > 1) and increase with decreasing (a/c). for (a/t > 0.4), the inverse is happening, where β is decreasing for (a/c ≥ 1) and approximately steady for (a/c < 1). this means that the influence of crack shape factor is not same for all configurations of cracks when sif is calculated in surface point. although, comparing values of reliability index for different depth ratio, it seems that β decrease with increasing depth as showed in fig. 5. as consequence, calculation of reliability index in deep point illustrates a monotonic effect of shape factor variability on structural reliability analysis. another point should be noted, for high shape ratio (a/c ≥ 1), reliability index in surface βa is lower than those in deep point βc; while βa for surface point is higher than βc for (a/c < 1). this remarque implies that considering sif in surface point results in high or less conservatism then deep point according to the considered crack shape ratio. figure 6: variation of reliability index with different cases of shape factor at constant a/t breliability fatigue assessment in this second part, the fatigue life time of cracks with two different shape factors is calculated based on paris crack growth expressed in eqn. (6): * * m a a m c c da c k dn dc c k dn         (7) where: ca=cc are paris crack growth rates in deep and surface directions, they are assumed to be equal. ∆ka, ∆kc are the change in applied stress intensity factor in deep and surface point respectively. paris crack growth expressed in eqn. (6) considers tow dimensional crack growth. simultaneous evolution of crack depth and length can reflect the crack shape evolution. tow configurations of initial shape are presented in tab. 2. the first is a small crack with semicircular shape, the second is a shallow crack with an aspect ratio a/c=0.2. an applied 150 mpa equivalent cycles is used to represent the stress severity indicator in term of number of cycle during fatigue life of the pipeline. a. guillalet alii, frattura ed integrità strutturale, 49 (2019) 341-349; doi: 10.3221/igf-esis.49.34 348 variables description μ cov std distribution a1 crack depth (mm) 4 / / fixed c1 crack length (mm) 4 / / fixed a2 crack depth (mm) 4 / / fixed c2 crack length (mm) 20 / / fixed d outside diameter (mm) 1219,2 0.0 0,0121 normal t pipe thickness (mm) 12,1 0,605 normal p maximum operating pressure (mpa) 8 fixed ∆σ applied pipeline wall stress range (mpa) 150 fixed kic fracture toughness (mpa.m1/2) 137 13.7 normal ca=cc fatigue crack growth rate (mm/cycle) 5*10-9 fixed m fatigue exponent 3.1 fixed table 2: input parameters for fatigue calculations. a target reliability index of 3.1 is fixed for comparison purpose. calculations are made using the same reliability method and input variables presented in tab. 2. variation of reliability index is plotted against number of experienced cycles for both configurations of crack. according to fig. 7, crack with initial a/c = 0.2 and a/c = 1 have a fatigue life time of 5*104 and >2.4*105 respectively. this results can be interpreted according to fig. 5, where β for shape ratio a/c = 0.5 is less than β for a/c = 1, so the first case reach the target reliability index before the second. also, these results seems to be in difference with those in [11] where the authors fixed the aspect ratio for all fatigue life. he found that semicircular crack had a shorter life time then shallow crack. this disagreement may be attributed to the assumption of fixed shape factor. stress intensity factor is estimated with less accuracy. the authors in [11] made the rest of his calculations with constant shape factor a/c=0.62 following recommendations in [18] in order to not shadow the influence of others parameters of study. figure 7: fatigue life time of cracks with different shape factor conclusion n this article, effect of crack shape factor in reliability analysis of axially cracked pipeline was illustrated. shape and depth crack ratio were varied to cover different crack shape and growth ranges. reliability index was plotted against different configurations of shape and depth ratio. according to the variation of reliability index calculated in deep point, this later is greatly influenced by the crack shape and depth ratio. shallow cracks have lower reliability index followed by deep cracks .as consequences, it seems that shallow cracks are more susceptible to cause fracture then deep cracks. reliability index calculated in deep point decrease with increasing of depth ratio for all crack shape. the reliability i a. guillalet alii, frattura ed integrità strutturale, 49 (2019) 341-349; doi: 10.3221/igf-esis.49.34 349 index calculated in surface point has a variation that is not similar for all shape and depth ratio configurations. as a conclusion, consideration of results from deep point reflects the sensitivity of reliability index to crack configuration while calculations in surface point reflects change in dependency of reliability index to the crack shape. fatigue life calculation shows that variation of crack shape factor can influence reliability index estimation. initial shallow crack was revealed to have shorter life time then initial semicircular crack differently from results in [11]. finally, an accurate correlation between a/t and a/c can give more precision in service life estimation of cracked pipeline. references [1] zhang, k., ferguson, j. (2017). crack shape development in fatigue growth assessment for pipelines, presented at the corrosion 2017, new orleans, louisiana, usa, [2] mahmoud, m. a. (1988).quantitative prediction of growth patterns of surface fatigue cracks in tension plates, engineering fracture mechanics, 30, pp. 735-746. doi: 10.1016/0013-7944(88)90134-8. [3] newman, j. c. and raju, i. s. (1981). an empirical stress-intensity factor equation for the surface crack, engineering fracture mechanics, 15, pp. 185-192. doi: 10.1016/0013-7944(81)90116-8. [4] boukharouba, t., azouaoui, k., gilgert, j., azari, z., and pluvinage, g. (2008). some insights into the fatigue crack propagation in tubes under internal pressure—proposition of predicting models, in safety, reliability and risks associated with water, oil and gas pipelines, ed: springer, p.^pp. 183-204. doi: 10.1007/978-1-4020-6526-2. [5] zhu, l. and tao, j. (2016). comparison of stress intensity factors of part surface flaws at stress concentration in plate and pipe between fe analysis and weight function approach, p. v01at01a010. doi: 10.1115/pvp2016-63262. [6] el amine, m., seghier, b., bettayeb, m., bouali, e. and gaceb, m. (2017). probabilistic approach evaluates reliability of pipelines with corrosion defects. [7] el amine, m., seghier, b., keshtegar, b. and elahmoune, b. (2018). reliability analysis of low, mid and high-grade strength corroded pipes based on plastic flow theory using adaptive nonlinear conjugate map, engineering failure analysis, 90, pp. 245-261. doi: 10.1016/j.engfailanal.2018.03.029. [8] el amine, m., seghier, keshtegar, b., correia, j. a., lesiuk, g. and de jesus, a. m. (2019). reliability analysis based on hybrid algorithm of m5 model tree and monte carlo simulation for corroded pipelines: case of study x60 steel grade pipes, engineering failure analysis, 97, pp. 793-803. doi: 10.1016/j.engfailanal.2019.01.061. [9] kocańda, d. and jasztal, m. (2012). probabilistic predicting the fatigue crack growth under variable amplitude loading, international journal of fatigue, 39, pp. 68-74. doi: 10.1016/j.ijfatigue.2011.03.011. [10] bettayeba, m., bouali, e., abdelbaki, n. and gaceb, m. (2012). establishment of a database and a classification of the defects in the metal of pipes according to their severity, procedia engineering, 42, pp. 607-615. doi: 10.1016/j.proeng.2012.07.453. [11] leander, j. and al-emrani, m. (2016). reliability-based fatigue assessment of steel bridges using lefm–a sensitivity analysis, international journal of fatigue, 93, pp. 82-91. doi: 10.1016/j.ijfatigue.2016.08.011. [12] kirkemo, f. (1988). applications of probabilistic fracture mechanics to offshore structures, applied mechanics reviews, 41, pp. 61-84. doi: 10.1115/1.3151882. [13] el amine, m., seghier, b., bettayeb, m., correia, j., de jesus, a. and calçada, r. (2018). structural reliability of corroded pipeline using the so-called separable monte carlo method, the journal of strain analysis for engineering design, 53(8), pp. 730-737. doi: 10.1177/0309324718782632. [14] keshtegar, b., el amine, m., seghier, b., (2018). modified response surface method basis harmony search to predict the burst pressure of corroded pipelines, engineering failure analysis, 89, pp. 177-199. doi: 10.1016/j.engfailanal.2018.02.016. [15] abdelkhalak el, h., changwu, h. and bouchaïb, r. (2017). overview of structural reliability analysis methods part ii sampling methods, incertitudes et fiabilité des systèmes multiphysiques, 1. doi: 10.21494/iste.op.2017.0116. [16] guillal, a., abdelbaki, n., gaceb, m. and bettayeb, m. (2018). effects of martensite-austenite constituents on mechanical properties of heat affected zone in high strength pipeline steels-review, chemical engineering transactions, 70, pp. 583-588. doi: 10.3303/cet1870098. [17] briottet, l., batisse, r., de dinechin, g., langlois, p. and thiers, l. (2012). recommendations on x80 steel for the design of hydrogen gas transmission pipelines, international journal of hydrogen energy, 37, pp. 9423-9430. doi: 10.1016/j.ijhydene.2012.02.009. 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/hrv (za stvaranje adobe pdf dokumenata najpogodnijih za visokokvalitetni ispis prije tiskanja koristite ove postavke. stvoreni pdf dokumenti mogu se otvoriti acrobat i adobe reader 5.0 i kasnijim verzijama.) /hun 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can be opened with acrobat and adobe reader 5.0 and later.) >> /namespace [ (adobe) (common) (1.0) ] /othernamespaces [ << /asreaderspreads false /cropimagestoframes true /errorcontrol /warnandcontinue /flattenerignorespreadoverrides false /includeguidesgrids false /includenonprinting false /includeslug false /namespace [ (adobe) (indesign) (4.0) ] /omitplacedbitmaps false /omitplacedeps false /omitplacedpdf false /simulateoverprint /legacy >> << /addbleedmarks false /addcolorbars false /addcropmarks false /addpageinfo false /addregmarks false /convertcolors /converttocmyk /destinationprofilename () /destinationprofileselector /documentcmyk /downsample16bitimages true /flattenerpreset << /presetselector /mediumresolution >> /formelements false /generatestructure false /includebookmarks false /includehyperlinks false /includeinteractive false /includelayers false /includeprofiles false /multimediahandling /useobjectsettings /namespace [ (adobe) (creativesuite) (2.0) ] /pdfxoutputintentprofileselector /documentcmyk /preserveediting true /untaggedcmykhandling /leaveuntagged /untaggedrgbhandling /usedocumentprofile /usedocumentbleed false >> ] >> setdistillerparams << /hwresolution [2400 2400] /pagesize [612.000 792.000] >> setpagedevice microsoft word numero_34_art_8 r. brighenti et alii, frattura ed integrità strutturale, 34 (2015) 80-89; doi: 10.3221/igf-esis.34.08 80 focussed on crack paths a unified approach for static and dynamic fracture failure in solids and granular materials by a particle method roberto brighenti, andrea carpinteri, nicholas corbari university of parma, italy brigh@unipr.it, andrea.carpinteri@unipr.it, nicholas.corbari@gmail.com abstract. the material structure at the microscale reveals the particulate nature of solids. by exploiting the discrete aspect of materials, the so-called particle methods developed and applied to the simulation of solids and liquids have attracted the attention of several researchers in the field of computational mechanics. in the present paper, a particle method based on a suitable force potential is proposed to describe the nature and intensity of the forces existing between particles of either the same solid or different colliding solids. the formulation applies to problems involving both granular materials and solids interacting with granular materials. the above approach is applied to simulate different problems dealing with the 3d dynamic fracture and failure of solids. keywords. particle method; discrete finite element; fracture, contact, dynamic failure. introduction he particle methods have attracted the attention of several researchers in the field of computational mechanics [1, 2]. it is straightforward when the material has to be described at the nanoscale where the molecular dynamic method can easily be applied [3]; however, this discrete description can successfully be applied even at the macroscale [4, 5]. accordingly, a discrete approach can replace the traditional continuous modelling of a solid, and allows us to examine complex phenomena such as failure, fracture, and interaction with other bodies [4]. the formulation applies to problems involving both granular materials [6-8] and solids interacting with granular materials. the need to solve mechanical problems has solicited the development of several numerical techniques aimed at assessing the response of materials both during service and at their ultimate conditions. to this purpose, various computational tools have been proposed: the finite element method (fem), the finite difference method, the finite volume method, the more recent boundary element method, meshless method [9] and natural element method [10], just to cite the main tools. problems involving mechanical systems characterized by large displacements, high velocity impact, fracture, failure, fragmentation, clustering, fluid-solid interaction, and so on, cannot be solved through classical numerical techniques in the context of the so-called lagrangian approach, because the severe distortion of the discretized domain leads to a lack of consistency between the numerical modelling and the physics problem. this issue has partially been overcome by using special remeshing techniques and the fe method, but that presents some drawbacks. the discretization through only nodal points – i.e. without mesh connectivity – represents a possible approach to solve this problem. in this context, the so-called smoothed particle hydrodynamics (sph) has been one of the first particle meshless methods in computational mechanics [11, 12]. the original idea of the developers of the above method lies in t r. brighenti et alii, frattura ed integrità strutturale, 34 (2015) 80-89; doi: 10.3221/igf-esis.34.08 81 the fact that the collective motion of particles in particle-wise systems (such as the movement of liquid, gas flow, particulate assemblies, etc.) may physically be modeled by the governing equations of classical newtonian hydrodynamics. such mesh-free lagrangian methods are characterized by variable nodal connectivity; the material is discretized with interacting particles and the method transforms a discrete field into a continuum one by using a localized kernel function that operates as a smoothing interpolation. the method can be applied to discrete systems but also to continuum ones, where the nodal points are not directly associated with the single particle composing the matter [13-15]. the noticeable advantages of such a method became clear after its first introduction, suddenly leading to its extension to the solution of a wide range of physics and engineering problems, well beyond the initial classical hydrodynamics field [16, 16]. the discrete nature of solid matters is evident at the microscale or at the molecular level [17]. on the other hand, the matter is typically modeled as continuous medium at the macroscale, suggesting the use of continuous computational techniques such as the fem. however, discrete models can conveniently be applied even in macroscopically continuum systems where each representative particle can be associated to a cluster of continuum elements. discrete element methods (dems) sometimes also called particle methods (pms), are numerical procedures to solve different engineering problems: the main assumption for this class of methods consists in the description of the material through an assemblage of separate discrete elements, such as atoms, molecules, grains, particle solid elements, etc. according to the scale of observation adopted [1, 17]. in the discrete approach, non-linear interactions between bodies and within bodies are numerically simulated in order to get their non-linear differential equations of motion. it is worth mentioning that the discrete nature of materials is well evident for some classes of them, such as the granular ones: geomechanical and powders materials can be studied by exploiting their noticeable granular nature [18, 19]. discrete methods have usefully been applied to solve problems at the macroscale such as mineral processing, rock and concrete blasting and crushing, sand mechanics, failure and fracture of compact or granular bodies [20, 21], problems involving fluid materials like liquids and gases [16, 22]. a generic solid can also be assumed to have a particle structure with a proper nature of particles’ interaction forces. from this remark, the mechanical behaviour of a material can range from very incoherent behaviour (characteristic of fluids, granular, powders, etc) up to compact behaviour (typical of polycrystalline materials), respectively. therefore, a discrete model can be used to simulate different classes of solids, by properly choosing the nature of the interaction forces between their discrete constituent elements. such an approach permits to get the overall response of the material at the macroscale, which is the main interest of materials science and mechanics of materials. moreover, the particle discretisation for a solid allows us to tackle the problem from a dynamic point of view, enabling to solve high strain rate, impact, large displacements and large strains problems involving history-dependent behaviour, plasticity, etc., that are more naturally expressed in a lagrangian computational framework. it should also be considered that discrete methods allow us to deal with short range forces (such as contact forces) and long range forces (such as the electrostatic ones). that enables to represent the physical nature of materials at the small or nano scales, where interatomic forces obeying such a non-local interaction relationship exist. in the present paper, a discrete element approach for the mechanical simulation of either continuum or granular-like materials (formulated on the basis of the force potential interaction concept) is proposed and applied to analyse dynamic fracture and failure of both granular materials and compact solids. a brief introduction related to the forces existing in continuum solids and discrete incoherent aggregates – modeled through discrete particles – is presented by taking into account the dynamic nature and large strain characteristics of the problem. finally, some examples demonstrating the versatility and the capability of the proposed approach are discussed. potential-force formulation for particle-particle interaction s is recalled above, the particle approach is straightforward when the material is really composed by several discrete elements as at the nano/microscale (for both solids and granular-like matters), where the particles can immediately be identified as the atoms/molecules or grains in the matter. however, a continuous solid can also be idealized as a cluster of elements reciprocally joined by forces depending on the particles relative positions: if the particles tend to approach to each other, a repulsive force arises (typical of compact solids and granular materials), while an attractive force appears when they tend to move far away (typical of compact solids and cohesive granular materials). the above interacting forces can be thought to have a local nature when they are associated to the direct contact between elements (for instance when granular materials are examined), while they assume a longer range characteristic in the case a r. brighenti et alii, frattura ed integrità strutturale, 34 (2015) 80-89; doi: 10.3221/igf-esis.34.08 82 of continuous materials. this remark suggests to adopt a unified potential-based formulation for the assessment of the interparticle actions, by properly choosing the distance of influence for the transmission of forces. as is typically done in the atomic description of solids where the material can be characterized by a potential energy functional ( ) x , it can be assumed the existence of a similar potential function at the meso or macro-scale. the equilibrium equations, referred to the discrete element i, correspond to the configuration of minimum energy of the system: ( ) 0tot tot i i i e       x p x x with iitottote xpxx  )()( (1) where ( )tot x and ip are the strain energy and the force applied to the particle i, respectively. by writing the power series expansion of the potential energy function, starting from its equilibrium state identified by the position vector 0x , the stationary condition of the above functional identifies the equilibrium configuration as follows: 00 0 2 2 0 0 02 2 ( ) ( ) ( )tot tot tot e e                xx x x x x x p k x x p x x x (2) where 0 /tote  xx 0 at the equilibrium, and the stiffness matrix of the system is indicated with 2 2/ /ij tot i j tot i je        k x x x x . at the atomic scale, various potential functions have been proposed in order to represent the mechanical behaviour of materials, such as the lennard-jones (lj) potential and the morse potential [23]. figure 1: scheme of pair-wise interparticle forces. the simplest mechanical model describing the stress-strain behaviour of a continuum linear elastic solid is the generalized hooke’s law that assumes the force between two infinitely closed material points to be proportional, through proper coefficients, to the strain value estimated in such a small region (fig. 1). the region of material – representative of a small region (of a continuum solid) lying between two particles i, j – is subjected to the deformation (evaluated with respect to the equilibrium distance er ) given by: 2 2 1 1 2 2 e e e e e e e e r r r r s s s s r r s s                    (3) r. brighenti et alii, frattura ed integrità strutturale, 34 (2015) 80-89; doi: 10.3221/igf-esis.34.08 83 where 0 0,i j e i jr r   x x x x are the distances between the particle centers in a generic state and at the equilibrium state, respectively, whereas , es s are the corresponding effective distances counterparts (fig. 2) defined as 2 ( ) / 2 2 2i js r d d r r        , 2 2e es r r   . in order to account for the no-penetration condition, the maximum co-penetration depth 1 2 r       is expressed as a fraction  of the averaged radius r of the particles. eq. (3) is written by taking into account the large displacements effect, whereas the maximum co-penetration distance enables to avoid the complete penetration condition between particles. figure 2: (a) a couple of particle at the equilibrium distance. (b) maximum co-penetration corresponding to 0( )f r r   . (c) generic particles relative position with geometrical parameters. by assuming the linear stress-strain relationship, the following expression for the force acting along the line joining the particle centers can be written: 2 infl infl 1 ' if 2 2 2 ( ) 0 if 2 2 i je e ij e e i j d ds s s s a e s r s s f s d d s r                              (3) where ija and 0'( ) ( )e s c s e  are the cross-section and the elastic modulus of a bar element that represents the material connecting the particles ,i j . the young modulus '( )e s is assumed to depend on s in order to take into account the no-penetration condition: it increases when 0s  (i.e. ( ) c s   if 0s  ), whereas ( ) 1c s  when s increases. the assumption of the no-penetration condition ( 0s  or 0 2w   ) entails an unlimited compressive strength of the particles when they are in contact, up to the limit 0s  (i.e. 2w  or 0r r ), w being the particles overlapping and 0r being the minimum allowed distance between particles. the force-potential and the corresponding stiffness, according to eq. (3), can be written as follows: 32 2 ( )1 1 ( ) ' 2 6 e ij e e e s ss s a e s s s s                 , 2 2 2 ( )( ) 1 ( ) ' eij e e s sd s k s a e ds s s                (4) in eq. (3) the influence radius inflr indicates the maximum interacting distance between two particles, i.e. it is the maximum distance beyond which two particles are not interacting. this assumption is suitable to represent long distance forces, such as in continuum materials, since the internal actions between the material points act also if such points are not in direct reciprocal contact (non-local interaction). in fig. 3a the distance dependence of the potential, of the force and of the stiffness are displayed for the linear elastic particles interaction related to the representative equilibrium distance / 1e is d  , while the same functions are reported in fig. 3b for the case of no-penetration constraint. in order to correctly represent the elastic behaviour of the material described through bar elements connecting the particles, a suitable choice of the cross section area ija of such elements must be done. since the bar arrangement in the r. brighenti et alii, frattura ed integrità strutturale, 34 (2015) 80-89; doi: 10.3221/igf-esis.34.08 84 3d space depends on the influence radius inflr and on the particles distribution (the bar connecting two particles exists only if the particles are within their influence distance), we can assume infl 0 ,( )ij ija a r a  , where the reference area is 2 0, ( ) / 8ij i ja d d    , i.e. the cross section of the cylindrical region of material placed between two particles with diameter equal to the mean value of the particles diameters. the function infl( )a r is evaluated by best fitting procedure once the particles arrangement in the space and their influence distance are assumed. dimensionless effective distance between particles surface, s / di in te rp a rt ic le s fo rc e , f co n ta ct s tif fn e s s, k f o rc e p o te n ti a l,  f(s) (s) (a) k(s) se / di = 1 1.0 0.0 dimensionless effective distance between particles surface, s / di in te rp a rt ic le s fo rc e , f co n ta ct s tif fn e s s, k f o rc e p o te n ti a l,  f(s) (s) (b) k(s) se / di = 1 1.0 0.0 figure 3: force potential and corresponding forces and stiffness according to the linear elastic behaviour for an equilibrium distance / 1e is d  , (a) without and (b) with the no-penetration condition. the above potential formulation can also be adopted for granular materials, where the internal forces act only when the particles are in reciprocal contact and their motion make them approach. in these cases, an influence distance can be adopted ( infl / ( / 2)ir d lower than or equal to about 2), i.e. the interaction of particles occurs only when they are in contact under compression condition, while no forces exist when ' 0s  . further, a tangential force can be assumed to exist between the colliding particles when ' 0s  (ref. [22]):  , ,( ) sign( ) min , ( )t rel t rel mdt w f w     u u (5) where  is the viscosity coefficient, md is the dynamic friction coefficient of the materials, ,t relu is the relative tangential velocity between the two particles in contact. note that eq. (5) provides a tangential force as the minimum value between the dynamic friction and the viscosity action. the present authors have verified that the function infl( )a r , for a given particles arrangement, is almost independent of the particles arrangement in the space and depends on inflr only [24]. on the other hand, the poisson’s coefficient tends to 1/3 as the influence radius increases, irrespective of the particles layout used to represent the domain of the problem of interest. when compact materials have to be simulated, a suitable choice of the influence radius value is infl / ( / 2) 4ir d  (corresponding to the correction function value equal to about infl( ) 0.4a r  for both cubic and tetrahedral arrangements), i.e. the interaction forces exist for neighbor particles even if they are not in direct contact. granular materials can be simulated by assuming infl / ( / 2) 2ir d  and infl( ) 1.0a r  , i.e. the interaction of particles exists only when they are in reciprocal compressive contact, while no forces are present when ' 0s  . it is worth noting that the particle-boundary simulation can be tackled in the same way as the particle-particle interaction. sph property of the potential force approach smoothing particle hydrodynamic (sph) approximation of a function and of its n-th derivative at a point ix in the region  can be written as follows [13]: r. brighenti et alii, frattura ed integrità strutturale, 34 (2015) 80-89; doi: 10.3221/igf-esis.34.08 85 ( ) ( ) ( ) ( ) ( )i i if f d f w d          x x x x x x x , ( ) ( )( ) ( ) ( )n ni if f w d     x x x x (6) where ( )i x x is the dirac delta function that is numerically approximated by adopting a proper decreasing function ( )iw x x of the distance ix x ( w is also called kernel or smoothing function), and h is the smoothing length (or support dimension). the numerical evaluation of eq. (61) is expressed as follows: ( ) ( ) ( , )ki k k i k k f f m w h     x x x x (7) where the index k spans all the particles over the neighbors of that placed at ix because of the compact support of the kernel function. the parameters , ,k k km x are the position, mass and density of the generic particle k , respectively, and ( )kf x is the function value at kx . by using a sph approximation for the material’s stress field and inserting it in the dynamic equilibrium equation, , 0ij j i ix b    , the following expression can be obtained: , ( )( ) ( , ) 0p k ij k j k p p p i p p i k pm v v w h v x v b                x x x  , 1, 2, 3i  (8) where pv represents the volume of the particle p and /k k km v  . by using the potential formulation presented above, we get: , , [ ] 2 ( ) ( )0, ( ) [ ] ( ) ( ) ( ) ( , ) ( ) ( , ) ( ) ' 1 2 ij k j k p p k ij k j k p k p k p e kp k p e kpmk p k i kp k p k p e kp e kp w h v v w h s sa h a e v v q v v s s                                x x x x x x x x x x  (9) where ( )i kpq is the i-th component of the versor connecting the particles k and p, and [ ]k p indicates the generic particle k falling within the neighbor of particle p. dynamic equilibrium equations he dynamic governing equations of the discretized problem are given by: i d e b     m x f f f f 0 or tm x f (10) where m is the mass matrix, x is the vector of the particles center acceleration (the rotation degrees of freedom are neglected since particles with small rotational inertia are assumed). further, , ,i d ef f f , bf are the internal force vector (see previous sections), the damping force vector, the external force vector and the vector of actions due to the collision of the particle with the elastic boundaries, respectively. the numerical integration of the motion equations can explicitly be done for each particle, once the force vector acting on it is known. explicit time integration methods, even if conditionally stable, are usually adopted in particles simulations to avoid the use of large matrices such as the stiffness one. t r. brighenti et alii, frattura ed integrità strutturale, 34 (2015) 80-89; doi: 10.3221/igf-esis.34.08 86 in the present particle approach, the explicit leapfrog method (the verlet integration scheme) is adopted [25], which allows a satisfactory numerical stability, provides time-reversibility and preservation of the symplectic form on the phase space. the word leapfrog recalls that even derivatives of position are known at on-step points, whereas odd derivatives are known at mid-step points. the particle acceleration at time step n , the velocity at time step 1/ 2n  and the position of particle i at time step 1n  are given by: , , , /i n t i n imx f , , 1/2 , 1/2 ,i n i n i nt    x x x   ,  , 1 , , 1/2 ,i n i n i n i nt t      x x x x  (11) where , 1/2 , , 1( ) /i n i n i n t   x x x   is the mean velocity vector across the time step 1n n  . in order to determine stable results, an upper limit of the time step size /t m k   in the dem approach is generally obtained from the natural oscillating period of a couple of particles: in the above expression, the minimum ratio /m k among all the particles constituting the discretized solid must be taken into account, and 1  is an appropriate constant to be introduced. numerical applications granular material cutting simulations his example considers the cutting of a granular material that resembles the fracture phenomenon in solids. a vertical flat blade with a constant horizontal velocity equal to 10 mm s-1 [26] drives particles that move, leading to some failure lines in the body. an initial volume of particles (fig. 4) under the gravity action is assumed to be placed inside a box, and the vertical blade is placed at the left side position. the simulation consists in moving the blade, causing the material inside the box to redistribute. the performed dynamic analysis is aimed at determining the particles configurations at different time instants. the material of the particles (assumed with a mass density equal to 855 kgm-3) is supposed to have an elastic modulus equal to 62.76 10e pa  and a negligible tensile strength (or, equivalently, no cohesion). the force potential is used to describe the particles interaction by adopting an influence distance of the particles equal to inflr d , and the box and the blade are supposed to have elastic modulus equal to 83.0 10e pa  . the particles volume is modeled through about 1162 spheres with diameter size equal to 20 mm, initially arranged in a cubic fashion. the geometry of the system is depicted in fig. 4. the integration time step is taken equal to 0.2 mst  and the final blade displacement is equal to 200mm, with an analysis duration equal to 2.0 s. the damping coefficient for the dynamic analyses is assumed equal to 0.20d  , and the two coefficients of dynamic friction (between particle and particle, and between particle and planes) are supposed to be 0.10d  . the obtained arrangement of the particles shows a behaviour similar to that of the soil cutting case analysed in ref. [26]. note that the blade in the present study is shorter than that in the literature test, causing a little difference in the disposition of the particles near the blade. neglecting last aspect, the shape assumed by the particles representing the granular material in the present study is similar to the configuration presented in ref. [26]. in fig. 4e, f, the fracture lines arising in the material can be recognized, i.e. the cutting phenomenon can be thought as a crack appearance event inside a non-compact material. fracture of a brittle concrete beam under a dynamic impact this example examines the fracture behaviour of a compact material. this analysis is performed with the same potential approach described in the theoretical sections and used also for the previous numerical example. in the present numerical test, a simply supported plain concrete beam under impact load is taken into account [27]. the system is characterized by the reference size 0.3b m , whereas the mechanical properties of the materials are as follows: elastic modulus 103 10e pa  , poisson’s ratio 0.18  , tensile strength 62.7 10tf pa  and mass density equal to 2300 kgm-3 for the concrete material, whereas the falling hammer is supposed to be made of steel (with elastic modulus 112 10e pa  , mass density equal to 8000 kgm-3). the system is modelled with about 2200 particles with cubic arrangement and radius equal to 35mm each. the impact velocity of the steel mass is assumed to be equal to t r. brighenti et alii, frattura ed integrità strutturale, 34 (2015) 80-89; doi: 10.3221/igf-esis.34.08 87 0 2, 4, 6 and 8 /v m s . the force potential described above is used to quantify the particles interaction, by adopting an influence distance of the particles equal to infl 2r d and a time increment for the dynamic analysis equal to 5t s  . 0.10 0.15 0.20 figure 4: configuration of particles for a blade displacement equal to: (a, c) 10cm, (b, d) 20cm [25], (e, f) corresponding configurations provided by the present model. color scale indicates the horizontal displacement of the particles expressed in m. fig. 5 shows the configuration of the system at different time instants. in particular, the initial development of the elastic wave – propagating inside the beam – is shown in fig. 5a, whereas the failure pattern at t=0.125 s after the first impact is represented in fig. 5b. as can be observed, a wedge-like failure mechanism takes place producing the detachment of a wide bottom portion of the beam. moreover, a diffused separation of the bottom layer of the beam can also be acknowledged. in fig. 5c, the time history of the reaction force at support obtained by the discrete approach by using different discretizations is displayed and compared with the fe results provided in ref. [27]. it can be observed that, only after a first time interval equal to about 30 ms (when the reaction is practically zero due to the time required by the elastic wave to propagate from the stricken zone to the support), such a boundary force raises very quickly. of course, higher impact speeds correspond to higher reaction force values. the fracture pattern provided by the dem approach roughly corresponds to the literature results, despite the other fem approach is very different (fig. 5d) and does not allow us to determine the detachment of material portion produced by the fracture phenomenon. conclusions he particulate nature of solids, naturally acknowledged at the microscale in granular or fluid materials, can also be adopted conveniently for the mechanical description of compact matter at the macroscale. based on such an idea, a particle method can be applied to the simulation of a wide class of mechanical problems once the mechanical properties and governing equations have been established. t (a) (c) (d) (e) (f) (b) r. brighenti et alii, frattura ed integrità strutturale, 34 (2015) 80-89; doi: 10.3221/igf-esis.34.08 88 a discrete approach can replace the traditional continuous modeling of solids, allowing to examine complex phenomena such as failure, fracture, contact and interaction with other bodies, by also taking into account large strain and dynamic effects. 0 0.0002 0.0004 0.0006 time, t (s) -200 -150 -100 -50 0 50 100 v e rt ic a l r e a ct io n , r z (k n ) ref. [27] pres. res.v0 (m/s) 2 4 6 8 no. 3366 particles no. 5551 particles figure 5: (a) elastic wave propagation and (b) failure pattern for the case 0 2 /v m s . (c) time history of the reaction force at the beginning of the impact phenomenon for 0 2, 4, 6, 8 /v m s from the present model. (d) fe crack path reported in [26]. in the present study, a particle method – based on the description of the forces between discrete elements evaluated on the basis of a force potential – has been proposed. it has been emphasized that the formulation applies without changes to problems involving granular materials or solids interacting with granular materials. the above approach has been applied to the simulation of different problems dealing with the 3d fracture and failure of both granular materials and compact solids. the formulated discrete method shows a wide capability to deal with different complex mechanical problems by properly describing the evolution of the crack pattern under dynamic conditions. references [1] cundall, p.a., strack, o.d.l., a discrete numerical model for granular assemblies. geotechnique, 29(1) (1979) 47–65. [2] oñate, e., particle-based methods: fundamentals and applications. springer science & business media, (2011). [3] liu, b., huang, y., jiang, h., qu, s., hwang, k.c., the atomic-scale finite element method. comput. methods appl. mech. engng., 193 (2004) 1849–1864. [4] krivtsov, a., molecular dynamics simulation of impact fracture in polycrystalline materials, meccanica, 38 (2003) 6170. [5] onate, e., idelson, s.r., del pin, f., aubry, r., the particle finite element method. an overview. int. j. comput. meth., 1 (2004) 267–307. (a) t = 44.2 10 s (b) t = 0.125 s (d) (c) r. brighenti et alii, frattura ed integrità strutturale, 34 (2015) 80-89; doi: 10.3221/igf-esis.34.08 89 [6] tasora, a., anitescu, m., a convex complementarity approach for simulating large granular flows, j. comp. nonl. dyn., 5 (2010) 1–10. [7] rycroft, c.h., kamrin, k., bazant, m.z., assessing continuum postulates in simulations of granular flow. j. mech. phys. sol., 57 (2009) 828–839. [8] bui, h.h., fukagawa, r., sako, k., ohno, s., lagrangian meshfree particles method (sph) for large deformation and failure flows of geomaterial using elastic–plastic soil constitutive model. int. j. num. an. meth. geomech., 32(12) (2008) 1537–1570. [9] belytschko, t., krongauz, y., organ, d., fleming, m., krysl, p., meshless methods: an overview and recent developments. computer methods in applied mechanics and engineering, 139(1–4) (1996) 3–47. [10] sukumar, n., moran, b., belytschko, t., the natural element method in solid mechanics. int. j. num. meth. engng, 43(5) (1998) 839–887. [11] lucy, l.b., a numerical approach to the testing of the fission hypothesis. astron. j., 82 (1977) 1013–1024. [12] gingold, r.a., monaghan, j.j., smoothed particle hydrodynamics: theory and application to non-spherical stars, mon. not. r. astron. soc., 181 (1977) 375–89. [13] benz, w., smooth particle hydrodynamics: a review. in: numerical modeling of non-linear stellar pulsation: problems and prospects, kluwer academic, boston; (1990). [14] monaghan, j.j., why particle methods work. siam j. sci. and stat. comput., 3(4) (1982) 422–433. [15] monaghan, j.j., sph elastic dynamics. comput. methods appl. mech. engrg., 190 (2001) 6641–6662. [16] oñate, e., owen, r., particle-based methods: fundamentals and applications, springer, (2011). [17] curtin, w.a., miller, r.e., atomistic/continuum coupling in computational materials science, model. simul. mater. sci. eng., 11 (2003) r33–r68. [18] d’addetta, g.a., kun, f., ramm, e., on the application of a discrete model to the fracture process of cohesive granular materials, granular matter, 4 (2002) 77–90. [19] obermayr, m., dressler, k., vrettos, c., eberhard, p., a bonded-particle model for cemented sand, comp. and geotechnics, 49 (2013) 299–313. [20] krivtsov, a., molecular dynamics simulation of impact fracture in polycrystalline materials, meccanica, 38 (2003) 61– 70. [21] aubry, r., idelsohn, s.r., oñate, e., particle finite element method in fluid mechanics including thermal convectiondiffusion, comput. & struct., 83 (2005) 1459–1475. [22] brilliantov, n., spahn, f., hertzsch, j., pöshel, t., model for collision in granular gases, phys. rev. e, 53 (1996) 5382–5392. [23] morse, p.m., diatomic molecules according to the wave mechanics. ii. vibrational levels, phys. rev., 34 (1930) 57– 64. [24] brighenti, r., corbari, n., dynamic behaviour of solids and granular materials: a force potential-based particle method. int. j. num. meth. engng, (2015) in press (doi: 10.1002/nme.4998). [25] verlet, l., computer experiments on classical fluids. i. thermodynamical properties of lennard−jones molecules, phys. rev., 159 (1967) 98–103. [26] coetzee, c.j., discrete and continuum modelling of soil cutting, comp. part. mech., 1(4) (2014) 409–423. [27] travaš, v., ožbolt, j., kožar, i., failure of plain concrete beam at impact load: 3d finite element analysis, int. j. fract., 160 (2009) 31–41. microsoft word numero 25 art 8 j. lachambre et alii, frattura ed integrità strutturale, 25 (2013) 50-53; doi: 10.3221/igf-esis.25.08 50 special issue: characterization of crack tip stress field in situ 3d characterization of fatigue cracks displacement fields joel lachambre, jean-yves buffiere mateis lab. umr cnrs 5510 insa lyon france julien réthoré lamcos lab. umr cnrs 5259 insa lyon france arnaud weck univ. of ottawa canada abstract. the three dimensional growth of fatigue cracks in samples of nodular graphite cast iron is characterized using laboratory x-ray computed tomography. the cracks grow from laser machined artificial defects, their development is monitored in situ using laboratory x-ray computed tomography (lab. ct) and digital volume correlation (dvc). the combination of both techniques gives access to the 3d displacement field at the tip of the crack (mainly mode i opening). keywords. cast iron; digital volume correlation; crack tip displacement; in situ. introduction n their early stage of propagation, fatigue cracks have a strong three dimensional character. this is because, in structural materials, crack initiation occurs at heterogeneities such as holes, surface scratches, harder or softer second phase particles, well oriented grain etc. once initiated, such small cracks strongly interact with the first surrounding grains and, at low stress levels, a large number of fatigue cycles is necessary before the propagation rate of a crack at the specimen surface is comparable to the propagation rate in the bulk of the specimen. fatigue models tend to ignore this three dimensional aspect of crack growth partly because reliable experimental data was (and still is) lacking. this is a crucial issue because a very large fraction of the fatigue life of real components correspond to the growth of such small 3d cracks [1]. various 3d-imaging techniques have been used in previous studies to describe the 3d propagation of fatigue cracks. sem/fib observations: this destructive approach can provide very high resolution images of a restricted area (typically 20 µm3) around the crack tip but in situ experiment are obviously impossible. laboratory x ray computed tomography (lab. ct)is a non-destructive technique useful for long cracks. the resolution is still rather low for direct imaging of short cracks even under load. synchrotron radiation computed tomography (sr ct) has been used for in situ characterisation of crack initiation and growth; very good detectors coupled to phase contrast offer a better resolution than in the case of lab. ct but the price to pay is the small (sub millimetric) sample size and limited availability of relevant synchrotron beamlines. it has been shown in the past that lab. ct can be used to map displacement fields at the tip of through thickness fatigue cracks [2]. however so far, the studied cracks have been characterized in specimens carved out from larger samples and the influence of sample preparation (relaxation of stress) could not be excluded. in this work a method has been developed to initiate and grow a crack in a single sample thus providing a more reliable picture of the displacement field at the tip of a crack grown in situ. i http://www.gruppofrattura.it http://dx.medra.org/10.3221/igf-esis.25.08&auth=true j. lachambre et alii, frattura ed integrità strutturale, 25 (2013) 50-53; doi: 10.3221/igf-esis.25.08 51 experimental he material used in this study is a nodular graphite cast iron with a homogeneous dispersion of graphite nodules which are used as natural markers for dvc [2]. the cracks are initiated from artificial defects produced by laser machining [3]. the fatigue cycles are applied on small dog bone samples (square cross section 1.5 mm2) using a specially designed fatigue machine which allows to use a distance between the sample and the x-ray source lower than 20mm. a standard laboratory tomograph available at mateis [4] has been used. a current of 174µa and a mean of 3 radiography with an exposure time of 1 second have been used 720 angular positions have been recorded which corresponded to a scan time of 45 minutes. the reconstruction time (weighted filtered back projection, feldkamp algorithm) takes approximately 15 minutes for a 560×560×900 voxels 3d image. the crack shape evolution is studied through the residual of the dvc which correspond to the difference between the reference and the deformed and corrected volumes [2]. once the sample is set up in the tomograph, two scans are recorded at low stress (40 mpa) and a scan at high stress (290 mpa). the sample is cycled in situ at constant a stress amplitude of 300 mpa (load ratio: 0.1). in the beginning of the experiment 100,000 cycles are applied to the sample before a first scan is recorded. then 2 scans are recorded every 15 kcycles, one at 40 mpa and an other at 290 mpa, to monitor the crack evolution as described in [2]. a c8-dvc multiscale algorithm with an eight node cubic element is used to compute the displacement fields in the loaded specimen [5]. two kinds of correlation are performed during the experiment: first between a reference volume acquired before cycling under low stress and a deformed volume under high stress at each step of cycling. then a correlation between the volume at low stress and the volume at high stress is also performed at each step. the first kind of analysis gives access to the crack shape evolution while the second is used to map the crack opening displacement (cod). results he dvc analysis during cycling is carried out with 32 voxels elements, over a volume of 11×11×15 c8,elements. this mesh is quite coarse considering that, typically, at ~ 180 kc the crack is contained in only 8 elements. nevertheless the crack morphology can be estimated from the dvc residual. similar images have been obtained for the cracks emanating from a corner defect. figure 1: surface crack evolution at 160 kc, 175 kc, 190 kc, 205 kc and 240 kc obtained from dvc residuals (the cross section of the sample is 1.5x1.5 mm2). an extended version of dvc called x-dvc (based on the principle of the extended finite element method. [6]) is used to post process the 3d images recorded between the scans at low and high stress. the results of x-dvc on one corner and one surface crack can be visualised in fig. 2. as the position of the crack front is not known, a discontinuous enrichment is added over the whole cross-section. those displacement fields can be used to compute stress intensity factor values along the crack front using williams series [7] as described in [2]. in this previous work, stress intensity factors were computed within parallel reconstructed sections containing the stress axis and the crack front normal. the crack was assumed to be straight and the planes used for fitting the williams series were parallel. the crack front position was found by minimizing the super singular term n=-1 of the series for the mode i case. t t http://www.gruppofrattura.it http://dx.medra.org/10.3221/igf-esis.25.08&auth=true j. lachambre et alii, frattura ed integrità strutturale, 25 (2013) 50-53; doi: 10.3221/igf-esis.25.08 52 figure 2: mode i component of the displacement field of the corner crack after 180kc (left) and the surface crack after 200kc (right): x-dvc analysis. the scale is given in voxel (1voxel= 3.5µm). in this work, the studied cracks having a three-dimensional shape, a new method has been used for extracting k values (see fig. 3 for a summary). an approximate position of the crack front is first derived from the dvc residuals (fig. 2a). a series of regularly spaced planes is built along this first crack front and used to fit a first set of williams series. by a minimization of the super singular term n=-1 of the series, a new position of the front is found ( red line in fig. 3b) a new set of planes is build and the crack front detection is carried out again. the « correct » crack front position is found when the crack front position is stable between two iterations. the different mode i, ii and iii stress intensity factors can then be computed. figure 3: schematic illustration of the iterative crack front extraction process : an initial crack front position is assumed (a) to build a series of planes which will be used for fitting the williams series. once the new position of the front is found (b) (see the text for details) a new series of planes is build (c) ; for non planar cracks, the process can be carried out in 3d (d). examples of stress intensity profiles obtained along the crack fronts of the propagating cracks can be obtained with this method and used to plot local da/dn=f(dk) laws. summary he 3d propagation of small fatigue cracks initiating from an artificial defect in a cast iron sample has been characterized in situ and analyzed using laboratory x-ray computed tomography and dvc. the process of creating small artificial defects with laser beam gives an appropriate way to initiate a crack in this material. the dvc analysis with a relatively coarse mesh provides during cycling a valuable information on the crack propagation. the x-dvc analysis allows to estimate directly the crack opening displacement over the entire crack surface. displacement fields extracted by dvc can be used to compute local values of the stress intensity factor along the curved crack fronts. acknowledgements his work was funded by the french anr program (grant anr-09-blan-0009-01 rupxcube project). t t http://www.gruppofrattura.it http://dx.medra.org/10.3221/igf-esis.25.08&auth=true j. lachambre et alii, frattura ed integrità strutturale, 25 (2013) 50-53; doi: 10.3221/igf-esis.25.08 53 references [1] suresh, s., fatigue of materials cambridge univ. press (1998) [2] limodin, n., réthoré, j., buffière, j.-y., hild, f., roux, s., ludwig, w., rannou, j., gravouil, a., influence of closure on the 3d propagation of fatigue cracks in a nodular cast iron investigated by x-ray tomography and 3d volume correlation, acta materialia 58 (2010) 2957-2967. [3] weck, a., crawford, t.h.r., borowiec, a., wilkinson, d.s., preston, j.s., femtosecond laser-based fabrication of a new model material to study fracture, applied physics a: materials science and processing 86 (2007) 55-61. [4] buffiere, j.-y., maire, e., adrien, j., masse, j., boller, e., in situ experiments with x ray tomography: an attractive tool for experimental mechanics, 50 (2010) 289-305. [5] roux, s., hild, f., viot, p., bernard, d., three-dimensional image correlation from x-ray computed tomography of solid foam}, composites part a: applied science and manufacturing, 39 (2008) 1253-1265. [6] réthoré, j., tinnes, j.-p., roux, s., buffière, j.-y., hild, f., extended three-dimensional digital image correlation (x3d-dic) comptes rendus mécanique 336 (2008) 643-649. [7] williams, m., on the stress distribution at the base of a stationary crack l. jal. appl. mech., 24 (1957) 109-114 http://www.gruppofrattura.it http://dx.medra.org/10.3221/igf-esis.25.08&auth=true microsoft word numero_37_art_22 n.r. gates et alii, frattura ed integrità strutturale, 37 (2016) 160-165; doi: 10.3221/igf-esis.37.22 160 focussed on multiaxial fatigue and fracture interaction of shear and normal stresses in multiaxial fatigue damage analysis nicholas r. gates, ali fatemi mechanical, industrial and manufacturing engineering department, the university of toledo, 2801 w. bancroft street, toledo, oh 43606, usa ngates@eng.utoledo.edu, afatemi@eng.utoledo.edu abstract. due to the abundance of engineering components subjected to complex multiaxial loading histories, being able to accurately estimate fatigue damage under multiaxial stress states is a fundamental step in many fatigue life analyses. in this respect, the fatemi-socie (fs) critical plane damage parameter has been shown to provide excellent fatigue life correlations for a variety of materials and loading conditions. in this parameter shear strain amplitude has a primary influence on fatigue damage and the maximum normal stress on the maximum shear plane has a secondary, but important, influence. in this parameter, the maximum normal stress is normalized by the material yield strength in order to preserve the unitless feature of strain. however, in examining some literature data it was found that in certain situations the fs parameter can result in better fatigue life predictions if the maximum normal stress is normalized by shear stress range instead. these data include uniaxial loadings with large tensile mean stress, and some non-proportional axial-torsion load paths with different normal-shear stress interactions. this modification to the fs parameter was investigated by using fatigue data from literature for 7075-t651 aluminum alloy, as well as additional data from 2024-t3 aluminum alloy fatigue tests performed in this study. keywords. multiaxial fatigue; critical plane; fatemi-socie; mean stress; load path interaction. introduction lthough there are many different steps in the fatigue life estimation process, relating the variation of stresses and strains to the fatigue damage that occurs within a material is the most fundamental part of any fatigue life analysis. due to the abundance of engineering components subjected to complex multiaxial loading histories, being able to accurately estimate fatigue damage under multiaxial stress states is especially important. to this end, significant effort in the last few decades has been put into developing damage parameters which reflect the actual damage mechanisms of the fatigue failure process [1,2]. chief among these are critical plane approaches, which build on the observation that fatigue cracks tend to initiate on preferred planes within a material. critical plane approaches are typically based on the idea of crack initiation occurring on or around either the maximum principal plane or maximum shear plane. as a result, these approaches have the added benefit of being able to predict failure plane orientation, which is useful if a subsequent crack growth analysis is to be performed. a popular critical plane-based parameter for computing multiaxial fatigue damage in materials exhibiting shear failure mechanisms is the fatemi-socie (fs) parameter [3]. this parameter was formulated based on the idea that while alternating shear strain is the primary driving force behind fatigue crack initiation, the maximum normal stress on the a n.r. gates et alii, frattura ed integrità strutturale, 37 (2016) 160-165; doi: 10.3221/igf-esis.37.22 161 crack plane also affects the nucleation and growth of small cracks by influencing the amount of friction and interlocking between opposing crack faces. therefore, the inclusion of a maximum normal stress term is able to account for the effects of mean stress in a manner that holds physical significance. the fs parameter predicts fatigue life in terms of shear fatigue properties based on the following equation:                  ' ,max 'max 1 2 2 2 b cf o on f f f y k n n g (1) where δγmax is the maximum range of shear strain experienced on any plane, σn,max is the maximum normal stress occurring on the same plane for the cycle of interest, σy is the material yield strength, and k is a material dependent parameter reflecting the influence of normal stress on fatigue damage. the maximum normal stress is normalized by yield strength as a means of preserving the unitless feature of strain. the right hand side of eq. 1 represents the shear strain-life curve for the material under consideration. in the event that shear fatigue properties are not available for damage calculation, the right side of eq. 1 may alternatively be expressed in terms of uniaxial fatigue properties as follows:                                            ' ' ,max 'max 1 1 2 1 2 1 2 2 2 b c bf fn e f p f f f y y k n n k n e (2) where νe is elastic poisson’s ratio, νp is poisson’s ratio for fully plastic conditions, usually taken to be 0.5, and all other fatigue properties correspond to the fully-reversed uniaxial strain-life equation. since the normal stress term is multiplied by a strain term, the fs parameter is also able to account for changes in fatigue damage brought about by cyclic and/or non-proportional hardening. damage parameters based on only stress or only strain terms, on the other hand, cannot reflect these changes in material constitutive behavior. additionally, because the normal stress term is multiplied by the shear strain range, the fs parameter assumes that cyclic shear strain must be present in order for fatigue damage to occur. this is important because it prevents the prediction of fatigue damage in situations where only a static axial stress may exist on a plane. overall, the fs parameter, based on either shear or uniaxial fatigue properties, has been shown to correlate experimental and predicted fatigue lives well for a variety of materials and loading conditions. despite this fact, when analyzing some recent literature data, e.g. [4,5], it was found that the parameter can result in non-conservative life predictions when significant tensile mean stress is present. although increasing the k value in the fs parameter can improve mean stress correlation by increasing the influence of the maximum normal stress term, this has a detrimental effect on the correlation of fatigue data generated under other multiaxial loading paths. as a result, in the first part of this study, modifications to the fs parameter are investigated in an attempt to improve fatigue life predictions. in addition to mean stress effects, shamsaei [6] performed fatigue tests on 1050 steel for different multiaxial loading paths which produced the same fatigue damage predictions based on the fs parameter. from the results of these tests, however, it was found that the average experimental fatigue life for cyclic torsion with static tension loading was around half of the life predicted for in-phase axial-torsion loading at the same damage value. conversely, the average life for cyclic torsion with pulsating tension loading was around a factor of 2.5 longer than for in-phase loading. although a factor of ±2.5 error is still very reasonable for multiaxial fatigue life predictions, these results suggest that there is room for some improvement in fatigue damage calculation with respect to the quantification of normal-shear stress/strain interaction. considering the load path dependence of fatigue damage, the second part of this study focuses on a limited number of fatigue tests designed to differentiate between the original fs parameter and the modified parameter developed in the first part of the study. these tests were performed using tubular specimens of 2024-t3 aluminum alloy under loading conditions which result in the same damage value based on the original fs parameter, but different damage values for the modified parameter. differences in experimental lives were then compared to predictions to determine which parameter more closely reflects the fatigue damage variation between loading paths. material and testing procedures he material chosen for the fatigue tests performed in this study was aluminum alloy 2024-t3. mechanical properties for the material include a yield strength (0.2% offset) of 330 mpa, ultimate tensile strength of 495 mpa, and modulus of elasticity of 73.7 gpa. additional deformation and fatigue properties can be found in [7]. all tests t n.r. gates et alii, frattura ed integrità strutturale, 37 (2016) 160-165; doi: 10.3221/igf-esis.37.22 162 were performed using un-notched specimens of a thin-walled tubular geometry. the specimens feature a 30 mm long gage section with an outside diameter of 29 mm and an inside diameter of 26 mm, resulting in a wall thickness of 1.5 mm. additional details, including complete specimen geometry, can be found in [8]. while mean stress effects were not studied for the 2024-t3 aluminum alloy tested in the current study, several constant amplitude fully-reversed fatigue tests were performed under a variety of loading paths. these tests were performed in load control and include uniaxial (12 tests) pure torsion (15 tests), torsion with static axial stress (8 tests), in-phase axial-torsion (6 tests), and 90° op axial-torsion (7 tests) loading conditions. additional tests were also performed using triangular load paths (4 tests total) in order to study the effects of axial and shear stress interaction on fatigue damage. all testing was carried out in a closed loop servo-hydraulic axial-torsion load frame with a dynamic rating of 100 kn axial load and 1 kn·m torsional load. load train alignment was carefully maintained throughout testing to produce no more than 5% bending at 1000 microstrain. the definition of crack initiation was considered to be a 3% change in displacement or rotation amplitude when compared to a stable reference cycle. this generally corresponded to final crack lengths of approximately 10–15 mm, with growth from 1 mm to final length occurring very rapidly. in addition to the 2024-t3 tests data generated in this study, literature data for 7075-t651 (σy = 501 mpa, σu = 561 mpa), reported by zhao and jiang [4], were also analyzed. loading conditions included were similar to those for the 2024-t3 tests: uniaxial (131 tests), torsion (17 tests), torsion with static axial stress (9 tests), in-phase (9 tests), and 90° op axialtorsion (7 tests). uniaxial fatigue tests were conducted at r ratios ranging from -∞ to 0.7, while tests for all other loading paths were performed under fully-reversed conditions. mean stress effects on damage calculation s mentioned in the introduction, although the fatemi-socie parameter has been shown to provide excellent fatigue life correlations under a variety of loading conditions, for 7075-t651 fatigue data reported in [4], it was found that the parameter resulted in non-conservative life predictions when significant tensile mean stress was present. correlation of this test data using the fs parameter (k = 1) is shown in fig. 1(a). data for tests with experimental lives less than 50 cycles are excluded from the figure due to the possibility of unstable material behavior when maximum stresses are near the ultimate strength of the material. additionally, data from runout tests are also excluded. it is clear from this figure that, despite reasonably good correlation between the different multiaxial load paths under fully-reversed conditions, life predictions are increasingly non-conservative for uniaxial loading conditions as the r ratio, and thus tensile mean stress, is increased. a similar trend of non-conservative fatigue life predictions in the presence of tensile mean stress was also observed for ductile cast iron data reported by meyer [5]. figure 1: fatigue life correlations for 7075-t651 aluminum alloy based on (a) fs and (b) modified fs parameters with uniaxial strainlife properties and k = 1. although increasing the k value in the fs parameter can improve the correlation of mean stress data by increasing the influence of the maximum normal stress term, this also has a detrimental effect on the correlation of fatigue data generated under other multiaxial loading paths. this is especially true for pure torsion loading where the maximum normal stress on the maximum shear plane is zero. it should also be noted that the accuracy of life predictions based on shear a (a) (b) n.r. gates et alii, frattura ed integrità strutturale, 37 (2016) 160-165; doi: 10.3221/igf-esis.37.22 163 strain-life properties is more sensitive to changes in k value. this is because the γ-n life prediction curve (eq. 1) does not change with the k value in the same manner that the uniaxial life prediction curve (eq. 2) does. given these results, modifications to the fs parameter were investigated in an attempt to improve life predictions. because life predictions were found to be non-conservative in the presence of significant tensile mean stress, it was apparent that the effect of maximum normal stress should be increased when such conditions exist. however, in order to maintain good fatigue life correlations for fully-reversed and multiaxial loading conditions, the influence of the normal stress term should not change in these cases. it was determined that substituting the yield strength in the fs equation for a quantity based on stress amplitude/range could achieve this effect. in addition, it can also be observed in fig. 1(a) that the correlation between fully-reversed axial and torsion fatigue data begins to degrade in the high cycle fatigue regime. therefore, substituting yield strength for a value based on shear stress was thought to be beneficial. this was based on the idea that the ratio of normal stress to shear stress could allow for better consideration of interaction effects between the two types of stresses. through some trial and error, it was found that replacing σy in eq. 1 with gδγ, where δγ is the shear strain range on the maximum shear strain plane, resulted in improved fatigue life correlations in the presence of mean stress. this yields the following equation for multiaxial fatigue damage calculation:               ' ,max 'max 1 2 2 2 b cf o on f f fk n n g g (3) shear stress range was expressed using gδγ, as opposed to δτ, in order to account for the effect that changes in material constitutive behavior can have on fatigue damage. although gδγ is equal to δτ at longer lives, where deformation is elastic, normalizing σn,max by a quantity based on strain predicts an increase in damage when cyclic and/or nonproportional hardening occur. normalizing σn,max by δτ, on the other hand, would result in the same damage value in situations where the two stress components change proportionally as a material hardens. this modified damage parameter maintains all of the advantages and physical interpretations of the original fs parameter, as discussed in the introduction, without introducing any additional empirical fitting constants. additionally, from a physical standpoint, the reduction of the normal stress term with increasing shear stress/strain range may reflect the idea that as shear stress/strain increases, larger local shear deformations are able to overcome some of the resistance caused by friction and interlocking between opposing crack faces. although there is a possibility for unrealistically large damage values to be computed as the shear strain range approaches zero, this mathematical issue can be overcome by imposing appropriate limits on the shear strain range required to produce fatigue damage. for example, in situations where the shear strain range is below its fatigue limit value, the damage parameter can be assumed to take a value of zero. the right-hand side of eq. 3, which relates the value of the damage parameter to fatigue life based on shear strain-life properties, can alternatively be expressed in terms of uniaxial fatigue life properties as follows:                                 ' ' ,max 'max 1 1 2 1 2 2 2 4 b c bf fn e f p f f fk n n k n g e g (4) by recalculating fatigue damage for the 7075-t651 test data, improvements offered by the modified fs parameter become evident in fig. 1(b). a k value of 1 was used in all modified parameter damage calculations. fatigue life correlations are not only qualitatively improved, with a tighter grouping of test data from all loadings conditions, but the overall accuracy of predictions is also increased. additionally, comparisons between modified parameter calculations based on the inclusion of δτ versus gδγ revealed that differences in life predictions were negligible above 1000 reversals, and within a factor of around 1.5 at lives on the order of 50 reversals. load path effects on damage calculation n addition to improved mean stress consideration, multiaxial fatigue life correlations and predicted failure planes under fully-reversed loading conditions remain very similar to the already accurate predictions based on the original fs parameter. in fact, fully-reversed data correlations were even found to improve slightly using the modified version i n.r. gates et alii, frattura ed integrità strutturale, 37 (2016) 160-165; doi: 10.3221/igf-esis.37.22 164 of the parameter. this is especially evident in the comparison between fully-reversed axial and torsion loading conditions in figs. 1(a) and 1(b). in order to further evaluate the characteristics of the proposed modified fs parameter, a limited number of fatigue tests were also performed in this study using specialized load paths meant to differentiate between the two different versions of the parameter. these tests featured loading conditions which result in the same damage value based on the original fs parameter, but different damage values based on the modified parameter. differences in experimental lives were compared to predictions to determine which parameter more closely reflects the fatigue damage variation between loading paths. these tests were conducted using a triangular shaped load path in shear versus axial stress space. this path, along with its corresponding stress-time history, is shown in fig. 2(a) based on normalized axial and shear stress variations. figure 2: (a) triangular load path in terms of stress-time history and shear vs. axial stress path, and (b) experimental and predicted fatigue life for discriminating load path tests. in analyzing potential load paths, it was found that by changing the ratio of applied shear to axial stress, relatively large differences in predicted fatigue damage could be obtained between the original and modified fs parameters. therefore, the same loading path was used in these tests, but with two different ratios of applied shear to axial stress, λ = τ/σ = 2 and λ = 0.5. stress values were carefully selected so that each path would result in the same fatigue damage value according to the fs parameter. additionally, experimental results from fully-reversed torsion tests with static tensile stress were also available for comparison at the same damage value. this additional loading path allows for the evaluation of damage predictions for cycles containing different load-time interaction between shear and normal stress components. the results of each of these tests are shown in fig. 2(b) along with life predictions from both the fs and modified fs damage parameters. results from the triangular load path tests (tri), at both nominal stress ratios, along with results from torsion with static tension loading (stsa), are included. a k value of 1 and uniaxial fatigue life properties were used for all analyses. in this figure, gray columns represent the average experimental fatigue life from two duplicate tests, while error bars indicate the individual life of each test. from these results, it is clear that variations in experimental fatigue damage exist between the different loading conditions. while the fs parameter in its original form does not account for these differences, the modified form of the parameter reflects the observed differences in fatigue life relatively well for each loading path considered. given the improvements in life predictions obtained when using the modified fs parameter to calculate fatigue damage, one final step was to analyze the remaining fully-reversed fatigue data generated for the 2024-t3 aluminum alloy tested in this study. these data, plotted against the original fs parameter in fig. 3(a), are presented again in fig. 3(b) with damage calculated using the modified form of the parameter. similar to the 7075-t651 data, it can be seen from these figures that the modified fs parameter provides somewhat improved fatigue life correlations for the 2024-t3 data. this is, again, evidenced by the slightly tighter grouping of test data from all loadings conditions. overall life prediction accuracy, however, is similar to that obtained using the original form of the parameter. summary and conclusions n this paper, the effects of mean stress and normal-shear stress interaction on multiaxial fatigue damage were investigated. based on literature data for 7075-t651 aluminum alloy, the fatemi-socie critical plane damage parameter was found to produce non-conservative life predictions in cases where significant tensile mean stress was present. while increasing the k value can improve uniaxial mean stress data correlation, this results in worse predictions i (a) (b) n.r. gates et alii, frattura ed integrità strutturale, 37 (2016) 160-165; doi: 10.3221/igf-esis.37.22 165 for other multiaxial loading conditions. it was found that by changing σy to gδγ in the fs parameter, the correlation of high tensile mean stress data was improved while retaining all the same physical interpretations of the parameter and adding no new material constants. additionally, a limited number of discriminating load path tests, performed using 2024t3 aluminum alloy, suggest that the modified fs parameter may also be able to better account for some of the effects of axial and shear stress interaction on fatigue damage. although the results of this study are encouraging, more experimental data and analysis are still needed, for different materials and loading conditions, to verify these findings. figure 3: fatigue life correlations for 2024-t3 aluminum alloy based on (a) fs and (b) modified fs parameters with uniaxial strain-life properties and k = 1. acknowledgements pecial thanks are given to the united states naval air systems command (navair) for financial support of this study and to nam phan for serving as a technical point of contact. references [1] you, b.-r., lee, s.-b., a critical review on multiaxial fatigue assessments of metals, int. j. fatigue 18 (1996) 235–244. [2] socie, d.f., marquis, g.b., multiaxial fatigue, society of automotive engineers inc., warrendale, pa, (2000). [3] fatemi, a., socie, d.f., a critical plane approach to multiaxial fatigue damage including out-of-phase loading, fatigue fract. eng. mater. struct. 11 (1988) 149–165. [4] zhao, t., jiang, y., fatigue of 7075-t651 aluminum alloy, int. j. fatigue 30 (2008) 834–849. [5] meyer, n., effects of mean stress and stress concentration on fatigue behavior of ductile iron, msc thesis, university of toledo, toledo, oh, (2014). [6] shamsaei, n., multiaxial fatigue deformation including non-proportional hardening and variable amplitude loading effects, phd dissertation, university of toledo, toledo, oh, (2010). [7] gates, n.r., fatemi, a., multiaxial variable amplitude fatigue life analysis including notch effects, int. j. fatigue (in press 2016). doi: 10.1016/j.ijfatigue.2015.12.011. [8] gates, n.r., fatemi, a., friction and roughness induced closure effects on shear-mode crack growth and branching mechanisms, int. j. fatigue (in press 2016). doi: 10.1016/j.ijfatigue.2016.01.023. s (a) (b) << /ascii85encodepages false /allowtransparency false /autopositionepsfiles true /autorotatepages /none /binding /left /calgrayprofile (dot gain 20%) /calrgbprofile (srgb iec61966-2.1) /calcmykprofile (u.s. web coated \050swop\051 v2) /srgbprofile (srgb iec61966-2.1) /cannotembedfontpolicy /error /compatibilitylevel 1.4 /compressobjects /tags /compresspages true /convertimagestoindexed true /passthroughjpegimages true /createjobticket false /defaultrenderingintent /default /detectblends true /detectcurves 0.0000 /colorconversionstrategy /cmyk /dothumbnails false /embedallfonts true /embedopentype false /parseiccprofilesincomments true /embedjoboptions true /dscreportinglevel 0 /emitdscwarnings false /endpage -1 /imagememory 1048576 /lockdistillerparams false /maxsubsetpct 100 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/hrv (za stvaranje adobe pdf dokumenata najpogodnijih za visokokvalitetni ispis prije tiskanja koristite ove postavke. stvoreni pdf dokumenti mogu se otvoriti acrobat i adobe reader 5.0 i kasnijim verzijama.) /hun 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can be opened with acrobat and adobe reader 5.0 and later.) >> /namespace [ (adobe) (common) (1.0) ] /othernamespaces [ << /asreaderspreads false /cropimagestoframes true /errorcontrol /warnandcontinue /flattenerignorespreadoverrides false /includeguidesgrids false /includenonprinting false /includeslug false /namespace [ (adobe) (indesign) (4.0) ] /omitplacedbitmaps false /omitplacedeps false /omitplacedpdf false /simulateoverprint /legacy >> << /addbleedmarks false /addcolorbars false /addcropmarks false /addpageinfo false /addregmarks false /convertcolors /converttocmyk /destinationprofilename () /destinationprofileselector /documentcmyk /downsample16bitimages true /flattenerpreset << /presetselector /mediumresolution >> /formelements false /generatestructure false /includebookmarks false /includehyperlinks false /includeinteractive false /includelayers false /includeprofiles false /multimediahandling /useobjectsettings /namespace [ (adobe) (creativesuite) (2.0) ] /pdfxoutputintentprofileselector /documentcmyk /preserveediting true /untaggedcmykhandling /leaveuntagged /untaggedrgbhandling /usedocumentprofile /usedocumentbleed false >> ] >> setdistillerparams << /hwresolution [2400 2400] /pagesize [612.000 792.000] >> setpagedevice microsoft word numero_60_art_xx_3137.docx o. shallan et al., frattura ed integrità strutturale, 60 (2022) 1-12; doi: 10.3221/igf-esis.60.01 1 interaction diagram for rc column strengthened by steel angles and strips osman shallan, thrwat sakr, mahmoud khater, ahmed ismail department of structural engineering, university of zagazig, zagazig, egypt osmanshalan@yahoo.com, thsakr@gmail.com, khater_civil@yahoo.com a.es.gabr@gmail.com, https://orcid.org/0000-0002-5942-5340 abstract. this paper presents an analytical model to construct the interaction diagrams (normal force and moment) for the rc column strengthened using the steel jacket technique. the proposed model is defined using the strain distribution block by determining the location of the neutral axis in the concrete section. the proposed analytical formulation is verified by experimental results performed by previous researches and numerical models using the nonlinear program ansys. the factors affecting the capacity of the strengthened column are taken into consideration, such as the amount of loads resisted by the steel cage, steel strips spacing, and the effect of concrete confinement. the results of the proposed model are in good agreement with the results from the experimental and numerical work used in verification. a practical design formula has been presented for strengthened columns. keywords. reinforced concrete; strengthening; steel angles; strips; eccentricity; interaction diagrams. citation: shallan, o., sakr, t., khater, m., ismail, a., proposed design criteria for column strengthened using steel angles and strips , frattura ed integrità strutturale, 60 (2022) 1-12. received: 18.07.2021 accepted: 05.01.2022 online first: 22.01.2022 published: 01.04.2022 copyright: © 2022 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. introduction c columns usually require strengthening to increase their capacities to sustain loads. for rc columns strengthened by steel angles and strips, four steel angles are fixed at the rc column corner and steel strips spaced at a suitable spacing and welded to the angles to form the steel jacket in this technique. grouting is used to fill the small gaps between the steel cage and the concrete column. this strengthening system requires a limited area around the column section when compared with concrete jackets. many researchers studied the behavior and efficiency of the strengthened column using the steel jacket under purely axial loads [1–5]. they studied the strengthening parameters as the size of the angles and strips, concrete strength, steel strips spacing, and direct or indirect loading on steel angles. analytical models for determining the capacity of the strengthened column using the steel jacket under axial load were also carried out [4, 6–9]. they discussed the factors affecting the capacity of the strengthening columns as the amount of load resisted by the steel angles, the effect of steel strips spacing, the effect of direct and indirect loading on the steel cage, and the effect of concrete confinement. for studying the strengthened column using steel jacketing under the eccentric load and slender column, some researchers conducted experimental and numerical studies to determine the capacity and mode failure of these columns [10,11]. others r https://youtu.be/jkyxxpdifpq osman s et al., frattura ed integrità strutturale, 60 (2022) 1-12; doi: 10.3221/igf-esis.60.01 2 construct the interaction diagram n-m using the experimental and numerical investigation to predict the capacity of the strengthened column for different eccentricities [12–15]. in this study, a practical analytical formulation is presented to construct the interaction diagram for columns strengthened using steel jackets. the proposed formulation is practical for determining the capacity of the strengthened columns under different eccentricities. the proposed model is verified using previous experimental work results done by [10, 12, 14, 16]. finite element models using the ansys program were also used to validate the proposed design formula . studying the behavior of strengthened columns using steel jacketing n order to study the behavior of concrete columns strengthened using steel jacketing (steel angles and strips), two main factors would be discussed. the first factor is the amount of load that the steel jacket can resist. the second factor is the improvement in concrete strength due to the confinement caused by the steel jacket. the majority of the researches conducted is carried out in their formulation of the ultimate load capacity of the strengthened column based on two basic modes of failure, failure caused by yielding of steel angles and failure caused by yielding in steel strips as follows. failure in the strengthened column due to yield in angles. in case of failure due to yielding in angles, local buckling occurs in angles. subsequently, the steel jacket is no longer able to confine the column. this behavior is based on the assumption that there are three points between every two strips, the two points at each strip are assumed to be hinged, while the point in the middle of the distance between strips is considered as a weak point in the angles as shown in fig. (1). figure 1: (a) the equilibrium model for the local buckling of the steel angles failure prediction. (b) failure of the strengthened column due to local buckling in steel angles experimental work of tarabia and albakry [8]. figure 2: failure of the strengthened column due to failure in strips experimental work tarabia and albakry [8] i o. shallan et al., frattura ed integrità strutturale, 60 (2022) 1-12; doi: 10.3221/igf-esis.60.01 3 failure in the strengthened column due to yield in strips. in this case, failure caused by yielding in strips due to the compression load on the column which leads to lateral strain in the concrete column and the steel jacket and causes an elongation in the strips subsequently the steel jacket isn't able to confine the column and the failure of the strengthened column occurred as shown in fig. (2). analytical models for load-carrying capacity: elow are some of the analytical expressions for determining the ultimate load for the strengthened column using steel angles and strips, which would be used to produce the proposed formula. fig. (3) shows the dimensions of the strengthened column using steel angles and strips used in the equations. figure 3: main dimensions of the strengthened column using steel angles and strips. eurocode (2008) [17]: some researchers consider the column strengthened by steel angle and strips as a composite column. according to eurocode, the ultimate load of composite columns can be expressed by the following equation:            0.85 / / 2.5    /ec c c s ys s l ap b d f a f b d f (1) where c, s, and a are the reduction factors for concrete, reinforcement, and structural steel strength at the ultimate limit states in practical design. however , for real comparison with the experimental work, these factors can be dispensed with. there are two main differences between the composite column behavior and the column strengthened by steel angle and strips, the first difference is the behavior of the composite action between the steel jacket and the concrete column. the second difference is the improvement of the concrete properties and strength due to the confinement of steel jacketing on the column, which would be addressed in the following researches. calderon et al. [6] calderon et al. [6] proposed a design formulation for determining the ultimate load carried by the strengthened column using steel angles and strips. the formula is based on the failure mode analysis observed in a numerical and experimental study presented in his research. the proposed design equation is expressed by the following equation:           0.85 2.5   ca c s ys l lp b d f a f b d f n (2) the factors nl (axial load carried by steel angles) and fl (confinement pressure) are calculated by two possible failure modes: failure due to material yielding of strips or yielding in angles as formed in the following equation. aa steel strips s steel angles l1xl1xt14l b h l1 s 2 l1 l1 sec a-a t2 t1 s2 x t2 b osman s et al., frattura ed integrità strutturale, 60 (2022) 1-12; doi: 10.3221/igf-esis.60.01 4      1 1.5  2 2.  .  .  . s b l ystrip t s f f e s b (3) where: (fl) when failure due to yield in strips          2 16. 2 1  . p l c m f f b s s (4) where: (fl) when failure due to yield in angles. badalamenti et al. [7] badalamenti et al. [7] proposed a design equation for determining the ultimate load that is carried by the rc column strengthened with steel angles and strips based on the effect of concrete confinement and load carried by the steel angles. the formula is expressed as the following equation :           campione 1 18cc s ys a ylp b d f a f n l t f (5) where, fcc = compressive strength of confined concrete; na = maximum axial force in angles; na and fcc are calculated by using the following formula.        0.87   1 4.74   lcc co co f f f f (6)             2 2 1 1 1 1 1   3   1 2 max yl yl a yl q s t f t f l n l t f (7) campione [18] campione [18] proposed an equation for calculating the capacity of the strengthened column using steel jacketing. to determine the confinement pressure, it is assumed that the confinement pressure is reduced in steel strips suddenly while it remains constant along the steel angle. the effect of concrete confinement and composite action between the concrete column and steel jacketing is taken into consideration, as the following equation :   1 1. . . . 8. . . .ult c a ys l ylp n b d f n l t f a f (8) where, n is the dimensionless load capacity of confined concrete core and na is the maximum axial force available indirectly loaded angles in the dimensionless as the following equation:                   0.87 1.5   1 1.42      s cc b cc s cd f f e f (9)                   1.5 11 1 2 2 1 1 1 0.63   0.5b t s b a s n e b lt l s s t (10) o. shallan et al., frattura ed integrità strutturale, 60 (2022) 1-12; doi: 10.3221/igf-esis.60.01 5 tarabia a. m. and albakry h. f. [8] tarabia a. m. and albakry h. f. [8] proposed an equation for determining the carried load by a column strengthened by steel angles and strips, compared to that proposed equation in calderon et al. [6] only with different in determining confinement effect on concrete core and load carried by steel jacketing, as the following equation.              2 2 2.     1 2 c l c s n f b b s e s t e (11) the load carried by the steel jacketing when axial compression of the column happens called direct loading, in this case, the steel jacket resists load with the concrete column from the beginning the load carried by the strengthened column, as the following equation.    1 12ult ylp l t f (12) campione et al. [14] campione et al. [14] proposed a design formula to define a plane fiber-section model of the column cross-section and take into consideration the frictional action along the column-angle face. the proposed formula is calibrated and validated by experimental results. the simple analytical stress-block procedure to derive continuous and simplified axial force bending moment domains is illustrated as a method for the hand-verification of reinforced cross-sections. the stress-strain laws assumed for the materials, the equilibrium equations of a reinforced cross-section written in the following form.                  \ \ \ \u c cc s s a a s s a an b x f a a a a (13)                                                     \ \ \ \ 2 4 1 4 2 c u c cc s s a a a a u x l m b x f d a d a d t l d a n (14) where xc = concrete block neutral axis from compression zone; σ's and σs = steel stress for top and bottom reinforcement; a's and as = steel bars areas respectively; σ'a and σa = steel stresses for top and bottom angles. salman and sherrawi [15] salman and sherrawi [15] performed a nonlinear numerical analysis in order to determine the carried load of the highstrength column with steel angles in the corner of the column. their numerical model takes into consideration the confinement effect of the concrete column due to existing steel angles and local buckling of it. they proposed a numerical method to predict the load capacity of the composite column at failure and study the efficiency of the steel angles in confining the concrete core. according to the numerical models, the column carried a large load after concrete cover spalling as discussed in their research. proposed analytical model numerical method will be discussed to construct the interaction diagram (m-n) for the strengthened column using steel angles and strips as shown in fig. (4). the axial load is plotted versus the bending moment m till failure. this method is based on the stress-strain compatibility procedure [17]. the effect of confinement on the concrete core, a osman s et al., frattura ed integrità strutturale, 60 (2022) 1-12; doi: 10.3221/igf-esis.60.01 6 the carried load by the steel jacket, the reduction in compression load in the steel jacket, and the steel jacket parameters are taken into consideration. the formulation is produced using the main four points from a to d as following . figure 4: main points used to plot the interaction diagrams for the strengthened column using steel angles and strips. point a (pure compression load: point a will be plotted as a point referring to pure compression failure. the maximum load-carrying capacity of the strengthened column takes into consideration the main parameters such as the concrete strength, the amount of steel reinforcement in the column, the steel yield stress, the effect of confinement on the concrete core, the carried load by steel jacket, the dimension of the steel angles and strips, and the composite action between the concrete column and steel jacket. the design model of campione, [18] will be used to calculate the ultimate carried load capacity of the strengthened column with the equation’s parameters shown in the previous section as following :            u cc a s angles y angles s ysp f b h n a f a f (15) point b (compression failure assumed) : point b will be plotted as a point referring to compression failure with a minimum eccentricity of the strengthened column. the compression failure is assumed to occur when the depth of the neutral axis is greater than its depth at the balanced position, fig. (5). figure 5: stress-strain distributions of point b which are used to plot the interaction diagrams for the strengthened columns. o. shallan et al., frattura ed integrità strutturale, 60 (2022) 1-12; doi: 10.3221/igf-esis.60.01 7 in this case, the tension steel stress in the steel angles and reinforcement is below the yield stress, and for simplicity, the neutral axis position is chosen at the tension steel location (c=d). thus, the developed force in the tension steel is equal to zero. the ultimate load and moment will be illustrated as follows:        \ \ \ \au cc sc sc s ysp f b a f a f (16)                          \ 2 2 2 2 u c s c h a h h m c c d s x (17) point c (balanced failure assumed) point c refers to the balanced failure of the column section. the failure of the balanced section occurs when the concrete reaches its maximum strain simultaneous with the yield strain in steel fig. (6). by definition, the point at the balanced section, the strain in the tension steel equals (s). thus, the stress in the tension steel equals (fy). the ultimate load and moment will be illustrated as follows:             au c c s t s cc bp c s c s t f b (18)                         \a 2 2 2 2 2 b u c s c h h h m c c d s x (19) figure 6: stress-strain distributions of point c which are used to plot the interaction diagrams for the strengthened column. point d (pure bending) in the case of a column subjected to pure bending or infinity eccentricity, the axial load is considered to be zero fig. (7). the locating of the neutral axis must be performed by applying the equilibrium equation as following:     c c s t sc s c s t (20)                  \ 0.8 cc c s c s s ys st yst c d c x a f b c e e a f a f c c (21) verification of the analytical proposed formula n order to verify the results of the proposed model in this study, some experimental researches work and numerical models have been concerned with stresses, strains, and deflections for the strengthened column to verify the proposed i osman s et al., frattura ed integrità strutturale, 60 (2022) 1-12; doi: 10.3221/igf-esis.60.01 8 formula. in this study, strengthened columns are modeled and studied using the commercial finite element software (ansys -version 19.2). figure 7 : stress-strain distributions of point c which are used to plot the interaction diagrams for the strengthened column. verification using finite element models. in order to verify the proposed model finite element models established in this paper using ansys software, the experimental researches work used in verification has been concerned with stresses, strains, and deflections for the strengthened column. the methods for implementing the test, and the quality of the materials, and the configuration of the specimens. solid element 65 is used to define concrete in 3d, link element 180 is used for steel reinforcement, solid 185 is defined for steel angles and strips, and steel plates for load distribution are defined as solid element 45. the components of the model, elements used, and boundary conditions are shown in fig. 8. figure 8: the numerical model’s component used in the verification. o. shallan et al., frattura ed integrità strutturale, 60 (2022) 1-12; doi: 10.3221/igf-esis.60.01 9 verification using previous experimental work. experimental work results of previous researches will be used to validate the proposed analytical model. the first experimental work was taken from montuori et al.[16], their specimens were (e-r1, d-r1, a-r1, and b-r1a) the second experimental work was taken from elsamny et al.[12] their specimens were (cl t3, c2 t5, c3 t7, c4 t3, c5 t5 , c6 t7, c7 t3, c8 t5, and c9 t7) . the third experimental work was taken from ezz-eldeen . [10] their specimens were (cs22e1 ,cs22e2, cs22e3 and cs22e4) . the fourth experimental work was taken from compaine et al. [14] their specimens were (rcaex1 ,rcaey1 ,rcbex1 and rcbey1). tab. 1 shows the specimen's details and experimental work results. the results of the finite element models will be discussed in the next section. failure load comparison ref. specimen column section fc' steel bars steel angles strips fya e n n n exp fem design mm mpa mm mm mpa mm kn kn kn montuori  et al.[16]  e-r1 150×150x500 26.4 4 φ 16 mm 4 l 30×2 15x3@125 mm 353 50 745 782.7 630 0.85 0.80 d-r1 150×150x500 26.4 4 φ 16 mm 4 l 30×2 15x3@125 mm 353 75 556 583.5 530 0.95 0.91 a-r1 150×150x500 26.4 8 φ 10 mm 4 l 30×2 15x3@125 mm 353 50 717 752.6 620 0.86 0.82 b-r1a 150×150x500 26.4 8 φ 10 mm 4 l 30×2 15x3@125 mm 353 75 524 550.1 520 0.99 0.95 elsamny et al.[12] cl t3 120×120x1000 15 4 φ 8 mm 4 l 20×2 20x2@490 mm 320 10 390 409.5 325 0.83 0.79 c2 t5 120×120x1000 15 4 φ 8 mm 4 l 20×2 20x2@245 mm 320 10 360 378 310 0.86 0.82 c3 t7 120×120x1000 15 4 φ 8 mm 4 l 20×2 20x2@164 mm 320 10 340 357 305 0.90 0.85 c4 t3 120×120x1000 15 4 φ 8 mm 4 l 20×2 20x2@490 mm 320 20 290 304.5 235 0.81 0.77 c5 t5 120×120x1000 15 4 φ 8 mm 4 l 20×2 20x2@245 mm 320 20 250 262.5 225 0.90 0.86 c6 t7 120×120x1000 15 4 φ 8 mm 4 l 20×2 20x2@164 mm 320 20 250 262.5 215 0.86 0.82 c7 t3 120×120x1000 15 4 φ 8 mm 4 l 20×2 20x2@490 mm 320 30 255 267.8 185 0.73 0.69 c8 t5 120×120x1000 15 4 φ 8 mm 4 l 20×2 20x2@245 mm 320 30 210 220.5 170 0.81 0.77 c9 t7 120×120x1000 15 4 φ 8 mm 4 l 20×2 20x2@164 mm 320 30 210 220.5 160 0.76 0.73 ezz‐ eldeen .  [10]  cs22e1 120×160x1000 28 4 φ 8 mm 4 l 20×2 20x2@250 mm 380 10 643 675.2 575 0.89 0.85 cs22e2 120×160x1000 28 4 φ 8mm 4 l 20×2 20x2@250 mm 380 20 552 579.6 510 0.92 0.88 cs22e3 120×160x1000 28 4 φ 8 mm 4 l 20×2 20x2@250 mm 380 30 474 497.7 455 0.96 0.91 cs22e4 120×160x1000 28 4 φ 8mm 4 l 20×2 20x2@250 mm 380 40 420 441 410 0.98 0.93 compaine  et al. [14]  rcaex1 220x300x820 12.7 6 φ 12 mm 4 l 50×5 40x4@136 mm 275 65 1048 1100 1150 1.10 1.05 rcaey1 220x300x820 12.7 6 φ 12 mm 4 l 50×5 40x4@136 mm 275 55 1205 1266 1175 0.97 0.93 rcbex1 220x300x820 24 6 φ 12 mm 4 l 50×5 40x4@136 mm 275 65 1370 1439 1250 0.91 0.87 rcbey1 220x300x820 24 6 φ 12 mm 4 l 50×5 40x4@136 mm 275 55 1476 1550 1350 0.91 0.87 table 1: specimens details and experimental work results and numerical models results. results and discussion he comparison between the result of the proposed interaction diagram, experimental and numerical models is shown in tab. 1. it can be seen that the results obtained using the proposed interaction diagram give a difference from 2 % to 30 % with an average difference of 12 % as illustrated in tab. 1. it can be seen that the value of the experimental and numerical is bigger than the value of the proposed model, which is considered as an advantage of the proposed method as a conservative design approach. it is also noticed that the results of the strengthened column with big eccentricity have a small difference with the proposed model results than the column with small eccentricity. fig. from (9-12) shows the comparison between the proposed interaction diagram and the experimental work of the researches used in verification. t 𝑁 𝑑𝑒𝑠𝑖𝑔𝑛 𝑁 𝐹𝐸𝑀 𝑁 𝑑𝑒𝑠𝑖𝑔𝑛 𝑁 𝐸𝑥𝑝 osman s et al., frattura ed integrità strutturale, 60 (2022) 1-12; doi: 10.3221/igf-esis.60.01 10 figure 9: comparison between the proposed i-d and the experimental work of ezz-eldeen, [10]). figure 10: comparison between the proposed i-d and the experimental work of elsamny et al.[12] ) figure 11: comparison between the proposed i-d and the experimental work of (montuori, and rizzano [16]). figure 12: comparison between the proposed i-d and the experimental work of compaine et al. [14]. as shown in fig. (9-12), the interaction diagram constructed from the proposed model comparison with the experimental work results are in good agreement and gives a practical design method for determining the capacity of the strengthened column under the different cases of loading. it can be noticed that the first point (a) which refers to pure axial load is almost underestimation, while the other points have a good agreement with the experimental and numerical results. fig. 13 shows the results of the numerical work using the finite element program. o. shallan et al., frattura ed integrità strutturale, 60 (2022) 1-12; doi: 10.3221/igf-esis.60.01 11 figure 13: deformation in strengthened column specimen (c1 t3) at failure comparison between numerical and experimental results for verification. conclusions his paper presents an analytical design formulation to construct the interaction diagrams (n-m) for the rc column strengthened by steel angles and strips, and the following conclusions can be drawn within the scope of this study:  the proposed analytical interaction diagram is efficient in determining the capacity of columns strengthened using steel jackets in different eccentricities.  the proposed analytical formula takes into consideration the factors affecting the behavior and the capacity of the strengthened column as the amount of loads resisted by the steel angles, the effect of steel strips spaci ng, and the effect of concrete confinement.  the proposed analytical formula was verified using experimental and numerical models with a good agreem ent with the difference from 2 % to 25 % with an average difference of 12 %.  the finite element models using the ansys program give a variety in studying the parameters affecting the behavior of the strengthened column under different eccentricities and valuable for constructing and verific ation the proposed analytical formulation. references [1] belal, m. f., mohamed, h. m. and morad, s. a. (2015) ‘behavior of reinforced concrete columns strengthened by steel jacket’, hbrc journal, 11(2), pp. 201–212. doi: 10.1016/j.hbrcj.2014.05.002. [2] saraswathi, m., saranya, s. and saranya, s. (2016). strengthening of rc square column using steel angles, international journal of emerging technology in computer science & electronics, 20(3), pp. 226–231. [3] khalifa, e. s. and al-tersawy, s. h. (2014) ‘experimental and analytical behavior of strengthened reinforced concrete columns with steel angles and strips’, international journal of advanced structural engineering, 6(2). doi: 10.1007/s40091-014-0061-6. [4] campione, g. (2012). strength and ductility of r.c. columns strengthened with steel angles and battens, construction and building materials, 35, pp. 800–807. doi: 10.1016/j.conbuildmat.2012.04.090. [5] giménez, e. et al. (2009). full-scale testing of axially loaded rc columns strengthened by steel angles and strips ester, advances in structural engineering, 12(2), pp. 169–181. doi: 10.1260/136943309788251704. [6] adam, j. m. et al. (2009). axially loaded rc columns strengthened by steel caging. finite element modelling, construction and building materials, 23(6), pp. 2265–2276. doi: 10.1016/j.conbuildmat.2008.11.014. t osman s et al., frattura ed integrità strutturale, 60 (2022) 1-12; doi: 10.3221/igf-esis.60.01 12 [7] badalamenti, v., campione, g. and mangiavillano, m. l. (2010). simplified model for compressive behavior of concrete columns strengthened by steel angles and strips, journal of engineering mechanics, 136, pp. 230–238. doi: 10.1061/asceem.1943-7889.0000069. [8] tarabia, a. m. and albakry, h. f. (2014). strengthening of rc columns by steel angles and strips, alexandria engineering journal, 53(3), pp. 615–626. doi: 10.1016/j.aej.2014.04.005. [9] cavaleri, l., trapani, f. di and ferrotto, m. f. (2016). steel jacketing of rc columns: reliability of capacity laws for concrete, in environment international conference, pp. 93–104. [10] ezz-eldeen (2016). steel jacketing technique used in strengthening reinforced concrete rectangular columns under eccentricity for practical design applications, international journal of engineering trends and technology, 35(5), pp. 195–204. doi: 10.14445/22315381/ijett-v35p243. [11] nimnim, h. t. and al-bahadli, h. a. (2019) ‘structural behavior of slender high-strength rc columns strengthened by steel angles’, 23(4), pp. 1–12. doi: 10.1061/(asce)sc.1943-5576.0000393. [12] elsamny, m. k. et al. (2013). experimental study of eccentrically loaded columns strengthened using a steel jacketing technique, international journal of civil, architectural, structural and construction engineering, 7(12), pp. 1–8. [13] al-sherrawi, m. h. and salman, h. m. (2015). analytical model for construction of interaction diagram for rc columns strengthened by steel jacket, international journal of science and research, 6(10), pp. 2319–7064. doi: 10.21275/art20177139. [14] campione, g. et al. (2017). frictional effects in structural behavior of no-end-connected steel-jacketed rc columns: experimental results and new approaches to model numerical and analytical response, journal of structural engineering (united states), 143(8), pp. 1–15. doi: 10.1061/(asce)st.1943-541x.0001796. [15] salman, h. m. and al-sherrawi, m. h. (2018). interaction diagram for a reinforced concrete column strengthened with steel jacket, international journal of civil engineering and technology, 9(6), pp. 1369–1377. [16] montuori, r., piluso, v. and rizzano, g. (2004). ultimate resistance of reinforced concrete columns strengthened with angles and battens: theoretical model and experimental validation, 3 th world conference on earthquake engineering. [17] british standards institution and for, c. (2005). eurocode 8, design of structures for earthquake resistance. part 3, general rules, seismic actions and rules for buildings. london: british standards institution. [18] campione, g. (2013). rc columns strengthened with steel angles and battens: experimental results and design procedure, practice periodical on structural design and construction, 18(1), pp. 1–11. doi: 10.1061/(asce)sc.1943-5576.0000125. << /ascii85encodepages false /allowtransparency false /autopositionepsfiles true /autorotatepages /none /binding /left /calgrayprofile (dot gain 20%) /calrgbprofile (srgb iec61966-2.1) /calcmykprofile (u.s. web coated \050swop\051 v2) /srgbprofile (srgb iec61966-2.1) /cannotembedfontpolicy /error /compatibilitylevel 1.4 /compressobjects /tags /compresspages true /convertimagestoindexed true /passthroughjpegimages true /createjobticket false /defaultrenderingintent /default /detectblends true /detectcurves 0.0000 /colorconversionstrategy /cmyk /dothumbnails false /embedallfonts true /embedopentype false /parseiccprofilesincomments true /embedjoboptions true /dscreportinglevel 0 /emitdscwarnings false /endpage -1 /imagememory 1048576 /lockdistillerparams false 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can be opened with acrobat and adobe reader 5.0 and later.) >> /namespace [ (adobe) (common) (1.0) ] /othernamespaces [ << /asreaderspreads false /cropimagestoframes true /errorcontrol /warnandcontinue /flattenerignorespreadoverrides false /includeguidesgrids false /includenonprinting false /includeslug false /namespace [ (adobe) (indesign) (4.0) ] /omitplacedbitmaps false /omitplacedeps false /omitplacedpdf false /simulateoverprint /legacy >> << /addbleedmarks false /addcolorbars false /addcropmarks false /addpageinfo false /addregmarks false /convertcolors /converttocmyk /destinationprofilename () /destinationprofileselector /documentcmyk /downsample16bitimages true /flattenerpreset << /presetselector /mediumresolution >> /formelements false /generatestructure false /includebookmarks false /includehyperlinks false /includeinteractive false /includelayers false /includeprofiles false /multimediahandling /useobjectsettings /namespace [ (adobe) (creativesuite) (2.0) ] /pdfxoutputintentprofileselector /documentcmyk /preserveediting true /untaggedcmykhandling /leaveuntagged /untaggedrgbhandling /usedocumentprofile /usedocumentbleed false >> ] >> setdistillerparams << /hwresolution [2400 2400] /pagesize [612.000 792.000] >> setpagedevice microsoft word 2343 m. bezzerrouki et alii, frattura ed integrità strutturale, 48 (2019) 491-502; doi: 10.3221/igf-esis.48.47 491 innovative geometric design improves the resistance of simple metal / metal lap joint mehadjia bezzerrouki, kouider madani, abderrahmane sahli university of djillali liabes, lmpm laboratory, sidi bel abbes, algeria m_bezzerrouki@yahoo.fr, koumad10@yahoo.fr, sahliabderahmen@yahoo.fr sébastien touzain, stéphanie mallarino university of la rochelle, lasie laboratory, la rochelle, france sebastien.touzain@univ-lr.fr , stephanie.mallarino@univ-lr.fr abstract. bonded assemblies are widely used in many industrial sectors mainly in the aerospace field. many researches in these domains are focused on evaluating the stresses in the adhesive layer in order to achieve maximum strength and long service life. factors that affect joint design are the mechanical and physical properties of the adhesive and the substrate. the reduction of stress concentration at the edges of the adhesive provides the strength of the adhesive layer. our work fits in this context, based on the astm d1002 standard. the innovative idea of this paper is to bring geometric improvements to an assembly system type aluminum/aluminum 2024-t3 bonded with an adhesive adekit a-140. the analysis of the stress distribution is performed by the three-dimensional finite element method using the abaqus calculation code. the geometric improvements presented in this work are beneficial and the results show a good reduction of the stress concentration along overlap length. keywords. single lap joint; adhesive; stresses; overlap length. citation: bezzerrouki, m., madani, k., sahli, a., touzain, s., mallarino, s., innovative geometric design improves the resistance of simple metal/metal lap joint, frattura ed integrità strutturale, 48 (2019) 491-503. received: 02.01.2019 accepted: 12.02.2019 published: 01.04.2019 copyright: © 2019 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. introduction he principal aims of adhesive bond are to ensure a uniform distribution of stress along overlap length and transmit a maximum of them to minimize a stress concentration which causes damage [1]. structural adhesive are strong, with a specifics characterizations which respond for the needs of different fields. the study of the influence of shear and peel stresses are very interesting in the fracture mechanics. the astm is an international standards organization that prepares and produces technical standards for materials, systems and products, it’s developed for testing and t http://www.gruppofrattura.it/va/48/2343.mp4 m. bezzerrouki et alii, frattura ed integrità strutturale, 48 (2019) 491-502; doi: 10.3221/igf-esis.48.47 492 classifying different materials used normalized specimen. the astm d1002 [2] is used for testing shear stress strength of adhesive for single lap joint made of two normalize plates adhesively bonded under tensile load. one presents here a brief outline of previous related works in the same domain. goland and reissner worked on the behavior of flexible adhesive using a normal stress [3]. hart-smith studied the shear and peel stresses distributions and gives a simplification for uncoupling shear and peel stresses [4]. he also developed solutions for stepping a single lap joint [5]. bigwood and crocombe [6] presented general elastic, shear and peel analysis for single lap joint using finite element analysis. chiu and jones [7] applied a finite element method to study a shear stress using a thick adherend test for a single and a symmetrical double lap joint. pereira and morais [8] conducted an experimental study using a double cantilever beam tests for single and double lap joints measured the critical strain energy-release rate and numerical one with finite element analysis using abaqus code to explain a strength behavior and peel stresses at the edges of overlap area. setoodeh, a. r and al. [9] used numerical and analytical methods for double lap joints to calculate peel stress using crack closure integral method and jintegral approach. nunes, s.l.s and al. [10] a numerical analysis was used to compares the tensile performance of different chosen adhesives for single and double-lap joints by varying the overlap length to express normal and shear stresses over adhesive thickness and the cohesive zone modeling approach is introduced to estimate the joint strength. recently, several studies have been made to try to reduce the stress concentration at the edges of the adhesive by the geometric modification of the edges of the plate by bevelling and or bead of the adhesive [11, 12] or by the combination of two modifications. others have tried to improve the overlap length by geometrical modification for the adhesive and adherends edge such a waved, beveled or notched which presented a significant decrease in peel and shear stresses and ameliorate the quality and the durability of the structural adhesive joints [13], as well as the assembly of composite materials, attempts have been made to introduce hybrid composite materials and to change fiber orientations in the different adhesive layers. madani, k. and al. [14] studies the effect of the geometry of the edge adhesive and adherend on reducing von mises, peel and shear stresses in the adhesive layer, several forms were considered namely bead of adhesive, internal and external beveling of the plate and the combination of an adhesive bead and beveling of the plate [15]. our work fits in this context; the aim of this study is to improve the bonding techniques by introducing geometric modifications on astm-d1002 single-lap-joint making with 2024-t3 aluminum specimens bonded with adekit a140 adhesive. two modifications are made to the single-lap-joint astm-d1002, the first is a reduction of thicknesses of plates along overlap length and the second one is to apply a reduction for only one plate for the assembly. the specimens were simulated numerically by the three-dimensional finite element method using the abaqus calculation software. the results clearly show that these two modifications bring about a considerable reduction of the stresses at the edge and the depth of the adhesive. geometrical model and mechanical properties ne considers an assembly of two 2024-t3 aluminum plates bonded with adekit a-140 adhesive. the basic geometric model is the astm d1002 single-lap-joint. the dimensions of the different substrates of the astm d1002 single-lap-joint without modification are shown in fig. 1 and it is called in this paper: model 1. the fixations localized are gives at grips areas and the stress are applied at one side along x axis using variable values. figure 1: basic geometrical model astm d1002 (model 1). o mm grip area grip area overlap area lo=12.7 63.5 mm 190.5 mm 139.7 mm 25 4 mm 25.4 mm 63.5 mm 25.4 mm overlap area 2 mm 0.2 mm 2 mm σ x y z m. bezzerrouki et alii, frattura ed integrità strutturale, 48 (2019) 491-502; doi: 10.3221/igf-esis.48.47 493 adekit a-140 adhesive presents a high mechanical performance and is used in several industrial sectors, in aeronautics. among these advantages:  excellent mechanical and thermal performances up to 100°c  excellent strength to dynamic loads (vibrations and impacts)  product adapted to stringent ageing and aggressive environments the mechanical properties of the various substrates are taken from the tensile curves of aluminum plates and mass specimens of adhesive adekit a-140 which are represented in fig. 2, [16]. (a) (b) figure 2: stress/strain curves: a) aluminum plate 2024-t3; b) adhesive adekit a-140 [16]. materials e: young modulus (gpa) g: shear modulus (gpa) : poisson coefficient aluminum: 2024-t3 69 36.92 0.3 adhesive: adekit a-140 2.690 0.99 0.3 table 1: elastic properties of the aluminum plate and the adhesive [16]. the adhesive bonded joints have several advantages compared to the mechanical assemblies (riveting and bolting) which ensures uniform stress distribution and transfer over the bonded surface following the absence of holes and avoids overweight bolts but it is necessary to prevent the stress concentration at the edge and the environment effects (temperature, moisture) which causes a degradation of their mechanical properties and which will consequently have a bad transfer of load and thus a disband. for our study, we tried to present a method for the bonding of the aluminum plates on the damaged surface; this method consists to remove a material from the aluminum plate over overlap area with a thickness of 0.2 mm on a single plate, which illustrated at assembly named: model 2, as shown in the fig. 3. and the second modification is to remove a thickness of 0.1mm of aluminum material from each plate which represented at assembly called: model 3, as shown in the fig. 4. this procedure covers the adhesive layer which can protect the assembly from the aging following the effect of temperature and moisture. figure 3: model 2: astm d1002 modified (reduction of 0.2 mm for one plate) 0.2 mm lo 2 mm 2 mm 0.2 mm overlap area overlap area. m. bezzerrouki et alii, frattura ed integrità strutturale, 48 (2019) 491-502; doi: 10.3221/igf-esis.48.47 494 figure 4: model 3: astm d1002 modified (reduction of 0.1 mm for both of plates). finites elements models he models are simulated with a three dimensional finite element method analysis using abaqus software [17]. a refined mesh is presented at the adhesive layer and plates to determine the maximum stresses which are located at the adhesive interface / adheres to the free edge. indeed, the refinement of the mesh is of great importance for the analysis of the structure. the linear elements (c3d8r) are used for the mesh of all parts of the models studies. the number of elements over parts of aluminum plate and the adhesive layer are respectively 14240 and 1275 for the model 1, 16167 and 1275 for model 2 and 3. the fig. 5 shows the detail of the meshed models. each layer is considered as an individual three-dimensional structure under a state of plane-stress and can be connected with adhesive bonds. the adhesive layer is homogeneous, elastoplastic, isotropic and deforms under shear and peel stresses. figure 5: mesh of the single-lap-joint and the detail at the overlap joint. in the finite element model the nodes are common between the aluminum plate and the adhesive layer so that there is a continuity of deformation and stress. this technique of the three layers modelling was used by naboulsi and mall [18]. the advantage of modelling the adhesive is to provide a continuous body to be able to capture the characteristics of the adhesive which are required for considering the progressive damage, heating effects, a nonlinear behavior of material, etc. results and analysis he overlap length is an important parameter in the strength of the assembly, for the astm d1002 there are a small overlap length compared to the length of plates and therefore a large load transfer through the adhesive layer. t t 2 mm overlap area 2 mm lo overlap area. 0.1 mm 0.1 mm m. bezzerrouki et alii, frattura ed integrità strutturale, 48 (2019) 491-502; doi: 10.3221/igf-esis.48.47 495 the analysis of the stress distribution in the bonded assemblies is essential in order to predict the level of stress intensity for each substrate. almost all the applied load will be transmitted to the adhesive which is the weak link of the structure seen these weak mechanical properties comparing to those of the plates. the adhesive will be subjected to a set of stresses, mainly the shear and peel stresses caused by the non-linearity of the two forces. one exposed the fig. 6 to explain the difference of stresses between the zones a and b. the stress distribution is not symmetrical because the two edges of the adhesive are not included at the same zone of the plate. fig. 6a shows an example of von-mises stresses distribution for an applied stress of 20 mpa for model 1. the stress distribution in the adhesive layer for the single lap joint is not homogeneous. in our study the stress distribution was determined along the ab segment on the adhesive / plate contact area represented in the fig. 6b. noting that the points a and b represented the zones a and b respectively. the point a is on the free side at the edge of the adhesive and the plate, so we have high stresses due to the edge effect. on the other side, the point b is on the plate and at the limit only of the adhesive where the stresses are lower compared to the point a. (a) (b) figure 6 : (a) von-mises stresses distribution, (b) representation of zones a et b. study of the stress distribution for model 1 one knows that the area stressed in the adhesive increase proportionally with applied stress and it is the same for the shearing and peeling stresses. fig. 7 shows the variation of von-mises stress, shear and peel stresses at the adhesive layer. one note that shear stresses remain almost low than von-mises and peel stresses. we clearly notice that whatever the value of the applied stress is the stress concentrations are localized at the edge adhesive layer. the depth of the adhesive remains inactive for low stress applied. an applied stress of 10 mpa generates a stress of 15 mpa in the adhesive. while the increase of the stress applied to 20 mpa generates almost 30 mpa what causes a degradation of the adhesive and makes work in its field of rupture. the bending moment caused by the nonlinearity of the forces causes high values of peel stresses, since the overlap length is minimal comparing to the lengths of the plates. inactive area zone a zone b m. bezzerrouki et alii, frattura ed integrità strutturale, 48 (2019) 491-502; doi: 10.3221/igf-esis.48.47 496 -2 0 2 4 6 8 10 12 14 0 5 10 15 20 25 30 (a) zone b zone a =10mpa =15mpa =20mpa v o n -m is e s s t r e s s ( m p a ) overlap length (mm) 0 2 4 6 8 10 12 14 0 2 4 6 8 10 12 14 16 (b) zone b zone a =10mpa =15mpa =20mpa s h e a r s tr e ss  xz (m p a ) overlap length (mm) -2 0 2 4 6 8 10 12 14 -5 0 5 10 15 20 25 (c) zone b zone a =10mpa =15mpa =20mpa p e e l s tr e ss  zz ( m p a ) overlap length (mm). figure 7: variation of a) von-mises, b) shear and c) peel stresses in the adhesive layer along the overlap length (case of model 1). m. bezzerrouki et alii, frattura ed integrità strutturale, 48 (2019) 491-502; doi: 10.3221/igf-esis.48.47 497 (a) (b) (c) figure 8: variation of a) von-mises, b) shear and c) peel stresses in the adhesive layer along the overlap length (case of model 2). m. bezzerrouki et alii, frattura ed integrità strutturale, 48 (2019) 491-502; doi: 10.3221/igf-esis.48.47 498 study of the stress distribution for model 2 the fig. 8 represents the variation of the stresses in the adhesive layer after modification in one of the two plates by removal of the material with a thickness of 0.2 mm so that the adhesive is entirely placed in one of the two plates, this will allow the adhesive to be exposed on one side to temperature and humidity. this method reduces the stresses at one of the two edges by reducing the bending moment. likewise, the increase in the applied stress increases the value of the various stresses in the adhesive layer. the depth of the adhesive will be less stressed comparing to the case of model1. the shear stress becomes a little weak in the adhesive and whatever the value of the stress applied at the edge and the core of the adhesive. likewise for peeling stresses, the values become weaker and the risk of peeling becomes negligible even for high stresses. adding that as the first model the distribution of stresses remain unsymmetrical. study of the stress distribution for model 3 the fig. 9 shows the variation of different stresses for the third model. it is clearly seen that the modification made to the two plates by removing the 0.1 mm material on each side of the plates has a considerable reduction in the various stresses at the edge and at the depth. in addition, symmetry is present in the stress distribution at the adhesive layer. we also note that the increase in the various stresses (von-mises, shearing and peeling) is low especially compared to model 1. it is concluded that the risk of separation is almost negligible in model 3. (a) (b) (c) figure 9: variation of a) von-mises, b) shear and c) peel stresses in the adhesive layer along the overlap length (case of model 3). m. bezzerrouki et alii, frattura ed integrità strutturale, 48 (2019) 491-502; doi: 10.3221/igf-esis.48.47 499 comparison of stresses at edge and depth of assembly along overlap length for the 3 models in order to clearly present the effect of the modifications made to the plates under the variation of the stresses, figs. 10 and 11 present the comparisons of the stresses at the edge and the depth of the adhesive. it is clear that increasing the applied stress considerably increases the various stresses at the edges. the percentage increase varies depending on the applied stress and the model used. one remark that; the first model has the highest rate for the different stresses in the adhesive layer and the lowest values are noted for the model 3. (a) (b) (c) figure 10: comparison of the stresses (a) -von-mises, (b) -shearing and (c) – peeling at edge for the 3 models of assembly according to the stresses applied. analyzing now the fig. 11 which gives the comparisons of the stresses inside the adhesive layer for the 3 models. it is noted that the stresses on the depths of the adhesive layers have low augmentation with the increase of applied stresses. for models 2 and 3 the stress curves coincide for the three types of stresses. comparison of inactive lengths in single-layer assemblies, adhesive is the weakest link in the structure where its mechanical properties are lower than those of the two plates and therefore the risk of cracking or separation of the plates is high. most research in this area is aimed at reducing edge stresses and working the central part of the adhesive, which in most cases remains inactive. m. bezzerrouki et alii, frattura ed integrità strutturale, 48 (2019) 491-502; doi: 10.3221/igf-esis.48.47 500 the purpose of this document is to modify the thickness of the two plates at the overlap length to minimize the concentration of stresses at the free edges that cause deflection and to try to work the central part of the adhesive. for this purpose, the ratio of the inactive length of the adhesive to the total length of the adhesive was represented to illustrate the effect of this geometric modification on the thickness of the two plates. thus introducing an idea of the comparison of inactive lengths that represent the variation of the inside length of the adhesive which is the safety zone to ensure the strength and adhesion of the assembly. the inactive length is shown in fig. 6a. the fig. 12 represents the variation of the ratio of the inactive length and the overlap length (linactive/l0 ) for the different stresses (von-mises, shear and peel). it is noted that the increase in the applied stresses surely generates a decrease of the ratio linactive/l0 but the difference remains weak comparing the three models which confirms the effectiveness of models 2 and 3. and on another side, one conclude that the changes made to the overlap part in the plates cause stresses in the entire overlap area and therefore the depth of the adhesive becomes active, which reduces the stresses at the edges. (a) (b) (c) figure 11: comparison of the stresses (a) -von-mises, (b) -shearing and (c) – peeling to the depths for the 3 models of assembly according to the stresses applied. conclusion n this study, the recapitulation of comparison of results for the models study gives following conclusions:  at the edges of the adhesive layer, the model 01 has the highest rate for the different stresses (von-mises, shear and peel), and the lowest values of this stresses are noted for the model 3 which attest the efficiency of the modification affected to the single-lap-joint. i m. bezzerrouki et alii, frattura ed integrità strutturale, 48 (2019) 491-502; doi: 10.3221/igf-esis.48.47 501 (a) (b) (c) figure 12: comparison of the ratio linactive / l0 according to the stresses applied of the 3 models for the stresses of: (a) vonmises, (b) shearing and (c) peeling.  at the depth of the adhesive layer, different stresses analyzed have low augmentation with the increase of stresses studied. noting also that a same behaviors for models 2 and 3 for the three types of stresses.  for the comparison of inactive length, the increase in the applied stresses surely generates a decrease of the ratio linactive / l0 but the difference remains weak comparing the three models which confirms the effectiveness of models 2 and 3.  the modification made to the plate considerably reduces the stresses at the edge of the adhesive and therefore makes the depth of the adhesive work, which balances the stresses along overlap length. references [1] baker, a., rose, f., jones, r. (2002). advances in the bonded composite repair of metallic aircraft structures. 1-2. elsevier. [2] astm standards (1999). standard test method for apparent shear strength of single-lap-joint adhesively bonded metal specimens by tension loading (metal-to-metal). https://www.admet.com/how-to-perform-an-adhesive-lap-joint-shear-strength-test-astm-d1002/ [3] goland, m. and reissner, e. (1944). j. appl. mech., (11), pp. a17–a24. [4] hart-smith, l. j. (1973). technical report nasa cr 112236, douglas aircraft company m. bezzerrouki et alii, frattura ed integrità strutturale, 48 (2019) 491-502; doi: 10.3221/igf-esis.48.47 502 [5] hart-smith, l. j. (1973). technical report nasa cr 112237, douglas aircraft company [6] bigwood, d. a. and crocombe, a. d. (1989). elastic analysis and engineering design formulae for bonded joints, j. adhes. adhes., (9), pp. 229–242, doi:10.1016/0143-7496(89)90066-3 [7] chiu, w. k. and jones, r. (1992). numerical study of adhesively bonded lap joints, j. adhes. adhes., (12), pp. 219– 225, doi: 10.1016/0143-7496(92)90057-3. [8] pereira, a. b. and morais, a. b. (2003). strength of adhesively bonded stainless steel joints, j. adhes. adhes., (23), pp. 315–322, doi: 10.1016/s0143-7496(03)00049-6. [9] setoodeh, a. r., hadavinia, h., biglari, f. r. and nikbin, f. k. (2005). comparison of analytical, numerical, and experimental methods in deriving fracture toughness properties of adhesives using bonded double lap joint specimens, j. adhes. adhes., (81), pp. 529–553, doi: 10.1080/00218460590944963. [10] nunes, s.l.s., campilho, r.d.s.g., da silva f.j.m., de sousa c.c.r.g., fernandes t.a.b., banea m.d., da silva l.m.f. (2015). comparative failure assessment of single and double-lap joints with varying adhesive systems, the journal of adhesion, doi:10.1080/00218464.2015.1103227. [11] elhannani, m., madani, k., chama, z., legrand, e., touzain, s., & feaugas, x. (2017). influence of the presence of defects on the adhesive layer for the single-lap bonded joint—part ii: probabilistic assessment of the critical state. j. aerosp. sci. technol., (63), pp . 372–386. doi:10.1016/j.ast.2016.12.020. [12] elhannani, m., madani, k., legrand, e., touzain, s., & feaugas, x. (2017). numerical analysis of the effect of the presence, number and shape of bonding defect on the shear stresses distribution in an adhesive layer for the single-lap bonded joint; part 1. j. aerosp. sci. technol., (62), pp. 122–135. doi:10.1016/j.ast.2016.11.024. [13] elhannani, m., madani, k., mokhtari, m., touzain, s., feaugas, x., cohendoz, s. (2016). a new analytical approach for optimization design of adhesively bonded single-lap joint. j. structural engineering and mechanics, 59(2), pp. 313326. doi : 10.12989/sem.2016.59.2.313. [14] [14] madani, k., mokhtari, m., belhouari, m., and hannani, m. (2013). effect of modifying the edges of the adherends and the adhesive on the stress distribution over the width and length of recovery, case of a single lap joint j. of mining, metallurgy & mechanical engineering (ijmmme). 1(4). [15] mokhtari, m., madani, k., belhouari, m., touzain, s., feaugas, x., ratwani, m. (2013). effects of composite adherend properties on stresses in double lap bonded joints. j. materials and design. (44), pp. 633-639, doi:10.1016/j.matdes.2012.08.001. [16] madani, k., touzain, s., feaugas, x., cohendouz, s., & ratwani, m. (2010). experimental and numerical study of repair techniques for panels with geometrical discontinuities. computational materials science, 48(1), pp. 83–93. doi: 10.1016/j.commatsci.2009.12.005 [17] abaqus/cae, ver 6.13 user’s manual, hibbitt, karlsson & sorensen, inc. [18] naboulsi, s., mall, s. (1996). modeling of a cracked metallic structure with bonded composite patch using the three layers technique. j. compos struct; (35), pp. 295–308. << /ascii85encodepages false /allowtransparency false /autopositionepsfiles true /autorotatepages /none /binding /left /calgrayprofile (dot gain 20%) /calrgbprofile (srgb iec61966-2.1) /calcmykprofile (u.s. web coated \050swop\051 v2) /srgbprofile (srgb iec61966-2.1) /cannotembedfontpolicy /error /compatibilitylevel 1.4 /compressobjects /tags /compresspages true /convertimagestoindexed true /passthroughjpegimages true /createjobticket false /defaultrenderingintent /default /detectblends true /detectcurves 0.0000 /colorconversionstrategy /cmyk /dothumbnails false /embedallfonts true /embedopentype false /parseiccprofilesincomments true /embedjoboptions true /dscreportinglevel 0 /emitdscwarnings false /endpage -1 /imagememory 1048576 /lockdistillerparams false /maxsubsetpct 100 /optimize true /opm 1 /parsedsccomments true 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/hrv (za stvaranje adobe pdf dokumenata najpogodnijih za visokokvalitetni ispis prije tiskanja koristite ove postavke. stvoreni pdf dokumenti mogu se otvoriti acrobat i adobe reader 5.0 i kasnijim verzijama.) /hun 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can be opened with acrobat and adobe reader 5.0 and later.) >> /namespace [ (adobe) (common) (1.0) ] /othernamespaces [ << /asreaderspreads false /cropimagestoframes true /errorcontrol /warnandcontinue /flattenerignorespreadoverrides false /includeguidesgrids false /includenonprinting false /includeslug false /namespace [ (adobe) (indesign) (4.0) ] /omitplacedbitmaps false /omitplacedeps false /omitplacedpdf false /simulateoverprint /legacy >> << /addbleedmarks false /addcolorbars false /addcropmarks false /addpageinfo false /addregmarks false /convertcolors /converttocmyk /destinationprofilename () /destinationprofileselector /documentcmyk /downsample16bitimages true /flattenerpreset << /presetselector /mediumresolution >> /formelements false /generatestructure false /includebookmarks false /includehyperlinks false /includeinteractive false /includelayers false /includeprofiles false /multimediahandling /useobjectsettings /namespace [ (adobe) (creativesuite) (2.0) ] /pdfxoutputintentprofileselector /documentcmyk /preserveediting true /untaggedcmykhandling /leaveuntagged /untaggedrgbhandling /usedocumentprofile /usedocumentbleed false >> ] >> setdistillerparams << /hwresolution [2400 2400] /pagesize [612.000 792.000] >> setpagedevice microsoft word numero_33_art_31 m. vormwald, frattura ed integrità strutturale, 33 (2015) 253-261; doi: 10.3221/igf-esis.33.31 253 focussed on multiaxial fatigue multi-challenge aspects in fatigue due to the combined occurrence of multiaxiality, variable amplitude loading, and size effects m. vormwald technische universität darmstadt, materials mechanics group, franziska-braun-str. 3, d-64287 darmstadt, germany vormwald@wm.tu-darmstadt.de abstract. the three major issues which contribute to uncertainties in fatigue life estimations are the limited transferability of material data obtained in a laboratory for describing the fatigue behavior of components, the lack of damage accumulation rules to realistically take into account the effects of various load sequences, and the uncertainty in the assessment of multiaxial stress states. the three issues contribute to life prediction errors in a balanced way. some modeling effort was spent in joining solution proposals in a unifying short crack model. the actual state is presented in the paper together with some ideas for further improvement as well as simplification for promoting the model’s acceptance in practical applications. keywords. multiaxial fatigue; short crack; critical plane. introduction or the stage of technical fatigue crack initiation conventional approaches like the local strain approach are applied which do not explicitly refer to the physical process of defect growth. this stage is treated as a black box where the failure process is disguised behind strain or stress life curves, damage accumulation rules, and multiaxial failure hypotheses. in such simulations, three major issues contribute to uncertainties in fatigue life estimations, the limited transferability of material data obtained in a laboratory for describing the fatigue behavior of components, the lack of damage accumulation rules to realistically take into account the effects of various load sequences, and the uncertainty in the assessment of multiaxial stress states. in a multi-scale modeling of the fatigue process, the next smaller scale of observation is the short crack growth regime. a large amount of research was dedicated to the investigation and accompanying modeling of short crack growth behavior with the aim to reduce the inaccuracies of conventional fatigue life estimation approaches. the accuracy of damage accumulation rules under variable amplitude loading was significantly enhanced by modeling the sequence-dependent opening and closure of short cracks. origins of limited transferability of material data may be identified in the size effect, the roughness effect, or the presence of residual stresses. some of these influences can be well explained using a short crack approach. for example, the non-homogeneous stress field in notches affects the crack driving force. considerable effort has been dedicated to model the statistical size effect, too. from the viewpoint of a short crack approach, the probability of exposure of a strength-reducing defect increases with the surface of the highly stressed material. finally, the short crack approach was introduced for the assessment of multiaxial fatigue. the three mentioned issues contribute to life prediction errors in a balanced way. some modeling effort was spent by hertel and vormwald [1,2] during the last years in joining solution proposals in a unifying short crack model. the actual state is presented together with some ideas for further improvement and simplification for promoting the model’s acceptance in practical applications. f m. vormwald, frattura ed integrità strutturale, 33 (2015) 253-261; doi: 10.3221/igf-esis.33.31 254 multiaxial fatigue crack initiation he macroscopic appearance of early fatigue crack initiation is similar under uniaxial, proportional, or nonproportional loading. in all cases short cracks initiate at microscopically small defects. a stage of stable fatigue crack growth follows. the crack selects a plane of growth which is usually termed critical plane. therefore, the critical plane approaches to multiaxial fatigue assessment are among the most preferred approaches. variants of this approach are explained in the standard text book of socie and marquis [3]. as an example, fig. 1 shows fatigue cracks initiated under uniaxial and severely non-proportional multiaxial loading. the crack growth has been monitored by hoffmeyer [4] who applied the replica technique. a part of this investigation has been published earlier in references [5] and [6] where more details can be found. a) 50 m b) figure 1: appearance of short fatigue cracks in aw5083 (also nominated as almg4.5mn or al5083), a) uniaxial loading with 0.3 %a  , b) multiaxial non-proportional pseudo-random strain sequence, straight-line cumulative frequency distribution ,max 0.346 %a  , ,max 0.6 %a  and a phase shift of 90° between the normal and the shear strain signal, hoffmeyer [4]. challenge 1: crack driving force it suggested itself to model the mechanisms by means of fracture mechanics [7-19]. naturally initiating cracks require stress and strain amplitudes of a magnitude that usually prevents the application of linear elastic fracture mechanics. a crack driving force from the collection of elastic-plastic fracture mechanics is selected. the first challenge is to define a reasonable and applicable formulation. strain based intensity factors and variants of the cyclic j -integral are used. here, some results are reported which adapted a formulation based on approximation formulas assumed to provide an estimate of the j -integral. 2 i,eff i ,eff2 xj y w a   (1) 2 ii,eff ii eff/ (1 ) xzj y w u a     (2) 2 iii,eff iii effxyj y w u a   (3) these formulas are supposed to be valid for semi-circular surface cracks. the x-coordinate is perpendicular to the crack area. besides geometry factors y for the three opening modes, the estimates rely on a proportionality between the direction-related portions of the strain energy density range, ijw , and the corresponding mode-related j -integral. a numerical check of the accuracy of this assumption is pending. t m. vormwald, frattura ed integrità strutturale, 33 (2015) 253-261; doi: 10.3221/igf-esis.33.31 255 challenge 2: effective ranges from uniaxial loading it is known that cracks only grow when their crack flanks do not touch, see e.g. [20]. little is known concerning crack closure under multiaxial loading. an example has been presented by hoffmeyer [4]. a thin-walled tube from steel s460n was tested under stain control with a butterfly strain sequence, fig. 2, two shear strain cycles, , were applied during one normal strain cycle,. thirty-three surface replicas of a naturally initiated crack were taken during a butterfly cycle at the - combinations indicated by dots in fig. 2. the snapshots are grouped together in an animation provided by a link. 0.0 30 25 20 15 510 1 0.2 0.4-0.2-0.4 0.00 0.25 0.50 -0.25 -0.50  in %  in % 300 m cr ac k c lo se d cr ac k o p en 1  cy clest2  cy clend figure 2: strain sequence, indicating (by dots) the - combinations of replicas, left, and inspection area of crack opening displacement evaluation, right, hoffmeyer [4]. 0 1 2 3 4 30 25 20 15 10 5 1 1  cy cle 2  cy cle c m sd 2  in %  in % 0.0 0.2 0.4-0.2-0.4 5 6 c m o d i n  m c m sd i n  m 0 1 2 3 4 5 6 0.0 0.2 0.4-0.2-0.4 0.6-0.6 10 1 20 30 st nd c m sd 1crack closed crack closed figure 3: crack mouth opening and sliding displacements, hoffmeyer [4]. the crack mouth opening and sliding displacements, cmod and cmsd, have been measured. in fig. 3 the local crack flank displacements (taken in the middle of the section shown by a white square in fig. 2 right) are plotted over the applied global strains. the crack flanks are in contact when the minimum normal strain is applied. the vertical line in fig. 2 gives an estimate of the crack opening and closure strain. crack flank sliding occurs while crack flanks are in contact, fig. 3 right. however, sliding is reduced, cmsd2, compared to a shear cycle without any contact, cmsd1. such observations of crack closure led to a phenomenological description of effective ranges in eq. (1) to (3). for the mode i loading portion the crack opening and closure global strain ( ,opx and ,clx are assumed to coincide) are modelled by first calculating an opening stress with ,op ,max 0 1 eqv,max max,eff( / ) for 0x x a a r r       0 max,eff f0.535 cos ( ) / ( 2 )a   1 max,eff f0.344( ) / ( 2 )a   (4) 2 2 2 max,eff ,max 3( )x xy xz      2 2 2 2 2 2 eqv,max ,max ,max( ) ( ) ( ) 6( ) / 2x y x z y z xy xz yz                  http://www.gruppofrattura.it/video/fis33/vormwald/vw2.html m. vormwald, frattura ed integrità strutturale, 33 (2015) 253-261; doi: 10.3221/igf-esis.33.31 256 where the x-coordinate is the crack area normal direction. the stress tensor components have to be provided in this coordinate system. next, the crack opening strain is determined in the ascending x-x path. the effective crack driving force is determined on the descending x-x path,   ,cl ,max ,eff ,max d x x x x x xw        . (5) the effective ranges associated with shear modes are estimated by defining an efficiency factor with            1 1eff fric f fric fln cos ( / 2 ) / 2( ) / ln cos ( / 2) / 2u                , (6) where fric act n,max    (7) is a model parameter requiring two fitting constants, act and , and n,max is the maximum normal stress during a shear cycle. these remarks on the crack closure phenomenon and the corresponding effective ranges should have made clear that the problems is away from being solved generally and provides another challenge for future research. challenge 3: definition of a damaging event – or a cycle most procedures apply rainflow counting of stress or strain components acting on the critical plane. there is hardly an alternative for defining a cycle although the physical basis of the rainflow algorithm is lost in non-proportional loading. a desirable approach would yield an incremental crack growth for an infinitesimal variation of the crack driving force. such an approach has been proposed for example by lu and liu [21] for uniaxial loading. for multiaxial loading some trials have been published, e.g. [22], to use plastic work as the responsible quantity for incrementally increasing the fatigue damage. the models have not yet achieved a wide acceptance. challenge 4: stress-strain paths the input for the cycle identification and counting must be provided by a calculation of components of the stress and strain tensor as a function of time. solving this task requires application of a cyclic plasticity model. contrary to a uniaxial case, the differential equations of incremental plasticity have to be solved. these models should address two phenomena which emerge in non-proportional loading: multiaxial ratcheting and non-proportional hardening. here, a model suggested by döring et al. [23] was used. fig. 4 shows a comparison of measured and calculated stresses for a strain controlled butterfly path. an animation showing the calculated stress path together with the kinematics of the yield surface is provided by link. the accuracy is better than acceptable; the numerical expense is enormous. -500 -250 0 250 500 -300 -200 -100 0 100 200 300  in m p a  in mpa measured calculated elastic   figure 4: measured and calculated stress response, strain controlled butterfly loading of a thin-walled tube, s460n, döring et al. [23]. challenge 5: mixed mode hypothesis the combined effect of mode-related crack driving forces on the crack increment has to be evaluated. little is known concerning mixed mode hypotheses for non-proportional fatigue [24]. generally, the hypothesis has to specify the crack http://www.gruppofrattura.it/video/fis33/vormwald/vw1.html m. vormwald, frattura ed integrità strutturale, 33 (2015) 253-261; doi: 10.3221/igf-esis.33.31 257 advance direction and the increment. in the crack initiation stage kinking in the critical plane is excluded and therefore only the increment must be calculated. it is not much more than a working hypothesis to simply add contributions of each mode according to m m m i,eff ii,eff iii,effd / da n c j c j c j      , (8) where m is the exponent of a power-law type crack growth rate formulation in terms of the j-integral. transfer of material data for describing the fatigue behavior of components he information gained by investigating material’s fatigue behavior under multiaxial fatigue must be made available for calculating fatigue lives of components. several tasks have to be fulfilled before arriving at a result. generally, a local stress or strain based approach is used. this implies the assumption that the life of a component can be determined from the failure life of a material element at the location of severest local stress and strain history. challenge 6: identification of critical locations it is not possible to identify the critical location only on the basis of quasi-static calculations of stresses and strains in the component, even after having gained the solutions for all loading cases. the fatigue live calculation for possibly very many locations has to be performed. the shortest of all lives obtained will determine the component’s life. challenge 7: calculation of local stress-strain time histories the method for calculating local stress and strain sequences might be the application of the finite element technology. however, the computational costs of such an approach are still too high for practical application. all actual software packages in the field heavily rely on approximations of the local elastic-plastic stress-strain histories on the basis of the knowledge of a hypothetical or pseudo linear elastic local stress histories,  e ij t . for all unit load cases, lk=1, the transformation factors, (cij)k, are calculated. the local pseudo-elastic stress time sequences are calculated by superposition,       1 l e ij ij kk k t c l t    (9) köttgen et al. [25] suggested two approaches, the pseudo stress and the pseudo strain based approach. both approaches are based on a two-step procedure. first, the relation between the loads and local stresses or plastic strains has to be established. second, the latter are related to its local counterpart. the term “relation” means application of an incremental plasticity model. in the pseudo stress approach loads are expressed in terms of pseudo stresses according to eq. (9), in the pseudo strain approach loads are expressed as pseudo strains. buczynski and glinka’s [26] extended neuber’s rule to non-proportional loading. the authors assume that the total of the distortional strain energy in an increment of loading is equal for elastic-plastic and linear elastic deformation. more precisely, the assumed identity is formulated for each component of the deviatoric stress and strain tensors individually. hertel et al. [27] compared the results of various approaches for a notched shaft under non-proportional tensioncompression and torsion. the results for a butterfly-type loading are redrawn in fig. 5. the accuracy of all approaches is comparable. the differences in predicted stress-strain paths are in the same order of magnitude as differences between measured and fe-calculated paths. some more comparisons can be found in [28]. challenge 8: size effects in the literature on size effects in fatigue several types of size effect are distinguished [29]. most important are the types taking into account the stress gradient and the highly stressed surface. although fracture mechanics is the favorite method for describing the stress gradient effect, the required solutions for the crack driving forces in non-homogeneous stress fields have not yet been developed. in the uniaxial case, only very sharp gradients have a considerable effect on crack initiation lives [29]. here, gradient effect has not yet been taken into account. fatigue life calculations based on defect growth considerations require the definition of an initial defect size. the initial crack depth for starting the simulation, a0, has to be determined. it is chosen in such a way that the life calculation model provides a realistic strain life curve of the material under consideration. the initial crack depth is regarded as a weibulldistributed random variable. the probability of finding an initial crack with a depth larger then a0 is written as t m. vormwald, frattura ed integrità strutturale, 33 (2015) 253-261; doi: 10.3221/igf-esis.33.31 258 0 0 κ( ) exp( ( / ) )p a a a   (10) the distribution parameter a and the weibull-exponent  are determined based on a statistical evaluation of the scatter of the initial crack depths from scatter of strain-life data. the initial crack depth for a component with any highly stressed surface a can be calculated by 1/ 0 0, ref ref( / )a a a a  (11) here a0,ref and aref are the initial crack depth and the highly stressed surface of the reference or material specimen. the variables a0 and a are the initial crack depth and the highly stressed surface of the structure under investigation. the component’s fatigue life therefore differs from material specimen’s fatigue for identical local stress and strain histories. s in mpa -200 0 200 -200 0 200 -200 0 200 -400 0 400 -0.8 -0.4 0.0 0.4 0.8 -0.5 0 0.5  in % experiment t i n m p a  in mpa  in m p a  in % pseudo-strain-app. pseudo-stress-app. fe-c alculation strain-energy -app. figure 5: local, notch root stress, , and strain, , states for a notched shaft under load controlled butterfly loading with tensioncompression (nominal stress s) and torsion (nominal stress t), s460n, hertel et al. [27]. sequence effects in variable amplitude loading wo major sources of sequence effect have been identified, either cyclic plastic deformation or geometric issues like a changing geometry of the structure during the fatigue process [30]. some of the sequence effects are severe. mean stress re-arrangement and plasticity induced crack closure as well as the continuous decrease of the technical endurance limit very strongly influence variable amplitude fatigue lives. challenge 9: sequence effects due to plasticity induced crack closure in the section on challenge 2 the determination of effective ranges for constant amplitude loading has been described. the crack opening strain x,op (or x,cl, respectively) discriminates effective and non-effective portions of a cycle. under variable amplitude loading the crack opening strain is considered to depend on the load sequence. two main cases are distinguished. if the constant amplitude crack opening strain of a cycle is smaller than the crack opening strain of previous cycles the crack opening strain is set to its constant amplitude value. this case is typical for large cycles following small cycles. if, however, the constant amplitude crack opening strain of a cycle is greater than the crack opening strain of previous cycles, the effective range of the actual cycle is computed using the old, lower crack opening strain. this case is typical for small cycles following large cycles. in this case effective ranges and crack growth increments of the proceeding small cycles are larger than they would be under constant amplitude conditions. an accelerating sequence effect is modeled. the small cycles following a large cycle continuously restore their constant amplitude crack opening strain level. the algorithm is described in more detail in reference [1]. it relies on rainflow cycle counting of the strain sequence. challenge 10: sequence effects due to increasing crack size a major issue in the assessment of variable amplitude loading is to realistically account for the damage contribution of load cycles with amplitudes smaller than the constant amplitude endurance limit. a fracture mechanics based assessment offers a natural solution of this problem. the threshold condition discriminates between growing and non-growing cracks. t m. vormwald, frattura ed integrità strutturale, 33 (2015) 253-261; doi: 10.3221/igf-esis.33.31 259 with the increasing crack length more and more smaller cycles contribute to crack growth. here, crack growth is calculated only for cycles for which the crack driving force is larger than its threshold. special attention must be paid to the fact that a short crack (sc) growth threshold is smaller than the long crack (lc) growth threshold. its dependence on the crack depth a is described by an empirical equation, eff,th,sc eff,th,lc / ( *)j j a a l     (12) the size of l* is determined by the fatigue strength of the material and the long crack growth threshold. results he notes on the challenging tasks listed above should have made clear that accurate life prediction results cannot be expected, yet. too many assumptions and simplifications had to be introduced. nevertheless, comparisons of experimentally and numerically determined crack initiation lives have been performed. the results for the most challenging cases of notched components under multiaxial variable amplitude loading are revisited, fig. 6. cy cles to crack initiation n o m in al m ax im u m n o rm al st re ss a m p li tu de s a, m ax i n m p a 200 400 600 800 1000 1200 cy cles to crack initiation 30 100 200 400 600 104 105 106 107 108 cy cles to crack initiation t a / sa = 0.873 s460n 50 100 200 400 500 300 50c rm o4v t a / sa = 0.5 g-a lsi7mg0.3 t a / sa = 1 104 105 106 107 108104 105 106 107 108 figure 6: experimentally ([1, 31]) and numerically ([1, 2]) determined crack initiation lives of shouldered shafts under non-proportional variable amplitude loading, nominal normal stress s and nominal shear stress t, phase shift 90°, pseudo random sequence with gaussian cumulative frequency distribution. a tendency of underestimating fatigue lives is observed. it might be attributed to the assessment of accelerating sequence effects. besides, the overall acceptable accuracy is certainly due to annihilation of errors gathered by imperfectly coping with the ten challenges. conclusion n the assessment of fatigue of components under multiaxial variable amplitude loading a list of challenges has been identified. any method is obliged to provide answers to all challenges. the list is incomplete. for example, the role of the inhomogeneous microstructure has not been addressed in this paper. however, it might have special influence. many materials are anisotropic featuring special weak planes of preferred crack growth. the actual experience leads to a ranking of the challenges with respect to their importance for the accuracy of the calculated lives. the mixed mode hypothesis should be appropriate – and at the same time it is the theory with weakest support for non-proportional loading. the crack closure plays a dominant role in connection with mixed mode and variable amplitude sequence effects. and the interaction with size effect assessment methods is highly speculative. on the other hand, the models for describing cyclic plastic deformation and for local strain estimation are well validated. a second ranking occurs to be performed with respect to simplifying the algorithms in order to accelerate the computation and promote acceptance. here, the models for describing cyclic plasticity rank first. most desirable would be an acceleration of the search of the critical plane orientation. and finally, the tracking of sequence effects calls for speeding up. t i m. vormwald, frattura ed integrità strutturale, 33 (2015) 253-261; doi: 10.3221/igf-esis.33.31 260 references [1] hertel, o., vormwald, m., short-crack-growth-based fatigue assessment of notched components under multiaxial variable amplitude loading, engineering fracture mechanics, 78 (2011) 1614–1627. [2] hertel, o., vormwald, m., multiaxial fatigue assessment based on a short crack growth concept, theoretical and applied fracture mechanics, 73 (2014) 17–26. [3] socie, d.f., marquis, g.b., multiaxial fatigue, sae warrendale, isbn 0-7680-0453-5, (2000). [4] hoffmeyer, j., anrisslebensdauervorhersage bei mehrachsiger beanspruchung auf basis des kurzrisskonzepts, institut für stahlbau und werkstoffmechanik, tu darmstadt, report 72 (in german), (2005). [5] hoffmeyer, j., döring, r., seeger, t., vormwald, m., deformation behaviour, short crack growth and fatigue lives under multiaxial nonproportional loading, int. j fatigue, 28 (2006) 508-520. [6] döring, r., hoffmeyer, j., seeger, t., vormwald, m., short fatigue crack growth under nonproportional multiaxial elastic-plastic strains, int. j fatigue, 28 (2006) 972-982. [7] socie, d.f., hua, c., worthem, d., mixed mode small crack growth, fat. fract. eng. mat. struct., 10(1) (1987) 1-16. [8] reddy, s., fatemi, a., small crack growth in multiaxial fatigue, in: astm stp 1122, advances in fatigue lifetime prediction techniques, (1992) 276-298. [9] socie, d.f., furman, s., fatigue damage simulation models for multiaxial loading, in: fatigue 96, 6th int. fatigue congress, berlin, (1996) 967-976. [10] de los rios, e., hussain, j., miller, k., a micro-mechanics analysis for short fatigue crack growth, fat. fract. eng. mat. struct., 8(1) (1985) 49-63. [11] zenner, h., pötter, k., schram, a., suhartono, h., simulation des mikrorisswachstums unter schwingbeanspruchung, materialwiss. u. werkstofft. , 32 (2001) 845-857. [12] ahmadi, a., zenner, h., düwel, v., mikrorissentstehung und mikrorisswachstum in aluminiumlegierungen bei zyklischer beanspruchung – werkstoffliche untersuchung und simulation, mat.-wiss. u. werkstofftech, 33 (2002) 265275. [13] hoshide, t., socie, d.f., crack nucleation and growth modelling in biaxial fatigue, engineering fracture mechanics, 29(3) (1988) 287-299. [14] hoshide, t., kusuura, t., life prediction by simulation of crack growth in notched components with different microstructures and under multiaxial fatigue, fat. fract. eng. mat. struct., 21(2) (1998) 201-214. [15] mcdowell, d.l., a shear stress based critical-plane criterion of multiaxial fatigue failure for design and life prediction, fat. fract. eng. mat. struct., 11(12) (1994), 1475-1485. [16] mcdowell, d.l., bennett, v.p., microcrack growth law for multiaxial fatigue, fat. fract. eng. mat. struct., 19(7) (1996) 821-837. [17] mcdowell, d.l., multiaxial small fatigue crack growth in metals, int. j. fat., 19 (1997) 127-135. [18] savaidis, g., seeger, t., consideration of multiaxiality in fatigue life prediction using the closure concept, fat. fract. eng. mat. struct., 20(7) (1997) 985-1004. [19] bonnen, j.j.f, topper, t.h., experimental determination and modeling of long crack crack-face interference-free crack propagation behavior in normalized sae 1045 steel, engineering fracture mechanics, 75 (2008) 804-820. [20] zhang, w., liu, y., investigation of incremental fatigue crack growth mechanisms using in situ sem testing, int. j. fatigue, 42 (2012) 14-23. [21] lu, z., liu, y., small time scale fatigue crack growth, int. j. fatigue, 32 (2012) 1306-1321. [22] jiang. y., ott, w., baum, chr., vormwald, m., nowack, h., fatigue life predictions by integrating evicd fatigue damage model and an advanced cyclic plasticity theory, int. j. plasticity, 25(5) (2009) 780–801. [23] döring, r., hoffmeyer, j., seeger, t., vormwald, m., a plasticity model for calculating stress-strain sequences under multiaxial nonproportional cyclic loading. computational materials science, 28(3-4) (2003) 587-596. [24] zerres, p., vormwald, m., review of fatigue crack growth under non-proportional mixed-mode loading, int. j. fatigue, 58 (2014) 75–83. [25] köttgen, v.b., barkey, m.e., socie, d.f., pseudo stress and pseudo strain based approaches to multiaxial notch analysis, fatigue fract. engng. mater. struct., 18(9) (1995) 981-1006. [26] buczynski, a., glinka, g., an analysis of elasto-plastic strains and stresses in notched bodies subjected to cyclic nonproportional loading paths, biaxial/multiaxial fatigue and fracture, elsevier (2003), [27] hertel, o., vormwald, m., seeger, t., döring, r., hoffmeyer, j., notch stress and strain approximation procedures for application with multiaxial nonproportional loading, materials testing, 47(5) (2005) 268-277. m. vormwald, frattura ed integrità strutturale, 33 (2015) 253-261; doi: 10.3221/igf-esis.33.31 261 [28] ye, d., hertel, o., vormwald, m., a unified expression of elastic-plastic notch stress-strain calculation in bodies subjected to multiaxial cyclic loading, int. j. solids and structures, 45(24) (2008) 6177-6189. [29] vormwald, m., hertel, o., kaffenberger, m., transferability of fatigue data, in: proc. xiii portuguese conf. on fracture, (2012) 13-21. [30] vormwald, m., classification of load sequence effects in metallic structures, procedia engineering, 101 (2015) 534542. [31] franz, r., xin, p., verbesserung der lebensdauerabschätzung für mehrachsig belastete sicherheitsbauteile aus schmiedestahl und aluminiumguss durch auswahl zutreffender berechnungsalgorithmen, forschungskuratorium maschinenbau e.v., frankfurt/m, germany (2013), fkm-net.de, report 319. microsoft word numero_46_art_12n s. mokadem et alii, frattura ed integrità strutturale, 46 (2018) 113-123; doi: 10.3221/igf-esis.46.12 113 developments in the fracture and fatigue assessment of materials and structures effect of the angles of the cracks of corroded plate in bonded composite repair salem mokadem, berrahou mohamed, mechab belaïd, belabbes bachir bouadjra university of djillali liabes, lpmm laboratory, sidi bel abbes, algeria moka_salem@yahoo.fr, berrahou22@ yahoo.com, bmechab@yahoo.fr, bachirbou@yahoo.fr abstract. in this study a three-dimensional finite element method analysis of repairing plate with bonded composite patch subjected to tensile load was presented. the effect of the corrosion on the damage of the adhesive (fm73) in the length of inclined crack is presented. the obtained results show that the increase of (dr) is due to the increase of the inclination of the crack against it leads to the decrease of the values of the stress intensity factor in mode i (ki). keywords. composite repair; corrosion; damage ratio; finite element method (fem); stress intensity factor in mode i and mode ii (ki, kii). citation: salem, m., berrahou, m., mechab, b., bachir bouadjra, b., effect of the angles of the cracks of corroded plate in bonded composite repair, frattura ed integrità strutturale, 46 (2018) 113-123. received: 23.05.2018 accepted: 18.06.2018 published: 01.10.2018 copyright: © 2018 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. introduction onded composite repairs of metallic structure have become a useful aircraft structural life extension solution over the last two decades. these repairs provide an efficient method for restoring the ultimate load capability of the structure [1]. alan baker [2, 3] was the first otherwise the pioneer of these searches in the aeronautical and maritime research laboratory of the royal australian air force. the first published study on the corrosion of composite metal matrix (cmm) materials was probably that of porter and wolff in 1967. current cmm corrosion resistance publications focus on matrix materials for the most part of aluminum reinforced with carbon or silicon carbide, with fibrous or particulate form. composite materials with aluminum matrix reinforced with carbon fibers (c/al) are the subject of this publication work. composite materials (c/al) clearly show very low resistance to corrosion in chloride media, whether in marine atmosphere, salt spray or immersion in seawater [4]. the various journals, gathering the results obtained on this topic before (1997), distinguish two main forms of corrosion in these materials: the hydrolysis of aluminum carbides (al4c3) and the galvanic corrosion between carbon and aluminum [5, 6].corrosion of composite materials (c/al) is a topic that cannot be addressed without studying the influence of alloy reinforcement on corrosion resistance. the vast majority of authors are interested in the chemical nature of the b http://www.gruppofrattura.it/va/46/12.mp4 s. mokadem et alii, frattura ed integrità strutturale, 46 (2018) 113-123; doi: 10.3221/igf-esis.46.12 114 reinforcements (silicon carbide, carbon, alumina, boron), but few of them have studied their volume fraction in the material, their morphology and the fiber / matrix interfaces. recently, some studies have taken into account the effect of corrosion on composite patch repair. berrahou and bachir bouiadjra [7] analysed the damage of the adhesive for different forms of patch in the repair of aluminum plates by composites, the obtained results show that the adhesive damage localized at the level of corrosion and in the sides of the patch, and the rectangular patch offers high safety it reduces considerably the risk of the adhesive failure. in another study, berrahou et al [8] studied the effect of the corrosion of plate with double cracks in bonds composite repair the obtained results show that the crack on the left side creates a very extensive area of the damaged zone and gives values of the stress intensity factor (sif) higher than that on the right side. we can conclude that the left crack is more harmful (dangerous) than that on the right side. the protection of aluminum alloys against marine corrosion is a topic that has been widely studied to date. the books dedicated to this subject are numerous and exhaustive [9]. the usual techniques used to protect aluminum have been tested on composite materials (c / al). about the effect of the patch form, bachir bouiadjra et al [10] compared the two rectangular and trapezoidal patch forms. they showed that the trapezoidal shape improves the efficiency and durability of repair. the finite element method has been used for the study of the crack patching by many authors, we can quote: many researchers have studied crack reinforcement of stiffeners or pre-stresses on the stress intensity factor at the cracks tip or notches by the optical method of caustics [11-13]. the damaged area criterion has been proposed to analyse the damage in the adhesive [14, 15]. this criterion assumes that the material breaks once the measured stress exceeds the ultimate strength of the material. damage in the adhesive layer occurs when the deformations or stresses in the adhesive are locally larger than the ultimate properties of the materials. the break in the adhesive does not occur by the propagation of cracks in the substrate, but rather by the initiation and propagation of the damaged area in the layer containing defects such as micro-cracks or voids [16]. the surface area of the adhesive is defined by a surface, where the deformations of the maximum permissible deformation and the breaking load of the glue joints have been determined experimentally. this model has been widely used in the literature to predict the detachment of the adhesive. chang-su ban et al [17] introduced modifications on the model of the damage zone of sheppard et al [15]. the ratio of the damaged area has been suggested for the prediction of the breaking load of the glue joint. for the epoxy adhesive (fm 73), it has been shown that the ratio of the damaged area corresponding to the failure of this adhesive is 0.247. apalak et al [18] used the damaged zone theory to analysis of the effects of thermal stresses in the glue joint. they showed that damage can be expected in composites as well as in the adhesive when using soaked adhesives. recently, several papers describing the damage zone theory published. we note the work of [7, 8] which work on the effect of the corrosion on the damage of the adhesive (fm73) on the repair efficiency and we noted also that [19] has estimated the adhesive damage and failure in the bonds composite repair of aircraft structures using modified damage zone theory. benyahia et al. and ramji et al. [20, 21] analysed four different shapes (rectangular, trapezoidal, circular and elliptical). benyahia and fari bouanani [22] evaluated the effect of water absorption on the adhesive damage in the bonds composite repair of aircraft structures. in this study, a three-dimensional finite element method is used to analyse the effect of the corrosion on the damage of the fm73 epoxy adhesive of bonded composite repair of aircraft structures. after variation of the crack inclination θ = (15-30-45-60-75)°, and determination of different graphs of the ratio of the damaged zone and the curves of variation of stress intensity factor, one proceeds to the comparison between the different forms of the patch to determine the effect of the angle of the crack. geometrical and fe models or the study of the repaired mode ii crack behaviour, we consider an aluminum plate (al 2024-t3) having the following dimensions: hpl=254mm, wpl=254mm and epl=5mm, with a crack inclined at an angle θ. the plate is subjected to uniaxial load σ = 100mpa presented in fig. 1. the crack is repaired with a patch boron / epoxy, the thickness epa= 1.5 mm and the adhesive (fm-73) properties gpa= 0.420gpa and the thickness of adhesive it’s ead = 0.15mm. the mechanical properties of the patch plate and of the adhesive are shown in tab. 1. the geometric shape of the corrosion used is randomly in 3d with a thickness 0.25mm, before repairing the structure, the corroded area is cleaned to remove the corrosion film and keep the same mechanical properties. f s. mokadem et alii, frattura ed integrità strutturale, 46 (2018) 113-123; doi: 10.3221/igf-esis.46.12 115 the considered plate was subjected to uniaxial tensile load in the vertical direction under a stress      100 mpa  . the commercial finite elements code abaqus v.6.11 was used for computation abaqus [23]. the mesh model contains 47150 linear hexahedral elements of type c3d8r and 35965 quadratic tetrahedral elements of type c3d10 (8 nodes biquadratic plane stress with reduced integration) with a grid refined and structured in the vicinity of the notch as shown in fig. 1. total number of nodes 124248. in the presence of principal crack, the number of the quadrilateral elements of type cps3 (3 nodes linear plane stress triangle). plane stress conditions were assumed. figure 1: geometrical model. the singularity at the crack tip by special quarter-point elements [24]. the parameters of crack, ki and kii are given by the stresses at the crack tip. at the crack tip 160 quadrilateral linear elements were considered fig. 1. however, to generate crack front some brick elements are replaced by “crack-blocks”. these crack-blocks are meshes of brick elements, which are mapped into the original element space and merged with surrounding mesh. the mesh was refined near the crack tip area with an element dimension of 0.05 mm using at least fifteen such fine elements in the front and back of the crack front. fig. 2 shows the total mesh of the corroded plate and the mesh for different forms of glue. the stress intensity factor (sif) at the crack front was extracted using the virtual crack closure technique (vcct). the crack tip stress intensity factors are calculated using the virtual crack closure technique (vcct) on the basis of the energy balance. in this technique, the stress intensity factors are obtained for the three failure modes according to the equation:  t i ii iiig g g g   (1) and 2 i i k g e  (2) where ig is the rate of energy restitution for mode  i , ik is the stress intensity factor for mode i i, ii, iii) and e is the modulus of elasticity. results and discussion n theory, it is stipulated that after the development of a damaged area there is an appearance of crack initiation in the patch glued with an adhesive. by applying a low intensity charge the damage is observed at the edges of the patch. this damage occurs because the material is subjected locally to deformations higher than the deformation. under average load, damaged areas grow in size and the concentration of points in damaged areas increases. because the breaking load is reached, the damaged area within the adhesive gets a critical size and with the merging of the individual i s. mokadem et alii, frattura ed integrità strutturale, 46 (2018) 113-123; doi: 10.3221/igf-esis.46.12 116 components a crack is formed. numerically, the damaged zone can be identified by the marking of the elements for which a criterion of rupture is exceeded. the analysed adhesive is a ductile adhesive. therefore, the failure criterion used for cohesion damage of the adhesive layer is equivalent to the von mises deformation criterion. (a) trapezoïdal adhesive rectangular adhesive circular adhesive (b) ellipsoidal adhesive figure 2: (a) mesh of the corroded plate, (b) mesh for different shapes of glue. property material description aluminum (al t2024) boron/epoxy adhesive fm 73 e1 72 200 4.2 young's modulus in x direction (gpa) e2 19.6 young's modulus in y direction (gpa) e3 19.6 young's modulus in z direction (gpa) ν12 0.33 0.3 0.32 poisson's ratio in x-y plan ν13 0.28 poisson's ratio in x-z plan ν23 0.28 poisson's ratio in y-z plan g12 7.2 shear modulus in x-y plan (gpa) g13 5.5 shear modulus in x-z plan (gpa) g23 5.5 shear modulus in y-z plan (gpa) table 1: mechanical proprieties of materials. s. mokadem et alii, frattura ed integrità strutturale, 46 (2018) 113-123; doi: 10.3221/igf-esis.46.12 117 2 2 2 1 2 2 3 3 2 1 ( ) ( ) ( ) 2(1 ) equi p p p p p px               (3) with εequi it’s the equivalent deformation, εpi are the plastic deformations in the different directions and  the poisson's ratio. for the epoxy adhesive (fm 73), the damaged area is defined as a domain in which the deformation exceeds the ultimate deformation of 7.87% chang-su ban et al [17] see fig. 3. the adhesive failure criterion for the damaged area should be used. for isotropic materials, fracture criteria such as von-mises and tresca can be used to better understand the take-off of the adhesive. in addition, the detachment of the joints can be predicted using the damaged area ratio method defined as follows. . i r a d l w   (4) figure 3: stress-strain curve of fm 73 epoxy adhesive. effect of crack inclination on the variation of the ratio of the damaged area of the adhesive the effect of the inclination of the crack is shown in figs. (4, 6, 8 and 10). these show the variations of the damaged area of the adhesive as a function of the slope of the crack ( ) for a constant length (a = 30 mm) repaired by simple patch. the thickness of the adhesive ead = 0.15 (mm) and the thickness of the patch epa = 1.5 mm was fixed for different patch shapes (rectangle, trapezium, circle and ellipse) and for an applied load equal to 100 mpa, firstly, then the crack inclinations θ = (15-30-45-60-75) ° were varied, after the determination of different ratio graphs of the damaged zone and the factor variation curves. the intensity of constraints one can make a comparison between the different forms of the patch to determine the effect of the crack inclination. rectangular patch fig. 4 shows the evolution of the damaged area according to the slope of the crack. in general, we find that the more the crack inclination increases more than the area of the damaged area increases. in the case of θ = 15o we note the presence of a very small damaged area surrounding the crack and the periphery of the patch. comparing the obtained results for the inclinations θ = 45o and θ = 75o to those of θ = 15 °, we notice an increase in the size of the progressively damaged zone and a slight increase in the area around the periphery of the patch. fig. 5 highlights the ratio of the damaged area as a function of crack inclination. a steep slope is observed at the beginning of the graph, which explains the rapid increase. then, it slows down gradually to 35%, which is equivalent to a 4% decrease in the damaged area. for comparison between the values observed for the inclinations of (θ) ranging from 15o to 30o on the one hand and from 40o to 75o on the other hand. for the first case we have (dr) which varies from 0.23 to 0.241, the increase is large and very fast, as for the second case the variation of the ratio of the damaged zone is not significant because the (dr) varies from 0.2415 to 0.242. the obtained results in this study are always lower than the critical value (drc) and this whatever the value of the inclination of the crack. s. mokadem et alii, frattura ed integrità strutturale, 46 (2018) 113-123; doi: 10.3221/igf-esis.46.12 118 (a) (b) (c) figure 4: damaged zone for a rectangular patch (a) θ = 15o, (b) θ = 45o and (c) θ = 75o. figure 5: ratio of the damaged area as a function of the crack tilt. trapezoidal patch the problem is to know the extent of the damaged area of adhesive as it was done before. fig. 6 notes that we have the same behavior observed in fig. 4. we note proportionality between the inclination of the crack and the damaged area. comparing the cases of fig. 6.a and 6.c it is clear the increase of the damaged area (shown in gray) as well as a slight increase of the damaged area at the edges of the patch. (a) (b) c) figure 6: damaged zone for a trapezoidal patch (a) θ = 15o, (b) θ = 45o and (c) θ = 75o. as it was observed previously in the case of fig. 5, the (dr) increases with the increase of the inclination of the crack. fig. 7 shows the variation of the ratio of the damaged area as a function of crack inclination. we observe two distinct parts of the first curve between θ = 15o and θ = 30o where the slope is small and therefore a small variation of the dr (0.25-0.27). in the second part of the curve between θ = 30o and θ = 75o we note that the slope is significant and constant the values of dr (0.27-0.42). all values of (dr) obtained are greater than that of drc for all angles of inclination. circular patch fig. 8 shows the variation of the damaged area using a circular patch. the findings made previously are very clearly visible here. increasing the crack tilt directly leads to an increase in the size of the damaged area. the increase in the damaged area at the periphery of the patch is very visible compared to rectangular and trapezoidal shapes. s. mokadem et alii, frattura ed integrità strutturale, 46 (2018) 113-123; doi: 10.3221/igf-esis.46.12 119 figure 7: ratio of the damaged zone according to the crack tilt. (a) (b) (c) figure 8: damaged zone for a circular patch (a) θ = 15o, (b) θ = 45o and (c) θ = 75o. the fig. 9 shows the variation of the ratio of the damaged zone as a function of the inclination. whatever the value of the inclination of the crack, it is noted that the critical value drc has not been reached, and that the increase in the crack inclination directly leads to the increase of dr. figure 9: ratio of the damaged zone according to the crack tilt. s. mokadem et alii, frattura ed integrità strutturale, 46 (2018) 113-123; doi: 10.3221/igf-esis.46.12 120 elliptical patch fig. 10 illustrates the distribution of the damaged area of the adhesive for the following inclinations (θ = 15o, θ = 45o and θ = 75o). by comparing the results found previously for patches of shapes (rectangular, trapezoidal and circular) to those of the elliptical we notice the appearance of the damaged area at the level of corrosion. this zone is visibly clear for θ = 75o that θ = 45o. same remarks as the previous cases, an increase in the inclination of the crack causes the increase of the damaged area surrounding crack as well as the area of the patch device. (a) (b) (c) figure 10: damaged zone for a circular patch (a) θ = 15o, (b) θ = 45o and (c) θ = 75o. curve 11 represents the values of the ratio of the damaged area of the adhesive which increase progressively with increasing crack inclination. starting from the value of dr = 0.0795 for θ = 15o until reaching the maximum value of dr = 0.083 for θ = 75o. note the critical value of the ratio (drc = 0.247) is not reached. figure 11: ratio of the damaged zone according to the crack tilt. comparison between the different (dr) according to the inclination of the crack for the different forms of patch in order to see the effect of the ratio of the damaged area for different inclinations of the crack the graph of fig. 12 is analysed. it is noted that the increase of the crack inclination leads to an increase of (dr) for all the different forms of patch used. the dr recorded for the trapezoidal shape is greater than the critical value which is a risk of detachment of the patch from which this form is to be avoided for repair. on the other hand all the other forms give values of dr lower than the critical value (drc = 0.247). among the results obtained the elliptical form is the best because it gives the minimum value of dr. effect of the inclination of the crack on the variation of the sif the figs. 13 and 14 respectively represent the variations of the sif in mode i and ii as a function of the inclination of the crack for respective thicknesses of the adhesive and of patch ead= 0.15 mm, epa= 1.5 mm and a crack size a = 30mm. s. mokadem et alii, frattura ed integrità strutturale, 46 (2018) 113-123; doi: 10.3221/igf-esis.46.12 121 figure 12: ratio of the damaged zone according to the crack tilt for the different patch shapes. figure 13: variation of the (sif) in mode i of the inclined crack for the different shape of patch (a = 30 mm) figure 14: variation of the (sif) in mode ii of the inclined crack for the different shape of patch (a = 30mm). s. mokadem et alii, frattura ed integrità strutturale, 46 (2018) 113-123; doi: 10.3221/igf-esis.46.12 122 fig. 13 shows that the ki value for different patch shapes decreases with increasing angle . the reduction of the sif values between the ellipsoid and circular shaped patch is evaluated at 85% and about 20% for the trapezoidal and rectangular shapes. when the value goes to the angle θ= 75 ° the value of sif tends to zero. for angle θ=0 ° we have a pure mode i from which the opening of the crack is maximum with high sif values. for angle θ = 75 °, the crack being at a position almost parallel to the loading the sif values tend to zero. concerning the mixed mode of sif, according to fig. 14, this factor (characterizing the sliding of the crack) is zero when the crack is perpendicular to the direction of loading, which passes through a maximum then tends towards a minimum when the inclination the crack tends to the angle θ= 75 °. the value of kii is maximum for the angle θ= 45 ° for all forms. circular and ellipsoidal shapes give higher kii values than rectangular and trapezoidal shapes. conclusion his work involves evaluating the damaged area of the adhesive from the effect of crack tilt. the objective is to calculate the ratio of the damaged area and to determine the stress intensity factor, then compare the results for the different shapes of the patch (rectangular, trapezoidal, circular and ellipsoidal), with an inclined crack (mixed mode) the results obtained allow the following conclusions: -the increase of the crack inclination leads to an increase of dr for all the different forms of patch used. -the risk of detachment of the patch can be observed for the trapezoidal shape which is due to dr greater than the critical value for the different θ. the ki value decreases with the increase of the angle and the kii value is maximum for the angle θ = 45 ° for all the shapes of the patch. references [1] bachir bouiadjra, b.b., achour, t., berrahou, m., ouinas, d. and feaugas, x. (2010). numerical estimation of the mass gain between double symmetric and single bonded composite repairs in aircraft structures, mater. des., 31, pp. 3073-3077. doi: 10.1016/j.matdes.2010.01.006. [2] baker, a. (1984). repair of cracked or defective metallic aircraft components with advanced fiber composites-an overview of australian work, j. compos. struct., 2, pp. 153-8. doi: 10.1016/0263-8223(84)90025-4. [3] baker, a. (1995). bonded composite repair of metallic aircraft components overview of australian activities, agard-cp-550, pp. 1-14. [4] pfeifer, w.h. (1977). graphite/aluminum technology development, hybrid and select metal matrix composites: a state-of-the-art review, pp. 159 – 252. [5] turnbull, a. (1992). review of corrosion studies on aluminum metal matrix composites, british corrosion journal, 27, pp. 27-35. doi: 10.1179/000705992798268864. [6] jones, r. and chiu w.k. (1999). composite repairs to crack in thick metallic components, compos. struct., 44, pp. 17-29. doi: 10.1016/s0263-8223(98)00108-1. [7] berrahou, m. and bachir bouiadjra b. (2016). analysis of the adhesive damage for different patch shapes in bonded composite repair of corroded aluminum plate, techno. press., 59, pp. 123-132.doi: 10.12989/sem.2016.59.1.123. [8] berrahou, m., m, salem., m., mechab, b. and bachir bouiadjra b. (2017). effect of the corrosion of plate with double cracks in bonded composite repair, techno. press., 64, pp. 323-328.doi: 10.12989/sem.2017.64.3.323. [9] vargel, c. (1999). corrosion de l'aluminium, corrosion reviews, paris, pp. 154-176. [10] bachir bouiadjra, b., fari, bouanani., m, albedah., a, benyahia., f and es-saheb, m. (2011). comparison between rectangular and trapezoidal bonded composite repairs in aircraft structures: a numerical analysis, mater. des., 32, pp. 3161–3166. doi: 10.1016/j.matdes.2011.02.053. [11] salem, m., bachir bouiadjra, b.b., mechab, b. and kaddouri, k. (2015). elastic-plastic analysis of the j integral for repaired cracks in plates, adv .mater .res., 4, pp. 87-96. doi: 10.12989/amr.2015.4.2.000. [12] mechab, b., chama, m., kaddouri, k. and slimani, d. (2016). probabilistic elastic-plastic analysis of repaired cracks with bonded composite patch, steel. compos. struct. int. j., 20, pp. 1173-1182. doi:10.12989/scs.2016.20.6.1173. [13] serier, n., mechab, b., m’hamdia, r. and serier, b., (2016). a new formulation of the j integral of bonded composite repair in aircraft structures, struct. eng. mech., 58, pp. 745-755. doi: 10.12989/sem.2016.58.5.745. t s. mokadem et alii, frattura ed integrità strutturale, 46 (2018) 113-123; doi: 10.3221/igf-esis.46.12 123 [14] crocombe, a. and richardson, g. (1995). a unified approach for predicting the strength of cracked and non-cracked adhesive joints, int. j. adhes., 49, pp. 211–44. doi: 10.1080/00218469508014357. [15] sheppard, a., kelly, d. and tong, l. (1998). a damage zone model for the failure analysis of adhesively bonded joints, int. j. adhes., 18, pp. 385–400. doi: 10.1016/s0143-7496(98)00024-4. [16] magalhães, a.g. and de moura m.f.s.f., gonçalves, jpm. (2005). evaluation of stress concentration effects in single-lap bonded joints of laminate composite materials, int. j. adhes. 25, pp. 313–319. doi: 10.1016/j.ijadhadh.2004.10.002. [17] chang-su, b.,young-hwan, l., jin-ho, c. and jin-hwe, k. (2008). strength prediction of adhesive joints using the modified damage zone theory, compos. struct., 86, pp. 96–100. doi: 10.1016/j.compstruct.2008.03.016. [18] kemal apalak, m., gul apalak, z. and gunes, r. (2004). thermal and geometrically nonlinear stress analyses of an adhesively bonded composite, tee joint with double support, thermoplast. compos. mater. 17, pp. 103–36. doi: 10.1177/0892705704033337. [19] fari bouanani, m., benyahia, f., albedah, a., aid, a., b. bachir bouiadjra, b.b., belhouari, m. and achour, t. (2013). analysis of the adhesive failure in bonded composite repair of aircraft structures using modified damage zone theory, mater. des., 50, pp. 433–439. doi: 10.1016/j.matdes.2013.03.017. [20] ramji, m., srilakshmi, r. and bhanu prakash, m. (2013). towards optimization of patch shape on the performance of bonded composite repair using fem, compos. b. eng., 45, pp. 710–20. doi: 10.1016/j.compositesb.2012.07.049. [21] benyahia, f., fari bouanani, m., albedah, a., bachir bouiadjra, b. b. and achour, t., (2014). effect of water absorption on the adhesive damage in bonded composite repair of aircraft structures, mater. des., 57, pp. 435–441. doi: 10.1016/j.matdes.2013.12.081. [22] benyahia, f., albedah, a. and bachir bouiadjra, b.b., (2014). analysis of the adhesive damage for different patch shapes in bonded composite repair of aircraft structures, mater. des., 54, pp. 18-24. doi: 10.1016/j.matdes.2013.08.024. [23] abaqus, abaqus standard/user’s manual, version 6.11. hibbit karlsson & sorensen, inc., pawtucket, ri, usa, (2007). [24] henshel, r. d. and shaw, k. g., (1975). crack tip finite elements are unnecessary, int. j. num. meth. eng., 9, pp. 495507. doi: 10.1002/nme.1620090302. << /ascii85encodepages false /allowtransparency false /autopositionepsfiles true /autorotatepages /none /binding /left /calgrayprofile (dot gain 20%) /calrgbprofile (srgb iec61966-2.1) /calcmykprofile (u.s. web coated \050swop\051 v2) /srgbprofile (srgb iec61966-2.1) /cannotembedfontpolicy /error /compatibilitylevel 1.4 /compressobjects /tags /compresspages true /convertimagestoindexed true /passthroughjpegimages true /createjobticket false /defaultrenderingintent /default /detectblends true /detectcurves 0.0000 /colorconversionstrategy /cmyk /dothumbnails false /embedallfonts true /embedopentype false /parseiccprofilesincomments true /embedjoboptions true /dscreportinglevel 0 /emitdscwarnings false /endpage -1 /imagememory 1048576 /lockdistillerparams false /maxsubsetpct 100 /optimize true /opm 1 /parsedsccomments true 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/pdfxoutputintentprofileselector /documentcmyk /preserveediting true /untaggedcmykhandling /leaveuntagged /untaggedrgbhandling /usedocumentprofile /usedocumentbleed false >> ] >> setdistillerparams << /hwresolution [2400 2400] /pagesize [612.000 792.000] >> setpagedevice microsoft word numero_46_art_28 a. deliou et alii, frattura ed integrità strutturale, 46 (2018) 306-318; doi: 10.3221/igf-esis.46.28 306 fatigue crack propagation in welded joints x70 adel deliou, benattou bouchouicha laboratory of materials and reactive systems lmsr, university djillali, liabes, sidi bel-abbes, algeria . del032003@yahoo.fr, benattou_b@yahoo.fr abstract. structural failure assessment approaches take into account local parameters, specimen geometry, loading and material. in the case of welded joints, in addition to these parameters, consideration must be given to the effect of the heterogeneity of properties due to welding. the objective of our work is to study the fatigue crack propagation of welded joint in api x70 pipeline steel. this experimental study focused on welded joints in the different parts, base metal, weld metal and heat affected zone. the concepts of fracture mechanics are used to analyze the harmfulness of defects in welded joints and the main part of fatigue life falls on the crack propagation. the results obtained show that the fatigue crack propagation rate of cracks in the heat affected zone is delayed compared to the other zones. the effect of the microstructure and the quality of submerged arc welding of the studied x70 steel are significant. tensile tests, hardness and measurement of energetically parameters complemented this work. keywords. x70; mechanical behaviors; fatigue crack propagation; energy. citation: deliou, a., bouchouicha, b., fatigue crack propagation in welded joints in x70, frattura ed integrità strutturale, 46 (2018) 306-318. received: 16.08.2018 accepted: 03.09.2018 published: 01.10.2018 copyright: © 2018 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. introduction elding is one of the important assembly methods for manufacturing in steel structures. in current industrial practice, welded joints are an integral section of these complex configurations [1]. in general, fatigue behavior of welded materials is complicated by large variation in nature and properties of materials, presence of geometric defects and many factors intrinsic (inclusions, lack of penetration, gas pore), etc. [2-8]. many studies show that, from such defects, the stage of initiation of the fatigue crack can be reduced [9] and that consequently a large part of the life of the welded joints subjected to fatigue propagation occurs [10]. for the design of these assemblies, it is interesting to use the crack propagation laws given by the linear elastic fracture mechanics [lefm]. in order to estimate the life of the joints, by calculating the number of cycles needed to propagate a crack from these defects until the rupture [11-21]. welded structures present a gradient of microstructure and mechanical behaviors from the weld metal to base metal. important studies regarding the microstructural change and the mechanical behaviors of api x70 steel have been executed [2224]. nanninga [25] examined the fatigue crack propagation of api x42 and apix70 pipelines at a load ratio r = 0.1 under h2 or n2 environment. the presence of hydrogen shows an important damage compared to nitrogen. the w http://www.gruppofrattura.it/va/46/28.mp4 a. deliou et alii, frattura ed integrità strutturale, 46 (2018) 306-318; doi: 10.3221/igf-esis.46.28 307 fatigue crack propagation fcp tested under the same type of environment (hydrogen or nitrogen) is higher than the api 5l x70 steel because of the microstructure and the chemical composition. the effect of toughness and microstructure on fatigue crack propagation rate in different steels x60 and x70 investigated by y. zhong et al. [26]. the results demonstrated that the toughness and strength have a significant influence to the fatigue behavior of pipeline steels. maamache [27] inspected the influence of successive welding repairs on the microstructure and mechanical properties of the heat affected zone haz of an api 5lx70 steel. microstructural analysis has shown that beyond the second repair, the haz microstructure undergoes a significant change in grain morphology and size that increases with the number of repairs. as a result, the yield strength and toughness of the repaired specimens were degraded. after the second repair, the properties of the welded joints do not meet the acceptability criteria defined by the standards applied by api. fatoba [28] studied the oligocyclic fatigue behavior of api 5l x65 pipeline steel at room temperature. the author has shown that the increase in the amplitude of total deformation has the effect of decreasing the life of fatigue oligocyclic, and the amplitude of stress increases with the amplitude of plastic deformation. the investigation [29] showed that the cracking rate of x65 steel is influenced by the crack direction. the parameters of the propagation model have been determined admitting to the paris law and show that the t-s direction has an excellent resistance to fatigue cracking with respect to the t-l direction (rolling direction). kim [30] characterized the fatigue of the x65 steel in the three regions base metal, welded and heat affected zone, he noticed that the difference in the cracking rate decreases when the values of the stress intensity factor k increase. the finite element analysis performed by hadjoui [30] for the x60 and x70 steels for a load ratio r = 0.2 shows that the x70 presents a better resistance to fatigue. recently maachou [31] analyzed the fatigue crack growth behavior under constant amplitude and variable amplitude loading using terms of energy parameters. the main objective of this work is to study the fatigue crack growth rate of low-carbon micro alloyed steel x70 welded joints used in pipeline manufacturing. this experimental study focused on the welded joints in the three different parts, namely in the unaffected base metal, the heat affected zone and the weld metal. mechanical properties materials he studied material is a microalloyed steel, api 5l x70 grade, used in pipeline manufacturing. the pipe is spirally welded by submerged arc welding saw process. chemical composition in order to evaluate if the chemical composition of our material conforms to the specification imposed by api 5l, an analysis by optical emission spectroscopy has been used. the chemical compositions of x70 pipeline steel and of saw weld metal in weight percent are shown in the tabs. 1 and 2 respectively. c mn si cr ni mo v al ti nb cu p sn s 0.064 1.640 0.290 0.051 0.009 0.021 0.050 0.038 0.020 0.056 0.023 0.011 0.036 0.004 table 1: chemical composition of x70 (base metal, bm; wt%). c mn si cr ni mo v al ti nb cu p sn s 0.070 1.610 0.250 0.035 0.030 0.133 0.060 0.017 0.017 0.040 0.046 0.014 0.003 0.004 table 2: chemical composition of filler metal (weld metal, wm; wt%). the equivalent carbon contents of the base metal and that of weld metal calculated to the expression (1) below proposed by the international institute of welding [32] are respectively 0.36% and 0.39%. t a. deliou et alii, frattura ed integrità strutturale, 46 (2018) 306-318; doi: 10.3221/igf-esis.46.28 308 6 5 15 eq mn cr mo v ni cu c c        (1) tensile test in order to evaluate the load strain curve and mechanical properties of x70, flat specimens according to api requirements were used .the tensile tests were carried out in 600 kn capacity, mfl uhp prufsysteme servo hydraulic testing machine, at room temperature with a low displacement rate(1mm/min). figure 1: schematic of the sampling direction of the specimens. the samples were taken in the rolling direction (fig.1). the dimensions of weld metal specimens used according to astm a370 and api 5l standard are presented in fig. 2. tab. 3 and fig. 3 present the results of conventional and true tensile of evolution of the stresses according to the deformation in base metal x70, where e the young module, ν the poisson's ratio, 𝜎 the yield strength, 𝜎 ultimate strength, a% the ductility and k and n being hollomon's parameters. tab. 4 shows the mechanical properties of the welded metal obtained. figure 2: diagram and dimensions of weld metal specimens used for tensile tests. figure 3: conventional and true tensile curve of x70 a. deliou et alii, frattura ed integrità strutturale, 46 (2018) 306-318; doi: 10.3221/igf-esis.46.28 309 e [gpa] ν   y [mpa]   u [mpa] a (%) k n 221 0.3 500.3 573.14 33 840 0.25 table 3: tensile properties of x70. material yσ [mpa] uσ [mpa] elongation (mm) wm 603.44 642.80 6.33 table 4: tensile properties of weld metal microstructure analysis in order to carry out the microstructural study of our material, we performed optical microscope observations on polished sections (1 μm) then etched with 3% nital at the transverse surface of the welded joint (fig. 4). examinations performed on unaffected sections reveal the presence of numerous alignments of mns inclusions in the base metal and globular oxides in the welded metal. optical micrograph shows an increase in grain diameter from the base metal to the weld joint. according to fig. (5.a), the microstructure of the base metal consists as expected essentially of polygonal ferrite grains (white) and pearlite (black) organized in strips. this structure is produced by the segregation of mn and p during rolling [34-37]. at the approach of the weld we find a more homogeneous organization of the grains the microstructure of the region near base metal consisted by equiaxed very fine grains of ferrite and pearlite.. for the heat affected zone (haz) (fig. 5b), they appear acicular ferrite grains in the form of needles with coarse polygonal ferrite grains. the microstructure of the weld metal (wm) consists of dominant polygonal ferrite, acicular ferrite around the inclusions, and islands of pearlite (fig.5c). the microstructure obtained is agreed with a number of studies oriented towards the analysis of the structure [26], [38-41]. figure 4: transversal section for micrographic examinations and hardness measurement figure 5: welded joint microstructure as observed through optical microscopy: (a) base metal (m: x200) (b) heat affected zone (m: x200) and the weld metal (m: x500) (c) a. deliou et alii, frattura ed integrità strutturale, 46 (2018) 306-318; doi: 10.3221/igf-esis.46.28 310 hardness measurement vickers hardness filaments were carried out in the thickness on a cross section of the weld joint. the measurements are taken under 10 kgf of load using a zwick zhv10 type durometer, the step is 0.5 mm in the haz and 1 mm in the base metal and the weld metal. the hardness profile measured across the average diameter changes to a letter m as shown in fig. 6. in addition, tab. 5 shows the average values of the vickers hardness for each region of the welded joint. the large values of hardness of haz zone related to the existence of acicular ferrite in its microstructure (presents the greatest value of the mechanical properties by virtue of the fine-grained and interlocked microstructures) [42-44], on the other hand, the low values are in the bm respect to welded joint can be related by the reverse cold deformation caused by the rolling (bauschinger effect). the hardness results representing the weld seam showed a uniformity of values between base metal and seam weld sign a good property. figure 6: hardness profile of the welded joint. region average value bm 207 haz 230 wm 227 table 5: results of hv10 hardness along the weld joint fatigue tests atigue cracking tests were performed on ct50 specimen’s thickness of 7 mm, in accordance with astme-e647 whose dimensions given by the fig. 7. these tests were carried out in laboratory of materials and reactive systems (lmsr), mechanical department of university of sidi belabbes. these tests were conducted in ambient air for the same load ration value r at a nominal frequency of 20hz in the three zones. welded structures present a gradient of microstructure and mechanical behaviours from the weld metal to base metal. the study of fatigue crack growth in welded joints of pipeline steels, particularly in the heat affected zone, is difficult research field. in order to more clearly compare the evolution of the cracking rate in the three zones, we chose to represent them by their respective linear regression lines obtained from the experimental points (seven point method) on the linear parts of the curves. f a. deliou et alii, frattura ed integrità strutturale, 46 (2018) 306-318; doi: 10.3221/igf-esis.46.28 311 figure 7: diagram and dimensions of ct50 specimens used for cracking tests figure 8: orientation of the ct specimens with respect to the welded joints according to the recommendations of astm e399 and afnor a03 404, the values of the stress intensity factor k in the case of ct geometry are calculated using the following relationship: 3 2 2     1 a p aw k f w a b w w               (2) where 𝑃 the amplitude of loading [n], w is the width of specimen [m], b is thickness of specimen [m] and a, is the crack length. the compliance function a f w       is on the form [26, 45]: 2 3 4 0.886 4.46  13.31 14.72   5.6 a a a a a f w w w w w                                  (3) a. deliou et alii, frattura ed integrità strutturale, 46 (2018) 306-318; doi: 10.3221/igf-esis.46.28 312 figure 9: evolution of the crack length according to the number of cycles. in order to explore the field of medium and high cracking rates, we imposed a sinusoidal load of constant amplitude 7p kn  for the duration of the test, with a load ratio 0.1r  . the curves of evolution of the length of the crack “a” as a function of number of cycles of bm, wm and haz regions of welded joint are presented in fig 9. the difference in advanced of the crack between these curves in higher as the number of cycles increases. these results influenced on the evolution of the nominal cracking rate versus plotted on a bilogarithmic curve shown in fig. 10. values of da dn are between 10-6 and 10-2 mm/cycle and the values of k values change from: 13.8 to 36.9 mpa m in the heat affected zone. 13.2 to 36.6 mpa m in the weld metal. 11.7 to 35.4 mpa m in the base metal. the curves have an almost rectilinear look on a big part of the explorer domain, which can be presented a law of paris of the form [46]:     m da c k dn   (4) the results of the fatigue tests obtained in the three zones recorded respectively in tab. 6. table 6: paris law in the different zones studied. regions paris law bm  4.87  111.1   da e k dn   wm  4.55  115.2  da e k dn   haz  3.82  118.1   da e k dn   a. deliou et alii, frattura ed integrità strutturale, 46 (2018) 306-318; doi: 10.3221/igf-esis.46.28 313 figure10: fatigue crack growth rates for as a function of δk for the three zones studied the results of fig. 10 have shown that the welded metal and heat affected zone have an important higher crack propagation resistance at the small δk values (the mechanical properties of weld material are better (tabs. 3 and 4). the paris equation coefficients obtained for the different x70 welded joint regions mentioned in tab. 6 indicate that the growth rate of the crack influenced by the microstructure of the welded joint zones. the high resistance to propagation of heat affected zone can be related to the existence of acicular ferrite in microstructure (acicular ferrite microstructure in heat-affected zone give high mechanical behaviors in terms of strength and toughness) [47-49]. at the high values of δk, the affinity between cracking rate plots can be related for the decrease of crack closure. for low values of δk this phenomenon as more marked by the crack tip plasticity following its advance (thus forming a wake plasticized). these results are in good agreement with the results of beltrao et al.[50] but, they noticed that the fatigue crack propagation is get more independent from the high load ratio values(r=0.5) evolution of energy parameters arious experimental techniques have been developed to measure the surface creation energy u. most of these techniques are based on stable mechanical hysteresis loops, which measure work in an area near the crack. ikeda et al. [51] had measured the quantity for steel of low carbon content and for high resistance aluminium alloy from hysteresis loops in the plastic zone using strain micro gages. using the differential method of kikukawa et al. [52], ranganathan measured the hysteric work u [53], which represents the dissipated energy in the plastic zone by unit created surface on the aluminium alloy (2024 t351), testing ct specimens modified in order to be able to measure the crack tip opening displacement (ctod) in the loading axial direction. the progression of the crack tip opening displacement δ, and δ’ with respect to the load p were registered at a frequency of 0.05 hz (δ evaluated by a clip gage). the differential displacement δ’ is calculated by the expression: δ δ α p   (5) : the specimen compliance at a singular crack length. the measurements were realized during one cycle for constant amplitude. characteristic δ and δ’ with respect to the load p layouts for constant amplitude loading are shown in fig. 11. (crack opening load pop was measured at the beginning of the horizontal segment on δ’ with respect to p diagram [54]. fig. 12 shows the evolution of the hysteretic energy q dissipated during a cycle as a function of δk, for a load ratio r = 0.1, in the three zones studied. this energy is determined by a numerical integration of the cycles (pδ‘), its expression is obtained by calculating the area of this loop obtained by acquisition and processing by a program written under labview. v a. deliou et alii, frattura ed integrità strutturale, 46 (2018) 306-318; doi: 10.3221/igf-esis.46.28 314 figure 11: diagrams of δ and δ 'with respect to charge p. figure12: evolution of the hysterical energy of the crack as a function of δk the advantage of this program is to be able to estimate this hysteretic energy for the low values of δk. we notice that q increases when δk increases for the three zones studied. fig. 13 represents the evolution of the specific energy expended u per cycle in function of δk in the three zones studied. this energy is given by the following relation [31], [55]: a. deliou et alii, frattura ed integrità strutturale, 46 (2018) 306-318; doi: 10.3221/igf-esis.46.28 315             ‘        2 2 area of the curve pq u da da b b dn dn                (6) where b the specimen thickness and da dn is the fatigue crack growth. u decreases with k at small k values to achieve a constant value at high k levels. these results indicated that the specific energy for the different zones of the weld joint studied is not a constant and depends the microstructure and on the decrease of crack closure phenomenon. these results are consistent with the work of [53], [57-58] where they consider that the hysterical work is essentially dispelled in the plasticized zone and that in the case where the closing phenomena are important, it is conceivable that a part of the energy u is dissipated in the zone situated in the wake plasticized along the crack front. figure 13: evolution of specific energy as a function of δk conclusion atigue behavior of welded structures is a more complicated than that of base material due to the presence of heterogeneous metallurgical zones produced during the welding process. fatigue crack propagation in base metal bm, weld metal wm and heat affected zone haz of welded joints of an api x70 pipeline steel was investigated. the most generally model used for the fatigue crack growth based is lefm and the crack propagation is the dominant stage of the fatigue life. the fatigue crack growth behavior of welded joints api x70 pipeline steel affected by variation of microstructure, weld materials and the loading parameter. fatigue crack propagation in heat affected zone of x70 steel is delayed compared to the propagation to the other zones. the hysteretic energy q dissipated during one cycle increases when δk increases for the three zones studied and specific energy u reaches a constant value at high δk levels. references [1] nykanen, t., li, x., bjork, t. and marquis, g. (2005). a parametric fracture mechanics study of welded joints with toe cracks and lack of penetration, engineering fracture mechanics, 72, pp.1580–1609. f a. deliou et alii, frattura ed integrità strutturale, 46 (2018) 306-318; doi: 10.3221/igf-esis.46.28 316 doi: 10.1016/j.engfracmech.2004.11.004. [2] ferreira, j. a. m. and branco, c. a. m. (1989). influence of the radius of curvature at the weld toe in the fatigue strength of fillet welded joints. int. j. of fatigue, 11, pp. 29-36. doi: 10.1016/0142-1123(89)90044-3. [3] janosh, j. j. (1990). study of the fatigue strength of welded joints at angles (made of steel e 36-4), according to the size of the penetration of welds, in the case of a combined stress of traction and flexion., ph.d. dissertation, university of metz, metz. [4] otegui, j. l., h.w. kerr, d. j. burns, mohaupt, u. h. (1998). fatigue crack initiation from defects at weld toes in steel, int. j. pres .ves. &piping, 38, pp.385-417. doi: 10.1016/0308-0161 (89)90048-3. [5] nguyen, n.t. (1990). advanced modeling fatigue of butt-welded structures”, ph.d. dissertation, university of adelaide, adelaide. [6] yee, r., burns, d. j., mohaupt, u. h., bell, r. and vosikovsky, o. (1990).thickness effect and fatigue crack development in welded t joints, journal of offshore mechanics and arctic engineering, 112, pp. 341-351. doi: 10.1115/1.2919876. [7] kambouz, y.m. benguediab, b. bouchouicha and mazari, m. (2017). numerical study of the mechanical behavior and fatigue in a weld bead by friction stir for a 6082-t6 aluminum alloy, periodica polytechnica mechanical engineering, 61(1), pp. 36-43. doi: 10.3311/ppme.9212. [8] srivastava, y. p. and garg, s. b. l. (1985). influence of r on effective stress range on effective stress range ratio and crack growth, engineering fracture mechanics, 22(6), pp. 915-926. doi: 10.1016/0013-7944 (85)90032-3. [9] benachour, m., m. benguediab, hadjoui, f. and benachour, n. (2008). fatigue crack growth of a double fillet weld, computational materials science, 44, pp.489–495. doi: 10.1016/j.commatsci.2008.04.015. [10] ngoula, d. t., h. t. beier and vormwald, m. (2017). fatigue crack growth in cruciform welded joints: influence of residual stresses and of the weld toe geometry, international journal of fatigue, 101(part 2), pp.253-262. doi: 10.1016/j.ijfatigue.2016.09.020. [11] al-haidary, j.t., wahab, a.a. and. abdul salam, e.h. (2006). fatigue crack propagation in austenitic stainless steel weldments, metallurgical and materials transactions a, 37a, pp. 3206-3214. doi: 10.1007/bf02586155. [12] bussu, g. and irving, p.e. (2003).the role of residual stress and heat affected zone properties on fatigue crack propagation in friction stir welded 2024-t351aluminium joints, international journal of fatigue, 25, pp.77–88. doi: 10.1016/s0142-1123(02)00038-5. [13] chattopadhyay, a., glinka, j., elzine, g. m., qian, j. and formas, r. (2011). stress analysis and fatigue of welded structures, welding in the world, 50(7&8), pp. 120. doi: 10.1007/bf03321326. [14] chrysanthopoulos, m.k. and righiniotis, t.d. (2006). fatigue reliability of welded steel structures, journal of constructional steel research, 62, 2006, pp.1199–1209. doi: 10.1016/j.jcsr.2006.06.007. [15] kainuma, s. and mori, t. (2008). a study on fatigue crack initiation point of load-carrying fillet welded cruciform joints, international journal of fatigue, 30, pp.1669–1677. doi: 10.1016/j.ijfatigue.2007.11.003. [16] mann, t., tveiten, b. w. and harkeegard, g. (2006). fatigue crack growth analysis of welded aluminium rhs tjoints with manipulated residual stress level, fatigue fract engng mater struct, 29, pp. 113–122. doi: 10.1111/j.1460-2695.2006.00970.x. [17] richards, c.e. and lindley, t.c. (1972). the influence of stress intensity and microstructure in fatigue crack propagation in ferritic materials, engineering fracture mechanics, 4, 1972, pp. 951-978. doi: 10.1016/0013-7944(72)90028-8. [18] trudel, a., sabourin, m., levesque, m. and brochu, m. (2014). fatigue crack growth in the heat affected zone of a hydraulic turbine runner weld, international journal of fatigue, 66, pp.39-46. doi: 10.1016/j.ijfatigue.2014.03.006. [19] tsay, l.w., liu, y.c, young, m.c. and lin, d. y. (2004).fatigue crack growth of aisi 304 stainless steel welds in air and hydrogen, materials science and engineering a, 374, pp.204-210. doi: 10.1007/bf02586155. [20] tveiten, b. w., fjeldstad, a., harkegard, g., myhr, o. r. and bjorneklett, b. ( 2006).fatigue life enhancement of aluminium joints through mechanical and thermal prestressing, international journal of fatigue, 28, pp.1667–1676. doi: 10.1016/j.ijfatigue.2006.01.006. [21] ural, a., krishnan, v. r. and papoulia, k. d. (2009). a cohesive zone model for fatigue crack growth allowing for crack retardation, international journal of solids and structures, 46, pp. 2453–2462. doi: 10.1016/j.ijsolstr.2009.01.031. [22] bordbar, s., alizadeh, m. and hashemi, s. h. (2013). effects of microstructure alteration on corrosion behavior of welded joint in api x70 pipeline steel, materials and design, 45, pp. 597-604. doi: 10.1016/j.matdes.2012.09.051. [23] hwang, b., kim, y. g, lee, s., kim, y. m., kim, n. j. and yoo, j. y. (2005). effective grain size and charpy impact properties of high-toughness x70 pipeline steels”, metallurgical and materials transactions a, 36a, pp. 2107-2114. a. deliou et alii, frattura ed integrità strutturale, 46 (2018) 306-318; doi: 10.3221/igf-esis.46.28 317 [24] hejazi, d., haq, a.j., yazdipour, n., dunne, d.p., calka, a, barbaro, f., pereloma, e.v.(2012). effect of manganese content and microstructure on the susceptibility of x70 pipeline steel to hydrogen cracking, materials science and engineering a, 551, pp.40– 49. doi: 10.1016/j.msea.2012.04.076. [25] nanninga, n., slifka, a. levy, y. and white, c. (2010). a review of fatigue crack growth for pipeline steels exposed to hydrogen, journal of research of the national institute of standards and technology, 115(6), pp.437-452. doi: 10.6028/jres.115.030. [26] zhong, y., shan, y., xiao, f. and yang, k. (2005). effect of toughness on low cycle fatigue behavior of pipeline steels, materials letters, 59, pp.1780– 1784. doi: 10.1016/j.matlet.2005.01.066. [27] maamache, b., (2017). structural and mechanical behavior of successive weld bead repairs in hsla steel, ph.d. dissertation, university of blida. [28] fatoba, o. and akid, r. (2014). low cycle fatigue behavior of api 5l x65 pipeline steel at room temperature, procedia engineering, 74, pp.279 – 286. doi: 10.1016/j.proeng.2014.06.263. [29] neves, m. a. (2005). fatigue crack propagation of longitudinal welded steel tubes, grade api 5l x70, ph.d. dissertation, university of federal university of rio de janeiro. [30] kim, y. p. kim, c. m., kim, w. s. and shin, k. s. (2007). fatigue crack growth behavior in girth weld of natural gas transmission pipelines, key engineering materials, 345-346, pp. 303-306. doi: 10.4028/www.scientific.net/kem.345-346.303. [31] hadjoui, f., benachour, m. and benguediab, m. (2012). fatigue crack growth on double butt weld with toe crack of pipelines steel, materials sciences and applications, 3, pp.596-599. doi: 10.4236/msa.2012.39085. [32] maachou, s. benguediab, m., mazari, m. ranganathan, n. (2014). fatigue crack propagation under variable amplitude loading amplitude loading analyses based on plastic energy approach, materials engineering, 21, 2014, pp.68-79. available online: http://fstroj.uniza.sk/journal-mi/pdf/2014/11-2014.pdf [33] association de recherche sur les structures métalliques arsem -guide pratique sur les ouvrages en mer, assemblage tubulaire soudé (1985), edition technip, paris. [34] carboni, a, pigani, a., paul, s. k. and megahed, g.m. (2008). casting and rolling of api x 70 grades for arctic applications in a thin slab rolling plant, millennium steel, pp.131-136. [35] bulger, j. t., lu, b. t. and luo, j. l. (2006). microstructural effect on near-neutral ph stress corrosion cracking resistance of pipeline steels, j mater sci., 41, pp. 5001–5005. doi: 10.1007/s10853-006-0131-7 [36] kumar, s. shukla, s. k., de, s. k., saxena, a., jha, b. k , mishra, b. verma, a. and mallik, s.( 2013). api x 70 grade hr coils for erw pipes, international journal of metallurgical engineering, 2(2), pp.179-187. doi:10.5923/j.ijmee.20130202.09. [37] feng, r., li, s., zhu, x. and ao, q. (2015). microstructural characterization and formation mechanism of abnormal segregation band of hot rolled ferrite/pearlite steel”, journal of alloys and compounds, 646, pp.787-793. doi: 10.1016/j.jallcom.2015.05.128. [38] beltrao, m. a. n., castrodeza, e. m., filho, f. d.m. and bastian, f. l. (2005).fatigue behavior of api grade 5l x65 and x-70 steels welded under variable amplitude loading, proceedings of cobem 2005 18th international congress of mechanical engineering , abcm november 6-11 , ouro preto, brazil. [39] tassadit, d, (2013). study of the harmfulness of defects in pipelines under hydrogen environments), ph.d. dissertation, university of tizi ouzou. [40] hashemi, s.h., sedghi, s., soleymani, v. and mohammadyani, d. (2012).ctoa levels of welded joint in api x70 pipe steel, engineering fracture mechanics, 82, pp. 46–59. doi: 10.1016/j.engfracmech.2011.11.022. [41] omale, j.i., ohaeri, e.g., tiamiyu, a.a., eskandari, m., mostafijur, k.m. and szpunar, j.a.(2017).microstructure, texture evolution and mechanical properties of x70 pipeline steel after different thermomechanical treatments, materials science & engineering a, 703, pp. 477-485. doi: 10.1016/j.msea.2017.07.086. [42] dowling, j. m., corbett, j.m. and kerr, h.w. (1986). inclusion phases and the nucleation of the acicular ferrite in submerged arc welding in high strength low alloy steel, metallurgical transaction a, 17a, pp.1611-1623. [43] shin, s.y., hwang, b., lee, s., kim, n. j. and ahn , s. s.( 2007).correlation of microstructure and charpy impact properties correlation of microstructure and charpy impact properties in api x70 and x80 line-pipe steels, materials science and engineering a, 458, pp.281–289. doi: 10.1016/j.msea.2006.12.097. [44] zhong, y., xiao, f., zhang, j., shan, y., wang, w. and yang, k. (2006). in situ tem study of the effect of m/a films at grain boundaries on crack propagation in an ultra-fine acicular ferrite pipeline steel, acta materialia, 54, pp.435–443. doi: 10.1016/j.jallcom.2015.05.128. [45] zeghloul, a. and petit j. (1989).influence de l’environnement sur la propagation des fissures courtes et longues dans un alliage léger type 7075, revue phys. appl., 24, pp.893-904. a. deliou et alii, frattura ed integrità strutturale, 46 (2018) 306-318; doi: 10.3221/igf-esis.46.28 318 [46] paris, p.c. and erdogan, f. (1963). a critical analysis of crack propagation law, j basic eng. (asme), 85, 1963, pp.528-533. doi:10.1115/1.3656900. [47] wan, x.l., wang, h.h., cheng, l. and wu, k.m. (2012). the formation mechanisms of interlocked microstructures in low-carbon high-strength steel weld metals, materials characterization, 67, pp.41-51. doi: 10.1016/j.matchar.2012.02.007. [48] ricks, r.a., howell, p. r. and barritte, g.s. (1982).the nature of acicular ferrite in hsla steel weld metals, journal of materials science, 17, pp.732-740. doi: 10.1007/bf00540369. [49] sorrija, b.a. and nascimento, m. p.d. (2015). fatigue crack growth rate analysis in an api 5l x70 steel pipe, rio pipeline conferences & exposition. [50] beltrao, m. a. n., castrodeza, e. m. and bastian, f. l. (2010). fatigue crack propagation in api 5l x-70 pipeline steel longitudinal welded joints under constant and variable amplitudes, fatigue & fracture of engineering materials & structures, 34,pp.321–328. doi: 10.1111/j.1460-2695.2010.01521.x. [51] ikeda, s., izumi, y. fine, m.e. (1977). plastic work during fatigue crack propagation in a high strength low alloy steel and in 7050 al-alloy, engineering fracture mechanics, 9, pp.123-136. [52] kikukawa, m., jono, m. and hora, h. (1977). fatigue crack propagation and closure behavior under plane strain condition, international journal of fracture, 13, pp. 699-701. doi: 10.1007/bf00017303. [53] ranganathan, n., chalon, f. and meo, s. (2008).some aspects of the energy based approach to fatigue crack propagation, international journal of fatigue, 30, pp. 1921–1929. doi: 10.1016/j.ijfatigue.2008.01.010. [54] benguediab, m, bouchouicha, b., zemri, m., mazari, m. (2012). crack propagation under constant amplitude loading based on an energetic parameters and fractographic analysis, materials research, 15 (4), pp.544-548. doi: 10.1590/s1516-14392012005000072. [55] mazari, m., bouchouicha, b., zemri, m., benguediab, m, ranganathan, n. (2008). fatigue crack propagation analysis based on plastic energy approach, comput mater sci, 41, pp.344–349. doi: 10.1016/j.commatsci.2007.04.016. [56] ranganathan, n. (1985). contribution to the development of an energy approach to the propagation of a fatigue crack, ph.d. dissertation, university of poitiers. [57] bouchouicha, b. 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can be opened with acrobat and adobe reader 5.0 and later.) >> /namespace [ (adobe) (common) (1.0) ] /othernamespaces [ << /asreaderspreads false /cropimagestoframes true /errorcontrol /warnandcontinue /flattenerignorespreadoverrides false /includeguidesgrids false /includenonprinting false /includeslug false /namespace [ (adobe) (indesign) (4.0) ] /omitplacedbitmaps false /omitplacedeps false /omitplacedpdf false /simulateoverprint /legacy >> << /addbleedmarks false /addcolorbars false /addcropmarks false /addpageinfo false /addregmarks false /convertcolors /converttocmyk /destinationprofilename () /destinationprofileselector /documentcmyk /downsample16bitimages true /flattenerpreset << /presetselector /mediumresolution >> /formelements false /generatestructure false /includebookmarks false /includehyperlinks false /includeinteractive false /includelayers false /includeprofiles false /multimediahandling /useobjectsettings /namespace [ (adobe) (creativesuite) (2.0) ] /pdfxoutputintentprofileselector /documentcmyk /preserveediting true /untaggedcmykhandling /leaveuntagged /untaggedrgbhandling /usedocumentprofile /usedocumentbleed false >> ] >> setdistillerparams << /hwresolution [2400 2400] /pagesize [612.000 792.000] >> setpagedevice microsoft word numero_46_art_6 m. hack et alii, frattura ed integrità strutturale, 46 (2018) 54-61; doi: 10.3221/igf-esis.46.06 54 developments in the fracture and fatigue assessment of materials and structures a progressive damage fatigue model for unidirectional laminated composites based on finite element analysis: theory and practice m. hack, d. carrella-payan, b. magneville siemens plm software, germany michael.hack@siemens.com, https://orcid.org/0000-0003-3919-1118, t. naito, y. urushiyama honda r&d co ltd, tochigi, japan w. yamazaki, t. yokozeki university of tokyo, japan w. van paepegem ghent university, belgium abstract. the simulation of the fatigue damage of laminated composites under multi-axial and variable amplitude loadings has to deal with several new challenges and several methods of damage modelling. in this paper we present how to account for the complex loading by using the damage hysteresis operator approach for fatigue. it is applied to a fatigue model for intra-laminar damage based on stiffness degradation laws from van paepegem [1]and has been extended to deal with unidirectional carbon fibres. the parameter identification method is presented here and parameter sensitivities are discussed. the initial static damage of the material is accounted for by using the ladevèze damage model and the permanent shear strain accumulation based on van paepegem’s formulation. this approach has been implemented into commercial software. the intra-laminar fatigue damage model combines efficient methods with a low number of tests to identify the parameters of the stiffness degradation law, this overall procedure for fatigue life prediction is demonstrated to be cost efficient at industrial level. keywords. composite; fatigue; variable amplitude; stiffness degradation. citation: hack, m., carrella-payan, d., magneville, b., naito, t., urushiyama, y., yamazaki, w., yokozeki, t., van paepegem, w, a progressive damage fatigue model for unidirectional laminated composites based on finite element analysis: theory and practice, frattura ed integrità strutturale, 46 (2018) 5461. received: 07.03.2018 accepted: 20.04.2018 published: 01.10.2018 copyright: © 2018 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. introduction he increase of lightweight material in transportation industries is today facing greater scrutiny on fatigue life prediction of composite structures based on realistic load situations. the critical step towards accurate prediction is to reproduce the loading conditions undergone by the composite component. in automotive applications, the t http://www.gruppofrattura.it/va/46/6.mp4 m. hack et alii, frattura ed integrità strutturale, 46 (2018) 54-61; doi: 10.3221/igf-esis.46.06 55 challenge is related to the variability of those conditions: non proportional and variable amplitude loading leading to multiaxial local stress states and long duration fatigue loading. this is why siemens plm software [2] has developed an innovative composite fatigue cae methodology (patent pending) keeping track of the material degradation under such conditions. sevenois and van paepegem [3] reviewed and compared the state of the art for fatigue model techniques of woven and ud composite. the study concluded that out of the four modelling methodology  fatigue life (sn curve based),  residual strength,  residual stiffness  (micro-)mechanics model the residual stiffness models are most suitable for mechanical performance using experimental data and can also be combined with a residual strength approach. the presented methodology is based on residual stiffness fatigue laws combined with an efficient damage operator approach to calculate the progressive damage and residual stiffness. this approach is able to perform fatigue simulations for variable amplitude loads and allows ply-stacking optimization without additional testing or material characterizations. intra-laminar fatigue solution: the model n the following sections, the fatigue model strategy will be presented from the load definition, stiffness degradation theory, calculation optimisation algorithm to the parameter identification procedure. fatigue damage laws the damage evolution law is based on the work of van paepegem [1] for woven glass fibres that has been verified in several projects (e.g. [4][5]). three intra-laminar damage variables 11d , 22d and 12d are defined at ply level and linked to the stress tensor by the following behaviour law, eqn.(1)    phch    (1) where c is the stiffness tensor, p is a permanent strain tensor and h is defined as 11 22 12 1 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 1 d d h d                     (2) in [1] the damage variables ijd were split into a positive and a negative part ( ijd  and ijd  ), where the positive part increases when the stress is positive, and the negative one when it is negative. at the end the two parts were added, including a crack closure coefficient for the combination of tension and compression. in this work, only positive stress ratios are used, which means that there is no switch between tension and compression over a cycle and simplifies the problem. either the stress is always positive and the damage ijd is equal to ijd  ; or it is always negative and it is equal to ijd  , eqn.(3) . furthermore, the formulations of van paepegem [1] must be adapted to unidirectional plies. first of all, to account for the high in-plane orthotropic behaviour of unidirectional plies, independent ic parameters are defined for the three components of the damage. therefore, fifteen parameters are used ( ,i jkc ) instead of five. for the same reason, the coupling between 11d and 22  d which was implemented for woven is not included for ud: in woven fabrics, matrix de-cohesion clearly affects i m. hack et alii, frattura ed integrità strutturale, 46 (2018) 54-61; doi: 10.3221/igf-esis.46.06 56 the stiffness in longitudinal and transverse directions, whereas in unidirectional plies, the effect of matrix degradation on longitudinal behaviour can be neglected. however, the coupling between 22d and 12d remains mandatory and has been maintained. finally, the deletion of this coupling imposes the addition of a propagation term in the formulation of 12d , so that a pure shear load in a ply remains able to lead to its collapse. with these assumptions applied to the formulations taken from [1], the evolution laws for the damage variables become:  211 111,11 11 2,11 3,11  11 11 5,11 11 4 ,11 11 ( )   d d d c exp c c d exp c c dn                     3 5,11211 11 1,11 11 2,11 3,11  11 11 11 4 ,11 11 ( )   3 cd d d c exp c c d exp c dn                                 2 222 221,22 12 22 2,22 3,22  22 22 5,22 22 4 ,222 12 22 ( ) 1   1 f f d d d c d exp c c d exp c c dn d                           3 5,222 222 22 1,22 12 22 2,22 3,22  22 22 22 4 ,222 12 22 ( ) 1   31 f f cd d d c d exp c c d exp c dn d                               (3)      2 212 121,12 12 12 2,12 3,12  12 12 5,12 12 4 ,122 12 12 ( ) 1   2 1 d d d c d exp c c d exp c c dn d                              2 212 121,12 12 12 2,12 3,12  12 12 5,12 12 4 ,122 12 12 ( ) 1   2 1 d d d c d exp c c d exp c c dn d                         where ,i jkc are the 15 fatigue material coefficients that must be identified, the fatigue failure indices ij give the connection to residual strength as the ratio between the effective stress and the (actual) ultimate strength of the material in the ij component, and defined as ij ij cycle ij ij max              ; ij ij cycle ij ij max              (4) where 0,   0   ,   0 ij ij ij ij        accumulated permanent strain in addition to these damage evolution laws, the model takes into account the permanent strain which appears in the ply due to a cyclic shear loading. some matrix debris formed by the shear stress is accumulated in the opening matrix cracks during tension stress [1], which leads to a non-reversible deformation of the ply. the 9c parameter drives the fatigue permanent strain accumulation following the formulation: m. hack et alii, frattura ed integrità strutturale, 46 (2018) 54-61; doi: 10.3221/igf-esis.46.06 57 12 12 12 9 12 9 12    p t t d dd dd c max c max dn dn dn         (5) initial degradation of the ply it is also important to consider the effect of the first static loading of the ply on its fatigue damage and strain behaviour, as it is not included in the fatigue degradation. therefore, the static damage and permanent strain are evaluated with a static damage model [1] by first running an initial non-linear analysis up to the peak load of the cyclic fatigue analysis. the resulting initial damage and permanent strain are imposed as initial state of the fatigue analysis and the first cycle can be computed with a correct stress distribution. the fatigue damage tensor fd is then added to the initial damage tensor sd        s fd d d  (6) the permanent strain is handled in the same way calculation optimisation: from n-jump to damage jump n this section we introduce a new methodology of handling stiffness degradation methods efficiently with variable amplitude load situations figure 1: effect of the n-jump algorithm on stiffness degradation. block loading: n-jump for this we start from the methodology for block loads, the n-jump algorithm. the purpose of the n-jump algorithm as presented in [1] is to avoid running a full fe analysis at each load cycle and to deliberately choose a few relevant load cycles only. the cycles with no significant damage growth are “jumped”. from a first fe analysis, at each gauss point of the fe model, the theoretical number of cycles to jump njump1 is estimated by extrapolating the damage, eqn. (7) and applying to eqn. (3) 20 1 10     0     0.5    0 0.2 0.1    0.2 n njump n if d d d d d if d if d              (7) i m. hack et alii, frattura ed integrità strutturale, 46 (2018) 54-61; doi: 10.3221/igf-esis.46.06 58 a global cycle jump njump is defined such that p% of gauss points verify njump1 < njump for the three components. the value of p has been set to 5% in this study. the damage is finally extrapolated after njump, using again the progressive damage formulations eqn.(3). to validate this algorithm and the value of p, three similar fatigue analyses (three point bending) have been run on the first 100 loading cycles with a 45 degree ply layup; one without n-jump, one with p=1% and one with p=5% see fig. 1. [1] compares the stiffness degradation observed in the three analyses and validates the accuracy of the n-jump algorithm. variable amplitude load in the automotive industry, the synthesis of realistic fatigue loading involves complex load schedules for different roads with variable loading (see fig. 2 and [15]). however, the common efficient way to simulate input fatigue loading is to consider block loading with a set of constant maximum stress amplitude sequences. nevertheless, this method is not able to accurately predict the damage progression and stress redistribution under real life variable amplitude. figure 2. variable amplitude example in automotive application. many different load events, many loads – shown here is just a short sequence of the wheel forces at one wheel new method: the damage accumulation jump in the case of variable amplitude, traditional fatigue approaches for metallic material use sn curves, linear miner-palmgren (see [6]) damage accumulation and cycle count (rainflow counted cycles [7]) based damage evaluations. in 1945, miner developed a linear damage accumulation method, based on the work of palmgren and added the contribution of various stress amplitude loading to the damage. however, as for sn curves, the loading history of the material is not accounted for. in rainflow counting methods the damage level depend on full closing hysteresis loop of load cycles (fig. 3). in the case of composite materials, the fatigue behaviour is changing over time due to changes in the matrix damage state. when applying variable amplitude loading, the largest load cycles – that contribute to the larger amount of damage – commonly take a very long time to complete, due to the many nested cycles. in this case the approach to only consider cycles when they are completed can no longer be justified. in the 1990ies brokate and krejci applied the mathematical toolset of hysteresis operators to fatigue theory (see [8, 9]) analysing the linear damage accumulation and analogies between damage accumulation and energy dissipation. based on this work it is possible to extend the rainflow based methodology to non-linear damage accumulation in a both mathematical and methodological sense: (see [10-13]) the damage hysteresis operator approach. m. hack et alii, frattura ed integrità strutturale, 46 (2018) 54-61; doi: 10.3221/igf-esis.46.06 59 the idea is based on the hysteresis operators for kinematic hardening (i.e. to calculate elastic-plastic stress-strain behaviour from pseudo elastic stress histories) and how dissipated energy is calculated in these models. the new idea is to replace the constitutive laws of elasto-plastic stress-strain behaviour with constitutive laws for a “stress-damage potential” behaviour (see [8,10]). the hysteresis operator approach is able to calculate damage at any time increment instead of ‘closed cycle increment’. the extensions explained in [10] and [11] allow the damage status and the damage behaviour to be updated depending on internal (i.e. pre-damage) and any external factors (i.e. temperature, humidity, etc.) therefore this approach is also suited to follow the progressive damage curves and also including the damage history of the material. figure 3. illustration of rainflow method based on stresses/strains with nested cycles. this approach was verified to give good prediction when applied to temperature dependent fatigue analysis with non-linear damage accumulation (see overview of results in [14]) and for full car structures with full load histories (e.g. [15]). it is also applied for modelling the stiffness degradation in short fibre reinforced plastics [16]. parameter identification procedure test protocol n this study, two different test protocols are proposed. the first is a traditional approach with tensile tests on five layups and five load levels per layup capturing a representative span of fatigue life (based on test method [17]). this results in twenty-five configurations. the second is an application of a more innovative approach again based on ideas in [1] with one-sided bending tests on the same five layups, but with only one load level for each layup, so only five configurations. the idea is to assess if the load distribution on this kind of specimen can provide enough information to feed the damage model, as a three-points-bending test results in progressive load levels along the same specimen, both in tension and compression. figure 4: effect of 2,12c (left) and 4 ,12c (right) on numerical stiffness degradation i m. hack et alii, frattura ed integrità strutturale, 46 (2018) 54-61; doi: 10.3221/igf-esis.46.06 60 peak data such as load, displacement, strains from extensometers and gauges, temperature are measured from these tests at several representative cycles. the stiffness degradation of each specimen can be estimated from these evolutions. additionally, running-in and unloading raw data are extracted to analyse the initial stiffness drop of the specimens and their final permanent strain. parameter identification protocol the parameter identification consists of an fe-based optimization of the fifteen fatigue parameters to fit simulated stiffness degradation with experimental results. a step-by-step methodology identifying the parameters one by one from specific experimental data has been setup. as illustrated by two examples in [1], each ci parameter has a specific contribution on the numerical stiffness degradation, and therefore can be adjusted to fit with experimental results. therefore, two volume finite element models reproducing the two testing procedures have been created, and the nonlinear fatigue solver with n-jump algorithm is used to correlate the stiffness degradation of each testing configuration by adjusting the fifteen ,i jkc parameters (note that the n-jump is herein used as tests are carried out under constant amplitude loading). an illustration of the resulting correlation between experimental and simulated stiffness evolutions is given in [17]. finally, the parameter 9c is estimated by crosschecking the raw data of the unloading of the specimens. validation and application he first validation has been conducted on a coupon under constant amplitude loading. the same three point bending analysis as above is run to 80 000 cycles at an imposed load level. a more complex quasi-isotropic layup [0/60/-60] 4s is now studied. the resulting stiffness degradation is compared to experimental data [17]. the good predictability illustrates the main interest of a ply-level damage law: identification is performed on specific layups, and the resulting material data remains available for any layup without additional identification. figure 5: correlation between experimental and simulated stiffness evolutions ([0]20 layup in 3 point bending). figure 6: predictability of stiffness reduction of a 3 point bending quasi-isotropic coupon. t m. hack et alii, frattura ed integrità strutturale, 46 (2018) 54-61; doi: 10.3221/igf-esis.46.06 61 further validation cases on component like (i.e. flat and v-shaped components) have been conducted. in these cases the overall stiffness degradation contribution from the fatigue loading were quite small. the comparison of the predicted and measured stiffness reduction showed good coincidence. as the failures in these examples were not initiated from fatigue failure due to intra-ply damage but due to the inter-laminar delamination from the edge, the examples were not sufficient to fully validate the methodology. so the authors decided that additional validation cases are needed and under investigation. conclusion new methodology to efficiently analyse the fatigue damage by stiffness reduction under variable amplitude was introduced. it combines the efficiency of the n-jump algorithm with complex load scenarios under variable and non-proportional loading. first validations show good coincidence between simulated and measured global stiffness behaviour. further investigation are needed that also include the inter-ply behaviour and the initiation of delamination. this introduces new challenges to extend this methodology to a complete intra-laminar and inter-laminar fatigue damage solution for variable amplitude and multi-axial loadings. the first steps have been already done but further validation of these extensions is still needed. references [1] van paepegem, w. (2002). development and finite element implementation of a damage. phd thesis, 2002, u gent. [2] siemens plm software: wikipedia [3] sevenois, r.b. and van paepegem, w. (2015). fatigue damage modeling techniques for textile composites: review and comparison with unidirectional composite modeling techniques. asme. appl. mech. rev. 67(2), 020802020802-12. doi: 10.1115/1.4029691. [4] xu, j., lomov, s.v., verpoest, i. daggumati, i., paepegem, w. van and degrieck, j. (2009). meso-scale modeling of static and fatigue damage in woven composite materials with finite element method.” presented in 17th international conference on composite materials (iccm-17). [5] xu, j. (2011). meso finite element fatigue modelling of textile composites, ph. d. thesis, dept mtm, katholieke universiteit leuven, belgium. [6] miner, m.a. (1945). cumulative damage in fatigue, journal of applied mechanics 67, pp. a159-a164. [7] matsuishi, m. and endo, t. (1968). fatigue of metals subjected to varying stresses, japanese society of mech. eng., fukuoka, japan. [8] brokate, m. and sprekels, j. (1996). hysteresis and phase transitions, series applied mathematical sciences, 121. [9] brokate, m., dressler, k. and krejci, p. (1996). rainflow counting and energy dissipation for hysteresis models in elastoplasticity, eur. j. mech. a/solids 15, pp. 705-737. [10] hack, m. (1998). schädigungsbasierte hysteresefilter, phd thesis, tu kaiserslautern. [11] nagode, m. and hack, m. (2011). the damage operator approach: fatigue, creep and viscoplasticity modeling in thermo-mechanical fatigue, sae int. j. of mat. & manuf., 4(1), pp. 632-637, 2011, doi:10.4271/2011-01-0485. [12] nagode, m., hack, m. and fajida, m. (2010). low cycle thermo‐mechanical fatigue: damage operator approach, fat. fract mat. struct. 33(3), pp. 149-160. doi: 10.1111/j.1460-2695.2009.01424.x. [13] nagode, m., hack, m. and fajida, m. (2009). high cycle thermo‐mechanical fatigue: damage operator approach, fat. fract mat. struct. 32(6), pp. 505-514. doi: 10.1111/j.1460-2695.2009.01353.x. [14] šeruga, d., hack, m. and nagode, m. (2016). thermomechanical fatigue life predictions of exhaust system components, mtz worldwide, 77(3), pp. 44-49. doi:10.1007/s38313-015-0102-y. [15] brune, m., fiedler, b., köttgen, v.b. and reißel, m. (1998). fem based durability analysis of the knuckle of the 5 series bmw, fatigue design’98, helsinki. [16] hack m., korte w., straesser s. and teschner m. (2018). fatigue simulation of a short fiber reinforced oil-filter under high temperature and pressure loads, procedia engineering 213c, pp. 207-214. doi: 10.1016/j.proeng.2018.02.022. 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/hrv (za stvaranje adobe pdf dokumenata najpogodnijih za visokokvalitetni ispis prije tiskanja koristite ove postavke. stvoreni pdf dokumenti mogu se otvoriti acrobat i adobe reader 5.0 i kasnijim verzijama.) /hun 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/pdfxoutputintentprofileselector /documentcmyk /preserveediting true /untaggedcmykhandling /leaveuntagged /untaggedrgbhandling /usedocumentprofile /usedocumentbleed false >> ] >> setdistillerparams << /hwresolution [2400 2400] /pagesize [612.000 792.000] >> setpagedevice microsoft word numero 22 articolo 9.doc d. gentile et alii, frattura ed integrità strutturale, 22 (2012) 85-92; doi: 10.3221/igf-esis.22.09 85 design and realization of a multisamples rotating high cycle fatigue machine domenico gentile dicem – university of cassino – via g. di biasio, 43 – 03043 cassino, italy massimo martorelli dime – university of naples federico ii – school of engineering, p.le v. tecchio 80 80125 naples, italy massimo.martorelli@unina.it abstract. in this work the design and the technical characteristic of a moore rotating bending machine are presented. the machine has been realized at the university of cassino in order to run tests on multiple specimens at different temperature. the user can choose independently the load and the temperature for each specimen. the machine has been designed to produce in short time a several numbers of data of materials fatigue strength at low costs. the machine is in assembling step at the laboratory of industrial design of the university of cassino. keywords. fatigue; wholer; test machine; product design process. introduction atigue research has been conducted on a multitude of testing machine ranging from rotating bending loading, axial loading, repeating bending loading and torsional loading. the design varies according to the nature and combination of load and components, to the type of fatigue test (high cycle, low cycle, thermal fatigue), to the scale (small specimens, full scale components). in this work the design of a low-cost and reliable rotating bending fatigue testing machine that meets the following criteria has been issued: 1. minimum mass so that high cycle fatigue testing can be done on this machine. 2. constant bending moment on specimen throughout testing. 3. up to 5 samples tested in the same time. 4. commercially available components adopted where possible. 5. designs, material selection, machinery specifications for unavailable components. 6. possibility to update easily the machine. 7. possibility to run tests at different temperature the idea is to realize a low cost machine that should be extremely adaptable. rotating machine configuration is one of the simplest and efficient in order to test a sample by a time variable load under constant amplitude, fig. 1. first machine has been design by wöhler [1]. the simplest configuration has been proposed from moore and krouse [2] that reached speed of the order of 30.000 rpm. the machine, using four point bending system, allows to load the sample with a constant stress on the full measure zone. leher [3] and next moore developed solutions in this way. this f http://dx.medra.org/10.3221/igf-esis.22.09&auth=true http://www.gruppofrattura.it d. gentile et alii, frattura ed integrità strutturale, 22 (2012) 85-92; doi: 10.3221/igf-esis.22.09 86 configuration can be adapted easily in order to test more samples together. prot [4] developed a machine able to test up to 30 samples in the same time. basically a simple bending moment is applied to a specimen gripped at both ends to a rotating shafts, fig. 1. this configuration has been modified every time following the needed. recently irfan et al. [5], has been realized a rotating bending fatigue machine able to test at the same time up to 16 laminated composite samples. new machines, d. brandolisio et al. [6], realized recently show that design process requires a specific analysis of the new mechanical components available commercially. a previous analysis on the materials used to realize the shaft has been conducted following a methodology proposed from bonora et al. [7-10]. today the use of parametric cad models plays an essential role in the product design process, mainly, but not only [11], in the industrial field [12, 13]. having the parametric cad model of the product, it is possible to make any virtual simulations on it, also in terms of fatigue lifetime [14]. although the fatigue virtual simulations are very useful, the experimental tests are fundamental to validate the results. in the paper the analysis have been carried out using cad parametric models and electronic calculus sheets formatted following the project desiderata. figure 1: basic design of a r.r. moore fatigue testing machine. geometry and components definition n order to take into account all the specifications required has been realized an electronic work sheet containing all the calculations and all the characteristic of the components adopted for the design. in this way every time there was a needed of a change of component in order to, for example, minimize cost, all the analysis come out automatically. in order to calculate the bending moment and rotation, the bearing life, the spring requirements and the chassis design, has been used the classic mechanical laws such as:   1 2 2 3 3 16 4 3 ys m t d n   (1) where m is the bending moment, t is the torsional moment, sy is the yield stress of the material, n is the safety factor and d is the minimum diameter. or the more useful following equation that allows to estimate an initial shaft size early in the design process: 1 32 32 3 4 f e yt k mn t d s s                 (2) where se is the material ultimate endurance limit, syt is the yield stress to torsion and kf is the stress intensity factor under cyclic load. this equation gives the minimum diameter shaft that will result in infinite fatigue life, and appears in the ansi standard. first question was to ensure the constant bending load. this specification can be met if the specimen grips can avoid inflection and rotation of the specimen. for this reason commercial grips have been adopted these grips are produced i http://dx.medra.org/10.3221/igf-esis.22.09&auth=true http://www.gruppofrattura.it d. gentile et alii, frattura ed integrità strutturale, 22 (2012) 85-92; doi: 10.3221/igf-esis.22.09 87 from cepi (commercial code 32, patented) according to din 6499 class 2 standards in order to grant seal and centering and that was also able to allow different specimen’s geometry, fig. 2. next step has been to design the shafts. analyses have been conducted following the classical mechanical laws, realizing parametric cad models that allow to change one or more dimensions. electronic sheets have been implemented in order to take into account the mechanical materials parameters and all the costs: commercial part, machine working of components, etc. in tab. 1 is reported a worksheet sample of stress analysis; in tab. 2 a sample of cost analysis. figure 2: grips: a) geometry; b) dimension as din6499 standard (all the measure are in millimeter). cepi catalog. material data commercial name elastic modulus e [mpa] failure stress [mpa] yield stress [mpa] endurance limit [mpa] material 1 210000 400 250 180 material 2 210000 600 480 300 geometrical data von mises stress diameter 1 25 mm section 1/2 296 mpa diameter 2 28 mm section 2/3 195 mpa diameter 3 30 mm section 3/4 173 mpa diameter 4 32 mm radius 2/1 2 mm material 1 material 2 radius 3/2 2 mm safe factor 1/2 0.84 1.62 radius 4/3 2 mm safe factor 2/3 1.28 2.45 d2/d1 1,12 safe factor 3/4 1.44 2.77 d3/d2 1.07 d4/d3 1.07 load 1800 n stress concentration factors bending torsion distance 100 mm kt (2/1) 1.80 1.60 bending 180000 nmm kt (3/2) 1.70 1.45 torsion 400000 nmm kt (4/3) 1.82 1.61 table 1: example of the work sheet implemented for calculus. http://dx.medra.org/10.3221/igf-esis.22.09&auth=true http://www.gruppofrattura.it d. gentile et alii, frattura ed integrità strutturale, 22 (2012) 85-92; doi: 10.3221/igf-esis.22.09 88 component unit. cost (€) total number total amount (€, no tax) total amount (€, 21% vat) carriage 4 linear recirculating ball bearing units 31.56 20 631.20 763.75 linear guidance systems with recirculating ball bearing units 24.48 10 244.80 296.21 self-lubricating kit 27.91 20 558.24 675.47 cover 15 0.16 50 8.00 9.68 ring nut 14.69 10 146.88 177.72 belt 340 4.80 1 4.80 5.81 belt 525 5.70 1 5.70 6.90 belt 400 5.10 4 20.40 24.68 pulley 30 3.90 10 39,00 47.19 timing-belt pulley 4.80 2 9.60 11.62 bearing 3.30 2 6.60 7.99 choke ring 1.50 20 30.00 36.30 bearing 3203 17.79 20 355.80 430.52 bearing 22206 39.81 20 796.20 963.40 choke ring a25 1.20 5 6.00 7.26 encoder+fan 1050.00 1 1050.00 1270.50 lsmv 80 222.30 1 222.30 268.98 sub-total 4135.52 5003.98 min (€) max (€) min + tax (€) max + tax (€) machinery 10000.00 € 10000.00 € 12000.00 € 12100.00 software 3000.00 € 5000.00 € 3600.00 € 6050.00 € 15600.00 € 18876.00 total amount € 20603.98 € 23879.98 table 2: example of the work sheet implemented for cost analysis. this procedure allowed to have a clear process of realization: clear components, clear machinery work, clear costs, clear assembling and verification. components that were not possible or convenient to have commercially, have been designed and realized very accurately in order to ensure constant bending at high fatigue cycles. one of these parts is the spindle body with the related shafts and supports. part of spindle is reported on fig. 3. also shafts have been realized in house. following classical mechanical formulae in order to verify strength and stiffness the shaft reported in fig. 4 has been defined. other fundamental components are the bearings. among the solutions available bearings by skf have been used. from skf catalogue have been selected the following: spherical roller bearings skf 22206 e (ccw33), angular contact ball bearings, double row skf 3203 atn9 in order to support spindle’s shaft, and deep groove ball bearings, single row skf 6004-2rsh as support of connectors between engine and pulleys. in order to have a very useful machine in different conditions, as for example fatigue tests at high temperature, a system with a single engine has been preferred to realize, five different load cells have been used, one for each sample. this allowed to realize a modular machine able to work for one or “n” samples depending of the mounted spindles. concerning the fatigue tests a different temperatures, this machine is able to test each specimen at different temperature in a single test. http://dx.medra.org/10.3221/igf-esis.22.09&auth=true http://www.gruppofrattura.it d. gentile et alii, frattura ed integrità strutturale, 22 (2012) 85-92; doi: 10.3221/igf-esis.22.09 89 in fig. 5 the spindles group has been reported. all the spindles are connected at the same asynchronous engine capable to reach a 4500 rpm speed. load cells are connected under the spindles plane, (not reported in the figure), counterbalanced by special gas springs in order to grant better applying load method. best operating conditions for this machine are: 5 specimens and 3000 rpm engine’s speed. figure 3: spindle body. figure 4: driven shaft. http://dx.medra.org/10.3221/igf-esis.22.09&auth=true http://www.gruppofrattura.it d. gentile et alii, frattura ed integrità strutturale, 22 (2012) 85-92; doi: 10.3221/igf-esis.22.09 90 gas spring has been selected from commercials catalogue by ace: maximum extension range 100 mm, maximum load 1440 n, fig. 6. power transmission has been realized by a system of toothed belts and pulleys, fig. 7. belts are made in “polychloroprene” with steel core. pulleys has type hdt (european standards) with 5 mm pitch for belts 15 mm width. (a) (b) figure 5: spindles group: a) total view; b) load system details. figure 6: gas spring. (ace commercial catalog). figure 7: belts and pulleys. most of the commercial components, like load cells or springs has been assembled in order to allow their substitution for eventual upgrades. spindles are mounted on rails to allow different sample’s length. also the control system has been designed in order to allow easy upgrade: for each sample there is a cycles counter and an encoder connected with a computer that allows to control separately each related load cell by a dedicated software. control system provides the possibility to send external trigger at defined numbers of cycles in order to allow measure by video camera or other kind of instruments. http://dx.medra.org/10.3221/igf-esis.22.09&auth=true http://www.gruppofrattura.it d. gentile et alii, frattura ed integrità strutturale, 22 (2012) 85-92; doi: 10.3221/igf-esis.22.09 91 a schema of a possible configuration has been reported in fig. 8. as a sample break, cycles counting will stop. the related shaft will stop leaving the others shafts to run without changing load or speed. gas spring and related connectors will avoid load cell drop and will allow his repositioning to a virtual zero. the machine is equipped with a spindle’s safety blocking system by a micrometer screw that prevents shaft bending up to defined limits. pc and  controller  engine sample video camera  encoder  thermal  control  figure 8: functional scheme. complete system is mounted on a single steel chassis, which is possible to fix on the floor by screws and dumping interfaces. in order to run tests at different temperature a system using oil is in the process design at the moment (a procedure to obtain a patent has been started). the idea is that different temperature can be applied to specimens by oil in different heaters, one for each specimen. conclusion n this work the executive project has been presented in order to realize a rotating fatigue bending machine. the aim was to develop a machine at low costs and capable to test many specimens at the same time and eventually at different temperature. at the present the machine is being tested at the lab. of industrial design of the university of cassino in collaboration with crea (center of reverse engineering applications) lab. of the university of naples federico ii for cad/fem simulations. cost and construction time are less than similar commercial machine that are able to test only one specimen. the machine can be used changing many parameter’s test and is already predisposed to run test at high temperature. this part will be completed after the preliminary tests. the possibility to combine different loads and temperature with a single test controlling independently the load cells and the warming room with a single asynchronous engine is very interesting. references [1] wöhler, z. baaw. 8 (1858-1870) 641. [2] h. f. moore, g. n. krouse university of illinois, engng. exp. sta. circ., 23 (1934) 7. [3] f. lehr die abkürzungsverfahren zur ermittlung der schwingungsfestigkeit von materialien, dr. ing. diss. th., stuttgart (1925) [4] f. m. prot, rev. métall., 34 (1937) 440. [5] a. irfan, s. raif, o. güven, materials and design, 29 (2008) 397. [6] d. brandolisio, g. poelman, g. de corte, j. symynck, m. juwet, f. de bal, fatimat project, http://mechanics.kahosl.be/fatimat/, (2009) [7] n. bonora, a. ruggiero, d. gentile, s. de meo, strain, 47 (2011) 241, doi: 10.1111/j.1475-1305.2009.00678.x 253 [8] n. bonora, a. ruggiero, l. esposito, d. gentile, int. j. of plasticity, 22(11) (2006) 2146. [9] n. bonora, a. ruggiero, int. j. of solids and structures, 42(5-6) (2005) 1401. i http://dx.medra.org/10.3221/igf-esis.22.09&auth=true http://www.gruppofrattura.it d. gentile et alii, frattura ed integrità strutturale, 22 (2012) 85-92; doi: 10.3221/igf-esis.22.09 92 [10] n. bonora, a. ruggiero, composites science and technology, 66 (2) (2006) 323. [11] p. ausiello, p. franciosa, m. martorelli, d. c. watts, dental materials, 28(8) (2012) 919. [12] s. gerbino, m. martorelli, d. oliviero, in: proc. of international design conference, design 2006, dubrovnik, may 15-18, isbn 953-6313-82-0 (2006) [13] m. martorelli, d. oliviero, journal of mechanics engineering and automation, 2(4) (2012) 213. [14] p. ausiello, p. franciosa, m. martorelli, d. c. watts, dental materials, 27(5) (2011) 423. http://dx.medra.org/10.3221/igf-esis.22.09&auth=true http://www.gruppofrattura.it microsoft word 2291 r. nikhil et alii, frattura ed integrità strutturale, 48 (2019) 523-529; doi: 10.3221/igf-esis.48.50 523 focused on “showcasing structural integrity research in india” limit load based evaluation of plastic η factor for c(t) specimen with a mismatched weld r. nikhil, s.a. krishnan, g. sasikala, a. moitra materials development and technology division, indira gandhi centre for atomic research, kalpakkam 603102, tamil nadu, india rnikhil@igcar.gov.in, sakrish@igcar.gov.in, gsasi@igcar.gov.in, moitra@igcar.gov.in abstract. plastic η factor is adopted to account for crack tip plasticity while evaluating the fracture toughness of the materials as per astm e1820. it is valid only for homogeneous materials. the plastic η factor for compact type (c(t)) geometry with type 316ln stainless steel weld has been evaluated based on elastic-plastic fe analysis. the incremental elastic-plastic material model with various values for strength mismatch ratio (m) i.e. ratio of yield strength of weld metal to that of base metal, from 1.2 to 2.2 have been considered. the weld width (h) parallel to the crack plane is varied from 4 mm to 16 mm. the η values thus obtained are analyzed and the inferences are discussed. keywords. limit load; plastic η; elastic-plastic; strength mismatch level. citation: nikhil, r., krishnan, s.a., sasikala, g., moitra, a., limit load based evaluation of plastic η factor for c(t) specimen with a mismatched weld, frattura ed integrità strutturale, 48 (2019) 523-529. received: 28.11.2018 accepted: 28.02.2019 published: 01.04.2019 copyright: © 2019 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. introduction eld joints are more likely to contain flaws or defects. the fracture toughness of weldment under the influence of base material strength is an essential input for integrity assessment of welded structures. j-integral as a measure of fracture toughness is generally determined according to astm e1820. it is a fracture characterizing parameter based on non-linear elastic material model applied to elastic-plastic materials. the j-integral is divided into elastic (linear), je and plastic (non-linear), jp components. the elastic component of j ( ' 2 e k je  ) is same as griffith energy release rate and the plastic part is given ( bb a j p p   ), where η is a geometry normalizing parameter to account crack tip plasticity i.e. spread of plastic zone around the crack tip. it is influenced by geometry of the test specimen. for compact tension (ct) specimens, astm has adopted an expression (eqn. 1) as obtained by landes and clarke [1].        w b 522.02 (1) w http://www.gruppofrattura.it/va/48/2291.mp4 r. nikhil et alii, frattura ed integrità strutturale, 48 (2019) 523-529; doi: 10.3221/igf-esis.48.50 524 this expression is valid for specimens made of homogenous material. wang and co-authors [2] proposed ctod equations expressed in terms of weld height, mismatch level and strain hardening rate for specimens made of non-homogeneous and strain hardening materials. smith [3], panontin and co-authors [4], cassanelli and co-authors [5], kim and co-authors [6], davies and co-authors [7], have proposed analytical and numerical solution to η expression for even match (m=1) c(t) specimens but varying strain hardening exponent. xuan and co-authors [8] and marie & nedelec [9] have performed fe based analysis for various mismatch factors from 0.25 to 2 and 2.3 respectively. a literature review of η solution for c(t)specimen in tabular form is provided by h. zhou and co-authors [10]. they have analyzed the influence of mismatch factor, weld height, material hardening exponent and a/w ratio effect on η solution. astm type 316ln stainless steel is a major structural material for fast breeder reactor being commissioned at kalpakkam, india. the m value for 316ln weld is found to vary across the weld thickness [11] and found to be as high as 2.2. in the present study, plane strain fe analysis have been carried out to assess the η factor for c(t) geometry with weld width to specimen width ratio, h/w varying from 0.08 to 0.32 and crack depth to width ratio, a/w varying from 0.45 to 0.7 for strength mismatch m =1.2,1.4,1.6,1.8,2 and 2.2. theoretical background or homogeneous material, as per astm experimental load, load line displacement (crack opening displacement) and crack length data are obtained to evaluate j-integral values for a growing crack. a typical plot is shown in fig. 1. figure 1: area under the load-displacement plot. j-integral consists of an elastic component and a plastic component. pe jjj  (2) where ' 2 e k je  such that ee ' for plane stress  2 ' 1   e e for plane strain (3) bb a j p p   (4) f r. nikhil et alii, frattura ed integrità strutturale, 48 (2019) 523-529; doi: 10.3221/igf-esis.48.50 525 as per ernst et al. [12,13], if limit load (pl)can be expressed in terms of independent functions of crack length (a) and loadline displacement (δpl) then η can be calculated based on pl.    pll gafp  . (5) assuming the material behavior to be ideal plastic, chattopadhyay et al. [14] proposed η as a p p l l    1  (6) knowing pl, the eq. (6) issued for heterogeneous c(t) specimens. pl could be evaluated by analytical solutions available in open literature [15] or twice elastic slope (tes) / twice elastic deflection (ted) or fe based yield contour (fyc) plot across the ligament. in present study pl has been obtained (i) based on tes method from fem simulated load-displacement plots and (ii) fe-yield contour plot across the ligament of c(t) specimen. figure 2: meshed ct geometry with constraints. figure 3: limit load vs a/w using various approaches. figure 4: schematic of weld c(t) specimen. figure 5: bilinear stress strain plot. r. nikhil et alii, frattura ed integrità strutturale, 48 (2019) 523-529; doi: 10.3221/igf-esis.48.50 526 figure 6(a): ac yield plot for a/w=0.5, h/w=0.08 and m=1.6 figure 6(b): ac yield plot for a/w=0.7, h/w=0.32 and m=2.2 figure 7(a): pl vs a for h/w=0.08 and m=1.6 figure 7(b): pl vs a for h/w=0.32 and m=2.2 fem analysis d fe analysis for standard c(t) geometry with base and base-weld metal configuration consisting of h/w ratio (0.08, 0.16, 024 and 0.32), a/w (0.45, 0.5, 0.55, 0.6, 0.65 and 0.7) and m (1.2, 1.4, 1.6, 1.8, 2 and 2.2) has been carried out using abaqus. loading pins of the specimen are modeled as rigid bodies and loaded by applying displacement while all other motions of the pins are restrained. surface-to-surface contact with a finite-sliding formulation is defined between the pins and the specimen hole. a typical c(t) geometry mesh model with constraints highlighted is shown in fig. 2. as per astm e1820, high stress triaxiality at crack tip is ensured in c(t) specimens by side grooving. hence in the present study the analysis is restricted plane strain (cpe4) condition. elastic-perfect plastic simulations have been carried out to evaluate limit load for homogeneous c(t) specimens with a/w ratios (0.45, 0.5, 0.55, 0.6, 0.65 and 0.7). flow stress of 410 mpa has been input for analysis. the limit load obtained using analytical formula, twice elastic slope (tes) and fe based yield contour (fyc) approaches are compared. fyc is obtained using ac yield parameter in abaqus which provides the extent of yielding of various elements. the pl values are shown in fig. 3. it is observed that the pl values based fyc are in good agreement with those obtained from tes and analytical solutions. therefore, the fem procedure adopted to evaluate the limit load could be extended to the heterogeneous c(t)specimens. towards this, elastic-plastic simulations have been carried out for c(t)specimens with weld width as shown in fig. 4. the yield stress, uts and % elongation obtained from all weld tensile test is 462 mpa, 658 mpa and 28% elongation respectively. based on these values a bi-linear true stress-plastic strain data generated considering identical hardening behaviour for all m values as shown in fig. 5 is used as material model input. a typical fyc corresponding to the limit load obtained for weld specimen with h/w = 0.08, a/w = 0.5, m = 1.6 is shown in fig. 6(a) and for h/w = 0.32, a/w = 0.7, m = 2.2 is shown in fig. 6(b). for a given load line displacement, the spread of yield contour is attributed to m and h, in case of specimen with 2 r. nikhil et alii, frattura ed integrità strutturale, 48 (2019) 523-529; doi: 10.3221/igf-esis.48.50 527 m=1.6 and h=4 mm, the yield contour crosses the interface boundary and spreads to base material to a larger area compared to specimen with m=2.2 and h=16 mm. results and discussion ypical pl vs. a plot for m=1.6, h/w=0.08 and m=2.2, h/w=0.32 is shown in figs. 7(a)and 7(b). these values are fitted to a second order polynomial. as per the eqn. 6, η values are calculated for all configurations of c(t)specimens. for the homogeneous c(t)specimens, the calculated η values are in close agreement of ±4% with astm proposed η values as given eq. (1). similar observation has been reported by zhou and co-authors [10]. the estimated η values for various configurations of weld c(t)specimen are given in table 1. table 1: η values calculated for heterogeneous specimens using fyc approach. t η for m=1.2 η for m=1.8 h/w 0.08 0.16 0.24 0.32 h/w 0.08 0.16 0.24 0.32 b/w b/w 0.3 2.096 1.910 1.809 2.338 0.3 2.081 1.795 1.597 1.767 0.35 2.185 2.106 1.975 2.202 0.35 2.130 1.892 1.746 1.787 0.4 2.231 2.185 2.121 2.116 0.4 2.153 1.906 1.795 1.767 0.45 2.262 2.239 2.173 2.040 0.45 2.170 2.001 1.952 1.758 0.5 2.302 2.303 2.238 2.008 0.5 2.202 2.036 1.947 1.778 0.55 2.259 2.273 2.225 1.993 0.55 2.169 2.019 1.985 1.815 ηmean 2.223 2.169 2.090 2.116 ηmean 2.151 1.941 1.837 1.778 η for m=1.4 η for m=2 h/w 0.08 0.16 0.24 0.32 h/w 0.08 0.16 0.24 0.32 b/w b/w 0.3 2.088 1.869 1.735 2.121 0.3 1.866 1.970 1.767 1.550 0.35 2.156 2.045 1.829 2.029 0.35 2.041 1.942 1.823 1.649 0.4 2.190 2.108 1.911 1.991 0.4 2.101 1.929 1.801 1.695 0.45 2.214 2.154 2.003 1.938 0.45 2.146 1.875 1.824 1.756 0.5 2.251 2.215 2.046 1.928 0.5 2.199 1.856 1.849 1.799 0.55 2.213 2.197 2.038 1.916 0.55 2.189 1.880 1.851 1.819 ηmean 2.185 2.098 1.927 1.987 ηmean 2.090 1.908 1.819 1.711 η for m=1.6 η for m=2.2 h/w 0.08 0.16 0.24 0.32 h/w 0.08 0.16 0.24 0.32 b/w b/w 0.3 2.082 1.834 1.815 1.838 0.3 1.868 1.751 1.640 1.536 0.35 2.140 2.003 1.886 1.798 0.35 2.034 1.832 1.713 1.633 0.4 2.168 2.056 1.864 1.854 0.4 2.088 1.898 1.752 1.674 0.45 2.188 2.098 1.904 1.903 0.45 2.128 1.980 1.794 1.705 0.5 2.222 2.157 1.918 1.881 0.5 2.181 1.956 1.845 1.761 0.55 2.188 2.148 1.924 1.897 0.55 2.172 2.002 1.846 1.777 ηmean 2.164 2.049 1.885 1.862 ηmean 2.079 1.903 1.765 1.681 r. nikhil et alii, frattura ed integrità strutturale, 48 (2019) 523-529; doi: 10.3221/igf-esis.48.50 528 for a given strength mismatch level, the η values have been found to decrease as the weld width is increased from 4 mm to 16 mm. this result is in agreement with literature [9,10]. further the η values have been found to decrease with strength mismatch except between m=2 & 2.2 where they are quite insensitive to mismatch. the similar trend has been reported in literature [10]. the η values vary with configurations, however the mean η value follow a trend line for m=1.6, 1.8, 2.0 and 2.2. the mean η value for m=1.2 is nearly constant for various h/w ratios, for m=1.4 it varies between 2.185 to 1.927. it is also observed that η decreases monotonically with increasing m, except for intermediate weld width i.e. h/w = 0.16 and 0.24 as shown in fig. 8. for c(t)configurations with m=1.6 to 2.2, there is a similarity and decreasing trend as the h/w ratio increases. the maximum mean η value is 2.16 and the minimum of 1.68. figure 8: η vs m for b/w=0.45. conclusion he following important conclusions are drawn based on present study. 1. a validated finite element analysis yield contour (fyc) approach based on elastic-plastic material model is used to estimate limit load. 2. the plastic η factors for various configurations of c(t) specimen with weldment parallel to crack plane has been proposed to evaluate plastic j-integral. 3. for smaller strength mismatch ratio, m≤1.4 the variation of mean η value is 2.2 to 1.93 hence evaluating configuration specific plastic η factor may not influence severe on j-estimation. 4. for larger values of m>1.4 the plastic η factor vary from 2.16 to 1.68, hence the values are c(t) configuration specific. references [1] clarke, g.a. and landes, j.d. (1979). evaluation of the j integral for the compact specimen, journal of testing and evaluation, jteva, 7(5), pp. 264–269. doi:10.1520/jte10222j. [2] wang, y.y., reemsnyder, h.s. and kirk, m.t. (1997). inference equations for fracture toughness testing: numerical analysis and experimental verification, astm special technical publication (1321), pp. 469–484. doi: 10.1520/stp12325s . [3] smith, e. (1992). the use of eta factors to describe the j integral: the astm 1152 standard for the compact tension specimen, engineering fracture mechanics, 41(2), pp. 241-246. doi: 10.1016/0013-7944(92)90184-g. [4] panontin, t.l., makino, a. and williams, j.f. (2000). crack tip opening displacement estimation formulae for c(t) specimens, engineering fracture mechanics, 67, pp. 293-301. doi: 10.1016/s0013-7944(00)00048-5. [5] cassanelli, a.n., cocco, r. and de vedia, l.a. (2003). separability property and ɳpl factor in astm a387-gr22 steel plate, engineering fracture mechanics, 70(9), pp. 1131-1142. doi: 10.1016/s0013-7944(02)00095-4. [6] kim, y.j., kim, j.s. and cho, s.m. (2004). 3-dconstraint effects on j testing and crack tip constraint in m(t), se(b), se(t) and c(t) specimens: numerical study, engineering fracture mechanics, 71(9–10), pp. 1203–1218. doi: 10.1016/s0013-7944(03)00211-x. t r. nikhil et alii, frattura ed integrità strutturale, 48 (2019) 523-529; doi: 10.3221/igf-esis.48.50 529 [7] davies, c., kourpetis, m., o’dowd, n. and nikbin, k.m. (2007). experimental evaluation of the j or c* parameter for a range of cracked geometries, fatigue & fracture mechanics, 35, pp. 321–340. doi: 10.1520/jai13221. [8] xuan, f.z., tu, s.t. and wang, z.d. (2005). a modification of astm e 1457 c* estimation equation for compact tension specimen with a mismatched cross-weld, engineering fracture mechanics, 72(17), pp. 2602–2614. doi: 10.1016/j.engfracmech.2005.05.002. [9] marie, s. and nedelec, m. (2011). mismatch effect on c(t)specimen mechanical effect and consequences on the weld toughness characterization, in asme conference proceedings, 44533, pp. 449–458. doi: 10.1115/pvp2011-57168. [10] zhou, h., biglari, f., davies, c.m., mehmanparast, a. and nikbin, k.m. (2014). evaluation of fracture mechanics parameters for a range of weldment geometries with different mismatch ratios, engineering fracture mechanics, 124, pp. 30–51. doi: 10.1016/j.engfracmech.2014.03.006. [11] hongo, h., yamazaki, m., watanabe, t., tabuchi, m. and albert, s.k. (2014). evaluation of local fluctuation of creep properties in weld joint of 18cr-12ni-mo-medium n low c steel, pressure vessels and piping: manufacturing and performance, narosa pub., pp. 307-316. [12] ernst, h.a. and paris, p.c. (1980). techniques of analysis of load–displacement records by j-integral methods, us nuclear regulatory commission, nureg/cr 1222. [13] paris, p.c., ernst, h.a. and turner, c.e. (1980). in: fracture mechanics, twelfth conference, astm stp 700, philadelphia, american society for testing and materials, pp. 338–351. doi: 10.1520/stp700-eb. [14] chattopadhyay, j., dutta, b.k. and kushwaha, h.s. (2004). new ‘ɳpl’ and ‘γ’ functions to evaluate j-r curves from cracked pipes and elbows: part i–theoretical derivation, engineering fracture mechanics 71, pp. 2635–2660. doi: 10.1016/j.engfracmech.2004.01.011. [15] kumar, v., german, m.d. and shih, c.f. (1981). an engineering approach for elastic–plastic fracture analysis, eprinp-1931, project 1287-1, topical report, electric power research institute, palo alto, ca. << /ascii85encodepages false /allowtransparency false /autopositionepsfiles true /autorotatepages /none /binding /left /calgrayprofile (dot gain 20%) /calrgbprofile (srgb iec61966-2.1) /calcmykprofile (u.s. web coated \050swop\051 v2) /srgbprofile (srgb iec61966-2.1) /cannotembedfontpolicy /error /compatibilitylevel 1.4 /compressobjects /tags /compresspages true /convertimagestoindexed true /passthroughjpegimages true /createjobticket false /defaultrenderingintent /default /detectblends true /detectcurves 0.0000 /colorconversionstrategy /cmyk /dothumbnails false /embedallfonts true /embedopentype false /parseiccprofilesincomments true /embedjoboptions true /dscreportinglevel 0 /emitdscwarnings false /endpage -1 /imagememory 1048576 /lockdistillerparams false /maxsubsetpct 100 /optimize true /opm 1 /parsedsccomments true 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/pdfxoutputintentprofileselector /documentcmyk /preserveediting true /untaggedcmykhandling /leaveuntagged /untaggedrgbhandling /usedocumentprofile /usedocumentbleed false >> ] >> setdistillerparams << /hwresolution [2400 2400] /pagesize [612.000 792.000] >> setpagedevice microsoft word numero_57_art_05_3055 t. boudina et alii, frattura ed integrità strutturale, 57 (2021) 50-62; doi: 10.3221/igf-esis.57.05 50 optimization of high-performance-concrete properties containing fine recycled aggregates using mixture design modeling tounsia boudina research laboratory of civil engineering (lrgc), university of biskra, pobox 145, 07000 biskra algeria boudina_tounsia@yahoo.fr; boudina.tounsia@univ-biskra.dz dalila benamara laboratory of civil engineering at the university of djelfa, pobox 3117, 17000 djelfa algeria benamaradalila2018@gmail.com; d.benamara@univ-djelfa.dz rebih zaitri civil engineering department, university of djelfa, pobox 3117, 17000 djelfa algeria. and structures rehabilitation and materials laboratory, university of laghouat, laghouat, algeria zrebih@yahoo.fr abstract. this investigation means to optimize the properties of highperformance-concrete (hpc) containing fine aggregates from concrete and brick wastes for different recycled aggregates substitution rates, using mixture design modeling. to succeed this, the design of experiments (doe) method was used. it is observed that slump, flexural and compressive strength of recycled concrete are significantly influenced by the content of natural sand (ns), recycled concrete aggregates (rca) and recycled brick aggregates (rba). the experimentally measured responses were successfully studied to develop a polynomial model, which represents slump, flexural strength and compressive strength at 7 day and 28 day of hpc. the significance and accuracy of the model was confirmed by statistical analysis and experimental verification. under optimal conditions, the maximum desirability is 0.65, which can be obtained by using only recycled sands, i.e. rba (9.5%) and rca (90.5%), and no natural sand. the statistical results show that the proposed models are well correlated with the experimental data. keywords. high performance concrete; recycled aggregates; mixture design modelling; physico-mechanical properties; optimization. citation: boudina, t., benamara, d., zaitri, r., optimization of high-performanceconcrete properties containing fine recycled aggregates using mixture design modeling, frattura ed integrità strutturale, 57 (2021) 5062. received: 01.04.2021 accepted: 11.05.2021 published: 01.07.021 copyright: © 2021 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. https://youtu.be/mq1-53itdja t. boudina et alii, frattura ed integrità strutturale, 57 (2021) 50-62; doi: 10.3221/igf-esis.57.05 51 introduction everal research studies have been carried out in many countries for the purpose of studying the possibility of recovering construction and demolition wastes and use them as aggregates in new types of concrete [1-8]. the recycling of construction waste as aggregates plays an important role in protecting the environment. since it allows, on one hand, to get rid of the debris resulting from the demolition of old buildings and / or from natural disasters, and on the other hand, to protect nature against the excessive exploitation of natural aggregate reserves. however, the problem of recycled aggregates from concrete and brick is the adhered mortar and its increased water absorption, which affected the properties of recycled concrete [9-10]. in algeria, most of the concrete used is exclusively made with alluvial sand. it is worth acknowledging that many parts of the country suffer from a remarkable lack of good quality alluvial sand. in addition, environmental requirements, production costs, depletion of alluvial deposits and remoteness of construction sites with respect to these deposits are also factors that encourage practitioners to search other types of sand [11]. currently, the use of high-performance concretes (hpcs), thanks to their high strength, offers good long-term durability to construction structures and allows saving up to 40% of materials [12-13]. for these reasons, the present work aims to investigate the effects of recycled sand from construction sites on -the physico-mechanical properties of high performance concretes. for this purpose, two types of recycled materials were been studied, namely recycled brick aggregates (rba) and recycled concrete aggregates (rca). recently, design of experiments doe method has attracted the attention of many researchers in the construction field; [14-17]. this statistical method allows for a good control of the process, while performing a minimum number of tests; it also helps to determine the impact of each parameter when acting separately and when interacting with other parameters. however, in the field of recycled concrete, just few studies have used it [18-21]. in this article, a 3-factor, 4-level network mixture design-model based on the experimental design methodology was been applied. the factors for studying mixture design are the proportions of the constituents of the mixture (ns, rba and rca), these constituents are independent of each other. moreover, the level represents the degree of accuracy levels chosen (25%, 50%, 75% and 100% in this study). the results obtained from the experimental tests and statistical analysis are presented as indicated by their substitution rates. so as to correctly valorise the incorporation of the aggregates of crushed brick and concrete, and to choose the most efficient optimal couples in the fresh and hardened states of concrete. it was decided to assess their impacts on the slump, the flexural and compressive strengths of concrete, at 7 and 28 days, in the form of a ternary iso-response diagram. the developed models were then compared with regard to their capacity to predict the intended responses, by analysing the coefficient of determination (r2), adjusted coefficient of determination (r2 adj), root mean square error (rmse), residual variance (p-values < 0.05) and the graph of residuals according to the expected responses. to the best of knowledge, this is the first report using the modelling approach for mixture design with several statistical parameters, in forecasting the physical and mechanical properties of high performance concretes (hpcs) including recycled sand. investigated materials aggregates hree types of fine aggregates were then selected:  the natural sand (ns) used is an alluvial sand, with nominal size of 4 mm; the sand was dried at 105°c.  two type of recycled fine aggregates (sands) were used in this research. the recycled concrete aggregates rca 0/4 and the recycled brick aggregates rba 0/4 was obtained by crushing an ordinary concrete and bricks respectively, using a jaw crusher. both rca and rba were dried at 105°c. two fraction size (4/8 and 8/16 mm) of natural coarse aggregates (nca) were used. the nca are a crushed limestone obtained from a local quarry in algeria. the physical properties of fine and coarse aggregates are shown in tab. 1. the grain size curves are plotted according to the recommendations of standard nf en 933-1; they are shown in the fig. 1. cement the cement used is of type cemi 52.5 n, produced by the local cement plant in algeria, with a fineness of 3461 cm2/g and density of 3150 kg/m3 was used in accordance with standard en 196-3 and 6. s t t. boudina et alii, frattura ed integrità strutturale, 57 (2021) 50-62; doi: 10.3221/igf-esis.57.05 52 adjuvant the adjuvant used is a new generation high-water-reducing superplasticizer of the medaflow 145 type. it is a solution of polycarboxylates, 31% dry extract, light pitch color, and ph between 5 and 6. silica fume the apparent density of silica fume is 650 (kg/m3), the actual density is 2240 (kg/m3) and its blaine specific surface is 23000 (cm2/g). tab. 2 presented the chemical compositions of cement and silica fume (sf). type of aggregate norme fine aggregates coarse aggregates characteristics / ns rca rba nca 4/8 nca 8/16 fineness modulus nf en 12620 3.51 4.51 3.53 absolute density (g/cm3) nf en 1097-6 2.68 2.57 2.32 2.55 2.62 apparent density (g/cm3) nf en 1097-6 1.53 1.131 1.23 1.19 1.60 sand equivalent (%) nf en 933-8 75.89 75.93 88.22 compactness (%) nf p 18-555 58 50.93 40.46 water absorption (%) nf en 1097-6 1 8 14 0.04 0.03 table 1: physical and mechanical characteristics of fine and coarse aggregates. figure 1: grading curves of fine and coarse aggregates used. the samples sio2 % ai2o3 % fe2o3 % cao % mgo % so3 % na2o % k2o % p.a.f. % cement (c) 21.70 4.27 4.83 64.11 1.35 1.59 0.08 0.32 0.99 silica fume (sf) 93.17 0.60 1.25 1.40 1.02 2.30 1.00 table 2: chemical compositions of the constituents. 0,00 10,00 20,00 30,00 40,00 50,00 60,00 70,00 80,00 90,00 100,00 0,01 0,1 1 10 p e rc e n ta g e  p a ss in g  ( % ) sieve size (mm) ns 0/4 rba 0/4 rca 0/4 nca 4/8 nca 8/16 t. boudina et alii, frattura ed integrità strutturale, 57 (2021) 50-62; doi: 10.3221/igf-esis.57.05 53 sample preparation method he formulation of high-performance concretes (hpcs) is based on the composition method developed by aïtcin at the university of sherbrooke [12]. a control concrete hpc 15 (cc) was prepared with natural aggregates, crushed gravel and alluvial sand (nca 4/8, nca 8/16 and ns). the replacement of natural sand by recycled one, was done by replacing a percentage of ns by its equivalent volume of rba and rca. only recycled sands were pre-wetted, for a period of 24 h before mixing, in order to avoid the possible absorption of mixing water by recycled aggregates [22]. they were then introduced into the mixer on a saturated-surface dry state; the other aggregates were used in their natural condition. fig. 2 shows concrete composition for fifteen hpcs with various compositions (natural sand/ recycled sand). figure 2: representation of the triangular network with 15 combinations (15 tests). the present work is expected to deal with a mixed-level design with 3 factors, i.e. natural sand (ns 0/4), and the two type of recycled fine aggregates, i.e. recycled brick aggregates rba and recycled concrete aggregates rca, taken in mass proportions; their sum must be equal to unity, with 75% substitution of alluvial sand. a constraint was put on the proportion of one-constituent (substitution of ns sand does not exceed 75 % in this case); a coding of the proportions was required. by considering, the remaining quantity that represents the unit, and the proportions of the points of experiments was deduced from the classic mixture design (tab. 3). it is worth noting that these factors are dependent on each other. the experimental domain must therefore satisfy the following condition:   %ns %rba %rca 100% (1) a second-order polynomial model was used with three non-independent variables. the proportions of these factors are presented in fig. 2. test methods he experimental program aimed to perform three physico-mechanical characterization tests: workability, compressive strength and flexural strength at 7 and 28 days. the workability tests were carried out by measuring the slump using the abrams slump cone test. for this, the concrete was introduced into a standardized conical mold in accordance with the lcpc technique and in conformity with standard nf en 12350-2. it is worth indicating that the abrams cone test is very simple to perform, rapid and relatively reliable. t t 15 13 10 6 1 14 11 7 2 12 8 3 9 4 5 ns rca rba t. boudina et alii, frattura ed integrità strutturale, 57 (2021) 50-62; doi: 10.3221/igf-esis.57.05 54 on the other hand, the mechanical characterization was accomplished once the compressive and flexural strengths were measured at 7 and 28 days. the mechanical behavior of all the hpc mixtures was investigated in simple bending (3 points) and uniaxial compression on prismatic test specimens of dimensions (70x70x280 mm3). moreover, three samples were tested, at each deadline, in simple bending on the bending frame of a matest press with a maximum capacity of 25 kn. it should be noted that the change rate was set at 0.05 ± 0.01mpa/s until failure, in accordance with the recommendations of standard nf p 18-407. the six half-test pieces resulting from bending failure were then subjected to uniaxial compression on the compression frame of a double-quadrant controls brand press that has a maximum capacity of 200 kn, at a loading speed of 0.5 kn/s. the specimens were cured in water until the age of testing. mixture cement (kg/m3) silica (kg/m3) ns (kg/m3) rba (kg/m3) rca (kg/m3) nca 4/8 (kg/m3) nca 8/16 (kg/m3) w (l/m3) w/c sp (l) hpc1 450 50 182.70 0 532.32 273 777 150 0.3 6 hpc2 182.70 120.05 399.24 hpc3 182.70 240.10 266.16 hpc4 182.70 360.15 133.08 hpc5 182.70 480.20 0 hpc6 321.16 0 399.24 hpc7 321.16 120.05 266.16 hpc8 321.16 240.10 133.08 hpc9 321.16 360.15 0 hpc10 459.61 0 266.16 hpc11 459.61 120.05 133.08 hpc12 459.61 240.10 0 hpc13 598.07 0.00 133.08 hpc14 598.07 120.05 0 hpc15 736.53 0 0 table 3: mixture proportions for 1 m3 of concrete [kg/m3]. results and discussion ccording to the mixture design modelling, the responses as a function of the substitution rate for the three factors, i.e. ns, rba and rca. witch can be fully exploited in the development of the mathematical models and predict the properties of concrete mixtures (slump, compressive strength and flexural strength) for different parameters process values. these models make it easier to assess the effect of each factor separately, and in combination with the other factors. tab. 4 depicts the results of the experimental characterization tests carried out in the laboratory; these results were obtained on the basis of the developed mixture design. effect of rca and rba on slump the measured slump changed from very plastic workability to plastic workability, for the different substitution rates of recycled sands. a t. boudina et alii, frattura ed integrità strutturale, 57 (2021) 50-62; doi: 10.3221/igf-esis.57.05 55 mixture s (cm) cs at 7 d (mpa) cs at 28 d (mpa) fs at 7 d (mpa) fs at 28 d (mpa) hpc1 18 58.76 82.54 7.40 12.13 hpc2 16.5 55.52 82.8 8.02 11.37 hpc3 13 52.07 81.72 7.75 11.52 hpc4 9 51.6 81.83 7.97 11.58 hpc5 6 46.88 77.1 7.55 11.53 hpc6 14 54.97 76.45 7.52 10.17 hpc7 10 52.4 78.14 7.74 10.29 hpc8 8 47.32 77.1 7.33 10.3 hpc9 7 45.49 75 7.17 10.72 hpc10 9 50.35 72.1 7.72 9.97 hpc11 8 50.22 74 7.42 10.87 hpc12 8 43.83 74.26 7.07 10.91 hpc13 9 55.33 71.84 8.21 10.86 hpc14 10 53.55 76.3 7.62 11.63 hpc15 16 63.2 80.24 8.75 12.55 table 4: experimental results of characterization tests. summary of adjustment r2 0.955131 r2 adjusted 0.930203 root of the mean squared error 0.994628 average response 10.76667 observations (or weighted sums) 15 table 5: model estimation parameters for the slump under consideration the concrete slump values were measured during the tests, which were compared with the results predicted by the generated model. the analyses of statistical parameters presented in tab. 5 and fig. 3(a) indicate that the eq. (2) represent adequately the actual relationship between the independent variables and the responses. the anova results for the slump show p-value < 0.0001 (fig. 3(a)), which implies that the r2 and adjusted coefficients (r2 adj) were calculated to check the adequacy and fitness of the model. the values of (r2) and (r2 adj) are close to 1, which implies also, that there are excellent correlations between the predicted and experimental models (fig. 3(a)). the mathematical model used in the slump test is given by the following equation:                            15.064285714 ns 6.2071428571 rba 19.171428571 rca ns 11.71428571 ns 31.85714286 0.1428751429 s cm rba rca rba rca (2) t. boudina et alii, frattura ed integrità strutturale, 57 (2021) 50-62; doi: 10.3221/igf-esis.57.05 56 this model, as expressed by eq. (2), allows observing that the slump value is strongly conditioned by the increase in the mass proportion of rca first, and then by the proportioning of ns and rba. it is worth mentioning that the slump increase is mainly attributed to the physical behavior of rca fines. therefore, increasing the rca content could result in a significant growth in workability values. it is widely acknowledged that sands from demolition concrete are rich in fines, and can therefore be used to significantly increase the workability of concrete. moreover, it should be noted that the couples of factors (ns*rba, ns*rca and rba*rca) in the polynomial have negative effects. this may be assigned to the high quantity of fines which were responsible for the higher water demand. indeed, when the content of recycled binary mixtures increases, the quantity of water required for wetting the entire surface of grains gets higher; this leads to slump decline in the manufactured concretes. furthermore, the iso-response curves of slump for high performance concretes (hpcs) are function to the percentage of substitution of the three types of sand are depicted in fig. 3(b). which suggests that the existence of recycled aggregates reduces the workability of concrete in the fresh state, particularly for rba proportions greater than 75%, i.e. 56.25% of the total sand mass, with a small percentage of rca with respect to reference concrete (hpc15). whereas, it is noted that demolished waste concrete fines significantly improve the workability of concrete, especially for rca dosages greater than 75%, i.e. hpc2 and hpc6 which exhibit the highest slump values, i.e. 16.5cm and 14 cm, respectively, in comparison with the other types of concrete under study. (a) (b) figure 3: (a) graphical representation of observed and predicted slump for the 15 tests, (b) iso-response curves of slump of hpcs as function of substitution rates of the three types of sand (ns, rba, rca). effect of rca and rba on compressive and flexural strength mechanical characterization was carried out using compressive and flexural strength measurements to assess the effect of rca and rba recycled aggregates. summary of adjustment cs at 7 d cs at 28 d r2 0.940175 0.942657 r2 adjusted 0.906939 0.9108 root of the mean squared error 1.566473 1.099557 average response 52.09933 77.448 observations (or weighted sums) 15 15 table 6: compressive strength model parameter estimates (cs at 7 d and cs at 28 d), summary of adjustment. t. boudina et alii, frattura ed integrità strutturale, 57 (2021) 50-62; doi: 10.3221/igf-esis.57.05 57 summary of adjustment fs at 7 d fs at 28 d r2 0.938866 0.922873 r2 adjusted 0.904902 0.880024 root of the mean squared error 0.132442 0.259156 average response 7.682667 11.09333 observations (or weighted sums) 15 15 table 7: flexural strength model parameter estimates (fs at 7 d and fs at 28 d), summary of adjustment. as clearly indicated in tabs. 6-7, the models simulated show a good regression model with a large value of the correlation coefficients i.e r² = 0.9401, 0.9426, 0.9388 and 0.9228 for cs at 7 d, cs at 28 d, fs at 7 d and fs at 28 d, respectively. the results obtained from experimental trials using mixture design models for cs at 7d and cs at 28d have been predicted by using the eqns. (3) – (4):                           7     63.055286 ns 47.311714 rba 58.871714 rca ns 36.04857 ns 34.10571 1.1371429      cs at d mpa rba rca rba rca (3)                            28     79.258 ns 77.443714286 rba 82.763 rca ns 14.10857143 ns 34.82 10.951428571 cs at d mpa rba rca rba rca (4) based on these models, it can be noted that cs at 28 d is first conditioned by the rca content, next by the increase in the ns content, then by the rba content and finally by the coupled effect of the rba * rca. on the other hand, it was found that the effects of the couple ns * rba and ns * rca cause a reduction in the compressive strength. the experimental results obtained for the mechanical strength are compared with the expected responses given by the jmp7 [23] software, they are represented graphically in fig. 4. the models developed were then compared with respect to their ability to predict the expected responses such as presented in tabs. 6-7. and by analysing the graph of the residues of expected results. one can clearly assert that since the graphical representation of the residues in terms of the expected values (fig. 5) has a random shape, the fluctuations of residues are relatively small and regular for cs and fs at 28 days. in both cases, the developed models exhibit a slight deviation, there is no information left to extract. (a) cs at 28 d (b) fs at 28 d figure 4: graph representing the observed values as a function of the predicted values for the mechanical strength. t. boudina et alii, frattura ed integrità strutturale, 57 (2021) 50-62; doi: 10.3221/igf-esis.57.05 58 (a) cs at 28 d (b) fs at 28 d figure 5: graph perform the residues as a function of the predicted values at 28 days. figs. 6 and 7 clearly show that with experimental designs method, one obtains the maximum information with the minimum number of experiments. the prediction profiler is used to study the impact of changes in study factors on predicted values. the curves in the profiler show the power of the impact of changes in each factor on responses. the prediction profiler of the compressive strength (cs) as a function of the substitution percentages for the three factors is shown in fig. 8. this prediction profiler clearly indicates that the maximum of cs at 28 d can be achieved when the proportions of the three factors are 0% for ns, 25% for rba and 75% for rca; for these three substitution percentages, the compressive strength (cs) reaches a maximum value of 83.48 mpa, as shown in fig. 8. note that the incorporation of rca above 75% slightly reduced the compressive strength. on the other hand, it is considerable to mention that rba has a negative effect on the compressive strength cs in 28 days as it continuously generates lower responses than that of control concrete. this decrease can also be explained by the fact that recycled aggregates are less resistant, especially the brick sands, and therefore the mechanical strength of concrete should decrease. according to the statistical model resulting from the response studied, it is clear that the resistance at 7 days has a very different trend on the ternary iso-response curve than the resistance at 28 days, as indicated by the coefficients of each factor and the negative influences of different coupled effects. if we are aiming for a high value of the compressive strength studied at 7 days, it will be necessary to choose a mixture with high rba contents. if a high response of cs at 28 days desired, a mixture rich of ns and rca will be chosen. in conclusion, the factors do not influence by the same value at 7 and 28 days. rba sand speeds the strength of concrete at 7 days while rca gives an improved strength at 28 days. the prediction eqn. (5)-(6) shows the evolution of the flexural strengths at 7 and 28 days:                         7     8.7431429 ns 7.5938571 rba 7.4781429 rca ns 4.368571 ns 1.425714 1.7028571    fs d mpa rba rca rba rca (5)                         28     12.721428571 ns 11.499285714 rba 11.911428571 rca ns 4.768571429 +ns 9.291425871 1.151428571 fs d mpa rba rca rba rca (6) furthermore, it is worth adding that the flexural strength fs at 7 days is also influenced by the percentages of the substitution of rba and rca. one may observe that after 7 days, the flexural strengths of hpc’s with the substitution of rba sand, achieved higher values of fs, than hpc’s with rca sand at the same percent of substations of these two sands presented in eq. (5). this is mainly attributed to the pozzolanic reaction of fines from rba brick waste sand i.e. calcined clay [24-26], which will have the effect of lowering the rate of portlandite (ch) and the production of new cshs. this has led to better densification of the cement matrix. t. boudina et alii, frattura ed integrità strutturale, 57 (2021) 50-62; doi: 10.3221/igf-esis.57.05 59 0,1 0,1 0,1 0,2 0,2 0,2 0,3 0,3 0,3 0,4 0,4 0,4 0,5 0,5 0,5 0,6 0,6 0,6 0,7 0,7 0,7 0,8 0,8 0,8 0,9 0,9 0,9 rba ns r c a 0,1 0,1 0,1 0,2 0,2 0,2 0,3 0,3 0,3 0,4 0,4 0,4 0,5 0,5 0,5 0,6 0,6 0,6 0,7 0,7 0,7 0,8 0,8 0,8 0,9 0,9 0,9 rba ns r c a 0,1 0,1 0,1 0,2 0,2 0,2 0,3 0,3 0,3 0,4 0,4 0,4 0,5 0,5 0,5 0,6 0,6 0,6 0,7 0,7 0,7 0,8 0,8 0,8 0,9 0,9 0,9 rba ns r c a 0,1 0,1 0,1 0,2 0,2 0,2 0,3 0,3 0,3 0,4 0,4 0,4 0,5 0,5 0,5 0,6 0,6 0,6 0,7 0,7 0,7 0,8 0,8 0,8 0,9 0,9 0,9 rba ns r c a figure 6: iso-response curves for the flexural strength at 7 days and 28 days. figure 7: iso-response curves for the compressive strength at 7 days and 28 days. optimization he search for the optimal proportions of fine recycled aggregates leading to the optimization of the recovery of fine recycled aggregates (rba and rca) having optimal responses, from previously established models, was done using the response profiler whose desirability value close to 1 corresponds to the maximum values of the physicomechanical properties. the optimization was performed using the desirability function which combines all the optimization targets into one (desirability). according to this study, the maximum desirability is 0.65 (prevision profiler) which can be reached for hpc without natural sand, by mixing the two recycled sands 9.5% of rba and 90.5% of rca. the optimized composition of the mixture gives: slump=17.94 cm, fs 7d= 7.63mpa, fs 28d=11.77 mpa, cs 7d =57.86 mpa et cs 28d=83.20 mpa. fs 7d 7,2 7,4 7,5 7,7 8 fs 28d 10,2 10,5 10,75 11 11,5 cs 28d 73 74 75 77 80 cs 7d 45 48 50 52 55 t t. boudina et alii, frattura ed integrità strutturale, 57 (2021) 50-62; doi: 10.3221/igf-esis.57.05 60 furthermore, this optimization also showing that hpc can be produced with recycled sands from brick and concrete waste and makes it possible to achieve better properties to natural hpcs (hpc 15). figure 8: prevision profiler for predicting optimal conditions for the formulation of recycled fine aggregate bhp. conclusions he present research aimed mainly at assessing the effects of incorporating brick waste aggregates and concrete demolition waste aggregates on the physico-mechanical properties of concrete. through experimental tests and analyses of each formulation, which contains different factors, with various substitution rates, and using the mixture design approach, it was found that a good agreement exists between the results of the mathematical models and those of the experimental tests, which validates the various considerable data on the effects of each of the recorded parameters. in light of the outcomes got right now, the following ends could be drawn: the modelling of the mixture design method utilized right now has demonstrated to be a powerful procedure for considering the impacts of the three types of sand (ns 0/4, rba 0/4 and rca 0/4) in binary and ternary frameworks on the fresh and hardened concrete states. the advantage of modelling results studied using the 4 8 12 16 20 s lu m p 1 7 ,9 4 65 7 ± 1, 4 92 5 7 3 70 74 78 82 c s a t 2 8 d a ys 8 3, 2 00 7 5 ±1 ,6 5 0 0 3 2 9,5 10,5 11,5 12,5 f s a t 2 8 d a ys 1 1, 7 72 7 ±0 ,3 8 8 8 9 8 45 50 55 60 65 c s a t 7 d a y s 5 7, 8 66 7 ±2 ,3 5 0 7 0 2 7 7,5 8 8,5 9 f s a t 7 d a y s 7 ,6 3 61 8 3 ±0 ,1 9 8 7 4 6 0 0 ,5 1 d és ir a b ilit é 0 ,6 4 9 79 0 0 ,2 0, 4 0 ,6 0 ,8 1 0 ns 0 0 ,2 0, 4 0 ,6 0 ,8 1 0,095431 rba 0 0 ,2 0, 4 0 ,6 0 ,8 1 0,904569 rca 0 0, 2 5 0 ,5 0 ,7 5 1 désirabilité t d e si ra b ili ty   desirability  t. boudina et alii, frattura ed integrità strutturale, 57 (2021) 50-62; doi: 10.3221/igf-esis.57.05 61 prediction equation is that it can evaluate all possible responses without carrying out all experiments. the measurements obtained during the tests allow developing polynomial models of prediction for the slump and mechanical strength of hpc’s with fine recycled aggregates. it should also be noted that the compressive strength of the formulated concrete is comparable to that of control concrete. moreover, it was found that following 28 days, the compressive strength (cs) reached a maximum value of 83.48 mpa with factors values of 25% rba, and 75% rca. and hpc’s based on rba sand presented greater values of flexural strength at 7 days than hpc’s based on rca sand, it was revealed that this is due to the rba fines pozzolanic reaction and the production of new cshs, which leads to better cement matrix densification. these findings demonstrate the robustness and usefulness of mixture design to model, predict and optimize the hpcs fine aggregate composition using rca and rba sands. it can therefore be concluded that hpc can be produced with recycled aggregates which has better properties. substitution of natural aggregates with recycled aggregates for the production of the new concrete offers a new aggregate resource and allows saving natural materials. it is worth mentioning that the physical and mechanical properties of the formulated concretes are encouraging. moreover, the economic, environmental and technical aspects are also very interesting, which supports this initiative of recovering brick waste and concrete demolition waste to be used as building materials. nomenclature ns: natural sand rba: recycled brick aggregates rca: recycled concrete aggregates nca: natural coarse aggregates hpc: high performance concrete sf: silica fume sp: superplasticizer c: cement (w/c): (water / cement) ratio s (cm): slump cs at 7d: compressive strength at 7 days. cs at 28d: compressive strength at 28 days. fs at 7d: flexural strength at 7 days. fs at 28d: flexural strength at 28 days. doe: design of experiments. references [1] tayeh, b. a. m. al saffar, d. m. and alyousef, r. (2020). the utilization of recycled aggregate in high performance concrete: a review. j. of mat. res. and tech., 9(4), pp. 8469–8481. doi: 10.1016/j.jmrt.2020.05.126. [2] anamarie, c.r. saylisse, d.w. torres, g. and arsenio, c.f. (2020). experimental design of concrete mixtures using recycled plastic, fly ash, and silica nanoparticles. construction and building materials., 254, 119207. doi: 10.1016/j.conbuildmat.2020.119207 [3] silva, r.v. de brito, j. and dhir, r.k. (2018). fresh-state performance of recycled aggregate concrete: a review. j. constr. and build. mater., 178, pp. 19–31. doi: 10.1016/j.conbuildmat.2018.05.149. [4] zheng, c. lou, c. du, g. li, x. liu, z. li, l. (2018). mechanical properties of recycled concrete with demolished waste concrete aggregate and clay brick aggregate, results in physics. doi: 10.1016/j.rinp.2018.04.061. [5] job thomas, nassif nazeer thaickavil and p.m. wilson. (2018). strength and durability of concrete containing crushed concrete aggregates, j. of build. eng., doi: 10.1016/j.jobe.2018.05.007. [6] omary, s. ghorbel, e. and wardeh, g. (2016). relationships between recycled concrete aggregates characteristics and recycled aggregates concretes properties. j. constr. and build. mater., 108, pp. 163–174. doi: 10.1016/j.conbuildmat.2016.01.042. t. boudina et alii, frattura ed integrità strutturale, 57 (2021) 50-62; doi: 10.3221/igf-esis.57.05 62 [7] kenai, s. and debieb, f. (2011), caractérisation de la durabilité des bétons recyclés à base de gros et fins granulats de briques et de béton concassé, mater. & structr., 44, pp. 815–824. doi: 10.1617/s11527-010-9668-7. [8] berredjem, l. arabi, n. molez, l. and jauberthie, r. (2015). propriétés mécaniques et durabilité des bétons à base de graviers et sables recyclés issus de béton de démolition. deuxième conférence internationale francophone nouveaux matériaux et durabilité (nomad 2015), nov 2015, douai, france. nouveaux matériaux et durabilité, https://hal.archives-ouvertes.fr/hal-01366521. [9] juan, m.s. and gutiérrez, p.a. (2009). study on the influence of attached mortar content on the properties of recycled concrete aggregate, constr. build. mater. 23, pp. 872–877. doi: 10.1016/j.conbuildmat.2008.04.012. [10] tu, t.y. chen, y.y. and hwang, c.l. (2006). properties of hpc with recycled aggregates, cem. concr. res, 36, pp. 943–950. doi: 10.1016/j.cemconres.2005.11.022. [11] shi, x. mukhopadhyay, a. zollinger, d. grasley, z. (2019). economic input-output life cycle assessment of concrete pavement containing recycled concrete aggregate. journal of cleaner production, 225, pp. 414–425. doi: 10.1016/j.jclepro.2019.03.288. [12] aitcin, c. p. (2001), bétons haute performance, edition eyrolles, ibsn 2-21201323-x, pp. 683, paris. [13] manikanta, d. ravella, d. p. yadav, j. m. (2021). mechanical and durability characteristics of high performance selfcompacting concrete containing flyash, silica fume and graphene oxide. j. of materials today. doi: 10.1016/j.matpr.2021.01.684. [14] goupy, j. and creighton, l. (2007). introduction to design of experiments with jmp examples. 3rd ed. cary (nc): sas institute, pp. 438. https://trove.nla.gov.au/version/43645151. [15] mayandi venkatesan, qammer zaib, izhar hussain shah, hung suck park. (2019). optimum utilization of waste foundry sand and fly ash for geopolymer concrete synthesis using d-optimal mixture design of experiments. resources, conservation & recycling, 148, pp. 114–123. doi: 10.1016/j.resconrec.2019.05.008. [16] varanda, c. portugal, i. ribeiro, j. silva, a.m.s. silva. c.m. (2017). optimization of bitumen formulations using mixture design of experiments (mdoe). j. constr. and build. mater., 156, pp. 611-620. doi: 10.1016/j.conbuildmat.2017.08.146. [17] bun kim ngun, hasmaliza mohamad, ken-ichi katsumata, kiyoshi okada, zainal arifin ahmad. (2014) using design of mixture experiments to optimize triaxial ceramic tile compositions incorporating cambodian clays. applied clay science 87, pp. 97–107. doi: 10.1016/j.clay.2013.11.037. [18] cabral, a. e. b., schalch, v., dal molin, d. c. c., ribeiro, j. l. d. (2010), mechanical properties modeling of recycled aggregate concrete, j. constr. and build. mater., 24, pp. 421–430, doi: 10.1016/j.conbuildmat.2009.10.011. [19] lovato, p. s., possan, e. dal molin, d. c. c., masuero, â. b., ribeiro, j. l. d. (2012), modeling of mechanical properties and durability of recycled aggregate concretes, j. constr. and build. mater., 26, pp. 437–447. doi: 10.1016/j.conbuildmat.2011.06.043. [20] hammoudi, a. moussaceb, k. belebchouche, c. and dahmoune, d. (2019). comparison of artificial neural network (ann) and response surface methodology (rsm) prediction in compressive strength of recycled concrete aggregates. j. constr. and build. mater., 209, pp. 425–436. doi: 10.1016/j.conbuildmat.2019.03.119. [21] gabriella puente de andrade, gabriela de castro polisseni, marco pepe, romildo dias toledo filho. (2020). design of structural concrete mixtures containing fine recycled concrete aggregate using packing model. j. constr. and build. mater., 252, 119091. doi: 10.1016/j.conbuildmat.2020.119091. [22] arabi, n. and berredjem, l. (2011). valorisation des déchets de démolition comme granulats pour bétons, déchets revue francophone d’écologie industrielle, 60, pp. 25–30, https://doi.org/10.4267/dechets-sciences-techniques.2765. [23] jmp (2018), version 14.0. sas institute inc., cary, nc, 1989-2019. [24] bazaz, j. b and khayati m. (2012). properties and performance of concrete made with recycled low-quality crushed brick. j. mater. civ. eng., 24(4), pp. 330–338. doi: 10.1061/(asce)mt.1943-5533.0000385. [25] ge, z. gao, z. sun, r. zheng, l. (2012). mix design of concrete with recycled clay-brick-powder using the orthogonal design method. j. constr. and build. mater., 31, pp. 289–293. doi: 10.1016/j.conbuildmat.2012.01.002. [26] afshinnia, k and poursaee, a. (2015). the potential of ground clay brick to mitigate alkali–silica reaction in mortar prepared with highly reactive aggregate. j. constr. and build. mater., 95, pp. 164–170. doi: 10.1016/j.conbuildmat.2015.07.155. microsoft word numero_59_art_13_3237.docx t.-h. nguyen et alii, frattura ed integrità strutturale, 59 (2022) 172-187; doi: 10.3221/igf-esis.59.13 172 focussed on steels and composites for engineering structures weight optimization of steel lattice transmission towers based on differential evolution and machine learning classification technique tran-hieu nguyen, anh-tuan vu hanoi university of civil engineering, viet nam hieunt2@nuce.edu.vn, https://orcid.org/0000-0002-1446-5859 tuanva@nuce.edu.vn abstract. transmission towers are tall structures used to support overhead power lines. they play an important role in the electrical grids. there are several types of transmission towers in which lattice towers are the most common type. designing steel lattice transmission towers is a challenging task for structural engineers due to a large number of members. therefore, discovering effective ways to design lattice towers has attracted the interest of researchers. this paper presents a novel method that integrates differential evolution (de), a powerful optimization algorithm, and a machine learning classification model to minimize the weight of steel lattice towers. a classification model based on the adaptive boosting algorithm is developed in order to eliminate unpromising candidates during the optimization process. a feature handling technique is also introduced to improve the model quality. an illustrated example of a 160-bar tower is conducted to demonstrate the efficiency of the proposed method. the results show that the application of the adaptive boosting model saves about 40% of the structural analyses. as a result, the proposed method is 1.5 times faster than the original de algorithm. in comparison with other algorithms, the proposed method obtains the same optimal weight with the least number of structural analyses. keywords. structural optimization; machine learning classification; differential evolution; transmission tower. citation: nguyen, t.-h., vu, a.-t., weight optimization of steel lattice transmission towers based on differential evolution and machine learning classification technique, frattura ed integrità strutturale, 59 (2022) 172-187. received: 19.08.2021 accepted: 12.10.2021 published: 01.01.2022 copyright: © 2022 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. introduction lectricity is an essential part of modern life. electricity is not only a big part of daily life in homes but also plays an important role in industrial production. the electrical grid consists of two components which are the electric power transmission and the electric power distribution. the transmission network carries electricity from power plants to substations, while the distribution network delivers electricity from substations to customers. nowadays, due to the increasing demand for energy as well as the exploitation of new energy sources such as wind power, solar power, the transmission network is constantly being upgraded and expanded. e https://youtu.be/kejsdoe45bi t.-h. nguyen et alii, frattura ed integrità strutturale, 59 (2022) 172-187; doi: 10.3221/igf-esis.59.13 173 in the transmission network, the power is usually transported at high voltages through overhead power lines due to the lower installation cost comparing with the underground systems. overhead power lines are supported by transmission towers which are often steel lattice truss structures. designing steel lattice transmission towers is always a challenging task for structural engineers due to a large number of design variables. in addition, a typical design of a tower is applied many times in the transmission lines. therefore, minimizing the weight of typical tower results in a significant economic effect. because of the above reasons, the weight optimization of steel lattice transmission towers is an interesting topic for a long time. numerous outstanding studies in this field can be listed as follows. in 1995, rao [1] applied the hookes-jeeves method to optimize the shape of a 400 kv transmission tower. the weight of the optimized tower is 12% less than the initial design. in 2004, taniwaki and ohkubo [2] considered the node coordinates, the cross-sectional areas, and the materials of members as design variables when optimizing the weight of transmission towers subject to simultaneously static and seismic loads. the optimization process was separated into two stages, in which the first stage aims to optimize the shape and the sections of the tower when the materials are fixed. at the second stage, the best pair of the cross-section and material for each member is identified while maintaining the shape of the tower. shea and smith [3] developed a new method that combines structural grammars and the simulated annealing (sa) algorithm for optimizing the topology and the shape of transmission towers. the weight of an existing tower in switzerland was reduced by 16.7% after optimizing by the proposed method. in [4], four types of optimization including sizing optimization, shape optimization, topology optimization, and configuration optimization are carried out based on the adaptive genetic algorithm (ga). kaveh et al. [5] presented the multi metaheuristic-based search method in which several metaheuristic algorithms are simultaneously employed on subsets of the initial population in order to increase the diversity over the design space. the proposed method was applied to optimize four different steel towers. souza et al. [6] proposed a new method to optimize the size, shape, and topology of steel towers based on the firefly algorithm and the backtracking search algorithm. in this proposed method, the considered tower is divided into modules and the configuration of each module is selected from pre-established templates. tort et al. [7] developed a tool that integrates the finite element analysis commercial software pls-tower and the sa algorithm for optimizing transmission towers. recently, khodzhaiev and reuter [8] used a modified version of the ga to optimize the topology, shape, and sizes of towers. based on the literature, it can be seen that the meta-heuristic algorithms have been commonly used in studies related to the optimization of steel towers due to their simplicity and ease of implementation. however, one of the disadvantages of metaheuristic algorithms is that the computing time is prohibitively long due to a huge number of structural analyses. as an illustration, in ref. [6], 180,000 structural analyses were performed when optimizing the 115 kv transmission tower. several studies have been carried out with the aim of reducing the number of structural analyses. for example, couceiro et al. [9] integrated the sensitivity analysis into the sa algorithm in order to accelerate the optimization process. this technique reduced the computing time from 109,095 s to 8850 s for a real 220 kv transmission tower containing 684 elements. in recent years, machine learning (ml) has been increasingly used in structural engineering. several common types of ml tasks include regression, classification, dimensionality reduction, etc. ml regression models are frequently used to simulate complex data which are difficult to derive explicit formulas such as characteristics of a material [10,11], load-bearing capacities of a structural member [12], or a whole structure [13]. unlike regression, the classification aims to predict a discrete class label like the failure mode of concrete columns [14] or the safety state of structures [15]. another ml task is to reduce the complexity of the data. some dimensionality reduction techniques can be listed: principal component analysis (pca), linear discriminant analysis (lda), and proper orthogonal decomposition (pod), in which the pod technique has been widely employed in the crack identification [16] as well as the damage detection [17]. it is noted that damage detection is formulated as an optimization problem with the aim of minimizing errors between measured values and calculated values. therefore, meta-heuristic algorithms are often applied to increase the precision of the damage detection as slime mould algorithm by tiachacht et al. [18], atom search optimization (aso) by khatir et al. [19]. additionally, the combination of a ml model with a meta-heuristic algorithm has gained increasing attention in recent times. some recognized works in this field are carried out by khatir et al. [20-22], by zenzen et al. [23]. regarding the structural optimization of steel towers, ml has been used to construct surrogate models in order to reduce the computational cost. for instance, kaveh et al [24] used neural networks (nns) as a structural analysis tool when optimizing the shape and size of transmission towers. in 2019, taheri, ghasemi, and dizangian [25] used radial basis function (rbf) neural networks to approximate the response of towers. the developed rbf networks were then combined with the artificial bee colony (abc) algorithm to shorten the computing time. similarly, hosseini, ghasemi, and dizangian [26] introduced the bbo-anfis optimization method in which the adaptive neuro-fuzzy inference system (anfis) models were embedded to the biogeography based optimization (bbo) algorithm to save the optimization time. although the application of surrogate modeling is very time-efficient, the designs found by the surrogate-assisted methods are not the optimal solutions due to the approximation of the structural behavior [25,26]. t.-h. nguyen et alii, frattura ed integrità strutturale, 59 (2022) 172-187; doi: 10.3221/igf-esis.59.13 174 this paper aims to present a hybrid method for the sizing optimization of transmission towers. different from previous studies, this study uses a ml classification technique called adaptive boosting to evaluate the safety state of transmission towers. the developed model is then integrated into the differential evolution algorithm to discard the unnecessary structural analyses. the proposed method is used to minimize the weight of a 160-bar tower. the obtained designs are then compared with previous designs in the literature to illustrate the effectiveness of the proposed method. formulation of the weight optimization problem of transmission towers n general, the overall cost of a transmission tower consists of several components such as the material cost, the manufacturing cost, the transportation cost, the erection cost, as well as the maintenance cost. however, there exists a linear relationship between the overall cost and the weight of the structure. therefore, the weight of structural members is frequently used as the objective function of optimization problems. because steel transmission towers are not constrained by architectural and aesthetic requirements, optimizing their shape and topology has been received great attention from researchers. however, there is a fact that the complex configurations obtained from the shape and topology optimization are difficult to apply in practice. hence, only cross-sectional areas of tower members are considered as design variables in the present work. the weight optimization of transmission towers is formulated as follows:                   1 1 1 2 find | 1, 2,..., to minimize ( ) subject to ( ) 0| 1, 2, ..., , , ..., i nm ing i j i j k i d a i ng w a l g k nc a s s s α a a s (1) where: a represents the vector containing ng design variables; ai is a design variable which denotes the cross-sectional area of members of the i-th group; ng is the number of member groups; w(a) is the weight of the tower;  is the unit weight of steel; nm(i) is the number of members belong to the i-th group; lj represents the length of j-th member; gk(a) is the k-th constraint; nc is the number of constraints; ai is selected from the set s containing d profiles. design constraints of transmission towers include stress, slenderness, buckling, displacement, as well as natural frequency limitations. the formula of each constraint condition depends on the design specification used in the project. the most widely used specification for steel lattice towers is asce 10-97 [27]. in addition, there are also geometric requirements in which the lower leg members must be larger than the upper ones. to apply meta-heuristic algorithms for solving this problem, some techniques should be employed. firstly, the penalty function method is often used for dealing with constraints. in more detail, the objective function is modified by adding a term to penalize when there is any constraint violation:                1 max max 0, jjfit w pf ga a a (2) in which: fit(a) is called the fitness function; w(a) is the objective function that is the weight of the tower in this case; pf is the penalty factor. in this work, pf is a very large value. by this setting, the selection between two candidates complies with the following rules:  between two feasible candidates, the one having the lower value of the objective function is selected,  between two infeasible candidates, the one having the lower degree of constraint violation is selected,  between a feasible candidate and an infeasible candidate, the feasible one is selected. besides, for handling discrete optimization problems, the design variable ai is replaced by the sequence number ii representing the position of ai in the list s. i t.-h. nguyen et alii, frattura ed integrità strutturale, 59 (2022) 172-187; doi: 10.3221/igf-esis.59.13 175 the proposed method he proposed method combines differential evolution (de), a powerful optimization algorithm, and the adaptive boosting classification technique. in the following sections, the de algorithm and the adaboost technique are briefly presented. next, the proposed method is introduced. differential evolution algorithm the de algorithm was developed by price and storn [28]. basically, the de algorithm consists of four basic operators: initialization, mutation, crossover, and selection. there exist many mutation strategies such as “rand/1”, “rand/2”, “best/1”, “best/2”, etc. in the present work, the variant “target-to-best/1” of the de algorithm is employed. first of all, the de generates an initial population of np individuals {xk(0)|k=1,2,...,np} using the following operator:     ( 0 ), rand 0,1k i i i ix l u l (3) where: xk(0) is a d-dimensional vector representing a solution of the optimization problem; xk,i(0) is the i-th component of xk(0); rand[0,1] is a uniformly distributed random real value in the range [0,1]; li and ui are the min. and max. bounds of xk,i, respectively. at the generation t, a trial vector uk(t) which is different from the target vector xk(t) is produced using two operators of mutation:          ( ) ( ) ( ) ( ) ( ) ( )1 2t t t t t tk k best k r rf fv x x x x x (4) and crossover:        ( ) ,( ) , ( ) , if or rand 0,1 otherwise t k it k i t k i v i k cr u x (5) where: r1  r2  k are randomly selected between 1 and np; f is the scaling factor; xbest(t) is the best individual of the t-th population; uk,i(t), vk,i(t), and xk,i(t) are the i-th component of uk(t), vk(t), xk(t), respectively; k is a randomly chosen integer in the interval [1,d]; and cr is the crossover rate. the k-th individual of the (t+1) generation xk(t+1) is selected using the operator selection as follows:         ( ) ( ) ( ) ( 1) ( ) if otherwise t t t k k kt k t k fit fitv u x x x (6) in which: fit(.) is the fitness function. the final optimal solution is obtained after repeatedly performing three operators of mutation, crossover, and selection for (max_iter-1) times. adaptive boosting the ensemble method adaptive boosting (a.k.a adaboost) was developed by freund and schapire in 1997 [29]. despite this method can handle both regression tasks as well as multi-label classification tasks, this study only employs the adaboost binary classifier. the idea behind this method is to create a strong classifier based on multiple weak classifiers that are sequentially trained on the weighted dataset as clearly illustrated in fig. 1. at the first step, every sample of the training data is weighted a uniform value and a classifier is trained by the whole data. then, the samples that are wrongly predicted by the first classifier are re-weighted with a higher value. it helps these samples get the attention of the next classifier. this process is repeatedly carried out to obtain a number of classifiers. each classifier is also assigned a weight based on its accuracy. the final prediction is made by the weighted majority voting technique. the implementation process of the adaboost binary classifier is shortly presented as follows. t t.-h. nguyen et alii, frattura ed integrità strutturale, 59 (2022) 172-187; doi: 10.3221/igf-esis.59.13 176 dataset weighted dataset weak classifier #1 strong classifier weighted dataset weak classifier #2 weak classifier #3 figure 1: illustration of the adaboost. assume that the training dataset contains n samples {(xi, yi}|i=1,…,n} where xi is a vector that comprises input features, yi{+1,1} is the output feature. firstly, a set of the same weight d1={w1,i=1/n|i=1,…,n} is assigned to all samples. a weak classifier c1 is then trained by the weighted dataset. secondly, the error rate of the trained classifier c1 is determined using the following formula:      1 1, 1 1 n i i i i err w i c yx (7) where: i(.) is a function that returns 0 if the prediction is correct while 1 if the prediction is wrong. third, the weight 1 of the weak classifier c1 is computed from its error rate:         1 1 1 11 ln 2 err err (8) next, the set of weights is adjusted to d2={w2,i|i=1,…,n} for the second iteration, in which the weight w2,i is calculated as follows:        1, 1 1 2, 2, 1 expi i i i n i i w y c w w x (9) the weak classifier c2 is then trained by the new weighted dataset. after t iterations, there are totally t weak classifiers that are sequentially trained. for new sample xnew, the label ynew is estimated by taking the weighted sum of the predictions of these weak classifiers:            1 sign t new t t new t y c x (10) where: sign(.) is a function that extracts the sign of a real number. the weak classifier used in the adaboost can be any machine learning classification algorithm, but the decision tree is commonly used. the background theory of the decision tree is not presented here since it is out of the scope of this article. t.-h. nguyen et alii, frattura ed integrità strutturale, 59 (2022) 172-187; doi: 10.3221/igf-esis.59.13 177 adaboost classification-assisted differential evolution the idea to use the machine learning classification technique to distinguish and discard unpromising candidates has been presented in ref. [30]. in the previous study, a deep nn model is developed to predict the safety state of structures. the optimization process is separated into two stages. the first stage employs the original de algorithm with the aim of exploring the design space. in the second stage, each trial vector produced by the mutation and crossover operators is preliminarily assessed by the neural network model. if it is predicted to violate any constraint and its objective function is larger than that of the target vector, the trial vector is eliminated without conducting the exact fitness evaluation. using the nn model during the optimization process can reduce unnecessary fitness evaluations. the numerical example of a planar 47-bar tower conducting in ref. [30] shows that the reduction rate reaches 20%. however, it can be observed that the fitness evaluations performed in the first stage can be used as the training data of the classification model. secondly, the neural network model used in ref. [30] has low accuracy. therefore, in the present work, some modifications are proposed to enhance the optimization process:  during the first stage, every trial vector is exactly evaluated and saved into the database. at the end of stage i, the collected data is used for training the machine learning model.  a previous study [31] demonstrates the superiority of the adaboost model over other ml models like nn or support vector machine (svm) in evaluating the safety state of trusses. therefore, the adaboost model is employed instead of the nn model in order to improve the classification accuracy in this study. the proposed method is called the adaboost-de (short for adaboost classification-assisted differential evolution) and its flowchart is presented in fig. 2. stage ii stage iinitial population exact evaluation assign label: label = “+1” if all constraints are satisfied label = “-1” otherwise mutation crossover exact evaluation selection training data i > n_iter1 mutation crossover elimination predicted label = “-1” w(u) > w(x) evaluate using adaboost model predicted label = “+1” exact evaluation selection i > max_iter end adaboost model y y n y n n figure 2: flowchart of the adaboost-de. t.-h. nguyen et alii, frattura ed integrità strutturale, 59 (2022) 172-187; doi: 10.3221/igf-esis.59.13 178 numerical example design data 160-bar transmission tower is carried out to demonstrate the efficiency of the proposed method. this structure has been optimized using numerous algorithms, such as the multi-metaheuristic based search method (mmsm) [5], the rank-based ant system (rbas) [32], the adaptive elitist de (aede) [33], the modified symbiotic organisms search (msos) algorithm [34], and the particle swarm optimizer cultural (psoc) [35]. the configuration of the tower is presented in fig. 3. the tower consists of 52 nodes and 160 members in which the information of nodes and members are listed in tab. 1 and tab. 2. the density of the steel material equals =0.00785 kg/cm3, and the modulus of elasticity is equal to e=2.047e+06 kgf/cm2. this tower subjects to eight independent load cases which are introduced in tab. 3. this problem has 38 design variables corresponding to cross-sectional areas of 38 member groups as shown in tab. 2. the list of 42 available profiles used in this tower is given in tab. 4. members in the tower are designed according to the tensile stress and buckling stress conditions. the limitation of the tensile stresses equals 1500 kgf/cm2 for all members while the critical buckling stresses of the members can be determined using the following equation:            2 27 1300 / /24 if / 120 10 / / otherwise b kl r kl r kl r (11) in which: k is the effective length factor which is assumed to be 1.0 for all members; l is the length of the member; r is the radius of gyration of the member’s section. it must be noted that constraints on displacement, natural frequency, as well as geometric requirements need to be considered in practice. however, these constraints are neglected as in previous studies [32-35] for a fair comparison. z x z y 2100 2100 2140 2070 ± 0.000 +1.750 +3.500 +5.350 +7.100 +8.725 +10.275 +11.055 +12.565 +13.465 +14.365 +15.265 +16.150 25 28 37 52 52 37 25 28 800800 figure 3: layout of the 160-bar tower. a t.-h. nguyen et alii, frattura ed integrità strutturale, 59 (2022) 172-187; doi: 10.3221/igf-esis.59.13 179 node x (cm) y (cm) z (cm) node x (cm) y (cm) z (cm) node x (cm) y (cm) z (cm) 1 -105.000 -105.000 0.000 19 60.085 60.085 710.000 37 -207.000 0.000 1256.500 2 105.000 -105.000 0.000 20 -60.085 60.085 710.000 38 40.000 40.000 1256.500 3 105.000 105.000 0.000 21 -49.805 -49.805 872.500 39 -40.000 40.000 1256.500 4 -105.000 105.000 0.000 22 49.805 -49.805 872.500 40 -40.000 -40.000 1346.500 5 -93.929 -93.929 175.000 23 49.805 49.805 872.500 41 40.000 -40.000 1346.500 6 93.929 -93.929 175.000 24 -49.805 49.805 872.500 42 40.000 40.000 1346.500 7 93.929 93.929 175.000 25 -214.000 0.000 1027.500 43 -40.000 40.000 1346.500 8 -93.929 93.929 175.000 26 -40.000 40.000 1027.500 44 -26.592 -26.592 1436.500 9 -82.859 -82.859 350.000 27 40.000 -40.000 1027.500 45 26.592 -26.592 1436.500 10 82.859 -82.859 350.000 28 214.000 0.000 1027.500 46 26.592 26.592 1436.500 11 82.859 82.859 350.000 29 40.000 40.000 1027.500 47 -26.592 26.592 1436.500 12 -82.859 82.859 350.000 30 -40.000 40.000 1027.500 48 -12.737 -12.737 1526.500 13 -71.156 -71.156 535.000 31 -40.000 -40.000 1105.500 49 12.737 -12.737 1526.500 14 71.156 -71.156 535.000 32 40.000 -40.000 1105.500 50 12.737 12.737 1526.500 15 71.156 71.156 535.000 33 40.000 40.000 1105.500 51 -12.737 12.737 1526.500 16 -71.156 71.156 535.000 34 -40.000 40.000 1105.500 52 0.000 0.000 1615.000 17 -60.085 -60.085 710.000 35 -40.000 -40.000 1256.500 18 60.085 -60.085 710.000 36 40.000 -40.000 1256.500 table 1: nodal coordinates. element no. group node element no. group node element no. group node element no. group node i j i j i j i j 1 1 1 5 11 2 4 5 21 4 7 12 31 6 10 15 2 1 2 6 12 2 1 8 22 4 8 11 32 6 11 14 3 1 3 7 13 3 5 9 23 4 8 9 33 6 11 16 4 1 4 8 14 3 6 10 24 4 5 12 34 6 12 15 5 2 1 6 15 3 7 11 25 5 9 13 35 6 12 13 6 2 2 5 16 3 8 12 26 5 10 14 36 6 9 16 7 2 2 7 17 4 5 10 27 5 11 15 37 7 13 17 8 2 3 6 18 4 6 9 28 5 12 16 38 7 14 18 9 2 3 8 19 4 6 11 29 6 9 14 39 7 15 19 10 2 4 7 20 4 7 10 30 6 10 13 40 7 16 20 table 2: element connectivity. t.-h. nguyen et alii, frattura ed integrità strutturale, 59 (2022) 172-187; doi: 10.3221/igf-esis.59.13 180 element no. group node element no. group node element no. group node element no. group node i j i j i j i j 41 8 13 18 71 14 24 26 101 22 33 38 131 31 38 39 42 8 14 17 72 14 21 30 102 22 34 39 132 31 39 35 43 8 14 19 73 15 26 27 103 23 33 39 133 32 40 44 44 8 15 18 74 15 27 29 104 23 32 35 134 32 41 45 45 8 15 20 75 15 29 30 105 23 31 36 135 32 42 46 46 8 16 19 76 15 30 26 106 23 34 38 136 32 43 47 47 8 16 17 77 16 25 26 107 24 32 38 137 33 40 45 48 8 13 20 78 16 27 28 108 24 33 36 138 33 41 46 49 9 17 21 79 16 25 30 109 24 34 35 139 33 42 47 50 9 18 22 80 16 29 28 110 24 31 39 140 33 43 44 51 9 19 23 81 17 25 31 111 25 37 35 141 34 44 45 52 9 20 24 82 17 28 32 112 25 37 39 142 34 45 46 53 10 17 22 83 17 28 33 113 26 37 40 143 34 46 47 54 10 18 21 84 17 25 34 114 26 37 43 144 34 44 47 55 10 19 24 85 18 26 31 115 27 35 40 145 35 44 48 56 10 20 23 86 18 27 32 116 27 36 41 146 35 45 49 57 11 18 23 87 18 29 33 117 27 38 42 147 35 46 50 58 11 19 22 88 18 30 34 118 27 39 43 148 35 47 51 59 11 20 21 89 19 26 32 119 28 35 38 149 36 45 48 60 11 17 24 90 19 27 31 120 28 36 39 150 36 46 49 61 12 21 26 91 19 29 34 121 29 36 40 151 36 47 50 62 12 22 27 92 19 30 33 122 29 38 41 152 36 44 51 63 12 23 29 93 20 27 33 123 29 39 42 153 37 48 49 64 12 24 30 94 20 29 32 124 29 35 43 154 37 49 50 65 13 21 27 95 20 30 31 125 30 40 41 155 37 50 51 66 13 22 26 96 20 26 34 126 30 41 42 156 37 48 51 67 13 23 30 97 21 26 29 127 30 42 43 157 38 48 52 68 13 24 29 98 21 27 30 128 30 43 40 158 38 49 52 69 14 22 29 99 22 31 35 129 31 35 36 159 38 50 52 70 14 23 27 100 22 32 36 130 31 36 38 160 38 51 52 table 2: element connectivity (continued). t.-h. nguyen et alii, frattura ed integrità strutturale, 59 (2022) 172-187; doi: 10.3221/igf-esis.59.13 181 load case node px py pz load case node px py pz lc1 52 -868 0 -491 lc5 52 -917 0 -491 37 -996 0 -546 37 -951 0 -546 25 -1091 0 -546 25 -1015 0 -546 28 -1091 0 -546 28 -636 1259 -428 lc2 52 -493 1245 -363 lc6 52 -917 0 -491 37 -996 0 -546 37 -572 1303 -428 25 -1091 0 -546 25 -1015 0 -546 28 -1091 0 -546 28 -1015 0 -546 lc3 52 -917 0 -491 lc7 52 -917 0 -491 37 -951 0 -546 37 -951 0 -546 25 -1015 0 -546 25 -1015 0 -546 28 -1015 0 -546 28 -636 1303 -428 lc4 52 -917 0 -546 lc8 52 -498 1460 -363 37 -572 1259 -428 37 -951 0 -546 25 -1015 0 -546 25 -1015 0 -546 28 -1015 0 -546 28 -1015 0 -546 table 3: load cases (unit: kgf). no. a (cm2) r (cm) no. a (cm2) r (cm) no. a (cm2) r (cm) no. a (cm2) r (cm) 1 1.84 0.47 12 7.44 1.26 23 21.12 2.16 34 46.94 2.94 2 2.26 0.57 13 8.06 1.36 24 23.2 2.36 35 51 2.92 3 2.66 0.67 14 8.66 1.46 25 25.12 2.57 36 52.1 3.54 4 3.07 0.77 15 9.4 1.35 26 27.5 2.35 37 61.82 3.96 5 3.47 0.87 16 10.47 1.36 27 29.88 2.56 38 61.9 3.52 6 3.88 0.97 17 11.38 1.45 28 32.76 2.14 39 68.3 3.51 7 4.79 0.97 18 12.21 1.55 29 33.9 2.33 40 76.38 3.93 8 5.27 1.06 19 13.79 1.76 30 34.77 2.97 41 90.6 3.92 9 5.75 1.16 20 15.39 1.95 31 39.16 2.54 42 94.13 3.92 10 6.25 1.26 21 17.03 1.74 32 43 2.93 11 6.84 1.15 22 19.03 1.94 33 45.65 2.94 table 4: list of available profiles. t.-h. nguyen et alii, frattura ed integrità strutturale, 59 (2022) 172-187; doi: 10.3221/igf-esis.59.13 182 feature handling for machine learning models when developing a machine learning model, the input features should be identified. numerous studies used the crosssectional areas of truss members as inputs [24-26,30]. however, as can be seen in eq. (11), the critical buckling stress of a member depends on its effective length kl and the radius of gyration r. among the two parameters, the effective length does not change during the sizing optimization process, but the radius of gyration r varies according to the profile of the member. therefore, the radius of gyration r is also an important characteristic that should be included in the machine learning model. in the present work, a feature handling technique is proposed to improve the accuracy of the machine learning model. in particular, there are 38 input features x={xi|i=1,2,…,38} that are fed into the model, in which each feature xi represents the ratio of the area and the radius of gyration of a profile used in this structure:  ii i a x r (12) where: ai, ri are the cross-sectional area and the radius of gyration of the profile, respectively. in this way, the model can learn both important characteristics including the cross-sectional area and the radius of gyration while keeping the number of input features. setups to exhibit the advantages of the proposed method, the 160-bar tower is optimized according to both the original de algorithm and the adaboost-de algorithm. the parameters of the two algorithms are the same as follows: the scaling factor f=0.8, the crossover rate cr=0.9, the population size np=50, the maximum number of generations max_iter=750. particularly for the adaboost-de algorithm, the number of generations of the first stage is set to be n_iter1=50 which means that the amount of samples of the training data equals 1000. the adaboost classification model consists of t=100 weak classifiers in which each weak classifier is a decision tree with the maximum depth max_depth=1. both the de and the adaboost-de algorithms are written in python programming language and performed by the personal computer having the system configuration as follows: processor intel core i5 2.5 ghz, ram 4.00 gb. the adaboost classification model is developed using the machine learning library scikit-learn [36]. the in-house python code for finite element analysis (fea) is based on the direct stiffness method. results the statistical results of 30 independent runs are summarized in tab. 5. the results of the previous studies are also presented in tab. 5 for comparison. the value in bold indicates this is the best result among the compared algorithms. fig. 4 plots the convergence histories of the de and the adaboost-de, in which fig. 4(a) shows the relationship of the weight and the number of structural analyses that must be carried out during the optimization process while fig. 4(b) displays the reduction of the weight over computing time. rbas [32] aede [33] msos [34] present work de adaboost-de weight (kg) best 1336.7493 1336.634 1336.634 1336.634 1336.634 mean 1342.6083 1355.875 1338.245 1350.648 1353.370 worst 1353.4686 1410.611 1343.821 1464.828 1475.435 sd 18.805 2.080 22.728 26.491 average number of structural analyses 90,000 23,925 24,000 37,500 22,488 average computing time (s) 3036.6 2024.5 table 5: statistical results for the optimization of the 160-bar transmission tower. t.-h. nguyen et alii, frattura ed integrità strutturale, 59 (2022) 172-187; doi: 10.3221/igf-esis.59.13 183 figure 4: convergence curves of the adaboost-de and the de. tab. 5 shows that the optimal results of the adaboost-de, the de, the aede, and the msos are the same and better than the rbas (1336.634 kg for the adaboost-de, the de, the aede, the msos, and 1336.7493 kg for the rbas). the optimal weights found by the mmsm (1329.715 kg) [5] and by the psoc (1327.048 kg) [35] are smaller than the optimal weight found in the present work. however, according to our verification, these designs slightly violate the buckling constraint at elements 52 and 80. thus, they are not reported in tab. 5. despite having the same optimal results, the advantage of the proposed method is the speed. the adaboost-de conducts 22488 structural analyses while the required number of structural analyses of the rbas, the de, the aede, the msos are 90000 times, 37500 times, 23925 times, and 24000 times, respectively. fig. 4 clearly exhibits the benefit of integrating the adaboost classification technique into the de algorithm. during 750 iterations, the de requires 37500 analyses while the adaboost-de performs only 22488 analyses. in other words, the application of the adaboost technique reduces 40% of structural analyses. compared with the results in ref. [30], the modifications proposed in the present work increase the reduction rate from 20% to 40%. regarding the computing time, although the proposed method requires additional time for training and employing the machine learning model, it is still more time-efficient than the original de algorithm. according to tab. 5, the average time consumed by the de and the adaboost-de are 3036.6 s and 2024.5 s, respectively. it means the adaboost-de is approximately 1.5 times faster than the de in terms of computing time. validation of the optimal design using the commercial software in this section, the best solution found by the adaboost-de is re-checked using the commercial software csi sap2000. this is a well-known software that has been widely utilized by structural engineers over the world. the section properties including sectional areas as well as the radius of gyration of 38 member groups of the best solution found by the adaboostde are reported in tab. 6. a 3d model containing 52 nodes and 160 elements is simulated by using sap2000 as schematized in fig. 5(a). the material steel used in this model is specified with the following properties: the modulus of elasticity e=2.047e+06 kgf/cm2 and the weight per unit volume =7.85e-03 kg/cm3. elements of the model are assigned to 38 different sections with the section properties as presented in tab. 6. eight static load cases are defined where the force magnitudes of these load cases are taken from tab. 3. the model is linearly analyzed and the stress contour of the envelope load combination is plotted in fig. 5(b). next, the tensile stress and buckling stress constraints are checked based on the obtained results. the maximum tensile stress found at element 86 reaches 912.1 kgf/cm2, which equals 61% of the limitation. the critical element according to the buckling stress condition is element 105. the compression stress in this element is equal to -386.3 kgf/cm2, achieving 100% of the allowable buckling stress. thus, the optimal design does not violate any design constraints. furthermore, the stresses of 160 elements obtaining by sap2000 and by in-house fea code are compared in fig. 6. the coefficient of determination r2=0.9996 is very close to 1.0 indicating the high similarity of sap2000 and the developed fea code. t.-h. nguyen et alii, frattura ed integrità strutturale, 59 (2022) 172-187; doi: 10.3221/igf-esis.59.13 184 group a (cm2) r (cm) group a (cm2) r (cm) group a (cm2) r (cm) group a (cm2) r (cm) 1 19.03 1.94 11 5.75 1.16 21 2.66 0.67 31 2.26 0.57 2 5.27 1.06 12 12.21 1.55 22 8.06 1.36 32 3.88 0.97 3 19.03 1.94 13 6.25 1.26 23 5.75 1.16 33 1.84 0.47 4 5.27 1.06 14 5.75 1.16 24 6.25 1.26 34 1.84 0.47 5 19.03 1.94 15 3.88 0.97 25 5.75 1.16 35 3.88 0.97 6 5.75 1.16 16 7.44 1.26 26 2.26 0.47 36 1.84 0.47 7 15.39 1.95 17 1.84 0.47 27 4.79 0.97 37 1.84 0.47 8 5.75 1.16 18 8.66 1.46 28 2.66 0.67 38 3.88 0.97 9 13.79 1.76 19 2.66 0.67 29 3.47 0.87 10 5.75 1.16 20 3.07 0.77 30 1.84 0.47 table 6: section properties of the best solution. figure 5: model in sap2000. t.-h. nguyen et alii, frattura ed integrità strutturale, 59 (2022) 172-187; doi: 10.3221/igf-esis.59.13 185 figure 6: comparison between the stresses obtained from sap2000 and in-house fea code. conclusions n this paper, a method that combines the differential evolution algorithm and the adaptive boosting classification technique to minimize the weight of steel lattice towers is proposed. in the sooner generations, the original differential evolution with four basic operators is employed with the aim of exploring the design space and collecting training data. an adaptive boosting model is trained by the obtained data and then utilized to discard worse candidates in the later generations. additionally, a feature handling technique is introduced for the purpose of improving the quality of the machine learning model. the proposed method is applied to a 160-bar tower to illustrate its effectiveness. the optimal design found by the adaboostde is as good as the results obtained by other meta-heuristic algorithms. however, the advantage of the adaboost-de is the fast convergence speed. this advantage is achieved because the adaboost-de reduces the number of structural analyses by approximately 40% compared to the original differential evolution algorithm. consequently, the optimization time of the adaboost-de is significantly shortened. the numerical example conducted in this paper indicates that the adaboostde is an efficient method to optimize steel lattice towers. despite the advantages mentioned above, the proposed method also has some disadvantages. first, the integration of the adaboost model into the de increases the complexity of the algorithm. this makes it difficult for structural engineers who are not familiar with advanced programming techniques. next, the proposed method needs to set seven parameters instead of four as in the original de. consequently, the hyperparameter tuning process consumes more computational cost. finally, the adaboost-de requires additional time for training ml models. in general, the proposed method is suitable for problems where the design constraint verification is very time-consuming. the potential of the adaboost-de for the optimization of large-scale towers should be further investigated. acknowledgment he author t.-h. nguyen was funded by vingroup joint stock company and supported by the domestic ph.d. scholarship programme of vingroup innovation foundation (vinif), vingroup big data institute (vinbigdata) code vinif.2020.ts.134. i t t.-h. nguyen et alii, frattura ed integrità strutturale, 59 (2022) 172-187; doi: 10.3221/igf-esis.59.13 186 references [1] rao, g.v. (1995). optimum designs for transmission line towers. computers & structures, 57(1), pp.81-92. doi: 10.1016/0045-7949(94)00597-v. [2] taniwaki, k. and ohkubo, s. (2004). optimal synthesis method for transmission tower truss structures subjected to static and seismic loads. structural and multidisciplinary optimization, 26(6), pp.441-454. doi: 10.1007/s00158-003-0367-7. [3] shea, k. and smith, i.f. (2006). improving full-scale transmission tower design through topology and shape optimization. journal of structural engineering, 132(5), pp.781-790. doi: 10.1061/(asce)0733-9445(2006)132:5(781). [4] guo, h.y. and li, z.l. (2011). structural topology optimization of high-voltage transmission tower with discrete variables. structural and multidisciplinary optimization, 43(6), pp.851-861. doi: 10.1007/s00158-010-0561-3. [5] kaveh, a., kalatjari, v.r. and talebpour, m.h. (2016). optimal design of steel towers using a multi-metaheuristic based search method. periodica polytechnica civil engineering, 60(2), pp.229-246. doi: 10.3311/ppci.8222. [6] de souza, r.r., miguel, l.f.f., lopez, r.h., miguel, l.f.f. and torii, a.j. (2016). a procedure for the size, shape and topology optimization of transmission line tower structures. engineering structures, 111, pp.162-184. doi: 10.1016/j.engstruct.2015.12.005. [7] tort, c., şahin, s. and hasançebi, o. (2017). optimum design of steel lattice transmission line towers using simulated annealing and pls-tower. computers & structures, 179, pp.75-94. doi: 10.1016/j.compstruc.2016.10.017. [8] khodzhaiev, m. and reuter, u. (2021). structural optimization of transmission towers using a novel genetic algorithm approach with a variable length genome. engineering structures, 240, p.112306. doi: 10.1016/j.engstruct.2021.112306. [9] couceiro, i., parís, j., martínez, s., colominas, i., navarrina, f. and casteleiro, m. (2016). structural optimization of lattice steel transmission towers. engineering structures, 117, pp.274-286. doi: 10.1016/j.engstruct.2016.03.005. [10] nguyen, h., vu, t., vo, t. p. and thai, h. t. (2021). efficient machine learning models for prediction of concrete strengths. construction and building materials, 266, 120950. doi: 10.1016/j.conbuildmat.2020.120950. [11] ouladbrahim, a., belaidi, i., khatir, s., magagnini, e., capozucca, r., and wahab, m. a. (2021). prediction of gurson damage model parameters coupled with hardening law identification of steel x70 pipeline using neural network. metals and materials international, 2021, pp.1-15. doi: 10.1007/s12540-021-01024-4. [12] degtyarev, v. v. (2021). neural networks for predicting shear strength of cfs channels with slotted webs. journal of constructional steel research, 177, 106443. doi: 10.1016/j.jcsr.2020.106443. [13] truong, v. h., vu, q. v., thai, h. t., and ha, m. h. (2020). a robust method for safety evaluation of steel trusses using gradient tree boosting algorithm. advances in engineering software, 147, 102825. doi: 10.1016/j.advengsoft.2020.102825. [14] mangalathu, s., and jeon, j. s. (2019). machine learning–based failure mode recognition of circular reinforced concrete bridge columns: comparative study. journal of structural engineering, 145(10), 04019104. doi: 10.1061/(asce)st.1943-541x.0002402. [15] shen, z., pan, p., zhang, d., and huang, s. (2020). rapid structural safety assessment using a deep neural network. journal of earthquake engineering, 2020, pp.1-17. doi: 10.1080/13632469.2020.1785586. [16] benaissa, b., hocine, n. a., belaidi, i., hamrani, a., and pettarin, v. (2016). crack identification using model reduction based on proper orthogonal decomposition coupled with radial basis functions. structural and multidisciplinary optimization, 54(2), pp.265-274. doi: 10.1007/s00158-016-1400-y. [17] samir, k., brahim, b., capozucca, r., and wahab, m. a. (2018). damage detection in cfrp composite beams based on vibration analysis using proper orthogonal decomposition method with radial basis functions and cuckoo search algorithm. composite structures, 187, pp.344-353. doi: 10.1016/j.compstruct.2017.12.058. [18] tiachacht, s., khatir, s., le thanh, c., rao, r. v., mirjalili, s., and wahab, m. a. (2021). inverse problem for dynamic structural health monitoring based on slime mould algorithm. engineering with computers, 2021, pp.1-24. doi: 10.1007/s00366-021-01378-8. [19] khatir, s., tiachacht, s., le thanh, c., tran-ngoc, h., mirjalili, s., and wahab, m. a. (2021). a new robust flexibility index for structural damage identification and quantification. engineering failure analysis, 2021, 105714. doi: 10.1016/j.engfailanal.2021.105714. [20] khatir, s., tiachacht, s., thanh, c.l., bui, t.q. and wahab, m.a., (2019). damage assessment in composite laminates using ann-pso-iga and cornwell indicator. composite structures, 230, p.111509. doi: 10.1016/j.compstruct.2019.111509. t.-h. nguyen et alii, frattura ed integrità strutturale, 59 (2022) 172-187; doi: 10.3221/igf-esis.59.13 187 [21] khatir, s., boutchicha, d., le thanh, c., tran-ngoc, h., nguyen, t.n. and abdel-wahab, m., (2020). improved ann technique combined with jaya algorithm for crack identification in plates using xiga and experimental analysis. theoretical and applied fracture mechanics, 107, p.102554. doi: 10.1016/j.tafmec.2020.102554. [22] khatir, s., tiachacht, s., le thanh, c., ghandourah, e., mirjalili, s. and wahab, m.a., (2021). an improved artificial neural network using arithmetic optimization algorithm for damage assessment in fgm composite plates. composite structures, p.114287. doi: 10.1016/j.compstruct.2021.114287. [23] zenzen, r., khatir, s., belaidi, i., le thanh, c., & wahab, m. a. (2020). a modified transmissibility indicator and artificial neural network for damage identification and quantification in laminated composite structures. composite structures, 248, 112497. [24] kaveh, a., gholipour, y. and rahami, h. (2008). optimal design of transmission towers using genetic algorithm and neural networks. international journal of space structures, 23(1), pp.1-19. doi: 10.1260/026635108785342073. [25] taheri, f., ghasemi, m.r. and dizangian, b., 2020. practical optimization of power transmission towers using the rbfbased abc algorithm. structural engineering and mechanics, 73(4), pp.463-479. doi: 10.12989/sem.2020.73.4.463. [26] hosseini, n., ghasemi, m.r. and dizangian, b., 2021. anfis-based optimum design of real power transmission towers with size, shape and panel variables using bbo algorithm. ieee transactions on power delivery. doi: 10.1109/tpwrd.2021.3052595. [27] asce, 2000, march. design of latticed steel transmission structures. american society of civil engineers. [28] storn, r. and price, k. (1997). differential evolution–a simple and efficient heuristic for global optimization over continuous spaces. journal of global optimization, 11(4), pp.341-359. doi: 10.1023/a:1008202821328. [29] freund, y. and schapire, r.e. (1997). a decision-theoretic generalization of on-line learning and an application to boosting. journal of computer and system sciences, 55(1), pp.119-139. doi: 10.1006/jcss.1997.1504. [30] nguyen, t.-h., and vu, a.-t. (2022). application of artificial intelligence for structural optimization. in: modern mechanics and applications, singapore, springer, pp. 1052-1064. doi: 10.1007/978-981-16-3239-6_82. [31] nguyen, t.-h. and vu, a.-t. (2021). evaluating structural safety of trusses using machine learning. frattura ed integrità strutturale, 15(58), pp. 308–318. doi: 10.3221/igf-esis.58.23. [32] capriles, p.v., fonseca, l.g., barbosa, h.j. and lemonge, a.c. (2007). rank‐based ant colony algorithms for truss weight minimization with discrete variables. communications in numerical methods in engineering, 23(6), pp. 553575. doi: 10.1002/cnm.912. [33] ho-huu, v., nguyen-thoi, t., vo-duy, t. and nguyen-trang, t. (2016). an adaptive elitist differential evolution for optimization of truss structures with discrete design variables. computers & structures, 165, pp.59-75. doi: 10.1016/j.compstruc.2015.11.014. [34] do, d.t. and lee, j. (2017). a modified symbiotic organisms search (msos) algorithm for optimization of pin-jointed structures. applied soft computing, 61, pp.683-699. doi: 10.1016/j.asoc.2017.08.002. [35] jafari, m., salajegheh, e. and salajegheh, j., (2021). optimal design of truss structures using a hybrid method based on particle swarm optimizer and cultural algorithm. structures, 32, pp. 391-405. doi: 10.1016/j.istruc.2021.03.017. [36] pedregosa, f., varoquaux, g., gramfort, a., michel, v., thirion, b., grisel, o., blondel, m., prettenhofer, p., weiss, r., dubourg, v. and vanderplas, j. 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can be opened with acrobat and adobe reader 5.0 and later.) >> /namespace [ (adobe) (common) (1.0) ] /othernamespaces [ << /asreaderspreads false /cropimagestoframes true /errorcontrol /warnandcontinue /flattenerignorespreadoverrides false /includeguidesgrids false /includenonprinting false /includeslug false /namespace [ (adobe) (indesign) (4.0) ] /omitplacedbitmaps false /omitplacedeps false /omitplacedpdf false /simulateoverprint /legacy >> << /addbleedmarks false /addcolorbars false /addcropmarks false /addpageinfo false /addregmarks false /convertcolors /converttocmyk /destinationprofilename () /destinationprofileselector /documentcmyk /downsample16bitimages true /flattenerpreset << /presetselector /mediumresolution >> /formelements false /generatestructure false /includebookmarks false /includehyperlinks false /includeinteractive false /includelayers false /includeprofiles false /multimediahandling /useobjectsettings /namespace [ (adobe) (creativesuite) (2.0) ] /pdfxoutputintentprofileselector /documentcmyk /preserveediting true /untaggedcmykhandling /leaveuntagged /untaggedrgbhandling /usedocumentprofile /usedocumentbleed false >> ] >> setdistillerparams << /hwresolution [2400 2400] /pagesize [612.000 792.000] >> setpagedevice microsoft word 2237 p. gallo et alii, frattura ed integrità strutturale, 47 (2019) 408-415; doi: 10.3221/igf-esis.47.31 408 focussed on “crack paths” experimental characterization at nanoscale of single crystal silicon fracture toughness pasquale gallo, takashi sumigawa, takayuki kitamura kyoto university, kyoto-daigaku-katsura, nishikyo-ku, kyoto-shi 615-8540, japan pasquale.gallo@aalto.fi, http://orcid.org/0000-0001-5742-8647 sumigawa@cyber.kues.kyoto-u.ac.jp kitamura@kues.kyoto-u.ac.jp abstract. the work reviews some preliminary recent micromechanical tests aimed at the evaluation of the fracture toughness of silicon. pre-cracked nano specimens and alternatively notched nano specimens combined with the theory of critical distances (tcd) are compared. the results show that the fracture toughness of silicon is approximately 1 mpa·m0.5, regardless of the procedure involved (i.e., pre-cracked samples or tcd). this value agrees with macro counterpart, i.e., 0.75-1.08 mpa·m0.5, and therefore the kic is independent of the size and crystal orientation. however, by employing the tcd, the accurate control of the final crack tip which is currently very challenging, is overcome by using notched specimens. additionally, the results give information about the crack propagation at the nanoscale. it seems that although the specimen axis deviates from the (011), the crack propagates along the cleavage plane (011) and the process develops very fast by breaking covalent bond at the crack tip. a brief discussion on beyond the breakdown of continuum theory and challenges toward nanometer scale fracture mechanics concludes the paper. keywords. fracture nanomechanics; silicon; nanoscale; fracture toughness; citation: gallo, p., sumigawa, t., kitamura, t., experimental characterization at nanoscale of single crystal silicon fracture toughness, frattura ed integrità strutturale, xx (2019) 408-415. received: 26.10.2018 accepted: 07.11.2018 published: 01.01.2019 copyright: © 2019 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. introduction onventional fracture mechanics [1] has been primarily investigated starting from the ii world war and developed in the well-known linear elastic fracture mechanics (lefm). however, in the last decade, new challenges have arisen. indeed, the miniaturization of electronic devices driven by the increasing demand for high-density integrations have brought problems of material behavior at very small scales into the domain of the conventional fracture mechanics [2]. moreover, recent literature suggests that in many applications at the macroscale, reliable engineering for entire component lifetime depends on accurate prediction of fracture from the smallest size until final failure [3]. while numerical simulations have spread rapidly [4], the small sizes of micro and nanocomponents still impose several challenges for the experimental study of their mechanical properties. the mechanical characterization at the micro and nanoscale (or even at atomic scale [5]) provides essential parameters for the design of components such as micro/nanoc http://www.gruppofrattura.it/va/47/2237.mp4 p. gallo et alii, frattura ed integrità strutturale, 47 (2019) 408-415; doi: 10.3221/igf-esis.47.31 409 electro-mechanical systems (mems, nems), but gives us an insight into the breakdown of the continuum fracture mechanics. for these reasons, fracture nanomechanics has sparked the increasing interest of the scientific community. while effort has been primarily devoted to determining young’s modulus and tensile strength of silicon and other materials [6,7], the fracture properties and fracture process at the nanoscale have been marginally treated. recent results suggest that at micro and nanoscale the material still fails by nucleation and propagation of cracks [2] and therefore some local approaches, commonly employed at the macroscale, can be directly scaled down [8]. however, there is a limit below which the continuum assumption of the lefm has to face the discrete nature of atoms [9]. in the above background, the experimental characterization of fracture behavior at the nanoscale and the investigation of the low limit of the continuum theory are at the present relevant and challenging aspects. therefore, this contribution presents a synthesis of experimental tests on the evaluation of single crystal silicon fracture toughness at the nanoscale [10,11]. first, results obtained from pre-cracked samples are reviewed and crack propagation is commented. later, results from notched nano-cantilever beams by using the theory of critical distances (tcd) are presented. at the end, the procedures are compared to highlight the pros and cons. the work also provides an insight into the micro-mechanisms of crack propagation in brittle materials. fabrication of the specimens he specimen fabrication is depicted in fig. 1. the pre-cracked samples and the notched nano-cantilever beams have similar procedures of fabrication with substantial differences only in the final steps. first, a block is generally carved out from a single-crystal si (100) plate. the block is then deposited on a flat end of a gold (au) wire and stabilized by tungsten vapor deposition. in this phase, the orientation of the sample can be re-arranged if needed. the block is then processed by fib (focused ion beam) to obtain the final specimen. in the case of pre-cracked specimens, a trapezoidal plate is generated, and v-shape grooves are introduced in the vertical direction. these grooves are used as a guide for the generation of the pre-crack. a notch is introduced at the top surface, and a wedge-shaped indenter is employed to apply an opening displacement until crack propagation is detected. finally, the top part of the specimen can be cut to obtain the desired crack-length. the process of pre-crack generation is in general quite difficult and time-consuming since precise control of the geometry with the fib is problematic at this small scale. in the case of notched specimens, the cantilever beam is cut from the block in several steps, and a notch is finally introduced. in the generation of the notch, attention should be paid to obtain a good level of symmetry on the two lateral surfaces. this aim is achieved by tilting the stage to correct the beam angle. it should be pointed out that also in this case the control on the notch root radius is very difficult, especially when the generation of sharp notches is needed. because of the extremely small sizes of the samples, even the smallest radius currently achievable with fib could not be simplified and considered as “zero”. the procedure is, however, faster than the fabrication of pre-cracked specimens and, as is shown in next sections, accurate control of the notch geometry is not needed when applying the tcd. figure 1: example of fabrication of specimens. t p. gallo et alii, frattura ed integrità strutturale, 47 (2019) 408-415; doi: 10.3221/igf-esis.47.31 410 evaluation of fracture toughness using nanoscale pre-cracked specimens hree micro-specimens were fabricated by a focused ion beam (fib) processing system (see previous section). vshape grooves were used as a guide for straight pre-crack introduction, and a notch was then introduced at the top of the specimen. the notches were, on average, 100 nm wide (mouth width) and 700 nm deep. example of the specimen is depicted in fig. 2(a) together with material properties, while geometrical parameters are reported in tab. 1. the pre-crack was realized by applying an opening displacement with a wedge-shaped indenter according to fig. 2(c). the upper part of the specimen was later cut by fib to obtain shorter pre-cracks. the experiments were conducted using a sample holder with a loading device inserted in a tem (transmission electron microscope) provided with in situ observation camera. the opening displacement was applied to the sample by pushing the wedge-shape indenter in the precrack mouth while a sensor beneath the indenter detected the applied load (see visual abstract). the stress in the specimens was later re-analyzed by finite element method (fem) by properly considering the material anisotropy and 3d model was used. the material constants and the model employed are reported in fig. 2(b). the fracture toughness was evaluated by the intensity of the singular field at the critical load (at crack propagation). the results are summarized in tab. 1 which reports the fracture toughness kic, the length of the singular stress field λk and the critical crack opening displacement δc. from the results, it is possible to conclude that the average fracture toughness kic is 1 mpa·m0.5. this value agrees with the bulk silicon value, i.e., 0.75-1.08 mpa·m0.5 [12–14]. this finding proves that the fracture toughness is independent of the size. the kic is also independent of the length of the singular stress field. results in tab. 1 are, indeed, all very close to the same average value of 1 mpa·m0.5. these results have been recently further confirmed by additional experiments and sophisticated first-principles density functional theory (dft) simulations [10,15] which considered the discrete nature of atoms. in those works, griffith criterion was applied to 4 nm stress singularity, and the fracture toughness resulted in being 0.95 ± 0.07 mpa·m0.5, in agreement with values presented here. figure 2: example of (a) nanoscale notched specimen, (b) 3d fe model and (c) introduction of pre-crack. a (nm) w (nm) t (nm) λk (nm) δc (nm) kic (mpa·m0.5) specimen 1 3982 830 580 23 205 0.83 specimen 2 1412 600 480 25.4 62 1.09 specimen 3 4359 474 302 57.5 237 1.08 table 1: pre-crack length a and width w; thickness of the thinned region t; synthesis of the results: length of singular stress field λk and critical crack opening displacement δc. t precrack material constants c11=167.4 gpa c12=65.23 gpa c44=79.57 gpa (a) (b) 1 μm 1 μm (c) indenter notch crack p. gallo et alii, frattura ed integrità strutturale, 47 (2019) 408-415; doi: 10.3221/igf-esis.47.31 411 evaluation of fracture toughness using nanoscale notched specimens t very small scale, even a small notch radius can drastically change the stress singularity, and the fracture toughness obtained [16,17]. at the same time, the realization of crack is difficult and very challenging. for this reason, it is worth of investigating alternative procedures for the determination of those mechanical properties that would overcome these difficulties. among the methods available in the literature, the theory of critical distances (tcd) has proved to be very versatile and simple. first developments on “material length parameters” were addressed by neuber [18] and peterson [19]. the recent history of the tcd, instead, was formalized by taylor [20] and susmel [21]. tcd in the form of the point method assumes that “failure occurs when the linear elastic maximum principal stress at a given distance l/2 from the notch root equals the inherent material strength of the material σ0”. l is the so-called material characteristic length, and it takes the following form under static loading [22]: 2 0 1 ickl          (1) from eqn. (1), it is clear that when the material characteristic length and the inherent stress are known, the fracture toughness can be quickly evaluated as: 0ick l  (2) susmel at al. [22,23] and taylor et al. [20,24] proposed an efficient strategy to evaluate the material characteristic length and the inherent material stress. at least two static tests considering notch of different sharpnesses need to be carried out to determine the static strengths. subsequently, the linear elastic stress fields of the two notches under incipient failure conditions can be plotted and overlapped in a single picture. the intersection of the two stress distributions permits to evaluate both σ0 and l. once these two parameters are defined, eqn. (2) can be employed. the advantages tied-in to the procedure in the realization of simple geometries are relevant and worth of investigating. therefore, to determine the fracture toughness of single crystal silicon, two notched nano-cantilever beams of different sharpnesses were realized by focused ion beam (fib) processing system. the fabrication process reported in [11] was followed. the specimens had a notch radius ρ of 6.3, 20.2 nm and opening angle 2α of 68° and 59°, respectively. these geometries gave stress concentration factor ktn (net section) of 4.9 and 2.9, respectively. the specimens were later loaded into the tem by using an indenter provided with a load sensor (see visual abstract). fig. 3(a) presents a sample during the experiment. deflection at failure δf and load at failure pf were obtained. the results are summarized in tab. 2. following the definition provided earlier, the fracture toughness kic and the material characteristic length l were determined as is shown in fig. 3(b). the value of the fracture toughness was 1.05 mpa·m0.5, while l was 1.8 nm. the inherent material strength σ0 was approximately 14 gpa. these results have been further confirmed by additional tests in [11,25]. figure 3: example of (a) nanoscale notched specimen (tem image) and (b) synthesis by using the tcd. a (a) (b) indenter tip 1.e+02 1.e+03 1.e+04 1.e+05 0.01 0.1 1 10 100 distance from notch root [nm] sharp blunt 105 102 σ 1 [m p a] ktn = 4.9 ktn = 2.9 σ0 ≈ 14 gpa l/2 = [0.9] nm kic = 1.05 mpa∙m 0.5kic = σ0 (πl) 0.5 p. gallo et alii, frattura ed integrità strutturale, 47 (2019) 408-415; doi: 10.3221/igf-esis.47.31 412 ρ (nm) 2α (deg) ktn δf (nm) pf (μn) specimen 1 6.3 68 4.9 83.74 30.84 specimen 2 20.2 59 2.9 115.59 65.11 table 2: geometry of the notches, deflection at failure δf and load at failure pf. discussion: nanocracking in silicon s is well-known, tensile strength and fracture toughness are fundamental mechanical properties. while tensile strength has been investigated in several works/materials and its scale dependence observed [26,27], the fracture toughness has not been investigated in detail up to the present. the reasons are the well-known difficulties in the fabrication of very small specimens and in the realization of an effective pre-crack at the nanometer level. at very small scale, indeed, even a small notch radius can drastically change the stress singularity and the fracture toughness [16,17]. ando et al. [16], for example, found that the kic changes with the crystal orientation, with maximum and minimum values of approximately 2 and 1.2 mpa·m0.5, respectively. li et al. [17] found a value of the fracture toughness of approximately 1.6 mpa·m0.5, in apparent disagreement with bulk silicon value. the results presented here show that, if an effective precrack is realized, the nanoscale si fracture toughness agrees with the macro counterpart. however, the realization of precrack is still very challenging and time-consuming. alternatively, it is shown that by employing the tcd, the demanding accurate control on the specimens geometry can be avoided since the fracture toughness is evaluated using at least two generic notches of different sharpnesses, leaving the user free to employ any obtained geometry. fig. 3(b) shows a fracture toughness in excellent agreement with macro counterpart value and the previous experiments on pre-cracked samples. additional experiments conducted by [10,11,15,25] further confirm the results presented here. useful information on crack propagation can be obtained by the experiments conducted on pre-cracked samples. fig. 4(a) refers to the sample 2 in tab. 1 and shows that although the not perfect specimen orientation, a stable crack propagation occurred along the cleavage plane (011). once the critical crack opening displacement was reached (see tab. 1), unstable crack propagation and subsequent final failure were observed. the propagation once started, is very fast and brings to the final failure rapidly. as is well-known, the fracture is usually studied on the assumption that fracture takes place from preexisting defects of flaws. defects, however, vary in number and severity depending on the volume and size of the sample. ideally, at the nanoscale, the inherent material strength σ0 can be considered to be the upper limit of fracture stress of components having no defect, i.e., ideal fracture stress [28]. the micro-mechanisms governing the crack propagation in such small components should be located therefore at a smaller level, i.e., atomic structure level. a more in-depth investigation can only be conducted if the discrete nature of atoms is considered, by using numerical experiments. indeed, recent density functional theory (dft) calculations showed that the nanocracking in silicon is due to the breaking of a covalent bond at the crack tip. when the applied stress intensity factor ki reaches the critical value of 1 mpa·m0.5 the bond is broken and the crack propagates instantaneously along the cleavage plane (011). this result was further confirmed with additional dft simulations considering different models and molecular dynamics (md) simulations, where the stress is calculated atom-by-atom using the virial theorem. regardless of size, geometry and loading conditions, the simulations confirmed that the nanoscale crack always starts to propagate when the atomic stress at the tip reaches its ideal (bond) strength [9,15]. fig. 4(b) represents the fracture mode displacements at the onset of nanocracking and schematically shows the crack advancement by atomic bond breaking. in the light of crack ultimately governed by atomic bond breaking and therefore by atomic level, it is natural to wonder whether the continuum theories should be applied at such small scales, if there is any limitation to the continuum theories and how eventually evaluate this limit. theory of critical distances lies between continuum mechanics theories and micro-mechanistic approaches. the material characteristic length should be considered therefore a representative length scale parameter that changes as the mechanisms of fracture do [29,30]. l, therefore, can somehow be representative of the low limit of continuum fracture mechanics. validation of this hypothesis can be done by comparison with a recent relevant work by shimada et al. [9]. those authors proposed an interesting study based on sophisticated dft and md calculations on cracked specimens. several samples were studied by varying the size. it was shown that the length of the singular stress field becomes smaller as the width of the specimen does, while the fracture process zone (defined as the zone where the discrete motion of atoms is concentrated) remains constant. when approaching a critical singular stress field length, continuum theory breaks down. this limit was quantified in 3-6 times the fracture process zone, and therefore in the case of silicon is 1.5-3 nm approximately, with a fracture process zone of 0.4-0.6 nm on average. interestingly, l falls within the range of that limit, being 1.8 nm, while l/2 is close to the fracture a p. gallo et alii, frattura ed integrità strutturale, 47 (2019) 408-415; doi: 10.3221/igf-esis.47.31 413 process zone value. with the quantification of low limit of continuum theory, it is possible to assume that method such as the tcd can be applied successfully at very small scale; however, once the limitation is reached, discrete nature of atoms cannot be neglected and other methods should be developed. it should be noted that other approaches have similitude with the tcd [31] and therefore have an excellent potential to be applied at small scales considered here. finite fracture mechanics (ffm) [32], for example, shares several aspects with the tcd and its consideration is left as future work. figure 4: tem image of (a) crack propagation of specimen 2 and (b) fracture mode displacements at the onset of nanocrack. beyond the breakdown of the continuum theory his contribution has shown that some continuum theories could be directly extended to micro and nanoscales until their low limit is reached but it does beg the question of how to approach lower scales, where the discrete nature of atoms must be considered. as is shown before, experimental testing is very challenging at the microscale, becomes tough at nanometer-scale and extremely tough at lower scales. however, atomic simulations have developed considerably in the last decade supported by the advancement of computing power and numerical techniques. these simulations, based on interatomic potentials, have drawn considerable attention in the scientific community because of their versatility in the reproduction of qualitative phenomena and are nowadays a reliable tool. when approaching atomic scale and in general beyond the breakdown of continuum theory, the validity and definitions of usual macromechanics parameters (e.g., stress, strain, elastic constant) should be reconsidered. approaches based on energy, instead, seem to be very versatile and their concepts showed to be easily extensible and valid at the atomic level. if one considers the brittle fracture of silicon, the griffith criterion, energy release rate (err) and others have been reformulated successfully to take into account the atomic structure and validated by using atomic simulations [9,15,33]. as a straightforward extension of the continuum concepts, for example, err has been reformulated based on atomic potential energy [34], showing to be more general than continuum counterpart and valid regardless of considered scales. a similar idea is under development by the present authors by considering the strain energy density and preliminary results should be soon available. the silicon, however, is relatively easy to be treated because of its intrinsic “ideal” brittle behavior: the fracture process does not involve dislocations but develops clearly by atomic bond breaking along the cleavage plane. in the fracture nanomechanics, fracture of silicon represents the most fundamental and straightforward research target. challenges toward nanometer scale fracture mechanics rapidly increase when plastic phenomena (e.g., emission of dislocation [35]) and more complex load conditions (e.g., mode ii, mode iii, mixed mode) have to be considered. ultimately, the definition of these primary mechanisms will depend on the realization of atomic-level fracture mechanics experiments with in situ observation. this final task will require a total reconsideration and improvement of current experimental equipment and techniques. the investigation of atomic fracture mechanics might bring great advancements not only in several academic fields (e.g., multi-physics) but also in industrial miniaturization of future electronic devices. conclusions his contribution has presented a synthesis of some recent micromechanical tests aimed at the evaluation of the fracture toughness of silicon by using pre-cracked nano specimens and alternatively notched nano specimens combined with the theory of critical distances (tcd). t t propagation δ c/2 δ c/2 crack tip (a) (b) [011] [011] [100] . p. gallo et alii, frattura ed integrità strutturale, 47 (2019) 408-415; doi: 10.3221/igf-esis.47.31 414 the results can be summarized as follows:  the fracture toughness of silicon is 1 mpa·m0.5 and is independent of the size and crystal orientation;  while accurate control of the geometry in the specimen fabrication is challenging, small crack tip radius has a relevant influence on the fracture toughness value when pre-cracked samples are employed;  the tcd simplifies the experimental procedure for the evaluation of the fracture toughness by employing notched specimens instead of pre-cracked samples;  the crack propagation at this small scale, where ideally there is no defect, is due to the breaking of atomic bonds along the cleavage plane;  the tcd also yields a good approximation of the magnitude of the fracture process zone, defined as the zone near the crack tip or notch root where the discrete motion of atoms is highly concentrated;  the results obtained here agree with those reported in the literature that define the breakdown of continuum fracture mechanics when the k-dominant region critical size is in the range of 3 to 6 times the fracture process zone. acknowledgments ideos of experiments are available in the visual abstract. the authors are grateful to the japan society for the promotion of science (jsps) for supporting the present research (grant-in-aid for jsps fellows no. 16f16366, p16366). references [1] liebowitz, h. (1968). fracture, new york, academic press. [2] kitamura, t., sumigawa, t., hirakata, h., shimada, t. (2016). fracture nanomechanics, singapore, pan stanford publishing. [3] wilson, d., zheng, z., dunne, f.p.e. (2018). a microstructure-sensitive driving force for crack growth, j. mech. phys. solids. doi: 10.1016/j.jmps.2018.07.005. [4] mosby, m., matouš, k. (2016). computational homogenization at extreme scales, extrem. mech. lett., 6, pp. 68–74. doi: 10.1016/j.eml.2015.12.009. [5] shimada, t., kitamura, t. (2015). fracture mechanics at atomic scales. in: altenbach, h., matsuda, t., okumura, d., (eds.), advanced structured materials, 64, pp. 379–396. [6] sato, k., yoshioka, t., ando, t., shikida, m., kawabata, t. (1998). tensile testing of silicon film having different crystallographic orientations carried out on a silicon chip, sensors actuators a phys., 70(1–2), pp. 148–152. doi: 10.1016/s0924-4247(98)00125-3. [7] yi, t., li, l., kim, c.-j. (2000). microscale material testing of single crystalline silicon: process effects on surface morphology and tensile strength, sensors actuators a phys., 83(1–3), pp. 172–178. doi: 10.1016/s0924-4247(00)00350-2. [8] gallo, p., sumigawa, t., kitamura, t., berto, f. (2016). evaluation of the strain energy density control volume for a nanoscale singular stress field, fatigue fract. eng. mater. struct., 39(12), pp. 1557–1564. doi: 10.1111/ffe.12468. [9] shimada, t., ouchi, k., chihara, y., kitamura, t. (2015). breakdown of continuum fracture mechanics at the nanoscale, sci. rep., 5(1), pp. 8596. doi: 10.1038/srep08596. [10] sumigawa, t., ashida, s., tanaka, s., sanada, k., kitamura, t. (2015). fracture toughness of silicon in nanometerscale singular stress field, eng. fract. mech., 150, pp. 161–167. doi: 10.1016/j.engfracmech.2015.05.054. [11] gallo, p., yan, y., sumigawa, t., kitamura, t. (2018). fracture behavior of nanoscale notched silicon beams investigated by the theory of critical distances, adv. theory simulations, 1(1), pp. 1700006. doi: 10.1002/adts.201700006. [12] yasutake, k., iwata, m., yoshii, k., umeno, m., kawabe, h. (1986). crack healing and fracture strength of silicon crystals, j. mater. sci., 21(6), pp. 2185–2192. doi: 10.1007/bf00547968. [13] wong, b. (1987). microindentation for fracture and stress-corrosion cracking studies in single-crystal silicon, j. electrochem. soc., 134(9), pp. 2254. doi: 10.1149/1.2100861. [14] dukino, r.d., swain, m. v. (1992). comparative measurement of indentation fracture toughness with berkovich v p. gallo et alii, frattura ed integrità strutturale, 47 (2019) 408-415; doi: 10.3221/igf-esis.47.31 415 and vickers indenters, j. am. ceram. soc., 75(12), pp. 3299–3304. doi: 10.1111/j.1151-2916.1992.tb04425.x. [15] sumigawa, t., shimada, t., tanaka, s., unno, h., ozaki, n., ashida, s., kitamura, t. (2017). griffith criterion for nanoscale stress singularity in brittle silicon, acs nano, 11(6), pp. 6271–6276. doi: 10.1021/acsnano.7b02493. [16] ando, t., li, x., nakao, s., kasai, t., tanaka, h., shikida, m., sato, k. (2005). fracture toughness measurement of thin-film silicon, fatigue fract. eng. mater. struct., 28(8), pp. 687–694. doi: 10.1111/j.1460-2695.2005.00920.x. [17] li, x., kasai, t., nakao, s., tanaka, h., ando, t., shikida, m., sato, k. (2005). measurement for fracture toughness of single crystal silicon film with tensile test, sensors actuators, a phys., 119(1), pp. 229–235. doi: 10.1016/j.sna.2003.10.063. [18] neuber, h. (1958). theory of notch stresses: principles for exact calculation of strength with reference to structural form and material, berlin, springer verlag. [19] peterson, r.e. (1959).notch sensitivity. in: sines, g., waisman, j.l., (eds.), metal fatigue, new yorl, mcgraw-hill, pp. 293–306. [20] taylor, d. (2007). the theory of critical distances: a new perspective in fracture mechanics, oxford. [21] susmel, l. (2008). the theory of critical distances: a review of its applications in fatigue, eng. fract. mech., 75(7), pp. 1706–1724. doi: 10.1016/j.engfracmech.2006.12.004. [22] susmel, l., taylor, d. (2008). on the use of the theory of critical distances to predict static failures in ductile metallic materials containing different geometrical features, eng. fract. mech., 75(15), pp. 4410–4421. doi: 10.1016/j.engfracmech.2008.04.018. [23] susmel, l., taylor, d. (2010). the theory of critical distances as an alternative experimental strategy for the determination of kic and δkth, eng. fract. mech., 77(9), pp. 1492–1501. doi: 10.1016/j.engfracmech.2010.04.016. [24] taylor, d. (2008). the theory of critical distances, eng. fract. mech., 75(7), pp. 1696–1705. doi: 10.1016/j.engfracmech.2007.04.007. [25] gallo, p., sumigawa, t., kitamura, t., berto, f. (2018). static assessment of nanoscale notched silicon beams using the averaged strain energy density method, theor. appl. fract. mech., 95, pp. 261–269. doi: 10.1016/j.tafmec.2018.03.007. [26] bažant, z.p. (2005). scaling of structural strength, elsevier. [27] bažant, z.p. (1999). size effect on structural strength: a review, arch. appl. mech., ingenieur arch., 69(9–10), pp. 703–725. doi: 10.1007/s004190050252. [28] kamigaito, o. (1988). ideal fracture stress of brittle material having no defect, j. mater. sci. lett., 7(5), pp. 529–531. doi: 10.1007/bf01730717. [29] pugno, n.m., ruoff, r.s. (2004). quantized fracture mechanics, philos. mag., 84(27), pp. 2829–2845. doi: 10.1080/14786430412331280382. [30] taylor, d. (2017). the theory of critical distances: a link to micromechanisms, theor. appl. fract. mech., 90, pp. 228–233. doi: 10.1016/j.tafmec.2017.05.018. [31] campagnolo, a., berto, f. (2017). some recent criteria for brittle fracture assessment under mode ii loading, eng. solid mech., pp. 31–38. doi: 10.5267/j.esm.2016.10.002. [32] carpinteri, a., cornetti, p., pugno, n., sapora, a., taylor, d. (2008). a finite fracture mechanics approach to structures with sharp v-notches, eng. fract. mech., 75(7), pp. 1736–1752. doi: 10.1016/j.engfracmech.2007.04.010. [33] huang, k., shimada, t., ozaki, n., hagiwara, y., sumigawa, t., guo, l., kitamura, t. (2017). a unified and universal griffith-based criterion for brittle fracture, int. j. solids struct., 128, pp. 67–72. doi: 10.1016/j.ijsolstr.2017.08.018. [34] kitamura, t., sumigawa, t., shimada, t., lich, l. van. (2018). challenge toward nanometer scale fracture mechanics, eng. fract. mech., 187, pp. 33–44. doi: 10.1016/j.engfracmech.2017.10.009. [35] rice, j.r. 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/hrv (za stvaranje adobe pdf dokumenata najpogodnijih za visokokvalitetni ispis prije tiskanja koristite ove postavke. stvoreni pdf dokumenti mogu se otvoriti acrobat i adobe reader 5.0 i kasnijim verzijama.) /hun 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/pdfxoutputintentprofileselector /documentcmyk /preserveediting true /untaggedcmykhandling /leaveuntagged /untaggedrgbhandling /usedocumentprofile /usedocumentbleed false >> ] >> setdistillerparams << /hwresolution [2400 2400] /pagesize [612.000 792.000] >> setpagedevice microsoft word numero_49_art_67_2516 a. en-najiet alii, frattura ed integrità strutturale, 49 (2019) 748-762; doi: 10.3221/igf-esis.49.67 748 prediction of thermomechanical behavior of acrylonitrile butadiene styrene using a newly developed nonlinear damage-reliability model a. en-naji laboratory of control and mechanical characterization of materials and structures, national higher school of electricity and mechanics, bp 8118 oasis, hassan ii university, casablanca, morocco abdenaji14@gmail.com , arrahma78@yahoo.fr n. mouhib laboratory of control and mechanical characterization of materials and structures, national higher school of electricity and mechanics, bp 8118 oasis, hassan ii university, casablanca, morocco higher institute of maritime studies isem, casablanca, morocco h. farid laboratoire de nanotechnologie et bioplasturgie, université du québec en abitibitémiscamingue uqat, boulevard de l'université, rouyn-noranda, québec j9x 5e4, canada m. el ghorba laboratory of control and mechanical characterization of materials and structures, national higher school of electricity and mechanics, bp 8118 oasis, hassan ii university, casablanca, morocco abstract.the aim of this work was to evaluate the influence of temperature on the mechanical behavior of an amorphous polymer, namely acrylonitrile butadiene styrene (abs), based on a series of uniaxial tensile tests on smooth specimens at different temperatures. the results demonstrate that the behavior of the polymers is strongly dependent on the temperature. its influence on the physical characteristics during the study of polymer behaviors cannot be denied, particularly when the processes of shaping are investigated, which require significant contributions of heat and mechanical effort. for this reason, this study consists of predicting the evolution of abs damage in two main zones. the first is the industrial zone, in which the configuration of macromolecular chains is largely immobile, and the temperature is below the glass temperature (tg = 110°c). in this zone, a damage model based on the obtained experimental results allowed us to determine three stages of damage evolution, and then to specify the critical fraction of life, at which the material becomes unstable and defective, for the purpose of predictive maintenance. the second zone is that of thermoforming, in which the temperature is above the glass temperature, tg. in this zone, the macromolecular chains tend to citation: en-naji, a., mouhib, n., farid, h., elghorba, m., prediction of thermomechanical behavior of acrylonitrile butadiene styrene using a newly developed nonlinear damage-reliability model, 49 (2019) 748-762. received: 08.05.2019 accepted: 17.05.2019 published: 01.07.2019 copyright: © 2019 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. http://www.gruppofrattura.it/va/49/2516.mp4 a. en-najiet alii, frattura ed integrità strutturale, 49 (2019) 748-762; doi: 10.3221/igf-esis.49.67 749 move more freely as the temperature increases. the same damage model was adopted to follow the flow process according to the fraction of life that represents the critical material parameter. this study also includes a comparison between the static (experimental) damage models and unified theory (theoretical) damage models. keywords. abs; damage; flow; stress; reliability; temperature; thermomechanical behavior; tensile testing. introduction he prediction and evaluation of material thermomechanical behavior have long been serious concerns. thus, numerous models have been developed in to quantify the damage caused by steel materials, with reference to either linear or nonlinear models. miner (1944) was the first author to formulate a fatigue damage law mathematically, and its linear formulation of the damage as a function of the fraction of the total work absorbed by the material made it a simple and obvious law to use. other authors, including quoc et al. (1971), proposed modeling of the damage depending on the loading conditions, stress level, and material characteristics. the models of henry (1955), lemaitre and chaboche (1979), and gatt (1961) can also be cited as representative damage models. zgoul and habali (2008) applied these different theories to steel materials and their alloys. to adapt these theories to polymer materials, we applied these to anacrylonitrile butadiene styrene (abs) thermoplastic polymer. a substantial amount of research has been conducted on this material to quantify its mechanical behavior. gonzalo et al (2015) evaluated the effect of the ultrasonic fatigue endurance of polymeric material abs, and the general mechanisms of crack initiation and propagation, when specimens were tested by being immersed in water and oil, to limit the temperature increase induced by the high mechanical vibration of ultrasonic fatigue testing. joseph et al. studied the effects of the toxicity of abs combustion products. bohatka et al (1995) evaluated the damage formation differences during fatigue crack propagation in abs polymer, using tests both fulfilling and not fulfilling the linear elastic fracture mechanics requirements, which related to differences in the crack propagation behavior through the crack layer. boldizar et al. (2003) studied the degradation of abs during repeated treatments and accelerated aging, whereby the abs material was subjected to a series of six combined cycles of extrusion and air aging as well as high temperatures, and observed changes in the tensile and flow properties. from the second to the sixth cycle, the elongation at break decreased considerably owing to aging, while it increased as a result of the extrusion step. shen et al. (1966) and merah et al. (2003) studied the temperature and weld-line effects on the mechanical properties of chlorinated pvc(cpvc).they investigated the effects of temperatures ranging from -10 to 70°c and injectionmolded weld lines on the mechanical properties of cpvc used in pipe fittings. in their studies, they demonstrated that brittle fracture occurred at temperatures below room temperature, while ductile failure occurred at temperatures above 23°c. at temperatures below 50°c, the fracture stress increased in small amounts. a significant increase in the fracture deformity occurred between 50 and 70°c. plastic deformation at these high temperatures was accompanied by considerable shrinkage. our work is based on thermomechanical characterization of the material. several series of tests were carried out in a temperature range of 25 to 170°c, passing through the glass transition temperature (tg) close to 110°c. for each temperature value, the curves relating to the thermomechanical characteristics such as the stress, elastic modulus, and elongation were plotted to identify the measurements in question for analyzing the material thermomechanical behavior. thereafter, an extensive analysis of the damage was performed using static damage-reliability modeling. the results of comparing the damage of three parameters, namely the ultimate stress, elastic modulus, and elongation, according to the fraction of life, allowed us to predict the thermomechanical behavior of this polymer in the industrial and thermoforming zones. material and experimental methods he material used in this work was abs, which is an amorphous polymer produced by emulsification or bulk polymerization of acrylonitrile and styrene in the presence of polybutadiene. t t a. en-najiet alii, frattura ed integrità strutturale, 49 (2019) 748-762; doi: 10.3221/igf-esis.49.67 750 the tensile specimens, illustrated in fig.1, were prepared according to the astm standard d638-03 [14] method of tests for the tensile properties of plastics. figure 1: dimensions of specimens according to astm d638-03[14]. symbol description size (mm) l0 total lengh 75 d initial distance between jaws 42 l lengh of the calibrated part 25 g lenth between landmarks 20 w with of the calibrated 4 r small radius of curvature 8 w0 widths at the ends 14 b thikness 2 table 1: the dimensions of dumbbell specimen for tensile test. fig.2 illustrates the evolution of the stress applied to the specimens (mpa) as a function of the deformation, ℇ(%). the general appearance of this curve exhibits ductile behavior. figure 2: tensile stress-deformation curvedumbbell specimen. it can be observed from fig. 2 that the curve includes four zones, each of which reveals a particular mechanical behavior of the material (abs) during the tensile test. zone 1 (linear): this is the reversible elastic deformation of the material owing to the amorphous phase. a. en-najiet alii, frattura ed integrità strutturale, 49 (2019) 748-762; doi: 10.3221/igf-esis.49.67 751 zone 2: the force decreases, indicating the beginning of the constriction, which corresponds to heterogeneous deformation of the material. zone 3: the constriction zone increases along the specimen until stabilization. zone4: the stretching force increases, and the deformation again becomes homogeneous owing to the structural hardening linked to the orientation of the macromolecular chains in the stretching direction; the material febrile fraction increases until rupture. the results presented in fig. 2 enabled us to determine the mechanical properties of the studied material. these properties include the elastic limit, elasticity modulus, and breaking stress, which are provided in tab. 2. young’s modulus poisson’s ratio elastic limit ultimate stress e=2.08gpa 0.3  e =32mpa u = 37.63 mpa table 2: characteristics of abs material. the mechanical properties of polymers are strongly dependent on the temperature. for this reason, the tensile test was carried out under different temperature conditions (elevated temperature tensile testing). the thermal enclosure required for this purpose was controlled by testxpert ii. the enclosure had a temperature range of -80 to +250°c (fig. 3). * figure 3: thermal enclosure assembly with tensile test machine. polymers exhibit very precise temperature possibilities for the movements of radicals or pieces of molecular chains; that is, the polymer mechanical behavior will be affected (fig. 4). figure 4: test specimens subjected to tensile tests as function of temperature. a. en-najiet alii, frattura ed integrità strutturale, 49 (2019) 748-762; doi: 10.3221/igf-esis.49.67 752 results and discussion temperature effect on mechanical behavior for abs o take into account the influence of the temperature on the abs mechanical properties, several series of tests were carried out on dumbbell specimens in a temperature range from 25°c (laboratory temperature) to 170°c, through the glass transition temperature tg = 110°c. the variations in the ultimate stress, elastic modulus, and elongation according to the temperature are presented in figs. 5, 6, and 7, respectively. several features of these figures are worth noting: for example, increasing the temperature produces a decrease in the elastic modulus, a reduction in the tensile strength, and an enhancement in the elongation. figure 5: loss of ultimate stress according to temperature. figure 6: loss of young's modulus according to temperature. we can observe the existence of two zones: zone i corresponds to a temperature that lies between the laboratory temperature ta = 25°c and glass transition temperature tg = 110°c. corresponding to a rigid (glass) state, the molecules of the amorphous part are deformed (industrial zone). zone ii is above the glass temperature and corresponds to a transition state in which chain movements become possible, allowing for greater and easier deformations. the mechanical properties t a. en-najiet alii, frattura ed integrità strutturale, 49 (2019) 748-762; doi: 10.3221/igf-esis.49.67 753 decrease in this phase; that is, that the mechanical behavior of the polymers is affected. this is a non-industrial zone (which could be exhibited as a thermoforming zone). furthermore, figs. 5 and 6 indicate a sudden decrease in both the ultimate stress and young's modulus with an increase in temperature, which accelerates once the tg range is exceeded. however, fig. 7 illustrates a pseudo-linear variation in the elongation as a function of the temperature, for temperatures below tg, while the evolution retains a slight slope with an elongation above 10%. when approaching tg, the elongation values increase more significantly to the melting zone; in this case, we refer to rubbery behavior, which corresponds to a flow owing to the disentanglement of macromolecular chains [15]. figure 7: evolution of the elongation modulus according to the temperature. thermomechanical behavior of abs material in the industrial zone (25°c to 110 °c)  adimensional loss of mechanical properties by fraction of life in order to normalize the values of the ultimate stress, young's modulus, and elongation, the ratio xur/xu was examined as a function of the fraction of life [16]. xur: either residual ultimate stress(ur), residual ultimate young's modulus (eur) or residual ultimate elongation (lur) xu: either ultimate stress (u), ultimate young's modulus (eu) or ultimate elongation (lu) the fraction of life β is expressed for the curves of the stress and young's modulus, as follows[16]: ti ta β tg ta    (1) where: ta : ambient temperature ; ti : instantaneous temperature ; and tg : glass temperature however, we observe that the elongation increases gradually with an increase in the temperature, for which we used the fraction of life[16] ti ta β 1 tg ta      (2) the results of the adimensional loss of the three studied mechanical properties xur/xu by the fraction of life are presented in fig.8. firstly, we can observe that the curves of the stress and young's modulus of the abs decrease as the fraction of life increases: virgin abs at room temperature (from 25°c) has an ultimate stress of 32 mpa and a young’s modulus of 2000 mpa (σur/σu = eur/eu = 1). these adimensional ratios decrease remarkably as a function of the fraction of life β, until the same value a. en-najiet alii, frattura ed integrità strutturale, 49 (2019) 748-762; doi: 10.3221/igf-esis.49.67 754 of 0.5 is obtained for a fraction of life equal to 1, which has a critical material temperature, beyond which the material exhibits no significant resistance. the shape of the curves in the interval β =0 to 0.4 with t = 44°cappears to indicate that the molecular chains are deformed: at very low relative evolution of the mobility of the molecular chains, the material mechanical behavior resembles that of fragile material. the increase in temperature may particularly increase the mobility and deformation of the molecular chains in the polymer to subsequently generate β> 0.4, a plasticizing phase that is more decisive for the loading amplitude. this general pattern of the deterioration of the polymers under the temperature effect makes it possible to explain the faster failure rate of the test specimens. however, the shape of the elongation curve in the interval β’ =0 to 0.5 indicates that the increase in temperature exhibits an evolutionary effect of the microcracking manifested in the abs material. figure 8: adimensional loss of abs mechanical properties.  comparison between theoretical and experimental adimensional loss of mechanical properties by means of analogy with the modified bui quoc law (1971)[17] and bathias (2013), a mathematical expression describing the rate of adimensional loss of the mechanical properties as a function of the fraction of life was exploited to provide a benchmark for comparison between the present theory and experimental results. the loss rate is represented by the following mathematical expression[17]: 1 1 1 1 m ur u m u x x                              (3) in which xur: either residual ultimate stress (ur), residual young's modulus (eur) or residual elongation (lur); xu:eitherultimate stress (u), ultimateyoung'smodulus (eu) or ultimateelongation (lu) ; γu :  either  non-dimensional stress ( σu )  σa , non-dimensional young’s modulus ( a eu e   ), or non-dimensional elongation (lu/la) ; γ :   instantaneous non-dimensional endurance limit : either σur   σa , a eur e   or(lur/la) ; a. en-najiet alii, frattura ed integrità strutturale, 49 (2019) 748-762; doi: 10.3221/igf-esis.49.67 755 σu, eu : endurance limit of the virgin material and lu: value of the elongation modulus at critical temperature; σur, eur, lur :residual ultimate stress, young’s modulus, and residual elongation of material at different temperatures; σa, ea: values of stress and young's modulus directly before rupture; and m: a material parameter, with m = 1 for amorphous polymers, according to [18]. graphical representations of the theoretical adimensional loss of the mechanical properties compared to the experimental loss are presented in fig. 9 below. figure 9: theoretical and experimental adimensional loss of mechanical properties ibe observed from the comparison in fig. 9 that the increase in temperature induces a greater reduction in both the theoretical and experimental residual stress and elastic modulus, and an evolution of the abs elongation. moreover, it is observed that the theoretical curves are situated slightly above the experimental curves. for a low β value (β < 0.2), the theoretical curves agree with the experimental curves. for a mean β (0.2 < β < 0.7), the experimental curves tend to overestimate the resistance loss. however, this tendency is reversed for a value close to 1, and the theoretical points are slightly lower than the experimental ones. consequently, the results demonstrate that the deviation between the theoretical and experimental curves is more or less remarkable at the beginning of the damage, following which the deviation narrows and the curves decrease proportionally in value directly before the break. it can be concluded that the modified bui quoc model accurately describes the loss of the adimensional mechanical properties of the abs material and can be used in the case of static loading coupled with temperature variations.  quantification of damage damage is a physical phenomenon [19] that can be determined quantitatively and qualitatively by measuring certain physical properties, particularly mechanical properties such as the yield stress, resistance to rupture, young's modulus, and elongation modulus. the static damage model consists of determining the evolution of the thermomechanical characteristics of the abs material as a function of the fraction of life. the static damage (d), based on variations in the stress, young's modulus, and elongation, was developed to predict the damage evolution and impact of artificial pre-loading, which is represented by the temperature variation. during the test, we observed the phenomenon of damage between the virgin state at an ambient temperature until the state of the test piece at a glass temperature of 110°c, by measuring the abs mechanical properties for each temperature variation. the static damage model d is represented in eqn. (4) [20-23]: 1 1 xur xud xa xu    (4) a. en-najiet alii, frattura ed integrità strutturale, 49 (2019) 748-762; doi: 10.3221/igf-esis.49.67 756 with: xur: either residual ultimate stress (ur), residual ultimate young's modulus (eur) or residual ultimate elongation (lur); xu: either ultimate stress (u), ultimate young's modulus (eu) or ultimate elongation (lu); and xa:either stress (a), young's modulus (ea) or elongation (la) of the material directly before the end of its life. figure 10: evolution of the static damage depending on life of fraction fig. 10 illustrates the evolution of the normalized experimental damage as a function of the fraction of life β, using one of the studied mechanical properties each time. the damage process is schematized by a concave curve, which means that the damage accelerates towards the end of the material life at d = 1. the increase in damage means an increase in the elongation, and a decrease in the stress and elastic modulus in the static tensile tests of the abs specimens. this is damage with appreciable irreversible deformations, which reduces the material ultimate strength. the damage briefly increases from zero (laboratory temperature) to its critical glass temperature. the damage shape and level at the end of the material life (d = 1, β = 1) provide this experimental damage model with certain credibility, which is consistent with the literature in an equivalent study on metals. having determined the normalized damage, we have an experimental reference necessary for the validation of theoretical models or other measurement approaches for experimental damage. it is remarkably interesting to be able to correlate the damage process to the three stages of damage. by observing the damage curves represented by the stress and young’s modulus, we can note the following characteristics: at the initiation of the damage, namely the end of the stage ι, in which the fraction of life β = 30%, the damage increases in a concave and slow manner. in the progressive zone, namely stage π, which is in the interval of β= [30%, 75%], the damage progressively evolves to 0.8. at the moment of sudden propagation (stage ш), in which the fraction of life β> 75% for d = 0.8, the damage accelerates considerably. the purple appearance illustrates the evolution of the static damage of the elongation as a function of the fraction of life (β’= 1-β). although the damage scenario has been established as the measure of the residual elongation, we also distinguish three stages:  stage 1: the damage evolves linearly between 0 and 0.3 for fractions of life β’ < 0.36.  stage 2: the damage increases gradually from 0.3 to 0.5 for fractions of life 0.3 <β’ < 0.7, and the temperature effect appears clearly as the temperature increases, while the damage within the material evolves significantly.  stage 3: for β’> 0.7 the damage accelerates rapidly until rupture.  relationship betweenstatic damage and static reliability when a system is in service under static stress, its physical properties undergo progressive degradation. it is often necessary to reduce the probability of sudden failure. consequently, reliability assessment becomes indispensable in any study of the a. en-najiet alii, frattura ed integrità strutturale, 49 (2019) 748-762; doi: 10.3221/igf-esis.49.67 757 mechanical behavior of the components. in this section, we present a reliability study to reduce the probability of sudden failure. the reliability r is a statistical parameter, which follows the evolution of the material deterioration. the relationship between these two parameters can be expressed as follows: r (β) + d (β) = 1 (5) [21]. using eqn. (5) to plot the different reliability curves corresponding to the various parameters studied, the following figures illustrate the variations in the reliability and damage as a function of the fraction of life in the industrial zone. we note that the damage always evolves in the opposite direction to the reliability as the temperature increases. figure 11: evolution of damageand reliability as function of fraction of life . the present work provides the opportunity to discuss the mechanical behavior of a well-known polymer that is extensively used in industrial areas; specifically, in the manufacture of cars. to facilitate quality control without the need for an expensive dynamic test, we conducted a study to compare the mechanical characteristics with the aid of elevated temperature tensile testing. the analysis of the static and thermic tests allowed us to evaluate the negative effects of the increase in temperature on the abs mechanical behavior more significantly. indeed, the curves in fig. 11illustrate that the stress and young's modulus parameters exhibit comparable damage, regardless of the fraction of life. to overcome the challenges of dynamic tests, we modified the unified theory controlled by elongation, to consider a new parameter relating to the mobility of molecules and the constriction of material. although the results obtained from the three parameters are in harmony, the use of elongation remains less precise and exhibits a phase shift compared to the other parameters (young's modulus and stress). thermomechanical behavior of abs material in thermoforming zone (non-industrial zone, t>tg) the degradation of the mechanical properties is always remarkable. the elastic stress, ultimate stress, tensile strength, and elasticity decrease more significantly as the temperature increases, and the material begins to deform permanently. the intrinsic softening zone corresponds to the beginning of the nonlinear distortion (this softening of the plastic flow threshold is mainly owing to the change in the material microscopic structure), and this deformation continues with a remarkable increase in temperature. thereafter, it falls towards the point at which it stabilizes and remains constant with an increasing elongation. the plastic deformation is owing to the material rubbery state, and this deformation is localized on the section of the sample in a region known as the curing zone. the rubbery state is a result of the amorphous phase, and exists in practically all polymers; it generally begins around the glass transition temperature and is limited by the melting temperature or thermal decomposition temperature. in the amorphous phase, the molecular organization is constantly changed by displacement of the molecules, owing to thermal activation or the applied stress (constraint). this state change with respect to the vitreous state described above is accompanied by rupturing of certain weak bonds (van der waals) between molecules by means of thermal agitation, and a significant increase in the polymer volume. this results in greater ease of movement of the molecules, so that the very low molecular mobility in the vitreous state increases with an increasing temperature. a. en-najiet alii, frattura ed integrità strutturale, 49 (2019) 748-762; doi: 10.3221/igf-esis.49.67 758 as mentioned previously, the rubbery state is owing to the amorphous phase; it is a consequence of the molecular mobility, which allows the chains to be unfolded in the direction of the applied stress, thereby causing deformation. when this constraint is released, it returns to the initial state. a higher cross-linking ratio results in a greater length of the chains between two cross-linking nodes. however, if the nodes of the cross-links are removed, the memory of the initial state disappears, as well as the reversibility of the deformation. in the following, similar to the damage study in the industrial zone, the flow evolution in the thermoforming zone is reported using the same three parameters. in this zone, we define the fraction of life θ for the curves of the stress and young's modulus, as follows [16]: ti tg θ                     tc tg    (6) where: tg :glass temperature; tc :critical temperature; and ti :instantaneous temperature. moreover, for elongation, we use the following expression for the determination of the fraction of life [16]: ti tg θ' 1    tc tg     (7)  adimensional loss of mechanical properties by fraction of life the variation in the abs mechanical properties as a function of the fraction of life is illustrated in fig.12. figure 12: adimensional loss of abs mechanical properties in non-industrial zone. the loss of the adimensional stress and young's modulus increases with the temperature and becomes increasingly important when approaching the thermoforming temperature. however, we note evolution of the adimensional elongation, which appea to indicate that the molecular chains are deformed, and the mechanical behavior of the material resembles that of caotechoutic material. the comparison between the theoretical model (previously defined by eqn. (3)) and experimental results, illustrated in fig. 13exhibits strong agreement, which allows us to confirm the effectiveness of the model used in our study for the mechanical behavior of abs material. a. en-najiet alii, frattura ed integrità strutturale, 49 (2019) 748-762; doi: 10.3221/igf-esis.49.67 759 figure 13: theoretical and experimental adimensional losses of mechanical properties in non-industrial zone.  quantification of static flow as the study in this case is focused on the non-industrial zone, in which the temperature exceeds that of glass temperature, we no longer refer to the damage, but rather the flow. the static flow based on changes in the abs mechanical properties was developed to predict the evolution of the hightemperature polymer (t>tg). the static flow model is presented in eqn. (8), [20]. x ur 1 x uf             x a 1 x g        (8) where: x'ur :either residual ultimate stress (’ur), residual ultimate young's modulus (e’ur) or residual ultimate elongation (l’ur); x’u :either ultimate stress (’u), ultimate young's modulus (e’u) or ultimate elongation (l’u); and x’a:either stress (’a), young's modulus (e’a) or elongation (l’a) of the material directly before the end of its life. fig.14 illustrates the variation in the flow rate as a function of the fraction of life in the non-industrial zone. figure 14: evolution of flow as function of fraction of life β’ in thermoforming zone a. en-najiet alii, frattura ed integrità strutturale, 49 (2019) 748-762; doi: 10.3221/igf-esis.49.67 760 the comparison of the abs mechanical properties demonstrates that, for fractions with a short lifetime (0% <θ <30%), the flow calculated using the stress and young's modulus is similar. with an increase of the fraction of life θ, the stress flow curve is less significant compared to that calculated by the young's modulus. thereafter, it exceeds the stress curve and it is overlapped with the elongation curve at the end of the lifetime θ’. by observing the flow curves represented by the stress and young's modulus, we can note the following characteristics:  from the beginning of the flow to the end of stage ι, in which the fraction of life is approximately θ’= 30%, the flow increases linearly and slowly.  in the progressive flow zone, namely stage π, which is in the interval of θ’ =[30%, 85%], the flow increases concisely and progressively.  at the end of the lifetime (stage ш), in which the fraction of life θ’> 85%, the flow accelerates very clearly until the break.  relationship between static flow and static reliability the reliability varies inversely with the damage (in this case, the flow) [24]. intuitively, a relationship must exist between these two parameters. this allows us to write: rs (θ) + f (θ) = 1 the resulting equation allows us to plot the variation in the reliability. a decrease in the reliability means a loss of the material mechanical properties, and this loss evolves as the temperature becomes more important. the advantage of determining the reliability lies in the fact that it makes it possible to establish the critical damage in particular. indeed, this information is crucial for preventive maintenance, in order to intervene in a timely manner and change the damaged part. figure 15: evolution of flow with respect to reliability as function of fraction of life calculated using material parameters fig. 15 distinctly represents the evolution of the flow reliability as a function of fraction of life for each mechanical property parameter. regardless of the parameter used, the flow gradually increases from 0 (vitreous temperature material) to its critical value of 1. in fact, the increase in temperature induces a greater decrease in the abs mechanical characteristics. this confirms the ability of this tensile mechanical characteristic to follow the degradation evolution reliably owing to the temperature increase. the paces calculated using the stress and elasticity modulus are similar they intersect at 50% reliability, with a relative difference for the fraction of life in the order of 10%.the two models proposed in this study provide an overview of the flow condition and tend to overestimate the material loss. however, the flow reliability calculated by the elongation model does not describe the material state correctly, as there is no sophisticated means for exact determination of the elongation. we can conclude that the two models (stress and elasticity modulus) describe the loss of the studied material quite correctly: as the specimen temperature increases, its stability decreases and it becomes uncontrollable. a. en-najiet alii, frattura ed integrità strutturale, 49 (2019) 748-762; doi: 10.3221/igf-esis.49.67 761 conclusion and outlook he objective of this work was to characterize the thermal and mechanical behavior of a thermoplastic flat sheet. the elevated temperature tensile test was considered as the most practical and accurate approach for the actual deformation state during loading, and this technique was used to describe the damage to the various thermomechanical characteristics: resistance, elasticity modulus, and elongation. a comparison of the abs mechanical characteristics enabled us to determine the performance of this material by exposing it to a tensile test coupled with temperature until the material was damaged. the evolution of the different parameters obtained allowed us to compare the temperature effects on the abs mechanical behavior. thereafter, we confirmed the ductile behavior of these, and we focused on comparing and processing the obtained curves. the increase in temperature demonstrated the critical impact on the material parameters and failure time. indeed, the proposed approach consists of analyzing the evolution of the global geometry of the curves by considering the zones and characteristic points of these curves, and also takes into account the temperature effect, following the damage evolution by means of a static model. two main zones were distinguished: the industrial zone, in which the configuration of the macromolecular chains was largely immobile and the temperature was below the glass temperature tg = 110°c; and the thermoforming zone, in which the temperature was above the glass temperature tg = 110°c. the macromolecular chains then tended to move more freely as the temperature increased, and thereafter the different stages of the process were determined. using the results of this work, we can construct a solid maintenance strategy and make the work with polymers more efficient and simpler. moreover, the simplified approaches proposed allow for clients and industrial companies to evaluate the damage based on static tests alone, without performing dynamic tests. furthermore, these can provide a tool that can aid in conducting rapid and relevant checks for the quality control of this material. finally, these results have demonstrated the feasibility of the applied damage approach. the proposed approach involves the material intrinsic parameters (elasticity modulus, elongation, and temperature), which enables a rigorous description of the material damage conditions. these preliminary studies are essential steps for complete realization of our medium-term objectives for the implementation and development of modeling and simulation tools for thermoplastic forming processes. nomenclature γe=σe/σa: non-dimensional endurance limit γu= σu/σa: parameter reflecting strength of material in virgin state γ=σur/σa: parameter characterizing effect of damage on material mechanical characteristics σu: endurance limit of the virgin material σur: residual ultimate stress of material at different hole diameters σa: applied stress level m: material parameter d: damage (d = 0 for neat material, d = 1 for completely damaged material) β: life fraction for stress and young's modulus in the industrial zone β': life fraction for elongation in the industrial zone. θ: life fraction for stress and young's modulus in the thermoforming zone θ': life fraction for elongation in the thermoforming zone tg: glass transition temperature tf: melting temperature ta: ambient temperature ti: instant temperature references [1] lligadas, g., ronda, j. c., galia, m. (2013). renewable polymeric materials from vegetable oils: a perspective caradiz materials today, 16(9). doi: 10.1016/j.mattod.2013.08.016. t a. en-najiet alii, frattura ed integrità strutturale, 49 (2019) 748-762; doi: 10.3221/igf-esis.49.67 762 [2] christensen, r., (1980). discussion: a nonlinear theory of viscoelasticity for application to elastomers, journal of applied mechanics, 47, pp. 682-683. [3] bui-quoc, t., dubuc, j., bazergui, a., biron, a., (1971). cumulative fatigue damage under stress-controlled conditions, j. basic eng. trans. [4] henry, d. l. (1955). a theory of fatigue damage accumulation in steel, trans. of the asme, 77, pp. 913-918. [5] gatts, r. r., (1961). application of cumulative damage concept to fatigue. asme journal of basic engineering. 83, pp. 529-540. [6] lemaitre, j., chaboche, j.l., (1979), a nonlinear model of creep-fatigue damage cumulation and interaction, national office for aerospace studies and research, pp. 1-30. [7] zgoul, m.h., habali, s.m., (2008). an invistigation into pipes ashot water transporters in domestic and industrial applications, jordan journal of mechanical and industrial engineering, 2, pp. 191 – 200. [8] joseph, v. rutkowski and barbara, c. (1986). acrylonitrile-butadiene-styrene copolymers (abs): pyrolysis and combustion products and their toxicity-a review of the literature; levint us department of commerce, national bureau of standards, national engineering laboratory, center for fire research, gaithersburg, md 20899 [9] domínguez almaraz, g. m. e., correa gómez, j.c., verduzco juárez, j.l., avila ambriz, (2015). crack initiation and propagation on the polymeric material abs (acrylonitrile butadiene styrene), under ultrasonic fatigue testing; avila ambriz university of michoacán (umsnh), santiago tapia no. 403, col. centro, 58000, morelia, michoacán, mexico. [10] bohatka, t. j., moet, a.,(1995). crack layer analysis of fatigue crack propagation in abs polymer ;department of macromolecular science, the case school of engineering, case western reserve university, cleveland, oh 44106, usa, 30(18), pp 4669–4675. [11] boldizar, a., möller, k.,(2003). degradation of abs during repeated processing and accelerated ageing, polymer degradation and stability, 81, pp. 359-366. [12] gibbs, j., (1961). the scientific papers of j. willard gibbs . dover publications, new york. [13] shen, m.c., eisenberg, a.,(1966). glass transitions in polymers, in progress in solid state chemistry, 3, pergamon press. [14] astm d638-03 standard test method for tensile properties of plastics. [15] rault, j., (2002). les polymères solides, amorphes, élastomères, semi-cristallins, propriétés microscopiques et macroscopiques, cépaduéséditions. [16] déformables, the abs data sheet. [17] bathias, c., bailon, j., (1980). the fatigue of materials and structures, pp. 328-330. [18] hicham, f., (2015). behavior and damage of membranes thermoplastics in large deformations. [19] ladeveze, p., (1986). damage mechanics for composite materials, 5ème journées nationales sur les composites, paris. [20] abderrazak, en-naji et al., (2019). change of experimental young’s modulus with increasing temperature for an abs material subjected to tensile test; arpn journal of engineering and applied sciences; 14(3), issn 1819-6608. [21] majid, f., et al., (2018). continuum damage modeling throughtheoretical and experimental pressure limit formulas, frattura ed integrità strutturale, 43, pp. 79-89; doi: 10.3221/igf-esis.43.05 [22] ouardi, a., majid, f. et alii. (2018). residual life prediction of defected polypropylene random copolymer pipes (ppr), frattura ed integrità strutturale, 43, pp. 97-105; doi: 10.3221/igf-esis.43.07. [23] majid, f., elghorba, m. (2016). hdpe pipes failure analysis and damage modeling, doi: 10.1016/j.engfailanal.2016.10.002. [24] chapouille, p. et depazzis, p., (1968). fiabilité des systèmes, editions masson. << /ascii85encodepages false /allowtransparency false /autopositionepsfiles true /autorotatepages /none /binding /left /calgrayprofile (dot gain 20%) /calrgbprofile (srgb iec61966-2.1) /calcmykprofile (u.s. web coated \050swop\051 v2) /srgbprofile (srgb iec61966-2.1) /cannotembedfontpolicy /error /compatibilitylevel 1.4 /compressobjects /tags /compresspages true /convertimagestoindexed true /passthroughjpegimages true /createjobticket false /defaultrenderingintent /default /detectblends true /detectcurves 0.0000 /colorconversionstrategy /cmyk /dothumbnails false /embedallfonts true /embedopentype false /parseiccprofilesincomments true /embedjoboptions true /dscreportinglevel 0 /emitdscwarnings false /endpage -1 /imagememory 1048576 /lockdistillerparams false /maxsubsetpct 100 /optimize true /opm 1 /parsedsccomments true /parsedsccommentsfordocinfo true /preservecopypage true /preservedicmykvalues true 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/hrv (za stvaranje adobe pdf dokumenata najpogodnijih za visokokvalitetni ispis prije tiskanja koristite ove postavke. stvoreni pdf dokumenti mogu se otvoriti acrobat i adobe reader 5.0 i kasnijim verzijama.) /hun 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/pdfxoutputintentprofileselector /documentcmyk /preserveediting true /untaggedcmykhandling /leaveuntagged /untaggedrgbhandling /usedocumentprofile /usedocumentbleed false >> ] >> setdistillerparams << /hwresolution [2400 2400] /pagesize [612.000 792.000] >> setpagedevice microsoft word numero_59_art_16_3213.docx a. houari et alii, frattura ed integrità strutturale, 59 (2022) 212-231; doi: 10.3221/igf-esis.59.16 212 numerical analysis of the elastic-plastic behavior of a tubular structure in fgm under pressure and defect presence a. houari, a.s. bouchikhi department of mechanical engineering, laboratory – lmss. bp 89, sidi bel-abbes, algeria amingenie14@gmail.com, asbouchikhi@yahoo.fr m. mokhtari ecole nationale polytechnique maurice audin, oran 31000, algeria mohamed.mokhtari@enp-oran.dz k. madani department of mechanical laboratory lmpm, sidi bel abbes 22000, alegria koumad10@yahoo.fr abstract. given the field of application and the many advantages, the use of fgm (functionally graded materials) has recently been extended in several components and more particularly in cylindrical structures, which have been the subject of several recent studies. our work aims to use the finite element method to analyze a cylindrical structure in fgm with properties gradated in the direction of the radius (thickness) solicited purely in internal pressure by the implementation of a umat subroutine in the calculation code abaqus. the elasto-plastic behavior of the fgm is described by the flow theory represented by the equivalent stress of von mises and an incremental hardening variable. the tto model (tamura-tomotaozawa) was used only to determine the elastic-plastic properties of the fgm. the radial, tangential and axial stresses according to the thickness were evaluated in the first part of our work. in the second part, these stresses are evaluated under the same conditions but with the presence of a micro-cavity. the results obtained show clearly that these stresses are in direct relation not only with the thickness and properties of the fgm tube but also with the presence of the cavity. keywords. fgm (functional graded materials); umat (user materials); defect (closed pores). citation: houari. a., bouchikhi, a. s., mokhtari, m., madani, k., numerical analysis of the elastic-plastic behavior of a tubular structure in fgm under pressure and defect presence, frattura ed integrità strutturale, 59 (2022) 212-231. received: 02.08.2021 accepted: 04.10.2021 published: 01.01.2022 copyright: © 2022 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. introduction ith industrial development, pressure vessels and tubes are widely used in reactor technology, chemical industries, marine engineering and aerospace. since in most applications the vessels must operate under extreme thermal and mechanical loads, any failure or fracture will be an irreparable disaster. consideration of w https://youtu.be/kntyotsewqk a. houari et alii, frattura ed integrità strutturale, 59 (2022) 212-231; doi: 10.3221/igf-esis.59.16 213 the strength of these components is therefore very important to ensure a long service life. fgms represent a new generation of composite materials because of their many advantages. the most important feature of fgms is the variable and continuous distribution of the material, which is advantageous for their application under adverse conditions such as high temperatures and pressures, excessive wear and corrosion while maintaining their structural properties, machinability and thermal conductivity. these fgms have been fabricated using many techniques including gas, liquid, and solid phase methods [1]. processes such as centrifugal casting, sedimentation casting, directional solidification, and infiltration processing are the popular processing methods generally employed [2]. the gradation of the two materials can be controlled by selected laws such as the power law (volume fraction law) and the law of exponentials (ghannad and gharooni [3], durmus and keles [4]) ). thick cylinders as structures are the subject of our study which are used in various industrial fields. the analysis of these structures under internal pressure and by the presence of defects, such as micro-cavities, which generate a high stress concentration which can become important if the structure, is subjected to high stress. several studies have focused on the analysis of cylindrical fgm structures such as (tounsi and bedia [5], wu and liu [6], bich and tran [7]) which have analyzed the effect of the gradation of a cylindrical fgm structure depending on the thickness. kordkheili et al [8] and safari et al [9] presented a solution by an analytical method for the mechanical behavior of a cylindrical structure in fgm, while sharma et al [10] and you et al [11] consider in their analysis a purely elastic behavior on a spherical structure under internal pressure. similarly, the work of foroutan et al [12] present in their static analysis of fgm cylinders subjected to internal and external pressure, a method without mesh. they assumed that the mechanical properties of the cylinders were variable in the radial direction and consider that the results obtained for these cylinders were compared to the analytical solutions and a very good agreement was observed between them. while some researchers ( ghannad and nejad [13], eraslan [14], ghannad et al [15], chen [16]) have invested in the analysis of cylinders under non-uniform internal pressure, others like bayat et al [17] and carrera et al [18] analyzed the mechanical behavior of tubular structures in fgm using the analytical and numerical method under transverse load. on the other hand, other studies (cinefra and belouettar [19], houari and tounsi [20], otbi and bedia [21], barka, and tounsi [22]) introduce the effect of thermo-mechanical loading on the response of a thick plate in fgm. kaci et al [23] analyzed the nonlinear bending behavior of a cylindrical structure with exponential functional gradation (simply called e-fg) of variable thickness; they assume that the material properties of functionally graduated plates, at the except the poisson's ratio, vary continuously on the thickness of the plate according to the exponential law of distribution. kerimcan et al [24] have used the method of complementary functions (cfm) to determine the thermal and mechanical stresses in onedimensional steady state for different values of constant of inhomogeneity in a thick hollow sphere in functionally graded material (fgm) where they assumed that the mechanical properties obey exponential variations in the radial direction. sharma et al [25] and wang et al [26] used the finite element method to analyze the response of an fgm structure subjected to a combined stress of torsion and internal and external pressure. the plasticity of the metal plays a major role in the behavior of the fgm. several researchers have shown their interest in this area as praveen and reddy [27]. a large part of the studies on the elasto-plastic behavior on fgm cylinders has been carried out numerically, namely the work of horgan et al [28] and figueredo et al [29] who have proposed a numerical methodology to predict the behavior of elastic stress -plastic functionally graded cylindrical vessels subjected to internal pressure. for the nonlinear analysis of the fgm, the work of trabelsi et al [30] and kar et al [31-32] is devoted to the use of the shell element in the modeling of structures under different types of stresses as well as on nonlinear thermal analyzes of fgm structures under different types of mechanical and thermal stresses. while hanen et al [33] use the extended finite element method to analyze both geometrical and material nonlinear behavior of general plate-shell type structures in functionally classified material, amir et al [34] proposes a new solution of elasto-plastic stress in axisymmetric problems (rotating disc, cylindrical and spherical vessel). the study of nonlinear vibrations in fgm was the basis of the research of kutlu [35] and hadji et al [36]). recently khalid et al [37] implemented a umat in the code of abaqus to study the flexion and the free vibration of the plate in fgm. other research, using the finite element method, have analyzed the effect of porosity in the analysis of inter-facial stresses of fgm beams perfectly reinforced with a plate of porous materials with functional gradation, whereas benferhat et al [38-39] studied the effect of shapes and the distribution of porosity on the bending behavior of a plate in fgm and developed a general model to predict the distribution of the interfacial shear stress and the normal stresses of the beam (fg) reinforced by porous fgm plates under mechanical loading. they showed that the normal and shear stresses at the interface are influenced by the material parameters and that the inhomogeneities play an important role in the distribution of these interfacial stresses. therefore, they have shown that functionally graded panel reinforcement systems in the presence of porosity are effective in improving the bending behavior of reinforced fgm beams. benferhat et al [39] proposed a modification of the mixing a. houari et alii, frattura ed integrità strutturale, 59 (2022) 212-231; doi: 10.3221/igf-esis.59.16 214 law to describe an approximation on the material properties of fgm plates with porosity phases. nguyen et al [40] analyzed the behavior of the porous fgm and they assumed two different porosity distributions according to the direction of the thickness (regular and unequal) while jae-chul [41] concluded that the distribution of porosity in the cylinder in fgm is nonlinear. we also cite other analyses on fgms by introducing the porosity effect such as the work of (benferhat et al [39] ). the work of bekki et al [42] aims to study the effect of the shapes of the porosity distribution on the bending behavior of the simply supported fg plate; they developed a refined theory of shear deformation to study the effect of the shape of the porosity distribution on the static behavior of fgm plates. it has been found that the shape of the porosity distribution significantly influences the mechanical behavior of fgm plates in terms of deformation and normal and shear stresses. our work fits within this context; we aim to analyze, by the finite element method using the abaqus code, the variation of circumferential, radial and axial stresses in a tubular structure in fgm. the material of the cylinder is assumed to be isotropic and heterogeneous, sollicited only under internal pressure, its mechanical properties vary radially along the thickness according to a power function; the elasticity modulus and the poisson's ratio are variable. in the first part of our analysis, the variation of the different stresses is presented as a function of the relationship between the outside and inside diameters as well as the gradation exponent "n". in the second part, we assume the presence of defects (cavity) in different positions in the fgm, the axial and radial stresses were evaluated under these different effects. formulation of the problem n our work, we consider a thick axisymmetric cylinder in non-homogeneous fgms subjected to a uniform pressure on the interior surface. let us take an element of infinitely small volume, see fig.1 (a): the linear relation between the stresses and strains is given by the hook's law. in order to implement a umat subroutine in the abaqus calculation code in the form of a numerical algorithm, it is necessary to use the elasticity relation isotropic in three dimensions given by the expression:      2σ λ r δ ε g r εij ij kk ij                    (1)  ij : is the true stress in the material,  ij the strain tensor, ij the kronecker delta. where the two lame coefficients: ( )r and ( )g r are expressed as a function of the young's modulus ( )e r and the poisson's ratio ( )v r which are continuously graded by the coordinates ( , , )r z in the umat:     ( ) ( ) (1 ( ))(1 2 ( )) e r r v r v r   and    ( ) ( ) 2(1 ( )) e r g r v r (2) i (a) cylindrical representation of the stresses, (b) deformation of the cylinder under the effect of internal pressure figure 1: cylindrical presentation. a. houari et alii, frattura ed integrità strutturale, 59 (2022) 212-231; doi: 10.3221/igf-esis.59.16 215 under the effect of pressure the internal diameter increases, giving rise to the radial stresses r and tangential  (fig. 1(b)), after deformation, a moves in a' and b in b'. from the geometric relations in fig.1, we have:  ( ) ( )r du r drr ,  ( ) ( )r u r r ,  ( )r dw dzz z   and     ( ) ( ) ( ) d r r r rr dr                    (3) the components of the tensor of the cauchy stresses are as follows:         ( ) ( ) ( ) ( ) ( )21 ( ) e r r r r rr rv r            (4.a)          ( ) ( ) ( ) ( ) ( )21 ( ) e r r r r rrv r                    (4.b)      ( ) ( ) ( ) ( )r v r r rz r                                (4.c) where  ( )r r ,  ( )r and  ( )z r are the radial, circumferential, and axial stresses, respectively, as a function of ( )r ,  ( )r r and  ( )r are the radial and circumferential strain, respectively, as a function of ( )r , while z is the axial strain and is assumed to be constant, taking the large length-radius ratio into consideration, and whereas ( )u r is the radial displacement as a function of ( )r and ( )w z is the axial displacement as function of length. ( )v r is the poison’s ratio. according to the infinitesimal strain theory, the equilibrium equation and the strain displacement relations for an axisymmetric structure can be written, respectively, as:    0 dσ (r) σ (r) σ (r) r r θ dr r                                             (5) in our analysis, the elastic-plastic behavior of a metal matrix fgm reinforced with ceramic particles is described with a flow surface represented by an equivalent von mises stress and an isotropic hardening variable of our fgm. the hardening subroutine (uhard) is used to check whether the material has undergone plastic deformation. the total deformation ( )r in the corotational coordinate system of an fgm as in all elastic-plastic materials has a reversible elastic part  ( )e r and an irreversible plastic part  ( )p r , according to the next equation:    ( ) ( ) ( )p er r rr r r                                (6.a)     ( ) ( ) ( ) p er r r                                (6.b)    ( ) ( ) ( )p er r rz z z                                (6.c) by replacing respectively the eqns. (4) in eqns. (6):       1( )( ) ( ) ( ) ( ). ( ) p r r re rr r r v r r                                (7)        1( )( ) ( ) ( ) ( ). ( ) p r re rr r r v r r                                (8) the relation between the stresses and the plastic strains is determined from subtraction the eqns. (7) and (8): a. houari et alii, frattura ed integrità strutturale, 59 (2022) 212-231; doi: 10.3221/igf-esis.59.16 216              ( ) ( ) ( )1( ) ( ) ( ) pd r d r d rpp rr r rr dr e r dr dr     ( ) ( ) ( ). ( )2 ( ) r de r r v r rr dre r            (9) to solve this differential equation, one uses the criterion of plasticity determined by the flow surface and is given according to the criterion of von mises by:     ( , ) 0f r eq r (10) ( , )f r : is the yield function,  eq : is the equivalent stress von mises of fgm and r : represents the radius of the yield surface. if ( , )f r is negative then the behavior of the material is elastic, if not ( , )f r remains zero, there will be plastic flow. from eqn. (11), we define the equivalent von mises stress  eq and the deviator (s) by:   2 .3 s seq ,                   2 221 2eq r z r z                               (11)                                                 2 3 2 3 2 3 r z s r r z s s s z z r                               (12) the evolution of the plastic strain  pd is governed by a normal flow law of the plasticity criterion:            2, 3 p p f sd d n n eq f d                                                                     (13) as a function of the tensor pde , the term  p d can be written as follows:   32 p d p p dp de de (14) where n is the gradient of the yield function with respect to the stress tensor,  p d is the (scalar) equivalent plastic strain rate. the isotropic hardening function  ( )r of the fgm will be described as:   ( ) ( ) ( )0r r r py and ( ) .r p h p (15) where 0 ( )y r is the initial yield stress of the fgm and ( )r p is the isotropic hardening. to obtain the plastic multiplier d , it is therefore sufficient to express the law of evolution of the variable ( )r p as a function of the flow variables. using the prandtl-reuss law to determine the evolution of the variable in our case in uniaxial tension, the equality  ( , ) 0f r can be summed up in the form:    ( ) ( ) ( )0 p r r ry and    ( ) p r h p d (16) a. houari et alii, frattura ed integrità strutturale, 59 (2022) 212-231; doi: 10.3221/igf-esis.59.16 217 where h is the hardening modulus of fgm and  pd is the plastic strain rate, the plastic multiplier can then be easily proven to be equal to the rate of the accumulated plastic strain, using eqns. (13), (14) and eqn.(12):                      2 3 3 2 2 3 2 2 3 d s d s s s dp d eq eq eq eq   dp d and dp : is the plastic multiplier (17) the plastic multiplier  p d in eqn.(14) is determined by using the consistency condition, which leads to:         . . 0 f f r r and    . .r r p p (18) and making use of eqn.(18) and eqn.(14) along with substitutions, we obtain the following expression for the plastic multiplier  d dp :      : : : : n c d d d n c n h (19) at the end, prandtl-reuss law makes possible to determine the 3d expression of the plastic strain rate, in the form:      : : : : n c dp d d n n c n h (20) to solve eqn.(20) we use the 'backward euler' integral method, eqn.(13), gives:     p p n (21) combining this with the deviatoric elasticity eqn. (11) and the integrated strain rate decomposition eqn. (21) gives:    ˆ2 ( )ps g n where:     ˆ e (22)  : is the new total strain increment. thereafter using the integrated flow rule eqn.(13), together with the von mises definition of the flow direction, (in eqn. 22), this becomes:              3 ˆ1 2 pg s g eq (23) the product of eqn.(23) with itself gives us newton's nonlinear equation:       2 3p pg geq (24) the term 2 peqg represent the value of eq at the start of each step and  ( ) p : is the new stress which must verify the uniaxial relation. we solve eqn.(24) by newton’s method:              ( ) 3 3 3 p p g feq g h g h  where         ( ) p p d h (25) a. houari et alii, frattura ed integrità strutturale, 59 (2022) 212-231; doi: 10.3221/igf-esis.59.16 218      p p (26) where, h is the hardening modulus recalculated at the end of each iteration. by substituting eqn.(26) into eqn.(1) one obtains:    ( . )pd c d n (27) we can obtain the complete elasto-plastic incremental stress-strain relation:   epd c d and     29 . 2( 3 ) g s sep c c g h eq (28) epc :is the fourth –order tensor known as the elasto-plastic tangent operator. finally the new stresses ( ) at the end of the time step ( )t can then be written as:    1 dt t (29) the index ( 1)t denotes the values at the end of the time increment. in the tto (tamura-tomota-ozawa) model (carpenter et al [43]), the mixture of materials is treated as elasto-plastic with isotropic linear hardening, for which the stresses and deformations are related to the constituent efforts  ,m c and  ,m c :    v vm m c c (30)    v vm m c c (31) where the subscripts c and m indicate the ceramic and metal, respectively. the volume fraction of metal is denoted by mv , where:  ,m c and  ,m c : are the average stresses and strains in metal and ceramic, respectively. in the tto model an additional parameter ( )q is introduced which represents the ratio of stress to strain transfer, note that:      ( ) / ( )c m c mq ,  0 q (32) we are interested here mainly in the plastic part, the properties of the fgms are described by the following relations:                  ( ) (1 ) / (1c cm m c m m m m m q e q e e r e v e v v v q e q h (33)          ( ) (1 )m cy m m m c m q e e r v v q e e (34)                  ( ) (1 ) / (1c cm m c m m m m m q e q e h r h v e v v v q h q h (35) where ( )e r is the young’s modulus of the composite fgm.  ( )y r is the yield stress of the fgm. the poison’s ratio ( )v r of the composite just follows a rule of mixtures in the tto model: a. houari et alii, frattura ed integrità strutturale, 59 (2022) 212-231; doi: 10.3221/igf-esis.59.16 219  ( ) m m c cv r v v v v (36) the empirical parameter ( )q depends on many factors including material composition, microstructural arrangement, and internal stresses. in our analysis, it is assumed that the elasto-plastic behavior of the fgm cylinder in ceramic matrix reinforced by ceramic particles varies continuously over the entire thickness of radius ( )r . in the inner radius inr the metal distribution  0mv and in the outer radius exr the metal fraction  1mv a function of the volume fraction of the constituent materials, according to the following ratio:    / nm in ex inv r r r r (37) mv is the volume fraction of metal, ( )r is the tube thickness and ( )n is an exponent of the volume fraction that adjusts the variation of the material profile across the thickness of the fgm layer. using matlab, we find that the distribution of elasticity modulus along the radius by the power law of  0.65n see fig.2, is similar to that of the exponential law. remember that the expression of the exponential distribution is given by:  .( ) rme r e e and      1 log c ex in m e r r e (38) where ( )e r is the young’s modulus of the fgm, me is the young’s modulus of the metal and ec is the young’s modulus of the ceramic. the elastic properties of ceramic-metal fgm are chosen from the work of kalali and al [44], are listed in tab. (1). ceramic tib metal ti [43] young's modulus poison’s ratio e = 316000 mpa ν = 0.17 e = 107000 mpa ν = 0.34 yield stress σ 450 mpa hardening modulus h = 10000 mpa table 1: the main mechanical properties. the parameter « q » may be approximated by calibration of experimental data from tensile test performed on monolithic composite specimens. for example, a value of q=4500 mpa is used for a tib/ti composite. the choice of titanium boride at room temperature (tib) as reinforcement in monolithic ti-mmcs has several distinct figure 2: variation of the young's modulus of the power law (image defined for the gradation exponent n = 1 with statev1). 0,0 0,2 0,4 0,6 0,8 1,0 1,5x10 5 2,0x10 5 2,5x10 5 3,0x10 5 normalized radial distance, (r-r in )/(r ex -r in ) r ex /r in =1.2 y ou ng 's m od ul u s e ( m p a) n=0.1 n=0.65 n=1 n=2 n=10 a. houari et alii, frattura ed integrità strutturale, 59 (2022) 212-231; doi: 10.3221/igf-esis.59.16 220 advantages over other possible titanium (ti) compounds; there is a dramatic increase in strength when tib whiskers are added to ti by itself. [45]. description of model geometry he geometries of the tubular structure with these standardized dimensions are illustrated in fig.3. its mechanical characteristics are quoted in tab. (1). the ceramic was graded in the metal according to the thickness of the inner inr outward exr by the choice of three different cases: by the fixed inner radius dimension of inr 50 mm and varying the outside exr 55,  60 and  65mm  , making a ratio of ex inr / r 1.1 , ex inr / r 1.2 and ex inr / r 1.3 . the length of the cylinder is l=200 mm is sufficient to ensure that no stress interference exists in the region from the ends. this length of the cylinder should only act as a means of attachment to limit only the pressure effect on the microcavity presence of our studied fgm structure. the numerical analysis of the behavior of the tubular structure was evaluated under the effect of internal pressure. the shape of the cavity is considered a spherical defect of dimension 0.5 mm taken for each location in the fgm and for each variation in the geometric ratio ex inr / r   and the gradation exponent. the micro-cavity was positioned in the middle of the pipe length and along the radius in: a) near inside diameter (ceramic), b) in the middle of the thickness and c) near the outside diameter (metal), see fig.4. figure 4: spherical micro-cavity position according to the thickness of pipes in fgm. since the elasto-plastic behavior of the metal was introduced into the fgm, the internal pressure level was chosen at 100 mpa in order to cause plasticization in the cavity and in particular when the defect moves away from the ceramic part of the cylinder (outside diameter). for all the situations studied, the loading conditions are as follows: fasteners applied to the ends of one side, the three directions    r zu u u 0 and on the other side only the two directions   ru u 0 to release the deformation in the direction zu . it is reported that all situations studied are under pressure. in this analysis, the mesh of the structure is refined around the zone of defect in order to have the concentrations of the stresses in a precise way at best. the convergence of the numerical calculations is obtained with difficulty according to the mesh architecture because of the small dimension of the micro-cavity. the behavior of fgm was presented using c3d8r solid elements. the number of elements used in the structure is 57970 elements for / 1.1ex inr r , of 93954 elements for / 1.2ex inr r and of 49464 elements for / 1.3ex inr r fig.5 shows the detail of the mesh used for the calculations. t figure 3: overview of the studied geometry. a. houari et alii, frattura ed integrità strutturale, 59 (2022) 212-231; doi: 10.3221/igf-esis.59.16 221 because of these numerous advantages, the typical gradation of fgms in tubular systems is widely used; it becomes important to study their behavior elasto-plastic in the presence of defects under internal pressure. these defects by their location, combine both effects the location itself and the gradation of fgm; hence, the main problem in our work is to identify the effect of default in different cases. our study is conducted by three locations following the thickness (fig.5). the quality defect is a void which always remains trapped in the thickness. this numerical computation modality gave us the reliable advantage of creating defects in complex geometrical and loading situations without having a problem of convergence. figure 5: details of the mesh around the cavity. figure 6: presentation of the algorithm for the integration of stresses in the fgm (umat and hard). plan a-a a. houari et alii, frattura ed integrità strutturale, 59 (2022) 212-231; doi: 10.3221/igf-esis.59.16 222 numerical implementation of the model n fig.6, we have presented the numerical model used in this study as an algorithm for the umat technique which shows all the key steps structured and dependent on each other. these steps are necessary for the modeling of a structure. the elastoplastic behavior of the structure is used by two subroutines umat and hard introduce into the calculation code abaqus. the equations as well as the conditions presented in the algorithm are well detailed in the previous study sections and which summarize the elastic corrections, localized plasticization of our studied fgm structure. results and analysis model valıdatıon or the reliability of our results, the present method is compared with the numerical results obtained by the work of kalali and al [44] by taking into account the dimensions of the normalized model under the effect of internal pressure and by taking a distribution of the following mechanical properties the thickness of the cylinder for an exponent of the power law n = 2 and 100% ceramic (f0= 1). the results obtained represent a very good agreement with those of kelali et al [44] (fig. 7). we notice that the current solution is closer to the numerical solution proposed by kalali and al [44]. this is mainly due to the different numerical analysis methods used in the simulations. the analysis of sensitivity to the mesh and cde onvergence of the results for the structure in three demensions led us to carry out three analyzes using elements c3d8 and c3d8r and 1000 increments of deflection / time. the elements of c3d8r have been shown to have excellent accuracy and moderate mesh dependence (fig. 7). the aim of developing the c3d8r elements was to increase the efficiency of calculations without losing precision. the c3d8r-type mesh sensitivity was measured until further improvement in the mesh caused stability in the determination of the von mises stress in the fgm plate. the effect of the mesh element density presented in fig. 7 has shown a strong link between the numerical analysis and that of the experimental one and presents a good validation with the work of kalali and al [44]. note that when it comes to a large percentage of ceramic (outer face of the cylinder), the two results are much closer compared to that of the interior where the percentage of plasticity is important (presence of metal) . in fact, the plastic behavior of the metal inside the cylinder displays stresses conditioned by the plasticity criterion introduced in the calculation. this is a better way to select a good selection of mesh elements with an appropriate density. for our analysis the choice was on the elements of c3d8r with a density of 40,000 elements in the structure. which brings us back to the end of concluding that our numerical approach with the parameters introduced is reliable. figure 7: von mises stress along the thickness in the fgm cylindrical vessel subjected to internal pressure (properties listed in tab. 1). i f a. houari et alii, frattura ed integrità strutturale, 59 (2022) 212-231; doi: 10.3221/igf-esis.59.16 223 effect of volume fraction exponent "n" fig.8 shows the variation of the different stresses ( radial, circumferential, and axial for different values of the volume fraction exponent "n" for a cylinder radius ratio r_ex⁄r_in =1.1. note that we set the same conditions in percentage of ceramic and metal in the ends of the cylinder thickness of 15% metal in the interior (85% ceramic) and 100% metal in the exterior under 100 mpa pressure. radial, circumferential, and axial stresses were evaluated under radial gradation of the ceramic into the metal from the inside to the outside. the radial stresses are greater from the inside to the outside and decrease with increasing value of the gradation exponent "n". this means that if the structure is ceramic rich, the compressive stresses are low. similarly, the effect of the exponent "n" of the gradation has a great impact on the tangential stresses, which occur with large values compared to those of the radial and axial. figure 8: the variation of radial, circumferential and axial of stress according to the thickness of fgm pipe (with ratio of diameter kept constant   ex inr / r 1.2 and n variable). important values are noted for "n = 1". the axial stresses clearly marked the effect of the gradation, for the exponent n=1 the axial stresses according to the thickness are all of tension by cons they are of tension and compression for the other values of "n". we also note that when the structure is rich in ceramic, the stresses are important from the inside. effect of thickness under gradation under an internal pressure of 100 mpa and under a gradation exponent of  0.65n , local plasticity occurred in some situations. fig.9 shows the evaluation of the stresses according to the thickness of the cylinder under the effect of both the thickness and the graduation. the collection of these results from the inside to the outside has been made in the middle of the length of the cylinder so that we can ascertain that they come from the pure effect of the internal pressure. fig.9 shows that the radial or compressive stresses according to the thickness are more important from the outside, 100% metal inwards 85% ceramic. according to the thickness of the cylinder, the variation of the stresses has been done by effect of stiffness of the thickness and that of the graduation. circumferential stress recorded higher values than radial and a. houari et alii, frattura ed integrità strutturale, 59 (2022) 212-231; doi: 10.3221/igf-esis.59.16 224 axial stresses. more particularly for small thicknesses, these stresses are constant as a function of thickness, except that they decrease towards the outside for larger thicknesses where the effect of the gradation appears slightly. the longitudinal or axial stresses vary from the inside to the outside depending on the thickness by compressive stresses towards tensile stress. if the thickness of the cylinder is important, the presence of ceramic is dominant and therefore more rigidity, which leads to a reduction in the values of the axial stresses. figure 9: the variation of radial, circumferential and axial of stress according to the thickness of fgm pipe (with ratio of diameter  ex inr / r variable and n kept constant=0.65) effect of the defect location under the gradation radial, circumferential and axial stresses are taken according to the thickness near to the defect, where the maximum values are presented. to better compare the effect of the three locations of the defect in the fgm, a stress distribution without defects was introduced; that of the fgm and that of the pure metal because the metal is the base of the fgm (15% of the interior and 100% of the outside). the presence and location of defects in fig.10 shows clearly their effect on the level and distribution of radial stresses. the defect to be localized is increased by the stresses in its zone and will be more important where the defect approaches towards the end of the thickness. when the defect appears in a rigid zone or rich in ceramic, the compressive stresses will be important, and the more it moves away to the outside, the more important it is also. the defect in the middle marks a slight decrease in compressive stresses along the thickness near the defect. the circumferential stresses presented in fig.11 recorded much larger values than those of the radial and axial stresses. however, they are always raised towards the outside of the cylinder except for the fault, which is in the middle. the defect effect represented by a peak explains the elongation of defect in the circumferential direction in elliptical form and a significant tension at these ends. since the material is made of fgm at the base of a metal graduated with ceramic, it always marks values slightly higher than those of pure metal. a. houari et alii, frattura ed integrità strutturale, 59 (2022) 212-231; doi: 10.3221/igf-esis.59.16 225 figure 10: the variation of radial stress according to the thickness for the three positions of the defect (with ratio of radius  ex inr / r constant and n kept constant=0.65). figure 11: the variation of circumferential stress according to the thickness for the three positions of the defect (with ratio of radius  ex inr / r constant and n kept constant=0.65). a. houari et alii, frattura ed integrità strutturale, 59 (2022) 212-231; doi: 10.3221/igf-esis.59.16 226 figure 12: the variation of axial stress according to the thickness for the three positions of the defect (with ratio of radius  ex inr / r constant and n kept constant=0.65). figure 13: equivalent plastic strain distribution in fgm cylinder (n=0.65) in fig.12, the axial stresses are clearly affected by the presence and location of defects that amplify the level and distribution of stresses. the peaks of the stresses explain the compression in the form of elongation in a direction slightly a. houari et alii, frattura ed integrità strutturale, 59 (2022) 212-231; doi: 10.3221/igf-esis.59.16 227 oriented by the gradation effect of fgm around the defect. the latter is accompanied with a concentration in these extremities. when the defect is close to the end of the thickness, the peaks are large with a weak change at the ends, unlike the one in the middle of the thickness. it is important subsequently to analyze the plastic deformation of these structures because the behavior of the metal is plastic and which is also part of the fgm. in addition, the presence of a defect depending on the thickness of the structure did indeed cause this deformation. according to the parameters introduced into the structure such as the volume fraction, the dimension of the cylinder as well as the applied pressure, we have presented in fig.13 the variation of the plastic deformation under the effect of the location of defect according to the thickness of the cylinder. it can be noted that the plasticity of the metal is graduated according to the thickness of the structure, it is clearly noted that in the vicinity of the defect, the plasticity displays peaks of stresses which are important in the case where the defect is close to the high percentage metal in the cylinder. validation of the fgm numerical model by stress-strain curves in fig. 14 we have presented the elastoplastic behavior of the fgm for our model. the purely elastic behavior of the ceramic tib and that of the metal ti, and by using the law of homogenization that of tto, we determined the elastoplastic behavior of the graduated fgm at different volume fraction and under the effect of different situations, without and with presence of defects in different locations; close to ceramic, close to metal, and in the middle of the cylinder thickness. figure 14: the true stress-strain curve of fgm ti/tib for n=0.65 and curve of ti and tib. we clearly notice in fig. 14 for a volume fraction n = 0.65 that is to say the fgm is rich in metal, that the presence of the defect as well as its location according to the thickness considerably influences the value of the various stresses in the cylinder.indeed, the stress-strain response of structure with the presence of defects displays relatively lower values, especially when it is a defect close to the metal side. this result clearly explains that the presence of a defect is a lack of materials in the structure which absorbs the stresses by plastic deformation much more. this fig.15 shows the radial, tangential and axial stresses for different locations of the defect according to the thickness of the fgm pipe. it also shows the location of higher and lower stress concentration. conclusion study based on finite element analysis was carried out to understand the influence of the position of a spherical cavity in a tubular fgm structure of type tib/ti subjected only to internal pressure. the analysis takes into account the elastoplastic behavior of the cylinder by introducing the mechanical properties of the two metals (ceramic and metal) in the calculation code abaqus. the umat analysis technique was used and compared with the literature for the von mises stress and with the experimental stress-strain curve of the structure in order to validate the numerical model where we can note a good agreement. a a. houari et alii, frattura ed integrità strutturale, 59 (2022) 212-231; doi: 10.3221/igf-esis.59.16 228 we were able to validate our numerical model following a study of sensitivity of mesh elements and we chose the element of type c3dr8 the most used and effective for the structures in fgm. the umat technique presents a good efficiency in the modeling of a tubular structure in fgms. the results obtained allowed us to evaluate the different parameters influencing the distribution of radial, tangential and axial stresses of the structure. the technique of modeling the behavior of a fgm structure by umat in abaqus has shown its effectiveness against the experimental and it could be extended for more application especially in the modeling of cancellous bones. the tto model has proven to be effective in determining the behavioral parameters of fgms by including the plasticity of the metal and using solid elements of the c3dr8 type. for a cylinder under pressure, depending on its thickness, the radial, circumferential and axial stresses are tensioncompression and shear stresses respectively. the tubular structure undergoes more circumferential stresses in tension than by the other stresses. the gradation exponent "n" plays an important role on the stress levels and distribution, the more concentrated the fgm is in a stiff material the stiffer it becomes and the more the structure as a function of stress type gives large values. if the thickness of the cylinder increases, the fgm structure becomes more and more rigid. this rigidity is amplified by the presence of the ceramic material which then gives higher stresses. in the fgm, if the micro-cavity is lodged towards the graduated rigid element, the stress concentration is important. a peak of overstress appears at the level of the cavity where its value depends on the position of the cavity in relation to the metal or ceramic the position of the defect according to the thickness of the metal towards the ceramic generates important values of the circumferential stresses which will cause a deterioration of the structure for more pressure. in addition, the presence of a void at the different locations can generate low or high stresses depending on the presence of ceramic or metal. figure 15: presentation of the stresses level around cylinder thickness for the three positions of the defect. a. houari et alii, frattura ed integrità strutturale, 59 (2022) 212-231; doi: 10.3221/igf-esis.59.16 229 references [1] hirai, t. (1991). fabrication and properties of functionally gradient materials, journal stage., 99 (1154), pp. 10021013. doi: 10.2109/jcersj.99.1002. [2] watanabe, y., inaguma, y. and sato, h. (2009). a novel fabrication method for functionally graded materials under centrifugal force: the centrifugal mixed-powder method, materials., 2(4), pp.2510–2525. doi:10.3390/ma2042510. [3] mehdi, g. and hamed, g. (2014). displacements and stresses in pressurized thick fgm cylinders with exponentially varying properties based on fsdt, journal structural engineering and mechanics., 51(6), pp.939-953. doi:10.12989/sem.2014.51.6.939. [4] kerimcan, c., durmus, y. and ibrahim, k.(2016). a unified method for stresses in fgm sphere with exponentiallyvarying properties, structural engineering and mechanics., 57(5), pp.823-835. doi:10.12989/sem. 2016.57.5.823. [5] abdelhakim, k., khalil, b., abdelouahed, t. and el abbes, b.(2014). nonlinear cylindrical bending analysis of e-fgm plates with variable thickness, steel and composite structures., 16(4), pp.339-356. doi: 10.12989/ scs.2014.16.4.339. [6] chih-ping,w. and yan-cheng, l. (2016). a state space meshless method for the 3d analysis of fgm axisymmetric circularplates, steel and composite structures., 22(1), pp.161-182. doi:10.12989/scs.2016.22.1.161. [7] bich, d.h., ninh, d.g. and tran, i.t. (2016).non-linear buckling analysis of fgm toroidal shell segments filled inside by an elastic medium under external pressure loads including temperature effects, composites part b. engineering., 87, pp.75-91. doi:10.1016/j.compositesb.2015.10.021. [8] kordkheili, s.a.h., naghdabadi, r. (2007). thermoelastic analysis of a functionally graded rotating disk, composite structures.,79(4), pp. 508–516. doi:10.1016/j.compstruct.2006.02.010. [9] safari, a., tahani, m ., hosseini.(2011). two-dimensional dynamic analysis of thermal stresses in a finite-length fg thick hollow cylinder subjected to thermal shock loading using an analytical method, acta. mech., 220(1-4), pp. 299314. doi:10.1007/s00707-011-0478-y. [10] sharma, s., s, yadav., r, sharma. (2017). thermal creep analysis of functionally graded thickwalled cylinder subjected to torsion and internal and external pressure, journal of solid mechanics., 09(2), pp. 89-98. doi: 10.22059/jcamech.2017.233633.143. [11] you, l.h., zhang, j.j., you, x.y. (2004). elastic analysis of internally pressurized thick-walled spherical pressure vessels of functionally graded materials, international journal of pressure vessels and piping., 82(5), pp.347–354. doi:10.1016/j.ijpvp.2004.11.001. [12] foroutan, m., r, moradi. and r, sotoodeh-bahreini. (2011). static analysis of fgm cylinders by a mesh-free method, steel and composite structures., 12(1), pp. 1-11. doi:10.12989/scs.2011.12.1.001. [13] gharooni, h., ghannad, m., and nejad, m.z. (2016). thermo-elastic analysis of clamped-clamped thick fgm cylinders by using third-order shear deformation theory, latin american journal of solids and structures., 13(4), pp. 750-774. doi:10.1590/1679-78252254. [14] ahmet, n.e. (2007). stresses in fgm pressure tubes under non-uniform temperature distribution, structural engineering and mechanics., 26(4), pp. 393-408. doi:10.12989/sem.2007.26.4.393. [15] ghannad et al. (2012). elastic analysis of exponential fgm disks subjected to internal and external pressure, open engineering., 03(3), pp. 459-465. doi:10.2478/s13531-013-0110-0. [16] chen, y.z. (2018). transfer matrix method for solution of fgms thick-walled cylinder with arbitrary inhomogeneous elastic response, smart structures and systems., 21(4), pp. 469-477. doi: 10.12989/sss.2018.21.4.46. [17] bayat, y., ghannad, m. and torabi, h. (2012). analytical and numerical analysis for the fgm thick sphere under combined pressure and temperature loading, arch appl mech., 82, pp. 229–242. doi:10.1007/s00419-011-0552-x. [18] carrera, e., brischetto, s. and robaldo, a. (2008). variable kinematic model for the analysis of functionally graded material plates, aiaa journal., 46(1), pp. 194–203. doi:10.2514/1.32490. [19] cinefra, m., carrera, e. and brischetto, s. (2010). analyse thermomécanique des coquilles fonctionnellement calibrées, journal of thermal stresses., 33(10), pp. 942–963. doi :10.1080/01495739.2010.482379. [20] bachir, b., mohammed, s., ah, h. and abdelouahed, t. (2013). thermomechanical bending response of fgm thick plates resting on winkler-pasternak elastic foundations, steel and composite structures., 14(1), pp. 85-104. doi: 10.12989/scs.2013.14.1.085. [21] otbi, b., khalil, b., abdelouahed, t. and el abbes, a.b. (2015). numerical analysis of fgm plates with variable thickness subjected to thermal buckling, steel and composite structures., 19 (3), pp. 679-695. a. houari et alii, frattura ed integrità strutturale, 59 (2022) 212-231; doi: 10.3221/igf-esis.59.16 230 doi: 10.12989/scs.2015.19.3.679. [22] merbouha, b., kouider, h.b., ahmed, b. and abdelouahed, t. (2016). thermal post-buckling behavior of imperfect temperature-dependent sandwich fgm plates resting on pasternak elastic foundation, steel and composite structures, 22 (1), pp. 91-112. doi: 10.12989/scs.2016.22.1.091. [23] abdelhakim, k., khalil, b., abdelouahed, t and el abbes, a.b. (2014). nonlinear cylindrical bending analysis of efgm plates with variable thickness, steel and composite structures, 16(4), pp. 339-356. doi:10.12989/scs.2014.16.4.339. [24] kerimcan, c., durmus, y. and ibrahim, k. (2016). a unified method for stresses in fgm sphere with exponentiallyvarying properties, structural engineering and mechanics.,57(5), pp. 823-835. doi:10.12989/sem. 2016.57.5.823. [25] sharma, s., yadav, s., sharma, r. (2017). thermal creep analysis of functionally graded thick-walled cylinder subjected to torsion and internal and external pressure, journal of solid mechanics., 9(2) , pp. 302–318. [26] wang, z.w., zhang, q., xia, l.z., wu, j.t., liu, p.q. (2015). stress analysis and parameter optimization of an fgm pressure vessel subjected to thermo-mechanical loadings, procedia, eng., 130, pp. 374–389. doi: 10.1016/ j.proeng .2015.12.230. [27] praveen, g. n., chin, c.d. and reddy, j.n. (1999). thermoelastic analysis of functionally graded ceramic-metal cylinder, journal of engineering mechanics., 125(11), pp. 125:11. doi: 10.1061/(asce)0733-9399. [28] horgan, c.o., chan, a.m. (1999). the pressurized hollow cylinder or disk problem for functionally graded isotropic linearly elastic materials, journal of elasticity., 55(1), pp. 43–59. doi:10.1023/a:1007625401963. [29] figueiredo, f., borges, l. and rochinha, f. (2008). elasto-plastic stress analysis of thick-walled fgm pipes, aip conference proceedings., 973(1), pp. 147. doi:10.1063/1.2896766. [30] trabelsi, s., frikha, a., zghal, s. and dammak, f. (2018). thermal postbuckling analysis of functionally graded material structures using a modified fsdt, int j mech sci., 144, pp. 74-89. doi:10.1016/j.ijmecsci.2018.05.033. [31] kar, v.r., panda, s. (2015). large deformation bending analysis of functionally graded spherical shell using fem, struct. eng. mech., 53(4), pp. 661–679. doi:10.12989/sem.2015.53.4.661. [32] kar, v.r., panda, sk. (2016). post-buckling behaviour of shear deformable functionally graded curved shell panel under edge compression, int.j.mech.sci., 115-116, pp. 318–324. doi: 10.1016/j.ijmecsci.2016.07.014. [33] hanen, j., jamel, m., mondher, w. and fakhreddine, d. (2018). an extended finite element method for modeling elastoplastic fgm plate-shell type structures, structural engineering and mechanics, 68(3), pp. 299-312. doi: 10.12989/sem.2018.68.3.299. [34] amir, t., kalali, saied., hadidi, moud. and behrooz, hassani. (2016). elasto-plastic stress analysis in rotating disks and pressure vessels made of functionally graded materials, latin american journal of solids and structures., 13 (5). doi:10.1590/1679-78252420. [35] kutlu, d. (2015). vibration analysis of functionally graded material (fgm) grid systems, steel and composite structures., 18(2), pp.395-408. doi:10.12989/scs.2015.18.2.395. [36] hadji, l., daouadji, t.h., tounsi, a. and bedia, e. (2014). a higher order shear deformation theory for static and free vibration of fgm beam, steel and composite structures., 16(5), pp. 507-519, doi:10.12989/scs.2014.16.5.507. [37] khalid, m., abdelkrim, b. and youcef, b. (2018). three dimensional finite elements modeling of fgm plate bending using umat, structural engineering and mechanics., 66(4), pp. 487-494. doi:10.12989/sem .2018.66.4.487. [38] benferhat, r., hassaine, t., hadji, l, and mansour, m. s. (2016). static analysis of the fgm plate with porosities, steel and composite structures., 21(1), pp. 123-136. doi:10.12989/scs.2016.21.1.123 . [39] benferhat, r., tahar, h. daouadji. and rabahi, a. (2019). effect of porosity in interfacial stress analysis of perfect fgm beams reinforced with a porous functionally graded materials plate, structural engineering and mechanics., 72(3), pp. 293-304. doi:10.12989/sem.2019.72.3.293. [40] nguyen, n.v., nguyen, h.x., lee, s. and nguyen-xuan, h. (2018). geometrically nonlinear polygonal finite element analysis of functionally graded porous plates, adv. eng. softw., 126, pp. 110–126. doi:10.1016/j.advengsoft.2018.11 .005. [41] jae-chul, l. (2015). sintering behavior and material properties of nickel/alumina functionally graded materials fabricated by pressureless sintering method, school of mechanical and aerospace engineering, china. [42] bekki, h., benferhat, r. and tahar, h. d. (2019). influence of the distribution shape of porosity on the bending fgm new plate model resting on elastic foundations, structural engineering and mechanics., 72(1), pp. 61-70. doi:10.12989/sem.2019.72.1.061. [43] carpenter, d., liang, w., paulino, g. h., gibeling, j. c. and munir, z. a. (1999). fracture testing and analysis of a layered functionally graded ti/tib beam in 3-point bending, materials science forum., pp. 837–842. doi: 10.4028/www.scientific.net/msf.308-311.837. a. houari et alii, frattura ed integrità strutturale, 59 (2022) 212-231; doi: 10.3221/igf-esis.59.16 231 [44] kalali, a.t., hassani, h. and saied, h. (2016). elastic-plastic analysis of pressure vessels and rotating disks made of functionally graded materials using the isogeometric approach, journal of theoretical and applied mechanics., 54(1), pp. 113-125. doi:10.15632 / jtam-pl.54.1.113. [45] panda, k.b., chandran, k.s. (2003). titanium-titanium boride (ti-tib) functionally graded materials through reaction sintering: synthesis, microstructure, and properties, metall. mater. trans., 34, pp. 1993–2003. doi:10.1007/s11661-003-0164-3. [46] jin, zh., paulino, gh. and dodds, rh. (2003). cohesive fracture modeling of elastic–plastic crack growth in functionally graded materials, engineering fracture mechanics.., 70(14), pp. 1885–1912. doi:10.1016/s0013-7944 (03) 00130-9. [47] houari, a., mokhtari, m., bouchikhi, a.s., polat, a. and madani, k. 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<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> /enu (use these settings to create adobe pdf documents best suited for high-quality prepress printing. created pdf documents can be opened with acrobat and adobe reader 5.0 and later.) >> /namespace [ (adobe) (common) (1.0) ] /othernamespaces [ << /asreaderspreads false /cropimagestoframes true /errorcontrol /warnandcontinue /flattenerignorespreadoverrides false /includeguidesgrids false /includenonprinting false /includeslug false /namespace [ (adobe) (indesign) (4.0) ] /omitplacedbitmaps false /omitplacedeps false /omitplacedpdf false /simulateoverprint /legacy >> << /addbleedmarks false /addcolorbars false /addcropmarks false /addpageinfo false /addregmarks false /convertcolors /converttocmyk /destinationprofilename () /destinationprofileselector /documentcmyk /downsample16bitimages true /flattenerpreset << /presetselector /mediumresolution >> /formelements false /generatestructure false /includebookmarks false /includehyperlinks false /includeinteractive false /includelayers false /includeprofiles false /multimediahandling /useobjectsettings /namespace [ (adobe) (creativesuite) (2.0) ] /pdfxoutputintentprofileselector /documentcmyk /preserveediting true /untaggedcmykhandling /leaveuntagged /untaggedrgbhandling /usedocumentprofile /usedocumentbleed false >> ] >> setdistillerparams << /hwresolution [2400 2400] /pagesize [612.000 792.000] >> setpagedevice microsoft word numero_30_art_19 a. spagnoli et alii, frattura ed integrità strutturale, 30 (2014) 145-152; doi: 10.3221/igf-esis.30.19 145 focussed on: fracture and structural integrity related issues thermal degradation in carrara marbles as the cause of deformation of cladding slabs a. spagnoli dipartimento di ingegneria civile, dell’ambiente del territorio e architettura, università di parma spagnoli@unipr.it m. migliazza, m. zucali dipartimento di scienze della terra “ardito desio”, università di milano a.m. ferrero dipartimento di scienze della terra, università di torino abstract. marble slabs, typically used as façade panels to externally cover buildings, might permanently deform after a certain time of environmental exposure. this phenomenon, called bowing, is generally accompanied by a reduction of strength which increases with increasing degree of bowing. in the present paper, a theoretical model to calculate the progressive bowing of marble slabs submitted to temperature cycles is briefly recalled and applied to a specific carrara marble sample. the marble is investigated by a microscopic analysis of thin sections cut along three orthogonal directions. the digital photographs are treated by an image analysis code which is capable of extracting grain size and shape distributions. in this way the anisotropic microstructure of the marble is quantified and taken into account in the numerical analyses. the influence of size distribution of grains as well as of their distribution of optic axis orientation on the slab bowing is discussed with the attempt of offering a quantitative tool for a better understanding of in situ bowing measurements. keywords. bowing; crack propagation; fracture mechanics; marble; thermal cycles. introduction arble slabs are often used as façade panels to externally cover buildings. they are subjected to different actions that deteriorate the material, including: temperature (daily and seasonal excursions, through-thickness gradient), mechanical loads (wind, self-weight), chemical attacks (acid rain), humidity changes. temperature may induce stresses due to thermal expansion (restraint effects of the anchorage system, nonlinear temperature fields, nonuniform thermal expansion). one visible phenomenon linked to deterioration of marble is bowing, which is characterised by permanent out-of-plane deflections. bowing is generally accompanied by an overall reduction of strength which increases with increasing degree of bowing, while at the material microstructural level the bowing is characterized by a decohesion of calcite grains. in order to understand the phenomenon of bowing in marble slabs, several experimental and theoretical studies [1-8] have been carried out, starting with the pioneering work of rayleigh [9]. the results of these studies show that the strength of m a. spagnoli et alii, frattura ed integrità strutturale, 30 (2014) 145-152; doi: 10.3221/igf-esis.30.19 146 marble after environmental exposition decreases due to grain decohesion. for instance, royer-carfagni [3] showed that thermal action produces self-equilibrated stress states at calcite grain (whose size ranges typically between 100 and 500 m) interfaces, which are responsible of progressive damage in the material leading to initiation and propagation of intergranular cracks. in the present paper, following some recent works by the authors [10-11], a theoretical model to estimate the progressive bowing and the thermal fatigue of marble slabs submitted to temperature cycles is briefly recalled and applied to a carrara marble sample whose microstructure is experimentally analysed in details. the model, developed within the framework of lefm, takes into account the mechanical microstructural characteristics of the marble as well as the actual cyclic temperature field in the material. the slabs are subjected to a thermal gradient along their thickness as well as to thermal fluctuation on the two sides of the slab due to daily and seasonal temperature excursions. this thermal action causes a stress field which can locally determine microcracks due to decohesion of grains. stress intensification near the cracks occurs and leads to crack propagation in the slab. such crack propagation under thermal actions is evaluated and the corresponding deflection (bowing) is calculated. a monte carlo simulation, where the orientation distribution of grain optic axis along the slab thickness is varied randomly, is performed in order to quantify the scatter of bowing evolution. the mechanics of thermal degradation one-dimensional theoretical model of a marble slab is considered. the thickness of the slab is h, while x and z are the through-thickness and longitudinal axis, respectively (x = 0 corresponds to the inner surface of the slab). the kinematic assumptions are those of beam theory. the material is mechanically linear elastic, homogeneous and isotropic, while the thermal expansion is heterogeneous along the panel thickness. the resulting longitudinal normal stress is ( )(1 ) ( , ) ( , ) ( , ) (1 2 )(1 ) (1 2 ) z z z x ee x t x t t x t              (1) where t(x, t) is the temperature function of time t and space x. considering the relevant case of a slab with hinged ends, we have ( , ) ( ) ( )z x t a t x b t   where a and b, functions of time, are determined by the condition of axial force and bending moment being equal to zero at the slab ends. as has been mentioned in the introduction section, the thermal expansion of calcite grains is anisotropic. in the present model, where thermal expansion is assumed to be heterogeneous and hence the coefficient z is a function of the through-thickness coordinate x, the thermal expansion heterogeneity is linked to the aforementioned thermal anisotropy of calcite grains. now let us assume that the thermal expansion of calcite grains is orthotropic (1-2 are the material thermal expansion axes, characterized by the coefficients 1 and 2 , respectively), the longitudinal thermal expansion coefficient along the z-axis z is obtained from 4 4 1 2( ) cos ( ) sin ( )z x x x      (2) where  is the angle formed by the material thermal expansion axes with the longitudinal axis z. in the light of the above, the thermal expansion heterogeneity (see ( )z x ) is due to the different orientation (see ( )x ) of the material thermal expansion axes of each grain. therefore ( )z x is hereafter assumed to be a stepwise varying function where a jump in such a function occurs at each calcite grain boundary. assuming a geometrically simple grain arrangement for our model, we might have a stack of layers with different values of z in each layer, where the layer thickness might be taken as the calcite grain mean dimension d. in the following, we consider a random distribution of thermal axis orientation in each grain with some specific statistical characteristics. under environmental exposure a diffuse cracking, mainly developing at the calcite grain boundaries, can take place at the external surface of the marble slab. such a diffuse cracking can be incorporated in the present model to calculate the consequent convex bowing of the slab due to thermal loading. intergranular cracking due to decohesion of calcite grains are treated as equivalent multiple edge cracks. to this end a crack density parameter n, corresponding to a number of equivalent external edge cracks, can be defined. assuming hence that intergranular cracking occurs, the crack density a a. spagnoli et alii, frattura ed integrità strutturale, 30 (2014) 145-152; doi: 10.3221/igf-esis.30.19 147 parameter can be correlated with the specific surface ss of the grains (i.e. the total surface area of the grains per unit volume of material) as follows for a slab of length l (fig. 1) 2 ss ln   (3) consider now an external edge crack of depth a submitted to mode i (opening) load due to the thermal stress ( , )z x t of eq. 1 ( ( , )z x t is the stress acting in the solid slab along the line where the crack is assumed to be located). the mode i stress intensity factor (sif) of the crack can be calculated as follows [12] 3 202 , 2 1 ( , ) ( , ) 1 1 a i z a a g a h k a t a t da a a a h a                       (4) where , a a g a h       is a dimensionless function of the crack geometry ( a = h–x). at this point, in might be worth considering the influence of calcite grain shape on the mechanical performances of marble (marble microstructures do present sometimes different geometric features ranging from the extreme cases of xenoblastic textures, characterized by wavy contours, and homoblastic textures, characterized by gently curving boundaries). generally speaking, xenoblastic marbles tend to exhibit a higher resistance to mechanical actions [3]. in order to consider such an aspect, for two-dimensional models it might be appropriate to use a shape parameter like the parameter equal to area/(perimeter)2, which has an upper limit corresponding to the value for a smooth circle ( max 1/ (4 ) 0.080   ) and tends to zero ( min 0  ) for extremely rough boundaries. typically, homoblastic marbles are characterized by 0.045  and xenoblastic marbles by 0.030  . figure 1: schematics on the intergranular equivalent cracking. the degree of roughness of grain boundaries tends to enhance the interlocking resistance of intergranular cracks. to include such an interlacing effect in the model, it is believed that the driving force can somehow be reduced as a function of fracture surface roughness. the concept of roughness-induced crack closure, largely used for fatigue crack propagation a. spagnoli et alii, frattura ed integrità strutturale, 30 (2014) 145-152; doi: 10.3221/igf-esis.30.19 148 problems (e.g. see [13]), can be borrowed for the present context. the following empirical linear relation is proposed to reduce the effective sif with respect to the actual sif [11]: min max min ieff ik k        (5) the crack-induced elastic deflection of marble slab can be determined from energy considerations. accordingly, the central deflection 1 crackf in the slab due to the presence of a single external edge crack is [10] 2 min 1 2 0 max min 3 ( , ) ( , ) a crack i l a f a t k a t a f da heh                     (6) where the sif ( , )ik a t is that of eq. 4 related to the thermal stress field,  f a h is a dimensionless function of the crack geometry dependent on the sif due to an outward point force applied to the centre of the slab [12], and the corrective factor of the effective sifs (see eq. 5) is considered. in the case of multiple equally spaced cracks, eq. 5 becomes 2 min 2 0 max min 3 ( , ) ( , ) 2 a n cracks i nl a f a t k a t a f da heh                     (7) finally, the maximum value during a temperature cycle of the crack-induced deflection for a crack of length a is given by ( ) max ( , )ncracks t f a f a t . it is well known that under cyclic loading conditions, stable propagation of cracks might occur. according to the paris law [14], the crack growth rate (expressed as the derivative da dn of crack length a with respect to the number of cycles n) is a function of the range of the effective sif (eq. 5) in a loading cycle ( )ieffk a (where ,max ,min( ) ( ) ( )ieff ieff ieffk a k a k a   ), that is  mieffda dn c k  where c and m are material constants. propagation of microcracks is an irreversible phenomenon, so that it is deemed to be reasonable to correlate the increment of slab deflection due to crack propagation to the slab bowing, which is characterized by permanent deflections. in other words, bowing ( )b n after a given number of cycles n is taken to be equal to 0[ ( )] ( )f a n f a . the experimental observation of marble microstructure n the following, numerical simulations of bowing using the present theoretical model are illustrated. as a reference, a specific marble used in the vertical cladding slabs (of thickness 30mm and span l corresponding to the vertical distance between anchorages equal to 0.6 m) of a building located in the central part of italy [15] is considered. the anchorages are modeled as hinges. the applied thermal cycles on the external and internal surfaces have a variation range of ±11 °c and ±9 °c, respectively. these temperature ranges are characteristic of diurnal temperature excursions in the marble claddings under consideration [15]. in the present simulations, the initial cracking depth is taken as equal to the mean value of the average grain size d (see below), namely a0 = 125 m. the values of material parameters obtained from experimental tests conducted by the authors are [16]: e = 52 gpa,  = 0.16, m = 4, c = 3x10-4 (for da/dn expressed in m/cycle and ki in mpam0.5) kic = 1.35 mpam0.5 (incidentally, it is intriguing to report that the experimental fatigue crack growth results of ref. [16] have been exploited in [17] to interpret the process of regolith generation on small asteroids). as for thermal expansion, we assume 1 = 25 m/m/°c, 2 = -6 m/m/°c [9]. three orthogonal thin sections are cut from the marble slab of the building under consideration [15], fig. 2. from a qualitative viewpoint, the three photographs show common features of calcite grains with granoblastic texture and anhedral grain shape. the grain size distribution is characterized by the prevalence of large grains (200-300µm), followed by smaller grains (30-50µm). grain boundaries are typically ranging from polygonal shape to interlobate one in both large and small crystals. a third group of calcite grains is detected as fine grained aggregates (<10µm) commonly rimming large porphyroblasts. i a. spagnoli et alii, frattura ed integrità strutturale, 30 (2014) 145-152; doi: 10.3221/igf-esis.30.19 149 in order to quantify the grain-size distribution and preferred orientation of calcite we perform two sets of microstructural analyses, devoted to i) define the grain edges in order to quantify the distributions of some grain geometric parameters and ii) quantify the optic preferred orientation by individuating three main extinction directions (a, b, c) and quantifying the number of grains falling in each direction class. figure 2: view of the three orthogonal thin sections being analysed the pictures of the three thin sections are image processed. automatic processing functions available in the freeware software gwyddion [18] are used to detect grain edges and to calculate the min/max size, area and perimeter of each grain. the frequency distributions of some geometrical parameters of the automatically detected grains are analysed. from the observation of the distribution of min and max grain sizes for each section, it can be noticed that the size distribution of grains is quasi-isotropic as there is little differences between the three sections. the results indicate a gaussian-like distribution of grain sizes. the mean value and standard deviation of the max grain size dmax distribution are equal to 157 and 77 m, respectively. for the min grain size dmin distribution such parameters are equal to 93 and 46 m, respectively. the mean value of the average grain size dave ( max min( ) / 2aved d d  ) is 125 m. such a mean value of grain size is adopted in the numerical simulations for grain size d and initial crack length a0. figure 3: frequency distributions and distribution as a function of average grain size dave for the three thin sections of the following grain geometric parameters: area a, specific surface ss and shape parameter . a. spagnoli et alii, frattura ed integrità strutturale, 30 (2014) 145-152; doi: 10.3221/igf-esis.30.19 150 fig. 3 depicts the distributions of three geometric parameters of calcite grains: area a, specific surface ss (equal to perimeter-to-area ratio) and the shape parameters  defined above, as a function of the average grain size dave. the mean values of ss and  are equal to 72.7 mm-1 and 0.034, respectively. such values are used to work out (see eq. 3) n = 21810 and to calculate the effective sif (see eq. 5 where the reduction factor is equal to  (0.034 0) / 0.08 0 0.425   ). some lattice/crystallographic preferred orientations may be inferred from microstructural analysis by separating groups of crystals on the basis of the orientation of twin/cleavage planes and of similar birefringence/extinction directions. in particular three groups of birefringence of large crystals may be identified: class a with orientation angle in the range 060°, class b with orientation 60-120° and class c with orientation 120-180°. the frequency distribution of grain orientation for the three classes is reported elsewhere [11]. as has been discussed above, calcite grains exhibit anisotropic thermal expansion whose principal axes are linked to the optic orientation of grains. the present simulations concentrate on the random distribution of grain orientation in the material, whilst the distributions of grain size and shape are disregarded here by considering their mean values. although the present experimental findings highlights some non-uniform distribution of grain orientation [11], for the sake of simplicity in the following a uniform distribution is considered. more in details, a uniform probability density function (pdf) for the orientation of thermal expansion axes of calcite grains with respect to the longitudinal axis z of the slab is assumed, that is  ( ) 1p   with 0    . monte carlo simulation n the following simulations, as far as thermal expansion is concerned, we analyse a random case where 4 4 1 2( ) cos ( ) sin ( )z x x x      and ( )x distribution follows a uniform pdf. random values of ( )x are generated, so that their sequences along the slab thickness can be regarded as a stochastic process. a monte carlo simulation is performed by considering a relatively large number (say 20) of realizations of this stochastic process. in this way statistical distribution of the number of thermal cycles producing a given bowing level can be worked out. more in details, the pdf of n for ( ) /b n l (being 0( ) [ ( )] ( )b n f a n f a  ) equal to e.g. 0.1% (1mm/m) can be analysed. fig. 4 shows the relative bowing ( ) /b n l of slab against the number of thermal cycles n for 20 different random distributions of grain orientation. in general, the curves are characterized by an initial stage where the bowing rate is either accelerating or decelerating, followed by some retardation stage (see the plateaus in the curves) where the rate is nearly null; some phases of strong bowing acceleration (see the steps in the curves) are also evident. the final stage leading to failure is characterized by vertical slopes of the curves, indicating a large scatter in the number of cycles to failure (ranging from 105 to 108 cycles). such a three order of magnitude scatter of the number of cycles to failure points out the dramatic variability of bowing evolution of slabs despite the relatively homogeneous nature of carrara marble. a useful tool that might be applied to interpret in-situ measurements is given in fig. 5 where the logarithmic frequency distribution of the number of cycles required to attain a relative bowing ( ) /b n l of 0.1%, according to the 20 simulations of grain orientations being performed, is reported. in the plot, the dispersion of the number of cycles leading to a certain bowing level can clearly be observed, offering a direct indication of the data scatter that can be obtain in an insitu measurement campaign. conclusions he paper analyses the influence of the material microstructure on the bowing of cladding marble slabs applying a theoretical model developed by the authors and taking into account the results of microscopic image processing of thin sections in terms of grain geometrical features and grain optic orientation. the model is based on lefm concepts applied to marble slabs where grain decohesion due to surface damage can occur. the model is able to estimate the stress intensification near the crack tip and to compute the stress which leads to crack propagation in the slab. such crack propagation under thermal actions is evaluated and the corresponding bowing is calculated. some examples, where a random distribution between calcite grains of the thermal expansion coefficient is considered (this being a reasonable description of the actual anisotropic thermal expansion of grains), have been presented to show the strong influence of material microstructure on the degree of bowing. i t a. spagnoli et alii, frattura ed integrità strutturale, 30 (2014) 145-152; doi: 10.3221/igf-esis.30.19 151 the obtained results can be utilised as an interpretation tool for in-situ bowing measurements which often show a wide dispersion even under nominally equal environmental condition. the proposed methodology based on standard microscopic analysis of marble microstructure and on the application of an image processing code can be suggested as a first attempt for a better understanding and forecasting of the bowing evolution of monitored slabs in building façades. 101 102 103 104 105 10 6 107 108 number of cycles [-] 0.0001 0.001 0.01 0.1 1 10 100 1000 r el at iv e bo w in g, b/ l [m m /m ] figure 4: relative bowing b/l vs number of cycles for 20 different realizations of grain orientation distribution along the slab thickness. 4 5 6 7 8 log of number of cyles at b/l=0.001 [-] 0 0.1 0.2 0.3 r el at iv e fr eq ue nc y [-] figure 5: frequency distribution of the number of cycles (log scale) required to attain a relative bowing b/l of 0.1%, according to the 20 simulations of grain orientations being performed. references [1] ferrero, a.m., marini, p., experimental studies on the mechanical behaviour of two thermal cracked marbles, rock mechanics and rock engineering, 34 (2001) 57-66. [2] leiss, b., weiss, t., fabric anisotropy and its influence on physical weathering of different types of carrara marbles, journal of structural geology, 22 (2000) 1737-1745. [3] royer-carfagni, g., on the thermal degradation of marble, international journal of rock mechanics and mining science, 36 (1999) 119-126. a. spagnoli et alii, frattura ed integrità strutturale, 30 (2014) 145-152; doi: 10.3221/igf-esis.30.19 152 [4] widhalm, c., tschegg, e., eppensteiner, w., anisotropic thermal expansion causes deformation of marble claddings, asce journal of performance of constructed facilities, 10 (1996) 5-10. [5] saylor, d.m., fuller, e.r., weiss, t., thermal-elastic response of marble polycrystals: influence of grain orientation configuration, international journal of materials research, 98 (2007) 1256-1263. [6] weiss, t., siegesmund, s., fuller, e.r., thermal degradation of marble: indications from finite-element modeling, building and environment, 38 (2003) 1251–1260. [7] siegesmund, s., ullemeyer, k., weiss, t., tschegg, e.k., physical weathering of marbles by anisotropic thermal expansion, international journal of earth sciences, 89 (2000) 170-182. [8] chau, k.t., shao, j.f., subcritical crack growth of edge and center cracks in façade rock panels subject to periodic surface temperature variations, international journal of solids and structures, 43 (2006) 807-827. [9] raileigh, a., the bending of marble, proceeding royal society of london, 19 (1934) 266-279. [10] spagnoli, a., ferrero, a.m., migliazza, m., a micromechanical model to describe thermal fatigue and bowing of marble, international journal of solids and structures, 48 (2011) 2557-2564. [11] ferrero, a.m., migliazza, m., spagnoli, a., zucali, m., micromechanics of intergranular cracking due to anisotropic thermal expansion in calcite marbles, engineering fracture mechanics, article in press (2014) http://www.scopus.com/inward/record.url?eid=2-s2.084893189538&partnerid=40&md5=200ab6486acc34bdc94057648918bf89 [12] tada, h., paris, p.c., irwin, g.r., the stress analysis of crack handbook. del research corporation, st.louis (1985). [13] suresh, s., ritchie, r.o., a geometric model for fatigue crack closure induced by fracture surface roughness, metallurgic transactions a, 13 (1982) 1627-1631. [14] paris, p.c., gomez, m.p., anderson, w.p., a rational analytic theory of fatigue, the trend in engineering, 13 (1961) 9-14. [15] ferrero, a.m., migliazza, m., spagnoli, a., theoretical modelling of bowing in cracked marble slabs under cyclic thermal loading, construction and building materials, 23 (2009) 2151-2159. [16] migliazza, m., ferrero, a.m., spagnoli, a., experimental investigation on crack propagation in carrara marble submitted to cyclic loads, international journal of rock mechanics and mining, 48 (2011) 1038-1044. [17] delbo, m., libourel, g., wilkerson, j., murdoch, n., michel, p., ramesh, k.t., ganino, c., verati, c., marchi, s., thermal fatigue as the origin of regolith on small asteroids. nature, 508 (2014) 233. [18] nečas, d., klapetek, p., gwyddion: an open-source software for spm data analysis, cent. eur. j. phys., 10 (2012) 181-188. microsoft word numero 1 notiziario.doc gruppo italiano frattura 2 notiziario i g f n. 18 luglio 2007 in questo numero 1) editoriale del presidente igf; 2) cariche sociali biennio 2005-2007; 3) verbale dell’assemblea annuale dei soci 2006; 4) verbali dei consigli di presidenza; 5) resoconti delle attività del 2006; 6) xix convegno nazionale igf – milano 2007; 7) convocazione assemblea annuale dei soci 2007; 8) calendario congressi internazionali ; 9) modulo di iscrizione igf-esis. presidente igf: giuseppe ferro, dipartimento di ingegneria strutturale e geotecnica, politecnico di torinocorso duca degli abruzzi, 24 10129 torino. tel. 0115644885, fax 011-5644899, e-mail: ferro@polito.it segretario igf curatore del notiziario: francesco iacoviello, di.m.s.a.t. università di cassino, via g. di biasio 43, 03043 cassino (fr). tel. 0776-2993681, fax 0776-2993733, e-mail: iacoviello@unicas.it (1) editoriale del presidente igf nel primo consiglio di presidenza svolto in via telematica (divertente esperienza iniziata con il sottoscritto connesso con abbondante ritardo e con firrao in veste di ascoltatore non microfonato che conferiva via sms, telefono e posta elettronica) è stata varata con molto entusiasmo da parte di tutti i membri del consiglio la rivista on-line del gruppo italiano frattura. la rivista si chiamerà frattura ed integrità strutturale. avrà una cadenza trimestrale e vedrà l’attuale segretario del gruppo nonché primo proponente, francesco iacoviello, nella veste di editor della rivista. questo editoriale inaugura il numero zero della nuova rivista. il comitato scientifico sarà costituito dai membri del consiglio di presidenza e dai più eminenti e autorevoli esperti di meccanica della frattura attivi in italia. la rivista sarà pubblicata facoltativamente in ltaliano o in inglese con sommario obbligatoriamente bilingua. cosa si può dire e augurare ad un progetto così ambizioso? sicuramente questa iniziativa darà l’opportunità a tutti i soci igf di poter pubblicare in un ambito molto indirizzato agli aspetti applicativi e industriali. usando un termine molto adoperato in questo periodo, la rivista aiuterà il trasferimento tecnologico nell’ambito dell’integrità strutturale in italia, dal momento che l’accesso alla rivista sarà libero e fortemente pubblicizzato per via telematica sfruttando gli importanti indirizzari telematici che siamo riusciti a costruirci nel corso di questi ultimi anni. il battesimo ufficiale della rivista avverrà nel corso del prossimo congresso nazionale che quest’anno si svolgerà a milano presso la sede del politecnico della bovisa. un concerto jazz presso il famoso locale blue note di milano rappresenterà l’aspetto mondano della festa. al congresso nazionale, molto ben organizzato da stefano beretta, le letture plenarie invitate saranno tenute da wolfgang brocks (recentemente insignito della griffth medal da parte dell’esis) e da hugo ernst. i due colleghi stranieri verranno nominati soci onorari del gruppo e si aggiungeranno ai precedenti soci onorari nominati nelle precedenti edizioni dei congressi nazionali (robert ritchie, yiu-wing may, david taplin, emmanuel gdoutos, george sih). un grosso lavoro è stato compiuto dal consiglio di presidenza in questi due anni di attività relativamente al nuovo sito igf (www.gruppo frattura.it) all’interno del quale sono stati inseriti gli atti dei congressi svolti nell’ultimo decennio (cassino 1997, trento 1998, bari 2000, catania 2002, bologna 2004, cosenza 2006) oltre al migliaio di paper presentati al congresso mondiale icf xi svoltosi a torino nel 2005, reperibili al sito www.icf11.com. entro il 2007 è nostra intenzione informatizzare tutti gli atti dei primi 12 congressi nazionali per rendere accessibili a tutti gli articoli che hanno fatto la storia della meccanica della frattura in italia, secondo lo spirito del nostro statuto. giuseppe ferro presidente igf e segretario esis gruppo italiano frattura 3 (2) cariche sociali biennio 2005-2007 presidente: • giuseppe ferro -politecnico di torino. consiglio di presidenza: • stefano beretta politecnico di milano; • francesco iacoviello università di cassino (segretario); • franco furgiuele università della calabria; • donato firrao politecnico di torino (vice presidente); • angelo finelli enea (tesoriere); • mario marchetti università di roma la sapienza (vice presidente); • lorenza barsanti – snam retegas; • roberto frassine politecnico di milano; revisori dei conti: • giuseppe demelio – politecnico di bari; • vincenzo sglavo università di trento; probiviri: • prof. alberto carpinteri politecnico di torino; • prof.sergio reale università di firenze; • prof. roberto roberti università di brescia. a norma di statuto il recapito dell'igf è presso il segretario: la quota annuale di iscrizione è di 30 euro (comprensiva di iscrizione esis), esente iva a norma dell'art.2 del dpr 26/10/72 e successive modifiche. la quota potrà essere versata a: gruppo italiano frattura mediante bonifico bancario su cc. n. 100940 del credito cooperativo bolognese, ag. via arcoveggio 56/22 bologna intestato al gruppo (abi 7082 cab 02402). (3) verbale dell’assemblea annuale dei soci verbale dell’assemblea ordinaria dei soci del 31 maggio 2006 l’assemblea ha inizio alle ore 18.00 del 31 maggio 2006 presso l’hotel san michele, cetraro (cs), sede del convegno nazionale igf xviii, con il seguente ordine del giorno: 1. approvazione verbale dell’assemblea dei soci di ferrara. 2. comunicazioni. 3. relazione revisore dei conti 4. presentazione bilancio consuntivo 2005 5. indirizzo attività per il biennio 2006-07 6. varie ed eventuali. 7. attribuzione “premio giovani” risultano presenti i seguenti consiglieri: ferro (presidente), barsanti, finelli, firrao, frassine, furgiuele, iacoviello. assenti giustificati: beretta, marchetti risultano presenti i seguenti soci: clubi vincenzo, colombo daniele, comino luca, esposito luca, fersini davide, gentile domenico, ghedini andrea, guagliano mario, iovani giuseppe, la vecchia marina, labanti martino, madia mauro, pasta antonino, peghini marco, piacente valentino, trentini elena punto 1 all’o.d.g.: approvazione verbale del consiglio di ferrara. il consiglio di presidenza approva il verbale. punto 2 all’o.d.g.: comunicazioni. il presidente comunica all’assemblea la recente scomparsa del prof. miller. l’assemblea osserva un minuto di silenzio. il presidente comunica che è attivo il sito internet all’indirizzo www.gruppofrattura.it e che, a breve, conterrà tutti i lavori presentati nei convegni nazionali e nelle giornate di studio. vengono distribuite a tutti i partecipanti le copie della relazione dei revisori dei conti e del bilancio consuntivo. punto 3 all’o.d.g.: relazione dei revisori dei conti. il revisore dei conti, sglavo, presenta all’assemblea la relazione dei revisori allegata al presente verbale, e ne propone l’approvazione. l’assemblea approva all’unanimità. punto 4 all’o.d.g.: presentazione bilancio consuntivo. il tesoriore, finelli, presenta all’assemblea il bilancio consuntivo, allegato al presente verbale, proponendone l’approvazione. l’assemblea approva all’unanimità. il presidente ricorda all’assemblea che la quota annuale ammonta a 30€, di cui 10€ vengono versati all’esis per l’iscrizione, e propone di mantenere la quota invariante anche nel prossimo anno. l’assemblea approva all’unanimità. punto 5 all’o.d.g.: indirizzo attività biennio 2006-2007. il presidente presenta all’assemblea l’attività svolta all’interno dell’esis, evidenziando il fatto che l’organizzazione igf è stata presa a modello da altri 16 paesi europei e sollecita l’assemblea per la proposta di attività da attivare nel prossimo biennio. barsanti propone l’organizzazione, in collaborazione con beretta, di una giornata di studio da svolgersi a milano ed avente come oggetto la gruppo italiano frattura c/o francesco iacoviello di.m.s.a.t. università di cassino via g. di biasio 43, 03043 cassino (fr). tel./fax 0776-2993681 e-mail: iacoviello@unicas.it gruppo italiano frattura 4 fatica e la frattura nelle strutture saldate da tenersi nella prima settimana di febbraio 2007. la giornata, in funzione del numero di partecipanti, si svolgerà nel centro ricerche di bolgiano (san donato milanese) oppure a piacenza. donzella e dogliano propongono un’altra giornata da organizzare a brescia a fine novembre – inizio dicembre 2006 ed avente come argomento l’integrità strutturale all’interfaccia ruota – rotaia. il presidente presenta da parte di beretta la candidatura della sede di milano ad organizzare il convegno nazionale igf xix nel mese di giugno 2007. l’assemblea approva all’unanimità tutte le attività proposte. punto 6 all’o.d.g.: varie ed eventuali. il presidente sollecita l’assemblea ad una discussione sulla missione del igf, ricordando all’assemblea l’importanza della partecipazione alle attività presenti nei tc – esis. inoltre propone che l’igf si presenti come autorevole interlocutore per contribuire alla stesura di normative. firrao interviene ricordando l’attività igf negli ultimi anni e propone all’assemblea una maggiore partecipazione alle attività a livello europeo. frassine propone un maggior legame con l’industria, proponendo che l’igf organizzi attività formative organizando scuole tematiche presso aziende interessate e partecipando a mostre. punto 7 all’o.d.g.: attribuzione “premio giovani” il cdp, dopo lunga ed approfondita discussione, decide di attribuire i due “premi giovani” ai seguenti autori: f. caimmi, autore del lavoro “sull’applicabilità della prova cens allo studio della tenacità interlaminare in modo ii di laminati in composito” e. trentini, autrice del lavoro “mechanical behaviour of a sicf/sic composite for nuclear applications at high temperature” il presidente scioglie l’assemblea alle ore 19.30. allegato a assemblea di bilancio 2005 relazione del tesoriere l’esercizio economico dell’anno 2005 mostra fra le uscite oltre ad un saldo di spesa relativo alla stampa di 1200 copie degli atti igf17, distribuite al convegno internazionale icf 11 di torino, le spese relative all’organizzazione della giornata sulla “fatica multiassiale” tenutasi presso la facoltà di ingegneria dell’università di ferrara nello scorso mese di giugno ed il contributo ad esis relativo all’iscrizione dei nostri soci. le entrate sono invece costituite dalle quote associative, dalle iscrizioni alla giornata su menzionata e da un nuovo prestito contratto con esis per un importo di 6000 €. e’ inoltre, secondo il mio parere, spiacevole dover notare come un evento importante come icf 11, nonostante una partecipazione elevata ed al di là delle più rosee previsioni, abbia garantito un introito pari solamente alla quota di partecipazione di 14 ospiti provenienti da paesi dell’est europeo. come si può notare dal rendiconto economico l’anno finanziario si chiude con un passivo di € 5.557,92, praticamente imputabili alla spesa per la stampa degli atti igf 17. l’andamento del mercato borsistico, ha, ancora una volta, sconsigliato il realizzo dei fondi investito in titoli, anche se, come già segnalato nella precedente assemblea, il suddetto mercato ha continuato a registrare un andamento positivo. su decisione dell’assemblea di catania del 2002, a bilancio viene comunque riportato il capitale inizialmente versato a cui viene detratto il valore di un prelievo effettuato nel 2003. il conto profitti o perdite verrà quantificato al momento di un eventuale completo realizzo. il capitale del gruppo passa pertanto da €. 50.802,07 a € 45.089,88 (11,2%). il giro di affari della gestione 2005, rilevabile dal bilancio consuntivo, è stato pari a € 80.898,43. il tesoriere: angelo finelli allegato b bilancio 2005 relazione dei revisori dei conti il bilancio 2005 chiude con entrate per € 13.086,72 e uscite per € 19.184,64. tenendo conto dell'avanzo di € 50.802,07 della gestione precedente, la presente gestione si chiude con un avanzo di € 45.089,88 che è stato iscritto alla voce bilancio del giornalmastro all'inizio dell'anno 2006. nel corso dell'anno 2005 abbiamo verificato che la contabilità del gruppo è stata tenuta regolarmente e che gli adempimenti fiscali del gruppo sono stati regolarmente ottemperati. riteniamo pertanto che il bilancio rifletta conti sinceri in accordo con la realtà dell'associazione e vi invitiamo ad approvarlo. i revisori dei conti: vincenzo m. sglavo e giuseppe demelio (4) verbali dei consigli di presidenza verbale del consiglio di presidenza del 20 marzo 2007 la riunione ha inizio alle ore 11.00 presso il politecnico di milano (sede bovisa), con il seguente ordine del giorno: 1. comunicazioni. 2. congresso nazionale igf 19 3. notiziario 4. sito web conosci i tc dell’esis ? www.esisweb.org gruppo italiano frattura 5 5. programmazione attività 07-08 6. varie ed eventuali. risultano presenti i seguenti consiglieri: ferro (presidente), beretta, frassine, finelli, firrao. sono inoltre presenti in audioconferenza iacoviello e furgiuele punto 1 all’o.d.g.: comunicazioni. ferro comunica che il convegno bilaterale italia russia previsto a san pietroburgo non avrà luogo a causa di problemi organizzativi presso il comitato russo. punto 2 all’o.d.g.: congresso nazionale igf 19 beretta riferisce che sono stati ricevuti fino al momento 33 abstract e che sono prevedibili circa una quarantina di lavori. il consiglio valuta l’opportunità di strutturare il convegno nazionale su due giorni pieni o lasciarne la calendarizzazione su tre giornate: la scelta finale sarà effettuata in base ai lavori presentati, considerando la durata di ogni presentazione pari a quindici minuti. beretta riferisce che le spese previste ammontano a circa 23 k€, parzialmente coperte dagli sponsor, comprensive delle spese relative al viaggio e soggiorno dei relatori delle memorie invitate, della cena sociale, della produzione dei cd contenenti gli atti e della stampa degli atti cartacei. a questo proposito, il consiglio richiede a furgiuele un preventivo del medesimo tipografo utilizzato per il precedente convegno nazionale, risultato in precedenza particolarmente conveniente. punto 3 all’o.d.g.: notiziario. il consiglio decide che il prossimo notiziario, oltre a contenere i verbali dei cdp e dell’ultima assemblea dei soci, dovrà contenere anche i resoconti dei tc esis cordinati da pavan, alberto carpinteri ed andrea carpinteri, delegando iacoviello (ed in subordine ferro) a contattare i colleghi per ottenere tale documentazione. punto 4 all’o.d.g.: sito web igf frassine rinuncia al ruolo di webmaster. il consiglio decide di delegare il presidente nell’identificazione di un gestore professionale, raccogliendo i preventivi dai candidati. il consiglio sottolinea la necessità di inserire sul sito almeno gli indici degli atti dei convegni nazionali e delle giornate disponibili solo in formato cartaceo. il consiglio discute quindi la proposta inviata nei giorni precedenti da iacoviello di inserire all’interno del sito una rivista on line, dotata di un comitato redazionale molto snello ed in grado di effettuare portare un lavoro in pubblicazione entro un mese dal primo invio (referaggio incluso). il consiglio ritiene tale proposta interessante, discutendo se dare a questa rivista un taglio maggiormente scientifico oppure divulgativo. il consiglio delega iacoviello alla preparazione di un paio di progetti da sottoporre al consiglio medesimo. punto 5 all’o.d.g.: programmazione attività 0708 ferro evidenzia il fatto che nell’ultimo periodo a causa di una serie di motivi contingenti sia diminuita l’attività igf tradizionalmente legata all’organizzazione di giornate seminariali, e propone l’organizzazione di una attività congiunta con l’associazione medici ortopedici italiani. il consiglio condivide la proposta. punto 6 all’o.d.g.: varie ed eventuali. non essendovi varie ed eventuali, il presidente scioglie il consiglio alle ore 16.00. verbale del consiglio di presidenza del 10 aprile 2007 la riunione ha inizio alle ore 10.00 in via telematica, con il seguente ordine del giorno: 1. rivista on line. 2. congresso nazionale 2007. 3. varie ed eventuali. risultano presenti i seguenti consiglieri: ferro (presidente), beretta, finelli, firrao, furgiuele, iacoviello. punto 1 all’o.d.g.: rivista on line. iacoviello espone al consiglio un resoconto delle procedure finalizzate alla attivazione di una rivista on-line. il consiglio dopo ampia ed approfondita discussione, decide unanimamente: di fondare una rivista on line dal titolo “frattura ed integrità strutturale – rivista ufficiale del gruppo italiano frattura”, con pubblicazione trimestrale; che la pubblicazione su questa rivista sia gratuita per tutti i membri igf ed esis; che la lingua ufficiale sia l’italiano, con abstract anche in inglese, e che siano accettati anche lavori in inglese; che il direttore editoriale sia iacoviello; che iacoviello sia delegato all’espletamento degli aspetti burocratico-amministrativi (attribuzione issn ed acquisto doi; accertamento delle eventuali procedure di registrazione della rivista, presso il tribunale, e del direttore, presso l’ordine dei giornalisti); su proposta di firrao, inoltre, il consiglio decide di verificare la possibilità di indicare all’interno del doi la dicitura italian group on fracture igf, member of esis; che il comitato editoriale sia costituito dal consiglio di presidenza e da una serie di personalità identificate dal consiglio medesimo; di delegare ferro a contattare le seguenti personalità per completare il comitato editoriale: carpinteri alberto, carpinteri andrea, firrao, fossati, gabetta, maier, pavan, rinaldi, roberti, sglavo, taylor. di produrre il primo numero in occasione del prossimo convegno nazionale (luglio 2007), producendo anche una cinquantina di copie gruppo italiano frattura 6 cartacee, contenente: un editoriale del presidente; un articolo elsevier (beretta si interesserà per i diritti e provvederà a trasmetterli a iacoviello); due articoli della esis newsletter (cui verranno attribuiti due doi igf; beretta provvederà a trasmetterli a iacoviello); le informazioni relative al convegno nazionale; i verbali dell’ultimo anno di attività del consiglio di presidenza. di utilizzare come formato della rivista quello trasmesso da iacoviello al consiglio con la denominazione “guida 3”. diversi consiglieri evidenziano l’importanza di un aggiornamento continuo e rapido del sito istituzionale dell’igf. ferro e iacoviello danno la loro disponibilità a recepire dei preventivi per una gestione professionale del sito dell’associazione. contestualmente ricercheranno la disponibilità di un grafico per la copertina della rivista da utilizzare anche per le comunicazioni via mail. punto 2 all’o.d.g.: convegno nazionale 2007. a seguito della proposta di iacoviello di procedere alla registrazione video del prossimo convegno nazionale ed alla loro pubblicazione in streaming sul sito, beretta propone di procedere comunque alla registrazione delle presentazioni invitate, previa autorizzazione dei relatori. il consiglio approva. per quanto riguarda la stampa degli atti cartaceo, furgiuele comunica che in giornata dovrebbe avere disponibile un preventivo dalla medesima tipografia utilizzata nel precedente convegno nazionale e provvederà a trasmetterlo al consiglio punto 3 all’o.d.g.: varie ed eventuali. non essendovi varie ed eventuali, il presidente scioglie il consiglio alle ore 12.00. (5) resoconti delle attività del 2006 esis (tc3) “fatigue of engineering materials and structures” chairmen: an. carpinteri, l.p.pook secretary: a. spagnoli activities during 2006 (a) professor cetin morris sonsino (darmstadt), professor h. zenner (clausthal-zellerfeld), professor andrea carpinteri (parma), professor les p. pook (london): guest editors of a special issue of the “international journal of fatigue (ijf)” (esis special technical publication), under the title “multiaxial fatigue and fracture”, with 26 papers selected from those presented at the 7th international conference on multiaxial fatigue and fracture (icbmff 7), held in berlin in june 2004. such a special issue of ijf has been published as issue nos 5-6, volume 28, 449-674, 2006. (b) professor andrea carpinteri (parma) and professor les p. pook (london): chairmen of the 2nd international conference on “crack paths (cp 2006)”, held in parma, italy, thursday 14th to saturday 16th september, 2006. present and future activities (a) professor andrea carpinteri (parma), professor les p. pook (london) and professor andrea spagnoli (parma) : guest editors of a special issue of the international journal “engineering fracture mechanics”, under the title “crack paths”, with papers selected from those presented at the international conference on “crack paths (cp 2006)”, held in parma, italy, thursday 14th to saturday 16th september, 2006. (b) dr upul fernando (sheffield hallam university, sheffield), professor mike w. brown (university of sheffield, sheffield), dr brian tomkins (aea technology plc): chairmen of the eighth international conference on multiaxial fatigue and fracture (icmff 8, http://www.icmff8.org.uk), to be held in sheffield, 10th to 14th june, 2007. (c) professor andrea carpinteri (parma) and professor les p. pook (london): chairmen of the 3rd international conference on “crack paths (cp 2009)”, september 2009. esis (tc4) “polymer and polymer composites” chairmen: j.g. williams, a. pavan. secretary: b.r.k. blackman. tc4 met twice during 2006, continuing their work on many of the existing project areas. in addition, polymer cutting and scratch testing have been proposed as new work areas for the committee. test protocols for these test methods are under development. ongoing work areas include mode i delamination at high test rates, quasi-static mode ii delamination in composites and structural adhesive joints, the peel testing of structural adhesives using 90 degree peel, t-peel and the mandrel test, j-crack growth resistance testing of polymers, high rate testing of polymers at greater than 1m/s, the essential work of fracture method, impact testing of short fibre composites and delamination fatigue. in 2007, the committee will meet on the following occasions: 23rd -25th may 2007 (regular tc4 committee meeting): les diablerets, switzerland. 17th-19th october 2007 (regular tc4 committee meeting): les diablerets, switzerland. the meetings are open to all. please contact the technical secretary for details and agenda. in 2008, the 5th international conference on fracture of polymers, composites and adhesives will be held in les diablerets, switzerland from 7th11th september 2008. www.tc4pca.elsevier.com (deadline for the submission of abstracts is 2nd november 2007). gruppo italiano frattura 7 esis (tc20) "role of defects and inclusions" chairmen: y. murakami, c.w. anderson secretary: s. beretta a meeting of tc20 was held on 13th september ’06 in politecnico di milano, dipartimento di meccanica (milan, italy) the participants of which were: y. murakami (kyushu university), s. beretta and f. benzoni (politecnico di milano), j. butler (corus group), d. girodin (snr roulements), e. henault (creas ascometal) f. cirilli (csm), e. paravicini (tenaris). round robin #1 (corus steel) murakami presents the results of measurements in his lab for the first round robin. beretta summarizes the results obtained in the first round robin by the different participants and the following discussion emphasizes the scatter of the results and the need of a confirmation by fatigue tests. it is then agreed to write a journal paper presenting the results of this round-robin on a suitable journal in order to have the widest circulation of results. some particpants (cirilli, henault) agree on carrying out a second series of measurements for estimating in-lab variability. round robin #2 (ascometal bearing steel) butler presents the results about automatical defect evaluation and the differences of corus measurements between 2005 and 2006 . girodin then presents some results obtained on a bearing steel and henault shows some interesting results obtained by simulations of measurements. the following discussion pin-point that there is a big difference in image analysis results and classification of the different inclusion types. it is agreed to circulate a cd containing the images by the different participants in order to have a direct comparison of measurements. future events cirilli briefly describes the evir+ project proposal presented at eccs. it is agreed to prepare a joint paper about rr#1 for spring 2007 esis (tc24) "integrity of railway structures” chairmen: e. smith, u. zerbst the annual meeting of tc24 was held in brescia (italy) on 29th november 06 with participants: u. zerbst – gkss (germany) r.a. smith – imperial college (uk) s. beretta – politecnico di milano (italy) l. drewitt – corus group (uk) g. donzella – università di brescia (italy) m. guagliano – politecnico di milano (italy) f. lombardo – lucchini sidermeccanica (italy) a. mazzu – università di brescia (italy) 1. future plans • zerbst proposes to hold next workshop/tc24 meeting in paris on spring 2007, in concomitance with the conclusion of a frenchgerman jointed research project on rails • beretta proposes a workshop/tc24 meeting in spring 2008 in milan, focussed on axles, summarizing the results of widem and deufrako projects; • smith proposes a future workshop/tc24 meeting in london entitled “load and infracstructure in railway application”, including several topics, like fatigue and fracture of rails, crashworthiness, structures (bridges), multiaxial fatigue of wheels, load spectra, climate changes, lightweighting, non-destructive controls. 2. proposals for reports from the committee it has been discussed about the best way to present the activities of the tc24 members, wich at the moment seems to be the special issues of elsevier journals. the space reserved by elsevier for esis could be used to announce these special issues and future tc24 meetings. 3. membership of the committee in the past, the requirement for tc24 membership was the esis membership, i.e. the participation to the correspondent national esis-related groups. anyway, a better definition of tc24 permanent membership is worthwhile. it would be usefull a revision of the tc24 mailing list, including people interested in the committee activities and people attending past meetings. workshop on the following day a workshop entitled “structural integrity of railway wheels and wheel/rail interface” was held at the university of brescia with an attendance of approx. 60 delegates. the following presentations were done: “railway wheels: the background” r.smith, imperial college “influence of the contact pressure distribution on the behavior of internally cracked railway wheels” m.guagliano, l.vergani , politecnico di milano “a numerical 3d model to study plastic ratchetting damage of a tramcar line” s.beretta, g.bucca, s.foletti, politecnico di milano “rcf-wear competition in railway wheel-rail interface” g.donzella, m.faccoli, a.mazzù, c.petrogalli, r.roberti, università di brescia “ultrasonic analysis of wheel-rail contact” b.leban, m.pau, università di cagliari “a simple approach to indirect control of railway vehicles rolling surfaces” r.ciuffi, f.piccioli, università di firenze “investigations on railway components some progress”, u.zerbst, gkss, geesthacht “innovative bainitic steel grade for solid wheels tested in artic heavy haul operations” gruppo italiano frattura 8 a.ghidini*, a.gianni*, a.ekberg**, lucchini sidermeccanica and chalmers university “photoelastic analysis of railway wheels in presence of cracks” c.colombo, m.guagliano, m. sangirardi, l.vergani, politecnico di milano tc24 members attendinding the workshop in brescia (from right): zerbst (chairman), drewitt, smith (chairman), guagliano, donzella, and beretta. (6) xix congresso nazionale igf – milano 2007 politecnico di milano, campus bovisa sud 2-4 luglio 2007 il gruppo italiano frattura (igf) organizza il prossimo convegno nazionale, giunto ormai alla sua xix edizione, al politecnico di milano, presso la nuovo campus bovisa sud (milano). il convegno nazionale rappresenta un’occasione per l’incontro, il dibattito e l’aggiornamento fra esperti provenienti dal mondo della ricerca e dell’industria. la finalità è quella di promuovere e diffondere studi ed applicazioni relativi alla meccanica della frattura e del danno in materiali, al calcolo e verifica di integrità strutturale, ai modelli computazionali avanzati. letture plenarie prof. wolfgang brocks is professor for mechanics of materials at the christianalbrechts-university, kiel (germany), where he teaches engineering mechanics and finite element method, and head of the department "modelling of solids and structures" at the institute of materials research in the gkss research centre, geesthacht. in 2002, professor brocks was awarded by esis the “griffith medal” for his outstanding research work in the field of deformation and fracture of metals and in the numerical modeling of ductile an brittle fracture. dr. hugo ernst has been: senior scientist, westinghouse r&d center pittsburgh, pa, usa; director of research fracture proof design corporation, st. louis; and full tenured professor at the georgia institute of technology, atlanta, georgia, usa. since february 1993, he works at the siderca r&d center. he is now head of the structural integrity department. dr. ernst has received the astm sam tour award, for the best paper in corrosion, published by the society in 1994; and the astm george irwin fracture mechanics medal in 1991. (7) convocazione assemblea annuale dei soci 2007 l’assemblea si riunirà in 1a convocazione lunedì 2 luglio 2007 alle ore 17.00 presso il politecnico di milano – campus bovisa sud. in mancanza del numero legale (metà dei soci), l’assemblea si riunirà in 2a convocazione, qualunque sia il numero dei soci presenti, alle ore 17.15 dello stesso giorno, nella stessa sede. ordine del giorno: 1 approvazione dell’ordine del giorno; 2approvazione del verbale dell’assemblea dei soci del 31 maggio 2006 3 comunicazioni del presidente; 4 relazione annuale del presidente; 5 relazione dei revisori dei conti; 6approvazione del bilancio consuntivo 2006; 7indirizzi dell’attività dell’associazione nell’anno 2007; 8previsione finanziaria e quota associativa 2008 9rinnovo delle cariche sociali; 10. varie ed eventuali. nuovo sito igf: www.igfweb.org www.gruppofrattura.it gruppo italiano frattura 9 ß (8) calendario congressi internazionali icmff8-2007 8th international conference on multiaxial fatigue and fracture 10th 14th june 2007 sheffield hallam university, sheffield, uk further details from: icmff8-2007 conference secretariat, sheffield hallam university, city campus, room 5503, surrey building, sheffield s1 1wb, uk. tel.: +44 114 225 5338; fax: +44 114 225 5337; e-mail: conference21@shu.ac.uk web: http://www.icmff8.org.uk/ framcos6-2007 6th international conference on fracture mechanics of concreteand concrete structures 17-22 june 2007 catania, italy further details from: web: http://www.icmff8.org.uk icem 13 international conference on experimental mechanics: experimental analysis of nano and engineering materials and structures 1–6 july 2007 alexandroupolis, greece further details from: professor e.e. gdoutos, school of engineering, democritus university of thrace, greece. e-mail: egdoutos@civil.duth.gr web: http://www.icem13.gr implast 2007 symposium on plasticity and impact mechanics 21–24 august 2007 bochum, germany further details from: professor dr. otto t. bruhns, lehrstuhl fu¨ r technische mechanik, fakulta¨t fu¨ r bauingenieurwesen, ruhr-universita¨ t bochum, d 44780 bochum, germany. tel.: +49 234 32 23080; fax: +49 234 32 14229; e-mail: implast07@tm.bi.rub.de complas 2007 9th international conference on computational plasticity 5–7 september 2007 barcelona, spain further details from: web: http://congress.cimne.upc.es/comp las07 semc 2007 the third international conference on structural engineering, mechanics and computation 10–12 september 2007 cape town, south africa further details from: professor a. zingoni, department of civil engineering, university of cape town, rondebosch 7701, cape town, south africa. e-mail: azingon@ebe.uct.ac.za web: http://www.semc2007.uct.ac.za dtas 2007 international conference on damage tolerance of aircraft structures () 25–28 september 2007 delft, the netherlands further details from: conference secretariat, d&g partners, ms. dineke heersma, ms. gemma van der windt tel: +31(0)6 27227520; fax: +31(0)10 5112119; e-mail: info@dtas2007.nl http://www.dtas2007.nl icfc4 fourth international conference on fatigue of composites 26–28 september 2007 kaiserslautern, germany further details from: conference secretariat, c/o dr n. himmel, institut fuer verbundwerkstoffe gmbh. fax: +49-631-2017-199; e-mail: icfc4@ivw.uni-kl.de www.ivw.uni-kl.de/icfc4 icmobt2 second international conference on mechanics of biomaterials and tissues 9–13 december 2007 lihue, kaua’i, hawaii, usa further details from: nina woods, icmobt conference secretariat, elsevier, the boulevard, langford lane, kidlington, oxford, ox5 1gb, u.k. tel.: +44 (0) 1865 843297 fax: +44 (0) 1865 843958 e-mail: n.woods@elsevier.com http://www.icmobt.elsevier.com dfe2008 international conference on design, fabrication and economy of welded structures 24–26 april, 2008 miskolc, hungary further details from: professor k. jarmai, university of miskolc, miskolc, hungary. e-mail: dfe2008@uni-miskolc.hu website: http://www.alt.unimiskolc. hu/dfe2008 ichmm–2008 second international conference on heterogeneous materials mechanics 3–8 june 2008 huangshan, china further details from: web: http://ichmm 2008.ustc.edu.cn/ichmm2008/ pcf 2008 11th portuguese conference on fracture 13 15 february 2008 lisbon, portugal further details from: rui fernando martins departamento de engenharia mecânica e industrial faculdade de ciências e tecnologia universidade nova de lisboa campus de caparica 2829-516 monte de caparica portugal e-mail: rfspm@fct.unl.pt web: http://eventos.fct.unl.pt/pcf2008 gruppo italiano frattura 10 esis procedures and documents (www.esisweb.org) two kinds of documents are produced by esis technical committees with the following designatory system: esis p2-92 or esis p4-92d, where: 1) p means "procedure", and 2 and 4 are the current numbers, while 92 is the year of issue. 2) d following the year (eg: 92d) means "draft", ie: not yet approved, while 3) d prior to the year (eg: d1-92) means "document" other than test methods. p1-92 esis recommendations for determining the fracture resistance of ductile materials. responsible body: tc1 subcommittee on fracture mechanics testing standards. p2-92 esis procedure for determining the fracture behaviour of materials. responsible body: tc1 subcommittee on fracture mechanics testing standards. p3-03d draft unified procedure for determining the fracture behaviour of material. responsible body: tc1 subcommittee on fracture mechanics testing standards (under preparation not available). p4-92d esis recommendations for stress corrosion testing using pre-cracked specimens. responsible body: tc10 committee on environmental-assisted cracking. p5-00/vamas procedure for determining the fracture toughness of ceramics using the sevnb method . responsible body: tc6 committee on ceramics. p6-98 esis procedure to measure and calculate material parameters for the local approach to fracture using notched tensile specimens. responsible body: tc8 committee on numerical methods. p7-00 esis procedure for dynamic tensile tests responsible body: tc5 subcommittee on dynamic testing at intermediate strain rates. p8-99d esis draft code of practice for the determination and interpretation of cyclic stress-strain data. responsible body: tc11 committee on high temperature mechanical testing. p9-02d guidance on local approach of rupture of metallic materials. (under preparation not available). p10-02 a code of practice for conducting notched bar creep rupture tests and interpreting the data. responsible body: tc11 high temperature mechanical testing committee. p11-02 technical recommandations for the extreme value analysis of data on large nonmetallic inclusions responsible body: tc20 committee on inclusions. d1-92 fracture control guidelines for stress corrosion cracking of high strength alloys. responsible body: tc10 committee on environmental assisted cracking. d2-99 fracture toughness of ceramics using the sevnb method; round robin, test programme. the esis tc6 and vamas twa3 developed a test method and conducted a round robin for its validation. d2-99 presents a detailed documentation of this activity. the final form of the test method has appeared as p5-00. responsible body: tc6 committee on ceramics. gruppo italiano frattura 11 (9) modulo di iscrizione igf-esis gruppo italiano frattura modulo di iscrizione 2007 la quota annuale di iscrizione è di 30 euro (comprensiva di iscrizione esis, european structural integrity society), esente iva a norma dell'art.2 del dpr 26/10/72 e successive modifiche. modalità di pagamento: bonifico bancario su cc. n. 100940 del credito cooperativo bolognese, ag. via arcoveggio 56/22, intestato al gruppo italiano frattura (abi 7082 cab 02402 cin k). paypal, dal sito www.gruppofrattura.it assegno non trasferibile, intestato a gruppo italiano frattura carta di credito. autorizzo il pagamento di 30 € mediante carta di credito eurocard master card visa american express scadenza cognome ……………………………….. nome ……………………. titolo ……… affiliazione ……………………………………………………………………………… indirizzo ………………………………………………………………………………… e-mail …………………………………….. tel …………………. fax ……………… firma ……………………………………… data ………………………………………: inviare il modulo a: segretario igf prof. francesco iacoviello di.m.s.a.t. università di cassino via g. di biasio 43, 03043 cassino (fr) tel./fax 0776-2993681 iacoviello@unicas.it(per cortesia, riempire in stampatello) n° sicurezza microsoft word numero_50_art_28_2520 f. larbi chaht et alii, frattura ed integrità strutturale, 50 (2019) 331-341; doi: 10.3221/igf-esis.50.28 331 using a hashin criteria to predict the damage of composite notched plate under traction and torsion behavior fouzia larbi chaht, mohamed mokhtari, habib benzaama ecole nationale polytechnique maurice audin, algeria fouzialose@hotmail.com, mokhtarimohamed44@yahoo.fr, habenza@yahoo.fr abstract. the volume fraction effect of carbon fiber in an epoxy matrix in the vicinity of the notch on the traction and torsion behavior were studied. this volume fraction which increases with the reduction of the thickness is a parameter which proved effective on the capacity of resistance. the calculations are done with the numerical code abaqus 2009 [1]. using the model hashin with shell elements of the structure. the objective of this study is to simulate the damage of stratified composite materials, the effect of several parameters such as the stacking sequence and the increase of the thickness of the folds having the same orientation of the structure, were evaluated and presented by load-displacement curves. the results obtained from the study illustrate the variation of damage as a function of these effects which act simultaneously and which also show that these modifications have a higher absorption capacity than that without modifications. keywords. fem (finite element method); hashin criteria; shell element; reinforcement. citation: larbi chaht, f., mokhtari, m., benzaama, h., using a hashin criteria to predict the damage of composite notched plate under traction and torsion behavior, frattura ed integrità strutturale, 50 (2019) 331-341. received: 16.05.2019 accepted: 18.08.2019 published: 01.10.2019 copyright: © 2019 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. introduction he use of composite materials has been increasing since their appearance. this use is justified by many advantages, the most remarkable is the relationship between resistance and weight saving. composite materials are an important research area (report 1989) [2], from which many researchers are attracted by the study of their damage [3]. this gives them special importance for the design, production, certification and monitoring of a growing variety of structures. in laminates there is a diversity in the mechanisms of damage produced by several parameters. these parameters are probably affected by the presence of the notch which causes an imbalance of the resistance around their zones. studies have been conducted by researchers to better characterize this phenomenon. lu studied the phenomenon of concentration and distribution of stresses around a hole [4]. subsequently, analytical solutions have been progressively developed by researchers for increasingly complex geometries. madani [5] have greatly contributed to the knowledge and development of this field by performing a systematic analysis of the main geometries and shapes. t http://www.gruppofrattura.it/va/50/2520.mp4 f. larbi chaht et alii, frattura ed integrità strutturale, 50 (2019) 331-341; doi: 10.3221/igf-esis.50.28 332 several researchers have studied the effect of the stacking sequence on the behavior of composite structures such as mokhtari [6] and the use of stratified composite with change in ply thicknesses mokhtari [7]. these techniques have been expanded by the use of strengthening or repair patch by ait kaci [8]and benzaama [9]. in the damage the models are implemented on formulations of solid type donado [10], and more often of the shell type, these two-dimensional elements peter linde [11] with a geometrically zero thickness are used for problems of thickness and displacement more or they can greatly reduce the calculation time elangovan [12].but in the case where the shear deformation occurs in structures with a larger thickness, we must opt for the use of solid elements which give results that can't be obtained by shell elements yong guo [13]. on which rests a good accuracy. the hashin criterion barberon [14] seen improvements in its prediction ability through the quadratic interaction criterion between the different tractions; that of the fiber and the matrix acting on the plane of damage until the introduction of the criteria which distinguish between the tension and the compression of fiber and the matrix, and this by using a quadratic interaction between stress invariants. according to the researchers, the latter is not always appropriate in the case of matrix or fiber compression, and which does not take into account the effects of shear in the plane which significantly reduces the compressive strength of a composite layer. this prompted several researchers to propose modifications to the hashin criteria in order to improve their predictive abilities carlos [15]. we use this hashin damage criterion for unidirectional fiber composites: this is a criterion that interacts with more than one stress component to evaluate different fracture modes. this criterion was originally developed for unidirectional polymer composites, and other types of non-polymeric laminates. failure indices for the hashin criteria are related to fiber and die failures and involve four failure modes. the maximum stress criteria are used for the transverse normal stress component that respond to threedimensional problems. notches are inevitable in the design of structures. this is the problematic of our work because are the areas where the initiation and the propagation of the cracks will take place. this approach, which can practically be difficult to achieve, is approved by the numerical results and can also be a solution to other problems in composite structures. the originality of our work is the improvement of the resistance of a composite structure notched by modifications both geometric and others whose parameters of the material in use is the criterion of haschin. this objective will take place if the architecture parameters of the composite are optimized because the competition between the reduction of thickness and the increase of the volume fraction of the fibers amply show results which are highly evaluative by their parameters. hashing criteria and input parameter he growth prediction and the damage trajectory are implemented by an intra-laminar damage criterion that is implemented in the standard abaqus calculation code [16]. the input data for the hashin criteria given in the tables are longitudinal tensile and compressive strengths, transverse tensile and compressive strengths, and longitudinal and transverse shear strengths. all resistance values are assumed to be positive sokolinsky [17]. in this criterion of damage there is no inter-laminar propagation path, no separation or existence of the interface but the damage is continuous in the structure by degradation of rigidity or by removal of the elements of the structure. several modes of damage can occur such as the breaking of the fiber and that of the matrix in tension and in compression. in most of cases these modes occur simultaneously, hence the importance of opting for the hashin criterion which introduces six criteria for initiation of tension and compression damage for fiber and matrix and at the interface level. this is to predict the multimodal phenomenon of composite damage. the hashin criteria used are quadratic, not because of their mechanical behavior may be the fit of the curve pederson [18]. these criteria of damage have the following general forms: 1. tensile fiber failure for σ11 ≥ 0 2 2 2 12 1311 2 12 1 failure 1 no failuretx s            (1) 2. compressive fiber failure for σ11 < 0 2 11 1 failure 1 no failurecx          (2) t f. larbi chaht et alii, frattura ed integrità strutturale, 50 (2019) 331-341; doi: 10.3221/igf-esis.50.28 333 3. tensile matrix failure for σ22 + σ33 > 0   13 2 2 22 1222 33 23 22 33 2 2 2 23 12 1 failure 1 no failurety s s               (3) 4. compressive matrix failure for σ22 + σ33 < 0   13 2 2 2 22 1222 3322 33 23 22 33 2 2 2 23 23 23 12 1 failure 1 1 no failure2 4 c c y s y s s s                                 (4) 5. interlaminar tensile failure for σ33 > 0 2 33 1 failure 1 no failuretz          (5) 6. interlaminar compression failure for σ33 < 0 2 33 1 failure 1 no failurecz          (6) the numerical prediction presents reliable simulations not only in the sense of the geometry of the numerical model which has been realized by a unique structure in shell elements but also with the criterion of damage related to this region. in other words, no interface between the folds or between the fibers and the matrix. add to this that our search result was in the overall response of the structure under loading and its failure load. so the numerical computation parameters were in agreement with the convergence of computation, which allows us moreover to go to the evaluation of several geometrical parameters hardly supported by numerical computations. the parameters introduced in the abaqus calculation code are: ** materials *material, name=material-1 *damage initiation, criterion=hashin 2050.,1200., 62., 190., 81., 81. *damage evolution, type=energy 45., 45., 0.6, 0.6 *damage stabilization 0.003,0.003,0.003,0.003 *elastic, type=engineering constants 170000.,9000.,9000., 0.34, 0.34, 0.34,4800.,4800.4500., description of model geometry and material properties he geometric finite element model is shown in figure 1. material and strength properties for the composite patch material (carbon / epoxy) are shown in tables 1, 2 and 3 respectively. the laminated carbon / epoxy composite sheet having the following dimensions: height h = 140 mm, width w = 50 mm, thickness e = 2 mm. a single circular shape with only one dimension of the notch is taken for each stacking sequence. these plates are subjected to an imposed displacement, equal to 2 mm. the modification is positioned around the notch to reinforce and reduce the tension of the damaged area in the course of loading (figure 1). the dimensions of the thicknesses of this modification are according to the volume fraction of fiber and which are as follows: 0.25 mm for a fraction of 50%, 0.2 mm for a fraction of 70% and 0.125 mm for a fraction of 90%. in the tensile behavior, the fixing and loading conditions consist in fixing the structure at one edge in the vertical and longitudinal direction and a traction displacement on the opposite edge, the same thing in the torsional behavior except that the loading is in rotation around the center of the plate. in the case where both types of loading are applied, traction and rotation must be in the same direction. t f. larbi chaht et alii, frattura ed integrità strutturale, 50 (2019) 331-341; doi: 10.3221/igf-esis.50.28 334 the elastic and carbon resistance properties of the epoxy are chosen from the library of the cadec [19] which determines, according to the volume fraction, the properties of the carbon / epoxy composite, and which allows us to calculate the resistance parameters by changing the thickness. figure 1: geometrical modification of the composite plate e1 = 170000mpa ν12 = 0.342 g12 = 4800mpa xt =2050 yt=62 e2 = 9000mpa ν13 = 0.342 g13 = 4800mpa xc=1200 yc=190 e3 = 9000mpa ν23 = 0.342 g23 = 4500mpa sl =81 st=81 table 1: for a 65% fraction and 0.25mm thickness [20]. e1 = 195000mpa ν12 = 0.32 g12 = 8167mpa xt = 2500 yt=74 e2 = 13450mpa ν13 = 0.32 g13 = 8167mpa xc= 1500 yc=224 e3 = 13450mpa ν23 = 0.32 g23 = 7137mpa sl =90 st=90 table 2: for a 75% fraction and a 0.2mm thickness. e1 = 221500mpa ν12 = 0.31 g12 = 13540mpa xt = 3000 yt=82 e2 = 21670mpa ν13 = 0.31 g13 = 13540mpa xc= 2200 yc=236 e3 = 21670mpa ν23 = 0.31 g23 = 11790mpa sl = 97 st=97 table 3:for a fraction of 85% and thickness of 0.125mm. e: young’s modulus, ν: poisson’s ratio, g: shear modulus xt: longitudinal tensile strength, xc: longitudinal compressive strength, yt: transverse tensile strength yc: transverse compressive strength, sl: longitudinal shear strength, st: transverse shear strength different ply orientations of the composite adherent are considered in this study to investigate their effect on the failure load. the value of θ (orientation angle) is taken from the longitudinal direction of the structure (x-axis) and varied from 0◦ to 90◦ (table 1,2,3) with step of 15◦. then, in the second case, some modifications were introduced and presented in fig.8. all layers have the same matrix (epoxy) and the same fiber materials (carbon). f. larbi chaht et alii, frattura ed integrità strutturale, 50 (2019) 331-341; doi: 10.3221/igf-esis.50.28 335 1 2 3 4 5 plies sequences (0)s (0/-15/15/90)s (0/-30/30/90)s (0/-45/45/90)s (0/-60/60/60/90)s table 4: the sequences of the plies used. the different configurations of the architecture composite structures are proposed to evaluate the behavior of their damaged. first, we used a structure plate with the same thickness and natureof fiber but the thickness of the layers changes around the notch simultaneously with different other parameters and with different orientations (figure 1). figure 2: the stacking sequence of composite used. for the configuration n°1 of the laminate, the thickness of all layers is identical of each layer and equal to 0.25 mm (fig. 1). for the configuration n°2 and n°3, the thicknesses of the several layers of the laminate are not identical; we can found two models ; when the thickness increase progressively around the notch from 0.125mm to 0.25mm going through 0.20 mm (fig. 3), we call it configuration n°2 and when the thickness is decrease around the notch from 0.25mm to 0.125mm going through 0.20 mm (fig.3), we call it configuration n°3. figure 3: detail of the mesh of each area. in this analysis, the mesh of the structure is refined around the area of the notch in order to accurately capture the area of damage. to simulate the damage in the plate, the linear behavior of the composite was presented using s4r shell elements (zero thickness) or the thickness of the structure was introduced into the properties of the composite. the number of elements is 13428 elements. the hashin criterion is implemented in the structure studied, and for each modification of f. larbi chaht et alii, frattura ed integrità strutturale, 50 (2019) 331-341; doi: 10.3221/igf-esis.50.28 336 the properties of the structure, the same number of elements is used. figure 3 shows a detail of the mesh used for the calculations. results and analysis enerally in structures, the geometric discontinuity such as the notch, has a weakness that quickly promotes their damage. these structures do not only undergo traction, which is the most dangerous solicitation, but also other loads that can undoubtedly accelerate their failure. during loading, the participants (stacking sequence / hybrid / geometric modification) play a determining role in the values of the resistance and the structural reaction to loading, are the parameters that have been evaluated in this work. it is by design that these cuts impose their existence in the structures, where often their damage will begin. from this problem, it is essential to look for a solution that takes the objective of reinforcement in order to delay the damage. referring to the work of benzaama[9].where the shape and size of the notch has been widely studied. in this study, only the reinforcement with the circular shape around the circular notch is limited by evaluating only the competition effect between the reduction of the thickness and the increase of the fiber volume fraction. figure 4: geometrical modification around the notch. figure 5: load displacement curve under tension loading. we made two changes: first when the thickness decreases and second when the thickness increases. the continuity of the fibers in the zones modified by a change of volume fraction and effectively of the thickness is ensured numerically by a change in the properties of rigidity and fracture of the composite if not, the calculation will take a discontinuity of the g f. larbi chaht et alii, frattura ed integrità strutturale, 50 (2019) 331-341; doi: 10.3221/igf-esis.50.28 337 fibers. the use of the computer aided design environment for composites (cadec 2014) will allow us in advantage to have the stiffness properties as well as the strength of the composite when loading at the notch. effect of loading type and geometric modifications on the behavior damage of the laminate plate notching often researchers are interested in structures that are subjected to loadings only in traction to determine their behavior. what is new in this part of the work is to add, not only another rarely studied behavior, but also to associate these two types of loading traction with rotation and likewise to make a comparison between these different types of loading in order to have a prediction of the damage of a notched laminate structure. first, each geometric model takes are evolution to the predicted damage that is presented by the load-displacement curves, these geometric models are: simple model without modification, we took it as a witness in order to compare it with the other models those of renamed modifications 1 and 2. for modification 1; we increased the thickness with the decrease in the volume fraction near the notch to keep the fiber continuity numerically. for modification 2; it is the opposite of the modification 1, we decreased the thickness and increased the volume fraction in the vicinity of the notch. the proposition of these geometric shapes with the simple form allows us to better compare and better understand how the damage occurs in nonlinear (geometric and property) situations. figure 5 shows the reaction of the structure to the imposed loading type traction and with circular notch. it can be seen that the effect of the proposed geometries is directly proportional to the strength of the structure; for geometric modification 1 where we have a reduction of the thickness at the notch which has a reduction which remains very small, the change of the load response of the structure appears beyond a displacement of 0.2mm. modification 2 presents a whole change in the response to loading and subsequently in its resistance levels; less resistance more elongation in the structure. b) a) figure 6:(a) load displacement curve under torsion loading; (b) load displacement curve under mixed loading. in the figure 6-a, the proposed reinforcements not only increase the rigidity of the structure but also the resistance to damage. the proposed reinforcing capacity and in particular the modification 2 does not have any advantage in the resistance to damage. while the modification 1 is more resistant if and only if, the size of modification widens or is optimized, the same remarksare noted in the two types of loading applied; traction and torsion. on the other hand, what is different in the results is that the response to the loading for the behavior in torsion and purely linear with the fast damage. figure 6-b shows the mixed stress of the notched plate: traction and rotation with the same pitch not to favor one over the other. it is also noted that the capacity of reinforcement by the proposed modifications on the structural resistance is conditioned much more by the type of loading than by the geometrical modifications. f. larbi chaht et alii, frattura ed integrità strutturale, 50 (2019) 331-341; doi: 10.3221/igf-esis.50.28 338 effect of stacking sequence and composite hybrid of the plate notched on the behavior damage : in this part of the study we are interested in the stacking effect of the structure itself and the change of nature of the fiber in some folds of laminates as a determining parameter that can give more resistance to the damage of the structure notched. the load transfer in the structure around the notch is ensured by its rigidity which is ensured by the orientation of the fibers and thus the objective is to evaluate the value of the breaking load by the modification of the stiffness of the composite (stacking sequence). 0° 60° (a) 0° 60° (b) 0° 60° (c) figure 7:(a) load displacement curve under tension loading of simple geometry;(b) load displacement curve under tension loading of modification1;(c) load displacement curve under tension loading of modification 2. f. larbi chaht et alii, frattura ed integrità strutturale, 50 (2019) 331-341; doi: 10.3221/igf-esis.50.28 339 these figures7-a-b-c show the effect of stacking on the resistance of these geometrically modified plates at the notch under the traction load. the catches are presented for each case and only for the damage of the fibers in tension which are responsible for the overall damage of the structure. for all cases of modification, we notice a linear behavior until the damage. for the simple geometry with the stacking effect we notice different values in the damage force as in the displacement at break. these stacks significantly improve the overall strength throughout the structure and particularly at the notch relative to the 0 and l orientation stacks. the stacks of 15 and 30 are more resistant than those of 45 and 60,which remain remarkable for the geometry of the first modification 1 with a different magnitude, except for the second modification which largely favors the stacking effect of all fiber orientation angles. in the end, we can see that with the geometric modifications and its optimized stacks we can obtain a higher resistance than the structures without modification. figure 8: reinforcement of the thickness of some layers (the modifications are symmetric in the other side). in this part of our study, we modified the mechanical properties of different layers by choosing a hybrid composite as shown in the following stacking sequences: (0/-30/30/90)s (0r/-30/30/90)s (0/-30r/30r/90)s (0/-30/30/90r)s where r stays for the reinforced thickness of layers in the composite. we change only the thickness of two layers which have the same fiber orientations for the three stacking sequences of structure (fig. 8). hence, we get 8 plies of composite. (a) (b) figure 9: (a) load displacement curve under tension loading of hybrid mod1. (b) load displacement curve under tension loading of hybrid mod2. f. larbi chaht et alii, frattura ed integrità strutturale, 50 (2019) 331-341; doi: 10.3221/igf-esis.50.28 340 in figure 9, force / displacement curves for structures with modification 1 and 2 have been presented with the stacks which each have a high optimized resistance (15° and 60°). subsequently, the thickness of the folds, which have the same fiber orientations for each case, has been reinforced as an evaluative parameter, which makes it possible to have their effects on the resistance of the structure. note that for the two curves, the reinforcement 0° and 90° folds have significant values than other angles except those without modification. conclusion his work has demonstrated the effectiveness of a 2d numerical approach with the use of hashin criterion of damage and with shell elements in laminated composite structures notches. it is also demonstrated the effectiveness of the reinforcement by geometric modifications that summarize our objective. • the use of the hashin criterion gives the advantage of analyzing the damage of composite structures with complex geometries. •the geometrical propositions studied can be accompanied by several parameters that make them more useful in the resistance of notched composite structures. • the value of the failure load is influenced by the type of the load applied and impalement sequence. •the introduced changes present a change in the response of the structure to the changes. • the carbon/epoxy composite absorbs better the stress than the aramid/epoxy and therefore a reduction in the value of load is observed. •the damage value and the propagation path follow the orientation of the fibers in the stress concentration zone. • the rack birth and its propagation depend directly on the fiber orientation at of the notch tip. references [1] abaqus, abaqus version (2009). 6.9 documentation. providence, ri: dassault systems simulia corporation. [2] bureau of accident investigation. (1989). aircraft accident report: aloha airlinesflight 243 boeing 737-200. national transportation and safety office. available at: https://www.faa.gov/about/initiatives/maintenance_hf/library/documents/media/human_factors_maintenance/air craft_accident_report--aloha_airlines.flight_243.boeing_737-200.n73711. near_maui.hawaii.april_28. 1988. [3] ponces camanho, p. (2002). failure criteria for fibre-reinforced polymercomposites, demegi. [4] lu, j., lieurade, h p., tehniques de l’ingénieur, concentration de contraintes, génie mécanique bm 5, 40, pp. 1–24. [5] madani, s., touzain, x., feaugas, s., cohendouz, m., ratwani, m. (2010) experimental and numerical study of repair techniques for panelswith geometrical discontinuities. computational materials science (48), pp.83–93. doi: 10.1016/j.commatsci.2009.12.005 [6] mokhtari, m., madani, k., benzaama, h., malarino, s.(2017).effects of the composite stacking sequence on the failure load of the single lap bonded joint. journal of theoretical and applied mechanics, 55(4), pp. 1257-1268. [7] mokhtari,m., madani, k., belhouari ,m., touzain, s., feaugas, x., ratwani ,m .(2013).effects of composite adherend properties on stresses in double lap bonded joints. materials and design, 44, pp. 633–639. doi: http://dx.doi.org/10.1016/j.matdes.2012.08.001. [8] ait kaci, d., madani, k., mokhtari, m., feaugas,x. ,touzain,s.(2017) .impact of composite patch on the j-integralin adhesive layer for repaired aluminum plate. advances in aircraft and spacecraft science,4(6),pp. 679-699. [9] benzaama, a., mokhtari,m., benzaama, h., gouasmi, s., tamine, t. (2018).using xfem technique to predict the damage of unidirectional cfrp composite notched under tensile load. advances in aircraft and spacecraft science,5(1), pp. 129-139. [10] donadon, m. v., de almeida, s f m., arbelo,m a., orúe, a b. (2009). a three-dimensional ply failure model for composite structures. international journal of aerospace engineering. doi: 10.1155/2009/486063. [11] linde, p., de boer, h. (2011). behaviour of solid like shell elements in simulation of composites in aircraft structures.16th international conference on composite structures iccs 16 a. j. m. ferreira (editor) feup, porto, portugal. [12] elangovan, p. (2012). a study on solid and shell material model in stamping simulation. stamping simulation engineer valeo india private limitedblock a, 4th floor, tecci park no. 176 rajiv gandhi salai sozhanganallur chennai ,pp.600-119. india, hts. t f. larbi chaht et alii, frattura ed integrità strutturale, 50 (2019) 331-341; doi: 10.3221/igf-esis.50.28 341 [13] guo ,y . ( 2000).eight-node solid element for thick shell simulations, livermore software technology corporation livermore, california, usa, 8, pp. 46. [14] barberon, e., shahbazi, m .(2017). determination of material properties for ansys progressive damage analysis of laminated composites. composite structures, 176, pp. 768–779. [15] davila,c g., camanho, p p., rose, c a .(2005). failure criteria for frp laminates. journal of composite materials. doi: 10.1177/0021998305046452. [16] abaqus finite element programs. abaqus istandard 5.6. hibbitt. pawtucket, ri 028: karlsson and sorensen, inc. [17] sokolinsky, v. (2013). using failure criteria for unidirectional fiber composite in abaqus, simulia. [18] pederson, j. (2006).finite element analysis of carbon composite ripping using abaqus. masters diss, clesmo university. available at: https://tigerprints.clemson.edu/cgi/viewcontent.cgi?article=1512&context=all_theses. [19] computer aided design environment for composites, cadec 14.1.6521.18183. available at: http://en.cadec-online.com/. [20] trigo, j.(1996). dimentional stability characterization of carbon fiber with epoxy and cyanate ester resin laminates due to moisture absorption.space craft structures. materials and mechanical engineering, proceedings of the conference held by esa, cnes and dara in noordwijk, paris. << /ascii85encodepages false /allowtransparency false /autopositionepsfiles true /autorotatepages /none /binding /left /calgrayprofile (dot gain 20%) /calrgbprofile (srgb iec61966-2.1) /calcmykprofile (u.s. web coated \050swop\051 v2) /srgbprofile (srgb iec61966-2.1) /cannotembedfontpolicy /error /compatibilitylevel 1.4 /compressobjects /tags /compresspages true /convertimagestoindexed true /passthroughjpegimages true /createjobticket false /defaultrenderingintent /default /detectblends true /detectcurves 0.0000 /colorconversionstrategy /cmyk /dothumbnails false /embedallfonts true /embedopentype false /parseiccprofilesincomments true /embedjoboptions true /dscreportinglevel 0 /emitdscwarnings false 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/hrv (za stvaranje adobe pdf dokumenata najpogodnijih za visokokvalitetni ispis prije tiskanja koristite ove postavke. stvoreni pdf dokumenti mogu se otvoriti acrobat i adobe reader 5.0 i kasnijim verzijama.) /hun 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can be opened with acrobat and adobe reader 5.0 and later.) >> /namespace [ (adobe) (common) (1.0) ] /othernamespaces [ << /asreaderspreads false /cropimagestoframes true /errorcontrol /warnandcontinue /flattenerignorespreadoverrides false /includeguidesgrids false /includenonprinting false /includeslug false /namespace [ (adobe) (indesign) (4.0) ] /omitplacedbitmaps false /omitplacedeps false /omitplacedpdf false /simulateoverprint /legacy >> << /addbleedmarks false /addcolorbars false /addcropmarks false /addpageinfo false /addregmarks false /convertcolors /converttocmyk /destinationprofilename () /destinationprofileselector /documentcmyk /downsample16bitimages true /flattenerpreset << /presetselector /mediumresolution >> /formelements false /generatestructure false /includebookmarks false /includehyperlinks false /includeinteractive false /includelayers false /includeprofiles false /multimediahandling /useobjectsettings /namespace [ (adobe) (creativesuite) (2.0) ] /pdfxoutputintentprofileselector /documentcmyk /preserveediting true /untaggedcmykhandling /leaveuntagged /untaggedrgbhandling /usedocumentprofile /usedocumentbleed false >> ] >> setdistillerparams << /hwresolution [2400 2400] /pagesize [612.000 792.000] >> setpagedevice microsoft word numero_50_art_4_2560 g. khandouzi et alii, frattura ed integrità strutturale, 50 (2019) 29-37; doi: 10.3221/igf-esis.50.04 29 numerical simulation of crack propagation behavior of a semicylindrical specimen under dynamic loading ghorban khandouzi school of mining engineering, college of engineering, university of tehran, tehran, iran gh.khandouzi@ut.ac.ir mohsen mollashahi department of mining and metallurgical engineering, amirkabir university of technology, tehran, iran mohsenmollashahi@aut.ac.ir mojtaba moosakhani school of mining engineering, college of engineering, university of tehran, tehran, iran mj.moosakhani@gmail.com abstract. to design and evaluate the analytical crack propagation of a specimen under dynamic load, measurement of dynamic fracture parameters is necessary. however, analytical methods have significant complexity, and experimental methods are also time-consuming that require high precision and considerable funding. therefore, numerical methods can be used to solve these problems. the extended finite element method (x-fem) as a powerful and efficient tool can be used for this purpose. in this paper, x-fem code in abaqus software was used in order to simulate crack growth in a semi-circular specimen with pre-existed crack and also intact specimen to determine dynamic stress intensity factor (dsif) using displacement extrapolation method. to verify the numerical modeling output, the curve of crack surface opening displacement (csod) in x-fem model has been compared with the experimental curve. moreover, concrete damage plastic (cdp) model was used to validate xfem simulation results. the results show that the dsif for a cracked sample under a maximum dynamic load 3000 n is equal to 0.5 mpa m . comparison between the cdp and x-fem results showed that in both approaches, the same area for crack propagation was also determined. keywords. extended finite element method (x-fem); concrete damage plastic (cdp); displacement extrapolation; dynamic stress intensity factor (dsif); crack surface opening displacement (csod). citation: khandouzi, g., mollashahi, m., moosakhani, m., numerical simulation of crack propagation behavior of a semicylindrical specimen under dynamic loading, frattura ed integrità strutturale, 50 (2019) 29-37. received: 10.05.2019 accepted: 09.07.2019 published: 01.10.2019 copyright: © 2019 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. http://www.gruppofrattura.it/va/50/2560.mp4 g. khandouzi et alii, frattura ed integrità strutturale, 50 (2019) 29-37; doi: 10.3221/igf-esis.50.04 30 introduction n most civil or mining projects such as blasting, road tunnels excavation, flying rocks and support systems, the type of the forces applied are dynamic. there are several methods to predict the effect of dynamic loads on structures with a flaw. one of the most important of these methods is introduced by the international society of rock mechanics (isrm) in 2012. this method uses semicircular specimens with a pre-existing crack under dynamic load. measurement of dynamic failure parameters such as stress intensity factor, crack start and crack propagation velocity when analyzing the behavior of a dynamically loaded structure is important. while a dynamic load distribution model increases the level of complexity and the existing analytical solutions are mainly suitable for simple problems, numerical modeling is considered as a suitable tool for solving these problems. according to jing [1], a valid numerical model requires complete knowledge of the geometric and physical properties of fractured rock masses. the main challenge is not to build a perfect model, but to create a model that is suitable for the main purpose [1]. for analyzing the fracture, there are a variety of numerical methods for cracking process modeling such as nmm (numerical manifold method) [2], dda (discontinuous deformation analysis) [3], bem (boundary element method) [ 4], rfpa (rock failure process analysis) [5], pfc (particle flaw code) [6], x-fem [7, 8], and several other in-house codes based on the lefm criteria [9]. in addition to creating system equations, two main tasks include evaluating the stress intensity factors (sif) and fracture growth simulation based on determining the mode of fracture (i, ii and iii) and different criteria for fracture growth such as maximum tensile strength or energy release rate [1]. so, based on the requirements listed above, as well as jing expressed in numerical modeling, in this study, xfem method is used for modeling crack propagation. failure mechanism consists of two parts start failing and the damage assessment based on the maximum principal stress fracture and power-law fracture criteria. the displacement extrapolation method has been used to determine initiation stress intensity factor and csod plot for modeling verification. cdp model is adapted to estimate the failure area in the specimen and comparison between kinetic energy and internal energy for verification of the cdp model. extended finite element method odeling of fixed discontinuities, such as cracks, using the conventional finite element method, requires that the mesh is compatible with geometric discontinuities. therefore, a high mesh density is required in the neighborhood of the crack edge to capture the singular asymptotic fields properly. moreover, modeling of a growing crack is even more complex as the mesh ought to be updated continuously to fit the geometry of the fracture as the crack progresses [10]. the extended finite element method (xfem) reduces the problems associated with the meshing of crack surfaces [10]. nowadays, the x-fem has developed as a powerful numerical method for the analysis of crack propagation [11]. this method mixed finite element and meshless method. modeling of crack explicitly in this method isn't by the mesh, but it uses the crack geometry implicit description, compatible with any crack path, regardless of its prior condition [12-13]. one of the major benefits of x-fem on finite element method is the flexibility and versatility in modeling, which does not need to be aligned with the element edges. this method is based on the enrichment of the fe model with additional degrees of freedom (dof) connected with the nodes of the elements intersected to the discontinuity [14]. failure criterion in x-fem x-fem model uses the maximum principal stress criterion for the damage initiation criterion and also a power-law criterion for calculation of damage assessment law. eqn. (1) illustrates the maximum principal stress criterion : 0 max max f          (1) where 0maxσ shows the maximum principal stress allowed. the macaulay bracket with the ordinary interpretation is represented by the symbol   . to signify compressive stress that does not initiate damage the macaulay brackets are used. initiation of damage is assumed to begin when the maximum stress ratio is equal to one [10]. the abaqus uses the power law model described in eqn. (2): i m g. khandouzi et alii, frattura ed integrità strutturale, 50 (2019) 29-37; doi: 10.3221/igf-esis.50.04 31 0 ( ) n m equiv i ii iii equivc ic iic iiic g g g g g g g g                 (2) for defining power-law model or equation, icg , iicg , iiicg , m α , n α and 0α must be provided; power-law criterion is described in wu and reuter (1965) by eqn. (2) [10], this equation is very practical in fracture problem and has been applied by elder et al (2004), zou (2002) and lammerant & verpoest (1996) [15]. specimen modeled in abaqus software he isrm has proposed two standard methods for determining static fracture toughness in rocks. they suggest that core-based prototypes experiments be performed on a typical laboratory compression or tension load frame [16]. these proposed specimens are used by iqbal and mohanty in the experimental calibration [17]. they contend that the deviation between different results stems from the specimen size, the rock anisotropy, and the dimensionless parameter in the equation of fracture toughness calculation in the ccnbd test [17]. another method has been introduced by kuruppu and et.al in 2013 using the same semi-circular bend specimen that introduced by zhao and et.al (2012) to determine the rock dynamic fracture toughness [18]. the benefits of semi-circular sample (scb) instead of cb (chevron bend), sr (short rod) & ccnbd (crack chevron notched brazilian disc) in determining of static fracture toughness are the low requirement of material per each specimen (for meeting the requirements in linear elastic fracture mechanics (lefm)), simple test setup, and the synchronization of the maximum compressive load with initiation cracking[16]. in some of the cases such as blasting, support system design, explosives storage and rock bursts under dynamic load in seismic events, the dynamic parameters instead of static parameters need to be determined. furthermore, zhao et.al has proposed a method to determine dynamic stress intensity factor using semi-circular bending specimen with a straight notch as geometry specimen shown in (fig. 1). figure 1: the scb specimen [18] figure 2: loads applied to the specimen (30000 left and 3000 right). mechanical and geometrical characterizations of specimen simulation using x-fem are presented in tab. 1 which has resulted from various laboratory tests. in this paper, the rock materials are considered isotropic, homogeneous, and elastic. the maximum principal stress failure criterion is selected for damage initiation and an energy-based damage evolution law based on a power-law t g. khandouzi et alii, frattura ed integrità strutturale, 50 (2019) 29-37; doi: 10.3221/igf-esis.50.04 32 fracture criterion is chosen for damage propagation. these criteria have been described in the previous section. the relevant material data are presented in tab. 1 resulted from various laboratory tests. the impact loads applied to the specimen are shown in (fig. 2). scb specimen mechanical & geometry characterization diameter 40 mm 2 4 thickness 20 mm distance between two supports 24 mm notch length 7 mm density 2400 kg/ 3m elastic modulus 3137e7 n/ 2m poison ratio 0.19 maxσ 10 (mpa) icg 42200 (n/m) iicg 42200(n/m) iiicg 42200(n/m) mα 1 nα 1 0α 1 table 1: mechanical and geometrically characterization of the scb specimen the loads applied on numerical samples are the same as the experimental load shape that measured in split hopkinson pressure bar test. this setup had been used to measure dynamic load by chen et al (2009) [19], dai et al (2010) [20] and dai et al (2011) [21]. measurement dynamic stress intensity factor and crack surface opening displacement (csod) isplacement extrapolation technique has been used for calculation of the intensity of dynamic initiation stress, as shown in eqn. (3). 2 / 1 b a y y i u u k r k        (3) where ik is the factor of stress intensity,  μ represents shear modules, r defines the distance from the crack tip, b yu and ayu show displacements at y-direction in the points marked on the model and    k 3 / 1    is used for plane stress and  k 3 4  for plane strain, and  shows the poison ratio. according to this method, points positioned in the model, which is shown in (fig. 3), are used to calculate the dynamic stress intensity factor. the displacement curve in one direction at four points to determine the stress intensity factor of the crack start is shown in fig. (6). however, before the crack reaches to horizontal directions of above-mentioned points shown in (fig. 4), displacement has linear form due to elastic deformation of the specimen while when the crack reaches these points, displacement curve turns into non-linear form. the final result for this strategy is presented in (fig. 6). d g. khandouzi et alii, frattura ed integrità strutturale, 50 (2019) 29-37; doi: 10.3221/igf-esis.50.04 33 moreover, the crack path after the simulation is shown in (fig. 4). stress intensity factor according to (fig. 5) is also presented in eqn. (4). figure 3: using displacement extrapolation in order to define stress intensity factor [22]. figure 4: points and direction for displacement extrapolation method and crack path simulation. figure 5: stress intensity factor according to displacement extrapolation.        &   iif y k x r  (4)  60      8 * 10 * 0 499032      0.5 id idr k k mpa m     . to verify numerical simulation in this paper, experimental data, csod graph, as shown in (fig. 7) , is obtained and compared with experimental results measured by chen et al (2009) [19], dai et al (2010) [20] and dai et al (2011) [21]. there is a good agreement between curves’ trends of numerical and experimental results. also, the crack path and crack initiation angle in the x-fem code is compared and verified with the experimental results of kalthoff and winkle (1987) and john and shah (1990) [10]. g. khandouzi et alii, frattura ed integrità strutturale, 50 (2019) 29-37; doi: 10.3221/igf-esis.50.04 34 figure 6: displacement – time curve for four points on fig. 6. figure 7: csod curve for scb specimen in x-fem model [19]. comparisons between damage and x-fem method he concrete damage plasticity (cdp) model herein has just been used to validate x-fem simulation results. (fig. 8) illustrates internal energy and kinetic energy for scb specimen in the cdp model. these curves are used for verification of cdp numerical modeling. according to the cdp model, internal energy has to be 8-10 times of the kinetic energy. in (fig. 8) internal energy fluctuates between 0 and 1.6 (kj) and kinetic energy varies between 0-0.2 (kj). according to these results, the internal energy is 8 times kinetic energy. as it can be seen in (fig. 9-b), the area with red colour is considered as the crushed area in the cdp model. the same load of 30000 n used in the x-fem model (fig. 9-a). the green area is regarded as a crack propagation area under the same load in x-fem code. comparison of two figures show the same areas of crack propagation under the dynamic load. dynamic loads of 3000 n and 30000 n have been exerted to the models as shown in (fig. 10-a) and (fig. 10-b), respectively. under the dynamic load of 3000 n the specimen doesn’t fail completely (fig. 10-a) while under the load of 30000 n the specimen completely failed (fig. 10-b). increasing in the load that needs for the propagation of a crack in intact specimen rather than the specimen with initial crack is due to the existence of initial flaw. t g. khandouzi et alii, frattura ed integrità strutturale, 50 (2019) 29-37; doi: 10.3221/igf-esis.50.04 35 figure 8: internal energy and kinetic energy for scb specimen figure 9: damage model for scb specimen-(a) x-fem & (b) cdp model figure 10: scb specimen without crack under 3000 n (a) & 30000 n(b) comparison between cdp and x-fem results (green area in (fig. 8-a) and (fig. 10-b)) showed the same area for crack propagation. therefore, the numerical method is a practical & powerful method for solving dynamic failure problems. conclusions  the cracked semicircular specimen completely failed under the dynamic load of 3000 n whilst, for intact specimen, it failed under the dynamic load of 30000 n. consequently, it illustrate that existence of any flaw in specimens will decrease the dynamic load required for crack propagation.  before the crack was initiated, displacement – time curve is linear, while it becomes nonlinear when the crack starts to grow. g. khandouzi et alii, frattura ed integrità strutturale, 50 (2019) 29-37; doi: 10.3221/igf-esis.50.04 36  the dynamic stress intensity factor required for crack initiation was calculated by the displacement extrapolation method. according to the obtained results, the dsif equals 0.5 mpa√m.  comparison between damage and x-fem models results presents the same area for crack propagation.  csod curve for x-fem code shows good agreement with experimental test.  according to the cdp model, the internal energy must to be 8-10 times of kinetic energy. the results demonstrate that internal energy is 8 times of kinetic energy.  the numerical method is a practical & powerful method for solving dynamic failure problems. references [1] jing, l. (2003). a review of techniques, advances and outstanding issues in numerical modelling for rock mechanics and rock engineering, international journal of rock mechanics and mining sciences, 40(3), pp. 283– 353. doi:10.1016/s1365-1609(03)00013-3. [2] zhang, h.h., li, l.x., an, x.m. and ma, g.w. (2010). numerical analysis of 2-d crack propagation problems using the numerical manifold method, engineering analysis with boundary elements, 34(1), pp. 41–50. doi:10.1016/j.enganabound.2009.07.006. [3] pearce, c.j., thavalingam, a., liao, z. and bićanić, n. (2000). computational aspects of the discontinuous deformation analysis framework for modelling concrete fracture, engineering fracture mechanics, 65(2), pp. 283–298. doi:10.1016/s0013-7944(99)00121-6. [4] chen, c.-s., pan, e. and amadei, b. (1998). fracture mechanics analysis of cracked discs of anisotropic rock using the boundary element method, international journal of rock mechanics and mining sciences, 35(2), pp. 195–218. doi:10.1016/s0148-9062(97)00330-6. [5] tang, c. (1997). numerical simulation of progressive rock failure and associated seismicity, international journal of rock mechanics and mining sciences, 34(2), pp. 249–261. doi:10.1016/s0148-9062(96)00039-3. [6] potyondy, d.o., and cundall, p.a., (2004). a bonded-particle model for rock, international journal of rock mechanics and mining sciences 41(8), pp. 1329–1364. doi:10.1016/j.ijrmms.2004.09.011. [7] rannou, j., limodin, n., réthoré, j., gravouil, a., ludwig, w., baïetto-dubourg, m.-c., buffière, j.-y., combescure, a., hild, f. and roux, s. (2010). three dimensional experimental and numerical multiscale analysis of a fatigue crack, computer methods in applied mechanics and engineering, 199(21) , pp. 1307–1325. doi: 10.1016/j.cma.2009.09.013. [8] guohua, c., and linjie, c. (2013). dynamic fracture research based on xfem and its application on discharge valve guard of hydrogen compressor, engineering failure analysis, 34(1), pp. 59–68. doi:10.1016/j.engfailanal.2013.07.002. [9] li, h., and yuen wong, l. n. (2012). influence of flaw inclination angle and loading condition on crack initiation and propagation, international journal of solids and structures, 49(18), pp. 2482–2499. doi:10.1016/j.ijsolstr.2012.05.012. [10] abaqus/ cae (2017) user s manual 6.10, product of dassault systems simulia corp., providence. [11] giner, e., sukumar, n., tarancón, j.e. and fuenmayor, f.j. (2009). an abaqus implementation of the extended finite element method, engineering fracture mechanics, 76(3), pp. 347–368. doi:10.1016/j.engfracmech.2008.10.015. [12] grégoire, d., maigre, h., réthoré, j. and combescure, a. (2007). dynamic crack propagation under mixedmode loading – comparison between experiments and x-fem simulations, international journal of solids and structures, 44(20), pp. 6517–6534. doi:10.1016/j.ijsolstr.2007.02.044. [13] mohammadi, soheil, ed., (2008). extended finite element method, doi:10.1002/9780470697795. [14] zamani, a., and eslami, m. r. (2010). implementation of the extended finite element method for dynamic thermoelastic fracture initiation, international journal of solids and structures, 47(10), pp. 1392–1404. doi:10.1016/j.ijsolstr.2010.01.024. [15] abrate, serge, ed. (2011). impact engineering of composite structures, cism international centre for mechanical sciences, doi:10.1007/978-3-7091-0523-8. [16] kuruppu, m. d., obara, y., ayatollahi, m. r., chong, k. p. and funatsu, t. (2013). isrm-suggested method for determining the mode i static fracture toughness using semi-circular bend specimen, the isrm suggested methods for rock characterization, testing and monitoring, pp. 107–114. doi:10.1007/978-3-319-07713-0_8. [17] iqbal, m. j., and mohanty, b. (2006). experimental calibration of isrm suggested fracture toughness measurement techniques in selected brittle rocks, rock mechanics and rock engineering, 40(5), pp. 453–475. doi:10.1007/s00603-006-0107-6. g. khandouzi et alii, frattura ed integrità strutturale, 50 (2019) 29-37; doi: 10.3221/igf-esis.50.04 37 [18] zhou, y.x., xia, k., li, x.b., li, h.b., ma, g.w., zhao, j., zhou, z.l. and dai, f. (2012). suggested methods for determining the dynamic strength parameters and mode-i fracture toughness of rock materials, international journal of rock mechanics and mining sciences, 49, pp. 105–112. doi:10.1016/j.ijrmms.2011.10.004. [19] chen, r., xia, k., dai, f., lu, f. and luo, s.n. (2009). determination of dynamic fracture parameters using a semi-circular bend technique in split hopkinson pressure bar testing, engineering fracture mechanics, 76(9), pp. 1268–1276. doi:10.1016/j.engfracmech.2009.02.001. [20] dai, f., chen, r., iqbal, m.j. and xia, k. (2010). dynamic cracked chevron notched brazilian disc method for measuring rock fracture parameters, international journal of rock mechanics and mining sciences, 47(4) pp. 606–613. doi:10.1016/j.ijrmms.2010.04.002. [21] dai, f., xia, k., zheng, h. and wang, y.x. (2011). determination of dynamic rock mode-i fracture parameters using cracked chevron notched semi-circular bend specimen, engineering fracture mechanics, 78(15), pp. 2633–2644. doi:10.1016/j.engfracmech.2011.06.022. [22] saouma, v.e., and zatz i.j. 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can be opened with acrobat and adobe reader 5.0 and later.) >> /namespace [ (adobe) (common) (1.0) ] /othernamespaces [ << /asreaderspreads false /cropimagestoframes true /errorcontrol /warnandcontinue /flattenerignorespreadoverrides false /includeguidesgrids false /includenonprinting false /includeslug false /namespace [ (adobe) (indesign) (4.0) ] /omitplacedbitmaps false /omitplacedeps false /omitplacedpdf false /simulateoverprint /legacy >> << /addbleedmarks false /addcolorbars false /addcropmarks false /addpageinfo false /addregmarks false /convertcolors /converttocmyk /destinationprofilename () /destinationprofileselector /documentcmyk /downsample16bitimages true /flattenerpreset << /presetselector /mediumresolution >> /formelements false /generatestructure false /includebookmarks false /includehyperlinks false /includeinteractive false /includelayers false /includeprofiles false /multimediahandling /useobjectsettings /namespace [ (adobe) (creativesuite) (2.0) ] /pdfxoutputintentprofileselector /documentcmyk /preserveediting true /untaggedcmykhandling /leaveuntagged /untaggedrgbhandling /usedocumentprofile /usedocumentbleed false >> ] >> setdistillerparams << /hwresolution [2400 2400] /pagesize [612.000 792.000] >> setpagedevice shot peening processes to obtain nanocrystalline surfaces in metal alloys: c. huang et alii, frattura ed integrità strutturale, 45 (2018) 108-120; doi: 10.3221/igf-esis.45.09 108 a new viscoelastic mechanics model for the creep behaviour of fiber reinforced asphalt concrete chunshui huang college of civil engineering, xuchang university, xuchang 461000, china; school of civil engineering, zhengzhou university, zhengzhou 450001, china chunshuihuang@163.com fangtao wang, tao gao henan province highway engineering bureau group co., ltd, zhengzhou 450052, china 1092366742@qq.com, 240286295@qq.com danying gao school of civil engineering, zhengzhou university, zhengzhou 450001, china gdy@zzu.edu.cn abstract. based on the burgers model, by adding a damper unit, this paper proposes a new viscoelastic model with five units and eight parameters to characterize the viscoelastic deformation of fiber reinforced asphalt concrete (frac). according to the creep tests of frac beams, this paper studies both the parameters in the model and the viscoelastic behaviour of frac with different fiber volume fraction and aspect ratio. in this model, this paper establishes the viscoelastic constitutive equation of asphalt concrete, which takes into account the impacts of fiber content characteristic parameter. both the experimental study and theoretical analysis show that the new model has a high correlation with the results of creep experiment and plays a key role in describing the whole creep process of frac. the fiber content characteristic parameter can comprehensively reflect the effects of the fiber volume fraction and aspect ratio on the viscoelastic behaviour of frac. within the range of this test, the optimum fiber volume fraction, fiber aspect ratio and fiber content characteristic parameter are 0.35%, 324 and 1.13, respectively. keywords. fiber reinforced asphalt concrete; viscoelastic model; viscoelastic performance; creep test; fiber content characteristic parameter. citation: huang, c., wang, f., gao, t., gao, d., a new viscoelastic mechanics model for the creep behaviour of fibre reinforced asphalt concrete, fratturaed integrità strutturale, 45 (2018) 108-120. received: 22.03.2015 accepted: 21.04.2018 published: 01.07.2015 copyright: © 2018 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. introduction t normal temperature around 15°c, asphalt concrete (ac) and fiber reinforced asphalt concrete (frac) are typical viscoelastic materials. the various viscoelastic mechanics models can be formed by combining the basic a http://www.gruppofrattura.it/va/45/15.mp4 c. huang et alii, frattura ed integrità strutturale, 45 (2018) 108-120; doi: 10.3221/igf-esis.45.09 109 viscoelastic mechanics elements such as spring and dampers [1-4]. generally, the model parameters can be obtained by uniaxial compression creep test, triaxial compression creep test and beam bending creep test [5-11]. besides, the influence of stress level, temperature and fiber content on the model parameters and the viscoelastic behavior of ac can also be achieved by above mentioned tests. over the years, many models have been developed to study the properties of ac and frac. for instance, the burgers model [2] reveals that the permanent deformation of frac has a linear positive correlation with loading time and a linear negative correlation with viscosity, and that the viscosity increases with the extension of loading time. however, some of the modelling results differ from the deformation features of frac during creep, such as the negative correlation between permanent strain and loading time, the absence of constant velocity creep, and the accelerated creep process. in the four-element five-parameter model [2], the viscosity increases with loading time, and the permanent strain increment exhibits an opposite trend; under the infinite loading time, the permanent strain increment gradually approximates zero; in this case, the deformation features are close to those of constant velocity creep rather than those of frac during accelerated creep. reference [8] examines the effects of fiber volume ratio and length-diameter ratio on ac viscoelasticity, but fails to characterize the overall effects of the two ratios with one parameter. thus, the understanding of the viscoelastic behavior of ac and frac is still very limited. in this paper, a new viscoelastic mechanics model with five units and eight parameters for frac was employed by analyzing the viscoelastic behavior of frac. the parameters of this model were obtained by beam bending creep tests with different fiber volume fraction and aspect ratio. the efficiency and validity of the present model were demonstrated by comparing the results of the model with those of burgers model and modified burgers model. at last, the effects of fiber volume fraction and fiber aspect fraction on the model parameters and the viscoelastic properties at loading and unloading creep stage of ac were studied by using the model. viscoelastic mechanic model with five units and eight parameters t is known that ac exhibits high time-dependent deformation process which called creep process and can be divided into two stages: loading creep and unloading creep. the curve of the whole creep process of frac beam bending in fig. 1 shows that the creep deformation in loading is similar to that of ac and it also includes three stages [1, 3]: (1) the stage of deceleration creep during the beginning of loading (migration period). polyester fiber reinforced asphalt concrete (pfrac) beam produces instantaneous elastic deformation under creep loading in this period, and the span deflection increases with time, while the creep rate gradually decreases with time. (2) the stage of constant speed creep (stable creep period). creep deformation continues to increase with time elapsing, while the incremental rate of creep deformation keeps constant approximately and the deformation-time curve is a straight line. (3) the stage of accelerating creep (undermine period). with the deformation gradually increasing, the slippage among the beam internal aggregates begins to take place and the cracks found in the bottom of test specimen begin to propagate gradually. it is noted that creep rate increases gradually and the deformation-time curve deviates from the straight line. an inflection point can be easily observed in the transition from the stable creep to accelerated creep in the deformationtime curve, and the corresponding loading time at the inflection point is named rheology time ft of frac [11]. obviously, ft is the time that the creep rate reduced to the minimum and the start time that frac begin to enter the stage of the accelerated creep. the creep rate increases after the inflection point of time. during the stage of creep unloading, the elastic deformation immediately recovered and the viscoelastic deformation gradually restored with time. however, the plastic deformation cannot be restored and become permanent deformation. both burgers model and modified burgers model are widely used to describe the viscoelastic deformation characteristics of ac in engineering. burgers model is a combination of two springs and two dampers [2], as shown in fig. 2. the creep equation of the model in loading stage is: 0 1 1 2 1 1 ( ) ( ) t t e t     − − = + +   (1) the creep rate is: 0 1 2 1 ( ) ( ) 0 t e t      − = +  (2) i c. huang et alii, frattura ed integrità strutturale, 45 (2018) 108-120; doi: 10.3221/igf-esis.45.09 110 figure 1: typical creep curve. figure 2: burgers model. the creep acceleration is: 0 2 2 2 ( ) 0 t e t      − −  =  (3) where 0 is the loading stress; t is the loading time; e1 and e2 are the elastic modulus of elements 1 and 2, respectively;  and  are the viscosities of elements 3 and 4, respectively; and =e2/2. in eqn. (1), the permanent deformation of frac is a linear function of time t and the reciprocal of viscosity 1/1. with time elapsing, the viscosity increases while the permanent stress increment decreases. both the stages of the stable creep and accelerated creep do not exist during the creep process. there is no inflection point in the creep deformation-time curve noticing from eqn. (2) and (3). therefore, the model does not present the rheological time characteristics of viscoelastic material and does not match the creep deformation characteristics of frac. based on burgers model, a modified model with four-unit and five-parameter was proposed through a nonlinear modification on the viscosity of the external damper with the viscous flow deformation characteristics of material [2], as shown in fig. 3. the viscosity of the external damper in this model is: c. huang et alii, frattura ed integrità strutturale, 45 (2018) 108-120; doi: 10.3221/igf-esis.45.09 111 1( ) bt t ae = (4) during the loading stage, equations of the creep, the creep rate and the creep acceleration can be expressed as: 0 1 2 1 1 1 ( ) ( ) bt t e e t ab    − − − − = + +   (5) 0 2 ( ) ( ) 0 bt t e e t a     − − = +  (6) 2 0 2 2 ( ) ( ) 0 tbt ebe t a      −−  = − +  (7) where 1(t) is the viscosity of external viscous component of modified model; a and b are the viscosity parameters of viscous elastic element 4, as shown in fig.3. from eqn. (4) and (5), it can be found that with the loading time increasing, the viscosity of element 4 increases and the permanent strain decreases. when the loading time tends to infinity, the strain increment tends to zero. the equations can be used to characterizes the consolidation effect of frac [4], which is similar to the deformation characteristics of stable creep stage. however, eqn. (4) and eqn. (5) still cannot describe the deformation characteristics of the accelerated creep stage of frac. from eqn. (6) and eqn. (7), the demarcation point of stable creep and accelerated creep do not present in the curve of creep deformation and time of frac, so the model cannot be used to describe the rheological time characteristics of viscoelastic material. figure 3: modified burgers model. figure 4: five units and eight parameters model in order to effectively describe the deformation feature of the whole creep process of frac and construct the rheological time parameters of viscoelastic material, a viscoelastic model with five units and eight parameters by adding a viscous component 5 is adopted based on burgers model, as shown in fig. 4. in this model, the viscosity of element 5 increases with time firstly and then decreases, that is: 0 3 2 ( )t at bt c   = − + (8) where, 0 is the initial viscosity of element 5; α, b and c are the viscosity parameters of element 5, moreover, α>0, b>0, c>0, and. b2-4c0 the creep equation of the model with five units and eight parameters can be expressed as for the loading stage, c. huang et alii, frattura ed integrità strutturale, 45 (2018) 108-120; doi: 10.3221/igf-esis.45.09 112 3 2 0 1 1 2 0 1 1 3 2( ) ( ) t a b t t ct t e t      − − + − = + + +   (9) for the unloading stage, 3 2 ( ) 0 0 00 0 0 0 1 2 0 (1 ) 3 2( ) t t t a b t t ct t e e t       − − −   − +  − = + +      (10) the creep speed during the loading stage is 2 0 1 2 0 1 ( ) ( ) t e at bt c t       − − + = + + (11) for the creep accelerator during the loading stage is 2 0 2 2 0 2 ( ) ( ) t e at b t       − − − = + (12) where t0 is the total loading time. in eqn. (12), if (t)=0, then 0 2 2 22 2 tb t e a a    − − = (13) * t in eqn. (13) can be solved by newton iterative method. obviously, if * 0 t t  , then 0  , 0  and 0  . if * t t , then 0  , 0  and 0  . so * t is the onset time of inflection point in the curve of creep strain and time, and is the demarcation point between the stable creep and the accelerated creep. also, the creep rate become the minimum at * t . after this point, the creep speed gradually increases and the rheological time of frac ft= * t . this model theoretically constructs the demarcation point between stable creep and accelerated creep, which cannot be seen in burgers model and modified burgers model, and it matches the characteristics of typical creep deformation and time curve, as shown in fig. 1. frac viscoelastic analysis and validation of the model parameters n the model with five units and eight parameters of frac, the resistance to elastic deformation is stronger as e1 gets larger. in the condition of same load and same time with increases, the permanent deformation decreases, and the resistance to viscous flow deformation tends to be stronger. when the relaxation time becomes larger, the increase of viscous flow deformation over time becomes slower, and then frac has a greater ability to resist rutting deformation. when the delay time becomes larger, the deformation development over time becomes slower, and then the resistance to viscoelastic deformation of frac becomes greater. when b is larger, a becomes smaller, while b becomes larger resulting in a larger rheological time, and then the resistance to viscous flow deformation of frac becomes stronger [12]. to verify the validity of the model expressed in eqn. (9) and (10), the creep test of frac was carried out. a-70 asphalt and polyester fiber (pf) with various aspect ratios and volume fractions were used in this test. the length of polyester fiber is 3mm，9mm and 12mm respectively, the ratio of length to diameter is 162，486 and 649, and the ratio of fiber to mineral mass is 0.2%.the volume ratio of fiber is 0.35%; for polyester fiber with length of 6mm, the ratio of length to diameter is 324, and the fiber content is 0.1%，0.2%，0.3% and 0.4% respectively, and the corresponding fiber volume i c. huang et alii, frattura ed integrità strutturale, 45 (2018) 108-120; doi: 10.3221/igf-esis.45.09 113 ratio is 0.17%，.0.35%，0.52% and 0.69%, respectively. according to jtj e20-2011 [13], the optimum asphalt content (oac) of matrix asphalt mixture, fiber aspect fraction and volume fraction of asphalt mixes were determined. rolling molding the test specimen of 300mm300mm50mm, and then were cut into a 250mm30mm35mm beam specimen. 15c creep tests were performed by using a multifunctional material testing machine. the creep load is 10% of the beam bending failure load in the same condition, as shown in fig. 5. span deflection for the creep test of small beams is collected by using a dial gauge connected to the data acquisition system. then the span deflection-time curve and the flexural tensile strain–time curves were drawn. when the beam specimens enter into the stage of accelerated creep stage then unload, and the test data were continued collecting for 30min. based on the results of the creep test and assumed initial values of the model parameters in eqn. (9) and (10), the nonlinear method of origin 8.5 is used to obtained a best fitting between the theoretical results of the mechanical model and those from tests. the fitting effect is controlled by adjusting the model parameters. if the results match well, the viscoelastic parameters of the mechanical model can be achieved. figure 5: creep test. rheological time heological time from eqn. (13) and the rheological time corresponding to the creep stability based on the measured creep deformation–time curves are listed in tab. 1. it can be seen that the present model can calculate the rheological time efficiently and accurately, and the relative error is less than 10% between the values calculated by the present model and results from the tests. the rheological time is the start time of the destruction of ac under creep loads [1], the larger the value is, the longer the time taken to deform the test piece is and the stronger the ability to resist deformation of ac is. the test results show that, when the fiber volume fraction is 0.35% and the aspect ratio is 324, the rheological time of frac is the largest and frac has the best resistance to deformation. the variation of creep strain–time curves is shown in fig. 6. it can be observed that when fiber volume fraction is 0.35% and the aspect ratio of fiber is 324, its curve is lower than others, and it means that frac has the best resistance to deformation at this moment. it is in accordance with the resistance to deformation from the present model based on the rheological time. tab. 1 also shows the results of burgers model and modified burgers model. in comparison, the data from the present model is the closest to that of the stage of creep load among the three models, and the data of burgers model has the largest deviation from the test data. the fitting curves of frac creep stain–time by using origin8.5 software is shown in fig. 7. it can be seen that the fitting curve of the burgers model during the stage of deceleration creep is below the test curve, and model characterization of frac creep deformation is less than the actual deformation. in the stage of stable creep model, the model curve is above the experimental curve, and the creep deformation of model characterization is greater than that of the actual deformation. in the stage of accelerating creep, the deformation of model characterization is less than the actual deformation of ac and model curve is below the experimental curve. it should be noticed that the difference between the test curve and the model curve will be more significant until specimen fracture. the fitting curve from the modified burgers and that from burgers are somewhat alike in relation to the test curve, while the difference is r c. huang et alii, frattura ed integrità strutturale, 45 (2018) 108-120; doi: 10.3221/igf-esis.45.09 114 that the creep strain–time curve of modified burgers model is closer to the test curve in the stages of decelerating creep and stable creep, and the modified burgers model can better describe deceleration and constant velocity creep deformation characteristics of frac. the fitting curve of the new model almost coincides with the measured test curve. the present model greatly increases the fitting accuracy and can describe the viscoelastic deformation characteristics of the whole creep process of frac very well. fv /% ar test rheology time /s calculation rheology time /s 2r burgers model modified burgers model five units and eight parameters model/s burgers model modified burgers model five units and eight parameters model 0 0 1450 / / 1320 0.99912 0.99930 0.99975 0.17 324 7500 / / 7332 0.99815 0.99930 0.99966 0.35 324 10200 / / 10996 0.99540 0.99926 0.99988 0.52 324 7200 / / 7739 0.99923 0.99958 0.99996 0.69 324 3200 / / 2986 0.99913 0.99925 0.99984 0.35 162 5500 / / 6045 0.99936 0.99951 0.99987 0.35 486 9000 / / 8532 0.99746 0.99924 0.99990 0.35 649 8000 / / 7501 0.99118 0.99905 0.99981 table 1: relationship between model index with fiber content and fiber aspect. figure 6(a): fiber volume ratio. figure 6(b): fiber aspect ratio. figure 7(a): burgers model. figure 7(b): modified burgers model. c. huang et alii, frattura ed integrità strutturale, 45 (2018) 108-120; doi: 10.3221/igf-esis.45.09 115 figure 7(c): five units and eight parameters model. load phase he model parameters of frac in eqn. (9) with different vf and ra were obtained from fitting the experimental data and listed in tab. 2. it can be noticed that the e1 and 1 firstly increase and then decrease with the increase of vf . when vf is 0.35%, e1 and 1 are at peak values and frac has stronger resistance to both elastic deformation and permanent deformation. when vf is 0.69%, e1 and 1 of frac are smaller than those of ac matrix. it indicates that fiber can enhance the elasticity and viscosity of the frac only with proper fiber volume fraction; excessive fiber may decrease the resistance of ac to the instantaneous elastic and viscous flow deformation. both the relaxation time 1/e1 and the delay time 2/e2 firstly increase and then decrease with the increase of vf . it means that a certain vf can increase the anti-rutting deformation capacity of frac. when vf is 0.35%, both the relaxation time and delay time are at maximum, and frac has the highest temperature stability at this time [12]. the a firstly decrease and then increase with the increase of vf , while 0, b, and b/2a firstly increase and then decrease with increase of vf . it indicates that rheological time of frac first increases and then decreases with increasing vf . it is worth mentioning that when vf is 0.35%, rheological time reaches the maximum value and frac show the best resistance to permanent deformation. when fiber aspect ratio increase, e1, 1, 1/e1, 2/e2 , 0, a, b and b/2a have the similar trend with vf varying. when ra is 324, frac has better resistance to elastic deformation, viscous flow deformation, viscoelastic deformation and rutting deformation capacity. the viscoelastic properties of frac described by the present model coincide with that performed by the creep strain–time curve shown in fig. 6. unloading phase y using eqn. (10) to simulate the test data, the model parameters of frac with different fiber volume fraction and aspect ratio are shown in tab. 3. obviously, it can be observed that e2, 1, 2, 0, a, b, and c have the same pattern as that of the creep loading stage. when fiber volume fraction and aspect ratio increase. when fiber volume fraction is 0.35% and fiber aspect ratio is 324, e2, 1, 2, 0, b, and c reach the maximum while a is the minimum. at the same time, frac has better deformation recovery performance. by comparing with the stage of the creep loading, the model parameters e2,2, and delay time 2/e2 in the unloading phase are greatly reduced, 1 and 0 decrease a little, while a, b, and c increase a lot. the reason is that the stage of accelerating creep is the stage of creep damage of frac, and after deceleration and constant velocity creep processes, its internal slippage occurs between the aggregates which result in the damage of the creep beam structure and attenuation of material properties. the actual permanent deformation characterized by the model parameters in the stage of unloading stage is bigger than the theoretical permanent deformation characterized by the same parameters in the stage of the uploading and actual deformation recovery rate is smaller than the theoretical deformation recovery rate of loading phase by the same parameter characterization, but it is not suitable to use the model parameters in the stage of creep loading to study the characteristics of the actual deformation of frac after unloading. from tab. 3, it should be noticed that the correlation between the test data of unloading phase and the eqn. (10) model decreases and t b c. huang et alii, frattura ed integrità strutturale, 45 (2018) 108-120; doi: 10.3221/igf-esis.45.09 116 frac exhibits more complex viscoelastic properties during the creep deformation recovery process after experiencing creep load damage. fv /% ar model parameters relaxation time/s delay time/s 1  /mpa 1 /mpa·s 2 /mpa 2 /mpa·s a/ 2 s − b/ 1 s − c 0 /mpa·s 0 0 591 332893 143 4996813 3.04e-06 0.00179 3.18 1.13e+09 563 34943 0.17 324 668 417152 156 8456622 8.21e-07 0.00612 4.40 3.11e+09 624 54209 0.35 324 820 556709 171 17987114 5.30e-07 0.00891 6.68 5.78e+09 679 105188 0.52 324 670 343284 129 6904945 5.81e-07 0.00689 5.70 2.22e+09 512 53527 0.69 324 576 234039 107 2871943 3.54e-06 0.00251 3.82 1.61e+09 406 26847 0.35 162 713 456829 158 15366364 6.60e-07 0.00651 5.17 2.35e+09 641 97255 0.35 486 708 402514 142 6006080 1.15e-06 0.00687 5.68 3.98e+09 569 42296 0.35 649 566 215312 108 2431274 3.10e-06 0.00229 3.89 3.38e+09 380 22512 table 2: relationship between model parameters of eqn. (9) with fiber contents and fiber aspect ratio. fv /% ar model parameters delay time/s 2 r 1 /mpa·s 2 /mpa 2 /mpa·s a/ 2 s − b/ 1 s − c 0 /mpa·s 0 0 114606 0.62 242 4.36e-04 0.97 210 4.27e+07 390 0.98478 0.17 324 318572 0.96 428 2.40e-04 2.92 584 1.03e+08 448 0.97522 0.35 324 553520 1.15 593 3.17e-05 4.66 925 1.51e+08 515 0.99166 0.52 324 320593 0.93 412 1.58e-04 2.56 775 9.88e+07 442 0.98287 0.69 324 99117 0.61 218 3.08e-04 0.73 544 3.75e+07 356 0.98899 0.35 162 211117 0.91 369 3.45e-04 1.41 391 8.90e+07 404 0.98453 0.35 486 218774 0.81 341 1.95e-04 1.67 757 7.20e+07 423 0.99532 0.35 649 113860 0.66 227 3.12e-04 0.91 502 3.92e+07 342 0.98252 table 3: relationship between model parameters of eqn. (10) with fiber contents and fiber aspect frac viscoelastic constitutive relation he above analysis shows that fiber volume fraction and aspect ratio are important factors, which affect the viscoelastic properties of the ac and the influence of fiber volume fraction and aspect ratio on the model parameters is consistent. therefore, fiber content characteristic parameter f(f=vfra) can be used to represent the combined effects of the fiber volume fraction and fiber aspect ratio. by nonlinear fitting of the experimental data in this paper, the relationship between model parameters of eqn. (9) and the fiber content characteristic parameters are as follow: 2 1( ) 577.8 327.4 149.1f f f   = + − (14) 2 2 ( ) 142.6 48.4 29.7f f f   = + − (15) 2 1( ) 324331.1 334911.7 172179f f f   = + − (16) 2 2 ( ) 4267638 17376388 8264399f f f   = + − (17) 6 6 6 2 ( ) 3.09 10 5.4 10 2.47 10f f fa    − − − =  −  +  (18) t c. huang et alii, frattura ed integrità strutturale, 45 (2018) 108-120; doi: 10.3221/igf-esis.45.09 117 2 ( ) 0.0016 0.0118 0.005f f fb   = + − (19) 2 ( ) 2.88 5.32 2.18f f fc   = + − (20) 9 9 9 2 0 ( ) 1.11 10 5.92 10 2.7 10f f f   =  +  −  (21) the relationship between model parameters of eqn. (10) and the fiber content characteristic parameter are as follow: 2 2 ( ) 0.615 0.884 0.401f f f   = + − (22) 2 1( ) 97153.9 675179.3 305297f f f   = + − (23) 2 2 ( ) 232.1 559.4 256.2f f f   = + − (24) 4 4 4 2 ( ) 4.5 10 5.9 10 2.37 10f f fa    − − − =  −  +  (25) 2 ( ) 0.89 5.74 2.64f f fb   = + − (26) 2 ( ) 191.1 1027 391.6f f fc   = + − (27) 7 8 7 2 0 ( ) 4.01 10 1.75 10 8 10f f f   =  +  −  (28) by substituting eqn. (14)-(21) and (22)-(28) into (9) and (10) respectively, the creep equations of present model of frac with consideration of fiber content characteristic parameter effect can be obtained: load phase: 3 2 0 1 1 2 0 ( ) ( ) ( ) 1 1 3 2( , ) ( ) ( ) ( ) ( ) f f t f f f f f f a b t t c t t e t              −   − + − = + + +        (29) unload phase: 3 2 ( ) 0 0 00 0 0 0 1 2 0 ( ) ( ) ( ) (1 ) 3 2( , ) ( ) ( ) ( ) f f t t t f f f f f a b t t c t t e e t              − − −   − + − = + +       (30) where, 2 2 ( ) ( ) f f e     = . taking derivative of t in eqn. (29) and (30), differential constitutive equation of frac can be obtained, which is characterized by the present model and considered the influence of fiber content characteristic parameter: load phase: c. huang et alii, frattura ed integrità strutturale, 45 (2018) 108-120; doi: 10.3221/igf-esis.45.09 118 2( ) 0 1 2 0 ( ) ( ) ( )1 ( , ) / ( , ) ( ) ( ) ( ) t f f f f f f f f f a t b t ce d t dt t                 − − +  = = + +    (31) unload phase: ( ) ( )0 0 0 2 ( 1) ( , ) / ( , ) ( ) t t tf f f f e e d t dt t           − − − −  = =    (32) fig. 8 displayed the variation of the creep strain and fiber content characteristic parameter with different loading stress and time, which is derived from eqn. (29). it can be seen that the creep strain increases with the increase of loading stress and prolonged the load time, while it firstly decreases and then increases with the increase of the fiber content characteristic parameter. it should be noted that when fiber content characteristic parameter is 1.13, the creep strain with different loading stress and the loading time achieved the minimum, at this time the frac exhibits good deformation resistance. the variation between the value of creep speed and the fiber content characteristic parameter in the stage of loading, derived from eqn. (31), is shown in fig. 9. it can be seen that the creep speed increases with the increase of load stress, while the creep rate firstly decreases and then increases with the increase of fiber content characteristic parameter under the same loading conditions. it should be noted that when fiber content characteristic parameter is 1.13 under different creep load, the rate of creep deformation reaches minimum. it can also be noticed that, the creep rate gradually decreases firstly and then goes to a stable value. finally, the creep rate increases with the increase of load time. it is worth to mentioning that the above phenomenon is consistent with the three-phase character of the creep curve in the stage of loading from test. figure 8(a): different stress. figure 8(b): different loading time figure 9: relationship between creep speed and f. figure 10: relationship between creep speed and f. c. huang et alii, frattura ed integrità strutturale, 45 (2018) 108-120; doi: 10.3221/igf-esis.45.09 119 the variations of the creep strain with the fiber content characteristics for 4 loads in unloading phase are plotted in fig. 10. it can be observed that within 30min after unloading, the greater the stress is, the greater both the damage of the frac at creep loading process and residual creep strain is. at the same time, the larger the loading stress is, the greater the elastic deformation is, and as a result, the inertia of the recovery elastic deformation after unloading causes that the recovery creep rate increases with the increase of stress. it should be mentioned that the residual strain of frac under the same creep loading stress decreases firstly and then increases with the increase of the fiber content characteristic parameter after unloading, while the creep recovery rate increases firstly and then decreases under the same condition. in addition, when the fiber content characteristic parameter is about 1.13, the residual creep strain of frac is at minimum and the creep deformation recovery rate reaches maximum, the frac shows better recovery performance of the viscoelastic deformation in this case. it can be concluded from eqn. (32) that the viscoelastic deformation recovery rate decreases gradually at the beginning with the uninstall time elapsing, and then goes to a stable value, that is consistent with test results. conclusions y adding viscous unit into burgers model, the new model with five units and eight parameters can effectively present the deformation characteristics of frac during the whole creep process in the stage of loading. the rheological time of frac calculated from the model is consistent with that from test results, and the curves from the present model coincide well with the curve of tests. the creep tests of frac show that with the increase of fiber content and aspect ratio, frac beam the curve of bottom flexural tensile strain and time is firstly reduced and then elevated. when the fiber content is 0.35% and its aspect ratio is 324, corresponding curves of creep deformation and time are in the lowest position and frac has a larger resistance to deformation, which is consistent with the influence of the fiber content and aspect ratio on the viscoelastic properties of ac obtained from the present model. fiber content characteristic parameter can comprehensively reflect the effect of fiber content and aspect ratio. the differential constitutive equation of frac performed through the present model by considering the influence of fiber content characteristic parameter can be characterized by eqn. (31) and (32). both the theoretical analysis and experimental studies show that: the creep strain, creep speed, the damage in frac, and the residual strain after unloading increase with the increasing of the loading stress and the loading time. it should be mentioned that under the same condition of load stress, the load creep strain, creep rate, and residual strain after unloading decreases firstly and then increases with the increase of fiber content characteristic parameter, while creep deformation recovery rate increases firstly and then decreases with the increase of fiber content characteristic parameter. when the fiber content characteristic parameter is 1.13, frac has better abilities of both anti-deform and creep deformation recovery. acknowledgments he authors gratefully acknowledge the financial support of the project from the colleges and universities key scientific research projects of henan province (grant no. 16b580003) and horizontal research project of xuchang university (grant no. 2017hx029). references [1] popoola, a. o., baoku, i. g. and olajuwon, b. i., (2016). heat and mass transfer on mhd viscoelastic fluid flow in the presence of thermal diffusion and chemical reaction, international journal of heat and technology, 34, pp. 15-26. [2] xu, s. f. (1992). a rheological model representing the deformation behavior of asphalt mixtures, mechanics and engineering, pp. 1437-1440. [3] yang, t. q. (1990). viscoelastic mechanics, central china university of technology press, wuhan. [4] yang, y. (2009). experience study on the visco-elastoplastic constitute model of asphalt mixture, huazhong university of science and technology, wuhan. [5] mitra, k., das, a., basu, s. (2012). mechanical behavior of asphalt mix: an experimental and numerical study, construction and building materials, 27, pp. 545-552. b t c. huang et alii, frattura ed integrità strutturale, 45 (2018) 108-120; doi: 10.3221/igf-esis.45.09 120 [6] bandyopadhyaya, r., das, a. and basu, s., (2008). numerical simulation of mechanical behaviour of asphalt mix, construction and building materials, 22, pp. 1051-1058. [7] gonzález, j.m., miquel canet, j., oller, s. and miró, r. (2007). a viscoplastic constitutive model with strain rate variables for asphalt mixtures-numerical simulation, computational materials science, 38, pp. 543-560. [8] guo, n. s., zhao and y. h. (2004). study on creep performance of fiber reinforced asphalt concrete, journal of china & foreign highway, 1, pp. 124-127. [9] rahmani, e., darabi, m. k., abu al-rub, r. k., kassem, e., masad, e. a. and little, d. n. (2013). effect of confinement pressure on the nonlinear-viscoelastic response of asphalt concrete at high temperatures, construction and building materials, 47, pp. 779-788. [10] stastna, j., zanzotto, l. and vacin, o. j. (2003). viscosity function in polymer-modified asphalts, journal of colloid and interface science, 259, pp. 200-207. [11] sun l. and zhu, y. (2013). a serial two-stage viscoelastic–viscoplastic constitutive model with thermodynamical consistency for characterizing time-dependent deformation behavior of asphalt concrete mixtures, construction and building materials, 40, pp. 584-595. [12] ming, z. h., huang, w. and qian, z. d. (2007). analysis on mechanics model of viscoelasticity behaviors for epoxy resin asphalt mixture, journal of highway and transportation research and development, 24(6-9), pp. 34. [13] ministry of transport of the people's republic of china, standard test methods of bitumen and bituminous mixtures for highway engineering, jtg e20-2011, china communications press, beijing, (2001). nomenclature tr rheological time (s), tf = t  0 creep test loading stress 1e , 2e elastic modulus of elements 1 and 2 (mpa) 1 , 2 , 3 viscosities of elements 3 ,4 and 5 (mpa·s)  2 2e  (s -1) a, b the viscosity coefficient of element 4 0 initial viscosity of element 5 a, b, c viscosity coefficient of element 5 ( )t creep strain ( )t creep speed ( )t acceleration of creep t  solution of formula (13), tr = t  tr relaxation time (s): 1 1/  td delay time (s): 2 2  ar ratio of fiber length to diameter fp fiber content: fiber to mineral mass ratio fv volume ratio of fiber to mixture ( )d t creep trabecular mid-span deflection 2 r square of correlation coefficient f fiber content characteristic parameter, f f av r =  ( , )ft  the creep strain when characteristic parameter of fiber content is f and time is t ( , )ft  the creep velocity when characteristic parameter of fiber content is f and time is t 0 loading stress (mpa) microsoft word numero_30_art_47 d. nappini et alii, frattura ed integrità strutturale, 30 (2014) 394-402; doi: 10.3221/igf-esis.30.47 394 focussed on: fracture and structural integrity related issues evaluation of the material’s damage in gas turbine rotors by instrumented spherical indentation d. nappini, g. zonfrillo department of industrial engineering, university of florence, via s.marta 3, florence, italy duccio.nappini@unifi.it, giovanni.zonfrillo@unifi.it f. mastromatteo, i. giovannetti ge oil&gas, florence, italy francesco.mastromatteo@ge.com, iacopo.giovannetti@ge.com abstract. experimental indentations are carried out on items of two different materials, taken in several location of various components from high pressure gas turbine rotor which have seen an extensive service. the components object of investigation consisted in 1st and 2nd high pressure turbine wheels made in nickel-base superalloy (inconel 718), the spacer ring (inconel 718) and the compressor shaft made in crmov low alloy steel (astm a471 type10). aim of the work is to set up the capability of the instrumented spherical indentation testing system to evaluate variations in the material properties due to damage, resulting from temperature field and stresses acting on components during service. to perform this task load-indentation depth curves will be acquired in various zones of the above mentioned components. the analysis of the results has allowed to identify an energy parameter which shows a linear evolution with the mean temperature acting on the components. keywords. instrumented indentation; depth-sensing indentation; material characterization. introduction eavy-duty and aircraft-derivative gas turbines rotors for power generation and industrial applications are among the most critical and highly stressed components of the plants and they are expected to reliably operate for a period which may be in excess of thirty years. over the turbine’s life the structural integrity of rotor materials naturally declines when subjected to the harsh conditions of gas turbine operation; high temperatures exposure, mechanical stress and startup/shutdown cycles result in the initiation and growth of flaws, which can eventually compromise the machine’s safety and integrity. remaining life assessment methodologies employ a combination of traditional and high-tech non-destructive tools and methods to evaluate the mechanical integrity of rotors; therefore, they can be used to confirm the safety of continued operation or to recommend necessary restoration [1-4]. the measure of material’s mechanical properties are a fundamental task in safety design and lifetime assessment of industrial components and among the in-field inspection and real-time monitoring non-destructive methods indentationh d. nappini et alii, frattura ed integrità strutturale, 30 (2014) 394-402; doi: 10.3221/igf-esis.30.47 395 based technique for materials characterization are a promising and attractive tool nowadays available in materials engineering and science [5-9]. instrumented indentation holds several advantages: they are inexpensive, non destructive and it does not require specimen preparation; therefore, it may be used to investigate the material properties on small volumes, such as thin films, and soft tissues on small scales by just one simple impression test. indentation tests can be used to probe hardness of materials, toughness, elastic modulus, elasto-plastic behaviour and constitutive laws evaluation by different reverse analysis methods of indentation load-displacement curve [10-16]. aim of the work is to set up the capability of the instrumented spherical indentation testing system to evaluate variations in a gas turbine rotor material properties due to damage resulting from temperature field and stresses acting on components during long time service. to perform this task load-indentation depth curves were acquired in several location of various components made in in718 and crmov from high pressure gas turbine rotor. conventional hardness measurements were also carried out, in order to verify if a correlation can be obtained between these tests and indentations. finally, whole results will be analysed to assess the material damage. materials and methods indentation testing apparatus xperimental indentations were carried out using an instrumented indentation testing equipment developed by university of pisa, university of trento and scienza machinale s.r.l, able to performs a maximum indentation load of 2000 n with a resolution of the order of 0.2 n during the experimental tests. with this device it is possible to investigate the behaviour of the hardest metallic materials. indentations were performed via a spherical tungsten-carbide ball having a diameter of 2.5 mm. the relative displacement between indenter and target was continuously measured by two lvdt transducers ensuring an accuracy of 4 µm and a resolution of 0.2 µm. tests were carried out in displacement control at a speed of 1µm/s, thus ensuring that the data were collected under quasi static condition and no potential strain-rate effects were involved. the technical specifications of the testing machine are summarized in tab. 1. a detailed description of the design solutions can be found in [17]. load cell loading axis indenter maximum load 2000 n maximum linear excursion 2 mm tungsten-carbide ball maximum error 1.5 n accuracy 4 µm diameter 2.5 mm resolution 0.2 µm table 1: technical specification of instrumented indentation apparatus (“diaptometro”). test procedure overview indentations were performed on items sampling on 1st and 2nd stage turbine discs and on the spacer ring made in nickelbase superalloy (inconel 718) from an high pressure ge turbine rotor which have seen an extensive service (over 105 hours). moreover some test were carried out on the compressor aft stub shaft made in crmov low alloy steel (astm a471 type10) belonging to the same machine. the items were machined so as to be free from thermal or mechanical alteration due to working process and to obtain a tolerance parallelism between surfaces minor of 0.05 mm and a tolerance flatness lower than 0.02 mm. also, in order to achieve the right surface finishing, the items were polished. for each tested item a set of about 40 instrumented indentations and 15 conventional hbw hardness measurements were performed in significant areas, subjected during service to different values of stress and temperature. in order to asses a statistical dispersion of indentation response, before the aforementioned testing campaign a set of measures was carried out on forging ring pieces of astm a182f22. to perform this task the items were machined to obtain the same surface conditions and tolerances. load-indentation depth (p-δ) curves and conventional hbw hardness acquired in the various zones of test samples were analysed as described in the following. e d. nappini et alii, frattura ed integrità strutturale, 30 (2014) 394-402; doi: 10.3221/igf-esis.30.47 396 direct analysis parameters evaluated from load-indentation depth curves nstrumented indentation is widely used to probe the elastic and plastic properties of engineering materials. the indentation test can only provide the characteristic load p vs. penetration depth δ curve, a sequence of measured values ( exp expi ip ,δ ), and a reverse analysis is therefore required to estimate the mechanical properties of materials (fig. 1). figure 1: (a) scheme of spherical indentation on a homogeneous, isotropic semi-infinite bulk specimen; (b) typical indentation load– depth curves obtained from an experiment; (c) the uniaxial stress–strain (σ–ε) curve of a power-law hardening solid. elastic modulus, e, has been widely employed to obtain damage evolution, using the fact that it shows a progressive degradation with damage. therefore, by measuring the value of e it is possible to indirectly measure the value of damage according to the following common equation: 0 dm 1 e e   where e is the effective modulus of damaged material and e0 is the modulus of virgin material. the stress–strain (σ-ε) curves of the materials are represented in hollomon like power law form, identified by three parameters: the young modulus, the stress of proportionality limit, σ0, and the strain-hardening exponent, n. the σ-ε curve can be deduced from indentation test by means an optimization algorithm that minimize the function exp exp 0 i iχ( e, n,σ , p ,δ ) , which represents the global distance between the measured points and the theoretical curve defined by the material properties e, σ0, n [18-20]. the reverse analysis of the indentation test involves three-axial stress state, as well as the highly nonlinearity of material behaviour, and the complexity of contact problem due to the presence of friction and size effect. therefore it is the critical step of the whole procedure. by evaluating e by means of indentation tests it is possible to estimate the damage. the promising potential of the idea is related to the possibility to correlate the damage parameter to stress and temperature fields, but the measurement of the elastic modulus obtained from σ-ε curves were not considered in this work enough accurate in consequence of a substantial data dispersion. in order to set up the effective capability of the instrumented spherical indentation testing system to evaluate variations in the material properties due to damage resulting from long time service, the collected load-indentation depth curves were systematically analysed. in particular the parameters below listed were evaluated (fig. 2): the maximum displacement, δmax. the final depth, δf, i.e. the permanent depth of penetration after the indenter is fully unloaded. the elastic unloading contact stiffness, s (dp/dδ), defined as the slope of the portion of the curve during the initial stages of unloading. the value δi of the intercept on x-axes of the line with slope s starting from the maximum of the curve. the area included by loading and unloading curve corresponding to the total work done by the indenter, w. the value of diameter at the rim of the impression, d, evaluated in function of the value of penetration depth δ acquired by the lvdt transducers: i a) b) c) d. nappini et alii, frattura ed integrità strutturale, 30 (2014) 394-402; doi: 10.3221/igf-esis.30.47 397 d 2   δ ( d δ)    in which d indicates the indenter diameter. some parameters calculated by the standard brinnell formulation:   max max 2 2 0.102 p 0.102 2p h   a πd  d   d d       in which pmax indicates the maximum value of the applied force (n), d and d are expressed in mm. replacing d with the previous expression, the relationship obtained is:   max 2 0.102 2p h πd  d   d 4(δ ( d δ)        using different values for the displacement δ three separate parameters h1, h2, h3 were defined. in particular in h1 the variable δ were set to δmax value, in h2 δ = δf, whereas in h3 the value δ = δi were used. figure 2: parameters evaluated from load-indentation depth curves. note that because these definitions of “hardness” are not based on the contact area after unloading, they deviate from the traditional hardness measurement. moreover, during the test the maximum value of the load is not maintained for a specific dwell time as the astm standard testing requires. so any evaluated hardness value cannot be in agreement with the standard, however the evaluated h parameters could be indicative of the material hardening. in all cases the penetration depth is calculated starting from the value of displacement at the first contact, assumed in correspondence of p = 1 n (fig. 3). figure 3: estimation of penetration value δ at the first contact for p = 1 n used to calculate the parameters. d. nappini et alii, frattura ed integrità strutturale, 30 (2014) 394-402; doi: 10.3221/igf-esis.30.47 398 experimental procedure initially, in order to asses a statistical dispersion of indentation response a set of measures was performed on a forging ring piece of astm a182f22 in “as is” conditions. a set of 25 indentation measurements were carried out using a maximum load of 1800 n and the maximum indenter penetration depth was measured. tab. 2 and fig. 4 respectively show an overview of the obtained values and the related gaussian distribution, highlighting as the dispersion of indentation response is low. min max aver. st.dev. 112.2 115.9 114.2 1.11 table 2: statistical parameters of the indentation response [µm] on a set of 25 measurements. figure 4: gaussian curve of indentation response. aim of the research is to investigate the capability of the instrumented spherical indentation system to evaluate variations in the material properties, due to damage resulting from stresses and temperature fields during long time service. to perform this task, the sites of indentation were chosen considering both the thermal and the mechanical gradients on components, obtained from fem analysis. for each component, the measurements were performed in order to analyse the whole surface. in particular, points positioned on lines parallel to the direction of the gradients were selected. also conventional hardness measurements were carried out using the same criteria. overall 130 spherical indentation and 50 conventional hardness measurements were performed in order to map the significant areas on the components. fig. 5a clarify the scheme of spherical indentation of the 1st stage turbine disc, underlining where sets of measure were carried out. fig. 5b shows the dimensionless temperature profile obtained for an average engine running in iso condition for, while fig. 5c shows the results of the 2d axial-symmetric elastic analysis at steady state condition. figure 5: a) positions of spherical indentation (red points) on item. in the yellow points are carried out conventional brinnel tests b) positions of spherical indentation (black points) overlying on thermal analysis c) positions of spherical indentation overlying on structural analysis. 0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40 111 112 113 114 115 116 117 g a u ss ia n d is tr ib u ti o n [ 1/ μ m ] max indenter penetration [μm] a) b) c) d. nappini et alii, frattura ed integrità strutturale, 30 (2014) 394-402; doi: 10.3221/igf-esis.30.47 399 result and discussion data analysis he comparison between the load-indentation depth curve obtained for astm a471 and in718 was shown in fig. 6. the sensibility of instrumented indentation testing system to characterise different materials is highlighted. the analysis of the p–δ raw data is a good way to find promising indicators which might be useful to describe the behaviour of superalloy as well as alloy steel. figure 6: comparison between the load-indentation depth curve for astm a471 and in718 alloys. an accurate analysis of all the previous detailed quantities obtainable from the load-indentation depth curves was performed for each items, to evaluate the possibility to correlate some parameters to damage. conventional hardness measurements were also carried out in order to find a relationship between these tests and indentations parameters. in fact, the hardness characteristic is correlate, to a certain extent, with the characteristics of many mechanical properties of a material, but the measured values was exhibit low sensitivity to structural transformations related to ageing in service, as observed also by the work of lebedev [21]. the damage resulting in a serviced component is a function of time, stress and temperature. turbine wheels and the spacer ring had seen the same extensive serviced time, about 105 hours, so it could not be a variable. also the material was the same, so the variables of interest were the stress and the temperature fields. as examples of the obtained results, in fig. 7 was reported for the rotor of the first stage the evolution of δmax, δi and δf as function of stress, while the fig. 8 shows the variation with temperature of hb1, hb2 and hb3. figure 7: evolution of penetration values δ in function of the stress field for the 1st stage wheel. figure 8: evolution of hardness values in function of the temperature field for the spacer ring. since an indentation test is not very appropriate for detecting a mechanical damage, such voids or micro-cracks, firstly the stress was not considered in the analysis and the results were modelling as a function of the temperature. 0 10 20 30 40 50 60 70 80 90 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 δ [μ m ] dimensionless stress δmax δf δi 200 300 400 500 600 700 800 0.80 0.84 0.88 0.92 0.96 1.00 h a rd n e ss  [ n /m m 2 ] dimensionless temperature h1 h2 h3 t d. nappini et alii, frattura ed integrità strutturale, 30 (2014) 394-402; doi: 10.3221/igf-esis.30.47 400 moreover, indentation sites at the same temperature performed on the spacer ring and on the 1st and 2nd stage of turbine wheels were considered equivalent points of measure. for each variable, the mean values among equivalent points were calculated and reported in function of the temperature. the analysis of all defined parameters had allowed to identify those which showed a monotonic and regular function. among them, the most significant are the elastic unloading contact stiffness and the area included by loading and unloading curve (fig. 2). a good fit solution was performed using a linear functions of mean data. fig. 9 shows the obtained trend. the quantities s and w extrapolated from the p– δ curves could be used for a first assessment of the mean temperature of the component in the site of analysis, so these parameters are also promising indicators to material damage estimation due to extensive service. figure 9: total work done by the indenter a) and elastic unloading contact stiffness b) as function of mean temperature in indentation zone for serviced material (in718). following this analysis, various objective function f(temperature, stress) were tested in order to include the stress field effect on damage. the stress acting on components was not considered as important as the temperature; its effect was therefore introduced as an amplification factor of the temperature values. in particular the functions shown in fig. 10a. evolutions of the various parameters vs. the modified temperature were carried out and the accuracy of the fits was determined by the correlation coefficient r2. all the factors performed an improvement of the correlation coefficient, but the better result were obtained using the amplification factor σ σmax as shown in fig. 10b for the s parameter. figure 10: a) comparison between three amplification factors proposed to include stresses effect; b) the relation between the elastic unloading stiffness and the modified temperature in indentation zone for in718 in serviced condition. conclusion n accurate analysis of several quantities evaluated from the load-indentation depth curve were performed on items sampling on turbine component in inconel 718, with the aim to assess the capability of spherical indentation testing system to evaluate variations in the material properties due to damage resulting from service. r² = 0.9451 75 75.5 76 76.5 77 77.5 0 0.1 0.2 0.3 0.4 0.5 0.6 s  ( d p /d δ ) modified temperature s, raw data a b)a) a) b) d. nappini et alii, frattura ed integrità strutturale, 30 (2014) 394-402; doi: 10.3221/igf-esis.30.47 401 indentation sites at the same temperature performed on the rotor components were considered equivalent points of measure and the resulting average values were reported in function of temperature. the most significant parameters related to temperature damaging are the elastic unloading contact stiffness and the area included by loading and unloading curve. these variables showed a linear behaviour with the temperature; after a calibration step, indentation tests may be used as an index of the average temperature acting on the component. so, these parameters are also promising indicators to material damage due to extensive service. the stress acting on components was considered an amplification factor of the temperature field. using the linear factor σ/σmax an improvement of the correlation was obtained. the correlations proposed should be clearly verified with other tests. in fact, it is obviously that the performed study is still far from obtaining an analytical relation between a parameter, derived from the indentation test, and damage of the component; however, it demonstrates the feasibility of this task. references [1] dowson, p., dowson, j., remaining life assessment technology applied to steam turbines and hot gas expanders, asme proceedings, structures and dynamics, paper no. gt2011-45324, (2011) 47-61. [2] viswanathan, r., damage mechanisms and life assessment of high temperature components, asm international, metals park, (1989). [3] de prosperis, r., di sisto, p., borkowski m., gas turbine life prediction and optimization device and method, patent wo 2013014202 a1, nuovo pignone spa [it], (2013). [4] fujiyama, k., fujiwara, t., damage in high temperature components and the life assessment technologies, icf10, honolulu, (2001). [5] cheng, y.t., page, t., pharr, g.m., swain, m., wahl, k.j. (eds.), fundamental and applications of instrumented indentation in multidisciplinary research, journal of material research, 19 (2004). [6] baker, s.p., cook, r.f., corcoran, s.g., moody, n.r., fundamentals of nanoindentation and nanotribology ii, materials research society symposium proceedings, vol. 649 (2001). [7] van landingham, m.r., review of instrumented indentation, journal of research of the national institute of standards and technology, 108 (4) (2003) 249-265. [8] fischer-cripps, a.c., critical review of analysis and interpretation of nanoindentation test data, surface & coatings technology, 200 (14-15) (2006) 4153-4165. [9] li, x., bhushan, b., a review of nanoindentation continuous stiffness measurement technique and its applications, materials characterization, 48 (1) (2002) 11–36. [10] li, j., li, f., he, m., xue, f., zhang, m., wang, c., indentation technique for estimating the fracture toughness of 7050 aluminum alloy with the berkovich indenter, materials and design, 40 (2012) 176–184. [11] oliver, w.c., pharr, g.m., measurement of hardness and elastic modulus by instrumented indentation: advances in understanding and refinements to methodology, journal of materials research, 19 (1) (2004) 3-20. [12] nayebi, a., el abdi, r., bartier, o., mauvoisin, g., new procedure to determine steel mechanical parameters from the spherical indentation technique, mech. mater. 34 (4), (2002) 243-254. [13] moussa, c., bartier, o., mauvoisin, g., pilvin, p. , delattre, g., characterization of homogeneous and plastically graded materials with spherical indentation and inverse analysis, journal of materials research 27 (1) (2012) 20-27. [14] lee, j.h., kim, t., lee, h., a study on robust indentation techniques to evaluate elastic-plastic properties of metals. int. j solids struct. 47 (2010) 647-664. [15] chicot, d., gil, l., silva, k., roudet, f., puchi-cabrera, e.s., staia, m.h., teer, d.g., thin film hardness determination using indentation loading curve modelling, thin solids films, 518, (2010) 5565-5571. [16] zhang, m., li, f., yuan, z., li, j., wang, s., effect of heat treatment on the micro-indentation behavior of powder metallurgy nickel based superalloy fgh96, materials & design, 49 (2013) 705–715. [17] di gioia, a., progetto costruttivo di un indentatore sferico strumentato”, bachelor’s degree dissertation, university of pisa, faculty of engineering, pisa, (2005). [18] beghini, m., bertini, l., fontanari, v., evaluation of the stress–strain curve of metallic materials by spherical indentation, international journal of solids and structures, 43 (7-8) (2006) 2441–2459. [19] beghini, m., bertini, l., fontanari, v., mechanical characterization of metallic materials by instrumented spherical indentation, proceedings of sem annual conference & exposition on experimental & applied mechanics, (2009) 110. d. nappini et alii, frattura ed integrità strutturale, 30 (2014) 394-402; doi: 10.3221/igf-esis.30.47 402 [20] beghini, m., bertini, l., fontanari, v., analysis of the elastic-plastic properties of metallic materials by instrumented spherical indentation testing, procedia engineering, 10 (2011) 1679-1684. [21] lebdev, a.a., muzyka, n.r., volchek, n.l., determination of damage accumulated in structural materials by the parameters of scatter of their hardness characteristics, strength of materials, 34 (4) (2002) 317-321. microsoft word numero_30_art_59 w. changfeng et alii, frattura ed integrità strutturale, 30 (2014) 486-494; doi: 10.3221/igf-esis.30.59 486 effect of nonlinearity of restrainer and supports on the elasto-plastic seismic response of continuous girder bridge wang changfeng school of civil engineering, yantai university, yantai, china wangchang-f@126.com zhu long, chen xingchong school of civil engineering, lanzhou jiaotong university, lanzhou, china 932570069@qq.com, chenxingchong@263.net abstract. during an earthquake, the nonlinearity of the bridge structure mainly occurs at the supports, bridge piers and restrainers. when entering nonlinear stage, members of the bridge structure affect the elasto-plastic seismic response of the whole structure to a certain extent; for multi-span continuous bridges, longitudinal restrainers can be installed on the movable piers to optimise the distribution of seismic force and enable the movable piers to bear a certain amount of seismic effect. in order to evaluate the effect of nonlinearity of restrainer and supports on the elasto-plastic seismic response of continuous girder bridge, analytical models of continuous girder bridge structure considering the nonlinearity of movable supports, restrainers and bridge piers were built and the nonlinear time history analysis was conducted to evaluate the effect of nonlinearity of restraining devices and supports on the elasto-plastic seismic response of continuous girder bridge. relevant structural measures and recommendation were made to reduce the seismic response of the fixed piers of the continuous girder bridge. keywords. restraining devices; supports; elasto-plastic seismic response; continuous girder bridge. introduction he investigations of previous seismic hazards showed that the damage of the bridge piers were not significant if failure occurred at the support, which suggests that the response of supports and bridge pier is interrelated; meanwhile, caging devices play a certain role in distributing the seismic force to each piers and abutments. under earthquake action, the girder, supports, piers, substructure and connecting members (restraining blocks and girderconnection devices) act as an integrated structure. as a certain portion of energy will be dissipated by movable supports during earthquake and a part of the inertia force of the superstructure will be passed to movable piers, especially when the movable supports fail and lose the sliding capacity, in which case the seismic force passed from the failed support to the movable pier would be magnified [1], the seismic response of the whole bridge structure will change. when studying the elasto-plastic seismic response of bridge structures, the effect of the nonlinearity of each component in the bridge structure on elasto-plastic seismic response of bridge structures should be considered [2]. t w. changfeng et alii, frattura ed integrità strutturale, 30 (2014) 486-494; doi: 10.3221/igf-esis.30.59 487 in bridge engineering, restraining blocks are often used to prevent the falling of the girder and increase the safety of the supports during earthquake. for large-span long continuous bridge structures, the self-load of the integrated girder body is high, resulting in a substantial horizontal seismic force mainly concentrated on the fixed supports. to optimise the distribution of seismic force for each pier, anti-seismic pins or restraining blocks can be installed. at the same time, a certain gaps between the blocks (pins) and the girder should be preserved, so that the movable pier is able to carry a part of the horizontal seismic force without affecting the normal stretching of the girder, as shown in fig. 1. it is pointed out by [3] that if the expected plastic hinge is located in the pier, more piers should be arranged to carry the horizontal seismic force. an ideal way is to install laminated rubber supports on all piers but the number of horizontal force bearing piers may be limited by other design factors which should be taken into consideration during design. xie xu [4] stated that horizontal seismic force produced by the superstructure of the continuous bridge is good to be carried by all piers and abutments to prevent overbearing of the fixed piers. relevant engineering procedures such as restraining devices were proposed. (a) (b) (c) figure 1: seismic tectonic measure at movable piers. (a) longitudinal seismic pin; (b) lateral seismic pin; (c) restrainer. at present, few studies are carried out to evaluate the effect of restraining devices and supports on the nonlinear seismic response of the bridge structure. restraining blocks are only considered as structural component without analysing the effect of them during seismic resisting process according to the seismic resistant standard of bridge engineering in china. studies focusing separately on the nonlinearity of supports, seismic mitigation and isolation, restraining devices or elastoplasticity of bridge piers are common [5,6] but studies considering simultaneously the nonlinearity of supports, contact of restraining devices and material nonlinearity are rare. studies concerning the interaction of the nonlinearity of supports, restraining devices and the elasto-plastic analysis of bridge piers are also rare. at present, the effect of friction at supports and the nonlinearity of restraining devices on the elasto-plastic seismic response of the bridge are rarely considered during the elasto-plastic seismic response of continuous bridge. in this study, on the basis of considering the nonlinearity of supports, piers and restraining devices, the effect of restraining devices and nonlinearity of supports on the elasto-plastic seismic response of continuous girder bridge is evaluated and structural procedures to reduce the seismic response of the fixed piers of continuous girder bridge are proposed. analytical models of each element support elements onlinear supports can be simulated by springs with bilinear hysteretic relationship. to simulate the sliding kinetic performance of the support in earthquake, bilinear hysteretic sliding support element [7] is used and the hysteretic model of the element is shown in fig. 2. laminated rubber supports which are normally positioned at the top of the piers are not bolted with the top of the pier or the bottom of the girder. if the seismic force exceeds the critical sliding force between the supports and the surfaces of the pier or the beam bottom, sliding will occur. the laminated rubber supports in this case can be simulated by bilinear model; for tetrafluoroethylene movable supports, the support element is also simulated by bilinear model. the stiffness of movable support after sliding is taken as 0, which is the coulomb friction model. n w. changfeng et alii, frattura ed integrità strutturale, 30 (2014) 486-494; doi: 10.3221/igf-esis.30.59 488 shear force displacement k1 k 2 f cr o figure 2: bilinear element model of the support. contact and impact elements presently, analytical methods for contact and impact are mainly: coefficient of reconstitution, lagrange multiplier and contact finite element method. the contact finite element method is mainly based on kelvin impact model. kelvin impact model is a parallel connection of spring and damper. the main parameters include: initial impact stiffness k1, yield stiffness k2, damping c and initial gap d0. the nonlinearity of the restraining devices is generally not considered in existing studies. in this study, considering that the restraining device can be nonlinear, the element and hysteretic model is given in fig. 3 [8, 9]. 0 1 2 y 0 y 1 2 (a) (b) figure 3: contact element: (a) mechanical model of the contact element; (b) hysteresis curve of the contact element. the above model was used to simulate the impact of girder and restraining devices and the impact force is given in eq. (1) [10, 11]: 1( ) ( ) 0 0 0 i j i j i j i j f k u u d c u u u u d f u u d                (1) in which: k1: is the contact and impact stiffness; d: initial gap; c: damping factor 1 21 1 2 2 m m c k m m   , 2 2 ln (ln ) e e      ; e is the hysteretic factor which can be taken as 0.65 for concrete; ui, uj: are respectively the end displacement of the adjacent girder of the contact element; ui, uj: are respectively the end velocity of the adjacent girder of the contact element. elasto-plastic reinforced concrete model the elasto-plasticity of bridge pier is simulated by takeda tri-linear model and the skeleton curve of the element is controlled by the moment and curvature at cracking, yield and damage points, as shown in fig. 4. w. changfeng et alii, frattura ed integrità strutturale, 30 (2014) 486-494; doi: 10.3221/igf-esis.30.59 489 m o m en t curvature crack point yield point damage point figure 4: takeda tri-line hysteresis model. finite element modelling project background he superstructure of a 60+100+60 m prestressed concrete continuous railway girder bridge was selected as the background project. the pier has a height of 20 m. the cross-section of the pier is rectangular with a dimension of 6.75×2.8 m for side piers and 6.8×4.0m for middle piers. the girder is variable-section boxed girder with single cell box and vertical webs. the girder has a total weight of 14367248 kg. the vertical reaction force for side supports is 8793.74 kn and 63042.5 kn for middle supports. the effect of ground and pier foundation is simplified as foundation springs applied at the cushion cap bottom. the proportionality factor is taken as 20000 kpa/m2 according to the foundation factor. the spring stiffness is calculated by “m” method [12]. the nonlinearity of ground and pier foundation is ignored and the rotation spring stiffness of the cushion cap bottom is taken as identical for each model. analytical model nonlinear takeda model is used for all bridge piers. only longitudinal seismic response of the continuous bridge is studied in this research [13]. the length of the plastic hinge of the bridge pier is taken as 1.0 d ( d is the height of calculation of the cross-section) and the plastic hinge is located at the bottom of the pier. the elasto-plasticity of the pier structure is considered within the range of plastic hinge and the nonlinearity is ignored outside the range. the reinforcement ratio of the bridge pier is taken as 0.5% and the control points of the moment-curvature curve of the crosssection of pier bottom are given in tab. 1. pier cracking moment (kn·m) cracking curvature (rad/m) yield moment (kn·m) yield curvature (rad/m) ultimate moment (kn·m) ultimate curvature (rad/m) side pier 33265 0.00014 59050 0.00087 83684 0.03649 middle pier 102917 0.00012 203459 0.00068 237879 0.0081 table 1: control points of the moment-curvature curve for the bottom section of bridge pier. the beam and piers were simulated by spatial beam element, the beam was separated into 83 elements and each pier was separated into 12 elements. the numerical fe model was shown in fig. 5. in actual design, the effect of transversal seismic and vertical load is both considered and thus the reinforcing ratio of the fixed pier and middle movable piers are normally identical. therefore, the same moment-curvature model is used for both middle movable piers and the fixed piers. five different calculating models are incorporated for different scenarios where the nonlinearity of support is considered or not as well as different installation of restraining devices. (1) model 1: the nonlinearity of movable supports is ignored. only the vertical degree of freedom of the movable supports is coupled with the girder, while both the vertical and horizontal degrees of freedom of the fixed supports are linked with the girder. t w. changfeng et alii, frattura ed integrità strutturale, 30 (2014) 486-494; doi: 10.3221/igf-esis.30.59 490 figure 5: numerical fe model. (2) model 2: the friction of the movable supports is considered with coefficient of friction taken as 0.02, 0.05, 0.10, 0.15, 0.20. no restraining devices are provided. as the stiffness of the supports is large before slipping occurs, the initial stiffness of the middle movable supports is taken as 1e6 kn/m and side movable supports, 4e5 kn/m during the analysis. (3) model 3: the elastic effect of the restraining devices is considered. when slipping occurs for a certain distance, the relative displacement of the girder and piers is restrained by the restraining devices. the restraining devices are considered elastic with a stiffness of 1e6 kn/m. the failure of the restraining devices is not considered. (4) model 4: the nonlinearity of the restraining devices is considered and the initial stiffness of the restraining devices is set identical as in model 3. on the basis that the horizontal sliding force of the supports is considered, the critical yield force of the restraining devices is taken as 30% of the horizontal sliding force of the supports. in actual engineering, the critical yield force of the restraining devices can be determined by its mechanism. the analytical model of model 4 is given in fig. 6. (5) model 5: no longitudinal restraining devices are provided for side piers and only the friction of side movable supports is considered. the movable supports are identical as in model 4. both the friction of support and the nonlinearity of the restraining devices are considered. during the time history analysis, three rare artificial seismic waves and tianjin wave are incorporated with the peak value of the seismic wave adjusted to 0.4g. takeda model coupled degree of freedom hysteretic model pier #1 pier(#2) movable supports restrainers movable pier pier #3 pier #4 takeda model takeda model takeda model fixed pier movable pier movable pier fixed bearing movable supports restrainers hysteretic model hysteretic model figure 6: calculation diagram for model 4. effect of nonlinearity of supports and restraining devices on the elasto-plastic seismic response of bridge structure comparison of calculated moment and curvature of the bottom section of the fixed pier hen the nonlinearity of the movable supports and restraining devices is considered, the hysteretic energy dissipation of movable supports affects the energy dissipating mechanism of the bridge structure. the existence of restraining devices results in the redistribution of seismic effect on each pier and thus the seismic w w. changfeng et alii, frattura ed integrità strutturale, 30 (2014) 486-494; doi: 10.3221/igf-esis.30.59 491 response of the structure (moment and curvature of the bottom section of the fixed pier and the displacement of the girder) is different from models where the friction of supports and the distribution of seismic force by the restraining devices are not considered. results show that the analytical results and trend for the four seismic waves are basically identical and the analytical results of the seismic response for the first artificial seismic wave and tianjin wave are shown in fig. 7 and 8. the initial gap of the restraining devices is taken as ±10 cm . 210 212 214 216 218 220 222 224 226 0 0.05 0.1 0.15 0.2 m o m en t (m n ·m ) μ moment of the bottom section of the fixed pier model 1 model 2 model 3 model 4 model 5 0.002 0.003 0.004 0.005 0.006 0 0.05 0.1 0.15 0.2 c u rv at u re (1 /m ) μ curvature of the bottom section of the fixed pier model 1 model 2 model 3 model 4 model 5 (a) (b) figure 7: moment and curvature of the bottom section of the fixed pier under the first artificial seismic wave. 40 45 50 55 60 65 70 0 0.05 0.1 0.15 0.2 m om en t (m n ·m ) μ moment of the bottom section of the 1# pier model 1 model 2 model 3 model 4 model 5 0.000 0.001 0.002 0.003 0.004 0 0.05 0.1 0.15 0.2 c u rv at u re (1 /m ) μ curvature of the bottom section of the 1# pier model 1 model 2 model 3 model 4 model 5 (a) (b) 211 212 213 214 215 216 217 0 0.05 0.1 0.15 0.2 m om en t (m n ·m ) μ moment of the bottom section of the fixed pier model 1 model 2 model 3 model 4 model 5 0.0020 0.0022 0.0024 0.0026 0.0028 0.0030 0.0032 0.0034 0.0036 0 0.05 0.1 0.15 0.2 c u rv at u re (1 /m ) μ curvature of the bottom section of the fixed pier model 1 model 2 model 3 model 4 model 5 (c) (d) 0 50 100 150 200 250 0 0.05 0.1 0.15 0.2 m om en t (m n ·m ) μ moment of the bottom section of the 3# pier model 1 model 2 model 3 model 4 model 5 0.000 0.001 0.002 0.003 0 0.05 0.1 0.15 0.2 c u rv at u re (1 /m ) μ curvature of the bottom section of the 3# pier model 1 model 2 model 3 model 4 model 5 (e) (f) figure 8: moment and curvature of the bottom section under tianjin seismic wave. w. changfeng et alii, frattura ed integrità strutturale, 30 (2014) 486-494; doi: 10.3221/igf-esis.30.59 492 it can be seen from fig. 7 and 8 that when the effect of the supports and restraining devices is considered: (1) for movable piers, due to the effect of friction at movable supports, the moment and curvature of bottom section of the piers when the effect of friction at movable support is considered (model 2) are larger than that in the case when the friction at movable supports is not considered (model 1), and the seismic response increases with the increase of coefficient of friction; for fixed piers, under the action of artificial wave, the moment and curvature of bottom section of the piers when the effect of friction at movable supports is considered are smaller than that in the case when friction at movable supports is not considered, and the response decreases with the increase of coefficient of friction. however, the seismic response of the bottom section of the fixed piers when the friction at movable supports is considered under tianjin wave increases, which suggests that the friction at movable supports is not always favorable for the seismic resistance of bridge structure. the effect of friction at movable supports on the seismic resistance performance of bridge structures depends on the spectrum of the seismic wave and the characteristics of the structure. it is recommended that for structures of which the natural vibration period is similar to the period of the surrounding ground when the contribution of stiffness of movable supports is considered, or structures on soft ground foundation, the effect of friction at movable supports should be considered. (2) when the effect of friction at movable supports and the elasticity of restraining devices are considered, the moment and curvature of bottom section of the movable piers increase and the response increases with the increase of the coefficient of friction at movable supports; the seismic response at the bottom section of the fixed piers in the case when restraining devices are considered (models 3 to 5) is smaller than that in the case when only the friction at movable supports is considered (model 2). (3) when the nonlinearity of the restraining devices is considered (model 4), the seismic response of the bottom section of the movable piers is smaller or similar with that in the case when the elasticity of restraining devices is considered; the seismic response of the bottom section of the fixed piers is slightly larger than that in the case when the elasticity of restraining devices is considered due to the fact that the restraining devices are in nonlinear stage which limits the bearing of seismic force by movable supports. the restrainers should be designed energy intensive to protect the movable pier from being destroyed by the violet pounding force, so model 4 was suggested in practice [14-16]. the bump rubber can be also used to decrease the pounding force. (4) if only the restraining effect of the middle piers is considered (model 5), the seismic response of the bottom section of the side movable piers is smaller than that in the case where the nonlinearity of the restraining devices is considered (model 4) but the seismic response of the middle movable piers and fixed piers increase. (5) for side movable piers, the seismic response in the case when the effect of supports and elasticity of restraining devices is considered (model 3) is the largest; for middle movable piers, the seismic response in the case when only the restraining effect of the 3# piers is considered (model 5) is the largest; for fixed piers, the seismic response in the case when the effect of supports and elasticity of restraining devices is considered (model 3) is the smallest, suggesting that restraining devices effectively reduce the seismic response of the bottom section of the fixed piers and enable the movable piers to bear a part of the seismic input energy to distribute and isolate the seismic effect. comparison of displacement of the girder and shear displacement of the supports the vertical displacement of the girder and shear displacement of the movable supports in different models are given in fig. 9 to 10. 0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40 0.45 0 0.05 0.1 0.15 0.2 d is p la ce m en t( m ) μ displacement of the girder under the first artificial wave model 1 model 2 model 3 model 4 model 5 0.20 0.22 0.24 0.26 0.28 0.30 0.32 0 0.05 0.1 0.15 0.2 d is p la ce m en t( m ) μ displacement of the girder under tianjin wave model 1 model 2 model 3 model 4 model 5 (a) (b) figure 9: comparison of displacement of girder in each model. w. changfeng et alii, frattura ed integrità strutturale, 30 (2014) 486-494; doi: 10.3221/igf-esis.30.59 493 0.00 0.05 0.10 0.15 0.20 0.25 0.30 0 0.05 0.1 0.15 0.2 s h ea r d ef le ct io n ( m ) μ shear deflection of 1# support model 2 model 3 model 4 model 5 0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0 0.05 0.1 0.15 0.2 s h ea r d ef le ct io n ( m ) μ shear deflection of 3# support model 2 model 3 model 4 model 5 (a) (b) figure 10: shear deflection of movable supports under tianjin wave. it can be seen from fig. 9 to 10 that: (1) the effect of restraining devices on the displacement of the girder is significant. the displacement of the girder in models with restraining devices is smaller than in models without them. the displacement of the girder in model 3 where the friction of movable supports and elasticity of restraining devices are both considered is the smallest. (2) the restraining devices have a certain level of effect on limiting the shear deflection of the movable supports. with the existence of restraining devices, the shear deflection of movable supports is mainly related to the initial gap between the restraining devices. (3) the variation trend of displacement of the girder is similar to that of the moment of the bottom section of the fixed pier. the increase of displacement of the girder under tianjin wave is witnessed when friction at movable supports is considered. conclusions he effect of nonlinearity of supports and restraining devices on the elasto-plastic seismic response of continuous girder bridge is evaluated in this study. finite element models considering the elasto-plasticity of supports, restraining devices and bridge piers are proposed. elaso-plastic seismic response is analysed and the following conclusions are drawn: (1) results show that analysis ignoring the effect of friction at movable supports is not safe in some circumstances. as the friction of movable supports exists, when analysing bridge structures built on soft ground and structures with first order natural vibration period close to the predominant period of the ground when the stiffness contribution of movable supports is considered, the effect of friction at movable supports should be considered. (2) in practical design, the restrainers installed on the movable pier should be designed energy intensive to protect the movable pier from being destroyed by the violet pounding force, so model 4 was suggested to analyse the seismic distribution of the seismic force for each pier. (3) restraining devices are effective in limiting the displacement of the girder in multi-span girder bridge, reducing the seismic response of the fixed piers and balancing the seismic distribution of each pier; for different structures, detailed finite element analysis can be conducted to modify the initial gap and stiffness of the restraining devices as well as the coefficient of friction and stiffness of the supports to reduce the seismic response of the fixed pier, balance the distribution of seismic input energy at each pier and prevent the input seismic effect from being carried by only the fixed piers. acknowledgements his research is sponsored by project supported by national natural science foundation of china (51108220). t t w. changfeng et alii, frattura ed integrità strutturale, 30 (2014) 486-494; doi: 10.3221/igf-esis.30.59 494 references [1] sang-hyo, ho-seong, m., sang-woo, l.,effects of bearing damage upon seismic behaviors of a multi-span girder bridge, engineering structures, 28 (2006) 1071-1080. [2] japan railway technical research institute, seismic design standards and explanations for railway structures, (2000), in japanese. [3] kehai, w., research on anti-seismic analysis of bridge, china railway press, (2007), in chinese. [4] xie xu, seismic response and earthquake resistant design of bridges, china communications press, (2006), in chinese. [5] trochalakis, p., o eberhard, m., stanton, j. f., design of seismic restrainers for in-span hinges, structural engineering, 123(4) (1997). [6] zhu, p., abe, m., fujino, y., modelling three dimensional nonlinear seismic performance of elevated bridges with emphasis on pounding of girders, earthquake engng struct. dyn., 31 (2002) 1891-1913. [7] filipov, e. t., fahnestock, l.a., steelman, j. s., evaluation of quasi-isolated seismic bridge behavior using nonlinear bearing models, engineering structures, 49 (2013) 168-181. [8] desroches, r., muthukumar, s., effect of pounding and restrainers on seismic response of multiple-frame bridges, journal of structural engineering, 128 (2002) 860-869. [9] schiehlen, w., seifried, r.. three approaches for elasto-dynamic contact in multibody systems, multibody system dynamics, 12(1) (2004) 1-16. [10] tkada, s., hozumi, m., ivanov, r., seismic force acting on bridge restrainers and reliability evaluation, memoirs of the cosntruction engineering research institute, 43b (2001) 69-82. [11] saiidi, m., randall, m., maragakis, e., seismic restrainer design methods for simply supported bridges, journal of bridge engineering, 6 (2001) 307-315. [12] frechette, d., behavior of lateral loaded drilled shaft groups. tempe: arizona state university , (2001). [13] kim, s.-h., lee, s.-w., mha, h.-s., dynamic behaviors of bridges considering pounding and friction effects under seismic excitations, structural engineering and mechanics, 10(6) (2000) 621-633. [14] kima, j. m., fengb, m. q., shinozukac, m., energy dissipating restrainers for highway bridges, soil dynamics and earthquake engineering, 19 (2000) 65-69. [15] desroches, r., fenves, g. l., design of seismic cable hinge restrainers for bridges, journal of structural engineering, 120 (2000) 500-509. [16] tobias d. h., anderson, r. e., hodel c. e., overview of earthquake resisting system design and retrofit strategy for bridges in illinois, practice periodical on structural design and construction, 13(3) (2008) 147-158. microsoft word numero 25 art 9 f. v. antunes et alii, frattura ed integrità strutturale, 25 (2013) 54-60; doi: 10.3221/igf-esis.25.09 54 special issue: characterization of crack tip stress field effect of crack propagation on crack tip fields f.v. antunes, a.g. chegini cemuc, department of mech eng, university of coimbra, rua luís reis santos, pinhal de marrocos, 3030-788 coimbra, portugal l.m. correia, a.l. ramalho cemuc, escola superior de tecnologia do instituto politécnico de castelo branco, av. do empresário, 6000 767 castelo branco, portugal abstract. crack closure influences fatigue crack growth rate and must be included in the design of components. plasticity induced crack closure is intimately linked with the crack tip plastic deformation, which becomes residual as the crack propagates. the objective here is to study numerically the effect of crack propagation on crack tip fields. the transient effect observed at the beginning of crack propagation is linked to the hardening behavior of material. the effect of mesh refinement is studied, and a singular behavior is evident, which is explained by the sharp crack associated with mesh topology, composed of a regular pattern of square elements. the plastic zone size measured perpendicularly to crack flank in the residual plastic wake is quantified and compared with literature models. finally, the removal of material at the first node behind crack tip with load cycling was observed for plane strain state and some hardening models in plane stress state. keywords. plasticity induced crack closure; crack tip; plastic deformation. introduction rack closure is a phenomenon which consists of the contact of the fracture surfaces during a portion of the load cycle. this contact affects the local stress and plastic deformation fields near the crack tip, and therefore, the intrinsic micromechanisms responsible for fatigue propagation (cyclic plastic deformation, oxidation, creep, etc.). according to elber’s understanding of crack closure [1], as the crack propagates due to cyclic loading, a residual plastic wake is formed. the deformed material acts as a wedge behind the crack tip and the contact of fracture surfaces is forced by the elastically deformed material. plasticity induced crack closure (picc) is intimately related with the monotonic and reversed plastic deformation occurring at the crack tip. the forward or monotonic plastic zone is constituted by the material near the crack tip undergoing plastic deformation during loading. major parameters are the maximum load, the stress state and the isotropic component of hardening. on the other hand, the reversed plastic zone is formed by the material near the crack tip undergoing compressive yielding during unloading. the amplitude of stress intensity factor, k, the stress state and the kinematic hardening are expected to have a major influence on reversed plastic deformation. however, the plastic deformation at a gauss point is a complex phenomenon, occurring progressively as the crack tip approaches it, depending on the hardening model, loading parameters and finite element mesh, among other parameters. the main objective here is to study numerically the effect of crack propagation on crack tip fields. the effect of mesh refinement, stress state and hardening model are considered. the numerical simulations were performed with a threedimensional elasto-plastic finite element program (dd3imp) that follows a fully implicit time integration scheme. c http://www.gruppofrattura.it http://dx.medra.org/10.3221/igf-esis.25.09&auth=true f. v. antunes et alii, frattura ed integrità strutturale, 25 (2013) 54-60; doi: 10.3221/igf-esis.25.09 55 numerical model middle-tension (m(t)) specimen, in agreement with astm e647 standard, is studied here. an initial crack length of a0=5 mm was assumed. due to symmetry conditions, only 1/8 of the mt specimen was simulated, considering adequate symmetry conditions. the material used for this research was the 6016-t4 aluminium alloy (hv0.5=92). in order to model the hardening behaviour of this aluminium alloy, three types of mechanical tests were performed: uniaxial tensile tests and monotonic and bauschinger shear tests. from the experimental data and curve fitting results, for different constitutive models, it was determined that the mechanical behaviour of this alloy is better represented using an isotropic hardening model described by a voce type equation: 0 (1 ) p vn saty y r e    (1) combined with a non-linear kinematic hardening model described by a saturation law:   p x sat x x c x x            (2) in previous equations y is the equivalent flow stress, p is the equivalent plastic strain, y0 is the initial yield stress, rsat is the saturation stress, n, cx and xsat are material constants, σ is the deviatoric stress tensor, x is the back stress tensor, p the equivalent plastic strain rate and p the equivalent stress. the materials constants determined for the batch of material in study, that were used in the numerical simulations, are: y0=124 mpa, rsat=291 mpa, n= 9.5, cx= 146.5 and xsat= 34.90 mpa [2]. fig. 1 presents the finite element mesh, which was refined at the crack front to model the severe plastic deformation gradients and enlarged at remote positions to reduce the numerical effort. the size considered for the linear isoparametric square elements around the crack front was l1=8 m, 16 m or 16 m. to overcome convergence difficulties, crack propagation was simulated by successive debonding of nodes at minimum load. each crack increment (ai) corresponded to one finite element and two load cycles were applied between increments. in each cycle, the crack propagates uniformly over the thickness by releasing both current crack front nodes. figure 1: finite element mesh. a) frontal view. b) detail of frontal view. the numerical simulations were performed with the three-dimensional elasto-plastic finite element program (dd3imp) that follows a fully implicit time integration scheme [3, 4]. the mechanical model and the numerical methods used in the finite element code dd3imp, specially developed for the numerical simulation of metal forming processes, takes into account the large elastic-plastic strains and rotations that are associated with large deformation processes. to avoid the locking effect a selective reduced integration method is used in dd3imp18. the optimum values of the numerical parameters of the dd3imp implicit algorithm have been already established in previous works, concerning the numerical simulation of sheet metal forming processes [5] and plasticity induced crack closure [6]. numerical results ig. 2a and 2b show stress-strain curves registered for a gauss point when the crack propagates approaching it, as illustrated in fig. 2c. the gauss point suffers plastic deformation at the first load cycle, which indicates that it is within the first forward plastic zone, but it doesn’t experience reversed plasticity. as the crack tip approaches the a f a) b) http://www.gruppofrattura.it http://dx.medra.org/10.3221/igf-esis.25.09&auth=true f. v. antunes et alii, frattura ed integrità strutturale, 25 (2013) 54-60; doi: 10.3221/igf-esis.25.09 56 gauss point, the monotonic plastic deformation increases and reversed plastic deformation starts. the plastic deformation has he highest magnitude when the gauss point is immediately ahead of crack tip (position n in fig. 2c). the comparison of fig. 2a and 2b indicates that plastic deformation level is significantly higher for a mesh with 8 m elements (m8) compared with a mesh with 32 m elements (m32). in fact, the reduction of mesh size approaches the gauss tip to crack flank, which increases the stress concentration factor. additionally, more load cycles are applied when the crack approaches the gauss point. other gauss points have similar behavior; however the levels of monotonic and reversed plastic deformation, and therefore the residual plastic deformation, vary. -4 -3 -2 -1 0 1 2 3 4 5 0.00 0.01 0.02 yy yy / ys -4 -3 -2 -1 0 1 2 3 4 5 0.00 0.01 0.02 yy y y / ys gp 1 5 n figure 2: influence of finite element mesh on stress-strain curves. a) mesh m32. b) mesh m8. c) position of the gauss point. (a=10mm; w=30 mm; max=47.5 mpa; min=0.8 mpa). the location of the gauss point relatively to the initial crack tip position has a major influence on residual plastic deformation. fig. 3 presents the equivalent plastic strain along crack flank, which remains after crack propagation. a peak is evident at the beginning of crack propagation (a0=5 mm), which is followed by a progressive decrease until a stabilization is reached. the material hardening model influences the plastic deformation level, but not the global trend. the kinematic hardening model gives higher plastic deformation levels, which is linked to the occurrence of reversed plastic deformation during unloading. fig. 4 shows the effect of stress state and mesh refinement. a peak still is observed at the beginning of crack propagation, but the deformation increases with crack propagation for the plane strain state which wasn’t expected. the use of finite elements with 8 m at the crack tip (mesh m8) instead of 16 m elements (mesh m16) increases the plastic deformation level. this could be expected since the decrease of element size approaches the gauss points to the crack tip and additionally more load cycles are applied because the crack increments are smaller. therefore the monotonic and reversed plastic deformation levels, and consequently the maximum stress and plastic deformation, are higher for mesh m8 compared to the mesh m16. fig. 5b presents normalized stress-strain curves (yy-yy), registered as the crack propagates under plane stress conditions, for gauss points (gp) in different elements ahead of the initial crack tip (e1, e2, e8 in fig. 5a). the crack is initially at position c0 indicated, and propagates ahead of element 8 (e8). the non-linear behaviour of the yy-yy curves at the first loading indicates the occurrence of yielding in all the elements analysed, i.e., that the initial monotonous plastic deformation extends ahead of element 8. however, the plastic deformation level is significantly higher for element e1, because it is closer to the crack tip. when the crack is extended one element, element e2 is immediately ahead of crack tip but the deformation does not reach the level obtained previously for element e1, which is due to the previous hardening. http://www.gruppofrattura.it http://dx.medra.org/10.3221/igf-esis.25.09&auth=true f. v. antunes et alii, frattura ed integrità strutturale, 25 (2013) 54-60; doi: 10.3221/igf-esis.25.09 57 this phenomenon explains the peak values observed in fig. 3 and 4 at the beginning of crack propagation. the difference between elements e2 and e8 is relatively small, which explains the stabilization observed in fig. 3 and 4. 0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 4.9 5.1 5.3 5.5 5.7 5.9 6.1 x [mm] p ,e q kinematic mixed isotropic 0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 4.9 5.1 5.3 5.5 5.7 5.9 6.1 x [mm] p ,e q plane strain, m8 plane stress, m8 plane stress, m16 figure 3: equivalent plastic strain along crack flank (max=47.5 mpa; min=0.8 mpa, mesh m16). figure 4: equivalent plastic strain along crack flank (mixed hardening, max=47.5 mpa; min=0.8 mpa). as already observed in fig. 2a and 2b, the size of finite elements at the crack tip has a major influence on plastic deformation level. fig. 6 shows the effect of element reduction down to nanometer sizes on maximum plastic deformation. there is a progressive increase of plastic deformation with mesh refinement without convergence, typical of a singular behavior. the finite element mesh used to model crack propagation, composed of a regular pattern of square elements ahead of initial crack tip, as can be seen in fig. 1 and 5a, assumes a sharp crack, which has a singular behavior. assuming a finite value for the crack tip radius, convergence is obtained with mesh refinement. however, depending on radius, the mesh required may be quite refined and the modeling of crack propagation to form the residual plastic wake is not easy with a finite crack tip radius. -5 -4 -3 -2 -1 0 1 2 3 4 5 0.00 0.02 0.04 0.06 0.08 0.10 yy  yy /  ys e1e2e8 figure 5: a) near crack tip elements. b) stressstrain curves (mixed hardening, max=47.5 mpa; min=0.8 mpa). e1 e2 e8 c0 http://www.gruppofrattura.it http://dx.medra.org/10.3221/igf-esis.25.09&auth=true f. v. antunes et alii, frattura ed integrità strutturale, 25 (2013) 54-60; doi: 10.3221/igf-esis.25.09 58 another relevant aspect is the size of crack tip plastic zone. fig. 7 shows the effect of load level and stress state on plastic zone size measured in the residual plastic wake perpendicularly to crack flank. the boundary was defined for a plastic deformation of 0.2%, which is usually considered to be the onset of plastic deformation in tension tests. the monotonic plastic zone increases with load level and, for the maximum load studied (kmax=11.9 mpa.m1/2; max/ys=70%), a size of 1.27 mm was observed. lower values were obtained for plane strain state, but the effect of load is clearly dominant in fig. 7. the size of crack tip plastic deformation zone has been widely studied for static loads, being usually represented in the form: 2( )p ys k r    (3) where k is the stress intensity factor and ys is material’s yield stress. considering only the singularity stress field, =1/6 for plane strain state and three times larger for plane stress state (=1/2) [7]. however, clavel et al. [8] proposed a factor of two. considering the stress redistribution produced by plastic deformation, rice [9] proposed =1/3 and =1/ for plane strain and plane stress states, respectively, assuming small scale yielding and a perfectly plastic behaviour. dugdale [10] proposed =/8 for plane strain state. for steels and aluminium alloys and plane strain state, dias et al. [11] proposed: 2 0.196 129 0.928 ced ced           (4) fig. 7 shows the results obtained with the models of dugdale and dias, which are significantly different from the numerical predictions. however, notice that the literature models were obtained for =0º, i.e., ahead of crack tip, and for static loads. in picc studies the size perpendicularly to crack flank, i.e., for =90º, is more relevant. the sizes proposed here for plane stress and plane strain states are, respectively: 2 0.11 ys k            (5) 3.1 1.64 ys k            (6) 0 0.5 1 1.5 2 2.5 0 5 10 15 20 25 30 35 l1 [m] p ,e q série1 figure 6: effect of mesh refinement on maximum equivalent plastic strain. the crack profile is also a main issue. a phenomenon of material removal was observed numerically under specific conditions, having a major influence of the closure level. fig. 8 shows the variation of the near crack tip profile in a numerical simulation performed considering pure kinematic hardening behaviour and plane stress state. the crack was submitted to 15 propagations with 2 load cycles between each, and after that, 20 load cycles were applied without propagation. as can be concluded from the figure, the increasing number of load cycles affects the position of the node immediately behind the crack tip, moving it upward. therefore, the first two loading cycles produce plastic deformation, http://www.gruppofrattura.it http://dx.medra.org/10.3221/igf-esis.25.09&auth=true f. v. antunes et alii, frattura ed integrità strutturale, 25 (2013) 54-60; doi: 10.3221/igf-esis.25.09 59 and consequently, crack closure. subsequent unloading and loading cycles takes material from behind the crack tip reducing closure. a similar phenomenon was observed for elastic-perfectly plastic behaviour. for plane strain state was observed independently of material model, however this affects the extent of the phenomenon. the same phenomenon has been reported also by antunes et al. [12] and jiang et al. [13] for pure kinematic hardening models in 2d plane stress analysis. toribio et al. [14] developed a high-resolution finite-element simulation of a plane-strain tensile crack with finite radius. elastic-perfectly plastic behaviour was assumed and deformed shapes revealed the mechanism of material transfer from the crack front onto lateral faces of the crack. 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 0.01 0.03 0.05 0.07 0.09 kmax/ys [m 0.5] p ,e q plane stress plane strain [11] [10] 0 0.0005 0.001 0.0015 0.002 0.0025 5.75 5.8 5.85 5.9 5.95 6 6.05 6.1 x [mm] d y [m m ] figure 7: size of plastic zone perpendicularly to crack flank. figure 8: effect of load cycles without propagation on crack profile (pure kinematic hardening, plane stress, l1=16 m). conclusions lasticity induced crack closure is intimately linked to crack tip plastic deformation. along crack flank, the plastic deformation presents an initial peak of plastic deformation. this peak was explained by the initial plastic deformation occurring at the first loading. the elements suffering progressive increase of load level showed lower plastic deformation levels as a consequence of hardening. the crack propagation stabilizes the plastic deformation and the plasticity induced crack closure (picc). the decrease of mesh size was found to increase progressively the maximum plastic deformation without convergence, which is typical of a singular behavior. convergence is achieved considering a finite value for the crack tip radius, but conciliate crack propagation modeling with a finite crack tip radius is not easy. the size perpendicularly to crack flank was measured and compared with literature models. significant differences were found relatively to literature models. however these models were defined for =0º, i.e., ahead of crack tip, and for static loads, while the present results were obtained for a residual plastic wake formed by crack propagation. aknowldgments he authors are indebted to the portuguese foundation for the science and technology (fct) and to feder (european regional development fund) for the financial support (project ptdc/eme-pme/114892/2009; compete: fcomp-01-0124-feder-015171) references [1] elber, w., fatigue crack closure under cyclic tension, engng fracture mechanics, 2 (1970) 37-45. p t http://www.gruppofrattura.it http://dx.medra.org/10.3221/igf-esis.25.09&auth=true f. v. antunes et alii, frattura ed integrità strutturale, 25 (2013) 54-60; doi: 10.3221/igf-esis.25.09 60 [2] bouvier, s., haddadi, h., levée, p., teodosiu, c., simple shear tests: experimental techniques and characterization of the plastic anisotropy of rolled sheets at large strains. journal of materials processing technology, 172 (2006) 96–103. [3] menezes, l.f., teodosiu, c., three-dimensional numerical simulation of the deep-drawing process using solid finite elements, journal of materials processing technology, 97 (2000) 100-106. [4] oliveira, m.c., alves, j.l., menezes, l.f., improvement of a frictional contact algorithm for strongly curved contact problems, international journal for numerical methods in engng, 58 (14) (2003) 2083-2101. [5] oliveira m.c., menezes, l.f., automatic correction of the time step in implicit simulations of the stamping process, finite elements in analysis and design, 40 (2004) 1995–2010. [6] antunes, f.v., rodrigues, d.m., numerical simulation of plasticity induced crack closure: identification and discussion of parameters, engineering fracture mechanics, 75 (2008) 3101–3120. [7] mcclung r.c., thacker b.h., roy, s., finite element visualization of fatigue crack closure in plane stress and plane strain, international journal of fracture, 50 (1991) 27–49. [8] clavel m., pineau a., fatigue behavior of two nickel-base superalloys i: experimental results on low cycle fatigue fatigue crack propagation and substructures, materials science and engineering, 55(2) (1982) 157-171. [9] rice, j.r., mechanisms of crack tip deformation and extension by fatigue, fatigue crack propagation, astm stp 415 (1967) 247-309. [10] dugdale, d.s., yielding of steel sheets containing slits, j. mech. phys. solids, 8 (1960) 100-108. [11] dias, a., lebrun j.l., bignonnet, a., x-ray diffraction studies on fatigue crack plastic zones developed under plane strain state conditions, fatigue and fracture of engng mat. structures, 22 (1999) 133-144. [12] antunes, f.v., borrego, l.f.p., costa, j.d., ferreira, j.m., a numerical study of fatigue crack closure induced by plasticity. fatigue and fracture of engng materials and structures, 27(9) (2004) 825-836. [13] jiang, y., feng, m., ding f., a re-examination of plasticity-induced crack closure in fatigue crack propagation. international journal of plasticity, 21 (2005) 1720-1740. [14] toribio, j., kharin, v., large crack tip deformations and plastic crack advance during fatigue. materials letters, 61 (4– 5) (2007) 964–967. http://www.gruppofrattura.it http://dx.medra.org/10.3221/igf-esis.25.09&auth=true microsoft word 2197 j.p.s.m.b. ribeiro et alii, frattura ed integrità strutturale, 48 (2019) 332-347; doi: 10.3221/igf-esis.48.32 332 focused on the “portuguese contributions for structural integrity” validation of fracture envelopes of structural adhesives for mixedmode strength prediction of bonded joints j.p.s.m.b. ribeiro departamento de engenharia mecânica, instituto superior de engenharia do porto, instituto politécnico do porto, portugal 1120523@isep.ipp.pt r.d.s.g. campilho departamento de engenharia mecânica, instituto superior de engenharia do porto, instituto politécnico do porto, portugal inegi – pólo feup raulcampilho@gmail.com, https://orcid.org/0000-0003-4167-4434 r.j.b. rocha inegi – pólo feup, portugal ricardojbragarocha@gmail.com a.j.s. leal, f.a.l. viana departamento de engenharia mecânica, instituto superior de engenharia do porto, instituto politécnico do porto, portugal alb.leal@gmail.com, 1120367@isep.ipp.pt abstract. in the design of adhesive structures, it is extremely important to accurately predict their strength and fracture properties (critical strain energy release rate in tension, gic, and shear, giic). in most cases, the loads occur in mixed-mode (tension plus shear). thus, it is of great importance the perception of fracture in these conditions, namely of the strain energy release rates in tension, gi, and shear, gii, relative to different crack propagation criteria or fracture envelopes. this comparison allows to determine the most suitable energetic propagation criterion to be used in cohesive zone models (czm). the main objective of this work is to verify, by czm, which is the power parameter () that best suits the energetic crack propagation criterion for czm modelling, using single-lap joints (slj) and double-lap joints (dlj) with aluminium adherends and bonded with three different adhesives. with this purpose, numerical simulations of the slj and dlj are carried out, and the maximum load (pm) is compared with experiments. for the araldite® av138 and araldite® 2015, the energetic criterion resulting from the experimental work provided matching numerical results and, thus, the fracture envelopes were validated. the sikaforce® 7752 results were slightly offset due to czm law shape issues. citation: ribeiro, j.p.s.m.b., campilho, r.d.s.g., rocha, r.j.b., leal, a.j.s., viana, f.a.l., validation of fracture envelopes of structural adhesives for mixed-mode strength prediction of bonded joints, frattura ed integrità strutturale, 48 (2019) 332-347. received: 24.09.2018 accepted: 28.10.2018 published: 01.04.2019 copyright: © 2019 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. http://www.gruppofrattura.it/va/48/2197.mp4 j.p.s.m.b. ribeiro et alii, frattura ed integrità strutturale, 48 (2019) 332-347; doi: 10.3221/igf-esis.48.32 333 keywords. bonded joint; finite element analysis; cohesive zone models; mixed-mode fracture; fracture envelope. introduction n the present time, adhesively-bonded joints are used in numerous industrial fields due to several advantages over other joining methods, e.g. welding, riveting and fastening. in fact, from a simple shoe to a space shuttle, adhesives are employed to bond similar and dissimilar materials. the aeronautic industry, continuously looking for new techniques to reduce fuel consumption and costs, was the one that most contributed to the development of adhesive joints [1]. moreover, the use of composite materials such as carbon fibre reinforced polymers (cfrp) in structures has significantly increased during the last years. in the automotive industry, cfrp is usually joined to other composites, aluminium or steel through adhesive bonds [2]. this technique’s advantages include preserving the integrity of the parent materials, since it avoids any structural damage (i.e. no holes or heating), thus providing a better stress distribution along the bonded area [3]. additionally, improved strength-weight and cost-effectiveness ratios can be attained, which are highly relevant for the industry and designers in the pursuit of better products [1]. few other benefits such as flexible gap filing, noise and vibration damping, excellent insulation and improved aesthetics are inherent to this method. nevertheless, some drawbacks still persist, such as the requirement of a surface treatment, disassembly issues without causing damage, low resistance to temperature and humidity, and joint design orientated towards the elimination of peel stresses [4]. a number of joint architectures is available depending on the different applied loads. among those, the slj is the most studied one. in fact, slj are simple to manufacture, although the adherends are not aligned, causing major peel (y) stresses at the overlap ends [3]. the dlj, slightly more difficult to produce, manages to decrease the bending moment due to its balanced design, thus reducing both y and shear (xy) stresses. despite that, internal bending moments may occur, triggering y stresses at the ends of the inner adherend. the scarf joint, which also presents manufacturing difficulties (in cutting the taper angle) keeps the loading axis collinear with the joint, therefore promoting more uniform y stresses in the adhesive layer and helping the joint to endure higher strengths compared to lap joints [5]. moreover, one may find commonly other joint architectures, such as butt, strap, step, tubular and t-joints. the development of trustworthy predictive methods is required for a widespread use of adhesively-bonded joints. despite few analytical solutions being capable to quickly predict the joints’ behaviour, the process could become extremely complex when composite adherends are used or in the presence of adhesives with high plasticity. the finite element (fe) method is capable to overcome such issues and is by far the most common technique used in bonded joints [6]. several approaches were developed along the years, such as continuum mechanics, fracture and damage mechanics techniques. later, during the sixties, barenblatt [7] and dugdale [8] proposed the concept of cohesive zone to describe damage under static loads. this method simulates the damage along a predefined crack path thru the establishment of a load-displacement (p-) correlation, known as traction-separation law. these laws associate the cohesive tractions (tn for tension and ts for shear) with the relative displacements (δn for tension and δs for shear). to obtain good agreement between the predicted strength and the experiments, a truthful estimation of the cohesive strengths in tension and in shear (tn0 and ts0, respectively), and gic and giic is essential. usually, an adhesive joint may be put under y or xy stresses, although in most cases it is subjected simultaneously to both, thereby creating a mixed-mode loading. despite the importance of the correct estimation of the czm parameters, standardized methods are not yet available [9]. nevertheless, few techniques are available to assess the cohesive parameters: the property identification method, the direct method and the inverse method [1]. the property identification technique involves the separated calculation of each one of the cohesive law parameters by proper tests. this approach is particularly critical if bulk tests are used due to reported deviations between the bulk and thin adhesive bond cohesive properties [10]. the direct method provides the precise shape and the complete czm laws by measuring the jintegral and crack-tip normal or shear displacements, through the differentiation of gi or gii with respect to δn or δs, respectively [11]. on the other hand, the inverse method involves estimating the czm parameters by iterative fitting the fe prediction with experimental data (e.g. the r-curve, the crack opening profile or the p-δ curve), considering a precise description of the experimental geometry and approximated cohesive laws [12]. the value of gic or giic is input in the fe model and, to completely define the czm law, approximate bulk values can be used for tn0 or tns for the initiation of the trial and error iterative process. i j.p.s.m.b. ribeiro et alii, frattura ed integrità strutturale, 48 (2019) 332-347; doi: 10.3221/igf-esis.48.32 334 several tensile fracture characterization tests to evaluate gic are available, such as the double-cantilever beam (dcb), the tapered double-cantilever beam (tdcb), the compact tension (ct) and the single-edge notched bending (senb). the dcb test became the most used, being supported by the bsi 7991:20001 [13], astm d3433 [14] and iso 25217 [15] standards, providing guiding processes for the experiments and data reduction. this test requires an initial crack introduced during the fabrication process at the adhesive-free edge of the specimen, which will propagate by applying an opening load at the specimen’s edge. the r-curve plots the gi against the crack length (a). in theory, this curve provides a perfectly horizontal gi-a curve during damage growth, whose steady-state value gives the measurement of gic. shear fracture testing is considerably more complex and is yet to be standardized [16]. nonetheless, several different tests have been proposed: end-notched flexure (enf), 4-point end-notched flexure (4enf) and end-loaded split (els). among those, the most commonly used is the enf, which presents a simple three-point bending setup and reliable data reduction methods. it requires a pre-cracked specimen and a constant measurement of p,  and a. since adhesive joints are typically subjected to mixed-mode, few tests are also available to evaluate the mixed-mode strain energy release rate (g), such as the asymmetric double-cantilever beam (adcb), the mixed-mode flexure (mmf), the mixed-mode bending (mmb) and the single-leg bending (slb). the mmb test is the only standardized test available to estimate g of composites, referred in astm d6671 [17]. a combination of the dcb and enf is the basis of the mmb test [18], and allows to change the mixed-mode ratio almost without limit between the pure mode i and pure mode ii loading conditions [19]. hence, it provides a complete understanding of the joints’ fracture behaviour under different loadings, known as fracture envelope. the slb test is simpler than the mmb as it does not require special jigs. however, is more limited with respect to the change of the mixed-mode ratio. jung lee et al. [9] suggested a systematic procedure to evaluate the czm parameters of an adhesive bond, using slb tests for the extrapolation of the pure-mode laws, hence simplifying the inverse fitting method. co-cured specimens were made of steel and unidirectional carbon fibre reinforced material. measurement of g was carried out from the test data, and the mixed-mode was defined from the classical beam theory. a mixed-mode czm was applied to reproduce the experiments, including a triangular law shape, the quadratic nominal stress criterion for damage initiation and the linear power law criterion for damage growth. the missing cohesive parameters (stiffness in tension, knn, stiffness in shear, kss, tn0 and ts0) were assessed by the design of experiments (doe) and kriging metamodel (km) techniques. the authors concluded that the proposed procedure accurately described the fracture behaviour of mixed-mode joints, attaining predictions within 15% of the experimental data. moreover, it had the advantage of non-requirement of two separate tests (e.g., dcb for tensile and enf for shear characterization). rodrigues et al. [20] determined the fracture envelope of an aluminium adhesive bonded joint in dry and wet conditions, enabling to predict the humidity effect on g. after assessing the adhesive moisture absorption capability, dcb and enf fracture tests were performed for mode i and ii, respectively. for the mixed-mode test, an apparatus described in reference [21] was used that allows to test within a range of mode combinations between pure-modes i and ii. the dry and wet fracture envelopes showed the ageing effect on the pm and p- curves. moreover, the applied methodology enabled obtaining the full fracture envelope with a linear correlation between the pure and mixedmode data points. nunes and campilho [22] estimated the fracture envelope of joints bonded with three adhesives with different ductility using the asymmetric tapered double-cantilever beam (atdcb) mixed-mode test. pure-mode tdcb tests and the corrected beam theory (cbt) were used to assess gic, and the enf test together with the compliance-based beam method (cbbm) served to estimate giic. czm laws were built based on a triangular law and the power law mixedmode growth criterion, and the respective numerical results were compared with the experiments. this enabled to validate the czm laws and the mixed-mode propagation criterion of each adhesive. some inconsistencies were detected in the stiffness and pm of the most ductile adhesive, since the triangular law was not suitable to capture the plasticity inherent to theses adhesives [23]. however, the authors manage to prove that the data reduction method used for the atdcb specimens is accurate and quick. the main objective of this work is to verify, by czm, which is the  value that best suits the energetic crack propagation criterion for czm modelling, using slj and dlj with aluminium adherends and bonded with three different adhesives. with this purpose, numerical simulations of the slj and dlj are carried out, and pm is compared with experiments. experimental work joint materials (fracture tests and lap joints) he dcb, enf and slb adherends, used to build the fracture envelopes of the adhesives, were manufactured from cfrp plates. the composite plates were fabricated using 20 plies with 0.15 mm thickness each, stacked by handlay-up using unidirectional layers. the seal® texipreg hs 160 rm pre-preg was used in this process. the curing t j.p.s.m.b. ribeiro et alii, frattura ed integrità strutturale, 48 (2019) 332-347; doi: 10.3221/igf-esis.48.32 335 process took 1 hour to accomplished and was carried out in a hot-plates press under a temperature and pressure of 130ºc and 2 bar, respectively. tab. 1 describes the elastic-orthotropic properties of an cfrp unidirectional layer fabricated under similar conditions [24]. the slj and dlj tested in this work for validation purposes were fabricated from an aluminium alloy sheet metal with reference aw6082-t651. this alloy is produced using a method of artificial ageing, carried at a temperature of 180ºc. this material presents several important features, which were relevant during the material selection, such as the good mechanical properties and the wide field of structural applications in the laminated form. this alloy was characterized in a previous study [25], on bulk specimens, from which the results depicted in tab. 2 were obtained. ex=1.09e+05 mpa xy=0.342 gxy=4315 mpa ey=8819 mpa xz=0.342 gxz=4315 mpa ez=8819 mpa yz=0.380 gyz=3200 mpa table 1: elastic orthotropic properties of a unidirectional carbon-epoxy ply aligned in the fibres direction (x-direction; y and z are the transverse and through-thickness directions, respectively) [24]. properties aluminium alloy aw6082 t651 young’s modulus, e [gpa] 70.07±0.83 poisson ratio,  0.3 tensile yield stress, y [mpa] 261.67±7.65 tensile failure stress, f [mpa] 324.00±0.16 tensile failure strain, f [%] 21.70±4.24 vickers hardness, [hv] 100 table 2: properties for the aluminium alloy aw6082 t651 [25]. three adhesives were tested, in order of increasing ductility: araldite® av138, araldite® 2015 and sikaforce® 7752. the use of these adhesives allowed testing different materials behaviours. their tensile mechanical properties, such as the young’s modulus (e), tensile yield stress (y), tensile strength (f) and tensile failure strain (f), were defined in previous studies [2628]. this was accomplished by tensile testing bulk specimens with a dogbone shape, produced in accordance with the french standard nf t 76-142, in a servo-hydraulic machine. example tensile stress-tensile strain curves (-) are represented in fig. 1. figure 1: example of - curves of the adhesives araldite® av138, araldite® 2015 and sikaforce® 7752. to characterize the adhesives’ shear properties, the thick adherend shear test (tast) was used in former studies [26-28]. to estimate gic and giic, dcb and enf tests were performed, respectively. the specimens were fabricated and tested as described in reference [28]. the gathered adhesives’ properties are described in tab. 3. 0 10 20 30 40 50 0 0.05 0.1 0.15 0.2  [m p a]  araldite® av138 araldite® 2015 sikaforce® 7752 j.p.s.m.b. ribeiro et alii, frattura ed integrità strutturale, 48 (2019) 332-347; doi: 10.3221/igf-esis.48.32 336 property av138 2015 7752 young’s modulus, e [gpa] 4.89±0.81 1.85±0.21 0.49±0.09 poisson’s ratio,  0.35 a 0.33 a 0.30 a tensile yield stress, y [mpa] 36.49±2.47 12.63±0.61 3.24±0.48 tensile strength, f [mpa] 39.45±3.18 21.63±1.61 11.48±0.25 tensile failure strain, f [%] 1.21±0.10 4.77±0.15 19.18±1.40 shear modulus, g [gpa] 1.81 b 0.70 b 0.19 b shear yield stress, y [mpa] 25.1±0.33 14.6±1.3 5.16±1.14 shear strength, f [mpa] 30.2±0.40 17.9±1.8 10.17±0.64 shear failure strain, f [%] 7.8±0.7 43.9±3.4 54.82±6.38 toughness in tension, gic [n/mm] 0.20 c 0.43±0.02 2.36±0.17 toughness in shear, giic [n/mm] 0.38 c 4.70±0.34 5.41±0.47 a manufacturer’s data b estimated from the hooke’s law using e and  c estimated in reference [26] table 3: mechanical and fracture properties of the adhesives araldite® av138, araldite® 2015 and sikaforce® 7752 [26-28]. joint dimensions, fabrication and testing fig. 2 illustrates the dimensions and geometry of dcb, enf and slb specimens, whereas fig. 3 represents the geometry and dimensions of the slj and dlj. figure 2: geometry and dimensions of the dcb (a), enf (b) and slb specimens (c). the specimens’ dimensions were as follows next (in mm): total length or mid-span l=180 (slj and dlj), l=140 (dcb) or l=100 mm (enf and slb), initial crack length a0≈40 mm (dcb) or a0≈60 mm (enf and slb), adherends’ thickness h=3, adhesive thickness ta=0.2, joints’ width b=25 and overlap length lo=12.5, 25, 37.5 and 50 (slj and dlj only). in the present work, the dlj were fabricated with equal h in the middle and outside adherends, which is not consistent with the j.p.s.m.b. ribeiro et alii, frattura ed integrità strutturale, 48 (2019) 332-347; doi: 10.3221/igf-esis.48.32 337 existence of cross-section balanced adherends. this occurs if the middle adherend has twice h than the outer adherends [29]. however, this was a testing choice that does not compromise the fracture envelopes’ validation purpose that this work aims to. six specimens for each condition were tested for the fracture tests, while five specimens were evaluated for the lap geometries. figure 3: geometry and dimensions of the single (a) and double-lap joint (b). figure 4: test setup for the slb specimens. for both cfrp and aluminium adherends, the surface preparation prior to bonding was similar: the bonding surfaces were manually abraded using a fine sandpaper to completely remove the shiny surface or aluminium oxide layer, respectively, followed by cleaning and degreasing with acetone. for all tests, and to promote a reliable and dimensionally accurate bonding, the joined parts were placed in a steel mould during the curing process. to guarantee a correct value of ta, for the dcb, enf and slb specimens, calibrated metallic spacers were placed between the superior and inferior adherends’. before their placement, the spacers were coated with demoulding agent to simplify their extraction after curing. these specimens shared the same pre-crack induction method, which consisted in the placement of spacers, in which the crack-tip spacer had a centred sharp razor blade. nonetheless, to avoid any blunting effects, in each specimen the crack was manually propagated for a length between 1 and 3 mm, and only after the a0 measurement took place. in the case of the slj and dlj, ta was achieved using metallic blocks that were placed in the mould. regardless the joint type, after pouring the adhesive in one of the adherends, the two adherends were joined and pressured until there was contact with the spacers. this process had to be repeated one more time for the dlj. then, the curing process initiated. this took place over one week for all joints. after curing, the spacers or blocks were removed, and the excess adhesive was removed using milling techniques. to allow the measurement of a, one side of the dcb, enf and slb joints was painted with a brittle white paint and a numbered scale was glued on that side to allow tracking crack propagation. all specimens were tested in an electro-mechanical testing machine shimadzu ag-x 100 equipped with a 100 kn load cell. the fracture tests were documented by taking pictures with 5 s intervals, using a digital 18 mpixel camera with no zoom and placed at a focal distance of 100 mm. the dcb, slj (a) (b) j.p.s.m.b. ribeiro et alii, frattura ed integrità strutturale, 48 (2019) 332-347; doi: 10.3221/igf-esis.48.32 338 and dlj specimens were tested in conventional tension, while the enf and slb specimens were tested using a three-point bending (3pb) setup. all tests were carried at room temperature and 1 mm/min of velocity. the manual a measurement in the dcb, enf and slb tests was done by approximating the crack tip to the nearest 1/8 of mm in the scale, which was made possible by the resolution of the images (0.02 mm/pixel). the 3pb setup is depicted in fig. 4 for the case of a slb specimen. fracture toughness estimation the linear elastic fracture mechanics (lefm) approach is a simple approach to estimate g for strength prediction purposes [30]. however, difficulties arise when dealing with materials (e.g., adhesives) with ductility. on the other hand, typically failure in adhesive bonds takes place under mixed-mode due to the different properties of the joints’ components, the applied load and joint architecture, which demands the knowledge of both gic and giic, and also the use of mixedmode criteria [22]. in this work, the cbbm data reduction method was selected to estimate gic and giic from the dcb and enf tests, respectively, and gi and gii from the slb tests. the cbbm provides the fracture measurements only from the experimental compliance (c) measured during the tests [31]. this method procedure includes an equivalent crack length (aeq), which is defined from the p- curve. moreover, it accounts for the fracture process zone (fpz), which generates around the crack tip due to the materials’ plasticity, otherwise neglected in the analysis when considering the measured value a. for the dcb specimen, gic is calculated as eq ic f 22 2 2 xy 26 1 5 ap g gb h h e         (1) where ef is a corrected flexural modulus to account for stress concentrations at the crack tip and stiffness inconsistency between specimens, and gxy is the shear modulus of the adherends. full derivation can be found in the study of constante et al. [32]. applied to the enf test, giic can be obtained by the following expression eq f 2 2 iic 2 3 9 . 16 p a g b e h  (2) a detailed description of the method can be found in reference [31]. the cbbm applied to the slb specimens, detailed by fernández et al. [33], is based on the beam theory of szekrényes and uj [34]. application of the irwin-kies expression gives the total energy release rate (gt) which, after equation splitting according to szekrényes and uj [34], provides gi and gii f f 2 2 2 22 eq eq i ii2 3 2 2 3 xy 12 93 and . 16 10 16 p a p ap g b e h g b h b e h   g (3) numerical work models’ construction umerical simulations were undertaken in abaqus® to simulate the slj and dlj, in order to validate the experimentally estimated fracture envelopes further in this work. the two-dimensional models included geometrical non-linearities. the models were based on plane-strain elements (cpe4 of abaqus®) for the adherends with elastic-plastic continuum formulation and cohesive elements (coh2d4 of abaqus®) for the adhesive layer. in fig. 5 it is possible to find a typical mesh for the dlj with lo=25 mm. it should be stressed that, for all dlj models, horizontal symmetry was applied to reduce the computational effort. the mesh refinement described next always assured mesh convergence. the elements’ size at the adhesive layer’s edges was 0.2 mm × 0.2 mm, thus, only a single row of czm elements was used to populate the adhesive layer thickness. this corresponds to using the continuum czm approach, in which the czm laws should reproduce the constitutive behaviour of the full adhesive layer, including the ta-dependent stiffness. for all the models, a total of 8 elements was considered in the adherends through-thickness, whereas between 40 and 160 solid elements were introduced length-wise in the adhesive layer length (between the smallest and largest lo). to speed up the simulations, although without compromising the analysis results, the fe mesh was graded horizontally and vertically (this effect is visible in fig. 5). all models were fixed at one edge while a vertical restraint and tensile displacement n j.p.s.m.b. ribeiro et alii, frattura ed integrità strutturale, 48 (2019) 332-347; doi: 10.3221/igf-esis.48.32 339 were applied at the opposite edge. in the following section, the triangular czm formulation, applied in all models and incorporated in abaqus®, is presented. figure 5: mesh detail for the lo=25 mm double-lap joint (czm failure analysis). mixed-mode triangular model czm are based on a relationship between stresses and relative displacements (in tension or shear) connecting paired nodes of cohesive elements (fig. 6), to simulate the elastic behaviour up to tn0 in tension or ts0 in shear and subsequent softening, to model the degradation of material properties up to failure. the shape of the softening region can also be adjusted to conform to the behaviour of different materials or interfaces [35]. the areas under the traction-separation laws in tension or shear are equalled to gic or giic, by the respective order. under pure loading, damage grows at a specific integration point when stresses are released in the respective damage law. under a combined loading, stress and energetic criteria are often used to combine tension and shear [36]. the triangular law (fig. 6) assumes an initial linear elastic behaviour followed by linear degradation. elasticity is defined by a constitutive matrix (k) containing the stiffness parameters and relating stresses (t) and strains () across the interface [37] n nn ns n s ns ss s . t k k t k k                       kt  (4) tn and ts are the current tensile and shear tractions, respectively, and n and s the corresponding strains. a suitable approximation for thin adhesive layers is provided with knn=e, kss=gxy and kns=0 [25]. damage initiation can be specified by different criteria. in this work, the quadratic nominal stress criterion was considered for the initiation of damage, already shown to give accurate results [25] and expressed as [37] n s n s 22 0 0 1. t t t t             (5) are the macaulay brackets, emphasizing that a purely compressive stress state does not initiate damage. after the mixedmode cohesive strength is attained (tm0 in fig. 6) by the fulfilment of eqn. (5), the material stiffness is degraded. complete separation is normally predicted by a linear power law form of the required energies for failure in the pure modes by considering the power law exponent =1 [37] i ii ic iic 1. g g g g                (6) results fracture envelopes of the adhesives he present section aims at estimating the most suitable propagation criterion exponent using the fracture envelope analysis. with this purpose, the pure-mode toughnesses (gic and giic) and mixed-mode toughnesses (gi and gii) are first required. t j.p.s.m.b. ribeiro et alii, frattura ed integrità strutturale, 48 (2019) 332-347; doi: 10.3221/igf-esis.48.32 340 figure 6: traction-separation law with linear softening law available in abaqus®. gic and giic calculation by the dcb and enf tests gic and giic were calculated by the cbbm data reduction method using the dcb and enf tests, respectively. the p- curves obtained for both tests were all consistent between specimens joined with each adhesive. regarding damage growth of the specimens bonded with araldite® av138, all attained a brittle failure, which grows abruptly throughout the bondline. on the other hand, both araldite® 2015 and sikaforce® 7752 suffered a gradual failure accompanied by a reduction of p. the r-curves depicted the expected steady-state crack growth for both loading modes, which represent the gic and giic values [38]. nevertheless, crack propagation presented few oscillations mainly owing to small fabrication defects and imperfections, adhesive mixing variations and crack arrest phenomena [39]. in the enf test, giic can be measured up to the crack reaching the proximity of the loading cylinder, because at this zone the almost pure-shear stress state is cancelled due to the compression effect. tab. 4 presents the average gic and giic and respective deviation of all specimens bonded with the three adhesives. the highest standard deviation, normalized over the average fracture toughness, was 10.4% for the araldite® av138 (giic), depicting the repeatability of the experimental tests. comparing these values with the ones presented in tab. 3, the following deviations were found for gic: -30.0, +25.6 and +60.4% for the adhesives araldite® av138, araldite® 2015 and the sikaforce® 7752, respectively. regarding the deviations for giic, the values were: -7.4, -37.1 and +2.6% in the same order. these differences are justified by the dependence of gic and giic with the specimens’ geometry, more specifically with h and ta, given that these parameters influence fpz’ size in the vicinity of the crack tip [40]. adhesive araldite® av138 araldite® 2015 sikaforce® 7752 fracture toughness gic giic gic average 0.140 0.352 0.540 deviation 0.012 0.037 0.041 table 4: average values of gic and giic and respective deviation [in n/mm] obtained by the dcb and enf tests, respectively. gi and gii calculation by the slb tests the p- curves of the slb specimens bonded with the araldite® av138 are depicted in fig. 7 as an example of the repeatability between specimens of each adhesive. generally, a good reproducibility was found between specimens bonded with same adhesive regarding the elastic stiffness (up to pm). the only exception occurs with an araldite® av138 specimen due to a higher a0 value, nonetheless, this does not affect the measurements. crack growth was usually stable, apart from few araldite® av138 specimens in which, after pm is attained, the load falls abruptly due to crack growth instability associated to the brittleness of this adhesive. this can also be indicative that this particular adhesive is affected by the presence of small defects that trigger this behaviour [32]. the crack growth behaviour was also similar between specimens bonded with the same adhesive. on the other hand, the ductility of the araldite® 2015 and the sikaforce® 7752 led to a softening near pm. fig. 8 shows example tensile (a) and shear (b) experimental r-curves for an slb specimen with the adhesive araldite® av138. one may notice that crack propagates at a fairly accurate steady-state value of gi or gii (for 130≤aeq≤180). this constant crack growth region was the one considered to estimate both gi or gii values. in fact, when the adhesives’ fpz spreads to the loading cylinder, the toughness artificially increases owing to the compression effects of the applied load. the r-curves for the joints bonded with the araldite® 2015, compared to the ones showed in fig. 8, j.p.s.m.b. ribeiro et alii, frattura ed integrità strutturale, 48 (2019) 332-347; doi: 10.3221/igf-esis.48.32 341 presented a reduction of the constant gi and gii extent because of the inherent ductility of this adhesive. on the other hand, the sikaforce® 7752 r-curves showed a minor increasing trend of gi and gii with a in line for the large dimensions of the fpz. figure 7: p- curves obtained for the slb specimens with the adhesive araldite® av138. fig. 8: example of tensile (a) and shear (b) experimental r-curves for an slb specimen with the adhesive araldite® av138. fracture envelope the fracture envelopes of the three tested adhesives depicted in fig. 9 were constructed from the mixed-mode results of the slb tests and also the pure-mode gic and giic values. in all cases, the cbbm data reduction method was used. four theoretical fracture envelopes are presented, by applying an energetic crack propagation criterion of the type of eqn. (6) with the exponents =1/2, 1, 3/2 and 2. this will enable framing the behaviour of each adhesive in the most appropriate criterion. regarding the araldite® av138, a small relative standard deviation of the experimental data was attained, i.e., 5.2 and 5.9% for gi and gii, respectively. oppositely, the other two adhesives presented a higher scatter in the experimental outcomes, even though this was still satisfactory. actually, the deviation found for gi and gii was by 9.4% and 9.2%, respectively, for the araldite® 2015, and 3.7% and 3.6% for the sikaforce® 7752, in the same order. the energetic propagation criterion with =1/2 provides a good agreement to the behaviour of the araldite® av138. the same exponent is also the best solution for the araldite® 2015, even though the correlation is not as obvious as for the araldite® av138. on the other hand, the sikaforce® 7752 presents a noticeably different mixed-mode behaviour compared to that of the other adhesives, in such a way that the mixed-mode energies during propagation largely exceed the linearity between the corresponding pure-mode values. in fact, for this adhesive, the best propagation criterion exponent to be used in mixedmode simulations is =2. validation with lap geometries this section aims at validating the estimated mixed-mode crack propagation criteria defined for each adhesive. with this purpose, initially the experimental pm results for the slj and dlj are presented and discussed. following, pm prediction takes place for all tested conditions, and the relevant conclusions are taken. 0 20 40 60 80 100 0 1 2 3 4 p [n ] δ [mm] 0 0.02 0.04 0.06 0.08 0.1 120 130 140 150 160 170 180 g i o r g ii [n /m m ] aeq [mm] gi gii j.p.s.m.b. ribeiro et alii, frattura ed integrità strutturale, 48 (2019) 332-347; doi: 10.3221/igf-esis.48.32 342 experimental strength fig. 10 provides the experimental pm of the slj (a) and dlj (b) bonded with the three adhesives as a function of lo. for both slj and dlj, the behaviour highly differs depending on the adhesive. here, the values of e and gxy have a major influence on the stress distributions and, thus, on pm. actually, adams [4] proved that a smaller adhesive stiffness is linked to more uniform stresses along lo. in view of this, the joints with the araldite® av138 should have higher peak stresses. it is also known that y and xy peak stresses in the overlap increase with lo [41], turning pm in joints with large lo highly dependent on the plasticization ability while, in joints with short lo, pm is mostly dependent on the adhesive strength. moreover, joints with a brittle adhesive should fail when the adhesive’s strength is attained. joints with ductile adhesives undergo plasticity at the bond edges at the same time that the inner bond becomes increasingly loaded, which is usually linked to an increase in pm [42]. a) b) c) figure 9: idealised fracture envelopes and experimental gi/gii data points for each of the adhesives: (a) araldite® av138, (b) araldite® 2015 and (c) sikaforce® 7752. in view of this, the slj results of fig. 10 (a) reveal that the strong and brittle araldite® av138 shows higher pm for lo=12.5 mm compared to the less strong but ductile araldite® 2015 (difference of 2.5%). the increase of peak stresses for higher lo [41] inhibits large pm improvements with lo for the joints with the araldite® av138. as a result, the araldite® 2015 progressively performs better than the araldite® av138 by increasing lo, due to its ductility. the difference between these two adhesives attains 62.5% for lo=50 mm. the sikaforce® 7752 is the less strong adhesive but, on the other hand, it is highly ductile, enough for the adhesive layer to fracture under generalized plasticization conditions up to large lo. thus, for small lo this adhesive is not competitive due to failure being governed by the strength rather than the toughness. the pm offset, for lo=12.5 mm, is 33.1% to the araldite® av138 and 31.4% to the araldite® 2015. on the other hand, due to its marked ductility, pm increases nearly linearly with lo. for lo=50 mm, pm is proximal to that of the araldite® 2015 (difference of only 5.3%), while it is higher than the araldite® av138 by 54.0%. for the dlj (fig. 10 b) and lo=12.5 mm, the araldite® av138 is also close to the araldite® 2015 (pm of the araldite® av138 only excels by 1.0%). however, the pm vs. lo plots gradually deviate with the increase of lo due to the less marked pm increase for the araldite® av138 (the approximate differences attained 30%). apart from this, the plastic deformation initiated at p16 kn in the inner adherend, while tensile net failure of the same adherend occurred at p24 kn. this occurrence was responsible for the disruption of the pm vs. lo curves of both the araldite® 2015 and sikaforce® 7752, and it also affected the behaviour of the joints bonded with the araldite® av138, even for small adherend plasticization. the j.p.s.m.b. ribeiro et alii, frattura ed integrità strutturale, 48 (2019) 332-347; doi: 10.3221/igf-esis.48.32 343 joints bonded with the araldite® 2015 suffered significant plasticization for lo=25 mm, although failing cohesively in the adhesive layer, while tensile adherend failure was encountered for lo>25 mm. thus, the pm vs. lo curve presents a steadystate pm for lo≥25 mm. using the sikaforce® 7752 led to a diminished pm for lo=12.5 mm because of the adhesive strengths. despite this fact, due to its toughness, this adhesive has an improved performance for bigger pm. this improvement is nearly linear up to lo=37.5 mm. bigger lo promote the inner adherend’s failure and limit pm to 24 kn. a) b) figure 10: experimental pm values for the slj (a) and dlj (b) bonded with the three adhesives. mixed-mode crack propagation criterion validation fig. 11, and fig. 12, fig. 13 show the comparison between the pm values obtained experimentally with the numerical ones for the different lo and  exponents for the slj (a) and dlj (b) bonded with the araldite® av138, araldite® 2015 and sikaforce® 7752, respectively. the pure-mode czm laws of the adhesives were inserted by the definition of e, gxy, tn0, ts0, gic and giic. these properties were all taken from the data of tab. 3, with the particularity that tn0 and ts0 are made equal to f and f, respectively [26]. the mixed-mode behaviour is defined from the damage initiation criterion (quadratic stress criterion in this case) and damage growth criterion (power law criterion with the user specification of ). for the araldite® av138 (fig. 11), and first considering the slj, it can be concluded that the experimental pm points are closest to the numerical predictions with =0.5. as a result, the experimentally obtained fracture envelope is considered valid, since the experimental and the numerical behaviours were in agreement. the largest percentile deviation between these two sets of values was -4.94% (lo=12.5 mm). the highest offset was found for =2, with a maximum deviation of +36.43% (lo=50 mm). identically, for the dlj, the numerical curve relating to =0.5 also proved to be the most accurate, and showed a maximum deviation to the experiments of -5.00% (lo=50 mm). it should be mentioned that, for lo≥25 mm, pm becomes affected by adherends’ plasticization for =1, 1.5 and 2, which prevents predicted pm with a larger offset than that depicted in the figure. as a result of this discussion, the formerly obtained experimental envelope is validated. the results for the araldite® 2015 (fig. 12) showed that, for the slj, the most suitable  is also 0.5, as predicted in the formerly discussed fracture tests, and that it gives a good representation of the experimental behaviour. the predicted pm are always above the experiments, with relative differences that range between +4.90% (lo=37.5 mm) to +14.39 (lo=12.5 mm). this enables validating the mixed-mode criterion for crack propagation. on the other hand, the other tested  revealed higher deviations by increasing  up to a value of 2. here, the maximum offset was +40.74%, for lo=50 mm. an identical agreement was also found for the dlj. however, for lo≥25 mm, the joints’ failure becomes governed by the net adherends’ fracture, and the pm results between different  become insignificant. also because of this, the deviations are generally not relevant. for =0.5, the maximum error was -3.55% for lo=50 mm. between all , the maximum error was +5.46% (=2 and lo=25 mm). as a result of this discussion, the formerly obtained experimental envelope is validated. in opposition to these two adhesives, for the sikaforce® 7752, =2 is the best solution. however, it was found that, for the joints bonded with the sikaforce® 7752, the change of  does not result in large pm changes. actually, for the slj, the offset between the tests and predictions steadily increased with lo, up to a maximum of -16.58, -15.84, -15.74, and -15.71% for lo=50 mm and increasing  from 0.5 up to 2. the dlj are affected by the adherends’ failure at lo=50 mm. the maximum errors were obtained for lo=37.5 mm for all , and took values of -15.50, -15.40, -15.39, and -15.39% by increasing order of . on the other hand, for the joints bonded with the other two adhesives, the modification of  revealed a great influence on pm. a more detailed study showed that the influence of this parameter on pm gradually diminishes with the adhesives’ 0 5 10 15 20 25 30 0 12.5 25 37.5 50 p m [k n ] lo [mm] araldite® av138 araldite® 2015 sikaforce® 7752 0 5 10 15 20 25 30 0 12.5 25 37.5 50 p m [k n ] lo [mm] araldite® av138 araldite® 2015 sikaforce® 7752 j.p.s.m.b. ribeiro et alii, frattura ed integrità strutturale, 48 (2019) 332-347; doi: 10.3221/igf-esis.48.32 344 ductility. on the other hand, the slight deviations between the experiments and simulations were found to due to using a triangular czm to model a highly ductile adhesive [35]. a) b) figure 11: comparison between experimental and numerical pm values for the slj (a) and dlj (b) bonded with the araldite® av138, considering different . a) b) figure 12: comparison between experimental and numerical pm values for the slj (a) and dlj (b) bonded with the araldite® 2015, considering different . a) b) figure 13: comparison between experimental and numerical pm values for the slj (a) and dlj (b) bonded with the sikaforce® 7752, considering different . 0 5 10 15 20 25 30 0 12.5 25 37.5 50 p m [k n ] lo [mm] av138 exp 0.5 1 1.5 2 0 5 10 15 20 25 30 0 12.5 25 37.5 50 p m [k n ] lo [mm] av138 exp 0.5 1 1.5 2 0 5 10 15 20 25 30 0 12.5 25 37.5 50 p m [k n ] lo [mm] 2015 exp 0.5 1 1.5 2 0 5 10 15 20 25 30 0 12.5 25 37.5 50 p m [k n ] lo [mm] 2015 exp 0.5 1 1.5 2 0 5 10 15 20 25 30 0 12.5 25 37.5 50 p m [k n ] lo [mm] 7752 exp 0.5 1 1.5 2 0 5 10 15 20 25 30 0 12.5 25 37.5 50 p m [k n ] lo [mm] 7752 exp 0.5 1 1.5 2 j.p.s.m.b. ribeiro et alii, frattura ed integrità strutturale, 48 (2019) 332-347; doi: 10.3221/igf-esis.48.32 345 conclusions he proposed work aimed at experimentally defining the most suitable  parameter for the mixed-mode crack propagation prediction of three structural adhesives. with this purpose, pure and mixed-mode fracture tests were undertaken that enabled building the fracture envelopes of the three adhesives. brittle crack propagation issues were detected in some specimens bonded with the araldite® av138, due to its brittleness. on the other hand, the araldite® 2015 and sikaforce® 7752 revealed a ductile failure, which, together with the gi/gii and gic/giic values obtained, confirmed their expected ductile behaviour. the r-curves enabled estimating the data points that were on the basis of the built fracture envelopes. the experimental data points revealed a different mixed-mode behaviour, with =0.5 giving a close match for the araldite® av138 and araldite® 2015, while =2 closely represented the sikaforce® 7752. validation of this data was undertaken with slj and dlj. however, a previous experimental data discussion was presented, enabling to realize that the lap-joints’ behaviour is highly dependent on the adhesive type and lo. more particularly, it was found that strong yet brittle adhesive behave well for short lo, while this is not true for large lo. for these geometries, less strong but ductile adhesives take advantage, on view of the ability to endure loads after damage onset takes place. after this analysis, numerical simulations of the slj and dlj were made with different , and pm was compared with experiments. for the araldite® av138 and araldite® 2015, the energetic criterion resulting from the experimental work provided matching numerical results and, thus, the fracture envelopes were validated. for these two adhesives and the chosen , the deviations were mostly under 10%. the sikaforce® 7752 results were slightly offset due to czm law shape issues. in the end, this work made possible, by czm, to estimate the most suitable  parameter to use in crack propagation of adhesive joints under mixed-mode conditions. references [1] da silva, j.f.m.g., öchsner, a., adams, r.d. handbook of adhesion technology. heidelberg: springer; 2011. [2] loureiro, a.l., da silva, l.f.m., sato, c., figueiredo, m.a.v. (2010). comparison of the mechanical behaviour between stiff and flexible adhesive joints for the automotive industry. j adhesion. 86, pp. 765-87. doi: 10.1080/00218464.2010.482440. [3] petrie, e.w. (1999). handbook of adhesives and sealants. 2nd ed ed. new york: mcgraw-hill. [4] adams, r.d. (2005). adhesive bonding: science, technology and applications. cambridge: woodhead publishing limited. [5] kinloch, a.j. (1987). adhesion and adhesives: science and technology. heidelberg: springer. [6] he, x. (2011). a review of finite element analysis of adhesively bonded joints. int j adhes adhes. 31, pp. 248-64. doi: 10.1016/j.ijadhadh.2011.01.006. [7] barenblatt, g.i. (1959). the formation of equilibrium cracks during brittle fracture. general ideas and hypotheses. axially-symmetric cracks. journal of applied mathematics and mechanics. 23, pp. 622-36. doi: 10.1016/0021-8928(59)90157-1. [8] dugdale, d.s. (1960). yielding of steel sheets containing slits. j mech phys solids. 8, pp. 100-4. doi: 10.1016/0022-5096(60)90013-2. [9] jung lee, m., min cho, t., seock kim, w., chai lee, b., ju lee, j. (2010). determination of cohesive parameters for a mixed-mode cohesive zone model. international journal of adhesion and adhesives. 30, pp. 322-8. doi: 10.1016/j.ijadhadh.2009.10.005. [10] andersson, t., stigh, u. (2004). the stress–elongation relation for an adhesive layer loaded in peel using equilibrium of energetic forces. int j solids struct. 41, pp. 413-34. doi: 10.1016/j.ijsolstr.2003.09.039. [11] pandya, k.c., williams, j.g. (2000). measurement of cohesive zone parameters in tough polyethylene. polymer engineering & science. 40, pp. 1765-76. doi: 10.1002/pen.11308. [12] banea, m.d., da silva, l.f.m., campilho, r.d.s.g. (2011). mode i fracture toughness of adhesively bonded joints as a function of temperature: experimental and numerical study. int j adhes adhes.31, pp. 273-9. doi: 10.1016/j.ijadhadh.2010.09.005. [13] bs 7991:2001 standard. determination of the mode i adhesive fracture energy, gic, of structural adhesives using the double cantilever beam (dcb) and tapered double cantilever beam (tdcb) specimens. london, united kingdom: british standards institution; 2001. [14] astm d3433-99 standard. standard test method for fracture strength in cleavage of adhesives in bonded metal joints. west conshohocken, pa: astm international; 2012. t j.p.s.m.b. ribeiro et alii, frattura ed integrità strutturale, 48 (2019) 332-347; doi: 10.3221/igf-esis.48.32 346 [15] iso 25217 standard. adhesives determination of the mode 1 adhesive fracture energy of structural adhesive joints using double cantilever beam and tapered double cantilever beam specimens. geneva, switzerland: international organization for standardization; 2009. [16] sistaninia, m., sistaninia, m. (2015). theoretical and experimental investigations on the mode ii fracture toughness of brittle materials. international journal of mechanical sciences.98, pp. 1-13. doi: 10.1016/j.ijmecsci.2015.04.003 [17] astm, d. (2001). 6671-01, standard test method for mixed mode i–mode ii interlaminar fracture toughness of unidirectional fiber reinforced polymer matrix composites. annual book of astm standards.15, pp. 03. [18] choupani, n. (2008). mixed-mode cohesive fracture of adhesive joints: experimental and numerical studies. engineering fracture mechanics.75, pp. 4363-82. doi: 10.1016/j.engfracmech.2008.04.023. [19] chaves, f.j.p., da silva, l.f.m., de moura, m.f.s.f., dillard, d.a., esteves, v.h.c. (2014). fracture mechanics tests in adhesively bonded joints: a literature review. j adhesion.90, pp. 955-92. doi: 10.1080/00218464.2013.859075. [20] rodrigues, t.a.f., chaves, f.j.p., silva, l.f.m.d., costa, m., barbosa, a.q. (2017). determination of the fracture envelope of an adhesive joint as a function of moisture. materialwissenschaft und werkstofftechnik.48, pp. 1181-90. doi: doi:10.1002/mawe.201700571. [21] costa, m., carbas, r., marques, e., viana, g., da silva, l.f.m. (2017). an apparatus for mixed-mode fracture characterization of adhesive joints. theor appl fract mec.91, pp. 94-102. doi: 10.1016/j.tafmec.2017.04.014. [22] nunes, f.a.a., campilho, r.d.s.g. (2018). mixed-mode fracture analysis of adhesively-bonded joints using the atdcb test specimen. international journal of adhesion and adhesives.85, pp. 58-68. doi: 10.1016/j.ijadhadh.2018.05.019. [23] rocha, r.j.b., campilho, r.d.s.g. (2018). evaluation of different modelling conditions in the cohesive zone analysis of single-lap bonded joints. j adhesion.94, pp. 562-82. doi: 10.1080/00218464.2017.1307107. [24] ribeiro, t.e.a., campilho, r.d.s.g., da silva, l.f.m., goglio, l. (2016). damage analysis of composite–aluminium adhesively-bonded single-lap joints. compos struct. 136, pp. 25-33. doi: 10.1016/j.compstruct.2015.09.054 [25] moreira, r.d.f., campilho, r.d.s.g. (2015). strength improvement of adhesively-bonded scarf repairs in aluminium structures with external reinforcements. engineering structures. 101, pp. 99-110. doi: 10.1016/j.engstruct.2015.07.001. [26] campilho, r.d.s.g., banea, m.d., pinto, a.m.g., da silva, l.f.m., de jesus, a.m.p. (2011). strength prediction of singleand double-lap joints by standard and extended finite element modelling. int j adhes adhes.31, pp. 363-72. doi: 10.1016/j.ijadhadh.2010.09.008 [27] campilho, r.d.s.g., banea, m.d., neto, j.a.b.p., da silva, l.f.m. (2013). modelling adhesive joints with cohesive zone models: effect of the cohesive law shape of the adhesive layer. int j adhes adhes.44, pp. 48-56. doi: 10.1016/j.ijadhadh.2013.02.006. [28] faneco, t., campilho, r., silva, f., lopes, r. (2017). strength and fracture characterization of a novel polyurethane adhesive for the automotive industry. j test eval.45, pp. 398-407. doi: 10.1520/jte20150335. [29] markolefas, s.i., papathanassiou, t.k. (2009). stress redistributions in adhesively bonded double-lap joints, with elastic– perfectly plastic adhesive behavior, subjected to axial lap-shear cyclic loading. int j adhes adhes.29, pp. 737-44. doi: 10.1016/j.ijadhadh.2009.04.001. [30] andré, a., haghani, r., biel, a. (2012). application of fracture mechanics to predict the failure load of adhesive joints used to bond cfrp laminates to steel members. construction and building materials.27, pp. 331-40. doi: 10.1016/j.conbuildmat.2011.07.040. [31] de moura, m.f.s.f., campilho, r.d.s.g., gonçalves, j.p.m. (2009). pure mode ii fracture characterization of composite bonded joints. int j solids struct.46, pp. 1589-95. doi: 10.1016/j.ijsolstr.2008.12.001. [32] constante, c.j., campilho, r.d.s.g., moura, d.c. (2015). tensile fracture characterization of adhesive joints by standard and optical techniques. eng fract mech.136, pp. 292-304. doi: 10.1016/j.engfracmech.2015.02.010. [33] fernández, m.v., de moura, m.f.s.f., da silva, l.f.m., marques, a.t. (2013). mixed-mode i + ii fatigue/fracture characterization of composite bonded joints using the single-leg bending test. composites part a: applied science and manufacturing.44, pp. 63-9. doi: 10.1016/j.compositesa.2012.08.009. [34] szekrényes, a., uj, j. (2004). beam and finite element analysis of quasi-unidirectional composite slb and els specimens. composites science and technology.64, pp. 2393-406. doi: 10.1016/j.compscitech.2004.05.002. j.p.s.m.b. ribeiro et alii, frattura ed integrità strutturale, 48 (2019) 332-347; doi: 10.3221/igf-esis.48.32 347 [35] kafkalidis, m.s., thouless, m.d. (2002). the effects of geometry and material properties on the fracture of single lapshear joints. int j solids struct.39, pp. 4367-83. doi: 10.1016/s0020-7683(02)00344-x. [36] feraren, p., jensen, h.m. (2004). cohesive zone modelling of interface fracture near flaws in adhesive joints. eng fract mech.71, pp. 2125-42. doi: 10.1016/j.engfracmech.2003.12.003. [37] abaqus®. documentation of the software abaqus®. dassault systèmes. vélizy-villacoublay 2013. [38] ameli, a., papini, m., schroeder, j.a., spelt, j.k. (2010). fracture r-curve characterization of toughened epoxy adhesives. eng fract mech.77, pp. 521-34. doi: 10.1016/j.engfracmech.2009.10.009. [39] blackman, b.r.k., kinloch, a.j., rodriguez sanchez, f.s., teo, w.s., williams, j.g. (2009). the fracture behaviour of structural adhesives under high rates of testing. engineering fracture mechanics.76, pp. 2868-89. doi: 10.1016/j.engfracmech.2009.07.013. [40] pardoen, t., ferracin, t., landis, c.m., delannay, f. (2005). constraint effects in adhesive joint fracture. j mech phys solids.53, pp. 1951-83. doi: 10.1016/j.jmps.2005.04.009. [41] nunes, s.l.s., campilho, r.d.s.g., da silva, f.j.g., de sousa, c.c.r.g., fernandes, t.a.b., banea, m.d., et al. (2016). comparative failure assessment of single and double-lap joints with varying adhesive systems. j adhesion.92, pp. 61034. doi: 10.1080/00218464.2015.1103227. [42] adams, r.d., peppiatt, n.a. (1974). stress analysis of adhesive-bonded lap joints. the journal of strain analysis for engineering design.9, pp. 185-96. doi: 10.1243/03093247v093185. << /ascii85encodepages false /allowtransparency false /autopositionepsfiles true /autorotatepages /none /binding /left /calgrayprofile (dot gain 20%) /calrgbprofile (srgb iec61966-2.1) /calcmykprofile (u.s. web coated \050swop\051 v2) /srgbprofile (srgb iec61966-2.1) /cannotembedfontpolicy /error /compatibilitylevel 1.4 /compressobjects /tags /compresspages true /convertimagestoindexed true /passthroughjpegimages true /createjobticket false /defaultrenderingintent /default /detectblends true /detectcurves 0.0000 /colorconversionstrategy /cmyk /dothumbnails false /embedallfonts true /embedopentype false /parseiccprofilesincomments true /embedjoboptions true /dscreportinglevel 0 /emitdscwarnings false /endpage -1 /imagememory 1048576 /lockdistillerparams false /maxsubsetpct 100 /optimize true /opm 1 /parsedsccomments true 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/hrv (za stvaranje adobe pdf dokumenata najpogodnijih za visokokvalitetni ispis prije tiskanja koristite ove postavke. stvoreni pdf dokumenti mogu se otvoriti acrobat i adobe reader 5.0 i kasnijim verzijama.) /hun 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/pdfxoutputintentprofileselector /documentcmyk /preserveediting true /untaggedcmykhandling /leaveuntagged /untaggedrgbhandling /usedocumentprofile /usedocumentbleed false >> ] >> setdistillerparams << /hwresolution [2400 2400] /pagesize [612.000 792.000] >> setpagedevice microsoft word numero 22 articolo 10.doc d. cerniglia et alii, frattura ed integrità strutturale, 22 (2012) 93-101; doi: 10.3221/igf-esis.22.10 93 rilievo in tempo reale di difetti superficiali su corpi in movimento a velocità elevata con ultrasuoni senza contatto real-time non-contact ultrasonic detection of surface defects on objects moving at high speed d. cerniglia, v. nigrelli, a. mancuso, a. alberti dipartimento di ingegneria chimica, gestionale, informatica, meccanica, università degli studi di palermo, viale delle scienze, 90128 palermo, italy vincenzo.nigrelli@unipa.it abstract. the detection of surface defects during periodic inspection is important because, usually, the stresses are higher at the surface, thus affecting the growth of the discontinuity. surface defects can be detected using some traditional non-destructive testing methods, such as eddy current, dye penetrant, magnetic particle and ultrasonic. some of these methods can be used only in static conditions; the others have limitations for the dynamic inspection. the recent progress in the field of non-contact ultrasonic sensors has led us to develop a simple system for the real-time inspection of moving bodies at a high speed. the paper presents the possibility of using, with the developed system, two methodologies, based on non-contact ultrasound, to detect surface defects on objects moving at 100 km/h, so that in service inspection is possible. a methodology, based on laser and air-coupled sensors, uses the advantages of laser-generated surface waves; the analysis is done on the reflected wave, created by the interaction of the surface wave with the defect. the inspected surface layer can be selected from the wavelength of the surface wave. the other methodology, based on air-coupled sensors, uses the disadvantages of the ultrasound transmission at the air/metal interface; the analysis is done on the diffraction of the wave reflected from the surface. the execution of the inspection is simple with both techniques. the experimental results indicate a good efficiency of the two methodologies proposed for the real-time detection of surface defects on objects moving at high speed. sommario. il rilievo di difetti superficiali durante le ispezioni periodiche è importante poiché in genere le sollecitazioni sono maggiori in superficie e possono accelerare la crescita delle discontinuità. i difetti superficiali possono essere rilevati utilizzando alcuni metodi tradizionali di controllo non distruttivo, quali correnti indotte, liquidi penetranti, polveri magnetiche ed ultrasuoni. alcuni tra questi metodi possono essere usati solo in condizioni statiche; gli altri presentano delle limitazioni per l’ispezione dinamica. i progressi recenti nel campo dei sensori ultrasonori senza contatto ci hanno permesso di sviluppare un sistema semplice per l’ispezione in tempo reale di corpi in movimento a velocità elevata. nel lavoro viene presentata la possibilità di usare, col sistema sviluppato, due metodologie, basate sugli ultrasuoni generati e ricevuti senza contatto con la struttura, per rilevare difetti superficiali su corpi in movimento a 100 km/h, così da poter effettuare l’ispezione anche in servizio. una metodologia, basata sull’uso di laser e trasduttori senza contatto, utilizza i vantaggi delle onde superficiali generate con il laser; l’analisi viene fatta sull’onda riflessa, creata dall’interazione dell’onda superficiale con il difetto. lo spessore superficiale ispezionato è selezionabile dalla lunghezza d’onda dell’onda http://dx.medra.org/10.3221/igf-esis.22.10&auth=true http://www.gruppofrattura.it d. cerniglia et alii, frattura ed integrità strutturale, 22 (2012) 93-101; doi: 10.3221/igf-esis.22.10 94 superficiale generata. l’altra metodologia, basata sull’uso di trasduttori senza contatto, sfrutta gli svantaggi della trasmissione degli ultrasuoni all’interfaccia aria/metallo; l’analisi viene fatta sulla diffrazione dell’onda riflessa dalla superficie. l’esecuzione delle ispezioni risulta semplice con entrambe le tecniche. i risultati sperimentali indicano una buona efficienza delle due metodologie proposte per il rilievo, in tempo reale, di difetti superficiali su corpi in movimento ad alta velocità. parole chiave. ultrasuoni; laser; sensori senza contatto; difetti superficiali; ispezione dinamica. introduzione l rilievo di difetti superficiali durante le ispezioni periodiche è importante poiché in genere le sollecitazioni sono maggiori in superficie e possono accelerare la crescita delle discontinuità. i difetti superficiali possono essere rilevati utilizzando alcuni metodi tradizionali di controllo non distruttivo, quali correnti indotte, liquidi penetranti, polveri magnetiche ed ultrasuoni. alcuni tra questi metodi possono essere usati solo in condizioni statiche; gli altri presentano delle limitazioni per l’ispezione dinamica. le tecniche ad ultrasuoni in cui la trasmissione di energia nel materiale avviene tramite contatto, nonostante siano caratterizzate da affidabilità e semplicità, limitano notevolmente la velocità di ispezione su oggetti in movimento ed anche il rilievo di difetti superficiali, poiché i segnali di eco dei primi millimetri di superficie non sono visibili. inoltre, in generale, l’ispezione è influenzata dalle condizioni di contatto quali superficie del pezzo in esame, pressione della sonda, mezzo di accoppiamento ed area di contatto. negli ultimi decenni l’interesse è stato focalizzato verso metodi e sensori non a contatto poiché consentono di superare questi limiti. in particolare, grazie ai progressi su nuovi materiali per dispositivi acustici e su nuove tecnologie di fabbricazione, si è avuto un crescente sviluppo di nuove sonde [1]. con aria come mezzo di accoppiamento, la distanza dei trasduttori dalla superficie dei corpi da ispezionare dipende dalla frequenza utilizzata. inoltre, poiché l’attenuazione delle onde varia con il quadrato della frequenza, si ha un limite alle frequenze rilevabili. è infatti impossibile ricevere onde con alta frequenza (maggiore di 5 mhz) senza portare il trasduttore quasi a contatto con la superficie. un altro limite principale associato all’impiego dei trasduttori senza contatto è la grande differenza di impedenza acustica all’interfaccia aria/metallo. l’onda riflessa dal metallo (per esempio alluminio) è pari al 99.99% dell’energia incidente; mentre quella che arriva al trasduttore, dopo aver attraversato metallo ed aria, è prossima al 10-6%. la combinazione del laser per generare e del sensore senza contatto per ricevere è più efficiente poiché gli ultrasuoni sono prodotti direttamente nel metallo. eliminando una interfaccia aria/alluminio, l’energia che arriva al trasduttore è pari allo 0.01%. la generazione di onde acustiche tramite laser è ormai ben caratterizzata [2-7]. la propagazione di onde generate tramite laser nei metalli, la loro interazione con i difetti e la trasmissione in aria sono state studiate tramite simulazione numerica in [8,9]. l’uso del laser nei sistemi di controllo ad ultrasuoni mostra anche un interesse crescente nel settore industriale poiché consente l'ispezione remota ed automatizzata, realizzabile su corpi in movimento. i progressi recenti nel campo dei sensori ultrasonori senza contatto ci hanno permesso di sviluppare un sistema semplice per l’ispezione in tempo reale di corpi in movimento a velocità elevata. nel lavoro viene presentata la possibilità di usare, col sistema sviluppato, due metodologie per il rilievo di difetti superficiali, in tempo reale, su componenti in movimento alla velocità di 100 km/h. la prima usa i vantaggi delle onde superficiali generate con il laser [10-11] ed analizza l’onda riflessa, creata dall’interazione dell’onda superficiale con il difetto. la seconda sfrutta gli svantaggi della trasmissione degli ultrasuoni all’interfaccia aria/metallo ed analizza la diffrazione dell’onda riflessa dalla superficie. il caso esaminato è quello in cui i sensori sono stazionari e il corpo ruota ad elevata velocità; caso per esempio di una stazione di ispezione per le ruote ferroviarie. questo lavoro è stato motivato da precedenti studi relativi ad onde ultrasonore per l’ispezione dinamica di rotaie e ruote ferroviarie [12-14]. prove e risultati sperimentali er l’esecuzione delle prove sono stati utilizzati due dischi in alluminio con diametro esterno 201.2 mm e spessore 15 mm: uno integro e l’altro con un difetto superficiale passante, largo 0.5 mm e profondo 2 mm. i dischi, calettati sull’albero di un motore elettrico, sono stati messi in rotazione con una velocità angolare pari a 2800 giri/min (velocità periferica pari a 106 km/h). per il rilievo del difetto sono state usate due diverse metodologie. la prima utilizza, i p http://dx.medra.org/10.3221/igf-esis.22.10&auth=true http://www.gruppofrattura.it d. cerniglia et alii, frattura ed integrità strutturale, 22 (2012) 93-101; doi: 10.3221/igf-esis.22.10 95 in un’unica ispezione, onde superficiali che si propagano in direzione circonferenziale; la seconda realizza un’ispezione continua sull’intera circonferenza, lungo la generatrice del disco. il primo setup sperimentale è mostrato in fig. 1. le onde superficiali di rayleigh sono generate tramite un laser pulsato e acquisite tramite due trasduttori piezoelettrici. le onde superficiali si propagano solo nello strato superficiale dei solidi, seguendone il profilo, e penetrano nel materiale per una profondità pari alla lunghezza d’onda, in relazione quindi alla frequenza di ispezione utilizzata [2]. l’ampiezza dello spostamento delle particelle decresce dalla superficie verso l’interno del mezzo. il laser utilizzato opera a 1064 nm con un’energia massima di 900 mj, frequenza 10 hz e durata dell’impulso di 5 nsec. i sensori registrano un segnale proporzionale alla pressione acustica, che è la deviazione locale della pressione rispetto a quella ambiente causata dall’onda ultrasonora. hanno una frequenza nominale di 1.5 mhz, larghezza di banda (a -6 db) 240 khz e diametro 12 mm. la distanza di ciascun trasduttore dalla superficie del disco è 5.5 mm. i sensori hanno una disposizione simmetrica (fig. 1) rispetto al piano su cui è il fascio laser, con 1=2=. si è assunto 140°, definito in maniera arbitraria. il trasduttore 1 è inclinato in modo da favorire la ricezione delle onde che viaggiano in verso orario, mentre il trasduttore 2 (inclinato dello stesso angolo) favorisce la ricezione delle onde antiorarie. il disco viene ispezionato per una profondità di 1.9 mm, pari alla lunghezza d’onda dell’onda superficiale data dal rapporto tra la velocità dell’onda superficiale nell’alluminio (val = 2.9 mm/s) e la frequenza dell’onda (1.5 mhz). in condizioni statiche, in conseguenza alla loro disposizione simmetrica rispetto al punto di origine delle onde ultrasonore, i due trasduttori acquisiscono le stesse forme d’onda sul disco integro (fig. 2). la prima onda (r1) ha il seguente tempo di volo (tof): t     ariaalr1 al aria ss 245.6 5.5 of 101 μs v v 2.9 0.33 dove sal ed saria sono la distanza percorsa nel disco e in aria, varia la velocità dell’onda in aria. la seconda onda (r2), ovvero la prima che si presenta nuovamente al sensore dopo aver percorso tutta la circonferenza del disco, ha tempo di volo pari a: 632 319dt t    r2 r1 al s of of 101 μs v 2.9 dove con sd si è indicata la lunghezza della circonferenza del disco. il tempo necessario affinché l’onda percorra un giro completo della superficie del disco è pari a 218 s. inoltre, nel caso statico, si hanno fenomeni di interferenza delle due onde propaganti in senso opposto, caratterizzate da identici tempi di volo, tali da provocare aumenti dell’ampiezza delle stesse ad ogni mezza rivoluzione (rilevabile con un sensore posto a 180°). figura 1: configurazione per il rilievo di difetti superficiali con onda che si propaga in direzione circonferenziale. figure 1: setup to detect surface defects using the wave propagating along the circumferential direction. http://dx.medra.org/10.3221/igf-esis.22.10&auth=true http://www.gruppofrattura.it d. cerniglia et alii, frattura ed integrità strutturale, 22 (2012) 93-101; doi: 10.3221/igf-esis.22.10 96 figura 2: segnale acquisito dai trasduttori 1 e 2 sul disco integro in condizioni statiche. figure 2: signal acquired by transducers 1 and 2 in the pristine disk in static conditions.. posto in rotazione il disco a 2800 giri/min, secondo verso antiorario in fig. 1, sono stati acquisisti i segnali in condizioni dinamiche. la fig. 3 confronta il segnale acquisito, sul disco integro, in condizione statica (blu) e dinamica (verde). figura 3: confronto tra i segnali acquisiti dal trasduttore 1 e 2 in condizione statica e dinamica. figure 3: comparison between the signals acquired by transducers 1 and 2 in static and dynamic conditions. come si evince dalla fig. 3, in condizione dinamica si rileva un ritardo (anticipo) nei tempi di arrivo delle onde acquisite dal sensore 1 (sensore 2), proporzionale alla distanza percorsa dalle stesse. i tempi di volo misurati per le onde r1 e r2 per il trasduttore 1 valgono stofr 1.1021  e stofr 2.3222  . in condizione dinamica il tempo necessario affinché l’onda ultrasonora oraria percorra tutta la circonferenza del disco è pari a 220.1 s. i valori dei tempi di volo relativi al trasduttore 2 sono stofr 9.971  e stofr 6.3132  . l’onda ultrasonora antioraria percorre la circonferenza del disco in 215.7 s. le misure di tali variazioni concordano con i valori ricavati dalle relazioni analitiche nel caso di onda superficiale che si propaga nello stesso verso di rotazione del disco e in verso opposto. l’interferenza delle due onde propaganti in senso opposto si presenta anche nel caso dinamico, ma non si ha la periodicità prima descritta in conseguenza della variazione dei tempi di volo delle due onde. in conseguenza al moto relativo tra onda superficiale e corpo, si genera inoltre una variazione della frequenza del segnale, noto come effetto doppler. tale effetto è risultato del tutto trascurabile per la velocità considerata. la stessa tipologia di prove è stata eseguita nel disco con difetto. si è prima analizzato il provino in condizione statica, posizionando il difetto in diversi punti ed acquisendo il segnale in arrivo ai due trasduttori. in particolare, indicando con γ l’anomalia del piano contenente il difetto (fig. 1) e definendo positivi gli angoli in verso orario, sono stati acquisiti segnali http://dx.medra.org/10.3221/igf-esis.22.10&auth=true http://www.gruppofrattura.it d. cerniglia et alii, frattura ed integrità strutturale, 22 (2012) 93-101; doi: 10.3221/igf-esis.22.10 97 ponendo il difetto in diverse posizioni corrispondenti a γ = ± 20°, ± 45°, ± 70°, ± 120°, ± 150°, ± 180°. viene riportata solamente una delle configurazioni, con difetto posto a γ= -70°. il segnale acquisito dal trasduttore 1 (fig. 4) contiene quattro onde: la prima è l’onda diretta (r1) che, generata dal fascio laser incidente sul disco, si propaga in verso orario. la seconda è l’onda riflessa (tof=185.7 s) generata dal difetto, ovvero l’onda che, generata dal laser, propaga inizialmente in senso antiorario e poi, in conseguenza alla riflessione in corrispondenza del difetto, prosegue verso il trasduttore propagando in senso orario. le ultime due sono rispettivamente l’onda diretta (r2) e l’onda riflessa che, riuscendo ad oltrepassare il difetto, si ripresentano al trasduttore dopo aver percorso tutta la circonferenza del disco (in ritardo quindi rispetto alle prime di 218 s). queste ultime risultano notevolmente attenuate in conseguenza della trasmissione sul difetto. analoghi risultati si ottengono con riferimento ai segnali acquisiti dal trasduttore 2 (fig. 5). in questo caso le onde chiaramente distinguibili sono quattro e relative, in sequenza d’arrivo, all’onda diretta che propaga in senso antiorario (r1) e riesce ad oltrepassare il difetto; all’onda che dopo aver percorso la superficie del disco in senso orario viene riflessa dal difetto e si propaga in senso antiorario verso il trasduttore (tof=234.6 s). la terza è l’onda diretta (r2) che oltrepassa nuovamente il difetto e si ripresenta in corrispondenza del trasduttore e, infine, l’onda riflessa dal difetto che compie l’intera rivoluzione, passando il difetto (tof = 452.2 s). mediante la valutazione dei tempi di volo dell’onda riflessa è possibile individuare univocamente la posizione del difetto, anche con un’unica ispezione. in presenza di più difetti lungo la circonferenza, il numero delle onde riflesse/trasmesse non permetterebbe più di individuare la posizione del difetto dal tempo di volo. in tal caso, si dovrebbe optare per una finestra temporale più stretta e più acquisizioni lungo la circonferenza. ad ogni modo, per un’ispezione affidabile dovrebbero essere fatte almeno due acquisizioni a 180° una dall’altra, per evitare che particolari posizioni del difetto (per esempio in corrispondenza della sorgente) diano segnali diversi. figura 4: segnale acquisito dal trasduttore 1. disco fermo con difetto in γ=-70°. figure 4: signal acquired by transducer 1. static disk with defect at γ=-70°. figura 5: segnale acquisito dal trasduttore 2. disco fermo con difetto in γ=-70°. figura 5: signal acquired by transducer 2. static disk with defect at γ=-70°. dalle acquisizioni realizzate con il disco in rotazione si sono ottenuti segnali con onde riflesse caratterizzate da tempi di volo diversi. ognuna di queste ha comunque permesso di individuare la presenza del difetto e di risalire alla sua posizione in quell’istante. per effettuare un confronto con l’acquisizione realizzata in condizioni statiche si riportano i segnali relativi alla posizione del difetto a γ=-70°. il calcolo dei tempi di volo delle onde r1 e r2 si esegue allo stesso modo, visto nel caso di disco senza difetto, in quanto esse propagano sempre in un verso. la determinazione dei tempi di volo delle onde riflesse risulta invece più complessa, in quanto la rotazione del disco tende a ritardarne l’arrivo nelle fasi in cui propagano in senso orario e ad anticiparlo nelle fasi in cui propagano in senso antiorario. tenendo conto di tale aspetto si sono misurati i tempi di volo di tutte e quattro le onde, ottenendo una buona corrispondenza con i valori teorici (fig. 6 e 7). la seconda metodologia consiste nell’utilizzare due sensori, uno come emettitore e l’altro come ricevitore, in modalita pitch-catch, ispezionando con continuità la superficie del disco, lungo la generatrice (fig. 8). l’onda analizzata è il fascio ultrasonoro riflesso dalla superficie del disco. http://dx.medra.org/10.3221/igf-esis.22.10&auth=true http://www.gruppofrattura.it d. cerniglia et alii, frattura ed integrità strutturale, 22 (2012) 93-101; doi: 10.3221/igf-esis.22.10 98 i trasduttori sono di tipo capacitivo con frequenze emesse e rilevate nel range 0.1  2.25 mhz [15, 16]. entrambi i trasduttori sono stati disposti con assi giacenti su uno stesso piano, parallelo al piano orizzontale, ed inclinati simmetricamente rispetto al piano τ (normale all’asse del disco e passante per la mezzeria dello spessore) con angolo =45°, come mostrato schematicamente in fig. 8. il piano contenente gli assi dei trasduttori è stato inclinato di un angolo 45°, rispetto alla normale alla superficie del provino. figura 6: segnale acquisito dal trasduttore 1. disco rotante con difetto in γ=-70°. figure 6: signal acquired by transducer 1. rotating disk with defect at γ=-70°. figura 7: segnale acquisito dal trasduttore 2. disco rotante con difetto in γ=-70°. figure 7: signal acquired by transducer 2. rotating disk with defect at γ=-70°. figura 8: configurazione per il rilievo di difetti superficiali con ispezione continua lungo la circonferenza del disco. figure 8: setup to detect surface defects with continuous inspection along the circumference of the disc. per eseguire l’ispezione con continuità lungo la circonferenza del disco bisogna scegliere un generatore con frequenza di ripetizione opportuna; se la frequenza è minore si ha probabilità di non rilevare il difetto posto tra due impulsi consecutivi. a tal fine è necessario considerare la velocità di rotazione del disco, il diametro del disco e le dimensioni dell’area attiva dei trasduttori. nel caso in esame la velocità periferica del disco è pari a 0.0294 mm/s e la lunghezza della circonferenza del disco è pari a sd=632 mm. il tempo necessario affinché (in una rivoluzione del disco) il difetto si riporti nello stesso punto è quindi pari a 0.0215 s. avendo i trasduttori un’area sensibile con diametro di 10 mm, per avere la certezza di ispezionare tutta la superficie del disco, è necessario avere un numero di impulsi n pari a 63.2. per essere in grado di individuare il difetto in una rivoluzione del disco, è necessario avere n impulsi ogni 0.0215 secondi, ovvero 2939 impulsi al secondo. il trasduttore emettitore è stato collegato ad un generatore con massimo valore della frequenza di ripetizione di 2 khz. con tale strumentazione si ha quindi una probabilità pari al 68% di individuare il difetto in una rivoluzione del disco. http://dx.medra.org/10.3221/igf-esis.22.10&auth=true http://www.gruppofrattura.it d. cerniglia et alii, frattura ed integrità strutturale, 22 (2012) 93-101; doi: 10.3221/igf-esis.22.10 99 si sono quindi acquisiti i segnali sul disco in condizione statica in due distinte configurazioni: fascio ultrasonoro diretto su una porzione integra della superficie del disco e poi sul tratto di disco nel quale è presente il difetto. si riportano in fig. 9 e 10 i segnali ottenuti e le rispettive trasformate di fourier. figura 9. segnale acquisito con disco fermo in assenza di difetto e relativa trasformata di fourier. figure 9. signal acquired on the static disk, without defect, and its fourier transform. figura 10: segnale acquisito con disco fermo in presenza del difetto e relativa trasformata di fourier. figure 10: signal acquired on the static disk, with defect, and its fourier transform. nel caso in cui il difetto si trova nella regione ispezionata dai trasduttori si ha una variazione della forma del segnale acquisito per la presenza delle onde diffratte ed una variazione del suo contenuto in frequenza. la nascita di onde diffratte, dovute alla discontinuità superficiale, produce infatti un aumento dell’ampiezza dei picchi nei campi di frequenza pari a 150200 khz e 250300 khz. caratterizzato il provino in condizioni statiche, si sono acquisiti i segnali con il disco in rotazione. si riportano in fig. 11 e 12 i segnali acquisiti e le rispettive trasformate di fourier rispettivamente per le acquisizioni in cui il fascio ultrasonoro ha inciso sul disco in rotazione in tratti di superficie integra e in corrispondenza del difetto. dal confronto con le acquisizioni relative al caso statico, nell’istante in cui il difetto si viene trovare in corrispondenza dei trasduttori si osserva una variazione del segnale nel dominio del tempo ed in quello della frequenza. per il monitoraggio continuo, il criterio da utilizzare per discriminare in tempo reale i segnali acquisiti dalle aree integre da quelle con discontinuità è stabilire delle soglie per le ampiezze delle componenti di frequenza a 150200 khz e 250300 khz (ad esempio, rispettivamente, 0.6 v e 0.4 v per il caso in esame). l’informazione sulla posizione del difetto può essere fornita da un sensore angolare. poiché l’indicazione di difetto viene data da onde che sono riflesse da discontinuità superficiale, allora elevata rugosità superficiale o scalfiture pronunciate possono influenzare il segnale. pertanto le soglie dei picchi di frequenza devono essere calibrate sul difetto di interesse. studi sistematici dovrebbero essere eseguiti per una valutazione quantitativa. http://dx.medra.org/10.3221/igf-esis.22.10&auth=true http://www.gruppofrattura.it d. cerniglia et alii, frattura ed integrità strutturale, 22 (2012) 93-101; doi: 10.3221/igf-esis.22.10 100 figura 11: segnale acquisito con disco rotante in assenza di difetto e relativa trasformata di fourier. figure 11: signal acquired on the rotating disk, without defect, and its fourier transform. figura 12: segnale acquisito con disco rotante in presenza del difetto e relativa trasformata di fourier. figure 12: signal acquired on the rotating disk, with defect, and its fourier transform. conclusione l rilievo di difetti superficiali durante le ispezioni periodiche è importante poiché in genere le sollecitazioni sono maggiori in superficie e possono accelerare la crescita delle discontinuità. i metodi tradizionali di controllo non distruttivo, utilizzabili per i difetti superficiali, sono le correnti indotte, i liquidi penetranti, le polveri magnetiche e gli ultrasuoni. alcuni tra questi metodi possono essere usati solo in condizioni statiche; gli altri presentano delle limitazioni per l’ispezione dinamica. i progressi recenti nel campo dei sensori ultrasonori senza contatto ci hanno permesso di sviluppare un sistema semplice per il rilievo in tempo reale di difetti superficiali in corpi in movimento ad elevata velocità. nel lavoro sono state presentate due metodologie di rilievo impiegabili col sistema sviluppato. entrambe utilizzano onde ultrasonore, generate e rilevate con sonde senza contatto con la struttura. in una si sono utilizzati un laser pulsato e due trasduttori piezoelettrici, per generare ed analizzare l’onda superficiale che si propaga lungo la circonferenza, con una singola acquisizione. l’altra metodologia, sfruttando gli svantaggi della trasmissione degli ultrasuoni all’interfaccia aria/metallo, utilizza una coppia di trasduttori in modalità pitch-catch con ispezione continua lungo la circonferenza, valutando il fascio riflesso dalla superficie del disco. le metodologie sono state provate in laboratorio su due dischi in rotazione, di cui uno con difetto superficiale; entrambe si sono mostrate efficaci nell’individuazione del difetto in condizioni dinamiche, alla velocità di 100 km/h, con ottima ripetibilità dei risultati. l’esecuzione delle ispezioni risulta semplice con entrambe le tecniche. la preferenza di una all’altra è esclusivamente legata alla specifica applicazione. in un caso, il corpo viene ispezionato per una profondità pari alla lunghezza d’onda dell’onda superficiale generata; nell’altro l’ispezione è solo superficiale. entrambe le metodologie i http://dx.medra.org/10.3221/igf-esis.22.10&auth=true http://www.gruppofrattura.it d. cerniglia et alii, frattura ed integrità strutturale, 22 (2012) 93-101; doi: 10.3221/igf-esis.22.10 101 permettono di rilevare in tempo reale e localizzare accuratamente la posizione del difetto. con la configurazione sensore/sensore, per effettuare la scansione di tutta la superficie è necessario che la coppia di sensori si porti in corrispondenza di ogni suo punto, con ovvio aumento dei tempi d’ispezione rispetto alla configurazione laser/sensore. tuttavia, la configurazione sensore/sensore permette di segnalare distintamente discontinuità multiple; tale attività diviene più complessa con l’altra configurazione. bibliografia [1] m. c. bhardwaj, non-contact ultrasound: the last frontier in non-destructive testing and evaluation, encyclopedia of smart materials, john wiley & sons, new york, (2001). [2] c.b. scruby, l.e. drain, laser ultrasonics: techniques and applications, adam hilger (1990). [3] d.a. hutchins, c.b. scruby, r.j. dewhurst, s.b. palmer, j. acoust. soc. am., 70(5) (1981) 1362. [4] l.f. bresse, d.a. hutchins, j. appl. phys., 65(4) (1989) 1441. [5] d. cerniglia, a. pantano, c. mineo, appl. phys. a, mater. sci. process., 105 (2011) 959. [6] m. arone, d. cerniglia, v. nigrelli, j. mater. process. technol., 176 (2006) 95. [7] d. cerniglia, n. montinaro, v. nigrelli, j. adhesion, 84 (2008) 811. [8] a. pantano, d. cerniglia. appl. phys. a, mater. sci. process., 91 (2008) 521. [9] a. pantano, d. cerniglia. appl. phys. a, mater. sci. process., 98 (2010) 327. [10] i. a. viktorov, rayleigh and lamb waves: physical theory and applications (plenum press, new york, 1967). [11] d. clorennec, d. royer. appl. phys. lett., 82 (2003) 4608. [12] s. kenderian, b.b. djordjevic, d.cerniglia, g. garcia. insight 48, (2006) 336. [13] d. cerniglia, a. pantano, m.a. vento. j. nondestruct. eval., 31(3), (2012) 245. [14] s. kenderian, d. cerniglia, b.b. djordjevic, g. garcia, j. sun, m. snell, materials evaluation, 61 (10) (2003) 1129. [15] d.w. schindel. ultrasonics, 35 (1997) 179. [16] w.m.d. wright, d.w.schindel, d.a. hutchins. j. acoust. soc. am., 95 (1994) 2567. http://dx.medra.org/10.3221/igf-esis.22.10&auth=true http://www.gruppofrattura.it microsoft word numero_50_art_2_2528 m.f. borges et al., frattura ed integrità strutturale, 50 (2019) 9-19; doi: 10.3221/igf-esis.50.02 9 focused on crack tip fields effect of yield stress on fatigue crack growth m.f. borges, f.v. antunes, p. prates, r. branco, m.c. oliveira university of coimbra, portugal micaelfriasborges@outlook.pt fernando.ventura@dem.uc.pt, http://orcid.org/0000-0002-0336-4729 pedro.prates@dem.uc.pt, ricardo.branco@dem.uc.pt, marta.oliveira@dem.uc.pt abstract. fatigue crack growth (fcg) depends on loading, geometry and also material properties. since fcg is supposedly linked to crack tip plastic deformation, material’s yield stress, y0, is an important parameter. the main objective here is to develop a parametric study focused on the effect of y0 on fcg. the study is based on the plastic ctod, p, determined numerically using the finite element method. the increase of y0 was found to decrease p, and therefore fcg rate. the variation is non-linear, being more important for lower values of y0. the effect of y0 was found to be much more relevant for the 7050 aluminium alloy than for the 304l stainless steel, which indicated a major influence of isotropic saturation stress. with the inclusion of crack closure, the reduction of p is kept, but there is a substantial reduction of p and therefore of fcg rate. keywords. fatigue crack growth; plastic ctod; yield stress; crack closure. citation: borges, m.f., antunes, f.v., prates, p., branco, r., oliveira, m.c., effect of yield stress on fatigue crack growth, frattura ed integrità strutturale, 50 (2019) 919. received: 24.05.2019 accepted: 01.07.2019 published: 01.10.2019 copyright: © 2019 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. introduction atigue crack growth (fcg) greatly depends on material parameters, however most of the studies are related to loading and geometrical parameters. studies based on material parameters are less common in literature due to the difficulty of implementing parametric experimental tests because the parameters cannot be changed one by one. also, the numerical tools available are typically devoted to studying the effect of loading parameters. this article is centered on the study of the effect of yield stress on fcg, using a numerical approach. since fcg is related to non-linear and irreversible phenomena acting at the crack tip, it makes sense that the yield stress is an important parameter. the methodology proposed by antunes et al., based on plastic ctod, was used to develop this parametric study 1. this approach is based on the assumption that fcg is linked to crack tip plastic deformation, and that the plastic ctod quantifies this deformation. the plastic ctod includes crack closure in a natural way and excludes the elastic deformation, which is not expected to contribute to fcg. f http://www.gruppofrattura.it/va/50/2528.mp4 m.f. borges et al., frattura ed integrità strutturale, 50 (2019) 9-19; doi: 10.3221/igf-esis.50.02 10 numerical model o study the effect of the yield stress on fcg, two materials were considered: the 7050-t6 aluminium alloy (aa) and the 304l stainless steel (ss). to avoid the influence of geometry and loading, the same ct specimen (see fig. 1) and loading conditions were used. the specimen had a width, w, of 50 mm, an initial crack length, a0, of 24 mm, therefore a0/w is 0.48. to reduce numerical effort and since the specimen in question is symmetric relatively to two planes, only ¼ of the specimen was considered. also to reduce the numerical effort, only a 0.1 mm of the thickness of the specimen was modelled. adequate boundary conditions were implemented to reproduce the symmetry of the specimen and state of stress. fig. 1b shows a lateral view of the specimen with symmetry conditions for plane stress state. for plane strain state an additional out of plane condition was implemented to avoid deformation along the thickness direction. the load was applied at the hole of the specimen and varied between 4.167 n and 41.67 n, therefore the load ratio was r=0.1 and kmax, kmin and k were 18.3; 1.83 and 16.5 mpa.m0.5, respectively. material hooke´s law voce law armstrong-frederick law e ν y0 ysat cy cx xsat [gpa] [-] [mpa] [mpa] [-] [-] [mpa] aa7050-t6 reference 420.50 420.50 0.50y0 210.25 210.25 0.75y0 71.70 0.33 315.38 315.38 0 228.91 198.35 1.25y0 525.63 525.63 1.50y0 630.75 630.75 ss304l reference 117 0.50y0 58.50 0.75y0 196 0.30 87.75 204 9 300 176 1.25y0 146.25 1.50y0 175.50 table 1: material parameters used in the analysis of the effect of the yield stress on fatigue crack growth. the mechanical behavior of the materials was assumed to be elastic-plastic. the isotropic elastic domain was defined by the generalized hooke’s law elastic parameters young’s modulus (e) and poisson’s ratio (ν). the plastic behavior was described by von mises yield criterion coupled with a mixed hardening model using voce isotropic and armstrongfrederick kinematic hardening laws, under an associated flow rule. voce isotropic hardening law is given by:      p p0 sat 0 yy ε =y + y -y [1-exp -c ε ] where y0, ysat, and cy are the material parameters of voce law and pε is the equivalent plastic strain. the armstrongfrederick kinematic hardening law can be written:   psat x x =c -x -x ε σ       x σ  t m.f. borges et al., frattura ed integrità strutturale, 50 (2019) 9-19; doi: 10.3221/igf-esis.50.02 11 where cx and xsat are the material parameters, σ is the equivalent stress and pε is the equivalent plastic strain rate. tab. 1 shows the values of reference of the elastic-plastic properties discussed before and the variations made in the yield stress. the material constants for the 7050-t6 aluminium alloy and for the 304l stainless steel were obtained in previous works of the authors 2,3. variations of +50%, +25%, -25% and -50% were considered relatively to the references values. the aa7050-t6 has a pure kinematic behavior, therefore the variation of y0 was accomplished by the variation of the saturation value (ysat). on the oher hand, for the 304l stainless steel only y0 was changed, since the saturation value is always above y0. the finite element mesh, illustrated in fig. 1a, comprised 7287 3d linear isoparametric elements and 14918 nodes. at the crack tip, the mesh was refined with square elements that had 8 8 μm2 to simulate strain gradients and local stress. a coarser mesh was used in the remaining volume of the body to reduce computational overhead. along the thickness, only one layer of elements was used. crack propagation was simulated by successive debonding at minimum load of both current crack front nodes. two load cycles were applied between each crack increment corresponding to one finite element. a total number of 320 load cycles were performed, corresponding to a crack advance of 320 δa= -1 ×8=1272 μm 2       , since in the first block there was no crack propagation. to eliminate crack closure phenomenon, in some numerical simulations the contact of crack flanks was removed. this permits the study of the effect of y0 without the interference of crack closure phenomenon. the three-dimensional finite element software used to implement the numerical model was the dd3imp in-house code, originally developed to simulate sheet metal forming processes [4-6]. this software takes into account large elastic-plastic deformations and rotations and assumes that the elastic strains are negligibly small with respect to unity. to simulate friction contact, the software uses the augmented lagrangian method. the nonlinear system obtained is solved with the newton-raphson method. the contact of the crack flanks is modeled considering a rigid body (plane surface) aligned with the crack symmetry plane. figure 1: model of the c(t) specimen. (a) load and boundary conditions. (b) boundary conditions for plane stress state. (c) boundary conditions for plane strain state. (d) and (e) details of finite element mesh. z y f a0=24 mm (a) (b) (c) (d) w=50 mm m.f. borges et al., frattura ed integrità strutturale, 50 (2019) 9-19; doi: 10.3221/igf-esis.50.02 12 1 2 3 4 5 6 0 0.2 0.4 0.6 0.8 1 1.2 0 10 20 30 40 50 c t o d  [ μ m ] f [n] 1 3 4 5 3p 4p 5p ‐0.6 ‐0.3 0 0.3 0.6 0.9 1.2 1.5 0 10 20 30 40 50 c t o d  [ μ m ] f [n] results typical ctod curves ig. 2a plots a typical curve of ctod versus the force applied on the specimen made of aa7050-t6 in a numerical simulation with contact at the crack flanks. it is noteworthy that the measuring of ctod was performed at the first node behind the tip because it is the node that better illustrates the behavior at the tip. this curve was obtained after a crack growth of 1.272 mm, corresponding to 159 crack increments of 8 m each. the simulation starts at point 1, and between stretch 1-2 the ctod is equal to zero, although the continuous increase of applied load, which means that the crack is closed during this range of load. at point 2, the crack opens and exhibits an elastic behavior between points 2 and 3. in this stretch, ctod increases linearly with the load and only occurs elastic deformation at the tip. point 3 is defined as the transition of elastic-plastic behavior. in this paper, the transition was assumed to occur for a plastic ctod equal to 0.001 μm. when the tip enters the plastic regime, the linear increase of ctod is no longer observed. point 4, is the point where the load reaches its maximum value and also corresponds to the point where the displacement at the tip is maximum. after point 4, the discharge begins and the linear behavior characteristic of elastic deformation is again observed, until point 5, with a slope identical to the one previously verified. between stretch 5 and 6, occurs reversed plastic deformation and at point 6 ctod reaches zero, which means that the crack closes. the total range of elastic and plastic deformation are marked as δe and δp, respectively. figure 2: (a) ctod versus load with contact; (b) ctod and plastic ctod versus load without contact (aa7050-t6; plane stress; a=1.272 mm). a ctod versus force curve in a simulation without contact at the crack flanks is illustrated at fig. 2b. simulations with no contact at the crack flanks are not physically possible but can be processed in numerical studies. the artificial removal of the contact is particularly interesting because it isolates the results from the effect of crack closure. the points represented in this curve, are identical to the ones with contact. the simulation starts at point 1 and the crack opens at this minimum load, therefore comparing with the previous figure, points 1 and 2 are coincident. at point 3, the tip enters the elastic-plastic regime and crack opens progressively until point 4 where the maximum load is reached. in stretch 4-1, begins the discharge with elastic deformation happening first, followed by plastic deformation. the separation of regimes occurs at point 5. fig. 2b also plots the plastic ctod versus load. as can be seen, before the transition point, 3p, there is no plastic deformation. after that, occurs a quick increase of the plastic deformation with the increase of applied load, reaching the maximum value at 4p. the rate of variation of plastic deformation increases up to the maximum load, which means that deformation is progressively easier. between 4p and 5p, the plastic deformation remains constant as the load applied decreases, because as already mentioned, in this stretch only elastic deformation occurs. f (a) (b) δp node 1 ctod δe δp m.f. borges et al., frattura ed integrità strutturale, 50 (2019) 9-19; doi: 10.3221/igf-esis.50.02 13 effect of y0 without contact of crack flanks the contact between crack flanks can be avoided numerically, which is very interesting because it eliminates the crack closure phenomenon, as already mentioned. therefore, the effect of material’s yield stress can be studied singly. variations of the yield stress (cases “0.75y0”, “ref” and “1.25y0”, in fig. 3) were made to compare different curves of ctod and plastic ctod versus load in simulations without contact. the curves are shown in fig. 3 (a) and (b). from fig. 3(a), as can be seen, the curves start apart and tend to approach for higher loads. the slope in the elastic regime is almost the same for the three situations. this is logical since this regime is greatly dependent on young’s modulus, which is not changed. an increase of the yield stress causes the material to enter the plastic regime for higher values of load and less plastic ctod range is achieved, as it is shown in fig. 3(b). in other words, as expected, the elastic regime (i.e., the region between points 2 and 3 in fig. 2) extends with the increase of material’s yield stress. it was also found that these curves were almost overlapped for ss304l. figure 3: (a) ctod versus load; (b) plastic ctod versus load (aa7050-t6; plane stress; no contact). fig. 4a presents the variation of plastic ctod range, p, with yield stress, y0. p is intimately related with fcg, as was studied in previous works of the authors 2,3. in this picture, points located at 0% means that the yield stress assumes the reference value. the other four points correspond to more and less 25% and 50% of the elastic limit, as indicated in tab. 1. it is observed a decrease of plastic ctod with the increase of the yield stress, as could be expected. looking to the results of the aa7050, it is possible to see that the variation is non-linear, being more important at lower values of y0. the decrease is more significant for aa7050-t6 than for the ss304l, and for this case is quite small. this indicates that the influence of y0 greatly depends on other material properties. looking to tab. 1, it is possible to see that the ss304 has a constant value of saturation stress, ysat, therefore this parameter is probably more relevant than y0. the analysis of the range of elastic deformation, e, showed that this does not change significantly. this could be expected since this deformation greatly depends on young’s modulus, which was kept constant. fig. 5a shows stress-strain curves for a gauss point located at a distance of 1.184 mm from the initial crack tip position. the location of the gauss point and the successive positions of the tip are schematically shown at fig. 5b. since the elements have dimensions 8 8 μm2, 148 crack increments were performed. as it is shown, the effect of the variation on the yield stress can be seen since the first cycle, where for a fixed value of plastic deformation, the increase of the elastic limit causes an increase of the stress required to achieve that value of deformation. the plastic deformation in the first cycle also indicates that the gauss point is inside the first monotonic plastic zone. as the crack propagation occurs, the range of stresses increases, causing more deformation. compressive stresses increase in magnitude, beginning to produce inverse deformation. the largest values of stress happen when the gauss point is immediately ahead of the crack tip. the two load cycles applied between crack increments are now clearly visible. larger values of plastic deformation are achieved for the reference curve which has a lower yield stress, as was expected. ‐0.6 ‐0.1 0.4 0.9 1.4 0 10 20 30 40 50 c t o d [μ m ] f [n] 1.25y0 0.75y0 ref 0 0.1 0.2 0.3 0.4 0.5 0 10 20 30 40 50 c t o d p   [μ m ] f [n] 1.25y0 0.75y0 ref (a) (b) m.f. borges et al., frattura ed integrità strutturale, 50 (2019) 9-19; doi: 10.3221/igf-esis.50.02 14 figure 4: (a)plastic ctod range, δp, versus the variation of the yield stress relative to the reference value in percentage, (plane stress; no contact). figure 5: (a) stress-strain curves for the reference value of the yield stress and 1.25 times that value (b) schematic representation of gauss point, at a distance of 1.184 mm ahead of the initial crack tip position, and crack growth (ss304l; plane stress; no contact). figs. 6a and 6b plot load above onset of plastic deformation versus ctodp for ss304l and aa7050, respectively, in plane stress conditions. the objective is to study the material hardening at the crack tip, as a function of the yield stress. further increases in load are required to increase the plastic ctod. also, the rate of variation of plastic ctod increases with the decrease of the yield stress. the curves are nearly coincident for lower values of applied load in ss304l, which 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 ‐60 ‐40 ‐20 0 20 40 60 δ p [μ m ] variation of yield stress [%] aa7050‐t6 ss304l -1000 -800 -600 -400 -200 0 200 400 600 800 1000 0 0.005 0.01 0.015 0.02 0.025 σ y y [m p a ] εyy [-] y025 ref gp 1 148 (a) (b) (a) m.f. borges et al., frattura ed integrità strutturale, 50 (2019) 9-19; doi: 10.3221/igf-esis.50.02 15 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0 10 20 30 40 50 c t o d [μ m ] f [n] ref 0.75y0 1.25y0 0 5 10 15 20 25 30 35 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 f  [ n ] ctodp [μm] 1.50y0 1.25y0 ref 0.75y0 0.50y0 0 5 10 15 20 25 30 35 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 f  [ n ] ctodp [μm] 1.50y0 1.25y0 ref 0.75y0 0.50y0 0 0.05 0.1 0.15 0.2 0.25 0.3 0 5 10 15 20 25 30 35 40 45 c t o d p   [ μ m ] f [n] ref 0.75y0 1.25y0 means that in these conditions, for a fixed value of the load, a variation in the yield stress practically does not change the plastic ctod. this is according the results of fig. 4. the separation of the curves is more prominent for the aa7050 and this effect begins to be seen in lower values of applied loads. figure 6: load versus plastic ctod. (a) ss304l; plane stress; (b) aa7050-t6; plane stress (without contact). figure 7: (a) ctod versus load; (b) plastic ctod versus load (aa7050-t6; plane stress; contact) effect of crack closure three curves of ctod versus applied load were plotted in a graph shown in fig. 7a. each curve corresponds to one value of initial yield stress which took the following values: 87.75 mpa, 117 mpa, and 146.25 mpa. as can be seen, the increase of yield stress for a constant load range causes a reduction of the ctod, and higher crack opening and closure levels. the curves are almost overlapped for small values of the applied load. the separation of the curves occurs for relatively high values of load, when plastic deformation is notable, as shown in fig. 7b, that illustrates the plastic ctod versus the applied load, for the same cases of the previous figure. it seems to exist more discrepancy of the curves during (a) (b) (a) (b) m.f. borges et al., frattura ed integrità strutturale, 50 (2019) 9-19; doi: 10.3221/igf-esis.50.02 16 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 ‐60 ‐40 ‐20 0 20 40 60 δ p [μ m ] variation of yield stress [%] aa7050‐t6 aa7050‐t6; no contact 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 ‐60 ‐40 ‐20 0 20 40 60 δ p [μ m ] variation of yield stress [%] ss304l ss304l; no contact unloading. higher values of yield stress imply larger elastic regime at the crack tip, which causes the tip to enter plastic deformation for higher loads. fig. 8 plots uclos versus the variation of the yield stress in percentage for the cases with contact between crack flanks. uclos=(fopen-fmin)/(fmax-fmin) is the portion of the load cycle during which the crack is closed. the yield stress has a great influence on the level of crack closure for the aa7050-t6. increasing the elastic limit from -50% to 50% causes a 30% decrease in crack closure level. on the other hand, for the ss304l, an increase of the elastic limit from -50% to 50% causes an increase of 10% in crack closure level. therefore, the crack closure level seems to be also more affected by ysat than by y0. figure 8: crack closure versus the variation of the yield stress relative to the reference value in percentage (ss304l; plane stress and aa7050-t6; plane stress) figure 9: plastic ctod range, δp, versus the variation of the yield stress relative to the reference value in percentage (plane stress) (a) aa7050-t6; (b) ss304l. fig. 9 plots p versus yield stress, without and with contact of crack flanks, in order to understand the effect of crack closure phenomenon. the first aspect is that crack closure has a great influence on p, and therefore on fcg rate. for the 0 10 20 30 40 50 ‐60 ‐40 ‐20 0 20 40 60 u cl o su re  [ % ] variation of yield stress [%] ss304l aa7050‐t6 (a) (b) m.f. borges et al., frattura ed integrità strutturale, 50 (2019) 9-19; doi: 10.3221/igf-esis.50.02 17 0 5 10 15 20 25 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 f  [ n ] ctodp [μm] 1.50y0 1.25y0 ref 0.75y0 0.50y0 0 5 10 15 20 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 f  [ n ] ctodp [μm] 1.50y0 1.25y0 ref 0.75y0 0.50y0 aa7050-t6 the decrease of p is much more evident for relatively low values of y0. this is according fig. 8, which shows higher values of crack closure level for lower values of y0. at relatively high values of y0, uclos10%, i.e., is relatively small, therefore there is a minor effect on p. for the 304l stainless steel, the opposite trend is observed, i.e., the increase of y0 increases the influence of crack closure, which is also according fig. 8. figure 10: load versus plastic ctod. (a) 304l; plane stress contact; (b) aa7050-t6; plane stress with contact. figs. 10a and 10b plot load versus ctodp for ss304l and aa7050, respectively, in plane stress conditions. the objective is to study the material hardening at the crack tip, as a function of the yield stress. further increases in load are required to maintain the increase in plastic ctod. also, the rate of variation of plastic ctod increases with the decrease of the yield stress. the curves are nearly coincident for lower values of applied load in ss304l, which means that in these conditions, for a fixed value of the load, a variation in the yield stress practically does not change the plastic ctod. the separation of the curves is more evident for the aa7050 and this effect begins to be seen in lower values of applied loads. sensitivity analysis a sensitivity analysis was developed (see fig. 11) to quantify the relative importance of the different material parameters. local sensitivity analysis aims at estimating the influence of the input parameters on the output quantities in one particular point of the input parameter space 7. the non-dimensional sensitivity of p relatively to the different material parameters is expressed as follows: p p p p m f m       where ∇f is the sensitivity coefficient and mp represents the material parameter. this analysis was made for the 304l stainless steel in a simulation with no contact of crack flanks. from the analysis of the figure, it can be concluded that the yield stress of the material has a relatively low influence on plastic ctod. the isotropic saturation stress (ysat) has a higher influence, similar to the influence of kinematic saturation stress (xsat). on the other hand, even though, the young´s modulus is an elastic parameter it has a relatively high influence on plastic ctod. (a) (b) m.f. borges et al., frattura ed integrità strutturale, 50 (2019) 9-19; doi: 10.3221/igf-esis.50.02 18 figure 11: sensitivity of the plastic ctod range for young´s modulus, kinematic hardening parameters and yield stress (ss304l; plane stress; no contact), calculated at the reference point (see tab. 1). conclusions numerical study was developed to quantify the effect material’s yield stress on plastic ctod and therefore on fatigue crack growth rate. two base materials were studied: the 7050-t6 aluminium alloy and the 304l stainless steel. the increase of y0 was found to decrease p, and therefore fcg rate. the variation is non-linear, being more important for lower values of y0. the effect of y0 was found to be much more relevant for the 7050 aluminium alloy than for the 304l stainless steel, which indicates a major influence of other material properties, namely the saturation stress. with the inclusion of crack closure, the reduction of p with y0 was kept, but there is a substantial reduction of p and therefore of fcg rate. acknowledgements his work was financially supported by: project ptdc/ctm-ctm/29101/2017 – poci-01-0145-feder-029101 funded by feder funds through compete2020 programa operacional competitividade e internacionalização (poci) and by national funds (piddac) through fct/mctes. references [1] antunes, f.v., branco, r. prates, p.a. and borrego, l. (2017) fatigue crack growth modelling based on ctod for the 7050-t6 alloy, fatigue fract engng mater struct, 40, pp. 1309-1320. [2] antunes, f.v., ferreira, m.s.c., branco, r., prates, p., gardin, c. and sarrazin-baudoux, c. (2019). fatigue crack growth versus plastic ctod in the 304l stainless steel, engineering fracture mechanics, 214, pp. 487–503. [3] antunes, f.v., branco, r., prates, p.a. and borrego, l. (2017). fatigue crack growth modelling based on ctod for the 7050-t6 alloy, fatigue fract engng mater struct, 40, pp. 1309-1320. [4] menezes, l.f. and teodosiu, c. (2000). three-dimensional numerical simulation of the deep-drawing process using solid finite elements, j mater process technol., 97(1-3), pp. 100-106. a t 0.0 0.5 1.0 1.5 2.0 2.5 3.0 ∇ f e xsat cx ysat cy y0 m.f. borges et al., frattura ed integrità strutturale, 50 (2019) 9-19; doi: 10.3221/igf-esis.50.02 19 [5] oliveira, c., alves, j.l. and menezes, lf. (2008). algorithms and strategies for treatment of large deformation frictional contact in the numerical simulation of deep drawing process, archiv comput methods eng., 15(2), pp. 113162. [6] neto, d.m., oliveira, m.c., menezes, l.f., alves, j.l. (2014) applying nagata patches to smooth discretized surfaces used in 3d frictional contact problems, comput methods appl mech eng., 271, pp. 296-320. [7] tortorelli, d. and michaleris, p. 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can be opened with acrobat and adobe reader 5.0 and later.) >> /namespace [ (adobe) (common) (1.0) ] /othernamespaces [ << /asreaderspreads false /cropimagestoframes true /errorcontrol /warnandcontinue /flattenerignorespreadoverrides false /includeguidesgrids false /includenonprinting false /includeslug false /namespace [ (adobe) (indesign) (4.0) ] /omitplacedbitmaps false /omitplacedeps false /omitplacedpdf false /simulateoverprint /legacy >> << /addbleedmarks false /addcolorbars false /addcropmarks false /addpageinfo false /addregmarks false /convertcolors /converttocmyk /destinationprofilename () /destinationprofileselector /documentcmyk /downsample16bitimages true /flattenerpreset << /presetselector /mediumresolution >> /formelements false /generatestructure false /includebookmarks false /includehyperlinks false /includeinteractive false /includelayers false /includeprofiles false /multimediahandling /useobjectsettings /namespace [ (adobe) (creativesuite) (2.0) ] /pdfxoutputintentprofileselector /documentcmyk /preserveediting true /untaggedcmykhandling /leaveuntagged /untaggedrgbhandling /usedocumentprofile /usedocumentbleed false >> ] >> setdistillerparams << /hwresolution [2400 2400] /pagesize [612.000 792.000] >> setpagedevice microsoft word numero_41_art_59.docx f. berto, frattura ed integrità strutturale, 41 (2017) 475-483; doi: 10.3221/igf-esis.41.59 475 cracked components under anti-plane loading: recent outcomes and future developments f. berto norwegian university of science and technology ntnu, department of engineering design and materials, trondheim, 7491, norway abstract. the existence of three-dimensional effects at cracks has been known for many years, but understanding has been limited, and for some situations still is. understanding improved when the existence of corner point singularities and their implications became known. increasingly powerful computers made it possible to investigate three-dimensional effects numerically in detail. despite increased understanding, three-dimensional effects are sometimes ignored in situations where they may be important. the purpose of the present investigation is to study by means of accurate 3d finite element (fe) models a coupled fracture mode generated by anti-plane loading of a straight through-the-thickness crack in linear elastic plates. an extended version of the present work has recently been published in the literature. the results obtained from the highly accurate finite element analyses have improved understanding of the behaviour of through cracked components under anti-plane loading. the influence of plate bending is increasingly important as the thickness decreases. it appears that a new field parameter, probably a singularity, is needed to describe the stresses at the free surfaces. discussion on whether kiii tends to zero or infinity as a corner point is approached is futile because kiii is meaningless at a corner point. the intensity of the local stress and strain state through the thickness of the cracked components has been evaluated by using the strain energy density (sed) averaged over a control volume embracing the crack tip. the sed has been considered as a parameter able to control fracture in some previous contributions and can easily take into account also coupled three-dimensional effects. calculation of the sed shows that the position of the maximum sed is independent of plate thickness. both for thin plates and for thick ones the maximum sed is close to the lateral surface, where the maximum intensity of the coupled mode ii takes place. keywords. fracture mechanics; finite element analysis; anti-plane loading; stress intensity factor; corner point effects. citation: berto, f., cracked components under anti-plane loading: recent outcomes and future developments, frattura ed integrità strutturale, 41 (2017) 475-483. received: 15.05.2017 accepted: 26.07.2017 published: 01.07.2017 copyright: © 2017 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. f. berto, frattura ed integrità strutturale, 41 (2017) 475-483; doi: 10.3221/igf-esis.41.59 476 introduction rack tip surface displacements in the vicinity of a corner point in which a crack front intersects a surface are often of practical interest. assuming that poisson’s ratio, v > 0, then kinematics considerations for an antisymmetric loading [1-2] show that modes ii and iii crack tip surface displacements cannot exist in isolation. mode ii induces mode iiic and mode iii induces mode iic. these induced modes are sometimes called coupled modes, indicated by the superscript c. the existence of three-dimensional effects at cracks has been known for many years [3,4], but understanding has been limited, and for some situations still is. understanding improved when the existence of corner point singularities [5] and their implications became known [6]. despite increased understanding, three-dimensional effects are sometimes ignored in situations where they may be important. within the framework of linear elastic fracture mechanics [7] the stress field in the vicinity of a crack tip is dominated by the leading term of a series expansion of the stress field [8]. this leading term is the stress intensity factor, k. in three dimensional geometries, the derivation of stress intensity factors makes the implicit assumption that a crack front is continuous. this is not the case in the vicinity of a corner point, and the nature of the crack tip singularity changes. the resulting corner point singularities were described in detail in 1979 by bažant and estenssoro [5]. some additional results were given by benthem in 1980 [9]. for corner point singularities, the polar coordinates in fig. 1 are replaced by spherical coordinates (r, , ) with origin at the corner point. the angle  is measured from the crack front. there do not appear to be any exact analytic solutions for corner point singularities. in their analysis bažant and estenssoro [5] assumed that all three modes of crack tip surface displacement are of the form rλρpf(θ, ), where ρ is distance from the crack tip, and p is a given constant. they then calculated λ numerically for a range of situations: λ is a function of poisson’s ratio, υ. for the antisymmetric mode, λ = 0.598 for υ = 0.3. benthem [9] made an equivalent assumption but used a different numerical method to calculate . the stress intensity measure, k, may be used to characterise corner point singularities, where  can be regarded as a parameter defining the corner point singularity. however, expressions for numerical values of k, and associated stress and displacement fields, do not appear to be available. at the present state of the art the extent of a corner point singularity dominated region has to be determined numerically. at a corner point stresses are a singularity. they must be either infinite or zero,  is indeterminate, and it is reasonable to speak of stress intensity factors in an asymptotic sense [3]. in the limit, as a crack front is approached, displacement fields must be those of a stress intensity factor [9]. hence, there is an infinitesimal k-dominated region within the core region of a corner point singularity. the stress intensity factors are proportional to s0.5 λ where s is the distance from the surface along the z axis [9]. hence, for the antisymmetric mode kii and kiii both tend to infinity as a corner point is approached. further, as a corner point the ratio kiii/kii tends to a limiting value which is a function of v. for v = 0.3 the limiting ratio is 0.5 [9]. benthem points out that kii and kiii lose their meaning at a corner point [9]. dhondt suggests that modes iic and iiic might not be singular [10]. the predicted tendency to infinity is reasonable for kii since relevant stresses are in plane and disclinations are zero [3]. from a linear elastic viewpoint the predicted tendency of kiii to infinity cannot be correct [4]. at a surface shear stresses perpendicular to the surface are zero, which implies that kiii tends to zero as the surface is approached. mode iii is a torsion problem [11]. under mode iii (anti-plane) loading initially plane cross sections, including the surface at a corner point, do not remain plane under load [4] and disclinations appear. it is well known that serious error can arise if warping of non-circular cross sections under torsion is not taken into account in stress analyses [12]. warping of the surface under mode iii means that τyz at the surface does not have to be zero, and finite values of kiii are possible. the implication is that the non linearities cannot be regarded as being in a core region within a corner point singularity dominated region and that bažant and estenssoro’s prediction that kiii tends to infinity as a corner point is correct. the alternative view, which is supported by a large body of evidence [4], is that apparent values of kiii decrease towards the surface in the z direction. this implies that kiii tends to zero as a corner point is approached, which is intuitively correct. it also implies that non linearities can be regarded as being within a core region, but does not explain why bažant and estenssoro’s analysis does not give the correct limit. nevertheless, this alternative view may well be adequate when considering practical implications. this paradox needs to be resolved so that the results of finite element analysis can be interpreted correctly. there does not appear to have been a systematic investigation of the extent to which bažant and estenssoro’s initial assumption is justified. their assumption does appear to be satisfactory for the symmetric mode (mode i) in that their analysis leads to useful results [4]. the purpose of the present investigation is to study a coupled fracture mode generated c f. berto, frattura ed integrità strutturale, 41 (2017) 475-483; doi: 10.3221/igf-esis.41.59 477 by anti-plane loading of a straight through-the-thickness crack in linear elastic plates by means of accurate threedimensional finite element (fe) models. an extended version of the present work has recently been published in the literature [3]. the material is assumed to be a homogeneous isotropic continuum, and its behaviour is assumed to be linearly elastic. due to the uncertainties in the definition of the stress intensity factors on the free surfaces, as stated above, the strain energy averaged in a control volume (sed) has been employed in the present contribution to quantify the stress intensity through the thickness of the plate. for a review of the sed the reader can refer to [13]. this parameter has been successfully used by lazzarin and co-authors to assess the fracture strength of a large bulk of materials, characterized by different control volumes, subjected to wide combinations of static loading [14 16] and the fatigue strength of notched components [17, 18]. as described in [13, 19] an intrinsic advantage of the sed approach is that it permits automatically to take into account higher order terms and three-dimensional effects. the parameter is easy to calculate in comparison with other well-defined and suitable 3d parameters [20, 21] and can be directly obtained by using coarse meshes [13, 19]. another advantage of the sed is that it is possible to easily understand whether the through-the-thickness effects are important or not in the fracture assessment for a specific material characterized by a control volume depending on the material properties. some brittle materials are characterized by very small values of the control radius and are very sensitive to stress gradients also in a small volume of material [13]. on the other hand more ductile materials have the capability of stress averaging in a larger volume and for this reason are less sensitive to the variations of the stress field through the thickness of the plate. the sed, once the control volume is properly modeled through the thickness of the plate, is able to quantify the 3d effects in comparison with the sensitivity of the specific material so providing precious information for the fracture assessment. finite element modelling n the present calculations, stresses, stress intensity factors and displacements are examined in detail for 100 mm square plates of various thicknesses under anti-plane (nominal mode iii) loading. one half of the plate geometry used is shown in fig. 2. the thickness is t. a through thickness crack has its tip at the centre of the plate, so its length, a, is 50 mm. calculations are carried out using ansys 11 for t/a = 0.25, 0.5, 0.75, 1, 1.25, 1.5, 1.75, 2, 2.25, 2.5, 2.75 and 3. poisson’s ratio is taken as 0.3 and young’s modulus as 200 gpa. a displacement of 10-3 mm is applied to the edge of the plate. stress intensity factors are calculated from stresses on the crack surface near the crack tip using standard equations [7,11]. the strain energy density is calculated from a control volume at the crack tip. one quarter of the plate is modelled. an overall view of the finite element mesh is shown in fig. 3. details of the mesh at the outer surface and crack tip are shown in the figure. figure 1: notation for crack tip stress field. i f. berto, frattura ed integrità strutturale, 41 (2017) 475-483; doi: 10.3221/igf-esis.41.59 478 figure 2: plate geometry. figure 3: overall view of finite element mesh. detail of finite element mesh at outer surface and at crack tip. results rack surface stresses, τyz and τxy (fig. 1) were extracted from the finite element results at distances, s, from the plate surfaces of 0 mm, 0.25 mm, 1 mm and 2 mm. results for t/a = 1, plotted on logarithmic scales, are shown in figs. 4-6. results for other values of t/a are generally similar, but with some differences in detail. when the plot is a straight line its slope is -λ. values of λ taken from straight line plots are shown in tabs. 1 and 2. where no value is shown the plot could not be regarded as a straight line. for s = 0.25 mm, 1 mm and 2 mm λ calculated from τxy is close to the theoretical value of 0.5 for a stress intensity factor singularity (tab. 1). hence, realistic values of kii can be calculated. for s = 0 mm the value of λ has a maximum for t/a = 0.25, and decreases as t/a increases. the values of λ are all significantly less than the theoretical value of 0.598 for a corner point singularity. realistic values of kii can probably be calculated for t/a > 2. realistic values of kiii can be calculated from τyz for s = 1 mm and 2 mm. the results for s = 0 mm (fig. 4) show that τyz is slightly lower than τxy for small x, and decreases as x increases. realistic values of kiii cannot be calculated. the presence of finite values of τyz, linked to finite values of kiii, appears because of the appearance of mode i disclinations, which are rotations about the y axis. differentiating the expression for the displacement uz gives the amount of this rotation which increases towards the crack tip, with a concomitant increase in τyz at a surface. this accounts qualitatively for the observed distributions of τyz at a surface. c f. berto, frattura ed integrità strutturale, 41 (2017) 475-483; doi: 10.3221/igf-esis.41.59 479 t/a s = 0 mm s = 0.25 mm s = 1 mm s = 2 mm 0.25 0.538 0.498 0.497 0.497 0.5 0.527 0.498 0.497 0.497 0.75 0.523 0.498 0.497 0.497 1 0.520 0.498 0.497 0.497 1.25 0.517 0.498 0.497 0.497 1.5 0.515 0.498 0.497 0.497 1.75 0.513 0.498 0.497 0.497 2. 0.512 0.498 0.497 0.497 2.25 0.510 0.498 0.497 0.497 2.5 0.510 0.498 0.497 0.497 2.75 0.509 0.498 0.497 0.497 3 0.508 0.498 0.497 0.497 table 1: values of λ for τxy, s is the distance from surface in the z direction. t/a s = 0 mm s = 0.25 mm s = 1 mm s = 2 mm 0.25 0.507 0.504 0.5 0.506 0.503 0.75 0.506 0.502 1 0.506 0.502 1.25 0.506 0.502 1.5 0.506 0.502 1.75 0.506 0.502 2 0.506 0.502 2.25 0.506 0.502 2.5 0.505 0.502 2.75 0.506 0.502 3 0.506 0.502 table 2: values of λ for τyz, s is the distance from surface in the z direction. figure 4: stresses τyz and τxy on crack surface at s = 0 mm from plate surface, t/a =1. xy yz f. berto, frattura ed integrità strutturale, 41 (2017) 475-483; doi: 10.3221/igf-esis.41.59 480 figure 5: stresses τyz and τxy on crack surface at s = 0.25 mm from plate surface, t/a =1. figure 6: stresses τyz and τxy on crack surface at s = 2 mm from plate surface, t/a =1. figure 7: through thickness distribution of kii and kiii for: t/a = 1, x = 0.05 mm. f. berto, frattura ed integrità strutturale, 41 (2017) 475-483; doi: 10.3221/igf-esis.41.59 481 through-the-thickness distributions of kii and kiii for t/a = 1 is shown in fig. 7. from tabs. 1 and 2 the values of kii are not realistic for s < 0.25 mm and the values of kiii are not realistic for s < 1 mm. the distribution of kiii presents a maximum at the centre line, but kiii then remains nearly constant for about half the distance to the plate surface. the influence of plate bending means that maxima steadily decrease as t/a decreases. as a surface is approached kiii first decreases slightly then increases to a maximum at about 0.15 mm from the surface. there is then an abrupt drop which is within the region where realistic values of kiii cannot be calculated. plate bending theory [2] suggests that kii should be zero on the centre line, with a linear increase towards a surface. kii does indeed increase linearly for much of the thickness with a greater increase as the surface is approached. this is within the region where realistic values of kii cannot be calculated. the extent of the linear portion, in terms of plate thickness, decreases as t/a increases but is still present when t/a = 3. maximum values of kii are at the surface. this is within the region where calculated kii values are not realistic so caution is needed in the interpretation of results. discussion here has been a lot of discussion on whether kiii tends to zero or infinity as a corner point is approached [3]. when apparent kiii values are calculated from stresses at a constant distance from the crack tip then kiii appears to tend to zero as the model surface is approached (fig. 7), in accordance with the linear elastic prediction. however, apparent values of kiii at the surface, linked to finite values of τyz (fig. 4), increase strongly as the distance from the crack tip at which they are calculated decreases. these results can be interpreted as indicating that kiii tends to infinity at a corner point in accordance with bažant and estenssoro’s prediction. the results in fig. 7 also show that kii does appear to tend to infinity as the surface is approached, in accordance with bažant and estenssoro’s prediction. the discussion is futile because, as pointed out by benthem [9], kiii is meaningless at a corner point and there is no paradox. for s ≥ 0.2 mm λ calculated from τxy is close to the theoretical value of 0.5 for a stress intensity factor singularity so kii provides a reasonable description of the crack tip stress field. similarly, kiii provides a reasonable description of the crack tip stress field for s ≥ 1 mm. at the surface values of λ obtained from τxy are always less than the theoretical value for a corner point singularity, and decrease with increasing plate thickness. the distribution of τyz at the surface (fig. 4) cannot be accounted for on the basis of bažant and estenssoro’s analysis. there is clear evidence of a boundary layer effect whose extent is independent of plate thickness. the only available characteristic dimension controlling the boundary layer thickness is the crack length, a. strain energy density through the plate thickness he intensity of the local stress and strain state through the plate thickness can be easily evaluated by using the strain energy density (sed) averaged over a control volume embracing the crack tip (see ref. [13] for a review of the sed approach). the main advantage with respect to the local stress-based parameters is that it does not need very refined meshes in the close neighbourhood of the stress singularity [19]. furthermore the sed has been considered as a parameter able to control fracture and fatigue in some previous contributions [14-16, 34-35] and can easily take into account also coupled three-dimensional effects [4,22]. with the aim to provide some numerical assessment of the contribution of the three-dimensional effects, specifically the coupled fracture mode, kii, the local energy density through the plate thickness is evaluated and discussed in this section. fig. 8 shows the local sed variation across the plate averaged over a cylindrical volume having radius r0 and height h, with h about equal to r0. in refs [13, 14-16, 17-18] r0 was thought of as a material property which varies under static and fatigue loading but here, for the sake of simplicity, r0 and h are simply set equal to 1.0 mm, only to quantify the threedimensional effects through the disc thickness. the influence of the applied mode iii loading combined with the induced singular mode ii loading is shown in fig. 8. it is evident that the position of the maximum sed is the same in all cases. it is close to the lateral surface, where the maximum intensity of the coupled mode ii takes place, both for thin plates, t/a=0.5 and 1.0, and for thick ones, t/a=2 and 3. in fact, as can be seen from fig. 7, the maximum contribution of the coupled mode ii, at the lateral surface, is significantly higher (about 4 times) compared to the maximum contribution of the applied mode iii, at the mid plane. t t f. berto, frattura ed integrità strutturale, 41 (2017) 475-483; doi: 10.3221/igf-esis.41.59 482 figure 8: through the thickness sed distribution for t/a = 0.50, 1, 2, 3. control radius r0 = 1.00 mm. conclusions (1) the results obtained from the highly accurate finite element analyses have improved understanding of the behaviour of through cracked plates under anti-plane loading. in particular, it is confirmed that mode iii does induce coupled mode iic. (2) the influence of plate bending is increasingly important as plate thickness decreases. the anti-plane loading used is a nominal mode iii loading. for thin plate it is a mixed modes iii and ii loading, in which mode iii induces mode iic and vice versa. at the present state of the art it is not possible to separate the coupled modes from the applied modes. (3) bažant and estenssoro’s analysis works well for the symmetric mode (mode i), but it is incomplete for the asymmetric mode (a combination of modes ii and iii). (4) discussion on whether kiii tends to zero or infinity as a corner point is approached is futile because, as pointed out by benthem, kiii is meaningless at a corner point. (5) the present results do not confirm the existence of a corner point singularity dominated region within a k-dominated region. it appears that a new field parameter, probably a singularity, is needed to describe the stresses at the plate surfaces. (6) calculation of the strain energy density (sed) in a control volume at the crack tip shows that the position of the maximum sed is independent of plate thickness. both for thin plates and for thick ones the maximum sed is close to the lateral surface, where the maximum intensity of the coupled mode ii takes place. (7) under the anti-plane loading used theoretical understanding of the stress field in the vicinity of a corner point is still incomplete. references [1] kotousov, a., lazzarin, p., berto, f., harding, s., effect of the thickness on elastic deformation and quasi-brittle fracture of plate components, eng. fract. mech., 77 (2010) 1665-1681. [2] kotousov, a., lazzarin, p., berto, f., pook, l. p., three-dimensional stress states at crack tip induced by shear and anti-plane loading, eng. fract. mech., 108 (2013) 65-74. [3] pook, l. p., campagnolo, a., berto, f., lazzarin, p., coupled fracture mode of a cracked plate under anti-plane loading, eng. fract. mech., (2015) doi:10.1016/j.engfracmech.2014.12.021. [4] pook, l. p., a 50-year retrospective review of three-dimensional effects at cracks and sharp notches, fatigue fract. engng. mater. struct., 36 (2013) 699-723. [5] bažant, z. p., estenssoro, l. f., surface singularity and crack propagation, int. j. solids struct., 15 (1979) 405-426. [6] pook, l. p., some implications of corner point singularities, eng. fract. mech., 48 (1994) 367-378. [7] pook, l. p., linear elastic fracture mechanics for engineers. theory and applications, wit press, southampton (uk), (2000). f. berto, frattura ed integrità strutturale, 41 (2017) 475-483; doi: 10.3221/igf-esis.41.59 483 [8] williams, m. l., on the stress distribution at the base of a stationary crack, j. appl. mech., 24 (1957) 109-114. [9] benthem, j. p., the quarter-infinite crack in a half-space; alternative and additional solutions, int. j. solids struct., 16(2) (1980) 119-130. [10] dhondt, g., on corner point singularities along a quarter circular crack subject to shear loading, int. j. fract., 89 (1998) l13-l18. [11] paris, p. c., sih, g. c., stress analysis of cracks, in: fracture toughness testing and its applications, astm stp 381, american society for testing and materials, philadelphia (usa), (1965) 30-81. [12] timoshenko, s. p., goodier, j. n., theory of elasticity, third ed., mcgraw-hill book company, new york (usa), (1970). [13] berto, f., lazzarin, p., recent developments in brittle and quasi-brittle failure assessment of engineering materials by means of local approaches, mater. sci. eng. r, 75 (2014) 1-48. [14] lazzarin, p., berto, f., elices, m., gómez, j., brittle failures from uand v-notches in mode i and mixed, i+ii, mode. a synthesis based on the strain energy density averaged on finite size volumes, fatigue fract. engng mater. struct., 32 (2009) 671–684. [15] torabi, a. r., campagnolo, a., berto, f., mode ii brittle fracture assessment of key-hole notches by means of the local energy, j. test. eval., 44 (2016) doi: 10.1520/jte20140295. [16] torabi, a. r., campagnolo, a., berto, f., local strain energy density to predict mode ii brittle fracture in brazilian disk specimens weakened by v-notches with end holes, mater. design, 69 (2015) 22-29. [17] berto, f., lazzarin, p., yates, j. r., multiaxial fatigue of v-notched steel specimens: a non-conventional application of the local energy method, fatigue fract. engng. mater. struct., 34 (2011) 921-943. [18] berto, f., campagnolo, a., lazzarin, p., fatigue strength of severely notched specimens made of ti-6al-4vunder multiaxial loading, fatigue fract. engng. mater. struct., (2015) doi: 10.1111/ffe.12272.   [19] lazzarin, p., berto, f., zappalorto, m., rapid calculations of notch stress intensity factors based on averaged strain energy density from coarse meshes: theoretical bases and applications, int. j. fatigue, 32 (2010) 1559-1567. [20] yosibash, z., shannon, s., computing edge stress intensity functions (esifs) along circular 3-d edges, eng. fract. mech., 117 (2014) 127-151. [21] omer, n., yosibash, z., on the path independency of the point-wise j integral in three dimensions, int. j. fracture, 136 (2005) 1-36. [22] campagnolo, a., berto, f., lazzarin, p., the effects of different boundary conditions on three-dimensional cracked discs under anti-plane loading, eur. j. mech. – a/solids, 50 (2015) 76-86. << /ascii85encodepages false /allowtransparency false /autopositionepsfiles true /autorotatepages /none /binding /left /calgrayprofile (dot gain 20%) /calrgbprofile (srgb iec61966-2.1) /calcmykprofile (u.s. web coated \050swop\051 v2) /srgbprofile (srgb iec61966-2.1) /cannotembedfontpolicy /error /compatibilitylevel 1.4 /compressobjects /tags /compresspages true /convertimagestoindexed true /passthroughjpegimages true /createjobticket false /defaultrenderingintent /default /detectblends true /detectcurves 0.0000 /colorconversionstrategy /cmyk /dothumbnails false /embedallfonts true /embedopentype false /parseiccprofilesincomments true /embedjoboptions true /dscreportinglevel 0 /emitdscwarnings false /endpage -1 /imagememory 1048576 /lockdistillerparams false /maxsubsetpct 100 /optimize true 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/hrv (za stvaranje adobe pdf dokumenata najpogodnijih za visokokvalitetni ispis prije tiskanja koristite ove postavke. stvoreni pdf dokumenti mogu se otvoriti acrobat i adobe reader 5.0 i kasnijim verzijama.) /hun 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can be opened with acrobat and adobe reader 5.0 and later.) >> /namespace [ (adobe) (common) (1.0) ] /othernamespaces [ << /asreaderspreads false /cropimagestoframes true /errorcontrol /warnandcontinue /flattenerignorespreadoverrides false /includeguidesgrids false /includenonprinting false /includeslug false /namespace [ (adobe) (indesign) (4.0) ] /omitplacedbitmaps false /omitplacedeps false /omitplacedpdf false /simulateoverprint /legacy >> << /addbleedmarks false /addcolorbars false /addcropmarks false /addpageinfo false /addregmarks false /convertcolors /converttocmyk /destinationprofilename () /destinationprofileselector /documentcmyk /downsample16bitimages true /flattenerpreset << /presetselector /mediumresolution >> /formelements false /generatestructure false /includebookmarks false /includehyperlinks false /includeinteractive false /includelayers false /includeprofiles false /multimediahandling /useobjectsettings /namespace [ (adobe) (creativesuite) (2.0) ] /pdfxoutputintentprofileselector /documentcmyk /preserveediting true /untaggedcmykhandling /leaveuntagged /untaggedrgbhandling /usedocumentprofile /usedocumentbleed false >> ] >> setdistillerparams << /hwresolution [2400 2400] /pagesize [612.000 792.000] >> setpagedevice microsoft word numero_30_art_29 n. petrone et alii, frattura ed integrità strutturale, 30 (2014) 226-236; doi: 10.3221/igf-esis.30.29 226 focussed on: fracture and structural integrity related issues field load acquisition and variable amplitude fatigue testing on maxi-scooter motorcycles n. petrone university of padova, italy nicola.petrone@unipd.it m. saraceni enginlab, italy m.saraceni@enginlab.com abstract. aim of the present work was the instrumentation of a maxi scooter for the field collection of service loads acting on the scooter main components such as frame, fork, handlebar, rear frame and suspension. service loads were collected on an instrumented yamaha tmax scooter equipped with 22 channels during a set of field tests that were representing a predefined road mix, covering a mileage of 270 km. field load histories were used to develop an accelerated test procedure for the accelerated bench fatigue testing of a new model prototype whose mission was set to 50000 km. the acceleration procedure allowed a time reduction from 1600 hrs to 122 hrs bench equivalent testing. both the benchmark scooter tmax and a maxi-scooter prototype under development underwent the bench variable amplitude fatigue testing. the results of the fatigue tests on the prototype allowed to identify some critical bolted connections and to reduce some stress concentration features causing the appearance of small cracks that were found also after during 50000 km of driving tests. keywords. motorcycle; field data collection; accelerated variable amplitude fatigue; cracked components. introduction he development of a new motorcycle model is a long and complex process that involves several fields of knowledge ranging from the styling, the design of frame-suspensions-engine components, the virtual assessment of components, the prototyping, the bench testing and the final driving tests: in that process, manufacturers can rely on their former experience and on the support of component manufacturers, depending on their industrial size and historic production. usually, experiences from a small vehicle are useful but not enough to develop a more powerful vehicle: on the other side, also strong experiences in the automotive or motorcycle market may not be enough to enter in a new market as, for instance, the maxi-scooter market that is nowadays bridging between the small city scooter vehicles and the road motorcycle family. over the last decades, a lot of investigation was carried out by manufacturers and researchers in order to establish a proper set of methodologies supporting the development of motorcycles, nowadays usually implemented in the industry. the first set of information needed by engineers regarded the loads acting on the components of scooter or motorcycles: this was approached by the application of sensors to the component of the vehicle [1-4] or in some cases by the t n. petrone et alii, frattura ed integrità strutturale, 30 (2014) 226-236; doi: 10.3221/igf-esis.30.29 227 development of customized load cells to be applied to the vehicle components for the complete measurement of loads acting on the vehicle interfaces with the ground [5,6] or with the rider [7]. on the basis of this set of information, engineers can develop methods for the virtual assessment of main components of the motorcycle such as frames and suspensions [7-9] by using multibody codes for the prediction of vehicle dynamics or finite element analysis for the assessment of frame stiffness properties and fatigue life of casted, cnc machined and welded components. the use of laboratory tests has always been supported by manufacturers as a tool for ensuring experimentally the durability of their product, despite the lack of mandatory regulation from an international body. manufacturers are responsible for any damage that customers can encounter during the supposed use of their vehicle, therefore they have to ensure the degree of safety of the product under their responsibility. laboratory tests however, as we can find in the manufacturers or research centers laboratory, can range from simple single channel constant amplitude fatigue tests [8,10], to multiple channels variable amplitude fatigue tests [11-15] of the full vehicle [11,15] or of its components [12,13]. within the different experiences developed throughout the world, further distinction can be made between the benches involving a dummy in the tests, therefore using inertial forces to reproduce the actions stressing the vehicle [3,11], and the benches involving a reaction frame around the component [10,12,13,14]. variable amplitude testing of full motorcycles, despite its appealing ability of reproducing exactly the load histories measured in the field, require acceleration procedures to ensure that the mileage demanded from the component assessment may be reproduced in a reasonable and industrially sustainable amount of time. very few information are available in the literature regarding these acceleration procedures [14,15] as this may be the bottleneck of the procedure or the real know-how that companies tend to protect. aim of the present work was the instrumentation of a maxi scooter for the field collection of service loads acting on the scooter’s main components such as frame, fork, handlebar, rear frame and suspension. service loads collected during a representative amount of field tests were used to develop an accelerated test procedure for the accelerated bench fatigue testing of a new model prototype comparison. overall method description he method adopted for the study was defined starting from the request of a motorcycle manufacturer for the fatigue assessment of a new prototype of maxi-scooter that was under development (prototype p1), whose final version was not yet equipped for road tests. the manufacturer wanted to make sure that the prototype p1, supposed to be used for the early design stage road tests, would ensure to test drivers the proper fatigue durability and survive a 50’000 km drive test campaign without any failure on main safety components. the study then was based on a service loads collection campaign using an existing maxi-scooter produced by a competitor, chosen by the prototype manufacturer as similar in dimensions and performances. the scooter was a yamaha tmax, 500 cc: two samples of this motorcycle were available for the study. the first sample, named tmaxs was instrumented and calibrated for the field data collection. the instrumented scooter tmaxs was also used to tune the fatigue test bench and to verify the amount of fatigue damage that was applied by the accelerated test load histories on the bench with respect to the target fatigue damage as collected from the field tests. the second sample, named tmaxd, was used for the fatigue testing of the commercial scooter. the prototype sample p1 underwent the same fatigue tests of the tmaxd to verify its ability to survive to the assumed target life. vehicle instrumentation he maxi-scooter tmaxs was prepared for the application of a large number of channels, in order to have a certain degree of redundancy in the evaluation of loads and solicitations acting on the scooter. the full list of applied channels, their name and units, the type of sensor used are listed in tab. 1. the location and sign convention of most of them are presented in fig. 1. as it can be appreciated, most of the channels were strain gauge channels directly applied to the motorcycle components: as a measuring principle, the intrinsic compliance of the component under single load components was used to obtain a channel calibrated in the assembled configuration of the scooter. t t n. petrone et alii, frattura ed integrità strutturale, 30 (2014) 226-236; doi: 10.3221/igf-esis.30.29 228 figure 1: location and sign convention of channels applied to scooter yamaha tmaxs. signal obtained from the field were therefore converted into mechanical loads on the basis of a calibration procedure aiming to apply known single load components to the assembled vehicle. only few channels were based on load cells intentionally designed for the quantity under measurement: this was the case of the rear damper force as well as the front and the rear brakes. in fact, in the case of the rear damper, the solid shaft at the damper extremity was notched by a trough hole in order to create a bending component to be sensed by means of half brigde (longitudinal & transverse grids, fig. 2.c). regarding the front and rear brake calipers, the arms connecting the caliper to the fork or the swing arm were slimmed in such a way that the tangential force acting on the calipers was creating a cantilever action on the arms, therefore making the full bridge unbalanced under the effect of the braking load. vehicle calibration alibration constants of single component strain gauge bridges were obtained as inverse values of channel sensitivity, intended as the linear regression slope between the electrical output [mv] of the channel and the known applied forces [n] or bending moment [nm]. in the case of coupling between the channels, as in the case of the handlebar or the rear wheel axle, a matrix approach was adopted. calibration tests were performed on the fully equipped scooter, ready to ride. this allowed to avoid the effect of reassembling the component after calibration, but introduced the complexity regarding the alignment of loads and the restraining of the vehicle. calibration loads were applied by deadweights and pulleys or by means of hydraulic actuators. only exception was the rear damper, calibrated by means of a tensile machine as it was working in tension (see the sketch in fig. 1). examples of some calibration test setups are reported in fig. 2. plots of the calibration results are presented in fig. 3. c legend = force = acceleration = stroke = bending component on cross section = axial component on cross section 20 = velocity 1-2 3 4 6 5 7 8 9 10 11 12 13 14 15 17 21 = distance 18 19 16 note: the arrow direction indicates the channel positive output x z n. petrone et alii, frattura ed integrità strutturale, 30 (2014) 226-236; doi: 10.3221/igf-esis.30.29 229 ch. n° channel description name unit sensor type 1 front fork tube right c 01_ffr [nm] half bridge strain gage 2 front fork tube left c 02_ffl [nm] half bridge strain gage 3 front brake force c 03_bf [n] half bridge strain gage 4 front fork stroke c 04_ffstk [mm] linear potentiometer (150mm) 5 front wheel accelerometer, z’ direction c 05_fwaz [g] capac. accelerometer (100g) 6 front wheel accelerometer, x’ direction c 06_fwax [g] capac. accelerometer (100g) 7 handlebar left force z direction c 07_hlfz [n] half bridge strain gage 8 handlebar left force x direction c 08_hlfx [n] half bridge strain gage 9 frame (telaio) bending moment c 09_tbm1 [nm] full bridge strain gage 10 frame (telaio) upper axial strain c 10_tua [e] full bridge strain gage 11 frame (telaio) lower axial strain c 11_tla [e] full bridge strain gage 12 front vertical force on saddle c 12_sfv [n] half bridge strain gage 13 rear vertical force on saddle c 13_srv [n] half bridge strain gage 14 rear damper stroke c 14_rdstk [mm] linear potentiometer (50mm) 15 rear damper force c 15_rdf [n] half bridge strain gage 16 rear brake force c 16_br [n] half bridge strain gage 17 rear wheel accelerometer vertical c 17_rwaz [g] capac. accelerometer (100g) 18 rear wheel right force z direction c 18_rwrfz [n] half bridge strain gage 19 rear wheel right force x direction c 19_rwrfx [n] half bridge strain gage 20 velocity sensor c 20_speed [km/h] native tmax inductive sensor 21 distance c 21_dist [m] digital counter table 1: list of channels applied to scooter yamaha tmaxs. (a) (b) (c) figure 2: examples of calibration tests on scooter yamaha tmaxs. (a) front fork and frame channels calibration. (b) handlebar horizontal calibration. (c) rear damper tensile calibration. +fwfn n. petrone et alii, frattura ed integrità strutturale, 30 (2014) 226-236; doi: 10.3221/igf-esis.30.29 230 (a) (b) figure 3: examples of calibration tests results with sensitivity values obtained by linear regression from tmaxs channels output. (a) handlebar horizontal calibration tests (fig. 2.b). (b) rear damper calibration tests (fig. 2.c). as it can be appreciated from the plots of fig. 3, the strain gauged components presented in general a good linearity and sufficient load decoupling for the purpose of the study. field load acquisition he field load acquisition sessions were carried out by two expert riders on the instrumented scooter tmaxs. an imc cronos pl3 was placed in the helmet housing and collected 16 analog channels at 1 khz per channel for each run. an onboard camera was placed on the scooter windshield for filming each driving event and surface. the road mix assumed for the study is summarized in fig. 4.a. the mix was obtained mainly by combining city driving (fig. 4.b.c.d), extraurban (fig. 4.e), highway and a small amount (6%) of offroad driving, as the target was the european market. the city driving included a 2,6 % of city pave (fig. 4.d) and a 3.3 % of bumps that were collected both using the typical 3mtm bumps (fig. 4.b) and the pedestrian crossings (fig. 4.c). a total amount of 270 km were recorded: 83 % of them were collected with two persons on the vehicle. road mix of maxi-scooter field tests [in % ] city, 26.1 offroad, 6.0 pavè, 2.6 bumps, 3.3 extraurban 32.1 highways 29.9 bumps pavè city offroad highways extraurban (a) figure 4: field tests information. (a) road mix adopted for the study. (b) example of 3mtm road bump encountered in city runs. (c) example of pedestrian crossing encountered in city runs. (d) example of city pavè. (e) example of extraurban driving road. results of the field tests were the raw signals from all the scooter components: they were zeroed, verified in terms of spikes and zeroing errors, converted into mechanical quantities such as loads, strokes, acceleration or strain. further analysis of data regarded the searching for special event that could be significant for defining the component strength t (c) (d) (e) (b) (c) n. petrone et alii, frattura ed integrità strutturale, 30 (2014) 226-236; doi: 10.3221/igf-esis.30.29 231 static tests. the results of this analysis have been collected for four channels in tab. 2 and 3. the max and min values correspond to the positive and negative peaks recorded during the event (bumps & braking) or the portions of tracks that were recognized as representing the different surfaces and conditions (1 person or 2 persons). rng values correspond to the maximum range values recorded during the considered track portion and correspond to the largest cycles that the components underwent during their recorded fatigue life history. events with the largest ranges are reported as bold in the table. ave correspond to the mean values recorded during the track portion, as well as std correspond to the standard deviation from the track portion. bending moment at front fork ffr_c 01 [nm] horizontal force at the handlebar hlfx_c08 [n] event max min rng ave std max min rng ave std bump 3m 1p (50 km/h) 1097 -720 1817 243 120 133 -156 289 6 27 bump 3m 2p (50 km/h) 957 -351 1308 265 92 183 -105 287 8 26 pedestrian bump 1p 777 -267 1044 244 70 170 -171 341 -12 38 pedestrian bump 2p 838 -233 1071 270 74 162 -89 251 7 25 front brake 2p 760 -1187 1947 -450 622 322 -27 349 184 130 rear brake 2p 490 212 278 394 49 224 -40 263 142 48 pavè 1p 947 -1482 2429 176 189 407 -203 610 0 49 pavè 2p 1151 -1747 2898 208 164 446 -216 663 -7 42 highway 2p 671 -102 773 256 35 38 -56 94 -14 10 urban external ring 2p 1329 -1070 2399 251 60 170 -107 277 -9 17 offroad 814 -235 1049 253 111 175 -124 298 13 36 deep pothole 731 -367 1097 249 135 298 -304 603 10 63 table 2: max, min, range, mean and stdev values of channels ffr and hlfx across the different types of tracks and events. bending moment at front frame tbm_c 09 [nm] rear damper force rdf_c 15 [n] event max min rng ave std max min rng ave std bump 3m 1p (50 km/h) 1569 -488 2057 559 137 10241 -1535 11777 4225 1110 bump 3m 2p (50 km/h) 1460 -195 1655 576 123 11992 -1462 13454 6650 1204 pedestrian bump 1p 1344 -153 1497 572 128 10732 -1209 11941 4620 1484 pedestrian bump 2p 1263 8 1256 614 106 15529 1722 13807 7479 1634 front brake 2p 1086 -804 1890 -89 592 8983 3881 5102 5517 1437 rear brake 2p 930 521 410 762 69 9584 6587 2998 8232 528 pavè 1p 1347 -1167 2515 487 198 9035 -763 9799 4376 843 pavè 2p 1740 -1328 3068 534 166 12985 -971 13956 6383 886 highway 2p 1015 180 836 595 46 9641 4311 5330 7375 327 urban external ring 2p 1740 -887 2627 588 73 11834 -688 12523 6679 527 offroad 1255 107 1148 703 132 12305 242 12063 7056 1287 deep pothole 2141 112 2029 674 211 40057 -372 40428 7468 2614 table 3: max, min, range, mean and stdev values of channels tbm and rdf across the different types of tracks and events. n. petrone et alii, frattura ed integrità strutturale, 30 (2014) 226-236; doi: 10.3221/igf-esis.30.29 232 laboratory fatigue test setup horizontal test bench description he scooter tmaxs was assembled on the fatigue test bench as shown in fig. 5.a. the frame was loaded by the fx force (bench fx force) at the front fork axle, after locking the front fork excursion at the static nominal length. loads were applied by means of a 15 kn mts 242 hydraulic cylinder. the cylinder was under force control by the mts testar ii m system. deadweights were applied at the rider (95 kg) and passenger (85 kg) locations as indicated by the manufacturer in order to reproduce the static frame bending moment at channel 9 (tbm). this channel was eventually adopted as the master channel to be taken as the reference channel: being able to reproduce the bending moment load history at channel tbm was assumed to be stressing the frame-fork connections and the frameengine connections in an equivalent manner. the frame front fork axle was fixed on a horizontal slider. the rear wheel (inflated at prescribed pressure) was clamped on a rigid plane applied to the bench, after preloading the tyre with 5000 n. the rear damper was substituted by a stiff rigid rod of the same dimensions. (a) (b) figure 5: horizontal fatigue test bench (a) sketch of the horizontal fatigue test bench. (b) yamaha tmaxd undergoing the horizontal fatigue test. overall description of the variable amplitude fatigue test procedure the test procedure was defined by combining the information collected during the field tests and the laboratory calibration tests with the required target fatigue life and the bench fatigue tests data. the overall procedure can be divided in several steps of the study. 1. field data analysis a. the strain data recorded in the field at channel #9 (tbm), (field measured signals), corresponding to the front frame bending moment at a significant location (down tube of tmaxs), were used as reference data. b. the field measured signals from the different available road tests were joined to obtain a total track of 270 km, corresponding to a total recorded time of 518.74 min (8,645 h). c. the field measured signals was rainflow counted (range only method) to produce the field measured spectrum. d. the field measured spectrum corresponding to 270 km was extended for nbtl= 185 times to reach 50000 km target life. e. the extended spectrum corresponding to 50000 km was compared with a virtual fatigue curve of a welded frame with wohler exponent k=4, as from previous experience with welded motorcycle frames and components [10,16]. linear damage summation and miner rule were used to estimate the minimum required frame strength corresponding to a target life of 50000 km. t n. petrone et alii, frattura ed integrità strutturale, 30 (2014) 226-236; doi: 10.3221/igf-esis.30.29 233 f. the results of such analysis were that the virtual fatigue curve corresponding to a life of 50000 km would be described by a slope of k=4, and a reference range of tbm [nm] = 906 nm at 2 106 cycles. 2. test acceleration procedure a. to reproduce the field measured signals corresponding to 270 km up to the required life of 50000 km with a 1:1 time scale, a total number of 1599,3 hrs would have been needed. this test duration would not be sustainable; therefore a test acceleration procedure was developed. b. test acceleration was obtained by means of the following actions: (i) peak-valley counting of field signals, (ii) generation of command signal, (iii) interpolation of command peaks & valleys, (iv) amplification of command signals, (v) reproduction of command signals. c. peak valley counting was performed on the field measured signal of tbm using a hysteresis threshold of 494 nm (corresponding to the 16% of the maximum recorded range of tbm), leading to a total fatigue damage reduction from 1.0 to 0.9. this allowed to reduce the field measured signal of tbm to a peak-valley signal containing a total number of 11604 peaks and valleys. d. the tbm signal was converted into a horizontal force signal fx by means of the transformation constant obtained during static calibration on the tmaxs scooter after application of fx forces and recording of tbm signals. the result was a peak-valley signal that could be used to command the bench. e. for the bench variable amplitude fatigue, the sine interpolation of peaks and valley was adopted as implemented in the mts control: this produced a sinusoidal command file where peaks were reproduced at an average frequency of 7 hz. f. the mts control was tuned with the pid values in order to match the applied loads with the command loads. to help this procedure, due to the hydraulic pid control and the test frequency, an amplification factor of 1.22 was introduced to optimize the applied fx signal. g. the result of this procedure was that a block corresponding nominally to 270 km could be reproduced with a nominal duration of 30 minutes. the target life of 50000 km could be nominally reached after application of 185 blocks, corresponding to duration of 90 hrs. h. the force fx really applied to the frame was recorded during the test as bench measured signal fx. this was different from the target signal. to take into account these differences, the tbm signal measured on the tmaxs mounted on the bench was recorded, rainflow counted and compared with the reference virtual fatigue curve. i. the number of blocks needed for a fatigue damage equivalent to 50’000 km was then recalculated based on the ratio between the road measured damage and the effective bench measured damage. this lead to increase the initially estimated number of 185 blocks to a number of 245 blocks to be applied (corresponding to duration of 122 hrs). vertical test bench description the scooter was assembled on the fatigue test bench as shown in fig. 6.a. the frame was loaded by the sfz force (bench sfz force) on the saddle structure. loads were applied by means of a 15 kn mts 242 hydraulic cylinder joined on a customized loading structure positioned over the rear frame without stiffening effects. the cylinder was under force control by the mts testar iim system. no deadweights were applied in this case: the mean value of saddle loads was obtaind by the mean value of the actuator. the frame front fork was fixed on a horizontal slider, with free displacement in x direction, zero load control. the frame rear axle was fixed on a rigid post applied to the bench. particular care was adopted in the definition of the vertical load sfz location: static calibrations with vertical loads were applied to the saddle at three different locations: the driver, the passenger and an intermediate. this allowed to compare the relative response of channels c_12 and c_13 during static calibrations and to locate the cylinder at a representative location able to stress adequately the saddle upper frame and the rear suspension. channel c 18_rwrfz was adopted as the master channel for the convergence of the vertical variable fatigue tests: being able to reproduce a vertical load history at channel rwrfz was assumed to be stressing the rear swing arm, the swing arm connections to the engine, the saddle frame and its connections to the engine in an equivalent manner. vertical fatigue test procedure the strain data recorded in the field at channel #18 rwrfz, corresponding to the rear wheel force measured at the axle, were used as reference data. this signal was available only from the tmaxs vehicle. so, after converging with the damage calculated at rwrfz on the tmaxs scooter, following the same acceleration procedure presented for the horizontal fatigue test, the saddle force history sfz was saved and reapplied to both the tmaxd scooter and the prototype p1. n. petrone et alii, frattura ed integrità strutturale, 30 (2014) 226-236; doi: 10.3221/igf-esis.30.29 234 (a) (b) figure 6: vertical fatigue test bench. (a) sketch of the vertical fatigue test bench. (b) tmaxs undergoing the vertical fatigue test setup. variable amplitude fatigue tests he variable amplitude fatigue tests were performed up to the target life of 50’000 km on two maxi-scooter frames. both the horizontal and vertical variable amplitude fatigue tests were performed in sequence on the tmaxd scooter and on the prototype scooter p1. the failure criteria was assumed as the presence of 10 mm visible cracks at any location of the frame. the components were periodically visually inspected during working hours. the frame stiffness decrease along the tests was in parallel considered as an indicator of failure, due to an increased compliance of cracked components. the 20 % reduction of initially settled stiffness was adopted as the test stop. as a results of the fatigue tests on the tmaxd frame, no failures were detected at the main frame, the swingarm nor the saddle frame. this was corresponding to the expectations as the scooter was a very well established product, circulating worldwide in the market since several years and was chosen by the manufacturers as a benchmark competitor. differently, the prototype p1, at its very early stage of development, presented a few localized failures during the vertical fatigue stage: after a variable amplitude fatigue equivalent to 15600 km, a bolt failure was experienced at the connection between the saddle frame and the mainframe. this resulted in the decision by the manufacturer to increase the diameter of all connection bolts at that location. the prototype did not show any stiffness decrease after the variable amplitude laboratory tests nor visible cracks were detected at any accessible component: the road tests campaign with drivers was then permitted and drivers started to test the behaviour of all motorcycle components, from the fork-frame assembly to the engine and cooling systems, from the braking systems to the electric components. interestingly, after 50’000 km of road tests on a fully equipped prototype, while investigating about the wear of different component on a fully disassembled vehicle, manufacturers discovered the presence of a small crack at the foot of the fillet of a reinforcing web in the inner portion of the frame end piece, connecting the rear swing arm to the main frame (fig. 7.a). the corresponding piece of the prototype p1 that underwent the horizontal and vertical fatigue was then reanalysed after disassembly: effectively, at the corresponding location of the frame end piece, a small crack of 5 mm depth was observed and confirmed subsequently by dye penetrant inspection (fig. 7.b). this evidence, initially not captured during the overall visual crack inspection nor revealed by any stiffness reduction of the assembly, confirmed the ability of the developed procedure to reproduce the fatigue damage accumulated by the vehicle during the 50’000 km test drive in the accelerated laboratory tests. as a result of this evidence, design engineers modified the fillet radius at the web and on following prototypes and series vehicle the new component presented a modified shape, as shown in fig. 7.c: the following drive and bench tests never produced cracks at that location (fig. 7.c). t n. petrone et alii, frattura ed integrità strutturale, 30 (2014) 226-236; doi: 10.3221/igf-esis.30.29 235 (a) (b) (c) figure 7: crack detection and redesign. (a) crack detected after disassembly of prototype undergoing 50000 km drive tests. (b) crack detected at the same location after 50000 km equivalent variable amplitude fatigue bench tests. (c) modified component with increased fillet radius to avoid stress concentration. discussion he fatigue design and testing of motorcycle components is a complex task regarding which most manufacturer usually develop a complete procedure consisting of field data acquisition, fatigue life estimation and fatigue bench testing, based on former experiences: these information are rarely available or are supplied by specialized companies once expensive test bench and control software are purchased [15] together with even more expensive dynamometric hubs to be applied at the wheel axles [6]. the present work intended to give a contribution regarding the complete approach to the problem, by presenting step by step the procedure and describing some passages in detail, similarly to what was performed on a simpler case such as the seatpost of a mountain bike experiencing a general recall after field failures [4]. it can be adopted by manufacturers, designer, test institutes in developing an accelerated test procedure. the main limitation of the study was its single axis testing approach. the horizontal and vertical testing were performed in sequence: more sophisticated methods (based however on dummy loaded motorcycles) are able to synchronously reproduce the field load histories on different components of the motorcycle. these benches however require in any case a similar procedure for the acceleration of the test. the method proposed can be unified in a single test provided that the damage contribution on the two master channels considered for the horizontal and the vertical test tuning will be arriving to the same summation after each block. in addition to that, the availability of poor components of short field fatigue life is very useful in the tuning of the method, as their known finite fatigue life will be assessed in the accelerated tests, therefore confirming the overall procedure as it happened with the present prototype frame. conclusions tmax maxi-scooter was equipped with 22 channels applied to the scooter main components such as frame, fork, handlebar, rear frame and suspension. service loads were collected during 270 km of field tests including city, extraurban, highway and offroad riding in order to represent an assigned road mix. field load histories were used to develop an accelerated test procedure for the accelerated bench fatigue testing of a new model prototype whose mission was set to 50000 km. a two stage variable amplitude fatigue test was applied to the benchmark scooter tmax and to a maxi-scooter prototype p1 under development. the time reduction obtained by implementing the proposed procedure was from 1600 hrs to 122 hrs bench equivalent testing for horizontal test. the results of the fatigue tests on the prototype were validated after the appearance of small cracks at a notched component that were found also after 50000 km of driving tests. t a n. petrone et alii, frattura ed integrità strutturale, 30 (2014) 226-236; doi: 10.3221/igf-esis.30.29 236 references [1] meneghetti, g., petrone, n., analisi di prestazione e durata su componenti motociclistici, parte i: acquisizione dati, mototecnica, xi(11) (1997) 104-112; parte ii: l’analisi di prestazione, mototecnica, xi(12) (1997) 116-119; parte iii: la durata, mototecnica, xii(2) (1998) 106-111. [2] forni, a., meneghetti, g., petrone, n., structural behaviour of a sport motorcycle in typical road events, in: proceedings of “power two wheels”, ata international conference, pisa, italy, (1998) 135-144. [3] petrone, n., biliato, n., toselli, g., fazi, f., acquisizione ed analisi dei carichi su scooter 125 in prove su pista e su banco a rulli, in: xxix° convegno nazionale aias, lucca, (2000) 545-554. [4] saraceni, m., petrone, n., un sensore per ogni parametro: parte 1 e 2. mototecnica. parte i: 18(10) (2004) 100-106; parte ii: 18(11) (2004) 110-113. [5] saraceni, m., petrone, n., sviluppo di un sistema di celle dinamometriche per la misura completa dei carichi agli assi ruota di uno scooter 150 cc., in: atti del xxxii convegno nazionale aias, salerno, (2003). [6] http://www.mts.com/ucm/groups/public/documents/library/dev_004781.pdf (2014). [7] capitani, r., meneghin, a., rosti, d., virtual prototyping of a two wheeled vehicle, sae technical paper 2003-010672, (2003). doi:10.4271/2003-01-0672. [8] mauro, l., meneghetti, g., petrone, n., structural analysis and fatigue life prediction on a welded tubular motorcycle frame, in: virtual prototyping today: industrial impact and future trend, bergamo, (2002) 341-352. [9] zhang, l., lu, c., kiet tieu, a., fatigue analysis of a motorcycle frame system based on a road test and the finite element method, materials science forum, 773 – 774 (2013) 842-850. doi:10.4028/www.scientific.net/msf.773774.842. [10] petrone, n., saraceni, m., cecchetto, m., pegoraro, d., sviluppo di un banco prova per l’analisi strutturale ed a fatica di telai motociclistici, in: xxx° convegno nazionale aias, alghero, (2001) 407-416. [11] tuluie, r., ericksen, g., racing motorcycle design process using physical and virtual testing methods, sae technical paper 2000-01-3576, (2000). doi:10.4271/2000-01-3576. [12] petrone, n., saraceni, m., metodologie di acquisizione su strada e riproduzione al banco di sollecitazioni complesse su componenti motociclistici soggetti a fatica, in: ia giornata studio “progettazione a fatica in presenza di multiassialità tensionali”, ferrara, (2005). [13] petrone, n., saraceni, m., crugnola, f., progetto e costruzione di un simulatore di strada multicanale per forcelle motociclistiche, in: xxxiv° convegno nazionale aias, politecnico di milano, ed grafiche g.s.s., bergamo, (2005). [14] franch, v., petrone, n., acquisizione su strada dei carichi al tubo reggisella di telai di mtb biammortizzate e verifica a fatica ad ampiezza variabile, rivista italiana saldatura, 2 (2006) 227-237. [15] http://www.mts.com/europeanmotorcycleseminar/download/mts_durability.pdf (2014). [16] petrone, n., susmel, l., biaxial testing and analysis of bicycle-welded components for the definition of a safety standard, fatigue and fracture of engineering material and structures, 26 (2003) 491-505. microsoft word numero_45_art_11 a. benyahia et alii, frattura ed integrità strutturale, 45 (2018) 135-146; doi: 10.3221/igf-esis.45.11 135 influence of limestone dust and natural pozzolan on engineering properties of self-compacting repair mortars amar benyahia, said choucha, mohamed ghrici geomaterials laboratory, hassiba benbouali university of chlef, algeria a.benyahia@univ-chlef.dz , said_choual@hotmail.fr, m.ghrici@univ-chlef.dz ahmed omran department of civil engineering, university of sherbrooke, canada a.omran@usherbrooke.ca abstract. the main goal of this work is to develop self-compacting repair mortars (scrms) containing limestone dust (ld) and natural pozzolan (np). therefore, a three different mortar (scrm0, scrm-10ld and scrm-20np) were prepared and tested according to en 1504-3. the results of the experimental study showed that the produced repair materials fulfilled the performances requirements for structural repair products, class r4. in addition, complete composite specimens for the slant shear, showed a good bond strength between the scrms and existing substrate concrete (subc) at 28-days and the fractures were only occurred in the subc, which means that the substrate is the weakest link in the repair system. keywords. self-compacting mortar; limestone dust; natural pozzolan; composite; bond strength; repair. citation: benyahia, a., choucha, s., ghrici, c.., omran, a., influence of limestone dust and natural pozzolan on engineering properties of self-compacting repair mortars, frattura ed integrità strutturale, 45 (2018) 135-146. received: 05.02.2018 accepted: 07.06.2018 published: 01.07.2018 copyright: © 2018 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. introduction n the last decades, the number of houses in the developing countries has increased dramatically due to the increase in the average income. these structures should be preserved in good conditions for longer life spans by carrying out periodical maintenance and rehabilitation. if the structures are made of concrete, high quality of care should be given, because concrete deterioration can be caused by a variety of factors, including natural hazards, climate changes, overloading, etc. these conditions could result in corrosion, cracking, local damages, or in extreme cases which can all lead to concrete failure however a crack maybe the first sign of a serious defect which may affect the serviceability or the stability of the building [1]. the cracks can be prohibited or at least minimized by the inclusion of fibers in the cementitious matrix. fibers can improve several mechanical properties of the hardened mortar such as post-cracking response, toughness, flexural strength and ductility; they can also reduce the water permeability and the creep [2]. currently, there are a large variety of i http://www.gruppofrattura.it/va/45/6.mp4 a. benyahia et alii, frattura ed integrità strutturale, 45 (2018) 135-146; doi: 10.3221/igf-esis.45.11 136 fiber options for reinforcing concrete, available in the marketplace including steel, glass, synthetic, and natural fibers. among them, the polypropylene fibers (ppf), as one of the synthetic fibers, is the most frequently used type due to its affordable cost, better distribution in concrete, and avoidance of corrosion spots on the concrete surface which could be made by using the steel fibers. singh et al. [3]. reported that the fracture, impact resistance toughness and fatigue properties can be improved significantly when using polypropylene fibers in the cement mortar mixture. however, the fiber addition can reduce the mortar workability. the better dispersion of fibers in a mortar and more workability characteristics are the key factors to obtain successful fiber-reinforced mortar for repair applications [4]. the self-compacting mortar mixture (scm) can provide many advantages. self-compacting mortar, as the name indicates is a highly flowable mortar which can be placed without any external consolidation [5]. nowadays, the self-compacting mortar is specially designed for repair applications [6]. the scrm technology can provide better filling capacity, especially in the heavily reinforced sections and the narrow spaces [7, 8]. the scms mix requires a significant amount of mineral admixtures content compared to the ordinary mortar [9]. the use of mineral admixtures in self-compacting mortars mix can improve rheological and mechanicals properties and durability. since that cement is one of the most expensive components of concrete or mortar, the use of mineral admixture as a replacement of cement is one of the economic solutions. however, mineral admixtures are not available in all regions and would be expensive if imported which makes their imports more expensive. this promotes the valorization of other available local materials (natural, waste or by-products) which can be used as mineral additives for the production of repair materials. therefore, due to their high availability in algeria, limestone dust (ld) and natural pozzolan (np) could be successfully and economically used as mineral admixtures in self-compacting mortar production. during extraction and processing of limestone rocks, huge amounts of fines called limestone dust (ld) are generated forming unsold stocks. therefore, in the presence of wind, these fines are transported and can affect the health workers as well as the people living near quarries [10]. incorporation of limestone dust in construction works will solve the problem of disposal of these fines. limestone dust has been successfully used in concrete or mortar as a sand replacement. however, few researches have been conducted in the area of scc using this fines as a partial cement replacement. zhu and gibbs[11]. observed that incorporating limestone powder in scc can accelerate cement hydration and improve the early strength. chi et al., 2004 reported that it is possible to use up to 15% of limestone fines in concrete manufacture without compromising its mechanical strength. felekoglu et al. [12]. investigated the effect of quarry dust on scc mix. they stated that quarry dust powder reduced the superplasticizer content and enhanced the 28-day’s compressive strength. dehwah [13]. reported that using of quarry dust in scc mix enhances their mechanical properties. natural pozzolans are siliceous or siliceous and aluminous materials produced during magmatic eruptions. these materials do not harden themselves when mixed with water, but when finely ground the desired fineness and in presence of water, they react with dissolved calcium hydroxide (ca(oh)2) at ordinary temperatures to form strength-developing calcium silicate (c-s-h gel) and calcium aluminate compounds. natural pozzolans have been used successfully since a long time as cement replacement in concrete industry for many purposes to bring down the cost of opc [14] as well as to produce more environmental friendly concretes [15]. in addition, its engineering properties have been also subjected to investigation [16, 17]. indeed, these materials have been used to reduce the hydration heat evolution and to increase strength and durability characteristics of mortar. but only a few studies[18-21 ] were carried out to investigate the effect of natural pozzolans on scc . the main goal of this research is to develop self-compacting repair mortars with available local materials such as limestone dust and natural pozzolan, and the study of the engineering properties behavior of the produced repair materials. the main goal of this research is to investigate the engineering properties behavior of self-compacting repair mortars made by the available local materials such as limestone dust and natural pozzolan. materials, mixture proportions and testing methods materials used ll the repair mortars mix were prepared using ordinary portland cement cem i 42,5 in accordance with en 1971[22]. the chemical composition and physical characteristics of opc were obtained from the lab result and given in tab. 1. two types of local mineral admixtures; limestone dust and natural pozzolan were used. these materials were milled to a particle-size distribution with a mean-particle diameter (d50) of 125µm. tab. 1 also presents the chemical composition and physical properties of these two fillers. modern superplasticizers based on chains of modified polycarboxylic ethers in accordance with en 934-2 [23], with a solid content of 30% and density of 1.065 g/cm3 was used. a short ppf fiber with a length of 12mm, diameter of 0.3mm, modulus of elasticity of 3 kn/mm2 and density of a a. benyahia et alii, frattura ed integrità strutturale, 45 (2018) 135-146; doi: 10.3221/igf-esis.45.11 137 0.9g/m3 was used. coarse aggregates used in the formulations of repair materials mix were crushed limestone gravel, with dmax of 15 mm and specific gravity of 2.56. siliceous river sand, with a specific gravity of 2.42, dmax of 3 mm and fineness modulus of 1.65 was used. particles size distribution of coarse and fine aggregates are also presented in fig.. 1. physical properties cement limestone dust pozzolan specific gravity 3.10 2.72 2.63 specific surface area (m2/kg) 350 470 550 compressive strength (mpa) 42.5 chemical properties (%) cao 63.91 52.57 10.88 sio2 21.58 4.58 48.1 al2o3 4.44 0.41 18.83 so3 1.93 0.01 0.51 fe2o3 5.36 0.42 10.6 mgo 1.64 0.22 4.38 na2o 0.11 0.01 0.80 k2o 0.22 0.13 0.20 loss of ignition 0.78 41.6 5.70 table 1: characteristics of ordinary cement, limestone dust and natural pozzolan. figure 1: grading of gravel and sand. mixture proportions in order to evaluate the influence of local mineral admixtures on the properties of repair mortar (scrms), two types of mortar mixtures containing 10% ld and 20% np as partial opc replacements were prepared in comparison with a control mortar (tab. 2). the water-to-powder ratio and the volume fraction of polypropylene fibers were kept constant in all the scrms mixtures. appropriate adjustments were conducted in the amount of sp in each mixture to achieve rheological properties as recommended by the efnarc (2005). the substrate concrete (subc) is an ordinary portland cement concrete usually used in the construction. the mix proportion of the subc is also presented in tab. 2. repair materials cement ld np p water sand gravel w/p sp ppf scrm-0 685 00 00 685 260 1274 -0.38 7.55 1.2 scrm-10ld 616.5 68.5 00 685 260 1274 -0.38 6.50 1.2 scrm-20np 548 00 137 685 260 1274 -0.38 8.45 1.2 subc 340 ---170 720 1130 0.5 -- table 2: mixture proportions of scrms and subc (kg/m3). a. benyahia et alii, frattura ed integrità strutturale, 45 (2018) 135-146; doi: 10.3221/igf-esis.45.11 138 testing methods the self-compactness characteristics of all the repair materials mix were evaluated by using a mini-slump flow and mini-vfunnel flow time tests according to efnarc [24]. the mini slump-flow was used to describe the ability of the fresh mix to deform under its own weight in unconfined conditions. the mini v-funnel flow time can be used to evaluate the flowability or viscosity of the repair materials mix. the fresh unit weight of repair mortars was determined according to en 1015-6 [25]. compressive and flexural strengths tests of scrms samples were conducted in accordance to en 121906 [26]. three prism specimens measuring 40×40×160 mm was cast for both compressive and flexural strengths, for each repair mortar. all the repair mortars samples were demolded and tested in the laboratory after 1, 7 and 28 days. the mechanical properties of substrate concrete (subc) such as compressive and splitting-tensile strengths were determined on 100 mm diameter and 200 mm height cylinder specimens after 28-days. the flexural strength test was determined on 70×70×280 mm3 beam samples at 28 days. the dynamic modulus of elasticity for all the repair mortars was determined after 28 days by the resonant frequent method using the ultrasonic pulse velocity test [27] (fig. 2). figure 2: test on dynamic modulus of elasticity of scrms samples. the specimen was a cylinder with a diameter of 50 mm and height of 60 mm. after determining the ultrasonic velocity through the specimen, the ed is calculated as follow: 2 d e ρv (1) where, ed is the elastic modulus (gpa), ρ is the density of the dry samples (kg/m3) and v is the ultrasonic velocity (m/s). in order to evaluate the durability characteristics of the produced repair mortars, the capillary water absorption coefficient was measured according to en 1015-18 [28]. after 28-days of curing, the scrms prism specimens (40×40×80 mm) were introduced in the oven at 60°c until mass stabilization. a resin layer covered the lateral sides of the prisms. the dry mass of the prisms was noted, where these prisms were vertically placed over a grid in a watertight tray containing 5mm water depth. the capillary water absorption coefficient of the mixtures at 28 days was calculated as follows: m c a t  (2) the adhesion between produced repair materials (scrms) and concrete substrate (subc) was evaluated by the slant shear test procedure according to astm-c882 [29]. the quantification of bond strength by this test was justified by the excellent results reported in previous studies [30, 31]. in the slant shear test, each type of repair mortar was bonded to a substrate concrete sample which has slant plane inclined at 30° angle from vertical axis. it should be noted that before casting the repair materials, the concrete substrates were surface treated by the sandblasting then by dry brushing to ensure a better bond strength [32, 33]. the composite samples were 76 mm in diameter and 152 mm in height thus obtained (see fig. 3) were tested under a compressive load using the conventional procedure according to astm c39 [34]. the bond strength can be calculated as follow: maxfs a  (3) a. benyahia et alii, frattura ed integrità strutturale, 45 (2018) 135-146; doi: 10.3221/igf-esis.45.11 139 where, s is the bond strength (mpa), fmax is the maximum applied compressive force (kn) and a is the area of the interface. the slant surface area is given: 2π a 4 sin30      (4) figure 3: composite cylinder samples subjected to slant shear. results and discussion mini-slump flow he results of the mini-slump flow test for all tested repair materials mixtures are plotted in fig. 4. all a repair mortars were designed to satisfy the requirement of scms limits [24], which were obtained by adjusting the content of the sp. it can be seen from the fig. 4 that mixtures containing 10% ld showed a better flowability when compared to the mixture containing 20% np. the required amount of sp to achieve the target flowability for scrm-10 ld decreased by 0.9 liters compared to the control mortar mix (see tab. 2). this can be explained by the higher fineness of the ld filler particles compared to the cement, which improves the packing density of cement, leading to decreasing the retained water in the mortar skeleton. this was also reported by several researchers such as fujiwara et al. [35] and ellerbrock et al. [36]. however, scrm-20np mix required a slightly higher amount of sp (1.05 liter) than that used for the scrm0 mix to achieve the desired flowability. this behavior can be attributed to the higher fineness and the irregular particles shape of np. this also confirms the results of previous works on the natural pozzolan [37-39]. figure 4: mini-slump flow for scrms. mini v-funnel flow time the flow time results obtained from the mini v-funnel showed that the observed values for all scrms mixtures are included in the efnarc specifications (fig. 5). the incorporation of 10% ld in the scrm1 mix resulted in a flow time t a. benyahia et alii, frattura ed integrità strutturale, 45 (2018) 135-146; doi: 10.3221/igf-esis.45.11 140 very close then that of control mortar mix. in contrast, the scrm-20np mixture showed a slightly higher flow time. this is in agreement with previous works [40,18]. figure 5: mini v-funnel flow time for scrms. fresh unit weight the measured unit weight values for the scrm-0, scrm-10ld and scrm-20np mix were 2210, 2115, and 2193 kg/m3, respectively. from these results, it can be seen that cement replacement with 10% ld and 20% np yielded about 4.3% and 1.0% reduction in the density for fresh scrm-10 and scrm-20np mix respectively, compared to that of the control mortar mix. this was due to the lower density values of the ld and np particles compared to the cement particles (see tab. 1). cement replacement with 10% ld in the scrm-10ld mix did not increase fresh density compared to that obtained by 20% np in the scrm-20np, despite the density of the ld which was higher than that of the np. this can be justified by the higher fineness of the np particles (550 m2/kg) compared to that of the ld (470 m2/kg) which led to a higher matrix densification of scrm-20np. figure 6: variation of compressive strength with age for scrms. compressive strength fig. 6 shows the measured compressive strength of produced repair mortars (scrms) at 1, 7 and 28 days. the compressive strength of mortar mix containing 10% ld and 20% np was lower than that of the control mortar mix at all ages. the highest compressive strength was obtained by the control mortar mix, followed by the mortar containing 20%np and then that containing 10% ld. except for 1-day of curing, the compressive strength of scrm-10 ld was close (16.87 mpa) to that of the control mortar (17.34 mpa) but exceeded that of the scrm-20np (12.81mpa). this result is consistent with previous studies [41, 16]. this behavior can be attributed to the fact that hydration provides/produces monocarbo-aluminate, when the finely limestone dust (caco3) reacts with c3a [42, 43]. moreover, the decrease in the compressive strength of the scrm-20np at 1-day can be attributed to the slowness of the pozzolanic reaction [44]. however, the strength gain was more pronounced for scrm-20np beyond 7 days of curing. the compressive strength of scrm-20np was 47 mpa and continues to increase and reached 56 mpa at 28-days of curing which was slightly lower a. benyahia et alii, frattura ed integrità strutturale, 45 (2018) 135-146; doi: 10.3221/igf-esis.45.11 141 than those of the control mixture (57.6 mpa). this can be attributable to the higher rate of c-s-h gel formed during cement hydration [45, 46]. however, when the curing age extends from 7 to 28-days, the strength gain for scrm-10ld was only 13%. further, at 28 days, the compressive strength of scrm-10ld was 20% lower that that of the control mixture. the compressive strength reduction of scrm-10ld can be attributed to the lower fineness and the slowness of the pozzolanic reaction of the ld (see tab. 1) compared to that of the np [47]. in addition, fig. 6 shows that all the produced repair materials have high compressive strength values which can meet the requirement for class r4 specified by the en 1405-3 [48]. flexural strength the results of flexural strength of repair mortars at 1, 7 and 28-days are shown in fig. 7. it can be seen that both compressive strength and flexural strength development show a similar trend. for instance, at 1-day of curing, the flexural strength of scrm-20np is approximately 20%, higher than that of scrm-10ld. however, for scrm-10ld mixture, no significant flexural strength gain was observed beyond 7-days. this result was in accordance with the findings reported by [9]. in addition, at 28-days of curing, using 20% np in scrm-20np mix showed flexural strength values very close (9.1 mpa) to that of scrm-0 (9.5 mpa). the increase in scrm-20np strength can be explained by the improvement of the aggregate (sand)-paste bond due to the densification of the transition zone (itz) and the formation of more secondary cs-h gel [41]. figure 7: variation of flexural strength with age for scrms. figure 8: variation of dynamic modulus of elasticity with age for scrms. dynamic elastic modulus for all repair mortars, the dynamic elastic modulus (ed) for all repair mortars was measured at 7 and 28-days and the results are presented in fig. 8. in general, the results clearly showed the effect of mineral additions on the development of the ed with time. the obtained results showed that the ed decreases with increasing the replacement rate of cement by ld and np. the highest modulus values were obtained by the control repair mix at all ages, due to the high amount of cement content (0% replacement). the 7 and 28-days ed values determined for the scrm-10ld were 6% and 9% a. benyahia et alii, frattura ed integrità strutturale, 45 (2018) 135-146; doi: 10.3221/igf-esis.45.11 142 respectively, lower than those measured for the scrm-0. the corresponding reductions for the scrm-20np were 5% and 8%. this finding was consistent with that obtained by [49]. in summary, the ed of scrm-0, scrm-10ld and scrm-20np at 28-days are 28gpa, 26.5 gpa and 25.8 gpa respectively, which were higher than the lower limit (20 gpa) required by the en 1504-3 standards for class r4 repair mortars. water absorption the capillary water absorption test was carried out over a 24-hour period for the three investigated mortars. the capillary absorption coefficient values after the 24-hour ranged between 0.30 and 0.48 kg/m2/h0.5, as shown in fig. 9. the lowest capillary absorption coefficient of 0.30 kg/m2/h0.5 was obtained by the scrm-20np (27% less than the scrm-0), which indicates a lower porosity. najimi et al. [14] reported that np can reduce significantly the concrete porosity due to its filling effect and pozzolanic reaction (the formation of secondary c–s–h gel), which can reduce the water mobility inside the mortar matrix and hence, reduce the capillary absorption. on the other side, the highest capillary absorption coefficient was obtained by the scrm-10ld (0.48 kg/m2/h0.5). this might have occurred due to the lake of the ld particles to block effectively the capillary pores. as a conclusion, all of the tested mortar samples meet the requirement for class r4 according to the en 1504-3. the en 1504-3 specifies 0.5 kg/m2/h0.5 as an upper limit for the water absorption after 24h of testing. figure 9: evolution of water absorption after 24 hours for scrms. slant-shear strength tab. 3 presents the development of bond strength in the various composite cylinders specimens (scrms/subc) at 7 and 28-days. at all ages, the slant shear strength values of composite cylinders scrm-10ld/subc and scrm-20np/subc were less than the control composite specimens scrm-0/subc. the 7-days slant shear strength of the control composite specimens was 20.1 mpa, whereas scrm-10ld/subc and scrm-20np/subc specimens showed a decrease of 10% and 28%, respectively, compared to the control composite specimens. at 28-days, the bond strength values of scrm10ld/subc and scrm-20np/subc specimens kept on increasing and reached 21.1 mpa and 20.4 mpa, respectively, which are 9% and 12% lower than that of the scrm-0/subc. the slant shear strength improvement of scrm10ld/subc specimens could be explained by the higher stiffness (higher ed) of repair material with 10% ld (scrm10) than the mortar containing 20% np (scrm-20np). another explanation for this, that the textural shape and angularity of the ld particles can increase the friction at the interface between repair material (scrm-10ld) and existing concrete, thus leading to an improvement of the bond strength [50]. furthermore, the significant bond strength gain of scrm-20np/subc composite at 28-days, as seen in tab. 3 (up to 2 times larger than that of the scrm-10ld/subc) may be due to the high pozzolanic effect that improved the microstructure at the itz between the scrm-20np mix and subc. besides, the slant shear test, composite cylinder specimens showed two different failure modes (please see tab. 4), monolithic failure and failure in the substrate. at 7-days, all composite cylinder specimens exhibited a monolithic rupture mode, where cracking and fracturing can be observed in both the repair materials and substrate concrete. at 28-days, all the fractures were occurred in the substrate concrete, which clearly indicated that the substrate concrete was weaker than the produced repair materials. based on the results presented in tabs. 3 and fig. 10, it can be concluded that using 10% ld or 20% np are considered as suitable materials for use as cement replacement to produce self-compacting repair mortars, because all the repair materials developed in this study using ld and np, meet the standards requirements for aci [51]. a. benyahia et alii, frattura ed integrità strutturale, 45 (2018) 135-146; doi: 10.3221/igf-esis.45.11 143 composite samples slant-shear strength s, mpa 7-days 28-days scrm-0/subc 20.1 23.2 scrm-10ld/subc 18.2 21.1 scrm-20np/subc 14.5 20.4 aci bond strength range 6.9-12.4 13.8-20.1 table 3: slant shear strength results.   table 4: failure mode for composite samples in slant-shear test (a), (b) and (c) monolithic failure at 7-days, and (d), (e) and (f) substrate failure at 28-days conclusions and future trends he main conclusions according to the experimental results are summarized next: 1) it has been observed that the efficiency of modified polycarboxylic scwms decreases compared to the control mortar with replacement cement content up to 10% ld, and vice-versa, with np content up to 20%, in comparison with control mortar mix. 2) although the density of the ld is higher than the np, the use of 10% of ld in the scrm-10np mix has no significant effect on the wet density compared to the 20% np in the scrm-20np mix, due to the higher fineness of the np which leads to a higher matrix densification. t a. benyahia et alii, frattura ed integrità strutturale, 45 (2018) 135-146; doi: 10.3221/igf-esis.45.11 144 3) both limestone dust and natural pozzolan affect the compressive strength of scrms mix. at 1-day of curing, the compressive strength of scrm-10 ld was close (16.87 mpa) to that of control mortar (17.34 mpa). from 7 to 28-days, using 20%np contributes significantly to the strength development of the scrm-20np mix, compared to that of the mortar containing ld. the compressive strength of scrm-20np was 47 mpa and kept on increasing and reached 56 mpa at 28-days of curing with only 3% decrease compared to that of the control mortar (57.6 mpa). however, all the produced repair mortars showed compressive strength values higher than the lower limit of the class r4 (en 1504-3). 4) the dynamic modulus of elasticity decreases with increasing the substitution rate of cement with ld and np. the incorporation of 10% of ld led to an increase in the ed at 7 and 28 days higher than 20% np addition. it should be noted that at 28 days, all repair mortars produced, showed higher ed than the lower limit (20 gpa) specified by the en 1504-3 standard for class r4. 5) for a good durability of repair materials used in structural applications as class r4. en 1504-3 standard requires maximum water absorption value 0.5 kg/m2/h0.5 at 24 h. this study showed that all tested repair mortars meet this requirement. the scrm-20np exhibited the lowest capillary absorption coefficient than scrm-10ld, due to the filling effect of ultrafine particles and the pozzolanic reaction (the formation of secondary c–s–h gel) of the np. 6) in 7-days slant shear tests, it has been noticed an increment of bond strength in shear of the scrm-10ld/subc specimens. but after this age (28-days), a slight increase of bond strength value was observed. whereas, the scrm20np/subc specimens showed a bond strength gain two times larger than that of the scrm-10ld/subc at 28-days. additionally, all composite specimens exhibited monolithic rupture mode at 7-days and substrate failure at 28-days without interface failure between repair materials and substrate. finally, it is important to note that this study does not cover all the required characteristics to examine repair materials for damaged concrete structures. furthers investigations on compatibility issues such as dimensional change/stability of the self-compacting repair mortars-based ld or np are recommended. references [1] schlangen, e. and joseph, c. (2009). self-healing processes in concrete. self-healing materials fundamentals, design strategies and applications, s. k. ghosh ed, willey press, weinheim, pp. 141–179. doi: 10.1002/9783527625376.ch5. [2] yazıcı, ş., arel, h. ş. and. tabak ,v. (2013). the effects of impact loading on the mechanical properties of the sfrcs. construction and building materials, 41, pp. 68-72. doi : 10.1016/j.conbuildmat.2012.11.095. [3] singh, s., shukla, a. and brown, r. (2004). pullout behavior of polypropylene fibers from cementitious matrix. cement and concrete research, 34, pp. 1919-1925. doi: 10.1016/j.cemconres.2004.02.014. [4] kuder, k.g., ozyurt, n., mu, e.b. and shah, s.p. (2007). rheology of fiber-reinforced cementitious materials. cement and concrete research. 37, pp. 191-199. doi: 10.1016/j.cem.con.res.2009.08.032. [5] kanadasan, j., fauzi, a.f.a., razak, h.a., selliah, p., subramaniam, v. and yusoff, s. (2015). feasibility studies of palm oil mill waste aggregates for the construction industry. materials. 8, pp. 6508–6530. doi: 10.3390/ma8095319 [6] courard, l., darimont, a., willem, x., geers, c. and degeimbre, r. (2002). repairing concretes with self-compacting concrete: testing methodology assessment. proceeding of the first north american conference on the design and use of self-consolidating concrete, pp. 267–274. http: hdl.handle.net/2268/59165. [7] cyr, m., legrand, c. and mouret, m. (2000). study of the shear thickening effect of superplasticizers on the rheological behavior of cement paste containing or not mineral admixtures. cement and concrete research, 30, pp. 1477–1483. doi: 10.1016/s0008-8846(00)00330-6. [8] khayat, k.h. and de schutter, g. (2014). mechanical properties of self-compacting concrete. rilem state-of-theart reports, pp. 271, isbn: 978-3-319-03245-0. [9] erdoğan, t.y. (1997). admixture for concrete. metu press. turkey. [10] azad, s. a and mittal, a. (2006). the stone quarrying industry around delhi-impact on worker and the environment. [11] zhu, w., and gibbs, j. c. (2005). use of different limestone and chalk powders in self-compacting concrete. cement and concrete research, 35, pp. 1457–1462, doi: 10.1016/j.cemconres.2004.07. [12] felekoglu, b., tosun, k., baradan, b., altun, a. and uyulgan, b. (2006). the effect of fly ash and limestone fillers on the viscosity and compressive strength of self-compacting repair mortars. cement and concrete research, 36, pp. 1719–1726. doi:10.1016/j. cemconres.2006.04.002. a. benyahia et alii, frattura ed integrità strutturale, 45 (2018) 135-146; doi: 10.3221/igf-esis.45.11 145 [13] dehwah, h.a.f. (2011). mechanical properties of self-compacting concrete incorporating quarry dust powder, silica fume or fly ash. construction and building materials, 26, pp. 47–551. doi: 10.1016/j.conbuildmat.2011.06.056. [14] najimi, m., sobhani, j., ahmadi, b. and shekarchi, m. (2012). an experimental study on durability properties of concrete containing zeolite as a highly reactive natural pozzolan. construction and building materials, 35, pp. 10231033. doi: 10.1016/j.conbuildmat.2012.04.038. [15] meyer, c. (2009). the greening of the concrete industry. cement and concrete composites, 31, pp. 601605. doi:10.1016/j. cemconcomp.2008.12.010. [16] ghrici, m., kenai, s., said mansour, m., and kadri, e. (2006). some engineering properties of concrete containing natural pozzolana and silica fume. journal of asian architecture and building engineering. 5, pp. 349-354. doi: 10.3130/jaabe.5.349. [17] kaid, n., cyr, m., julien, s. and khelafi, h. (2009). durability of concrete containing a natural pozzolan as defined by a performance-based approach. construction and building materials, 23, pp.3457-3467. doi: 10.1016/j.conbuildmat.2009.08.002. [18] belaidi, a., azzouz, l., kadri, e. and kenai, s. (2012). effect of natural pozzolana and marble powder on the properties of self-compacting concrete. construction and building materials, 31, pp. 251-257. doi : 10.1016/j.conbuildmat.2011.12.109. [19] behfarnia, k. and farshadfar, o. (2013). the effects of pozzolanic binders and polypropylene fibers on durability of scc to magnesium sulfate attack. construction and building materials, 38, pp. 38:64-71. doi: 10.1016/j.conbuildmat. 2012.08.035. [20] shamsad, a., saheed, a., maslehuddin, m., kalam, a. (2014). properties of self-consolidating concrete made utilizing alternative mineral fillers. construction and building materials, 68, pp. 268-276. doi: 10.1016/j.conbuildmat.2014.06.096. [21] saheed, a., shamsad, a., maslehuddin, m. and al-gahtani, hj. (2015). properties of scc prepared using natural pozzolana and industrial wastes as mineral fillers. cement and concrete composites, 62, pp.125-133. doi:10.1016/j. cemconcomp.2015.06.001. [22] en 197-1(2000). cement, composition, specifications and conformity criteria for common cements. [23] en 934-2 (2009). admixtures for concrete, mortar and grout part 2: concrete admixtures definitions, requirements, conformity, marking and labeling. [24] efnarc. (2005). the european guidelines for self-compacting concrete: specification, production and use. european federation for specialist construction chemicals and concrete systems. [25] en 1015-6 (1999). methods of test for mortar for masonry. determination of bulk density of fresh mortar. [26] en 12190-6 (1999). products and systems for the protection and repair of concrete structures-test methods determination of compressive strength of repair mortar. [27] en 12504-4 (2004). testing concrete. determination of ultrasonic pulse velocity. [28] en 1015-18. (2002). methods of test for mortar for masonry. determination of water absorption coefficient due to capillary action of hardened mortar. [29] astm c882. (1999). standard test method for bond strength of epoxy-resin systems used with concrete by slant shear. [30] climaco, j. and regan, p. (1989). evaluation of bond strength between old and new concrete proc. 4th int. conf. on structural faults and repair, london, pp.115-122. doi: https://doi.org/10.1680/macr.2001.53.6.377. [31] knab, l. and spring, c. (1989). evaluation of test methods for measuring the bond strength of portland cement based repair material to concrete. cement and concrete aggregate, 11, pp. 3-14. doi: 10.1520/cca10096j. [32] castillo, l. s. and aguado, de c. a. (2012). bi-layer diaphragm walls: evolution of concrete-to-concrete bond strength at early ages. construction and building materials, 31, pp. 29-37. doi: 10.1016/j.conbuildmat.2011.12.090. [33] santos, d. s., santos, p. m. d., and dias-da-costa d. (2012). effect of surface preparation and bonding agent on the concrete-to-concrete interface strength. construction and building materials, 37, pp. 102-110. doi: 10.1016/j.conbuildmat.2012.07.028. [34] astm c39-03. (2003). standard test method for compressive strength of cylindrical concrete specimens. [35] fujiwara, h., nagataki, s., otsuki, n. and endo, h. (1996). study on reducing unit powder content on high-fluidity concrete by controlling powder particle size distribution. proceeding of japan society of civil engineering, 30, pp.117-127. doi:10.2208/jscej.1996.532_67. [36] ellerbrock, h. g., and spung, s. (1990). particle size distribution and properties of cement: part iii influence of grinding process. zement-kalk-gips, 43, pp.13-19. [37] uzal, b., turanli, l., mehta, pk. (2007). high-volume natural pozzolan concrete for structural applications. aci a. benyahia et alii, frattura ed integrità strutturale, 45 (2018) 135-146; doi: 10.3221/igf-esis.45.11 146 materials joural, 104, n0 5, pp. 535–8. [38] feng, n., li, g. and zang, x. (1990). high-strength and flowing concrete with a zeolitic mineral admixture., cemet and concrete aggregate, 12, pp. 61–69. doi: 10.1520/cca10273j. [39] kaid, n., cyr., m. and khelafi, h. (2015). characterization of an algerian natural pozzolan for its use in eco-efficient cement. international journal of civil engineering, 13(4a), http: ijce.iust.ac.ir/article-1-974-en.html. doi: 10.22068/ijce.13.4.444. [40] benabed, b., soualhi, h., belaidi, a. s. e., azzouz, l. and kenai, s. (2016). effect of limestone powder as a partial replacement of crushed quarry sand on properties of self-compacting repair mortars. journal of building materials and structures, 1, pp.15-30. [41] shannag, m j. (2000). high strength concrete containing natural pozzolan and silica fume. cement and concrete composite, 22, pp. 399-406. doi: 10.1016/s0958-9465(00)00037-8. [42] bonavetti, v., donza, h., rahhal, v. and irassar, e. (2000). influence of initial curing on the properties of concrete containing limestone blended cement. cement and concrete research, 30, pp. 703-708. doi: 10.1016/s0008-8846(00)00217-9. [43] temiz, h., kantarcı, f. (2014). investigation of durability of cem ii b-m mortars and concrete with limestone powder, calcite powder and fly ash, construction and building materials, 68, pp. 517-524. doi:10.1016/j. conbuildmat.2014.06.078. [44] lemonis, n., tsakiridis, p.e, and katsiotis, n.s., antiohos, s., papageorgiou, d., katsiotis, m.s. and beazi-katsioti, m. (2015). hydration study of ternary blended cements containing ferronickel slag and natural pozzolan. construction and building materials, 81, pp. 130-139. doi: 10.1016/j.conbuildmat.2015.02.046. [45] lawrence, p., cyr, m. and ringot, e. (2005). mineral admixtures in mortars effect of type, amount and fineness of fine constituents on compressive strength. cement and concrete research, 35, pp. 1092-1005. doi: 10.1016/j.cemconres.2004.07.004. [46] guru, j.j., sashidhar, c., ramana, r.i.v., annie, p. j. (2013). micro and macrolevel properties of fly ash blended selfcompacting concrete. materials and design, 46, pp. 696-705. doi: 10.1016/j.matdes.2012.11.027. [47] sarıdemir, m. (2013). effect of silica fume and ground pumice on compressive strength and modulus of elasticity of high strength concrete. construction and building materials, 49, pp. 484-489. doi: 10.1016/j.conbuildmat.2013.08.091. [48] en 1504-3 (2006). products and systems for the protection and repair of concrete structures. definitions, requirements, quality control and evaluation of conformity. structural and non-structural repair. [49] turk, k. (2012). viscosity and hardened properties of self-compacting mortars with binary and ternary cementitious blends of fly ash and silica fume. construction and building materials, 37, pp. 326-334. doi:10.1016/j. conbuildmat.2012.07.081. [50] aliabdo, a. and elmoaty, m. a. (2012). experimental investigation on the properties of polymer modified scc. construction and building materials, 34, pp. 584-592. doi: 10.1016/j.conbuildmat.2012.02.067. [51] aci committee 546. (2004). concrete repair guide (aci 546r-04). american concrete institute, farmington. << /ascii85encodepages false /allowtransparency false /autopositionepsfiles true /autorotatepages /none /binding /left /calgrayprofile (dot gain 20%) /calrgbprofile (srgb iec61966-2.1) /calcmykprofile (u.s. web coated \050swop\051 v2) /srgbprofile (srgb iec61966-2.1) /cannotembedfontpolicy /error /compatibilitylevel 1.4 /compressobjects /tags /compresspages true /convertimagestoindexed true /passthroughjpegimages true /createjobticket false /defaultrenderingintent /default /detectblends true /detectcurves 0.0000 /colorconversionstrategy /cmyk /dothumbnails false /embedallfonts true /embedopentype false /parseiccprofilesincomments true /embedjoboptions true /dscreportinglevel 0 /emitdscwarnings false /endpage -1 /imagememory 1048576 /lockdistillerparams false /maxsubsetpct 100 /optimize true /opm 1 /parsedsccomments true /parsedsccommentsfordocinfo true /preservecopypage true /preservedicmykvalues true 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/hrv (za stvaranje adobe pdf dokumenata najpogodnijih za visokokvalitetni ispis prije tiskanja koristite ove postavke. stvoreni pdf dokumenti mogu se otvoriti acrobat i adobe reader 5.0 i kasnijim verzijama.) /hun 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can be opened with acrobat and adobe reader 5.0 and later.) >> /namespace [ (adobe) (common) (1.0) ] /othernamespaces [ << /asreaderspreads false /cropimagestoframes true /errorcontrol /warnandcontinue /flattenerignorespreadoverrides false /includeguidesgrids false /includenonprinting false /includeslug false /namespace [ (adobe) (indesign) (4.0) ] /omitplacedbitmaps false /omitplacedeps false /omitplacedpdf false /simulateoverprint /legacy >> << /addbleedmarks false /addcolorbars false /addcropmarks false /addpageinfo false /addregmarks false /convertcolors /converttocmyk /destinationprofilename () /destinationprofileselector /documentcmyk /downsample16bitimages true /flattenerpreset << /presetselector /mediumresolution >> /formelements false /generatestructure false /includebookmarks false /includehyperlinks false /includeinteractive false /includelayers false /includeprofiles false /multimediahandling /useobjectsettings /namespace [ (adobe) (creativesuite) (2.0) ] /pdfxoutputintentprofileselector /documentcmyk /preserveediting true /untaggedcmykhandling /leaveuntagged /untaggedrgbhandling /usedocumentprofile /usedocumentbleed false >> ] >> setdistillerparams << /hwresolution [2400 2400] /pagesize [612.000 792.000] >> setpagedevice microsoft word numero 25 art 23 c. j. christopher et alii, frattura ed integrità strutturale, 25 (2013) 161-166; doi: 10.3221/igf-esis.25.23 161 special issue: characterization of crack tip stress field extension of the cjp model to mixed mode i and mode ii c. j. christopher, g. laboviciute, m. n. james university of plymouth, drake circus, plymouth pl4 8aa, uk mjames@plymouth.ac.uk e. a. patterson university of liverpool, brownlow hill, liverpool, l69 3gh, uk abstract. the present authors have previously proposed a novel ‘plastic inclusion’ approach for dealing with the local plasticity which occurs at the tip of a growing fatigue crack. this meso-scale model provides a modified set of crack tip stress intensity factors that include the magnitude of plastic wake-induced crack tip shielding and which have the potential to help resolve some long-standing controversies associated with plasticity-induced closure. the present work extends the cjp model to deal with the case of mixed mode i and mode ii loading and thus opens up enhanced possibilities for testing it on inclined cracks in metallic specimens. this extension requires the addition of only one new force parameter to the model, i.e. an anti-symmetric shear force on either side of the crack. keywords. mixed mode fatigue; cjp crack tip stress model; plastic inclusion; crack tip shielding. introduction he present authors have previously proposed a novel ‘plastic inclusion’ approach for dealing with the local plasticity which occurs at the tip of a growing fatigue crack [1]. localised plasticity arises from crack growth mechanisms and essentially blunts the crack, creates a reversed cyclic plastic zone, and induces shear along the crack flanks, along with the possible generation of wake contact stresses which act on the applied elastic stress field at the boundary of the elastic-plastic enclave surrounding the crack. the outcome of this meso-scale model is a modified set of crack tip stress intensity factors that include the magnitude of plastic wake-induced crack tip shielding and which have the potential to help resolve some long-standing controversies associated with plasticity-induced closure. a full-field approach has been developed for stress using photoelasticity and also for displacement using digital image correlation. this model has been termed the cjp model by the authors, and is independent of the mechanisms of plastic deformation and is therefore potentially applicable to a variety of materials. the definition of the forces on the crack allows roughness-induced closure to also be accounted for in the calculated stress intensity factors. the model can also be used to mathematically explore the effect on shape of the crack tip stress field of changes in magnitude of the various parameters; for, example, the effect of variation in magnitude of increasing positive or negative t-stress on crack tip fringe patterns. under mode i loading, the new model uses four parameters to characterize the stress fields generated by the forces in fig. 1; an opening mode stress intensity factor kf, the shear stress intensity factor ks, the retardation stress intensity factor kr, and the t-stress. in applications involving the dic technique, stress intensity factors in the new four-parameter model can be solved directly from measured displacement fields using muskhelishvili’s potential functions. t http://dx.medra.org/10.3221/igf-esis.25.23&auth=true http://www.gruppofrattura.it c. j. christopher, frattura ed integrità strutturale, 25 (2013) 161-166; doi: 10.3221/igf-esis.25.23 162 figure 1: schematic idealisations of forces acting at the interface of the plastic enclave and the surrounding elastic material, where fa is the mode i applied force generating the crack tip stress field usually characterized by ki, fb is the additional applied force induced by mode ii loading, ft represents the force due to the t-stress shown in this example as positive, fs is the interfacial shear force between the elastic and plastic zones, fc and fp together create the shielding effect. fp is the force generated by the constraint of compatibility on the plastically deformed material and fc is the contact force between the flanks of the crack generated by the interference of the plastic zones along the flanks [1]. the present work extends the cjp model to deal with the case of mixed mode i and mode ii loading and thus opens up enhanced possibilities for testing it on inclined cracks in metallic specimens. this extension requires the addition of only one new force parameter to the model, shown as fb in fig. 1, i.e. an anti-symmetric shear force on either side of the crack. the cjp model under biaxial (mode i and mode ii) loading he cjp model [1] is defined as: 1 3 1 3 02 2 2 2 y x xy2i az z z cb ln(z)z dz z z ln(z)e            (1) the extension to the model was obtained by making the coefficients a and b complex and making the assumptions biara i3 , b bbr i i  , d e 0  . 1 3 1 3 02 2 2 2 y x xy r i r i2i ( a i3b )z ib )z z cz dz z z ln(z( )b ln(z) e               (2) the elastic stress fields near the crack tip are given by: forces on plastic field forces on elastic field maximum applied load minimum applied load fs fs fs fs fs fs fs fs fay fay fay fay fax fax fpy fpy fpx fpx fpy fpy fc fc fc fc ft ft ft ft ft ft notational boundary of  plastically deformed material closed crack with flank contact ft open crack  ft forces on plastic field forces on elastic field maximum applied load minimum applied load fs fs fs fs fs fs fs fs fay fay fay fay fax fax fpy fpy fpx fpx fpy fpy fc fc fc fc ftft ftft ftft ftft ftft ftft notational boundary of  plastically deformed material closed crack with flank contact ftft open crack  ftft t http://dx.medra.org/10.3221/igf-esis.25.23&auth=true http://www.gruppofrattura.it c. j. christopher et alii, frattura ed integrità strutturale, 25 (2013) 161-166; doi: 10.3221/igf-esis.25.23 163 1 1 1 2 2 2 y r r r i 1 1 2 2 1 1 1 2 2 2 r r ix r 1 1 5 1 5 ( a cos b b sin 2 2 2 2 2 2 2 1 5 5 e 4b 8e )r r cos r sin r ln(r ) cos sin ) 4b 8e)r r c 5cos 5sin o(r 2 2 2 2 2 1 1 5 1 5 ( a cos b bos r si 7sin 2 2 n 2 2 2 2 2                                                          1 1 2 2 1 1 2 2 xy r r i 1 1 2 2 1 5 5 e 3cos 3sin c o(r 2 2 2 2 2 1 5 1 5 r b b r cos 3cos 2 2 2 2 2 2 3 3 e ln(r )cos sin o r ln(r ) cos sin ) a sin s (r 2 2 in r sin )                                                            (3) fk is defined from the asymptotic limit of y as x 0  , along y 0 , i.e. towards the crack tip from the front along the crack line: r 0 1 2 f y r rk lim 2er ln(r ))2 r ( ( a 3b 8e ) 2               (4) rk was obtained by evaluating x in the limit as x 0  , along y 0 , i.e. towards the crack tip from behind along the crack flank: r i r x 0 2 rk lim (2b e 2 4 )            (5) s k is derived from the asymptotic limit of xy as x 0  , along y 0 , i.e. towards the crack tip from behind along the crack flank: s 0 xy r r r 2 rk l a )im ( b 2           (6) the +ve sign indicates y 0 , and a –ve sign that y 0 . the quantity ii k characterizes mode ii loading, and is derived from the asymptotic limit of xy as x 0  , along y 0 , i.e. towards the crack tip from the front along the crack line: xyi ii r 0 2 r 2 bk lim 2        (7) t-stress is the transverse stress which is added to x as a constant term and is given by t c  (8) the new five-parameter model can be solved for displacement fields: http://dx.medra.org/10.3221/igf-esis.25.23&auth=true http://www.gruppofrattura.it c. j. christopher, frattura ed integrità strutturale, 25 (2013) 161-166; doi: 10.3221/igf-esis.25.23 164 1 1 2 2 x y r i 1 1 2 2 r i 1 1 1 2 2 2 r i c (u iu ) 2(b ib )z z 4 c z (b ib 2e)z z ln(z) 4 c ( a i3b )z z ln(z 2 2ez ln( ) z) e d 2d z z 2                                  (9) where xu and yu are the horizontal and vertical displacements respectively, e 2(1 )     ; 3 4   (plane strain) or 3 1       (plane stress). xu and yu are shown explicitly below with the assumption d e 0  . 1 1 1 2 2 2 x r r i i r 1 1 2 2 i 2 ( a (2b (b 2e)cos b sin e ln(r ) 3 u r 2b 2e )cos r 3b )sin r 2 2 2 3 3 3 r r (1 2 )cos sin (1 2 )sin 2 2 2 2 2 c r(1 )c 4 co os s                                            (10) 1 1 1 2 2 2 i i r r r 1 1 2 2 i y2 ( 2b ( a (b 2e )sin b cos e ln(r ) 3 u r 3b )cos r 2b 2e )sin r 2 2 2 3 3 3 r r sin (1 2 )sin (1 2 )cos 2 2 2 2 2 c r(3 )sin 4 cos                                             (11) application of the model to mixed mode crack growth hus far, the model has been tested against limited data obtained from an inclined crack in a 2mm thick 2024-t6 aluminium ct specimen with non-standard dimensions, which is shown in fig. 2. a jeweller’s saw with blade thickness of 0.15 mm was used to extend the notch tip into a 45° slit some 5 mm long, which is schematically shown in fig. 2. a fatigue crack some 2 mm long was then grown in mode i collinear with this slit. this was achieved by starting with a larger dimension ct specimen with additional loading holes in a similar fashion to the disk-shaped compact specimen described by ding et al [2]. the specimen was then machined to final dimensions and approximately 100 cycles of loading was applied in the usual orientation, so as to put the fatigue crack under a combination of mixed mode i and mode ii loading. the applied load ratio was r = 0.1 and the peak load was 1.2 kn. a dantec digital image correlation (dic) system operating in 2d mode was used to measure the crack tip displacement field and to compare the predictions of the cjp model with the measured strain field data. a facet size of 17 pixels with a centre-line pitch of 17 pixels was used with a scale of 107 pixels per millimetre. it is acknowledged that this method of cracking is not optimum, as it produces a mode i plastic wake, rather than one that reflects mixed mode loading. however, the technique gives data for a mixed mode crack tip strain field and a mode i crack wake and this is not dissimilar to the data acquired by many other workers, e.g. [2]. attention will be given in the immediate future to testing cracks of various inclinations, i.e. various mode-mixity ratios, which have been developed under true mixed mode loading, as well as under mode i loading. fig. 3 presents a comparison between the measured x and y components of the crack tip displacement and those predicted by the 5-parameter cjp mixed mode model, whilst fig. 4 show typical stress intensity data measured through a loading half cycle. in fig. 4 the stress intensity factors are all defined with respect to the local crack plane, i.e. kf and kii values are defined as respectively being perpendicular to, and parallel with, the plane of the inclined crack. the stress intensity factors can be fairly easily re-defined using simple geometry, with cartesian coordinates defined in terms of the load line t http://dx.medra.org/10.3221/igf-esis.25.23&auth=true http://www.gruppofrattura.it c. j. christopher et alii, frattura ed integrità strutturale, 25 (2013) 161-166; doi: 10.3221/igf-esis.25.23 165 and the plane of the original notch in the ct specimen, e.g. kf = (kf+kii)/√2 and kii = (kf-kii)/√2 (or the negative of this, depending on how the force directions were chosen). however, the belief of the present authors is that it is more useful to define stress intensity factors in terms of the local crack plane, because crack growth rate is governed by these local conditions. : geometry and dimensions (in millimetres) of the polycarbonate compact tension (ct) specimens used in this work. note figure 2 that the notch length (equal to the initial crack length) ai = 20 mm and the width b = w = 72 mm are defined from the centreline of the holes. dic: y-displacement a) cjp model: yb) dic: x-displacement c) cjp model: xd) : comparison between dic and cjp model predictions of the x and y-displacement fields at the tip of a crack under mixed figure 3 mode fatigue loading. http://dx.medra.org/10.3221/igf-esis.25.23&auth=true http://www.gruppofrattura.it c. j. christopher, frattura ed integrità strutturale, 25 (2013) 161-166; doi: 10.3221/igf-esis.25.23 166 : stress intensity values given by the mixed-mode cjp equation, with kf defined perpendicular to the 45° slant crack and kii figure 4 defined parallel with the slant crack in the ct specimen. conclusions he cjp model has been extended to deal with fatigue cracking under mixed mode i and ii conditions, by incorporating an additional anti-symmetric horizontal shear force into the analysis. the model appears able to accurately predict the x and y-displacement fields ahead of the tip of a crack under mixed mode loading. further work is on-going to explore the accuracy of the predictions, the values of the mixed mode stress intensity factors and their use in predicting fatigue crack growth rates. references [1] james, m.n., christopher, c.j., lu, y. and patterson, e.a., local crack plasticity and its influences on the global elastic stress field. int. j. fatigue, 46 (2013) 4-15. [2] ding, f, zhao, t. and jiang, y., a study of fatigue crack growth with changing load direction. engng fract. mech., 74 (2007) 2014-2029. t http://dx.medra.org/10.3221/igf-esis.25.23&auth=true http://www.gruppofrattura.it microsoft word numero_50_art_10_2420 r. boutelidja et alii, frattura ed integrità strutturale, 50 (2019) 98-111; doi: 10.3221/igf-esis.50.10 98 focused on fracture mechanics versus environment environmental effects on the reliability of an aisi 304 structure boutelidja racim university of badji mokhtar, department of mechanical engineering, annaba, algeria boutelidja.racim@gmail.com guedri abdelmoumene, belyamna mohammed amine university of soukahras, infra-res laboratory, soukahras, algeria guedri_moumen@yahoo.fr, beelyamina@gmail.com merzoug bachir university of badji mokhtar, department of mechanical engineering, annaba, algeria merzougbachir@yahoo.fr abstract. this work is based on the application of probabilistic fracture mechanics models to predict the reliability of pressure pipelines in nuclear power reactors. the simulation of cracking of stainless steel piping under the conditions of intergranular stress corrosion cracking (igscc) is based on the improved modified piping reliability analysis including seismic events (praise) code. the igscc is characterized by a unique damage parameter that depends on residual stresses and environmental conditions. case studies of igscc failures in nuclear power plants are presented and the contribution of environmental effects on crack initiation and leakage is discussed. for small damages we observed that the change in temperature or oxygen concentration does not affect the initiation process but their decrease contribute favourably to the decrease in the leakage probabilities. keywords. modified praise code; stress corrosion cracking environment; reliability. citation: boutelidja, r., guedri, a., belyamna, m. a., merzoug, b., environmental effects on the reliability of an aisi 304 structure, frattura ed integrità strutturale, 50 (2019) 98-111. received: 02.03.2019 accepted: 16.04.2019 published: 01.10.2019 copyright: © 2019 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. introduction amage detection and quantification mean knowing when and where it initiates; determining its propagation mode(s) and its interactions with the microstructure. thus, it leads us to the understanding, modelling, and prediction of environmentally assisted cracking processes, i.e., stress corrosion, fatigue-corrosion, and hydrogen embrittling. it is, therefore, possible to evaluate the respective role of the different chemical, mechanical, and metallurgical intervening parameters, and necessary steps to establish phenomenological models. it made enables us to quantify the effect of these d http://www.gruppofrattura.it/va/50/2420.mp4 r. boutelidja et alii, frattura ed integrità strutturale, 50 (2019) 98-111; doi: 10.3221/igf-esis.50.10 99 parameters in order to take them into account in a micromechanical modelisation. stress corrosion cracking (scc) is one of the important mechanisms in the degradation of steels. this mechanism induces material cracking due to a combined action of a sensitive material, a tensile stress, and corrosive environment (see fig. 1). in the piping of a boiling water reactor, the sensitive material in the vicinity of welds is the stainless steel aisi 304. figure 1: main types of aging and damage. the sensitivity of this material to cracking by scc is due to the precipitation of chromium carbide at the grain joints immediately adjacent to the area with lower chromium grade [1]. zhang and al. have done experimental verifications to determine the initiation time and the propagation rate of igscc in sensitized stainless steel type aisi 304 in diluted sulfate solutions [2]. many researchers have approached the probabilistic analysis of components failure due to scc based on fracture mechanics [3-10]. piping component failure probabilities under scc, including the effects of residual stresses, have been realized by guedri and al. using monte carlo simulation techniques (mcs). the results of these studies have been used to develop the input data for the analysis of failure probabilities [11-12]. the present study is incorporated in a research topic involving the optimal conception and the reliability study of precracked mechanical structures, aiming; in particular, at its application in austenitic steels under complicated solicitations. this paper is structured as follows: the first part presents relevant generalities on reliability, the second part is a general description of the piping reliability model, and the third part presents an application example with an analysis of the results. finally, a general conclusion synthesizes the analysis methodology and the main results. reliability evaluation he present section describes probabilistic fracture mechanics calculations that were performed for selected components using the praise computer code. the calculations address the failure mechanisms of stress corrosion cracking and intergranular stress corrosion cracking for components and operating conditions that are known to make particular components susceptible to cracking. comparisons with field experience showed that the praise code predict relatively high failure probabilities for components under operating conditions that have resulted in field failures. it was found that modeling assumptions and inputs tended to give higher calculated failure probabilities than those derived from data on field failures. sensitivity calculations were performed to show that uncertainties in the probabilistic calculations were sufficiently large to explain the differences between predicted failure probabilities and field experience. overview of the praise code the first version of praise [13] was developed in the 1980s by lawrence livermore national laboratory under contract to nrc, with the initial application to address seismic-induced failures of large-diameter reactor coolant piping. this version of the code addressed failures (small leaks and ruptures) associated with fabrication flaws in welds that were allowed to grow as fatigue cracks until they either caused the pipe to leak or exceed a critical size needed to result in unstable crack growth and pipe rupture. the next major enhancement to the code [14] addressed igscc and simulated t r. boutelidja et alii, frattura ed integrità strutturale, 50 (2019) 98-111; doi: 10.3221/igf-esis.50.10 100 both crack initiation and crack growth. the enhanced code allowed for crack initiation at multiple sites around the circumference of a girth weld and simulated linking adjacent cracks to form longer cracks more likely to cause larger leaks and pipe ruptures. in the early 1990s a version of praise (pc-praise) was developed to run on personal computers [15]. the mid-1990s saw the development of methods for risk-informed in-service inspection, for which there were many new applications of praise. a new commercial version of praise (win praise) was made available by dr. david harris of engineering mechanics technology that simplified the input to the code with an interactive front end [16]. during this, same time period, pnnl made numerous applications of praise to apply probabilistic fracture mechanics to support the development of improved approaches to in-service inspection [17-24]. the objective of this work was to ensure that changes to inspection requirements could be justified in terms of reduced failure probabilities for inspected components. other work at pnnl for nrc the aim of this work is to evaluate the effects of the environment changes in terms of failure probabilities. khaleel et al. [19] involved evaluations of fatigue critical components that could potentially attain calculated fatigue usage factors in excess of design limits (usage factors greater than unity).the most recent upgrades to praise [19] were developed to support these fatigue evaluations, with the upgrade consisting of a model similar to that for igscc but directed at predicting the probabilities of initiating fatigue cracks. this new model was used to develop the technical basis for changes to appendix l of american society of mechanical engineers (asme) section xi that addresses fatigue critical locations in pressure boundary components [25]. however, the code has not been maintained and upgraded in an ongoing manner. upgrades have been performed to meet the needs of immediate applications of the code and as such have served to fill very specific gaps in capabilities of praise. in the early 2012s an improved modified praise version (m-praise) [4, 11, and 12] was developed. in m-praise the modifications in the praise code included the adjustment of residual stress factors to better fit experimental data and the change of the stress intensity factors expressions to ameliorate the previous more conservative ones. other probabilistic fracture mechanics codes for piping have been developed to calculate failure probabilities for piping. the srra code [26] developed by westinghouse follows much the same approach as the praise code, but is limited to failures associated with cyclic fatigue stresses considers only preexisting fabrication flaws. fatigue crack initiation has been approximated by assuming a very small initial crack, but with only one initiation site per weld. stress corrosion cracking is similarly treated by postulating a very small initial crack, and growing the crack according to user-specified parameters for a crack growth equation. the srra code includes an importance sampling procedure that gives reduced computation times compared to the monte carlo approaches used by praise. also the model can simulate uncertainties in a wide range of parameters such as the applied stresses. the european nurbim [27] has looked at a number of codes including praise as part of an international benchmarking study. included were a swedish code nurbit [28], the prodigal code from the united kingdom [29], a code developed in germany by grs [30], a swedish code prosacc [31] and another code (struel) from the united kingdom [32]. this review concluded that none of the other benchmarked codes provided capabilities significantly different than or superior to the capabilities of m-praise. in any case, the predictions of all such codes are limited in large measure by the quality of the values that can be established for the input parameters, as well as the validation with service experience. stress corrosion cracking model the aim of this work is to evaluate the effects of the environment changes in terms of failure probabilities. the improved modified praise version (m-praise) [4, 11, and 12] takes into account the initiation in multiple sites by dividing the piping circumference. in m-praise, the occurrence of scc modulated by considering it as a two-step process: first crack initiation which is followed, in a second step, by crack propagation. time to initiation time to initiation of stress corrosion crack is considered as a function of damage parameter, dsigma, which represent effects of loading, environment and material variables on igscc. the damage parameter is given by ) (loadingent) x f (environm) x f (material = fd 321sigma (1) where f1, f2 and f3 are given by (pa) c =f 2c11 (2) where pa is a measure of degree of sensitization, given by electrochemical potentiokinetic reactivation (in c/cm2). r. boutelidja et alii, frattura ed integrità strutturale, 50 (2019) 98-111; doi: 10.3221/igf-esis.50.10 101 ( )[ ] ( ) γclog273+tcexpo =f 63 c54c22 (3) where o2 is oxygen concentration in ppm, t is temperature in degrees centigrade, and γ is water conductivity in μs/cm. the loading term f3 is considered to be a function of stress. for constant applied load case, f3 is given by ( ) σc=f 79 cc83 (4) where σ is stress in mpa. c1 to c9 are constants whose values depend on type of material. values for these constants are presented in tab.1. constant c1 c2 c3 c4 c5 c6 c7 c8 c9 value 23.0 0.51 0.18 −1123.0 8.7096 0.35 0.55 2.21 ×10−15 6.0 table 1: numerical values of constants ci used for predicting the initiation and propagation of scc for aisi304[15] the time to initiation ti for a given dsigma is considered as a random variable following lognormal distribution. the mean and standard deviation of log (ti) are given by: mean value of ( ) ( )sigmai dlog4.21 -3.10 -=tlog (5) standard deviation of ( ) 3081.0=tlog i crack size at initiation in pc-praise, shape of surface crack initiated due to igscc is considered to be semi-elliptical (fig.2), which is also consistent with shapes of stress corrosion cracks reported by helie [33] and by lu [34]. surface length of initiated cracks, (l = 2b), is assumed to be log normally distributed with a median value of 3.175 mm and a shape parameter of 0.85 [15]. depth of initiated crack is taken to be 0.0254 mm. figure 2: geometry of the part-through circumferential crack considered crack growth model the growth of very small cracks that have just initiated cannot be treated from a fracture mechanics standpoint [1]. therefore, an initiation velocity is assigned to newly initiated cracks ( ) ( ) sigma1 dlogg+j=νlog (6) where j is normally distributed and g is a constant. it can be noted that eqn. (6) is similar in form (power law) as that proposed by helie [33], based on experimental observations. for aisi 304 austenitic stainless steel, j has a mean of 2.551 and standard deviation of 0.4269, and g = r. boutelidja et alii, frattura ed integrità strutturale, 50 (2019) 98-111; doi: 10.3221/igf-esis.50.10 102 1.3447 [15]. from parametric studies carried out, a value of 5% coefficient of variation of log (ν1) was found to be critical to life of piping component [35], and hence this value is used in this study. the procedure followed for transition from initiation to fracture mechanics crack growth rate in the present study is: pre-existing cracks always grow at fracture mechanics velocity. initiation velocity is always assigned to initiate cracks. at any given time, if fracture mechanics velocity (ν2) is greater than initiation velocity (i.e. ν2 >ν1) and depth of crack is greater than 2.54 mm, that particular crack grows at fracture mechanics velocity thereafter. if the stress intensity factor for a crack is negative, the crack will not grow. fracture mechanics based crack growth velocity, ν2 (inches/year), is given by harris [15]: ( ) k15142 dc+c=νlog (7) where dk is the damage parameter given by kc+))entenvironnem(flog(c=d 13212k (8) where k is stress intensity factor, c12, c13 and c15 are constants and c14 is normally distributed. for aisi 304 austenitic stainless steel, c12 = 0.8192, c13 = 0.03621 and c15 = 1.7935; mean value of c14 = -3.1671 and standard deviation of c14 =0.7260 [15]. from a probabilistic failure analysis of austenitic nuclear pipe against scc, priya in [35] inferred that expressions given in praise for computation of stress intensity factors for modeling crack propagation need modification. this modification has been introduced by using well-accepted expressions given in asm handbook [36], and with modified praise approach, stochastic propagation of stress corrosion cracks with time has been studied. it has been noted that trend of distribution of crack depths at initial stages is in satisfactory agreement with relevant experimental observations reported in literature. multiple cracks in materials subjected to igscc, many cracks would initiate successively and propagate simultaneously, and hence multiple cracks can be present in a given weld. the expressions, given in praise, for determining statistical properties of ti are mainly based on data from laboratory experiments on specimens about 50 mm long. hence, these expressions are applicable to specimens of about 50 mm only. this is taken into account in praise, by considering a given weld in the pipe to be composed of 50 mm segments adding up to length of weld. initiation time for each segment is assumed to be independent and identically distributed. coalescence of crack the multiple cracks that may be present can coalesce as they grow. linkage of two cracks takes place if spacing between them is less than the sum of their depths. after coalescence of two cracks, the dimensions of modified crack are given by eq. (9). greateriswhich,aora=a,depthandl+d+l=l length, 2121 (9) where l1 and l2 are lengths of two cracks under consideration, a1 and a2 are crack depths and d is spacing between them. the operating conditions and environmental conditions show variations during the lifetime of the power plant [9]. also, there will be variations in micro-structural properties of the material of piping component. these variations should be taken into account while assessing the safety of the piping component against scc. various researchers have carried out studies on failure analysis against scc in different types of components of power plants by considering different basic variables (such as those associated with material properties and applied loading) as random, [15, 35]. however, safety assessment of nuclear power plant pipelines also involves information from expert judgment and/or data from in-service inspections. residual stresses residual stresses influence both crack initiation and propagation. the damage parameter dsigma is a function of the stress, which consists of both the applied (service-induced pressure and thermal) and residual stresses. r. boutelidja et alii, frattura ed integrità strutturale, 50 (2019) 98-111; doi: 10.3221/igf-esis.50.10 103 the crack-tip stress-intensity factor is given by resap k+k=k (10) where kap and kres are the stress-intensity factors attributable to the applied stress and residual stresses, respectively. the calculations reported here are concerned with the stress corrosion cracking behavior of small pipes [15] (102 ≤ outside diameter ≤ 254 mm). the local residual stresses at the inside surface of small pipe is treated as being normally distributed. the through–thickness distributions of stress are assumed to be linear variations between local values sampled for the inner and outer surfaces. for small pipes, the mean value of residual stress at the inner surface was 168 mpa with a standard deviation of 100 mpa. the independently sampled stress at the outside surface was 168 mpa with a standard deviation of 98 mpa. in our case, to limit the disagreement between predicted and observed leak probabilities, the adjusted residual stress level used was set at 75% of their original values. failure criteria the part-through initial stress corrosion cracks considered can grow and become unstable part-through cracks or stable or unstable through-wall cracks. the stability of the part-through or through-wall crack is checked by comparing net-section stress with the flow stress of the material. the net-section stress criterion is applicable to very tough material, and the failure is due to the insufficient remaining area to support the applied loads given by eqs. (11) and (12) (i.e. net-section stress due to applied loads becomes greater than the flow stress of the material σf ). for leakage failure, the criterion was that of a crack depth equal to the pipe-wall thickness. f crp plc net σ> aa aσ =σ (11) ( ) r a +2ab=a,h+2rhπ=a i crip (12) where ri is the internal radius of pipe, h is the pipe wall thickness, ap is the cross-section area of the pipe, acr is the area of crack, σlc and σf are the load-controlled components of stress and the flow stress, respectively. the flow stress of the material σf used in eq. (11) was taken to be normally distributed, with an expected value of 296 mpa and a standard deviation of 29 mpa. for leakage failure criterion was that a crack depth equal to the pipe-wall thickness. monte carlo simulation monte carlo simulation (mcs) is a compurized mathematical technique that takes into account the risk in the quantitative analysis and the decision making. the diverse professionals in the fields of finance, project management, energy, production, engineering, research and development, insurances, gas and oil industry, transportation and environment, have recourse to this technique. as all numerical methods, mcs has advantages and drawbacks. one within the main advantages: mcs allows to use explicit as well as implicit variables in the performance function. concerning its precision; mcs is considered as a reference method by most researchers in the fields of structural reliability. results and analysis example he application problem illustrates the use of m-praise to simulate the initiation and the growth of cracks in a welding due to the stress corrosion cracking mechanism. the necessary material properties for the initiation and growth of cracks under scc in aisi 304 steel are pre-selected in this case and introduced in the code. the only used loading cycle is the heating-cooling cycle. the used fracture criteria are presented in the section fracture criterion. the main input related to the pipe geometry, pipe material, and the working conditions for the basic case are described below (tab. 2). t r. boutelidja et alii, frattura ed integrità strutturale, 50 (2019) 98-111; doi: 10.3221/igf-esis.50.10 104 conditions for the basic case pipe geometry inner radius = 7.16 (in) wall thickness = 0.84 (in) loading stress total loading = 15.23 (ksi) working pressure = 1250 (psi) (1 (psi) = 0.00689476 (mpa)) material flow stress mean value = 44.9 (ksi) standard deviation = 1.9 (ksi) scc parameters oxygen at the start= 8 (ppm) stable oxygen at steady state = 0.2 (ppm) (1(ppm) = 0.001(g/l)) water temperature at steady state = 550 (°f) ((°f-32)*5/9 = °c) heating time = 5 (hours) cooling liquid conductivity = 0.2 (μs/cm) table 2: conditions for the basic case a lifetime of 20 years is simulated and the results printed every two years. the maximal time step for the growth of cracks under stress corrosion cracking is limited to 0.1 year, which means that during a long period of operation at steady state, the crack size, the stress intensity factors, and other computations are updated every 0.1 year. in the output file, there is a description of the data. other than the initiation probability, leak probabilities as a function of time are represented in this file. unlike the case of pre-existing cracks with a stratified sampling, the leak probability and the failure probability are obtained in the same sequence printing. in the application example, we have proceeded as follow: 1generation of pipe samples for the probabilistic analysis as showed in fig. 3. 2generation of (1000 x 10 x n) times of initiations from 1000 values of the damage parameter d. (see fig. 4). 3generation of (1000 x 10 x n) times of initiation rates from 1000 values of the damage parameter d (see fig. 5). 4computation of the cracks propagation rate based on fracture mechanics, for (1000x 10 x n) generated cracks using the values of σ, a and b. (see fig. 6). 5computation of the probabilities of initiation, leak, big leak, and of failure according to the used failure criteria. figure 3: generation of tube samples for the probabilistic analysis – schematic representation. figure 4: generation of (1000 x 10 x n) times of initiations from 1000 values of the damage parameter. r. boutelidja et alii, frattura ed integrità strutturale, 50 (2019) 98-111; doi: 10.3221/igf-esis.50.10 105 figure 5: generation of (1000 x 10 x n) times of initiation rates from 1000 values of the damage parameter, d figure 6: computation of the cracks propagation rate based on fracture mechanics, for (1000 x 10 x n) generated cracks using the values of σ, a and b. analysis of the results the objective of this work is to study the influence of the parameters characterizing the environment modification and particularly the change in the oxygen concentration and temperature during operation. effects of the change in the oxygen concentration for a temperature of 550 (°f), tab. 3 resumes the steady state oxygen concentrations used to illustrate the effect of their variation. studied case case1 case12 case13 case14 case15 oxygen concentration (ppm) 0.2 0.05 0.01 0.1 1 table 3: studied cases fig. 7 presents some information on the number of initiated cracks at the beginning of the time increment during the experiment (first number of cracks), and fig. 8 presents the number of initiated cracks in the time increment (total initiated cracks: initiation and coalescence). these results are printed at each evaluation time for case1, case12, case13 and case14. for a given value of the damage d, figs (9 to 11) show the probability of failure as a function of time. hence besides the crack initiation probability, the probability of leak (crack crossing the wall) is evaluated for the 4 cases (1, 12, 13 and 14) respectively. for weak damages (fig. 13) the variation of oxygen concentrations does not affect the initiation process (fig. 12). r. boutelidja et alii, frattura ed integrità strutturale, 50 (2019) 98-111; doi: 10.3221/igf-esis.50.10 106 figure 7: numbers of initiated cracks. figure 8: total number of initiated cracks with time. figure 9: cumulative probability of initiation or leak (case1). r. boutelidja et alii, frattura ed integrità strutturale, 50 (2019) 98-111; doi: 10.3221/igf-esis.50.10 107 figure 10: cumulative probability of initiation or leak (case12). figure 11: cumulative probability of initiation or leak (case13 and case14). figure 12: probability to initiate a leak (case 1, case12, case13 and case14). r. boutelidja et alii, frattura ed integrità strutturale, 50 (2019) 98-111; doi: 10.3221/igf-esis.50.10 108 figure 13: damage versus o2 concentration. figure 14: probability to have a leak (case1, case12, case13 and case14). fig. 14 regroups the leak cumulative probabilities for the treated examples. if we suppose that case1 is a reference (o2 concentration = 0.2 ppm) one notes that when the transient regime concentration is approached (case14: o2 concentration = 0.1 ppm) the leak probability is reduced by 12 times. moreover, when we are below the transient regime concentration (case13: o2 concentration = 0.01 ppm) the leak probability is reduced by 87 times. effects of temperature change for an oxygen concentration of 0.2 ppm, tab. 4 resumes the temperatures used to illustrate the effect of their variations. temperatures used and cases studied studied case case 1-550 case 12-560 case 13-479 case 14-480 case 15-450 temperature, (°f) 550 560 479 480 450 table 4: temperatures used and cases studied fig. 15 regroups the initiation probability curves for the 5 cases studied. results are printed at each evaluation time for case1-550, case12-560, case13-479, case14-480 and case15-450. for weak damages (fig. 16) the variation of temperature does not affect the initiation process (fig. 15). r. boutelidja et alii, frattura ed integrità strutturale, 50 (2019) 98-111; doi: 10.3221/igf-esis.50.10 109 figure 15: probability to initiate a leak. fig. 17 regroups the leak probability curves for the 4 cases studied. the effect of temperature depends on the triggering temperature of the heat-up and cool-down cycle. figure 16: damage versus temperature. figure 17: probability to have a leak. r. boutelidja et alii, frattura ed integrità strutturale, 50 (2019) 98-111; doi: 10.3221/igf-esis.50.10 110 conclusions n this study we used m-praise computation program upgraded over the last few years to allow checking initiation and propagation of cracks in a variety of materials for under pressure piping and in boiling water reactors ( bwr) to predict and analyze the reliability of pipes under pressure based on fracture mechanics. the subroutine for initiation has been used in conjunction with monte carlo simulation to estimate the probability of failure as a function of time. in addition to the probability of crack initiations, the probabilities to have a leak in the piping have been evaluated. the study and the analysis of the results obtained from the treated cases show the influence of the variation of the environmental parameters on leakage probability. most figures present statistics on initiated cracks as a function of time. many cracks are predicted to initiate, but none could grow to become a crossing crack during the pipe lifetime, which is simulated to 20 years. lastly, for small damages we observed that the change in temperature or oxygen concentration does not affect the initiation process but their decrease contribute favorably to the decrease in the leakage probabilities. references [1] andresen, p.l., ford, f.p. (1994). fundamental modeling of environmental cracking for improved design and lifetime evaluation in bwrs, int. j. press. vessel. pip., 59(1–3), pp. 61–70, doi: 10.1016/0308-0161(94)90142-2. [2] zhang, s., shibata, t., haruna, t. (1997). initiation and propagation of igscc for sensitized type 304 stainless steel in dilute sulfate solutions, corros. sci., 39(9), pp. 1725–1739, doi: 10.1016/s0010-938x(97)00078-4. [3] harris, d.o., dedhia, d.d., eason, e.d. (1986a). probabilistic analysis of initiation and early growth of stress corrosion cracks in bwr piping. american society of mechanical engineers, new york. asme paper 86-pvp-11. [4] guedri, a., djebbar, y., khaleel, m., zeghloul, a., (2012). structural reliability improvement using in-service inspection for intergranular stress corrosion of large stainless steel piping, in: applied fracture mechanics. intech. doi: 10.5772/48521. [5] ting, k. (1999). the evaluation of intergranular stress corrosion cracking problems of stainless steel piping in taiwan bwr-6 nuclear power plant, nucl. eng. des., 191(2), pp. 245–254, doi: 10.1016/s0029-5493(99)00146-6. [6] rahman, s., ghadiali, n., wilkowski, g.m., paul, d. (1997). a computer model for probabilistic leak-rate analysis of nuclear piping and piping welds, int. j. press. vessel. pip., 70(3), pp. 209–21, doi: 10.1016/s0308-0161(96)00032-4. [7] helie, m., peyrat, c., raquet, g., santarini, g., sornay, p. (1996). phenomenological modelling of stress corrosion cracking. first global internet corrosion conferences. [8] lu, b.t., chen, z.k., luo, j.l., patchett, b.m., xu, z.h. (2005). pitting and stress corrosion cracking behavior in welded austenitic stainless steel, electrochim. acta, 50(6), pp. 1391–1403, doi: 10.1016/j.electacta.2004.08.036. [9] anoop, m.b., balaji rao, k., lakshmanan, n. (2008). safety assessment of austenitic steel nuclear power plant pipelines against stress corrosion cracking in the presence of hybrid uncertainties, int. j. press. vessel. pip., 85(4), pp. 238–247, doi: 10.1016/j.ijpvp.2007.09.001. [10] guedri, a., zeghloul, a., merzoug, b. (2009). reliability analysis of bwr piping including the effect of residual stresses. international review of mechanical engineering 3, pp. 640–645. [11] guedri, a. (2013). reliability analysis of stainless steel piping using a single stress corrosion cracking damage parameter, int. j. press. vessel. pip., 111–112, pp. 1–11, doi: 10.1016/j.ijpvp.2013.03.011. [12] guedri, a. (2013). effects of remedial actions on small piping reliability, proc. inst. mech. eng. part o j. risk reliab., 227(2), pp. 144–161, doi: 10.1177/1748006x13477798. [13] harris, d.o., lim, e.y., dedhia, d.d. (1981). probability of pipe fracture in the primary coolant loop of a pwr plant: probabilistic fracture mechanics analysis load combination program project 1 final report. nureg/cr2189, 5. u.s. nuclear regulatory commission, washington, d.c., doi: 10.2172/5341468. [14] harris, d.o., dedhia, d.d., eason, e.d., patterson, s.d. (1986b). probability of failure in bwr reactor coolant piping: probabilistic treatment of stress corrosion cracking in 304 and 316ng bwr piping weldments. nureg/cr-4792, 3. u.s. nuclear regulatory commission, washington, d.c. [15] harris, d.o., dedhia, d.d., lu, s.c. (1992). theoretical and user’s manual for pc-praise, a probabilistic fracture mechanics computer code for piping reliability analysis. nureg/cr-5864. u.s. nuclear regulatory commission, washington, d.c. [16] harris, d.o., dedhia, d.d. (1998). winpraise 98 praise code in windows. engineering mechanics technology, inc., usa. i r. boutelidja et alii, frattura ed integrità strutturale, 50 (2019) 98-111; doi: 10.3221/igf-esis.50.10 111 [17] khaleel, m.a., simonen, f. (1994a). the effects of initial flaw sizes and inservice inspection on piping reliability. in service experience and reliability improvement: nuclear, fossil, and petrochemical plants, american society of mechanical engineers, new york, pvp, 288, pp. 95-107. [18] khaleel, m.a., simonen, f.a. (1994b). a parametric approach to predicting the effects of fatigue on piping reliability. in service experience and reliability improvement: nuclear, fossil, and petrochemical plants, american society of mechanical engineers, new york, pvp, 288, pp. 117-125. [19] khaleel, m.a., simonen, f.a. (2000). effects of alternative inspection strategies on piping reliability, nucl. eng. des., 197(1–2), pp. 115–140, doi: 10.1016/s0029-5493(99)00261-7. [20] khaleel, m.a., simonen, f.a, harris, d.o., dedhia, d. (1995). the impact of inspection on intergranular stress corrosion cracking for stainless steel piping. in risk and safety assessments: where is the balance?, american society of mechanical engineers, new york, pvp296, pp. 411-422. [21] simonen, f.a, khaleel, m.a. (1998a). a probabilistic fracture mechanics model for fatigue crack initiation in piping.” in fatigue, fracture and residual stress, american society of mechanical engineers, new york, pvp-373, pp. 27-34. [22] simonen, f.a., khaleel, m.a. (1998). effects of flaw sizing errors on the reliability of vessels and piping, j. press. vessel technol., 120(4), pp. 365, doi: 10.1115/1.2842345. [23] simonen, f.a., harris, d.o., dedhia, d.d. (1998). effect of leak detection on piping failure probabilities. in fatigue, fracture and residual stress, american society of mechanical engineers, new york, pvp-373, pp. 105-113. [24] khaleel, m.a., simonen, f.a., phan, h.k., harris, d.o., dedhia, d. (2000). fatigue analysis of components for 60year plant life. nureg/cr-6674, pnnl-13227. u.s. nuclear regulatory commission, washington, dc. [25] gosselin, s.r., simonen, f.a., carter, r.g., davis, j.m., stevens, g.l. (2005). enhanced asme section xi appendix l flaw tolerance procedure. 1: codes and standards, asme, pp. 5–16. doi: 10.1115/pvp2005-71100. [26] bishop, b.a. (1997). an updated structural reliability model for piping risk informed isi, in fatigue and fracture, american society of mechanical engineers, new york, pvp, 346(2), pp. 245-252. [27] brickstad, b., zang, w. (2001). nurbit nuclear rbi analysis tool, a software for risk management of nuclear components. technical report no 10334900-1. dnv, stockholm, sweden. [28] brickstad, b., chapman, o.j.v., schimpfke, t., schulz, h., muhammed, a. (2004). review and benchmarking of srm and associated software. nurbim final report d4, contract fiks-ct-2001-00172. dnv, stockholm, sweden. [29] bell, c.d., chapman, o.j.v. (2003). description of prodigal. nurbim report d4/appendix f. rolls-royce plc., derby, united kingdom. [30] schimpfke, t. (2003). a short description of the piping reliability code prost. nurbim report d4/appendix c. gesellschaft fur anlagen-und reaktorsicherheit (grs), berlin, germany. [31] dillstrom, p. (2003). a short description of prosacc. nurbim report d4/appendix g. dnv, stockholm, sweden. [32] mohammed, a.a. (2003). a short description of struel. nurbim report d4/appendix h. the welding institute, cambridge, united kingdom. [33] helie, m., peyrat, c., raquet, g., santarini, g., sornay, p. (1996). phenomenological modelling of stress corrosion cracking. intercorr/96 first global internet corrosion conference. [34] lu, b.t., chen, z.k., luo, j.l., patchett, b.m., xu, z.h. (2005). pitting and stress corrosion cracking behavior in welded austenitic stainless steel, electrochim. acta, 50(6), pp. 1391–1403, doi: 10.1016/j.electacta.2004.08.036. [35] priya, c., rao, k.b., anoop, m.b., lakshmanan, n., gopika, v., kushwaha, h.s., saraf, r.k. (2005). probabilistic failure analysis of austenitic nuclear pipelines against stress corrosion cracking, proc. inst. mech. eng. part c j. mech. eng. sci., 219(7), pp. 607–624, doi: 10.1243/095440605x31526. [36] asm international handbook committee. 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can be opened with acrobat and adobe reader 5.0 and later.) >> /namespace [ (adobe) (common) (1.0) ] /othernamespaces [ << /asreaderspreads false /cropimagestoframes true /errorcontrol /warnandcontinue /flattenerignorespreadoverrides false /includeguidesgrids false /includenonprinting false /includeslug false /namespace [ (adobe) (indesign) (4.0) ] /omitplacedbitmaps false /omitplacedeps false /omitplacedpdf false /simulateoverprint /legacy >> << /addbleedmarks false /addcolorbars false /addcropmarks false /addpageinfo false /addregmarks false /convertcolors /converttocmyk /destinationprofilename () /destinationprofileselector /documentcmyk /downsample16bitimages true /flattenerpreset << /presetselector /mediumresolution >> /formelements false /generatestructure false /includebookmarks false /includehyperlinks false /includeinteractive false /includelayers false /includeprofiles false /multimediahandling /useobjectsettings /namespace [ (adobe) (creativesuite) (2.0) ] /pdfxoutputintentprofileselector /documentcmyk /preserveediting true /untaggedcmykhandling /leaveuntagged /untaggedrgbhandling /usedocumentprofile /usedocumentbleed false >> ] >> setdistillerparams << /hwresolution [2400 2400] /pagesize [612.000 792.000] >> setpagedevice microsoft word 2188 s. akbari et alii, frattura ed integrità strutturale, 47 (2019) 39-53; doi: 10.3221/igf-esis.47.04 39 novel weight functions and stress intensity factors for quarterelliptical cracks in lug attachments s. akbari, s.m. nabavi faculty of aerospace engineering, malek ashtar university of technology, tehran, iran saleh_akbari66@yahoo.com nabavi@mut.ac.ir, http://orcid.org/0000-0002-3803-843x h. moayeri department of mechanical engineering, west tehran branch, islamic azad university, tehran, iran. moayeri.hamed@wtiau.ac.ir abstract. in this paper, a general weight function is developed to calculate the stress intensity factors (sifs) for quarter-elliptical cracks in a wide range of lug attachment family. for this purpose, a series of finite element analyses are performed. finally, using this unique extracted weight function, the influence of the pin loading model and crack parameters (aspect ratio and relative depth of the quarter-elliptical crack) on the sifs is evaluated in the cracked lug attachments. the results of the present work are compared with some data available in the literature, and the agreement is satisfactory. keywords. attachment lug; quarter-elliptical crack; weight function; stress intensity factor; 3d finite element analysis citation: akbari, s., nabavi, s. m., moayeri, h., novel weight functions and stress intensity factors for quarter-elliptical cracks in lug attachments, frattura ed integrità strutturale, 47 (2019) 39-53. received: 06.09.2018 accepted: 20.10.2018 published: 01.01.2019 copyright: © 2019 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. introduction ug-type joints are one of the most useful and serviceable types of attachments in aerospace industries, which play an important role in the integrity of mechanical structures. because of their application and loading condition, these parts are very critical. the stress distribution around the hole of lugs and the complexity of pin loading makes these parts critical and may result in cracks initiation. to evaluate the crack growth, firstly a fracture study should be done, which leads to fatigue life estimation. for this study, calculation of stress intensity factor (sif) is very important and should be achieved precisely to ensure the precision of the results of next stages. it is helpful to perform stress analysis before starting from a fracture study. jiang et.al[1] performed a 3d numerical analysis using finite element method (fem) to investigate the effect of geometrical parameters of a lug on its stress concentration factor (scf). they found that sif is very sensitive to the change of these parameters. in addition, they reported that sif has almost a linear relation with the friction coefficient. wang [2] studied the stress fields in a lug under various loading conditions, such as the contact and clearance between the lug and a pin. it was shown that the effect of rigidity between the l http://www.gruppofrattura.it/va/47/2188.mp4 s. akbari et alii, frattura ed integrità strutturale, 47 (2019) 39-53; doi: 10.3221/igf-esis.47.04 40 pin and lug on stress distribution is small. grant and flipo [3] made a parametric analysis to study the change of interference between a pin and a lug hole, together with the effect of the radius of the hole and thickness of the lug on the stress. this paper takes into account both 2d and 3d fem models and their results. studying the fracture of a lug due to its loading condition as mentioned earlier is necessary. there are many approaches to obtain sif in a cracked lug to evaluate its fracture. kathiresan et al. [4] used a 2d fe fracture analysis on a tapered lug. results show that in a tapered lug, sif has a lower value than a straight lug for symmetric loading. a similar work were performed by hsu [5] on a tapered and a straight lug. the effect of lug and crack parameters on the stress distributions and sif were determined in both cases. kathiresan et al. [6] obtained sif solutions for through cracks in lugs using the green's function method and correction factors. narayana et al. [7] analyzed the presence of cracks in metallic and composite lugs using finite element analysis. boljanović and maksimović [8] and boljanović et al. [9] carried out two similar investigations, in which they obtained the sifs for both through and surface cracks using 3d fem analysis. naderi and iyyer [10] used three type of pin loadings such as full contact problem, cosine pressure distribution and uniform pressure distribution in their xfem model. results confirmed that sifs came from full contact loading of the pin is higher from those two other models. also, naderi et al. [11] used an extended isogeometric analysis in order to calculate sif in lug attachments which uses some new functions. the resulted sifs were used to study the crack growth of straight attachment lugs. rigby and aliabadi [12] used the boundary element method and the j-integral to obtain sifs in a single quarter elliptical and symmetrical quarter elliptical cracks in a lug. wang [13] extracted a weight function (wf) for a wide range of through cracks in a lug based on the boundary element method. mikheevskiy et al. [14] employed the wf technique for fatigue crack growth analysis of a cracked lug using the load-shedding effect. the shape of crack changed from a quarter circular to an edge crack in the crack growth process of that quarter elliptical crack. wu and tong [15] provided a 1d wf to calculate the crack surface displacements of cracks in radial. xu et al. [16] developed an analytical 1d wf for a pin-loaded specimen with a single crack at mixed mode condition. bahloul et al. [17] considered crack tip residual stress field and material dispersion in their fracture modelling of a lug. the proposed approach was able to predict the fatigue crack growth in lug attachments with a good reliability. there are some similar works like the newman's papers [18, 19] that formulated sifs in finite plates which contain a hole with cracks. these formulas could not be used for lug parts because of the difference in geometry, boundary condition and also the ratio of hole radius to the width of lug. in a different work, chikmath and dattaguru [20] used a prognostic analysis to monitor the criticalities in lug attachments during fatigue crack growth. in this paper, they made it possible to change the contact condition between lug and pin during the fatigue loading. the goal of present work is to compute a weight function to predict stress intensity factors in a wide range of lug attachments family, which is very useful in their life estimation. the considered flaw configuration is a quarter-elliptical crack which is located inside the lug. extraction of the wf is based on the 3d fe analyses. the computed wfs can be employed for both surface and deepest points of the quarter-elliptical cracks. the proposed wf could be used for the cracks in lugs having different ratios of width to radius in the lug’s hole, as well as different aspect ratios and depth ratios for the crack. because of these characteristics, the extracted wf is a unique and independent tool, which could be used in many problems with different loading condition, lug geometries, and crack configurations. it means that in the literatures there is no similar wf, which could cover a wide range of lugs and be presented in the paper with its educational aspects. the outcomes of the present wf are compared with special cases in the literature to verify the results of this paper. the results obtained are in good agreement with those available in literature. the derived wf can play an important role to assess fatigue crack growth in attachment lug. finally, the effects of loading types on the sifs are studied as an application of present wf. the characteristics and novelties of the wf presented in this study could be summarized as:  capability in calculating sifs in the lugs containing quarter-elliptical corner cracks subjected to complex stress distributions.  feasibility to be used in a board range of lug’s family with different geometries having various quarter-elliptical cracks’ parameters.  proposal of efficient wfs for the estimation of crack growth in lug attachments. geometry of the attachment lug and the material properties he examined lug is made of al 7075 t7351 and shown in fig.1. ro is the outer radius of the lug, ri is the radius of lug hole, and b is the thickness of lug. in order to extract a wf valid for a range of lug parameters, values of ro and ri are not constant. the parameters of the quarter elliptical crack in this lug are a and c as described in fig.1. further, a and c are involved in the wf achievement process, they have variable values which will be presented in the wf later. the cracked lug is made of t s. akbari et alii, frattura ed integrità strutturale, 47 (2019) 39-53; doi: 10.3221/igf-esis.47.04 41 7075 t7351 aluminium alloy. poisson's ratio and young's modulus of this material are 0.32 and 71 gpa, respectively. linear elastic fracture mechanics analyses are employed to determine the sifs. figure 1: schematic of a straight attachment lug with a quarter-elliptical crack. weight function extraction procedure n this section, all related steps to achieve the wf are presented. during the first step of the process, a numerical analysis (fea) should be used to determine the sifs for two reference loads. considerable attention must be paid when 3d fea results are sensitive to element size and convergence. at this point, the results of the analysis are employed to obtain the wf. at the end of these steps, further verifications are performed on the computed results. finite element analysis in order to achieve a wf it is very important to have enough results, at those ranges of parameters that would be the variants of the function. here, three variables are considered, which are: ro/ri, a/c and c/b. their ranges are defined according to literatures. these ranges are 1.5 to 3, 0.2 to 1 and 0.2 to 0.8 for ro/ri, a/c and c/b, respectively. by considering a constant value of b, the other parameters could be calculated according to that. the considered variation of these parameters is presented in tab. 1 for one family of the cracked lugs. parameter value aspect ratio of quarter-elliptical crack (a/c) 0.2, 0.4, 0.6, 0.8, 1 depth ratio of the quarter-elliptical crack (c/b) 0.2, 0.4, 0.6, 0.8 ratio of outer to inner radius of the lug’s hole (ro/ri) 1.5, 2.25, 3 radius of the lug’s hole (ri) 19.05 mm thickness of the lug (b) 12.7 mm table 1: geometrical parameters of the cracked lug. according to these parameters, 3d finite element models are developed in abaqus [21] fe program to obtain sifs corresponded to each condition. because of the location and the shape of crack in the lug, same as the schematic in fig. 1, the complete model is employed. 3d meshes are implemented for these analyses as shown in fig. 2. 20-node brick elements are used for all parts of the lug, except the region around the crack tip. collapsed wedge-shaped elements, which midpoints are shifted to quarter points, are implemented for crack tip region due to the singularity. there are three general methods for calculating stress intensity factors from fea. these methods are: displacement extrapolation (de), the stiffness derivative technique (sdt), and the j-integral technique. both the de method and the sdt are sensitive to mesh accuracy i s. akbari et alii, frattura ed integrità strutturale, 47 (2019) 39-53; doi: 10.3221/igf-esis.47.04 42 around crack front using singular elements. the j-integral method, instead, reduces this problem. j-integral method is chosen in abaqus for calculating the sifs in these analyses. figure 2: typical fem mesh for the complete cracked lug. the sifs due to reference loading are calculated for determining the wf. the stress distributions across the plane of the crack specify are regarded as reference loads. the crack face is subjected to a general power-law stress distribution. the general equation to introduce the reference loading is given by: 0( ) (1 / ) nx x a   (1) where n is a positive integer number and is equal to 0 and 1 for uniform and linear reference loadings, respectively. x is the distance from the inner surface of the hole (moving positive towards), 𝜎0 is the amplitude of the loading, and a is the crack length according to fig.1. abaqus has this ability to give sifs directly, but sifs are achieved from j-integral as follows: 2/ (1 )ik je   (2) about eqn. (2) it should be noted that, this equation is valid for the points which have singularity with the power of 0.5, but for the end points of the crack front the power of singularity is not equal to 0.5. therefore, the results will be extracted near these end points on the crack front to have accurate results [22-24]. the results from the uniform and linear reference loadings would be used in the process of fitting curves for extracting the wf. verification of fem results because fem results are the base part of this work, a separate verification is done. in order to verify the resulted sifs of this work, refs. [6, 8] are used (tab. 2). the lug is subjected to the pin loading. the rigid pin was considered to fit in the lug hole with zero clearance and frictionless. in this case the pin has contact with the hole of lug (both have equal radius) and the applied force is in the y-direction, according to fig.1. the surface and deepest points of the crack (a and b) are introduced (fig.3) for this comparison. the results are normalized (kn=ki/ brσ . πa which 𝜎br=p/ (2.ri. b) and p is the total pin load in the lug). sifs here obtained are compatible with those reported in refs. [6, 8]. it is obvious that the results of the present fe model are compatible with analytical and fe results of mentioned references and the maximum difference is about 4 percent. s. akbari et alii, frattura ed integrità strutturale, 47 (2019) 39-53; doi: 10.3221/igf-esis.47.04 43 figure 3: surface point (a) and the deepest point (b) on the quarter-elliptical crack in the attachment lug. ro/ri c/b location kn fem (present work) analytical [6] fem [8] 2.0 0.22 surface 1.28 1.32 2.0 0.22 deepest 1.69 1.75 2.25 0.50 surface 0.97 1.01 2.25 0.50 deepest 1.31 1.34 2.25 0.78 surface 1.01 0.98 2.25 0.78 deepest 1.36 1.41 table 2: comparison of the obtained sifs for the quarter-circular crack (a/c=1) in a lug under the pin loading. the weight function extraction the basis of the wf method is the sif calculation process, which is independent of the loading shape. the sif corresponding to 𝜎(x) (see eqn. (3)) can be determined for arbitrary loading on the considered points on the crack front (here deepest and surface points) by a single integration: 0 ( ). ( , ) a k x m x a dx  (3) where k is the sif for an arbitrary loading, 𝜎(x) is the stress distribution equation on the crack plane for the un-cracked lug and m(x,a) is the appropriate wf for this geometry. for a corner crack, this wf would be determined as: ( , ) ( , ) u x ah m x a k a    (4) where h is a constant of material and can be expressed by: h e for plain stress (5.a) 2/ (1 )h e   for plain strain (5.b) u is the crack face displacement which has the effects of boundary condition inherently. according to ref. [26] the general form of wf for corner cracks at the surface and deepest points are given by: 1/2 3/2 1 2 3 2 1 2 ( ) ( , ) (1 ) (1 ) (1 )a a a am m m a x x x x m x a a a a            (6) s. akbari et alii, frattura ed integrità strutturale, 47 (2019) 39-53; doi: 10.3221/igf-esis.47.04 44 1/2 3/2 1 2 3 2 ( , ) 1 ( ) ( ) ( )b b b bx a m m m x x x x m a a a       (7) where mia and mib (with i = 1,2,3) are constants of the wf for the surface and the deepest point of the crack respectively, and could be calculated using two reference loadings (uniform and linear) and an added condition. the added condition for calculating the constants of the wf for surface point of the crack [27] is that the second derivative of wf should be zero at x=0: 2 2 ( , ) 0a m x a x    at x=0 (8) the condition for the deepest point of the crack is that the value of the wf at x=a should be zero. ( , ) 0bm x a  at x=a (9) the obtained equations from these two conditions are 2 3am  (10) 1 2 3 1 0b b bm m m    (11) if eqns. 10 and 11 are used, only two reference stress intensity factors have to be known. by considering 𝜎(x), when n is equal to 0 (uniform stress) and 1 (linear stress), the sifs are for the surface point of crack: 0 0uniform surface ak y q   (12.a) 0 1linear surface ak y q   (12.b) whereas for the deepest point of the crack are: 0 0uniform deepest ak f q   (13.a) 0 1linear deepest ak f q   (13.b) where y0, y1, f0 and f1 are correction factors that can be obtained from curve fitting of fem results (uniform and linear) and are function of ro/ri, a/c and c/b . q is the shape parameter for elliptical crack, which is based on a series expansion of an elliptic integral of the second kind and can be approximated as [25]: 1.65 1 1.464( )q a c   0 1a c  (14) substituting eqns. 6 and 12 into eqn. 3, the wf constants for the surface point of the crack can be found as 1 0 1(4 6 ) 6.252a m y y q     (15.a) 2 3am  (15.b) s. akbari et alii, frattura ed integrità strutturale, 47 (2019) 39-53; doi: 10.3221/igf-esis.47.04 45 3 0 1( 6 12 ) 1.62a m y y q     (15.c) in the same way, substituting eqs. 7 and 13 into eqn. 3 and using eqn. 11, the constants mib for the deepest point of the crack can be determined as 1 1 0(30 18 ) 82b m f f q    (16.a) 2 0 1(60 90 ) 152b m f f q    (16.b) 3 0 1(42 60 ) 82b m f f q    (16.c) four equations are obtained by curve fitting on the fem results under uniform and linear reference loadings in order to achieve y0, y1, f0 and f1. these fitting equations are function of ro/ri, a/c and c/b. the concluded wf specifications which are the novel results of this work and given by: 3 3 3 1 1 1 1 1 1 ( ) ( ) ( )i j lok kijl i j l i r a c y a r c b         0,1k  (17) 3 3 3 1 1 1 1 1 1 ( ) ( ) ( )i j lok kijl i j l i r a c f b r c b         0,1k  (18) in addition, values of coefficient akijl and bkijl are listed in tab. 3 and tab. 4, respectively. k i j l 1 2 3 0 1 1 0.921 0.227 0 2 0.161 1.884 0 3 0 0 0 2 1 0.004 0.067 0 2 0.027 1.572 0.897 3 0 0.161 0 3 1 0 0 0 2 0 0.358 0.339 3 0 0.017 0.372 1 1 1 0.250 0.055 0 2 0.063 1.080 0 3 0 0 0 2 1 0.016 0.023 0 2 0.001 0.893 0.5 3 0 0.221 0 3 1 0 0 0 2 0 0.223 0.221 3 0 0.003 0.338 table 3: coefficient akijl in the boundary correction factor for the reference loads. s. akbari et alii, frattura ed integrità strutturale, 47 (2019) 39-53; doi: 10.3221/igf-esis.47.04 46 k i j l 1 2 3 0 1 1 0.374 0.376 0 2 0.739 2.314 0 3 0 0 0 2 1 0.036 0.1395 0 2 0.075 0.594 0.077 3 0 1.685 0 3 1 0 0 0 2 0 0.217 0.324 3 0 0.2104 1.199 1 1 1 0.292 0.034 0 2 0.662 1.444 0 3 0 0 0 2 1 0.044 0.072 0 2 0.097 0.784 0.144 3 0 1.043 0 3 1 0 0 0 2 0 0.328 0.243 3 0 0.001 1.22 table 4: coefficient bkijl in the boundary correction factor for reference loads. a set of computations have been accomplished to identify the accuracy of the derived wf expressions. the stress distribution is applied as an input to calculate the sifs using the wf integral in eqn. 3. the sifs are computed from wf for the quadratic and cubic stress distribution acting on the crack faces using n=2 and 3 in eqn. 1 respectively. the calculated sifs were compared with the fem results, and these comparisons are shown in tab. 5-7, for ro/ri=1.5, 2.25 and 3.0, respectively. the comparison between the computed and fea results point out that the derived wf can be applied for reliable calculation of the lug with quarter-elliptical crack. the maximum difference does not exceed more than 7 percent. a/c c/b location kn=ki/  0 . /a q  parabolic cubic wf fem wf fem 0.2 0.2 surface 0.203 0.210 0.142 0.150 deepest 0.470 0.464 0.436 0.445 0.4 surface 0.197 0.202 0.137 0.144 deepest 0.463 0.448 0.428 0.413 0.6 surface 0.195 0.201 0.137 0.143 deepest 0.457 0.451 0.422 0.417 0.8 surface 0.202 0.212 0.142 0.150 deepest 0.454 0.466 0.420 0.429 1 0.2 surface 0.192 0.187 0.130 0.129 deepest 0.868 0.839 0.766 0.750 0.4 surface 0.240 0.235 0.169 0.166 deepest 0.879 0.846 0.789 0.756 0.6 surface 0.337 0.318 0.245 0.247 deepest 0.969 0.991 0.864 0.841 0.8 surface 0.478 0.497 0.358 0.379 deepest 1.132 1.156 0.997 1.008 table 5: comparison between the sifs calculated by the wf and fem for the parabolic and cubic loading at ratio r0/ri=1.5. s. akbari et alii, frattura ed integrità strutturale, 47 (2019) 39-53; doi: 10.3221/igf-esis.47.04 47 a/c c/b location kn=ki/  0 . /a q  parabolic cubic wf fem wf fem 0.2 0.2 surface 0.197 0.190 0.137 0.133 deepest 0.452 0.459 0.419 0.417 0.4 surface 0.190 0.192 0.132 0.134 deepest 0.449 0.449 0.415 0.414 0.6 surface 0.189 0.195 0.131 0.135 deepest 0.442 0.450 0.407 0.420 0.8 surface 0.193 0.200 0.135 0.142 deepest 0.435 0.456 0.401 0.421 1 0.2 surface 0.169 0.177 0.111 0.117 deepest 0.834 0.822 0.757 0.739 0.4 surface 0.199 0.205 0.134 0.138 deepest 0.812 0.858 0.733 0.768 0.6 surface 0.270 0.276 0.190 0.196 deepest 0.859 0.863 0.769 0.775 0.8 surface 0.382 0.374 0.279 0.275 deepest 0.978 0.975 0.869 0.867 table 6: comparison between the sifs calculated by the wf and fem for the parabolic and cubic loading at ratio r0/ri=2.25. a/c c/b location kn=ki/  0 . /a q  parabolic cubic wf fem wf fem 0.2 0.2 surface 0.197 0.204 0.138 0.141 deepest 0.447 0.450 0.416 0.413 0.4 surface 0.192 0.194 0.133 0.137 deepest 0.456 0.428 0.417 0.390 0.6 surface 0.193 0.194 0.135 0.137 deepest 0.455 0.426 0.420 0.395 0.8 surface 0.192 0.197 0.137 0.139 deepest 0.445 0.453 0.413 0.418 1 0.2 surface 0.185 0.181 0.124 0.125 deepest 0.868 0.823 0.788 0.748 0.4 surface 0.202 0.208 0.137 0.142 deepest 0.810 0.819 0.729 0.724 0.6 surface 0.244 0.255 0.170 0.176 deepest 0.827 0.831 0.740 0.735 0.8 surface 0.310 0.314 0.227 0.229 deepest 0.916 0.936 0.818 0.828 table 7: comparison between the sifs calculated by the wf and fem for the parabolic and cubic loading at ratio r0/ri=3.0. s. akbari et alii, frattura ed integrità strutturale, 47 (2019) 39-53; doi: 10.3221/igf-esis.47.04 48 verification of the weight function the dimensionless sif results extracted from the present study under real pin loading by using both the wf and fe analysis are compared with those of ref. [28] in fig. 4 for ro/ri=2, a/c = 1 and 0.2≤c/b≤0.8 . kc and ka represent the sifs in the deepest and the surface points of the crack, respectively. the pin loading is modeled as a contact problem with zero friction. the sifs obtained from the wf method, fea and analytical results of ref. [28] are approximately the same and are also given in fig. 4 for comparison purpose. figure 4: dimensionless sifs under the real pin loading at point a and c (ro/ri=2). in addition, dimensionless sifs (kn=ki/(𝜎br√𝜋a)) under a real pin loading with frictionless contact are compared with those of ref. [6] for ro/ri=2.25 , a/c = 1 and 0.2≤c/b≤0.8 for the surface and the deepest points of the crack, listed in tab. 8 and tab. 9. the maximum difference of the sifs obtained from wf and the analytical results of ref. [6] is less than 8%. c/b kn=ki/  .br a  fem (present work) wf (present work) analytical [6] 0.2 1.27 1.29 1.38 0.4 1.04 1.09 1.07 0.6 0.96 0.98 0.93 0.8 0.89 0.93 0.86 table 8: sifs of the surface point of the crack under real pin loading with contact r0/ri=2.25. c/b kn=ki/  .br a  fem (present work) wf (present work) analytical [6] 0.2 1.43 1.41 1.51 0.4 1.38 1.35 1.41 0.6 1.31 1.29 1.38 0.8 1.26 1.205 1.33 table 9: sifs of deepest point of the crack under real pin loading with contact at r0/ri=2.25. a comparison is done between the results of the wf and those in ref. [14] for a lug with a quarter-circular crack subjected to a constant gross stress. the values of a/c and ro/ri are 1 and 2.7, respectively. the results are compared in tab. 10. s. akbari et alii, frattura ed integrità strutturale, 47 (2019) 39-53; doi: 10.3221/igf-esis.47.04 49 c/b kn=ki/  .br a  surface point deepest point wf (present work) wf[14] wf (present work) wf [14] 0.2 0.993 0.951 1.24 1.18 0.4 0.805 0.788 1.18 1.15 0.6 0.702 0.675 1.15 1.06 0.8 0.636 0.617 1.13 1.06 table 10: sifs of the surface point of the quarter-circular crack under real pin loading with contact r0/ri=2.7. other approaches for simulating the pin loading are constant pressure and cosine pressure in the lug hole in the direction of pin load, which are also modeled in this work. the resulted sifs are calculated using the wf according to rigby and aliabadi’s work [12]. the presented cosine pressure loading in this study is defined as 0 cosc   (19) where 0 2 ( )i p r b  (20) in which p is resultant load in the y-direction and θ is the angle from pin loading direction according to coordinate system in fig.1. a comparison between the present wf results and those in ref. [12] is made in tab. 11 and 12. the results are dimensionless according to ref. [12]. the comparison of the results shows that the maximum difference between calculated sifs using the present wf with those computed using bem in ref. [12] is about 7 percent. ro/ri location kn=ki/  .br a  cosine pressure uniform pressure wf bem [12] wf bem [12] 1.5 surface 4.16 4.29 3.05 3.13 deepest 2.49 2.61 2.21 2.36 2.25 surface 1.58 1.66 1.19 1.23 deepest 1.17 1.21 0.91 0.99 3 surface 1.09 1.15 0.83 0.87 deepest 0.79 0.84 0.67 0.71 table 11: comparison between the resulted sifs of cosine pressure loading and uniform pressure loading for present wf and bem of ref.[12] for a/c=1 and c/b=0.5. ro/ri location kn=ki/ σ . √πa cosine pressure uniform pressure wf bem [12] wf bem [12] 1.5 surface 4.15 4.21 1.17 1.23 deepest 3.23 3.37 1.16 1.21 2.25 surface 1.59 1.68 0.83 0.87 deepest 1.45 1.51 0.83 0.87 3 surface 1.12 1.17 1.18 1.23 deepest 0.99 1.06 1.13 1.21 table 12: comparison between the resulted sifs of cosine pressure loading and uniform pressure loading for present the wf and bem of ref.[12] for a/c=0.66 and c/b=0.5. s. akbari et alii, frattura ed integrità strutturale, 47 (2019) 39-53; doi: 10.3221/igf-esis.47.04 50 evaluating the effect of pin loading conditions and crack parameters variation n order to model pin loading in the attachment lug, three methods could be implemented. these three methods are the real pin loading (contact between pin and lug hole), the constant pressure and the cosine pressure. here a study is done to evaluate the effect of each loading conditions on the resulted sifs. the results are calculated for ro/ri=2, a/c=1, 0.2≤c/b≤0.8, 9.6 kpa gross stress, which are presented in tabs. 13 and 14. it is evident that the real pin loading has the largest values for sifs than the other two methods. among the three common types of loading in the lug hole, the real pin loading condition has the largest magnitude of the sifs. further, it is obvious that when c/b increases, values of sifs increase in both deepest and surface points of the crack because of the effect of crack depth on the sif. c/b real pin loading constant pressure cosine pressure 0.2 0.0615 0.0603 0.0591 0.4 0.0718 0.0683 0.0677 0.6 0.0926 0.0902 0.0891 0.8 0.1178 0.1143 0.1121 table 13: sifs (mpa(mm)0.5) for surface point of the crack under three types of pin loading for r0/ri=2 and a/c=1. c/b real pin loading constant pressure cosine pressure 0.2 0.0708 0.069 0.061 0.4 0.101 0.098 0.092 0.6 0.129 0.121 0.117 0.8 0.1562 0.1518 0.148 table 14: sifs (mpa(mm)0.5) for deepest point of the crack under three types of pin loading for r0/ri=2 and a /c=1. in order to study the effect of a/c and c/b on the sifs, a comparison is done for different values of a/c and c/b using the wf method. the results are shown in fig. 5 and fig. 6 for the real pin loading model. it could be concluded that by changing the shape of the crack from a quarter circle to a quarter ellipse, the values of the sifs for surface points of the crack increase despite the fact that the sif values for deepest points of the crack decrease. also for both points when a/c<1, by increasing the a/c, sif values increase. it is obvious that increasing the c/b would increase the value of sifs in surface and deepest points. figure 5: variation of sifs vs. c/b for the surface point of the crack under the real pin loading for different a/c ratios. i s. akbari et alii, frattura ed integrità strutturale, 47 (2019) 39-53; doi: 10.3221/igf-esis.47.04 51 figure 6: variation of sifs vs. c/b for the deepest point of the crack under the real pin loading for different a/c ratios. evaluating the effect of bush and interference fitting ne of the cases for the contact between the lug and the pin is when the diameter of the pin is a little larger than the lug hole, which is called interference loading. another approach is when a bush exists between the pin and lug hole (in this case the bush would have interference contact with the hole of lug) and the contact between the pin and the bush is neat. in this paper the amount of interferences for both cases is considered 0.1 mm and the consequence effects are studied for different values of a/c, c/b and fixed value of ro/ri=2.25. the thickness of bush is 1 mm and it is made of the same material as the lug. the analysis was performed for 100 kn force of pin. the results are compared with the those obtained from neat loading condition without any interferences and bush in tab. 15. it is obvious that the values of sifs for neat contact between the pin and the lug are more than the case of interference contact and the bush existence. that is the reason why these two cases are used in fatigue conditions for increasing the life time. by comparing the results between the interference contact of the pin and the lug and the case that the bush exists, it can be understood that in the presence of bush, the values of sifs are lower than the other. this is a study for this case of loading and for choosing an appropriate value for the interference to have a benefit effect on the fatigue life of the lug, the extracted wf could be used to avoid the time consumer modelling and analysing. a/c c/b point location ki  mpa mm neat loading interference with bush 0.2 0.2 surface 426.972 378.88 370.98 deepest 218.556 192.959 188.99 0.4 surface 576.559 517.312 506.279 deepest 323.459 287.412 277.315 0.6 surface 693.524 628.975 615.364 deepest 412.142 364.62 351.471 0.8 surface 794.21 728.448 712.531 deepest 487.162 432.112 417.291 1 0.2 surface 654.173 610.42 607.183 deepest 718.31 638.72 625.38 0.4 surface 854.616 826.41 824.37 deepest 1012.92 914.711 895.211 0.6 surface 1030.5 1008.37 987.51 deepest 1283.41 1173.69 1148.81 0.8 surface 1248.31 1121.21 1106.14 deepest 1591.54 1196.32 1138.26 table 15: sifs (mpa(mm)0.5) for crack under the pin loading in three conditions. o s. akbari et alii, frattura ed integrità strutturale, 47 (2019) 39-53; doi: 10.3221/igf-esis.47.04 52 conclusion n the present work, a wf has been proposed to predict the stress intensity factor for cracked lugs with various geometrical parameters. a quarter-elliptical crack was considered at the inner surface of the attachment lug. for this aim a series of 3d fe analyses have been done for two reference loadings (uniform and linear). lug parameters and their ranges which have been considered as variants in these analyses were 1.5≤ro/ri≤3, 0.2≤a/c≤1 and 0.2≤c/b≤0.8 . the achieved wf has been considered a function of these three parameters, which gives this ability to predict the sifs in lugs with different loading condition, geometries and crack configurations. this characteristic helps to study this wide range of lug family, without any need to other time consumer approach and beside that, the accuracy of this method is confirmed. it has been validated by comparing the calculated sifs of wf and those reported in the literatures. it was evident that the results had good agreement with considering the average of the differences. in addition, the effects of three approaches of pin loading model on the sifs values have been studied using the extracted weight function. these three types of the pin loading have been modeled as the real pin loading with contact to the lug hole, the constant pressure and the cosine pressure on the lug hole. the results have shown that the real pin loading gives the largest values of sifs and it is the accurate approach in life estimation. in the next part of the paper, the effects of the variation of crack parameters (a/c and c/b) on sif values have been studied. at the end of this paper in order to study the effect of the interference between the pin and the lug contact and also the effect of bush existence on the sifs variation, the extracted weight function in present study has been applied. it have been observed that the values of sifs for neat contact between the pin and the lug are more than the case in the presence of interference and bush with interference in contact condition. for the considered loading it is obvious that the use of interference in lug and pin contact and also the use of bush with interference between them can improve the fatigue life of the lug. it should be noted that the value of interference should be calculated in order to have a beneficial effect on the life of the lug. therefore the extracted weight function could be used without any extra modelling and time consuming analysis for different cases. references [1] jiang, y., she, c., yu, p. and guo, w. (2011). three-dimensional stress concentrations at circular pin holes in clearancefit lugs. fatigue fract eng mater struct, 34(8), pp. 573-580. doi: 10.1111/j.1460-2695.2011.01548.x. [2] wang, g. s. (1994). stress analysis for a lug under various conditions. j. strain anal eng, 29(1), pp. 7-16. doi: 10.1243/03093247v291007. [3] grant, r. j. and flipo, b. c. d. (2009). parametric study of the elastic stress distribution in pin-loaded lugs modelled in two and three dimensions and loaded in tension. j. strain anal eng, 44(6), pp. 473-489. doi: 10.1243/03093247jsa501. [4] kathiresan, k., hsu, t. m. and rudd, j. l. (1984). stress and fracture analysis of tapered attachment lugs. fracture mechanics: fifteenth symposium. astm stp 833, r. j. sanford, ed., american society for testing and materials, philadelphia. [5] hsu, t. m. (1981). analysis of cracks at attachment lugs. j. aircraft, 18(9), pp. 755-760. doi: 10.2514/3.57558. [6] kathiresan, k., brussat, t. r. and rudd, j. l. (1985). crack growth analyses and correlations for attachment lugs, j. aircraft, 22(9), pp. 818-824. doi: 10.2514/3.45207. [7] narayana, k. b., dayananda, t. s., dattaguru, b., ramamurthy, t. s. and vijayakumar, k. (1994). cracks emanating from pin-loaded lugs. eng fract mech, 47(1), pp. 29-38. doi: 10.1016/0013-7944(94)90235-6, [8] boljanović, s. and maksimović, s. (2016). fatigue failure analysis of pin-loaded lugs. frattura ed integrità strutturale, 35, pp. 313-321. doi: 0.3221/igf-esis.35.36 [9] boljanović, s., maksimović, s. and djurić, m. (2016). fatigue strength assessment of initial semi-elliptical cracks located at a hole. int j fatigue, 92, part 2, pp. 548-556. doi: 10.1016/j.ijfatigue.2016.04.011. [10] naderi, m. and iyyer, n. (2015). fatigue life prediction of cracked attachment lugs using xfem. int j. fatigue, 77, pp. 186-193. doi: 10.1016/j.ijfatigue.2015.02.021. [11] naderi, m., sarkar, s., amiri, m. & iyyer, n. (2016). extended isogeometric analysis (xiga) of fatigue life in attachment lug. j fail anal prev, 16(4), pp. 601–611. doi: 10.1007/s11668-016-0125-y [12] rigby, r. and aliabadi, m. h. (1997). stress intensity factors for cracks at attachment lugs. eng fail anal, 4(2), pp. 133146. doi: 10.1016/s1350-6307(97)00004-6. i s. akbari et alii, frattura ed integrità strutturale, 47 (2019) 39-53; doi: 10.3221/igf-esis.47.04 53 [13] wang, g. s. (1992). weight functions and stress intensity factors for the single crack round-ended straight lug. int j fract, 56(3), pp. 233-255. doi: 10.1007/bf00012329. [14] mikheevskiy, s., glinka, g. and algera, d. (2012). analysis of fatigue crack growth in an attachment lug based on the weight function technique and the unigrow fatigue crack growth model. int j fatigue, 42, pp. 88-94. doi: 10.1016/j.ijfatigue.2011.07.006. [15] wu, x. r. & tong, d. h. (2018). evaluation of various analytical weight function methods base on exact k-solutions of an edge-cracked circular disc. eng fract mech, 189, pp.64-80. doi: 10.1016/j.engfracmech.2017.09.024. [16] xu, w., wu, x. r., yu, y. and li, z. h. (2018). a weight function method for mixed modes hole-edge cracks. fatigue fract eng mater struct, 41, pp. 223-234. doi: 10.1111/ffe.12674. [17] bahloul, a., benahmed, a. and bouraoui, c. (2018). an engineering predictive approach of fatigue crack growth behavior: the case of the lug-type joint. comptes rendus mécanique, 346(1), pp. 1-12. doi: 10.1016/j.crme.2017.10.003. [18] fawaz, s. a., andersson, b. and newman jr, j. c. (2003). experimental. verification of stress intensity factor solutions for corner cracks at a hole. subject to general loading. icaf, fatigue of aeronautical structures as an engineering challenge. [19] newman, j. c., jr and raju, i. s. (1984). stress-intensity factor equations for cracks in three-dimensional finite bodies subjected to tension and bending loads. nasa; united states. [20] chikmath, l. and dattaguru, b., (2017). prognostic analysis of fastener joints in straight attachment lugs. int j struct inte, 8(3), pp. 404-422. doi: 10.1108/ijsi-09-2016-0031 [21] abaqus. (2012). dassault systèmes inc., usa. [22] pook, l. p. (1994). some implications of corner point singularities. eng fract mech, 48, pp. 367-378. doi: 10.1016/0013-7944(94)90127-9 [23] nabavi, s. m. and shahani, a. r. (2014). dynamic stress intensity factors for a longitudinal semi-elliptical crack in a thick-walled cylinder. int j eng sci technol, 6(5), pp. 57-77. [24] pook, l. p. (2000). crack profiles and corner point singularities. fatigue fract eng mater struct, 23(2), pp. 141-150. doi: 10.1046/j.1460-2695.2000.00249.x. [25] anderson, t.l. (2017). fracture mechanics: fundamentals and applications, 4th edition, boca raton, crc press. [26] shen, g. and glinka, g. (1991). weight functions for a surface semi-elliptical crack in a finite thickness plate. theor appl fract mech, 15(3), pp. 247-255. doi: 10.1016/0167-8442(91)90023-d. [27] fett, t., mattheck, c. and munz, d. (1987). on the calculation of crack opening displacement from the stress intensity factor. eng fract mech, 27(6), pp. 697-715. doi: 10.1016/0013-7944(87)90159-7. [28] kim, j.-h., lee, s.-b. and hong, s.-g. (2003). fatigue crack growth behavior of al7050-t7451 attachment lugs under flight spectrum variation. theor appl fract mech, 40(2), pp. 135-144. doi: 10.1016/s0167-8442(03)00041-7. << /ascii85encodepages false /allowtransparency false /autopositionepsfiles true /autorotatepages /none /binding /left /calgrayprofile (dot gain 20%) /calrgbprofile (srgb iec61966-2.1) /calcmykprofile (u.s. web coated \050swop\051 v2) /srgbprofile (srgb iec61966-2.1) /cannotembedfontpolicy /error /compatibilitylevel 1.4 /compressobjects /tags /compresspages true /convertimagestoindexed true /passthroughjpegimages true /createjobticket false /defaultrenderingintent /default /detectblends true /detectcurves 0.0000 /colorconversionstrategy /cmyk /dothumbnails false /embedallfonts true /embedopentype false /parseiccprofilesincomments true /embedjoboptions true /dscreportinglevel 0 /emitdscwarnings false /endpage -1 /imagememory 1048576 /lockdistillerparams false /maxsubsetpct 100 /optimize true /opm 1 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can be opened with acrobat and adobe reader 5.0 and later.) >> /namespace [ (adobe) (common) (1.0) ] /othernamespaces [ << /asreaderspreads false /cropimagestoframes true /errorcontrol /warnandcontinue /flattenerignorespreadoverrides false /includeguidesgrids false /includenonprinting false /includeslug false /namespace [ (adobe) (indesign) (4.0) ] /omitplacedbitmaps false /omitplacedeps false /omitplacedpdf false /simulateoverprint /legacy >> << /addbleedmarks false /addcolorbars false /addcropmarks false /addpageinfo false /addregmarks false /convertcolors /converttocmyk /destinationprofilename () /destinationprofileselector /documentcmyk /downsample16bitimages true /flattenerpreset << /presetselector /mediumresolution >> /formelements false /generatestructure false /includebookmarks false /includehyperlinks false /includeinteractive false /includelayers false /includeprofiles false /multimediahandling /useobjectsettings /namespace [ (adobe) (creativesuite) (2.0) ] /pdfxoutputintentprofileselector /documentcmyk /preserveediting true /untaggedcmykhandling /leaveuntagged /untaggedrgbhandling /usedocumentprofile /usedocumentbleed false >> ] >> setdistillerparams << /hwresolution [2400 2400] /pagesize [612.000 792.000] >> setpagedevice microsoft word 2345 p. dhaka et alii, frattura ed integrità strutturale, 48 (2019) 630-638; doi: 10.3221/igf-esis.48.60 630 focused on “showcasing structural integrity research in india” effect of contact geometry on the contact stresses in a flat with rounded edge contact pankaj dhaka, raghu v. prakash indian institute of technology madras, india pdhakanith@gmail.com, https://orcid.org/0000-0001-7250-7845 raghuprakash@iitm.ac.in, https://orcid.org/0000-0002-8888-022x abstract. the blade-disc dovetail interface in an aero-engine compressor is characterized by a non-uniform pressure distribution which can be obtained by an equivalent flat with rounded edge-on-plate configuration. the contact tractions for a mating pair are affected by many parameters which include, contact geometry, loading conditions, and material properties; with contact geometry being one of the prominent factors. in the present work, a 2-d elastic and elasto-plastic finite element analysis has been carried out for a rounded contact geometry to study the influence of the radius of the corners ‘r’ and length of the flat region ‘2a’. it is observed that the peak tensile stress in the fretting direction decreases with increasing ‘a’ (for constant ‘r’) which is likely to delay the crack initiation. also, as compared to elasto-plastic analysis, elastic analysis overestimates peak tensile stress and possibly gives a conservative estimate for the fretting fatigue life. further, the effect of modelling elastic-plastic behaviour is significant for low a/r ratio (for constant ‘r’). however, opposite trend was observed when ‘r’ was varied keeping ‘a’ constant. also, it is found that the effect of contact geometry cannot be characterized using a single parameter like a/r ratio or contact area. keywords. dovetail; flat with rounded edge; fretting; contact geometry. citation: dhaka, p., prakash, r.v., effect of contact geometry on the contact stresses in a flat with rounded edge contact, frattura ed integrità strutturale, 48 (2019) 630-638. received: 04.01.2019 accepted: 25.01.2019 published: 01.04.2019 copyright: © 2019 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. introduction nvestigation of the contact behaviour is an indispensable exercise for many applications ranging from aero-engine and automotive components to orthopedic implants, hoists, power plant and electronic components [1-6]. the detrimental effect of a poor contact could be either loss of clearance in assemblies due to wear at the interface [2, 3, 6] or complete failure due to crack initiation and propagation at the mating interface [1, 4]. the damage gets even more aggravated in the fretting regime where the sliding between the contact pair is of small amplitude (ranging between few microns to about 200 microns) because of smaller contact zone size which leads to highly localized stresses. the contact i http://www.gruppofrattura.it/va/48/2345.mp4 p. dhaka et alii, frattura ed integrità strutturale, 48 (2019) 630-638; doi: 10.3221/igf-esis.48.60 631 behaviour of a mating pair is affected by many parameters which include material properties, contact geometry, and loading conditions, with contact geometry being one of the crucial parameters. contact geometry directly affects the completeness and conformality of a contact. in case of a complete contact, the nominal area of contact is fixed geometrically and is independent of normal load whereas, for an incomplete contact, the contact area increases with an increase in normal load. further, if the largest characteristic dimension of the contact zone (contact radius) is considerably smaller than the smallest radius of the curvature of a mating pair, then the contact becomes non-conformal contact while vice-versa forms a conformal contact [7]. most of the studies reported in the literature have generally focused on non-conformal and incomplete contacts viz. cylinder on plate configurations, with very few studies on conformal and complete contact. a flat with rounded edge-on plate contact is a type of conformal and partially complete contact. the relevance of analyzing flat with rounded edge contact lies in the fact that it is impractical to machine a flat surface with perfectly sharp corners owing to machining constraints which inevitably leads to corner radii. another interesting application is in the case of an aero-engine compressor where the contact pressure distribution at the blade-disc dovetail interface can be represented by a flat-withrounded-edge geometry [8]. while in the case of a flat punch with sharp corners, singularity is present at contact edge and asymptotic contact pressure distribution is obtained, the rounding of the corners in a flat with rounded-edge leads to contact pressure falling to zero at the edge of the contact. this results in a non-uniform pressure distribution with constant pressure at the center and pressure peaks at the corners [9]. ciavarella et al. [9-11] in one of their seminal works, proposed the analytical solution for the contact tractions in the case of partially flat contacts subjected to oscillating tangential and bulk load. further, warmuth et al. [12] observed that fretting in less conforming contacts leads to considerably higher wear rates compared to conformal contacts. they proposed that the difference in contact pressure because of different contact geometry was not the contributory factor for different wear rates rather it was attributed to the effect of contact geometry on debris flow in the contact zone. many researchers [13, 14] studied the effect of radii of corners in the partially flat pad on fretting fatigue life and found that, in general, fretting fatigue life drops with an increase in corner radii which was attributed to increased stresses with rounding. in the present work, effect of both half-length of central flat region (‘a’) and corner radii (‘r’) has been studied to understand its influence on the contact tractions and explore the possibility of quantifying the effect of contact geometry using a single parameter like a/r ratio or contact zone size. finite element analysis was carried out for the both elastic and elasto-plastic case to understand the interrelation between yielding and contact geometry. methodology inite element methods tend to be quite advantageous in analyzing the contact problems which, otherwise are either infeasible to deal using experimental methods or prove to be cumbersome when subtle information regarding contact tractions is required. in the present work, a two-dimensional finite element analysis was carried out for a flat-with-rounded-edge pad on plate configuration. the geometric dimensions for flat-with-rounded-edge pad were taken from fouvry et al. [9] which is a scaled-down model and represents the contact pressure distribution for a real blade-disc dovetail interface. the central flat region ‘2a’ was taken as 3 mm while the radius at the corners(‘r’) was 1.35 mm. the plate was modelled with width ‘l’ and depth ‘b’ of 20 mm and 10 mm respectively. the model was meshed using 2-d plane strain, first order quadrilateral elements with reduced integration (cpe4r) and triangular elements (cpe3). these elements are generally preferred over second-order elements which give fluctuating pressure distribution for contact problems with friction [15]. the mesh was sufficiently refined in the contact zone and mesh size of 2 µm was used while regions away from the contact zone were meshed using coarser mesh. the geometry and meshed model are shown in fig. 1 (a) and 1 (b) respectively. the material behaviour for the flat with rounded edge pad and plate was modelled using ti6al-4v which is one of the widely used titanium alloys in aero-engines for fretting prone assemblies. the elasto-plastic behaviour of ti-6al-4v was modelled using ramberg-osgood law with material properties as given in tab. 1 [16]. the ramberg-osgood deformation plasticity model available in abaqus® is generally used to describe elastic-plastic behaviour in applications pertaining to fracture mechanics and doesn’t require separate definition for elastic and plastic segment of the stress-strain curve [17]. the ramberg-osgood coefficient and exponent were obtained by fitting a power law relationship in plastic strain vs. true stress response normalized with respect to corresponding yield point values using the following equation [18]: 0 0 n p           f p. dhaka et alii, frattura ed integrità strutturale, 48 (2019) 630-638; doi: 10.3221/igf-esis.48.60 632 where, p is plastic strain,  is true stress, 0 , 0 are yield point values for true stress and true strain respectively, and  , n are ramberg osgood coefficient and exponent respectively (a) (b) figure 1: (a) schematic of flat-with-rounded-edge on plate configuration, (b) meshed model young’s modulus (gpa) poisson’s ratio yield strength (mpa) α n 121 0.29 677.6 0.43 10 table 1: material properties of ti-6al-4v. for validation of fem effect of contact geometry s. no. ‘a’ ‘r’ s. no. objective ‘a’ ‘r’ 1 1.5 1.35 11 effect of ‘a’ 1 1.35 2 0.5 1.35 12 2.7 1.35 3 0.1 1.35 13 4.05 1.35 4 0.005 1.35 14 effect of ‘r’ 1.5 1 5 0.0005 1.35 15 1.5 0.75 6 1.5 0.135 16 1.5 0.5 7 1.5 2 17 effect of a/r ratio 1 2 8 1.5 4 18 0.5 1 9 1.5 6 19 2 1 10 1.5 8 20 1 0.5 table 2: analysis cases for the validation of finite element model the frictional interaction between the fretting pad and the plate was defined using coulomb’s law of friction with a constant friction coefficient of 0.8; a value typically observed in experimental studies [8]. combined penalty (for shear traction) and augmented lagrange (for normal contact) algorithm was used for contact formulation. the combined algorithm has been found particularly suitable for the fretting contact problems and computationally more efficient as compared to pure penalty formulation or pure lagrange method [19]. a constant normal load (p) of 750 n has been p. dhaka et alii, frattura ed integrità strutturale, 48 (2019) 630-638; doi: 10.3221/igf-esis.48.60 633 applied on the top of the flat-with-rounded-edge pad and the pad is constrained to move in the vertical direction only. the bottom edge of the plate has been restrained from moving in both horizontal and vertical direction. the validation of present finite element model was carried out using two approaches: first, the contact pressure distribution obtained from the elastic finite element analysis was compared with the analytical results proposed in the literature [10]; secondly, the length of the central flat region and corner radii were collapsed independently to make it tend towards the cylinder-on-plate and flat punch respectively. the results were compared with the analytical solution proposed by hertz for cylinder-on-plate configuration [20, 21]. further, the effect of contact geometry was studied by varying either ‘a’, keeping ‘r’ as constant or by varying ‘r’, keeping ‘a’ as constant. the analysis was extended further to the elasto-plastic case to understand the interrelation between material yielding and contact geometry. all the analysis cases are tabulated in tab. 2. results and discussion he analysis results from the present study are presented in three different sections as follows: finite element validation fig. 2(a) shows the comparison between the contact pressure distribution obtained from finite element analysis and the analytical solution proposed by ciavarella et al. [10]. it can be observed that the contact pressure distribution obtained from analytical and finite element analysis correlate well at the rounded corners but show significant deviation in the central contact zone. the possible reasons for the deviation could be: first, as the analytical solution proposed by ciavarella et al. [10] is an approximate solution and involves calculation of many variables through an iterative approach which is likely to cause an error. secondly, for higher values of a/r ratio, the half-plane idealization doesn’t hold well. to further substantiate this argument and validate the present finite element model, the analysis was carried out with reduced values of ‘a’. fig. 2(b) depicts the evolution of contact pressure distribution for different values of ‘a’, keeping ‘r’ as constant. it can be observed that, as the length of the central flat region is reduced keeping radii of corners as constant, the contact pressure distribution starts approaching towards that for a cylinder-on-plate configuration. further, the solution agrees very well with the hertz analytical solution [20] for cylinder-on-plate configuration. (a) (b) figure 2: (a) comparison between finite element analysis and analytical results, and (b) evolution of contact pressure distribution with reducing ‘a’. also, when the radius of corners was reduced, the contact pressure distribution tends towards that of the flat punch-onplate with the deviation from analytical results [21] being approximately 8% as shown in fig. 3. t p. dhaka et alii, frattura ed integrità strutturale, 48 (2019) 630-638; doi: 10.3221/igf-esis.48.60 634 figure 3: evolution of contact pressure distribution with reducing ‘r’ effect of contact geometry the contact zone size in case of a flat-with-rounded-edge geometry is a function of two characteristic geometric dimensions viz. length of the flat region, ‘2a’ and corner radii, ‘r’, in contrast to the case of a cylinder-on-plate configuration where radius of the cylinder is the only characteristic geometric dimension. to investigate whether the influence of contact geometry in case of a flat-with-rounded-edge geometry can be quantified using a single parameter like contact area or a/r ratio, elastic finite element analyses were carried out for different contact geometries by varying ‘a’ and ‘r’ independently. from fig. 4(a), it can be observed that the maximum contact pressure in the contact zone decreases with an increase in ‘a’ for a constant value of ‘r’. this is because of the proportional increase in the contact area with an increase in ‘a’ as shown in fig. 4(b). also, as ‘a’ tends towards zero, the maximum contact pressure approaches hertzian pressure [20] for a cylinder with radius ‘r’, as marked with in the fig. 4(a). (a) (b) figure 4: (a) variation of maximum contact pressure with ‘a’, and (b) contact zone size variation with ‘a’ further, the analysis was repeated by varying the value of ‘r’, keeping ‘a’ as constant. fig. 5(a) shows the variation of maximum contact pressure, mean pressure in the central flat region and analytical mean pressure (i.e. p/2a for unit thickness) with an increasing value of ‘r’. it can be observed that the maximum contact pressure decreases with an increase in ‘r’, tending towards a constant value for higher values of ‘r’. this can be explained by the evolution of contact zone size with ‘r’ which also shows a similar trend and starts saturating for the higher value of ‘r’ as shown in fig. 5(b). further, the mean contact pressure in the central flat region starts approaching theoretical value of mean pressure as corner radius is decreased below half-length of the flat region. also, from the slope of the curves in fig. 4(a), (b) and 5(a), (b), it can be inferred that effect of varying ‘a’ is more prominent on contact pressure and contact area than varying ‘r’. fig. 5(c) shows the variation of maximum contact pressure with a/r ratio for two different cases viz. for variable ‘a’, keeping ‘r’ as constant, and variable ‘r’, keeping ‘a’ as constant. it can be observed that both the curves intersect at a single point only i.e. approximately at a/r=1. further, only single point of intersection was found between the curves of p. dhaka et alii, frattura ed integrità strutturale, 48 (2019) 630-638; doi: 10.3221/igf-esis.48.60 635 variable ‘a’ and variable ‘r’ when normalized contact pressure was plotted against the normalized contact area as shown in fig. 5(d). the normalization of maximum contact pressure and contact area has been done with respect to maximum contact pressure and contact area obtained from the reference condition of a=1.5 mm and r=1.35 mm. thus, it can be inferred that, for a flat-with-rounded-edge geometry, the effect of contact geometry cannot be quantified using a single parameter like a/r ratio or contact area, apart from the only case when both ‘a’ and ‘r’ are approximately equal. (a) (b) (c) (d) figure 5: (a) variation of maximum contact pressure with ‘r’, (b) contact zone size variation with ‘r’, (c) variation of maximum contact pressure with a/r ratio, and (d) normalized contact pressure variation with the normalized contact area. (a) (b) figure 6: (a) normal stress distribution on plate surface in xdirection, and (b) variation of maximum normal stress (in x-direction) with a/r ratio p. dhaka et alii, frattura ed integrità strutturale, 48 (2019) 630-638; doi: 10.3221/igf-esis.48.60 636 further, for the same normal load of 750 n, a fully reversed tangential displacement of 15 µm (triangular waveform with 5 hz frequency) was applied to the flat-with-rounded edge pad in the x-direction and one fretting cycle with elasto-plastic material behavior was simulated. the normal stress distribution was extracted from plate surface after quarter stroke in the forward direction. fig. 6(a) shows the typical stress distribution for contact geometry with a=1.5 mm and r=1.35 mm. a tensile stress peak is observed on the trailing edge which is generally considered critical from the viewpoint of crack initiation [22]. fig. 6(b) shows the variation of peak tensile stress with a/r ratio for both the cases, viz., variable ‘a’, constant ‘r’ and variable ‘r’, constant ‘a’. it can be observed that peak tensile stress decreases with an increase in a/r ratio. at a constant value of ‘r’, increase in a/r ratio means, increase in ‘a’ i.e. half-length of the flat region, which means that as the contact geometry becomes flatter/more conformal at the center, the tendency for crack initiation decreases. similarly, at constant ‘a’ value, increase in a/r ratio means, decrease in ‘r’ i.e. radius of contact edge, which implies that as the corners become sharper, the resistance for crack initiation increases. this is surprising because in general, filleting at the corners is considered as a measure to relieve the stresses at the contact edges but that is not always true and it may even lead to an increase in stresses. further, it agrees with the observations reported in the literature [13, 14] where researchers have found that fretting fatigue life decreases with the increase in the corner radius and it was attributed to increased stresses due to filleting at the corners. effect of material yielding to check whether yielding of the material has any implications on the analysis presented in the previous section, finite element analyses were also carried out using elasto-plastic material behaviour. the elasto-plastic behaviour of material was modelled using ramberg osgood law. from fig. 7(a), it can be observed that elasto-plastic analysis results deviate from elastic analysis results for lower values of a/r ratio for variable ‘a’ and constant value of ‘r’. this is because, with the decrease in ‘a’, contact geometry starts approaching cylinder-on-plate configuration and thus leading to increased non-conformality of the contact. this results in higher stresses which lead to sufficient yielding of material and hence, elasto-plastic analysis results deviate from the elastic analysis. further, fitting a logarithmic trend line to the contact pressure variation obtained from elastic analysis shows that as ‘a’ tends to zero, contact pressure approaches to that of a cylinder-on-plate case with radius ‘r’ as 1.35 mm. from fig. 7(b), it can be seen that when ‘r’ is varied keeping ‘a’ as constant, the elasto-plastic analysis results deviate from elastic analysis results at higher values of a/r ratio. this is because, with reduction in ‘r’, the contact geometry tends towards the flat-punch-on-half plane case, leading to highly localized stresses at the corners. hence, the elasto-plastic analysis results deviate significantly from the elastic analysis results. interestingly, the deviation between elastic and elastoplastic analysis results becomes significant only about a/r value of approximately equal to one. further, the elastic analysis predicts higher contact pressure and stresses as compared to elasto-plastic analysis and is likely to give the conservative estimate for the fretting wear volume and fretting fatigue life which are dependent on contact pressure and tensile stress in fretting direction respectively. (a) (b) figure 7: effect of material yielding on the variation of maximum contact pressure with a/r ratio for (a) variable ‘a’ and constant ‘r’=1.35 mm, and (b) variable ‘r’ and constant ‘a’=1.5 mm. p. dhaka et alii, frattura ed integrità strutturale, 48 (2019) 630-638; doi: 10.3221/igf-esis.48.60 637 conclusions wo-dimensional finite element analysis was carried out for a flat-with-rounded-edge contact to study the influence of contact geometry on contact tractions. the finite element analysis results were compared with the analytical results and reasonable agreement was found between them. further, the influence of geometric parameters viz. ‘a’ and ‘r’ was studied. a comparison was also made between finite element analyses carried out using elastic and elastoplastic material behavior. following conclusions can be drawn from the present study:  the finite element analysis results give better correlation with analytical results for lower value of a/r ratio.  the effect of ‘a’ is more prominent on contact pressure than varying ‘r’ because of the greater influence of ‘a’ on the contact zone size.  the effect of contact geometry on the contact stresses cannot be quantified using a unified parameter like a/r ratio or contact area under the present loading conditions.  lesser filleting at the corners is found to be more beneficial as compared to generous fillets because it leads to a decrease in the peak tensile stresses. this is likely to delay the crack initiation and hence, longer fretting fatigue life. further research is required to determine the extent of filleting which can be applied for a particular contact geometry.  both elastic and elasto-plastic analysis give identical results and the deviation becomes significant only when the contact geometry starts approaching either non-conformal contact or flat punch with sharp corners.  the elastic analysis overpredicts the contact pressure and peak tensile stresses which is likely to result in a conservative estimate for fretting wear volume and fretting fatigue life. references [1] papanikos, p., meguid, s.a., stjepanovic, z. (1998). three-dimensional nonlinear finite element analysis of dovetail joints in aero-engine discs, finite elem. anal. des., 29(3–4), pp. 173–186, doi: 10.1016/s0168-874x(98)00008-0. [2] söderberg, a., andersson, s. (2009). simulation of wear and contact pressure distribution at the pad-to-rotor interface in a disc brake using general purpose finite element analysis software, 267, pp. 2243–2251, doi: 10.1016/j.wear.2009.09.004. [3] bitter, t., khan, i., marriott, t., lovelady, e., verdonschot, n., janssen, d. (2018). finite element wear prediction using adaptive meshing at the modular taper interface of hip implants, j. mech. behav. biomed. mater., 77(may 2017), pp. 616–623, doi: 10.1016/j.jmbbm.2017.10.032. [4] cruzado, a., urchegui, m.a., gómez, x. (2012). finite element modeling and experimental validation of fretting wear scars in thin steel wires, wear, 289, pp. 26–38, doi: 10.1016/j.wear.2012.04.018. [5] kim, h.k., lee, y.h., lee, k.h. (2008). on the geometry of the fuel rod supports concerning a fretting wear failure, nucl. eng. des., 238(12), pp. 3321–3330, doi: 10.1016/j.nucengdes.2008.08.010. [6] shinde, d.u. (2008). wear simulation of electric contacts subjected to vibrations, auburn university. [7] hills, d.a. (1994). mechanics of fretting fatigue, 175, pp. 107–113. [8] fouvry, s., paulin, c., deyber, s. (2009). impact of contact size and complex gross-partial slip conditions on ti-6al4v/ti-6al-4v fretting wear, tribol. int., 42(3), pp. 461–474, doi: 10.1016/j.triboint.2008.08.005. [9] ciavarella, m., hills, d.a., monno, g. (1998). the influence of rounded edges on indentation by a flat punch, inst. mech. engrs., 212, pp. 319-328. [10] ciavarella, m., demelio, g. (2001). a review of analytical aspects of fretting fatigue, with extension to damage parameters, and application to dovetail joints, intnl. j. solids and structures, 38, pp. 1791-1811. [11] ciavarella, m., macina, g. (2003). new results for the fretting-induced stress concentration on hertzian and at rounded contacts, 45, pp. 449–467, doi: 10.1016/s0020-7403(03)00061-4. [12] warmuth, a.r., pearson, s.r., shipway, p.h., sun, w. (2013). the effect of contact geometry on fretting wear rates and mechanisms for a high strength steel, wear, 301(1–2), pp. 491–500, doi: 10.1016/j.wear.2013.01.018. [13] juoksukangas, j., lehtovaara, a., mäntylä, a. (2013). the effect of contact edge geometry on fretting fatigue behavior in complete contacts, wear, 308(1–2), pp. 206–212, doi: 10.1016/j.wear.2013.06.013. [14] mall, s., naboulsi, s., namjoshi, s.a. (2008). contact geometry effects on fretting fatigue crack initiation behaviour of ti–6al–4v, tribol. mater. surfaces interfaces, 2(1), pp. 25–32, doi: 10.1179/175158308x320755. t p. dhaka et alii, frattura ed integrità strutturale, 48 (2019) 630-638; doi: 10.3221/igf-esis.48.60 638 [15] ding, j., leen, s.b., mccoll, i.r. (2004). the effect of slip regime on fretting wear-induced stress evolution, int. j. fatigue, 26(5), pp. 521–531, doi: 10.1016/j.ijfatigue.2003.09.001. [16] ambrico, j.m., begley, m.r. (2000). plasticity in fretting contact, j. mech. phys. solids, 48(11), pp. 2391–417. [17] abaqus 6.12-1 documentation. [18] james, l.a., steel, a.a. (2017). ramberg-osgood strainhardening characterization, j. pressure vessel technology 117, pp. 341–345. [19] anandavel, k., prakash, r. v. (2011). effect of three-dimensional loading on macroscopic fretting aspects of an aeroengine blade – disc dovetail interface. tribiology int., 44(11), pp. 1544–1555, doi: 10.1016/j.triboint.2010.10.014. [20] hertz, h. (1882). on the contact of elastic solids, j. pure and applied mathematics, 92, pp. 156-171. [21] k. l. johnson. (1985). contact mechanics, cambridge, cambridge university press. [22] mcveigh, p. a., farris, t.n. 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can be opened with acrobat and adobe reader 5.0 and later.) >> /namespace [ (adobe) (common) (1.0) ] /othernamespaces [ << /asreaderspreads false /cropimagestoframes true /errorcontrol /warnandcontinue /flattenerignorespreadoverrides false /includeguidesgrids false /includenonprinting false /includeslug false /namespace [ (adobe) (indesign) (4.0) ] /omitplacedbitmaps false /omitplacedeps false /omitplacedpdf false /simulateoverprint /legacy >> << /addbleedmarks false /addcolorbars false /addcropmarks false /addpageinfo false /addregmarks false /convertcolors /converttocmyk /destinationprofilename () /destinationprofileselector /documentcmyk /downsample16bitimages true /flattenerpreset << /presetselector /mediumresolution >> /formelements false /generatestructure false /includebookmarks false /includehyperlinks false /includeinteractive false /includelayers false /includeprofiles false /multimediahandling /useobjectsettings /namespace [ (adobe) (creativesuite) (2.0) ] /pdfxoutputintentprofileselector /documentcmyk /preserveediting true /untaggedcmykhandling /leaveuntagged /untaggedrgbhandling /usedocumentprofile /usedocumentbleed false >> ] >> setdistillerparams << /hwresolution [2400 2400] /pagesize [612.000 792.000] >> setpagedevice microsoft word numero_37_art_23 n.r. gates et alii, frattura ed integrità strutturale, 37 (2016) 166-172; doi: 10.3221/igf-esis.37.23 166 focussed on multiaxial fatigue and fracture fatigue crack growth behavior under multiaxial variable amplitude loading nicholas r. gates, ali fatemi mechanical, industrial and manufacturing engineering department, the university of toledo, 2801 w. bancroft street, toledo, oh 43606, usa ngates@eng.utoledo.edu, afatemi@eng.utoledo.edu nagaraja iyyer technical data analysis, inc. (tda), 3190 fairview park drive, suite 650, falls church, va 22042, usa. niyyer@tda-i.com nam phan us naval air systems command, 48110 shaw road, building 2187, suite 2320a, patuxent river, md 20670, usa. nam.phan@navy.mil abstract. this study compares both uniaxial and multiaxial variable amplitude experimental crack growth data for naturally initiated fatigue cracks in tubular specimens of 2024-t3 aluminum alloy to predictions based on two state-of-the-art analysis codes: unigrow and fastran. for variable amplitude fatigue tests performed under pure axial nominal loading conditions, both unigrow and fastran analyses were found to produce mostly conservative growth life predictions, despite good agreement with constant amplitude crack growth data. for variable amplitude torsion and combined axial-torsion crack growth analyses, however, the conservatism in growth life predictions was found to reduce. this was attributed to multiaxial nominal stress state effects, such as t-stress and mixed-mode crack growth, which are not accounted for in either unigrow or fastran, but were found in constant amplitude fatigue tests to increase experimental crack growth rates. since cracks in this study were initiated naturally, different initial crack geometry assumptions were also investigated in the analyses. keywords. fatigue crack growth; multiaxial; variable amplitude; fastran; unigrow. introduction ost engineering components and structures are subjected to variable amplitude cyclic loadings throughout their service lives. due to the nature of these loadings, they typically result in multiaxial stress states, and individual stress components can vary in a non-proportional manner. when such components are operating under a damage tolerant design philosophy, being able to predict how fatigue cracks will grow under these complex loading conditions is a topic of particular interest. one of the key requirements for the application of fracture mechanics concepts in a fatigue crack growth analysis is that conditions of similitude should be retained. similitude implies that for a particular value of driving force parameter (e.g. jm n.r. gates et alii, frattura ed integrità strutturale, 37 (2016) 166-172; doi: 10.3221/igf-esis.37.23 167 integral, stress intensity factor (sif), crack tip opening displacement (ctod), etc.), the state of stress surrounding the crack tip is uniquely described by the value of that parameter. however, for variable amplitude loading, load history dependence may alter the local stress state at a crack tip allowing the possibility for multiple crack growth rates to occur at the same nominal driving force. because of this, the amount of crack growth experienced in a variable amplitude loading history cannot be accurately assessed by simply summing the nominal crack growth increment for each applied cycle. load sequence effects have been attributed to a number of mechanisms including: crack blunting, compressive residual stresses in front of the crack tip, changes in plasticity induced crack closure due to varying amounts of residual deformation in the crack wake, crack deflection (i.e. increased roughness induced closure), and strain hardening effects. although all of these mechanisms may contribute in some degree, residual stresses and changes in closure levels tend to be the favored explanations [1]. in addition to load sequence effects on mode i crack growth under uniaxial nominal loading, multiaxial nominal stress states can also affect growth rates. for example, gladskyi and fatemi [2] studied axial and torsion load sequence effects on mode i crack growth and found that for cracks growing in mode i under pure torsion and pure axial loadings, cracks in pure torsion tests grew faster despite the same maximum principal stress range. additionally, the insertion of blocks of pure torsion cycles into an otherwise uniaxial loading history was shown to increase crack growth rate, while the insertion of uniaxial cycles into a pure torsion loading history was shown to decrease crack growth rate. most of these effects were explained in terms of the stress state at the crack tip. for mode i cracks growing under nominal torsion loading, it was speculated that the presence of a tangential stress (t-stress) component, acting parallel to the direction of crack growth, increased crack tip driving force for a given value of nominal sif. crack growth rate correlations for the various loading histories were found to improve when considering the effects of t-stress on plastic zone size. in this study, crack growth data were generated under a variety of variable amplitude loading conditions using notched tubular specimens of 2024-t3 aluminum alloy. given the complexity of such an analysis, two state-of-the-art analysis codes were used in order to compare the experimentally measured crack growth lives to predictions based on two fundamentally different crack growth models. unigrow [3] is based on the idea that residual stress distributions surrounding the crack tip are responsible for causing load sequence effects in variable amplitude crack growth, while fastran [4] attributes these effects to varying degrees of plasticity induced closure in the crack wake. since both analysis programs are meant for application to crack growth under uniaxial loading conditions, variable amplitude crack growth trends for multiaxial nominal loadings are compared with those for constant amplitude loading conditions in order to help interpret the analysis results. material and testing procedures he material chosen for all fatigue tests performed in this study was aluminum alloy 2024-t3. tests were performed using notched specimens of a thin-walled tubular geometry. the specimens feature a 30 mm long gage section with an outside diameter of 29 mm and an inside diameter of 25.4 mm, resulting in a wall thickness of 1.8 mm. to serve as a stress concentrator, a 3.2 mm diameter circular transverse hole was produced using a drilling and reaming operation through one side of the specimen gage section. material properties and complete specimen geometry can be found in [5]. all variable amplitude fatigue tests were based on a single stress-based simulated service loading history representing the nominal axial and shear loading conditions on the lower wing skin of a long-range military patrol aircraft. a variety of take-off, landing, and in-flight maneuvers are represented in the history. in its entirety, the loading history contains around 915000 data points, with each point approximately corresponding to one loading reversal on the axial stress channel. the maximum and minimum axial stresses in the unscaled history are 144.8 mpa and -51.3 mpa, respectively, while the maximum and minimum shear stresses are 67.0 mpa and -15.9 mpa, respectively. plots showing the time history of a 1000 reversal segment taken from the loading history, along with the axial-shear stress path for this same segment, are shown in fig. 1. the loading segment shown in this figure is representative of the loading patterns repeated throughout the remainder of the full history. from the stress path, it can be seen that the loading history contains significant nonproportional loading events. different loading conditions were obtained in testing by using the axial loading channel only, the torsion channel only, or the combined axial-torsion loading. variable amplitude fatigue tests were performed using a closed loop servo-hydraulic axial–torsion load frame by repeatedly applying the entire load history in nominal load control until a tip-to-tip crack length of 15 mm was reached. for each test, the entire loading history was scaled by an appropriate factor to obtain stress levels that would produce fatigue lives ranging from less than one block to around 10 blocks. a summary of the applied loading conditions for all t n.r. gates et alii, frattura ed integrità strutturale, 37 (2016) 166-172; doi: 10.3221/igf-esis.37.23 168 tests can be found in [5]. in addition to the variable amplitude fatigue tests, a variety of constant amplitude fatigue tests were also performed on notched specimens under fully-reversed axial, torsion, and combined axial-torsion loading. some results from these tests are presented herein as a basis for evaluating the variable amplitude crack growth predictions. crack initiation and growth were monitored by using a digital microscope camera, capable of 10–230x optical zoom levels. crack lengths were then measured using digital image analysis software. figure 1: representative loading segment from the variable amplitude service loading history in terms of (a) applied stresses vs. time and (b) axial-shear stress path. modeling procedures ecause constant amplitude crack growth rate data for the specimens tested in this study were only generated under fully-reversed loading conditions, they are not ideal for computing crack growth properties for either the unigrow or fastran software. as a result, the unigrow analyses performed in this study (version 2014-02-09) utilized material properties for a 2024-t351 aluminum alloy, which were already included in the unigrow material library. similarly, fastran (version 5.42) analyses were based on crack growth properties reported in literature for 2024-t3 [6]. the mechanical and crack growth properties for the materials used in both programs were found to be very similar to those measured experimentally for the 2024-t3 alloy used in this study. consequently, using the material data from literature is not expected to have a significant effect on the accuracy of crack growth predictions presented in the following section for either program. crack growth was only measured on the outer surface of the specimens tested in this study. therefore, it is reasonable to assume that while cracks were short, their geometry was either that of a through thickness crack or corner crack growing from the edge of the hole. additionally, since cracks were observed to grow from both sides of the hole, the assumption of diametrically opposite symmetric cracks was considered reasonable. as a result, two different specimen geometries were used in the following analyses: a circumferential through crack in a tube (tt), and two symmetric semi-elliptic corner cracks at a hole in a plate subjected to remote tensile stress (cch). the cch geometry was assumed to transition to the tt geometry after cracks became through thickness. the same sif solutions were defined as custom inputs in each crack growth program. because stress intensity factors for short cracks are lower for the cch geometry, the predicted crack growth lives are longer than those based on the tt crack geometry assumption. since it is possible for actual cracks to assume either of these geometries, or a combination of both, crack growth predictions based on both tt and cch sif solutions should provide an approximate upper and lower bounds for experimentally observed crack growth curves, so long as the crack growth models are accurate. for each nominal loading history, stresses were projected onto the maximum principal stress plane (consistent with observed crack growth planes) and input into the crack growth programs for analysis. this corresponds to the 0° plane (perpendicular to the specimen axis) for axial and combined variable amplitude loading histories, and the 45° plane for pure torsion loading. crack growth lives were compared from an initial half crack length of 1.8 mm (0.2 mm excluding the hole radius) to a length of 7.5 mm. b (a) (b) n.r. gates et alii, frattura ed integrità strutturale, 37 (2016) 166-172; doi: 10.3221/igf-esis.37.23 169 crack growth prediction results n order to establish some baseline crack growth prediction results, both unigrow and fastran were used to analyze crack growth under simple constant amplitude loading conditions. these results, shown in fig. 2 for the both tt and cch crack geometries, are useful when interpreting the results of subsequent variable amplitude analyses. figure 2: constant amplitude crack growth life predictions based on (a) fastran and (b) unigrow analyses. from these results, it is clear that both unigrow and fastran are capable of producing fairly accurate crack growth predictions under constant amplitude loading conditions. while unigrow gives slightly more conservative crack growth predictions than fastran, fig. 2 shows that the majority of life predictions are still within a factor of ±3 of experimental results, regardless of crack geometry assumption. additionally, the fact that most experimental crack growth lives fall between the tt and cch life predictions supports the idea that these predictions can be used to represent the lower and upper bounds for crack growth life, respectively. the first variable amplitude loading conditions analyzed were those corresponding to the pure axial (a) nominal loading history. plots of experimental versus predicted crack growth life for each analysis performed are shown in fig. 3 for both crack geometries. additionally, experimental versus predicted crack growth curves are shown in fig. 4(a) for the lowest applied loading level. from these results, both unigrow and fastran are generally found to produce conservative crack growth predictions for the loading history utilized, regardless of the assumed crack geometry. this is despite the fact that, for both programs, experimental crack growth lives under constant amplitude loading conditions were generally found to fall between predictions based on the tt and cch crack geometry assumptions. in general, the degree of conservatism in crack growth predictions tends to increase with decreasing stress levels. by comparing these results to the constant amplitude baseline analyses, the effects of the variable amplitude loading history are found to be greater for life predictions based on the unigrow crack growth model than for those based on fastran. while fastran growth life predictions for constant amplitude tests were, on average, a factor of 1.1 times longer than unigrow predictions, this difference increased to an average of 1.8 times longer for variable amplitude tests. the fact that variable amplitude growth life predictions for both analysis programs are closer to the experimentally measured lives as the loading level increases suggests that increased plasticity is likely not the cause for the prediction error. in addition to tests performed under axial only loading conditions, crack growth for the pure torsion (t) variable amplitude loading histories was also analyzed, shown in fig. 3. from figs. 3 and 4(b), crack growth predictions for the nominal torsion loading histories are found to be significantly different than those for axial loading. instead of being consistently conservative, the torsion growth predictions tend to be non-conservative based on fastran analyses, and fairly accurate based on unigrow analyses. additionally, the shift in conservatism is notably larger for the fastran analyses than for the unigrow analyses. while fastran life predictions for the axial loading history were an average of 1.9 times longer than unigrow predictions, this increases to a factor of 8.5 for the torsion loading history analyses. based on the differences between crack growth conditions under the pure axial and pure torsion loading histories applied in this i (a) (b) n.r. gates et alii, frattura ed integrità strutturale, 37 (2016) 166-172; doi: 10.3221/igf-esis.37.23 170 study, the cause for these shifts in prediction accuracy can be narrowed down to two likely sources: multiaxial stress state effects, such as the presence of t-stress, and/or differences in loading history profile. figure 3: variable amplitude crack growth life predictions based on (a) fastran and (b) unigrow analyses. figure 4: variable amplitude crack growth curves for lowest loading level (a) axial, (b) torsion, and (c) combined axial-torsion loading. concerning loading history profile, the axial channel of the variable amplitude service loading history, as shown in fig. 1(a), is composed of smaller cycles with significant tensile mean stress mixed with occasional larger cycles at a much smaller r ratio. the shear channel, on the other hand, is composed of small amplitude cycles, ranging between approximately zero to minimum conditions, mixed with occasional larger amplitude cycles of an approximate zero to maximum range. given these differences, significantly more crack closure would be expected for mode i crack growth under pure torsion loading due to the smaller tensile mean stress values. this agrees with the more conservative fastran life predictions for the axial loading history, as compared to the shear history. residual stresses, on the other hand, are most significantly affected by the maximum stress values in a loading history. therefore, the effect of the (a) (b) (a) (b) (c) n.r. gates et alii, frattura ed integrità strutturale, 37 (2016) 166-172; doi: 10.3221/igf-esis.37.23 171 loading history profile is not expected to have as large of an effect on residual stress distributions so long as the frequency and magnitude of maximum stress cycles are similar, which is the case in this study. as such, the fact that growth life predictions are more consistent between axial and torsion loading histories for unigrow analyses, as compared to fastran analyses, is not surprising. in addition to load history profile, even for constant amplitude loading conditions, mode i crack growth rates for nominal torsion loading of the notched tubular specimens were considerably higher than those for axial nominal loading at the same applied sif range. this was attributed to the presence of compressive tangential stress (t-stress) at the crack tip, resulting in an increased plastic zone size and crack driving force under multiaxial nominal stress states. because unigrow and fastran are both meant to model crack growth under uniaxial nominal loading conditions, neither program accounts for multiaxial stress state effects, such as t-stress, on mode i crack growth rates. therefore, for a given sif range, both models will predict lower crack growth rates than what would be expected in experiments for torsion and combined axial-torsion nominal loadings. as a result, the overall reduction in conservatism for the pure torsion variable amplitude growth life predictions is to be expected. finally, crack growth analyses were performed for the variable amplitude combined axial-torsion (at) loading histories. given the tension dominated nature of the variable amplitude loading history applied in this study, crack growth behavior for the combined loading tests is expected to be similar to that observed for the axial only tests. by studying the results, this is found to be generally true. figs. 3 and 4(c) show that crack growth life predictions for both axial only and combined loading tests tend to be conservative based on both fastran and unigrow analyses. additionally, the degree of conservatism is found to increase with decreasing loading levels in both cases. while crack growth prediction trends are qualitatively similar for the axial only and combined loading conditions, growth life predictions are generally found to be less conservative for combined loading tests. similar to the growth life predictions for the pure torsion tests, some of this difference is likely due to the crack growth models’ inability to account for increased growth rates due to the effect of t-stress on mode i crack growth. however, there are also additional factors that can contribute to this discrepancy which are only brought about under combined loading situations. fig. 1(b) shows that the variable amplitude service loading history investigated in this study contains a number of significant non-proportional loading events. when non-proportionally varying stresses are present in a crack growth analysis, it becomes especially difficult to calculate crack driving forces. because the principal stress directions are not constant under non-proportional loading conditions, a growing crack is continuously subjected to varying degrees of mixed-mode loading, regardless of its orientation. additionally, the tendency of a mode i crack to grow under the influence of maximum principal stress can cause increased crack meandering and crack face roughness as cracks try to align with the changing principal stress direction. while there are many factors, in addition to plasticity induced closure and residual stress effects, which have the potential to influence crack growth behavior under variable amplitude combined loading conditions, some of these effects act to increase crack growth rates (e.g. t-stress and mixed-mode loading), while others tend to hinder crack growth (e.g. crack path meandering). for the loading conditions and specimen geometry of interest in the current study, the combined effect of all of these mechanisms appears to result in less conservative crack growth predictions for combined loading histories than for axial only histories. this agrees with the higher crack growth rates observed at higher sif ranges for both inphase and 90° out-of-phase constant amplitude combined loading conditions, when compared to those for axial loading. summary and conclusions n general, variable amplitude crack growth predictions based on both fastran and unigrow analyses were found to be conservative, regardless of the initial crack geometry assumption, for both axial and combined axial-torsion loading conditions. the accuracy of crack growth predictions for pure torsion loading conditions, however, was found to vary depending on the crack growth model, although all predictions were less conservative than in the case of axial and combined loadings. this is despite the fact that, for both programs, the majority of experimental crack growth lives under constant amplitude axial loading conditions were predicted within a factor of ±3 and generally found to fall between predictions based on the tt and cch crack geometry assumptions. additionally, comparisons with constant amplitude crack growth data show that the shift in conservatism between the different nominal loading conditions can likely be attributed to multiaxial stress state effects on mode i crack growth, such as the presence of t-stress and the potential for mixed-mode crack growth conditions. these effects are not accounted for in either crack growth model investigated. i n.r. gates et alii, frattura ed integrità strutturale, 37 (2016) 166-172; doi: 10.3221/igf-esis.37.23 172 acknowledgements .s. naval air systems command (navair) provided financial support for this study. references [1] geary, w., a review of some aspects of fatigue crack growth under variable amplitude loading, int. j. fatigue, 14 (1992) 377–386. [2] gladskyi, m., fatemi, a., load sequence effects on fatigue crack growth in notched tubular specimens subjected to axial and torsion loadings, theor. appl. fract. mech. 69 (2014) 63–70. [3] mikheevskiy, s., glinka, g., elastic-plastic fatigue crack growth analysis under variable amplitude loading spectra, int. j. fatigue 31 (2009) 1828–1836. [4] newman, j.c. jr., fastran-ii a fatigue crack growth structural analysis program, nasa tm 104159, hampton, va, (1992). [5] gates, n.r., fatemi, a., multiaxial variable amplitude fatigue life analysis including notch effects, int. j. fatigue (in press 2016). doi: 10.1016/j.ijfatigue.2015.12.011. [6] newman, j.c. jr., phillips, e.p., swain, m.h., fatigue-life prediction methodology using small-crack theory, int. j. fatigue 21 (1999) 109–119. u << /ascii85encodepages false /allowtransparency false /autopositionepsfiles true /autorotatepages /none /binding /left /calgrayprofile (dot gain 20%) /calrgbprofile (srgb iec61966-2.1) /calcmykprofile (u.s. web coated \050swop\051 v2) /srgbprofile (srgb iec61966-2.1) /cannotembedfontpolicy /error /compatibilitylevel 1.4 /compressobjects /tags /compresspages true /convertimagestoindexed true /passthroughjpegimages true /createjobticket false /defaultrenderingintent /default /detectblends true /detectcurves 0.0000 /colorconversionstrategy /cmyk /dothumbnails false /embedallfonts true /embedopentype false /parseiccprofilesincomments true /embedjoboptions true /dscreportinglevel 0 /emitdscwarnings false /endpage -1 /imagememory 1048576 /lockdistillerparams false /maxsubsetpct 100 /optimize true /opm 1 /parsedsccomments true 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can be opened with acrobat and adobe reader 5.0 and later.) >> /namespace [ (adobe) (common) (1.0) ] /othernamespaces [ << /asreaderspreads false /cropimagestoframes true /errorcontrol /warnandcontinue /flattenerignorespreadoverrides false /includeguidesgrids false /includenonprinting false /includeslug false /namespace [ (adobe) (indesign) (4.0) ] /omitplacedbitmaps false /omitplacedeps false /omitplacedpdf false /simulateoverprint /legacy >> << /addbleedmarks false /addcolorbars false /addcropmarks false /addpageinfo false /addregmarks false /convertcolors /converttocmyk /destinationprofilename () /destinationprofileselector /documentcmyk /downsample16bitimages true /flattenerpreset << /presetselector /mediumresolution >> /formelements false /generatestructure false /includebookmarks false /includehyperlinks false /includeinteractive false /includelayers false /includeprofiles false /multimediahandling /useobjectsettings /namespace [ (adobe) (creativesuite) (2.0) ] /pdfxoutputintentprofileselector /documentcmyk /preserveediting true /untaggedcmykhandling /leaveuntagged /untaggedrgbhandling /usedocumentprofile /usedocumentbleed false >> ] >> setdistillerparams << /hwresolution [2400 2400] /pagesize [612.000 792.000] >> setpagedevice shot peening processes to obtain nanocrystalline surfaces in metal alloys: z.-q. wang et alii, frattura ed integrità strutturale, 53 (2020) 81-91; doi: 10.3221/igf-esis.53.07 81 low cycle fatigue damage model and sensitivity analysis of fatigue crack initiation by finite element approach zhi-qiang wang, xiao-guang huang*, dian-hao zhang college of pipeline and civil engineering, china university of petroleum (east china), qingdao, 266580, china. huangxg@upc.edu.cn, huangxg@upc.edu.cn, 918052605@qq.com abstract. to meet the design requirements, different types of defects are often machined on the surface of fatigue components. local stress concentration formed at the notch accelerates the initiation of fatigue crack, therefore greatly shortens the service lives of such components. based on the theory of continuous damage mechanics and the principle of irreversible thermodynamics, the damage evolution model of low cycle fatigue is investigated. by programming the damage evolution model as a umat subroutine and coupling it to abaqus, the fatigue damage and crack initiation life of notched p92 steel samples under specific loads are simulated, and the crack initiation location is determined. furthermore, the damage evolution and crack initiation sensitivity of notch morphology are considered. the results show that the crack initiation occurs easily in the notch root where the damage reaches the maximum and the plastic strain accumulates most quickly under cyclic loading. the fatigue damage accumulates slowly at the initial stage, but the damage accumulates rapidly after the cumulative damage reaches a critical value. the fatigue damage evolution and fatigue initiation life are very sensitive to the notch morphology parameters. the notch morphologies need to be analyzed carefully, to improve the fatigue life of the notched samples. keywords. defect; damage evolution model; low cycle fatigue; crack initiation; sensitivity. citation: wang, z. q., huang, x. g., zhang, d.h., low cycle fatigue damage model and sensitivity analysis of fatigue crack initiation by finite element approach, frattura ed integrità strutturale, 53 (2020) 81-91. received: 16.12.2019 accepted: 09.04.2020 published: 01.07.2020 copyright: © 2020 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. introduction atigue is a common failure behavior of metal materials under an alternating load. with the widespread application of metal materials in automobiles, machinery, aerospace, etc., fatigue failure has gradually become one of the main failure modes of such components [1]. generally, fatigue failure can be divided into three stages: crack initiation, crack propagation and fracture. for those materials without initial damage, the crack initiation life usually accounts for more than 80% of the total life. hence, it is of great significance to study the crack initiation life of metal materials [5]. according to the relationship between stress, strain and fatigue life, the corresponding fatigue life models have been gradually established to solve the high cycle or low cycle fatigue life prediction of the structural components. the mansonf https://youtu.be/7tobkfvr4s0 z.-q. wang et alii, frattura ed integrità strutturale, 53 (2020) 81-91; doi: 10.3221/igf-esis.53.07 82 coffin model is commonly used in the low cycle fatigue life prediction [6]. in recent decades, the application of continuous damage mechanics to fatigue damage evolution has been considered as one of the most effective methods to predict fatigue life, and has attracted extensive attentions [8]. memon [11] studied the influence of loading sequence on the fatigue life using damage mechanics-finite element method, and verified that the damage mechanics-finite element method based fatigue lives were consistent with the experimental results. tommy et al. [12] proposed the concept that the detailed fatigue damage analysis in some key areas could greatly simplify the calculation process and solve the practical engineering problems effectively. based on the concept of damage step size, zheng et al. [13] deduced the fatigue crack nucleation and propagation prediction formula, and predicted the whole life of 2024 and 7075 notched plate specimens with various geometric parameters. guan et al. [14] proposed a new low cycle fatigue damage evolution model according to the theoretical continuous damage mechanics and energy principle, which was verified to predict the low cycle fatigue life of metal materials effectively. however, to meet the requirements of engineering design, fatigue components inevitably have different notch morphologies. when under cyclic loads, the cracks often initiate at the structural notch on account of the local stress concentration [15]. therefore, it is extremely important to design the notch shape to improve the fatigue life of the notch members. xie [16] used the modified tanaka-mura model to reveal the effect of gradient hardening thickness on the initiation location and lifetime of fatigue cracks. xing [17] et al. predicted the crack initiation life of notched plate specimens under high-low cycle fatigue load. however, the influence of notch and its morphology on crack initiation life has attracted very limited attention. in this paper, the low cycle fatigue damage evolution law derived from the theory of damage mechanics is established and the influence of notch morphology on the crack initiation life of p92 steel is analyzed. in consequence, the low cycle fatigue damage evolution law derived from the theory of continuous damage mechanics is written as a umat subroutine and coupled to abaqus software in this paper, so as to analyze the influence of different notch morphology on crack initiation life. the analysis results are helpful to the durability design of fatigue parts with notch. fatigue damage model damage evolution theory ccording to the classical damage theory, damage is usually defined as a phenomenon of deterioration of the internal properties of materials caused by the generation of micro-cracks and micro-cavities under external loads. by introducing the damage definition of lemaitre [18], the damage variable d for uniaxial samples can be expressed as follows: d=1-sd/s （1） where sd and s represent the effective bearing area of the damaged material, and the cross-sectional area of the material under no damage, respectively. there is no damage to the material when d=0, whereas, the material completely fails when d=1. fatigue damage is always caused by the cumulative plastic strain. according to the continuous damage theory, the low cycle fatigue damage can be performed by an energy dissipative potential, i.e. e p p a ( )φ = φ ε, t,ε ,ε ,ε , d, ... （2） where  is the total strain, t is the temperature, e, p, and ap represent the elastic, plastic and accumulative strain, respectively. and the fatigue damage evolution can be derived from the established energy dissipative potential. based on the theory of continuous damage mechanics, the damage evolution dynamics law can be written as  = −  φ d y （3） where y denotes strain energy release rate. in general, the expression of dissipative potential is a z.-q. wang et alii, frattura ed integrità strutturale, 53 (2020) 81-91; doi: 10.3221/igf-esis.53.07 83 ( ) =  2 0 2 1 0α y p φ s d （4） where s0 and 0 are the material constants, and p represents the plastic strain rate. correspondingly, the strain energy release rate y is demonstrated as follows: ( ) 2 eq v 2 = 2 1 σ r y e d （5） where eq and e denote the equivalent stress and young's modulus, respectively, and rv is the parameter describing the triaxial stress effect with the following expression: ( ) ( )         2 h v eq 2 = 1+ + 3 1+ 2 3 σ r ν ν σ （6） with  being the poisson’s ratio, and h representing the average stress. by substituting eqns. (4)-(5) into eqn. (3), the fatigue damage evolution law can be obtained as ( ) = α σ p d r es d 0 2 eq v+1 0 2 1 （7） assuming that the stress-strain relationship of the material under cyclic loading can be characterized by the rambergosgood cyclic constitutive model, so the plastic strain of each stable cycle is 2 2 p       n σ k 1/ δ δ = （8） where p and  represent cyclic strain amplitude and cyclic stress amplitude respectively, k is cyclic strength coefficient and n denotes cyclic strain hardening index. by introducing the concept of damage, the plastic strain per cycle under a proportional loading or uniaxial stress can be rewritten as ( ) eq 2 2 p        n σ = k d 1/ δδ 1 （9） the change of damage is very small in a cycle, therefore, the damage variable d is approximately considered as an invariant. differentiating both sides of eqn. (9), one can obtain the plastic strain rate expressed as ( ) ( ) eq eq p        nσ = σ nk d k d 1/ 1 1 d d 1 1 （10） for a symmetric fatigue cycle, the hysteresis loop is centrosymmetric. by integrating eqn. (7) in one stress cycle and bringing eqn. (10) into it, the low-cycle fatigue damage per cycle can be obtained z.-q. wang et alii, frattura ed integrità strutturale, 53 (2020) 81-91; doi: 10.3221/igf-esis.53.07 84 2 eq 0 ( ) ( ) (2 1)  n+ n+ +αn σ rd = nes k d n +0 1/ v 1/ 11/ d dn 1 （11） hence, the expression of fatigue damage accumulation per cycle combined with eqn. (9) is given as follows: ( ) ( ) ( )( ) d d n γ α α d k p p r r n es d n ω γ d 0 0 2 2 +1 +1 v v 0 δ δ = = 2 1 2 + 1 + 1 1 （12） where  and  are the material constants, 0 2 2es ω = k , 2γ = n [19]. damage evolution simulation by finite element approach and the implementation method n this paper, the bilaterally notched plate specimens of p92 steel were selected to simulate the fatigue damage evolution and analyze the influence of notch morphology on fatigue crack nucleation life. three main notch shapes, namely, cnotched, u-notched and v-notched are included. to describe the notch clearly h, , and r, which respectively mean the notch depth, the opening angle, and the root radius, are adopted to describe the notch type, as shown in fig. 1. different values of parameters correspond to different types of notch: the notch is v-notched when the opening angle is greater than 0. while the opening angle is equal to 0 and the depth is greater than the radius of the root, the notch belongs to u-notched, otherwise it is called a c-notched. the mechanical properties of p92 steel are listed in tab. 1 [21]. moreover, the cyclic load with a stress range of 131mpa and stress ratio of -1 is applied to the ends of the sample, as shown in fig. 2. figure 1: the morphology of symmetrically notched specimen. figure 2: schematic diagram of loading model. parameter e (mpa)  k n   0 value 125000 0.3 234 0.119 12.57 0.273 7.56 table 1: the mechanical property of p92. under the fatigue loading, the damage in each element accumulates with the loading cycles. when the damage of the element reaches 1, the element fails and the micro fatigue crack initiates. since there is no identical engineering standard for critical crack length for crack initiation, micro-crack length up to 0.1-0.2mm is usually referred to the initiation size of crack [22. in this paper, the crack initiation life of notched specimen is studied by coding a umat subroutine of the fatigue damage  r h -70 -35 0 35 70 0 1 2 3 4 5 6 s tr e ss / m p a time/s cyclic loading cyclic loading i z.-q. wang et alii, frattura ed integrità strutturale, 53 (2020) 81-91; doi: 10.3221/igf-esis.53.07 85 evolution law derived above. crack initiation is considered when the failure element size reaches a critical crack initiation size. the calculation flow chart of abaqus umat subroutine is shown in fig. 3. figure 3: umat calculation flow chart. numerical simulation of fatigue damage fem results he finite element 1/8 model of plate sample with length of 40mm, width of 20mm, thickness of 5mm and a bilateral semicircular notch (c-notched, r=3mm ) in the middle was established, as shown in fig. 4. the symmetric constraints were applied in the directions of model x, y and z. the solid model was divided into a series of three dimensional 8-node reduced integration (c3d8r) elements. to verify the effect of element size on calculation accuracy, a convergence analysis was conducted. we found the analysis results were enough accurate when the mesh size near the notch root is refined to 0.02mm. the maximum stress, plastic strain state of this model at the first cycle are shown in figs. 5-6, respectively. the stress and strain concentrations are obvious, because the mises stress and plastic strain at the notch root are 129.9mpa and 4.2e-5, respectively. the accumulation of plastic deformation per cycle promotes the continuous evolution of fatigue damage, and the accumulated fatigue damage at the middle of the notch root firstly reach 1, indicating the fatigue crack firstly initiates from this position, as shown in fig. 7. figure 4: the 1/8 fem model. job submission call parameters calculate the plastic strain calculate fatigue damage critical damage? crack initiation size? yes end calculate fatigue life no no t z.-q. wang et alii, frattura ed integrità strutturale, 53 (2020) 81-91; doi: 10.3221/igf-esis.53.07 86 figure 5: the stress distribution. figure 6: the plastic strain distribution. figure 7: the fatigue damage distribution. lateral viewmain view main view lateral view lateral viewmain view z.-q. wang et alii, frattura ed integrità strutturale, 53 (2020) 81-91; doi: 10.3221/igf-esis.53.07 87 parametric study ig.8 shows the fatigue damage accumulation of semi-circular notched specimen with cycle numbers. the notch depth is 2mm and the root radii are 2mm, 3mm, and 4mm, respectively. we can see that the fatigue damage accumulation is very dependent on the notch root radius, and more fatigue loading cycles are needed to reach a certain damage under a bigger root radius. all the damages accumulate very slowly at the primary stage, whereas, as the number of cycles increases, the damage accumulation also accelerates until the failure of the unit at the critical damage stage. fig. 9 illustrates the fatigue damage evolution with different notch depths. the influence of notch depth on fatigue damage is as similar as that of the notch radius, which can be contributed to this result that the notch depth and root radius are the most important parameters deciding the stress and strain concentration effect, as well as the damage evolution. figure 8: fatigue damage at different root radius. figure 9: fatigue damage at different root depths. besides, the damage distribution and cyclic plastic strain distributions in the n, z and x directions of the c-notched specimen with r=3mm and h=2mm are extracted respectively, as shown in figs. 10-11, where o is the center of the sample. as can be seen, the maximum value occurs when the displacement is 0, i.e. the central position of the notch root. the variation trend of the fatigue damage in the three directions is similar, i.e., the damage decreases rapidly with the increase of the distance away from the center. the results indicate that the damage of the notch root element is the largest during the process of cyclic loading, and crack will initiate at the notch root first. the plastic strain distributions in three direction are similar as that of damage, which is consistent with the fatigue damage theory. f z.-q. wang et alii, frattura ed integrità strutturale, 53 (2020) 81-91; doi: 10.3221/igf-esis.53.07 88 figure 10: fatigue damage in different directions. figure 11: plastic strain in different directions. furthermore, the fatigue damage of u-notched sample is also discussed. three types of u-notched, i.e., h=1.5mm, 2.0mm, and 2.5mm were selected to investigate the effect of notch depth h on crack initiation life. the variation in the damage with the cycle number as shown in fig. 12, where the radius is maintained as 1mm. it can be clearly noted that the specimen with a notch depth of 2.5mm gets to critical damage value at about 1200 cycles, while the specimen experienced almost no damage even after 3000 cycles when the notch depth decreases to 1.5mm. however, as seen in fig. 13, the fatigue crack initiation seems to be more sensitive to the notch depth, when compared with fig. 12. figure 12: fatigue damage in different notch depths (u-notched). z.-q. wang et alii, frattura ed integrità strutturale, 53 (2020) 81-91; doi: 10.3221/igf-esis.53.07 89 figure 13: fatigue damage in different notch radii (u-notched). fig. 14 demonstrates the influence of notch dimension on the fatigue damage evolution of v-notched samples. as shown in fig. 14(a), with the decrease of opening angle, the stress concentration increases and the fatigue damage undergoes rapid evolution accordingly. fig. 14(b) shows the influence of notch depth on the damage evolution (θ=90°) and fig. 14(c) depicts the influence of root radius on the damage evolution (h=2mm). comparative analysis shows that the fatigue damage evolution of among the v-notched sample are very sensitive to the three mentioned notch morphology parameters. in other words, the reasonable notch morphology is needed to improve the fatigue life of this notched sample. (a) (b) (c) figure 14: fatigue damage evolution of v-notched samples: (a) notch angle, (b) notch depth, (c) notch radius. conclusions ased on the theory of continuous damage mechanics and the principle of irreversible thermodynamics, the damage evolution model of low cycle fatigue is investigated. by programming the damage evolution model with abaqus umat subroutine, the fatigue damage evolution and crack initiation life of symmetrically notched p92 steel samples under cyclic loads are simulated, and the following conclusions obtained are listed as follows: (1) the maximum fatigue damage always occurs at the root of the notch, no matter what the notch morphology is. the variations of equivalent stress and cyclic plastic strain along different direction of notch are consistent with that of the fatigue damage. (2) the fatigue damage accumulates slowly at the initial stage, but the damage accumulates rapidly with the number of cycles after the cumulative damage reaches a critical value. (3) no matter what type the notch is, the fatigue damage evolution and fatigue initiation life are very sensitive to the notch morphology parameters. the fatigue nucleation lives decrease with the increase of h/r in c and u notched samples, and the fatigue nucleation lives of v-notched samples are more sensitive to opening angle than root radius and notch depth. b z.-q. wang et alii, frattura ed integrità strutturale, 53 (2020) 81-91; doi: 10.3221/igf-esis.53.07 90 therefore, to improve the fatigue life of the notched sample, the notch morphology need to be carefully designed. acknowledgments he research work was supported by the fundamental research funds for the central universities of china (no.17cx02065), and the national natural science foundation of china (no.51404286). references [1] xu j. q. (2017). mechanics of fatigue. beijing: science press. (in chinese) [2] chow c. l., wei y. a model of continuum damage mechanics for fatigue failure. international journal of fracture, 1991, 50 (4), pp. 301-316. doi: 10.1007/bf00032199. [3] fatoba o., akid r. (2018). uniaxial cyclic elasto-plastic deformation and fatigue failure of api-5l x65 steel under various loading conditions. theoretical and applied fracture mechanics, 94, pp. 147-159. doi: 10.1016/j.tafmec.2018.01.015. [4] song w., liu x., berto f., wang p., fang h. (2012). fatigue failure transition analysis in load-carrying cruciform welded joints based on strain energy density approach. fatigue & fracture of engineering materials & structures 40(7), pp. 1164-1177. doi: 10.1111/ffe.12588. [5] huang x.g., and xu j.q. (2012). pit morphology characterization and corrosion fatigue crack nucleation analysis based on energy principle. fatigue & fracture of engineering materials & structures, 35(7), pp.606-613. doi: 10.1111/j.1460-2695.2011.01654.x. [6] wang, y.y., and susmel, l. (2016). the modified manson–coffin curve method to estimate fatigue lifetime under complex constant and variable amplitude multiaxial fatigue loading. international journal of fatigue, 83(2), pp. 135149. doi: 10.1016/j.ijfatigue.2015.10.005. [7] zhu s. p., and huang h. z., (2010). a generalized frequency separation–strain energy damage function model for low cycle fatigue–creep life prediction. fatigue & fracture of engineering materials & structures, 33(4), pp. 227-237. doi: 10.1111/j.1460-2695.2009.01431.x. [8] herwig, m. (2009). fatigue damage of low amplitude cycles in low carbon steel. journal of materials science, 44, pp. 4919-4929. doi: 10.1007/s10853-009-3751-x. [9] volkov, i.a., korotkikh, y.g., tarasov, i.s., and shishulin d. n. 2011. numerical modeling of elastoplastic deformation and damage accumulation in metals under low-cycle fatigue conditions. strength of materials, 43, pp. 471485. doi: 10.1007/s11223-011-9317-6. [10] chen, h. shang, d. g., tian, y. j., and liu j. z. (2012). comparison of multiaxial fatigue damage models under variable amplitude loading. journal of mechanical science and technology, 26(11), pp. 3439-3446. doi: 10.1007/s12206-012-0872-y. [11] memon, i. r., zhang, x., and cui, d.y., (2002). fatigue life prediction of 3-d problems by damage mechanics with two-block loading. international journal of fatigue, 24(1), pp. 29-37. doi: 10.1016/s0142-1123(01)00057-3. [12] tommy, h.t., chan, l., and guo, l., (2003). finite element modelling for fatigue stress analysis of large suspension bridge. journal of sound and vibration, 261(3), pp. 443-464. doi: 10.1016/s0022-460x(02)01086-6. [13] zhang, y.j., zhang, m., and hu, w.p., (2011). fatigue life prediction of the joint plate based on damage mechanics method. journal of mechanical strength, 33(3), pp. 443-449. (in chinese) [14] guan, d., sun, q., and yang, f. p., (2013). a modified low cycle fatigue damage model for metals. chinese journal of solid mechanics, 34(6), pp. 571-578. (in chinese) [15] bao, z.q., (2014). effect of notch geometry to high cycle fatigue strength of tc4 and prediction. dissertation of nanjing university of aeronautics and astronautics, nanjing. (in chinese) [16] xie, j.j. (2017) numerical simulation study on fatigue life of notch specimens with surface gradient reinforcement. journal of aeronautical materials, 37, 41-49. doi: 10.11868/j.issn.1005-5053.2017.000094. (in chinese) t https://link.springer.com/journal/10704 https://link.springer.com/journal/10704/50/4/page/1 http://xueshu.baidu.com/s?wd=author%3a%28fatoba%2c%20olusegun%29%20&tn=se_baiduxueshu_c1gjeupa&ie=utf-8&sc_f_para=sc_hilight%3dperson http://xueshu.baidu.com/s?wd=author%3a%28%20akid%2c%20robert%29%20&tn=se_baiduxueshu_c1gjeupa&ie=utf-8&sc_f_para=sc_hilight%3dperson http://www.sciencedirect.com/science/article/pii/s0167844217300575 http://www.sciencedirect.com/science/article/pii/s0167844217300575 https://www.sciencedirect.com/science/journal/01678442 https://www.researchgate.net/journal/8756-758x_fatigue_fracture_of_engineering_materials_structures http://www.researchgate.net/publication/229945587_a_generalized_frequency_separationstrain_energy_damage_function_model_for_low_cycle_fatiguecreep_life_prediction http://www.researchgate.net/publication/229945587_a_generalized_frequency_separationstrain_energy_damage_function_model_for_low_cycle_fatiguecreep_life_prediction https://www.researchgate.net/journal/1460-2695_fatigue_fracture_of_engineering_materials_structures http://www.sciencedirect.com/science/article/pii/s0142112301000573 http://www.sciencedirect.com/science/article/pii/s0142112301000573 z.-q. wang et alii, frattura ed integrità strutturale, 53 (2020) 81-91; doi: 10.3221/igf-esis.53.07 91 [17] xing, j., han, y.d., xu, l. c., jin, z. h., li, c. c., and zhao, l. (2017). high cycle and low cycle hybrid fatigue damage based on continuum damage mechanics. transactions of the china welding institution, 38(7), pp. 63-66. doi: 10.12073/j.hjxb.20150708001. [18] lemaitre, j. (1990). mechanics of solid material. cambridge university press, cambridge. [19] yang, x. h., li, n., jin, z. h., and wang, t. j., (1997). a continuous low cycle fatigue damage model and its application in engineering materials. international journal fatigue, 19(10), pp. 687-692. doi: 10.1016/s0142-1123(97)00102-3. [20] song, s., han, y.d., xu, l.y., jing, h.y., zhao, l., (2019), analysis on low cycle fatigue damage of ti-6al-4v based on combined hardening model. transactions of the china welding institution, 40(1): 43-49. (in chinese) [21] kannan, r., sankar, v., sandhya, r., and mathew, w. d., (2013). comparative evaluation of the low cycle fatigue behaviours of p91 and p92 steels. procedia engineering, 55, pp. 149 -153. doi: 10.1016/j.proeng.2013.03.234. [22] goodall, i. w., and ainsworth, r.a., (2003). r5: assessment procedure for the high temperature response of structure (issue 3). british energy, gloucester, uk. [23] goodall, i. w., and ainsworth, r.a., (1991). an assessment procedure for the high temperature response of structures. in: życzkowski m. (eds) creep in structures. international union of theoretical and applied mechanics. springer, berlin, heidelberg. doi: 10.1007/978-3-642-84455-3_35. http://dx.doi.org/10.12073/j.hjxb.20150708001 http://dx.doi.org/10.1007/978-3-642-84455-3_35 404 not found microsoft word numero_58_art_20_3238.docx m. azadi et alii, frattura ed integrità strutturale, 58 (2021) 272-281; doi: 10.3221/igf-esis.58.20 272 focussed on fracture and structural integrity bending cyclic behavior and scatter-band analysis of aluminum alloys under beneficial and detrimental conditions through highcycle fatigue regime mohammad azadi faculty of mechanical engineering, semnan university, semnan, iran m_azadi@semnan.ac.ir, http://orcid.org/0000-0001-8686-8705 hanieh aroo faculty of mechanical engineering, semnan university, semnan, iran abstract. this article presents the bending fatigue behavior and the scatterband analysis of aluminum alloys under beneficial conditions of nano-clayparticles and heat-treating, compared to detrimental conditions of the mechanical stress and the corrosion. moreover, the sensitivity analysis was also done on the stress level, the pre-corrosion phenomenon, the addition of nano-particles, and applying the heat treatment on the high-cycle bending fatigue lifetime of the aluminum-silicon alloy. for this objective, gravity and stir-casting processes were done for aluminum alloy and nano-clay-composite specimens and then, standard samples were machined from initial casted cylinders. furthermore, rotary fatigue tests were performed under cyclic bending loadings, through the high-cycle fatigue regime. some samples were pre-corroded in the sulfuric acid for 200 hours. based on the sensitivity analysis on experimental data by the minitab software, the obtained results indicated that the stress level was the effective parameter on the fatigue lifetime. the meaningful regression model was calculated and calibrated on the logarithmic scale of the fatigue lifetime. then, the second sensitive parameter was demonstrated as the pre-corrosion, which caused significant degradation of fatigue properties in the material. the last-ranked factor was related to nano-particles for the beneficial effect on the improvement of the high-cycle fatigue lifetime. the scatter-band analysis illustrated that nanoparticles and heat-treating changed the scattering behavior of experimental data. keywords. bending fatigue; scatter-band analysis; aluminum alloy; nanoclay-particles; heat-treating; corrosion. citation: azadi, m., aroo, h., bending fatigue behavior and scatter-band analysis of aluminum alloys under beneficial conditions of nano-clay-particles and heat-treating, compared to detrimental conditions of mechanical stress and corrosion, frattura ed integrità strutturale, 58 (2021) 272-281. received: 19.08.2021 accepted: 27.08.2021 published: 01.10.2021 copyright: © 2021 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. https://youtu.be/niwpokkkj44 m. azadi et alii, frattura ed integrità strutturale, 58 (2021) 272-281; doi: 10.3221/igf-esis.58.20 273 introduction orrosion damages are one problem in aluminum-based mechanical structures. one case study is the cylinder head in a diesel engine, which is arrested by the corrosive fuel environment besides cyclic mechanical loadings. therefore, knowing the corrosion-fatigue behavior of the material could be useful for designer engineers [1-2]. moreover, the improvement in the corrosion-fatigue lifetime of components is to be noticed in the automotive industry. various ways to increase the service lifetime are heat treatments, in addition to the recent knowledge edge of nano-particles [3]. in this field of study, different articles have been widely published until now. guerin et al. [4] investigated the corrosionfatigue lifetime of 2050 aluminum-copper-lithium alloy, in the chloride solution. they indicated that t34 and t84 states were respectively susceptible to inter and intragranular corrosion in the material. moreover, the fatigue lifetime of the t34 heat-treated alloy was most affected by the fatigue-corrosion phenomena. since the propagation of the intergranular corrosion was assisted by cyclic mechanical loading. chen et al. [5] found the effect of the pre-deformation on the precorrosion multiaxial fatigue behaviors of 2024-t4 aluminum alloy. their results illustrated a reduction percentage of precorroded fatigue lifetime with the pre-deformation level due to the pitting marks caused by the corrosion. they showed that the combination of pre-deformation and pre-corrosion was more detrimental than that of either one acting separately. rodriguez et al. [6] performed a study on corrosion effects on the low-cycle fatigue behavior of dissimilar friction stir welding of high-strength aluminum alloys. the immersion in 3.5% nacl for various exposure times resulted in the localized corrosion damage in the thermo-mechanically affected and heat-affected zones. they observed corrosion damages such as general pitting, pit clustering, and exfoliation, which caused a decrease in the fatigue lifetime. azadi et al. [2] compared the high-cycle fatigue lifetime in un-corroded and corroded piston aluminum alloys, within the diesel engine application. their results showed higher weight losses for 200 hours immersion times, which resulted in the lifetime decrease in pre-corrosive samples. in the literature review, almost all works were presented through qualitative analysis. in only rare articles such as azadi et al. [3], the quantitative analysis was performed on fatigue and corrosion-fatigue phenomena of materials. based on a claimed novelty in this research, the sensitivity analysis of the stress, the pre-corrosion, the addition of nano-particles, and the heat treatment was done on the fatigue lifetime of aluminum alloys. as another novelty, the corrosive environment was salts or acids, in the literature review. however, in this article, the influence of sulfuric acid was considered due to the diesel fuel and the combustion products. the third novelty is to analyze the scatter-band for fatigue experimental data for different conditions of studied materials. it should be mentioned that this research is an extended article from the previously published literature [7]. notably, the third novelty based on the scatter-band analysis of experimental data is the extended text for fatigue and corrosion-fatigue testing. materials and experiments he fatigue and corrosion-fatigue behaviors of the alsi12cunimg aluminum alloy (the european name of the material: ac48000) were studied in this research. this aluminum-silicon alloy has been widely used for the engine piston in the automotive industry. the chemical composition was 12.70 wt.% si, 1.16 wt.% cu, 1.00 wt.% mg, 0.80 wt.% ni, 0.56 wt.% fe and the remainder was the aluminum element. in order to fabricate the metal-based nano-composite, 1 wt.% of nano-clay-particles was added to the aluminum melt, during the stir-casting technique. for this objective, melting of aluminum bars was done firstly at 700˚c for about 2 h. then, pre-heated nano-particles at 400˚c were added to the melt. after 20 min of stirring, a steady condition was obtained for the melt and cylindrical samples were cast in a cast-iron mold. in this regard, more details could be found in the literature [8]. it should be noted that the expectation of adding nano-clay-particles to aluminum alloys is to increase the hardness, strength, and fatigue lifetime. such an advantage by the nanotechnology could be utilized in the engine piston, which is working under high-temperature cyclic loadings. since the clay type as a ceramic (metal oxides) was considered and selected for the nano-particle, the strength and the low-cycle fatigue lifetime of the material would enhance, especially at high temperatures [8]. similar components could be fabricated from such a nano-composite, where high temperatures occur. for the corrosion study, the acid amount of 0.00235% from the sulfuric acid was considered and a pre-corrosion process was performed for 200 hours before fatigue testing, to illustrate the corrosion effect on the fatigue lifetime of materials. then, rotary high-cycle bending fatigue testing was performed on standard samples, either from the base material, the corroded sample, the reinforced specimen, and the corroded nano-composite. the dimension of the cylindrical specimen was 76 mm of the total length, 18 mm of the gauge length, and also 4 mm and 9 mm of the smallest and largest diameters, c t m. azadi et alii, frattura ed integrità strutturale, 58 (2021) 272-281; doi: 10.3221/igf-esis.58.20 274 respectively. it should be noted that fatigue testing was carried out based on the iso-1143:2010 standard [9], under 4 stress levels by the sft-600 rotary bending fatigue machine. these bending stress levels were 120, 150, 180, and 210 mpa. more details for the fabrication of the studied materials could be found in the literature by aroo et al. [1], azadi et al. [3], rezanezhad et al. [10], and zolfaghari et al. [11]. in addition, more details of fatigue testing and the geometry of standard cylindrical samples could be followed in the literature by parast et al. [12], sharifi et al. [13], and khisheh et al. [14]. after testing, a regression curve-fitting process was done for the sensitivity analysis on experimental data. this job was performed in the minitab software, using regression analysis. in this study, the value of the risk level was usually 0.05. therefore, the p-value in the sensitivity analysis should be less than 0.05 to claim that one input parameter was sensitive and effective on outputs. moreover, higher f-value amounts mean higher effects of inputs on outputs. in this case of study, inputs included the stress, the pre-corrosion, the addition of nano-particles, and the heat treatment. then, the output was the fatigue lifetime in both normal and logarithmic scales. to present data in a better manner, some abbreviations were used, which could be seen in tab. 1. these abbreviations were used for different samples and various types of fatigue testing. no. abbreviations explanations 1 pf pure bending fatigue testing 2 cf corrosion-fatigue testing with pre-corroded samples 3 alsi_n0_t0 aluminum-silicon alloy 4 alsi_n1_t0 aluminum-silicon alloy, reinforced with nano-clay-particles 5 alsi_n1_t6 aluminum-silicon alloy, reinforced with nano-clay-particles and the heat treatment table 1: abbreviations for tests and samples in this study. usually, experimental fatigue data have high scattering, especially in the high-cycle fatigue regime. therefore, the fatigue lifetime of materials is described by statistical functions such as weibull or normal [15-17]. for these distribution functions, the averaged value (  ) and the standard deviation ( ) are considered for recorded data. to analyze the scatter-band of fatigue experimental data, for each lifetime ( x ), there are several models [17]. however, in this research, eq. (1) was utilized for the scatter-band analysis, which could be written as follows [16,17],     x z (1) where the z value could be found from the literature [16,17] and the confidence level. in this research, the confidence level was considered as 85, 90, and 95% for the normal distribution function. when the confidence level increases, the scatterband will be wider. it should be noted that the z value is 1.44, 1.65, and 1.96 when the confidence level is 85, 90, and 95%, respectively [16,17]. finally, the scatter-band could be written as   n z , where n is the fatigue lifetime at each stress level. results and discussion ig. 1 presents the curve of the stress versus the fatigue lifetime of studied materials, as a first result. it should be noted that obtained results in fig. 1 are for both fatigue and corrosion-fatigue phenomena. as another note in this figure, the averaged value of lifetime data was considered. the variation of the fatigue lifetime was also studied in the section that is related to the scatter-band analysis. therefore, the standard deviation is not shown in fig. 1, in order to avoid data cluttering in the chart. considering a logarithmic function, curve-fitting between the stress and the fatigue lifetime was properly carried out by high values of the coefficient of determination (r2), higher than 93%. as it could be seen from obtained results in fig. 1, the slope of the curves under fatigue and corrosion-fatigue testing was almost similar for one type of material. moreover, the heat-treated nano-composite had a higher fatigue lifetime, compared to the base material, especially for the low-cycle fatigue regime or under higher stress levels. however, only the addition of f m. azadi et alii, frattura ed integrità strutturale, 58 (2021) 272-281; doi: 10.3221/igf-esis.58.20 275 nano-particles to the aluminum matrix had a reverse effect and decreased the fatigue lifetime. such trends could be also for the corrosion-fatigue lifetime of studied materials. in other words, the slope of the curves for one type of testing was different for all types of studied materials. it means that the addition of nano-clay-particles and the heat treatment changed the slope of the stress-lifetime curve. comparing results in fig. 1 showed that the corrosion effect on the fatigue lifetime was negative and detrimental and therefore, the degradation of the material performance occurred, either in different types of alloys. under high-stress levels and through the low-cycle fatigue regime, the corrosion-fatigue lifetime of aluminum-silicon alloys (reinforced with nanoparticles and the heat treatment) increased, compared to that of aluminum-silicon alloys, as also claimed by rezanezhad et al. [10]. considering obtained results for fatigue and corrosion-fatigue testing for comparison, the corrosion-fatigue lifetime was less than the fatigue lifetime in all cased, as also reported by guerin et al. [4], chen et al. [5], rodriguez et al. [6], and azadi et al. [1]. figure 1: the curve of the stress amplitude ( as ) versus twice times of the fatigue and corrosion-fatigue lifetimes ( 2 fn ) in a logarithmic scale, considering the averaged value. the main objective of this article was the sensitivity analysis of inputs on outputs. the obtained results from the regression analysis on experimental data could be found in tab. 2, respectively for normal and logarithmic scales. for this order, the coefficient of determination (r2) was calculated as 42.78 and 86.98%, respectively. this means that the logarithmic scale of the fatigue lifetime had a meaningful trend, compared to the normal scale. it should be noted that the p-value of the regression analysis was less than 0.05 and therefore, the sensitivity analysis was meaningful for both scales. based on the p-value in the normal scale of the fatigue lifetime, the stress and the pre-corrosion were effective parameters, since they had a p-value lower than 0.05. however, the effect of both reinforcements was not significant on the fatigue lifetime of studied materials. considering the f-value, the effect of the stress was higher than the pre-corrosion influence of the fatigue performance of the material. besides, according to the p-value in the normal scale of the fatigue lifetime, all input parameters were effective on the fatigue performance of the material. the f-value indicated that the most effective parameter was the stress, the pre-corrosion, the heat treatment, and lastly, nano-particles. as another observation from these results, the influence of beneficial conditions (the heat treatment and nano-particles) was less than that of detrimental conditions (the stress, the pre-corrosion) on the fatigue lifetime. the applied stress was the first factor, which had detrimental effects on the fatigue lifetime. the other harmful parameter is the pre-corrosion, since the additional damage like pits decreased the fatigue lifetime, besides the effect of the applied stress. these corrosion pits could be a location for the stress concentration and the potential region for the crack initiation, sooner than the condition of having no pre-corrosion. the heat treatment was the third factor, which had m. azadi et alii, frattura ed integrità strutturale, 58 (2021) 272-281; doi: 10.3221/igf-esis.58.20 276 beneficial effects on the fatigue lifetime. since the hardness of the material increased by heat-treating, fatigue properties would improve, especially through the high-cycle fatigue regime. the last-ranked useful parameter was nano-particles. however, this factor could be a detrimental condition. since if there was any agglomeration in the microstructure, they could be a potential location for the stress concentration and the crack initiation. parameter the normal scale of the fatigue lifetime the logarithmic scale of the fatigue lifetime f-value p-value f-value p-value regression 12.71 0.000 113.07 0.000 stress 37.34 0.000 216.82 0.000 pre-corrosion 11.32 0.001 72.76 0.000 nano-particles reinforcement 1.81 0.184 22.39 0.000 heat treatment reinforcement 2.04 0.158 62.61 0.000 table 2: the sensitivity analysis for normal and logarithmic scales of the fatigue lifetime. to find the qualitative trend of input parameters on the output, fig. 2 is presented. based on these results, as expected, by increasing the stress, the fatigue lifetime decreased. however, by the addition of nano-particles, the fatigue lifetime reduced. by the heat treatment, the fatigue lifetime of the material enhanced. finally, by the pre-corrosion, the degradation occurred in the material performance. as a note, the stress was a continuous parameter and therefore, a continuous line was used in the regression analysis. for other parameters, data were discrete and two points could be observed for each state. increasing the fatigue lifetime of aluminum alloys by the reinforcement was also reported by rezanezhad et al. [10], sharifi et al. [13], and khisheh et al. [14], which could be claimed as an agreement with obtained results in this research. the reason for such an improvement was due to the microstructural changes in the microstructure of the aluminum alloy. the heat treatment and the addition of nano-particles led to a decrease in the size of the grain in the material microstructure. moreover, checking the interaction effect of input parameters on the logarithmic scale of the fatigue lifetime indicated that since no crossed lines could be observed; therefore, no interaction of parameters could be claimed on the fatigue performance of studied materials. figure 2: the qualitative trend of input parameters on the logarithmic scale of the fatigue lifetime. in fig. 3, the scatter-band of fatigue data is presented for the aluminum alloy, the nano-composite, and the heat-treated nano-composite, on a logarithmic scale and for different confidence levels. similar to these results, fig. 4 depicts the scatterband of corrosion-fatigue data for studied materials. obtained results indicated that the fatigue scatter-band of the nano-composite was narrower than those of two other materials. however, the heat-treated nano-composite had a wider fatigue scatter-band, especially in the high-cycle fatigue regime. in other words, the heat treatment led to scattered experimental data. such a discussion could not be claimed for corrosion-fatigue data and the scatter-band was almost similar for all studied materials. as another note, the aluminum alloy had a homogeneous scatter in both fatigue and corrosion-fatigue phenomena through both lowand high-cycle fatigue regimes. however, adding nano-particles and the heat treatment caused changes in this behavior through lowand highcycle fatigue regimes. the reason could be the formed defects during the stir-casting process, which had higher numbers of parameters, compared to the gravity casting of the aluminum alloy. m. azadi et alii, frattura ed integrità strutturale, 58 (2021) 272-281; doi: 10.3221/igf-esis.58.20 277 (a) (b) (c) figure 3: the scatter-band for fatigue data of (a) the aluminum alloy, (b) the nano-composite, and (c) the heat-treated nano-composite (note: the horizontal axis includes the logarithmic value of the fatigue lifetime). m. azadi et alii, frattura ed integrità strutturale, 58 (2021) 272-281; doi: 10.3221/igf-esis.58.20 278 (a) (b) (c) figure 4: the scatter-band for corrosion-fatigue data of (a) the aluminum alloy, (b) the nano-composite, and (c) the heat-treated nanocomposite (note: the horizontal axis includes the logarithmic value of the fatigue lifetime). m. azadi et alii, frattura ed integrità strutturale, 58 (2021) 272-281; doi: 10.3221/igf-esis.58.20 279 as another result by comparing the scatter-band in both figs. 3 and 4, it could be claimed that wider scattering data occurred and were obtained under fatigue testing. the scatter-band of corrosion-fatigue data was narrower since the root cause under the corrosive environment could be more. the corrosion pits could increase the probability of the damage, in addition to the failure of the crack initiation due to mechanical loading and the maximum bending stress on the sample surface. therefore, a higher probability of damages under corrosion-fatigue testing led to a narrower scatter-band, compared to that of pure fatigue testing on studied materials, as all detrimental conditions. however, as a beneficial condition, nano-clay-particles decreased the scatter-band of experimental data for fatigue and corrosion-fatigue testing. this could be due to finer grains in the material microstructure, as reported in the literature [10]. against such a description, morel et al. [18] showed that the microstructure and the defect could reflect the scatter-band, observed in the fatigue strength of metallic materials. this scatter-band is often explained by the anisotropic behavior of the material. shlyannikov et al. [19] found that there was a steady relationship between the crack growth rate and the plastic stress intensity factor in the form of the general curve, within a relatively narrow scatter-band for all tested specimens of 2024 and 7075 aluminum alloys, at different temperatures. as another reason, farzannasab et al. [20] illustrated that results usually have had remarkable scatter-bands, due to the lack of repeatability of testing. in other words, the number of fatigue testing could influence the scatter-bank analysis. in the present work, 4 stress levels were considered for bending fatigue testing under 120, 150, 180, and 210 mpa. moreover, under each stress level, 3 samples were tested. if the number of such a test with similar loading conditions increases, the scatter-band would be changed for the studied materials. one way to have a deep investigation on the scatter-band is to analyze the microstructure of the material. since the obtained trends could be attributed to the microstructure of the studied aluminum alloy. in addition, the effect of the nano-particles addition or the applied heat treatment could be found from the microstructure. moreover, the role of casting defects could not be ignored for their influences on the scatter-band of the fatigue lifetime. in this regard and for some cases, the microstructural study of the material was presented in the literature [8]. for further investigations and in order to continue this work, the failure probability could be calculated, in addition to the reliability [21] for each stress level. this job could be done for various distribution functions including normal, weibull, extreme maximum value (emv), and smallest extreme value (sev) distributions [20]. then, the probability density function (pdf) could be obtained based on the distribution function and the cumulative distribution function (cdf), and also the reliability could be calculated for failures. conclusions n the present article, the sensitivity analysis was performed for the stress, the pre-corrosion, nano-particles, and the heat treatment on the fatigue lifetime of aluminum alloys. obtained results could be highlighted as follows,  fatigue and fatigue-corrosion lifetimes of the aluminum alloy, reinforced with nano-particles and the heat treatment process increased by 128 and 114%, respectively, under high-stress levels, compared to the base aluminum alloy. however, under low-stress levels and through the high-cycle fatigue regime, such a behavior was not observed.  the reduction in the fatigue lifetime was significant for 200 hours of immersion time, especially through the highcycle fatigue regime, which equaled lower stress levels. the reason was due to the surface damage and pits caused by corrosion reactions.  when the normal scale of the fatigue lifetime was considered, reinforcing parameters were not effective. however, all four parameters of the stress, the pre-corrosion, the addition of nano-particles to the aluminum matrix and the heat treatment had effects on the logarithmic scale of the fatigue lifetime of studied materials.  the scatter-band analysis revealed that the addition of nano-particles and the heat treatment could change the scatter-band of fatigue and corrosion-fatigue experimental data, compared to the aluminum alloy. that is due to the probable defects during the stir-casting process. acknowledgement uthors would tend to acknowledge motorsazi pooya neyestanak (mpn) company, located in isfahan, iran for providing raw materials and also dr. mahboobed azadi at semnan university for the scientific support on this research. i a m. azadi et alii, frattura ed integrità strutturale, 58 (2021) 272-281; doi: 10.3221/igf-esis.58.20 280 references [1] aroo, h., azadi m., azadi, m. (2021). corrosion effects on high-cycle fatigue lifetime and fracture behavior for heattreated aluminum-matrix nano-clay-composite compared to piston aluminum alloy. silicon. doi: 10.1007/s12633-021-01129-w. [2] azadi, m., aroo, h., azadi, m., parast, m.s.a. (2021). comparing of high-cycle fatigue lifetimes in un-corroded and corroded piston aluminum alloys in diesel engine application. archives of foundry engineering, 21, pp. 89–94. doi: 10.24425/afe.2021.136083. [3] azadi, m., zomorodipour m., fereidoon, a. (2021). sensitivity analysis of mechanical properties and ductile/brittle behaviors in aluminum-silicon alloy to loading rate and nano-particles, considering interaction effects. engineering reports, 3(6), e12341. doi: 10.1002/eng2.12341. [4] guerin, m., alexis, j., andrieu, e., blanc, c., odemer, g. (2015). corrosion-fatigue lifetime of aluminum-copperlithium alloy 2050 in chloride solution. materials and design, 87, pp. 681–69. doi: 10.1016/j.matdes.2015.08.003. [5] chen, y., zhou, j., liu, c., wang, f. (2018). effect of pre-deformation on the pre-corrosion multiaxial fatigue behaviors of 2024-t4 aluminum alloy. international journal of fatigue, 108, pp. 35–46. doi: 10.1016/j.ijfatigue.2017.11.008. [6] rodriguez, r.i., jordon, j.b., allison, p.g., rushing, t., garcia, l. (2019). corrosion effects on fatigue behavior of dissimilar friction stir welding of high-strength aluminum alloys. material science and engineering a, 742, pp. 255– 268. doi: 10.1016/j.msea.2018.11.020. [7] azadi, m., aroo, h. (2021). sensitivity analysis of stress, pre-corrosion, nano-particles and heat treatment on fatigue lifetime of aluminum alloy. structural integrity procedia, igf26 26th international conference on fracture and structural integrity. [8] azadi, m., bahmanabadi, h., gruen, f., winter, g. (2020). evaluation of tensile and low-cycle fatigue properties at elevated temperatures in piston aluminum-silicon alloys with and without nano-clay-particles and heat treatment. materials science and engineering a, 788, 139497. doi: 10.1016/j.msea.2020.139497. [9] metallic materials – rotating bar bending fatigue testing, (2010). iso-1143:2010 standard, available at: https://www.iso.org/standard/41875.html. [10] rezanezhad, s., azadi, m., azadi, m. (2021). influence of heat treatment on high‑cycle fatigue and fracture behaviors of piston aluminum alloy under fully‑reversed cyclic bending. metals and materials international, 27, pp. 860–870. doi: 10.1007/s12540-019-00498-7. [11] zolfaghari, m., azadi, m., azadi, m. (2021). characterization of high-cycle bending fatigue behaviors for piston aluminum matrix sio2 nano-composites in comparison to aluminum-silicon alloys. international journal of metalcasting, 15, pp. 152–168. doi: 10.1007/s40962-020-00437-y. [12] parast, m.s.a., khameneh, m.j., azadi, m., azadi, m., mahdipanah m.h., roostaie, s. (2021). effect of plasma nitriding on high‐cycle fatigue properties and fracture behaviors of gjs700 nodular cast iron under cyclic bending loading. fatigue and fracture of engineering materials and structures, 44(8), pp. 2070–2086. doi: 10.1111/ffe.13479. [13] sharifi, m.j., azadi, m., azadi, m. (2020). fabrication of heat-treated nano-clay-composite for improving high-cycle fatigue properties of alsicu aluminum alloy under stress-controlled fully-reversed bending loads. proceedings of the institution of mechanical engineers, part c: journal of mechanical engineering science. doi: 10.1177/0954406220969731. [14] khisheh, s., khalili, k., azadi, m., hendouabadi, v.z. (2021). influences of roughness and heat treatment on highcycle bending fatigue properties of a380 aluminum alloy under stress-controlled cyclic loading. materials chemistry and physics, 264, 124475. doi: 10.1016/j.matchemphys.2021.124475. [15] zhai, j.m., li, x.y. (2012). a methodology to determine a conditional probability density distribution surface from sn data. international journal of fatigue, 44, pp. 107–115. doi: 10.1016/j.ijfatigue.2012.05.008. [16] khameneh, m.j., azadi, m. (2018). reliability prediction, scatter-band analysis and fatigue limit assessment of highcycle fatigue properties in en-gjs700-2 ductile cast iron. matec web of conferences, 12th international fatigue congress, 165, 10012. doi: 10.1051/matecconf/201816510012. [17] lee, y.l., pan, j., hathaway, r., barkey, m. (2004). fatigue testing and analysis. john wiley and sons, usa. [18] morel, f., guerchais, r., saintier, n. (2015). competition between microstructure and defect in multiaxial high cycle fatigue. fracture and structural integrity, 33, pp. 404–414. doi: 10.3221/igf-esis.33.45. [19] shlyannikov, v., yarullin, r., ishtyryakov, i. (2017). effect of different environmental conditions on surface crack growth in aluminum alloys. fracture and structural integrity, 41, pp. 31–39. doi: 10.3221/igf-esis.41.05. m. azadi et alii, frattura ed integrità strutturale, 58 (2021) 272-281; doi: 10.3221/igf-esis.58.20 281 [20] farzannasab, m., azadi, m., bahmanabadi, h. (2020). study of high-cycle fatigue properties in bovine tibia bones based on reliability and scatter-band predictions. mechanics of advanced composite structures, 7(2), pp. 255–261. doi: 10.22075/macs.2019.18248.1215. [21] yang, g. (2007). life cycle reliability engineering. john wiley and sons, usa. microsoft word numero 25 art 14 a. spagnoli et alii frattura ed integrità strutturale, 25 (2013) 94-101; doi: 10.3221/igf-esis.25.14 94 special issue: characterization of crack tip stress field on a kinked crack model to describe the influence of material microstructure on fatigue crack growth andrea spagnoli, andrea carpinteri, sabrina vantadori department of civil-environmental engineering & architecture (dicatea), university of parma abstract. threshold condition and rate of fatigue crack growth in both short and long crack regime appear to be significantly affected by the degree of crack deflection. in the present paper, a theoretical model of a periodically-kinked crack is presented to describe the influence of the degree of crack deflection on the fatigue behavior. the kinking of the crack is due to a periodic self-balanced microstress field having a length scale, d. by correlating the parameter d with a characteristic material length (e.g. average grain size in metals, maximum aggregate dimension in concrete), the possibility of using the present model to describe some experimental findings related to crack size effects in fatigue of materials is explored. well-known experimental results concerning two different situations (fatigue threshold and fatigue crack growth in the paris regime) are briefly analysed. keywords. kinked crack; crack size effect; fatigue crack growth; fatigue threshold; microstress field. introduction nder fatigue loading, cracks in both brittle and ductile materials tend to deflect because of far-field multiaxial stresses, microstructural inhomogeneities (grain boundaries, interfaces, etc.), residual stresses, etc. threshold condition and rate of fatigue crack growth in both short and long crack regime appear to be significantly affected by the degree of crack deflection [1]. this might be induced by the fact that the value of the near-tip stress intensity factor (sif) of kinked fatigue cracks can be considerably different from that of a straight crack of the same projected length. in the case of bidimensional elastic problems, analytical solutions for sif of kinked cracks are available in the literature [27]. some of such results have been used to gain a quantitative understanding of the relation between fatigue crack growth rate and the degree of crack deflection in the fatigue crack path (e.g. see ref. [8]). a description of actual irregularities of kinked crack surfaces has been carried out by using the fractal geometry [9]. successful applications of the fractal geometry to size effect-related fatigue problems have been proposed by the present authors in the past few years [10-16]. in this paper, a theoretical model of a periodically-kinked crack is discussed in order to describe the influence of the degree of deflection on the fatigue behavior. the kinking of the crack is due to a periodic self-balanced microstress field having a length scale, d [17]. by correlating the parameter d with a characteristic material length (e.g. average grain size in metals, maximum aggregate dimension in concrete), the possibility of using the present model to describe some experimental findings related to crack size effects in fatigue of materials is explored. well-known experimental results concerning two different situations (fatigue threshold and fatigue crack growth in the paris regime) are briefly analysed. u http://www.gruppofrattura.it http://dx.medra.org/10.3221/igf-esis.25.14&auth=true a. spagnoli et alii, frattura ed integrità strutturale, 25 (2013) 94-101; doi: 10.3221/igf-esis.25.14 95 the kinked crack model self-balanced microstress field consider an infinite cracked plate described by the xy coordinate system in fig. 1, exposed to remote tensile stress ( )y  along the y-axis and shear stress ( )xy  . assume that material microstructural features create a self-balanced (residual) microstress field, which is characterized by a length scale, d , related to a characteristic material length, and amplitudes e.g. governed by material properties’ dispersion. further let us assume that such a microstress field is a one-dimensional function (of the x coordinate), defined by the following stress tensor: x xy x ,a xy ,a xy y xy ,a y ,a x ( x) f d                           t         (1) without lack of generality, we describe the plane microstress field by taking into account the following two non-zero stress components: y af ( x / d )      and xy af ( x / d )      . an attempt to correlate the above self-balanced microstress to some heterogeneity features of the material microstructure is presented in ref. [18]. figure 1: nomenclature for the kinked crack in an infinite plate (y-axis of symmetry). approximate stress intensity factors in the kinked crack according to the present model, the central crack might kink as a result of both remote and microstess fields (see fig. 1). as will be shown below, the local stress intensity factors (sifs) at the crack tips ( ik and iik ) can be expressed as a function of those ( ik and iik ) of a straight crack having length equal to the projected length of the kinked crack [2-7]. the total values of sifs defined with respect to the projected crack are the sum of two contributions (due to remote and microstress fields, respectively), that is: ( ) i i i ( ) ii ii ii k k k k k k         (2) the remote sifs are defined with respect to the projected crack of semi-length l, aligned with the x axis (fig. 1). hence, under the uniform remote stresses ( ) ( )y    and ( ) ( )xy    , we have : l ( ) ( ) ( ) i 2 20 l ( ) ( ) ( ) ii 2 20 l 1 k 2 dx l l x l 1 k 2 dx l l x                       (3) ki ki a b l 1 2   kii ki kii ki kii kii x y 0   1 2 http://www.gruppofrattura.it http://dx.medra.org/10.3221/igf-esis.25.14&auth=true a. spagnoli et alii frattura ed integrità strutturale, 25 (2013) 94-101; doi: 10.3221/igf-esis.25.14 96 the condition for self-balanced stress is that the function  f x / d is periodic (with material microstructure period d ). for the sake of simplicity, we assume    f x / d cos 2 x d (this could be regarded as a first order approximation through fourier series of a general periodic function). now, since the above  f x / d is a even function with respect to x, we have that the value of the sifs (i.e. referring to the projected crack) are (using buckner’s superposition principle, which is based on the stresses in the uncracked body along the crack lines):         l l l i a a a 02 2 2 2 2 20 0 0 l l l ii a a a 02 2 2 2 2 20 0 0 f x d cos 2 x d 2 ll l l k 2 dx 2 dx 2 dx l j dl x l x l x f x d cos 2 x d 2 ll l l k 2 dx 2 dx 2 dx l j dl x l x l x                                                       (4) where 0j is the zero order bessel function. in such a self-balanced microstress field, it can be reasonably assumed that the crack symmetrically kinks (due to the mixed mode of fracture) with respect to the y-axis and at each material microstructure semi-period, i.e. at each reversal in the microstress spatial courses (a = d/2 in fig. 2). in the case of a singly-kinked crack (of projected crack length 2l , as is reported in fig. 1), the sifs at the tips of the inclined part of the crack can be expressed through the sifs ik and iik of a straight crack of length equal to the projected length of the kinked crack [2-7] :         i 11 i 12 ii ii 21 i 22 ii k a , b a k a , b a k k a , b a k a , b a k         (5) where ija are coefficients depending on the slant angle  (positive counter-clockwise for tip coordinate x > 0) and the length ratio b a between the deflected leading segment and the horizontal trailing segment. if a geometry different from that of an infinite plate with a central crack is examined, the geometric factor of the sifs defined with respect to the projected crack would be different from the unity, but the expression in eq. 5 would not change. figure 2: mixed-mode crack growth in the self-balanced microstress field. the coefficients ija for b a   (and, with good approximation, also for b a 0.3 ) are [2]:         3 2 1 2 11 12 1 2 1 2 21 22 a cos a 2 sin cos a sin cos a cos 2 cos                 (6) l   x y 0 d/2 x d 2 1 n a ~ a ~ x a ~ a ~         3 )/(~ dxfa )/(~ dxfa http://www.gruppofrattura.it http://dx.medra.org/10.3221/igf-esis.25.14&auth=true a. spagnoli et alii, frattura ed integrità strutturale, 25 (2013) 94-101; doi: 10.3221/igf-esis.25.14 97 note that the local sifs in eqs 5 and 6 are equal to those of an inclined straight crack of projected semi-length l forming an angle 2  with respect to the loading axis of ( )  [2]. it is reasonable to assume that, as the crack propagates following the path in fig. 2, only its latter deflection influences the stress field near the crack tips (for example, the local sifs at the crack tip 3 in fig. 2 are assumed to be equal to those of a singly-kinked crack with an inclined segment corresponding to the segment 2-3, and by taking b a 0.3 , see eq. 6) [19]. the approximate computation is thus based on the assumption that the near-tip stress field depends on the local crack direction at the crack tip. the local sifs at the crack tip are assumed to be expressed by eqs 5 and 6 for deflected (mode i+ii) segments (see segments 1-2 and 1 2  in fig. 1), despite the fact that the length ratio b a between the leading segment and preceding segment might in general vary from 0 to  during propagation (in fig. 1, for example, b is the running quantity for the crack propagating along the deflected segment 1-2 so that b a ranges from 0 to a value greater than the unity). direction of growth of the kinked crack and effective sif as is mentioned above, the crack might kink at each material microstructure semi-period, namely at each reversal in the microstress spatial courses. the classical criterion of erdogan and sih [20] is applied herein to describe the mixed-mode crack propagation. accordingly the kinking angle , defined with respect to the general inclined axis of the crack (fig. 1), is expressed by 2 i i ii ii k k1 1 2 arctan 8 4 k 4 k            (7) where the sifs values appearing in eq. 7 are those determined according to eqs 5 and 6. the angle  is positive counterclockwise and is in the range – and +. the sign in eq. 7 is chosen so as to have the smallest absolute value of . once the freshly formed kinked segment develops to a finite length, an equivalent sif eqk can be calculated according to eqs 5 and 6. an effective driving force can be determined by applying the coplanar strain energy release rate theory [21], that is, the equivalent sif eqk is given by 2 2 eq i iik k k  (8) fatigue growth in nominally mode i kinked cracks ow let us restrict our attention to nominally mode i cracks, i.e. cracks submitted to a remote mode i fatigue loading ( )  . hence, for an infinite plate, we have the following sifs related to the projected crack of semilength l : ( ) ( )a a i 0 i 0( ) ( ) ( ) ( )a a ii 0 i 0( ) ( ) 2 l 2 l k l 1 j k 1 j d d 2 l 2 l k l j k j d d                                                                             (9) in eq. 9, we assume that the microstress field (e.g. a a a t pt p max (t ) min (t )         ) is time-varying and proportional to the applied remote loading of period p (constant amplitude fatigue loading). under remote mode i loading and a superimposed shear microstress field, cracks propagate ‘on average’ along the x axis following a zig-zag pattern (the same pattern is followed also in the presence of superimposed normal microstress). in general, it turns out that the crack slanting angle decreases as the crack length increases with respect to the material microstructural length d, namely ( l / d)  . obviously, crack kinking occurs only in the presence of a multiaxial stress field. therefore, for the simplest case of uniaxial remote and microstress fields, a complanar growth of cracks occurs ( 0  ) and, according to eq. 8, eq ik k   n http://www.gruppofrattura.it http://dx.medra.org/10.3221/igf-esis.25.14&auth=true a. spagnoli et alii frattura ed integrità strutturale, 25 (2013) 94-101; doi: 10.3221/igf-esis.25.14 98 with ik obtained from eq. 9 (which includes the effect of the bessel function 0j ). no crack kinking occurs in such a case, but sifs are not proportional to the square root of the crack length. consequently, it can be shown that, in the bilogarithmic idl / dn δk plane, crack growth does not follow a linear relationship (e.g. see barenblatt’s model to describe short fatigue crack growth in ref. [19]). 0 10 20 30 40 normalized projected crack length, l/d -40 -20 0 20 40 60 s la nt a ng le ,  [° ] figure 3: example of slant angle variation under nominally mode i loading (d = characteristic material length). weighted average of effective stress intensity factor a weighted average value eqk of the equivalent sif range eqk along the straight segments is introduced. recognizing a repetitive pattern constituted by n segments in the crack profile, we have : n i i 1 eq , i i 1 eq n (s s ) k k s        (10) where eq , ik (see eq. 8) is the equivalent sif value along the straight segment of length i i 1(s s ) , s being the curvilinear coordinate along the crack path (fig. 4). figure 4: fatigue growth of the kinked crack. if the repetitive pattern is that of a zig-zag crack (this has been demonstrated to occur for remote/nominal mode i load superimposed to any normal/shear microstress field), we have :   n eq , i i 1 ( ) ( ) ( )i eq i a an i 1 i kd 2 cos k k f , l d , , d 1 2 cos                          (11) 1 2 1  ki 3 l  s kii kii 0 ki http://www.gruppofrattura.it http://dx.medra.org/10.3221/igf-esis.25.14&auth=true a. spagnoli et alii, frattura ed integrità strutturale, 25 (2013) 94-101; doi: 10.3221/igf-esis.25.14 99 where the function  ( ) ( )a af f , l d , ,           highlights the dependence of eqk on the relevant parameters. note that the kinking angle is itself a function of l d . geometric effects of kinking on crack growth rate considering the fact that, when the kinked crack spans a distance s , then the projected straight crack spans a distance l , the following relationship holds (between the crack growth rate, ds dn , for the kinked crack and the nominal crack growth rate, dl dn , for the projected straight crack) : ds s dl dn l dn  (12) note that the crack rate dl dn is always smaller than ds dn . now, for a zig-zag crack with slant angle  , we have : n i 1 i d 1 2 cosds dl ddn dnn 2   (13) kinetics of fatigue crack growth now let us apply the paris law to the periodically-kinked crack : m eq ds c k dn   (14) where c and m are material constants. by substituting eqs 11 and 13 in eq. 14, the following fatigue crack growth law in terms of the nominal quantities dl dn and ik is determined for a zig-zag kinked crack : m eqn i 1 i dl n c k 1dn cos    (15) and hence, by using eq. 11, we get :   m n eq , i m mi 1 ( ) ( ) ( )i a a in n i 1 i 1i i k cosdl n c c f , l d , , k 1 1dn cos cos                                           (16) two applications of the kinked crack model to experimental evidences or illustrative purposes, the present model is applied to some fatigue experimental evidences demonstrating crack size effects. the aim is to discuss whether the present model is able to follow some trend of behavior observed in the experimental tests. the comparison is carried out by considering, in the theoretical model, nominally mode i cracks (the acting remote fatigue load is ( )  ) under a shear microstress field with ( )a    arbitrarily taken to be equal to 2. the first experimental data being analysed concern the fatigue threshold condition for mild steel [22]. such data are related to ferritic and pearlitic steels with carbon content of 0.20% and grain size d of the ferritic phase equal to 7.8 m (small-size grain) and 55 m (large-size grain), respectively (see ref. [12] for details of experimental data elaboration). for various values of the crack length (ranging from 6 to 1383 m), the threshold stress intensity factor range thk was f http://www.gruppofrattura.it http://dx.medra.org/10.3221/igf-esis.25.14&auth=true a. spagnoli et alii frattura ed integrità strutturale, 25 (2013) 94-101; doi: 10.3221/igf-esis.25.14 100 experimentally evaluated (the threshold stress intensity th ,0k for long cracks is equal to 5.21 mpa m and 6.20 mpa m for small-size grain and large-size grain material, respectively). figure 5a reports, in a normalized form, the above experimental data along with the corresponding theoretical curve of the kinked model. such a curve (normalized in so that the ratio th th ,0k k  tends to the unity for l d   ) is determined by posing the weighted average effective sif of eq. 11 equal to the threshold sif range for long cracks th ,0k (the remote sif ( ) ik  corresponds to the threshold sif range thk ), that is :   th ( ) th ,0 a k 1 k f , l d ,         (17) it can be seen that the experimentally observed reduction of the threshold stress intensity factor with respect to that of long cracks (reduction occurring as the crack length decreases) is correctly captured by the present model, although to a smaller extent. further experimental data being analysed concern fatigue crack growth in the paris regime [23, 24]. such data are related to fatigue crack propagation in three-point bend specimens made of normal-strength (ns) plain-concrete [23] and highstrength (hs) plain-concrete [24]. for each concrete type, three series of two-dimensional geometrically similar cracked specimens with height h equal to 38, 76, 152mm and to 38, 108, 304mm for ns and hs concrete, respectively, span = 2.5h, initial crack length l0 = 0.16h, thickness = 38 mm. by elaborating the experimental data through a best-fit procedure (see ref. [13] for details), it is shown that the paris parameter m is independent of the initial crack length (m is equal to 10.4 and 8.2 for ns and hs concrete, respectively), while the paris parameter c turns out to be dependent on such a length. figure 5b plots the experimental best-fit values of c (for crack growth rate expressed in m / cycle and stress intensity range in mpa m ) as a function of the normalized initial crack length (the characteristic material length is taken to be equal to the maximum aggregate dimension, 12.7 and 9.5mm for ns and hs concrete, respectively), along with the best-fit curves of the present model (see eq. 16, where the crack-size dependent paris coefficient is   m ( ) ( ) a ac f , l d , ,             ). the experimental evidence seems to be well described by the present kinked model in the range of crack sizes being considered. (a) (b) figure 5: (a) fatigue threshold results for mild steel [22]; (b) fatigue crack growth results in the paris regime for concrete [23, 24]. conclusions n the present paper, irregular morphology of fracture surfaces is described via a two-dimensional model of a periodically-kinked crack, where its kinking is due to a periodic self-balanced microstress field having a length scale, d. on the basis of some geometrical and mechanical arguments, the model allows us to quantify the influence of the deflection degree on the fatigue threshold condition and fatigue crack growth. by correlating the parameter d with a characteristic material length (e.g. average grain size in metals, maximum aggregate dimension in concrete), the possibility of using the present model to describe some experimental findings related to crack size effects in fatigue of materials is explored. some experimental results related to crack-size effects in fatigue threshold condition for metals as well as i http://www.gruppofrattura.it http://dx.medra.org/10.3221/igf-esis.25.14&auth=true a. spagnoli et alii, frattura ed integrità strutturale, 25 (2013) 94-101; doi: 10.3221/igf-esis.25.14 101 fatigue crack growth in the paris regime for concrete seem to be in favour of the present model, in the range of the crack sizes being considered. acknowledgements he authors gratefully acknowledge the financial support of the italian ministry of education, university and research (miur) under the project prin 2009 no. 2009z55nwc_003. references [1] suresh, s., fatigue of materials, 2nd edition, cambridge university press, cambridge, (1998). [2] kitagawa, h., yuuki, r., ohira, t., crack-morphological aspects in fracture mechanics, engng fract. mech. 7, (1975) 515-529. [3] bilby, b.a., cardew, g.e., howard, i.c., stress intensity factors at the tips of kinked and forked cracks, in: d.m.r. taplin (ed), fracture 3, pergamon press, new york, (1977) 197-200. [4] lo, k.k., analysis of branched cracks, j. app. mech., 45 (1978) 797-802. [5] cotterell, b., rice, j.r., slightly curved or kinked cracks, int. j. fract., 16 (1980) 155-169. [6] suresh, s., shih, c.f., plastic near-tip fields for branched cracks, int. j. fract., 30 (1986) 237-259. [7] chen, y.z., stress intensity factors for curved and kinked cracks in plane extension, theor. and appl. fract. mech., 31 (1999) 223-232. [8] suresh, s., crack deflection: implications for the growth of long and short fatigue cracks, metallurgical transactions, 14a (1983) 2375-2385. [9] carpinteri, al., scaling laws and renormalization groups for strength and toughness of disordered materials, int. j. sol. and struct., 31 (1994) 291-302. [10] carpinteri, an., spagnoli a., vantadori, s., an approach to size effect in fatigue of metals using fractal theories, fat. & fract. engng mat. & struct., 25 (2002) 619-627. [11] carpinteri, an., spagnoli, a., a fractal analysis of size effect on fatigue crack growth, int. j. fat., 26 (2004) 125-133. [12] spagnoli, a., fractality in the threshold condition of fatigue crack growth: an interpretation of the kitagawa diagram, chaos, sol. and fract., 22 (2004) 589-598. [13] spagnoli, a., self-similarity and fractals in the paris range of fatigue crack growth, mech. mat., 37 (2005) 519-529. [14] carpinteri, an., spagnoli, a., vantadori, s., viappiani, d., influence of the crack morphology on the fatigue crack growth rate: a continuously-kinked crack model based on fractals, engng fract. mech., 75 (2008) 579-589. [15] carpinteri an., spagnoli a., vantadori s., size effect in s-n curves: a fractal approach to finite-life fatigue strength, int. j. fat. , 31 (2009) 927-933. [16] carpinteri, an., spagnoli, a., vantadori, s., a multifractal analysis of fatigue crack growth and its application to concrete, engng fract. mech., 77 (2010) 974-984. [17] carpinteri, an., spagnoli, a., vantadori, s., correlating the fractal dimension of a continuously-kinked fatigue crack with some material microstructural features, in: proceedings of the 13th international congress on mesomechanics vicenza, italy, (2011). [18] barenblatt, g. i., on a model of small fatigue cracks, engng fract. mech., 28 (1987) 623-626. [19] brighenti, r., carpinteri, a., spagnoli, a., scorza, d., crack path dependence on inhomogeneities of material microstructure, frattura ed integrità strutturale, 20 (2012) 6-16. [20] erdogan, f., sih, g.c., on the crack extension in plates under plane loading and transverse shear, j. basic engng., 85 (1963) 519–527. [21] sih, g.c., strain-energy-density factor applied to mixed mode crack problems, int. j. fract., 10 (1974) 305-321. [22] tanaka, k, nakai, y, yamashita, m., fatigue growth threshold of small cracks, int. j. fat., 17 (1981) 519–33. [23] bazant, z.p., xu, k., size effect in fatigue fracture of concrete, aci mat. j., 88 (1991) 390-399. [24] bazant, z.p., shell, w.f., fatigue fracture of high-strength concrete and size effect, aci mat. j., 90 (1993) 472-478. t http://www.gruppofrattura.it http://dx.medra.org/10.3221/igf-esis.25.14&auth=true microsoft word numero_30_art_20 c. madrigal et alii, frattura ed integrità strutturale, 30 (2014) 163-161; doi: 10.3221/igf-esis.30.20 153 focussed on: fracture and structural integrity related issues numerical implementation of a multiaxial cyclic plasticity model for the local strain method in low cycle fatigue c. madrigal, v. chaves, a. navarro university of seville, dpto. ing. mecánica y fabricación, escuela técnica superior de ingeniería. avda. camino de los descubrimientos, s/n. 41092. seville. cmadrigal@us.es abstract. very often computations on structural elements or machine components subjected to variable loading require using an advanced finite element model. this paper reports the numerical implementation of a model for multiaxial cyclic elasticplastic behaviour developed to extend the tools of the local deformation method under fatigue to multiaxial conditions. a basic computer code for axialtorsional loads was developed with the commercial software matlab and a more sophisticated code based on the finite element model for general multiaxial loads was developed as a umat subroutine in abaqus. stress integration was introduced in the two usual forms: implicitly and explicitly. a comparison of the results obtained with the implicit and explicit formulations revealed that, under certain loading conditions, the outcome of the process depends on the particular integration scheme used. keywords. cyclic plasticity; numerical implementation; multiaxial fatigue; umat user subroutine. introduction he cyclic plastic behaviour of some materials can be defined via so-called “cyclic stress-strain curves”, which are widely used in fatigue studies to introduce steady-state cyclic behaviour in computations of fatigue life at small numbers of cycles in the local strain method [1–3]. using cyclic stress-strain curves in combination with hysteresis cycles, neuber’s rule, memory rule and n  curves allows one to calculate local stresses and strains at the edge of a notch and lives under uniaxial loading. this is in fact the procedure of choice for a number of sectors in the automobile, aeronautical and aerospatial industries. in previous work [4–8], we developed a plasticity model to simulate the behaviour of materials under multiaxial loads from cyclic stress-strain curves obtained in uniaxial loading tests with a view to extending the applicability of the local strain method to multiaxial loading. this computational procedure for fatigue life is included in some commercial software packages. in fact, any custom model to be used for this purpose should run in at least one. also, validating a mathematical model for fatigue life entails performing numerical simulations for comparison with experimental results in order to define the scope of the model. for these reasons, in this work we implemented the proposed model in two different commercial software packages, namely: matlab, which is useful for computations at specific points under combined tensile–torsional loads, and abaqus/standard, which was used to produce a umat subroutine for whole elements under general multiaxial loads. t c. madrigal et alii, frattura ed integrità strutturale, 30 (2014) 163-161; doi: 10.3221/igf-esis.30.20 154 model he stress tensor is represented by a point in the stress space. applying a load causes the point to move to another location in the space. the proposed model assumes that the plastic strain caused by the applied load depends on the distance between the starting and ending point in the stress space. if a load-free initial state (i.e., the space origin) is assumed, then application of a load at a given point will result in the point being displaced and in the distance from the origin dictating the beginning of plastic behaviour. thus, the yield criterion establishes that plastic behaviour starts when the distance q reaches a value  k , which is a property of the material dependent on its extent of cumulative hardening. q is calculated from the following equation: i j ijq g k   σ (1) where ijg are the components of the fundamental or metric tensor g in the stress space. this formula contains einstein’s summation convention and can be rewritten in the form of a pseudo-vector with the following components: 1        2        3        4        5   6         7         8         9      x y z xy yx yz zy zx xz                   (2) figure 1: successive unloading process. applying a load to a load-free specimen causes the point representing the stress state at each time to move from the origin and result in an elastic deformation. the distance from the origin increases with increasing loading until the point reaches the yield surface, which is a hypersphere centred in the origin. under sustained loading, the hypersphere increases in size but continues to contain the load point. if the load is removed, however, the point approaches the origin and the previous equations are inapplicable as the distance ceases to be measured with respect to the origin; also, a new hypersphere forms tangentially to the previous one at the return point mσ (see fig. 1), which illustrates the situation with two successive unloading events. the unloading distance is defined as the diameter q of the new inner hypersphere, which is calculated from       0   cos 2 i mi i mim cai mi cai mi q q                σ σ (3) where mσ is the return point, caσ the centre of the previous hypersphere of diameter 0q and  the angle between the    mσ σ segment and the line joining mσ with caσ . the amount of plastic strain resulting from loading or unloading is given by the following flow rule: p j i i jd n n d   (4) t c. madrigal et alii, frattura ed integrità strutturale, 30 (2014) 163-161; doi: 10.3221/igf-esis.30.20 155 where  is equal to  φ q under loading conditions and   2/ cosq  under unloading conditions.  φ q and  q are the hardening modulus of the material with and without loading, respectively, and can be calculated numerically or empirically from the cyclic stress-strain curve of the material under uniaxial loading; and n is the vector normal to the yield surface, which is defined by its gradient, i.e., by the gradient of the distance function in eq. (1) under loads 1   j ii iji q n g q q         (5) and eq. (3) in their absence     0 2 2  i i mi cai min q q        (6) the stress corresponding to a given deformation increment can be calculated by expanding eq. (4) with the elastic strain as defined in hooke’s law and solving the resulting expression as follows:   1j ij i j id h n n d      (7) where  ijh denotes the components of the (9 9) hooke matrix. a more detailed description of the model can be found elsewhere [4-8]. matrix notation s shown in the previous section, the proposed model was defined in 9 dimensions because the stress tensor had 9 components. however, the symmetry of the tensor made using a reduced number of dimensions (6) more practical. this required rewriting the previous equations in matrix form and using an ancillary matrix s to provide for duplicate tangential terms: 1 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 = 0 0 0 2 0 0 0 0 0 0 2 0 0 0 0 0 0 2                    s with this definition, eq. (1) is written in matrix form as  q   t tσ σ s gsσ (8) and its differential q ddq     σ sn σ (9) under unloading conditions, diameter q was expressed as         0 2 m m ca m m q q      t t t t σ σ s gs σ σ σ σ s gs σ σ (10) or, in differential form, as 2   q d cos dq     σ sn σ (11) a c. madrigal et alii, frattura ed integrità strutturale, 30 (2014) 163-161; doi: 10.3221/igf-esis.30.20 156 the flow rule took the form  pd d ε sn sn σ (12) where  is equal to  φ q with loading and   2/ cosq  in the absence of loads. the normal vector was formulated as q  gsσ n (13) with loads and as     0 2 2 m ca m q q    n gs σ σ gs σ σ (14) without them. combining the elastic and plastic terms, and inversion, yielded the stress increment:   1d d   σ h sn sn ε (15) where h is a (6 6) hooke matrix. numerical implementation he previous equations were implemented numerically in two different commercial software packages. thus, matlab was used to implement the particular equations for combined axial–torsional loads, which accurately reflect the behaviour of a material under multiaxial loads and considerably simplify the model equations. this enables easy numerical integration by effect of the vector space being reduced to two dimensions. also, most experimental results at low cycle fatigue under multiaxial loads are obtained by subjecting hollow tubes to combined tensile–torsional loads; as a consequence, these simulations are highly suitable for expeditious validation of models. figure 2: flow chart for the code. t c. madrigal et alii, frattura ed integrità strutturale, 30 (2014) 163-161; doi: 10.3221/igf-esis.30.20 157 calculating the amount of deformation in a whole element entails implementing the proposed equations in finite element software. we used a umat subroutine for abaqus/standard for this purpose. the scheme of fig. 2 depicts a very simplified version of the flow chart for the code. on calling the subroutine, the software feeds it with a given total strain increment that is used to calculate the corresponding stress increment. the procedure is identical with and without loads. the total strain increment is used in combination with eq. (9) and (11) to calculate the distance increment ( dq or dq ). if the increment is positive, then the hypersphere continues to grow and eq. (15) is integrated to calculate the associated stress increment. under unloading conditions, the hypersphere must be checked not to grow as much as needed to exceed the size of the following outer hypersphere otherwise, unloading is finished, the inner hypersphere is closed and the process continues with the outer hypersphere in order to record the memory effect. if dq (or dq ) is negative, then unloading starts and an inner hypersphere forms tangentially to the previous one at the load return point. integration e used two different integration modes. the explicit formulation was more simple and expeditious but conditionally stable; also, the precision was dependent on the size increment chosen —which should therefore be not too large. the implicit formulation was more computationally expensive but afforded a greater integration step and led to faster solutions; also, it was unconditionally stable and ensured that the increment end-point was on the yield surface by effect of all terms and variables being assessed at the end of the increment. explicit formulation the explicit formulation was based on euler’s direct first-order scheme, which involves updating stresses at the end of step 1nσ from those at the start (i.e., those calculated at the previous step, nσ ): 1 d  n n  σ σ σ (16) where the stress increment resulting from the total deformation increment, d ε , was calculated from eq. (15). it should be borne in mind that all properties included in the equations are assessed at the start of the increment, which can lead to gross errors if the deformation step is very large. implicit formulation one of the most widely used methods for implicit integration is based on radial return [9–11], which forces the stress point to remain on the yield surface. stresses at the end of the increment are calculated with provision for the fact that the deformation increment can be split into an elastic component and a plastic component. therefore, 1 e e e e p n n nd d d     ε ε ε ε ε ε (17) so thus  1 e p tr pn n d d d     σ d ε ε d ε σ d ε (18) where  d is the elastic constant matrix and trσ the trial stress or elastic estimator, which coincides with the stress level that would be reached if the strain increment were purely elastic. since part of the deformation is plastic, the test stress falls off the yield surface and must be combined with the second term (the plastic corrector) to bring it back on the surface. these non-linear equations can be solved by using the newton–raphson method, which uses an iterative procedure to calculate stresses at the end of the increment, 1nσ . in what follows, 1nσ is denoted in simplified form by σ . the final stress at the end of the increment will be the σ value reached at the end of the iterative process. such a value is calculated from a residual stress ψ given by 0tr pd   ψ σ σ d ε (19) substitution of the plastic strain increment (eq. (12)) into which yields   0 0tr      ψ σ σ d sn sn σ σ (20) w c. madrigal et alii, frattura ed integrità strutturale, 30 (2014) 163-161; doi: 10.3221/igf-esis.30.20 158 where the stress differential term is simply the difference between the values at the start ( 0σ ) and end of the increment. the residual stress can be approximated via the taylor series 0      ψ ψ σ σ (21) which can be solved for the stress increment upon each iteration: 1       ψ ψσ σ (22) the final stress is updated in each iteration by using the increment in (22). thus, 1k k   σ σ σ (23) and the updated stress is used to recalculate the residual and update the stress iteratively until the preset tolerance level is reached. 1210tr pd    ψ σ σ d ε (24) each iteration updates all terms in the equations. as a result, the stress at the end of the increment, 1nσ , is calculated from the material properties at the corresponding stress level. validation of the code he proposed code was validated by comparison of its numerical output with experimental values. a number of simulations spanning a wide range of complexity from uniaxial, proportional loads to complex, non-proportional loads were conducted to this end. by way of example, fig. 3 shows the simulation of a complex loading history reported by lamba et al. [12]. the process, implemented in abaqus, involved modelling a tube mimicking the straight portion of the gauge cross-section of the specimens used in the experimental tests that was 1.15 cm in outer radius, 0.95 cm in inner radius and 3.6 cm in length. the mesh was constructed from three-dimensional c3d20r solid elements, which allow the presence of a thickness stress gradient. boundary conditions were applied by linking the upper and lower surface to a reference node each allowing for radial motion. the reference node for the lower surface was fixed whereas that for the upper surface was allowed to move vertically and rotate about the same axis in order to facilitate recording of the whole loading history. therefore, the boundary conditions involved node displacement rather than deformation. figure 3: loading history imposed in the experiments and simulations. t c. madrigal et alii, frattura ed integrità strutturale, 30 (2014) 163-161; doi: 10.3221/igf-esis.30.20 159 fig. 3 shows the loading history together with the deformations imposed in the tests and the matlab simulation. as can be seen, the amount of deformation recorded by the abaqus simulation was not identical with that applied in the tests. this was a result of the boundary conditions in abaqus being imposed via displacements rather than directly as deformations. the axial displacement to be applied was calculated as the product of the gauge length by the desired axial strain. the shear strain was calculated from the relation between the rotation angle  and the cross-section of radius ( r ) and gauge length ( l ):   /l r  . the resulting estimates led to axial strains nearly identical with the experimentally determined values and shear strains slightly lower than their experimental counterparts. figure 4: comparison of the experimental and numerical results for the loading history shown in fig. 3. the abaqus and matlab predictions are compared with the experimental results of lamba et al. [1] in fig. 4. as can be seen, both numerical simulations led to very similar results that were also similar to the experimental values. the two curves differed in the torsional branch by effect of slight differences in their imposed shear deformation. the difference could be lessened by using a finer mesh containing several elements across its thickness in order to more accurately simulate its deformation gradient. influence of the integration mode nce the required equations were implemented and the resulting code was verified, the influence of the particular integration mode used on the numerical results was examined in various types of tests. with uniaxial and proportional loads, the integration mode had no effect on the results. fig. 5 illustrates a simulated test involving proportional loads and both integration modes. the graph only shows the torsional loops. as can be seen, the curves were virtually indistinguishable. on the other hand, the outcome of the tests with non-proportional loads was strongly affected by the integration mode used. fig. 6 shows its influence on the results of a 90 out-of-phase loading test. thus, explicit integration failed to predict the empirically observed levelling of stresses. by contrast, implicit integration of the same load history led to a stable stress orbit. this was a result of the out-of-phase test involving a continuous neutral load once stresses peaked. explicit integration calculated the increment from the values of the variables at the start. with a neutral load, this caused the loading point in the stress space to move tangentially to the yield surface at the start of the step. with a finite increment, the end point obviously lay off the yield surface, the displacement from each increasing on each successive integration step. explicit integration should therefore be avoided when the loading history includes a substantial neutral load. implicit integration corrects the initial estimate by forcing the point to return to the yield surface iteratively before a new step is taken. therefore, implicit integration is mandatory in simulating out-of-phase loading tests. o c. madrigal et alii, frattura ed integrità strutturale, 30 (2014) 163-161; doi: 10.3221/igf-esis.30.20 160 figure 5: implicit and explicit simulation of a proportional test. torsional branch. figure 6: simulations of a 90 out-of-phase test. conclusions mplementing a non-standard plasticity model in commercial software enabled application of constitutive equations to elements under various types of loads. a simplified matlab scheme allowed the stress status at a preset point under axial and torsional loading to be determined; also, a umat subroutine in abaqus/standard allowed simulation of components subjected to general multiaxial loads. stresses in both codes were integrated explicitly and implicitly. the codes were validated by simulating various loading histories and comparing the outcome with experimental values. based on the results, the umat subroutine is accurate and applicable to any type of multiaxial load, whether proportional or otherwise. the integration mode used was found to have a strong impact on the simulated results for non-proportional loading histories involving substantial segments of neutral loads. under these conditions, the explicit scheme cannot retain i c. madrigal et alii, frattura ed integrità strutturale, 30 (2014) 163-161; doi: 10.3221/igf-esis.30.20 161 stresses on the yield surface and considerable errors in the simulated values arise as a result. with uniaxial, proportional loads, however, the two integration modes provide essentially identical results. acknowledgements he authors would like to thank the spanish ministry of education for its financial support through grant dpi2011-27019. references [1] wetzel, r. m., fatigue under complex loading: analyses and experiments, advances in engineering 6, society of automotive engineers, (1977). [2] dowling, n. e., mechanical behavior of materials. engineering methods for deformation, fracture, and fatigue, prentice-hall, (1993). [3] bannantine, j. a., comer, j. j., handrock, j., fundamentals of metals fatigue analysis, prentice-hall, inc., (1990). [4] navarro, a., brown, m. w., a constitutive model for elastic-plastic deformation under cycling multiaxial straining, fatigue fract. eng. mater. struct., 20 (1997) 747–758. [5] navarro, a., giráldez, j. m., vallellano, c., a constitutive model for elastoplastic deformation under variable amplitude multiaxial cyclic loading, int. j. fatigue, 27 (2005) 838–846. [6] navarro, a., madrigal, c., ecuaciones de flujo plástico para el método de las deformaciones locales con carga multiaxial, anal. mec. fract, 26-ii (2009) 417–423. [7] madrigal, c., navarro, a., distancia en el espacio de tensiones y criterios de plastificación, anal. mec. fract, 28-ii (2011) 571–576. [8] madrigal, c., chaves, v., navarro, a., aplicación de ecuaciones de flujo plástico basadas en la distancia en el espacio de tensiones a ensayos cíclicos en acero f125, anal. mec. fract, 30-i (2013) 187–192. [9] doghri, i., fully implicit integration and consistent tantent modulus in elasto-plasticity, int. j. numer. meth. eng., 36 (1993) 3915–3932. [10] hopperstad, o. s., remseth, s., a return mapping algorithm for a class of cyclic plastticity models, int. j. numer. meth. eng., 38 (1995) 549–564. [11] kobayashi, m., ohno, n., implementation of cyclic plasticity models based on a general form of kinematic hardening, int. j. numer. meth. eng., 53, (2002) 2217–2238. [12] lamba, h. s., sidebottom, o. m., cyclic plasticity for nonproportional paths: part 1 cyclic hardening, erasure of memory, and subsequent strain hardening experiments, j. eng. mater. technol., 100 (1978) 96–103. t microsoft word 2262 h.s. bedi et alii, frattura ed integrità strutturale, 48 (2019) 571-576; doi: 10.3221/igf-esis.48.55 571 focused on “showcasing structural integrity research in india” interfacial shear strength of carbon nanotubes based hybrid composites: effect of loading rate harpreet singh bedi, beant kaur billing, prabhat k. agnihotri mechanics of advanced materials laboratory, department of mechanical engineering, indian institute of technology ropar, punjab, india harpreet.bedi@iitrpr.ac.in, https://orcid.org/0000-0001-5662-0071 beant.kaur@iitrpr.ac.in prabhat@iitrpr.ac.in, https://orcid.org/0000-0002-8332-9279 abstract. interfacial interaction is investigated between the two basic constituents in carbon fiber reinforced plastics (cfrps). efforts have been made to quantify the interfacial shear strength (ifss) between individual carbon fiber (cf) and epoxy matrix in cfrps by performing single fiber micro-droplet debond test. initially, ifss of the epoxy composites reinforced with unsized or heated carbon fiber (hcf) is assessed. study is then extended to assess the ifss of carbon nanotubes (cnts) based cfrp hybrid composites. the hybrid composites are prepared by reinforcing epoxy matrix with cnt grafted carbon fibers (cntcf). the versatile, simple and time effective method of chemical vapor deposition is used to synthesize cnts directly on the surface of cf. ifss is found to enhance after the inclusion of grafted cnts in cfrp composites. keeping in mind the application view point of cfrps to put up with varying loads, effect of loading rate on the ifss of cfrps is also examined. to this end, both hcf/epoxy and cntcf/epoxy composites are debonded at cross-head rates varying by two orders of magnitude and ifss values are compared. finally, scanning electron microscopy of debonded fibers is carried out to understand the interfacial failure mechanism in various composites. keywords. carbon fiber; cfrp; cnts; epoxy; ifss; microbond. citation: bedi, h.s., billing, b.k.., agnihotri, p.k., interfacial shear strength of carbon nanotubes based hybrid composites: effect of loading rate, frattura ed integrità strutturale, 48 (2019) 571-576. received: 17.11.2018 accepted: 16.02.2019 published: 01.04.2019 copyright: © 2019 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. introduction ue to increasing popularity and demand, carbon fiber reinforced plastics (cfrps) are finding their way in applications that are likely to comprise high strain rate loading [1]. so, it becomes a necessity for cfrps to be able to bear the complex environmental and loading conditions and their properties must not deteriorate at varying strain rates. thus, to serve better the ever widening scope of engineering applications, it is vital for the composite materials to retain their mechanical performance at both quasi-static and/or dynamic loading conditions. this is d http://www.gruppofrattura.it/va/48/2262.mp4 h.s. bedi et alii, frattura ed integrità strutturale, 48 (2019) 571-576; doi: 10.3221/igf-esis.48.55 572 imperative for cfrps so as to avoid any chances of premature and unexpected failure [1]. in order to sustain the structural integrity of a composite member at varying load conditions, the fiber/matrix bond strength is an important parameter which if optimized improves the mechanical performance of the composite [2]. the average mechanical properties of cfrp laminated composites largely depend on the direct interaction and extent of bonding between the individual reinforcing fiber and the surrounding matrix [3]. stronger the interfacial interaction better the composite properties. interfacial bond strength can be tailored in many ways such as by texturing the fiber surface [4], modifying the matrix [5], functionalization of fiber surface, type of fiber, modification of fiber sizing [2] etc. the exceptional properties of carbon nanotubes (cnts) [6] have made them a superior candidate in improving the mechanical properties of cfrps. the potential of cnts is harnessed in cfrps in two ways: by preparing polymer nanocomposites [7] by dispersing cnts in polymer matrix and by growing cnts directly on the surface of carbon fiber (cf) [8]. in both the cases, bonding between fiber and matrix is affected by the presence of cnts [3] at the interface. interfacial strength primarily depends on the area of contact available on the fiber surface to interact with the matrix [9] which can be increased by synthesizing cnts on the surface of fiber [10, 11]. additionally, grafted nanotubes improve the wettability of fiber with matrix by increasing the surface energy of unsized carbon fiber [10] ultimately enhancing the ability of the fiber to attract the matrix [14] and spread it more efficiently. this leads to an improvement in stress transfer between fiber and matrix through an enhanced interfacial area, mechanical interlocking and localized stiffening of the matrix [8]. a direct measure of the interfacial bond strength can be estimated from interfacial shear strength (ifss) at the fiber/matrix interface with the help of single fiber micro-droplet debond test or simply microbond test [12]. accordingly, debond tests are performed on epoxy matrix composites reinforced with single unsized/heated carbon fiber (hcf) and cnt grafted carbon fiber (cntcf) and hence ifss is evaluated from the load-displacement data so obtained. furthermore, the effect of load rate variation on the ifss of both the composites is also evaluated. scanning electron micrographs of debonded hcf and cntcf help us to better understand interfacial failure mechanism in unsized and hybrid composites. experimental preparation of cnt grafted carbon fiber he as-received carbon fabric (hindoostan technical fabrics, india) is firstly heated at 450˚c to make it free from the sizing layer applied on it. a bunch of heat treated sizing free or unsized carbon fibers (hcf) is then separated from the heated fabric and is coated with nickel catalyst for synthesizing cnts on fiber surface using dip coating method. the details of preparation of catalyst solution and the dip coating process are described in ref. [13]. once the unsized fibers are coated with catalyst, they are subjected to the reactive environment of argon, hydrogen and acetylene gases inside a chemical vapour deposition (cvd) reaction chamber (technos instruments, india) as per the procedure detailed in ref. [14]. after the successful completion of a cvd cycle, the catalyst coated cfs gets transformed into cnt coated cfs. surface morphology of as-received (ar-cf), unsized (hcf) and cnt grafted carbon fiber (cntcf) can be seen in fig. 1. where, as-received fibers appear smooth (fig. 1a) because of the sizing layer on their surface, the rough surface of unsized fiber helps in retaining the catalyst particles in a better way (fig. 1b). it is clear from fig. 1c that the synthesized cnts uniformly cover the fiber surface. composites are then prepared with both unsized and cnt grafted cf using epoxy as matrix as described in the next section. figure 1: sem micrograph of: (a) as-received, (b) unsized and (c) cnt grafted carbon fiber. t h.s. bedi et alii, frattura ed integrità strutturale, 48 (2019) 571-576; doi: 10.3221/igf-esis.48.55 573 interfacial characterization in order to evaluate the shear strength of the fiber/matrix interface, micro-droplet debond tests are carried out with both hcf/epoxy as well as cntcf/epoxy composites. schematic of sample preparation is shown in fig. 2a where the ends of a single cf filament (unsized or cnt grafted) are first attached to a channel section stand with the help of a quick setting adhesive. epoxy matrix is prepared by mixing epoxy besphenol resin with polyamine hardener in a ratio of 1:2 by weight. as soon as a drop of matrix is poured on a fiber it disintegrates into multiple micro-droplets as shown in fig. 2a. figure 2: schematic of single fiber micro-droplet debond test: (a) polymer micro-droplets adhering the surface of single carbon fiber filament. (b) test specimen undergoing debond test. (c) representative load (f) vs. displacement (δ) curve for the debond test. afterwards, the specimens are allowed to cure at atmospheric conditions for at least 24 hr followed by post curing in an electric oven at 60°c for 4 hr. during this period of curing, matrix droplets set and get hard, adhering the fiber surface to the best of their potential. debond test is then performed on a universal testing machine (shimadzu, japan) as illustrated in fig. 2b. crosshead speed is varied from 0.05 to 5 mm/min and load (f) vs. displacement (δ) data is logged corresponding to each speed and for each sample. a typical load/displacement curve obtained from such a test is shown in fig. 2c. peak force (fmax) required to debond a micro-droplet from the fiber is obtained from these curves and interfacial shear strength (ifss) is then evaluated using eqn. (1). max   e f ifss dl (1) where, d is the fiber diameter and le is the embedded length of a polymer micro-droplet on the carbon fiber (see fig. 2b for detail). the small rise after the abrupt drop in load (f) corresponds to frictional sliding effects. results and discussion oad or stress transfer from matrix to fiber in cfrps critically depends on the strength of the fiber/matrix interface. single fiber micro-droplet debond test is a simple way to measure the interfacial shear strength (ifss) in cfrp composites. figs. 3a and 3b show the variation of maximum debond force fmax as a function of varying embedded length le of polymer micro-droplet for each fiber/matrix composite. the results of debond test are fitted well with linear interpolation, indicating the direct proportionality between peak load and embedded length of the microdroplet. therefore, ifss of each composite is evaluated from the slope of a linear fit to the experimental data (markers in figs. 3a and 3b) and average ifss with standard deviation is shown in fig. 3c. on increasing the loading speed from 0.05 to 5 mm/min the ifss of hcf/epoxy composite rises from 50 mpa to 54 mpa (figs. 3a and 3c) by 8%. similarly, the ifss of cntcf/epoxy composite increases by 6% from 66 mpa (at 0.05 mm/min) to 70 mpa (at 5 mm/min) (see figs. 3b and 3c). it is observed from figs. 3a and 3b that at higher speed of loading the slope of the linear fit is higher than the one obtained at lower speed. this corresponds to an increase in ifss with loading speed irrespective of the type of fiber (hcf or cntcf) used to reinforce epoxy. this could be attributed to increased yielding of the matrix due to strain hardening effects at higher load speeds, resulting in more energy required to fracture [15]. the energy to fail the composite is determined from area under the load-displacement curve (fig. 2c) which shows an increasing trend when the rate of loading is increased and/or cnts are grafted on fiber surface. l h.s. bedi et alii, frattura ed integrità strutturale, 48 (2019) 571-576; doi: 10.3221/igf-esis.48.55 574 however, at a particular loading rate, composites reinforced with cnt grafted carbon fiber show enhanced ifss than the ones having just unsized fiber (fig. 3c). compared to hcf/epoxy composites, increments of 32% and 30% are observed for ifss of cntcf/epoxy composites at 0.05 and 5 mm/min crosshead speeds, respectively. moreover, the elastic interaction between the reinforcing fiber and matrix governs the strain rate dependence [1]. thus, changes in ifss are expected when the fiber/matrix interfacial interaction is modified by incorporating grafted cnts in the composite system. one of the reasons behind this observation is the increase in fiber surface area [16] due to cnt grafting, which improves the wettability of cnt grafted carbon fiber with epoxy matrix [17] and hence the mechanical properties of the hybrid composite [14]. therefore, cnt grafting proves to be effective in improving the shear strength of cfrps at all loading rates considered in this study and facilitates their usage under situations of low and/or high strain rates. one more advantage of using grafted carbon nanotubes is the resistance that they offer to brittle failure in cfrp composites. the outwardly projecting grafted cnts mechanically interlock with the surrounding matrix and offer frictional sliding after fiber gets debonded from the matrix [13], consequently preventing catastrophic failure either by avoiding or delaying the crack propagation. figure 3: maximum debond force (fmax) versus embedded length (le) for epoxy composite reinforced with: (a) unsized carbon fiber (hcf) and (b) cnt grafted carbon fiber (cntcf). (c) interfacial shear strength (ifss) of various composites at different load speeds. figure 4: sem micrographs of single fiber filament after debond test: (a) unsized and (b) cnt grafted carbon fiber debonded from epoxy droplet. inset shows the optical image (dino-lite, taiwan) of drop on fiber before testing. in order to get some idea about the observed differences in ifss of cfrps reinforced with or without cnts, sem h.s. bedi et alii, frattura ed integrità strutturale, 48 (2019) 571-576; doi: 10.3221/igf-esis.48.55 575 analysis is performed on the failed fiber surfaces. fig. 4 presents the analysis of the surface of debonded fibers using sem, throwing some more light on the failure mechanism of different fiber/epoxy composites. the presence of matrix debris adhering the surface of cnt grafted cf debonded from epoxy (fig. 4b) implies that failure occurs at the interface of nanotubes and matrix away from the cf/epoxy interface [13]. whereas, the clean surface of debonded fiber in hcf/epoxy composites (fig. 4a) suggests failure taking place at the fiber/epoxy interface. this implies poor interfacial bond in hcf/epoxy composites and lower ifss as compared to cntcf/epoxy composites. conclusion he effect of loading rate and grafted cnts on the interfacial shear strength (ifss) of carbon fiber reinforced epoxy composites is studied. single fiber micro-droplet debond tests are carried out on unsized and cnt grafted carbon fiber epoxy composites at two displacement rates of 0.05 and 5 mm/min. an increase in ifss is observed by increasing the test speed for both unsized and cnt grafted carbon fiber reinforced epoxy composites. the benefit of incorporating grafted cnts in the composite system is clear from the high values of ifss for cntcf/epoxy composites than hcf/epoxy composites. ifss of cnt based hybrid composites are approximately 30% higher than their non-cnt counterparts. at higher speeds of loading, matrix is found to play a more significant role in the failure process by yielding more to increase the energy of fracture and hence the ifss of the composite. acknowledgement uthors would like to thank the financial support and lab facilities provided by indian institute of technology ropar to carry out this research work. references [1] jacob, g.c., starbuck, j.m., fellers, j.f., simunovic, s. and boeman, r.g. (2004). strain rate effects on the mechanical properties of polymer composite materials, j. appl. polym. sci., 94(1), pp. 296-301. [2] sockalingam, s. and nilakantan, g. (2012). fiber-matrix interface characterization through the microbond test, international journal of aeronautical and space sciences, 13(3), pp. 282-295. [3] qian, h., bismarck, a., greenhalgh, e.s., kalinka, g. and shaffer, m.s. (2008). hierarchical composites reinforced with carbon nanotube grafted fibers: the potential assessed at the single fiber level, chem. mater., 20(5), pp. 18621869. [4] gao, x., jensen, r., li, w., deitzel, j., mcknight, s. and gillespie jr, j. (2008). effect of fiber surface texture created from silane blends on the strength and energy absorption of the glass fiber/epoxy interphase, journal of composite materials, 42(5), pp. 513-534. [5] chandrasekaran, v., advani, s. and santare, m. (2011). influence of resin properties on interlaminar shear strength of glass/epoxy/mwnt hybrid composites, composites, part a, 42(8), pp. 1007-1016. [6] breuer, o. and sundararaj, u. (2004). big returns from small fibers: a review of polymer/carbon nanotube composites, polym. compos., 25(6), pp. 630-645. [7] winey, k.i. and vaia, r.a. (2007). polymer nanocomposites, mrs bull., 32(04), pp. 314-322. [8] qian, h., greenhalgh, e.s., shaffer, m.s. and bismarck, a. (2010). carbon nanotube-based hierarchical composites: a review, j. mater. chem., 20(23), pp. 4751-4762. [9] li, m., gu, y.z., liu, y.n., li, y.x. and zhang, z.g. (2013). interfacial improvement of carbon fiber/epoxy composites using a simple process for depositing commercially functionalized carbon nanotubes on the fibers, carbon, 52, pp. 109-121. [10] li, q., church, j.s., naebe, m. and fox, b.l. (2016). interfacial characterization and reinforcing mechanism of novel carbon nanotube–carbon fibre hybrid composites, carbon, 109, pp. 74-86. [11] jiang, d., liu, l., long, j., xing, l., huang, y., wu, z., yan, x. and guo, z. (2014). reinforced unsaturated polyester composites by chemically grafting amino-poss onto carbon fibers with active double spiral structural spiralphosphodicholor, compos. sci. technol., 100, pp. 158-165. t a h.s. bedi et alii, frattura ed integrità strutturale, 48 (2019) 571-576; doi: 10.3221/igf-esis.48.55 576 [12] an, f., lu, c., guo, j., he, s., lu, h. and yang, y. (2011). preparation of vertically aligned carbon nanotube arrays grown onto carbon fiber fabric and evaluating its wettability on effect of composite, appl. surf. sci., 258(3), pp. 1069-1076. [13] agnihotri, p., basu, s. and kar, k. (2011). effect of carbon nanotube length and density on the properties of carbon nanotube-coated carbon fiber/polyester composites, carbon, 49(9), pp. 3098-3106. [14] bedi, h.s., padhee, s.s. and agnihotri, p.k. (2018). effect of carbon nanotube grafting on the wettability and average mechanical properties of carbon fiber/polymer multiscale composites, polym. compos., 39(s2), pp. e1184-e1195. [15] okoli, o.i. (2001). the effects of strain rate and failure modes on the failure energy of fibre reinforced composites, composite structures, 54(2-3), pp. 299-303. [16] bedi, h.s., tiwari, m. and agnihotri, p.k. (2018). quantitative determination of size and properties of interphase in carbon nanotube based multiscale composites, carbon, 132, pp. 181-190. [17] bedi, h.s., padhee, s.s. and agnihotri, p.k., editors. on the nature of interface of carbon nanotube coated carbon fibers with different polymers. iop conference series: materials science and engineering; 2016: iop publishing; 2016. << /ascii85encodepages false /allowtransparency false /autopositionepsfiles true /autorotatepages /none /binding /left /calgrayprofile (dot gain 20%) /calrgbprofile (srgb iec61966-2.1) /calcmykprofile (u.s. web coated \050swop\051 v2) /srgbprofile (srgb iec61966-2.1) /cannotembedfontpolicy /error /compatibilitylevel 1.4 /compressobjects /tags /compresspages true /convertimagestoindexed true /passthroughjpegimages true /createjobticket false /defaultrenderingintent /default /detectblends true /detectcurves 0.0000 /colorconversionstrategy /cmyk /dothumbnails false /embedallfonts true /embedopentype false /parseiccprofilesincomments true /embedjoboptions true /dscreportinglevel 0 /emitdscwarnings false /endpage -1 /imagememory 1048576 /lockdistillerparams 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can be opened with acrobat and adobe reader 5.0 and later.) >> /namespace [ (adobe) (common) (1.0) ] /othernamespaces [ << /asreaderspreads false /cropimagestoframes true /errorcontrol /warnandcontinue /flattenerignorespreadoverrides false /includeguidesgrids false /includenonprinting false /includeslug false /namespace [ (adobe) (indesign) (4.0) ] /omitplacedbitmaps false /omitplacedeps false /omitplacedpdf false /simulateoverprint /legacy >> << /addbleedmarks false /addcolorbars false /addcropmarks false /addpageinfo false /addregmarks false /convertcolors /converttocmyk /destinationprofilename () /destinationprofileselector /documentcmyk /downsample16bitimages true /flattenerpreset << /presetselector /mediumresolution >> /formelements false /generatestructure false /includebookmarks false /includehyperlinks false /includeinteractive false /includelayers false /includeprofiles false /multimediahandling /useobjectsettings /namespace [ (adobe) (creativesuite) (2.0) ] /pdfxoutputintentprofileselector /documentcmyk /preserveediting true /untaggedcmykhandling /leaveuntagged /untaggedrgbhandling /usedocumentprofile /usedocumentbleed false >> ] >> setdistillerparams << /hwresolution [2400 2400] /pagesize [612.000 792.000] >> setpagedevice microsoft word numero_54_art_01_2787 t. i. j. brito et alii, frattura ed integrità strutturale, 54 (2020) 1-20; doi: 10.3221/igf-esis.54.01 1 on the lumped damage modelling of reinforced concrete beams and arches thalyson issac de jesus brito, danilo menezes santos, fabio augusto silva santos, rafael nunes da cunha, david leonardo nascimento de figueiredo amorim laboratory of mathematical modelling in civil engineering, post-graduation programme in civil engineering, department of civil engineering, federal university of sergipe, são cristóvão, brazil britothalyson@gmail.com, http://orcid.org/0000-0003-0884-2950 dmsantosse@gmail.com, http://orcid.org/0000-0002-3165-7553 fabioaugustoufs@gmail.com, http://orcid.org/0000-0003-0554-2119 fael3005ufs@academico.ufs.br, http://orcid.org/0000-0003-2503-6758 david.amorim@ufs.br, http://orcid.org/0000-0002-9233-3114 abstract. the analysis of reinforced concrete structures can be performed by means of experiments or numerical studies. the first way is usually quite expensive, so the second one sometimes is a good option to understand the physical behaviour of actual structures. lumped damage mechanics appears as one of the latest nonlinear theories and presents itself as an interesting alternative to analyse the mechanical behaviour of reinforced concrete structures. the lumped damage mechanic applies concepts of the classic fracture and damage mechanics in plastic hinges for nonlinear analysis of reinforced concrete structures. therefore, this paper deals with a novel physical definition of the correction factor γ for cracking evolution that ensures the presented lumped damage model depicts accuracy when it is compared to experimental observations of reinforced concrete beams and arches. based on such experiments, the numerical analysis showed that γ value has upper and lower thresholds, depending on the physical and geometric properties of the reinforced concrete element. notwithstanding, for γ values inside of the proposed interval, there is a best value of γ. keywords. plastic hinges; lumped damage mechanic; reinforced concrete; beams; arches. citation: brito, t.i.j., santos, d.m., santos, f.a.s., cunha, r.n., amorim, d.l.n.f., on the lumped damage modelling of reinforced concrete beams and arches, frattura ed integrità strutturale, 54 (2020) 1-20. received: 13.04.2020 accepted: 29.06.2020 published: 01.10.2020 copyright: © 2020 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. introduction einforced concrete structures are worldwide used. in order to understand the behaviour of reinforced concrete structures due to different loading conditions, several experimental researches were carried out during the last decades. for instance, vecchio and emara [1] analysed a reinforced concrete frame with monotonic and cyclic loads. carpinteti et al. [2] studied the scale effect in concrete specimens under uniaxial compression. marsavina et al. [3] measured the chloride penetration in concrete structures. sharifi [4] studied the influence of self-consolidating concrete in r https://youtu.be/bgx5m9yrjbu t. i. j. brito et alii, frattura ed integrità strutturale, 54 (2020) 1-20; doi: 10.3221/igf-esis.54.01 2 reinforced concrete beams. caratelli et al. [5] and abbas et al. [6] analysed the performance of precast tunnel segments actually built in italy [5] and canada [6]. finally, ruggiero et al. [7] carried out full scale explosion experiments in reinforced concrete slabs. since experimental research is usually quite expensive, numerical studies are often feasible to understand the physical behaviour of actual structures. among several possibilities, theory of plasticity, fracture and damage mechanics are usually chosen. theory of plasticity is probably the most known nonlinear principle. in such theory the inelastic effects are quantified by plastic strains e.g. the nonlinear behaviour of the reinforced concrete slabs during the direct contact explosion were modelled by ruggiero et al. [7] throughout the theory of plasticity coupled with a three-dimensional finite element analysis. fracture mechanics [8] were developed in order to quantify the propagation of discrete cracks in continuum media. for instance, shi et al. [9] analysed a plain concrete tunnel lining with tens of thousands of finite elements with a fracture model. note that the numerical response [9] is quite close to the experimental one [10]. damage mechanics [11] introduces a variable, called damage, which quantifies the micro-crack density for concrete-like materials or micro-voids for metallic ones. in such theory, these micro-cracks are not small enough to be neglected but not big enough to be considered as discrete cracks. several damage models were proposed in literature [12-20]. despite the accuracy of the plastic, damage and fracture models, due to the material complexity of reinforced concrete structures, such models are usually not suitable for practical applications. alternatively, lumped damage mechanics (ldm) applies some key concepts of classic fracture and damage mechanics in plastic hinges. ldm was firstly formulated for reinforced concrete structures under seismic loads [21-23]. afterwards, ldm was rapidly expanded for other reinforced concrete structures [24-32], as well as steel frames [33-36], plain concrete tunnel linings [37] and masonry arches [37-38]. note that ldm models present objective solutions [39-41]. for reinforced concrete structures the damage variable quantifies the concrete cracking and the plastic rotation variable accounts for the reinforcement yielding. such damage variable takes values between zero and one. therefore, the generalised griffith criterion is used as an energy balance to crack propagation i.e. damage evolution. the plastic rotation evolution is accounted for a kinematic plastic law. note that the evolution laws for damage and plastic rotation on the referred papers [21-32] and the references therein varies due to the purpose of each study and the applications per se. perdomo et al. [23] proposed evolution laws that the model parameters can be easily associated to classic reinforced concrete theory. despite such model’s [23] accuracy for bearing load capacity of reinforced concrete structures, service loads are often not well estimated. as an attempt to present a simple calibration of this model, alva and el debs [27] proposed a correction factor that enhances the damage evolution law leading to solutions that are even more accurate. however, alva and el debs [27] do not present the physical meaning of such factor, which might be an issue to this model reach practical engineering applications. in the light of the foregoing, this paper aims to propose a novel understanding of the physical meaning of the correction factor presented by alva and el debs [27]. therefore, such correction factor is widely analysed using some experiments in order to deepen knowledge on the model and facilitate its application in practical engineering problems. lumped damage mechanics statics of circular arch elements onsider the structure depicted in fig. 1a, which is composed by m circular arch elements connected by n nodes. external forces can be applied at each node, as illustrated for node j (puj, pwj and pθj). note that the first index of the applied force describes its direction and the second one the node e.g. pwj is the force at the node j parallel to the zaxis. generically, the applied loads are gathered in the matrix of external forces, given by:    1 1 1 ... ... ... t u w ui wi i uj wj j un wn np p p p p p p p p p p p   p (1) where the superscript t means “transpose of”. consider a circular arch element b between nodes i and j, as the one presented in fig. 1. a circular arch element is defined by its arc angle (χb), a radius (rb) and an angle between the z-axis and z-axis (βb). such element presents internal forces with respect to the global xz system as depicted in fig. 1b. then, the matrix of internal forces is given as follows:    tui wi i uj wj jb q q q q q q q (2) c t. i. j. brito et alii, frattura ed integrità strutturale, 54 (2020) 1-20; doi: 10.3221/igf-esis.54.01 3 where qui is the internal force at the node i in the x-axis direction, qwi is the internal force at the node i in the z-axis direction and so on. now, adopting the same notation proposed by powell [42], another set of static variables is introduced (fig. 1c) which are called as generalised stresses. then, the matrix of generalised stresses gathers two bending moments at the edges of the element (mi and mj) and an axial force at the node i (ni) i.e.    ti j ib m m nm (3) (a) (b) (c) figure 1: (a) structure composed by circular arch finite elements, (b) internal forces and (c) generalised stresses. regarding the equilibrium of the element, the internal forces and the generalised stresses can be expressed as [31]:      tb b bq b m (4) where [b]b is the transformation matrix, given by: t. i. j. brito et alii, frattura ed integrità strutturale, 54 (2020) 1-20; doi: 10.3221/igf-esis.54.01 4                                                         sin cos 1 sin sin sin cos 0 sin sin cos 1 sin cos 1 cos cos sin 0 sin sin cos cos sin sin cos cos 0 sin sin cos cos sin b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b r r r r r r r r r                                                           b                               sin cos cos 1 sin sin cos 1 sin cos 1 cos cos sin 0 sin sin b b b b b b b b b b b b b b b b b b b b b b b b r r r                                          (5) then, the equilibrium relation of the structure is given by:     1 m e b b  p q (6) being {qe}b the expanded internal forces matrix, given as follows:   1 {0 0 0 0 0 0}te ui wi i uj wj jb node node i node nnode j q q q q q q q      (7) therefore, the equilibrium relation can be expressed as:       1 m t e bb b  p b m (8) where [be]b is the expanded transformation matrix, given in a similar way of {qe}b. kinematics of circular arch elements consider again the structure depicted in fig. 1a, the node i presents two translations parallel to the global xand z-axes (ui and wi, respectively) and a rotation in the xz plane (θi). such translations and rotation are here called generalised displacements. then, the generalised displacements of all nodes of the structure are gathered in the generalised displacements matrix, given by:    1 1 1 ... ... ... t i i i j j j n n nu w u w u w u w   u (9) now, the generalised deformations are defined as conjugate quantities of the generalised stress i.e. i, j and δi are conjugated to mi, mj and ni, respectively. such quantities are gathered in the generalised deformations matrix:    ti j ib   φ (10) therefore, the mechanical power of the element is expressed as: t. i. j. brito et alii, frattura ed integrità strutturale, 54 (2020) 1-20; doi: 10.3221/igf-esis.54.01 5          t t eb bbb  φ m u q m  (11) assuming small displacements and small deformations, the matrix of generalised deformations is given by:      eb bφ b u (12) elasticity of circular arch elements consider an elastic circular arch element with its internal forces at edges in the local coordinate system as the one depicted in fig. 2a. thus, the strain energy of the element is expressed by:    2 2 0 2 2 b b b m n u r d ei ae               (13) where n(ψ) and m(ψ) are the normal force and bending moment for a cross section ψ, respectively, ae is the axial stiffness and ei is the flexural stiffness of the element. note that n(ψ) and m(ψ) can be obtained by equilibrium (fig. 2b): ( ) ( 1 cos ) ( ) (1 cos ) sin sin sin ( cos ) ( ) cos sin i j i b b i i b b i i b i b b j i b b m m n r m m n r m n r n r m n n r                       (14) figure 2: elastic circular arch element: (a) internal forces and (b) stresses at any cross section. where v(ψ) is the shear force for a cross section ψ. by applying castigliano’s theorem, the elastic generalised deformations are given by:       2 2 2 2 2 2 2 02 2 2 2 2 b b b b i j i iie i i i e e b b b b j j bbb j i j j ije i bi b b b b i i i j i i u u uu m m m nmm m u u u u m m m m m nm n u u u u n m n m n n                                                                            φ f m (15) t. i. j. brito et alii, frattura ed integrità strutturale, 54 (2020) 1-20; doi: 10.3221/igf-esis.54.01 6 being [f0]b the elastic flexibility matrix, expressed as follows [38]:     2 2 2 2 2 2 2 0 2 2 2 2 2 22 2 2 2 2 4 sin 3 2 cos 3sin cos sin cos1 1 2 2sin sin b b b i j i ii b b b b i j j ij b b b i i j i i b b b b b b bb b b b i b b b b i u u u m m m nm u u u m m m nm u u u m n m n n ru m ei r ae u m m                                                             f       2 2 2 22 2 2 2 2 2 2 sin sin cos sin cos1 1 2 2sin sin 5sin 5 cos cos 3 2 cos1 2 sin sin sin cos cos1 2 sin sin cos s1 1 2 2sin b b b b b b b b j b b b b b b b b b b b bb i i b b b b b b b b b b b bb j b r ei r ae ru m n ei ae ru m ei                                                         2 22 2 2 3 22 2 2 in cos sin sin cos sin cos1 2 sin sin sin cos cos1 2 sin 3sin cos cos 2 3sin cos sin sin sin cos c b b b b b b b b b b b bb j i b b b b b b b b b b b b b b b b bb i b b b b b b b r ae ru m n ei ae ru n ei r                                                            2 os sin b bae   (16) deformation equivalence hypothesis for the sake of simplicity, consider initially a uniaxial problem where a damaged straight bar is axially loaded. by definition, the damage variable ω represents the micro-cracks density [11]. then, such bar resists to the axial force by means of the effective stress i.e. the cauchy stress σ divided by (1 – ω). the following expression, named strain equivalence hypothesis [11], is given by substituting the effective stress in the hooke’s law:   1 pe           (17) where e is the young’s modulus, ε is the total strain and εp is the plastic strain. the previous relation can be rewritten as follows:    1 1 p p e d p e e e                      (18) t. i. j. brito et alii, frattura ed integrità strutturale, 54 (2020) 1-20; doi: 10.3221/igf-esis.54.01 7 therefore, by assuming the strain equivalence hypothesis the total strain can be expressed by a sum of three parts: elastic, damaged and plastic ones. note that if ω = 0 then εd = 0; on the other hand, if ω tends to one, εd tends to infinity, which represents that the straight bar is now broken into two parts. analogously, for a circular arch element the deformation equivalence hypothesis can be defined as:        e d pb b b b  φ φ φ φ (19) being {φe}b, {φd}b and {φp}b the elastic, damaged and plastic generalised deformations matrices, respectively. for the lumped damage framework, {φd}b and {φp}b describe the inelastic effects that are concentrated at two hinges at the edges of the element (fig. 3). in this paper it is assumed that the plastic deformations account for the reinforcement yielding and the lumped damage variables represent the concrete cracking. assuming that the plastic elongations at both hinges can be neglected [38], the plastic generalised deformation matrix is given by:    0 tp p pi jb  φ (20) where ip and jp are the plastic relative rotations at the edges i and j of the element, respectively. the damaged generalised deformation matrix is expressed as:       2 2 2 2 0 0 1 0 0 , 1 0 0 0 i b i i i jd b j i j bb b j j i b d u d m m d u m d d d m n                             φ c m (21) being [c(di,dj)]b the compliance matrix and di and dj the lumped damage variables at the hinges i and j, respectively. note that if there is no damage at the element then [c(di,dj)]b is null; on the other hand, if the damage variables tend to one then the non-zero terms of [c(di,dj)]b tend to infinity, which represents that the inelastic hinges are close to perfectly hinges. then, by substituting (15), (20) and (21) in (19), the constitutive relation is given by:              0 , ,p i j i jb b bbb b bd d d d         φ φ f m c m f m (22) where [f(di,dj)]b is the flexibility matrix with damage, written as:   2 2 2 2 2 2 2 2 2 2 2 2 1 1 1 , 1 b b b i i j i ii b b b i j b i j j j ij b b b i i j i i u u u d m m m nm u u u d d m m d m nm u u u m n m n n                                           f (23) t. i. j. brito et alii, frattura ed integrità strutturale, 54 (2020) 1-20; doi: 10.3221/igf-esis.54.01 8 figure 3: elastic circular arch element with two inelastic hinges. model reduction to straight elements a particular characteristic of the presented lumped damage model is that the circular arch element can degenerate to a straight element [37]. therewith, if rb tends to infinity then χb tends to zero, rbsinχb tends to the length of the element lb and βb becomes its orientation. then, the transformation and flexibility matrices are given as follows:     sin cos sin cos 1 0 sin cos sin cos lim 0 1 cos sin 0 cos sin 0 1 0 1 3 6 1 lim , 0 6 1 3 0 0 b b b b b b b b b b b b b b br b b b b b b b b b b i b b i j r b j b l l l l l l l l l l d ei ei l l d d ei d ei l ae                                                        b f (24) damage evolution law the complementary energy of the element is given by:          1 1 , 2 2 t tp i jb b bb b w d d     m φ φ m f m (25) since the lumped damage variable accounts for the concrete cracking, its evolution law is given by the generalised griffith criterion for each hinge i.e. t. i. j. brito et alii, frattura ed integrità strutturale, 54 (2020) 1-20; doi: 10.3221/igf-esis.54.01 9             2 2 2 2 2 2 2 2 0 0 2 1 0 0 2 1 i i i i b i i ii i i i j j j j b j j jj j j j d g y d m uw g d mg y d d d d g y d m uw g d mg y d d d                             (26) where gi and gj are the damage driving moments for the hinges i and j, respectively, and y(di) and y(dj) are the cracking resistance functions. the cracking resistance function for a hinge i was obtained by means of experiments on reinforced concrete beams [23]:     0 ln 1 1 i i i d y d y q d     (27) being y0 and q model parameters. in order to generalise the previous equation, alva and el debs [27] proposed the following relation:       0 ln 1 exp 1 1 i i i i d y d y q d d          (28) where γ is an empiric parameter introduced as an attempt to ensure a better fitting between numerical and experimental responses for service loads. plastic evolution law the plastic evolution laws for each hinge of the element are given by: 0 0 0 0 0 10 0 0 0 0 10 0 p i i pi i ip ii i p j j j p j jp jj j f m f c k df f m f c k df                                 (29) being fi and fj the yield functions for the hinges i and j, respectively, and c and k0 model parameters. model association with reinforced concrete theory n evident advantage of the lumped damage models for reinforced concrete structures is that the model parameters can be easily associated to the classic reinforced concrete theory. an engineer in practice knows how to calculate four key quantities for any reinforced concrete element: first cracking moment (mr), ultimate moment (mu), plastic moment (mp) and ultimate plastic rotation (up) [43]. considering an inelastic hinge i, cracks start to nucleate when the first cracking moment is reached i.e. 2 2 02 0 2 r b i r i i m u m m d y m        (30) then, the parameter y0 is defined as the first cracking resistance. a t. i. j. brito et alii, frattura ed integrità strutturale, 54 (2020) 1-20; doi: 10.3221/igf-esis.54.01 10 note that the analysed cross section (hinge i) has a load bearing capacity, therefore the ultimate moment (mu) is associated to a certain cracking level, which is quantified by the ultimate damage (du). therewith, the generalised griffith criterion is expressed as:      2 2 02 2 ln 1 exp 1 12 1 uu b i u i u u uiu dm u m m d d y q d dmd              (31) where q and du are the unknown variables. since the load bearing point (du, mu) is the local maximum point of the moment-damage curve, another equation may be defined as:          00 2 1 1 ln 1 1 ln 1 exp 1 0 i u i u i u u u u u m mi d d m y d q d d d d d                        (32) then, with eqns. (31) and (32) the variables q and du can be calculated. note that the parameter q is related to an additional cracking resistance due to the reinforcement. analogously to the load bearing point, the plastic moment (mp) is associated to the plastic damage (dp). thus, dp is calculated by the generalised griffith criterion i.e.       2 2 02 2 ln 1 exp 1 12 1 pp b i p i p p pip dm u m m d d y q d dmd              (33) at this stage, the reinforcement starts yielding, therefore: 00 0 1 pp i p i i p m m m f k d         (34) where k0 is defined as the effective plastic moment. finally, for the load bearing capacity the plastic evolution law is expressed by: 0 1 0 1 p p u i p i u i p uu m m m f c k d                 (35) being c then defined. examples cantilever beam [43] lórez-lópez et al. [43] presents the test of a cantilever reinforced concrete beam subject to a lateral concentrated load as illustrated in fig. 4. the beam properties are shown in tab. 1 and the yield and rupture tensions of the steel bars are 412 mpa and 520 mpa, respectively. the numerical analyses carried out in this example vary the value of γ. the comparison among experimental and numerical responses is shown in fig. 5. beam fc' (mpa) as a's h (cm) b (cm) 1 26.0 3 ø 12.5mm 3 ø 12.5mm 20 20 table 1: geometric and material proprieties of the beam [43] f t. i. j. brito et alii, frattura ed integrità strutturale, 54 (2020) 1-20; doi: 10.3221/igf-esis.54.01 11 figure 4: test set-up [43] figure 5: convergence of results to the experimental for the cantilever beam [43] for γ = 0, it may be noted that the results are very close to the experimental data, presenting good fitting for the three stages, reaching the rupture load. for γ ≠ 0, it can be observed that all analysis reached the rupture load acquired from experimental data. in cases where the range for γ values are lower than zero, the curves present a high stiffness at cracking concrete stage, not fitting well to the experimental result. on the other hand, for the range where γ values are higher than zero, there is a decrease in the stiffness response for elastic and cracking stages, but in tertiary stage the similarity with the experimental results is recovered. furthermore, the bending moment vs damage results are presented in fig. 6. as shown in fig. 6, the ultimate damage (du) for γ = 0 is near to 0.6. in comparison, for different γ values, it is noted that the damage variable is directly proportional to the coefficient γ. in the same way, seen in fig. 6 when attributed γ equal to 10, leads to a physical divergence where it occurs damage growth in parallel bending moment decreases. this fact leads the conclusion that γ has a maximum limit. for this, it is necessary to obtain the moment equation that is done by equalling the damage driving moment (g) to cracking resistance function (y). then, the upper-limit for γ is given by the following criterion: aa fix rigid base p ø10.0mm @ 8.0cm 3ø12.5mm 2 0 20 3ø12.5mm cross section a-a 1 4 0 dimensions in centimeters t. i. j. brito et alii, frattura ed integrità strutturale, 54 (2020) 1-20; doi: 10.3221/igf-esis.54.01 12   2 0 2 exp 0 i upperi r i bd r i qm m d u m m           (36) figure 6: bending moment vs. damage response the following equation shows the result obtained: 2 2 2 ln r bupper i m u q m          (37) the lower-limit for γ is obtained by the following criterion:     2 2 0 0 0 0 1 2 exp exp i b r i i i d lower lower u m d m m y q              (38) which leads to: lower   (39) despite γlower, when γ values are negative occurs numerical instabilities in the analysis process, leading to values of ultimate damage and plastic damage tending to zero. therefore, from now on, only positive values for γ are adopted in this paper. meneghetti [44] a simply supported experimental beam under a four point bending test was carried out by meneghetti et al. [44], which has as cross section dimensions 15 cm x 30 cm, total length 300 cm and distance between supports 285 cm. for the design due to bending were defined two longitudinal lower bars with 12.5 mm diameter, 317 cm total length and 10 cm anchorage at each edge; two longitudinal upper bars with 6.3 mm diameter, 297 cm total length. for the design due to shearing were calculated 42 stirrups with 6.3 mm diameter, 7 cm spacing, 90 cm total length and 6cm anchorage at each tip and the covering adopted was 15 mm (see fig. 7). results of strength limits, 6.3 mm steel bars acquired the followed magnitude tensions, 508 mpa and 713 mpa, yield and rupture, respectively. 12.5 mm bars acquired yield tension value 578 mpa and t. i. j. brito et alii, frattura ed integrità strutturale, 54 (2020) 1-20; doi: 10.3221/igf-esis.54.01 13 806 mpa in rupture. the concrete used achieved average values of 41.4 mpa in the experiments of compressive strength and 37.6 gpa as elasticity modulus. the beam was loaded at its first and second third of its length between supports. figure 7: geometry and typical reinforcement arrangement [44] fig. 8 shows a sequence of curves with increasing coefficient γ in comparison to the experimental curve. as the coefficient increases it is noticed the numerical model convergence to the experimental loading-displacement curve in this example. alva [45] suggests that each structure analysed has its optimum coefficient (γopt), which might be acquired through repeatedly iterations in a programming routine. the choice of γ parameter aim the best numerical fitting to the experimental response. the comparison between the force-displacement curve of the theoretical model and the experimental curve indicates that the lumped damage model is able to approximately reproduce the nonlinear behaviour of the structure, both in the cantilever beam (previous example) and in the current one, which deals with a four-point bending test. it is important to emphasise that all parameters from the numerical model were calculated based on average values of strength and deformability for the structural materials, since the objective was a comparison with experimental results. figure 8: convergence of results to the experimental beam [44] yasser sharifi beams [4] sharifi [4] studied the influence of self-consolidating concrete in reinforced concrete beams. for this, a series of experiments in beams, with different reinforcement ratios, were executed, tested under four points bending test. the typical geometry of the beams and its typical arrangement of reinforcement are shown in fig. 9. the properties of the beams analysed are presented in tab. 2 and the average yield strength of the longitudinal reinforcement was approximately 400 mpa. 15 cross section a-a 7.57.5 285 102.5 95 a a 3 0 ø6.3mm @ 7.0cm 2ø12.5mm 2ø6.3mm dimensions in centimeters 102.5 t. i. j. brito et alii, frattura ed integrità strutturale, 54 (2020) 1-20; doi: 10.3221/igf-esis.54.01 14 figure 9: geometry and typical reinforcement arrangement of the beams [4]. beam fc' (mpa) as a's d (mm) d' (mm) b1 31.6 2 ø 14 2 ø 14 258 42 b2 28.84 2 ø 18 + 2 ø 16 + 2 ø 14 2 ø 14 + 2 ø 18 256 43 b3 29.53 2 ø 22 2 ø 14 + 2 ø 25 254 45 table 2: geometric and material proprieties of the sharifi’s beams [4]. for the specimen b1 it was observed that all analyses had good approximation with the experimental results for the three stages and reached the collapse load. the obtained results are shown in fig. 10. figure 10: convergence of results to the experimental beam b1 [4] furthermore, all curves present closer results to the experimental curve at primary stage, but for higher values of γ, the stiffness is closest than the others. for b2, the results of load-displacement are shown in fig. 11. dimensions in centimeters 15 270 15 120 60 120 3 0 20 3 0 20 cross section b-b b b a a cross section a-a t. i. j. brito et alii, frattura ed integrità strutturale, 54 (2020) 1-20; doi: 10.3221/igf-esis.54.01 15 figure 11: convergence of results to the experimental b2 [4] it may be noticed by the experimental data that this beam has a higher stiffness. thus, γ = 0 provides better results. moreover, the results obtained by using γ ≠ 0, due to their lower inclination, reaches the collapse load only for higher values of displacement, not fitting well for the three stages. for b3, with results of load-midspan displacement, presented in fig. 12, can be observed a less-rigid behaviour. therefore, the numerical simulation gives better results for higher γ values. figure 12: load-displacement curve b3 [4] brennero base segment tunnel [5] aiming to analyse the performance of a precast tunnel, caratelli et al. [5] carried out a full-scale test of a tunnel segment. in its totality, the tunnel has 55 km long, with external diameter equal to 6 meters and total circumference length equal to 19 m. the diameter was divided in 6 segments, where only one was experimentally tested under three points bending, getting the midspan displacement. the set-up of the test is shown in fig. 13 and its orthogonal view is shown in fig. 14, where “t” is the thickness and “l” is the length between hinge supports. t. i. j. brito et alii, frattura ed integrità strutturale, 54 (2020) 1-20; doi: 10.3221/igf-esis.54.01 16 figure 13: test set-up [5, 6] figure 14: view of the segment of tunnel, in meters the considered segment thickness is equal to 200 mm, the length between hinge supports and the width are equal to 204 cm and 150 cm, respectively. its average cubic compressive strength of concrete reached 50 mpa and the yielding strength of the longitudinal reinforcement is 450 mpa. the reinforced is composed with 8 mm rebars, spaced of 20 cm and with open stirrups, used as splitting reinforcement, as shown in fig. 15. figure 15: geometry and typical reinforcement arrangement of the brennero base segment tunnel [5] 1 5 0 365 20 1 0 dimensions in centimeters t. i. j. brito et alii, frattura ed integrità strutturale, 54 (2020) 1-20; doi: 10.3221/igf-esis.54.01 17 the mid-span displacement of brennero base segment tunnel [5] is shown in fig. 16 for the experimental response and numerical analyses. figure 16: convergence of results to the experimental of brennero base segment tunnel [5] it can be observed that the results of all analysis were close one another, losing the similarity in the second stage. however, for γ equal to 4, the curve was closer to the experimental data than the others. furthermore, for all models, the collapse load was bigger than the experimental results, increasing safety. canada underground tunnel [6] abbas et al. [6], aiming to study the behaviour of a precast concrete tunnel lining, had modelled a full-scale arc segment from a subway extension tunnel in canada. for this, they had executed a flexural monotonic and cyclic load test. the arch had distance between supports, width and thickness equal to 300 cm, 150 cm and 235 mm, respectively. the compressive concrete strength equal to 60 mpa and yielding strength of reinforcement equal to 450 mpa. the reinforcement arrangement was made with 8.6 mm, 11.3 mm, 14 mm rebars and is shown in fig. 17. figure 17: geometry and typical reinforcement arrangement of the canada underground segment tunnel [6] 318 ø14mmø11.3mm 15 ø 8.6mm @ 18.4cm dimensions in centimeters 8 .3 1 0 2 6 .5 1 2 2 4 .8 1 2 2 6 .5 1 0 8 .3 1 5 0 t. i. j. brito et alii, frattura ed integrità strutturale, 54 (2020) 1-20; doi: 10.3221/igf-esis.54.01 18 the experimental test took place similarly to brennero base segment tunnel [5], tested under three points bending, as shown in fig. 13, and results for the mid-span displacement. the results of the experimental test and the models analysed are presented in fig. 18. figure 18: convergence of results to the experimental of canada underground tunnel [6] note that, the precast segment tunnel was less rigid than brennero base segment tunnel [5], so γ > 0 gives better approximation for the results in the curve load-displacement. furthermore, it is shown in fig. 16, that the results for γ = 0 lost the similarity on cracking and ultimate stages. however, for γ > 0, this similarity is approximate for higher values of γ, in especial for γ equal to 4, the results are closer than the others. furthermore, all models could reach to the collapse load, for similar displacements. concerning the experimental responses of tunnel lining segments tested by caratelli et al. [5] and abbas et al. [6], there are several differences in both set-ups. note that the geometry of the test is quite different, where the span, thickness and the arc radius of both specimens are 2.04 m, 20.0 cm and 5.90 m [5] and 3.00 m, 23.5 cm and 2.40 m [6], respectively. such characteristics imply that the tunnel segment tested by abbas et al. [6] is approximately 2.56 times more flexible than the one tested by caratelli et al. [5]. conclusions his work intended to present a physical meaning for the empiric coefficient proposed by alva and el debs [27], which was analysed from comparisons with experiments obtained in the literature. even though it is not observed by alva and el debs [27], that the proposed model presents limitations of range for the γ value model, once adopting negative values, the plastic and ultimate damage tend to null values, which does not have physical significance. while, for positive values of γ, when analysing the moment-damage curve, it is observed that, for very high values of γ, the curve does not represent the actual structural behaviour, i.e., for the increase in the value of the damage, the bending moment presents a decreasing rate. the maximum value of γ varies according the structural flexibility, first cracking moment, the increase in strength of the structure due to longitudinal reinforcement and the ultimate bending moment. applying γ = 0 and γ ≠ 0 approaches to the experiments, a good approximation of both for the experimental results was observed. however, cases which the structures were more rigid, the first model (γ = 0) achieved better results in primary and secondary stages, reaching good stiffness results, while for less rigid structures the second model (γ ≠ 0) presented better approximations for higher values of γ. for the analysed experiments, γ = 0 presents better solutions for the cantilever beam [43], the first and the second beams presented by sharifi [4] and the tunnel lining segment tested by caratelli et al. [5]. on the other hand, better numerical solutions are obtained with γ = 10 for the beam tested by meneghetti et al. [44], γ = 3 for the third beam presented by sharifi [4] and γ = 4 for the tunnel lining segment tested by abbas et al. [6]. t t. i. j. brito et alii, frattura ed integrità strutturale, 54 (2020) 1-20; doi: 10.3221/igf-esis.54.01 19 furthermore, both models reached the collapse load for all examples; however, for the cases where the values of γ were higher, also higher values of deformation were needed to reach the maximum load. it is recommended for future works to make modifications to the cracking strength equation, in order to obtain results that reach good approximations in comparison with results obtained experimentally, especially for the secondary stage. references [1] vecchio, f.j., emara, m.b. (1992). shear deformations in reinforced concrete frames, aci struct. j., 89(1), pp. 46–56, doi: 10.14359/1283. [2] carpinteri, a., ferro, g., monetto, i. (1999). scale effects in uniaxially compressed concrete specimens, mag. concr. res., 51(3), pp. 217–225, doi: 10.1680/macr.1999.51.3.217. [3] marsavina, l., audenaert, k., de schutter, g., faur, n., marsavina, d. (2009). experimental and numerical determination of the chloride penetration in cracked concrete, constr. build. mater., 23(1), pp. 264–274, doi: 10.1016/j.conbuildmat.2007.12.015. [4] sharifi, y. (2012). structural performance of self-consolidating concrete used in reinforced concrete beams, ksce j. civ. eng., 16(4), pp. 618–626, doi: 10.1007/s12205-012-1517-5. [5] caratelli, a., meda, a., rinaldi, z., romualdi, p. (2011). structural behaviour of precast tunnel segments in fiber reinforced concrete, tunn. undergr. sp. technol., 26(2), pp. 284–291, doi: 10.1016/j.tust.2010.10.003. [6] abbas, s., soliman, a.m., nehdi, m.l. (2014). mechanical performance of reinforced concrete and steel fiber-reinforced concrete precast tunnel lining segments: a case study, aci mater. j., 111(5), pp. 501–510, doi: 10.14359/51687101. [7] ruggiero, a., bonora, n., curiale, g., de muro, s., iannitti, g., marfia, s., sacco, e., scafati, s., testa, g. (2019). full scale experimental tests and numerical model validation of reinforced concrete slab subjected to direct contact explosion, int. j. impact eng., 132 (september 2018), doi: 10.1016/j.ijimpeng.2019.05.023. [8] broek, d. (1984). elementary engineering fracture mechanics, martinus nijhoff. isbn: 978-94-009-4333-9. [9] shi, z., ohtsu, m., suzuki, m., hibino, y. (2001). numerical analysis of multiple cracks in concrete using the discrete approach, j. struct. eng., 127(9), pp. 1085–1091, doi: 10.1061/(asce)0733-9445(2003)129:3(324). [10] abo, h., tanaka, m., yoshida, n. (2000). development of a maintenance system for waterway tunnels. electric power civ eng, 287, 424-6. [11] lemaitre j, chaboche jl (1985). mécaniques des matériaux solides. paris: dunod. isbn: 978-2100013975. [12] bonora, n., (1997). a nonlinear cdm model for ductile failure. engineering fracture mechanics, 58, pp. 11-28, doi: 10.1016/s0013-7944(97)00074-x. [13] ragueneau, f., la borderie, c., mazars, j. (2000). damage model for concrete-like materials coupling cracking and friction, contribution towards structural damping: first uniaxial applications, mech. cohesive-frictional mater., 5(8), pp. 607–625, doi: 10.1002/1099-1484(200011)5:8<607::aid-cfm108>3.0.co;2-k. [14] comi, c., perego, u. (2001). fracture energy based bi-dissipative damage model for concrete, int. j. solids struct., 38(36–37), pp. 6427–54, doi: 10.1016/s0020-7683(01)00066-x. [15] bažant, z.p., jirásek, m. (2002). nonlocal integral formulations of plasticity and damage: survey of progress, j. eng. mech., 128(11), pp. 1119–1149, doi: 10.1061/(asce)0733-9399(2002)128:11(1119). [16] proença, s.p.b., pituba, j.j.c. (2003). a damage constitutive model accounting for induced anisotropy and bimodular elastic response, lat. am. j. solids struct., 1(1), pp. 101–117. [17] comi, c., perego, u. (2011). anisotropic damage model for concrete affected by alkali-aggregate reaction, int. j. damage mech., 20, pp. 598–617, doi: 10.1177/1056789510386857. [18] farahani, b. v., belinha, j., pires, f.m.a., ferreira, a.j.m., moreira, p.m.g.p. (2017). a meshless approach to non-local damage modelling of concrete, eng. anal. bound. elem., 79, pp. 62–74, doi: 10.1016/j.enganabound.2017.04.002. [19] testa, g., ruggiero, a., iannitti, g., bonora, n., gentile, d. (2018). modification of the bonora damage model for shear failure, frat. ed integrita strutt., 12(44), pp. 140–150, doi: 10.3221/igf-esis.44.11. [20] majid, f., elghorba, m. (2018). continuum damage modeling through theoretical and experimental pressure limit formulas, frat. ed integrita strutt., 12(43), pp. 79–89, doi: 10.3221/igf-esis.43.05. [21] flórez-lópez j. (1993) modelos de daño concentrado para la simulación del colapso de pórticos planos. rev int mét num cálc dis ing. ;9(2):123–139. [22] cipollina, a., lópez-inojosa, a., flórez-lópez, j. (1995). a simplified damage mechanics approach to nonlinear analysis of frames, comput. struct., 54(6), pp. 1113–1126, doi: 10.1016/0045-7949(94)00394-i. t. i. j. brito et alii, frattura ed integrità strutturale, 54 (2020) 1-20; doi: 10.3221/igf-esis.54.01 20 [23] perdomo, m.e., ramírez, a., flórez-lópez, j. (1999). simulation of damage in rc frames with variable axial forces, earthq. eng. struct. dyn., 28(3), pp. 311–328, doi: 10.1002/(sici)1096-9845(199903)28:3<311::aid-eqe819>3.0.co;2d. [24] liu y. -b., liu j. -b. (2004). a damage beam element model for nonlinear analysis of reinforced concrete member. j earthquake eng eng vib., 24(02), pp. 95–100. [25] araújo f, proença s.p.b. (2008). application of a lumped dissipation model to reinforced concrete structures with the consideration of residual strains and cycles of hysteresis. j mech mater struct., 3(5), pp. 1011–1131, doi: 10.2140/jomms.2008.3.1011. [26] rajasankar j, iyer nr, prasad ap. (2009). modelling inelastic hinges using cdm for nonlinear analysis of reinforced concrete frame structures. comput concr.,6(4), pp. 319–431, doi: 10.12989/cac.2009.6.4.319. [27] alva, g.m.s., el debs, a.l.h. de c. (2010). application of lumped dissipation model in nonlinear analysis of reinforced concrete structures, eng. struct., 32(4), pp. 974–981, doi: 10.1016/j.engstruct.2009.12.024. [28] faleiro, j., oller, s., barbat, a.h. (2010). plastic-damage analysis of reinforced concrete frames, eng. comput., 27(1), pp. 57–83, doi: 10.1108/02644401011008522. [29] yang, t. -s., wang, j. -l. (2010). damage analysis of three-dimensional frame structure suffering from impact. j vib shock, 29(12), pp. 177–180. [30] perdomo, m.e., picón, r., marante, m.e., hild, f., roux, s., flórez-lópez, j. (2013). experimental analysis and mathematical modeling of fracture in rc elements with any aspect ratio, eng. struct., 46, pp. 407–416, doi: 10.1016/j.engstruct.2012.07.005. [31] amorim, d.l.n.f., proença, s.p.b., flórez-lópez, j. (2013). a model of fracture in reinforced concrete arches based on lumped damage mechanics, int. j. solids struct., 50(24), pp. 4070–4079, doi: 10.1016/j.ijsolstr.2013.08.012. [32] teles, d.v.c., oliveira, m.c., amorim, d.l.n.f. (2020). a simplified lumped damage model for reinforced concrete beams under impact loads, eng. struct., 205, doi: 10.1016/j.engstruct.2019.110070. [33] guerrero, n., marante, m.e., picón, r., flórez-lópez, j. (2007). model of local buckling in steel hollow structural elements subjected to biaxial bending, j. constr. steel res., 63(6), pp. 779–790, doi: 10.1016/j.jcsr.2006.08.006. [34] bai, y., kurata, m., flórez-lópez, j., nakashima, m. (2016). macromodeling of crack damage in steel beams subjected to nonstationary low cycle fatigue, j. struct. eng., 142(10), pp. 1–13, doi: 10.1061/(asce)st.1943-541x.0001536. [35] bai, y., guan, s., flórez-lópez, j. (2017). development of a damage model for assessing fracture failure of steel beamto-column connections subjected to extremely low-cycle fatigue, eng. fail. anal., 82, pp. 823–834, doi: 10.1016/j.engfailanal.2017.07.032. [36] bazán, j.a.v., beck, a.t., flórez-lópez, j. (2019). random fatigue of plane frames via lumped damage mechanics, eng. struct., 182, pp. 301–315, doi: 10.1016/j.engstruct.2018.12.008. [37] amorim, d.l.n. d. f., proença, s.p.b., flórez-lópez, j. (2014). simplified modeling of cracking in concrete: application in tunnel linings, eng. struct., 70, pp. 23–35, doi: 10.1016/j.engstruct.2014.03.031. [38] amorim, d.l.n.f., proença, s.p.b., flórez-lópez, j. (2014). lumped damage mechanics as an alternative to analyse masonry arches. international collaboration by young researchers for “application of structural engineering and structural health monitoring to historic buildings, pp. 19–25. [39] toi, y., hasegawa, k. (2011). element-size independent, elasto-plastic damage analysis of framed structures using the adaptively shifted integration technique, comput. struct., 89(23–24), pp. 2162–2168, doi: 10.1016/j.compstruc.2011.09.002. [40] amorim, d.l.n.f. (2016). on the lumped damage mechanics for nonlinear structural analyses: new developments and applications. escola de engenharia de são carlos. [41] amorim, d.l.n.f., piedade neto, d., proença, s.p.b., flórez-lópez, j. (2018). the extended lumped damage mechanics: a new formulation for the analysis of softening with fe size-independence, mech. res. commun., 91, pp. 13–18, doi: 10.1016/j.mechrescom.2018.05.001. [42] powell, h.g. (1969). theory for nonlinear elastic structures, j. struct. div.-asce, 95 (st12), 2687-2701. [43] flórez-lópez, j., marante, m.e., picón, r. (2015). fracture and damage mechanics for structural engineering of frames: state-of-the-art industrial applications, engineering science reference. isbn: 978-1466663794. [44] meneghetti, l.c. (2007). análise do comportamento à fadiga de vigas de concreto armado reforçadas com prf de vidro, carbono e aramida. universidade federal do rio grande do sul. [45] alva, g.m.s. 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can be opened with acrobat and adobe reader 5.0 and later.) >> /namespace [ (adobe) (common) (1.0) ] /othernamespaces [ << /asreaderspreads false /cropimagestoframes true /errorcontrol /warnandcontinue /flattenerignorespreadoverrides false /includeguidesgrids false /includenonprinting false /includeslug false /namespace [ (adobe) (indesign) (4.0) ] /omitplacedbitmaps false /omitplacedeps false /omitplacedpdf false /simulateoverprint /legacy >> << /addbleedmarks false /addcolorbars false /addcropmarks false /addpageinfo false /addregmarks false /convertcolors /converttocmyk /destinationprofilename () /destinationprofileselector /documentcmyk /downsample16bitimages true /flattenerpreset << /presetselector /mediumresolution >> /formelements false /generatestructure false /includebookmarks false /includehyperlinks false /includeinteractive false /includelayers false /includeprofiles false /multimediahandling /useobjectsettings /namespace [ (adobe) (creativesuite) (2.0) ] /pdfxoutputintentprofileselector /documentcmyk /preserveediting true /untaggedcmykhandling /leaveuntagged /untaggedrgbhandling /usedocumentprofile /usedocumentbleed false >> ] >> setdistillerparams << /hwresolution [2400 2400] /pagesize [612.000 792.000] >> setpagedevice shot peening processes to obtain nanocrystalline surfaces in metal alloys: a. ouladbrahim et alii, frattura ed integrità strutturale, 58 (2021) 442-452; doi: 10.3221/igf-esis.58.32 442 focussed on steels and composites for engineering structures sensitivity analysis of the gtn damage parameters at different temperature for dynamic fracture propagation in x70 pipeline steel using neural network abdelmoumin ouladbrahim, idir belaidi department of mechanical engineering, university m’hamed bougara boumerdes, lemi laboratory, 35000 boumerdes, algeria. moumindoc@gmail.com; https://orcid.org/0000-0003-4729-298x idir.belaidi@gmail.com; https://orcid.org/0000-0003-3160-1135 samir khatir, magd abdel wahab soete laboratory, faculty of engineering and architecture, ghent university, technologiepark zwijnaarde 903, b-9052, zwijnaarde, belgium; khatir.samir@hotmail.fr; https://orcid.org/0000-0002-8101-3633 magd.abdelwahab@ugent.be; https://orcid.org/0000-0002-3610-865x erica magagnini, roberto capozucca dicea, structural section, polytechnic university of marche, italy abstract. in this paper, the initial and maximum load was studied using the finite element modeling (fem) analysis during impact testing (cvn) of pipeline x70 steel. the gurson-tvergaard-needleman (gtn) constitutive model has been used to simulate the growth of voids during deformation of pipeline steel at different temperatures. fem simulations results used to study the sensitivity of the initial and maximum load with gtn parameters values proposed and the variation of temperatures. finally, the applied artificial neural network (ann) is used to predict the initial and maximum load for a given set of damage parameters x70 steel at different temperatures, based on the results obtained, the neural network is able to provide a satisfactory approximation of the load initiation and load maximum in impact testing of x70 steel. keywords. steel x70; impact test (cvn); gtn parameters; fem; artificial neural network. citation: ouladbrahim, a., belaidi, i, khatir, s., wahab, m. a., magagnini, e., capozucca, r., sensitivity analysis of the gtn damage parameters at different temperature for dynamic fracture propagation in x70 pipeline steel using neural network, frattura ed integrità strutturale, 58 (2021) 442-452. received: 27.08.2021 accepted: 04.09.2021 published: 01.10.2021 copyright: © 2021 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. https://youtu.be/nfs6wqfsa8s a. ouladbrahim et alii, frattura ed integrità strutturale, 58 (2021) 442-452; doi: 10.3221/igf-esis.58.32 443 introduction he importance in the design of the current pipelines is the sufficient resistance of steels against fractures and ductile rupture of the pipelines should be avoided and their catastrophic consequences with the initiation of the rupture and the propagation of the fracture of the pipeline, while this requires a value of the minimum toughness of the steel necessary to arrest a long-lasting ductile fracture. the mechanical characterizations deduced from tensile testing in the pipeline manufacturing laboratory may be insufficient because breaks can be obtained below the yield strength under normal and special conditions rendering the material in a brittle state. the impact test is a main complement to the tensile test. the impact bending test or the impact test on a notched charpy specimen is intended to measure the resistance of a material to sudden rupture. the impact test represented by the charpy v-notch (cvn) (astm international) [1]is used to determine the fracture value of the toughness of a considerable material in the frame that it is an easy and more economical method to perform experiments. the high cost of large-scale experimental campaigns has driven the development of more economical laboratory-scale tests such as the well-known charpy v-notch (cvn) impact test, drop weight tear test (dwtt) [2]and more recently the dynamic tear test (dt3) [3]. for modern pipelines with a wall thickness reaching over 20mm, the cvn has a relatively small standard specimen size with a cross section of 10mm × 10mm [4]. in addition, limited by the test conditions, the results of the charpy impact test will be affected by certain factors, which have been investigated by many of the researchers. it is also of great research value to transform non-standard test results into standard results. li [5]studied the influence of the radius of the striker on the energy absorbed by the impact of x80 steel for pipelines; madhusudhan[6] presented the variation of energy absorbed by changing the pendulum speeds of 5 m/s, 6 m/s, 7 m/s and 9 m/s of maraging steel 300 using abaqus software. for x70 pipeline steel, there is a lack of comprehensive and systematic analysis of factors influencing the results of charpy impact testing; so the corresponding damage models can be validated and / or calibrated to be implemented in more complex simulations. the gurson-tvergaard-needleman (gtn) [7] damage model is well-known and widely applied and it is used to simulate dynamic ductility fracture propagation [8]. due to the limited parameter set in this model, it is often adopted in the industry field. in this article, the application of the gtn damage model for the dynamic propagation of fractures in the charpy test case is studied and the influence of the damage parameters on the initial and maximum fracture load will be quantified. at failure are applied to a high strength pipe material, namely x70 through a numerical study of a cvn impact experiment. a sensitivity analysis of the gtn damage constants is carried out to evaluate their influence on the initial and maximum load expected at failure. to analyze the simulation data obtained, machine learning approaches are applied and represented by an artificial neural network in order to identify the relative influence of the values of the gtn parameters and in temperature change on the initial and maximum load of the rupture. the potential predictive capacity of our model is tested by analyzing the outputs of our neural network for the proposed gtn parameter sets. finite element model e analysis of tensile test for base metal is performed using commercially available abaqus software; the charpy tensile and impact part is modeled as deformable. a 3d solid finite element model was implemented with the aim to reproduce the laboratory scale fracture toughness experiment (cvn). the abaqus/explicit solver permitted the application of the gtn damage model for the simulation of the dynamic propagation of fractures. the geometry was created based on the standard dimensions of the specimen as shown in the fig. 1 below. in each model, the mesh was created using linear 8 node brick elements with reduced integration. the mesh size is of significant importance when the gtn damage model is implemented [9]. in this study, an element size of 0.25 mm was used (see fig. 1). the condition of zero penetration between the hammer and the test specimen has been implemented [10]. in addition, friction has been taken into account using a penalty function with a coefficient of friction equal to 0.1. due to the impact load in the cvn, the acceleration and, as consequence, force measurements can show pronounced oscillations. therefore, the velocity data was extracted and derived to obtain acceleration and force data. this method reduced the presence of oscillations and made it possible to construct the force-displacement curves for each respective simulation. t f a. ouladbrahim et alii, frattura ed integrità strutturale, 58 (2021) 442-452; doi: 10.3221/igf-esis.58.32 444 the charpy impactor impact test is modeled as discrete rigid. the assigned physical material properties are shown in tab. 1. current stress and charpy impact models are subjected to plastic strain, therefore plasticity material properties at different temperatures (-20, -10, 0 and 20 ° c) for base metal are assigned using tensile test result data as shown in fig. 2. figure 1: a scheme of impact test specimen dimension and mesh used in finite element simulation. young’s modulus 210 gpa e =210 gpa poisson’s ratio ν =0.3 isotropic hardening =485 mpa k= 795 mpa n= 0.13 strain rate effect d=55 p=5 table 1: mechanical properties for x70 grade steels [11]. figure 2: true stress vs true strain at different temperatures. the thermophysical properties of api 5l x70 steel using for this simulation is shown in tab. 2.  yld a. ouladbrahim et alii, frattura ed integrità strutturale, 58 (2021) 442-452; doi: 10.3221/igf-esis.58.32 445 material conductivity (w / m° c) specific heat (j / kg ° c) thermal expansion (u m /m° c) api x70 52 420 8.5 table 2: thermophysical properties of api grade x70 steel [12]. temperature parameters q1 q2 n  fn fc parameters q1 q2 n  fn fc step1:20 °c; step2:0 °c; step3: -10 °c; step4: -20 °c. 1 1.5 1 0.3 0.012 0.0002 39 1.43 0.95 0.5 0.02 0.0042 2 1.47 1 0.3 0.012 0.0002 40 1.5 0.95 0.5 0.02 0.0042 3 1.43 1 0.3 0.012 0.0002 41 1.47 0.95 0.5 0.02 0.0042 4 1.4 1 0.3 0.012 0.0002 42 1.4 0.95 0.5 0.02 0.0042 5 1.5 0.975 0.3 0.012 0.0002 43 1.43 1 0.5 0.02 0.0042 6 1.5 0.95 0.3 0.012 0.0002 44 1.43 0.975 0.5 0.02 0.0042 7 1.5 0.925 0.3 0.012 0.0002 45 1.43 0.925 0.5 0.02 0.0042 8 1.5 1 0.4 0.012 0.0002 46 1.43 0.95 0.3 0.02 0.0042 9 1.5 1 0.5 0.012 0.0002 47 1.43 0.95 0.4 0.02 0.0042 10 1.5 1 0.7 0.012 0.0002 48 1.43 0.95 0.7 0.02 0.0042 11 1.5 1 0.3 0.016 0.0002 49 1.43 0.95 0.5 0.012 0.0042 12 1.5 1 0.3 0.02 0.0002 50 1.43 0.95 0.5 0.016 0.0042 13 1.5 1 0.3 0.024 0.0002 51 1.43 0.95 0.5 0.024 0.0042 14 1.5 1 0.3 0.028 0.0002 52 1.43 0.95 0.5 0.028 0.0042 15 1.5 1 0.3 0.012 0.0022 53 1.43 0.95 0.5 0.02 0.0002 16 1.5 1 0.3 0.012 0.0042 54 1.43 0.95 0.5 0.02 0.0022 17 1.5 1 0.3 0.012 0.005 55 1.43 0.95 0.5 0.02 0.005 18 1.5 1 0.3 0.012 0.0062 56 1.43 0.95 0.5 0.02 0.0062 19 1.5 1 0.3 0.012 0.008 57 1.43 0.95 0.5 0.02 0.008 20 1.47 0.975 0.4 0.016 0.0022 58 1.4 0.925 0.7 0.024 0.005 21 1.5 0.975 0.4 0.016 0.0022 59 1.5 0.925 0.7 0.024 0.005 22 1.43 0.975 0.4 0.016 0.0022 60 1.47 0.925 0.7 0.024 0.005 23 1.4 0.975 0.4 0.016 0.0022 61 1.43 0.925 0.7 0.024 0.005 24 1.47 1 0.4 0.016 0.0022 62 1.4 1 0.7 0.024 0.005 25 1.47 0.95 0.4 0.016 0.0022 63 1.4 0.975 0.7 0.024 0.005 26 1.47 0.925 0.4 0.016 0.0022 64 1.4 0.95 0.7 0.024 0.005 27 1.47 0.975 0.3 0.016 0.0022 65 1.4 0.925 0.3 0.024 0.005 28 1.47 0.975 0.5 0.016 0.0022 66 1.4 0.925 0.4 0.024 0.005 29 1.47 0.975 0.7 0.016 0.0022 67 1.4 0.925 0.5 0.024 0.005 30 1.47 0.975 0.4 0.012 0.0022 68 1.4 0.925 0.7 0.012 0.005 31 1.47 0.975 0.4 0.02 0.0022 69 1.4 0.925 0.7 0.016 0.005 32 1.47 0.975 0.4 0.024 0.0022 70 1.4 0.925 0.7 0.02 0.005 33 1.47 0.975 0.4 0.028 0.0022 71 1.4 0.925 0.7 0.028 0.005 34 1.47 0.975 0.4 0.016 0.0002 72 1.4 0.925 0.7 0.024 0.0002 35 1.47 0.975 0.4 0.016 0.0042 73 1.4 0.925 0.7 0.024 0.0022 36 1.47 0.975 0.4 0.016 0.005 74 1.4 0.925 0.7 0.024 0.0042 37 1.47 0.975 0.4 0.016 0.0062 75 1.4 0.925 0.7 0.024 0.0062 38 1.47 0.975 0.4 0.016 0.008 76 1.4 0.925 0.7 0.024 0.008 table 3: gtn parameters used in the simulation. a. ouladbrahim et alii, frattura ed integrità strutturale, 58 (2021) 442-452; doi: 10.3221/igf-esis.58.32 446 the finite element analysis of the impact test specimen was performed using the mesh size of 0.2 mm around the notch area. the simulation parameters at different temperatures of (-20, -10.0 and 20 ° c) are shown in tab. 3. the gtn damage model parameters are: q1, q2 and q3: related to the strengthening of the matrix material. and : mean equivalent plastic strain and the standard deviation. fn , fc : volume fraction of the critical voids. f f: the failure volume fraction of the material failure. in this work we consider that these parameters are fixed =0.1, and f f =0.18. test material the investigation of our study concerns manganese carbon steel used for the transport of hydrocarbons (gas and oil) under a working pressure of 70 bars with the name api 5l x70. the material meets the specification imposed by the standard api 5l [13]. tab. 4 shows the chemical composition of the steel used. c 0.125 mn 1.680 si 0.270 cr 0.051 ni 0.040 mo 0.021 s 0.005 s 0.005 cu 0.045 ti 0.003 nb 0.033 al 0.038 table 4: chemical composition requirement for analyzes (api 5l x70; wt%; fe is bal.). effect of specimen at different temperatures several impact tests were performed at different temperatures and the specimens were cooled using a special type of cooler designed to provide cooling temperatures down to -60 ° c. these tests are carried out on a charpy machine. we have carried out tests [-20 c; +20 c] at the alfapipe mechanical test laboratory, in accordance with api 5l x70. the dimensions of the test piece are given in fig. 1, the resilience test was carried out on standard cvn 10 * 10 test specimens, the geometry of which according to api 5l. from tab. 5, it is shown that as the temperature of the specimen keeps high values, the corresponding impact energy required for failure increases rapidly due to the steel being moved to the ductile zone. at high temperatures, while at low temperatures, steel behaves like a brittle material which requires quite a bit of energy to fracture. t, oc energy (j/cm²) energy (j/cm²) test 1 test 2 test 3 average (1,2,3) base metal (bm) 20 262.8 254.1 266.5 261.13 0 248 242 238 242.67 -10 216 210 210 212 -20 206 205 203 204.67 table 5: macro-characteristics of charpy specimens cut from x70 pipe steel tested for impact toughness-experimental. results simulated load-displacement/time curve ypical load vs displacement/time curve obtained from the fem simulation is shown in fig. 3. similar to the analysis of the experimental results, the load-displacement curve is divided into three parts: i-before the general yield point, ii-between the general yield point and the peak point, and iii-after the maximum point till the final fracture. all points are marked in fig. 3. it can be seen in fig. 3 that the load increases linearly with the displacement in part i. between the general yield point and the peak point the material starts to be deformed plastically. in part iii, the crack propagates and the load decreases to end of impact and the final separation is observed. all results at different temperatures and gtn parameters values of fem simulated load values are summarized in tab. 6. n ns ns t a. ouladbrahim et alii, frattura ed integrità strutturale, 58 (2021) 442-452; doi: 10.3221/igf-esis.58.32 447 figure 3: the simulated load-displacement curve, impact testing-x70. material specimen temperature experiment fem simulated general yield min-max (kn) peak load min-max (kn) general yield min-max (kn) peak load min-max (kn) group1 20 °c 17.78 18.65 19.05 19.98 14.07 15.15 15.01 24.22 group2 0 °c 16.66 17.36 17.85 18.6 14.72 15.67 15.53 25.33 group3 -10 °c 14.7 15.12 15.75 16.2 15.64 16.11 15.96 26.92 group4 -20 °c 14.21 14.42 15.225 15.45 15.85 16.37 16.23 27.28 table 6: summary of experiment and fem simulation results for the impact testing specimen. fig. 4 represented examples of the effect of the value of gtn parameters on the resulting fracture surface for charpy specimen, and fig. 5 shows the simulated impact test and the experimentally tested one. they are in very good agreement. two faces fracture area can be observed in both pictures. predict and analysis of initiation and maximum impact loading artificial neural network (ann) he fracture simulation by gtn model in abaqus software provides detailed information and data of the load fracture initiation and propagation in a ductile impact testing specimen. in this case, the development of ann application depends on a good selection of training data. in this work, ann model has been developed to predict the initial and maximum values of loading in impact test at different temperatures. the percentage by weight of gtn parameters was considered as the inputs and the initial and maximum load were considered as the outputs as shown in the fig. 6. t a. ouladbrahim et alii, frattura ed integrità strutturale, 58 (2021) 442-452; doi: 10.3221/igf-esis.58.32 448 max parameter value min parameter value q1 q2 fn fc figure 4: examples of the effect of the value of gtn parameters on the resulting fracture surface. (a) (b) figure 5: the fractured impact testing specimen: tested specimen (a); simulated specimen (b).  n a. ouladbrahim et alii, frattura ed integrità strutturale, 58 (2021) 442-452; doi: 10.3221/igf-esis.58.32 449 figure 6: architecture of neural network. anns have been widely used in several research studies to study the correlation between numerical input data elements and target orientation [14–16]. we try to use ann to study the relationship and the sensitivity between the gtn parameters and the initial and maximum load for the specimen fracture. thus, in our study, the 80% of the data provided in tab. 3 is used for training and 20% for testing and validation of neural networks for the prediction of initial and maximum load at different temperatures. in matlab the desired inputs and outputs or targets are imported into the workspace and the network "nntool" is created using inputs and targets. the ann model has a multi-layered structure, which is connected by nodes with three main layers, namely the input layer (6), the hidden layer (s) (12 neurons) and the output layer (2 neurons) as shown in fig 6. the mass percentage values of api x70 steel elements are inputs: q1, q2, , fn, fc, and t(°c). the output layer represents the initial and maximum load values: and the obtained results with the regression analysis (see fig 7(a)) and performance analysis (see fig 7(b)) for the prediction of the initial and maximum load values in impact testing at different temperatures of api x70 steel as a function of gtn model parameters are provided using ann. aregression analysis bperformance analysis figure 7: the results obtained for the prediction of initial and maximum load.  n initialf maximumf a. ouladbrahim et alii, frattura ed integrità strutturale, 58 (2021) 442-452; doi: 10.3221/igf-esis.58.32 450 the test input is considered (gtn model parameters) to predict different values of load (initial and maximum) and at different temperatures. the provided results are plotted in fig. 8 and 9. figure 8: the initial and maximum load with number of parameters gtn model (min and max values). figure 9: the maximum load at different temperatures and max gtn parameters values of impact testing. conclusion n artificial neural network model was developed in this work to predict the initial and maximum load and analysis of the gtn damage parameters at different temperatures for dynamic fracture propagation in x70 pipeline steel. based on the data obtained, the following conclusions can be drawn: • the calibration of certain parameters requires data and experimental tests and therefore the result of this calibration depends on the latter which varies according to the condition of the tests. so in this work we try to predict and analyze the influences of number gtn parameters on the initial and maximum load and in a temperature range in the charpy impact test using modelization of neural network which gives better results and makes it possible to minimize the number of simulations. • from the results, we can say that each gtn model parameter influences the final results by different percent and this allows taking the sensitivity of the parameters in consideration in the calibration part. • use of the damage model exists in many studies and researches but the values of the gtn parameters in the calibration of the models are not fixed and equal in them so our study goes through the study of the sensitivity of a a. ouladbrahim et alii, frattura ed integrità strutturale, 58 (2021) 442-452; doi: 10.3221/igf-esis.58.32 451 the initial and maximum load in the test of the impact according to the changes of the values of the parameters of the model gtn and in a limited temperature interval. • the developed model has a great capacity to make the prediction of the results before making calibration and determines the variation between different parameters by the simulation according to the mechanical properties of x70 steel. acknowledgement he third author, samir khatir, acknowledges the funding of the postdoctoral fellowship bof20/pdo/045 provided by bijzonder onderzoeksfonds (bof), ghent university. references [1] mitchell, e.b., lucon, e., collins, l.e., clarke, a.j., clarke, k.d. (2021). microstructure and thickness effects on impact behavior and separation formation in x70 pipeline steel, jom, 73(6), pp. 1966–1977, doi: 10.1007/s11837-021-04562-9. [2] skalny, p. (2016). evaluation and identifying the ductile fracture area of x70 steel from dwtt broken specimens, procedia struct. integr., 2, pp. 3727–3734, doi: 10.1016/j.prostr.2016.06.463. [3] simha, c.h.m., xu, s., tyson, w.r. (2015). computational modeling of the drop-weight tear test: a comparison of two failure modeling approaches, eng. fract. mech., 148, pp. 304–323, doi: 10.1016/j.engfracmech.2015.06.085. [4] mortazavi, e., najafabadi, r.a., meysami, a. (2017). effect of heat input on microstructure and mechanical properties of dissimilar joints of aisi 316l steel and api x70 high-strength low-alloy steel, j. iron steel res. int., 24(12), pp. 1248–1253, doi: 10.1016/s1006-706x(18)30024-4. [5] cao, y., zhen, y., song, m., yi, h., li, f., li, x. (2020). determination of johnson–cook parameters and evaluation of charpy impact test performance for x80 pipeline steel, int. j. mech. sci., 179(august 2019), doi: 10.1016/j.ijmecsci.2020.105627. [6] madhusudhan, d., chand, s., ganesh, s., saibhargavi, u. (2018). modeling and simulation of charpy impact test of maraging steel 300 using abaqus, iop conf. ser. mater. sci. eng., 330(1), doi: 10.1088/1757-899x/330/1/012013. [7] yoon, s.h., ryu, t.-y., kim, m.k., choi, j.-b., kim, i.-j. (2019). development of gtn model parameters for simulating ductile fracture behavior of x 70 carbon steel sent specimens, asme 2019 press. vessel. pip. conf., doi: 10.1115/pvp2019-93542. [8] jang, y.-y., moon, j.-h., huh, n.-s., kim, k.-s., cho, w.-y., lee, m.-w., kim, y.-j. (2019). evaluations of ductile and cleavage fracture using coupled gtn and beremin model in api x70 pipelines steel, asme 2019 38th int. conf. ocean. offshore arct. eng., doi: 10.1115/omae2019-96483. [9] gholipour, h., biglari, f.r., nikbin, k. (2019). experimental and numerical investigation of ductile fracture using gtn damage model on in-situ tensile tests, int. j. mech. sci., 164, pp. 105170, doi: 10.1016/j.ijmecsci.2019.105170. [10] kim, j.-s., kim, y.-j., lee, m.-w., kim, k.-s., shibanuma, k. (2020). fracture simulation model for api x80 charpy test in ductile-brittle transition temperatures, int. j. mech. sci., 182, pp. 105771, doi: 10.1016/j.ijmecsci.2020.105771. [11] rahman, k.m.m., mohtadi-bonab, m.a., ouellet, r., szpunar, j. (2019). a comparative study of the role of hydrogen on degradation of the mechanical properties of api x60, x60ss, and x70 pipeline steels, steel res. int., 90(8), pp. 1900078, doi: 10.1002/srin.201900078. [12] raafat, e., nassef, a., el-hadek, m., el-megharbel, a. (2019). fatigue and thermal stress analysis of submerged steel pipes using ansys software, ocean eng., 193(october), pp. 106574, doi: 10.1016/j.oceaneng.2019.106574. [13] carla silva de araújo, l., cândido, l.c., trindade, v.b., porcaro, r.r. (2017). evaluation of the influence of post welding heat treatments on microstructure and mechanical properties of api 5l x70q weld joints, weld. int., 31(4), pp. 251–258, doi: 10.1080/09507116.2016.1218609. [14] hojjat, g., shahram, s., mohammad, s. (2020). predicting the burst pressure of high-strength carbon steel pipe with gouge flaws using artificial neural network, j. pipeline syst. eng. pract., 11(4), pp. 4020034, doi: 10.1061/(asce)ps.1949-1204.0000478. [15] abarghouee, h., arabi, h., seyedein, s.h., mirzakhani, b. (2021). modelling of hot flow behavior of api-x70 t a. ouladbrahim et alii, frattura ed integrità strutturale, 58 (2021) 442-452; doi: 10.3221/igf-esis.58.32 452 microalloyed steel by genetic algorithm and comparison with experiments, int. j. press. vessel. pip., 189, pp. 104261, doi: 10.1016/j.ijpvp.2020.104261. [16] ouladbrahim, a., belaidi, i., khatir, s., magagnini, e., capozucca, r., wahab, m.a. (2021). prediction of gurson damage model parameters coupled with hardening law identification of steel x70 pipeline using neural network, met. mater. int., doi: 10.1007/s12540-021-01024-4. microsoft word numero 25 art 10 p. lazzarin et alii, frattura ed integrità strutturale, 25 (2013) 61-68; doi: 10.3221/igf-esis.25.10 61 special issue: characterization of crack tip stress field recent developments in multi-parametric three-dimensional stress field representation in plates weakened by cracks and notches p. lazzarin, m. zappalorto, f. berto university of padua, department of management and engineering, stradella san nicola 3, 36100, vicenza, italy abstract. the paper deals with the three-dimensional nature and the multi-parametric representation of the stress field ahead of cracks and notches of different shape. finite thickness plates are considered, under different loading conditions. under certain hypotheses, the three-dimensional governing equations of elasticity can be reduced to a system where a bi-harmonic equation and a harmonic equation have to be simultaneously satisfied. the former provides the solution of the corresponding plane notch problem, the latter provides the solution of the corresponding out-of-plane shear notch problem. the analytical frame is applied to some notched and cracked geometries and its degree of accuracy is discussed comparing theoretical results and numerical data from 3d fe models. keywords. three-dimensional elasticity; stress fields; antiplane solution; plane solution. introduction pioneering analytical framework was proposed by dougall [1] to evaluate the three-dimensional stress fields in plates; dougall’s method was later applied by green [2] to the stress analysis of a thick isotropic elastic plate weakened by a cylindrical hole. the same problem was discussed later also by sternberg and sadowsky [3] and by folias and wang [4]. as common denominator, these works have a sound discussion on the role played by the plate thickness on the hole tip stresses. as is well known, an approach providing a general solution for three-dimensional problems of elasticity was developed by papkovich [5] and neuber [6]. it is based on a general three-dimensional stress function. by using three harmonic functions, the fourth one being equal to zero, and different curvilinear coordinate systems, neuber was able to provide some solutions for the three-dimensional problem, in particular those related to the axisymmetric hyperboloidal ligament and the axisymmetric ellipsoidal cavity in an infinite elastic body. dealing with cracked components, hartranft and sih gave the approximate stress fields near the tip of a through crack in a thin elastic plate using a variational principle [7] and a refinement of the reissner theory [8]; fundamental contributions are also the extension to the three-dimensional crack case [9] of williams’ two dimensional eigenfunction series [10] as well as the application of the papkovich-neuber method to the same case [11]. among the recent papers we remember here the work by yang and freund [12] who took advantage of the kane and mindlin hypothesis [13] to analyse the state of stress in a tensioned thin elastic plate containing through-cracks. by using the fourier transform and the wiener-hopf technique they demonstrated the existence of a generalised plane strain field at the crack tip, and confirmed hartranft and sih’s previous findings [7]. the same result was found numerically also by nakamura and parks [14]. in parallel, discussing results from 3d finite element analyses on thin cracked elastic plates remotely subjected to mode ii anti-symmetrical loading, nakamura and parks [15] found that the asymptotic stress fields were characterized by a combination of plane strain mode ii and antiplane mode iii singular fields. their analyses put into light, for the first time, the existence of “local induced modes” due to three-dimensional effects. a http://www.gruppofrattura.it http://dx.medra.org/10.3221/igf-esis.25.10&auth=true p. lazzarin et alii, frattura ed integrità strutturale, 25 (2013) 61-68; doi: 10.3221/igf-esis.25.10 62 in the same period pook analysed the stress and displacement distributions in three-dimensional plates weakened by cracks and narrow notches [16, 17]. from the results of 3d finite element analyses pook [17] noted that in a plate under a nominal, far applied, mode ii loading there was a zone, close the notch tip (the notch tip radius being small but different from zero), where mode iii displacements were induced. the kane and mindlin theory was applied by kotousov and lew [18] to analyse the stress singularities related to angular corners in plates of arbitrary thickness subjected to in-plane loadings and various boundary conditions. the new singular stress states were referred to as the out-of-plane singularities and the corresponding fracture mode as the out-of-plane singular mode or ko mode. the intensity of local out-of-plane stress fields at the tip of pointed v-notches in 3d plates under remote mode ii loading was widely documented in refs. [19-21] on the basis of detailed three-dimensional fe analyses. cracks, blunt cracks as well as a variety of notches, sharp and blunt, were considered in these contributions. also the role played by higher order terms of the stress field was analysed in detail with reference to the crack case. in the presence of a notch tip radius equal to zero, the out-of-plane stress singularity arising at a small distance from the free surfaces, prior to these ones, was found to match that of the sharp v-notch problem under pure antiplane elasticity. when the v-notch opening angle is large enough to make non singular the mode ii stress distribution, the induced mode iii stress field remains singular. the local interaction between loading modes has been recently justified analytically by lazzarin and zappalorto [22] for pointed and sharply radiused notches in finite thick plates. on the basis of a generalised plane strain assumption, it was demonstrated that the governing equations of three-dimensional elasticity can be reduced in complexity solving, in combination, a bi-harmonic equation and a harmonic equation. the former provides the solution to the corresponding plane notch problem, the latter that of the antiplane elasticity problem for the same notch geometry. the two equations have to be simultaneously satisfied in a 3d problem, thus justifying theoretically the mutual interaction between mode ii and mode iii. this result was supported by a number of finite element analyses carried out on mode ii loaded thick plates with sharp and blunt notches [22, 23]. as a result, some previous closed-form solutions [24,25] obtained for axi-symmetric bodies under torsion can be used to analyse the out-of-plane stress distributions in 3d plates. starting from the analytical frame provided in [22], the aim of the present work is to present the 3d stress fields in some cases of practical interest. in the first case the stress fields close to a rectangular hole in a plate of finite thickness under tension is investigated. the second example deals with a finite thickness plate weakened by a crack. two forces are applied to generate mode iii loading conditions on the plate and the automatically generated coupled mode ii is investigated paying also attention to the scale effect governing the induced mode. a new frame for the analysis of the three-dimensional stress field new approach to the analysis of the three-dimensional notch problems has been recently proposed in ref. [22]. according to a generalized plane strain hypothesis, the displacement components are given by: ( , ) ( , ) ( , )x y zu u x y u v x y u bz w x y    (1) where z is the through-the-thickness coordinate and b is a constant term. doing so, the normal strains xx, yy, zz as well as xy are independent of z. taking advantage of the stress-strain relationships it was demonstrated that also the stress components xx, yy, xy and zz are independent of z, whereas the out-of-plane shear stress components depend on z according to the following expressions: yz xz w w g bz g bz y x           (2) then the equilibrium equation in the z direction simply gives [22]: 2 0w  (3) where 2 denotes the two-dimensional laplacian operator. differently, invoking eq. (3), the equilibrium equations in the x and y directions give: 2 22 2 2 2 0 yy xyxx y xx y           (4) eq. (4) is automatically satisfied by the classic airy stress function x,y: a http://www.gruppofrattura.it http://dx.medra.org/10.3221/igf-esis.25.10&auth=true p. lazzarin et alii, frattura ed integrità strutturale, 25 (2013) 61-68; doi: 10.3221/igf-esis.25.10 63 2 2 2 2 2xx yy xy x yy x                 (5) at the same time, accounting for the generalised hooke law for stresses and strains, the in-plane compatibility equation can be written in the form [22]: 4 2 0zz      (6) where the equality to zero is guaranteed by the third of beltrami-mitchell’s equations. as a result, the three dimensional notch problem can be converted into a bi-harmonic problem and a harmonic problem being valid the following differential equation system: 4 2 0 0w      (7a-b) here w and  are implicitly defined according to eqs. (2) and (5), respectively. note that eq. (7a) is the common biharmonic equation governing the solution of the plane problem; eq. (7b) is, instead, the harmonic equation governing the antiplane elasticity problem. it was demonstrated [22, 23] that this new frame is effective not only in the presence of pointed notches (sharp cracks or re-entrant corners) but also in the case of sharply radiused notches. the range of applicability does mainly depend on the notch tip radius. one should note that, in order to guarantee all the fundamental equations of 3d elasticity, eq. (7a) and eq. (7b) must be simultaneously satisfied. this allows to explain an important feature of three-dimensional stress distributions in plates: far applied loads resulting in local skew-symmetric function (mode ii stress components) inherently provoke a local skewsymmetric w function (mode iii stress components). viceversa, far applied loads resulting in local skew-symmetric wfunction (twisting) inherently provoke a local skew-symmetric function (mode ii stress components). the same holds valid, obviously, for symmetric loading conditions. far applied loads resulting in a local symmetric function (mode i stress components) results in a local symmetric w function, which is non-singular also in the presence of a singularity point. this justifies by a theoretical point of view the mutual interaction between loading modes shown numerically in refs. [19-21] and allows to understand why nisitani and chen [26] discussed, in principle, about four distinct loading modes. it is also worth mentioning that the proposed solution is not valid on the free surfaces of plates, where some edge effects, like the corner point singularities noted by benthem [27], might arise. it is valid up to a small distance from the free-surfaces. in the next sections two examples are provided with the aim to discuss the degree of accuracy of the newly developed three-dimensional theory. the spatial rectangular hole problem he plane problem of a plate weakened by a rectangular hole has been analysed by savin [28]. the mapping function approximating the rectangular hole was constructed on the basis of the schwarz-christoffel transformation and the complex functions used to determine the stress state according to the kolosofmuskelisvily method were given explicitely. in this section savin’s two dimensional analysis is extended to the threedimensional case. for more details, see ref. [23]. in particular, a rectangular hole in a finite thickness plate loaded in tension is considered (figure 1a). the rectangle corner can be regarded as a pointed v-notch of which the bisector is 45° inclined with respect to the loading direction. as a consequence, the uniaxial remote applied tension induces local in-plane mixed mode stresses (mode i plus mode ii), which can be described, according to eq. (7a), using williams’ plane solution for re-entrant corners. for a fixed value of the through-the-thickness coordinate, z, taking advantage of a polar reference system centred at the notch tip (see figure 1b), the in-plane stresses must vary according to williams’ singularity degrees, 1-1 for mode i and 12 for mode ii; in parallel, the stress field intensities can be quantified by the corresponding notch stress intensity factors (nsifs) [29]. however, the three-dimensional nature of the problem induces, besides the in-plane stresses, the out-of-plane shear stress components, zr and z which do not belong, by nature, to the williams solution. these stress components can be obtained by the following w function [26]: t http://www.gruppofrattura.it http://dx.medra.org/10.3221/igf-esis.25.10&auth=true p. lazzarin et alii, frattura ed integrità strutturale, 25 (2013) 61-68; doi: 10.3221/igf-esis.25.10 64    3 , 3 ,3, 3,cos sins as s a aw d r d r      (8) where 3, 3,2 /s a     , so that only the skew-symmetric part of w contributes to the singular behaviour of stress fields. accordingly the antiplane mode iii shear stresses close to the tip can be determined as: (a) (b) figure 1: thick plate weakened by a rectangular hole under tension (a); coordinate system used for stress components (b). 3, 3 ,1 1 3 3 3, 3, (z) (z) sin cos 2 2 a a zr a z a k r k r               (9) where: 3 , 1 3 0( ) lim 2 ( , 0) a r zk z r r        (10) is the mode iii nsif, to be thought of as the natural extension to the out-of-plane mode of gross and mendelson’s definitions given for the in-plane modes. in order to validate these theoretical results, a detailed finite element analysis on the geometry shown in figure 1a has been carried out. 20 node brick elements have been used with a very fine mesh pattern, in order to get the desired degree of accuracy. the material has been modelled according to a linear elastic behaviour, with e=206000 mpa and =0.3. 0.1 1 10 100 1000 10000 0.0001 0.001 0.01 0.1 1 s tr es s co m po n en ts [ m p a] distance from the notch tip, r [mm]  r z 100 mpa 100 mpa slope: 0.456 slope: 0.333 slope: 0.091 figure 2: plots of the stress components z and r along the notch bisector line of a rectangular hole in a thick plate under tension. distance from the mid plane z=2.5 mm. applied tension =100 mpa. http://www.gruppofrattura.it http://dx.medra.org/10.3221/igf-esis.25.10&auth=true p. lazzarin et alii, frattura ed integrità strutturale, 25 (2013) 61-68; doi: 10.3221/igf-esis.25.10 65 -300 -200 -100 0 100 200 300 -140 -100 -60 -20 20 60 100 140 s h ea r st re ss c o m po ne n ts [ m p a]  [°] z zr xy r  solid lines: eqs. (9) symbols: fem 100 mpa 100 mpa figure 3: plots of the stress components z and zr along a circular path of radius r = 0.001 mm centred at the notch tip, 135° ≤  ≤135°, and comparison with eq. (9). rectangular hole in a thick plate under tension. distance from the mid plane z=2.5 mm. nominal stress n=100 mpa. the stresses have been evaluated initially along the notch bisector line, with reference to the distance z=2.5 mm from the mid-plane. results are shown in figure 2 where that the singularity degree of in-plane stresses is shown to be in agreement with the williams solution. it is worth noting that the stress components , linked to the local mode i, is much higher than the mode iii stress component z antiplane shear stresses from fea have been evaluated also on a circular path of radius r=0.001 mm centred at the notch tip and compared to the theoretical prediction based on eq. (9). the comparison, shown in figure 3, documents a satisfactory agreement. figure 4 shows the through the thickness variation of the nsifs, k1, k2, k3. it can be seen that the hypothesis postulated in the previous section are verified on the major part of the plate thickness: the in-plane nsifs are almost constant while k3 varies linearly with z up to a maximum value which is located in the vicinity of the free surface. 0 10 20 30 40 50 60 70 0 100 200 300 400 500 600 0 0.5 1 1.5 2 2.5 3 k 3 [m p a m m 0 .3 3 3 3 ] k 1 [m p a m m 0 .4 5 6 ], k 2 [m p a m m    ] distance from mid plane [mm] k1 k2 k3 rectangular hole tension loadings figure 4. nsifs plotted along the thickness of the plate. rectangular hole in a thick plate under tension. nominal stress =100 mpa. 3d v-notched plate under torsion loading n this session another example of coupled mode generation is discussed. a finite thickness plate weakened by a crack has been modeled and two forces have been applied to generate mode iii loading on the plate (see fig. 5). the values of the stress intensity factors, tied to the generating and the coupled mode and normalized by kiii, appl., defined i http://www.gruppofrattura.it http://dx.medra.org/10.3221/igf-esis.25.10&auth=true p. lazzarin et alii, frattura ed integrità strutturale, 25 (2013) 61-68; doi: 10.3221/igf-esis.25.10 66 as the maximum value of kiii at the mid plane, have been plotted through the plate thickness for different values of the poisson’s ratio (see fig. 6). as it can be observed from the figure also the limit case =0 has been considered. the figure refers to a distance x=0.1 mm from the crack tip fully included in the zone governed by the leading order terms. the analysis shows that by applying a remote mode iii loading automatically a coupled mode ii is generated in the plate. as well visible from the figure the coupled mode is only slightly influenced by the poisson’s ratio and that, more important, it arises also when =0. by considering different plate thicknesses it is possible to investigate the scale effect when an externally applied mode iii induces a coupled mode ii. figure 7 reports the induced in plane shear stress component xy for different plate thicknesses (h=2.5, 10 and 40 mm). it is evident that decreasing the plate thickness the intensity of the induced stress increases according to the square root of the ratio between the considered plate thicknesses. figure 5: three-dimensional plate weakened by crack under torsion loading. two forces have been applied in z-direction while all displacements have been constrained on the dashed surface opposite to the notch. figure 6: variations of the stress intensity factors (mode iii and coupled mode) along the plate thickness. conclusions n this paper a stress field theory for plates of finite thickness is revisited and applied to some cases of practical interest. according to this theory the three-dimensional governing equations of elasticity can be simplified into a biharmonic equation and a harmonic one. the former provides the solution of the corresponding plane notch i http://www.gruppofrattura.it http://dx.medra.org/10.3221/igf-esis.25.10&auth=true p. lazzarin et alii, frattura ed integrità strutturale, 25 (2013) 61-68; doi: 10.3221/igf-esis.25.10 67 problem, the latter that of the corresponding out-of-plane notch problem. the two mentioned differential equations must be solved simultaneously, thus justifying by a theoretical point of view the mutual interaction between loading modes shown numerically by other authors. the capability of the new frame to describe the local stress fields in plates of arbitrary thickness under various loading conditions has been verified by some practical examples. 0.1 1 10 100 0.001 0.01 0.1 1 10 in p la n e sh ea r st re ss  xy (m p a) distance from the crack tip (mm) yy = yz = 0 iii = 0.5 h=10 mm h=2.5 mm h=40 mm scale factor 2 h-decreasing figure 7: scale effect on in-plane shear stresses (plate thickness h=40, 10 and 2.5 mm) induced by mode iii loading with kiii=1 mpa mm0.5. xy was plotted at z/h=0 (free surface) where the maximum effect due to induced mode ii occurs. the plate sizes are scaled by a factor 1/4 while the resulting stresses are scaled by a factor 2. references [1] dougall, j., an analytical theory of the equilibrium of an isotropic elastic plate, trans. roy. soc., edinburgh, 41 (1904) 129–228. [2] green, a.e., three-dimensional stress systems in isotropic plates, i. philos. trans. r. soc., london, ser a 240 (1948) 561-97. [3] sternberg, e., sadowsky, m.d., three-dimensional solution for the stress concentration around a circular hole in a plate of arbitrary thickness, j. appl. mech., 16 (1949) 27-38. [4] folias, e.s., wang, j-j., on the three-dimensional stress field around a circular hole in a plate of arbitrary thickness. comput. mech., 6 (1990) 379-91. [5] papkovich, p.f., solution générale des équations differentielles fondamentales d'élasticité exprimée par trois fonctions harmoniques, compt. rend. acad. sci. paris, 195 (1932) 513–15. [6] neuber, h., theory of notch stresses, berlin: springer-verlag; (1958). [7] hartranft, r.j., sih g.c., an approximate three-dimensional theory of plates with application to crack problems, int. j. eng., science 8 (1970) 711-29. [8] hartranft, r.j., sih g.c., effect of plate thickness on the bending stress distribution around through cracks, j. math. phys., 47 (1968) 276-91. [9] hartranft, r.j., sih, g.c., the use of eigenfunction expansions in the general solution of three-dimensional crack problems, j. math. mech., 19 (1969) 123-38. [10] williams, ml., stress singularities resulting from various boundary conditions in angular corners of plate in extension, j. appl. mech., 19 (1952) 526–534. [11] kassir, m.k., sih g.c., application of papkovich-neuber potentials to a crack problem, int. j. solids struct., 9 (1973) 643-54. [12] yang, w., freund, l.b., transverse shear effects for through-cracks in an elastic plate, int. j. solids struct., 21 (1985) 977–94. [13] kane, t.r., mindlin, r.d., high frequency extensional vibrations of plates, j. appl. mech., 23 (1956) 277–83. [14] nakamura, t, parks, dm., three-dimensional stress field near the crack front of a thin elastic plate, j. appl. mech., 55 (1988) 805–13. http://www.gruppofrattura.it http://dx.medra.org/10.3221/igf-esis.25.10&auth=true p. lazzarin et alii, frattura ed integrità strutturale, 25 (2013) 61-68; doi: 10.3221/igf-esis.25.10 68 [15] nakamura, t., parks, d.m., antisymmetrical 3-d stress field near the crack front of a thin elastic plate, int. j. solids struct, 25 (1989)1411–26. [16] pook, l.p., some implications of corner point singularities, eng. fract. mech., 48 (1994) 367-78. [17] pook, l.p., finite element analysis of corner point displacements and stress intensity factors for narrow notches in square sheets and plates, fatigue fract. engng. mater. struct., 23 (2000) 979–92. [18] kotousov, a., lew, y.t., stress singularities resulting from various boundary conditions in angular corners of plates of arbitrary thickness in extension. int. j. solids. struct., 43 (2006) 5100–09. [19] berto, f., lazzarin, p., harding, s., kotousov, a., out-of-plane singular stress fields in v-notched plates and welded lap joints induced by in-plane shear load conditions, fatigue fract. engng. mater. struct., 34 (2011) 291-304. [20] berto, f, lazzarin, p, kotousov, a, pook, l., on mode o existence at the tip of blunt cracks and u-notches under inplane shear loading, fatigue fract. engng. mater. struct., 35 (2012) 538–555. [21] berto, f., lazzarin, p., kotousov, a., on higher order terms and out-of-plane singular mode, mech. mater., 43 (2011) 332-342. [22] lazzarin, p., zappalorto, m., a three-dimensional stress field solution for pointed and sharply radiused v-notches in plates of finite thickness, fatigue fract. engng mater. struct. 35 (2012) 1105–19. [23] zappalorto, m., lazzarin, p., three-dimensional elastic stress fields ahead of notches in thick plates under various loading conditions, eng. fract. mech., accepted for publication. [24] zappalorto, m., lazzarin, p., filippi, s., stress field equations for u and blunt v-shaped notches in axisymmetric shafts under torsion, int. j. fract. 164 (2010) 253-69. [25] zappalorto, m., lazzarin, p., stress fields due to inclined notches and shoulder fillets in shafts under torsion, j. strain. anal. eng. des., 46 (2011) 187-99. [26] chen, d., nisitani, h., singular stress field near a corner of jointed dissimilar materials under antiplane loads. bull japan soc. mech. eng., 35 (1992) 399-403. [27] benthem, j.p., state of stress at the vertex of a quarter-infinite crack in half space. int. j. solids struct. 13 (1977) 479– 92. [28] savin, g.n., stress concentration around holes. new york; pergamon press, (1961). [29] gross, r., mendelson a., plane elastostatic analysis of v-notched plates. int. j. fract. mech., 8 (1972) 267–276. http://www.gruppofrattura.it http://dx.medra.org/10.3221/igf-esis.25.10&auth=true microsoft word numero_46_art_14 n. c. m. ibrahim et alii, frattura ed integrità strutturale, 46 (2018) 140-149; doi: 10.3221/igf-esis.46.14 140 developments in the fracture and fatigue assessment of materials and structures analysis of the crack-crack interaction effect initiated in aeronautical structures and repaired by composite patch nour chafak mohamed ibrahim, serier boualem, mechab belaïd university of djillali liabes, lpmm laboratory, sidi bel abbes, algeria nor_achafak@yahoo.fr, serielem@ yahoo.com, bmechab@yahoo.fr abstract. in this work, we analyze three dimensionally, by the finite element method, the performance of the repair of aeronautical structures damaged by cracking and repaired by patch of composite materials. the effect of crack-crack interaction according to their position and interdistance was analyzed. the criterion of rupture retained for this study is the factor of intensity of constraints. we show that this factor increases considerably and reaches a critical threshold when the two cracks develop towards each other. the repair of such damage using a composite patch ensures the stability of this structure during the commissioning process. the sharp fall in the stress intensity factor is characteristic of this stability. keywords. plate; repair; adhesive; patch; composite materials; crack; finite elements; stress intensity factor. citation: ibrahim, n. c. m., serier, b., mechab, b., analysis of the crack-crack interaction effect initiated in aeronautical structures and repaired by composite patch, frattura ed integrità strutturale, 46 (2018) 140-149. received: 05.06.2018 accepted: 12.07.2018 published: 01.10.2018 copyright: © 2018 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. introduction echniques for repairing and reinforcing damaged structures by bonding composite patches are increasingly used in industry, with the aim of delaying the appearance or propagation of fatigue cracks. in this technique, a composite patch is assembled to the damaged part with an adhesive, the aim of which is to transmit the maximum of stresses of the plate to the patch through the adhesive in order to reduce them to the tip of the crack. the notches are the main cause of the initiation of the crack and thus the repair with composite patches can play an important role, on the other hand, in reducing the stress concentration at the tip of the crack, and on the other hand of the reduction of the intensity of the stresses at the crack tip. therefore, the bonding assembly has several advantages, the possibility of assembling different materials, weight reduction, high stiffness, good fatigue strength, shock reduction and ease of bring together the most complex shapes. this technique has been extensively studied, where the stress intensity factor is considered an important factor in estimating the residual lifetime of cracked structures. in order to improve this technique, several experimental, numerical and even analytical studies have been devoted to the study of this behavior. the work was launched, in 1984, by baker at the australian research laboratory arl. [1, 2]. analytically, several works have been devoted to understanding this class of problems represent the effect of the patch on the crack tip stress intensity factor such as, mitchell and al. [3], jones and callinan [4], rose [5 7], young and al. [8, 9], rooke and al [10], ramesh chandra and al., [11] liu and fan [12], arendt and sun [13]. numerically, several authors have shown that the stress intensity factor depends on several parameters, the size and position of the crack, the patch and adhesive dimensions, the t http://www.gruppofrattura.it/va/46/14.mp4 n. c. m. ibrahim et alii, frattura ed integrità strutturale, 46 (2018) 140-149; doi: 10.3221/igf-esis.46.14 141 mechanical properties of the patch, the adhesive and of the structure itself, and have shown that, after repair, the stress intensity factor exhibits asymptotic behavior when the length of the crack increases as fekirini and al.[14], belhouari and al.[15] et bachir bouiadjra [16] which also showed that an adhesive with a high shear modulus gives a low stress intensity factor at the end of the repaired cracks. therefore, they recommend the use of these types of adhesives to increase the performance of the repair. however, the higher the adhesive shear modulus leads to higher adhesive stresses, which increases the risk of adhesive failure. they also analyzed the thickness importance of the adhesive and concluded that the adhesive properties should be optimized to improve repair performance and avoid adhesive breaking. ouinas and al. [17] made a comparison between the boron / epoxy patch and the graphite / epoxy patch for repairing aircraft structures. they indicated that the reduction of the stress intensity factor at the crack tip is more important for the boron / epoxy patch. ouinas and al. [18,19], mhamdia and al. [20] they analyzed the effect of the shape of the composite patch on the repair of aircraft structures. these authors analysed the performance of the repair is related to the patch shape, where they showed that the effectiveness of the rectangular shape of the plate can be greatly improved if this shape is modified in "h" or arrow shapes. the latter shape reduces: the stress intensity factor at the tip of the crack, the mass of the composite patch and therefore the repair cost, the adhesive stresses what improves the durability of the repair. the repair of doubly cracked structures is the objective of this study, where the interconnection of these cracks leads to the ruin of the structure. thus, the presence of a crack in the vicinity close to another leads to an increase in the probability of instability of these cracks by an intensification of the fic. the subcritical size of this narrow crack is about 3 times when the cracks are close to each other. such a fissure arrangement can be fatal to the structures, thus leading to their break. in order to delay this interconnection during commissioning and consequently to improve the service life. the latter is analyzed in terms of stress intensity factor, which depends on the stress applied, the size of the cracks, and their interdistance. figure: 1 geometrical models containing, (a) central crack of size "a", (b) two parallel cracks, (c) two parallel central fissures distant from (dx) and (dy). n. c. m. ibrahim et alii, frattura ed integrità strutturale, 46 (2018) 140-149; doi: 10.3221/igf-esis.46.14 142 geometrical and fe models he geometric model of the 2024 t3 aluminum alloy plate cracked repaired by boron-epoxy composite patch is shown in fig. 1. the plate is characterized by its height hp = 254 mm, its width wp = 254 mm and its thickness ep = 3 mm. the patch of dimensions hr = 75 mm, wr = 160 mm, er = 3 mm is bonded to the plate by an adhesive type fm73 of thickness ea = 0.26 mm. the unrepaired and repaired cracked plate is subjected to uniaxial tension efforts of varying amplitude. the mechanical properties of the plate, the patch and the adhesive are shown in tab. 1. the complete structure was modeled by cubic elements (hexahedrons) at eight nodes for the analysis of the stress intensity factor (fig. 2a, fig. 2b, fig. 2c). the rectangular shape of the composite patch is identifiable in this figure, a regular mesh is made for the whole structure, this mesh remains the same throughout the calculation. the crack results in a geometric singularity causing a concentration of stress. therefore, a refined mesh is made around the crack. the total number of elements of the structure containing: a central crack of size "a" (fig. 1a) is equal to 22716. two central and parallel cracks, distant from '' dx '' (fig. 1b) is equal to 26160. two central and parallel cracks distant from dx '' and '' dy '' (fig. 1c) is equal to 51960. (a) (b) (c) figure 2: meshing models containing, (a) central crack of size "a", (b) two parallel cracks, (c) two parallel central fissures distant from (dx) and (dy). results and discussion a central crack of size "a" effect of loading three-dimensional numerical analysis by the finite element method of the breaking mechanical behavior of an aluminum plate al 2024 t3 containing a central crack of size "a" initiated perpendicular to the direction of stresses and subjected to uniaxial tensile load. the criterion of rupture selected for this study is the factor of stress intensity in mode of opening (mode i). the results thus obtained are represented in fig. 3a. the latter shows that t a n. c. m. ibrahim et alii, frattura ed integrità strutturale, 46 (2018) 140-149; doi: 10.3221/igf-esis.46.14 143 an increase in this crack results in an intensification of this factor. this behavior is accentuated by an increase in mechanical efforts. property material description aluminum (al t2024) boron/epoxy adhesive fm 73 e1 72 200 2.55 young's modulus in x direction (gpa) e2 25 young's modulus in y direction (gpa) e3 25 young's modulus in z direction (gpa) ν12 0.33 0.21 0.32 poisson's ratio in x-y plan ν13 0.21 poisson's ratio in x-z plan ν23 0.21 poisson's ratio in y-z plan g12 7.2 shear modulus in x-y plan (gpa) g13 5.5 shear modulus in x-z plan (gpa) g23 5.5 shear modulus in y-z plan (gpa) table 1: mechanical proprieties of materials. (a) (b) figure 3: variation of stress intensity factor in crack heads as a function of crack size and mechanical loading intensity: (a) unrepaired, (b) repaired. the area of the plate initially damaged by cracking is repaired by patch of composite material and then tested in uniaxial tension. in fig. 3b are shown the results obtained from this analysis. this figure clearly shows that the repair begets a large reduction (about ten times) in the stress intensity factor. the variation of this rupture criterion with the size of the crack is an asymptotic variation. such behavior shows that the crack propagation kinetics are greatly reduced, thus resulting in crack stability. the durability of such a structure is therefore considerably increased, and this for large size defects subjected to heavy loading. crack-crack interaction two central and parallel cracks in this part of the work, we analyze the rupture behavior of an al 2024t3 plate containing two cracks aligned on the same axis perpendicular to that of the mechanical stresses. this structure is tested in uniaxial tension (fig. 1b). the fig. 4a illustrates the variation in the stress intensity factor in the opening mode in heads of the first unrepaired crack (fig. 1b) as a function of the distance separating it from the second. this figure shows that a growth of the latter towards the first 0,00 0,01 0,02 0,03 0,04 0,05 0,06 0,07 0,08 0,09 0,10 0,11 0 10 20 30 40 50 60 70 80 k i (m p a. (m )1 /2 ) a (m)  = 50mpa  = 100mpa  = 150mpa 0,00 0,01 0,02 0,03 0,04 0,05 0,06 0 1 2 3 4 5 6 7 8 9 10 k i (m p a .( m )1 /2 ) a (m)  = 50mpa  = 100mpa  = 150mpa n. c. m. ibrahim et alii, frattura ed integrità strutturale, 46 (2018) 140-149; doi: 10.3221/igf-esis.46.14 144 greatly increases the mechanical energy in crack heads. the stress intensity factor doubles practically in intensity when the two cracks are located in the vicinity close to each other. there is thus an interdistance between these two defects beyond which this criterion of rupture increases very strongly. this increase is all the more important as the plate more strongly mechanically solicited. the increase of this rupture criterion is explained by the simultaneous interaction of the stress fields in the heads of these two cracks. the increase of this rupture criterion is explained by the simultaneous interaction of the stress fields in the heads of these two cracks. this shows that a development from one fissure to another causes their instability and favors their coalescence. the interaction effect tends to disappear when these two defects are located far from one another. this structure, containing two cracks, is repaired using a patch made of composite material (fig. 2b) of the same size as that used for the repair of a crack and then subjected to traction. the variation of the stress intensity factor in mode i in the tip of the first repaired crack as a function of the distance with respect to the second crack is illustrated in fig. 4b. the repair leads to a considerable fall of this criterion of rupture. a large part of the mechanical energy concentrated in crack tips is absorbed by the patch through the adhesive. this leads to the stability of these two cracks and therefore to their non-coalescence, thus leading to an increase in the duration of such a structure. (a) (b) figure 4: variation of the stress intensity factor in heads of the first crack as a function of the distance with respect to the second crack: (a) unrepaired, (b) repaired. for an illustration of the effect of the repair we have shown in the fig. 5 is the variation of the stress intensity factor in the opening mode in heads of the first crack as a function of the distance separating it from the second initiated crack in a non-repaired and repaired plate. this figure shows that the adhesion of a composite patch to the damaged part by cracking of the plate, as a repair technique, leads to a very great reduction in this rupture criterion, approximately eight times smaller than that resulting from cracks not repaired. beyond a certain distance between these two cracks the stress intensity factor varies very little with the reduction with this distance. the effect of the size of the first crack on the localized stress intensity factor at a distance "dx" from the second crack is illustrated in fig. 6a. we note that a development of this defect leads to an increase in mechanical energy in crack tips and that this energy is all the more significant as this crack approaches the second. the stress intensity factor is closely related not only to the size of the crack, is propagating but also to the distance separating it from the second crack. the interaction of the stress fields in points of the two cracks leads to an increase in the stress intensity factor. the variation of this factor resulting from such a plate containing two repaired cracks, as a function of the size of the first crack and its distance from the second defect, is shown in fig. 6b. the latter shows that repair has considerably reduced this factor. a very high proportion of stresses in crack tips is transferred from the damaged plate to the composite patch through the adhesive, thus causing the stability of these two defects and consequently the increase in the duration of these structures. the effect of the size of the second crack on the stress intensity factor in the heads of the first crack initiated in an unrepaired plate is shown in fig. 7a. the latter shows that a development of the second crack towards the first favors its instability characterized by an increase of this criterion of rupture. indeed, the field of stresses in points of the first crack is all the more important as the second crack propagates in the direction of the first. the level of these constraints increases 0,00 0,01 0,02 0,03 0,04 0,05 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 a1= a2=30mm  = 50mpa  = 100mpa  = 150mpa dx (m) k i (m p a .( m )1 /2 ) 0,00 0,01 0,02 0,03 0,04 0,05 2 3 4 5 6 7 8 9 10 11 a1= a2= 30mm ; dy=0 dx (m) k i (m p a .( m )1 /2 )  = 50mpa  = 100mpa  = 150mpa n. c. m. ibrahim et alii, frattura ed integrità strutturale, 46 (2018) 140-149; doi: 10.3221/igf-esis.46.14 145 considerably when the second tends towards the first. this behavior favors their coalescence. the fig. 7b shows the variation in the stress intensity factor resulting from the same structure but repaired. the analysis of this figure shows the beneficial effect of the repair. the stress intensity factor in points of the first crack fell sharply, regardless of the size of the second crack. under the effect of the repair, the zone of strong of stresses interaction was strongly relaxed. this clearly shows that the repair technique considerably reduces the risk of coalescence of cracks resulting from the mechanism of interaction between stress fields in crack heads. figure 5: variation of the stress intensity factor in the heads of the first crack as a function of the distance separating it from the second initiated in an unrepaired and repaired plate. (a) (b) figure 6: variation of the stress intensity factor in heads of the first crack as a function of its size: (a) unrepaired, (b) repaired. the effect of the simultaneous propagation of the two unrepaired cracks on the stress intensity factor in spikes of the first crack is illustrated in fig. 8a. we note, however, that the risk of instability of the first crack is all the higher as the second propagates in its direction and these two defects develop simultaneously towards each other. the stress intensity factor resulting from the first crack increases with the growth of these two cracks. such behavior promotes their coalescence by interaction effect. a patch repair of such a structure leads to a strong of stresses relaxation in crack tips characterized by a low stress intensity factor irrespective of the size of these two defects (fig. 8b). 0,00 0,01 0,02 0,03 0,04 0,05 14 21 28 35 42 49 56 63 70 77 84 91 98 105 a2=30 mm  = 150mpa a1=10mm a1=20mm a1=30mm a1=40mm a1=50mm k i (m p a .( m )1 /2 ) dx (m) 0,00 0,01 0,02 0,03 0,04 0,05 7 8 9 10 11 12 dx (m) k i (m p a .( m )1 /2 ) a2=30 mm  = 150mpa a1=10mm a1=20mm a1=30mm a1=40mm a1=50mm n. c. m. ibrahim et alii, frattura ed integrità strutturale, 46 (2018) 140-149; doi: 10.3221/igf-esis.46.14 146 (a) (b) figure 7: variation of the stress intensity factor in heads of the first crack as a function of the size of the second crack: (a) not repaired, (b) repaired. (a) (b) figure 8: variation of the stress intensity factor in heads of the first crack as a function of the size of two cracks: (a) unrepaired, (b) repaired two central and parallel cracks distant from dx '' and '' dy '' the fig. 9 shows that the mode i stress intensity factor at the point of the mobile crack decreases as it tends to approach the immovable defect. the interaction effect disappears when these defects tend to coalesce. such an arrangement of these two cracks are dangerous as when they are parallel and opposite. in this case these two defects behave one only one. the repair by composite patch of this plate containing such cracks results in a marked improvement in its durability by a strong reduction of this breaking criterion as shown in fig. 9. in this part of the work, the stress intensity factor in heads of the first crack is analyzed as a function of the two distances (horizontal and vertical denoted dx and dy respectively) separating it to a second crack. the results thus obtained are illustrated in fig. 10a. we note that a strong reduction of these two geometric parameters leads to a sudden increase of this criterion of rupture. such a localization favors their instability by intensifying the mechanical energy in crack tips. this strong interaction of the energies leads to the coalescence of these two defects and therefore to the sudden rupture of the plate. the repair of such a structure results in a clear decrease in the stress intensity factor (fig. 10b). the shear stresses in the adhesive are relatively low as shown in fig. 11. this figure clearly illustrates that the transfer of stress resulting from the interaction effect between two cracks, from the plate to the patch, is done easy way. the transfer 0,00 0,01 0,02 0,03 0,04 0,05 0 20 40 60 80 100 120 140 d = 1mm = 150mpa a1 (m) k i (m p a .( m )1 /2 ) a2=10mm a2=20mm a2=30mm a2=40mm a2=50mm 0,00 0,01 0,02 0,03 0,04 0,05 3 4 5 6 7 8 9 10 11 12 13 14 d = 1mm = 150mpa a2=10mm a2=20mm a2=30mm a2=40mm a2=50mm a1 (m) k i (m p a .( m )1 /2 ) n. c. m. ibrahim et alii, frattura ed integrità strutturale, 46 (2018) 140-149; doi: 10.3221/igf-esis.46.14 147 is explained by low values of the greatest tangential stresses in the adhesive layer. even the strongest interactions between the two cracks, defined here by d = 1 mm (fig. 1), induce relatively high shear stresses in the glue. it is clear that the refraction of such cracks (interaction of two cracks), initially highly unstable, (fic in mode i) high disadvantaged their coalescence and ensures their stability. the stresses generated for such a location in the adhesive are relatively and do not present any risk of damage to the adhesive by cohesive or adhesive rupture. figure 9: variation of the stress intensity factor in heads of the first crack as a function of the size of two repaired and unrepaired cracks. (a) (b) figure 10: variation of the stress intensity factor in the heads of the first crack as a function of the distances ‘’dx’’ and ‘’dy’’ separating it from the second crack of a structure: (a) unrepaired, (b) repaired the stress relaxation in the near vicinity of interacting cracking fronts (low mode i fic) and tangential stresses in the adhesive layer promotes performance, reliability and durability of the repair. conclusion he results obtained in this work lead to the conclusion that: -the stress intensity factor depends not only on the stress applied, on the size of the cracks, initiated along the transverse axis of the plate but also on their interdistance. it is the horizontal distances "dx" and vertical "dy" that t 0,00 0,01 0,02 0,03 0,04 0,05 30 35 40 45 50 55 60 65 70 75 80 85 k i (m p a .( m )1 /2 ) dx (m) dy=1mm dy=5mm dy=10mm dy=20mm dy=30mm 0,00 0,01 0,02 0,03 0,04 0,05 7,5 8,0 8,5 9,0 9,5 10,0 10,5 11,0 11,5 12,0 12,5 13,0 k i (m p a .( m )1 /2 ) dx (m) dy=1mm dy=5mm dy=10mm dy=20mm dy=30mm n. c. m. ibrahim et alii, frattura ed integrità strutturale, 46 (2018) 140-149; doi: 10.3221/igf-esis.46.14 148 separate these cracks which determine the value of the stress intensity factor. simultaneous reduction of these two geometric parameters leads to a strong increase in the stress intensity factor reaching the critical breaking threshold 0,0 0,2 0,4 0,6 0,8 1,0 -10 -5 0 5 10   ( m p a ) normalized distance dx=1mm dx=3mm dx=5mm dx=7mm dx=10mm dx=20mm dx=30mm dx=40mm dx=50mm figure 11: variation of shear stresses in the adhesive. -the repair with composite patch of such a structure leads to a very great reduction in the stress intensity factor. the cracks initially highly unstable, characterized by a steep slope at the curve ki = f (d), see their kinetics of propagation greatly delayed. these defects do not have enough energy to propagate. -the stress intensity factor resulting from a crack, distant from "dx" of another crack, increases with the mutual increase of these cracks. it reaches its maximum value when, during their growth, these two defects propagate towards each other. to the repair of such cracks results in a highly reduced stress intensity factor. this leads to a slowing down of the coalescence phenomenon of these two cracks; -the stress relaxation in the near vicinity of interacting cracking fronts (low mode i fic) and tangential stresses in the adhesive layer promotes performance, reliability and durability of the repair. references [1] baker, a.a. (1984). repair of cracked or defective metallic aircraft components with advanced fibre composites an overview of australian work. compos struct. pp. 2153 –2581. doi: 10.1016/0263-8223(84)90025-4. [2] baker, a.a. and chester, r.j. (1993). recent advances in bonded composite repair technology for metallic aircraft components. in: chandra t, dhingra ak, editors. proceedings of the international conference on advanced composite materials, pp. 45–49. [3] mitchell, r.a., woolley, r.m. and chwirut, d.j. (1975). analysis of composite reinforced cut-outs and cracks, aiaaj.,13, pp. 744–749. doi: 10.2514/3.60431. [4] jones, r. and callinan, r.j. (1979). finite element analysis of patched cracks, j. struct.mech. 7, pp. 107-130. doi: 10.1080/03601217908905315. [5] rose, l. r. f. (1981). an application of inclusion analogy for bonded reinforcement. int. j. of solids struct., 17827-838. doi: 10.1016/0020-7683(81)90091-3. [6] rose, l. r. f. (1982). a cracked plate repaired by bonded reinforcements, int. j. frac., 18, pp. 135-144. doi:10.1007/bf00019638. [7] rose, l. r. f. (1987). crack reinforcement by distributed spring. j. mech. phys. solid.,3, pp. 5383-5340. doi: 10.1016/0022-5096(87)90044-5. [8] young. a, cartwright, d.j. and rooke, d. p. (1985). model studies of repair patches. proc of int. conf. on fatigue, corrosion, cracking, fracture mechanics and failure analysis, salt lake city, 339-346. n. c. m. ibrahim et alii, frattura ed integrità strutturale, 46 (2018) 140-149; doi: 10.3221/igf-esis.46.14 149 [9] young. a, rooke, d. p. and cartwright, d.j. (1989). numerical study of balanced patch repairs to cracked sheet. aero. j., pp. 327334. doi: 10.1017/s0001924000017255. [10] rooke, d. p., young, a. and courtney, t.j. (1992). effect of repair patches on fatigue lifetimes. durability of metal aircraft structures, ed: atluri, s. n., harris, c.e., hoggard, a., miller, n/ and sampath, s. g., atlanta technology publications, pp. 132-145. [11] ramesh c., murthy, m. v. v., ramamurthy, t. s. and rao, a. k. (1985). analytical estimation of stress intensity factors in patched cracked plates. eng. frac. mech., 21, pp. 479-494. doi: 10.1016/s0013-7944(85)80041-2. [12] liu, t. and fan, w. (1994). analysis for an adhesively bonded finite strip repair to a cracked plate. eng. frac. mech., 47, pp. 629-637. doi: 10.1016/0013-7944(94)90154-6. [13] arendt, c. and sun, c. t. (1994). bending effects of unsymmetric adhesively bonded composite repairs on cracked aluminium panels. nasa cp 3274, pp. 33-48. [14] fekirini, h., bouiadjra, b. b., belhouari, m., boutabout, b., serier, b. (2008). numerical analysis of the performances of bonded composite repair with two adhesive bands in aircraft structures, composite structures, pp. 8284-8289. doi: 10.1016/j.compstruct.2006.12.004. [15] belhouari, b. b. and serier, b., (2004). comparison of double and single bonded repairs to symmetric composite structures: a numerical analysis, composite structures, 65, pp. 47–53. doi: 10.1016/j.compstruct.2003.10.005. [16] bachir b. b., belhouari, m. and serier, b. (2002). computation of the stress intensity factors for repaired cracks with bonded composite patch in mode i and mixed mode. composite structures, 56, pp. 401-406. doi: 10.1016/s0263-8223(02)00023-5. [17] ouinas, d., bouiadjra, b.b., serier, b. and said bekkouche, m. (2007). the effects of disbands on the stress intensity factor of aluminium panels repaired using composite materials. compos struct. 78, pp. 278–84. doi: 10.1016/j.commatsci.2006.09.006. [18] ouinas, d., hebbar, a. and vina olay j. (2006). fracture mechanics modelling of cracked aluminium panel repaired with bonded composite circular patch. journal of applied science 9, pp. 2088-2095. doi: 10.3923/jas.2006.2088.2095 [19] ouinas d., ramdane, z. and sahnoun m. (2011). effet de la forme géométrique du patch sur la réduction du fic en mode i. journées d’etudes nationales de mécanique, jenm’2011 ouargla, algérie. [20] mhamdia, r., bouiadjra, b.b., serier, b. and belhouari, m. (2012). the patch shape effects on the performances of bonded composite repair in aircraft structures. proceedings of the international conference on industrial engineering and operations management istanbul, turkey. << /ascii85encodepages false /allowtransparency false /autopositionepsfiles true /autorotatepages /none /binding /left /calgrayprofile (dot gain 20%) /calrgbprofile (srgb iec61966-2.1) /calcmykprofile (u.s. web coated \050swop\051 v2) /srgbprofile (srgb iec61966-2.1) /cannotembedfontpolicy /error /compatibilitylevel 1.4 /compressobjects /tags /compresspages true /convertimagestoindexed true /passthroughjpegimages true /createjobticket false /defaultrenderingintent /default /detectblends true /detectcurves 0.0000 /colorconversionstrategy /cmyk /dothumbnails false /embedallfonts true /embedopentype false /parseiccprofilesincomments true /embedjoboptions true /dscreportinglevel 0 /emitdscwarnings false /endpage -1 /imagememory 1048576 /lockdistillerparams false /maxsubsetpct 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/hrv (za stvaranje adobe pdf dokumenata najpogodnijih za visokokvalitetni ispis prije tiskanja koristite ove postavke. stvoreni pdf dokumenti mogu se otvoriti acrobat i adobe reader 5.0 i kasnijim verzijama.) /hun 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can be opened with acrobat and adobe reader 5.0 and later.) >> /namespace [ (adobe) (common) (1.0) ] /othernamespaces [ << /asreaderspreads false /cropimagestoframes true /errorcontrol /warnandcontinue /flattenerignorespreadoverrides false /includeguidesgrids false /includenonprinting false /includeslug false /namespace [ (adobe) (indesign) (4.0) ] /omitplacedbitmaps false /omitplacedeps false /omitplacedpdf false /simulateoverprint /legacy >> << /addbleedmarks false /addcolorbars false /addcropmarks false /addpageinfo false /addregmarks false /convertcolors /converttocmyk /destinationprofilename () /destinationprofileselector /documentcmyk /downsample16bitimages true /flattenerpreset << /presetselector /mediumresolution >> /formelements false /generatestructure false /includebookmarks false /includehyperlinks false /includeinteractive false /includelayers false /includeprofiles false /multimediahandling /useobjectsettings /namespace [ (adobe) (creativesuite) (2.0) ] /pdfxoutputintentprofileselector /documentcmyk /preserveediting true /untaggedcmykhandling /leaveuntagged /untaggedrgbhandling /usedocumentprofile /usedocumentbleed false >> ] >> setdistillerparams << /hwresolution [2400 2400] /pagesize [612.000 792.000] >> setpagedevice microsoft word numero_52_art_18_2751 n. hebbar et alii, frattura ed integrità strutturale, 52 (2020) 230-246; doi: 10.3221/igf-esis.52.18 230 numerical modeling of bending, buckling, and vibration of functionally graded beams by using a higher-order shear deformation theory nabil hebbar department of civil engineering and architecture, university of abdelhamid ibn-badis, mostaganem, algeria. nabil_al@hotmail.fr, https://orcid.org/0000-0001-7648-9875 imène hebbar department of mechanical engineering, university of sidi bel abbes, sidi bel abbes, algeria. imhebbar@gmail.com djamel ouinas department of mechanical engineering, university of abdelhamid ibn-badis, mostaganem, algeria. douinas@netcourrier.com mohamed bourada department of civil engineering, university of sidi bel abbes, sidi bel abbes, algeria. med_bourada@yahoo.fr abstract. the objective of this work is to analyze the behavior beams functionally graded, simply supported, under different conditions such as bending, buckling, and vibration and this by use shear deformation theories a two-dimensional (2d) and quasi-three-dimensional (quasi-3d). the proposed theories take into account a new field of displacement which includes indeterminate whole terms and contains fewer unknowns, compared to other theories of the literature; by taking account of the effects of the transverse shears and the thickness stretching. in this theory, the distribution of the transverse shear stress is hyperbolic and satisfies the boundary conditions on the upper and lower surfaces of the beam without the need for a shear correction factor. in this type of beam the properties of the materials vary according to a distribution of the volume fraction, the hamilton principle is used to calculate the equations of motion, and in order to check the accuracy of the theory used comparison is made with the studies existing in the literature. keywords. functionally graded beams; bending; buckling; vibration; hyperbolic theory of shear deformation. citation: hebbar, n., hebbar, i., ouinas, d., bourada, m., numerical modeling of bending, buckling, and vibration of functionally graded beams by using a higher-order shear deformation theory, frattura ed integrità strutturale, 52 (2020) 230-246. received: 12.02.2020 accepted: 16.02.2020 published: 01.04.2020 copyright: © 2020 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. https://youtu.be/urlpfedge4m n. hebbar et alii, frattura ed integrità strutturale, 52 (2020) 230-246; doi: 10.3221/igf-esis.52.18 231 introduction n recent decades, a new class of composite materials has emerged from a group of researchers at the national aerospace laboratory (sta) in japan, where they have developed a functionally graded materials with characteristics to withstand with thermal and mechanical stresses[1], since the classic materials, despite their advantages of high rigidity, high and low mechanical resistance, do not always meet the required requirements, these functionally graded materials have a microstructure that varies gradually and constantly through the thickness in order to optimize their performances whether mechanical or thermal or both at the same time. fig.1 shows the microstructure of functionally graded materials [2]. figure 1: the microstructure of functionally graded materials. today, structures in advanced composite materials attract several researchers who are immersed in this vast field of research where they have developed several models in order to study the behavior of beams, plates and shells in different applications such as koizumi [3-5], karama et al.[6] and aydogdu et al. [7] where they used a first-order parabolic and the exponential deformation theory to study the free vibration behavior of a functionally graded and simply supported material beam. bernoulli [8] and euler [9] have developed a classical theory (cbt) for the analysis of isotropic and anisotropic beams but unfortunately, this theory does not take into account the effect of transverse shear deformation. in order to overcome these limitations, several researchers have introduced the theory of shear deformation which takes into account the effect of transverse shear for the first-order theory and higher-order (hsdt). timoshenko [10] introduced in his first-order theory the effect of shear deformation but always remains that he must add a correction factor and this is due to the shear stress that is constant across the thickness. these difficulties are eliminated by the introduction of the theory of higher-order shear deformation by researchers reddy [11] and touratier [12] they proposed work in bending, buckling and free vibration. matsunaga [13] investigated the buckling and free vibration of fgm plates using a twodimensional deformation theory. vidal et al.[14] carried out an evaluation of the sine model for nonlinear analysis of composite beams. şimşek [15] used the different higher-order theories to study the dynamic responses of beams in functionally graded materials. talha et al.[16] studied the static and dynamic response of fgm plates using the theory of higher-order shear strain. hosseini-hashemi et al. [17] investigated the free vibration of rectangular-type fgm plates using the first-order shear deformation theory. hosseini-hashemi et al. [18] proposed a new analytical approach to study the free vibration of rectangular reissner-mindlin plates. xiang et al. [19] provided a theory of n-shear deformation for the purpose of studying the free vibration of sandwich plates. thai and vo [20] have worked on the analysis of the buckling and vibration of beams in functionally graded materials by using higher-order shear deformation theory for beams. reddy et al. [21] proposed a theory of torque stress depended on the microstructure of functionally graded beams. eltaher et al. [22] determined the position of the neutral axis and its effect on the eigenfrequencies of functionally graded macros/nano-beams. li and batra [23] proposed a relational analysis between the critical buckling loads of a timoshenko theory of beams and euler-bernoulli for different boundary conditions. nguyen et al. [24] used the theory of first-order shear deformation to analyze the vibration of beams in graded functional materials to obtain an analytical solution i n. hebbar et alii, frattura ed integrità strutturale, 52 (2020) 230-246; doi: 10.3221/igf-esis.52.18 232 according to navier's solution. hadji et al. [25] have developed a new model of first-order and higher-order shear deformation to analyze the vibration of functionally graded beams. yaghoobi et al. [26] developed an analytical study on the analysis of nonlinear free vibrations after beam buckling in functionally graded materials resting on a non-linear elastic foundation under thermo mechanical loading using vim. rahmani and pedram [27] they analyzed by modeling the effect of size on the vibration of functionally graded nano-beams based on the nonlocal timoshenko beam theory. alkhateeb and zenkour [28] presented a refined four-variable theory for the analysis of flexion of resting plates on elastic foundations in hygrothermal environments. vo et al. [29, 30] developed a finite element model based on a refined theory of shear deformation in order to study the static and dynamic behavior of beams under different boundary conditions. meradjah et al. [31] proposed a new theory of shear deformation for the study of beams in functionally graded materials with a consideration of the stretching effect. vo et al. [32] developed a quasi-3d theory for the study of buckling and vibration of sandwich beams. zemri, a et al. [33] proposed an unrefined theory of theory for static analysis, buckling and free vibration of beams in nanometrically functionally graded materials. al-basyouni et al. [34] analyzed flexion and vibration as a function of the size of functionally graded micro-beams based on the modified theory of torque stress and neutral surface position. ebrahimi and dashti [35] explored the effects of linear and non-linear distributions of temperature on the vibration of nano-beams in functionally graded materials. kar and panda [36] studied the vibration and nonlinear shear bending of a spherical shaped, shell panel is functionally graded materials. bourada et al. [37] presented a new simple and refined higher-order trigonometric theory for the analysis of free bending and vibration of beams in functionally graded materials taking into account the effect of stretching the thickness. celebi et al. [38] proposed a unified method for studying the constraints in a sphere of functionally graded materials with properties that vary exponentially. boukhari et al. [39] proposed a thermal study on wave propagation in fgm functionally graded materials plates based on the neutral surface position. ebrahimi and barati [40] have studied the influence of the environment on the damping vibration of nano-beams in functionally graded materials. ahouel et al. [41] investigated the size-dependent mechanical behavior of trigonometrically shear functional and trigonometric shear nano-beams, including the concept of the neutral surface position. shafiei et al. [42] studied the nonlinear vibrations of conical micro-beams in functionally graded imperfect and porous materials based on modified torque constraints and euler-bernoulli theories. raminnea et al. [43] used the non-linear reddy theory of higher-order for the study of the vibration and instability of embedded pipes carrying a fluid as a function of temperature. ghumare and sayyad [44] developed a new theory for the study of fifth-order shear deformation and normal deformation for the analysis of flexion and free vibration of fgm beams. benadouda et al. [45] proposed a theory of shear deformation for the study of wave propagation in beams in functionally graded materials with porosities. bellifa et al. [46] used a theory of simple shear deformation as well as the concept of the position of the neutral surface for the analysis of flexion and free vibration of plates made of functionally graded materials. akbaş [47, 48] studied the vibratory response of viscoelastic beams and wave propagation in a beam made of functionally graded materials in thermal environments. bellifa et al. [49] used the theory of non-local zero-order shear strain for the non-linear post-buckling of nano-beams. li et al. [50] studied the effect of thickness on the mechanical behavior of nano-beams. sayyad and ghugal [51] developed a theory of unified shear deformation for the study of the bending of beams and plates in functionally graded materials. aldousari [52] studied the bending analysis of different material distributions in a functionally graded beam. bouafia et al. [53] developed a non-local quasi-3d theory to study the behavior of the free bending of nano-beams in functionally graded materials. zidi et al. [54] have proposed a new simple two-unknown theory for studying the hyperbolic shear deformation of beams in functionally graded materials. fouda et al. [55] proposed a porosity model to study shear deformation in the static case, buckling and free vibration of porous beams in functionally graded materials based on the euler bernoulli method and finite elements. a study on the free vibration of beams in functionally graded materials is presented by zaoui et al. [56] where they used a theory of higher-order shear deformation. mouffoki et al. [57] studied the analysis of the free vibration of nano-beams under a hygro-thermal loading using a new theory of trigonometric beams with two unknowns. recently, sayyad and ghugal [58] studied the bending, buckling and free vibration responses of the hyperbolic shear deformation of fgm beams. kaci. a. et al. [59] have studied the post-buckling analysis of shear-deformable composite beams using a new, simple two-unknown theory. dragan et al. [60] developed a new function for the purpose of analyzing plate bending in functionally graded materials. the effect of shear deformation of structures in functionally graded materials requires more investigation. in our study, a theory of 2d and quasi-3d three-variable shear deformation for the analysis of beams in functionally graded materials is presented. the motion equations are derived from the hamilton principle. navier's solutions are also presented. displacements, stresses, critical buckling loads and frequencies obtained using the current beam theory of functionally graded materials in which the properties of materials vary with the power-law (p-fgm) are compared with other results in order to demonstrate the effectiveness of the proposed theory. numerical examples will be presented for the study of the shear deformation of beams in functionally graded materials in the case of bending, buckling and vibration. n. hebbar et alii, frattura ed integrità strutturale, 52 (2020) 230-246; doi: 10.3221/igf-esis.52.18 233 -0.5 -0.4 -0.3 -0.2 -0.1 0.0 0.1 0.2 0.3 0.4 0.5 -0.1 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 p=0.1 p=0.5 p=1 p=2 p=5 p=10 vc(z) z/ h mathematical modeling formulation of the problem onsider a beam of functionally graded materials of uniform length (a) width (b) and thickness (h), it is represented in the fig.2. the cartesian coordinate system x, y, z at z = 0 the plane x, y coincides with the median surface of the beam. figure 2: the geometry of functionally graded beam. the characteristics of the material can change according to the thickness and the function given in the following equations [24, 57, 61, 62, 63]:   ( ) (1 / 2) ( / ) pm c me z e e e z h    (1)   ( ) (1/ 2) ( / ) pm c mz z h       (2)   ( ) (1/ 2) ( / ) pm c mg z g g g z h    (3) where: ec and em present the property of the upper and lower faces of the beam respectively and p is the exponent which specifies the distribution profile of the material in the thickness. in this work, young's modulus e and the shear modulus g, change according to the problem case according to eqn. (1), and the poisson's ratio  is considered constant. figure 3: variation of the volume fraction vc across the thickness of a beam in fg for different values of the index of the power-law. c n. hebbar et alii, frattura ed integrità strutturale, 52 (2020) 230-246; doi: 10.3221/igf-esis.52.18 234 basic assumptions he hypotheses of the present theory are as follows; the origin of the cartesian coordinate system is taken on the neutral axis of the beam in functionally graded materials; the displacements are small in comparison with the thickness of the beam thus the deformations involved are infinitesimal; displacements (u) in the x direction consist of extension, bending and shear components. kinematic and constitutive equation n the basis of the assumptions made in the previous section, the displacement field can be presented as follows: 0 0 ( , ) ( , , ) ( , ) ( ) ( , ) ,a w x t u x z t u x t z k f z x t dx x        (4a) ( , , ) 0,x z t  (4b)  0( , , ) ( , ) ( , ),w x z t w x t g z x t  (4c) where: u0 is the axial displacement in the median plane, and t represents the time. in this study, f (z) represents the shape function determining the distribution of transverse shear deformation as follows: 22 ( ) ( ) , ( ) 3 4 z z f zh f z g z h z           (5) the deformations associated with displacements in eqn. (4) are: 0 ( ) , x x x xzk f z     0( ) xzxz f z z      (6) where: 0 0 x u x     , 2 0 2x w k x     , x ak a  , 0 ( , )xz ak x t dx   (7) and 0 0 ( )'( ) , , '( ) z zz g z g z g z z          (8) the navier method is used to solve the integrals defined in the equations [64]: adx x      (9) where the coefficient a' is considered according to the type of solution used, in this case via the navier method. consequently, a′ and ka are expressed as follows: 2 2 1 a , ak     (10) the beam in functionally graded materials obeys hooke's law, so the behavioral relations can be given as follows: t o n. hebbar et alii, frattura ed integrità strutturale, 52 (2020) 230-246; doi: 10.3221/igf-esis.52.18 235 11 13 13 33 55 ( ) ( ) 0 ( ) ( ) 0 0 0 ( ) x x z z x z x z q z q z q z q z q z                              (11) with (𝜎x, 𝜎z, 𝜏xz) and ( x , z , xz ) are respectively the stresses and the deformations. the expressions ijq depends on the normal deformation z : in the case of two-dimensional shear deformation (2d) the normal deformation z = 0, therefore:         11 55 and 2(1 ) e z q z e z q z     (12) in the case of quasi-three-dimensional shear deformation (quasi-3d) the normal deformation z  0, therefore:               11 33 13 11 552 , and 2(1 )1 e z e z q z q z q z q z q z       (13) equation of motion he hamilton principle is used in this study to derive the equations of motion; it can be given in the following analytic form [65]:   0 0 t u v k dt    (14) where: δu is the variation of the strain energy,δv is the variation of the kinetic energy and δk is the variation of the potential energy. the variation of the deformation energy of the beam can be defined as follows: /2 /2 0 /2 /2 ( ) l b h x x xz xz b h u dzdydx           (15) 2 0 0 2 0 ( ) l x z b s d u d w d u n m m m q dx dx dxdx           (16) with: nx, mb, ms and q are the resultants of the stress in terms of axial force, bending moment, higher-order moment and shear force, respectively:      /2 /2 , , 1, , h x b s x h n m m z f z dz    (17a) t n. hebbar et alii, frattura ed integrità strutturale, 52 (2020) 230-246; doi: 10.3221/igf-esis.52.18 236   2 0 0 11 11 112 /2 2 0 0 11 11 112 /2 2 0 0 11 11 112 1 s x h s b x h s s s s du d w d a b b dx dxdx n du d w d m z dz b d d dx dxdx m f z du d w d b d h dx dxdx                                         (17b)     /2 /2 /2 /2 ' , h h z z xz xz h h n g z dz q b g z dz       (17c) the variation of the kinetic energy is expressed by: 0 l v q w dx   (18) furthermore, the potential energy of the distributed load is expressed by:   /2 0 /2 ( ) l h h k u u w w z dzdx            (19) substitute the expressions displacement by deformation as well as stress by deformation which are respectively defined by the eqns. (16), (18) and (19) in eqn. (14) and by integrating by parts while putting the coefficients u, v, w and equal to zero. as a result, the governing equations obtained are given as follows: 0 0 0 0 1 1 : xn wu i u i j x x x              (20a) 2 2 2 0 0 0 0 0 0 0 1 2 22 2 2 : b m u u w w q n i w i j i x xx x x                              (20b) 2 0 1 0 2 2 : a xzs a z a a qm w k n k j u k j k x x x                 (20c) with:     /2 /2 11 11 11 11 /2 /2 /2 /2 2 11 11 11 11 /2 /2 /2 /2 2 11 11 11 11 /2 /2 /2 2 55 55 /2 ( ) , ( )z , ( ) , ( ) ( ) , ( ) ( ) , ( ) ( ) , ( ) ( ) h h h h h h s h h h h s s h h h s h a b q z dz b b q z dz d b q z z dz b b q z f z dz d b q z z f z dz h b q z f z dz a b q z g z dz                      (21) n. hebbar et alii, frattura ed integrità strutturale, 52 (2020) 230-246; doi: 10.3221/igf-esis.52.18 237 where: (z) is the density and i0, i1, j1, i2, j2 and k2 are the coefficients of inertia as defined below: /2 /2 /2 0 1 1 /2 /2 /2 /2 /2 /2 2 2 2 2 2 /2 /2 /2 ( ) , ( ) , ( ) ( ) , ( ) , ( ) ( ) , ( ) ( ) h h h h h h h h h h h h i b z dz i b z z dz j b f z z dz i b z z dz j b zf z z dz k b f z z dz                         (22) analytical solution he motion equations admit navier's solutions for simply supported beams. the variables u0, w0 and ϕcan be written assuming the following variations: 0 0 1,3,5 cos sin cos i t m i t m m i t m u xeu w w xe xe                             (23) with:   i = 1 and α = mπ/l the transverse load q is also expressed by the double series of fourier sine as follows: 0 1,3,5 4 sin m q q x m       (24) substitute the expressions u0, w0 and ϕ of eqn. (23) in the equation of motion (20). the analytical solution is given in the following form: 11 12 13 11 12 13 2 0 12 22 23 12 22 23 13 23 33 13 23 33 0 4 0 m m m s s s m m m u q s s s m m m w m s s s m m m                                                   (25) in which: s11= a11 α2, s12= -b11 α3, s13= ak a'd11 α2, s22= ak bs11 α2, s23= ak a'ds11 α2, s33= 2 ak a'2hs11 α2 + 2 ak a' as55 (26) m11 = i0, m12 =i1 α, m13 = ak a' j1 α2, m22 = i2 α2 + i0, m23 = j2 α2, m33 = 2 ak a'2k2 α2 numerical results and discussion n this section, various numerical examples are presented to verify the accuracy of the theory presented for the purpose of predicting bending, buckling, and vibration responses of a simply supported fg beam. the properties of the materials change through the thickness of the beam according to a power-law. the lower surface of the beam is rich in aluminum and the upper surface of the beam is rich in alumina. for convenience, the following dimensionless form is used: 3 3 22 0 4 4 3 0 00 0 100 100 12 (0, 0, ) , ( , 0, 0) , ( , 0, ) , (0, 0, 0) , , 2 2 2 2            m m x x mx xz cr m m w e h w e h h h p n ah l l h l u w n q l q l h eq l q l e h (27) t i n. hebbar et alii, frattura ed integrità strutturale, 52 (2020) 230-246; doi: 10.3221/igf-esis.52.18 238 0.0 0.2 0.4 0.6 0.8 1.0 0 2 4 6 8 10 12 14 t ra ns ve rs e di sp la ce m en t (w ) x/l p=0 p=1 p=2 p=5 p=10 material properties young’s modulus (gpa) poisson’s ratio mass density (kg/m3) aluminum (al) 70 0.3 2702 alumina(al2o3) 380 3960 table 1: materials properties used in the fg beams. bending analysis ab. 2 presents a comparison of dimensionless displacements and stresses of al/al2o3 functionally graded materials beams, simply supported and subjected to uniformly distributed loads with different exponent values of the power-law p and for ratios. l/h = 5 and 20. it can be seen through the results obtained that displacements and stresses increase as the power-law index increases and takes a maximum value when p takes the value of one and a minimum value in the case where p takes the value of zero, this interpretation is due to the ductility of the beam since the more the material index is increasing, the more the beam becomes more ductile. the results obtained are compared with other results from the literature such as hsdt of reddy [11], hsdt of hadji et al. [25], and hsdt of a.s. sayyad and y.m. ghugal [58]. it can also be noted that the two-dimensional (2d) shear deformation theory is in good agreement with the other theories of shear deformation, whereas the results obtained by the theory of quasi-shear deformation threedimensional (quasi-3d) are slightly larger compared to that of the literature and this is due to the effect of normal transversal deformation which is not neglected (εz 0) compared to other theories where the effect normal transversal deformation is neglected (εz = 0). fig. 4 shows the variation of the transverse displacement across the length of the beam made of al/al2o3 functionally graded materials, subjected to a uniformly distributed load. it is noted that the transverse displacement increases with the increase of the index of the power-law p and reaches a maximum value. the traced curve takes a parabolic form. figure 4: variation of dimensionless transverse displacement (w) along the length of the beam subjected to uniformly distributed load with a ratio (l/h=5). fig. 5 shows the variation of the axial displacement across the length of the beam in al/al2o3 functionally graded materials, subjected to a uniformly distributed load, for different values of the index of the power-law p. it can be seen that the axial displacement is maximum when the index of the power-law takes the value of one and it is minimal in the case where the index of the power-law takes the value of zero. fig. 6 shows the variation of the axial displacement of a beam made of al/al2o3 functionally graded materials, subjected to a uniformly distributed load, for different values of the power-law index p which takes the values 0, 1, 2, 5 and 10 with a ratio of (l/h = 5). it can be seen through these curves that the axial displacement is influenced by the index of the t n. hebbar et alii, frattura ed integrità strutturale, 52 (2020) 230-246; doi: 10.3221/igf-esis.52.18 239 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 -4 -3 -2 -1 0 1 2 3 4 a xi al d is p la ce m en t (u ) x/l p=0 p=1 p=2 p=5 p=10 power-law p since the dimensionless displacement increases as the index of the power-law increases and precisely in the two upper and lower parts of the beam. p theory l/h=5 l/h=20 u w x xz u w x xz 0 present (εz0) 0.8569 2.9063 3.8071 0.7325 0.2098 2.6372 15.0143 0.7455 present (εz=0) 0.9397 3.1654 3.8019 0.7332 0.2306 2.8962 15.0129 0.7437 hadji et al. [25] 0.9400 3.1654 3.8019 0.7330 0.2305 2.8962 15.0129 0.7437 a.s. sayyad and y.m.ghugal [58] 0.9274 3.1224 3.7529 0.7259 0.2275 2.8585 14.8179 0.7259 reddy [11] 0.9397 3.1654 3.8019 0.7330 0.2306 2.8962 15.0129 0.7437 1 present (εz0) 2.0993 5.7397 5.8924 0.7325 0.5174 5.2852 23.2076 0.7455 present (εz=0) 2.3038 6.2594 5.8835 0.7330 0.5685 5.8049 23.2051 0.7437 hadji et al. [25] 2.3038 6.2594 5.8835 0.7330 0.5685 5.8049 23.2051 0.7437 a.s. sayyad and y.m.ghugal [58] 2.2735 6.2586 5.8077 0.7187 0.5611 5.7292 22.9038 0.7259 reddy [11] 2.3036 6.2594 5.8836 0.7330 0.5686 5.5685 23.2051 0.7432 2 present (εz0) 2.8363 7.4016 6.8940 0.6699 0.6999 6.7760 27.1021 0.6828 present (εz=0) 3.1129 8.0677 6.8824 0.6704 0.7366 7.2558 27.0989 0.6812 hadji et al. [25] 3.1129 8.0677 6.8824 0.6704 0.7366 7.2558 27.0989 0.6812 a.s. sayyad and y.m.ghugal [58] 3.0720 7.9627 6.7938 0.6573 0.7591 7.3450 26.7470 0.6648 reddy [11] 3.1127 8.0677 6.8824 0.6704 0.7691 7.4421 27.0989 0.6812 5 present (εz0) 3.3815 9.0403 8.1272 0.5898 0.8313 8.0.06 31.8173 0.6025 present (εz=0) 3.7100 9.8281 8.1104 0.5904 0.9134 8.8182 32.8127 0.6013 hadji et al. [25] 3.7100 9.8281 8.1104 0.5904 0.9134 8.8182 32.8127 0.6013 a.s. sayyad and y.m.ghugal [58] 3.6612 9.6986 8.0059 0.5786 0.9014 8.7031 31.3997 0.5863 reddy [11] 3.7097 9.8281 8.1104 0.5904 0.9134 8.8182 31.8127 0.6013 10 present (εz0) 3.5434 10.0733 9.7310 0.6459 0.8679 8.8259 38.1434 0.6599 present (εz=0) 3.7462 10.9381 9.7123 0.6467 0.9536 9.6905 38.1387 0.6600 hadji et al. [25] 3.8863 10.9381 9.9878 0.7064 0.9262 9.5513 38.1382 0.6586 a.s. sayyad and y.m.ghugal [58] 3.8351 10.7949 9.5870 0.6412 0.9412 9.5641 37.6432 0.6426 reddy [11] 3.8859 10.9381 9.7119 0.6465 0.9536 9.6905 38.1382 0.6586 table 2: comparison of the dimensionless displacements and stress of the fg beams subjected to uniformly distributed load with various power-law exponent values. figure 5: variation of dimensionless axial displacement (u) along the length of the beam subjected to uniformly distributed load with a ratio (l/h=5). n. hebbar et alii, frattura ed integrità strutturale, 52 (2020) 230-246; doi: 10.3221/igf-esis.52.18 240 figure 6: variation of the dimensionless axial displacement (u) across the thickness of an fg beam subjected to uniformly distributed load with a ratio (l/h = 5). the fig. 7 illustrates the variation of the axial stress of a beam made of al/al2o3 functionally graded materials, subjected to a uniformly distributed load, for different values of the index of the power-law p which takes the values 0, 1, 2, 5 and 10 with a ratio of (l/h = 5). it can be deduced that the upper part is towed and the lower part is compressed and between these two parts the curve takes a parabolic form. figure 7: variation of the dimensionless axial stress across the thickness of the fg beam subjected to uniformly distributed load with a ratio (l/h =5). the fig. 8 shows the variation of the transverse shear stress of a beam in al/al2o3 functionally graded materials, subjected to a uniformly distributed load for different values of the index of the power-law p which takes the values of 0, 1, 2, 5 and 10 with a ratio of (l/h = 5). it is observed that the plot of the transverse shear stress does not take a parabolic form as in the case of homogeneous beams of metal and ceramic, it can also be noted that the neutral axis is eccentric towards the upper part. -0.50 -0.25 0.00 0.25 0.50 -4 -2 0 2 4 axial displacement (u)  t h ic kn es s co o rd in at e( z/ h ) p=0  p=1  p=2  p=5  p=10 n. hebbar et alii, frattura ed integrità strutturale, 52 (2020) 230-246; doi: 10.3221/igf-esis.52.18 241 -0.50 -0.25 0.00 0.25 0.50 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 transverse shear stress ( xz ) t h ic kn es s co o rd in at e (z /h ) p=0 p=1 p=2 p=5 p=10 figure 8: variation of the dimensionless transverse shear stress through the thickness of the fg beam subjected to uniformly distributed load with a ratio (l/h = 5). buckling analysis n this part we have studied the comparison of dimensionless critical buckling loads ( ncr ) for al/al2o3 type functionally graded beams, simply supported and subjected to axial forces (n0) with respect to different values of the exponent of the law of power p for the ratios l/h= 5 and 10. it is observed that the critical load of dimensionless buckling decreases with the growth of the index of the law of power p and it increases with the increase of the ratio (l/h). the results of the critical buckling load obtained in tab. 3 are compared with other results of the literature such as hsdt of reddy [11], fsdt of touratier [12], hsdt of a.s. sayyad and y.m. ghugal [58], fsdt of li and batra [23], and hsdt of vo et al. [30]. it can also be noted that the theory of two-dimensional shear deformation (2d) is in good agreement with the other theories of shear deformation, whereas the results obtained by the theory of quasi-threedimensional shear deformation (quasi-3d) are slightly larger than those of the literature and this is due to the effect of the normal transversal deformation which is not neglected (εz0) compared to other theories where the effect of the normal transverse deformation is neglected (εz=0). l/h theory p 0 1 2 5 10 5 present (εz0) 52.916 26.805 20.783 17.002 15.253 present (εz=0) 48.596 24.584 19.071 15.645 14.052 a.s. sayyad and y.m. ghugal [58] 48.596 24.584 19.071 15.645 14.052 reddy [11] 48.596 24.584 19.071 15.643 14.051 touratier [12] 48.835 24.687 19.245 16.024 14.427 li and batra [23] 48.835 24.687 19.245 16.024 14.427 vo et al. [30] 48.840 24.691 19.160 16.740 14.146 10 present (εz0) 57.262 28.666 22.330 18.714 16.974 present (εz=0) 52.238 26.141 20.366 17.082 15.500 a.s. sayyad and y.m. ghugal [58] 52.238 26.141 20.366 17.082 15.500 reddy [11] 52.238 26.141 20.366 17.082 15.499 touratier [12] 52. 309 26.171 20.416 17.192 15.612 li and batra [23] 52. 309 26.171 20.416 17.194 15.612 vo et al. [30] 52. 308 26.172 20.393 17.111 15.529 table 3: comparison of the dimensionless critical buckling loads ( ncr ) of the fg beams subjected to axial forces in regards to various power-law exponent values. i n. hebbar et alii, frattura ed integrità strutturale, 52 (2020) 230-246; doi: 10.3221/igf-esis.52.18 242 vibration analysis n this third part of our work, we studied the first three fundamental dimensionless frequencies of al/al2o3 type functionally graded materials beams for various exponent values of the power-law p and the ratio (l/h). l/h mode theory p 0 1 2 5 10 5 1 present (εz0) 5.3781 4.1677 3.7867 3.5470 3.4203 present (εz=0) 5.1527 3.9904 3.6264 3.4014 3.2816 a.s. sayyad and y.m.ghugal [58] 5.1527 3.9904 3.6264 3.4014 3.2816 reddy [11] 5.1527 3.9904 3.6264 3.4012 3.2816 touratier [12] 5.1531 3.9906 3.6263 3.3997 3.2811 simsek [15] 5.1527 3.9904 3.6264 3.4012 3.2816 thai and vo [20] 5.1527 3.9904 3.6264 3.4012 3.2816 vo et al. [29] 5.1526 3.9711 3.6050 3.4012 3.2962 vo et al. [30] 5.1527 3.9716 3.5979 3.3742 3.2653 timoshenko [10] 5.1524 3.9902 3.6343 3.4311 3.3134 bernoulli-euler [9] 5.3953 4.1484 3.7793 3.5949 3.4921 2 present (εz0) 17.514 14.531 13.105 11.932 11.380 present (εz=0) 17.881 14.010 12.640 11.544 11.024 a.s. sayyad and y.m.ghugal [58] 17.881 14.010 12.640 11.544 11.024 reddy [11] 17.881 14.010 12.640 11.543 11.025 touratier [12] 17.887 14.014 12.641 11.532 11.021 thai and vo [20] 17.881 14.009 12.640 11.544 11.024 bernoulli-euler [9] 20.618 15.798 14.326 13.587 13.237 3 present (εz0) 35.173 27.930 25.052 22.289 21.061 present (εz=0) 34.209 27.098 24.316 21.720 20.556 a.s. sayyad and y.m.ghugal [58] 34.202 27.098 24.316 21.720 20.556 reddy [11] 34.209 27.098 24.315 21.716 20.556 touratier [12] 34.234 27.115 24.324 21.694 20.558 thai and vo [20] 34.208 27.097 24.315 21.718 20.556 bernoulli-euler [9] 43.348 33.027 29.745 28.085 27.475 20 1 present (εz0) 5.7222 4.4069 4.0202 3.8232 3.7083 present (εz=0) 5.4603 4.2050 3.8361 3.6485 3.5389 a.s. sayyad and y.m.ghugal [58] 5.4603 4.2050 3.8361 3.6485 3.5390 reddy [11] 5.4603 4.2050 3.8361 3.6485 3.5389 touratier [12] 5.4603 4.2051 3.8361 3.6484 3.5389 simsek [15] 5.4603 4.2050 3.8361 3.6485 3.5389 thai and vo [20] 5.4603 4.2050 3.8361 3.6484 3.5389 vo et al. [29] 5.4603 4.2038 3.8349 3.6490 3.5405 vo et al. [30] 5.4603 4.2038 3.8342 3.6466 3.5378 timoshenko [10] 5.4603 4.2050 3.8367 3.6508 3.5415 bernoulli-euler [9] 5.4777 4.2163 3.8472 3.6628 3.5547 2 present (εz0) 22.587 17.420 15.877 15.046 14.574 present (εz=0) 21.573 16.643 15.161 14.374 13.926 a.s. sayyad and y.m.ghugal [58] 21.573 16.643 15.161 14.374 13.926 reddy [11] 21.573 16.634 15.162 14.374 13.926 touratier [12] 21.574 16.635 15.162 14.373 13.925 thai and vo [20] 21.573 16.643 15.161 14.374 13.926 bernoulli-euler [ 9] 21.843 16.810 15.333 14.595 14.167 3 present (εz0) 49.761 38.458 35.003 32.998 31.899 present (εz=0) 47.593 36.768 33.469 31.579 30.095 a.s. sayyad and y.m.ghugal [58] 47.593 36.768 33.469 31.579 30.095 reddy [11] 47.593 36.768 33.469 31.578 30.537 touratier [12] 47.595 36.769 33.468 31.570 30.534 thai and vo [20] 47.593 36.767 33.469 31.5789 30.537 bernoulli-euler [ 9] 48.899 37.617 34.295 32.6357 31.688 table 4: comparison of the first three dimensionless fundamental frequencies of the fg beams in regards to various power-law exponent values. i n. hebbar et alii, frattura ed integrità strutturale, 52 (2020) 230-246; doi: 10.3221/igf-esis.52.18 243 0 2 4 6 8 10 10 20 30 40 50 60 c ri ti ca l b uc kl in g lo ad ( n cr ) power‐ law exponent p l/h=5 l/h=10 0 2 4 6 8 10 3 4 5 6 n at ur al f re qu en ci es ( w ) power‐law  exponent p l/h=5 l/h=10 observe that the fundamental non-dimensional frequencies for the first three modes decrease with the growth of the power-law index and they increase with the increase of the ratio (l/h), this is because of an increase in the power-law index p makes the beam more flexible. the results of the fundamental frequencies obtained in tab. 4 are compared with other results such as hsdt of reddy [11], hsdt of a.s. sayyad and y.m. ghugal [58], fsdt of touratier [12], hsdt of simsek [15], hsdt of thai and vo [20], fsdt of vo et al. [29], hsdt of vo et al. [30], fsdt of timoshenko [10], and cbt of bernoulli-euler [9]. it can also be noted that the two-dimensional shear deformation theory (2d) is in good agreement with that of the literature, whereas the results obtained by the theory of quasi-three-dimensional shear deformation (quasi-3d) are slightly larger compared to that of the literature and this is due to the effect of normal transversal deformation which is not neglected (εz 0) compared to other theories where the effect of normal transversal deformation is neglected (εz=0). fig. 9 illustrates the variation of the buckling critical load and the dimensionless fundamental natural frequency with respect to the index of the power-law p for different values of the ratio (l/h) by the use of the deformation theory shearing. it can be seen through these plots that the critical load and the frequency decreases with the growth of the index of the law of power p, it is maximum when the law of power p takes the value of zero in this case, the beam is entirely ceramic and is minimal in the case where the index of the power-law p takes the value of one, in this case, the beam is entirely metal, this is due to the increase in the value of the index of the power-law which causes a decrease in the value of the modulus of elasticity. it can also be seen that the ratio (l/h) has a considerable effect on the critical buckling load and the fundamental dimensionless fundamental frequency when it is reduced, the value of the ratio (l/h) decreases. this dependence is related to the effect of shear deformation. (a) (b) figure 9: variation in dimensionless critical buckling loads (a) and natural frequencies (b) with respect to the power-law exponents of exponents of simply supported fg beams. conclusions he aim of our work is to study the bending, buckling, and vibration of beams functionally graded using a twodimensional (2d) and quasi-three-dimensional shear deformation theory (quasi-3d), without a need for introducing a shear correction factor. these beams are subjected to uniformly distributed loads. the principle of virtual works is used to solve equilibrium equations using the navier approach with simply supported boundary conditions. the equations of motion are derived from the hamilton principle. parametric studies were carried out to examine the influence of the power-law index, and the beam aspect ratio (l/h) on the variation of dimensionless displacements as well as the distribution of dimensionless stresses across the thickness of a beam made of al/al2o3 type functionally graded materials. the results obtained are in good agreement with the results of the literature. it can be said that the present theory of shear deformation with the taking into account the stretching effect is not only precise, but also provides an easily feasible approach for the simulation of the mechanical behavior of structures in order to design weak structures which can be used in several fields such as automotive, aeronautical, marine, medical and nuclear. in futuristic work, we envisage the study of these mechanical behaviors with other boundary conditions and different loadings that are mechanical or/and thermal. t n. hebbar et alii, frattura ed integrità strutturale, 52 (2020) 230-246; doi: 10.3221/igf-esis.52.18 244 references [1] niino, m., hirai, t., watanabe, r. (1987). the functionally gradient materials, j.jpn. soc. compos. mater. 13, 257– 264. [2] hashmi, s., gilmar, f.b., van tyne, c.j., yilbas, b.s. (2014). comprehensive materials processing livre électronique, oxford, walltham, ma. elsevier. [3] koizumi m. (1993). the concept of fgm. ceramic transactions, functionally gradient materials. 34(1):3–10. [4] koizumi, m., niino, m. (1995). overview of fgm research in japan. mrs bull. 20, 19–24. [5] koizumi m. 1997. fgm activities in japan. composites part b. 28, pp. 1–4. [6] karama, m., afaq, k.s., mistou, s. (2003). mechanical behavior of laminated composite beam by the new multilayered laminated composite structures model with transverse shear stress continuity, int. j. solids struct. 40(6), 1525–1546. doi: 10.1016/s0020-7683(02)00647-9. [7] ayadoglu. m and tashkin v. (2007). free vibration analysis of functionally graded beams with simply supported edges. materials and design. 28, 1681-1656. doi: 10.1016/j.matdes.2006.02.007. [8] bernoulli, j. (1694). curvatura laminate elasticae. acte eruditorum lipsiae. 3(6), 262-276. [9] euler, l. (1744). method usin venien diline ascurvas maximum inimive proprietate gaudentes.lausanne and geneva. [10] timoshenko, s. p. (1921). on the correction for shear of the differential equation for transverse vibrations of prismatic bars. philosophical magazine. 41, 742–746. doi: 10.1080/14786442108636264. [11] reddy j.n. (1984). a simple higher order theory for laminated composite plates. j of applied mechanics. 51, pp. 745– 752. doi: 10.1115/1.3167719. [12] touratier m. (1991). an efficient standard plate theory. int j engineering science. 29, pp. 901–916. doi: 10.1016/0020-7225(91)90165-y. [13] matsunaga, h., (2008). free vibration and stability of functionally graded plates according to a 2-d higher-order deformation theory, compos struct. 82, pp. 499 – 512. [14] vidal, p., polit, o. (2009). assessment of the refined sinus model for the non-linear analysis of composite beams, compos. struct. 87, pp. 370–381. [15] şimşek m. (2010). fundamental frequency analysis of functionally graded beams by using different higher order beam theories, nuclear engineering and design. 240(4), pp. 697.705. doi: 10.1016/j.nucengdes.2009.12.013. [16] talha, m., singh, b.n., (2010). static response and free vibration analysis of fgm plates using higher-order shear deformation theory, appl. math. model. 34(12), 3991–4011. doi: 10.1016/j.apm.2010.03.034. [17] hosseini-hashemi, s., rokni damavandi taher, h., akhavan, h., omidi, m., (2010). free vibration of functionally graded rectangular plates using first-order shear deformation plate theory, appl. math. model. 34(5), pp. 1276–1291. doi: 10.1016/j.apm.2009.08.008. [18] hosseini-hashemi, s., fadaee, m., atashipour, s.r., (2011a). a new exact analytical approach for free vibration of reissner–mindlin functionally graded rectangular plates, int. j. mech. sci. 53(1), pp. 11-22. doi: 10.1016/j.ijmecsci.2010.10.002. [19] xiang, s., jin, y.x., bi, z.y., jiang, s.x., yang, m.s., (2011). a nth-order shear deformation theory for free vibration of functionally graded and composite sandwich plates, compos. struct. 93(11), pp. 2826–2832. doi: 10.1007/s11012-012-9563-0. [20] thai, h. t., & vo, t. p. (2012). bending and free vibration of functionally graded beams using various higher-order shear deformation beam theories. international journal of mechanical sciences. 62, pp. 57–66. doi: 10.1016/j.ijmecsci.2012.05.014 [21] reddy,j.n., (2011). microstructure-dependent couple stress theories of functionally graded beams. journal of the mechanics and physics of solids. 59(11), pp. 2382-2399. doi: 10.1016/j.jmps.2011.06.008 [22] eltaher, m.a., alshorbagy, a.e., mahmoud, f.f., (2013). determination of neutral axis position and its effect on natural frequencies of functionally graded macro/nano-beams, compos. struct. 99, pp. 193-201. [23] li, s. r., & batra, r. c. 2013. relations between buckling loads of functionally graded timoshenko and homogeneous euler– bernoulli beams. composite structures. 95, pp. 5–9. doi: 10.1016/j.compstruct.2012.07.027. [24] nguyen, t. k., vo, t. p., & thai, h. t. (2013). static and free vibration of axially loaded functionally graded beams based on the first-order shear deformation theory. composites part b engineering. 55, pp. 147–157. doi: 10.1016/j.compositesb.2013.06.01. [25] hadji, l., daouadji, t. h., meziane, m. a. a., tlidji, y., & bedia, e. a. a. (2016). analysis of functionally graded beam using a new first-order shear deformation theory. structural engineering and mechanics. 57, pp. 315–325. n. hebbar et alii, frattura ed integrità strutturale, 52 (2020) 230-246; doi: 10.3221/igf-esis.52.18 245 doi: 10.12989/sem.2016.57.2.315. [26] yaghoobi, h., valipour, m.s., fereidoon, a. and khoshnevisrad, p., (2014). analytical study on post-buckling and nonlinear free vibration analysis of fg beams resting on nonlinear elastic foundation under thermo-mechanical loading using vim, steel compos. struct. 17(5), pp. 753-776. doi: 10.12989/scs.2014.17.5.753 [27] rahmani, o. and pedram, o. (2014). analysis and modeling the size effect on vibration of functionally graded nanobeams based on nonlocal timoshenko beam theory. international journal of engineering science. 77, pp. 55-70. doi: 10.1016/j.ijengsci.2013.12.003 [28] alkhateeb et zenkour. (2014). a refined four-unknown plate theory for advanced plates resting on elastic foundations in hygrothermal environment. composite structures. 111, pp. 240–248. doi: 10.1016/j.compstruct.2013.12.033 [29] vo, t. p., thai, h. t., nguyen, t. k., & inam, f. (2014a). static and vibration analysis of functionally graded beams using refined shear deformation theory. meccanica. 49, pp. 155–168. [30] vo, t. p., thai, h. t., nguyen, t. k., maheri, a. and lee, j. (2014b). finite element model for vibration and buckling of functionally graded sandwich beams based on a refined shear deformation theory. engineering structures. 64, pp. 12–22. doi: 10.1016/j.engstruct.2014.01.029. [31] meradjah, m., kaci, a., houari, m.s.a., tounsi, a. and mahmoud, s.r. (2015). a new higher order shear and normal deformation theory for functionally graded beams, steel compos. struct. 18(3), pp. 793-809. doi: 10.12989/scs.2015.18.3.793. [32] vo, t. p., thai, h. t., nguyen, t. k., inam, f., & lee, j. (2015). a quasi-3d theory for vibration and buckling of functionally graded sandwich beams. composite structures. 119, pp. 1–12. doi: 10.1016/j.compstruct.2014.08.006. [33] zemri, a., houari, m.s.a., bousahla, a.a., tounsi, a. (2015). a mechanical response of functionally graded nanoscale beam: an assessment of a refined nonlocal shears deformation theory beam theory, structural engineering and mechanics. 54(4), pp. 693-710. doi: 10.12989/sem.2015.54.4.693. [34] al-basyouni, k.s., tounsi, a. and mahmoud, s.r. (2015). size dependent bending and vibration analysis of functionally graded micro beams based on modified couple stress theory and neutral surface position, compos. struct. 125, pp. 621-630. doi: 10.1016/j.compstruct.2014.12.070. [35] ebrahimi, f. and dashti, s. (2015). free vibration analysis of a rotating non-uniform functionally graded beam, steel compos.struct.19(5), pp. 1279-1298. doi: 10.12989/scs.2015.19.5.1279. [36] kar, v.r. and panda, s.k. (2015). nonlinear flexural vibration of shear deformable functionally graded spherical shell panel, steel compos. struct., int. j.18(3), pp. 693-709. doi: 10.12989/scs.2015.18.3.693. [37] bourada m., kaci a., houari m.s.a., tounsi a. (2015). a new simple shear and normal deformations theory for functionally graded beams, steel and composite structures. 18(2), pp. 409-423. doi: 10.12989/scs.2015.18.2.409. [38] celebi, k., yarimpabuc, d., keles, i. (2015). a unified method for stresses in fgm sphere with exponentially-varying properties, struct. eng. mech. 57(5), pp. 823-835. doi: 10.12989/sem.2016.57.5.823. [39] boukhari, a., fouad, b., djalil, b.a., mohamed, b.b., abdelouahed, t., bedia, e.a. (2016). the thermal study of wave propagation in functionally graded material plates (fgm) based on neutral surface position, mathematical modelling of engineering problems. 3(4), pp. 202-205. doi: 10.18280/mmep.030410. [40] ebrahimi and barati. (2016a). a nonlocal higher-order shear deformation beam theory for vibration analysis of sizedependent functionally graded nanobeams. arabian journal for science and engineering. 41(5), pp. 1679-1690. doi: 10.1007/s13369-015-1930-4. [41] ahouel. m., mohammed sid ahmed houari, e.a. adda bedia and abdelouahed tounsi, (2016), size-dependent mechanical behavior of functionally graded trigonometric shear deformable nano-beams including neutral surface position concept. steel and composite structures. 20(5), pp. 963-981. doi: 10.12989/scs.2016.20.5.963. [42] shafiei navvab, alireza mousavi, majid ghadiri, (2016), on the size-dependent nonlinear vibration of porous and imperfect functionally graded tapered microbeams, international journal of engineering science. 106, pp. 42-56. doi: 10.1016/j.ijengsci.2016.05.007 [43] raminnea, m., biglari, h. and vakili tahami, f. (2016). nonlinear dynamics nonlinear higher order reddy theory for temperature-dependent vibration and instability of embedded functionally graded pipes conveying fluid. structural engineering & mechanics. 59(1), pp. 153-186. doi: 10.12989/sem.2016.59.1.153. [44] ghumare and sayyad. (2017). bending, buckling and free vibration of laminated composite and sandwich beams: a critical review of literature. composite structures. 171, pp. 486-504. doi: 10.1016/j.compstruct.2017.03.053. [45] benadouda, m., ait atmane, h., tounsi, a., bernard, f., mahmoud, s.r. (2017). an efficient shear deformation theory for wave propagation in functionally graded material beams with porosities, earthquakes and structures. 13(3), pp. 255-265. doi: 10.12989/eas.2017.13.3.255. n. hebbar et alii, frattura ed integrità strutturale, 52 (2020) 230-246; doi: 10.3221/igf-esis.52.18 246 [46] bellifa, h., benrahou, k.h., hadji, l., houari, m.s.a., tounsi, a. (2016). bending and free vibration analysis of functionally graded plates using a simple shear deformation theory and the concept the neutral surface position, j braz. soc. mech. sci. eng. 38, pp. 265–275. doi: 10.1007/s40430-015-0354-0. [47] akbaş, ş.d. (2015). wave propagation of a functionally graded beam in thermal environments, steel compos. struct. 19(6), pp. 1421-1447. [48] akbaş, ş.d. (2016). forced vibration responses of functionally graded viscoelastic beams under thermal environment, international journal of innovative research in science, engineering and technology. 5(12), pp. 36 – 46. doi: 10.1142/s1758825117501009. [49] bellifa, h., benrahou, k.h., bousahla, a.a., tounsi, a., mahmoud, s.r. (2017b). a nonlocal zeroth-order shear deformation theory for nonlinear postbuckling of nanobeams, structural engineering and mechanics. 62(6), pp. 695 702. doi: 10.12989/sem.2017.62.6.695. [50] li, l., tang, h. and hu, y. (2018). the effect of thickness on the mechanics of nanobeams. international journal of engineering science. 123, pp. 81-91. doi: 10.1016/j.ijengsci.2017.11.021. [51] sayyad, a. s., & ghugal, y. m. (2017b). a unified shear deformation theory for the bending of isotropic, functionally graded, laminated and sandwich beams and plates. international journal of applied mechanics. 9(1), pp. 1–36. doi: 10.1142/s1758825117500077. [52] aldousari, s.m. (2017). bending analysis of different material distributions of functionally graded beam, appl. phys. a. 123, pp. 296. [53] bouafia, k., kaci, a., houari, m. s. a., benzair, a., tounsi, a. (2017). a nonlocal quasi-3d theory for bending and free flexural vibration behaviors of functionally graded nanobeams, smart structures and systems. 19(2), pp. 115-126. doi: 10.12989/sss.2017.19.2.115 [54] zidi, m., houari, m.s.a., tounsi, a., bessaim, a., mahmoud, s.r. (2017). a novel simple two-unknown hyperbolic shear deformation theory for functionally graded beams, struct. eng.mech. 64(2), pp. 145-153. doi: 10.1016/j.ast.2014.02.001. [55] fouda noha, tawfik el-midany, a. m. sadoun, (2017), bending, buckling and vibration of a functionally graded porous beam using finite elements, journal of applied and computational mechanics. 3, pp. 274-282. doi: 10.22055/jacm.2017.21924.1121. [56] zaoui f. zohra, hanifi h. a. lemya, younsi abderahman, meradjah mustapha, tounsi abdelouahed, ouinas djamel, (2017). free vibration analysis of functionally graded beams using a higher-order shear deformation theory, mathematical modelling of engineering problems. 1(1), pp.7-12. doi: 10.18280/mmep.040102. [57] mouffoki, a., adda bedia, e.a., houari, m.s.a., tounsi, a., mahmoud, s.r. (2017). vibration analysis of nonlocal advanced nanobeams in hygro-thermal environment using a new two-unknown trigonometric shear deformation beam theory, smart structures systems. 20(3), pp. 369-383. doi: 10.12989/sss.2017.20.3.369. [58] sayyad, a. s., & ghugal, y. m. (2018). bending, buckling and free vibration responses of hyperbolic shear deformation fgm beams. mechanics of advanced composite structures. 5, pp. 13-24. doi: 10.22075/macs.2018.12214.1117. [59] kaci, a., houari, m.s.a., bousahla, a.a., tounsi, a., mahmoud, s.r. (2018). post-buckling analysis of sheardeformable composite beams using a novel simple two-unknown beam theory, structural engineering and mechanics.65(5), pp. 621-631. doi: 10.12989/sem.2018.65.5.621. [60] dragan cukanovic, aleksandar radakovic´, gordana bogdanovic´, milivoje milanovic´, halit redžovi´c and danilo dragovi´c. (2018). new shape function for the bending analysis of functionally graded plate, materials. 11, pp. 2381. doi: 10.3390/ma11122381. [61] bouremana, m, houari, m.s.a., tounsi, a.,kaci, a. and adda bedia, e.a. (2013), a new first shear deformation beam theory based on neutral surface position for functionally graded beams, steel compos. struct., 15(5), pp. 467479. doi: 10.12989/scs.2013.15.5.467. [62] ould, l.l., kaci, a., houari, m.s.a. and tounsi, a. (2013), an efficient shear deformation beamtheory based on neutral surface position for bending and free vibration of functionally graded beams, mech.bas.des.struct., 41(4), pp. 421-433. doi: 10.1080/15397734.2013.763713. [63] şimşek, m.and yurtcu, h.h. (2013), analytical solutions for bending and buckling of functionally graded nanobeams based on the nonlocal timoshenko beam theory, compos. struct., 97, pp. 378-386. doi: 10.1016/j.compstruct.2012.10.038 [64] mantari jl, granados ev. (2016). an original fsdt to study advanced composites on elastic foundation. thinwalled structures;107: 80e9. doi: 10.1016/j.tws.2016.05.024. [65] reddy jn. 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/hrv (za stvaranje adobe pdf dokumenata najpogodnijih za visokokvalitetni ispis prije tiskanja koristite ove postavke. stvoreni pdf dokumenti mogu se otvoriti acrobat i adobe reader 5.0 i kasnijim verzijama.) /hun 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can be opened with acrobat and adobe reader 5.0 and later.) >> /namespace [ (adobe) (common) (1.0) ] /othernamespaces [ << /asreaderspreads false /cropimagestoframes true /errorcontrol /warnandcontinue /flattenerignorespreadoverrides false /includeguidesgrids false /includenonprinting false /includeslug false /namespace [ (adobe) (indesign) (4.0) ] /omitplacedbitmaps false /omitplacedeps false /omitplacedpdf false /simulateoverprint /legacy >> << /addbleedmarks false /addcolorbars false /addcropmarks false /addpageinfo false /addregmarks false /convertcolors /converttocmyk /destinationprofilename () /destinationprofileselector /documentcmyk /downsample16bitimages true /flattenerpreset << /presetselector /mediumresolution >> /formelements false /generatestructure false /includebookmarks false /includehyperlinks false /includeinteractive false /includelayers false /includeprofiles false /multimediahandling /useobjectsettings /namespace [ (adobe) (creativesuite) (2.0) ] /pdfxoutputintentprofileselector /documentcmyk /preserveediting true /untaggedcmykhandling /leaveuntagged /untaggedrgbhandling /usedocumentprofile /usedocumentbleed false >> ] >> setdistillerparams << /hwresolution [2400 2400] /pagesize [612.000 792.000] >> setpagedevice microsoft word numero_30_art_48 n. mortas et alii, frattura ed integrità strutturale, 30 (2014) 403-408; doi: 10.3221/igf-esis.30.48 403 focussed on: fracture and structural integrity related issues impact response of balsa core sandwiches nurdane mortas department of mechatronics engineering, university of gaziosman paşa nurmortas@gmail.com paulo n.b. reis department of electromechanical engineering, university of beira interior preis@ubi.pt josé a.m. ferreira cemuc, department of mechanical engineering, university of coimbra martins.ferreira@dem.uc.pt abstract. the benefits of resins nano-enhanced on the impact response of sandwich composites made by fiber glass/epoxy skins and balsa wood core were studied. afterwards, the influence of the core's discontinuity was analyzed in terms of impact strength. for better dispersion and interface adhesion matrix/clay nanoclays were previously subjected to a silane treatment appropriate to the epoxy resin. resins enhanced by nanoclays promote higher maximum impact loads, lower displacements and the best performance in terms of elastic recuperation. the core's discontinuity decreases the impact strength, but the resin enhanced by nanoclays promotes significant benefits. keywords. sandwich composites; nanoclays; impact behaviour. introduction tructural sandwich composites have been widely used in many engineering applications as consequence of their superior structural capacity in carrying transverse loads, superior bending stiffness, low weight, excellent thermal insulation and acoustic damping [1, 2]. these materials combine thin skins (to promote high in-plane mechanical properties) with low density cores (to fix the skins and to carry the transverse shear load or to provide other structural/functional duties). for this purpose a large variety of materials can be used. usually, the skins are made of metal alloy sheet or fiber-reinforced polymer laminates and, in terms of core, metallic honeycomb, polymer foam, syntactic foam, nomex and balsa wood can be used. for example, balsa is the lightest woods available and it offers salient mechanical and physical properties. however, sandwich composites are very susceptible to the impact loads that occur during the operational or maintenance activities. to improve the impact performance of those materials many researchers propose the addition of low concentrations of nanoparticles into polymers without compromising density, toughness or the manufacturing process [27]. montmorillonite (mmt) clay is the most popular nanoreinforcement for polymeric nanocomposites as consequence of its relatively high ion exchange capacity, high aspect ratio and economic advantages [8]. s n. mortas et alii, frattura ed integrità strutturale, 30 (2014) 403-408; doi: 10.3221/igf-esis.30.48 404 in this context, hosur et al. [9, 10] showed that the sandwich composites with nano phased foam sustain higher loads and present lower damage areas as compared with neat sandwiches. avila et al. [11] reported benefits in terms of energy absorption and failure modes with the nanoclays fillers on fiber glass/nano-modified epoxy face sheets and polystyrene foams. according to reis et al. [2], the lowest displacements and the highest elastic recuperation occur for sandwiches with resin nano-enhanced. the best performance of the sandwiches with epoxy resin enhanced by nanoclays was also confirmed by the residual flexural strength, which increases with the introduction of the nanoclays [2]. on the other hand, avila et al. [12] observed that the natural frequencies of the structural sandwich composites are altered by the addition of nano-reinforcements. however, the balsa planks (boards) present finite dimensions. consequently, there are discontinuities of the core that affect the mechanical properties. therefore, the aim of this work is study the effect of these discontinuities (gap between cores) on the impact performance. for this purpose, a gap with 20 mm of length will be analyzed and the results will be compared with other ones obtained for sandwiches manufactured with continuous cores (control samples). the benefits of resins nano-enhanced on the impact response of sandwich composites made by fiber glass/epoxy skins and balsa wood core will be studied. the epoxy resin was enhanced by nanoclays with special treatment to improve their dispersion and interface adhesion. the results are discussed in terms of load-time, load-displacement and energy-time diagrams. experimental procedure he sandwich composite specimens were fabricated using skins of glass fibre/epoxy resin and core of balsa wood with 6 mm of thickness. the skins are composited by six ply laminates, all in the same direction, of woven bidirectional glass-fibre 1195-1000 (195 g/m2). sr 1500 epoxy resin and a sd 2503 hardener, supplied by sicomin, were used. the system was placed inside a vacuum bag and a load of 2.5 kn was applied during 24 hours in order to maintain a constant fibre volume fraction and uniform laminate thickness. during the first 10 hours the bag remained attached to a vacuum pump to eliminate any air bubbles existing in the composite. the post-cure was followed according to the manufacturer`s datasheet (epoxy resin) in an oven at 40 ºc for 24 hours. in order to improve the dispersion and interface adhesion matrix/clay, nanoclays were previously subjected to a special treatment appropriate to the epoxy resin. more details about the treatment and the dispersion/exfoliation on the epoxy matrix can be found in [3, 4]. the nanoclays content used in present study is 3 wt.% because, according with studies developed by the authors [4], is the best amount for this epoxy system. fig. 1 shows the square specimens, with 100 mm side and 8 mm thickness (100x100x8 mm3), used in the present study. low-velocity impact tests were performed using a drop weight-testing machine imatek-im10. more details of the impact machine can be found in [13]. impactor diameter of 10 mm with masses of 2.903 kg was used. the tests were performed on square section samples of 75x75 mm and the impactor stroke at the centre of the samples obtained by centrally clamping the 100x100 mm specimens. the impact energies used in the tests were 5 j. this energy was previously selected in order to enable the measuring of the damage area, but without promote full perforation of the specimens. for each condition, five specimens were tested at room temperature. a) b) figure 1: a) control samples; b) samples with different gap lengths (0 = 20 mm). t 6 m m 10 0 m m 100 mm 8 mm 10 0 m m 100 mm 6 m m 8 mm 0 n. mortas et alii, frattura ed integrità strutturale, 30 (2014) 403-408; doi: 10.3221/igf-esis.30.48 405 results and discussion mpact tests were carried and fig. 2 shows the load-time, load-displacement and energy-time curves for sandwiches with pure epoxy resin and epoxy enhanced by nanoclays. these diagrams are representative of all specimens tested and they agree with the literature [2-4, 14-15]. 0 0.5 1 1.5 2 2.5 0 2 4 6 8 10 l o ad [ kn ] time [ms] 0 0.5 1 1.5 2 2.5 0 2 4 6 l o ad [ kn ] displacement [mm] a) b) 0 1 2 3 4 5 6 0 10 20 30 e n er gy [ j] time [ms] c) figure 2: a) typical load-time curves; b) typical load-displacement curves; c) typical energy-time curves. in detail, it is possible to observe that the force increases up to a maximum value (pmax) followed by a drop after the peak load. the impact energy was not high enough to infiltrate full penetration, because the impactor sticks into specimens and rebound always. the beginning of the plateau coincides with the loss of contact between the striker and the specimen, so, this energy coincides with that absorbed by the specimen [3, 4, 16]. the addition of nanoclays promotes major maximum impact loads with values, relatively to the control samples, around 11.9% higher. these results agree with the studies developed by reis et al. [3] where, for example, the addition of clays promoted maximum loads around 16.1% highest than occurred in kevlar with pure epoxy resin. for gustin et al. [17] the differences observed in maximum forces results in the different failure modes, because each sample type has different tensile and shear properties. in terms of displacement, sandwiches manufactured with pure resin presented values about 17.0% higher. this phenomenon is interesting, because the displacement should be controlled, sometimes, in terms of design [3]. finally, the elastic energy is calculated as the difference between the absorbed energy and the energy at peak i with nanoclays with nanoclays with nanoclays without nanoclays without nanoclays without nanoclays n. mortas et alii, frattura ed integrità strutturale, 30 (2014) 403-408; doi: 10.3221/igf-esis.30.48 406 load [3, 4]. when the fillers are added better results can be found. the sandwiches manufactured with epoxy resin enhanced by nanoclays presents best performance in terms of elastic recuperation with values about 25.7% higher. however, in real applications, the planks (boards) of balsa wood have finite lengths. in this case there are discontinuities between the cores of the sandwiches, because the boards do not touch. this absence of material, in terms of core, affects the mechanical properties of the sandwich, especially the impact strength. in order to detect the effect of the gap’s dimension, fig.3 shows the typical load-time, load-displacement and energy-time curves. in this case, the control samples are compared against the specimens containing a gap of 20 mm for sandwiches manufactured with pure resin (fig. 3). 0 0.5 1 1.5 2 2.5 0 2 4 6 8 10 l o ad [ kn ] time {ms] 0 0.5 1 1.5 2 2.5 0 2 4 6 l o ad [ kn ] displacement [mm] a) b) 0 1 2 3 4 5 6 0 10 20 30 e n er gy { j] time [ms] c) figure 3: comparison of the gap’s effect in terms of a) load-time curves; b) load-displacement curves; c) energy-time curves. these curves and the curves shown on fig. 2 are very similar but with different values. the gap promotes a decrease of the maximum impact loads and elastic recuperation (energy dissipated) but the opposite tendency occurs for displacement and contact time. as consequence of a lower energy dissipated, the damage increases. tab. 1 shows the average values observed and the benefits promoted by the resin nano-enhanced. if, in terms of control samples, the benefits obtained with resin nano-enhanced were previously analyzed, the effect of the gap follows the same tendency. in both cases, the gap promotes a decreasing of the maximum impact load with values around 29.4%, for the sandwiches manufactured with pure resin, and about 24.3% for the other ones with nanoclays. on the other hand, in terms of displacement, the opposite tendency was observed. in this case, the displacement increases for both conditions, but with higher values for the sandwiches with pure resin. values around 22.9% were found, while an increasing about 22% was observed for the sandwiches with resin nano-enhanced. this small difference in terms of displacement, however, was sufficient to promote the lowest damage areas when the resin was enhanced by the nanoclays. in fact, the gap with 20 control samples control samples control samples 0 = 20 mm 0 = 20 mm 0 = 20 mm n. mortas et alii, frattura ed integrità strutturale, 30 (2014) 403-408; doi: 10.3221/igf-esis.30.48 407 mm length promoted a decreasing about 48.2% and 41.5% of the energy dissipated, respectively, for sandwiches with pure resin and resin nano-enhanced. these results were expected, because the matrix enhanced by clays present higher stiffness and, consequently, its ductile behavior decreases [3, 4, 18]. therefore, the failure occurs along the matrix cracking promoted by the impact load [2]. sandwiches pmx [kn] sd [kn] displacement [mm] sd [mm] energy dissipated [%] sd [mm] cs without nanoclays 2.35 0.06 4.75 0.24 34.99 2.68 cs with nanoclays 2.63 0.05 4.06 0.11 43.98 1.51 0 = 20 mm without nanoclays 1.66 0.19 5.84 0.44 18.13 8.63 0 = 20 mm with nanoclays 1.99 0.15 4.96 0.31 25.72 0.52 table 1: effect of the gap on the different impact parameters. conclusions he present work studied the benefits of resins nano-enhanced, and the discontinuities of the cores (gap between cores), on the impact response of sandwich composites made by fibre glass/epoxy skins and balsa wood core. nanoclay cloisite 30b, specially modified for better dispersion and interface adhesion matrix/clay, were dispersed in 3% of resin weight. the maximum impact loads were obtained with resin enhanced by nanoclays. the opposite tendency was observed for the displacement at peak load, where the lower values were found for nanoclays filled sandwiches. finally, sandwich composites manufactured with epoxy resin enhanced by 3 wt.% of nanoclays presents the best performance in terms of elastic recuperation. in terms of core's discontinuity, the absence of material decreases the impact strength, but the resin enhanced by nanoclays promotes significant benefits in this context. references [1] atas, c., sevim, c., on the impact response of sandwich composites with cores of balsa wood and pvc foam, compos. struct., 93 (2010) 40-48. [2] reis, p.n.b., santos, p., ferreira, j.a.m., richardson, m.o.w., impact response of sandwich composites with nanoenhanced epoxy resin, j. reinf. plast. comp., 32 (2013) 898-906. [3] reis, p.n.b., ferreira, j.a.m., santos, p., richardson, m.o.w., santos, j.b., impact response of kevlar composites with filled epoxy matrix, compos. struct., 94 (2012) 3520-3528. [4] reis. p.n.b., ferreira, j.a.m., zhang, z.y., benameur, t., richardson, m.o.w., impact response of kevlar composites with nanoclay enhanced epoxy matrix, compos. part b-eng., 46 (2013) 7-14. [5] luo, j.-j., daniel, i.m., characterization and modeling of mechanical behaviour of polymer/clay nanocomposites, compos. sci. technol., 63 (2003) 1607-1616. [6] giannelis, e.p., polymer layered silicate nanocomposites, adv. mater., 8 (1996) 29-35. [7] saber-samandari, s., khatibi, a.a., basic, d., an experimental study on clay/epoxy nanocomposites produced in a centrifuge, compos. part b-eng., 38 (2007) 102-107. [8] shi, h.z., lan, t., pinnavaia, t.j., interfacial effects on the reinforcement properties of polymer-organoclay nanocomposites, chem. mater., 8 (1996) 1584-1587. [9] hosur, m.v., mohammed, a.a., zainuddin, s., jeelani s., impact performance of nanophased foam core sandwich composites, mater sci eng a, 498 (2008) 100-109. [10] hosur, m.v., mohammed, a.a., zainuddin, s., jeelani, s., processing of nanoclay filled sandwich composites and their response to low velocity impact loading, compos. struct., 82 (2008) 101-116. t n. mortas et alii, frattura ed integrità strutturale, 30 (2014) 403-408; doi: 10.3221/igf-esis.30.48 408 [11] avila, a.f., carvalho, m.g.r., dias, e.c., da cruz, d.t.l., nano-structured sandwich composites response to low velocity impact, compos. struct., 92 (2010) 745-751. [12] avila, a.f., donadon, l.v., duarte, h.v., modal analysis on nanoclay epoxy-based fiber-glass laminates, compos. struct., 83 (2008) 324-333. [13] amaro, a.m., reis, p.n.b., magalhães, a.g., de moura, m.f.s.f., the influence of the boundary conditions on lowvelocity impact composite damage, strain, 47 (2011) e220-e226. [14] iqbal, k., khan, s.-u., munir, a., kim, j.-k., impact damage resistance of cfrp with nanoclay-filled epoxy matrix, compos. sci. technol., 69 (2009) 1949-1957. [15] aslan, z., karakuzu, r., okutan, b., the response of laminated composite plates under low-velocity impact loading, compos. struct., 59 (2003) 119-127. [16] río, t.g., zaera, r., barbero, e., navarro, c., damage in cfrps due to low velocity impact at low temperature, compos. part b-eng., 36 (2005) 41-50. [17] gustin, j., joneson, a., mahinfalah, m., stone, j., low velocity impact of combination kevlar/carbon fiber sandwich composites, compos. struct., 69 (2005) 396-406. [18] ferreira, j.a.m., reis, p.n.b., costa, j.d.m., richardson, m.o.w., fatigue behavior of kevlar composites with nanoclay filled epoxy resin, j. compos. mater., 45 (2013) 1885-1895. microsoft word numero 25 art 4 yu. g. matvienko et alii, frattura ed integrità strutturale, 25 (2013) 20-26; doi: 10.3221/igf-esis.25.04 20 special issue: characterization of crack tip stress field determination of fracture mechanics parameters on a base of local displacement measurements yu. g. matvienko mechanical engineering research institute of the russian academy of science (imash ran). 4 m. kharitonievsky per., 101990 moscow, russia. e-mail: matvienko7@yahoo.com. v.s. pisarev, s. i. eleonsky central aero-hydrodynamics institute named after prof. n.e. zhukovsky (tsagi). 1 zhukovsky street, zhukovsky 140180 moscow region, russia. e-mail: vsp5335@mail.ru. abstract. new experimental technique for a determination of the stress intensity factor (sif) and t-stress values is developed and verified. the approach assumes combining the crack compliance method and optical interferometric measurements of local deformation response on small crack length increment. initial experimental information has a form of in-plane displacement component values, which are measured by electronic speckle-pattern interferometry at some specific points located near a crack tip. required values of fracture mechanics parameters follow from the first four coefficients of williams’ series. a determination of initial experimental data at the nearest vicinity of notch tip is the main feature of the developed approach. that is why it is not necessary to involve complex numerical models, which include global geometrical parameters, loading and boundary conditions of the object under study, in a stage of experimental data interpretation. an availability of high-quality interference fringe patterns, which are free from rigid-body motions, serves as a reliable indicator of real stress state around a crack tip. a verification of the technique is performed by comparing experimental results with analogous data of fem modelling. experimentally determined mode i sif for dcb specimen with end crack is in 5 per cent agreement with the numerically simulated case. proposed approach is capable of estimating an influence of the notch radius on fracture mechanics parameters. comparing sif and t-stress obtained for u-notches of different radius both in actual and residual stress field confirms this statement. keywords. stress intensity factor; t-stress; crack compliance method; in-plane displacement components; electronic speckle-pattern interferometry. introduction xperimental determination of stress intensity factor (sif) and t-stress for a crack of constant length under external load increment is of considerable current interest [1-8]. at the same time the crack compliance method is capable of sif deriving by local crack length increasing under constant load conditions [9-10]. this presentation is devoted to a development and verification of new technique for a determination of sif and t-stress values by combining the crack compliance method and optical interferometric measurements of local deformation response on small crack length increment. e http://www.gruppofrattura.it http://dx.medra.org/10.3221/igf-esis.25.04&auth=true yu. g. matvienko et alii, frattura ed integrità strutturale, 25 (2013) 20-26; doi: 10.3221/igf-esis.25.04 21 main principals and relations odified version of the crack compliance method resides in recording interference fringe patterns, which correspond to a difference between two in-plane displacement component fields. each field is referred to a crack of close but different length. the first exposure is made for a crack of initial length an-1 (see fig. 1). then initial crack length is increased by small increment δan so that new total crack length becomes equal to an=an-1+δan and the second exposure is performed. required interference fringe patterns are visualized by numerical subtraction of two images recorded for two cracks [11]. two interferograms, which are obtained by this way for thin plate with through edge crack of mode i, are shown in fig. 2. positive direction of x-axis in fig. 1 and fig. 2 coincides with a direction of the crack propagation. figure 1: polar co-ordinate system related to a crack tip and the notation adopted. (a) (b) figure 2: specimen #3v. interference fringe pattern obtained in terms of in-plane displacement component u (a) and v (b). initial crack length a4 = 7.18 mm with increment δa5 = 1.81 mm procedure of deriving required fracture mechanics parameters from interference fringe patterns is based on williams’ formulation [12]. in-plane displacement field near a crack tip is expressed as an infinite series for each in-plane displacement component. when x-direction coincides with the crack line these series for mode i condition have the following form: m http://www.gruppofrattura.it http://dx.medra.org/10.3221/igf-esis.25.04&auth=true yu. g. matvienko et alii, frattura ed integrità strutturale, 25 (2013) 20-26; doi: 10.3221/igf-esis.25.04 22 2 1 2 1 (1 ) ( 4 ) ( 1) cos cos 2 2 2 2 (1 ) ( 4 ) ( 1) sin sin 2 2 2 2 n n n n n n n n r nn n n u a k e r nn n n v a k e                                   (1) where u and v are in-plane displacement component in direction of x and y axis, respectively; μ is the poisson’s ratio; e is the elasticity modulus; k = (3–μ)/(1+μ) for plane stress and k=(3–4μ) for plane strain conditions; an are constants to be determined; r and θ are radial and angular distance from the crack tip as it is shown in fig. 1. values of stress intensity factor (sif) ki and t-stress t are connected with coefficients of infinite series (1) by the following way [7]: 1 2ik a  , 24t a (2) generally initial experimental information represents a difference in absolute values of in-plane displacement components ( , )nu r  and ( , )nv r  for two cracks of length na and 1na  : 1( , ) ( , ) ( , )n n nu r u r u r    , 1( , ) ( , )n n nv v r v r   (3) where 1 1( , ), ( , )n nu r v r   and ( , ), ( , )n nu r v r  are absolute values of in-plane displacement components in a point with polar co-ordinates ( , )r  for a crack of 1na  and na length, respectively. eq. (3) are valid for any point belonging to the proximity of crack tip located at point n. but right hand sides of eq. (3) include relative values of displacement components, which can not be directly used for a determination of an-values from decomposition (1). the key point of the developed approach resides in the fact that each interference fringe pattern of type shown in fig. 2 contains a set of specific points located at a crack border immediately. absolute values of in-plane displacement components and then coefficients an from formulae (1) for a crack of na length can be determined at these points. first, specific points are located along the crack line between point n–1 and point n where displacement component 1( , )nv r  equals to zero before making a crack length increment. thus, interference fringe pattern shown in fig. 2b allows determining absolute values of ( , )nv r  -component for each point with polar co-ordinates 0 ≤ r ≤ δan and θ=π. developed approach employs four first coefficients of series (1) for deriving required fracture mechanics parameters. a distribution of ( , )nv r  -displacement component along the crack line (θ=π, see fig. 1) is expressed as: 1 3 4 4 ( , ) 0( )n nn r r r v r a a r e e      (4) relation (4) shows that deriving ki value from eq. (3) demands a determination of ( , )nv r  -values at two points belonging to the interval 0 ≤ r ≤ δan, θ=π, as minimum. it is conveniently to use two points with polar coordinates (r =δan, θ=π) and (r=δan/2, θ=π). substituting these co-ordinates into relation (4) forms a system of linear algebraic equations, a solution of which is:     1 0.5 1 3 1 0.5 2 2 8 2 4 n n n n n n n n n e a v v a e a v v a a                 (5) where an1 and an3 are coefficients of decomposition (1) for a crack of an length; δvn-1 = 2vn(r=δan, θ=π) and δvn-0.5 = 2vn(r=δan/2, θ=π) are crack opening values from eq. (4), which have to be experimentally determined. sif value for a crack of an length follows from combining the first relations from eqs. (2) and (5):  0.5 12 2 2 8 n i n n n e k v v a        (6) http://www.gruppofrattura.it http://dx.medra.org/10.3221/igf-esis.25.04&auth=true yu. g. matvienko et alii, frattura ed integrità strutturale, 25 (2013) 20-26; doi: 10.3221/igf-esis.25.04 23 taking into account only the first term from eq. (1) leads to well-known westergaard relation: * 1 2 8 n n i n v e k a   (7) a characterisation of t-stress values t is based on a determination of u-displacement component directed along x-axis. a distribution of ( , )nu r  -displacement component for points belonging to the crack line (θ=π, see fig. 1), which corresponds to the second and the fourth terms of infinite series (1), is expressed as: 2 3 4 4 4 ( , ) 0( )n nn r r u r a a r e e       (8) absolute value of u-component for a crack of an length can be again obtained at point n –1 with polar co-ordinates r=δan and θ=π because at this point 1( , ) 0nu r   . a substitution of nr a  and 1( , )n n nu r a u      in eq. (8) and taking into account the first from relations (3) lead to the following relation: 2 1 2 4 4 4( )n nn n n a a u a a e e       (9) eq. (9) gives us the first equation essential for a determination of t-stress value t when displacement component value un1 is experimentally obtained. it should be noted that all experimental parameters needed for relations (5)-(7) and eq. (9) can be derived from two interferograms, which correspond to δan crack length increment. a formulation of the second required equation demands involving interference fringe pattern, which corresponds to crack length increasing from point n to point n+1 by δan+1 increment (see fig. 1). for point n+1 with polar co-ordinates (r =δan+1, θ=0) the first eq. (4) can be written as: 1 1 1 1 1 1( ; 0) ( ; 0) 0 ( ; 0)n n n n n n n nu u r a u r a u r a u                      (10) combining relations (1) and (10) gives: 2 1 1 1 1 1 2 1 1 3 4 2 (1 ) 4 4( )(1 ) 2n n n n nn nn n n a a a u a a a a a a e e e e                   (11) where 1nu  is the absolute value of ( , )nu r  displacement component at point n+1 (see fig. 1). relation (11) represents the second equation essential for a determination of t-stress because the values of coefficients a1 and a3 are already known from formulae (5) note that a value of 1nu  has to be experimentally derived from interference fringe pattern of type shown in fig. 2a, which are recorded for δan+1 crack length increment. if an estimation of t-stress value is restricted by coefficient an2 only, the following simplified formula is valid: n n n u t e a    (12) the t-stress value in eq. (12) can be determined by using interference fringe pattern of type shown in fig. 2a recorded for crack length increment δan only. electronic speckle-pattern interferometry (espi) serves for a determination of in-plane displacement components [11]. well-known optical system with normal illumination with respect to plane object surface and two symmetrical observation directions is used. when a projection of illumination directions onto plane surface of the investigated object coincides with ξ-direction, interference fringe pattern is described as: 2 sin d n    (12) where dξ is in-plane displacement component in ξ-direction; n = 1; 2; 3, … are the absolute fringe orders;  = 0.532 μm is the wavelength of laser illumination;  = 45 degrees is the angle between inclined illumination and normal observation directions. when ξ-direction coincides with x-axis and y-axis displacement component u and v can be derived accordingly to formula (13), respectively. http://www.gruppofrattura.it http://dx.medra.org/10.3221/igf-esis.25.04&auth=true yu. g. matvienko et alii, frattura ed integrità strutturale, 25 (2013) 20-26; doi: 10.3221/igf-esis.25.04 24 metrological verification etrological verification of the developed approach is performed by using specially designed specimen #3v made from 2024 aluminium alloy (e = 74000 mpa, μ = 0.33) shown in fig. 3. working part of this specimen is a thin plate of dimensions 120x48x5 mm3. a u-notch of length a0 = 20 mm is initially made in the middle of the shortest side in a direction of the symmetry cross-section. the specimen is loaded by transverse force directed orthogonally to the notch line as it is shown in fig. 3. step-by-step notch increase process is firstly performed by narrow jewellery saw of width b1 = 0.3 mm (notch radius ρ1~0.15 mm). a scheme of the experiment involved resides in the following. external transverse load pn1 is applied to the specimen. the first exposure is made for a notch of current length an-1. then notch length is increased by small increment δan and the second exposure is made for a notch of the final length an = an-1 + δan. during a process of notch length increasing a value of acting force is slightly decreased to pn2 due to a compliance of the force gage. two interference fringe patterns recorded for the 4th notch length increment are shown in fig. 2. interference fringe patterns are recorded for 7 notch length increments starting from initial notch length a0 = 20 mm up to a0+an = 32.9 mm. experimental data are obtained for the same loading conditions: pn1 = 0.930 kn and pn2 = 0.846 kn. dependences of sif ki and t-stress t values from total notch length constructed accordingly to relation (6) and relations (9)-(11), respectively, are shown in fig. 4. note that sif values obtained by formula (6) coincide with analogous data from formula (7) within 5 per cent because an3 values are practically equal to zero for all steps considered. this fact gives us a capability of reliable comparing experimentally obtained sif values with analogous results of numerical simulation on a base of nastran computer codes. figure 3: drawing specimen #3v and a scheme of its loading. (a) (b) figure 4: dependencies of sif ki (a) and t-stresses t (b) from total notch length for specimen #3v and specimen #4v. m http://www.gruppofrattura.it http://dx.medra.org/10.3221/igf-esis.25.04&auth=true yu. g. matvienko et alii, frattura ed integrità strutturale, 25 (2013) 20-26; doi: 10.3221/igf-esis.25.04 25 comparing the results of two types is performed for the fourth notch length increment with total notch length a0+a4 = 27.2 mm. finite element mesh consists of 162000 plane shell elements of cquad 4 type. boundary conditions correspond to real geometry of the specimen shown in fig. 3. local area including a notch tip is simulated by twodimensional notch tip element crac2d. this element is capable of sif calculation accordingly to formula (7) only. numerical sif value 6.48femik mpa m coincides with analogous experimental value 4 6.14ik mpa m within five per cent. this result proves a high accuracy and reliability of the developed approach. influence of the notch width on fracture mechanics parameters eveloped approach is capable of determining fracture mechanics parameters for notches as well as cracks in both actual and residual stress field. it is also possible to estimate an influence of notch radius on sif and t-stress values obtained through the use of formula (5) and relations (9)-(11), respectively. the first step in this way is made for actual stress field in specimen #4v, geometrical parameters and loading conditions of which completely coincide with scheme shown in fig. 3. the main difference resides in using a saw of width b3 = 1.0 mm (notch radius ρ3~0.50 mm) for incremental crack length increasing. dependences of sif ki and t-stress t values obtained accordingly to formula (6) and relations (9)-(11) from total notch length for specimen #4v are also shown in fig. 4. a difference in sif values reaches 10 per cent with notch width increasing leads to sif decreasing. average t-stress values calculated for the first six steps are tnav = –67.2 mpa and tnav = –76.8 mpa for specimens #3v and #4v, respectively. thus, notch width increasing gives a decrease of negative t-stress values by 12.5 per cent. a study of notch increase in residual stress field is performed for two welded thin plates of dimensions 200x100x4 mm3 made from aluminium alloy (e=72000 mpa, μ=0.33). these plates are denoted as specimen #015 (notch width b2 = 0.6 mm, notch radius ρ2~0.30 mm) and specimen #016 (notch width b1 = 0.3 mm, notch radius ρ1~0.15 mm). weld seam of lengths 100 mm coincides with one from symmetry cross-section of each specimen. notches in both specimens are increased from a centre of the weld along the second symmetry cross-section orthogonally to the weld direction. preliminary determination of maximal residual stress values σymax acting along the weld in both specimens serves for estimating an identity of residual stress fields. these values determined at points with co-ordinate x = 9 mm equal to σymax = 130 and σymax = 139 mpa for specimen #015 and #016, respectively. data are obtained by combining the hole drilling method and espi. holes are drilled in specimen’s area, which does not contain a notch. (a) (b) figure 5: dependences of sif ki (a) and t-stress t (b) values form total notch length. experimental technique and a procedure of sif and t-stress determination completely corresponds to the approach described above. dependences of sif ki and t-stress t values from total notch length are shown in fig. 5a and fig. 5b, respectively. these results show that co-ordinate of points where ki = 0 and t = 0 do not depend on the notch radius and correspond to notch length as = 16÷18 mm. maximal sif values for specimen #016 (ki=17.8 mpa·m0.5) and specimen d http://www.gruppofrattura.it http://dx.medra.org/10.3221/igf-esis.25.04&auth=true yu. g. matvienko et alii, frattura ed integrità strutturale, 25 (2013) 20-26; doi: 10.3221/igf-esis.25.04 26 #015 (ki=14.3 mpa·m0.5) differ by 20 per cent. a difference in maximal values of t-stress for specimen #016 (t = –188 mpa) and specimen #015 (t = –120 mpa) reaches 30 per cent. distributions of ki in fig. 5a are constructed by using formula (6). t-stresses shown in fig. 5b are derived on a base of relations (9)-(11). it should be specially noted that formula (12) gives t = 0 for both specimens and any notch length increment. conclusions ew technique for a determination of fracture mechanics parameters is developed. its essence resides in a measurement of local deformation response on small crack length increment by electronic speckle-pattern interferometry. obtained experimental information is capable of deriving the first four coefficients of williams’ asymptotic series and further calculations of stress intensity factor and t-stress values. developed approach allows estimating dependencies of fracture mechanics parameters from a real width of the u-notch and/or notch radius. acknowledgement resented study is performed in the framework of rfbr grant #10-08-00393-а and the program of joint investigations of central aero-hydrodynamics institute and mechanical engineering research institute of the russian academy of science. references [1] maleski, m.j., kirugulige, m.s., h.v. tippur, h.v., a method for measuring mode i crack tip constraint under static and dynamic loading conditions, exp. mech., 44 (2004) 522-532. [2] hild, f., roux, s., measuring stress intensity factors with a camera: integrated digital image correlation (i-dic), c. r. mecanique, 334 (2006) 8-12. [3] yoneyama, s., morimoto, y., takashi, m., automatic evaluation of mixed-mode stress intensity factors utilizing digital image correlation, strain, 42(2006) 21-29. [4] yoneyama, s., ogawa, t., kobayashi, y., evaluating mixed-mode stress intensity factors from full-field displacement fields obtained by optical methods, eng. fracture mech., 74(2007) 1399-1412. [5] réthoré, j., roux, s., hild, f., noise-robust stress intensity factor determination from kinematic field measurements, eng. fracture mech., 75(2008) 3763-3781. [6] lópez-crespo, p., burguete, r.l., patterson, e.a., shterenlikht, a., withers, p.j., yates, j.r., study of a crack at a fastener hole by digital image correlation. exp. mech., 49(2009) 551–559. [7] yates, j.r., zanganeh, m., tai, y.h., quantifying crack tip displacement fields with dic, eng. fracture mech., 77(2010) 2063-2076. [8] hadj meliani, m., azari, z., pluvinage, g., matvienko, yu.g., the effective t-stress estimation and crack paths emanating from u-notches, eng. fracture mech., 77(2010) 1682–1692. [9] schindler, h.-j., determination of residual stress distributions from measured stress intensity factors. int. j. of fracture, 74(1995) r23-r30. [10] schindler, h.-j., cheng, w., finnie, i., experimental determination of stress intensity factors due to residual stresses. exp. mech., 37(1997) 272-277. [11] rastogi, p., digital speckle pattern interferometry and related techniques. wiley, west sussex, (2001). [12] williams, m.l., on the stress distribution at the base of a stationary crack. asme j. of applied mech., 24(1957) 109– 114. n p http://www.gruppofrattura.it http://dx.medra.org/10.3221/igf-esis.25.04&auth=true microsoft word numero_51_art_10_2657 s. k. kourkoulis et alii, frattura ed integrità strutturale, 51 (2020) 127-135; doi: 10.3221/igf-esis.51.10 127 focussed on igf25 – fracture and structural integrity international conference 2019 a biomechanical study of the role of sitagliptin on the bone characteristics of diabetic rats stavros k. kourkoulis, ermioni d. pasiou national technical university of athens, laboratory for testing and materials, unit of biomechanics, greece stakkour@central.ntua.gr, https://orcid.org/0000-0003-3246-9308 epasiou@teemail.gr, https://orcid.org/0000-0003-1580-3415 arezoo abdi, despoina n. perrea national and kapodistrian university of athens, medical school, laboratory for experimental surgery & surgical research “n.s. christeas”, greece aabdi@med.uoa.gr, dperrea@med.uoa.gr john vlamis university of athens, kat general hospital, 3rd orthopaedic department, greece jvlamis@email.com abstract. an experimental protocol is described aiming to explore the influence of type 2 diabetes mellitus on the biomechanical response of the bone tissue and, also, to quantify the potential beneficial role of a pharmaceutical treatment, based on sitagliptin, a diabetes drug that increases the levels of natural substances called incretins. twenty eight male, 10-week old wistar rats were used, divided into three groups, i.e., the control one, the group including the diabetic rats and, finally, the group including the diabetic rats which were treated using sitagliptin. the biomechanical study was based on a series of three-point bending tests of the femora of the sacrificed rats and the analysis of the experimental data was implemented in terms of the actual geometry of the fractured cross-section. it was concluded that diabetic bones undertake larger forces despite the fact that the “diameter” of their crosssection was somehow smaller. on the contrary, the slope of the load-deflection curve (corresponding to a measure of the stiffness) of diabetic bones is slightly lower compared to the control bones. finally, it seems that treating diabetic animals with sitagliptin only partly reverses the effect of type 2 diabetes mellitus on their bone tissue, at least concerning its strength and stiffness. keywords. male wistar rats; type-2 diabetes; sitagliptin; biomechanics; three point bending; video-extensometer. citation: kourkoulis, s.k., pasiou, e.d., abdi, a., perrea, d.n., vlamis, j., a biomechanical study of the role of sitagliptin on the bone characteristics of diabetic rats, frattura ed integrità strutturale, 51 (2020) 127-135. received: 13.10.2019 accepted: 05.11.2019 published: 01.01.2020 copyright: © 2020 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. http://www.gruppofrattura.it/va/51/2657.mp4 s. k. kourkoulis et alii, frattura ed integrità strutturale, 51 (2020) 127-135; doi: 10.3221/igf-esis.51.10 128 introduction iabetes mellitus is a disease which increases the blood glucose levels of the patient. there are mainly two types of diabetes, i.e., type 1 (insulin is not produced at all) and type 2 (the total amount of insulin required cannot be produced). insulin is a hormone produced in the pancreas and its role is to move glucose from the blood into cells, regulating blood sugar levels. the amount of insulin released is augmented by metabolic hormones, the incretins, which are some of the gut hormones (secreted after glucose consumption) stimulating insulin secretion together with hyperglycemia. glucose-dependent insulinotropic polypeptide (gip) and glucagon-like peptide-1 (glp-1) are known incretin hormones from the upper (gip, k cells) and lower (glp-1, l cells) gut [1]. these two hormones together create the incretin effect, namely, a twoto three-fold higher insulin secretory response to oral as compared to intravenous glucose administration. it is known that, in subjects with type 2 diabetes this incretin effect is diminished or even no longer present. once released to the blood stream, these two hormones are rapidly degraded by an endopeptidase, the dipeptidylpeptidase 4 (dpp-4) [1]. glucagon-like peptide-1 receptor agonists (glp-1 ra) and dipeptidyl peptidase-4 inhibitors (dpp-4i) are new incretin-based drugs which have emerged as a potentially new class of drugs for the management of the type 2 diabetes mellitus (t2dm), and were received with enthusiasm by the medical community due to their extra-pancreatic effects. the present study focuses on t2dm, taking into account that t2dm patients are the majority (>90%) of diabetic patients, where inadequate insulin is produced, less sugar is moved into cells and therefore blood glucose levels increase. nowadays, plenty of drugs are used for the treatment of diabetic patients, including dpp-4 inhibitors, such as sitagliptin used in this protocol, which blocks the enzyme dipeptidyl peptidase-4 (dpp-4), delaying the deactivation of incretins. during the last decades there has been increased interest in the relationship of bone metabolism with diabetes. due to the increased prevalence of diabetes mellitus globally, research on some of the lesser-known effects, including impaired bone health, is gaining a lot of attention. the actual effect of diabetes on bone fragility and fractures, as well as the implications of various therapeutic strategies on the bone, remain unclear [2, 3]. all studies agree that patients with t2dm have 40-70% increased fracture risk, however their bone mineral density is normal or increased. this suggests that other factors, besides bone quality, affect bone fragility [4, 5]. animal and human diabetic subjects have consistently lower bone formation, however the findings on bone resorption are not so clear. most animal studies reveal increased bone resorption in diabetic subjects, whereas clinical studies show decreased bone turnover in general [6, 7]. in the direction of gaining deeper insight in this issue, an experimental protocol is presented in this study, aiming to study the influence of t2dm on the biomechanical response of the bone tissue and, also, to quantify the potential beneficial role of a pharmaceutical treatment, based on sitagliptin. as with most similar studies, the fracture load is considered as the criterion for assessing the quality of bone tissue. it is mentioned, however, that the load, expressed in terms of the fracture force, does not take into consideration the geometrical characteristics and anatomic variations of bones, quite often shadowing the conclusions of biomechanical studies. in fact, from the mechanics of materials point of view, it is the fracture stress rather than the fracture force that characterizes the strength of any given material. in this context, the fracture stress, as obtained from series of three-point bending tests, is used for the quantification of the role of t2dm and sitagliptin on the mechanical quality of bone tissue. the specific test is chosen due to its simplicity and, also, due to its wide application in similar protocols worldwide. the main challenge of the study was the accurate determination of the geometrical features of the fractured cross-section, in an attempt to avoid adopting simplifying assumptions, like, for example, to consider the cross-section as a circular or elliptic ring. in this direction, the approach suggested by biewener [8] (permitting determination of the area, the centroid, the second moment of area and the coordinates of the points with the maximum distance from the neutral plane), was adopted and developed further, for the calculation of the fracture stress. the study enlightens interesting aspects of the role of t2dm and sitagliptin on the quality of the bone tissue of diabetes patients, which are not always in line with the respective ones of already published studies. the experimental protocol animals wenty eight (28) male 10-week old wistar rats were used in the present study. the animals were divided into three (3) groups: (a) the control (c) one, (b) the diabetic (d) one and (c) the diabetic one, the animals of which after having become diabetic were treated using sitagliptin (d-s). more specifically, twenty (20) of the rats were made diabetic by adding fructose in their drinking water and, also, by injecting streptozotocin (stz) [9]. on the contrary, the rats of the control group were drinking normal tap water and they received a vehicle buffer injection (in other words, they received a normal saline injection). d t s. k. kourkoulis et alii, frattura ed integrità strutturale, 51 (2020) 127-135; doi: 10.3221/igf-esis.51.10 129 one week after the injection, the animals with non-fasting blood glucose levels higher than 300 mg/dl were considered diabetic. the injection was repeated if necessary. as a next step and after diabetes was confirmed, twelve (12) of the diabetic rats were treated with sitagliptin per os for eight (8) weeks. the remaining eight (8) diabetic rats and the control ones did not receive any drug treatment. tab. 1 recapitulates the three groups of animals, as well as the treatment offered to each group. all animals were fed normal pellet diet and eight (8) weeks after their 8-week treatment they were sacrificed. it should be underlined that during the whole protocol, all regulations for animal protocols were followed (i.e., all animal procedures were approved by the national bioethics council of the greek ministry of education). group number of rats water injection treatment control (c) 8 normal drinking water vehicle buffer injection (ip) diabetic (d) 8 water with 10% frustose ad libitum single injection (ip) of streptozotocin (stz) (40 mg/kg b.w.) dissolved in citrate buffer (ph 4.4) diabetic-sitagliptin (d-s) 12 sitagliptin per os (10 mg/kg/day) table 1: the groups of animals tested and the treatment taken. experimental procedure the sacrifices of the animals were made in the “laboratory for experimental surgery & surgical research ‘n. s. christeas’ ” of the “national and kapodistrian university of athens”. after each sacrifice, the right femur of the rat was removed and it was transferred in normal saline solution to the “laboratory for testing and materials” of the “national technical university of athens” within the next 30 minutes, in order to study their mechanical behaviour under three point bending. all experiments were carried out using an mts electromechanical loading frame and a specially designed apparatus for supporting the bones (figs.1(a,b)) dictated by the relatively small size of the femora. the distance between the supports was set equal to 20 mm and it was kept constant in all experiments. the load was applied monotonically up to the fracture of the specimens with the aid of a punch of rounded tip. all tests were carried out under displacement-control mode, at a constant rate of 0.5 mm/min, simulating quasi-static loading conditions. the deflection of the bones at their mid-span was measured with the aid of a contactless video-extensometer by limess (fig.1c). the advantage of using the specific technique will be discussed in next section. (a) (b) (c) figure 1: (a,b) both sides of the experimental set-up used; (c) a typical image taken by the video-extensometer during the experiment. the perimeter of the cross-section of the diaphysis of long bones is usually of irregular shape, as it can be clearly seen in figs.2(a-c). it is only in very few cases that the perimeter can be considered (with a satisfactory level of approximation) of elliptical shape (see the white dotted ellipse in fig.2d). therefore, the exact settlement of the bone on the supports is not a priori known. this means that, for the majority of specimens, the loading axis does neither coincide with one of the two principal axes of the cross-section nor it passes through the centroid of the cross-section (generating, thus, shear stresses, in addition to the normal ones). furthermore, and taking into account that all geometrical characteristics of the cross-sectional area (like for example the tensor of the second moments of area) are unknown, calculating the magnitude of the stresses developed (normal ones due to bending and shear ones due to parasitic torsion) becomes a challenging task. to cope with these problems, the procedure proposed by biewener’s [8], as it was refined by kourkoulis et al. [10], was adopted. as a first step, the bone was placed on the supports of the experimental apparatus and a pre-load (lower than 5 n, i.e., lower than 3% of the maximum load undertaken by the specimens) was applied on the femur in order to stabilize it. in s. k. kourkoulis et alii, frattura ed integrità strutturale, 51 (2020) 127-135; doi: 10.3221/igf-esis.51.10 130 this position, the point of the bone at which the tip of the loading punch was coming in contact, was marked red. then, the respective point at the lower level of the femur was marked black, as it can be seen in fig.2e for the cross-section at the midspan of a typical femur. the specific procedure permitted determination of the direction of the loading axis. after the end of the experiments, one of the two fractured parts of each specimen was placed vertically in a plastic cup which was then filled with molten resin (fig.3a). after the curing time of the resin, as it is dictated by the manufacturer, the construct, i.e., the bone and the surrounding resin, was removed from the cup (figs.3(b,c)). the free surface of the construct was then grinded by means of a series of abrasive papers of increasing smoothness up to the level of the marked points mentioned in the previous paragraph (i.e., the marks determining the loading axis). finally, the polished surface of the construct were photographed with the aid of a stereoscope (figs.2(a-d) and fig.3d). (a) (b) (c) (d) (e) figure 2: (a-c) typical cross-sections of the bones tested; (d) the approximation of the cross-section using an ellipse; (e) the loading axis as it was determined for a typical cross-section of a femur. (a) (b) (c) (d) figure 3: (a) the fractured bones surrounded by the resin in the plastic caps; (b,c) typical bone-resin construct; (d) photo of the polished surface of a typical construct. obtaining the geometrical data of the fractured cross-sections of the specimens each photo taken by the stereoscope was imported in the autocad software and both the outer and inner perimeters of the femur’s fractured cross-section were drawn, together with the line corresponding to the loading axis, as it was indicated by the previously mentioned coloured marks (fig.4a). taking advantage of these drawings, the cross-sectional area, the centroid of the cross-section (and therefore the eccentricity of the loading axis with respect to the centroid, e), the average thickness of the cortical bone and the area enclosed by the median line were calculated (figs.4(b,c)) for each specimen. having determined the centroid of the cross-section, a system xccyc is initially chosen, with the yc-axis to be parallel to the loading axis (fig.5a) and the second moment of area about the centroidal axes were calculated, i.e., ixcxc, iycyc, ixcyc. as a next step, the principal second moments of area were determined, i.e., ixpxp=imin, iypyp=imax, together with the respective orientations (fig.5b). taking advantage of the above data, the bending moments about the principal axes were calculated according to eqs.(1) (figs.5(c,d)), together with the respective (parasitic) torsional ones, which were calculated according to eq.(2) (fig.5d).  , 4 4 yx y x p lp l m m (1) torsionalm pe (2) applying now the concepts of the bernoulli-euler technical bending theory (and according to the specific conventions adopted for the bending moments in fig. 5d) the neutral line (zero normal stress line) is determined, according to eq.(3), as it is demonstrated in fig.6a for the specific bone (specimen) presented here.    0 0 p p p p yx bending x x y y mm y x i i  (3) s. k. kourkoulis et alii, frattura ed integrità strutturale, 51 (2020) 127-135; doi: 10.3221/igf-esis.51.10 131 (a) (b) (c) figure 4: (a) the “imprint” of the cross-section of a typical bone, as it was obtained using the autocad software; (b) the centroid of the cross-section and the eccentricity of the loading axis; (c) the thickness measured in various locations of the cross-section in order to determine the cortical bone’s average thickness and, finally, the area needed for the calculation of the shear stress. (a) (b) (c) (d) figure 5: (a) the auxiliary centroidal system initially chosen arbitrarily (the loading axis is, also, shown); (b) the principal centroidal system determined; (c) the components of the applied load (analyzed along the principal centroidal axes); (d) the bending and the torsional moments developed. (a) (b) figure 6: (a) determination of the neutral line (zero normal stress locus); (b) locating the point most distanced from the neutral line, at which the maximum normal (tensile) stress is developed. then, as a last step, the maximum normal (tensile) stress at point k, i.e., the most distanced one from the neutral line (fig. 6b), is calculated, together with the respective (parasitic) shear stress, according to eqs.(4,5), where xk and yk represent the coordinates of point k.   p p p p yx bending k k x x y y mm y x i i  (4)   2 torsional torsional m m a t (5) it is clarified at this point that the stresses calculated with the aid of eq.(5) are caused by the torsional moment developed due to the inevitable eccentricity of the loading axis with respect to the centroid of the cross section. on the contrary, the shear stresses due to the internal resultant shear force, v (stresses provided by the familiar formula τ=vq/it, where i is the respective second moment of area of the cross section, q is the first moment of area of the part of the cross section located above or below the point at which the stresses are calculated, and t the width of the section at the specific point) were ignored, given that the length over “height” ratio exceeds well the limit of 4 (below which these stress are worth being taken into account). s. k. kourkoulis et alii, frattura ed integrità strutturale, 51 (2020) 127-135; doi: 10.3221/igf-esis.51.10 132 results efore proceeding to the discussion of the results obtained from this study, it is mentioned that the mean values of all quantities (either measured or calculated, tabulated in the respective tables of this section) were obtained after rejecting experiments that were suspicious for biased errors, according to chauvenet’s criterion. in addition, the percentage difference of all quantities between the groups is added in the tables next to the respective mean value. specifically, the data of the row corresponding to the diabetic rats are compared to the control ones while the data for the diabeticsitagliptin group are compared to both the control and the diabetic animals. for this reason, two percentage differences are presented in the row corresponding to the diabetic-sitagliptin group: the first number in the parenthesis is the comparison to the control group and the second one is the comparison to the diabetic group. the mean values of the geometrical characteristics of the bones tested, i.e., their cross-sectional area and their average thickness, are presented in tab. 2 for the three groups of animals tested. the first conclusion that can be drawn is that the cross-sectional area of the diabetic femora is 16% smaller than the respective one of the control bones. in addition, the bones of the diabetic animals are 13% thinner than the control ones. on the other hand, both the cross-sectional area and the thickness of the animals treated with sitagliptin are even smaller compared to the respective quantities of the diabetic rats. the average thickness seems to be the quantity most affected. group cross-sectional area [mm2] average thickness [mm] control 7.846 0.81 diabetic 6.581 (-16.0%) 0.71 (-13.0%) diabetic-sitagliptin 6.466 (-18.0% / -1.7%) 0.66 (-18.0% / -7.0%) table 2: the geometrical characteristics of the groups tested. group deflection at max load [mm] stiffness [n/mm] control 0.346 576.37 diabetic 0.300 (-13.0%) 670.13 (+16.0%) diabetic-sitagliptin 0.295 (-14.5% / -1.7%) 644.38 (+12.0% / -3.8%) table 3: the deflection at the maximum load and the stiffness of all groups. similar conclusions can be drawn concerning the deflection measured at the maximum load attained (tab. 3). the diabetic femora were definitely proven to be more brittle than the control ones (their deflection was 13% smaller) and the treatment with sitagliptin seems not to “cure” the bone. on the contrary, the bones belonging to the diabetic-sitagliptin group were slightly more brittle. it is here recalled, that the deflection of the femora was measured using the video-extensometer (as it was already mentioned previously). the advantage of using this technique is that actual deflection of the femur is provided relieved from any parasitic influences due to deformation of any other element/component of the experimental set-up etc. the astonishing difference between the deflection measured by the video-extensometer and that provided directly by the software of the loading frame is shown in fig.7a. it is seen that for the specific specimen, the difference between the deflections provided by the extensometer and that provided by the loading frame approaches 40%. it is mentioned, however, that even higher differences have been reported in the literature [10]. typical load-deflection curves of all three groups tested are shown in fig.7b. based on these plots, the stiffness of each femur was calculated. contrary to what was observed for the three quantities described up to this point (i.e., the crosssectional area, the average thickness and the deflection at the maximum load), diabetes mellitus increases about 16% the stiffness of the diabetic bones when they are compared to the control ones as it can be seen in tab. 3. in addition, the use of sitagliptin seems to decrease the stiffness (about 4% compared to the diabetic femora) approaching to some extent the respective one of the control rats. interesting results were obtained concerning the maximum load attained by each group of animals. as it is seen in tab. 4, the diabetic femora sustain 7% larger load when they are compared to the maximum load sustained by the femora of the control group. on the other hand, the maximum load recorded for the bones that were treated with sitagliptin is only slightly (1.5%) higher compared to that of the control ones. b s. k. kourkoulis et alii, frattura ed integrità strutturale, 51 (2020) 127-135; doi: 10.3221/igf-esis.51.10 133 (a) (b) figure 7: (a) the load-deflection curves obtained by the video-extensometer and the loading frame for a typical diabetic femur; (b) typical load-deflection curves for the three animal groups of the present study. group load [n] bending strength [mpa] shear stress [mpa] equivalent stress [mpa] control 173.63 211.04 3.71 211.20 diabetic 186.44 (+7.0%) 268.53 (+27.0%) 6.26 268.83 (+27.0%) diabetic-sitagliptin 176.31 (+1.5% / -5.4%) 247.29 (+17.0% / -7.9%) 7.16 247.69 (+17.0% / -7.9%) table 4: the load and the stresses developed in the three groups tested. similar results, but with greater percentage difference, are observed concerning the bending stress calculated. surprisingly enough, the bending strength of the diabetic rats seems to be increased with respect to the ones of the control group by about 27%. moreover, the use of sitagliptin only partly reverses the effect of diabetic mellitus, leading to 17% greater bending strength compared to the control bones. the same differences can be seen for the equivalent von mises stresses. this was expected since the shear stresses produced by the torsional moment developed were proven not significant in this protocol (their magnitude was of the order of about 2.5% of the respective equivalent stress) and therefore they do not distort the conclusions drawn based on the normal stress. it is herewith recalled that the shear stresses due to the internal resultant shear force were ignored in the analysis of the results on the basis of purely geometrical arguments (the length over “height” ratio of the specimens tested definitely exceeds the critical limit of 4, beyond which the specific “family” of shear stresses are of ignorable magnitude compared to the respective normal stresses). discussion he target of the present study was two-folded: on the one hand it was attempted to quantify the potentially harmful role of type 2 diabetes mellitus on the biomechanical properties of the bone tissue. on the other hand, it was attempted to check whether some of these damages can be restored with the aid of a widely used treatment against diabetes, based on sitagliptin. to achieve these targets, three groups of male 10-week old wistar rats were used (control, diabetic and diabetic treated with sitagliptin). taking into account that some of the findings of the experimental protocol (especially the ones concerning the relation between geometric characteristics and mechanical properties) could be considered as “unexpected”, an attempt to gain deeper insight into the role of t2dm and sitagliptin is undertaken. in this direction two critical geometrical characteristics of the femora, i.e., the cross-sectional area and the second principal moments of area, were considered against the respective average value of the weight of the animals of the three groups. the results of this correlation are plotted in figs.8a for the cross sectional area and in fig.8b for the second moment of area. it is definitely concluded that t2dm significantly contributes to loss of weight of the sufferers. treating them with sitagliptin increases further the loss of weight as it is also mentioned by other researchers [16, 17]. similarly, t2dm decreases the second moments of area. sitagliptin does not reverse this trend. 0 70 140 210 0.0 0.2 0.4 0.6 0.8 l o ad [ n ] deflection [mm] mts video-extensometer 0 70 140 210 0.0 0.2 0.4 0.6 l o ad [ n ] deflection [mm] c d d-s t s. k. kourkoulis et alii, frattura ed integrità strutturale, 51 (2020) 127-135; doi: 10.3221/igf-esis.51.10 134 (a) (b) figure 8: the average weight of the animals of the three groups versus the respective average value of (a) the femora’s cross-sectional area and (b) the femora’s principal second moments of area. at this point it is obvious that a kind of paradox comes into fora: while the geometrical characteristics of diabetic bone tissue are considerably downgraded, the respective load carrying capacity increases. obviously this controversial behaviour cannot be explained on purely engineering terms. histopathological studies, in parallel with the respective biomechanical ones, seems to be “sine qua non” in order to clearly understand the damage mechanisms activated by t2dm. concluding remarks he basic conclusions drawn from this study can be categorized into two groups, i.e., one concerning the geometrical features of the critical cross section of the femora and a second one concerning the mechanical properties of the specific bone as a structure under mechanical load. concerning geometry, it was concluded that the cross-sectional area of diabetic femora is almost 16% smaller compared to that of the control bones. moreover, the bone of diabetic animals is about 13% thinner than that of the control ones. for the diabetic animals treated with sitagliptin the cross-sectional area and the thickness of the bone are even smaller compared to the respective quantities of diabetic rats. concerning the mechanical properties and parameters, it is to be accepted that some of the conclusions drawn from the present protocol are not in full accordance with what was perhaps expected. namely, the fact that the femora of diabetic animals sustain 7% higher load with respect to that of the control group, was, indeed, somehow unexpected. one could anticipate that this increase could be just the result of increased cross-sectional area (or increased second moment of area) of the femora of diabetic rats, but this is not the case. expressing the fracture load in terms of the respective normalized quantity (ultimate normal bending stress or bending strength) provides even more surprising results: the bending strength of the femora of the diabetic animals appears almost 27% higher than that of the femora of the animals of the control group. along the same lines, it seems that diabetes mellitus increases the stiffness (about 16%) of the bone tissue with respect to that of the control animals. again, sitagliptin does not bring things in their initial status (i.e., to that of the control group): although the bone tissue stiffness of animals treated with sitagliptin is almost 4% lower compared to that of the diabetic animals it is still almost 12% higher compared to that of the control animals. the above conclusions may sound peculiar but this is not the first time that similar findings are reported in international literature. for example prisby et al. [11], as well as reinwald et al. [12], observed a similar behaviour. on the contrary, other researchers have reported opposite experimental results indicating either negative role of t2dm on bone quality [13, 14] or negligible influence [12, 15]. in any case, it is beyond discussion that the role of t2dm on the quality of the bone tissue must be further studied before definite conclusions are drawn. the current consensus in the medical community is that patients with t2dm have 40-70% increased fracture risk (which in terms of mechanics of materials could be translated to increased brittleness); however, their bone mineral density is normal or increased (which, again in terms of mechanics of materials could be translated to increased bending strength). this suggests that there are other factors besides bone quality that affect bone fragility. it is here mentioned that this is not the case for patients with type i diabetes, who are characterized by low bone mineral density and a six-fold increased fracture risk, implying that chronic hyperglycemia is not the main pathophysiological mechanism 6.0 6.5 7.0 7.5 8.0 0.50 0.55 0.60 0.65 c ro ss -s ec ti o n al a re a [m m 2 ] weight [kg] c d d-s 4 8 12 16 0.50 0.55 0.60 0.65 i [m m 4 ] weight [kg] c d d-s i max i min y=11.99x+0.26 y=5.92x+2.56 y=20.54x-0.16 t s. k. kourkoulis et alii, frattura ed integrità strutturale, 51 (2020) 127-135; doi: 10.3221/igf-esis.51.10 135 of increased fracture risk in diabetic patients [4, 5]. the above consensus concerning brittleness was definitely supported by the present protocol. indeed, it was indicated that the deflection at the maximum load of the diabetic femora was 13% smaller compared to that of the control group. unfortunately, it was concluded (also beyond any doubt) that sitagliptin does not cure the problem of increased brittleness of diabetic bone tissue. references [1] nauck, m.a. and meier, j.j. (2018). incretin hormones: their role in health and disease, diabetes obes. metab., 20, pp. 5–21. doi: 10.1111/dom.13129. [2] janghorbani, m., van dam, r.m., willett, w.c. and hu, f.b. (2007). systematic review of type 1 and type 2 diabetes mellitus and risk of fracture. am. j. epidemiol., 166, pp. 495–505. doi: 10.1093/aje/kwm106. [3] napoli, n., chandran, m., pierroz, d.d., abrahamsen, b., schwartz, a.v., ferrari, s.l. and iof bone and diabetes working group (2017). mechanisms of diabetes mellitus-induced bone fragility, nat. rev. endocrinol., 13, pp. 208– 219. doi: 10.1038/nrendo.2016.153. [4] hofbauer, l.c., brueck, c.c., singh, s.k. and dobnig, h. (2007). osteoporosis in patients with diabetes mellitus, j. bone miner. res., 22, pp. 1317–1328. doi: 10.1359/jbmr.070510. [5] napoli, n., strotmeyer, e.s., ensrud, k.e. et al. (2014). fracture risk in diabetic elderly men: the mros study, diabetologia, 57, pp. 2057–2065. doi: 10.1007/s00125-014-3289-6. [6] purnamasari, d., puspitasari, m.d., setiyohadi, b., nugroho, p. and isbagio, h. (2017). low bone turnover in premenopausal women with type 2 diabetes mellitus as an early process of diabetes-associated bone alterations: a crosssectional study, bmc endocr. disord., 17, article number: 72. doi: 10.1186/s12902-017-0224-0. [7] krakauer, j.c., mckenna, m.j., buderer, n.f., rao, d.s., whitehouse, f.w. and parfitt, a.m. (1995). bone loss and bone turnover in diabetes, diabetes, 44, pp. 775–782. doi: 10.2337/diab.44.7.775. [8] biewener, a.a. (1982). bone strength in small mammals and bipedal birds: do safety factors change with body size?, j. exp. biol., 98, pp. 289–301. [9] yabe, d. and seino, y. (2013). incretin actions beyond the pancreas: lessons from knockout mice, curr. opin. pharmacol., 13, pp. 946–953. doi: 10.1016/j.coph.2013.09.013. [10] kourkoulis, s.k., kouvaka, a., andriakopoulou, ch. and dontas, i. (2016). an alternative approach for the interpretation of data from three-point bending of long bones, engineering transactions, 64(4), pp. 401–407. [11] prisby, r.d., swift, j.m., bloomfi eld, s.a., hogan, h.a. and delp, m.d. (2008). altered bone mass, geometry and mechanical properties during the development and progression of type 2 diabetes in the zucker diabetic fatty rat, j endocrinol., 199(3), pp. 379–388. doi: 10.1677/joe-08-0046. [12] reinwald, s., peterson, r.g., allen, m.r. and burr, d.b. (2009). skeletal changes associated with the onset of type 2 diabetes in the zdf and zdsd rodent models, am. j. physiol. endocrinol. metab., 296(4), pp. e765–774. doi: 10. 1152/ajpendo.90937.2008. [13] gallant, m.a., brown, d.m., organ, j.m. et al. (2013). reference-point indentation correlates with bone toughness assessed using whole-bone traditional mechanical testing, bone, 53(1), pp. 301–305. doi: 10.1016/j.bone.2012.12.015. [14] hamann, c., rauner, m., höhna, y. et al. (2013). sclerostin antibody treatment improves bone mass, bone strength, and bone defect regeneration in rats with type 2 diabetes mellitus, j. bone miner. res., 28(3), pp. 627–638. doi: 10. 1002/jbmr.1803. [15] hill gallant, k.m., gallant, m.a., brown, d.m. et al. (2014). raloxifene prevents skeletal fragility in adult female zucker diabetic sprague-dawley rats, plos one, 9(9), e108262. doi: 10.1371/journal.pone.0108262. [16] gül, ö.ö., kıyıcı, s., ersoy, c. et al. (2011). effect of sitagliptin monotherapy on serum total ghrelin levels in people with type 2 diabetes, diabetes res. clin. pr., 94(2), pp. 212–216. doi: 10.1016/j.diabres.2011.07.031. [17] yanai, h., adachi, h., hamasaki, h. et al. (2012). effects of 6-month sitagliptin treatment on glucose and lipid metabolism, blood pressure, body weight and renal function in type 2 diabetic patients: a chart-based analysis, j. clin. med. res., 4(4), pp. 251-258. doi: 10.4021/jocmr975w. << /ascii85encodepages false /allowtransparency false /autopositionepsfiles true /autorotatepages /none /binding /left /calgrayprofile (dot gain 20%) /calrgbprofile (srgb iec61966-2.1) /calcmykprofile (u.s. web coated \050swop\051 v2) /srgbprofile (srgb iec61966-2.1) /cannotembedfontpolicy /error /compatibilitylevel 1.4 /compressobjects /tags /compresspages true /convertimagestoindexed true /passthroughjpegimages true /createjobticket false /defaultrenderingintent /default /detectblends true /detectcurves 0.0000 /colorconversionstrategy /cmyk /dothumbnails false /embedallfonts true /embedopentype false /parseiccprofilesincomments true /embedjoboptions true /dscreportinglevel 0 /emitdscwarnings false /endpage -1 /imagememory 1048576 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/hrv (za stvaranje adobe pdf dokumenata najpogodnijih za visokokvalitetni ispis prije tiskanja koristite ove postavke. stvoreni pdf dokumenti mogu se otvoriti acrobat i adobe reader 5.0 i kasnijim verzijama.) /hun 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can be opened with acrobat and adobe reader 5.0 and later.) >> /namespace [ (adobe) (common) (1.0) ] /othernamespaces [ << /asreaderspreads false /cropimagestoframes true /errorcontrol /warnandcontinue /flattenerignorespreadoverrides false /includeguidesgrids false /includenonprinting false /includeslug false /namespace [ (adobe) (indesign) (4.0) ] /omitplacedbitmaps false /omitplacedeps false /omitplacedpdf false /simulateoverprint /legacy >> << /addbleedmarks false /addcolorbars false /addcropmarks false /addpageinfo false /addregmarks false /convertcolors /converttocmyk /destinationprofilename () /destinationprofileselector /documentcmyk /downsample16bitimages true /flattenerpreset << /presetselector /mediumresolution >> /formelements false /generatestructure false /includebookmarks false /includehyperlinks false /includeinteractive false /includelayers false /includeprofiles false /multimediahandling /useobjectsettings /namespace [ (adobe) (creativesuite) (2.0) ] /pdfxoutputintentprofileselector /documentcmyk /preserveediting true /untaggedcmykhandling /leaveuntagged /untaggedrgbhandling /usedocumentprofile /usedocumentbleed false >> ] >> setdistillerparams << /hwresolution [2400 2400] /pagesize [612.000 792.000] >> setpagedevice microsoft word numero_30_art_24 j. toribio et alii, frattura ed integrità strutturale, 30 (2014) 182-190; doi: 10.3221/igf-esis.30.24 182 focussed on: fracture and structural integrity related issues evolution of crack paths and compliance in round bars under cyclic tension and bending j. toribio, j.c. matos, b. gonzález, j. escuadra university of salamanca, spain toribio@usal.es abstract. the aim of this paper is to calculate how the surface crack front and the dimensionless compliance evolve in cracked cylindrical bars subjected to cyclic tension or bending with different initial crack geometries (crack depths and aspect ratios). to this end, a computer application (in the java programming language) that calculates the crack front’s geometric evolution and the dimensionless compliance was made by discretizing the crack front (characterized with elliptical shape) and assuming that every point advances perpendicularly to the crack front according to the paris law, and using a three-parameter stress intensity factor (sif). the results show that in fatigue crack propagation, relative crack depth influences more on dimensionless compliance than the aspect ratio, because the crack front tends to converge when the crack propagates from different initial geometries, showing greater values for tension than for bending. furthermore, during fatigue crack growth, materials with higher values of the exponent of the paris law produce slightly greater dimensionless compliance and a better convergence between the results for straight-fronted and circular initial cracks. keywords. cracked round bar; numerical modelling; paris law; fatigue crack growth; dimensionless compliance. introduction he problem of fatigue crack propagation in round bars is of great interest in fracture mechanics, applied to linear structural elements. these components, usually subjected to oscillating load, may fracture after surface fatigue crack growth, frequently with semi-elliptical flaws contained in a plane perpendicular to the loading axis. several criteria have been stated in the past to characterize fatigue crack growth in these geometries, e.g., prediction of the 90º intersecting angle of the crack with the surface or the iso-k criterion along the crack front [1]. the most used are those based on the paris-erdogan law [2-6], requiring the knowledge of the dimensionless stress intensity factor (sif), y, along the crack front in the round cracked bar. it has been deducted by several authors following different procedures: compliance methods, finite element analysis, boundary integral equation methods, experimental techniques, etc. [1, 7-10]. dimensionless compliance in round cracked bars under tension or bending depends on the crack geometry. if the crack is characterized by an elliptical shape, there are two factors exerting influence: the relative crack depth (crack depth divided by the diameter), which causes an increase of its value, and the aspect ratio (ratio between the crack depth and the other semiaxis of the ellipse), which causes a decrease of its value [3, 11]. thus, there is a relation between the change in compliance during fatigue crack growth and the crack geometry evolution, depending on the specimen material, the initial crack geometry and the type of applied load [10, 12]. t j. toribio et alii, frattura ed integrità strutturale, 30 (2014) 182-190; doi: 10.3221/igf-esis.30.24 183 numerical modelling computer program in the java programming language was developed to determine the geometrical evolution of the crack front according to the paris law, for a transverse surface crack in a cylindrical geometry subjected to cyclic tension loading or cyclic bending moment (fig. 1). this would be the basis to determine the change taking place in the dimensionless compliance of the round bar during the fatigue crack propagation process. figure 1: cracked bar under tension loading (left) and bending moment (right). aspect ratio the basic hypothesis of the modelling consisted of assuming that the crack front can be modelled as an ellipse with centre on the bar surface [12] and the fatigue propagation takes place in a direction perpendicular to this crack front, following a paris-erdogan law [13],   m d d a c k n (1) every elliptical arc of the crack front was divided in z segments with exactly the same length using the simpson’s rule in order to discretize the front. the point on the round bar surface was not taken into account, since it presents some difficulties regarding the computation of the dimensionless sif (there is a plane stress state on the crack surface). after that, every single point was shifted according to the paris-erdogan law perpendicular to the front and so as to keep constant the maximum crack depth increment, δa(max) ≡ max δai, all over the process [6]. the advance of every front point, δai, can be obtained from the maximum crack increment and the ratio of the dimensionless sifs, i          m i (max) (max) y a a y (2) the newly obtained points, fitted by the least squares method, generate a new ellipse with which the process is repeated iteratively until the desired crack depth is reached. due to the existing symmetry, only half of the problem was used for the computations. dimensionless sif the dimensionless sif, y, depends on three-parameters for the crack modelled as an ellipse with centre on the round bar surface and its value depends on the crack geometry (depth and aspect ratio) and on the point on the front where it is calculated. the dimensionless sif used in the computations is that proposed by shin and cai [10] obtained by the finite element method and the virtual crack extension technique, whose value is function of the relative crack depth a/d, the crack aspect ratio a/b, and the position of the point considered on its front x/h (fig. 2). figure 2: elliptical crack model used by shin and cai. a j. toribio et alii, frattura ed integrità strutturale, 30 (2014) 182-190; doi: 10.3221/igf-esis.30.24 184 the fitting of the results provides a three-parametrical expression which is defined as a function of the coefficients mijk for tension with free sample ends [10], i.e., unrestrained bending during tension, i j k ijk                       i j k 2 7 2 0 0 0 a a x y m b d h (3) and the coefficients nijk for bending [10], i j k ijk                       i j k 2 6 2 0 0 0 a a x y n b d h (4) dimensionless compliance experimentally the geometrical evolution of the crack front in a cylindrical bar can be observed post mortem (once fractured) and there are several techniques to mark the front according to the material studied. it is possible to relate the crack front geometry with compliance, one of the few characteristics which can be measured during the crack propagation [14]. if tensile load is applied, it is obtained that the local displacement u is related to the applied force f through compliance λ as follows: u λf (5) if bending is applied, in this case the angle φ is related to the applied moment m through compliance λ as follows: φ λm (6) the strain energy u can be expressed taking into account the equivalence between the energy release rate g and the sif in plane strain k, 2 2(1 ) d d d k ν u g a a e    (7) where v is the poisson coefficient and da the differential of the cracked area. on the other hand, the strain energy for a cracked bar subjected to tensile load is, introducing the value du from eq. (5), 2 1 1 d d d 2 2 u f u f λ  (8) and the strain energy for a cracked bar subjected to bending is, introducing the value du from the eq. (6), 2 1 1 d d d 2 2 u m φ m λ  (9) the sif in plane strain for the geometry of the study can be obtained as follows: πk yσ a (10) where the stress σ for axial tension is calculated as: 2 4 π f σ d  (11) and the maximum stress σ for bending is calculated as: 3 32 π m σ d  (12) if equations for strain energy are made equal and introducing values k and σ, the isolated compliance is obtained for tension loading:  2 2 4 0 32 1 d π aν λ y a a d e   (13) and for bending moment, j. toribio et alii, frattura ed integrità strutturale, 30 (2014) 182-190; doi: 10.3221/igf-esis.30.24 185  2 2 6 0 2048 1 d π aν λ y a a d e   (14) solving the integral which appears in eq. (13) and (14) is not trivial. in order to achieve that, the cartesian coordinates (x, y) were change into parametrical coordinates (a, θ), relating themselves through the expressions: cosx b θ (15) siny a θ (16) where the correspondence between angles δ and θ, deducted from fig. 3, is as follows, tan tan y a δ θ x b   (17)   b h y x figure 3: relationship between δ and θ angles. the differential of the ellipse area modelling the crack advance is:  d d da x y (18) differentiating the coordinates (x, y) according to the new coordinates (a, θ), d ( )cos d sin dx b a θ a b θ θ (19) d sin d cos dy θ a a θ θ  (20) and substituting these expressions on the eq. (18), it is obtained:  2 2d ( )cos sin d da ab a θ b θ a θ   (21) the problem that arises in calculating eq. (21) can be found in the previous knowledge of the variation of the parameter b with the crack depth a. the definition of the derivative at a point can be used to this purpose, ( ) ( ) ( ) b a a b a b a a      (22) introducing eq. (21) in eq. (13), that allows the computation of the compliance in a cracked round bar subjected to axial tensile loading, it is obtained:     0 2 π/2 2 2 2 4 cos 64 1 ( )cos sin d d π h a b ν λ y a ab a θ b θ θ a d e    a (23) introducing eq. (21) in eq. (14), which allows calculating compliance in a cracked round bar subjected to bending loading, it is obtained: j. toribio et alii, frattura ed integrità strutturale, 30 (2014) 182-190; doi: 10.3221/igf-esis.30.24 186     2 π/2 2 2 2 3 0 cos 4096 1 ( )cos sin d d π a h a b ν λ y a ab a θ b θ θ a d e    (24) where f is defined as the dimensionless compliance due to tensile or bending load:   π/2 2 2 2 3 0 cos ( )cos sin d d a h a b a f y ab a θ b θ θ a d    (25) the dimensionless compliance value can be calculated incrementally with the crack growth, where the integral, i 1 i π/2 cos d d a i ha a b f r θ a      (26) it is solved using the trapezoidal rule (where r is the corresponding expression according to eq. (25)), following the scheme on fig. 4, dividing every crack increment in eight parts for half of the problem, so they correspond with the coordinate’s isolines (a, θ). (i,j) (i,j+1) (i+1,j) (i+1,j+1) a  i+1 a i j  j+1 figure 4: divisions with the isolines used in the trapezoidal rule. the compliance increment in every crack advance is calculated using the following expression,                       = 7 8 7 i 1 i j 1 j 0 , , 1 1, 1, 1 ,7 1,7 ,84 2 3i j r i j r i j r i j r i j r i r i r iθ θ f a a θ θ                   (27) in order to obtain the dimensionless compliance of the initial crack, the process is similar to that just described, but easier, because it considers that every previous crack front has the same aspect ratio as the initial one. numerical results and discussion fatigue cracking paths he study of the convergence was performed to obtain the number of segments in which each ellipse is divided, z=14, and the value of the maximum crack increase, δa(max)=d/1000. the geometrical evolution of the crack front, characterized as part of the ellipse, was determined for every relative crack depth, a/d, through the aspect ratio, a/b, for materials with paris exponent m=2, 3 and 4, starting from different initial crack geometries (corresponding to the beginning of each curve) under cyclic tension loading and cyclic bending moment (figs. 5 to 7). under fatigue loading, different initial crack configurations tend to a preferential path (in a plot a/b-a/d), the convergence being faster for higher values of the m coefficient of the paris law and greater for the bending loading than for the tensile loading. when subjected to bending, growth curves generally present lower values for the a/b parameter than under tension, with the exception of the deepest cracks growing from an initial crack aspect ratio (a/b)0≈0. if the initial crack is circular, the aspect ratio a/b diminishes with the crack growth, whereas when the initial crack is quasi-straight, the aspect ratio a/b increases at the beginning and decreases later (with the exception of initially deep cracks with (a/d)0≈0.5, where the aspect ratio a/b always increases), cf. figs. 5 to 7. it is observed that results depend on the exponent of the paris law, so that for m=2 and m=3 the crack fronts are more distant between them than for m=3 and m=4, where the m=3 front is between m=2 and m=4. in the case of growth from circular initial cracks, the maximum discrepancy with regard to the crack fronts appears for intermediate cracks (a/d~0.5), a/b being lower for higher values of m-exponent in the paris law. in the case of growth from quasi-straight initial cracks, the maximum discrepancy in t j. toribio et alii, frattura ed integrità strutturale, 30 (2014) 182-190; doi: 10.3221/igf-esis.30.24 187 the matter of the crack fronts appears for short ((a/b)0~0.3) and long ((a/b)0~0.7) cracks, whereas for intermediate ((a/b)0~0.5) cracks the results for different paris coefficient m almost match. for short cracks a/b is higher for greater m; whereas for long cracks a/b is higher for lower values of m (again with the exception of initially deep cracks with (a/d)0≈0.5). dimensionless compliance the evolution of the dimensionless compliance f during fatigue crack propagation is shown in figs. 8 to 10, for different initial crack depths, initial crack aspect ratios (quasi-straight front and circular front), and different loading conditions (tension and bending). in cracked cylindrical bars, dimensionless compliance f depends on the loading conditions, on the relative crack depth a/d and on the crack aspect ratio a/b. during fatigue crack growth starting from different initial crack geometries, it is observed how the dimensionless compliance f increases with the relative crack depth a/d and how the influence of the crack aspect ratio a/b is lower as the crack grows, due to the marked geometrical convergence taking place for the deepest cracks, in which the compliance reaches the highest values. the dimensionless compliance f for initially quasi-straight cracks is approximately twice than that for initially circular crack, both being really small at the beginning (initial cracks) and increasing clearly and approaching between them under fatigue. the dimensionless compliance f in the cracked bars is higher under tensile loading than under bending moment, the ratio being as high as five for the deepest cracks of the present analysis (a/d=0.7). the f-a/d plots starting from an initially circular crack front and from an initially quasi-straight crack front are closer when (i) the applied load is bending instead of tension, (ii) the exponent m of the paris law is higher, (iii) the initial crack depth (a/d)0 is lower. furthermore, during fatigue crack growth, materials with higher values of the paris parameter m produce slightly greater dimensionless compliance. 0.0 0.2 0.4 0.6 0.8 1.0 0.0 0.2 0.4 0.6 0.8 1.0 a/d a/ b m=2 0.0 0.2 0.4 0.6 0.8 1.0 0.0 0.2 0.4 0.6 0.8 1.0 m=2 a/d a/ b figure 5: evolution of the aspect ratio a/b with crack growth (represented by the relative crack depth a/d) for m=2, starting from different initial crack geometries under tension loading (left) and bending moment (right). 0.0 0.2 0.4 0.6 0.8 1.0 0.0 0.2 0.4 0.6 0.8 1.0 m=3 a/d a/ b 0.0 0.2 0.4 0.6 0.8 1.0 0.0 0.2 0.4 0.6 0.8 1.0 m=3 a/d a/ b figure 6: evolution of the aspect ratio a/b with crack growth (represented by the relative crack depth a/d) for m=3, starting from different initial crack geometries under tension loading (left) and bending moment (right). j. toribio et alii, frattura ed integrità strutturale, 30 (2014) 182-190; doi: 10.3221/igf-esis.30.24 188 0.0 0.2 0.4 0.6 0.8 1.0 0.0 0.2 0.4 0.6 0.8 1.0 m=4 a/d a/ b 0.0 0.2 0.4 0.6 0.8 1.0 0.0 0.2 0.4 0.6 0.8 1.0 m=4 a/d a/ b figure 7: evolution of the aspect ratio a/b with crack growth (represented by the relative crack depth a/d) for m=4, starting from different initial crack geometries under tension loading (left) and bending moment (right). 0.0 0.4 0.8 1.2 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 (a/b) 0 =0.08 (a/b) 0 =1.00 a/d f m=2 0.0 0.1 0.2 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 (a/b) 0 =0.08 (a/b) 0 =1.00 m=2 a/d f figure 8: evolution of the dimensionless compliance f with crack growth (represented by the relative crack depth a/d) for m=2, starting from different initial crack geometries under tension loading (left) and bending moment (right). 0.0 0.4 0.8 1.2 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 (a/b) 0 =0.08 (a/b) 0 =1.00 m=3 a/d f 0.0 0.1 0.2 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 (a/b) 0 =0.08 (a/b) 0 =1.00 m=3 a/d f figure 9: evolution of the dimensionless compliance f with crack growth (represented by the relative crack depth a/d) for m=3, starting from different initial crack geometries under tension loading (left) and bending moment (right). j. toribio et alii, frattura ed integrità strutturale, 30 (2014) 182-190; doi: 10.3221/igf-esis.30.24 189 0.0 0.4 0.8 1.2 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 (a/b) 0 =0.08 (a/b) 0 =1.00 m=4 a/d f 0.0 0.1 0.2 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 (a/b) 0 =0.08 (a/b) 0 =1.00 m=4 a/d f figure 10: evolution of the dimensionless compliance f with crack growth (represented by the relative crack depth a/d) for m=4, starting from different initial crack geometries under tension loading (left) and bending moment (right). conclusions he following conclusions have been drawn from this work regarding the evolution of crack paths and compliance in round bars under cyclic tension or cyclic bending:  according to the paris-erdogan law, in fatigue propagation the different initial crack geometries tend to a unique path on the a/b vs. a/d plot, this convergence being faster for higher coefficients m of paris and quicker for bending than for tension loading.  with quasi-circular initial geometries, the crack aspect ratio a/b diminishes with the crack growth, whereas when the initial crack is quasi-straight, the aspect ratio increases at the beginning and decreases at the end (with the exception of initially deep crack).  in fatigue crack propagation, relative crack depth a/d influences more on dimensionless compliance f than the aspect ratio a/b, because the crack fronts tend to converge as the cracks propagate from different initial geometries.  the f-a/d plots starting from an initially circular crack front and from an initially quasi-straight crack front are closer when the applied load is bending, the exponent m of the paris law is higher or the initial crack depth (a/d)0 is lower. acknowledgements he authors wish to acknowledge the financial support provided by the following spanish institutions: micyt (grant mat2002-01831), mec (grant bia2005-08965), micinn (grants bia2008-06810 and bia2011-27870) and jcyl (grants sa067a05, sa111a07 and sa039a08). references [1] carpinteri, a., shape change of surface cracks in round bars under cyclic axial loading, int. j. fatigue, 15 (1993) 21-26. [2] shih, y.-s., chen, j.-j., analysis of fatigue crack growth on a cracked shaft, int. j. fract., 19 (1997) 477-485. [3] couroneau, n., royer, j., simplified model for the fatigue growth analysis of surface cracks in round bars under mode i, int. j. fatigue, 20 (1998) 711-718. [4] lin, x.b., smith, r.a., shape growth simulation of surface cracks in tension fatigued round bars, int. j. fatigue, 19 (1997) 461-469. [5] shin, c.s., cai, c.q., evaluating fatigue crack propagation properties using a cylindrical rod specimen, int. j. fatigue, 29 (2007) 397-405. [6] toribio, j., matos, j.c., gonzález, b., escuadra, j., numerical modelling of crack shape evolution for surface flaws in round bars under tensile loading, eng. fail. anal., 16 (2009) 618-630. [7] astiz, m.a., an incompatible singular elastic element for twoand three-dimensional crack problems, int. j. fract., 31 (1986) 105-124. [8] carpinteri, a., elliptical-arc surface cracks in round bars, fatigue fract. eng. mater. struct., 15 (1992) 1141-1153. t t j. toribio et alii, frattura ed integrità strutturale, 30 (2014) 182-190; doi: 10.3221/igf-esis.30.24 190 [9] levan, a., royer, j., part-circular surface cracks in round bars under tension, bending and twisting, int. j. fract., 61 (1993) 71-99. [10] shin, c.s., cai, c.q., experimental and finite element analyses on stress intensity factors of elliptical surface crack in a circular shaft under tension and bending, int. j. fract., 129 (2004) 239-264. [11] rubio, l., muñoz-abella, b., loaiza, g., static behaviour of a shaft with an elliptical crack, mech. syst. signal process., 25 (2011) 1674-1686. [12] toribio, j., matos, j.c., gonzález, b., escuadra, j., compliance evolution in round cracked bars under tensile fatigue, eng. fract. mech., 78 (2011) 3243-3252. [13] paris, p.c., erdogan, f., a critical analysis of crack propagation laws, j. basic eng., 85d (1963) 528-534. [14] cai, c.q., shin, c.s., a normalized area-compliance method for monitoring surface crack development in a cylindrical rod, int. j. fatigue, 27 (2005) 801-809. microsoft word numero_50_art_40_2615 a. kakaliagos et alii, frattura ed integrità strutturale, 50 (2019) 481-496; doi: 10.3221/igf-esis.50.40 481 focused on the research activities of the greek society of experimental mechanics of materials damage and failure of orban’s gun during the bombardment of constantinople walls in 1453 aristotle kakaliagos senior structural engineer, greece nninis@culture.gr nikolaos ninis civil engineer, greek ministry of culture and sports, athens, greece nninis@culture.gr abstract. in this paper the bombardment of the constantinople theodosian walls by the great cannon of orban is numerically reproduced deploying structural mechanics. overall gun dimensions were assessed based on historical reports, whereby, the gunpowder charge p was estimated at 177 kg, and the gun was placed at 500 m from the inner walls. gun ballistics and effect on target have been evaluated analytically. the analysis has verified orban’s gun muzzle velocity, cannonball trajectory and its effect on constantinople walls by successfully calculating the length of the breach in the wall, referred in historical reports, as well as the cannon ball penetration into soil. the evaluated sound pressure level inside constantinople, produced by the bombard, confirmed the tremendous psychological effect of the cannon’s blast on the city’s population. a numerical effort was made to assess the combined effect of powder chamber internal pressure with associate temperature produced by powder ignition. keywords. bombard damage; medieval gun ballistics. citation: a. kakaliagos, n. ninis, damage and failure of orban’s gun during the bombardment of constantinople walls in 1453, frattura ed integrità strutturale, 50 (2019) 481-496. received: 28.01.2019 accepted: 29.05.2019 published: 01.10.2019 copyright: © 2019 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. introduction t the dusk of the late medieval period, during the first half of the 15th century, guns with enormous proportions appeared in the european battlefields. these guns manufactured by craftsmen originating from the traditional bell manufacturers in europe were called bombards. manning and serving the bombards was a difficult task, demanding excessive use of manpower, logistic and supply train, as well as skilled bombardiers who started rising from the ranks of craftsmen and combatants. those heavy guns were mainly deployed during city sieges, hurling stone cannonballs of very large diameters. rate of fire of those guns was slow and aiming on the target was also cumbersome requiring several trial shots to identify the successful cannonball trajectory. however, when used skillfully, the bombards could catapult stone cannonballs with enormous strike power on the enemy defenses. the bombards often carried names, demonstrative of their tremendous effect, in order to spray fear into the enemy ranks and press negotiations to surrender, well before a http://www.gruppofrattura.it/va/50/2615.mp4 a. kakaliagos et alii, frattura ed integrità strutturale, 50 (2019) 481-496; doi: 10.3221/igf-esis.50.40 482 their deployment. female gun names were typical such, as “dulle griete”, the angry margherit, from the city of ghent in today belgium, casted in 1452, “mons meg” from edinburgh castle in scotland casted in 1449, “griete” from the duchy of burgundy casted in 1431 and “signora amedea”, bombard deployed by the duke of savoy in 1426. occasionally, some bombards carried bizarre names such as “il deluvio”, the downpour, or “non piu parole”, hence, no more talks. the fall of constantinople can be considered as a bench mark in city siege warfare in the european theater of operations. passing the mid of the 15th century, stone throwing bombards were deployed more often in several city sieges in europe. typical example of late medieval siege in italy, is the assault on the fortified position of rocca di castelletto. herein, on may 28, 1464, francesco sforza deployed massively bombard artillery against this position. the bombards “corona”, the crown and “liona”, the lioness, both from pavia, “la bissona”, the bison, of milan, together with “san giorgina” and “golia”, the goliath, both from genova, were deployed. the bombards devastated the heavy wall fortification after only 4 hours of bombardment and opened a wide gap in the fortified wall of 3.6 m thickness (12 piedi romani, an italian foot equals to 0.30 m). the deployment of bombards against roman type fortifications, which typically projected heavy stone walls perpendicular to the enemy attacking effort and line of advance, had catastrophic results on the city defenses, as roman city walls could no more block and repel an attacker. the use of bombards posed a type of asymmetrical threat to fortified positions equipped with roman type fortifications. this threat was to be mastered years later by sébastien marquis de vauban (1633-1707), whose innovative fortification system counterbalanced the strength of the siege artillery. during the siege of constantinople in 1453, a bombard with huge dimensions was deployed. the gun was ordered by sultan mehmet ii and manufactured by orban, a skilled master craftsman from hungary. bombards often tended to explode inflicting severe casualties to friend and foe. the dangerous situation develops during the ignition of the gunpowder placed inside the gunpowder chamber. according to historical reports, orban’s gun had the same fate, killing both orban and the gun crew. the present paper deals with the investigation of the causes who potentially may have led to a fatal failure of orban’s gun. in order to focus on the structural response of the gun powder chamber, as this part of the gun was suspect for potential gun failure, it was necessary to numerically reconstruct the weapon and evaluate gun ballistics and effect on target. the results were compared to contemporary to the siege, byzantine and italian historical reports, thus identifying gun dimensions, gunpowder charge and force capacity of the exploding gunpowder inside the gun chamber. with those factors confirmed, powder chamber structural response was analyzed considering the combined action of blast pressure inside the powder chamber together with associated temperature effects produced by powder ignition. orban’s gun reconstruction verall gun dimensions were assessed on the basis of historical reports and were compared to the existing dardanelles gun at fort nelson museum, u.k (voice of the guns gallery, object number: xix.164), an ottoman bombard casted in 1464. additionally, orban gun dimensions were cross checked using the contemporary to the siege gun classification system proposed by francesco giorgio martini [7]. it was considered that orban’s gun consisted of two parts, casted separately, with the cannon powder chamber shorter than the barrel. the split cannon was assembled insitu after transportation as reported by critovoulos [3]. the gunpowder charge p was estimated at 177 kg, adequate to fire a granite cannonball with a diameter at 752 mm and a corresponding projectile weight b of 600 kg (table 1) see barbaro [1], chalkokondyles [2], critovoulos [3]. information given by the venetian physician n. barbaro [1] (venice, 1420-1494) dealing with size of the cannonball and cannon overall dimensions when compared to numerical results of present paper lead to the conclusion that barbaro had actually measured the size and weight of the cannonballs. based on the geometrical data for orban’s bombard as presented in table 1, it was verified that the ratio of powder chamber thickness t1=648mm to barrel thickness t=200 mm was at a ratio of 3.24, thus, corresponding on the average to 2φ, where φ equals 1.618, the golden ratio. correspondingly, the ratio of total gun length at 9200 mm to barrel length at 5800 mm is close to φ (table 1). lg (mm) l (mm) c (mm) b (kg) p (kg) d (mm) d (mm) d1 (mm) d2 (mm) t (mm) t1 (mm) k (mm) 9200 8552 2752 600 117 752 248 1152 1544 200 648 648 table 1: schematic representation of orban’s bombard and geometrical parameters. o a. kakaliagos et alii, frattura ed integrità strutturale, 50 (2019) 481-496; doi: 10.3221/igf-esis.50.40 483 orban’s gun interior ballistics the force of the expanding gunpowder gas during ignition of the charge creates a force which in turn accelerates the cannonball inside the barrel towards the muzzle. integrating the work produced by the cannon ball running across the barrel and setting this work equal to the projectile kinetic energy, the muzzle velocity is calculated (in m/sec) with eq.(1). herein, r is a factor accounting for the effect of hot gunpowder expanding gases after ignition inside the gunpowder chamber (robins [8], collins [9]). this factor captures the initial ratio of gunpowder chamber hot gas pressure to atmospheric pressure, with the atmospheric pressure set at 101,325 pa. in addition, factor r reflects the quality of the gunpowder, the gunpowder charge compaction and the skill of the gun crew. the dimensionless factor ψ equals 6.13 for granite cannon balls capturing projectile density ρ at 2,700 kg/m3. 12 2 676 1 αψ λ v r lnα β         where: l c   , d d   , l d   (gun caliber) and 𝜓 0.00227𝜌 (1) in the above expression an effective projectile weight was employed, typically corresponding to the original projectile weight increased by one third of the gunpowder weight, with gunpowder density at approximately 881 kg/m3. (taylor [16]). this effective cannonball weight increase models the energy consumption which is required to accelerate the burning powder and hot gas along the barrel as well as the cannonball. the phenomenon was also monitored for the 17th and 18th century smooth bore cannons, with cannon bore and cannonball manufactured with cast iron (collins [9]). it was considered that orban’s gun was manufactured in bronze with granite cannonball ammunition (critovoulos [3]). admittedly, both materials employed differ from cast iron. however, effects such as pronounced gun thermal effects and projectile surface imperfections present in orban’s gun, ultimately decelerated projectile’s forward accelerated motion inside the barrel after ignition. these factors ultimately counterbalanced the associated effects as introduced by cast iron material. it is considered, that under repeated gun firing, residual thermal stresses and corresponding dilatations and/or microdistortions of the cannon bore, may have resulted ultimately in imperfections of the original cannon bore geometry. those factors lead to pronounced contact friction of granite cannonball to internal bore surface. according to historical reports, the gun produced a pronounced increase in temperature along the barrel, effect which in turn, may have resulted in an early explosion of the gun (chalkokondyles [2], phrantzes [6]). it was considered that orban’s gun cannonballs were manufactured by stone masons. this procedure may not necessarily have resulted in an absolutely perfect smooth cannonball surface when compared to cast iron cannonball projectiles. as a result of this, an increased friction would be present at granite cannonball contact to bore internal surface. the deployment of an effective cannonball weight was deemed necessary in order to realistically model gun firing capability. using data from table 1 together with r=1,000, the cannonball muzzle velocity results 216 m/sec with the corresponding time for cannonball exit from bombard bore at 44.8 msec. pressure inside the gunpowder chamber in order to estimate the pressure inside the gunpowder chamber, hence, the factor r from eq.(1), information from full scale gun testing of a medieval cannon was used. the tested gun was a replica of the medieval loshult gun (ho group [12], mclachlan [11]). the loshult gun originating from sweden, was known and apparently used in france with the name “pot de fer” and in italy with the name “vasi”. the gun was tested using early gunpowder recipes from the 14th century with different proportions of saltpeter, firing a 184 g lead ball with 50 g of gunpowder (table 3). using the geometrical properties of the gun the input parameters for eq.(1) were evaluated (table 2). they were used together with the experimentally recorded muzzle velocity to solve eq.(1) for the corresponding r value (table 3). it must be emphasized that the loshult test results were furnished with a total of 19 shots and they should be treated with caution. however, an overall trend is identified where r is increasing when the corresponding saltpetre portion in the gunpowder mix is increased (table 3). considering the fact that the results from table 2 demonstrate the average effectiveness of the 14th century gunpowder recipes, it can be expected that the corresponding r value for orban’s gun could be marginally higher as gunpowder production techniques were further developed in the 15th century. admittedly, powder chamber internal pressure as result of gunpowder ignition is also function of powder chamber volume and propellant characteristics (culver [10]). it was recognized, that for the early 18th century u.k smooth bore guns, muzzle velocities could be evaluated with an r value at approximately 1,500, whereby, for the early 19th century guns, an r value of 1,600 would be appropriate (collins [9]). a. kakaliagos et alii, frattura ed integrità strutturale, 50 (2019) 481-496; doi: 10.3221/igf-esis.50.40 484 lg (mm) l (mm) c (mm) b (g) p (g) d (mm) d (mm) d1 (mm) d2 (mm) t (mm) t1 (mm) k (mm) 300 270 65 184 50 31 36 65 110 22 37 30 table 2: schematic representation of loshult gun and geometrical parameters. powder type year saltpetre kno3 (%) sulphur s (%) charcoal c (%) computed r (---) rouen 1338 50 25 25 127 lille 1340 55.6 22.2 22.2 167 marcus graecus 1350 66.7 11.1 22.2 186 rothenburg 1380 75 12.5 12.5 212 table 3: values of r for different types of 14th century gunpowder mix proportions. aiming to get an estimate for r corresponding to a powder recipe closer to the date of the siege at 1453 it was decided to simulate numerically available information from a 16th century full-scale gun fire test. this would yield chamber pressures corresponding to an improved powder recipe when compared to the recipes originating from the 14th century (table 3). in september 1544, a full-scale gun fire test with a venetian navy cannon was executed in venice close to the church of san niccolò di lido. the bronze gun used in the test was a colubrina bastarda legittima da 50 of caliber 32, firing a 16.4 kg iron cannonball with 13.12 kg gunpowder at 7.5 degrees gun elevation. the gunpowder recipe was according to the venetian recipe 5-asso-asso, corresponding to 71.4% saltpetre, 14.3% sulphur and 14.3% charcoal. finally, engaging the geometrical properties of the cannon together with an r value at 1,550 and eq.(1), the muzzle velocity at 685 m/sec was confirmed (santarini [17]). in general, it was considered that there was a rapid increase of gunpowder quality and associated methods of gunpowder production and handling, as well as a drastic improvement in the procedures for servicing a gun from the 13th century (r=212, table 3) till the 16th century (r=1,550, venice test). on the average it was concluded that the corresponding r value for orban’s gun could be set close to the mean value between 212 and 1,550. consequently, the r value for orban’s gun was estimated approximately at 1,000, realizing that the improvement of gunpowder production and handling was not a linear process over time. the use of r at 1,000, could reflect approximately a saltpeter portion in the gunpowder mix between 66.7 and 75%, together with certain impurities, typically present for the 15th century gunpowder. in the ensuing sections of present paper r was set at 1,000 and the bombarding effect on constantinople wall was evaluated. in general, evaluated bombard ballistics and associated computed effects on target when compared to information from eyewitness historical reports confirmed the use of r at a value of 1,000. orban’s gun external ballistics – cannonball aerodynamics the cannonball trajectory after leaving the barrel can be expressed by newton's equations of motion. herein, an additional drag force fp is acting on the cannon ball as a result of the air resistance to the projectile forward motion. considering the air density ρα=1.225 kg/m3, the instantaneous projectile velocity v, the cannonball diameter d and the aerodynamic drag ca(m), the drag force fp can be computed using eq.(2) as function of the corresponding mach number m. the aerodynamic drag for spherical projectile ca(m) was modelled with eq.(3), valid up to mach 1.5. given the muzzle velocity, the initial position of the gun and the elevation of the barrel, the trajectory of the cannonball is evaluated using a linear step by step numerical procedure with a time integration step of 0.001 sec. this provision was necessary in order to provide a numerically stable trajectory path. muzzle velocity at 216 m/sec was used to evaluate the corresponding cannonball trajectory and resulting cannon range. herein, the average firing position of the gun was set at a. kakaliagos et alii, frattura ed integrità strutturale, 50 (2019) 481-496; doi: 10.3221/igf-esis.50.40 485 1.5 m above ground in order to reflect historical reports (table 4). it was reported that the ottoman combat engineers had constructed a prepared position with a ditch protecting the gun crew having thus potentially placed the gun on an elevated ramp of soil and gravel (phrantzes [6], chalkokondyles [2]). according to doukas [4], on january 1453, orban executed full-scale fire testing of the bombard at sultan’s palace in adrianople with sultan mehmet present. herein, a maximum range of 1 mile was reported which corresponds to 1,479 m, based on agrippa’s imperial roman mile. this result corresponds to the numerically evaluated gun range at 12 degrees cannon elevation (table 4). admittedly, with increasing gun elevation, corresponding range can be increased, however, at 12 degrees gun elevation the maximum effort for the construction of an elevated earth ramp is typically reached, requiring the construction of a 2 m high well compacted earth ramp with associated heavy fixed supports necessary to nail the gun in position and absorb bombard recoil. this reflects the maximum effort siege engineers could deliver. 𝐹 0.393𝜌 𝐶 𝑀 𝑣 𝜋𝑑 (2) 𝐶 𝑀 0.7229𝑀 3.3061𝑀 4.9596𝑀 2.6087𝑀 0.558𝑀 0.4485 (3) cannon elevation maximum ordinate range impact velocity on ground arrival time on ground (deg) (m) (m) (m/sec) (sec) 5 18.41 744 180.43 3.794 8 43.18 1,096 166.65 5.876 10 65.04 1,306 159.28 7.227 gun in firing position 12 90.79 1,498 153.12 8.550 table 4: orban’s gun ballistics. bombardment of constantinople inner walls the bombardment of the constantinople theodosian walls by the great cannon of orban is hereby treated as a full-scale experiment and is numerically reproduced deploying structural mechanics. a ballistic scenario has been adopted in order to check orban’s gun bombarding effect on constantinople inner walls on april 24, 1453, as reported by iskanter [5], who was an eyewitness of the historical events. this procedure was necessary in order to check and verify both muzzle velocity and the r factor, reflecting the pressure rise in the gunpowder chamber (eq.(1)). securing r, would lead subsequently to an assessment of the resulting stress situation in the gunpowder chamber. as reported in the russian chronicle of nestor iskanter, on april 24, 1453, orban’s gun fired twice on the inner wall (iskanter [5]). following the first shot the inner wall started tilting, whereby, after the second shot a large portion of the wall collapsed. herein, the cannonball opened a gap in the wall with the total height of the breach, measured from the ramparts, at 5 fathoms (9.15 m) approximately. iskanter scenario was reconstructed analytically. for this purpose, the canon was placed at a distance of 500 m from the inner walls. the elite condottieri force led by giovanni giustiniani longo (genova 1418-1453 chios) was positioned facing orban’s gun, at the mesotechion wall portion of the theodosian walls and at the saint romanos gate. the selected gun position was outside the range of giustiniani’s genoese crossbowmen, which was estimated at 400 yards from the outer wall ramparts (fig.1). in general, genoese crossbowmen were considered as the most formidable elite unit of the era, capable of firing up to 10-12 shots per minute with armor piercing darts, capable of penetrating all types of armor of the late medieval period. due to this fact, the decision to place the gun outside the range of this weapon but close enough to maintain line of sight to the wall, was justified. according to historical records the ottoman trenches were at very close distance from the walls (chalkokondyles [2]). the ottoman bombard crew, although close to the walls, could only see the upper section of the inner wall, as the line of sight to the lower portion of the inner wall was blocked by the outer wall towers and the paratechion ramparts. a target was selected which still could be spotted from the gun crew (fig.1). using the computer model presented previously, the gun “fired” with the muzzle velocity at 216 m/sec. gun elevation was selected as input variable and several trial shots on the wall were executed in order to identify the appropriate gun elevation adequate to hit the target. there was a very delicate balance in selecting the appropriate gun elevation. the cannonball was cruising at a very low altitude over the outer wall ramparts with high probability to hit the outer wall instead of the target or shoot over the inner wall ramparts. a. kakaliagos et alii, frattura ed integrità strutturale, 50 (2019) 481-496; doi: 10.3221/igf-esis.50.40 486 historical records report that orban’s gun could fire only three up to a maximum of seven shots per day (chalkokondyles [2], iskanter [5]). this situation reflects the effort of the gun crew to identify the appropriate gun elevation. finally, at 4.620 gun elevation the projectile hit the target after 2.47 sec with an impact velocity at 191 m/sec (fig.1). for the successful shot the maximum range was at 680m and the corresponding impact velocity on ground 183m/sec. at target impact, the projectile delivered a total kinetic energy at 11,163 knm, value which is comparable to modern artillery shell ammunition. figure 1: bombardment of constantinople inner walls. lateral resistance and force capacity of inner wall masonry the projectile upon reaching the target can either open a breach in the wall and/or impose a global wall overturning mechanism. considering the large size of the wall it was assumed that the delivered projectile kinetic energy would actually impose a punching shear mechanism on the wall solid (fig.2a). it was realized that the inner wall would have a block masonry outer skin at both exterior wall faces and an inner masonry core. this inner core would consist of natural stone masonry with compacted soil fill. the quality and strength of the outer skin would define the overall wall load capacity and strength. in general, inner wall material properties were addressed deploying eurocode 6 (design of masonry structures) considering a wall structure at category 1. using an average compressive strength for the masonry fb=20 mpa and mortar compressive strength fm=1.0 mpa, the characteristic masonry compressive strength fwk equals 3.5 mpa. the overall wall density was set at 20 kn/m3 approximately. the characteristic masonry shear strength was estimated at fs=0.12 mpa with eq.(4), whereby, σd=0.12 mpa was considered as the mean axial wall compressive stress acting over the total wall thickness. this axial wall stress reflected the dead load effect of the wall solid above cannonball impact area. 𝑓 0.075 0.4𝜎 (4) the constant factor in eq.(4) is taken as the average of the code provisions for masonry shear strength evaluation considering vertical joints with and without mortar. this provision reflects reports, where the strength of the wall fortifications was deteriorating and urgent wall repair and strengthening was required – phrantzes [6]. assuming an impact stress distribution under 450 into the wall solid, the punching shear capacity vm of the inner wall is computed with eq.(5) (fig.2b). setting tw=5 m, d=0.752 m and fs=0.12 mpa the corresponding punching shear capacity yields vm=10,837 kn. 𝑉 𝜋 𝑡 𝑑 𝑡 𝑓 (5) the wall structure would resist the implied force of projectile impact by providing adequate punching shear resistance. in case of overstress, the punching shear cylinder may slide by a certain displacement s towards the wall’s outer surface (fig. 2a). this procedure reflects wall stiffness deterioration due to cannonball impact. during this action, energy would be absorbed due to mobilization of shear sliding mechanisms in the wall between the stone blocks at the contact interface area of punching shear cylinder area to surrounding wall solid. after sliding, the punching shear cylinder may establish a new equilibrium, whereby a reduced punching shear cylinder area shall resist the implied impact force. the reduced punching shear resistance vred was computed with eq.(6). considering energy equilibrium during cannonball impact on the wall together with cannonball mass m and associated impact velocity v yields the required setback s (eq.(7)): a. kakaliagos et alii, frattura ed integrità strutturale, 50 (2019) 481-496; doi: 10.3221/igf-esis.50.40 487 𝑉 𝜋 𝑡 𝑑 𝑡 𝑠 𝑓 (6) 0.5𝑚𝑣 𝑠𝑉 where: 𝑠 0.5𝑡 0.5 𝑡 𝑡 4𝑠∗ and 𝑠∗ (7) (a) (b) (c) figure 2: (a) punching shear cylinder at cannonball impact area; (b) formation of punching shear cylinder; (c) wall breach. the above equations can be used to simulate continuous bombardment on the wall. to do this, in the follow up shots, wall thickness is set equal to the reduced wall thickness and vm in eq.(7) is replaced with vred from the corresponding previous shot. in case wall thickness is reduced at or below 4s* in eq.(7), equilibrium is not produced. this serves as an indication that the projectile has opened a breach in the wall. to simulate the first shot of orban’s gun, input values with tw=5.0 m, d=0.752 m, fs=0.12 mpa, projectile weight b=6.0 kn, g=9.81 m/sec2 and v=191 m/sec were considered. the result of the first shot, calculated with eq.(7), yields: s=1.45 m, vred=7,694 kn and a reduced wall thickness at 3.55 m. it was concluded that after the first shot the outer wall masonry skin was destroyed and the projectile penetrated into the wall solid. considering s=1.45 m as wall load eccentricity in general, this value is close to 1/3 of the wall thickness of 1.67m, where wall stability limit is reached. this result confirms eyewitness report that the wall started tilting after the first shot [5]. to simulate the second shot, wall thickness was set at tw=3.55 m and wall punching shear capacity at vm=7,694 kn. equilibrium was not delivered with eq.(7) and it was concluded that the projectile had opened a breach in the wall (fig. 2c). herein, the total breach height at 8.88m confirms eye witness report, where the height of the breach was at 9.15 m (iskanter [5]). during the procedure of continuous bombardment wall overturning did not occur. the inner wall was considered as cantilever structure, whereby the connection to adjacent towers and associated arching effects were not mobilized. a typical portion of the inner walls between adjacent towers with a mean total length at 50 m was considered. cannonball impact on the wall with a force at 10,837 kn, thus at wall punching shear capacity on the impact area, yields a maximum compressive stress at wall base was at 0.97 mpa. the associated vertical load eccentricity due to imposed overturning moment was at 1.35 m, fair below 1.67 m, which corresponds to the general acceptable wall stability eccentricity limit at 30% of wall thickness. orban’s gun projectile penetration into soil the cannonball would impact on ground and penetrate into soil in case aiming was not appropriate. to simulate this effect, cannonball was treated as a single mass m, punching the ground with an impact velocity v, with soil stiffness simulated by a single translational spring. considering energy equilibrium during cannonball impact on ground together with cannonball weight b, diameter d and soil subgrade modulus ks, projectile penetration into soil δf results with eq.(8): 2 2 2 s f bv πd k δ 2g 4  and 0 5 f s v b δ 0 255 d k . .        (8) during gun fire testing as reported by doukas [4], the cannonball touched down after 1 mile (1479m) and penetrated one fathom into the ground. deploying impact velocity on ground at v=153 m/sec (table 4), b=6.0 kn, g=9.81 m/sec2, d=0.752 m and ks=10,000 kn/m3 for loose sand, δf results at 1.27 m. this result corresponds approximately to one fathom (1.83 m). soil subgrade modulus was selected accordingly to reflect loose soil conditions close to earth surface, such as crop fields with top organic soil layer. a. kakaliagos et alii, frattura ed integrità strutturale, 50 (2019) 481-496; doi: 10.3221/igf-esis.50.40 488 psychological impact sound effect of orban’s gun the peak blast overpressure corresponding to the rise of atmospheric pressure inside the gun was converted to an equivalent sound pressure level pspl measured in db. the sound pressure level pspl was computed at 254 db using the atmospheric pressure patm=101,325 pa together with r=1,000 and p0=2x10-5 n/m2 the reference sound pressure level at zero db (eq.(9)). sound pressure level decay was captured with eq.(10), whereby, l1 is the sound pressure at distance r1 from blast source and l2 the corresponding sound pressure at distance r2 respectively. 𝑃 20 𝑙𝑜𝑔 (9) 𝐿 𝐿 20 𝑙𝑜𝑔 (10) decibel (db) units of sound pressure level are atmospheric decibels and, therefore, do not necessarily express what the listener would experience. however, they serve as indication in order to evaluate a sound impact on the human ear (table 5). sound pressure level at various constantinople locations was computed (fig.3). results confirm reports whereby orban’s gun could be heard even at a distance of 40 stadia (chalkokondyles [2]). sound pressure at st. romanus gate and at the mesotechion portion of the theodosian walls was at 120 db, value extremely high for the human ear (iskanter [5]). in constantinople, sound pressure level was extremely disturbing for the human ear and was in the range of 100-110db, with sound pressure level at aghia sofia at 100 db. it can be understood that people inside the city were afraid and women fainted due to the cannon roar (phrantzes [6], barbaro [1]). sound pressure level (db) effect on human ear 30 totally quiet nighttime in desert 85 beginning of hearing damage, earplugs should be worn 100 normal average car or house stereo at maximum volume 104-107 the beginning of pain at the most sensitive frequency of 2750 hertz 107-114 a very large, powerful portable radio 116 human body begins to perceive vibration in the low frequencies 120 200 front row in rock concert f16 sonic boom 235 earthquake intensity 5 on richter scale table 5: sound pressure level effect on human ear. # location sound pressure level (db) 1 st. romanus gate 120 2 phanarion 108 3 vlachernae palace 106 4 column of marcian 105 5 golden gate 103 6 forum theodosius 102 7 galata tower 101 8 forum constantine 101 9 aghia sofia 100 10 diplokionion 98 11 at 40 stadia, 7.5 km distance from blast 97 figure 3: orban’s gun sound pressure level. a. kakaliagos et alii, frattura ed integrità strutturale, 50 (2019) 481-496; doi: 10.3221/igf-esis.50.40 489 gunpowder chamber structural response he pressure inside the gunpowder chamber due to gunpowder ignition is increasing the atmospheric pressure of 101,325 pa by a factor r (eq.(1)). consequently, the internal pressure q results at 101.325 mpa (14.70 ksi), with r at 1,000. considering the gunpowder chamber as a thick cylinder under internal pressure, maximum stresses result at the inner surface of the cylinder (timoshenko and goodier [13]). herein, for a cylinder without connection to cannon breech, the circumferential stress is at 107 mpa, the radial stress at 101 mpa and the axial stress at 2.7 mpa, respectively. these stresses produce a maximum von mises stress σv at 180 mpa (fig.4). under this plane stress condition, with both cylinder ends capped, the dilatation of the inner gunpowder cylinder surface results at 169 microns and 35 microns at the outer gunpowder cylinder surface, respectively. stress concentration appears at the connection of gunpowder cylinder to cannon breech along the gunpowder cylinder inner perimeter. at this location the circumferential stresses bottleneck in order to further stream into the connected cannon breech solid and typically act locally as shear stresses. as a result of this, the von mises stress peaks at 211 mpa (fig.4). in order to verify the local von mises stress increase at the connection of gunpowder chamber to cannon breech, a finite element computer model under internal pressure was employed. the internal pressure q was set at 101.325 mpa. herein, a 10o cylinder slice was used, with the finite element mesh tuned to yield the theoretically stresses derived previously for a cylinder under internal pressure without connection to cannon breech (figs.4,5a). the model had fixed base supports, whereby 24,026 eight node solid elements and 48,813 nodes were employed. figure 4: gun powder chamber stresses under internal pressure during powder ignition. figure 5: (a) computer model; (b) gunpowder chamber stresses and (c) gunpowder chamber internal surface distortions. t a. kakaliagos et alii, frattura ed integrità strutturale, 50 (2019) 481-496; doi: 10.3221/igf-esis.50.40 490 bombard stress powder chamber connection to breech no yes bronze material strength analytical fem yield tensile von mises stress [mpa] 180 211 219 220 240 fraction to yield 0.81 0.96 0.99 1.0 1.09 table 6: stresses in the gunpowder chamber. the computer model revealed that the maximum von mises stress at gunpowder chamber connection to cannon breech was at 219 mpa (fig.5b, table 6). moving towards the gun muzzle, distortions of bore internal diameter were progressively increasing, reaching the maximum value of 169 microns at 900 mm from cannon breech. this value corresponds to the maximum dilatation of the inner cylinder surface for a cylinder without connection to cannon breech (fig.5c). it was concluded that the maximum von mises stress at the connection of gunpowder chamber internal surface to cannon breech was close to gun material yield strength. herein, ancient bronze material yield strength was considered at 220 mpa with 240 mpa tensile strength, reflecting bronze made up of copper, tin and small amounts of lead. bronze elastic modulus was set at 100,000 mpa and poisson ratio at 0.3. realizing that under internal blast pressure with r set at 1,000 the von mises combined stress is close to bronze yield limit, it was concluded that the rise of atmospheric pressure in the gun powder chamber due to powder ignition could be set at this value, producing ultimately a muzzle velocity at 216 m/sec (eq.(1)). this result is in agreement to the overall firing capacity of smooth barrel guns, as they can deliver a muzzle velocity in the range of 0.3 to 2.0 mach (collins [9]). powder chamber nonlinear response under internal pressure aiming to approach nonlinear effects which potentially could imply a premature failure of the gun, the powder chamber was considered as a thick cylinder under internal pressure, whereby, at the inner portion of the cylinder a plastic zone was formed (fig.6). the plastic-elastic interface is defined by a cylindrical surface of radius rp, which effectively divides the cylinder cross sectional area into two separate adjacent zones, hence, cylindrical rings. in the inner ring, the material is in plastic state and at the outer cylindrical ring, the gun material behaves elastically (liu [15]). the internal blast pressure qp which brings the plastic boundary interface at a certain plastic radius rp is defined with eq.(11). correspondingly, the radial displacement δp at the boundary interface and the associated radial displacement δ at the inner surface of the plastic ring are evaluated with eqs.(12,13), respectively. the resulting radial displacement at any radial distance r from the elastic-plastic boundary zone till gunpowder chamber outer surface is defined with eq.(14). in eqs.(11-14), e is the bronze elastic modulus, σy the corresponding yield stress, poisson’s ratio equals 0.3, whereby, b is the internal powder chamber radius and 𝛼 the external radius respectively (vullo [14]). the elastoplastic push over curve for the unrestrained powder chamber cylinder, hence, without connection to gun breech was evaluated using e=100,000 mpa, σy=220 mpa, with a=772 mm and b=124mm (curve a fig.7). it was identified that the yield pressure for this curve was at 123.67 mpa with corresponding radial displacement δ=206 microns. in general, the stresses in the plastic zone, hence, the circumferential stress σ1 and the radial stress σ2 together with the axial stress σ3 were defined with eqs.(15-17) (vullo [14]). as identified previously in figs.4,5, the von mises combined stress due to gunpowder chamber connection to gun breech was close to yield limit (table 6). to capture this effect a point on the elastic branch of curve a (fig.7) with coordinates qp=101,325 mpa and δ=169 microns adequate to reflect yielding of gunpowder chamber connection to gun breech was identified (fig.7). realizing the fact that a premature local yielding occurs when the powder chamber is connected to gun breech (figs.4,5), it was decided to produce a new curve, hence, curve b, by scaling down the “original” push over curve a by a load factor of 1.22 (fig.7). this load factor reflects the ratio of yielding pressures for the powder chamber with and without connection to the breech, hence, 123,670/101,325=1.22. the developed curve b would use the same elastic path as curve a and enter yield phase at δ=169 microns (fig.7). this procedure was considered adequate for the purposes of present analysis, in order to derive first hand data for the nonlinear powder chamber response with connection to gun breech subjected to blast internal pressure. considering the input from fig.7 it was assumed that the radial displacement δ occurs at a location approximately 900 mm from gun breech, as derived previously, for the elastic case, in fig.5c. push over curve b shall be used subsequently in order to assess the combined action of internal pressure and induced temperature due to powder ignition inside the chamber. a. kakaliagos et alii, frattura ed integrità strutturale, 50 (2019) 481-496; doi: 10.3221/igf-esis.50.40 491 𝑞 √ 𝜎 1 2𝑙𝑛 (11) 𝛿 √ 𝜎 0.4 1.3 (12) 𝛥 𝛿 (13) 𝛿 √ 𝜎 0.4 1.3 (14) 𝜎 √ 𝜎 1 2𝑙𝑛 (15) 𝜎 √ 𝜎 1 2𝑙𝑛 (16) 𝜎 √ 𝜎 2𝑙𝑛 (17) figure 6: plastic zone in gunpowder chamber. figure 7: push over curve gunpowder chamber elastoplastic response under internal pressure. temperature effects in powder chamber during firing of orban’s bombard a significant temperature could develop inside the gun due to gunpowder ignition. depending on the powder burning characteristics, the temperature inside the gun could be expected to rise significantly a. kakaliagos et alii, frattura ed integrità strutturale, 50 (2019) 481-496; doi: 10.3221/igf-esis.50.40 492 over a short period of time, typically within a time window of certain fragments of milliseconds. the maximum developing temperature is related to the adiabatic gas temperature of the hot expanding gases produced during ignition and the gunpowder burning characteristics. in general, the associated temperature profile inside the gun is subjected to an exponential decay over time. the total event of temperature rise in the powder chamber, hence, from the abrupt temperature rise during powder ignition to the temperature drop close to ambient temperature is typically affected by gunpowder chamber volume, charge weight and propellant burning characteristics (bannister et al [18]). assuming that the adiabatic gas temperature is approximately at tm =2,000 k (1,728 oc) and using an ambient temperature ta=20o c, the temperature rise t inside the bombard powder chamber over time t can be approximated with eq.(18). this expression is used to simulate the situation with orban’s gun and compare the resulting effects with corresponding historical reports. 𝑇 𝑇 𝑇 ⁄ 𝑏𝑒𝑓𝑜𝑟𝑒 𝑏𝑢𝑟𝑛𝑖𝑛𝑔 𝑡 𝑡 𝑇 𝐵 𝑎𝑓𝑡𝑒𝑟 𝑏𝑢𝑟𝑛𝑖𝑛𝑔 𝑡 𝑡 𝑡 (18) where: 𝑡 𝐴 𝑡 , 𝑡 𝑡 𝐴⁄ , 𝑡 𝑡 𝐴⁄ , 𝐵 . in the above equation tw is the time window, hence, the estimated total time required for the temperature inside the bombard powder chamber to drop at ambient temperature level. additionally, tb is the estimated time at which the propellant is all burned, tm is a scaled time, te =44.8 msec is the time of cannonball exit from the bombard muzzle, a1, a2 and a3 are constants, whereby, γ =1.36 is the gas effective ratio of specific heats. parameter a1 was selected at 20,000 to set the time window tw at 15 minutes, large enough to monitor the temperature decay. it was considered that a relatively quick burning powder was present. consequently, the time tb was estimated at 8.96 msec with a2=5, time which corresponds approximately to the cannonball travel at 0.5 m inside bore (fig.8a). considering the size of the powder chamber and the total weight of the propellant it was assumed that approximately around time tb the temperature in the powder chamber could be set close to the adiabatic gas temperature. this decision was supported by the method of powder preparation and compaction into the chamber as described in detail in historical reports. herein, the bombard crew compacted extremely well the powder inside the chamber with a piece of wood and used that piece to seal the circular hole entrance to the chamber, using this piece apparently also as a stopper for the exact position of the cannonball inside the barrel (critovoulos [3]). consequently, parameter a3 was set at 2,000 to yield a scaled time tm at 0.00240 msec. the model from eq.(18) kept track of the developed temperature at time tx=2.5sec after ignition, time which corresponds to the time when the cannonball hits the walls. this time marks the termination of the shot and is used as reference to check if the situation was safe for the crew to approach the bombard in order to cool the gun and launch preparations for the next shot. the developed temperature at time tb, when the propellant is all burned, was at 2,018o c dropping significantly at 1,122 o c at time te, when the cannonball exits the muzzle. it should be emphasized that from the time of ignition till time te, at 44.8 msec, the resulting temperatures were substantially higher than the bronze melting temperature at approximately 900 oc. with continuous firing of the weapon this effect would certainly result in wear of the bombard. the resulting temperature at time tx was recorded at 248o c. correspondingly, the recorded temperature after 30 sec from ignition was at 90 oc, at 60 sec around 71 oc and at 5 minutes at ambient temperature (fig.8b). it was realized that a variation of parameter a3 from 2,000 up to 5,000 yields the same picture as presented previously, 1,708 oc temperature at time tb, 207 oc at 2.5 sec and at ambient temperature after 5 minutes. it was noted, that the developed temperature at the end of the shot, hence at time tx, was approximately around 200 oc, a reference value where bronze material properties are not affected by temperature. the picture emerging from the model supports a situation whereby the gun crew could approach the gun almost immediately after firing in order to cool the bombard. after each shot the bombard crew would soak the bombard in oil in an effort to cool the weapon. although the model from eq.(18), shows that the temperature inside the chamber had dropped at ambient temperature after 5 minutes, the amount of heat accumulated inside the powder chamber solid during the firing process would subsequently radiate and propagate towards the exterior chamber surface, hence, producing significant amount of heat. this is supported by the significant average chamber temperature at 3890c as expressed from the temperature impulse from time tb till tx divided by the time interval of approximately 2.5 sec. considering the fact that at time tx the chamber temperature was approximately at 200 oc and the average chamber temperature at 389 0c, as presented previously, it was decided that a temperature in the powder chamber at 200 oc could be addressed as reference temperature. it was considered that this temperature, when combined with powder chamber stresses due to internal pressure, could capture the associated effects of accumulated temperature and heat radiation a. kakaliagos et alii, frattura ed integrità strutturale, 50 (2019) 481-496; doi: 10.3221/igf-esis.50.40 493 towards chamber exterior surface. additionally, the mechanical properties and associated material strength of bronze are not influenced by temperature up to approximately 200 oc. exceeding this temperature, a gradual drop of material strength and properties is expected. (a) (b) figure 8: (a) cannonball velocity inside bombard bore; (b) temperature inside powder chamber. for subsequent evaluation of temperature effects combined with powder chamber stresses due to internal pressure the powder chamber was set conservatively in a condition of steady heat flow. herein, the temperature to is the temperature of the inner surface of the chamber cylinder, whereby, the temperature on the outer surface is set at zero. to is set at 200 oc as evaluated previously and reflects the temperature difference between the temperature at the end of the event and the ambient temperature at 20 oc. in this situation the temperature t at any point inside the powder chamber solid, with distance r from the center of the cylinder is expressed with eq.(19), whereby the resulting tangential stress σ1, radial stress σ2 and axial stress σ3 are evaluated with eqs.(20-22), with poisson’s ratio ν=0.3 and coefficient of linear expansion for bronze αt=20×10-6 oc-1 (timoshenko and goodier [13]). the corresponding radial displacement δt at any point located at a certain radial distance r can be evaluated with eq.(23) (vullo [ 14]): 𝑇 ⁄ 𝑙𝑛 where: 𝑏 𝑟 𝑎 (19) 𝜎 ⁄ 1 𝑙𝑛 1 𝑙𝑛 (20) 𝜎 ⁄ 𝑙𝑛 1 𝑙𝑛 (21) 𝜎 ⁄ 1 2𝑙𝑛 𝑙𝑛 (22) 𝛿 ⁄ 1 𝜈 𝑙𝑛 𝑙𝑛 1 2𝜈 (23) the von mises combined stress resulting from the individual chamber temperature stresses from eqs.(20-21) was evaluated in fig.9. herein, the situation at 200 oc yields a significant plastic zone extending from 286 mm till chamber exterior surface. this effect is marginally pronounced at temperature 400 oc, a value close to the average temperature at 389 oc evaluated previously. with the cooling effort by the bombard crew, the von mises combined stress would gradually drop from 200 oc, the temperature after the shot at 2.5 sec, thus, effectively bringing the developed combined stress below yield at 100 oc (fig.9). a. kakaliagos et alii, frattura ed integrità strutturale, 50 (2019) 481-496; doi: 10.3221/igf-esis.50.40 494 figure 9: temperature effect on gunpowder cylinder – von mises combined stresses powder chamber without connection to gun breech. the temperature stresses used in the combined stress effect from fig.6 were combined with the corresponding stresses from internal pressure in fig.5 and presented in fig.10. the formation of a plastic zone is recorded, extending from 240 mm up to chamber exterior surface (fig.10). as the temperature stresses were evaluated for chamber without connection to the breech, the radial stresses which are typically zero at the internal and external chamber surface, are expected to rise when the corresponding radial constraint is activated to the connected gun breech. this procedure would increase the effect of radial stresses in the evaluation of the von mises combined stress as presented previously with a simultaneous increase of the plastic zone width. it should be emphasized that during the cooling procedure, which is typically executed fast during a battle situation, residual stresses are expected to develop in the powder chamber at the interior and exterior chamber surface. these residual stresses would combine their effect with the subsequent shot, hence, deteriorating the situation as presented in figs.5,10. figure 10: combined effect of internal pressure and temperature – von mises combined stress powder chamber without connection to gun breech. to capture the temperature effect on the chamber considering the connection to cannon breech it was decided to apply a displacement-based procedure. herein, the evaluated radial displacement, as computed with eq.(23) at 200 oc, was used as imposed displacement on the push over curve b from fig.11. the evaluated radial displacement δτ at the inner chamber surface was at 159 microns and 991 mm at the outer surface correspondingly. for ensuing considerations, the average value of evaluated radial displacements was used, hence, at 575 microns. considering the radial displacement at 169 microns due to internal pressure together with the average imposed displacement due to temperature at 575 microns the total displacement results at 744 microns. using this value as imposed displacement in fig.11 the plastic radius rp is at 218 mm with the corresponding stress situation (point 1, fig.11) at curve b close to d/250, thus, yielding a situation where a. kakaliagos et alii, frattura ed integrità strutturale, 50 (2019) 481-496; doi: 10.3221/igf-esis.50.40 495 the chamber is entering the yield plateau of curve b (fig.11). admittedly, the situation described above occurs after one bombard shot. additional gun shots and residual plastic dilatations caused by the combined action of temperature and internal pressure would further push point (1) in fig.11 towards the yield plateau of curve b, hence, increasing the potential of gun failure. after each individual gunshot, unloading would result following a typical unloading stiffness parallel to the original stiffness of the gunpowder chamber. this procedure yields residual plastic deformations of the chamber. herein, the elastic stiffness of the gun can be computed as 101.325 mpa/169 microns, hence, 600 mpa/mm (figs.7,11). in situations where powder chamber dilation exceeds d/500 and after repeated firing of the gun, residual plastic deformations and associated stresses and strains due to combined action of internal pressure and temperature together with successive loading and unloading in the push over curve can contribute to the overall structural deterioration of the gunpowder chamber (curve b, figs.7,11). recognizing the fact that bronze material as produced during the late medieval period could not exhibit a significant strain hardening behavior and considering the effect of imposed dilations due to internal blast combined with temperature, it can be concluded that exceeding deformation limit at d/100 failure of the gun can be expected. admittedly, the situation as presented above actually occurs within a time frame of certain milliseconds. considering the time of cannonball exit from gun bore te at 44.8 msec, the time frame for peak blast pressure occurrence can be roughly estimated at te/100. although this time window is small and strain rate effects can play a role in the whole procedure, in general it is not expected that imposed stresses and strains would not produce effects as presented above. the situation as presented above supports historical reports that the bombard exploded killing both the gun crew and orban himself (phrantzes [6]). figure 11: combined effect of internal pressure and temperature. conclusions he objective of the analysis presented in this paper was to treat the historical records concerning the bombardment of constantinople walls in 1453 as a full-scale numerical experiment. its aim was to verify gun capacity as well as firing strength, check the validity of the corresponding historical records and focus on structural design aspects which potentially may have led to premature bombard failure. orban’s gun dimensions and overall size have been reconstructed numerically based on historical reports. gun ballistics and effect on target have been evaluated analytically. a numerical model was evaluated to assess wall collapse mechanisms during bombardment. the analysis has verified orban’s gun muzzle velocity, cannonball trajectory and its effect on constantinople walls. the analytical results have verified the authenticity of the historical reports and proved that these sources are accurate and correct. the sound effect of orban’s gun has been evaluated numerically. the analysis confirmed the tremendous psychological effect of the cannon’s blast on the city’s population, as mentioned in historical records. the stress situation in the powder chamber under combined action of blast internal pressure and induced temperature due to powder ignition was evaluated. it was identified that combined internal pressure and t a. kakaliagos et alii, frattura ed integrità strutturale, 50 (2019) 481-496; doi: 10.3221/igf-esis.50.40 496 temperature induced residual plastic deformations, which in turn could produce residual stresses in the chamber. as the gun crew tried to cool the bombard within a short period of time, residual stresses were potentially increased. successive firing of the bombard resulted in a continuous deterioration of powder chamber structural response. references [1] barbaro, p.v., niccolò (1856). giornale dell' assedio di costantinopoli 1453, corredato di note e documenti di enrico cornet. vienna, libreria tendler & comp. [2] chalkondyles, l. (1996). a translation and commentary of the demonstrations of histories, h’ (320b [201p] – 403b [214p] translation nikolaos nikoloudis, athens [3] critovoulos, m. (1983). critobuli imbriotae historiae, α’ (17,1 – 72,3), reinsch, d.r. (ed.), corpus fontium historiae byzantinae 22, berlin – new york [4] doukas, m. (1834). byzantine history, ducae historia byzantina, cshb, editor i. bekker, bonnae [5] iskanter, n. (1998). the tale of constantinople of its origin and capture by the turks in the year 1453, editors walter k. hanak and marios philippides, publisher: a. d. caratzas [6] phrantzes, g. (1838). the siege of constantinople, annales georgii phrantzae protovestiarii, bonn [7] martini, f. g. (1841). trattato di architettura, ingegneria e arte militare, torino [8] robins benjamin (1742). new principles of gunnery. london [9] collins, a. r. (2018). smooth bore cannon ballistics, www.arc.id.au [10] culver, r. o. (1972). velocity and pressure effects on projectiles due to variation of ignition parameters. naval postgraduate school, monterey california, december [11] mclachlan, s. (2010). medieval handgonnes, the first black powder infantry weapons, osprey publishing [12] medieval gunpowder research group (2002). the ho experiments, report number 1, september 2002 [13] timoshenko, s.p and goodier, j.n. (1951) theory of elasticity, mac graw hill, 3rd edition [14] vullo, v. (2014). circular cylinders and pressure vessels – stress analysis and design, springer series in solid and structural mechanics 3, springer [15] liu, c. k. (1965). stress and strain distributions in a thick walled cylinder of strain hardening material elasticplastically strained. nasa tn d-2941. washington d. c., august 1965 [16] taylor, w.c., amcp 706-150, interior ballistics of guns, us army material command, 1965, 2-3 & 2-19 [17] santarini, m. (2011). le artiglierie della marina veneta nel xvi secolo. ufficio storico della marina militare, dicembre [18] bannister, e. l., jones, n. r., bagwell, w. d. (1963). heat transfer, barrel temperatures and thermal strains in guns. ballistic research laboratories, maryland. report no 192. << /ascii85encodepages false /allowtransparency false /autopositionepsfiles true /autorotatepages /none /binding /left /calgrayprofile (dot gain 20%) /calrgbprofile (srgb iec61966-2.1) /calcmykprofile (u.s. web coated \050swop\051 v2) /srgbprofile (srgb iec61966-2.1) /cannotembedfontpolicy /error /compatibilitylevel 1.4 /compressobjects /tags /compresspages true /convertimagestoindexed true /passthroughjpegimages true /createjobticket false /defaultrenderingintent /default /detectblends true /detectcurves 0.0000 /colorconversionstrategy /cmyk /dothumbnails false /embedallfonts true /embedopentype false /parseiccprofilesincomments true /embedjoboptions true /dscreportinglevel 0 /emitdscwarnings false /endpage -1 /imagememory 1048576 /lockdistillerparams false /maxsubsetpct 100 /optimize true /opm 1 /parsedsccomments true /parsedsccommentsfordocinfo true 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can be opened with acrobat and adobe reader 5.0 and later.) >> /namespace [ (adobe) (common) (1.0) ] /othernamespaces [ << /asreaderspreads false /cropimagestoframes true /errorcontrol /warnandcontinue /flattenerignorespreadoverrides false /includeguidesgrids false /includenonprinting false /includeslug false /namespace [ (adobe) (indesign) (4.0) ] /omitplacedbitmaps false /omitplacedeps false /omitplacedpdf false /simulateoverprint /legacy >> << /addbleedmarks false /addcolorbars false /addcropmarks false /addpageinfo false /addregmarks false /convertcolors /converttocmyk /destinationprofilename () /destinationprofileselector /documentcmyk /downsample16bitimages true /flattenerpreset << /presetselector /mediumresolution >> /formelements false /generatestructure false /includebookmarks false /includehyperlinks false /includeinteractive false /includelayers false /includeprofiles false /multimediahandling /useobjectsettings /namespace [ (adobe) (creativesuite) (2.0) ] /pdfxoutputintentprofileselector /documentcmyk /preserveediting true /untaggedcmykhandling /leaveuntagged /untaggedrgbhandling /usedocumentprofile /usedocumentbleed false >> ] >> setdistillerparams << /hwresolution [2400 2400] /pagesize [612.000 792.000] >> setpagedevice microsoft word numero_50_art_35_2610 v. kytopoulos et alii, frattura ed integrità strutturale, 50 (2019) 414-422; doi: 10.3221/igf-esis.50.35 414 focused on the research activities of the greek society of experimental mechanics of materials a sem-x-ray assisted experimental approach for the determination of mechanical and thermal load – induced damage in mmcs victor n. kytopoulos, emilios sideridis, john venetis, chrysoula riga department of mechanics, national technical university of athens, 5 heroes of polytechnion avenue, athens, greece victor@central.ntua.gr alexandros altzoumailis school of chemical engineering, national technical university of athens, 5 heroes of polytechnion avenue, athens, greece ajumaily@central.ntua.gr abstract. an experimental technique is presented to evaluate mechanical and thermal load-induced microstructural damage, based on the electron probe micro-analysis (epma) principle, by which certain analytical potentialities of scanning electron microscopy (sem) are used. the aim of the study is to apply this technique in the case of metal matrix composites (mmcs). based on earlier findings it is shown that by this technique the damage-controlled microstructural integrity distribution ahead of an edge-notch under tension is determined with sufficient reliability. to demonstrate this fact two mmcs were tested. dog-bone specimens with an edge notch were subjected to slow tension up to their ultimate stress, the loading process was terminated and the epma technique was applied. the procedure was also applied after sudden cooling of the specimens by immersion in liquid hydrogen. it is shown that the mmc with larger differences between the elastic and plastic constants of the inclusion and the matrix exhibit increased proneness to mechanical and thermal load-induced damage. the findings obtained are discussed on the basis of the dominating combined influence of macro-microscopic mechanical and thermo-elastic stress concentration processes on the matrix-particle interfacial fracture strength. keywords. (micro)-damage; x rays; mmcs; thermal shock-stress; process zone; microstructural integrity. citation: kytopoulos, v.n., sideridis, e. venetis, j., riga, ch.., altzoumailis, a., a sem x-ray assisted experimental approach for the determination of mechanical and thermal load induced damage in metal matrix composites, frattura ed integrità strutturale, 50 (2019) 414422. received: 24.01.2019 accepted: 28.05.2019 published: 01.10.2019 copyright: © 2019 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. introduction odern materials such as aluminum-alloy-based metal matrix composites are the new candidates for a variety of engineering applications. aluminum and its alloys have been used as the main constituent due to their wide application in advanced structural, automotive, aviation, aerospace, marine and defense sectors. the mechan-m http://www.gruppofrattura.it/va/50/2610.mp4 v. kytopoulos et alii, frattura ed integrità strutturale, 50 (2019) 414-422; doi: 10.3221/igf-esis.50.35 415 ical and tribological properties of the matrix material can be improved by adding various reinforcements ranging from very soft materials, like graphite, to high hardened ceramic particulates like sic. in recent years particulate reinforced aluminum-alloy composites have shown significant improvement in tribological properties, including sliding wear, abrasive wear, friction and seizure resistance [1-4]. a problem of major importance, especially in high temperature power and tribological technology, is to record and estimate the development of surface damage in severely mechanically and thermally loaded components made of these materials during service. for instance, in tribological applications [2, 4] due to high level of localization of the micro-cracks or crack-like micro effects mainly at the surface, the ability of a correct recording and estimation of surface damage becomes a challenging task. such recording of damage would make it possible to retain the components in service until replacement is indicated by the damage level approaching a critical value. in this direction, various techniques, like for example sonic inspection, have a long tradition and constitute a strong base in engineering practice of damage control. however, very often micro-cracks and pores, which constitute basic material damage may not be detected or measured by sonic and other non-destructive techniques. in this context, it is noted that today there are several “common” macroscopic techniques for damage control and evaluation working on the macro-and meso-scale level [5, 6]. at the same time, there also exist a lot of advanced physical techniques for surface microanalysis of solids [7-11]. however, very few references could be found in the literature concerning the application of the present sem-epma technique to mechanical and thermal load-induced damage evaluation and characterization of materials [12-14]. in spite of this scarceness, it is to be accepted that convenient combination of this technique with other similar ones [13,1519], could provide valuable relationships between damage and other basic parameters of fracture mechanics such as crack opening displacement (cod), the length of the damage zone etc. therefore, it would be of importance to establish certain complementary experimental techniques for surface damage evaluation and characterization at microscopic level. such a technique, called scanning electron microscopy-aided electron probe microanalysis (sem-epma), was used for this purpose in the present study. earlier attempts in this direction have shown that this technique can be a powerful tool providing valuable information about surface damage at microscopic level [12-14]. therefore, in the present study a further attempt is made to apply an improved version of this technique for a deeper insight into the damage processes to be obtained. in particular, the proper application of this technique on a tensile loaded edge-cracked (notched) specimen was found to allow the evaluation, in a semi quantitative way, of the continuous distribution of mechanical and thermal load-induced micro-damage and hence the description of the microstructural integrity changes, ahead of the notch root. theoretical considerations basic damage aspects he material damage due to quasi-static increase of loading is brought about by the progressive nucleation and growth of microscopic cavities in the materials as a result of its elastic-plastic deformation, and is either elasticbrittle damage or elastic-plastic damage. the microscopic features of the nucleation and growth of such cavities vary significantly depending on the type of material, its macrostructure, the loading conditions, environmental and other factors. the elastic-plastic damage in composite materials is an extremely complicated process originating from the generation of various faults such as matrix cracking, interface degradation, delamination, fiber breakage, fiber-matrix debonding and other processes. this is in contrast to the damage development in geological materials [20] and structures made of geological materials [21] like and metals, where damage under a given loading scheme develops according to a single or a limited number of damage mechanisms. in general, it can be said that the process of gradual loss of integrity of a solid may be attributed to the increasing concentration of micro-cracks due to: • the existence of initial cracks associated with the manufacturing process or the previous loading histories, • highly localized deformations and the attendant stress concentrations, • substantial differences in fracture toughness and elastic-plastic constants of the constituent phases, and • large fluctuations of the stresses which may be attributed to the inhomogeneity of the meso-scale structure. x-ray generation approaches the x-ray quanta are generated at different depths in the material and theoretically can be described by the so-called mass-depth distribution function φ(ρz), where the depth is characterized by the effective variable, ρz, in units of mg/cm2. x-rays generated at a depth z and collected at a given take-off angle are absorbed along the path length up to the surface layer [22-23]. the absorption process is characterized by an exponential decrease of the function of the linear-absorption (attenuation) coefficient μ, of the material and, is the average of these coefficients for all the elements of the material. in a t v. kytopoulos et alii, frattura ed integrità strutturale, 50 (2019) 414-422; doi: 10.3221/igf-esis.50.35 416 simple, first-order approximation model the distribution function φ (ρz) of x-rays generation can be described by a single exponential decrease [23]:   zz e     (1) where σ is a material-instrument set-up constant and ρ the mass density of material. at the same time the attenuation (absorption) processes is given by beer’s law as exp[-μz], where z is the x-ray travelling depth. thereafter the emitted and detected x-ray intensity can be described, at first, as: emi   e e dz    xz   ρz μz 0 (2) where the mass density ρ is assumed in a first approximation to remain constant along the x-ray generation path z. nevertheless, the presence of crack-like micro-defects, i.e., volumetric damage in the material, imposes a related local variation of the mass density ρ. as such, the above integration should be made with respect to the “effective” variable, ρz, called mass-depth. therefore the above integral takes the final form:   xz z z emi    k e e d z          0 (2a) where /   is the so-called mass absorption (attenuation) coefficient, which is a very important material constant for the non-destructive testing given that it is independent of the physical and/or chemical state of the material [22-24]. the constant kσ takes into account the atomic mass and number as well as fluorescence effects [23] while zx is the maximum effective depth of x-rays generation. integration with respect to (ρz) yields:   x z em k i      e             1 (3) furthermore, it is valid that maximum mass-depth ρzx is almost constant under the same experimental set-up conditions [23]. on the basis of this fact, one may similarly assume that the effective mass-volume mx of x-rays generation, sampled by the electron beam, remains almost constant. hence, one may write: x x xm v      z    const    3 (3a) where vx≈zx3 is the associated effective maximum volume of x-rays generation. using now eq.(3a) and substituting zx=(const/ρ1/3) into eq.(3) one arrives at the final-general form of emitted x-ray signal intensity: a   emi  a e              2 3 1 (4) constants a, α take into account all constants of eq.(3). as such, the basic eq.(4) implies that the emitted and detected signal intensity should increase (decrease) monotonically with increasing (decreasing) local mass density ρ. since damage can be assumed to be (in a first approximation) inversely proportional to the local mass density it means that the measured damage degree should monotonically increase (decrease) with decreasing (increasing) signal emission intensity, given by eq.(4). experimental details methods he x-rays used are generated and emitted from a specimen bombarded with a focused electron beam of the scanning electron microscope. the x-ray generation and emission is a result of complex electron beam-specimen interactions, which describe the mechanisms for both characteristic and continuum x-ray production. in this study t v. kytopoulos et alii, frattura ed integrità strutturale, 50 (2019) 414-422; doi: 10.3221/igf-esis.50.35 417 both of these x-ray productions were taken into consideration, which means that the x-ray signal intensity used consists of the overlapping of characteristic and continuum x-ray of the material. in this way the applied manner of measurements exhibits a great advantage over the usually applied elemental x-ray microanalysis technique where the imposed measuring conditions and the precautions including atomic number, absorption and fluorescence factors (zaf) are much more stringent [22]. in this study, the x-ray detection was made by using a microspec 201-type wavelength dispersive spectrometer with special analyzing crystals. this spectrometer was attached to a cambridge-s4-10-type, sem, installed in the laboratory of strength and materials of the national technical university of athens. the edge-notched specimens, of dog-bone geometry, were loaded in tension using a specially designed servo-motor device and examined in-situ in the sem-epma system. fig.1 shows the geometry of the sampled region by sem-electron beam ahead of the notch root of the specimen. the electronic scan frame and line set-up on the sem were adequately selected to allow convenient measurements imposed by the conditions of x-ray signal collection. for instance, since electronic deflection of the beam can lead to defocusing of the x-ray spectrometer the desired line scans were performed by stepping the sample under a static electron beam. figure 1: electron beam of scanning – stepping set up principle. the stepping procedure was made by means of a high-precision micro-positioning system of the loading stage. in this context, it is noted that the emitted x-ray beam intensity is strongly depended on the electron beam intensity and because of this the measurements were performed for fixed electron intensity. this was made by monitoring the electron beam by means of a special specimen current apparatus of high sensitivity ±10-12 amp attached to the sem. furthermore, because of the statistical nature of the x-ray emission phenomenon the counting error is independent of counting time, it is beneficed to record a pre-determined fixed number of counts rather than to operate for a fixed time period [10]. in this sense the measured x-rays emission intensity should be appropriately scaled with the corresponding time signal variation. for this reason the measurements were carried out by introducing a time-converted signal given as:  i em i ot i   i constant (5a) i i   t  1 (5b) where i0 is the predetermined fixed number of counts, iem i is the emission intensity from the “i” point on the surface of the specimen and ti is the corresponding measured specific accumulation time. thus, the main measurement parameter in eq. (5b), ĩ, is the so-called specific accumulation rate. taking into account, the discussion concerning eq.(4), one can generally state that the specific parameter ĩ, may reflect a measure of the damage-controlled microstructural integrity change in the material. the data presented are the result of the average of measurements taken from three specimens. materials in this study, two mmcs were tested, namely the 8090-al-li and 2124-al-cu. both were fabricated by liquid metallurgy. this method is the most economical to fabricate composite materials. the mixed molten metal at 710 oc was poured into v. kytopoulos et alii, frattura ed integrità strutturale, 50 (2019) 414-422; doi: 10.3221/igf-esis.50.35 418 the pre-heated iron molds. the matrix was reinforced with 20 % volume fraction sic particles of radius about 3μm. the composites were prepared by bp-international by mixing and blending of al matrix alloy and sic powders followed by canning, vacuum de-gassing and consolidation and then hot rolling to plate and sheet. the basic mechanical properties of these two materials are given in table 1. the specimens were dogbane-shaped in accordance with the requirements of the grips of the loading device (of load capacity equal to 2.5 kn) specially designed for in-situ observations by sem. the edgenotch was machined very carefully by means of a rotating diamond disc-slow cutting apparatus (in order to avoid any parasitic damage). type of mmc-material al-li 8090 al-cu 2124 constituents alloy mmc change (%) alloy mmc change (%) elastic modulus (gpa) 92.5 114.0 23 80.0 109.9 37 tensile strength (mpa) 428 575 34 435 622 43 ductility (%) 4.5 4.0 -11 6.7 4.9 -27 table 1: mechanical properties of the materials tested. results and discussion n figs.2(a,b) the data obtained from the measurements of micro-damage controlled micro-structural integrity distribution ahead of the notch root for a 2124 mmcand a 8090 mmc-specimen, respectively are presented. taking into consideration the discussion concerning eqs.(5), one can clearly observe that this distribution, measured by the specific-count accumulation rate ĩ shows a distinct decrease towards notch root. also this signal tends to equilibrate at certain distance ρz away of notch root. at this distance the damage has a vanishing limit value. the parameter ρz, called fracture process zone, is an important factor in the experimental fracture mechanics of materials [7,19,25]. the fracture process or cohesive zone is a small characteristic region surrounding the crack tip or notch where micro-fracture develops mainly through the successive stages of inhomogeneous void growth and coalescence and bound breaking on atomic scale. in this context, the increased size, of about 5 times, of the process zone of the 8090 mmc, compared to the 2124 mmc specimen is to be properly highlighted. 3 2 1 0 i [s ec -1 ] 0 100 200 300 400 ρz [μm] 2.4 1.6 0.8 0 i [s ec -1 ] 0 30 60 90 ρz [μm] ĩ [s ec -1 ] ĩ [s ec -1 ] (a) (b) figure 2: reduced structural integrity change distribution ahead of notch root for material (a) 2124 mmc and (b) 8090 mmc. note that the strain rate for both cases was equal to 10-5 sec-1. as shown in fig.3 the proposed damage degree number qd=ad/a0 was determined, where a0 is the total sampled area and ad is the damage-controlled integrity loss area. in table 2 one can see the larger damage degree number obtained for the 2124 mmc material compared to the 8090 mmc, for the same strain rate conditions (of 10-5/s). comparing now the two parameters ρz and qd of these materials one can deduce that a larger damage degree or integrity loss is developed in 2124 mmc “along” a smaller fracture process zone. i v. kytopoulos et alii, frattura ed integrità strutturale, 50 (2019) 414-422; doi: 10.3221/igf-esis.50.35 419 0 100 200 300 400 ρz [μm] 3 2 1 0 i [s ec -1 ] ĩ [s ec -1 ] figure 3: integral area principle for calculation of damage or integrity loss number qd. to further enlighten this fact a new parameter, the specific damage number δ=qd/ρz, is introduced, describing the intensity of damaging processes. thereafter it seems that the 2124 mmc with higher matrix ductility (table 1), responds to loading with a larger specific damage number than the 8090 mmc, which has lower matrix ductility. a reasonable explanation for this interesting behavior could be given as follows: the more ductile metal matrix is associated with a higher strain hardening rate-induced dislocation motion activity [26]. this means that in this matrix (compared to less ductile ones) larger dislocation piling-up accumulations at metal matrix-sic particle interface sites may occur at early stages of loading. the high level of dislocation accumulation, in turn, produces strong stress concentration fields at these sites, promoting premature and intensive interfacial degradation activity, reflected by rapid lowering of the interfacial strength [27]. this implies, in turn, strong matrix-particle debonding-decohesion and micro-voids formation effects, which on further loading induce linkage of debonded particles followed by rapid crack initiation and propagation and final fracture. in this case, the related elastic-plastic damage processes are associated with energy absorption, by which a significant portion of the total micro-fracture energy flows into the crack-tip region dissipated within a “restricted” and characteristic damage process zone-volume, screened from the outer undamaged region, leading to intensive micro-failure events reflected by a large specific damage number. ιn figs.4(a,b) the damage controlled integrity change distribution ahead of notch root in 2124 mmc and in 8090 mmc, respectively for a higher strain rate is presented. one can observe the dramatic reduction of the fracture process zone compared to the lower stain rate (see figs.2(a,b)). in this context, in table 2 one can observe the increased specific damage number for both mmc materials with increasing strain rate of deformation. from the above findings the obvious embrittling influence of strain rate on the damage process can be deduced. this may be due to the dominating quasi-adiabatic process where high deformation rates limit the dissipation time required for the absorbed micro-failure energy to form new surfaces. hence the corresponding effective-specific damage process volume is reduced, a fact that is experimentally observed by the reduction of the measured process zone length ρz. moreover the high deformation rate seems to exhibit a lower embrittling influence on 8090 mmc. this is reasonable, since at high deformation rates the dislocation motion activity in the less ductile matrix (compared to the more ductile one) is subjected to a larger fractional reduction, a fact that (as was explained earlier) should induce corresponding micro-damage activity with reduced intensity. 0 10 20 30 ρz [μm] 1.5 1.0 0.5 0 i [s ec -1 ] ĩ [s ec -1 ] 1.8 1.2 0.6 0 i [s ec -1 ] 0 5 10 15 ρz [μm] ĩ [s ec -1 ] 0 (a) (b) figure 4: reduced structural integrity change distribution ahead of notch root for material (a) 2124 mmc and (b) 8090 mmc. note that the strain rate for both cases was equal to 10-2 sec-1. v. kytopoulos et alii, frattura ed integrità strutturale, 50 (2019) 414-422; doi: 10.3221/igf-esis.50.35 420 material and strain rate damage number qd=ad /a0 specific damage number δ= qd / ρz mmc 8090 (strain rate 10 -5/sec) 0.27 9 x 10-4 mmc 8090 (strain rate 10-2/sec) 0.37 3.1 x 10-2 mmc 2124 (strain rate 10-2/sec) 0.58 3.8 x 10-2 mmc 2124 (strain rate 10-5/sec) 0.33 5.5 x 10-3 table 2: basic, final results of micro-damage evaluation measurements of the investigated materials, before thermal shock. furthermore, in an isotropic body subjected to a non-uniform temperature distribution, the elements attempt to undergo dilation (or shrinkage) as a result of the temperature changes from an initially uniform temperature. however, the elements cannot dilate (or shrink) in an unrestricted manner. since the body must remain continuous during the temperature change there will be partial constraint internally, even if the body externally is unconstrained, as to change in geometry. one can then introduce in this way a general stress field in the body, with a parameter called thermal stress [28]. highspeed aircraft and space vehicles are subjected to considerable thermal stress from aerodynamic or solar heating on the outside surfaces and from the heat originating in propulsion system. furthermore, even without external constraint, thermal shock can occur due to the steep temperature gradients created because of a finite thermal conductivity. again, such a thermal shock is the stress state resultant of combined thermal conductivity and steep temperature gradient effect. for example, rapid cooling of the surface of a high-temperature wall is accompanied by surface tensile stresses. the surface contracts more than the interior, which is still relatively hot. as a result, the surface “pulls” the interior, into compression and “pulls” itself into tension. with the inevitable presence of griffith flaws at the surface, this surface tensile stress creates the clear potential for brittle fracture. the ability of a material to withstand a given temperature change depends on a complex combination of thermal expansion, thermal conductivity, overall geometry, and the inherent brittleness of the material. the presence of griffith flaws in solids in form of cracks or crack-like defects are usually classified as microscopic, meso-scopic and macroscopic according to crack length [5]. microscopic cracks in the sub-micrometer range often exist as a result of the material production processes. on thermal loading of materials, surface cracks propagate and additional cracks can be generated, which may finally lead to fracture. in other words, with thermal shock, stresses are caused by heterogeneous thermal expansion of the loaded material, which may be a result of both a heterogeneous material structure and a heterogeneous (local) energy load. moreover, the above described thermal cracking damage, is very critical in many primary and secondary manufacturing processes of materials such as casting, forging and welding where due to the improper related parameter such a damage can develop [29]. in fig.5 the measured x-ray intensity before tensile loading ahead of edge notch for the heat treated specimens by sudden cooling in liquid hydrogen at -196 oc temperature is presented. thus sudden cooling in this case produces the so called thermal shock by which, due to high thermal stresses, the fracture of material may occur. the produced thermal stresses are proportional to δαδτ where δτ is the temperature difference between cooling agent (196 oc) and specimen (20 oc) and δα the thermal expansion coefficient of the mmc material. in this case two dominant parallel processes may occur: a fracture mechanics controlled macroscopic thermo-elastic stress concentrations around a cut [30] and a damage mechanics controlled microscopic one around inclusions (sic particle) [5] .the microscopic process is characterized by highly localized thermal shock stresses produced between sic particle and matrix where due to large differences between thermal expansion coefficients, δα, of particle and matrix these stresses may lead to intensive and rapid mechanical degradation of interphase microstructure. the combined effect of these two thermal stress concentration processes result in the interfacial damage controlled structural integrity change shown in fig.5. one can see in this figure that mmc-2124 material shows a distinct higher thermal damage response than the other one. thus, one can argue that the composite material with large differences between the components (sic and matrix) concerning the tensile moduli and ductility, are more prone to thermal shock damage. in fig.6 the increased damage response is presented for the same specimens as in fig.5 after tensile loading to ultimate stress. this was expected since damage accumulated by thermal shock, on tensile loading, acts as an initial – present damage in the material. the basic data for the specimens after thermal shock treating are given in table 3. one can deduce that the initial presence of damage in the material, after thermal shock, exhibits a considerable influence on the subsequently tensile load – induced damage. in this aspect one can at first observe the increased proneness to thermal shock of the mmc2124 material compared to the other one. moreover, the combined effect of tensile load and thermal shock induced damage is larger for the mmc2124 material. this can be seen first by the large shift of both curves to lower values of measured count accumulation intensity and v. kytopoulos et alii, frattura ed integrità strutturale, 50 (2019) 414-422; doi: 10.3221/igf-esis.50.35 421 0.80 0.85 0.90 0.95 0 50 100 150 ḹ[ se c1 ] ρz [μm] mmc-2124 mmc-8090 0.25 0.50 0.75 1.00 0 150 300 450 ῑ[ se c1 ] ρz [μm] mmc-2124 mmc-8090 ĩ [s ec -1 ] ĩ [s ec -1 ] (a) (b) figure 5: reduced structural integrity changes ahead of notch root after thermal shock process (a) before tensile loading and (b) after subsequent tensile loading. reduction to unity of undamaged (virgin) material. strain rate 10-5 sec-1. table 3: basic final results of micro-damage evaluation measurements of the investigated materials, after thermal shock. second by the formation of an increased process zone ahead of the notch root. thereafter, by comparing the data presented in tables 2 and 3, one can generally state that the combined (superimposed) mechanical and thermal damage processes seems to influence more the mmc 2124 and less the mmc8090 material. conclusions the experiments conducted showed that, within the experimental scatter of the proposed semi-quantitative approach and under the same experimental conditions, the mmc with higher ductility of the matrix exhibits a higher proneness to mechanical load induced damage compared to the mmc material with lower ductility. based on the principle of elasticplastic damage, this behavior can be explained by the general fact that larger differences in ductility between matrix and sic particles may result to a larger misfit and accommodation loss between inclusion and matrix. this, in turn, leads to an associated intensive micro-cracking and debonding damage activity, taking place within the matrix-particle interface of the composite. in this aspect strain hardening rate effects seem to play a decisive role. furthermore, it was shown that increasing deformation rate leads to significant changes of the damage activity ahead of the edge-crack, a fact that is equivalent to a strain rate induced embrittlement of the material. this behavior seems to be more pronounced in mmcs with higher matrix ductility. at the same time, it is concluded that the material with larger differences in the elastic-plastic parameter of its constituent phases seems to exhibit a larger proneness to thermal shock damage. in general, the observed proneness to thermal shock damage may be explained by the combined effect of macroscopic and microscopic thermo-elastic stress concentration processes which may promote at first the physico-mechanical degradation of the particle-matrix interphase. in general, it can be stated that the proposed technique can give a reliable semi-quantitative approach for micro-damagecontrolled structural integrity evaluation and characterization of materials. material damage number qd specific damage number δ=qd /ρz mmc 8090 thermal shock 0.13 3.0 x 10-4 mmc 2124 thermal shock 0.19 2.3 x 10-2 mmc 8090 thermal shock and tensile load 0.33 1.3 x 10-2 mmc 2124 thermal shock and tensile load 0.57 2.7 x 10-3 v. kytopoulos et alii, frattura ed integrità strutturale, 50 (2019) 414-422; doi: 10.3221/igf-esis.50.35 422 references [1] stachowiak, g. and batchelor, a.w. (2013). engineering tribology, 3rd edition, oxford, uk, elsevier-butterworthheinemann [2] stachowiak, g. (ed) )2005). wear-materials, mechanisms and practice. john willy & sons ltd, england [3] shizhu wen, ping huang (2018). principles of tribology, 2nd edition john wiley & sons, singapore [4] hutchings, i., shipway, p. (2017). tribology-friction and wear of engineering materials, 2nd edition. elsevier, butterworth-heinemann, united states [5] krajcinovic, d. (1985). continuous damage mechanics revisited: basic concepts and definitions, journal of applied mechanics, 52, pp. 829-834 [6] yang, q., chen, x., zhou, w. (2005). on microscopic thermodynamic mechanisms of damage evolution laws, international journal of damage mechanics, 14, pp. 261-293 [7] kytopoulos, v.n. (1991). contribution of sem-technique to investigation of elastic-plastic micro-failure processes in materials, phd thesis, laboratory of strength of materials, national technical university of athens, greece [8] vickerman, j., gilmore, i. (2009). surface analysis the principal techniques, john wiley & sons [9] yacobi, b.g. and holt, d.b. (1994). an introduction to microanalysis of solids. in: yacobi b.g., holt d.b., kazmerski l.l. (eds.) microanalysis of solids. springer, boston, ma. [10] flewitt, p.e. and wild, r.k. (1994). physical methods for materials characterization, institute of physics publishing, bristol and philadelphia [11] wetzig, k. and schulze, d. (eds.) (1995). in situ scanning electron microscopy in materials reseaech, akademie verlag, berlin. [12] papadopoulos, g. and kytopoulos, v.n. (2001). micro-failure behavior of al2o3-ceramics studied by x-ray epma. icce/8, annual international conference, spain, 5-11/8/2001, pp. 715-716 [13] riga, ch. (2007). msc-thesis, school of applied mathematics and physics, section of mechanics, national technical university of athens, greece [14] kytopoulos, v.n., riga, ch. and kourkoulis, s.k. (2007). notch root opening displacement versus damage for particulate mmc. in: gdoutos e.e. (ed.) experimental analysis of nano and engineering materials and structures, springer, dordrecht, pp. 133-135 [15] andrianopoulos, n.p., kourkoulis and s.k., saragas, s. (1997). cod measurements and optimum exploitation of metal matrix composites for aerospace applications, engineering fracture mechanics, 57, pp. 565-576 [16] kourkoulis, s.k. and andrianopoulos, n.p. (2000). plastically induced anisotropy on metal matrix composites, mechanics of composites materials and structures, 7(1), pp. 1-18 [17] kourkoulis, s.k. (2001). the influence of cracks on the mechanical behavior of particulate mmcs: an experimental study, archives of mechanics, 53(4-5), pp. 439-456 [18] kourkoulis, s.k. (2002). quantifying the plastic anisotropy for particulate metal matrix composites, advanced composites letters, 11(4), pp. 153-163 [19] kourkoulis, s.k. (2003). the process zone around the tip of cracks in metal matrix composites. archives of mechanics, 55(5-6), 407-430 [20] kourkoulis, s.k., prassianakis, i., agioutantis, z. and exadaktylos, g.e. (2006). reliability assessment of the ndt results for the internal damage of marble specimens, international journal of material and product technology, 26 (1/2), pp. 35-56 [21] kourkoulis, s.k., ganniari-papageorgiou, e. and mentzini, m. (2010). dionysos marble beams under bending: a contribution towards understanding the fracture of the parthenon architraves, engineering geology, 115(3-4), pp. 246-256 [22] goldstein, j.i. (1992). scanning electron microscopy and x-ray microanalysis: a text for biologists, material scientists and geologists, 2nd edition, plenum press-new york [23] reimer, l. (1998). scanning electron microscopy, physics of image formation and microanalysis, 2nd edition, springerverlag [24] mcgonnagle, w.j. (1971). nondestructive testing, gordon and breach, science publ., new york, london, paris [25] hellan, k. (1984). introduction to fracture mechanics, mcgraw-hill, new york [26] polukhin, p., gorelik, s., and vorontsov, v. (1983). physical principles of plastic deformation, mir publishers, moscow [27] hertzberg, r.w. (1989). deformation and fracture of engineering materials, willey, 1989 [28] shackelford, j.f. (2001). introduction to materials science for engineers, 5th edition, prentice hall inc [29] das, a.k. (1996). metallurgy of failure analysis. mc graw-hill [30] parton, v.z. and morozov, e.m. 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can be opened with acrobat and adobe reader 5.0 and later.) >> /namespace [ (adobe) (common) (1.0) ] /othernamespaces [ << /asreaderspreads false /cropimagestoframes true /errorcontrol /warnandcontinue /flattenerignorespreadoverrides false /includeguidesgrids false /includenonprinting false /includeslug false /namespace [ (adobe) (indesign) (4.0) ] /omitplacedbitmaps false /omitplacedeps false /omitplacedpdf false /simulateoverprint /legacy >> << /addbleedmarks false /addcolorbars false /addcropmarks false /addpageinfo false /addregmarks false /convertcolors /converttocmyk /destinationprofilename () /destinationprofileselector /documentcmyk /downsample16bitimages true /flattenerpreset << /presetselector /mediumresolution >> /formelements false /generatestructure false /includebookmarks false /includehyperlinks false /includeinteractive false /includelayers false /includeprofiles false /multimediahandling /useobjectsettings /namespace [ (adobe) (creativesuite) (2.0) ] /pdfxoutputintentprofileselector /documentcmyk /preserveediting true /untaggedcmykhandling /leaveuntagged /untaggedrgbhandling /usedocumentprofile /usedocumentbleed false >> ] >> setdistillerparams << /hwresolution [2400 2400] /pagesize [612.000 792.000] >> setpagedevice microsoft word numero_49_art_10_2522 s. seitl et alii, frattura ed integrità strutturale, 49 (2019) 97-106; doi: 10.3221/igf-esis.49.10 97 focused on crack tip fields approximation of the crack-tip field in fatigue cracks in bridge steel specimens: dic analysis of different constraint levels s. seitl, p. miarka academy of sciences of the czech republic, institute of physics of materials, v. v. i., žižkova 22, 616 62 brno, czech republic and brno university of technology, faculty of civil engineering, institute of structural mechanics, veveří 331/95, 602 00 brno, czech republic seitl@ipm.cz, http://orcid.org/0000-0002-4953-4324 petr.miarka@vut.cz http://orcid.org/0000-0002-4953-4324 v. růžička, l. malíková, brno university of technology, faculty of civil engineering, institute of structural mechanics, veveří 331/95, 602 00 brno, czech republic ruzicka@musicer.net, https://orcid.org/0000-0002-1954-6340 malikova.l@fce.vutbr.cz, http://orcid.org/0000-0001-5868-5717 a. s. cruces, p. lopez-crespo department of civil and materials engineering, university of malaga, c/dr ortiz ramos s/n, 29071 malaga, spain ascruces@uma.es plopezcrespo@uma.es, https://orcid.org/0000-0002-5897-5615 abstract. a study on the accuracy of the approximation of the displacement field around of crack tip in a sample made from bridge steel (s355) is main objective of contribution. linear elastic fracture mechanics (lefm) theory in framework of multi-parameter formulation, i.e. postulated by williams is used to determine of coefficients of williams power series terms. over deterministic method was used to calculate the terms based on the least squares regression technique, applied on data from numerical simulation and experiment on s355 steel grades. comparison between the stress fields (by principal stress 1 and von mises stress hmh) obtain from experimental measurement dic, hybrid method and obtain from reconstruction by using various number of williams power terms are quantified in order to get key information around the crack tip region on bridge steel specimens. keywords. displacement; crack-tip stress fields; dic; high order terms; multi-parameter approximation accuracy; williams power series. citation: seitl, s., miarka, p., ruzicka, v., malikova, l., cruces, as. lopez-crespo, p. approximation of the crack-tip field in fatigue cracks in bridge steel specimens: dic analysis of different constraint levels, frattura ed integrità strutturale, 49 (2019) 97-106. received: 16.05.2019 accepted: 22.05.2019 published: 01.07.2019 copyright: © 2019 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. http://www.gruppofrattura.it/va/49/2522.mp4 s. seitl et alii, frattura ed integrità strutturale, 49 (2019) 97-106; doi: 10.3221/igf-esis.49.10 98 introduction on-destructive inspections of fatigue loaded components or civil engineering structures are usually performed to predict the size and the locations of cracks that are created from singular stress concentrator/defects during the manufacturing process or service life. the existence of cracks changes predictable load-bearing capacity and service interval [1-4] of the civil engineering components especially during the fatigue loading. characterisation of stress fields near crack tip has been studied for many decades; see for example a short state-of-art [5] where an over deterministic method (odm) is presented to evaluate the combination of mode i and mode ii by using photo-elasticity for drawing isoline and given number of we terms [6]. the odm has also been employed successfully to analyse bulk strain data obtained with synchrotron tests [7, 8]. understanding the evolution of higher order terms for different geometries is key to predict the constraint of elastic-plastic crack tip fields [9]. consequently, a large effort has been devoted in recent times to develop algorithms for fast determination of higher order terms and to improve the accuracy in the estimation of higher order terms [10-13] both quasi-statically [14] and in dynamic situations [15]. digital image correlation technique (dic) was applied successfully on niti pseudoelastic alloy for evaluation of fracture toughness and another fracture properties [16]. in the papers [17, 18, 23-27], the displacement field in the surrounding of a crack tip of single edge geometry specimens was employed in conjunction with williams power series to estimate the stress intensity factor (sif). the higher-order terms effects were analysed by using williams expansion (focusing of t-stress) for various sizes of the crack tip distance of applied region for fitting data. a comparison between the sif results and the analytical solution was established. the aim of this contribution is to analyse the various stress fields in the vicinity of the crack tip that were constructed from the data obtained from measurement of the displacement field by dic by comparing the crack tip field approximations obtained with the odm [28] and hybrid element method [29, 30]. the displacement field in the vicinity of the crack tip, which is necessary for the following analysis, was measured in a standard compact tension (ct-[31]) specimen made of s355 j2 under the constant value of stress intensity factor ki=15 mpa√m.(according astm e647, [32]). the linear elastic fracture mechanics (lefm, [38]) theory was applied on calculation of displacement vector components to be more precisely the multi-parameter formulation given by williams [39] is applied. calculation of terms coefficients of williams power series was applied the least squares-based regression technique marked odm, [28] for which displacements data obtained experimentally from optical measurements are taken as inputs. the influence of the number of terms considered for the power series reconstruction of two kinds of definition for the stress fields for the calculation of the values of coefficients of those terms are investigated in the current paper. steel c (max. %) mn (max. %) si (max. %) p (max. %) s (max. %) n (max. %) cu (max. %) cev (max. %) s355 j2 0.2 1.6 0.55 0.03 0.03 0.55 0.47 table 1: chemical composition in percentage by weight (wt. %) of the used steel grades according to en 10025-2:2004 standard. young’s modulus yield stress uts elongation at break poisson’s ratio 205.4 ±7.4 gpa 381.94±6.22 mpa 554.41±1.62 mpa 34.22 ±1.54 % 0.3 [1] table 2: mechanical properties of s355 j2 mean values with standard deviation. experimental study material s355 j2 and method of measurement he experiments were conducted on a compact tension (ct) geometry that were machined in the t-l direction that is the rolling direction was parallel to the crack growing direction. the specimen was machined according to astm e647 [32]. the material was s355 j2 structural steel that is commonly used offshore, marine and structural applications. the chemical composition of the steel grade is specified in en 10025-2:2004 standard and is presented in [33]. chemical composition of the experimental material was verified by producer, and it is in agreement with the standard presented in this paper and measured mechanical properties of the s355 j2 are summarized in tab. 2, the fatigue properties were published e.g. [34-37]. n t s. seitl et alii, frattura ed integrità strutturale, 49 (2019) 97-106; doi: 10.3221/igf-esis.49.10 99 the tested ct specimens had dimensions: l = 62.5 mm, w = 50 mm, b = 10 mm, an = 12.5 mm, h/2 = 30 mm and the angle 1 = 60°, fig. 1. figure 1: schematic of the compact tension (ct) specimen employed, including the dimensions. astm e647 [32] was followed in the machining of the specimen. the rolling direction is also shown in the figure. specimens were prepared from a metal sheet in two different orientations to the sheet rolling direction. specimens were marked with letters “a-crack propagating along rolling direction” and “b-crack propagating across to rolling direction” to see the influence of the material structure orientation on the crack propagation rate. in case of the specimens marked with letter “a”, the initial crack (notch) is oriented parallel to rolling direction, whereas with letter “b” the initial crack (notch) is oriented perpendicular to the rolling direction (rotated by 90°), the microstructure of s355 j2 for different rolling direction is shown in fig. 2. a) s355 j2a b) s355 j2b figure 2: figure structure of the s355 j2 steel grade, the crack was propagating in the horizontal direction; etched with 2% nital, light optical microscope a/w 0.310 0.350 0.390 0.450 0.490 0.650 0.690 0.750 pmax 6.490 5.860 5.280 4.490 4.000 2.220 1.830 1.300 pmin 0.649 0.586 0.528 0.449 0.400 0.222 0.183 0.130 p 5.841 5.274 4.752 4.041 3.600 1.998 1.647 1.170 table 3: examples of forces values (pmax, pmin and p) versus relative crack length (a/w) applied for ct specimen for constant range of stress intensity factor ki=15 mpa√m according astm e647 [32]. the fatigue propagation test was conducted on a 100 kn instron sevo-hydraulic rig. the precracking was implemented for 120,000 cycles, a frequency of 20hz and a load ratio, r, of 0.1. attention was paid throughout the test to fulfil small scale yielding conditions (see the paragraph entitled justification of using lefm). the value of stress intensity has changed each 1 mm of crack growing to be at given point 15 mpam1/2. the selected values of forces for relative crack length, calculated for given range of k according astm e647 [32], are mentioned in tab. 3. s. seitl et alii, frattura ed integrità strutturale, 49 (2019) 97-106; doi: 10.3221/igf-esis.49.10 100 justification of using lefm condition of small scale yielding is a very useful concept [38], which has been used to describe that the linear extension of the plastic region is small compared to significant dimensions of the body, particularly the crack length 2 2.5 i y k a         (1) due to the high gradient that takes place at the crack tip because of the crack tip singularity, a certain plastic deformation will occur. the extension of this plastic deformation was estimated with irwin’s model where the plastic radius can be inferred along the x-axis, by equating the stresses acting on the crack opening direction to the yield stress of the material: 2 1 2 i p y k r         – plane stress, (2) 2 1 6 i p y k r         – plane strain. (3) in eqns. 2 and 3, ki is stress intensity factor and y is yield stress. therefore, valid points from used dic measurement were taken in higher distance than 0.25 mm. full-field experimental measurement of displacements key experimental information of the displacement field around the crack tip was obtained with digital image correlation (dic). the study was conducted for various crack lengths and one load level (see tab. 3). dic is a powerful full-field technique that enables the in-plane displacement field between two different strain states to be measured. dic technique works by splitting the image of the analysed surface into a small squared images also called interrogation windows. it is based on the cross-correlation function [40] that evaluates the similarity between the different interrogation windows during the different strain states:       2 2 2 2 ,  , , n n x y a b n n x y c u v i x y i x u y v          , (4) where c is the cross-correlation function that depends on the horizontal, u, and vertical, v, displacement vectors that join the centre of all interrogation windows in the two different strain states. ia and ib are distributions of the intensity across the two images captured in the two different strain states. n is the total number of interrogation windows included in each image. the maximum of the cross-correlation function indicates the most likely displacement vector for all the interrogation windows. figure 3: set up for fatigue measurement with digital image correlation (dic) s. seitl et alii, frattura ed integrità strutturale, 49 (2019) 97-106; doi: 10.3221/igf-esis.49.10 101 the experimental setup is shown in fig. 3. fig. 3 shows the loading fixture employed to apply mode i loading on the ct geometry and the dic experimental system. this includes the digital camera, the macro-lens and fibre-optics co-axial illumination. the camera was positioned so that the crack propagation direction was parallel to the positive x coordinate. the crack opening direction was parallel to the y coordinate [17]. such pre-arranging simplifies the post-processing of the results [18], in particular for non pure mode i cracks (i.e. for mixed mode cracks, e.g. [19, 20]. unlike most previous works where speckle pattern was obtained by spraying the surface with black and white paint [21, 22], here we obtain a random pattern in the studied surface by abrading the surface with different grades sic papers [23, 24]. such procedure yielded excellent results in the past with similar types of alloys [25]. moreover, the recommendations generated in previous studies were incorporated in the tests [26]. the digital images were acquired with a 2452×2052 pixels ccd camera with 8-bit dynamic range. the frame rate of the camera was set to 12. overall the camera/sample/illumination/loading rig setup was analogous to that employed previously [10, 27]. in order to not introduce additional sources of error, the raw information measured by dic, was fed into the elastic analytical model to conduct the fracture mechanics analysis (see following section). that is, horizontal, u, and vertical, v, displacement information was used, rather than strain information that requires an additional step. theoretical background: multi-parameter fracture mechanics stress and displacement field near crack tip for mode i he stress and displacement distribution near crack tip can be written by a power series that was introduced by williams in [39]. in a homogeneous linear-elastic isotropic material (described by e – young modulus and  – poisson ratio for the crack loaded by mode i loading, the stress field/displacement field around the crack tip can be expressed by following williams eigenfunction expansion:       1 2 1 2 1 cos 1 1 cos 3 2 2 2 2 2 1 cos 1 1 cos 3 2 2 2 2 2 1 sin 1 1 sin 3 2 2 2 2 n x n n y n n xy n n n n n n n n n n r a n n n n                                                                                                                      . (5) similarly, the displacement vector can be written as:     /2 1 1 cos cos 2 2 2 2 2 2 1 sin sin 2 2 2 2 2 n n n nn n n n n u r a v n n n n                                                      . (6) in eqns. 5 and 6, r and θ are polar coordinates with the start of coordinate system in the crack tip),  is shear modulus defined as  = e/2(1+), where n denotes the index of the term in the series development and  is the kolosov constant defined for plane stress ((3- or plane strain (3-4 conditions. coefficients of we marked an depend on relative crack length  = a/w. the start of polar coordinate system was positioned at the crack tip [40] and curvature of crack was not considered [41]. it is good to mention, that bulk effect was not taken in account like in [42]. the used shortened form of the wps used n terms is applied on description of approximation of stress/displacement fields. when the crack is loaded by mixed-mode [44], eqns. 5 and 6 have to include a shear mode terms, see e.g. [45, 46]. over-deterministic method (odm) in the scientific literature [29, 30, 47, 48], various numerical procedures for calculation of the coefficients of the williams power series can be found. some of them are based on the hybrid crack elements, boundary collocations or other mathematically more difficult definitions and techniques. contrary to that, there exist a relatively simple method that can utilize the basic results of data postprocessing included in each commercial finite element software. the method is called t s. seitl et alii, frattura ed integrità strutturale, 49 (2019) 97-106; doi: 10.3221/igf-esis.49.10 102 over-deterministic (odm) [28], because the coefficients are obtained from an over-determined system of equation. these equations are formed based on eqn. 6. the principle consists in choosing a set of particular nodes around the crack tip. the number of nodes, k, corresponds to the number of williams expansion terms, n, that should be determined (it has to hold that 2k  n + 1 for mode i configurations). the displacements of these nodes obtained experimentally from the dic measurements are used as inputs for eqn. 6 together with their polar coordinates (the total number of nodes between the radius from 0.25 up 1 mm around the crack tip was approximately 120 for each configuration). thus, the coefficients an could be calculated, which was programmed in wolfram mathematica code [49] and php software [50]. more details on advantages, restrictions and accuracy of the odm can be found in [10-13]. methods of reconstruction of stress fields in vicinity of a crack tip the knowledge of higher-order terms of the we from eqn. 5 allow us to plot the stress isolines for given values of stress. in the contribution, two methods of approximation are used: the principal stress 1 and von mises stress hmh. the following equations show how to calculate these stress values: 2 2 1 2 2 x y x y xy                (7) 2 2 2 hmh 3x x y y xy         (8) where x, y are normal stress components in x and y direction and xy is shear stress component. for comparison of stress distribution around the crack tip, the coefficients of the we obtain via the hybrid crack elements for a normalized ct specimen were taken from the literature [29]. results and discussion stress intensity factor (sif) if values obtain from various methods were compared, see tab. 4. the suggested values 15 mpam1/2 obtained according astm e647 [32] ct fatigue tests (see tab. 3) are compared to sif values obtain by using combination of dic and odm methods and sif values obtained by using the hybrid crack elements like knésl & bednář in [29]. a [mm] a/w [1] p [kn] fracture test k [mpa m1/2] optical measurements (dic)  [mpa m1/2] optical measurements (dic) t-stress [mpa] knésl & bednář [29]  [mpa m1/2] knésl & bednář [29] t-stress [mpa] 16 0.32 5.70 15 15.05 19.34 15.01 20.07 26 0.52 3.28 15 14.82 25.23 14.93 28.71 35 0.70 1.56 15 15.01 26.02 14.96 26.24 43 0.86 0.47 15 15.03 40.36 15.02 45.12 table 4: values of the stress intensity factors (sifs) in mpa√m and t-stress mpa for selected crack length obtained: from fracture tests astm e647, [32], combination of dic and odm methods and sif values obtained by using the hybrid crack elements like knésl & bednář in [29]. t-stress for ct specimen fig. 4 shows the value of t-stress versus a/w for ct specimen in case of static load ki=15 mpa m1/2. therefore, the presented results are for selected relative crack lengths a/w where level of constraint (t-stress) is different, see tab. 3. s s. seitl et alii, frattura ed integrità strutturale, 49 (2019) 97-106; doi: 10.3221/igf-esis.49.10 103 comparison of stress fields in vicinity of a crack tip for comparison of experimentally obtain data and numerically calculated, the relative crack length 0.86 were selected due to maximal value of constraint (t-stress), see tab. 3 and fig. 4. in fig. 5, σ1 and σhmh the approximation of the crack tip stresses taking into account one and two terms of the williams power series on specimen are shown: a) stress values calculated from the coefficients determined theoretically [29]; b) stress values computed from the coefficients that were calculated through the odm from the experimental displacement information. figure 4: value of t-stress versus relative crack length a/w for ct specimen in case of static load ki=15 mpa m1/2.  1  h m h a) knésl & bednář [29] b) dic + odm figure 5: σ1 and σhmh crack tip stress approximation considering one (thick lines) and two (dashed lines) initial terms of the williams expansion on specimen with the relative crack length 0.86: a) isoline of stresses calculated from the coefficients determined theoretically [29]; b) isoline of stresses calculated from the coefficients calculated by odm from the dic measurements. s. seitl et alii, frattura ed integrità strutturale, 49 (2019) 97-106; doi: 10.3221/igf-esis.49.10 104 conclusion his work presents an investigation regarding the stress distribution around a fatigue crack tip. the study has been conducted on a s355 steel often used in offshore, marine and structural applications. the experimental program is based on ct specimens analysed by means of dic full-field technique. different cases with constant stress intensity factor, k = 15 mpam1/2, were analysed. one of the main outputs has been inferring the fourier coefficients that are required to approximate the williams expansion describing the field. this has allowed the crack tip stress field distribution for be reconstructed for a real fatigue crack. the results have been validated by comparison between the williams based analysis and theoretical solutions. the current research is part of a broader investigation program aimed at multi-parameter characterisation of failure in metals. acknowledgements inancial support from the czech science foundation (project no. 17-01589s), and from ministerio de economia y competitividad through grant reference mat2016-76951-c2-2-p is gratefully acknowledged. this paper has been worked out under the "national sustainability programme i" project "admas up – advanced materials, structures and technologies" (no. lo1408) supported by the ministry of education, youth and sports of the czech republic and brno university of technology. references [1] krejsa, m. brozovsky, j. lehner, p. seitl, s. and kala, z. (2018) stochastic analysis for short edge cracks under selected loads, aip conference proceedings, 1978, art. no. 150006, doi: 10.1063/1.5043797 [2] lehner, p. křivý, v. krejsa, m. pařenica, p. and kozák, j (2018) stochastic service life prediction of existing steel structure loaded by overhead cranes, procedia structural integrity, 13, pp. 1539–1544. doi: 10.1016/j.prostr.2018.12.314 [3] janas, p. krejsa, m. sejnoha, j. and krejsa, v. (2017) doproc-based reliability analysis of structures, structural engineering and mechanics, 64(4), pp. 413–426. doi: 10.12989/sem.2017.64.4.413 [4] kala, z. (2018) probabilistic modelling of fatigue crack some observations about conditional probability, international journal of mechanics, 12, pp. 121–130. [5] stepanova, l. and roslyakov, p. (2016) multi-parameter description of the crack-tip stress field: analytic determination of coefficients of crack-tip stress expansions in the vicinity of the crack tips of two finite cracks in an infinite plane medium, int. j. solids struct., 100, pp. 11–28. [6] ramesh, k. gupta, s.and kelkar, a. a. (1997) evaluation of stress field parameters in fracture mechanics by photoelasticity—revisited, eng. fract. mech., 56(1), pp. 25–45. [7] lopez-crespo, p. peralta, j.v. and withers, p.j. (2018) synchrotron x-ray diffraction based method for stress intensity factor evaluation in the bulk of materials. theoretical and applied fracture mechanics, 98, pp. 72–77. [8] lopez-crespo, p. peralta, j.v. and withers, p.j. (2019) in situ through-thickness analysis of crack tip mechanics with synchrotron x-ray diffraction. international journal of fatigue, to appear. 2019. [9] sgambitterra, e. lesci, s. and maletta, c. (2015) effects of higher order terms in fracture mechanics of shape memory alloys bydigital image correlation, procedia eng., 109, pp. 457–464. [10] seitl, s. malíková, l. růžička, v. moreno, b. and lopez-crespo, p. (2018) williams' expansion-based approximation of the displacement field in an al 2024 compact tension specimen reconstructed from optical measurements, fatigue and fracture of engineering materials and structures, 41(10), pp. 2187–2196, doi: 10.1111/ffe.12842 [11] šestáková, l. (2013) how to enhance efficiency and accuracy of the over-deterministic method used for determination of the coefficients of the higher-order terms in williams expansion,” appl. mech. mater., 245, pp. 120–125, doi http://dx.doi.org/10.4028/www.scientific.net/amm.245.120 [12] šestáková, l. and veselý, v. (2013) convergence study on application of the over-deterministic method for determination of near-tip fields in a cracked plate loaded in mixed-mode,” appl. mech. mater., 249–250, pp. 76–81, doi http://dx.doi.org/10.4028/www.scientific.net/amm.249-250.76 [13] růžička, v. malíková, l. and seitl, s. (2017) over-deterministic method: the influence of rounding numbers on the accuracy of the values of williams’ expansion terms, frattura ed integrita strutturale, 11(42), pp. 128–135, doi: t f s. seitl et alii, frattura ed integrità strutturale, 49 (2019) 97-106; doi: 10.3221/igf-esis.49.10 105 10.3221/igf-esis.42.14 [14] mokhtarishirazabad, m. lopez-crespo, p. moreno, b. lopez-moreno, a. and zanganeh., m. (2017) optical and analytical investigation of overloads in biaxial fatigue cracks. international journal of fatigue, 100(2), pp. 583–590. [15] mokhtarishirazabad, m. lopez-crespo, p. and zanganeh, m. (2018) stress intensity factor monitoring under cyclic loading by digital image correlation. fatigue and fracture of engineering materials and structures, 41, pp. 2162–2171. [16] clocksin, w. f. da fonseca, j. q. withers, p. j.a nd torr, p. h. s. (2002) image processing issues in digital strain mapping, in proceedings of spie, application of digital image processing xxv, 4790, pp. 384–395. [17] mokhtarishirazabad, m. lopez-crespo, p. moreno, b. lopez-moreno, a. and zanganeh, m. (2017) optical and analytical investigation of overloads in biaxial fatigue cracks, int. j. fatigue, 100(2), pp. 583–590. doi http://dx.doi.org/10.1016/j.ijfatigue.2016.12.035 [18] lopez-crespo, p. moreno, b. lopez-moreno, a and zapatero, j. (2015) study of crack orientation and fatigue life prediction in biaxial fatigue with critical plane models, eng. fract. mech., 136, pp. 115–130. [19] lopez-crespo, p. and pommier, s. (2008) numerical analysis of crack tip plasticity and history effects under mixed mode conditions, journal of solid mechanics and materials engineering. 2, pp. 1567–1576. [20] lopez-crespo, p. burguete, r.l. patterson, e.a. shterenlikht, a. withers, p.j. and yates, j.r. (2009) study of a crack at a fastener hole by digital image correlation, experimental mechanics. 49, pp. 551–559. [21] yoneyama, s. ogawa, t. and kobayashi, y. (2007) evaluating mixed-mode stress intensity factors from full-field displacement fields obtained by optical methods, eng. fract. mech., 74, pp. 1399–1412. [22] lopez-crespo, p. moreno, b. lopez-moreno, a. and zapatero, j. (2015) characterisation of crack-tip fields in biaxial fatigue based on high-magnification image correlation and electro-spray technique, int. j. fatigue, 71, pp. 17–25. [23] lopez-crespo, p. burguete, r.l. patterson, e.a. shterenlikht, a. withers, p.j. and yates, j.r. (2009) study of a crack at a fastener hole by digital image correlation, exp. mech., 49, pp. 551–559. [24] lopez-crespo, p. shterenlikht, a. yates, j.r. patterson, e.a. and withers, p.j. (2009) some experimental observations on crack closure and crack-tip plasticity, fatigue fract. eng. mater. struct., 32, pp. 418–429. [25] lopez-crespo, p. moreno, b. lopez-moreno, a. and zapatero, j. (2015) characterisation of crack-tip fields in biaxial fatigue based on high-magnification image correlation and electro-spray technique,” int. j. fatigue, 71, pp. 17–25. [26] mokhtarishirazabad, m. lopez-crespo, p. moreno, b. lopez-moreno, a. and zanganeh, m. (2016) evaluation of crack-tip fields from dic data: a parametric study, int. j. fatigue, 89, pp. 11–19. [27] lopez-crespo, p. garcia-gonzalez, a. moreno, b. lopez-moreno, a. and zapatero, j. (2015) some observations on short fatigue cracks under biaxial fatigue, theor. appl. fract. mech., 80, pp. 96–103. [28] ayatollahi, m. r. and nejati, m. (2011) an over-deterministic method for calculation of coefficients of crack tip asymptotic field from finite element analysis, fatigue fract. eng. mater. struct., 34(3), pp. 159–176. [29] knésl, z. and bednář, k. (1998) two-parameter fracture mechanics: determination of parameters and their values (in czech), ipm as cr, v. v. i. brno. [30] xiao, q. z. karihaloo, b. l and liu, x. y. (2004) direct determination of sif and higher order terms of mixed mode cracks by a hybrid crack element, int. j. fract., 125(3), pp. 207–225. [31] farahani, b.v. tavares, p.j. belinha, j. and moreira, p.m.g.p. (2018) compact tension fracture specimen: experimental and computational implementations on stress intensity factor, journal of strain analysis for engineering design, 53(8), pp. 630–647. doi: 10.1177/0309324718763189 [32] astm e647 (2005) standard test method for measurement of fatigue crack growth rates. [33] european committee for standardization (cen) (2005) en1993-1-9: eurocode 3: design of steel structures, part 19: fatigue. brussels. european standard. [34] rozumek, d. marciniak, z. lesiuk, g. and correia, j. a. f. o. (2017) mixed mode i/ii/iii fatigue crack growth in s355 steel, procedia structural integrity, 5, pp. 896–903. [35] de jesus, a. m. p. matos, r.b. fontoura, .f.c. rebelo, c. simoes da silva, l. and veljkovic, m. (2012) a comparison of the fatigue behavior between s355 and s690 steel grades, journal of construction steel research, 79, pp. 140–150. [36] seitl, s. miarka, p. klusák, j. fintová, s. and kunz, l. (2018) comparison of the fatigue crack propagation rates in s355 j0 and s355 j2 steel grades. in local mechanical properties xiii. key engineering materials (web). trans tech publications, switzerland, 784, pp. 91–96. [37] seitl, s. miarka, p. blasón, s. and canteli, a. (2019) evaluation of fatigue properties of s355 j2 and s355 j0 by using profatigue software, book title: mechanical fatigue of metals, chapter 28. [38] anderson, t.l. (1995) fracture mechanics: fundamentals and applications. crc press. isbn 978-0849316562 [39] williams, m. l (1957) on the stress distribution at the base of a stationary crack,” j. appl. mech., 24(1), pp. 109–114. [40] clocksin, w. f. da fonseca, j. q. withers, p. j. and torr, p. h. s. (2002) image processing issues in digital strain s. seitl et alii, frattura ed integrità strutturale, 49 (2019) 97-106; doi: 10.3221/igf-esis.49.10 106 mapping, in proceedings of spie, application of digital image processing xxv, 4790, pp. 384–395. [41] zanganeh, m. lopez-crespo, p. tai, y.h. and yates, j. r. (2013) locating the crack tip using displacement field data: a comparative study, strain, 49, pp. 102–115. [42] camas, d. lopez-crespo, p. gonzalez-herrera, a. and moreno, b. (2017) numerical and experimental study of the plastic zone in cracked specimens, eng. fract. mech., 185, pp. 20–32, doi http://dx.doi.org/10.1016/j.engfracmech.2017.02.016 [43] lopez-crespo, p. mostafavi, m. steuwer, a. kelleher, j.f. buslaps, t. and withers, p. j. (2016) characterisation of overloads in fatigue by 2d strain mapping at the surface and in the bulk, fatigue fract. eng. mater. struct., 39(8), pp. 1040–1048. [44] lopez-crespo, p. and pommier, s (2008) numerical analysis of crack tip plasticity and history effects under mixed mode conditions, j. solid mech. mater. eng., 2(12), pp. 1567–1576. [45] yoneyama, s ogawa, t. and kobayashi, y. (2007) evaluating mixed-mode stress intensity factors from full-field displacement fields obtained by optical methods,” eng. fract. mech., 74, pp. 1399–1412. [46] lopez-crespo, p. shterenlikht, a. patterson, e. a. withers, p.j. and yates, j. r. (2008) the stress intensity of mixed mode cracks determined by digital image correlation, j. strain anal. eng. des., 43, pp. 769–780. [47] tong, p. pian, t. h. h. and lasry, s. j. (1973) a hybrid-element approach to crack problems in plane elasticity,” int. j. numer. methods eng., 7(3), pp. 297–308. [48] xiao, q. z. karihaloo, b. l. liu, x. y. (2004) direct determination of sif and higher order terms of mixed mode cracks by a hybrid crack element, int. j. fract., 125(3), pp. 207–225. [49] c. wolfram research, inc., ed., wolfram mathematica documentation center. 2007. 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/hrv (za stvaranje adobe pdf dokumenata najpogodnijih za visokokvalitetni ispis prije tiskanja koristite ove postavke. stvoreni pdf dokumenti mogu se otvoriti acrobat i adobe reader 5.0 i kasnijim verzijama.) /hun 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/pdfxoutputintentprofileselector /documentcmyk /preserveediting true /untaggedcmykhandling /leaveuntagged /untaggedrgbhandling /usedocumentprofile /usedocumentbleed false >> ] >> setdistillerparams << /hwresolution [2400 2400] /pagesize [612.000 792.000] >> setpagedevice microsoft word numero 14 articolo 4 b. l 36 h us br fed bra lob ab hyd in com and and mo lim fac to pre ke in bri sen imp unn ho val dec in tho (iii) t lobato da silva high-cyc sed in h raitner lob deral universi asília, brazil, batoae@gmail. bstract. t draulic comp that sense, mponents w d the consid d 2.42. in o ood, stairca mit. for such ctor were co results obta ediction of t eywords. n ntroductio he fatigu these co invariab ttle materials nsitivity to ge portant trans notched spec owever, the m lue is practica crease quickly 1 f k   f s k s  the last 40 ye ose considera ) stress field t et alii, frattura cle notc hydroge bato da silv ity of brasília, 70940-910. com.br, jorge@ the presenc ponents is a , specimens was tested. t dered stress order to dete se method w h geometry a ompared thro ained it was the peterson notch, fatigu on ue analysis in omponents a bly occur at st s due to the f eometric disc sformation fa cimen, sfe. th most definitio ally unaffecte y with respect  1 t q k  f fe s s ears many ex ations, they ca intensity mo ed integrità stru ch sensi enator tu va, jorge l mechanical e @unb.br, alex e of notche a current pro s of the as the specimen concentratio ermine the f was used. t at least 8 spe ough fatigue s possible to n and neube ue strength, n turbine blad are designed tress concent fatigue. ther continuities. i actor that rel his relation c on accepts is ed for 106 to t the cycle nu xpressions hav an be classifie odels [2]. in utturale, 14 (201 tivity of urbine c luiz de alm engineering d x07@unb.br es and othe oblem in eng stm a743 ns were test on factors, k fatigue limit this approac ecimens wer e notch redu o conclude r’s empirical staircase me des and other to operate b trators. in th refore, the str in that sense lates the fati an be expres the relation 108 cycles. in umber [1]. ve been deve ed in three m this work, w 10) 36-44; doi: f alloy s compon meida ferr department, ca er stress co gineering. it ca6nm a ted under un kt, values, c for such no ch is based re tested. in uction factor that the tes l models. ethod, up an r hydraulic no below its en he cases that t ress concentr e, appears th igue strength ssed by eq. 1 showed by e n addition, w eloped to the models: (i) av we work onl 10.3221/igf-esi teel ast nents reira, josé ampus univer oncentration t causes a re alloy steel u niaxial fatigu calculated wi otch type, a on the assu addition, th r, kf, obtain sted materia d down met otch compon ndurance limi the loading is ration factor he fatigue not h of notch sp 1, where q is eq. 2. exper when the fatig notch fatigu verage stress m ly with avera is.14.04 tm a74 alexander rsitário darcy ns in turbin duction of e using in sev ue loading w ith respect t reduction d umed target he peterson a ned from exp al is less sen thod, astm nents is a ver it and becau s dynamic, th should be m tch reduction pecimen, sf, the notch s rimental inve gue life is les ue notch redu models, (ii) f age stress mo 43 ca6n r araújo ribeiro, e blades an endurance li veral hydrog with a load ra to net area, data method distribution and neuber perimental d nsitive to no m a743 ca6n ry important p use fatigue fa he ductile ma modified accor n factor, kf. with the fat ensibility fact stigations ind ss that 106 cy uction factor, fracture mech odels: neube nm nd other no imit of mate genator turb atio equal to were 1.55, 2 d by dixon n of the fati r’s notch fati data. accord otches than nm. problem beca ailures in ser aterials behav rding to mat it establishes tigue strength tor and 0 q dicate that th ycles, the kf v (1) (2) kf. accordin hanic models r and peters otch erial. bine o -1, 2.04 and igue igue ding the ause rvice ve as terial s an h of 1 . he kf value ng to and on’s http://www.gruppofrattura.it http://dx.medra.org/10.3221/igf-esis.14.04&auth=true mailto: lobatoae@gmail.com.br mailto: jorge@unb.br mailto: alex07@unb.br rela fati sm not ne of pet fati ho con ex ma ten are t ation. the fir igue failure o mooth specime tch opening a 1 f k   euber formula tensile streng 1 f k   10 n a  terson assum igue strength owever, peter nstant materia 1 f k   0 p a        xperiment aterial he teste turbine properti nsile strength, e showed in t t rst model sho occur when th en sf. the eq angle, and a 1 1 t k a w        ated the eq. 3 gth, srt, for ste 1 1 t n k a     134 5860 rts med that the fa h of a smooth rson proposed al and it can b 1 1 ,t r p k s a           700 0,185 207 0, 0254 rt rt s s         tal proced ed material w components ies according , srt, and yield tab. 2 and ta c 0 b. lo ws by kuhn he average st q. 3 presents a is a material c a  3 as the eq. eels with srt > atigue failure h specimen [5 d that the stre be estimate in 1520mpa rt  1.8 , 0 , 700 9 7 t rt rt s s         dure was a steel allo s and it requ g to astm a d strength, sy.) b. 3, respectiv c mn 0.06 1.00 table 1: che e (gp 198  table 2: me obato da silva et and hardrah tress about ch an obtained e constant that 4 [4], where > 550 mpa, ac occur when 5]. obviously ess near to no n function of 0mpa 00mpa oy, astm a uests high m a 743/a 743 ) and fatigue vely. c si 1.00 11 emical properti pa) sy (m  4 575  echanical prope alii, frattura ed t [3] became haracteristic l expression by is a function   rtn a f s i ccording to e the stress at y, the peterso otch decrease tensile streng a743 ca6nm mechanical str m [6] are sh properties ba omposition ( cr ni 1.5-14 3.5–4 ies of astm a mpa) srt (mp  35 918  erties of astm d integrità struttu base for aver ength from r y kuhn and h n of the tensile s a constant m eq. 5 distance d0 fr on’s model is e linearly. th gth according m, which has rength and t howed in tab ased on paral (%) i mo 4.5 0.4–1.0 a743 ca6nm pa) hardnes 1 273.0  m a743 ca6n urale, 14 (2010) rage stress mo root notch eq hardraht, whe e strength. material that rom root notc a particular e eq. 6 expre g to eq. 7. been used in that it resist b. 1. the mec llel-projected p 0.04  alloy steel [6]. ss (hb)  7.0 nm alloy steel. ) 36-44; doi: 10 odels. this m quals the end ere  is root n can be quant ch is equal or case of avera ess this relatio n the fabricat the corrosio chanical (you method acco s 0.03 .3221/igf-esis. model assumes durance limit notch radius, (3) tified in func (4) (5) r more than l age stress mo on, where ap (6) (7) tion of hydra on. its chem ung modulus ording to silva 14.04 37 s the of a w is ction limit odel. p is a aulic mical s, e, a [7] http://www.gruppofrattura.it http://dx.medra.org/10.3221/igf-esis.14.04&auth=true b. l 38 ac ho this fig fac sta th his alte obs stre tw mo dis pro wo th init thr wil dep inc lobato da silva cording to p owever, silva s work. the s g. 1 and its g ctor calculated 3. t k  aircase method he staircase m storically, its ernative but s serving the re ess or dose, f wo methods o ood [15] and tribution of t ovides better ork. he dm metho tial stress for rough of para ll be tested at pends on the creased or dec et alii, frattura ta parallel-projec et al. predict specimens we geometric par d by eq. 8 [10 065 3.370    kt 2.4 2.0 1.5 d method has be origin is ass similar biolog eaction that i for that an acc of data reduct zhang-kecec the fatigue lim and more co od was popul r a specific f allel-projected t a lower stre previous tes creased [17].t ed integrità stru parame a b able 3: basquin cted method 360.1 14.0 m ere produced rameters are 0]. 2 0.647 a c        t a (mm) 42 3.00 4 5.00 5 8.00 een recomme sociated to b gical stimuli. i s produces in ceptable prop tion for statis cioglu [16]. b mit, normal a onservative pr arized by litt fatigue life. i d or s-n curv ess level. oth st results and the stress inc utturale, 14 (201 eter estim estimate 1659.1 -0.108 n’s fatigue para for fatigue l mpa accordin d in accordanc shown in ta 2 2 0.658 a c       figure b (mm) c ( 80.00 3 80.00 3 80.00 3 table 4: s nded by man biological assa in other word n a living orga portion of spe stical properti both approach and weibull, redictions tha tle [18]. it use initially, the f ve. if the spec herwise, a new the experime crements are 10) 36-44; doi: mate value e deviation 116.4 0.006 ameter obtaine life of 2.106 ng to staircas ce with astm ab. 4. in addi 3 2 8 a c       1: flat plate sp (mm) d (mm 0.00 7.50 0.00 7.50 0.00 7.50 specimen geom ny standards [ ay. biologica ds, it is basica anism [14]. in ecimens survi ies of fatigue hes are based respectively. an zhang-ke es a simple sy fatigue limit cimen fails be w test will be ent continues usually cons 10.3221/igf-esi confidence lower 1416.3 -0.120 ed of parallel-p cycles, the e e method [8] m e 466-96 [ ition, tab. 4 pecimen. m) e (mm) 0 160.00 0 160.00 0 160.00 metric data. [11-13] to eva al assay is a ally the measu n both cases, ives. strength at a d on maximum according to cecioglu meth ystematic me and its stand efore to infini conducted a s in this mann stant and are is.14.04 intervals upper 1901.9 -0.097 projected meth endurance lim . therefore, t [9] and forged presents the net area (m 105.00 150.00 180.00 aluate the fatig set of techni urement of th , one want to specific fatig m likelihood o lin [17], the hod (zk). th ethodology wh dard deviatio ite life (say 2· at upper stres ner in sequen in the range hod. mit is 344.00 this is the fati d into flat pla e analytic stre mm2) gue limit stati iques used in he potency of o determine th gue life are m estimation an e dixon-moo herefore it wi here the spec on are estima 106 cycles), th ss level. in th nce with the of half to tw 0 24.13 mpa igue limit use ates as shows ess concentra (8) tistical proper n comparison f any stimulu he level stimu most used: dix nd assume ta od method (d ill be used in cimen is teste ate, for exam he next specim hat way, each stress level b wice the stand [7]. ed in s the ation rties. n of us by ulus, xonarget dm) this ed at mple, men test eing dard http://www.gruppofrattura.it http://dx.medra.org/10.3221/igf-esis.14.04&auth=true dev rec sta th lim the th equ dis nor bro de 9 a th oth or th to fati acc ord be th dev ten a m ló con in viation of th commends ru atistical analys he dm metho mit. it requires e survivals or he stress levels uations propo tributed; (ii) rmal distribu ownlee [21] a enoting by ni t and 10, respec i a   i b   he eq. 11 sho herwise, it is u dm s  1 dm   0 dm   he staircase m predict estim igue [22]. thi curate standar der to evaluat an improvem he eq. 14 sho viation by di nd increase th sl   modified corr ren correctio nstants depen pc a  this work the e fatigue lim unning the tes sis od provides a s that the two only the failu s s spaced eq osed by dix the sample s ution should b assures that th the number o ctively. i in 2 i i n ows the estim used minus si 0 i a s d n       1.62 b n d n      0.53d if methods are n mate accurate is method con rd deviation. te and to imp ment in all ma ows the estim ixon-mood a he deviation e 3 dm n n         rection was d on. the form ndent on the n 3 dm n a n        e largest devia b. lo mit. lee [19] st at least 15 s approximate o statistical p ures. qually with a xon and moo size should b be grossly es he samples fro of the less fre mate of the ign. the eqns 1 2      2 2 0.029 i i a n     2 2 i i b n a n   notably accura e of fatigue l ncentrates th braam and v prove the relia aximum-likelih mate of stand nd n is the t stimate by di developed wh of the propo number of sa m dmb d       ation will be u obato da silva et recommends specimens. formulas to properties be chosen increm od [15] respe be big, aroun stimated prev om 5 to 10 sp equent event mean, where s. 12 and 13 s 9    if  b  0.3 ate and efficie limit standard e most exper van der zwaag ability of stan hood evaluati dard deviation total specime ixon-mood. hich attempted osed standard amples, see t used, sl or alii, frattura ed s a value 5% calculate the determined b ment d are nu ect three assu nd 40 to 50 s viously in ord pecimens are at the stress l e the plus sig show the estim  2 2 0. i i n a n     ent in terms d deviation u rimental point g [23], svenss ndard deviatio ion procedur n corrected b en number. t d to allow a g d deviation es ab. 5. pc . d integrità struttu % less than fa mean, dm , a by using the d umbered i wh umptions: (i) specimens or der to specify reliable to de level i, two qu gn is used if mate of stand .3 to quantify th using these m ts near the m son and de m on and propo res. by svensson-l this correctio greater range stimate, pc , i urale, 14 (2010) atigue limit i and standard data of the le here i=0 for t the fatigue r more and ( y the step of etermine the m uantities can f the more fr dard deviation he mean fatig methods with mean therefore maré [24], lin sed a linear c lóren [26], on is a strictly of unbiased e is shown in e ) 36-44; doi: 10 nitially estim deviation,  ess frequent e the lowest str strength sho (iii) the stand f stress increm mean fatigue be calculated requent even n. gue strength h small samp e is more diffi [17] and rab correction fac sl , where d y function of estimation th eq. 15, where .3221/igf-esis. mated. collin dm ,of the fat event, either o ress level s0. ould be norm dard deviation ments. howe limit. d: a and b, e (9) (10) nt is survival (11) (12) (13) but very diffi les at high c ficult to obtain bb [25] worke ctor and foun dm is the stand f sample size (14) an the svenss e a, b, and m (15) 14.04 39 [20] tigue only the mally n of ever, eqns. and ficult cycle n an ed in nd to dard and sonm are http://www.gruppofrattura.it http://dx.medra.org/10.3221/igf-esis.14.04&auth=true b. l 40 fa in stre stan the lim 5% re en en fig dix exp abo nor con wit wit t lobato da silva tigue testing order to dete ess ratio, r, ndard deviati e percentile b mit intervals ar % of fatigue lim notch t esults and ndurance limit f hree exp the stair ndurance limit f g. 3 plots the xon-mood a perimental tim ove average f rmal distribu nstant. it can th specimens th less accura t et alii, frattura ermine experi of -1 at a fr ion number u between step re presented mit initially es h radius (mm 3 51 52 8 table 6: exper d discussio for notch radi perimental ge rcase testing r figur for notch radi staircase test and svensson me, the tests s fatigue streng ution. in addi be verified th 6 to 10. the cy in the stan ed integrità stru table 5: con imentally the requency of used to determ size and mat too in the sam stimated by s m) deviation 1.6 1.6 2.2 1.6 rimental param n ius of 8 mm eometric cond results for no e 2: plot of sta ius of 3 mm ting results fo n-lóren equ started from b gth estimate, ition, from s hat experimen erefore, in thi ndard deviatio 203 214 225 236 247 258 270 281 292 303 0 s tr es s le v el ( m p a) utturale, 14 (201 specimens 8 10 12 15 20 nstants used in fatigue limit 15 hz with mine the clas terial enduran me table. it c staircase meth n class d 10 3 10 5 10 1 10 1 meters of stairc ditions were t otch radius of aircase testing or notch radi uations, respe bigger class. i the probabil second specim ntal results fo is case five sp on. 1 2 3 failure su 10) 36-44; doi: # (n) a 1.30 1.08 1.04 0.97 1.00 n proposed stan of notched m a universal s ss of staircase nce limit for 2 can be observ hod in silva [8 (mm) fd  3.99 1. 5.47 1. 1.82 0. 1.18 3. case method (1 tested in this f 8 mm. the f results for not ius of 3 mm. ectively, for it can be obs lity of experi men to eight or the specim pecimens wer 3 4 5 specimen uspension 10.3221/igf-esi b m 1.2 1.72 1.2 1.10 4 1.2 0.78 1.2 0.55 1.2 0.45 ndard deviation materials for servo-hydraul e method; the 2.106 cycles. ved from tab 8] as lee reco f (%) uppe .1 .5 .5 .0 fist testing sta study and th fatigue limit f ch radius of 8 the average this case a served that th imental limit th specimen ens from 1 to re sufficiently 6 7 8 number is.14.04 n correction [2 2.106 cycles, lic mts mac e quantity of in addition, b. 6 that the s ommends [19 r lim. (mpa) 190.2 223.0 228.5 303.2 age and 2 secon he results are for this case is mm for 2.106 fatigue limit are 184.2 2. his class corre fatigue is un the experim o 5 is statistic y to determine 9 10 1 22]. all testing wa chine. the t class used, s the upper an stress increme 9]. lower lim. 154.3 173.8 212.1 202.6 nd testing stage shown in ta s 355.1 19.1 cycles. and its scatte .6 mpa. in o sponds 1.6 st nder is more ental behavio ally similar to e the average 1 as performed tab. 6 shows s; the step siz nd lower stair ents are less t (mpa) 3 8 1 6 e). ab. 9. fig. 2 p mpa. er determined order to red tandard devia than 89% f or is regular o results obtai e fatigue limit at a the ze, d; rcase than plots d by duce ation for a and ined t but http://www.gruppofrattura.it http://dx.medra.org/10.3221/igf-esis.14.04&auth=true en sta spe the sec th inc of no ac dec ndurance limit f arting from th ecimens were e result was r cond stage is he results obta crement of th step size is re otch strength a cording to o crease in endu for notch radi he obtained re e used and the refined and m 214.6 1.2 m fi ained in secon he staircase m esponsible for nd notch fatigu obtained resu urance limit w fi b. lo figure 3: pl ius of 5 mm esults previou e endurance l more five spe mpa. igure 4: plot of nd stage pres method. the s r this fact. ue reduction st ults starting f when notch ra igure 5: plot of 154 158 162 166 170 174 178 182 186 190 0 1 s tr es s le ve l (m p a) 174 179 185 190 196 201 207 212 218 223 0 1 s tr es s le v el ( m p a) fa 212 214 216 218 219 221 223 225 227 228 0 1 s tr es s le v el (m p a) obato da silva et lot of staircase usly the stairc limit determin ecimens were f staircase testi sented a reduc standard devi trength, kf , b from experim adius decreas f staircase testi 2 3 2 3 ilure suspens 1 2 3 alii, frattura ed e testing results case method f ned was 220. e tested as it ing results for ction at avera iation decreas behavior mental data an se for astm ing results for 4 5 6 specimen numb 4 5 6 specimen numb sion 4 5 6 specimen numb d integrità struttu s for notch rad for notch rad 3 3.6 mpa. f can be seen notch radius o age endurance sed three tim nd shown in a743 ca6nm notch radius o 7 8 9 ber failure su 6 7 8 ber 6 7 8 ber failure sus urale, 14 (2010) dius of 3 mm. dius was execu fig. 4 shows in fig. 5. th of 5 mm (stage e limit becaus mes in relation n tab. 7 and m alloy steel. of 5 mm (stage 10 11 spension 9 10 9 10 spension ) 36-44; doi: 10 uted at two st the testing re he fatigue lim e 1). se the refinem n to first stag d fig. 6 we c . e 2). .3221/igf-esis. tages. firstly, esults. follow mit taken acco ment in the st ge. the decrea can to observ 14.04 41 five wing, ount tress ased ve a http://www.gruppofrattura.it http://dx.medra.org/10.3221/igf-esis.14.04&auth=true b. l 42 tab pet not em lobato da silva b. 8 and fig. terson and n tch size the mpirical model et alii, frattura . 7 show an neuber’s empi notch factor ls shows that table 8: e figure 7: com 150. 200. 250. 300. s fe ( m p a) k f ed integrità stru not table 7: end increase of n irical models r are more d astm a743 figure 6: com notch radiu 3 5 8 experimental an mparison betw 3.02.00 0 0 0 0 32.00 1.00 2.00 3.00 utturale, 14 (201 tch radius (mm 3 5 8 durance limit f notch fatigue are statistica different. the 3 ca6nm all mparison betwe us (mm) ex 1 2 1 nd theory fatig ween experimen 00 4.00 3.00 4.00 10) 36-44; doi: m) enduran mean 184.2 214.6 255.1 for each notch reduction st ally very simil e comparison oy steel is les een endurance fatigue notc xperimental eq. 2 .96  0.08 2.04  0.07 .55  0.12 gue notch redu ntal and theory 5.00 notch radiu 5.00 notch radius 10.3221/igf-esi nce limit. sfe (m n deviatio 2 2.6 6 1.2 1 19. based on stair trength with lar when notc n between ex s sensitive th limits of notch ch reduction neuber eq. 4 2.27  0.03 1.95  0.05 1.51  0.06 uction factor es y models for no 76.00 us (mm) 7.006.00 s (mm) is.14.04 mpa) on 6 2 .1 rcase method. decrease of n ch radius is b xperimental an prediction hed specimens factor. kf peterson eq. 6 2.37  0.03 2.02  0.05 1.54  0.06 stimate for each otch fatigue re .00 8.00 experimen 0 8.00 experime neuber peterson notch radius. big. however notch fatigue ns (fig.7). s. h geometry. duction factor 9.00 ntal data 9.00 ental in addition, r, when decre e factor and . , the eases the http://www.gruppofrattura.it http://dx.medra.org/10.3221/igf-esis.14.04&auth=true co pro aro dec rad em mo ac re [1] [2] [3] [4] [5] [6] [7] [8] [9] t t n specim 1 2 3 4 5 6 7 8 9 10 sf (m onclusion he aim o staircase sizes. a operties are e ound average creases as it w dius, the pred mpirical model odels used. cknowledg his proje are grate eferences a. buch, fa w. yao, k. p. kuhn, h naca tn h. neuber, r. e. peters astm/a74 resistant fo b. l. silva, j mechanical b. l. silva, j engineering astm/e46 (2002). t t notch radius men # s (m 1 190 2 186 3 182 4 186 5 182 6 186 7 182 8 186 9 182 0 178 mpa) 1 ns of this work w e method wa reduction da easily determ e. however, was waited. t dictions are s ls does not p gements ect was suppo efully acknow s atigue strengt xia, y. gu, i h. f. hardrat 2805, langley int. j. of app son, in: meta 43/a743m – or general ap j. l. a. ferre engineering j. l. a. ferre g, gramado, r 66-96, standa b. lo (3 mm) mpa) cycles .19 1.2.106 .19 1.4.106 .20 run ou .19 8.1.105 .20 run ou .19 1.2.106 .20 run ou .19 9.1.105 .20 1.7.106 .21 7.5.105 184.2  2.6 table was to evalua as used to det ata method b mined and the the standard therefore, th tatistically sim predict correc orted by cen wledged. we a th calculation int. j. fatigue th, an engin y aeronautica plied mec., 2 al fatigue, g. – 06, standard pplication, (20 eira, f. olivei , gramado, r eira, j. a. araú rio grande d ard practice obato da silva et not specimen 6 1 6 2 t 3 5 4 t 5 6 1 t 2 5 3 6 4 5 5 sf (mpa) 9: staircase te ate the effect termine the e y dixon and e mean value d deviation d e notch fatig milar and can tly. in additi trais elétricas are thankful t n, trans tech e, 17 (1994) 2 neering metho al laboratory 8 (1961) 544. sines & j. l. d specification 006). ira, j. a.araúj rio grande d újo, in: proce do sul, brazil for conducti alii, frattura ed tch radius (5 m n # s (mpa) 223.03 217.56 223.03 217.56 223.03 221.20 219.38 217.56 215.73 213.91 ) 214. sting results fo of notch fati endurance lim mood was v e is has very does not reli gue reduction n to predict t ion, the alloy s do norte do o god for th h publications 245. od for estim y, washington waisman edi n for casting jo, in: procee o sul, brazil ( eedings of co l (2009). ing constant d integrità struttu mm) ) cycles 8.2.105 run out 5.2.105 run out 4.0.105 7.4.105 7.6.105 4.5.105 9.4.105 run out 8  1.2 or 2.106 cycles igue behavior mit and its sta very efficientl y accuracy be iable. the fa factor decre the fatigue be steel tested in o brasil s. a. he blessing of s, switzerland mating the no n (1952). itors, new yo gs, iron–chro edings of co (2009). obem 2009, t amplitude a urale, 14 (2010) notch specimen # 1 2 3 4 5 6 7 8 9 10 sf (mpa) (r=-1). r of astm a andard deviat ly to determin ecause the te atigue limit d eases when no ehavior, othe n this researc eletronorte to live, to pro d (1988). otch-size effe ork, mcgraw omium, ironobem 2009, 2 20th internat axial fatigue ) 36-44; doi: 10 radius (8 mm s (mpa) 258.49 269.67 280.86 269.67 258.49 269.67 280.86 269.67 258.49 247.30 255.1  a743 ca6nm tion for three ne fatigue lim echnique con decreases wh otch radius in erwise peterso ch is less sens e and finatec oduce and to fect in fatigu w hill, (1959) chromium-n 20th internatio tional congre e tests of m .3221/igf-esis. m) cycles run out run out 1.1.106 9.6.105 run out run out 15.105 4.1.105 2.2.105 run out 19.1 m alloy steel. e different no mit. the statis ncentrates po hen notch ra ncreases. for on and neub sitive than the c. these supp develop scie e tests on s 293. nickel, corro onal congres ess of mechan metallic mater 14.04 43 the otch tical oints adius r big ber’s eory ports ence. steel, sion ss of nical rials, http://www.gruppofrattura.it http://dx.medra.org/10.3221/igf-esis.14.04&auth=true b. l 44 [10 [11 [12 [13 [14 [15 [16 [17 [18 [19 [20 [21 [22 [23 [24 [25 [26 re t lobato da silva 0] w. c. youn 1] british stan keynes: bri 2] standard m 3] normalizati normalisati 4] d. j. finney 5] w. j. dixon 6] j. zhang, d washington 7] s-k. lin, y 8] r. e. little, 9] y-l. lee, j butterworth 0] j. a. collin wiley and s 1] k. a. brow 2] r. pollak, a 3] j. j. braam, 4] t. svensson 5] b. r. rabb, 6] t. svensson esponsibili he autho t et alii, frattura ng, r. g. bud ndard 3518: m itish standard method of stati ion francais ion (1991). y, probit ana n, a. m. moo d. b. kececio n, (1998) 297. y-l. lee, m-w , statistical d j. pan., r. b h-heinemann n, failure of sons. inc. (19 wnlee, j. l. ho a. palazotto, t s. van der zw n, s. lorén, j. , trans. eng. n, s. lorén, j. ity notice ors are the on ed integrità stru dynas, roark’s methods of fa d institution ( istical fatigue e a 03-405: alysis, cambri od, j. amer st oglu, in: the . w. lu, int. j. o esign of fatig b. hathaway, n, oxford, uk materials in 93) odges jr., m. r t. nicholas, m wang, j. testi . de maré, ex sci., 40 (2003 . de maré, b. e nly responsibl utturale, 14 (201 s formulas fo atigue testing; (1966). e testing, jsm essais de f idge universit tar assoc., 43 4th issat in of fatigue, 23 gue experime m. e. bark k (2005). mechanical d rosenblatt, j. mechanical o ing eval., 26 xtremes, 2:2 ( 3) 447. wadman, ex le for the prin 10) 36-44; doi: or stress & st ; part 5: guide e s 002, japa fatigue, tou ty press, cam 3 (1948) 109. nternational c 3 (2001) 75. ents, john wi key, fatigue design – anal . am. stat. a of material, 38 (1998)125. (1999) 165 xtremes, 2 (20 nted material 10.3221/igf-esi train, 7th ed., m e to the appli an society of ur europe. p mbridge (1971 conference on iley & sons, n testing and lysis. predicti ssoc., 48 (195 8 (2006) 1170 000) 165. included in th is.14.04 mcgraw-hill ication of sta mechanical e paris la defe 1). n reliability a new york (19 analysis (th ion. preventio 53) 262. 0. his paper. l (2002). atistics, linfor engineers (19 fense: l’assoc and quality i 975). heory and pr on, 2nd ed., n rd wood, mi 981),. ciation franc in design, se ractice), else new york: j ilton caise eatle, evier john http://www.gruppofrattura.it http://dx.medra.org/10.3221/igf-esis.14.04&auth=true << /ascii85encodepages false /allowtransparency false /autopositionepsfiles true /autorotatepages /none /binding /left /calgrayprofile (dot gain 20%) /calrgbprofile (srgb iec61966-2.1) /calcmykprofile (u.s. web coated \050swop\051 v2) /srgbprofile (srgb iec61966-2.1) /cannotembedfontpolicy /error /compatibilitylevel 1.4 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/hrv (za stvaranje adobe pdf dokumenata najpogodnijih za visokokvalitetni ispis prije tiskanja koristite ove postavke. stvoreni pdf dokumenti mogu se otvoriti acrobat i adobe reader 5.0 i kasnijim verzijama.) /hun 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can be opened with acrobat and adobe reader 5.0 and later.) >> /namespace [ (adobe) (common) (1.0) ] /othernamespaces [ << /asreaderspreads false /cropimagestoframes true /errorcontrol /warnandcontinue /flattenerignorespreadoverrides false /includeguidesgrids false /includenonprinting false /includeslug false /namespace [ (adobe) (indesign) (4.0) ] /omitplacedbitmaps false /omitplacedeps false /omitplacedpdf false /simulateoverprint /legacy >> << /addbleedmarks false /addcolorbars false /addcropmarks false /addpageinfo false /addregmarks false /convertcolors /converttocmyk /destinationprofilename () /destinationprofileselector /documentcmyk /downsample16bitimages true /flattenerpreset << /presetselector /mediumresolution >> /formelements false /generatestructure false /includebookmarks false /includehyperlinks false /includeinteractive false /includelayers false /includeprofiles false /multimediahandling /useobjectsettings /namespace [ (adobe) (creativesuite) (2.0) ] /pdfxoutputintentprofileselector /documentcmyk /preserveediting true /untaggedcmykhandling /leaveuntagged /untaggedrgbhandling /usedocumentprofile /usedocumentbleed false >> ] >> setdistillerparams << /hwresolution [2400 2400] /pagesize [612.000 792.000] >> setpagedevice microsoft word numero_35_art_21 j. albinmousa, frattura ed integrità strutturale, 35 (2016) 182-186; doi: 10.3221/igf-esis.35.21 182 focussed on crack paths multiaxial fatigue crack path prediction using critical plane concept jafar albinmousa (http://orcid.org/0000-0002-2395-5008) king fahd university of petroleum & minerals, dhahran 31261, saudi arabia binmousa@kfupm.edu.sa abstract. prediction of fatigue crack orientation can be an essential step for estimating fatigue crack path. critical plane concept is widely used due to its physical basis that fatigue failure is associated with certain plane(s). however, recent investigations suggest that critical plane concept might need revision. in this paper, fatigue experiments that involve careful measurement of fatigue crack were reviewed. predictions of fatigue crack orientation using critical plane concept were examined. projected length and angle were used to characterize fatigue crack. considering the entire fatigue life, this average representation suggests that it is more reasonable to assume the plane of maximum normal strain as the critical plane even though fundamentally the plane of maximum shear strain is more likely to be the critical one at early initiation stage. keywords. multiaxial fatigue; crack growth; critical plane; crack path. introduction here is still no unified definition of fatigue crack initiation. yet, there is an agreement that there are three classes of fatigue crack growth: microscopic, small and macroscopic [1]. still these classes are not exactly defined and there is an overlap between them. in general, cracks with lengths less than 102 μm are considered microscopic and their growth is governed by the microstructure texture. based on the literature, such crack size marks the initiation size [2]. cracks with lengths between 102 to 103 μm are considered small and such range represents what is so-called early growth stage [3, 4]. it is widely accepted that fatigue correlations are valid during initiation and early growth stages. after that, fracture mechanics is used to predict propagation life that is dominated by growth of macroscopic cracks. the concept of critical plane was developed based on the experimental observations that fatigue cracks initiate at specific planes [3, 5]. the current practice for evaluating critical plane models consists of three steps. considering a maximum shear strain damage parameter, the first step is to search for critical plane by transforming hysteresis loops at different planes using plane stress-strain transformation relations. the critical plane is the plane at which shear strain is maximum. this plane may only correspond to the orientation of the inception or early initiation of crack, with length scale in the order of microns. in the second step the corresponding axial and shear stresses are obtained from the hysteresis loops on this critical plane. finally, fatigue life is predicted by coupling the damage with a life equation. this procedure implies that crack will initiate at the plane of maximum shear strain and it will grow, within early growth stage, in the same orientation. of course, this is not always the case as fatigue cracks may grow in a zigzag paths. recently, albinmousa and jahed [6] examined the predictions of fatigue crack orientation on smooth specimens subjected to multiaxial loading using critical plane concept. they showed that reversed analysis for predicting fatigue life by assuming the critical plane as the experimentally observed plane showed that the predictions of strain-based models were mostly non-conservative. t j. albinmousa, frattura ed integrità strutturale, 35 (2016) 182-186; doi: 10.3221/igf-esis.35.21 183 conversely, satisfactory predictions were obtained by evaluating the jahed–varvani [7] energy model on the observed planes. albinmousa and jahed suggested that the assumption of critical plane based on maximum driving parameter such as normal or shear strains might be idealistic. it was rather suggested that redefining the physical size of the analysis by adopting an average measure could resolve the aforementioned conflict. they proposed that if a crack grows in zigzag path, in average and for a limited size it could still be considered as a single crack with a single orientation as illustrated in fig. 1. in this figure, the projected crack length, lp, is defined as the straight distance between the tips of the crack and the orientation of this line is defined by the angle β. the objective of this study is to investigate the applicability of the proposed idea by albinmousa and jahed [6]. β1 β2 β3 β4 β5 n1 n2 n3 n4 n5 figure 1: definition of the projected crack length, lp, and its orientation, β. ni+1>ni. experiment and results ecause the focus of this paper is fatigue, which includes both initiation and early growth stages, tests should be performed on smooth specimens. unlike fracture mechanics experiments in which a determined flaw size is required or introduced before the application of loading, detection and monitoring fatigue crack growth in fatigue tests is a demeaning task. experimental analysis considered in this study was conducted by hoffmeyer et al. [8]. combined axial-torsional cyclic tests were performed on smooth specimens machined from and aluminum al5083 (almg4.5mn). the monotonic and cyclic properties of this alloy are as listed in tab. 1 [8]. summary of investigated cases in this paper is listed in tab. 2. monotonic cyclic e (mpa) 68,000 k’ (mpa) 544 ν 0.33 n’ 0.075 sy0.2% (mpa) 169 σ’f (mpa) 780.3 sut (mpa) 340 ε’f 1.153 %ar 20 b -0.114 table 1: monotonic and cyclic properties al5083 aluminum [8]. incremental measurements of actual crack length, projected crack length lp and orientation β were performed for the tests listed in tab. 2. variations of projected angle β and crack actual crack length with cycling are plotted in fig. 2. in addition, planes of maximum normal and maximum shear strains were also determined for each case. three general observations can be made from fig. 2. fatigue crack grows exponentially with cycling. the variation of the projected angle β with cycling is relatively steady and closer to the plane of maximum normal strain than the plane of maximum shear. b j. albinmousa, frattura ed integrità strutturale, 35 (2016) 182-186; doi: 10.3221/igf-esis.35.21 184 no. loading εa (%) γa (%) σa (mpa) τa (mpa) nf 1 axial 0.300 0.00 207.1 0.0 28,600 2 0 0.231 0.40 161.0 103.0 47,500 3 0 0.202 0.35 138.0 103.1 57,845 4 90 0.346 0.60 247.7 157.8 2,700 5 90 0.231 0.40 161.8 105.9 28,500 6 90 0.202 0.35 143.8 113.8 40,860 7 45 0.231 0.40 163.9 131.8 20,900 table 1: summary of cyclic tests for almg4.5mn [8]. figure 2: variations of projected angle β and crack length with cycling. planes of maximum normal and maximum shear strains are indicated by red-dashed and green-dashed lines, respectively. 0 75 150 225 -90 -60 -30 0 30 60 90 0.0 0.2 0.4 0.6 0.8 1.0 c ra ck l en g th ( μ m ) o ri en ta ti o n ( °) n/nf no. 1 beta max normal max shear length exp fit 0 500 1000 1500 -90 -60 -30 0 30 60 90 0.0 0.2 0.4 0.6 0.8 1.0 c ra ck l en g th ( μ m ) o ri en ta ti o n ( °) n/nf no. 2 beta max normal max shear length exp fit 0 40 80 120 160 -90 -60 -30 0 30 60 90 0.0 0.2 0.4 0.6 0.8 1.0 c ra ck l en g th ( μ m ) o ri en ta ti o n ( °) n/nf no. 3 beta max normal max shear length exp fit 0 75 150 225 -90 -60 -30 0 30 60 90 0.0 0.2 0.4 0.6 0.8 1.0 c ra ck l en g th ( μ m ) o ri en ta ti o n ( °) n/nf no. 4 beta max normal max shear length exp fit 0 500 1000 1500 2000 -90 -60 -30 0 30 60 90 0.0 0.2 0.4 0.6 0.8 1.0 c ra ck l en g th ( μ m ) o ri en ta ti o n ( °) n/nf no. 5 beta max normal max shear length exp fit 0 40 80 120 160 -90 -60 -30 0 30 60 90 0.0 0.2 0.4 0.6 0.8 1.0 c ra ck l en g th ( μ m ) o ri en ta ti o n ( °) n/nf no. 6 beta max normal max shear length exp fit 0 400 800 1200 1600 -90 -60 -30 0 30 60 90 0.0 0.2 0.4 0.6 0.8 1.0 c ra ck l en g th ( μ m ) o ri en ta ti o n ( °) n/nf no. 7 beta max normal max shear length exp fit j. albinmousa, frattura ed integrità strutturale, 35 (2016) 182-186; doi: 10.3221/igf-esis.35.21 185 discussion here is no single fatigue failure model that can be viewed as widely accepted by the research community to be applicable to varieties of materials and loading conditions. because it has been found that the effectiveness of an individual fatigue model depends on the material, the loading conditions and the failure mechanisms involved. experimental observations on fatigue failure indicate that fatigue crack nucleation occurs at the persistent slip bands (planes). the critical plane approach was originated on the basis of this observation. as a result, component of stress or strain are evaluated at specific planes for fatigue damage calculation. the fact that critical plane models can predict both fatigue life as well as fatigue cracking plane gives these models an advantage over other models that provide predictions for only fatigue life. critical plane models became popular because of their success in predicting fatigue life for various engineering materials and under different loading conditions [5, 9, 10]. however, it was pointed out by several investigations [4, 6, 9] that even though these models can predict fatigue life with good accuracy (as compared to experimental observations) they may not succeed in providing acceptable estimations of the fatigue cracking planes. for example, models that assume the maximum tensile plane as the critical plane fail to predict the cracking plane of material that fails under shear mode and vice versa. furthermore, in a recent experimental investigation [6] the fatigue crack planes were determined using uniaxial and multiaxial cyclic loading tests and then fatigue lives were successfully predicted using critical plane approach. however, the predictions of fatigue lives were far from being reasonable by pre-defining the critical plane as the measured cracking plane. the discrepancy in the aforementioned experimental observations suggests that damage parameters in critical plane models need revision or the definition of critical plane needs revision. however, this argument is still subject to valid criticism due to the size range of the measured crack. metallurgical factors such as texture, grain size, grain boundary, defects and inclusion, and second phase particles can influence the fatigue cracking behavior. also, as crack length increases the size of the plastic zone around the crack tip increases that can also influence the fatigue cracking behavior. incorporating all of the aforementioned factors in a single fatigue model is a challenging task. an incremental fatigue model might be a suitable tool to predicting both fatigue life and crack path. on the other hand, the proposed method can be considered as an average approach. in general, the results in fig. 2 indicate that by considering a crack size of about 103 μm, it is more reasonable for the critical plane to be assumed as the plane of maximum normal strain even though fundamentally the plane of maximum shear strain is more likely to be the critical one. fatigue cracks initiate at the plane of maximum shear strain where slip bands occur, however, they change their direction quickly approaching the plane of maximum normal strain. the exponential growth rate of fatigue crack length with cycling has long been observed and modelled in literature [1, 11]. a comprehensive investigation with detailed real time measurements of crack evolution is needed. summary atigue experiments on smooth specimens machined from aluminum al5083 (almg4.5mn) were analyzed. specimens were tested under multiaxial cyclic loading. detailed measurements of crack length and orientation were made. fatigue crack was characterized using an average projected crack length and an angle. such representation suggests that plane of maximum normal strain could be used as the critical plane for fatigue damage calculations. further detailed investigation is required to examine the applicability of the proposed idea and to determine both fatigue damage parameter and fatigue life equation. acknowledgement he author would like to acknowledge the support of king fahd university of petroleum & minerals (kfupm) for supporting this work under sabic fast track, an internally funded project from dsr (project no. sb121003). a special thank is due to prof. michael vormwald from darmstadt university of technology in germany for providing detailed images of crack growth on which the present analysis was conducted. t f t j. albinmousa, frattura ed integrità strutturale, 35 (2016) 182-186; doi: 10.3221/igf-esis.35.21 186 references [1] shamsaei, n., fatemi, a., small fatigue crack growth under multiaxial stresses, international journal of fatigue, 58 (2014) 126-135. [2] sakane, m., zhang, s.d., kim, t., notch effect on multiaxial low cycle fatigue, international journal of fatigue, 33 (2011) 959-968. [3] socie, d., critical plane approaches for multiaxial fatigue damage assessment, astm special technical publication, 1191 (1993) 7-7. [4] reis, l., li, b., de freitas, m., analytical and experimental studies on fatigue crack path under complex multi-axial loading, fatigue & fracture of engineering materials & structures, 29 (2006) 281-289. [5] fatemi, a., shamsaei, n., multiaxial fatigue: an overview and some approximation models for life estimation, international journal of fatigue, 33 (2011) 948-958. [6] albinmousa, j., jahed, h., multiaxial effects on lcf behaviour and fatigue failure of az31b magnesium extrusion, international journal of fatigue, 67 (2014) 103-116. [7] jahed, h., varvani-farahani, a., upper and lower fatigue life limits model using energy-based fatigue properties, international journal of fatigue, 28 (2006) 467-473. [8] hoffmeyer, j., döring, r., seeger, t., vormwald, m., deformation behaviour, short crack growth and fatigue livesunder multiaxial nonproportional loading, international journal of fatigue, 28 (2006) 508-520. [9] jiang, y.y., hertel, o., vormwald, m., an experimental evaluation of three critical plane multiaxial fatigue criteria, international journal of fatigue, 29 (2007) 1490-1502. [10] albinmousa, j., jahed, h., lambert, s., cyclic behaviour of wrought magnesium alloy under multiaxial load, international journal of fatigue, 33 (2011) 1127-1139. [11] navarro, a., de los rios, e.r., short and long fatigue crack growth: a unified model, philosophical magazine a, 57 (1988) 15-36. << /ascii85encodepages false /allowtransparency false /autopositionepsfiles true /autorotatepages /none /binding /left /calgrayprofile (dot gain 20%) /calrgbprofile (srgb iec61966-2.1) /calcmykprofile (u.s. web coated \050swop\051 v2) /srgbprofile (srgb iec61966-2.1) /cannotembedfontpolicy /error /compatibilitylevel 1.4 /compressobjects /tags /compresspages true /convertimagestoindexed true /passthroughjpegimages true /createjobticket false /defaultrenderingintent /default /detectblends true /detectcurves 0.0000 /colorconversionstrategy /cmyk /dothumbnails false /embedallfonts true /embedopentype false /parseiccprofilesincomments true /embedjoboptions true /dscreportinglevel 0 /emitdscwarnings false /endpage -1 /imagememory 1048576 /lockdistillerparams false /maxsubsetpct 100 /optimize true /opm 1 /parsedsccomments true /parsedsccommentsfordocinfo true 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/hrv (za stvaranje adobe pdf dokumenata najpogodnijih za visokokvalitetni ispis prije tiskanja koristite ove postavke. stvoreni pdf dokumenti mogu se otvoriti acrobat i adobe reader 5.0 i kasnijim verzijama.) /hun 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/pdfxoutputintentprofileselector /documentcmyk /preserveediting true /untaggedcmykhandling /leaveuntagged /untaggedrgbhandling /usedocumentprofile /usedocumentbleed false >> ] >> setdistillerparams << /hwresolution [2400 2400] /pagesize [612.000 792.000] >> setpagedevice microsoft word numero_49_art_70_2530 c. bellini et alii, frattura ed integrità strutturale, 49 (2019) 791-799; doi: 10.3221/igf-esis.49.70 791 friction influence on the aa6060 aluminium alloy formability costanzo bellini, gillo giuliano, luca sorrentino university of cassino and southern lazio, department of civil and mechanical engineering, italy costanzo.bellini@unicas.it, http://orcid.org/0000-0003-4804-6588 gillo.giuliano@unicas.it luca.sorrentino@unicas.it, http://orcid.org/0000-0002-5278-7357 abstract. using a finite element calculation code, this work analyses the influence of friction during a stamping test conducted on the aa6060 aluminium-based alloy. the study focuses on phenomena happening when the sheet necking appears. this condition, based on the hill’s localized necking theory and the swift’s diffuse necking theory, is dependent on the material hardening index. this work shows that the punch stroke at the necking condition point is maximum when the main strain measured on the sheet surface is unbalanced and close to a balanced biaxial tension condition. keywords. aa6060 aluminium alloy; forming process; friction influence; formability limit curve. citation: bellini, c., giuliano, g., sorrentino, l., friction influence on the aa6060 aluminium alloy formability, frattura ed integrità strutturale, 49 (2019) 791-799. received: 02.05.2019 accepted: 19.06.2019 published: 01.07.2019 copyright: © 2019 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. introduction n the last decades, the use of aluminium alloys has considerably grown in the automobile and aerospace industries due to its high strength-to-weight ratio and corrosion resistance [1, 2]. the sheet metal stamping operation represents one of the most important processing techniques [3]. the manufacturing process design phase makes use of increasingly accurate models to evaluate the appropriate variables of the product production process. the use of software based on the finite element method (fem) allows significant savings in time and cost, including the limitation of the onerous "trial-and-error" operations. in [4], the authors highlighted how the material constants that characterize the behaviour of aluminium alloys can influence the results of the erichsen test. the effect of the temperature on formability is important too; in fact, the mechanical behaviour of different aluminium alloys at “warm” process temperature was studied by li and ghosh [5], an increase in the flow stress with the decreasing deformation temperature was found by lu et al. [6], while an increased formability in warm temperature condition was found by wang et al. for aa7075 [7]. the effect of the metal microstructure on formability at high temperature was investigated by wang et al. [8] and rokni et al. [9]. furthermore, the behaviour of the aa5083 and aa2017 alloys was also examined in hot pressing processes [10, 11]. the sheet propensity to undergo deformations without incurring the fracture is preserved in the design phase of a stamping process with the use of the formability limit curve (flc). fig. 1 shows a typical formability limit curve. it is i http://www.gruppofrattura.it/va/49/2530.mp4 c. bellini et alii, frattura ed integrità strutturale, 49 (2019) 791-799; doi: 10.3221/igf-esis.49.70 792 represented, in terms of main strain measured in the sheet plane (maximum strain and minimum deform strain), by a graph of the necking and/or fracture conditions. in order to ascertain the success of a sheet metal forming process, the adopted finite element code is equipped with an flc dependent on the mechanical properties of the material. fem verification involves a comparison between the calculated strain during the stamping process and the flc for that material. the flc can be derived from hill’s localized necking theory and swift’s diffuse necking one [12, 13]. it depends on the hardening index obtainable from the results of a tensile test on the studied material. figure 1: typical formability limit curve of metal sheets. β represents the ratio between the principal strains, that are εmax and εmin, evaluated in the sheet plane: min max     (1) while the formability limit parameter can be calculated through the following relation: max min( ) flp flc    (2) in which flc (εmin) constitutes an analytical description of the flc as a function of the principal strain εmin. therefore, on the assumption that β≤0, it can be stated that: min( ) 1 n flc     (3) while, for β>0, it is: 2 min 2 1 ( ) 2 (1 )( 2 2 ) flc n             (4) the use of the flp allows monitoring, by means of fem analysis, the moment and the position in which the instability condition arises (flp = 1) during a plastic deformation process. the flc can be determined using experimental methods [14], theoretical (that is based on necking or fracture criteria of the material) [12, 13, 15] and hybrids [16] (that is combining experimental results with analytical or numerical methods). c. bellini et alii, frattura ed integrità strutturale, 49 (2019) 791-799; doi: 10.3221/igf-esis.49.70 793 both marciniak and nakajima tests can be used for flc experimental determination [17]; banabic's work [18] examines different methods for determining the flc. the simplest experimental method for calculating the flc of a sheet is the nakazima test. this test consists in the movement, at constant speed, of a hemispherical punch against the sheet metal clamped between the die and the blank holder. the sheet is thus subjected to stretching up to the onset of the necking or fracture. to induce different deformation states in the material, the test is carried out on rectangular specimens with different width-length ratio. to detect strains on the sheet metal, a reference grid is drawn on the samples before performing the test. in this work, adopting the fem code and the experimental results presented in [19], the friction influence on the formability of the aa6060 aluminium alloy is highlighted. the friction effects on sheet formability are very important [20]; in fact, yan et al. presented a scale factor to adjust the wanheim/bay friction model [21], ma et al. studied the effect of temperature on the tribological behaviour in tube forming [22], wang et al. investigated the substitution of zinc phosphate precoat with another lubricant coating [23], hol et al. introduced a physical based model for friction simulation in fullscale modelling, taking into consideration the surface topography variation [24], wang et al. examined the dry forming process carried out by means of a coated tool [25], hol et al. presented an advanced friction model, based on coulomb law, suitable for large-scale forming modelling [26], zhang et al. studied the effect of reciprocal speed and surface roughness on the coulomb friction coefficient through fem simulations [27] and wang et al. performed a study on the challenges and trends of friction analysis in sheet metal forming [28]. experimental activity he material considered in this study is the aluminium-magnesium-silicon alloy named aa 6060. it is characterized by the following chemical composition by weight: al 0.6% si-0.3% fe-0.1% mn-0.6% mg-0.1% cu-0.15 % zn0:05% cr-0.1% ti. the constitutive law of the material was determined by the tensile test according to the european standard uni en 10002-1. the results of the tensile test, carried out on 1 mm thick specimens, are reported in [19]. the material is thus characterized in the plastic field by a constitutive equation that can be expressed by the power law: nk  (5) where ε and σ are the equivalent strain and the equivalent stress, respectively; while k is the strength coefficient and n is the hardening index of the material. the experimental activity involves the execution of a stamping operation performed on square-shaped specimens clamped between the die and the blank holder, both presenting a circumferential shape with a radius of approximately 83 mm, and subjected to the action of a hemispherical punch with a radius of 60 mm. the tests are conducted using the equipment designed at the dicem laboratory of the university of cassino. this apparatus is equipped with a load cell that allows detecting the force-stroke curve of the punch. further details on the experimental equipment are reported in [19, 29]. the tests are conducted both in the absence and in the presence of lubrication, in the latter case by using a polytetrafluoroethylene sheet (ptfe) as a lubricant between the punch and the sheet. the influence of friction on the results of the erichsen test conducted on sheets made of different aluminium alloys and on dc05 steel was studied by the authors in [29, 30]. in order to determine the principal strain in the fracture conditions of the material, a grid of circles with a diameter of about 3 mm is drawn on the specimens before executing the forming test. the sheets are cut according to the scheme shown in fig. 2. numerical activity he stamping test is simulated by fem model using the commercial calculation code msc.marc 2005. it consists of a trial similar to the nakazima test considering only the geometry shown in fig. 2. in [19] it is shown that the results of the numerical simulation conducted by means of a two-dimensional analysis (which uses axisymmetric elements) are identical to those achieved through a three-dimensional analysis, that requires shell elements, that are heavier than the axisymmetric ones. therefore, all the results cited below refer to the lighter two-dimensional analysis. fig. 3a shows the layout of the equipment used as well as the sheet discretized with axisymmetric finite elements. t t c. bellini et alii, frattura ed integrità strutturale, 49 (2019) 791-799; doi: 10.3221/igf-esis.49.70 794 figure 2: geometry of the tested specimens. a) b) figure 3: a) scheme of the equipment (punch and matrix) and of the sheet metal discretized with axisymmetric finite elements; b) achievement the necking condition. the sheet metal nodes on the outer edge are constrained to simulate the presence of the blank holder, while the nodes on the symmetry axis are not allowed to move along the direction orthogonal to the symmetry axis itself. the punch and the die are considered as rigid bodies. to analyse the influence of the friction coefficient on the formability of the aluminium alloy aa6060, the modified coulomb friction model is considered, whose relationship between the tangential force ft and the normal one fn is as follows: 2 r t n sv v f f arctg r             (5) c. bellini et alii, frattura ed integrità strutturale, 49 (2019) 791-799; doi: 10.3221/igf-esis.49.70 795 in which vr is the relative sliding speed and rsv is the relative sliding speed below which the friction force tends to vanish. the value of the friction coefficient μ varies between 0 and 0.3. in particular, the friction coefficient assumes the values of 0, 0.025, 0.05, 0.1, 0.2 and 0.3. a user-defined subroutine is used to introduce the most suitable flc in the model. analysis of numerical and experimental results he fem modelling and the experimental tests conducted on the aa6060 aluminium alloy produce the following results: 1. the flc is reached through a deformation path that varies according to the adopted friction coefficient; 2. the distance between the symmetry axis and the point where the flp is equal to 1 decreases as the friction coefficient decreases from the value 0.1 to the value 0, while it is almost constant for a value of the friction coefficient including between 0.1 and 0.3; 3. the experimental results determined in the fracture condition [19] confirm what was found in point 2; 4. the stroke of the punch (measured as the condition flp = 1 is reached) is maximum for a value of the friction coefficient different from zero, that is when the principal strains measured on the sheet surface are unbalanced. fig. 3b shows, in yellow, the achievement of the instability condition (flp = 1) near the sheet symmetry axis and in perfect lubrication conditions (μ = 0). in order to confirm what stated in point 1, fig. 4 shows the deformation paths followed in the different friction conditions simulated in the work. figure 4: deformation paths followed in different friction conditions and flc relevant to the aa6060 aluminium alloy represented in the positive half-plane. in fig. 5, the achievement of the condition flp = 1 in the various friction conditions is observable in yellow. it is possible to point out that the yellow zone moves from the centre to the periphery of the specimen as the friction coefficient increases from 0 to 0.1. fig. 6 shows the distance between the centre of the specimen and the fracture line in a sheet subjected to the experimental test conditions. in [19] it has been observed, through experimental tests, that the fracture line approaches the sheet symmetry axis if the lubrication conditions between the punch and the sheet are improved (theoretically approaching friction coefficient values equal to 0). moreover, the punch stroke measured at the fracture attainment varies from about 26 mm, in the condition of lubrication absence, to about 30 mm, in the case a polytetrafluoroethylene sheet (ptfe) is used as a lubricant. fig. 7 shows the punch stroke trend, measured when the flp = 1 condition is reached, as a function of the friction coefficient. from the figure it is possible to highlight what stated in point 4. this result is a direct consequence of the followed deformation path varying the friction coefficient, reported in fig. 4. in fact, in the positive half-plane, the flc can be represented by the curve passing through the points a-b-c-d. the a-b section of the flc curve is characterized t c. bellini et alii, frattura ed integrità strutturale, 49 (2019) 791-799; doi: 10.3221/igf-esis.49.70 796 by increasing maximum and minimum strain, moving from a to b point. therefore, in this section, the punch stroke required to reach the necking condition increases. in the b-d section, the maximum strain tends to decrease while the minimum strain increases, producing a situation in which the punch stroke increases until it reaches a maximum point (point c) and then it decreases to point d. figure 5: achievement of the condition flp = 1 adopting a value of the friction coefficient equal to 0, 0.05 and 0.1, respectively. figure 6: photo of the specimen where the distance between the fracture line and the sheet centre is showed. figure 7: punch stroke as a function of the friction coefficient. c. bellini et alii, frattura ed integrità strutturale, 49 (2019) 791-799; doi: 10.3221/igf-esis.49.70 797 the fem results of fig. 8 highlight how the distance measured from the centre of the specimen to the point in which flp = 1 varies for different values of the friction coefficient. fig. 9 shows the strain values measured in fracture conditions of the sheet tested using the polytetrafluoroethylene sheet as a lubricant. figure 8: distance evaluated by fem between the flp = 1 point and the specimen centre at the friction coefficient varying. figure 9: strain s at break measured in experimental tests compared to the flc of the necking condition (flp = 1). conclusions n this work, a fem-based two-dimensional model is chosen to analyse the friction influence on the stamping process of circular sheet metal. the sheet is modelled with the mechanical characteristics of the aa6060 aluminium alloy. in addition to the constitutive equation of the material (obtained from the tensile test), the limit formability curve (flc) for the condition of material necking is considered. this curve depends on the hardening index of the tested material. the numerical and experimental results highlight the dependence of some characteristic parameters (such as the punch stroke, the distance between the specimen centre and the necking point) on the friction coefficient value assumed in numerical simulations. i c. bellini et alii, frattura ed integrità strutturale, 49 (2019) 791-799; doi: 10.3221/igf-esis.49.70 798 references [1] tisza, m. and czinege, i. (2018). comparative study of the application of steels and aluminium in lightweight production of automotive parts. j. light mater. manuf., 1(4), pp. 1-10. doi: 10.1016/j.ijlmm.2018.09.001. [2] hirsch, j. (2014). recent development in aluminium for automotive applications. t. nonferr. metal. soc., 24(7), pp. 1995-2002. doi: 10.1016/s1003-6326(14)63305-7. [3] rong, h.h, hu, p., ying, l., hou, w., zhang, j. (2019). thermal forming limit diagram (tfld) of aa7075 aluminum alloy based on a modified continuum damage model: experimental and theoretical investigations, int. j. mech. sci., 156, pp. 59-73. doi: 10.1016/j.ijmecsci.2019.03.027. [4] giuliano, g. (2012). influence of the metal sheet parameters on the results of the erichsen test, appl. mech. mater., 217-219, pp. 2444-2447. doi: 10.4028/www.scientific.net/amm.217-219.2444. [5] li, d. and ghosh, a. (2003). tensile deformation behavior of aluminum alloys at warm forming temperatures, mater. sci. eng. a, 352 (1–2), pp. 279-286. doi: 10.1016/s0921-5093(02)00915-2. [6] lu, j., song, y., hua, l., zheng, k., dai, d. (2018). thermal deformation behavior and processing maps of 7075 aluminum alloy sheet based on isothermal uniaxial tensile tests, j. alloy. compd., 767, pp. 856-869. doi: 10.1016/j.jallcom.2018.07.173. [7] wang, h., luo, y., friedman, p., chen, m., gao, l. (2012). warm forming behavior of high strength aluminum alloy aa7075, t. nonferr. metal. soc., 22(1), pp. 1-7. doi: 10.1016/s1003-6326(11)61131-x. [8] wang, l., strangwood, m., balint, d., lin, j., dean, t.a. (2011). formability and failure mechanisms of aa2024 under hot forming conditions, mater. sci. eng. a, 528(6), pp. 2648-2656. doi: 10.1016/j.msea.2010.11.084. [9] rokni, m.r., zarei-hanzaki, a., roostaei, a.a., abedi, h.r. (2011). an investigation into the hot deformation characteristics of 7075 aluminum alloy, mater. des., 32(4), pp. 2339-2344. doi: 10.1016/j.matdes.2010.12.047. [10] giuliano, g. and samani, f. (2016). comparison between superplastic and non-superplastic grade aa 5083, j. test. eval., 44(6), pp. 2114-2119. doi: 10.1520/jte20150299. [11] giuliano, g. (2016). on the constitutive equation of aa2017 aluminium alloy at high temperature, manuf. lett., 10, pp. 10-13. doi: 10.1016/j.mfglet.2016.08.003. [12] hill, r. (1952). on discontinuous plastic states with special reference to localized necking in thin sheets, j. mech. phys. solids., 1(1), pp. 19-30. doi: 10.1016/0022-5096(52)90003-3. [13] swift, h.w. (1952). plastic instability under plane stress, j. mech. phys. solids., 1(1), pp. 1-18. doi: 10.1016/0022-5096(52)90002-1. [14] banabic, d., lazarescu, l., paraianu, l., ciobanu, i., nicodim, i., comsa, d. (2013). development of a new procedure for the experimental determination of the forming limit curves, cirp ann. manuf. techn., 62(1), pp. 255258. doi: 10.1016/j.cirp.2013.03.051. [15] marciniak, z. (1994). stability of plastic shells under tension with kinematic boundary condition, arch. mech., 17, pp. 577-592. [16] situ, q., jain, m., metzger, d. (2011). determination of forming limit diagrams of sheet materials with a hybrid experimental-numerical approach, int. j. mech. sci., 53(4), pp. 707-719. doi: 10.1016/j.ijmecsci.2011.06.003. [17] abovyan, t., kridli, g.t., friedman, p.a., ayoub, g. (2015). formability prediction of aluminum sheet alloys under isothermal forming conditions, j. manuf. process., 20, pp. 406-413. doi: 10.1016/j.jmapro.2014.08.003. [18] banabic, d. (2010). sheet metal forming processes constitutive modelling and numerical simulation, berlin, springer. doi: 10.1007/978-3-540-88113-1. [19] giuliano, g., bellini, c., sorrentino, l., turchetta, s. (2018). forming process analysis of an aa6060 aluminum vessel, fract. struct. int., 45, pp. 164-172. doi: 10.3221/igf-esis.45.14. [20] nielsen, c.v. and bay, n. (2018). review of friction modeling in metal forming processes, j. mater. process. tech., 255, pp. 234-241. doi: 10.1016/j.jmatprotec.2017.12.023. [21] yan, w., han, j., zheng, w., wang, g.,wu, t. (2018). establishment of friction model and calculation of size factor in micro/meso forming processes, int. j. adv. manuf. tech., 98 (9-12), pp. 3061-3069. doi: 10.1007/s00170-018-2441-8. [22] ma, j., li, h., wang, d., fu, m.w., tao, z.j. (2018). tribological behaviors in titanium sheet and tube forming at elevated temperatures: evaluation and modeling, int. j. adv. manuf. tech., 97 (1-4), pp. 657-674. doi: 10.1007/s00170-018-1985-y. [23] wang, z.g., komiyama, s., yoshikawa, y., suzuki, t., osakada, k. (2015). evaluation of lubricants without zinc phosphate precoat in multi-stage cold forging, cirp ann.-manuf. techn., 64 (1), pp. 285-288. doi: 10.1016/j.cirp.2015.04.130. c. bellini et alii, frattura ed integrità strutturale, 49 (2019) 791-799; doi: 10.3221/igf-esis.49.70 799 [24] hol, j., meinders, v.t., de rooij, m.b., van den boogaard, a.h. (2015). multi-scale friction modeling for sheet metal forming: the boundary lubrication regime, tribol. int., 81, pp. 112-128. doi: 10.1016/j.triboint.2014.07.015. [25] wang, z.g., yoshikawa, y., suzuki, t., osakada, k. (2014). determination of friction law in dry metal forming with dlc coated tool, cirp ann.-manuf. techn., 63 (1), pp. 277-280. doi: 10.1016/j.cirp.2014.03.050. [26] hol, j., cid alfaro, m.v., de rooij, m.b., meinders, t. (2012). advanced friction modeling for sheet metal forming, wear, 286-287, pp. 66-78. doi: 10.1016/j.wear.2011.04.004. [27] zhang, s., hodgson, p.d., cardew-hall, m.j., kalyanasundaram, s. (2003). a finite element simulation of micromechanical frictional behaviour in metal forming, j. mater. process. tech., 134 (1), pp. 81-91. doi: 10.1016/s0924-0136(02)00926-3. [28] wang, d., yang, h., li, h. (2014). advance and trend of friction study in plastic forming, t. nonferr. metal. soc., 24 (5), pp. 1263-1272. doi: 10.1016/s1003-6326(14)63188-5. [29] giuliano, g. (2015). evaluation of the coulomb friction coefficient in dc05 sheet metal forming, stroj. vestn.-j. mech. e., 61(12), pp. 709-713. doi: 10.5545/sv-jme.2015.2733. [30] giuliano, g. and samani, f. 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can be opened with acrobat and adobe reader 5.0 and later.) >> /namespace [ (adobe) (common) (1.0) ] /othernamespaces [ << /asreaderspreads false /cropimagestoframes true /errorcontrol /warnandcontinue /flattenerignorespreadoverrides false /includeguidesgrids false /includenonprinting false /includeslug false /namespace [ (adobe) (indesign) (4.0) ] /omitplacedbitmaps false /omitplacedeps false /omitplacedpdf false /simulateoverprint /legacy >> << /addbleedmarks false /addcolorbars false /addcropmarks false /addpageinfo false /addregmarks false /convertcolors /converttocmyk /destinationprofilename () /destinationprofileselector /documentcmyk /downsample16bitimages true /flattenerpreset << /presetselector /mediumresolution >> /formelements false /generatestructure false /includebookmarks false /includehyperlinks false /includeinteractive false /includelayers false /includeprofiles false /multimediahandling /useobjectsettings /namespace [ (adobe) (creativesuite) (2.0) ] /pdfxoutputintentprofileselector /documentcmyk /preserveediting true /untaggedcmykhandling /leaveuntagged /untaggedrgbhandling /usedocumentprofile /usedocumentbleed false >> ] >> setdistillerparams << /hwresolution [2400 2400] /pagesize [612.000 792.000] >> setpagedevice microsoft word numero_35_art_8 s s. el kabir et alii, frattura ed integrità strutturale, 35 (2016) 64-73; doi: 10.3221/igf-esis.35.08 64 focussed on crack paths numerical study of crack path by mmcg specimen using m integral s. el kabir, r. moutou pitti université clermont auvergne, université blaise pascal, institut pascal, pb 10448, 63000, clermont-ferrand, france cnrs, umr 6602, institut pascal, 63171, aubière, france soliman.elkabir@yahoo.fr, rostand.moutou_pittil@univ-bpclermont.fr n. recho université clermont auvergne, université blaise pascal, institut pascal, pb 10448, 63000, clermont-ferrand, france cnrs, umr 6602, institut pascal, 63171, aubière, france recho@moniut.univ-bpclermont.fr and epf ecole d’ingénieurs, sceaux, france naman.recho@epf.fr y. lapusta french institute of advanced mechanics, université clermont auvergne, institut pascal umr 6602 /ubp /cnrs / ifma, pb 265, 63175, aubière, france lapusta@ifma.fr f. dubois gemh laboratory, limoges university, civil enginering center, 19300, egletons, france frederic.dubois@unilim.fr abstract. the mixed mode loading configuration occurs in many civil engineering and mechanical applications. in wood material, the study of this problem is very important due to the orthotropic character and the heterogeneity of the material. in order to study the mixed mode loading in wood material, moutou pitti et al [1] have proposed a new specimen called mixed mode crack growth (mmcg). the main goal of this geometry is to propose a decrease of the energy release rate during the crack growth process. in this case, the fracture parameters can be decoupled into mode i and mode ii in order to determine the impact of time during creep crack test. the present work proposes to study the crack path stability in mmcg specimen for different sizes and thicknesses. the mθ integral, combining real and virtual mechanical displacement fields is used in order to separate numerically mode i and mode ii in the mixed mode ratio. the stability is shown for the opening mode (mode i), the shear mode (mode ii), and the mixed mode of 15°, 30°, 45°, 60°, 75° by computing the energy release rate versus the crack length. finally, it is shown that the mmcg specimen can be reduced in various shape and used for example in small climate chamber in order to perform creep test at different temperature and moisture content levels. keywords. crack stability; mmcg specimen; m integral; energy release rate. s. el kabir et alii, frattura ed integrità strutturale, 35 (2016) 64-73; doi: 10.3221/igf-esis.35.08 65 introduction ivil engineering and mechanical structures are usually submitted to mixed mode loading. as a consequence, a mixed mode crack growth process occurs. this fact appears again as an important key in the case of wood material due to its orthotropic behavior and heterogeneous character of the material. also, in order to know the real impact of time effects on the damage process during creep crack growth tests, it is necessary to separate fracture effects and time effect. in this case, moutou pitti & al [1] have proposed new specimen for mixed mode fracture of wood called mixed mode crack growth (mmcg), fig. 1 (c). this specimen is a combination of a modified double cantilever beam (dcb) developed by dubois, but just usable in opening mode [2], fig. 1 (a), and a cantilever tension shear (cts) specimen developed by richard [3,4] and used by ma and zhang for metallic material [5] and adapted by valentin and caumes for timber material [3], fig. 1 (b). (a) (b) (c) figure 1: (a) modified double cantilever beam dcb specimen [2]. (b) cantilever tension shear cts specimen [6]. (c) mixed mode crack growth mmcg specimen [1]. although, according to its large sizes, the mmcg specimen developed by moutou pitti & al [1] is not adapted to all humidity and temperature test chambers. it is necessary to have specimens with various dimensions to realize experiment tests in different configurations, in order to evaluate fracture parameters, and to study thermo-mechanics and mechano-sorptive effects [2]. based on the previous specimen [1], we propose to study three different size ratios and three thickness ratios ¾, ½, ¼, according to the initial mmcg geometry. for each case we plot the evolution of the energy release rate versus the crack length. the numerical analyses of crack path under mixed mode loading are performed as function of contour integral. the mθ integral allows determining the crack growth behavior under mixed mode ratio. the computation is realized for an orthotropic elastic material assuming a plane stress state. in the present work, in order to determine the crack stability in the opening mode, shear mode and mixed mode, we analyze several new sizes and thicknesses of the mmcg specimen. the first section recalls some integral parameters that we use in calculating the energy release rate around the crack tip. the second part presents a mmcg specimen as proposed by moutou pitti e& al [1], including its design and geometry and some results under mixed mode for 45°. the last section introduces some new dimensions of a mmcg specimen under different loadings and gives for each case the evolution of the energy release rate versus the crack length. crack growth stability in mixed mode is justified by the decrease of the energy release rate along the crack path. integral parameter n this section we present the path integral which enabled us to obtain the energy release rate g under mixed mode solicitation. a path independent integral is equivalent to the energy release rate. for cracked linear elastic material, rice [7] have used j-integral to compute energy release rate for curvilinear contour. j-integral takes the following notation: 1 1 1 i ij j j u j f n n n d g a            (1) l r c i s s. el kabir et alii, frattura ed integrità strutturale, 35 (2016) 64-73; doi: 10.3221/igf-esis.35.08 66 where γ1 is arbitrary curvilinear contour oriented by its normal vector n  , f denotes the helmholtz strain energy density, ui is the displacement component and σij is the stress component. m and mθ integral m-integral is an energetic approach that allows studying stress field around crack tip. it is developed by chen and shield [8] in order to separate mixed mode fracture [8] and is a combination between real and virtual strain fields which enables computing fracture parameter. based on a conservative law, m-integral enables to separate fracture mode under creep mixed load [9]:  ,1 ,1 1 2 v u ij j ij i jm u v n d         (2) where ij and ,1 v ij are real and virtual stresses associated with the real and virtual displacements fields u and v. the curvilinear integral (2) is difficult to realize in the finite element method [1, 2, 9]. in order to make easy numerical integration destuynder [10] proposed mθ integral. this integral is obtained by ostrogradski transformation and defined at a surface contour containing the crack tip. figure 2: integral domain of mθ .  , , ,1 2 u v ij i k ij k i k j v m v u dv        (3) where θ is a continuous and derivable scalar field. it forms a crown around the crack tip as shown in fig. 2. energy release rate in general case the energy release rate, denoted g, traduces the energy release by the material during an unitary crack growth process. according to this definition, the energy release rate, is the energy consumed by the crack growth δa [16] and takes the following expression potw g a    (4) dwpot is the variation of the potential energy. in simple mode solicitation, the energy release rate can be defined by eq. (1) or eq. (4). however, in mixed mode loading, using the superposition principle one can write the following relation [11]:   1 2, 8 8 u v u v i i ii iik k k km u v c c     (5) s. el kabir et alii, frattura ed integrità strutturale, 35 (2016) 64-73; doi: 10.3221/igf-esis.35.08 67 c1 and c2 are the reduced elastic compliances and k1 and k2 and are the stress intensity factors in opening mode and shear mode, respectively. in order to decouple each fracture mode and obtain the reel stress intensity factors uik and u iik , we perform two computations of particular values of virtual stress intensity factors vik and v iik [1] as follows     1 2 1, 0 0, 1 8 and 8 v v v v i ii i iiu u i ii m k k m k k k k c c        (6) finally, we can compute the energy release rate for each mode by combining expressions (4) and (5) according to real intensity factors:    2 2 1 2 8 8 u u i ii i ii k k g g g c c      (7) mmcg specimen design and geometry s described in introduction, the mixed mode crack growth (mmcg) specimen is a combination between modified dcb and cts [1]. in this part, we recall the wood specimen dimensions of mmcg device. fig. 3 presents the dimensions in millimeters of the initial wood specimen proposed in [1]. in this wood specimen, four holes are machined in order to fixe the arcan device. this allows a various mixed ratio with seven loading fixations with angle θ = (0° ; 15° ; 30° ; 45° ; 60° ; 75° ; 90°). the geometry of the mmcg specimen has been optimized by using a finite element computation. the main goal of this specimen is to obtain a stable crack growth rate during propagation. figure 3: mmcg specimen. the finite element computation is realized in plane stress state for an elastic orthotropic behavior. wood material used is douglas fire and has the following elastic characteristics: longitudinal modulus ex=14100 mpa, transversal modulus ey=2040 mpa, shear modulus gxy=925 mpa, poisson ratio nuxy=0.4. crack growth stability mmcg specimen was designed in order to obtain the crack growth stability. the decrease of the energy release rate translates stability of the crack growth. in mixed mode loading and according to the griffith approach, moutou pitti et al. have introduced f threshold function [1] such as: 1 2 1 2 s s g g f k g g   (8) a s s. el kabir et alii, frattura ed integrità strutturale, 35 (2016) 64-73; doi: 10.3221/igf-esis.35.08 68 1 sg and 2 sg are the critical values of the energy release rate in each mode respectively. they are parameters depend your material characteristics. the factor k is the mixed mode ratio equal to 1 in the present work. according to equation (7), the crack growth process obeys to the three different cases:  crack growth initiation f < 1  crack growth stability f = 1 and 0 f a     crack growth instability f > 1 and 0 f a    where a is the crack length. new specimen dimensions and crack growth stability design and geometry n order to prove the efficiency of new specimen, various size and thickness parameters of mmcg are presented in fig. 4 for mixed loading mode at 45°. figure 4: geometric definition of mmcg specimen for: (a): different size coefficients a, (b): different thicknesses coefficients b and (c): a combination of both. i s. el kabir et alii, frattura ed integrità strutturale, 35 (2016) 64-73; doi: 10.3221/igf-esis.35.08 69 the initial crack length is fixed to 49 *mm a , with the coefficient a = 1; ¾; ½ ; ¼ . the factor b is used to modify the thickness and takes the following values b = 1; ¾; ½. for different mmcg specimens, the simulation presents a crack growth process to a final crack length of 70 iterations. in the literature, the initial arcan fixture is proposed by [1]. in this work, new shapes and dimensions of the experimental loading device are proposed, see e.g. fig. 5. the system allows considering, during the test, the specimens for the factor a= ½ and a = 1, and different thicknesses for mmcg specimen. figure 5: mmcg specimen and loading device adapted for 1a  and 1 2 a  . numerical results in this section, the results of parametrical study are exposed. in order to observe the stability of mmcg specimen, the energy release rate is computed for different sizes and thicknesses of the mmcg specimen. finite element computation is realized with the software cast3m, produced by french energy atomic commission cea [12]. for some significant cases, we plot the evolution of the energy release rate as function of the crack growth. the decrease of the energy release rate for specimen of new sizes translates the stability of the crack growth. the computation is realized assuming a plane stress state. radial meshes and θ field are shown in fig. 6. in fig 6 (a), the size of radial mesh and the field θ are the same, and the mesh is constructed with 10 elements around the crack tip. greater is the number of elements, more accurate is mθ value. for more stability, mθ field has to be included inside the radiating mesh as seen in fig 6 (b). mesh density and mθ field are two parameters which allow less disruption and more numerical stability. figure 6: mθ field around the crack tip and outside radial meshes (a), or inside radial meshes (b). fig. 7 presents the contributions of the opening mode and the shear mode to the energy release rate for the mixed mode ratio of 45° for different size coefficients a and the same thickness. in fig. 7 (a), results for three different sizes versus crack length are presented and we show that the value of g increases when the size increases. simultaneously, fig. 7 (b) and (c) (a) (b) s s. el kabir et alii, frattura ed integrità strutturale, 35 (2016) 64-73; doi: 10.3221/igf-esis.35.08 70 show stable crack growth zones for 2 sizes. the results are summarized in table 1 where different new size parameters are given versus stable crack growth zones. fig. 8 (a) illustrates the evolution of the energy release rate versus the crack length for several mmcg specimen thicknesses b and size a=1. g1 and g2 are the parts of opening and shear in the mixed mode 45°. we observe that the values of g increase when the thickness decreases. stable crack growth zones are also presented in fig. 8 (b) and (c). figure 7: normalized elastic energy release rate g1 and g2 versus mixed mode ratio for various sizes parameter 3 1 3 1 1; ; and b 1 (a), for and 1 (b), for and 1(c) 4 2 4 2 a a b a b           . size parameter a stable zone g1 (mm) length of stable zone g1 (mm) stable zone g2 (mm) length of stable zone g2 (mm) 1 [54:82] 28 [93:114] 21 0.75 [40.5:61.5] 21 [69.75:85.5] 15.75 0.5 [27:41] 14 [46.5:57] 10.5 0.25 [13.5:20.5] 7 [23.25:28.5] 5.25 table 1: stable crack growth zones for different size parameter and 1b  . s. el kabir et alii, frattura ed integrità strutturale, 35 (2016) 64-73; doi: 10.3221/igf-esis.35.08 71 tab. 1 shows the stable crack growth zones for various new size parameters. the lengths are proportional to size parameter and greater for g1 than for g2. figure 8: normalized elastic energy release rate g1 and g2 versus mixed mode ratio for various thickness parameters 3 1 1 1 3 1 1 1; ; and (a), for and (b), for and (c) 4 2 2 2 4 2 2 b a a b a b           . comparison between g1 and g2 shows that the opening mode needs 10 times more energy than the shear mode. thickness parameter b stable zone g1 (mm) stable zone g2 (mm) 1 [27:41] [46.5:57] 0.75 [27:41] [46.5:57] 0.5 [27:41] [46.5:57] 0.25 [27:41] [46.5:57] table 2: stable crack growth zone for different size parameter and 1 2 a  . s s. el kabir et alii, frattura ed integrità strutturale, 35 (2016) 64-73; doi: 10.3221/igf-esis.35.08 72 tab. 2 shows the stable crack growth zones for various new thickness parameters. the length of stable zones is the same for all cases. let us analyze now the influence of the thickness on the energy release rate. as shown in fig. 9, a thickness change results in a new value of the energy release rate. figure 9: influence of /a b ratio on the energy release rate evolution the evolution of the energy release rate are not linearly dependent on the /a b ratio, see fig. 9. the change of thickness has an impact on the mmcg specimen. we consider, in numerical computation by integral under the plane stress assumption, that the effort is divided by thickness. dependencies of g1 and g2 versus /a b ratio are posted in fig. 9 (a) and (b) respectively. we show the influence of the thickness parameter b on the mmcg specimen stability for various cases of the size parameter a. conclusion and future extensions n this work, different sizes and thicknesses of mixed mode crack growth (mmcg) specimen have been studied numerically. the evolution of the energy release rate versus the crack length for each new size and thickness of a new mmcg specimen have been determined. numerical calculations have been performed for the ratio of mixed mode 45°. the stability is justified by the decrease of g versus crack length during the growth process in each mode. this parametric study shows the impact of size, thickness, and both parameters combined on the energy release rate coupled with the crack stability. the following conclusions can be drawn:  the mmcg specimen is stable for the parameters studied;  the smaller are the dimensions of the mmcg specimen, the more the stability is reduced;  the variation in thickness impacts the evolution of the energy release rate g. in future work, it will be necessary to extend the numerical computation to a pure opening mode, pure shear mode, and different angles in mixed mode in order to optimize mmcg specimen for larger stability zone. also, experimental tests will be necessary to validate the numerical results. this study can be extended to perform new crack extension criteria under mixed mode loading [13, 14] for composite materials [15]. references [1] moutou pitti, r., dubois, f., pop, o., a proposed mixed-mode fracture specimen for wood under creep load, int. j. fract., 167(2011) 195–209. [2] dubois, f., chazal, c., petit, c., viscoelastic crack growth process in wood timbers: an approach by the finite element method for mode i fracture, int. j. fract., 113(4) (2002) 367-388. [3] richard, h., benitz, k., a loading device for the creation of mixed mode in fracture mechanics, int. j. fract., 22 (1983) 55-58. [4] richard, h., a new compact shear specimen int. j. fract., 17 (1981) 105-107 [5] ma, s., zhang, x., recho, n., li, j., the mixed-mode investigation of the fatigue crack in cts metallic specimen, int. j. fatig., 28 (2006) 1780–1790. 0 0,2 0,4 0,6 0,8 1 0 0,5 1 1,5 2 2,5 3 0 0,05 0,1 0,15 0,2 0 0,5 1 1,5 2 2,5 3 g1 j / n 2  a  1 4 a  1 2 a b a  3 4 (a) g2 j / n 2  a  1 4 a  1 2 a  3 4 a b (b) i s. el kabir et alii, frattura ed integrità strutturale, 35 (2016) 64-73; doi: 10.3221/igf-esis.35.08 73 [6] valentin, g., caumes, p., crack propagation in mixed mode in wood: a new specimen, wood science and technology, 23 (1989) 43-53. [7] rice, j.r., a path independent integral and the approximate analysis of strain concentrations by notches and cracks, j. appl. mech., 35 (1968) 379–386. [8] chen f.m.k., shield, r.t., conservation laws in elasticity of j-integral type, j. appl. mech. phys., 28 (1977) 1–22. [9] moutou pitti, r., dubois, f., petit, c., sauvat, n., pop, o., a new m-integral parameter for mixed-mode crack growth in orthotropic viscoelastic material, eng. fract. mech., 75 (2008) 4450–4465. [10] destuynder, ph., djaoua, m., lescure, s., quelques remarques sur la mécanique de la rupture élastique, j. de mécanique théorique et appliquée, 2 (1983) 113–135. [11] moutou pitti, r., dubois, f., petit, c., sauvat, n., mixed mode fracture separation in viscoelastic orthotropic media: numerical and analytical approach by the mθv-integral, int. j. fract., 145 (2007) 181–193. doi:10.1007/s10704-0079111-4. [12] cea commissariat de l’energie atomique, http://www-cast3m.cea.fr/index.php?xml=download1, france (2014). [13] li, j., zhang, x. b., recho, n., j–mp based criteria for bifurcation assessment of a crack in elastic-plastic materials under mixed mode i-ii loading, eng. fract. mechanics, 71 (2004) 329-343. [14] zhang, x., ma, s., recho, n., li, j., bifurcation and propagation of a mixed-mode crack in a ductile material, (2006) 1925–1939. [15] lapusta, y., henaff-gardin c., an analytical model for periodic alpha-layer cracking in composite laminates, international journal of fracture, 102 (2000) 73-76. [16] griffith, a. a., the phenomena of rupture and flow in solids, philosophical transactions of the royal society, 221 (1921) 163-198. << /ascii85encodepages false /allowtransparency false /autopositionepsfiles true /autorotatepages /none /binding /left /calgrayprofile (dot gain 20%) /calrgbprofile (srgb iec61966-2.1) /calcmykprofile (u.s. web coated \050swop\051 v2) /srgbprofile (srgb iec61966-2.1) /cannotembedfontpolicy /error /compatibilitylevel 1.4 /compressobjects /tags /compresspages true /convertimagestoindexed true /passthroughjpegimages true /createjobticket false /defaultrenderingintent /default /detectblends true /detectcurves 0.0000 /colorconversionstrategy /cmyk /dothumbnails false /embedallfonts true /embedopentype false /parseiccprofilesincomments true /embedjoboptions true /dscreportinglevel 0 /emitdscwarnings false /endpage -1 /imagememory 1048576 /lockdistillerparams false /maxsubsetpct 100 /optimize true /opm 1 /parsedsccomments true /parsedsccommentsfordocinfo true 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/hrv (za stvaranje adobe pdf dokumenata najpogodnijih za visokokvalitetni ispis prije tiskanja koristite ove postavke. stvoreni pdf dokumenti mogu se otvoriti acrobat i adobe reader 5.0 i kasnijim verzijama.) /hun 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can be opened with acrobat and adobe reader 5.0 and later.) >> /namespace [ (adobe) (common) (1.0) ] /othernamespaces [ << /asreaderspreads false /cropimagestoframes true /errorcontrol /warnandcontinue /flattenerignorespreadoverrides false /includeguidesgrids false /includenonprinting false /includeslug false /namespace [ (adobe) (indesign) (4.0) ] /omitplacedbitmaps false /omitplacedeps false /omitplacedpdf false /simulateoverprint /legacy >> << /addbleedmarks false /addcolorbars false /addcropmarks false /addpageinfo false /addregmarks false /convertcolors /converttocmyk /destinationprofilename () /destinationprofileselector /documentcmyk /downsample16bitimages true /flattenerpreset << /presetselector /mediumresolution >> /formelements false /generatestructure false /includebookmarks false /includehyperlinks false /includeinteractive false /includelayers false /includeprofiles false /multimediahandling /useobjectsettings /namespace [ (adobe) (creativesuite) (2.0) ] /pdfxoutputintentprofileselector /documentcmyk /preserveediting true /untaggedcmykhandling /leaveuntagged /untaggedrgbhandling /usedocumentprofile /usedocumentbleed false >> ] >> setdistillerparams << /hwresolution [2400 2400] /pagesize [612.000 792.000] >> setpagedevice microsoft word numero_45_art_8 x. z. wang, frattura ed integrità strutturale, 45 (2018) 100-107; doi: 10.3221/igf-esis.45.08 100 research on anchor service life base on grey prediction model xinzheng wang academy of civil engineering and architecture, nanyang normal university, nanyang 473061, china wxz791023@126.com abstract. with the wide application of anchored structures in various engineering, their durability and service life have become an important issue in the development of anchoring technique. according to the corrosion experiment results on different working conditions (close and damp, permanently soaked in water, wet and dry alternately, weak acidity aqueous soaking), and on the basis of determining the loss rate threshold of anchor steel reinforcement bearing capacity, this paper first test the experiment data and then predict the service life of anchor steel on four different working conditions by adopting gm (1,1) model. the results indicate that the grey prediction has high accuracy. keywords. anchor; service life; grey prediction; gm (1,1). citation: wang, x.z., research on anchor service life base on grey prediction model, frattura ed integrità strutturale, 45 (2018) 100-107. received: 29.03.2018 accepted: 11.06.2018 published: 01.07.2018 copyright: © 2018 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. introduction he bolt and cable supporting is convenient and fast in construction, low in cost and adaptable to engineering [1-3]. it is widely used in rock and soil slope supporting engineering in water conservancy and hydropower, railway, highway, construction and other industries. in the course of using the anchor structure, how long their residual life is, and whether they will suddenly failure one day has become a common concern. therefore, it is of great importance significance to study the durability and service life of the anchor. by combining the indoor experiment with theoretical analysis, this paper analyzes the experimental result indoors through the use of grey theory, and based on the experimental result of limit tension anchor rod on site, studies the durability and service life of anchored structures. according to the corrosion experiment results on different work condition (close and damp, permanently soaked in water, wet and dry alternately, weak acidity aqueous soaking)) and on the base of determining the critical breakage of carrying capacity loss rate, this paper first examines the experiment data and then predict the service life of anchor rod on 4 different work conditions by adopting gm(1,1) model. at last, the predicting result is compared with the testing result of the anchor rod. the results indicate that the grey prediction has high accuracy. overview of grey system theory the concept of grey prediction he grey theory studies few data and indetermination. it understands and knows the world by creating and opening out the “part” known information, and then it can correctly hold and depict the functional behavior and evolutive rules of the system. it can successfully solve many practical problems in production, life and scientific ret t http://www.gruppofrattura.it/va/45/19.mp4 x.z. wang, frattura ed integrità strutturale, 45 (2018) 100-107; doi: 10.3221/igf-esis.45.08 101 search. this theory has been broadly used in many engineering fields. grey prediction is based on the processing of raw data and the establishment of grey model, find and master the development law of the system, and make a scientific and quantitative prediction of the future state of the system [4-7]. grey prediction model generally refers to gm (1,1) model. gm (1,1) model make x(0) is the modeling sequence of gm(1,1): ( 0 ) ( 0 ) ( 0 ) ( 0 )( (1), ( 2), , ( ))x x x x n  , and make x(1) is the ago sequence of x(0): (1) ( 1) (1) (1)( (1), ( 2), , ( ))x x x x n  , ( 1) ( 0 )(1) (1)x x , ( 1) ( 0 ) 1 ( ) ( ) k m x k x m    (1) make z(1)(k) is the mean sequence of x(1)(k) (1) (1) (1)( ) 0.5 ( ) 0.5 ( 1)z k x k x k   (2) (1) ( 1) (1) (1)( ) ( ( 2), (3), , ( ))z k zx zx zx n  (3) the definition type of gm (1,1), that is, the grey differential equation model of gm (1,1) is: (0) (1)( ) ( )x k az k b  , 1, 2, ,k n  (4) in the formula: a and b are constants, among them, a is development coefficient, b is grey influencing coefficients. the gm (1,1) definition equation can be transformed into matrix equations. ny bp (5) t(0) (0) (0) n (2), (3), , ( )y x x x n    (6) (1) (1) (1) ( 2) 1 (3) 1 ( ) 1 z z b z n                (7) . a p b        (8) under the least square criterion, the solution of yn=bp is: 1. ( )t t n a p b b b y b       (9) substitute b and yn into the formula, it can calculate the value of a and b. the detailed formula of (1,1)gm grey prediction model is obtained. when k=0, 1, 2, …, n, the original sequence fitting value is obtained, for k=n+1, a prediction value of the original sequence is obtained, and a multi-step prediction can be obtained at one time. x. z. wang, frattura ed integrità strutturale, 45 (2018) 100-107; doi: 10.3221/igf-esis.45.08 102 corrosion test of anchor steel orrosion is the most important factor affecting the service life of anchor steel. when the corrosion is slight, the tensile capacity of the steel bar is calculated according to the remaining cross-sectional area, without considering the strength reduction of the steel bar. when the steel bar is corroded to a certain extent, not only the sectional area of the steel bar is decreased, but also the strength and ductility of the steel bar have different rate reduce. when the steel corrosion is serious, the stress-strain curve of the steel bar has changed greatly. there is no obvious yield point on the curve, and the yield strength is very close to the tensile strength, it is very easy to cause the sudden brittle fracture of the structure [8-10]. steel bar corrosion mechanism the chemical composition and mechanical properties of the steel used in the test are shown in tab. 1. chemical composition rel/mpa rm/mpa 20°c impact energy/ak/j c si mn s p v 0.26 0.56 1.57 0.011 0.024 0.107 705 875 35 table 1: the chemical composition and mechanical properties of the steel. the corrosion of anchor steel is an electrochemical corrosion process, mainly through the following four processes. (1) the process of anodic reaction. the iron atom in the anode region is transformed into cationic, and the electron is released. the equation of reaction is: 2 22fe fe e   (10) (2) the process of electron transport. the electrons which released from anode region are transferred through steel to the cathode region. (3) the process of cathode region. in the vicinity of the cathode region, the oxygen dissolved in the pore water absorbs electrons and occurs reduction reaction. the equation of reaction is: 2 22 4 4o h o e oh     (11) the ohproduced at the cathode is sent to the anode through the liquid phase in the concrete pore, thus, a closed loop of corrosion current is formed [11-15]. (4) the formation process of corrosion products. the fe2+ generated in the anode region diffused and migrated in the aqueous solution, the ohgenerated in the cathode zone diffuses through the pores in the concrete to the anode region. near the anode, fe2+and ohform insoluble 2( )fe oh ,and oxidize to 3( )fe oh under oxygen enrichment. 2 22 ( )fe oh fe oh    (12) 2 2 2 34 ( ) 2 4 ( )fe oh o h o fe oh   (13) after fe(oh)3 dehydration, it becomes loose and porous red embroidered fe2o3, that is: 3 2 3 22 ( ) 3fe oh fe o h o  (14) under the condition of less oxygen, fe(oh)2 oxidation is not complete, and part of fe(oh)2 forms fe3o4, that is: 2 2 3 4 26 ( ) 2 6fe oh o fe o h o   (15) therefore, the final corrosion product depends on the oxygen supply. c x.z. wang, frattura ed integrità strutturale, 45 (2018) 100-107; doi: 10.3221/igf-esis.45.08 103 experimental design the dimension of the specimen steel is φ8×40 mm. clean the oil of the specimen bar and place it in a dry container. specimens were placed in four environments: close and damp, permanently soaked in water, wet and dry alternately, weak acidity aqueous soaking. the close and damp means that the specimen is hung above the water surface in the sealed container. the permanently soaked in water means that the specimen is located below the water level in the sealed container. the wet and dry alternately means that the specimen is located below the water level for 7 days, and the other 7 days is located above the water level in the container, and so on alternately, the container is open. the weak acidity aqueous soaking means that the dilute sulfuric acid and tap water was used to prepare soaking solution, and the soaking solution is used to simulate the acid environment, immerse the specimen permanently below the surface of the acid solution in the sealed container. all of the above corrosion environments change soaking liquid once a month [16-20]. experimental result the experimental results are shown in fig. 1. (1) as can be seen from fig. 1, in the four different corrosion environments, the weight loss rate of steel is the largest in the weak acid aqueous solution and the minimum in the close and damp environment. figure 1: distribution of anchor steel weight loss rate with time (2) the rate of weight loss of steel in wet and dry alternately is almost the same as that in permanently soaked in water, but the growth rate of weight loss rate in the wet and dry alternately condition is greater than the permanently soaked in water condition. (3) the weight loss rate of the anchor steel in close and damp condition is only about 1/5 of the anchor steel in the condition of permanently soaked in water condition and wet and dry alternately condition. (4) in any experimental environment, the weight loss rate of anchor steel increases with time, but the increase rate decreases with time. the analysis of grey prediction determination of the bearing capacity loss threshold of steel bars n practical engineering, the bearing capacity of steel bars direct influence on the structural safety, therefore, the bearing capacity loss rate of the steel bars is taken as the damage criterion. the bearing capacity loss rate of steel bars can be expressed as: %100 δ 0y0 1 ' y0y0    sf sfsf p p (16) in the formula, p —the decrement of bearing capacity (kn); p— initial bearing capacity (kn); fy0—initial strength of the steel bars(n/mm2); 'yf —strength damage threshold of steel bars (n/mm2); s0—initial sectional area of steel i x. z. wang, frattura ed integrità strutturale, 45 (2018) 100-107; doi: 10.3221/igf-esis.45.08 104 bars(mm2); s1—sectional area after failure(mm2). select the strength standard value of the steel bar as its initial strength that is kyy ff ,0  (17) the safety factor is 1.2, so that the strength damage threshold of the steel bar is: 2.1/' y ys ff  (18) when other factors are not considered, the sectional area of steel bars has not changed, s0=s1. substituting formula (17) and formula (18) into formula (16), the threshold value of bearing capacity loss rate is calculated to be 16.67%. in the case of corrosion, not only the sectional area of steel will decrease, but also the yield strength will decrease. when the corrosion rate of steel bar is greater than 10% and less than 60%, the yield strength before and after corrosion has the following relations: ky, s s ys 1 1.0280.985 f ρ ρ f    (19) in the formula, fys—yield strength of corroded steel bars: fy,k—yield strength of steel bar before corrosion: ρs—cross sectional loss rate of steel bar. substituting formula (19) into formula (16), the following formula can be obtained. s 0ky, 1ys0ky, 1.0280.015 δ ρ sf sfsf p p    (20) when the loss rate threshold value of bearing capacity is 16.67%, the corresponding steel section loss rate is obtained by formula (20), and it is 14.76%. because the test steel is completely immersed in water, it is considered that the corrosion of steel bar is overall and uniform, and the weight loss rate is linear with the cross-section loss rate of steel bar. thus, the weight loss rate of the steel bar is 14.76%, which is used as the threshold value of the grey prediction data sequence. feasibility test of the grey prediction according to the characteristics of matlab, two file functions are compiled, namely greycch and greynum, and their basic algorithms are the same. greycch is used to judge the feasibility of modeling, and greynum is used to sequence grey prediction. the data sequence for the gm (1,1) model under different corrosion conditions is shown in tab. 2. when the absolute value of the development coefficient is less than or equal to 0.3, it is feasible to predict the weight loss rate of anchor specimens in the medium and long term by gm (1,1) model. in order to further verify the feasibility of grey prediction by using the corrosion test data of steel bars, the first part of the original data sequence is used as the modeling data, and the rest of the experimental data is used as prediction and verification. the results are shown in tab. 3, the first 8 sets of data were used to predict the latter 3 sets of data, the predicted value and the actual value are relatively close, and the error is small. it shows that the grey prediction method is feasible and has high confidence. results and analysis of grey prediction with the weight loss rate as the prediction sequence, the parameters, test indexes and prediction results of the model are shown in tab. 4. (1) from the parameters of gm (1,1) model, it can be seen that the absolute values of the development coefficient are much less than 0.3, which shows that the model can be used for medium and long-term prediction. at the same time, the average precision of the model is more than 0.95, and the maximum deviation of the average class ratio is only 0.0373, which meets the requirements of modeling and the accuracy of the model is higher. (2) from the comparison between the prediction curve and the original data points (as shown in fig. 2-5), it can be seen that the prediction curve passes through the original data points and then develops upwards, and the development trend x.z. wang, frattura ed integrità strutturale, 45 (2018) 100-107; doi: 10.3221/igf-esis.45.08 105 of the prediction curve and the original data points are consistent. in different working conditions, the development trend of curves is obviously different, but they are not linear, which is closer to the actual situation. data sequence weight loss rate /% serial number time/month close and damp permanently soaked in water wet and dry alternately weak acidity aqueous soaking 1 1 0.043 9 0.660 9 0.424 4 1.140 8 2 1.5 0.060 8 0.661 4 0.497 3 1.466 2 3 2 0.074 3 0.662 2 0.563 0 1.714 7 4 2.5 0.085 1 0.663 6 0.621 4 1.904 6 5 3 0.093 8 0.665 9 0.672 4 2.049 6 6 3.5 0.100 7 0.669 6 0.716 1 2.160 4 7 4 0.106 3 0.675 8 0.752 6 2.245 0 8 4.5 0.110 8 0.685 9 0.781 7 2.309 6 9 5 0.114 4 0.702 7 0.803 6 2.359 0 10 5.5 0.117 3 0.730 3 0.818 1 2.396 7 11 6 0.119 6 0.775 8 0.825 4 2.425 5 table 2: data sequences modeled by gm (1,1). corrosion environment test 1 test 2 test 3 predicted value /% actual value /% error /% predicted value /% actual value/% error /% predicted value /% actual value/% error /% close and damp 0.1241 0.1144 -8.48 0.1333 0.117 -13.64 0.1428 0.120 -19.40 permanently soaked in water 0.6846 0.7027 2.32 0.6886 0.730 5.71 0.6925 0.776 10.74 wet and dry alternately 0.8592 0.8036 -6.92 0.9224 0.818 -12.75 0.9902 0.825 -19.97 weak acidity aqueous soaking 2.5547 2.359 -8.30 2.7192 2.397 -13.46 2.8912 2.426 -19.32 table 3: feasibility verification of grey prediction. corrosion environment translation value development coefficient grey influencing coefficients mean accuracy mean stepwise ratio deviation predicted life /a close and damp 0.2 -0.020 7 0.263 5 0.984 0 0.014 7 8.2 permanently soaked in water 0 -0.015 9 0.625 5 0.979 6 0.014 9 8.4 wet and dry alternately 0 -0.049 8 0.523 4 0.956 7 0.037 3 3.2 weak acidity aqueous soaking 1 -0.009 0 11.483 5 0.991 4 0.006 8 2.4 table 4: parameters and grey prediction results of gm (1,1) model. (3) from the predicted results, according to the selected weight loss rate threshold value, under the permanently soaked in water condition, the life of anchor steel bar is the longest, reaching 8.3 years; the life of anchor bar under close and damp condition is 8.2 years; the life of anchor bar under weak acidity aqueous soaking condition is the shortest, only 2.4 x. z. wang, frattura ed integrità strutturale, 45 (2018) 100-107; doi: 10.3221/igf-esis.45.08 106 years. this is because under the weak acid environment, the oxide film passivation layer formed on the steel bar surface is easily destroyed by acid water, which leads to faster corrosion and shorter service life of steel bars. figure 2: the prediction curve and original data point at close and damp environment. figure 3. the prediction curve and original data point at permanently soaked in water environment. figure 4. the prediction curve and original data point at wet and dry alternately environment. figure 5. the prediction curve and original data point at weak acidity aqueous soaking environment. conclusion ased on the combination of laboratory test and theoretical analysis, the durability and service life of the anchor structure are analyzed comprehensively by the grey system theory. the main conclusions are as follows: (1) in four different corrosive environments (close and damp, permanently soaked in water, wet and dry alternately, weak acidity aqueous soaking), the weight loss rate of the anchor in weak acidity aqueous soaking environment is the biggest, and the weight loss rate of the anchor in close and damp environment is the smallest. in any environment, the weight loss rate of anchor increases with time, but the increase rate decreases with time. (2) the gm (1,1) model is used to test the data of another part by using some experimental data. the results are relatively close. it shows that it is feasible to predict the service life of anchor structures by using the gm (1,1) model. (3) based on the existing test data, the grey prediction of the anchor service life under four conditions after the test period is carried out. the service life prediction results of the anchor under four conditions have high confidence. acknowledgments he authors are grateful to the anonymous referees for their valuable remarks and helpful suggestions, which have significantly improved the paper. this research is supported by the science and technology project of henan province (grant no: 172102310748); the young backbone teacher support program of henan province colleges and universities (grant no: 2015ggjs-120); the key research project of the henan education department (grant no: b t x.z. wang, frattura ed integrità strutturale, 45 (2018) 100-107; doi: 10.3221/igf-esis.45.08 107 15b560008): and the natural science basic research projects of the henan education department (grant no. 2010b410004). references [1] wang, j.h., yan, s., zeng, x.m. and li, s.m. (2006). study and application of compound soil nail support in china, construction technology, 35(1), pp. 15–19. [2] liu, b. and wang, h. (2012). application of gray system theories in forecasting daily output of oil, journal of chengde petroleum college, (2), pp. 9–12. doi: 10.13377/j.cnki.jcpc.2012.02.026 [3] wang, f.j., li, t.q. and yu, c.z. (2006). grey verhulst predictive model of road traffic accidents, journal of traffic and transportation engineering, 6(1), pp. 122–126. [4] yang, m.g. and yang, x.x. (2010). prediction for inbound tourism flow of chongqing based on grey prediction model, journal of southwest china normal university (natural science edition), 35(3), pp. 259–263. doi: 10.13718/j. cnki. xsxb. 2010.03.064 [5] wang, l., ding, w., ma, y.f. and zhang, j.r. (2011). probabilistic model of shear resistance degradation for corroded reinforced concrete beam, journal of changsha university of science and technology (natural scienc), 8(4), pp. 34– 41. [6] xiao, c.y., du, z.y., guo, c. and xia, j.b. (2008). the computational analysis of flexural bearing capacity of corroded reinforced concrete beams, journal of hubei university of technology, 28(1), pp. 25–27. [7] zhang, y.h., meng, q.f. and li, y.q. (2002). the nonlinear analysis of concrete simple-supported beams strengthened by external prestressing, building science research of sichuan, (1), pp. 27–29, 34. [8] zeng, x.m., chen, z.y., wang, j.t. and du, y.h. (2004). research on safety and durability of bolt and cablesupported structures, chinese journal of rock mechanics and engineering, 23(13), pp. 2235–2242. [9] [9] hong, h.c. and xu, w.y. (2008). research on service life of wholly bonded prestressed cable when corrosion expansion cracking, rock and soil mechanics, 29(4), pp. 949–953. doi: 10.16285/j.rsm.2008.04.032 [10] zhao, j., ji, w.z., xiao, l., liang, s.f., yan, s., wang, j.h. and zeng, x.m. (2006). in-situ experimental study on anchor durability, chinese journal of rock mechanics and engineering, 25(7), pp. 1377–1385. [11] prosek, t., le bozec, n. and thierry, d. (2014). application of automated corrosion sensors for monitoring the rate of corrosion during accelerated corrosion tests, materials and corrosion, 65(5), pp. 448–456. [12] montoya, p., diaz, i., granizo, n., fuente, d.d.l. and morcillo, m. (2013). a study on accelerated corrosion testing of weathering steel, materials chemistry and physics, 142(1), pp. 220–228. [13] pacheco, a.r. and schokker, a.j. (2007). revisions to accelerated corrosion test method for post tensioning grout, aci materials journal, 104(2), pp. 123–128. [14] rahman, m.s., divi, s., chandra, d. and daemen, j. (2008). effect of different salts on the corrosion properties of friction type a607 steel rock bolt in simulated concentrated water, tunnelling and underground space technology, 23(6), pp. 665–673. [15] darmawan, m.s. and stewart, m.g. (2007). spatial time dependent reliability analysis of corroding pretensioned prestressed concrete bridge girders, structural safety, 29(1), pp. 16–31. [16] divi, s., chandra, d. and daemen, j. (2011). corrosion susceptibility of potential rock bolts in aerated multiionic simulated concentrated water, tunnelling and underground space technology, 26(1), pp. 124–129. [17] kim, j. and west, r.c. (2010). application of the viscoelastic continuum damage model to the indirect tension test at a single temperature, journal of engineering mechanics, 136(4), pp. 496–505. [18] lopez, c.m., carol, i. and aguado, a. (2008). meso-structural study of concrete fracture using interface structure elements. ii: compression, biaxial and brazilian test, materials and structures, 41(3), pp. 601–620. [19] mashayekhi, m., ziaei rad, s., parvizian, j., niklewicz, j. and hadavinia, h. (2007). ductile crack growth based on damage criterion: experimental and numerical studies, mechanics of materials, 39(7), pp. 623–636. [20] zhang, j. and lounis, z. 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can be opened with acrobat and adobe reader 5.0 and later.) >> /namespace [ (adobe) (common) (1.0) ] /othernamespaces [ << /asreaderspreads false /cropimagestoframes true /errorcontrol /warnandcontinue /flattenerignorespreadoverrides false /includeguidesgrids false /includenonprinting false /includeslug false /namespace [ (adobe) (indesign) (4.0) ] /omitplacedbitmaps false /omitplacedeps false /omitplacedpdf false /simulateoverprint /legacy >> << /addbleedmarks false /addcolorbars false /addcropmarks false /addpageinfo false /addregmarks false /convertcolors /converttocmyk /destinationprofilename () /destinationprofileselector /documentcmyk /downsample16bitimages true /flattenerpreset << /presetselector /mediumresolution >> /formelements false /generatestructure false /includebookmarks false /includehyperlinks false /includeinteractive false /includelayers false /includeprofiles false /multimediahandling /useobjectsettings /namespace [ (adobe) (creativesuite) (2.0) ] /pdfxoutputintentprofileselector /documentcmyk /preserveediting true /untaggedcmykhandling /leaveuntagged /untaggedrgbhandling /usedocumentprofile /usedocumentbleed false >> ] >> setdistillerparams << /hwresolution [2400 2400] /pagesize [612.000 792.000] >> setpagedevice microsoft word numero 25 art 19 j. toribio et alii, frattura ed integrità strutturale, 25 (2013) 130-137; doi: 10.3221/igf-esis.25.19 130 special issue: characterization of crack tip stress field role of plasticity-induced crack closure in fatigue crack growth jesús toribio, viktor kharin university of salamanca, spain abstract. the premature contact of crack surfaces attributable to the near-tip plastic deformations under cyclic loading, which is commonly referred to as plasticity induced crack closure (picc), has long been focused as supposedly controlling factor of fatigue crack growth (fcg). nevertheless, when the plane-strain near-tip constraint is approached, picc lacks of straightforward evidence, so that its significance in fcg, and even the very existence, remain debatable. to add insights into this matter, large-deformation elastoplastic simulations of plane-strain crack under constant amplitude load cycling at different load ranges and ratios, as well as with an overload, have been performed. modeling visualizes the laird-smith conceptual mechanism of fcg by plastic blunting and re-sharpening. simulation reproduces the experimental trends of fcg concerning the roles of stress intensity factor range and overload, but picc has never been detected. near-tip deformation patterns discard the filling-in a crack with material stretched out of the crack plane in the wake behind the tip as supposed picc origin. despite the absence of closure, load-deformation curves appear bent, which raises doubts about the trustworthiness of closure assessment from the compliance variation. this demonstrates ambiguities of picc as a supposedly intrinsic factor of fcg and, by implication, favors the stresses and strains in front of the crack tip as genuine fatigue drivers. keywords. crack closure; crack-tip strains; fatigue cracking. introduction he capability of opposite crack surfaces to contact prematurely at unloading due to particular patterns of the neartip plastic straining under cyclic loading, the so called plasticity induced crack closure (picc), is believed to be the intrinsic feature of fatigue crack growth (fcg), cf., e.g., the overview [1], although not everybody involved in fatigue studies shares this conviction [2-4]. despite the phenomenon of crack closure has been focused for decades since its raising by elber [5], neither agreement between evaluations by different ways nor consensus about the relevance, and even the very existence, of picc in the course of fcg do exist, cf. [1-3,6,7]. conclusions about the picc mechanisms based on both dislocation and continuum plasticity analyses are contradictory, cf., e.g., deshpande et al. [8] or pippan and riemelmoser [9] vs. louat et al. [3] or bjerkén and melin [10], budianski and hutchinson [11] vs. noroozi et al. [12], and mcclung et al. [13] vs. toribio and kharin [14]. picc is used to be accepted as the factor directly responsible for the dependence of fcg, apart from the load range, on the load maximum or ratio, as well as on overor under-loads along the loading routes, forming thus the framework to interpret fcg trends. crack closure, which can arise from various origins (incidental ones, such as in-crack debris, oxides or other in-crack depositions, as well as ubiquitous ones, such as the crack surface roughness), seems to be out of doubts as a phenomenon that can accompany fcg and affect it under certain circumstances. nevertheless, specifically picc remains questionable as the universal intrinsic mechanism that controls fcg. a deal of uncertainty owes here to the difficulties of straightforward evidence of the crack closure phenomenon. reviews [1,6,7] catalogued a variety of ways of the crack closure verification and assessment ranging from deductions based on the crack growth behavior (i.e., on the presumption of the role of closure in the process) to interpreting the compliance measurements on the assumption that t http://www.gruppofrattura.it http://dx.medra.org/10.3221/igf-esis.25.19&auth=true j. toribio et alii, frattura ed integrità strutturale, 25 (2013) 130-137; doi: 10.3221/igf-esis.25.19 131 the experienced nonlinearity of the load-deformation curves (as obtained with the use of displacement or strain gauges, interferometry, or other devices to monitor deformations) “indicates that there is a progressive change in geometry of the specimen, which must be caused by the closing of the crack” [5]. this way, the very identification of picc lacks of direct evidence and its responsibilities in fcg remain debatable. since in situ visualization of the near-tip deformations is hardly feasible in the places where the plane-strain situation is approached, computational simulation turns out to be the right way to determine them. accounting for both constitutive (inelasticity) and geometrical (large displacements and strains) nonlinearities is here essential. for cracks growing by means of local material rupture, the alteration of solid boundary via crack advance by bond breaking is the third nonlinearity. then, the most precise revelation of the near tip situation would be achieved taking into account all three mentioned nonlinearities. up to date, among available analyses of fatigue cracks, some of them have not accounted for large deformations (such as, e.g., [13, 15, 16]), whereas others (e.g., [14, 17-24]), although fulfilling this deficiency, presented partial data about cracks under cyclic loading. anywise, common shortcoming is the lack of realistic treatment of the crack growth by means of bond breaking. this latter was simulated usually by cutting the material bonds fairly subjectively along finite-size steps via finite element node release to the analyst’s discretion at the bottom, mid or top points of designated loading cycles irrespectively of both the material and applied load (cf., e.g., [13, 16, 21, 24]), and thus, having hardly whatsoever to do with the physics of crack advance. the efforts involving more realistic mechanisms of material damage and bond breaking directly in the modeling of fcg have been undertaken since nearly a decade (e.g., [25, 26]) usually by substantial computational expenses. however, these relatively few attempts are at rather early stage of development and encounter conceptual and technical difficulties on the way to implement damage mechanics in large-deformation formulations. finally, having difficulties with direct involvement of realistic material rupture modeling into simulation of fcg, another approach counts on the stress-, strainor energy-based variables as fatigue damage monitors [27-30]. however, the evolution of a tip of a growing crack cannot be solved there straightforwardly. obviously, ignoring any of the three commented nonlinearities worsens the resolution of the crack-tip fields. disregard among them of the crack growth via bond breaking, modeling of which is surrounded by the most controversy, may have significance for the simulation outcome. however, would consequent inaccuracy be more or less substantial in comparison with faultiness of unrealistic modeling of the bond breaking merely by making use of a “virtual knife” in analyst’s hands has to be verified through much advanced analyses involving duly all three concerned nonlinearities. meanwhile, among conceptual mechanisms of fcg, the one, which was suggested by laird and smith [31] and reaffirmed by pelloux [32] and neumann [33], and which was emphasized as the rational physical model for fcg in ductile materials [2, 10, 22, 23, 34, 35], relies solely on the near tip plastic deformations under cyclic loading without involvement of pullapart bond breaking. then, high-resolution large-deformation elastoplastic simulation is the right way to visualize this mode of fcg. recent advances in large-strain elastoplastic analyses of cracks under cyclic loading [14,17-20,22,23] revealed various aspects of fcg according to the laird-smith concept. the scope of this paper is to narrate the results of modeling of cracks under cyclic loading, which are in particular association with the matter of picc verification and assessment, and have not been revealed in previous presentations [14,18-20] of the performed simulations. deformations near the crack subjected to mode i cyclic loading under plane strain and small scale yielding (ssy) are described with the intention to bring insight into some long-standing controversies about the crack blunting re-sharpening and picc under load cycling. model material parameters correspond here to medium-high strength steel. notwithstanding, using common normalization techniques, generated solutions are applicable not to this sole material but to a similitude class fixed by the magnitudes of pertinent dimensionless parameters, such as the ratio of young modulus e to the yield stress y, poisson coefficient , and so on. modelling he results presented herein proceed from the extensive modeling of the mode i crack tip fields in elastoplastic material under ssy in terms of the crack tip autonomy dominated solely by the stress intensity factor (sif) k [36]. model design (geometry, loading and constitutive material model) and the large-strain analysis procedure were basically the same as presented and substantiated elsewhere [14,18-20]. their outline is as follows. at large strains, material hardening approaches saturation, so that elastic perfectly-plastic constitutive model can be an acceptable approximation, provided the value of y corresponds not to the initial yield point, but to some saturation stress level, the "effective" yield stress as modified by strain-hardening. then, the model of ideal elastoplastic solid having e = 200 gpa,  = 0.3 and y = 600 mpa with von mises yield surface and associated flow rule was chosen. t http://www.gruppofrattura.it http://dx.medra.org/10.3221/igf-esis.25.19&auth=true j. toribio et alii, frattura ed integrità strutturale, 25 (2013) 130-137; doi: 10.3221/igf-esis.25.19 132 the simulations were performed for constant amplitude loadings at different sif ranges k = kmax – kmin, and ratios r = kmin/kmax, and the effect of a single overload was considered, too, along the following load cases: (i) k = 2k0, r = 0, (ii) k = k0, r = 0, (iii) k = k0, r = 0.5, (iv) k = k0, r = 0, with an overload to kov = 2k0 at a single cycle of the loading path, where the reference value k0 = 30 mpam corresponds to loading regimes of fatigue cracking in steels [2,34]. the model of undeformed crack was parallel-flanks slot of the width b0 with semicircular tip, fig. 1(a), as it has been repeatedly substantiated and used in analyses of cracks, e.g., by mcmeeking [37], needleman and tvergaard [38], rice et al. [39], or toribio and kharin [14,18-20]. the value of b0 = 5 m was taken as a reasonable choice for steels [40]. model design was subdued to ensuring the ssy in terms of the k-dominated crack tip autonomy [36]. the choice was made [19,20] in favor of full-scale specimens, which were double-edge-cracked panel (decp) and central-cracked panel (ccp) under remote traction by uniform stress ap, fig. 1(b). due to specimen symmetries, the boundary-value problems were stated for the same region –a  x  w – a, 0  y  h (fig. 1(b), shadowed), being a the initial crack size, 2w and 2h the panel width and height, respectively. boundary conditions were posed according to the specimen symmetries and loading, fig. 1(c). to ensure the ssy, the model sizes were a = 15000b0, a/w = 0.2 and w = h. the sif calibrations were specified using the specimen geometry factor according to the compendium [41] for decp and ccp, respectively. the textbook [34,36] estimation for the monotonic plastic zone dimension under plane strain, ry = k2/(3y2), renders for the chosen material, geometry and loading max{ry/a, ry/h, ry/w}  0.014 << 1, which ensures the ssy. figure 1: model geometry and boundary conditions: (a) crack, (b) decp and ccp specimens, (c) global view of the fe model of the specimen quarters shadowed in (b) with respective boundary conditions for ccp and decp test-pieces, (d) near tip mesh refinement. large-deformation elastoplastic solutions were generated using a finite element (fe) code with updated lagrangian formulation and additive decomposition of strain rates. the fe mesh design followed previous studies of large near tip deformations [37-39]. to overcome numerical problems associated with mesh degeneration at the crack tip, extensive trials were accomplished to ensure the solution mesh convergence for acceptable number of loading cycles. re-meshing was considered to be not a suitable means to improve the fe model performance because of substantiated doubts [42] that, under the propensity to solution bifurcation of certain elastoplasticity problems due to their loss of ellipticity [43,44], small perturbations by re-meshing of the deformed tip shape in relation to the "true" one (yet unknown) can harm the results victim to pitfalls of a re-meshing technology. this later can break against mesh-sensitivity, which is rooted in the potential non-uniqueness of corresponding field solutions, to the extent that the relation between solution of the original continuum-mechanics problem and of its fe approximation may become questionable. to this end, it must not surprise to meet severe discrepancies between near tip deformations obtained using different mesh layouts, fe formulations and re-meshing procedures, which rendered crack faces folding without closure at the very first load cycles [17], as well as smooth surfaces arriving at closure at fairly large number of cycles [22, 23]. a variety of meshes permanently embedded in the material were explored attending the roles of fe size and shape, as well as of the interpolation order and integration scheme, as described elsewhere [42]. to postpone mesh degeneration, fe models of full-integration bi-linear quadrilateral elements were elaborated using rather high grade of element refinement http://www.gruppofrattura.it http://dx.medra.org/10.3221/igf-esis.25.19&auth=true j. toribio et alii, frattura ed integrità strutturale, 25 (2013) 130-137; doi: 10.3221/igf-esis.25.19 133 and relying on suitable initial element shaping trying to ascertain the near tip deformation patterns yet to come in the deformed configuration in order to maintain the accumulated fe distortions within tolerable limits. results and discussion enerated near tip solutions turned out to be fairly insensitive to the specimen geometry and loading in pertinent aspects. this way, the k-dominance over the crack tip zone was confirmed. for all geometry-and-loading cases, the crack-tip deformations evolved similarly to what is shown in fig. 2. plastic crack growth ap is there appreciated as an advancement of the tip apex a0 deeper into material. this way, the laird-smith conceptual scheme, which is considered to be one of the intrinsic mechanisms of fcg in ductile materials [2,31-35], is visualized. simulations evidence that the crack does grow under cyclic loading, although with no bond breaking. figure 2: crack tip deformations at unloading after accomplishing the first (a) and fifth (b) cycles of the load case i (decp specimen); undeformed mesh fragment and tip contours are shown near the image center in (a) and in the bottom-left corner in (b), respectively, together with the positions of material points a0, b0 and b1 in the initial and deformed configurations. the plastic crack advancements ap vs. cycle number n are presented in fig. 3. the slopes of these curves render corresponding rates of plastic crack growth (da/dn)p. its acceleration with k is there evident, whereas the effect of r is rather vague. calculated (da/dn)p values are of the order of 10–6 m/cycle, which is proper for the paris regime in steels [2,34]. the paris-like equation (da/dn)p = c k m fits the numerical results at m  2.25, which is reasonable for many alloys [34]. this mode of crack extension is sensible to an overload, which halts the crack advance (fig. 3, load case iv). this way, the effects of k and overload on fcg obtained by simulations agree with common experimental trends [2,34]. figure 3: crack growth ap vs. cycle number n along indicated loading routes in ccp specimen (the points correspond to the crack tip positions at the load cycle ends). no signs of picc have ever occurred during simulated crack growth at r  0. although cracks upon unloading shrink in a wake behind the tip more than at the tip itself in all load cases (fig. 2), deformed crack faces have never and nowhere got to the initial crack width, and so, no contact between crack surfaces could be approached. this holds for an appreciable crack advancement ap leaving a considerable plastic wake behind the tip, as it can be appreciated from fig. 4 which displays crack penetration through substantial fraction of the plastic zones created in the first load cycle, the g http://www.gruppofrattura.it http://dx.medra.org/10.3221/igf-esis.25.19&auth=true j. toribio et alii, frattura ed integrità strutturale, 25 (2013) 130-137; doi: 10.3221/igf-esis.25.19 134 forward (monotonic) and the reverse ones, as well as the move forward of the actual cyclic plastic zone together with the crack tip, having these zones determined according to the criterion of non-zero equivalent plastic strain rate [20]. figure 4: plastic zones near the tip of the grown crack in the deformed solid configuration (meshed area) after accomplishing of 90 loading cycles along the route ii: actual cyclic (reversed) plastic zone at the end of the 90th cycle (white contour line) and the material which was involved in plastic flow in the first loading cycle at its top (monotonic plastic zone, light-grey area) and bottom (reversed plastic zone at unloading, dark-grey area). undeformed crack contour is present at the figure bottom. although presented modeling agrees with experimental trends of fcg, crack advancement by blunting re-sharpening can hardly be the entire mechanism of every fcg occurrence, as far as fatigue cracks usually evidence, e.g., by means of fractography, the signs of material damage and fracture. this may be the reason why simulated solely plastic crack growth is insensitive to the load ratio or manifests negative crack growth rate after an overload (fig. 3). fcg is seen [2,4,34] to proceed usually by various mechanisms of deformation, damage and bond breaking which go on synergistically. as well, crack closure upon unloading can arise owing to a series of causes, both intrinsic (such as fracture surface roughness originated from various microstructural damage and fracture events, or stress-induced phase transformations, etc.) and extrinsic (e.g., in-crack debris, oxides, and so long) ones. however, presented results imply that crack closure can be neither a necessary requisite nor a decisive factor for the mentioned fcg trends. indeed, the plastic advancement of a crack behaves per se in agreement with well known experimental fcg trends, but with no signs of picc. this latter may happen at larger number of cycles, as it occurred in simulations by tvergaard [22,23], as well as may not. the supposed consequences of closure in fcg (e.g., the overload retardation or arrest [34]) do appear with no closure. accordingly, the practiced indirect assessments of picc-related issues from fcg behaviour [7] acquire a deal of spuriousness, which can make them artifacts. displayed results fairly agree in all pertinent aspects with other large-strain analyses of cracks under cyclic loading [22,23], but challenge those smalland finite-strain simulations (such as, e.g., [13,16,21,24]), where crack growth was imposed by means of cutting the material arbitrarily with a "virtual knife" in analyst's hands counting on neither the material nor the applied load. so, all these latter models were intrinsically unable to render per se any effect of the loading route on fcg, such as the influence of k or overload. in contrast, presented modeling does this. moreover, by virtue of the permanent gluing of fe meshes to the material, it is revealed here how the crack grows by plastic straining, which renders material transfer from the crack front onto its lateral surfaces, as it does a neighborhood of the material point b1 in fig. 2. material "bricks" situated initially a little bit aside the top a0 of the arc b0b1a0, which shapes the crack tip, move there sideways and build the crack flanks up, i.e., contribute to crack enlargement. this is lengthened additionally by stretching of these material “bricks”, which are placed to form the crack flanks, fig. 5(a), where large tensile plastic strain 0pyy  in the in-plane of the crack direction is observed, fig. 5(b), which implies negative axial strain yy  xx < 0 near the crack tip by virtue of plane-strain large incompressible plasticity. this latter result agrees with experimental x-ray diffraction study of the strain fields near fatigue cracks, which reported the "negative anomaly" in yy strain behind the tip [45], but contradicts the results of small-strain numerical analysis [13] schematized in fig. 5(c). this way, performed large-deformation simulations discard the mechanism of picc implied from the small-strain modeling [13], where material elements behind the crack tip underwent out-of-plane plastic stretching 0pyy  accompanied by shrinking along the crack surfaces 0p pxx yy    by virtue of the plane-strain incompressible plasticity, fig. 5(c). accordingly, it was argued that this out-of-plane stretched material on the growing crack surfaces behind the tip could fillhttp://www.gruppofrattura.it http://dx.medra.org/10.3221/igf-esis.25.19&auth=true j. toribio et alii, frattura ed integrità strutturale, 25 (2013) 130-137; doi: 10.3221/igf-esis.25.19 135 in the crack, and this way enable the opposite crack surfaces to contact prematurely at unloading, i.e., produce picc. evidently, this contradicts to figs. 2 and 5(a,b), where large displacements and rotations in the crack tip vicinity make material not to fill-in the crack behind the tip and render picc, but to increment the crack flanks, i.e., they make the crack advance. this gives the reason to consider the suggested picc origin as an artifact [13], as far as it appears to be not the naturally present feature of a crack under cyclic loading but a product of an analysis method. figure 5: deformations near the crack tip under cyclic loading: (a) crack-tip large-deformation patterns with a scheme showing how and where do material "bricks" with their glued local material frames ( , )x y go by translation and rotation (arrows) from the initial configuration to make the crack grow; (b) contour bands of the plastic strain pxx at the end of the sixth cycle of the route i in deformed solid configuration (undeformed crack tip is seen in the bottom-left corner) to illustrate the contribution of the "bricks" stretching to crack lengthening, but not to its closure; (c) scheme of the small-deformation results [13, fig. 8] used to substantiate the suggested origin of picc in the supposed filling-in the crack with stretched material behind the tip; the squares shaded in gray and rectangles filled with line pattern represent in (a) and (c) the same material elements in the initial and deformed states, respectively. conclusions he crack becomes larger after every cycle, i.e., it grows, as suggested the laird-smith concept, by means of plastic straining with certain rate (da/dn)p. this growth reproduces the key experimental trends of fcg, such as the acceleration with k and the hindering by overload, which have been repeatedly attributed to the crack closure. specimen compliance changes, which are frequently considered, following elber [5], to be the evidences of crack closure, do occur in simulations. despite all that, no picc has appeared, and revealed deformation patterns discard its supposed origination from filling-in the crack with plastically stretched material in the wake. it does not matter now whether picc could occur at substantially larger number of cycles or longer crack growth, or whether local material fracture through bond breaking is a necessary requisite for picc to arise, but the point is that the supposed consequences of picc do take place with no closure behind them, thereby bringing doubts about picc. acknowledgements he authors wish to acknowledge the financial support provided by the following spanish institutions: ministry for science and technology (mcyt; grant mat2002-01831), ministry for education and science (mec; grant bia2005-08965), ministry for science and innovation (micinn; grants bia2008-06810, and bia2011-27870) and junta de castilla y león (jcyl; grants sa067a05, sa111a07, and sa039a08). references [1] overview. advances in fatigue crack closure measurement and analysis, astm stp 1343, r.c. mcclung, j.c. newman, eds., astm international, west gonshohocken, (1999) xi. [2] ritchie, r. o., mechanisms of crack propagation in ductile and brittle solids, int. j. of fract., 100 (1999) 55-83. t t http://www.gruppofrattura.it http://dx.medra.org/10.3221/igf-esis.25.19&auth=true j. toribio et alii, frattura ed integrità strutturale, 25 (2013) 130-137; doi: 10.3221/igf-esis.25.19 136 [3] louat, n., sadananda, k., duesbery, m., vasudevan, a. k., a theoretical evaluation of crack closure, met. trans., a24 (1993) 2225-2232. [4] vasudevan, a. k., sadananda, k., glinka, g., critical parameters for fatigue damage, int. j. of fatigue, 23 (2001) s39s53. [5] elber, w., fatigue crack growth under cyclic tension, eng. fract. mech., 2 (1970) 37-45. [6] macha, d. e., corbly, d. m., jones, j. w., on the variation of fatigue-crack-opening load with measurement location, exp. mech., 19 (1979) 207-213. [7] xu yigeng, gregson, p. j., sinclair, i., systematic assessment of compliance-based crack closure measurements in fatigue, mater. sci. and eng., a284 (2000) 114-125. [8] deshpande, v. s., needleman, a., van der giessen, e., a discrete dislocation analysis of near-threshold fatigue crack growth, acta mater., 49 (2001) 3189-3203. [9] pippan, r., riemelmoser, f. o., visualization of the plasticity-induced crack closure under plane strain conditions, eng. fract. mech., 60 (1998) 315-322. [10] bjerkén, c., melin, s., growth of a short fatigue crack – a long term simulation using a dislocation technique, int. j. of solids and struct., 46 (2009) 1196-1204. [11] budiansky, b., hutchinson, j. w., analysis of closure in fatigue crack growth, j. of appl. mech., 45 (1978) 267-276. [12] noroozi, a. h., glinka, g., lambert, s., prediction of fatigue crack growth under constant amplitude loading and a single overload based on elasto-plastic crack tip stresses and strains, eng. fract. mech., 75 (2008) 188-206. [13] mcclung, r. c., thacker, b. h., roy, s., finite element visualisation of fatigue crack closure in plane stress and plane strain, int. j. of fract., 50 (1991) 27-49. [14] toribio, j., kharin, v., large crack-tip deformations and plastic crack advance during fatigue, mater. lett., 61 (2007) 964-967. [15] ellyin, f., wu, j., elastic-plastic analysis of a stationary crack under cyclic loading and effect of overload, int. j. of fract., 56 (1992) 189-208. [16] wu, j., ellyin, f., a study of fatigue crack closure by elastic-plastic finite element for constant-amplitude loading, int. j. of fract., 82 (1996) 43-65. [17] levkovitch, v., sievert, r., svendsen, b., simulation of fatigue crack propagation in ductile metals by blunting and resharpening, int. j. of fract., 136 (2005) 207-220. [18] toribio, j., kharin, v., high-resolution numerical modelling of stress-strain fields in the vicinity of a crack tip subjected to fatigue, fracture from defects, emas, (1998) 1059-1064. [19] toribio, j., kharin, v., role of fatigue crack closure stresses in hydrogen assisted cracking, advances in fatigue crack closure measurement and analysis, astm stp 1343, r.c. mcclung, j.c. newman, eds., astm international, west gonshohocken, (1999) 440. [20] toribio, j., kharin, v., finite deformation analysis of the crack-tip fields under cyclic loading, int. j. of solids and struct., 46 (2009) 1937-1952. [21] roychowdhury, s., dodds, r. h., a numerical investigation of 3-d small-scale yielding fatigue crack growth, eng. fract. mech., 70 (2003) 2363-2383. [22] tvergaard, v., on fatigue crack growth in ductile materials by crack-tip blunting, j. mech. and phys. of solids, vol. 52, 2004, pp. 2149-2166. [23] tvergaard, v., overload effects in fatigue crack growth by crack-tip blunting, int. j. of fatigue, 27 (2005) 1389-1397. [24] lei, y., finite element crack closure analysis of a compact tension specimen, int. j. of fatigue, 30 (2008) 21-31. [25] lynn, a. k., duquesnay, d. l., computer simulation of variable amplitude fatigue crack initiation behaviour using a new strain-based cumulative damage model, int. j. of fatigue, 24 (2002) 977-986. [26] nguyen, o., repetto, e., ortiz, m., radovitzky, r., a cohesive model of fatigue crack growth, int. j. of fract., 110 (2001) 351-369. [27] chalant, g., remy, l., model of fatigue crack propagation by damage accumulation at the crack tip, eng. fract. mech., 18 (1983) 939-952. [28] chan, k. s., lankford, j., a crack tip strain model for the growth of small fatigue cracks, scripta met., 17 (1983) 529532. [29] fan, f., kalnaus, s., jiang, y., modelling of fatigue crack growth of stainless steel 304l, mech. of mater., 40 (2008) 961-973. [30] hurtley, p. j., evans, w. j., a new method for predicting fatigue crack propagation rates, mater. sci. and eng., a466 (2007) 265-273. [31] laird, c., smith, g. c., crack propagation in high stress fatigue, phil. mag., 8 (1962) 847-857. http://www.gruppofrattura.it http://dx.medra.org/10.3221/igf-esis.25.19&auth=true j. toribio et alii, frattura ed integrità strutturale, 25 (2013) 130-137; doi: 10.3221/igf-esis.25.19 137 [32] pelloux, r. m. n., crack extension by alternating shear, eng. fract. mech., 1 (1970) 697-704. [33] neumann, p., new experiments concerning the slip process at propagating fatigue cracks, acta met., 22 (1974) 11551165. [34] suresh s., fatigue of materials, cambridge university press, cambridge, (1991) 617. [35] riemelmoser, f. o., pippan, r., stüwe, h. p., an argument for a cycle-by-cycle propagation of fatigue cracks at small stress intensity ranges, acta mater., 46 (1998) 1793-1799. [36] kanninen, m.f., popelar, c.h., advanced fracture mechanics, oxford university press, new york, (1985) 562. [37] mcmeeking, r. m., finite deformation analysis of crack tip opening in elastic-plastic materials and implications for fracture, j. mech. and phys. of solids, 25 (1977) 357-381. [38] needleman, a., tvergaard, v., crack-tip stress and deformation fields in a solid with vertex on its yield surface, elastic-plastic fracture: second symposium inelastic crack analysis, astm stp 803, c.f. shih, j.p. gudas, eds., astm international, 1 (1983) 80. [39] rice, j. r., mcmeeking, r. m, parks, d. m., sorensen, e. p., recent finite element studies in plasticity and fracture mechanics, comput. meth. applied mech. and eng., 17/18 (1979) 411-442. [40] handerhan, k. j., garrison, w. m., jr., a study of crack tip blunting and the influence of blunting behavior on the fracture toughness of ultra high strength steels, acta met. et mater., 40 (1992) 1337-1355. [41] savruk, m. p., stress intensity factors in solids with cracks, naukova dumka, kiev, (1988) 619 [42] toribio, j., kharin, v., comments on simulations of fatigue crack propagation by blunting and re-sharpening: the mesh sensitivity, int. j. of fract., 140 (2006) 285-292. [43] hill, r., acceleration waves in solids, j. mech. and phys. of solids, 10 (1962) 1-16. [44] rice, j. r., the localization of plastic deformation, theoretical and applied mechanics, north-holland, amsterdam, (1977) 207-220. [45] croft, m., zhong, z., jisrawi, n., zakharchenko, i., holtz, r.l., skaritka, j., fast, t., sadananda, k., lakshmipathy, m., tsakalakos, t., strain profiling of fatigue crack overload effects using energy dispersive x-ray diffraction, int. j. of fatigue, 27 (2005) 1408-1419. http://www.gruppofrattura.it http://dx.medra.org/10.3221/igf-esis.25.19&auth=true microsoft word numero_30_art_31 p. lopez-crespo et alii, frattura ed integrità strutturale, 30 (2014) 244-251; doi: 10.3221/igf-esis.30.31 244 focussed on: fracture and structural integrity related issues study of short cracks under biaxial fatigue p. lopez-crespo, b. moreno, a. garcia-gonzalez, j. zapatero department of civil and materials engineering, university of malaga, c/dr ortiz ramos s/n, 29071 malaga, spain plopezcrespo@uma.es a. lopez-moreno department of materials science and metallurgy engineering, university of jaen, campus las lagunillas 23071 jaen, spain abstract. in this paper a methodology for evaluating crack initiation under biaxial conditions is presented. the methodology consists of evaluating the crack length automatically with digital processing of highmagnification images of the crack. the methodology was applied to study five different strain conditions on a low carbon ferritic-pearlitic steel specimen with tubular shape. a hole of 150 μm diameter was drilled to enforce the crack to initiate at a particular spot. different combinations of axial and torsional strains were analysed during the initiation stage of the crack. the setup employed allowed detection of the crack to within 6 μm from the edge of the hole on average and monitoring of the crack during early stages. fatigue crack propagation curves clearly showed oscillations due to microstructure. it was also observed that these oscillations decreased as the torsional component of the strain was increased. keywords. biaxial fatigue; proportional loading; fatigue crack growth; crack initiation introduction nderstanding the behaviour of engineering components under biaxial load is crucial for a number of industries, including aerospace, automobile and power generation industries. different models have been proposed in an attempt to characterise the behaviour under such conditions [1]. stress-based models can be used to predict the fatigue life if the plastic strains are small [2]. strain-based models are typically employed in the low-cycle fatigue regime where significant plasticity may occur [3]. within strain-based models, critical plane approaches aim at predicting not only the fatigue life but also the crack direction of the crack [4, 5]. energy models are based on evaluating the energy accumulated per cycle on the material, and use it as a damage parameter [6, 7]. depending on the loading regime, an important portion of the life can be consumed in the initiation stage of the crack. initiation stage includes crack nucleation and micro-crack growth up to a length of around 1 mm. during the initiation stage, the aforementioned models for predicting crack propagation under biaxial loads no longer can be applied, because they are based on continuum mechanics. the material microstructure and the surface morphology are critical to the crack growth during the initiation stage [8]. during the initiation, fatigue crack growth is different to that predicted by the above mentioned models, and oscillations are commonly observed on the growth curves. these are caused by grain and phase boundaries and other micro-structural features that continuum mechanics models do not take into account [9]. the current work aims at studying the fatigue crack growth behaviour of small cracks under different biaxial conditions. u p. lopez-crespo et alii, frattura ed integrità strutturale, 30 (2014) 244-251; doi: 10.3221/igf-esis.30.31 245 material and specimen low carbon steel (st-52-3n) was examined in this investigation. this material is often employed in structural components. the composition of the steel is shown in tab. 1. fig. 1 shows a micrograph of the st-52-3n steel. ferrite and pearlite bands can be seen in fig. 1 as vertical bands in white and black respectively. c si mn p s cr ni mo 0.17 0.225 1.235 0.010 0.0006 0.072 0.058 0.16 table 1: chemical composition in weight % of st-52-3n steel. the balance is fe. figure 1: optical micrograph of st-52-3n steel used in all tests. tubular hollow specimens were used in this work to apply different combinations of torsion and tensile loads. a schematic of the geometry is shown in fig. 2. all experiments were conducted with mts 809 servo-hydraulic loading rig, allowing different biaxial loads to be applied on the specimens. biaxial extensometer epsilon 3550 was used to measure axial and angular strains. all the crack measurements were made with a black and white 1.2 megapixel digital camera coupled to a long distance microscope. co-axial illumination was used to acquire all images. moreover, two additional led 3 w lamps were also used to improve light distribution on the surface and remove reflections. fig. 3 shows the setup employed in the experiment with all the different elements used. figure 2: geometry of the dog-bone shaped tubular hollow specimen used in the experiments. all dimensions are in mm. a p. lopez-crespo et alii, frattura ed integrità strutturale, 30 (2014) 244-251; doi: 10.3221/igf-esis.30.31 246 figure 3: experimental setup employed in this work. experiments he initiation stage of the crack growth was studied under combined proportional tension-compression and torsion tests [10]. all experiments were conducted under strain control mode with the help of the biaxial extensometer, with cyclic sinus signal with zero mean strain (r = -1). the aim of the work was to study a wide range of biaxial loads, with angle between shear and axial strains, φ, going from 0 to 90º in 15º increments (see fig. 4). imaging of the crack during initiation was possible by drilling a 150 μm diameter hole on the outer surface of the specimen [11]. the long-distance microscope was then focused on the hole, so that the crack initiation could be acquired. the hole on the surface looked like those shown in fig. 5. the hole served as a stress raiser thus increasing the chances of the crack nucleating there. the size of the hole was chosen so that fatigue behaviour remains the same as that of the specimen without the hole, but large enough so that nucleation of the crack occurs at the hole. the hole influence on the fatigue life is negligible, as shown previously [12]. the setup allowed detection of the crack a few microns away from the edge of the hole. on average, detection of the crack was possible at distances of 6 μm from the edge of the hole. in practice, the crack did not nucleate at the hole in around 50% of the specimens tested. only the samples where crack nucleated at the hole are reported here. when the shear component was increased beyond φ = 60º, it was not possible to nucleate the crack around the hole. instead, the crack appeared either on the inside of the specimen or elsewhere. consequently, it was not possible to conduct experiments with angle greater than φ = 60º. tab. 2 summarises the different tension-compression and torsion strain combination studied. figure 4: definition of angle between axial and shear strain amplitudes. t p. lopez-crespo et alii, frattura ed integrità strutturale, 30 (2014) 244-251; doi: 10.3221/igf-esis.30.31 247 sample no. φ (º) εa γa nf (cycles) s1 0 0.005 0 875 s2 15 0.0048 0.022 950 s3 30 0.043 0.043 1400 s4 45 0.035 0.061 1850 s5 60 0.025 0.075 2425 table 2: summary of five samples employed in this work, showing the angle (φ) between axial strain amplitude (εa) and shear strain amplitude (γa), as well as the fatigue life (nf) of each sample. fatigue crack measurements he setup described previously (fig. 3) allowed acquisition of high-magnification images while the specimens were being strained. magnification factor of 1.1 μm/pixel was achieved with working distance of approximately 380 mm, resulting in a field of view of 2 × 1.5 mm2. in addition, the surface of the specimen was etched for 30 seconds with nitric acid diluted with ethanol to create a random pattern of the surface. this pattern can be used for obtaining displacement and strain fields with digital image correlation (dic). however, no dic results are shown here and only the crack propagation results will be shown and discussed. fig. 5 shows some examples of images acquired during the experiment. figure 5: images acquired for samples a) s2 and b) s4 after 950 and 1300 cycles respectively. the diameter of the hole in both images is 150 μm. around 120 images similar to those shown in fig. 5 were acquired every 25 cycles. the image of maximum strain was then selected (fig. 6.a) and analysed with an image processing algorithm. the algorithm evaluated the darkest pixels (minimum value in the grey scale) of the image and assumed they were inside the crack. subsequently 20 grey values were added the minimum value to account for small intensity differences occurring within the crack. this information was employed for binarising the image, as has been done in previous works [13]. the binarised image was then analysed with an edge-finding routine to detect the edges which coincide with the crack edges (fig. 6.b) [14, 15]. finally, the detected crack was superimposed on the original image (fig. 6.c). the algorithm allowed automatic evaluation of the crack length for all images acquired. t p. lopez-crespo et alii, frattura ed integrità strutturale, 30 (2014) 244-251; doi: 10.3221/igf-esis.30.31 248 figure 6: image of sample s1 at maximum strain after applying 800 cycles. a) raw image, b) image of the crack detected with the algorithm and c) detected crack superimposed on original image. the diameter of the hole is 150 μm. the results of monitoring the crack length against the number of cycles during the early stages of the crack are shown in fig. 7. the crack growth rates were computed from a-n curves by numerical differentiation following astm standard [16] and are shown in fig. 8. figure 7: crack length versus number of cycles for samples a) s1, b) s2, c) s3, d) s4 and e) s5. discussion t is observed in tab. 2 and fig. 7 that fatigue lives increase from 875 to 2425 cycles as the angle φ increases from 0 to 60º. that is, for the strain ranges studied, increasing the shear component produces longer fatigue lives. fig. 7 also shows that the growth of the cracks emanating to the right hand and left hand of the hole are similar for samples s1, s2 and s5. differences between right and left cracks are observed for samples s3 and s4. i p. lopez-crespo et alii, frattura ed integrità strutturale, 30 (2014) 244-251; doi: 10.3221/igf-esis.30.31 249 figure 8: fatigue crack propagation rates (da/dn) versus crack length for samples a) s1, b) s2, c) s3, d) s4 and e) s5. fig. 8 shows oscillations in the growth rate. these oscillations are due to microstructure and are often observed during crack initiation. the barrier effect is produced by the pearlite bands which are the phases with greatest strength [12]. since the propagation rate curves are plotted on logarithmic scale, it is not easy to compare the magnitude of oscillations for the different angles. thus the average oscillation for all angles was computed. the extent of each oscillation was obtained subtracting each local minimum to the subsequent local maximum. the average extent of the oscillations for all angles studied are shown in fig. 9. these values are an estimate of how large acceleration and retardation transients are. large oscillations are indicative of great accelerations and/or great retardations. it can be seen in fig. 9 that acceleration and retardation transients increase as the angle φ decreases. that is, increasing the axial component of the strain produces stronger accelerations and retardations. the more damaging effect of lower angle φ is evident from fig. 7 since lower angles φ yield shorter fatigue lives. accordingly, the combination of strains applied at lower angles φ (i.e. with higher tensile component) produces an overall higher level of stresses. nevertheless, the current tests do not seem to follow the trend depicted by mcdowell model (fig. 10) [17, 18]. the model predicts higher level of oscillations as the load is increased. however, the data shown previously seems to follow a different trend. it is possible that increasing the torsional component, reduces the oscillations typically observed in small cracks and the effect of the torsional component is more pronounced than the mean stress effect. nevertheless, further experiments should be conducted in order to evaluated both effects separately. figure 9: average oscillation on da/dn curve for the five different angles, φ, studied. p. lopez-crespo et alii, frattura ed integrità strutturale, 30 (2014) 244-251; doi: 10.3221/igf-esis.30.31 250 figure 10: typical evolution of crack growth rate as a function of crack length and stress amplitude. adapted from [17]. concluding remarks methodology for characterising crack initiation under biaxial loading conditions has been described. it included automatic evaluation of crack length with digital processing algorithms and edge-finding routine. the setup allowed detection of the crack within 6 μm from the edge of a hole drilled so that the crack could be observed from its early stages. different biaxial conditions were investigated in five tubular specimens of low carbon ferriticpearlitic steel. strains ranged from pure tension-compression axial strain to strain states with an increasing torsional component and a decreasing axial component. typical oscillations with acceleration and retardation transients were observed throughout all the strains states studied. these oscillations were ascribed to grain or phase boundaries existing in the material. the retardations seem to appear when the crack meets a pearlite band. in addition, the magnitude of the oscillations decreases with increasing torsional component. it was not possible to correlate the different oscillation levels with previous models describing crack growth at the initiation stage. acknowledgements inancial support of junta de andalucía through proyectos de excelencia grant reference tep-3244 and of spanish ministerio de economía y competitividad through grant reference dpi2012-33382 is greatly acknowledged. experimental help of mr pablo cobos-rodriguez and mr hector martin is also greatly acknowledged. references [1] you, b. r., lee s. b., a critical review on multiaxial fatigue assessments of metals, international journal of fatigue, 18(4) (1996) 235-244. [2] mcdiarmid, d. l., a general criterion for high cycle multiaxial fatigue failure, fatigue and fracture of engineering materials and structures, 14(4) (1991) 429-453. [3] socie, d. f., marquis, g. b., multiaxial fatigue, warrendale, pa (usa), society of automotive engineers, inc., (2000). [4] brown, m. w., miller, k. j., a theory for fatigue under multiaxial stress-strain conditions, in: proceedings of the institution of mechanical engineers, 187 (1973) 745-755. [5] fatemi, a., socie, d.. a critical plane approach to multiaxial fatigue damage including out-of-phase loading, fatigue and fracture of engineering materials and structures, 11(3) (1988) 149-165. [6] garud, y. s., a new approach to the evaluation of fatigue under multiaxial loadings, journal of engineering materials and technology, 103 (1981) 118-126. [7] ellyin, f., kujawski, d., amultiaxial fatigue criterion including mean-stress effect. in: astm stp 1191. mcdowell dl, ellis r, editors. west conshohocken, (1993) 55-66. a f p. lopez-crespo et alii, frattura ed integrità strutturale, 30 (2014) 244-251; doi: 10.3221/igf-esis.30.31 251 [8] suresh, s., ritchie, r.o., propagation of short fatigue cracks, international materials reviews, 29(1) (1984) 445-475. [9] mcdowell, d.l., multiaxial small fatigue crack growth in metals, international journal of fatigue, 19 (1987) s127s135. [10] lopez-crespo, p., moreno, b., lopez-moreno, a., zapatero, j., study of crack orientation and fatigue life prediction in biaxial fatigue with critical plane models, engineering fracture mechanics, (2014) to appear. [11] moreno, b., lopez-crespo, p., zapatero, j., high magnification crack-tip field characterisation under biaxial conditions, frattura ed integrità strutturale, 25 (2013) 145-152. [12] lopez-crespo, p., moreno, b., lopez-moreno, a., zapatero, j., characterisation of crack-tip fields in biaxial fatigue based on high-magnification image correlation and electro-spray technique, international journal of fatigue, manuscript accepted (2014), http://dxdoiorg/101016/jijfatigue201402016. [13] withers, p. j., lopez-crespo, p., kyrieleis, a., hung, y.-c., evolution of crack-bridging and crack-tip driving force during the growth of a fatigue crack in a ti/sic composite, in: proceedings of the royal society a, mathematical, physics & engineering sciences, (2012), doi: 101098/rspa20120070. [14] lopez-crespo, p., shterenlikht, a., patterson, e. a., withers, p. j., yates, j. r., the stress intensity of mixed mode cracks determined by digital image correlation, journal of strain analysis for engineering design, 43 (2008) 769-780. [15] lopez-crespo, p., burguete, r. l., patterson, e. a., shterenlikht, a., withers, p. j., yates, j. r., study of a crack at a fastener hole by digital image correlation, experimental mechanics (2008). [16] astm e647 standard test method for measurement of fatigue crack growth rates, (2003). [17] mcdowell, d. l., bennett, v. p., a microcrack growth law for multiaxial fatigue, fatigue and fracture of engineering materials and structures, 19(7) (1996) 821-837. [18] mcdowell, m. l., an engineering model for propagation of small cracks in fatigue, engineering fracture mechanics, 56(3) (1997) 357-377. microsoft word numero_44_art_3 a. saoud et alii, frattura ed integrità strutturale, 44 (2018) 25-34; doi: 10.3221/igf-esis.44.03 25 mechanical behavior of wood subjected to mode ii fracture, using an energetic criterion: application on thuja of morocco amal saoud, abdelhamid elamri, khadija kimakh, m'hamed chergui university of hassan ii, national superior school of electricity and mechanics casablanca (ensem), lccmms, morocco. saoudamal22@gmail.com http://orcid.org/ 0000-0002-2139-2627 khadija.kimakh@gmail.com http://orcid.org/ 0000-0002-2418-1307 mohsine ziani institut national des sciences de l'archéologie et du patrimoine (insap)/rabat, morocco. moussa elmatar centre technique d’industrie du bois et d’ameublement (ctiba)/casablanca, morocco. abstract. shear strength is one of the properties often used to qualify a wood species for use in industry. but until now there is no standardized test which allows understanding this phenomenon. this paper constitutes a new approach to study the behavior of the wood material subjected to the mode ii fracture. for that we designed and realized a new prototype of a wooden specimen that we tested in our laboratory which gives rise to an evaluation of the fracture until separation by pure shear of the specimen in the tl plane. the experimental data from a first series of tests on thuja wood (tetraclinis articulata (vahl) masters) as a test material as well as the calculation of mode ii initiation fracture toughness and the critical stress intensity factor are presented in this paper. keywords. shear; mode ii fracture; tetraclinis articulata; moroccan thuja wood; experimental testing. citation: saoud, a., elamri, a., kimakh, k., chergui, m., ziani, m., elmatar, m., mechanical behavior of wood subjected to mode ii fracture, using an energetic criterion: application on thuja of morocco, frattura ed integrità strutturale, 44 (2018) 25-34. received: 16.09.2017 accepted: 15.01.2018 published: 01.04.2018 copyright: © 2018 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. introduction t the beginning of the 21st century, environmental issues require the special attention of researchers. the process of transformation of wood has been proved to be the least expensive in terms of energy. the study of the mechanical behavior of wood is rising especially after recommendations following the conference of parties (cop): kyoto, rio, paris and marrakech. it is for this reason that the environmental commitments of the participating countries further stimulate scientific research on wood material for a more massive use in the context of reasonable logging. a a. saoud et alii, frattura ed integrità strutturale, 44 (2018) 25-34; doi: 10.3221/igf-esis.44.03 26 the study of this heterogeneous material requires knowledge of its behavior in the face of different solicitations, while knowing that wood as a natural material contains many defects, the application of the theory of fracture mechanics, which is a mean of estimating the stability of cracks in the immediate vicinity of the defects, is essential. it also makes it possible to predict the critical propagation length as a function of the loading applied. accordingly, it is fundamental to provide accurate measurements of the fracture properties such as initiation fracture toughness under mode i, mode ii, mixed mode i + ii and mode iii. the mode i fracture has been widely studied by different researchers using several types of standard specimens namely: compact tension (ct), single-edge notched tension (sent), double-edge notched tension (dent), single-edge notched three-point bending (senb) tests [1-5] and the double cantilever beam (dcb). concerning the dcb test specimen, its efficiency has been universally accepted thanks to its simplicity of design and realization for the measurement of toughness (gic and kic) by the simple beam theory [6]. wood fracture behavior under shear is one of the phenomena until now not fully controlled, that is why several prototypes have been proposed to approach closely the nature of the fracture in mode ii of rupture, the three main tests are based on flexure: the most commonly used test is the end-notched flexure (enf) which is a beam-like test specimen containing an artificial crack on one side and is loaded under three-point bending. the application of the load is rather simple, the propagation of the crack from the initial crack is unstable except for the very large notch lengths a/l> 0.7 [7]. studies using enf have been performed with an a/l ratio of 0.5 [8-10], so the propagation is unstable. other researchers use end loaded split (els) [11]: the sound side of a prismatic/beam specimen is clamped while the side containing the artificial defect is loaded in the direction of thickness. the loading is generally applied to the test specimen via a load block. the els test makes it possible to obtain a stable crack propagation in mode ii if the condition a/l>0.55 is respected [7]. nevertheless, it requires a rather complicated assembly to maintain the boundary conditions. finally, there is the most recent 4-point bend end-notched flexure (4enf) test specimen: a specimen containing an artificial defect on one side and loaded under four-point bending; this prototype has the advantage of being the most stable, but the acquisition of results requires sophisticated equipment. in this paper, a new test prototype is presented which is easy to use and stable and in which the rupture of the specimen can be perceived under mode ii. (a) (b) (c) figure 1: mode ii test configurations. (a) end notched flexure (enf), (b) four-point end notched flexure (4enf) and (c) end loaded split (els). a. saoud et alii, frattura ed integrità strutturale, 44 (2018) 25-34; doi: 10.3221/igf-esis.44.03 27 material and methods he experimental work consisted in subjecting thin, notched flat specimens with different cut lengths to mode ii tensile tests. all specimens and the gripping device were specially designed and produced for the purpose of this research. test material the material used is moroccan thuja "tectracanalis articulata" from the middle atlas plateau (khemissat region). in morocco, thuja occupies a total area of about 680 000 ha (equivalent to 11.7% of the total area covered by the moroccan forest) and plays an important socioeconomic role in the satisfaction of local needs of riparian populations for rangelands, firewood and various service woods [12]. these trees have no defects or rot. by respecting the various dimensions according to the specificities of the test, the test specimens were made from 25 mm thick ridges. in order to better characterize the material, physical and mechanical characterization tests.  physical measurements the moisture, the densities and the shrinkage along the three axes are determined on cubic specimens (20 mm × 20 mm × 20 mm) respectively according to standards nf b 51-004, nf b 51-005 and nf b 51-006.  mechanical measurements the longitudinal elastic modulus el and the static flexural strength σfs were determined by 4-point bending tests using prismatic specimens of (20 mm × 20 mm × 360 mm) cut aligned to the three symmetry directions of the wood in compliance with standard nf b51-008. compression tests were carried out to determine the stress at break σa according to the nf b 51-007 standard and finally shear tests on test pieces whose dimensional specificities are detailed in standard nf b 51-012 were also performed to evaluate the longitudinal shear strength, rlc. dh g/cm³ d0 g/cm³ rv(%) rt(%) rr(%) anisotropy el (mpa) σa (mpa) σfs (mpa) rlc (mpa) average 0.68 0.63 4.98 2.9 1.83 0.64 7437 35 82.22 30 standard deviation 0.03 0.02 0.46 0.45 0.06 0.11 148.1 0.38 25.93 2.41 dh: density of the specimen in the moisture state h, d0: density of the specimen in the anhydrous state, rv(%):volumetric shrinkage , rt(%):tangential shrinkage ,rr(%):radial shrinkage, el: longitudinal young's modulus, σa: compressive stress σfs: static bending strength rlc: longitudinal shear strength. table 1: main physical and mechanical characteristics of thuja. figure 2: representation of the test specimen. t a. saoud et alii, frattura ed integrità strutturale, 44 (2018) 25-34; doi: 10.3221/igf-esis.44.03 28  prototype of the fracture specimen designed the fracture specimens used were made from logs of thuja trees from the plateau of the middle atlas of morocco. these specimens are intended for crack propagation under mode i+ii but dominated by mode ii. fig. 2 illustrates the geometry and dimensional characteristics are presented in tab. 2. symbol description dimensions (mm) accuracy of ±0.1mm w width of the specimen 20 b thickness of the specimen 10 e the width of the groove 10 d the depth of the groove 10 l length of the specimen 234 z the area of damage 20 a length of notch  6 a 12 a gripping area 97 table 2: dimensional characteristics of the fracture specimen.  principle of the test the specimens are provided by a mechanical cut made using a jigsaw. a suitable device has been set up to have a precise notch depth and to ensure a displacement parallel to the base plane of the groove; the details of this mechanical notch are shown in fig. 3. figure 3: representation of the proposed test specimen. figure 3: realization of the notch with (a) blade 1 mm thick, (b) test specimen for mode ii fracture characterization and (c) slip gauge. this operation was reproduced on twenty-five specimens that were placed in a climatic chamber at a temperature of 10 ° c and 74% of humidity until material stabilization at moisture content of 15%. before each test, a razor blade was used to increase the sharpness of the mechanical notch, granting consistency with the linear fracture mechanics.  conduction of tests the test specimens were placed in a universal test machine type "mts 810", which allows the conduction of controlled tensile tests. this machine is equipped with a computer with control software which gives the recordings of the variation of the applied load as a function of the spacing of the lips of the crack for each specimen under test. this applied load is a. saoud et alii, frattura ed integrità strutturale, 44 (2018) 25-34; doi: 10.3221/igf-esis.44.03 29 measured by the load cell installed on the upper cross-member of the machine. load-displacement records are viewed on a computer screen and then stored for analysis. the two ends of the test specimen are then introduced into the gripping device as illustrated in fig. 4. figure 4: gripping device. the gripping device uses two ball-joints to ensure the alignment between the axis of the cross-member and that of the jack. the assembly has been placed in the tensile machine shown in the fig. 5. figure 5: (a) photo of mounted test specimen, (b) kinematic diagram of the test specimen mounted in the gripping device: (1) machine jaws; (2) ball joint connection; (3) gripping area; (4) grooves; (5) pivot pin; (6) loading direction; (7) test specimen; (8) mechanical notch. the testing machine allowed the application of an axial tensile force parallel to the wood grain on a series of 25 test specimens with a constant speed of 0.5 mm/min. this loading allowed the propagation of the crack until a shear rupture surface was created. results and discussion he experimental results of a test carried out under the same conditions are presented in the following. force-displacement curves fig. 6 illustrates typical force/displacement curves. t a. saoud et alii, frattura ed integrità strutturale, 44 (2018) 25-34; doi: 10.3221/igf-esis.44.03 30 figure 6: load-displacement curves for a = 6mm and a=4mm. the behaviour of our test piece during the test can be qualified as elastic under the action of the applied load. fig. 6 shows the superposition of the load / displacement curve obtained for thuja wooden specimens. it is noted that the crack propagates linearly until reaching the maximum load. it is also noted that the curve experiences oscillations during loading which can be explained by heterogeneities of wood, internal defects, variability in growth rings. cracks tend to propagate in growth rings corresponding to early wood (low intensity). to ensure the validity of our results and to consider the scatter, the tests were carried out on batches of 25 test pieces, taking care to distribute them in five small batches of five test pieces each with a notch length a (a = 4, 6, 8, 10, 12 mm). fig. 7 shows the load-displacement curves for different initial crack sizes of the test specimens tested. with a constant test speed of 0.5 mm / min as previously reported, the average tensile load decreases as the crack length increases as shown in tab. 3. figure 7: the load-displacement curves for the different lengths of initial notches. it is noted that the maximum loads vary from one test to another with the same notch length and under the same conditions; a normal thing due to the high heterogeneity of the wood material but the appearance of the curves remains consistent. the giic mode ii initiation fracture toughness and the kiic stress intensity factor of the thuja massive wood. experimental approach has helped to determine two important parameters, namely the strain energy release rate and the stress intensity factor. to do this, we started by determining the compliance as a function of the crack size. the set of loaddisplacement curves provides several values of the compliance ci (ai), defined by the slope of the load-displacement curve c = δ/p (see fig. 8), where δ and p represent the displacement and the applied load, respectively. the experimental points were smoothed using a polynomial of order 3. a. saoud et alii, frattura ed integrità strutturale, 44 (2018) 25-34; doi: 10.3221/igf-esis.44.03 31 crack length a (mm) critical load (kn) average load (kn) standard deviation (kn) a=4 1 0.81 1.14 0.95 0.13 0.98 0.80 a=6 0.882 1 0.90 0.88 0.07 0.85 0.801 a=8 0.57 0.59 0.60 0.59 0.01 0.60 0.57 a=10 0.54 0.54 0.54 0.55 0.01 0.55 0.57 a=12 0.51 0.40 0.47 0.51 0.07 0.54 0.61 table 3: evolution of the maximum load for each test. figure 8: the experimentally defined compliance as a function of the crack length. to perform the calculations, the following assumptions were assumed:  wood is a homogeneous material because the dimensions of the specimen are large compared to the difference between the diameters of two consecutive rings.  the elastic behavior is valid.  the orthotropic stiffness matrix is known.  the elastic constants used hereinafter, listed in tab. 4, were determined using the predictive model developed by a. saoud et alii, frattura ed integrità strutturale, 44 (2018) 25-34; doi: 10.3221/igf-esis.44.03 32  guitard, knowing that the density of wood is d = 0.60 g / cm 3[14]. to facilitate the comparison of results with the literature, while knowing that almost most researchers in this component uses this database. s11-1 (mpa) s22-1 (mpa) s33-1 (mpa) s12-1 (mpa) s23-1 (mpa) s31-1 (mpa) s44-1 (mpa) s55-1 (mpa) s66-1 (mpa) 1355.5 922.5 19355 2842 45950 51750 893.35 1173 117.8 sij: the components of the compliance matrix which are in function of the elastic constants of the wood table 4: elastic constants of thuja.  the giic mode ii initiation fracture toughness. g, the initiation fracture toughness corresponding to a small crack increment can be computed using the analytical form according to irwin-kies [6]:    p c b a 2 iig 2 (1) where b is the thickness of the specimen; p is the applied load and a the crack length.     c a ac c g b a 2 iic p 2 (2) the critical value of gii, giic, is then found by measuring the critical load pc needed to fracture a specimen containing a crack of length ac, and using the slope of the compliance curve at this same value of a[13] : we note that: c = ma3 + c0 (3) where m and c0 are determined by a linear regression of the experimental curve c as a function of a3 the critical stress intensity factor kiic mode ii initiation fracture toughness gii and stress intensity factor kii, assuming elastic linear behavior, are related to each other. the relationship between these two quantities is obtained using the following equation [14]:               1 1 2 2 2 12 66iic 11 22 iic 11 11 2s sk s s g s 2s2 (4) table 5: mode ii initiation fracture toughness and corresponding stress intensity factors. a(mm) gii n/m mean value standard deviation kii mpa.√m mean value standard deviation 4 113.95 33.37 0.40 0.06 6 221.99 37.14 0.56 0.05 8 174.65 9.20 0.50 0.05 10 237.20 11.87 0.58 0.05 12 267.06 62.51 0.61 0.02 a. saoud et alii, frattura ed integrità strutturale, 44 (2018) 25-34; doi: 10.3221/igf-esis.44.03 33 we set the mean value of the mode ii initiation fracture toughness giic and the kiic critical stress intensity factor determined using respectively the formulas cited previously in (3) and (4) in tab. 5. knowing that a material subjected to stresses contains stored elastic energy stored, during material cracking, there is an energy release. in fig. 9 a dispersion is observed for each value of a, except for the values of 8 and 10 mm, this dispersion is less visible. it is also observed that the propagation of the crack is stable from the ratio a=6mm. hence a quasi-stability of our prototype, we can conclude that for values greater than a / w = 0.3 gii and kii, are a characteristic of the wood material. figure 9: evolution of the energy restitution rate gii and kii as a function of the crack length. we cannot conclude without comparing our results with the literature. however, the wood has a lot of inter and intra-tree dispersal; moreover the moisture rate and the conditions in which the tests were carried out have a great influence on the results. we can only compare orders of magnitude. in tab. 6 we compare our results with the literature. specimens wood species reference giic els pinus pinaster [11] 0.319 enf pinus pinaster [16] 0.637 3enf stika spruce [10] 0.39 our work thuya of morroco 0.202 table 6: the comparative table of our results with the literature. conclusion new test method for the study of the behavior of wood material subjected to a shear stress in the longitudinal plane was developed. the experimental protocol of this test was applied to a first series of a resinous species: thuja of morocco. we were able to determine giic and kiic from the typical recording of the load-displacement curve during the stable propagation of the crack and using the method of complacency. these results were compared with the literature where it was observed that our approach presents an ease in the production and application of the specimens for mode ii propagation. unlike other devices previously presented the comparison of the results shows a high consistency. references [1] schniewind, a.p. and pozniak, r.a. (1971). on the fracture toughness of douglas-fir wood, engineering fracture mechanics, 2, pp. 223-230. doi: 10.1520/acem20120045. [2] mall, s., murphy, j.f. and shottafer, j.e. (2016). criterion for mixed mode fracture in wood. materials science and engineering: a, 527, pp. 27–28. doi: 10.1016/j.msea.2010.08.004. [3] triboulot, p., jodin, p. and pluvinage, g. (1984). validity of fracture mechanics concepts applied to wood by finite element calculation, wood scitechnol, 18, pp. 51–58. doi: 10.1007/bf00632130. a a. saoud et alii, frattura ed integrità strutturale, 44 (2018) 25-34; doi: 10.3221/igf-esis.44.03 34 [4] kretschmann, d.e. and green, d.w. (1985). modeling moisture content mechanical property relationships for clear southern pine. wood fiber science. [5] king, m.j., sutherland, i.j. and le-ngoc, l. (1995). fracture toughness of wet and dry pinus radiate,european journal of wood and wood product, 57, pp. 235–240. doi: 10.1007/s001070050 . [6] dourado, n., morel, s., de moura, m.f.s.f., valentin, g. and morais, j. (2008). comparison of fracture properties of two wood species through cohesive crack simulations, composites part a, 39, pp. 415-427. doi: 10.1016/j.compositesa.2007.08.025. [7] yoshihara, h. (2007). simple estimation of critical stress intensity factors of wood by tests with double cantilever beam and three-point end notched flexure. holzforschung, 61, pp. 182–189. doi: 10.1515/hf.2007.032 . [8] davies, p., blackman, b.r.k. and brunner (1998). standard test methods for delamination resistance of composite materials, applied composite materials, 5, pp.345. doi 10.1023/a:1008869811626. [9] davies, p., blackman, b.r.k. and brunner, a.j. (2001).mode ii delamination. european structural integrity society, 28, pp. 307-333. doi: 10.1016/s1566-1369(01)80039-x. [10] silva, m.a.l., de moura, m.f.s.f. and morais, j.j.l. (2006). numerical analysis of the enf test for mode ii wood fracture composites part a, 37, pp. 1334–1344.doi: 10.1016/j.compositesa.2005.08.014. [11] yoshihara, h. and ohta, m. (2000). measurement of mode ii fracture toughness of wood by the end-notched flexure test, j wood sci, 46, pp. 273. doi:10.1007/bf00766216. [12] silva, m.a.l., morais, j.j.l., de moura, m.f.s.f. and lousada, j.l. (2007) mode ii wood fracture characterization using the els test.engineering fracture mechanics, 74, pp. 2133-2147 doi: /10.1016/j.engfracmech.2006.10.012 . [13] ellatifi, m. (2012). l’économie de la forêt et des produits forestiers au maroc: bilan et perspectives. [14] roylance, d. (2001). introduction to fracture mechanics, department of materials science and engineering massachusetts institute of technology cambridge, ma 02139. [15] guitard, d. and el amri, f., (1987). modèles prévisionnels de comportement élastique tridimensionnel pour les bois feuillus et les bois résineux, annals of forest science, 44, pp. 335-358. doi: 10.1051/forest:19870305. [16] yoshihara, h. 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can be opened with acrobat and adobe reader 5.0 and later.) >> /namespace [ (adobe) (common) (1.0) ] /othernamespaces [ << /asreaderspreads false /cropimagestoframes true /errorcontrol /warnandcontinue /flattenerignorespreadoverrides false /includeguidesgrids false /includenonprinting false /includeslug false /namespace [ (adobe) (indesign) (4.0) ] /omitplacedbitmaps false /omitplacedeps false /omitplacedpdf false /simulateoverprint /legacy >> << /addbleedmarks false /addcolorbars false /addcropmarks false /addpageinfo false /addregmarks false /convertcolors /converttocmyk /destinationprofilename () /destinationprofileselector /documentcmyk /downsample16bitimages true /flattenerpreset << /presetselector /mediumresolution >> /formelements false /generatestructure false /includebookmarks false /includehyperlinks false /includeinteractive false /includelayers false /includeprofiles false /multimediahandling /useobjectsettings /namespace [ (adobe) (creativesuite) (2.0) ] /pdfxoutputintentprofileselector /documentcmyk /preserveediting true /untaggedcmykhandling /leaveuntagged /untaggedrgbhandling /usedocumentprofile /usedocumentbleed false >> ] >> setdistillerparams << /hwresolution [2400 2400] /pagesize [612.000 792.000] >> setpagedevice microsoft word numero_51_art_22_2683 r. massabò et alii, frattura ed integrità strutturale, 51 (2020) 275-287; doi: 10.3221/igf-esis.51.22 275 focussed on igf25 – fracture and structural integrity international conference 2019 local zigzag effects and brittle delamination fracture of n-layered beams using a structural theory with three displacement variables roberta massabò, ilaria monetto department of civil, chemical and environmental engineering, university of genova, italy roberta.massabo@unige.it, http://orcid.org/0000-0002-9746-1801 abstract. equivalent single layer theories for layered beams effectively and accurately predict global displacements and internal force and moment resultants using a limited number of displacement variables. however, they cannot reproduce local effects due to material architecture or weak/imperfect bonding of the layers, such as zigzag displacement fields, displacement jumps at the layer interfaces and complex transverse stress fields, nor can they simulate delamination damage growth. in this work we will present some applications and discuss advantages and limitations of a recently formulated zigzag model. the model, through a modification of the equilibrium equations of an equivalent single layer theory, which maintains the same number of variables, reproduces local effects and delamination fracture under mode ii dominant conditions. the approach is based on a local enrichment of the displacement field of first order shear deformation theory, the introduction of cohesive interfaces and homogenization. keywords. structural theory; zigzag; homogenization; cohesive zone model; brittle fracture; laminate. citation: massabò, r., monetto, i., local zigzag effects and brittle delamination fracture of n-layered beams using a structural theory with three displacement variables, frattura ed integrità strutturale, 51 (2020) 275-287. received: 13.11.2019 accepted: 27.11.2019 published: 01.01.2020 copyright: © 2020 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. introduction he mechanical response of layered structures, such as laminates, sandwich composites, laminated glass, and laminated wood, is controlled by local effects due to the elastic mismatch of the layers, the presence of thin interlayers (adhesives, resin rich regions, polymeric layers), and interfacial imperfections, defects and delaminations, which are typical consequences of manufacturing processes. zigzag displacement fields and complex transverse stress distributions, which are due to the multilayer architecture, and displacement discontinuities, due to the presence of interlayers or interfacial damage/delaminations, are not captured by the widely used equivalent single layer theories (eslt), such as first order shear deformation theory (fsdt). these theories assume a c1 continuous displacement field through the thickness which introduces discontinuities in transverse stresses and the impossibility to satisfy local equilibrium. modeling local effects requires the use of layerwise, discrete-layer or 2d/3d finite-element models, where layers and interfacial regions between layers are distinctly modelled and continuity of displacements, but not of their derivatives (slopes), is imposed at the interfaces [1]. modeling delamination evolution using these techniques requires in addition a t http://www.gruppofrattura.it/va/51/2683.mp4 r. massabò et alii, frattura ed integrità strutturale, 51 (2020) 275-287; doi: 10.3221/igf-esis.51.22 276 cohesive zone approach to capture the displacement discontinuities and an in-plane discretization to follow the evolution of the cracks. the main drawback of these approaches is that the number of displacement variables is related to the number of mathematical layers and to the kinematics assumed to describe the layers. to model a n-layered beam with perfectly bonded layers and transverse inextensibility using timoshenko beam theory in each layer leads to a total of (n+2) displacement unknowns (namely (2n+1) initial displacements minus (n-1) displacement continuity conditions at the interfaces). delamination damage evolution in the beam can be studied by releasing the displacement continuity at the layer interfaces and introducing cohesive interfacial tractions, normal and tangential, and cohesive traction laws which relate the tractions to the relative sliding and opening displacements [2–4]. this approach requires 3n unknowns for each beam region (or (2n+1) unknowns for mode ii dominant problems, where crack opening is neglected and a single displacement variable describes the transverse displacements of the layers). an effective approach for modeling multilayered structures was proposed in the early works in [5,6] and is known in the community as “zigzag approach”. the basic idea of the global-local zigzag approach is to enrich the displacement field of an equivalent single layer theory (elst) by local zigzag functions [5,6, and subsequent works] in order to account for the effects of the multilayer structure (zigzag). this adds a large number of local kinematic variables to the global variables, which are then removed from the problem by imposing continuities conditions on interfacial tractions at the layer interfaces [6]. variational techniques are then used to derive the equilibrium equations, which depend on the global variables only. other refined approaches have been proposed, e.g. [7,8], which introduce additional global variables to try and overcome some drawbacks of the original theories. the presence of thin interlayers and interfacial damage has been modelled following two different techniques. the first, known as “compliant layer concept”, is based on a description of thin interlayers or interfacial damaged regions as regular layers of the stack, with elastic constants apt to describe their response; the method then essentially follows the procedure described above for fully bonded structures [9,10]. the second technique, known as “spring-layer approach”, introduces zero thickness interfaces and interfacial traction laws which describe the response of the interlayer/damaged regions [11– 14]. in addition to the zigzag functions, the displacement field of the global equivalent single layer theory is then enriched by interfacial jumps. considering the n-layered plate in fig. 1a, the displacements ( )k v (=1,2,3) in an arbitrary layer k , with upper and lower coordinates 13 kx  and 3 kx , are described by the following equations: 1 1 ( ) 1 1 2 3 01 1 2 3 1 1 2 1 1 2 3 3 1 1 2 1 1 ˆ( , , , ) ( , , ) ( , , ) ( , )( ) ( , , ) k k k i i i i i v x x x t v x x t x x x t x x x x v x x t            1 1 ( ) 2 1 2 3 02 1 2 3 2 1 2 2 1 2 3 3 2 1 2 1 1 ˆ( , , , ) ( , , ) ( , , ) ( , )( ) ( , , ) k k k i i i i i v x x x t v x x t x x x t x x x x v x x t            (1) 1 1 ( ) 3 1 2 3 0 1 2 3 3 1 2 3 1 2 3 3 3 1 2 1 1 ˆ( , , , ) ( , , ) ( , , ) ( , )( ) ( , , ) k k k i i i i i v x x x t w x x t x x x t x x x x v x x t            where 01 02 0 1 2 3, , , , ,v v w    are the primary variables of the equivalent single layer model (here a first order shear and normal deformation plate theory), 1 2 3 3( , )( ) i ix x x x  for 1, 2, 3  and 1,..., 1i n  are piecewise linear zigzag functions and ( 1) ( ) 1 2 3 3 3 3ˆ ( , , ) ( ) ( ) i k k k kv x x t v x x v x x       for 1, 2, 3  and 1,..., 1i n  are displacement jumps at the layer interfaces [14]. higher order equivalent single layer models can be used which increase the number of the global variables and better describe the transverse stresses in fully bonded problems [1]. zigzag functions and displacement jumps are then defined by imposing continuity of transverse shear and normal tractions at the layer interfaces and the interfacial constitutive laws to relate tractions and jumps. this yields the macro-scale displacement field and homogenized equilibrium equations which depend on the global variables only. using this second approach care must be put on properly accounting for the strain energy absorbed during deformation within the interface [15] in the variational equations used for the derivation of the equations of motion. this term was neglected in the early models in [11–13] and corrected only later in [14]. zigzag models have been formulated to study interfacial damage evolution using the compliant-layer concept and continuum damage approaches in [9,16,17]. recently, the model in [14], which uses a cohesive zone approach and the zigzag kinematic approximation in eqn. (1), has been applied to simulate single and multiple delamination growth under mode ii dominant conditions in wide plates within the framework of fracture mechanics [18]. r. massabò et alii, frattura ed integrità strutturale, 51 (2020) 275-287; doi: 10.3221/igf-esis.51.22 277 in this paper the model in [14] is briefly reviewed, the equations which describe the response of n-layered beams with imperfect interfaces and delaminations under mode ii dominant conditions, as shown in figs. 1b,c, are recalled and some applications of the model, novel and from the literature, are presented and discussed. the applications are chosen in order to highlight the applicability of the homogenized approach to predict local stress and displacement fields in layered beams with imperfect interfaces and delaminations and to analyze single and multiple delamination crack propagation in homogeneous and layered beams with different boundary conditions. the results are used to discuss advantages and limitations of the homogenized approach. figure 1: (a) n-layered plate with weakly bonded layers modelled as imperfect interfaces and delaminations; (b1,2) n-layered beam with imperfect interfaces and related homogenized description; (c1,2) n-layered beam with imperfect interfaces and delaminations and related homogenized description. the homogenized description eliminates the need for through-thickness and longitudinal discretization in the presence of continuous imperfect interfaces (b2), and requires only longitudinal discretization in the presence of delaminations, (c2). (a) (b) figure 2: (a) exemplary interfacial traction laws used to describe a n-layered beam with continuous fully bonded, imperfectly bonded and fully detached interfaces, as shown in fig. 1b (after [14]); (b) interfacial traction law used to analyze perfectly brittle fracture in the n-layered beam in fig. 1c; the crack tip is defined at the coordinate where the sliding displacement becomes critical, . 2 2ˆ ˆ cv v ., and the area under the first branch up to 2ˆ cv is the critical energy release rate or mode ii fracture toughness of the interface (after [18]). multiscale structural model for n-layered beams with interfacial imperfections and delaminations n this section the equations of the model formulated in [14] for plates with weakly bonded layers, oriented along the geometrical axes, and delaminations shown in fig. 1a are particularized to a beam (wide plate) with imperfect sliding interfaces and delaminations and used to describe the two schematics shown in figs. 1b and 1c. assuming transverse inextensibility and the absence of normal separation between the layers, in order to describe mode ii dominant problems with layers in constrained contact, the displacement field in eqn. (1) modifies since the dependence on 1x is removed and 3 3 3ˆ 0 i iv     , for 1,..., 1i n  . the displacement unknowns of the problem are then the global displacements 02 0 2, ,v w  , the zigzag functions 2 3 3( ) i ix x  for 1,..., 1i n  and the jumps 2ˆ iv for 1,..., 1i n  , for a total of i r. massabò et alii, frattura ed integrità strutturale, 51 (2020) 275-287; doi: 10.3221/igf-esis.51.22 278 3 2( 1)n  . the ( 1)n  zigzag functions are defined in terms of the global variables by imposing continuity of the shear tractions at the ( 1)n  layer interfaces (the shear tractions are calculated using the elastic constitutive laws in eqn. (7) in the appendix). the remaining local unknowns, which describe the interfacial jumps, depend on the mechanisms acting at the interfaces which are described through piece-wise linear interfacial traction laws relating interfacial shear tractions and jumps. to describe the beam in fig. 1b, with continuous imperfect interfaces, such as those due to thin elastic interlayers (adhesives, resin rich layers), the linear traction laws shown in fig. 2a, 2ˆ ˆ k k k s sk v  , are used, which relates k sk , the interfacial stiffness of the interface k, and the jump 2ˆ kv ; the interfacial stiffness may be different in the different interfaces and 0ksk  is used to describe fully debonded layers, so that 2ˆ ˆ0, 0 k k s v   , while 1/ 0 k sk  describes perfect bonding, where 2ˆ 0 kv  . in the beam in fig. 1c, with imperfect interfaces and delaminations, the interfacial stiffness also varies between the different longitudinal regions and a longitudinal discretization of the problem is required; different interfacial traction laws are used to define the traction free delaminations and the bonded or partially bonded ligaments ahead of the delamination tips. to simulate perfectly brittle fracture of the layers, the law in fig. 2b, with 1/ 0ksk  in the intact regions and 0 k sk  along the traction free delaminations, is used and the critical energy release rate is defined by the area under the first branch. the crack tips are located where the crack sliding displacement equals the critical value, 2 2ˆ ˆ k cv v . the interfacial jumps are defined in terms of the global variables by imposing equilibrium conditions at the interface boundaries, which relate interfacial tractions and shear stresses in the layers. using eqns. (1) and (7), the macroscale displacement field then takes the form:  ( ) 2 2 3 02 2 3 2 2 0 2 2 2 2 22 3 ( ) 3 2 0 2 ( , ) ( ) ( ) , ( ) ( ) ( ) ( ) ( ) k k s k v x x v x x x w x x r x v x w x       (2) with   ( 1)1 (1) (1)23 22 3 23 3 3 23( 1) ( ) ( 1) ( ) 1 123 23 23 23 1 1 1 1 ( ) 1 ik i k i s i i i j j i js g r x g x x g g g k g g                               (3) where ( ) 23 i g is the shear modulus of the layer i. in a beam with layers having the same elastic properties, as a unidirectionally reinforced laminate, ( 1) ( )23 23 k kg g  and eqn. (3) simplifies in ( 1)22 3 231.. 1( ) / k i i s si k r x g k     ; in the intact portions, where 1/ 0ksk  , 22 3( ) 0 k sr x  and the displacement field coincides with that of first order shear deformation theory. if the elastic constants of the layers differ, in the intact portions of the plate where 1/ 0ksk  the displacement field coincides with that assumed by the original zigzag theory in [6]. the low order of the global model and eqns. (2),(7) imply that the shear strains obtained from (2) through compatibility are constants in and between the layers in the intact regions and vanish in the delaminated regions. following the approach which is commonly used for the structural low order theories, accurate shear stresses and strains can be obtained a posteriori through the imposition of local equilibrium: ( ) ( )22 2 23 3, , 0 k k post   and ( ) ( ) ( )23 23 23 2 / k post k post k g  . on the other hand, the absence of shear strains in the delaminated regions induces under-predictions of the transverse displacements in shear deformable plates and the need for corrections or adjustments [19,20]. the problem will be discussed later. variationally consistent equilibrium equations and boundary conditions are derived through the principle of virtual works [14]. they are shown below for a beam subjected to distributed transverse load, 3 2( )f x : 22 2 2 22 2 2 2 2 2 2 2 3 2 22 2 2 02 02 22 2 2 2 2 2 2 3 0 0 22 2 2 0 2 0 2 , ( ) 0; , ( ) ( ) 0; , ( ) ( ) 0 or ; or ; or ; or , , b g g b b zs zs g n x m x q x q x f x n n n v v m n m q n n w w m n m w w                    (4) r. massabò et alii, frattura ed integrità strutturale, 51 (2020) 275-287; doi: 10.3221/igf-esis.51.22 279 where 22 22 2, , b gn m q are axial force, bending moment and generalized shear force, given by (8) in the appendix, where the tilde defines prescribed values at the beam edges and 2 1n   is the second component of the outward unit normal. the equations have the same form of those of first order shear deformation theory and the effects of the local enrichments (zigzag and interfacial jumps) enter the generalized shear force, eqn. (8), which is variationally consistent and coincides with the resultant of the a posteriori calculated shear stresses, 3 1 3 ( ) 2 23 31.. k k x k post g k n x q dx     , as in classical structural theories. the constitutive equations of the homogenized beam have been derived in [18]:   0 0 22 22 22 02 2 02 22 1 1 0 1 2 2 22 22 22 2 2 2 44 2 0 2 2 22 0 1 2 2 0 22 0 22222 , , , ; , , , , s s b s s s s s s g zs s s s s n a b c c v v m b d c c q a w c c c c w wm c c c c                                               (5) with 3 1 3 ( ) 2 22 22 22 22 3 3 3 44 44 44 1 , , d ) (1, , ) ; ( k k n xk p s x k c x x dx a ka b c c       where  ( )( ) 22 22 23 32 33/ kk c c c c c  with ( )k ijc the coefficients of the 6×6 stiffness matrix in the layer k ; the remaining coefficients are given in (10) in the appendix; 44k is a shear correction factor which can be set equal to 5/6, as for a homogeneous beam, since the effects of the layered structure are already accounted for through the zigzag functions. the equilibrium equations in terms of global displacement variables (for a beam subjected to transverse surface tractions, 3 2( )f x ) are [19]: 0 0 22 02 22 22 2 22 0 222 0 1 2 1 2 22 02 22 22 2 22 0 222 44 0 2 2 0 1 2 2 02 222 2 222 0 2222 44 0 22 2 2 3 , ( ) , , 0 ( ) , ( 2 ) , ( ) , ( , ) 0 , ( ) , , ( , , ) 0 s s s s s s s s s s s a v b c c w b c v d c c c c w a w c v c c c w a w f                          (6) they return the equilibrium equations of first order shear deformation theory in a n-layered beam with equal fully bonded layers, where all coefficients with upper index s vanish. and they return the equilibrium equations of the zigzag theory in [6] for fully bonded unequal layers. local stress and displacement fields and delamination fracture of n-layered beams n this section various applications of the model are presented in order to highlight its main features. stress and displacement fields in n-layered beams subjected to mechanical loadings the equilibrium eqns. (6) with boundary conditions in (4) are easily solved for n-layered beams and wide plates with continuous imperfect interfaces, shown in fig. 1(b); the model is applicable to beams with various boundary conditions (simply supported, clamped) and loadings (distributed, concentrated loads). exemplary closed form solutions have been presented in [19] for simply supported plates under thermo-mechanical loadings; in [21] closed form solutions have been derived for the wave propagation problem. the model accurately captures the transverse displacements in fully bonded beams while requires a correction in shear deformable beams with fully debonded or weakly bonded interfaces where the i r. massabò et alii, frattura ed integrità strutturale, 51 (2020) 275-287; doi: 10.3221/igf-esis.51.22 280 effects of the shear strains on the global transverse displacement are not fully captured. the local fields are accurately captured also in very thick beams and wide plates. predictions are less accurate near clamped edges, due to the presence of boundary regions which will be discussed later [19,20,22]. the diagrams in fig. 3 show transverse shear stresses through the thickness in a unidirectionally reinforced orthotropic wide plate with fibers (l) along 2x , two layers (n=2) and one interface. results in the figure refer to a simply supported plate subjected to a sinusoidal transverse load. the solutions of the homogenized zigzag model are compared with exact elasticity solutions for perfectly bonded, partially bonded and fully debonded layers, after [14]. geometry and elastic constants are defined in the caption. fig. 4 shows axial displacements and transverse shear stresses in a thick wide-plate with three symmetrically oriented orthotropic layers (0/90/0) and two equally spaced weak interfaces. the boundary conditions are the same of the previous case. the homogenized model accurately captures the local effects due to the material architecture, e.g. the zigzag displacements, the jumps at the layers interfaces and their effects on transverse shear stresses. figure 3: dimensionless transverse shear stresses shown through thickness at 2x l in the thick unidirectionally reinforced wide plate with two layers and one imperfect interface shown on the right. the plate is subjected to a sinusoidal transverse load, 0 2sin( / )p q x l  . materials and geometry: / 5l h  , / 25t le e  , / 50lt lg e  , , 0.25lt tt   (modified after [14] ). figure 4: axial displacements and transverse shear stresses at 2x l shown through thickness in a three-layer laminate (0/90/0), thick simply supported wide plate subjected to sinusoidal transverse load, 0 2sin( / )p q x l  . materials and geometry: / 4l h  , / 25t le e  , / 50lt lg e  , / 125tt lg e  , 0.25lt tt   (modified after [19]). r. massabò et alii, frattura ed integrità strutturale, 51 (2020) 275-287; doi: 10.3221/igf-esis.51.22 281 single and multiple delamination fracture in n-layered beams the equilibrium eqns. (6) can be applied directly to study the response of beams (wide plates) with stationary delaminations, which are regions where the layers are fully debonded, as shown in fig. 1c. for these problems a discretization in the axial direction is required, as shown in fig. 1c2 since the coefficients in eqns. (6) and (4) differ between regions. continuity conditions between the different regions are then applied and the problem is solved analytically or semi-analytically. displacement and stress fields accurately reproduce the 2d elasticity solutions but for boundary regions, which occur near clamped edges or crack tip cross sections, and will be discussed later in the paper. the energy release rate for the collinear propagation of the delaminations can be calculated using different techniques, namely the compliance method and the jintegral along different paths [18]. different fracture problems have been examined in [18]: bend beams with two and three layers (sandwiches), with single and multiple delaminations and various boundary conditions (simply supported and clamped). here two relevant applications after [18] are recalled and novel applications are presented in order to highlight the capability of the model, which uses only three displacement variables as a classical single layer theory, to describe the discrete event of brittle delamination fracture, to reproduce the interaction effects of multiple delaminations and to follow the evolution of multiple cracks, in homogeneous and layered beams. (a) (b) figure 5: (a) critical load for crack propagation versus load point displacement in a enf specimen (modified after [18] ). geometry and materials: l = 50 mm, 2h = 3.4 mm, 0 25a  mm, b = 25 mm (width). graphite/epoxy as-4/828 with 139 16.7le   gpa and 6ltg  gpa and mode ii fracture energy 1.04 0.17iic  g n/mm [24]. (b) dimensionless critical load for crack propagation versus crack length in an end load split specimen. unidirectional e-glass-epoxy with 41le  gpa, 10.4te  gpa, 4.3ltg  gpa , 0.28, 0.5lt tt   . exact solution in [27]. crack propagation in unidirectionally reinforced end-notched flexure and end-load split specimens fig. 5a shows the macro-structural response of the unidirectional end-notched flexure (enf) specimen shown in the inset, through the critical load for crack propagation versus load-point deflection (after [18]). the layup and elastic constants are described in the caption. the energy release rate has been obtained using the compliance method and the transverse displacement calculated through eqns. (6). local effects in the layers due to the presence of the delamination are well captured by the model and the distribution of the shear stresses is qualitatively similar to that presented in fig. 3. this is a pure mode ii problem and the dimensionless critical load is obtained in closed form and is 2/cr iicp he g  4 / 3 /h a with iicg the critical fracture toughness [18]. the critical load coincides with predictions using classical structural mechanics assumptions and a discrete-layer approach. the exact solution of the problem [23] has two additional terms, which account for the effects of crack tip shear on the near tip deformations and are important when the crack is short. the response diagram is compared with the experimental results on a graphite/epoxy [0]24 laminate tested in [24]. the two theoretical curves shown in the diagram have been obtained using the average values of the elastic constants and energy release rate, r. massabò et alii, frattura ed integrità strutturale, 51 (2020) 275-287; doi: 10.3221/igf-esis.51.22 282 red dashed lines model (a), and the maximum values, black solid lines model (b). the experimental results, obtained under displacement, control show a load drop in the critical load at the onset of propagation; this is due to an unstable propagation of the crack which grows catastrophically and arrests near the mid-span. the homogenized model, which is under cracklength control [18,25], is able to capture the snap-back instability and follow the virtual branch where crack growth is associated to a reduction of the load-point displacement. crack propagation is modelled also in the region beyond the midspan to show that the curve stably approaches the limiting solution (dotted line) corresponding to two fully delaminated layers. fig. 5b shows the critical load for crack propagation in an end loaded split (els) specimen. the material is a unidirectional e-glass-epoxy laminate with elastic constants given in the caption of fig. 5b. this is a pure mode ii problem. local effects are similar to those of the enf specimen and described in fig. 3. the critical load for crack propagation obtained using the homogenized model is /cr iic lp he g  2 / 3 /h a . the solution coincides with predictions using discrete models and elementary beam theory. an accurate solution of the els specimen based on dimensional analysis, orthotropy rescaling and 2d finite element analyses has been obtained in [26] and has been recently confirmed by the analytical solution in [27]. for the e-glass-epoxy examined here, the exact solution is /cr iic lp he g   1/42 / 3 / (1 ( ) / )iih a y h a   , with 1/40.33, =2.56 and ( ) 0.4iiy      . the 2d solution accounts for the near tip deformations which are not accounted for in the homogenized solution since continuity conditions at the crack tip are imposed on global quantities. the relative error on the critical load for crack propagation is 4%, 2%,1% for / 10, 20, 40a h  , respectively. (a) (b) figure 6: (a) critical load for crack propagation versus load point displacement in the els specimen tested in [28]. geometry and materials: l = 130 mm, 2h = 5.98 mm, 0 60a  mm, b = 20 mm. cross-ply carbon/epoxy laminate with layup [(02/90)7/02//02/(90/02)7] and 144le  gpa, 10te  gpa, 4.2lt ttg g  gpa, 0.25lt  and 0.3tt  . mode ii fracture energy 0.5, 0.45iic g n/mm. (b) comparison of theoretical results using the homogenized model and 2d finite element models. crack propagation in end-load split cross-ply laminate [(02/90)7/02//02/(90/02)7] the diagram in fig. 6 shows the critical load for crack propagation versus load point displacement in the end load split (els) specimen tested in [28]. the material is a cross ply laminate with 46 unidirectional carbon plies of thickness 0.13 mm, layup [(02/90)7/02//02/(90/02)7] and elastic constants given in the caption of fig. 6. the specimen has total length 160tl  mm , width 20b  mm and initial crack length 0 60a  mm. the theoretical results have been obtained by assuming that a part of the specimen, of length 30 mm, has been clamped so that the free length is 130l  mm (this is necessary to match 2d finite element results to the slope of the experimental linear branch; using tl would produce unacceptably large r. massabò et alii, frattura ed integrità strutturale, 51 (2020) 275-287; doi: 10.3221/igf-esis.51.22 283 displacements). the diagrams show the critical load for crack propagation versus load-point deflection obtained using the homogenized model, the compliance method, the crack propagation criterion ii iicg =g and crack length control [18,25]. the results are compared with the experimental results in [28] and 2d finite element results obtained here. the finite element results have been obtained by using ansys, the vcct technique, the crack propagation criterion ii iicg =g and a crack length control. the finite element model uses plane strain isoparametric and quadrilateral 8-noded elements to mesh each layer of the beam with elements of equal size 0.075 0.13 mm in order to ensure convergence on both load point displacement and energy release rate. the results of the homogenized model agree well with the finite element predictions and the relative error on the critical load is always less than 3%; this error is due to an underestimation of the compliance in the homogenized model which neglects shear deformations along the delaminated portion of the specimen. the theoretical curves are presented for two values of the mode ii fracture energy 0.45iic g n/mm and 0.5iic g n/mm. the first value better matches the experimental results at crack initiation and the second the post-critical branches; this difference is probably due to the presence of nonlinear cohesive mechanisms which are not reproduced by the linear elastic fracture mechanics solutions. the theoretical curves, obtained under crack length control, show snap-back instabilities, with virtual branches having negative slope, which are also evident in the almost vertical drops of some of the experimental curves obtained using displacement control. in the simulations in [28] the fracture toughness was assumed as 0.7iic g n/mm; according to the lefm analyses, this large value of iicg could be explained only if crack propagation occured under large scale bridging, with a large process zone, during the entire loading process. further analyses are required to clarify this point; however propagation under extensive large scale bridging appears to be supported by the experimental measurements of the traction free crack lengths during propagation, which are shorter than those obtained using linear elastic fracture mechanics (not shown here). (a) (b) figure 7: critical load for crack propagation versus load point displacement in the homogeneous and isotropic cantilever beams with multiple delaminations shown in the insets (results for homogenized model in [18] and discrete layer model in [4]): (a) symmetrically positioned cracks; (b) asymmetrical positioned cracks (lengths and positions in the main text). interaction effects of multiple delaminations fig. 7 (after [18]) is used to highlight the capability of the homogenized model to analyze multiple delamination fracture and reproduce the effects of the interaction between delaminations. the dimensionless diagrams depict the critical load for the propagation of the cracks in the homogeneous and isotropic cantilever beams in the insets in fig. 8 versus load-point displacement. the diagram (a) refers to a beam where ( 2 ) (1) 2h h  , ( 3 ) (1) 1h h  and the initial upper and lower crack lengths are 0 / 5.5ua h  and 0 / 6la h  . the diagram (b) refers to a homogeneous isotropic beam where ( 2 ) (1) ( 3 ) (1) 1/ 3h h h h  and the initial upper and lower crack lengths are 0 / 5ua h  and 0 / 4la h  . the delaminations r. massabò et alii, frattura ed integrità strutturale, 51 (2020) 275-287; doi: 10.3221/igf-esis.51.22 284 are assumed to propagate when the energy release rate, calculated using the compliance method, approaches the critical value, ii iicg g . the results of the homogenized model in [18] are compared with the results of the discrete-layer cohesivecrack model with spring-contact in [4]. a local snap-through instability is observed in the diagram (a) when the upper crack starts to propagate in a and approaches the lower crack tip, in b. then the load to propagate the crack must be increased, due to a shielding phenomenon, up to point c where the two cracks propagate together unstably. in the diagram (b) the lower crack, which is shorter, starts to propagate at the maximum load, point a; crack propagation is unstable and characterized by a snap-back instability up to point b. then there is a sudden drop in the load, to point c, caused by a sudden amplification discontinuity. after point c the lower crack continues to propagate alone. discussion he homogenized model uses a zigzag kinematic approximation based on first order shear deformation theory (fsdt) which is enriched by local zigzag functions and interfacial jumps, as shown in eqn. (1). the low order of the global model and the small number of unknowns, which are those of fsdt, implies that shear strains are constants in and between the layers in the intact regions of the beam and vanish in the delaminated regions. following the approach which is commonly used for the structural low order theories, accurate shear stresses and strains can be obtained a posteriori through the imposition of local equilibrium. the diagrams in figs. 3 and 4 show that the complex local fields which arise in multilayered wide plates with imperfect or fully debonded interfaces are accurately reproduced, also in very thick and highly anisotropic cases. however, stress recovery using the equation above is not very accurate in a finite element framework [8] and this limits the applicability of the model. the introduction of a shear correction factor, 44 5 / 6k  , in the equilibrium eqns. (6) allows to account for the shear strains in the solution of the problem and the displacements of fully bonded beams are accurately predicted. on the other hand, due to the vanishing of the shear strains in the delaminated regions of the beams, the transverse displacements in eqn. (3) and the equilibrium eqns. (6) will only account for the bending contributions and this may affect the load re-distribution between different regions in statically indeterminate systems. this problem cannot be solved by increasing the order of the esl theory used as global model and, in our opinion, could be solved only by modifying the zigzag formulation and leaving the displacement jumps as part of the unknowns of the problem, as it has been done for instance in [29]. another approach to solve this problem could be through the use of the refined zigzag theory [7]; however, preliminary analyses in [20,30] highlight other still unresolved difficulties of the approach in dealing with in-plane discontinuities. the effects of neglecting shear deformations along the delaminated portions of the beam, however, are not relevant in all problems dominated by bending defomations (as in the fracture analyses of the cross ply laminated els specimen in fig. 6). another limitation of the homogenized approach presented here is related to the imposition of continuity and boundary conditions in terms of global quantities, either displacement or force and moment resultants. this implies that continuity is not satisfied at the local level and displacements and force sub-resultants within the single layers may differ. this typically occurs near the crack tip and clamped ends, within boundary regions whose size depends on the mismatch of the elastic constants of the layers and on the stiffness of the interfaces and is very small when the mismatch is small and the interfacial stiffness is very large or very small [20,22]. the model and analyses presented here are limited to mode ii dominated problems, were transverse extensibility of the layers and interfacial openings may be neglected. the homogenized approach is currently being extended (work in progress [31]) to general mixed-mode problems using the extended formulation in [14], which uses first order shear, first order normal deformation theory as global model. conclusions homogenized structural model based on a zigzag approach has been presented for the analysis of beams with imperfect interfaces and delaminations and layers oriented along the geometrical axes. the model enriches the displacement field of first order shear deformation theory, in order to introduce zigzag effects due to the layered architecture and interfacial sliding jumps due to the presence of soft interlayers, imperfections or delaminations. piece-wise linear cohesive traction laws describe the constitutive behavior of the interfaces. homogenization and variational techniques are used to define the local variables in terms of the global variables and derive the equilibrium equations of the problem. the model has been validated through various novel applications and using experimental results and 2d elasticity solutions. t a r. massabò et alii, frattura ed integrità strutturale, 51 (2020) 275-287; doi: 10.3221/igf-esis.51.22 285 advantages and limitations of the approach have been discussed. local stress and displacement fields are accurately predicted also in very thick and highly anisotropic beams and wide plates with continuous imperfect interfaces and delaminations. crack propagation under mode ii dominant conditions has been successfully reproduced in various fracture specimens and bend beams: unidirectionally reinforced end-notched flexure and end-load split specimens; end-load split specimen made of a 46-layers cross-ply laminate; isotropic cantilever beams with multiple delaminations interacting during propagation. the solution is analytical or semi-analytical, requires only in-plane discretization of the problem and the displacement unknowns are only three as in first order shear deformation theory. acknowledgements upport by the u.s. navy office of naval research, grant n00014-17-1-2914 and by the italian dept. for university and scientific and technological research, miur prin15 project 2015lyyxa8. references [1] abrate, s., di sciuva, m. (2018).multilayer models for composite and sandwich structures. comprehensive composite materials ii, (editors zweben, c.h., beaumont, p.w.r.), elsevier, usa, pp. 399–425. [2] williams, t.o., addessio, f.l. (1997). a general theory for laminated plates with delaminations, int. j. solids struct., 34(16), pp. 2003–2024, doi: 10.1016/s0020-7683(96)00131. [3] andrews, m.g., massabò, r., cavicchi, a., cox, b.n. (2009). dynamic interaction effects of multiple delaminations in plates subject to cylindrical bending, int. j. solids struct., 46(9), pp. 1815–1833, doi: 10.1016/j.ijsolstr.2008.11.027. [4] andrews, m.g., massabò, r. (2008). delamination in flat sheet geometries with material imperfections and thickness variations, compos. part b eng., 39(1), pp. 139–150, doi: 10.1016/j.compositesb.2007.02.017. [5] murakami, h. (1986). laminated composite plate theory with improved in-plane responses, j. appl. mech. trans. asme, 53(3), pp. 661–666, doi: 10.1115/1.3171828. [6] di sciuva, m. (1986). bending, vibration and buckling of simply supported thick multilayered orthotropic plates: an evaluation of a new displacement model, j. sound vib., 105(3), pp. 425–442, doi: 10.1016/0022-460x(86)90169-0. [7] tessler, a., di sciuva, m., gherlone, m. (2009). a refined zigzag beam theory for composite and sandwich beams, j. compos. mater., 43(9), pp. 1051–1081, doi: 10.1177/0021998308097730. [8] tessler, a. (2015). refined zigzag theory for homogeneous, laminated composite, and sandwich beams derived from reissner’s mixed variational principle, meccanica, 50(10), pp. 2621–2648, doi: 10.1007/s11012-015-0222-0. [9] averill, r.c. (1994). static and dynamic response of moderately thick laminated beams with damage, compos. eng., 4(4), pp. 381–395, doi: 10.1016/s0961-9526(09)80013-0. [10] groh, r.m.j., tessler, a. (2017). computationally efficient beam elements for accurate stresses in sandwich laminates and laminated composites with delaminations, comput. methods appl. mech. eng., 320, pp. 369–395, doi: 10.1016/j.cma.2017.03.035. [11] di sciuva, m. (1997). geometrically nonlinear theory of multilayered plates with interlayer slips, aiaa j., 35(11), pp. 1753–1759, doi: 10.2514/2.23. [12] cheng, z.q., jemah, a.k., williams, f.w. (1996). theory for multilayered anisotropic plates with weakened interfaces, j. appl. mech. trans. asme, 63, pp. 1019–1026, doi: 10.1115/1.2787221. [13] schmidt, r., librescu, l. (1996). geometrically nonlinear theory of laminated anisotropic composite plates featuring interlayer slips, n j math game theory algebr., 5, pp. 131–137. [14] massabò, r., campi, f. (2015). assessment and correction of theories for multilayered plates with imperfect interfaces, meccanica, 50(4), pp. 1045–1071, doi: 10.1007/s11012-014-9994-x. [15] shu, x., soldatos, k.p. (2001). an accurate stress analysis model for angle-ply laminates with weakly bonded layers, acta mech., 150(3-4), pp. 161–178, doi: 10.1007/bf01181809. [16] eijo, a., oñate, e., oller, s. (2013). a numerical model of delamination in composite laminated beams using the lrz beam element based on the refined zigzag theory, compos. struct., 104, pp. 270–280, doi: 10.1016/j.compstruct.2013.04.035. [17] groh, r.m.j., weaver, p.m., tessler, a. (2015). application of the refined zigzag theory to the modeling of delaminations in laminated composites, nasa/tm-2015-218808, pp. 1–22, doi: 10.13140/rg.2.1.3147.0804. s r. massabò et alii, frattura ed integrità strutturale, 51 (2020) 275-287; doi: 10.3221/igf-esis.51.22 286 [18] massabo, r, darban, h. (2019). mode ii dominant fracture of layered composite beams and wide-plates: a homogenized structural approach, eng. fract. mech., 213, pp. 280–301, doi: 10.1016/j.engfracmech.2019.03.002. [19] pelassa, m., massabò, r. (2015). explicit solutions for multi-layered wide plates and beams with perfect and imperfect bonding and delaminations under thermo-mechanical loading, meccanica, 50(10), pp. 2497–2524, doi: 10.1007/s11012-015-0147-7. [20] darban, h., massabò, r. (2018). a homogenized structural model for shear deformable composites with compliant interlayers, multiscale multidiscip. model. exp. des., 1, pp. 269–290, doi: 10.1007/s41939-018-0032-x. [21] massabò, r. (2017). propagation of rayleigh-lamb waves in multilayered plates through a multiscale structural model, int. j. solids struct., 124, pp. 108–124, doi: 10.1016/j.ijsolstr.2017.06.020. [22] massabò, r. (2014). influence of boundary conditions on the response of multilayered plates with cohesive interfaces and delaminations using a homogenized approach, frat. ed integrita strutt., 8(29), pp. 230–240, doi: 10.3221/igf-esis.29.20. [23] andrews, m.g., massabò, r. (2007). the effects of shear and near tip deformations on energy release rate and mode mixity of edge-cracked orthotropic layers, eng. fract. mech., 74(17), pp. 2700–2720, doi: 10.1016/j.engfracmech.2007.01.013. [24] madhukar, m.s., drzal, l.t. (1992). fiber-matrix adhesion and its effect on composite mechanical properties: iv. mode i and mode ii fracture toughness of graphite/epoxy composites, j. compos. mater., 26(7), pp. 936–968, doi: 10.1177/002199839202600701. [25] monetto, i., campi, f. (2017). numerical analysis of two-layer beams with interlayer slip and step-wise linear interface law, eng. struct., 144, pp. 201–209, doi: 10.1016/j.engstruct.2017.04.010. [26] suo, z., bao, g., fan, b., wang, t.c. (1991). orthotropy rescaling and implications for fracture in composites, int. j. solids struct., 28(2), pp. 235–248, doi: 10.1016/0020-7683(91)90208-w. [27] ustinov, k.b., massabò, r., lisovenko, d.s. (2019). orthotropic strip with central semi-infinite crack under arbitrary loads applied far apart from the crack tip. analytical solution, submitted. [28] tawk, i., navarro, p., ferrero, j.f., barrau, j.j., abdullah, e. (2010). composite delamination modelling using a multilayered solid element, compos. sci. technol., 70(2), pp. 207–214, doi: 10.1016/j.compscitech.2009.10.008. [29] kim, h.s., chattopadhyay, a., ghoshal, a. (2003). characterization of delamination effect on composite laminates using a new generalized layerwise approach, comput. struct., 81(5), pp. 1555–1566, doi: 10.1016/s0045-7949(03)00150-0. [30] flores, f.g., oller, s., nallim, l.g. (2018). on the analysis of non-homogeneous laminates using the refined zigzag theory, compos. struct., 204, pp. 791–802, doi: 10.1016/j.compstruct.2018.08.018. [31] massabò, r. (2019). mixed-mode delamination in layered beams using a homogenized structural approach, internal report. university of genova, italy. appendix relevant constitutive, equilibrium and compatibility equations in layer k: ( ) ( ) ( ) 22 22 22 k k kc  ; ( ) ( ) ( )23 23 232 k k kg  ; ( ) ( ) 22 2 23 3, , 0 k k   ; (7)     22 2 2, k k v  ;      23 2 3 3 22 , , k k kv v   force and moment resultants:    3 1 3 ( ) 22 22 22 3 3 2 2 2 2 2 2 22 2 2 2 2 1 ˆ, 1, ; ( ) ( ) ( ) , ( ) ( ) k k n xb k b z zs gx k n m x dx q x q x q x m x x         (8) with: r. massabò et alii, frattura ed integrità strutturale, 51 (2020) 275-287; doi: 10.3221/igf-esis.51.22 287 3 3 1 1 3 3 3 1 3 ( ) ( ) 2 23 3 22 22 22 3 1 1 1 ( ) (1) ( 1) (1) 2 23 23 3 2 23 23( 1) ( ) ( 1) ( ) 1 1 123 23 23 23 ; 1 1 1 1 ˆ ; 1 k k k k k k n nx xb k zs k k sx x k k n k kxz k k i i j jx k i j q dx m r dx q g dx g g g g g g                                     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can be opened with acrobat and adobe reader 5.0 and later.) >> /namespace [ (adobe) (common) (1.0) ] /othernamespaces [ << /asreaderspreads false /cropimagestoframes true /errorcontrol /warnandcontinue /flattenerignorespreadoverrides false /includeguidesgrids false /includenonprinting false /includeslug false /namespace [ (adobe) (indesign) (4.0) ] /omitplacedbitmaps false /omitplacedeps false /omitplacedpdf false /simulateoverprint /legacy >> << /addbleedmarks false /addcolorbars false /addcropmarks false /addpageinfo false /addregmarks false /convertcolors /converttocmyk /destinationprofilename () /destinationprofileselector /documentcmyk /downsample16bitimages true /flattenerpreset << /presetselector /mediumresolution >> /formelements false /generatestructure false /includebookmarks false /includehyperlinks false /includeinteractive false /includelayers false /includeprofiles false /multimediahandling /useobjectsettings /namespace [ (adobe) (creativesuite) (2.0) ] /pdfxoutputintentprofileselector /documentcmyk /preserveediting true /untaggedcmykhandling /leaveuntagged /untaggedrgbhandling /usedocumentprofile /usedocumentbleed false >> ] >> setdistillerparams << /hwresolution [2400 2400] /pagesize [612.000 792.000] >> setpagedevice microsoft word numero_30_art_21 a. chmel et alii, frattura ed integrità strutturale, 30 (2014) 162-166; doi: 10.3221/igf-esis.30.21 162 focussed on: fracture and structural integrity related issues damage initiation in brittle and ductile materials as revealed from a fractoluminescence study alexandre chmel, igor’ shcherbakov fracture physics department, ioffe physico-technical institute 26 polytekhnicheskaya, st. petersburg, russia 194021 chmel@mail.ioffe.ru abstract. a set of heterogeneous and homogeneous materials differing in their brittle and ductile characteristics (granite, marble, silica ceramics, silicon carbide, organic glass) were subjected to impact damaging by a falling weight. multiple chemical bond ruptures produced by elastic waves propagating from a damaged zone were accompanied by the photon emission generated throughout the sample (triboor fractoluminescence, fl). the statistical analysis of the fl time series detected with high resolution (10 ns) showed that the energy release distributions in brittle solids follow the power law typical for the correlated nucleation of primary defects. at the same time, the formation of damaged sites in ductile materials (marble and organic glass) was found to be fully random. keywords. impact fracture; fractoluminescence; time series; random statistics; correlated statistics. introduction loaded body is open thermodynamic system, in which along with non-reversible changes, such as ruptures of structural links, the self-organizing of the ensemble of newly-formed defects proceeds with maintaining the metastable (critical) state of the stressed structure. an origin of self-organizing is so-called long-range interactions between initial damages when these ones affect each other at distances exceeding the radius of a damaged site. in contrast to short-range cross-feed in equilibrium (unloaded) structures, which decay exponentially with distance, the power law dependence of the energy release on damage size (scaling) manifests itself under conditions of the external energy income. thus, the scaling phenomena occur over an area much greater than is predicted by elasto-dynamic interactions [1]. as far as multiple interactions implies the abundance of damaged sites, the scaling effect during straining and fracturing is inherent in heterogeneous materials, such as building materials [2], ceramics [3], composites [4], rocks [5], etc., in which the multi-site damaging takes place. fractured brittle homogeneous solids exhibit this phenomenon only at the macroscopic scale level – when the number of fragments of a broken body reaches the statistical significance [6]. at the same time, even conventionally homogeneous materials display pronounced heterogeneity at the nanostructural scale level. therefore, the scaling effect could manifest itself during the primary defect accumulation even in structurallyordered materials. this scale level is available for studying with the help of the fractoluminescence technique, which is sensitive to the nanostructural degradation in stressed solids [7]. chemical bond breakage is accompanied by the photon emission from reconfiguring electronic structures. amplitudes of light pulses are proportional to quantity of counted photons, and, correspondingly, to the energy released in events of primary damage nucleation. a a. chmel et alii, frattura ed integrità strutturale, 30 (2014) 162-166; doi: 10.3221/igf-esis.30.21 163 a historical term for the light emission from mechanically treated solids is “triboluminescence”; however, in recent decades the definition of the effect has been subject to some refinement. the term “triboluminescence” is commonly referred to the light generated through rubbing a material, while the photon emission from deformed or fractured solids is more frequently called “mechanoluminescence”. kawaguchi [8] introduced a narrower term “fractoluminescence” (fl) to stress the difference between the strainand fracture-induced effects. the latter term seems to be mostly adequate to experiments presented in this communication. in this work, five materials substantially differing in their physical and mechanical characteristics (heterogeneous brittle and ductile rocks, ceramics; homogeneous single crystal and organic glass) were damaged by falling weight, and the highly resolved fl time series were recorded. the fl amplitude distributions in the time series were constructed in order to establish a prevailing statistical law that governs the energy release in primary damage events occurring in different materials. samples and equipment ested brittle solids were granite, silica ceramics, and silicon carbide; marble and poly (methylmethacrylate) (pmma) represented ductile materials. the samples were shaped to blocks of approximately 202030 mm with polished faces. a schematic diagram of the experimental setup is depicted in fig. 1a. the samples were placed on a massive metal support covered with a grease layer in order to reduce parasitic vibrations. a surface damage was produced by the pointed striker positioned on the upper face of the sample, on which a 100 g weight dropped. the data acquisition system was triggered in the moment of contact between the weight and the striker. photographs of damaged samples are shown in fig. 1 (cutoff). figure 1: schematic diagram of the experimental setup and photographs of impact-induced damages in granite (a), silica ceramics (b), silicon carbide (c), marble (d), and organic glass (e). the fl radiation was collected from the side face of the sample by a quartz lens and directed onto a photomultiplier feu136. thus, only the light excited by bond breakage at the lateral surface of the sample, which was optically isolated from the damaged surface, was detected. an analogue-to-digital converter ask-3106 provided the dynamic range 2 mv to 10 v (70 db) in the time range 10 ns to 100 c. the converted (digital) fl signals were directed to and stored in a pc. the duration of all recorded time series was 1.3 ms. t a. chmel et alii, frattura ed integrità strutturale, 30 (2014) 162-166; doi: 10.3221/igf-esis.30.21 164 time series ig. 2 shows the ae time series from impact fractured samples. a delay of about 70-90 s between the instance of weight-striker contact and the series beginning was determined by the traveling time of the elastic wave through the figure 2: time series of fl signals from fracturing samples. striker. the impact produced a localized “macroscopic” damage on the sample surface, and generated microscopic failures throughout the sample including lateral faces, from which the emitted light was collected. the signal intensity depended both on the sample hardness (which influences the damage size), and on the quantum yield of luminescence. the fl amplitude is proportional to the energy release in damage events. therefore, the amplitude time series were used for constructing the energy distributions in the form of dependence log10n(e>e) versus log10e, where n(e>e) is the number of events characterized with the energy e exceeding a threshold value e. each energy distribution was plotted both in doubleand semi-logarithmic coordinates (fig. 3a and 3b, respectively). one can see that the distributions belonging to brittle materials contain log-linear portions (fig. 3a), which represent the dependence: log10n(e>e)  – b log10e (1) (here b is the constant). eq. (1) can be rewritten in the form of the power law: n(e>e)  e-b. (1a) f a. chmel et alii, frattura ed integrità strutturale, 30 (2014) 162-166; doi: 10.3221/igf-esis.30.21 165 (a) (b) figure 3: the same experimental dependences n(e>e) versus e plotted in double-logarithmic (a) and semi-logarithmic (b) coordinates; straight lines in (a) and (b) fit eq. (1) and eq. (2), respectively. in ductile marble and pmma, the log10n(e>e) versus log10e graphs do not exhibit log-linear dependences but being replotted in semi-logarithmic coordinates (with linear scale along the energy axis, fig. 3b) these ones become well approximated with straight lines according to the relation: log10n(e>e)  – ae (2) where a is the constant. relation (2) is equivalent to the exponential law n(e>e)  exp(-ae) (2a) which is specific for random events occurrence. correspondingly, neither brittle materials exhibit the exponential dependence (2), nor the energy distributions in ductile materials follow the power law (1). (we remind that the consideration concerns primary damage events detected at the nanostructural scale level.) a. chmel et alii, frattura ed integrità strutturale, 30 (2014) 162-166; doi: 10.3221/igf-esis.30.21 166 discussion he statistical analysis of the time series showed that the energy distributions of fl pulses in both heterogeneous and homogeneous brittle materials follow the power law indicative of long-range interactions between primary damage events. random (exponential) energy distributions were found in experiments with marble and organic glass that is in materials with pronounced plasticity. the absence of the correlated damage accumulation in this case was quite surprising because these materials exhibited the fl series evidencing multiple (statistically significant) bond breakage. however, this result points out a necessity to introduce some corrections in common interpretations of the role of structural heterogeneities, which were developed for explaining some cooperative phenomena in fracture. the cooperative effects result from the interactions between multiple individual failures, which are realized through propagating elastic waves excited by local structural perturbations [9, 10]. high plastic deformation prior to the bond rupture suppresses the elastic excitations thus disturbing dynamic cross-coupling between nucleating defects. as a result, the damage accumulation in ductile materials proceeds in an extensive manner that is the appearance of a defect does not affect efficiently the nucleation of other ones. this means that the prevalence of either correlated or random damage initiation at the scale level of basic structural heterogeneity (at the nanostructural level) depends on the degree of microplasticity in the given material, which determines the efficiency of long-range elastic interactions conclusion ractoluminescence is the effective method for monitoring the nucleation of defects in deformed/fractured dielectrics at the level of basic structural links. the fl sensitivity depends on the damage size and quantum yield of luminescence. in this work, the fl technique was applied for studying the primary damage accumulation in a set of solids differing in their mechanical properties. the statistical analysis of the fl time series emitted from impact damaged solids revealed the power law energy release distributions (scaling) in brittle materials, and exponential (poissonlike) distributions in ductile materials. at the same time, the microscopic heterogeneity of materials did not determine the prevailing (correlated or random) energy pattern at the nanostructural scale level. references [1] bowman, d.d., ouillon, g., sammis, c.g., sornette, a., sornette, d. an observational test of the critical earthquake concept, j. geophys. res., 103 (1998) 24359-24372. [2] carpinteri, a., puzzi, s., complexity: a new paradigm for future mechanics, frattura integrità strutturale, 10 (2009) 311. [3] mamalimov, r.i., sinani,a.b., chmel, a.e., shcherbakov, i.p., initiation of impact fracture in sio2 ceramics, tech. phys., 58 (2013) 1453-1458. [4] momon, s., moevus, m., godin, n., r’mili, m., reynaud, p., fantozzi, g., fayolle, g., acoustic emission and lifetime prediction during static fatigue tests on ceramic-matrix-composite at high temperature under air, composites part a: appl. sci. manufacturing, 41 (2010) 913-918. [5] amitrano, d., rupture by damage accumulation in rocks, intern. j. fract., 139 (2003) 369-381. [6] davydova, m., uvarov, s., fractal statistics of brittle fragmentation, frattura ed integrità strutturale, 24 (2013) 60-68. [7] chandra, b.p., mechanoluminescence in luminescent solids, in d.r. vij (ed.), luminescence of solids, plenum press, new york, (1998) 301-345. [8] kawaguchi, y., time-resolved fractoluminescence spectra of silica glass in a vacuum and nitrogen atmosphere, phys. rev. b, 52 (1995) 9224-9228. [9] kuksenko, v., tomilin, n., chmel, a., the rock fracture experiment with a drive control: a spatial aspect, tectonophysics, 431 (2007) 123-129. [10] telesca, l., lovallo, m., investigating non-uniform scaling behavior in temporal fluctuations of seismicity, nat. hazards earth system sci., 8 (2008) 973-976. t f microsoft word numero_41_art_61.docx v. rizov, frattura ed integrità strutturale, 41 (2017) 491-503; doi: 10.3221/igf-esis.41.61 491 analysis of longitudinal cracked two-dimensional functionally graded beams exhibiting material non-linearity victor rizov department of technical mechanics, university of architecture, civil engineering and geodesy, 1 chr. smirnensky blvd., 1046 – sofia, bulgaria. v_rizov_fhe@uacg.bg abstract. an analytical study of longitudinal fracture in two-dimensional functionally graded cantilever beam configurations is carried-out with taking into account the non-linear behavior of material. a longitudinal crack is located arbitrary along the beam cross-section height. the material is functionally graded along the width as well as along the height of beam. the external loading consists of a bending moment applied at the free end of lower crack arm. fracture is studied in terms of the strain energy release rate by considering the beam complementary strain energy. the solution derived is verified by analyzing the longitudinal crack with the help of the j-integral. the distribution of j-integral value along the crack front is studied. the effects of crack location, material gradients and non-linear behavior of material on the fracture are elucidated. the analysis reveals that the material non-linearity has to be taken into account in fracture mechanics based safety design of structural members and components made of two-dimensional functionally graded materials. keywords. functionally graded beam; crack; material non-linearity; analytical solution. citation: rizov, v., analysis of longitudinal cracked two-dimensional functionally graded beams exhibiting material non-linearity, frattura ed integrità strutturale, 41 (2017) 491-503. received: 23.04.2017 accepted: 28.05.2017 published: 01.07.2017 copyright: © 2017 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. introduction he functionally graded materials are new inhomogeneous materials produced by mixing of two constituent materials in different proportions in order to satisfy the requirements of material properties in different parts of a structural member [1-12]. since the composition of constituent materials varies continuously along one or more spatial coordinates during manufacturing without sudden changes of material properties, the interfaces and stress concentrations are largely avoided in contrast to laminated composite materials [13-15]. besides, the performance of functionally graded structural members and components to the external load can be optimized by tailoring the variation of material properties in a desired way during manufacturing. therefore, the functionally graded materials have been widely applied as advanced structural materials in aeronautics, electronics, nuclear energy, optics, engineering and biomedicine for t v. rizov, frattura ed integrità strutturale, 41 (2017) 491-503; doi: 10.3221/igf-esis.41.61 492 the last three decades [16]. fracture behavior is crucial for structural integrity and functionality of members and components made of functionally graded materials. therefore, considerable attention has been paid to fracture in these novel materials by the international research community [17-22]. the present paper is concerned with a longitudinal fracture analysis of a two-dimensional functionally graded cantilever beam configuration with taking into account the non-linear behavior of material. fracture is analyzed in terms of the strain energy release rate. the material is functionally graded along the height as well as along width of the beam. the mechanical behavior of material is described by a power-law stress-strain relation. an additional fracture analysis is carried-out by applying the j-integral approach and the results obtained are compared with the strain energy release rate. the effects of material gradients, crack location and material non-linearity on the fracture behavior are elucidated. analysis of the strain energy release rate he present paper analyses the longitudinal fracture in the two-dimensional functionally graded cantilever beam configuration shown schematically in fig. 1. figure 1: the geometry and loading of the two-dimensional functionally graded cantilever beam. a longitudinal crack of length, a, is located arbitrary along the beam cross-section height (it should be mentioned that the present paper is motivated also by the fact that functionally graded materials can be built up layer by layer [16] which is a premise for appearance of longitudinal cracks between layers). the lower and upper crack arms have different thicknesses denoted by 1h and 2h , respectively. the beam is loaded by one bending moment, ym , applied at the free end of lower crack arm (fig. 1). thus, the upper crack arm is free of stresses. the beam has a rectangular cross-section of width, b, and height, 2h. the beam is clamped in section, d. the beam non-linear mechanical behavior is described by the following power-law stress-strain relation [23]: mb  (1) where σ is the longitudinal normal stress, ε is the longitudinal strain, b and m are material properties. zircona-titanium is one of the functionally graded materials which exhibit non-linear mechanical behavior. data for mechanical properties of zircona-titanium can be found in [24]. the material is functionally graded along the width as well as along the height of the beam (fig. 1). the distribution of material property, b, in the beam cross-section is expressed as a function of 3y and 3z by the following quadratic law: t v. rizov, frattura ed integrità strutturale, 41 (2017) 491-503; doi: 10.3221/igf-esis.41.61 493 2 2 3 3 0 1 22 2 4 y z b b b b b h    , (2) where 3 2 2 b b y   , 3h z h   . (3) in (2), 0b is the value of b in the centre of the beam cross-section, 1b and 2b are material properties which govern the material gradients along axes, 3y and 3z , respectively (fig. 1). figure 2: distribution of the material property, b, in the beam cross-section. it should be mentioned that eq. (2) is suitable for two-dimensional functionally graded beam configurations which have high mechanical properties at the lower, upper and lateral surfaces of the beam as shown in fig. 2. the fracture behavior is studied in terms of the strain energy release rate. for this purpose, an elementary increase, da , of the crack length is assumed (the external load is kept constant). the strain energy release rate, g, is expressed via the changes of external work, extdw , and strain energy, du , as extdw dug da   (4) where the increase of crack area is da bda (5) the change of external work is written as * extdw du du  (6) where *du is the change of complementary strain energy. by combining of (4), (5) and (6), the strain energy release rate can be expressed as *du g bda  (7) it should be noted that the present analysis holds for non-linear elastic behavior of material. the analysis is applicable also for elastic-plastic behavior of material if the beam considered undergoes active deformation, i.e. if the external loading increases only [25]. it should also be mention that the present study is based on the small strains assumption. v. rizov, frattura ed integrità strutturale, 41 (2017) 491-503; doi: 10.3221/igf-esis.41.61 494 figure 3: the free end of the lower crack arm (. 1 1n n . is the neutral axis). the beam complementary strain energy, *u , is written as   22 2 2 * 01 2 2 2 2 1 * 0 * 1 1 dzdyualdzdyuau h h b b u h h b b l                             (8) where * 0lu and * 0uu are the complementary strain energy densities in the lower crack arm and the un-cracked beam portion  lxa  3 , respectively. axes, 1y and 1z , are shown in fig. 3, 2y and 2z are the centroidal axes of the crosssection of the un-cracked beam portion. in principle, the complementary strain energy density is equal to the area oqr that supplements the area opq, enclosed by the stress-strain curve, to a rectangle (fig. 4). therefore, the complementary strain energy density in the lower crack arm is written as ll uu 0 * 0   (9) where the strain energy density, lu0 , is equal to the area opq    0 0 )( du l (10) from (1), (9) and (10), the complementary strain energy density can be obtained as 1 1 * 0    m m bu m l  (11) the strain distribution is analyzed by applying the bernoulli’s hypothesis for plane sections since the span to height ratio of the beam under consideration is large. concerning the application of the bernoulli’s hypothesis in the present study, it should also be noted that since the beam is loaded in pure bending (fig. 1) the only non-zero strain is the longitudinal strain, ε. therefore, according to the small strain compatibility equations, ε is distributed linearly along the height of the beam cross-section. thus, ε in the lower crack arm is written as v. rizov, frattura ed integrità strutturale, 41 (2017) 491-503; doi: 10.3221/igf-esis.41.61 495  1 1 11nz z   (12) where 1 1nz is the coordinate of the neutral axis, 1 1n n , (the neutral axis shifts from the centroid since the material is functionally graded (fig. 3)), 1 is the curvature of the lower crack arm. figure 4: schematic of a non-linear stress-strain curve ( 0u and * 0u are the strain energy density and the complementary strain energy density, respectively). the following equilibrium equations of the lower crack arm cross-section (fig. 3) are used in order to determine 1 1nz and 1 : 1 2 2 1 1 1 1 2 2 h b h b n dy dz                 (13) 1 2 2 1 1 11 1 2 2 h b y h b m z dy dz                 (14) where 1n and 1ym are the axial force and the bending moment, respectively. it is obvious that 1 0n  , 1y ym m (15) by using (2), the distribution of material property, b, in the lower crack arm cross-section is written as  22 11 0 1 22 2 4 r zy b b b b b h     (16) where 1 2 2 b b y   , 1 1 1/ 2 / 2h z h   , 1 2 h r h  . (17) by substituting of (1), (12) and (16) in (13) and (14), one derives v. rizov, frattura ed integrità strutturale, 41 (2017) 491-503; doi: 10.3221/igf-esis.41.61 496       2 1 10 1 1 1 2 1 1 1 221 3 1 1 m m m m mb b b b b brn m m h m                       12 2 1 12 1 11 2 1 22 2 1 2 1 m nm m m m zb br m mh                   (18) 3 3 2 2 12 1 1 1 2 1 22 21 3 2 f q f q f q f q m nq q q qzb b q f q f qh                                  2 1 1 1 2 f q f q n q qz f q               2 2 21 1 2 1 0 1 1 221 1 3 2 m m m m m y b b b br m b b mh                   3 3 1 1 11 2 1 1 2 1 22 2 1 1 3 f q f q m n q qm m z b br q m f qh                          2 2 2 1 11 1 1 2 1 2 2 2 f q f q f q f q n nq q q qz z f q f q                           (19) 4 4 3 3 12 1 1 1 2 1 22 31 4 3 f q f q f q f q m nq q q qzb b q f q f qh                                 2 22 3 1 11 1 1 2 1 2 3 2 f q f q f q f q n nq q q qz z f q f q                            where 1 1 1 1/ 2 nh z   , 2 1 1 1/ 2 nh z    and /f q m ( f and q are positive integers). in (19), 1n and 1ym are determined by (15). it is obvious that at m=1 the non-linear stress-strain relation (1) transforms into the hooke’s law, assuming that b=e (here e is the modulus of elasticity). this means that at m=1 eq. (19) should transform into the formula for curvature of linear-elastic beam. indeed, at m=1, 0b e and 1 2 0b b  eq. (19) yields 11 3 1 12 ym ebh   (20) which is exact match of the formula for curvature of a linear-elastic homogeneous beam of width, b, and height, 1h . eqs. (18), and (19) should be solved with respect to 1 1nz and 1 by using the matlab computer program. by substituting of (12) and (16) in (11) the distribution of complementary strain energy density in the lower crack arm is written as     1 122 1 1 111* 1 0 0 1 22 2 4 1 m m n l m z zr zy u b b b mb h             (21) v. rizov, frattura ed integrità strutturale, 41 (2017) 491-503; doi: 10.3221/igf-esis.41.61 497 formula (21) can also be applied to obtain the distribution of complimentary strain energy density, *0uu , in the un-cracked beam portion. for this purpose, r , 1y , 1z , 1 1nz and 1 have to be replaced with 0 , 2y , 2z , 2 2nz and 2 , respectively ( 2 2nz is the neutral axis coordinate of the cross-section of un-cracked beam portion, 2 is the curvature of un-cracked beam portion). the quantities, 2 2nz and 2 , can be determined from eqs. (18) and (19). for this purpose, r , 1 1nz , 1h and 1 have to be replaced with 0 , 2 2nz , 2h and 2 , respectively. finally, by substituting of *0lu , * 0uu and (8) in (7), one derives         21 1 10 1 21 1 221 1 3 1 1 m m mu u u u u b b b b b brm g b m m m h m                       12 2 1 12 11 2 1 22 2 1 2 1 nm m m mu u u u u u zb br m mh                  3 3 2 2 12 1 1 2 1 22 21 3 2 f q f q f q f qu u u u u u u u nq q q qu u u u u u u u u zb bq f q f qh                                 2 1 1 1 2 f qf q u uu u n qq u u u z f q               (22)       1 1 10 12 1 2 1 1 3 1 m m mu u u u u u b b b bm b m m m                  3 3 2 2 22 2 1 2 1 22 21 3 2 f q f q f q f qu u u u u u u u nq q q qu u u u u u u u u u u u u zb bq f q f qh                                 2 2 2 1 2 f qf q u uu u n qq u u u u u z f q               where 1um m  , /u u uf q m ( uf and uq are positive integers), 1 2 2u nh z   and 2 2 2u nh z    . formula (22) calculates the strain energy release rate in the beam configuration shown in fig. 1 when the beam mechanical behavior and the material gradient are described by formulae (1) and (2), respectively. it should be noted that at m=1, 0b e , 1 2 0b b  and 1h h formula (22) yields 2 2 3 21 4 ym g eb h  (23) which is exact match of the expression for the strain energy release rate when the beam considered is linear-elastic and homogeneous [26]. in order to verify (22), the fracture is analyzed also by using the j-integral written as [27] 0 cos x y u v j u p p ds x x               (24) v. rizov, frattura ed integrità strutturale, 41 (2017) 491-503; doi: 10.3221/igf-esis.41.61 498 where γ is a contour of integration going from the lower crack face to the upper crack face in the counter clockwise direction, 0u is the strain energy density, α is the angle between the outwards normal vector to the contour of integration and the crack direction, xp and yp are the components of stress vector, u and v are the components of displacement vector with respect to the crack tip coordinate system xy (x is directed along the crack), ds is a differential element along the contour. the j-integral is solved by using an integration contour, γ, that coincides with the beam contour (fig. 1). it is obvious that the j-integral value is non-zero only in segments 1 and 2 of the integration contour. therefore, the j-integral solution is written as 1 2 j j j   (25) where 1 j and 2j are the j-integral values in segments 1 and 2 , respectively ( 1 and 2 coincide with the free end of lower crack arm and the clamping, respectively). the components of j-integral in segment, 1 , of the integration contour are written as (fig. 3) xp   mb  , 0yp  (26) 1ds dz , cos 1   (27) where 1z varies in the interval 1 1[ / 2, / 2]h h . partial derivative, /u x  , in (24) is found as  1 1 11n u z z x        (28) where 1 1nz and 1 are obtained from eqs. (18) and (19). the strain energy density is calculated by substituting of (1) in (10) 1 0 1 mb u m     (29) by substituting of (1), (12), (16), (26), (27), (28) and (29) in (24) and integrating in boundaries from 1 / 2h to 1 / 2h , one derives         2 21 1 10 1 1 21 1 22 21 4 1 1 1 1 m m mu u u u u b y b b rm j m m b m h m                          12 2 1 12 11 2 1 22 2 1 2 1 nm m m mu u u u u u zb r m mh                  3 3 2 2 12 1 1 2 1 22 21 3 2 f q f q f q f qu u u u u u u u nq q q qu u u u u u u u u zb q f q f qh                                 (30) 2 1 1 1 2 f qf q u uu u n qq u u u z f q               v. rizov, frattura ed integrità strutturale, 41 (2017) 491-503; doi: 10.3221/igf-esis.41.61 499 where 1y varies in the interval  / 2, / 2b b . the j-integral solution in segment, 2 , of the integration contour (fig. 1) can be determined by (30). for this purpose, r , 1 1n z , 1 , 2 and 1 have to be replaced with 0 , 2 2nz , 1u , 2u and 2 , respectively. besides, the sign of (30) must be set to „minus” because the integration contour is directed upwards in segment, 2 . the j-integral final solution is found by substituting of 1 j and 2j in (25)         2 21 1 10 1 1 21 1 22 2 4 1 1 1 1 m m mu u u u u b y b b rm j m m b m h m                       12 2 1 12 11 2 1 22 2 1 2 1 nm m m mu u u u u u zb r m mh                  3 3 2 2 12 1 1 2 1 22 21 3 2 f q f q f q f qu u u u u u u u nq q q qu u u u u u u u u zb q f q f qh                                 2 1 1 1 2 f qf q u uu u n qq u u u z f q               (31)       21 1 10 1 12 1 22 4 1 1 1 m m mu u u u u u b y bm m m b m                  3 3 2 2 22 2 1 2 1 22 21 3 2 f q f q f q f qu u u u u u u u nq q q qu u u u u u u u u u u u u zb q f q f qh                                 2 2 2 1 2 f qf q u uu u n qq u u u u u z f q               formula (31) describes the distribution of the j-integral value along the crack front. the average value of the j-integral along the crack front is written as 2 1 2 1 b av b j j dy b    (32) it should be noted that the j-integral solution derived by substituting of (31) in (32) is exact match of the strain energy release rate (22). this fact verifies the fracture analysis developed in the present paper. results he distribution of j-integral value along the crack front is analyzed. for this purpose, calculations are performed by using formula (31). it is assumed that b=0.020 m, h=0.004 m, m=0.7, f=7, q=10, 1.7um  , 17uf  , 10uq  and 20ym  nm. the j-integral value is presented in non-dimensional form by using the formula,  0/nj j b b . the material gradient along the beam width is characterized by 1 0/b b ratio. fig. 5 shows the distribution of the j-integral value in nont v. rizov, frattura ed integrità strutturale, 41 (2017) 491-503; doi: 10.3221/igf-esis.41.61 500 dimensional form along the crack front for two 1 0/b b ratios at 1 / 2 0.75h h and 2 0/ 2b b  . only the right-hand half of the crack front is shown in fig. 5 since the distribution is symmetrical with respect to the crack front centre. the horizontal axis is defined such that 12 / 0.0y b  is in the crack front centre. thus, 12 / 1.0y b  is in the right-hand lateral surface of the beam. one can observe in fig. 5 that for 1 0/ 1.2b b  , the j-integral value is maximum in the crack front centre and decreases towards the right-hand lateral surface (this is due to the fact that for 1 0/ 1.2b b  the material property, b, is minimum in the crack front centre and increases towards the beam lateral surfaces). fig. 5 shows that for 1 0/ 0.4b b   , the j-integral value increases from its minimum in the crack front centre towards the right-hand lateral surface of the beam. figure 5: the distribution of the j-integral value in non-dimensional form along the crack front (curve 1 at 1 0/ 1.2b b  , curve 2 – at 1 0/ 0.4b b   ). the effects of the material gradient and the crack location on the strain energy release rate are evaluated too. for this purpose, calculations of the strain energy release rate are carried-out by using formula (22). the strain energy release rate is presented in non-dimensional form by using the formula,  0/ng g b b . figure 6: the strain energy release rate in non-dimensional form plotted against 1 0/b b ratio at three 1 / 2h h ratios. v. rizov, frattura ed integrità strutturale, 41 (2017) 491-503; doi: 10.3221/igf-esis.41.61 501 the crack location along the height of the beam cross-section is characterized by 1 / 2h h ratio. in the calculations, 0b is kept constant. therefore, 1b is varied in order to generate various 1 0/b b ratios. the strain energy release rate in nondimensional form is plotted against 1 0/b b ratio at three 1 / 2h h ratios and 2 0/ 2.0b b  in fig. 6. the curves in fig. 6 indicate that the strain energy release rate decreases with increasing of 1 / 2h h ratio. this finding is attributed to the increase of the lower crack arm stiffness. it can be observed also in fig. 6 that the strain energy release rate decreases with increasing of 1 0/b b ratio. the influence of non-linear behavior of the material on the fracture is also analyzed. for this purpose, the strain energy release rate in non-dimensional form is presented as a function of 2 0/b b ratio at 1 / 2 0.5h h  and 1 0/ 0.5b b  in fig. 7. it can be observed that the strain energy release rate decreases with increasing of 2 0/b b ratio (fig. 7). the strain energy release rate obtained assuming linear-elastic behavior of the two-dimensional functionally graded material is also presented in fig. 7 for comparison with the non-linear solution (the linear-elastic solution is derived by substituting of m=1 in formula (22)). the curves in fig. 7 indicate that material non-linearity leads to increase of the strain energy release rate. figure 7: the strain energy release rate in non-dimensional form presented as a function of 2 0/b b ratio (curve 1 – at non-linear elastic behavior of material, curve 2 – at linear-elastic behavior of material). conclusions he longitudinal fracture behavior of two-dimensional functionally graded cantilever beam that exhibits material non-linearity is investigated analytically. the beam is loaded by a bending moment applied at the free end of the lower crack arm. the fracture is studied in terms of the strain energy release rate. the beam mechanical behavior is described by using a power-law stress-strain relation. the material property, b, varies continuously in the beam crosssection according to a quadratic law. the solution derived is applicable for longitudinal crack located arbitrary along the height of the beam cross-section. in order to verify the solution, the fracture is analyzed also by applying the j-integral approach. the distribution of the jintegral value along the crack front is investigated. the physical meanings of the dependence of the j-integral value on material gradient are discussed. the effects of material gradients and crack location along the beam height on the fracture behavior are also analyzed. the analysis revealed that the strain energy release rate decreases with increasing of the lower crack arm thickness. it is found also that the strain energy release rate decreases with increasing of 1 0/b b and 2 0/b b ratios. this finding is attributed to the increase of the beam stiffness. the influence of material non-linearity on the fracture is studied too. it is found that the material non-linearity leads to increase of the strain energy release rate. therefore, non-linear behavior of the material has to be taken into account in fracture mechanics based safety design of structural members and components made of two-dimensional functionally graded materials. the results obtained in the t v. rizov, frattura ed integrità strutturale, 41 (2017) 491-503; doi: 10.3221/igf-esis.41.61 502 present study indicate that the longitudinal fracture in two-dimensional functionally graded beams with material nonlinearity can be efficiently regulated in their design stage by employing appropriate material gradients. besides for the beam shown in fig. 1, the analysis developed in the present paper can be applied to determine the strain energy release rate for longitudinal cracks in two-dimensional functionally graded non-linear elastic beam configurations loaded in pure bending (for instance, the double cantilever beam loaded with uneven bending moments, the four-point bending beam when the crack tip is located in middle beam portion which is loaded in pure bending). it should be noted that the approach developed in the present paper is applicable also for beam configurations loaded by a vertical load when the shear stresses can be neglected, i.e. when the span to height ratio of the beam is large. acknowledgments he present study was supported financially by the research and design centre (cnip) of the uaceg, sofia (contract bn – 198/2017). references [1] butcher, r.j., rousseau, c.e., tippur, h.v., a functionally graded particulate composite: measurements and failure analysis, acta matererialia, 47 (1999) 259-268. [2] gasik, m.m., functionally graded materials: bulk processing techniques, international journal of materials and product technology, 39 (1995) 20-29. [3] hirai, t., chen, l., recent and prospective development of functionally graded materials in japan, material science forum, 308-311 (1999) 509-514. [4] mortensen, a., suresh, s., functionally graded metals and metal-ceramic composites: part 1 processing, international materials review, 40 (1995) 239-265. [5] nemat-allal, m.m., ata, m.h., bayoumi, m.r., khair-eldeen, w., powder metallurgical fabrication and microstructural investigations of aluminum/steel functionally graded material, materials sciences and applications, 2 (2011) 1708-1718. [6] neubrand, a., rödel, j., gradient materials: an overview of a novel concept, zeit f met, 88 (1997) 358-371. [7] suresh, s., mortensen, a., fundamentals of functionally graded materials, iom communications ltd, london (1998). [8] tokova, l., yasinskyy, a., ma, c.-c, effect of the layer inhomogeneity on the distribution of stresses and displacements in an elastic multilayer cylinder, acta mechanica, (2016) doi: 10.1007/s00707-015-1519-8, 1 – 13. [9] tokovyy, y., ma, c.-c, three-dimensional temperature and thermal stress analysis of an inhomogeneous layer, journal of thermal stresses, 36 (2013) 790 – 808, doi: 10.1080/01495739.2013.787853. [10] tokovyy, y., ma, c.-c, axisymmetric stresses in an elastic radially inhomogeneous cylinder under length-varying loadings, asme journal of applied mechanics, 83 (2016), doi: 10.1115/1.4034459. [11] uslu uysal, m., kremzer, m., buckling behaviour of short cylindrical functionally gradient polymeric materials, acta physica polonica a, 127 (2015) 1355-1357, doi:10.12693/aphyspola.127.1355. [12] uslu uysal, m., buckling behaviours of functionally graded polymeric thin-walled hemispherical shells, steel and composite structures, an international journal, 21 (2016) 849-862. [13] szekrenyes, a., fracture analysis in the modified split-cantilever beam using the classical theories of strength of materials, journal of physics: conference series, 240 (2010) 012030. [14] szekrenyes, a., vicente, w.m., interlaminar fracture analysis in the gii-giii plane using prestressed transparent composite beams, composites part a: applied science and manufacturing, 43 (2012) 95-103. [15] szekrenyes, a., semi-layerwise analysis of laminated plates with nonsingular delamination the theorem of autocontinuity, applied mathematical modelling, 40 (2016) 1344 – 1371. [16] bohidar, s.k., sharma, r., mishra, p.r., functionally graded materials: a critical review, international journal of research, 1 (2014) 289-301. [17] erdogan, f., fracture mechanics of functionally graded materials, computational engineering, 5 (1995) 753-770. [18] paulino, g.c., fracture in functionally graded materials, engineering fracture mechanics, 69 (2002) 1519-1530. t v. rizov, frattura ed integrità strutturale, 41 (2017) 491-503; doi: 10.3221/igf-esis.41.61 503 [19] shi-dong pan, ji-cai feng, zhen-gong zhou, wu-lin-zhi, four parallel non-symmetric mode –iii cracks with different lengths in a functionally graded material plane, strength, fracture and complexity: an international journal, 5 (2009) 143-166. [20] tilbrook, m.t., moon, r.j., hoffman, m., crack propagation in graded composites, composite science and technology, 65 (2005) 201-220. [21] upadhyay, a.k., simha, k.r.y., equivalent homogeneous variable depth beams for cracked fgm beams; compliance approach, international journal of fracture, 144 (2007) 209-213. [22] uslu uysal, m., güven, u., a bonded plate having orthotropic inclusion in adhesive layer under in-plane shear loading, the journal of adhesion, 92 (2016) 214-235, doi:10.1080/00218464.2015.1019064. [23] petrov, v.v., non-linear incremental structural mechanics, infra-injeneria, m. (2014). [24] tsukamoto, h., mechanical properties of zirconia – titanium composites, international journal of materials science and applications, 3 (2014) 260-267. [25] lubliner, j., plasticity theory (revised edition), university of california, berkeley, ca (2006). [26] hutchinson, w., suo, z., mixed mode cracking in layered materials, advances in applied mechanic, 64 (1992) 804– 810. 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/hrv (za stvaranje adobe pdf dokumenata najpogodnijih za visokokvalitetni ispis prije tiskanja koristite ove postavke. stvoreni pdf dokumenti mogu se otvoriti acrobat i adobe reader 5.0 i kasnijim verzijama.) /hun 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can be opened with acrobat and adobe reader 5.0 and later.) >> /namespace [ (adobe) (common) (1.0) ] /othernamespaces [ << /asreaderspreads false /cropimagestoframes true /errorcontrol /warnandcontinue /flattenerignorespreadoverrides false /includeguidesgrids false /includenonprinting false /includeslug false /namespace [ (adobe) (indesign) (4.0) ] /omitplacedbitmaps false /omitplacedeps false /omitplacedpdf false /simulateoverprint /legacy >> << /addbleedmarks false /addcolorbars false /addcropmarks false /addpageinfo false /addregmarks false /convertcolors /converttocmyk /destinationprofilename () /destinationprofileselector /documentcmyk /downsample16bitimages true /flattenerpreset << /presetselector /mediumresolution >> /formelements false /generatestructure false /includebookmarks false /includehyperlinks false /includeinteractive false /includelayers false /includeprofiles false /multimediahandling /useobjectsettings /namespace [ (adobe) (creativesuite) (2.0) ] /pdfxoutputintentprofileselector /documentcmyk /preserveediting true /untaggedcmykhandling /leaveuntagged /untaggedrgbhandling /usedocumentprofile /usedocumentbleed false >> ] >> setdistillerparams << /hwresolution [2400 2400] /pagesize [612.000 792.000] >> setpagedevice microsoft word numero_30_art_15 j. vázquez et alii, frattura ed integrità strutturale, 30 (2014) 109-117; doi: 10.3221/igf-esis.30.15 109 focussed on: fracture and structural integrity related issues effect of the model’s geometry in fretting fatigue life prediction j. vázquez, c. navarro, j. domínguez departamento de ingeniería mecánica, universidad de sevilla, e.t.s.i. camino de los descubrimientos s/n, c.p. 41092, sevilla, españa jesusvaleo@us.es, cnp@us.es, jaime@us.es abstract. this paper analyses the influence that the type of geometry used to obtain the stress/strain fields in a cylindrical contact has on fretting fatigue life predictions. in addition, this work considers the effect that the fatigue crack shape assumed has on these fretting fatigue life predictions. the strain/stress fields are calculated using a series of finite elements models that consider the following three types of behaviour: plane stress, plane strain (2d geometries) and 3d. each of these models gives a different crack initiation life and a different evolution of the stress intensity factor (sif), which are calculated using the weight function method. these models therefore provide different fretting fatigue life predictions. finally, the lives obtained using the numerical models are compared with experimental lives. keywords. fretting fatigue; geometrical effects; fatigue life model. introduction retting is a superficial damage phenomenon that is found in certain mechanical joints when are subjected to fluctuating loads. consequently, time variable contact stress distributions arise at the contacting surfaces, potentially leading to surface crack formation [1]. if there is a bulk tension at the joint in addition to the contact stress field, surface cracks may cause mechanical failure at the joint [2]. this phenomenon is referred to as fretting fatigue. because the most common form of transmitting forces between solids is mechanical contact, fretting or fretting fatigue is present in a wide variety of mechanical components. due to this commonality, fretting fatigue is the focus of many studies [3-5]. with the research aim of predicting the failure of mechanical components, a series of fatigue life prediction models have been developed [6-10]. in many circumstances, these models are applied to geometries and load systems whose behaviour can be assumed to be in plane stress or plane strain conditions, as observed in 2d models with actual 3d geometries. the focus of this work is to analyse the effect produced by the geometry of the model (2d or 3d) on fatigue life prediction. for this task, fatigue life predictions were completed over a series of experimental tests, considering both 2d and 3d models. tests were performed using cylindrical contact in which a cylindrical element was pressed against a dogbone type fatigue test specimen while a static normal load, n, was applied. both components were made of al 7075-t651 alloy. the test specimen was then subjected to a cyclic axial stress, , and due to the assembly used and the friction between the contact pair, generates a tangential cyclic load q (fig. 1). more details about the experimental set up can be found in [11]. f j. vázquez et alii, frattura ed integrità strutturale, 30 (2014) 109-117; doi: 10.3221/igf-esis.30.15 110 figure 1: scheme of the experimental assembly. fatigue life prediction model he fretting fatigue life predictions model used in these analyses is based on a previous model proposed by the authors [7]. this model combines the crack initiation and crack propagation phases by analysing each phase independently. using fracture mechanics procedures, the crack propagation phase is calculated using a curve. this curve offers the crack propagation cycles, np(a), that are required to grow a crack from an initial length, a, to the final fracture crack length at which the test specimens fails. this curve is obtained by integrating the crack propagation law between a and the final crack length. moreover, the crack initiation phase offers the number of crack initiation cycles, ni(a), required to nucleate/generate a crack of length equal to a. the ni(a) curve is obtained by considering the stress and strain fields along the prospective crack path. the total fatigue life, nt, is obtained by adding the curves, nt(a)=ni(a)+np(a). as a result, the total fatigue life, nt(a), is a function of the crack length, a, which defines when the crack initiation phase ends and the crack propagation phase begins. depending on the value assumed for the initial crack length, a, the total fatigue life estimated is different, and the curve nta can be obtained by repeating the calculation process using diverse values of a. as shown in [7], close to the contact surface the fatigue life is controlled by the crack initiation process, and far from it by the crack propagation. therefore, the value of a that produces the minimum of the curve nt(a) is considered the nexus between the crack initiation and the crack propagation phases [8]. for this reason, and because it is the crack initiation length that offers the most conservative prediction, the minimum value of nt is established as the fatigue life prediction. crack propagation phase a fracture mechanics-based law reflecting a generic initial crack length, a, is used to calculate the crack propagation phase. because the value of a can be measured on the order of microns, the proposed law also tries to model the short crack growth phase. for this reason, a modified threshold dependent on the actual crack length is introduced into the crack growth law [9]. 1/2 0 0 th nff n i i f f f da a c k k dn a a l                   (1) in eq. (1), thi k   is the threshold sif range for long cracks, f is a parameter equal to 2.5 [10], l0 is the distance between the surface and the first microstructural barrier (a grain boundary), c and n are the paris’ crack growth parameters and a0 is the el haddad’s parameter, which is defined by 2 0 1 thi fl k a           (2) in which fl is the stress range at the fatigue limit. the factor that multiplies thik  in eq. (1) is based on a theoretical approximation of the kitagawa-takahashi diagram that considers the threshold stress to be a function of the crack length. t j. vázquez et alii, frattura ed integrità strutturale, 30 (2014) 109-117; doi: 10.3221/igf-esis.30.15 111 many different options were considered to model the short crack growth phase [9], but it was found that one offers the best results is that shown in eq. (1). figure 2: mesh in the 2d models. figure 3: mesh in the 3d models. to study the effect exerted by the model geometry (2d or 3d) on the crack growth phase, sif values were calculated according to the type of geometry used to model the contact pair that was used between the pad and the test specimen. in those models with a plane stress or a plane strain formulation, the sif was obtained using the weight function proposed by orynyak [12] and calculated as follows:      ,ik y w g da      (3) where  represents the surface crack,  is the angle for a certain point along the crack front, σ(y) is the normal stress distribution along the prospective crack faces and g symbolises the crack geometry. in the case of a 2d model, this stress distribution only varies with the y coordinate. conversely, when a 3d model is applied, the sif is obtained by adapting eq. (3) to the bidimensional stress field along the crack surface:      , ,ik y z w g da      (4) where the normal stress σ(y,z) is the bidimensional stress distribution on the crack surface. obtaining sif using eq. (3) and (4) is only valid until the crack becomes a through crack. from that moment forward, the sif is calculated using the unidimensional weight function proposed by bueckner [13]: j. vázquez et alii, frattura ed integrità strutturale, 30 (2014) 109-117; doi: 10.3221/igf-esis.30.15 112       0 , l k l y w y l dy  (5) in eq. (5), σ(y) is the normal stress distribution along the prospective crack path. in 3d cases, this stress distribution is averaged through the test specimen thickness. figure 4: crack configuration in the models. both stress distributions, σ(y) (for eqs. (3) and (5)) and σ(), have been obtained from a series of elastic-plastic finite element analyses, which simulate the mechanical behaviour of the contact pair between the pad and the test specimen. the software used for the finite element models (fem) was ansys® 14.0. fig. 2 shows the mesh and boundary conditions used in the 2d fem. in these cases and due to the symmetrical conditions of the actual contact pair, only half of the test specimen has been introduced into the models. in the 3d models, these symmetrical conditions allow to consider only half of the pad and a quarter of the test specimen during modelling. the fem mesh for 3d case modelling is shown in fig. 3. based on experimental observation in both models (2d and 3d), the cracks have been modelled as surface cracks that are semi-elliptical and centred along the test specimen thickness and emanating from the contact trailing edge (fig. 1 and 4). it is further experimentally observed that the crack shape evolves as a crack grows; thus, for the sif calculations, a variable crack aspect ratio, b/a, has been considered. the evolution of the crack aspect ratio can be obtained from the following equation:       1/2 /2 0 0 1/2 0 0 0 , / , / th th nffn i i f f f nffn i i f f f a k a b a k a a lb db a da a k a b a k a a l                                     (6) in this equation, it is implicitly assumed that the crack grows according to the same law at the surface point ( =π/2) and at the deepest point ( =0) of the crack front. according to eq. (6), the procedure used to calculate the crack aspect evolution is as follows: 1. using the present crack length, a, and aspect ratio, b/a, the sif values at the surface and the deepest point of the crack front are calculated. 2. a small crack length increment δa is imposed; in the present case, δa =1 µm. 3. assuming that the sif values remain unchanged during the increment δa, δb is obtained from eq. (6). suspecting that the assumed initial crack aspect ratio could have a potential influence on the a/b evolution, a series of simulations were carried out while considering different initial crack aspect ratios. the result of one of these simulations is shown in fig. 5, in which an initial crack length, a, of 1 µm has been considered for all cases. these simulations prove that the assumed initial crack aspect ratio only affects the aspect ratio at any length for cracks smaller than 20 µm. j. vázquez et alii, frattura ed integrità strutturale, 30 (2014) 109-117; doi: 10.3221/igf-esis.30.15 113 figure 5: crack aspect evolution for different initial crack aspect. crack initiation phase to analyse the crack initiation phase, the fatigue model here applied takes ideas from the work of mcclung et al. [14]. the first step is to obtain from smooth fatigue test specimens the fatigue curve nsmooth(ε,a). this curve gives, as a function of the applied strain range, ε, the number of cycles needed to initiate a crack of length a in smooth test specimens. for each value of ε and a, the number of fatigue cycles, nsmooth(ε,a), is calculated as follows:          0 0 , , , fa smooth smooth smooth smooth p a dl n a n n a n f l               (7) in eq. (7), nt smooth(ε) represents the total number of fatigue cycles obtained in a smooth test specimen subjected to a strain range ε. np smooth(ε,a) is the number of cycles required to propagate the crack from a to the final fracture crack length, af, for a smooth test specimen subjected to ε. finally, f(ε,a) represents the fatigue crack growth law eq. (1), in which ki is calculated according to the applied ε and the geometry of the smooth fatigue test specimen. for the al 7075-t651 alloy, the initiation curves nsmooth(ε,a) for different initiation cracks lengths are represented in fig. 6. the nt smooth(ε) curve is also plotted in this figure. figure 6: initiation crack curves for al 7075-t651 alloy. in the case where a multi-axial stress/strain state and a stress/strain gradient are present, as in fretting fatigue, the same procedure can be applied, but with some changes. first, a multi-axial fatigue parameter should be used. in this work, the j. vázquez et alii, frattura ed integrità strutturale, 30 (2014) 109-117; doi: 10.3221/igf-esis.30.15 114 fatemi-socie parameter (fs) has been used [15]. using the set of nsmooth(ε,a) curves, a new set of nsmooth(fs,a) curves are obtained. however, in a fretting fatigue situation where a stress/strain gradient with depth is present, the fs parameter also varies with depth. therefore, the crack initiation life depends on where the parameter is evaluated. considering the results from previous works [16], the mean value of the fs parameter between the surface and a depth equal to the prospective crack initiation length, a, is considered the most appropriate option. with this average value and the set of nsmooth(fs,a) curves, the number of cycles required to initiate a crack with a length equal to a is obtained. because a mean value is used, the calculation is approximate in nature. with this option, it is the hypothesis that zones with the same mean value of the parameter require the same number of cycles to initiate a crack. combination of the crack initiation and crack propagation phases when the curves ni(a) and np(a) are acquired, these values are added to obtain a new curve nt(a)= ni(a)+np(a), which gives the total number of fatigue cycles needed as a function of the assumed initial crack length, a. the value of a that minimises the total number of cycles is considered the crack initiation length. the minimum value of nt is the fatigue life. this fatigue model presents the advantage that there is no need to determine a priori when the crack initiation phase finishes and, hence, when the crack propagation phase starts. the decision is made based on the value of a that minimises the total fatigue life nt. fig. 7 shows the curves ni(a), np(a) and nt(a) obtained in a simulation of the test type 3, using a 3d model. the parameters defining this type of test will be shown further in this document. in the following figure, it is observed that the crack initiation length, i.e., the value of a that minimises nt, is approximately equal to 65 µm. figure 7: curves ni(a), np(a) and nt(a) obtained in a 3d simulation. fatigue tests ollowing the same procedure described in [11], a series of fretting fatigue tests were performed. the data for completed tests are shown in tab. 1. seven varying load combinations were applied to meet two main fretting fatigue test goals: completing tests with a wide range in fatigue lives and carrying out tests with varying predominate loads. fatigue life predictions he fretting fatigue life predictions were performed using the mechanical and fatigue properties for the al 7075t651, as shown in tab. 2 [17]. in this table, the σf´, b, εf´ and c are parameters defining the δε-n curve, and the constants k´ and n´ define the stress-strain ramberg-osgood curve. f t j. vázquez et alii, frattura ed integrità strutturale, 30 (2014) 109-117; doi: 10.3221/igf-esis.30.15 115 test type n(n)/q(n) σ(mpa) nexp 1 1 5800 / 850 40 1070886 2 1 5800 / 850 40 1793368 3 2 5800 / 850 50 577540 4 2 5800 / 850 50 382064 5 2 5800 / 850 50 676704 6 3 5800 / 1100 70 303509 7 3 5800 / 1100 70 347072 8 4 5800 / 1100 55 252878 9 4 5800 / 1100 55 283110 10 5 5800 / 1350 70 167324 11 5 5800 / 1350 70 165421 12 6 4750 / 1100 110 52440 13 6 4750 / 1100 110 57032 14 7 3690 / 1350 110 32395 15 7 3690 / 1350 110 57479 table 1: loads (n and q), axial stress (σ) and experimental fatigue cycles (nexp). e ν σu σy 70 gpa 0.33 572 mpa 503 mpa c n δkth δσfl 8.83·10-11 3.322 2.1 mpa√m 169 mpa σf´ b εf´ c 1231 -0.122 0.26 -0.806 k´ n´ 694 mpa 0.04 table 2: mechanical and fatigue properties for the al 7075-t651. the fretting fatigue predictions obtained for the 2d (plane stress or plane strain) and 3d models, are shown in tab. 3. in addition, tab. 3 indicates the experimental lives. to consider the full picture of the behaviour offered by each model (2ds or 3d), fig. 8 presents the predictions, npred, versus the experimental lives, nexp, for all cases. this plot illustrates the solid predictions obtained using both 2d models; furthermore, it illustrates that both models provide similar predictions. regarding the 3d model, this plot also indicates good behaviour; however, for test type 2, the results were worse than those obtained using the 2d models. to complete the prediction obtained using the models, fig. 9 represents the percentage of ni and the crack initiation length as a function of the predicted life npred. this plot shows that the crack initiation lengths are continuously longer than 20 m, justifying the low influence exerted on the fatigue predictions by the assumed initial crack aspect ratio. similarly, this plot displays that the comparative relevance of both the crack initiation and the crack propagation phases can vary across test results. this fact shows that it is not possible to ignore either the crack initiation phase or the crack propagation phase when conducing these tests. finally, fig. 9 also indicates that the crack initiation length is always shorter than 70 µm; a model that considers the short crack growth phase is expedient. j. vázquez et alii, frattura ed integrità strutturale, 30 (2014) 109-117; doi: 10.3221/igf-esis.30.15 116 type nexp plane stress plane strain 3d 1 1070886 949195 876623 1997908 1793368 2 577540 564307 530292 1017824382064 676704 3 303509 150253 132687 179496 347072 4 252878 236057 205330 294700 283110 5 167324 94757 87313 104212 165421 6 52440 67845 61666 69356 57032 7 32395 55983 51213 48948 57479 table 3: fretting fatigue life predictions. figure 8: npred vs. nexp. figure 9: crack initiation length vs. npred and ni(%) vs. npred. conclusions n this work, the effect that the model’s geometry has on the fretting fatigue life predictions has been studied. for the cylinder-plane contact pair considered, all of the models give similar results. these results are proven to be virtually identical in the 2d cases. these results additionally justify the use of a 2d fem that provides the advantage of lower computational cost compared with 3d models. references [1]waterhouse, r.b., fretting fatigue, applied science publisher, (1981). [2]nishioka, k., hirakawa, k., fundamental investigation on fretting fatigue—part 4. the effect of mean stress, bull. jpn. soc. mech. eng., 12 (1969) 408–414. i j. vázquez et alii, frattura ed integrità strutturale, 30 (2014) 109-117; doi: 10.3221/igf-esis.30.15 117 [3]navarro, c., muñoz, s., domínguez, j., propagation in fretting fatigue from a surface defect, tribol. int., 39 (2006) 1149–1157. [4]hattori, t., kien, v.t., yamashita, m., fretting fatigue life estimations based on fretting mechanisms, tribol. int., 44 (2011) 1389–1393. [5]hills, d.a. et al., correlation of fretting fatigue experimental results using an asymptotic approach, int. j. fat., 43 (2012) 62–75. [6]szolwinski m., farris t., observation, analysis and prediction of fretting fatigue in 2024-t351 aluminum alloy, wear, 221 (1998) 24–36. [7]navarro, c., garcía, m., domínguez, j., a procedure for estimating the total life in fretting fatigue, fat. fract. engng. mater. struct., 26 (2003) 459-468. [8]socie d.f., morrow, j., chen, w.c., a procedure for estimating the total fatigue life of notched and cracked members, engng. fract. mech., 11 (1979) 851-859. [9]muñoz, s., navarro, c., domínguez, j., application of fracture mechanics to estimate fretting fatigue endurance curves, engng. fract. mech., 74 (2007) 2168-2186. [10]vallellano, c., domínguez, j., navarro, a., on the estimation of fatigue failure under fretting conditions using notch methodologies, fat. fract. engng. mater. struct., 26 (2003) 469-478. [11]tam, r. et al., caracterización de una máquina para realizar ensayos de fretting fatiga con contacto cilíndrico, anales de la mecánica de la fractura, (2011) 323-328. [12]orynyak, i.v., borodii, m.v., torop, v.m., approximate construction of a weight function for quarter-elliptical, semi-elliptical and elliptical cracks subjected to normal stresses. eng. fract. mech., 49 (1994) 143-151. [13]bueckner, h.j., sih, g.c. (ed.), methods of analysis and solutions of crack problems, noordhoff int. publishing, (1973). [14]mcclung, rc, francis, wl, hudak, jr. sj, a new approach to fatigue life prediction based on nucleation and growth. in: 9th international fatigue congress, atlanta, 2006. [15]fatemi, a. socie, d. a., critical plane approach to multiaxial fatigue damage including out-of-phase loading, fatigue. fract. eng. mater. struct., 11 (1998) 145–65. [16]navarro, c., muñoz, s., domínguez, j., influence of the initiation length in predictions of life in fretting fatigue, strain, 47 (2011) 283–91. [17]navarro, c., vázquez, j., domínguez, j., 3d vs. 2d fatigue crack initiation and propagation in notched plates, int. j. fat, 58 (2014) 40-46. m. laredj et alii, frattura ed integrità strutturale, 48 (2019) 193-207; doi: 10.3221/igf-esis.48.21 193 prediction and optimizing residual stress profile induced by cold expansion in aluminum alloys using experimental design m. laredj, a. miloudi university of djillali liabes, sidibel abbès, laboratory of lmsr algeria laredjmustapha@gmail.com, miloudidz@yahoo.fr a. lousdad laboratory of mechanics of structures and solids (lmss), faculty of technology – department of mechanical engineering university djilali liabes of sidi bel abbes, b.p 89 cité ben m’hidi sidi belabbes 22000 algeria a_lousdad@yahoo.com m. benguediab university of djillali liabes, sidibel abbès, laboratory of lmsr algeria benguediab_m@yahoo.fr abstract. cold expansion by hardening is a common process used in the aerospace industry to extend the fatigue lifetime of drilled assemblies due to the existence of a field of high compressive tangential residual stresses. the understanding and the control of the residual stresses are thus important, since it can be beneficial to improve the reliability and lifetime of the structures. the main objective of this work is to establish and validate a predictive model of residual stresses generated by cold hardening. this technique will be useful for industrial application since it allows the estimation of the fatigue lifetime of parts with respect to the process parameters. this tool can also be used to determine the optimal parameters in order to maximize the fatigue lifespan. an experimental setup was used to highlight the effect of the expansion degree, the thickness of the part and the yield strength on the residual stresse profiles. moreover, the proposed mathematical models are used to determine the optimal values of the process parameters and predict the residual stress in order to achieve a maximum service life of cracked structure after repair. also it aims to delay crack initiation and growth in riveted or bolted structures. moreover, the modelling allows to highlighting the effect of these factors and their interactions on the residual stresses profiles. keywords. cold expansion; residual stress; prediction; experimental design; interaction; fatigue life. citation: laredj, m., miloudi, a., benguediab, b., lousdad, a., prediction and optimizing residual stress profile induced by cold expansion in aluminum alloys using experimental design, frattura ed integrità strutturale, 48 (2019) 193-207. received: 31.10.2018 accepted: 18.02.2019 published: 01.04.2019 copyright: © 2019 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. mailto:laredjmustapha@gmail.com mailto:miloudidz@yahoo.fr mailto:a_lousdad@yahoo.com http://www.gruppofrattura.it/va/48/2241.mp4 m. laredj et alii, frattura ed integrità strutturale, 48 (2019) 193-207; doi: 10.3221/igf-esis.48.21 194 introduction atigue cracks in mechanical structures primarily begin at stress concentration tips such as rivet holes and / or geometric discontinuities. hole cold expansion process is a very useful technique to extend fatigue life of structural assemblies. hence, in the case of crack detection, a hole in the front of the crack will be created to reduce the concentration of local stresses leading to a delay of the propagation. this improvement is explained by lower notch sharpness and the presence of residual stresses introduced by the plastic deformation at the edge of the hole [1, 2]. hence, the role of compression residual stresses is to reduce the effective stress level. cold expansion hardening (ceh) is a process used in the aerospace industry to extend the life of riveted and bolted structures by applying a high field of tangential compressive residual stresses. consequently, residual stresses have a major role for determining the surface micro-cracks growth rate and thus on fatigue lifetime. therefore residual stress analysis is a mandatory step in the design and manufacture of components. numerous studies based on experimental measurements [3, 4] or on numerical finite elements calculations [5, 6, 7, and 8] studied separately the influence of several factors on the technique of cold expansion hardening. j vogvell [2] simulated the expansion of a hole by a steel ball assumed undeformable on an aluminium 7075 t6 alloy plate. numerical modelling is done using 3d finite elements. three cases of plate thicknesses (2. 5and 10 mm) and three degrees of expansion (2, 4 and 6%) were studied. the authors concluded that, increasing the degree of expansion does not have a significant influence on fatigue life. contrary, amrouche and al [9] performed fatigue tests with the following degrees of expansion 1.7, 3.4 and 4.3% to study the influence of the number cycles leading to fatigue crack initiation for aluminium alloy 6082 t6 plate. the authors showed that the increase of the expansion degree leads to the retardation of crack initiation. in at özdemir’s work [10] fatigue tests were also carried out on aluminium alloy t651 8090 plates and aluminium alloy 7050 plate of thickness 1.6 and 5 mm respectively with 4% expansion degree in addition to aluminium alloy 7010 of 19 mm thickness and 3% of expansion degree to investigate the effect of the plate thickness. they showed that the 3% expansion for the 19 mm thick plate gives a greater compression stress comparing to thinner plates of 1.6 and 5 mm with the expansion of 4%. salvati and all [11] proposed eigenstrain field to the evaluation of residual strain within an additively anufactured nickel superalloy compressor blade that was subsequently subjected to shot peening treatment. eigenstrain variation is described by a continuous function of the distance from the boundary of the bject in a twodimensional model of its cross‐section. the authors showed that eigenstrain method for the in‐plane strain reconstruction was successfully applied to a real case study of compressor blade section. the eigenstrain profile induced by shot peening was assessed, and the predicted residual elastic strain distribution compared to experimental measurements. acceptable overall agreement was found. dewald and hill [12] presents a methodology for predicting the residual stress within threedimensional parts caused by laser peening treatment. the eigenstrain is input into the finite element model in stated treatment areas where laser peening is applied. the authors concluded the model has a fair amount of agreement with the measurements over the range of geometry studied. but there is disagreement between the measurements and the predictions with respect to the relation between radius size and depth of compressive residual stress for the corner radius geometry. renan and all [13] predict that the residual stresses arising from cold expansion by using two different finite element (fe) approaches and compare the obtained results to measurement data obtained by the contour method. the first fe approach considers process modeling, and includes elasticplastic behaviour. the second approach is based on the eigenstrain method and includes only elastic behavior. the results obtained from the fe models are in good agreement with one another as well as with the measurement data. the eigenstrain method was found to be very useful, providing generally predictions of residual stress. both models were found to give reasonable residual stress estimates. thus, the model results give confidence to estimate the residual stress. the residual stresses produced by cold expansion hardening depend on several intrinsic or extrinsic factors of the material which complicate and make the modelling of the stresses difficult. the present work deals with the influence of three factors that affect cold expansion hardening process and the distribution of stresses around a hole using 3d finite element model. the main parameters analyzed in this work are the thickness, the degree of expansion as well as the yield strength. the experimental design methodology is used for modelling and predicting residual stresses in the input face. the approach allows the determination of the values of these factors which ensure the improvement of the service life. f m. laredj et alii, frattura ed integrità strutturale, 48 (2019) 193-207; doi: 10.3221/igf-esis.48.21 195 process choice any cold expansion approaches have been developed and investigated according to the diverse expansion tools. the most widely used methods in practice are: ball expansion, direct mandrel expansion, hole edge expansion and split sleeve expansion processes [14, 15, 05]. in the present work the expansion by a mandrel with sleeve has been chosen in order to avoid direct contact between the workpiece and the mandrel to prevent both mandrel wear and the damage of hole surface. the cold expansion hardening is carried out by inserting a mandrel with a sleeve through the hole of a tool (a conical mandrel with sleeve) of greater diameter “d” than the initial diameter of the hole “d” as shown in figure (1). split sleeve cold expansion is accomplished by pulling a tapered mandrel pre-fitted with a lubricated split sleeve through a hole. the function of the disposable split sleeve is to reduce mandrel pull force, ensure correct radial expansion of the hole, preclude damage to the hole and allow one-sided processing [16]. the expansion is obtained by interference of the initial hole diameter (d) and the maximum mandrel diameter (d) taking into account the sleeve thickness (t). the degree of expansion is defined as a percentage by the following expression: ( )2 % 100 d t d de d + − =  (1) d : maximum mandrel diameter t : thickness of the sleeve d : hole diameter before hardening figure 1: drilling of cold expansion process overview [17]. model description and mechanical properties everal studies have been conducted to compare the results of 2d and 3d hole hardening finite element models [15, 05, 18]. all these previous studies consider the process as a generated axisymmetric stress state. a conclusion consensus of the different researchers’ works that two-dimensional finite element models predict quietly different tangential residual stresses when compared to the surface results of 3d models. a 3-d model was preferred to the axisymetric 2-d one because of rectangular plate shape. this observation justifies the 3d models to simulate this phenomenon. the models consisted of square plates with 70 mm length, three thickness 3, 5 and 7mm with 6 mm diameter hole centrally located. models had undergone a cold expansion hardening by mandrel with sleeve elastically deformable. the sleeve wall thickness is 0.25 mm and the mandrel diameter has a variable diameter depending on the degree of expansion (2, 4 and 6%). the expansion was simulated using the commercial code abaqus 11 [19]. the materials used in our 3d simulation work are aluminum alloys 6005-t6, 6082-t6 and au 4g. the mandrel is supposed to be perfectly rigid. the sleeve has been modeled as an elastic body with the steel material properties (young's modulus of 220 gpa and a poisson's ratio of 0.3). the friction coefficient between the contact surfaces is taken equal to 0.1. the friction is generally present between the handle and the plate but often neglected between the mandrel and the handle since it is lubricated. m s m. laredj et alii, frattura ed integrità strutturale, 48 (2019) 193-207; doi: 10.3221/igf-esis.48.21 196 a displacement in the z direction is applied from the input face to the output face on the mandrel to simulate the expansion process. the johnson-cook is used for the numerical simulation in order to take into account the parameters of the dynamic hardening and the speed of plate deformation, the johnson-cook parameters of the three aluminum alloys are shown in table (1). a(mpa) b(mpa) n c m tf(k) ta(k) . p al au 4g [20] 350 440 0.41 0.0083 1 911 293 1 al 6005-t6 [21] 270 134 0.52 0.015 0.859 893 293 1 al 6082-t6 [22] 428 327 1.008 0.00747 1.31 855 293 1 table 1: johnson-cook parameters. with: a, b and n: are constants that describe hardening m = hardening exponent tf : melting temperature ta: ambient temperature . p  : is the reference strain rate figure 2: finite element model boundary conditions: (b) plane xy; (c) plane yz. m. laredj et alii, frattura ed integrità strutturale, 48 (2019) 193-207; doi: 10.3221/igf-esis.48.21 197 due to the symmetry with respect to the x-z, y-z planes, only a quarter of the specimen and sleeve are considered. this allows a much greater mesh refinement around the hole and reduces the required computational resources. a highly refined fe model is required to ensure convergence of the given solution at the area of high located deformation around the hole. for this reason, a non-uniform mesh distribution was used. smaller elements were taken near the entrance and exit surfaces and longer elements away from the hole. the workpiece was discretized using linear brick elements (c3d8r) with reduced integration. this type of element is adapted in the case of elasto-plastic calculations and also is well conjugated with contact elements. in the case of a thickness equal to 3 mm, this latter is divided into 10 elements. the model mesh is illustrated in figure (2-a) consisting of 17749 elements and 23043 nodes. surface to surface contacts were used to represent the interaction between the different elements (hole surface – sleeve and sleeve – mandrel). figures (2-b-c) illustrate the geometry and the boundary conditions of the 3d fea contact model of the mandrel and the handle. figure (3) shows the residual stress field with a 3.36% cold expansion degree for the 6005t6 aluminum alloy with a 5 mm thickness. the deformed zone generates compressive residual stresses at the edge of the hole. we find that the residual circumferential stresses are not uniform through the thickness. hence, figures (4) shows that the level of compressive residual stresses on the entrance face is lower than that at mid-thickness. the stress varies between a maximum value of approximately 320 mpa around the hole in the exit face and with minimum value of 140 mpa at the entrance face. the difference in the residual stresses in the two specimen faces is explained by the level of retained expansion combined to the material volume carried by the mandrel movement during the cold expansion process. this result is in agreement with the works of liu [23] and elajrami [24]. these results lead to conclude that the entrance face is less resistant to fatigue than the exit face. therefore, we chose the study of the residual stresses in the entrance face. figure (5) illustrates an example of typical tangential residual stress distribution around an expanded hole. the important factors of the residual results profile (outputs simulations results) are summarized in table (2). figure 3: distribution of circumferential residual stresses on the three faces 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 -400 -300 -200 -100 0 100 entry face mid-thickness exit face distance from hole edge(mm) r e s id u a l ta n g e n ti a l s tr e s s ( m p a ) figure 4: tangential residual stress distribution at three different planes of the plate m. laredj et alii, frattura ed integrità strutturale, 48 (2019) 193-207; doi: 10.3221/igf-esis.48.21 198 figure 5: typical distribution of tangential residual stress around an-expanded hole factors outputs results 1 crseh compressiveresidual stress at the edge of the hole 2 mcrs maximum compressive residual stresses 3 dmcrs the depth of the maximum compressive residual stress 4 crsz the compressive residual stress zone 5 mt the maximum tension 6 pdz the plastic deformation zone table 2: output simulations results experimental design approach he experimental design is necessary to identify relevant information to establish a relationship between the input variables thickness (t), cold expansion (ce) and yield strength (ys)) and the output variables (crseh, mcrs, dmcrs, crsz, mt and pdz). in order to predict the amount of residual stresses each parameter was tested at three different levels: the thickness (3,5,7 mm), cold expansion (2,4, 6) and yield strength (270, 349.25 ,428.5 mpa). the responses were calculated using the finite element method. the experimental design matrix of the experiments is given by modde 5.0 (modeling and design) software [25-26]. we have adopted a complete experimental design [27] of three factors at two levels. the mode of the experimenter is quadratic and has the following form: 3 3 2 0 1 1 3 1 i i ij i j ii i i i j i y a a x a x x a x e =    = = + + + +   (2) where i, j vary from 1 to the number of process variables (3), y is the response of the process. the coefficient is the average of all the responses for the whole experiment; the coefficients represent the effect of the variable and are the regression coefficients that represent the effects of the interactions of the variables and e is the experimental error. the polynomial model proposed by modde 5.0 describes the variations of the response function to the factors (ys), (ce) and (t) is of the following form: 2 2 2 0 1 2 3 12 13 23 11 22 33response . . . a a t a ys a ce a t ys a t ce a ys ce a t a ys a ce= + + + + + + + + + (3) t m. laredj et alii, frattura ed integrità strutturale, 48 (2019) 193-207; doi: 10.3221/igf-esis.48.21 199 the experimental plans used in this study are a complete quadratic plan which a mathematical model of the second degree. by removing the non-significant effects we obtain the following mathematical models: ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) 2 2 2 114.75 5.56 38.64 15.46 9.86 . 13.59 . 7.7 9.08 20.38( ) crseh t ce ys t ys ce ys t ce ys = − − + − + + + + + + (4) ( ) ( ) ( ) ( ) ( ) ( ) 2 2 238.07 21.49 8.11 26.34 7.43 . 12.82 5.9 16.15( )mcrs t ce ys t ce t ys= − + + − + + + + + (5) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) 2 2 2 1.44 0.08 0.49 0.2 0.08 . 0.03 . 0.02 4 0.04( )dmcrs t ce ys t ce ce ys t ce ys= + + − + − + − + (6) ( ) ( ) ( ) ( ) ( ) ( ) ( ) 2 2 2 3.38 0.16 0.43 0.29 0.14 . 0.11 0.17 0.1( )crsz t ce ys t ce t ce ys= + + − + − − − (7) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) 2 2 2 47 7.5 14.23 8.05 2.15 . 4.17 . 2.13 0.32 0.3( )mt t ce ys t ce t ys t ce ys= − + + − + + + − (8) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) 2 2 2 3.88 0.09 0.5 0.21 0.13 . 0.08 . 0.03 . 0.019648 0.13 0.05( ) pdz t ce ys t ce t ys ce ys t ce ys = + + − + − + + − − − (9) analysis of the results rom the graphical analysis we can determine the influence of each factor on the response by plotting the response variation according to these factors. the evolution of surface residual stresses at the edge of the hole after expansion as a function of the thickness (t), the degree of expansion and the yield strength are presented respectively in the figures (6-a), (6-b) and (6-c). the analysis of figure (6-a) shows that an increase in the thickness causes an increase of the residual stresses (absolute value) at the edge of the hole after expansion crseh. figure 6: the compressive residual stress at the edge of the hole after expansion from the results one can deduct the existence of the critical thickness (t = 4.92mm) of the material and beyond this value the crseh is almost independent of this geometrical parameter. the result show a good agreement with v. nigrelli et al work [28] which illustrated through fe analysis carried out on plate thicknesses of 3, 5 and 10 mm considering a f m. laredj et alii, frattura ed integrità strutturale, 48 (2019) 193-207; doi: 10.3221/igf-esis.48.21 200 constant hole diameter d = 5.8 mm. the authors concluded that the increase of thickness leads to an increase of residual compression stresses at the edge of the hole. in the following the influence of the (ce) on the crseh is investigated. this study was carried out for an expansion degree ranging from 2 to 6. figure (6-b) illustrates the variation of the crseh as function of the (ce). we found that, the stresses decrease with the increase of the expansion degree (absolute value). moreover, the effect of yield strength according to the variation (crseh) is analysed and illustrated in figure (6-c). this figure shows that an increase in the yield strength reduces the crseh after expansion. the process is valid between [240340 mpa]. however, in the range [340-430 mpa] the (crseh after the expansion increases slightly depending on the value of yield strength. it should be noted that no experimental or numerical study had examined the effect of the degree of expansion and the yield strength on crseh. regarding the second factor (mcrs), which represents an important parameter for the residual stress profiles, we studied the variation this factor with respect to the (t), (ce) and (ys). the analysis results are illustrated respectively in figures (7-a), (7-b) and (7-c). we find that an increase of the thickness and the degree of expansion lead to reducing the maximum compressive residual stresses (in absolute value) which is less marked in the case of the degree of expansion. hence, the increase of these parameters leads to the increase of the lifetime of the structure. these results are in agreement with the findings research of z. semari and j. vogwell [29-2] concluding that the compression stresses are inversely proportional to the degree of expansion. unlike the other effects, we found that the increase of the yield strength causes an increase of the mcrs (in absolute value) which confirms the conclusions of others authors [30 .1], performing several tests and simulations on aluminium alloys and some steels. figure 7: the variation of the maximum compressive residual stress after expansion in the following section, we have studied the effects of the (t), (ce) and (ys) on the depth variation of the maximum compressive residual stress. the examination of the figure (8a), permit us to notice that the thickness has a minor influence on the compressive residual stress. in fact the increase of thickness by 133 % leads to an increase of 7.05% in the (dmcrs). the figure (8-b) shows clearly that the degree of expansion has a higher influence on dmcrs. according to the figure (8c), we notice that the increase of the yield strength leads to a decrease of dmcrs. in this part, we are interested in studying the evolution of other important parameter on residual stress profiles which is the compressive residual stresses zone. the results in the figure (9-a) indicate that an increase of the thickness leads to an increase of crsz. consequently, the use of thicker structure conducts to an important improvement of lifetime. therefore we can also indicates that there exist a critical thickness (t = 4.93 mm) beyond which the crsz is almost independent of this geometrical parameter. the results obtained are consistent with the work of v. nigrelli, a.t. özdemir and [28-10]. regarding the degree of expansion, we notice that it had an important effect on the compressive residual stresses zone. these results are in agreement with the results of a.amrouche and m. su [32, 31] who found that the degree of expansion has a significant influence on crsz. also, the authors had shown, based on experimental measurements and finite element numerical calculations study that the growth of crsz stops at ce = 5%. it can be interpreted as the convergence difficulty of 3d calculation. on the other hand, beyond the degree of expansion value 4 the influence of the m. laredj et alii, frattura ed integrità strutturale, 48 (2019) 193-207; doi: 10.3221/igf-esis.48.21 201 latter on crsz is insignificant. consequently, an increase in the degree of expansion by 50% leads only to an increase of 7.46% of the compressive residual stresses zone. figure 8: the depth variation of the maximum compressive residual stress in figure (9-c) illustrates the effect of the yield strength on crsz. contrary to the other parameters, an increase in the yield strength leads to a decrease of the compressive residual stresses zone. in fact, a 72% increase in the yield point leads to a 20% decrease in the crsz. it had been demonstrated that the mechanical characteristics have an influence on the distribution of the circumferential residual stresses. several investigations carried by z. semari and m. su [29-31] have focused on the study of the effect of the mechanical characteristics on residual stress profiles. therefore all studies agree that the increasing of the yield strength causes a decrease in crsz. figure 9: the variation of the compressive residual stresses zone the evolution of the plastic deformations zone as a function of the (t), (ce) and (ys) are presented respectively in the figures (10-a), (10-b) and (10-c) . figure (10-a) illustrates the evolution of the plastic deformations zone with respect to the thickness. we note that the increase of the thickness causes a small increase of pdz. these results are in agreement with the work of v. nigrelli [28]. figure (10-b) illustrates the effect of the degree of expansion on the pdz. we see that an increase of the expansion degree leads to an increase of the plastic deformations zone which provokes the deceleration of the propagation kinetics of the defects and thus the increase of the lifetime of the structures. these results are in accordance with the work results of z. semari [29]. m. laredj et alii, frattura ed integrità strutturale, 48 (2019) 193-207; doi: 10.3221/igf-esis.48.21 202 figure (10-c) shows the variation of the plastic deformations zone as function of the yield strength. according to this figure we note that the yield strength increase results a small decrease of pdz which is verified by the results of m. su and al [31] by performing expansion by a numerical simulation for different degrees of expansion: 1.7, 3.4, 4.3, 5, and 6% on aluminium alloys 6082, 6005 and steel a42. they have demonstrate that crack initiation can be obtained by a lower number of cycles in the case of the yield strength increasing than by the increase of the degree expansion. figure 10: the plastic deformations zone in the last analysis we study the evolution of the maximum tension according to the three previous parameters. in figure (11-a) we observe that the decrease in the mt caused by increasing of thickness. thus, the thicker structure presents the lower mt. on the other hand, in figures (11-b) and (11-c) we observe that, an increase of the degree expansion and the yield strength leads to an increase of the maximum tension. this effect is more marked in the case of the expansion degree. figure 11: the variation of the maximum tension after the expansion in the first case of interactions, the parameters variation of residual stress profiles according to the three factors: (ce), (ys) and (t) is investigated. therefore, the plan calculates the effects of both factors and their interaction using a regression model. in this study, we only present the prediction curves shown in the figures (12, 13) which show the influence of the most important points in the residual stress profile enumerated as following: • the maximum compressive residual stresses • the compressive residual stresses zone. figure (12) shows the predicted response of the mcrs according to the variation of the three factors. the investigation of this curve shows that, to produce a maximum value of compressive residual stress (in absolute value) it is necessary to m. laredj et alii, frattura ed integrità strutturale, 48 (2019) 193-207; doi: 10.3221/igf-esis.48.21 203 maintain value of the degree of expansion between 3 and 4%, the thickness between 3 and 6 mm and to keep the yield strength between 345 and 430 mpa. figure 12: prediction of maximum compressive residual stress as a function of the three factors in the last of interaction analysis, we focus on the compressive residual stress zone variation according to the three factors as shown in figure (13). the results clearly show that the increase of the degree of expansion and the thickness cause to a larger area of the crsz. however the reduction of the yield strength leads to an increase of this zone. figure 13: prediction of the compressive residual stresses zone. by introducing the results in the modde 5.0 software to examine the different effects, the results given in figs. 14 and 15 corresponding respectively to the maximum compressive residual stress and the compressive residual stress zone were obtained. the effects of factors are presented using a bar graph. this diagram gives the effects in descending order of their importance in absolute value. figure 14: effects of factors on mcrs. the analysis of these figures shows that the classification of dominant factors on the maximum compressive residual stresses is as the following: (ys), (t) and (ce). on the other hand, for the case of the compressive residual stresses zone and the other points of the residual stress profile, the order of dominant factors are as following: (ce), (ys) and (t). m. laredj et alii, frattura ed integrità strutturale, 48 (2019) 193-207; doi: 10.3221/igf-esis.48.21 204 hence, we note that the effect of the degree of expansion on the improvement of the service life is more significant than the yield strength and the thickness. from the obtained models we can determine the optimal values of the various factors (t), (ce) and (ys) to predict the residual stresses obtained from factor values. figure 15: effects of factors on crsz. according to the analysis performed by the "modde5.0" software we can verify easily the optimal points of the responses. consequently, according to the table (3) these values are obtained by maximizing the residual stress profile. the process can be carried out by the experiment which comprises the values of the thickness equal to 4.93 mm, the degree of expansion which is equal to 4.04 and the yield strength which is equal to 347.082 mpa. these findings are very close to the results of a. amrouche and m. su [32-31] showing through an experimental study that the existence of critical degree of expansion ce = 4.3% increases the lifetime by about 3.5 times comparing to the drilling without expansion. on the other hand, beyond this critical value the expansion process becomes detrimental on lifetime and the crack propagation rate after its initiation. thickness ce % ys crseh mcrs dmcrs drsz mt pdz 6.6328 2.331 251.191 62.6207 156.727 1.2626 2.9075 13.5694 3.4623 6.3866 5.7463 313.173 52.3595 174.271 2.2156 3.999 51.4983 4.5646 4.8038 2.8226 358.838 143.368 248.403 0.9815 2.835 39.2896 3.3622 6.6137 5.876 311.975 45.0092 163.664 2.3023 4.0605 51.2529 4.6291 4.939 4.0448 347.082 115.912 241.729 1.4309 3.3315 48.4612 3.8708 7 5.5078 250.008 10.0388 112.273 2.5006 4.2592 34.2554 4.7822 5.5529 2.0674 368.755 161.045 239.242 0.6452 2.3531 32.5068 2.8971 4.5671 4.2187 357.05 109.586 -248.24 1.4403 3.2879 52.9058 3.869 table 3: optimal values of residual stress profiles the validation of the models is done by comparing the results obtained by simulations and the predicted models. table (4) illustrating the comparison of an expansion of a 5mm thick plate with a 4% degree of expansion made of aluminium alloy 6082-t6. figure 16 shows a good correlation between residual stress profiles obtained by simulation and predicted models. m. laredj et alii, frattura ed integrità strutturale, 48 (2019) 193-207; doi: 10.3221/igf-esis.48.21 205 response predicted value numerical value difference % crseh -110 -100 10% mcrs -248 -238 4.2% dmcrs 1.286611 1.21198 6.15% crsz 2.987402 2.78 7.46% mt 54.74 62 11.7 % pdz 3.61 3.333 8.47 % table 4: predicted and numerical values. figure16: predicted and numerical values of residual stress this small difference between the simulation and the predicted models confirms the excellent effectiveness of the mathematical models established by the experimental design method. conclusion n this work, the study focuses to establish and validate a predictive model of residual stresses generated from cold hardening. thus the assessment allows industrialists to predicting the fatigue lifetime duration of riveted or bolted structures. an experimental setup was used to points out the effectiveness of degree of expansion, thickness of the part as well as the yield strength on the residual stresses profiles. the application of numerical with the experimental method allows determining the optimal values of the different factors to predict the residual stress profiles for any values of the factors. by proposing a mathematical model that takes into account these factors the latter allowed us to obtain a better description of the residual stress profile. the validation of the model confirms the excellent quality of the mathematical model established by the experimental design method. based on our assessment, the effect of the degree of expansion on the improvement of the service lifetime is clearly significant than the yield strength and the thickness. therefore, the classifications of impact parameters are in the following order: degree of expansion, the yield strength and the thickness of the structure. i m. laredj et alii, frattura ed integrità strutturale, 48 (2019) 193-207; doi: 10.3221/igf-esis.48.21 206 references [1] chakherlou, t.n. and vogwell, j. (2003). the effect of cold expansion on improving the fatigue life of fastener holes, engineering failure analysis, 10, pp. 13–24 [2] vogwell, j., chakherlou, t.n. and minguez, j.m. (2001). the effect of cold expansion on fatigue resistance of fastener holes, the 10 th international congress of fracture. [3] caron, i., fiori, f., mesmacque, g., pirling, t., su, m. (2004). expanded hole method for arresting crack propagation: residual stress determination using neutron diffraction, physica b 350 pp. e503–e505. doi: 10.1016/j.physb.2004.03.132. [4] stefanescu, d., santisteban, j.r., edwards, l. and fitwpatrick, m. e. (2004). residual stress measurement and fatigue crack growth prediction after cold expansion of cracked fastener holes, journal of aerospace engineering, 17 pp. 91-97. doi: 10.1061/(asce)0893-1321(2004)17:3(91) [5] papanikos, p., and meguid, s.a. (1998). three dimensional finite element analysis of cold expansion of adjacent holes, international journal of mechanical science, 40, pp. 1019-1028 [6] yongshou, l., shao, x., liu, j. and yue, z. (2010). finite element method and experimental investigation on the residual stress fields and fatigue performance of cold expansion hole, materials and design, 31, pp. 1208–1215. doi: 10.1016/j.matdes.2009.09.031 [7] cheol, k., dae-jin, k., chang-sung, s. and won-ho, y. (2004). finite element analysis of the residual stress by cold expansion method under the influence of adjacent holes, journal of materials processing technology, pp 986–991. doi: 10.1016/j.jmatprotec.2004.04.271 [8] aghdam, a.b., chakherlou, t.n. and saeedi, k. (2010). an fe analysis for assessing the effect of short-term exposure to elevated temperature on residual stresses around cold expanded fastener holes in aluminum alloy 7075-t6.materials and design, 31, pp. 500–507. doi:10.1016/j.matdes.2009.06.024 [9] amrouche, a., mesmacque, g., garcia, s. and talha, a. (2003), cold expansion effect on the initiation and the propagation of the fatigue crack, international journal of fatigue, 25, pp. 949–954. doi:10.1016/s0142-1123(03)00127-0. [10] özdemir, a.t. and hermann, r. (1999). effect of expansion technique and plate thickness on near-hole residual stresses and fatigue life of cold expanded holes, journal of materials science, 34. pp. 1243 – 1252. [11] salvati, e., lunt, a.j.g., ying, s., sui, t., j.zhang, h., heason, c., baxter, g. and korsunsky, a.m. (2017). eigenstrain reconstruction of residual strains in an additively manufactured and shot peened nickel superalloy compressor blade, journal of computer methods in applied mechanics and engineering, 320, pp 335-351. doi: 10.1016/j.cma.2017.03.005. [12] dewald, a t., hill, m r. (2008) eigenstrain-based model for prediction of laser peening residual stresses in arbitrary three-dimensional bodies part 2: model verification, journal of strain analysis for engineering design, 44, pp.13-27. doi: 10.1243/03093247jsa420. [13] renan, l., ribeiro and michael, r. hill. (2017). residual stress from cold expansion of fastener holes: measurement, eigenstrain, and process finite element modeling, j. eng. mater. technol 139(4), 041012, paper no: mats-17-1032. doi: 10.1115/1.4037021. [14] matos, p. d., moreira, p., camanho, p. and de castro, p. (2005). numerical simulation of cold working of rivet holes, finite elements in analysis and design, 41, pp. 989-1007. [15] kang, j., johnson, w.s. and clark, d.a. (2002). three-dimensional finite element analysis of the cold expansion of fastener holes in two aluminum alloys, journal of engineering materials and technology, 124, pp. 140-145. [16] bernard, m., bui-quoc, t., julien, d. and forgues, sa. (1993). feasibility study of cold expansion process modelling. canadian department of defence, research and development air, cont. rep. w8477-1-ac89101-ss; [17] burlat, m., julien, d., lévesque, m., bui-quoc, t. and bernard, m. (2008). effect of local cold working on the fatigue life of 7475-t7351 aluminium alloy hole specimens, engineering fracture mechanics, 75, pp. 2042–2061. doi: 10.1016/j.engfracmech.2007.10.011 [18] mahendra babu, n., jagadish, t., ramachandra, k. and sridhara, s. (2008). a simplified 3-d finite element simulation of cold expansion of a circular hole to capture through thickness variation of residual stresses, engineering failure analysis, 15, pp. 339-348. [19] abaqus standard user's manual, karlsson and sorensen, (2005). [20] laroche, y. and narcisse, j. (2011) rapport : projet de fin d’etude simulation numérique de l’usinage avec abaqus, polytech tours. https://www.sciencedirect.com/science/article/pii/s0045782516318461#! https://www.sciencedirect.com/science/article/pii/s0045782516318461#! https://www.sciencedirect.com/science/article/pii/s0045782516318461#! https://www.sciencedirect.com/science/article/pii/s0045782516318461#! https://www.sciencedirect.com/science/article/pii/s0045782516318461#! https://www.sciencedirect.com/science/article/pii/s0045782516318461#! https://www.sciencedirect.com/science/article/pii/s0045782516318461#! https://www.sciencedirect.com/science/article/pii/s0045782516318461#! https://www.sciencedirect.com/journal/computer-methods-in-applied-mechanics-and-engineering https://doi.org/10.1016/j.cma.2017.03.005 https://journals.sagepub.com/author/dewald%2c+a+t https://journals.sagepub.com/author/hill%2c+m+r https://doi.org/10.1243%2f03093247jsa420 http://materialstechnology.asmedigitalcollection.asme.org/solr/searchresults.aspx?author=renan+l.+ribeiro&q=renan+l.+ribeiro http://materialstechnology.asmedigitalcollection.asme.org/solr/searchresults.aspx?author=michael+r.+hill&q=michael+r.+hill m. laredj et alii, frattura ed integrità strutturale, 48 (2019) 193-207; doi: 10.3221/igf-esis.48.21 207 [21] clausen, a. h., borvik, t., hopperstad, o. s. and langseth, m (2003) impact resistance of aa6005 panels , journal . iv france 110, doi: 10. 1051/p4 : 20030774. [22] jaspers, s.p.f.c., dautzenberg, j.h. (2002). material behavior in conditions similar to metal cutting: flow stress in the primary shear zone, journal of materials processing technology, 122, pp. 322-330. [23] liu, j., shao, x.j., liu, y.s. and yue, z.f (2008). effect of cold expansion on fatigue performance of open holes, materials science and engineering, a 477, pp. 271–276. doi:10.1016/j.msea.2007.05.034 [24] elajrami, m., miloud, r., melouki, h. and boukhoulda, f. (2013) numerical study of the effect of doublecold expansion of rivet hole on the residual stresses distribution, journal of engineering manufacture, 227(4), pp. 621–626. doi: 10.1177/0954405412472179. [25] eriksson, l., johansson, e., kettaneh-wold, n., wikström, c. and wold, s., (2000). design of experiments: principles and applications, stockholm, learnways ab. [26] https://www.dynacentrix.com/telecharg/modde/livredoe.pdf. [27] modde 5.0, modelling and design, umetrics ab, umea, sweden. (1999). [28] medjdoub, s. and bouadjra, b., (2018). optimization of the geometrical parameters of bonded composite wrap for repairing cracked pipelines, j. frattura ed integrità strutturale, 46, pp. 102-112; doi: 10.3221/igf-esis.46.11. [29] nigrelli, v. and pasta, s. (2008). finite-element simulation of residual stress induced by split-sleeve cold-expansion process of holes, journal of materials processing technology, 205, pp. 290–296. doi:10.1016/j.jmatprotec.2007.11.207. [30] semari, z. influence des perçages, avec et sans expansion, en fond de fissure sur la propagation des fissures de fatigue. cas des alliages d’aluminium a6082 et a6005. etude expérimentale et numérique,thèse de doctorat, jui 2013, université des sciences et technologies de sidi bel abbés. [31] semari, z., aid, a., benhamena, a., amrouche, a., benguediab, m., sadok, a. and benseddiq, n. (2013). effect of residual stresses induced by cold expansion on the crack growth in 6082 aluminum alloy, engineering fracture mechanics, 99, pp. 159–168. doi: 10.1016/j.engfracmech.2012.12.003. [32] matos, p.f.p., mcevily, a.j., moreira, p.m.g.p. and castro, p.m.s.t. (2007). analysis of the effect of cold-working of rivet holes on the fatigue life of an aluminum alloy.international journal of fatigue, 29, pp. 575–586. doi: 10.1016/j.ijfatigue.2006.04.004 [33] man, s. (2005). etude de l’influence et de l’optimisation du degré d’expansion à froid dans les mécanismes de réamorçage d’une fissure : etude numérique et expérimentale, thèse de doctorat, université des sciences et technologies de lille. [34] amrouche, a., su, m., aid, a. and mesmacque, g.(2008). numerical study of the optimum degree of cold expansion: application for the pre-cracked specimen with the expanded hole at the crack tip, journal of materials processing technology, 197, pp. 250–254. doi: 10.1016/j.jmatprotec.2007.06.030. microsoft word numero_46_art_33 h. zhu et alii, frattura ed integrità strutturale, 46 (2018) 361-370; doi: 10.3221/igf-esis.46.33 361 stress performance of embedded carbon fiber reinforced plastics plate consolidated reinforced concrete structure hua zhu school of civil engineering, yancheng institute of technology, yancheng, jiangsu, 224051, china huazhu74@126.com abstract. with the development of the building industry, various novel building materials have emerged. modern buildings requires higher on performance of building materials, and the performance of old buildings has not been able to keep up the pace of the times. extending the service time of old buildings by repairing and reinforcing is inevitable. in this study, 10 reinforced concrete beams including 2 ordinary reinforced concrete beams and 8 carbon fiber reinforced plastics (cfrp) plate reinforced test beams were manufactured. three-dimensional finite element model was established using finite element software to simulate and compare the stress performance of the strengthening beams with different number of cfrp plate, size, number of groove and shear span ratio. the results demonstrated that the ultimate carrying capacity of the embedded cfrp plate reinforced beams was obviously superior to that of the ordinary reinforced concrete beams; two plates and two grooves were appropriate; the larger the shear span ratio, the better the bearing performance and the smaller the deformation. cfrp plate consolidated reinforced concrete can effectively stabilize buildings which need repairing and reinforcement. keywords. cfrp plate consolidation; reinforced concrete; threedimensional finite element model; stress performance. citation: zhu, h., stress performance of embedded carbon fiber reinforced plastics plate consolidated reinforced concrete structure, frattura ed integrità strutturale, 46 (2018) 361-370. received: 25.07.2018 accepted: 12.09.2018 published: 01.10.2018 copyright: © 2018 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. introduction ith the acceleration of urbanization, the performance of many old buildings has not been able to satisfy the requirements of the society. therefore reinforcement is needed to recover their performance. the emergence of novel building materials provides a better choice for building reinforcement. fiber reinforce plastic (frp) has favorable mechanical performance and corrosion resistance performance. embedded carbon fiber reinforced plastics (cfrp) plate reinforcement is a prospective method in the reinforcement of reinforced concrete beams. motavalli et al. [1] made multi-aspect studies on the development of cfrp plate in the field of concrete. they developed w http://www.gruppofrattura.it/va/46/33.mp4 h. zhu et alii, frattura ed integrità strutturale, 46 (2018) 361-370; doi: 10.3221/igf-esis.46.33 362 a gradient prestressing technique without end anchorage plates and investigating confinement technique using nonlaminated thermoplastic cfrp straps. raoof et al. [2] compared the flexural properties of textile-reinforced mortar (trm) versus fibre-reinforced polymers (frp) and found that frp was more superior in improving the flexural bearing capacity of reinforced concrete beams than trm through experiments. to analyze the effect of cfrp in enhancing the carrying capacity of beams during bending, khelifa et al. [3] developed a numerical program to simulate the bending behaviors of beams. rezazadeh m et al. [4] designed an experimental procedure to evaluate the influence of prestress technology on the bending performance of the embedded cfrp plate consolidated reinforced concrete beams and found that prestressing could improve the load carrying capacity corresponding to the concrete cracking and steel yielding initiations. after reviewing the articles concerning about cfrp consolidated reinforced concrete beams and reinforced concrete slab, jumaat et al. [5] put forward a simple cfrp reinforcement method to strengthen the negative moment regions of continuous t beams and attempted to address an important practical issue that is encountered in strengthening the negative moment region of rc continuous t beam. dias et al. [6] studied the effect of cfrp in reinforcing reinforced concrete beams in aspects of the percentage and inclination of cfrp laminates and percentage of stirrups and found that embedded cfrp had better efficacy in strengthening reinforced concrete beams. in this study, the finite element analysis software ansys was used for simulation, and the simulated values were compared with the test values to verify the effectiveness of the model; moreover the stress performance of cfrp plates in different structures was also simulated using finite element model to analyze the influence of different number of cfrp plate, grooving mode and shear span ratio on beams and explore the best reinforcement way of embedded cfrp plate. embedded cfrp plate rp which is composed of fiber materials and resin is prone to be installed on irregular surface and has advantages of higher strength and strong corrosion resistance [7, 8]. it was found that the application of frp can recover or improve the original strength of beams [9]. frp can be divided into cfrp, glass fiber reinforced plastics (gfrp), aromatic polyamide fiber reinforced plastics (afrp), etc. cfrp has stronger tensile and bending resistance compared to other materials. frp reinforcement includes frp surface pasting method and frp embedded reinforcement. the procedures of embedded reinforcement are as follows. firstly, concrete cover was grooved. after the dust in the groove was cleaned, half of the groove was filled with cementing material, for example, resin. then frp was added and pressed. figure 1: the schematic diagram of embedded reinforcement. frp reinforcement can effectively strengthen the bending and shear resistance performance of reinforced concrete beams [10], which has many advantages compared to other reinforcement methods. embedded frp avoids contact with the outside world, i.e., reduce the influence of external environment on the performance of materials. the complete contact of frp and binding materials reduces the possibilities of debonding failure. it is suitable for strengthening the negative moment region of structural components. when frp reinforcement is used, the workload of processing concrete surface is light, saving time and cost. f h. zhu et alii, frattura ed integrità strutturale, 46 (2018) 361-370; doi: 10.3221/igf-esis.46.33 363 analysis on the failure mode of embedded cfrp plate consolidated reinforced concrete beams bending failure hen the length of cfrp plate is enough and its binds well with concrete, strengthening beams may have bending failure, i.e, the shear bearing capacity of strengthening beams is larger than the bending bearing capacity, tensile reinforcement yields, and concrete is crushed or cfrp plate breaks. when the crushing of concrete and the fracture of cfrp plate happen simultaneously, then [11]: * 0.8 cu c y s cu fu f f f bh f a a f          where fu stands for the ultimate strain of cfrp plate, cu stands for the ultimate strain of concrete, b stands for the width of beam section, h stands for the height of beam section, fc stands for the design value of cube compressive strength of concrete under uniaxial stress, fy stands for the design value of tensile strength of rebars, and as stands for the cross sectional area of rebars. when *f fa a , concrete is crushed; when * f fa a , cfrp plate fractures. shear failure when the stirrup ratio is not enough or shear is the first to exceed other resistances, strengthening beams are very likely to have shear failure. the shear failure of strengthening beams indicates beams have excellent bending resistance, and the values of cfrp are given full play. debonding failure debonding failure is a special failure mode in embedded cfrp plate reinforcement method and also the main failure mode. cfrp plate reinforcement includes the mutual contact of three materials, i.e., contact between cfrp plate and binding materials and contact between binding materials and concrete. the hardness and strength of binding materials are very likely to decrease with the increase of temperature [12]. the main manifestations of failure include failure of connection between cfrp plate and resin, failure of connection between resin and concrete, failure of resin and failure of concrete. finite element analysis establishment of finite element model inite element method which is a practical numerical calculation method has been applied in many fields. in this study ansys was used for simulating and analyzing embedded cfrp plate consolidated reinforced beams. concrete solid65 element in ansys was used for simulating concrete material. the cracking of concrete was observed via the equivalent value of plastic strain. damaged plasticity model (dilatancy angle: 45°, eccentricity ratio: 0.1, viscous parameter: 0.005) was used. during modeling, a rectangle with a size of 150 * 300 mm was drawn, and then it was stretched for 2400 mm to form a concrete beam. rebars link8 element was used for simulating rebars. the rebars born under uniaxial tension and compression and could move freely in the directions of x, y and z. the plasticity, expansion and deformation of rebars were simulated. the parameters of rebars are shown in tab. 1. w f h. zhu et alii, frattura ed integrità strutturale, 46 (2018) 361-370; doi: 10.3221/igf-esis.46.33 364 materials compressed rebar tension rebar stirrup specification hrb4002  10 hrb4002  14 hpb300  8 elasticity modulus se ( 5 210 /n mm ) 2.00 2.00 2.20 the design value of tensile strength 2( / )yf n mm 360 360 280 the design value of compressive strength ' 2( / )yf n mm 360 360 280 table 1: the parameters of rebars. cfrp plate and binding material cfrp plate and binding material were regarded as a whole and simulated using solid45 element. the ultimate tensile strength of cfrp plate fuf was 2860 n/mm2, elasticity modulus cfe was 1.47 ×105 n/mm2, and poisson's ratio was 0.3. the poisson's ratio and elasticity modulus of binding material was 0.25 and 3500 n/mm2 respectively. cushion block to prevent stress concentration induced local damage, rigid cushion blocks were used at the support and loading points. it was simulated using solid45 element. the poisson's ratio and elasticity modulus of cushion block was 0.3 and 2.0 × 105 n/mm2. modeling and solution process mapping meshing was used. the position of node generation should ensure the sharing nodes of different materials were at the same position after connection. taking the position of rebars and the size of groove as an example, concrete, resin and cushion blocks were divided into hexahedral element. nodes were established in the space firstly. then rebars generated via the nodes. plane net was established on the plane which the top of the beam and cushion blocks lie; after stretching, concrete and cushion blocks were established, and the position of groove should be left. after merging of the nodes, cfrp element was established at the pre-aside position for groove. then mid-span symmetry was performed to simulate the whole beam. displacement control was used in the simulation process, and the maximum displacement value was 0.05 m. after modeling, data were analyzed using finite element solver via static. the calculation results were extracted using post1. design of component the size of the component was 150 mm * 300 mm * 2300 mm. the calculated net span of the beam was 2100 mm. the size of tension rebar of the test beam and erection rebar was 2  25 (as=980 mm2) and 2  6.5 (as=65 mm2) respectively. unilateral stirrup reinforcement was used, and the reinforcement zone was  6.5@50, and the nonreinforcement zone was  6.5@200. the thickness of the protective layer at the lower layer of the concrete beam was 30 mm, and the protective layer at the upper layer was 20 mm. finite element analysis results analysis of concrete failure he failure process of the strengthening beam was as follows. in the initial stage, the tension on the beam is shared by rebars, concrete and cfrp plate. with the increase of load, concrete in the tension zone fractured. in the middle stage, the stress on the rebars and cfrp plate became layer, and the tension mainly relied on rebars and cfrp plate. with the increase of the load, the rebars reached the yield stress. in the late stage, the strain on the cfrp t h. zhu et alii, frattura ed integrità strutturale, 46 (2018) 361-370; doi: 10.3221/igf-esis.46.33 365 plate increased, the stress on the rebars stopped increasing, bond slip happened to the rebars and concrete, the cfrp plate shouldered the main tension. at that moment, the ultimate carrying capacity and failure mode of the strengthening beam mainly depended on whether the binding between the cfrp plate and concrete was tight. the main failure modes included crushing of concrete beam, fracture of cfrp plate, debonding of cfrp plate and binding materials, debonding of the protective layer of concrete and debonding of concrete and binding materials. comparison between simulated values and test values to verify the accuracy of the finite element model, the analysis results of l1, l2 and l3 beams were firstly selected. the specific parameters of the beams are shown in tab. 2. no. of test specimen l1 l2 l3 width of cfrp plate (mm) 10 10 10 number of cfrp plate (n) 6 4 4 the embedding angle of cfrp plate 90 90 90 spacing between cfrp plate (mm) 100 150 150 depth of groove (mm) 20 20 20 shear span ratio(a/h0) 2.33 2.33 2.71 table 2: the parameters of the verified beams. the mid-span vertical displacement of the model beam was extracted as the mid-span deflection of the beam. the 2-fold value of the reactive force at the cushion blocks was taken as the concentrated load of the beam. the load-deflection curve of the strengthening beam was drawn. the test values were compared with the simulated values to verify the accuracy of the model. the comparison results are shown in fig. 2, 3 and 4. figure 2: the load-deflection curve of l1. it could be noted from the load-deflection curves that the differences between the simulated values and test values were small, suggesting the high accuracy of the finite element model. the comparison results of the ultimate load values of the test beams and simulated beams are shown in tab. 3. h. zhu et alii, frattura ed integrità strutturale, 46 (2018) 361-370; doi: 10.3221/igf-esis.46.33 366 figure 3: the load-deflection curve of l2. figure 4: the load-deflection curve of l3. no. of test specimen l1 l2 l3 the test value of the ultimate load (kn) 334.68 289.54 279.61 the simulated value of the ultimate load (kn) 339.02 308.52 286.37 error (%) 1.30 6.56 2.42 table 3: the comparison of the test values and simulated values of the beams. tab. 3 suggests that the test values were close to the simulated values, and the errors were all lower than 10%. the strains of the rebars and cfrp plates were analyzed using universal methods, and there were also small errors between the tested values and simulated values. the results suggested that the finite element model had a high accuracy. h. zhu et alii, frattura ed integrità strutturale, 46 (2018) 361-370; doi: 10.3221/igf-esis.46.33 367 analysis on the mechanical performance o determine the best reinforcement method of cfrp plate, different embedded cfrp plates were studied using finite element model. taking reinforced concrete beam as an example, six reinforcement methods were designed to analyze and compare the mechanical performance of the beam. the model parameters are shown tab. 4. no. of test specimen reinforced concrete beam a b c d e f size of test specimen (mm) 200*250* 1800 200*250* 1800 200*250* 1800 200*250* 1800 200*250* 1800 200*250* 1800 200*250* 1800 size of cfrp plate (mm) 1.2*20*1800 1.2*20*900 1.2*20*900 1.2*20*600 1.2*20*600 1.2*20.900 number of cfrp plate (n) 1 2 2 3 3 2 number of grooves (n) 1 1 2 1 3 2 size of groove (mm) 20*20*1800 20*20*900 20*20*900 20*20*600 20*20*600 20*20*900 shear span ratio (a/h0) 2.32 2.32 2.32 2.32 2.32 2.73 spacing between grooves (mm) 80 60 80 table 4: the model parameters. fig. 5 shows the load-deflection curves of the strengthening beams of different kinds. with the increase of the load, the load-deflection curves of different beams gradually changed: the concrete at the bottom of the beam fractured, and the mechanical performance of the beam changed. the deflection of the strengthening beams increased slower than that of the non-strengthening beams, indicating that cfrp plate could effectively reduce the mid-span displacement of beams. different reinforcement methods of beams had different influence on the carrying capacity and failure modes of beams. in the aspect of groove mode, the effect of multiple grooves and plates was better than that of single groove and multiple plates. cfrp plate could inhibit the growth of cracks, but too many grooves was not beneficial to the integral rigidity of beams; therefore two grooves was the best. in the aspect of shear span ratio, the larger the shear span ratio. tab. 5 shows the ultimate carrying capacity, improvement amplitude and failure mode of the strengthening beams of different kinds. under the same load, the mid-span displacement of the strengthening beams was smaller than that of the nonstrengthening beams. the improvement amplitudes of beam c and f was the largest, but beam f was more obvious. i indicated that the larger the shear span ratio, the better then reinforcement effect. as to the failure mode, beam e had bending failure, and the other beams had debonding failure. it might be because the increased number of grooves. moreover debonding failure of the protective layer of concrete can be avoided only when the length of the cfrp plate was enough. the cfrp plate, rebars and concrete strains of the reinforced beam, beam c and beam f were further compared, and the comparison results are shown in fig. 6. it could be noted from fig. 6 that the strain value of the cfrp plate strengthening beam was larger than that of the reinforced concrete beam. under the same load, the strain of the cfrp plate was larger than that of the rebars as the bottom tension was bore by the cfrp plates and rebars after the cracking of concrete, the relative distance of the cfrp plates was large, and the elasticity modulus was low. the strain of beam f was larger than the strain of beam c, indicating that the larger the shear span ratio, the better the mechanical performance. t h. zhu et alii, frattura ed integrità strutturale, 46 (2018) 361-370; doi: 10.3221/igf-esis.46.33 368 figure 5: the load-deflection curve of different beams no. of test specimen rc a b c d e f ultimate load (kn) 89 110 127 140 106 115 152 improvem ent amplitude (%) 23.6 42.7 57.3 19.1 29.21 70.79 failure mode 1 2 2 3 2 2 table 5: the results of different beams. note: 1. crushing failure of concrete beams; 2. debonding failure of concrete and binding materials; 3: debonding failure of the protective layer of concret.e figure 6: the comparison results of strains of different beams. h. zhu et alii, frattura ed integrità strutturale, 46 (2018) 361-370; doi: 10.3221/igf-esis.46.33 369 discussion and conclusion rp as a novel building material suggests favourable performance in reinforcing reinforced concrete beams. to prevent the failure of binding materials, embedded cfrp plate strengthening is an advantageous method [13]. to fully understand the performance of cfrp plate, multi-aspect studies need to be made. the application of finite element software can reduce test materials and workload. many scholars have studied the functions of finite element software in the simulation of cfrp plate strengthening. dirar et al. [14] analyzed the shear capacity of reinforced concrete beams using finite element analysis method and compared the simulated values and test values of shear force, shear force-deflection curve, crack mode and failure mode via modeling to understand the shear capacity. taghia et al. [15] explored the influence of cfrp plate on reinforced concrete short columns using finite element software, studied different aspects of constraint effect such as difference of sectional dimension, number of carbon fiber cloth and volume ratio of carbon fiber cloth, and found that outside sticking of carbon fiber cloth was quite effective in improving the axial strength and ductility of concrete short columns. in this study, the model was established using ansys. to verify the reliability of the model, the test values and simulated values of three beams were compared, and it was found that the two groups of data basically fitting. the existence of error might be because the test beams were affected by factors such as temperature and proportion of concrete, the finite element model ignored the bond slipping between different interfaces of the beams, and partial parameters were excessively ideal. but overall, the results could verify that the finite element model had high accuracy and reliability. to study the mechanical performance of embedded cfrp plate reinforcement method, six reinforcement methods which involved different length of cfrp plate, number of cfrp plate, number of grooves and shear span ratio were compared. the results demonstrated that different reinforcement methods had different influences on the carrying capacity and failure mode of beams; proper increase of length of cfrp plate could avoid the debonding failure of the protective layer of concrete; multiple plates and grooves could increase the surface of plates and inhibit the growth of cracks at the bottom of concrete, but too many grooves was not beneficial to the integral rigidity of beams and might lead to decrease of the ultimate carrying capacity (for example, beam e); the larger the shear span ratio, the higher the ultimate carrying capacity of beams and the lower the possibility of deformation (for example, beam f). the beams except beam a had debonding failure, which might be because the sufficient length of anchoring of the cfrp plates of beam a reduced the possibilities of debonding failure. it indicated that the embedded length of the cfrp plate might be in an obvious correlation with the possibilities of debonding failure. the comparison of strain between the rebars, concrete and cfrp plate suggested that embedded cfrp plate reinforcement was significantly effective in increasing the strain of the beams, and the strain of the cfrp plate was larger than that of the rebars. in conclusion, embedded cfrp plate strengthening was effective in enhancing the mechanical performance of reinforced concrete beams. embedded cfrp plate strengthening beams with favourable mechanical performance has a broad development prospect in repairing old buildings. in this study, the mechanical performance of the beams which applied different strengthening methods was compared in aspects of the number, size, grooving mode and shear span ratio of the cfrp plate after the effectiveness of the model was verified. the results demonstrated that the ultimate carrying capacity of the embedded cfrp plate strengthening beams was significantly superior to that of ordinary reinforced concrete beams, the reinforcement method of two cfrp plates and two grooves was the best, and the larger the shear span ratio, the higher the carrying capacity and the lower the possibility of deformation. embedded cfrp reinforcement technology has more possibilities, and its application values need to be explored through more studies in the future. references [1] motavalli, m., czaderski, c. and pfyl-lang, k. (2011). prestressed cfrp for strengthening of reinforced concrete structures — recent developments at empa switzerland. journal of composites for construction, 15(2), pp. 194205. [2] raoof, s.m., koutas, l.n. and bournas, d.a. (2017). textile-reinforced mortar (trm) versus fibre-reinforced polymers (frp) in flexural strengthening of rc beams. construction & building materials, 151, pp. 279-291. [3] khelifa, m. and celzard, a. (2014). numerical analysis of flexural strengthening of timber beams reinforced with cfrp strips. composite structures, 111(1), pp. 393-400. [4] rezazadeh, m., costa, i. and barros, j. (2014). influence of prestress level on nsm cfrp laminates for the flexural strengthening of rc beams. composite structures, 116 (1), pp. 489-500. f h. zhu et alii, frattura ed integrità strutturale, 46 (2018) 361-370; doi: 10.3221/igf-esis.46.33 370 [5] jumaat, m.z., rahman, m.m. and alam, m.a. (2010). flexural strengthening of rc continuous t beam using cfrp laminate: a review. international journal of physical sciences, 5(6), pp. 619-625. [6] dias, s.j.e. and barros, j.a.o. (2012). nsm shear strengthening technique with cfrp laminates applied in highstrength concrete beams with or without pre-cracking. composites part b, 43(2), pp. 290-301. [7] elchalakani, m. (2014). cfrp strengthening and rehabilitation of degraded steel welded rhs beams under combined bending and bearing. thin-walled structures, 77(4), pp. 86-108. [8] belarbi, a. and acun, b. (2013). frp systems in shear strengthening of reinforced concrete structures. procedia engineering, 57(1), pp. 2-8. [9] parvin, a. and brighton, d. (2014). frp composites strengthening of concrete columns under various loading conditions. polymers, 6(4), pp. 1040-1056. [10] burke, p.j., bisby, l.a. and green, m.f. (2013). effects of elevated temperature on near surface mounted and externally bonded frp strengthening systems for concrete. cement & concrete composites, 35(1), pp. 190-199. [11] ou, j.p., wang, b., he, z., zhang, x. and qian, m. (2004). load-deflection response of concrete beams reinforced with frp bars. advances in structural engineering, 7(5), pp. 427-436. [12] stratford, t.j. and bisby, l.a. (2012). effect of warm temperatures on externally bonded frp strengthening. journal of composites for construction, 16(3), pp. 235-244. [13] wu, z., iwashita, k., sun, x. and kobayashi, a. (2010). development of structural strengthening method with prestressed near-surface mounted cfrp tendons. kozo kogaku ronbunshu a, 56, pp. 630-643. [14] dirar, s., lees, j.m. and morley, c. (2013). phased nonlinear finite-element analysis of precracked rc t-beams repaired in shear with cfrp sheets. journal of composites for construction, 17(4), pp. 476-487. [15] taghia, p. and bakar, s.a. (2013). mechanical behaviour of confined reinforced concrete-cfrp short columnbased on finite element analysis. world applied sciences journal, 24(7), pp. 960-970. << /ascii85encodepages false /allowtransparency false /autopositionepsfiles true /autorotatepages /none /binding /left /calgrayprofile (dot gain 20%) /calrgbprofile (srgb iec61966-2.1) /calcmykprofile (u.s. web coated \050swop\051 v2) /srgbprofile (srgb iec61966-2.1) /cannotembedfontpolicy /error /compatibilitylevel 1.4 /compressobjects /tags /compresspages true /convertimagestoindexed true /passthroughjpegimages true /createjobticket false /defaultrenderingintent /default /detectblends true /detectcurves 0.0000 /colorconversionstrategy /cmyk /dothumbnails false /embedallfonts true /embedopentype false /parseiccprofilesincomments true /embedjoboptions true /dscreportinglevel 0 /emitdscwarnings false /endpage -1 /imagememory 1048576 /lockdistillerparams false /maxsubsetpct 100 /optimize true /opm 1 /parsedsccomments true 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/hrv (za stvaranje adobe pdf dokumenata najpogodnijih za visokokvalitetni ispis prije tiskanja koristite ove postavke. stvoreni pdf dokumenti mogu se otvoriti acrobat i adobe reader 5.0 i kasnijim verzijama.) /hun 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can be opened with acrobat and adobe reader 5.0 and later.) >> /namespace [ (adobe) (common) (1.0) ] /othernamespaces [ << /asreaderspreads false /cropimagestoframes true /errorcontrol /warnandcontinue /flattenerignorespreadoverrides false /includeguidesgrids false /includenonprinting false /includeslug false /namespace [ (adobe) (indesign) (4.0) ] /omitplacedbitmaps false /omitplacedeps false /omitplacedpdf false /simulateoverprint /legacy >> << /addbleedmarks false /addcolorbars false /addcropmarks false /addpageinfo false /addregmarks false /convertcolors /converttocmyk /destinationprofilename () /destinationprofileselector /documentcmyk /downsample16bitimages true /flattenerpreset << /presetselector /mediumresolution >> /formelements false /generatestructure false /includebookmarks false /includehyperlinks false /includeinteractive false /includelayers false /includeprofiles false /multimediahandling /useobjectsettings /namespace [ (adobe) (creativesuite) (2.0) ] /pdfxoutputintentprofileselector /documentcmyk /preserveediting true /untaggedcmykhandling /leaveuntagged /untaggedrgbhandling /usedocumentprofile /usedocumentbleed false >> ] >> setdistillerparams << /hwresolution [2400 2400] /pagesize [612.000 792.000] >> setpagedevice microsoft word numero_53_art_11_2753 e. nurullaev et alii, frattura ed integrità strutturale, 53 (2020) 134-140; doi: 10.3221/igf-esis.53.11 134 physical parameters of polymer composite materials created on the basis of low and high molecular weight rubbers e. nurullaev, n. y. lyubimova, t. a. gertsen perm national research polytechnic university, russia ergnur@mail.ru , https://orcid.org/0000-0001-6525-3090. ninalubimova@yandex.ru tanger59perm@yandex.ru, https://orcid.org/0000-0002-6420-0592 abstract. the objective of this work is the further development theoretical foundations of structural and mechanical behavior of the filled three-dimensionally cross-linked elastomers. the use of mathematical modeling it was possible to create three-dimensionally cross-linked, filled with dispersed particles, frost-resistant elastomers based on low and high molecular weight rubbers at the minimal cost. theoretical and experimental data are compared and their good convergence is shown. a comparison of the physical parameters of the composites showed that the deformation characteristics of the composite based on high molecular rubbers are many times higher than composites based on low molecular weight rubbers, and also their glass transition temperatures differ sharply. the created composites are recommended as a structural material in relation to the engineering problem of creating wear-resistant parts and components of automobile and aviation vehicles operating in a wide temperature range, including in the far north and the arctic. keywords. deformation; mechanical stress; filler; high molecular weight rubber; low molecular weight rubber; fracture energy. citation: nurullaev, e., lyubimova, n. y., gertsen, t. a., physical parameters of polymer composite materials created on the basis of low and high molecular weight rubbers, frattura ed integrità strutturale, (2020) 134 140. received: 14.02.2020 accepted: 26.03.2020 published: 01.07.2020 copyright: © 2020 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. introduction lastomeric materials are an important type of polymer composite materials. they are widely used to create automobile tires [1-3]. at present, one of the main problems associated with the development of frost-resistant structural material for parts and assemblies of various types of automobile and air transport, operated in the far north and in the arctic at operating temperatures up to 170-223k is an increase in their wear resistance and economy. the most promising direction for solving this problem is the use of high molecular weight synthetic hydrocarbon rubbers in the form of copolymers that do not crystallize in a wide temperature range of operation as a polymer base of composites [4]. experimental values of the real and imaginary components of the dielectric permittivity of carbon nanofibers (cnfs) and nanotubes (cnts) composites in polymethylmethacrylate and polyaniline are given in [5]. both frequency dependences in the range from 8 to 12 ghz and concentration dependences are determined. e https://youtu.be/vijptid2fwq e. nurullaev et alii, frattura ed integrità strutturale, 53 (2020) 134-140; doi: 10.3221/igf-esis.53.11 135 currently, materials that cover a wide range of frequencies [6, 7], up to almost 70 ghz have been developed. the purpose of the study was to create a frost-resistant (with a glass transition temperature of ~ 170k), elastic (composite deformation of at least 70% at t ~ 223k) polymer composite material. therefore, the following tasks were solved: 1. new equation formula was developed and mathematical modeling of the dependence of mechanical stress on deformation was carried out, the influence of structural parameters on the mechanical characteristics of polymer composites was studied; 2. based on the results of theoretical calculations, a model of a polymer composite material is constructed that meets the goal, and a frostresistant and flexible polymer composite is experimentally created; 3. the materials were tested using a tensile testing machine, and the results were compared with the calculated data. material, samples and equipment he polymeric basis is formed by copolymerized low-molecular rubbers with epoxy (pdi-3b) and carboxyl skdktr) end groups, transversely cross-linked by an eet-1 three-functional epoxy resin. the filler is a mixture of two fractions of silica: natural macro crystalline quartz (500-1500 μm), and a highly dispersed pyrogenetic amorphous quartz of trademark “aerosil-380” (35-40 nm) in the ratio 80:20. the volume fraction of filler was 0.712. the glass transition temperature of the resulting elastomer is 213 k. material based on a high molecular weight three-dimensionally cross-linked elastomer polydivinyl isoprene brand skdil, plasticized with dioctylsebacinate and filled with three fractional silicon dioxide rubber, has the following characteristics: skid-l copolymer with a molecular weight of 286000, a glass transition temperature of 178k, a density of 900 kg/m3 and a volume fraction of 0.4; plasticizer dioctyl sebacyanate with a glass transition temperature of 169 k, a density of 910 kg/m3 and a volume fraction of 0.6; filler is the silicon dioxide with fractional composition fraction no.1 (1 μm) with an optimal volume fraction of 0.2 fraction no.2 (8 μm) and with an optimal volume fraction of 0.8. the elastomeric composite was made in laboratory conditions using the lsp-5 mixer at the research institute of polymer materials. the method of obtaining a polymer composite material based on a high molecular weight copolymer skid-l is given in tab. 1. no the operation duration of operation, [s] component temperature, т [к] mixture temperature, т [к] 1 loading of a copolymer skid-l no more than 900 900 – 2100 – 2 loading of a plasticizer dioctylsebatsionat no more than 900 288 – 308 – 3 loading the rest of the filler 1800 – 3600 – 303 – 313 4 download 1/3 of the filler no more than 900 288 – 308 – 5 stirring 600 – 900 – 293 – 308 6 loading the rest of the filler no more than 900 288 – 308 7 stirring 600 – 900 – 293 – 308 8 stirring, evacuation 3000 – 3600 – 293 – 308 table1: conditions for preparing a polymer composite. physical and mathematical description he structural-mechanical behavior of a three-dimensionally cross-linked plasticized elastomer filled with solid particles in uniaxial tension is considered in [8]. the elastic potential of a spatial polymer network, on the basis of which mooney and rivlin deduced their equation, is shown below: t t e. nurullaev et alii, frattura ed integrità strutturale, 53 (2020) 134-140; doi: 10.3221/igf-esis.53.11 136 1 1 2 2( 3) ( 3)u c i c i    (1) the parameters 2c1 and 2c2 allowed mooney and rivlin to write their equation in the form 1 2 1 2(2 2 )( )c c        (2) σ is the conditional stress (tensile force related to the initial cross section). up to now, the parameters 2с1 and 2с2 have been associated with the chemical and “physical” (intermolecular) components of transverse bonds in the polymeric basis of a binder. really, from eq. (2) formally follows the expression: 2 1 2 1 22 ( ) 2 ( )c c            (3) the first term corresponds to the case of elasticity theory of cross-linked rubbers (resins) at a test temperature close to the equilibrium one: t∞=tg +2000 (tg is the temperature of structural glass transition of a polymer). then, as follows from [6]: 2 2 2 12 ( ) ( ) ( )ch a chc kn t rt                   (4) here, νch is the molar concentration of chemical transverse bonds in the cross-linked polymer; k is the boltzmann constant; na is the avogadro number; r is the gas constant per mole; α=(1+ε/100) is the relative elongation as a function of strain. to verify the applicability of mooney–rivlin eqn. (2) to the case of a filled elastomer and the effect of the second term in eq. (3), we put to use its linear form: 2 1 1 2 / ( ) 2 2       c c (5) in view of dependence (6), the mooney–rivlin equation is refined regarding the influence of the “physical” (intermolecular interaction) component of transverse bonds in the polymeric binder:  1/ 3 3 2 1 1 21 29 exp 0, 225 10 ( ) ( )ch r grt t t a                   (6) here, for a plasticized elastomer, φr=(1-φsw) 1 is the volume fraction of the polymeric base of binder; φsw is the volume fraction of softener in the elastomer; т is the test temperature, aά-1 is the shift factor take φsw into account the effect of strain rate (equal to unity for the standard rate of uniaxial tension). experimental results (reconstructed tension diagrams) for an elastomeric composition filled with silica are presented in fig. 1. the physical and chemical features of the composition are as follows. the polymeric basis is formed by copolymerized low-molecular rubbers with epoxy (pdi-3b) and carboxyl skd-ktr) end groups, transversely cross-linked by an eet-1 three-functional epoxy resin. the filler is a mixture of two fractions of silica: natural macro crystalline quartz (5001500 μm) and highly dispersed pyrogenetic amorphous quartz of trademark “aerosil-380” (35-40 nm) in the ratio 80:20. the volume fraction of filler was 0.712. it is seen that, also in the case of the type of filled elastomer considered, the test data are rather well described by the mooney–rivlin equation. this allows us, taking into account formula (5), to determine the parameters 2с1 and 2с2 graphically. the 2с2 value in eq. (5), which is related to the viscous (relaxation) component of the initial viscoelastic modulus (e=dϭ/dα at α =1), tends to zero (intermolecular bonds fail) with rising temperature and decreasing strain rate (fig. 1). in addition, the 2с1 value associated with the elastic component of the initial viscoelastic modulus, remains practically constant. the coefficient of the inversible temperature dependence of change in 2с2 for a filled elastomer can be written as at=(2c1+2c2)/2c1 in the temperature range from tg to t∞, approximately equal to 200k for the majority of 30 crosslinked polymers. this fact leads to a 30-fold change in the total number of chemical (constant) and “physical” (inversibly varying) bonds. tab. 2 shows the values of the coefficients 2c1 and 2c2. the linear dependences (5) necessary for this were constructed from the data of the tension curves (fig. 1). e. nurullaev et alii, frattura ed integrità strutturale, 53 (2020) 134-140; doi: 10.3221/igf-esis.53.11 137 figure 1: relationships ϭ/(α-α-2)=f(α-1) (reconstructed tension diagrams) for an elastomeric composition filled with silica at т = 323 (1), 293 (2, 4, 6), 273 (3), 253 (5), 233 (7), and 223 k (8) and strain rates 1,2·10-3 s-1; –3 (1-3, 5, 7, 8), 4.6·10–4 (4), and 4.6·100 s–1 (6). the axes are the dimensionless relative values. temperature stretching sample, [к] parameter 2с1, [mpa] parameter 2с2, [mpa] coefficient temperature offsets аt=(2с1+2с2)/2с1 323 0.009 0.001 1.159 293 0.010 0.003 1.476 253 0.011 0.010 2.587 243 0.012 0.025 3.968 223 0.010 0.110 17.460 table 2: parameters of the mooney-rivlin equation for the pcm based on skd-ktr and pdi-3b tab. 2 includes only operating temperatures. data at room temperature is not of practical interest for the creation and use of polymer composite materials according to customer conditions. expression (6) is equivalent to the parameter 2с2. in view of dependence (6), the mooney–rivlin equation is refined regarding the influence of the “physical” (intermolecular interaction) component of transverse bonds in the polymeric binder:  1/ 3 3 2 1 1 21 29 exp 0, 225 10 ( ) ( )ch r grt t t a                   (7) engineering application he use of mathematical modeling [8, 9] allowed the authors, at the lowest cost, to create a material, based on a high molecular weight three-dimensionally cross-linked elastomer polydivinyl isoprene of the skdi-l brand, plasticized with dioctylsebacinate and filled with three fractional silicon dioxide rubber. circles and squares in fig.2 are intermediate points for theoretical calculations. the choice of the stretching speed is determined by the specific application of the studied polymer composite as a standard. fig. 2 shows the experimental and calculated diagrams of uniaxial tension at various temperatures samples of the composite based on high molecular copolymer scdi-l. for comparison, fig. 3 shows the envelopes of points of discontinuity of elastomeric composite materials by t. smith [12] on the basis of a mixture of low molecular weight rubber skd-ktr and pdi 3b and high molecular weight copolymer scdi – l. t e. nurullaev et alii, frattura ed integrità strutturale, 53 (2020) 134-140; doi: 10.3221/igf-esis.53.11 138 σ,mpa εb, % in contrast to the “traditional” effect of the test temperature on the type of tensile curves of polymer composites in the highly elastic region of the thermomechanical curve (fig. 3), a composite based on a high molecular weight copolymer with decreasing temperature becomes more and more elastic. at the same time, both breaking stress and tensile deformation increase. figure 2: stress σ as a function of strain ε for the composite based on skdi-l 10–3 s–1; solid lines: experimental data; dashed lines: data of the numerical experiment. figure 3: envelopes of the break points (according to t. smith) of elastomer composite materials based on (1) a blend of skd-ktr and pdi-3b low-molecular-mass rubbers and (2) skdi-l high-molecular-mass copolymer. (σ) stress and (εb) strain. such frost resistance of the elastomeric composite may be associated with an extremely low structural glass transition temperature of the polymer binder. undoubtedly, also, quinol ether as a crosslinking agent exerted the indicated thermomechanical behavior of the composite based on the skdi-l copolymer. in contrast to the latter, sulfur curing systems for rubbers form less strong transverse chemical bonds [4]. the corresponding envelopes of t. smith breakpoints in the tensile diagrams of both types of composites show significantly higher tensile strains of the composite based on the high molecular weight copolymer skdi-l than in the case of the composite based on a mixture of low molecular weight rubbers skd-ktr and pdi-3b, with a small difference in values breaking stresses. however, when curve 2 is extrapolated to a region of lower temperatures, up to the σ ,mpa ε ,% e. nurullaev et alii, frattura ed integrità strutturale, 53 (2020) 134-140; doi: 10.3221/igf-esis.53.11 139 εb, % w, kj structural glass transition temperature, a composite based on skdi-l may exceed the strength of a composite based on a mixture of skd-ktr and pdi-3b. all data points and completely all studies whose results are given in this work belong only to the indicated authors. for a comprehensive engineering assessment of the influence of the basic structural parameters of an elastomeric composition on its mechanical characteristics, the envelopes of fracture points in tensile diagrams according to smith t. are still most widely used [10, 11]. however, they do not fully reflect the physical nature of the process of destruction of the polymer composite as energy costs (work). the equation for calculating the energy of mechanical failure was first deduced by the authors [12, 13] and has the form:   2 2 2 23 1 2 3 2 2 3 1 29 exp 0, 225 10 2 2 b b b b g b b w t t a                                    2 1/ 3 /1 1, 25 1 . / m ch r m rt                (8)             the experimental and calculated dependences of the energy of mechanical failure on the tensile strain are shown in fig.4. it can be seen that with decreasing test temperature and, naturally, an increasing in intermolecular interaction, the energy of mechanical destruction, which determines the operational life of the material increases. there is good agreement between the theoretical and experimental research data. the discrepancy is about 5%, which is satisfactory for engineering problems. figure 4: mechanical failure energy w is as a function of breaking strain εb for the composite based on skdi-l at different temperatures. solid lines: experimental data; dashed lines: calculated data; conclusion 1. the theoretical foundations of the structural and mechanical behavior of filled three-dimensionally cross-linked elastomers are supplemented. the corresponding numerical experiments were carried out. 2. based on the results of a numerical experiment, a frost-resistant, three-dimensionally cross-linked, plasticized elastomer filled with three-fraction silicon dioxide is proposed. 3. the theoretical and experimental results of the study are compared. satisfactory agreement between theoretical and experimental data is shown. 4. the composite is recommended as a structural material in relation to the engineering problem of creating wearresistant parts and assemblies of automobile and aviation vehicles operating in a wide temperature range, including the far north and the arctic. e. nurullaev et alii, frattura ed integrità strutturale, 53 (2020) 134-140; doi: 10.3221/igf-esis.53.11 140 references [1] dick, j.s. (2005). rubber technology: compounding and testing for perfomance. hanser publishers, minich, p. 620 [2] jones, e.m., burak erman and erlich, f.r. (2005). science and technology of rubber/elsevier inc. all rights, reserved. p. 767. [3] dementiev, s. a. (2008). development of tread rubbers using domestic silica filler rosil 175 and bifunctional silane k-69: dis. candidate of technical sciences kazan: knitu, p.120. [4] dogadkin, b.a., dontsov, a.a., and shershnev, v.a. (1981). khimiya elastomerov (elastomer chemistry), moscow: khimiya. [5] makeiff, d.a., huber, t.and saville, p. (2005). complex permittivity of polyaniline−carbon nanotube and nanofibre composites in the x-band: pmma composites. defence r&d canada−atlantic, technical memorandum, drdc atlantic tm. p.124 [6] mills, d.l.l. bland, a.c. (2006). nanomagnetism: ultrathin films, multilayers and nanostructures j. amsterdam: elsevier, p. 348. [7] mohn, p. (2006). magnetism in the solid state: an introduction. ney york: springer. p. 229. [8] treloar, i. r. g. (1974). the elasticity and related properties of rubbers, rubber rew., 47, pp. 625-696. doi: 10.5254/1.3540456. [9] ermilov, a. s., nurullaev, e. m mechanical properties of elastomers filled with solid particles, mechanics of composite materials, 48(3), . (2012). 243-252. doi: 10.15593/2224-9982/2015.41.10 [10] certificate no. 2012613349 rf a software for determination and optimization of packing density of solid. disperse fillers of polymer composite materials / ermilov a. s., nurullaev e. m, and duregin k. a. priority of 09.04.2012 ermilov, a.s., nurullaev, e.m., subbotina, t.e., and duregin, k.a., certificate of official registration of computer program no. 2011615640. [11] smith, t. l. (1964). ultimate tensile properties of elastomers. ii. comparison of failure envelopes for unfilled vulcanizates. journal of applied physics 35, p. 27. doi: 10.1063/1.1713094. [12] ermilov, a. s. and nurullaev, e. m. (2016). optimizing the composition of elastomer composites for the fracture energy, (mechanics of composite materials. 52(2) 325-334. doi: 10.1007/s11029-016-9575-2 . [13] ermilov, a. s. and nurullaev, e. m. numerical simulation and derivation of an equation for calculation of the mechanical fracture energy of elastomer filled with multifractional silica russian journal of applied chemistry. 87(4). 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/hrv (za stvaranje adobe pdf dokumenata najpogodnijih za visokokvalitetni ispis prije tiskanja koristite ove postavke. stvoreni pdf dokumenti mogu se otvoriti acrobat i adobe reader 5.0 i kasnijim verzijama.) /hun 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can be opened with acrobat and adobe reader 5.0 and later.) >> /namespace [ (adobe) (common) (1.0) ] /othernamespaces [ << /asreaderspreads false /cropimagestoframes true /errorcontrol /warnandcontinue /flattenerignorespreadoverrides false /includeguidesgrids false /includenonprinting false /includeslug false /namespace [ (adobe) (indesign) (4.0) ] /omitplacedbitmaps false /omitplacedeps false /omitplacedpdf false /simulateoverprint /legacy >> << /addbleedmarks false /addcolorbars false /addcropmarks false /addpageinfo false /addregmarks false /convertcolors /converttocmyk /destinationprofilename () /destinationprofileselector /documentcmyk /downsample16bitimages true /flattenerpreset << /presetselector /mediumresolution >> /formelements false /generatestructure false /includebookmarks false /includehyperlinks false /includeinteractive false /includelayers false /includeprofiles false /multimediahandling /useobjectsettings /namespace [ (adobe) (creativesuite) (2.0) ] /pdfxoutputintentprofileselector /documentcmyk /preserveediting true /untaggedcmykhandling /leaveuntagged /untaggedrgbhandling /usedocumentprofile /usedocumentbleed false >> ] >> setdistillerparams << /hwresolution [2400 2400] /pagesize [612.000 792.000] >> setpagedevice microsoft word numero_35_art_5 chahardehi et al, frattura ed integrità strutturale, 35 (2016) 41-49; doi: 10.3221/igf-esis.35.05 41 focussed on crack paths fatigue crack growth under remote and local compression – a state-of-the-art review a. chahardehi (http://orcid.org/0000-0002-7823-7484) atkins energy, euston tower, 286 euston road, london nw1 3at, uk amir.chahardehi@atkinsglobal.com a. mehmanparast (http://orcid.org/0000-0002-7099-7956) cranfield university, uk a.mehmanparast@cranfield.ac.uk abstract. there is an ever increasing need for accurate understanding of the fatigue crack growth behaviour in major engineering materials and components. with the move towards more complex, probabilistic assessments, the traditional ‘safe’ or conservative approach for prediction of fatigue crack growth rate may no longer be attractive. current codes and standards tend to be ambiguous about the treatment of compressive stress cycles: on the one hand code guidance on fatigue crack initiation may be non-conservative, while assessment of crack propagation may be inconsistently conservative. where codes are non-conservative they could lead to dangerous assessments. the current paper provides a critical review of state-of-the-art in literature and a study of current code implications. keywords. fatigue crack growth; compressive stress; closure; r-ratio; paris law; design codes. introduction ost common engineering predictions of fatigue crack growth (fcg) rate demand a high level of accuracy. the need for accuracy may be perceived to be of two apparently distinct natures: on the one hand the scientist and the academic is interested in deeper understanding of the fundamental behaviour of materials in order to progress what may be termed the ‘frontier of science’, while on the other hand the engineer is interested to utilise this, or any usable understanding in the most effective way in practical applications. in offshore applications such as for oil & gas platforms, where cost saving considerations merit it, the move towards risk-based inspections and complex probabilistic assessments relies fundamentally on accurate knowledge of the fatigue crack growth behaviour. nevertheless deterministic predictions of fatigue crack growth for safety applications have traditionally relied on inherent conservatisms in the paris law coefficients used in the ‘design’ fatigue crack growth laws (fracture mechanics-based fatigue assessment), often taking the prediction curve two standard deviations away from the mean of data. m chahardehi et al, frattura ed integrità strutturale, 35 (2016) 41-49; doi: 10.3221/igf-esis.35.05 42 therefore it is understandable that the apparent bias in design codes and standards, when treating the fatigue crack growth phenomenon, has been towards conservatism in the prediction of growth rates. as such, emphasis has usually not been placed on treatment of some of the beneficiary features of fatigue such as closure or the treatment of compressive stress cycles. in some engineering components, where a crack grows in the parent material, away from any residual stresses due to welds (and the larger inherent scatter in the fatigue behaviour in this region), the mean stress could be low or even compressive (e.g. self weight) and therefore benefit may be taken from the effect of fully compressive or part-compressive stress cycles. although fatigue crack initiation has been observed under purely compressive remote stress cycles, current code recommendation could be misinterpreted, assuming no damage accumulation during a fully compressive stress cycle. conversely, most national standards do not allow accounting for the beneficial effect of closure, and some even ignore the partial benefit of the compressive stress cycles in fatigue cracks growth. in bs7910 : 2013 [1], which more closely reflects uk experience and practice, the recommended fcg curves are presented for the cases of r0.5 and r<0.5. the r0.5 is recommended for welded joints, and data for this family of curves is gathered from results of tests on welded samples. the data for r<0.5 are gathered from a pulsating tension (minimum stress = 0 ~ 0.1) [2] taking into account the full stress intensity range [3]. no data has been used with inclusion of compressive stresses in the loading. the esdu data sheet item 80036 [4] notes two options for calculation of k when the stress cycle is partly compressive: calculating the range from the tensile part only, and calculating it from full range. the key is that the same method should be used both for predicting growth and in the presentation of the basic data. this is also in accordance with the guidance of astm e647 [5]. the dnv classification note 30.2 (1984) [6] stated that compressive stresses do not contribute to crack propagation, but the recommendation was that the whole of the stress cycle should be considered. the current paper provides a critical state-of-the-art review of current understanding, with a view to highlighting current issues and challenges which may complicate more accurate modelling of the fatigue crack growth phenomenon in codes and standards. note – in keeping with the accepted nomenclature, r-ratio is defined as the ratio of the minimum to maximum stress in a give load cycle, and u is defined as the ratio of the effective stress intensity factor and the total stress intensity factor ranges. effects of compressive loading – timeline of observations atigue crack initiation and propagation under cyclic compression has been reported and investigated as early as the 60’s. almen [7] shows examples of cracks generated under compressive loading such as compressive cracking of coil springs and ‘shelling’ in rails. gerber [8] and hubbard [9] and a number of other authors observed fatigue crack initiation under compression in laboratory and components, and this is a well-documented phenomenon. see for example the works of suresh [10] and fleck [11] for crack initiation in steels, and solis et al [12] for initiation in ceramics, to give a few examples. these tests are generally conducted on notched samples, under remote compressive stress cycles. the observations from the tests were cracks that initiated at the notch, and grew to a small length and would then arrest – the final length before arrest was 0.6mm from suresh’s work [13] and between 0.68mm and 2.48mm in fleck’s tests [11]. the experiments performed by fleck [11], suresh [10], pippan [12], hermann [14] and kasaba [15], all resulting in nucleation and growth of cracks, were all performed under fully compressive loading. in all of these experiments, the cracks grew with decreasing growth rate until complete crack arrest at a certain crack length. yu et al [16] demonstrated the significance of the compressive stress on fatigue crack propagation rate of aluminium alloy 2024-t351. tests performed by tack and beevers [17] showed that the fatigue crack propagation rate under a negative stress ratio r is greater than that for r=0.1. pommier [18] showed that the addition of a compressive part to the loading could increase the crack growth rate by a factor of five. the observed behaviour was attributed to plastic properties of the material and its kinematic hardening. the general outcome of these observations is that compressive loading in notched samples can lead to fatigue crack initiation, and in the presence of purely compressive loading the crack would grow to a finite albeit small size before arrest. the fact that crack initiation and growth occurs under compressive loading is significant because in some engineering application, not foreseeing this crack could cause unexpected loss of the component. in the following sections, the factors affecting growth and subsequent arrest of these cracks are reviewed. f chahardehi et al, frattura ed integrità strutturale, 35 (2016) 41-49; doi: 10.3221/igf-esis.35.05 43 residual stresses and plastic zone size ahead of crack any authors have associated the growth (and subsequent arrest) of compressive cracks to the residual stress field and the plastic zone generated at the notch due to the remote compressive loading, and the state-of-the art is reviewed in this section. saal [19] proposed a model where the residual stresses at the notch root, generated from maximum compressive load were calculated. it was assumed that under fully compressive cyclic loading, cracks would stop growing at the boundary of the plastically deformed zone. saal’s study was restricted to constant amplitude cyclic loading. it is different from hubbard’s work [9], where the residual stress field in the vicinity of the notch is not released as the crack grows. experimental work by saal [19] showed where no tensile stress component is present, the crack stops at the elastic-plastic boundary. fleck et al [11] used dugdale’s strip yield model [20] and back-calculated the effective stress intensity factor range (and hence inferred the residual stresses) from crack growth test results, using bueckner’s principle of weight function [21-22]. they found that residual stresses found by this method are greater than those calculated from dugdale’s model [11]. jones et al [23] suggest that since negative r-ratio effects are considered to be principally caused by crack closure, a tight crack should produce more significant crack closure and hence negative r-ratio effects. however data from their tests [23] show that results from tight cracks and notches do not significantly alter negative r-ratio effects. assuming that the reason behind this observation by is that the extent of residual stresses due to the compressive loading remains unchanged, the work of saal [19] may explain this phenomenon. saal shows that the condition of a specimen with a straight cut will be a reasonable approximation of calculating the plastic zone size of any elastic-perfectly plastic notched specimen. saal’s observation is further supported by libatskii [24], who showed that the yield behaviour of static tensile tests of notched specimens of mild steel was very close to that described by dugdale’s model. an important work was reported by reid et al [25], which is the first work to report measured values of residual stress at a notch, generated by compressive loading, and to use this in the analysis of crack growth under cyclic compression. the measurement method has been explained in [26]. furthermore, neutron diffraction was also used to obtain the residual stress field. it was found that the general shape of the stress distribution was independent of the pre-load used. not surprisingly, the residual stress magnitude increased with the pre-load. the region of tensile stress near the uncracked notch tip increased in size with the value of the pre-load but in each case it was significantly smaller than the final crack length [26]. this contradicts the views of gerber et al [8] and suresh [10]. reid et al [25] argue that it is possible for the crack tip to remain in a region of tension because the growth of a crack redistributes the original tensile stress to larger distances from the notch. a number of authors have used numerical tools to model the generated residual stress field ahead of the crack, due to the compressive loading. among them, zhang et al [27] developed an elastic-plastic finite element model to study the compressive stress effect on fatigue crack growth under applied tension-compression loading. prior to this, silva [28] had concluded that to predict fatigue crack growth behaviour under applied tension-compression loading, models based on fatigue crack closure were not suitable, and models need to be developed which are based on material’s cyclic plastic properties. the discussions above are all for fatigue crack growth. one finding worth mentioning here is by iswanto et al [29], who found that the effect of residual stress caused by roller-working on s-n fatigue was similar to the effect of compressive mean stress. however, chahardehi et al [30] conclude that the compressive residual stresses caused by laser peening do not influence fatigue crack growth in the way that was previously expected, i.e. superposition of stresses is not sufficient. modelling the r-ratio effect arious authors recognized the r-ratio dependence of fcg rates, and several models have been presented to include this behaviour. generally, equations of the paris law type that account for the effect of r-ratio can be divided into the following three types: 1) stress intensity factor range is defined as per the conventional definition k=kmax-kmin and paris law coefficients are dependent on r-ratio. this is the approach taken in the bs7910 : 2013 recommendation [1] and astm e647 [5]. m v chahardehi et al, frattura ed integrità strutturale, 35 (2016) 41-49; doi: 10.3221/igf-esis.35.05 44 2) the effective stress intensity factor range keff is defined as a function of k and r-ratio. this is the method employed by walker [31], and by kurihara [32] and eason [33], in the form of an effective coefficient u where keff =u.k. 3) equations where the general form is similar to the paris law but includes other terms such as the material toughness and kmax, such as forman’s equation [34], the relationship proposed by mcevily et al [35] and a number of other authors. for a review of some of the famous fatigue crack growth rate equations see the works of bloom [36] and huang [37]. the equations are mainly based on empirical plasticity-induced crack closure models. additional mechanisms include asperity-induced and oxide-induced closure [36]. the two parameter models, e.g. as proposed by vasudevan [38] can either be deemed to be among the second group of methods (above), or the third type of methods. kurihara [32] predicts that for fully reversed loading (r = -1.0), only 39 percent of the stress intensity factor range is effective for crack growth. however, not many empirical models are based on experimental data for part compressive stresses (and fully compressive stresses, for that matter). jones et al [23] found that by using a form of equation suggested by eason [33], and finding the coefficients from experimental data, the effects of negative r-ratio on the fatigue crack growth rates for even the high stress range tests could be bounded by correlating the foregoing equation to only positive r-ratio test results and extending the resulting equations into negative r-ratio regime. factors affecting fcg in compressions discussion eal life applications where fatigue loading is involved present a number of complicating problems e.g. variable amplitude loading, and residual stresses, to name a couple, and some of there factor are examined in the rest of this section. the examination is by no means exhaustive, but each sub-section provides a meaningful understanding to the whole topic: variable amplitude loading – effect of overload and underload variable amplitude loading itself poses a number of complications. variable amplitude cycles would in reality have a variable r-ratio, whereas cycle-by-cycle analysis using an r-ratio dependent growth law is tedious. indeed, to overcome this particular issue, the loading histogram (stress range vs. number of occurrence) could be rearranged and grouped into separate subsets with similar r-ratios for ease of calculation. however, another complicating factor, which is less easily surmountable, is the influence of the previous stress cycle on the increment of growth. to demonstrate the effect of load history on fatigue, mcevily et al [39] argue that if several alloys are ranked in terms of fatigue crack growth resistance under constant amplitude loading conditions, the same order of rating may not apply under variable amplitude loading, based on findings of minakawa et al [40]. this observation also confirms a deeper material dependence of fatigue behaviour. to provide an explanation for the effect of overload and underload (i.e. compressive overload), silva proposed as a competition between a damage accumulation effect and a residual stress effect [41]. in a study by stephens et al [42] it is experimentally shown that compressive loading greatly reduces the tensile overload effect. this is shown in fig. 1 taken from stephens [42]. mcevily et al [39] argue that “… the influence of compressive overloads or various combinations of compression-tension overloads is generally of lesser significance than a single tensile overload, an effect which can be related to a reduction of the crack opening level as the results of a compressive cycle.”. material-dependence of the overload and underload behaviour silva maintains that the difference in the sensitivity of different materials to negative loads may be due to the bauschinger effect [41]. based on test results, silva [43] also found that materials exhibiting strong cyclic hardening and a high bauschinger effect were strongly affected by the compressive load while materials exhibiting no cyclic hardening were relatively insensitive to applied compressive load. jones et al [23] observe that experimental results found from a specific material do not necessarily generalise, i.e. do not predict the behaviour of other alloys because with the exception of corrosion-induced blunting, crack-tip blunting and crack-tip plasticity behaviour are governed by the toughness/yield ratio of the material. in their review of fatigue crack growth, allen et al [44] argue that where stress ratio dependence is observed, such as the forman equation [34], it is usually associated with additional cyclic crack extension by brittle fracture or microvoid coalescence. see for example [45-46]. where neither mechanism is operative there is generally no stress ratio r chahardehi et al, frattura ed integrità strutturale, 35 (2016) 41-49; doi: 10.3221/igf-esis.35.05 45 dependence. as an example, frost et al [47] found no r-ratio dependence in pure aluminium, copper, or titanium. in these materials, therefore, there is a mechanistic difference between higher r-ratios and cycles including negative stress, compared to materials where r-ratio dependence is observed. it may be concluded that where empirical formulae are derived base on positive r-ratio data, extension of these formulae to negative r-ratios is not justified. figure 1: crack growth at different r-ratios following single tensile overload in 2024-t3 aluminium alloy, overload ratio =2.0 [42]. reprinted, with permission, from astm stp 595 fatigue crack growth under spectrum loads, copyright astm international, 100 barr harbor drive, west conshohocken, pa 19428. a note on residual stresses when a component contains tensile residual stresses, such as is common in weldments, the r-ratio is always assumed to be greater than 0.5. the rationale for this is that since welds can contain residual stresses of the order of the yield strength of the material, most general engineering cyclic loading cases, when superimposed on the residual stress, would result in a fully tensile cycle with high mean stresses. however, as allen et al [48] point out, the potential for conservative prediction should be noted. presence of tensile residual stresses implies the presence of balancing compressive stresses, which is usually not assessed in fatigue in the conservative assumption, whereas in reality in a stress-relieved weld, the crack may close during the compression cycle, therefore removing the stress concentration at the crack tip. on the other hand, where a non-redundant structural component is welded, far-reaching residual stresses due to the misfits (or geometrical incompatibility) of the set up may be generated which have not been calculated in the modelling phase, say by using finite element method. presence of this type of stress would increase the mean stress, and therefore should not be overlooked in assessment. effect of thickness some authors have correlated certain experimental observations to thickness effect see for example [49]. however these explanations do not sufficiently deal with acceleration under plane strain conditions [41], and the question is still partly unanswered. effect of stress range crooker [50] showed that compressive part of the loading is more influential for low-cycle fatigue. jones et al [23] have examined the effect of high stress ranges in fatigue crack growth, for r=-1.0. the results suggest that there is a significant difference between fatigue crack growth rate curves for small and large stress ranges, and whether the initial stress cycle closes or opens the crack: less benefit is seen when the first cycle closes the crack. jones’s suggestion is in keeping with crooker’s observation [50]. effect of crack length kurihara et al [32] performed experiments where they could show that the u parameter (ratio of effective stress intensity factor range and mathematical stress intensity factor range) is dependent on crack length (for smaller cracks), and this dependence is stronger for smaller (more negative) r-ratios. fig. 2 shows this behaviour. chahardehi et al, frattura ed integrità strutturale, 35 (2016) 41-49; doi: 10.3221/igf-esis.35.05 46 figure 2: dependence of u on crack length. reprinted with permission from [32]. copyright (1985) the society of materials science, japan. during early stages of crack growth, the effective stress range ratio (u) decreases with an increase in crack length. this parameter then approaches a constant value. for more negative r-ratios, this decrease continues over a longer crack size. this is believed to be due to the larger size of the zone of residual stress due to compressive loading at more negative rratios [32]. effect of loading mode only uniaxial loading is considered in the present work under mode i, i.e. ‘opening mode’ loading. work on biaxial stress fields has shown similar r-ratio dependence of fatigue crack growth [51]. chung-seong et al [52] looked at the effect of loading mode (pure bending vs. axial loading) in closure behaviour of surface and through-thickness cracks. the loading mode does not seem to affect the relative ratio of crack opening in through-thickness and surface cracks. however, effect of loading mode on residual stresses from compressive cycle is not directly obtained. therefore one hypothesis may be that the shape and extent of the residual stress field developed due to compressive stress could be dependent on loading mode. miscellaneous considerations care should be exercised when dealing with closure in corrosive environment, as the mechanisms involved may not have been fully understood. also, sensitivity of closure behaviour to waveform and frequency has not been experimentally investigated, however it may be assumed that mechanistically the behaviour should not be dependent on these two parameters, as is the case in general crack growth under constant amplitude loading. compressive behaviour at variable amplitude has also not been investigated. conclusions he two important features recognized in fatigue of compressively loaded components are the beneficial effect of closure (for low r-ratio loads with a tensile part), and the finite albeit limited growth in fully compressive stress mode. the current papers highlights the observations, performed over the last five decades, among with some of the explanations given for certain features. fatigue crack growth in compression is clearly confirmed to be a complicated phenomenon, where a simple, broad-brush method for its assessment has not been developed. observations include the t chahardehi et al, frattura ed integrità strutturale, 35 (2016) 41-49; doi: 10.3221/igf-esis.35.05 47 influences of crack length, stress range, thickness, and material properties, providing a complicated picture. however, some of the better-established trends have not been transferred to codes and standards. a full review of the existing empirical formulae based on r-ratio, and also a full review of historic evolution of codes and standards is beyond the scope of the paper, and should be conducted in the future. acknowledgement he authors would like to personally thank prof feargal brennan of cranfield university and mr david linkens of atkins for their support. references [1] bs7910 : 2013 – guide to methods for assessing the acceptability of flaws in metallic structures, british standards institution (2013). [2] maddox, s.j., the effect of mean stress on fatigue crack propagation – a literature review, int. j. frac., 11 (1975) 389408. [3] king, r.n., a review of fatigue crack growth rates in air and seawater, hse offshore technology report oth 511 (1998), health and safety executive, uk. [4] esdu 80036 with amendments a and b, introduction to the use of linear elastic fracture mechanics in estimating fatigue crack growth rates and residual strength of components, engineering science data unit (1996). [5] astm e647-13 ae1, standard test method for measurement of fatigue crack growth rates, american society for testing and materials (2013). [6] dnv, fatigue strength of mobile offshore units, classification note no. 30.2, det norske veritas, norway (1984). [7] almen, j.o., black, p.h., residual stresses and fatigue in metals, mcgraw-hill, new york (1963). [8] gerber, t.l., fuch, h.o., analysis of nonpropagating fatigue cracks in notch parts with compressive mean stress, j. mat., 3 (1968) 359-374. [9] hubbard, r.p., crack growth under cyclic compression, j. basic eng., trans. asme, series d, 91 (1969) 625631. [10] suresh, s., crack initiation in cyclic compression and its application, eng. frac. mech., 21 (1985) 453-463. doi:10.1016/s0013-7944(85)80038-2 [11] fleck, n.a., shin, c.s., smith, r.a., fatigue crack growth under compressive loading, eng. frac. mech., 21 (1985) 173-185. doi:10.1016/0013-7944(85)90063-3 [12] solis, j., lapetra c., dominguez j., crack initiation under compression fatigue in tough ceramics, 9th eur. conf. frac (1992). [13] pippan, r., the growth of short cracks under cyclic compression, fatigue frac. eng. mat. struc., 9 (1987) 319-328. doi: 10.1111/j.1460-2695.1987.tb00459.x [14] hermann, r., fatigue crack growth in ductile materials under cyclic compressive loading, fatigue frac. eng. mat. struc., 17 (1994) 93-103. doi: 10.1111/j.1460-2695.1994.tb00775.x [15] kasaba, k., sano, t., kudo, s., shoji, t., katagiri, k., sato, t., fatigue crack growth under compressive loading, j. nuclear mat. 258-263 (1998) 2059-63. [16] yu, m.t., topper, h., au, p., the effect of stress ratio, compressive load and underload on the threshold behaviour of a 2024-t351 aluminium alloy, fatigue 84 – 2nd int. conf. fatigue and fatigue threshold, birmingham (1984) 179190. [17] tack, a.j., beevers, c.j., the influence of compressive loading on fatigue crack propagation in three aerospace bearing steels, 4th int. conf. fatigue and fatigue threshold, honolulu (1990) 1179-1184. [18] pommier, s., cyclic plasticity and variable amplitude fatigue, int. j. fatigue, 25 (2003) 983-997. doi:10.1016/s01421123(03)00137-3. [19] saal, h., fatigue crack growth in notched parts with compressive mean load, j. basic eng. 94 (1972) 243-247. doi:10.1115/1.3425376 [20] dugdale, d.s., yielding of steel sheets containing slits, j. mech. phys. solids, 8 (1960) 100-104. doi: 10.1016/00225096(60)90013-2. t chahardehi et al, frattura ed integrità strutturale, 35 (2016) 41-49; doi: 10.3221/igf-esis.35.05 48 [21] bueckner, h.f., a novel principle for the computation of stress intensity factors, zeitschrift fur angewandte mathematik und mechanik, 50 (1970) 529-546. [22] nelson, d.v., effect of residual stress on fatigue crack propagation, in residual stress effects in fatigue, astm stp, 776 (1982) 172-184. [23] jones, d.p., hoppe, r.g., hechmer, j.l., james, b.a., an experimental study on the effects of compressive stress on the fatigue crack growth of low-alloy steel, j. pres. vessel tech., asme, 116 (1994) 317-323. doi:10.1115/1.2929595. [24] libatskii, l.l., determination of the length of slip bands in a plate with a circular hole, soviet materials science, 2 (1966) 31-34. [25] reid, c.n., moffatt, j., hermann, r., fatigue under compressive loading and residual stress, scripta metallurgica, 22 (1988) 1743-1748. doi: 10. 1016/s0036-9748(88)80276-x. [26] reid, c.n., a method for mapping residual stress in a compact tension specimen, scripta metallurgica, 22 (1988) 451 456. doi:10.1016/0036-9748(88)90004-x. [27] zhang, j., he, x.d., sha, y., du, s.y., the compressive stress effect on fatigue crack growth under tension compression loading, int. j. fatigue, 32 (2010) 361-367. doi:10.1016/j.ijfatigue.2009.07.008. [28] silva, f.s., crack closure inadequacy at negative stress ratios, int. j. fatigue, 26 (2004) 241-252. doi:10.1016/s0142 1123(03)00162-2. [29] iswanto, p.t., nishida, s., hattori, n., effect of compressive mean stress and compressive residual stress on fatigue properties of stainless steel sus304, proc. 12th int. offshore and polar eng. conf., kitakyushu, japan, (2002) 209213. [30] chahardehi, a., brennan, f.p., steuwer, a., the effect of residual stresses arising from laser shock peening on fatigue crack growth, eng. frac. mech., 77 (2010) 2033-2039. doi:10.1016/j.engfracmech.2010.03.033. [31] walker, k., the effect of stress ratio during crack propagation in cycle-loaded structures, j. basic eng., 89 (1967) 459 464. [32] kurihara, m., katoh, a., kawahara, m., effects of stress ratio and step loading on fatigue crack propagation rate, materials research series, current research on fatigue cracks, the society of materials science, japan, 1 (1985) 217233. [33] eason, e.d., gilman, j.d., jones, d.p., andrew, s.p., technical basis for a revised fatigue crack growth rate reference curve for ferritic steels in air, j. press. vessel tech., 114 (1992) 8086. doi: 10.1115/1.2929016. [34] forman, r.g., kearney, v.e., eagle, r.h., numerical analysis of crack propagation in cyclic loaded structures, transactions of asme (series d), 69 (1967) 459-463. [35] mcevily, a.j., gregor, j., on the threshold for fatigue-crack growth, 4th int. conf. frac, waterloo, 2 (1977) 12931298. [36] bloom, j.m., an approach to account for negative r-ratio effects in fatigue crack growth calculations for pressure vessels based on crack closure concepts, trans. asme, 116 (1994) 30-35. [37] xiaoping huang, fatigue crack growth rate recommended in bs7910 and an unique crack growth rate curve under different load ratios, proc. of pvp2007 – san antonio (2007). [38] vasudevan, a.k., sadananda, k., louat, n., two critical stress intensities for threshold crack propagation, scritpta metallurgica, 28 (1993) 65-70. doi: 10. 1016/09656-716x(93)90538-4. [39] mcevily, a.j., minakawa, k., crack closure and variable-amplitude fatigue crack growth, in basic questions in fatigue, astm stp 924, fong, j.t., fields, r.j., american society for testing and materials, i (1988) 357-376. [40] minakawa, k., levan, g., mcevily, a.j., the influence of load ratio on fatigue crack growth in 7090-t6 and in 9021t4 p/m aluminium alloys, metallurgical and mat. trans. a, 17 (1986) 1787-1795. [41] silva, f.s., fatigue crack propagation after overloading and underloading at negative stress ratios, int. j. fatigue, 29 (2007) 1757-1771. doi:10.1016/j.ijfatigue.2007.03.012. [42] stephens, r.i., chen, d.k., hom, b.w., fatigue crack growth with negative stress ratio following single overloads in 2024-23 and 7057 t6 aluminum alloys, in fatigue crack growth under spectrum loads, astm stp 595 (1976), 2740. [43] silva, f.s., the importance of compressive stresses on fatigue crack propagation rate, int. j. fatigue, 27 (2005) 1441 1452. doi:10.1016/j.ijfatigue.2005.07.003. [44] allen, r.j., booth, g.s., julta, t., a review of fatigue crack growth characterisation by linear elastic fracture mechanics (lefm). part i – principles and methods of data generation, fatigue frac. eng. mat. struc., 11 (1988) 45-69. doi: 10.1111/j.1460-2695.1988.tb01219.x chahardehi et al, frattura ed integrità strutturale, 35 (2016) 41-49; doi: 10.3221/igf-esis.35.05 49 [45] richards, c.e., lindley, t.c., the influence of stress intensity and microstructure on fatigue crack propagation in ferritic materials, eng. frac. mech., 4 (1972) 951-978. [46] ritchie, r.o., knott, j.f., effects of fracture mechanisms on fatigue crack propagation, conf. mechanics and mechanisms of fatigue crack growth, cambridge, british steel corporation, (1973) 12. [47] frost, n.e., pook, l.p., denton, k., a fracture mechanics analysis of fatigue crack growth data for various materials, eng. frac. mech., 3 (1971) 109-126. doi:10.1016/0013-7944(71)90003-8. [48] allen, r.j., booth, g.s., julta, t., a review of fatigue crack growth characterisation by linear elastic fracture mechanics (lefm). part ii – advisory documents and applications within national standards, fatigue frac. eng. mat. struc., 11 (1988) 71-108. doi: 10.1111/j.1460-2695.1988.tb01162.x. [49] makabe, c., purnowidodo, a., mcevily, a.j., effects of surface deformation and crack closure on fatigue crack propagation after overloading and underloading, int. j. fatigue, 26 (2004) 1341-1348. doi:10.1016/j.ijfatigue.2004.03.017. [50] crooker, t.w., effect of tension-compression cycling on fatigue crack growth in high-strength alloys, naval research laboratory report 7220 (1971). [51] zamrik, s.y., shabara, m.a., the effect of stress ratio on fatigue crack growth in a biaxial stress field, j. pres. vessel tech. 99 (1977) 137-143. doi:10.1115/1.3454497. [52] chung-seong oh, ji-ho song, crack growth and closure behaviour of surface cracks under pure bending loading, int. j. fatigue, 23 (2001) 251-258. doi:10.1016/s0142-1123(00)00090-6. << /ascii85encodepages false /allowtransparency false /autopositionepsfiles true /autorotatepages /none /binding /left /calgrayprofile (dot gain 20%) /calrgbprofile (srgb iec61966-2.1) /calcmykprofile (u.s. web coated \050swop\051 v2) /srgbprofile (srgb iec61966-2.1) /cannotembedfontpolicy /error /compatibilitylevel 1.4 /compressobjects /tags /compresspages true /convertimagestoindexed true /passthroughjpegimages true /createjobticket false /defaultrenderingintent /default /detectblends true /detectcurves 0.0000 /colorconversionstrategy /cmyk /dothumbnails false /embedallfonts true /embedopentype false /parseiccprofilesincomments true /embedjoboptions true /dscreportinglevel 0 /emitdscwarnings false /endpage -1 /imagememory 1048576 /lockdistillerparams false /maxsubsetpct 100 /optimize true /opm 1 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can be opened with acrobat and adobe reader 5.0 and later.) >> /namespace [ (adobe) (common) (1.0) ] /othernamespaces [ << /asreaderspreads false /cropimagestoframes true /errorcontrol /warnandcontinue /flattenerignorespreadoverrides false /includeguidesgrids false /includenonprinting false /includeslug false /namespace [ (adobe) (indesign) (4.0) ] /omitplacedbitmaps false /omitplacedeps false /omitplacedpdf false /simulateoverprint /legacy >> << /addbleedmarks false /addcolorbars false /addcropmarks false /addpageinfo false /addregmarks false /convertcolors /converttocmyk /destinationprofilename () /destinationprofileselector /documentcmyk /downsample16bitimages true /flattenerpreset << /presetselector /mediumresolution >> /formelements false /generatestructure false /includebookmarks false /includehyperlinks false /includeinteractive false /includelayers false /includeprofiles false /multimediahandling /useobjectsettings /namespace [ (adobe) (creativesuite) (2.0) ] /pdfxoutputintentprofileselector /documentcmyk /preserveediting true /untaggedcmykhandling /leaveuntagged /untaggedrgbhandling /usedocumentprofile /usedocumentbleed false >> ] >> setdistillerparams << /hwresolution [2400 2400] /pagesize [612.000 792.000] >> setpagedevice microsoft word numero 12 art 6 a. namdar et alii, frattura ed integrità strutturale, 12 (2010) 57-62; doi: 10.3221/igf-esis.12.06 57 tsunami numerical modeling and mitigation abdoullah namdar, asima nusrath university of mysore, mysore, india. ab_namdar@yahoo.com; sina_a_n@yahoo.com abstract. the numerical modeling and wave theory are used in tsunami mitigation analysis. it is assumed sea forest is simulating offshore structure submitted to wave loads. the sea forest acts simulate break waves in conservation of coastal territory and facility installed over there. the result reveal that mathematical modeling and numerical simulation can be used to understand tsunami ability in design and urban construction, the research indicates reduction of water deep by sea forest resulted in reducing geometry and all wave ability. keywords. tsunami; wave theory; offshore structure; urban design. introduction he tsunami has brought lot of suffering to people residing in the coastal areas. an estimated 489 cities within the pacific states of alaska, california, hawaii, oregon, and washington are susceptible to floods, cyclones and tornadoes, and as many as 900,000 residents of these cities would be inundated by a height of 50-foot wave striking these coasts. it has been reported by the testing of “tsunami resistant model house” that the impact on a new ‘tsunami resistant model house’ design house was far less than that on a typical coastal house. this model was developed in the usa and now built in sri lanka. digital images recorded during the test reveal how the tsunami wave passed through the new house design without damaging [1]. on the morning of sunday, december 26, 2004 an earthquake registering 9.0 on the richter scale struck off the western coast of north sumatra, triggering massive waves that devastated coastal regions throughout the indian ocean rim. indonesia’s aceh province suffered the greatest mortality with widespread destruction extending along more than 1,000 kilometers of coastline. approximately one year after the tsunami, indonesian government estimates a total of 129,775 deaths, 38,786 missing and 504,518 tsunami-displaced in aceh province [2]. the implementation of urban planning and design particularly for mitigating tsunami has been applied by various researchers [3-5]. the urban design is the main and primary concept of social life. in this investigation authors have made an attempt to mathematically calculate tsunami force and found ways to disable its force before reaching the coastline of urban area. this paper is attempting to propose method to improve urban design by utilizing the polluted coastal areas which will not only serve to increase the ecological condition by developing and implementing the concept of green belts but also serve as a barrier of the oceanic waves to enter the coast. methodology and modeling here is two methods in understanding wave force applied to the structure or to any natural barrier, the first one is application of way theory and second is using fundamental fluid dynamics equations. here, the application of wave theory is considered. t t http://dx.medra.org/10.3221/igf-esis.12.06&auth=true http:/www.gruppofrattura.it a. namdar et alii, frattura ed integrità strutturale, 12 (2010) 57-62; doi: 10.3221/igf-esis.12.06 58 the winds, waves, currents, ice, earthquake, soil movement and ship collision could be analysis and modeled by mathematical method. the morison equation could be used in estimating of wave force acting on offshore structure, it may be written as [6]. f=0.5ρcdap|u|u+ρ cm (du/dt) ρ = density cd = 0.6 – 1.2 ap = projected frontal area u = velocity of the ambient flow cm = inertia coefficient = 2 = displaced of volume of structure (du/dt) = assumed ∂u/∂t and also the isaacson (1979) equation is complete expression for the inertial force in the x direction of wave [6]. it is assumed that the wave is bi-dimensional, x and y being the 2d coordinates, all the formulae can be used in the two directions, and this maintains permanent form and also incompressible, inviscid and the flow is irrotational. l =wave length = t√(gd) h =wave height t =wave period z =h/2 c =wave speed = (l/t) range of validity; kd< (π/10) (d/l) < (1/20) (d/gt2) < 0.0025 p = pressure = ρgz + 0.5ρgh cosθ e = average energy density = 0.125 ρgh2 sxx = radiation stress = 1.5 e syy = radiation stress = 0.5 e sxy =syx = radiation stress =0 results and discussion he mathematical modeling and numerical simulation of wave can be performed to understand wave characteristics. the result of tab. 1-3 and fig. 1-3 indicate that the wave length has a direct correlation with dangerous wave effects. sl. no wave length (m) wave speed (m/s) pressure (kg/m2) average energy density (kg/m3) radiation stress in x direction (kg/m2) radiation stress in y direction (kg/m2) 1 10 2.21 26.39 10.20 15.31 5.10 2 20 3.13 52.79 40.83 61.25 20.41 3 30 3.83 79.18 91.88 137.82 45.94 4 40 4.42 105.58 163.34 245.01 81.67 5 50 4.95 131.97 255.22 382.835 127.61 6 60 5.42 158.37 367.52 551.28 183.76 7 70 5.85 184.76 500.23 750.35 250.11 8 80 6.26 211.16 653.37 980.05 326.68 9 90 6.64 237.55 826.92 1240.38 413.46 10 100 7 263.95 1020.89 1531.34 510.44 table 1: mathematical characteristics of wave in shallow water. t http://dx.medra.org/10.3221/igf-esis.12.06&auth=true http:/www.gruppofrattura.it a. namdar et alii, frattura ed integrità strutturale, 12 (2010) 57-62; doi: 10.3221/igf-esis.12.06 59 figure 1: mathematical characteristics of wave in shallow water. sl. no wave length (m) wave speed (m/s) pressure (kg/m2) average energy density (kg/m3) radiation stress in x direction (kg/m2) radiation stress in y direction (kg/m2) 1 100 7 263.95 1020.89 1531.33 510.44 2 200 9.899 527.90 4083.57 6125.35 2041.78 3 300 12.12 791.86 9188.03 13782.05 4594.01 4 400 14 1055.82 16334.29 24501.43 8167.14 5 500 15.65 1319.77 25522.33 38283.49 12761.16 6 600 17.15 1583.73 36752.15 55128.23 18376.07 7 700 18.52 1847.68 50023.76 75035.65 25011.88 8 800 19.8 2111.64 65337.16 98005.74 32668.58 9 900 21 2375.59 82692.35 124038.52 41346.17 10 1000 22.14 2639.55 102089.32 153133.98 51044.66 table 2: mathematical characteristics of wave in shallow water. figure 2: mathematical characteristics of wave in shallow water. http://dx.medra.org/10.3221/igf-esis.12.06&auth=true http:/www.gruppofrattura.it a. namdar et alii, frattura ed integrità strutturale, 12 (2010) 57-62; doi: 10.3221/igf-esis.12.06 60 sl. no wave length (m) wave speed (m/s) pressure (kg/m2) average energy density (kg/m3) radiation stress in x direction (kg/m2) radiation stress in y direction (kg/m2) 1 1000 22.14 2639.55 102089.323 153133.98 51044.66 2 2000 31.3 5279.09 408357.29 612535.93 204178.64 3 3000 38.34 7918.64 918803.90 1378205.85 459401.95 4 4000 44.27 10558.2 1633429.16 2450143.74 816714.58 5 5000 49.5 13197.75 2552233.06 3828349.59 1276116.53 6 6000 54.22 15837.3 3675215.61 5512823.41 1837607.80 7 7000 58.57 18476.85 5002376.81 7503565.20 2501188.40 8 8000 62.61 21116.4 6533716.64 9800574.96 3266858.32 9 9000 66.41 23755.95 8269235.13 12403852.69 4134617.56 10 10000 70 26395.50 10208932.3 15313398.39 5104466.12 table 3: mathematical characteristics of wave in shallow water. figure 3: mathematical characteristics of wave in shallow water. to reduce of wave length as per mathematical equation, one way is to reduce the water depth, this subsequently leads to reduction geometry and all dangerous wave effects. the bandarabbas city of iran with geographical condition placed in front of the geshm island with minimum of 1km distance. this geographical position increases tsunami wave if it occur between the geshm island of 120 km length and bandarabbas coastal, this is a factor make complicate tsunami wave behavior. this geographical condition could be bringing back wave from one coastal to other (fig 4). figure 4: satellite image of persian gulf. figure 5: mangrove root shape. http://dx.medra.org/10.3221/igf-esis.12.06&auth=true http:/www.gruppofrattura.it a. namdar et alii, frattura ed integrità strutturale, 12 (2010) 57-62; doi: 10.3221/igf-esis.12.06 61 the mangrove root shape (fig 5) is similar coarse aggregate, this shape increases soil foundation bearing capacity and tree stability and this could control land slide, deformation, settlement and increases soil cohesion which is needed in standing of trees subjected to dynamic force. the mangrove root strength can be find from laboratory experiments: the process is statistic and experimental is similar to approach other construction material such as steel. the advantage of coastal area is mangrove root not affect to any structure foundation. density of mangrove jungle is depending on plan the height of mangrove could be reach average up to 15 ft, all assumption can be lead to reach a hypothesis for considering jungle as a solid area in wave height reduction. another idea about mangrove in tsunami mitigation is similarity to dense wall installed in subsoil for reduction of dynamic stress created under shaking table function this method reduces soil deformation mitigation as well as seismic force. the mangrove root function in tsunami is simulate soil nailing or micro pile in ground stabilization and improvement, this reduce all kind of geotechnical problem faces subsoil during the tsunami, this is simulate of passing vehicle on the subsoil which create of dynamic force at any moment. the mathematically calculation water self weight shown in fig. 6, it is exhibited reducing the lateral pressure of water in the static position if area have been under plantation, it is clear the tsunami is in the dynamic form, and need of calculation of tsunami speed reduction, it has direct correlation with strength, diameter, root, height, density and body tree. the soil texture has independently affect in stability of tree which soil consists of clay mineral with high level of cohesion helps in standing tree submitted to the dynamic force. 40,71 1*57*40.71=2320.47/2=1160.24 kg 1160.4*19=22044.56 kg/m 50 total bending moment 1750*23.33=40827.5kg/m total lateral pressure 1*70*50=3500/2=1750 kg 7 0 plantation area 5 7 total bending moment total lateral pressure figure 6: water force model before and after plantation. the figures 7-9 are shown different types of mangrove. due to creation of jungle, the urban area take advantage of approaching better environment, the another advantage of this urban design method is to have an attractive tourist place with job creation and it lead to improve of economically development of coastal region. in the coastal territory with land shortage for green belt, this method is applicable and will have significantly affect on maintain of climate which is one of the important problem in recent century society faces. figure 7: mangrove tree in coastal area. http://dx.medra.org/10.3221/igf-esis.12.06&auth=true http:/www.gruppofrattura.it a. namdar et alii, frattura ed integrità strutturale, 12 (2010) 57-62; doi: 10.3221/igf-esis.12.06 62 figure 8: mangrove tree in coastal area. figure 9: mangrove tree in coastal area. conclusion the result reveals mathematical modeling and numerical simulation could be used to understand dangerous wave effects in design and urban construction. the research indicates reduction of water deep by sea forest results in reducing geometry and all dangerous wave effects. the method could be applied in reduction of air pollution and the control of tsunami force. the method will create attractive tourist places. the method is fruitful to develop the economy of coastal regions. if the tsunami not occur in the region the society could use advantage of the improvement of climate. it is possibility to have green belt in the coastal territory if faces of land shortage. references [1] i. proce navaratnam et al., civil engineering, 161 (2008) 77. [2] united nations information management service (unims) in collaboration with the rehabilitation and reconstruction agency (brr). tsunami recovery status report, 8 december 2005 [3] fig. the contribution of the surveying profession to disaster risk management, a publication of fig working group 8.4 international federation of surveyors (fig) (2006). [4] m. pelling, the vulnerability of cities: natural disasters and socialresilience, london: earthscan publications (2003). [5] jica. the study on the urgent rehabilitation and reconstruction support program for acehprovince and affected areas in north sumatra. japan international cooperation agency (jica), badan perencanaan pembangunan nasional (bappenas), and provincial government of nanggroe aceh darussalaam, banda aceh working report (2005). [6] t. sarpkaya, m. isaacson, mechanics of wave forces on offshore structures, van nostrand reinhold co, (1981) 295. http://dx.medra.org/10.3221/igf-esis.12.06&auth=true http:/www.gruppofrattura.it shot peening processes to obtain nanocrystalline surfaces in metal alloys: k. li et alii, frattura ed integrità strutturale, 51 (2020) 386-397; doi: 10.3221/igf-esis.51.28 386 the development and application of an original 3d laser scanning: a precise and nondestructive structural measurements system kexin li, jun wang college of civil engineering, northeast forestry university, harbin 150000, china like@nefu.edu.cn, http://orcid.org/0000-0003-3854-1710 jun.w.619@163.com dawei qi school of science, northeast forestry university, harbin 150000, china qidw9806@126.com abstract. recently, a number of non-destructive testings (ndts) equipment which can partially replace human-conducted on-site inspections has been implemented for detecting modern civil architectural structures. however, the situation of implementing 3d laser scanning measurement technology worldwide is not optimistic: several inconvenient flaws are troubling users (e.g., heavy, costly, hard to move, hard to inspect and etc.). therefore, a new equipment to address the problems is urgently demanded. a 3d laser scanning system is designed composed of high precision elevating platform and small 2d laser ranging sensor. manufacture process of the 3d laser scanning system is described in detail. a comparative analysis with other non-contact measurement experiments based on the bending fatigue load test, the scanning designed efficiency and feasibility has been proved. the information of micro-damage and depth of the structure can be quickly captured by the designed 3d laser scanning system. its detecting performance is better than the traditional methods. to overcome the challenges of the 3d laser scanning on-site measurement technology, this paper proposes the manufacture process of the 3d scanning system with a high precision, miniaturization and lightweight. keywords: structure detection; 3d laser scanning; nondestructive testing; digital image process; measurement on site. citation: li, k., wang, j., qi, d., the development and application of an original 3d laser scanning: a precise and nondestructive structural measurements system, frattura ed integrità strutturale, 51 (2020) 386-397. received: 15.10.2019 accepted: 01.12.2019 published: 01.01.2020 copyright: © 2020 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. introduction uilding structure testing can provide a reliable basis for the quality assessment of engineering structures, the identification of existing structural properties and the verification of structural calculation theory [1]. the building structure is inspected on site through various measurement techniques. the structural related parameters are obtained. the effective feature information reflecting the current state of the structure is captured. and the relationship b http://orcid.org/0000-0003-3854-1710 mailto:%20%3cqidw9806@126.com%3e http://www.gruppofrattura.it/va/51/2658.mp4 k. li et alii, frattura ed integrità strutturale, 51 (2020) 386-397; doi: 10.3221/igf-esis.51.28 387 between the structure and the resistance is analyzed. it is used to promote the comprehensive judgment and evaluation of the safety and reliability of the structure. [2]. however, the detection process is limited by the complex constraints of the engineering site. the traditional structure detection technology cannot fully meet the requirements of modern building structure detection in terms of measuring dimensions, range and frequency [3]. for example, the progressive collapse study, which has received extensive attention from the international civil engineering community. the dynamic response of the structure is triggered by the initial initialization of the test component's own components, resulting in high frequency vibration and large deformation. the dynamic strain and the displacement are required to be measured, which exceed the application range of traditional measurement technology [4]. therefore, it is very necessary to develop precision detection devices and related measurement technologies in combination with various emerging fields. thereby, the non-destructive detection and reliability identification of modern building structures can be realized efficiently [5]. as one of the latest advances in the field of structural measurement, non-contact measurement technology has the advantages of undamaged, accuracy and objectivity [6]. among them, digital image correlation (dic) has been widely used in structural detection experiments [7]. however, dic technology requires higher illumination conditions for the detection environment. it generally requires multiple devices to work together to obtain spatial deformation information [8]. and the 3d laser scanning measuring device has the following advantages: 1) non-destructive: getting rid of installing the sensor on the object to be detected; 2) strong environmental adaptability: the laser itself can be used as a light source to resist interference; 3) efficient detection: can achieve 3d information acquisition of a single device [9-12]. therefore, the 3d laser scanning technology have lately received great attention in the field of building structure inspection [13, 14]. park [15] applied 3d laser scanning technology to structural health monitoring, and verified the effectiveness of the method based on the static loading test of simply supported steel beams. olsen [16] used 3d laser scanning technology to quantitatively describe the structural damage based on the reinforced concrete frame joint test. dai [17] obtained the 3d laser scanning data of the steel beam structure and extracted the deformation field information of the structure. the widespread application of commercial, integrated 3d laser scanners to structural testing are facing numerous challenges: 1) scanners are usually expensive, bulky, and complex; 2) the detection environment is limited, and it is difficult for the inspectors to operate flexibly; 3）usually, the scanner scans large structures, and it is difficult to accurately construct a three-dimensional model of the structural test object. therefore, it is worthwhile devoting much effort to develop a 3d laser scanning device that is miniaturized, lightweight, high precision and low-cost, thereby achieving accurate modeling of modern structural tests [18]. the laser ranging sensor is characterized by accuracy and efficiency. therefore, it plays an important role in measurement, navigation and security [19]. among them, the 2d laser ranging sensor can form a single complete scanning plane by single line scanning. we can independently design a 3d scanning device that drives the 2d laser sensor to move up and down according to the needs of the detection object and the environment.20]. the designed scanning device is more adaptable and flexible, can accurately construct a 3d model based on lower cost. the 3d scanning device integrated by 2d laser sensor has been widely used in environmental modeling, mechanical automation and other fields. for example, the fraunhofer institute for autonomous intelligent systems in germany developed an autonomous mobile robot with a 2d laser range finder and successfully applied it to 3d exploration and digital simulation for indoor environments [21]. chou [22], etc., installed a 2d laser sensor on a rotating four-bar linkage to create an indoor 3d mapping automatic scanning robot. cai jun [23] developed a 3d laser scanning system consisting of a high-precision rotating head and a small 2d laser ranging sensor to achieve high-precision automation environment modeling. the detection technology of 3d laser scanning by adding 2d laser sensor to the 1d transmission actuator has achieved good research results [24-25]. however, despite these considerable advantages, this technology has not been widely promoted in structural testing studies. in summary, it is essential to independently develop a 3d laser scanning system for modern structural inspection. the stepper motor drives the fine movement of the sliding group to realize the lifting and scanning of the two-dimensional laser ranging sensor. this system is portable, more accurate, more adaptable and less costly. it realizes non-destructive, efficient and accurate detection of structural damage 3d information. based on the rpc bending fatigue test, the reliability of the 3d modeling and structural damage information measurement data of the device was verified. 3d laser scanning system design principles of system design he 3d laser scanning system designed in this paper is mainly composed of a 2d laser ranging sensor, a sliding mold combination, a bracket, a control box and a computer, as shown in figure 1. the scanning system is divided into four parts: a transmission actuator, a transmission control device, a laser ranging sensor, and a sensor control t k. li et alii, frattura ed integrità strutturale, 51 (2020) 386-397; doi: 10.3221/igf-esis.51.28 388 interface. the transmission actuator is driven by a stepping motor to output a high-precision, controllable lifting movement. the drive control unit consists of a stepper motor driver, plc and related components. the control slider performs a uniform linear ascending and descending motion on the slide rail through the m programming language. in order to control the uniform linear lifting scanning action of the laser ranging sensor, it is fixedly mounted on the slider through the connecting plate. the sensor scan plane is parallel to the ground and perpendicular to the drive direction. the parameters of the laser sensor are set on the surface of the sensor control interface, so that the scanning optical center lifting speed is consistent with the linear sliding group motion output. figure 1: design drawing of 3d laser scanning system. system measurement principle two coordinate systems for the structural characteristics of the 3d laser measurement system are defined as followed: 1) the coordinate system of laser ranging sensor position: {oa-xayaza}; 2) the coordinate system of the image acquired by laser scanning: {o-xyz}. the origin of the {oa-xayaza} coordinate system is located at the sensor transmission port, xaoaya is parallel to the scanning surface of the two-dimensional laser, and za is the transmission direction. the moving speed of the laser sensor in the z direction is v (m / s), and the movement time is t (s). in the initial state, the laser emitting end (red circle) coincides with the origin. the angle between the laser emitted by the transmitting end and xa is α, and the coordinate of the intersection with the object to be detected is s (xa,xb,xc). the laser is emitted to the object, and the reflected light on the object is reflected to the receiving end (green circle). the angle between the emitted light and the reflected light is θ. the x-axis of the {o-xyz} coordinate system is parallel to the intersection of the scanning plane and the detected object. the y-axis is parallel to the scanner drive direction. the z-axis represents the distance from the laser emitting end of the scanning plane to the detected object. figure 2: laser ranging sensor coordinate system {oa-xayaza} k. li et alii, frattura ed integrità strutturale, 51 (2020) 386-397; doi: 10.3221/igf-esis.51.28 389 in the {oa-xayaza} coordinate system, the three-dimensional coordinates of s (xa, xb, xc) are expressed as follows:      = = = vtz y x a a a   sin cos (1) the distance from the sensor to the surface of the object can be expressed by equation (2):  tand= (2) therefore, the position coordinates of any light spot s can be expressed as:        = = = vtz dy dx a a a     tan sin tan cos (3) then the laser scanned image is obtained and establish the coordinate system {o-xyz} is established, as shown in fig. 3. figure 3: laser scanning image coordinate system {o-xyz}. the laser scanned image is an object model that is recombined by laser spots. therefore, the detection data of the structure can be acquired by the position change information of any two points p1(x1, y1, z1) and p2(x2, y2, z2) on the image. the deformation information of the structure can be calculated by the formula (4). 2 12 2 1212 )()( yyxxpp −+−= (4) where y = vt, x is related to the variables α, θ and the size of the detected object. the variation of the structure elevation information can be obtained by formula (5). 12 zzd −= (5) where tandz = . therefore, the established 3d laser scanning system can detect structural damage by acquiring the positional changes of the spots on the laser scanned image. k. li et alii, frattura ed integrità strutturale, 51 (2020) 386-397; doi: 10.3221/igf-esis.51.28 390 implementation of 3d laser scanning system bracket he bracket is used to support and stabilize the transmission actuator, including the main body of the bracket, the base and the wheel. the overall composition is shown in figure4. figure 4: bracket composition. the main body of the bracket is made up welded i-shaped steel with a total length of 1200mm. the overall height of the bracket is 1300mm. in order to facilitate the installation and movement of the sliding group, a hole is placed on each side of the struts 50mm apart, for a total of 23 holes. the maximum effective detection height is 2000mm, and can be adjusted arbitrarily according to the on-site inspection environment. in order to ensure good stability and portability of the struts, the struts and the base are fixed by welding. the pulleys are installed on the four corners of the base. sliding module the combination of sliding mode is as the basic support of the transmission system, including the strut, stepper motor, slider, screw, as shown in figure 5. in order to ensure a perfect nested connection between the sliding group and the bracket body, m4 nut slots corresponding to the bracket body are disposed on both sides and the rear of the pillar. for the purpose of improving module accuracy, a 1200 rpm stepper motor and a grade c7 & g1610 ball screw are provided. the slider is a rectangular parallelepiped with a threaded hole in the center that can pass through the screw. connection and fixation there is a nested connection between the bracket and the sliding group. there is a fixed connection between the stand and the scanner. these two types of connections directly affect the scanning accuracy of the entire drive system. in order to ensure accurate nesting connection between the bracket and the sliding group, the drilling of the nested connection is set, and the specific connection manner is shown in figure. 6(a). for the purpose of calibrating the flatness of the back of the laser sensor, a connecting plate in which the laser sensor is fixedly connected to the slider is fabricated. the four connection holes in the middle of the connecting plate are subjected to countersinking treatment, and the specific connection form is shown in figure. 6(b). t k. li et alii, frattura ed integrità strutturale, 51 (2020) 386-397; doi: 10.3221/igf-esis.51.28 391 figure 5: slide group detail. (a) nested loops join (b) connecting the fixed figure 6: connection and fixation. control box the transmission control device composed of the control box and its internal components is shown in figure 7. in order to control the operation of the transmission system, the built-in transformer of the control box provides a regulated power supply for the stepper motor. the controller sends a stable pulse signal to the driver, which converts the signal to an angular displacement and transmits it to the stepper motor. a button capable of controlling the direction of the driver is provided outside the cabinet. k. li et alii, frattura ed integrità strutturale, 51 (2020) 386-397; doi: 10.3221/igf-esis.51.28 392 (a) external (b) internal figure: 7 detail of the drive actuator. parameter setting and automatic data collection the gocator-2080 laser sensor is connected to the power supply in the control box via a 19-pin cable, connected to the computer by the m12 cable. the scanning speed, exposure and other parameters are set on the laser ranging sensor setting interface. figure 8 shows a full view of the 3d laser scanning system. the position of the main body of the stent is adjusted, the structure to be inspected in the effective area of the scan is placed , and data automatically is collected. the 3d scan information of the detected object are obtained. and the data storage is completed . figure 8: 3d laser scanning system. application in order to fully verify the reliability and practicability of the structure detection of the 3d laser scanning system. based on the concrete bending fatigue test, the concrete structure damage detection is carried out. it is the first time, the 3d laser scanning system was used to detect fatigue damage of the structural. • automatic data collection the structure is located in the scanning sector detection area by adjusting the horizontal position of the holder body. in order to ensure complete structural modeling information, the effective detection range in the vertical direction is greater than the height of the detected object. figure 9 shows the data acquisition process. k. li et alii, frattura ed integrità strutturale, 51 (2020) 386-397; doi: 10.3221/igf-esis.51.28 393 figure 9: data acquisition. the data of the damaged area can be automatically collected through the buttons on the control box. • 3d image efficient acquisition figure 10 shows a scanned point cloud image of the structure acquired in the {o-xyz} coordinate system. in order to compare the measurement accuracy of the 3d laser scanning system, based on the bending fatigue loading test, 100 laser scanning experiments were performed for each group of structural tests. figure 10: structure point cloud diagram. the 3d image of the damaged area is quickly displayed on the computer interface with an average efficiency of 3s per image. the performance of the scanning system was verified. based on this experiment, the performance of the scanning system was verified. the high-frequency vibration of the detection object can be neglected, the scanning precision is high, and the scanning speed is fast; damage information on the plane and space of the damaged area can be obtained, and the damage situation can be more comprehensively analyzed; the position of the scanner can be arbitrarily adjusted according to the conditions of the on-site inspection site, which is convenient for movement; it is not affected by environmental factors of the detection site, and has strong adaptability. the scanning effective area is a fan-shaped space of 350-750 mm from the scanning sensor with an accuracy of 0.005 mm. the scanning accuracy is high, but the area is small. it is not suitable for scanning large structures. this problem can be improved by replacing the model of the scanning sensor. the effective height of the scan is affected by the length of the slide group. the improvement of this problem can be achieved by increasing the length of the sliding group to meet the engineering structure detection needs. k. li et alii, frattura ed integrità strutturale, 51 (2020) 386-397; doi: 10.3221/igf-esis.51.28 394 results and discussion defect detection he structure contains depressions, holes, and crack defects caused by fatigue loading. the region of interest (roi) of each defect point cloud image is extracted, and the defect detection is performed according to the formula (4) and the formula (5), as shown in figure 11. figure 11: defect detection result. the specific detection results of each defect are marked in figure.11, including the size and elevation data information. analysis of results the measurement results are obtained based on digital image correlation (dic） technology and the yernier caliper detection method based on traditional detection technology respectively. the test results and analyze test performance is compared. the detection method based on dic technology needs sufficient illumination. moreover, structural damage information needs to be obtained in conjunction with digital image correlation techniques. and the conventional measurement method needs a professional inspector. the scanning device designed in this study is consistent with the defect detection results obtained by each detection means. the rationality and reliability of the system are fully proved. at the same time, the scanning device designed in this study is superior to other detection technologies in performance. the comparison of performance as shown in table 1. the data in table 1 shows that the traditional measurement method and the flaw detection instrument combined with dic have higher requirements on the light source, lower objectivity and efficiency, and it is difficult to capture the elevation information of the defect. the 3d laser scanning system developed in this paper realizes the modeling of the measurement structure. it can achieve more accurate detection results under any condition. and it has the advantages of wide measurement range and high accurate of detection. it has no blind spot area and high detection efficiency. in this comparative analysis experiment, the 3d laser scanning system showed stronger environmental adaptability and higher detection efficiency. the developed scanning system has high scanning accuracy and fast scanning speed. it can t k. li et alii, frattura ed integrità strutturale, 51 (2020) 386-397; doi: 10.3221/igf-esis.51.28 395 comprehensively analyze the changes of damage in the plan and space. and it is not affected by the environmental factors of the test site and has high adaptability. type condition accuracy(mm) range efficiency（s） depth gocator2080 ±0.005mm level: 0-120° vertical: 0-2000mm 3 available hcck102 light source ±0.01mm 0-8mm 45 paola5385 professional ±0.03mm 0-150mm 60 table 1: measurement performance comparison. conclusions his paper developed a 3d laser scanning structure test measuring device independently, which can widely adapt to the testing conditions of modern structural tests. the 3d laser scanning system consist of a linear slide group and a 2d laser ranging sensor. the stepping motor controls the fine movement of the sliding group screw to realize the lifting and scanning of the laser ranging sensor. the following conclusions were made: 1) the 3d coordinate system of the laser scanning measuring device is established, and the calculation formula for detecting the structure size and elevation data information is obtained. 2) the whole process of developing the scanning system is summarized, including the construction of the bracket system, the construction of the transmission device, the simulation of the control device and the connection and fixing of various parts. 3) based on the rpc bending fatigue test, the scanning platform of this experiment was compared with the traditional method and dic technology to verify the reliability and superiority of the operating system. the results show that the system achieves 3d modeling of structural inspection objects compared to other detection techniques. it has stronger environmental adaptability, higher measurement accuracy and lower cost. the developed 3d laser scanning system can overcome the constraints of environmental constraints and hardware equipment, and realize the efficient and accurate measurement of modern structural tests. acknowledgments his work was supported by general program of the natural science foundation project of heilongjiang province (zd2019e001), national natural science foundation of china (51778186) and heilongjiang post-doctoral research foundation project (lbh-q 15011). reference [1] cha, y. j., buyukozturk, o. (2015). structural damage detection using modal strain energy and hybrid multiobjective optimization. computer-aided civil and infrastructure engineering, 30(5), pp. 347-358. [2] abdeljaber, o., avci, o., kiranyaz, s., et al (2017). real-time vibration-based structural damage detection using onedimensional convolutional neural networks. journal of sound & vibration,388, pp.154-170. [3] zhao, l., et al. (2017). a review on measurement technology for structure in civil engineering. journal of xi'an university of architecture & technology (natural science edition.49, pp. 48-55. [4] daigoro, i. (2018). progressive collapse analysis of structures. numerical codes and applications, 12(2), pp.59-66. [5] zhao, x., li, q. (2017). a review on measurement technology for structural testing in civil engineering. j. xi'an univ. of arch. &. tech. (natural science edition), 49(01), pp. 48-55 t t https://www.sciencedirect.com/science/article/pii/b9780128129753000062?via=ihub#! https://www.sciencedirect.com/science/book/9780128129753 k. li et alii, frattura ed integrità strutturale, 51 (2020) 386-397; doi: 10.3221/igf-esis.51.28 396 [6] chen, c., li, q, yan, q. (2018). mobile robot simultaneous localization and mapping based on heterogeneous sensor information fusion. science technology and engineering, 18 (13), pp.86-91 [7] shang, m. y., weizhong, c., diansen, y. (2017). experimental study of brittle rock failure based on three-dimensional digital image correlation technique. rock and soil mechanics, 38(01), pp.117-123 [8] pan, b., qian, k., xie, h. (2009). two-dimensional digital image correlation for in-plane displacement and strain measurement: a review. measurement science & technology, 20(6), pp. 062001 [9] yan, t., wang, x., zhu, h., et al (2018). evaluation of object surface edge profiles detected with a 2-d laser scanning sensor. sensors, 18(11). [10] niclass, c., rochas, a., besse, p. a., et al. (2005). design and characterization of a cmos 3-d image sensor based on single photon avalanche diodes. ieee journal of solid-state circuits, 40(9), pp. 0-1854. [11] monserrat, o., crosetto, m. (2008). deformation measurement using terrestrial laser scanning data and least squares 3d surface matching. isprs journal of photogrammetry and remote sensing, 63(1), pp. 142-154. [12] zhe, c., fumin, z., xinghua, q., et al (2015). fast measurement and reconstruction of large workpieces with freeform surfaces by combining local scanning and global position data. sensors, 15(6), pp. 14328-14344. [13] nagarajaiah, s., yang, y. (2017). modeling and harnessing sparse and low rank data structure: a new paradigm for structural dynamics, identification, damage detection, and health monitoring. structural control & health monitoring, 24(1). [14] yong-shang, m. a., wei-zhong, c., dian-sen, y., et al (2017). experimental study of brittle rock failure based on three-dimensional digital image correlation technique. rock & soil mechanics. [15] park, h. s., lee h. m., adeli, h., et al (2007). a new approach for health monitoring of structures: terrestrial laser scanning. computer-aided civil and infrastructure engineering, pp. 22(1), 19-30. [16] olsen, m. j., kuester, f., chang, b. j., et al (2010). terrestrial laser scanning-based structural damage assessment. journal of computing in civil engineering, 24(3), pp. 264-272. [17] dai, et al (2017). application of gray information in lidar scan point cloud data for structural deformation field calculation. journal of building structures. 38 (3), pp. 151-157. [18] aytekin, c., rezaeitabar, y., dogru, s., et al (2015). railway fastener inspection by real-time machine vision. ieee transactions on systems man & cybernetics systems, pp. 45(7), 1101-1107. [19] pejic, m., ogrizovic, v., bozic, b., et al (2014). a simplified procedure of metrological testing of the terrestrial laser scanners. measurement, 53, pp. 260-269. [20] soudarissanane, s. s., lindenbergh, r. c. (2012). optimizing terrestrial laser scanning measurement set-up. isprs international archives of the photogrammetry, remote sensing and spatial information sciences [21] surmann, h., nüchter, a., hertzberg, j. (2003). an autonomous mobile robot with a 3d laser range finder for 3d exploration and digitalization of indoor environments. robotics and autonomous systems, 45(3-4), pp. 181-198. [22] chou, y. s., liu, j. s. (2013). a robotic indoor 3d mapping system using a 2d laser range finder mounted on a rotating four-bar linkage of a mobile platform. international journal of advanced robotic systems, pp.10. [23] cai, et al (2018). a 3d laser scanning system design and parameter calibration. journal of beijng university of aeronautics and astronautics, 44 (10), pp.2208-2216 [24] yongkun, w., ju, h., xingshun, w. (2014). a real-time robotic indoor 3d mapping system using duel 2d laser range finders. chinese control conference. ieee [25] petr, o., michal, k., pavel, m., et al (2016). calibration of short range 2d laser range finder for 3d slam usage. journal of sensors, pp. 1-13. nomenclature ndt non-destructive testing dic digital image correlation plc programmable logic controller roi region of interesting {oa-xayaza} coordinate system of laser ranging sensor position. {o-xyz} coordinate system of the image acquired by laser scanning. k. li et alii, frattura ed integrità strutturale, 51 (2020) 386-397; doi: 10.3221/igf-esis.51.28 397 t (s) movement time of the sensor v (m/s) speed of sensor movement α angle between the laser emitted by the transmitting end and xa s (xa,xb,xc) coordinate of the intersection with the object θ angle between the emitted light and the reflected light p2p1 plane distance d height difference m4 screw type 1200 rpm speed of stepper motor c7&g1610 type of ball screw gocator-2080 model of laser sensor 40x 40 times magnification microsoft word numero 23 articolo 6 a. spaggiari, frattura ed integrità strutturale, 23 (2013) 57-61; doi: 10.3221/igf-esis.23.06 57 scilla 2012 the italian research on smart materials and mems properties and applications of magnetorheological fluids a. spaggiari dept. of engineering sciences and methods, university of modena and reggio emilia, italy andrea.spaggiari@unimore.it abstract. this brief introduction describes the mechanical, rheological and magnetic properties of the magnetorheological (mr) fluids for feasible engineering applications. the typical modes of exploiting this technology are shown and discussed. an increasing number of industrial applications illustrate how the mr fluids peculiar properties may be used to provide optimal performance in semi active damping and dissipative devices. keywords. magnetorheological fluids; pressure; shear mode; interaction; experimental. properties of magnetorheological fluids agnetorheological (mr) fluids are smart and controllable materials, even though at the first glance they do not look so impressive. they are a non colloidal mixture of ferromagnetic particles randomly dispersed in oil or water (fig. 1a), plus some surfactants useful to avoid the settling of the suspended particles. the overall aspect is like a greasy quite heavy mud, since mr fluids density is more than three times the density of water. this material becomes suddenly smart and interesting as soon as a magnetic field passes through it. the ferromagnetic particles feel the induction field and acquire a magnetic bipole, then they move and redesign their arrangement start to flow and to form chains and linear structures (fig. 1b). these microscopic chains have a the macroscopic effect to change the apparent viscosity of the fluid. the size of the particles is around 10 micron for the so called mr fluids (fig. 2a) mainly produced by [1], while the nanosized particles produces a similar substance called ferrofluid (fig. 2b), produced by [2]. while the applications of mr fluids are relevant for engineers and can be used in many damping devices, the ferrofluids are mainly a fancy stuff to play with for artist and kids. the reason for this distinction is simple: there is a huge difference in the yield shear stress of the mr and ferrofluids, which affects the maximum force the fluid can provide. (a) (b) figure 1: microfotography of a mr fluid with no magnetic field, where particles are randomly dispersed (a). microphotography mr fluid with an applied magnetic field with parallel chains of carbonyl iron (b). m http://www.gruppofrattura.it http://dx.medra.org/10.3221/igf-esis.23.06&auth=true a. spaggiari, frattura ed integrità strutturale, 23 (2013) 57-61; doi: 10.3221/igf-esis.23.06 58 (a) (b) figure 2: magneto rheological fluid (a) from lord [1] and ferrofluid (b), produced by [2]. the yield shear stress is the main figure of merit of a mr fluid and derives from the non newtonian behaviour of these fluids. the mr fluid behaves following a so called bingham law, which means that it exhibits a non zero shear stress value for a zero shear rate [3], behaving more like a solid than like a liquid, as shown in fig. 3a. the value of the shear stress at no shear rate is called yield stress of the mr fluid and is controlled by the applied magnetic field as shown in fig. 3b. the larger the field, the higher the yield stress. the higher the yield stress the higher the force the material can withstand without flowing. bearing a load is possible only because mr fluids can modify their aggregations states changing from a viscous free-flow liquid to a quasi solid state. (a) (b) figure 3: bingham model of mr fluid (a) and effect of the magnetic field on the yield stress (b). in order to exploit mr fluids properties there are three main way envisioned in current engineering applications [4]: a) flow mode, shown in fig. 4a; b) shear mode, shown in fig. 4b; c) squeeze mode, shown in fig. 4c. flow mode, also called valve mode, exploits the fluid between two fixed walls, the magnetic field is normal to the flow directions and is typical for linear damper applications. shear mode is mainly used in rotary application such as brakes and clutches and the fluid is constrained between two walls which are in relative motion with the magnetic field normal to the wall direction. squeeze mode is used mainly for bearing applications, is able to provide high forces and low displacements having the magnetic field normal to walls directions. in all the above mentioned cases the working principle is the same: the applied magnetic field regulates the yield stress of the fluid and changes its apparent viscosity. so the amount of http://www.gruppofrattura.it http://dx.medra.org/10.3221/igf-esis.23.06&auth=true a. spaggiari, frattura ed integrità strutturale, 23 (2013) 57-61; doi: 10.3221/igf-esis.23.06 59 dissipated energy of the system is simply controllable by acting on the coil current and the system can provide semi-active behaviour. (a) (b) (c) figure 4: typical using modes for mr fluids, flow (a), shear (b) and squeeze (c) mode. applications of magnetorheological fluids he sudden change in the mr behaviour (few milliseconds) due to the magnetic field application, makes this material attractive for damping and dissipative devices. the mr fluids can be used to build integral, silent, quick mechanical systems enhanced by means of electronic controls. the mr applications in the field of are semi-active control devices which offer the flexibility and versatility of the active systems and the reliability of the passive ones. there are two main ways to exploit the mr fluids in engineering applications. (b) (a) figure 5: schematic of single ended mr damper and double ended mr damper, both produced by lord [1]. t http://www.gruppofrattura.it http://dx.medra.org/10.3221/igf-esis.23.06&auth=true a. spaggiari, frattura ed integrità strutturale, 23 (2013) 57-61; doi: 10.3221/igf-esis.23.06 60 linear mr devices one of the most interesting engineering applications of mr fluid is the construction of smart and controllable mr linear dampers. the main asset of a mr based damper is the controllability of the system, which can be adjusted in order to provide the desired level of damping by simply changing the supply current. the main idea is to obtain the desired level of damping by varying the magnetic induction in an orifice between two separated mr fluid chambers. the orifice acts like a magnetic valve for the fluid, regulated by the current and thus exploits the mr fluid in flow mode. two many architectures are envisioned for this purpose: the single ended damper (fig. 5a) and the double ended damper (fig. 5b). the single ended damper has only one reservoir for the mr fluid which is transferred through an orifice from on chamber to another. since the rod volume is just on one side the system accounts for the change in volume that results from piston rod movement. in order to accommodate this change in reservoir volume, an accumulator is usually used. the accumulator provides a barrier between the mr fluid and a compressed gas (usually nitrogen) that is used to accommodate the necessary volume changes. moreover the accumulator pressure can be used to enhance the performance of the mr system, as shown in [5]. the double-ended mr damper has piston rods of the same diameter that protrude through both ends of the damper. in this case there is no change in volume as the piston rod moves, the doubleended damper does not require an accumulator or other similar device. the applications of the single ended damper are mainly in the vibration suppression of mechanical components like seat suspension, car suspensions, and industrial vibration suppression, while the double ended damper is mainly used for bicycle applications, gun recoil applications, and for stabilizing buildings and bridges during earthquakes. the output forces of such a devices can range from quite low forces (hundreds of newtons) in case of light suspension system up to 20 tons in case of civil applications, in which they must compensate the incredibly large forces cause by the shaking of entire buildings. (a) (b) figure 6: picture and schematic of mr based brake (a) and clutch, both produced by lord [1]. rotary mr devices the other main application exploits the mr fluid in shear mode to realize a sort of hydraulic brakes and clutches with mr fluids. the aim is to obtain a precise control of the braking torque (in case of brakes) or transmitted torque (in case of clutches) with no moving parts by simply varying the current in the coils. the typical architecture for a mr based brake is depicted in fig. 6a, where the basic idea is clearly depicted. the magnetic flux path passes through the chassis and the http://www.gruppofrattura.it http://dx.medra.org/10.3221/igf-esis.23.06&auth=true a. spaggiari, frattura ed integrità strutturale, 23 (2013) 57-61; doi: 10.3221/igf-esis.23.06 61 rotating disk and the fluid is sheared between these elements. the braking force depends on the yield stress of the fluid making the system controllable. the mr based clutch is ideally described by fig. 6b, the fluid is between the input disk and the output disk and the amount of transmitted torque is proportional to the yield stress of the fluid. no moving part are used to change the transmitted torque and the torque value can be smoothly controlled through the coil current. even though multidisc applications can be used to increase the output torque, the typical application of rotary mr fluid devices is in the high precision and low power range. for example the rheoknee, developed by ossur [6] is the first prosthetic knee which allow the amputee to have a normal leg motion even in case of stairs. the mr knee exhibits a very low torque when is not active enabling the leg to move forward freely and in a few millisecond the mr is able to carry all the human weight to complete the step. the overall performance is outstanding and shows how the smartness of mr fluid can improve human condition. conclusion he world of dissipative and damping device is full of potential mr fluid applications, especially when it is desirable to control motion. traditional viscosity based system with moving parts can be easily replaced by a mr fluid with changing viscosity as function of current, obtaining an improvement in functionality and a costs reduction. the mr fluid main features are: fast response, simple interface between electrical power input and the mechanical power output, controllability and integration in complex system. nowadays mr fluid are a reliable technology for many engineering applications. flow mode (used in dampers) and shear mode (used in brakes and clutches) have been studied thoroughly and several products are already present in the market. references [1] lord corp. http://www.lord.com/products-and-solutions/magneto-rheological-%28mr%29.xml [2] apexmagnets llc http://apexmagnets.com/index.php?main_page=index&cpath=7 [3] e. dragoni, progettare, 332 (2009). [4] m. r. jolly, j. w. bender, j. d. carlson, j. intell. mater. syst. struct., 10 (1999) 5. [5] a. spaggiari, e. dragoni, asme j. fluids eng., 134 (2012) 091103. [6] ossur company http://www.ossur.com/?pageid=15766 t http://www.gruppofrattura.it http://dx.medra.org/10.3221/igf-esis.23.06&auth=true numero_45_art_7 q.-c. li et alii, frattura ed integrità strutturale, 45 (2018) 86-99; doi: 10.3221/igf-esis.45.07 86 investigation method of borehole collapse with the multi-field coupled model during drilling in clayey silt hydrate reservoirs qing-chao li, yuan-fang cheng, qiang li school of petroleum engineering, china university of petroleum (east china), qingdao, shandong 266580, china. b16020053@s.upc.edu.cn http://orcid.or/ 0000-0001-7373-4046 yfcheng@upc.edu.cn http://orcid.org/0000-0001-7181-9919 fu-ling wang college of science, china university of petroleum (east china), qingdao, shandong 266580, china. chuang zhang, chuan-liang yan school of petroleum engineering, china university of petroleum (east china), qingdao, shandong 266580, china. abstract. the global reserves of natural gas hydrates are extremely abundant, but hydrate reservoirs are usually clayey silt hydrate reservoirs with low strength, and borehole collapse is a key issue during the drilling operation. in the present work, both the investigation method and the finite element model that used for investigating borehole collapse in hydratebearing sediment are developed, and the superiority of the investigation method developed herein is also analyzed. the results show that changes in temperature and/or pore pressure do not necessarily lead to the hydrate dissociation. hydrate dissociation occurs only when both temperature and pore pressure satisfy the conditions of hydrate dissociation. moreover, the applicability of the investigation method developed herein is verified by comparing the equivalent plastic strains obtained by the coupled model developed in this paper and the simplified model respectively. in addition, the simplified model overestimates the extent of the wellbore collapse for the drilling operation in hydrate-bearing sediments. all these results demonstrate that both the investigation method and the finite element model can be used for borehole stability simulation in hydrate-bearing sediments. keywords. hydrate-bearing sediments; hydrate dissociation; wellbore instability; borehole collapse; finite element analysis. citation: li, q. c., cheng, y. f., li, q., wang, f. l., wei, j., ding, j. p., zhang, h. w., song, b. j., zhang, c., yan, c. l., investigation method of borehole collapse with the multi-field coupled model during drilling in clayey silt hydrate reservoirs, frattura ed integrità strutturale, 45 (2018) 8699. received: 19.05.2018 accepted: 25.05.2018 published: 01.07.2018 copyright: © 2018 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. introduction atural gas hydrates are crystalline structures formed by natural gases (mainly methane, generally more than 96%) and pure water under the conditions of low temperature and high pressure [1-3]. more and more attention has been paid to methane hydrate development from hydrate-bearing sediments in deep water for its clean property n http://www.gruppofrattura.it/va/45/31.mp4 q.-c. li et alii, frattura ed integrità strutturale, 45 (2018) 86-99; doi: 10.3221/igf-esis.45.07 87 and the vast reserves. although the estimation of global hydrate reserves is uncertain, according to incomplete statistics, the energy stored in natural gas hydrates all over the world is at least twice as much as that stored in fossil fuels currently known [4-6]. although various countries have conducted a series of hydrate production test activities recently (especially china and japan), the current research on methane hydrates is generally in the stage of theoretical research and laboratory exploration. the production test activities are listed in tab. 1. canada u.s.a japan china 1st test 2nd test 1st test 1st test 2nd test 1st test time 2002 2007 2012 2013 2017 2017 test area mackenzie delta north slope of alaska nankai trough shenhu area lithology sandy sandy sandy clayey silt method hot water circulating depressurization replacement+ depressurization depressurization fluid extraction production time 5d 6d 30d 6d 36d 60d cumulative gas 516m3 13000m3 24000m3 120000m3 235000m3 309000m3 reasons for stop sand production table 1: production test activities of natural gas hydrates worldwide [7]. some development strategies have been studied by numerous experts for the development of natural gas hydrates, of which the depressurization method is the most effective and the most commonly used one [8]. however, hydrate reservoirs in deep water are generally low-strength formations, which make the wellbore collapse to be a commonly occurred issue during hydrate production process [9-12]. in addition, hydrate dissociation during hydrate production operation is another contributor to both the complex accidents within the borehole (i.e., borehole instability and casing damage, etc.)[13-17] and the geological disasters (such as slope slide and submarine earthquakes)[18, 19]. hydrate dissociation at high temperature and/or low pressure determines that drilling operation in hydrate reservoirs is more difficult than conventional oil and gas reservoirs. the caliper logging curve at the sh4 site in shenhu area of the south china sea shows that serious borehole collapse and borehole enlargement has emerged during the drilling process within the hydrate interval [20]. therefore, exploration of a method for borehole stability investigation in hydrate reservoirs and thorough analysis of borehole collapse mechanism are of great importance to ensure the construction safety in hydrate reservoirs. up to now, the main focuses of numerous scholars have been paid on gas production from hydrate-bearing sediments, and different production strategies have been investigated in detail [7, 21-25]. however, the threat of hydrate dissociation to the stability of both the reservoir and wellbore is an important research topic in the development of natural gas hydrates. on the one hand, hydrate dissociation leads to changes in both the pore pressure and the effective stresses within hydrate reservoir. on the other hand, hydrate dissociation also weakens the reservoir strength, which severely affects the strata stability. in spite of this, the investigations of wellbore behavior caused by hydrate dissociation during hydrate development in deep water only attract a few scholars’ interests [13-17, 26, 27]. although these studies are valuable for studying borehole behavior during a drilling operation in hydrate formation, nearly all these related investigations did not integrate three physical fields of seepage, deformation, and heat transfer to thoroughly analyze borehole stability in hydrate reservoirs. in this paper, the finite element (fe) model used for investigating borehole stability during the drilling operation in hydrate reservoirs is established by integrating seepage, deformation, and heat transfer. based on this, the results of borehole collapse are compared when the coupled fe model (investigated herein) and the simplified model (both seepage and heat transfer are neglected) are used respectively, then the applicability of the investigation method can be verified. moreover, the yield range evolution within the near-wellbore area is also investigated with the coupled fe model. q.-c. li et alii, frattura ed integrità strutturale, 45 (2018) 86-99; doi: 10.3221/igf-esis.45.07 88 fundamental theory borehole instability in hydrate reservoirs ellbore instability usually manifests as shear failure and/or tensile failure. borehole collapse generally occurs in the direction of the minimum principal stress due to the stress concentration caused by the low drilling mud density [28, 29]. hydrate reservoirs are usually sandstone reservoirs with high porosity, and borehole collapse is the main form of borehole instability in hydrate formations. hydrate dissociation results in the changes of both pore pressure and the effective stresses. therefore, hydrate dissociation within the near-wellbore region during drilling operation can aggravate the borehole collapse. and, borehole collapse in hydrate reservoirs depends on the initial formation conditions and the conditions of drilling mud within the wellbore. schematic diagram of borehole instability while drilling in hydrate reservoirs is shown as fig.1. therefore, determining the collapse area during a drilling operation in hydrate reservoirs needs to consider the effect of hydrate dissociation caused by the invasion of drilling mud. during the determination of collapse area, the equivalent plastic strain is used as the parameter for judging the collapse of a wellbore. when the surrounding rock shows a positive equivalent plastic strain value, it is considered that the borehole may collapse. figure 1: schematic diagram of borehole instability while drilling in hydrate reservoirs. figure 2: schematic diagram of the relationship between various coordinate systems. effective stresses around arbitrary borehole the effective stress is the key for wellbore stability, and the relationship between the total stress, the effective stress and the pore pressure can be expressed by the principle of effective stress, which is shown as the following equation. w q.-c. li et alii, frattura ed integrità strutturale, 45 (2018) 86-99; doi: 10.3221/igf-esis.45.07 89 tot eff pp = + (1) in order to accurately determine the effective stresses around the arbitrary borehole, four coordinate systems (fig.2) are defined, that is, the in-situ stress coordinate system (xs-ys-zs), the geographic coordinate system (xg-ygzg), the borehole coordinate system (xb-yb-zb) and the wellbore polar coordinate system (r-θ-zb). the in-situ stresses (σh, σh, and σv) can be transformed from the in-situ stress coordinate system to the borehole coordinate system with two transformation steps [30]. firstly, the in-situ stresses are transformed from the in-situ stress coordinate system to the geographic coordinate system. then the stresses in geographic coordinate system are transformed from the geographic coordinate system to the borehole coordinate system. the whole transformation process can be expressed by the following equation. x t = = xx y xz b b b yx yy yz t b b b b b s p s b zx zy zz b b b r r r r                        (2) where the tensor rs and rb are expressed as eqn. (3) and eqn. (4). = + s cos cos sin cos sin r cos sin sin sin cos sin sin sin cos cos cos sin cos sin cos sin sin sin sin cos cos sin cos cos                                                    (3) ( ) ( ) ( ) ( ) ( ) = ( ) ( ) 0 ( ) ( ) ( ) ( ) ( ) b cos az cos inc sin az cos inc sin inc r sin az cos az cos az sin inc sin az sin inc cos inc           (4) the stresses around borehole in the cylindrical coordinate system can be expressed as eqn. (5) when the drilling fluid pressure is pm [31]. ( ) ( ) ( ) y y x = = + -2 2 -4 2 = -2 2 +2 2 =2 r m p xx yy xx yy x b b b b b m p zz xx yy x z b b b b p yz z z b b p p cos sin p p cos sin p cos sin                             (5) the maximum and minimum effective principal stresses need to be determined when mohr-coulomb criterion is used for borehole stability analysis. however, determining the three effective stresses around borehole (σi, σj and σk) in borehole cylindrical coordinate system is the basis, which can be calculated using eqn. (6). ( ) ( ) ( ) ( ) 2 2 2 2 = = =0.5 + +0.5 +4 =0.5 + 0.5 +4 i r m p j z z z k z z z p p                    − (6) the maximum and minimum effective principal stresses can be obtained by comparing these three effective stresses. q.-c. li et alii, frattura ed integrità strutturale, 45 (2018) 86-99; doi: 10.3221/igf-esis.45.07 90 conditions for hydrate stability loh et al. investigated the dissociation of seawater hydrates (3.03 wt% nacl) and gave the empirical phase boundary equation for methane hydrate in porous media, which is shown as eqn. (7) [32]. the equation shows that the hydrate will dissociate when the temperature t exceeds the phase equilibrium temperature teq under the corresponding pore pressure pp. ( )1.3 1.66exp 0.141eq eqp t= + (7) eqn. (7) can be used for determining whether the methane hydrate dissociate or not. finite element model efore the establishment of the fe model, some assumptions are made to simplify the investigation problem. firstly, investigation of borehole stability while drilling in hydrate-bearing sediments can be simplified as the plane strain problem. furthermore, hydrate reservoir is thought of as the isotropic porous media. also, the temperature of the drilling mud is constant during the whole drilling operation. finally, the effects of hydrate dissociation on both the temperature and the pore pressure of hydrate reservoir are neglected. however, no matter how the investigation problem is simplified, it is a complex physical process involving physical fields such as seepage, deformation and heat transfer. the established 2d fe model is displayed as fig.3. as can be seen from fig.3, the wellbore is assumed as the vertical openhole one drilled in the clayey silt hydrate reservoir. moreover, the diameter of the borehole is the same as that of the drill bit, and it is 8 1/2 inches. in order to ensure that the temperature and pore pressure at the outer boundaries are not affected during the entire simulation, both the length and width of the fe model are 20m. herein, the widely used mohrcoulomb constitutive model has been used herein to describe the relationship between the stress and the strain of the porous media. figure 3: schematic of borehole stability model during a drilling operation in hydrate reservoir. boundary conditions and the initial conditions the entire simulation process can be divided into two steps, namely, the geostatic step and the borehole stability analysis step. in the first step, the normal displacements at the outer boundaries of the fe model are fixed. the borehole also needs to be fixed in this step to simulate the state that the hydrate reservoir has not been disturbed. fig.4 shows the boundary conditions of the fe model in the first step. and, in order to clearly show the boundary condition of the borehole in this step and the detailed elements within the near-wellbore area, fig.4b demonstrates the mesh model of the near-wellbore area. b q.-c. li et alii, frattura ed integrità strutturale, 45 (2018) 86-99; doi: 10.3221/igf-esis.45.07 91 in the fe model, 4500 stress/pore pressure elements are obtained to simulate the borehole collapse in hydrate formation. since the hydrate dissociation during drilling operation mainly occurs in the near-wellbore area (fig.4b), the elements within the near-wellbore area are denser than other area. figure 4: the boundary conditions in the first step (the geostatic step). (a): the whole model, (b) elements in the near-wellbore area. just as the first step, fig.5 demonstrates the boundary conditions of the fe model in the second step (the borehole stability step). in the borehole stability step, the boundary conditions are listed as the following items: (1) the fixed displacement of borehole should be removed first, which is an alternative to drilling operation; (2) then, boundary conditions of both the temperature and pore pressure should be applied to the borehole; (3) also, boundary conditions of both the temperature and pore pressure should be applied to the outer boundaries synchronously; (4) besides, the bottom-hole pressure pm generated by the gravity of the drilling fluid needs to be applied to the borehole. figure 5: the boundary conditions in the second step (the borehole stability step). the initial conditions herein are the initial pore pressure and the initial temperature within the hydrate-bearing sediments. in addition, the in-situ stresses also need to be determined. the initial conditions and the boundary conditions can be determined by the logging data and/or the seismic data obtained from exploration activities. q.-c. li et alii, frattura ed integrità strutturale, 45 (2018) 86-99; doi: 10.3221/igf-esis.45.07 92 simulation methodology and workflow according to the load, the initial conditions and the boundary conditions described in these two simulation steps, the investigation methodology and workflow herein is presented as fig.6. firstly, the initial stress state without human disturbance within the investigation model for wellbore stability simulation can be generated by the geostatic step. then, based on the results obtained by the first step, the borehole collapse can be investigated by the second analysis step. however, the focus of the whole simulation is the coupling of the three physical fields of heat transfer, seepage, and deformation. figure 6: workflow of borehole simulation in hydrate-bearing sediments. case study basic input data for simulation he basic input data for investigation of borehole stability in the clayey silt hydrate-bearing sediments are listed in tab. 2 and tab. 3 [33]. however, the physical parameters of hydrate-bearing sediments are different from each other in different area all over the world for the difference in so many factors such as the lithology or hydrate saturation. therefore, a series of empirical formulae describing the characteristics of hydrate reservoirs have been obtained from the research on artificial or natural hydrate samples. parameter value unit parameter value density, ρ 2000 kg/m3 thermal conductivity, λ 1.5 w/(m·k) initial young's modulus, e0 625 mpa specific heat capacity, csh 1362 j/(kg·k) initial dilation angle, ψ 17.46 ° drilling mud pressure, pm 15.5 mpa poisson's ratio, v 0.35 drilling mud temperature, tm 18.79 °c friction angle, ϵ 25 ° drilling time, td 3 h initial cohesion, c0 1.25 mpa bias ratio 5 table 2: physical parameters of investigation model before hydrate dissociation and the drilling conditions. t q.-c. li et alii, frattura ed integrità strutturale, 45 (2018) 86-99; doi: 10.3221/igf-esis.45.07 93 the relationship between young's modulus of hydrate-bearing sediments e and hydrate saturation sh can be expressed by eqn. (8) [34]. 125 1000 he s= +  (8) the cohesion c also changes with hydrate saturation, and it can be expressed by the following equation 2.5 hc mpa s=  (9) in addition, change of dilation angle caused by hydrate can be expressed by eqn. (10). sin 0.05 0.5 hs = +  (10) parameter value unit parameter value unit void ratio 0.8512 initial hydrate saturation, sh0 47 % initial pore pressure 14.64 mpa max. horizontal stress, σh, (y) 0.9 mpa vertical effective stress, σv 1.1 mpa min. horizontal stress, σh, (x) 0.6 mpa initial permeability, k0 10-14 m2 initial temperature, t 14.79 °c initial porosity, ϕ0 45.98 % table 3: initial conditions of the fe model. hydrate dissociation during the drilling operation in this case, the bottom-hole pressure (pm) is 15.5mpa, which is larger than the initial pore pressure (14.64mpa). therefore, the investigation case can be defined as the overbalanced drilling operation (odb). the properties of hydrate-bearing sediments listed in tab. 2 and tab. 3 have been as close as possible to that of the hydrate reservoirs in the south china sea. although it is odb case, the conditions of drilling mud pressure (i.e., 15.5mpa) and its temperature (17.79℃, which is higher than the phase equilibrium temperature calculated by drilling mud pressure) can result in the dissociation of seawater hydrates. fig.7 shows the temperature distribution of at different drilling times along a path extending radially from the borehole. figure 7: temperature distribution of at different drilling times along a path extending radially from the borehole. q.-c. li et alii, frattura ed integrità strutturale, 45 (2018) 86-99; doi: 10.3221/igf-esis.45.07 94 from fig.7, the temperature front gradually moves forward from the borehole, but its speed gradually slows down. when the formation is drilled for 10 min, the temperature front reached a position of 4.30 cm from the borehole. however, the temperature front reaches the position of 35.72 cm when the hydrate-bearing sediment has been drilled for 3 hours. however, the temperature disturbance in the hydrate reservoir does not imply the hydrate dissociation. fig.8 shows the dissociation range of hydrate-bearing sediments within the near-wellbore area at different times. it can be seen from fig.8 that drilling operation only results in the hydrate dissociation within a range of 17.94 cm around the borehole in the nearwellbore area, which indicates the fact mentioned above that the temperature disturbance in the hydrate reservoir does not imply the hydrate dissociation. therefore, only when both the pore pressure and temperature reach the dissociation condition of methane hydrates, hydrate dissociation can occur. by comparing the simulation results shown in fig.7 and fig.8, it can be seen that the dissociation speed of seawater hydrates in hydrate-bearing sediments during the drilling operation is similar to that of temperature front, and both speeds slow down as drilling operation continues. figure 8: dissociation range of hydrate-bearing sediments within the near-wellbore area. yield area caused by hydrate dissociation the area where the equivalent plastic strain (peeq) generated is the area that borehole collapse may occur. therefore, the equivalent plastic strain can be used as an important parameter to describe the borehole collapse/instability during a drilling operation in hydrate reservoirs. the evolution of yield range (where the peeq value is positive) within the nearwellbore area during the drilling operation in hydrate-bearing sediments of the south china sea is demonstrated in fig.9. as can be seen from fig.9, within half an hour of the whole drilling operations, not only the yield range of the nearwellbore region, but also the maximum equivalent plastic strain continuously increase as drilling operation continues. however, although the yield range within the near-wellbore area changes little after half an hour of the drilling operation, the equivalent plastic strain (peeq) continues to increase rapidly. in spite of this, larger yield area where borehole collapse may occur can present with the increase of the dissociation area. superiority and applicability of the coupled fe method in order to verify the superiority of the simulation method developed herein, results obtained from two different fe models are compared. among them, a model is the finite element model proposed in this paper that couples seepage, deformation and heat transfer together (which is named as “model 1”). the other is a simplified model that ignores seepage and heat transfer (which is defined as “model 2”). fig.10 shows the comparison results of equivalent plastic strain at last between these two different models described above. from fig.1, the maximum collapse area should present at the direction of the minimum horizontal principal stress. however, as shown in fig.10b, when the fe model neglects seepage and the heater transfer (model 2), the yield area is evenly distributed along the borehole. therefore, as can be seen from fig.10, simulation of borehole collapse during the drilling operation in hydrate reservoirs is more realistic using the coupled fe model (model 1) that integrates seepage, deformation and heat transfer. in addition, borehole collapse simulation with the fe model neglects seepage and the heater transfer (model 2) overestimates the borehole collapse. therefore, all these comparison results indicate the applicability of both the coupled fe method and the investigation method established herein. q.-c. li et alii, frattura ed integrità strutturale, 45 (2018) 86-99; doi: 10.3221/igf-esis.45.07 95 figure 9: equivalent plastic strain (peeq) within the near-wellbore area during drilling operation in hydrate-bearing sediments. (a): 1min, (b): 10min, (c): 30min, (d): 1h, (e): 2h, (f): 3h figure 10: comparison results of equivalent plastic strain at the last (drilling in hydrate formation for 3h) of the drilling operation between these two different models. (a): peeq of model 1, (b): peeq of model 2. effect of mesh size on hydrate dissociation and borehole collapse effect of mesh size on hydrate dissociation and borehole collapse are shown as fig.11 and fig.12 respectively. herein, the bias ratio (1 and 10 are investigated herein) has been defined a parameter to describe the size ratio between the maximum and the minimum elements within the near-wellbore region. it can be seen from fig.11 that hydrates dissociate more when mesh quality of the fem is not very good (bias ratio is equal to 1). this is because hydrate dissociation within hydrate-bearing sediments during the analysis process is based on the temperature and pore pressure of each mesh element. the poor mesh quality makes the element interval within the near-wellbore area larger, resulting in faster hydrate q.-c. li et alii, frattura ed integrità strutturale, 45 (2018) 86-99; doi: 10.3221/igf-esis.45.07 96 dissociation. conversely, the better mesh quality within the near-wellbore area means that the mesh size increases from the borehole radially outward, which makes the hydrate dissociation simulation closer to the actual situation. figure 11: dissociation range of hydrate-bearing sediments within the near-wellbore area when the bisa ratio is different. fig.12 displays the equivalent plastic strain of the hydrate formation within the near-wellbore area at the last of the drilling operation when the mesh size is different. as can be seen from fig.12, the equivalent plastic strain is larger when the mesh quality is good (when the basi ratio is 5), this is related to the hydrate dissociation in fig.11. when the mesh quality is poor, more hydrate dissociation leads to more severe wellbore collapse and instability. for example, when the basi ratio is 10, the maximum equivalent plastic strain is 2.977×10-2, but the maximum equivalent plastic strain increases to 3.051×10-2 when the basi ratio changes to 5. in addition, the yield range caused by hydrate dissociation changes little for models with two different mesh sizes. all these results indicate that mesh size is an important factor when the fem was used to investigate wellbore stability in hydrate-bearing sediments. figure 12: comparison results of equivalent plastic strain at the last (drilling in hydrate formation for 3h) of the drilling operation between these two different mesh size within the near-wellbore area. (a): peeq when basi ratio is 10, (b): peeq when basi ratio is 5. conclusions and suggestions he major results are as follows: (1) the investigation method of borehole collapse in hydrate-bearing sediments is developed, and a twodimensional seepage-deformation-heat transfer coupled finite element model is also established. (2) hydrate stability depends on so many factors, such as the temperature and the pore pressure. only when both the pore pressure and temperature reach the dissociation condition of methane hydrate, hydrate dissociation can occur. (3) equivalent plastic strain caused by hydrate dissociation increases with the continuous drilling operation in hydratebearing sediments. and, borehole collapse first occurs at the intersection of the minimum horizontal principal stress direction with the borehole. t q.-c. li et alii, frattura ed integrità strutturale, 45 (2018) 86-99; doi: 10.3221/igf-esis.45.07 97 (4) it is impractical to investigate borehole collapse using the simplified model that neglects both the seepage and the heat transfer (i.e., model 2 in this paper). by comparison, the coupled finite element model and the investigation method established herein are feasible for simulating borehole instability during the drilling operation in hydrate-bearing sediments. (5) poor mesh quality is not conducive to realistically simulating the hydrate dissociation during the drilling operation and the resulting wellbore collapse. mesh size is also an important factor when the fem was used to investigate wellbore stability in hydrate-bearing sediments. although the research method proposed in this paper has some advantages compared with previous studies, there are still many shortcomings and need further improvement: (1) effect of the anisotropy of reservoir properties on borehole collapse needs to be investigated. (2) effect of hydrate dissociation on temperature and pore pressure must be considered to realistically simulate the actual situation. (3) a temperature change of drilling mud during mud circulation also a limitation requires to be considered. funding his work is supported by program for the changjiang scholars and innovative research team in university (irt_14r58) ，the national natural science foundation project of china (51704311), the fundamental research funds for the central universities (grant no. 16cx06033a), national key research and development program (grant no. 2016yfc0304005), the national basic research program of china (973 program) (grant no. 2015cb251201) and qingdao science and technology project (grant no. 15-9-1-55-jch). acknowledgements his work should be thankful for the help from rock mechanics laboratory in china university of petroleum (east china). references [1] gai, x. and sánchez, m. (2017). a geomechanical model for gas hydrate-bearing sediments, journal of environmental geotechnics, 4(2), pp.143-156. doi: 10.1680/jenge.15.00050. [2] klar, a., soga, k. and ng, mya. (2017). coupled deformation–flow analysis for methane hydrate extraction, géotechnique, 60(10), pp.765-776. doi: 10.1680/geot.9.p.079-3799. [3] lu, s. (2015). retracted: a global survey of gas hydrate development and reserves: specifically in the marine field, renewable & sustainable energy reviews, 41, pp.884-900. doi: 10.1016/j.rser.2014.08.063. [4] li, g., li, x. zhang, k. li, b. and zhang, y. (2013). effects of impermeable boundaries on gas production from hy drate accumulations in the shenhu area of the south china sea, energies, 6, pp. 4078-4096. doi: 10.3390/en6084078. [5] merey, s. (2016). drilling of gas hydrate reservoirs, journal of natural gas sciences & engineering, 35, pp.1167-1179. doi: 10.1016/j.jngse.2016.09.058. [6] milkov, av. (2004). global estimates of hydrate-bound gas in marine sediments: how much is really out there, earth science reviews, 66(3), pp.183-197. doi: 10.1016/j.earscirev.2003.11.002. [7] zhang, w., bai, f. shao, m. and tian, q. (2017). progress of offshore natural gas hydrate production tests in japan and implication, marine and geology quaternary geology, 37(5), pp.27-33. (in chinese) [8] li, g., moridis, gj. zhang, k. and li, xs. (2011). the use of huff and puff method in a single horizontal well in gas production from marine gas hydrate deposits in the shenhu area of south china sea, journal of petroleum science & engineering, 77(1), pp.49-68. doi: 10.1016/j.petrol.2011.02.009. [9] cha, y., yun, ts. kim, yj. lee, jy. and kwon, t. (2016). geomechanical, hydraulic and thermal characteristics of deep oceanic sandy sediments recovered during the second ulleung basin gas hydrate expedition, energies, 9(10), pp. 775. doi: 10.3390/en9100775. t t q.-c. li et alii, frattura ed integrità strutturale, 45 (2018) 86-99; doi: 10.3221/igf-esis.45.07 98 [10] rutqvist, j. and moridis, gj. (2007). numerical studies on the geomechanical stability of hydrate-bearing sediments. spe journal, 14(2), pp.267-282. doi: 10.2118/126129-pa. [11] klar, a., uchida, s. soga, k. and yamamoto, k. (2013). explicitly coupled thermal flow mechanical formulation for gas-hydrate sediments, spe journal, 18(2), pp.196-206. doi: 10.2118/162859-pa. [12] pook, les. (2015). crack paths and the linear elastic analysis of cracked bodies, frattura ed integrità strutturale, 9, pp.150-159. doi: 10.3221/igf-esis.34.16. [13] berto, f., campagnolo, a. and pook, l. (2015). three-dimensional effects on cracked components under anti-plane loading, frattura ed integrità strutturale, 33, pp.17-24. doi: 10.3221/igf-esis.33.03. [14] qiu, k. b., yamamoto, k. birchwood, r. a. and chen, y. r. (2015). well integrity evaluation for methane hydrate production in the deepwater nankai trough, spe drilling & completion, 30(1), spe-174081-pa. doi: 10.2118/174081-pa. [15] ning, f.l., zhang, k.n. wu, n.y. zhang, l. li, g. jiang, g. s. yu, y.b. liu, l. and qin, y.h. (2013). invasion of drilling mud into gas-hydrate-bearing sediments. part i: effect of drilling mud properties, geophysical journal international, 193(3), pp.1370–1384. doi: 10.1093/gji/ggt015. [16] ning, f.l, wu, n.y. yu, y.b. zhang, k.n. jiang, g.s. zhang, l. sun, j.x. and zheng, m.m. (2013). invasion of drilling mud into gas-hydrate-bearing sediments. part ii: effects of geophysical properties of sediments, geophysical journal international, 193(3), pp.1385–1398. doi: 10.1093/gji/ggt016. [17] fereidounpour, a., and vatani, a. (2015). designing a polyacrylate drilling fluid system to improve wellbore stability i n hydrate bearing sediments, journal of natural gas science and engineering, 26, pp. 921-926. doi: 10.1016/j.jngse.2015.06.038. [18] matsuda, h., yamakawa, t. sugai, y.c. and sasaki, k. (2016). gas production from offshore methane hydrate layer and seabed subsidence by depressurization method, engineering, 8, pp.353-364. doi: 10.4236/eng.2016.86033. [19] mcconnell, d.r., zhang, z.j. and boswell, r. (2012). review of progress in evaluating gas hydrate drilling hazards, marine & petroleum geology, 34, pp.209-223. doi: 10.1016/j.marpetgeo.2012.02.010. [20] wang, x.j., lee, m. collett, t. yang, s.x. guo, y.q. and wu, s.g. (2014). gas hydrate identified in sand-rich inferred sedimentary section using downhole logging and seismic data in shenhu area, south china sea, marine and petroleum geology, 51, pp.298-306. doi: 10.1016/j.marpetgeo.2014.01.002. [21] su, z., moridis, g.j. zhang, k.n. yang, r. and wu, n.y. (2010). ss-gas hydrate: numerical investigation of gas production strategy for the hydrate deposits in the shenhu area, in: proceding of offshore technology conference, houston, usa, otc-20551-ms. doi: 10.4043/20551-ms. [22] su, z., huang, l. wu, n.y. and yang, s.x. (2013). effect of thermal stimulation on gas production from hydrate dep osits in shenhu area of the south china sea, science china earth sciences, 56(4), pp.601–610. doi: 10.1007/s11430-013-4587-4. [23] moridis, g.j. and reagan, m.t. (2007). strategies for gas production from oceanic class 3 hydrate accumulations, in: proceding of offshore technology conference, houston, usa, otc-18865-ms. doi: 10.4043/18865-ms. [24] khanna, a., luong, h. kotousov, a. nguyen, g. and rose, l. (2017). residual opening of hydraulic fractures created using the channel fracturing technique, international journal of rock mechanics and mining sciences, 100, pp.124137. doi: 10.1016/j.ijrmms.2017.10.023. [25] bortolan neto, l. and kotooussov, a. (2012). residual opening of hydraulically stimulated fractures filled with granular particles, journal of petroleum science and engineering, 100, pp.24-29. [26] freij-ayoub, r., tan, c. clennell, b. tohidi, b. and yang, j.h. (2007). a wellbore stability model for hydrate bearing sediments, journal of petroleum science and engineering, 57, pp.209-220. doi: 10.1016/j.petrol.2005.10.011. [27] meneghetti, g., campagnolo, a., berto, f. and tanaka, k. (2017). crack initiation life in notched ti-6al-4v titanium bars under uniaxial and multiaxial fatigue: synthesis based on the averaged strain energy density approach, frattura ed integrita strutturale, 11, pp.8-15. doi: 10.3221/igf-esis.41.02. [28] bradley, w. (1979). failure of inclined boreholes, journal of energy resources technology, 101(4), pp.232-239. doi: 10.1115/1.3446925. [29] liu, x., zeng, w. liang, l. and lei, m. (2016). wellbore stability analysis for horizontal wells in shale formations, journal of natural gas science & engineering, 31, pp.1-8. doi: 10.1016/j.jngse.2016.02.061. [30] liu, m., yan, j. lu, y. chen, m. hou, b. chen, w. wen, x. and yu, x. (2016). a wellbore stability model for a deviated well in a transversely isotropic formation considering poroelastic effects, rock mechanics and rock engineering, 49(9), pp.3671–3686. doi: 10.1007/s00603-016-1019-8. [31] aadnoy, b.s., and chenevert, m.e. (1987). stability of highly inclined boreholes, spe drilling engineering, 2, pp.364374. doi: 10.2118/16052-pa. https://doi.org/10.2118/174081-pa https://doi.org/10.1093/gji/ggt015 https://doi.org/10.1093/gji/ggt016 https://doi.org/10.1016/j.jngse.2015.06.038 https://doi.org/10.4236/eng.2016.86033 https://doi.org/10.1016/j.marpetgeo.2012.02.010 https://doi.org/10.1016/j.marpetgeo.2014.01.002 https://doi.org/10.4043/20551-ms https://doi.org/10.1007/s11430-013-4587-4 https://doi.org/10.4043/18865-ms https://doi.org/10.1016/j.petrol.2005.10.011 https://doi.org/10.1115/1.3446925 https://doi.org/10.1115/1.3446925 https://doi.org/10.1016/j.jngse.2016.02.061 https://doi.org/10.1007/s00603-016-1019-8 https://doi.org/10.2118/16052-pa q.-c. li et alii, frattura ed integrità strutturale, 45 (2018) 86-99; doi: 10.3221/igf-esis.45.07 99 [32] loh, m., falser, s. babu, p. linga, p. palmer, a. and tan, t. s. (2012). dissociation of freshand seawater hydrates along the phase boundaries between 2.3 and 17 mpa, energy & fuels, 26(10), pp.6240-6246. doi: 10.1021/ef3008954. [33] li, q., cheng, y. li, q. zhang, c. ansari, u. and song, b. (2018). establishment and evaluation of strength criterion for clayey silt hydrate bearing sediment, energy sources, part a: recovery, utilization, and environmental effects, 40(6), pp.742-750. doi: 10.1080/15567036.2018.1457742. [34] ng, m.y.a., klar, a. and soga, k. (2008). coupled soil deformation-flow-thermal analysis of methane production in layered methane hydrate soils, in proceedings of the offshore technology conference, houston, tx, usa, 5–8. nomenclature symbol interpretation symbol interpretation σtot the total stress, mpa az and inc the azimuth and the inclination, ° σeff the effective stress, mpa pm drilling mud pressure, mpa pp the pore pressure, mpa v the poisson's ratio σp the in-situ stress tenser, mpa θ the polar angle in borehole cylindrical coordinate system rs and rb the transformation matrices teq equilibrium temperature of methane hydrate α, β and γ three rotation angles, ° peq equilibrium pressure of methane hydrate https://doi.org/10.1021/ef3008954 https://doi.org/10.1080/15567036.2018.1457742 microsoft word numero 25 art 12 j.t.p de castro et alii, frattura ed integrità strutturale, 25 (2013) 79-86; doi: 10.3221/igf-esis.25.12 79 special issue: characterization of crack tip stress field is notch sensitivity a stress analysis problem? jaime tupiassú pinho de castro, marco antonio meggiolaro mechanical engineering department, pontifical catholic university of rio de janeiro (puc-rio), brazil abstract. semi–empirical notch sensitivity factors q have been widely used to properly account for notch effects in fatigue design for a long time. however, the intrinsically empirical nature of this old concept can be avoided by modeling it using sound mechanical concepts that properly consider the influence of notch tip stress gradients on the growth behavior of mechanically short cracks. moreover, this model requires only wellestablished mechanical properties, as it has no need for data-fitting or similar ill-defined empirical parameters. in this way, the q value can now be calculated considering the characteristics of the notch geometry and of the loading, as well as the basic mechanical properties of the material, such as its fatigue limit and crack propagation threshold, if the problem is fatigue, or its equivalent resistances to crack initiation and to crack propagation under corrosion conditions, if the problem is environmentally assisted or stress corrosion cracking. predictions based on this purely mechanical model have been validated by proper tests both in the fatigue and in the scc cases, indicating that notch sensitivity can indeed be treated as a stress analysis problem. keywords. notch sensitivity; stress gradient effects; non-propagating short cracks. introduction emi-empirical notch sensitivity factors 0  q  1 have been long used to relate linear elastic (le) stress concentration factors (scf) kt = max/n, to their corresponding fatigue scf kf = 1 + q(kt – 1) = sl(r)/slntc(r), where max and min are the maximum and minimum le stress at the notch root caused by n, the nominal stress that would act at that point if the notch did not affect the stress field around the notch, whereas sl(r) and slntc(r) are the fatigue limits measured on standard (smooth and polished) and on notched test specimens (ts), respectively, at a given r = min/max ratio. despite their empirical nature, such kf values are still widely used to quantify notch effects on the fatigue strength of structural components [1]. on the other hand, it is well known that the notch sensitivity in fatigue can be associated with the relatively fast generation of tiny non-propagating cracks at notch roots when sl(r)/kt < n < sl(r)/kf, see fig. 1 [2]. based on this behavior, a model has been proposed to calculate the q values from the fatigue behavior of short cracks emanating from notch tips, using only relatively simple but sound mechanical principles, which do not require heuristic arguments, neither any arbitrary data-fitting parameter [3-5]. in particular, this model does not require a critical distance concept, a good idea which originally assumed that the notch sensitivity should be dependent on some (yet never discovered) microstructural parameter [6-10]. in fact, to operationalize the critical distance concept it needs in practice to be fitted to the measured material properties, not to its microstructural parameters. the alternative explanation proposed here may be appealing for those who tackle such problems from a more mechanical viewpoint. such an approach allowed it to explain notch effects not only on fatigue, but also on environmentally assisted cracking problems. indeed, it is claimed here that notch sensitivity exists on such problems as well, and that it can be described using the same techniques successfully applied to model the fatigue problem. in fact, this can be done by just considering the proper resistances to crack initiation and to crack propagation in the given material/environment pair, both standard well-defined mechanical properties. data is already available to support the proposed model predictions both in fatigue and scc conditions. s http://www.gruppofrattura.it http://dx.medra.org/10.3221/igf-esis.25.12&auth=true j.t.p de castro et alii, frattura ed integrità strutturale, 25 (2013) 79-86; doi: 10.3221/igf-esis.25.12 80 figure 1: classical data showing that non-propagating fatigue cracks are generated at the notch roots if sl/kt < n < sl/kf [2, 7]. analysis of notch effects on the fcg behavior of short cracks he generation of non-propagating fatigue cracks shown in figure 1 indicates that whereas crack initiation by fatigue is controlled by the stresses acting at notch tips, the fatigue crack growth (fcg) behavior of short cracks emanating from them should be affected by the stress gradients around them too. it also indicates that notch sensitivity is caused by the existence of those non-propagating cracks. indeed, to start a crack at a notch tip and then stop it after a short growth, its driving force must decrease in spite of its growing size. as the cracking driving force depends on the crack size and on the stress acting on it, the only mechanical explanation for such an apparently odd behavior is that the stresses ahead of the notch tip must decrease more than the crack growth contribution. therefore, the stress gradients ahead of the notch tips must be as important as their scf to understand the notch sensitivity behavior. indeed, based on this sensible argument, even before developing its mechanics it could be claimed that, contrary to the traditional practice, for any given material the notch sensitivity value q should depend not only on the notch tip radius , but also on its depth b, since both affect the stress gradients around notch tips. this means that shallow and elongated notches of same  may have quite different q. but before jumping to conclusions, let’s work out this mechanical model. first note that short fatigue cracks must behave differently from long cracks, since their fcg threshold must be smaller than the long crack threshold kth(r) [11], otherwise the stress range  required to propagate them would be higher than the material fatigue limit sl(r). indeed, assuming as usual that the fcg process is primarily controlled by the stress intensity factor (sif) range, k  (a), if short cracks with a  0 had the same kth(r) threshold of long cracks, their propagation by fatigue would require   , clearly a nonsense. note also that the word “short” is used here to mean “mechanical” and not “microstructural” small cracks, since material isotropy is assumed in their modeling, a simplified hypothesis corroborated by the tests. the fcg threshold of short fatigue cracks under pulsating loads kth(a, r  0) can be modeled using el haddad-topper-smith (ets) characteristic size a0 [12], which is estimated from s0  sl(r  0) and k0  kth(r  0). this clever trick reproduces the kitagawa-takahashi plot trend [13], see fig. 2, using a modified sif range k’ to describe the fatigue propagation conditions of any crack, short or long, defined by: 0( )k a a     , where    2 0 0 01a k s   (1) this k’ has been deduced for the griffith’s plate sif, k = (a). to deal with other geometries it should be rewritten using the non-dimensional geometry factor g(a/w) of the cracked component: 0( ) ( )k g a w a a     , where     2 0 0 01 ( )a k g a w s     (2) but the tolerable stress range  under pulsating loads only tends to the fatigue limit s0 when a  0 if  is the notch root (instead of the nominal) stress range. however, most g(a/w) expressions found in tables include the notch scf, thus they use  instead of n as the nominal stress. a clearer way to define the short crack characteristic size a0 when the short crack departs from a notch root is to explicitly recognize this practice, separating the geometry factor g(a/w) into two t http://www.gruppofrattura.it http://dx.medra.org/10.3221/igf-esis.25.12&auth=true j.t.p de castro et alii, frattura ed integrità strutturale, 25 (2013) 79-86; doi: 10.3221/igf-esis.25.12 81 parts: g(a/w) = (a), where (a) describes the stress gradient ahead of the notch tip, which tends to the scf as the crack length a  0, whereas  encompasses all the remaining terms, such as the free surface correction: 0( ) ( )k a a a        , where     2 0 0 01a k s      (3) figure 2: kitagawa-takahashi plot describing the fatigue propagation of short and long cracks under pulsating loads (r = 0) in ht80 steel with k0 = 11.2 mpam and s0 = 575 mpa. operationally, the short crack can be better treated by letting the sif range retain its original form, while modifying the fcg threshold expression to become a function of the crack length a, namely k0(a), resulting (under pulsating loads) in:  0 0 0( )k a k a a a     (4) the ets equation can be seen as one possible asymptotic match between the short and long crack behaviors. following bazant’s idea [14], a more general equation can be used introducing an adjustable parameter  to fit experimental data:   1/2 0 0 0( ) 1k a k a a         (5) equations (1) to (4) result from (5) if   2. the bi-linear limit, (a  a0)  s0 for short cracks and k0(a  a0)  k0 for the long ones, is obtained if g(a/w)  (a)  1 and   . most short crack fcp data is fitted by k0(a) curves with 1.5    8, but   6 better reproduces classical q-plots based on data measured by testing semi-circular notched fatigue ts [3-5]. using (5) as the fcp threshold, then any crack departing from a notch under pulsating loads should propagate if:     12 0 0 0( ) 1k a a k a k a a                    (6) where   1.12 is the free surface correction. as fatigue depends on two driving forces,  and max, (6) can be extended to consider max (indirectly modeled by the r-ratio) influence in short crack behavior. first, the short crack characteristic size should be defined using the fatigue limit sr and the fcp threshold for long cracks kr  kth(a >> ar, r), both measured or properly estimated at the desired r-ratio:     2 r r1 1.12ra k s     (7) likewise, the corresponding short crack fcp threshold should be re-written as:   1/2 ( ) 1r r rk a k a a         (8) according to tada [15], the sif of a crack with size a that departs from a circular hole of radius  given within 1% by: 2 3 6 1.1215 ( ), 0.2 0.3 1( ) 2 2.354 1.206 0.221(1 )(1 ) 1 1 1 ik a x x a x x x x xx x x x                                              (9) http://www.gruppofrattura.it http://dx.medra.org/10.3221/igf-esis.25.12&auth=true j.t.p de castro et alii, frattura ed integrità strutturale, 25 (2013) 79-86; doi: 10.3221/igf-esis.25.12 82 so, for circular holes (x  0)  3 and (x )  1/1.12152  0.63. since to propagate by fatigue any crack its sif must be larger than its threshold, then for pulsating loads:     1//2 0 0( ) 1i thk a a k a k a a                     (10) note that a0 cannot depend on the stress gradient factor (a/w), otherwise it would not be a material property. the fcg criterion can thus be rewritten using two dimensionless functions, one related to the notch stress gradient (a/w), and the other g(s0/, a/, k0/s0, ) which includes the applied stress range , and depends on the crack size, on the notch radius , on the fatigue resistances k0 and s0, and on the data fitting exponent  (if it is used):           0 0 0 0 0 1/ 0 0 0 , , , s k s s ka a g s a k s                                      (11) therefore, if x  a/ and   k0/s0  (a0/), a fatigue crack departing from a kirsch hole under pulsating loads grows whenever (x)/g(s0/, x, , ) > 1. figure 3 plots some /g functions for several fatigue strength to loading stress range ratios s0/ as a function of the normalized crack length x, assuming a small notch root radius compared to the short crack characteristic size with  1.40a0, and a material with   1.5 and   6 [5]. figure 3: cracks that can start from the border of a (small) circular hole may propagate by fatigue and then stop if their /g< 1. for high applied stress ranges , the strength to load ratio s0/ is small, and the corresponding /g curve is always higher than 1, so cracks initiate and propagate from this kirsch hole border without stopping during this process. small stress ranges with load ratios s0/  kt  3 have /g < 1, meaning that such loads cannot initiate a fatigue crack from this hole, and that small enough cracks introduced there by any other means will not propagate at such low loads. intermediate load ranges can initiate and propagate a fatigue crack from this hole border, until the decreasing /g ratio reaches 1, where the crack stops because the stress gradient ahead of its small root is sharp enough to eventually force ki(a) < kth(a). finally, the curve is tangent to the /g  1 line identifies the smallest pulsating stress range that can cause crack initiation and propagation (without arrest) from the notch border by fatigue alone. hence, by definition, it is associated to this hole fatigue scf kf. moreover, the abscissa of its tangency point gives the largest non-propagating crack size that can arise from it by fatigue alone, amax. for any other /a0, , and  combination, kf and amax can always be found by solving the system           max max max max , , ,1 0 , , , f f x g x kg g x x x g x k x                     (12) kirsch holes induce relatively mild stress gradients. larger holes compared with the short crack characteristic size, with radii  >> a0, are associated to small  values and do not induce short crack arrest. that is a nice way to mechanically http://www.gruppofrattura.it http://dx.medra.org/10.3221/igf-esis.25.12&auth=true j.t.p de castro et alii, frattura ed integrità strutturale, 25 (2013) 79-86; doi: 10.3221/igf-esis.25.12 83 interpret the notch sensitivity concept. in other words, if the system {/g  1, (/g)x  0} is solved for a given  and several tip radii using k0/s0, then the notch sensitivity factor q is obtained by: ( , ) [ ( , ) 1] ( 1)f tq k k      (13) this approach has 4 advantages: (i) it is an analytical procedure; (ii) it considers the effect of the fatigue resistances to crack initiation and propagation on q; (iii) it can use the exponent  used to modify the original ets model to better fit short fcg data; and (iv) it can be easily extended to other notch geometries. for example, the sif of cracks that depart from a semi-elliptical notch with semi-axles b and c, with b collinear with the crack a and perpendicular to the (nominal) stress n, can be described by:  i ,k f a b c b a      (14) where   1.1215 is the free surface correction factor and f(a/b, c/b) is the geometrical factor associated to the notch stress concentration effect. such notches scf kt is given by [15]:   2.51 2 1 0.1215 (1 )tk b c c b       (15) using s  a/(a + b) two analytical expressions for f(a/b, c/b) were obtained in [3] by fitting results obtained by a series of finite elements (fe) analyses for several types of semi-elliptical notches:       2 2 2 22 2 , , 1 exp( ) ( ), 1 exp( ) ( , ) , 1 exp( ) , t tt t s t t t t t f a b c b f k s k k s k s c b k s f a b c b f k s k k c b k s                         (16) note that traditional notch sensitivity estimates, like peterson’s q  (1 + /)-1, where  is a length parameter obtained by fitting only 7 experimental points, suppose that the notch sensitivity depends only on the notch tip radius  and on the steel tensile strength (and only on  for al alloys). the model proposed here, on the other hand, recognizes that q depends on , s0, and k0 (and in , if it is used). there are reasonable relations between s0 and su, the ultimate tensile strength, but none between k0 and su. this means that two steels of same su, but very different k0, should behave identically according to peterson-like q estimates, for example, not a reasonable assumption. further details on this model are available on [3], and experimental evidence that supports its predictions in fatigue is presented in [4-5]. its extension for stress corrosion cracking conditions is developed in [16]. influence of short cracks on the fatigue strength of structural components he traditional sn and n fatigue design methods are used to analyze supposedly crack-free pieces, but very often it is not possible to fulfill this requisite in practice. in fact, it is impossible to guarantee that a component is really free of cracks smaller than the detection threshold of the non-destructive method used to identify them. nevertheless, most structural components are still designed against fatigue crack initiation using procedures that do not recognize such small cracks. hence, their “infinite life” predictions may become unreliable when they are introduced by any means during manufacture or service, and not quickly detected and properly removed. but while large cracks may be easily detected and dealt with, small cracks may pass unnoticed, even in careful inspections. therefore, structural components that must last for very long fatigue lives should be designed to be tolerant to undetectable short cracks, since continuous work under fatigue loads cannot be guaranteed if any of the cracks they might have can somehow propagate during their service lives. despite being self-evident, this requirement is still not included in most fatigue design routines used in practice. indeed, most long-life designs just intend to maintain the service stresses at the structural component critical point below its fatigue limit,  < sl(r)/f, where f is a suitable safety factor. such calculations can become quite involved when designing e.g. against fatigue damage caused by random non-proportional loads, but their safe-life philosophy remains the same. however, in spite of not recognizing any cracks, most long-life designs work just fine. this means that they are somehow tolerant to undetectable or to functionally admissible short cracks. but the question “how much tolerant” t http://www.gruppofrattura.it http://dx.medra.org/10.3221/igf-esis.25.12&auth=true j.t.p de castro et alii, frattura ed integrità strutturale, 25 (2013) 79-86; doi: 10.3221/igf-esis.25.12 84 cannot be answered by sn or n procedures alone. such problem can be avoided by adding short crack concepts to their “infinite” life design criteria which, in its simplest version, may be given by [5]:   12( ) 1r f rk a g a w a a            (17) where   1/2 ( ) 1r r rk a k a a         , and    2 1r r ra k s    since the fatigue limit sr sl(r) already reflects the effect of the microstructural defects inherent to the material, equation (17) complements it by describing the tolerances to small cracks that may pass unnoticed in actual service conditions. the practical usefulness of this sensible criterion is well illustrated by a practical example, as follows. due to a rare manufacturing problem, a batch of an important component left the factory with tiny surface cracks (only detectable by a microscope), causing some unexpected and embarrassing failures. hence, it became necessary to properly quantify the actual effect of such tiny cracks in that component fatigue strength. assume its rectangular cross-section has 2 by 3.4mm; its (uncracked) fatigue limit is sl = 246mpa; and it is made from steel with su = 990mpa. this measured fatigue limit is about ¼ of the steel su/4, whereas it would be traditionally estimated by sl  su/2  495mpa. this difference may be due to a surface finish factor ksf  0.5, a value between those proposed by juvinall for su  1gpa steels with cold-drawn (ksf  0.45) and machined surfaces (ksf  0.7) [17]. the surface finish should not affect cracks, but as this difference could be due to other factors too, like tensile residual stresses, the only safe option is to use sl = 246mpa to evaluate the tiny crack effects. therefore, by goodman sl(r) = sr = slsu(1 – r)/[su(1 – r) + sl(1 + r)] for r1 (or m  0), for example. the fcg threshold kr is also needed to model short crack effects, but if data is not available, as in this case, it must be estimated e.g. by kr(r  0.17)  k0  6mpam and kr(r > 0.17)  7(1 0.85r) [18]. this practice increases the predictions uncertainty, but it is the only option available. besides, it tends to be conservative. moreover, it assumes that kr(r < 0)k0, a safe estimate too (except if the load history contained severe compressive underloads which might accelerate the crack, not the case here.) using the sif of an edge cracked strip of width w loaded in mode i, then the tolerable stress ranges under pulsating loads shown in fig. 4 are estimated within a fatigue safety factor f as:  0 0 12 3 02[ 0.752 2.02 0.37(1 sin ) ]sec tan 1 2 2 2 fk a aa a a w a w aw w w a                       (18) figure 4: larger stress ranges tolerable under several r–ratios by the analyzed component considering it contains an edge crack with size a, for w  3.4mm,   1.12, k0  6mpam, a0  59m,   6, and f  1.6. notch sensitivity in environmentally assisted cracking problems he behavior of materials on aggressive environments is an important problem for many industries, because the costs and specially the delivery times for special eac-resistant alloys keep increasing. major problems occur e.g. in the oil industry, where oil and gas fields can contain considerably amounts of h2s, and in the aeronautical t http://www.gruppofrattura.it http://dx.medra.org/10.3221/igf-esis.25.12&auth=true j.t.p de castro et alii, frattura ed integrità strutturale, 25 (2013) 79-86; doi: 10.3221/igf-esis.25.12 85 industry, where very light structures must operate in saline environments. but environmentally assisted cracking problems have been treated so far by simplistic structural integrity assessment procedures based on an overly conservative policy of totally avoiding material-environment pairs susceptible to eac conditions. when such conditions are unavoidable during the service life of the structural component in question, the standard solution is just to choose a nobler material to build it, one that is resistant or immune to crack initiation and propagation by eac in the operational environment. alternatively, the solution may be to recover the structural component surface with a suitable properly adherent and scratch resistant eac-resistant coating. but in many cases there are no such coatings available in the market. such inflexible design criteria may be safe, but they can also be too conservative if the material is summarily disqualified when it may suffer eac in the service environment, without considering any stress analysis issues. such decisions may cause severe cost penalties. indeed, even though eac conditions may still be difficult to define, due to the number of metallurgical, chemical, and in particular mechanical variables that affect them, structural integrity assessment procedures should always be used on the design stage to define a maximum tolerable flaw size. in fact no crack can grow unless driven by a tensile stress, caused by the superposition of applied loads, residual stresses induced by previous loads or overloads, and maintenance or manufacturing procedures. thus eac cracks cannot be properly evaluated neglecting the stress and strain fields that may drive them. but such uneconomical decisions can be avoided, since we already know how different the behavior of deep and shallow fatigue cracks is, and how it can be treated in structural design. therefore, it is now possible to propose an extension of the proved criteria for accepting shallow fatigue cracks to environmentally assisted cracking problems, assuming they also present a notch sensitivity behavior that can be mechanically described. if cracks behave well under eac conditions, then a kitagawa-like diagram can be used to quantify tolerable stresses, using the material eac resistances to define a “short crack characteristic size under eac conditions” by:  20 (1/ ) ieac eaca k s    (19) in this way all corrosion features are assumed to be properly described by the resistance to crack propagation kieac and by the resistance to crack initiation seac under fixed stress conditions in the analyzed material-environment pair. in other words, this model supposes that the mechanical parameters that govern the environmentally assisted cracking problem behave analogously to the equivalent parameters kth(r) and sl(r) that control the fatigue problem, see fig. 5. figure 5: a kitagawa-takahashi-like plot proposed to describe the environmentally assisted cracking behavior of short and deep flaws for structural design purposes. consequently, if cracks loaded under eac conditions behave mechanically as they should, i.e. if their driving force is indeed the stress intensity factor applied on them; and if the chemical effects that influence their behavior are completely described by the material resistance to crack initiation from smooth surfaces quantified by seac, and by its resistance to crack propagation measured by kieac; then it can be expected that eac cracks may depart from sharp notches and then stop, due to the stress gradient ahead of the notch tips, eventually becoming non-propagating cracks, as it occurs in the fatigue case. hence, if the size of non-propagating short cracks can be calculated using the same procedures useful for fatigue case, then the resistance to that kind of defect can be properly quantified using an eac notch sensitivity factor in structural integrity assessments. therefore, a criterion for the maximum tolerable crack size under eac conditions can be proposed as: 1 2 max 0(1 ) (1 ) ( )ieaca k a a a g a w          (20) http://www.gruppofrattura.it http://dx.medra.org/10.3221/igf-esis.25.12&auth=true j.t.p de castro et alii, frattura ed integrità strutturale, 25 (2013) 79-86; doi: 10.3221/igf-esis.25.12 86 conclusions generalized el haddad-topper-smith’s parameter was used to model the crack size dependence of the threshold stress intensity range for short cracks, as well as the behavior of non-propagating environmentally assisted cracks. this dependence was used to estimate the notch sensitivity factor q of shallow and of elongated notches, from studying the propagation behavior of short non-propagating cracks that may initiate from their tips. it was found that the notch sensitivity of elongated slits has a very strong dependence on the notch aspect ratio, defined by the ratio c/b of the semi-elliptical notch that approximates the slit shape having the same tip radius. these predictions were calculated by numerical routines. based on this promising performance, a criterion to evaluate the influence of small or large surface flaws in fatigue and in environmentally assisted cracking problems was proposed. such results indicate that notch sensitivity can indeed be properly treated as a mechanical problem. references [1] peterson, r.e., stress concentration factors, wiley (1974). [2] frost, n.e., marsh, k.j., pook, l.p., metal fatigue, dover (1999). [3] meggiolaro, m.a., miranda, a.c.o., castro, j.t.p., short crack threshold estimates to predict notch sensitivity factors in fatigue, int. j. fatigue, 29 (2007) 2022–2031. [4] wu, h., imad, a., nouredine, b., castro, j.t.p., meggiolaro, m.a., on the prediction of the residual fatigue life of cracked structures repaired by the stop-hole method, int. j. fatigue, 32 (2010) 670-677. [5] castro, j.t.p., meggiolaro, m.a., miranda, a.c.o., wu, h., imad, a., nouredine, b., prediction of fatigue crack initiation lives at elongated notch roots using short crack concepts, int. j. fatigue, 42 (2012) 172-182. [6] taylor, d., the theory of critical distances: a new perspective in fracture mechanics. elsevier (2007). [7] taylor, d., geometrical effects in fatigue: a unifying theoretical model, int. j. fatigue, 21 (1999) 413–420. [8] atzori, b., lazzarin, p., fillipi, s., cracks and notches: analogies and differences of the relevant stress distributions and practical consequences in fatigue limit predictions, int. j. fatigue, 23 (2001) 355-362. [9] atzori, b., lazzarin, p., meneghetti, g., a unified treatment of the mode i fatigue limit of components containing notches or defects, int j fracture, 133 (2005) 61-87. [10] susmel, l., the theory of critical distances: a review of its applications in fatigue, eng. fract. mechanics 75 (2008) 1706-1724. [11] lawson, l., chen, e.y., meshii, m., near-threshold fatigue: a review. int. j. fatigue, 21 (1999) 15-34. [12] el haddad, m.h., topper, t.h., smith, k.n., prediction of non-propagating cracks. eng. fract. mechanics, 11 (1979) 573-584. [13] kitagawa, h., takahashi, s., applicability of fracture mechanics to very small crack or cracks in the early stage. proceedings of the 2nd international conference on mechanical behavior of materials. asm (1976) 627-631. [14] bazant, z.p., scaling of quasibrittle fracture: asymptotic analysis. int. j. fracture, 83 (1977) 19-40. [15] tada, h., paris, p. c., irwin, g. r., the stress analysis of cracks handbook, del research (1985). [16] castro, j.t.p., leite, j.c.c., does notch sensibility exist in environmentally assisted cracking (eac)?, j. mat. research and technology, in press, (2013). [17] juvinall, r.c., marshek, k.m., fundamentals of machine component design, 4th ed., wiley (2005). [18] barsom, j.m., rolfe, s.t., fracture and fatigue control in structures, 3rd ed., astm (1999). a http://www.gruppofrattura.it http://dx.medra.org/10.3221/igf-esis.25.12&auth=true microsoft word numero_30_art_65 c. yunyu, frattura ed integrità strutturale, 30 (2014) 545-551; doi: 10.3221/igf-esis.30.65 545 an analysis research of the stiffness characteristics of hospital building materials chen yunyu the first affiliated hospital of wenzhou medical university, 325000, china cyy@hosp1.ac.cn abstract. this paper primarily aims to introduce different stiffness ratio requirements for hospital buildings of various structural styles, to achieve a new standard. the requirements of each stiffness ratio are analyzed, according to the specification formulas and illustrations. and whether the structural deformation situation complies with the code requirement or dissatisfies the specification requests can be intuitively reflected through the application of the chart form, respectively. the corresponding measures complying with the code requirement and the matters needing attention in the schematic design phase are proposed. the comparison analysis for the lateral rigidity and lateral stiffness ratios is performed by applying different methods for the project cases of shear wall, frame tube and partial frame shear wall structures. the proposed computing method may better reflect the stiffness characteristics of the component’s cross-section, with regard to vertical layer, storey height and materials, as well as the actual situation of the turning constraint on both ends. the result thus determined can better reflect the real lateral rigidity of the construction, which is available as a benchmark for engineers designing hospital building structures. keywords. hospital building; stiffness properties; material. introduction tiffness and strength are two basic concepts in structural design work. strength reflects the load resistance ability of a structural component, while stiffness reflects its ability to resist transformation. previously, when designing ordinary and non-seismic multilayer reinforced concrete and brick structures, the component strength requirement was generally emphasized, while the rigidity requirement was ignored. but in the case of hospital building the horizontal load has become the control factor, due to its high altitude and to the fact that it has to bear a relatively high horizontal load (wind load and earthquake action), thus the horizontal load has become the control factor, and its ability to resist deformation under a horizontal load, namely, overall lateral stiffness, has become an important indicator of design control. rigidity not only influences structural deformation, but also exerts great effect on the load-carrying capacity of structural components [1]. structures with high stiffness feature limited deformation and a large load-carrying capacity, while structures with low stiffness feature significant deformation and a small load-carrying capacity. thus, the ability to better control the stiffness of the whole structure and the relative rigidity of its components is a prerequisite for determining whether the building’s structural system is safe, economic and reasonable [2]. materials and methods t present, the rigidity of the later layers of hospital building structures is usually measured with the following formula: s a c. yunyu, frattura ed integrità strutturale, 30 (2014) 545-551; doi: 10.3221/igf-esis.30.65 546 i i i v k   (1) where: ik is the lateral rigidity in the thi layer; iv is the shearing force of the thi layer influenced by a horizontal earthquake (lateral force); i is the inter-story displacement of the thi layer relative to the 1thi  layer influenced by a lateral force[3]. for theoretical analysis purposes, the following problems arise among the computing methods for calculating the lateral layer stiffness of hospital building structures: (1) the rigidity of the structural component or lateral layer is the only parameter related to the physical and geometric characteristics of the component and its composing structure, namely once the structure takes shape it becomes the inherent characteristic of the structure itself, which is only related to its own physical geometric characteristics and has nothing to do with the external load, but both iv and i in type (1) are the calculation results determined by the lateral force, and they are inevitably related with the external load, which changes along with lateral layer rigidity [4]. (2) in type (1), inter-story displacement i is caused by a lateral force (horizontal earthquake action), when calculating the inter-story displacement i in the thi layer. its value inevitably contains the mechanical deformation influence of many vertical components in the other storeys and, therefore, cannot reflect the contribution of the vertical component’s mechanical deformation in the thi layer, while it is the integration of both mechanical and nonmechanical deformation. as a result, lateral rigidity ik in the thi layer, calculated by applying i , will inevitably be on the low side [5]. (3) the research indicates that the inter-story displacement i in type (1) is the combined result of the component’s mechanical and non-mechanical deformation. the displacement between the upper storeys in hospital building structures is primarily the result of the components' non-mechanical deformation, while mechanical deformation tends to account for a very small proportion of the displacement; thus, as the vertical component’s cross-section in this regional floor decreases or storey height increases, the rigidity of the components is significantly weakened. but the lateral layer stiffness calculated according to type (1) is almost the same or changes only slightly, which probably results in what would appear to be a deviation or miscalculation when determining the location of the weak structural layer. and the collapse in the upper floors of many hospital buildings during the kobe earthquake in japan is a good representative example of this [6]. (4) under the effects of a horizontal earthquake, the story shear iv of the structural top floor would change greatly, when the component rigidity itself of vertical layer in this area does not changes a lot, but the lateral layer rigidity calculated according to type (1) would change a lot, which is also the unreasonable representation of this method . (5) the seismic safety of the bottom floors of hospital building structures is the concerned question of seismic design, when the storey height at the bottom of the structure has larger demands, due to building function, it tends to form a weak storey at the bottom, the lateral rigidity at the bottom determined by type (1) would be misjudged, as it does not conform to physical truth at this moment, thus it will produce problems in respect of structural seismic safety [7]. the preliminary validation method ig. 1 shows the vertical component of different rotational restraints on both the upper and lower ends, although the component itself has the same condition, the lateral rigidity of these components needs to be calculated using different formulas (the influence of shear deformation is excluded). 3 1 3k ei h (2) 3 2 112 4k ei h k  (3) 3 12 1 01 ( ) k k k k k h    (4) f c. yunyu, frattura ed integrità strutturale, 30 (2014) 545-551; doi: 10.3221/igf-esis.30.65 547 where: e is the elasticity modulus of the component; i is component’s cross sectional moment of inertia; h is the component height; 0k is the bending constraint's stiffness at the bottom, when 0k   , 3 1k k . any floor in a hospital building structure is composed of many vertical components (walls and columns) and coterminous horizontal components. lateral layer stiffness must be the summation of the lateral rigidity of the rotational constraints on both ends considered by this group of vertical components. thus we can infer that when determining the lateral rigidity of the thi layer ,its calculation model is shown as fig. 2, the thi layer will generate a unit horizontal displacement, while the 1thi  has no lateral displacement, the horizontal force needed to impose on the thi layer is the lateral rigidity ik of the thi layer. the lateral rigidity of the thi layer, determined based on this calculation model (fig. 2), contains the contribution of all vertical component stiffness values on this floor and considers the influence of rotating constraints on both ends. it is only the shape constant which is related to the geometric physical properties and bending constraint on both ends of the structural component in this layer, but it is unrelated with the external load. this definition could be considered to be the generalization of the single vertical component’s lateral stiffness in the hospital building’s structure layer. (a) (b) (c) figure1: the schematic diagram of lateral stiffness meaning for different rotational restraint components on both upper and lower end: (a) the top is free and the bottom is fixed; (b) the top is sliding and the bottom is fixed; (c) the top is sliding and the bottom is spring 1i 01  i 1k figure 2: the calculation model of lateral rigidity in the thi layer the following takes the shear wall structure of a 4-storey hospital as an example (7 degrees, ii type site). its structural typical floor plane is shown in fig. 3 (the thickness of the shear wall is 100 mm, the main sectional dimensions of the girders are 100×400, 100×350), the lateral layer stiffness and the ratio between them is obtained through the respective calculation by adopting the method in this paper, and type (1) is shown in fig. 4 and 5. the calculations indicate that the lateral layer stiffness obtained according to type (1) (the new high gauge formula) is generally relatively lower. and on the c. yunyu, frattura ed integrità strutturale, 30 (2014) 545-551; doi: 10.3221/igf-esis.30.65 548 upper floor, due to that inter-story displacement i , the value is heavily affected by the non-mechanical deformation of the storey’s vertical component, as well as the overall structural bending; the calculation results of the inter-story displacement show a significant increase, as a result of which the calculation results of the lateral layer stiffness will be considerably low, the difference from the bottom to the top being about 2.7~16 times. figure 3: the comparison results of storey’s lateral rigidity calculated with two methods. figure 4: the calculation results of a storey’s lateral stiffness ratio. results and discussion ith regard to the high gauge calculation of the lateral rigidity of a hospital building’s structural layer, the following type is applied to obtain the lateral layer stiffness ratio i between the next floor (the thi layer) and the adjacent upper floor (the 1thi  layer): 1 1 i i i i i v v       (5) through observing the size of lateral layer stiffness ratio i , whether the thi layer will form weak storeys or not, due to relative low rigidity, should be determined according to the limiting value specified by the high gauge, and corresponding seismic strengthening measures should be adopted, thus the calculation results of the stiffness ratio for the lateral layers will directly influence structural design. the ratio between interlayer displacements angles should be the basis for determining whether the thi layer will appear as a weak storey, the specifications are shown in the following type: 1 1 i i i i i h h       (6) the calculation results of type (5) and (6) feature obvious qualitative differences under certain situations. for the structure of box shear, shear wall and frame-tube etc in the high gauge, the original stiffness ratio of the lateral layer is added with the storey height ratio as its amendment, compared with the formula [type (5)], the following formula will be adopted to calculate the lateral layer stiffness ratio: 1 1 1 i i i i i i i v h v h        (7) the type (5) and type (7) in the new high gauge will be compared; it is not difficult to see that their difference only regards the storey's shear ratio 1i iv v  in type (5), which is amended by the storey height ratio 1i ih h  in type (7). the partial framed shear wall with transformation storey is widely applied in hospital building structures, as the shear wall of the partial transformation storey cannot collapse, thus the number of shear walls under the transformation storey decreases and the lateral layer stiffness of the storey is weakened, which requires the calculation of the method of lateral layer stiffness for both upper and lower storeys, in order to accurately determine whether the weak layer will appear on the w c. yunyu, frattura ed integrità strutturale, 30 (2014) 545-551; doi: 10.3221/igf-esis.30.65 549 transformation layer or not and what measures should be adopted to strengthen it, all of which are very important to guarantee the seismic safety of the structures [8]. figure 5: the comparison of the lateral layer stiffness ratio the lateral layer stiffness comparison of the upper and lower structure layers in the transformation layer generally only considers the shear deformation of the shear wall. if we suppose that both ends of the column undergo no rotation, the calculation formula for the approximate layer’s total lateral stiffness ik of bending deflection will be considered, namely: i i i ga k h  (8) where: i wji wi j a a a  , wia is the effective cross-section area of the entire shear wall on the thi storey along the calculation direction (excluding the flange area); ih is the storey height of the thi layer; g is the shearing modulus of elasticity of the shear wall concrete on the thi storey. when the storey features columns, ia should still contain the lateral rigidity when assuming that both ends of the pillar have no rotation, which is approximated by the following type: i wi ij cij j a a c a  (9) 22.5( ) cij ij i h c h  (10) where: cijh is the cross-section height of the thj pillar on the thi storey along the calculation direction. it is explicitly stipulated in new high gauge that when the transformation storey is on the 1th and 2th layer, the equivalent shear stiffness ratio between the transfer storey and its adjacent superstructure could be adopted to represent the upper and lower structural change of structural stiffness on the transfer storey. when the transfer storey is on the 1th storey, 1 1 2 1 2 2 1 g a h g a h   (11) where: 1 2,h h is the storey height of the 1 th and 2th layer. when the transfer storey is on the 2th layer, 32 2 2 2 3 2 hg a g a h   (12) c. yunyu, frattura ed integrità strutturale, 30 (2014) 545-551; doi: 10.3221/igf-esis.30.65 550 where: 3h is the storey height of the 3 th layer. eq. (8) ~ (12) indicate that the lateral layer stiffness of the transfer storey is obtained by supposing that the shear wall’s vertical components on this floor only consider the shear deformation. and supposing that there is no relative sideway unit generated from the corner of the pillar’s two ends, the shearing force at that moment is its lateral rigidity [9]. the merit of this calculation method is to denote the lateral rigidity of the structural sheaf with the only related shape constant to the geometry and physical properties of the structure layer’s vertical component itself, while it has nothing to do with the external load. this is correct, but the essence of this method is to assume the rotation constraint of the vertical component’s two ends as infinite rigidity constraints, and that the overall horizontal component is not in a rotational state. when the thi storey generates a sideway unit 1i  , the horizontal force needed to be exerted is ik , as it is shown in fig. 6. it is not in accordance with fig. 6, especially when it is on the upper and lower floor of the transfer storey (when the transfer storey is on the 2th storey), the flexural rigidity of the horizontal component is generally not large, but quite at odds with the assumed infinite rigidity, even though the flexural rigidity of the beam and slab on the transfer storey is relatively large, it also has a large gap with the infinite rigidity assumption, as a result of which the rationality and accuracy of this calculation methods still needs further research [10]. ik 1i figure 6: calculation model of the new and old high guage’s lateral rigidity based on the above analysis, we can see that the meaning of stiffness ratio is different for different structures, which means that the calculation results may vary widely, which deserves attention in the design phase. hospital buildings should first consider using uniform stiffness to achieve uniform deformation, meanwhile with the increase in height a more rigid structure should be adopted to reduce the deformation. when the structure of framed shear wall must be adopted, the location of the transfer storey should be reduced as far as possible to decrease the number of weak storeys and overall structural deformation, which is beneficial to structural safety. when there is an annex, the transfer storey should be set up on the annex’s surface. if the annex area is large, the pillar and shear wall etc. must have many components to resist lateral force, and rigidity will be greater. the transfer storey should be set up on this layer in favor of resistance to lateral forces, meanwhile it is relatively easy to comply with the specification about the stiffness ratio. in addition, for the structure of the framed shear wall, the storey height of the upper layer on the transfer storey should be enhanced as much as possible. the equipment interlayer with the short storey height must not be built up on the upper layer of the transfer storey. as the equipment interlayer is the shear wall structure, which itself is very rigid, in addition to its short storey height and little deformation, all of which would intensify the stiffness and deformation mutation of the transfer storey, which is not beneficial to the safety of the transfer storey. meanwhile, in order to make the overall structure comply with the specification about the related requirements of the stiffness ratio between the layers, higher construction costs should be added. according to the above analysis, we can see that structural stiffness and deformation are mainly related to the number of shear walls and storey height. thus dissatisfaction with the stiffness ratio’s requirement should be managed by regulating the number of shear walls and storey height. conclusions his paper has discussed the calculation methods of lateral rigidity and its ratio on hospital building’s structural layers and pointed out that some problems exist in this respect, as well as suggested methods for their solution [11]. furthermore, it points out that the calculation method of the structural lateral rigidity on the transfer storey t c. yunyu, frattura ed integrità strutturale, 30 (2014) 545-551; doi: 10.3221/igf-esis.30.65 551 is essentially the calculation method of the layer shear stiffness, assuming that the transfer storey and horizontal component stiffness of its corresponding upper and lower storey is infinitely rigid. although it reflects the stiffness characteristics of the vertical component’s cross-section, storey height and material, the rotation constraints on both ends are supposed to be infinitely stiff, which is not in accordance with reality, and results in too high a lateral layer stiffness, the imbalance range is different in different cases, thus it would result that the calculation results of the lateral layer stiffness ratio is too small or big, so it is difficult to determine beforehand and is disadvantageous for the accuracy and reliability of physical design. adopting the suggested calculation methods could better reflect the component cross-section of the vertical layer, storey height and stiffness characteristics of material, as well as the actual state of the rotation constraints on both ends, thus the calculation results could better reflect the real lateral stiffness of the transfer storey’s structure, which could solve the existing confusion in the engineering field with regard to this problem [12]. references [1] lian, w., the symposium about the displacement control of hospital building structure, architectural structure, 30(6) (2000) 27-30. [2] xin, w., hao, z., yun, g., study on the safety assessment system of buildings, industrial safety and environment protection, 36(9) (2010) 56-57. [3] baojun, p., tao, z., shanyi, d., analysis for the mesoscopic computational mechanics of effective elastic modulus in three-dimensional and multi-directional braided composites, chinese journal of computational mechanics, 18(2) (2001) 231-234. [4] shanyuan, w., ruguang, z., et al., fibre reinforced composite material, china's textile industry university press, (2008) version 1. [5] ko, f. k., three-dimensional fabrics for composites-an introduction to the magnaweave structure, proc. iccm-4, japan soc. composite material, tokyo, japan, (2012). [6] ko, f. k., pastore, c. m., structure and properties of and integrated3-d fabric for structural composites, in recent advances in composites in the united states and japan, astmstp 864, vinson, j. r. & taya, m. editors, philadelphia: american society for testing and materials, (2005) 428-439. [7] ma, c. l., yang, j. m., chou, t. w., elastic stiffness of three-dimensional braided textile structure composites, in composite materials: testing and design (seventh conference), astm stp, philadelphia, 893 (1986), 404-421. [8] lian, w., sen, w., renfan, s., computing method research for lateral rigidity of high-rise building structure layer, architectural structure, 44(6) (2014) 4-9. [9] kostar, t. d., chou, t. w., design and automated fabrication of 3-d braided performs for advanced structural composites, computer aided design in composite material technology iii, elsevier science, (2009) 63-78. [10] hongchang, w., analysis and design for combined action of supporting column transfer beam and upper frame, hunan university, (2012). [11] wang, y. q., sun, x., determining the geometry of textile performs using finite element analysis, in: proceedings of the american society for composites, college station, texas, september 25-27, (2009) 485-492. microsoft word numero_44_art_13 g. testa et alii, frattura ed integrità strutturale, 44 (2018) 161-172; doi: 10.3221/igf-esis.44.13 161 equation chapter 1 section 1 numerical simulation of self-piercing riveting process (srp) using continuum damage mechanics modelling gabriel testa, nicola bonora, gianluca iannitti, andrew ruggiero, domenico gentile university of cassino and southern lazio, cassino i-03043, italy gabriel.testa@unicas.it, http://orcid.org/0000-0001-2345-6789 abstract. the extended bonora damage model was used to investigate joinability of materials in self-piercing riveting process. this updated model formulation accounts for void nucleation and growth process and shearcontrolled damage which is critical for shear fracture sensitive materials. potential joint configurations with dissimilar materials have been investigated computationally. in particular the possible combination of dp600 steel, which is widely used in the automotive industry, with al2024-t351, which is known to show shear fracture sensitivity, and oxygen-free pure copper, which is known to fail by void nucleation and growth, have been investigated. preliminary numerical simulation results indicate that the damage modelling is capable to discriminate potential criticalities occurring in the spr joining process opening the possibility for process parameters optimization and screening of candidate materials for optimum joint. keywords. self-piercing; riveting; cdm; ductile damage; shear fracture. citation: testa, g., bonora, n., ruggiero, a., gentile, d., numerical simulation of selfpiercing riveting process (srp) using continuum damage mechanics modelling, frattura ed integrità strutturale, 44 (2018) 161-172. received: 02.02.2018 accepted: 25.03.2018 published: 01.04.2018 copyright: © 2018 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. introduction elf-piercing riveting (spr) is a cold-forming operation used to fasten two or more sheets of material by driving a semi-tubular rivet through the top sheet(s), piercing the bottom sheet, and spreading the rivet skirt under the guidance of a suitable die. as the process relies on a mechanical interlock rather than fusion, it can be used for a wide range of advanced materials that are dissimilar, coated, and hard to weld. unlike the “traditional” riveting process, no pre-process, such as hole drilling and alignment, is necessary. the complex joint geometry and its three-dimensional nature combine to increase the difficulty of obtaining an overall system of governing equations for predicting the properties of the spr joints. the effective way to analyze spr joint during forming process is to perform numerical simulation. this has been addressed by several authors using different numerical techniques. mori et al. [1] used finite element simulation to optimize the die shape provided the mechanical properties of the rivet. they found that the strength of the joint is influenced by both mechanical properties of the sheet metals and the ratio of the lower sheet thickness and the overall thickness. atzeni et al. [2] investigated the possibility to predict the strength of a srp joint simulating both process and shear test finding a reasonable agreement with experiments in terms of deformed geometry and force-displacement response. more recently, he et al. [3] simulated spr s g. testa et alii, frattura ed integrità strutturale, 44 (2018) 161-172; doi: 10.3221/igf-esis.44.13 162 process in al 5754 using ls-dyna showing the possibility to reproduce with good accuracy the load vs displacement response during the process. a) b) c) d) figure 1: schematic representation of srp fastening process: a) the semi-tubular rivet is place in the holder; b) applied load forces the rivet to deform with the metal sheets that eventually pierce, c) usually, only the first sheet is pierced and while the rivet lock-in the second metal sheet, d) the load is finally released [4]. however, finite element analysis can be particularly useful in providing a better understanding of the potential mechanisms and conditions that may result in a poor joining. in fact, several defects may occur during srp. these include: the penetration through the lower sheet, the necking of the lower sheet, and the separation of sheets. in the penetration through the lower sheet, the leg of the rivet goes out from the bottom surface of the lower. this is found to be a driver for corrosion in service. the necking of the lower sheet is a thinning phenomenon, similar to the penetration defect. in the separation of the sheets, the spread of the leg of the rivet is too small to join the sheets, and the riveted sheets are easily separated [5]. a sketch of these defects is shown in fig. 2. a) b) c) figure 2: typical defects in spr: a) penetration, b) necking and c) separation. the spr technique is mainly applied to joining of two sheets, although application of this technique to multi-layer sheets has also been investigated [6]. the possibility to achieve a joint without defects defines the “joinability” of candidate materials. at present, for given materials (i.e. steel and aluminum), this ability seems to depends on the ratio between the upper and the lower sheets thickness. for steel-aluminum it was found that penetration, necking and separation are caused by small total thickness, small thickness of the lower sheet and large total thickness, respectively [5]. the possibility to predict the occurrence of such defects by means of numerical simulation relies mainly in the ability to model plastic deformation in the materials and the capability to predict the occurrence of fracture phenomena. this requires an accurate description of material flow curve and a failure model. in spr of joinable materials, the upper sheet material initially flows around the rivet with a progressive reduction of the ligament eventually followed by fracture. in the literature, this process has been simulated using arbitrary separation criteria based on geometrical consideration. cacko [7] presented a review of selected material separation criteria available in commercial msc software applied for the spr process simulation. his conclusions confirm that geometrical separation criteria, although very simple to use, relays on experiments for calibration. this makes simulation suitable for reproducing a known process but incapable of any prediction for different scenarios in which process parameters or material characteristics are changed or unknown. alternatively, the conditions for separation, occurring in the material under large plastic deformation as such in spr process can be accurately predicted using continuum damage mechanics (cdm). in this field, there is an extensive literature on modelling ductile damage in metals and alloys. among available approaches to model ductile damage and its effects, bonora [8], in the framework of cdm introduced by lemaitre [9], proposed a damage model formulation in which a general non-linear law of evolution for damage that was demonstrated to be suitable to predict ductile fracture in g. testa et alii, frattura ed integrità strutturale, 44 (2018) 161-172; doi: 10.3221/igf-esis.44.13 163 different classes of metals and alloys under variable geometry and loading conditions [10-15]. very recently, testa et al. [16] extended the original bonora damage model in order to account for the effect of the third invariant of the deviatoric stress tensor on the fracture strain of shear fracture sensitive materials. this new feature is particularly suited to investigate fracture in deformation processes largely dominated by shear such as those occurring in the self-piercing process. in this work, the extended bonora damage model (xbdm) was used to investigate the joinability of materials in the spr process. to this purpose, an extensive numerical investigation was performed analyzing different combinations of material sheets including also materials that are known to show susceptibility to shear controlled fracture. results seem to indicate that the model is capable to predict the occurrence of damage during the process and in particular before the rivet flaring stage. the possibility to predict the poor joinability of materials is also shown. damage modelling he bonora damage model (bdm) is derived according to the thermodynamics framework of continuum damage mechanics (cdm) initially introduced by lemaitre [17]. in this context, from the definition of the potential of dissipation, the evolution law for the damage, which is a state variable, can be derived. under the assumption of isotropic damage, d is a scalar defined as the ratio between the damaged and the nominal net resisting area of the material reference volume element (rve), 0 dad a  (1) d ranges from 0, for the material in the undamaged state, to crd at rupture where the material has zero load carrying capability. testa et al. [16] proposed the following expression for the damage dissipation potential,     1 2 0 0 0 0 1 2 1 1ˆ cr k d d ds sy y f a d s d s dp                                  (2) here, y is the damage associated variable, which represents the strain energy density release rate, derived from the state potential [18], (1 ) 2 r y d e   (3) where, e is the young’s modulus and r is the function that accounts for stress triaxiality effects,     22 1 3 1 2 3 r       (4) where  is the poisson’s ratio and  is the stress triaxiality factor defined as the ratio of the means stress m and equivalent von mises stress  , m    (5) the first term on the right hand side is the original expression of damage dissipation potential proposed by bonora [8]. this accounts mainly for the dissipation associated with damage state ascribable to nucleation and growth of microvoids (nag) and it is led by stress triaxiality. here, p̂ is the “active plastic strain” defined as the equivalent plastic strain that accumulates under tensile state of stress (t≥0), t g. testa et alii, frattura ed integrità strutturale, 44 (2018) 161-172; doi: 10.3221/igf-esis.44.13 164 2ˆ 3 p p eq eqp t d d dt   (6) is the heaviside function that is equal to 1 when the stress triaxiality is positive and 0 otherwise. the unilateral condition for damage states that under compressive state of stress, damage does not accumulate and its effects are temporarily restored ( 0 & 0d d  ). the second term on the right hand side of eqn. (2) accounts for dissipation associated with void sheeting under shear dominated stress state. here,  is the parameters, bounded between 0 and 1, that accounts for the for the influence of the third invariant of the deviatoric stress tensor j3 on material ductility, which is defined as a function of the lode parameter l as, 21 l   (7) where 3 3 27 2 j l    (8) the damage evolution law is obtained from the generalized normality rule     1/ 11 ˆ 1 ˆ 1ln kcrd cr ff th d df p d d d r d d d p y p                               (9) where  is the plastic multiplier equal to the equivalent plastic strain rate scaled by damage effect,  1p d    (10) for constant  and t (>0) deformation process, the damage rate equation can be integrated to obtain the following expression for damage evolution, 1 1ln 1 1 ln k th cr f th f p d d r p                                   (11) here, , dcr, th, f, f, , k are the material damage parameters: th is the plastic strain threshold under uniaxial state of stress at which damage process is initiated, f is the failure strain under constant stress triaxiality equal to 1/3,  is the damage exponent that defines the shape of damage evolution law for nag,  and k are the damage exponents for shear controlled damage contribution, and f is the critical strain for pure shear. these parameters can be determined performing selected experimental tests. in particular, th and f can be determined by fitting on the stress triaxiality vs failure strain plot of fracture data obtained with round notched bar in tension for which w=0, using the expression for the failure locus 1 rf f th th p           (12) similarly, f and k can be determined on the same plot fitting fracture data in the negative stress triaxiality regime with the following expression of the fracture locus, g. testa et alii, frattura ed integrità strutturale, 44 (2018) 161-172; doi: 10.3221/igf-esis.44.13 165 f f k p    (13) other damage parameters, which define the shape of the evolution of different damage contribution with plastic strain, can be determined performing measurement of loss of stiffness as discussed in [19]. in a first approximation, =0.3 is a suitable value for several classes of materials. more difficult is the determination of . barsoum and faleskog [8] found that at low levels of stress triaxiality, failure seems to be governed by a simple criterion based on a critical measure of plastic shear deformation. therefore, following the occam’s razor principle, =0 is assumed. figure 3: h4 c-skr rivet type. d=5.0 mm, h=5.45 mm, b=7.67 mm. figure 4: self-piercing riveting configuration for fem analysis. case upper sheet lower sheet 1 steel (dp600) al2024 2 steel (dp600) ofhc cu 3 al2024 al2024  ofhc cu steel (dp600) table 1: summary of investigated spr configurations. self-piercing riveting simulation geometry he self-piercing riveting process was simulated with fem using xbdm model. all finite element simulations have been performed with msc marc v2017.1. in this fem code, the bdm is ready available, however the xbdm was implemented using user subroutines. here, a self-pierce h4 c-skr rivet was selected to simulate joining of t g. testa et alii, frattura ed integrità strutturale, 44 (2018) 161-172; doi: 10.3221/igf-esis.44.13 166 different combinations of hard to soft metal sheets. the reference self-piercing riveting configuration is shown in fig. 4. here, the holder and the punch are simulated as rigid bodies while deformable-deformable contact is considered between the rivet, the upper, and the lower metal sheets. since the problem is axisymmetric, all simulations have been performed using 2d four node axisymmetric elements. this element type has four gauss points, bilinear shape functions and it is particularly suited for large strain and contact problems. analyses have been carried out using large displacement, finite strain and lagrangian updating. since elements in the metal sheets undergo large plastic deformation, automatic remeshing was used to avoid severe element distortion and analysis interruption due to the impossibility to reach convergence. remeshing was performed using advanced front quadrilateral prescribing the average (0.04 mm) and minimum element size (0.01 mm) for the new created elements. in order to investigate the modelling capabilities to predict different material joinability, the combinations of materials given in tab. 1, have been investigated. the upper and lower sheet thicknesses are 27 mm and 15 mm, respectively. these are unchanged during the analyses. figure 5: true stress-strain curves for materials used in the simulation. materials materials considered in this study are dp600, al 2024-t351 and ofhc 99.98% pure copper. the dp600 is a dual phase steel consisting of a ferrite matrix containing a hard second phase, usually islands of martensite, widely used in the automotive industry for different parts and safety cage components (b-pillar, floor panel tunnel, engine cradle, front subframe package tray, shotgun, seat). compared with high strength low alloy steels (hsla), dp steel exhibits higher initial work hardening rate, higher ultimate tensile strength, and higher ultimate stress over yield stress ratio than a similar yield strength hsla. al 2024-t351, usually provided as plate or sheet, is ideal for everyday applications where a high strength to weight ratio is necessary. the material offers a fair level of workability as well as high level of corrosion resistance. this alloy is used in a variety of applications such as fuselage structurals, wing tension members, shear webs and ribs, and structural areas where stiffness, fatigue performance, and good strength are required. this material has been widely characterized. it susceptibility to shear controlled fracture was investigated in [20] while testa et al. [16] identified the xbdm model parameters. ofhc 99.8% cu has been characterized extensively for application in the dynamic deformation range. [21-27]. bonora et al. [28] determined the bdm model parameters for ofhc cu in the fully annealed state. this material was selected because fracture process is controlled by nag and does not show shear sensitivity. flow curves for these material at room temperature and low strain rate (10-3/s) is given in fig. 5. dp600 damage parameters identification damage parameters for al 2024 and ofhc were identified elsewhere. for dp600, the experimental data given in [29] where used for the identification of damage parameters. authors performed tensile tests on several specimen geometries to obtain different combinations of stress triaxiality and lode parameter. among all available experimental data, those relative to geometries for which w=0, i.e. axisymmetric round notched bar (rnb), have been selected to determine the damage parameters for dt. damage parameters for d, would requires experimental data in the regime for t<0. unfortunately, no such data where available. therefore, k could not be fitted and was assumed equal to 0.1 which sounds g. testa et alii, frattura ed integrità strutturale, 44 (2018) 161-172; doi: 10.3221/igf-esis.44.13 167 reasonable for the few data reported in the near zero stress triaxiality range. the choice of this value was verified simulating with fem some of the flat notched samples tested by basaran and weichert [29] that in fig. 6 showed a failure strain in the intermediate stress triaxiality range. figure 6: comparison of predicted failure locus for shear and nag dominated regimes and experimental data for dp600. in fig. 6 the comparison of predicted failure locus for shear and stress triaxiality controlled stress states with available experimental data is plotted. here, the red line is the failure locus given by eqn. (12) where there is no contribution of the third invariant of deviatoric stress (w=0) while the blue line is the failure locus predicted for shear controlled fracture (=1) without the contribution of damage due to stress triaxiality under the assumption of plane stress condition (3=0). light symbols are relative to specimen geometries in which both t and  contribute. in fig. 6 the traced failure loci have to be interpreted as follow. for the stress triaxiality range where only a solution is drawn, this represents the locus where fracture strain is expected to occur. in the range of stress triaxiality where the two solutions superimpose, fracture strain will be determined by the concurrent action of stress triaxiality and lode parameter. therefore, the expected fracture strain in this range is much lower than the values retuned by the two limit solutions. in tab. 2, the summary of damage parameters for dp600 is given. damage parameters th 0.098 f 3.11 dcr 0.1  0.3  0.0 f 0.105  0.10 table 2: summary of damage model parameters for dp600. g. testa et alii, frattura ed integrità strutturale, 44 (2018) 161-172; doi: 10.3221/igf-esis.44.13 168 results and discussion n fig. 7 the calculated global response in terms of applied punch force vs vertical displacement for different combination of materials sheets in the joint is given. figure 7: comparison of punch force vs displacement curves for different combinations of materials. these results are in a general good agreement with the response measured in experiments. for instance, for the dp600ofhc combination, all the essential phases of the process can be recognized: 1) clamping, 2) piercing, 3) rivet flaring and 4) compression. when less joinable materials are used, some of the phases no longer occur. for instance, for al2024al2420 configuration, the shear sensitivity of the material causes the aluminum sheet to fracture when in contact with the rivet. in this case full penetration occurs without rivet flaring. on the opposite side, if the material in contact with the rivet is ductile but with lower strength, piercing occurs during clamping and the compression phase starts well before the rivet has begun to flare. in fig. 8 the comparison of the calculated damage contour map for the different material combination for a punch vertical displacement of 1.25 mm is shown. here, it can be noted that for shear sensitive materials (al-al), damage controlled by lode parameter accumulates almost immediately resulting in the piercing at the contact without appreciable deformation of the metal sheets. opposite situation is predicted for the ofhc-dp600 configuration. here the ductility of the upper sheet combined with that of dp steel, result in much larger deformation in the die with a limited indentation of the rivet. this indentation is larger for the dp600-al configuration. in fact, the limited deformability of the al restraints that of the upper steel plate promoting the rivet penetration at this stage. increasing the punch displacement (=2.26 mm), the rivet is predicted to penetrate without any relevant deformation in the al-al configuration, while in the dp600-ofhc the lower sheet has touched the die and the complete penetration of the upper sheet has not occurred yet fig. 9. it is interesting to note the difference in the deformed shape of the upper sheet material that flow into the rivet for the ofhc-dp600 and dp600-ofch. in the latter case, shear bands (damage contours) initiated from the rivet edge and developing along the upper metal sheet are clearly visible while in ofhcdp600 configuration, damage is much more localized along the contact surface between the copper and the rivet. interestingly, in the case of dp600-al, damage start to accumulate on the back surface of the al sheet. this damage state is mainly controlled by stress triaxiality and it is due to the plastic strain accumulation due to the local bending. increasing further the punch displacement, fig. 10 and fig. 11, fracture is predicted to occur in al-al on both metal sheets with almost no deformation of the rivet. similar fracture is predicted to occur for the dp600-al configuration. the main difference is that in the al-al damage is driven by shear in the dp600-al manly by nag. complete clutching is predicted to occur for the dp600-ofhc, although extensive damage bands along the ligament of the lower metal sheet is predicted to develop. i g. testa et alii, frattura ed integrità strutturale, 44 (2018) 161-172; doi: 10.3221/igf-esis.44.13 169 ofhc-dp600 al-al dp600-ofhc dp600-al figure 8: comparison of deformed state for different material combinations at the end of the clamping stage, punch displacement: 1.25 mm. ofhc-dp600 al-al dp600-ofhc dp600-al figure 9: comparison of deformed state for different material combinations during the piercing stage, punch displacement: 2.26 mm. g. testa et alii, frattura ed integrità strutturale, 44 (2018) 161-172; doi: 10.3221/igf-esis.44.13 170 ofhc-dp600 al-al dp600-ofhc dp600-al figure 10: comparison of deformed state for different material combinations at the end of the piercing stage, punch displacement: 3.00 mm. ofhc-dp600 =3.85 mm al-al =3.45 mm dp600-ofhc =5.67 mm dp600-al =2.38 mm figure 11: comparison of deformed state at final stage (different punch displacement in each case). g. testa et alii, frattura ed integrità strutturale, 44 (2018) 161-172; doi: 10.3221/igf-esis.44.13 171 video1: steel-al video 2: steel-cu video 3: al-al video 4: cu-steel conclusions n this work, the possibility to predict the joinability of different materials for self-piercing riveting process by means of damage mechanics has been investigated. to this purpose, the extended version of the bonora damage model was used. this model formulation allows accounting also for shear-controlled fracture in materials that suffer shear fracture sensitivity. srp process, with several combinations of materials, has been investigated to demonstrate that the model is capable to predict different piercing characteristics that could not be predicted with simple separation criteria. numerical simulation results show that it is possible to anticipate the behavior of the material during the joining process allowing to tune process parameters and to screen materials in a virtual environment. of particular interest is the case of al2024-t351. this material showed to result in uncomplete joint when coupled with another al or dp steel sheet but for completely different mechanisms. further experimental investigation may provide indications to support model validation. references [1] mori, k., kato, t., abe, y. and ravshanbek, y. (2006). plastic joining of ultra high strength steel and aluminium alloy sheets by self piercing rivet. cirp annals-manufacturing technology, 55, pp. 283-286. [2] atzeni, e., ippolito, r. and settineri, l. (2007). fem modeling of self-piercing riveted joint. key engineering materials, trans tech publ, 655-662. [3] he, x., xing, b., zeng, k., gu, f. and ball, a. (2013). numerical and experimental investigations of self-piercing riveting. the international journal of advanced manufacturing technology, 69, pp. 715-721. [4] su, z.-m., lin, p.-c., lai, w.-j. and pan, j. fatigue analyses of self-piercing rivets and clinch joints in lap-shear specimens of aluminum sheets. international journal of fatigue, (2015) 72, pp. 53-65. [5] abe, y., kato, t. and mori, k. (2006). joinability of aluminium alloy and mild steel sheets by self piercing rivet. journal of materials processing technology, 177, pp. 417-421. [6] kato, t., abe, y. and mori, k. (2007). finite element simulation of self-piercing riveting of three aluminium alloy sheets. key engineering materials, trans tech publ, 1461-1466. [7] cacko, r. (2008). review of different material separation criteria in numerical modeling of the self-piercing riveting process–spr. archives of civil and mechanical engineering, 8, pp. 21-30. [8] bonora, n. (1997). a nonlinear cdm model for ductile failure. engineering fracture mechanics, 58, pp. 11-28. [9] lemaitre, j. (1985). a continuous damage mechanics model for ductile fracture. journal of engineering material and technology, 107, pp. 83-89. [10] iannitti, g., bonora, n., ruggiero, a. and testa, g. (2014). ductile damage in taylor-anvil and rod-on-rod impact experiment. journal of physics: conference series, 500. [11] iannitti, g., bonora, n., bourne, n., ruggiero, a. and testa, g. (2017). damage development in rod-on-rod impact test on 1100 pure aluminum. aip conference proceedings. [12] carlucci, a., bonora, n., ruggiero, a., iannitti, g. and testa, g. (2014). crack initiation and propagation of clad pipe girth weld flaws. american society of mechanical engineers, pressure vessels and piping division (publication) pvp. [13] testa, g., bonora, n., gentile, d., ruggiero, a., iannitti, g., carlucci, a. and madi, y. (2017). strain capacity assessment of api x65 steel using damage mechanics. frattura ed integrita strutturale, 11, pp. 315-327. [14] bonora, n., gentile, d., ruggiero, a., testa, g., folgarait, p. and calatroni, a. (2013). failure assessment of pipe tee element using continuum damage mechanics. american society of mechanical engineers, pressure vessels and piping division (publication) pvp. [15] ruggiero, a., iannitti, g., testa, g., limido, j., lacome, j. l., olovsson, l., ferraro, m. and bonora, n. (2014). high strain rate fracture behaviour of fused silica. journal of physics: conference series, 500. i http://www.gruppofrattura.it/pdf/rivista/numero44/video/steelal/steelal.html http://www.gruppofrattura.it/pdf/rivista/numero44/video/steelcu/steelcu.html http://www.gruppofrattura.it/pdf/rivista/numero44/video/alal/alal.html http://www.gruppofrattura.it/pdf/rivista/numero44/video/custeel/custeel.html g. testa et alii, frattura ed integrità strutturale, 44 (2018) 161-172; doi: 10.3221/igf-esis.44.13 172 [16] testa, g., ruggiero, a., iannitti, g., bonora, n. and gentile, d. (2018). modification of the bonora damage model for shear failure. frattura ed integrità strutturale, 44, pp. 140-150. [17] lemaitre, j. (1990). micro-mechanics of crack initiation. international journal of fracture, 42, pp. 87-99. [18] lemaitre, j. (2012). a course on damage mechanics, springer science & business media. [19] bonora, n., ruggiero, a., de meo, s., gentile, d. and esposito, l. (2008). a revised approach to damage measurement based on stiffness loss technique. asme 2008 pressure vessels and piping conference, pp. 195-199. [20] bao, y. and wierzbicki, t. (2004). on fracture locus in the equivalent strain and stress triaxiality space. international journal of mechanical sciences, 46, pp. 81-98. [21] hörnqvist, m., mortazavi, n., halvarsson, m., ruggiero, a., iannitti, g. and bonora, n. (2015). deformation and texture evolution of ofhc copper during dynamic tensile extrusion. acta materialia, 89, pp. 163-180. [22] bonora, n., testa, g., ruggiero, a., iannitti, g., mortazavi, n. and hörnqvist, m. (2015). numerical simulation of dynamic tensile extrusion test of ofhc copper. journal of dynamic behavior of materials, 1, pp. 136-152. [23] bonora, n., ruggiero, a., esposito, l. and iannitti, g. (2009). damage development in high purity copper under varying dynamic conditions and microstructural states using continuum damage mechanics, pp. 107-110. [24] bonora, n., ruggiero, a., iannitti, g. and testa, g. (2012). ductile damage evolution in high purity copper taylor impact test. aip conference proceedings, pp. 1053-1056. [25] chiantoni, g., bonora, n. and ruggiero, a. (2010). experimental study of the effect of triaxiality ratio on the formability limit diagram and ductile damage evolution in steel and high purity copper. international journal of material forming, 3, pp. 171-174. [26] danian, c., chunlei, f., shugang, x., jinwei, h., shanxing, w., huanran, w., hua, t. and yuying, y. (2007). study on constitutive relations and spall models for oxygen-free high-conductivity copper under planar shock tests. journal of applied physics, 101, pp. 063532-9. [27] ruggiero, a., bonora, n., esposito, l. and gray iii, g. t. (2009). ductile damage evolution assessment in high purity copper and stainless steel subjected to different shock-loading profiles using cohesive modeling, pp. 1073-1076. [28] bonora, n., ruggiero, a., esposito, l. and iannitti, g. (2009). damage development in high purity copper under varying dynamic conditions and microstructural states using continuum damage mechanics. aip conference proceedings, pp. 107-110. [29] basaran, m. and weichert, d. (2011). stress state dependent damage modeling with a focus on the lode angle influence, lehrstuhl und institut für allgemeine mechanik. << /ascii85encodepages false /allowtransparency false /autopositionepsfiles true /autorotatepages /none /binding /left /calgrayprofile (dot gain 20%) /calrgbprofile (srgb iec61966-2.1) /calcmykprofile (u.s. web coated \050swop\051 v2) /srgbprofile (srgb iec61966-2.1) /cannotembedfontpolicy /error /compatibilitylevel 1.4 /compressobjects /tags /compresspages true /convertimagestoindexed true /passthroughjpegimages true /createjobticket false /defaultrenderingintent /default /detectblends true /detectcurves 0.0000 /colorconversionstrategy /cmyk /dothumbnails false /embedallfonts true /embedopentype false /parseiccprofilesincomments true /embedjoboptions true /dscreportinglevel 0 /emitdscwarnings false /endpage -1 /imagememory 1048576 /lockdistillerparams false /maxsubsetpct 100 /optimize true /opm 1 /parsedsccomments true /parsedsccommentsfordocinfo 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/hrv (za stvaranje adobe pdf dokumenata najpogodnijih za visokokvalitetni ispis prije tiskanja koristite ove postavke. stvoreni pdf dokumenti mogu se otvoriti acrobat i adobe reader 5.0 i kasnijim verzijama.) /hun 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/pdfxoutputintentprofileselector /documentcmyk /preserveediting true /untaggedcmykhandling /leaveuntagged /untaggedrgbhandling /usedocumentprofile /usedocumentbleed false >> ] >> setdistillerparams << /hwresolution [2400 2400] /pagesize [612.000 792.000] >> setpagedevice microsoft word numero_52_art_15_2711 a. drai et alii, frattura ed integrità strutturale, 52 (2020) 181-196; doi: 10.3221/igf-esis.52.15 181 finite element modeling of the behavior of polymethyl-methacrylate (pmma) during high pressure torsion process ahmed drai mechanical engineering department, university of mascara, 29000, labab laboratory of enpo, algeria. draiahmed14@yahoo.fr, http://orcid.org/ 0000-0001-6091-9519 benaoumeur aour laboratory of applied biomechanics and biomaterials (labab), enp oran, bp1523 el mnaour, oran, 31000, algeria. benaoumeur.aour@enp-oran.dz, http://orcid.org/0000-0002-2345-6790 naima belayachi université d’orléans, laboratoire de mécanique gabriel lamé polytech orléans, 45072 orléans, france. naima.belayachi@univ-orleans.fr, http://orcid.org/0000-0002-2345-6791 abderrahim talha ecole des hautes etudes d’ingénieur (hei), 13 rue de toul, 59046 lille, lille mechanics unit, university of lille, france abderrahim.talha@hei.fr, http://orcid.org/0000-0003-2345-6792 noureddine benseddiq lille mechanics unit, university of lille, france noureddine.benseddiq@univ-lille1.fr, http://orcid.org/0000-0003-2345-6793 abstract. high pressure torsion (hpt) is a highly effective super-plastic deformation process for obtaining nano-materials with high performance mechanical properties. in view of its optimization, it is of paramount importance to evaluate the relations between the behavior of the material under the effects of different processing parameters. in this context, this work aims to highlight the plastic strain distribution in the deformed material as a function of the hydrostatic pressure, the torsion angle and the temperature of the material applied during the process. a typical amorphous polymer (polymethyl-methacrylate: pmma) has been tested. firstly, in order to identify the material parameters of a phenomenological elasto-viscoplastic model compression tests at different temperatures and strain rates have been carried out. then, the distributions of the effective plastic strain, the equivalent plastic strain rate and the hydrostatic stress were analyzed using finite elements method. recommendations on process conditions were citation: drai, a., aour, b., belayachi, n., talha, a., benseddiq, n., numerical modeling of polymethyl-methacrylate (pmma)behavior during high pressure torsion process, frattura ed integrità strutturale, 52 (2020) 181-196. received: 20.12.2019 accepted: 10.02.2020 published: 01.04.2020 copyright: © 2020 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. https://youtu.be/30ua-qbjqwy a. drai et alii, frattura ed integrità strutturale, 52 (2020) 181-196; doi: 10.3221/igf-esis.52.15 182 proclaimed at the end of this work according to the obtained numerical results. keywords. hpt; finite elements; pmma; behavior; plastic strain. introduction here have been extensive investigations over the last two decades into the production of bulk ultrafine-grained (ufg) materials through the application of severe plastic deformation (spd) [1, 2]. recently, spd techniques have been used in the modification of microstructure. they made possible to produce nano-crystalline (nc) microstructures out of metallic materials [3, 4]. such spd methods include high pressure torsion (hpt), equal channel angular pressing (ecap), accumulative roll bonding (arb), multiple forging, twist extrusion (te) and some others. among the various spd techniques, equal-channel angular pressing (ecap) and high pressure torsion (hpt) are the most common [5]. to date, processing by hpt has proven to be the most effective of all the spd methods in producing bulk nanostructured materials [6]. its principle consists in putting a disk between two massive anvils under a simultaneously or successively action of high compression and torsion as shown in fig. 1. the occurrence of superplasticity was reported not only after hpt processing of thin disc specimens [7,8], but also using the ring samples [9,10], bulk samples [11, 12] as well as after continuous high-pressure torsion extrusion [13]. different materials have been tested experimentally [14] and theoretically [15] through the application of hpt process such as aluminum alloys [8, 16], nickel [17], copper [15], titanium alloys [3, 18], polymers [19], zirconium [20, 21], magnesium alloys [22], aluminum-zinc alloys [23], intermetallics [24, 25] and others (see [26, 27]). figure 1: schematic illustration of hpt process. in the past, fem simulations of the spd processes were performed with the purpose of analysis and optimization of the spd processing variables and prediction of the mechanical and microstructural characteristics of the spd processed samples [15]. for example, for hpt, the effects of processing parameters, such as geometries of the disc [28], applied pressure [29], temperature distribution [30, 31], rotation rate [31], friction conditions [32], material porosity and properties [32, 33] and slope of the inclined anvil's surface [34] on the plastic strain behavior were reported in the literature extensively. this work is devoted to study the behavior of polymethyl-methacrylate (pmma) during hpt process. it is important to note that the behavior of this amorphos polymer is sensitive to the strain rate, temperature, hydrostatic pressure and torsion angle [35]. a three-dimensional finite element analysis has been conducted using hexahedral element with 8-nodes. our particular attention has been focused on the distribution of the plastic strain in the deformed material as a function of the different parameters of the process, namely, the sequence of the different phases, the hydrostatic pressure, the torsion angle and the temperature of the material during the process. t a. drai et alii, frattura ed integrità strutturale, 52 (2020) 181-196; doi: 10.3221/igf-esis.52.15 183 constitutive modeling o model the pmma behavior during hpt process, the elasto-viscoplastic model of perzyna has been used [36]. the material parameters of this model have been identified using compressive tests on pmma cylindrical specimens at different temperatures and strain rates. the experimental protocol used for this solicitation mode was also presented in details in the next section. the perzyna model considers the hypo-elastic relation, and the additive decomposition of the tensor of the strain rates to write [36]: . 4σ h : (d d )vp  (1) with h is the hooke tensor (tensor of elasticity) given by: 2 h ( ) 2(1 ) 1 2 ik jl il jk ij kl e                  (2) where e and represent respectively the young's modulus and the poisson's ratio and  is the kronecker symbol. the viscoplastic deformation rate is given by the rule of normality. its direction is normal to the surface flow in the stress space f    , f being the surface flow. by introducing the hypothesis that the function f is independent of the deformations, and supposing the von mises criterion [37], the viscoplastic strain is formulated as follows: d φ( )vp f f     (3) with f    = 1 in the case of a perfectly viscoplastic material. where φ(f) is a function generally chosen as a power function: 1 0 ( ) 1 m f           (4) then, we obtain: 1 0 d 1 m vp          (5) where m and  are respectively the hardening parameter and the viscosity (strain rate sensitivity parameters),  is the flow stress and 0 is the static elastic limit. the perzyna model describes only the sensitivity of the yield stress to the strain rate, then it is necessary to introduce the post yield softening and hardening. the finite element program used allows us to take into account this post-flow behavior. a multilinear isotropic hardening combined with the von mises criterion has been adopted. it should be noted that in this study, we assume that the viscoelastic part of the response does not significantly affect the global results and the pre-yield response is assumed to be linear and elastic. the behavior in large deformations of viscoplastic solids is described by the constitutive equations, for which analytical solutions are difficult to obtain, even for simplified problems. this model has attracted a lot of attention in the literature because it was validated experimentally in the work of perzyna [38]. in addition, its simplicity of writing made it easier to t a. drai et alii, frattura ed integrità strutturale, 52 (2020) 181-196; doi: 10.3221/igf-esis.52.15 184 implement in simulation codes. peric et al. [39] have used this model in their numerical studies to adapt to large deformations the behavior of materials depending on time and the history of deformation. the work of van der sluis et al. [40, 41] on polycarbonate loaded with elastomer particles has brought an interesting approach based on the perzyna model and a nonlinear hardening which has shown the efficiency of the use of this models type for polymers. experimental procedure for material parameters identification o identify the parameters of the elasto-viscoplastic constitutive law presented in the previous paragraph, we used compression tests at different strain rates and different temperatures conducted on polymethyl-methacrylate (pmma) samples. noting that compressive loading, unlike traction, provides (or delays as much as possible) the damage mechanisms. material properties the material studied (pmma) was supplied by the goodfellow© company in the form of a cylindrical bar of 8 mm in diameter and 1000 mm in long, with a molar mass of the order of 65 kg.mol-1. the glass transition temperature is about 120°c. the mechanical properties of this material are shown in tab. 1. mechanical properties of pmma density (g cm-3) 1.19 coefficient of friction 0.25 – 0.4 hardness rockwell 92-100 impact resistance izod (j m-1) 16-32 poisson coefficient 0.35 – 0.4 elongation at fracture (%) 2.5-4 traction module (gpa) 2.4-3.3 tensile strength (mpa) 80 table 1: mechanical properties of the studied polymer (pmma). description of the mechanical test in order to determine the three parameters ( 0 , m,  ) of the elasto-viscoplastic model, the pmma sample was tested at strain rates ranging from 10-5 s-1 to 10-2 s-1 at a room temperature (25°c) and high temperatures (40°c, 60°c and 80°c). the uniaxial compression tests are performed on an instron 5867 tensile/compression machine using a 10 kn cell to measure the applied force. the acquisition of experimental data in stresses and strains at each moment during the test was recorded using the bluehill software. the displacement of the upper plate is controlled with a translational speed of the crossbar calculated from the speed of deformation. all samples were compressed up to 40% of deformation using two parallel compression trays. to study the dependence of the polymer behavior at a high temperature, we used a thermal enclosure allowing tests with temperatures up to 250°c. to ensure the homogeneity of the temperature in the specimen, it was maintained for about 15 minutes at the desired temperature before starting the test. the upper end of the sample is left free during the heating phase to allow thermal expansion to take place freely. to investigate the influence of the temperature increase on the stress-strain curve, the pmma sample was tested at temperatures ranging from 25°c to 100°c at a constant strain rate. from the registration of the cross-bar displacement and the measurement of the force f during the test, the nominal strainstress curves are deduced using the bluehill software integrated in the electromechanical testing machine. to make the necessary transformations in true quantities (true stress, true strain), it is assumed that the material is incompressible and isotropic, and the deformation is supposed to be homogeneous. the extensometer allows to measure the displacement δl and by knowing the initial height of the sample l0, the true axial strain is obtained from the following expression: 0 1zz l ln l         (6) the true stress becomes: t a. drai et alii, frattura ed integrità strutturale, 52 (2020) 181-196; doi: 10.3221/igf-esis.52.15 185 0 . 1zz n l l          (7) where 0n f s  , is the nominal stress and s0 is the initial section. fig. 2 shows the axial stress-strain curves resulting from the tests at different temperatures and a speed of 10-3 s-1. from this graph, we can notice that the stress level decreases when the temperature increases. in addition, the curves confirm the very marked nonlinearity of the pmma behavior, and a weak softening followed by a noticeably observed hardening. figure 2: true axial stress-strain curves at different temperatures and a strain rate of 10-3 s-1 on a pmma samples. by plotting on a graph the evolution of the stress as a function of the deformation (fig. 3), for different strain rates, and for the same temperature, we have been able to highlight the dependence of pmma behavior on strain rate. these curves show that the elastic limit, the young's modulus, and the hardening decreases with the decrease of the strain rate. the curves show a peak which is slightly pronounced at room temperature and becomes more significant with the increase of the temperature. parameters identification and validation of the model he identification of viscoplastic parameters for pmma goes through the classical process using linear least squares regression from pmma strain-strain curves at different strain rates. we draw the following function: 1 d 1 0 mvp ln f                     (8) for the three strain rate values 10-4, 10-3, and 10-2 s-1, this evolution is a linear function y=a.x+b which allows us to determine the coefficients a and b. finally the parameters are deduced as follows: γ = exp(b) , m = 1/a (9) the values of the parameters obtained for each temperature are given in tab. 2. t a. drai et alii, frattura ed integrità strutturale, 52 (2020) 181-196; doi: 10.3221/igf-esis.52.15 186 parameter t=25°c t=60°c t=80°c e (mpa) 2565 1084 833  0.32 0.33 0.33 m 0.346 0.294 0.295  0.027 0.0137 0.0298 0 (mpa) 89 40 29 table 2: material parameters of elastic-viscoplastic model for pmma at different temperatures. to validate the viscoplastic model, we simulated compression tests performed on pmma sample at different strain rates and at study temperatures {t = 25, 60 and 80°c}. we have examined the macroscopic behavior of pmma with the set of parameters reported in tab. 2. as can be seen in fig. 3, there is an acceptable agreement between experimental data and simulation results. for high strain rates and at 25°c and 80°c, the predicted flow yield is near to the experimental measurements, but the hardening deviates from it. this difference can be explained by the experimental calculation of the stresses from a rectangular surface, whereas the sample has a barrel shape with a section which changes and becomes more important in the middle. (a) t=25°c (b) t=60°c (c) 80°c figure 3: stress-strain curves of the pmma for different strain rates and at temperatures of: (a) 25°c, (b) 60°c and (c) 80°c. a. drai et alii, frattura ed integrità strutturale, 52 (2020) 181-196; doi: 10.3221/igf-esis.52.15 187 simulation of the hpt process he simulations were performed by the finite element code msc.marc using eight (8) nodes hexahedral elements. the initial dimensions of the pmma samples used are 20 mm in diameter and 10 mm in thickness. it should be noted that the mesh size selected is largely sufficient to show accurately the distribution of localized plastic strain within the samples. the upper and lower anvils were considered as rigid bodies in the finite element simulations. the upper anvil is subjected to an imposed displacement of compression, while the lower anvil is subjected to rotation. the effects of the hydrostatic pressure applied and the torsion angle on the evolution of the equivalent plastic strain were highlighted in this numerical investigation of pmma behavior during hpt process. effect of the hydrostatic pressure to highlight the effect of hydrostatic compression, four different vertical displacements were imposed by the upper anvil. a constant rotation speed of 0.2618 rad/sec was applied during the torsion. the results obtained for the evolution of the equivalent plastic strain along the radial distance from the center for various imposed compression displacements combined with a 30° of torsion angle are illustrated in fig. 4. it may be noted that the equivalent plastic strain increases with the increase of the imposed compressive displacement. in addition, it can be seen that the influence of this parameter becomes significant by moving away from the center of the specimen and likewise for the heterogeneity of the plastic strain distribution. indeed, for an imposed displacement of 1 mm, an equivalent plastic strain (εp) of 1.49 was obtained, whereas, for the one of 2.5 mm, εp=1.91. figure 4: distribution of the equivalent plastic strain along the radial distance of the disk for different imposed vertical displacements. the distributions of the equivalent plastic strain in the deformed geometries of the sample at the end of the process for imposed displacements of 1mm, 1.5mm, 2mm and 2.5mm are illustrated in fig. 5. it can be noted that the highest deformation values are located in the lower and upper regions of the sample. therefore, in order to improve the level of the plastic strain distribution, it is necessary to increase the torsion angle. furthermore, it should be interesting to remember that the decrease of the sample thickness contributes also to the increase of the plastic strain as it has been highlighted by drai and aour [42]. effect of torsion angle in order to illustrate the effect of torsion angle on the evolution of equivalent plastic strain a vertical displacement of 1 mm was imposed by the upper anvil on the sample and was maintained during the torsion with different angles of the lower anvil (15°, 30°, 45° and 60°). the simulations were performed with low angular velocity of 0.26 rad/sec in order to conduct the process in isothermal conditions. t a. drai et alii, frattura ed integrità strutturale, 52 (2020) 181-196; doi: 10.3221/igf-esis.52.15 188 (a) (b) (c) (d) figure 5: distribution of the equivalent plastic strain as a function of the imposed displacements on the deformed pmma sample at the end of hpt process in the case of: (a) 1 mm, (b) 1.5 mm, (c) 2 mm and (d) 2.5 mm. evolution of equivalent plastic strain fig. 6 shows the distribution of the equivalent plastic strain along the sample radius for an imposed displacement of 1 mm and different torsion angles. it can be observed that the accumulated plastic deformation increases with the increase of the torsion angle and becomes very important at the edge of the sample. fig. 7 illustrates the isovalue contours of the equivalent plastic strain distribution in the pmma samples deformed during the hpt process, in the case of 1mm imposed displacement and a torsion angle of: (a) 15°, (b) 30°, (c) 45° and (d) 60°. from fig. 8, it can be observed that after the vertical compressive displacement of 1 mm the plastic strain is very low and its maximum value does not exceed 0.3. in addition, at this stage, the plastic strain induced by a simple compression remains very low especially in the middle of the sample. however, after the application of torsion under high pressure, the plastic strain increases with the increase of the torsion angle  and becomes very high in the upper and lower areas, where it reaches a maximum value of 4.72 when  = 60°. on the other hand, in the center it is always weak. therefore, it is advised to use small a. drai et alii, frattura ed integrità strutturale, 52 (2020) 181-196; doi: 10.3221/igf-esis.52.15 189 thicknesses in the case of pmma samples, to obtain a good homogeneity and a large plastic strain in the sample processed by hpt. figure 6: evolution of the equivalent plastic strain as a function of the radial distance for different torsion angles at the end of hpt process. evolution of the mean normal stress in order to study the state of the stresses in the pmma sample, the distributions of mean normal stresses along the diameter of the upper face at the end of hpt process using an imposed compressive displacement of 1mm of compression with different torsion angles are presented in fig. 9. it can be seen that as the torsion angle increases, the compression stress increases at the central portion of the upper surface of the sample. (a) (b) a. drai et alii, frattura ed integrità strutturale, 52 (2020) 181-196; doi: 10.3221/igf-esis.52.15 190 (c) (d) figure 7: distribution of the equivalent plastic strain in the deformed sample during hpt process in the case of an imposed compressive displacement of 1mm with a torsion angle of: (a) 15°, (b) 30°, (c) 45° and (d) 60°. figure 8: evolution of the equivalent plastic strain at the beginning and the end of torsion during hpt process at the upper area of the sample. figure 9: evolution of the average normal stress along the diameter of the upper face at the end of hpt process using a compressive displacement of 1mm with different torsion angles. fig. 10 illustrates the contours plots of the mean normal stress distribution in the pmma sample deformed during hpt process. it can be observed that the central part of the sample is stressed in compression, however the peripheral region (in yellow color) is under tensile stress and this zone increases with the increase of the torsion angle. this explains the heterogeneity of the equivalent plastic strain distribution. in addition, the maximum value is always located in the central part of the sample-anvil interfaces for the four torsion angles. effect of temperature from the macroscopic point of view, the behavior of pmma is highly dependent on temperature. it is the site of behavioural transitions that can be associated with different molecular relaxations. it is the site of behavioral transitions that can be associated with different molecular relaxations, i.e. activation of changes in local conformations, resulting in the most brutal behavior changes in certain temperature ranges. to study the dependence of pmma behavior during hpt process under a. drai et alii, frattura ed integrità strutturale, 52 (2020) 181-196; doi: 10.3221/igf-esis.52.15 191 the effect of temperature, a series of numerical calculations was carried out for three different temperatures t = {25, 60 and 80°c}. noting that the same constitutive law described in the previous paragraph has been identified at different temperatures under isothermal conditions and the material parameters obtained are presented in tab. 2. the same operating conditions previously used (compression of 1 mm with a torsion angle of 15°) were applied for the simulation of the hpt process under different temperatures. (a) (b) (c) (d) figure 10: distribution of the average normal stress in the deformed sample during hpt process in the case of a 1mm of compression with a torsion angle of: (a) 15°, (b) 30°, (c) 45° and (d) 60°. distribution of the equivalent plastic strain in order to highlight the distribution of the plastic deformation in the pmma sample, the iso-value contours of this latter at the end of the process for three different temperatures are presented in fig. 11. it can be noted that the temperature has a slight influence on the magnitude of the plastic deformation during hpt process. a. drai et alii, frattura ed integrità strutturale, 52 (2020) 181-196; doi: 10.3221/igf-esis.52.15 192 (a) (b) (c) figure 11: distribution of the equivalent plastic strain in the deformed sample with a compression of 1mm and a torsion angle of 15 ° for different temperatures: (a) 25°c, (b) 60°c and (c) 80°c. this slight influence of temperature can be confirmed by plotting the distribution of the equivalent plastic strain along the radial distance from the upper surface of the sample as shown in fig. 12. a slight difference was found. in addition, the maximum value of equivalent plastic strain is approximately 2.36. figure 12: distribution of the equivalent plastic strain as a function of the radial distance in the upper surface of the sample during the hpt process for different temperatures: 25°c, 60°c and 80°c. evolution of applied load and torque fig. 13 shows the simulation results for the evolution of the compression load applied by the upper anvil as a function of the time during hpt process at various temperatures. the load required for each temperature in the ascending order (25°c, 60°c and 80°c) is respectively 11800, 16200 and 36000 n. we can see that when the temperature increases, the load required for hpt process decreases. for example, for a temperature of 25°c, the required load is more than three times of that required at room temperature. moreover, the load versus time evolution during the hpt process can be subdivided into four main stages. the first stage starts from the origin up to the end of compression phase. this stage corresponds to the elastic deformation of compression. the second stage corresponds to the increase of the load from the elastic limit of a. drai et alii, frattura ed integrità strutturale, 52 (2020) 181-196; doi: 10.3221/igf-esis.52.15 193 compression to the maximum value of the load. this stage corresponds to initiation and propagation of the plastic zone between the two upper and lower surfaces of the sample. the maximum force corresponds to the formation of the shear band along the cross-section of the sample, which precedes softening. the third stage corresponds to the decrease of the load from the peak to a minimum and is characterized by the initiation of the plastic flow. beyond (stage 4), the load remains almost constant. this stage corresponds to the steady-state of the plastic flow when the plastic strain reaches its saturation value. figure 13: evolution of the compression load applied by the upper anvil as a function of the time of hpt process for different temperatures. fig. 14 shows the actual values obtained by numerical simulation of the torque required for torsion phase of hpt process when it carried out at different temperatures (25°c, 60°c and 80°c). it can be noticed that there is an abrupt increase from the torsion phase followed by a plateau (a horizontal line) after about 1.8 sec. this aspect can be attributed to the plastic flow in the direction of rotation (when the elastic limit due to the torsion is exceeded). it should be noted that the conduct of the process with a temperature higher than room temperature and lower than the glass transition temperature of the pmma allows to reduce the pressure and the torque required for the deformation of the sample during hpt process. figure 14: evolution of the torque as a function of time process for different temperatures. a. drai et alii, frattura ed integrità strutturale, 52 (2020) 181-196; doi: 10.3221/igf-esis.52.15 194 three particular properties can be highlighted when the sample is deformed at high temperatures: (a) reduced plastic strain distribution in the sample, (b) decrease of the required load and (c) decrease of the required torque. furthermore, strain recovery during the cooling stage may affect the process. this point will be the subject of further mechanical and microstructural investigations. conclusion he aim of this work is devoted to study the applicability of hpt process for a typical amorphous polymer which is polymethyl-methacrylate (pmma). for this purpose, an identification of the parameters of a perzyna elastoviscoplastic phenomenological model was performed using compression tests at different temperatures and strain rates. after the identification of the parameters, a numerical investigation was carried out to highlight the effects of the main processing parameters in the case of an imposed compressive displacement and different torsion angles. from the results obtained, we can draw the following conclusions:  the equivalent plastic strain increases with the increase of the imposed compression displacement.  accumulated plastic deformation increases with the increase of torsion angle and becomes very important at the edge of the sample.  it is advised to use small thicknesses to obtain a good homogeneity of the plastic deformation.  the temperature has a slight effect on the evolution of the plastic deformation. however, it can be used to reduce the force and torque required for hpt process if necessary. acknowledgments his research was supported by the general directorate of scientific research and technological development (dgrsdt : direction générale de la recherche scientifique et du développement technologique) of algeria. the authors gratefully acknowledge the scientific support of the two research teams from the lille mechanics unit (france) and the laboratory of applied biomechanics and biomaterials (labab) of oran (algeria). references [1] alhajeri, s.n., khaled, j., al-fadhalah, a., almazrouee, i. and langdon, t.g. (2016). microstructure and microhardness of an al-6061metal matrix composite processed by high-pressure torsion, mater. charact. , 118, pp. 270–278. doi: 10.1016/j.matchar.2016.06.003. [2] beloshenk, v., vozniak, iu., beygelzimer, y., estrin, y. and kulagin, r. (2019). severe plastic deformation of polymers, mater. trans., 60(7), pp. 1192-1202. doi: 10.2320/matertrans.mf201912 [3] um, h.y., park, b.h., ahn, d.h., abdelaal, m.i., park, j., kim, h.s. (2017). mechanical and biological behavior of ultrafine-grained ti alloy aneurysm clip processed using high-pressure torsion, j. mech. behav. biomed. mater. , 68, pp. 203–209. doi: 10.1016/j.jmbbm.2017.02.002. [4] peitang, w., cheng, l., kiet t., lihong, s., guanyu, d., and wenbin, h. (2017). a study on the texture evolution mechanism of nickel single crystal deformed by high pressure torsion, mater. sci. eng. a, 684, pp. 239–248. doi: 10.1016/j.msea.2016.11.098. [5] yu, i., kulagin, r., fedorov, v., mazilkin, a., scherer, t., baretzky, b. and hahn, h. (2016). high pressure torsion extrusion as a new severe plastic deformation process, mater. sci. eng. a, 664, pp. 247–256. doi: 10.1016/j.msea.2016.04.008. [6] figueiredo, r.b., pereira, p.h.r., aguilar, m.t.p., cetlin, p.r. and langdon, t.g. (2012). using finite element modeling to examine the temperature distribution in quasi-constrained high-pressure torsion, acta mater., 60, pp. 3190–3198. doi: 10.1016/j.actamat.2012.02.027. [7] valiev, r.z., song, c., mcfadden, s.x., mukherjee, a.k. and mishra, r.s. (2001). tem/hrem observations of nanostructured superplastic ni3al, philos. mag. a, 81, pp. 25–36. doi: 10.1007/s10853-014-8204-5. t t a. drai et alii, frattura ed integrità strutturale, 52 (2020) 181-196; doi: 10.3221/igf-esis.52.15 195 [8] xu, c., dobatkin, s.v., horita, z. and langdon, t.g. (2009). superplastic flow in a nanostructured aluminum alloy produced using high-pressure torsion, mater. sci. eng. a, 500, pp. 170–175. doi: 10.1016/j.msea.2008.09.049. [9] harai, y., edalati, k., horita, z., and langdon, t.g. (2009). using ring samples to evaluate the processing characteristics in high-pressure torsion, acta mater., 57, pp. 1147–1153. doi: 10.1016/j.actamat.2008.10.046. [10] edalati, k., horita, z., furuta, t. and kuramoto, s. (2013). dynamic recrystallization and recovery during high-pressure torsion: experimental evidence by torque measurement using ring specimens, mater. sci. eng. a, 559, pp. 506–509. doi: 10.1016/j.msea.2012.08.132. [11] horita, z. and langdon, t.g. (2008). achieving exceptional superplasticity in a bulk aluminum alloy processed by highpressure torsion, scr.mater., 58, pp. 1029–1032. doi: 10.1016/j.scriptamat.2008.01.043. [12] faraji, g., kim, h.s., and kashi, h.t. (2018). severe plastic deformation methods for bulk samples, book chapter: severe plastic deformation, pp. 37-112. doi: 10.1016/b978-0-12-813518-1.00002-3. [13] ivanisenko, y., kulagin, r., fedorov, v., mazilkin, a., scherer, t., baretzky, b. and hahn, h. (2016). high pressure torsion extrusion as a new severe plastic deformation process, mater. sci. eng. a , 664, pp. 247-256. doi: 10.1016/j.msea.2016.04.008. [14] zhilyaev, a.p., and langdon, t.g. (2008). using high-pressure torsion for metal processing: fundamentals and applications, prog. mater. sci., 53, pp. 893–979. doi: 10.1016/j.pmatsci.2008.03.002. [15] lee, d.j., yoon, e.y., ahn, d.h., park, b.h., park, h.w., park, l.j., estrin, y. and kim, h.s. (2014). dislocation density-based finite element analysis of large strain deformation behavior of copper under high-pressure torsion, acta mater., 76, pp. 281-293. doi: 10.1016/j.actamat.2014.05.027. [16] vafai, r., toroghinejad, m.r. and pippan, r. (2012). evaluation of mechanical behavior of nano-grained 2024 al alloy during high pressure torsion (hpt) process at various temperatures, mater. sci. eng. a, 536, pp. 73-81. doi: 10.1016/j.msea.2011.12.064. [17] peitang, w., cheng, l., kiet, t., lihong, s.,guanyu, d. and wenbin, h. (2017). a study on the texture evolution mechanism of nickel single crystal deformed by high pressure torsion, mater. sci. eng. a, 684, pp. 239-248. doi: 10.1016/j.msea.2016.11.098. [18] dimic, i., cvijovic-alagic, i., volker b., hohenwarter, a., pippan, r., veljovic, d., rakin, m. and bugarski, b. (2016). microstructure and metallic ion release of pure titanium and ti–13nb–13zr alloy processed by high pressure torsion, mater design., 91, pp. 340-347. doi: 10.1016/j.matdes.2015.11.088. [19] draï, a. and aour, b. (2013). analysis of plastic deformation behavior of hdpe during high pressure torsion process, eng. struct., 46, pp. 87-93. doi: 10.1016/j.engstruct.2012.06.033. [20] zhao, y. and zhang, j. (2007). enhancement of yield strength in zirconium metal through high-pressure induced structural phase transition, appl. phys. lett., 91, pp. 201907. doi: 10.1063/1.2802726. [21] feng, b., levitas, v.i. and kamrani, m. (2018). coupled strain induced alpha to omega phase transformation and plastic flow flow in zirconium under high pressure torsion in a rotational diamond anvil cell, mater. sci. eng. a, 731, pp. 623633. doi: 10.1016/j.msea.2018.06.061. [22] seenuvasaperumal, p., doi, k., basha, d.a., singh, a., elayaperumal, a. and tsuchiya, k. (2018). wear behavior of hpt processed ufg az31b magnesium alloy, mater lett., 227, pp. 194-198. doi: 10.1016/j.matlet.2018.05.076. [23] alhamidi, a., edalati, k., horita, z., hirosawa, s., matsuda, k. and terada, d. (2014). softening by severe plastic deformation and hardening by annealing of aluminum–zinc alloy: significance of elemental and spinodal decompositions, mater. sci. eng. a, 610, pp. 17-27. doi: 10.1016/j.msea.2014.05.026. [24] edalati, k., matsuo, m., emami, h., itano, s., alhamidi, a., staykov, a., smith, d.j., orimo, s., akiba, e. and horita, z. (2016). impact of severe plastic deformation on microstructure and hydrogen storage of titanium-ironmanganese intermetallics, script.mater., 124, pp. 108-111. doi: 10.1016/j.scriptamat.2016.07.007. [25] nikitina, m.a., r. islamgaliev, k., and sitdikov, v.d. (2016). thermal stability of tial-based intermetallic alloys subjected to high pressure torsion, mater. sci. eng. a, 651, pp. 306-310. doi: 10.1016/j.msea.2015.10.121. [26] matsunoshita, h., edalati, k., furui, m., and horita, z. (2015). ultrafine-grained magnesium-lithium alloy processed by high-pressure torsion: low-temperature superplasticity and potential for hydroforming, mater. sci. eng. a, 640, pp. 443-448. doi: 10.1016/j.msea.2015.05.103. [27] edalati, k. and horita, z. (2016). a review on high-pressure torsion (hpt) from 1935 to 1988, mater. sci. eng. a, 652, pp. 325-352. doi: 10.1016/j.msea.2015.11.074. [28] figueiredo, r.b., aguilar, m.t.p., cetlin, p.r. and langdon, t.g. (2012). analysis of plastic flow during high-pressure torsion, j. mater. sci., 47, pp. 7807–7814. doi: 10.1007/s10853-012-6506-z. a. drai et alii, frattura ed integrità strutturale, 52 (2020) 181-196; doi: 10.3221/igf-esis.52.15 196 [29] wang, w., song, y., gao, d., yoon, e.y., lee, d.j., lee, c. and kim, h.s. (2013). analysis of stress states in compression stage of high pressure torsion using slab analysis method and finite element method, met. mater. int., 19, pp. 1021-1027. doi: 10.1007/s12540-013-5014-2. [30] edalati, k., miresmaeili, r., horita, z., kanayam, h., and pippan, r. (2011). significance of temperature increase in processing by high-pressure torsion, mater. sci. eng. a, 528, pp. 7301–7305. doi: 10.1016/j.msea.2011.06.031. [31] pereira, p.h.r., figueiredo, r.b., huang, y., cetlin, p.r., and langdon, t.g. (2014). modeling the temperature rise in high-pressure torsion, mater. sci. eng. a, 593, pp. 185-188. doi: 10.1016/j.msea.2013.11.015. [32] kamrani, m., levitas, v.i., and feng, b. (2017). fem simulation of large deformation of copper in the quasi-constrain high pressure-torsion setup, mater. sci. eng. a, 705, pp. 219–230. doi: 10.1016/j.msea.2017.08.078. [33] kulagin, r., zhao, y., beygelzimer, y., toth, l.s. and shtern, m. (2017). modeling strain and density distributions during high-pressure torsion of pre-compacted powder materials, mater. res. lett. 5, pp. 179–186. doi: 10.1080/21663831.2016.1241318. [34] lee, d.j. and kim, h.s. (2014). finite element analysis for the geometry effect on strain inhomogeneity during high pressure torsion, j. mater. sci., 49, pp. 6620-6628. doi: 10.1007/s10853-014-8283-3. [35] belayachi, n., benseddiq, n. and nait-abdelaziz, m. (2008). behavior of the heterogeneous glassy polymers: computational modeling and experimental approach, compos. sci. technol. 68, pp. 367–375. doi: 10.1016/j.compscitech.2007.07.002 [36] perzyna, p. (1985). on constitutive modelling of dissipative solids for plastic flow, instability and fracture. in: a. sawczuk (eds), (1985), plasticity today-modelling, methods and applications, pp. 657-679. [37] perzyna, p. (1966). fundamental problems in viscoplasticity, in: advances in applied mechanics, academic press in new york., 9, pp. 243-377. doi: 10.1016/s0065-2156(08)70009-7. [38] perzyna, p., and pecherski, r. (1983). modified theory of viscoplasticity. physical foundations and identification of material functions for advanced strains, arch. mech., 35, pp. 423-436. [39] peric, d., owen, d.r.j. and honnor, m.e. (1992). a model for finite strain elasto-plasticity based on logarithmic strains: computational issues. computer methods in applied mechanics and engineering, 94, pp. 35-61. doi: 10.1016/0045-7825(92)90156-e. [40] sluis, o.v.d., schreurs, p.j.g, brekelmans, w.a.m. and meijer, h.e.h. (2000). overall behavior of heterogeneous elastoviscoplastic materials: effect of microstructural modeling. mech. mat., 32, pp. 449-462. doi: 10.1016/s0167-6636(00)00019-3. [41] sluis, o.v.d., schreurs, p.j., and meijer, h.e.h. (2001). homogenisation of structured elastoviscoplastic solids at finite strains, mech. mat., 33, pp. 499-522. doi: 10.1016/s0167-6636(01)00066-7. [42] draï, a. and aour, b. (2017). analysis of the temperature effect on the plastic strain of polymers during high pressure torsion (hpt) process, icontes2017: international conference on technology, engineering and science, october 26 29, 2017 antalya/turkey, the eurasia proceedings of science, technology, engineering & mathematics (epstem), 1, pp. 40-51. << /ascii85encodepages false /allowtransparency false /autopositionepsfiles true /autorotatepages /none /binding /left /calgrayprofile (dot gain 20%) /calrgbprofile (srgb iec61966-2.1) /calcmykprofile (u.s. web coated \050swop\051 v2) /srgbprofile (srgb iec61966-2.1) /cannotembedfontpolicy /error /compatibilitylevel 1.4 /compressobjects /tags /compresspages true /convertimagestoindexed true /passthroughjpegimages true /createjobticket false /defaultrenderingintent /default /detectblends true /detectcurves 0.0000 /colorconversionstrategy /cmyk /dothumbnails false /embedallfonts true /embedopentype false /parseiccprofilesincomments true /embedjoboptions true 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/hrv (za stvaranje adobe pdf dokumenata najpogodnijih za visokokvalitetni ispis prije tiskanja koristite ove postavke. stvoreni pdf dokumenti mogu se otvoriti acrobat i adobe reader 5.0 i kasnijim verzijama.) /hun 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can be opened with acrobat and adobe reader 5.0 and later.) >> /namespace [ (adobe) (common) (1.0) ] /othernamespaces [ << /asreaderspreads false /cropimagestoframes true /errorcontrol /warnandcontinue /flattenerignorespreadoverrides false /includeguidesgrids false /includenonprinting false /includeslug false /namespace [ (adobe) (indesign) (4.0) ] /omitplacedbitmaps false /omitplacedeps false /omitplacedpdf false /simulateoverprint /legacy >> << /addbleedmarks false /addcolorbars false /addcropmarks false /addpageinfo false /addregmarks false /convertcolors /converttocmyk /destinationprofilename () /destinationprofileselector /documentcmyk /downsample16bitimages true /flattenerpreset << /presetselector /mediumresolution >> /formelements false /generatestructure false /includebookmarks false /includehyperlinks false /includeinteractive false /includelayers false /includeprofiles false /multimediahandling /useobjectsettings /namespace [ (adobe) (creativesuite) (2.0) ] /pdfxoutputintentprofileselector /documentcmyk /preserveediting true /untaggedcmykhandling /leaveuntagged /untaggedrgbhandling /usedocumentprofile /usedocumentbleed false >> ] >> setdistillerparams << /hwresolution [2400 2400] /pagesize [612.000 792.000] >> setpagedevice microsoft word numero_59_art_31_3287.doc e.s.m.m. soliman, frattura ed integrità strutturale, 59 (2022) 471-485; doi: 10.3221/igf-esis.59.31 471 mode i stress intensity factor with various crack types ehab samir mohamed mohamed soliman mechatronics and robotics department, faculty of engineering, egyptian russian university, badr city, cairo, 11829, egypt. swgezumo@yahoo.com, https://orcid.org/0000-0001-6427-3022 abstract. presence of cracks in mechanical components needs much attention, where the stress field is affected by cracks and the propagation of cracks may be occurred causing the damage. the objective of this paper is to present an investigation of crack type effect on crack severity in a finite plate. three cases of cracked plate with three different types of cracks are assumed in this work, i.e., single edge crack, center crack and double edge crack. 2d numerical models of cases of cracked plate are established in finite element analysis (fea), ansys software by adopting plane 183 element. values of fea mode i stress intensity factor sif and von-mises stress at crack apex are determined for cases of cracked plate under tensile stress with different values. to identify the crack severity, the comparison of fea results for different cracked cases is made. the comparison showed that, single edge cracked plate (secp) has the maximum values of mode i sif and von-mises stress at crack apex, i.e. the greatest crack severity is considered. also, values of fea von-mises stress at crack apex for center cracked plate (ccp) are moderate and for double edge cracked plate (decp) are the minimum. besides, in case of high crack lengths, it is found that, fea results of mode i sif in case of (ccp) are higher than those of in case of (decp). consequently, crack severity is considered as moderate in case of (ccp) and the minimum in case of (decp). empirical formulas are used to approximately estimate mode i sif for all the case studies of cracked plate in this study and the results are compared to those of fea. a good agreement between analytical and fea results has been showed by this comparison. keywords. stress intensity factor (sif); cracked plate; crack severity; vonmises stress; crack apex. citation: soliman, e.s.m.m., mode i stress intensity factor with various crack types, frattura ed integrità strutturale, xx (2022) 471-485. received: 01.10.2021 accepted: 09.12.2021 published: 01.01.2022 copyright: © 2022 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. introduction racks in engineering components often cause serious local stress concentration and may finally cause to fracture damage and consequently to failure of these components [1]. the failure of cracked components is due to the propagation of cracks and the singular (first term) stress near the crack tip is characterized by the stress intensity c https://youtu.be/l7pxkkd_r7i e.s.m.m. soliman, frattura ed integrità strutturale, 59 (2022) 471-485; doi: 10.3221/igf-esis.59.31 472 factor sif [2]. in an elastic body, the stress intensity factors refer to the stress singularities arising from the crack tips and specify stress fields near crack tips [3]. the failure of material due to the presence of cracks can be predicted by evaluation of an important parameter in fracture mechanics i.e. stress intensity factor (sif) [4]. in the application of the principles of linear elastic fracture mechanics to practice, the stress intensity factor (sif) plays a vital role and hence the determination of its value is crucial important [5]. many researchers have investigated the evaluation of stress intensity factor for cracked plate using finite element method [6−9]. ismail et al. [10] modeled single edge cracked plate and calculated the stress intensity factors of mode i and mode ii at different crack slanted angles using ansys finite element program. their study showed that, higher relative crack depths produced higher stress intensity factors for mode i and mode ii. they concluded that, when the crack slanted angles is increased, then the mode i stress intensity factors reduce and the mode ii stress intensity factors increase. the stress intensity factors are the most important parameters in fracture analysis and provide fundamental information on how the crack is going to propagate in the elastic fracture analysis [11]. in the fracture mechanics field, the mode i stress intensity factor is a key parameter and the knowing of whether the crack is stable or not in respect to the toughness of the kic material, is predicted by it [12]. the plane strain fracture toughness (kic) is defined as a material property which measures crack resistance, where the crack propagation occurs when mode i sif ≥ kic, which is a failure criterion for brittle materials [13]. the stress intensity factor is affected by the different parameters such as crack length, crack location in the geometry, crack inclination, number of cracks and boundary conditions [14]. ensure of the reliability and integrity of mechanical structures, can be determined by successfully using of the stress intensity factor (sif), which is one of the most important cracks driving force [15]. zhu et al. [16] introduced a new approach to calculate stress intensity factors for three different cases of cracked plate by using peridynamic (pd) theory and displacement extrapolation method (dem). in the analysis, they considered plate with a central crack, plate with an edge crack and plate with a slanted crack as three problems. they compared sifs results of proposed approach against analytical and fem results and the comparison showed a good agreement. mohsin [17] calculated the stress intensity factors mode i for finite center cracked plate subjected to uniform tensile loading, by finite element and analytical solution for different crack lengths and plate dimensions. he inferred that, the value of mode i intensity factor increased as the crack length and applied stresses increased. the severity of the crack is denoted by the stress intensity factor [18], so in the present work, evaluation of mode i sif using finite element method is carried out to investigate the effect of crack type on crack severity in a 2d finite plate subjected to tensile uniaxial loading. for this purpose, the 2d numerical models of single edge cracked plate (secp), center cracked plate (ccp) and double edge cracked plate (decp) are developed using finite element analysis (fea), ansys. fea results of mode i sif and von-mises stress at crack apex are obtained for the three cases of cracked plate and the fea results are compared. also, analytical solution for mode i sif for the cases of cracked plate is carried out and a comparison between fea results of mode i sif and those of analytical for cases of cracked plate is made. a flow chart of this present work structure is shown in fig. 1. figure 1: flow chart of the present work e.s.m.m. soliman, frattura ed integrità strutturale, 59 (2022) 471-485; doi: 10.3221/igf-esis.59.31 473 governing equations n this study, the displacement and stresses near the crack apex are described. consequently, the co-ordinate systems and contour around the crack apex are adopting as depicted in fig. 2. figure 2: crack apex co-ordinate systems the displacement and stress fields near the tip of the crack with traction-free faces known as williams expansion, originally introduced by [19-21] and can be written as [22]:                                                       2 1 cos cos 20 0 2 2 2 221 1 sin sin 2 2 2 2 2 n r n n n nnu u y a knn n n n nn b kn (1)                                                         2 1 sin sin 20 0 2 2 2 221 1 cos cos 2 2 2 2 2 n r n n n nnx a knn n n n nn b kn (2)                                                                             1 2 2 1 cos 1 1 cos 3 2 2 2 221 2 1 sin 1 1 sin 3 2 22 2 n n n n n nnr anx n n nn nn bn (3)                                                                             1 2 2 1 cos 1 1 cos 3 2 2 2 221 2 1 sin 1 1 sin 3 2 22 2 n n n n n nnr any n n nn nn bn (4) i e.s.m.m. soliman, frattura ed integrità strutturale, 59 (2022) 471-485; doi: 10.3221/igf-esis.59.31 474                                                                              1 2 1 sin 3 1 sin 1 2 2 2 221 1 cos 3 1 cos 1 2 2 2 2 n n n n n nnr anxy n n n n nnbn (5)     2 1e (6)          3 4 plane strain 3 plane stress 1 k (7) where (x, y) is the cartesian coordinate and the crack with faces exists on the negative x-axis; (r, ɵ) is polar coordinate and ɵ is measured from x-axis in direction of counterclockwise; k is kolosov constant; μ is shear modulus; e and ν are young’s modulus and poisson’s ratio, respectively; u0 and υ0 are displacements at the crack tip; an and bn are coefficients and θ0 is the rigid body rotation with respect to the crack tip. the coefficients of the leading (singular) terms, a1 and b1, which are relevant to the mode i and mode ii stress intensity factors can be expressed as [22]:  1 2 kia (8)  1 2 kiib (9) where ki and kii are mode i and mode ii stress intensity factors (sifs) respectively. zhao et al. [1] utilized an extrapolation procedure in fe software ansys using nodal displacements of a few nodes away from the singularity point at the crack tip. they established a local coordinate where the crack tip lies on origin and the crack faces lie on the negative x-axis. they are selected five nodes; one node at the crack tip and two nodes on each side of the crack face. the stress intensity factor (sif) at the crack tip has been extrapolated by them as the following [1]:                         3 31 22 1 cos cos 2 3 sin sin 4 2 2 2 4 2 2 2 k kr r u k k g g (10)                          3 31 22 1 sin sin 2 3 cos cos 4 2 2 2 4 2 2 2 k kr r k k g g (11) where: r and θ are the polar coordinates, g is the shear modulus, u and ʋ are nodal displacement of these nodes, k1 and k2 are sifs for mode i and mode ii. for a cracked body, the equations of corresponding displacement fields near the crack tip, for the plane strain condition, originally introduced by karihaloo and xiao [21] and can be expressed as [2]:                                           3 3 5 8 cos cos 9 8 sin sin 4 2 2 2 4 2 2 2 3 22 1 cos 4 sin k kr ri iiux r t b o rn e (12) e.s.m.m. soliman, frattura ed integrità strutturale, 59 (2022) 471-485; doi: 10.3221/igf-esis.59.31 475                                               3 3 7 8 sin sin 3 8 cos cos 4 2 2 2 4 2 2 2 3 2 1 sin 4 1 cos k kr ri iiu y r t b o rn e (13) where: bn is the coefficient relevant to williams’ expansion in anti-symmetric mode. µ is the shear modulus; e is young’s modulus; ν is poisson’s ratio; t is a constant that acts parallel to the crack surfaces; ux and uy are displacement fields, for the plane strain condition; (r, θ) is the polar coordinate and ki and kii are the mode i and mode ii sif. the determination of sif using the crack flank displacements may be obtained as [2]:              , , 1 2 k u r u ry yi r (14)              , , 1 2 k u r u rx xii r (15) the first order stress field equations for mode i can be expressed as [13]:                                   3 1 sin sin 2 2 3 cos 1 sin sin 2 2 22 3 sin cos 2 2 xx ki yy r xy (16) the stress in the z-direction can be written as [13]:               2 cos (for plane strain) 22 0 (for plane stress) ki xx yy rzz (17) for a double edge cracked plate with two symmetric edge cracks having two symmetrical axes, the general stress functions can be written as [23]:                             cos ( 2 )2 1 2 2 2 1 2 1sin 02 1 11 sin ( 2 ) m mz bb k kz e i z c e z f zk kk ka b (18)                             cos ( 2 )2 1 2 2 2 1 2 1sin 02 1 11 sin ( 2 ) m mz bb k kz e i z c f z f zk kk ka b (19) e.s.m.m. soliman, frattura ed integrità strutturale, 59 (2022) 471-485; doi: 10.3221/igf-esis.59.31 476                                                    1 2 2 2 cos cos sin 02 2 2 2 2 2 2 2 2 2 2 1 2 1 2 2 1 1 z z a z e b b b m mi k k ke kz c k z k f zk k k kz c (20)         2 2lim i k e z c z i z c (21)  z x iy  1i  c b a where: φ (z), ϕ (z) and ω (z) are complex stress functions, c is the half length of the ligament, 2b is width of the plate, a is the length of each edge crack, ek and fk are coefficients, ki is the stress intensity factor, α is an angle of inclination of the crack with the x axis, k is kolosov constant. empirical formulas for mode i sif, for a finite cracked plate under tensile stress, σ, can be written as [24]: in case of single edge crack                   2 3 4 1.122 0.231 10.550 21.710 30.382a a a ak a b b b bi (22) in case of center crack                      2 3 1 0.5 0.370 0.044 1 a a a b b bk ai a b (23) where: 2a is the length of crack, 2b is the width of plate in case of double edge crack having two symmetric edge cracks                      2 3 1.122 0.561 0.015 0.091 1 a a a b b bk ai a b (24) where: a is the length of each edge crack, 2b is the width of plate methodology d plane strain models of single edge cracked plate (secp), center cracked plate (ccp), and double edge cracked plate (decp) under tensile stress, are executed in ansys, fea to determine the numerical values of mode i stress intensity factor ki. the material of the plate is steel with properties young’s modulus of elasticity (e) = 200gpa 2 e.s.m.m. soliman, frattura ed integrità strutturale, 59 (2022) 471-485; doi: 10.3221/igf-esis.59.31 477 and poisson’s ratio (ν) = 0.3. the geometry and parameters of the plate are length = width = (2b) = 0.72 m, the crack length = (2a), crack length ratio = (a/b) and uniform tensile stress in the y–direction = (σ). in case of double edge cracked plate (decp), the length of each edge crack = (a), where the length (2a) is divided into two equal lengths for two cracks at plate edges. in this analysis, the plate is loaded under loads (σ) of 50mpa, 220mpa and 350mpa. for every load, the crack length ratio was varied as 0.1, 0.25, 0.4, 0.55 and 0.7. based on symmetry of the plate, half model was considered in case of (secp) and quarter model was considered in case of (ccp) and (decp). the plane strain condition is considered and 2d finite element model is established. eight-node plane 183, 2d, structural solid element, was employed in the finite element analysis (fea) where it is a suitable singular element for accuracy simulation the singularity property at the crack tip [1]. the options for plane 183 element assumed in this analysis are quadrilateral of element shape, plane strain of element behavior and pure displacement of element formulation. there are both strain and stress singularities around an elastic crack tip [5]. a much attention for the region around the crack tip must be considered during the meshing in the finite element analysis to produce the singularity in the stresses and strains at the crack tip [25]. in this analysis, the mesh of the region around crack tip was generated using singular elements but irregular elements are used for the generation mesh of the rest region as [15]. hence, the concentration keypoint at the crack tip has been created. the fracture toughness ki was calculated during finite element analysis using the kcalc command as [26]. geometry, finite element mesh and symmetry boundary conditions for cases (secp), (ccp), and (decp), respectively are shown in figs. 3, 4 and 5, respectively. figure 3: single edge cracked plate (secp): (a) full model, (b) symmetry boundary conditions of half model and (c) fe mesh of half model e.s.m.m. soliman, frattura ed integrità strutturale, 59 (2022) 471-485; doi: 10.3221/igf-esis.59.31 478 the fea results of von-mises stress at crack apex for the cases of (secp), (ccp) and (decp), respectively are indicated in tabs. 1, 2 and 3, respectively. from these tables it is noticed that the values of von-mises stress are the maximum in the case of (secp) and the minimum in the case of (decp). the mode i stress intensity factor ki is calculated by using the kcalc command for two cases of (ccp) and (decp) is depicted in fig. 6. the fea von-mises stress contour for some cases of (secp), (ccp) and (decp) as shown in fig. 7, indicated that the maximum von-mises stress occurs at crack apex. figure 4: center cracked plate (ccp): (a) full model, (b) symmetry boundary conditions of quarter model, (c) fe mesh of quarter model, and (d) singular elements around crack apex e.s.m.m. soliman, frattura ed integrità strutturale, 59 (2022) 471-485; doi: 10.3221/igf-esis.59.31 479 figure 5: double edge cracked plate (decp): (a) full model, (b) symmetry boundary conditions of quarter model, and (c) fe mesh of quarter model crack length ratio (a/b) single edge cracked plate von-mises stress (pa) σ = 50 (mpa) σ = 220 (mpa) σ = 350 (mpa) 0.1 0.144×109 0.633×109 0.101×1010 0.25 0.185×109 0.813×109 0.129×1010 0.4 0.241×109 0.106×1010 0.169×1010 0.55 0.341×109 0.150×1010 0.239×1010 0.7 0.651×109 0.286×1010 0.456×1010 table 1: fea von-mises stress at crack apex for the case of (secp). e.s.m.m. soliman, frattura ed integrità strutturale, 59 (2022) 471-485; doi: 10.3221/igf-esis.59.31 480 crack length ratio (a/b) center cracked plate von-mises stress (pa) σ = 50 (mpa) σ = 220 (mpa) σ = 350 (mpa) 0.1 0.135×109 0.594×109 0.945×109 0.25 0.145×109 0.639×109 0.102×1010 0.4 0.163×109 0.716×109 0.114×1010 0.55 0.188×109 0.825×109 0.131×1010 0.7 0.226×109 0.995×109 0.158×1010 table 2: fea von-mises stress at crack apex for the case of (ccp). crack length ratio (a/b) double edge cracked plate von-mises stress (pa) σ = 50 (mpa) σ = 220 (mpa) σ = 350 (mpa) 0.1 0.134×109 0.59×109 0.939×109 0.25 0.140×109 0.618×109 0.983×109 0.4 0.147×109 0.645×109 0.103×1010 0.55 0.149×109 0.657×109 0.104×1010 0.7 0.154×109 0.68×109 0.108×1010 table 3: fea von-mises stress at crack apex for the case of (decp). figure 6: mode i stress intensity factor (ki): (a) (ccp); (a/b) = 0.25; σ = 350 mpa, (b) (decp); (a/b) = 0.7; σ = 220 mpa e.s.m.m. soliman, frattura ed integrità strutturale, 59 (2022) 471-485; doi: 10.3221/igf-esis.59.31 481 figure 7: von-mises stress contour: (a) (secp); (a/b) = 0.4; σ = 220 mpa, (b) (ccp); (a/b) = 0.55; σ = 50 mpa, (c) (decp); (a/b) = 0.55; σ = 350 mpa. results and discussions s this work focuses on study the influence of crack type, i.e. single edge crack, center crack and double edge crack on crack severity in a finite plate. hence, this section indicates a comparison of numerical results obtained for (secp), (ccp) and (decp) to investigate crack severity. fea results of fracture toughness (mode i stress intensity factor) for cracked cases of plate with values of tensile stress 50mpa, 220mpa and 350mpa, respectively are shown in figs. 8, 9 and 10, respectively. these figures revealed the comparison of sifs obtained from fea in the following ways: 1. when the tensile stress is kept constant and the crack length is increased, then mode i sif i.e., fracture toughness at crack apex increases. 2. when the crack length is kept constant and the tensile stress is increased, then the fracture toughness at crack apex increases. 3. when the tensile stress and the crack length are kept constant, the case of single edge cracked plate has the maximum value of fracture toughness at crack apex. 4. when the tensile stress is kept constant and at (a/b) = 0.55 and at (a/b) = 0.7, the case of double edge cracked plate has the minimum value of fracture toughness at crack apex. 5. when the tensile stress is kept constant, the sifs for double edge cracked plate are higher with a small difference than those for center cracked plate in case of (a/b) = 0.1, (a/b) = 0.25 and (a/b) = 0.4. the results showed little different of sifs obtained from the double edge and center cracks in case of (a/b) = 0.1, (a/b) = 0.25 and (a/b) = 0.4. hence, in case of small size cracks the effect of double edge and center cracks on the structural performance of the plate is neearly the same. on the other hand, in case of high size cracks the influence of center cracks on the plate is greater than those of double edge cracks. from the results, a great significant effect is observed in case of single edge cracks on the deterioration of structural performance. a e.s.m.m. soliman, frattura ed integrità strutturale, 59 (2022) 471-485; doi: 10.3221/igf-esis.59.31 482 figure 8: fea fracture toughness values at σ = 50mpa. figure 9: fea fracture toughness values at σ = 220mpa. figure 10: fea fracture toughness values at σ = 350mpa e.s.m.m. soliman, frattura ed integrità strutturale, 59 (2022) 471-485; doi: 10.3221/igf-esis.59.31 483 analytical solution for sif calculation his section validates the numerical results of mode i sif obtained from finite element analysis (fea). for this purpose, the values of mode i sif were approximately calculated for (secp), (ccp) and (decp), respectively using eqn. (22) [24], eqn. (23) [24] and eqn. (24) [24], respectively. the comparison between analytical and numerical values of mode i sif is indicated in tabs. (4), (5) and (6). it is observed that the results of ki obtained from finite element analysis using software ansys are with good agreement to those of analytical results and thus verifies the acceptance of the fea used in the calculation of fracture toughness. crack length ratio (a/b) ki (pa√m) for single edge cracked plate σ = 50 mpa σ = 220 mpa σ = 350 mpa analytical eq (22) [24] fea error (%) analytical eq (22) [24] fea error (%) analytical eq (22) [24] fea error (%) 0.1 0.282×108 0.27570×108 2.2 0.124×109 0.12131×109 2.2 0.197×109 0.19299×109 2 0.25 0.57×108 0.58468×108 2.6 0.25×109 0.25726×109 2.9 0.4×109 0.40928×109 2.3 0.4 0.1×109 0.10318×109 3.2 0.44×109 0.45397×109 3.2 0.7×109 0.7222×109 3.2 0.55 0.187×109 0.18026×109 3.6 0.82×109 0.79313×109 3.3 0.13×1010 0.12618×1010 2.9 0.7 0.376×109 0.36778×109 2.2 0.165×1010 0.16182×1010 1.9 0.263×1010 0.25745×1010 2.1 table 4: mode i stress intensity factor values obtained analytically and by fea for the single edge cracked finite plate. crack length ratio (a/b) ki (pa√m) for center cracked plate σ = 50 mpa σ = 220 mpa σ = 350 mpa analytical eqn. (23) [24] fea error (%) analytical eqn. (23) [24] fea error (%) analytical eqn. (23) [24] fea error (%) 0.1 0.169×108 0.1615×108 4.4 0.744×108 0.711×108 4.4 0.118×109 0.11304×109 4.2 0.25 0.276×108 0.2732×108 1.01 0.121×109 0.12021×109 0.65 0.193×109 0.19125×109 0.91 0.4 0.372×108 0.3864×108 3.9 0.164×109 0.170×109 3.7 0.260×109 0.27048×109 4.03 0.55 0.488×108 0.522×108 6.97 0.215×109 0.22967×109 6.8 0.341×109 0.36539×109 7.2 0.7 0.663×108 0.70257×108 5.97 0.292×109 0.30913×109 5.87 0.464×109 0.4918×109 6 table 5: mode i stress intensity factor values obtained analytically and by fea for the center cracked finite plate. crack length ratio (a/b) ki (pa√m) for double edge cracked plate σ = 50 mpa σ = 220 mpa σ = 350 mpa analytical eqn. (24) [24] fea error (%) analytical eqn. (24) [24] fea error (%) analytical eqn. (24) [24] fea error (%) 0.1 0.189×108 0.18091×108 4.3 0.831×108 0.796×108 4.2 0.132×109 0.12664×109 4.1 0.25 0.302×108 0.3019×108 0.03 0.133×109 0.13284×109 0.12 0.211×109 0.21133×109 0.16 0.4 0.391×108 0.40722×108 4.1 0.172×109 0.17918×109 4.2 0.274×109 0.28506×109 4.04 0.55 0.484×108 0.50434×108 4.2 0.213×109 0.22191×109 4.2 0.339×109 0.35304×109 4.1 0.7 0.612×108 0.61169×108 0.05 0.269×109 0.26914×109 0.05 0.428×109 0.42818×109 0.04 table 6: mode i stress intensity factor values obtained analytically and by fea for the double edge cracked finite plate. conclusion ea were performed for cases of cracked finite plate with three types of crack, single edge crack, center crack and double edge crack under tensile stress with different values, then the numerical values of von-mises stress and mode i sif are obtained. from the comparison of the fea results for the three types of crack, it is observed that the fea values of von-mises stress and mode i sif at crack tip are the maximum in case of single edge cracked plate. fea values of von-mises stress at crack tip are moderate in case of center cracked plate and the minimum in case of t f e.s.m.m. soliman, frattura ed integrità strutturale, 59 (2022) 471-485; doi: 10.3221/igf-esis.59.31 484 double edge cracked plate. as the severity of crack is proportional to values of fracture toughness and von-mises stress at crack apex, hence from the previous observations of the results, it can be considered that severity of single edge crack type is the maximum. on the other hand, the crack severity in case of center crack is moderate and in case of double edge crack is the minimum. the crack geometry which is asymmetry in case of (secp) and symmetric in the two cases (ccp) and (decp) was vital to interpret the variation in the obtained results for sif. as a result, when plate having a single edge crack, there would be high significant effect on sif and this effect would be less in the two cases with double edge crack and center crack. the accuracy of numerical models is validated by comparing values of mode i sif obtained by analytical and fea, where the comparison exhibited a good convergence. references [1] zhao, f., aiqun, l., haiying, b., hao, w. (2018). calculation of stress intensity factor in two-dimensional cracks by strain energy density factor procedure. sci. china technol. sci. 61(4), pp. 542–550, doi: 10.1007/s11431-017-9186-9. [2] chen, c.-h., wang, c.-l. (2008). stress intensity factors and t-stresses for offset double edge-cracked plates under mixed-mode loadings. int. j. fract. 152, pp. 149–162, doi: 10.1007/s10704-008-9276-5. [3] yamamoto, y., tokuda, n. (1973). determination of stress intensity factors in cracked plates by the finite element method. int. j. numer. methods eng. 6, pp. 427-439. [4] zhong-liang, r., hong-bo, z., shun-de, y. (2013). evaluation of mixed-mode stress intensity factors by extended finite element method. j. cent. south univ. 20, pp. 1420−1425, doi: 10.1007/s11771-013-1630-8. [5] mukhopadhyay, n.k., maiti, s.k., kakodkar, a. (2000). a review of sif evaluation and modelling of singularities in bem. comput. mech. 25, pp. 358-375, doi: 10.1007/s004660050483. [6] byskov, e. (1970). the calculation of stress intensity factors using the finite element method with cracked elements. int. j. fract. mech. 6(2), pp. 159-167, doi: 10.1007/bf00189823. [7] mohammed, b., boualem, s., mokadem, s., bouchra, z., khacem, k. (2019). modeling of a cracked and repaired al 2024t3 aircraft plate: effect of the composite patch shape on the repair performance. frattura ed integrità strutturale, 50, pp. 68-85, doi: 10.3221/igf-esis.50.08. [8] bhagat, r.k., singh, v.k. (2013). effect of specimen geometry on stress intensity factors of inclined crack by finite element method. j. fail. anal. prev. 13(4), pp. 463–469. doi: 10.1007/s11668-013-9697-y. [9] lou, b., barltrop, n. (2020). universal hybrid method and approximate closed-form solution for v-notched and vnotch-cracked plate under tensile and in-plane bending. theor. appl. fract. mech. 108, 102579, doi: 10.1016/j.tafmec.2020.102579. [10] ismail, a.e., awang, m.k., tobi, a.m., ahmad, m.h. (2017). mode i stress intensity factors of slanted cracks. arpn j. eng. appl. sci. 12(10), pp. 3189-3194. [11] souiyah, m., alshoaibi, a., muchtar, a., ariffin, ak. (2008). finite element model for linear-elastic mixed mode loading using adaptive mesh strategy. j. zhejiang univ. sci. a 9(1), pp. 32-37, doi: 10.1631/jzus.a072176. [12] el fakkoussi, s., moustabchir, h., elkhalfi, a., pruncu, c.i. (2019). computation of the stress intensity factor ki for external longitudinal semi-elliptic cracks in the pipelines by fem and xfem methods. int. j. interact. des. manuf. (ijidem) 13, pp. 545–555, doi: 10.1007/s12008-018-0517-1. [13] perez, n. (2004). fracture mechanics, boston, kluwer academic publishers. [14] arunkumar, s., nithin, v.k. (2020). estimation of stress intensity factor of multiple inclined centre cracks under biaxial loading. j. fail. anal. prev. 20(6), pp. 2040–2058, doi: 10.1007/s11668-020-01019-0. [15] azlan, m.a., ismail, a.e. (2015). effect of mechanical mismatch on the stress intensity factors of inclined cracks under mode i tension loading. appl. mech. mater. 773-774, pp. 129-133, doi: 10.4028/www.scientific.net/amm.773-774.129. [16] zhu, n., oterkus, e. (2020). calculation of stress intensity factor using displacement extrapolation method in peridynamic framework. j. mech. 36(2), pp. 235-243, doi : 10.1017/jmech.2019.62. [17] mohsin, n.r. (2015). static and dynamic analysis of center cracked finite plate subjected to uniform tensile stress using finite element method. int. j. mech. eng. technol. 6(1), pp. 56-70. [18] soliman, e.s.m.m. (2019). investigation of crack effects on isotropic cantilever beam. j. fail. anal. prev. 19(6), pp. 1866–1884, doi: 10.1007/s11668-019-00796-7. [19] williams, m.l. (1957). on the stress distribution at the base of a stationary crack. j. appl. mech. 24(1), pp. 109–114, doi: 10.1115/1.4011454. e.s.m.m. soliman, frattura ed integrità strutturale, 59 (2022) 471-485; doi: 10.3221/igf-esis.59.31 485 [20] owen, d.r.j., fawkes, a.j. (1983). engineering fracture mechanics: numerical methods and applications, swansea, u.k., pineridge press ltd. [21] karihaloo, b.l., xiao, q.z. (2001). accurate determination of the coefficients of elastic crack tip asymptotic field by a hybrid crack element with p-adaptivity. eng. fract. mech. 68(15), pp. 1609–1630, doi: 10.1016/s0013-7944(01)00063-7. [22] xiao, q.z., karihaloo, b.l., liu, x.y. (2004). direct determination of sif and higher order terms of mixed mode cracks by a hybrid crack element. int. j. fract. 125, pp. 207–225, doi: 10.1023/b:frac.0000022229.54422.13. [23] cheung, y.k., woo, c.w., wang, y.h. (1988). the stress intensity factor for a double edge cracked plate by boundary collocation method. int. j. fract. 37, pp. 217-231, doi: 10.1007/bf00045864. [24] tada, h., paris, p.c., irwin, g.r. (2000). the stress analysis of cracks handbook, third ed., asme press. [25] soliman, e.s.m.m. (2020). investigation of modal and damage parameters of isotropic cantilever beam under double-sided crack. j. fail. anal. prev. 20(1), pp. 120–136, doi: 10.1007/s11668-020-00806-z. [26] begum, y., bharath, k.n., doddamani, s., rajesh, a.m., kaleemulla, k.m. 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can be opened with acrobat and adobe reader 5.0 and later.) >> /namespace [ (adobe) (common) (1.0) ] /othernamespaces [ << /asreaderspreads false /cropimagestoframes true /errorcontrol /warnandcontinue /flattenerignorespreadoverrides false /includeguidesgrids false /includenonprinting false /includeslug false /namespace [ (adobe) (indesign) (4.0) ] /omitplacedbitmaps false /omitplacedeps false /omitplacedpdf false /simulateoverprint /legacy >> << /addbleedmarks false /addcolorbars false /addcropmarks false /addpageinfo false /addregmarks false /convertcolors /converttocmyk /destinationprofilename () /destinationprofileselector /documentcmyk /downsample16bitimages true /flattenerpreset << /presetselector /mediumresolution >> /formelements false /generatestructure false /includebookmarks false /includehyperlinks false /includeinteractive false /includelayers false /includeprofiles false /multimediahandling /useobjectsettings /namespace [ (adobe) (creativesuite) (2.0) ] /pdfxoutputintentprofileselector /documentcmyk /preserveediting true /untaggedcmykhandling /leaveuntagged /untaggedrgbhandling /usedocumentprofile /usedocumentbleed false >> ] >> setdistillerparams << /hwresolution [2400 2400] /pagesize [612.000 792.000] >> setpagedevice microsoft word numero_52_art_04_2565 o. kryvyi et alii, frattura ed integrità strutturale, 52 (2020) 33-50; doi: 10.3221/igf-esis.52.04 33 thermally active interphase inclusion in a smooth contact conditions with transversely isotropic half-spaces oleksandr kryvyi national university «odesa maritime academy», 65029, odessa, didrikhson str., 8, ukraine krivoy-odessa@ukr.net, kryvyi-od@math.onma.edu.ua, http://orcid.org/0000-0001-2345-6789 yurii morozov odesa national polytechnic university, 65044, odesa, boulevard of shevchenko, 1, ukraine morozov@opu.ua, morozovyu@gmail.com, https://orcid.org/0000-0003-4027-2353 abstract. an exact solution of the stationary thermoelasticity problem is constructed for the interfacial circular absolutely rigid inclusion, while it is in the smooth contact conditions in a piecewise homogeneous transversely homogeneous space. with the help of the constructed discontinuous solution, by the method of singular integral relations, the task is reduced to a system of singular integral equations (sie).an exact solution has been built for the specified sie, and as a result, dependences of translational displacement of the inclusion on temperature, the resultant load, main moment and thermomechanical characteristics of transversely isotropic materials have been obtained. keywords. thermoelasticity problem; interphase circular inclusion; singular integral equations; piecewise-homogeneous transversely isotropic space. citation: kryvyi, o., morozov yu., thermally active interphase inclusion in a smooth contact conditions with transversely isotropic half-spaces, frattura ed integrità strutturale, 52 (2020) 32-50. received: 16.07.2019 accepted: 24.01.2020 published: 01.04.2020 copyright: © 2020 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. introduction he modern construction is widely using composite anisotropic materials and heterogeneous structures that contain constructive or technological interphase heat-active inclusions (defects, fibers, reinforcement elements) and are under conditions of power and temperature loading with various types of contact interaction with the medium. these inclusions are significant stress concentrators and can lead to structural failure as well as to a the destruction of structures. at the same time stress concentration is significantly affected as a form of contact interaction of the inclusion with the medium so are the ratio of thermoelastic constants of the matrix. such problems arise [1, 2], particularly, in geophysics, during the operation of nuclear power plants, in welded bridge structures and when using modern reinforced materials. one of the methods of repairing damaged structures of long-term operation is injection technologies [3], according to which the damaged areas of concrete and reinforced concrete structures and structures are filled with special materials, turning over time into rigid heat-emitting inclusions that may have different contact with the matrix. t https://youtu.be/fxvu1yjmyd4 o. kryvyi et alii, frattura ed integrità strutturale, 52 (2020) 33-50; doi: 10.3221/igf-esis.52.04 34 therefore, an important scientific and technical task for of predicting the possible destruction of structures during their operation and design is a study of the stress-strain state of bodies in the presence of interphase heat-emitting or heatinsulated inclusions in anisotropic piecewise homogeneous media. in particular, the study of the effects on deformation and the distribution of stresses around the specified inclusions of thermoelastic parameters of anisotropic media and the type of interaction contact of inclusions with the medium. in the general this kind of finite bodies problems in the presence of many inclusions, can have only a numerical solution, . however, the presence of exact solutions for single inclusions allows not only to study the stress concentration around the defect, but also improve the efficiency of numerical methods. concentration of tensions near defects such as cracks or inclusions in the composite media have been investigated by many authors. in particular, in [5] non-axisymmetric problems on various interfacial defects in a composite isotropic space are reduced to systems of two-dimensional singular integral equations (sie), and for circular defects a method for their exact solutions is proposed. in [6], the axisymmetric problem of the theory of elasticity for a rigid circular inclusion located at the interface between two perfectly connected dissimilar isotropic elastic half-spaces is considered, the solution for which was obtained using the hankel transform. in papers [7–9], using the method of potential and the fourier transform, the problems of stationary thermoelasticity for absolutely rigid inclusion in unbounded isotropic space, and in [6] in transversely isotropic space under the action of a heat flux, are reduced to a system of related two-dimensional singular integral equations for jumps of stress. in [1, 2], consider stationary thermal elasticity problems for the body with a thermally permeable disk inclusion, between the surfaces where there is an imperfect thermal contact, as well as with a thin heat-active disk inclusion. the posed problems are reduced to hypersingular integral equations of the first and second kind, for which an exact solution has been obtained. in works [11-14], problems on of nonaxisymmetric interphase defects such as cracks or absolutely rigid inclusions, for different types of contact interaction (full coupling, smooth contact, mixed conditions) with various transversely isotropic half-spaces using the method of singular integral relations (sir) [15] are being reduced to two-dimensional sie systems. a method of constructing exact solutions of these sia systems for circular defects has been proposed, which has allowed to determine the singularity of the stress and displacement fields around the cracks and inclusions under arbitrary load. an analysis of well-known publications shows that nonaxisymmetric problems of thermoelasticity for piecewise homogeneous transversely isotropic media in the presence of interfacial defects are not well-studied.have not been extencively studied. especially it concerns a smooth (sliding) contact of the inclusion with the medium, despite the importance of such a solution [16]. in this paper, for the first time, we consider the non-axisymmetric stationary thermoelasticity problem for a composite transversely isotropic space containing a heat radiating circular inclusion having a smooth contact with the medium. the problem, using the sir method, is reduced to the sie system. an exact solution to the indicated sie system was obtained, which made it possible to study the fields of stresses, strains, and temperatures around the inclusion. formulation of the problem et in the plane everywhere except the circular area have the perfect contact of two different transversely isotropic half-spaces. for stress tensor components: vector of movements temperature and heat flux , we introduce the notation:  8 8 1,80{ } { } , { , , } { , , , , , , , }k k k z yz xz zkz x y z u v w t q          v (1) in view of the notation (1), the conditions for perfect contact of various transversely isotropic half-spaces outside the area can be written as ( , ) 0, ( 1, 7),k x y k    3 2 7 3 2 7( , , 0) ( , , 0),x y x y          ( , ) ,x y  (2) where       , , , , 1,8k k k kx y x y x y k          (3)  0z   2 2: { },x y a   , , ,z yz xz , , ,u v w t zq  l o. kryvyi et alii, frattura ed integrità strutturale, 52 (2020) 33-50; doi: 10.3221/igf-esis.52.04 35 3   coefficient of thermal conductivity along the axis , respectively, for the upper and lower half-space. the area contains a heat-active absolutely rigid inclusion (fig. 1), being in smooth contact with the medium. the shape of inclusion faces is described by functions thus except for that we shall consider satisfied a condition: 0 0( , ) 0.25 , ( ( , ) ( , ) ( , )).x y a x y x y x y          (4) figure 1: caption is missing. if condition (4) is satisfied, the inclusion can be considered thin, and since it is absolutely rigid, the effect of its faces on half-spaces (boundary conditions) can be carried on the planes: this approach is some simplification of the mechanical model, however, as shown by the comparison with the solution of individual problems in the general arrangement [17], the error is not significant and tends to zero with reduction of the inclusion thickness. at the same time, with this approach, the mathematical model of the problem is greatly simplified, which allows to obtain its exact solution. this approach, in particular, was applied in [18] to study the dependence on the form of inclusion of the stress concentration in the neighborhood of interfacial defects in a composite anisotropic medium. let's assume that on infinity to the environment along the axis normal compressive load applied 0 ( , )p x y which on inclusion leads to the resultant force zp and the main moments xm , ym and on the inclusion the heat flow is se ( , )q x y . as a result of such a force and thermal actions, the positions of the inclusion faces will be described by the functions 0 0 6 6 0 6( , ), , ( , )z y xx y y x x y              , (5) where ,,z x y   translational displacements and turning angles of the inclusion around the corresponding axes, for determine of which are use force and moment equilibrium equations 1 1( , ) , ( , ) . y z x mx x y dxdy p x y dxdy y m                   (6) z   0 ( , ), ( , ) ,x y x y   0 ( , ) 0,x y   0 ( , ) 0,x y   0, ( , ) ..z x y z o. kryvyi et alii, frattura ed integrità strutturale, 52 (2020) 33-50; doi: 10.3221/igf-esis.52.04 36 with this formulation of the problem, the tangent stresses are equal to zero on the inclusion faces, normal displacements and heat flux are also specified. according to the notation (1) and (3), we formulate these conditions 0 6 6 8( , ) 0, 2, 3, ( , ) ( , ) (1 1) , ( , , 0) ( , ), ( , ) .k x y k x y x y x y q x y x y                (7) unknown in the area for the task will be jumps of normal stresses, tangential displacements and temperature: ( , ),( 1, 4, 5, 7)k x y k   (8) reduction of the problem to a two-dimensional system of sie and construction of its exact solution. onditions (7) make it possible to use the approach proposed in [11-14] to reduce the problem to a twodimensional system of sie relatively unknown jumps (8). this approach is based on the generalized functions of slow growth constructed in [15] in the space discontinuous solutions and sis for a piecewise homogeneous transversely isotropic space. it should be emphasized that solutions were built in space of to strictly justify all constructions and prove the existence of solutions in the respective classes. following [15], an sis (a.11) was obtained in the appendix, relating jumps and sums (3) of the thermoelastic characteristics of the medium. the second, third, fourth and sixth equality from (a.11), as well as conditions (7), allowed us to obtain relatively about unknown , the next system of four two-dimensional sie 223 23 21 1 24 6 25 7 223 23 21 1 24 6 25 7 43 41 1 6 44 6 45 7 65 7 8 d d dd d d , 2 2 d dd d d d , 2 2 [ ] [d [ ] d [ ]] [ ], 2 dd [ ] ( 2 q q q u u q q q q q u u q q q q u u q q q                                                                                              , ),( , ) .x y x y  (9) here, operators and defined by relations (а.10) and (а.12). let's consider for definiteness, that a heat flux in the area of changes under the linear law: 0 10 01( , ) (1 ).q x y q d x d y   (10) we obtain the exact solution to system (9) using the approach described in [11-14]. to do this, we turn to the thermoelastic characteristics of space in cylindrical coordinates jumps and the sums at transition through a plane we shall designate as follows: in polar coordinate system instead of unknown functions (8) we will enter new unknown functions: 1 1 3 5 7( , ) ( cos , sin ), ( , ) ( cos , sin ), ( , ) ( cos , sin ). iv r v r e u v r                        (11) functions (11) are searched in the form of    ,ρ, v ρ ,j inj n n v e        (12)   3( )r  3( )r 1      4 5 ,u i   7 d    ( , , ),z  0z                                   8{ , , , , , , , } { ( , )} .z z z ku u w t q v  ( , ) c o. kryvyi et alii, frattura ed integrità strutturale, 52 (2020) 33-50; doi: 10.3221/igf-esis.52.04 37    , 1v ρ, , 1, 3, 5, 2 j in n n j jv v e d j                          3, 3, 3, 3v v , v .n n n n v              for determination of coefficientв in expansions (12), we move on in system (9) to polar coordinates and apply the finite fourier transform. then, taking into account formulas [19] ( ) 2 2 0 1 ( ) ( ) , 2 cos( ) , ik k k k e j t j t dt                    0 0 1, * * * 0 w ( , ), w ( , ) ( ) ( ) , i m m m kn k ni e d j t j t dt e                       of representation (12), and the convolution theorem, after simple transformations, we obtain the following system of integral equations 1, 1 4 4w [u] , w [u ] g , 0 , 0, 1, 2, ,nn n n n n n a n       b g   (13) here we use the notation 1, * * 1 2 3 1 3 3u {u , u , u }, u ( ), u 0.5(u ( 1) u ), 2, 3, j n n n n n jn n nv j        * 1 1 3, * 1 1 3, 5, 3 3 4u ( ) [ v ( )] , u ( ) [ v ( )] , u [ v ( )] n n n n n n n n n n n n                            5,1 24 25 , 3 0 0, 23 0.5 g 0.5 w [v ], g , ,n nnn n n n n n n n n n c с q f q c c c q                     5, 2 44 3 0 12 1 45 ,g ( ) ( ) 2 w [v ], ( ) [ ],n n n n n n n n n nf q f q f                   2 00 00 4 0 10 1, 1, 01 1, 1, , * * * * 65 0 g { [ ( )) ( )]}, w [ ] ( ) w ( , ) , 2 4 a n n n n n n n n kn q d d id f f d q                   21 23 3 1 * 321 23 41 43 2 21 43 41 23 23 23 23 41 43 2 0 2 { } 0 , 2 , ( ), { } 0 0 1 jm jm q q q q b q q q q q q q q q b q q                          b b     ,j n  kronecker symbol; nc  constants that are determined from conditions * 1 3 0 ( ) 0 a n nu d     (14) for the operator there is an inverse [19], which is an isomorphism in and allows the representation 11 2 * , 1 1 2 1 22 2 2 2 0 ( )2 w [ ( )] ( ) ( ) a t ll l l l ft dt d f d dtt t                  (15) ,v (ρ)jn     ( 0, 1, 2, 3, )n ,wl l  3( )r o. kryvyi et alii, frattura ed integrità strutturale, 52 (2020) 33-50; doi: 10.3221/igf-esis.52.04 38 the latter makes it possible, after reducing the matrix to a diagonal form, to obtain a solution to system (13): * * 1 2 12 1 3 02 2 * * 5, , 2 1 1 3 2 2 23 2 0 4 00 0 10 1 1 012 2 2 2 65 2 ( ) { 0.5 ( 2 )} w [ ( ) ( )] v ( ), 1, 2; u ( ) , 4 u ( ) {2 [ ( )) ( 3 n jn j n n j n n n n j n j n j n n n n n n n n n u b с b a b f s f s j c q a q d d id q a a                                                       1 1 )]}n n (16) where * * * * 1 1 24 2 44 1 1 25 2 45 5, 2 2 2 20 00 0, 10 1, 1, 01 1, 1, 65 ( 2 1)( 2 )!! , , . ( 2 1)!! 4 v ( ) {2 [ ( )) ( )]} 3 n j j j j j j n n n n n n n n s b q b q s b q b q n q d a a d id q                            equality 1,w ( , ) ( ) n n n n           which is true in 3( )r , and representation (17) allow to write expressions for the coefficients in the expansion (12) so ( 0, 1, 2,n    , 0 a  ) 1, 3, 3, 1 1, 2 3 1, 2 3v ( ) u , v ( ) w [u u ], v ( ) w [u u ].n n n n n n n n n n n n             (17) the number of compounds in the decomposition (12) depends both on the heat flux on it and on the form of inclusion, and is generally limited. in particular, for the axial symmetric inclusion and heat flux (10), three components will remain in decomposition (12), . the jumps in normal stresses and tangential displacements in this case can be represented as follows:   '0 1 11 0 11 52 2 2 221 2 2 2 2 2 2 2 0 2 3 4 2 2 2 2 2 2 2 0 3 2 4 ( ) ( [ ( )]) ( , ), 2 { [ ( )] } re( )[ (5 ( ) 3 ) ] re( ) , im( )( (3 5 ( )) z n i i xy i m m s l f s v a s u l f f a a q de m a a m a m e u a q de m a m a a m                                                              2 2 2 20 00 10 01 65 im( ) . 8 {2 ( cos sin ) } 3 i xy e q t d a d d a q               (18) here we use the notation 10 01 0 0 * 02 2 2 2 2 2 0 0 , , , ( ) ( )1 , [ ( )] , xy y x xy y x a a t d d id m m im i tf t dt ft d f l f dt d a dta t t t                              2 20 0( , ) ( ),x y x y         0,( ) [ ] ( )n n nf f  1, 0,1n o. kryvyi et alii, frattura ed integrità strutturale, 52 (2020) 33-50; doi: 10.3221/igf-esis.52.04 39 2 2 00 0 11* 0 11 0 11 1 3 65 65 * * 21 21 1 1 22 2 3 2 4 1* * 65 21 1 21 1 23 2 4 3 4 , ( ) re( ) re( ), 2 3 154 ( ) 44 1 , , , . 45 2( ) ( ) z i i xy p d q sf a a m s q s m m e de q qa s b g g b m m m m g q b g b g q                       in the case of a penny-shaped inclusion of thickness h     0 1 11 11 52 2 2 2 2 2 2 2 2 2 2 2 221 0 2 3 4 2 2 2 2 2 2 2 0 3 2 4 0 00 65 ( ) ( , ), 2 (1 ) re( )[ (5 ( ) 3 ) ] re( ) , im( )( (3 5 ( )) im( ) . {2 z i i xy i i xy m m s h s v a a hs u a a a q de m a a m a m e u a q de m a m a a m e q t d a q                                                              2 2 2 2 10 01 8 ( cos sin ) } 3 d d a        for z , x , y using conditions (6), the following expressions are obtained 21 2 2 2 * 5 0 00 6 7 0 10 8 7 0 01 83 3 , , , 8 z y x z y x p b m m f m a q d m m a q d m m a q d m a a a              (19) where * * * *2 2 11 21 11 21 5 11 21 11 21 6 65 * * * 721 1 11 21 21 1 11 7 8* * * * * * 6512 21 12 1 11 22 21 1 ( ) ( ), , 2 6 3( ) ( )4 , . 154( ) ( ) s b b s m s b b s m q mb g b s b g s m m qb b b g b b b g                   note that the exact solutions obtained are rigorously justified using the theory of generalized functions and the riemann boundary value problem. the reliability of the results obtained also confirms their coincidence with the results of [20], in which a particular case of this problem for a homogeneous transversely isotropic medium is considered. numerical results and their analysis. sing the solution obtained, we investigate the behavior the jump of normal stresses in the neighborhood of inclusion. we assume that the load applied to the inclusion is linearly distributed, and in polar coordinates has the form: , in this case, the resulting force and moments allow representations: , , . calculations were performed for the combination of materials. cadmium (material ), magnesium (material ), al2o3 (material ), zn (material ) tab. 1 shows the values of thermoelastic constants of these materials. calculations were performed with , for different values figs. 2-13, for the combination of materials m1 (upper half space),  m2 (lower half space), figs. 14-19, for the combination m3  m4. figs. 2, 4, 6, 8, 10, 12 shows the dependences on the polar angle or different values of the polar radius , figs. 3, 5, 7, 9, 11, 13 show dependencies on the polar radius or different values of the polar angle. in addition,   z       0 0 01 10( , ) (1 ( sin( ) cos( ))p p s s  2 0zp a p  4 0 100.25ym a p s  4 0 010.25xm a p s 1m 2m 3m 4m  01 101 3, 1 7 ,d d  01 101 5 , 1 7 ,s s  1a 0 ,q 0 ,p   z     z  u o. kryvyi et alii, frattura ed integrità strutturale, 52 (2020) 33-50; doi: 10.3221/igf-esis.52.04 40 in figs. 2, 3, the indicated dependences were obtained for ; in figs. 4, 5, 14, 15 with ; in figs. 6, 7 with ; in figs. 8, 9, 16, 17 with ; in figs. 10, 11, with ; in figs. 12, 13, 18, 19 with .. 11 210ijc n m  5 0 110 ( )j c  0j w mc material 11c 12c 13c 33c 44c 55c 1 2  3 1 2  3 1m 1.08 0.389 0.375 0.46 0.156 0.156 54 20.2 93 94 2m 0.5952 0.256 0.214 0.6147 0.1647 0.1647 27.7 20.2 159 160 3m 4.6 1.74 1.27 5.095 1.269 1.269 77 85 2.6 3.5 4m 1.581 0.314 0.474 0.614 0.4 0.4 6.43 1.6 119 119 table 1: material properties of transversely isotropic materials. figure 2: 0 00, 70p q  figure 3: 0 00, 70p q    figure 4: 0 00.5, 70p q  figure 5: 0 00.5, 70p q     0 00, 70p q  0 00.5, 70p q  0 00.7, 70p q  0 01, 70p q  0 00, 150p q  0 01, 150p q o. kryvyi et alii, frattura ed integrità strutturale, 52 (2020) 33-50; doi: 10.3221/igf-esis.52.04 41 figure 6: 0 00.7, 70p q  figure 7: 0 00.7, 70p q    figure 8: 0 01, 70p q  figure 9: 0 01, 70p q    figure 10: 0 00, 150p q  figure 11: 0 00, 150p q    o. kryvyi et alii, frattura ed integrità strutturale, 52 (2020) 33-50; doi: 10.3221/igf-esis.52.04 42 figure 12: 0 01, 150p q  figure 13: 0 01, 150p q    figure 14: 0 00.5, 70p q  figure 15: 0 00.5, 70p q    figure 16: 0 01, 70p q  figure 17: 0 01, 70p q    o. kryvyi et alii, frattura ed integrità strutturale, 52 (2020) 33-50; doi: 10.3221/igf-esis.52.04 43 figure 18: 0 01, 150p q  figure 19: 0 01, 150p q    the purpose of the calculations was to establish the influence on the distribution of normal stresses in the neighborhood of the inclusion of the force and temperature fields, as well as the inhomogeneity of the matrix.. the degree of heterogeneity of the matrix in the direction perpendicular to the inclusion, the coefficient are determines: which characterizes the difference between the elastic properties of half-spaces in the direction of the axis z. so, for the combination of materials m1-m2, the value , for the combination m3-m4, the value , i.e., the elastic properties of the half spaces in the z-axis direction, for the second combination m3-m4 are much more different than for the first m1-m2. it has been established (see figs. 2, 3, and 10, 11) that in the absence of force action with the growth of thermal radiation, an increase in stress and a change in the nature of its distribution are observed, which is obviously due to the inhomogeneity of the medium. with fixed thermal radiation and growthing of the force loading for the first combination: , (see figs. 2, 4, 6, 8 and 3, 5, 7, 9) a significant change in the direction of the gradient of normal stresses are observed, while for the second combination, (figs. 14, 16 and 15, 17) such changes are less pronounced. obviously, this regularity is explained by a much greater rigidity (almost an order) of the material of the upper half-space for the second combination, which leads to a more stable direction of increase in stresses. however, in this case, the opposite quantitative picture of the stress change is observed (see figs. 12, 13 and 18, 19): for the second combination of materials, the normal stresses are four times higher for the same values of the parameters of the force and heat exposure. note that the regularities found could be identified due to the general non-axisymmetric formulation of the problem. conclusions n accurate solution to the non-axisymmetric problem of circular heat radiating inclusion at arbitrary loading, which is in smooth contact with different transversely isotropic spaces, has been designed. the latter allowed, in particular, to investigate the features of the field of normal stresses and their distribution around the inclusion. the resulting expressions for translational and circular movements , show that the translational movements depends on the resulting stress and the amount of heat flux, and the circular movements respective to their resulting moments , as well as the heat flux. the proposed approach allows one to obtain the exact solutions of nonaxisymmetric problems of stationary thermoelasticity for interphase inclusions for other types of contact interaction (perfect contact, delamination, etc.) with various transversely isotropic half-spaces. the existence of such solutions makes it possible not only to identify critical loads and calculate structural elements for strength, but also to expand the theoretical base for the application of technical remote monitoring methods for the state 33 33 ,z с с   0 .7 4 8 3z  8.2981z  0 .7 4 8 3z  8.2981z  z  ,x y zp  ,x y ,x ym m a o. kryvyi et alii, frattura ed integrità strutturale, 52 (2020) 33-50; doi: 10.3221/igf-esis.52.04 44 of various structures for long-term operation [3]. in particular, methods of thermographic and acoustic control, based on knowledge of the distribution of stress and temperature gradients around various internal defects (cracks, inclusions for different types of contact interaction with the medium). these methods form the foundation of operation of various thermal imagers and flaw detectors [3]; therefore, the proposed solutions make it possible to improve the operation of remote monitoring the state of various structures. references [1] kit, g.s., o. p. sushko, o.p. (2011). problems of stationary heat conduction and thermoelasticity for a body with a heat permeable disk-shaped inclusion (crack), j math sci. 174(3), pp. 309-319. doi: 10.1007/s10958-011-0300-3. [2] kit, g. s., sushko, o. p. (2011). axially symmetric problems of stationary heat conduction and thermoelasticity for a body with thermally active or thermally insulated disk inclusion (crack), j math sci. 176(4), pp. 561-577. doi: 10.1007/s10958-011-0422-7. [3] marukha v.i., panasyuk v.v., sylovaniuk v.p. (2009). injection technologies of damaged long-term operation structures renewal. volume 12, in facture mechanic and strength of materials: reference book (editor-in-chief v.v. panasyuk) lviv: ph “spolom”, 262 c. [4] sylovanyuk, v.p., marukha, v.i., yukhym, r.y. (2010) strengthening of concrete as a result of filling of the pores and cavities, mater sci 46: pp. 70-75. doi: 10.1007/s11003-010-9265-5. [5] efimov, v.v., krivoj, a.f., popov, g.ya. (1998). problems on the stress concentration near a circular imperfection in a composite elastic medium, mechanics solids, 33(2), pp. 35-49. [6] li, x.f., fan, t.y. (2001). the asymptotic stress field for a rigid circular inclusion at the interface of two bonded dissimilar elastic half-space materials, international journal of solids and structures, 38, pp. 8019-8035. doi: org/10.1016/j.ijsolstr.2009.01.002/. [7] kaczynski, a., kozlowski, w. (2009). thermal stresses in an elastic space with a perfectly rigid flat inclusion under perpendicular heat flow, international journal of solids and structures, 46, pp. 1772-1777. doi: 10.1016/s0020-7683(01)00010-5. [8] kaczynski, a., monastyrsky, b. (2013). a rigid inclusion in an elastic space under the action of a uniform heat flow in the inclusion plane, international journal of solids and structures, 50(16-17), pp.2631-2640. doi: 10.1016/j.ijsolstr.2013.04.012. [9] kaczynski, a. (2016). on 3d symmetrical thermoelastic anticrack problems archives of mechanics, 68(2), pp. 99-112. [10] kaczynski, a. (2014). thermal stress analysis of a three-dimensional anticrack in a transversely isotropic solid, international journal of solids and structures, 51(13), pp. 2382-2389. doi: 10.1016/j.ijsolstr.2014.03.004. [11] kryvyy o.f. (2011). singular integral relations and equations for a piecewise homogeneous transversally isotropic space with interphase defects, j math sci. 176(4), pp 515--531. doi: 10.1007/s10958-011-0419-2. [12] kryvyy, o.f. (2012). interface circular inclusion under mixed conditions of interaction with a piecewise homogeneous transversally isotropic space, j math sci. 184(1), pp. 101-119. doi: 10.1007/s10958-012-0856-6. [13] kryvyi, o.f. (2012). interface crack in the inhomogeneous transversely isotropic space, mater sci. 47(6), pp. 726-736. doi: 10.1007/s11003-012-9450-9. [14] kryvyi, o.f. (2014). delaminated interface inclusion in a piecewise homogeneous transversely isotropic space, mater sci. 50(2), pp. 245-253. doi: 10.1007/s11003-014-9714-7. [15] kryvyy, o. (2009). the discontinuous solution for the piece-homogeneous transversal isotropic medium, operator theory: advances and applications, 191. pp. 387 – 398. doi: 10.1007/978-3-7643-9921-4_25. [16] mikhas’kiv, v.v. & stasyuk, b.m. (2015) elastic state of a sliding short fiber inclusion in three-dimensional matrix, int appl mech, 51(6), pp. 640-647. doi: 10.1007/s10778-015-0720-8 [17] panasyuk, v.v., stadnyk m. m., sylovaniuk, v.p. (1986) концентрация напряжений в трехмерных телах с тонкими включениями. к.: наук. думка. [18] krivoi, a.f., radiollo, m.v. (1984) specific features of the stress field near inclusions in a composite anisotropic plane, izv. akad. nauk sssr, mekh. tverd. tela, 3. pp. 84-92. [19] popov g.ya. (1982). the stress concentration near punches, sections, thin inclusions and supports. m.: nauka. [20] selvadurai a.p.s. (1980) asymmetric displacements of a rigid disc inclusion embedded in a transversely isotropic elastic medium of infinite extent, int. j. engng sci., 18 (7), pp. 979-986, doi: 10.1016/ 0020-7225(80)90070-1. [21] nowacki, w. (1986). thermoelasticity (2nd ed.). warszawa: pwn-polish scientific publishers. 25, 373 o. kryvyi et alii, frattura ed integrità strutturale, 52 (2020) 33-50; doi: 10.3221/igf-esis.52.04 45 [22] haojiang ding, weiqiu chen, l. zhang (2006). elasticity of transversely isotropic materials published by springer, p.o. box 17, 3300 aa dordrecht, the netherlands. doi: 10.1007/1-4020-4034-2. appendix a: construction of a discontinuous solution and singular integral relations for a piecewise homogeneous transversely isotropic body in 3( )  elative to the components of the displacement vector 3 33{ } { }j ju   u and temperature t using the duhamelneumann relations [21], we obtain, with 0,z  system of differential equations    1 2 3 1 2 3, , , , , 0, 0d t p t z        u β (a.1) where 3 2 2 2 1 2 3 1 2 3 3 1 2[ , , ] { } , [ , , ] ( ),kjd l p              1 2 3, , x y z            2 2 2 2 2 11 11 1 66 2 44 3 12 12 66 12 13 44 13 13, ( ) , ( ) , jk kjl c c c l c c l c c l l             2 2 2 2 2 2 2 22 66 1 11 2 44 3 23 44 23 23 33 55 1 44 2 33 3, ( ) , ,l c c c l c c l c c c               1 3 23 13 55 44 22 11, θ( ) θ( ) , θ( ) θ( ) , , ,kj kj kj j j jc z c z c z z c c c c c c                   1 2 3{ , , } , θ( ) θ( ) t j j jz z          β , 1 2  , θ( ) θ( )j j jz z       , 1 11 1 12 2 13 3 ,c c c       3 13 1 23 2 33 3c c c       , k jc   elastic constants, respectively, of the upper and lower half-spaces. other components of the vector v from (1.2) can be found by the formulas       1 13 1 1 2 2 33 3 3 3 2 44 3 2 2 3 3 44 1 3 3 1 8 3 , , , z c u u с u t c u u c u u k t                       (a.2) based on the representation of the solutions of eqns. (a.1) for a homogeneous space [22], the components of the vector v are 0 1 2 3[ , , , ], 1, 8, 0j j j z        (a.3) here we use the notation 0 1 2 3 0 1 2 3 0 1 2 3[ , , , ] θ( ) [ , , , ] θ( ) [ , , , ]j j jz z                   2 2 1 0 1 2 3 3 0 [ , , , ] k k k            , 2 6 0 1 2 3 1 3 0 [ , , , ] ,k k k            2 2 2 1 0 1 2 3 44 3 3 1 23 1 1 0 [ , , , ] (( 1) ), 1, 1, 2jj j k k k k k c j                         r o. kryvyi et alii, frattura ed integrità strutturale, 52 (2020) 33-50; doi: 10.3221/igf-esis.52.04 46 2 1 3 0 1 2 3 3 3 0 [ , , , ] ( 1) , 1, 2jj j j k k j                2 7 0 1 2 3 02 3 0[ , , , ]          , 28 0 1 2 3 02 3 0[ , , , ]        2 2 2θ( ) θ( ) ,j j jz z       1 1 1θ( ) θ( ) ,j j jz z       0,1, 2j  , 2 2 2 13 33 1 3 2 1 2 1 1 ( ) ( ), , 0,1, 2 j j j j j j j b a c c j b a                          2 2 0 33 44 0 11 33 13 13 44 11 44 02 12 222 1 0 1 ( ( ( 2 ))) , 0 ( ) c c c c c c c c c b a                             , 1 3 13 44 1 33( ) ,b c c c         2 3 44 ,b c    1 1 44 ,a c   2 3 11 1 13 44( )a c c c         , 2 1 0 1 3( ) ( ) ,k k     2 13 66 44( ) ( ) ,c c     constants j  ( 1, 2j  ) are solutions of equations 4 2 33 44 13 13 44 11 33 11 44( ) [ ( 2 ) ]( ) 0.j jc c c c c c c c c                 the functions , 0,1, 2, 3j j  satisfy the differential equations:  1 2 3, , 0, 0j jp z     (a.4) θ( ) θ( ) ,j j jp z p z p     2 2 2 23 1 2( ) ( )j jp         , 2 2 2θ( )( ) θ( )( )j j jz z       . following [15] we let's pass in the eqns. (a.4) to the space of generalized functions 3( ),  as a result, we obtain boundary value problems for the functions ,( 0,1, 2, 3)j j    1 1 3 1 2 3 3 2 0 [ , , ] , ( ) , ( )k kj j j j j j k p f f z                 (a.5) 3 0 1 2 3 0 1 2 3[ , , , ] [ , , , ] ( , ), ( ), 1, 8,j j j jx y j                              (a.6) we obtain operators j  by replacing in operators j  ordinary derivatives k with generalized ones k . applying the three-dimensional fourier transform to eqns. (a.5) we obtain the riemann problem in the space 3( ),  by parameter 3 to determine the transformants of the functions , 0,1, 2, 3j j  . , 0, 3j j jp p q j          (a.7) o. kryvyi et alii, frattura ed integrità strutturale, 52 (2020) 33-50; doi: 10.3221/igf-esis.52.04 47 to solve the riemann problem (a.7) using the method proposed in [13], we obtain        1 01 1 2 0 3 ( , ) kk j jk j k j j j ir r                       (a.8) where 0 1 2( , )jk    unknown functions; 2 2 1 2r    , j ji    , 0,1, 2, 3j  . unknown functions 0jk , following [15], are expressed through transformants of jumps of thermoelastic characteristics: 1 2 2( , ) f [ ( , )]j j x y      , which allowed, using formulas (a.3), to obtain such expressions for the transformant 1 2 2( , , ) ( ) [ ]j jv z z f       : 3 1, 2, 1 3, 1 1 1, 1 1, 2 2 1 3 1, 1 4 2 5 1 4 , 5, 6, 1 1, 6 1, 7 1, 8 ( ) ( ) { (( ) ( ) ) (( ) ( ) ) }, k k k k k k k k v z z e q r q r i i q i i q r q q r                                                 3 3 2 2 2, 2 1, 2 2, 1, 2 2 2 1 2, 1 3 1,3 1 2 3 1 2, 3 1,3 1 1 3 1 3, 2, 1 2 1 2 4 1 2, 3 1,3 5 2 1 1 ( ) ( ){ [ ( ) ( ) ] ( )( ) [ ] ( )( ) [ ] [ ( ) k k k k k k k k k k v z z r i e q i e q i i r e q e q i i r e q e q r i e q                                                                 3 3, 2 2, 2, 1 3 1,3 1 3 1, 1 4 , 5, 1 6, 2 1 2, 2 1 2, 2 6 2, 2 7 2, 2 8 1 ( ) ] [ ( ) ( ) ( ) ( ) ]}, k k k k k k k k i e q e q i r q i q i r q i r                                          3 3 3 2, 1, 3 2 2, 2 1, 4 2 1 2 1 3, 3 2,3 3 1 1 3, 3 2 2,3 1 1 3 2 2 3, 2 2, 2 4 1 1 3, 2 3 2,3 2 1 5 1 ( ) ( ){( )( ) [ ] [( ) ( ) ] [( ) ( ) ] ( )( ) k k k k k k k k k v z z i i r e q e q r i e q e i q r i e q i e q i i r                                                                3 3, 2, 1 3, 3 2,3 1 3 1, 2 4 , 1 5, 2 6, 3 1 3, 1 1 3, 1 6 3, 1 7 3, 1 8 1 [ ] [ ( ) ( ) ( ) ( ) ]}, k k k k k k k k k e q e q e q i r q i r q i r q i r                                          3 1, 1 2 2 2, 6 1 4 , 1 2 2 1 3 4 , 1 1 1 3, 4 , 5, 1 6, 2 1 4 2 5 4 , 4 , 6 4 , 7 4 , 8 ( ) ( ) { (( ) ( ) ) (( ) ( ) ) }, k k k k k k k k v z z e q r i r i r q i r i r q q q r q r                                                     3 3 5 1 6 5 6 7 1 7 5, 8 5, 8 1 7 6, 8 6, 1 1 ( ) ( ) { }, ( ) ( ) { }k k k k k k k k v z z e q r q v z z e r q q                        (a.9) where ,ki rzke e     2, 2, 30 31 1, 1, 30 31 , jks                        s s s s     ,   * * 11 121 * * * *, 1,2 21 22 ,jk j k s s s s s             s s       o. kryvyi et alii, frattura ed integrità strutturale, 52 (2020) 33-50; doi: 10.3221/igf-esis.52.04 48   1, 1, 1, 1, 1, 1, 00 01 10 11 20 21 2, 2, 2, 2, 2, 2, 00 01 10 11 20 21 1, 1, 1, 1, 1, 1, 00 01 10 11 20 21 2, 2, 2, 2, 2, 2, 00 01 10 11 20 21 3, 3, 3, 3, 3, 3, 00 01 10 11 20 21 3 00 , jks                                                                     s s s s  1 * * , 3, 3, 3, 3, 3, 01 10 11 20 21 , jks                                   s s ,  1, , k j jk j j i                 12, , k j j j jk j j i i                    2 23, ( ) k j j j jk j j i               , 2, 1,3 44 3 ( ),k k kc i         1, 1, 2, 3,13 33 3jk jk j jk jkc c i                , 2, 2, 1,44 [ ( )]jk jk jk jc          , 3, 3,3( )jk j jki        , 2 4 6 2 , * , * , * , * 1, 2, 3, 3, 1 3 5 1 , , ,p p p pk kn np k kn np k kn np k kn np n n n n q s s q s s q s s q s s                     the formulas for the definition 3 ( )v z  and 5 ( )v z  we obtain respectively from the formulas for 3 ( )v z  and 5 ( )v z  , by permutations 2 3    , 4 5    , 1 2  . using expressions (a.9), we compose the transformants of the sums of limiting values: 0z   thermoelastic characteristics of the space, and proceed to the originals. as a result, we obtain singular integral relations in 3( ),  connecting jumps and the sum of the components of the stress tensor, displacement vectors, temperature and heat flux in the plane: 5 1 11 1 13 3 15 7 12 2 2 3 1 14 6 16 83 4 0 0 00 1 1 1 1 1 ( , ) { [ ] } , 2 j j j x y q q q q q q dtd r r rr                                 2 22 2 24 2 6 21 1 2 2 22 1 11 2 22 3 22 2 2 0 0 0 0 2 2 2 23 4 12 5 23 2 12 1 25 7 2 26 8 2 0 0 0 0 0 1 1 ( , ) { [ ] 2 1 1 1 1 [ ] } , yx t x t x y q q q q q q r r r r y q q q q q dtd r r r r r                                                        3 22 3 24 1 6 22 2 1 3 22 2 11 12 2 2 0 0 0 2 2 2 4 23 1 12 2 21 1 1 23 5 12 25 7 1 26 8 2 0 0 0 0 0 0 1 ( , ) { [ ] 2 1 1 1 1 1 [ ] } , y y x t x y q q q q q r r r x t q q q q q q dtd r r r r r r                                                          4 31 1 32 2 2 3 32 1 21 2 34 6 12 0 0 0 0 0 4 33 2 22 1 33 5 2 35 7 36 8 33 42 2 2 2 0 0 0 0 0 1 1 ( , ) { [ ] 2 [ ] } , y yx t x t x y q q q q q r r r r r y x t x t x t x t q q q q q dtd q r r r r r                                                            o. kryvyi et alii, frattura ed integrità strutturale, 52 (2020) 33-50; doi: 10.3221/igf-esis.52.04 49 5 31 1 2 32 2 21 1 32 3 1 33 4 12 2 0 0 0 0 0 5 33 1 22 2 34 6 2 35 7 36 8 1 2 33 52 2 2 0 0 0 0 0 1 ( , ) { [ ] 2 1 [ ] } , y y y yx t x y q q q q q r r r r r y y yx t q q q q q d d q r r r r r                                                                6 44 6 41 1 42 2 3 43 4 1 5 22 2 0 0 00 0 45 7 46 8 0 0 1 1 1 1 ( , ) { [ ] [ ] 2 1 ln( )} , y x t x y q q q q r r rr r q q r dtd r                                     56 65 7 55 7 8 8 66 8 7 3 0 0 1 1 ( , ) , ( , ) , 2 2 q q x y q dtd x y q dtd r r                        (a.10) where 6 2 2 * , , 0 ,3 ,3 1 ( ) ( ) , , , ,p pkp kn np kp kp kp kp k k n r x t y q s s q q q q q q                    22 22 11 23 23 12 32 32 21 33 33 22, , , .q q q q q q q q q q q q               differentiation operators in space 3( ),  have readily verifiable properties  2 1 2 1 1 22 2 2 2 0 0 0 0 0 0 , , 2 , , y y yx t x t x t x t y r r r r r r                       2 2 1 2 1 2 0 1 23 0 0 0 00 0 0 1 1 1 1 1 , , d d , d yx t r i r r r rr r r               2 0 1 1 d d 0, ( ) ( , .x t i y r            (a.11) using properties (a.11), with respect to complex combinations of jumps and sums: 3 2 4 5, ,i u i              ratio (a.10) can be rewritten as 13 12 1 11 1 14 6 15 7 16 8(d d ) (d [ ] d [ ]) d d [ ] [ ], 2 2 q q q u u q q q                          223 2322 22 24 6 21 1 0 25 7 26 0 8 d d [ ] d [ ] dd [ ] d [ ] 2 2 2 2 d [ ] [ ], q qq q q q u u q q                                   223 2322 22 24 6 21 1 0 25 7 26 0 8 d d [ ] d [ ] dd [ ] d [ ] 2 2 2 2 d [ ] [ ], q qq q q q u u q q                                   o. kryvyi et alii, frattura ed integrità strutturale, 52 (2020) 33-50; doi: 10.3221/igf-esis.52.04 50 33 32 32 33 31 0 1 0 34 6 35 0 7 36 8 d d d 2 2 2 2 , q q q q u u q u q q q                                                            33 32 32 33 31 0 1 0 34 6 35 0 7 36 8 [ ] [ ] d [ ] d [ ] d [ ] 2 2 2 2 [ ] [ ], q q q q u u q u q q q                                    42 43 6 44 6 41 1 0 0 45 7 46 1 8 [ ] [ [ ] [ ]] [d [ ] d [ ]] 2 2 [ ] [ ], q q q q u u q q                                 7 55 7 56 8 8 66 8 65 7[ ], d d [ ].q q q q                 (a.12) here we use the notation 0 1 0 0 ( , ) ( , )1 1 1 [ ] , [ ] , [ ] ( , ) ln( ) . 2 2 2 j j j j j j t t dtd dtd t r dtd r                                  the obtained sis (a.9) and (a.11) generalize the sis obtained in [15], and allow thermoelasticity problems on interfacial defects in a piecewise homogeneous transversely isotropic space to be reduced directly to sie systems. << /ascii85encodepages false /allowtransparency false /autopositionepsfiles true /autorotatepages /none /binding 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<feff04120438043a043e0440043804410442043e043204430439044204350020044604560020043f043004400430043c043504420440043800200434043b044f0020044104420432043e04400435043d043d044f00200434043e043a0443043c0435043d044204560432002000410064006f006200650020005000440046002c0020044f043a04560020043d04300439043a04400430044904350020043f045604340445043e0434044f0442044c00200434043b044f0020043204380441043e043a043e044f043a04560441043d043e0433043e0020043f0435044004350434043404400443043a043e0432043e0433043e0020043404400443043a0443002e00200020042104420432043e04400435043d045600200434043e043a0443043c0435043d0442043800200050004400460020043c043e0436043d04300020043204560434043a0440043804420438002004430020004100630072006f006200610074002004420430002000410064006f00620065002000520065006100640065007200200035002e0030002004300431043e0020043f04560437043d04560448043e04570020043204350440044104560457002e> /enu (use these settings to create adobe pdf documents best suited for high-quality prepress printing. created pdf documents can be opened with acrobat and adobe reader 5.0 and later.) >> /namespace [ (adobe) (common) (1.0) ] /othernamespaces [ << /asreaderspreads false /cropimagestoframes true /errorcontrol /warnandcontinue /flattenerignorespreadoverrides false /includeguidesgrids false /includenonprinting false /includeslug false /namespace [ (adobe) (indesign) (4.0) ] /omitplacedbitmaps false /omitplacedeps false /omitplacedpdf false /simulateoverprint /legacy >> << /addbleedmarks false /addcolorbars false /addcropmarks false /addpageinfo false /addregmarks false /convertcolors /converttocmyk /destinationprofilename () /destinationprofileselector /documentcmyk /downsample16bitimages true /flattenerpreset << /presetselector /mediumresolution >> /formelements false /generatestructure false /includebookmarks false /includehyperlinks false /includeinteractive false /includelayers false /includeprofiles false /multimediahandling /useobjectsettings /namespace [ (adobe) (creativesuite) (2.0) ] /pdfxoutputintentprofileselector /documentcmyk /preserveediting true /untaggedcmykhandling /leaveuntagged /untaggedrgbhandling /usedocumentprofile /usedocumentbleed false >> ] >> setdistillerparams << /hwresolution [2400 2400] /pagesize [612.000 792.000] >> setpagedevice microsoft word numero_30_art_25 g. meneghetti et alii, frattura ed integrità strutturale, 30 (2014) 191-200; doi: 10.3221/igf-esis.30.25 191 focussed on: fracture and structural integrity related issues the specific heat loss combined with the thermoelastic effect for an experimental analysis of the mean stress influence on axial fatigue of stainless steel plain specimens g. meneghetti, m. ricotta, b. atzori university of padova, department of industrial engineering, via venezia 1, 35131, padova, italy giovanni.meneghetti@unipd.it, mauro.ricotta@unipd.it; bruno.atzori@unipd.it abstract. the energy dissipated to the surroundings as heat in a unit volume of material per cycle, q, was recently proposed by the authors as fatigue damage index and it was successfully applied to correlate fatigue data obtained by carrying out fully reversed stressand strain-controlled fatigue tests on aisi 304l stainless steel plain and notched specimens. the use of the q parameter to analyse the experimental results led to the definition of a scatter band having constant slope from the lowto the high-cycle fatigue regime. in this paper the energy approach is extended to analyse the influence of mean stress on the axial fatigue behaviour of unnotched cold drawn aisi 304l stainless steel bars. in view of this, stress controlled fatigue tests on plain specimens at different load ratios r (r=-1; r=0.1; r=0.5) were carried out. a new energy parameter is defined to account for the mean stress effect, which combines the specific heat loss q and the relative temperature variation due to the thermoelastic effect corresponding to the achievement of the maximum stress level of the stress cycle. the new two-parameter approach was able to rationalise the mean stress effect observed experimentally. it is worth noting that the results found in the present contribution are meant to be specific for the material and testing condition investigated here. keywords. dissipated energy density; mean stress effect; fatigue; thermoelastic temperature; fatigue life estimation; thermometric methods. introduction he fatigue damage monitoring and the fatigue life assessment of materials and components can be experimentally performed by using the surface temperature. in fact for a given set of boundary conditions (i.e. load test frequency, room temperature, specimen geometry), the temperature of a material undergoing fatigue increases as the applied stress amplitude increases. stoymeyer [1] adopted the dissipated energy to evaluate the fatigue limit of plain steel specimens; in particular he measured the temperature increase of a steady stream of water covering the specimen. more recently, curti et al. proposed the “limit temperature” [2] and later la rosa and risitano suggested an experimental procedure for the rapid determination of the material fatigue limit [3], based on the temperature measurement by using an infrared camera. recently risitano et al. proposed a fatigue life assessment method valid for variable amplitude fatigue [4] and a thermographic method to evaluate the material fatigue limit by means of a static tensile test [5]. curà et al. developed a methodology for the rapid determination of the material fatigue limit, based on an iterative method to t g. meneghetti et alii, frattura ed integrità strutturale, 30 (2014) 191-200; doi: 10.3221/igf-esis.30.25 192 recognise the temperature measurements obtained from specimens loaded by stress amplitude higher or lower than the fatigue limit [6]. giancane et al. analysed the non-uniform temperature distribution in the case of aluminium alloys [7]. in ref. [8] an experimental procedure was proposed to evaluate the energy dissipated as heat in a unit volume of material per cycle, q, starting from temperature measurements. the q parameter was then adopted as a new experimental damage index useful for fatigue life estimations. recently, the use of the q parameter enabled us to rationalise several experimental results generated from constant amplitude, push-pull, stressor strain-controlled fatigue tests on plain and notched hot rolled aisi 304 l stainless steel specimens [9, 10] as well as from cold drawn un-notched bars of the same steel under fully-reversed axial and torsional fatigue loadings [11]. here we recall that notched specimens had either lateral uor vnotches, with root radii equal to 3 or 5 mm, or a central hole with radius equal to 8 mm. fig. 1 shows the axial and the torsional fatigue test results in terms of net-section stress amplitude an or a, respectively, the mean fatigue curves and the 10%-90% scatter bands. the figure reports also the inverse slope k of the curves, the stress-based scatter index t=a,10%/a,90% (t) and the life-based scatter index tn, (tn,). in the case of strain-controlled fatigue tests, the stress amplitude reported in fig. 1 is the value measured at half the fatigue life. fig. 2 shows the same fatigue data re-analysed in terms of the q parameter. in particular, the 10%-90% scatter band shown in the figure was fitted only on the fatigue data published in [10]. however, fig. 2 shows that fatigue data obtained under axial and torsional fatigue tests [11] can be interpreted by the same scatter band. more than 120 fatigue data are included in the figure. 100 700 300  an ,  a [m p a] 200 500 102 103 104 105 106 107 nf, number of cycles to failure strain controlled stair case: broken, unbroken plain material k=17.2; t=1.19; tn,=20.0 hole, r=8 mm: k=8.9; t=1.18; tn,=4.3 u-notch, r=5 mm v-notch, r=3 mm k=5.8 t=1.30 tn,=4.5 load ratio: -1 axial load: k=18.9, t=1.13, tn,=10.0 torsional load: k=18.7, t=1.13, tn,=9.02 scatter bands: 10% 90% survival probabilities. data from [9,10]data from [11] na figure 1: fatigue data analysed in terms of net-section stress amplitude. scatter bands are defined for 10% and 90% survival probabilities. it is worth noting that the q parameter is independent of the mechanical and thermal boundary conditions such as the specimen’s geometry, load test frequency and room temperature [10]. by applying the energy balance equation, it was shown [8] that q can be evaluated by stopping the fatigue test and then measuring the cooling gradient immediately after the test has been interrupted, according to eq. (1): t q f c t         (1) where f is the load test frequency, t is temperature, t is time,  is the material density c is the material specific heat. concerning the stainless steel material analysed in the present paper, the material density  and the specific heat c were experimentally measured and resulted 7940 kg/m3 and 507 j/(kg k), respectively [12]. according to eq. (1), it is possible to evaluate the thermal power (q·f) dissipated in steady state conditions by measuring the cooling gradient just after the g. meneghetti et alii, frattura ed integrità strutturale, 30 (2014) 191-200; doi: 10.3221/igf-esis.30.25 193 test interruption. eq. (1) enables one to measure readily and in-situ the specific heat loss q at any point of a specimen or a component undergoing fatigue loadings. 0.01 0.1 1 10 102 103 104 105 106 107 nf, number of cycles to failure strain controlled plain material hole, r=8 mm u-notch, r=5 mm v-notch, r=3 mm load ratio: -1 qa,50%=0.133 [mj/(m 3cycle)] tq=2.04 scatter bands:10% 90% survival probabilities, from [10] data from [9,10] tn,q=4.50 stair case: broken; unbroken 1 2.11 axial load torsional load data from [11] q [ m j/ (m 3 · cy cl e) ] na figure 2: fatigue data shown in fig. 1 analysed in terms of energy released as heat by a unit volume of material per cycle. scatter bands are defined for 10 and 90% survival probabilities. recently, the energy-based approach has been extended in order to take into account the presence of non-zero mean stresses [13]. in literature sound stress/strain-based approaches are available that include the influence of mean stresses; a common feature of them is to combine different mechanical parameters. smith, watson and topper [14] proposed the swt parameter to extend the manson-coffin approach: max aswt e    (2) where a is the applied strain amplitude, e the material elastic modulus, max the maximum stress. among the fracture mechanics-based approaches, walker [15] and more recently vasudevan et al. [16], kujawsky [17, 18] and stoychev and kujawsky [19] proposed the parameter:  1 maxeqvk k k                (3) to rationalise fatigue crack growth rate data, characterised by different values of the mean stress. in eq. (3), k and kmax are the range and the maximum value of the stress intensity factor, respectively, and  is a best fitting parameter to determine from the experimental data. eq. (2) and (3) show that the driving force of the crack nucleation, eq. (2), and propagation, eq. (3), is characterised by two parameters: the amplitude (or range) of the driving force and its level (i.e. its maximum value). both the parameters involved in eq. (2) and eq. (3) were interpreted by the authors of this paper in terms of energy, i.e. the hypothesis was formed that the fatigue strength depends on a thermodynamic exchange variable as well as on a state variable. after that, the q parameter was identified as the exchange variable, whereas the thermoelastic temperature tthe was assumed as the state variable. the thermoelastic temperature tthe is the temperature that would be achieved by the material when loaded at the maximum stress level of the fatigue cycle, max, in an adiabatic process. tthe can be evaluated analytically or experimentally by loading the material in its elastic field and then by extending the temperature-applied stress relation up to the max value. the applied stress rate must be properly set in order to reduce the heat transfer between material and the surroundings, i.e. to make the loading process adiabatic. as it will be discussed in a dedicated section, it was found that such nearly adiabatic conditions can be reached in standard laboratory tests, at least for the material analysed in this paper. g. meneghetti et alii, frattura ed integrità strutturale, 30 (2014) 191-200; doi: 10.3221/igf-esis.30.25 194 alternatively, the thermoelastic temperature tthe can be easily calculated from eq. 4, which relates tthe to the maximum applied stress [20]: max max 0 the m t k t c               (4) where t0 is the material temperature when the applied stress is equal to zero and  the material thermal expansion coefficient. therefore the new equation proposed in the present paper to rationalise the mean stress influence on axial fatigue of stainless steel plain specimens is:   f 0 n cost mh mthe f t q n q t               (5) where h and m are material constants to evaluate by fitting the experimental data. material, specimens’ geometry and test procedure he material selected for the experimental tests consisted of 25-mm-diameter aisi 304 l cold drawn bars, having a engineering tensile strength, rm, and an engineering proof stress, rp02, equal to 691 mpa and 468 mpa, respectively. the material adopted in this work is different from that analysed in [10], characterised by rm=700 mpa and rp02 = 315 mpa. as to the material analysed in the present paper, the mechanical properties, the chemical composition, the vickers hardness and the average grain size are listed in tab. 1 [11]. e [mpa] rp02 [mpa] rm [mpa] a [%] hv30 c [%] si [%] mn [%] cr [%] mo [%] ni [%] cu [%] average grain size* [m] 192200 468 691 43 199 0.013 0.58 1.81 18.00 0.44 8.00 0.55 35 table 1: aisi 304 l material properties (*according to astm e 112 [21]). constant amplitude, stress-controlled fatigue tests were carried out on a servo-hydraulic mfl machines equipped with a 250 kn load cell and a mts testar iim digital controller. three different load ratios r (r=-1, r=0.1 and r=0.5) were adopted. in the case of load ratio equal to r=-1 and r=0.1, the specimens’ geometry is shown in fig. 3a, whereas that adopted for r=0.5 is reported in fig. 3b. the load test frequency was selected in the range 1-30 hz and as high as possible in order to maintain the stabilised temperature of the material below 70°c during the whole fatigue test. then the fatigue test was suddenly stopped to measure the cooling gradient and to evaluate the q parameter, according to the experimental procedure proposed in [8]. the fatigue tests were run until the specimen’s failure or to 2 million cycles (runout specimen). 230 130 50 50 ø 2 5 r425 ø 1 5 (a) 230 130 50 50 ø 2 5 r285 ø 1 0 (b) figure 3: specimens’ geometry adopted for fatigue tests having a) load ratio r=-1 e r=0.1 and b) r=0.5. to evaluate the thermoelastic material constant km, eq. (4), load controlled ramps were executed at different load rates by means of a servo-hydraulic schenck hydropuls psa 100 machine equipped with a 100 kn load cell and a trio sistemi rt3 digital controller. during all tests, the specimen’s temperature was measured by using a copper-constantan thermocouple having diameter of 0.127 mm, which was fixed at the specimen’s centre by means of a silver-loaded conductive epoxy glue. temperature t g. meneghetti et alii, frattura ed integrità strutturale, 30 (2014) 191-200; doi: 10.3221/igf-esis.30.25 195 signals generated by the thermocouples were acquired by means of a data logger agilent technologies hp 34970a operating at a maximum sample frequency, facq, of 22 hz (accuracy equal to 0.02 °c). fatigue test results ig. 4 shows the fatigue test results and reports the mean curves in terms of the engineering stress amplitude a, the 10%-90% survival probability scatter bands, the inverse slope k, the reference fatigue strength a,50% evaluated at na= 2 million cycles with a survival probability equal to 50%, and the stressas well as the life-based scatter index t and tn, respectively. the experimental data were statistically re-analyzed under the hypothesis of log-normal distribution of the number of cycles to failure with a 95% confidence level. it can be seen that the fatigue behaviour of the analysed material is significantly affected by the load ratio: in fact a,50% evaluated under push-pull fatigue test (r=-1) is reduced of a factor equal to 1.27 and 1.86, in the case of r=0.1 and r=0.5, respectively. it is worth noting that in all fatigue tests carried out by imposing a load ratio equal to r=0.5 and in many tests conduced at r=0.1, the maximum stress was higher than the material proof stress. therefore, the cyclic material stabilisation was monitored by considering the axial displacement measured by the displacement transducer of the test machine. after stabilisation, the reduction of the specimen diameter ranged from 4.5% to 19.5% with respect to the initial diameter, depending on the applied stress amplitude. 100 103 104 105 106 107  a [m p a] 200 300 600 r=-1; k=18.7; a,50%=288 mpa; t=1.13; tn=9.83 r=0.1; k=22.6; a,50%=227 mpa; t=1.11; tn=10.6 r=0.5; k=22.7; a,50%=155 mpa nf, number of cycles to failure na figure 4: fatigue data analysed in terms of engineering stress amplitude for different load ratios. scatter bands are defined for 10% and 90% survival probabilities. energy-based fatigue test results n order to evaluate the evolution of q parameter, each fatigue test was interrupted several times. fig. 5 shows some characteristic examples of q values plotted against the number of cycles normalised with respect to the number of cycles to failure or, in the case of run-out specimens, with respect to 2 millions. one can observe that the q values span in a range between 0.01 and 5 mj/(m3·cycle) by considering the different load ratio analysed in this paper, in spite of a variation of a from 155 to 400 mpa. according to [8], the fatigue test results were re-analysed in terms of the characteristic value of q measured at 50% of the number of cycles to failure or, in the case of run-out specimens, at 1 million cycles. fig. 6 shows the results of the statistical analysis in the hypothesis of log-normal distribution of the number of cycles to failure nf and constant scatter with respect to the energy dissipation level. the mean and the 10% 90% survival probability curves fitting the experimental results with a confidence level of 95% have the following expression: cosk fq n t  (6) the figure reports the inverse slope k of the curves, the mean energy value qa,50% at the reference fatigue life na of two million cycles and the energyas well as the life-based scatter index tq and tn,q, respectively. fig. 6 shows that the data f i g. meneghetti et alii, frattura ed integrità strutturale, 30 (2014) 191-200; doi: 10.3221/igf-esis.30.25 196 obtained by carrying out fatigue tests at different load ratios cannot be rationalised in a single scatter band by using the q parameter. 0.1 1 0 0.25 0.5 0.75 1 n/nf r=-1 r=0.1 r=0.5 q [ m j/ (m 3 ·c y cl e) ] 10 0.01 figure 5: measured q trends against the number of cycles normalised with respect to the number of cycles to failure, nf. 0.1 1 10 103 104 105 106 107 nf, number of cycles to failure r=-1: k=1.98; qa,50%=0.133 mj/(m 3·cycle); tq=2.99; tn,q=8.75 r=0.1: k=3.08; qa,50%=0.026 mj/(m 3·cycle); tq=2.88; tn,q=26.0 q [ m j/ (m 3 · cy cl e) ] 0.01 r=0.5: k=5.51; qa,50%=0.012 mj/(m 3·cycle) na figure 6: fatigue data analysed in terms of energy released as heat by a unit volume of material per cycle. scatter bands are defined for 10 and 90% survival probabilities. experimental evaluation of the thermoelastic constant o experimentally evaluate the thermoelastic constant km (see eq. 4), load-controlled ramps at different load rates were carried out, aiming at the evaluation of the minimum stress-rate  required to achieve adiabatic test conditions. five stress rates were applied, namely  = 5, 19, 37, 54 and 73 mpa/s. the tests were conduced by applying an initial compressive stress equal to –150 mpa, followed by a ramp up to 150 mpa. the value of 150 mpa was chosen to guarantee the linear elastic behaviour of the analysed material. the adopted procedure can be summarised as follows: application of a compressive stress equal to –150 mpa applied to the specimen; holding of the compressive stress to allow for material thermal equilibrium with the surroundings (reference temperature t0); execution of a tensile ramp up to 150 mpa with given  value and measurement of the corresponding temperature drop. since t0 is the reference temperature at a stress of –150 mpa, the thermoelastic temperature tthe reached at the end of the test will be referred to a stress of 300 mpa. fig. 7 shows as an example the results of a test conduced at  = 54 mpa/s. within the time window (tf-ti), it can be observed that the temperature decreases from the initial value t0=301.25 k. the stress range adopted to evaluate km corresponds to the stress variation in the time window t=tf-ti, (=(tf)-(ti)), that is 297 mpa in fig. 7. t g. meneghetti et alii, frattura ed integrità strutturale, 30 (2014) 191-200; doi: 10.3221/igf-esis.30.25 197 -150 -100 -50 0 50 100 150 -1 t=ti 1 2 3 4 5 -1.2·10-3 -10-3 -8·10-4 -6·10-4 -4·10-4 -2·10-4 0 2·10-4  [ m p a] t th e/ t 0 time [s] = 297 mpa mpa/s 54 t0=301.25 k t=tf figure 7: example of static test and measured thermoelastic temperature variation. the km values measured in all static tests are collected in fig. 8. it can be observed that by increasing the applied stress rate, the scatter of the km values decreases and that a 5.4% variation of the km mean value was noticed (from 3.86·10-12 to 3.65·10-12 pa-1), by increasing the stress rate of a factor about 2 (from 37 to 73 mpa/s). therefore from an engineering point of view, it can be concluded that adiabatic conditions can be reached by imposing a stress rate higher than 37 mpa/s, at least for the material and test conditions analysed in this paper. the final km value adopted was equal to 3.75·10-12 pa-1, being the mean value measured for  =37, 54 e 73 mpa/s; it is in good agreement with the theoretical value of 3.97·10-12 pa-1 that can be calculated by using eq. (4) and assuming =16·10-6 k-1. 3 3.25 3.5 3.75 4 4.25 4.5 4.75 5 0 20 40 60 80 5 mpa/s 19 mpa/s 37 mpa/s 54 mpa/s 73 mpa/s k m [ 1 0 -1 2 p a1 ] [mpa/s]  figure 8: experimental evaluation of the thermoelastic constant km of the analysed material. the new two-parameter, energy-based approach applied to the experimental results fter evaluating the thermoelastic constant km, the thermoelastic temperature relevant to each specimen was calculated according to eq. (4). having in hands q, 0 thet t and the number of cycles to failure nf for each coupon, the parameters h and m of eq. (5) were calculated. in more detail, the experimental results were plotted in a q0/thet t plane, for a given number of cycles to failure, as shown in fig. 9. by considering the available number of data and independently of the load ratio r, the fatigue results were divided in 4 groups, characterized by a different range of the number of cycles to failure (nf ≤ 10000 cycles; 20000 ≤ nf ≤ 60000 cycles; 80000 ≤ nf ≤ 120000 cycles e 300000 ≤ nf ≤ 800000 cycles). a g. meneghetti et alii, frattura ed integrità strutturale, 30 (2014) 191-200; doi: 10.3221/igf-esis.30.25 198 0.01 0.1 1 10 10-3 5·10-3 q [ m j/ (m 3 ·c y cl e) ] 0t thet 60000fn20000  120000fn80000  800000fn300000  h=6.05 h=4.36 h=4.57 h=4.66 h=3.63 10000n2900 f  figure 9: evaluation of the h constant, eq. (5). dashed regression lines in fig. 9 (a log-log diagram) were calculated for each group. by considering the reduced variation among the h values from an engineering point of view, a unique h value was calculated and resulted equal to 4.57 (continuous line in fig. 9). after that, all available data were plotted in a q -nf plane (see eq. 5, h=4.57) and re-analyzed as a single population, independently of the load ratio, under the hypothesis of log-normal distribution of the number of cycles to failure and with a 95% confidence level. the result is shown in fig. 10, where the mean line, the 10% 90% survival probability curves, the inverse slope m, the equivalent energy q t and the life-scatter tn indexes are plotted. 10-3 10-2 10-1 1 10 103 104 105 106 107 nf, number of cycles to failure q [ 1 0 -1 2 m j/ (m 3 · cy cl e) ] m = 1.69 tn = 10.7 tq = 4.07 na qa,50%=0.0148·10 -12 [mj/m3·cycle)] r-1 r=0.1 r=0.5 5.69·10-16 [mj/m3·cycle)] figure 10: fatigue data of fig. 4 analysed in terms of the equivalent energy released as heat by a unit volume of material per cycle q . scatter bands are defined for 10 and 90% survival probabilities. by considering the stress amplitude as well as the dissipated energy-based curves (plotted in fig. 4 and fig. 6, respectively), one can appreciate that the new q parameter collapses all the fatigue data into a single scatter band having a constant slope from 103 to 2·106 cycles, despite the different load ratios involved. moreover, it is worth noting that the scatter index tn in fig. 10 is very close to that relevant to the “r=-1” and “r=0.1” series presented in terms of stress amplitude (see fig. 4) as well as to the “r=-1” series expressed in terms of q parameter (see fig. 6). g. meneghetti et alii, frattura ed integrità strutturale, 30 (2014) 191-200; doi: 10.3221/igf-esis.30.25 199 conclusions n this paper a two parameter, energy-based approach has been presented to rationalise the influence of the load ratio on the fatigue behaviour of aisi 304 l cold drawn steel bars. three different load ratios (namely r=-1, r=0.1 and r=0.5) were applied in the constant amplitude fatigue tests. the mean stress influence was considered by combing the specific heat loss with the thermoelastic temperature relevant to the maximum stress of the load cycle. the new twoparameter, energy-based method enabled us to collapse all fatigue test results in a single scatter band having a constant slope from 103 to 2·106 cycles. the scatter index resulted equal to that of single test series expressed in terms of stress amplitude. static tests at different stress rate were carried out to experimentally measure the thermoelastic constant of the material, which is needed to calculate the thermoelastic temperature. it was observed that adiabatic test conditions required to measure the thermoelastic constant can be achieved by using a standard laboratory environment. this new approach has not been tested yet against materials different from that analysed in the present paper. acknowledgements his work was carried out as a part of the italian research program prin 2009z55nwc of the ministry of university and scientific research. the authors would like to express their gratitude for financial support. references [1] stoymeyer, c.e., the determination of fatigue limits under alternating stress conditions, proceedings of the royal society of london. series a, 90 (1914) 411-425. [2] curti, g., geraci, al., risitano, a., a new method for rapid determination of the fatigue limit, ingegneria automotoristica, 42 (1989) 634–636. in italian. [3] la rosa, g., risitano, a., thermographic methodology for rapid determination of the fatigue limit of materials and mechanical components, int j fatigue, 22 (2000) 65-73. [4] risitano, a., risitano, g., cumulative damage evaluation of steel using infrared thermography, theor appl fract mec, 54 (2010) 82-90. [5] risitano, a., risitano, g., determining fatigue limits with thermal analysis of static traction tests, fatigue fract eng mater struct, 36 (2013) 631-639. [6] curà, f., curti, g., sesana, r., a new iteration method for the thermographic determination of fatigue limit in steels int j fatigue, 27(4) (2005) 453-459. [7] giancane, s., chrysochoos, a., dattoma, v., wattrisse, b., deformation and dissipated energies for high cycle fatigue of 2024-t3 aluminium alloy, theor appl fract mec, 52 (2009) 117-121. [8] meneghetti g., analysis of the fatigue strength of a stainless steel based on the energy dissipation, int j fatigue, 29 (2007) 81-94. [9] meneghetti, g., ricotta, m., the use of the specific heat loss to analyse the lowand high-cycle fatigue behaviour of plain and notched specimens made of a stainless steel, eng fract mec, 81 (2012) 2-17. [10] meneghetti, g., ricotta, m., atzori, b., a synthesis of the push-pull fatigue behaviour of plain and notched stainless steel specimens by using the specific heat loss, fatigue fract eng mater struct, 36 (2013) 1306-1322. [11] meneghetti, g., ricotta, m., negrisolo, l., atzori, b., a synthesis of the fatigue behavior of stainless steel bars under fully reversed axial or torsion loading by using the specific heat loss, key engineering materials, 577-578 (2014) 453456. [12] atzori, b., meneghetti, g., ricotta, m., analysis of the fatigue strength under two load levels of a stainless steel based on energy dissipation. in: proceedings of 14th international conference on experimental mechanics icem14, poitiers, france, (2010). [13] meneghetti, g., ricotta, m., negrisolo, l., sottana, g., atzori, b., sintesi del comportamento a fatica di un acciaio inossidabile aisi 304l a diversi rapporti di ciclo mediante l’uso combinato dell’energia dissipata e dell’effetto termoelastico, in: proceedings of the 42° aias national conference, salerno (italy), (2013). [14] smith, kn., watson, p., topper, th., a stress-strain function for the fatigue of metals, j mater, 5 (1970) 767-778. i t g. meneghetti et alii, frattura ed integrità strutturale, 30 (2014) 191-200; doi: 10.3221/igf-esis.30.25 200 [15] walker, k., the effect of stress ratio during crack propagation and fatigue for 2024-t3 and 7075-t6 aluminum, astm stp, 462 (1970) 1-14. [16] vasudevan, a.k., sadananda, k., glinka, g., critical parameters for fatigue damage, int. j. fatigue, 23s (2001) s39s53. [17] kujawski, d., a new (δk+·kmax)0.5 driving force parameter for crack growth in aluminum alloys, int j fatigue, 23 (2001) 733-740. [18] kujawski, d., a fatigue crack driving force parameter with load ratio effects, int. j. fatigue, 23 (2001) s239-s246 [19] stoychev, s., kujawski, d., analysis of crack propagation using k and kmax, int. j. fatigue, 27 (2005) 1425-1431. [20] audenino, a. l., goglio, l., rossetto, m., metodi sperimentali per la progettazione, levrotto&bella, torino, italy (1997). [21] astm e112 12 standard test methods for determining average grain size. microsoft word numero_44_art_14 v. di cocco et alii, frattura ed integrità strutturale, 44 (2018) 173-182; doi: 10.3221/igf-esis.44.14 173 a simple model to calculate the microstructure evolution in a niti sma vittorio di cocco università di cassino e del lazio meridionale, dicem, via g. di biasio 43, 03043 cassino (fr), italy v.dicocco@unicas.it, https://orcid.org/0000-0002-1668-3729 stefano natali university of rome “la sapienza”, dicma, via eudossiana 18, roma, italy stefano.natali@uniroma1.it, https://orcid.org/0000-0002-2742-0270 abstract. shape memory alloys (smas) are a wide class of materials characterized by the property to recover the initial shape. this property is due to ability of alloys to change the microstructure from a “parent” microstructure (usually called “austenite”) to a “product” microstructure (usually called “martensite”). considering the tensile resistance, smas stress strain curves are characterized by a sort of plateau were the transformations from austenite to martensite (in loading condition) and from martensite to austenite (in unloading condition) take place. in this work a simple model to predict the microstructure modification has been proposed and verified with an equiatomic niti alloy characterized by a pseudo-elastic behavior. keywords. shape memory alloy; austenite; martensite; microstructure transitions. citation: di cocco, v., corbo esposito, a., natali, s., a simple model to evaluate the microstructure modification in a niti sma, frattura ed integrità strutturale, 45 (2018) 173-182. received: 01.03.2018 accepted: 19.03.2018 published: 01.04.2018 copyright: © 2018 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. introduction hape memory alloys (smas) are an interesting class of materials which is usually employed in many fields of the aerospace and civil industry. thanks to the high resistance against corrosion in many aggressive environments, smas are also used in medicine for construction of prosthesis [1, 2]. in the last years, the use of smas in electric field is more and more increased, especially in piezoelectric and in self-healing devices. in the last decades, several investigations have been carried out in order to characterize such alloys and take advantage of their peculiar properties in different applications [3-7]. in particular, smas are able to recover the original shape, even after severe deformations. the explanation of this peculiar behavior is due to both crystallography and thermodynamic properties of smas which allow a reversible phase transition from the parent phase (austenite) to the product phase (martensite) [8-13]. note that the twinning deformation mode characterizes the above transition. this is a reversible deformation process and differs from other irreversible processes, such as the slip deformation mode [9, 11]. it is important to underline that smas deformations can be recovered as follows [7-9]: s v. di cocco et alii, frattura ed integrità strutturale, 44 (2018) 173-182; doi: 10.3221/igf-esis.44.14 174 1) shape memory effect, where the recovery of initial shape depends on the material heating up to a critical temperature; 2) pseudoelastic effect, where the recovery of initial shape is due to the unloading process, being the critical temperature lower than the environment temperature. the microstructure transformation takes place at the material strain threshold up to this deformation level, the stressstrain behavior is linear with the austenite young modulus. over this strain value, the transformation of austenite in martensite takes place, and the stress-strain behavior is quite similar to a plateau. when the transformation of austenite to martensite is completed, the stress-strain behavior becomes linear according to the young modulus of martensite. in this work, the austenite and martensite volume fractions were measured using xrd analyses for different imposed strains both in loading and in unloading conditions. furthermore, the influence of cycling was analyzed and a simple model able to calculate the microstructure quantities was proposed. investigated alloy and methods n this work, an equiatomic niti shape memory alloy, characterized by a pseudoelastic behavior, is investigated. the alloy was obtained by using a vacuum furnace where a crucible made of ittria was charged using pure ni and pure ti powders. the cast was obtained from melted alloy using centrifugal force obtained by high crucible rotation. the melting was cooled in a graphite casting molds in rectangular mini-ingots (40x30x10 mm). from the casting ingots, flat tensile specimens characterized by the shape in fig. 1 were obtained by electrical discard machining (edm). figure 1: mini dog-bone tensile specimens: thickness 1 mm. tests were performed by means of patented mini-tensile machine that is characterizes by a removing frame (fig. 2) able to keep the specimens under scheduled deformation in order to analyze the microstructure. figure 2: removing frame of tensile minimachine. diffractions measurements were performed step by step corresponding to 1, 10, 50 and 100 cycles both in loading and in unloading conditions. for each investigated loading step, the loading frame containing the specimen was removed from the testing machine, at fixed values of deformation. the specimens, under load condition, were analyzed using a diffractometer to evaluate xrd spectra. xrd measurements were performed using a philips x-pert diffractometer equipped with a vertical bragg–brentano powder goniometer. a step–scan mode was used in the 2θ range from 40° to 30 mm 16 mm 2 mm 2  m m 1 0  m m i v. di cocco et alii, frattura ed integrità strutturale, 44 (2018) 173-182; doi: 10.3221/igf-esis.44.14 175 90° with a step width of 0.02° and a counting time of 2 s per step. the employed radiation was monochromated cukα (40 kv – 40 ma). the investigated steps are loading and unloading conditions. the analyzed diffraction steps conditions are shown in tab. 1. εeng. in loading conditions [%] εeng. in unloading conditions [%] 0.00 -- 2.50 9.15 3.33 8.32 4.16 7.49 5.00 6.66 5.83 5.83 6.66 5.00 7.49 4.16 8.32 3.33 9.15 2.50 10.00 0.00 table 1: xrd analyzed deformations steps in loading and in unloading condition a 1 and 50 cycles. results and discussion x-ray diffractions spectra onsidering the equiatomic niti investigated alloy, the diffraction spectrum of the initial unloaded specimen is shown in fig. 3 (cycle 1,  = 0%). in this spectrum the main peak is measured corresponding to 2θ=42.27° and a secondary peak is measured at 2θ=43.21°. figure 3: diffraction spectra of equiatomic niti at εeng=0% and at εeng=10% for the first cycle: peaks of austenite (corresponding to εeng=0%) and martensite (corresponding to εeng=10%) c v. di cocco et alii, frattura ed integrità strutturale, 44 (2018) 173-182; doi: 10.3221/igf-esis.44.14 176 these peaks correspond to the austenite phase, and no evidence of a different microstructure is shown in the spectrum in the analyzed angles range. the spectrum corresponding to higher deformation value (εeng=10%) shows the presence of a single peak in the investigated range (fig. 3 cycle 1,  = 10.00%). this peak corresponds to a fully martensitic structure. both spectra imply a microstructure modification from a fully austenitic to a fully martensitic one due to the effect of deformation. removing the imposed deformations, the initial shape is completely recovered, and the spectrum obtained in unloading conditions (fig. 4 – cycle 1,  =0.00% unloading) is similar to the initial spectrum (fig. 3 – cycle 1 eps 0.00%). this result implies that the microstructure is fully changed from martensite to austenite phase. this behavior corresponds to a pseudoelastic sma behavior, and the differences between the spectra in fig. 4 are due to the damage generated by the first loading-unloading cycle as already observed in di cocco et al. [12]. as shown in fig. 5, the spectra obtained after 50 cycles are different from to the spectra obtained after 1 cycle (fig. 3). however the ability to recover the initial austenitic structure is not compromised as shown on fig. 6, where the spectrum obtained at εeng=0.00% is quite similar to the spectrum obtained in unloading condition at εeng=0.00% (after 50 cycles). figure 4: diffraction spectra of equiatomic niti at εeng=0% both before and after the first cycle. figure 5: comparison between spectra obtained for at cycle 50: at εeng=0.00% and εeng=10.00% v. di cocco et alii, frattura ed integrità strutturale, 44 (2018) 173-182; doi: 10.3221/igf-esis.44.14 177 figure 6: comparison between spectra obtained for at cycle 50 at εeng=0.00% both in loading and in unloading conditions. differences in diffraction spectra are not only due to the cycling damage of the investigated alloy but are also due to the hysteresis as shown in fig. 7, where the spectrum corresponding to εeng=6.66% in loading condition is compared to the spectrum obtained at same strain in unloading condition. the presence of different mean peaks implies that the hysteresis phenomenon allows two different microstructure equilibrium conditions (under loading and unloading conditions, respectively). figure 7: comparison between spectra obtained for the first cycle at εeng=6.66% both in loading and in unloading conditions. microstructure evaluation considering all the spectra obtained in the xrd analyses for each investigated condition (tab. 1), the quantification of microstructure is performed by means of measure of amplitude of main austenite and martensite peaks. in order to evaluate the amplitude of main peaks, a ground signal is subtracted from the measure of each peak. the ground values are obtained from the spectrum at εeng=0.00% for the martensite and from the spectrum obtained at εeng=10.00% for the austenite. both the quantification of austenite and the martensite are obtained normalizing to 1 the amplitude of corresponding mean peaks. in addition, considering that only two phases were observed (austenite and/or martensite), the measure of microstructure contents is assumed as complement to 1 to the structure characterized by a peak better identified in xrd analysis. v. di cocco et alii, frattura ed integrità strutturale, 44 (2018) 173-182; doi: 10.3221/igf-esis.44.14 178 as an example, results of structure quantifications, in terms of volumetric quantification, are shown in fig 8 for the first cycle and in fig. 9 for the cycle 50. a) b) figure 8: quantification of microstructure corresponding to the first cycle: a) loading condition, b) unloading condition. a) b) figure 9: quantification of microstructure corresponding to the cycle 50: a) loading condition, b) unloading condition. microstructure prediction model in this work, a function e is assumed to be associated to microstructural changing in smas alloys (eq. 1). this function depends on the engineering strain ε and by the austenite a or martensite m volume fractions (normalized to 1).  , ,e a m (1) the infinitesimal variation of eq. 1 is due to three different contributions: 1) the first one is the contribution of imposed strain and it is assumed in proportional form using a constant c which depends on materials and their conditions (e.g. damage, cycling, and so on); v. di cocco et alii, frattura ed integrità strutturale, 44 (2018) 173-182; doi: 10.3221/igf-esis.44.14 179 2) the second one is the variation of austenite (austenite volume fraction); 3) the third contribution is the variation of martensite (martensite volume fraction). in the loading conditions the microstructure transition is from austenite to martensite; for this reason, the contribution of austenite variation is assumed as positive and the contribution of martensite variation is assumed negative as shown in eq. (2)  , , da dm de a m cd a m     (2) to evaluate the equilibrium conditions of structure the differential form of eq.2 is imposed to zero as shown in eq. 3. the integration of eq. 3 is shown in eq. 4, and the integrated form is shown in eq. 5. 0 da dm de cd a m     (3) da dm cd d a m       (4) a d c lna lnm c ln m       (5) expliciting eq. 5 in terms of a/m ratio (eq. 6) and considering the volume fraction of the austenite as a complement to 1 of martensite volume fraction (under the hypothesis of presence of only austenite and martensite without any other phases) the austenite/martensite ratio can be expressed by eq. 7.     d c c a a ln d c e de m m         (6) 1 cm de m   (7) from eq. 7 is trivial to evaluate the content of martensite (eq. 8) and of austenite (eq. 9) 1 1 c m de    (8) 1 1 1 1 1 c c c de a m de de              (9) the evaluation of parameters c and d is obtained by minimizing square errors of values obtained from eq. 8 and eq. 9 and the experimental microstructure quantifications. for example in fig. 10 the results obtained by eq. 8 and 9 are plotted whit the corresponding experimental results shown in figs. 8 and 9. considering all the investigated cycles (1, 10, 50 and 100) the evaluation of c and d parameters are shown in table 2, where the parameter d can assume only two values (700 in loading conditions and 70 in unloading conditions). this parameter indicates the hysteresis phenomena of the microstructure transition and it doesn’t depend on the cycles. the effect of the cycles is taken into account by the parameter c, which is influenced by the cumulative cyclic damage. plotting the parameter c as a function of loading cycles in a bi-logarithmic plane, a linear correlation is obtained (fig. 11). more evident differences of the c parameter are observed corresponding to low cycles (between 1 and 10 cycles) where the main damages are observed [12, 13]. v. di cocco et alii, frattura ed integrità strutturale, 44 (2018) 173-182; doi: 10.3221/igf-esis.44.14 180 a) b) c) d) figure 10: comparison of microstructure quantifications: a) cycle 1 loading conditions, b) cycle 1 unloading condition, c) cycle 50 loading condition, d) cycle 50 unloading condition. cycle c d loading/unloading 1 1 700/70 10 0.9 700/70 50 0.85 700/70 100 0.8 700/70 table 2: evaluation of c and d parameters. conclusion n this work, the microstructure modification of a pseudoelastic equiatomic niti alloy was investigated by means of xrd diffraction on tensile dog-bone specimens using a non standard mini-tensile machine. following this procedure, it was possible to obtain the diffraction spectra under imposed deformations. the measured spectra were i v. di cocco et alii, frattura ed integrità strutturale, 44 (2018) 173-182; doi: 10.3221/igf-esis.44.14 181 elaborated to evaluate the austenite and martensite volume fractions for each investigated deformation value (both in loading and in unloading conditions). the analyses were performed after 1, 10, 50 and 100 loading cycles. the results of experimental quantification of austenite and martensite volume fractions showed a non linear modification of the microstructure due to imposed strain and the influence of hysteresis. a simple model was proposed in order to calculate the austenite and martensite volume fractions at different imposed strains both in loading and in unloading conditions. the model takes into account both the hysteresis phenomenon and the cycling damage of material by using two parameters: 1) the parameter c (it takes into account the damage due to the cyclic loading); 2) the parameter d (it takes into account the hysteresis). figure 11: influence of cycling on c parameter. references [1] bogue, r. (2014). smart materials: a review of capabilities and applications, assembly automation., 34, pp. 16-22. [2] ogai, h. and bhattacharya, b. (2018). introduction to smart materials, intelligent systems, control and automation., science and engineering, 89, pp. 123-151. [3] amariei, d., frunzaverde, d., vela, i. and gillich, g.r. (2010). educational stand using shape memory alloys to enhance teaching of smart materials., procedia social and behavioral sciences, 2, pp. 5104-5108. [4] lemmens, r.j., dai, q. and meng, d.d. (2014). side-groove influenced parameters for determining fracture toughness of self-healing composites using a tapered double cantilever beam specimen., theoretical and applied fracture mechanics, 74, pp. 23–29. [5] bhargava, rr. and verma, p.r. (2016). strip-electro-mechanical yield model for transversely situated two semipermeable collinear cracks in piezoelectric strip., theoretical and applied fracture mechanics, 81, pp. 32–49. [6] hu, k., and chen, z. (2016). boundary effect on crack kinking in a piezoelectric strip with a central crack., theoretical and applied fracture mechanics, 81, pp. 11–24. [7] oudah, f. and el-hacha, r. (2017). joint performance in concrete beam-column connections reinforced using sma smart material., engineering structures 151, pp. 745–760. [8] shaw, j.a. and kyriakides, s. (1995). thermomechanical aspects of niti., journal of the mechanics and physics of solids 43(8), pp. 1243-1281. [9] otsuka, k. and ren, x. (1999). recent developments in the research of shape memory alloys., intermetallics, 7 pp. 511-528. [10] liang, w., zhou, m. and ke, f. (2005). shape memory effect in cu nanowires., nano letters, 5(10), pp. 2039-2043. [11] otsuka, k. and ren, x. (2005). physical metallurgy of ti–ni-based shape memory alloys., progress in materials science, 50, pp. 511–678. c  p a ra m e te r cycles 0.0105 0.0100 0.0095 0.0090 0.0085 0.0080 0.0075 1 5 10 50 100 v. di cocco et alii, frattura ed integrità strutturale, 44 (2018) 173-182; doi: 10.3221/igf-esis.44.14 182 [12] di cocco, v., iacoviello, f., maletta, c. and natali s. (2014). cyclic microstructural transitions and fracture micromechanisms in a near equiatomic niti alloy., international journal of fatigue, 58, pp. 136–143. http://dx.doi.org/10.1016/j.ijfatigue.2013.03.009 [13] di cocco, v., vantadori, s., carpinteri, a., iacoviello, f. and natali, s. (2018). fatigue analysis of a near-equiatomic pseudo-elastic niti sma., theoretical and applied fracture mechanics, 94, pp. 110-119. https://doi.org/10.1016/j.tafmec.2018.01.012. << /ascii85encodepages false /allowtransparency false /autopositionepsfiles true /autorotatepages /none /binding /left /calgrayprofile (dot gain 20%) /calrgbprofile (srgb iec61966-2.1) /calcmykprofile (u.s. web coated \050swop\051 v2) /srgbprofile (srgb iec61966-2.1) /cannotembedfontpolicy /error /compatibilitylevel 1.4 /compressobjects /tags /compresspages true /convertimagestoindexed true /passthroughjpegimages true /createjobticket false /defaultrenderingintent /default /detectblends true /detectcurves 0.0000 /colorconversionstrategy /cmyk /dothumbnails false /embedallfonts true /embedopentype false /parseiccprofilesincomments true /embedjoboptions true /dscreportinglevel 0 /emitdscwarnings false /endpage -1 /imagememory 1048576 /lockdistillerparams false /maxsubsetpct 100 /optimize true /opm 1 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/hrv (za stvaranje adobe pdf dokumenata najpogodnijih za visokokvalitetni ispis prije tiskanja koristite ove postavke. stvoreni pdf dokumenti mogu se otvoriti acrobat i adobe reader 5.0 i kasnijim verzijama.) /hun 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can be opened with acrobat and adobe reader 5.0 and later.) >> /namespace [ (adobe) (common) (1.0) ] /othernamespaces [ << /asreaderspreads false /cropimagestoframes true /errorcontrol /warnandcontinue /flattenerignorespreadoverrides false /includeguidesgrids false /includenonprinting false /includeslug false /namespace [ (adobe) (indesign) (4.0) ] /omitplacedbitmaps false /omitplacedeps false /omitplacedpdf false /simulateoverprint /legacy >> << /addbleedmarks false /addcolorbars false /addcropmarks false /addpageinfo false /addregmarks false /convertcolors /converttocmyk /destinationprofilename () /destinationprofileselector /documentcmyk /downsample16bitimages true /flattenerpreset << /presetselector /mediumresolution >> /formelements false /generatestructure false /includebookmarks false /includehyperlinks false /includeinteractive false /includelayers false /includeprofiles false /multimediahandling /useobjectsettings /namespace [ (adobe) (creativesuite) (2.0) ] /pdfxoutputintentprofileselector /documentcmyk /preserveediting true /untaggedcmykhandling /leaveuntagged /untaggedrgbhandling /usedocumentprofile /usedocumentbleed false >> ] >> setdistillerparams << /hwresolution [2400 2400] /pagesize [612.000 792.000] >> setpagedevice microsoft word numero_54_art_16_2792 m.a. warda et al., frattura ed integrità strutturale, 54 (2020) 211-225; doi: 10.3221/igf-esis.54.16 211 optimum sustainable mix proportions of high strength concrete by using taguchi method m.a. warda, h.s. khalil, seleem s. e. ahmad materials department, faculty of engineering, university of zagazig, egypt mamabowarda@gmail.com, http://orcid.org/0000-0001-2345-6789 hossamkhalil_m@yahoo.com, http://orcid.org/0000-0002-2345-6790 seleemahmad62@yahoo.com, http://orcid.org/0000-0002-2345-6791 i.m. mahdi structural eng. and construction management dept., future university, egypt ibrahimmahdi@gmail.com, http://orcid.org/0000-0003-2345-6792 abstract. in this study, mix proportion parameters of high strength concrete (hsc) were analyzed by using the taguchi’s experiment design methodology for optimal design. for that purpose, mixtures are designed in a l27 orthogonal array with six factors, namely, ‘silica fume’, ‘steel fiber’, ‘super-plasticizer’, ‘maximum aggregate size (ag)’, ‘water / cementitious material (w/c) ratio’, ‘fly ash’. the mixtures were extensively tested to meet technical requirements of hsc. the experimental results were analyzed by using the taguchi experimental design methodology. the best possible levels for mix proportions were determined for maximization of compressive strength at 7, 28, 56, 90 days, splitting tensile strength at 28 days, flexural strength at 28 days, and the slump. also the best possible levels for mix proportions were determined for minimization of the production cost. it was found that steel fibers and fly ash are the most dominant factors in the process of optimization. the advantage of using steel fiber and fly ash was the reduced energy and cost associated with the raw materials which meant more sustainable concrete could be attained. it was also found that there is a necessity to apply a multiresponse optimization to get the best mix proportions. keywords. high strength concrete; taguchi method; optimal mix design. citation: warda, m. a., khalil, h.s., ahmad s.s.e., mahdi, i.m., optimum sustainable mix proportions of high strength concrete by using taguchi method, frattura ed integrità strutturale, 54 (2020) 211-225. received: 16.04.2020 accepted: 27.08.2020 published: 01.10.2020 copyright: © 2020 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. introduction lam et al., [1] in their research illustrated that the countries need to create a healthy and sustainable economy to achieve sustainable development (sd). the industries policymakers are now making the concept of sd as an important objective [2]. wced [3] defined sd as development that meets the demand of the present generations a https://youtu.be/qgns4ucjfdc m.a. warda et al., frattura ed integrità strutturale, 54 (2020) 211-225; doi: 10.3221/igf-esis.54.16 212 without arbitrating the future generations to meet their demands. nowadays, the sd has been the subject of discussion and debate within government, non-government, and academic circles, leading concentration of national and international economy, social and environmental agendas [4]. hence, sd can be viewed as the satisfaction of present needs without compromising the ability of future generations to meet their own needs. sustainability is referred to as the triple bottom line (tbl) of an organization [5], which includes the three dimensions: environment, economic and social [6] and [7]. it also promotes by giving an opportunity to create occupant friendly buildings and environment responsible ones [6]. concrete sustainability is still a hot topic in spite of progress achieved in this area because of concrete industry still faces challenges. several evaluation methods have been proposed in responses to these challenges, but the lack of a complete framework for sustainable concrete material remains. because of these issues, the strategy of this research is to reduce the level consumption of resources to utilize it for present and future needs. this means reaching to an optimum of mix proportions for high strength concrete. in detection of achieving this objective, sustainable concrete is found as the best key to avoid depletion of resources. sustainable material selection is found as a vital strategy in construction. high strength concrete (hsc) is considered to be a concrete having a high strength at 28 days (typically greater than 40 mpa compressive strength or a low water / cement ratio (less than 0.35)). in order to reach high strength levels using a regular water reducer, the concrete composition had to be very carefully optimized and a stringent quality control program had to be implemented. the idea was conceived to produce the highest possible compressive strength through lowering the water / binder ratio as much as possible. the direct measurement of the tensile strength of usual concrete is not easy because of the complicated set-up that must be used. therefore, tensile strength is usually calculated using indirect measurements, such as the measurement of the modulus of rupture (mor) (astm c78) and/or the splitting tensile strength (astm c496). performing the mor and splitting tensile strength measurements does not present any special difficulties in the case of high strength concrete, so that the same set-ups and procedures used for usual concrete can also be used for high strength concrete. when bouygues of france decided to cast the prefabricated box girders for the ile de re bridge with 70 mpa concrete instead of the design 40 mpa, the unit-cost increase per cubic meter of concrete was small compared with the savings resulting from faster casting, [8]. choosing high performance concrete for two union square in seattle was based more on high elastic modulus than high strength, even though these two properties are somewhat related. the high elastic modulus was required to increase the building rigidity to dampen swaying in high winds. the top of the empire state building sways about two feet (600 mm) during a storm, [9]. high performance concrete not only reduces the dead load of offshore platforms but also ensures outstanding durability, especially in the critical splash zone, where it is subjected to very severe exposure (this was the case for the hibernia offshore platform in canada), [8]. several researchers studied mechanical properties of concrete by using taguchi method. ozbay et. al. [10], analyzed mix proportion parameters of high strength self-compacting concrete (hsscc) by using the taguchi’s experiment design methodology for optimal design. khiabani et. al. [11], presented the results of the effect of high temperatures on the retained mechanical properties of high strength concrete (hsc) using taguchi method. they found that the water to binder ratio is the most important factor in mix proportion in both compressive and tensile strength. hashemi et. al. [12], investigated optimizing mix proportions using taguchi method. they concluded that taguchi method has a powerful potential for estimating optimum mix-design of hsc. also they concluded that taguchi method saves energy, cost and time by reducing number of experiments. emara et. al. [13] investigated the effect and optimization of using selfcompacting rubberized concrete by using taguchi method. their study considered examining the influence of different concrete mix proportioning parameters that included fine rubber, coarse rubber, fly ash and viscocrete contents on the studied mechanical and fresh properties. kumari et. al. [14] optimized the cement content in concrete using pozzolanic materials as reduction of co2 released during the production of cement is major issues of construction industry. their study showed that both mineral and chemical admixtures can be effectively used to reduce the cement content in concrete. tan et. al. [15] investigated the effect of the bentonite (b), fly ash (fa), and silica fume (sf) on the bleeding of cement-based grouts. the optimum conditions were determined for three different water to solids ratios. they found that silica fume is the most effective factor for bleeding. also they observed that to reduce the bleeding in grout mixes and to carry out a successful injection it is useful to use silica fume and bentonite. hinislioglu et. al. [16] optimized the early flexural strength of concrete pavement (cp) by using the taguchi method. they found the optimum conditions to be 0.35 water / cementitious ratio, gradation with minimum content of fine aggregates, 5% fly ash content, and 0% silica fume content at 7 days curing. maximum flexural strength of 5.31 mpa was achieved at the optimum conditions. in this study, 27 different mixes were produced according to aforementioned hsc concrete criteria. the experimental work was so designed that the experiments gave the best possible working conditions of the parameters that affect the mechanical properties, using the taguchi method. in this research, 40-84 mpa 28 days compressive strength concrete samples were produced according to the high strength concrete properties. not only, compressive strength at 28 days, but m.a. warda et al., frattura ed integrità strutturale, 54 (2020) 211-225; doi: 10.3221/igf-esis.54.16 213 also compressive strength at 7 days, compressive strength at 56 days, splitting tensile strength at 28 days, flexural strength at 28 days, production cost, and slump were considered. the experimental results were analyzed according to the taguchi method. using taguchi method, mix proportions were set to best possible levels for the maximization of compressive strength, splitting tensile strength, flexural strength, and slump results. also mix proportions were set to their best possible levels for the minimization of production cost. methodology taguchi method he taguchi method reduces the number of trials by design of experiments. the number of possible trials for p parameter at l level as per factorial method design is n=lp where l= number of levels for each factor and p= number of factors involved. for example, if we have 6 parameters at 3 levels then total number of combinations = 36 = 729 but with the help of orthogonal array (oa), a minimum number of trials for these combinations is required. in an experimental study, in order to determine the effects of various factors, which are affecting the results of experiments, different methods and approaches are used. the fundamentals of these methods are the full factorial design and fractional factorial design. in the traditional approach, which is also known as full factorial design, the experiments are performed for each condition, which consists of all factors. in the experiments where the number of factor and their levels are few, the full factorial experimental design may be applied to the design. dr. taguchi started to develop new methods to optimize the process of engineering experimentation in japan after world war ii. he developed techniques which are known as the taguchi method [17]. with this method, which can be applied easily by the researcher, the results obtained are possible to be standardized. standard tables known as orthogonal arrays (oa) are used for the design of the experiments in the taguchi method. an oa with a three level and six factors are shown in tab. 1. this oa is particularly designed with the symbol of l27. each row in the array represents a trial condition with the factor levels, which are indicated by the numbers in the row. the columns correspond to the factors specified in the study and each column contains nine level 1, nine level 2 and nine level 3 conditions (a total of 27 conditions) for the factors assigned to the column. thus, the evaluation of results has been standardized by this method, which can easily be applied by researchers. taguchi method uses the s/n ratio (signal-to-noise), which is a performance characteristic, instead of the average value to interpret the trial result data into a value for the evaluation characteristics in the optimum setting analysis. this ratio expresses the scatter around a target value. there are three categories of performance characteristics; the larger-the better, the smaller-the better and the nominal-the better. these performance characteristics are evaluated by using the following equations; larger the better 10 21 1 1 / 10 log ( )  n i i s n n y    (1) smaller the better 2 10 1 1 / 10 log ( ) n ii s n y n     (2) and the nominal the better 2 10 1 1 s / n 10 log ( ( ) ) n i oi y y n     (3) , where s/n are performance statistics, defined as the signal to noise ratio (s/n unit: db), n is the number of repetitions for an experimental combination, and yi is a performance value of the i th experiment and yo is the nominal value desired. from doe (design of experiment), the present work utilized orthogonal array to study the following six variables:  silica fume (s.fume)  steel fiber (s.fiber) t m.a. warda et al., frattura ed integrità strutturale, 54 (2020) 211-225; doi: 10.3221/igf-esis.54.16 214  super-plasticizer (sp)  maximum aggregate size (ag)  water to cementitious materials ratio (w/c)  fly-ash mix no. s.fume s.fiber sp ag w/c flyash a b c d e f 1 1 1 1 1 1 1 2 1 1 1 1 2 2 3 1 1 1 1 3 3 4 1 2 2 2 1 1 5 1 2 2 2 2 2 6 1 2 2 2 3 3 7 1 3 3 3 1 1 8 1 3 3 3 2 2 9 1 3 3 3 3 3 10 2 1 2 3 1 2 11 2 1 2 3 2 3 12 2 1 2 3 3 1 13 2 2 3 1 1 2 14 2 2 3 1 2 3 15 2 2 3 1 3 1 16 2 3 1 2 1 2 17 2 3 1 2 2 3 18 2 3 1 2 3 1 19 3 1 3 2 1 3 20 3 1 3 2 2 1 21 3 1 3 2 3 2 22 3 2 1 3 1 3 23 3 2 1 3 2 1 24 3 2 1 3 3 2 25 3 3 2 1 1 3 26 3 3 2 1 2 1 27 3 3 2 1 3 2         table 1: a three-level orthogonal array (l27). the levels and values for the considered parameters are shown in tab. 2 and 3. according to the parameters and their variation levels, l27 orthogonal array is used. tab. 3 shows the defined mix proportions. parameters levels s.fume % steel fiber % sp % ag (mm) w/c ratio fly-ash % 1 0 0 0.3 20 0.27 0 2 5 1 0.5 14 0.31 10 3 10 2.5 0.7 10 0.35 20 table 2: mix parameters and levels. materials the cement used in this research was sinai@ cem i 52.5n. fineness of the cement as shown in tab. 4 and cement setting time test is shown in tab. 4 also. also compressive strength for used cement is shown in tab. 6 and 7. steel fibers m.a. warda et al., frattura ed integrità strutturale, 54 (2020) 211-225; doi: 10.3221/igf-esis.54.16 215 were supplied from nassar group@. their aspect ratio is equal to 30. their length is 24 mm and diameter is 0.80 mm. the steel fiber has tensile strength not less than 1000 mpa. a third generation super-plasticizer for homogenous concrete sika@ viscocrete@-3425 was used in all concrete mixtures. natural river sands were used as fine aggregate in the concrete mixtures with specific gravity 2.6. the coarse aggregate was dolomite with maximum size of 20 mm and specific gravity 2.68. fine aggregate to coarse aggregate ratio ranges from 0.37 to 0.39. the aggregate grading is shown in tab. 5. mix no. s.fume s.fiber sp ag mm w/c fly-ash % cement % % cement ratio % cement 1 0 0 0.3 20 0.27 0 2 0 0 0.3 20 0.31 10 3 0 0 0.3 20 0.35 20 4 0 1 0.5 14 0.27 0 5 0 1 0.5 14 0.31 10 6 0 1 0.5 14 0.35 20 7 0 2.5 0.7 10 0.27 0 8 0 2.5 0.7 10 0.31 10 9 0 2.5 0.7 10 0.35 20 10 5 0 0.5 10 0.27 10 11 5 0 0.5 10 0.31 20 12 5 0 0.5 10 0.35 0 13 5 1 0.7 20 0.27 10 14 5 1 0.7 20 0.31 20 15 5 1 0.7 20 0.35 0 16 5 2.5 0.3 14 0.27 10 17 5 2.5 0.3 14 0.31 20 18 5 2.5 0.3 14 0.35 0 19 10 0 0.7 14 0.27 20 20 10 0 0.7 14 0.31 0 21 10 0 0.7 14 0.35 10 22 10 1 0.3 10 0.27 20 23 10 1 0.3 10 0.31 0 24 10 1 0.3 10 0.35 10 25 10 2.5 0.5 20 0.27 20 26 10 2.5 0.5 20 0.31 0 27 10 2.5 0.5 20 0.35 10 table 3: mix proportions. item result egyptian code of practice % retained on sieve no. 170 10% % passing from sieve no. 170 90% initial setting time 95 minute >45 minute final setting time 345 minute < 600 minute 3 days compressive strength 21.9 n/mm2 >18 n/mm2 7 days compressive strength 29.1 n/mm2 >27 n/mm2 table 4: cement properties test report m.a. warda et al., frattura ed integrità strutturale, 54 (2020) 211-225; doi: 10.3221/igf-esis.54.16 216 preparation of the specimens concrete ingredients were mixed thoroughly for about seven minutes using a rotating mixer. the binder, i.e. cement, fine aggregate, coarse aggregate, sf, and fa were first mixed for 1 min without water. afterwards, water and super-plasticizer were gradually added in 30 s followed by a 1 min mixing. then 20% of steel fiber were added and mixed for 2 min. at last, all the remaining fibers were added to the flow able mortar and mixed for another 2 min to obtain a homogeneous dispersion. sieve size maximum aggregate size (mm) fine (mm) 20 mm 14 mm 10 mm aggregate 20 100 100 100 100 14 74 100 100 100 10 10 31 100 100 5 3 6 55 100 2.36 11 97 1.18 86 0.6 48 0.3 25 0.15 2 table 5: aggregate grading (% passing). the slump test was performed directly after mixing and then specimens were casted and vibrated using the vibrations table. we followed the prescription of the slump test as it is mentioned in astm c 143-90a and bs 1881: part 102: 1983. the slump test is very useful on the site as a check on the batch-to-batch or hour-to-hour variation in the materials being fed into the mixer. too high or too low a slump gives immediate warning and enables the mixer operator to remedy the situation. this study included 27 design mixes and the following specimens were performed in this study: ‐ eighty-one cubic specimens having dimensions 100×100×100 mm3, three specimens for each mixture, designated for 7-day compressive strength test. ‐ eighty-one cubic specimens having dimensions 100×100×100 mm3, three specimens for each mixture, designated for 28-day compressive strength test. ‐ eighty-one cubic specimens having dimensions 100×100×100 mm3, three specimens for each mixture, designated for 56-day compressive strength test. ‐ eighty-one cubic specimens having dimensions 100×100×100 mm3, three specimens for each mixture, designated for 90-day compressive strength test. ‐ eighty-one cylindrical specimens having dimensions 100 mm in diameter and 200 mm in height, three specimens for each mixture, to be subjected to 28-day splitting tensile strength test. ‐ eighty-one prism specimens having dimensions 100×100×500 mm3, three specimens for each mixture, designated for 28-day flexural strength test. specimens were demolded after 24 hours from casting and then stored in water until the age of testing and then mechanical tests were conducted. testing procedure to investigate the compressive strength on 7 day, 28 day, 56 day, and 90 day after casting, uniaxial compression tests were carried out. we followed bs 1881: part 108: 1983 by filling the moulds in three layers. each layer of concrete was compacted by a vibrating table. ramming continued until full compaction without segregation to ensure that the test result is to be representative of the properties of fully-compacted concrete. according to bs 1881: part 111: 1983, after the top surface of the cube has been finished by means of a float, the cubes were stored undisturbed for 24±4 hours at a temperature of 20±5 ºc and a relative humidity of not less than 90 per cent. at the end of this period, the moulds were stripped and the cubes were further cured in water at 20±2 ºc. according to bs 1881: part 116: 1983, the loads on each cube was applied at a constant rate of stress equal to 0.2 to 0.4 mpa/second. also our tests conform to bs en 12390-3. the tests were conducted by a hydraulic machine with a capacity of 3000 kn. the maximum load was recorded by a m.a. warda et al., frattura ed integrità strutturale, 54 (2020) 211-225; doi: 10.3221/igf-esis.54.16 217 pointer. splitting tensile strength was conducted using the same testing machine. where cylindrical specimens were placed horizontally between the upper and lower bearing surfaces. in the splitting tensile strength test, we followed a rate of loading which was prescribed by astm c 496-90 and by bs 1881: part 117: 1983, and conform to bs en 12390-6. the splitting test is simple to perform and gives more uniform results than other tension tests. the strength determined in the splitting test is believed to be close to the direct tensile strength of concrete 5 to 12 per cent higher. flexural strength tests were also carried out by means of another hydraulic testing machine with a maximum load capacity set as 50 kn in this test, a plain concrete beam is subjected to flexure. because the load points are spaced at one-third of the span, the test is called a third-point loading test. the theoretical maximum tensile stress reached in the bottom fibre of the test beam is known as the modulus of rupture. if fracture occurs within the central one-third of the beam, the modulus of rupture is calculated on the basis of ordinary elastic theory. our tests conform to bs en 12390-5 and bs 1881: part 118. mix no. c7 c28 t28 f28 c56 c90 pc s mpa mpa mpa mpa mpa mpa le/m3 mm 1 18.33 57.98 3.5 7.27 55.65 64.15 915.9 30 2 34.66 57.65 3.08 6.45 52.65 69.65 1637 40 3 26.66 40.32 2.65 6.07 44.32 55.98 2309.5 40 4 36.16 52.65 3.02 7.8 70.65 69.15 4186.1 40 5 41.99 50.99 2.33 5.92 54.32 60.65 4983.2 40 6 22.33 35.32 1.49 5.06 39.32 36.66 5579.9 100 7 59.65 70.65 6.58 8.85 70.98 77.98 9037.5 150 8 36.32 58.82 5.62 8.14 62.98 62.98 9744.5 100 9 21.33 23.99 4.35 6.07 36.32 39.32 10320.2 80 10 48.65 61.32 1.7 6.19 72.65 81.98 2841.9 100 11 32.66 43.32 2.18 7 48.32 44.65 3396.5 50 12 38.99 52.32 1.59 5.05 38.66 63.65 1507.5 120 13 40.65 40.99 3.18 6 51.98 53.15 5805.7 70 14 33.99 40.99 3.18 4.51 51.65 55.48 6313.6 150 15 29.32 36.99 3.71 6.9 41.99 46.65 4612.2 50 16 53.65 82.64 6.16 8.67 84.98 87.81 10654.8 30 17 31.32 42.65 5.2 7.14 42.65 44.32 11197.9 20 18 40.99 47.99 5.31 5.86 60.98 51.98 9309.7 30 19 24.66 30.32 1.7 4.35 41.15 42.99 4399 100 20 49.32 50.65 3.18 6.25 55.65 76.98 2336.4 150 21 28.99 51.98 3.5 6.61 42.82 49.99 2857.9 130 22 42.99 31.99 3.82 4.35 53.98 65.65 7911.9 40 23 33.66 37.99 4.88 7.18 41.49 46.65 5539.8 30 24 31.99 52.32 5.62 6.04 53.32 54.82 6104 150 25 38.66 56.32 6.47 9.9 58.48 59.98 12031 40 26 54.57 75.64 6.9 10.42 79.81 81.14 10029.5 50 27 34.66 46.65 6 8.05 52.82 51.82 10520.5 50 table 6: test results of concrete (where c7: compressive strength at 7 days, c28: compressive strength at 28 days, t28: tensile strength at 28 days, f28: flexural strength at 28 days, c56: compressive strength at 56 days, c90: compressive strength at 90 days, pc: production cost, and s: slump in mm). m.a. warda et al., frattura ed integrità strutturale, 54 (2020) 211-225; doi: 10.3221/igf-esis.54.16 218 results and discussion he test results on concrete specimens are shown in tab. 6, in which compressive strength, splitting tensile strength, and flexural strength values were obtained from the average of three specimens for each of them. the optimum possible mix proportion levels were investigated for the maximum compressive strength, splitting tensile strength, flexural strength, and slump by using taguchi method. the ‘larger the better’ type of quality characteristic situation was evaluated. also the optimum possible mix proportion levels were investigated for the minimum production cost by using taguchi method. the ‘smaller the better’ type of quality characteristic situation was evaluated. the commercial software minitab was adopted to conduct taguchi method. the best possible mix parameter combinations of the high strength concrete (hsc) could be determined from the main effect plots for each response as shown in figs. 1 8. in these figures, the highest point for each factor indicates the optimal settings. their abscissa values are the levels of parameters to choose. for example, in fig. 6, maximum 90 days compressive strength is obtained at 10 % silica fume, 2.5% steel fiber by volume, 0.5% super-plasticizer, 20 mm maximum aggregate size, 0.27 water to cement ratio, and 0 % fly ash. the optimal mix designs are shown in tab. 10. as can be seen in figs. 1-6, increasing the steel fiber content from 1% to 2.5% increased the compressive strength at 7 days, the compressive strength at 28 days, the splitting tensile strength at 28 days, the flexural strength at 28 days, the compressive strength at 56 days and the compressive strength at 90 days significantly. the reason is the bonding effect of steel fibers. also it can be noticed that for the compressive strength at 7 days, 28 days, and 56 days, increasing the silica fume from 5% to 10% decreases the compressive strength for the aforementioned ages. the reason is the cement effect on strength. the compressive strength of the mix design proportion with the finest aggregate (10 mm) is lower, which is due to a larger specific area of fine aggregates leading to a lower flow ability of concrete. figure 1: main effect plot for signal to noise ratio for 7 days compressive strength. figure 2: main effect plot for signal to noise ratio for 28 days compressive strength t m.a. warda et al., frattura ed integrità strutturale, 54 (2020) 211-225; doi: 10.3221/igf-esis.54.16 219 figure 3: main effect plot for signal to noise ratio of 28 days splitting tensile strength. figure 4: main effect plot for signal to noise ratio for 28 days flexural strength. figure 5: main effect plot for signal to noise ratio of 56 days compressive strength. m.a. warda et al., frattura ed integrità strutturale, 54 (2020) 211-225; doi: 10.3221/igf-esis.54.16 220 figure 6: main effect plot for signal to noise ratio for 90 days compressive strength. figure 7: main effect plot for signal to noise ratio of production cost. figure 8: main effect plot for signal to noise ratio of slump. m.a. warda et al., frattura ed integrità strutturale, 54 (2020) 211-225; doi: 10.3221/igf-esis.54.16 221 optimal mix proportions silica fume steel fiber superplasticizer maximum aggregate size (mm) water to cement ratio fly ash vf % %cement c7 5 2.5 0.5 10 0.27 10 c28 5 2.5 0.5 20 0.27 10 t28 10 2.5 0.3 20 0.31 0 f28 0 2.5 0.5 20 0.31 0 c56 5 2.5 0.5 20 0.27 10 c90 10 2.5 0.5 20 0.27 0 pc 0 0 0.3 20 0.35 0 s 10 0 0.7 10 0.35 10 table 7: optimal mix design proportions for the measured quality characteristics of hsc percentage contribution of individual parameter can be well determined using anova (analysis of variance). tabs. 8 15 present the results of anova. the f-test is used for comparing the factors of the total deviation. p-value indicates the significance of parameters. the contribution percentage of factors gives an idea of the significance of factors to strength, production cost, and slump. as s summary, steel fiber content and fly ash are the most influencing factors on compressive strength, splitting tensile strength, and flexural strength. also steel fiber is the most influencing factor on production cost. for the slump the most effective factor is super-plasticizer. these are rational results. source df seq ss adj ms f-value p-value contribution s.fume 2 89.88 44.94 0.36 0.706 6.11% s.fiber 2 111.03 55.52 0.44 0.652 7.54% sp 2 89.49 44.75 0.36 0.707 6.09% ag 2 175.99 88 0.7 0.514 11.95% w/c 2 282.77 141.39 1.12 0.353 19.20% fly ash 2 722.94 361.47 2.87 0.09 49.11% error 14 1762.97 125.93 table 8: analysis of variance for 7 days compressive strength. source df seq ss adj ms f-value p-value contribution s.fume 2 150.1 75.07 1.47 0.263 3.47% s.fiber 2 1175.5 587.77 11.51 0.001 27.23% sp 2 281.4 140.69 2.76 0.098 6.52% ag 2 144.6 72.29 1.42 0.275 3.34% w/c 2 650.3 325.14 6.37 0.011 15.06% fly ash 2 1916.4 958.21 18.77 0 44.38% error 14 714.7 51.05 table 9: analysis of variance for 28 days compressive strength. m.a. warda et al., frattura ed integrità strutturale, 54 (2020) 211-225; doi: 10.3221/igf-esis.54.16 222 source df seq ss adj ms f-value p-value contribution s.fume 2 5.5882 2.7941 4.09 0.04 7.77% s.fiber 2 51.709 25.8545 37.85 0 71.92% sp 2 5.8866 2.9433 4.31 0.035 8.19% ag 2 1.7363 0.8682 1.27 0.311 2.41% w/c 2 0.2947 0.1474 0.22 0.809 0.41% fly ash 2 6.6807 3.3403 4.89 0.025 9.29% error 14 9.5639 0.6831 table 10: analysis of variance for 28 days splitting tensile strength. source df seq ss adj ms f-value p-value contribution s.fume 2 1.393 0.6963 0.34 0.717 2.36% s.fiber 2 32.935 16.4673 8.07 0.005 55.71% sp 2 7.375 3.6873 1.81 0.2 12.47% ag 2 4.335 2.1673 1.06 0.372 7.33% w/c 2 5.007 2.5037 1.23 0.323 8.47% fly ash 2 8.072 4.0362 1.98 0.175 13.66% error 14 28.564 2.0403 table 11: analysis of variance for 28 days flexural strength. source df seq ss adj ms f-value p-value contribution s.fume 2 2.72 1.36 0.01 0.992 0.12% s.fiber 2 197.05 98.525 0.6 0.562 8.92% sp 2 94 47 0.29 0.755 4.27% ag 2 80.18 40.088 0.24 0.787 3.63% w/c 2 1019.46 509.728 3.1 0.077 46.14% fly ash 2 815.74 407.871 2.48 0.119 36.94% error 14 2298.87 164.205 table 12: analysis of variance for 56 days compressive strength. source df seq ss adj ms f-value p-value contribution s.fume 2 18.01 9.004 0.07 0.934 0.79% s.fiber 2 191.35 95.675 0.73 0.498 8.30% sp 2 54.65 27.327 0.21 0.814 2.37% ag 2 24.95 12.474 0.1 0.909 1.08% w/c 2 926.81 463.403 3.55 0.057 40.16% fly ash 2 1092.26 546.132 4.18 0.038 47.33% error 14 1828.5 130.607 table 13: analysis of variance for 90 days compressive strength. m.a. warda et al., frattura ed integrità strutturale, 54 (2020) 211-225; doi: 10.3221/igf-esis.54.16 223 ource df seq ss adj ms f-value p-value contribution s.fume 2 9425297 4712649 317.43 0 3.08% s.fiber 2 280369997 140184998 9442.43 0 91.77% sp 2 14864 7432 0.5 0.617 0.00% ag 2 279413 139707 9.41 0.003 0.09% w/c 2 1213075 606538 40.85 0 0.40% fly ash 2 14203210 7101605 478.34 0 4.65% error 14 207848 14846 table 14: analysis of variance for production cost. source df seq ss adj ms f-value p-value contribution s.fume 2 1066.7 533.3 0.34 0.714 3.63% s.fiber 2 2466.7 1233.3 0.8 0.47 8.41% sp 2 18866.7 9433.3 6.1 0.012 64.31% ag 2 5066.7 2533.3 1.64 0.23 17.26% w/c 2 1400 700 0.45 0.645 4.78% fly ash 2 466.7 233.3 0.15 0.861 1.60% error 14 21666.7 1547.6 table 15: analysis of variance for slump. evaluation of factor effects ‐ effect of silica fume the test results demonstrated that sf replacement at most levels is not clear on the compressive strength and flexural strength (figs 1, 2, 4, 5, 6). these results are near to the results obtained by [16]. hinislioglu et. al [16] found reduction in 7 days flexural strength of pavement concrete with 10%, 20%, and 30% sf is 2%, 11%, and 18%, respectively. they interpret that due to their extreme fineness, the water requirement of sf is very high. furthermore, the addition of sf to the cement matrix may result in micro-shrinkage cracking. ‐ effect of steel fiber as shown in figs. 1-6, increasing the steel fiber content from 0% to 1% to 2.5% increases the compressive, splitting tensile, flexural strengths significantly. the reason was the bonding effect of steel fibers. these results were similar to certain extent to results obtained by [18] for compressive strength. from fig. 11, steel fiber increased the production cost of the mixes which contains it. from fig. 12, increasing steel fiber decreased the workability significantly. ‐ effect of super-plasticizer as shown in figs. 1, 2, 4, 5, 6, increasing the super-plasticizer content from 0.3 to 0.5% increases the compressive, and flexural strengths. however, further increasing from 0.5% to 0.7% the compressive strength, splitting tensile strength, and flexural strength decreased. also it can be seen from fig. 12 that increasing the super-plasticizer 0.7% enhanced the workability greatly as it is expected. ‐ effect of maximum aggregate size the compressive strength, splitting tensile strength, and flexural strength of the mix-design proportion with the finest aggregate (10 mm) were lower, which might be due to a larger specific area of fine aggregates leading to a lower flowability of concrete. these results were similar to the test results obtained by [18]. ‐ effect of water / cementitious materials the effect of w/c ratio on the compressive strengths, splitting tensile strength, and flexural strength are shown in figs. 16. according to anova, water contents affects significantly on the properties of concrete (tabs. 8 to 15). it has been known that compressive strength, splitting tensile strength, and flexural strength vary inversely with the w/c ratio for m.a. warda et al., frattura ed integrità strutturale, 54 (2020) 211-225; doi: 10.3221/igf-esis.54.16 224 concrete [19]. in another word, while w/c ratio decrease strength of concrete increase. from the test results, first level of w/c ratio (0.27) maximizes the s/n as it is expected. ‐ effect of fly ash the effect of fa on compressive strength, splitting tensile strength, and flexural strength is given in figs. 1-6. test results showed that after 10% replacement of fa the strength development decreases. also test results for splitting tensile strength, flexural strength, and compressive strength at 90 days showed that all levels of fa replacement decreased aforementioned strengths when compared with control concrete. conclusions 1an experimental study was carried out to optimize the mix design proportions for high strength concrete (hsc) so as to maximize the compressive strength at 7, 28, 56, 90 days, splitting tensile at 28 days, flexural strength at 28 days and slump. mix proportions are also set to minimize production cost. taguchi method with l27 orthogonal array was used to investigate the ranking of different hsc parameters. the most important parameters affecting all the three mechanical properties were steel fiber, fly ash, and water to cement ratio respectively. 2after analyzing the results, it was found that higher maximum aggregate size yielded better strength. 3it is found that super-plasticizer is the most effective parameter for the slump. 4the effect of the steel fiber on the strength does not appear at early ages. 5steel fiber is the most effective factor on splitting tensile strength and flexural strength. 6steel fiber is the most effective factor on production cost. 7the strength of fly ash concrete will depend on whether a water reduction is achieved, plus the pozzolanic performance of the cement/fly ash combination. fly ash is able to reduce the heat of hydration very effectively. using fly ash in concrete will increase the setting time compared with an equivalent grade of pc concrete. this increased setting time reduces the rate of workability loss. formwork striking times at lower ambient temperatures may have to be extended in comparison to pc concrete. 8fly ash is the most effective factor on compressive strengths at all ages. this does not mean increase the strengths but fa replacement decreased the strengths. 9high strength is generally the first property associated with silica fume concrete. an increase in the compressive strength using silica fume will result in a similar relative increase in the tensile and flexural strength. this plays a strong role when silica fume concrete is used in flooring, bridging or roadway projects. 10the inclusion of silica fume in concrete causes significant changes in the structure of the matrix, though both physical action and a pozzolanic reaction, to produce a densified, refined pore system and greater strength. 11the study showed that taguchi method can be used effectively and economically for designing the experiments and for determining the optimum process parameters. references [1] alam, s., fatima, a. and butt, m.s. (2007). sustainable development in pakistan in the context of energy consumption demand and environmental degradation, journal of asian economics, 18(5), pp. 825-837. [2] singh, r.k., murty, h.r., gupta, s.k. and dikshit, a.k. (2009). an overview of sustainability assessment methodologies, ecological indicators, 9(2), pp. 189-212. [3] wced (1987), our common future, report of the world commission on environment and development, world commission on environment and development. [4] wang, j.-j., jing, y.y., zhang, c.f. and zhao, j.h. (2009). review on multi-criteria decision analysis aid in sustainable energy decision-making, renewable and sustainable energy reviews, 13(9), pp. 2263-2278. [5] kleindorfer, p.r., singhal, k. and wassenhove, l.n. (2005). sustainable operations management,production and operations management, 14(4), pp. 482-492. [6] bansal, s., biswas, s. and singh, s.k. (2017). fuzzy decision approach for selection of most suitable construction method of green buildings, international journal of sustainable built environment, 6(1), pp. 122-132. [7] govindan, k., shankar, k.m. and kannan, d. (2016). sustainable material selection for construction industry – a hybrid multi criteria decision making approach, renewable and sustainable energy reviews, 55, pp. 1274-1288. [8] aitcin, p-c. (2004) high performance concrete, taylor & francis e-library, isbn 0-203-78327-1. m.a. warda et al., frattura ed integrità strutturale, 54 (2020) 211-225; doi: 10.3221/igf-esis.54.16 225 [9] gordon, j. e. (1991). structures or why things don’t fall down, penguin books, london, isbn 01401.3628 2, 174 pp. [10] ozbay, e, oztas, a, baykasoglu, a, ozbebek, h. (2009). investigating mix proportions of high strength selfcompacting concrete by using taguchi method, construction and building materials, 23, pp. 694-702. [11] khiabani, a.c., bastami, m., baghbadrani, m., kordi, m. (2011). optimization of the concrete mix proportions centered on performance after exposure to high temperature, advanced materials research, 268-270, pp. 372-376. [12] hashemi, s.h., soleymani, a. (2013). optimization of hsc compressive strength by taguchi method, applied mechanics and materials, 253-255, pp. 572-575. [13] emara, m.a., eid f.m., nasser a.a., safaan m.a. (2018). prediction of self-compacting rubberized concrete mechanical and fresh properties using taguchi method, j. of civil & environmental engineering, 8(2). [14] kumari, s., palamu, t. (2013). optimization of cement content in concrete using additives, 3rd international conference on sustainable construction materials and technologies, http://www.claisse.info/proceedings.htm. [15] tan, o., zaimoglu, a. s., hinislioglu, s., altun s. (2005). taguchi approach for optimization of the bleeding on cement –based grouts, tunneling and underground space technology, 20, pp. 167-173. [16] hinislioglu, s., bayrak, o. u. (2004). optimization of early flexural strength of pavement concrete with silica fume and fly ash by the taguchi method, civil engineering and environmental systems, 21(2), pp. 79-90. [17] kackar, r.n. (1986). taguchi’s quality philosophy : analysis and commentary, american society for quality control. [18] ye, l., hai, t.k., dong, z. (2016). optimization of compressive strength and tensile strength of ultra-high performance concrete, hipermat proceedings, kassel, germany. [19] bayrak, o.u., hattatoglu, f., hinislioglu, s. (2010). determination of modulus of rupture of pavement concrete with silica fume and fly ash using taguchi technique, international journal of civil and structural engineering, 1(3). [20] neville, a.m. (2002). properties of concrete, british library, isbn 0-582-23070-5. [21] kaliyan mathiyazhagan, a., gnanavelbabu, b., lokesh prabhuraj (2018). a sustainable assessment model for material selection in construction industries perspective using hybrid mcdm approaches, journal of advances in management research. [22] behera, m., bhattacharyya, s.k., minocha, a.k., deoliya, r. and maiti, s. (2014). recycled aggregate from c&d waste and its use in concrete – a breakthrough towards sustainability in construction sector: a review, construction and building materials, 68, pp. 501-516. << /ascii85encodepages false /allowtransparency false /autopositionepsfiles true /autorotatepages /none /binding /left /calgrayprofile (dot gain 20%) /calrgbprofile (srgb iec61966-2.1) /calcmykprofile (u.s. web coated \050swop\051 v2) /srgbprofile (srgb iec61966-2.1) /cannotembedfontpolicy /error /compatibilitylevel 1.4 /compressobjects /tags /compresspages true /convertimagestoindexed true /passthroughjpegimages true /createjobticket false /defaultrenderingintent /default /detectblends true /detectcurves 0.0000 /colorconversionstrategy /cmyk /dothumbnails false /embedallfonts true /embedopentype false /parseiccprofilesincomments true /embedjoboptions true /dscreportinglevel 0 /emitdscwarnings false /endpage -1 /imagememory 1048576 /lockdistillerparams false /maxsubsetpct 100 /optimize true /opm 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/hrv (za stvaranje adobe pdf dokumenata najpogodnijih za visokokvalitetni ispis prije tiskanja koristite ove postavke. stvoreni pdf dokumenti mogu se otvoriti acrobat i adobe reader 5.0 i kasnijim verzijama.) /hun 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can be opened with acrobat and adobe reader 5.0 and later.) >> /namespace [ (adobe) (common) (1.0) ] /othernamespaces [ << /asreaderspreads false /cropimagestoframes true /errorcontrol /warnandcontinue /flattenerignorespreadoverrides false /includeguidesgrids false /includenonprinting false /includeslug false /namespace [ (adobe) (indesign) (4.0) ] /omitplacedbitmaps false /omitplacedeps false /omitplacedpdf false /simulateoverprint /legacy >> << /addbleedmarks false /addcolorbars false /addcropmarks false /addpageinfo false /addregmarks false /convertcolors /converttocmyk /destinationprofilename () /destinationprofileselector /documentcmyk /downsample16bitimages true /flattenerpreset << /presetselector /mediumresolution >> /formelements false /generatestructure false /includebookmarks false /includehyperlinks false /includeinteractive false /includelayers false /includeprofiles false /multimediahandling /useobjectsettings /namespace [ (adobe) (creativesuite) (2.0) ] /pdfxoutputintentprofileselector /documentcmyk /preserveediting true /untaggedcmykhandling /leaveuntagged /untaggedrgbhandling /usedocumentprofile /usedocumentbleed false >> ] >> setdistillerparams << /hwresolution [2400 2400] /pagesize [612.000 792.000] >> setpagedevice microsoft word 2210 f. v. antunes et alii, frattura ed integrità strutturale, 48 (2019) 676-692; doi: 10.3221/igf-esis.48.64 676 focused on the “portuguese contributions for structural integrity” stress intensity factor solutions for cts mixed mode specimen f.v. antunes, r. branco, j.a.m. ferreira, l.p. borrego university of coimbra, portugal fernando.ventura@dem.uc.pt, http://orcid.org/0000-0002-0336-4729 ricardo.branco@dem.uc.pt, http://orcid.org/0000-0001-2345-6789 martins.ferreira@dem.uc.pt, borrego@isec.pt abstract. the compact tension shear (cts) specimen is used to study fracture and fatigue under mixed mode i/ii loading conditions. the k solution available in literature was developed for fracture studies and does not consider the effect of crack deflection. the aim of present work is to develop ki and kii empirical solutions for cracks with different crack lengths, loading angles and crack orientations. a total number of 1120 cracked geometries were studied numerically with the finite element method and analytical solutions were fitted to the numerical predictions. an average difference of 0.53 % was found between numerical predictions and the analytical solution proposed for ki. for kii the difference is higher, but the equivalent stress intensity factor showed a difference of only 1% because kii is lower than ki. experimental work was developed to study fatigue crack growth in cts specimens. the cracks always adopted a direction approximately normal to loading direction, i.e., tend to propagate under mode i. keywords. cts specimen; stress intensity factor solution; mixed mode citation: antunes, f. v., branco, r., ferreira, j.a.m., borrego, l.p., stress intensity factor solutions for cts mixed mode specimen, frattura ed integrità strutturale, 48 (2019) 676-692. received: 06.10.2018 accepted: 28.11.2018 published: 01.01.2019 copyright: © 2019 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. introduction he majority of studies on fracture toughness and fatigue crack propagation are performed for mode i loading. however, there are situations where the cracks are not normal to maximum principal stress direction. furthermore, at microscale level, depending on microstructural details, deviations in crack direction may occur even under mode i loading. macroscopic crack deflection occurs due to asymmetry in stresses near the crack tip, resulting from multi-axial far field loading or from non-uniformity in mechanical properties near the crack tip. since mixed mode loading tests are not standardized, several specimens have been developed. a geometry widely used to study mixed mode i/ii loading, named compact tension shear (cts), was developed by richard 1. it is a rectangular specimen with through crack and three holes for fixing on each side. this geometry was used to study fracture toughness and fatigue crack growth of metallic materials 2,3, laminated composites 4, adhesive joints 5,6, ce-tzp/alumina composite 7, etc. banks-sills et al. 8 modified the cts specimen considering a lower width at the center of the t http://www.gruppofrattura.it/va/48/2210.mp4 f. v. antunes et alii, frattura ed integrità strutturale, 48 (2019) 676-692; doi: 10.3221/igf-esis.48.64 677 specimen, where the crack is positioned. recently, lo et al. 9 suggested a third version similar to the original one but with a different positioning of the holes. other geometries have been used to study mixed mode i/ii loading namely the compact mixed-mode specimen, cmm 10, the asymmetric three-point single edge notch bend specimen, asenb3, and the asymmetric four-point single edge notch bend specimen, asenb4 11. for mixed mode i/iii loading a modified compact tension specimen (mct) was developed 12. for materials submitted to compressive loads (like glass) alternative specimens were developed, namely the cracked brazilian disc specimen, cbd 13 and the double clivage drilled compression, dcdc 14. richard et al. 15 obtained ki and kii solutions for the original cts geometry, presented in appendix a, considering that the crack was plane and normal to lateral faces. these solutions are adequate for fracture studies, since pre-cracks are obtained under mode i loading therefore do not suffer crack deflection. however, cracks submitted to mixed mode fatigue loading change orientation searching mode i loading and richard’s solutions can be inadequate since they have been developed for straight cracks. therefore, the objective of the present work is the development of ki, kii solutions for the cts mixed mode specimen which include the influences of crack length, loading angle and crack orientation. this way, literature solution is extended for fatigue studies under mixed mode loading. several crack geometries were studied numerically by the finite element method in order to obtain ki, kii, and analytical solutions were fitted to the numerical predictions. numerical procedure ig. 1 presents the geometry of the compact tension shear (cts) specimen studied here. it has a width of 90 mm, a total height of 148 mm, and a thickness of 3 mm, and is identical to richard’s specimen 1, except in the thickness. the thickness affects the shape of crack front, but a reduced effect on crack orientation may be expected. a pre-crack submitted to cyclic loading changes its direction approaching direction normal to remote loading, i.e., approaching mode i. a main geometrical parameter is therefore the slope at the crack tip, . the specimens used in the experimental work had an initial notch depth a0=42.5 mm, however cracks with less extent were studied numerically to enable the reduction of initial notch depth in posterior studies. this specimen geometry was tested with the loading device shown in fig. 2. this apparatus was based on the mixed-mode fracture testing technique originally developed by richard 16. the loading device allows to apply pure mode-i, pure mode-ii, as well as mixed-mode loading to the cts specimen just by changing the loading angle  between the longitudinal axis of the specimen and the load direction applied by a uniaxial tension testing machine. fig. 3 defines load direction, , and boundary conditions. the specimen has circular holes but the loading device has elongated holes. the holes 1, 3, 4, 6 are elongated in the direction parallel to the crack so that forces f1, f3, f4 and f6 are normal to the crack plane. on the other hand, holes 2 and 5 are elongated perpendicular to the crack so that only the forces f2 and f5 parallel to the crack can be transmitted from the load device to the specimen. the uniaxial load f is related with punctual loads according 16: 1 c f f f.( cosα sin )1 6 2 b    2 5f f f.sinα  3 4 1 c f f f.( cosα sin ) 2 b    (1) the material studied was the almgsi1 (6082) aluminium alloy with a t6 heat treatment. the t6 heat treatment corresponds to a conversion of heat-treatable material to the age-hardened condition by solution treatment, quenching and artificial age-hardening. the chemical composition and the mechanical properties of the alloy are shown in tabs. 1 and 2, respectively. si mg mn fe cr cu zn ti other 1.05 0.80 0.68 0.26 0.01 0.04 0.02 0.01 0.05 table 1: chemical composition of 6082-t6 aluminium alloy (wt. %). f f. v. antunes et alii, frattura ed integrità strutturale, 48 (2019) 676-692; doi: 10.3221/igf-esis.48.64 678 figure 1: geometry and loading of cts specimen. figure 2: mixed-mode loading device (=60º). a 2d analysis was developed numerically, assuming a plane strain state. due to lack of symmetry in terms of loading and geometry of the crack, the whole specimen was analyzed. the boundary conditions considered are presented in fig. 3, and intend to avoid rigid body movement without affecting the global rigidity of the specimen. the material was assumed to be homogeneous, isotropic with linear elastic behaviour. the elastic properties considered were e=74000 mpa and =0.33. the physical model was analyzed using cosmosm 2.0, a commercial finite element package. quadrilateral isoparametric elements with 8 nodes were considered. singular elements with nodes at quarter-point positions were considered at the crack tip. fig. 4 presents the finite element mesh considered for x=52.5 mm, y=0 and =20º. the crack kinks at x=0, however the crack slope relevant is that at the crack tip. location of (x, y) cartesian coordinates and slope at the crack tip () are defined in fig. 1. the meshes had 4804 elements and 15075 nodes. the geometry of crack remote from its tip does not influence k values. si other tensile strength, uts [mpa] 3002.5 yield strength, ys [mpa] 2452.7 elongation,r [%] 9 cyclic hardening exponent, n' 0.064 cyclic hardening coefficient, k' [mpa] 443 fatigue strength exponent, b -0.0695 fatigue strength coefficient, 'f [mpa] 485 fatigue ductility exponent, c -0.827 fatigue ductility coefficient, 'f 0.773 table 2: mechanical properties of the 6082-t6 aluminium alloy 3. the accuracy of numerical predictions was checked by comparing with literature solution presented in appendix a for =0º 16. differences lower than 2% were obtained for ki and kii which is a good indication for the accuracy of the results. a numerical analysis was also done using marc-mentat 2000 considering square elements with 88 m at the crack tip for a total number of 6700 elements and 20727 nodes. mode i predictions were similar to cosmosm results. f. v. antunes et alii, frattura ed integrità strutturale, 48 (2019) 676-692; doi: 10.3221/igf-esis.48.64 679 figure 3: loading and boundary conditions of the cts specimen. figure 4: typical finite element mesh (x=52.5; y=0; =20º). presentation and analysis of numerical results he stress intensity factors (ki, kii) depend on: the geometry of the specimen, characterized by its width, w; the geometry of the crack, characterized by the cartesian coordinates of its tip (xp, yp) and by the slope at its tip ( in fig. 1); the magnitude and direction of the load, which can be characterized by  (=f/(wt), being t the thickness of the specimen) and (figs. 2 and 3), respectively: , ( , , , , , )k k f w x y i ii p p     (2) the number of independent variables can be reduced using buckingham’s theorem of non dimensional analysis 17. considering  and x the primary variables, the following non-dimensional relations can be obtained: k x yiy f( , ,α β,β)i w wσ. π.x    (3) k x yiiy f( , ,α β,β)ii w wσ. π.x    (4) this approach reduces the number of independent variables, and yi, yii are independent of unit system and can be used to specimens similar to present one, which is interesting since cts specimen is not a standard geometry. to obtain relations 3 and 4 several numerical analyses were performed in order to obtain yi and yii for the different independent parameters. the values considered for x were 32.5, 37.5, 42.5, 47.5, 52.5, 57.5, 62.5 and 67.5 mm, and for y were 0, 5, 10 and 15 mm. only zero and positive values were considered for y because crack deflects always towards mode t f. v. antunes et alii, frattura ed integrità strutturale, 48 (2019) 676-692; doi: 10.3221/igf-esis.48.64 680 i loading. different values of and  were considered for each of these 24 crack tip positions. the values considered for  were 0, 10, 20, 30, 40, 50 and 60º, while for  were 0, 10, 20, 30, 40, therefore a total number of 1120 numerical analysis were performed. j integral values (ji and jii) were obtained for each analysis, from which ki and kii were calculated according: e.jiki 21 υ   e.jiikii 21 υ   (5) finally, yi and yii were obtained using relations 3 and 4. tabs. b1 and b2 in appendix b present results obtained for yi and yii, respectively, with cosmosm software. typical variations of geometric factor, yi, with (-), , y and (w/(w-x))1.5 can be seen in figs. 5a, 5b, 5c and 5d, respectively. maximum values can be observed in fig. 5a for (-) close to zero, which could be expected as zero correspond to pure mode i loading. however, the maximum value is not always zero, which indicates that there are others aspects influencing the geometric factors apart from loading direction. a good fitting is obtained with second order polynomial or sinusoidal function. a second order polynomial also fits well to results in fig. 5b. it can be seen that the increase of slope at crack tip (), keeping all the others parameters fixed, reduces yi. the typical results presented in fig. 5c show a linear variation with y. finally, fig. 5d shows a linear variation of yi with (w/(w-x))1.5. this variation is related with the asymmetric geometry of the specimen, which imposes flexure to non-cracked section. the increase of crack length decreases the height of rectangular non-cracked section, and increases flexure moment. the comparison between figs. 5 indicates that highest variation of yi occurs with x and then with (-). figure 5: variation of yi with (a) () (for x=52.5 mm; y=0). (b) crack tip slope, () (for x=52.5 mm; y=0). (c) y (for x=37.5 mm; =0º). (d) (w/(w-x))1.5 (for y=0; =10º). a numerical solution with 39 constants was fitted to the numerical results presented in tab. 4 (appendix b) and illustrated in figs. 5: yi= m. 1.5(w / (w x)) +b (6) (a) (b) (c) (d) f. v. antunes et alii, frattura ed integrità strutturale, 48 (2019) 676-692; doi: 10.3221/igf-esis.48.64 681 m = am.(-)2+bm.(-)+cm am = mam.(y/w)+bam mam = 8.4471x10-9.2 4.6826x10-8. -1.5894x10-4 bam = 1.2076 x10-82 1.9219 x10-7. -1.3955 x10-4 bm = mbm.(y/w)+bbm mbm = -2.3457 x10-62 2.9335x10-4 + 4.1625 x10-2 bbm = 9.6990 x10-72 2.4575x10-4 2.8677 x10-4 cm = mcm.(y/w)+bcm mcm = -2.7508 x10-42 + 4.3628x10-2 3.7856 x10-2 bcm = -1.5507x10-42 9.5592 x10-4 + 1.0744 b = ab.(-)2+bb.(-)+cb ab = aab. 2+bab. +cab aab = 4.9864 x10-8.(y/w)+1.4723x10-8 bab = -2.9412 x10-6.(y/w) 1.9886x10-6 cab = -2.6726 x10-4.(y/w)+ 3.0499x10-5 bb = abb. 2+bbb. +cbb abb = -4.3391x10-5.(y/w)2+2.1155 x10-6.(y/w)-5.3868 x10-6 bbb=2.1858 x10-3.(y/w)2-9.6565x10-4.(y/w)+5.8686 x10-4 cbb = 5.7786 x10-2.(y/w)-2.6952e-03 cb = acb. 2+bcb. +ccb acb =-6.9194 x10-4. (y/w) + 2.6846e-04 bcb=7.8256 x10-2.(y/w) + 5.9363e-04 ccb == 2.0543.(y/w)2-6.2440 x10-3.(y/w)-1.5349x10-1 the units of  and  are degrees. the parametric region where this solution is valid is: 0, 60º; x/w  0.4, 0.75 mm; y/w  0, 0.167. this solution has an average difference of 0.53 % relative to numerical values, with maximum and minimum differences of +2.2 e -3.01, respectively. the average difference was obtained from the absolute values of the differences. typical variations of geometric factor, yii, with (-), , y and x can be seen in figs. 6a, 6b, 6c and 6d, respectively. yii has a complex variation with (-) as can be seen in fig. 6a. minimum values, close to zero were obtained for -0, as could be expected. as for yi, minimum values do not coincide exactly with =0, which is a consequence of the complexity of the situation. yii increase with crack length, x (fig. 6d). a good fitting to results in figs. 6b (), 6c (y) and 6d (x) was obtained with second order polynomials. the comparison between figs. 6 indicates that the highest variation of yii occur with (-), followed by x. the magnitudes of the variations of yii with x and  are similar. the complex variations of yii, namely with , complicated significantly the development of a regression function. since similar values of kii are expected for symmetrical values of (), this parameter was replaced by . besides since minimum values occur in general for 0, yii was studied as a function of  being the angle for minimum yii. considering this change of independent variable and adequate values for , the results of fig. 6a modify to results in fig. 7. all the results fall on the same trend, which indicates that the parameter proposed is adequate. an empirical expression with 54 constants was fitted to the numerical values of yii: yii=a.sin(--t) (7) a = aa.(x/w)2+ba.(x/w)+ca aa = aaa.2+baa.+caa aaa=-1709.472357 .(y/w)2+519.545852 (y/w )+ 21.384622 baa=959.716917.(y/w)2-249.236159 (y/w )+ 6.561228 caa=-98.482311.(y/w)2+4.234582(y/w )+ 1.006272 ba = aba.2+bba.+cba aba=1953.567396.(y/w)2-541.35909 (y/w )-19.747265 bba= -1101.79278.(y/w)2+255.808188(y/w )-7.044048 cba=113.285142.(y/w)2-3.803387 (y/w )+ 0.704463 f. v. antunes et alii, frattura ed integrità strutturale, 48 (2019) 676-692; doi: 10.3221/igf-esis.48.64 682 ca = aca.2+bca.+cca aca=-529.091514.(y/w)2+143.768493(y/w)+ 4.296419 bca=299.064879.(y/w)2-71.861075 (y/w)+ 1.74509 cca=-27.688878.(y/w)2+1.127385.(y/w)+ 0.773005 t = at.(x/w)2+bt.(x/w)+ct at = aat.2+bat.+cat aat= -31.328451.(y/w)2 189.201651(y/w) 13.342750 bat= -75.128472.(y/w)2 + 152.527046(y/w) + 11.48976 cat= 32.715576.(y/w)2 17.576125(y/w) 0.138782 bt = abt.2+bbt.+cbt abt=-15.361974.(y/w)2 + 209.112802(y/w) + 11.726069 bbt= 116.101593.(y/w)2 166.317934(y/w) 9.360830 cbt= -41.982624.(y/w)2 + 19.603112(y/w) + 0.083306 ct = act.2+bct.+cct aca= 31.329018.(y/w)2 53.553350(y/w) 2.292627 bca= -50.034429.(y/w)2 + 44.725843(y/w) + 1.819130 cct= 12.967452.(y/w)2 5.665219(y/w) 0.011360 the units of  and  are radians. the parametric region where this solution is valid is:0, 60º; x/w 0.4, 0.75 mm; y/w 0, 0.167. this solution has an average difference of 10.8 % relatively to the numerical values. this average was once again calculated using the absolute values of the differences. this difference is relatively high, however it is mainly a consequence of odd results obtained for a reduced number of the predictions. figure 6: variation of yii with (a) (-) (for x=52.5 mm; y=0). (b) crack tip slope () (for x=32.5 mm; y=0). (c) yp. (d) xp (for y=5 mm; =10º). (a) (b) c) (d) f. v. antunes et alii, frattura ed integrità strutturale, 48 (2019) 676-692; doi: 10.3221/igf-esis.48.64 683 figure 7: variation of yii with  (x=52.5 mm, y=0). furthermore, to evaluate the characteristics of mixed mode fatigue crack, it is necessary to introduce the comparative stress intensity factor kv considering mode i and mode ii simultaneously. the exact relation between kv, ki and kii depends on the criterion employed. the criterion of richard/henn 18 proposes: δk 1 2 2iδk δk 6 δkv i ii2 2    (8) the values of kii are in general much lower than the ones obtained for ki, therefore its influence on kv defined by eq. (8) is relatively low. the solutions presented here for yi and yii were used to obtain kv and this was compared with kv obtained directly from cosmosm results. maximum and minimum differences were found to be +10.63 and -4.5% respectively, but the average difference is 1.01 %, which is excellent. experimental fatigue results n experimental work was developed to study fatigue crack growth and fatigue crack closure under mixed mode loading in 6082-t6 aluminium alloy. the specimens were obtained in the transverse longitudinal (tl) direction from a laminated plate. the initial notch depth was 42.5 mm. before testing the specimen surfaces were polished mechanically. the experiments were performed in a servo-hydraulic, closed-loop mechanical test machine with 100 kn load capacity, interfaced to a computer for machine control and data acquisition. all tests were conducted in air and at room temperature. the tests were performed under load control mode and the load ratio for all loading angles was kept constant at 0.05. the loads were applied with a sinusoidal waveform at a frequency of 20 hz. fatigue pre-cracking was introduced under mode-i loading to an a/w ratio of 0.51, where a and w are the crack length and width of the specimen, respectively. the crack length was measured in both x and y directions using a travelling microscope (45) with a resolution of 10 m. the specimen was painted ahead of the crack tip (fig. 2) to enhance optical measurement of crack length. the maximum and minimum loads applied for each loading angle were chosen in order to have after fatigue pre-crack a comparative stress intensity factor, kv, defined by eq. (8) of approximately 6 mpa.m1/2, where the mode-i and mode-ii stress intensity factor ranges were calculated by the solutions presented in appendix a. tab. 3 summarizes the parameters of the experimental testes. further details can be found elsewhere 3. the k solutions developed here were applied to the treatment of the experimental results. the crack tip coordinates (x,y) and slope, , were measured directly on specimen’s surface using profilometer rodenstok rm 6003d. however,  could have been obtained from (x,y) values using a procedure similar to the calculation of da/dn 0 1 2 0 0.2 0.4 0.6 0.8 1 1.2 abs()-t [º] y ii [ -]      a f. v. antunes et alii, frattura ed integrità strutturale, 48 (2019) 676-692; doi: 10.3221/igf-esis.48.64 684 from (a,n) experimental results. fig. 8 presents experimental crack shapes for different loading directions, which are indicated for each case. the cracks adopted a direction approximately normal to loading direction, i.e., tend to propagate under mode i loading. however, () is not exactly zero and increases with  and with crack length. test  º f n r 1 30 1539 0.05 2 45 1900 0.05 3 60 2043 0.05 4 76 2394 0.05 table 3: experimental parameters used in the tests. figure 8: experimental crack shapes. figure 9: comparison of present solution with richard’s solution (=60º). 0 0.004 0.008 0.012 0.016 0.02 0.0425 0.0475 0.0525 0.0575 0.0625 0.0675 x [m] y [m ] =75º =30º =60º =45º =30º 75º 6 8 10 12 14 16 18 0.045 0.050 0.055 0.060 x [m] k v [ m p a. m 1/ 2] ] present solution; kv versus x richard's solution; kv versus x richard's solution; kv versus a -6% -31% f. v. antunes et alii, frattura ed integrità strutturale, 48 (2019) 676-692; doi: 10.3221/igf-esis.48.64 685 the values of x, y, ,  were applied in solutions 6 and 7 to obtain yi and yii, respectively. then considering experimental loads presented in tab. 3, ki and kii were calculated. finally, effective stress intensity factor was obtained using eqn. 8. fig. 9 compares the values of kv for =60º obtained with solutions 6 and 7, and with richard’s solution. two different approaches were considered when applying richard’s solution: consider x and consider crack length, a. significant differences were found, with maximum values of -6% and -31%, as indicated in fig. 9. differences are significantly reduced if total crack length, a, is used in richard’s solution instead of coordinate x. therefore, the present solution represents a significant improvement relatively to richard’s solution. notice that richard’s solution was obtained for y=0 and =0º. numerical prediction of crack path ropagation directions were also studied numerically using the solutions developed here for yi and yii. qian et al. 19 reviewed the criteria used to predict crack growth direction under mixed mode loading, which can be divided into two categories 20. the first includes the methodologies which consider the stress, the strain or the displacement as the driving parameters, namely the maximum tangential stress criterion (mts criterion), and the vector crack tip displacement criterion (ctd criterion). the second category contains the methodologies considering the total or the dilatational elastic strain as the driving parameters, namely the minimum strain energy density criteria (scriterion), the dilatational strain energy density criterion (t-criterion), the minimum accumulated elastic strain energy (p-criterion) and the j-criterion. the mts and s criteria are widely used. according s-criterion [21] the crack is assumed to grow along a direction that minimizes the strain energy density factor, s: 2 2 2s a k 2a k k a k a k11 1 12 1 2 22 2 33 3    (9) where aij are coefficients relating polar angle (), e and , and  k k / πi i . s includes the dilatational and the distortional strain energy. the j-criterion uses the line integral with the same name and states that crack extends along direction of vector: ˆ ˆj j .i j .ji ii   (10) figure 10: (a) crack direction predictions considering different criteria (=60º). (b) crack tip slopes () for different crack propagation criteria (=60º). notice that since k solutions were defined in terms of (), crack propagation increments must consider a rotation of cartesian coordinate system. in fact, jii=0 corresponds to a propagation along a direction normal to loading direction. p a) b) f. v. antunes et alii, frattura ed integrità strutturale, 48 (2019) 676-692; doi: 10.3221/igf-esis.48.64 686 the p-criterion 20 considers the accumulated elastic strain energy (p) within a circular core with radius r0 around the crack tip as the driving parameter. p-factor is given by: 2 2p λ k λ k1 i 3 ii  (11) being 1=0.0000191419 and 3=0.0000300746, as indicated by pavlou et al. 20. the crack is assumed to propagate along direction of minimum p-factor. another two criteria were used here: the maximum value of ki (ki-criterion) and the minimum value of energy release rate (g-criterion), being g obtained from effective stress intensity factor defined in eqn. 8. fig. 10a presents the results obtained for =60º considering different criteria and crack propagation increments of 0.5 mm. loading direction is also presented. it can be seen that all criteria, except j-criterion, predict crack slopes lower than experimentally observed. best predictions were obtained with p-criterion and g criterion, which gave similar results. finally, fig. 10b presents the variation of crack tip slope () with crack propagation. it can be seen that  reduces with crack propagation. the rate of variation of with crack growth predicted numerically is similar to that measured experimentally. conclusions he main conclusions of the present work are: ki, kii stress intensity factor solutions were obtained numerically for cts (compact tension shear) specimen. these solutions are valid for a wide range of x, y,  (load direction) and  (crack tip angle): 0, 60º; x/w  0.4, 0.75 mm; y/w  0, 0.167. the average accuracy of kv is expected to be 1.01 %; the solution developed was applied to crack profiles obtained experimentally in 6082-t6 aluminium alloy. as expected, significant differences were found between present solution and richard’s solution when  is different from zero. the differences reduce significantly when the whole crack length is used in richard’s solution; experimental work was developed to study fatigue crack growth in cts specimens. the cracks always adopted a direction approximately normal to loading direction, i.e., tend to propagate under mode i loading; the solution developed here was used to predict crack growth direction considering different criteria. best predictions were obtained with p-criterion and g-criterion. by request the authors will send by e-mail the solution developed here, implemented in an excel file. aknowledgements his research is sponsored by feder funds through the program compete (under project t44950814400019113) and by national funds through fct – portuguese foundation for science and technology, under the project ptdc/ems-pro/1356/2014. references [1] richard, h.a. (1981). a new compact shear specimen, international journal of fracture, 17, pp. r105-r107. [2] biner, s.b. (2001). fatigue crack growth studies under mixed-mode loading, international journal of fatigue, 23, pp. s259-s263. [3] borrego, l.p., antunes, f.v., ferreira, j.m. and costa, j.d. (2004). mixed-mode fatigue crack growth and closure in aluminium alloys, proc. 7th icbmffseventh international conference on biaxial/multiaxial fatigue fracture, berlin, germany, pp.1483-488. [4] rikards, r. et al. (1998). investigation of mixed mode i/ii interlaminar fracture toughness of laminated composites by using a cts type specimen, engineering fracture mechanics, 61, pp. 325-342. [5] madhusudhana, k.s. and narasimhan, r. (2002). experimental and numerical investigations of mixed mode crack growth resistance of a ductile adhesive joint, engineering fracture mechanics, 69, pp. 865-883. t t f. v. antunes et alii, frattura ed integrità strutturale, 48 (2019) 676-692; doi: 10.3221/igf-esis.48.64 687 [6] pirondi, a. and nicoletto, g. (2002). mixed mode i/ii fracture toughness of bonded joints, international journal of adhesion and adhesives, 22, pp. 109-117. [7] lin, g.-y. and shetty, d.k. (2003). transformation zones, crack shielding, and crack growth resistance of cetzp/alumina composite in mode ii and combined mode ii and mode i loading, engineering fracture mechanics, 70, pp. 2569-2585. [8] banks-sills, l. and arcan, m. (1986). a compact mode ii fracture specimen, fracture mechanics, 17, astm-stp 905, american society for testing and materials, pp. 347-363. [9] lo, k.w., gong, y.b., tamilselvan, t. and lai, m.o. (2003). a proposed specimen for kiic testing, international journal of fracture, 124, pp. 127-137. [10] hyde, t.h. and chambers, a.c. (1988). a compact mixed-mode (cmm) fracture specimen, journal of strain analysis, 23 (2), pp. 61-66. [11] choi, r.s., zhu, d. and miller, r.a. (2003). mode i, mode ii and mixed-mode fracture of plasma-sprayed thermal barrier coatings at ambient and elevated temperatures, proc. 8th international symposium on fracture mechanics of ceramics, university of houston, (nasa/tm 2003-212185). [12] patterson, e.a. and gungor, s. (1997). a photoelastic study of an angle crack specimen subjected to mixed mode iiii displacements, engineering fracture mechanics, 56, pp. 767-778. [13] ayatollahi, m.r. and aliha, m.r.m. (2005). cracked brazilian disc specimen subjected to mode ii deformation, engineering fracture mechanics, 75, pp. 493-503. [14] lardender, t.j., chakravarthy, j.d., quinn, j.d. and ritter, j.e. (2001). further analysis of dcdc specimen with an offset hole, international journal of fracture, 109, pp. 227-237. [15] richard, h.a. and benitz, k. (1983). a loading device for the creation of mixed mode in fracture mechanics, international journal of fracture, 22, pp. r55-r58. [16] richard, h.a. (1985). bruchvorhersagen bei überlagerter normalund schubbeanspruchung von risen, vdi forschungsheft 631, düsseldorf: vdi-verlag, pp. 1-60. [17] setién, j. and varona, j.m. (1996). on the use of dimensional analysis in fracture mechanics. proc. 11th biennial european conference on fracture (ecf11), poitiers, france, ed. by j. petit, vol.i, september 3-6, pp. 125-132. [18] richard, h.a., linnig, w. and henn, k. (1991). fatigue crack propagation under combined loading, forensic engineering, 3, pp. 99-109. [19] qian, j. and fatemi, a. (1996). mixed mode fatigue crack: a literature survey, engineering fracture mechanics, 55 (6), pp. 969-990. [20] pavlou, d.g. labeas, g.n., vlachakis, n.v. and pavlou, f.g. (2003). fatigue crack propagation trajectories under mixed mode cycling loading, engineering structures, 25, pp. 869-875. [21] sih, g.c. (1974). strain energy density factor applied to mixed mode crack problems, international journal of fracture, 10, pp. 305-321. appendix a: literature solution 15 he stress intensity factors for different loading angles considering =0º are: a 0.26 2.65 f cosα w ak π.ai a aw.t 1 a / w 21 0.55 0.08( ) w a w a        (a1) a 0.23 1.40 f sinα w ak π.aii a aw.t 1 a / w 21 0.67 2.08( ) w a w a         (a2) t f. v. antunes et alii, frattura ed integrità strutturale, 48 (2019) 676-692; doi: 10.3221/igf-esis.48.64 688 where f is the applied force, w is the width of the specimen, t is the thickness, a is the crack length,  is the angle of loading direction with respect to the crack plane. the degree of the mode-mixity is given by: i ii k2 m .a.tan( ) π k  (a3) f. v. antunes et alii, frattura ed integrità strutturale, 48 (2019) 676-692; doi: 10.3221/igf-esis.48.64 689 appendix b: numerical results x= 32.5 x= 37.5   0 10 20 30 40 50 60 0 10 20 30 40 50 60 0 1.97 1.91 1.8 1.63 1.41 1.15 0.86 2.27 2.22 2.1 1.91 1.67 1.37 1.04 10 1.94 1.94 1.87 1.75 1.58 1.35 1.09 2.24 2.24 2.18 2.04 1.85 1.6 1.3 y=0 20 1.87 1.91 1.9 1.82 1.7 1.52 1.29 2.16 2.22 2.2 2.12 1.98 1.77 1.51 30 1.76 1.84 1.87 1.85 1.76 1.62 1.44 2.04 2.14 2.17 2.14 2.05 1.89 1.68 40 1.6 1.72 1.79 1.81 1.76 1.67 1.52 1.87 2.01 2.09 2.1 2.06 1.95 1.78 0 1.97 1.99 1.94 1.84 1.68 1.46 1.21 2.28 2.3 2.25 2.13 1.95 1.71 1.42 10 1.95 2.02 2.02 1.96 1.84 1.67 1.44 2.25 2.33 2.34 2.27 2.13 1.94 1.68 y=5 20 1.89 2 2.04 2.03 1.96 1.82 1.63 2.18 2.31 2.36 2.35 2.26 2.1 1.88 30 1.78 1.93 2.02 2.05 2.01 1.92 1.77 2.06 2.23 2.33 2.36 2.32 2.21 2.03 40 1.63 1.81 1.93 2 2 1.95 1.83 1.9 2.1 2.24 2.32 2.32 2.25 2.11 0 1.98 2.07 2.09 2.05 1.94 1.78 1.56 2.29 2.39 2.41 2.37 2.25 2.06 1.81 10 1.97 2.1 2.17 2.18 2.11 1.99 1.8 2.28 2.43 2.51 2.51 2.43 2.29 2.07 y=10 20 1.91 2.09 2.2 2.25 2.23 2.14 1.98 2.21 2.41 2.54 2.59 2.56 2.45 2.27 30 1.81 2.02 2.18 2.26 2.28 2.23 2.11 2.1 2.37 2.51 2.6 2.62 2.55 2.41 40 1.66 1.91 2.09 2.21 2.26 2.24 2.16 1.94 2.21 2.42 2.55 2.6 2.57 2.47 0 2.01 2.16 2.25 2.27 2.23 2.11 1.93 2.32 2.49 2.59 2.62 2.56 2.42 2.22 10 2 2.2 2.34 2.41 2.4 2.32 2.17 2.31 2.54 2.69 2.77 2.75 2.66 2.48 y=15 20 1.95 2.2 2.38 2.48 2.52 2.47 2.35 2.25 2.53 2.73 2.85 2.88 2.82 2.68 30 1.85 2.13 2.35 2.5 2.56 2.56 2.47 2.14 2.46 2.7 2.86 2.93 2.92 2.81 40 1.71 2.02 2.26 2.43 2.53 2.56 2.5 1.99 2.34 2.61 2.8 2.91 2.93 2.86 x= 42.5 x= 47.5   0 10 20 30 40 50 60 0 10 20 30 40 50 60 0 2.64 2.59 2.46 2.25 1.98 1.64 1.26 3.14 3.09 2.94 2.7 2.38 1.98 1.53 10 2.61 2.62 2.55 2.39 2.17 1.88 1.53 3.11 3.11 3.03 2.85 2.58 2.24 1.83 y=0 20 2.52 2.59 2.57 2.47 2.3 2.07 1.76 3 3.07 3.04 2.93 2.72 2.43 2.07 30 2.38 2.49 2.53 2.49 2.37 2.19 1.93 2.83 2.96 2.99 2.93 2.78 2.55 2.24 40 2.19 2.34 2.43 2.44 2.37 2.24 2.03 2.61 2.78 2.86 2.86 2.77 2.59 2.34 0 2.65 2.68 2.63 2.5 2.29 2.01 1.67 3.15 3.18 3.12 2.97 2.72 2.4 1.99 10 2.63 2.71 2.72 2.64 2.48 2.25 1.95 3.12 3.22 3.22 3.12 2.93 2.65 2.29 y=5 20 2.54 2.68 2.74 2.72 2.62 2.43 2.17 3.02 3.18 3.24 3.2 3.07 2.84 2.53 30 2.4 2.59 2.7 2.73 2.68 2.54 2.33 2.86 3.07 3.18 3.2 3.12 2.95 2.68 40 2.22 2.45 2.6 2.67 2.66 2.57 2.41 2.65 2.89 3.05 3.12 3.09 2.97 2.76 0 2.67 2.78 2.81 2.75 2.61 2.39 2.1 3.16 3.29 3.32 3.25 3.08 2.82 2.47 10 2.65 2.82 2.91 2.91 2.82 2.64 2.38 3.15 3.34 3.43 3.42 3.3 3.08 2.77 y=10 20 2.57 2.8 2.94 2.99 2.95 2.82 2.6 3.06 3.31 3.45 3.5 3.44 3.27 3 30 2.44 2.71 2.9 2.99 3 2.92 2.74 2.9 3.2 3.4 3.49 3.48 3.37 3.15 40 2.26 2.56 2.79 2.93 2.98 2.93 2.8 2.69 3.03 3.27 3.41 3.44 3.38 3.21 0 2.7 2.9 3.01 3.03 2.96 2.8 2.55 3.2 3.42 3.55 3.56 3.47 3.27 2.97 10 2.69 2.95 3.12 3.19 3.17 3.05 2.84 3.19 3.48 3.66 3.74 3.7 3.55 3.29 y=15 20 2.62 2.93 3.15 3.28 3.31 3.23 3.06 3.11 3.45 3.7 3.83 3.84 3.74 3.52 30 2.5 2.85 3.12 3.29 3.36 3.33 3.19 2.96 3.35 3.64 3.82 3.89 3.83 3.66 40 2.33 2.71 3.01 3.21 3.32 3.33 3.24 2.76 3.18 3.51 3.73 3.84 3.83 3.7 f. v. antunes et alii, frattura ed integrità strutturale, 48 (2019) 676-692; doi: 10.3221/igf-esis.48.64 690 x= 52.5 x= 57.5   0 10 20 30 40 50 60 0 10 20 30 40 50 60 0 3.81 3.75 3.57 3.29 2.9 2.43 1.88 4.76 4.69 4.51 4.12 3.64 3.05 2.37 10 3.77 3.78 3.67 3.45 3.12 2.7 2.2 4.71 4.71 4.56 4.28 3.87 3.33 2.7 y=0 20 3.65 3.72 3.67 3.52 3.26 2.9 2.45 4.56 4.63 4.56 4.34 4 3.53 2.96 30 3.45 3.58 3.6 3.51 3.31 3.01 2.63 4.33 4.46 4.45 4.31 4.04 3.64 3.13 40 3.2 3.37 3.44 3.41 3.28 3.04 2.72 4.02 4.2 4.25 4.18 3.97 3.65 3.22 0 3.82 3.86 3.79 3.6 3.3 2.9 2.41 4.77 4.82 4.72 4.48 4.11 3.6 2.99 10 3.78 3.89 3.89 3.76 3.52 3.17 2.73 4.72 4.85 4.82 4.65 4.33 3.89 3.32 y=5 20 3.67 3.84 3.9 3.83 3.65 3.36 2.97 4.58 4.77 4.81 4.71 4.46 4.08 3.57 30 3.48 3.71 3.82 3.82 3.7 3.47 3.13 4.36 4.6 4.7 4.67 4.49 4.17 3.73 40 3.23 3.5 3.66 3.71 3.65 3.48 3.2 4.05 4.34 4.5 4.52 4.41 4.16 3.78 0 3.83 3.98 4.01 3.92 3.71 3.38 2.96 4.78 4.96 4.98 4.86 4.58 4.17 3.63 10 3.81 4.03 4.12 4.09 3.93 3.66 3.27 4.75 4.99 5.09 5.03 4.82 4.46 3.96 y=10 20 3.7 3.98 4.14 4.17 4.07 3.85 3.51 4.62 4.93 5.09 5.09 4.94 4.65 4.21 30 3.52 3.85 4.06 4.15 4.11 3.95 3.66 4.4 4.76 4.98 5.05 4.96 4.73 4.35 40 3.28 3.65 3.9 4.04 4.05 3.94 3.71 4.1 4.5 4.77 4.89 4.87 4.69 4.38 0 3.86 4.12 4.26 4.26 4.14 3.89 3.52 4.81 5.11 5.26 5.25 5.07 4.75 4.28 10 3.85 4.18 4.38 4.45 4.38 4.18 3.85 4.79 5.16 5.38 5.43 5.32 5.05 4.62 y=15 20 3.76 4.14 4.4 4.53 4.52 4.37 4.09 4.67 5.1 5.39 5.51 5.46 5.24 4.21 30 3.59 4.02 4.33 4.52 4.56 4.47 4.24 4.46 4.95 5.28 5.46 5.47 5.32 5 40 3.35 3.82 4.18 4.4 4.5 4.45 4.27 4.17 4.7 5.08 5.31 5.37 5.28 5.02 x= 62.5 x= 67.5   0 10 20 30 40 50 60 0 10 20 30 40 50 60 0 6.18 6.08 5.8 5.35 4.73 3.97 3.09 8.44 8.31 7.93 7.31 6.46 5.42 4.22 10 6.12 6.1 5.89 5.51 4.96 4.26 3.43 8.35 8.31 8.01 7.47 6.7 5.73 4.58 y=0 20 5.93 5.99 5.86 5.56 5.08 4.46 3.69 8.11 8.14 7.93 7.48 6.8 5.91 4.84 30 5.63 5.76 5.71 5.48 5.09 4.55 3.86 7.83 7.83 7.7 7.34 6.75 5.96 4.99 40 5.24 5.42 5.44 5.29 4.98 4.52 3.92 7.19 7.36 7.32 7.05 6.56 5.88 5.02 0 6.18 6.24 6.11 5.79 5.3 4.65 3.85 8.44 8.51 8.32 7.88 7.2 6.3 5.21 10 6.12 6.26 6.2 5.96 5.53 4.94 4.2 8.36 8.51 8.4 8.04 7.44 6.6 5.57 y=5 20 5.94 6.15 6.17 6 5.65 5.12 4.44 8.12 8.35 8.32 8.04 7.52 6.77 5.81 30 5.65 5.92 6.01 5.91 5.64 5.19 4.59 7.73 8.03 8.08 7.88 7.45 6.79 5.93 40 5.27 5.58 5.73 5.7 5.5 5.14 4.61 7.21 7.56 7.68 7.57 7.23 6.67 5.9 0 6.19 6.4 6.42 6.24 5.88 5.33 4.62 8.44 8.71 8.72 8.46 7.94 7.18 6.21 10 6.14 6.43 6.52 6.42 6.11 5.63 4.97 8.37 8.72 8.81 8.62 8.18 7.49 6.57 y=10 20 5.97 6.33 6.49 6.46 6.22 5.8 5.21 8.14 8.56 8.72 8.62 8.25 7.64 6.79 30 5.69 6.1 6.33 6.36 6.2 5.86 5.33 7.76 8.24 8.47 8.45 8.16 7.63 6.87 40 5.31 5.77 6.04 6.14 6.05 5.78 5.33 7.25 7.77 8.06 8.11 7.91 7.47 6.8 0 6.22 6.58 6.75 6.71 6.47 6.03 5.41 8.46 8.93 9.12 9.04 8.69 8.07 7.21 10 6.18 6.62 6.86 6.89 6.72 6.34 5.76 8.39 8.94 9.22 9.22 8.93 8.38 7.57 y=15 20 6.02 6.53 6.84 6.94 6.83 6.51 6 8.17 8.79 9.14 9.21 9 8.52 7.78 30 5.75 6.31 6.68 6.85 6.8 6.55 6.11 7.8 8.47 8.89 9.03 8.9 8.5 7.84 40 5.38 5.98 6.4 6.62 6.64 6.46 6.08 7.31 8.01 8.48 8.68 8.63 8.31 7.73 table b1: numerical values obtained for yi. f. v. antunes et alii, frattura ed integrità strutturale, 48 (2019) 676-692; doi: 10.3221/igf-esis.48.64 691 x= 32.5 x= 37.5   0 10 20 30 40 50 60 0 10 20 30 40 50 60 0 0.02 0.19 0.38 0.56 0.72 0.86 0.97 0 0.21 0.42 0.62 0.79 0.94 1.07 10 0.19 0 0.19 0.38 0.56 0.72 0.85 0.21 0.02 0.22 0.42 0.61 0.78 0.93 y=0 20 0.36 0.18 0 0.18 0.37 0.54 0.69 0.41 0.21 0.05 0.2 0.4 0.58 0.75 30 0.52 0.36 0.19 0.04 0.17 0.34 0.5 0.58 0.41 0.23 0.05 0.17 0.35 0.53 40 0.64 0.51 0.37 0.21 0 0.09 0.26 0.72 0.58 0.43 0.26 0.08 0.11 0.28 0 0.03 0.22 0.4 0.58 0.74 0.87 0.98 0.38 0.24 0.45 0.64 0.81 0.96 1.08 10 0.16 0 0.21 0.39 0.56 0.71 0.84 0.18 0.03 0.23 0.42 0.61 0.77 0.91 y=5 20 0.34 0.17 0 0.17 0.34 0.5 0.65 0.38 0.2 0.05 0.19 0.38 0.55 0.7 30 0.5 0.36 0.21 0.06 0.13 0.28 0.43 0.56 0.4 0.24 0.08 0.13 0.29 0.46 40 0.63 0.52 0.39 0.25 0.1 0 0.16 0.71 0.59 0.45 0.3 0.14 0.05 0.19 0 0.06 0.25 0.43 0.61 0.76 0.89 1 0.05 0.27 0.48 0.67 0.84 0.98 1.1 10 0.14 0.04 0.22 0.4 0.56 0.71 0.83 0.15 0.05 0.25 0.44 0.61 0.77 0.91 y=10 20 0.31 0.15 0 0.17 0.33 0.48 0.61 0.36 0.18 0.05 0.19 0.36 0.52 0.67 30 0.48 0.35 0.21 0.08 0.1 0.24 0.37 0.53 0.39 0.24 0.1 0.1 0.25 0.4 40 0.61 0.51 0.41 0.29 0.15 0 0.07 0.69 0.59 0.47 0.34 0.2 0.06 0.11 0 0.08 0.28 0.47 0.64 0.8 0.93 1.03 0.09 0.3 0.51 0.71 0.88 1.02 1.14 10 0.11 0.07 0.25 0.42 0.58 0.72 0.84 0.13 0.08 0.27 0.46 0.63 0.79 0.92 y=15 20 0.29 0.13 0 0.17 0.32 0.47 0.59 0.33 0.17 0.06 0.2 0.36 0.51 0.65 30 0.45 0.34 0.21 0.09 0.09 0.21 0.33 0.51 0.38 0.24 0.1 0.06 0.2 0.35 40 0.59 0.51 0.42 0.31 0.19 0.03 0 0.66 0.58 0.48 0.36 0.23 0.09 0 x= 42.5 x= 47.5   0 10 20 30 40 50 60 0 10 20 30 40 50 60 0 0 0.23 0.46 0.67 0.86 1.02 1.16 0 0.25 0.49 0.72 0.92 1.1 1.24 10 0.24 0.02 0.22 0.44 0.65 0.84 1 0.27 0.01 0.22 0.46 0.68 0.89 1.06 y=0 20 0.46 0.25 0.05 0.2 0.41 0.61 0.8 0.53 0.3 0.05 0.17 0.41 0.63 0.83 30 0.66 0.48 0.28 0.11 0.17 0.37 0.56 0.77 0.57 0.35 0.13 0.13 0.35 0.56 40 0.83 0.68 0.51 0.32 0.14 0.12 0.29 0.96 0.8 0.61 0.4 0.19 0.08 0.28 0 0.03 0.26 0.48 0.69 0.88 1.04 1.17 0.03 0.28 0.52 0.74 0.95 1.12 1.26 10 0.21 0.02 0.24 0.45 0.65 0.83 0.99 0.24 0 0.23 0.46 0.68 0.88 1.05 y=5 20 0.43 0.23 0.05 0.19 0.39 0.58 0.75 0.5 0.28 0.05 0.16 0.38 0.59 0.78 30 0.64 0.47 0.3 0.13 0.14 0.31 0.49 0.74 0.56 0.36 0.16 0.1 0.29 0.49 40 0.81 0.68 0.53 0.37 0.2 0.09 0.21 0.94 0.8 0.63 0.45 0.26 0.08 0.18 0 0.05 0.29 0.52 0.73 0.91 1.07 1.2 0.06 0.32 0.56 0.78 0.99 1.16 1.29 10 0.16 0.05 0.26 0.47 0.66 0.83 0.98 0.21 0 0.26 0.48 0.7 0.89 1.05 y=10 20 0.36 0.22 0.05 0.19 0.38 0.56 0.72 0.47 0.26 0.02 0.16 0.37 0.57 0.75 30 0.55 0.46 0.3 0.15 0.13 0.27 0.43 0.71 0.54 0.36 0.18 0.08 0.24 0.43 40 0.71 0.68 0.55 0.41 0.26 0.13 0.15 0.91 0.79 0.65 0.49 0.31 0.14 0.11 0 0.1 0.34 0.56 0.78 0.96 1.12 1.25 0.1 0.36 0.61 0.84 1.05 1.22 1.35 10 0.14 0.08 0.29 0.5 0.69 0.86 1 0.17 0.06 0.3 0.52 0.73 0.92 1.08 y=15 20 0.37 0.19 0.05 0.2 0.38 0.55 0.71 0.43 0.23 0 0.17 0.38 0.57 0.75 30 0.58 0.45 0.3 0.17 0.13 0.25 0.39 0.68 0.52 0.36 0.18 0.08 0.22 0.39 40 0.76 0.67 0.56 0.44 0.3 0.18 0.12 0.88 0.78 0.66 0.51 0.35 0.19 0.09 f. v. antunes et alii, frattura ed integrità strutturale, 48 (2019) 676-692; doi: 10.3221/igf-esis.48.64 692 x= 52.5 x= 57.5   0 10 20 30 40 50 60 0 10 20 30 40 50 60 0 0.31 0.26 0.52 0.76 0.98 1.17 1.32 0 0.28 0.56 0.81 1.05 1.25 1.41 10 0.32 0.06 0.2 0.46 0.7 0.92 1.12 0.39 0.11 0.17 0.45 0.71 0.96 1.17 y=0 20 0.63 0.38 0.13 0.13 0.39 0.63 0.86 0.76 0.5 0.22 0.07 0.35 0.62 0.87 30 0.9 0.69 0.45 0.2 0.05 0.31 0.56 1.1 0.87 0.6 0.32 0.04 0.26 0.54 40 1.14 0.96 0.75 0.52 0.27 0 0.24 1.39 1.19 0.96 0.69 0.41 0.12 0.2 0 0.03 0.3 0.55 0.79 1.01 1.19 1.34 0.03 0.31 0.59 0.84 1.07 1.27 1.43 10 0.29 0.03 0.22 0.47 0.7 0.92 1.1 0.36 0.09 0.19 0.45 0.71 0.94 1.15 y=5 20 0.6 0.37 0.12 0.12 0.36 0.59 0.81 0.7 0.49 0.21 0.05 0.32 0.57 0.81 30 0.87 0.68 0.46 0.23 0 0.24 0.48 1.07 0.86 0.62 0.36 0.1 0.18 0.45 40 1.11 0.96 0.77 0.57 0.34 0.1 0.12 1.36 1.2 0.99 0.75 0.5 0.23 0.07 0 0.07 0.33 0.59 0.84 1.05 1.23 1.38 0.06 0.35 0.63 0.88 1.11 1.31 1.47 10 0.26 0 0.25 0.49 0.72 0.93 1.11 0.33 0.06 0.21 0.47 0.72 0.95 1.15 y=10 20 0.56 0.34 0.11 0.12 0.35 0.57 0.78 0.7 0.46 0.21 0.05 0.3 0.54 0.77 30 0.84 0.66 0.46 0.25 0 0.19 0.41 1.04 0.85 0.63 0.39 0.14 0.12 0.37 40 1.08 0.95 0.79 0.6 0.4 0.18 0 1.33 1.19 1.01 0.8 0.57 0.32 0.07 0 0.11 0.39 0.65 0.9 1.12 1.3 1.45 0.11 0.4 0.68 0.94 1.18 1.37 1.53 10 0.21 0.03 0.53 0.53 0.76 0.96 1.14 0.28 0.02 0.25 0.51 0.76 0.98 1.17 y=15 20 0.52 0.31 0.08 0.14 0.37 0.58 0.77 0.65 0.43 0.19 0.07 0.31 0.54 0.77 30 0.8 0.64 0.45 0.25 0 0.16 0.37 0.99 0.82 0.61 0.39 0.16 0.09 0.32 40 1.05 0.93 0.79 0.63 0.44 0.24 0 1.29 1.17 1.01 0.83 0.62 0.39 0.15 x= 62.5 x= 67.5   0 10 20 30 40 50 60 0 10 20 30 40 50 60 0 0 0.3 0.59 0.87 1.12 1.33 1.5 0 0.33 0.64 0.94 1.21 1.44 1.63 10 0.49 0.19 0.12 0.42 0.71 0.98 1.22 0.65 0.33 0.03 0.35 0.68 0.98 1.26 y=0 20 0.96 0.68 0.37 0.06 0.27 0.58 0.87 1.28 0.96 0.62 0.26 0.13 0.49 0.84 30 1.39 1.13 0.84 0.52 0.19 0.16 0.49 1.86 1.56 1.23 0.85 0.45 0.08 0.39 40 1.77 1.54 1.27 0.96 0.63 0.27 0.11 2.36 2.1 1.78 1.41 0.99 0.55 0.11 0 0.02 0.33 0.62 0.9 1.14 1.35 1.52 0.01 0.35 0.66 0.96 1.23 1.46 1.64 10 0.47 0.18 0.13 0.42 0.7 0.96 1.19 0.63 0.32 0.05 0.34 0.65 0.94 1.21 y=5 20 0.94 0.67 0.39 0.11 0.23 0.52 0.8 1.26 0.97 0.65 0.31 0.08 0.4 0.73 30 1.37 1.14 0.87 0.58 0.27 0.08 0.37 1.83 1.58 1.28 0.94 0.57 0.2 0.23 40 1.74 1.55 1.32 1.04 0.74 0.41 0.09 2.34 2.13 1.85 1.52 1.15 0.74 0.31 0 0.06 0.36 0.66 0.93 1.18 1.39 1.56 0.04 0.37 0.69 0.99 1.25 1.48 1.66 10 0.43 0.15 0.15 0.43 0.7 0.95 1.17 0.61 0.31 0.07 0.33 0.63 0.92 1.17 y=10 20 0.9 0.65 0.39 0.12 0.2 0.47 0.73 1.23 0.96 0.67 0.36 0.09 0.32 0.63 30 1.33 1.13 0.89 0.62 0.34 0.06 0.27 1.8 1.58 1.32 1.01 0.68 0.33 0.12 40 1.71 1.55 1.35 1.11 0.84 0.54 0.22 2.3 2.14 1.91 1.63 1.29 0.92 0.52 0 0.1 0.41 0.71 0.98 1.23 1.44 1.61 0.08 0.41 0.73 1.03 1.3 1.52 1.71 10 0.39 0.1 0.17 0.45 0.72 0.96 1.18 0.57 0.28 0.09 0.35 0.64 0.91 1.16 y=15 20 0.86 0.62 0.36 0.08 0.17 0.44 0.69 1.19 0.94 0.67 0.38 0.13 0.28 0.57 30 1.1 1.1 0.88 0.63 0.37 0.07 0.17 1.75 1.57 1.33 1.06 0.75 0.43 0.15 40 1.66 1.53 1.36 1.15 0.9 0.62 0.33 2.25 2.13 1.95 1.7 1.41 1.07 0.7 table b2: numerical values obtained for yii. << /ascii85encodepages false /allowtransparency false /autopositionepsfiles true /autorotatepages /none /binding /left /calgrayprofile (dot gain 20%) /calrgbprofile (srgb iec61966-2.1) /calcmykprofile (u.s. web coated \050swop\051 v2) /srgbprofile (srgb iec61966-2.1) /cannotembedfontpolicy /error /compatibilitylevel 1.4 /compressobjects /tags /compresspages true /convertimagestoindexed true /passthroughjpegimages true /createjobticket false /defaultrenderingintent /default /detectblends true /detectcurves 0.0000 /colorconversionstrategy /cmyk /dothumbnails false /embedallfonts true /embedopentype false /parseiccprofilesincomments true /embedjoboptions true 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can be opened with acrobat and adobe reader 5.0 and later.) >> /namespace [ (adobe) (common) (1.0) ] /othernamespaces [ << /asreaderspreads false /cropimagestoframes true /errorcontrol /warnandcontinue /flattenerignorespreadoverrides false /includeguidesgrids false /includenonprinting false /includeslug false /namespace [ (adobe) (indesign) (4.0) ] /omitplacedbitmaps false /omitplacedeps false /omitplacedpdf false /simulateoverprint /legacy >> << /addbleedmarks false /addcolorbars false /addcropmarks false /addpageinfo false /addregmarks false /convertcolors /converttocmyk /destinationprofilename () /destinationprofileselector /documentcmyk /downsample16bitimages true /flattenerpreset << /presetselector /mediumresolution >> /formelements false /generatestructure false /includebookmarks false /includehyperlinks false /includeinteractive false /includelayers false /includeprofiles false /multimediahandling /useobjectsettings /namespace [ (adobe) (creativesuite) (2.0) ] /pdfxoutputintentprofileselector /documentcmyk /preserveediting true /untaggedcmykhandling /leaveuntagged /untaggedrgbhandling /usedocumentprofile /usedocumentbleed false >> ] >> setdistillerparams << /hwresolution [2400 2400] /pagesize [612.000 792.000] >> setpagedevice microsoft word numero_34_art_60 q. like et alii, frattura ed integrità strutturale, 34 (2015) 543-553; doi: 10.3221/igf-esis.34.60 543 meso-mechanics simulation analysis of microwave-assisted mineral liberation qin like, dai jun school of architecture and civil engineering xi’an university of science and technology, xi’an 710054, p.r china 422576294@qq.com yuan liqun school of architecture and civil engineering, liaocheng university, liaocheng 252059, p.r china abstract. microwave-assisted crushing and grinding can improve efficiency and reduce energy consumption. this paper takes rock grains with galena and calcite as the research object to establish a two-dimensional computational model through the finite difference software flac2d. it analyzes the process and law of mineral boundary failure under microwave irradiation, and assesses the effects of four factors, namely, microwave irradiation time, power density, mineral crystal size, and mineral content, on mineral boundary failure. results indicate an optimal microwave irradiation period for the rapid failure of mineral boundary. moreover, irradiation time and energy consumption can be reduced by increasing the microwave power density. however, irradiation time and energy consumption are basically unchanged when the microwave power density is above a certain threshold. mineral content slightly affects the microwave irradiation time, whereas mineral crystal size significantly affects the microwave irradiation time. in addition, a larger-sized mineral crystal requires less irradiation time and energy consumption to reach the same failure rate. however, irradiation time and energy consumption slightly change when the crystal size is larger than a certain value. keywords. microwave heating; assisted liberation; meso-mechanics simulation; irradiation time; energy consumption. introduction icrowave is an ultra-high frequency electromagnetic wave with a wavelength of 1 mm~1 m. it can be used for heating [1]. compared with conventional heating, microwave heating has advantages of internal heating, rapid heating, selective heating, and simple control; therefore, microwave heating is extensively used in various fields, such as food, agriculture, medical, and metallurgy [2-5]. microwave heating can also be utilized for sorting minerals, which can effectively improve sorting efficiency and reduce energy consumption. different minerals produce various heating characteristics under microwave irradiation due to diverse dielectric properties [6]. the results indicate that several gangue minerals, such as quartz, calcite, and muscovite, are classified as electromagnetic wave-transparent materials that are difficult to heat by microwave; however, some ores, primarily sulfide mineral, iron oxide ores, such as copper, lead sulfide, pyrite, manganese oxide, and many other useful minerals, are microwave-absorbing materials, which can be heated in a very short time in the microwave field [7, 8]. therefore, in the microwave irradiation process, a large temperature m q. like et alii, frattura ed integrità strutturale, 34 (2015) 543-553; doi: 10.3221/igf-esis.34.60 544 difference may form between the gangue and mineral, and a temperature stress may form, producing micro cracks on the mineral boundary and contributing to mineral liberation [9, 10]. testing and numerical methods nowadays are chiefly adopted in microwave-assisted grinding and crushing studies. the test method is primarily used for determining the mineral temperature rising curve and the effect of auxiliary grinding. some scholars have adopted the test method to examine the temperature rising characteristics of titanium concentrate and ilmenite in a microwave field using thermocouple [11, 12]. xiaojuan pan [13] investigated the temperature rising characteristics of manganese ore powder in a microwave field. mamdouh omranet et al. [14] placed the iron ore under microwave irradiation and scanned it via electron microscope (see fig. 1). their test results confirm that micro cracking occurs more easily between mineral and gangue through microwave heating than traditional heating. shenghui guo et al. [15] placed ilmenite under microwave irradiation and revealed that micro cracking occurs between useful mineral and gangue through microwave irradiation, which can effectively promote liberation between mineral and gangue. figure 1: bse image of micro crack distribution after microwave irradiation [14]. at present, measuring via tests the internal temperature and the stress and strain distribution of rocks under microwave irradiation is difficult. qualitative analysis can be performed through scanning electron microscope for the generation and development of micro cracks in minerals under microwave irradiation. however, conducting quantitative research in this manner is difficult. therefore, numerical methods have been primarily used for research in this field. huijun cui et al. [16] simulated the characteristic curve of the increasing temperature of carbon chrome ore powder in a microwave field using the finite element method. some scholars have studied the internal temperature and the stress and strain distribution characteristics of a single crystal mineral through the finite difference method and finite element method, respectively [1719]. a.y. ali et al. [20] confirmed the existence of micro cracks between mineral and gangue via the numerical method. whittles et al. [21] analyzed the change of rock strength under microwave irradiation using the finite difference method. although studies on microwave-assisted mineral liberation have achieved certain results, research on the characteristics and influencing factors of mineral liberation cracks remains scarce. thus, this study takes rock grains with galena and calcite as the research object to investigate the distribution and evolution characteristics of mineral boundary failure under microwave irradiation using the finite difference method. it seeks to ascertain the mineral liberation mechanism under microwave irradiation, and to provide a theoretical basis for the selection of microwave source and optimized design of microwave equipment. calculation model calculation principal he heat energy produced by microwave irradiation primarily depends on the microwave frequency and the electric field intensity. the quantity of heat produced by a material of unit volume can be calculated by the following formula: " 22d o r op f e   (1) where pd denotes the power density of microwave (w/m3), that is, the power of microwave transforming heat energy; f is the microwave divergence frequency (hz); " r is the dielectric coefficient in a vacuum (8.854×10 -12f/m); o is the medium dielectric loss factor; and eo is the effective value of the electric field (v/m). given that the dielectric loss factor of calcite is 4×10-4 and that of galena is 13, under the irradiation by microwave, calcite absorbs little energy from the microwaves, and the non-production of heat by calcite in the calculation may be assumed [22]. t q. like et alii, frattura ed integrità strutturale, 34 (2015) 543-553; doi: 10.3221/igf-esis.34.60 545 the differential expression of the energy balance in flac has the form t t v t q q t      (2) where tq is the heat-flux vector in (w/m2), tvq is the volumetric heat-source intensity (w/m 3) that is equated to the power density within the material, and t is the heat stored per unit volume (j/m3). in general, temperature changes may be spurred by changes in both energy storage and volumetric strain, and the thermal constitutive law relating those parameters may be expressed as t v t t m t t t            (3) where mt and βv are material constants, and t is temperature. flac considers a particular case of this law, for which βv = 0 and 1 t v m c  . ρ is the mass density of the medium (kg/m3), and cv is the specific heat at constant volume (j/kg°c). the hypothesis is that strain changes negligibly affect the temperature. such an assumption is valid for quasi-static mechanical problems involving solids. accordingly, we may express v t t c t t        . (4) the substitution of eq. (4) in eq. (2) yields the following energy-balance equation: t d v t q p c t       (5) after the material is heated by microwaves, the strain resulting from temperature change can be expressed as , , ,i j i j i jt   (6) where ,i j denotes the strain; ,i j is the thermal expansion coefficient (1/°c); and ,i jt is the temperature change. the stress produced by heat can be calculated by hooke’s law as follows. , , , ,(1 2 ) i j i j i j i j e     (7) where ,i j denotes the thermal stress of unit i, j; ,i je is the elastic modulus of unit i,j (pa); and ,i j is the poisson’s ratio of unit i, j. calculation model this paper takes the rock grains consisting of galena and calcite as the research object. the research object is simplified into a two-dimensional plane strain model, with a rock grain size of 10 mm × 10 mm, and square galena crystal’s side length of 0.6 mm. for mesh generation in flac2d, the unit length is 0.05 mm; after generation, the model contains 40,000 units and 40,401 nodes. by writing a random distribution subroutine, in the case of a given mineral content, the galena crystal is randomly distributed within the calcite crystal, without human intervention in the distribution process. after the model is determined, a calcite unit near a galena crystal is defined as a mineral boundary element, as shown in fig. 2. mineral boundary occupies only one element, with a width of 0.05 mm. q. like et alii, frattura ed integrità strutturale, 34 (2015) 543-553; doi: 10.3221/igf-esis.34.60 546 under microwave irradiation, the failure of mineral boundary elements is the root cause of the microwave-assisted mineral liberation. the calculation involves taking the mechanical state of the mineral boundary element as the monitoring object, and the ratio of the number of boundary elements around galena in the failure state to the total number of mineral boundary elements is defined as the mineral boundary element failure rate. during calculation and analysis, this study focused on mineral boundary element failure rate changes and the development law under different conditions of irradiation and mineral composition. under microwave irradiation, the heated rock generates thermal strain and thermal stress. an element after yield is considered to be a failure element in this paper. the calculation assumes several conditions. first, model boundaries are adiabatic, and no heat transfer occurs between the model and the surroundings. the initial temperature of the model is 25 °c. only galena absorbs microwave energy under microwave irradiation. the model boundary is free of any constraint. finally, contact between galena and calcite occurs in a fixed manner. figure 2: geometric plot of computed model material parameters the thermal conductivity and specific heat of galena and calcite are presented in tab. 1, whereas the thermal expansion coefficient is shown in tab. 2 [23, 24]. thermal conductivity coefficient (w/m °c) specific heat (j/kg °c) 25°c 100°c 227°c 25°c 227°c 727°c calcite 4.02 3.01 2.55 819 1051 1238 galena 2.78 2.23 1.92 209 212 234 table 1: thermal conductivity and specific heat capacity of the mineral [23, 24]. 100°c 200°c 400°c 600°c calcite 1.31 1.58 2.01 2.4 galena 6.12 6.1 6.32 6.68 table 2: thermal expansion coefficient of the mineral (10-5) [23, 24]. both galena and calcite adopt the strain-softening model. this model is based on the mohr–coulomb model with nonassociated shear and associated tension flow rules. fig. 3 shows the one-dimensional strain softening model. the curve is linear to the point of yield; within this range, the strain is elastic only, ee e . after yield, the total strain is composed of elastic and plastic parts, e pe e e  . the mechanical parameters are presented in tab. 3 [21, 25]. q. like et alii, frattura ed integrità strutturale, 34 (2015) 543-553; doi: 10.3221/igf-esis.34.60 547 figure 3: stress-strain curve with strain-softening model. density (kg/m3) bulk modulus (gpa) shear modulus (gpa) peak strength (after 1% strain) residual strength(after 1% strain) φ (°c) c(mpa) t(mpa) φr(°c) cr(mpa) tr(mpa) calcite 2680 73.3 32.0 54 25 15 54 0.1 0 galena 7597 58.6 31.9 54 25 15 54 0.1 0 table 3: mechanical parameters of the mineral [21, 25]. calculation results and analysis he major factors that influence microwave-assisted mineral liberation include microwave power density, irradiation time, mineral content, and mineral crystal size. mineral content pertains to the volume content, which is the ratio of the volume of mineral to that of total rock. to facilitate the comparison of the effects of different sizes of mineral crystals on mineral liberation, the size of crystals in the mineral herein is assumed to be similar. (a) t=5ms (b) t=15ms (c) t=20ms (d) t=25ms figure 4: distribution diagram of rock failure state (pd=109 w/m3). t q. like et alii, frattura ed integrità strutturale, 34 (2015) 543-553; doi: 10.3221/igf-esis.34.60 548 effect of irradiation time on mineral boundary failure fig. 4 shows the distribution of the mechanical state of rock at different irradiation times under the following conditions: mineral content of 5%, mineral crystal size of 0.6 mm, and microwave power density pd = 109w/m3. the figure demonstrates that as irradiation time increases, the rock changes from a completely elastic to a yield failure state. the boundary element around galena crystals near the rock border is destroyed first due to the free boundary of the mineral. other boundary elements of galena crystals are gradually destroyed as irradiation time increases. meanwhile, the failure elements among different crystals begin to link with each other. the development process of failure elements is similar to that obtained by mamdouh omran [14]. fig. 4 also shows that the failure regions in the rock are concentrated at the boundary elements of galena crystals, which clearly signifies that microwave irradiation benefits mineral liberation. as indicated by the failure type, both shear and tensile failures occur. tensile failure primarily occurs at the boundary regions of the sample and at the connecting regions of different mineral crystals. the rest of the failures are tensile. fig. 5 depicts the graph of mineral boundary failure rate over the irradiation time. the model consists of 728 mineral boundary elements. when irradiation time is 7.9 ms, some mineral boundary elements begin to step into a failure state. by contrast, when irradiation time is 12.5 ms to 20 ms, the mineral boundary failure rate rapidly increases from 11.67% to 91.07%, and mineral boundary element failure rate grows fastest during this irradiation period. when irradiation time is 28 ms, the boundary failure rate reaches 99.31%, after which time the rate does not increase further. this condition shows an optimal irradiation time for microwave-assisted mineral liberation. an irradiation time that is shorter than the optimal irradiation time averts the attainment of the mineral liberation effect. by contrast, an irradiation time that exceeds the optimal irradiation time wastes energy. therefore, microwave-assisted mineral liberation and energy saving should critically determine the beginning and completion times of mineral boundary failure. figure 5: relationship between failure rate around mineral boundary and irradiation time (pd=109 w/m3). effect of microwave power density on failure rate fig. 6 illustrates the relationship between mineral failure rate and irradiation time at different microwave power densities under the condition in which mineral content is 5% and mineral crystal size is 0.6 mm. the figure demonstrates that as the power density increases during the optimal irradiation time, the growth of the slope is larger and the boundary element requires a shorter time to complete the failure. when the power density reaches 12×109 w/m3, mineral boundary element failure requires 3.5 ms from beginning to completion. moreover, when the power density reaches 3×109 w/m3, the time required is 0.72 ms. meanwhile, as the power density increases, the beginning and completion times of mineral boundary element failure occur earlier. fig. 7 illustrates the relationship between irradiation time and power density when the mineral boundary failure reaches 95%. as shown in the figure, as power density increases, irradiation time decreases. when the power density increases from 0.5×109 w/m3 to 3×109 w/m3, irradiation time decreases most obviously from 83 ms to 4.95 ms. furthermore, when the power density is greater than 3×109 w/m3, irradiation time decreases within a very small range. fig. 8 shows the relationship between energy consumption and power density when the boundary failure reaches 95%. when the power density increases from 0.5×109 w/m3 to 12×109 w/m3, energy consumption decreases rapidly. when the power density is greater than 3×109 w/m3, energy consumption decreases slightly, and when it is more than 12×109 w/m3, energy consumption increases slowly. in general, when the microwave power density is greater than 3×109 w/m3, irradiation time and energy consumption slightly change. this condition signifies that irradiation time and energy consumption cannot be q. like et alii, frattura ed integrità strutturale, 34 (2015) 543-553; doi: 10.3221/igf-esis.34.60 549 decreased effectively by blindly increasing microwave power density. when the power density exceeds a threshold value, the excessive power density will increase the equipment cost. fig. 6 relationship between failure around mineral boundary and irradiation time. fig. 7 relationship between irradiation time and power density when the failure rate is 95%. fig. 8 relationship between energy consumption and power density when the failure rate is 95%. effect of mineral content on rock failure state fig. 9 depicts the stress state for different mineral contents when the power density reaches 7×109 w/m3 and irradiation time is 20 ms. as shown in the figure, the mineral contents are different; however, at the same irradiation time, the q. like et alii, frattura ed integrità strutturale, 34 (2015) 543-553; doi: 10.3221/igf-esis.34.60 550 mineral boundary failure rates are all 94.5%. this outcome is principally attributed to the fact that the microwave heating is categorized as internal heating; under the same mineral crystal size, a similar mineral liberation effect is generated. (a) 3% (b) 7% (c) 11% (d) 15% figure 9: distribution diagram of mechanical state of rock (pd=109 w/m3, t=20 ms). fig. 10 illustrates the relationship between mineral boundary failure rate and irradiation time with different mineral contents. although mineral content curves are slightly different at the failure rate growth phase, the beginning and completion times are similar, that is, the same optimal microwave irradiation period, which indicates that the mineral content has a slight effect on the failure rate of the mineral boundary failure element. figure 10: relationship between failure around mineral boundary and irradiation time with different mineral content effect of mineral crystal size on rock failure state figs. 11 to 14 depict the relationship between mineral boundary failure rate curve and irradiation time, with a mineral content of 5%, microwave power density of 1×109w/m3, and galena crystal sizes of 0.2 mm, 0.4 mm, 0.8 mm, and 1.0 mm, respectively. as the mineral grains become larger, the slope of the growth curve is greater in the optimal microwave irradiation time; the smaller the mineral crystal is, the later the mineral boundary failure begins, and the later the failure completes. moreover, as the mineral crystal is smaller, the irradiation time required by mineral boundary failure completion is longer. q. like et alii, frattura ed integrità strutturale, 34 (2015) 543-553; doi: 10.3221/igf-esis.34.60 551 figure 11: relationship between failure around mineral boundary and irradiation time (0.2 mm). figure 12: relationship between failure around mineral boundary and irradiation time (0.4 mm). figure 13: relationship between failure around mineral boundary and irradiation time (0.8 mm). figure 14: relationship between failure around mineral boundary and irradiation time (1.0 mm). figure 15: relationship between irradiation time and grain size when the failure rate reaches 95%. figure 16: relationship between energy consumption and grain size when the failure rate reaches 95%. fig. 15 illustrates the relationship between microwave irradiation time and grain size when the mineral failure rate reaches 95%. fig. 16 shows the relationship between the corresponding energy consumption and grain size. as shown in the figures, as the mineral crystal becomes larger, irradiation time becomes shorter when the mineral boundary failure rate reaches 95%, and energy consumption is lower. when irradiation time decreases from 650 ms to 22 ms, energy consumption decreases from 3250 j to 85 j. moreover, when the crystal size exceeds 0.6 mm, irradiation time and energy consumption substantially remain unchanged. the results of this method are consistent with those of other mineral q. like et alii, frattura ed integrità strutturale, 34 (2015) 543-553; doi: 10.3221/igf-esis.34.60 552 liberation methods, that is, the smaller the mineral crystal is, the harder the selection of mineral crystal becomes, and the more energy is consumed. conclusions his study takes the mineral consisting of galena and calcite as the research object to establish a two-dimensional plane strain model and analyze the effects of microwave irradiation time, power density, mineral content, and mineral crystal size on microwave-assisted mineral liberation. it draws the following major conclusions: (1) under the microwave irradiation, mineral boundary can be quickly destroyed in a specific period. an optimal irradiation period exists. when irradiation time is shorter than the beginning time of the optimal irradiation period, no failure occurs on the mineral boundary. by contrast, when irradiation time is longer than the end of the optimal irradiation period, more energy is wasted. (2) a greater microwave power density reduces the period for mineral boundary failure completion. the microwave irradiation time and energy consumption can be effectively reduced by improving the microwave power density. however, when the microwave power exceeds a certain value, the microwave irradiation period and energy consumption slightly change. (3) with the same microwave power density, when the mineral crystal size is constant, the mineral content has no effect on the optimal microwave irradiation time, and the beginning and completion times of failure exhibit no change. moreover, mineral crystal size significantly affects the microwave irradiation time and energy consumption; the larger the mineral crystal, the shorter the irradiation time is, and the less energy consumption the mineral boundary failure requires. when the mineral crystal size exceeds a certain value, both irradiation time and energy consumption essentially remain unchanged. acknowledgements his work was supported by the china postdoctoral science foundation (2015m572580), the foundation of shaanxi educational committee (15jk1471), and the national natural science foundation of china (no. 51174159). references [1] jin, q., microwave chemistry. science press, beijing, (1990) 214-216. [2] duan, b., zeng, l., liu, p., application and situation of microwave-assisted heating technology, ceramics, 12(3) (2005)11-15. [3] islam, m. m., design of a microstrip antenna on duroid 5870 substrate material for ku and k-band applications. tehnicki vjesnik, 6(2) (2013) 71-77. [4] lubikowski, k., seebeck phenomenon, calculation method comparison, journal of power technologies, 95(1) (2015) 63-67. [5] czaplicka, k., korol, k. b., et al., model of eco-efficiency assessment of mining production processes, archives of mining sciences, 1(2) (2015) 477-482. [6] kingman, s. w., vorster, w., rowson, n. a., the influence of mineralogy on microwave assisted grinding, minerals engineering, 22 (1) (2015) 160-163. [7] zhong, l., nano-structured si/c/n composite powder produced by radio frequency induction plasma and its microwave absorbing properties, journal of engineering science and technology review, 13(3) (2000) 313-327. [8] liu, q., xiong, y., research on application mechanism of microwave in iron ores selective grounding, yunnan metallurgy, 6 (3) (1997) 25-28. [9] kingman, s.w., rowson, n.a., microwave treatment of mineralsa review, minerals engineering, 11(11) (1998) 10811087 [10] kingman, s. w., jackson, k., recent developments in microwave assisted combination, international journal of mineral processing, 74 (2004) 71-83 t t q. like et alii, frattura ed integrità strutturale, 34 (2015) 543-553; doi: 10.3221/igf-esis.34.60 553 [11] huang, m., peng, j., lei, y., temperature rising behaviors and absorbing characteristics of titanium ore in microwave field, journal of sichuan university: engineering science edition, 39 (2) (2007) 111-115. [12] ouyang, h., yang, z., xiong, x., et al., research on the temperature rising curve and fluidizing leaching of ilmenite in microwave field, mining metallurgical engineering, 30 (1) (2010) 73-75. [13] pan, x., chen, j., zhao, m., zhao, j., research on temperature rising characteristics of carbon-bearing manganese carbonate powder after microwave heating, new technology & new process, 1 (2008) 55-58. [14] omran, m., fabritius, t., mattila, r., thermally assisted liberation of high phosphorus oolitic iron ore: a comparison between microwave and conventional furnaces, powder technology, 269 (2015) 7-14. [15] guo, s., chen, g., microwave assisted grinding of ilmenite ore, transactions of nonferrous metals society of china, 21 (9) (2011) 2122-2126 [16] cui, h., chen, j., feng, x., li, n., numerical simulation for temperature rising curve of carbon-bearing chromium powder in microwave field, china metallurgy, 17 (1) (2007) 30-35. [17] jones, d.a., kingman, s.w., whittles, d.n., understanding microwave assisted breakage, minerals engineering, 18 (2005) 659-669. [18] wang, g., radziszewski, p., ouellet, j., particle modeling simulation of thermal effects on ore breakage. computational materials science, 43 (2008) 892-901. [19] wang, y., djordjevic, n., thermal stress fem analysis of rock with microwave energy, international journal of mineral processing, 130 (2014) 74-81. [20] ali, a.y., bradshaw, s.m., quantifying damage around grain boundaries in microwave treated ores, chemical engineering and processing, 48 (2009) 1566-1573. [21] whittles, d.n., kingman, s.w., et al., application of numerical modelling for prediction of the influence of power density on microwave-assisted breakage international journal of mineral processing, 68 (2003)71-91. [22] chen, t.t., dutrizac, j.e., hague, k.e., et al., the relative transparency of minerals to microwave radiation, canadian metallurgical quarterly, 23 (3) (1984) 349-354. [23] touloukian, y. s., judd, w.r., physical properties of rocks and minerals, mcgraw-hill book company, new york, (1981) 56-63. [24] clark, s. p., handbook of physical constants. geological society of america, new york, (1966) 415-436. [25] bass, j.d., elasticity of minerals, glasses, and melts. in: t.j. ahrens, editor, handbook of physical constants, american geophysical union, washington, dc, (1995) 45-63. microsoft word numero_30_art_22 e. sgambiterra et alii, frattura ed integrità strutturale, 30 (2014) 167-173; doi: 10.3221/igf-esis.30.22 167 focussed on: fracture and structural integrity related issues stress induced martensite at the crack tip in niti alloys during fatigue loading e. sgambitterra, l. bruno, c. maletta dept. of mechanical, energy and management engineering, university of calabria, 87036 rende (cs), italy. esgambitterra@unical.it abstract. crack tip stress-induced phase transformation mechanisms in nickel-titanium alloys (niti) were analyzed by digital image correlation (dic), under fatigue loads. in particular, single edge crack (sec) specimens, obtained from a commercial pseudoelastic niti sheet, and an ad-hoc experimental setup were used, for direct measurements of the near crack tip displacement field by the dic technique. furthermore, a fitting procedure was developed to calculate the mode i stress intensity factor (sif), starting from the measured displacement field. finally, cyclic tensile tests were performed at different operating temperature, in the range 298-338 k, and the evolution of the sif was studied, which revealed a marked temperature dependence. keywords. shape memory alloys; fracture; digital image correlation; stress intensity factor. introduction n last decades, shape memory alloys (smas), and in particular the nickel titanium-based ones (niti), received big attention from scientific and engineering communities thanks to their unique characteristics, namely shape memory effect (sme) and superelastic effect (se) [1]. in particular, these properties allow large recoverable strains or large induced internal forces due to a reversible solid-state phase transformation between austenite and martensite; this transformation can be activated by a temperature variation (tim, thermally induced martensite) or by the application of external forces (sim, stress-induced martensite). due to these interesting features, as well as to their good mechanical performances and biocompatibility, niti alloys have seen growing use in many branches of engineering and medicine [23]. as a direct consequence of this interest, many studies were carried out to better investigate on the thermo-mechanical behavior of smas, in terms of both sme and se [1]. their mechanical properties were investigated using tensile (e.g. [4–5]) and fatigue testing (e.g. [6–11]), however, many aspects are still unknown, especially because the hysteretic stress and/or thermally induced phase transformations significantly affect the damage mechanisms occurring under fatigue loadings, i.e. the crack formation and propagation mechanisms. from a materials science point of view, an accurate knowledge of these topics is essential for predicting the functional and structural life of damaged structures as well as their failure modes, with the aim to improve the overall performances of niti-based components or structures. the fracture behavior of austenitic niti alloys strongly depends on the sim transformation which occurs in the crack tip region, as a consequence of the high values of local stresses. as a direct consequence of the marked non-linear and hysteretic behavior, classic elastic and/or elastic-plastic theories cannot be directly applied to smas. the constitutive laws implemented in commercial finite element software are based on phenomenological approaches and on theory of plasticity, i.e. they use plasticity-like concepts to describe the effects of phase transformation mechanisms on i e. sgambiterra et alii, frattura ed integrità strutturale, 30 (2014) 167-173; doi: 10.3221/igf-esis.30.22 168 the macroscopic response of niti alloys [12]. even though these numerical methods represent useful design tools to simulate the macroscopic response of simple or complex sma based systems, special care should be taken when they are used to study the local effects in the proximity of high stress concentration regions. in particular, it was demonstrated that the high values of local stresses arising in the crack tip region of niti alloys cause stress-induced phase transition mechanisms [13-30], which significantly affect the crack tip stress distribution and, consequently, the crack evolution under both static and fatigue loading conditions. despite the increasing number of research activities on fracture and fatigue of niti alloys in recent years, much effort should be devoted for an effective understanding of the role of the phase transformations in the crack formation and propagation mechanisms and in the stress state generated at the crack tip. within this context, the development and application of full field techniques to analyze the local transformation mechanisms near geometrical discontinuities and, in particular, in the crack tip region, represent a highly challenging scientific goal. for this purpose, synchrotron x-ray micro-diffraction (xrd) [13-15], infrared thermographic (ir) [16] and digital image correlation (dic) [18, 19] techniques were recently applied, to better understand the mechanisms of phase transformation in the notch and/or crack tip proximity. in particular, a pseudoelastic niti alloy for medical applications were analyzed in [13] by using miniature compact-tension (ct) specimens, which were directly obtained from thin-walled tubes, similar to those used for manufacturing self-expanding stents. xrd microdiffraction investigations of fatigue precracked specimens revealed that the crack tip local strain are due to both b2 to b19’ transformation and to the subsequent loading of the martensitic phase. strain and texture evolution near the crack tip of a martensitic niti alloy were analyzed in [14], by synchrotron x-ray experiments, after fatigue crack propagation in a compact-tension (ct) specimen; it was found that texture evolution is mainly due to detwinning, the main deformation mechanism in martensitic niti alloys. both martensitic and austenitic alloys were analyzed in [15], by using miniaturized ct specimens [19] after fatigue crack propagation, which revealed the presence of detwinned martensite at the crack tip of both martensitic and austenitic specimens. an austenitic niti alloy was analyzed in [17] by dic analysis of thin edge cracked specimen, which allowed direct measurement of the crack tip strain field related to stress-induced transformation. these experimental investigations, together with other several recent numerical [20-22] and analytical [23-30] studies, provide very useful information about the occurrence of crack tip transition mechanisms in niti alloys subjected to static and/or monotonic loads, and the effect of the operating temperature on the stress intensity factor (sif) and on the size of the transformation region was also numerically investigated in [30]. however, the role of these mechanisms on the fracture properties on niti alloys is not yet completely defined, i.e. no reliable methodologies were developed for an effective design against fracture. in addition, the evolution of microstructural changes at the crack tip occurring during fatigue loading, i.e. the thermal and mechanical hysteretic behavior, was not yet investigated. this topic is of major concern as the hysteretic nature of phase transitions is expected to play a significant role on the crack growth mechanisms. in this work the stress intensity factor evolution in a niti pseudoelastic alloy was investigated by means of a full field experimental techniques in particular, dic method was used to analyze the displacement field in the crack tip region by which, with a proper fitting procedure based on the william’s series expansion [31], the mode i stress-intensity factor (sif) was evaluated. different cyclic tests, a different operating temperatures, in the range 298-338 k, were performed and the effect of the temperature on the sif was investigated. material and methods commercial nickel-titanium sheet (thickness t=0.5 mm) with pseudoelastic properties at room temperature (austenite finish temperature af=286.7 k) was used in this investigation. fig. 1a shows the isothermal (t=298 k) stress strain () response of the material obtained from a complete loading-unloading cycle up to a maximum deformation of about 6.2 %, corresponding to a complete stress-induced martensite transformation. the figure also reports the values of the main thermo-mechanical parameters of the alloy: transformation stresses (sam, fam, sma and fma), tranformation strain (l), young’s moduli of austenite and martensite (ea and em) and clausius-clapeyron constants (ca and cm). edge-notched tension specimens were cut from a commercial plate by electrical discharge machining (edm) and a 0.1 mm edm wire was used to machine the notch. the specimen surface has been properly treated in order to provide a suitable speckle pattern for using dic, therefore, the specimens were not painted. a e. sgambiterra et alii, frattura ed integrità strutturale, 30 (2014) 167-173; doi: 10.3221/igf-esis.30.22 169 specimens were fatigued by using a servo hydraulic testing machine (instron 8500), at rate of 5 hz, to initiate and grow a crack from the edm notch tip at constant load amplitude and a load ratio, r=min/max, of roughly zero, in order to get a length ratio, a/w, close to 0.3 (see fig. 2). pre-cracked specimens were subsequently subjected to complete tensile loading-unloading cycles by using an electro-mechanical testing machine (mts criterion s42) equipped with 5 kn load cell; different tests were carried out at different operating temperature, in the range 298-338 k and with a maximum load p=300 n, corresponding to a maximum stress max=pmax/wt=60 mpa. figure 1: loading-unloading isothermal stress-strain cycle (298 k) figure 2: single edge crack specimen a digital camera (sony xcdx910 model) with a resolution of 1280 by 960 pixels of 4.65 m was used to capture images throughout measurement tests. the focus of the images was performed using a linos photonics microscope objective with a 4x magnification and a numerical aperture of 0.1, which ensures, in conditions of correct illumination, a resolution of approximately 2.5 m, and therefore lower than the pixel size of the camera. dic was performed on images from each test carried at different operating temperature using a special tool available in the matlab® software platform. the first image in the measurement cycle (at minimum load) was used as the reference image, and terms up to first order displacement gradients were used in all correlations. dic was used to obtain full-field displacements for each image throughout the cycle and the correlations were performed using a subset size with a radius of 42 pixels and a spacing of 2 pixels between subset centers. results and discussions yclic tensile tests were performed on a single edge crack specimen, at different operating thermal conditions in order to understand the effect of the temperature on the stress induced transformation mechanisms at the crack tip. three different values of temperature, in the range of 298-338 k, were adopted during the tests. to determine the effective stress intensity factor the specimen actually experiences, which could be different than the theoretical one determined by the linear elastic fracture mechanic (lefm) theory due to the marked non-linear behavior of niti alloys, a least squares regression was performed on the dic measured displacements. the displacement field, at the crack tip, proposed by williams [31],was used to fit the experimental data obtained from the tests. as the displacement field is not unique unless rigid body motion is also specified, two in-plane rigid motion terms, rotation, a, and rigid translation perpendicular to the crack line, b, have to be specified. furthermore, due to the low magnitude of the pictures, if the t-stress term is included, in order to improve the fitting of the analytical and experimental results, the asymptotic crack tip displacement equations become:      1 1sin 1 cos sin cos 2 2 2 2 2 1 ik r vv k tr ar b v                                 (1) where ki is the effective stress intensity factor, r is the distance from the crack tip, c e. sgambiterra et alii, frattura ed integrità strutturale, 30 (2014) 167-173; doi: 10.3221/igf-esis.30.22 170  is the angle from the crack line ahead of the tip,  is the poisson’s ratio,  is the shear modulus given by:  2 1 e v    (2) and k is given by: 3 1 v k v    (3) the vertical displacement filed, recorded at the maximum applied load (p=300 n) for a specimen with a/w=0.32, is given in fig. 3. the experimentally obtained and regressed displacements were plotted together to demonstrate the accuracy of the regression technique. in particular, blue contours represent the experimentally found displacements and the red contours represent the regressed displacement contours. as observed, the experimental and regressed displacement contours show good agreement. for a given value of the young’s modulus, which was assumed to be constant and equal to that of austenitic untransformed structure (ea=68gpa), the fitting procedure allows a direct estimation of the mode i stress-intensity factor (ki). however, it is important to underline that, due to the transformation mechanisms occurring in the crack tip region, the effective elastic properties changes, as consequence of the generation of the new phase and its variants reorientations, therefore further estimations should be carried out in this way to well characterize the real stress state involving the crack tip in a pseudoelastic niti alloy. figure 3: comparison between the experimental and regresses vertical displacements (v) near the crack tip. fig. 4, shows the evolution of the calculated ki as a function of the applied load during a complete loading-unloading cycle for all the investigated operating temperatures. as shown, all the curves exhibit two different slopes: a lower slope for load values lower than 50 n and an higher one for load values between 50 n and 300 n. this behavior can be attributed to the unique non-linear stress-strain behavior of niti alloys as well as to the crack opening and closure mechanisms. furthermore, it is possible to observe that the higher the operating temperature the lower the recorded stress intensity factor. in fig. 5, the stress intensity factor, recorded at the maximum applied load (p=300 n), is plotted in function of the temperature. results revealed that ki tends to decrease by increasing the temperature until the material exhibits pseudoelastic properties (t<320 k). for higher values of temperature (t>320 k), transformation mechanisms tends to e. sgambiterra et alii, frattura ed integrità strutturale, 30 (2014) 167-173; doi: 10.3221/igf-esis.30.22 171 vanish because the energy required to create slip plane is lower than the one needed to induce phase transformation, therefore the stress intensity factor (ki) tends to stabilize. figure 4: evolution of the calculated stress intensity factor (sif) in a cyclic test for different operating temperatures. figure 5: evolution of the stress intensity factor (sif), recorded at the maximum applied load (p=300 n), as a function of the operating temperature. conclusions igital image correlation technique was adopted in this investigation to study the phase transition mechanisms at the crack tip in niti alloys. to this aim single edge crack (sec) specimens, obtained from a commercial niti sheets with pseudoelastic behavior, were analyzed. dic method was used to analyze the displacement field in the crack tip region and a fitting procedures, based on the william’s series expansion, were properly implemented to estimate the mode i stress-intensity factor (sif). the effect of the operating temperature on the sif was investigated and results showed that the stress intensity factor decrease by increasing the temperature and it tends to stabilize when the pseudoelastic properties of the alloy vanish. d e. sgambiterra et alii, frattura ed integrità strutturale, 30 (2014) 167-173; doi: 10.3221/igf-esis.30.22 172 references [1] otsuka, k., ren, x., physical metallurgy of ti-ni based shape memory alloys, progress in material science, 50 (2005) 511. [2] otsuka, k., wayman, c.m., editors. shape memory materials, cambridge: cambridge university press, (1998). [3] duerig, t.w., melton, k.n., stokel, d., wayman, c.m., editors, engineering aspects of shape memory alloys, london: butterworth, (1990). [4] schmahl, w.w., khalil-allafi, j., hasse, b.,wagner, m., heckmann, a., somsen, c., investigation of the phase evolution in a super-elastic niti shape memory alloy (50.7 at.%ni) under extensional load with synchrotron radiation, materials science and engineering a, (2004), 378:81–5. [5] chen, j.h., sun, w., wang, g.z., investigation on the fracture behavior of shape memory alloy niti, metallurgical and materials transactions a, (2005) 36:941–55. [6] eggeler, g., hornbogen, e., yawny, a., heckmann, a., wagner, m., structural and functional fatigue of niti shape memory alloys, materials science and engineering a, (2004) 378:24–33. [7] maletta, c., sgambitterra, e., furgiuele, f., casati, r., tuissi, a., fatigue of pseudoelastic niti within the stressinduced transformation regime: a modified coffin-manson approach, smart materials and structures (21), (2012) 1– 9. art. no. 112001. [8] maletta, c., sgambitterra, e., furgiuele, f., casati, r., tuissi, a., fatigue properties of a pseudoelastic niti alloy: strain ratcheting and hysteresis under cyclic tensile loading, international journal of fatigue (66) 2014, 78-85. [9] melton, k.n., mercier, o., fatigue of niti thermoelastic martensites, acta metallurgica, (1978), 27:137–44. [10] sawaguchi, t., kaustrater, g., yawny, a., wagner, m., eggeler, g., crack initiation and propagation in 50.9 at. pct ni-ti pseudoelastic shape-memory wires in bending-rotation fatigue, metallurgical and materials transactions a (2003), 34:2847–60. [11] stankiewicz, j.m., robertson, s., ritchie, r.o., fatigue-crack growth properties of thin-walled superelastic austenitic nitinol tube for endovascular stents, journal of biomedical materials research part a (2006), 81:685–91. [12] paiva, a., savi, m.a., an overview of constitutive models for shape memory alloys, mathematical problems in engineering, art. no. 56876 (2006). [13] robertson, s.w., mehta, a., pelton, a.r., ritchie, r.o., evolution of crack-tip transformation zones in superelastic nitinol subjected to in situ fatigue: a fracture mechanics and synchrotron x-ray microdiffraction analysis, acta materialia, 55(18) (2007) 6198–6207. [14] daymond, m.r., young, m.l., almer, j.d., dunand, d.c., strain and texture increment during mechanical loading of a crack tip in martensitic shape-memory niti, acta materialia, 55 (11) (2007) 3929-3942. [15] gollerthan, s., young, m.l., baruj, a., frenzel, j., schmahl, w., eggeler, g., fracture mechanics and microstructure in niti shape memory alloys acta materialia, 57 (4) (2009) 1015-1025. [16] gollerthan, s., young, m.l., neuking, k., ramamurty, u., eggeler, g., direct physical evidence for the backtransformation of stress-induced martensite in the vicinity of cracks in pseudoelastic niti shape memory alloys acta materialia, 57 (2009) 5892–5897. [17] daly, s., miller, a., ravichandran, g., bhattacharya, k., an experimental investigation of crack initiation in thin sheets of nitinol, acta materialia, 55 (2007) 6322-6330. [18] gollerthan, s., herberg, d., baruj, a., eggeler, g., compact tension testing of martensitic/pseudoplastic niti shape memory alloys materials science and engineering a, 481–482 (2008) 156–159. [19] bewerse, c., gall, k.r., mcfarland, g.j., zhu, p., brinson, l.c., local and global strains and strain ratios in shape memory alloys using digital image correlation, materials science and engineering a, 568 (2013) 134–142. [20] wang, x.m., wang, y.f., baruj, a., eggeler, g., yue, z.f., , on the formation of martensite in front of cracks in pseudoelastic shape memory alloys materials science and engineering a, 394(1–2) (2005) 393–398. [21] maletta, c., falvo, a., furgiuele, f., leonardi, a., stress-induced martensitic transformation in the crack tip region of a niti alloy, journal of materials engineering and performances, 18(5–6) (2009) 679–685. [22] freed, y., banks-sills, l., crack growth resistance of shape memory alloys by means of a cohesive zone model, journal of the mechanics and physics and solids, 55 (2001) 2157–2180. [23] yi, s., gao, s., fracture toughening mechanism of shape memory alloys due to martensite transformation, international journal of solids and structures, 37(38) (2000) 5315–5327. [24] xiong, f., liu, y., effect of stress-induced martensitic transformation on the crack tip stress-intensity factor in ni-mn-ga shape memory alloy, acta materialia, 55(16) (2007) 5621–5629. e. sgambiterra et alii, frattura ed integrità strutturale, 30 (2014) 167-173; doi: 10.3221/igf-esis.30.22 173 [25] maletta, c., furgiuele, f., analytical modeling of stress-induced martensitic transformation in the crack tip region of nickel–titanium alloys, acta materialia, 58 (2010) 92-101. [26] maletta, c., furgiuele, f., fracture control parameters for niti based shape memory alloys, international journal of solids and structures, 48 (11) (2011) 1658-1664. [27] maletta, c., young, m.l., stress-induced martensite in front of crack tips in niti shape memory alloys: modeling versus experiments, journal of materials engineering and performances, 20 (2011) 597–604. [28] baxevanis, t., lagoudas, d., a mode i fracture analysis of a center-cracked in niti shape memory alloy panel under plane stress international journal of fracture, 175 (2012) 151–166. [29] maletta, c., a novel fracture mechanics approach for shape memory alloys with trilinear stress–strain behaviour, international journal of fracture, 177 (2012) 39–51. [30] maletta, c., sgambitterra, e., furgiuele, f., crack tip stress distribution and stress intensity factor in shape memory alloys, fatigue and fracture of engineering materials and strictires, 36 (9) (2013) 903-912. [31] eftis, j., subramonian, n., liebowitz, h., crack border stress and displacement equations revisited, engineering fracture mechanics, 9 (1977) 189-210. microsoft word numero_49_art_17_2462 m. zhelnin et alii, frattura ed integrità strutturale, 49 (2019) 156-166; doi: 10.3221/igf-esis.49.17 156 focused on russian mechanics contributions for structural integrity numerical analysis of application limits of vyalov’s formula for an ice-soil wall thickness m. zhelnin, a. kostina, o. plekhov, i. panteleev institute of continuous media mechanics of the ural branch of russian academy of science, russia zhelnin.m@icmm.ru, http://orcid.org/0000-0003-4498-450x kostina@icmm.ru, http://orcid.org/0000-0002-5721-3301 poa@icmm.ru, http://orcid.org/0000-0002-0378-8249 pia@icmm.ru, http://orcid.org/0000-0002-7430-3667 l. levin mining institute of the ural branch of russian academy of science, russia aerolog_lev@mail.ru abstract. artificial ground freezing is an efficient technique which allows one to sink the mine shafts under complex hydrogeological conditions. the aim of artificial ground freezing is a creation of a temporary wall of frozen soil around the intended excavation. to estimate an optimal thickness of an ice-soil wall, the vyalov’s formula is widely used by engineers. the article is devoted to analysis of vyalov’s formula on the basis of the numerical simulation. the numerical simulation has been conducted by the finite element method. for the simulation of a stress-strain state of an ice-soil wall a new computational scheme has been proposed. the scheme is based on vyalov’s design layout for a vertical shaft sinking and takes into account a soil layer beyond the excavation bottom. a mechanical behavior of frozen soil is described by vyalov’s constitutive relations. as a result, it has been shown that values of the wall thickness given by vyalov’s formula do not agree with the ones obtained by the numerical simulation. in order to conform results given by vyalov’s formula and the numerical simulation, two modifications of the formula have been proposed. keywords. artificial ground freezing; mine shaft; ice-soil wall: inelastic deformation; numerical simulation. citation: zhelnin, m., kostina, a., plekhov, o., panteleev, i., levin, l., numerical analysis of application limits of vyalov’s formula for an ice-soil wall thickness, frattura ed integrità strutturale, 49 (2019) 156-166. received: 04.04.2019 accepted: 22.05.2019 published: 01.07.2019 copyright: © 2019 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. introduction t the present time mineral deposits characterize of an increase of a depth of an occurrence and a complication of hydrogeological conditions of building of a vertical mine shaft for their elaboration. artificial ground freezing (agf) is an efficient technique which allows sinking of the mine shafts through weak, unstable, water saturation a m. zhelnin et alii, frattura ed integrità strutturale, 49 (2019) 156-166; doi: 10.3221/igf-esis.49.17 157 soil stratums. the aim of agf is a creation of a temporary wall of frozen soil around the intended excavation. ice in soil pores changes its mechanical and hydrodynamical properties, so at certain temperature the ice-soil wall can withstand rock pressure from unfrozen rock mass and eliminate groundwater filtration. the freezing of ground is carried out by a series of wells that are drilled around the excavation. due to circulation of liquid refrigerant inside the pipes, heat extracts from the near-wellbore domain and the ice-soil retaining structure is established. strength and reliability of the ice-soil wall determine safety of a shaft sinking and geotechnical works. mechanical behavior of the wall depends on properties of soil that its formed. presence of ice and unfrozen water in frozen soil leads to occurrence of rheological properties that characterize development of slow deformations (creep) and losing strength during a prolonged load action [1]. as a result, the ice-soil wall could significantly deform under rock pressure [2]. a lot of experimental studies have been carried out to study time-dependent deformation of frozen soil under uniaxial and multiaxial compression tests [1-10]. creep deformation of frozen soil depends on long-term strength limit [3]. if the stress does not exceed the long-term strength limit, deformation rate tends to zero and failure time is infinity. in the case evolution of deformation is characterized as attenuate creep. if the stress is larger than the long-term strength, nonattenuate creep develops. in general, the creep process can be divided on three stage: unsteady creep with a decreasing deformation rate, viscoplastic flow with an almost constant rate, and progressive flow with an increasing rate after that failure arises. in [1, 3] it is noted that the long-term strength limit of frozen soil significantly depends on temperature of frozen soil. in [4] from uniaxial creep tests of warm ice-rich sand it has been established that creep characteristics are affected by small temperature variation. in [5, 6] on the basis of triaxial tests it has been shown that a decrease of temperature leads to an improvement of strength properties. in [7] a study of an influence of thermal gradient on the frozen sand has been carried out. it has been determined that a decrease of thermal gradient leads to an increase of the long-term strength limit. in [8] it is noted that rheological properties of frozen soils also depend on ice and unfrozen water saturations, grain-size distribution, mineral content. in [9] it has been concluded that cryostructure has an influence on creep behavior of frozen soil. in [10] based on triaxial creep tests it has been shown that coarse-grained content in frozen silty clay causes a rise of it strength. for describing the phenomena of creep of frozen soils various constitutive relations have been developed. to reflect changes in soils that arises during creep process at the microscale into the macroscale, micromechanics [11], thermodynamics [12, 13] and damage mechanics [10] are used. however, to determine material parameters for this models difficult and costly experimental studies have to be conducted. as a result, for engineering purposes macroscale phenomenological models are widely used [14]. in [3, 14, 15] extensive reviews of various models describing creep under complex stress state and various stages of deformation are presented. it could be divided in two types: models that take into account an influence of confining pressure on creep deformation and models in that the influence is supposed to be negligible. in [16, 17] nishihara and burgers models have been improved to a new creep constitutive models that describe viscoplasticity deformation of frozen soils under high confining pressure. one of basic model for analysis of creep deformation of ice-soil retaining structure is vyalov’s constitutive relations [1,2]. the relations are based on the norton-bailey power law in that a modulus depends on time and temperature. an influence of confining pressure on creep of frozen soil is neglected. the advantage of the model is that material parameters for describing deformation in complex stress state can be estimated from simple uniaxial loading tests. experimental verification of the vyalov’s relations has been performed in uniaxial and multiaxial creep tests in wide range of temperature and ice saturation of frozen soils [1, 2, 18]. in [19] experimental values of creep deformation of beams of frozen soil have been compared to values obtained by a finite element modeling. in [20] experimental and numerical studies of interaction of footings with frozen sand have been performed. in [21, 22] an improvement of vyalov’s relations has been performed by consideration of an influence of volumetric ice content on creep deformation. in [1, 23] on the basis of vyalov’s relations an analytical formula for an estimation of an optimal thickness of an ice-soil wall from a condition of maximal creep deformation has been derived. nowadays vyalov’s formula is widely applied by engineers for design parameters of an ice-soil retaining structure and determination of agf regimes [24]. however, analytical derivation of the formula is accompanied by a series of strong assumptions that could not agree with real conditions of a shaft sinking. in [25] deformation of an ice-soil wall of callovian sandy loam has been estimated by numerical modelling with using vyalov’s relations for various depths of a shaft sinking. it has been shown that deformation of an ice-soil wall with thickness estimated by vyalov’s formula exceeds admissible values for depths of the sinking more than 100 meters. the present work is devoted to analysis of vyalov’s formula on the basis of numerical modeling. the simulation of a sinking of a vertical shaft under agf is performed according to vyalov’s design layout of a shaft sinking [1] modified by consideration of a soil layer beyond the excavation bottom. it is considered three type of soils: chalk, sand and clay that m. zhelnin et alii, frattura ed integrità strutturale, 49 (2019) 156-166; doi: 10.3221/igf-esis.49.17 158 are prevalent on potash deposits in the petrikov site in belarus. results of the numerical simulation is used for modifications of vyalov’s formula to reconcile values of the wall thickness obtained by the formula to the numerical ones. mathematical models for deformation of an ice-soil retaining structure n [1] a design layout for a vertical shaft sinking with using agf has been proposed fig. 1. the ice-soil retaining structure is a hollow cylinder of inner radius a and outer radius b that encloses unfrozen soil. as a shaft is sunk an inner surface of the cylinder is exposed. the shaft sinking is performed gradually with an installation of a shaft tubbing lining. therefore, only a height h of the inner surface is unsupported. this part of the surface is deformed under rock pressure p during the time prt that requests for building of the lining. at that the upper end of the cylinder is supposed to be fixed by the tubbing lining, as it prevents of deformation of the soil to the cylinder center. figure 1: vyalov’s design layout for a vertical shaft sinking with applied of agf. according to the scheme in [16] the following system of equation in axial-symmetric configuration for describing a stressstate state of an ice-soil wall has been proposed:            0 rzr r r r z , (1)      0 rz rz z r , (2) , , , , zr r r r z rz uu u u r r z z              (3) with boundary conditions          0r rz zr a r a z h , (4)    r r b p , (5)     0 0z zz z h u u , (6)   0r z hu , (7) where ( , , )r z – cylindrical coordinates, u – displacement vector, σ cauchy stress tensor, ε – strain tensor, a , b – inner radius and outer radius of the ice-soil cylinder. the geometry of the ice-soil cylinder is presented in fig 1. as it can i m. zhelnin et alii, frattura ed integrità strutturale, 49 (2019) 156-166; doi: 10.3221/igf-esis.49.17 159 be seen from (1)-(3) axial stress is supposed to be constant along the height of the cylinder and axial strain is supposed to be constant along the radius of the cylinder. the vyalov’s constitutive relations for frozen soil is generally accepted. the relationship between stress and strain are written as   ( , ) meff effa t t , (8) where   2 dev( ):dev( ) 3 eff ε ε is the equivalent strain,   3 dev( ):dev( ) 2 eff σ σ is the equivalent stress, dev – deviatoric part of a tensor,      1 2( , ) 3 ( 1) m a t t t t – deformation coefficient depending on temperature t of the frozen soil and time t of loading action, m ,  ,  – material constants. it is assumed that frozen soil is isotropic, homogenous material. the volumetric creep strain of frozen soil is taken to be zero: tr 0ε , (9) where tr – trace of a tensor. the hydrostatic stress trσ has no an influence on the strain. a contribution of the elastic strain is neglected. an additional hencky’s relations are taken into the account: tr     σ( ), , ,i i i r z (10) 2rz rz  , (11) from engineering practice and experiments on a physical modeling of an operation of an ice-soil wall it is well known that under an action of rock-pressure radial strain on the inner surface of the cylinder could attain significant values that threaten of failure of freezing pipes and deviation on designed characteristics of the mine shaft. therefore, the problem of estimation of the ice-soil wall thickness e b a  under that the radial displacement ru on the inner surface do not exceed a limiting value  is stated:   r r au . (12) on the basis of analytical solution of the problem (1)-(11) taking into account the condition (12) in [16] the following estimation of an optimal thickness e has been obtained: 1 1 1(1 ) 1 1 ( , ) m m m pr m ph e a a t t a                . (13) the formula (13) is named vyalov’s formula. to analytically solve the problem (1)-(11) a series of assumptions have been purposed. the key assumption relates to expression for distribution of shear strain rz on the upper end of the ice-soil cylinder. according to the assumption a distribution of the shear strain is approximated by the following expression: rz a rh    . (14) the assumption allows significantly simplifying mathematical treatment and obtaining formula convenient for engineering calculations. also it should be noted that the problem (1)-(11) has been solved for small neighborhoods of the ends of the ice-soil cylinder. m. zhelnin et alii, frattura ed integrità strutturale, 49 (2019) 156-166; doi: 10.3221/igf-esis.49.17 160 in order to analysis vyalov’s formula a numerical simulation of stress-strain state of the ice-soil cylinder has been carried out. vyalov’s design layout has been modified by taking into account a soil layer beyond the bottom of the excavation as usual it performs in modelling of vertical shafts (fig. 2). the layer also consists of the hollow ice-soil cylinder and unfrozen soil inside it. the system of equations considered in the simulation is written as: div 0σ , (15)   t 1 [grad ( grad ) ] 2 ε u u , (16) where grad – the gradient operator, div – the divergence operator. boundary conditions are identical to (5), (6). the other boundaries of the cylinder are free. figure 2: a scheme of an ice-soil wall that is used in the numerical simulation. the constitutive relations for describing inelastic strain of the ice-soil cylinder under the rock pressure coincide with vyalov’s relations. an additional it is taken into account elastic part of strain. the unfrozen soil it is supposed to be isotropic, homogenous material that can undergo only elastic deformation. the simulation is performed in axial-symmetric configuration with using the finite element method. the geometrical domain is divided on mapped elements of the second order. the rock pressure p acting on the ice-soil retaining structure is estimated by the standard engineering formula [26]:  l wp p p , (17)                  2tan 2 tan 2 2 l sp hg c , (18) w w wp gh , (19) where lp – effective lateral pressure, wp – hydrostatic pressure, h – depth of bottom of the soil stratum within that the ice-soil cylinder is placed, l – average density of soils in the rock mass where a vertical shaft is constructed,  – friction angle of unfrozen soil, c – cohesion coefficient of unfrozen soil, w – density of groundwater, wh – groundwater hydraulic head. results of the numerical simulation he numerical simulation has been conducted for three types of soils: clay, sand and chalk. elastic and rheological properties of the soils have been determined from uniaxial compression tests of cylindrical samples of core from the petrikov site of starobinsky potash deposit in belarus. this region is elaborated by belaruskali. the t m. zhelnin et alii, frattura ed integrità strutturale, 49 (2019) 156-166; doi: 10.3221/igf-esis.49.17 161 determined mechanical properties for frozen soils are listed in tab. 1 and for unfrozen soils in tab. 2. according to design documentations for building of a vertical mine shaft accepted by belaruskali, minimal temperature of frozen soil in an ice-soil wall must not exceed 8t c   , so the properties are determined at this temperature. the deformation coefficient is estimated for 24prt hour. technical parameters for a vertical shaft sinking with using agf given by the documentation are presented in tab. 3. the numerical simulation has been carried out for the depth h of soil stratums occurrence within the range from 100 m to 500 m. soil a , mpa k , gpa g , gpa m clay 9.37 0.86 0.73 0.47 sand 6.65 2.76 2.25 0.3 chalk 15.90 1.19 1.09 0.48 table 1: mechanical properties of the frozen soils at temperature 8  t c . a – deformation coefficient in the constitutive relation (8), k – bulk modulus, g – shear modulus, m – degree in in the constitutive relation (8). soil k , gpa g , gpa c , kpa  ,  clay 0.19 0.15 105 25 sand 0.27 0.12 9.6 30 chalk 0.33 0.11 1 31.5 table 2: mechanical properties of the unfrozen soils. k – bulk modulus, g – shear modulus, c – cohesion coefficient,  – friction angle. a , m h , m  , m 5.25 5 0.1 table 3: technical parameters for a vertical shaft sinking. in fig. 3 5 distributions of radial displacement ru in an excavation obtained by the numerical simulation are presented. the thickness s of the ice-soil wall is estimated by vyalov’s formula (13). for the depth up to 300 m vyalov’s formula gives an overvalued estimation of optimal thickness of the ice-soil wall independent on considered soil. in chalk stratum the obtained displacements do not exceed the admissible value for all considered range of the depths. at the depth 500 m the radial displacement of the ice-soil wall of frozen clay exceeds the admissible value by 1 cm. at the same time the displacement of the wall of frozen sand at this depth exceeds the admissible value more than two times. qualitatively the distributions for soils under consideration coincide. a maximum value of the displacement attains on the inner surface of the ice-soil cylinder. thus it can be concluded that vyalov’s formula gives an overvalued estimation of the optimal thickness of the wall of quasi-brittle carbonate rocks such as chalk. for more ductile soils such as clay and sand vyalov’s formula gives an overvalued estimation of the optimal thickness of the wall for the depths less than 300 m and an undervalued the one for the large depths. distributions of shear strain rz in depending on radius on the top end of the ice-soil cylinder are presented in fig 6. it can be seen that for soils under consideration values of the strain obtained by the numerical simulation significantly differ from the ones given by the eqn. (14). normalization of the distribution on the maximum value it allows one to conclude that there is a qualitative discrepancy between the numerical and analytical distributions (fig 7). m. zhelnin et alii, frattura ed integrità strutturale, 49 (2019) 156-166; doi: 10.3221/igf-esis.49.17 162 a b figure 3: distribution of radial displacement ru in excavation in a clay stratum at depth h 300 m (a) and 500 m (b). a b figure 4: distribution of radial displacement ru in excavation in a sand stratum at depth h 300 m (a) and 500 m (b). a b figure 5: distributions of radial displacement ru in excavation in a chalk stratum at depth h 300 m (a) and 500 m (b). a b c figure 6: distributions of shear strain rz in depending on radius on the top end of the ice-soil cylinder of frozen clay (a), sand (b), chalk (c). black curve is given by the expression (14). other curves are obtained by the numerical simulation. m. zhelnin et alii, frattura ed integrità strutturale, 49 (2019) 156-166; doi: 10.3221/igf-esis.49.17 163 a b c figure 7: normalized distributions of shear strain rz in depending on radius on the top end of the ice-soil cylinder of frozen clay (a), sand (b), chalk (c). black line is given by the expression (14), other lines are obtained by the numerical simulation. modifications of vyalov’s formula he results of the numerical simulation presented in the previous section show that for the thickness of the ice-soil wall given by vyalov’s formula the radial displacement either is less than the admissible value or exceeds it. thus to reconcile vyalov’s formula to the results of the numerical simulation it has to be modified. from the plots of the shear strain obtained by the numerical simulation (fig. 6, fig. 7) it can be seen that the all curves converge to a limit curve under the increasing of the depth. as a consequence, it can be concluded that at the large depth h the shear strain rz on the top end of the ice-soil cylinder do not reflect a relationship between a maximal value of the radial displacement ru of the inner surface of the cylinder and rock pressure p . thus a modification of eqn. (14) does not allow one to modify vyalov’s formula that it coincide with the result of the numerical modeling. fig. 8 shows estimations of the thickness e of the ice-soil wall obtained by vyalov’s formula and the numerical simulation on the basis of the condition (12) for clay, sand and chalk stratums. the rock pressure p corresponds to the depth h within the range from 100 m to 500 m. figure 8: estimations of the thickness e of the ice-soil wall obtained by vyalov’s formula (dashed curve) and the numerical modeling (solid line) based on the condition of limiting radial strain for clay, sand and chalk stratums. by analysis of the presented data it has been noted that for a certain value of the rock pressure vyalov’s formula can be conformed to the results of the numerical simulation by a simple way: 1 2 vyalove e  , (20) t m. zhelnin et alii, frattura ed integrità strutturale, 49 (2019) 156-166; doi: 10.3221/igf-esis.49.17 164 where vyalove – a value of the thickness given by vyalov’s formula (13), 1e – a modified value. in fig. 9 (a) for the soils under consideration values obtained with using the eqn. (20) is compared to the ones given by the numerical modeling. the presented plots show that independently on soil under consideration the eqn. (20) can be applied when vyalove is less than 11 m. for the larger values of vyalove the eqn. (20) gives an undervalued estimation of the wall thickness in comparison to the results of the numerical simulation. a b figure 9: (a) estimations of the thickness e of the ice-soil wall given by the eqn. (20) (solid line) and the results of the numerical simulation (markers; the abscissa of a marker is a value given by vyalov’s formula, the ordinate is a value obtained by the numerical simulation.). (b) estimations of the thickness e of the ice-soil wall given by the eqn. (20) (solid line) and the results of the numerical modeling (markers). a value vyalove depends on a value of the rock pressure acting on the ice-soil wall. therefore, it can be deduced that the eqn. (20) is correct within a range of the rock pressure. in order to describe the dependency of the thickness of the icesoil wall obtained by the numerical simulation within the all range of rock pressure the following modification of vyalov’s formula has been proposed:                1 1 1 2 (1 )1 1 ( ) 1 2 ( , ) m m m pr m ph e a g p a t t a . (21) here the function  ( )g g p is a quadratic function 2 2 1 0( )g p p p     , (22) where coefficients i , ( 1, 2, 3)i  , are depended on considered frozen soil. in tab. 4 values of the coefficients for clay, sand and chalk are listed. fig. 9 (b) shows estimations of the thickness of the ice-soil wall of frozen clay, sand and chalk given by the eqn. (21). it can be seen that the proposed equation allows one to describe the results of the numerical simulation both qualitatively and quantitatively. soil 131 10  , pa-2 7 2 10  , pa-1 3 clay 1.95 -6.02 1.31 sand 0.51 -2.16 1.20 chalk 1.00 -4.75 1.42 table 4: material coefficients  ,i ( 1, 2, 3)i  , for the eqn. (22). m. zhelnin et alii, frattura ed integrità strutturale, 49 (2019) 156-166; doi: 10.3221/igf-esis.49.17 165 conclusions his work is devoted to analysis of vyalov’s formula for determination of an optimal thickness of an ice-soil retaining structure on the basis of a numerical simulation. for the numerical simulation of a stress-strain state of the ice-soil wall a new computational scheme has been proposed. the scheme is based on vyalov’s design layout for a vertical shaft sinking and takes into account a soil layer beyond the excavation bottom. the layer consists of a hollow ice-soil cylinder and unfrozen soil inside it. a mechanical behavior of frozen soil is described in according to vyalov’s constitutive relations. in comparison with an analytical approach used for derivation of the formula in the numerical simulation it has not to make additional assumptions concerning to distributions of stress and strain. as a result of the numerical simulation it has been shown that if a depth of soil stratum occurrence is less than 300 m, vyalov’s formula gives an overvalued estimation of the wall thickness for the all soils under consideration. for chalk, radial displacement of the wall is less than an admissible value within all range of the studied depths. for sand and clay, the displacement exceeds the admissible value if the depth is large than 300 m. thus, in quasi-brittle carbonate rock stratum an ice-soil retaining structure with a wall thickness estimated by vyalov’s formula has excess margin of safety. in ductile soil stratums, that are occurrence at large depth, vyalov’s formula gives an understated estimation of the wall thickness. it has been studied of an analytical expression for distribution of shear strain on the top end of the cylinder. for soils and depths under consideration the distributions given by the expression do not coincide qualitatively and quantitatively with the ones obtained by the numerical simulation. since vyalov’s formula is derived on the basis of the analytical expression, this is a reason due that estimates of the wall thickness obtained by vyalov’s formula do not agree to the numerical results. in order to conform estimations of the wall thickness given by the vyalov’s formula to the results of the numerical simulations, two modifications of the formula have been proposed. the first modification could be useful for engineering computations. according to the modification if a value of a thickness of the ice-soil wall given by vyalov’s formula is less than 11 m than it has to be divided on 2 to coincide with the value given by the numerical simulation. this rule is fulfilled for the all studied soils. the second modification intends including in vyalov's formula a quadratic function on a rock pressure that acts on an ice-soil wall. coefficients of the function depends on soil from that consists of the ice-soil wall. the modification allows one to describe the results of the numerical simulation qualitatively and quantitatively within all range of the rock pressure. however, to determine the coefficients of the function the numerical simulations has to be conducted for typical stratums of an elaborated deposit. thus, it can be concluded that for soil stratums occurrence at small depths a use of vyalov’s formula in design computations causes overvalued costs on the agf process. to prevent dangerous breakdown at large depths of a shaft sinking, estimates given by vyalov’s formula should be corrected by the numerical simulation. acknowledgments his research was supported by 17-11-01204 project (russian science foundation). references [1] vyalov, s.s., zaretsky, y.k., gorodetsky, s.e. (1979). stability of mine workings in frozen soils, engineering geology, 13 (1-4), pp. 339-351. doi: 10.1016/0013-7952(79)90041-3. [2] vyalov, s.s. (1986). rheological fundamentals of soil mechanics. elsevier, amsterdam, the netherlands [3] lai, y., xu, x., dong, y., li, s. (2013). present situation and prospect of mechanical research on frozen soils in china, cold regions science and technology, 87, pp. 6-18. doi: 10.1016/j.coldregions.2012.12.001. [4] yang, y., lai, y., chang, x. (2010). experimental and theoretical studies on the creep behavior of warm ice-rich frozen sand. cold regions science and technology, 63(1-2), 61-67. doi: 10.1016/j.coldregions.2010.04.011. [5] zhou z., ma w., zhang s., du h., mu y., li g. (2016). multiaxial creep of frozen loess, mechanics of materials, 95, pp. 172-191. doi: 10.1016/j.mechmat.2015.11.020. t t m. zhelnin et alii, frattura ed integrità strutturale, 49 (2019) 156-166; doi: 10.3221/igf-esis.49.17 166 [6] esmaeili-falak m., katebi h., javadi a. (2018). experimental study of the mechanical behavior of frozen soils-a case study of tabriz subway, periodica polytechnica civil engineering, 62(1), pp. 117-125. doi: 10.3311/ppci.10960. [7] zhao, x., zhou, g. (2013). experimental study on the creep behavior of frozen clay with thermal gradient. cold regions science and technology, 86, 127-132. doi: 10.1016/j.coldregions.2012.10.012. [8] wang d.y., ma w., wen z., chang x.x. (2008). study on strength of artificially frozen soils in deep alluvium, tunnelling and underground space technology, 23(4), pp. 381-388. doi: 10.1016/j.tust.2007.06.010. [9] bray, m. t. (2012). the influence of cryostructure on the creep behavior of ice-rich permafrost. cold regions science and technology, 79, 43-52. doi: 10.1016/j.coldregions.2012.04.003. [10] hou, f., lai, y., liu, e., luo, h., & liu, x. (2018). a creep constitutive model for frozen soils with different contents of coarse grains. cold regions science and technology, 145, 119-126. doi: 10.1016/j.coldregions.2017.10.013. [11] lackner r., pichler c., kloiber a. (2008). artificial ground freezing of fully saturated soil: viscoelastic behavior, journal of engineering mechanics, 134(1), pp. 1-11. doi: 10.1061/(asce)0733-9399(2008)134:1(1). [12] andersland o.b., akili w. (1967). stress effect on creep rates of a frozen clay soil. geotechnique 17(1), pp. 27–39. doi: 10.1680/geot.1967.17.1.27. [13] fish a.m. (1984). thermodynamic model of creep at constant stress and constant strain rate, cold regions science and technology, 9(2), pp. 143-161. doi: 10.1016/0165-232x(84)90006-5. [14] qi j., wang s., yu f. (2013). a review on creep of frozen soils, in constitutive modeling of geomaterials. springer, berlin, heidelberg, pp. 129–133. doi: 10.1007/978-3-642-32814-5_6. [15] razbegin v.n., vyalov s.s., maksimyak r.v., sadovskii a.v., (1996). mechanical properties of frozen soils. soil mechanics and foundation engineering 33(2), pp. 35–45., doi: 10.1007/bf02354292. [16] li, d. w., fan, j. h., wang, r. h. (2011). research on visco-elastic-plastic creep model of artificially frozen soil under high confining pressures. cold regions science and technology, 65(2), 219-225. doi: 10.1016/j.coldregions.2010.08.006 [17] wang, s., qi, j., yin, z., zhang, j., & ma, w. (2014). a simple rheological element based creep model for frozen soils. cold regions science and technology, 106, 47-54. doi: 10.1016/j.coldregions.2014.06.007. [18] klein j. (1981). finite element method for time-dependent problems of frozen soils, international journal for numerical and analytical methods in geomechanics, 5(3), pp. 263-283. doi: 10.1002/nag.1610050304. [19] klein j., jessberger h.l. (1979). creep stress analysis of frozen soils under multiaxial states of stress. engineering geology, 13(1-4), pp. 353-365. doi: 10.1016/0013-7952(79)90042-5. [20] puswewala u.g.a., rajapakse, r.k.n.d., domaschuk l., lach r. p. (1992). finite element modelling of pressuremeter tests and footings on frozen soils. international journal for numerical and analytical methods in geomechanics, 16(5), pp. 351-375. doi: 10.1002/nag.1610160505. [21] arenson, l. u., springman, s. m. (2005). mathematical descriptions for the behaviour of ice-rich frozen soils at temperatures close to 0 c. canadian geotechnical journal, 42(2), 431-442. doi: 10.1139/t04-109. [22] bray, m. t. (2013). secondary creep approximations of ice-rich soils and ice using transient relaxation tests. cold regions science and technology, 88, 17-36. [23] vyalov s.s., gorodetsky, s.e., zaretsky yu.k., gmoshinsky v.g, grigoreva v.g., pekarskaya n.k., shusherina e.p., (1962). strength and creep of frozen soils and design of ice—soil retaining structures. u.s.s.r. acad. press, moscow (in russian). [24] andersland o.b., ladanyi b., 2013. an introduction to frozen ground engineering. chapman and hall, new york. [25] kostina a., zhelnin m., plekhov o., panteleev i., levin l. (2018). creep behavior of ice-soil retaining structure during shaft sinking, procedia structural integrity, 13, pp. 1273-1278. doi: 10.1016/j.prostr.2018.12.260. [26] terzaghi k., peck r.b., mesri g. 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can be opened with acrobat and adobe reader 5.0 and later.) >> /namespace [ (adobe) (common) (1.0) ] /othernamespaces [ << /asreaderspreads false /cropimagestoframes true /errorcontrol /warnandcontinue /flattenerignorespreadoverrides false /includeguidesgrids false /includenonprinting false /includeslug false /namespace [ (adobe) (indesign) (4.0) ] /omitplacedbitmaps false /omitplacedeps false /omitplacedpdf false /simulateoverprint /legacy >> << /addbleedmarks false /addcolorbars false /addcropmarks false /addpageinfo false /addregmarks false /convertcolors /converttocmyk /destinationprofilename () /destinationprofileselector /documentcmyk /downsample16bitimages true /flattenerpreset << /presetselector /mediumresolution >> /formelements false /generatestructure false /includebookmarks false /includehyperlinks false /includeinteractive false /includelayers false /includeprofiles false /multimediahandling /useobjectsettings /namespace [ (adobe) (creativesuite) (2.0) ] /pdfxoutputintentprofileselector /documentcmyk /preserveediting true /untaggedcmykhandling /leaveuntagged /untaggedrgbhandling /usedocumentprofile /usedocumentbleed false >> ] >> setdistillerparams << /hwresolution [2400 2400] /pagesize [612.000 792.000] >> setpagedevice microsoft word numero_37_art_24 p.s. van lieshout et al., frattura ed integrità strutturale, 37 (2016) 173-192; doi: 10.3221/igf-esis.37.24 173 focussed on multiaxial fatigue and fracture comparative study of multiaxial fatigue methods applied to welded joints in marine structures p.s. van lieshout, j.h. den besten, m.l. kaminski delft university of technology, netherlands p.s.vanlieshout@tudelft.nl, henk.denbesten@tudelft.nl, m.l.kaminski@tudelft.nl abstract. marine structures are particularly prone to action of waves, winds and currents with stochastically varying composition, intensities and directions. therefore, resultant stresses may cause multiaxial fatigue in specific welded structural details. for the assessment of multiaxial fatigue in welded joints, a wide variety of methods have been suggested. however, there is still no consensus on a method which can correctly account for non-proportional and variable amplitude loading. this paper beholds a comparative study of multiaxial fatigue methods applicable for design of marine structures. for the purpose of comparison several load cases were defined including non-proportional and variable amplitude loadings with different normal and shear stress amplitude ratios. three types of methods are compared: those described by three different codes (i.e. eurocode 3, iiw and dnv-gl), those described by three different multiaxial fatigue approaches from literature (i.e. modified carpinteri-spagnoli criterion, modified wohler curve method and effective equivalent stress hypothesis) and an approach based on path-dependent-maximum-range multiaxial cycle counting. from this study it has been concluded that non-proportional variable amplitude loading has a significant negative impact on the fatigue lifetime estimates, and that further research and experimental testing are essential to come to a consensus. keywords. multiaxial fatigue; welded joints; marine structures; non-proportional; variable amplitude loading; constant amplitude loading. introduction ost welds in structural details of marine structures are predominantly subjected to uniaxial stresses due to the stiffness distributions in typical structural member assemblies like stiffened panels, frames and trusses. however, there are also welds which could be subjected to multiaxial stresses induced either by geometry [1, 2] or loading. such stresses may lead to a significant reduction of the fatigue resistance of welded steel [3]. considering that the majority of marine structures are (relatively thick) plated structures, such fatigue lifetime reductions are generally caused by the combined effect of a dominant normal and shear stress (mixed mode-i and mode-iii). currently, fatigue design of marine structures is predominantly based on uniaxial fatigue criteria assuming a governing mode-i. these criteria are then used in combination with a damage accumulation hypothesis (e.g. miner’s rule) and cycle counting method (e.g. rainflow counting) to determine the fatigue lifetime. however, such an approach can be nonconservative for structural details where the welds are subjected to multiaxial stresses, especially when these are nonproportional, i.e. out-of-phase (op). over the last few decades intensive efforts have been made to develop multiaxial fatigue approaches which are able to deal with difficulties such as (random) variable amplitude (va) loading and non-proportionality. this has resulted, m p.s. van lieshout et al., frattura ed integrità strutturale, 37 (2016) 173-192; doi: 10.3221/igf-esis.37.24 174 amongst others, in multiaxial cycle counting methods [4-6], critical plane based criteria [3, 79] , invariant based criteria [10] and energy based criteria [11]. furthermore, spectral methods have been developed to assess multiaxial fatigue in the frequency domain, instead of the time domain [12]. however, still no consensus has been reached on an approach for the assessment of multiaxial fatigue in welded joints, whereby non-proportionality and variable amplitude loading can be accounted for correctly [13]. this study aims to identify the discrepancies resulting from the use of different multiaxial fatigue approaches for the fatigue analysis of welded joints in marine structures, considering proportionality and stress amplitude (ratio). the comparative study has been carried out using several conceptual constant (ca) and variable amplitude load cases. each ca case has been analysed using three different codes and three multiaxial fatigue methods from literature. the va cases have been analysed with an approach based on pdmr multiaxial cycle counting. theoretical background hen analysing the fatigue performance of a marine structure (i.e. ship or offshore structure) there are three preliminary steps which can be distinguished: 1. hydrodynamic analysis; the structural response is induced by exposure to (multiaxial) environmental loads (e.g. wind, current and waves) and operational loads. confused sea states and/or joint geometry can hereby lead to multiaxial stress states. with a hydrodynamic analysis the loads can be converted into time series or response transfer functions, consisting of raos (response amplitude operators) and phase angles, which describe the structural behaviour in all six degrees of freedom. 2. structural analysis; multiaxial stress states can be induced depending on the (combination of) loading and structural geometry at global and local level. in order to identify the locations where such multiaxial stresses occur, it is often required to execute a global and local structural analysis. 3. fatigue analysis; stress or strain time trace histories can be extracted (in a time domain analysis) or generated (in a frequency domain analysis) with the structural analysis and subsequently be used to estimate the fatigue performance of the structure. a multiaxial fatigue analysis is not a procedure with a univocal set of instructions. in fact, different decisions can be made at four elementary levels. in the first place it is of importance to narrow down the possibilities by defining the domain (time or frequency), joint type (welded or non-welded), material characteristics (ductile, semi-ductile or brittle) and scale (macro, meso or micro). this leads to the second level where it has to be decided whether an intact geometry parameter will be chosen, wherefore sn-curves will be used, or a crack damaged parameter, whereby fracture mechanics will be used [14]. marine structures typically deal with high cycle fatigue whereby fatigue crack initiation dominates the total fatigue life. this fatigue regime is generally described by stress ranges due to the fact that low stress amplitudes are encountered which cause elastic deformation of the material [15]. on the other hand, elastic-plastic deformations induce low cycle fatigue and is therefore generally described by strain ranges. an intact geometry parameter is most commonly applied for the fatigue design of welded joints in marine structures. generally, a fail-safe design approach is followed, meaning that the structural integrity can cope with the failure of an individual member [14, 15]. such a design approach is chosen because it is anticipated that imperfections are present in the material, induced by production and/or welding. using an intact geometry parameter, a distinction can be made between those who lead to a fatigue lifetime estimate (i.e. finite lifetime) and those who identify a ‘safe region’ without fatigue crack initiation (i.e. an infinite lifetime). this ‘safe region’ is then identified by a fatigue boundary definition. an example of such a definition is the dang van criterion [1619]. however, to obtain a fatigue lifetime estimate four steps have to be undertaken. in this fourth elementary level the fatigue damage parameter(s) should be identified (i.e. stress, strain or energy-a product of stress and strain) including the basis on which these parameters are being considered (i.e. a critical plane, an invariant, an integral). then, the cycle counting procedure (uniaxial or multiaxial), damage rule (linear of non-linear) and the reference sn-curve (considering separate modes or mixed modes) have to be chosen. in fig. 1 a schematic overview is given of the four elementary levels of decision making indicating the different options. one of the difficulties with multiaxial fatigue in welded marine structures is that the phenomenon of fatigue in welded joints cannot be scaled. plenty of research on multiaxial fatigue has been executed for the automotive and aerospace w p.s. van lieshout et al., frattura ed integrità strutturale, 37 (2016) 173-192; doi: 10.3221/igf-esis.37.24 175 industry but this knowledge, concerning thin plated structures, cannot be directly transferred to relatively thick plated marine structures. as elaborated in [15], fatigue resistance decreases with increasing plate thickness due to an increase in welded material volume, residual stress effects, surface quality and a larger stressed material volume. a total stress concept was developed to incorporate these effects. however, this concept was developed for welded aluminium joints subjected to uniaxial fatigue and has not yet been extended to steel joints facing multiaxial fatigue. figure 1: overview of the four elementary levels in a multiaxial fatigue analysis. in literature different fatigue damage models can be found which describe fatigue crack evolution as a combination of shear stress dominated crack initiation and normal stress dominated crack growth e.g. miller’s 2-stage concept and socie’s damage model [20]. this is based on the physical phenomenon whereby persistent slip bands (psb’s) form when a crystal is subjected to microscopic cyclic stresses. psb’s are parallel to the easy glide material plane which has, for example for mode i loading, typically a 45 degrees inclination with the normal. psb’s facilitate laminar flow under shear loading which p.s. van lieshout et al., frattura ed integrità strutturale, 37 (2016) 173-192; doi: 10.3221/igf-esis.37.24 176 causes the initiation of a fatigue crack: they follow the path of the least resistance. once a micro-crack has been formed the microscopic stress concentration moves with the crack tip until the crack reaches its next slip band. this also explains the +/45 degrees zig-zag crack profile that is often observed at microor meso-scale. therefore, fatigue crack initiation is shear stress governed and fatigue crack growth normal stress governed. at macro-scale the average profile is 0 degrees meaning perpendicular to the principal stress (and equal to the normal stress for a mode-i loading). therefore, fatigue crack initiation (at micro and meso scale) is shear stress governed and fatigue crack growth at macro-scale normal stress governed. moreover, this holds for different cracking modes. this is the underlying theory for including a normal and shear stress component in multiaxial fatigue models which aim to determine fatigue lifetime (i.e. fatigue crack initiation and growth). multiaxial fatigue methods implemented in codes mongst the codes which have been developed for the fatigue design of marine structures e.g. eurocode 3, iiw, dnv-gl-0005, two types of approaches can be distinguished. they use either standardized interaction equations or the maximum principal stress (together with its relative direction with respect to the weld toe) [21-23]. the sn-curves that are used in combination with these recommended approaches are obtained from experimental tests and are presented independent of a mean stress [24]. this is based on the presumption of high tensile residual stresses in the weld [19]. interaction equations originate from the empirical finding that under combined bending and torsional loading ductile materials (e.g. steel) show an ellipse shape of the fatigue limits in the normal/shear stress diagram [25-26]. this eventually resulted in the well-known empirical gough-pollard equation (i.e. gough ellipse), see eq. 1. for brittle materials this was not an ellipse shape but a parabola. therefore, the exponent of the normal stress term in the gough-pollard equation could be considered as a function of (the ratio of) the fatigue limits. this leads into the generic ellipse arc formulation provided in eq. 2 [27].                      2 2 ,  1 , 1 1 a a (1)                      2 ,  1 , 1 1 k a a (2)             ,  1 , 1 a a k f principal stress based approaches were developed from the experimental observation that fatigue cracks grow normal to the principal stress direction when it has a constant directionality [21]. this observation was then also used as a basis for the assessment of multiaxial fatigue with changing principal stress direction (e.g. non-proportionality). the size and orientation of the principal stress direction are then taken into account. eurocode 3 for the fatigue design of steel structures, the european union has established eurocode-3. this code advises to account for the combined effect of the normal and shear stress components, acting respectively perpendicular and parallel to the weld toe, through an interaction equation (eq. 3). in order to establish this relationship fatigue tests from large scale specimens were used, including geometrical and structural imperfections from material production. the constant amplitude equivalent normal stress range  eq and shear stress range  eq are related to the design resistances  r and  r defined at a certain number of stress cycles for a particular detail category. it can be seen from eq. 3, that two individual damage mechanisms are incorporated: two different exponents are used for respectively the normal stress term and the shear stress term. the selected values for the exponents originate from the fatigue resistance to shear stress which typically shows a slope of 5 and for normal stress a slope of 3. this diverges from the exponents suggested in the gougha p.s. van lieshout et al., frattura ed integrità strutturale, 37 (2016) 173-192; doi: 10.3221/igf-esis.37.24 177 pollard equation (eq. 1). however, it was concluded in a comparative study executed by [25] that eurocode 3 provides consistently less accurate results in comparison to two other interaction equations which use the exponents as suggested in the gough-pollard equation (i.e. iiw and sfs 2378). particularly for non-proportional combined loading, differences are observed when compared to experimental data from welded joints. it is therefore questionable whether the individual damage mechanisms remain unaffected by combined load cases.                    3 5 1 eq eq r r (3) iiw based on experimental investigations and recommendations from contributing researchers the international institute of welding (iiw) developed a similar relationship between the normal and shear stress component as eurocode 3. however, in comparison to eurocode 3, the interaction equation as defined by the iiw seems more advanced: eq. 4. the code allows for different material ductility (steel or aluminium), load characteristics (ca and va loading, both in combination with either in-phase (ip) or op loading), and a correction for fluctuating mean stress. for each particular case a critical miner’s damage sum (equating to 0.2; 0.5 or 1) and comparison value    0.5 or 1cv is advised. the design resistance of particular detail category is expressed by fat class. similar to the gough-pollard equation (eq. 1) there is no difference observed between the two damage mechanisms (i.e. shear and normal stress induced): both terms in the equation are raised to power of two. however, the interaction effect can be (partially) covered by the cv value and maximum damage sum that are used in the fatigue analysis.                    2 2 eq eq r r cv (4) figure 2: illustration clarifying how angle φ is used to determine the maximum principal stress direction σp1 with respect to the weld toe; reproduced from [21]. dnv-gl-rp-0005 dnv-gl has established a recommended practice for fatigue design of offshore steel structures based on the maximum principal stress and its direction. the use of principal stresses in the dnv recommended practice for marine structures originates from 1984 and originates from experimental observations that fatigue cracks grow perpendicular to the principal stress direction for uniaxial and proportional multiaxial load cases (i.e. the load cases where the direction of the principal stress doesn’t change (during one load cycle)). therefore, the direction of the principal stress range is taken into account by an angle   between the maximum principal stress  1 p and the normal to the weld toe  a (see fig. 2). once this angle exceeds a critical value, the notch at the weld toe may no longer be the critical location for fatigue. a higher reference sn-curve is then recommended depending on the detail category [21]. it should be noted that the same approach is considered applicable to non-proportional load cases whereby the principal stress changes direction in one load cycle. important to note is the fact that the fatigue assessment following this recommended practice is mode i based p.s. van lieshout et al., frattura ed integrità strutturale, 37 (2016) 173-192; doi: 10.3221/igf-esis.37.24 178 i.e. the angle relative to the normal of the weld seam is being considered. the interaction effect between mode i and mode iii is not taken into account. multiaxial fatigue methods from literature ultiaxial fatigue methods are often categorized on the basis of their fatigue damage parameter(s) and their approach, cf. section 2. critical plane based methods are considered promising for the analysis of multiaxial fatigue problems because they show good correlation with experimental observations [28]. moreover, they can incorporate non-proportionality and distinguish between phase shift induced non-proportionality and frequency induced non-proportionality. they originate from experimental observations where fatigue crack initiation (i.e. nucleation and early growth) appeared to occur on preferred material planes [29]. however, these observations were made in non-welded smooth specimens. many critical plane based methods were therefore originally developed for smooth and notched specimens. however, in welded joints the crack initiation and early crack growth phase are affected by the welding process. nowadays, several critical plane based methods have been explicitly developed or extended for welded joints. however, it is often not clear in literature in how far these approaches can be applied to multiaxial fatigue problems in welded joints. instead of identifying a particular critical plane it is suggested by some approaches to consider the interaction between the different material planes through integration. on these grounds, three methods have been selected for further investigation. modified carpinteri-spagnoli criterion the modified carpinteri-spagnoli criterion was originally found suitable for smooth and blunt notched specimens [30] and later extended for welded joints facing multiaxial fatigue [7]. the basis of the original criterion are experimental observations which demonstrated a correlation between the fatigue crack plane and the direction of the maximum principal stresses/strains and maximum shear stress/strain [30]. two stages were distinguished: shear stress driven crack initiation and fatigue crack growth in the plane normal to the direction of the maximum principal stress. interestingly, this criterion combines the different approaches that are suggested in the design codes (cf. section 3) by suggesting an interaction equation which considers the stress components acting on a critical plane which is directly related to the averaged principal stress direction. the modified carpinteri-spagnoli criterion (mcsc) is formulated as a quadratic combination of the maximum normal stress amplitude and shear stress amplitude acting on the critical plane [31]:                      2 2 , 1 , 1 1max a a a (5)      , 1                 1a fully reversed normal stress fatigue limit for bending r      , 1                 1a fully reversed shear stress fatigue limit for torsion r in order to define the directions of the averaged principal stresses it was initially suggested to apply an averaging procedure using weight functions which would result in three euler angles    ,  , determining the orientation of each averaged principal stress. however, from a parametric study it was found that the averaged principal stress direction almost coincides with the moment where the principal stress reaches its maximum value in a load cycle. this simplified the original calculation procedure [7]. in fig. 3a it can be seen how the directions of the averaged principal stresses (whereby   ' '1,   2,   3 ˆ ˆz x y ) are defined using the three euler angles   ,   and  which correspond to counter clockwise rotations about respectively the z -axis, the so called line of nodes n and the 'z -axis (i.e. rotated z -axis) [32]. based on experimental observations an empirical expression was formulated for the off angle  (resulting from a clockwise rotation around the 2̂ axis) between the normal to the critical plane w and the averaged direction of the maximum principal stress 1̂ . the empirical expression for  is given in eq. 6. furthermore, an additional counter clockwise angle about w is formulated. this angle  . enables to described the local coordinate system by the axes uvw as illustrated in fig. 3b. m p.s. van lieshout et al., frattura ed integrità strutturale, 37 (2016) 173-192; doi: 10.3221/igf-esis.37.24 179 different methods have been developed to determine the shear stress amplitude acting on a critical plane. in this comparative study the minimum circumscribed circle method was used. this method has been described in [7, 31, 33].                  2 , 1 , 1 3 45 1 2 af af (6)       , 1 , 1 1   1 3 af af whereby figure 3: representation of the counter clockwise rotations about the , z n and 'z axis, defined through three euler angles , ,   (a) relationship between the two spherical angles  and  with respect to the local coordinate system with axes uvw (b); reproduced from [32]. modified wohler curve method the mwcm considers the normal and shear stress components acting on a particular critical plane whereby the orientation of the critical plane is determined by a maximum variance method (mvm). this mvm is based on the experimental observation that fatigue damage shows proportionality with the variance of a random uniaxial load signal, both for gaussian and non-gaussian loadings [34]. therefore, the critical plane corresponds to the material plane which coincides with the direction along which the variance of the resolved shear stress is maximum. the complexity of the stress state is then expressed by the stress amplitude ratio    δ / δn which indicates the degree of nonproportionality. hereby,  n is the normal stress acting perpendicular to the critical plane and  is the resolved shear stress acting on the critical plane. the mwcm presumes that fatigue damage is independent of the (nominal) load path as long as the stress ratio and shear stress range relative to the critical plane are the same. therefore, a linear relationship is suggested for the construction of a modified load specific sn-curve [34]. fig. 4 illustrates how this load specific sn-curve is constructed based on the tension and torsional fatigue curves. the equations that represent this linear relationship are given in eq. 7 and 8.                , δ δ  δ   2 a a a a ref (7)        0 0  k k k k (8) the mvm describes the orientation of the critical plane using two polar angles  and  with respect to the local nab coordinate system of the critical plane. the angle  represents the angle between the normal to the critical plane and the z-axis of the global reference coordinate system, while angle  represents the angle between the projection of the normal p.s. van lieshout et al., frattura ed integrità strutturale, 37 (2016) 173-192; doi: 10.3221/igf-esis.37.24 180  n to the critical plane on the xy-plane in the global reference coordinate system. in addition, angle  is used to determine the orientation of the shear stress vector in the critical plane which corresponds with the maximum resolved shear stress along unit vector q . fig. 5a and 5b elucidates how the three angles  ,  and  are related to the critical plane and its local coordinate system. figure 4: constructing a load specific sn-curve using the curves for pure uniaxial and torsional loading following the modified wohler curve method; reproduced from [9]. figure 5: determination of the orientation of the normal to the critical plane using the angles  and  (a) determination of the orientation of the local coordinate system of the critical plane abn using angle  ; (b) reproduced from [35]. effective equivalent stress hypothesis from previous research it was concluded that the von mises equivalent stress encounters difficulties with nonproportional multiaxial loadings [3, 36]. the eesh was developed with the aim to improve the von mises equivalent stress formulation for cases of non-proportional multiaxial fatigue. the hypothesis tries to incorporate the detrimental effect of non-proportional loading on fatigue lifetime by considering the interaction of shear stress in different material planes. this is based on the consideration that for ductile materials shear stress initiates multiaxial fatigue failure . the maximum local stress in the weld toe is hereby presumed governing for fatigue life. therefore, the approach uses local stresses. p.s. van lieshout et al., frattura ed integrità strutturale, 37 (2016) 173-192; doi: 10.3221/igf-esis.37.24 181 originally, [3] included a square root term in the hypothesis to try to account for the influence of the maximum stressed material volume on the local stress. however, this term was found to be unsuccessful and got removed from the equation [37]. the eesh defines a local equivalent stress  eesh , based on the von mises stress equivalent which is determined as a function of the phase angle  (see eqs. 9-10). the interaction of the shear stresses acting at different material planes is incorporated by an effective shear stress term f which is also a function of the phase angle  . the effective shear stress is an integral of all shear stress components (i.e. n ) acting on the material planes (in two dimensional space) defined by their angle of rotation  . due to this integration procedure frequency induced non-proportionality is also covered in this hypothesis. however, as can be seen from eq. 11, the calculations become significantly more complex once variable amplitude loading is encountered. henceforth, damage calculation requires a local sn curve. such a local sn-curve was constructed with experimental data from a welded flange-tube specimen in sonsino & kueppers (2001).                   0 0 eesh eesh f f (9)             2 2 20   3eesh x y x y xy (10)            0 1 pf f d (11)                   , 1       :    1       :  n ls p n i s i for constant amplitude loading f for variable amplitude loading l            swhereby l sequence length of the load spectrum comparative study he stress state at a location of interest can be analyzed at different levels. in the current literature different methods have been developed based on nominal stress [38, 9], hot spot stress [38-41] or structural stress [42-44] and notch stress [19, 45-47]. they differentiate amongst one another in the amount of local stress information. the nominal stress approach only considers the membrane component of stress induced by the macro-geometry of the joint, excluding stress concentrations [23]. the hot spot or structural stress approach considers an equilibrium-equivalent structural stress part as a composition of a membrane and bending stress component. it uses linear extrapolation towards the weld toe in order to account for the membrane and bending component of stress (or through-thickness linearization), excluding the effect of the notch at the weld-toe transition. this means that only those stress concentrations are being considered which are caused by the structural detail of the joint [40]. the effective notch stress approach accounts for the additional stress peak induced by the notch at the weld-toe transition (i.e. self-equilibrating notch stress part). typically, the more local information is added the more accurate the fatigue lifetime estimates should become. however, at a certain point it is no longer worthwhile to add more local information because it cannot overcome statistical scatter in experiments [14]. this comparative study is based on nominal stresses. the reasoning behind this is that more local stress information (e.g hot spot/structural stress, notch stress) would require a specified joint geometry. the objective is to execute a comparative study which is independent of joint dimensions. moreover, the results can be considered conservative because more local stress information would improve the accuracy. constant amplitude loading five different conceptual ca load cases have been established presuming harmonic sinusoidal loading, see tab. 1. the stress amplitude ratio was set to   / 1 / 3a a (with a normal stress amplitude of   100 a mpa ) and a frequency ratio of   / 1f f . load case 5 is an exception whereby the frequency ratio is set to 2 . t p.s. van lieshout et al., frattura ed integrità strutturale, 37 (2016) 173-192; doi: 10.3221/igf-esis.37.24 182 reference sn-curves had to be selected for each code separately. for this purpose a non-load carrying fillet welded joint was presumed leading to cat 80, fat 80 and e category for eurocode 3, iiw and dnv-gl respectively. the reference sn curves were used to find the number of cycles  fn which meet the established criterion and were then transposed to fatigue damage using miner’s rule [48]. for lc 5 two different strategies have been applied. the first one is a conservative interpretation (referred to as lc 5.1), whereby the frequency of the normal stress component is presumed similar to the shear stress component (i.e. twice as high as actually is the case). the second strategy (referred to as lc 5.2) accounts the actual number of cycles of the shear stress component when finding agreement with the fatigue criterion. all damage sums have been normalized with the pure mode-i load case (i.e. lc 1), for each code separately, and are listed in tab. 2a. load case 1 (lc 1) pure tension load case 2 (lc 2) pure torsion load case 3 (lc 3) tension & torsion in-phase load case 4 (lc 4) tension & torsion out-of-phase load case 5 (lc 5) tension & torsion out-of-phase table 1: definition of ca load cases table 2a: normalized effect of stress multiaxiallity on fatigue damage predicted using selected codes – comparison between the different load cases. for the three selected multiaxial fatigue methods, particular reference sn-curves had to be used. for this purpose experimental data collected by [3] was used. run-outs were excluded. the use of this data set is favourable as the stress concentration factors for bending and torsion of this test specimen are known. this enables to determine the local stresses at the weld which are needed for application of the eesh. to determine fatigue damage a reference sn-curve based on the local equivalent stress amplitude could now be used. this sn-curve was defined earlier by [3]. for the mcsc and mwcm the pure mode-i and pure mode iii curve were used [34]. all normalized damage sums are listed in tab. 2b. it should be emphasized that the results listed in tabs. 2a and 2b show the relative differences between the different load cases. critical plane method lc 1 lc 2 lc 3 lc 4 lc 5 mcsc 1.0 0.15 2.7 2.3 2.7 mwcm 1.0 0.15 1.2 1.3 1.3 eesh 1.0 0.02 1.7 2.5 4.4 table 2b: normalized effect of stress multiaxiallity on fatigue damage predicted using selected multiaxial fatigue methods in addition, the codes and methods have been compared amongst each other for each individual load case. in tab. 3a the results from the selected codes are listed after normalization with the lowest fatigue damage. from the three selected 1 considering an in air environment s tr e ss [ m p a ] t 0 1 2 3 4 5 6 -100 -80 -60 -40 -20 0 20 40 60 80 100 code lc 1 lc 2 lc 3 lc 4 lc 5 lc 5.1 lc 5.2 eurocode 3 1.0 0.41 1.4 1.4 2.8 1.8 iiw 1.0 0.41 2.6 9.8 20 3.5 dnv-gl-rp-00051 1.0 0.14 1.1 1.0 1.0 p.s. van lieshout et al., frattura ed integrità strutturale, 37 (2016) 173-192; doi: 10.3221/igf-esis.37.24 183 multiaxial fatigue methods only the results from mcsc and mwcm were considered because they use the same reference sn-curve. including the results obtained with the eesh would not be just because this method is based on a local approach. the results were normalized with the lowest fatigue damage and are listed in tab. 3b. variable amplitude loading – case study in various previous studies on the applicability and validity of multiaxial fatigue methods conceptual load histories have been used [49-51]. however, difficulties start to arise when it is intended to execute a multiaxial fatigue analysis on a structure under op va loading, which is representative for the actual day-to-day loading on marine structures. for this purpose a case study was developed by the authors and was then used to investigate the effect of stress amplitude ratio on fatigue damage using pdmr based multiaxial cycle counting [52]. table 3a: normalized effect of stress multiaxiallity on fatigue damage predicted using selected codes – comparison between the different codes. critical plane method lc 1 lc 2 lc 3 lc 4 lc 5 mcsc 1.0 1.0 2.3 1.7 2.0 mwcm 1.0 1.0 1.0 1.0 1.0 table 3b: normalized effect of stress multiaxiallity on fatigue damage predicted using selected multiaxial fatigue methods – comparison between the different methods. marine structures are in reality subjected to a combination of stationary sea states whereby each sea state consists of one, two or several wave systems [53]. each wave system is then defined by a spectral density function. simultaneous wind seas and swells generally dominate the wave spectrum of floating marine structures. however, as a simplified approach, zou & kaminski (2016) suggest to use one expression to represent all swells by a particular spectrum with a mean wave direction. this suggestion is based on wave energy conservation the same assumption can be made for wind seas. in this case study this simplified approach has been followed. wind driven seas were described by the mean jonswap spectrum as advised by the 17th ittc in 1984 [54] and swell sea by a gaussian swell spectrum (see eqs. 8 and 9).                    2 , 5 4 jonswap 4 4 , , 320 1950 s ω s wind a p wind p wind h exp t t (8)                               2 ,  , 1 0.07   2   ; ;    0.09   , 2 pp wind p wind pp if whereby a exp ift wind                          2 2 ,  2 , ( / 4 ) 2 2 ps swell gaussian swellh s exp (9) 2 considering an in air environment code lc 1 lc 2 lc 3 lc 4 lc 5 lc 5.1 lc 5.2 eurocode 3 1.0 3.0 1.3 1.4 2.7 1.7 iiw 1.0 3.0 2.4 9.8 19 3.3 dnv-gl-rp-00052 1.0 1.0 1.0 1.0 1.0 p.s. van lieshout et al., frattura ed integrità strutturale, 37 (2016) 173-192; doi: 10.3221/igf-esis.37.24 184 this is in agreement with various guidelines for the marine industry (e.g. [55-56]). the directionality of the two spectra was fixed at a 180 degrees heading for wind seas and a 90 degrees heading for swell. it was assumed that wind driven and swell seas are long-crested and generate only normal and shear stresses, respectively. additionally, it was assumed that stress spectral density functions are the same as wave spectra meaning that unit response amplitude operators were assumed. normally, multiplication of the wave spectra with response amplitude operators slightly shifts the spectra towards another frequency range. therefore, it was necessary to choose the spectra parameters such that they correspond to a realistic structural response of a typical marine structure. the used spectra parameters are listed in tab. 4 and the corresponding energy density spectra are depicted in fig. 6. the selected va case is representative for a general fillet welded connection in a marine structure (see fig. 7). it is supposed that along the weld a multiaxial stress state is generated consisting of a normal stress induced by wind seas and a shear stress induced by a simultaneous swell. figure 6: energy density for wind seas and swell. parameter description value , p windt peak period of wind seas 8 s ,  p swellt peak period of swell seas 14 s , s windh significant wave height of wind seas 2 m ,s swellh significant wave height of swell seas 2 m g gravitational constant 29.81  /m s  gaussian spectral width 0.02  peakedness factor of jonswap spectrum 3.3 table 4: all parameters which have been used to describe the two spectra of swell respectively wind seas. p.s. van lieshout et al., frattura ed integrità strutturale, 37 (2016) 173-192; doi: 10.3221/igf-esis.37.24 185 figure 7: illustration of the local multiaxial stress components (normal and shear) with respect to a structural detail fatigue lifetime estimation multiaxial cycle counting he intricacy in processing the generated time traces lies in the cycle counting procedure. the authors used their own multiaxial cycle counting algorithm developed based on publications of the pdmr cycle counting method [52, 57, 58]. this algorithm was used to process time traces of normal and shear nominal stress which were generated with the two considered wave spectra. the generated time traces were scaled with four different stress amplitude ratios                  1 1 1 1   ;    ;    ;    ;  1 2 3 5 a a a a a a a a and then pdmr counted in   3 stress space. multiaxial damage accumulation for quantitative comparison, the pdmr cycle counting results were converted into an accumulated damage and then normalized with respect to pure normal stress. for this purpose miner’s linear damage accumulation rule was used in combination with a reference sn-curve. this reference sn-curve had to be compatible with the pdmr based cycle counting. therefore, the selected experimental data from [3] was used again. for the four load cases (i.e. pure bending, pure torsion, combined ip loading and combined op loading) the corresponding effective stress range was determined using pdmr cycle counting. in this case, these effective stress ranges correspond with the half-length of the load path in   3 stress-space. eventually, a mean sn-curve was establishing by making a linear regression as shown in fig. 8. tab. 5 lists the parameters of the mean sn-curve. accumulated fatigue damage was then calculated using the mean minus two times standard deviation sn-curve. figure 8: mean sn-curve used to determine the accumulated fatigue data and generated using data published in [3]. t p.s. van lieshout et al., frattura ed integrità strutturale, 37 (2016) 173-192; doi: 10.3221/igf-esis.37.24 186 parameter value  log c 17.2 m 4.45 sd 0.369 table 5: parameters of mean sn-curve. for comparison the ca load cases were also analysed using the pdmr based approach. the normalized results are listed in tab. 6 and show that the virtual path length, which is identified in this counting procedure, has a large effect on the damage calculation. for the va load cases twenty minute time traces were used of which a part of a typical realization is shown in fig. 9. in fig. 10 an example is given of a va multiaxial load path considering an amplitude ratio of 1. fig. 11 shows the histograms that resulted from pdmr cycle counting of the load path depicted in fig. 10 when the virtual path length is included and excluded. again a significant impact of the virtual load path on the accumulated fatigue damage was observed. furthermore, a peak is observed at very low stress ranges. this is caused by all the remaining small pieces of path length that result from ‘cutting’ the load path in the counting procedure. for twenty realizations the average fatigue damage was calculated using pdmr cycle counting including and excluding the virtual path length. the values were normalized with pure tension/bending (i.e. normal stress only) and are listed in tab. 7a. multiple realizations were needed because of unknown phases between the individual frequency components of the stress spectra. pdmr based method lc 1 lc 2 lc 3 lc 4 lc 5 including virtual path excluding virtual path normalized damage 1.0 1.0 5.0 6.7 38 7.1 normalized path length 1.0 1.0 1.4 1.5 2.7 2.2 scaled maximum range 2.0 2.0 2.8 3.1 5.2 3.2 number of half cycles 2 2 2 2 4 4 table 6: fatigue damage (info) obtained with pdmr cycle counting for ca load cases; results normalized with pure tension/bending figure 9: example of two typical time traces for sigma and tau which have been used for pdmr based cycle counting. figure 10: multiaxial load path of a twenty minute time trace from a three hour realization depicted in the 3  stress space whilst considering a stress amplitude ratio of 1. p.s. van lieshout et al., frattura ed integrità strutturale, 37 (2016) 173-192; doi: 10.3221/igf-esis.37.24 187 table 7a: average fatigue damage obtained with pdmr cycle counting for va loading considering different stress amplitude ratios; results normalized with pure tension/bending (i.e. normal stress only). from the results obtained from the va load cases an exponential trend was inferred between stress amplitude ratio and fatigue damage. therefore, an additional damage calculation was executed with a stress ratio of 0.8. the results are listed and compared with the other stress amplitude ratio’s in tab. 7b. an exponential increase of fatigue damage is indeed clearly shown in fig. 12. the power functions that corresponds with the two fitting curves correspond with the generic eq. 11.         50,  3.1       24,  3.1      b a b excluding virtual pathy a x a b including virtual path (11) figure 11: histograms resulting from pdmr cycle counting of the load path depicted in fig. 4 (right); virtual path included (left) and excluded (right). stress amplitude ratio a aτ /σ 1:5 1:3 1:2 4:5 1:1 avgd including virtual path 2.7 5.0 5.5 29 52 avgd excluding virtual path 1.5 2.3 2.1 14 25 table 7b: average fatigue damage obtained with pdmr cycle counting for va loading; results normalized with pure tension/bending (i.e. normal stress only). stress amplitude ratio a aτ /σ 1:5 1:3 1:2 1:1 avgd including virtual path 2.7 5.0 5.5 52 avgd excluding virtual path 1.5 2.3 2.1 25 p.s. van lieshout et al., frattura ed integrità strutturale, 37 (2016) 173-192; doi: 10.3221/igf-esis.37.24 188 discussion rom the three investigated codes it is found that eurocode 3 does not distinguish between proportional (lc3) and non-proportional (lc4) loadings while iiw does. this is resulting from the use of different critical values in their fatigue criterion. incorporating frequency induced non-proportionality using the conservative strategy (lc5.1), results in a doubling of the normalized damage obtained under phase shift induced non-proportionality. interestingly, using the alternative strategy (i.e. lc5.2), eurocode results in a higher damage, while iiw results in a lower damage than lc4. this is likely caused by the different damage mechanisms which are presumed (i.e. difference in exponents). a principal stress based approach, such as suggested by dnv-gl, results in a slight reduction of fatigue damage under nonproportional loading (lc 4 and 5) in comparison to proportional loading (lc 3) due to a reduced maximum principal stress range. furthermore, it does not distinguish between phase shift or frequency induced non-proportionality and due to the principal stress direction dependent reference sn-curve and mode-i based slope, pure torsional loading results in a lower damage compared to eurocode 3 or iiw. with iiw, non-proportionality has the highest impact on fatigue damage. comparison of the codes amongst each other per individual load case results in practically the same conclusions. looking at the results from the selected multiaxial fatigue methods, it appears that with the mcsc, the impact of nonproportionality on fatigue lifetime is less damaging or equally damaging to the proportional load case. the comparison between mcsc and mwcm for each individual load case lead to the same findings. however, this is in contradiction with experimental results of testing welded steel joints [3]. possibly the procedure which was selected to determine the normal and shear stress components acting on the critical plane should be changed. remarkable about the comparison between the normalized results for mcsc and mwcm is a factor two for all multiaxial load cases (lc3, 4 and 5), which could also be a result of this selected procedure. the mwcm is hardly capable of accounting non-proportionality due to the fact that the stress amplitude ratio does not depend on the type of loading. from the three considered multiaxial fatigue methods the eesh results seem to be most affected by (non-)proportionality. however, this method becomes more complex when va loading is under consideration. figure 12: graph showing the exponential increase of fatigue damage with increasing stress amplitude ratio considering pdmr based cycle counting in the pdmr based approach the virtual load path strongly affects the damage calculations. moreover, the averaged normalized damage sums that were obtained in this study would require more realizations to achieve full convergence for stress amplitude ratio 1:3 and 1:2. this causes the averaged damage sum at a ratio of 1:3 to be slightly higher than at a f p.s. van lieshout et al., frattura ed integrità strutturale, 37 (2016) 173-192; doi: 10.3221/igf-esis.37.24 189 ratio of 1:2 which seems contradictory. a non-linear relationship is observed between fatigue damage and the shear stress contribution (i.e. stress amplitude ratio) which can be described by a power function. this explains why codes and most multiaxial fatigue methods suggest a type of power function which relates fatigue damage to the two stress components: normal and shear. analysis of the constant amplitude load cases with the pdmr based approach showed that for nonproportional load cases the increased load path in combination with the reference sn-curve results in a significant increase in the normalized fatigue damage. interesting is that, for the va load cases, the power coefficients of both fitting curves (fig. 12) are smaller than the slope of the sn-curve that was used for damage calculation (fig. 8). the pdmr model takes only the fatigue strength aspect of multiaxiallity into account. the fatigue damage mechanism parameter (slope m) is a regression based value. it represents the average effective value of the load case specific slopes of the considered experimental (fatigue resistance) data. increasing the variety of load cases incorporated to construct the sncurve may result into an improved average effective slope value. in this study, the sn-curve was generated with data of only 1 stress amplitude ratio. however, the calculated damage (i.e. lifetime) estimates can still be conservative or nonconservative depending on the considered load case. a complete multiaxial fatigue resistance model should take both the load case specific fatigue strength and fatigue damage mechanism into account. conclusion n this study, a selection of codes and multiaxial fatigue methods for the marine industry were investigated considering (non-proportional) constant amplitude loading. furthermore, a case study was developed and used to examine the relationship between variable amplitude loading and fatigue damage based on pdmr cycle counting. from the most selected codes and multiaxial fatigue methods it appears that constant amplitude induced multiaxiallity can increase fatigue damage up to a factor of approximately four. the dnv-gl principal stress based approach seems to be on the non-conservative side while iiw could be on the conservative side. criteria which are based on a critical plane or consider interacting material planes aim to improve fatigue lifetime estimates based on the theory of cyclic deformation in crystals. for variable amplitude loading, a non-linear relationship (described by a power function) is observed between fatigue damage and stress amplitude ratio. furthermore, it has been shown that virtual path lengths can strongly affect the results from pdmr based cycle counting. it can be concluded that there are large discrepancies between the fatigue damages resulting from the application of codes, multiaxial fatigue methods and the pdmr based approach. all comparisons in this study are based on nominal stresses meaning that the use of more local stress information could improve the results. however, particularly experimental testing under (frequency induced) non-proportional multiaxial loading is expedient for validation, refinement or the development of existing and new methods. for this purpose the proposed case study provides a reasonable basis. acknowledgements his work was executed as part of the 4d-fatigue project and therefore the authors gratefully acknowledge the support from the dutch foundation for technological research (stw), industrial project participants and the delft university of technology. reference [1] hong, j. k., forte, t. p., fatigue evaluation procedures for multiaxial loading in welded structures using the battelle structural stress approach. in asme 2014 33rd international converence on ocean, offshore and arctic engineering (pp. 1–9). san fransisco, usa, (2014). [2] maddox, s. j., fatigue assessment of welds not oriented either normal or parallel to the direction of loading. cambridge, uk, (2010). [3] sonsino, c. m., kueppers, m. multiaxial fatigue of welded joints under constant and variable amplitude loadings. fatigue and fracture of engineering materials and structures, 24 (2001) 309–327. [4] anes, v., reis, l., de freitas, m., a new criterion for evaluating multiaxial fatigue damage under multiaxial random loading conditions. in fatigue 2014. melbourne, australia: fatigue 2014, (2014). i t p.s. van lieshout et al., frattura ed integrità strutturale, 37 (2016) 173-192; doi: 10.3221/igf-esis.37.24 190 [5] meggiolaro, m. a., tupiassú, j., de castro, p., an improved multiaxial rainflow algorithm for non-proportional stress or strain histories part ii: the modified wang-brown method. international journal of fatigue, (2011). http://doi.org/10.1016/j.ijfatigue.2011.10.012. [6] wei, z., dong, p., batra, r. c., nikbin, k., analysis of multi-axial test data using a path-dependent effective stress/strain definition. in asme 2013 pressure vessels and piping conference. paris, france: pvp2013-97630, (2013). [7] carpinteri, a., spagnoli, a., vantadori, s., multiaxial fatigue life estimation in welded joints using the critical plane approach. international journal of fatigue, 31 (2008) 188–196. http://doi.org/10.1016/j.ijfatigue.2008.03.024. [8] li, j., zhang, z.-p., sun, q., li, c.-w., multiaxial fatigue life prediction for various metallic materials based on the critical plane approach. international journal of fatigue, 33 (2011) 90–101. http://doi.org/10.1016/j.ijfatigue.2010.07.003. [9] susmel, l., tovo, r., on the use of nominal stresses to predict the fatigue strength of welded joints under biaxial cyclic loading. fatigue fracture of engineering materials structures, 27 (2004) 1005–1024. http://doi.org/10.1111/j.1460-2695.2004.00814.x. [10] cristofori, a., susmel, l., tovo, r., a stress invariant based criterion to estimate fatigue damage under multiaxial loading. international journal of fatigue, 30 (2007) 1646–1658. http://doi.org/10.1016/j.ijfatigue.2007.11.006. [11] macha, e., sonsino, c. m., energy criteria of multiaxial fatigue failure. fatigue and fracture of engineering materials and structures, 22 (1999) 1053–1070. [12] niesłony, a., comparison of some selected multiaxial fatigue failure criteria dedicated for spectral method. journal of theoretical and applied mechanics, 48(1) (2010) 233–254. [13] wang, y.-y., yao, w.-x. evaluation and comparison of several multiaxial fatigue criteria. international journal of fatigue, 26 (2004) 17–25. http://doi.org/10.1016/s0142-1123(03)00110-5. [14] besten, j. h. den. a total stress concept. delft university of technology, (2015). [15] suresh, s., fatigue of materials (second edi). cambridge, uk: cambridge university press, (1998). [16] callens, a., bignonnet, fatigue design of welded bicycle frames using a multiaxial criterion. procedia engineering, 34 (2012) 640–645. http://doi.org/10.1016/j.proeng.2012.04.109. [17] dang van, k., on a unified fatigue modelling for structural analysis based on the shakedown concept. mecamix, xtech. paris, france, (2014). [18] lieshout, p. s. van, besten, j. h. den, kaminski, m. l., validation of the corrected dang van multiaxial fatigue criterion applied to turret bearings of fpso offloading buoys. ships and offshore structures, to be publ., (2016). [19] radaj, d., sonsino, c. m., fricke, w., fatigue assessment of welded joints by local approaches. woodhead publishing limited, 53 (2006). http://doi.org/10.1017/cbo9781107415324.004. [20] susmel, l., lazzarin, p. a bi-parametric wöhler curve for high cycle multiaxial fatigue assessment. fatigue and fracture of engineering materials and structures, 25(1) (2002) 63–78. http://doi.org/10.1046/j.1460-2695.2002.00462.x [21] dnv-gl.,fatigue design of offshore steel structures. recommended practice dnvgl-rp-0005:2014-06, 1–126. (2005). retrieved from ftp://128.84.241.91/tmp/mse-4020/fatigue-design-offshore.pdf [22] eurocode 3. design of steel structures part 1-9: fatigue. (2005). [23] hobbacher, a., recomendations for fatigue design of welded joints and components. iiw document iiw-1823-07 ex xiii-2151r4-07/xv-1254r4-07. paris, france, (2008). [24] farajian, m., nitschke-pagel, t., boin, m., wimpory, r. c., relaxation of welding residual stresses in tubular joints under multiaxial loading. the tenth international conference on multiaxial fatigue fracture (icmff10), (2013). [25] backstrom, m., marquis, g., interaction equations for multiaxial fatigue assessment of welded structures. fatigue and fracture of engineering materials and structures, 27 (2004) 991–1003. http://doi.org/10.1111/j.1460-2695.2004.00811.x. [26] gaier, c., dannbauer, h., an efficient critical plane method for ductile , semiductile and brittle materials. in oral reference: ft436. elsevier ltd. (2006). [27] papadopoulos, i. v., panoskaltsis, v. p., gradient-dependent multiaxial high-cycle fatigue criterion. multiaxial fatigue and design, esis 21, edited by a. pineau, g. caileetaud, and t. c. lindley, (1996). [28] gustafsson, j., multi-axial fatigue in welded details-an investigation of existing design approaches. chalmers university of technology, (2007). [29] wang, y., susmel, l., the modified manson–coffin curve method to estimate fatigue lifetime under complex constant and variable amplitude multiaxial fatigue loading. international journal of fatigue, 83 (2016) 135–149. http://doi.org/10.1016/j.ijfatigue.2015.10.005. p.s. van lieshout et al., frattura ed integrità strutturale, 37 (2016) 173-192; doi: 10.3221/igf-esis.37.24 191 [30] carpinteri, a., brighenti, r., macha, e., spagnoli, a., expected principal stress directions under multiaxial random loading. part ii: numerical simulation and experimental assessment through the weight function method. international journal of fatigue, 21 (1999) 89–96. [31] carpinteri, a., spagnoli, a., multiaxial high-cycle fatigue criterion for hard metals. international journal of fatigue, 23 (2001) 135–145. retrieved from www.elsevier.com/locate/ijfatigue. [32] ronchei, c., carpinteri, a., fortese, g., spagnoli, a., vantadori, s., kurek, m., lagoda, t., life estimation by varying the critical plane orientation in the modified carpinteri-spagnoli criterion. frattura ed integrita strutturale, 9(34) (2015) 74–79. http://doi.org/10.3221/igf-esis.34.07. [33] papadopoulos, i., critical plane approaches in high-cycle fatigue: on the definition of the amplitude and mean value of the shear stress acting on the critical plane. fatigue fracture of engineering materials structures, 21(3) (1998) 269–285. http://doi.org/doi:10.1046/j.1460-2695.1998.00459.x. [34] susmel, l., tovo, r., benasciutti, d., a novel engineering method based on the critical plane concept to estimate the lifetime of weldments subjected to variable amplitude multiaxial fatigue loading. fatigue and fracture of engineering materials and structures, 32 (2009) 441–459. http://doi.org/10.1111/j.1460-2695.2009.01349.x. [35] susmel, l., a simple and efficient numerical algorithm to determine the orientation of the critical plane in multiaxial fatigue problems. international journal of fatigue, 32 (2010) 1875–1883. http://doi.org/10.1016/j.ijfatigue.2010.05.004. [36] sonsino, c. m., multiaxial fatigue of welded joints under in-phase and out-of-phase local strains and stresses. international journal of fatigue, 17 (1995) 55–70. [37] sonsino, c. m., wiebesiek, j., assessment of multiaxial spectrum loading of welded streel and aluminium joints by modified equivalent stress and gough-pollard algorithms. darmstadt, germany, (2007). [38] backstrom, m., multiaxial fatigue life assessment of welds based on nominal and hot spot stresses. lappeenranta university of technology, lappeenranta, finland, (2003). [39] fricke, w., recommended hot spot analysis procedure for structural details of fpsos and ships based on roundrobin fe analyses. in 11th internation offshore and polar engineering conference. stavanger, norway, (2001). [40] maddox, s. j., recommended hot-spot stress design s-n curves for fatigue assessment of fpsos. in 11th international offshore and polar engineering conference. stavanger, norway, (2001). [41] maddox, s. j., hot-spot stress design curves for fatigue assessment of welded structures. international journal of offshore and polar engineering, 12(2) (2002) 1053–5381. [42] kyuba, h., dong, p. equilibrium-equivalent structural stress approach to fatigue analysis of a rectangular hollow section joint. international journal of fatigue, 27 (2005) 85–94. http://doi.org/10.1016/j.ijfatigue.2004.05.008. [43] selvakumar, p., hong, j. k., robust mesh insensitive structural stress method for fatigue analysis of welded structures. procedia engineering, 55 (2013) 374–379. http://doi.org/10.1016/j.proeng.2013.03.268. [44] tveiten, b. w., moan, t., determination of structural stress for fatigue assessment of welded aluminum ship details. marine structures, 13 (2000) 189–212. http://doi.org/10.1016/s0951-8339(00)00022-8. [45] pedersen, m. m., multiaxial fatigue assessment of welded joints using the notch stress approach. international journal of fatigue, 83 (2016) 269–279. http://doi.org/10.1016/j.ijfatigue.2015.10.021. [46] radaj, d., sonsino, c. m., fricke, w., recent developments in local concepts of fatigue assessment of welded joints. international journal of fatigue, 31 (2008) 2–11. http://doi.org/10.1016/j.ijfatigue.2008.05.019. [47] sonsino, c. m., fricke, w., de bruyne, f., hoppe, a., ahmadi, a., zhang, g., notch stress concepts for the fatigue assessment of welded joints background and applications. international journal of fatigue, 34 (2012) 2–16. http://doi.org/10.1016/j.ijfatigue.2010.04.011. [48] exel, n., sonsino, c. m., multiaxial fatigue evaluation of laserbeam-welded magnesium joints according to iiwfatigue design recommendations. welding in the world, 58(4) (2014) 539–545. http://doi.org/10.1007/s40194-014-0139-6. [49] anes, v., reis, l., li, b., de freitas, m., new cycle counting method for multiaxial fatigue. international journal of fatigue, (2014). http://doi.org/10.1016/j.ijfatigue.2014.02.010. [50] anes, v., reis, l., li, b., fonte, m., de freitas, m., new approach for analysis of complex multiaxial loading paths. international journal of fatigue, 62 (2014) 21–33. http://doi.org/10.1016/j.ijfatigue.2013.05.004 [51] mamiya, e. n., castro, f. c., malcher, l., araújo, j. a., multiaxial fatigue life estimation based on combined deviatoric strain amplitudes. international journal of fatigue, 67 (2014) 117–122. http://doi.org/10.1016/j.ijfatigue.2013.11.002. [52] dong, p., wei, z., hong, j. k., a path-dependent cycle counting method for variable-amplitude multi-axial loading. international journal of fatigue, 32 (2009) 720–734. http://doi.org/10.1016/j.ijfatigue.2009.10.010. p.s. van lieshout et al., frattura ed integrità strutturale, 37 (2016) 173-192; doi: 10.3221/igf-esis.37.24 192 [53] zou, t., kaminski, m. l., validation of wavewatch-iii wave model for investigation of climate change effects on fatigue lifetime of offshore floating structures 2 wave data formats. to be published. (2016). [54] journée, j. m. j., pinkster, j., introduction in ship hydromechanics. tu delft, 1 (2002). http://doi.org/10.1111/ejh.12375. [55] dnv. environmental conditions and environmental loads, (2010). [56] kim, b., wang, x., shin, y.-s., extreme load and fatigue damage on fpso in combined waves and swells. abs technical papers. houston, texas, (2007). [57] wei, z., dong, p., a rapid path-length searching procedure for multi-axial fatigue cycle counting. fatigue and fracture of engineering materials and structures, 35 (2011) 556–571. http://doi.org/10.1111/j.1460-2695.2012.01649.x. [58] wei, z., dong, p., a generalized cycle counting criterion for arbitrary multi-axial fatigue loading conditions, journal of strain analysis for engineering design, 49 (2014) 325–341. << /ascii85encodepages false /allowtransparency false /autopositionepsfiles true /autorotatepages /none /binding /left /calgrayprofile (dot gain 20%) /calrgbprofile (srgb iec61966-2.1) /calcmykprofile (u.s. web coated \050swop\051 v2) /srgbprofile (srgb iec61966-2.1) /cannotembedfontpolicy /error /compatibilitylevel 1.4 /compressobjects /tags /compresspages true /convertimagestoindexed true /passthroughjpegimages true /createjobticket false /defaultrenderingintent /default /detectblends true /detectcurves 0.0000 /colorconversionstrategy /cmyk /dothumbnails false /embedallfonts true /embedopentype false /parseiccprofilesincomments true /embedjoboptions true /dscreportinglevel 0 /emitdscwarnings false /endpage -1 /imagememory 1048576 /lockdistillerparams false /maxsubsetpct 100 /optimize true /opm 1 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/hrv (za stvaranje adobe pdf dokumenata najpogodnijih za visokokvalitetni ispis prije tiskanja koristite ove postavke. stvoreni pdf dokumenti mogu se otvoriti acrobat i adobe reader 5.0 i kasnijim verzijama.) /hun 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/pdfxoutputintentprofileselector /documentcmyk /preserveediting true /untaggedcmykhandling /leaveuntagged /untaggedrgbhandling /usedocumentprofile /usedocumentbleed false >> ] >> setdistillerparams << /hwresolution [2400 2400] /pagesize [612.000 792.000] >> setpagedevice microsoft word 2264 m. peron et alii, frattura ed integrità strutturale, 47 (2019) 425-436; doi: 10.3221/igf-esis.47.33 425 focussed on “crack paths” assessment of tensile and fatigue behavior of peek specimens in a physiologically relevant environment mirco peron, jan torgersen, filippo berto department of mechanical and industrial engineering, norwegian university of science and technology (ntnu), richard birkelands vei 2b, 7034, trondheim, norway. mirco.peron@ntnu.no, jan.torgersen@ntnu.no, filippo.berto@ntnu.no abstract. in the last decades the necessity of implant devices is continuously increasing. the researchers have thus focused their attentions on the development of new biocompatible materials, in particular polymers. among them, polyetheretherketone (peek) has gained wide interest in loadbearing applications such as spinal cages due to its yielding behavior and its superior corrosion resistance. since such applications are characterized by notches and other stress concentrators weakening the implant resistance, a design tool for assessing their tensile and fatigue behavior, in the presence of such discontinuities, is highly claimed. to this aim, tensile and fatigue data available in literature related to neat and differently notched peek samples, experimentally tested in a phosphate-buffered saline (pbs) at 37 °c have been analyzed using the strain energy density (sed) approach. the method is shown to provide accurate results regardless of the different notch geometries, both in terms of tensile and fatigue behavior. concerning the former, the tensile strength was in fact estimated with an error lower than ±10%, whereas for the latter the sed approach was able to summarize the experimental fatigue data in a single narrow scatter band, independently from the notch geometry. keywords. peek; tensile; fatigue; notch; sed citation: peron, m., torgersen, j., berto, f., assessment of tensile and fatigue behavior of peek specimens in a physiologically relevant environment, frattura ed integrità strutturale, 47 (2019) 425-436. received: 19.11.2018 accepted: 02.12.2018 published: 01.01.2019 copyright: © 2019 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. introduction n recent years, the need of surgical procedures, and consequently the necessity of implant devices, have continuously increased [1]. these implants are generally used for applications that ensure a substantial improvement in patients’ quality of life, such as orthopedics, pacemakers, cardiovascular stents, defibrillators, neural prosthetics and drug delivery systems [2–5], but load-bearing implants are characterized by the highest annual growth rate [6] and, posing significant challenges, they have attracted large scale researcher efforts [4,7,8]. for example, artificial limbs have to fit i http://www.gruppofrattura.it/va/47/2264.mp4 m. peron et alii, frattura ed integrità strutturale, 47 (2019) 425-436; doi: 10.3221/igf-esis.47.33 426 perfectly to the patient specific site of interest and have to resemble the mechanical properties of the bone to avoid bone resorption due to the stress-shielding phenomenon [9–11]. moreover, load-bearing implants have to be characterized by sufficient strength since they are intermittently stressed due to weight and activity. for example, prostheses implanted to the lower extremities of the body have to withstand loads several times heavier than body weight [12–14]. in addition, the biologically-attractive implant design of these implants might cause challenging mechanical conditions leading to tensile and fatigue failure. for example, implant porosity is widely reported to enhance osseointegration and it is used to tailor the mechanical properties of the prosthesis to fit the biological site of interest [15]. however, such features lead to stress concentrators that reduces the strength of the components [16]. moreover, a high surface roughness has been reported to favor the cell adhesion and growth, but at the same time is known to lead to crack initiation [17–20]. these competing requirements are aggravated due to the corrosive environment in the human body, leading to effects such as corrosion fatigue and stress corrosion cracking [21,22]. sivakumar and rajeswari reported the failure due to the stress corrosion cracking phenomenon of a 316l stainless steel used for fixing a femoral fracture in a 27 years old man [23]. yokoyama et al. reported that the failure of a titanium occlusal screw failed after three years of implantation was due to the fatigue crack nucleation at the root of the thread [24]. moreover, chao and lopez reported that corrosion fatigue was responsible of the failure of almost 90% of ti-6al-4v hip prosthesis [25]. in this challenging scenario, a robust and reliable design tool for the prediction of implant tensile and fatigue strength is highly claimed, especially in the presence of stress concentrators. considering the developments obtained in the engineering field, many researchers and clinicians have tried to assess implant behavior of notched components using linear elastic fracture mechanics (lefm) theory and, in particular, the notch stress intensity factors (nsifs) [26]. concerning the tensile assessment, the nsif approach predict the failure of a component comparing the nsif at which the implant is subjected with a reference strength value obtained by testing samples weakened by the same notch geometry. concerning fatigue, instead, the nsif approach predicts the fatigue life of notched components comparing the nsif at which the implant is subjected with a reference fatigue curve determined from samples characterized by the same notch geometry [27,28]. however, the reliable applicability of the nsif approach requires to accurately evaluate the stress field ahead of the geometrical discontinuities, and the time-consuming stress field analyses has thus limited its development. in addition, the nsif-based criteria are dependent on the geometry and this represent another drawback of this approach. their unit depends in fact on the notch opening angle: the exponent β in their unit mpa(m)β is in fact equal to 1-λ1, where λ1 is the geometrical dependent williams’ eigenvalue [29]. the geometry dependence implies the necessity of ad hoc experimental data to use the nsif method, representing thus a complexity in its use. the theory of critical distance (tcd), that represents a set of methodologies, allows to overcome the geometry-dependence limitation. based on the definition of a material parameter (the critical distance l), the tcd states that failure of notched components subjected either to static or cyclic loadings occurs when the stress averaged over a line (line method, lm) or calculated at a certain distance from the notch root (point method, pm) equals the inherent material strength, σ0, or the plane specimen fatigue limit, δσ0, depending on whether tensile or fatigue assessment is considered. the applicability of the tcd to predict the strength of bio-materials has been assessed by kasiri and taylor [30]. they applied the lm to predict the fracture behavior of bones, weakened by different holes, and subjected to various loading scenario, but, although the general trend was well predicted, the results underestimated the fracture stress by 20–30%. in fact, it is generally acknowledged by proponents of critical distance methods that the point and line method are limitation of a more accurate approach that average stresses over a certain volume (or area in 2d problems) in the vicinity of the hot-spot. taylor [31] thus formalized the so-called area method (am), where the range of the maximum principal stress is averaged over a semicircular area. although the accuracy of the results increases considering the am, stress fields ahead of the notch still need to be accurately determined, resulting in high-performance hardware demand. however, although the accuracy of the results increases considering the am, stress fields ahead of the notch still need to be accurately determined, resulting in high-performance hardware demand. this has been overcome by the strain energy density (sed) approach, according to which failure occurs when the strain energy w (or strain energy range w for fatigue loadings) averaged in a control volume of radius, rc, ahead of the notch or crack tip reaches its critical value wc (or δwc for fatigue), independently from the notch geometry [32–34]. moreover, the strain energy range can either be obtained analytically, deriving the stress fields ahead of the geometrical discontinuity, or by means of fe analyses with a coarse mesh, being mesh-insensitive [35,36]. this tool has been widely reported to accurately predict the tensile and fatigue behavior of different notched materials [37–41] and for real component such as steel rollers [42], and its improvements with respect of the tcd methodologies has been reported in details in [43] for ti-6al-4v. in addition, it has recently been utilized to predict the fracture and fatigue behavior of plastics [44–46], including the biocompatible biopolymer polyetheretherketone (peek) [47,48]. in particular, sed approach has been reported to provide better assessment of the peek fatigue life compared to nsif and tcd approaches [48]. peek is considered an emerging material due to its yielding behavior and its superior m. peron et alii, frattura ed integrità strutturale, 47 (2019) 425-436; doi: 10.3221/igf-esis.47.33 427 corrosion resistance, also in physiologically relevant environments [4,49–52]. in particular, williams et al. reported the flexural strength to decrease from 156 mpa to 149 mpa after two months of immersion in simulated body fluid (sbf) at 37 °c [53]. due to its outstanding properties, peek, besides being studied as a substitute material for metals in gear wheels and food processing [54], has also gained interest in biomedical applications such as spinal cages [55] and dental implants [56,57]. peek is in fact characterized by an in vitro bone stimulation capacity comparable to that of cp ti grade 1 [58] and by an elastic modulus closer to that of human bones compared to that of metals, as reported in [11]. as a consequence, the bone resorption by the stress shielding effect induced by peek implant is significantly lower than that induced by titanium and zirconia implants, as assessed by lee et al. [59]. in addition, they reported un-notched peek components to be able to withstand static and cyclic loadings comparable to those deriving by bites in anterior dentitions. due to the increasing interests in peek for biomedical applications, a reliable failure criterion for this material is highly required, especially when weakened by notches, and the authors have herein decided to assess the reliability of the sed approach in predicting the tensile and fatigue behavior of peek materials in a physiologically relevant environment. for our reference, we employ the experimental data of sobieraj et al., that investigated peek tensile and fatigue behavior in a physiologically relevant environment in the presence of stress concentrators [60,61]. their tensile and fatigue data were here analyzed in terms of sed to assess the reliability of the method as a prediction model for biomaterials. experimental reference data tensile data obieraj et al. [60] examined the stress-strain behavior of neat and notched peek specimens under uniaxial loads in a corrosive environment (phosphate-buffered saline solution at 37 °c). the specimens were circumferentially grooved round bars with an 8 mm outer diameter, weakened by three different types of notches. these were circumferentially u-notched geometries with a 6 mm inner diameter, and moderate (0.9 mm) or deep (0.45 mm) notch radii. in addition, a circumferentially razor grooved dog-bone was investigated (fig. 1). a) b) c) d) figure 1: schematic view of the specimen geometries: a) neat sample; b) u-notched sample with notch radius of 0.9 mm; c) u-notched sample with notch radius of 0.45 mm; d) circumferentially razor grooved dog-bone. the specimens, made by optima lt1tm (invibio, inc., west conshohocken, pa, usa), were tested under strain control condition, with two different strain rates at 0.1 and 0.5 s−1. the ultimate tensile strength values, together with the experimental scatter, are listed in tab. 1. the young’s modulus and the yield stress were reported not to change with the strain rate, confirming the results obtained in ref. [6], where a strain rate from 0.00001 s−1 to 10 s−1 was reported to negligibly affect these properties. fatigue data sobieraj et al. [61] aimed to determine the s-n curve of peek in presence of stress concentrators and in a corrosive environment. they preconditioned the specimens for 8 weeks and then carried out fatigue tests in a 37 °c phosphatebuffered saline (pbs) bath. the samples tested were characterized by the same notched geometries reported in the previous section and shown in fig. 1. tension-tension fatigue tests were carried out aiming to assess the fatigue behavior, in a range of number of cycles to failure ranging from 1000 to 100,000, at a frequency of 2 hz, with a load ratio equal r ≤ s m. peron et alii, frattura ed integrità strutturale, 47 (2019) 425-436; doi: 10.3221/igf-esis.47.33 428 0.02. the fatigue data, shown in fig. 2, were fitted by sobieraj et al. [61] by means of the s-n basquin relationship [62] with good results being the mean squared error, r2, higher than 0.90 for all the notched geometry: d= an (1) where δσ is the stress range, n is the number of cycles to failure, and a and d are constants, listed in tab. 2. un-notched moderate deep razor strain rate (s-1) 0.1 0.5 0.1 0.5 0.1 0.5 0.1 0.5 max axial true stress (mpa) 211 ± 8.2 225 ± 5.4 132 ± 1.1 135 ± 0.4 127 ± 2.3 129 ± 1.4 119 ± 4.9 123 ± 4.3 table 1: tensile properties of notched and un-notched polyetheretherketone (peek) specimens under different strain rates. figure 2: experimental s-n curves for the three different notched geometries, i.e. moderate (u-notched with a notch radius of 0.9 mm), deep (u-notched with a notch radius of 0.45 mm) and razor (circumferentially cracked). modified from sobieraj et al. [61]. parameter moderate (radius 0.9 mm) deep (radius 0.45 mm) razor a (mpa) 152 120 131 d -0.043 -0.043 -0.063 r2 0.95 0.90 0.92 table 2: s-n basquin relationship constants. data taken from ref. [61]. analytical frame work sed approach under static loadings he sed criterion states that the failure of a component, subjected to tensile loading, occurs when the total strain energy, w , averaged in a circular control volume of radius rc (surrounding a crack or notch tip) reaches its critical value wc [63]. the critical sed parameters, i.e. the critical radius, rc, and the critical strain energy density, wc, are material dependent”[64], and they can be analytically derived with only few material properties [63]: the ultimate tensile t m. peron et alii, frattura ed integrità strutturale, 47 (2019) 425-436; doi: 10.3221/igf-esis.47.33 429 strength of the un-notched material, σt, the young’s modulus, e, and the fracture toughness, kic. in the case of ductile material, the ultimate tensile strength should be replaced with “the maximum normal stress existing at the edge at the moment preceding the cracking” as suggested by seweryn [65], or the equivalent material concept developed by torabi should be considered [66]. in agreement with beltrami [67], the critical value of the total strain energy can be computed by the following equation: 2 t c σ w = 2e (2) in plane problems, the control volume becomes a circular sector or a circle, for v-notches or cracks, respectively (fig. 3a and 3b). the critical radius, rc, is defined as follow [63]:    2 ic c t 1+ν 5 8ν k r = 4π σ       (3) where ν is the poisson’s ratio of the material. for a blunt v-notch or a u-notch (fig. 3c), the volume is assumed to be of a crescent shape, where rc is the depth measured along the bisector line. the outer radius of the crescent shape is equal to rc+r0, with r0 being the distance between the notch tip and the origin of the local coordinate system (fig. 3c). such a distance depends on the notch-opening angle, 2α, and the notch root radius, ρ, according to the expression:    0 π 2α r = ρ 2π 2α (4) a) b) c) figure 3: control volume under mode i loading for: (a) sharp v-notch, (b) crack case and (c) u notch . however, the fracture toughness is not always available due to the difficulties and time consuming calculations. yet, an estimate of the critical radius can be obtained as the radius at which the critical sed values (wc) for two different specimen geometries, are identical [27]. sed approach under fatigue loadings dealing with fatigue loadings, lazzarin and zambardi states that failure occurs when the strain energy density range, w , averaged in a control volume of radius rc (ahead of the notch or crack tip) reaches its critical value δwc. in ref. [63] a simple analytical formulation for the computation of the critical value of the strain energy density range, δwc, has been proposed: 2 a c δσ δw = 2e (5) m. peron et alii, frattura ed integrità strutturale, 47 (2019) 425-436; doi: 10.3221/igf-esis.47.33 430 where δσa is the fatigue limit of the material without geometric singularities for fully reversed normal stress. the control volume is defined, as in the previous section, with the only exception that now the formulation of critical radius, rc, is defined as follow: 1 1 1λ 1 1a c a 2e δk r = δσ        (6) where λ1 is williams’ eigenvalue for mode i [29], δk1a is the amplitude of the notch stress intensity factors (nsif) fatigue threshold, and e1 is a parameter dependent on the notch opening angle, 2α, and on the hypothesis considered (plane strain or plane stress), and on the poisson’s ratio ν (the reader should referred to ref. [63] for e1 formulation). also, in case of a blunt v-notch or a u-notch, the volume is assumed to be of a crescent shape and defined as for static loadings. as it can be noted from eqns. (5) and (6), that also in case of dynamic loadings the critical value of the strain energy density, and that of the radius of the control volume, are only dependent on the material [64]. however, in some cases not all the material parameters required to apply sed approach are available. recently, this shortcoming has been overcome thanks to the possibility provided by some fe codes to easily determined the strain energy within the control volume. berto et al. [68] analyzed the fatigue behavior of innovative alloys at high temperature and, using ansys® code, they obtained the critical radius value. this value was obtained varying the control volume until the sed value ( w ) for a notched specimen at a certain amount of cycles, matched the critical sed value (wc) obtained for a plain specimen, failed at the same number of cycles (eq. 5). in this work, neither nsif fatigue threshold nor fatigue limit of the material without geometric singularities are known, and thus the critical values are obtained using a similar approach to that reported in ref. [68]. the critical radius has been determined as the value at which the sed values (w ) for two different specimen geometries at the same number of cycles are equal. moreover, this sed value has been considered as the critical one. a deeper explanation will be provided in the next sections. a) b) figure 4: strain energy density (sed) mesh sensitivity: (a) number of elements = 2049, w = 2.8431 mj/m3; (b) number of elements = 23, w = 2.8398 mj/m3. m. peron et alii, frattura ed integrità strutturale, 47 (2019) 425-436; doi: 10.3221/igf-esis.47.33 431 finite element model n order to obtain the sed value (w ), axisymmetric linear elastic 2d analyses were performed on the notched models. due to the double symmetry of the geometry only one quarter of the specimens was modeled. the 8-nodes axisymmetric element plane 83 was selected for these analyses. in the fe code, the material was assumed isotropic, with the young’s modulus e = 3500 mpa and the poisson’s ratio ν = 0.36, as reported in ref. [60]. a mesh convergence study was undertaken to ensure that a proper number of elements was used in finite element modelling, with elements size at the crack tip ranging from about 10−3 mm to 10−1 mm. the results are independent from the mesh, being the difference only 0.11% between the sed value for a coarse mesh and that for a fine mesh (fig. 4), and thus a coarse mesh was adopted for the analyses. the mesh-insensitivity of the sed approach was previously verified also by berto and lazzarin [35], for cracked and notched specimens. this represents one of the main advantages of this approach, together with the capability of assessing the tensile behavior of different materials regardless of the geometry. fig. 5 illustrates the mesh pattern and the boundary conditions used for finite element analyses. symmetric boundary conditions were used for vertical and horizontal symmetry lines of the models (as indicated by the triangles in fig. 5). the top side of the model was able to move along the loading axis to simulate the application of the load. figure 5: typical mesh pattern of the finite element model near the notch tip and schematics of boundary conditions. results static loading obieraj et al. tested un-notched and notched peek specimens under different strain rates and in a corrosive environment, and in this section their results were analyzed in terms of sed. the application of the sed approach requires the computation of both the critical value of the radius, rc, of the control volume and that of the strain energy density, wc. the critical sed value, wc, can be simply evaluated using eqn. 2, leading to a critical sed value of 7.278 and 6.38 mj/m3 under a strain rate of 0.5 and 0.1 s−1, respectively. concerning the control volume, in reference [60] the fracture toughness has not been reported. eqn. 3 cannot thus be used, but it is possible to obtain the critical radius, rc, leveraging on fe analyses, by changing the radius of the control volume of the specimens with two different control radii and iteratively computing the sed value ( w )) until a satisfying convergence is reached. in this work, circumferentially razor-grooved dog-bone and u-notched specimen, with a notch root radius of 0.45 mm, have been modelled in ansys®. the simulations have been carried out for different values of rc, ranging from 0.1 to 0.2 mm, with a i s m. peron et alii, frattura ed integrità strutturale, 47 (2019) 425-436; doi: 10.3221/igf-esis.47.33 432 step of 0.01 mm, and the critical radius results to be equal to 0.13 and 0.12 mm for specimens tested at 0.1 and 0.5 s−1, respectively. the small difference in radius is due to the material’s limited strain rates sensitivity below 10 s−1 [69]. as the strain energy density is proportional to the square of the applied stress, the predicted tensile strength of the notched specimens, σuts,predicted, has been estimated with c uts, predicted unit_load w σ = w                   (7)    in which wc is the critical sed value (eqn. (2)) and wunit_load is the sed value determined by means of fe analyses applying a unit load. the sed prediction of the tensile failure for both the strain rates are reported in tab. 3. specimen geometry strain rate (s-1) experimental data (mpa) sed prediction (mpa) deviation (%) deep 0.1 127 118 -6.8 0.5 129 124 -4 moderate 0.1 132 132 -0.1 0.5 135 139 +3.3 razor 0.1 119 118 -0.8 0.5 123 124 +0.8 table 3: prediction of tensile failure of moderate, deep and razor specimens using the sed approach. for the geometries and test conditions reported in [60], the presented approach provides suitable prediction of tensile failure, where deviations (computed as the relative difference between the experimental and predicted values, and expressed in percentage) are generally lower than 4%, for predictions of moderate and razor grooved merely even below 1%. impacts of the corrosive test environment were successfully accounted for. a) b) figure 6: determination of the sed critical parameters: (a) the value of the critical radius rc has been varied with a step of 0.01 mm and (b) with a finer step of 0.001 mm. fatigue loading as mentioned earlier, neither the nsif fatigue threshold nor the fatigue limit of the plain material were available, and thus eqns. (5) and (6) could not be applied to determine the critical sed parameters. an alternative approach has thus been used using ansys®: the radius of the control volume has been varied until the sed values for two different specimen geometries, at the same number of cycles, were equal. in particular, circumferentially razor-grooved dog-bone and unotched specimen, with a notch root radius of 0.45 mm, have been modelled, and the critical radius has been varied from 0.01 to 0.1 mm, with a step of 0.01 mm (fig. 6a). then, in the range between 0.06 and 0.07 mm, where the difference m. peron et alii, frattura ed integrità strutturale, 47 (2019) 425-436; doi: 10.3221/igf-esis.47.33 433 between the sed values for the two geometries at 150000 cycles were lower, the simulations have been repeated with a step of 0.001 mm for the critical radius until a correspondence was found, resulting in rc = 0.067 mm and δwc = 3.23 mj/m3 at 150000 cycles (fig. 6b). once the critical radius was determined, the fatigue data shown in fig. 2 were analyzed in terms of sed range. fe analyses were carried out considering the experimental stress range as the applied load in the simulations, determining the corresponding sed range value, used to obtain the fatigue curve shown in fig. 7. figure 7: synthesis of peek fatigue data by means of sed approach. the fatigue results felt within a single narrow scatter band, with an inverse slope k = 8.091 and a strain energy density range referred to 2 million loading cycles and to a probability of survival of 50%. in fact, the scatter index tw, related to the two curves, with probabilities of survival ps = 2.3% and 97.7%, is equal to 1.484. tw = 1.484 becomes equal to 1.22 when reconverted to an equivalent local stress range being the sed proportional to the square of the stress (tσ = √1.484 = 1.22). comparing fig. 2 with fig. 7 it can be noted how the sed approach is able to summarize the fatigue data obtained by using different notch geometries within a single narrow scatter band, whereas the s-n curves, in fig. 2, show a different behavior for each notch geometry. this represents a milestone in the design of biomedical implants; once a δw-n curve had been obtained for any notch geometry, it can be considered as the sed fatigue master curve, which can be used as reference for every kind of notch geometries weakening the components. as it is evident from the just reported procedure, the advantages of sed approach lie on its simplicity and rapidity-to-use that could render it a breakthrough in the design procedures when compared to the methods so far used. conclusions he strain energy density (sed) approach has revealed in the past to greatly predict both the tensile and fatigue behavior of metals, weakened by different notch geometries. herein this approach has been extended to the assessment of the tensile and fatigue behavior of peek in corrosive environments. the authors have utilized a previously supplied dataset [60,61], where different notch geometries in a physiologically relevant environment have been tested under static and dynamic loadings. the approach has shown to capture both the strainand notch-sensitivity of the material. concerning static loadings, the predictive performance of the tensile strength of peek are characterized by a discrepancy to the experimental data in the range of ±10%, the performance range considered acceptable in many studies of a sed database, while, dealing with fatigue loadings, the sed criterion has been shown to summarize fatigue data for different notch geometries within a single narrow scatter band. compared with the classical nsif approach, the sed t m. peron et alii, frattura ed integrità strutturale, 47 (2019) 425-436; doi: 10.3221/igf-esis.47.33 434 criterion overcomes the nsif approach main limitation of the geometry dependency. in addition, both nsifs and tcd require high computational efforts, a fine mesh being required ahead of the notch tip, whereas the sed approach has revealed to be mesh-insensitive. this work introduces a milestone in the design of peek biomedical devices, providing a simple and rapid method for assessing the tensile and fatigue strength, overcoming the drawbacks of the other methods, and opening the road towards the use of this approach in corrosive environments. references [1] ginebra, m.p., traykova, t., planell, j.a. (2006). calcium phosphate cements as bone drug delivery systems: a review, j. control. release, 113(2), pp. 102–110. doi: 10.1016/j.jconrel.2006.04.007. [2] regar, e., sianos, g., serruys, p.w. (2001). stent development and local drug delivery., br. med. bull., 59, pp. 227–48. [3] greatbatch, w., holmes, c.f. (1991). history of implantable devices, ieee eng. med. biol. mag., 10(3), pp. 38–41. doi: 10.1109/51.84185. [4] long, p.h. (2008). medical devices in orthopedic applications, toxicol. pathol., 36(1), pp. 85–91. doi: 10.1177/0192623307310951. [5] khan, w., muntimadugu, e., jaffe, m., domb, a.j. (2014).implantable medical devices., springer us, pp. 33–59. [6] (n.d.). $21.12 billion implantable biomaterials market: global forecasts to 2023 miniaturization of implant devices and increasing minimally invasive surgery. available at: https://globenewswire.com/newsrelease/2017/03/10/934363/0/en/21-12-billion-implantable-biomaterials-market-global-forecasts-to-2023miniaturization-of-implant-devices-and-increasing-minimally-invasive-surgery.html. [accessed april 1, 2017]. [7] pruitt, l., furmanski, j. (n.d.). polymeric biomaterials for load-bearing medical devices, jom, 61(9), pp. 14–20. doi: 10.1007/s11837-009-0126-3. [8] evans, s.l., gregson, p.j. (1998). composite technology in load-bearing orthopaedic implants., biomaterials, 19(15), pp. 1329–1342. [9] nagels, j., stokdijk, m., rozing, p.m. (n.d.). stress shielding and bone resorption in shoulder arthroplasty. [10] huiskes, r., weinans, h., van rietbergen, b. (1992). the relationship between stress shielding and bone resorption around total hip stems and the effects of flexible materials., clin. orthop. relat. res., 274, pp. 124–134. [11] peron, m., torgersen, j., berto, f. (2017). mg and its alloys for biomedical applications: exploring corrosion and its interplay with mechanical failure, metals (basel)., 7(7), pp. 252. doi: 10.3390/met7070252. [12] niinomi, m. (mitsuo). (2010). metals for biomedical devices, crc press. [13] black, j. (2006). biological performance of materials : fundamentals of biocompatibility, crc taylor & francis. [14] ramakrishna, s., mayer, j., wintermantel, e., leong, k.w. (n.d.). biomedical applications of polymer-composite materials: a review. [15] fraldi, m., esposito, l., perrella, g., cutolo, a., cowin, s.c., esposito, l. (2010). topological optimization in hip prosthesis design, biomech model mechanobiol, 9, pp. 389–402. doi: 10.1007/s10237-009-0183-0. [16] peron, m., torgersen, j., ferro, p., berto, f. (2018). fracture behaviour of notched as-built ebm parts: characterization and interplay between defects and notch strengthening behaviour, theor. appl. fract. mech., 98, pp. 178–85. doi: 10.1016/j.tafmec.2018.10.004. [17] e murr, l., m gaytan, s., martinez, e., medina, f.r., wicker, r.b. (2012). fabricating functional ti-alloy biomedical implants by additive manufacturing using electron beam melting, j. biotechnol. biomater., 02(03). doi: 10.4172/2155-952x.1000131. [18] obaton, a.-f., fain, j., djemaï, m., meinel, d., léonard, f., mahé, e., lécuelle, b., fouchet, j.-j., bruno, g. (2017). in vivo xct bone characterization of lattice structured implants fabricated by additive manufacturing, heliyon, 3(8). doi: 10.1016/j.heliyon.2017.e00374. [19] smeets, r., stadlinger, b., schwarz, f., beck-broichsitter, b., jung, o., precht, c., kloss, f., gröbe, a., heiland, m., ebker, t., ebker, t. (2016). impact of dental implant surface modifications on osseointegration, biomed res. int., 2016, pp. 1–16. doi: 10.1155/2016/6285620. [20] albrektsson, t., wennerberg, a. (n.d.). oral implant surfaces: part 1--review focusing on topographic and chemical properties of different surfaces and in vivo responses to them., int. j. prosthodont., 17(5), pp. 536–43. [21] osman, r., swain, m. (2015). a critical review of dental implant materials with an emphasis on titanium versus zirconia, materials (basel)., 8(3), pp. 932–58. doi: 10.3390/ma8030932. [22] gil, f.j., herrero-climent, m., lázaro, p., rios, j. v. (2014). implant–abutment connections: influence of the design on the microgap and their fatigue and fracture behavior of dental implants, j. mater. sci. mater. med., 25(7), pp. m. peron et alii, frattura ed integrità strutturale, 47 (2019) 425-436; doi: 10.3221/igf-esis.47.33 435 1825–30. doi: 10.1007/s10856-014-5211-7. [23] sivakumar, m., rajeswari, s. (1992). investigation of failures in stainless steel orthopaedic implant devices: pit-induced stress corrosion cracking, j. mater. sci. lett., 11(15), pp. 1039–42. doi: 10.1007/bf00729754. [24] yokoyama, k., ichikawa, t., murakami, h., miyamoto, y., asaoka, k. (2002). fracture mechanisms of retrieved titanium screw thread in dental implant, biomaterials, 23(12), pp. 2459–65. doi: 10.1016/s0142-9612(01)00380-5. [25] chao, j., lópez, v. (2007). failure analysis of a ti6al4v cementless hip prosthesis, eng. fail. anal., 14(5), pp. 822– 30. doi: 10.1016/j.engfailanal.2006.11.003. [26] prawoto, y. (n.d.). integration of mechanics into materials science research : a guide for material researchers in analytical, computational and experimental methods, . [27] verreman, y., nie, b. (1996). early development of fatigue cracking at manual fillet welds, fatigue fract. eng. mater. struct., 19(6), pp. 669–681. doi: 10.1111/j.1460-2695.1996.tb01312.x. [28] lazzarin, p., tovo, r. (1998). a notch intensity factor approach to the stress analysis of welds, fatigue fract. eng. mater. struct., 21(9), pp. 1089–1103. doi: 10.1046/j.1460-2695.1998.00097.x. [29] williams, m.l. (1952). stress singularities resulting from various boundary conditions in angular corners on plates in extension, j. appl. mech., 19, pp. 526–528. [30] kasiri, s., taylor, d. (2008). a critical distance study of stress concentrations in bone, j. biomech., 41(3), pp. 603–9. doi: 10.1016/j.jbiomech.2007.10.003. [31] taylor, d. (1999). geometrical effects in fatigue: a unifying theoretical model, int. j. fatigue, 21(5), pp. 413–420. doi: 10.1016/s0142-1123(99)00007-9. [32] razavi, s.m.j., peron, m., torgersen, j., berto, f., mutignani, f. (2017). effect of hot dip galvanization on the fatigue strength of steel bolted connections, frat. ed integrita strutt., 11(41). doi: 10.3221/igf-esis.41.54. [33] razavi, s.m.j., peron, m., torgersen, j., berto, f. (2017). static multiaxial fracture behavior of graphite components: a review of recent results, key eng. mater., 754, pp. 35–38. doi: 10.4028/www.scientific.net/kem.754.35. [34] razavi, s.m.j., peron, m., mutignani, f., torgersen, j., berto, f. (2017). a study on the fatigue behavior of hot dip galvanized steel connections, key eng. mater., 754, pp. 241–243. doi: 10.4028/www.scientific.net/kem.754.241. [35] berto, f., lazzarin, p. (2009). a review of the volume-based strain energy density approach applied to v-notches and welded structures, theor. appl. fract. mech., 52(3), pp. 183–194. doi: 10.1016/j.tafmec.2009.10.001. [36] peron, m., razavi, s.m.j., berto, f., torgersen, j., colussi, m. (2017). fracture assessment of magnetostrictive materials, frat. ed integrita strutt., 11(42). doi: 10.3221/igf-esis.42.24. [37] campagnolo, a., razavi, s.m.j., peron, m., torgersen, j., berto, f. (2017). mode ii brittle fracture: recent developments, frat. ed integrita strutt., 11(42). doi: 10.3221/igf-esis.42.19. [38] razavi, s.m.j., peron, m., torgersen, j., berto, f. (2017). notched graphite under multiaxial loading, frat. ed integrita strutt., 11(41). doi: 10.3221/igf-esis.41.53. [39] peron, m., razavi, s.m.j., berto, f., torgersen, j. (2017). notch stress intensity factor under mixed mode loadings: an overview of recent advanced methods for rapid calculation, frat. ed integrità strutt., 42, pp. 196–204. [40] peron, m., razavi, s.m.j., berto, f., torgersen, j., mutignani, f. (2017). local strain energy density for the fatigue assessment of hot dip galvanized welded joints: some recent outcomes, frat. ed integrita strutt., 11(42). doi: 10.3221/igf-esis.42.22. [41] razavi, s.m.j., peron, m., mutignani, f., torgersen, j., berto, f. (2017). fatigue strength of hot-dip galvanized welded steel connections, key eng. mater., 754, pp. 244–7. doi: 10.4028/www.scientific.net/kem.754.244. [42] chebat, f., peron, m., viespoli, l., welo, t., berto, f. (2018). fatigue strength assessment of steel rollers: on the reliability of the strain energy density approach on real components, appl. sci., 8(7), pp. 1015. doi: 10.3390/app8071015. [43] peron, m., torgersen, j., berto, f. (2018). rupture predictions of notched ti-6al-4v using local approaches, materials (basel)., 11(5), pp. 663. doi: 10.3390/ma11050663. [44] (2012). fracture behaviour of notched round bars made of pmma subjected to torsion at room temperature, eng. fract. mech., 90, pp. 143–160. doi: 10.1016/j.engfracmech.2012.05.001. [45] berto, f., cendon, d.a., lazzarin, p., elices, m. (2013). fracture behaviour of notched round bars made of pmma subjected to torsion at 60°c. doi: 10.1016/j.engfracmech.2013.02.011. [46] peron, m., razavi, s.m.j., berto, f., torgersen, j., marsavina, l. (2017). local strain energy density for the fracture assessment of polyurethane specimens weakened by notches of different shape, 4232214223(10), pp. 214–22. doi: 10.3221/igf-esis.42.23. [47] peron, m., razavi, s., torgersen, j., berto, f. (2017). fracture assessment of peek under static loading by means m. peron et alii, frattura ed integrità strutturale, 47 (2019) 425-436; doi: 10.3221/igf-esis.47.33 436 of the local strain energy density, mater. 2017, vol. 10, page 1423, 10(12), pp. 1423. doi: 10.3390/ma10121423. [48] peron, m., torgersen, j., berto, f., peron, m., torgersen, j., berto, f. (2018). a novel approach for assessing the fatigue behavior of peek in a physiologically relevant environment, mater. 11, pp. 1923. doi: 10.3390/ma11101923. [49] ulery, b.d., nair, l.s., laurencin, c.t. (2011). biomedical applications of biodegradable polymers., j. polym. sci. b. polym. phys., 49(12), pp. 832–864. doi: 10.1002/polb.22259. [50] maitz, m.f. (2015). applications of synthetic polymers in clinical medicine, biosurface and biotribology, 1, pp. 161– 176. doi: 10.1016/j.bsbt.2015.08.002. [51] williams, d.f. (2009). on the nature of biomaterials, biomaterials, 30(30), pp. 5897–5909. doi: 10.1016/j.biomaterials.2009.07.027. [52] lendlein, a., rehahn, m., buchmeiser, m.r., haag, r. (2010). polymers in biomedicine and electronics, macromol. rapid commun., 31(17), pp. 1487–1491. doi: 10.1002/marc.201000426. [53] williams, d.f., mcnamara, a., turner, r.m. (1987). potential of polyetheretherketone (peek) and carbon-fibrereinforced peek in medical applications, j. mater. sci. lett., 6(2), pp. 188–190. doi: 10.1007/bf01728981. [54] platt, d.k., rapra technology limited. (2003). engineering and high performance plastics market report : a rapra market report, rapra technology ltd. [55] walter, j., kuhn, s.a., reichart, r., kalff, r., ewald, c. (2010). peek cages as a potential alternative in the treatment of cervical spondylodiscitis: a preliminary report on a patient series., eur. spine j., 19(6), pp. 1004–1009. doi: 10.1007/s00586-009-1265-5. [56] schwitalla, a., müller, w.-d. (2013). peek dental implants: a review of the literature, j. oral implantol., 39(6), pp. 743–749. doi: 10.1563/aaid-joi-d-11-00002. [57] rahmitasari, f., ishida, y., kurahashi, k., matsuda, t., watanabe, m., ichikawa, t. (2017). peek with reinforced materials and modifications for dental implant applications., dent. j., 5(4). doi: 10.3390/dj5040035. [58] sagomonyants, k.b., jarman-smith, m.l., devine, j.n., aronow, m.s., gronowicz, g.a. (2008). the in vitro response of human osteoblasts to polyetheretherketone (peek) substrates compared to commercially pure titanium, biomaterials, 29(11), pp. 1563–1572. doi: 10.1016/j.biomaterials.2007.12.001. [59] lee, w.-t., koak, j.-y., lim, y.-j., kim, s.-k., kwon, h.-b., kim, m.-j. (2012). stress shielding and fatigue limits of poly-ether-ether-ketone dental implants, j. biomed. mater. res. part b appl. biomater., 100b(4), pp. 1044–1052. doi: 10.1002/jbm.b.32669. [60] sobieraj, m.c., kurtz, s.m., rimnac, c.m. (2009). notch sensitivity of peek in monotonic tension., biomaterials, 30(33), pp. 6485–6494. doi: 10.1016/j.biomaterials.2009.08.020. [61] sobieraj, m.c., murphy, j.e., brinkman, j.g., kurtz, s.m., rimnac, c.m. (2010). notched fatigue behavior of peek, biomaterials, 31(35), pp. 9156–9162. doi: 10.1016/j.biomaterials.2010.08.032. [62] dowling, n.e. (2007). mechanical behavior of materials : engineering methods for deformation, fracture and fatigue, upper saddle river, nj, pearson prentice hall. [63] lazzarin, p., zambardi, r. (2001). a finite-volume-energy based approach to predict the static and fatigue behavior of components with sharp v-shaped notches, int. j. fract., 112(3), pp. 275–298. doi: 10.1023/a:1013595930617. [64] berto, f., lazzarin, p. (2014). recent developments in brittle and quasi-brittle failure assessment of engineering materials by means of local approaches, mater. sci. eng. r, 75(1), pp. 1–48. doi: 10.1016/j.mser.2013.11.001. [65] seweryn, a. (1994). brittle fracture criterion for structures with sharp notches, eng. fract. mech., 47(5), pp. 673–681. doi: 10.1016/0013-7944(94)90158-9. [66] fuentes, j., cicero, s., berto, f., torabi, a., madrazo, v., azizi, p. (2018). estimation of fracture loads in al7075t651 notched specimens using the equivalent material concept combined with the strain energy density criterion and with the theory of critical distances, metals (basel) 8(2), pp. 87. doi: 10.3390/met8020087. [67] beltrami, e., e. (1885). sulle condizioni di resistenza dei corpi elastici, nuovo cim., 18(1), pp. 145–155. doi: 10.1007/bf02824697. [68] berto, f., gallo, p., razavi, s.m.j., ayatollahi, m.r. (2017). fatigue behavior of innovative alloys at elevated temperature, procedia struct. integr., 3, pp. 162–167. doi: 10.1016/j.prostr.2017.04.029. [69] albérola, n.d., mélé, p., bas, c. (1997). tensile mechanical properties of peek films over a wide range of strain rates. ii, j. appl. polym. sci., 64(6), pp. 1053–1059. doi: 10.1002/(sici)1097-4628(19970509)64:6<1053::aid-app3>3.0.co;2-k. << /ascii85encodepages false /allowtransparency false /autopositionepsfiles true /autorotatepages /none /binding /left /calgrayprofile (dot gain 20%) /calrgbprofile (srgb iec61966-2.1) /calcmykprofile (u.s. web coated \050swop\051 v2) /srgbprofile (srgb iec61966-2.1) /cannotembedfontpolicy /error /compatibilitylevel 1.4 /compressobjects /tags /compresspages true /convertimagestoindexed true /passthroughjpegimages true /createjobticket false /defaultrenderingintent /default /detectblends true /detectcurves 0.0000 /colorconversionstrategy /cmyk /dothumbnails false /embedallfonts true /embedopentype false /parseiccprofilesincomments true /embedjoboptions true /dscreportinglevel 0 /emitdscwarnings false /endpage -1 /imagememory 1048576 /lockdistillerparams false /maxsubsetpct 100 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can be opened with acrobat and adobe reader 5.0 and later.) >> /namespace [ (adobe) (common) (1.0) ] /othernamespaces [ << /asreaderspreads false /cropimagestoframes true /errorcontrol /warnandcontinue /flattenerignorespreadoverrides false /includeguidesgrids false /includenonprinting false /includeslug false /namespace [ (adobe) (indesign) (4.0) ] /omitplacedbitmaps false /omitplacedeps false /omitplacedpdf false /simulateoverprint /legacy >> << /addbleedmarks false /addcolorbars false /addcropmarks false /addpageinfo false /addregmarks false /convertcolors /converttocmyk /destinationprofilename () /destinationprofileselector /documentcmyk /downsample16bitimages true /flattenerpreset << /presetselector /mediumresolution >> /formelements false /generatestructure false /includebookmarks false /includehyperlinks false /includeinteractive false /includelayers false /includeprofiles false /multimediahandling /useobjectsettings /namespace [ (adobe) (creativesuite) (2.0) ] /pdfxoutputintentprofileselector /documentcmyk /preserveediting true /untaggedcmykhandling /leaveuntagged /untaggedrgbhandling /usedocumentprofile /usedocumentbleed false >> ] >> setdistillerparams << /hwresolution [2400 2400] /pagesize [612.000 792.000] >> setpagedevice microsoft word numero_30_art_32 d. gentile et alii, frattura ed integrità strutturale, 30 (2014) 252-262; doi: 10.3221/igf-esis.30.32 252 focussed on: fracture and structural integrity related issues use of circumferentially cracked bar sample for ctod fracture toughness determination in the upper shelf regime d. gentile, i. persechino, n. bonora university of cassino and southern lazio gentile@unicas.it, i.persechino@unicas.it, nbonora@unicas.it g. iannitti techdyn engineering srl g.iannitti@techdyn.it a. carlucci saipem s.a. antonio.carlucci@saipem.com abstract. in this work, the use of circumferentially cracked bar (ccb) sample to determine material fracture toughness in the upper shelf regime for carbon steels has been investigated. since high fracture toughness materials are known to exhibit extensive crack tip blunting before ductile crack initiation, accurate specimen design is required to provide realistic fracture toughness measurement. here, a ccb was designed to have similar loss of constraint as for sent sample. continuum damage mechanics was used to predict the occurrence of ductile crack initiation and propagation. finite element analysis was performed to predict specimen response and to compare computed j-integral crack driving force with measured ctod. finally, experimental tests were performed on x65 carbon steel and the measured critical ctod was compared with available fracture data obtained with sent. keywords. circumferentially cracked bar; fracture; ctod; cdm. introduction he determination of material fracture toughness is coded in standards, such as astm e399. design codes and material testing standards provide also the sample geometry for fracture toughness determination. although, crack driving force solutions for a number of possible alternative geometries are available, compact tension (ct), single edge crack in tension (sent) or in bending (senb) are usually recommended. for instance, the latter two geometries are recommended in dnv-os-f101 standard for structural integrity assessment of subsea pipelines because they are characterized by geometry loss of constraint similar to that occurring in pipe welds circumferential flaws. t d. gentile et alii, frattura ed integrità strutturale, 30 (2014) 252-262; doi: 10.3221/igf-esis.30.32 253 in engineering practice, the use of ct, sen or sent is not always practicable especially when material availability is limited. this is the case of multi materials joints, such as bi-metallic girth welds, where the amount of each material is insufficient to machine even small size fracture samples. a possible alternative is given by the circumferential cracked bar (ccb) sample. this geometry is particularly simple in the design, it can be scaled according to the material availability, and it is free of three-dimensional effects because of radial symmetry. the idea of ccb as alternative fracture mechanics samples is not new. notched cracked bar have been used by stark and ibrahim [1], ibrahim and stark [2-3], and lam and ibrahim [4]. devaux et al [5] used axisymmetric cracked bar to determine local approach fracture parameters to compare with ct data. beremin [6] used ccb to predict the condition for initiation and stable crack growth in low alloy steels. giovanola and crocker [7] performed a study aimed to demonstrate the possibility to measure representative fracture toughness for nuclear pressure vessel materials using small cracked round bars at different temperatures. they found, over the entire temperature range, a good agreement between fracture toughness values measured with ccb and 1t-ct for both cleavage and ductile fracture. among the advantages offered by the ccb sample, they pointed out the possibility to achieve, under fully plastic regimes, a high degree of constraint at the crack tip even for small uncracked ligament and its use for the determination of the dynamic fracture toughness with split hopkinson pressure bar [8-10]. the same year, scibetta et al. [11] investigated computationally the loss of constraint in ccb sample in order to derive the conditions and specimen requirements for a valid measurement of plane strain fracture toughness. reviewed papers in the literature, mainly address the possibility to use circumferential cracked bar as alternative to measure fracture toughness in the lower shelf regime. authors used axisymmetric bar geometry differing in the notch or crack shape. most of them used v-notch while other used crack emanating from round notch. however, all of them agreed in using ki or ji as governing fracture parameters and this requires necessarily the use of finite element simulation for the determination of the effective crack driving force as a function of geometry parameters ( i.e. crack depth ration, sample height, etc.) and applied load. for instance, wang et al. [12] reported the following ki solution for v-notch circumferentially cracked bar under remote tension, 2 0.932 1.2 / 2.1 i p d k for d d d     (1) where d is the remote bar diameter, d is the minimum diameter at the v-notch, and p the maximum load. such general solutions based on fem analysis, depends on a number of computational issues. these includes the material model (elastic or elastic-plastic), the implementation of strain energy release method for contour integral determination, as well as other computational issues (element type, large or small strain formulations, etc.) inherently related to the code used at the time the simulation was performed. bonora et al. [10], proposed the use of ccb to determine material resistance using the critical crack tip opening displacement (ctod, c) as fracture parameter. they highlighted the possibility offered by such sample geometry to directly measure the material resistance using either the digital image correlation (dic) technique or alternatively, a high speed video camera avoiding numerical simulation or to refer to not well assessed analytical solutions. using well-known relationships between the ctod and ki and ji, material fracture resistance in the lower and upper shelf regime can be easily determined. the scope of this work was to investigate the use of ccb to determine fracture resistance of high toughness materials in the upper shelf regime. this task poses a number of complexities since these materials are known to show extensive blunting before ductile tearing initiation and propagation in association with substantial loss of constraint. in axisymmetric bar, the development of an extensive crack tip blunting may cause the flaw to behave like a notch and not like a crack triggering ductile failure in the center of the uncracked ligament. in addition, an excessive loss of constraint may lead to fracture toughness values which differs significantly from those measured in other geometries such as ct. therefore, an accurate design of ccb is required to provide realistic fracture strength measurement. sen(t) and ccb(t) analysis in the j-q space n design codes and standards for oil and gas application, as in os-dnv-f101, the use of sent is recommended for the experimental determination of the material critical crack tip opening displacement. from the design standpoint, outer circumferential weld crack subjected to remote axial strain loading, is one flaw configuration of major concern. loss of constraint in sent is similar to that occurring for this crack configuration in welded joints. although sent sample is relatively easy to be extracted for the base metal in the longitudinal direction of the pipe, it is often difficult or i d. gentile et alii, frattura ed integrità strutturale, 30 (2014) 252-262; doi: 10.3221/igf-esis.30.32 254 impossible to machine this sample geometry for girth weld or base metal along the circumferential direction. situation becomes even more complicated when dealing with the corrosion resistant alloy (cra) layer in clad pipe. in this case, 4 mm is a typical thickness for the clad and therefore it is impracticable to machine a sent sample with such limited material availability. specimen geometry, as well as crack depth ratio, has an effect on measured fracture toughness. a loss of constraint, resulting from large-scale yielding, relaxes the stress concentration for notched-tension panels and shallow-notch specimens, while deep-notch bend and compact specimens maintain a high level of crack tip constraint. this leads to an apparently increased fracture resistance in term of kic, jic and *c for the former configurations [13, 14]. t-stress and qparameter respectively in the k and j-controlled stress fields have been proposed to characterize the constraint effect on the crack tip. the t-stress and q-parameter at fracture are not material constants but depend on specimen geometry of specimens. since the objective of the work was the investigation of the ccb sample for the determination of fracture toughness in the upper shelf regime, the q-parameters was selected to characterize the constraint. an extensive finite element simulation analysis was performed to determine the j-q path in sent and ccb for varying crack depth ratio to verify if similar constraint can be realized for these geometry samples. for each selected crack depth ratio, the opening stress ( geomyy ) along the crack ligament was extracted as a function of the applied j-integral value. successively, a modified boundary layer (mbl) analysis was carried out inferring the same j-integral value and t-stress set to zero. again, the opening stress (  mblyy ) along the ligament was extracted. hence, the q-stress was determined according to: 0 geom mbl yy yy q      (2) since the opening stress varies with the distance from the crack tip, the q-stress was evaluated taking the stress field values at 0   and 02 /r j  , where 0 is the reference material yield stress. finite element simulations have been carried out with msc marc r2013 commercial fem code using fully integrated four node elements with bilinear shape functions. all elastic-plastic simulations were performed using large displacement, lagrangian updating and finite strain formulation. the j-integral was calculated using the domain integral formulation which ensures accurate estimation under general loading conditions. to account for extensive plastic zone developent at the tip, an initial blunting was introduced in the fem model. (a) (b) figure 1: finite element mesh for mbl: a) whole model, b) detail of the near tip region showing the initial crack blunting. arrows indicates symmetry boundary conditions applied as constrained displacement to the nodes. the initial blunt radius used in this work was r=0.01 mm. this value is small enough to follow accurately the transition from the linear elastic to the elastic-plastic stress field. for both specimen and mbl model the same mesh was used. boundary conditions were selected accordingly, fig. 1. the minimum element size at the tip was 0.0063 mm. for both sent and ccb, four crack depth ratios (a/w or a/r=0.2, 0.3, 0.4, and 0.5) have been investigated. reference dimensions for the sent were taken in accordance to [15]. for the ccb, there are no prescribed dimensions. for the purpose of the analysis, the mesh used for the ccb was the same as for sent. d. gentile et alii, frattura ed integrità strutturale, 30 (2014) 252-262; doi: 10.3221/igf-esis.30.32 255 figure 2: finite element mesh for sent and ccbt (a/w and a/r=0.5). same mesh but different element type: plane strain for sent, axisymmetric for ccbt. figure 3: comparison of the calculated j-q paths for sent and ccbt for different crack depth ratios. the j-q path for a outer circumferential girth weld crack is also shown. in fig. 3 the summary of the calculated j vs -q parameter for sent and ccb. is given. as anticipated, the q-parameter does not remain constant for increasing j-integral values. for each crack depth ratio, a saturation q value is reached for fully developed plastic zone. these results indicate that the loss of constraint in ccb is less severe than in sent, in general. j-q paths in sent have the tendency to converge for high j-integral values, resulting in similar values independently on the crack depth ratio. ccb j-q paths become steeper for deeper crack. however, it was found that in ccb shallow crack (a/r=0.2) result in similar constraint as for sent with a/w=0.5. in fig. 3, the j-q path for outer circumferential crack typically used in the engineering criticality assessment (eca) procedure is also plotted for comparison. based on this, it was decided to use ccb a/r=0.2 for investigating the critical ctod in carbon steel and to compare with fracture toughness data obtained with sent. c si mn p s cr ni cu 0.091 0.4 1.37 0.009 0.0007 0.024 0.27 0.17 table 1: chemical composition of the c-mn steel. material he material under investigation is c-mn x65 pipe steel grade with the nominal composition given in tab. 1. the material was fully characterized at rt and the flow curve was determined according to the procedure given in [10]. a two-term voce law was used as, 601 38(1 exp( / 0.012)) 250(1 exp( / 0.206))p p         (3) the measured flow stress was found to be higher than that expected for this steel grade. the nominal reference ductile-tobrittle trasition temperature is -100°c, consequently at rt the material is completely in the upper shelf regime. t d. gentile et alii, frattura ed integrità strutturale, 30 (2014) 252-262; doi: 10.3221/igf-esis.30.32 256 ductile tearing analysis uctile crack initiation and propagation analysis in ccb was performed using bonora’s damage model [16]. this model is derived in the framework of continuum damage mechanics and was verified for different classes of metals and alloys [17]. in this model, damage affects only the elastic stiffness while damage effects flow stress are taken into account in the definition of the material flow curve, leading to a non-softening formulation, which has the advantage to avoid mesh dependency of the solution. here, damage accumulates only under positive (tensile) state of stress while in compression damage effects are temporarily restored. the model requires only four material parameters to be determined: th the threshold strain at which damage processes initiates; f the failure strain under constant uniaxial constant stress triaxiality; crd , the critical damage at rupture and the shape factor  . these parameters are characteristic of the material and do not depend on the geometry [17]. the damage rate is given by the following expression,   1 1 ln( / ) p cr cr p f th d d r d d                 (4) the function r accounts for stress triaxiality effect,     2 2 1 3 1 2 3 h eq r                 (5) where h is the pressure and eq is the von mises stress and  is the poisson’s ratio. for the material under investigation, damage model parameters have been determined according to the procedure described in [18] and summarized in tab. 2. this procedure is based on fracture data, obtained from traction tests performed on smooth and round notched samples, and numerical simulation aimed to build the failure locus in terms of stress triaxiality vs average failure strain. threshold strain th failure strain f critical damage dcr  0.288 4.15 0.1 0.3 table 2: summary damage model parameters. a) b) c) d) figure 4: evolution of damage development at the crack tip of ccb a/r=0.2 under remote tension load: a) initial configuration; b) blunting development; c) crack initiation; d) crack propagation. d d. gentile et alii, frattura ed integrità strutturale, 30 (2014) 252-262; doi: 10.3221/igf-esis.30.32 257 finite element analyses were performed with msc marc 2013r1 in which the bonora’s damage model is available. numerical simulation of ccb incorporating damage was performed using the same computational parameters discussed in the previous paragraph. crack propagation was simulated using element removal technique: when the damage reaches its critical value at the element first gauss point, the element is removed and the stress and strain are set to zero. although the damage model formulation does not suffer mesh size dependence, the size of the element has direct influence on the crack growth rate. as rule of thumb, the minimum element size should not be smaller than the material average grain size. in fig. 5 the sequence of the deformation and damage development at the crack tip for the ccb a/r=0.2 is shown. this result showed that, although extensive blunting occurs at the tip prior tearing initiation, crack propagation starts at the tip and propagates along the ligament confirming that the blunted crack still behaves as a “crack”. numerical simulation have been repeated simulating partial unloading at prescribed remote imposed displacement in order to evaluate the change in the unloading compliance as a function of crack advance. this result was used to validate damage simulation comparing with predicted crack growth with experimental data. ccb design and experimental testing ased on computational analyses results, the geometry given in fig. 5, for the ccb was selected. the remote diameter was 6.0 mm, the crack depth ratio was 0.2 and the longitudinal gauge length was l=30 mm. the circumferential crack was machined using edm and no fatigue pre-cracking was prescribed. the nominal notch radius was 0.06 mm. for testing in the upper shelf regime, this value is small enough to be considered as a sharp crack. a) b) figure 5: a) ccb dimensions, b) detail of the crack tip. specimen ends where thread in order to avoid slip during loading. four samples were machined and their effective dimensions are summarized in tab. 3. of the four samples, two where monotonically loaded in tension up to failure while the other two were used for damage assessment performing partial unloading at prescribed remote imposed displacements. elongation was measured using an extensometer with a reference length of 12.5 mm. additionally, strain was measured using dic. high speed video camera was used to monitor crack tip blunting development and first crack initiation for ctod determination. in fig. 6 the ccb instrumented with the clip gauge is shown. in fig. 7 a sequence of crack blunting development observed with the video camera is given. specimen outer diameter (mm) minimum diameter (mm) edm notch radius (mm) ccb_b1 5.993 4.814 0.0595 ccb_b2 6.014 4.826 0.0605 ccb_b3 6.004 4.797 0.0590 ccb_b4 6.026 4.812 0.0610 table 3: specimen dimension. tensile test. b d. gentile et alii, frattura ed integrità strutturale, 30 (2014) 252-262; doi: 10.3221/igf-esis.30.32 258 figure 6: reference set-up for ccb. figure 7: sequence of crack tip blunting development and crack initiation observed with high speed camera. results and discussion or each test, the global response in terms of applied load vs elongation was recorded while the ctod at crack initiation was derived from the video recording. tests showed that crack initiation occurred beyond the maximum load indicating that some sort of necking develops in the minimum section. this was indeed confirmed by the video recording of the test and later verified also by fem analysis. in fig. 8, the comparison of the measured applied load vs average strain (from extensometer) and calculated response with fem is shown. here, it can be observed that specimens crb_b1, that was monotonically loaded up to fracture, and crb_b4, that was subjected to partial unloading, showed very similar responses. some differences were observed in specimen crb_b2 that showed a higher yield stress and more rapid load drop beyond maximum load. finite element simulation results were in a general good agreement with the experimental data although the calculated response was in a better agreement with that of crb_b2 sample. 0,000 0,025 0,050 0,075 0,100 0,125 0,150 0,175 0,200 0 2500 5000 7500 10000 12500 15000 17500 20000 l o a d [ n ] eng. strain l/l 0 crb_b1 crb_b2 crb_b4 (unloading compliance) fem (unloading compliance) figure 8: comparison of applied load vs strain response measured in the tests and predicted with fem. f d. gentile et alii, frattura ed integrità strutturale, 30 (2014) 252-262; doi: 10.3221/igf-esis.30.32 259 crack propagation as a function applied load was also compared with finite element prediction obtained with the damage model. in fig. 9, the comparison is given. here, experimental crack advance data have been obtained from the high speed camera filming. again the comparison with computational results is in a general good agreement considering that simulation have been performed using model parameters identified on different test types. the comparison is quite good up to 0.6 mm of crack advance that correspond to a crack depth ratio of 0.4. for larger crack advance the difference between the predicted and the measured response increases. this is probably due to the fact the fem do not reproduce accurately the global response in the final part of the load vs strain curve as shown in fig. 8. 0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 0 2500 5000 7500 10000 12500 15000 17500 20000 ccb_1 ccb_2 fem l o a d [ n ] crack advance a [mm] figure 9: comparison of predicted and measured applied load vs crack advance. 0,0 0,2 0,4 0,6 0,8 1,0 1,2 1,4 0,00 0,25 0,50 0,75 1,00 1,25 fem ccb_1 ccb_2 c m o d [ m m ] crack advance a (mm) figure 10: comparison of predicted and measured cmod vs crack advance. similar agreement was found for the crack mouth opening displacement (cmod) vs crack advance response, fig. 10. finally, results in terms of crack resistance curve were also provided. from the computational point of view, the j-integral was calculated using the domain integral formulation available in msc marc while the applied j-integral in the experiment was estimated using the relationship provided in [19]. d. gentile et alii, frattura ed integrità strutturale, 30 (2014) 252-262; doi: 10.3221/igf-esis.30.32 260   2 00 1 3 2 cr cr crj p d p r              (6) where p is the applied load, cr is the load point displacement which is function of the compliance of the uncracked specimen, and r0 is the uncracked ligament. results are provided in fig. 11. 0,0 0,2 0,4 0,6 0,8 1,0 1,2 1,4 0 250 500 750 1000 1250 1500 1750 2000 2250 2500 fem ccb_1 ccb_2 j -i n t e g r a l [ k j /m 2 ] crack advance a [mm] figure 11: comparison of calculated crack resistance and crack driving force obtained using unloading compliance values. 0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 0 250 500 750 1000 1250 1500 1750 2000 2250 2500 j -i n t e g r a l [ kj /m 2 ] crack advance a [mm] fem ccb_b1 compliance corrected figure 12: crack resistance curve calculated considering the change in the unloading compliance. it can be seen that the agreement is good up to j-integral values of ~600 n/mm, which correspond to the maximum load. this is coherent with eq. (6) that is valid up to the maximum load. beyond this point, eq. (6) shall be corrected considering the change in the unloading compliance due to crack advance. therefore, crack resistance data have been recalculated using the unloading compliance measured in the tests. the new crack resistance curve is shown in fig. 12. this time, a better agreement between the experimental values and the fem results is found up to ~1.0 mm of crack growth. d. gentile et alii, frattura ed integrità strutturale, 30 (2014) 252-262; doi: 10.3221/igf-esis.30.32 261 specimen ctod max load [mm] ctod fem max load [mm] critical ctod (a=0.1 mm) [mm] ctod fem (a=0.1 mm) [mm] ccb_b1 0.489 0.380 0.879 0.56 ccb_b2 0.458 0.380 0.784 0.56 ccb_b3 0.394 0.380 0.788 0.56 ccb_b4 0.365 0.380 0.852 0.56 sent (a/w=0.5) 0.460 0.40 table 4: summary of ctod measurement for ccb and sent. finally, the ctod measured in the tests was compared with data obtained on sent [20]. ctod for sent was measured, after cutting and polishing on an interrupted test at maximum load. this value is usually considered as design allowable ins several design codes. in tab. 4, the summary of the ctod at maximum load are given. in the table the estimated critical ctod for which crack propagation has occurred is given. the resolution of video recording is such that the crack advance can be estimated with a sensitivity of ±0.1 mm since this is the size of the pixel. the ctod at maximum load for ccb was 0.426 ± 0.057 mm that is in a good agreement with the value measured for sent, while the estimated critical ctod for a minimum of 0.1 mm crack advance was 0.826 ± 0.047 mm. the ctod at maximum load estimated with fem is in a very good agreement with the experimental data. on the contrary, the ctod for 0.1 mm of crack advance, is 30% less than the experimental measure. probably, this can be explained by the variability of the material plastic flow curve, which is also responsible for the differences observed in the predicted applied load vs elongation curve. conclusions n this work, the use of the circumferentially cracked bar sample to determine the ctod fracture toughness in the upper shelf regime, has been investigated. based on finite element simulation, the ccb crack depth ratio that exhibits the same q-parameter as for sent with a/w=0.5, was found a/r=0.2. it was verified that with such crack depth ratio, considering the extensive blunting occurring at the tip, the flaw in ccb still behaves as a crack (that is ductile tearing always occurs at the tip). experimental tests performed at rt on x65 carbon steel grade, showed ctod values in a very good agreement with that measured using standard sent geometry sample confirming the equivalence of ccb with sent. the critical ctod for 0.1 mm crack advance was found twice that at maximum load which is usually indicated as allowable value in the design practice. predictions performed with damage mechanics have been found to be in a very good agreement with experimental finding indicating that this approach is a mature tool for preliminary analysis and design of experiment in order to anticipate expected material/geometry behaviour and to reduce the experimental effort. references [1] stark h. l., ibrahim, r. n., estimating fracture toughness from small specimens, engineering fracture mechanics, 25 (1986) 395-401. [2] ibrahim r. n., stark, h. l., validity requirements for fracture toughness measurements obtained from small circumferentially notched cylindrical specimens, engineering fracture mechanics, 28 (1987) 455-460. [3] ibrahim r. n., stark, h. l., establishing k1c from eccentrically fatigue cracked small circumferentially grooved cylindrical specimens, int. j. of fracture 44, 179-188 (1990). [4] lam y. c., ibrahim, r. n., improvement of the fracture toughness of an aluminum alloy, fatigue fract. engng. mater. struct. 17 (1994) 277-284. [5] devaux, j. c., rousselier, g., mudry, f., pineau, a., an experimental program for the validation of local ductile fracture criteria using axisymmetrically cracked bars and compact tension specimens, engineering fracture mechanics, 21 (1985) 273-283. i d. gentile et alii, frattura ed integrità strutturale, 30 (2014) 252-262; doi: 10.3221/igf-esis.30.32 262 [6] beremin, f. m., calculation and experiment on axisymmetrically cracked tensile bars: prediction of initiation, stable crack growth and instability, in: transactions of the 6th int. conference on structural mechanics in reactor technology, l (1981) l 6/2. [7] giovanola, j. h., crocker, j. e., fracture toughness testing with cracked round bars: feasibility study, nureg/cr6342 ornl/sub/94-dhk60, us nuclear regulatory commission, washington dc, (2000). [8] costin, l. s., duffy, j., freund, l. b., fracture initiation in metals under stress wave loading conditions, in: fast fracture and crack arrest, astm stp 62 7, g. t. hahn and m. f. kanninen, eds., american society for testing and materials, philadelphia, (1977) 301-318 [9] hawley, r. h., duffy, j., shih, c. f., dynamic notched round bar testing, in: asm metals handbook, 9th ed., mechanical testing, american society for metals, metals park, ohio, 8 (1985) 275-282. [10] bonora, n., ruggiero, a., testa, g., iannitti, g. and gentile, d., dynamic crack tip opening displacement (dctod) as governing parameters for material fragmentation, j. of physics: conference series, 500(11) (2014). [11] scibetta, m., chaouadi r., van walle, e., fracture toughness analysis of circumferentially-cracked round bars, int. j. of fracture, 104 (2000) 145–168. [12] wang, c.h., introduction to fracture mechanics; stress analysis of cracked bodies, aeronautical and maritime research laboratory, victoria 3001, melbourne, dsto-gd-0103, (1996) 10-28. [13] minami, f., inoue, t., arimochi, k., constrain correction of fracture toughness ctod for fracture performance evaluation of structural components, in: 10th int. conference on fracture icf10 elsevier science, honolulu, hawaii, usa, 2001 (1-6). [14] betegòn, c., hancock, j. w., two parameter characterization of elastic-plastic crack tip fields, j. of applied mechanics, 58 (1991) 104-110. [15] dnv-os-f101, offshore standard submarine pipeline systems, (2012) 1-367. [16] bonora, n., a non-linear cdm damage model for ductile failure, engineering fracture mechanics, 58(1/2) (1997) 11–28 [17] bonora, n., ruggiero, a., esposito, l., gentile, d., cdm modeling of ductile failure in ferritic steels: assessment of the geometry transferability of model parameters, int. j. of plasticity, 22(11) (2006) 2015-2047. [18] carlucci, a., bonora, n., ruggiero, a., iannitti, g., crack initiation and growth in bimetallic girth welds, in: proc. proceedings of the asme 2014, 33rd int. conference on ocean, offshore, and artic engineering omae 2014, ed. asme, (2014) 1-5. [19] giovanola j. h., kobayashi, t., mechanics of deformation and ductile tearing in cracked round bar specimens, engineering fracture mech., 59(2) (1998) 117-136. [20] carlucci, a., bonora, n., ruggiero, a., iannitti, g., testa, g., crack initiation and propagation of clad pipe girth weld flaws, in: proc. of asme 2014 pressure vessel and piping division conference, pvp201, (2014) 28017. microsoft word numero_46_art_11 s.m. medjdoub et alii, frattura ed integrità strutturale, 46 (2018) 102-112; doi: 10.3221/igf-esis.46.11 102 developments in the fracture and fatigue assessment of materials and structures optimization of the geometrical parameters of bonded composite wrap for repairing cracked pipelines sidi mohamed medjdoub university of djillali liabes, sidi bel abbes, algeria medjdoubsm@gmail.com belabbes bachir bouadjra university of djillali liabes, lpmm laboratory, sidi bel abbes, algeria bachirbou@yahoo.fr miloudi abdelkader university of djillali liabes, lmsr laboratory, sidi bel abbes, algeria miloudidz@yahoo.fr abstract. in this study the finite element method is used to analyze the performances of bonded composite wrap repair of cracked steel pipelines. parametric analysis was performed in order to highlight the effects of the geometrical properties on the repair efficiency. the experimental design method is used to explore the effects of wrap dimensions (length, angle and thickness) in order to optimize the repair process. we showed in using the moode.5 software the most dominant geometrical parameters on stress intensity factor at the crack front which to determine the most important parameters on the repair efficiency. this optimization can help the composite wrap designers to improve the repair performance and rehabilitation. keywords. fracture mechanics; crack; composite; wrap; pipelines. citation: medjdoub, s.m., bachir bouadjra, b., miloudi, a., optimization of the geometrical parameters of bonded composite wrap for repairing cracked pipelines, frattura ed integrità strutturale, 46 (2018) 102-112. received: 06.05.2018 accepted: 28.06.2018 published: 01.10.2018 copyright: © 2018 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. introduction he oil and gas are transported by steel pipelines in industry better than the storage tanks. the operating conditions are in subjected to hard environments and extreme loading conditions. mechanical damages are common in operating pipelines. they are damage in the coating, erosion and corrosion which can lead principal problem met in industry to internal and external crack in the structure of the pipeline. according to the gravity of the problem, the harmful effects are the pressure bearing capability in the pipeline and they can reduce his lifespan or a failure of the structure [1-5]. the best means of reparation of canalization is the bonded composite wrap because he is installed during t http://www.gruppofrattura.it/va/46/11.mp4 s.m. medjdoub et alii, frattura ed integrità strutturale, 46 (2018) 102-112; doi: 10.3221/igf-esis.46.11 103 the continuity flow of the fluid and there is not hot work in order to avoid the risk of explosion. the use of the composite wrap as an alternative of the cracked replacement pipe often saves economical resources to immediately pay behind costs of repair [6-10]. after the realization of 2 to 65 composite wrap repairs on pipelines more than 300 mm of outer diameter can save 15.000 to 780.000 m3 of natural gas by year. in choosing the composite wrap, they saved 4 .106 m3 of gas during 5 years [11]. a study conducted by the us department of transportation showed repair costs can be reduced by 24% by using composite repair instead of welded steel sleeves. when compared to the replacement of the whole defective pipe section, the cost can be further reduced to approximately 73% [12]. the strength of the repair is governed by the thickness of composite wrap and the tensile stress at each layer of the wrap, where effective stress transfer initiates once plastic flow occurs in the repaired steel pipe [13,14]. murad et al [15] developed an integrated structural health monitoring approach for composite-based pipeline repair. however, the cumbersome process of installing electrical strain gauges on the steel pipe prior to the application of the composite repair greatly limits its adoption in offshore subsea application. numerical methods such as finite element method (fem) have grown considerably in recent years. several authors have used this method to analyze the performance of pipe repair by a composite patch [16-20]. the majority of these authors have used the linear mechanics of fracture approach to evaluate the reduction of stress intensity around the crack front by the composite wrap. benyahia et al [18] calculated the stress intensity factor (sif) at the front of repaired crack with bonded composite wrap in pipe subjected to internal pressure. they showed that the composite wrap repair leads to a significant reduction of the sif which improves the service life of the cracked pipe. the same conclusions were made by bezzerrouki et al [19] who studied the performances of bonded composite wrap on pipes subjected to traction. however, for pipe subjected to bending moment the repair efficiency is less significant according to achour et al [20]. a finite element study of cracked steel circular tube repaired by fiber reinforced polymer composite (frpc) patching is executed by lam et al [21]. it was shown that the mode i stress intensity factor (ki) of cracked steel members was found to be reduced with the application of frpc patching. using the ki and paris equation [22], the fatigue life of the cracked steel member was increased by 22 times with the application of frpc patching. the various works conducted have showed that application of frpc to reinforce structural element is a viable option. experimental testing can be used as a means of determining the effectiveness of the repair or reinforcement [23,24]. the use of numerical modelling can be a more cost effective solution where accurate results have been shown to be attainable through numerous previous studies [25,26]. the design of bonded frpc wrap for repairing damaged pipe line has not been studied enough in the literature. the use of fiber-reinforced polymer composite as a load bearing sleeve has emerged as a promising means of pipeline rehabilitation due to advantages such as high specific strength, high corrosion resistance, lightweight, do not require welding and are simple to install [27]. erdogan et al. [28,29] studied on the cracked panels using an analytical formulation for the fracture parameters such as stress intensity factor. other closed-form expressions for sifs are presented by zahoor [30], sanders [31] and forman [32] for cracked cylindrical pipes. zárate et al. [33] presented a framework to update and predict crack length as a function of the number of cycles in structural elements subjected to fatigue. in all previous researches of bonded composite repair of damaged pipe, the optimization of the repair parameters was not made. the objective of this work is to optimize the repair parameters in the technique of repair of cracked pipeline with composite wrap. to achieve this objective, a finite element study is used to analyze the performance of cracks repaired with composite patches by calculating the crack stress intensity factors in elastic behaviour. the effect of the geometrical properties on the reduction of the stress intensity factor at the crack tip is also analyzed. the obtained results are analyzed by the methodology of the experimental design to develop a constitutive mathematical model which controls the stress intensity factor as a function of the combination of three geometrical parameters of bonded frpc wrap: length, angle and thickness. this experimental design method was applied to optimize the frpc wrap size and to find the most influencing dimension on the repair efficiency. model description and mechanical properties onsider material alloy often used in gas pipelines, api 5l grade x65 containing a longitudinal external semielliptical crack of length (2c = 15.4 mm) and depth (a = 2.8 mm), he is repaired with a frpc wrap, the fibres are all oriented at 0° stuck around the entire circumference of the pipeline, the model is shown in fig. 1. the c s.m. medjdoub et alii, frattura ed integrità strutturale, 46 (2018) 102-112; doi: 10.3221/igf-esis.46.11 104 geometrical and mechanical characteristics of the pipeline, the composite wrap and the adhesive are shown in tab. 1 and 2 respectively. figure 1: repair by composite wrap of a semi-elliptical crack in a pressurized cylinder. symbol value description l 9000 pipeline length (mm) d 864 pipeline outside diameter (mm) di 847.44 pipeline inside diameter (mm) t 8.28 pipeline wall thickness (mm) a 2.8 crack depth (mm) c 7.7 half crack length (mm) lw [100-350 -600] composite wrap length (mm) tw [6-18-30] composite wrap thickness (mm) aw [30195 -360] composite wrap recovery angle(°) ta 0.1 adhesive thickness (mm) table 1: dimensions of typical repair of pipeline. property material description steel glass/epoxy adhesive e1 209000 159000 2400 young's modulus in x direction (mpa) e2 25400 young's modulus in y direction (mpa) e3 25400 young's modulus in z direction (mpa) ν12 0.3 0.28 0.3 poisson's ratio in x-y plan ν13 0.28 poisson's ratio in x-z plan ν23 0.15 poisson's ratio in y-z plan g12 7190 shear modulus in x-y plan (mpa) g13 5430 shear modulus in x-z plan (mpa) g23 5430 shear modulus in y-z plan (mpa) σy 456000 yield stress (mpa) table 2: mechanical proprieties of materials. s.m. medjdoub et alii, frattura ed integrità strutturale, 46 (2018) 102-112; doi: 10.3221/igf-esis.46.11 105 numerical modeling and boundary condition he pipeline is modelled in the commercial finite element software, abaqus [34]. continuum elements with eight nodes and reduced integration (c3d8r in abaqus) were used throughout the model. the total number of elements generated for the symmetrical model was 686950. the mesh is refined at the crack front, composite wrap and adhesive layer. the pipeline is subjected to internal compression pi = 0.57 mpa with distributed uniform stress. the model is shown in fig. 2. figure 2: finite element model of repaired crack by composite wrap. experimental design approach he experimental design is necessary to have relevant information, establish a relationship between the input variables, which are the geometrical parameters (the length, the thickness and especially the width of the recovery angle of the composite wrap bonded) and the output variables is the evolution of the mode i stress intensity factor (ki). in order to determination the optimum patch dimensions. each parameter was tested at three different levels: the length of wrap (100-350-600) thickness of wrap (6-18-30) and the recovery angle (30-195-360). the responses (stress intensity factor) were calculated using the finite element method. the experimental design matrix of the experiments is given by modde 5.0 (modelling and design) software [35,36] is presented in tab. 3. we have adopted a complete experimental design of three factors at two levels; the mode of the experimenter is quadratic and has the following form: 3 3 2 0 1 1 3 1 i i ij i j ii i i i j i y a a x a x x a x e             (1) where i, j vary from 1 to the number of process variables 3, y is the response of the process (stress intensity factor); the coefficient a0 is the means of answers for the whole experiment; the coefficient ai represents the effect of the variable xi and aij are the regression coefficients that represent the effects of the interactions of the variables xi xj and ai are the regression coefficients that represent the effects of the interactions of the variable xi xi and e is the experimental error. the polynomial model proposed by modde 5.0 describe the variations of the response function (stress intensity factor) ki to the factors lw, tw and aw is of the following form: 0 1 2 3 12 13 23 2 2 2 11 w 22 w 33 w a l a t a a i w w w w w w w w wk a a l a t a a a l t a l a a t a          (2) the experimental plans used in this study are a complete quadratic plan to say that we deal with a mathematical model of the second degree. tab. 4 presents the coefficients of the various parameters and their interactions. t t s.m. medjdoub et alii, frattura ed integrità strutturale, 46 (2018) 102-112; doi: 10.3221/igf-esis.46.11 106 the mathematical model proposed by modde 5.0 is expressed as follows: 2 2 2 w w w 21 3496 4.71944 14.7872 7.66384 3.41241 1.43191 3.47017 3.794 3.06383t 6.11351a i w w w w w w w w w k . l t a l t l a t a l           (3) exp. no lw (mm) tw (mm) aw (°) ki (mpa√m) 1 100 6 30 60.65 2 350 6 30 54.29 3 600 6 30 55.07 4 100 18 30 50.641 5 350 18 30 40.04 6 600 18 30 35.77 7 100 30 30 30.19 8 350 30 30 19.65 9 600 30 30 10.988 10 100 6 195 41.61 11 350 6 195 42.2 12 600 6 195 45.92 13 100 18 195 30 14 350 18 195 16.95 15 600 18 195 16.33 16 100 30 195 21.83 17 350 30 195 10.09 18 600 30 195 8.363 19 100 6 360 39.22 20 350 6 360 35.81 21 600 6 360 37.48 22 100 18 360 27.42 23 350 18 360 16.46 24 600 18 360 17.98 25 100 30 360 22.27 26 350 30 360 11.72 27 600 30 360 10.98 table 3: the conducted table experiments given by the experimental design. ki coeff. sc std. err. p conf. int(±) constant 21.3496 1.77809 9.97244e-010 3.75146 lw -4.71944 0.823094 2.43432e-005 1.73659 tw -14.7872 0.823094 1.71477e-012 1.73659 aw -7.66384 0.823094 4.36222e-008 1.73659 lw*lw 3.794 1.42564 0.0164509 3.00786 tw*tw 3.06383 1.42564 0.0463223 3.00786 aw*aw 6.11351 1.42564 0.000497399 3.00786 lw*tw -3.41241 1.00808 0.00351972 2.12688 lw*aw 1.43191 1.00808 0.173562 2.12688 tw*aw 3.47017 1.00808 0.00310919 2.12688 n = 27 q2 =0.919 cond. no. =5.2299 df = 17 r2 =0.967 y-miss =0 table 4: sif ki coefficients list. s.m. medjdoub et alii, frattura ed integrità strutturale, 46 (2018) 102-112; doi: 10.3221/igf-esis.46.11 107 results rom the graphical analysis it is possible to determine the influence of each factor on the response. the stress intensity factor responses are predicted by modde 5.0. effect of composite wrap thickness on sif the influence of the composite wrap thickness on the stress intensity factor is summarized in fig. 3. the results show a strong influence of the composite wrap thickness on the stress intensity factor, the higher the composite wrap thickness, the lower the stress intensity factor. a difference of about 400% in the stress intensity factor between the two composite wrap thicknesses (6 and 30) is observed. the analysis of this figure shows that an increase in the thickness of the wrap causes a decrease in the stress intensity factor. these results are in agreement with those of bezzerrouki et al [19]. if thicker wrap is used, the stress level at crack front decreases. this behaviour can be explained by the fact that the bonded composite wrap significantly reduces the mechanical energy at the crack front which attenuates the crack growth rate. this reduction is more significant when the wrap thickness increases. figure 3: sif vs composite wrap thickness. figure 4: sif vs composite wrap length. effect of composite wrap length on sif fig. 4 illustrates the influence of the composite wrap length on the stress intensity factor; we observe that an increase of this length leads to a decrease in the stress intensity factor. until reaching a minimum value of 21 mpa.m1/2, which corresponds to a value of lw = 350 mm, beyond this value the composite wrap length has no influence on the response ki. about the wrap length effects, it can be noted that the composite wrap length give weak stress intensity factors and consequently best repair efficiency. this is because with longer composite wrap the bonded area increases and the stress transfer from the pipe toward the composite wrap will be more significant. effect of composite wrap recovery angle on sif fig. 5 illustrates the effect of the composite wrap recovery angle of the stress intensity factor by analyzing this curve it can be said that the increase in the angle generates a considerable decrease in the stress intensity factor. indeed, an increase of 300° in the composite wrap recovery angle leads to a 75% decrease in the stress intensity factor. this effect is less marked for a composite wrap recovery angle of 233°. interaction effect of different parameters on sif in this analysis step we expand our comments taking into account this time an interaction between two factors while keeping the other two constant this decision allows us to visualize the variation of the stress intensity factor by a graph in three dimensions in fig. 6. f s.m. medjdoub et alii, frattura ed integrità strutturale, 46 (2018) 102-112; doi: 10.3221/igf-esis.46.11 108 figure 5: sif vs composite wrap recovery angle. figure 6: surface plot of sif vs thickness and length of wrap. fig. 7 is the projection of the surface 6 on the plane (iso-reponse), which presents the effect of the combination of the two factors for a constant value of wrap recovery angle aw = 195°, the composite wrap length and the composite wrap thickness on the stress intensity factor. in this case combination, the stress intensity factor is optimal when these two factors take maximum values. fig. 8 shows the effect of the combination of the two factors, the composite wrap length and the composite wrap recovery angle on the stress intensity factor. the results obtained show that the more these factors increase, more the stress intensity factor decreases, for a composite wrap length value between 400 and 600 mm, and for composite wrap recovery angle between 125° and 330 °. we conclude this analysis that to have a better reparation, it is necessary to have a maximum value of the composite wrap length and a value of the composite wrap recovery angle equal to 233°. fig. 9 illustrates the variation of the stress intensity factor as a function of the thickness composite wrap and the recovery angle. following this combination, it is found that the increase of these two factors causes a decrease in the stress intensity factor. concludes that to have a significant life time, composite wrap thickness maximized and the composite wrap recovery angle must be equal to 233°. figure 7: contour plot of sif for wrap recovery angle constant aw = 195°. figure 8: contour plot of sif for wrap thickness constant tw = 30 mm. by introducing the results into the modde 5.0 software to examine the different effects, the results obtained are given in fig. 10. this diagram shows the effects of all combinations of the factors performed (linear, crossed and quadratic). in s.m. medjdoub et alii, frattura ed integrità strutturale, 46 (2018) 102-112; doi: 10.3221/igf-esis.46.11 109 descending order of their importance in absolute value. by analyzing these results, we can say that the dominant factors on stress intensity factor are in the following order: 1composite wrap thickness. 2composite wrap recovery angle. 3composite wrap length. figure 9: contour plot of sif for wrap length constant lw = 600 mm. figure 10: effects of the different parameters on the stress intensity factor ki. optimal composite wrap dimension from the optimization software, we can deduce the minimal value of the sif which is equal to 4.9777 mpa.m1/2. this value gives the better repair efficiency (tab. 5). it is obtained from the following dimension of the composite wrap: length lw=599.413 mm, thickness tw=29.9999 mm and recovery angle aw = 233.967°. lw tw aw ki 550 30 228.594 5.1817 559.262 29.9031 275.268 5.5471 588.105 29.9992 236.796 4.999 566.146 29.5898 239.624 5.4477 599.413 29.9999 233.967 4.9777 556.166 29.8859 238.203 5.2314 600 30 228 4.9805 566.146 29.5898 239.624 5.4477 table 5: optimal frpc wrap sizes. t w ( m m ) aw (°) s.m. medjdoub et alii, frattura ed integrità strutturale, 46 (2018) 102-112; doi: 10.3221/igf-esis.46.11 110 the validity of the developed model can also be obtained from the fig. 11 which presents the relation between the values computed numerically and predicted from the proposed model. this curve indicates that the mathematical model developed shows a good agreement between the calculated and estimated values of the responses. 0 5 10 15 20 25 30 0 10 20 30 40 50 60 70 k i [m p a (m )1 /2 ] experiences abaqus model figure 11: comparison between the sif of different program execution and those obtained by mathematical model. discussion onded composite repair of cracked pipeline is an efficient technique to increases the lifespan of damaged pipe. the load transfer between the cracked pipe and the composite wrap can attenuate the stress intensity around the front of the repaired crack which leads to the improvement of the fatigue life of the pipeline [37]. it was shown by benyahia et al [18] in this study that the reduction of the stress intensity by the composite wrap repair is very significant at the external position of the crack compared to the internal crack position. the main disadvantage of the technique of bonded composite repair in pipe is the impossibility to bond double-sided composite wrap in order to equilibrate the stress transfer between the internal and external positions of the cracks [20]. to increase the repair efficiency, it is important to optimize the repair parameters since the stress intensity around the crack depends on all these parameters. the optimization of the mechanical properties of the adhesive and the composite patch can improve the repair and reinforcement performances and durability significantly. this optimization must equilibrate between the reduction in the stress intensity at the repaired defect and the reduction in the risk of adhesive layer failure [19]. the obtained results showed that the wrap length has a significant effect on the repair efficiency, the maximization of this parameter is essential to increase the repair performance. it was also shown that the wrap thickness must be also maximized to improve the repair efficiency. these results are in concordance with those of achour et al [20]. these authors studied the performances of bonded composite wrap of pipeline subjected to bending. they showed that the increase of the plies number of the composite wrap reduces significantly the stress intensity factor at the crack front. the relative reduction of the sif is about 30% when the plies number varies between 4 and 14 [20]. these results allow us to confirm that the choice of thicker wraps makes it possible to increase significantly their performances. the optimum of the recovery angle is 233° representing 65% if the global recovery. this is specific for pipe repair because in plate repair the total recovery is the optimum [21]. conclusion he objective of our study is to highlight the performance of the fibre-reinforced polymer composite wrap repair technique in a pipeline subjected to internal pressure. the analysis of the effect of various geometrical parameters of wrap on the repair efficiency has been studied numerically. the analysis of the influence of these parameters was performed by the method of experimental design. consequently, the following conclusions can be deduced: the bonded frpc wrap repair improves the lifespan of cracked pipe but the improvement rate strongly depends on the geometrical properties of the frpc wrap. the increasing of the wrap thickness leads to a considerable decrease of the sif at the crack tip. b t s.m. medjdoub et alii, frattura ed integrità strutturale, 46 (2018) 102-112; doi: 10.3221/igf-esis.46.11 111 the thickness has the most significant effect on the repair efficiency. an increase in the length of the wrap causes the decrease in the sif of the longitudinal crack; the use of a longer wrap in the axial direction is therefore beneficial for repaired structure. -in addition, increasing the recovery angle of the wrap on the outside circumference of the pipeline reduces the sif at the crack front. but we take into account the geometrical design limits of the frpc wrap for a recovery angle 65% (233°) to have an optimum in reducing the stress concentration at the crack front. optimization sizes reduce the use of the composite material with a gain of 35%. the non patched surface absorbs the energy around the crack front leading to a stress relaxation at this front. references [1] gerhardus, h.k., brongers, m.p.h., thompson, n.g., virmani, y.p. and payer, j.h., (2002). corrosion costs and preventive strategies in the united states, summary, pp. 1–12. doi: fhwa-rd-01-156. [2] mokhtari, m. and alavi nia, a., (2015). the influence of using cfrp wraps on performance of buried steel pipelines under permanent ground deformations, j. soil dynamics and earthquake engineering, 73, pp. 29–41. doi: 10.1016/j.soildyn.2016.04.009. [3] greenwood, c., (2001). composite pipe repair method shows versatility, long-lasting, j. pipeline gas, 228, pp. 58. [4] alexander, c. and wilson, f., (1999). development and testing of the armor plate pipeline repair system, in: proceedings of the asme energy sources technology conference, american society of mechanical engineers, petroleum division, houston. [5] alexander, c. and ochoa, o., (2010). extending onshore pipeline repair to offshore steel risers with carbon–fiber reinforced composites, j. composite structures., 92, pp. 499–507. doi: 10.1016/j.compstruct.2009.08.034. [6] mableson, a. r., dunn, k.r., dodds, n. and gibson, a.g., (2000). refurbishment of steel tubular pipes using composite materials, j. plastics rubber and composites, 29, pp. 558–565. doi: 10.1179/146580100101540770. [7] fazzini, p.g. and otegui, j.l., (2006). influence of old rectangular repair patches on the burst pressure of a gas pipeline, int. j. pressure vessels and piping, 83, pp. 27–34. doi: 10.1016/j.ijpvp.2005.10.004. [8] jodin, p., (2008). fracture mechanics analysis of repairing a cracked pressure pipe with a composite sleeve, in: pluvinage, g., elwany, m.h., (eds.), safety reliability and risks associated with water oil and gas pipelines, springer. doi: 10.1007/978-1-4020-6526-2_19. [9] smith, p. and cuthill, j., (2002). patching up pipework with carbon–fiber composites, mater. world, 10, pp. 28. [10] meriem-benziane, m., abdul-wahab, s. a., zahloul, h., babaziane, b., hadj-meliani, m. and pluvinage, g., (2015). finite element analysis of the integrity of an api x65 pipeline with a longitudinal crack repaired with singleand double-bonded composites, j. composites part b, 77, pp. 43-439. doi: 10.1016/j.compositesb.2015.03.008. [11] ngsp (2006). composite wrap for non-leaking pipeline defects, environmental protection agency, usa, pp. 5-7. [12] rspa (2000). pipeline safety: gas and hazardous liquid repair, department of transportation, 98-4733. [13] mazurkiewicz, l., małachowski , j., tomaszewski , m., baranowski , p. and yukhymets, p., (2018). performance of steel pipe reinforced with composite sleave, j. composite structures, 183, pp. 199–211. doi: 10.1016/j.compstruct.2017.02.032. [14] mazurkiewicz, l., tomaszewski, m., malachowski, j., sybilski, k., chebakov, m., witek, m., yukhymets, p. and dmitrienko, r., (2017). experimental and numerical study of steel pipe with part-wall defect reinforced with fibre glass sleeve, int. j. pressure vessels and piping, 149, pp. 108-119. doi: 10.1016/j.ijpvp.2016.12.008. [15] murad, m., frost, s. and brennan, f., (2013). bonding integrity study between steel pipeline and composite wraps using structural health monitoring technique, j. pipeline systems engineering and practice, 4, pp. 68-73. doi: 10.1061/(asce)ps.1949-1204.0000115. [16] duell, j.m., wilson, j.m. and kessler, m.r., (2008). analysis of a carbon composite overwrap pipeline repair system, int. j. pressure vessels and piping, 85, pp. 782-788. doi: 10.1016/j.ijpvp.2008.08.001. [17] wilson, j., (2006). characterization of a carbon fiber reinforced polymer repair system for structurally deficient steel piping, ph. d. thesis, university of tulsa, tulsa, 226. [18] benyahia, f., albedah, a. and bachir bouiadjra, b., (2014). stress intensity factor for repaired circumferential cracks in pipe with bonded composite wrap, j. pressure vessel technology, 136, 041201-1. doi: 10.1115/1.4026022. [19] bezzerrouki, m., albedah, a., bachir bouiadjra, b., ouddad, w. and benyahia, f., (2013). computation of the stress intensity factor for repaired cracks with bonded composite wrap in pipes under traction effect, j. thermoplastic composite materials, 26, pp. 831-844. doi: 10.1177/0892705711430428. s.m. medjdoub et alii, frattura ed integrità strutturale, 46 (2018) 102-112; doi: 10.3221/igf-esis.46.11 112 [20] achour, a., albedah, a., benyahia, a., bachir bouiadjra, b. and ouinas, d., (2016). analysis of repaired cracks with bonded composite wrap in pipes under bending, j. pressure vessel technology, 138 060909-6. doi: 10.1115/1.4033449. [21] lam, c., cheng, j. and yam, c., (2011). finite element study of cracked steel circular tube repaired by frp patching. procedia engineering, 14, pp. 1106-1113. doi: 10.1016/j.proeng.2011.07.139. [22] paris, p.c. and erdogan, f., (1963). a critical analysis of crack propagation laws, j. basic eng. trans. asme ser d, 85, pp. 528–534. [23] liua, j., qina, m., zhaob, q., chena, l., liub, p. and gao, j., (2017). fatigue performances of the cracked aluminumalloy pipe repaired with a shaped cfrp patch, j. thin-walled structures, 112, pp. 140–148. doi: 10.1016/j.tws.2016.11.008. [24] zarrinzadeh, h., kabir, m.z. and deylami, a., (2017). crack growth and debonding analysis of an aluminum pipe repaired by composite patch under fatigue loading, j. thin-walled structures, 112, pp. 140–148. doi: 10.1016/j.tws.2016.12.023. [25] da costa mattos, h.s., reis, j.m.l., paima, l.m., da silva, m.l., lopes junior, r. and perrut, v.a., (2016). failure analysis of corroded pipelines reinforced with composite repair systems, j. engineering failure analysis, 59, pp. 223– 236. doi: 10.1016/j.engfailanal.2015.10.007. [26] zarrinzadeh, h., kabir, m.z. and deylami, a., (2017). experimental and numerical fatigue crack growth of an aluminium pipe repaired by composite patch, j. engineering structures, 133, pp. 24–32. doi: 10.1016/j.engstruct.2016.12.011. [27] watanabe junior, m.m., reis, j.m.l. and da costa mattos, h.s., (2017). polymer-based composite repair system for severely corroded circumferential welds in steel pipes, j. engineering failure analysis, 81, pp. 135–144. doi: 10.1016/j.engfailanal.2017.08.001. [28] erdogan, f. and sih, g., (1963). on the crack extension in plates under plane loading and transverse shear, j. basic eng., 85, pp. 519–525. doi: 10.1115/1.3656897. [29] erdogan, f. and kibler, j., (1969). cylindrical and spherical shells with cracks, int. j. fract. mech., 5, pp. 229–286. doi: 10.1016/0029-5493(72)90031-3. [30] zahoor, a., (1985). closed form expressions for fracture mechanics analysis of cracked pipes, j. pressure vessel technol., 107, pp. 203–205. doi: 10.1115/1.3264435. [31] sanders, j. l., (1982). circumferential through-cracks in cylindrical shells under tension, j. appl. mech., 49, pp. 103– 107. doi: 10.1115/1.3161948. [32] forman, r., hickman, j. and shivaskumar, v., (1985). stress intensity factors for circumferential through cracks in hollow cylinders subjected to combined tension and bending loads, eng. fract. mech., 21, pp. 563–571. doi: 10.1016/s0013-7944(85)80049-7. [33] zárate, b. a., caicedo, j. m., yu, j. and ziehl, p., (2012). bayesian model updating and prognosis of fatigue crack growth, eng. struct., 45, pp. 53–61. doi: 10.1016/j.engstruct.2012.06.012. [34] abaqus standard user's manual, karlsson and sorensen, (2005). [35] eriksson, l., johansson, e., kettaneh-wold, n., wikström, c. and wold, s., (2000). design of experiments: principles and applications, stockholm, learnways ab, https://www.dynacentrix.com/telecharg/modde/livredoe.pdf. [36] modde 5.0, modelling and design, umetrics ab, umea, sweden. (1999). [37] abd-elhadya, a.a., sallama, h.e.m. and mubarakia, m.a., (2017). failure analysis of composite repaired pipelines with an inclined crack under static internal pressure, procedia structural integrity, 05, pp. 123–130. doi: 10.1016/j.prostr.2017.07.077. << /ascii85encodepages false /allowtransparency false /autopositionepsfiles true /autorotatepages /none /binding /left /calgrayprofile (dot gain 20%) /calrgbprofile (srgb iec61966-2.1) /calcmykprofile (u.s. web coated \050swop\051 v2) /srgbprofile (srgb iec61966-2.1) /cannotembedfontpolicy /error /compatibilitylevel 1.4 /compressobjects /tags /compresspages true /convertimagestoindexed true /passthroughjpegimages true /createjobticket false /defaultrenderingintent /default /detectblends true /detectcurves 0.0000 /colorconversionstrategy /cmyk /dothumbnails false /embedallfonts true /embedopentype false /parseiccprofilesincomments true /embedjoboptions true /dscreportinglevel 0 /emitdscwarnings false /endpage -1 /imagememory 1048576 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/hrv (za stvaranje adobe pdf dokumenata najpogodnijih za visokokvalitetni ispis prije tiskanja koristite ove postavke. stvoreni pdf dokumenti mogu se otvoriti acrobat i adobe reader 5.0 i kasnijim verzijama.) /hun 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can be opened with acrobat and adobe reader 5.0 and later.) >> /namespace [ (adobe) (common) (1.0) ] /othernamespaces [ << /asreaderspreads false /cropimagestoframes true /errorcontrol /warnandcontinue /flattenerignorespreadoverrides false /includeguidesgrids false /includenonprinting false /includeslug false /namespace [ (adobe) (indesign) (4.0) ] /omitplacedbitmaps false /omitplacedeps false /omitplacedpdf false /simulateoverprint /legacy >> << /addbleedmarks false /addcolorbars false /addcropmarks false /addpageinfo false /addregmarks false /convertcolors /converttocmyk /destinationprofilename () /destinationprofileselector /documentcmyk /downsample16bitimages true /flattenerpreset << /presetselector /mediumresolution >> /formelements false /generatestructure false /includebookmarks false /includehyperlinks false /includeinteractive false /includelayers false /includeprofiles false /multimediahandling /useobjectsettings /namespace [ (adobe) (creativesuite) (2.0) ] /pdfxoutputintentprofileselector /documentcmyk /preserveediting true /untaggedcmykhandling /leaveuntagged /untaggedrgbhandling /usedocumentprofile /usedocumentbleed false >> ] >> setdistillerparams << /hwresolution [2400 2400] /pagesize [612.000 792.000] >> setpagedevice microsoft word 2173 s. k. kourkoulis et alii, frattura ed integrità strutturale, 47 (2019) 247-265; doi: 10.3221/igf-esis.47.19 247 fracture and structural integrity: ten years of ‘frattura ed integrità strutturale’ analytical and numerical study of the stress field in a circular semi ring under combined diametral compression and bending stavros k. kourkoulis, ermioni d. pasiou, christos f. markides national technical university of athens, school of applied mathematical and physical sciences, department of mechanics, laboratory for testing and materials, 5, heroes of polytechnion avenue, zografou campus, theocaris building, 157 73, greece stakkour@central.ntua.gr, epasiou@teemail.gr, markidih@mail.ntua.gr abstract. the stress field developed in a circular semi-ring under the combined action of diametral compression and bending is explored both analytically and numerically. the analytic solution is implemented by means of the complex potentials technique as it was formulated by muskhelishvili, while for the numerical study a finite element model, properly validated based on experimental data, is used. the analytic solution provided closed formulae for the stress field along strategic loci of the specimen, while the numerical model permitted thorough parametric investigation of the dependence of critical quantities on geometrical and loading factors. the idea behind the study is to assess the potentialities of the circular semi-ring as a possible substitute of the familiar brazilian disc, in the direction of curing drawbacks of the latter. it was concluded that a circular semi-ring subjected to eccentric diametral compression provides reliable data for the tensile strength of very brittle materials, relieved from ambiguities characterizing the standardized brazilian-disc test. keywords. circular semi-ring; brazilian-disc test; tensile strength; complex potentials; finite element method; stress field. citation: kourkoulis s.k., pasiou e.d, markides ch.f., analytical and numerical study of the stress field in a circular semi-ring under combined diametral compression and bending, frattura ed integrità strutturale, 47 (2019) 247-265. received: 21.08.2018 accepted: 28.10.2018 published: 01.01.2019 copyright: © 2019 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. introduction he implementation of standardized uniaxial tensile tests, with specimens made of brittle materials (as for example various hard rocks and rock-like geomaterials), encounters insuperable difficulties, related mainly to local fragmentation of the specimens during gripping and, also, fracture of the specimens in the immediate vicinity of the gripping area (rendering the data of the tests unreliable, given that the stress field in these regions is not purely uniaxial). in an attempt to overcome the problem, the engineering community is long ago seeking for alternative configurations that could provide at least an estimation of the uniaxial tensile strength of very brittle structural materials. among the alternative configurations proposed, the one most widely accepted worldwide, is that of a circular disc compressed by diametral forces, t http://www.gruppofrattura.it/va/47/2173.mp4 s. k. kourkoulis et alii, frattura ed integrità strutturale, 47 (2019) 247-265; doi: 10.3221/igf-esis.47.19 248 c -p lower indenter upper indenter csrspecimen aβ d e e΄ d΄ y νcsr z aβ d e e΄ d΄ r θ-p pc -pc p y xo which is known as brazilian-disc test, honouring the brazilian engineer fernando carneiro [1] who was the first one that proposed the specific configuration as a substitute of the direct tension test, already since 1943 (almost simultaneously with the japanese engineer tsunei akazawa [2]). in spite of its wide acceptance (mainly due to the simplicity of the geometry of the specimens and of the experimental setup), the brazilian-disc test was strictly criticized almost immediately after it was introduced. the main points raising concerns about the validity of its outcome (and the relation of the quantity obtained with the tensile strength determined from a uniaxial tension test) are related to the fact that the stress field at the center of the disc is biaxial rather than uniaxial and, also, to the fact that (under specific conditions) fracture may originate from the immediate vicinity of the load application area (the vicinity of the points where the load is imposed) rather than from the center of the disc (rendering the validity of solutions [3-9] providing the “tensile strength” questionable [10-14]). in this direction, a variety of alternative configurations were gradually introduced, each one with its own pro and cons. among them one should mention the ring test [15, 16], the flattened brazilian-disc test [17] and the semi-circular bend test [18]. in the present study an alternative configuration is introduced, curing some drawbacks of previous attempts. the configuration proposed is that of a circular semi-ring (outer radius r2, inner radius r1, thickness 2h), which is loaded under compression, as it is shown in fig. 1a. the respective test will be denoted from here on as the circular semi-ring test (csr test). the main advantage of the specific test is that the stress field at the critical point a (i.e., the point at which fracture is expected to start) includes a single tensile component. in addition, the ratio between the maximum tensile stress (developed at point a) and the respective compressive one (developed at point b) is relatively easily controlled by the ratio ρ=r2/r1. moreover, the force required to cause fracture of the specimens is relatively low (compared to other more compact configurations). for the sake of generality, a non-zero eccentricity c of the applied load p, with respect to the vertical y-axis, has been considered (obviously, one can always assume c=0, simplifying significantly the analytic calculations). the similarity of the csr-configuration to the familiar arc-shaped notched tension specimen, proposed by astm [19] for the standardized determination of mode-i fracture toughness (astm e399-90 standard), is to be highlighted. (a) (b) figure 1: (a) the configuration proposed for the experimental implementation of the csr-test; (b) the ncsr configuration considered in the analytic solution of the problem. analytical considerations he stress field in the csr will be here obtained analytically by adopting muskhelishvili’s solution for a curved beam [20], assuming that the material of the csr is homogeneous, isotropic and linearly elastic. it is emphasized from the very beginning that, the configuration considered in the analytic solution of the problem (shown in fig. 1b) is somehow simplified compared to that of fig. 1a, which is, in fact, proposed for the laboratory implementation of the test. the configuration of fig. 1b will be denoted from here on as net circular semi-ring (ncsr), in order to be distinguished from that of fig. 1a. in this context, and taking into account the eccentricity c of the externally applied loading with respect to y-axis (which, for practical reasons, is very difficult to be avoided during the laboratory implementation of the experiments), the analytic solution deals with an ncsr, simultaneously subjected to bending by transverse forces –p, p and couples pc, –pc applied to its straight edges ed and e΄d΄ (fig. 1b). t s. k. kourkoulis et alii, frattura ed integrità strutturale, 47 (2019) 247-265; doi: 10.3221/igf-esis.47.19 249 in spite of the above mentioned difference between the csr-specimen and the ncsr-configuration, the theoretically predicted stresses in the vicinity of the critical cross-section ab (which is in fact the area of major interest for engineering applications) are expected to approach well the respective ones developed in the csr-specimen, provided that the width (w= r2-r1) of the ncsr is relatively small and that the resultant force and moment considered at its straight edges can efficiently replace the shaded parts of the csr-specimen (saint venant’s principle). as it will be seen by the comparative consideration of the results of the numerical and the analytical approaches, the above assumptions are well justified even in case the inner radius, r1, of the csr-specimen is equal to half of its outer one, r2. the analytic solution described in next sections is deduced from the respective one of the circular ring (cr) (in fact the ncsr is here considered as part of the cr [20]), under the admission of multi-valued displacements and the concept of dislocation, shortly recapitulated in the next paragraph. it is here recalled that the specific way of approaching this family of problems was first introduced by golovin [21] (together with a series of solutions for the problem of curved beams under various loading schemes). characteristics of the dislocation in this section a brief outline of the concepts of multi-valued displacements and dislocation will be given (together with a short description of the method adopted for obtaining the stress field in the ncsr through the solution of the respective cr problem), as they were analyzed in muskhelishvili’s milestone book [20]. in this context, a homogeneous, isotropic and linearly elastic cr, of inner and outer radii r1 and r2, respectively, is considered in equilibrium under an arbitrary in-plane loading scheme. assuming that the cross-section of the cr lies in the z=x+iy=reiθ plane, with its centre at the origin of the cartesian reference system, muskhelishvili’s general solution for the first fundamental problem for the cr is written as [20]: ( ) log , ( )k kk kz a z a z z a z           (1) the demand for the displacements to be single valued in the cr reads as [20]: 0, 0u u v v       (2) where u and v are the horizontal and vertical components of the displacement field, respectively, with (+), (–) indicating the two sides of a cut joining the outer and inner perimeters of the cr, converting it into a simply connected region (figs. 2 and 3). constants ak, ak΄ in eqs.(1) (excluding the imaginary part of a0 that remains arbitrary) are determined from the fulfillment of the boundary conditions for stresses and the following conditions, resulting from eqs.(2) [20]: 1 1 2 [(1 )(1 2 )], plane strain3 0, 0 , (1 ), plane stress e a a a e                         (3) in eqs.(3), e is the young’s modulus, ν the poisson’s ratio and μ the shear modulus. over-bar denotes the complex conjugate value. in case, now, multi-valued displacements are permitted in the cut cr, then instead of eqns. (2) it holds that [20]: ,u u y v v x             (4) in this context, the additional expressions, besides the boundary conditions, for obtaining ak, ak΄ of eqns. (1) (except the imaginary part of a0) are given (instead by eqns. (3)) by the following expressions [20]: 1 1 (1 ) , ( i ) i a a a                (5) in eqs.(4) and (5), ε (with dimensions of angle), and α, β (with dimensions of length), are arbitrary, infinitesimal, real constants, expressing the relative angle of rigid body rotation of the two sides of the cut about the origin, and the relative rigid s. k. kourkoulis et alii, frattura ed integrità strutturale, 47 (2019) 247-265; doi: 10.3221/igf-esis.47.19 250 +β<0 y xo cr cut along the negative x-axis overlapped parallel cut sides – -p p β>0 y xo cr cut along the negative x-axis gap between the parallel cut sides + – p -p ε>0 – + y xo cr cut along the negative x-axis overlapped radially cut sides pc -pc y xo cr cut along the negative x-axis gap between the radially cut sides + –ε<0 -pc pc body translation of the two sides of the cut along xand y-axis, respectively (figs. 2 and 3). the difference from the previous case (eqs.(2, 3)) is that by admitting the above multi-valued displacements in the cut cr, gaps or/and overlaps will appear (a) (b) figure 2: the nature of the β-dislocation and the resulting transverse forces for (a) negative and (b) positive values. (a) (b) figure 3: the nature of the ε-dislocation and the resulting couples for (a) positive and (b) negative values. between the sides of the cut, dictated by the values of ε, α and β and stresses will be developed within the cut cr, even in case of zero external forces. these stresses, due to ε, α and β (and not due to the application of some external loading scheme), are of particular interest in this study and will actually provide the stress field in the ncsr-configuration and in turn in the csr-specimen in question, at least approximately. before dealing with these stresses (as it is thoroughly described in next section), a few comments must be made for clarity on the nature of multi-valued displacements within the cut cr, which are due to muskhelishvili [20]. namely, it is mentioned that ε, α and β are the so-called “characteristics of the dislocation” (as named by love [22]) and it was timpe [23] who gave first a physical interpretation to these quantities in the case of the cr (later volterra [24] dealt with the general case of multiply connected regions). timpe [23] stated that even allowing multi-valued displacements, deformation can still be compatible assuming that one adds to (or/and removes from) the cut cr, strips of the same material, of dimensions ε, α and β and then rejoin the cut cr in one part. obviously, when ε, α and β are to cause a gap between the sides of the cut (figs. (2b, 3b)), a strip should be added between the sides of the cut and joined to them, whereas when ε, α and β are to cause overlapping of the sides of the cut (figs. (2a, 3a)), a strip should be removed from the sides of the cut and the generated new free sides of the cut should be brought into contact and joined together. in this way, the resulting cr will remain continuous after any actual deformation due to a non-zero external loading scheme, without gaps or overlaps, since the two sides of the cut will move as a single unit. the stress field in the ncsr due to the characteristics of the dislocation the next step is to return back to the initial problem, in order to describe the way the “characteristics of the dislocation” ε, α and β can provide the stress field in the csr-specimen. as it was mentioned in previous section, the stress field in the csr-specimen may (under certain conditions meeting saint venant’s principle) be provided approximately from the solution of the problem of the ncsr subjected simultaneously to transverse forces –p, p and couples pc, –pc at its straight s. k. kourkoulis et alii, frattura ed integrità strutturale, 47 (2019) 247-265; doi: 10.3221/igf-esis.47.19 251 edges ed and e΄d΄ (fig. 1b). on the other hand, as it will be shown below, suitable combinations of ε, α and β lead to effective solutions to the problems of the ncsr under transverse forces and couples at its straight edges, separately. in this context, two independent problems are considered next for the ncsr: (a) the problem of bending by transverse forces of magnitude p applied to its straight edges ed, e΄d΄ and (b) the problem of bending by couples of magnitude pc applied to its straight edges ed, e΄d΄. then within the framework of linear elasticity, the solution of the whole problem for the ncsr, approximating that of the csr, will be obtained by just superposing the solutions of these two problems. (a) bending of the ncsr by transverse forces applied to its straight edges assume that the cut cr is free from external forces and that ε=α=0 and β≠0. then the deformed cut cr would attain one of the configurations of fig. 2, depending on the sign of β, whereas stresses would occur in the cut cr due to β, given as [20]: 2 2 1 2 2 2 2 2 3 1 2 1 2 ( ) ( ) 1 1 cos ( 2 ) r r rr r r r r r r                   (6) 2 2 1 2 2 2 2 2 3 1 2 1 2 ( ) ( ) 1 3 1 cos ( 2 ) r rr r r r r r r                    (7) 2 2 1 2 2 2 2 2 3 1 2 1 2 ( ) ( ) 1 1 sin ( 2 ) r r rr r r r r r r                    (8) setting in eqns. (6-8) θ=±π/2, it is seen that the only non-zero stress-component on the cross-sections ed and e΄d΄of the cut cr is τrθ(β). moreover, integrating τrθ(β)2hdr over ed and e΄d΄, one can determine the transverse force acting on ed and e΄d΄ as follows [20]:    2 1 2 2 2 22 1 2 2 1 1 2 2 1 2 ( ) log 2 ( ) 2 2 d ( 2 ) r r r r r r r r h r p h r r r                      (9) then keeping from the cr the part between θ=±π/2, one obtains the ncsr configuration under transverse forces of magnitude p (p>0) at its straight edges ed and e΄d΄. moreover, as the fractions on the right-hand side of eqn.(9) are always positive, the sign of β will dictate the direction of p, and it is easily seen that for β<0, i.e., for (using eqn.(9)):   2 2 1 2 2 2 2 22 1 2 1 2 1 ( 2 ) 0 2 ( ) log r rp rh r r r r r                 (10) one arrives at the first problem in question for the ncsr under bending by transverse forces –p, p applied to its straight edges. (b) bending of the ncsr by couples applied to its straight edges assume that the cut cr is free from external forces and that ε≠0, α=β=0. in that case, the deformed cut cr would attain one of the configurations of fig. 3, depending on the sign of ε and stresses would appear in the cut cr due to ε, given as [20]: 2 2 2 2 1 2 2 2 2 1 1 2 2 2 2 2 12 1 2 1 ( ) ( ) log log1log log ( 2 ) r r r r r r r r r rr r r r r                   (11) 2 2 2 2 1 2 2 2 2 1 1 2 2 2 2 2 12 1 2 1 ( ) ( ) log log1log log 1 ( 2 ) r r r r r r r r rr r r r r                     (12) ( ) 0r   (13) s. k. kourkoulis et alii, frattura ed integrità strutturale, 47 (2019) 247-265; doi: 10.3221/igf-esis.47.19 252 from eqns. (11-13), it is immediately seen that by considering any isolated part of the cut cr, one has a curved beam, the only non-zero stress-component on the straight edges of which is σθ(ε). the distribution of that σθ(ε), attaining its extrema at the beam’s peripheries, is statically equivalent to counterbalancing couples at the beam’s straight edges of magnitude [20]:   2 1 2 22 2 2 2 2 2 1 1 2 1 2 2 2 1 ( ) 4 log ( ) 2 d 2 ( 2 ) r r r r r r r rh h r r r r                     (14) taking into account that according to the assumptions adopted this magnitude should be equal to pc, then equating eqn. (14) to pc and solving for ε, one obtains:   2 2 2 1 2 22 2 2 2 2 2 1 1 2 1 ( 2 )2 0 ( ) 4 log r rpc h r r r r r r                     (15) it is seen that for the above positive value of ε, and by considering the part of the cut cr between θ=±π/2, one obtains the second problem in question for the ncsr under bending by couples –pc, pc applied to its straight edges ed and e΄d΄. (c) the overall problem of the ncsr for bending by transverse forces and couples applied to its straight edges the overall stress field in the ncsr under transverse forces –p, p and couples pc, –pc at its straight edges ed and e΄d΄, approaching that of the csr-specimen, is given by superposing the respective stress components: σr=σr(β)+σr(ε) (eqns. (6, 11)), σθ=σθ(β)+σθ(ε) (eqns. (7, 12)) and τrθ=τrθ(β)+τrθ(ε) (eqns. (8, 13)), with β and ε given by eqs.(10, 15), respectively. it is mentioned that these stresses depend on the magnitude p of the transverse force, the eccentricity c, the ratio ρ=r2/r1, the thickness 2h of the csr, the loading conditions adopted (namely plane stress or plain strain), and, also, on the material (appearing in the expressions for the dislocations β, ε). it must be, also, mentioned that assigning to the parameters of the analysis arithmetic data corresponding to very brittle materials, the values calculated for β and ε (depending on the values of p and c considered) are extremely small, satisfying the principal assumptions governing the present study, i.e., the assumption of linear elasticity. effectiveness of the analytic solution the effectiveness of the analytic solution was assessed in terms of the data for the displacement field, as it was obtained from a recent experimental protocol [25]. csr-specimens made of pmma (e=3.2 gpa, ν=0.36) with 2h=10 mm, r1=25 mm, r2=50 mm, and c=6.25 mm were tested according to the scheme shown in fig. 1a. a 10 kn electromechanical frame was used to load the specimens and the displacement field was measured with the aid of the digital image correlation (dic) technique. the experimental set-up is shown in fig. 4a. all tests were quasi-static, implemented under displacement-control conditions, at a constant rate of 0.1 mm/min. a typical fractured specimen is shown in fig. 4b. during loading, series of successive photos of the specimens were taken permitting the determination of the displacement field by means of the software of the dic system. the experimental data for the displacements were then compared with the ones provided by the analytic solution (as it is analytically described by markides et al. [25]), which read as: (a) displacements due to bending of the ncsr by transverse forces applied to its straight edges   2 ( ) 2 2 1 2 2 2 2 1 2 2 2 22 2 1 21 2 ( ) 3 1 3 log 1 4 ( 2 ) 1 1 2 cos 2 2 r u r r r r r r r r rr r                                        (16) s. k. kourkoulis et alii, frattura ed integrità strutturale, 47 (2019) 247-265; doi: 10.3221/igf-esis.47.19 253 0.9 1.0 1.1 1.2 0 10 20 30 40 50 d is p la ce m en t a lo n g lo cu s a b , u x [m m ] r [mm] analytical solution dic data   2 22 ( ) 1 2 2 2 22 2 1 2 1 2 ( ) 3 1 3 1 1 1 sin 2 4 ( 2 ) 2 r rr v r r rr r                                   (17) (b) displacements due to bending of the ncsr by couples applied to its straight edges 2 2 ( ) 2 2 1 1 2 2 2 1 2 2 1 2 2 2 2 12 1 ( ) log log3 1 1 log cos 4 ( 2 ) 2 23 3 cos 1 sin cos log r r r r u r r r r r r r r r r rr r                                                     (18) 2 2 ( ) 2 2 1 1 2 2 2 1 2 2 1 2 2 2 2 12 1 ( ) log log3 1 1 log sin 4 ( 2 ) 2 23 3 sin 1 cos sin log r r r r v r r r r r r r r r r rr r                                                     (19) the results of the comparison are plotted in fig. 4c, in which the displacement ux≡u developed along the ab locus (see fig. 1a), is plotted according to both the analytic and the experimental data. the agreement is satisfactory almost all along the locus considered (which is, in fact the most crucial for practical applications), excluding a weak maximum recorded by the dic-system in the immediate vicinity of point b, which is not actually predicted by the analytic solution. (a) (b) (c) figure 4: (a) an overview of the experimental set-up; (b) a fractured csr specimen; (c) analytic versus experimental data for the displacement component developed along the critical locus ab. the stress field in the ncsr at some strategic points and along some critical loci of the csr in this paragraph the formulae obtained for the stress field in the ncsr are applied along some loci of particular practical (and engineering) interest. however, for a direct comparison between the data for the csrand the ncsr-configurations to be feasible, some preliminary remarks should be made. initially, one should consider the conditions related to the eccentric application of the compressive forces (fig. 1a) through the two cylindrical rods. let ro be the radius of the rods and assume that half of their profile is inserted into the respective congruent hollow cavity of the csr-specimen, at a given distance c on the left of y-axis (fig. 5). then, the points of contact of the csr with the indenters, corresponding to any specific eccentricity c, will be described as: s. k. kourkoulis et alii, frattura ed integrità strutturale, 47 (2019) 247-265; doi: 10.3221/igf-esis.47.19 254 -p upper indenter csrspecimen y d e ro θo θo c xo i / 2( )  cθ cr e ο ο 2 ο ο r r r θ θ -1 sintan cos rosinθo i (π/2 )e c± +c θz = r , 2 2 -1 -12 2 2 2 sin cos tan sin cos o o c o o o c o o o o r θ c r = r + r 2r r θ , θ =θ + , θ = r r θ r       (20) figure 5: the procedure adopted to specify the contact point i ( /2 )e ccz r   . moreover, it is noted that during the experimental implementation of the csr-test (as well as in the numerical model that will be described in next sections, which reproduces accurately the experimental procedure) both rods are restricted concerning their motion in the horizontal direction. in addition, the lower rod is fixed also concerning its vertical motion (i.e., it is assumed completely fixed, without any degree of freedom) and a vertical displacement vp is imposed to the csr-specimen, with the aid of the upper rod. on the contrary, in the analytic study, diametral compressive forces p and couples pc are imposed on both vertical edges of the ncsr. obviously, for comparison reasons, the magnitude of these forces and couples must produce a vertical displacement equal to (1/2)vp to the points where they are applied. in this direction, advantage is taken of the above mentioned formulae for the displacement field in the ncsr. more specifically, the ncsr is ideally extended to the csr-configuration with the supporting parts shown shaded in fig. 1a. the contact points i ( /2 )e ccz r    , mentioned previously, are assumed lying on the shadowed parts (which is always true since ncsr is part of the whole cut cr, to which the analytic solutions obtained before refer to). then, in accordance with the experimental procedure (and the respective numerical models), point i ( /2 )e ccz r    must be completely fixed while point +i ( /2 )e ccz r   must be fixed only in the x-direction. for this to be achieved one should subtract from the analytically determined displacement field the respective displacements of the points i ( /2 )e ccz r    , considering them as rigid-body ones. as a next step, the experimental/numerical value of vp must be introduced in the expression for the vertical displacement v of point +i ( /2 )e ccz r   providing the magnitude of the force p, corresponding to the specific value of vp. then, inserting this value of p (as well as the proper value of c, i.e., the value matching the experimental/numerical configuration), into eqs.(10, 15), ε and β and in turn the theoretical stresses (eqs.(6-8) and eqs.(11-13)) in the ncsr are obtained, in a manner comparable to the experimental and numerical ones for the csr-specimen. in this context, and in order for some features of the analytical solution to be quantitatively enlightened, an ncsr made of pmma (e=3.2 gpa, ν=0.36) is here considered with c=10 mm and vp=3 mm (corresponding to the data of the experimental protocol discussed previously and to the numerical models that will be described next). the force corresponding to these data (i.e., the force that has to be introduced in the analytic formulae for the stress field) is determined equal to p=1188.3 n for plane strain conditions and to p=994.5 n for plane stress ones. s. k. kourkoulis et alii, frattura ed integrità strutturale, 47 (2019) 247-265; doi: 10.3221/igf-esis.47.19 255 -80 -40 0 40 80 0 10 20 30 40 50 σ θ [m p a] r [mm] 0.7 0.5 0.3 0.1 r2/r1 = 1.43 2.00 3.33 10.0 a b ab adopting the above values the stress components at the two critical points of the configuration (namely points a(r2,0) and b(r1,0)) are calculated equal to: ‐ σθ(r2,0)=39.97 mpa, σθ(r1,0)= –75.98 mpa, for plane strain, ‐ σθ(r2,0)=33.45 mpa, σθ(r1,0)= –63.59 mpa, for plane stress. the ratio of the two stresses is equal to:     1 2 2 1 , 0 1.9, for 2 , 0 r r r r         (21) in other words, the ratio of the maximum compressive stress developed over the respective maximum tensile one, in a csr with ρ=2, is less than 2. compared to the respective ratio of the brazilian disc test, which at the center of the disc is equal to 3, one of the major advantages of csr-specimen is highlighted, since the csr-test can be used in a broader variety of materials concerning the ratio of compressive over tensile strength. regarding now the contribution of each one of the two constituent components (transverse forces and bending moments) of the overall stress field, it can be determined that for plane strain conditions it holds that: contribution of transverse forces, –p, p (β-dislocation): σθ(β)(r2,0)=30.62 mpa, σθ(β)(r1,0)= –61.24 mpa, ‐ contribution of couples, –pc, pc (ε-dislocation): σθ(ε)(r2,0)= 9.35 mpa, σθ(ε)(r1,0)= –14.74 mpa, while for plane stress it holds that: ‐ contribution of transverse forces, –p, p (β-dislocation): σθ(β)(r2,0)=25.62 mpa, σθ(β)(r1,0)= –51.25 mpa, ‐ contribution of couples, –pc, pc (ε-dislocation): σθ(ε)(r2,0)= 7.82 mpa, σθ(ε)(r1,0)= –12.34 mpa. in both cases (plane strain plane stress), it is determined that: point a: σθ(β)(r2,0) =0.77σθ(r2,0), σθ(ε)(r2,0)=0.23 σθ(r2,0), point b: σθ(β)(r2,0) =0.81σθ(r2,0), σθ(ε)(r2,0)=0.19 σθ(r2,0). in addition, for either plane strain or plane stress, it holds that: bending by transverse forces, –p, p (β-dislocation):     ( ) 1 2 ( ) 12 , 0 2 , 0 r r rr           , bending by couples, –pc, pc (ε-dislocation):     2 2 2 2 ( ) 2 1 2 1 1 ( ) 2 2 2 22 2 1 1 1 2 log , 0 1.58 , 0 2 log r r r r r r rr r r r r             . figure 6: the distribution of the transverse normal stress along the axis of symmetry (locus ab) of the csr for various ρ-values. s. k. kourkoulis et alii, frattura ed integrità strutturale, 47 (2019) 247-265; doi: 10.3221/igf-esis.47.19 256 as it has been already mentioned, the ratio of the maximum compressive stress developed in a csr over the respective maximum tensile one is controllable by a geometric parameter, namely the ratio ρ=r2/r1 of the specimen’s radii. in order to quantitatively explore this issue, the variation of the transverse stress, σθ, along the locus ab, is plotted in fig. 6, for a series of values of the ratio ρ, within the 1.43<ρ<10.00 range. it is seen from fig. 6 that, the transverse stress is tensile (as it is expected) at the outermost point a of the locus ab and its value gradually decreases as one moves towards the innermost point b. at a given r-value (r1<r<r2) (which is not constant but rather it depends on ρ), the stress is zeroed and then it becomes compressive of continuously increasing magnitude. as the csr becomes thinner (i.e., for r1 approaching r2) the ratio of the maximum stresses at points a and b tends to 1. obviously, testing specimens with ρ-values approaching unity is difficult; however, the fact that the maximum compressive stress developed is somehow controllable offers a serious advantage to the csr-test against the standardized brazilian-disc test for which such a control is not possible. numerical modeling s a next step, and in order to parametrically explore various aspects of the stress field, developed in a csr-specimen under eccentric diametral compression, the finite element method is employed. in this direction, the commercially available software ansys (v.11) was used. the problem is studied in three dimensions and every effort was paid to properly simulate the configuration of fig. 1a, i.e., the one proposed for the laboratory implementation of the csr-test. a csr with r1=25 mm, r2=50 mm and thickness 2h=10 mm (figs. 1a and 7a) was considered as the reference model of the numerical study. in this context, two cylindrical rods were also constructed and placed in circular grooves (of the same diameter with that of the rods) at a distance equal to c=10 mm from y-axis. all nodes of the lower cylinder were rigidly fixed and a vertical downwards displacement vp=3 mm was imposed on the nodes of the upper cylinder, the motion of which normally to y-axis is restricted. the specific value of the displacement imposed ensures that the material remains within its elastic regime during loading, as it has been indicated by a preliminary experimental protocol [25]. the mechanical properties assigned to the material of the csr-specimen are those of pmma (following the respective assignment of the analytical study, i.e., e=3.20 gpa, ν=0.36). the two load transferring cylinders were assumed to be made of steel (er=210 gpa, νr=0.3). pmma was modeled as linearly elastic material, taking into account that the csr-test is proposed for the determination of the tensile strength of brittle geomaterials, the mechanical response of which is properly described within the frame of linear elasticity. moreover, taking into account that the load required to cause fracture of a csr-specimen is very small, compared to that causing yield of the rods, steel was also modeled as a linearly elastic material. (a) (b) figure 7: (a) the three dimensional numerical model properly meshed with 155000 elements; (b) the dependence of the horizontal displacement ux≡u of point a on the number of elements used for meshing the numerical model. a s. k. kourkoulis et alii, frattura ed integrità strutturale, 47 (2019) 247-265; doi: 10.3221/igf-esis.47.19 257 convergence and validation of the numerical model solid185 element was used for meshing the model. the optimum element size was chosen after a proper convergence analysis. initially, the horizontal displacement of point a was taken into account. its dependence on the number of elements of the mesh is plotted in fig. 7b. it is seen that using models with about 150000 elements offers a satisfactory compromise between accuracy and cpu-time consumption. in fact, the reference model finally used (shown in fig. 7a) consists of about 155000 elements. the quality of convergence was further checked by considering the dependence of critical quantities along critical paths instead of single points. as such a path the locus ab was chosen. the variation of the maximum principal stress σ1 along ab is plotted in fig. 8 for models with increasing number of elements. it is seen that the differences between the models are worth noticing only in the immediate vicinity of point b and, also, at the point where the value of σ1 changes sign. again it is verified that models with about 150000 elements offer quite satisfactory accuracy. for the validation of the numerical model to be achieved, the results of the reference model with 155000 elements, concerning the displacement field, are compared against the respective ones recorded during a recently implemented experimental protocol [25]. attention is again focused to the critical path ab. the results for the horizontal displacement component are plotted in fig. 9. it can be seen that, from a qualitative point of view, the agreement is excellent; the two curves (numerical and experimental) match almost perfectly to each other. from a quantitative point the difference between numerical and experimental data is less than 20 μm. in other words, the experimental data exceed the respective numerical ones by less than 2%, all along the locus considered. taking into account the very small magnitude of the experimentally measured quantities, the agreement between numerical and experimental data can be safely considered as excellent. figure 8: the dependence of the maximum principal stress σ1, developed along the ab locus, on the number of elements used for meshing the reference model. figure 9: the horizontal component of the displacement field ux≡u developed along the ab locus determined numerically in juxtaposition to the respective one experimentally measured using the dic technique [25]. s. k. kourkoulis et alii, frattura ed integrità strutturale, 47 (2019) 247-265; doi: 10.3221/igf-esis.47.19 258 parametric analysis with the aid of the validated numerical model having the model validated, it is now possible to determine the distribution of any mechanical quantity, like stress or strain or displacement all over the volume of the csr-specimen, for any combination of the geometrical and loading parameters, as well as for any material of the csr-loading rods complex. as a first example, the distribution of displacements (both horizontal and vertical) in a csr with ρ=2.0 is shown in fig. 10, for a common externally imposed vertical displacement equal to 3.0 mm. as a second example the distribution of the von mises equivalent stress is plotted in fig. 11 for two different csr-specimens with ρ=2.0 and ρ=10.0, again for a common externally imposed displacement, equal now to 0.8 mm. besides highlighting the capabilities of the numerical model, fig. 11 vividly emphasizes the crucial role of the parameter ρ, on the overall distribution of the stress field in a csr-specimen, from both the qualitative and the quantitative points of view. it is worth mentioning that for r1 tending to zero (i.e., for very high ρ-values) the stress field starts resembling that of a circular disc with a small central hole and the contours of constant equivalent stress obtain the familiar form of the von mises plastic enclave, surrounding a discontinuity in the form of circular hole in an infinite plate under compression [26]. (a) (b) figure 10: the distribution of the (a) horizontal(ux≡u, upper scale) and the (b) vertical(uy≡v, lower scale) displacement components for a csr with ρ=2.0 for a common externally imposed displacement equal to 3.0 mm (scales in m). (a) (b) figure 11: the distribution of the von mises equivalent stress for a csr with (a) ρ=2.0 (corresponding to the upper scale) and (b) ρ=10.0 (corresponding to the lower scale), for a common externally imposed displacement equal to 0.8 mm (scales in pa). s. k. kourkoulis et alii, frattura ed integrità strutturale, 47 (2019) 247-265; doi: 10.3221/igf-esis.47.19 259 y = 0.793x-0.832 r² = 0.9993 0 0.2 0.4 0.6 0.8 0 3 6 9 12 |σ θ, α /σ θ, b | ρ 0 10 20 30 40 0 3 6 9 12 σ θ ,α [m p a] ρ ab a ab ab the as above validated numerical model is now used to explore the role of some critical parameters on the stress field developed in csr-specimens. two parameters are considered in this first attempt, namely, the inner radius of the ring, r1, and the horizontal distance of the load transferring rods from y-axis (in other words the eccentricity of the load applied). the values assigned to these parameters are recapitulated in table 1 (bold numbers correspond to the reference model). the outer radius and the thickness of the ring are assumed constant equal to r2=50 mm and 2h=10 mm, respectively. from here on, for comparison reasons, a common vertical downwards displacement is imposed on the nodes of the upper load transferring rod, equal to vp=3 mm, in all cases. parameter values r1 [mm] 5 15 25 35 c [mm] 7.5 10.0 12.5 15.0 table 1: the numerical values assigned to the parameters studied in the numerical analysis. the crucial role of the inner radius of the csr on the respective stress field is clearly highlighted in fig. 12, in terms of the ρ=r2/r1 ratio. in fig. 12a the tensile stress, σθ,α, developed at point a (namely the stress value, which at the fracture of the specimens is assumed to correspond to the tensile strength of the specimen’s material) is plotted versus ρ. it is observed that, for ρ-values lower than ρ=3.0 the specific stress component increases steadily with increasing ρ. on the contrary, for ρvalues exceeding ρ=3.0, the value of σθ,α tends to be stabilized at a value equal to about σθ,α≈36 mpa. the dependence of the magnitude of the ratio of the maximum tensile stress over the respective compressive one, i.e., of the ratio of the stresses developed at points a and b, is plotted in fig. 12b, again versus the ρ-ratio. it is observed that the relation of the ratio of maximum stresses and the ratio of the radii is excellently described by a power law, almost all over the range of ρ-values considered here. (a) (b) figure 12: the dependence of the (a) maximum tensile stress and (b) the ratio of the maximum tensile stress over the respective compressive one, on the values of the radii ratio ρ. in fig. 13 the polar distribution of the transverse stress σθ, along the outer perimeter of the csr (i.e., along the locus e΄ae, marked green in the sketch embedded in fig. 13) is plotted for four different values of the ρ-ratio. it is observed that for high ρ-values the specific stress component is positive (i.e., of tensile nature) almost all along the csr’s outer perimeter. for example, for ρ=10.0 no compressive stress appears for the whole range of θ-values (-90ο<θ<90ο). gradually, with decreasing ρ, stresses of compressive nature appear also. the angle θ, at which the transverse stress is zeroed, strongly depends on ρ. it is, also, worth noticing from fig. 13 that, for high ρ-values, the distribution of σθ, is characteristically flat almost all along the outer perimeter of the csr. it is mentioned, for example, that for ρ=10.0 the value of σθ varies in a relatively narrow s. k. kourkoulis et alii, frattura ed integrità strutturale, 47 (2019) 247-265; doi: 10.3221/igf-esis.47.19 260 -20 0 20 40 -90 -60 -30 0 30 60 90 σ θ [m p a] θ [deg] 0.7 0.5 0.3 0.1 r2/r1 = 1.43 2.00 3.33 10.0 f e θ x y y α x ε ε΄ interval from about 37 mpa at θ=0ο to about 30 mpa for θ=60o. this flatness is lost with decreasing ρ-values and the distribution of the transverse normal stress tends to obtain a bell-shaped form. figure 13: the polar distribution of the transverse normal stress along the outer perimeter of the csr for various ρ-values. (a) (b) figure 14: (a) the variation of the transverse stress along locus ab for four different values of the eccentricity c (in mm); (b) the dependence of the maximum tensile stress (i.e., the stress developed at point a) on eccentricity c. the next parameter studied is the eccentricity, c, of the pair of compressive forces loading the csr-specimen. to explore its role, the variation of the transverse stress, σθ, along the critical locus ab is plotted in fig. 14a, for four different values of c within the 0.015r2<c<0.030r2 range (or, alternatively, in the 7.5 mm<c<15.0 mm range). it can be observed from this figure that, with increasing c-values, the magnitude of the maximum tensile stress developed (i.e., that at point a) decreases (recall that the loading scheme consists of a constant vertical displacement imposed on the upper cylindrical rod) and the same is true for the magnitude of the maximum compressive stress (i.e., the one developed at point b). in other words, s. k. kourkoulis et alii, frattura ed integrità strutturale, 47 (2019) 247-265; doi: 10.3221/igf-esis.47.19 261 -20 0 20 40 -90 -60 -30 0 30 60 90 σ θ [m p a] θ [deg] f e θ x y y α x ε ε΄ c = 7.5 10.0 12.5 15.0 the slope of the plot is reduced with increasing c. moreover, it is to be highlighted that all plots share a common point at about r=0.8r2 for all values of c. on the other hand, the point at which the transverse stress, σθ, is zeroed, appears depending (though very slightly) on the value of the parameter c. the influence of c on the magnitude of the maximum tensile stress developed (i.e., the quantity of utmost practical importance) is more vividly shown in fig. 14b: at least for the range of c-values studied here, the relation between σθ,max≡σθ,α and c is perfectly linear. from a quantitative point, increasing the value of c by a factor of 2, i.e., by 100% (from 7.5 mm to 15.0 mm), results to a decrease of σθ,max from about 31.3 mpa to about 26.5 mpa, or in other words only by about 15%, indicating the rather minor influence of c on the quantity of importance (i.e., on σθ,α). in fig. 15 the polar distribution of the transverse stress σθ, along the outer perimeter of the csr (i.e., along the locus e΄αε, marked green in the sketch embedded in fig.15) is plotted for four different values of the eccentricity (the same with the ones considered in previous paragraph). all four curves are quite similar to each other with minor differences, of only quantitative nature. these differences are more or less negligible for the major portion of the range of θ considered and only for θ-values approaching ±90o do these differences increase significantly. all plots share two common points, symmetric with respect to the θ=0o line, located at about θ=±48ο. figure 15: the polar distribution of the transverse normal stress along the outer perimeter of the csr for various c-values (in mm). discussion and concluding remarks n alternative configuration for the laboratory determination of the tensile strength of brittle materials was proposed, consisting of a circular semi-ring (csr) subjected to diametral compression, either centrally or slightly eccentrically. the configuration is proposed as a possible substitute of the familiar standardized brazilian-disc test (bdt), taking into account severe criticism against it, concerning the validity of its results and the relation of its outcome with the actual tensile strength as it is obtained from a direct tension test [3-5]. an analytic solution was introduced for the stress field developed in the csr, based on the solution for the cut circular ring, following the approach introduced by golovin [21] and muskhelishvili [20]. the solution was checked against experimental data and the agreement was found very satisfactory. a three dimensional numerical model was then designed that permitted parametric exploration of the role of some geometrical and loading parameters on the distribution of stresses and their magnitude along various critical paths and strategic points of the csr-specimens. the data of the numerical model are here considered in juxtaposition to the respective ones of the analytic solution. this is achieved by plotting the transverse normal stress σθ along the critical path ab, according to both approaches (numerical and analytical). the plots are implemented for the reference model (r1=25 mm, r2=50 mm, 2h=10 mm) and the results are exhibited in next fig. 16. it is clear that the two approaches are extremely close to each other all along the locus considered. the maximum discrepancy is observed at r=50 mm (i.e., at point a) and it does not exceed 7%. a s. k. kourkoulis et alii, frattura ed integrità strutturale, 47 (2019) 247-265; doi: 10.3221/igf-esis.47.19 262 -80 -40 0 40 25 30 35 40 45 50 σ θ [m p a] r [mm] numerical model analytical solution a b ab the main advantage of the csr-configuration (compared to the bdt one) is that the stress field, at the point of expected fracture (namely point a in fig. 1a), includes a single component of tensile nature. therefore, by determining the force, fp , required to cause fracture of a csr-specimen of given geometry, one can determine the respective stress at point a, which can be assumed as representing the tensile strength of the specimen’s material. figure 16: the distribution of the transverse normal stress along the critical locus ab, according to the analytical solution and the data provided by the numerical model (for the reference configuration). according to the results of the theoretical analysis described in previous sections, this critical stress is given as:     2 2 2 2 2 1 1 2 2 1 2 1 2 2 2 2 2 2 22 2 2 2 2 2 1 2 1 21 2 1 2 11 2 2 log log4 log fultimate tensile r c r r r p r r r h rr r r r r rr r r r rr                               (22) considering a csr with ρ=2 and c=0.2r2 the above equation is rewritten in terms of the outer radius, r2, of the csr as:  2 2 fultimate tensile csr p k r h     (23) where kcsr is a numerical constant, depending on the pair of parameters ρ and c. for the above considered numerical values (i.e., ρ=2 and c=0.2r2, it holds that kcsr=16.812). at this point, it is worth highlighting that, eqn. (23) closely resembles the formula proposed by mellor and hawkes [14] for the tensile stress developed at the intersection of the loading diameter of a circular ring under diametral compression with the ring’s inner boundary (which when the force applied causes fracture is, also, supposed to provide the tensile strength of the ring’s material). this formula reads as:   f fultimatetensile circular ringcircular ring p p k k rt rt     (24) where, according to mellor and hawkes, k is a numerical constant (depending on the ratio of the ring’s radii), t is the ring’s thickness (it is recalled that, according to the notation of the present study, t≡2h) and r its outer radius. the above statement, i.e., that the csr-test can successfully provide the tensile strength of the specimen’s material, was experimentally assessed by submitting a number of csr-specimens (r1=25 mm, r2=50 mm, 2h=10 mm), made of pmma, to diametral compression. the average fracture force, pf, of all successful tests of that protocol was equal to s. k. kourkoulis et alii, frattura ed integrità strutturale, 47 (2019) 247-265; doi: 10.3221/igf-esis.47.19 263 about pf=1.79 kn. substituting this value of pf into eqn. (22), the maximum tensile stress at point a (in other words the tensile strength of the csr’s material) was calculated equal to about 60.2 mpa. a preliminary protocol of direct tension tests with standardized dog-bone specimens (of the same batch from which the csr-specimens were cut), provided a value for the tensile strength of the material equal to about 58.8 mpa, i.e., only 2.4% lower than that determined with the aid of the csr-test. on the other hand, a series of tests with compact discs (again made of the same batch of material and having diameter 2r equal to 100 mm and thickness t equal to 10 mm) subjected to brazilian disc test [1, 2], in accordance with the isrm suggestion, provided a fracture force equal to pbr=87.65 kn. adopting hondros’ familiar formula [3], the respective tensile strength is calculated equal to σbr=p/(πrt)=55.8 mpa, i.e., 5.1% lower than the value provided by the direct tension tests. the above mentioned inconsistency, between the data of the direct tension test and the csr-test, even though it is relatively small, could be justified by taking into account the role of another parameter (which was ignored up to this point), namely the thickness of the csr-specimens. in fact, the specimens tested in the experimental protocol had a thickness of 10 mm. they were neither very thin (plane stress) nor very thick (plane strain) for obvious practical reasons. the role of the specific parameter cannot be analytically explored (the analysis described is not actually three dimensional and the configurations considered must be characterized either as plane stress or plane strain). inevitably testing specimens of moderate thickness introduces some discrepancies. in this context, the role of thickness is here explored by taking advantage of the numerical model (previously validated), and more specifically of the respective reference configuration. in fig. 17a the variation of the horizontal displacement ux≡u along the axis of symmetry of the csr-specimen (locus ab) is plotted for both the front face (identical to the rear one) and the central section of the three dimensional numerical model. the difference between the two plots are by no means negligible, however, it is almost constant all along the locus considered. in the same figure the results of the analytical solution for the variation of ux≡u along locus ab are plotted, assuming either 2d-plane stress or 2d-plane strain conditions. the difference between the two cases is, now, not constant along the ab locus. it is zeroed for r=25 mm (inner contour of the csr) and increases gradually until r≈35 mm. then it starts decreasing until r=50 mm (outer contour of the csr). the respective plots for the transverse stress developed along the ab locus are exhibited in fig. 17b. as it is, perhaps, expected, the difference for the stresses between the central section and the two surface faces of the three dimensional numerical model are negligible. on the contrary, the difference between the plane strain and the plane stress assumptions is quite considerable, approaching 13% at points a and b (the points at which the maximum difference is observed). more specifically, the maximum tensile stress (i.e., that at point a) is equal to about 29.7 mpa for the 2d-plane stress scheme, while for the respective 2d-plane strain scheme it is equal to about 33.6 mpa. 1.000 1.025 1.050 1.075 1.100 25 30 35 40 45 50 u x [m m ] r [mm] 3d_central 3d_front 3d_back 2d_plane stress 2d_plane strain ab ab -80 -40 0 40 25 30 35 40 45 50 σ θ [m p a] r [mm] 3d_central 3d_front 3d_back 2d_plane stress 2d_plane strain ab ab (a) (b) figure 17: the variation of (a) the horizontal displacement ux≡u and (b) the normal transverse stress along the ab locus, according to the reference configuration of the numerical model, assuming either three dimensional conditions (the plots are realized for both the front and rear surfaces and also the central section) or two dimensional conditions (plane stress and plane strain). s. k. kourkoulis et alii, frattura ed integrità strutturale, 47 (2019) 247-265; doi: 10.3221/igf-esis.47.19 264 the above analysis clearly indicates that the thickness of the csr-specimens plays an important role, which should not be ignored in case the csr-test is to be used for the determination of the tensile strength. given that the analytic solution cannot be applied for intermediate states between plane-stress and plane-strain conditions, eqs.(22, 23) must be handled with caution. research in progress [27] aims to provide correction factors, following a hybrid analytic-numerical approach. coming to an end, it can be safely stated that the csr-test is indeed a flexible alternative for the determination of the tensile strength of brittle materials, the potentialities of which should be further explored, both experimentally (for specimens made of rocks and rock-like materials) and numerically (in the direction of quantifying the role of additional parameters). references [1] carneiro, f. l. l. b. (1943). a new method to determine the tensile strength of concrete, proc. 5th meeting of the brazilian association for technical rules, 3d. section, 16 september 1943, pp. 126–129 (in portuguese). [2] akazawa, t. (1943). new test method for evaluating internal stress due to compression of concrete (the splitting tension test) (part 1), j. japan soc. civil engrs, 29, pp. 777–787. [3] hondros, g. (1959). the evaluation of poisson’s ratio and the modulus of materials of a low tensile resistance by the brazilian (indirect tensile) test with particular reference to concrete, aust. j. appl. sci., 10, pp. 243–268. [4] markides, ch. f., pazis, d.n., kourkoulis, s. k. (2010). closed full-field solutions for stresses and displacements in the brazilian disk under distributed radial load, int. j. rock mech. min. sci, 47(2), pp. 227–237. [5] markides, ch. f., kourkoulis, s. k. (2012). the stress field in a standardized brazilian disc: the influence of the loading type acting on the actual contact length, rock mech. rock eng, 45(2), pp. 145–158. [6] kourkoulis s. k., markides, ch. f., chatzistergos, p. e. (2012). the brazilian disc under parabolically varying load: theoretical and experimental study of the displacement field, int. j. solids struct., 49(7-8), pp. 959–972. [7] markides, ch. f., pazis, d.n., kourkoulis, s. k. (2010). the brazilian disc under non uniform distribution of radial pressure and friction, int. j. rock mech. min. sci, 50, pp. 47–55. [8] kourkoulis, s. k., markides, ch. f., hemsley, j. a. (2013). frictional stresses at the disc-jaw interface during the standardized execution of the brazilian disc test, acta mechanica, 224(2), pp. 255–268. [9] kourkoulis, s. k., markides, ch. f., chatzistergos, p. e. (2012). the standardized brazilian disc test as a contact problem, int. j. rock mech. min. sci, 57, pp.132–141. [10] hobbs, d. w. (1964). the tensile strength of rocks, int. j. rock. mech. min. sci., 1, pp. 385–396. [11] fairhurst, c. (1964). on the validity of the ‘brazilian’ test for brittle materials, int. j. rock mech. min. sci., 1, pp. 535–546. [12] hobbs, d. w. (1965). an assessment of a technique for determining the tensile strength of rock, brit. j. appl. phys., 16, pp. 259–268. [13] hooper, j. a. (1971). the failure of glass cylinders in diametral compression. j. mech. phys. solids, 19, pp. 179–200. [14] mellor, m., hawkes, i. (1971). measurement of tensile strength by diametral compression of discs and annuli, eng. geol., 5, pp. 173–225. [15] ripperger, e., davis, n. (1947). critical stresses in a circular ring (paper no 2308), trans. am. soc. civil engrs, 112, pp. 619–627. [16] jaeger, j.c., hoskins, e. r. (1966). stresses and failure in rings of rock loaded in diametral tension or compression. brit. j. appl. phys., 17, pp. 685–692. [17] wang, q. z., jia, x. m., kou, s. q., zhang, z. x., lindqvist, p. a. (2004). the flattened brazilian disc specimen used for testing elastic modulus, tensile strength and fracture toughness of brittle rocks: analytical and numerical results. int. j. rock mech. min. sci., 41(2), pp. 245–253. [18] kuruppu, m. d., obara, y., ayatollahi, m. r., chong, k. p., funatsu, t. (2014). isrm-suggested method for determining the mode i static fracture toughness using semi-circular bend specimen. rock mech rock eng, 47(1), pp. 267–274. [19] astm e399 90 (1997). standard test method for plane-strain fracture toughness of metallic materials a5. special requirements for the testing of the arc-shaped tension specimen. [20] muskhelishvili, n. i. (1963). some basic problems of the mathematical theory of elasticity, noordhoff, groningen. [21] golovin, kh. (1882). a static problem of the elastic body. minutes of the technological institute, st. petersburg, 1880-1881, st. petersburg. [22] love, a. e. h. (1927). a treatise on the mathematical theory of elasticity, 4th ed., cambridge, 1927. s. k. kourkoulis et alii, frattura ed integrità strutturale, 47 (2019) 247-265; doi: 10.3221/igf-esis.47.19 265 [23] timpe, a. (1905). probleme der spannungsverteilung in ebenen systemen, einfach gelöst mit hilf der airyschen function, zeitschrift für mathematik und physik, 52, pp. 348–383. [24] volterra, v. (1907). sur l' équilibre des corps élastiques multiplement connexes. annales scientifiques de l' éqole normale supérieure, 24, pp. 401–517. [25] markides, ch. f., pasiou, e. d., kourkoulis, s. k. (2018), a preliminary study on the potentialities of the circular semi-ring test, by procedia structural integrity, 9, pp. 108–115. [26] pazis, d. n., agioutantis, z., kourkoulis s. k. (2011). the optical method of reflected caustics applied for a plate with a central hole: critical points and limitations, strain, 47(6), pp. 489–498. [27] kourkoulis, s. k., pasiou, e. d., markides, ch. f. 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/hrv (za stvaranje adobe pdf dokumenata najpogodnijih za visokokvalitetni ispis prije tiskanja koristite ove postavke. stvoreni pdf dokumenti mogu se otvoriti acrobat i adobe reader 5.0 i kasnijim verzijama.) /hun 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can be opened with acrobat and adobe reader 5.0 and later.) >> /namespace [ (adobe) (common) (1.0) ] /othernamespaces [ << /asreaderspreads false /cropimagestoframes true /errorcontrol /warnandcontinue /flattenerignorespreadoverrides false /includeguidesgrids false /includenonprinting false /includeslug false /namespace [ (adobe) (indesign) (4.0) ] /omitplacedbitmaps false /omitplacedeps false /omitplacedpdf false /simulateoverprint /legacy >> << /addbleedmarks false /addcolorbars false /addcropmarks false /addpageinfo false /addregmarks false /convertcolors /converttocmyk /destinationprofilename () /destinationprofileselector /documentcmyk /downsample16bitimages true /flattenerpreset << /presetselector /mediumresolution >> /formelements false /generatestructure false /includebookmarks false /includehyperlinks false /includeinteractive false /includelayers false /includeprofiles false /multimediahandling /useobjectsettings /namespace [ (adobe) (creativesuite) (2.0) ] /pdfxoutputintentprofileselector /documentcmyk /preserveediting true /untaggedcmykhandling /leaveuntagged /untaggedrgbhandling /usedocumentprofile /usedocumentbleed false >> ] >> setdistillerparams << /hwresolution [2400 2400] /pagesize [612.000 792.000] >> setpagedevice http://dx.medra.org/10.3221/igf-esis.04.02&auth=true http://www.gruppofrattura.it http://www.gruppofrattura.it shot peening processes to obtain nanocrystalline surfaces in metal alloys: f. stochino et alii, frattura ed integrità strutturale, 46 (2018) 216-225; doi: 10.3221/igf-esis.46.20 216 design of civil environmental engineering assessment of rc bridges integrity by means of low-cost investigations flavio stochino, maria luisa fadda, fausto mistretta department of civil environmental engineering and architecture university of cagliari fstochino@unica.it, http://orcid.org/00000002-0786-9070 mary.fadda@tiscali.it fmistret@unica.it, http://orcid.org/0000000 2-5238-7644 abstract. infrastructure aging is an important problem nowadays, in particular for countries like italy in which the main motorways were built 50 years ago. huge budgets are necessary to keep infrastructure and bridges in service. in addition, the lack of a proper and timely maintenance, entails an increase of the deterioration and therefore higher costs of repair. thus, the need of methods capable of assessing the reliability of the infrastructure in the frame of bridge management system (bms), is patent. the aim of this work is to provide a robust decision-support tool for the analysis of the data collected with field inspection. the innovative aspect of the proposal is the introduction of two factors which take into account the location of the damage, and the mechanical characterization of the material in the definition of a condition rating number (crn). the analysis of an existing reinforced concrete (rc) bridge network is presented in order to show the accuracy of this new method. keywords. bridges; concrete; bms; durability; inspection; maintenance. citation: stochino, f., fadda, m.l., mistretta, f. assessment of rc bridges deterioration by means of low-cost investigations, frattura ed integrità strutturale, 46 (2018) 216-225. received: 27.07.2018 accepted: 31.08.2018 published: 01.10.2018 copyright: © 2018 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. introduction he wear of an asset due to its prolonged use results in a gradual degradation of its performance. the aging of materials and asset technology yields to a decline in technical efficiency or technological obsolescence. chemical-physical tests have a fundamental role in the inspection and maintenance of installations and machines, see [1-2]. the continuous measurement of these quantities with automatic or semi-automatic methods allows to know the system state and can provide essential information for the policies on condition assessment from the maintenance point of view, see [3]. the same approach should be applied to concrete bridges networks. in fact, as well as industrial machines and equipment should be monitored continuously, also infrastructures require stringent inspections at regular intervals of all the elements. t http://www.gruppofrattura.it/va/46/20.mp4 f. stochino et alii, frattura ed integrità strutturale, 46 (2018) 216-225; doi: 10.3221/igf-esis.46.20 217 the main objectives of the bridges infrastructure networks maintenance strategies, are to ensure, in probabilistic terms, the safety of the individual citizen and the effectiveness of the transport system. in addition, in case of natural disasters (floods, earthquakes, etc.) or acts of terrorism, a good ability of infrastructural network to provide alternative routes (resilience), with primary focus on strategic activities (civil defense, hospitals, energy supply, waste disposal, etc.) see [4-6], is expected. in recent years, the importance of bridge management system (bms) has been increasing. bms is the set of inspection, investigation, maintenance, repair of a group of bridges or viaducts, organized according to priority, with the support of computer databases and algorithms officers. in most of cases, the condition of a structure is assessed by qualitative judgments. figure 1: bridge management system in a schematic way, see fig. 1, it can be said that a bms is composed of: inventory of bridges network; data analysis capabilities on the basis of deterioration models; cost models; optimization programs, which are based on previous assessments, help in planning characteristics and schedule of the retrofitting. therefore, a bms can be seen as a tool that can: o assess the condition and give an overview about the status of the structures; o formulate maintenance programs within predetermined cost limits and plan consequent actions; o schedule requests and fund appropriations. the main goal is to obtain a representative picture of each structure that will allow making adequate maintenance work or to underline the need for further in-depth investigation [7]. in order to prioritize maintenance investments bridge rating strategy is adopted in bms. usually, the rates of bridges can be compared at project or network level and can consider both serviceability and relevance. different methods can be found in the literature: an integrated bridge index (ibi) is presented in [8]. it takes into 
account the vulnerability risk and strategic importance of each net component. visual inspection, experts survey and regression analysis has been adopted for calibration. an effective approach for fast and automatic evaluation of bridges robustness and resilience is presented in [9], while multi-attribute utility theory (muat) is implemented in bridges ranking strategy in [10]. also fuzzy logic has been adopted in this context with some interesting results, see [11] and [12]. 
 f. stochino et alii, frattura ed integrità strutturale, 46 (2018) 216-225; doi: 10.3221/igf-esis.46.20 218 the concept that a condition rating method should be based on numerical evaluation of all those essential damage types revealed during inspection has been introduced in [13] by znidaric and perus. variations and applications of this approach has been published in the last years (see [14-16]). the authors proposed in [17] an improved version of the above-mentioned method which takes into account the mechanical degradation of materials and the location of the damages. in the present paper an application of this innovative method is described considering a net of bridges in sardinia (italy). 
 after a synthetic description of the proposed method the real case-study is analysed with the aim of proving the efficacy of the proposed approach. finally, some perspectives and conclusive remarks are presented. proposed method he proposed method is divided in three main steps: • thorough visual examinations aimed at detecting any damages in the structure. • development of non-destructive tests in order to assess the mechanical characteristics of materials. • evaluation of the condition rating number crn for each structure. crn is a non-dimensional number representing the damage degree of the analysed structure. it is defined by the following equation: 1 , 1 100 k d mm k d ref mm f crn f  = =    =        (1) where γ denotes an arbitrary scale constant that should be tuned for the considered case; fdm represents the condition rating number for the m-th-structural component and fd,refm is the corresponding maximum value. fdm is defined as follows: 2 3 1 n dm m i i i i i i f k b k k l t = =     (2) km denotes the importance of the considered element into the structure. its value spans between 0.1 and 1.2. for the sake of synthesis the complete description is not reported here. the interested reader can find the table with all values in [13] tab. a2 or in [17]. bi denotes the basic value associate to the type of defect "i". it expresses the potential effect of the damage type "i" on the safety and / or durability of the element observed. it varies between 1 and 4, see [13] tab. a1. the magnitude of the i-th damage is expressed by k2i. its values range between 0.5 and 2.0, the complete definition is reported in [13] tab. a3. k3i quantifies the extension of the damage along the structural element, as a number within the range 0 – 1 according to the indications reported in [13] tab. a4. criterion li damage not in a critical point 1 damage in a critical point 2 table 1: li parameter values representing the damages location importance. the main novelty of this method is the specification of the damage location and of the material properties degradation in each structural element. these two aspects can be respectively measured by li and ti. li denotes the position of the i-th damage in the structural element and it can assume binary values: 1 in case it is not a critical point, 2 if it is a critical point as reported in tab. 1. critical points are the parts of the single element that are “critical” for the structural safety. t f. stochino et alii, frattura ed integrità strutturale, 46 (2018) 216-225; doi: 10.3221/igf-esis.46.20 219 the material degradation is represented by ti whose values are reported in the following tab. 2. they depend on the ratio between the design material strength fmkd and the one measured by experimental tests developed on site: fmkexp (e.g. coring strength test, ultrasound pulse test, rebound index etc.). if it is not possible to obtain the design material strength, it is assumed equal to the minimum value required for the considered exposure class (see [18]). in case it is not possible to develop any experimental test on the structural element a conservative value of ti is 4. considering composite structures (e.g. rc) fmk represents the matrix (concrete) compressive cylindrical strength as a first approximation. if it is possible to have information on the reinforcements too it is the averaged mean of the matrix (concrete) and reinforcements (steel) mechanical properties as presented in eqn. (3): c mk ck yk s e f f f e = +  (3) where ec and fck respectively are the concrete young’s modulus and characteristic strength, while es and fyk are the ones corresponding to steel. eqn. (3) gives fmkexp, when the experimental mechanical characteristics are considered and fmkd when the materials design values are used. criterion fmkexp/fmkd ti high resistance >1 1 poor resistance from 0.66 to 1 2 low resistance from 0.33 to 0.66 3 no resistance from 0 to 0.33 4 table 2: material characteristics degradation: ti values. each structure component should be investigated rating any defects in order to provide a characteristic fdm and fd,refm, see eqn. (2). then the whole structure can be denoted by the value of crn defined by eqn. (1). according to this value the structure can included into one of the 4 damage categories presented in tab. 3. a higher value corresponds to a worst condition and vice versa. damage categories crn/γ in service 0.00 -1.36 little deterioration 1.36 -1.86 severe deterioration 1.86 – 2.27 urgent intervention 2.27 – 2.95 out of service >2.95 table 3: damage categories for the proposed method. application to a real case-study he proposed method has been applied to a set of rc bridges in sardinia (italy). the structural scheme is similar for every one: a horizontal slab supported by transverse and longitudinal beams simple supported by the lateral abutments, see figs. 2-4. t f. stochino et alii, frattura ed integrità strutturale, 46 (2018) 216-225; doi: 10.3221/igf-esis.46.20 220 figure 2: t1 type bridge. figure 3: t2 type bridge. considering the number of the transverse and longitudinal beams the bridges can be divided in three types as reported in tab. 4. the design material resistance is not available, thus given the exposure class xc4, see [18], the minimum resistance class was assumed as the material strength reference class c30/37. for the sake of simplicity, the scale constant γ has been considered equal to one. figure 4: t3 type bridge. f. stochino et alii, frattura ed integrità strutturale, 46 (2018) 216-225; doi: 10.3221/igf-esis.46.20 221 label long. beam transv. beam type p01 2 1 t1 p03 2 1 t1 p07 2 1 t1 p08 2 1 t1 p10 4 2 t2 p12 8 2 t3 p13 8 2 t3 table 4: bridge net description. figure 5: p08 bridge structural scheme. a set of destructive and not destructive tests (core compressive strength test, sclerometer, pull out, ultrasound wave velocity test, ecc) has been developed on each bridge. for the sake of synthesis, the average concrete resistance class obtained by the experimental results for each group is reported in the following tab. 5. this simplification is possible because bridges belonging to the same type are quite homogeneous. in general, bigger bridges (type t3-t2) present better mechanical characteristics in comparison to smaller ones (type t1). bridge type concrete class t1 c16/20 t2 c25/30 t3 c25/30 table 5: concrete class for each bridge group. in order to show the method, consider the case of bridge p08 that belongs to t1 type. fig. 5 presents its geometrical dimensions and structural scheme. the visual inspection enriched by the experimental tests produced a damage identification form for each structural component. some examples for abutment, beam and slab are reported in tab. 6-8. also, the value of location coefficient li and material degradation coefficient ti are reported in these tables. humidity spot have been detected in every structural component, concrete spalling is present in the abutments and in the slab. some transversal cracks are present in the longitudinal beams. most of damages were not located in critical points (li=1) while the information on materials yield to a value of ti=3 for the whole bridge. 10.00 5.00 3.00 0.24 long. beam 1 long. beam 2 t ra n s v e rs a l b e a m 0 .9 0 a b u tm e n t 1 a b u tm e n t 2 deck slab f. stochino et alii, frattura ed integrità strutturale, 46 (2018) 216-225; doi: 10.3221/igf-esis.46.20 222 damage b k2 k3 li rckexp rckd ti humidity spot 1 1.5 1.5 1 20 37 3 deteriorated concrete 1 1.5 1.5 1 spalling 2 1 0.5 1 rusted reinforcements 3 1 0.5 1 web fracture 1 horizontal cracks 1 vertical cracks 3 inclined cracks 3 rusted stirrups 3 1 0.5 1 deformed reinforcements 4 construction joint deterioration 1 impact damages 1 support damages – top edge 2 support damages – bottom edge 4 out of plumb 2 table 6: abutment damage identification form for bridge p08. damage b k2 k3 li rckexp rckd ti humidity spot 1 1 1.5 1 20 37 3 deteriorated concrete 1 beam/slab joint deterioration 2 freezing 2 de-icing salts 2 spalling 2 2 2 1 reinforcements corrosion 3 2 2 1 tendons corrosion 4 duct deficiency 2 web fracture 1 longitudinal cracks 3 vertical cracks 3 1.5 1.5 2 inclined cracks 3 rusted stirrups 3 2 2 1 deformed reinforcements 4 construction joint deterioration 2 impact damages 1 table 7: longitudinal beam damage identification form for bridge p08. f. stochino et alii, frattura ed integrità strutturale, 46 (2018) 216-225; doi: 10.3221/igf-esis.46.20 223 damage b k2 k3 li rckexp rckd ti humidity spot 1 2 2 2 20 37 3 deteriorated concrete 1 2 1.5 1 spalling 2 2 1.5 1 reinforcements corrosion 3 1.5 1.5 1 web fracture 1 longitudinal cracks 3 vertical cracks 3 inclined cracks 3 rusted stirrups 3 2 1.5 1 construction joint deterioration 3 table 8: slab damage identification form for bridge p08. the values of km, see eqn. (2), are: abutment 0.4, slab 0.4, longitudinal beam 0.6, transversal beam 0.3. tab. 9 presents the damage analysis for each structural component. for the specific case it is clear that the longitudinal beam 1 and the slab are the most damaged elements. element fdm fd,refm 100 fdm/ fd,refm abutment 1 10.20 512 1.99 abutment 2 4.80 512 0.94 slab 39.30 320 12.28 lon.beam 1 84.60 480 17.62 lon.beam 2 31.95 480 6.65 transv.beam 0.0 240 0.00 table 9: damage estimation for bridge p08 components. order of urgency bridge label crn 1° p13 10.51 2° p12 8.98 3° p07 8.06 4° p08 6.72 5° p10 2.95 6° p03 0.63 table 10: intervention order within the infrastructure network. f. stochino et alii, frattura ed integrità strutturale, 46 (2018) 216-225; doi: 10.3221/igf-esis.46.20 224 the global cnr for bridge p08 is 6.72, it requires immediate retrofitting. in particular, the above mentioned structural component should be analysed with higher accuracy in order to control the damage evolution and design the refurbishments operations. the same procedure can be applied to all other bridges and tab. 10 presents the synthetic results of the whole net assessment. bridge p13, p12, p07, p08 require immediate retrofitting, while p10 is in service even with urgent maintenance needs. only bridge p01 and p03 are in good condition. it is clear that this result can represent a starting point for the bridge net condition assessment. further investigations are advised for the bridges that require urgent or immediate retrofitting in order to design the necessary refurbishments. conclusions n this paper the application of a new method for fast and low-cost condition rating mark for rc bridge network has been described. this method is based on visual inspection and experimental on-site tests. it can be briefly described by the following steps: identification of the structural components of each bridge (or construction). weighting of each structural component for the whole structure safety. visual inspection, experimental testing (if possible), information collection. rating of each damage considering importance, extension and magnitude, position and material degradation. ranking of the structures belonging to the same net using eqns. (1) – (2). this rank can help bms decision makers in optimizing the allocation of available funds for maintenance and management costs (service interruption etc). main innovations of this approach are the parameters that take into account the location of the damage at the structural elements level and the mechanical degradation of materials. the application to a real case study proved the efficacy of this method giving an “urgency ranking” for retrofitting needs of a bridge net, but also a priority list of damaged elements among the same structure. in particular, during the structure life time [19], it is possible to “track” damages evolution creating an useful specific database. further developments are expected implementing the approach in an automatized algorithm that is capable of assessing the bridge condition using an inverse problem approach, [20]. in addition, the authors would like to extend the method to different kinds of materials (like steel, masonry) and other types of constructions (e.g. general buildings). references [1] carvalho, h., hallal fakury, r. and leite vilela, p. (2017). structural integrity assessment and rehabilitating of hercilio luz bridge. frattura ed integrità strutturale, 11(42), pp. 93-104. doi: 10.3221/igf-esis.42.11. [2] berto, f., razavi, j., jones, r. and peng, d. (2018). effect of corrosion and fatigue on the remaining life of structures and its implication to additive manufacturing. frattura ed integrità strutturale, 12(45), pp. 33-44. doi: 10.3221/igf-esis.45.03. [3] furlanetto, l., garetti, m. and macchi, m. (2007). ingegneria della manutenzione. strategie e metodi. milano: franco angeli. [4] stochino, f. and carta, g. (2014). sdof models for reinforced concrete beams under impulsive loads accounting for strain rate effects. nuclear engineering and design, 276, pp.74-86. doi: 10.1016/j.nucengdes.2014.05.022 [5] stochino, f. (2016). rc beams under blast load: reliability and sensitivity analysis. engineering failure analysis, 66, pp.544-565. doi: 10.1016/j.engfailanal.2016.05.003 [6] stochino, f., mistretta, f., meloni, p. and carcangiu, g. (2017) integrated approach for post-fire reinforced concrete structures assessment, periodica polytechnica civil engineering, 61(4), pp. 677-699. doi: https://doi.org/10.3311/ppci.9830. [7] fib (ceb-fip) (2002) management, maintenance and strengthening of concrete structures. [8] valenzuela, s., de solminihac, h. and echaveguren, t. (2010). proposal of an integrated index for prioritization of bridge maintenance. journal of bridge engineering, 15(3), pp. 337-343. doi: 10.1061/(asce)be.1943-5592.0000068. [9] liao h.k., yau n.j. (2011) development of various bridge condition indices for taiwan bridge management system, proceedings of the 28th isarc, seoul, korea, pp. 911-916. i f. stochino et alii, frattura ed integrità strutturale, 46 (2018) 216-225; doi: 10.3221/igf-esis.46.20 225 [10] abu dabous, s. and alkass, s. (2010). a multi‐attribute ranking method for bridge management. engineering, construction and architectural management, 17(3), pp. 282-291. doi: 10.1108/09699981011038079 [11] mistretta f., piras v., fadda m.l. (2014) a reliable visual inspection method for the assessment of r.c. structures through fuzzy logic analysis, proceedings of the 4th international symposium on life-cycle civil engineering, pp. 1154-1160. [12] fadda m.l., mistretta f., piras v. (2014) vulnerability assessment of concrete bridges using different methods of visual inspection. civil-comp proceedings, 105, 1759-3433. [13] znidaric j., perus i. (1998), condition rating methods for concrete structures, ceb bulletin no. 243: 
strategies for testing and assessment of concrete structures. [14] gattulli, v. and chiaramonte, l. (2005). condition assessment by visual inspection for a bridge management system. computer-aided civil and infrastructure engineering, 20(2), pp.95-107. doi: 10.1111/j.1467-8667.2005.00379.x. [15] kano h., morikawa h. (2007), condition rating methodology on rc bridges with chloride induced deterioration, in reliability and optimization of structural systems: assessment, design, and life-cycle performance, taylor & framcis group, pp. 113 -122 [16] kušar m., šelih j., (2014) analysis of bridge condition on state road network in slovenia. journal of the croatian association of civil engineers, 66(9), pp. 811-822. doi: 10.14256/jce.1047.2014 [17] stochino, f., fadda, m. and mistretta, f. (2018). low cost condition assessment method for existing rc bridges. engineering failure analysis, 86, pp. 56-71. doi: 10.1016/j.engfailanal.2017.12.021 [18] uni en 206-1:2006 concrete part 1: specification, performance, production and conformity. [19] biondini f., frangopol, d.m. (2018). life-cycle performance of civil structure and infrastructure systems: survey, journal of structural engineering (united states), 144(1), art. no. 06017008. doi: 10.1061/(asce)st.1943-541x.0001923. [20] turco e. (2017) tools for the numerical solution of inverse problems in structural mechanics: review and research perspectives. european journal of environmental and civil engineering, 21(5), pp. 509–554. doi: 10.1080/19648189.2015.1134673. microsoft word numero_52_art_20_2688 w. n. bouzitouna et alii, frattura ed integrità strutturale, 52 (2020) 256-268; doi: 10.3221/igf-esis.52.20 256 elastoplastic analysis of cracked aluminum plates with a hybrid repair technique using the bonded composite patch and drilling hole in opening mode i w. n. bouzitouna smart structures laboratory, univ ctr of ain témouchent, po box 284,46000, algeria hibanesrine@outlook.fr w. oudad mechanical engineering department, univ ctr of ain témouchent, po box 284,46000, algeria oudadw@gmail.com, https://orcid.org/0000-0002-3283-1322 m. belhamiani, d. e. belhadri smart structures laboratory, univ ctr of ain témouchent, po box 284,46000, algeria mbelhamiani@gmail.com, https://orcid.org/0000-0001-8951-032x djamelins@hotmail.fr l. zouambi mechanical physical materials laboratory, mechanical engineering department, (lmpm) university center of relizane, 48000, algeria zouambileila1071@gmail.com abstract. the objective of this study is to analyze the performance of composite bonding repair, hole drilling and the combination of the two techniques (hybrid repairs) by tensile tests and to show the interest of a hybrid repair versus other processes. these repair techniques can apply in different branches of engineering: mechanical, aerospace, civil, naval, etc. the finite element method with the abaqus code was used to model the mechanical behavior of the different repair techniques. the notch stress intensity factor (nsif) is adopted to model the behavior of the cracked notch based on the volumetric method. the size of the plastic zone, the intensity of the normal σyy stress, the peel stress and ctod are combined to model the proposed techniques repair. although the bonded composite is very strong, the application of a drilling hole results in additional energy absorption and reduces the level of the maximum normal stress by about 50% compared to a simple patch only. the use of a hybrid repair has a high resistance compared to other proposed methods, improves the mechanical strength and increases the life of the cracked structure compared to a single composite joint and a repair by drilling hole only. keywords. hybrid; bonded; composite; nsif; plastic zone; drilled. citation: bouzitouna, w. n., oudad, w., belhamiani, m., belhadri, d. e., zouambi, l., elastoplastic analysis of cracked aluminum plates with a hybrid repair technique using the bonded composite patch and drilling hole in opening mode i, frattura ed integrità strutturale, 52 (2020) 256-268. received: 17.11.2019 accepted: 13.02.2020 published: 01.04.2020 copyright: © 2020 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. https://youtu.be/4xstoifnbcs w. n. bouzitouna et alii, frattura ed integrità strutturale, 52 (2020) 256-268; doi: 10.3221/igf-esis.52.20 257 introduction amage to metal aircraft structures is often caused by corrosion, erosion, normal stress, and accidents and mishaps, which made the component susceptible to cracking in service. the replacement of the cracked component can be very costly, thus it’s important that metal structural repairs be made according to the best available techniques to expand its service life and investigate the satisfactory performance of an aircraft in a rapid way reducing the immobilization time of the device structure. numerous and varied crack repair techniques have been proposed for arresting or retarding crack propagation in structural components such as: i) the use of bonded composite patch repair, a baker and al [1] explain the concept of using bonded composite materials as a mean to maintain aging metallic aircraft. the reinforcements of composite patch repairs reduce stresses in the cracked region and keeps the crack from opening and therefore from growing; ii) the infiltration method, which is based on reinforcing the cracked body by depositing closure material like epoxy resin along the crack path. [2] stated that crack growth retardation is promoted by through the infiltration of closure materials into a crack, and the closure material properties play a dominant role in promoting the crack closure and the retardation. iii) drilling a hole at the crack tip is one of the easiest and most accessible crack arresting procedures. cracking resumes very shortly after drilling because of the high stress concentration associated with hole and this is why it remains temporary and relatively ineffective method [3, 4]; iv) a much superior approach is to stop drilling and then expand the stop hole, usually with a special sleeve to develop favorable compressive stresses that reduce or prevent crack opening, while this approach is often highly effective in stopping crack growth [4–6]. [5] studied the influence between the holes of different diameters and also between the expanded holes and non-expanded holes on arresting the crack propagation, finding that the number of cycles to initiate a new crack is three times longer than non-expanded holes; v) repair of corrosion types such as pitting or exfoliation in aluminum alloy structures generally involves the removal of visible damage by grinding followed by an extra confidence cut to ensure that all the corrosion is removed. the region is then treated, primed and painted. in the case of severe corrosion, panel thickness may be reduced below the allowable thickness and must be reinforced to make it airworthy [7–9]; vi) the overload repair is applied to the metallic structure in order to create a plastic zone over the crack-tip, this zone generates a residual compressive stress that leads to a decrease in the velocity of the crack growth, [10], that is explain by the closure of the crack caused by the plastic zone generated [11–14]; vii) another method based on the application of residual compressive stresses to reduce the crack growth rate is to press a steel ball in the crack-tip. [15,16], studied this phenomenon by leaving a brinell-type dimple of a certain diameter and showed that the greatest arrest of crack growth due to the compressive stresses was caused by forming the dimple. it is obvious that each repair procedure has advantages and disadvantages; this paper focuses on the requirement of hybrid repair method by combining a bonded patch with drilled stop hole, that enhances the residual strength of the damaged structures. the combination between two techniques can offer a possibility of complementarity and eliminate the weaknesses of the two techniques. few studies on this combination exist in the literature in fact, there are several studies concerning hybrid joints, we can mention the work of [17–19]. in this work, three-dimensional finite element analyzes are performed to compare the effectiveness of the hybrid repair technique with composite patches and the drilling hole to repair an aluminum plate containing u lateral notches. a volumetric approach is developed to obtain the notch stress intensity factor kρ in mode-i condition [20]. variation of notch bottom opening stress fields in the different methods was examined based on the notch stress intensity factor (nsif). the plastic zone at the u-notch front has been studied as part of a drill hole, bonded repair and hybrid method repair. in addition, the variation in peel stresses in the plate / adhesive interface area for single patch repair and hybrid repair has also been checked. volumetric method (kρ) the stress field around the notch-tip in mode i condition and subsequent evaluation of the notch stress intensity factor kρ are performed to describe the fracture criterion. the determination of the kρ is made using the volumetric approach [20], this method was chosen because it is feasible to give the appropriate kρ values before and after the repairs. it assumed that the fracture process needs a physical volume where the necessary fracture energy release rate is stored to launch the fracture phenomenon; it corresponds to the high stressed region in which the fracture notch effect is taking place. this leads to a volumetric approach; two parameters are describing this fracture criterion: the effective distance and the effective stress. a bi-logarithmic graph shown in fig. 1, represent the stress distribution at the notch tip where the stress normal to the notch plane is plotted versus the distance, and the effective stress and distance are also shown. d w. n. bouzitouna et alii, frattura ed integrità strutturale, 52 (2020) 256-268; doi: 10.3221/igf-esis.52.20 258 figure 1: stress distribution at the notch tip where the stress normal to the notch plane versus the distance from end notch [20] from the above graph, it can be distinguished three zones, i) the high stressed zone (zone i) in which the stress distribution achieves a maximum value offset by a distance from the notch root, ii) in the (zone ii) the stress value is decreasing to the outside of the notch root, iii) the evaluation of the stress (zone iii) takes a linear behavior. the effective distance was determined from the value of the minimum of the relative stress gradient χ defined by: 1 .  yy yy d dr     (1) where χ is the relative stress gradient and σyy is the maximum principal stress or opening stress. from the relative stress gradient plotted on logarithmic graph fig. 2, the effective distance xef was obtained with the minimum of χ. while from the plot of stress distribution over the effective distance, the effective stress for fracture δef was considered as the average value over the effective distance. the stress distribution is then given by:   0 1 . 1 .    efx ef yy ef r dr x     (2) however, the notch stress intensity factor is a function of the effective distance and the effective stress:  . 2 αef efk  σ πx  (3) where kρ is the notch stress intensity factor and σef and xef are the effective stress and effective distance, respectively, and α is the slope of the stress distribution in region iii. the exponent α depends on the notch angle and is equal to α = 0.5 if the sides of the notch are parallel. w. n. bouzitouna et alii, frattura ed integrità strutturale, 52 (2020) 256-268; doi: 10.3221/igf-esis.52.20 259 figure 2: stress distribution at the notch root together with relative stress gradient.[20] geometrical and material properties typical basic geometry and loading, adhesive layer and composite patch are shown in fig. 3, the plates were made of a 2024-t3 aluminum alloy containing lateral unotch repaired with boron/epoxy composites and bonded with a thin layer of fm73 adhesive, subjected to a uniaxial loading of 65 mpa. the plate has the following dimensions: length= 160 mm, width= 39 mm, thickness = 3 mm and the dimensions of the notch are: radius ρ= 0.25 mm, length= 9.75 mm the length of one side square patch repair is 25 mm and its thickness is 1.5 mm. the thickness of adhesive is 0.1 mm. material properties of the aluminum plate, adhesive and composite patch are given in tabs. 1 and 2. the plate and the adhesive are considered as isotrop while the composite patch is modeled as an orthotrop [21,22]. figure 3: geometry of the repaired model. (a) front view (b) side view (c) 3d view a w. n. bouzitouna et alii, frattura ed integrità strutturale, 52 (2020) 256-268; doi: 10.3221/igf-esis.52.20 260 parameters aluminum alloy 2024t3 adhesive fm73 e (gpa) 72 2.21 ʋ 0.3 0.43 table 1: material properties of 2024-t3 aluminium alloy and fm 73 adhesive. elasticity modulus (gpa) shear modulus (gpa) poisson’s ratio e11 200 g11 7.2 υ12 0.21 e22 25 g22 5.5 υ13 0.21 e33 25 g33 5.5 υ23 0.21 table 2: material properties of composite patch boron/epoxy finite element model finite element method (fem) using abaqus software suite is employed for modeling the notched plates; a typical finite element geometry, loading and mesh configuration of the notched plate are shown in fig. 3. the structure made up on the plate, the adhesive and the patch are subjected to uniform uniaxial tensile load of 65 mpa on the section of the plate in y direction, then clamped the down surface in the three directions. these conditions are represented in a 3d model as shown in fig. 3 the mesh was modeled in 3d stress element type with 20-node quadratic brick geometric order and with a hexagonal element shape. a very fine mesh was generated for the region close to the notch-tip with an element dimension of 0.05mm fig. 4. the tie between the plate–adhesive and patch-adhesive was created using “tie” constraint, which allows the part instances to combine together. in this analysis, the stress fields of the repaired plates are obtained to compare between the different repair techniques than to get the curve opening stresses versus the crack patch in order to extract the stress notch intensity factor kρ determined analytically using the volumetric approach. figure 4: finite element mesh of the notched plate. analysis and results he evaluation of the effectiveness of the repair of cracked structures by the method of drilling a hole, push us to adopt the volumetric technique as a criterion because it allows us to use the notch stress intensity factor this factor is assimilated to the stress intensity factor for an elastic material. this factor is one of the parameters which providing a characteristic of the stress field existing near the crack tip. a t w. n. bouzitouna et alii, frattura ed integrità strutturale, 52 (2020) 256-268; doi: 10.3221/igf-esis.52.20 261 validation of the choice of the drilling technique the ruins of cracked structures depend on several parameters, namely the size of the crack its geometry or shape, the type of loadings and its amplitude. the repair of a cracked structure by the hole drilling method at the bottom of the crack is based on the geometric modification of the crack eliminating the singularity in its tip, this causes a relief of the structure solicited and offers the possibility to leave the structure in service the time to prepare for its replacement otherwise the repair can be permanent. figure 1: the notch stress intensity factor kρ vs notch radius for three methods a, b and c . researchers boost this interesting technique. the [23] and [24] investigated the possibility of drilling several holes near the bottom of the crack. drilling a hole near the point of the crack increases the service life of the crack. structure and also influences the direction of propagation of the crack [6]. figure 2: plastic zone size vs drilled methods a, b and c. in the perspective of validating our numerical model. the choice of piercing method is compared with the results of [25]. fig. 5 presents the variation of the notch stress intensity factor as a function of the drilling radius for the three w. n. bouzitouna et alii, frattura ed integrità strutturale, 52 (2020) 256-268; doi: 10.3221/igf-esis.52.20 262 drilling methods proposed by [25], our results valid and confirm the conclusion of [25], indeed the notch stress intensity factor decreases only in method '' a '' as a function of drilling radius. in addition, the evaluation of the beneficial effect of the repair by drilling hole depending on the notch stress intensity factor kρ can be assessed by analyzing the distribution of axial stresses σ22 and the size of the plastic zone in the vicinity of the drilling hole. fig. 6. show the size of plastic zone (spz) for three drilled methods. as it, we can observe the development of plastic zones, because the presence of the weak concentrations of deformations in the bottom of the crack engendered by the removal of the material for the three methods of drilling, still with the size of plastic zone the technique of piercing (a) proves its interest. hybrid repair technic in recent years, several researchers have invested in assembling structures with joint or hybrid joints (weld + rivet, clinch + bonded [18], bonded + riveted [26], bonded + bolted [17]) to improve the individual performance of each type of joint. hybrid joint applications are of major interest in aerospace technology and engineering. experimental studies have demonstrated that certain assemblies can achieve high static strength over riveted, bonded, or bolted assemblies separately [27-29]. compared to a riveted structure only, the hybrid assembly reduces the number of rivets and improves the strength of the structure. however, the repair of cracked structures is one of the areas where hybrid assemblies or hybrid repair can be used, our study is aimed at this empty domain. we will investigate numerically in the hybrid repair (collage drilling) based on the notch intensity factor, the distribution of the σyy stress, the size of the plastic zone at the bottom of the notch, crack type opening displacement (ctod), finally the peel stress. distribution of σyy stress fig. 7 shows the distribution of the normal stress σyy , in fig. 7 (a) and the fig. 7(b) illustrates max σyy distribution through plate thickness the stress concentration at the bottom of the notch shows two stress levels in fig. 7(a), a maximum between 370 and 470 mpa and a second level between 148 and 250 mpa, we can also see that far from the notch bottom in the relaxation zone of plate, two other levels of stress appear, the non-repair plate is relaxing at a stress level of 120 mpa, the drilled plate has a lower level of 90 mpa, while the level of the constraints of the two repair techniques is practically superimposed view that in both techniques the composite absorbs virtually all the stresses generated by mechanical solicitation. plotting the max σyy in fig. 7 (b) and comparing these results it is found that the drilling plate provides a reduction of 21% of the max σyy, the second level offered by the two repair techniques, these techniques carries out reduced rates of 46% for single-composite repair and 68% for hybrid repair (single-patch drilling). figure 3: distribution of σyy stress along the ligaments of the crack (a), and variation of the max σyy for different cases (b) the distribution of the normal stress σyy along the plate thickness is plotted against all studied cases in fig. 8 (a), averaged σyy for same cases repairs technics in fig. 8(b). w. n. bouzitouna et alii, frattura ed integrità strutturale, 52 (2020) 256-268; doi: 10.3221/igf-esis.52.20 263 figure 4: normal stress σyy distribution along the plate thickness for all cases. a comparison of the normal stress level for the types of repair considered allows us to conclude that the majority of the resistance of the hybrid repair with a simple patch comes from the adhesive and proposed as the best compared to the others with 44% of reduction compared to the structure repaired by simple patch only. however, the addition of a second patch on the other side of the plate (double patch) increases greatly the energy absorption capacity of the hybrid repair. in the case considered, this increase was equal to 80%. notch stress intensity factor after analyzing the maximum normal stress σyy, we also analysed the notch stress intensity factor (nsif), which is another parameter of failure. the result above shows a strong decrease in stress concentration in the vicinity of the notch bottom caused by the application of the bonded composite. figure 5: the notch stress intensity factor kρ vs repair technics system. fig. 9 demonstrates the comparability of the notch stress intensity factor (nsif) kρ for the repair technics system, one can note that the drilling of the plate offers a reduction of the nsif of 10% compared to the unrepaired plate, for the repair system by patch only the rate of reduction is 83%, while the hybrid repair (simple patch + drilling) offers a drop of the nsif of the order 88% of the same hybrid repair (double patch + drilling) led to a further reduction of 90%. indeed, the singularity at the bottom of the notch removed by the piercing provides additional relaxation to the damaged structure. the central parts of the adhesive in the vicinity of the pierced zone are subjected to a low level of stress and do not support a high load, since the patch absorbs the majority of the stresses caused by the uniaxial solicitation. cod parameter ductile materials can break at relatively low stress levels since the deformation is limited to the vicinity of the relatively large crack tip. to characterize the fracture behaviour of these materials, we have used parameters similar to critical w. n. bouzitouna et alii, frattura ed integrità strutturale, 52 (2020) 256-268; doi: 10.3221/igf-esis.52.20 264 crack opening displacement (cod), critical-crack-tip opening displacement (ctod) or crack stretching (δ).the criticalcrack-tip opening displacement ctod can be converted into stress intensity after which it can be used directly to predict the breaking of large structures. the ctod value is extracted from a fixed node in face of the initial crack tip [30]. the cod value is extracted from a fixed node in the end line of the initial crack tip (fig. 10). the variation cod parameters for five cases studies is presented in fig. 11, it can be observed from fig. 11 that, for both simple patches only technic and hybrid technic (simple patch + drilled) the cod are comparatively similar, this is because most of the strength of the hybrid joint comes from the adhesive. however, the application of a second composite patch on the other side of the plate increases greatly the energy absorption capacity of the hybrid repair system (double patch + drilled). plastic zone it was pointed out that the analysis of the extent of the plastic zone has shown that the plastic zone has completely disappeared by applying the hybrid repair technic, for this reason it is wished to make a comparison with respect to the unrepaired face of the plate by a simple patch only and hybrid repair (simple patch + drilling). the results of fig. 11 show that the hybrid repair leads to the decrease of the cod parameter and consequent to the decrease in the size of the plasticized zone at the crack tip (fig. 12). this illustrates the extent of the plastic zone for different repair techniques. the extents of the plasticized areas were determined using the von mises criterion. figure 6: schematic plot of the cod-node. figure 7: variation of cod parameters for the five studied cases. w. n. bouzitouna et alii, frattura ed integrità strutturale, 52 (2020) 256-268; doi: 10.3221/igf-esis.52.20 265 figure 8: variation of plastic zone size for the three studied cases. at the crack tip the deformation fields are considerable and result in a larger area of the plastic zone [22]. in this case, the mechanical energy at the crack head is absorbed by the material in the form of defects. the higher this energy is, the higher of the defect density increases leading to a large size of the plastic zone. the sizes of the plasticized zones obtained for the hybrid technique are small compared to those obtained for the drilled hole repair and single patch only. indeed, the area of the plastic zone for the drilling hole technique is worth almost six times that of the hybrid technique, this confirms the effectiveness of the hybrid repair system. peel stress (σzz ) as we know, disband is one of the major weaknesses of bonded composite repair, these initiating causes are generally the bad preparation of bonding surfaces, the low resistance of the adhesive in shear load or peel stress, high concentration of stress at the crack tip, etc. on the other hand, the adhesive is the weak link of reinforcement by composite materials. it is a material with very low mechanical shear properties and it is known that takeoff is started with the development of peel stress concentrations (σzz) [32], [33]. in our study, we focus on the peel stress. fig. 13 shows the distribution of the peel stress (σzz) along the virtual line for tow type of repair systems (simple patch + drilling). we find that the distribution of stress peel is similar except at the tip of the notch for the hybrid repair with a reduction of 80%, it is clear that the use of a hybrid repair generates low peel stresses near the notch front and therefore decreases the probabilities of disband phenomena. the use of hybrid repair technic is recommended to extend the life of cracked structural components and give a better performance and eliminating the disadvantages of each type of repaired system (bonded composite and drilled hole). figure 9: peel stress (σzz) distribution along the virtual line. w. n. bouzitouna et alii, frattura ed integrità strutturale, 52 (2020) 256-268; doi: 10.3221/igf-esis.52.20 266 verification with other models fig.15 are plotted to see more clearly about the behaviour of different configurations of repair system, where the maximum values of the normal stress (σyy) are assembled in histograms forms. rodriguez-sanchez et al [31] proposed five drill crack repair configurations (fig. 14): (a) through hole, (b) bottom hole, (c) hole with notch to symmetric inclined faces, (d) hole with notch with asymmetrical inclined faces, (e) hole and inclined notch. in this analysis, we applied hybrid repair to these configurations for specific cases. fig. 15 shows a comparison between the repair proposed by rodriguez [31] and the application of the composite bonded on these same configurations for the cases chosen, this figure leads us to conclude that the hybrid configuration is the best whatever the model chosen, because it always reduces the stress concentrations in a significant way at the bottom of the notch. in the (e) model the maximum σyy value is significantly the bottom-most lower than the other models without bonded patch, so with the composite patch it decreases by seven times compared to the drilled hole case only. figure 10: equivalent notch configurations [31] figure 11: maximum σyy value for each type of repair systems. conclusion n this work crack repair by hole drilling, composite bonding and the combination of both (hybrid) have been studied numerically. the results obtained from finite element analysis in this paper lead us to the following conclusions: hybrid repairs (single and double patch + drilled hole) provide better static performance than other configurations. i w. n. bouzitouna et alii, frattura ed integrità strutturale, 52 (2020) 256-268; doi: 10.3221/igf-esis.52.20 267 the singularity at the bottom of the notch removed by the piercing provides additional relaxation to the damaged structure. the hybrid repair leads to the decrease of the cod parameter and consequently to decrease the size of the plasticized zone at the bottom of the crack. finite element analyzes have shown that the presence of the two-side bonded composite can reduce significantly the maximum peel stress at the interface (plate/adhesive), which helps attain better repair performance. references [1] baker, a. a., rose, l. r. f. and jones, r. (eds) (2002) advances in the bonded composite repair of metallic aircraft structure. 1st ed. amsterdam ; boston: elsevier. [2] song, p. s., hwang, s. and shin, c. s. (1998). effect of artificial closure materials on crack growth retardation, engineering fracture mechanics, 60(1), pp. 47–58. doi: 10.1016/s0013-7944(97)00180-x. [3] fu, z., ji, b., xie, s. and liu, t. (2017). crack stop holes in steel bridge decks: drilling method and effects, journal of central south university, 24(10), pp. 2372–2381. doi: 10.1007/s11771-017-3649-8. [4] murdani, a., makabe, c., saimoto, a., irei, y. and miyazaki, t. (2008). stress concentration at stop-drilled holes and additional holes, engineering failure analysis, 15(7), pp. 810–819. doi: 10.1016/j.engfailanal.2007.11.002. [5] ghfiri, r., shi, h.-j., guo, r. and mesmacque, g. (2000). effects of expanded and non-expanded hole on the delay of arresting crack propagation for aluminum alloys, materials science and engineering: a, 286(2), pp. 244–249. doi: 10.1016/s0921-5093(00)00805-4. [6] goto, m., miyagawa, h. and nisitani, h. (2007). crack growth arresting property of a hole and brinell-type dimple, fatigue & fracture of engineering materials & structures, 19(1), pp. 39–49. doi: 10.1111/j.1460-2695.1996.tb00930.x. [7] kirkhope, k. j., bell, r., caron, l., basu, r. i. and ma, k.-t. (1999). weld detail fatigue life improvement techniques. part 1: review, marine structures, 12(6), pp. 447–474. doi: 10.1016/s0951-8339(99)00013-1. [8] rodriguez-sanchez, j. (2004). application of short repairs for fatigue life extension, international journal of fatigue, 26(4), pp. 413–420. doi: 10.1016/j.ijfatigue.2003.07.002. [9] wu, h., benseddiq, n. and imad, a. (2010). fracture toughness prediction of a valve body: numerical analysis, engineering failure analysis, 17(1), pp. 135–142. doi: 10.1016/j.engfailanal.2009.04.010. [10] elber, w. (1971). the significance of fatigue crack closure, in rosenfeld, m. (ed.) damage tolerance in aircraft structures. 100 barr harbor drive, po box c700, west conshohocken, pa 19428-2959: astm international, doi: 10.1520/stp26680s. [11] newman, j. (1976). a finite-element analysis of fatigue crack closure’, in rice, j. and paris, p. (eds) mechanics of crack growth. 100 barr harbor drive, po box c700, west conshohocken, pa 19428-2959: astm international. doi: 10.1520/stp33952s. [12] newman, j. and elber, w. (eds) (1988) mechanics of fatigue crack closure. 100 barr harbor drive, po box c700, west conshohocken, pa 19428-2959: astm international. doi: 10.1520/stp982-eb. [13] robin, c., louah, m. and pluvinage, g. (1983). influence of an overload on the fatigue crack growth in steels, fatigue & fracture of engineering materials and structures, 6(1), pp. 1–13. doi: 10.1111/j.1460-2695.1983.tb01135.x. [14] smith, d. j., bourke, m. a. m., hodgson, a. p., webster, g. a. and webster, p. j. (1992). interpretation of residual stress distributions in previously loaded cracked beams, the journal of strain analysis for engineering design, 27(2), pp. 77–83. doi: 10.1243/03093247v272077. [15] van leeuwen, h. p., meulman, a. e. and schra, l. (1970) the repair of fatigue cracks in low-alloy steel sheet. [16] eggwerts, s., garfall, l. and wallgren, g. (1969). review of some swedish investigations on fatigue during the period april 1967 to march 1969. [17] fu, m. and mallick, p. k. (2001). fatigue of hybrid (adhesive/bolted) joints in srim composites, international journal of adhesion and adhesives, 21(2), pp. 145–159. doi: 10.1016/s0143-7496(00)00047-6. [18] moroni, f., pirondi, a. and kleiner, f. (2010). experimental analysis and comparison of the strength of simple and hybrid structural joints’, international journal of adhesion and adhesives, 30(5), pp. 367–379. doi: 10.1016/j.ijadhadh.2010.01.005. [19] venkateswarlu, s. v. (2013). modelling and analysis of hybrid composite joint using fem in ansys, iosr journal of mechanical and civil engineering, 6(6), pp. 1–6. doi: 10.9790/1684-0660106. [20] pluvinage, g. and gjonaj, m. (2001) notch effects in fatigue and fracture. doi:10.1007/978-94-010-0880-8. [21] hosseini-toudeshky, h., saber, m. and mohammadi, b. (2008). mixed-mode 3-d crack propagation of repaired thin aluminum panels using single-side composite patches, international journal of fracture, 153(2), pp. 105–116. doi: 10.1007/s10704-008-9303-6. w. n. bouzitouna et alii, frattura ed integrità strutturale, 52 (2020) 256-268; doi: 10.3221/igf-esis.52.20 268 [22] oudad, w., belhadri, d. e., fekirini, h. and khodja, m. (2017). analysis of the plastic zone under mixed mode fracture in bonded composite repair of aircraft structures, aerospace science and technology, 69, pp. 404–411. doi: 10.1016/j.ast.2017.07.001. [23] thomas, s. b., mhaiskar, m. j. and sethuraman, r. (2000). stress intensity factors for circular hole and inclusion using finite element alternating method, theoretical and applied fracture mechanics, 33(2), pp. 73–81. doi: 10.1016/s0167-8442(00)00002-1. [24] shin, c. (1996). fatigue damage repair: a comparison of some possible methods, international journal of fatigue, 18(8), pp. 535–546. doi: 10.1016/s0142-1123(96)00029-1. [25] khoshravan, m. r. and hamidi, a. (2007). numerical analysis of the influence of location of the stopping holes in the crack growth, journal of aerospace science and technologie, 4(1), pp. 9–16. [26] gómez, s., oñoro, j. and pecharromán, j. (2007). a simple mechanical model of a structural hybrid adhesive/riveted single lap joint, international journal of adhesion and adhesives, 27(4), pp. 263–267. doi: 10.1016/j.ijadhadh.2006.01.004. [27] kweon, j.-h., jung, j.-w., kim, t.-h., choi, j.-h. and kim, d.-h. (2006). failure of carbon composite-toaluminum joints with combined mechanical fastening and adhesive bonding, composite structures, 75(1–4), pp. 192–198. doi: 10.1016/j.compstruct.2006.04.013. [28] chan, w. s. and vedhagiri, s. (2001). analysis of composite bonded/bolted joints used in repairing, journal of composite materials, 35(12), pp. 1045–1061. doi: 10.1177/002199801772662325. [29] hart-smith, l. j. (1985). bonded-bolted composite joints, journal of aircraft, 22(11), pp. 993–1000. doi: 10.2514/3.45237. [30] kanninen, m. f., broek, d., marschall, c. w., rybicki, e. f., sampath, s. g., simonen, f. a. and wilkowski, g. m. (1976). mechanical fracture predictions for sensitized stainless steel piping with circumferential cracks. [bwr]. [31] rodriguez, j. e., brennan, f. p. and dover, w. d. (1998). minimization of stress concentration factors in fatigue crack repairs, international journal of fatigue, 20(10), pp. 719–725. doi: 10.1016/s0142-1123(98)00039-5. [32] ramji, m., srilakshmi, r. (2012). design of composite patch reinforcement applied to mixed-mode cracked panel using finite element analysis, j. reinf. plast. compos., 71(2), pp. 258–70, doi: 10.1177/0731684412440601. [33] oudad, w., belhadri, d.e., fekirini, h. and khodja, m. 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can be opened with acrobat and adobe reader 5.0 and later.) >> /namespace [ (adobe) (common) (1.0) ] /othernamespaces [ << /asreaderspreads false /cropimagestoframes true /errorcontrol /warnandcontinue /flattenerignorespreadoverrides false /includeguidesgrids false /includenonprinting false /includeslug false /namespace [ (adobe) (indesign) (4.0) ] /omitplacedbitmaps false /omitplacedeps false /omitplacedpdf false /simulateoverprint /legacy >> << /addbleedmarks false /addcolorbars false /addcropmarks false /addpageinfo false /addregmarks false /convertcolors /converttocmyk /destinationprofilename () /destinationprofileselector /documentcmyk /downsample16bitimages true /flattenerpreset << /presetselector /mediumresolution >> /formelements false /generatestructure false /includebookmarks false /includehyperlinks false /includeinteractive false /includelayers false /includeprofiles false /multimediahandling /useobjectsettings /namespace [ (adobe) (creativesuite) (2.0) ] /pdfxoutputintentprofileselector /documentcmyk /preserveediting true /untaggedcmykhandling /leaveuntagged /untaggedrgbhandling /usedocumentprofile /usedocumentbleed false >> ] >> setdistillerparams << /hwresolution [2400 2400] /pagesize [612.000 792.000] >> setpagedevice microsoft word numero_35_art_6 m.v. bannikov et alii, frattura ed integrità strutturale, 35 (2016) 50-56; doi: 10.3221/igf-esis.35.06 50 focussed on crack paths experimental investigation of crack initiation and propagation in highand gigacycle fatigue in titanium alloys by study of morphology of fracture m.v. bannikov, o. b. naimark, v.a. oborin institute of continuous media mechanics ub ras, 614013, ac. koroleva street, 1, perm, russia mbannikov@icmm.ru, naimark@icmm.ru, oborin@icmm.ru abstract. fatigue (highand gigacycle) crack initiation and its propagation in titanium alloys with coarse and fine grain structure are studied by fractography analysis of fracture surface. fractured specimens were analyzed by interferometer microscope and electronic microscope to improve methods of monitoring of damage accumulation during fatigue test and verify the models for fatigue crack kinetics. fatigue strength was estimated for high cycle fatigue (hcf) regime using the luong method [1] by “in-situ” infrared scanning of the sample surface for the step-wise loading history for different grain size metals. fine grain alloys demonstrated higher fatigue resistance for both hcf and gigacycle fatigue regimes. fracture surface analysis for cylindrical samples was carried out using optical and electronic microscopy method. high resolution profilometry (interferometerprofiler new view 5010) data of fracture surface roughness allowed us to estimate scale invariance (the hurst exponent) and to establish the existence of two characteristic areas of damage localization (different values of the hurst exponent). area 1 with diameter ~300 µm has the pronounced roughness and is associated with damage localization hotspot. area 2 shows less amplitude roughness, occupies the rest fracture surface and considered as the trace of the fatigue crack path corresponding to the paris kinetics. keywords. fractography; gigacycle fatigue; titanium alloy. introduction cf and vhcf are important fundamental and engineering problems for several areas o applications. catastrophic events caused by failure of gas-turbine motors, high costs of fatigue life-time estimation for constructions and potential cost of development of new constructions initiated perspective conceptions in the area of hcf and vhcf based on the fundamental research in fatigue damage and reliability prediction. the kernel aspects of such programs are development of approaches using the results of fundamental research, modern approaches in the laboratory modeling and structural analysis for the prediction of characteristic stages of fatigue damage and the criticality signs under damage-failure transition. high interest to vhcf is determined during last decade and explaining the opportunity to reach number of cycles 108-1010 for materials and constructions of gas-turbine motors due to the usage of fine-grain superalloys and advanced technologies providing vhcf limit. recently, an increase in the strength properties of structural materials has been achieved by the formation of micro-and nano-crystalline structure. however, traditional methods of testing do not provide an estimate of fatigue life in gigacycle loading conditions (109 cycles to failure) leading to the emergence of new techniques based on ultrasonic testing machines like [2] and studying the h m.v. bannikov et alii, frattura ed integrità strutturale, 35 (2016) 50-56; doi: 10.3221/igf-esis.35.06 51 morphology of the fracture surfaces by modern methods of structural analysis. the effect of microstructure in pure titanium including submicrocrystalline (smc) and ti6al4v alloy was studied in gigacycle fatigue regime and qualitative differences in the mechanisms of fatigue crack initiation in high-and gigacycle fatigue conditions established. experimental conditions and materials pecimens of pure titanium with different microstructure from original polycrystalline state with grain size of 25 μm to smc state obtained through equal channel angular extrusion (ecae) at different conditions: smc-1 state (annealing at t = 450 °c, 8 passes of ecae , drawing from 14 to 9 mm at t = 200 °c, the grain size: 100-150 nm) and smc-2 state (annealing at t = 450 °c, 4 passes of ecae, the warm rolling from 12 to 8 mm at t = 350 °c, the grain size of 200 nm) and specimens of titanium alloy ti6al4v were investigated in highand gigacycle fatigue regime using the ultrasonic testing machine. in order to establish the scale invariant parameter [3-5] of crack initiation and growth in high and gigacycle fatigue fracture surfaces of samples were analyzed. a) b) c) figure 1: structure of ti grade-4: a) optical microscopy image of initial state (grain size ~25 µm); b) tem-image of smc-1 state (grain size ~150-200 µm); c) tem-image of smc-2 (grain size ~200 µm) according to transmission electron microscopy the microstructure of smc-1 material is more homogeneous, grains have equiaxial shape in transverse and longitudinal sections. in the longitudinal section of rod in smc-2 state we can observe development metallographic structure, which is characterized by elongated grains with dislocation substructure as a result of rolling after ecae. figure 2: geometry of specimen. values of sizes r1, r2, l2, l1 is depends on parameters of material and calculates in formals at [5]. fatigue tests were carried out on the ultrasonic loading machine shimadzu usf-2000, which imposes special load conditions due to the geometry of the samples (fig.2). during the experiment, the sample and components of the machine are in resonant oscillations which form a standing wave. in this case peaks of displacement are located on ends of the sample and maximum amplitude of stress is located in the center of sample [5]. results of fatigue experiments he result of fatigue tests are shown in the fig. 3. fatigue failure of ti6al4v after 109 cycles occurred at stress amplitude 495 mpa. failure of samples of pure titanium after 109 loading cycles occurred at 275 mpa stress amplitudes for the initial state and 375 mpa and 340 mpa for the states smc-1 and smc-2, respectively. fatigue s t m.v. bannikov et alii, frattura ed integrità strutturale, 35 (2016) 50-56; doi: 10.3221/igf-esis.35.06 52 life of titanium alloy ti6al4v in gigacycle regime corresponds to the data of bathias [5]. the dependence of material microstructure on its fatigue strength during gigacycle fatigue agrees with data observed in [6]. the smc-1 titanium tigrade 4 with equilibrium grain boundaries exhibits highest fatigue properties compared to the smc-2 state with nonequilibrium grain boundaries and to the polycrystalline state (grain size of about 25 μm). figure 3: fatigue curve data for investigated materials: σ – applied mean stress, nf –number of cycles to failure. 1 – ti6al4v bathias [6]; 2 – ti6al4v; 3 – ti grade-4 initial state; 4 – ti grade-4 smc-1 state; 5 – ti grade-4 smc-2 state. mechanisms of initiation and propagation of fatigue cracks were investigated by means of qualitative and quantitative analysis of the morphology of fracture surfaces. the results of observation reported in [7] show that during stress cycles several fine subgrains having different crystal orientations are formed in a thin layer (thickness is 400 nm) around nonmetallic inclusion. the following mechanism of crack initiation under long cyclic loading was proposed: a fine granular layer caused by the intensive polygonization is gradually formed around the interior inclusion. the number of microdamage centers in this layer gradually increases and some of them coalesce. when damage spread over the entire fine granular layer the crack is finally formed around the interior inclusion. after the crack has grown to a critical size, it propagates in accordance with the paris law kinetics:    mda c kdn , (1) where da/dn is the fatigue crack growth rate, c and m are empiric constants depending on the material, k is the stress intensity factor. qualitative analysis was carried out by using optical and electron microscopy of the surface morphology. quality and quantitative analysis of fracture surfaces estruction in gigacycle fatigue regime usually forms a characteristic type of fracture surface "fish-eye"[6-7]. qualitative analysis by optical microscope allows us to separate zones with different reflectivity. first zone with a radius of 150 µm from the source of crack is very dark, then light and smooth area is followed, which is then replaced by darker area (fig.4). by substituting the radius of the borders in the formula (2) for the stress intensity factor of radial inner cracks   2 / [ / ( 2 )]k a f d a , (2) where f is normalization function [8], d is diameter of the sample, these zones can be associated with the stages of crack nucleation and propagation. radius a = 150 microns corresponds to the threshold value of the stress intensity factor δkth for this material at which the crack begins to grow. in the area between borders of 1 and 2, the crack grows steadily by d m.v. bannikov et alii, frattura ed integrità strutturale, 35 (2016) 50-56; doi: 10.3221/igf-esis.35.06 53 paris law (1). area between boundaries 2 and 3 corresponds to catastrophically fast growth of crack. the value of k with radius of crack 3 1400 µm corresponds to the fracture toughness. figure 4: fracture surface of ti6al4v in gigacycle fatigue regime. 1) a= 150 µm, δk = 6.88 mpam ≈ δkth ; 2) a= 750 µm, δk = 21.3 mpam; 3) a= 1400 µm, δk = 54.1 mpam ≈ δk1c . the surface roughness was analysed by interferometer-profiler new view 5010 to establish quantitative characteristics of the fracture surface. two distinct zones with strongly different roughness were observed (fig. 5): zone i of the size ~ 100300 μm, depending on testing material in the vicinity of the crack origin has high fracture surface roughness, which corresponds to the area of defect initiation and accumulation during cyclic loading; zone ii that covers rest of the fracture surface is smoother than the first, corresponds to the crack propagation according paris law (1). these results confirm the crack initiation mechanism described in [7]. to investigate scale-invariant properties of the fracture surface, one-dimensional profiles with different lengths were analyzed using two-dimensional profiles with the interferometer new view data (fig.2). figure 5: image of the fatigue crack origin in cylindrical samples (ti6al4v) by interferometer new view 2-d. marked zones i and ii are the areas of crack initiation and propagation, respectively. solid lines are cross-sections of surface roughness used for the estimation of scale invariance (the hurst exponent) the hurst exponent was defined from the slope of linear portion of the correlation function k(r) in logarithmic coordinates [4, 9-10]:       1/22( ( ) ( )) h x с r z x r z x r (3) where z (x) is the relief height, depending on the coordinate x; angular brackets denote averaging over x, h is the hurst exponent. in logarithmic coordinates the slope of the linear plot of this function determines the hurst exponent. the spatial range of linear part establishes the correlated behaviour of defect induced roughness in the direction of fatigue crack propagation. m.v. bannikov et alii, frattura ed integrità strutturale, 35 (2016) 50-56; doi: 10.3221/igf-esis.35.06 54 the influence of the window size (image resolution) on the value of hurst exponent was investigated by analysing the fracture surface with different resolution from 2.5 μm and 0.1 μm per pixel respectively. starting from the resolution 0.3 μm by 1 pixel and larger, the value of the hurst exponent remains practically constant (fig.6). in that case all calculation was carried out on images with 0.5 microns per pixel resolution. figure 6: value of hurst exponent versus resolution of image. the correlation function (3) calculated from the profiles for both zones has two linear portions with a break on the scale, which corresponds to change in the mechanisms of fracture surface topography. whereas functions (2) calculated separately for zones 1 and 2 reveal only one linear portion for each zone (fig. 7). the gigacycle fatigue cracks for titanium grade 4 were originated near the surface (70-150 μm) and the crack hotspot generally could not be detected based on the optical image. the roughness pattern analyzed according to the new view data allows one to differentiate between the zones of crack origination (size ~ 100 μm) characterized by roughness invariance and the rest of the crack propagation roughness zone. figure 7: correlation function built on profiles: а) inside zone 1; b) inside zone 2. in samples of pure titanium grade-4 under gigacycle fatigue regime of loading the crack was initiated at a depth of 70-150 µm below the surface. whereas characteristic feature of the fracture surface of such images unlike the alloy ti6al4v is the lack of an optical image of any zone boundaries (fig. 8,a). however, at the height map obtained using profilometer new view 5010 (fig.8,b) we can observe the characteristic crack initiation zone, which roughness is different from the rest of the zone of crack propagation, its radius is about to 50 microns. m.v. bannikov et alii, frattura ed integrità strutturale, 35 (2016) 50-56; doi: 10.3221/igf-esis.35.06 55 a) b) figure 8: fracture surface of ti grade-4 a)-optical image, b) new view image. roughness of fracture surfaces of samples with the surface fatigue crack (fig. 9) was also investigated by interferometer new view 5010 and analyzed with correlation function (3). the correlation function detects only one slope across the fracture surface of both near and far from the crack initiation point. the value of the hurst exponent calculated on linear part of the correlation function corresponds to the fractal dimension of the profile of the crack propagating through paris law like in second zone in previous case. the accumulation defects zone typical to internal crack initiation is not detected. this shows fundamentally different mechanisms for the fatigue crack initiation in the bulk and on the surface of material. figure 9: new view image of 2dprofile fracture surface of ti grade-4 with fatigue crack initiated from surface of the specimen. conclusions he analysis of scale-invariant properties of fracture surface allowed us to establish the qualitative difference in terms of the scale invariance (the hurst exponent) of the surface roughness for the areas of crack initiation and propagation. the crack initiation area can be identified as the zone with pronounced multiscale defect interaction providing correlated behaviour over characteristic scale. the size of this zone and collective defect growth kinetics were studied in [10] and associated with special type of spatial-temporal defect organization named as collective blow-up mode of defects. the scenarios of crack nucleation (in the bulk of specimen for gigacycle load and at the surface for hcf) reflect qualitative different kinetics of collective behaviour of defects in mentioned regimes caused by typical size of defects and interaction length. however, the scenario of crack propagation under gigacycle regime corresponds to the paris law that reflects the similarity in the mechanisms of plastic flow at the crack tip that still follows the stress induced singularity in term of the stress intensity factor increment. acknowledgements his study was supported by the russian science foundation, project no. 14-19-01173. t t m.v. bannikov et alii, frattura ed integrità strutturale, 35 (2016) 50-56; doi: 10.3221/igf-esis.35.06 56 references [1] luong, m. p., infrared thermographics scanning of fatigue in metals, nuclear engineering and design., 158 (1995) 363-376. [2] bathias, c., piezoelectric fatigue testing machines and devices, international journal of fatigue, 28 (2006) 1438-445. [3] barenblatt, g.i., scaling phenomena in fatigue and fracture, international journal of fracture, 138(1) (2004) 19-35. [4] bouchaud, e., scaling properties of cracks, j. phys.: condens. matter., 9 (1997) 4319–4344. [5] oborin, v.a., bannikov, m.v., naimark, o.b., palin-luc, t., scale invariance of fatigue crack grow in gigacycle loading, technical physics letters., 36(22) (2010) 76-82. [6] bathias, c., paris, p.c., gigacycle fatigue in mechanical practice, marcel dekker publisher co, (2005). [7] sakai, t., review and prospects for current studies on high cycle fatigue of metallic materials for machine structural use, jour. solid mech. and mat. eng., 3(3) (2009) 425-439. [8] cherepanov, g.p., mechanics of brittle fracture / moscow, «nauka», (1974) 640, in russian. [9] ritchie, r.o., incomplete self-similarity and fatigue-crack growth, international journal of fracture, 132(3) (2005) 197-203. [10] oborin, v., bannikov, m., naimark, o., froustey, c., long range correlation large scale interactions in ensembles of defects: estimating reliability of aluminum alloys under dynamic cycling and fatigue loading conditions, technical physics letters, 37(3) (2011) 241–243. << /ascii85encodepages false /allowtransparency false /autopositionepsfiles true /autorotatepages /none /binding /left /calgrayprofile (dot gain 20%) /calrgbprofile (srgb iec61966-2.1) /calcmykprofile (u.s. web coated \050swop\051 v2) /srgbprofile (srgb iec61966-2.1) /cannotembedfontpolicy /error /compatibilitylevel 1.4 /compressobjects /tags /compresspages true /convertimagestoindexed true /passthroughjpegimages true /createjobticket false /defaultrenderingintent /default /detectblends true /detectcurves 0.0000 /colorconversionstrategy /cmyk /dothumbnails false /embedallfonts true /embedopentype false /parseiccprofilesincomments true /embedjoboptions true /dscreportinglevel 0 /emitdscwarnings false /endpage -1 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can be opened with acrobat and adobe reader 5.0 and later.) >> /namespace [ (adobe) (common) (1.0) ] /othernamespaces [ << /asreaderspreads false /cropimagestoframes true /errorcontrol /warnandcontinue /flattenerignorespreadoverrides false /includeguidesgrids false /includenonprinting false /includeslug false /namespace [ (adobe) (indesign) (4.0) ] /omitplacedbitmaps false /omitplacedeps false /omitplacedpdf false /simulateoverprint /legacy >> << /addbleedmarks false /addcolorbars false /addcropmarks false /addpageinfo false /addregmarks false /convertcolors /converttocmyk /destinationprofilename () /destinationprofileselector /documentcmyk /downsample16bitimages true /flattenerpreset << /presetselector /mediumresolution >> /formelements false /generatestructure false /includebookmarks false /includehyperlinks false /includeinteractive false /includelayers false /includeprofiles false /multimediahandling /useobjectsettings /namespace [ (adobe) (creativesuite) (2.0) ] /pdfxoutputintentprofileselector /documentcmyk /preserveediting true /untaggedcmykhandling /leaveuntagged /untaggedrgbhandling /usedocumentprofile /usedocumentbleed false >> ] >> setdistillerparams << /hwresolution [2400 2400] /pagesize [612.000 792.000] >> setpagedevice microsoft word numero_30_art_16 r. baptista et alii, frattura ed integrità strutturale, 30 (2014) 118-126; doi: 10.3221/igf-esis.30.16 118 focussed on: fracture and structural integrity related issues design optimization of cruciform specimens for biaxial fatigue loading r. baptista, r. a. claudio estsetúbal, instituto politécnico de setúbal, campus do ips, estefanilha, 2914-508 setúbal, portugal icems & idmec, instituto superior técnico, universidade de lisboa, av. rovisco pais, 1049-001 lisboa, portugal ricardo.baptista@estsetubal.ips.pt, ricardo.claudio@estsetubal.ips.pt l. reis, i. guelho, m. freitas icems & idmec, instituto superior técnico, universidade de lisboa, av. rovisco pais, 1049-001 lisboa, portugal luis.g.reis@ist.utl.pt, ivo.guelho@ist.utl.pt, mfreitas@dem.ist.utl.pt j. f. a. madeira isel, instituto superior de engenharia de lisboa, rua conselheiro emídio navarro, 1, 1959-007 lisboa, portugal icems & idmec, instituto superior técnico, universidade de lisboa, av. rovisco pais, 1049-001 lisboa, portugal jaguilar@dem.ist.utl.pt abstract. in order to correctly assess the biaxial fatigue material properties one must experimentally test different load conditions and stress levels. with the rise of new in-plane biaxial fatigue testing machines, using smaller and more efficient electrical motors, instead of the conventional hydraulic machines, it is necessary to reduce the specimen size and to ensure that the specimen geometry is appropriated for the load capacity installed. at the present time there are no standard specimen’s geometries and the indications on literature how to design an efficient test specimen are insufficient. the main goal of this paper is to present the methodology on how to obtain an optimal cruciform specimen geometry, with thickness reduction in the gauge area, appropriated for fatigue crack initiation, as a function of the base material sheet thickness used to build the specimen. the geometry is optimized for maximum stress using several parameters, ensuring that in the gauge area the stress is uniform and maximum with two limit phase shift loading conditions. therefore the fatigue damage will always initiate on the center of the specimen, avoiding failure outside this region. using the renard series of preferred numbers for the base material sheet thickness as a reference, the reaming geometry parameters are optimized using a derivative-free methodology, called direct multi search (dms) method. the final optimal geometry as a function of the base material sheet thickness is proposed, as a guide line for cruciform specimens design, and as a possible contribution for a future standard on in-plane biaxial fatigue tests. keywords. biaxial fatigue; in-plane testing; specimen optimization; direct multisearch; renard series. r. baptista et alii, frattura ed integrità strutturale, 30 (2014) 118-126; doi: 10.3221/igf-esis.30.16 119 introduction he study of biaxial fatigue life behavior is very important, as shanyavskiy [1] and cláudio et al. [2] have demonstrated, when considering the main applications of aluminum alloys or composite materials. recently different types of specimens and biaxial fatigue testing machines have been developed by the scientific community and therefore new challenges must be solved in order to assess the material properties. using the latest generation of inplane biaxial fatigue testing machines, like the one developed by cláudio et al. [3], using smaller and more efficient electrical motors, requires new specimens, with an optimal geometry, allowing to attain higher stress levels using lower loads. the cruciform specimen, a two-dimensional analogue of the uniaxial tensile specimen, has been used by different authors, but there is not a design accepted by all. hanabusa et al. [4], developed a cruciform geometry using slits on the specimen arms in order to promote an uniform stress and strain distribution on the specimen center, and to reduce the stress concentration on the specimen arms corner, independently of the load ratio applied. on the other hand, müller et al. [5], used notches on the specimen arms corners as a mean to achieve higher stress levels on the specimen center and to reduce the stress concentration on the specimen arms. finally several different types of specimens with a reduce thickness in the center, have been reviewed by bruschi et al. [6] or leotoing et al. [7]. this reduction drives the maximum stress and strains to occur on the specimen center, rather than on the specimen arms, while it still allows for a uniform strain and stress level to occur. this reduction can be achieved using a straight or curved profile, but leotoing et al. [7] have achieved excellent results, using a revolved spline profile. unfortunately there is still no specimen design standard, and one must choose all the available design variables very wisely in order to achieve the best results possible. an optimization process is one of the possible solutions to solve this problem. yu et al. [8] developed an optimization process in order to produce optimal center thickness on their specimens, while smits et al. [9] and makris et al. [10] have also used an optimization process to develop optimal geometries for their cruciform specimens. the aforementioned specimens all use reduced central thicknesses and similar specimen arms fillets, in order to achieve higher stress levels on the specimen center, while maintain uniform strain distributions. in the present paper a cruciform specimen geometry design is optimized for the use with low capacity test machine, [3]. the optimization process used the direct multi-search methodology to obtain several pareto fronts relating to two objectives functions: a) maximizing the stress level on the specimen center; b) maximizing the stress uniformity on the specimen center. all the cruciform specimens use a reduced center thickness and elliptical fillet on the arms corners in order to drive the optimization process. cruciform specimen design he geometry presented in this paper (fig. 1) was achieved after an extensive literature review and using the authors previous experience, [11]. this geometry has proven to be efficient by poncelet et al. [12] and ackermann et al. [13], for metallic specimens, but also by lamkanf et al. [14] for composite materials specimens. there were two main goals to achieve with this geometry, the first one was to guarantee that the maximum stress level occurred on the specimen center, while the second one was to assure the stress distribution on the specimen center was almost uniform. therefore one can expect the fatigue crack initiation to occur exactly on the specimen center. the geometry is derived from a cruciform geometry, with reduced thickness in the center of the specimen and uses an elliptical fillet in order to reduce the stress concentration in the arms corners. therefore one can aim to achieve the maximum stress level on the center of the specimen, while the stress level on the arms will be considerably lower, as shown by cláudio et al. [2]. the specimen center reduced thickness is achieved by using a revolved spline, in order to reduce the stress concentration between the original material thickness and the specimen center, while it is also possible to achieve a uniform stress level on the specimen center, within a radius of 1 mm, as reported by makinde et al. [15]. this geometry is defined by nine variables. two of them where considered constant, the specimen arm length with a value of 200 mm and the specimen arm width with a value of 30 mm for finite element modeling purposes. these dimensions have no influence on the final results. the specimen arm width is also a possible variable for future optimization problems, as it will influence the applied load in order to achieve a desirable stress level. tab. 1 shows five of the other variables which were used in the optimization problem. the center thickness (tt) is a value of the arms thickness (t) (material base) and ratios of 15% and 17% were considered, while the spline exit angle (theta) is a very important variable ensuring a smooth geometrical transition to avoid stress concentration in the critical region. the center spline radius (rr) defines the area where the specimen thickness is reduced, using the above referenced revolved spline, that has a tangency t t r. baptista et alii, frattura ed integrità strutturale, 30 (2014) 118-126; doi: 10.3221/igf-esis.30.16 120 of 0º at the center. the elliptical fillet is centered between the specimen arms and is defined by three variables, the major ellipse radius (rm), the minor ellipse radius (rm) and the ellipse center (dd). figure 1: specimen geometry, dimensions in mm. arms thickness (t) center thickness (tt) spline exit angle (theta) centre spline radius (rr) major ellipse radius (rm) minor ellipse radius (rm) ellipse center (dd) min 1 mm 15% of t 30º 4 mm 56 mm 16 mm 46 mm max 10 mm 17% of t 90º 15 mm 70 mm 30 mm 60 mm table 1: design variables used in the specimen design geometry optimization. finally the specimen arms thickness (t) is also a variable and one of the most important. this was the base variable for all the optimizations performed in the present work. in order to achieve on the main goals, the arms thickness was chosen using the renard series of preferred numbers [16], which is used as a base for material standard presentation by sheet manufactures. therefore the present results may be directly used by the end user. tab. 2 shows the used arms thickness on the present paper, in order to optimize the geometry shown in fig. 1. r10″ 1 2 3 4 5 6 7 8 9 10 11 arms thickness (t) [mm] 1.00 1.20 1.50 2.00 2.50 3.00 4.00 5.00 6.00 8.00 10.00 center thickness (tt) [mm] 0.17 0.20 0.25 0.33 0.42 0.50 0.67 0.83 1.00 1.20 1.50 table 2: design variables used in the specimen design geometry optimization. the series chosen is the r10″, which is rounded, between 1 mm and 10 mm of the arms thickness. i order to simplify the optimization problem to five active variables, the problem was solved individually for each arm thickness and center thickness as provided in tab. 2. this variable can, and will also be explored in future works, but on the present paper was kept constant with a value of 17% of the arms thickness, except for the higher values of 8 and 10 mm, where it was kept constant on 15%, because the optimization convergence was not able to be met with the previous value. these ratios were considered from previous optimization results, where the arms thickness was an active variable, [11]. r. baptista et alii, frattura ed integrità strutturale, 30 (2014) 118-126; doi: 10.3221/igf-esis.30.16 121 multi-objective optimization constrained nonlinear multi-objective optimization problem (moo) can be mathematically formulated as, [17]: find n design variables:  1 2, ..., t nx x x x (1) which minimizes:         1 2 . . min , , ..., t k s t x f x f x f x f x   (2) involving k objective functions  : , 1, ...,njf j k       to minimize. recall that to maximize fj is equivalent to minimize -fj.  n     represents the feasible region. any or all functions fj, j=1,…,k can hold a nonlinear nature. in general, since in moo there are often conflicting objectives for each objective function, the concept of pareto dominance is used to characterize global and local optimality, [17]. a feasible solution of x is called a pareto optimal if there exists no other feasible solution y such that fi(y)≤fi(x) for all i={1,2,…,k} with fj(y) < fj(x) for at least one j, j ∈ {1,2,…,k}. the direct multisearch (dms) algorithm [17] is a derivative-free method for multiobjective optimization problems. this algorithm does not aggregate or scalarize any components of the objective function and it is inspired by the searchpoll paradigm of direct-search methods of directional type from single to multiobjective optimization. through the use of the concept of pareto dominance, this algorithm generates and maintains a list of feasible nondominated points from which it iterates and chooses new poll centers. the dms algorithm tries to capture the whole pareto dominance front from the polling procedure and at each iteration, if improvement is found, the new feasible evaluated points are added to the list (approximating the pareto front) and the dominated ones are removed. successful iterations then correspond to changes in the approximation of the pareto front meaning that a new feasible nondominated point was found, otherwise, the iteration is declared as unsuccessful. the search step is optional and set as to best fit to the optimization problem characteristics in order to improve the numerical performance. in direct multisearch, constraints are handled using an extreme barrier function:      , ..., f x if x f x otherwise      (4) which means that if a point is infeasible (not belonging to the predetermined feasible points universe or compromised by the problem constraints), the components of the objective function f are not evaluated and the values of f are set to +∞. this approach allows us to deal with black-box type constraints where only a yes/no answer is returned. optimization procedure the optimization procedure uses three different programs. initially matlab creates an input file with the initial design variables values. these variables, as referred in tab. 1, are the minor ellipse radius (rm), the major ellipse radius (rm), the ellipse center (dd), the center spline radius (rr) and the spline exit angle (theta), whose limits (introduced as restrictions) are given in tab. 1. using a python script the resulting geometry is created by finite element method (fem) code abaqus, as well as all the loads and boundary condition are applied to the model. the chosen material is an aluminium alloy with young modus of 69 gpa and poisson ratio of 0.3. once solved all the necessary stresses and strains are saved in to individual files, which are read by matlab in order to validate the solution and to calculate the two objective functions, using eq. (5) and (6): f1(x) = σmaximum von mises stress level on specimen center (5) f2(x) = max(δσcenter stress/σcenter stress) (6) the first objective function is the negative value of the maximum stress level on the specimen center, and the second objective function is the maximum stress level difference within a 1m radius of the specimen center. using the dms a r. baptista et alii, frattura ed integrità strutturale, 30 (2014) 118-126; doi: 10.3221/igf-esis.30.16 122 algorithm described above a new set of design variables are calculated, and by repeating this procedure the pareto front will be generated. load cases and boundary conditions the optimization process used a simplified version of the cruciform specimen for fem calculations. due to symmetry, 1/8 of the geometry was modeled and symmetry boundary conditions were applied to all three symmetry planes. 32315 tridimensional linear elements were used, with a total of 40548 nodes per simulation. also two different load cases were studied, the first load case is an in-phase (δ=0º) loading, with a 1 kn load applied in both directions. the second load case is an out-of-phase (δ=180º) loading, with a 1 kn load applied on one direction and a – 1 kn load applied to the second direction. for both load cases the validation conditions where the same. the difference between the maximum stress level on the specimen center and the arms must be higher than 20%, while the stress differences in both directions within a 1mm radius of the specimen center must be lower than 2%. therefore one can guaranty that the maximum stress level occurs on the specimen center, and is uniform enough in order for the geometry to be appropriated for fatigue crack initiation. specimen optimization results fter running the optimization procedure for every arms thickness on tab. 2, it was possible to obtain several optimized specimen geometry, as exemplified on tab. 3. each configuration of variables where chosen from each of the pareto fronts obtained for the renard series of tab. 2. they do not represent the global optimum solution for the maximum stress level, or stress uniformity level, they were chosen within the pareto front in order to produce a smooth evolution for every variable, as the arms thickness is changed. therefore it will possible to attain a relationship between those variables and the arms thickness. each configuration on tab. 3, represents a point on the pareto front (fig. 2) for the corresponding value of arms thickness, any point of the pareto front could have been chosen, as they all are mathematically equal. but the main goal of this paper is to establish a relationship between every specimen geometry variable and the arms thickness, therefore tab. 3 represents the best configurations possible to achieve this goal. t, mm (fixed) rm, mm rm, mm theta, º rr, mm dd, mm tt, mm (fixed) maximum stress, mpa/kn stress difference, % 1.0 61.7 22.5 71 5.9 51.3 0.166 146 0.657 1.2 62.2 21.9 68 5.0 52.0 0.200 109 0.931 1.5 62.7 22.0 64 5.0 52.4 0.250 87 0.859 2.0 63.9 22.3 36 5.8 52.4 0.334 76 0.587 2.5 61.6 22.3 60 5.5 51.7 0.416 53 0.784 3.0 60.1 22.3 66 5.2 51.7 0.500 37 0.753 4.0 58.7 25.8 38 9.1 51.3 0.666 29 0.284 5.0 56.0 25.8 45 9.6 49.9 0.834 22 0.616 6.0 56.7 25.8 43 9.8 50.1 1.000 19 0.825 8.0 63.4 28.6 72 9.8 55.1 1.200 15 0.715 10.0 65.1 28.6 70 9.9 57.6 1.500 10 0.932 table 3: optimal specimen geometry for each renard series value of arms thickness. a r. baptista et alii, frattura ed integrità strutturale, 30 (2014) 118-126; doi: 10.3221/igf-esis.30.16 123 arms thickness influence the arms thickness influence changes the optimal specimen geometry in different ways when one analyses the different variables used in this optimization. in fig. 3 it is possible to assess the influence of the arms thickness on the form and position of the elliptical fillet used between the specimen arms. one can see that for arm thickness values less than 2 mm, both the major and minor ellipse radius, rm and rm, increase with the arm thickness. then both these values decrease, between 2 and 6 mm of arm thickness, before they will increase again. in a different way the position of the center of the elliptical fillet position (dd) is directly proportional to the arms thickness. the variables used to define the revolved spline for the specimen center generation are also influenced by the arms thickness. the center thickness was considered constant in every optimization, therefore the centre spline radius and spline exit angle, rr and theta, variation can be found in fig. 4 and fig. 5. both these variables are related, as it will be discussed next, but their variation with the arms thickness is clear. the center spline radius is almost constant for thickness values less than 3 mm, before it starts to increase very rapidly between thicknesses of 4, 5 and 6 mm. then it is almost constant again for higher thickness values. the spline exit angle clearly decreases with the thickness, for values less than 4 mm, before it starts to increase again. some optimal configurations do not represent this behavior, but some of these exceptions can be justified by the spline exit angle and centre spline radius influence discussed next. lines plotted in fig. 3 to 5 represents the polynomial interpolation to the points. spline exit angle and centre spline radius influence the specimen geometry contain on its center a revolved spline defined by three variables. two of them are very important for the maximum stress level and stress uniformity level. considering all the points on the pareto fronts one can see that decreasing the spline exit angle, the maximum stress level on the specimen center increases, while the stress uniformity level decreases. in order to justify this effect, one must consider the spline profile. as the spline exit angle decreases, the slope around the specimen center becomes steeper, increasing the stress level but decreasing the stress uniformity. the center spline radius has the same effect. increasing the center spline radius, increases the size of the area where the thickness in reduce, therefore increasing the stress uniformity level while decreasing the maximum stress level. again the spline profile, is responsible for this effect. figure 2: pareto fronts for several arms thickness figure 3: arms thickness influence on the elliptical fillet. figure 4: arms thickness influence on the centre spline radius. figure 5: arms thickness influence on the spline exit angle. r. baptista et alii, frattura ed integrità strutturale, 30 (2014) 118-126; doi: 10.3221/igf-esis.30.16 124 combining both variables allows the optimization process to generate points where both the maximum stress level and the stress uniformity level are optimal. combining these points with the other variables, it is possible to obtain the pareto fronts provided on fig. 2. analyzing the pareto fronts it is possible to report that sometimes the optimization algorithm achieved better results by decreasing the value of the spline exit angle while increasing the value of the center spline radius, this happened for the arms thickness of 2 mm. unfortunately this behavior leads to a difficult correlation between the center spline radius or the spline exit angle variables and the arms thickness, as seen on fig. 4 and 5. center thickness influence the influence of the center thickness was studied in the preparation work for this paper. the center thickness is the most important variable on the specimen center maximum stress optimization. this variable dominates all the others and using it on the optimization process, means this variable will always assume the lower bound value. therefore decreasing the center thickness, increases the maximum stress level, while the stress uniformity decreases. considering the domination effect the center thickness was considered fixed on the present results. the authors decide to start with a relationship of 17% between the center thickness and the arms thickness, based on past works by cláudio et al. [11]. nevertheless as the arms thickness increases with the renard series number, for values of 8 and 10 mm, it was impossible to achieve convergence of the optimization process using a 17% ratio. the solution used was to decrease the center thickness, and a 15% ratio was used, as seen on tab. 3. future work planed by the authors will include the use of different ratios between the center and arms thickness, in order to establish the relationship between both these variables and the optimal specimen geometry. stress distribution on the specimen center the conditions for solution acceptance in the optimization process, included the center maximum stress to be 20% higher than the arms maximum stress (based on several experimental tests experience), and the stress differences on the specimen center to be less than 2% in 1 mm radius (accepted reasonable limit for the authors). considering that the stress uniformity level was an optimization objective, it was expected to achieve even lower center stress differences. fig. 6 shows the evolution of the center stress differences with the renard series thickness values (also according to tab. 3), one can see the maximum value is 0.93%. fig. 7 shows the von mises stress distribution around the center of a specimen with 5 mm of arms thickness for the first load case (proportional). it is possible to see how the stress level is almost constant on the specimen center, while the arms stress is always at an inferior level. by changing the loading conditions, one can see on fig. 8 how the stress distribution remains almost constant on the specimen center, even with the presence of nonproportional load case with a phase shift of 180º. finally fig. 9 shows the relationship between the arms thickness and the optimal maximum stress level on the specimen center. as expected the stress level decreases as the arms thickness increases. fig. 9 shows the maximum stress levels for the first load case, it can be shown that on the second load case, the von mises stress level is 3.4 time higher, while the normal stress levels are 2 times higher. final specimen optimal geometry following the present results it is possible to recommend the use of an optimal geometry as a function of the material arms thickness, using eq. (7) to (13), which are plotted in fig. 3 to 5: rm(t) = -0.0379t4 + 0.8223t3 5.5749t2 + 12.555t + 53.84 (7) rm(t) = -0.0236t3 + 0.3501t2 0.5036t + 22.185 (8) dd(t) = -0.021t4 + 0.4668t3 3.248t2 + 7.9452t + 46.224 (9) rr(t) = -1.2979t3 + 8.1814t2 16.157t + 15.071 for: 1 ≤ t ≤ 3 mm (10) rr(t) = 0.0171t3 0.3968t2 + 3.0199t + 2.2763 for: 4 ≤ t ≤ 10 mm (11) theta(t) = 2.0201t3 3.4534t2 14.954t + 87.4 for: 1 ≤ t ≤ 3 mm (12) theta(t) = -0.7621t3 + 15.484t2 92.774t + 211.78 for: 4 ≤ t ≤ 10 mm (13) these equation are valid for 1≤ t ≤ 10 mm and considering that tt is equal to 0.17t, for t<8 mm and tt equal to 0.15t if t≥8 mm. also these equations are not valid for t=2mm, as the behavior on this point is significantly different. future validation and extra work will allow to include on the previous equations the influence of the center thickness (tt), and therefore construct a standard cruciform specimen geometry for biaxial fatigue in-plane testing. r. baptista et alii, frattura ed integrità strutturale, 30 (2014) 118-126; doi: 10.3221/igf-esis.30.16 125 figure 6: center stress differences. figure 7: stress distribution in the optimized geometry, t=5mm, load case 1. figure 8: stress distribution in the optimized geometry, t=5mm, load case 2. figure 9: maximum center stress, load case 1. conclusions he direct multi-search model was able to produce several pareto fronts for a very complicated finite element problem, which included two objective function and five active design variables. each pareto front was obtained for each arms thickness, based on the renard series of preferred numbers, and therefore the specimen designer can obtain the optimal geometry as a function of the desired material thickness. within the pareto front all the specimen geometries configurations are mathematically equal, therefore the ones chosen in this paper represent the best possible correlation between the design variables and the arms thickness. it was possible to achieve a correlation between the arms thickness and the specimen elliptical fillet variable. on the other hand the relationship between the center spline radius or the spline exit angle and the arms thickness still need to be worked on. both these variables have the same effect on the maximum stress level and stress uniformity level on the specimen center. decreasing their value leads to an increase on the maximum stress level and a decrease on the stress uniformity level. therefore different combinations lead to similar results. decreasing the specimen center reduced thickness value leads to higher stress levels, but is was found that this is a dominating variable. therefore the center thickness was assumed constant, sa ratio of the arms thickness, in the optimization process. future work will require to achieve a correlation between this variable and the other specimen design variables. two different loading conditions were studied, and it is possible to report that the second load case produces higher stress levels on the specimen center. .as expected increasing arms thickness decreases the maximum stress level on the specimen. references [1] shanyavskiy, a., fatigue cracking simulation based on crack closure effects in al-based sheet materials subjected to biaxial cyclic loads, eng. fract. mech., 78 (8) (2011) 1516–1528. t r. baptista et alii, frattura ed integrità strutturale, 30 (2014) 118-126; doi: 10.3221/igf-esis.30.16 126 [2] cláudio, r. a., freitas, m., reis, l., li, b., guelho, i., multiaxial fatigue behaviour of 1050 h14 aluminium alloy by a biaxial cruciform specimen testing method, in: 10th int. conf. multiaxial fatigue fract., (2013). [3] cláudio, r., freitas, a. m., reis, l., li, b., guelho, i., antunes, v., maia, j., in-plane biaxial fatigue testing machine powered by linear iron core motors, sixth symp. appl. autom. technol. fatigue fract. test. anal., astm stp 1571 (2013). [4] hanabusa, y., takizawa, h., kuwabara, t., numerical verification of a biaxial tensile test method using a cruciform specimen, j. mater. process. technol., 213(6) (2013) 961–970. [5] müller w., pöhlandt, k., new experiments for determining yield loci of sheet metal, j. mater. process. technol., 60(i 996) (1996) 643–648. [6] bruschi, s., altan, t., banabic, d., bariani, p. f., brosius, a., cao, j., ghiotti, a., khraisheh, m., merklein, m., tekkaya, a. e., testing and modelling of material behaviour and formability in sheet metal forming, cirp ann. manuf. technol. (2014). [7] leotoing, l., guines, d., zidane, i., ragneau, e., cruciform shape benefits for experimental and numerical evaluation of sheet metal formability, j. mater. process. technol., 213(6) (2013) 856–863. [8] yu, y., wan, m., wu, x.-d., zhou, x.-b., design of a cruciform biaxial tensile specimen for limit strain analysis by fem, j. mater. process. technol., 123(1) (2002) 67–70. [9] smits, a., van hemelrijck, d., philippidis, t. p., cardon, a., design of a cruciform specimen for biaxial testing of fibre reinforced composite laminates, compos. sci. technol., 66(7–8) (2006) 964–975. [10] makris, a., vandenbergh, t., ramault, c., van hemelrijck, d., lamkanfi, e., van paepegem, w., shape optimisation of a biaxially loaded cruciform specimen, polym. test., 29(2) (2010) 216–223. [11] guelho, i., reis, l., freitas, m., li, b., madeira, j. f. a., cláudio, r. a., optimization of cruciform specimen for a low capacity biaxial testing machine, in: 10th int. conf. multiaxial fatigue fract., (2013). [12] poncelet, m., barbier, g., raka, b., courtin, s., desmorat, r., le-roux, j. c., vincent, l., biaxial high cycle fatigue of a type 304l stainless steel: cyclic strains and crack initiation detection by digital image correlation, eur. j. mech. a/solids, 29(5) (2010) 810–825. [13] ackermann, s., kulawinski, d., henkel, s., biermann, h., biaxial in-phase and out-of-phase cyclic deformation and fatigue behavior of an austenitic trip steel, int. j. fatigue, 67 (2014) 123–133. [14] lamkanfi, e., van paepegem, w., degrieck, j., ramault, c., makris, a., van hemelrijck, d., strain distribution in cruciform specimens subjected to biaxial loading conditions. part 1: two-dimensional versus three-dimensional finite element model, polym. test., 29(1) (2010) 7–13. [15] makinde, a., thibodeau, l., neale, k., development of an apparatus for biaxial testing using cruciform specimens, exp. mech., 32(2) (1992) 138–144. [16] o. for standardization, iso 3, preferred numbers — series of preferred numbers, (1973). [17] custódio, a.l., madeira, j.f.a., vaz, a.i.f., vicente, l.n., direct multisearch for multiobjective optimization, j. optim., (2011) 1–33. microsoft word numero_50_art_42_2617 v. saltas et alii, frattura ed integrità strutturale, 50 (2019) 505-516; doi: 10.3221/igf-esis.50.42 505 focused on the research activities of the greek society of experimental mechanics of materials the use of acoustic emissions technique in the monitoring of fracturing in concrete using soundless chemical demolition agent vassilios saltas, despoina peraki laboratory of geophysics and seismology – unesco chair in solid earth physics and geohazards risk reduction, technological educational institute of crete, greece vsaltas@chania.teicrete.gr, http://orcid.org/0000-0003-4958-2876 desnikper@gmail.com filippos vallianatos laboratory of geophysics and seismology – unesco chair in solid earth physics and geohazards risk reduction, technological educational institute of crete, greece dept of geophysics–geothermics, faculty of geology and geoenvironment, national and kapodistrian university of athens, greece fvallian@geol.uoi.gr abstract. soundless chemical demolition agents (scdas) have been used during the last decades in the demolition of boulders and concrete structures as well as in open-surface and sub-surface rock excavation, as an alternative to the use of explosives posing safety risks. however, the knowledge of the governing fracture mechanisms in brittle materials is rather limited. in the present work, we thoroughly investigate the use of the acoustic emission technique to study the scda-induced fracture process in concrete blocks. energy-related features and waveform parameters of the recorded ae activity are correlated to the fracture mode of the concrete where a quasi-static behavior is observed. monitoring of the progressive fracture is also achieved by the 3d localization of the ae sources. the distribution of the inter-event times of the recorded hits is further analyzed in the context of non-extensive statistical physics. keywords. acoustic emissions; fracture; soundless chemical demolition agent; concrete; non-extensive statistical physics; tsallis entropy. citation: saltas, v., peraki, d., vallianatos, f., the use of acoustic emissions technique in the monitoring of fracturing in concrete using soundless chemical demolition agent, frattura ed integrità strutturale, 50 (2019) 505-516. received: 29.01.2019 accepted: 27.05.2019 published: 01.10.2019 copyright: © 2019 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. introduction oundless chemical demolition agents (scdas) have been used during the last decades in the demolition of boulders and concrete structures as well as in open-surface and sub-surface rock excavation, as an effective alternative to the use of explosives posing safety risks [1-5]. recently, the potential application of scda fracking in unconventional oil and gas recovery as well as in mineral processing applications has been under investigation [5,6]. the effect of the nons http://www.gruppofrattura.it/va/50/2617.mp4 v. saltas et alii, frattura ed integrità strutturale, 50 (2019) 505-516; doi: 10.3221/igf-esis.50.42 506 explosive cracking agents on fracturing of the surrounding media inside a borehole is based on the volume thermal expansion of the cracking agent, caused by the exothermic hydration reaction of cao under confined conditions. in the proper mixing ratio of the cracking agent to water, the subsequent coagulation and rigidity of the mixture results in the development of high expansive pressures within the pre-drilled holes that eventually causes a complex fracture network in the concrete or the rock mass [7]. in addition to commercial use, non-explosive expansion material has been utilized in laboratory experiments to evaluate its fracturing capacity of synthetic specimens, and its potential application for fracturing coal roofs in coal mines has been proposed [8]. guo et al. used soundless cracking agent in laboratory scale experiments to form a fracture network in shale specimens, in order to establish an evaluation method for the hydraulic fracturing in shale reservoirs [9]. more recently, zhai et al. have proposed the application of non-explosive expansion method in the field of reservoir fracturing for the extraction of coal bed methane [10]. in the previous three cases, the acoustic emission (ae) technique was used for the dynamic monitoring and analysis of the fracture network formation. to the best of our knowledge, these are the only available studies where the effect of scdas in fracturing has been studied by means of the ae technique. although the optimum operation conditions of scdas, related to the external temperature, hole size and spacing, and mixing ratio of agent to water have been studied to some extent [2,11], the knowledge of the governing fracture generation and propagation mechanisms in concrete or rock masses is rather limited [5]. regarding fracture mechanisms, quasi-static conditions can be considered in scda-induced rock fracturing, due to the observed stable crack propagation at low crack velocities, and micro-crack based sliding models are likely to be applied [5]. in this direction, the well-established monitoring technique of ae can provide valuable information on the fracture mechanisms in rocks and concrete structures under the effect of scdas [12-14]. the present study explores the potential use of the ae technique to study the scda-induced fracture process in concrete samples. the generation and propagation of micro-cracks into concrete specimens in unconfined state due to the addition of expansion mortar to pre-drilled holes is monitored for a period of 24-h, by an array of ae sensors. the experimental data are analyzed using parameter-based and statistical methodologies of acoustic emissions. experimental setup oncrete blocks used for pavement cover were cut in prismatic shape and a cylindrical hole, of 10 mm diameter and a depth of a few cm, was drilled vertically to one of its surfaces (refer to fig.1a). the pre-drilled hole was filled with dexpan soundless chemical demolition agent [5,15], in the appropriate mixing ratio of water to cementitious powder (~3.5:10), to achieve maximum expansive strenght (124 mpa, according to the manufacturer). the monitoring of concrete fragmentation in the absence of any confinement, by the ae technique was carried out at ambient pressure and temperature. seven ae piezoelectric sensors operated at 200-750 khz (pico-sensors of physical acoustics corporation) were mounted with silicon glue on all the surfaces of the concrete specimen. pre-amplification of 40 db was used in all sensors and the threshold of detection was set at 39 db, to avoid the background noise. the ae activity of the concrete block was monitored continously under the effect of the expansive mortar, for a period of 24 hours. a pci-2 card based ae multichannel system (physical acoustics corporation) was used to record the detected signals (hits) in each sensor and the ae hit parameters (amplitude, duration, rising time, rising angle, etc) were automatically extracted and further analysed by dedicated software (aewin and noesis by mistras group). a characteristic recorded signal (hit) with the calculated based ae parameters is shown in fig.2. peak definition time (pdt), hit definition time (hdt) and hit lockout time (hlt) were set as 50, 200 and 300 μs, respectively. the sampling rate was set at 5 msamples/s. the acoustic wave velocity of concrete specimens was determined experimentally by using two of the ae sensors in pulse-receive mode and found to be (3120±70)m/s. we have to mention that the highly inhomogeneous concrete specimen combined with the finite size of the ae sensors inevitably introduces errors in determining the location of the ae sources. results and discussion a parameter-based analysis of acoustic emissions he time history of the ae activity, expressed as the number of hits in time bins and their amplitudes, recorded in all channels during the effect of the cracking agent on the concrete block for a 24-h monitoring period, is illustrated in fig.3, as a three-dimensional plot. from the recording time ti≈43618 sec (~12 h) a large number of hits with ampli c t v. saltas et alii, frattura ed integrità strutturale, 50 (2019) 505-516; doi: 10.3221/igf-esis.50.42 507 figure 1: (a) the concrete specimen with the ae sensors mounted on it. the arrow indicates the pre-drilled hole filled with the expansive mortar and the dashed circles indicate the positions of the visible ae sensors; (b) the concrete block at the end of the monitoring where the fracture plane is parallel to the y-z plane; (c) view of the two splitting pieces of the concrete block after its ultimate rupture. white arrows indicate main visible macro-cracks. figure 2: a representative recorded ae signal (hit) of moderate amplitude (61.4 db), recorded in channel 6, at relative recording time, t= 13675.24175475 s. rising angle (ra=1.2 μs/db) is defined as the ratio of rising time (rt=74.2 μs) to the corresponding amplitude. tudes up to 90 db starts to be observed, while afterwards, the recorded hits and their amplitudes are gradually decreased until the end of the monitoring test. this observed peak (refer to fig.3) is attributed to the initiation of cracks generation into the concrete specimen, which occurs when the expansion stress of the cracking agent exceeds the tensile strength of the concrete specimen. the initiation of the fracturing process is manifested by a concentrated ae activity, that is, 3.5 % (or 205 hits) of the total number of hits, over a short period of 0.5 sec. subsequently, a considerable ae activity is recorded (~45% of the total activity) that lasts for a long period of about 5.1 h. this is related to the additional generation of micro-cracks and their coalescence which leads to the formation of the major macro-cracks in the concrete specimen, as it is shown in fig.1(b, c). it should be noted here that the crack initiation was observed after 12 h which is far from the corresponding value suggested by the manufacturer, i.e. 2-8 h after the injection of scda. the latter, however, should be considered as the optimum value under certain operating conditions which are related to the ambient temperature, the water content and the diameter of the borehole. a low ae activity is occasionally recorded in all channels before the observed onset of the fracturing process and from the beginning of the monitoring test, corresponding to ~4% (i.e., 243 hits) of the total number of hits and to amplitudes ≤ 61 db. this activity should be associated with micro-cracks and friction effects, caused during the thermal expansion of the cracking agent within the pre-drilled hole of the concrete block. it is worth noting that there is no clear pre-failure activity, indicative of the upcoming fracturing process which started suddenly after about 12 h of the beginning of the monitoring test. the high recorded ae activity that is related to the initiation of the cracking process in the concrete block is also reflected to the duration of the recorded hits in each of the 7 channels, as it is illustrated in fig.4. according to fig.4, the hits recorded around the time 𝑡 43618 sec have duration as high as a few ms, while afterwards and for the rest of the monitoring v. saltas et alii, frattura ed integrità strutturale, 50 (2019) 505-516; doi: 10.3221/igf-esis.50.42 508 figure 3: time history of the distribution of amplitudes and the occurrence rate of the recorded ae hits in all channels, during the 24h monitoring of the fracturing process of the concrete specimen under the effect of the cracking agent. figure 4: 3d plot of the time evolution of the duration (in μs) of the hits in each recording channel, during the 24-h monitoring period of the concrete block subjected to the cracking agent charging. v. saltas et alii, frattura ed integrità strutturale, 50 (2019) 505-516; doi: 10.3221/igf-esis.50.42 509 figure 5: the cumulative absolute energy (in aj) in each recorded channel, during the monitoring test of the concrete specimen. the overall monitoring period is divided into 3 stages, a, b and c (see text for details). period, the recorded hits have substantially lower duration. prior to the onset of the intense ae activity, the duration of the occasional recording hits are limited to less than 1 ms, suggesting that the corresponding acoustic emissions have rather low energies and do not correspond to any significant precursory signal of the upcoming scda-induced cracking process. further information on the cracking process caused by the expansive agent in the concrete block can be derived from the time evolution of the cumulative absolute energy of the recorded hits in each channel, during the monitoring period (refer to fig.5). the highest cumulative energy is recorded in channel 6, which is closer to the hole filled with the expansive agent. in all sensors, however, the recorded energy variations exhibit the same characteristics. the overall monitoring period has been divided into 3 stages, depending on their specific characteristics. the “silent” stage a (0-43618 sec) that appears prior to the initiation of the cracking process, corresponds to a limited number of hits (~4% of the total number) with low amplitudes and short durations and thus to a cumulative energy close to zero. in stage b which lasts for 5.1 h, the cumulative energy of hits increases drastically exhibiting stepped-like behavior that corresponds to the formation of macro-cracks, as it is shown in figs.1(b,c). this stage of strong ae activity can be considered as the effective period of action of the expansive agent in the fracture of the concrete specimen. finally, in region c, although the recorded hits reach 20% of the total, the cumulative energy remains almost constant until the end of the monitoring test, due to the relatively short duration and the low amplitudes of the recorded hits. the separation of the monitoring period in the aforementioned stages, according to the values of the cumulative energy will be used later in the statistical analysis of the ae data. the characterization of the cracking mode (tensile or mode-i and shear or mode-ii) during the fracturing process of the concrete specimen can be achieved by correlating specific ae parameters, namely average frequency (af) and rising angle (ra) [16-19]. this classification is based on the fact that the slower shear waves transmit more energy than the faster tensile waves, resulting to longer rising time and to a low frequency content of the recorded waveform, in opposition to the tensile waves which correspond to short rising times and higher frequencies [16]. the average frequency as a function of the rising angle of the recorded hits in channel 6, for the stages a and b of the monitoring procedure is depicted in fig.6a. additionally, two representative recorded waveforms corresponding to different cracking modes and their frequency content are illustrated in figs.6(b,c). we observe that the majority of the recorded hits are characterized by low values of ra and af values in the low frequency range, i.e. 50-250 khz. according to the aforementioned classification, these recorded hits are due to the formation of tensile cracks inside the concrete specimen. this is in accordance to the shape of the specimen after fracture, as it is depicted in fig.1b. the compressive stresses that develop in the radial direction of the cylindrical hole and accumulate to the interface between the expansive agent and the walls, lead to indirect tensile stresses in the tangential direction of the hole which manifest as macro-cracks in the y-z plane. the latter is the predominant plane of fracture, since the distance of the cylindrical hole from the side surfaces of the specimen is minimal in the y-direction, corresponding to minimal confinement from the surrounding material. these observations are in agreement with published results stating that scda-induced initial cracking occurs when the mean value of the tangential stress reaches the splitting tensile strength of the specimen and the crack propagation is caused mainly by mode-i type of failure [5,11,20,21]. v. saltas et alii, frattura ed integrità strutturale, 50 (2019) 505-516; doi: 10.3221/igf-esis.50.42 510 as it is clearly observed in fig.1c, additional smaller macro-cracks were also propagated from the interface of the hole with the concrete, without however reaching the outer surface, due to the higher surrounding confinement. these cracks should be of shear and mixed-type and they are observed in a smaller percentage, as it is evident in fig.6a. their presence in random directions could be attributed to the heterogeneity of the concrete specimen. in both cases of tensile and shear cracks formed in the concrete specimen during the agent-induced fracturing, the different waveform features are clearly indicated in figs.6(b,c). the low value of rise-time and the broad frequency content are indicative of tensile cracks (see fig.6b). as for the shear cracks, rise-time is much longer and the frequency spectrum mainly contains low frequencies, as it is shown in fig.6c. figure 6: (a) average frequency versus rising angle of the hits recorded in channel 6 with amplitudes greater than 45 db, during the two stages of the fracturing process (stages a and b) of the concrete specimen. the dashed grey line separates the two cracking modes; (b), (c) two typical recorded waveforms [indicated by black arrows in (a)] attributed to tensile (b) and shear (c) cracking modes and their corresponding frequency spectra. the waveform characteristics are noted in each case. tct stands for the threshold crossing time; red dashed lines indicate the threshold of detection (39 db). the use of 7 sensors in the monitoring test has enabled the determination of the location of ae sources. the principle of ae source localization is based on the minimization of the following quantity, chi square (χ2), by using multiple regression analysis [22,23]: 𝜒 ∑ 𝛥𝑡 , 𝛥𝑡 , (1) where 𝛥𝑡 , 𝑡 𝑡 is the observed time difference calculated from the known arrival times in the first hit sensor and the ith sensor, and 𝛥𝑡 , is the calculated time difference, according to the following time-distance relationship 𝛥𝑡 , 𝑥 𝑥 𝑦 𝑦 𝑧 𝑧 𝑥 𝑥 𝑦 𝑦 𝑧 𝑧 /𝜐 (2) in eq.(2), 𝑥 , 𝑦 , 𝑧 and 𝑥 , 𝑦 , 𝑧 are the coordinates of the ith sensor and the unknown ae source location, respectively, in a 3d cartesian coordinate system, and υ is the acoustic wave velocity in the material under test, which is considered isotropic and homogenous. three-dimensional location patterns of ae events at different selected times of the monitoring test are illustrated in figs. 7(a-d). the ae data were filtered to discard events with amplitudes lower than 45 db, in order to improve the overall location pattern. we observe that the locations of events before the initiation time of the fracturing process, i.e. in the range a, are rather concentrated at the bottom of the hole filled with the expansive mortar (refer to fig.7a and fig.5). during the evolution of the fracturing process (range b), new micro-cracks were formed and propagated around the hole, possibly at the interface of the concrete with the expansive mortar [refer to snapshots (b) and (c) of fig.7]. these are reasonable findings, considering that the expansive pressure generated by the cracking agent is not uniformly distributed along 0 200 400 600 800 1000 -0.2 -0.1 0.0 0.1 0.2 0 200 400 600 800 1000 0 2 4 6 8 10 12 14 16 18 a m p ( v ) time (sec) duration: 1062.8 s amplitude: 66.8 db risetime: 19.2 s tct: 43623.7782835 sec (b) f f t m a g n itu d e frequency (khz) frequency centroid: 373.1 khz peak frequency: 143.7 khz average frequency: 160.9 khz 0 400 800 1200 1600 2000 0 100 200 300 400 500 600 tensile cracks stage a stage b a ve ra g e f re q u e n cy , a f ( kh z) rising angle, ra (ms/v) shear cracks (a) 0 200 400 600 800 1000 -0.03 -0.02 -0.01 0.00 0.01 0.02 0.03 0 200 400 600 800 1000 0 1 2 3 4 5 6 a m p ( v ) time (sec) duration: 632.2 s amplitude: 49.4 db risetime: 126 s (c) f f t m a g n it u d e frequency (khz) tct: 57549.507567 sec frequency centroid: 318.9 khz peak frequency: 148.3 khz average frequency: 68.0 khz v. saltas et alii, frattura ed integrità strutturale, 50 (2019) 505-516; doi: 10.3221/igf-esis.50.42 511 (a) recording time: 12:00:00 (43200 sec) (b) recording time: 12:11:13 (43873 sec) (c) recording time: 13:29:37 (48577 sec) (d) recording time: 17:58:41 (64721 sec) figure 7: 3d location patterns of cumulative events at different selected times, during monitoring of the fracturing process in the concrete specimen. the numbered green dots indicate the positions of the 7 ae sensors. the cylindrical hole was drilled along the z-direction (refer to fig.1). axes scale is in mm. the cylindrical hole, due to its finite length and the absence of any confinement on the upper side of the hole. thus, the expansive pressure should be higher in the inner part of the hole than at its edge. this results in the generation of microcracks starting from the inside and then extending towards the outside of the hole. as for the snapshot corresponding to the beginning of range c (fig.7d), the distribution of the events has been further extended, due to the formation of macrocracks in the concrete specimen (figs.1(b,c)).further estimation of the events localization should be no longer valid, as the specimen has started to be divided into 2 pieces (refer to fig.1b). non-extensive statistical analysis of acoustic emissions the concept of non-extensive statistical physics (nesp) has been successfully applied to the investigation of complex systems in different length-scales, such as earthquakes and fracturing experiments in brittle materials [24-29]. nesp has been introduced by tsallis in order to describe the non-equilibrium stationary states of a system which exhibits long-range interactions, memory effects and multifractality [30,31]. in this context, tsallis proposed replacing the classical boltzmangibbs entropy with the generalized q-entropy (or tsallis entropy) which is defined as: 𝑆 1 𝑝 𝑋 𝑑𝑋 (3) where 𝑘 is boltzmann’s constant, p(x) is the probability distribution function of the continuous variable x, and q is a real parameter which describes the degree of non-extensivity of the system under consideration. for q>1 or q<1, the system v. saltas et alii, frattura ed integrità strutturale, 50 (2019) 505-516; doi: 10.3221/igf-esis.50.42 512 has a sub-additive or super-additive behavior, respectively. if 𝑞 → 1, tsallis entropy reduces to the classical boltzman gibbs entropy. in the case of the recorded ae activity during the fracture of brittle materials (concrete and rocks), the continuous variable x corresponds to an ae parameter, such as the inter-event time or inter-event distance between two successive micro-cracks generated within the material, due to the applied mechanical stress [24,26,27]. the maximization of q-entropy under appropriate constraints generates probability distributions, the so-called q-distributions, such as q-exponential, q-gaussian, q-weibull distributions, etc [32-34]. the q-exponential distribution has been extensively used to describe the cumulative distribution functions (cdf) of seismic parameters in global and regional scale, and the ae activity in laboratory-scale fracturing experiments of rocks [24-28]. it is defined as follows 𝑃 𝑋 exp 𝛽𝛸 1 1 𝑞 𝛽𝑋 ⁄ (4) where the parameter β is related to the lagrange multiplier [27]. in the limit 𝑞 → 1, eq.(4) leads to the ordinary exponential distribution. in this study, nesp is applied to analyze the series of the inter-event times (it, i.e. the time interval between successive micro-cracks) of the hits recorded during the scda-induced fracturing process of the concrete specimen (stage b). specifically, we chose to use the sequence of the hits recorded to sensor with the maximum number of recorded hits, i.e., sensor 6. the time history of the inter-event times (τ) of the recorded hits in channel 6 during the monitoring test, is shown in fig.8a. the same data are also shown in a sequential order in fig.8b, to increase the resolution of observation during the fracture (stage b), where most ae activity is recorded. we observe that it values cover more than 6 orders of magnitude, spanning from hundreds of seconds down to the millisecond range. in range a, its have very high values, because of the rare occurrence of hits. instead, the initiation of the fracturing process (range b) causes an abrupt decrease of it of more than 4 orders of magnitude (from ~102 to less than 10-2 sec), as it is clearly observed in fig.8b. a subsequent characteristic decrease of it is observed at recording time 𝑡 43772 𝑠𝑒𝑐, i.e. after 154 sec of the cracks’ initiation (refer to fig.8b)]. the prolonged recording of it with low to intermediate values (~0.1-10 sec) suggests that a quasi-static fracture is taking place during the effect of the cracking agent to the concrete specimen. this is consistent with published reports stating that the quasi-static conditions should be taken into account in fracture modelling of rocks with scdas [5]. an alternative approach for presenting the ae activity in terms of the inter-event times has been recently proposed by triantis and kourkoulis [35]. according to this methodology, a time function f(τi) is introduced, which represents the average frequency of occurrence of ae hits, in a sliding time window of n consecutive hits with a mean value of the inter-event times, 𝜏 𝑡 𝑡 /𝛮. the time evolution of the function f of the recorded hits in channel 6 for n=10, during the stage b of the fracture process is illustrated in fig.8c. the observed peak of f at 43618 sec is associated with the initiation of the fracture process which is significant during the first few minutes, but decreases afterwards. this behavior is quite similar to the observed fluctuations of the smoothed curve of it, as it is shown in fig. 8b. depending on the low or higher values of n which adjusts the time resolution of the evolution of the recorded hits during the test, the details of the ae activity can be revealed or shadowed, respectively. in the present case, for the optimum selected value of n (n=10), the rate of ae hits as expressed by the function f exhibit the same characteristics as those seen in fig.3 and fig.8b. proceeding further with the analysis in the context of nesp, it should be noted that a single q-exponential function failed to fit the cumulative distribution of its in the entire region b. thus, the aforementioned observed fluctuations of it in region b have prompted us to separate this region into 2 different sub-regions. the 1st sub-region (b1), where it fluctuates considerably, includes hits from 71 to 470 and the 2nd sub-region (b2) the remainder. in the latter case, the majority of its exhibit higher values on average. this separation of region b is also consistent with the approach mentioned above, regarding the values of the function f in each sub-region [35]. in sub-region b1, the function f maintains relatively high values, while in sub-region b2, f has low values, without any significant fluctuations. the normalized cumulative distributions (p>τ) of it associated to the recorded hits in channel 6 are depicted in fig.9a,b, for the two distinct sub-regions of stage b, in a log-log representation. in fig.9a, for low values of it (𝜏 1 𝑠𝑒𝑐), the cumulative distribution was best fitted with a q-exponential function (red line), according to eq.(4), while for higher values of it, an ordinary exponential function (dashed green line) was sufficient to fit the data. subsequently, the entire distribution of its in region b2 (hits 471-1340) is best fitted with a single q-exponential function, as it is depicted in fig. 9b. in the latter case, the calculated q-value which is close to unity (q=1.12±0.03) indicates a rather weak q-exponential behavior, suggesting that long-range interactions should be also weak. on the contrary, the calculated high q-value (q=2.58±0.05) in region b1 for low values of it, suggests a highly sub-additive behavior, associated with a significantly well-organized fracturing process. however, the subsequent crossover to an exponential decay at higher it values is indicative of randomness in the fracturing process. actually, the behavior of the cdfs of v. saltas et alii, frattura ed integrità strutturale, 50 (2019) 505-516; doi: 10.3221/igf-esis.50.42 513 its in region b1 incorporates two different patterns, i.e. two regions of small and large values of it that could be related to the micro-cracks generation and propagation in random positions in the interface between the scda and the surrounding concrete. their subsequent coalescence in the macro-scale during the fracturing process resulting to ultimate failure, obeys a mechanism closer to a boltzman-gibbs statistics. a similar behavior of the q-index during three-point bending tests of cement mortar beams has been reported in ref.[36], where q-index was calculated in successive stages of the test, as the specimens approached failure, and was found to decrease, due to the different associated fracture mechanisms. more recently, nesp analysis was conducted at inter-event times of ae during repetitive loading/unloading cycles of cement mortar beams subjected to 3-point bending [37]. the experimental data were fitted by a q-exponential function; the entropic index q was found to increase in each repeated cycle, approaching a critical value (q=1.42) when the specimen reached ultimate failure. figure 8: (a) time evolution of the inter-event times of hits recorded to sensor with the maximum number of recorded hits (sensor 6) during the monitoring test of scda-induced concrete fracture. the 3 stages (a, b and c) refer to the separation applied in fig.5, according to the variation of the cumulative absolute energy of the recorded hits. (b) the same data as in (a), in sequential order. the blue line represents a smoothed curve with an averaging method of 20 points. a color scale is used to distinguish the hits with different amplitudes. only the data of stage b have been further analyzed in the context of nesp. (c) the function f(τ) of recorded hits in channel 6, for the stage b (43618 – 62145 s) of the monitoring test. the number of consecutive hits is n=10. the inset shows in greater detail the first 6 minutes of the fracture process. note the logarithmic scale in the vertical axis, in all cases. conclusions n the present work, the fracturing process of concrete specimens under the effect of a soundless chemical demolition agent was investigated by using the ae technique. real-time monitoring of a concrete block with a pre-drilled hole filled with scda was performed for a period of 24 h by an array of 7 ae sensors. the analysis of the experimental data 0 1 2 3 4 5 6 7 8 9 10-4 10-3 10-2 10-1 100 101 102 103 104 channel #6 in te re ve n t tim e ,  (s e c) time (x 104 sec) (a) a b c 0 200 400 600 800 1000 1200 1400 1600 10-4 10-3 10-2 10-1 100 101 102 103 104 (b) in te re ve n t tim e ,  (s e c) sequential number of hits 20 points smoothing 39 51 63 75 87 amplitude (db) region b 4.4 4.8 5.2 5.6 6.0 10-1 100 101 102 103 4.36 4.37 4.38 4.39 10-1 100 101 102 103 fu n ct io n f ( s -1 ) time (x 104 sec) (c) i v. saltas et alii, frattura ed integrità strutturale, 50 (2019) 505-516; doi: 10.3221/igf-esis.50.42 514 figure 9: the normalized cumulative distribution of the inter-event times (blue circles) of hits recorded in channel 6, during the two substages of region b of the monitoring test. the fitting curves (red and dashed green lines) are also shown. note the logarithmic scale in both axes. the fitting parameters are noted in each case. reveals that fracture is suddenly observed after 12 h, without any clear indication of pre-failure signals. the absolute energy and the inter-event times of the recorded hits have been used to distinguish the effective period of action of the cracking agent and the quasi-static behavior in the fracturing process, respectively. the correlation of the ae parameters (average frequency and rising angle) implies that the fracturing process is dominated by tensile cracks (mode-i type of fracture). the localization of the ae sources allows investigating the formation and propagation of micro-cracks around the pre-drilled hole. in this direction, we propose that the expansive agent placed into a hole of a solid material could be used as an artificial source of acoustic signals, in analogy to the lead pencil break tests (lpbt) for studying the propagation of elastic waves in materials. however, we have to point out that this proposed method, as a destructive test in contrast to the lpbt, cannot be used directly in the test specimens but should be applied separately to other suitably prepared specimens. additionally, the use of the expansive agent may not be appropriate in the case of the high anisotropic rocks and should only be used in artificial materials. the statistical analysis of ae data in the frame of nesp provides evidence that the scda-induced fracture of concrete is a complex process where the long-range interactions of the micro-cracks should play a significant role to any possible model of the fracturing process. the present investigation could be further extended to other brittle materials such as rocks and to complicated arrangement of holes that are used in practical applications, in order to monitor the evolution of the complex fracture network that will be developed under the effect of scdas. the influence of the essential parameters for the optimum usage of scdas, i.e. ambient temperature, water content, hole diameter and spacing between holes should be also investigated to reveal any possible correlations with the ae parameters. acknowledgements e acknowledge support of this work by the project ‘‘helpos – hellenic system for lithosphere monitoring, greece’’ (mis 5002697) which is implemented under the action ‘‘reinforcement of the research and innovation infrastructure’’, funded by the operational programme ‘‘competitiveness, entrepreneurship and innovation, greece’’ (nsrf 2014–2020) and co-financed by greece and the european union (european regional development fund). references [1] gambatese, j.a. (2003). controlled concrete demolition using expansive cracking agents, j. constr. eng. manag., 129(1), pp. 98–104, doi: 10.1061/(asce)0733-9364(2003)129:1(98). [2] laefer, d.f., ambrozevitch-cooper, n., huynh, m.p., midgette, j., ceribasi, s., wortman, j. (2010). expansive fracture agent behaviour for concrete cracking, mag. concr. res., 62(6), pp. 443–452, doi: 10.1680/macr.2010.62.6.443. [3] dessouki, a. el., mitri, h. (2011). rock breakage using expansive cement, engineering, 03(02), pp. 168–173, doi: 10.4236/eng.2011.32020. 10-4 10-3 10-2 10-1 100 101 102 103 10-3 10-2 10-1 100 exponential fitting (r2 = 0.997) 0.471(4)e-0.657(6) (a) ch#6: 71 470 hit data points q-exponential fitting (r2 = 0.978)  = 4.26(7) q = 2.58(5) n o rm a liz e d c u m u la ti ve d is tr ib u tio n , (p > ) inter-event time, (s) 10-4 10-3 10-2 10-1 100 101 102 103 10-3 10-2 10-1 100 data points curve fitting (r2 = 0.996)  = 0.0482(3) q = 1.12(3) n o rm a liz e d c u m u la tiv e d is tr ib u ti o n , (p > ) inter-event time, (s) ch#6: 471 1340 hit (b) w v. saltas et alii, frattura ed integrità strutturale, 50 (2019) 505-516; doi: 10.3221/igf-esis.50.42 515 [4] hasanipanah, m., jahed armaghani, d., monjezi, m., shams, s. (2016). risk assessment and prediction of rock fragmentation produced by blasting operation: a rock engineering system, environ. earth sci., 75(9), pp. 1–12, doi: 10.1007/s12665-016-5503-y. [5] de silva, r.v., gamage, r.p., anne perera, m.s. (2016). an alternative to conventional rock fragmentation methods using scda: a review, energies, 9(11), pp. 1–31, doi: 10.3390/en9110958. [6] guo, t., zhang, s., ge, h., qu, z. (2015). a novel “soundless cracking agent fracturing” for shale gas reservoir stimulation, int. j. environ. sci. dev., 6(9), pp. 681–7, doi: 10.7763/ijesd.2015.v6.680. [7] musunuri, a., mitri, h. (2009). laboratory investigation into rock fracturing with expansive cement, int. j. min. miner. eng., 1(4), doi: 10.1504/ijmme.2009.029318. [8] xu, j., zhai, c., qin, l., yu, g. (2017). evaluation research of the fracturing capacity of non-explosive expansion material applied to coal-seam roof rock, int. j. rock mech. min. sci., 94, pp. 103–111, doi: 10.1016/j.ijrmms.2017.03.004. [9] guo, t., zhang, s., ge, h., wang, x., lei, x., xiao, b. (2015). a new method for evaluation of fracture network formation capacity of rock, fuel, 140, pp. 778–787, doi: 10.1016/j.fuel.2014.10.017. [10] zhai, c., xu, j., liu, s., qin, l. (2018). fracturing mechanism of coal-like rock specimens under the effect of nonexplosive expansion, int. j. rock mech. min. sci., 103, pp. 145–154, doi: 10.1016/j.ijrmms.2018.01.037. [11] natanzi, a.s., laefer, d.f., connolly, l. (2016). cold and moderate ambient temperatures effects on expansive pressure development in soundless chemical demolition agents, constr. build. mater., 110, pp. 117–127, doi: 10.1016/j.conbuildmat.2016.02.016. [12] lockner, d. (1993). the role of acoustic emission in the study of rock fracture, int. j. rock mech. min. sci. geomech. abstr., 30(7), pp. 883–899, doi: 10.1016/0148-9062(93)90041-b. [13] shah, k.r., labuz, j.f. (1995). damage mechanisms in stressed rock from acoustic emission, j. geophys. res. solid earth, 100(b8), pp. 15527–15539, doi: 10.1029/95jb01236. [14] aggelis, d.g., soulioti, d. v., sapouridis, n., barkoula, n.m., paipetis, a.s., matikas, t.e. (2011). acoustic emission characterization of the fracture process in fibre reinforced concrete, constr. build. mater., 25(11), pp. 4126–4131, doi: 10.1016/j.conbuildmat.2011.04.049. [15] https://www.dexpan.com/collections/dexpan-demolition-agent [16] aggelis, d.g. (2011). classification of cracking mode in concrete by acoustic emission parameters, mech. res. commun., 38(3), pp. 153–157, doi: 10.1016/j.mechrescom.2011.03.007. [17] aggelis, d.g., mpalaskas, a.c., matikas, t.e. (2013). investigation of different fracture modes in cement-based materials by acoustic emission, cem. concr. res., 48, pp. 1–8, doi: 10.1016/j.cemconres.2013.02.002. [18] farhidzadeh, a., mpalaskas, a.c., matikas, t.e., farhidzadeh, h., aggelis, d.g. (2014). fracture mode identification in cementitious materials using supervised pattern recognition of acoustic emission features, constr. build. mater., 67(part b), pp. 129–138, doi: 10.1016/j.conbuildmat.2014.05.015. [19] tsangouri, e., aggelis, d., matikas, t., mpalaskas, a. (2015). acoustic emission activity for characterizing fracture of marble under bending, appl. sci., 6(1), pp. 6, doi: 10.3390/app6010006. [20] harada t., idemitsu t., watanabe a., takayama s. (1989). the design method for the demolition of concrete with expansive demolition agents. in: shah s.p., swartz s.e. (eds) fracture of concrete and rock. springer, new york. [21] shang, j., zhao, z., aliyu, m.m. (2018). stresses induced by a demolition agent in non-explosive rock fracturing, int. j. rock mech. min. sci., 107(december), pp. 172–180, doi: 10.1016/j.ijrmms.2018.04.049. [22] agioutantis, z., kaklis, k., mavrigiannakis, s., verigakis, m., vallianatos, f., saltas, v. (2016). potential of acoustic emissions from three point bending tests as rock failure precursors, int. j. min. sci. technol., 26(1), pp. 155–160, doi: 10.1016/j.ijmst.2015.11.024. [23] kaklis, k., mavrigiannakis, s., saltas, v., vallianatos, f., agioutantis, z. (2017). using acoustic emissions to enhance fracture toughness calculations for ccnbd marble specimens, frat. ed integrita strutt., 11(40), doi: 10.3221/igf-esis.40.01. [24] vallianatos, f., benson, p., meredith, p., sammonds, p. (2012). experimental evidence of a non-extensive statistical physics behaviour of fracture in triaxially deformed etna basalt using acoustic emissions, epl, 97(5), doi: 10.1209/ 0295-5075/97/58002. [25] vallianatos, f., sammonds, p. (2013). evidence of non-extensive statistical physics of the lithospheric instability approaching the 2004 sumatran-andaman and 2011 honshu mega-earthquakes, tectonophysics, 590, pp. 52–58, doi: 10.1016/j.tecto.2013.01.009. [26] vallianatos, f., papadakis, g., michas, g. (2016). generalized statistical mechanics approaches to earthquakes and tectonics, proc. r. soc. a math. phys. eng. sci., 472(2196), doi: 10.1098/rspa.2016.0497. v. saltas et alii, frattura ed integrità strutturale, 50 (2019) 505-516; doi: 10.3221/igf-esis.50.42 516 [27] saltas, v., vallianatos, f., triantis, d., stavrakas, i. (2018). complexity in laboratory seismology: from electrical and acoustic emissions to fracture, in: t. chelidze, l. telesca, f. vallianatos (eds.), complexity of seismic time series: measurement and application, 1st ed., elsevier, pp. 239–273, isbn: 978-0-12-813138-1. [28] chochlaki, k., vallianatos, f., michas, g. (2018). global regionalized seismicity in view of non-extensive statistical physics, phys. a stat. mech. its appl., 493, pp. 276–285, doi: 10.1016/j.physa.2017.10.020. [29] michas, g., vallianatos, f. (2018). stochastic modeling of nonstationary earthquake time series with long-term clustering effects, phys. rev. e, 98(4), pp. 042107, doi: 10.1103/physreve.98.042107. [30] tsallis, c. (1988). possible generalization of boltzmann-gibbs statistics, j. stat. phys., 52(1–2), pp. 479–87, doi: 10. 1007/bf01016429. [31] tsallis, c. (2009). nonadditive entropy and nonextensive statistical mechanics -an overview after 20 years, brazilian j. phys., 39(2a), pp. 337–356, doi: 10.1590/s0103-97332009000400002. [32] picoli, s, jr, mendes, r.s., malarne, l.c., santos, r.p.b. (2009). q-distributions in complex systems: a brief review, braz j phys, 39(2a), pp. 468–474, doi: 10.1590/s0103-97332009000400023. [33] vallianatos, f., sammonds, p. (2010). is plate tectonics a case of non-extensive thermodynamics?, phys. a stat. mech. its appl., 389(21), pp. 4989–4993, doi: 10.1016/j.physa.2010.06.056. [34] vallianatos, f. (2018). a non-extensive statistical mechanics view on easter island seamounts volume distribution, geosci., 8(2), doi: 10.3390/geosciences8020052. [35] triantis, d., kourkoulis, s.k. (2018). an alternative approach for representing the data provided by the acoustic emission technique, rock mech. rock eng., 51(8), pp. 2433–2438, doi: 10.1007/s00603-018-1494-1. [36] stergiopoulos, c., stavrakas, i., hloupis, g., triantis, d., vallianatos, f. (2013). electrical and acoustic emissions in cement mortar beams subjected to mechanical loading up to fracture, eng. fail. anal., 35, pp. 454–461, doi: 10.1016/ j.engfailanal.2013.04.015. [37] stavrakas, i., triantis, d., kourkoulis, s.k., pasiou, e.d., dakanali, i. 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can be opened with acrobat and adobe reader 5.0 and later.) >> /namespace [ (adobe) (common) (1.0) ] /othernamespaces [ << /asreaderspreads false /cropimagestoframes true /errorcontrol /warnandcontinue /flattenerignorespreadoverrides false /includeguidesgrids false /includenonprinting false /includeslug false /namespace [ (adobe) (indesign) (4.0) ] /omitplacedbitmaps false /omitplacedeps false /omitplacedpdf false /simulateoverprint /legacy >> << /addbleedmarks false /addcolorbars false /addcropmarks false /addpageinfo false /addregmarks false /convertcolors /converttocmyk /destinationprofilename () /destinationprofileselector /documentcmyk /downsample16bitimages true /flattenerpreset << /presetselector /mediumresolution >> /formelements false /generatestructure false /includebookmarks false /includehyperlinks false /includeinteractive false /includelayers false /includeprofiles false /multimediahandling /useobjectsettings /namespace [ (adobe) (creativesuite) (2.0) ] /pdfxoutputintentprofileselector /documentcmyk /preserveediting true /untaggedcmykhandling /leaveuntagged /untaggedrgbhandling /usedocumentprofile /usedocumentbleed false >> ] >> setdistillerparams << /hwresolution [2400 2400] /pagesize [612.000 792.000] >> setpagedevice microsoft word numero_30_art_66 m. rossi et alii, frattura ed integrità strutturale, 30 (2014) 552-557; doi: 10.3221/igf-esis.30.66 552 focussed on: fracture and structural integrity related issues identification of the plastic zone using digital image correlation m. rossi, m. sasso, g. chiappini, e. mancini, d. amodio polytechnic university of marche m.rossi@univpm.it. m.sasso@univpm.it, g.chiappini@univpm.it, e.mancini@univpm.it, d.amodio@univpm.it abstract. in this paper digital image correlation (dic) is used to study the evolution of the plastic zone close to a crack tip. a modified ct-specimen was used in order to fulfill the plane stress condition. the strain field around the crack tip was measured using two cameras and stereo dic, so that out-of-plane movements are taken into account. then, the virtual fields method was used to identify the plastic zone, looking at the parts of the specimen which deviates from the linear elastic behavior. with such approach, it was possible to individuate the onset of plasticity close to the crack tip and follow its evolution. a comparison with fem results is also provided. keywords. digital image correlation; plastic zone; virtual fields method; fracture mechanics. introduction he virtual fields method (vfm) is a technique that can be used to identify the mechanical properties of materials, starting from full field measurements [1]. during the years, such a technique was extended to many fields of mechanical engineering [2-5]. the vfm exploits the principle of virtual work to identify the material properties using experimental tests which produce heterogeneous strain fields. in the field of plasticity, the vfm is gaining increasing interest [6, 7] because large amount of information can be obtained from a single test, moreover the minimization procedure is usually faster than fe updating methods. in this paper, the vfm is used to identify the plastic zone on a crack tip. the transition between plastic and elastic behaviour can be easily obtained by fe computations but it is not possible to directly individuate it from experimental measurements of the strain field. the identification is performed starting from the strain field measured close to the crack tip. although this area is rather small, (1 ~ 4 mm2 ) the high resolution of recent digital cameras and the improvements in the full-field measurement techniques (e.g. dic, grid method) allow nowadays to very accurate strain measurements with a high grade of spatial resolution and noise reduction even on small surfaces [9, 10]. afterwards, in order to apply the vfm, suitable virtual fields are defined so that the contribution of the external forces is zeroed. these virtual fields are generated using piecewise functions [11], the virtual displacement on the nodes placed at the boundary of the inspected area are set to zero. an error function is then developed to assess the zones where the elastic behavior is not fulfilled. this error indicates the deviation from the linear elastic behavior, when it exceeds a threshold value, the corresponding material point is considered part of the plastic zone. it is worth noting that no force measurement is required with this approach. the procedure was validated by means of simulated experiments using a fe model [12]. in this paper the first experimental results are shown. a test was conducted on a modified ct specimen and the evolution of the plastic zone is evaluated. t m. rossi et alii, frattura ed integrità strutturale, 30 (2014) 552-557; doi: 10.3221/igf-esis.30.66 553 theoretical background the plastic zone is obtained applying the vfm. the vfm relies on the principle of virtual works that, for a solid of any shape of volume v and surface ∂v, if there are no body forces acting on the solid, can be written as * *: v v dv ds    σ ε t u (1) where σ is the stress tensor, t is a surface force acting at the boundary and u* and ε* are a kinematically admissible virtual fields and the corresponding virtual strain fields, respectively. in case of in-plane tests with constant thickness, the problem reduces to a 2-d situation and eq. 3 can be rewritten as: * *: s s t ds t dl    σ ε t u (2) where t is the specimen thickness. considering an isotropic elastic material behaviour, the stress tensor can be written as a function of strain field according to the constitutive equations, for plane stress it follows: 2 1 0 1 0 1 1 0 0 2 xx xx yy yy xy xy e                                        (3) with e and ν which are the young’s modulus and the poisson’s ratio, respectively. the strain field is the one measured during the experiment by a full-field optical technique. the virtual fields involved in eq. 4 can be arbitrarily chosen if they are kinematically admissible [1]. they can be defined using piecewise functions as it occurs in fe models [1,11]. in this case the virtual displacement u* is written as a function of the nodal coordinates u(e) of an element according to the element shape functions n: * ( )eu nu (4) the strain can be obtained as well from the nodal coordinates as: * ( )eε bu (5) in the present case a regular square grid of four elements was used, the 8 nodes at the boundary are kept fixed while the internal node is moved. in such a way the virtual displacement at the boundary is equal to zero and the second term of eq. 4 vanishes. 24 independent virtual fields were generated by varying the displacement u* of the central node as follows:  * cos , sin with [0 : / 12 : 2 [     u (6) when the material has a linear elastic behaviour, the equilibrium is respected and the first term of eq.4 is identically null in each zone of the specimen. close to the crack tip, however, the material behaviour deviates from elasticity because plastic deformation locally occurs. in this case, eq. 4 is not valid anymore, this discrepancy can be considered as an indication of the plasticity occurrence. with this assumption, an error function err is defined as: * 1 1 1 : vn i s v i err ds n s    σ ε (7) where nv is the number of independent virtual fields employed, i.e. 24 in this case. the unit of this error is a specific energy. the larger the error function the most likely the inspected zone undergoes plastic deformation. the error is normalized on the surface area s so that its value is not influenced by its size. indeed, the area can be varied in order to include more or less measurement points. the error functions is also influenced by the amount of strain in the investigated zone. in order to have a fair comparison between zones with different levels of strain, the normalization parameter  is also introduced defined as: m. rossi et alii, frattura ed integrità strutturale, 30 (2014) 552-557; doi: 10.3221/igf-esis.30.66 554 1 vm s ds s    (8) where vm is the equivalent von mises strain. it is worth underlying that no other assumptions are made on the plasticity law, therefore the identification of the plasticity material properties are not necessary to detect the plastic zone. the area of the virtual field is moved along the measured strain field as a sort of “probe” which detects the likelihood of plastic deformation occurrence inside the area. in such a way, it is possible to define an error map close to the crack tip. experiments modified ct-specimen was used in the experimental test. fig. 1 illustrates an example of ct-specimen according to the astm [13]. the dimension of the specimens depends on the parameter w, which allows to scale the specimen according to the thickness. in this case, since eq. 5 is only valid for plane stress, the ct-specimen was modified so that the thickness was small compared to the in-plane dimensions. the specimen was cut from a 3mm thick sheet metal of aisi 304 steel. a value of w=100mm is used for all the other dimensions. figure 1: scheme of the used ct-specimen. figure 2: experimental set-up. a m. rossi et alii, frattura ed integrità strutturale, 30 (2014) 552-557; doi: 10.3221/igf-esis.30.66 555 in fig. 2 the experimental set-up is shown, the modified ct-specimen was loaded using suitable fixture which guarantees an in-plane loading. buckling occurs at large deformation, however it was possible to apply up to 5 kn to the specimen before a consistent out of plane movement was measured. the strain field measurement was obtained by means of stereo dic. two cameras have been used with an angle of around 15°. a speckle pattern was sprayed onto the specimen surface. the investigated area is around 6 × 6 mm close to the crack tip. a global dic approach is used using a regular mesh of 32 × 32 pixels that corresponds to 0.8 × 0.8 mm in actual units. the strain at each pixel was then obtained using the shape function of the elements x -4 -2 0 -3 -2 -1 0 1 2 3 -2 0 2 4 6 x 10 -3 y -4 -2 0 -3 -2 -1 0 1 2 3 -2 0 2 4 6 8 x 10 -3 xy -4 -2 0 -3 -2 -1 0 1 2 3 -5 0 5 x 10 -3 figure 3: measured strain field. results and discussions he error function obtained from eq. 7 is plotted for different values of the tensile force, see fig. 4. the same contour limits are used for all graphs. as the force increases, the error function also increases close to the crack tip showing the evolution of the plastic zone. a certain amount of noise is present, but the evolution of the plastic zone is clearly visible. force: 1758 n -4 -2 0 -2 0 2 0 500 1000 1500 2000 force: 1991 n -4 -2 0 -2 0 2 0 500 1000 1500 2000 force: 2593 n -4 -2 0 -2 0 2 0 500 1000 1500 2000 force: 3231 n -4 -2 0 -2 0 2 0 500 1000 1500 2000 force: 3938 n -4 -2 0 -2 0 2 0 500 1000 1500 2000 force: 4662 n -4 -2 0 -2 0 2 0 500 1000 1500 2000 figure 4: identification of the plastic radius. t m. rossi et alii, frattura ed integrità strutturale, 30 (2014) 552-557; doi: 10.3221/igf-esis.30.66 556 in fig. 5, the plastic zone computed by fem for two levels of force, namely the first and the last of fig. 4, are illustrated. qualitatively, a reasonably good match is obtained with the experimental results. the fem model was built using the actual mechanical properties of the material obtained by means of uniaxial tensile tests. force 1758 n force 4662 n figure 5: plastic zone evaluated by fem for the same specimen and same load levels conclusions procedure to evaluate the plastic zone close to the crack tip starting from full field dic measurement data is presented. a modified ct specimen was used to ensure the plane stress condition in the area of interest. test were conducted at different load levels, stereo dic was used to extract the strain field close to the crack tip, then the vfm was used to look at the zones which deviate from the linear elastic behavior. qualitatively, a good match is found between the error maps and the plastic zone evaluated by fem. in future works more effort will be put on quantitatively evaluating the plastic zone setting a suitable threshold to the level of error measured. references [1] pierron, f., grédiac, m., the virtual fields method, springer, (2012). [2] palmieri, g., sasso, m., chiappini, g., amodio, d., virtual fields method on planar tension tests for hyperelastic materials characterisation, strain, 47 (2011) 196-209. [3] guélon, t., toussaint, e., le cam, j.-b., promma, n., grédiac, m., a new characterisation method for rubber, polymer testing, 28 (2009) 715-723. [4] pierron, f., forquin, p., ultra-high-speed full-field deformation measurements on concrete spalling specimens and stiffness identification with the virtual fields method, strain, 48 (2012) 388-405. [5] giraudeau, a., pierron, f., identification of stiffness and damping properties of thin isotropic vibrating plates using the virtual fields method. theory and simulations, j. sound. vib. 284 (2005) 757–781. [6] rossi, m., pierron, f., identification of plastic constitutive parameters at large deformations from three dimensional displacement fields, comput. mech., 49 (2012) 53-71. [7] grédiac, m., pierron, f., applying the virtual fields method to the identification of elasto-plastic constitutive parameters, int. j. plasticity, 22 (2006) 602–627. [8] avril, s., bonnet, m., bretelle, a. s., grédiac, m., hild, f., ienny, p., latourte, f., lemosse, d., pagano, s., pagnacco, e., pierron, f., overview of identification methods of mechanical parameters based on full-field measurements, exp. mech., 48 (2008) 381–402. [9] bornert, m., brémand, f., doumalin, p, dupré, j.-c., fazzini, m., grédiac, m., hild, f., mistou, s., molimard, j., orteu, j.-j., robert, l., surrel, y., vacher, p., wattrisse, b., assessment of digital image correlation measurement errors: methodology and results, exp. mech., 49 (2009) 353-370. a m. rossi et alii, frattura ed integrità strutturale, 30 (2014) 552-557; doi: 10.3221/igf-esis.30.66 557 [10] moulart, r., rotinat, r., pierron, f., lerondel, g., on the realization of microscopic grids for local strain measurement by direct interferometric photolithography, opt. laser. eng., 45 (2007) 1131–1147. [11] avril, s., grédiac, m., pierron,. f., sensitivity of the virtual fields method to noisy data, comput. mech., 34 (2004) 439–452. [12] rossi, m. fardmoshiri, m., sasso, m., amodio, d., application of the virtual fields method to fracture mechanics, in: convegno nazionale igf xxii, roma, italia, (2013) 322-331 [13] astm standards, standard test method for plane-strain fracture toughness of metallic materials, astm e39990, american society for testing and materials, philadelphia, (1997). microsoft word numero_50_art_7_2531 n. boychenko et alii, frattura ed integrità strutturale, 50 (2019) 54-67; doi: 10.3221/igf-esis.50.07 54 characterization of the stress-strain state in a gas turbine engine compressor disc taking into account damage accumulation natalia boychenko, ivan ishtyryakov institute of power engineering and advanced technologies, frc kazan scientific center, russian academy of sciences, russia nataboi@ya.ru, ivan_200999@mail.ru abstract. a stress-strain state analysis of a gas turbine engine compressor disc was conducted with consideration to the accumulation of damages under various loading conditions in the temperature range. characterization of constraint effects was performed using the local stress triaxiality h, tz-factor and in-factors for various crack sizes and different operation conditions. the distributions of elastic, plastic and creep stress intensity factors were determined by numerical calculation. results for several crack front positions, temperature values and disc rotation angular velocity were obtained. the differences in the behaviour of elastic and nonlinear fracture resistance parameters were observed on the basis of loading conditions, crack geometry and temperature. nonlinear stress intensity factors are preferred as the fracture resistance parameters of materials and structures. keywords. compressor disc; creep; damage; surface flaw; plastic stress intensity factor; creep stress intensity factor. citation: boychenko n., ishtyryakov i., parametric study of stress-strain state in gas turbine engine compressor disc taking into account damage accumulation, frattura ed integrità strutturale, 50 (2019) 54-67. received: 28.05.2019 accepted: 07.07.2019 published: 01.10.2019 copyright: © 2019 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. introduction as turbine engines (gte) are the main power plants in modern aviation. many types of engines in land and marine engineering are based on gtes. gtes are operated under extremely high temperatures and loads for long periods of time. the temperature ranges from -60°c to +1700°c, air pressure can reach 300 mpa, and gas flow rate exceeds the sonic velocity. the main loads are derived from centrifugal forces on the rotating parts of the rotor; a rotation frequency reaches 5000 1/s, and the circumferential speed is –450 m/s. high-strength materials, efficient technological processes and advanced design solutions are used to implement highly reliable parameters. titanium alloys and stainless steels are often used for highly loaded rotor components, and heat-resistant nickel-based alloys are used for high-temperature turbine components [1, 2]. when in operation, the discs subjected to centrifugal and thermal loads are the most loaded part of the rotors. the compressor disc has various concentrators in the form of grooves, holes, mating surfaces and recesses, etc. in some cases, stresses near concentrators may exceed the yield strength, and plastic stains will occur [3, 4]. g http://www.gruppofrattura.it/va/50/2531.mp4 n. boychenko et alii, frattura ed integrità strutturale, 50 (2019) 54-67; doi: 10.3221/igf-esis.50.07 55 this study aims to explore elastic and nonlinear fracture resistance parameters and analyse constraint parameters taking into account accumulation of damages under various loading conditions within a temperature range. the subject under study and material properties n this study, the stress-strain state and the fracture resistance parameters in an aircraft gte compressor disc (fig. 1a) were analysed. slot fillets under the blade are the concentrated stress areas in the compressor disc of the aircraft gte [3, 5-7]. the ‘dovetail’ type attachment had a broach angle of 26 at the axis of rotation, and partial-through surface cracks occurred in the disc and blade attachment [7, 8-10] (fig. 1b). the crack propagation usually starts from a quarter elliptical corner surface flows [9, 11]. crack developed in slot fillet near the disc outer surface. further, the growing crack intersected the entire thickness of the disc. as a result, the disc rim ruptured (fig. 1c) [9, 11]. a) b) c) figure 1: gte compressor disc (a) and operation damages of disc and «dovetail type» blade attachment (b, c). numerical analyses of the stress-strain state under the operating loading conditions were conducted in this study at various temperatures and crack sizes. the first part of numerical calculations focused on the stress-strain state analysis of the compressor disc without cracks. the second part was devoted to the analysis of the compressor disc with operational damage in the slot fillet of the – ‘dovetail’ type disc and its blade attachments. three types of curvilinear crack geometry were considered. all calculations were performed at room (23°с) and elevated (300°с and 370°с) temperatures with a rotor angular velocity of 925 and 1000 rad/sec. elastic, plastic and creep conditions were considered. damage accumulation was analysed in consideration of creep conditions. thus, numerical investigations were performed for given combinations of the main parameters, such as the angular velocity of the compressor disc, temperature, shape and size of the defect and the elastic, plastic and creep properties of the material. the combinations of the parameters used in the numerical calculations are presented in tab. 1. angular velocity, rad/s temp., °с disc without crack disc with surface crack: а=0.34mm, с=0.71mm а=0.76mm, с=1.32mm а=1.5mm, с=2.2mm elastic plastic creep damage elastic plastic creep damage 925 23 + + + + 300 + + + + + + + + 370 + + + + + + + + 1000 23 + + + + 300 + + + + + + + + 370 + + + + + + + + table 1: various parameters employed in the numerical calculations. the compressor disc considered for the numerical calculations was made of titanium alloy vt3-1. the main mechanical properties of the material analysed at three temperatures are summarized in tab. 2, where, σ0.2 – yield stress, σut – true ultimate tensile stress, е – young's modulus, n – strain hardening exponent, α – strain hardening coefficient. i n. boychenko et alii, frattura ed integrità strutturale, 50 (2019) 54-67; doi: 10.3221/igf-esis.50.07 56 temperature, °с 0.2 mpa ut mpa e gpa n α 23 1004 1602 100 12.88 1.11 300 753 1515 96 8.91 0.99 370 699 1500 97 8.43 0.97 table 2: summary of the main mechanical properties of titanium alloy vt3-1 at room and elevated temperatures. the norton law was used to describe a material’s behaviour under the creep conditions: n cr b   (1) where cr is the creep strain rate, b is the creep coefficient, ncr is the creep exponent, and σ is the stress. the creep properties for titanium alloy vt3-1 are listed in tab. 3. material temperature, °с creep equation creep constant b, (mpa)-n hour-1 ncr vt3-1 300 9 1.63423 10cr     3·10-9 1.6342 370 9 1.93371 10cr     10-9 1.9337 table 3: creep properties of titanium alloy vt3-1 at 300°с и 370°с. in this study, the model proposed by shlyannikov and tumanov for the damage accumulation rate [12, 13] was used to assess the creep damage behaviour:     1 / 1 1 n n i i в m f bd dt t                   (2) 22 1 3 i b     ;         2 2 1 1 1 1                ;   221 1 1 i            where 0 1  is the measure of damage, with 0  denoting the undamaged state and 1  the fully damaged state;  is the experimental material constant, which is determined as the ratio of uniaxial tensile strength to compression strength = t /c. for brittle fracture  = 0, whereas  = 1 is for ductile fracture tf is the time for the fracture to occur under creep conditions, m is the constant in the law of damage accumulation, 2 1    is the principal stress ratio, and  is the poisson's ratio. eqn. (2) allows us to consider the complex stress state. knowing only the constants of the norton law equation and the time to fracture at least at one level of the effective nominal stresses is enough to determine the constants of eqn. (2) [12, 13]. eqn. (2) was integrated into the ansys finite element (fe) code [14]. a full-field 3d fe analysis was conducted using the ansys code to determine the stress-strain state parameters of the gte compressor disc with the considered geometry. n. boychenko et alii, frattura ed integrità strutturale, 50 (2019) 54-67; doi: 10.3221/igf-esis.50.07 57 elastic-plastic stress fields in the gte compressor disc he first part of this study is concerned with the stress–strain state analysis of the compressor disc without cracks. fem calculations were performed to determine the stress and strain distributions under different loading conditions within a specified temperature range. the 3d segment of the disc with blades was simulated due to the cyclic symmetry property of the disc. a 20-node quadrilateral isoparametric 3d solid fe model represented the 3d compressor disc configuration (fig. 2). the displacements of the radial sections of the disc corresponded to the xoy, yoz and xoz planes and were limited under normal. the interaction between the blade root and the mounting holes of the disc was modelled using contact elements. the 3d fe model of the aircraft gte compressor disc d-36 are presented in fig. 2a. the global elastic–plastic equivalent, von mises stress distributions and local nonlinear strain zone in a compressor disc with an angular velocity of 925 rad/s at room temperature are shown in figs. 2b and 2c. a) b) c) d) figure 2: the 3d fe model (a), global von mises stress distributions (b), local nonlinear strains zone (c) and damage distribution (d) in aircraft gte compressor disc. results indicated that the main high-loaded areas of the disc are the slot fillets under the blade in which the maximum stresses exceed the yield strength of the titanium alloy vt3-1 at the temperature considered. a similar pattern was observed for all other combinations of the angular velocity and temperatures listed in tab. 1. the stress and strain level in the disc depends on the temperature and the angular velocity. t n. boychenko et alii, frattura ed integrità strutturale, 50 (2019) 54-67; doi: 10.3221/igf-esis.50.07 58 fig. 2d shows the damage field in the slot fillets of the compressor disc at 370°c. an area of defect nucleation in the slot fillet was determined on the basis of the maximum value of the damage. this area coincides with the localization of real cracks occurring in the compressor disc during the operation. the obtained area of defect nucleation was used as a basis for the second part of the work. stress-strain state of the gte compressor disc with operational damages he second part of the numerical study is concerned with the stress–strain state analysis of the gte compressor disc with cracks. the location of the surface defect was chosen in accordance with the direction previously determined at the first stage of this study. the initial crack inclination (nearly 45°) was defined in a manner consistent with the results of the full-size compressor disc’s experimental low cycle fatigue tests. the position of the quarter-elliptic crack fronts in the compressor disc and the size of the simulated defects are presented in fig. 3. the crack was modelled as a notch with a crack tip curvature radius r = 0.002mm, where a is the crack depth, and c is the crack size on the free surface of the disc. to compare the behaviour of the governing parameters along the corner quarter-elliptical crack front, we use normalized coordinates in the following forms: 0 0 0 0 cos , sinx y       cos , sin c c c c x y       cos , sini i i ix y       ,  0 0, , i c c         (3) 0 0 0 0 , i ii i c c x x y y x y x x y y        2 21 , 0,1 2 i i i ir x y r   where 0 is an angle denoting the position of the crack front point on the free surface of the disc. c is an angle that corresponds to the crack front point placed on the slot key’s surface (fig. 3). in this study, a dimensionless variable r was used in a range from 0 to 1, where r=0.0 indicates the exterior surface of the compressor disc (point b), and r=1.0 corresponds to the slot surface (point a). once the location of the crack and the size of the crack are identified, the region around the crack should be meshed appropriately to calculate the nonlinear fracture resistance parameters accurately. a quarter-elliptical part-though crack was inserted in the compressor disc fe model (fig. 4) in the area of the disc and blade attachment. a full-field 3d fe analysis was performed to obtain the stress and strain fields along the corner crack front in the compressor disc when subjected to different combinations of angular velocities, temperatures and crack front positions (tab. 1). fig. 5 shows typical plots of the nonlinear strain zones along the curvilinear crack front in the compressor disc for plastic, creep and damage solutions. the nonlinear strain zone pertains to when the zone within the total strain intensity exceeds the yield strain value. results show that under the operating loading conditions, the distribution of strains (fig. 5) were non-symmetrical due to mode mixity, and the nonlinear zone was larger in the slot key relative to the free surface of the disc. the maximum value of strain intensity was located in the slot fillet’s inner surface for all considered combinations of variable parameters and is presented in tab. 1. the crack was assumed to grow primarily along the thickness of the disc. this assumption was confirmed by the data on the crack paths in the slot key fillet [8]. the nonlinear strain zone under creep conditions was significantly larger than that under the plastic solution. strain intensity increased due to damages under creep conditions. thus, an account the damages allows a more conservative estimate of the degradation of the material properties and stress–strain state parameters. t n. boychenko et alii, frattura ed integrità strutturale, 50 (2019) 54-67; doi: 10.3221/igf-esis.50.07 59 crack front point a с, mm point b a, mm front 1 0.71 0.34 front 2 1.32 0.76 front 3 2.22 1.5 figure 3: crack front positions and sizes in the slot fillet of aircraft gte compressor disc. figure 4: the 3d fe meshes of slot fillet of compressor disc with а quarter-elliptical part-though crack. a b (b) (a) n. boychenko et alii, frattura ed integrità strutturale, 50 (2019) 54-67; doi: 10.3221/igf-esis.50.07 60 plastic solution creep damage figure 5: strains intensity distributions in the compressor disc with а crack in a slot fillet. figure 6: contours of creep damage around crack tip on slot fillet surface (point a) and free surface (point b) of compressor disc with angular velocity 925 rad/s. fig. 6 shows the contours of the damaged zones around the crack tip in the slot fillet of the compressor disc with an angular velocity of 925 rad/s at 300°c and 370°c. results are presented for two sections: the inner surface of the slot fillet (fig. 3 point a) and the free surface of the disc (fig. 3 point b). the crack front positions are indicated by the numbers 1 and 3, respectively. the contours of the damaged zone for the second crack front occupied an intermediate position. as shown in fig. 6, the measure of damage depended on the temperature, crack size and on the point along the crack front. the shape of the damage contours in the slot fillet and on the free surface (points a and b correspondingly) were significantly different. on the inner surface of the slot fillet, the damaged zone was close to symmetrical; meanwhile, substantial asymmetry was observed on the free surface of the disc. moreover, the asymmetry of the damaged zone on the free surface increased with the increasing crack size. n. boychenko et alii, frattura ed integrità strutturale, 50 (2019) 54-67; doi: 10.3221/igf-esis.50.07 61 nonlinear fracture resistance and constraint parameters in the gte compressor disc elastic and plastic stress intensity factors hlyannikov et al. [5] showed that the stress–strain state in the rotating disc obtained from fe calculations was biaxial indicating that the structure around the slot fillets of the key was subjected to radial and tangential stresses. stress biaxiality ratio rr    is a function of the current value of the disc radius and varies from η=−0.27 to η=+0.29 [3]. the data presented in fig. 8 also indicates a mixed mode behaviour along the crack front in the compressor disc. different from pure mode i, calculating the two fracture parameters was necessary to study the influence of the mixed mode loading conditions on fracture resistance parameters, namely, modes i and ii stress intensity factors (sifs) ki and k2. shlyannikov [15] generalised the numerical method of calculating the geometry-dependent correction factors y1 and y2 for sif ki and k2 under mixed mode fracture. this study directly used the results of the fe solution for calculating sif ki and k2 ahead of the crack tip (θ=0º):    2 22 2 21 2 1 24eqvk k k k k   (6) 1 2 femk r  2 2 fem rk r  where femi represents the stresses obtained from the fe solution, and r and θ – are the polar coordinates centred at the crack tip. the plastic stress intensity factor was introduced in [3, 16-17] as the unified fracture resistance parameter for fatigue crack growth rate characterization. for the compressor disc, the plastic sif kp in pure mode i (or pure mode ii) can be expressed directly in terms of the corresponding elastic equivalent sif keqv. this is shown in [18]:    1 2 1 1 1 4 n eqv p y n k k i w                 (7) where 3 4   ,  is the poisson’s ratio, in is the governing parameter of the elastic–plastic stress–strain fields in the form of in factor, α and n are the hardening parameters, y is the yield stress, and w is the characteristic size (in this case, the width of key). in the asymptotic hrr solution [19-21], the in is dependent only on the plastic properties of the material, namely, the strain-hardening exponent n. shih [22] modified the hrr solution for the plane strain problem and found that the in becomes dependent on the mode mixing parameter mp under mixed mode, small-scale yielding,. shlyannikov and tumanov [16] developed a method to determine the in factor. this method considers the influence of the specimen and crack geometry [16]:     , , , ( , , , )fem femn p pi m n a w m n a w d         (8)     1, , , cos 1 femfem n p e n m n a w n        sin fem fem fem fem fem femr rr r r du du u u d d                               (9)  1 cos . 1 fem fem fem fem rr r ru u n         s n. boychenko et alii, frattura ed integrità strutturale, 50 (2019) 54-67; doi: 10.3221/igf-esis.50.07 62 a detailed description of the governing parameter in the form of in-factor definition is given in [16]. it is shown that infactor is sensitive to the constraint effects and can be used as constraint parameter. stressstrain fields under extensive creep can be written in terms of creep stress intensity factor kcr in the following form [23]: 1 * 1 0 1 crn cr cr n c k bi l        (10) where b and ncr are creep constants, cr ni is the governing parameter of the stress–strain fields for power-law creeping materials, and с* is the с-integral under extensive creep. methods for determining c-integral at various creep stages and conditions are given in [23-26]. a numerical method was introduced by shlyannikov [23] to determine the governing parameters of the creep-crack tip fields in terms of the in integral for power-law creeping materials. this method can be also be used to analyse the creepdamaged material’s fracture resistance characteristics. kcr is the most effective crack tip parameter in correlating the creep– fatigue crack growth rates in power plant materials and can be used for practical purposes [23, 24]. constraint parameters distributions the stress-strain state analysis of the compressor disc with corner cracks should be performed taking into account inplane and out-of-plane constraint effects. shlyannikov et al. [27, 28] showed that different traditional approaches which can successfully describe the in-plane constraint are inaccurate for describing 3d surface cracks. in [29], constraint parameters were analysed as a function of cyclic tension loading and temperature conditions. characterization of the constraint effects in the present study was performed using the local stress triaxiality h, tz-factor, in-factor and cr ni for specified combinations of crack sizes and loading conditions. all parameters were determined at the crack tip distance range of r/a=0.01, where the numerical solution provides a stabilised result. a local parameter of the crack-tip constraint was proposed in [30] as a secondary fracture parameter because the validity of some concepts previously mentioned depends on the chosen reference field. this stress triaxiality parameter is described as follows: 3 3 2 kk ij ijh s s        (4) where kk and ijs are hydrostatic and deviatoric stresses, respectively. as the function of the first invariant of the stress tensor and the second invariant of the stress deviator, the stress triaxiality parameter is a local measure of the in-plane and out-of-plane constraint effects that is independent of any reference field. the tz-factor [31] has been recognized to present a measure of the out-of-plane constraint and can be expressed as the ratio of the normal stress components: zz z xx yy t      (5) where  is the poisson’s ratio, zz is the out-of-plane stress, and xx and yy are the in-plane stresses. fig. 7 depicts the effect of temperature on the constraint parameters for plastic and creep solutions. results for two crack front positions (initial and final [front 1 and 3, respectively]) are presented. the tz-factor and stress triaxiality h change in character along the crack tip from the free surface (r=0) and across the mid-plane (0<r<1) towards the slot surface (r=1). all considered factors, such as the crack front position, temperature and angular velocity, affect the constraint parameters. however, the crack front position has the most significant influence. whilst crack size increases, qualitative and quantitative changes in constraint parameters distributions occur. this occurrence contrasts with temperature and angular n. boychenko et alii, frattura ed integrità strutturale, 50 (2019) 54-67; doi: 10.3221/igf-esis.50.07 63 velocity, which only produce a quantitative effect on tz-factor and h. the tz-factor under creep conditions is nearly independent on the temperature within the considered range. figure 7: distribution of tz-factor and stress triaxiality h along the crack for plastic solution and creep in the temperature range. fig. 8 demonstrates the behaviour of constraint parameters under creep conditions for the damaged and undamaged states. at the initial and intermediate crack front positions (front 1 and 2), the damage on both parameters considered in this section is insignificant. for the third crack front position, the damages lead to an unsubstantial increase in the tzfactor and h. figure 8: impact of damage accounting on the constraint parameters behavior under creep conditions. thus, the tz-factor and h mainly reproduce the influence of crack front shape and position. the influence of loading conditions, temperature and damage of material is insignificant to these parameters. the governing parameters of the elastic-plastic stress field in and creep field cr ni distributions along the cracked front in the compressor disc with an angular velocity of 1000 rad/s are plotted in fig. 9. these distributions correspond to the different temperatures and crack front positions. the in-factor distributions are plotted against the normalized coordinates, where r= 0.0 is the free surface, and r = 1.0 is the inner surface of slot fillet. as shown in fig. 9, the infactor distributions essentially change along the crack front from the free surface towards the slot key. material properties n. boychenko et alii, frattura ed integrità strutturale, 50 (2019) 54-67; doi: 10.3221/igf-esis.50.07 64 relating to temperature and the crack front position have a significant influence on the distribution of the in and cr ni factors. figure 9: in and cr ni -factors distributions along the crack front in the temperature range. figure 10: impact of damage accounting on the crni -factor behavior. the behaviour of the crni -factor for damaged and undamaged states is depicted in fig. 10. in contrast to the traditional constraint parameters tz and h (fig. 8), the cr ni -factor is a function of the damage for all crack front positions, loading conditions and temperatures in the present study. damage accounting under creep conditions causes changes in the crni factor distributions for all the loading conditions and temperature combinations considered in this work. the crni -factor, which is used as the foundation for the creep stress intensity factor, is sensitive to in-plane and out-of-plane constraint effects. moreover, the crni -integral has advantages over the traditional constraint parameters considered in this study due to sensitivity to damage accumulation. elastic and plastic stress intensity factors distributions the behaviour of the elastic sifs along the crack front in the gte compressor disc under the considered loading conditions is shown in fig. 9. the elastic sifs change moderately as a result of the crack front position and angular velocity. at the same time, the elastic sif is not sensitive to temperature. for each considered crack front position, the same keqv distribution corresponds to three temperature values (20°с, 300°с, 370°с). this fact imposes significant restrictions on the use of the elastic stress intensity factor as a fracture resistance parameter. fig. 12 depicts the plastic stress intensity factor distributions along the crack front for different combinations of angular velocity, temperature and crack front position. plastic sif, as well as elastic sif, depend on the crack front position and angular velocity. however, in contrast to the elastic sif, the nonlinear sif kp is sensitive to the main material properties as a function of the compressor disc’s operating temperature. moreover, a significant change in kp is observed when the temperature rises from 20°c to 300°c. a further increase in temperature of up to 370°c has no substantial effect on the distribution of the plastic stress intensity factor. n. boychenko et alii, frattura ed integrità strutturale, 50 (2019) 54-67; doi: 10.3221/igf-esis.50.07 65 figure 11: elastic equivalent sif keqv distribution along the crack front in the temperature range. (1 – initial, 2 intermediate, 3 final crack fronts) figure 12: plastic sif kp distribution along the crack front in the temperature range. (1 – initial, 2 intermediate, 3 final crack fronts) as previously mentioned, loading conditions (namely the angular velocity) affect the distribution of the plastic stress intensity factor; however, the results presented in fig. 12 show that material properties related to temperature have a decisive influence on the kp value. these findings support the use of plastic sif as a useful parameter for the assessment of the fracture resistance of materials and structures. creep stress intensity factor distributions for two values of the disc rotational speed and temperature for damaged and undamaged states are shown in fig. 13. the factors considered in this work have a significant influence on the kcr distributions; these factors include angular velocity, temperature, crack size and position of the cross section in the disc. as shown in the presented data, kcr is sensitive to accumulated damage. damage accounting leads to an increase in the nonlinear creep stress intensity factor, thus allowing the researchers to conclude that damage accounting provides an opportunity to perform an objective carrying capacity assessment. these results support the use of the creep sif as a parameter for the assessment of the fracture resistance of materials and structures under high temperature conditions. n. boychenko et alii, frattura ed integrità strutturale, 50 (2019) 54-67; doi: 10.3221/igf-esis.50.07 66 figure 13: creep sif kcr distribution along the crack front in the temperature range taking into account damage accumulation. (1 – initial, 2 intermediate, 3 final crack fronts). conclusions n this study, a numerical analysis of an aircraft gte compressor disc was conducted under operation loading conditions taking into account damage accumulation. different combinations of disc rotation angular velocity, operating temperature, quarter elliptical crack form and size and elastic–plastic properties of the titanium alloy vt3-1 were compared. the constraint parameters in the form of the tz-factor, local stress triaxiality h and in and cr ni -factor were analysed for the specified combinations of crack sizes and temperature conditions. the crni -factor, used as the foundation of the creep stress intensity factor, is sensitive to damage accumulation. the distributions of the governing parameters for the crack tip were represented along the crack front in the form of elastic, plastic and creep sifs. a study under creep conditions were carried out taking into account the damage of material, revealing that elastic sif is not sensitive to temperature. the principal advantage of the plastic and creep stress intensity factors is its sensitivity to real material properties and temperature. damage accounting provides an opportunity to perform an objective carrying capacity assessment. nonlinear sifs are found to be attractive as a self-dependent unified parameter for the characterisation of fracture resistance under room and elevated temperatures. based on the obtained numerical results of the present study, an ongoing work of the author will include crack growth rate and lifetime prediction. references [1] makhutov, n.a., vorobyev, a.z., gadenin m.m. at al. (1983). prochnost' konstrukcij pri malociklovom nagruzhenii, moscow: nauka, 272p. [2] zharoprochnye splavy dlja gazovyh turbin, edited by shalin r.e. (1981). moscow: metallurgija, 479 p. [3] shlyannikov, v.n., zakharov, a.p., yarullin, r.r. (2016). structural integrity assessment of turbine disk on a plastic stress intensity factor basis, international journal of fatigue, 92 (part 1), pp. 234-245. doi: 10.1016/j.ijfatigue.2016.07.016. [4] kumar, r., ranjan, v., kumar, b., ghoshal, s.k. (2018). finite element modelling and analysis of the burst margin of a gas turbine disc using an area weighted mean hoop stress method, engineering failure analysis, 90, pp. 425-433. doi: 10.1016/j.engfailanal.2017.12.014. [5] shlyannikov, v.n., iltchenko, b.v., stepanov, n.v. (2001). fracture analysis of turbine disks and computational– experimental background of the operational decisions, engineering failure analysis, 8 (5), pp. 461-475. doi: 10.1016/s1350-6307(00)00041-8. [6] shlyannikov, v.n., yarullin, r.r., zakharov, a.p. (2015). fatigue life of power steam turbine disk material after loading history, transactions of academenergo, 3, pp. 78-91. i n. boychenko et alii, frattura ed integrità strutturale, 50 (2019) 54-67; doi: 10.3221/igf-esis.50.07 67 [7] papanikos, p., meguid, s.a., stjepanovic, z. (1998). three-dimensional nonlinear finite element analysis of dovetail joints in aeroengine discs, finite elements in analysis and design, 29, (3-4), pp. 173-186. doi: 10.1016/s0168-874x(98)00008-0. [8] shanyavsky, a.a., stepanov, n.v. (1995). fractographic analysis of fatigue crack growth in engine compressor disks of ti-6al-3mo-2cr titanium alloy, fatigue & fracture of engineering & material structures, 18 (5), pp. 539-550. doi: 10.1111/j.1460-2695.1995.tb01416.x. [9] farrahi, g.h., tirehdast, m., masoumi khalil abad, e., parsa, s., motakefpoor, m. (2011). failure analysis of a gas turbine compressor, engineering failure analysis, 18 (1), pp. 474-484. doi: 10.1016/j.engfailanal.2010.09.042. [10] giannella, v., citarella, r., perrella, m., shlyannikov. v. (2019). surface crack modelling in an engine compressor disc, theoretical and applied fracture mechanics, in press. doi: 10.1016/j.tafmec.2019.102279 . [11] shaniavski, a.a. (2003). tolerance fatigue failures of aircraft components. synergetics in engineering applications. in: monography, ufa, pp. 803 [12] shlyannikov, v.n., tumanov, a.v. (2018). force and deformation models of damage and fracture during creep, physical mesomechanics, 3, pp.70-85. [13] shlyannikov, v.n., tumanov, a.v. (2018). creep fracture resistance parameters determination based on stress and ductility damage models, fatigue & fracture of engineering & material structures, 41 (10), pp. 2110-2129. doi: 10.1111/ffe.12766. [14] ansys. theory reference. 001242. eleventh edition. (1999). sas ip inc. [15] shlyannikov, v.n. (2013). t-stress for crack paths in test specimens subject to mixed mode loading. engineering fracture mechanics, 108, pp. 3–18. doi: 10.1016/j.engfracmech.2013.03.011. [16] shlyannikov, v.n., tumanov, a.v. (2014). characterization of crack tip stress fields in test specimens using mode mixity parameters, international journal of fracture, 185, pp. 49-76. doi: 10.1007/s10704-013-9898-0. [17] shlyannikov, v.n., tumanov, a.v., zakharov, a.p. (2014). the mixed mode crack growth rate in cruciform specimens subject to biaxial loading, theoretical and applied fracture mechanics, 73, pp. 68-81. doi: 10.1016/j.tafmec.2014.06.016. [18] shlyannikov, v.n., zakharov, a.p. (2017). generalization of mixed mode crack behaviour by the plastic stress intensity factor, theoretical and applied fracture mechanics, 91, pp. 52-65. doi: 10.1016/j.tafmec.2017.03.014 . [19] hutchinson, j.w. (1968). plastic stress and strain fields at a crack tip, journal of mechanics and physics of solids, 16, pp. 337-347. [20] rice, j.r., rosengren, g.f. (1968). plane strain deformation near a crack tip in a power-law hardening material, journal of mechanics and physics of solids, 16, pp. 1-12. [21] hutchinson, j.w. (1968). singular behaviour at the end of a tensile crack in a hardening material, journal of mechanics and physics of solids, 16, pp. 13-31. [22] shih, c.f. (1974). small-scale yielding analysis of mixed mode plane-strain crack problems, fracture analysis, astm special technical publications, 560, pp.187-210. [23] shlyannikov, v.n., tumanov, a.v., boychenko, n.v. (2015). a creep stress intensity factor approach to creep-fatigue crack growth, engineering fracture mechanics, 142, pp. 201-219. doi: 10.1016/j.engfracmech.2015.05.056. [24] shlyannikov, v.n., tumanov, a.v., boychenko, n.v. (2018). creep-fatigue crack growth rate assessment using ductility damage model, international journal of fatigue, 116, pp.448-461. doi: 10.1016/j.ijfatigue.2018.07.003. [25] boychenko, n.v. (2017). parameters of cracked bodies behavior under creep conditions, transactions of academenergo, 1, pp. 104-118. [26] saxena, a. (1998). nonlinear fracture mechanics for engineers. boca raton, fl, crc press. [27] shlyannikov, v.n., tumanov, a.v., zakharov, a.p., gerasimenko, a.a. (2016). surface flaw behavior under tension, bending and biaxial cyclic loading, international journal of fatigue, 92 (part 2), pp.557-576. doi: 10.1016/j.ijfatigue.2016.05.003. [28] slyannikov, v.n., yarullin, r.r., ishtyryakov, i.s. (2015). surface crack growth in cylindrical hollow specimen subject to tension and torsion, frattura ed integrità structurale, 33, pp.335-344. doi: 10.3221/igf-esis.33.37. [29] yarullin, r.r., ishtyryakov, i.s. (2016). fatigue surface crack growth in aluminum alloys under different temperatures. procedia engineering, 160, pp.199-206. doi: 10.1016/j.proeng.2016.08.881. [30] henry, b.s., luxmoore, a.r. (1997). the stress triaxiality constraint and the q-value as fracture parameter, engineering fracture mechanics, 57, pp.375-390. doi: 10.1016/s0013-7944(97)00031-3. [31] guo, w.l. 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/hrv (za stvaranje adobe pdf dokumenata najpogodnijih za visokokvalitetni ispis prije tiskanja koristite ove postavke. stvoreni pdf dokumenti mogu se otvoriti acrobat i adobe reader 5.0 i kasnijim verzijama.) /hun 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can be opened with acrobat and adobe reader 5.0 and later.) >> /namespace [ (adobe) (common) (1.0) ] /othernamespaces [ << /asreaderspreads false /cropimagestoframes true /errorcontrol /warnandcontinue /flattenerignorespreadoverrides false /includeguidesgrids false /includenonprinting false /includeslug false /namespace [ (adobe) (indesign) (4.0) ] /omitplacedbitmaps false /omitplacedeps false /omitplacedpdf false /simulateoverprint /legacy >> << /addbleedmarks false /addcolorbars false /addcropmarks false /addpageinfo false /addregmarks false /convertcolors /converttocmyk /destinationprofilename () /destinationprofileselector /documentcmyk /downsample16bitimages true /flattenerpreset << /presetselector /mediumresolution >> /formelements false /generatestructure false /includebookmarks false /includehyperlinks false /includeinteractive false /includelayers false /includeprofiles false /multimediahandling /useobjectsettings /namespace [ (adobe) (creativesuite) (2.0) ] /pdfxoutputintentprofileselector /documentcmyk /preserveediting true /untaggedcmykhandling /leaveuntagged /untaggedrgbhandling /usedocumentprofile /usedocumentbleed false >> ] >> setdistillerparams << /hwresolution [2400 2400] /pagesize [612.000 792.000] >> setpagedevice microsoft word numero_35_art_9 l. songsong et alii, frattura ed integrità strutturale, 35 (2016) 74-81; doi: 10.3221/igf-esis.35.09 74 focussed on crack paths mechanism of crack branching in the fatigue crack growth path of 2324-t39 aluminium alloy lu songsong (http://orcid.org/0000-0001-7591-434x) bao rui (http://orcid.org/0000-0001-7170-082x) zhang ting fei binjun institute of solid mechanics, beihang university (buaa), 100191, beijing, china rbao@buaa.edu.cn abstract. the crack growth behavior in 2324-t39 aluminium alloy was experimentally investigated. two types of crack branching were observed. the mechanism of an uncommon crack branching which results from the link up of secondary crack with the main crack was focused on. the crack paths were observed with optical microscope and in-situ sem. finite element crack tip simulation was performed to investigate the relationship between plastic zone size and the location of the secondary crack. tests and analysis results indicate that the secondary crack initiates near the plastic zone boundary and from the subsurface. the mechanism of this kind crack branching relates to the interaction of grain size and plastic zone size. keywords. fatigue crack growth; crack path branching; mechanism analysis; 2324-t39 aluminium alloy. introduction lloy 2324-t39 plate is a higher strength version of alloy 2024-t351, and is a high-purity controlled composition varient of alloy 2024. both strength and fracture toughness properties are improved compared to 2024 plate via employing the t39 temper which was developed through special fabricating practices [1]. since this alloy was developed for tension-dominated, fatigue and fracture critical plate applications, most of the experimental investigations about it are most focused on the fatigue crack growth and fracture. william m. [2] and dawicke d s [3] report the fracture test results of 2324-t39 plate with difference thicknesses. stoychev s [4] investigates the effect of varying stress intensity factor range k on crack growth rate. bao r et al. [5-7] present the macroscopic crack path branching observed during the crack growth tests of 2324-t39 middle crack tension (m (t)) specimen under spectrum loading. according to achievements in fatigue theory and fracture mechanics, a through thickness middle crack in an isotropic thin plate subjected to remote tension-dominated loading should propagate perpendicular to the load direction, i.e., mode i. this is reasonable from a physical perspective because the tensile stress component, which opens the crack, will certainly promote the conversion of cyclic plastic deformation into crack extension [8]. at the macro level, crack kinking, bifurcation and branching are influenced by micro-structural irregularities, load effects (global and local multiaxial stress state, spectrum loading), and environmental factors [9-13]. though, the t39 temper was said to account for the fracture toughness improvement, there is no evidence found in the literature that the t39 temper will contribute to the macroscopic crack path change with respect to those of other al-cu-mg alloys, such as 2024-t351 and 2524-t3. a l. songsong et alii, frattura ed integrità strutturale, 35 (2016) 74-81; doi: 10.3221/igf-esis.35.09 75 in the microscopic perspective, a series of investigations on crack branching, e.g. in-situ sem tests of a nickel-based single crystal in ref [14] and ebsd tests on crack propagation path of 7050 alloy in ref [15], were carried out, which suggest that the crystallographic orientations and geometry of local microstructure, particularly the tilt and twist angle, differences of slip planes or crack planes, together with cooperation and competition between movement of slip systems and loading stress influence the crack propagation behavior. patton’s research indicated that crack bifurcation may be caused by plastic anisotropy and pre-existing defects in front of crack tip [16]. zhiyi liu’s research indicated that the extending potential decides the further extending of these bifurcated cracks [17]. the potential of the propagation concerns the tilt angle, twist angle and schmid factor differences between two neighboring grains. these factors, of commonsense, could result in kinking, bifurcation or branching in fatigue crack path, the appearance of which could be captured as soon as it arises [18]. however, ref. [6] reports that the crack branching observed in alloy 2324-t39 results from the linkup of secondary crack with the lead crack, the process of which is quite different from those common procedures found in the literatures, e.g. ref. [14-18]. ref. [7] presents the effect of overloads and k level on crack path change in alloy 2324-t39. for better understanding the mechanism of the uncommon macroscopic crack branching in 2324-t39 alloy, optical metallography analysis, in-situ sem crack growth tests and numerical simulations on crack tip stress field were carried out in this paper, which will reveal the differences in macroscopic crack morphologies and metallographic fracture characteristics of the two types of crack branching, as well as the effect of the less common crack branching on crack growth rate and some relationship between the appearance of the less common crack branching with the crack tip plastic zone size. experiments hree kinds of crack growth tests were carried out to investigate the crack growth behavior in 2324-t39, i.e. tests with m(t) specimen of 4.5mm in thickness under spectrum loading (stated as test type i), tests with relatively small specimens of 1.5mm in thickness with single edge notch under constant amplitude loading(stated as test type ii), and in-situ scanning electron microscope (sem) crack growth tests under constant amplitude loading(stated as test type iii). the details of the tests type i, such as specimen configuration, loading sequence, test procedures, etc., have been reported in ref. [6, 7]. the aims of designing the other two kinds of tests are 1) to eliminate the potential effects of specimen thickness and loading sequence on crack branching; 2) to rule out the effect of crack configuration, i.e. middle crack and edge crack, on crack branching; 3) to observe the position where the secondary crack appears and the linkup via in-situ sem test. the small specimens with single edge notch used in test type ii and iii were cut from the aforementioned m(t) specimen. the configurations of the specimens are designed to fit the loading facilities attached to test machines, which are given in fig. 1(a) for test type ii and fig. 1(b) for test type iii. all the specimens are in l-t orientation as demonstrated in fig. 1(c). the thickness of the specimen for test type ii is 1.5mm, while it is 0.7mm for test type iii. (a) (b) (c) figure 1: specimen dimensions and orientation (unit: mm). t l. songsong et alii, frattura ed integrità strutturale, 35 (2016) 74-81; doi: 10.3221/igf-esis.35.09 76 tests type ii were accomplished with mts880 servo hydraulic fatigue test system and an observation system consisting of a digital microscope, a servo motor and a raster ruler. constant amplitude (ca) loading cycles with stress ratio r = 0.06 were employed. two specimens, labelled as l-t-2-1 and l-t-2-2, were tested at the maximum stress max = 140 mpa and 150 mpa, respectively. all the tests were run at 20hz in laboratory air. test type iii were carried out with shimadzu ss-550 sem. the loading facility in the sem is a microscopic static and dynamic testing machine produced by shimadzu. constant amplitude loading cycles of r = 0.06 and max = 150 mpa was employed in the in-situ sem test. the test was run at 10hz in vacuum. the specimen tested in this case is marked with l-t-3-1. all the specimen was pre-cracked under constant amplitude load of r = 0.06 and max = 120 mpa, which resulted in an initial crack whose length is about 0.3 mm from the notch tip. crack branching process and mechanism ig. 2(a), (b) and (c) show the crack morphologies observed in test type i, ii and iii, respectively. two types of crack branching were observed in the crack paths corresponding to all the three test types. the ones marked by circle in fig. 2 are the familiar type of crack branching which were captured once they appeared. the intersection angles are usually less than 90 degree. however, the branches marked by square in fig. 2 are obviously different with those marked by circles. the following on discussion will centre on this type of crack branching. (a) (b) (c) figure 2: crack morphologies observed in (a) m(t) specimen under spectrum loading [7], (b) single edge notch specimen (l-t-2-2) tested under ca loading, and (c) l-t-3-1 specimen tested by in-situ sem under ca loading it can be seen from fig. 2, for the less familiar type of crack branching (marked by squares), the turning angles are almost 90 degree. the procedure of the appearance of such branches is also different to the common ones. the growth of the leading crack slowed down firstly, and a surface secondary crack was observed away from the leading crack tip, both of the leading crack and the secondary crack kept growing for several loading cycles and finally they linked up to each other. fig. 3 and fig. 4 give the observed crack branching procedures in test type i and iii, respectively, which indicate exactly the same manner. f l. songsong et alii, frattura ed integrità strutturale, 35 (2016) 74-81; doi: 10.3221/igf-esis.35.09 77 the surface secondary crack cannot be observed immediately after it initiates even in the in-situ tests. once it appears on the specimen surfaces, it is already in a certain length as shown in fig. 4(b). the crack growth of the secondary crack was transgranular, while the link up path was long the grain boundary. the omen of the appearance of surface secondary crack is the slowing down in the growth rate of the previously dominated crack, as shown in fig. 5. it can be seen from fig. 5 that there is a remarkable crack growth rate drop at about 3467 loading cycles, however, there was no abnormal observed around the crack tip in the picture corresponding to 5969 cycles in fig. 4(a). compare fig. 4(a) and (b), it can be found that there is little growth of previously dominated crack during the 2598 cycles. there is a sudden increase in crack length in fig. 5(a) at about 8567 cycles that is because of the appearance of the surface secondary crack of about 150m in fig. 4(b). from these clues, it can be deduce that the secondary crack initiates from subsurface at about 3467 cycles, which dissipates the energy and in consequence decreases the growth rate of the main crack. after the link up of secondary crack and the main crack, the crack growth rate recovers. (a) (b) (c) figure 3: appearance of secondary surface cracks and cracks linking up under spectrum loading [6]. (a) (b) figure 4: in-situ sem pictures on crack path of l-t-3-1 specimen (a) at 5969 cycles and (b) at 8567 cycles under constant amplitude loading. (a) (b) (c) figure 5: crack growth data for l-t-3-1 specimen, (a) crack length a vs. loading cycles n, (b) crack growth rate da/dn vs. loading cycles n and (c) crack growth rate da/dn vs. stress intensity factor range k to investigate the difference in mechanism of the uncommon kind of crack branching from the common ones, optical microscope observations on the grain shape and crack growth path were carried out on the single edge notch specimen after the crack growth test. metallographic samples were prepared etching with keller (1ml hf, 1.5ml hcl, 2.5ml hno3, 95ml h2o) for 3 minutes after the conventional mechanical polishing to observe the grain boundary. fig. 6(a), (b) and (c) demonstrate the microstructure on l-t, l-s and t-s metallographic planes, respectively, where s is the short transverse direction. it can be l. songsong et alii, frattura ed integrità strutturale, 35 (2016) 74-81; doi: 10.3221/igf-esis.35.09 78 seen from fig. 6 that the dimension of the grains in the l direction is remarkably longer than that in the t and s direction; it looks like a layered up structure in l-s plane. the observed crack paths in specimens l-t-2-1 and l-t-2-2, for which the applied max are 140 mpa and 150 mpa, respectively, are given in fig. 7 and fig. 8. the common type of crack branching, shown in fig. 7(b) and fig. 8(b), occurs at the grain boundary. for the weaker cohesion of grain boundary in this orientation, grain boundary becomes paths of easy propagation. whereas, for the less common type of crack branching, see fig. 7(c) and fig. 8(c), the growth of the main crack and the surface secondary crack show transgranular characteristic, though the linkup path was along the grain boundary. therefore, the reason for crack branching is not the weakness in grain boundaries. (a) (b) (c) figure 6: grain shape observations on (a) l-t, (b) l-s, (c) t-s metallographic planes of 2324-t39 alloy. (a) (b) (c) figure 7: crack growth path for l-t-2-1 specimen (ca loading, max = 140 mpa, r = 0.06). (a) (b) (c) figure 8: crack growth path for l-t-2-2 specimen (ca loading, max = 150 mpa, r = 0.06). l. songsong et alii, frattura ed integrità strutturale, 35 (2016) 74-81; doi: 10.3221/igf-esis.35.09 79 the position where the secondary crack appears t can be seen from fig. 2, 3, 4, 7 and 8 that the secondary cracks, on the l-t plane, located a certain distance away from the main cracks. analysis with empirical equations and finite element (fe) simulation were performed to investigate the relationship between the value of this distance and the crack tip plastic zone size. in the condition of small scale yielding, the curve equation of the crack tip plasticity boundaries, as shown in fig. 9, under mises criterion is as follows [18]:                       2 2 2i 2 s 2 22 2 p 2i s cos 1+ 3sin planestress 2πσ 2 2 cos 1 2ν + 3sin planestrain 2π r 2 2 = σ k θ θ k θ θ (1) where θ is defined as the upward inclination from the horizontal and ν is poisson's ratio. figure 9: sketch map of crack tip plastic zone. it is acceptable that the crack tip is in small scale yielding state for case of the edge notch specimens used in this study when the secondary cracks initiate on the surface. since the secondary cracks usually initiate above or below the main crack tip, θ in eq. (1) is set to be 90 degree in the calculation. the calculation results are listed in tab. 1 for specimen l-t2-1, l-t-2-2 and l-t-3-1. since the specimens are thin sheet, the calculation is based on the equation for plain stress. although the specimen configurations and the clapping mode were slightly different in test type ii and iii, the section as shown in fig. 10(a) could be regarded as an edge cracked plane subjected to uniaxial stress state. finite element simulation was performed for this section. considering the symmetry, a 1/2 plane model was used here and the boundary conditions and the meshing was illustrated in fig. 10(b) and (c). line ab is the crack surface. symmetry constraint was applied to line bc. constraint in x direction and uniformly distributed load in y direction are applied to line de. the three specimens, i.e. l-t-2-1, l-t-2-2 and l-t-3-1, are all simulated. the widths and crack lengths of the fe models and the applied stress levels are in accord with those in the corresponding tests. the material behavior is assumed to be elastic-plastic isotropic to acquire the crack tip stress field. the trilinear constitutive mode is adopted with e = 450 mpa, 0.2 = 481 mpa, b = 532 mpa, which were obtained from the - curve of the mechanical property test. (a) (b) (c)   figure 10: fe model and crack tip meshing (the meshing size of crack tip is 0.01mm). i l. songsong et alii, frattura ed integrità strutturale, 35 (2016) 74-81; doi: 10.3221/igf-esis.35.09 80 the fe calculated plastic zone sizes at θ =90° for the three specimens are listed in tab. 1, together with the results calculated by eq. (1). the distances from the surface secondary cracks to the main crack tips are also measured from the optical photographs and listed in tab. 1. the comparison in tab. 1 indicates that: 1) the fe simulation results are about 10% higher than the results obtained by empirical equation, that is because the elastic-plastic material model is used in the fe model; 2) the calculated plastic zone sizes at θ =90° by both eq. (1) and fe model match the measured distances from the surface secondary cracks to the main crack tips. that is to say, the secondary cracks initiation positions are near the plastic zone boundaries of the main crack. specimen measured distance between the secondary crack and the main crack calculated plastic zone size of plane stress state at θ =90° by eq. (1) calculated plastic zone size of plane stress state at θ =90° by fe model l-t-1 0.241 0.209 0.23 l-t-2 0.185 0.177 0.19 l-t-3 0.083 0.074 0.08 table 1: comparison of the plastic zone size of plane stress state at θ =90° with the measuring distance from the secondary crack to the main crack (mm). conclusions he following conclusions can be drawn from the experimental investigations and crack tip analysis: 1) the macroscopic crack branching in aa 2324-t39 results from two different types of mechanism. the uncommon kind of branching is resulted from the linking up of the secondary crack with the main crack, which is different from the intergranular crack branching. 2) the secondary cracks usually locate near the plastic zone boundaries of the main cracks and show transgranular growth characteristics. the initiation sites of the secondary cracks were deduced at the sub-surfaces of the specimen. 3) the grain shapes characteristics in different orientations of this alloy and their interaction with the plastic zone size contribute to the appearance of the second type of crack branching. acknowledgements he national natural science foundation of china is acknowledged for supporting the project (10802003). references [1] http://www.alcoa.com/mill_products/catalog/ pdf/alloy2324-t39techsheet. (2009) [2] johnston, w. m., newman, jr. j. c., fracture test results for 0.5, 0.7 and 0.9 inch thick 2324-t39 aluminium alloy material, (2001). [3] dawicke, d. s., fracture testing of 2324-t39 aluminium alloy, nasa tm-109183, (1995). [4] stoychev, s., kujawski, d., mallory, j., fatigue crack growth in 2324 aluminium alloy. mae-05-01, (2005). [5] hailing, tian, et al. influence of low load truncation level on crack growth for al 2324-t39 and al 7050-t7451. chinese journal of aeronautics, 22(4) (2009) 401-406. [6] rui, b., zhang, x., fatigue crack growth behaviour and life prediction for 2324-t39 and 7050-t7451 aluminium alloys under truncated load spectra, international journal of fatigue, 32(7) (2010) 1180-1189. [7] zhang, t., rui, b., binjun, f., load effects on macroscopic scale fatigue crack growth path in 2324-t39 aluminium alloy thin plates, international journal of fatigue, 58 (2014) 193-201. t t l. songsong et alii, frattura ed integrità strutturale, 35 (2016) 74-81; doi: 10.3221/igf-esis.35.09 81 [8] schijve, j., fatigue of structures and materials, springer, germany, (2009). [9] toribio, j., gonzález, b., matos, j. c., fatigue and fracture paths in cold drawn pearlitic steel. engineering fracture mechanics, 77(11) (2010) 2024-2032. [10] beretta, s., foletti, s., valiullin, k., fatigue crack propagation and threshold for shallow micro-cracks under out-ofphase multiaxial loading in a gear steel. engineering fracture mechanics, 77(11) (2010) 1835-1848. [11] schubbe, j. j., evaluation of fatigue life and crack growth rates in 7050-t7451 aluminium plate for tl and ls oriented failure under truncated spectra loading, engineering failure analysis, 16(1) (2009) 340-349. [12] hénaff, g., menan, f., odemer, g., influence of corrosion and creep on intergranular fatigue crack path in 2xxx aluminium alloys. engineering fracture mechanics, 77(11) (2010) 1975-1988. [13] pook, l. p., on fatigue crack paths, international journal of fatigue, 17(1) (1995) 5-13. [14] zhang, y., shi, h.-j., gu, j., li, c., kadau, k., luesebrink o., crystallographic analysis for fatigue small crack growth behaviors of a nickel-based single crystal by in situ sem observation, theoretical and applied fracture mechanics, 69 (2014) 80-89. [15] wei, lili, pan, q., huang, h., feng, l., wang, y., influence of grain structure and crystallographic orientation on fatigue crack propagation behavior of 7050 alloy thick plate, international journal of fatigue, 66 (2014) 55-64. [16] patton, g., et al. study of fatigue damage in 7010 aluminium alloy, materials science and engineering: a 254.1 (1998): 207-218. [17] liu, z., li, f., xia, p., bai, s., gu, y., yu, d., zeng s., mechanisms for goss-grains induced crack deflection and enhanced fatigue crack propagation resistance in fatigue stage ii of an aa2524 alloy, materials science and engineering, a 625 (2015) 271-277. 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can be opened with acrobat and adobe reader 5.0 and later.) >> /namespace [ (adobe) (common) (1.0) ] /othernamespaces [ << /asreaderspreads false /cropimagestoframes true /errorcontrol /warnandcontinue /flattenerignorespreadoverrides false /includeguidesgrids false /includenonprinting false /includeslug false /namespace [ (adobe) (indesign) (4.0) ] /omitplacedbitmaps false /omitplacedeps false /omitplacedpdf false /simulateoverprint /legacy >> << /addbleedmarks false /addcolorbars false /addcropmarks false /addpageinfo false /addregmarks false /convertcolors /converttocmyk /destinationprofilename () /destinationprofileselector /documentcmyk /downsample16bitimages true /flattenerpreset << /presetselector /mediumresolution >> /formelements false /generatestructure false /includebookmarks false /includehyperlinks false /includeinteractive false /includelayers false /includeprofiles false /multimediahandling /useobjectsettings /namespace [ (adobe) (creativesuite) (2.0) ] /pdfxoutputintentprofileselector /documentcmyk /preserveediting true /untaggedcmykhandling /leaveuntagged /untaggedrgbhandling /usedocumentprofile /usedocumentbleed false >> ] >> setdistillerparams << /hwresolution [2400 2400] /pagesize [612.000 792.000] >> setpagedevice microsoft word numero_41_art_18.docx s. e. ferreira et alii, frattura ed integrità strutturale, 41 (2017) 129-138; doi: 10.3221/igf-esis.41.18 129 focused on crack tip fields a model to quantify fatigue crack growth by cyclic damage accumulation calculated by strip-yield procedures samuel elias ferreira, jaime tupiassú pinho de castro, marco antonio meggiolaro pontifical catholic university of rio de janeiro, puc-rio, r. marquês de são vicente 225, rio de janeiro, 22451-900, brazil ferreirase@hotmail.com, jtcastro@puc-rio.br, meggi@puc-rio.br abstract. elber's hypothesis that keff can be assumed as the driving force for fatigue crack growth (fcg) is the basis for strip-yield models widely used to predict fatigue lives under variable amplitude loads, although it does not explain all load sequence effects observed in practice. to verify if these models are indeed intrinsically better, the mechanics of a typical strip-yield model is used to predict fcg rates based both on elber's ideas and on the alternative view that fcg is instead due to damage accumulation induced by the cyclic strain history ahead of the crack tip, which does not need or use keff ideas. the main purpose here is to predict fcg using the cyclic strains induced by the plastic displacements calculated by strip-yield procedures, assuming there are strain limits associated both the with the fcg threshold and with the material toughness. despite based on conflicting principles, both models can reproduce quite well fcg data, a somewhat surprising result that deserves to be carefully analyzed. keywords. fatigue crack growth models; strip-yield mechanics; crack closure; damage accumulation ahead of the crack tip. citation: ferreira, s.e., castro, j.t.p., meggiolaro, m.a., a model to quantify fatigue crack growth by cyclic damage accumulation calculated by strip-yield procedures, frattura ed integrità strutturale, 41 (2017) 129-138. received: 28.02.2017 accepted: 15.04.2017 published: 01.07.2017 copyright: © 2017 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. introduction aris and erdogan clearly demonstrated that stable fatigue crack growth (fcg) rates da/dn can be correlated to stress intensity factor (sif) ranges k, at least in the central region of typical da/dnk curves, where theirs da/dn  akm rule applies [1]. following their idea, many others proposed similar rules to consider the effects of other parameters that can affect fcg rates as well, such as the peak load kmax or the load ratio r kmin/kmax, fcg thresholds kth(r), and the toughness kc [2]. in particular, after discovering crack closure under tension loads, elber postulated that additional fatigue damage could only be induced after the crack tip is fully opened under loads greater than kop, the crack opening load [3-4]. his da/dn  f(keff  kmax  kop if kop > kmin) hypothesis can plausibly explain many characteristics of the fatigue cracking behavior, such as fcg delays and arrests induced by overloads (ol), reductions on ol-induced delays after underloads (ul), or the existence of r-dependent fcg thresholds, which can very much affect p s. e. ferreira et alii, frattura ed integrità strutturale, 41 (2017) 129-138; doi: 10.3221/igf-esis.41.18 130 fatigue lives under variable amplitude loads (val). the keff idea has been used since then in many semi-empirical fcg models, among them the strip-yield models (sym) that estimate kop and fcg lives using a suitable da/dnkeff rule properly fitted to experimental data [5-9]. works that support the da/dn  f(keff) hypothesis are extensively reviewed e.g. by kemp [10] and by skorupa [11-12], but many other works question it. fcg delays or arrests after ols under high r while the crack remains fully opened, always maintaining kmin > kop [13]; constant fcg rates induced by fixed {k, r}, but highly variable keff loadings [14-15]; cracks arrested at a given r that restart to grow at a lower r under the same keff [16]; or the r-insensibility of fcg in inert environments [17], are examples of fcg behaviors that cannot be explained by elber's postulate. although this work does not aim to support or to refute elber's idea, neither to review the works that support or question it, it can be claimed that there is no doubt it still remains controversial. in view of such doubts, this work first uses well-proved strip-yield mechanics [5-9] to model some da/dnk curves measured at low and high r. however, instead of just assuming that a reasonable description of some fatigue data confirms that the keff hypothesis is valid, the very same mechanics is then used to verify if the same data can be equally described by the alternative view that fcg, instead of controlled by keff, is due to damage accumulation ahead of the crack tip. this critical damage model (cdm) assumes that fatigue cracks grow by sequentially breaking small volume elements (ve) adjacent to the crack tip after they reach the critical damage the material can sustain. if properly applied, this alternative idea do not need the keff hypothesis or requires arbitrary data-fitting parameters [13, 18-20]. fcg models our fcg models are studied following: (i) the critical damage model (cdm) proposed in [18-20]; (ii) a strip-yield model (sym) based on [6]; (iii) a combination of the strip-yield with the critical damage model (sym-cdm) using fracture mechanics tools; and (iv) a modified strip-yield critical damage model (mod sym-cdm) proposed here. fig 1 illustrates the cdm principles that allow the use of n concepts, used to describe fatigue crack initiation, to model fcg as well. this simple model basically assumes that: (i) fatigue cracks grow by successively breaking small ve located ahead of their tips; (ii) such ve can be treated as tiny n specimens fixed along the crack path; (iii) these ve accumulate fatigue damage induced by variable strain ranges, which increase as the crack tip approaches them; and (iv) the fracture of the ve adjacent to the crack tip occurs because it accumulated the entire damage the material can tolerate. figure 1: schematics of the fcg process caused by successive fractures of the ve adjacent to the crack tip at every load cycle [2]. f s. e. ferreira et alii, frattura ed integrità strutturale, 41 (2017) 129-138; doi: 10.3221/igf-esis.41.18 131 since constant amplitude sif range induce constant fcg rates, the ve widths in such cases can also be assumed fixed and equal to the crack increment per cycle. any given ve suffers damage in each load cycle, caused by the strain loop range induced by that cycle, which depends on the distance xi between the i-th ve and the fatigue crack tip (fig. 1). the strain ranges acting in any given ve increase at every load cycle, as the crack tip approaches it. the fracture of the ve adjacent to the crack tip occurs when its accumulated damage reaches a critical value, estimated by the linear damage accumulation rule (or by any other suitable damage accumulation rule) as: (1) where ni(xi) is the number of cycles that the ith ve located at a distance xi from the crack tip would last if only that cycle loading would act during its whole life, and ni is the number of cycles that acted at that load, in this case just one. the cdm uses the elastoplastic strain distribution ahead of the crack tip to calculate damage in every ve. however, like in the le case, ep models for the stress and strain fields inside the plastic zones pz ahead of a crack tip assumed to have a zero tip radius  = 0, like the hrr field [21-22], are singular at x = 0 as well. to eliminate this undesired and physically inadmissible feature (since no loaded cracks can sustain infinite strains at their tips), the necessarily finite ep stress and strain fields can be estimated by shifting the hrr field origin into the crack by a distance x. this procedure is inspired by creager and paris’ idea originally used to estimate stress concentration factors kt from the sif of geometrically similar cracks [23]. under constant sif range conditions the crack advances a distance equal to the ve width in each cycle (ni  1), so the sum in eq. (1) can be approximated by an integral along, say, the reverse or cyclic plastic zone (pzr), neglecting in a first approximation fatigue damage induced outside it: (2) the hrr field origin shift can be estimated e.g. assuming x  /2, as creager and paris did, where  is the (finite) crack tip radius under the peak load kmax. to calculate the cyclic plastic strain range p ahead of the crack tip, the modification proposed by schwalbe [24] can be used as in [19]: (3) where syc is the cyclic yield strength of the material, e is its young's modulus, and hc is its ramberg-osgood strainhardening exponent. since the elastic strain amplitude inside the cyclic plastic zone is neglected in eq. (3), its associated fatigue life n(x + x) can be estimated from the plastic part of coffin-manson’s equation by n,x+x.=,1-2.,,,∆,ε-p.(x+x)-2,ε-c...-,1-c.. (4) where c and c are coffin-manson's plastic exponent and coefficient, respectively. hence, estimating the x displacement of the modified hrr field in the same way as creager and paris did with the le williams field, i.e. assuming it as   ctod/2, where ctod is schwalbe’s estimate for the crack tip opening displacement induced by kmax, then (5) the fcg rate induced by constant sif ranges, i.e. by fixed {k, r} conditions, can then be estimated by eq. (2)-(5). finally, these resulting da/dn values can be used to calculate the constant c in a modified mcevily’s rule that simulates all 3 phases of typical da/dnk curves, considering the fcg threshold kth and the toughness kc limits in fcg rates: (6)  ( ) 1i i ii n n x   0 pzrda dx dn n x x          1 12 hcp yc rx x s e pz x x             2 1 2 1 2 4 2 1 max yc c kctod x e s h               2th c c maxda dn c k k k k k         s. e. ferreira et alii, frattura ed integrità strutturale, 41 (2017) 129-138; doi: 10.3221/igf-esis.41.18 132 another less arbitrary and probably more reasonable way to estimate the x displacement of the hrr field origin (needed to remove the strain singularity at the crack tip) uses the strains induced by kmax at the crack tip predicted by a suitable strain concentration rule, as described in [19]. in any way, the whole da/dnk curve can be estimated using only welldefined materials properties, without the need for any data-fitting parameter. such equations describe the simplest formulation of this cdm, since they apply only to constant sif range conditions, but this model can be further developed to describe fcg under val as well, see [20]. strip-yield models, on the other hand, numerically estimate the kop needed to find keff using the classic dugdalebarenblatt's idea [25-26], modified to leave a wake of plastically deformed material around the faces of the advancing fatigue crack. dugdale's model estimates the plastic zone size in a griffith plate of an elastic perfectly plastic material under plane stress (pl-) conditions, assuming the pz formed ahead of both crack tips under a given kmax work under a fixed tensile stress equal to the material yield strength sy (neglecting strain-hardening and stress gradients inside the pz). there are several algorithms based on these ideas [5-9]. the sym algorithm implemented in this work is based in newman’s original work [6], but it uses the fcg rule and material parameters specified as in the nasgro code [27]. the validation of this home-made algorithm was performed by comparing its opening stress predictions under several load conditions with results from the literature [28-29]. newman’s original sym calculates pz sizes and surface displacements by superposition of two le problems: (i) a cracked plate loaded by a remote uniform nominal tensile stress and, (ii) a uniform stresses distributed over surface segments near the crack tip. fig 2 schematizes the crack surface displacements and the stress distributions around the crack tip at the maximum and minimum loads max and min. the plastic zones and the crack wakes left by previous cycles are discretized in a series of rigid-perfectly-plastic 1d bar elements, which are assumed to yield at the flow strength of the material, sfl = (sy + su)/2, to somehow account for the otherwise neglected strain-hardening effects – a first order approximation. these elements are either intact at the plastic zone or broken at the crack wake, keeping residual plastic deformations. if they are in contact, the broken bar elements can carry compressive stresses, and they can yield in compression when their stresses reach sfl. the elements along the crack face that are not in contact do not affect the crack surface displacements, neither carry stresses. figure 2: crack surface displacements and stress distribution along the crack line according to the sym [6]. it is important to somehow consider the effects of the actually 3d stresses around the crack tip, caused by transversal plastic restrictions induced by the high strain gradients that act there when the plate is thick and cannot be assumed to work under limiting pl- conditions. to do so in the 1d sym, it uses a thickness-dependent constraint factor  to s. e. ferreira et alii, frattura ed integrità strutturale, 41 (2017) 129-138; doi: 10.3221/igf-esis.41.18 133 increase the tensile flow stress sfl in the unbroken elements along the plastic zone during the loading. hence, this constraint factor should vary from   1 for plane stress conditions in thin plates, to up to   1/(1 2)  3 for plane strain limit conditions in thick plates, where  is poisson's coefficient (but in practice it is often used as an additional datafitting parameter). since there is no crack-tip singularity when the crack closes, this constraint factor is not used to modify the compressive yield strength during unloading, assuming the conditions around the crack tip tend to remain uniaxial. eq. (7) presented below governs the sym behavior by requiring compatibility between the le part of the cracked plate and all bar elements along the crack surfaces and inside the pz ahead of the crack tip. when the length of the wake elements lj is larger than their displacement vj under min, they contact and induce a stress j needed to force vj = lj. the influence functions f(xi) and g(xi, xj) used in eq. (7) are related to the plate geometry and its width correction, and are calculated like described in [6]. (7) to improve the resolution of the sym used here, the pz ahead of the crack tip is divided into 20 bar elements, or twice the number of elements used in the original newman’s model [6]. after calculating the pz size induced by the peak stress max applied in the current cycle, the widths of the bar elements inside the plastic zone are calculated by eq. (7), replacing the terms n by 20 and j by sf, see fig. 2a. when the plate is unloaded to the minimum load min (fig. 2b), the bar elements inside the pz are also unloaded until some of them near the crack tip start to yield in compression, because they try to reach a stress j ≤ sf. the size of this reverse plastic zone pzr depends on the amount of crack closure and on the transversal constraints induced by the plate thickness. the broken elements located inside the plastic wake formed along the crack surfaces, which store residual deformations, may come into contact and carry compressive stresses as well. some of these elements may also yield in compression, if they try to reach j ≤ sf. the stresses j at each of the n elements inside the plastic zone and along the plastic wake that surrounds the crack surfaces are calculated solving the system of equations from eq. 7 using vi  li (at max) and n min. crack opening loads and residual plastic deformations are calculated considering contact stresses. during the crack propagation stage, the opening stress is kept constant during a small arbitrary crack increment to save computer cost. the number of load cycles n required to grow the crack by this increment is calculated by by eq. (8) [27], in which the parameters cn, m, p and q are data-fitting constants, kc is the material toughness, and the fcg threshold kth can be estimated using a procedure described in [27]. (8) the combination of cdm with sym procedures uses the same strip-yield description adopted by the sym to calculate the plastic strain ranges and the consequent fatigue damage distribution ahead of the crack tip. this replace the displaced hrr strain field used by the original critical damage model [19]. this model estimates the fcg increments in a cycle-bycycle basis by a gradual damage accumulation process, but considering possible crack closure effects on the cyclic strain field ahead of the crack tip. the pz ahead of the crack tip is divided into small bar elements with constant width, whose quantity varies between 150 and 550, depending on the loading conditions. the plastic displacements within the sym strip-yield are transformed into plastic strains using a solution proposed by rice [30] to estimate the strain field based on ctod variations, properly modified to consider each bar element displacements by (9) the displacements lmax and lmin of the ith element inside the pz are calculated at the maximum and minimum applied stresses. the position of the elements starting from the crack tip, xct(i), is located at the center of each element. the strain range y that acts at each element center can be correlated to the number of cycles that would be required to break that element by the plastic part of coffin-manson’s rule (c&m) eq. (10), or else by swt rule eq. (11), to consider peak stress effects. notice that only the plastic part of the strain range can be considered by this sy-cdm, because the strain ranges estimated from the sym displacements are calculated assuming rigid-perfectly-plastic bar elements. the total damage accumulated by each element is evaluated by palmgren-miner’s rule eq. (1).     1 , n i n i j i j j v f x g x x            1 1m p qn eff th max cda dn c k k k k k         ( ) ( ) ( )2 2 ( ) ( )y max ct min ctlog l x li i i i ix      s. e. ferreira et alii, frattura ed integrità strutturale, 41 (2017) 129-138; doi: 10.3221/igf-esis.41.18 134 (10) (11) since the numerical model calculates fatigue damage at the central position of each ve, the crack increment induced by each load cycle is given by the location where the damage reaches one ahead of the crack tip. therefore, the damage value of the new first element are calculated using a linear interpolation procedure. as the number of elements is unchanged, to keep the width sum of all elements equal to the pz size, the first and the last element can have a variable width. moreover, since eq. (6) reproduces the sigmoidal shape of da/dnk curves, and since its only adjustable constant c can be directly calculated for any {k, r} combination from the n properties of the material, the cdm used here in fact have no datafitting parameters (whereas the nasgro fcg rule used at the sym needs 4 of them). the c constant (eq. 6) is found using several da/dn values calculated by sy-cdm procedures using c&m or swt rules. this process is similar to the adopted by the original cdm. the main difference here is the replacement of a shifted hrr strain field by a strain field derived from the displacement field of the sym. the new modification proposed here for the sy-cdm eliminates the need of assuming that the da/dn versus k curve of the material is always described by mcevily’s rule eq. (6). this can be achieved by assuming two new hypotheses, which are also based on the physics of the fcg process. the first supposes that there is a limit strain range below which the crack does not grow by fatigue, which is directly related to the sif range threshold kth. the second assumes the crack becomes unstable at a maximum plastic strain related to the critical stress intensity factor, or to the material toughness. these hypotheses are described by: (12) the plastic strain range calculated by eq. (12) is used by the modified sy-cdm to calculate the damage at each element by eq. (10) or (11). the interpolation routine was improved to work with a fixed number of elements (400) for any load condition and, due these hypotheses, one less step is required to estimate the fcg finally, a major fringe-benefit of all cdms used in this work must be emphasized: if they can reasonably estimate fcg rates for a given material, they do so using only its n, kth, and kc properties, without the need for any adjustable data-fitting parameters. therefore, these simple and sound models can indeed be called predictive, since they do not need or use actual fcg data points to estimate da/dn rates. the results presented next support this claim. experimental results and discussions hese four models are compared against experimental da/dnk data measured at r  0.1 and r  0.7 for two materials, a 7075-t6 al alloy and a 1020 low carbon steel, as described elsewhere [19]. these materials properties and the c values used by the c&p cdm (model i) are listed in tab. 1. fcg rates predictions by the sym (model ii) use material properties from nasgro version 4.02, as shown in tab. 2. but instead of using poisson's coefficients to estimate the constraint factor , its value was varied to verify its effect on fcg predictions. values  3 for 7075 and  2 for the 1020 resulted in good approximations and are adopted here. the kth(r) and kic from tab. 1 are used in eq. 8, since they approximate the data better than the values listed in nasgro. the constants c from eq. (6), model (iii), are listed in tab. 3. material sy (mpa) su (mpa) c (mpa) c b c kic (mpam) kth (mpam) c (for k in mpam) r  0.1 r  0.7 7075-t6 498 576 709 0.12 -0.056 -0.75 25.4 3.4 2.9 8.23e-09 1020 285 491 815 0.25 -0.114 -0.54 277 11.6 7.5 2.73e-10 table 1: material properties [19] and c values obtained by several strain concentration rules.   1( )) (1 2 2 cy cn ii        1 max( ) 1 2 ( ) ( ) 2 b c y c cn i i i        ,mod , , , ,max( ) ( ) ( ) ( ) ( ) ( )y y y th y cr y cr yi i i i i i                 t s. e. ferreira et alii, frattura ed integrità strutturale, 41 (2017) 129-138; doi: 10.3221/igf-esis.41.18 135 material sy (mpa) su (mpa) cn (for k in mpamm m p q 7075-t6 (m7ha03ab1) 461.9 524 9.68610-12 3 0.5 1 1015-1026 (c1bb11ab1) 262 399.9 1.51510-14 3.7 0.5 0.5 table 2: properties and forman-newman parameters from the nasgro 4.02 database [27]. n equation c (for k in mpam) 7075-t6 1020 c&m 8.73e-09 2.64e-09 swt 1.49e-08 4.50e-09 table 3: constant c for modified cdms obtained from sym-calculated cyclic strain fields. figs. 3 and 4 show the measured da/dnk points and the curves predicted by the original cdm based on creager and paris (c&p), by the original sym (assuming   3), by the sy-cdms (sy-c&m and sy-swt), and also by the modified sy-cdms proposed here (sy-c&m modified and sy-swt modified). the fcg data has been obtained under r  0.1 and r  0.7 using standard astm e647 procedures for a 7075-t6 al alloy and a 1020 steel, respectively. recall that the sy-cdm curves are predicted from the n damage induced by the cyclic strain fields generated by sym strip-yield procedures using coffin-manson or stw n rules. these models use only the plastic part of those n rules because the sym numerical procedures discretize the pz ahead of the crack tip using rigid-perfectly-plastic ve elements. recall as well that the modified sy-cdm proposed here does not need to use a previously chosen da/dnk rule (eq. 6) due the two limiting strain values introduced in the model, one for the fcg threshold and the other for the toughness. figure 3: strip-yield and critical damage models for the 7075-t6 at r = 0.1 and 0.7. s. e. ferreira et alii, frattura ed integrità strutturale, 41 (2017) 129-138; doi: 10.3221/igf-esis.41.18 136 notice in fig. 3 that the da/dnk curve estimated by the sy-c&m model is essentially equal to the curve generated by the original c&p cdm model. both estimates are quite reasonable for r 0.1, albeit not as good for r  0.7. the sym curve (generated assuming   3) describes better the data points measured at r  0.7. the swt n model estimates higher fcg rates than the c&m model for both r-ratios, as expected. the model proposed here (sy-c&m-modified, which does not need an assumed fcg rule) yielded the best estimates at r  0.1 and had a performance similar to the sym at r  0.7. the modified sy-cdms had in particular a better performance at the higher k ranges, where the original models systematically estimated fcg rates higher than the data. the original cdm [19] and sy-cdm models need a pre-chosen mcevily’-type da/dnk curve, whose single adjustable parameter can however be calculated by n procedures. their good performance certainly is not a coincidence, since they use no adjustable data-fitting parameters and their predictions are entirely based on measured n properties. in fact, when compared to sym estimates based on keff concepts and on a fcg rule that has 4 adjustable data-fitting parameters, not to mention the constraint factor  that in practice is frequently used as a 5th adjustable parameter, the cdm performance could be even qualified as quite impressive for a so simple model. the results for the 1020 steel are shown in fig. 4. the original cdm based on a creager and paris shift of the hrr field reproduced well the data trend, but yielded slight non-conservative fcg estimates at r  0.1. for r  0.7 it presented a still better performance. the original sym had a similar performance at r  0.1, but instead generated slight conservative predictions, which deviated from data at low k values. for r  0.7 its predictions were not good. the modified syc&m generated quite reasonable predictions for r  0.7, but for r  0.1 they were maybe too conservative. the other models yielded too conservative predictions for both r-ratios. figure 4: strip-yield and critical damage models for the 1020 steel at r = 0.1 and 0.7. two facts resulting from this academic exercise must be emphasized. first, their fcg estimates were quite reasonable, an indication that their ideas about the mechanics of the fcg process probably are reasonable as well. this at least may be seen as an indication that the procedures used in these simple models are at least coherent, a reassuring evidence. however, the second fact is still more interesting, since it could not be anticipated. the study presented above show that s. e. ferreira et alii, frattura ed integrità strutturale, 41 (2017) 129-138; doi: 10.3221/igf-esis.41.18 137 fcg rates estimated by opposing ideas can yield similarly reasonable results. moreover, when the sym and the cdm techniques are properly combined, they also generate reasonable predictions. this does not means that these methods are equivalent. indeed, while the cdm fcg rate estimates requires only measurable n properties and need no data-fitting parameters, the sym estimates use at least four data-fitting parameters in a pre-chosen fcg rule to achieve similar results. this is probably not a major problem from an engineering point of view, if such parameters are available. however, it is undeniable that to generate similar descriptions of measured fcg data using only standard n properties and basic mechanical principles is a point in favor of cdm ideas. finally, an additional point must be emphasized as well, although it is more philosophical than operational: the results presented here also indicate that a good description of some experimental data cannot be claimed as a conclusive proof of any model suitability, let alone of its prevalence. what is really important when discussing the performance of any given model is to clearly identify which set of properly measured experimental data it cannot describe well. this point is important, since after so many years still there is no consensus even about which are the true fatigue crack driving forces, let alone on the best fcg model. indeed, whereas many defend that fatigue cracks are driven by keff, others affirm that fatigue crack closure is not even a major issue in fcg. the authors hope this relatively straightforward modeling exercise can contribute at least to avoid the radical opinions that are still too common in this field. conclusions cg models based on critical damage and strip-yield procedures are used to estimate da/dnk curves of two materials under low and high r-ratios. these models are based on contradictory hypotheses about the cause for the fcg behavior. whereas the syms assume fcg is driven by keff, so that it depends on the interference of the plastic wakes left behind the crack tip along the crack surfaces, the cdms suppose fatigue cracks propagate by sequentially breaking volume elements ahead of the crack tip, which fail because they accumulate all the fatigue damage they could sustain. all fcg models studied here are compared against properly measured da/dnk curves of a 7075-t6 al alloy and of an aisi 1020 low carbon steel, which were experimentally obtained following standard astm e647 procedures. moreover, the n properties of such materials were also measured by standard procedures, following astm e606 recommendations. moreover, both the fcg and the fatigue crack initiation properties were measured in coupons machined from the same material lot, to avoid any inconsistency in the data. both the original cdms (based on the hrr field displaced to eliminate the strain singularity ate the crack tip) and syms can describe reasonably well the measured data, even though they are apparently contradictory from a conceptual point of view. this is certainly an indication that such models are not incompatible. this claim is verified here by mixing them, using the strip yield mechanics instead of the hrr field to generate the strain field ahead of the crack tip needed for the critical damage calculations. first, this is done maintaining the hypothesis that the fcg curves can be described by mcevily’s single parameter model. then, two new hypotheses are proposed to eliminate the need for such an assumption, namely (i) there is a limit strain range related to the threshold stress intensity factor range, and (ii) there is a maximum plastic strain related to the critical stress intensity factor. these limit strain values can be introduced in the n damage calculations, eliminating one calculation step and allowing the cdm to easier deal with variable amplitude loading problems, a feature that will be discussed in future works. finally, the quite reasonable performance of the predictions obtained from models based on so different hypothesis about the fcg driving forces also indicates that the good fitting of some properly obtained data set is not enough to prove which one is the best. references [1] paris, p.c., erdogan, f. a critical analysis of crack propagation laws. j basic eng 85 (1963) 528-534. [2] castro, j.t.p., meggiolaro, m.a., fatigue design techniques, volume 3: crack propagation, temperature and statistical effects. createspace (2016). [3] elber, w., fatigue crack closure under cyclic tension. eng fract mech, 2 1970) 37-45. [4] elber, w., the significance of fatigue crack closure. damage tolerance in aircraft structures, astm stp, 486 (1971) 230-242. f s. e. ferreira et alii, frattura ed integrità strutturale, 41 (2017) 129-138; doi: 10.3221/igf-esis.41.18 138 [5] dill, h.d., saff, c.r., spectrum crack growth prediction method based on crack surface displacement and contact analyses. fatigue crack growth under spectrum loads, astm stp 595 (1976) 306-319. [6] newman, jr, jc., a crack-closure model for predicting fatigue crack growth under aircraft spectrum loading. methods and models for predicting fatigue crack growth under random loading, astm stp 748 (1981) 53-84. [7] de koning, a.u., liefting, g.. analysis of crack opening behavior by application of a discretized strip yield model. mechanics of fatigue crack closure, astm stp 982 (1988) 437-458. [8] wang, g.s., blom, a.f., a strip model for fatigue crack growth predictions under general load conditions. eng fract mech, 40 (1991) 507-533. [9] beretta,s, carboni,m. a strip-yield algorithm for the analysis of closure evaluation near the crack tip. eng fract mech 72 (2005) 1222-1237. [10] kemp, p.m.j., fatigue crack closure – a review. tr90046, royal aerospace establishment, uk, (1990). [11] skorupa, m., load interaction effects during fatigue crack growth under variable amplitude loading a literature review part i: empirical trends, fatigue fract eng mater struct, 21 (1998) 987-1006. [12] skorupa, m., load interaction effects during fatigue crack growth under variable amplitude loading a literature review part ii: qualitative interpretation, fatigue fract eng mater struct, 22 (1999) 905-926. [13] castro, j.t.p., meggiolaro, m.a., miranda, a.c.o., singular and non-singular approaches for predicting fatigue crack growth behavior. int j fatigue, 27 (2005) 1366-1388. [14] castro, j.t.p., meggiolaro, m.a., gonzález, j.a.o., can keff be assumed as the driving force for fatigue crack growth? frattura ed integrità strutturale, 33 (2015) 97-104. [15] castro, j.t.p., gonzález, j.a.o., meggiolaro, m.a., gonzález, g.l.g., freire, j.l.f., some questions about assuming keff as the sole fcg driving force. submitted to int j fatigue, (2016). [16] chen, d.l., weiss, b., stickler, r., the effective fatigue threshold: significance of the loading cycle below the crack opening load. int j fatigue, 16 (1994) 485-491. [17] vasudevan, a. k., sadananda, k., holtz, r. l., analysis of vacuum fatigue crack growth results and its implications, international j. fatigue, 27 (2005) 1519-1529. [18] castro, j.t.p., kenedi, p.p., prediction of fatigue crack growth rates departing from coffin-manson concepts. j braz soc mech sci eng, 17 (1995) 292-303 (in portuguese). [19] durán, j.a.r., castro, j.t.p., payão filho, j.c., fatigue crack propagation prediction by cyclic plasticity damage accumulation models, fatigue fract eng mater struct, 26 (2003) 137-150. [20] castro, j.t.p., meggiolaro, m.a., miranda, a.c.o., fatigue crack growth predictions based on damage accumulation calculations ahead of the crack tip, comput mat sci, 46 (2009) 115-123. [21] rice, j.r., rosengren, g.f., plane strain deformation near a crack tip in a power-law hardening material, j mech phys solids, 16 (1968) 1-12. [22] hutchinson, j.w., singular behavior at the end of a tensile crack tip in a hardening material, j mech phys solids 16 (1968) 13-31. [23] creager, m., paris, p.c., elastic field equations for blunt cracks with reference to stress corrosion cracking, int j fract mech, 3 (1967) 247-252. [24] schwalbe, k.h., comparison of several fatigue crack propagation laws with experimental results, eng fract mech 6 (1974) 325-341. [25] dugdale, d. s., yielding of sheets containing slits, j mech phys solids, 8 (1960) 100-104. [26] barenblatt, g.i., the mathematical theory of equilibrium cracks in brittle fracture. advances in applied mechanics, 7 (1962) 55-192. [27] nasgro – fracture mechanics and fatigue crack growth analysis software, reference manual, version 4.02, (2002). [28] newman, j.c., fastran ii: a fatigue crack growth structural analysis program, nasa technical memorandum 104159, lrc hampton, (1992). [29] newman, j.c., a crack opening stress equation for fatigue crack growth. int j fract, 24 (1984) r131-r135. [30] rice, j.r., mechanics of crack tip deformation and extension by fatigue. fatigue crack propagation, astm stp 415 (1967) 247-311. << /ascii85encodepages false /allowtransparency false /autopositionepsfiles true /autorotatepages /none /binding /left /calgrayprofile (dot gain 20%) /calrgbprofile (srgb iec61966-2.1) /calcmykprofile (u.s. web coated \050swop\051 v2) /srgbprofile (srgb iec61966-2.1) /cannotembedfontpolicy /error /compatibilitylevel 1.4 /compressobjects /tags /compresspages true /convertimagestoindexed true /passthroughjpegimages true /createjobticket false /defaultrenderingintent /default /detectblends true /detectcurves 0.0000 /colorconversionstrategy /cmyk /dothumbnails false /embedallfonts true /embedopentype false /parseiccprofilesincomments true /embedjoboptions true /dscreportinglevel 0 /emitdscwarnings false /endpage -1 /imagememory 1048576 /lockdistillerparams false /maxsubsetpct 100 /optimize true /opm 1 /parsedsccomments true /parsedsccommentsfordocinfo true 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can be opened with acrobat and adobe reader 5.0 and later.) >> /namespace [ (adobe) (common) (1.0) ] /othernamespaces [ << /asreaderspreads false /cropimagestoframes true /errorcontrol /warnandcontinue /flattenerignorespreadoverrides false /includeguidesgrids false /includenonprinting false /includeslug false /namespace [ (adobe) (indesign) (4.0) ] /omitplacedbitmaps false /omitplacedeps false /omitplacedpdf false /simulateoverprint /legacy >> << /addbleedmarks false /addcolorbars false /addcropmarks false /addpageinfo false /addregmarks false /convertcolors /converttocmyk /destinationprofilename () /destinationprofileselector /documentcmyk /downsample16bitimages true /flattenerpreset << /presetselector /mediumresolution >> /formelements false /generatestructure false /includebookmarks false /includehyperlinks false /includeinteractive false /includelayers false /includeprofiles false /multimediahandling /useobjectsettings /namespace [ (adobe) (creativesuite) (2.0) ] /pdfxoutputintentprofileselector /documentcmyk /preserveediting true /untaggedcmykhandling /leaveuntagged /untaggedrgbhandling /usedocumentprofile /usedocumentbleed false >> ] >> setdistillerparams << /hwresolution [2400 2400] /pagesize [612.000 792.000] >> setpagedevice shot peening processes to obtain nanocrystalline surfaces in metal alloys: q. zheng et alii, frattura ed integrità strutturale, 53 (2020) 141-151; doi: 10.3221/igf-esis.53.12 141 fatigue life simulation and analysis of aluminum alloy sheet selfpiercing riveting qingchun zheng, naixin wang, peihao zhu*, jingna liu, wenpeng ma tianjin key laboratory for advanced mechatronic system design and intelligent control, school of mechanical engineering, tianjin university of technology, tianjin 300384, china national demonstration center for experimental mechanical and electric engineering education (tianjin university of technology) zhengqingchun@tjut.edu.cn, wangnaixin_up@163.com, zhupeihao_gp@163.com, liujingna2003@163.com, wenpengma@sina.com abstract. the fatigue life prediction model of self-piecing riveting components of aluminum alloy is established and the effects of roughness and residual stress on fatigue life are analyzed by the model. finite element software abaqus and fatigue analysis software fe-safe are used to study the effects of roughness and residual stress on the fatigue life of self-piecing riveting components through finite element simulation and mathematical statistics multivariate orthogonal regression experiment. the quantitative relations between fatigue life and three variables (roughness, residual stress and maximum stress) are fitted, and the variation trend of fatigue life with roughness and residual stress is obtained. the order of influence of roughness, residual stress, maximum stress and two interactions on fatigue life is as follows: residual stress, interaction between roughness and residual stress, roughness. when the maximum stress is fixed, the fatigue life increases with the decrease of residual stress with a certain roughness, and the fatigue life decreases with the increase of roughness with a certain residual stress. the average error between the fatigue experiment results and the simulation results is 9.27%, which proves that the simulation results are reliable. keywords. aluminum alloy; self-piecing riveting; surface roughness; residual stress; fatigue life; fe-safe. citation: zheng, q., wang, n., zhu, p., liu j., ma, w., fatigue life simulation and analysis of aluminum alloy sheet selfpiercing riveting, frattura ed integrità strutturale, 53 (2020) 141-151. received: 20.02.2020 accepted: 02.04.2020 published: 01.07.2020 copyright: © 2020 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. introduction he lightweight development of g-series high-speed railway has become an inevitable trend, among which aluminum alloy plays a more and more important part in the body materials of rail vehicles due to its low density, high specific strength and good wear resistance [1-3]. self-piecing riveting (spr) is the main connection method t mailto:zhengqingchun@tjut.edu.cn mailto:wangnaixin_up@163.com mailto:zhupeihao_gp@163.com mailto:liujingna2003@163.com mailto:wenpengma@sina.com https://youtu.be/fcyipakxw1w q. zheng et alii, frattura ed integrità strutturale, 53 (2020) 141-151; doi: 10.3221/igf-esis.53.12 142 of aluminum alloy thin plates at the present stage without punching being required. it adopts the principle of mechanical locking with a simple process, so that the thin plates can be effectively connected [4-6]. the fatigue life analysis of self-piercing riveting has been investigated by many scholars. liu [7] investigated the mechanical properties and failure mechanisms of self-piercing riveted-bonded hybrid joints with carbon fiber reinforced polymers/aluminum alloy 5754. zhang [8] studied the fatigue of self-piercing riveting joints connecting similar and dissimilar sheets of ta1 titanium alloy, al5052 aluminum alloy and h62 copper alloy. zhao [9] studied the influence of sheet thickness on the fatigue behavior and fretting of single-lap self-piercing riveted joints in aluminum alloy 5052. li huang [10] used experimental methods to study aa6111-t4 fatigue characteristics of aluminum alloy self-piercing riveting joints and fatigue prediction. xing baoying et al. [11,12] studied the influence of multiple rivet distributions on the mechanical properties and failure mechanism of joints, and thoroughly studied the macro and micro failure mechanisms of joints based on experiments. deng chengjiang et al. [13] studied the dynamic fatigue characteristics of self-piercing riveting allogeneic joints, and the results showed that the fatigue failure modes of aluminum alloy allogeneic joints were plate fracture. xing[14]studied fatigue performance and failure mechanism of aluminum alloy self piercing riveting head through fatigue testing, statistical methods, fracture analysis and elemental analysis of x-ray spectrometer. sun et al. [15] comparatively analyzed the effects of substrate connection form, orientation, sheet thickness, harw22dness and adhesive on the fatigue performance of joints. the results showed that different board thicknesses and connection directions have significant effects on the fatigue strength of joints. choi et al. [16] studied the effects of changes in riveting parameters on the mechanical properties of aluminum alloy self-piercing riveting joints and the mechanism of fatigue failure. it was found that when the fatigue cycle reached 75% of the total number, the fatigue strength of the joint gradually decreased, and at 90%, the strength suddenly decreased. di franco et al .[17] studied the fatigue characteristics of self-piercing riveted joints of 2024 aluminum alloy and cfrp(carbon fiber reinforced plastics) plates through experiments and simulations, and found that composite joints have good fatigue properties. ueda et al. [18] analyzed the fatigue characteristics of the joints of cfrp multilayer plates after optimized self-piercing riveting. the results showed that the rivets fail first at a load level lower than 80%, and at a load level higher than 80% cfrp multilayer materials failed first. gay et al. [19] studied the fatigue performance of heterogeneous self-piercing riveted joints of aluminum alloy and glass fiber thermoplastic composites, and investigated the effects of rivet shape and high temperature environment on joint performance. huang et al.[20] studied the fatigue performance of aluminum-steel heterogeneous metal self-piercing riveting joints with different thicknesses, and analyzed the fatigue failure mechanism of the upper and lower plate contact areas and the plate and rivet contact areas in detail. this paper studies the fatigue simulation of self-piercing riveting joints based on the surface roughness of 5083 aluminum alloy sheet and residual stress of the components, and quantitatively determines the relationship between the fatigue life and three variables which are the surface roughness, residual stress and maximum stress of the components through regression orthogonal experiments. according to the quantitative relationship formula of the fatigue life, the change trend of the fatigue life with respect to the roughness and the residual stress is obtained, so as to provide relevant references for the practical application of the new technology on rail vehicles. fatigue simulation based on abaqus and fe-safe n this paper, the fatigue analysis of self-piercing riveting joints is carried out by nominal stress method. the nominal stress method is based on the s-n curve of materials, taking into account the stress concentration factor and nominal stress at the dangerous position of structural fatigue, and adopts miner linear fatigue cumulative damage theory to calculate the fatigue life. the analysis process is shown in fig. 1. figure 1: flow chart of fatigue simulation analysis. i building a 3d solid model preprocessing postprocessing finite element model fatigue life calculation results stress and strain results fe-safe fatigue life analysis fatigue load material parameters abaqus q. zheng et alii, frattura ed integrità strutturale, 53 (2020) 141-151; doi: 10.3221/igf-esis.53.12 143 s-n curve correction the fatigue life of mechanical structural parts calculated from the material fatigue characteristic curve tends to be ideal, while factors such as stress concentration, shape size and surface processing technology of mechanical structural parts in actual engineering have a greater impact on fatigue strength. therefore, when predicting the fatigue life of structural parts, the material fatigue characteristic curve is corrected and converted into the fatigue characteristic curve of the corresponding structural part to obtain a more accurate analysis result. using the correction method proposed by zhao shaobian [21], in the number of cycles 4 10n  , the above-mentioned fatigue influencing factors have a small effect on the material, which can be ignored. when the number of cycles 4 10n  , the material fatigue strength will be reduced by a factor of k , calculation method such as（1） t 1 + 1 = k k   − （1） where tk is the theoretical stress concentration factor;  is the surface quality factor; and  is the dimensional coefficient of the structural part. query the appendix of "anti-fatigue design-methods and data"[21], the stress concentration factor of self-piercing riveted members is 2tk = ; according to the cold-working of self-piercing riveted members, the surface roughness is 2 m , and combined with the "anti-fatigue design-methods and data", the value is 0.5 = ;  can be calculated by the following empirical formula: 0.034 0 =    −       （2） where 0 is the material volume of parts subjected to the maximum stress of more than 95%;  is the material volume of standard samples similar to the geometry of parts subjected to the maximum stress of more than 95%. when the number of cycles is 7 10 , the fatigue limit correction formula is 1 1' k   −− = （3） where 1− is the initial fatigue correction factor; k is the factor of fatigue strength reduction. after the above correction method, the s-n curve of the standard sample material is corrected to obtain the s-n curve of the actual structural part, and the slope of the high-cycle fatigue interval line segment of the fatigue characteristic curve of the self-piercing riveted member is obtained through calculation: 1 1 4 7 lg lg ' lg 10 lg 10 reqs k  −− = − （4） the modified miner rule is used to modify the small load under the fatigue limit to obtain the s-n curve of the selfpiercing riveted member, as is shown in fig. 2. static analysis in order to more accurately simulate the stress and fatigue life of the self-piercing riveted piece, the fatigue simulation is performed using the size of the fatigue experimental sample, as is shown in fig. 3, and based on the mapping results, solidworks is used to establish a self-piercing riveting joint model, as is shown in fig. 4. in the actual fatigue experiment, the self-piercing riveting joint is fixed at both ends and pulled at the same time. therefore, in the static analysis, the left end of the component joint is fixed and the right end is subjected to a constant load with a load of 1kn. in order to improve the accuracy of the calculation, eight-node hexahedral solid elements are q. zheng et alii, frattura ed integrità strutturale, 53 (2020) 141-151; doi: 10.3221/igf-esis.53.12 144 used in the model, which is divided by the method of sweeping the mesh that is refined at the riveting point. the total number of elements is 124993 and the total number of nodes is 153607. figure 2: s-n curve of the joints. figure 3: size of the self-piercing riveting specimen. figure 4: self-piercing riveting 3d model. materials density（kg/m3） elastic modulus （mpa） poisson's ratio sheet 5083 aluminum 15 2.71 10 −  4 7 10 0.33 rivet 36mnb4 157.87 10 −  5 2.09 10 0.28 table 1: material parameters. fig. 6 shows the stress cloud diagram of the static simulation von mises. according to the stress cloud diagram, the most critical part of the riveting joint is the contact between the rivet leg and the plate, and the maximum stress is 283 mpa. q. zheng et alii, frattura ed integrità strutturale, 53 (2020) 141-151; doi: 10.3221/igf-esis.53.12 145 figure 5: mesh of the self-piercing riveting specimen. figure 6: stress cloud of the self-piercing riveting specimen. figure 7: fatigue simulation cloud of self-piercing riveting specimen q. zheng et alii, frattura ed integrità strutturale, 53 (2020) 141-151; doi: 10.3221/igf-esis.53.12 146 fatigue life simulation analysis based on the finite element analysis, fe-safe is used for full life (s-n) analysis. the software requires as inputs, the 5083 aluminum alloy’s tensile strength (uts) and the elastic modulus in the “material”, the s-n curve, shown in fig. 2 and the load history. the stress of fatigue simulation is the product of the stress of finite element analysis and the transient value of load history. the applied stress is the maximum load stress in the static analysis process, therefore, the load time history should be the unit load in the fatigue simulation. the load type is a sine wave, and the stress ratio is r=0.1, f=20hz. finally, define the surface state of the component, and input the surface roughness and residual stress in the surface and residual windows, respectively. the fatigue simulation results are shown in fig. 7 characterized by a maximum stress of 283mpa, a roughness of 1μm and a residual stress of -300mpa. it can be seen from the figure that the position with the minimum fatigue life is the lower part of the rivet leg that is in contact with the upper plate. the crack initiates in this area, then under the action of the alternating load, it continues to expand and finally breaks, causing the riveting failure. and the minimum fatigue life is 5.016 10 =103753 times. fatigue simulation experiment based on multiple orthogonal regression analysis method esidual stress in the riveting process and surface roughness of the thin plate are two important factors that affect the fatigue life. on the one hand, the residual stress can cause plastic deformation and disrupt the stress balance of the riveted components. on the other hand, due to the micro unevenness on rough surface, it is easy to form stress concentration, the formation of which accelerates the generation of cracks. these two factors generally affect the fatigue life in a comprehensive way, therefore, it is difficult to quantitatively evaluate the influence of a single factor. based on orthogonal experiments and regression analysis methods, this paper designs a multiple regression orthogonal experiment to fit a multiple linear regression equation to determine the fatigue life cyclesn and residual stress 1x , roughness 2x , maximum stress 3x and interaction 1 2x x , 1 3x x , 2 3x x functional relationship. during the riveting process, the surface roughness value zr of the aluminum plate ranges from 1 to 5 m , the residual stress value ranges from -300 to 100, and the maximum stress range is 100 to 500 amp . to facilitate the design of subsequent orthogonal experiments, the levels of each factor ( 1x , 2x , 3x ) is respectively encoded into 1z , 2z and 3z through formula (5). and the encoding results are shown in tab. 2. ( )j j j0 jz = x x−  (5) factor（ jx ） zr / m residual stress/ mpa maximum stress/ mpa top level（ j1x ） 5 100 500 bottom level （ ( )j 1x − ） 1 -300 100 zero level（ 0x ） 3 -100 300 change block（ j ） 2 200 200 table 2: the factor code table. based on the above experimental factors, an orthogonal table is selected, and after the code conversion, the regression orthogonal table shown in tab. 3 is obtained. columns 1, 3, and 5( 1z , 2z and 3z ) are codes corresponding to residual stress, roughness, and maximum stress. columns 2, 4, and 6( 1 2z z , 1 3z z and 2 3z z ), respectively, are interactions of two factors. the total number of tests is n=8. fe-safe is used to calculate the fatigue life under different conditions. the test results are shown in tab. 3. origin is used for regression analysis and variance analysis. see tab. 4 for the calculation process. the results of the orthogonal regression are shown in tab. 4 and tab.5. from tab.5, it can be seen that when the two factors interact, the interaction between roughness and residual stress is greater than the interaction between the other two r q. zheng et alii, frattura ed integrità strutturale, 53 (2020) 141-151; doi: 10.3221/igf-esis.53.12 147 factors because of 100165.1( 1 2z z )> 7605.13( 1 3z z )> 5961.13( 2 3z z ); when the single factor interacts, the effects of maximum stress, roughness, and residual stress increase sequentially because of 12482.1( 3z )>112798( 2z )>91024( 1z ); when comprehensively considered, residual stress> roughness and residual stress interaction> roughness. experiment number 1 z 1 2z z 2z 1 3z z 3z 2 3z z roughness / m residual stress/ amp maximum stress / amp fatigue life /time 1 1 1 1 1 1 1 5 100 500 459 2 1 1 1 -1 -1 -1 5 100 100 19929 3 1 -1 -1 1 1 -1 5 -300 500 5020 4 -1 1 -1 -1 1 -1 1 -300 500 123392 5 -1 -1 1 -1 1 1 1 100 500 606 6 -1 1 -1 1 -1 1 1 -300 100 436286 7 1 -1 -1 -1 -1 1 5 -300 100 65899 8 -1 -1 1 1 -1 -1 1 100 100 7220 table 3: ternary regression orthogonal experimental design and analysis of simulation results. parameter result multiple r 0.999703 r square 0.999406 adjusted tr square 0.995839 standard error 12419.98 observation value 8 table 4: ternary orthogonal regression analysis data sheet. coefficients p value intercept 119851.4 0.023314 1z -91024.6 0.028792 1 2z z 100165.1 0.027891 2z -112798 0.024771 1 3z z -7605.13 0.333352 3z -12482.1 0.21535 2 3z z 5961.13 0.404182 table 5: correlation coefficient and p value. q. zheng et alii, frattura ed integrità strutturale, 53 (2020) 141-151; doi: 10.3221/igf-esis.53.12 148 according to the results, an orthogonal regression equation is obtained, as is shown in formula (6). when the codes 1z , 2z , 3z are converted into 1x , 2x , 3x respectively, the formula (6) is transformed into formula (7), so that the quantitative relationship between fatigue life and residual stress, roughness, maximum stress is obtained. in the subsequent related research, the fatigue life of the rivet structure can be directly estimated by using matlab based on the quantitative relationship, saving a certain amount of experimental time and experimental cost. degree freedom stdev square mean square f statistics saliency regression analysis 6 2.5e+11 4.32e+10 280.22 0.0456 residual 1 1.5e+08 1.54e+08 total 7 2.6e+11 table 6: significance analysis. 1 1 2 2 1 3 3 2 3 =119851.4 97024.6 z 106151 z z 118783.7 z 12793.6 z z 6496.3 z 11149.6 z z −  +   −  −   −  +   cyclesn （6） where cyclesn is the fatigue life ; 1z is level code of the residual stress; 2z is the level code of the roughness; 3z is level code of the maximum stress. ( ) ( ) ( ) ( )( ) ( ) ( ) ( ) ( ) ( ) 1 1 2 2 1 3 3 2 3 =119851.4 97024.6 x 3 2 106151 x 3 2 x 100 200 112798 x 100 200 7605.13 x 3 2 x 300 200 12482.1 x 300 200 5961.13 x 100 200 x 300 200 −  − +  −  +           −  + −  −  −       −  − +  +  −           cyclesn （7） where cyclesn is the fatigue life; 1x is the residual stress; 2x is the roughness; 3x is the maximum stress. the maximum stress under working conditions is 450 mpa, and the change trend of fatigue life with respect to roughness and residual stress is shown in fig. 8. when the roughness is constant, as the residual stress decreases, the fatigue life gradually increases. under fatigue conditions, as the roughness increases, the fatigue life gradually decreases. figure 8: the relationship between fatigue life and roughness and residual stress under 450mpa. q. zheng et alii, frattura ed integrità strutturale, 53 (2020) 141-151; doi: 10.3221/igf-esis.53.12 149 fatigue experiment luminum plates with different roughness are selected and cut into specimens using electric spark cutting equipment, and riveted with different self-piercing riveting machines to make 5 different samples groups with different roughness and residual stress. and each group consists of three samples. roughness tester and x-ray diffraction stress tester are used to test the sample parameters. the mts landmark100 electro-hydraulic servo material testing machine is selected. the specimen is clamped in the machine as is shown in fig. 9. the maximum stress is 450mpa, the stress ratio is r=0.1 and the frequency is f=20hz. the sinusoidal stress is used for the tensile-tensile fatigue test. the failed spr joints for the fatigue tests are shown in fig. 10. figure 9: clamping specimen. figure 10: different failed spr joints for the fatigue tests. the experimental results are shown in tab. 7. under the conditions of preset roughness and residual stress, the simulation and experiments are performed on the self-piercing riveting members of aluminum alloy thin plates. the fatigue results of the two are in the same order of magnitude, and the average error is 9.27%. experiment examples roughness rz residual stress /mpa simulation results /time experimental result/time error/% （1） 4.16 60 10722 11689 8.3 56 11053 11867 6.9 50 10656 11689 8.8 （2） 3.28 37 34810 39654 12.2 30 34960 39088 11.3 28 35560 40887 13.0 （3） 3.12 -100 104326 114528 8.9 -110 114873 126347 9.1 -118 110287 124345 11.3 （4） 2.45 -150 172708 187368 7.8 -160 175623 189074 7.1 -145 179236 188659 5.0 （5） 1.34 -200 291486 329463 11.5 -220 292476 329793 11.3 -234 307563 328974 6.5 average error / / / / 9.27 table 7: fatigue test results. a q. zheng et alii, frattura ed integrità strutturale, 53 (2020) 141-151; doi: 10.3221/igf-esis.53.12 150 conclusion hrough the finite element simulation and mathematical statistical multiple orthogonal regression experiments, the fatigue life prediction model of aluminum alloy thin plate self-piercing riveting structure is analyzed, and the functional relationships of fatigue life on roughness, residual stress and maximum stress are fitted. the main influencing factors are residual stress, the interaction between roughness and residual stress, and roughness. the maximum stress is unchanged. in the range of lower roughness, the fatigue life increases as the residual stress decreases; when the residual stress is constant, the fatigue life decreases as the roughness increases. fatigue tests are performed on self-piercing riveting members with different roughness and residual stress. compared with the simulation results, the average error is 9.27%, indicating that the fatigue life simulation and analysis method of selfpiercing riveting of aluminum alloy sheet are reliable. acknowledgments he authors gratefully acknowledge the support from the national natural science foundation of china (grant no. 61941305), the tianjin science and technology project (grant no.19yffcys00110), and the natural science foundation of tianjin of china (grant no.18jcqnjc75000). references [1] li, y., li, y., lou, m., lin, z. (2012). lightweighting of car body and its challenges to joining technologies, jixie gongcheng xuebao/journal mech. eng., 48(18), pp. 44–54. doi: 10.3901/jme.2012.18.044. [2] he, x., wang, y., lu, y., zeng, k., gu, f., ball, a. (2015). self-piercing riveting of similar and dissimilar titanium sheet materials, int. j. adv. manuf. technol. 80 (9-12), pp.2105-2115. doi: 10.1007/s00170-015-7174-3. [3] zhang, c. yu., gou, r. bin., yu, m., zhang, y. jing., qiao, y. hu., fang, s. ping. (2017). mechanical and fatigue properties of self-piercing riveted joints in high-strength steel and aluminium alloy, j. iron steel res. int. 24(2), pp.214-221. doi: 10.1016/s1006-706x(17)30030-4. [4] carandente, m., dashwood, r.j., masters, i.g., han, l. (2016). improvements in numerical simulation of the spr process using a thermo-mechanical finite element analysis, j. mater. process. technol. 236, pp. 148-161. doi: 10.1016/j.jmatprotec.2016.05.001. [5] chrysanthou, a. (2014).fatigue behaviour of self-piercing riveted joints. self-piercing riveting: properties, processes and applications. doi:10.1533/9780857098849.1.33. [6] jeong, c.h., kim, d.y., oh, h.s., cheon, s.s. (2018). fe analysis of self-piercing rivet (spr) process and tensile behaviours, j. korean soc. precis. eng. doi: 10.7736/kspe.2018.35.9.875. [7] liu, y., zhuang, w. (2019). self-piercing riveted-bonded hybrid joining of carbon fibre reinforced polymers and aluminium alloy sheets, thin-walled struct. 144, pp. 106340. doi: 10.1016/j.tws.2019.106340. [8] zhang, x., he, x., xing, b., zhao, l., lu, y., gu, f., ball, a. (2016). influence of heat treatment on fatigue performances for self-piercing riveting similar and dissimilar titanium, aluminium and copper alloys, mater. des. doi: 10.1016/j.matdes.2016.02.075. [9] zhao, l., he, x., xing, b., lu, y., gu, f., ball, a. (2015). influence of sheet thickness on fatigue behavior and fretting of self-piercing riveted joints in aluminum alloy 5052, mater. des. 87, pp.1010-1017. doi: 10.1016/j.matdes.2015.08.121. [10] huang, l., lasecki, j., guo, h., su, x. (2014).fatigue and fretting of mixed metal self-piercing riveted joint. asme international mechanical engineering congress and exposition, proceedings (imece). doi: 10.1016/j.ijfatigue.2015.10.018. [11] xing, b., he, x., zeng, k., wang, y. (n.d.). mechanical properties of self-piercing riveted joints in aluminum alloy 5052, int. j. adv. manuf. technol., 75(1–4), pp. 351–61. doi: 10.1007/s00170-014-6152-5. [12] xing, b., he, x., wang, y., yang, h., deng, c. (2015). study of mechanical properties for copper alloy h62 sheets joined by self-piercing riveting and clinching, j. mater. process. technol. 216, pp. 28–36. doi: 10.1016/j.jmatprotec.2014.08.030. t t q. zheng et alii, frattura ed integrità strutturale, 53 (2020) 141-151; doi: 10.3221/igf-esis.53.12 151 [13] deng, c.j., he, x.c., xing, b.y., wang, y.q., zeng, k., ding, y.f. (2015). mechanical properties of self-piercing riveted lap joints in dissimilar metal sheets of aluminum and copper, jilin daxue xuebao (gongxueban)/journal jilin univ. (engineering technol. ed., 45(02), pp.473-480. doi: 10.13229/j.cnki.jdxbgxb201502021. [14] xing, b., he, x., wang, y., liu, f. (2016). fatigue properties and failure mechanisms of self-piercing riveted joints in aluminium alloy, hanjie xuebao/transactions china weld. inst.37(06), pp.50-54+131. [15] sun, x., stephens, e. v., khaleel, m.a. (2007). fatigue behaviors of self-piercing rivets joining similar and dissimilar sheet metals, int. j. fatigue,97, pp.20-28, doi: 10.1016/j.ijfatigue.2006.02.054. [16] choi, d.h., han, d.w., kim, h.k. (2017). fatigue life estimation of self-piercing riveted aluminum joints under mixed-mode loading, int. j. fatigue,97, pp.20-28. doi: 10.1016/j.ijfatigue.2016.12.019. [17] franco, g. di., fratini, l., pasta, a. (2012). fatigue behaviour of self-piercing riveting of aluminium blanks and carbon fibre composite panels, proc. inst. mech. eng. part l j. mater. des. appl. 226(3), pp. 230-241. doi: 10.1177/1464420712443753. [18] ueda, m., miyake, s., hasegawa, h., hirano, y. (n.d.). instantaneous mechanical fastening of quasi-isotropic cfrp laminates by a self-piercing rivet, compos. struct., 94(11),3388-3393. doi: 10.1016/j.compstruct.2012.04.027. [19] gay, a., lefebvre, f., bergamo, s., valiorgue, f., chalandon, p., michel, p., bertrand, p. (2016). fatigue performance of a self-piercing rivet joint between aluminum and glass fiber reinforced thermoplastic composite, int. j. fatigue 83, pp. 127-134. doi: 10.1016/j.ijfatigue.2015.10.004. [20] huang, l., shi, y., guo, h., su, x. (2016). fatigue behavior and life prediction of self-piercing riveted joint, int. j. fatigue 88, pp.96-110. doi: 10.1016/j.ijfatigue.2016.03.015. [21] yang, z., zhang, y., jiang, c. (2016). dynamic reliability analysis of mechanical parts under actual operation conditions.journal of northeastern university(natural science).40(11), pp.1584-1589. microsoft word numero_52_art_08_2660 m. saadatmand et alii, frattura ed integrità strutturale, 52 (2020) 98-104; doi: 10.3221/igf-esis.52.08 98 focussed on the 1st benelux network meeting and workshop on damage and fracture mechanics study on the thermal cycle of wire arc additive manufactured (waam) carbon steel wall using numerical simulation mohsen saadatmand, reza talemi department of material engineering, ku leuven, belgium mohsen.saadatmand@kuleuven.be, reza.hojjatitalemi@kuleuven.be abstract. the thermal behavior in waam process is a significant cause for thermal stress. in this paper, a 3d model of a four-layer wall is built in abaqus software in order to investigate the thermal behavior in a carbon steel (astm a36) waam wall. moreover, the effects of substrate preheating temperature and travel speed on the temperature distribution are studied. the modelling results show that with increase in number of deposited layers, the peak temperature increases but average cooling speed decreases. furthermore, substrate preheating increases peak temperature of fist layer and decreases its average cooling speed. regarding simulation results, the travel speed has major effects on the thermal behavior of deposited layers. keywords. additive manufacturing; wire arc additive manufacturing; finite element method; low carbon steel. citation: saadatmand, m., talemi, r., study on the thermal cycle of wire arc additive manufactured (waam) carbon steel wall using numerical simulation, frattura ed integrità strutturale, 52 (2020) 98-104. received: 24.10.2020 accepted: 19.12.2019 published: 01.04.2020 copyright: © 2020 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. introduction dditive manufacturing (am) processes have become very noteworthy in recent years. they have many advantages in comparison to conventional processes [1]. the production of complex and individual components is possible with additive manufacturing processes. wire arc additive manufacturing (waam) is a directed energy deposition (ded) method, which uses an electric arc for melting the metallic materials [2]. the arc-based heat sources have recently attracted a lot of attention since they have proven the ability to produce large metallic structures [3]. the hardware cost for the waam system is typically an order of magnitude less than the laser powder systems and it can achieve deposition rates two orders of magnitude higher than laser powder systems (typically 2-4 kg/hour) [4]. moreover, the waam process, in combination with a robot, also allows the production of complex geometries [5]. however, repeated heating and cooling cycles make a very large temperature gradient between the substrate and deposited layers, causing serious thermal stress, cracks, and even fracture of fabricated parts [6]. in order to manufacture a high-quality product, it is important to determine the interaction of each process parameter with the component properties. it is highly important to understand and control the temperature gradient and thermal stress for process optimization. according to thompson et al. [7], the mechanical properties of the fabricated part are directly influenced by the microstructure, which drastically depends on the thermal history. as reported by colegrove et al. [8], it is a https://youtu.be/zr2jqq8ipi0 m. saadatmand et alii, frattura ed integrità strutturale, 52 (2020) 98-104; doi: 10.3221/igf-esis.52.08 99 of great importance to have the process parameters and cooling rate under control and learn how they influence the properties of the material. besides experimental methods, numerical simulation has been demonstrated to be an efficient approach to study the thermal-mechanical behavior in additive manufacturing processes. zhao et al. [9] obtained a 3d heat transfer model with temperature dependent material properties for studying the thermal cycling effects. they concluded that the heat diffusion conditions deteriorate by the increase in the deposition height. xiong et al. [10] defined an finite element (fe) simulation for prediction of the heat dissipation mechanism in a tube of welds made using gas metal arc (gma)-waam. they demonstrated that the heat transport conditions in each layer are closely associated with the direction of deposition in the former layer. the substrate preheating is one of the most effective methods to mitigate the thermal stress and crack. therefore, it is important to explore the preheating impact on thermal behavior of waam parts. however, little has been done to model the effect of substrate preheating on thermal behavior in waam process [6]. xiong et al. [6] used a h08mn2s wire electrode and the commercial software msc marc was used for modelling of the waam process of a circular thin walled part. in this study, a 3d finite element model is developed in abaqus software to study the thermal behavior of low carbon steel waam wall (astm a36). the temperature distribution in the middle point of deposited layer is studied and effects of substrate preheating temperature and travel speed are discussed. simulation procedure in this section by using abaqus 2019 software, a 3d thermal elastic-plastic fe computational procedure was employed to simulate the temperature distribution in the waam wall of low carbon steel (astm a36) (wwls). the temperaturedependent thermal-mechanical properties of astm a36 were obtained from the literature [11] (tab. 1). the substrate and deposited material are assumed to have the identical material properties and to be isotropic. temperature (°c) specific heat (j/kg°c) thermal conductivity (w/m°c) density (kgm-3) yield stress (mpa) thermal expansion coefficient (10-5/°c) young modulus (gpa) poisson’s ratio 0 400 60 7880 250 1.15 210 0.3 100 500 50 7880 240 1.2 200 0.3 200 520 45 7800 230 1.42 200 0.3 400 650 38 7760 200 1.45 170 0.3 600 750 30 7600 180 1.45 80 0.3 800 1000 25 7520 150 1.45 35 0.3 1000 1200 26 7390 125 1.45 20 0.3 1200 1400 28 7300 80 1.45 15 0.3 1400 1600 37 7250 35 1.45 10 0.3 1550 1700 37 7180 30 1.45 10 0.3 table 1: the temperature-dependent thermal-physical properties of low carbon steel astm a36 [11] the model was developed for the wwls, containing 4 layers with a layer height of 2.5mm. the 3d finite element mesh model is shown in fig. 1. a symmetry plane was used to save computational time in the model of the wwls without sacrificing the physics of the process. the model was meshed with the eight-noded, three-dimensional brick element type. the mesh size for deposited layers was 1.25mm along the thickness of deposited layers and increased gradually away from the deposited layers. m. saadatmand et alii, frattura ed integrità strutturale, 52 (2020) 98-104; doi: 10.3221/igf-esis.52.08 100 figure 1: finite element mesh for the wwls the arc continuously moved along y direction (travel direction indicated in fig. 1) with no interlayer idle time (iit). a code written as subroutine (dflux) in the fortran programming language was used in order to apply a moving volumetric heat source for modelling of arc, based on the double ellipsoidal distribution proposed by goldak [12], which is expressed by the following equations. for the front heat source [12]: 2 22 2 2 2 3   6 3   f y zx a b cf f f f q q e abc            (1) and for the rear heat source [12]: 2 22 2 2 2 3   6 3  r y zx a b cr f r f q q e abc           (2) where q is the heat source power, x, y and z are the local coordinates of the double ellipsoid model aligned with the deposition line. the parameters a, br, bf and c are associated to the features of heat source, as indicated in fig. 2(a). these parameters were determined from results reported by nuraini et al. [13] (tab. 2). parameter value length of front ellipsoidal (bf) (mm) 10.1 length of rear ellipsoidal (br) (mm) 12.4 depth of the heat source (c) (mm) 6 half width of the heat source (a) (mm) 5 front heat fraction 0.4 rear heat fraction 1.6 energy input rate (w) 4752 table 2: the values for heat source parameters [13] the heat source model considers the heat flux losses by convection and radiation; thus, during the fe analysis, a convection heat transfer coefficient of 35 w/m2k, the radiative emissivity of 0.5, and the stefan-boltzmann constant of 5.67x10-8 w m-2k-4 were used for the external sides of the substrate and layers [14]. the parameters for heat loss were not applied to the longitudinal mid-plane because of the symmetry thermal boundary. the latent heat was considered as 250 kj/kg between the solidus temperature 1460°c and the liquidus temperature 1520°c [15]. to simulate material deposition and mimic the additive nature of the waam process, the element birth technique method was used. with the model change option in abaqus, all the elements of the deposited layers are deactivated at the initial step of the analysis, and then the elements of each layer are activated, simulating material deposition layer by layer stacked to each other. the initial temperature of the substrate and deposited layers were considered as 25°c. m. saadatmand et alii, frattura ed integrità strutturale, 52 (2020) 98-104; doi: 10.3221/igf-esis.52.08 101 in this study, the numerical temperature cycle at four distinct locations was computed during the waam process. fig. 2(b) represents the location of middle points of the first, second, third and fourth layer, namely, p1, p2, p3 and p4, respectively. to investigate effects of substrate preheating, the substrate was preheated at 200°c, 400°c and 600°c. also, travel speeds of 10mm/s, 12,5mm/s and 15mm/s were considered in order to investigate effects of travel speed on the thermal behavior of deposited layers. figure 2: (a) schematic diagram of goldak model [16], (b) the location of middle points of the first, second, third and fourth layer, namely, p1, p2, p3 and p4, respectively. results & discussion thermal cycles during waam process ig. 3 illustrates the thermal cycles of middle point of the four layers (deposited with the travel speed of 12.5 mm/s), namely, p1, p2, p3 and p4, as is showed in fig. 2. as indicated in fig 3, in the middle point of the first layer, the temperature increases sharply to the peak when the heat source approached. when the heat source travelled to the middle point of the second layer, the temperature of the middle point of first layer also increases. during the deposition of second layer, because of the preheating of the previous deposition (first layer), the peak temperature of the second layer increases to a higher value compared to that of first deposited layer (indicated by dashed line). also, the increase rate for reheating peak temperature seems to be slightly higher compared to that for first peak temperature. it can be attributed to this fact that for previously deposited layers the heat cannot escape so more increase in temperature is expected. as shown in fig. 3, every thermal cycling curve has two continues peaks exceeding the melting point, resulting in enough condition for metallurgy bonding. the peak temperatures of the middle point of first layer is lower due to the influence of the initial temperature of substrate. since the initial temperature of the substrate is lower (room temperature, 25℃), which makes the heat dissipation quickly, the average cooling speed for first layer is higher compared to that of subsequent deposited layers. the average cooling speed for first layer is about 123 °c/s which drops to 115 °c/s for the third layer. here, it should be noted that by increasing the number of deposited layers, the peak temperature will increase from 2518°c for the first layer to 2640°c for fourth deposited layer. for a substrate at room temperature, a large temperature gradient between the substrate and deposited layers causes serious thermal stress, cracking and even fracture of fabricated parts, as reported in the literature [6]. to mitigate the thermal stress and cracks, substrate preheating is one of the most effective methods. in the next part, the effects of substrate preheating temperature on the thermal behavior of deposited layers are investigated. effect of substrate preheating on the thermal cycle of deposited layers fig. 4 provides the thermal cycle of the middle point in the first layer for non-preheated and preheated substrate with temperature of 200 ℃, 400 ℃ and 600 ℃. the first peak temperature value varies from 2518 ℃ to 2537 ℃, 2567 ℃ and 2600 ℃ with the increase of the preheating temperature from non-preheated to 200 ℃, 400 ℃ and 600 ℃, respectively. also, with increase in preheating temperature to 600℃, the average cooling speed decreases gradually to 118°c/s. this can be explained by the fact that when the preheating temperature increases, the temperature difference between the substrate and the first layer decreases, resulting in a bad heat conduction condition of the deposited layer [17]. f m. saadatmand et alii, frattura ed integrità strutturale, 52 (2020) 98-104; doi: 10.3221/igf-esis.52.08 102 figure 3: computed thermal cycles of p1, p2, p3 and p4 with the travel speed of 12.5 mm/s. figure 4: thermal cycle of the middle point in the first layer for non-preheated and preheated substrate with temperature of 200 ℃, 400 ℃ and 600 ℃. figure 5: the peak temperature of middle point in the first layer for travel speed of 10 ,12.5 and 15 mm/s m. saadatmand et alii, frattura ed integrità strutturale, 52 (2020) 98-104; doi: 10.3221/igf-esis.52.08 103 effect of travel speed on thermal cycle of deposited layers the temperature distributions of p1 with different travel speeds are shown in fig. 5. as shown in fig 5, with increasing the travel speed, the maximum temperature for each point decreases. the reason is that as the travel speed reduces, the interaction time between arc and material increases. as a result, more energy transfers to the material, therefore temperature increases. also, with increase in travel speed from 10 to 15 mm/s, the average cooling speed increases from 118°c/s to 136°c/s for the middle point in the first layer. moreover, for the travel speed of 15mm/s, the second peak is approaching the melting point, so it influences the metallurgy bonding between deposited layers. conclusions n this work, a 3d finite element model has been developed to study the thermal cycle during the waam process along with the effects of substrate preheating temperature and travel speed on the thermal cycle of waam manufactured wall of low carbon steel (astm a36). it has been found that, during the waam process, the peak temperature of newly deposited layers increases (from 2518℃ to 2640℃) but the average cooling speed decreases (from 123 °c/s to 115 °c/s) due to the influence of previously deposited layers. moreover, with the increase of substrate’s preheating temperature, the peak temperature of first layer increases (from 2518℃ to 2600℃). in addition, the cooling rate of first layer decreases gradually from 123°c/s to 118°c/s with the increasing preheating temperature. furthermore, from the obtained numerical results it can be concluded that the travel speed has a major impact on the thermal behavior and metallurgical bonding of deposited layers. references [1] wu, b., pan, z., ding, d., cuiuri, d., li, h., xu, j., norrish, j. (2018). a review of the wire arc additive manufacturing of metals: properties, defects and quality improvement, j. manuf. process., 35(february), pp. 127–139, doi: 10.1016/j.jmapro.2018.08.001. [2] haden, c. v., zeng, g., carter, f.m., ruhl, c., krick, b.a., harlow, d.g. (2017). wire and arc additive manufactured steel: tensile and wear properties, addit. manuf., 16(2010), pp. 115–123, doi: 10.1016/j.addma.2017.05.010. [3] hejripour, f., binesh, f., hebel, m., aidun, d.k. (2019). thermal modeling and characterization of wire arc additive manufactured duplex stainless steel, j. mater. process. technol., 272(march), pp. 58–71, doi: 10.1016/j.jmatprotec.2019.05.003. [4] ding, j. (2012).thermo-mechanical analysis of wire and arc additive manufacturing process. cranfield university. [5] kazanas, p., deherkar, p., almeida, p., lockett, h., williams, s. (2012). fabrication of geometrical features using wire and arc additive manufacture, proc. inst. mech. eng. part b j. eng. manuf., 226(6), pp. 1042–1051, doi: 10.1177/0954405412437126. [6] xiong, j., lei, y., li, r. (2017). finite element analysis and experimental validation of thermal behavior for thin-walled parts in gmaw-based additive manufacturing with various substrate preheating temperatures, appl. therm. eng., 126, pp. 43–52, doi: 10.1016/j.applthermaleng.2017.07.168. [7] thompson, s.m., bian, l., shamsaei, n., yadollahi, a. (2015). an overview of direct laser deposition for additive manufacturing; part i: transport phenomena, modeling and diagnostics, addit. manuf., 8, pp. 36–62, doi: 10.1016/j.addma.2015.07.001. [8] colegrove, p.a., coules, h.e., fairman, j., martina, f., kashoob, t., mamash, h., cozzolino, l.d. (2013). microstructure and residual stress improvement in wire and arc additively manufactured parts through high-pressure rolling, j. mater. process. technol., 213(10), pp. 1782–1791, doi: 10.1016/j.jmatprotec.2013.04.012. [9] zhao, h., zhang, g., yin, z., wu, l. (2011). a 3d dynamic analysis of thermal behavior during single-pass multi-layer weld-based rapid prototyping, j. mater. process. technol., 211(3), pp. 488–495, doi: 10.1016/j.jmatprotec.2010.11.002. [10] xiong, j., li, r., lei, y., chen, h. (2018). heat propagation of circular thin-walled parts fabricated in additive manufacturing using gas metal arc welding, j. mater. process. technol., 251, pp. 12–19, doi: 10.1016/j.jmatprotec.2017.08.007. [11] stamenkovic, d., vasovic, i. (2009). finite element analysis of residual stress in butt welding two similar plates, sci. tech. rev., lix(1), pp. 57–60. [12] goldak, j., chakravarti, a., bibby, m. (1984). a new finite element model for welding heat sources, metall. trans. b, i m. saadatmand et alii, frattura ed integrità strutturale, 52 (2020) 98-104; doi: 10.3221/igf-esis.52.08 104 15(2), pp. 299–305, doi: 10.1007/bf02667333. [13] nuraini, a., zainal, a., azmahhanim, m. (2013). the effect of welding process parameter on temperature and residual stress in buttjoint weld of robotic gas metal arc welding, aust. j. basic appl. sci., 7(7), pp. 814–820. [14] graf, m., hälsig, a., höfer, k., awiszus, b., mayr, p. (2018). thermo-mechanical modelling of wire-arc additive manufacturing (waam) of semi-finished products, metals (basel)., 8(12), doi: 10.3390/met8121009. [15] eisazadeh, h., achuthan, a., goldak, j.a., aidun, d.k. (2015). effect of material properties and mechanical tensioning load on residual stress formation in gta 304-a36 dissimilar weld, j. mater. process. technol., 222(august), pp. 344– 355, doi: 10.1016/j.jmatprotec.2015.03.021. [16] nezamdost, m.r., esfahani, m.r.n., hashemi, s.h., mirbozorgi, s.a. (2016). investigation of temperature and residual stresses field of submerged arc welding by finite element method and experiments, int. j. adv. manuf. technol., 87(1– 4), pp. 615–624, doi: 10.1007/s00170-016-8509-4. [17] hu, z., qin, x., shao, t. 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can be opened with acrobat and adobe reader 5.0 and later.) >> /namespace [ (adobe) (common) (1.0) ] /othernamespaces [ << /asreaderspreads false /cropimagestoframes true /errorcontrol /warnandcontinue /flattenerignorespreadoverrides false /includeguidesgrids false /includenonprinting false /includeslug false /namespace [ (adobe) (indesign) (4.0) ] /omitplacedbitmaps false /omitplacedeps false /omitplacedpdf false /simulateoverprint /legacy >> << /addbleedmarks false /addcolorbars false /addcropmarks false /addpageinfo false /addregmarks false /convertcolors /converttocmyk /destinationprofilename () /destinationprofileselector /documentcmyk /downsample16bitimages true /flattenerpreset << /presetselector /mediumresolution >> /formelements false /generatestructure false /includebookmarks false /includehyperlinks false /includeinteractive false /includelayers false /includeprofiles false /multimediahandling /useobjectsettings /namespace [ (adobe) (creativesuite) (2.0) ] /pdfxoutputintentprofileselector /documentcmyk /preserveediting true /untaggedcmykhandling /leaveuntagged /untaggedrgbhandling /usedocumentprofile /usedocumentbleed false >> ] >> setdistillerparams << /hwresolution [2400 2400] /pagesize [612.000 792.000] >> setpagedevice microsoft word numero 25 art 11 v. veselý et alii, frattura ed integrità strutturale, 25 (2013) 69-78; doi: 10.3221/igf-esis.25.11 69 special issue: characterization of crack tip stress field multi-parameter crack tip stress state description for estimation of fracture process zone extent in silicate composite wst specimens václav veselý, jakub sobek, lucie šestáková, petr frantík brno university of technology, faculty of civil engineering, institute of structural mechanics, brno, czech republic stanislav seitl academy of sciences of the czech republic, v. v. i., institute of physics of materials, brno, czech republic abstract. for wedge splitting test specimens, the stress and displacement fields both in the vicinity and also in larger distance from the crack tip are investigated by means of numerical methods. several variants of boundary conditions were modeled. the stress intensity factor k, t-stress and even higher-order terms of william series were determined and subsequently utilized for analytical approximation of the stress field. a good fit between the analytical and numerical solution in dependence on the distance from the crack tip was shown, compared and discussed. presented approach is considered as suitable for estimation of the fracture process zone extent in silicate composite materials. keywords. near-crack tip fields; williams series; higher-order terms; stress field approximation; wedge splitting test; fracture process zone. introduction he research of the author’s collective is focused on estimation of the size, shape and other relevant properties of the zone with nonlinear material behaviour evolving at the tip of a propagating crack in composite materials with disordered internal structure, particularly those with quasi-brittle nature which exhibit strain softening. characteristics of the zone, in the case of the materials in question referred to as the fracture process zone (fpz), are intended to be utilized within methods for evaluation of fracture mechanical parameters in order to diminish the effects of the test specimen’s size, geometry and free boundaries on their values, mainly the fracture energy, determined from records of tests on laboratory-sized specimens. this topic is intensively researched in last decades [1–6]. a determination procedure taking into account the mentioned effects is currently under development by the authors [7,8] and outputs of individual parts of the procedure are being tested, verified and validated at present, both from the perspective of the fpz extent estimation [9–11] and also the crack tip stress state description [12–14]. this paper is particularly focused on investigation of differences in crack tip stress state caused by changes in the test geometry (the specimen’s shape and boundary conditions) resulting in differences in the shape and size of the fpz. variants of what is referred to as the wedge splitting test (wst) geometry are taking into account for this study. a precise description of the stress state in the cracked body is necessary for the procedure of the fpz extent estimation. for that purpose, multi-parameter fracture mechanics is employed as the size proportions of the fpz in relation to the whole specimen is much larger in the case of the studied quasi-brittle composites than that of e.g. plastic zone in metals. therefore, the fpz extent analysis is preceded by a detailed finite element method (fem) analysis of the stress and displacement fields in the test specimens serving as input to the over-deterministic method [15] for evaluation of higherorder terms of the williams power series [16] via which the fields are approximated. main attention is given to this issue in t http://www.gruppofrattura.it http://dx.medra.org/10.3221/igf-esis.25.11&auth=true v. veselý et alii, frattura ed integrità strutturale, 25 (2013) 69-78; doi: 10.3221/igf-esis.25.11 70 the paper; the accuracy of the approximation is investigated. some examples of results of the verification analyses are presented in conclusion. multi-parameter description of the stress and displacement fields in a cracked body multi-parameter fracture mechanics [17–19] is based on the analytical description of the stress and deformation fields in the body with crack by means of williams expansion [16]. this infinite power series for a homogeneous elastic isotropic body can be expressed for the stress tensor {} and deformation vector {u} as 1 2 1 2 ( 1) cos 1 1 cos 3 2 2 2 2 2 ( 1) cos 1 1 cos 3 2 2 2 2 2 ( 1) sin 1 1 sin 3 2 2 2 2 n x n n y n n xy n n n n n n n n n n r a n n n n                                                                                                                       (1)     /2 1 1 cos cos 2 2 2 2 2 2 1 sin sin 2 2 2 2 2 n n n nn n n n n u r a v n n n n                                                      (2) respectively, where r and  are polar coordinates centered at the crack tip (considering the direction of the crack propagation in positive x-axis),  is a shear modulus, e and  are young’s modulus and poisson’s ratio; n represents index of term of the power expansion and  is kolosov’s constant (depends on plane stress or plane strain state). coefficients an are functions of relative crack length . they can be with convenience expressed as dimensionless functions (with regard to the loading) in various ways. we alternatively employ the two most frequently used ones in this paper which are adopted from [20,21] and [22,23], and they are expressed here only for the parameters presented later in the paper. with respect to the mentioned references they can be written as    1 i 1 0 0 2 ( ) a k b k k       and         2 2 i i 4 ( ) a a t a b k k          (3) and   2 2( ) n n n a g w      for 1, 3, 4 ,n n  and  2 2 4 ( ) a g t      (4) respectively. in these formulas,  is nominal stress in the central plane of the specimen caused by (usually only the splitting component psp of) the applied load (i.e.  = psp/bw), k0 is the normalized stress intensity factor (i.e. 0 spk p b w ), ki is the stress intensity factor, t is t-stress, a is the crack length, w and b is the specimen’s width and breadth, respectively. the crack length a is defined as a distance from the point of the splitting force application to the crack tip, i.e. a = c + dn – h in the case of the wst, see fig. 3. consequently, the relative crack length  is defined as the ratio of the crack length a and the effective specimen width n ef ( )       c d ha w w h (5) http://www.gruppofrattura.it http://dx.medra.org/10.3221/igf-esis.25.11&auth=true v. veselý et alii, frattura ed integrità strutturale, 25 (2013) 69-78; doi: 10.3221/igf-esis.25.11 71 coefficients of the terms of the williams power expansion used/presented in this paper were determined using direct methods which evaluate results gained via fem computations. values of first two terms (k and t-stress) were computed both using the direct method (e.g. [24]) or determined with help of quarter-point crack-tip elements (e.g. [25]). for the latter case, following formulas are used to calculate k and t   ( c ) ( b ) ( a ) ( b ) ( c ) i 2 2 2 4 , 4 2 3(1 )(1 ) 2 1 i i i i i ve e k v t u u u l l                    (6) where l is the element length, u and v are displacement components in the x and y directions, respectively. the (a), (b), and (c) superscripts indicate the fe node positions as follows: a – node at the crack tip, b – node at a distance of 1/4l from the crack tip, and c – node at a distance of l. for the direct method [24] the estimation of the fracture parameters is derived directly from the stress description via eq. (1) (for max. n = 2). let us note that several alternatives to the methods used in this paper are available in literature, especially for the determination of k (e.g. [26]). coefficients of even the higher-order terms of the power expansion were calculated (alternatively to the previouslymentioned techniques for the first two ones, however, as the only used technique for the other ones) by using the overdeterministic method (odm) [15]. odm, based on the linear least-squares formulation, provides solution of the system of 2k equations (resulting from eq. (2)), where k represents the number of selected nodes around the crack tip, leading to values of n selected terms of the series. they can be calculated from the knowledge of the values of components u, v of the displacement vector and coordinates r,  of the selected nodes. similarly to the above-mentioned techniques, inputs to the odm were also obtained by fem computations. motivation of the determination of the higher-order of terms of the power series dwells in the requirements on the estimation of the crack-tip nonlinear zone extent. they must be taken into account in order to describe the fields in more distant surroundings of the crack tip, especially in the case of the quasi-brittle materials. wedge splitting test geometry – definition of numerical study edge splitting test is a convenient and popular configuration for estimation of fracture parameters of silicatebased composites, mainly building materials. it has been introduced in 80ies of the last century [27,28]. for its advantages it is often used as an alternative of standard three-point bending test of notched beams. the test can be performed on specimens of various shapes, however also the test setup, i.e. the boundary conditions, can significantly differ. and that is true both for the boundary conditions related to the load application (see fig. 1) and the specimen supports (see figs. 2 and 3). the differences in the load application and supporting are usually neglected, even fracture analyses utilizing functions of geometry corresponding to the compact tension test configuration are commonly published [29,30]. and if the kcalibration curves are computed for the wst geometry and presented in the literature (e.g. [31]), details of supports and load application are not properly taken into account. particularly, the compressive component of the loading force (pv in figs. 2 and 3) is ignored and only one central support is considered (except to [32], with regard to both aspects). karihaloo and co-workers published the stress and displacement field description using as many as five terms of the williams series [22,23]. two variants of supports were modeled, but the compressive component of the applied loading was not considered too. it is worth noticing that if a certain fracture analysis has to be conducted for which the stress/displacement fields in only the very vicinity of the crack tip is required (i.e. the case of brittle fracture with description of the fields via k only), the simplifications mentioned in previous paragraph are possible (to some extent, i.e. when t-stress value is not too low or high). in our work, three variants of supports (one central support, and two supports positioned 1/4w and 1/8w from the central plane, see figs. 2 and 3) and two alternatives of load imposition (via loading platens with bearings placed inside the specimen’s groove – platens i – and platens with bearings axes outside the groove – platens ii, see figs. 1, 3 left and right, respectively) are considered. the influence of the boundary conditions of the wst test was analyzed in several relevant aspects in detail in previous works by the authors [32–34, 12–14] and results were compared with the crack-tip fields descriptions published in literature. selected parts of the rather thorough study are presented in this paper. the study was first conducted in the w http://www.gruppofrattura.it http://dx.medra.org/10.3221/igf-esis.25.11&auth=true v. veselý et alii, frattura ed integrità strutturale, 25 (2013) 69-78; doi: 10.3221/igf-esis.25.11 72 framework of two-parameter fracture mechanics (investigation of the stress intensity factor k and the t-stress, or their normalized values b1 and b2, respectively). later, more terms of the williams series was considered and coefficients of the first several ones (up to around 10) were determined, again either in their absolute values an or expressed as the normalized shape functions gn. figure 1: variants of boundary conditions of the wst geometry in the area of the load application (compare (a), (b) vs. (c), (d)). (a) (b) (c) (d) http://www.gruppofrattura.it http://dx.medra.org/10.3221/igf-esis.25.11&auth=true v. veselý et alii, frattura ed integrità strutturale, 25 (2013) 69-78; doi: 10.3221/igf-esis.25.11 73 psp pv12 psp pv12 pv 1 2 pv 1 2 psp psp pv p p psp pv12 pv 1 2 pv 1 2 pv12 psp pv12 pv psp pv12 pv 1 2 pv 1 2 psp psp pv12 p p p figure 2: schemes of variants of boundary conditions of the wst geometry in both the area of the load application (differences between (a) vs. (b), (c) and (d) vs. (e) and (f)) and supports (differences between (a) vs. (b) and (e) vs. (d) vs. (c) and (f)). taking into account the vertical component of the loading force is essential. numerical modeling he test configuration in considered variants of boundary conditions and specimen dimensions corresponding to results showed below are indicated in fig. 3 and their values are summarized in tab. 1. dimensions [mm] w 100 b 100 a 20 ~ 80 dn 20 e 35 f 30 h 15 i 25 table 1: individual dimensions of the modeled wst specimen. t (a) (b) (c) (e)(d) (f) http://www.gruppofrattura.it http://dx.medra.org/10.3221/igf-esis.25.11&auth=true v. veselý et alii, frattura ed integrità strutturale, 25 (2013) 69-78; doi: 10.3221/igf-esis.25.11 74 d c w a e e w /4 w /2 w /4 w /2 w /2 w h i 1 2 p 1 2 p 1 2 pp f alt. breadth b w a e ef alt. breadth b h w /4 w /8 3w /8 w /2 w /2 w v psp n vvv 1 2 pv psp ppsp 1 2 pv d c w n ef w ef 1 2 p 1 2 pp vvv p w /4 (a) (b) figure 3: sketch of the modeled wst specimen with considered variants of boundary conditions. the numerical study was conducted in the ansys fem software [35]. all simulations were modeled in 2d under plane strain condition. the fe mesh was generated from 8-nodes isoparametric elements. linear elastic isotropic material of the cementitious composite specimen and the steel loading platens was defined by young’s moduli e = 40 and 210 gpa and poisson’s ratios  = 0.2 and 0.3, respectively. fig. 4a and b shows a static scheme and fe model for a variant of the wst with platens ii and one central support (a half of the specimen with symmetry conditions). a detail of the near-crack-tip fe mesh is depicted in fig. 4c and d. fig. 4d shows utilization of the quarter-point singular elements at the very crack tip (used for calculation of k and t, or b1 and b2, via the first two mentioned methods), in fig. 4c the (near-crack-tip) ring of nodes is indicated from which coordinates and computed displacements are used as inputs into the odm for determination shape functions gn. results and discussion, application of the multi-parameter fracture mechanics his section presents some of the results obtained within the conducted study. in agreement with the definition of the normalized dimensionless expressions of the coefficients of the williams series’ terms mentioned above, the influence of boundary conditions on the stress and displacement fields’ description is indicated in graphs in figs. 5 and 6. fig. 5 shows the parameters b1 and b2 as functions of the relative crack length . differences in the boundary conditions are apparently distinguishable for the latter one, particularly they are evident for short cracks (up to approx. a < 0.4, which corresponds to the influence of the loading platens, see differences between the "platens i" and "platens ii" cases) as well as long cracks (i.e. from approx. a > 0.4, influence of the number and mutual distance of supports). it is also clearly seen, and that is true for almost the whole studied range of , that the neglecting of the compressive force pv produces larger error if a single support is used. effect of boundary conditions on the first term of the series is rather low, as can be expected, since the singular term domain is the very vicinity of the crack tip only. the graphs in fig. 6 show shape functions corresponding to two selected higher-order terms coefficients, g4 and g7, and only the effect of supports can be investigated. both curves are from simulations with loading platens ii, therefore no differences between the curves are obvious up to a fracture process stage when the crack tip approaches the back-face of the wst specimen (see the magnified sections of the graphs in fig. 6b and d). differences are apparent only for the relative crack lengths around 0.9 and larger provided that compressive component of the loading force pv is considered. if t http://www.gruppofrattura.it http://dx.medra.org/10.3221/igf-esis.25.11&auth=true v. veselý et alii, frattura ed integrità strutturale, 25 (2013) 69-78; doi: 10.3221/igf-esis.25.11 75 pv is neglected, significant difference appears earlier, around  = 0.75 (see fig. 6a and b, where comparison with [23], which ignores pv, is shown). (a) (b) (c) (d) figure 4: 2d representation of the wst – static scheme with indication of boundary conditions (a) and corresponding fe model (b). example of the fe mesh around the crack tip: ring of selected nodes (at radius 5 mm from the crack tip) (c) and quarter-point cracktip elements (d). 0 25 50 75 100 125 150 175 200 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 b 1 [] α [-] platens i, psp platens i, psp + pv, 1 supp. platens i, psp + pv, 2 supp. (1/4) platens i, psp + pv, 2 supp. (1/8) platens ii, psp + pv, 1 supp. platens ii, psp + pv, 2 supp. (1/4) -0.50 -0.25 0.00 0.25 0.50 0.75 1.00 1.25 1.50 1.75 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 b 2 [] α [-] platens i, psp platens i, psp + pv, 1 supp. platens i, psp + pv, 2 supp. (1/4) platens i, psp + pv, 2 supp. (1/8) platens ii, psp + pv, 1 supp. platens ii, psp + pv, 2 supp. (1/4) (a) (b) figure 5: geometry factors b1 and b2 as functions of the relative crack length  for various considered boundary conditions. -50 0 50 100 150 200 250 300 0.2 0.4 0.6 0.8 g 4 [] α [-] 0.7 0.8 0.9 α [-] platens ii, psp + pv, 1 supp. platens ii, psp + pv, 2 supp. (1/4) distrib. load, psp, 2 supp. (1/4) (ref. karihaloo et al. 2003) -15000 -12500 -10000 -7500 -5000 -2500 0 2500 0.2 0.4 0.6 0.8 g 7 [] α [-] 0.850 0.875 0.900 0.925 α [-] platens ii, psp + pv, 1 supp. platens ii, psp + pv, 2 supp. (1/4) figure 6: shape functions g4 and g7 as functions of the relative crack length  for two support variants. an accurate knowledge of the mechanical fields in the cracked body is necessary for a relevant fracture analysis. as an example, a reconstruction of the stress fields in the wst (platens ii, one support, pv considered) is introduced. fig. 7 (a) (b) (c) (d) http://www.gruppofrattura.it http://dx.medra.org/10.3221/igf-esis.25.11&auth=true v. veselý et alii, frattura ed integrità strutturale, 25 (2013) 69-78; doi: 10.3221/igf-esis.25.11 76 displays distributions of selected stress components (in this case e.g. x, 1) over the specimen (symmetrical half) taking into account various ranges of terms of the williams series (whose coefficients were determined via methods mentioned above). the fields correspond to load psp = 1 kn. different relative crack lengths were chosen for each case. it is clearly visible that if the knowledge of the stress field is requested even in larger distance of the crack tip, the approximation of the field by higher number of terms of the series is essential. the isolines in the second row of fig. 7 may represent a nonlinear (plastic) zone extent provided that rankine failure criterion was applied. if the strength limit of the material were 2 (1 and 0.5) mpa, 4 (around 7 and more than 12, respectively) terms would be necessary for the accurate enough description of the nonlinear zone. n = 1 n = 2 n = 4 n = 7 n = 12 fem solution  = 0 .5 , σ x [pa]  = 0 .8 5 , σ 1 [pa] figure 7: comparison of stress fields (x, 1) in wst specimen reconstructed by means of williams power expansion using various ranges of terms of the series (from left 1, 2, 4, 7, and 12, respectively) with the numerical solution (right). the crack tip region is magnified in the second row (the axes scale is kept the same as in the first row). conclusions nalysis of the stress and displacement fields near a crack tip in a wst specimen is presented. for this purpose, multi-parameter fracture mechanics was applied. influence of the boundary conditions on the stress intensity factor and the t-stress (representing the first two terms of williams expansion) was investigated and several resulting conclusions discussed. moreover, even the higher-order terms of the series (up to order of 12) were calculated by means of the over-deterministic method. subsequently, various ranges of them were used for reconstruction of the stress field around the crack tip and compared with stress distribution obtained by means of fem. the results clearly show that especially for long cracks and/or in larger distances from the crack tip the accurate approximation of the stress field requires using more terms of the williams expansion than it is usual within classical fracture mechanical approaches. acknowledgements he work has been supported by the czech science foundation, the project no. 104/11/0833, and brno university of technology, specific research program, project no. fast-s-12-21/1653. a t http://www.gruppofrattura.it http://dx.medra.org/10.3221/igf-esis.25.11&auth=true v. veselý et alii, frattura ed integrità strutturale, 25 (2013) 69-78; doi: 10.3221/igf-esis.25.11 77 references [1] bažant, z.p., analysis of work-of-fracture method for measuring fracture energy of concrete, j. engng. mech. (asce), 122(2) (1996) 138–144. [2] hu, x.-z., wittmann, f.h., size effect on toughness induced by crack close to free surface, engng. fract. mech., 65 (2000) 209–221. [3] duan, k., hu, x.-z., wittmann, f.h., boundary effect on concrete fracture and non-constant fracture energy distribution, engng. fract. mech., 70 (2003) 2257–2268. [4] duan, k., hu, x.-z., wittmann, f.h., size effect on specific fracture energy of concrete, engng. fract. mech., 74 (2007) 87–96. [5] hu, x.-z., duan, k., size effect: influence of proximity of fracture process zone to specimen boundary, engng. fract. mech., 74 (2007) 1093–1100. [6] trunk, b., wittmann, f. h., influence of size on fracture energy of concrete, mater. struct., 34 (2001) 260–265. [7] veselý, v., frantík, p., keršner, z., cracked volume specified work of fracture, in: b.h.v. topping, l.f. costa neves, r.c. barros (eds.), proc. of 12th int. conf. on civil, structural and environmental engineering computing, funchal, portugal, civil-comp press, stirlingshire, uk, (2009) n.194. doi:10.4203/ccp.91.194. [8] veselý, v., frantík, p., an application for the fracture characterization of quasi-brittle materials taking into account fracture process zone influence, submitted to adv. eng. softw. (expected in 2013). [9] veselý, v., frantík, p., reconstruction of a fracture process zone during tensile failure of quasi-brittle materials, appl. comp. mech., 4 (2010) 237–250. [10] veselý, v., keršner, z., němeček, j., frantík, p., řoutil, l., kucharczyková, b., estimation of fracture process zone extent in cementitious composites, chem. listy, 104 (2010) s382–s385, [11] frantík, p., veselý, v., keršner, z., parallelization of lattice modelling for estimation of fracture process zone extent in cementitious composites. adv. eng. softw. (2013), http://dx.doi.org/10.1016/j.advengsoft.2012.11.020. [12] veselý, v., šestáková, l., seitl, s., influence of boundary conditions on higher order terms of near-crack-tip stress field in a wst specimen, key eng. mat., 488–489 (2012) 399–402. [13] veselý, v., sobek, j., šestáková, l., seitl, s., accurate description of near-crack-tip fields for the estimation of inelastic zone extent in quasi-brittle materials, key eng. mat., 525–526 (2013) 529–532. [14] šestáková, l., veselý, v., sobek, j., frantík, p., accuracy of approximation of stress field in cracked bodies for failure zone extent estimation. accepted to conference framcos-8, toledo, spain, 10–14 march 2013. [15] ayatollahi, m.r, nejati, m., an over-deterministic method for calculation of coefficients of crack tip asymptotic field from finite element analysis, fatigue fract. engng. mater. struct., 34 (2010) 159–176. [16] williams, m.l., on the stress distribution at the base of a stationary crack, j. appl. mech. (asme), 24 (1957) 109– 114. [17] berto, f., lazzarin, p., christopher, c.j., james, m.n., characterization of crack tip stress fields, forni di sopra (ud), italy, march 7–9, (2011) 88–95. [18] guagliano, m., sangirardi, m., sciuccati, a., zakeri, m., multiparameter analysis of the stress field around a crack tip, procedia engineering, 10 (2011) 2931–2936. [19] berto, f., lazzarin, p., multiparametric full-field representations of the in-plane stress fields ahead of cracked components under mixed mode loading, int. j. fatigue, 46 (2013) 16–26. [20] leevers, p.s., radon, j.c., inherent stress biaxiality in various fracture specimen geometries, int. j. fract., 19 (1983) 311–325. [21] knésl, z., bednář, k., two-parameter fracture mechanics: determination of parameters and their values (in czech), ipm as cr, v. v. i., brno, (1998). [22] karihaloo, b.l., xiao, q.z., higher order terms of the crack tip asymptotic field for a wedge-splitting specimen int. j. fract., 112 (2001) 129–137. [23] karihaloo, b.l., abdalla, h., xiao, q.z., coefficients of the crack tip asymptotic field for wedge splitting specimen, engng. fract. mech., 70 (2003) 2407–2420. [24] yang, b., ravi-chandar, k., evaluation of elastic t-stress by the stress difference method, engng. fract. mech., 64 (1999) 589–605. [25] tan, c.l., wang, x., the use of quarter-point crack-tip elements for t-stress determination in boundary element method analysis, engng. fract. mech., 70 (2003) 2247–2252. http://www.gruppofrattura.it http://dx.medra.org/10.3221/igf-esis.25.11&auth=true v. veselý et alii, frattura ed integrità strutturale, 25 (2013) 69-78; doi: 10.3221/igf-esis.25.11 78 [26] yang, z. j., chen, j. f., holt, g. d., efficient evaluation of stress intensity factors using virtual crack extension technique, comp. struct., 79(31) (2001) 2705–2715. [27] linsbauer, h.n., tschegg, e.k., fracture energy determination of concrete with cube-shaped specimens, zement und beton, 31 (1986) 38–40. [28] brühwiler, e., wittmann, f.h., the wedge splitting test, a new method of performing stable fracture mechanics test, engng. fract. mech., 35 (1990) 117–125. [29] reinhardt, h.w., xu, s., crack extension resistance based on the cohesive force in concrete, engng. fract. mech., 64 (1999) 563–587. [30] xu, s., reinhardt, h.w., determination of double-k criterion for crack propagation in quasi-brittle fracture, part iii: compact tension specimens and wedge splitting specimens, int. j. fract., 98 (1999) 179–193. [31] guinea, g.v., elices, m., planas, j., stress intensity factors for wedge-splitting geometry, int. j. fract., 81 (1996) 113– 124. [32] seitl, s., veselý, v., řoutil, l., two-parameter fracture mechanical analysis of a near-crack-tip stress field in wedge splitting test specimens, comp. struct., 89 (2011) 1852–1858. [33] seitl, s., dymáček, p., klusák, j., řoutil, l., veselý, v., two-parameter fracture analysis of wedge splitting test specimen, in: b.h.v. topping, l.f. costa neves, r.c. barros (eds.), proc. of 12th int. conf. on civil, structural and environmental engineering computing, funchal, portugal, civil-comp press, stirlingshire, uk, pap. 192 (10 p.), 2009. doi:10.4203/ccp.91.192. [34] seitl, s., hutař, p., veselý, v., keršner, z., t-stress values during fracture in wedge splitting test geometries: a numerical study, in: a. brandt, j. olek and i. h. marshall (eds.), proc. of int. symp. brittle matrix composites 9, warsaw, iftr and woodhead publ., 2009, 419–428. [35] ansys users manual version 10.0, swanson analysis system, inc., houston, 2005. http://www.gruppofrattura.it http://dx.medra.org/10.3221/igf-esis.25.11&auth=true microsoft word numero_46_art_31 y. yanya, frattura ed integrità strutturale, 46 (2018) 343-351; doi: 10.3221/igf-esis.46.31 343 blending ratio of recycled aggregate on the performance of pervious concrete yao yanya wuxi city college of vocational technology, wuxi, 214063, china yaoyanya66@163.com abstract. recycled pervious concrete as an environment-friendly and material-saving construction material can satisfy the current development demands of circular economy and environmental protection in china. but studies concerning the performance of recycled pervious concrete are not enough, which limits its application and promotion. in this study, waste prefabricated concrete beams were taken as the source of recycled aggregate and processed by crushing and screening to obtain recycled coarse aggregate. then pervious concrete was prepared using the recycled coarse aggregate. taking replacement rate and grain size grade as the running parameters, five groups of mix proportion were designed. moreover the physical, mechanical and permeability performance and the interrelation were analyzed by tests. the results demonstrated that the 24-hour water absorption rate of the recycled coarse aggregate was 12 times higher than that of natural aggregate, the porosity of the pervious concrete was between 14.2% and 20.44%, and the permeability coefficient was between 0.19 cm and 0.46 cm and increased with the increase of the porosity. the compressive strength of the pervious concrete increased with the increase of the replacement rate. when the replacement rate was 30%, the improvement amplitude was the largest. the compressive strength was improved 35.4% after double grain grade aggregate was mixed, but the permeability performance decreased. keywords. recycled aggregate; pervious concrete; permeability; strength. citation: yanya, y., blending ratio of recycled aggregate on the performance of pervious concrete, frattura ed integrità strutturale, 46 (2018) 343-351. received: 10.06.2018 accepted: 10.09.2018 published: 12.09.2018 copyright: © 2018 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. introduction emolition wastes has exceeded 1.5 billion tons in china every year with the acceleration of urbanization development, among which, 30%~50% is waste concrete; but the availability of the waste concrete is lower than 50% [1,2]. therefore, recycling of waste concrete has arisen the attentions of the world. it is common to apply waste concrete in road embankment or as concrete aggregate after crashing, screening and cleaning, which can promote the sustainable development of the construction industry and has significant economic and social benefits [3,4]. preparing d http://www.gruppofrattura.it/va/46/31.mp4 y. yanya, frattura ed integrità strutturale, 46 (2018) 343-351; doi: 10.3221/igf-esis.46.31 344 recycled concrete with waste concrete instead of natural aggregate has been tried in the 1950s. many scholars in china and abroad have studied the basic properties of recycled aggregate in recent years and gained substantial research achievements. silva et al. [5] and akbarnezhad et al. [6] found that the performance of recycled concrete was weaker than that of natural concrete. brito et al. [7] regarded waste concrete beams with high grade as the source of recycled aggregate and found that the mixing amount of recycled aggregate had insignificant influence on the strength of concrete. zhang et al. [8] considered that recycled aggregate could be used for preparing high-performance concrete. though the conclusions about the performance of recycled concrete in those studies are inconsistent, preparing concrete with recycled aggregate is extensively considered as feasible. but limited by technical and social factors, its application has not been extensively promoted [9]. pervious concrete refers to a kind of concrete with certain strength and permeability performance which is prepared by coating and binding aggregate particles with cement paste and adding or not adding fine aggregate and whose connected pores can rapidly drain away water. the porosity depends on the grain size of aggregate [10]. america has started to study and apply pervious concrete since 1970s and 1980s. china is promoting pervious concrete currently. low impact development construction in china greatly demands pervious concrete, which means large consumption of natural aggregate. replacing natural aggregated rocks with waste concrete totally or partially as the aggregate source of pervious concrete can save a large number of natural resources and generate significant ecological environmental benefits [11]. studies concerning the preparation of pervious concrete based on recycled aggregate is in the early stage. guneyisi e et al. [12] studied the influence of different replacement rates of recycled aggregate (25%, 50%, 75% and 100%) on pervious concrete and evaluated the performance of pervious concrete using general linear model-analysis of variance (glm-anova). the results demonstrated that the strength of pervious concrete increased firstly and then decreased and permeability coefficient increased with the increase of the replacement rate of recycled aggregate; the permeability performance of pervious concrete increased with the increase of water cement ratio under the same replacement rate. but zaetang et al. [13] considered that the compressive strength slightly increased when the replacement rate was lower than 60% and slightly decreased when the replacement ratio was 100%. zhu found that the compressive strength of pervious concrete was the largest when the replacement rate of recycled coarse aggregate was 30% and then decreased with the increase of the replacement rate through gaussian curve fitting. previous studies [14,15] considered that the basic performance of pervious concrete which was prepared using recycled aggregate could satisfy requirements; however the research methods are different, and the relationship between the replacement rate and the performance of pervious concrete has not been unified. therefore, the performance and replacement rate of recycled aggregate and the strength and permeability performance of graded recycled pervious concrete were studied by preparing graded aggregate based on waste prefabricated concrete beams through mechanical crushing and artificial screening, which provides a theoretical basis for the the application of recycled aggregate in pervious concrete and promote the recycling of waste concrete. test overview raw materials he raw materials included p·o 42.5 cement (henan mengdian group, china) whose 28-day compressive strength was 53 mpa and 28-day bending strength was 8.0 mpa, natural river sand (coarse sand), natural coarse aggregate (gravel with grain size between 5 mm and 10 mm) and recycled coarse aggregate (waste road concrete blocks). natural river sand was used as fine aggregate. the mixture of coarse sand was to ensure the strength of test specimens and improve the workability of pervious concrete and facilitate the forming of test specimens. the waste road concrete blocks were obtained by crushing with knobbling and y132s-4 jaw crusher (shanghai dezhong electric co., ltd., china) and screening aggregate with grain size between 5 mm and 10 mm and between 10 and 20 mm (in a small amount). design of mix proportion referring to relevant regulations and research achievements [16,17], water cement ratio was set as 0.30. the replacement rate of recycled aggregate was set as 0%, 30%, 50%, 100% single-sized and 100% double-sized, denoted as rc0, rc30, rc50, rc100 and rc100d. the double-sized recycled coarse aggregate included aggregate with grain size between 5 mm and 10 mm and between 10 mm and 20 mm (mass ratio: 6:4; with the maximum accumulation density). the 10-min water absorption rate of recycled aggregate usually can be 90% that of aggregate in saturation state; moreover concrete mixing can be completed within 10 min. to solve the problem of high water absorption of the recycled aggregate, added water was used in this study. the amount of added water was equal to the amount of 10-min water absorption. influence of the water absorption of natural aggregate was not considered. t y. yanya, frattura ed integrità strutturale, 46 (2018) 343-351; doi: 10.3221/igf-esis.46.31 345 to improve the mixing peaceability of recycled pervious concrete and ensure its strength, a small amount of coarse sand (natural river sand with fineness modulus of 3.3) was added (sand percentage: 10%) was added (tab. 1). the design of mix proportion is shown in tab. 2. aperture size/mm 9.5 4.75 2.36 1.18 0.60 0.30 0.15 type ii grading region requirement/% 0 0-10 0-25 10-50 4170 7092 90100 the first accumulative sieve residue percentage/% 0 0.5 11.8 41.9 65.2 80.4 92.6 the second accumulative sieve residue percentage/% 0 0.7 13.5 43.2 67.6 83.8 91.3 table 1: natural sand grain grading. no. replace ment rate/% sand percentag e/% material utilization amount per unit volume (kg/m3) ra1 ra2 na natural sand cement water involved in cement hydration added water rc0 0 10 0 0 1378 153 307 92 0 rc30 30 10 136 0 1240 153 307 92 3 rc50 50 10 415 0 968 153 307 92 10 rc100 100 10 1378 0 0 153 307 92 32 rc100d 100 10 826 550 0 153 307 92 28 table 2: mix proportion of recycled pervious concrete note: na: natural aggregate (5~10 mm); ra1: recycled coarse aggregate (5~10 mm); ra2: recycled coarse aggregate (10~20 mm) the forming and maintenance of test specimens all the concrete was mixed using a 50 l blender. firstly sand and cement were mixed evenly. then coarse aggregate and water were added. after 3 ~ 5 min of mixing, the slump degree was measured, about 35 mm~50 mm. after testing of the slump degree, the concrete mixture was poured into a steel mould and tamped; the surface was smoothed. the mould was removed after 24 hours. then it was maintained in a curing room (20±2 °c, humidity higher than 95%). after 28 days, all the test specimens were taken out for testing. test methods porosity and permeability coefficient he effective porosity of test specimens was calculated based on the mass variation of test specimens after being immersed in water and dried by air for 24 h. the calculation formula is: 2 1m[1 ( )] 100% w m p v     (1) where p stands for porosity (unit: %), m1 stands for the mass of test specimens in water (unit: g), m2 stands for the mass of test specimens after 24 hours of air drying (unit: g), v stands for the volume of test specimens (unit: cm3), and ρw stands for the density of water at room temperature (unit: g/cm3). permeability coefficient permeability coefficient was tested using constant water head method, and the test device is shown in fig. 1. pervious concrete was prepared using polyvinylchlorid pipe mould in a nominal outside diameter of 110 mm×150 mm. then the test specimens were vertically fixed at the stent in the middle of overflow gutter. valve for water supply was opened. after the volume of water flowing from the outflow ports of the overflow gutter and porous cylinder became stable, difference of the water levels of the porous cylinder and overflow gutter (h) was measured using a steel gauge. when the water levels were being stable for 30 s, a second chronograph was started; at the same time, water flowing from the water outlet was t y. yanya, frattura ed integrità strutturale, 46 (2018) 343-351; doi: 10.3221/igf-esis.46.31 346 collected using a measuring cylinder. the time (t) and the amount of effluent water (q) were recorded. each test specimen was measured thrice. the maximum and minimum values were removed from the test results, and the median was taken as the permeability coefficient of the test specimens. the calculation formula is: i ql k aht  (2) where ki stands f or the permeability coefficient at the i-th measurement (unit: cm/s), q stands for the amount of water passing through the test specimens in t seconds (unit: cm3), l stands for the height of the test specimens (unit: cm), a stands for the cross section area of the test specimens (unit: cm2), h stands for the difference of water level (unit: cm), and t stands for the measurement time (unit: s). figure 1. test device compressive strength and splitting tensile strength the compressive and splitting tensile strength of the recycled pervious concrete were tested using yaw6506 electrohydraulic servo compression testing machine according to standard for test method of mechanical properties on ordinary concrete (gb /t 50081-2002). test results and analysis the analysis results of the physical properties of coarse aggregate oarse aggregate acts as a skeleton in concrete, which determines the properties of concrete mixture and the mechanical and endurance properties after hardening. the main properties of the natural and recycled aggregate were detected using relevant regulations in this study, and the results are shown in tab. 3. physical property indexes water content/ % 10-min water absorption/% 24-h water absorption% apparent density/ (kg/m3) stacking density/ (kg/m3) porosity /% silt content/ % crush index/% recycled aggregate 2.9 5.0 5.6 2606 1262 51.62 0.25 35.07 natural aggregate 0.2 0.4 0.5 2728 1553 45.33 1.4 15.56 table 3: the physical properties of the natural aggregate and recycled aggregate. tab. 3 demonstrates that the water content of the recycled aggregate was 14 times that of the natural aggregate, the 24-h water absorption of the former was about 12 times that of the natural aggregate, and the 10-min water absorption of the recycled aggregate was 90 % that of recycled aggregate in saturated water absorption state. it was because that the hardened mortar on the surface of the recycled aggregate was so porous that the water absorbability was strong. the c y. yanya, frattura ed integrità strutturale, 46 (2018) 343-351; doi: 10.3221/igf-esis.46.31 347 findings were consistent with the research results of bhutta mar et al. [18]. tab. 3 also demonstrated that the apparent density and stacking density of the recycled aggregate was lower than those of the natural aggregate. the study of xu et al. [19] suggested that the apparent density and stacking density of the recycled aggregate were between 2310 kg/m3 and 2620 kg/m3 and between 1200 kg/m3 and 1470 kg/m3; and the apparent and stacking density of the recycled aggregate in this study were both within the ranges. moreover the crushing value of the recycled aggregate was apparently larger than that of the natural aggregate, about 2 times, and the silt content of the natural aggregate was 6 times that of the recycled aggregate. the analysis results of porosity and permeability coefficient a previous study [20] found that the porosity of recycled pervious concrete increased with the increase of replacement rate. the relationship between replacement rate and porosity obtained in this study was in line with that rule. the porosity and permeability coefficient of the recycled pervious concrete are shown in tab. 4. moreover it was found that the connected porosity increased with the increase of permeability coefficient (fig. 2), which was similar to the research results of zaetang et al. [13]. it was because that concrete with higher porosity had suffered smaller water resistance due to the larger effective wetted area. no. range of porosity/% average porosity/% average permeability coefficient (cm/s) rc0 17.02~19.18 17.8 0.28 rc30 14.56~15.68 14.96 0.26 rc50 14.94~18.55 16.18 0.27 rc100 18.75~22.2 20.43 0.47 rc100d 13.77~14.95 14.20 0.18 table 4: porosity and permeability coefficient. 1.8 1.6 1.4 1.2 1.0 0.8 0.6 0.4 0.2 0 14 16 18 20 22 24 26 28 porosity /% )(149.0021.0 vew  917.02 r figure 2: porosity and permeability coefficient the analysis of compressive and splitting tensile strength strength is an important parameter of pervious concrete. the application of recycled aggregate can provide enough strength for pervious concrete. the compressive strength of the recycled pervious concrete was between 3.6 mpa and 9.07 mpa in this study. the variation rule of the compressive strength under different replacement rate is shown in fig. 3 and 4. it could be noted from fig. 3 and 4 that the compressive strength of rc30, rc50, rc100 and rc100d were higher than rc0, which was consistent with the current research results [21,22]. it was because that the rough surface and porous internal structure of the recycled aggregate strengthened cementation, and the water absorbed by the aggregate during mixing released to promote the development of the compressive strength. moreover it was observed that the compressive strength gradually improved with the increase of the replacement rate; the improvement amplitude was the largest when the replacement rate was 30%, but kept unchanged when the replacement rate was higher than 30%. the compressive y. yanya, frattura ed integrità strutturale, 46 (2018) 343-351; doi: 10.3221/igf-esis.46.31 348 strength of rc100d was about 35.4% higher than that of rc100, indicating that grading adjustment could optimize the strength of pervious concrete. grading adjustment could improve the stacking density and decrease the crushing value, which could improve the compressive strength and reduce dispersion. c o m pr es si v e st re n g th / m p a figure 3: compressive strength of the recycled pervious concrete. 0 20 40 60 80 100 0 2 4 6 8 10 replacement rate/% rc0 rc30 rc50 rc100d rc100 figure 4: the diagram of the relationship between different replacement rate and compressive strength. the compressive strength was considered in an exponential relationship with the porosity, and the compressive strength decreased with the increase of the porosity [17]. the relationship between the porosity and compressive strength found in this study was basically consistent with previous studies (fig. 5 and 6). but rpc100 with the largest porosity, surprisingly, had the highest compressive strength. the compressive strength of porous pervious concrete is usually determined by the occlusion friction of coarse aggregate and the bounding strength between aggregate and cement mortar. the rough surface of rpc100 increased the occlusion friction between aggregate, and moreover the thickness of cement mortar between aggregate increased. c o m p re ss iv e st re n g th / m p a figure 5: porosity and compressive strength. y. yanya, frattura ed integrità strutturale, 46 (2018) 343-351; doi: 10.3221/igf-esis.46.31 349 porosity/% 14 15 16 17 18 19 2120 0 2 4 6 8 10 c o m p re ss iv e st re n g th /m p a rc100d rc30 rc50 rc0 rc100 figure 6: the diagram of the relationship between the porosity of the pervious concrete and compressive strength. the relationship between the compressive strength and splitting tensile strength of the pervious concrete is shown in fig. 7. the results demonstrated that the splitting tensile strength improved with the increase of the compressive strength. 513.01)(265.0 cst ff  748.02 r figure 7: compressive strength and splitting tensile strength conclusions he recycled aggregate was obtained by mechanically crushing and artificially screening the waste prefabricated concrete components in this study, and moreover it was tested and analyzed to explore the effects of the mixing amount of recycled aggregate on the strength and permeability performance of pervious concrete. the main conclusions are as follows. the water absorption of the recycled coarse aggregate was 13 times that of the natural aggregate, and its 10-min water absorption could be 90% of the recycled coarse aggregate in the saturated water absorption state. the apparent and stacking density of the recycled coarse aggregate was 95.5% and 81.2% that of the natural aggregate and the crushing value of the former was 2 times that of the latter. considering the high water absorption of the recycled coarse aggregate, added water whose amount was equal to the 10min water absorption of the recycled coarse aggregate was used to avoid region with low water cement ratio. the strength and water permeability of the recycled pervious concrete satisfied the regulations. the test results were superior to the pervious concrete prepared using natural aggregate in the same proportion. therefore it is feasible to prepare pervious concrete using recycled aggregate in the aspect of performance. the blending ratio of the recycled coarse aggregate was in no obvious relation with the porosity changes of the pervious concrete. the porosity was the largest when the replacement rate was 100%, but the permeability coefficient increased with the porosity. moreover the addition of double grain grade aggregate improved the compressive strength of the recycled pervious concrete and decreased the porosity and water permeability. t y. yanya, frattura ed integrità strutturale, 46 (2018) 343-351; doi: 10.3221/igf-esis.46.31 350 when the replacement rate of the recycled coarse aggregate was 30%, the compressive strength of the pervious concrete was the largest, 6.71 mpa; when the replacement rate became higher than 30%, the compressive strength stopped increasing. the splitting tensile strength was in a positive correlation with the compressive strength; the splitting tensile strength increased with the increase of the compressive strength. but the compressive strength was in a negative correlation with the porosity; the compressive strength decreased with the increase of the porosity. references [1] chen, z.p., zhou, c.h. and chen, y.l. (2014), mechanical property and strain-stress constitutive relationship of recycled pebble aggregate concrete, j. basic sci. engin., 22(4), pp. 763-774. [2] fan, j., chen, z.p. and chen, y.l. (2015), analysis of influencing factors on compression strength and bending strength of recycled aggregate wall materials, j basic sci engin, 23(6), pp. 1210-1220. [3] li, h. and zhai, b.h. (2015). policy research on promoting recycling construction waste in china, urban dev res, 22(3), pp. 119-124. [4] sun, j.k., ou, x.j., ma, h.p. (2016). research on the improvement of construction waste recovery process, environ. engin., 34(12), pp. 103-107. [5] silva, r.v., brito, j.d. and dhir, r.k. (2015). the influence of the use of recycled aggregates on the compressive strength of concrete:a review, eur j environ civ en, 19(7), pp. 825-849. [6] akbarnezhad, a., ong, k.c.g. and zhang, m.h. (2011). microwave-assisted beneficiation of recycled concrete aggregates, constr. build. mater., 25(8), pp. 3469-3479. [7] brito, j.d., ferreira, j. and pacheco, j. (2016). structural, material, mechanical and durability properties and behaviour of recycled aggregates concrete, j. build. engin., 6, pp. 1-16. [8] zhang, y.m., qin, h.g. and sun, w. (2002). preliminary study on mix proportion design of recycled concrete, china concrete cement prod, (1), pp. 7-9. [9] andreu, g. and miren, e. (2014). experimental analysis of properties of high performance recycled aggregate concrete, constr build mater, 52(2), pp. 227-235. [10] zhang, s.t., jia, x.y. and song, z. (2016). mix proportion design of sand free recycled pervious concrete, china concrete cement prod, (12), pp. 6-12. [11] chen, s.l., yang, q. and liu, q.c. (2017). experimental on the strength and permeability of recycled aggregate pervious concrete, trans chin so agricult eng., 33(15), pp. 141-146. [12] guneyisi, e., gesoglu, m. and kareem, q. (2016). effect of different substitution of natural aggregate by recycled aggregate on performance characteristics of pervious concrete, mater. struct., 49(1), pp. 521-536. [13] zaetang, y., sata, v. and wongsa, a. (2016). properties of pervious concrete containing recycled concrete block aggregate and recycled concrete aggregate, constr. build. mater., 111, pp. 15-21. [14] barnhouse, p.w. and srubar, w.v. (2016). material characterization and hydraulic conductivity modeling of macroporous recycled-aggregate pervious concrete, constr. build. mater., 110(02), pp. 89-97. [15] yang, x.g., hao, y.c. and xue, y. (2012). study on the basic properties of recycled aggregates, concrete, (2), pp. 6668. [16] zhang, x.c., yin, j. and chi, y. (2010). summary of performance for pervious concrete, concrete, 12 , pp. 47-50. [17] sriravindrarajah, r., wang, n.d.h. and lai, j.w.e. (2012). mix design for pervious recycled aggregate concrete, int j concrete struct mater, 6(4), pp. 239-246. [18] bhutta, m.a.r., hasanah, n. and farhayu, n. (2013). properties of porous concrete from waste crushed concrete (recycled aggregate), constr. build. mater., 47, pp. 1243-1248. [19] xu, y.z. and shi, j.g. (2006). analyses and evaluation of the behaviour of recycled aggregate and recycled concrete. concrete, (7), pp. 41-46. [20] omary, s., ghorbel, e. and wardeh, g. (2016). relationships between recycled concrete aggregates characteristics and recycled aggregates concretes properties, constr. build mater., 108, pp. 163-174. [21] cai, h.y., zhang, m. and dang, l.b. (2012). experimental study on compressive strength of recycled aggregate concrete with different replacement ratios, appl mechan mater., (6), pp. 1277-1280. [22] yao, y.f., jin, b.h. and zhang, h.g. (2016). influence of replacement rate of recycled coarse aggregate on mechanical properties of recycled concrete, j guangxi univ (nat sci ed), 41(4), pp. 1187-1193. y. yanya, frattura ed integrità strutturale, 46 (2018) 343-351; doi: 10.3221/igf-esis.46.31 351 appendix rc0 a pervious concrete sample which is composed of single-sized aggregate and whose replacement rate of recycled aggregate is 0% rc30 a pervious concrete sample which is composed of single-sized aggregate and whose replacement rate of recycled aggregate is 30% rc50 a pervious concrete sample which is composed of single-sized aggregate and whose replacement rate of recycled aggregate is 50% rc100 a pervious concrete sample which is composed of single-sized aggregate and whose replacement rate of recycled aggregate is 100% rc100d a pervious concrete sample which is composed of double-sized aggregate and whose replacement rate of recycled aggregate is 100% porosity the ratio of the volume of open pores inside the pervious concrete to the volume of the pervious concrete permeability coefficient a parameter representing the permeability performance of concrete, which refers to the volume of water passing through pervious concrete per unit area in unit time. << /ascii85encodepages false /allowtransparency false /autopositionepsfiles true /autorotatepages /none /binding /left /calgrayprofile (dot gain 20%) /calrgbprofile (srgb iec61966-2.1) /calcmykprofile (u.s. web coated \050swop\051 v2) /srgbprofile (srgb iec61966-2.1) /cannotembedfontpolicy /error /compatibilitylevel 1.4 /compressobjects /tags /compresspages true /convertimagestoindexed true /passthroughjpegimages true /createjobticket false /defaultrenderingintent /default /detectblends true /detectcurves 0.0000 /colorconversionstrategy /cmyk /dothumbnails false /embedallfonts true /embedopentype false /parseiccprofilesincomments true /embedjoboptions true /dscreportinglevel 0 /emitdscwarnings false /endpage -1 /imagememory 1048576 /lockdistillerparams 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/hrv (za stvaranje adobe pdf dokumenata najpogodnijih za visokokvalitetni ispis prije tiskanja koristite ove postavke. stvoreni pdf dokumenti mogu se otvoriti acrobat i adobe reader 5.0 i kasnijim verzijama.) /hun 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can be opened with acrobat and adobe reader 5.0 and later.) >> /namespace [ (adobe) (common) (1.0) ] /othernamespaces [ << /asreaderspreads false /cropimagestoframes true /errorcontrol /warnandcontinue /flattenerignorespreadoverrides false /includeguidesgrids false /includenonprinting false /includeslug false /namespace [ (adobe) (indesign) (4.0) ] /omitplacedbitmaps false /omitplacedeps false /omitplacedpdf false /simulateoverprint /legacy >> << /addbleedmarks false /addcolorbars false /addcropmarks false /addpageinfo false /addregmarks false /convertcolors /converttocmyk /destinationprofilename () /destinationprofileselector /documentcmyk /downsample16bitimages true /flattenerpreset << /presetselector /mediumresolution >> /formelements false /generatestructure false /includebookmarks false /includehyperlinks false /includeinteractive false /includelayers false /includeprofiles false /multimediahandling /useobjectsettings /namespace [ (adobe) (creativesuite) (2.0) ] /pdfxoutputintentprofileselector /documentcmyk /preserveediting true /untaggedcmykhandling /leaveuntagged /untaggedrgbhandling /usedocumentprofile /usedocumentbleed false >> ] >> setdistillerparams << /hwresolution [2400 2400] /pagesize [612.000 792.000] >> setpagedevice microsoft word numero_50_art_52_2569 p. livieri et alii, frattura ed integrità strutturale, 50 (2019) 613-622; doi: 10.3221/igf-esis.50.52 613 stress intensity factor for small embedded cracks in weldments paolo livieri university of ferrara, department of engineering, italy paolo.livieri@unife.it fausto segala university of ferrara, department of mathematic, italy fausto.segala@unife.it abstract. in the present work, the stress intensity factor (sif) of embedded small cracks placed at the weld toe is calculated by means of two procedures based on the oore-burns integral. in the first approach, the defect is considered as a circular disk and the sif is evaluated by means of the ooreburns weight function. by taking advantage of a suitable change of variable, the singularity of the weight function on the crack border can be removed. in this way, the numerical evaluation of the sif is possible without the use of specific integration algorithms, although the nominal stress field becomes singular when the crack approaches a v-sharpe notch. as an example, the obtained equations are applied to a defect located in the neighbourhood of a weld toe with an opening angle of 135 degrees under mode i loading. subsequently, for a crack similar to a star domain with a border expressed by means of the fourier series, the sif is given by means of an explicit equation based on the oore-burns weight function. keywords. weight function; stress intensity factor; three-dimensional crack; weld. citation: livieri, p., segala, f., stress intensity factor for small embedded cracks in weldments, frattura ed integrità strutturale, 50 (2019) 613-622. received: 19.07.2019 accepted: 17.08.2019 published: 01.10.2019 copyright: © 2019 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. introduction he safety factors in the presence of a defect can be verified by the knowledge of the stress intensity factor (sif) evaluated for an elastic linear material [1]. as proposed by bueckner [2] and rice [3], the sif calculation can be performed by means of the weight function technique. the numerical analysis is reduced to an evaluation of an integral exactly over the region covered by the crack. this method can be applied both for two-dimensional models (crack as a line) or for three-dimensional problems (crack as a surface). in the literature for two-dimensional cracks, there are many formulations in closed form obtained with different methodologies [4]. however, for the three-dimensional cracks, the number of proposed solutions is poor (see, for example, bibliographical references [5–6]). in fact, in many cases the use of t http://www.gruppofrattura.it/va/50/2569.mp4 p. livieri et alii, frattura ed integrità strutturale, 50 (2019) 613-622; doi: 10.3221/igf-esis.50.52 614 simplifications in the form of a defect is common and it is comparable to relatively simple geometric shapes of which the solution is already known. usually, by simplifying, the defect is compared to an elliptical equivalent crack [7], while in order to simulate the propagation phase, the defect is continuously assimilated to a succession of ellipses [8–9]. the weight function introduced by oore-burns (ob) allows the value of the sif of three-dimensional cracks under mode i loading with a generic shape to be calculated [10]. although not exact, this weight function, for the three-dimensional case [11], is an excellent approximation that retains all the typical characteristics of the weighted functions in [12]. in particular, in the case of a semi-axial ellipse (1, b), when eccentricity e tends to zero, the main contribution of the oore-burns integral differs from irwin’s analytical solution [13] for an amount equal to 2 20 e  [14]. the advantage offered by the oore-burns integral is to use a generic shape of the defect and the evaluation of sif at each point of the creak contour without the need to consider the elliptical shape. unfortunately, the difficulties associated with the analytical calculation of the integral result in the user choosing a particular grid [12, 15]. the resolution strategy proposed in [15] is not always easy to reach the convergence condition. however, it should be emphasised that the oore-burns integral is recommended by asm standards in the case of isolated three-dimensional cracks to have an estimate of the sif value throughout the profile of a real crack. the designer is therefore motivated to find a solution in closed form for a rapid evaluation of the sif of a crack with generic form [16]. in this paper, we first summarise an analytical technique to get the oore-burns integral as an exact solution. then, for a circular crack, a simple general equation for the sif estimation is proposed and, as an example, it is used in the case of welded structures. finally, the oore-burns integral is very well approximated by means of an explicit form for an irregular crack shape similar to a star domain under uniform tensile loading. analytical background et  be an open bounded simply connected subset of the plane as in fig. 1. we define: 2 ( ) ( ) ds f q q p s    (1) where ( , )q q x y  , s is the arch-length parameter and the point p(s) runs over the boundary  . in their famous work in 1980, oore-burns proposed the following expression for the mode i stress intensity factor for a crack subjected to a nominal tensile loading σn(q) evaluated without the presence of the crack: 2 ( )2 ( ') , ' ( ) ' n i q k q d q f q q q        (2) under reasonable hypothesis on the function σn(q), the integral (2) is convergent and the proof is based on the asymptotic behaviour of f(q) [17]. figure 1: inner crack l p. livieri et alii, frattura ed integrità strutturale, 50 (2019) 613-622; doi: 10.3221/igf-esis.50.52 615 oore-burns on a circular crack et ω be a fixed set. we can reconstruct the ob integral along the front crack ( )  by its values along  by the equation ( , ', ) (1, '/ , )i n ik q k q     (3) where ( )n q   with 0  if we “read” the boundary point q’ in terms of an angle α that is, for example ω is star shaped with respect to the origin, (3) takes the simplest form ( , , ) (1, , )i n ik k      (4) in the particular case when ω is a disk of radius a centred at the origin of the plane ( , )x y , we denote by (x,y) the system in dimensionless coordinates x= x a and y= y a (see fig. 2). figure 2: reference circular crack by definition, for the unit disk ω’, by (1) and (2) it follows:    2 2 ,0 2 2 1 2 ( , ) ( , ) ( ) cos sin i x y a x y h x y k dx dy x y            (5) with ( , ) 1/ ( , )h x y f x y (6)    2 2 ( , ) cos sin d f x y x y           (7) by introducing the change of variables     0, , 0, / 2     (1 sin )cos cos sin cos cos (1 sin )sin x r r y r r                (8) where l p. livieri et alii, frattura ed integrità strutturale, 50 (2019) 613-622; doi: 10.3221/igf-esis.50.52 616 22sin sinr   (9) by some simple calculations 4 sin sin cosdx dy r d d     (10) 21 2sinr r    (11) by using eqn. (8–11), we have the following expression for the stress intensity factors on the unitary disk 2 ,0 4 ( ) ( , ) sin cosik x y d d          (12) where the integral is computed on the “longitude”  0,  and the “latitude”  0, / 2  . moreover, the pressure σ(x,y) is “read” in the new coordinates (, φ) for any fixed α, in the sense that x and y are given by (8), with r being defined by (9). if the crack has a radius equal to a the stress intensity factor becomes 2 ,0 4 ( ) ( , ) sin cosi a k x y d d          (13) when  1  , from (13) we obtain the well-known result: ,0 2 ( ) 1.12837i a k a    (14) we may test the efficiency of eqn. (13) by comparison with the special cases of nominal stress distribution considered in the literature [18]. furthermore, many other new examples have been obtained in reference [19] by changing the shape of the nominal stress σ. sif for an irregular crack shape like a star domain or a crack like a star domain as reported in fig. 3, the oore-burns integral can be evaluated without a particular numerical procedure. the oore-burns integral will be approximated by means of riemann sums. let us use the cartesian reference system x,y, q’ is a point of coordinate (r,α) on  . now we consider a new orthogonal reference system u,v with origin in q’ with n tangent to  (see fig. 3). a mesh of size δ on  can be considered, where δ divides the length of  . qjk of coordinate (kδ, jδ) in the u,v plain, and also qjk = rδ(cos(jδ), sin(jδ)). pm in fig. 3 is a point of coordinate mδ with respect to the initial point po. the riemann sums ki(δ, q’) is given by: ( )2 ( , ') jk ij i q a k q k      (15) where   1 2 2 ij jk ma q p    (16) the sum (15) is made on 2 0 1, jkm q       . f p. livieri et alii, frattura ed integrità strutturale, 50 (2019) 613-622; doi: 10.3221/igf-esis.50.52 617 figure 3: mesh for riemann sums in a previous work [20], we showed that the stress intensity factor can be expressed in the following form: ( ') ( , ') ( ') ( )i ik q k q q c o      (17) where 3 2 2 2 2 1 3 3 2 c j i                 (18) with 0 sini d    , 1 0 j th d   and 1 2       is the well-known riemann function evaluated in 0.5 (c=0.930). if we know the polar equation of the crack border ( )r  , it is convenient to discretise the angle  instead of the arc length s. now we consider: 2 2( ) ( ) ' ( )r r     (19) the coefficients (16) assume the form 1 2 2 ( )jk jk mb q p m        (20) where pm is the point of the contour corresponding to m  . the coefficient c is then replaced by: 3 2 2 0.889 0.038 ( ) cos ( ) d              (21) where α indicates the position of q’ for a given origin on the crack border. the condition q  can be given in terms of a fourier series as a function of ( )r r  , so that:   0 ( ) cos sinr rr a r b r      (22) p. livieri et alii, frattura ed integrità strutturale, 50 (2019) 613-622; doi: 10.3221/igf-esis.50.52 618 by setting 2 2x y   , w x i y  , q  is equivalent to:  0 1 1 re imr rr rra a w b w      (23) for example, if ( ) 1 cosr a   with 1 0 2 a  , the condition q  becomes 2 0a x    (24) finally, the equation for sif assessments can be rewritten as: ( ') ( , ') ( ') ( )i ik q k q q d o      (25) with ( )2 ( , ') jk ij i q b k q k      (26) (for more details see reference [21]). numerical example n order to verify the accuracy of the proposed procedure, now we analyse two reference cases: the first is a circular defect at the weld toe, the second is an irregular crack under uniform tensile loading. fig. 4 shows a welded t-joint under tensile nominal stress. in fig. 4, a disc is put at the weld toe of the welded t-joint and the stress intensity factor is evaluated by considering the asymptotic stress field as reported in [22–23]. the crack lies along the bisector at variable distance d from the weld corner. the t-joint is subjected to a tensile nominal stress, but along the bisector of the weld corner the hoop stress assumes the simple form: 326.0399.0  rkn (27) where kn is the notch stress intensity factors of mode i and it is equal to 2.46 mpa mm0.326 for a nominal tensile stress σn of 1 mpa. this value was calculated by means of a careful notch stress analysis by considering the t-joints of fig. 5 as threedimensional components without taking into account the effects of the width as analysed in [24]. figure 4: welded t-joint under tensile loading. i p. livieri et alii, frattura ed integrità strutturale, 50 (2019) 613-622; doi: 10.3221/igf-esis.50.52 619 figure 5: circular crack at the weld toe of fig. 4. tab. 1 shows the comparison on the stress intensity factor prediction by means of eqn. (13) and the results obtained with fe analysis. an accurate mesh is considered and the strand of the principal stress along the crack direction is shown in fig. 6. the dimensions of smaller elements at the tip of the crack were in the order of 10-5 mm. fig. 7, as an example, shows the mesh used for point c. the difference between the analytical and numerical results is less than 7%. so that, from an engineering point of view, the simple eqn. (13) can be used for sif assessments of a small defect in the neighbourhood of the weld toe as made in references [8–9] for semi-circular cracks. if the crack has an irregular shape not approximable to a disc, eqn. (25) can be used. in order to estimate the fatigue limit for small cracks or defects under a uniform tensile stress, murakami and endo [25–27] proposed 4 area as an empirical parameter to estimate the maximum sif value of a convex-shaped crack. on the basis of numerous numerical analyses, murakami and nemat-nasser proposed a synthesis relation for the maximum value of the sif of superficial cracks in the form: ,maxik y area  , where y is a dimensionless factor that assumes the value of 0.629 for lateral cracks [25]. in the case of internal cracks, the value of y is approximated to 0.5 [25]. figure 6: principal stress σ1 along the bisector for point a of fig. 4 (a=0.1 mm; d=0.15 mm, opening angle 2α=135°). p. livieri et alii, frattura ed integrità strutturale, 50 (2019) 613-622; doi: 10.3221/igf-esis.50.52 620 figure 7: example of mesh used in the numerical fe analysis for the evaluation of sif for point c (the dimensions of smaller elements at the tip of the crack were in the order of 10-5 mma=0.3 mm, d=0.4 mm). a d a i n k  eqn. (13) c i n k  eqn. (13) a i n k  fe c i n k  fe [mm] [mm] [mm0.5] [mm0.5] [mm0.5] [mm0.5] 0.3 0.4 1.088 0.795 1.166 0.816 0.1 0.15 0.818 0.583 0.858 0.611 0.1 0.3 0.566 0.488 0.608 0.524 table 1: stress intensity factor at points a and c of fig. 5 for a nominal tensile loading σn (opening angle 135°). x y   0 30 60 90 120 150 180 210 240 270 300 330 1 0.5 0 [deg] figure 8: defects (maximum diameter 0.42 mm) figure 9: defect in dimensionless form obtained by dividing the radius by half the value of the maximum diameter. as an example, the calculation procedure described in the previous section is used to calculate the form factor y, which refers to a small defect detected inside a metallic material. fig. 8 reports an irregular defect of a maximum diameter equal to p. livieri et alii, frattura ed integrità strutturale, 50 (2019) 613-622; doi: 10.3221/igf-esis.50.52 621 0.42 mm. the dimensionless shape of the defects is reported in fig. 9, where the half maximum diameter is considered in the dimensionless operation. the numerical results are shown in fig. 10. the symbols represent the numerical values obtained by means of eqn. (25), whereas the continuous line is the sif calculated by considering the defect of fig. 8 as a first order deviation of a circle (see reference [28] for details). in this case after the reading of the border in the fourier series, the stress intensity factors are given as a sum of harmonic terms weighed by numerical coefficients derived from the oore-burns integral in a similar way to that obtained in references [29–30]. figure 10: sif of the crack of fig. 8 under uniform tensile loading σn. (a is half maximum diameter). conclusions he calculation of the stress intensity factor (sif) of small circular defects located at the weld toe is possible without the use of specific numerical procedures despite the singularity of the stress field when the distance from the notch tip becomes zero. if the defects do not have a circular form, by taking advantage of the oore-burns weight function, a procedure is developed for cracks similar to a star domain. in this way, a more precise evaluation of the sif is possible and the shape factor of non-convex defects should be estimated. the influence of mode ii will be take into account in the future. references [1] webster, s., bannister, a. (2000). structural integrity assessment procedure for europe – of the sintap programme overview, engineering fracture mechanics, 67(1), pp. 481–514. [2] bueckner, h.f. (1970). a novel principle for the computation of stress intensity factors, zamm 50, pp. 529–546. [3] rice, j.r. (1989). weight function theory for three-dimensional elastic crack analysis. astm stp1020, wei r.p. and gangloff r.p., eds. philadelphia, american society for testing and materials, pp. 29–57. [4] fett, t., munz, d. (1997). stress intensity factors and weight functions, computational mechanics publications. [5] mastrojannis, e.n., keer, l.m., mura, t. (1979). stress intensity factor for a plane crack under normal pressure, international journal of fracture, 15 (3), 247–258. [6] wen, p.h., aliabadi, m.h., rooke, d.p. (1998). mixed-mode weight functions in three-dimensional fracture mechanics: static, engineering fracture mechanics 59(5), pp 563–575. [7] hobbacher, a. (1995). recommendation on fatigue of welded components, iiw document xiii-153995/xv-845-95. [8] gurney, t.r. (1991). the fatigue strength of transverse fillet welded joints. abington publishing, abington, cambridge [9] maddox, s.j. (1987). the effect of plaste thickness on the fatigue strength of fillet welded joints. abington publishing, abington, cambridge. [10] livieri, p., segala, f. (2012). evaluation of stress intensity factors from elliptical notches under mixed mode loadings. engineering fracture mechanics, 81, pp. 110–119 t p. livieri et alii, frattura ed integrità strutturale, 50 (2019) 613-622; doi: 10.3221/igf-esis.50.52 622 [11] oore, m., burns, d.j., (1980). estimation of stress intensity factors for embedded irregular cracks subjected to arbitrary normal stress fields. journal of pressure vessel technology asme, 102, pp. 202–211. [12] livieri, p., segala, f. (2010). an analysis of three-dimensional planar embedded cracks subjected to uniform tensile stress, engineering fracture mechanics, volume 77, 2010, pages 1656-1664. [13] beghini, m., bertini, l., vitale, e. (1991). a numerical approach for determining weight functions in fracture mechanics. international journal for numerical methods in engineering, 32, pp. 395–607. [14] irwin, g.r., (1962). crack-extension force for a part-through crack in a plate. asme, journal of applied mechanics, pp. 651–654. [15] livieri, p., segala, f. and ascenzi, o. (2005). analytic evaluation of the difference between oore–burns and irwin stress intensity factor for elliptical cracks. acta mechanica, 176, pp. 95–105. [16] desjardins, j.l., burns, d.j., thompson j.c., (1991). a weight function technique for estimating stress intensity factors for cracks in high pressure, journal of pressure vessel technology, asme, 113, pp. 10–21. [17] asm handbook, (1996). fatigue and fracture. vol 19, asm international. [18] livieri, p., segala, s. (2016). stress intensity factors for embedded elliptical cracks in cylindrical and spherical vessels theoretical and applied fracture mechanics 86(1), pp. 260-266. [19] ascenzi, o., pareschi, l., segala, f. (2002). a precise computation of stress intensity factor on the front of a convex planar crack. international journal for numerical methods in engineering 54, pp. 241–261. [20] tada, h., paris, c.p., irwin, g.r. (2000). the stress analysis of cracks handbook. third edition, asme press. [21] livieri, p., segala, f. (2015). new weight functions and second order approximation of the oore-burns integral for elliptical cracks subject to arbitrary normal stress field, eng. fract. mech. 138, pp. 100–117. [22] livieri, p., segala, f. (2014). sharp evaluation of the oore-burns integral for cracks subjected to arbitrary normal stress field, fatigue & fracture of engineering materials & structures 37, pp. 95–106. [23] livieri, p., segala, f. (2018). an approximation in closed form for the integral of oore–burns for cracks similar to a star domain. fatigue fract eng mater struct, 41, pp. 3–19. [24] lazzarin, p., tovo, r. (1998). a notch intensity approach to the stress analysis of welds. fatigue and fracture of engineering materials and structures 21, pp. 1089–1104. [25] livieri, p., tovo, r. (2009). the use of the jv parameter in welded joints: stress analysis and fatigue assessment. international journal of fatigue, 31(1), pp. 153–163. [26] livieri, p., tovo, r. (2017). analysis of the thickness effect in thin steel welded structures under uniaxial fatigue loading. international journal of fatigue, 101(2), pp. 363–370. [27] murakami, y., endo, m. (1983a). quantitative evaluation of fatigue strength of metal containing various small defects or cracks. engineering fracture mechanics, 17 (1), pp. 1–15. [28] murakami, y., nemat-nasser, s. (1983b). growth and stability of interacting surface flaws of arbitrary shape. engineering fracture mechanics, 17 (3), pp. 193–210. [29] murakami, y, (2002). metal fatigue: effects of small defects and non-metallic inclusions, elsevier [30] livieri, p., segala, f. (2010). first order oore–burns integral for nearly circular cracks under uniform tensile loading. international journal of solids and structures. 47(9), pp. 1167–1176. [31] gao, h., rice, j.r. (1987). somewhat circular tensile cracks. international journal of fracture 33, pp. 155–174 [32] rice, j.r. (1985). first order variation in elastic fields due to variation in location of a planar crack front. asme journal of applied mechanics 52, pp. 571–579. << /ascii85encodepages false /allowtransparency false /autopositionepsfiles true /autorotatepages /none /binding /left /calgrayprofile (dot gain 20%) /calrgbprofile (srgb iec61966-2.1) /calcmykprofile (u.s. web coated \050swop\051 v2) /srgbprofile (srgb iec61966-2.1) /cannotembedfontpolicy /error /compatibilitylevel 1.4 /compressobjects /tags /compresspages true /convertimagestoindexed true /passthroughjpegimages true /createjobticket false /defaultrenderingintent /default /detectblends true /detectcurves 0.0000 /colorconversionstrategy /cmyk /dothumbnails false /embedallfonts true /embedopentype false /parseiccprofilesincomments true /embedjoboptions true /dscreportinglevel 0 /emitdscwarnings false /endpage -1 /imagememory 1048576 /lockdistillerparams false /maxsubsetpct 100 /optimize true /opm 1 /parsedsccomments true 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can be opened with acrobat and adobe reader 5.0 and later.) >> /namespace [ (adobe) (common) (1.0) ] /othernamespaces [ << /asreaderspreads false /cropimagestoframes true /errorcontrol /warnandcontinue /flattenerignorespreadoverrides false /includeguidesgrids false /includenonprinting false /includeslug false /namespace [ (adobe) (indesign) (4.0) ] /omitplacedbitmaps false /omitplacedeps false /omitplacedpdf false /simulateoverprint /legacy >> << /addbleedmarks false /addcolorbars false /addcropmarks false /addpageinfo false /addregmarks false /convertcolors /converttocmyk /destinationprofilename () /destinationprofileselector /documentcmyk /downsample16bitimages true /flattenerpreset << /presetselector /mediumresolution >> /formelements false /generatestructure false /includebookmarks false /includehyperlinks false /includeinteractive false /includelayers false /includeprofiles false /multimediahandling /useobjectsettings /namespace [ (adobe) (creativesuite) (2.0) ] /pdfxoutputintentprofileselector /documentcmyk /preserveediting true /untaggedcmykhandling /leaveuntagged /untaggedrgbhandling /usedocumentprofile /usedocumentbleed false >> ] >> setdistillerparams << /hwresolution [2400 2400] /pagesize [612.000 792.000] >> setpagedevice microsoft word numero_30_art_23 s. seitl et alii, frattura ed integrità strutturale, 30 (2014) 174-181; doi: 10.3221/igf-esis.30.23 174 focussed on: fracture and structural integrity related issues wedge splitting test method: quantification of influence of glued marble plates by two-parameter fracture mechanics s. seitl academy of sciences of the czech republic, v. v. i., institute of physics of materials, brno, czech republic and brno university of technology, faculty of civil engineering, institute of structural mechanics, brno, czech republic seitl@ipm.cz b. nieto garcía academy of sciences of the czech republic, v. v. i., institute of physics of materials, brno, czech republic and university of oviedo, department of construction and manufacturing engineering campus de viesques, gijón, spain uo209943@uniovi.es i. merta university of technology vienna, faculty of civil engineering, institute of building construction and technology, vienna, austria ildiko.merta@tuwien.ac.at abstract. in the present paper, the well-known wedge splitting test (wst) is applied on specimens with different geometries (s= 150, 200, 300 mm) and variants of the specimens’ configurations. k-calibration (b1) and t-stress (b2) calibration curves for such specimens are introduced. the objective was to compare and discuss the values of the calibration curves dependent on the specimen’s geometries and on three different specimens' configurations: homogenous specimen; specimen with marble plates forming the groove for load application and specimen with glued marble plates. keywords. wedge splitting test; stress intensity factor, t-stress; k-calibration curves; concrete fracture test. introduction he wedge splitting test (wst) is nowadays a popular test for measuring fracture properties of materials like concrete [7, 17, 18, 24]. the wst was developed by linsbauer and tschegg [22] and patented by tschegg in 1986 [30]. a modified wst with different wedge equipment was published by bruhwiler and wittmann in 1990 [5]. it is a very stable test for determining the fracture energy of concrete. the specimens used are very compact and require small amounts of material compared to the notched beams employed in three-point bending tests (3pbt). however, the implementation of this type of test requires more sophisticated tools than the 3pbt and the number of experimental results available in the literature obtained using the wst of concrete is very limited. calibration curves for the wst are not as widely reported. stress intensity factors (sif, k-factor) for particular variants of the wst (cube-shaped specimens) can be found in the literature, e.g. guinea et al. [10]. k and t-stress calibration curves for foam concrete with marble plates forming the rectangular groove on the upper side of wst specimens are presented in [29]. multi-parameter t s. seitl et alii, frattura ed integrità strutturale, 30 (2014) 174-181; doi: 10.3221/igf-esis.30.23 175 description of stress and displacement fields by means of the williams power series using also higher-order terms for homogenous specimens can be found in malíková and veselý [23]. coefficients of this series are determined via the overdeterministic method from the results of conventional finite element (fe) analysis. the lattice modeling of wst can be found in frantík et al. [9]. in the wst for the assembly of the load transmission pieces and of the wedge, a rectangular groove is needed on the upper side of the specimens. there are generally three ways (with their advantages and disadvantages) for preparation of the rectangular groove. according to the literature, the most traditional way is to cut this part out of the specimens with a diamond saw; see e.g. [7, 30]. however, this is a very time consuming and demanding procedure. another method is to form the groove in the specimens by placing a rectangular bar into the standard cube moulds when casting the specimens. in the paper by korte et al. [17, 18], the bar was attached to the side of the mould in order to obtain a plain top surface of the groove. the authors kim and kim used the 10-mm groove to insert the triagonal prism at each outer side. here, the initial notch was made by inserting a steel plate into the specimens during the casting and the plate was taken out after one day. the use of special moulds to produce notch and grooves in mortar samples has been widely reported [28]. however, this method is generally applicable for concretes with small aggregate size. when working with concretes of larger aggregate size the bars placed into the mould during the casting could have a significant influence on the distribution of the particles in the matrix resulting in non-realistic results of the experiments. the most convenient and easiest way to obtain the rectangular groove is to form it by gluing two marble plates on the upper side of the specimens, see [24]. first, a thin layer of the specimens should be cut off the top in order to obtain a completely plane surface and then the starter notch should be cut. the marble plates are then glued to the specimens with two-component glue. in this paper the parametrical study of the wst within the framework of two-parameter fracture mechanics is applied for the case where the rectangular groove on the upper side of the specimens was formed by gluing two marble pieces thereon and for the case where the rectangular groove was obtained by cutting it out from the specimens. the stress intensity factor calibration curves and the t-stress calibration curves are determined and compared among three variants of the wst configuration: i) homogenous specimen, ii) specimen where the rectangular groove is formed by two marble plates without glue (see fig. 1a) and iii) specimen with a glue layer between marble plates and concrete (see fig. 1b). note that in composite structures and materials, the weakest part is often the interface between different materials. note also that the fracture mechanics parameters of materials are important data for numerical calculation during the structural design [13,14,26,27] a) b) figure 1: wedge splitting specimen: a) photo and b) sketch: where the rectangular groove is formed by two marble plates glued on the upper side of the specimen. theoretical background ccording to the two-parameter fracture mechanics approach which uses t-stress as a constraint parameter [1,2,29,32], the stress field around the crack-tip of a two-dimensional crack embedded in an isotropic linear elastic body subjected to normal mode i loading conditions is given by the following expressions by williams [31]: a s. seitl et alii, frattura ed integrità strutturale, 30 (2014) 174-181; doi: 10.3221/igf-esis.30.23 176 i xx i yy i xy 3 cos 1 sin sin ( ) 2 2 22 3 cos 1 sin sin ( ) 2 2 22 3 cos sin cos ( ) 2 2 22 k t a r k b r k c r                                                                             (1) where r and θ are the polar coordinates and x and y are the cartesian coordinates, both with their origins at the crack tip. ki is the stress intensity factor for mode i and t is the t-stress. thus, in two-parameter based fracture mechanics, the stress field is expressed by means of these two parameters, the stress intensity factor ki and the t-stress (see e.g. [2]). according to leevers and radon [20] the sif and the t-stress may be normalized for the testing geometries in question to be dimensionless as follows: i 1 0 k b k  , where sp0 p k t w  (2) and 2 i t a b k   (3) where psp is the horizontal component of the loading (the splitting force), t is the specimen thickness, w is the fundamental specimen dimension (specimen size) and a represents the crack length. input material parameters n order to obtain the relevant calibration curves, a literature overview [4] of materials properties was conducted. the range of real materials properties are summarized in tab. 1. on the basis of this data the theoretically possible intervals of properties (young’s modulus and poisson’s ratio) for particular materials were selected as follow: the values of marble are e  <10; 100> gpa and  = 0.3, the values of epoxy in layer are e = 5 gpa and  = 0.4, the values of concrete are e  <1; 100> gpa and  = 0.2 and for steel parts the traditional values are used e = 210 gpa and  = 0.3. materials/elastic materials property young’s modulus [gpa] poisson ratio [1] marble in [8] georgia marble tennessee marble russian marble 23.442.1 53.176.5 9.020.7 marble in [16] 91.7 marble in [11] 0.2-0.3 epoxy inlayer in [6] 15 0.350.43 concrete in [3] 30.633.22 0.180.21 foam concrete [12] 18 high performance self-compacting concrete in [33] 3050 high performance concrete in [25] 5862 0.020.2 lightweight concrete in [19] 10.3935.92 0.2 ultra high performance concrete [15] 5075 ultra high performance concrete in [21] 95100 table 1: information of selected material properties. i s. seitl et alii, frattura ed integrità strutturale, 30 (2014) 174-181; doi: 10.3221/igf-esis.30.23 177 numerical simulation or numerical calculations of both boundary conditions the characteristic dimension, 150 mm (marked in the text as w), was used, see fig. 1. the values of forces during the numerical simulation are follow in splitting direction (axe y) is psp = 1000 n and the vertical load (axe x) is pv = 535.89 n according the equation: 1 2 v spp p k (4) where 2 tan 1 tan w c c w k        (5) the symbol w represents the angle of the wedge (w=15°, according to [24]) and c refers to friction in the roller bearings. note that the influence of friction was studied in [29] and is not the subject of this study. the selected numerical model with boundary conditions is shown in fig 2. the interfaces between materials were modeled as ideal adhesion (for both materials the same displacement and deformation values in transition nodes were used). the initiation notch length was modeled as a crack (i.e. of zero width). the material input data for the concrete, marble and glue layer used in the numerical simulation are mentioned in paragraph input material parameters. the stress intensity factor k and the t-stress values were computed using the direct method [32] and after that normalized according eqs. (2) and (3). figure 2: numerical model of wedge splitting specimens with boundary conditions, symmetrical half. f s. seitl et alii, frattura ed integrità strutturale, 30 (2014) 174-181; doi: 10.3221/igf-esis.30.23 178 results and discussion he numerically calculated values of the normalized sif (i.e. b1) and t-stress (i.e. b2) are plotted in figs. 3 and 4, respectively. in the present paper, two issues of the specimens’ shapes/arrangements on the calibration curves were investigated: i) the influence of the material inhomogenity of specimens, i.e. the homogeneous variant, the variant with marble parts and ii) the variant with marble parts glued by epoxy and change of length s = 150, 200 and 300 mm. the change of the wst specimen lengths in fig. 3 the dependencies of b1 as a function of ratio  has been plotted. the dependencies show practically the same trends, the functions of calibration curve for s = 150, 200 and 300 mm can be introduced as follows: 1(150) 11928 30294 30425 15149 81 4 462 24.573b                    (6) 1( 200) 11940 30409 30644 15319 3951 447.98 24.97b                  (7) 1(300) 11947 30414 30626 15295 942.7 4.77.98 24.889b                  (8) all three studied cases, except for length s, are for the rest of geometrical aspects similar and so similar values of the normalized stress intensity factor b1 were expected. this fact is obvious especially for long cracks ( > 0.6), where the influence of the length on the stress state around the crack tip can be supposed to vanish. figure 3: the values of normalized stress intensity factor b1 for three cases of homogeneous concrete specimens of lengths s =150, 200, 300 mm. the normalized t-stress values expressed in fig. 4 as the b2() functions vary from negative values for very short cracks to positive values for relative crack lengths larger than approximately 0.15 in all studied cases. 2 (150) 8.7758 20.471 56.862 43.872 20.216 7.9127 0.7082b                  (9) 2 ( 200) 49.463 101.89 70.194 6.3491 14.923 7.4399 0.6945b                  (10) 2 (300) 83.718 200.77 172.51 50.561 7.8443 6.9177 0.6806b                  (11) values of b2 (α) for all three geometries tend to be equal for very long cracks only (0.85). influence of material inhomogeneity in this study, the influence of the wst specimen composition on the near-crack tip stress field fracture parameters was investigated (wst specimen is made from: i) concrete, ii) concrete and marble iii) concrete, marble and epoxy). according to the paragraph input materials parameters, the various combinations of materials properties for selected part of wst were used. t s. seitl et alii, frattura ed integrità strutturale, 30 (2014) 174-181; doi: 10.3221/igf-esis.30.23 179 the b1 and b2 as a function of  has practically the same values for all cases, see fig. 5a and 5b, and the same calibration curve can be used for all three cases. this means that neither the use of marble parts nor the epoxy layer has an influence on the calibration curve. figure 4: the values of normalized stress intensity factor b2 for three cases of homogeneous concrete specimens of lengths s =150, 200, 300 mm (a) (b) figure 5: the values of normalized stress intensity factor b1 and t-stress b2 for w = 150 mm for three cases: i) concrete (e = 40 gpa), ii) concrete (e = 1 gpa) with marble parts (e = 100 gpa) and iii) concrete (e = 100 gpa) with marble parts (e = 10 gpa) glued by epoxy (e = 5 gpa). for quantification of the error caused by the various kinds of material the graphs of maximal deviation between the homogeneous specimen and with marble and epoxy part are plotted in fig. 6. in fig. 6, these show the maximal percentual difference for 0.3  α  0.8. the error is smaller than 1.5 % and it is possible to neglect it in the evaluation of fracture parameters (fracture energy, etc….). therefore, the polynomial approximations dependence on the length of specimen for both b1 and b2 can be used. (a) (b) figure 6: the maximal percentual difference for various wst specimen compositions: a) for biaxial parameter b1 and b) for biaxial parameter b2. s. seitl et alii, frattura ed integrità strutturale, 30 (2014) 174-181; doi: 10.3221/igf-esis.30.23 180 conclusions finite element analysis of the wedge splitting test on specimens modified by replacement of the load transmitting parts with a stiffer material was performed by means of a constraint-based two parameter fracture mechanics approach. the study focused on two aspects:  investigation of the influence of the length of the wst specimens (150, 200 and 300 mm)  investigation of the influence of the specimens’ inhomogeneity (different concrete, different marble, epoxy layer and steel) the principal conclusions derived from this work are the following:  the influence of the specimens’ length on the calibration curves values is not negligible and for each case a different polynomial function has to be used, see fig. and eq. (6-11).  the influence of the specimens’ inhomogeneity on the calibration curves’ values is negligible and the same polynomial function covers all cases, see fig. 5 and the possible mistake/deviation of results are smaller than 1.5 %. acknowledgements he investigation reported in this paper was supported by grants no. 7amb1 4at012, cz. 107/2.3.00/20.0197 and fast-s-14-2532. references [1] aliha, m.r.m., ayatollahi, m.r., two-parameter fracture analysis of scb rock specimen under mixed mode loading, engineering fracture mechanics, 103 (2013) 115–123. [2] anderson, t. l., fracture mechanics: fundamentals and applications. new york, crc press llc, (1995) 688. [3] bahr, o., schaumann, p., bollen, b., bracke, j. young’s modulus and poisson’s ratio of concrete at high temperatures: experimental investigations, materials and design, 45 (2013) 421–429. [4] boresi, a. p., schmidt, r. j., sidebottom, o. m. advanced mechanics of materials, wiley, (1993). [5] bruhwiler e., wittmann fh. the wedge splitting test: a new method of performing stable fracture mechanics tests, eng fract mech, 35 (1990) 117–125. [6] cease, h., derwent, p.f., diehl, h.t., fast, j., finley, d., measurement of mechanical properties of three epoxy adhesives at cryogenic temperatures for ccd construction, fermilab/tm/2366 a, (2006) 1–9. [7] cifuentes, h., karihaloo, b., determination of size/independent specific fracture energy of normaland highstrength self/compacting concrete from wedge splitting tests, construction and buildings materials, 48(2013) 548–553. [8] exadaktylos, g.e., vardoulakis, i., kourkoulis, s.k. influence of nonlinearity and double elasticity on flexure of rock beamsi. technical theory, international journal of solids and structures, 38 (2001) 4091–4117. [9] frantík, p., veselý, v., keršner, z. parallelization of lattice modelling for estimation of fracture process zone extent in cementitious composites, advances in engineering software, 60-61 (2013) 48–57. [10] guinea, g.v., elices, m., planas j. stress intensity factors for wedge-splitting geometry, int j fracture, 81 (1996) 113– 124 [11] http://www.engineeringtoolbox.com/poissons-ratio-d_1224.html. [12] jones, m.r., mccarthy, a., preliminary views on the potential of foamed concrete as a structural material, mag concr res, 57 (2005) 21–31. [13] katzer, j., domski, j., optimization of fibre reinforcement for waste aggregate cement composite, construction and building materials, 38 (2013) 790–795. [14] kim j., kim y., fatigue crack growth of high-strength concrete in wedge-splitting test, cement and concrete research, 29 (1999) 705–712. [15] kimbauer, j., vacuum mixing of ultra high performance concrete, doctoral thesis, vienna university of technology, faculty of civil engineering, (2013). a t s. seitl et alii, frattura ed integrità strutturale, 30 (2014) 174-181; doi: 10.3221/igf-esis.30.23 181 [16] koca, m.y., ozden, g., yavuz, a.b., kincal, c., onargan, t., kucuk, k., changes in the engineering properties of marble in fire-exposed columns, international journal of rock mechanics & mining sciences, 43 (2006) 520–530. [17] korte, s., boel, v., de corte, w., de schutter, g., static and fatigue fracture mechanics properties of selfcompacting concrete using three-point bending tests and wedge-splitting tests, construction and buildings materials, 57 (2014) 1–8. [18] korte, s., boel, v., de corte, w., de schutter, g., vibrated concrete vs. self-compacting concrete: comparison of fracture mechanics properties, key engineering materials, 601 (2014) 199–202. [19] kurugöl, s., tanacan, l., ersoy, h.y., young’s modulus of fiber-reinforced and polymer-modified lightweight concrete composites, construction and building materials, 22 (2008) 1019–1028. [20] leevers, p.s. radon, j.c. inherent stress biaxiality in various fracture specimen geometries, international journal of fracture, 19 (1983) 311–325. [21] leutbecher, t., rissbildung und zugtragverhalten von mit stabstahl und fasern bewehrtem ultrahochfesten beton (uhpc). kassel: kastel university press, (2008). [22] linsbauer h.n., tschegg, e.k., fracture energy determination of concrete with cube-shaped specimens, zement und beton, 31 (1986) 38–40. [23] malíková, l., veselý, v., the influence of higher order terms of williams series on a more accurate description of stress fields around the crack tip, fatigue and fracture of engineering materials and structure, (2014). doi: 10.1111/ffe.12221 [24] merta, i., tschegg, e.k., fracture energy of natural fibre reinforced concrete, construction and building materials, 40 (2013) 991–997 [25] persson, b., poisson’s ratio of high-performance concrete, cement and concrete research, 29(1999) 1647–1653. [26] pryl, d., červenka, j., pukl, r., material model for finite element modelling of fatigue crack growth in concrete. procedia engineering, 2 (2010) 203–212. [27] pryl, d., mikolaskova, j., pukl, r., modeling fatigue damage of concrete, key engineering materials, 577–578 (2014) 385–388. [28] ribeiro, s., de campos ribeiro, d., de souza dias, m.b., ribeiro garcia, g.c., bento dos santos, é.m., study of the fracture behavior of mortar and concretes with crushed rock or pebble aggregates, mat. res. são carlos, 14(1) (2011). [29] seitl, s., veselý, v., řoutil, l. two-parameter fracture mechanical analysis of a near-crack-tip stress field in wedge splitting test specimens, computers and structures, 89 (2001) 1852–1858. [30] tschegg, e., republik österreich. patent number 390328b, (1986). [31] williams, m.l., on the stress distribution at the base of a stationary crack, j appl mech, 24 (1957) 109–14. [32] yang, b., ravi-chandar, k., evaluation of elastic t-stress by the stress difference method, engineering fracture mechanics, 64 (1999) 589–605. [33] yurtdas, i., burlion, n., shao, j.f. li, a. evolution of the mechanical behaviour of a high performance selfcompacting concrete under drying, cement & concrete composites, 33(2011) 380–388. microsoft word numero_34_art_61 r. citarella et alii, frattura ed integrità strutturale, 34 (2015) 554-563; doi: 10.3221/igf-esis.34.61 554 robust design of a polygonal shaft-hub coupling r. citarella, m. perrella department of industrial engineering, university of salerno, via giovanni paolo ii 132, fisciano (sa), italy rcitarella@unisa.it abstract. in this work, the taguchi method is applied for the optimal choice of design parameter values for a polygonal shaft-hub coupling. the objective is to maximize a performance function, minimizing, at the same time, its sensitivity to noises factors (robust design). the design of experiments (doe) is adopted to set up a plan of numerical experiments, whose different configurations are simulated using the boundary element method (bem). keywords. robust design; boundary element method; taguchi method; polygonal shaft-hub coupling. introduction n polygonal shaft-hub couplings, the torque transmission takes place thanks to normal and friction forces at the interface between the joined components. the common features of these couplings include: compact construction, self-alignment, absence of protruding elements that may cause high stress levels, efficient transmission of static-oscillating torques even with small dimensions, easy hub interchangeability (in case of failure) and, for polygonal shapes, such as those with 4 lobes, the possibility of displacement under load [1]. these types of couplings are highly competitive when compared to traditional ones that use keys, fasteners and splined shafts. nevertheless, the difficult workability (with steel requiring special grinding machines) and laborious calculation of the stresses, due to the lack of rotation symmetry, along with a tri-axial stress state, discouraged designers and constructors in the past, with them preferring traditional couplings over polygonal ones. the development of cnc grinding machines, the introduction of sintered materials (allowing for production by moulding), along with the improvement of hardware and software resources, making it possible to carry out accurate assessments for the dimensioning, circumvented those drawbacks, making the use of polygonal couplings very appealing. the first analysis of the biaxial stress and strain states in the shaft-hub was proposed by mechnik that used the finite element method (fem) [2], followed by many literature works up to recent time [3]. the numerical analysis of the coupling by fem greatly reduced the simplification of the coupling model, with the results becoming reliable, as highlighted by the comparison of the fem numerical results against the experimental ones obtained from optical methods [4] and against bem (boundary element method) numerical results [5]. mechnik’s study, along with those that followed [6-7], dealt with shaft-hub couplings with the most commonly used p3g normalized polygonal profiles. figure 1 shows a normalized profile with 3 lobes, whilst its parametric equation, defined in 1959 by filemon [8] and valid in general for profiles with n lobes is reported in eq. (1), where the parameters dm and e are, respectively, the diameter and eccentricity of the profile. i r. citarella et alii, frattura ed integrità strutturale, 34 (2015) 554-563; doi: 10.3221/igf-esis.34.61 555 figure 1: polygonal profile with n = 3 lobes         2 2 m m d x e cos n cos n e sin n sin d y e cos n sin n e sin n cos                               (1) in the preliminary stages of designing a new component, when many engineering solutions are considered, the use of fem makes it difficult to quickly update a model subject to continuous shape optimisation. in these cases, it can be very advantageous to use bem that performs the numerical study of a component by discretizing only the boundary, with the volume not being affected by the meshing operation and with a consequent reduction of “pre-processing” time. in addition, bem, contrary to fem, allows calculating traction and displacements at shaft-hub interface with the same accuracy (they are both primary variables). for this reason, it is highly suitable when studying problems with high surface stress gradients, such as contact problems. in this paper a multi-objective optimization problem of a polygonal shaft-hub interference fit is analysed using the taguchi method (robust design) [9-11], and the bem commercial code beasy [12]. bem contact stress analysis odelling of nonlinear contact [13] at shaft-hub interface takes place by means of special constraints (“normal gap”), defined between pair of nodes (node to node contact) belonging to overlapped elements at the interface area between the two zones (shaft and hub) in which the entire domain of the coupling is divided. enforcing these constraints causes the code to consider the interface elements between the shaft and hub as separate, although initially coincident in modelling. then a condition of interference or clearance is modelled, depending on the value, respectively negative or positive, attributed to the “normal gap”. the contact problems are nonlinear due to the variation of the contact area in dependence of the applied load. therefore, the stress state at the interface depends on the friction coefficient, the load, the geometry as well as the material and extension of the contact area. the nonlinear behaviour of the coupling was studied by means of an incremental-iterative procedure, which is useful when following the evolution of the contact as a result of the gradual application of the load, even in the presence of friction, which can be modelled in both static and dynamic terms [14]. it is worth highlighting the convenience of using an adequate number of regularly distributed (without circumferential “grading”) linear elements rather than a smaller number of elements with higher polynomial order, on the interface area where the algorithm operates the contact. such choice can improve the solution convergence and avoid “hot spots” occurrence (local irregularities at stress-deformational level in the numerical outcome). m r. citarella et alii, frattura ed integrità strutturale, 34 (2015) 554-563; doi: 10.3221/igf-esis.34.61 556 the nature of the external applied load (torsional) requires for the remaining part of the surfaces a discretization with quadratic elements. in the application that follows, an interference fit is assumed, with the global stresses resulting from the superposition of interference fit and torsional load. problem description he problem relates to the optimal choice of the following design parameters of the coupling: 1. p3g profile of the coupling in terms of the eccentricity of the lobes (e); 2. type of lubricant interposed between the coupling surfaces, influencing the design friction coefficient (f); 3. coupling tolerances. the objective is to minimize the effects of uncontrolled variability of the so called “noise factors” on the performance of the coupling while maximizing the performance parameters. a doe (design of experiments) approach was adopted, to define different configurations to be tested in the structural simulations, based on the use of so-called “orthogonal matrices”. these simulations allow evaluating the performance parameters of the product, with particular reference to: 1. shaft-hub reciprocal circumferential sliding after loading, since limiting such sliding considerably increases the fatigue life of the joint; 2. maximum radial deformation of the hub, since excessive values could, for example, create malfunctioning if the hub is part of a kinematic chain (an alternative parameter may be the maximum error of circularity); 3. stress peaks in the hub (normally more stressed than the shaft), which must be limited in order to reduce its size and consequently the overall dimensions of the joint; 4. press fit force, since reduced values facilitate a possible isothermal assembly; this force (fpress fit) is evaluated as: fpress fit = pm*a*f where pm is the pressure at interface, assumed to be independent from the friction coefficient ( f ) and a is the contact surface. it is also worth noting that the aforesaid mean pressure is just slightly influenced by the eccentricity value, depending substantially on the interference value. corresponding to the two profiles with e=2.05mm and e=3mm, the perimeters are respectively p1=201 mm and p2=207 mm. the identified performance parameters should be limited as much as possible in absolute value (lower is better) but above all in terms of sensitivity to the varying “environmental” conditions (noise factors), so as to be able to predict with a reduced margin of uncertainty, the value that they will assume under operational conditions. the noise factors, suitably simulated in each numerical analysis, are related to: • the precision of the machining, which manifests itself through an interference fit value that is variable within the chosen tolerance zone; • the variability of torque (torque peaks or overload in general); • the variability of the friction coefficient compared to the nominal design value. finally, a series of numerical experiments l4 (23) were carried out, based on three independent control variables and three noise factors, each with two possible levels. in order to quantify the variability of the torque and the friction coefficient, a normal distribution was assumed, centred at the respective nominal values and with a variation coefficient of nearly 7%. for the effective dimensions of shaft and hub the concept of “natural tolerance” was used, according to which the width of the tolerance zone is equal to 6and the mean value of the analysed dimension, which is also distributed according to a gaussian function, is at the centre of the tolerance zone. the adopted tolerance bands were it7 (30 m) for the hub and it6 (19 m) for the shaft and the corresponding standard deviations  were equal to 30/6=5 m and 19/6=3.17 m respectively. the normal distribution of the interferences (i) was obtained by composing the distributions of the size of the shaft (da) and hub (dm) as follows: i = da-dm  i = da-dm i2 = da2+dm2 = 25+10 = 35 m2 t r. citarella et alii, frattura ed integrità strutturale, 34 (2015) 554-563; doi: 10.3221/igf-esis.34.61 557 applying these formulas for the two considered couplings, the levels of the noise factors i1 and i2 were obtained, assuming that they are separated from each other by 2and are equidistant from the mean: 1. interference fit h7/n6 (imax=39 m; imin = -10 m; imed=i=14.5 m; i=5.9 m): i11= i+i=20.4 m; i12= i-i=8.6 m; 2. interference fit h7/p6 (imax=51 m; imin=2 m; imed=i=26.5 m; i=5.9 m): i21= i+i = 32.4 m; i22 = i-i=20.6 m. regarding the applied torque, a nominal value mt=1543 nm was assumed (the chosen value does not affect the generality of the results). the values used in the simulation, again equidistant from the average value and each other distant 2, were mt1=1651 nm and mt2=1442 nm, with corresponding tractions on the external hub surface (fig. 2) respectively equal to t1=4.28 n/mm2 and t2=3.74 n/mm2. for the static friction coefficient that, as a control factor, was tested on two nominal levels f1=0.2 and f2=0.1, the corresponding levels of the noise factors were obtained with a variation of +/7% from such nominal values: f11=0.214 and f12=0.187, f21=0.107 and f22=0.0934, respectively. together with the static friction coefficients, also the dynamic friction coefficients were provided as input to the analysis: the latter were assumed 20% lower than the static ones. with reference to the geometry of the coupling, two different polygonal shaft-hub joints with three lobes were analysed: the first with eccentricity e=2.05 mm and the second with e=3 mm. the trochoidal profile of the shaft was realised using the system pro/engineer (p.t.c.) [5] and imported into the calculation program through the iges exchange format. the be analysis was initially carried out both with reference to the 3d (fig. 2) and 2d models (fig. 3), but for the sake of simplicity, the numerical experiments were carried out with reference to the 2d model. under the action of a static torque, applied to the outer surface of the hub, the coupling exhibits a 120° cyclic symmetry; consequently, in order to reduce the computational effort, the analysis was carried out on just 1/3 of the entire model, imposing the boundary conditions of cyclic symmetry. one end of the shaft was assumed to be clamped whereas the torque mt was introduced on the hub by means of tangential forces. figure 2: 3d polygonal coupling with highlight of boundary conditions. the two models considered (a and b) had the following common dimensions (figs. 1, 4): hub external diameter dh=87 mm, diameter of the circle inscribed to the profile di=60 mm, hub length l2=32.5 mm. the differences between the two models were related to: r. citarella et alii, frattura ed integrità strutturale, 34 (2015) 554-563; doi: 10.3221/igf-esis.34.61 558  model a: ea = 2.05 mm, dm = 64.1 mm (fig. 1);  model b: eb = 3 mm, dm = 66 mm. figure 3: mesh and boundary conditions of the coupling for the plane strain problem (symbols in red are representative of normal gap). figure 4: 3-lobe polygonal coupling parametric dimensions. the shaft and hub were both made of steel (42crmo4) with a young’s modulus e=216000 nmm-2, poisson’s ratio =0.3 and yield strength s=800 nmm-2. the analysis was carried out under the hypothesis of isotropy, homogeneity and linear elasticity of the material. in fig. 5 a 2d example of the stress state induced by the combined action of the interference and torque is shown. design of experiments and analysis of the results he operating procedure requires the carrying out of several preliminary stages in order to design the experiments: identify the objective functions or performance parameters to be optimized; identify the control and noise factors and the related levels. this phase involves the definition of the orthogonal matrix, which identifies the combinations of the control and noise factors relating to each simulation. for the design of numerical simulations, an orthogonal type l4 (23) matrix was adopted t r. citarella et alii, frattura ed integrità strutturale, 34 (2015) 554-563; doi: 10.3221/igf-esis.34.61 559 for both the control and noise factors. this matrix is suitable for the cases in question, since, in addition to providing a variation on two levels as required, it provides a number of simulations equal to the degrees of freedom and therefore just sufficient to ensure the conditions at the base of a correct use of the taguchi method. figure 5: von mises stress (mpa) state induced by the combined action of interference and torque, with the highlight of circumferential reciprocal sliding. regarding the equivalent (von mises) stress peaks, it is worth considering the following: there is an optimal exploitation of the material when said peaks reache the maximum value allowed for the material in question, for which the problem is considered as “nominal the best”; the length of the hub can be chosen as calibration factor because useful in bringing the mean stress value to the target value after optimization, thanks to its characteristics (presumed but eventually verifiable) of not affecting the sensitivity of the coupling to considered noises. thus, in the choice of the optimum combination of the design parameters, it is possible to neglect the distance between the target value and the effective mean value in the quality function. only at the end the length of the hub is defined, upon which the stress peaks depend in an inversely proportional manner. figs. 6-10 show the effects of the control factors on the mean values and on the scatter of the performance parameters: with reference to the latter, each bar of the histogram is representative of the mean (fig. 10) or the signal/noise ratio (figs. 6-9), recalculated in decibels (db), when the control factor, indicated on the abscissa, assumes a given value. thus, the individual contributions of the control factors on the performance of the overall mean and s/n ratio are identified, assuming no interaction between the control factors. tabs. 1-4 present all the simulation results. figure 6: s/n ratio for the radial expansion of the hub upon varying the design parameters. r. citarella et alii, frattura ed integrità strutturale, 34 (2015) 554-563; doi: 10.3221/igf-esis.34.61 560 figure 7: s/n ratio for the von mises stress peaks in the hub upon varying the design parameters. figure 8: s/n ratio for the tangential shaft-hub displacements upon varying the design parameters. figure 9: s/n ratio for the shaft-hub press fit force upon varying the design parameters. r. citarella et alii, frattura ed integrità strutturale, 34 (2015) 554-563; doi: 10.3221/igf-esis.34.61 561 figure 10: mean values for the shaft-hub press fit force upon varying the design parameters. control factors (matrix l4) noise factors (matrix l4) average press fit force (n) s/n ratio ( =20log10() ) f e shaft tolerance grade i1 i1 i2 i2 f1 f2 f1 f2 t1 t2 t2 t1 0.2 2.1 n6 1419 1240 589 515 941 6.29e+00 0.2 3 p6 2215 1935 1484 1297 1733 1.23e+01 0.1 2.1 p6 1118 976 753 657 876 1.24e+01 0.1 3 n6 642 561 281 246 432 6.76e+00 table 1: average press fit force for an isothermal joint for each of the 16 tested configurations. control factors (matrix l4) noise factors (matrix l4) average equivalent stress value eq (n/mm2) s/n ratio ( =20log10() ) f e shaft tolerance grade i1 i1 i2 i2 f1 f2 f1 f2 t1 t2 t2 t1 0.2 2.05 n6 334 321 315 388 340 20.17 0.2 3 p6 552 543 417 477 497 17.93 0.1 2.05 p6 610 580 467 534 548 18.89 0.1 3 n6 550 500 405 480 484 18.10 table 2: von mises stress peaks for each of the 16 tested configurations and relative sensitivity to noises. r. citarella et alii, frattura ed integrità strutturale, 34 (2015) 554-563; doi: 10.3221/igf-esis.34.61 562 control factors (matrix l4) noise factors (matrix l4) average displacement (mm) s/n ratio ( =-10log10((yi2)/n )f e shaft tolerance grade i1 i1 i2 i2 f1 f2 f1 f2 t1 t2 t2 t1 0.2 2.05 n6 1.25e-01 1.15e-01 2.20e-01 3.00e-01 1.90e-01 1.38e+01 0.2 3 p6 8.10e-02 7.90e-02 7.90e-02 1.14e-01 8.83e-02 2.10e+01 0.1 2.05 p6 2.80e-01 2.52e-01 2.59e-01 3.30e-01 2.80e-01 1.10e+01 0.1 3 n6 1.78e-01 1.50e-01 1.90e-01 2.35e-01 1.88e-01 1.44e+01 table 3: maximum shaft-hub tangential displacements (mm) for each of the 16 tested configurations. control factors (matrix l4) noise factors (matrix l4) average hub radial expansion (mm) s/n ratio ( =-10log10((yi2)/n) )f e shaft tolerance grade i1 i1 i2 i2 f1 f2 f1 f2 t1 t2 t2 t1 0.2 2.05 n6 3.60e-02 3.27e-02 4.38e-02 5.53e-02 4.20e-02 2.74e+01 0.2 3 p6 4.47e-02 4.45e-02 3.47e-02 4.26e-02 4.16e-02 2.76e+01 0.1 2.05 p6 7.01e-02 6.55e-02 5.84e-02 7.00e-02 6.60e-02 2.36e+01 0.1 3 n6 5.70e-02 5.05e-02 5.06e-02 6.10e-02 5.48e-02 2.52e+01 table 4: maximum hub radial expansion for each of the 16 tested configurations. the identified optimal level assumes the following combination of the control factors: • = 0.2 since it has a beneficial effect on all the performance parameters with the exception of the press fit force, which increases the mean value; • e = 3 since, while slightly increasing the sensitivity of the stresses to the noises and the press fit force, it determines a beneficial effect on the relative displacements as well as on the radial expansion of the hub; • interference fit h7/n6 since it reduces the stress state (it is worth recalling that stresses due to interference fit cannot be reduced by increasing the hub length), making it less sensitive to noises, even if the relative circumferential slidings increase, determining together with the eccentricity choice, a good compromise at the stress-strain level. this reduces the radial deformation of the hub as well as the press fit force that is already reduced by previous choices. it is evident that if the priority of the designer were the fatigue life of the coupling rather than the static resistance, it would be better to choose the coupling h7/p6, which ensures a better tightening of the coupling, useful in preventing the phenomena of “fretting” (damage due to wear from relative motion under normal load). confirmation experiment to validate the procedure t this point, it is possible to verify if the hypothesis of no interaction between the control factors are satisfied. this is achieved by the so-called confirmation experiment that simulates the behaviour of the joint in the identified optimal configuration by simultaneously superimposing noises. the obtained numerical results are then compared with those determined analytically to check their correspondence. if not verified, the assumptions made should be reviewed, resulting in the possible existence of interactions between the control factors or an incorrect setting of the objective functions. the optimum configuration is not present among those already simulated, with it being necessary to a r. citarella et alii, frattura ed integrità strutturale, 34 (2015) 554-563; doi: 10.3221/igf-esis.34.61 563 carry out four additional simulations, corresponding to the four combinations of noise levels defined in the numerical plan. the performance parameters corresponding to the optimal configuration will come out from an average of the results obtained from the four simulations. the confirmation experiment provided a positive assessment. conclusions he adopted values of the control factors are varying in a small range since this analysis is part of a refinement that starts from a prior knowledge of the phenomenon and allows an a priori restriction of the domain in which to search for the optimum. this also explains the use of only two levels for the control and noise factors. the doe approach allows to analyse a limited number of design configurations of the coupling without penalising the information content available from e.g. an extensive plan of numerical simulations, provided that there are no interactions (as in this case) between the control factors that would invalidate the applicability of the superposition principle. bibliography [1] orlov, p., fundamentals of machine design, mir publishers moscow, 4 (1989) 69-73. [2] mechnik, r.p., beitrag zur festigkeitsberechnung von polygon-welle-nabe-verbindungen unter reiner torsion, konstruktion, 43 (1991). [3] strozzi, a., baldini, a., giacopini, m., bertocchi, e., bertocchi, l., achievement of a uniform contact pressure in a shaft-hub press-fit, proceedings of the institution of mechanical engineers, part c: journal of mechanical engineering science, 227(3) (2013) 405-419. [4] caputo, f., giudice, g., profili poligonali per trasmissione di coppie: analisi delle tensioni e verifica sperimentale, in: proceedings of the xii aias conference, sorrento, italy, (1984). [5] citarella, r., gerbino, s., be analysis of shaft-hub couplings with polygonal profiles, journal of materials processing technology, 109 (2001) 30-37. [6] kollmann, f.g., chr. göttlicher, entwicklung einer verbesserten festigkeitsberechnung für p3g-polygon-wellenabe-verbindungen beikombinierter biegeund torsionsbanspruchung, zwischenber, dfg-forsch. vorhaben ko 634/34-1, th-darmastadt, (1992). [7] beitz, w., reinholz, r., tragfähigkeit von p3g-welle-nabe-verbindungen, konstr., 46 (1994). [8] filemon, e., production and analysis of polygon profiles, periodica polytechnica m iii/1, budapest, (1959). [9] taguchi, g., on robust technology development, asme press, 1993 [10] phadke, m. s. quality engineering using robust design, prentice hall, englewood cliffs, nj, usa, (1989). [11] park, s. h., robust design and analysis for quality engineering, chapman & hall, 2-6 boundary row, london, (1996). [12] beasy v10r14, documentation, c.m. beasy ltd, (2011). [13] adey, r.a., niku, s.m., boundary element stress analysis involving contact using beasy, in: proc. boundary element conference, southampton, uk, (1999). [14] man, k.w., aliabadi, m.h., rooke, d.p., analysis of contact friction using the boundary element method, in computational methods in contact mechanics, m.h. aliabadi and c.a. brebbia, eds, computational mechanics publications, southampton, elsevier applied science, london, (1993) 1-60. t microsoft word numero_37_art_25 v. shlyannikov et alii, frattura ed integrità strutturale, 37 (2016) 193-199; doi: 10.3221/igf-esis.37.25 193 focussed on multiaxial fatigue and fracture a plastic stress intensity factor approach to turbine disk structural integrity assessment v. shlyannikov, a. zakharov, r. yarullin kazan scientific center of russian academy of sciences, russia shlyannikov@mail.ru, alex.zakharov88@mail.ru, yarullin_r@mail.ru abstract. this study based on a new fracture mechanics parameter is concerned with assessing the integrity of cracked steam turbine disk which operate under startup-shutdown cyclic loading conditions. damage accumulation and growth in service have occurred on the inner surface of slot fillet of key. in order to determine elastic-plastic fracture mechanics parameters full-size stress-strain state analysis of turbine disk was performed for a quote-elliptical part-through cracks under considering loading conditions. as a result distributions of elastic and plastic stress intensity factors along crack front in slot fillet of key of turbine disk depending on surface crack form are defined. an engineering approach to the prediction of carrying capacity of cracked turbine disk which is sensitive to the loading history at maintenance is proposed. the predictions of the rate of crack growth and residual lifetime of steam turbine disk are compared for elastic and elastic-plastic solutions. it is shown that the previously proposed elastic crack growth models provide overestimate the lifetime with respect to the present one. an advantage to use the plastic stress intensity factor to characterize the fracture resistance as the self-dependent unified parameter for a variety of turbine disk configurations rather than the magnitude of the elastic stress intensity factors alone is discussed. keywords. structural integrity; turbine disk; plastic stress intensity factor; quote-elliptical part-through crack. introduction n power steam turbine components there is the possible occurrence of undetected defects that can propagate at each startup-shutdown cycle, and sequence, damage accumulation and growth acceptance criteria have to be defined for the turbine critical zones. the successful lifetime prediction for power engineering turbines required application of fracture mechanics methodology with knowledge of loading history at operation, local stress/strain in concentration zones, static and fatigue material properties, the stress intensity factors for the appropriate crack geometry and crack growth rate characterization for the material. accumulated experience with respect to turbine discs and blades based on the deterministic and probabilistic approaches has shown [1-6] that advance in fracture technology proceeds best through mutual interaction between analysis and experimental observations. very few investigations devoted to the nonlinear fracture mechanics analysis exist which refer to structural integrity turbine disc assessment. the typical operation damages in such stress concentration zones are part-through thickness corner cracks. the most approaches to the corner crack growth prediction in the turbine disc under cyclic loading contains simplified models of stress-strain state in the nonlinear region at the crack tip. from this disadvantage is free a nonlinear stress intensity factors introduced by shlyannikov et al. [7-10] for the conditions of plasticity and creep-fatigue interaction. these studies have focused on the background for the characterization of static and cyclic fracture resistance i v. shlyannikov et alii, frattura ed integrità strutturale, 37 (2016) 193-199; doi: 10.3221/igf-esis.37.25 194 materials and structures using one unified parameter in the form of the plastic and creep sif’s, which take into account both in-plane and out-of-plane constraint effects at fracture. the present work provide an appropriate theoretical and numerical investigations based on the limited experimental data substantially assist fracture mechanics technology in application especially to part-through surface cracks fatigue life predictions for rotating components of power steam turbines. the paper also concentrates on the residual life assessment aspect in greater detail of nonlinear fracture mechanics using power steam turbine disc as a case study. subject for study and material properties otor in power steam turbine experience both cyclic and sustained centrifugal and thermal loads due to the nature of the rotor operating cycles. the methodology describing in the present study is applied to a 100 mw steam turbine rotor shown in fig.1a. the turbine disc is loaded, in general, by thermal and mechanical stresses because it is operated at c.a. 550ºc and 3000 rpm. subject for analysis is the disk of 22nd stage turbine rotor with central bore and through-thickness key (fig.1b). operation damage in the form of corner crack with length on the free surface a =12 mm and depth along shaft thickness b = 23mm was detected in the slot fillet of key in the disc of 22nd stage (fig.1c). this stage is operated at about 140°c therefore the influence of temperature is not take into account. for the lifetime calculations, the following operating data were assumed: total operation time is 236607 hours, number of starts is 204. the material of turbine disc is steel 34хн3ма which main mechanical properties are listed in tab. 1. a) b) c) figure 1: 100 mw steam turbine rotor and disk of 22nd stage with operation damage. material young modulus e, (mpa) poisson’s ratio  yield stress σ0, (mpa) ultimate stress σf, (mpa) strain hardening exponent n strain hardening coefficient α steel 34хн3ма 196363 0.3 790 992 7.49 2.39 table 1: main mechanical properties. elastic-plastic stress fields in turbine disk rior to lifetime predictions, a 3d fe model of the 22nd stage turbine disc section generated was available and used for the purpose of this study. as shown in fig.2, the turbine disc and blades, as well as the rivets incorporated in the orignal 3d model. the startup power conditions was chosen in stress analysis as it represents the most severe combination of temperature and rotor speed in the operation profile. due to the planting disc onto the turbine shaft with a tightness, on the inner surface of the disc bore occur radial stresses with the magnitude of 50mpa, which are also taken into account in the calculations. r p v. shlyannikov et alii, frattura ed integrità strutturale, 37 (2016) 193-199; doi: 10.3221/igf-esis.37.25 195 figure 2: equivalent stress distribution for turbine disk. figure 3: coordinate systems at slot fillet. from fig.4, it was observed that the peak stresses mainly occur on the surface of the slot fillets of key (web and disc bore). in order to compare the parameter distributions along slot fillet on the free surface of the disk as well as along the disc hub in the thickness direction (fig.4) is convenient to introduce the dimensionless coordinates in the following form:  dll 2 , tsb  where l and s are current coordinates, t is hub thickness equal 180 mm, d is slot depth equal 15 mm. in such representation of numerical results, we will use variables and changing in the range from 0 to 1. it should be noted, as it follows from fig.4, that the stresses on the free surface and in the slot along hub thickness are higher than the yield stress of steel 34хн3ма. 0.0 0.2 0.4 0.6 0.8 1.0 -0.3 0.0 0.3 0.6 0.9 1.2 =0, p=50mpa 0.0 0.2 0.4 0.6 0.8 1.0 0.4 0.6 0.8 1.0 1.2 =0.6, p=50mpa r=0 r=0.7mm r=1.6mm r=3mm figure 4: hoop stress distributions along fillet and hub. v. shlyannikov et alii, frattura ed integrità strutturale, 37 (2016) 193-199; doi: 10.3221/igf-esis.37.25 196 elastic-plastic stress intensity factors ull-field elastic-plastic fea are performed using ansys finite element (fe) code to determine the stress-strain parameter distributions along of the crack-front for turbine disc of considered configuration. the elastic stress intensity factor (sif) k1 distribution around the corner crack is calculated for each of front profile and the results superimposed according to the desired hoop stress distribution in the uncracked disc σуп defined by the polynomial in the following form                       1 1 2 3 4yn a a b k l f f f f b w t (1) where a is the crack length, b is the crack depth,  is the elliptical crack angle, w is the hub width. fig. 5 shows the dependencies of elastic sif on the crack sizes for turbine disc considered configuration for two main points of the crack front, i.e. the free surface of hub and the slot surface of key. the special kind of nonlinear calculations accounting for the plastic material properties were performed to determine plastic stress intensity factors pk for the same crack front profiles in turbine disc after corresponding loading history at operation                       1 1 22 1 0 n yn p n k a k i w (2) where in is the governing parameter of elastic-plastic stress-strain field at the crack tip. fig. 6 represents the plastic sif distributions along the initial and final crack front profiles in the turbine disc. these results of elastic and elastic-plastic numerical solutions for the sif were employed to residual fatigue life prediction of turbine disc with operation damages. figure 5: elastic sif versus crack size in depth and length direction. figure 6: plastic sif as a function of crack size and front profile. f v. shlyannikov et alii, frattura ed integrità strutturale, 37 (2016) 193-199; doi: 10.3221/igf-esis.37.25 197 structural integrity assessment pplication of the strain energy density (sed) function for analyzing fatigue fracture has been made in work [11]. to extend the response to unloading, reloading and cyclic loading, making use of the cyclic stress and strain curves, a critical state of elastic-plastic hysteresis loop can be written in terms of the strain energy density as            4 2 m f f f c dw n dv (3) substituting into the left part of formula (3) the total sed we have got                     2 1 4 2 myn f f fs n e where                      2 12 1 11 1 1 2 1 ne n n k a s a k n w i (4) the crack growth rate per cycle, da/dn, is given by                 1 2 2 * * 2 4 m n th th f f s sda a dn e (5) the above rate of crack propagation law contains the mechanical properties of the material, e, cyclic properties **, , n, the governing parameters of elastic-plastic stress-strain field in and a length parameter c associated with the fracture process zone size. more details to determine the sed functions s , ths , the in-factor and equivalent stress e ~ for cracked body different configurations are given by refs. [7-11]. we have paid our attention on the combined method including the numerical stress-strain distribution in the parts and components of power steam turbine by using finite element analyses and limited experimental data related to elasticplastic material properties under uniaxial tension. within the current investigation a fatigue life estimation approach (eq.5) based on the fea results and experimental data is applied to predict residual durability of power steam turbine disk with take into account of operating time. the fatigue crack growth analysis was performed under harmonic loading using the elastic and elastic-plastic sif's distributions along different crack front profiles. an initial circumferential edge crack at the highest elastic-plastic stress location was chosen to be 1.6 mm in the depth and length direction, which is much smaller than the observed crack size at operation. it is found that the crack growth in the depth direction is much faster than that in the length direction as it shown in figs. 7 and 8. also it should be noticed that the two ends of the crack tend to place in the radial direction and this is believed to be due to the influence of the hoop stress. figure 7: crack growth rate comparison for elastic and elastic-plastic solutions. a v. shlyannikov et alii, frattura ed integrità strutturale, 37 (2016) 193-199; doi: 10.3221/igf-esis.37.25 198 figure 8: crack growth rate as a function of plastic sif. figure 9: lifetime prediction based on elastic and elastic-plastic solutions. fig. 9 represents the comparison between the predicted change in crack length a on the free surface of disc and the crack depth b along the slot of key as a function of fatigue load cycles for both type of solutions. the elastic-plastic solution on based on the plastic sif's show that the crack would grow on the free surface from 1.6 mm to 10 mm and in the depth direction from 1.6 mm to 20 mm in about 1,300 cycles. at the same time the elastic solution using the elastic sif's gives overestimate the lifetime in about 1,700 cycles. as the predicted crack growth rate according to nonlinear fracture mechanics approach is much faster that elastic modeling, this indicates that the plastic material properties have a significant effect on the damage accumulation and growth in an critical zone of turbine disc. it should be pointed out that the elastic solution is not accounted for the stressstrain state redistributions at the plastic zone close to the crack tip. the implications due to this limitation may give nonconservative predictions of crack growth rate for this case as the actual stress and strain may be higher than predicted by elastic solution. as the purpose for analyzing the edge crack in the turbine disc considered at the operation was to estimate the crack growth rate under extreme situation, the residual fatigue life should be determined based on the elasticplastic solution. summary study on residual life assessment of disc with initial flaws in a power plant steam turbine was carried using fullsize 3d analyses and fatigue crack growth predictions. the predictions of the rate of crack growth and residual lifetime of steam turbine disk are compared for elastic and elastic-plastic solutions. it is shown that the previously proposed elastic crack growth models provide overestimate the lifetime with respect to the present one. an advantage to use the plastic stress intensity factor to characterize the fracture resistance as the self-dependent unified parameter for a variety of turbine disk configurations rather than the magnitude of the elastic stress intensity factors alone is shown. the methodology of the lifetime assessment of steam turbine components presented in this study has considerable practical importance. the approach described in the present work is implemented in practical engineering tools, and its usefulness was illustrated with an example of its practical application to a steam turbine rotor. a v. shlyannikov et alii, frattura ed integrità strutturale, 37 (2016) 193-199; doi: 10.3221/igf-esis.37.25 199 acknowledgment he authors gratefully acknowledge the financial support of the russian foundation for basic researches under the project 16-08-00744. references [1] shlyannikov, v.n., iltchenko, b.v., stepanov n.v., fracture analysis of turbine disks and computational– experimental background of the operational decisions, eng. failure analysis, 8 (2001) 461-475. [2] kim, h., crack evaluation of the fourth stage blade in a low-pressure steam turbine, eng. failure analysis, 18 (2011) 907-913. [3] nurbanasari, m., abdurrachim, c., crack of a first stage blade in a steam turbine, eng. failure analysis, 2 (2014) 5460. [4] shlyannikov, v.n., yarullin, r.r., zakharov, a.p., fatigue of steam turbine blades with damage on the leading edge, proc. mater. science, 3 (2014) 1792-1797. [5] walz, g., riesch-oppermann, h., probabilistic fracture mechanics assessment of flaws in turbine disks including quality assurance procedures, struct. safety, 28 (2006) 273-288. [6] hu, d., wang, r., fan, j., shen x., probabilistic damage tolerance analysis on turbine disk through experimental data, eng. fract. mech., 87 (2012) 73-82. [7] shlyannikov, v.n., tumanov, a.v., characterization of crack tip stress fields in test specimens using mode mixity parameters, int. j. fract., 185 (2014) 49-76. [8] shlyannikov, v.n., tumanov, a.v., zakharov a.p., fracture analysis of turbine disks and computational– experimental background of the operational decisions, theoret. appl. fract. mech., 73 (2014) 68-81. [9] shlyannikov, v.n., boychenko n.v., tumanov, a.v., fernandez-canteli a., the elastic and plastic constraint parameters for three-dimensional problems, eng. fract. mech., 127 (2014) 83–96. [10] shlyannikov, v.n., tumanov, a.v., boychenko, n.v., a creep stress intensity factor approach to creep–fatigue crack growth, eng. fract. mech., 142 (2015) 201–219. 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can be opened with acrobat and adobe reader 5.0 and later.) >> /namespace [ (adobe) (common) (1.0) ] /othernamespaces [ << /asreaderspreads false /cropimagestoframes true /errorcontrol /warnandcontinue /flattenerignorespreadoverrides false /includeguidesgrids false /includenonprinting false /includeslug false /namespace [ (adobe) (indesign) (4.0) ] /omitplacedbitmaps false /omitplacedeps false /omitplacedpdf false /simulateoverprint /legacy >> << /addbleedmarks false /addcolorbars false /addcropmarks false /addpageinfo false /addregmarks false /convertcolors /converttocmyk /destinationprofilename () /destinationprofileselector /documentcmyk /downsample16bitimages true /flattenerpreset << /presetselector /mediumresolution >> /formelements false /generatestructure false /includebookmarks false /includehyperlinks false /includeinteractive false /includelayers false /includeprofiles false /multimediahandling /useobjectsettings /namespace [ (adobe) (creativesuite) (2.0) ] /pdfxoutputintentprofileselector /documentcmyk /preserveediting true /untaggedcmykhandling /leaveuntagged /untaggedrgbhandling /usedocumentprofile /usedocumentbleed false >> ] >> setdistillerparams << /hwresolution [2400 2400] /pagesize [612.000 792.000] >> setpagedevice microsoft word risitano-fargione-guglielmino-igf_pulito a. risitano et alii, frattura ed integrità strutturale, 30 (2014) 201-210; doi: 10.3221/igf-esis.30.26 201 focussed on: fracture and structural integrity related issues definition of the linearity loss of the surface temperature in static tensile tests a. risitano, g. fargione university of catania, department of industrial engineering, viale andrea doria, 6 95125 catania (italy) arisitan@diim.unict.it, gfargion@diim.unict.it e. guglielmino università degli studi di messina, dipartimento di ingegneria elettronica, chimica e ingegneria, industriale, contrada di dio (s. agata), 98166 messina, (italy), eguglie@unime.it abstract. static tensile tests on material for mechanical constructions have pointed out the linearity loss of the surface temperature with the application of load. this phenomenon is due to the heat generation caused by the local microplasticizations which carry the material to deviate from its completely thermoelastic behavior,. the identification of the static load which determines the loss of linearity of the temperature under stress, becomes extremely important to define a first dynamic characterization of the material. the temperature variations that can be recorded during the static test are often very limited (a few tenths of degree for every 100 mpa in steels) and they require the use of special sensors able to measure very low temperature variations. the experience acquired in such analysis highlighted that, dealing with highly accurate sensors or with particular materials, the identification of the first linearity loss (often by eye) in the temperature curves, can be influenced by the sensibility of the investigator himself and can lead to incorrect estimates. the aim of this work is to validate the above mentioned observations on different steels, by applying the autocorrelation function to the data collected during the application of a static load. this, in order to make the results of the thermal analysis free from the sensitivity of the operator and to make the results as objective as possible, for defining the closest time of the linearity loss in the temperature-time function. keywords. termoelasticity; fatigue; autocorrelation function. introduction and aim of the work he research of more simple and faster methodologies for the determination of the fatigue limit or, generally, the data characterizing the dynamic behavior of the materials, has been the subject of continued interest [1-10]. from more than 30 years, the authors work on the methodologies based on the energy factors such as the heat development during the fatigue tests (risitano method) [11-15] in order to define the fatigue curves in a very short time compared to the traditional method (stair case); the results of this method (risitano method) have been then studied and t a. risitano et alii, frattura ed integrità strutturale, 30 (2014) 201-210; doi: 10.3221/igf-esis.30.26 202 analyzed by many other researchers [16-28] and now this method is quite normal in use. the analysis of the phenomenon of the heat development has highlighted that the material which is subjected to a dynamic stress higher than its fatigue limit, shows the irreversible phenomena already during the first cycle of application of the fatigue loads. for this reason, the authors checked the first loading ramp for the detection of the first micro heat source, index of irreversible deformed states. thus, it seemed almost natural to think about the application of all methods able to capture this phenomena during the static test, and in particular to rely on infrared thermal sensors for the surface temperature survey. since the first analyses of this type which date back to 1987, it has been noted that, using this approach, it was possible to determine the region (stress-strain) in which the material follows the laws of the thermoelasticity [38, 39]. the thermal analysis applied to various steels during the static tensile test [29-34], showed that it was possible to define the “fatigue limit” by analyzing the temperature of the hottest point of the specimen surface and determining the point where the slope changes, in the temperature vs. stress curve. on the basis of the first results, other researchers [35, 36] tested the procedure on other materials, different from the steels (composite materials). until now, the point in which the slope changes was determined by plotting, in the stress-temperature diagram, the first part with a constant slope (part perfectly thermoelastic) and identifying the point where the curve deviates from the linear behavior. this work has a double aim: it wants to confirm the procedure to detect the fatigue limit on different steels and it intends to make the measurement independent by the experience of those who adopt this kind of analysis. it is thought that an analysis of the physical phenomenon could be more appropriate than the analytical study of the function. therefore, it has been proposed the application of the correlation function to the temperature-time data detected during the static tensile tests. in order to define a future test protocol, the authors would try to define a process methodology based on a method independent from the performer of the tests. this work describes how to use the correlation function for the surface temperature data, collected during a simple static uniaxial tensile test, we can define the point at which the slope of the stress-temperature curve, changes and, therefore, can be estimated the value of the fatigue limit. it has been verified, in fact, that the value of the load, which influences the loss of linearity in the temperature-load (stress) function, corresponds to zero of the autocorrelation function relative to the values that have been detected by the sensors used for the test surface temperature during a static tensile test ig. 1 shows the qualitative trend of the result () of a static monoaxial tensile test for a steel plate specimen. the same diagram shows the evolution of the surface temperature measured on the specimen during the test. in the diagram, p indicates where the temperature trend is not linear. at this point, the stress value is completely different from the limit yield strength and the corresponding deformation will be zero if the sample is unloaded. the analysis of the surface temperature curve while varying the load (in red in the diagram) is perfectly linear up to point p then the slope changes when it is still far from the classic value of yield stress. from that point onwards, the slope of the curve varies continuously until the failure of the specimen. analyzing the specimen from a physical point of view, during a static tensile test at a constant load speed [n/s], it is possible to characterize the behavior of the first phase as due to the perfectly elastic relation between the change of temperature t and the stresses (lord kelvin’ law): δt = -kmt σm (1) where t is the absolute temperature, km is the thermoelastic constant of the material (for steels 123.3 10 [pa-1]) σm is the average stress applied to the specimen [39]. after this first phase, starting at the point p (second phase) until the break of the specimen, the change of slope is due to the heat developed for the irreversible deformations, which affect more and more volume of the sample until its failure for this area (starting from point p) the following law can be applied [31]: 2 3 0 3 p m a r r r m a r r e t t m k t t tt t k t t                      (2) where:  dvp is the rate at which the volume v is plastically deformed (dvp=v-ve); f a. risitano et alii, frattura ed integrità strutturale, 30 (2014) 201-210; doi: 10.3221/igf-esis.30.26 203  s is the original cross-sectional area of the specimen (s=a·b);  a is the specimen width;  b is the specimen thickness;  sl is the lateral parallepiped surface (sl2v/b for a  b);  l0 is the original length of the specimen;  δlp is the plastic elongation;  εp is the plastic strain (εp = δlp/l0);  kc is the thermal convection coefficient;  dte is the temperature increment of the elastic crystal as it encounters the ambient temperature;  dt is the temperature increment of the volume v as it encounters the ambient temperature;  m is the conversion coefficient; and,  ρ1 is the density after deformation. 00 0 t t     (3) 0 0 p r p c l t v l t     (4) c r r s v t  (5) where, r is the fracture stress of the specimen and rt is the time in which the plasticization phenomenon starts. in accordance with the laws of the fracture mechanics, it has been supposed the following law for the plasticization volume: 2 2p r v v t t  (6) 2 2 r v v v t t    (7) the transition point between the two phases is where the microscopic deformative irreversible phenomena start and they can be appreciated just referring to non-conventional parameters. the experience gained during the fatigue tests with the evaluation of the damage parameters based on the energy methods, shows that the fatigue rupture occurs (even at a very high number of cycles) when, at a microscopic level, irreversible deformations due to the presence of external or internal defects (inclusions, dislocations, etc.) appear. these deformations, by applying cyclic loads, cause micro-cracks that increase in size (with heat development) until to the complete rupture of the material. the static tensile test, assumed as the first loading ramp of a tensile fatigue stress, can give information about the beginning of the internal heat generated by the local irreversible plastic deformations. if repetitive loads (fatigue load) are applied to the specimen with the macroscopic maximum value of stress equal to that of the first plasticization, the specimen, after a certain number of cycles (high or very high), will break. based on these considerations and using not conventional and more general definition, for risitano a. the fatigue limit at high (or very high) number of cycles, is the macroscopic stress for which in a well-defined point (crystal) of the material (even at the microscopic level), microplasticizzations appear . for stress value above this (0 in fig. 1) and for different values of load ratio r, the specimen will break at different nr cycles (fig. 2). and more, for stress value less than 0 failures will never happen; on the contrary, for  over 0, failures will always occur. we can assume the cycles number nr for r= -1, as the limit number nr(lim) (equivalent to the conventional value 2·106) and consequently at this nr(lim) number, the failures, for different loads ratio r, will occur but only for stress values over the fatigue limit (before defined). starting from the above mentioned observations, it is possible to define the beginning of the local plasticization phenomena as the stress range for which the fatigue failure can appear. for this purpose, the authors have for a long time identified the external temperature (on the surface of the specimen) as a significant parameter (also because it is more easily detectable) able to provide indications on the deformation state (even microscopic) of stressed material. a. risitano et alii, frattura ed integrità strutturale, 30 (2014) 201-210; doi: 10.3221/igf-esis.30.26 204 measurement of the temperature during a tensile test and autocorrelation function s it is well known, the autocorrelaction function is widely used in the signal theory [40]. it provides a measurement of how a signal auto correlates itself, it means how much it has in common with itself delayed by a time. it also provides the desired signal cleaned from the noise. finally, it contains the information about the variations on the time axis. for temperature data recorded during static tensile test, the autocorrelation function has been applied, to make free from the subjective effect, the identification of the point where the temperature-strain function (of the hottest point on the specimen surface), loses the perfectly linear trend, i.e the totally elastic behavior. the analysis of the static tests carried out on the specimen in order to determine the start of the thermal increment, requires the continuous monitoring during the test of three parameters: applied load, surface temperature and time. practically, the test machine is set on a constant load speed (n/s) and the temperature on the entire surface of the specimen is detected . once the thermal images are acquired, the analysis is performed starting from the last images and going back by detecting the temperature of the specimen surface at the points of interest. with this approach, the temperature-time (strain) function of the chose point can be built. the analysis of this function, in accordance with the laws of thermoelasticity, points out that, from a given point, the temperature function loses its linearity, in other words the derivative function for two successive points t(t) e t(t+) is not constant but it varies with a certain continuity. since the collected temperature data are real, in order to locate the first point to this variation and make free the reading from the sensitivity of the operator, it is thought to refer to the autocorrelation function. this choice, based on the physical data, does not introduce factors that can have influence on the value to define . in certain cases, in fact, considering the the sensors accuracy and the presence of background noises, an estimation by tracing the straight line which fits the part perfectly elastic and taking the point p at which the temperature-time function leaves the linear behavior, can lead to values with errors of subjectivity which do not affect the validity of the methodology, strictly linked to the physical phenomenon, but can make the procedure less effective. for the use of the autocorrelation function, it is necessary to record a number of acquisitions of the temperature in the first part of the curve (up to the classic limit yield point) sufficiently high. the commercial systems allow the acquisition of 30 frames per second, enough for this kind of analysis. in this work it was adopted 1 frame/s static tests analysis tatic mono-axial tensile tests were performed on aisi 1045 (c45) specimens, for which the tab. 1 reports the chemical composition and the tab. 2 the physical and mechanical properties. the shape and the dimensions of the specimens are those shown in fig. 3 and fig. 4. in particular, were performed two (2) test for each specimen type (notched and not). all static tests were carried out with the testing machine instrong 8501 of 100 kn. c si mn p s cr ni mo % 0.43-0.50 0.40 0.60-0.90 0.035 0.035 0.40 0.40 0.10 table 1: chemical composition. during the whole test, the surface temperature of the specimens has been detected by the thermo camera flir sc7000 lwir. the data acquisition and the analysis of the (acquired) images have been made with the altair software. the tests have been always performed with a slew rate imposed and constant equal to 115 n/s. the surface temperature, relative to applied loads, was continually recorded. the number of the images acquired per second was equal to 1. they have allowed to build diagrams like those of fig. from 5 to 10 where on the x axis is reported the time while on the y axis is reported the applied load ( in light blue) and the temperature of the chosen surface point ( in yellow). since the aim of the work was also the validation of the analysis capacity through the use of the autocorrelation function, in order to avoid the edge effects on the temperature values , for the three types of specimens (smooth and notched), the temperature values were measured at the centre of the specimen (see fig. 11). the collected data are those reported in the above mentioned diagrams (fig. from 5 to 10). a s a. risitano et alii, frattura ed integrità strutturale, 30 (2014) 201-210; doi: 10.3221/igf-esis.30.26 205 density g/cm3 7.87 brinell hardness 163 ultimate stress [mpa] 810 yield stress [mpa] 725 young modulus [gpa] 210 poisson modulus 0.29 ultimate elongation % 16 resilience (izod) [j] 30 thermal conductivity [w/m*k] 51.9 specific heat [j/g*k] 0.502 coefficient of linear expansion [1e-06/k] 15.1 electrical resistivity [ohm*cm] 1.42e-05 table 2: physical and mechanical properties.     sorge specimens autocorrelation “eye estimated” aisi 1045-p1 smooth (12.5x5) 164.5 172.0 aisi 1045-p2 smooth (12.5x5) 168.9 170.0 aisi 1045-p3 notched (10.9x5) 183.2 175.0 aisi 1045-p4 notched (10.9x5) 275.1 225.0 aisi 1045-p5 notched (8.3x5) 264.7 250.0 aisi 1045-p6 notched (8.3x5) 212.6 195.0 table 3: values of the detected stresses referred to the 6 (p1-p6) specimens. figure 1: qualitative stress-strain () curve and temperature-strain (t-) curve of a static monoaxial traction test (indication of0). a. risitano et alii, frattura ed integrità strutturale, 30 (2014) 201-210; doi: 10.3221/igf-esis.30.26 206 figure 2: qualitative failure number cycles for different ratio load but equal max (max  0). figure 3: shape and the dimensions of the specimens. figure 4: photos of the three types of specimens (smooth, notched). a. risitano et alii, frattura ed integrità strutturale, 30 (2014) 201-210; doi: 10.3221/igf-esis.30.26 207 figure 5: stress-time (t) curve and temperature-time (t) curve for aisi 1045-p1 smooth (12.5x5). figure 6: stress-time (t) curve and temperature-time (t) curve for aisi 1045-p1 smooth (12.5x5). figure 7: stress-time (t) curve and temperature-time (t) curve for aisi 1045-p3 notched (10.9x5). figure 8: stress-time (t) curve and temperature-time (t) curve for aisi 1045-p4 notched (10.9x5). figure 9: stress-time (t) curve and temperature-time (t) curve for aisi 1045-p5 notched (8.3x5). figure 10: stress-time (t) curve and temperature-time (t) curve for aisi 1045-p6 notched (8.3x5). figure 11: spot position. a. risitano et alii, frattura ed integrità strutturale, 30 (2014) 201-210; doi: 10.3221/igf-esis.30.26 208 figures from 5 to 10 report the results of the static tests. in each test is shown the applied load and the temperature detected at the centre of the specimen as a function of the time. in each figure, in correspondence of the time for which the autocorrelation function was zero, it is shown (in red) the vertical line which allowed to date back to the corresponding stress at the point defined by the autocorrelation function. in the diagrams, were reported the lines "by eye" for identification of the change of slope of the temperature and at the intersection of them, it has been identified the corresponding value of the stress (estimated). as before said, the values of the detected stresses, referred to the 6 specimens, are reported in tab. 3. in this table the first column characterizes the type of specimen, the second column shows the value of the stress estimated "by eye" (eye estimated), the third column shows the values determined by means of the autocorrelation function. the examination of the results of the two columns shows the applicability of the correlation function to the measured temperature data. the differences of the stress values are, in fact, always limited and just in a case there was difference more than 15%. the values determined for the smooth specimens are very close to each other and they are close to those estimated "by eye". the mean value (166.5 n/mm2) for which changes the slope of the curve is very close to the fatigue limit ([171 n/mm2) found for the same steel by the thermographic fatigue method (risitano method) . it is in the range (170-190 n/mm2), found in literature [41, 42], for a aisi 1045 steel with similar mechanical characteristics and determined by traditional test. as before said, for the notched specimen the analysis was carried out in correspondence to the central point and for this reason the values reported in the table do not represent the fatigue limit, as it was for the smooth specimens, but they are the values and trends depending on the local stresses which, as it is known, during the elastic phase, are less than the mean stress. an analysis carried out close to the edges would determine a different value (lower) of the load for which the change of slope there would be, as it has already reported in [44]. even for the notched specimens, it has been noticed a good correspondence between the values estimated "by eye" and those found using the autocorrelation function. conclusions n order to determining the "fatigue limit" (minimum), it has been proposed the use of the autocorrelation function to evaluate the point of the linearity loss of the temperature-time function of a surface point of the specimen during the application of the load in tensile tests. smooth specimens and notched specimens (2 different notch) were tested. for homogeneity, for each kind of specimen, the analysis has been referred to the central point of the specimen. for each specimen the value of, the change of slope of the temperature function over the time (load), corresponding to the end of perfectly and totally elastic behavior, has been identified (by the graphs) with an estimation by eye and by the analysis of the data temperature by means of the autocorrelation function. the results have pointed out the validity of the application of the autocorrelation function to the temperature data. it allows ,in fact, to make the results free from the sensitivity of the operator (estimation by eye). for all the examined cases, the values estimated from the graphs and defined by the autocorrelation function were very close. the obtained results confirm what it has already verified by other authors and also for materials different from the steels. it has confirmed, once again, that the thermal analysis of data collected during the simple static tests allows to estimate with a good approximation the “fatigue limit” of the material. for the aisi 1045 steel the value defined by the tensile test coincides with the value found by other authors [41, 42] who have applied the traditional fatigue tests [43] to the aisi 1045 steel having mechanical properties very similar to the steel used in the present work. references [1] locati, l., an aid for the determination of fatigue limit in research and production, metall. ital., 27 (1935) 188-204. [2] locati, l,. fatigue and other tests with progressively increasing load, eng. dig., 20 (1959) 337-339. [3] foppel, o., diedämpfungsfägsfähikeiteinesbaustahlesbeiwechselbeanspruchungen.v.d.i.z., 70(39) (1926) 12911296. [4] prot, m., the determination of the fatigue limit by progressively increased loading, misure et control, 13 (1948) 301309. [5] prot, m., fatigue testing under progressive loading.wadctr, (1952) 53-148. [6] föppl, o., ludwik, p., stoffprüngegezueinerwirklichkeitsgetreuenfestgkeitsrechnung.v.d.i.z., 76 (1932) 683-685. [7] delorme, j. f., sinicki, g., gobin, p., calorimetric study of the energy dissipated from a solid subjected to fatigue cycles, j. phys. d: appl. phys., 1 (1968) 1737-1742. i a. risitano et alii, frattura ed integrità strutturale, 30 (2014) 201-210; doi: 10.3221/igf-esis.30.26 209 [8] dengel, d., harig, h., estimation of the fatigue limit by progressively-increasing load tests, fatigue fract. eng. m.,3 (1980) 113–128. [9] kaleta, j., blotny, r., harig, h., energy stored in a specimen under fatigue limit loading conditions, j. test eval., 19 (1990) 326–333. [10] catalbiano, t., geraci, a., orlando m., analysis of the fatigue strength of specimens by means of the infrared technique, il progettista industriale, 2 (1984). [11] geraci, a., la rosa, g., risitano, a., l’infrarosso termico nelle applicazioni meccaniche, ata ingegneria automotoristica, 38 (1985) 8-9. [12] curti, g., la rosa, g., orlando, m., risitano, a., analisi tramite infrarosso termico della “temperatura limite” in prove di fatica, in: proceedings xiv convegno nazionale aias, (1986) 211-220. [13] curti, g., geraci, a., risitano, a.. un nuovo metodo per la determinazione rapida del limite di fatica.ata ingegneriaautomotoristica, 10 (1989) 634-636. [14] la rosa, g., risitano, a., thermographic methodology for rapid determination of the fatigue limit of materials and mechanical components, int. j. fatigue, 22 (2000) 65–73. [15] fargione, g., geraci, a., la rosa, g., risitano, a., rapid determination of the fatigue curve by the thermographic method, int. j. fatigue, 24 (2002) 11–19. [16] luong, m. p., fatigue limit evaluation of metals using an infrared thermographic technique, mech. mater., 28 (1988) 155–163. [17] luong, m. p., infrared thermography of fatigue in metals, spie, 1682 (1988) 222-223. [18] luong, m. p., dang-van, k., metal fatigue limit using infrared thermography, in: proceedings fondazione g. ronchi, il (1993). [19] luong, m. p., infrared scanning of fatigue in metals, nucl. eng. des., 158 (1995) 363–376. [20] blarasin, a., fracchia, r., pozzati, m., rapid determination of the fatigue limit of materials and components by means of the infrared technique, ata – ingegneria automotoristica, 51 (1988) 255–265. [21] curà, f., curti, g., sesana, r., a new iteration method for the thermographic determination of fatigue limit in steels, int. j. fatigue, 27 (2005) 453–459. [22] amiri, m., khonsari, m.m., rapid determination of fatigue failure based on temperature evolution: fully reversed bending load, int. j. fatigue, 32 (2010) 382-389. [23] liakat, m., khonsari, m. m., rapid estimation of fatigue entropy and toughness in metals, materials and design, 62 (2014) 149-157 [24] fatemi, a., yang, l., cumulative fatigue damage and life prection theories: a survey of the state of the for homogeneus materials, int. j. fatigue, 20 (1998) 9-34. [25] feltner, c. e., morrow, j. d., microplastic strain hysteresis energy as a criterion for fatigue fracture, j. basic. eng., 83 (1961) 15–22. [26] walter, f., eifler, d., short-time procedure for the determination of wöehler and fatigue life curves using mechanical, thermal and electrical data, jsmme, 2 (2008) 507-518. [27] atzori, b., meneghetti, g., energy dissipation in low cycle fatigue of austempered ductile irons, in: proceedings 5th international conference on low cycle fatigue, (2003) 147–152. [28] meneghetti, g., analysis of the fatigue strength of a stainless steel based on the energy dissipation, int. j. fatigue, 29 (2007) 81-94. [29] geraci, a., la rosa, g., risitano, a., correlation between thermal variation in static test and elastic limit of material using infrared imagery, in: proceedings 7th international conference on mechanical behaviour of material (1995). [30] risitano, a., risitano, g., clienti, c., determination of fatigue limit by mono-axial tensile specimens using thermal analysis, key engineering materials, 452-453 (2011) 361-364. [31] risitano, a., risitano, g., determining fatigue limits with thermal analysis of static traction tests, fatigue fract. eng. m., 36 (2013) 631-639. [32] risitano, a., mechanical design, first ed., crc press, new york (2011). [33] clienti, c., fargione, g., la rosa, g., risitano, a., risitano, g., eng. fract. mech., 77 (2010) 2158-2167. [34] risitano, a., corallo, d., risitano, g., sirugo, a., determinazione del limite di fatica mediante prove quasi-statiche, in: proceedings xxxix convegno nazionale aias, (2010). [35] bagheri, z., el sawi, i., bougherara, h., zdero, r., biomechanical fatigue analysis of an advanced new carbon fiber/flax/epoxy plate for bone fracture repair using conventional fatigue tests and thermography, j. of the mechanical behavior of biomedical materials, 35 (2014) 27-38. a. risitano et alii, frattura ed integrità strutturale, 30 (2014) 201-210; doi: 10.3221/igf-esis.30.26 210 [36] colombo, c., vergani, l., burman, m., static and fatigue characterisation of new basalt fibre reinforced composites, compos. struct., 94 (2012) 1165-1174. [37] libonati, f., vergani, l., damage assessment of composite materials by means of thermographic analyses, compos. part. b-eng., 50 (2013) 82-90. [38] houwink, r., burgers, w. g., elasticity, plasticity and structure of matter, university press, cambrige (1954). [39] nowacki, w., thermoelasticity. pergamon press, oxford (1986). [40] luise, m., vitetta, g. m., teoria dei segnali, mcgraw hill (2002). [41] su, y.l., yao, s.h.,wei, c.s., kao, w.h., wu, c.t., influence of singleand multilayer tin films on the axial tension and fatigue performance of aisi 1045 steel, thin solid films, 338 (1999) 177–184. [42] di schino, a., kenny j. m., grain size dependence of the fatigue behaviour of a ultrafine-grained aisi 304 stainless steel, mater. lett., 57 (2003) 3182–3185 [43] astm e 466-72, standard practice for conducting constant amplitude axial test of metallic materials. [44] risitano, a., fargione g., experimental method for the determination of the under-stress first-plasticization process parameters, in: proceedings igf xxii, rome (italy), (2013). microsoft word numero_53_art_33_2796 a. desai et alii, frattura ed integrità strutturale, 53 (2020) 426-433; doi: 10.3221/igf-esis.53.33 426 glass/epoxy fiber orientation effects on translaminar fracture toughness under mixed mode(i/ii) load using fpb specimen abilash desai department of mechanical engineering, sdmcet, dharwad, karnataka, india abilashdesai@gmail.com c. m. sharanaprabhu department of mechanical engineering, pesitm, shivamogga, karnataka, india cmsharanaprabhu@rediffmail.com s. k. kudari department of mechanical engineering, cvr college of engineering, hyderabad, telangana, india s.kudari@rediffmail.com abstract. to study glass/epoxy fiber orientation effects on translaminar fracture toughness under mixed mode(i/ii) load using asymmetric four point bend specimen. fracture toughness values for different fiber-oriented glass/epoxy laminates under mixed modes are compared with unidirectional glass/epoxy laminates. specimens were fabricated using hand layup technique with (0/45)° and (0/90)° fiber oriented glass fiber. the experimental study was conducted for 6 crack positions varying from s/d=0(mode-ii) to 1(mode-1) with an increment of 0.2 for four point bend specimen. the specimens were tested under universal testing machine to obtain peak loads and further evaluate fracture toughness. the experimental test results show fracture toughness can be increased by orienting the fiber in the laminate. fracture toughness is highly dominating for (0/90)° fiber-oriented laminates compared to 0° and (0/45)° glass/epoxy laminates. keywords. asymmetric four point bend; stress intensity factor; mixed mode i/ii. citation: desai, a., sharanaprabhu, c.m. kudari, s.k., glass/epoxy fiber orientation effects on translaminar fracture toughness under mixed mode(i/ii) load using fpb specimen, frattura ed integrità strutturale, 53 (2020) 426-433. received: 22.04.2020 accepted: 25.05.2020 published: 01.07.2020 copyright: © 2020 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. introduction racture mechanics role in providing engineers and researchers with vital informations for designing and prediction of crack initiation and orientation with its propagation path under mixed-mode loading is desirable for life prediction of engineering materials [1,2]. major failure modes revealed that laminated composite undergoes interlaminar, intralaminar and translaminar fracture. for translaminar fracture, very limited research has been carried out. f https://youtu.be/mmcnpzernfy a. desai et alii, frattura ed integrità strutturale, 53 (2020) 426-433; doi: 10.3221/igf-esis.53.33 427 hence for glass/epoxy polymer composites used in aerospace application comes under failure by mixed mode loading under translaminar fracture. hence, experimental investigation is necessary for glass/epoxy composites under mixedmode loading. he and hutchinson [2] provided accurate results for the stress intensity factors for the asymmetric four point bend (fpb) specimen with an edge crack. a basic solution for an infinitely long specimen loaded by a constant shear force and a linear moment distribution provides the reference on which the finite geometry solution is based. this note was prompted by a comparison of existing numerical solutions for the crack specimen known as the asymmetric four point bend (fpb) specimen. the specimen has distinct advantages for mixed mode testing, including the determination of mixed mode fatigue crack thresholds [3]. reeder presented an investigation for mixed mode bending test which comprises both mode-i and mode-ii loading simultaneously using a mixed mode bending apparatus [4]. kenane showed delamination fatigue-crack growth experiments have been carried out on unidirectional glass/epoxy laminates using different mixed mode loadings [5]. sham prasad illustrated the interlaminar fracture toughness by mixed mode using mixed mode bending tests for polymer-matrix composites [6]. rikards showed interlaminar fracture toughness for glass fiber reinforced composite was found by testing for mode-i to mixed mode then to mode-ii by using a compact tension shear (cts) specimen and finding critical energy release rate [7]. laffan showed translaminar fracture toughness measurement can be done in fiber reinforced polymers [8]. swolfs [9] showed the importance of translaminar fracture toughness for penetration impact behavior of woven carbon/glass hybrid composites. experimental work was carried out on unidirectional glass/epoxy laminates using fpb specimen and fracture toughness was calculated in our previous work [10]. orientation of fiber in laminates is important parameter which will affect fracture toughness. comparing different fiber-oriented laminates was done for compact tension shear and mixed mode bending specimens by earlier researchers [11,12]. thus, in the present investigation an effort is made to study translaminar fracture toughness for various fiberoriented glass/epoxy laminates in a four point bend specimen. experimentation is done for (0/45)° and (0/90)° fiber oriented glass/epoxy laminates and is compared with 0° fiber oriented glass/epoxy laminates in terms of fracture toughness from earlier research[10]. experimentation materials lass-epoxy reinforced polymers are type of laminated composites, which are becoming increasingly popular for various structural applications in the aerospace, automotive and other industrial sectors. the present investigation has been carried out with epoxy resin (lapox l12) at a room temperature with a curing hardener (h6). all these polymer products were supplied by atul limited, polymer division (gujarat, india). the unidirectional glass fiber of 220 gsm having thickness 0.25 mm was supplied from marktech composites, bangalore, india. fabrication of composite the aim of the test is to determine the fracture toughness of glass/epoxy composite material with different fiber orientation. to prepare the specimens by hand layup method, 36 layers of glass fiber having 0.25mm thickness with 320 mm length and 190 mm width were put together with epoxy and hardener to form a block with dimension of 320*190*9 mm for fracture test. later specimen was cut with dimension of 130*18*9 mm. for (0/45)° laminate, alternate layers of 0° and 45° oriented fiber direction were arranged with same dimensions. fig. 1 (a) shows laminate obtained in (0/45)° manner. in the same manner to achieve (0/90)° laminate, alternate layers of 0° and 90° oriented fiber direction were arranged with same dimensions. fig. 1 (b) shows laminate obtained in (0/90)° manner. fracture test mixed mode (i/ii) fracture toughness test for glass-epoxy composite was carried out as per he and hutchinson [3]. mixed-mode (i/ii) fracture tests were conducted on fpb specimens with a thickness of 9 mm (b/w=0.5) for both (0/45)° and (0/90)° fiber oriented glass/epoxy laminates. the initial crack of 9mm (a/w=0.5) is carefully introduced in specimen using a saw cutter of thickness 0.5 mm. the loadings on the specimen used are similar to the one used in the earlier work [13]. fig. 2 illustrates the major dimensions of the samples used in the tests and fig. 3 shows mixed mode testing fixture for accommodating all the mixed mode distances for fpb specimens from pure mode-i to pure mode-ii. in this test method, a notched specimen was loaded in compression that has been initially cracked. specimens prepared were loaded on a computer controlled universal testing machine. the specimens were loaded by fixture which were designed and fabricated using ms steel to perform the fracture test for mode-i and mode-ii. the tests were closely monitored and conducted at room temperature, since it is difficult to detect the first point of damage in laminated g a. desai et alii, frattura ed integrità strutturale, 53 (2020) 426-433; doi: 10.3221/igf-esis.53.33 428 composites. in order to overcome such difficulties, the applied loads are recorded. using recorded values of peak load, the fracture toughness kic and kiic will be calculated. the magnitudes of kic and kiic have been calculated by analytical formulations given in eqns. (1) and (2) [3]. figure 1: fiber directions of glass laminate obtained in (0/45)° and (0/90)° respectively the analytical formulations of ki and kii (he and hutchinson) [3] are as follows: 6 2 sq a a k fi i ww        (1) 3 / 2( / ) 1/ 2 1/ 2(1 / ) q a w a k fii ii ww a w       (2) where ( ) ( ) f l d q l d    (3) the functions fi and fii were defined by murakami [14], as polynomial functions: 2 3 4 5( / ) 1.122 1.121( / ) 3.740( / ) 3.873( / ) 19.05( / ) 22.55( / )   / 0.7 if a w a w a w a w a w a w for a w        (4) 2 3 4( / ) 7.264 9.37( / ) 2.74( / ) 1.87( / ) 1.04( / )    0   / 1 iif a w a w a w a w a w for a w        (5) 2 2k k keff i ii  (6) (a) (b) 45° lamina 0° lamina 45° lamina 0° lamina 0° lamina 90° lamina 0° lamina 90° lamina a. desai et alii, frattura ed integrità strutturale, 53 (2020) 426-433; doi: 10.3221/igf-esis.53.33 429 here ‘f’ is the peak load, ‘t’ is the thickness of the specimen and fi(a/w) and fii(a/w) are the non-dimensional geometrical factors for both pure mode-i and pure mode-ii. fracture tests were performed with a universal tensile testing machine under a loading speed of 2 mm per minute. tests were conducted three times for each specimen laminates. the critical stress intensity factor (kic & kiic) value was calculated from this peak load by equations that have been established on specimens of the type described in he and hutchinson [3]. figure 2: specimen configuration used in the analyses w=18mm, d= 26mm, l=52mm, a=9mm. figure 3: arrangement of fpb specimen loaded at utm results and discussions fracture behavior of glass-epoxy polymer composite he specimen is loaded for 6 different crack positions (i.e. d/w=1.5 constant for all the specimens). these 6 cases correspond to the different crack distances from the middle of the specimen by varying the s/d ratios from 0 to 1 by an increment of 0.2. fracture behavior of laminates for different loading positions in the specimen, showed that the crack in the specimen initiated at the crack tip and then propagated along the fibre/matrix interface. thus, for loading positions other than s/d=0 and s/d=1, the cracks propagate under mixed mode loading conditions. a set of five specimens were prepared for each loading conditions and the peak load experienced by the specimen is computed by the average of best three specimen results. it is observed that the deviation in the load is less than 2.5%. the estimated average load vs. displacement values is plotted in fig. 4 for (0/45)° and (0/90)° fiber oriented glass/epoxy. load is applied for various s/d ratios of the specimen to calculate the stress intensity factor (k). load displacement curves from the experimental fracture are gathered and from these curves, the peak loads (f) at fracture are used to compute critical mode-i and mode-ii stress intensity factors. tab. 1 and tab. 2 gives peak load values and corresponding stress intensity t compression plate fpb specimen fixture a. desai et alii, frattura ed integrità strutturale, 53 (2020) 426-433; doi: 10.3221/igf-esis.53.33 430 factors for corresponding s/d ratios for (0/45)° and (0/90)° laminates respectively. the magnitudes of kic and kiic have been calculated by analytical formulations given in eqns. (1) and (2) [3]. (a) (b) figure 4: load vs. displacement (0/45)° and (0/90)° fiber oriented glass/epoxy laminates s/d average peak load f(n) kic (mpa(m)1/2) kiic (mpa(m)1/2) keff (mpa(m)1/2) 0 15000 0.00 10.66 10.66 0.2 14250 19.14 10.13 21.65 0.4 13320 35.77 9.47 37.00 0.6 12690 51.12 9.02 51.91 0.8 11930 64.08 8.48 64.64 1 11310 75.94 0.00 75.94 table 1: mixed-mode critical loads (f) and average critical stress intensity factors (kic, kiic, keff) [mpa m0.5] for glass/epoxy (0/45)° laminate. s/d average peak load f(n) kic (mpa(m)1/2) kiic (mpa(m)1/2) keff (mpa(m)1/2) 0 16320 0.00 11.60 11.60 0.2 15420 20.71 10.96 23.43 0.4 14380 38.62 10.22 39.95 0.6 13650 54.99 9.70 55.84 0.8 12880 69.18 9.15 69.79 1 12140 81.51 0.00 81.51 table 2: mixed-mode critical loads (f) and average critical stress intensity factors (kic, kiic, keff) [mpa m0.5] for glass/epoxy (0/90)° laminate. a. desai et alii, frattura ed integrità strutturale, 53 (2020) 426-433; doi: 10.3221/igf-esis.53.33 431 fig. 5 shows kic vs. s/d for various fiber-oriented laminates. critical stress intensity factors are increasing from pure mode-ii to pure mode-i. fig. 6 shows kiic vs. s/d for various fiber-oriented laminates. critical stress intensity factors are decreasing from pure mode-ii to pure mode-i. also, we can observe (0/90)° fiber oriented laminate is dominant compared to other fiber oriented laminate. critical stress intensity factor is considered as fracture toughness. the failure under mixed mode loading i.e. variation of kiic vs. kic is depicted in fig. 7. this nature of variation of kiic vs. kic is in good agreement with the results shown by our earlier experimental work under mixed mode loading [10]. fracture toughness value of (0/90)° fiber oriented laminates are highest among other fiber oriented laminates. also, (0/90)° fiber orientation fabrication is simple compared to (0/45)° fiber orientation. hence (0/90)° fiber oriented laminates can be preferred for industrial purpose. fig. 8 shows keff vs. s/d for various fiber-oriented laminates. this figure indicates that, the effective stress intensity factor in mode-i is more than that of mode-ii which indicates specimen fails earlier in mode-i compared to mode-ii and mixed modes.. also, nature of variation of keff vs. s/d is similar to earlier researchers [2]. fig. 9 shows fracture behavior of laminates at different loading positions from s/d=0 to 1. from fig. 9 we can see that, for s/d=0, fracture takes in pure mode-ii. for s/d=1, fracture takes place in pure mode-i. for s/d=0.2, 0.4, 0.6 and 0.8 fracture takes place in mixed mode. as we have conducted experimentation on specimen using crack perpendicular to fiber direction, the nature of failure will be translaminar. after the experiment crack tip is examined through optical microscope having 100x magnification which reveals fiber breakage as is shown in fig. 10. figure 5: kic vs. s/d figure 6: kiic vs. s/d fiber figure 7: kiic vs. kic figure 8: keff vs. s/d a. desai et alii, frattura ed integrità strutturale, 53 (2020) 426-433; doi: 10.3221/igf-esis.53.33 432 figure 9: fracture behavior of laminates at different loading position figure 10: fiber breakage seen using optical microscope mode mixity (me) is calculated for different s/d ratios for fpb specimen [2] using eqn. (7). tab. 3 shows values for mode mixity for s/d ratios. 2 arctan ie ii k m k           (7) table 3: mode-mixity values for various s/d ratios conclusion he major conclusions in this investigation is that, the bearing load capacity for unidirectional (0/90)° fiber oriented laminate is more compared to 0° and (0/45)° unidirectional fiber oriented laminate for asymmetric four point bend mixed mode(i/ii) fracture specimen. consequently, the translaminar fracture toughness for (0/90)° is more compared to other fiber oriented laminates. in addition, fabrication process for (0/90)° fiber oriented laminate using hand layup technique is simple compared to (0/45)° fiber oriented laminate. hence, (0/90)° fiber oriented laminate is preferable for industrial application. s/d mode-mixity me 0 0 0.2 0.69 0.4 0.835 0.6 0.888 0.8 0.916 1 1 t mode-ii mode-i mixed modes fiber breakage a. desai et alii, frattura ed integrità strutturale, 53 (2020) 426-433; doi: 10.3221/igf-esis.53.33 433 acknowledgment uthors gratefully acknowledge the experimental facilities provided by the research centre, s.d.m. college of engineering & technology, dharwad, karnataka, india and research centre, pesitm, shivamogga, karnataka, india. references [1] laffan, m.j., pinho, s.t., robinson, p., mcmilllan, a.j. (2012). translaminar fracture toughness testing of composites: a review”, polymer testing, , pp. 481-489. doi: 10.1016/j.polymertesting.2012.01.002. [2] kudari, s. k., sharanaprabhu, c.m. (2010). on the relationship between stress intensity factor (k) and minimum plastic zone radius (mpzr) for four-point bend specimen under mixed mode loading, international journal of engineering, science and technology, 2(5), pp. 13-22. doi: 10.4314/ijest.v2i5.60095. [3] he, m. y., hutchinson, j.w. (2000). asymmetric four-point crack specimen. journal of applied mechanics, 67, pp. 207-209. doi: 10.1115/1.321168 [4] james, r. r. (1990). mixed-mode bending method for delamination testing, aiaa journal, 28(7), pp. 1270-1276. doi: 10.2514/3.25204 [5] kenane, m., benzeggagh, m. l. (1997). mixed-mode delamination fracture toughness of unidirectional glass/epoxy composites under fatigue loading, composites science and technology, 57 pp. 597-605. doi: 10.1016/s0266-3538(97)00021-3 [6] sham prasad, m.s., venkatesh, c.s. and jayaraju, t.(2011). experimental methods of determining fracture toughness of fiber reinforced polymer composites under various loading conditions, journal of minerals and materials characterization & engineering 10(13), pp. 1263-1275. doi: 10.4236/jmmce.2011.1013099 [7] rikards, r. (1998). investigation of mixed mode i/ii interlaminar fracture toughness of laminated composites by using a cts type specimen, engineering fracture mechanics, 61, pp. 325-342. doi: 10.1016/s0013-7944(98)00068-x. [8] laffan, m.j., pinho, s.t., robinson, p., mcmilllan, a.j. (2011). translaminar fracture toughness: the critical notch tip radius of 0° plies in cfrp, composites science and technology, 72, pp. 97-102. doi: 10.1016/j.compscitech.2011.10.006 [9] swolfs, y., geboes, y., gorabatikh, l., pinho, s. t. (2017). the importance of translaminar fracture toughness for the penetration impact behaviour of woven carbon/glass hybrid composites, composites part a, 103, pp. 1-8. doi: 10.1016/j.compositesa.2017.09.009 [10] desai, a., sharanaprabhu, c.m., kudari, s.k. (2018). experimental investigation on critical energy release rate for an asymmetric four point bending, national conference on advanced research in science, engineering and management, pesitm, shivamogga pp. 395-398. [11] desai, a., sharanaprabhu, c.m., kudari, s.k. (2019). experimental investigation on the effects of fiber orientation on mixed mode i/ii translaminar fracture toughness for glass-epoxy composites, advances in polymer composites, mechanics, characterization and applications, aip conf. proc.2057, 020010. doi: 10.1063/1.5085581. [12] naghipour, p., bartsch, m., chernova, l., hausmann, j., voggenreiter, h. (2010). effect of fiber angle orientation and stacking sequence on mixed mode fracture toughness of carbon fiber reinforced plastics: numerical and experimental investigations, materials science and engineering a, 527 pp. 509–517.  doi: 10.1016/j.msea.2009.07.069. [13] shahani, a.r., tabatabaei, s.a. (2009). effect of t-stress on the fracture of a four point bend specimen, materials and design, 30, pp. 2630-2635. doi: 10.1016/j.matdes.2008.10.031 [14] murakami ,y. stress intensity factors handbook, pergamon press, new york (1987) a << /ascii85encodepages false /allowtransparency false /autopositionepsfiles true /autorotatepages /none /binding /left /calgrayprofile (dot gain 20%) /calrgbprofile (srgb iec61966-2.1) /calcmykprofile (u.s. web coated \050swop\051 v2) /srgbprofile (srgb iec61966-2.1) /cannotembedfontpolicy /error /compatibilitylevel 1.4 /compressobjects /tags /compresspages true /convertimagestoindexed true /passthroughjpegimages true /createjobticket false /defaultrenderingintent /default /detectblends true /detectcurves 0.0000 /colorconversionstrategy /cmyk /dothumbnails false /embedallfonts true /embedopentype false /parseiccprofilesincomments true /embedjoboptions true /dscreportinglevel 0 /emitdscwarnings false /endpage -1 /imagememory 1048576 /lockdistillerparams 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can be opened with acrobat and adobe reader 5.0 and later.) >> /namespace [ (adobe) (common) (1.0) ] /othernamespaces [ << /asreaderspreads false /cropimagestoframes true /errorcontrol /warnandcontinue /flattenerignorespreadoverrides false /includeguidesgrids false /includenonprinting false /includeslug false /namespace [ (adobe) (indesign) (4.0) ] /omitplacedbitmaps false /omitplacedeps false /omitplacedpdf false /simulateoverprint /legacy >> << /addbleedmarks false /addcolorbars false /addcropmarks false /addpageinfo false /addregmarks false /convertcolors /converttocmyk /destinationprofilename () /destinationprofileselector /documentcmyk /downsample16bitimages true /flattenerpreset << /presetselector /mediumresolution >> /formelements false /generatestructure false /includebookmarks false /includehyperlinks false /includeinteractive false /includelayers false /includeprofiles false /multimediahandling /useobjectsettings /namespace [ (adobe) (creativesuite) (2.0) ] /pdfxoutputintentprofileselector /documentcmyk /preserveediting true /untaggedcmykhandling /leaveuntagged /untaggedrgbhandling /usedocumentprofile /usedocumentbleed false >> ] >> setdistillerparams << /hwresolution [2400 2400] /pagesize [612.000 792.000] >> setpagedevice microsoft word numero 12 art 7 m. angelillo et alii, frattura ed integrità strutturale, 12 (2010) 63-78; doi: 10.3221/igf-esis.12.07 63 numerical experiments in 2d variational fracture m. angelillo, a. fortunato università di salerno, dipartimento di ingegneria civile. e. babilio, m. lippiello università di napoli, dipartimento di costruzioni l. cardamone sissa trieste riassunto. in questo lavoro si presentano i risultati di alcuni esperimenti numerici ottenuti utilizzando un modello variazionale di frattura fragile alla griffith. l'analisi è basata essenzialmente sulla recente formulazione di francfort e marigo; la principale differenza consiste nel fatto che qui si ricercano minimi locali piuttosto che minimi assouluti. la propagazione quasi-statica della frattura viene simulata minimizzando, in un procedimento al passo, una forma di energia che è la somma di un termine di volume e di un termine di interfaccia. il problema è risolto numericamente adottando una discretizzazione ad elementi finiti discontinui e basati su di una mesh variabile, minimizzando l'energia, rispetto agli spostamenti e alla posizione dei nodi della mesh nella configurazione di riferimento, con un metodo di discesa. per uscire da eventuali buche di energia di piccola taglia si adotta una sorta di rilassamento, mesh dependent, della energia di interfaccia. abstract. in the present work we present some results of numerical experiments obtained with a variational model for quasi-static griffith-type brittle fracture. essentially the analysis is based on a recent formulation by francfort and marigo the main difference being the fact that we rely on local rather than on global minimization. propagation of fracture is obtained by minimizing, in a step by step process, a form of energy that is the sum of bulk and interface terms. to solve the problem numerically we adopt discontinuous finite elements based on variable meshes and search for the minima of the energy through descent methods. we use a sort of mesh dependent relaxation of the interface energy to get out of small energy wells. the relaxation consists in the adoption of a carefully tailored cohesive type interface energy, tending to the griffith limit as the mesh size tends to zero. keywords. griffith’s fracture; numerical methods; energy minimization; free discontinuities. introduction ur research group has developed in the last decade a computer model for fracture nucleation and propagation in 2d brittle solids, based on variational fracture (see [1], [2] and references therein). the present work reports some numerical results obtained with this computer model in quasi-static problems of fracture nucleation and o http://dx.medra.org/10.3221/igf-esis.12.07&auth=true http://www.gruppofrattura.it m. angelillo et alii, frattura ed integrità strutturale, 12 (2010) 63-78; doi: 10.3221/igf-esis.12.07 64 propagation. essentially the analysis is based on the formulation of francfort and marigo [3] the main difference being the fact that we rely on local rather than on global minimization. nucleation and propagation of fracture is obtained by minimizing in a step by step process a form of energy that is the sum of bulk and interface terms. recent attempts of producing numerical codes for variational fracture (see for example the works of bourdin [4] or del piero et al [5]) are based on the approximation of the energy, in the sense of gamma-convergence, by means of elliptic functionals (e.g. ambrosio-tortorelli approximations [6]). here instead we adopt discontinuous finite elements and search for local minima of the energy, close to equilibrium trajectories, through descent methods. in constructing such a numerical model there are two main questions that must be answered. 1. the variational model for fracture requires the ability to accurately approximate the location of cracks, as well as their length. cracks may not be restricted to propagate along the skeleton of a fixed finite element mesh. to overcome this difficulty our mesh is made variable in the sense that node positions in the reference configuration of the body are considered as further variables. 2. on adopting a griffith type interface energy the initiation of fracture in a previously virgin body is always "brutal", that is the system cannot proceed along neutral equilibrium paths or, in other words, descent directions toward local minima do not exist. to reach local minima the system must have the ability to surmount small energy barriers and then proceed through “non-equilibrium” descent paths. here we use a sort of mesh dependent relaxation of the interface energy to get out of small energy wells. the relaxation consists in the adoption of a carefully tailored cohesive type interface energy, tending to the griffith limit as the mesh size tends to zero. in the first part of the paper we give the main ingredients of the theory and of the model implementation. in the final part of the paper, some examples concerning fracture nucleation and propagation are presented. griffith’s versus variational fracture mechanics n the theory of brittle fracture due to griffith, cracking is associated to the existence of surface energy and the propagation of cracks to the competition between surface energy and potential energy release during an infinitesimal increase of the crack length “c”. a number of authors, since the pioneering work of ambrosio and braides [7] in 1995, has proposed variational models of brittle fracture based on global energy minimization with free discontinuities (for early thoughts on minimization with free discontinuities see de giorgi [8]). the basic idea is to use the competition between bulk and interface energy that is implicit in griffith’s theory, [9], as the driving criterion for optimal crack selection. global energy minimization remedies to two main shortcomings of griffith’s theory, namely  initiation: griffith’s is a model for crack growth from a pre-existing crack, not a model for crack nucleation. indeed the cost of surface energy for the creation of an infinitesimally long crack cannot be compensated by the elastic energy release in an originally “flawless” body.  crack path selection: griffith’s model is restricted to the study of crack propagation along a given path. in the original formulation the energy balance is expressed in terms of “c” only. the variational formulation based on global minimization which looks at the crack set as one of the sought unknowns, leads naturally to the search of crack paths without any restriction on crack topology, thus allowing, at least in principle, the study of initiation and, possibly, branching. there are two main criticisms to variational fracture: 1. the minimum energy formulation implies reversibility but fracture is an inherently irreversible phenomenon. 2. global minimality does not seem physically correct. the “infinitesimal” local minimality of the griffith’s theory is presumably not correct either but at least does not lead to paradoxes such as the impossibility of equilibrium under purely tensile loading. in 1998 francfort & marigo formulated a consistent variational model of fracture respecting the irreversibility of the phenomenon, but again based on global minimality. the problem is formulated as a quasi-static evolution problem in which the geometry and size of the cracks are limited by their precedessors. a more realistic approach that would investigate local minimizers still lacks of the necessary mathematical apparatus (though the recents attempts of dal maso & toader [10] and larsen [11] must be aknowledged). our work, as described in the introduction, is devoted to assess, through numerical experiments, the ability of a variational model of fracture based on local minimization to model fracture initiation and propagation. from the numerical point of view the main issue with local minimization is how the material moves from an equilibrium i http://dx.medra.org/10.3221/igf-esis.12.07&auth=true http://www.gruppofrattura.it m. angelillo et alii, frattura ed integrità strutturale, 12 (2010) 63-78; doi: 10.3221/igf-esis.12.07 65 state to another. though it seems natural to look at “gradient flows”, so that the material moves downhill in the steepest direction, in studying initiation (that is the onset of cracks in a previously flawless body) the crack cannot open up in any “nearby” optimal direction without having the energy to increase somewhere. a way out to restore physical plausibility is to assume that the system can overcome “small” energy barriers, where the term “small” refers both to the amount of the energy increase before the descent begins and to the length of the path leading to the point of descent. such a “smallness” could be measured by introducing a convenient barrier-norm to be compared with a given threshold specific of the material considered. since an increase in energy always requires the work of external active forces, these energy jumps should be actually forbidden in a quasi-static evolution and can be justified only admitting the presence of finite disturbances in the geometry and in the data. analytical and numerical formulation of the problem ur approach is reported in details in [2] and it will be briefly summarized for the reader’s convenience. preliminaries consider a two–dimensional body b occupying in the original configuration a bounded plane domain  and undergoing small deformations. let  be the infinitesimal strain tensor and u the displacement field defined over . the boundary of is partitioned into two parts where displacements u and tractions p are given. we admit that u may be discontinuous on a set  assumed to belong to an admissible set of cracks s(). the crack pattern is the most relevant unknown in variational fracture problems and the theorems of ambrosio [12], valid in particular for griffith’s type variational formulations based on global minimizers, ensure that  is sufficiently regular to be approximated by sets composed by regular arcs, such as line elements. therefore  is a 1d closed set and the unit normal n and tangent t exist a.e. along it. the jump of u across , denoted [[u]] = u+−u-, is resolved into two components relative to n, t [[u]] = an + bt (1) if a is positive the corresponding points on the two opposite sides of the interface  separate and determine a vacancy. finally we assume that u belongs to h1(\), that is u has the regularity required in linear elasticity away from . volume and surface energy densities the material is assumed to be elastic and isotropic, that is characterized by the elastic energy density )2)(*( 2 1 )( 2   tr (2) a scalar field defined over \. in (2)  and  are the elastic moduli for generalized plane stress. to model brittle fracture, we introduce on  the interface energy density 0 , 0, 0 ( , ) , 0 , 0 0 & 0 c a b a b g a a or a b           (3) where gc is the thoughness of the material and a,b are the components of the displacement jump along . typical boundary value problems we consider quasi–static bvp’s. a typical example is represented by the plane strip of height h and width b shown in fig. 1 to which we refer for notations. on the lateral sides of the rectangle the traction condition p = 0 is enforced and on the bases a combination of relative displacements u is given. we assume u to be time dependent. at any time t of the loading process we seek equilibrium states of the strip as points of local minima of the functional o http://dx.medra.org/10.3221/igf-esis.12.07&auth=true http://www.gruppofrattura.it m. angelillo et alii, frattura ed integrità strutturale, 12 (2010) 63-78; doi: 10.3221/igf-esis.12.07 66      \ ]]u([[)()u,(e dsda  (4) under the boundary conditions described above. space discretization to discretize the problem we split the domain into triangles, as shown in fig. 1, and identify  with the part of the skeleton of the triangulation that is not at the boundary of . in order to duplicate nodes and edges of the skeleton of the mesh, we introduce special interface elements with zero thickness placed along the edges of the continuous elements. a topological view of these elements is depicted in fig. 13a for a plane strip. figure 1: typical bvp: strip with a straight crack in “mixed” mode. in order to give to the skeleton the ability to choose optimal crack paths, the positions of the nodes of the triangulation in the reference configuration , are taken as further variables and can be moved to minimize the total energy. approximate interface (surface) energy density in the numerical applications we approximate the equilibrium trajectory of the system by considering crack propagation as based on critical points of the energy. to get out of possible small energy wells, either numerical (due to the finite element mesh) or physical (due to fracture initiation) on introducing the limit tensile stress °, the limit shear stress ° the thoughness =gc, the shear stiffness k and the functions (fig.2) 1 2 2 2 2 ( ) 2 arctan( ) 2 2 ( ) arctan( ) log (1 ( ) ) 2 2 a a a e e k b k b b k b k                                    (5) where  = 1.90086, we adopt the following approximate relaxed form of the surface energy density: )()(),( 21 baba   (6) (a) (b) figure 2: comparison between exact and relaxed interface energies. http://dx.medra.org/10.3221/igf-esis.12.07&auth=true http://www.gruppofrattura.it m. angelillo et alii, frattura ed integrità strutturale, 12 (2010) 63-78; doi: 10.3221/igf-esis.12.07 67 in (6)° represents the slope at the inflection point of the curve depicted in fig. 2a, ° the slope of the dotted lines in fig. 2b. notice that while  and k are constants, °, °, are actually mesh dependent, that is their values must be tuned depending on the current mesh size h and should tend to infinity as h tends to zero, linearly with1/h. although the density (13) has a shape close to that of the approximate surface energy density defined in [2], the main difference between them is that all parameters in the function (6) have a clear physical meaning and no shape parameter is needed. fracture nucleation in 1d he study of a simple 1d example can clarify the main ingredients of our approach. consider the long strip of brittle material depicted in fig. 3, modeled as a 1d continuous bar, fixed at the left end and subject to a given displacement u at the other end. figure 3: 1d bar: fe discretization. the bar has been discretized into two finite elements of length l/2. inside the elements the material is linearly elastic and characterized by the elastic energy density =1/2 ea 2. the spirit of our approximation is to consider that fractures, that is discontinuities in the displacements, may occur at the interface between elements (the skeleton of the mesh), that is at point 2. to allow for the interface energy at node 2 we must duplicate node 2 into two spatially coincident nodes in the reference configuration : 2’, 2”. therefore we are reduced to a two degrees of freedom structure. the two degrees of freedom we choose are {u,a} and are defined in terms of the displacements u(2’), u(2”) as follows: u= u(2’), a = u(2”)u(2’). then the total energy is 2 2 2 2 c 1 / 2 ea 2 u / l 1 / 2 ea 2 (u u) / l a = 0 e (u, a) 1 / 2 ea 2 u / l 1 / 2 ea 2 (u u a) / l g a 0 a 0             the graph of the energy (u,a) for a particular value of the given displacement u is depicted in fig. 4. in the figure are visible two minima: one is ½ ea u2l, the “elastic” minimum for a=0 and u=u/2 (point a), that is the one for which there is no discontinuity; the other one is gc, the minimum for a=u and u=0 (point b), that is the bar is completely fractured. for u small the “elastic” minimum is smaller than the “completly fractured” minimum. as the displacement u is gradually increased from zero, with the system sitting in the “elastic” minimum, the energy minimum rises and becomes larger than gc. as it is evident from fig. 4, wathever large be the elastic minimum with respect to gc, there is always an energy barrier to sormount to go from the local to the global minimum, that is there is no descent direction from a to b. figure 4: 3d plot of the energy  for u large. t http://dx.medra.org/10.3221/igf-esis.12.07&auth=true http://www.gruppofrattura.it m. angelillo et alii, frattura ed integrità strutturale, 12 (2010) 63-78; doi: 10.3221/igf-esis.12.07 68 the numerical method we propose to get out of the “elastic pocket” is to adopt for the interface energy the relaxed form depicted in fig. 2a. with such cohesive type energy the system will access a descent direction at u= l °/e. the stress thresold is set again to infinity as soon as the system accesses the gradient flow from a to b; the fractured minimum is reached through steepest descent. in this example the mesh skeleton is fixed, therefore the crack can open up only at point 2. a way to make the crack move is to consider the mesh 1, 2, 3 variable in the sense that the coordinate x(2) of point 2 is taken as a further variable in the energy:             2 2 2 2 c 1 / 2 ea u / x 2 1 / 2 ea (u u) / l x 2 a = 0 e (u, a, x 2 ) 1 / 2 ea u / x 2 1 / 2 ea (u u a) / l x 2 g a 0 a 0                and the minimum is searched with respect to u, a, x(2). actually all the fractured minima are equivalent if the bar is homogeneous and there is no reason for the bar to move the crack from the midpoint. this can be easily verified by preminimizing (u,a,x(2)) with respect to u (that gives u°=u x(2)/l) and substituting u° for u in the energy:   2 2 c 1 / 2 ea u / l a = 0 e (a) e (u u , a, x 2 ) 1 / 2 ea / l (u a) + g a 0 a 0           that is actually idependent of x(2). to make the node movements worthwile we consider that the bar is weackened at x=0.366l (fig. 5), that is the thoughness gc is not homogeneous and has a minimum at x=0.366l. the bar is discretized into 10 elements in such a way that there is no node at the weackest point. the energy is then a function of 27 variables: 9 node displacements, 9 displacement jumps, 9 node positions: {u(i), a(i), x(i)}, i=2,...,10. a value of the displacement u, large enough to have gc<1/2ea/l u2, is assigned and the minimum state is searched with a descent method using as starting state the displacement field depicted in fig. 6a. figure 5: weackened 1d bar: fe discretization. (a) (b) (c) figure 6: three snapshots of the evolution of the displacement u and of the node positions a(i), from starting point to convergence (diplacement is represented along the vertical axis). http://dx.medra.org/10.3221/igf-esis.12.07&auth=true http://www.gruppofrattura.it m. angelillo et alii, frattura ed integrità strutturale, 12 (2010) 63-78; doi: 10.3221/igf-esis.12.07 69 through descent the system evolves toward the minimum as showni in fig. 6. the evolution of the domain and of the node positions at five steps of the evolution is depicted in fig. 7. in particular in fig. 7 it can be seen how node 5 moves from the original position to the “weackest point” by creating an interface at x=0.366l. figure 7: five snapshots of the evolution of the domain from original domain to convergence. validation with classical linear fracture mechanics (clfm): propagation of a straight crack in mode i oving from 1d to 2d we enter a much more complex world. the ability of the method to mimic the onset of cracks in brittle materials in 2d becomes a difficult problem of approximation of the real quasi-static trajectory of the system with a step-wise sequence of states, and depends on a sensible choice of the parameters °, °. such parameters are mesh dependent, in the sense that must be tuned according to the mesh size h, in order to make the approximate solution mesh independent. we must say that the story of our “battle” to obtain sound numerical results from our experiments on fracture simulation is full of “casualties”. in scientific papers most often appears that the proposed numerical models are good enough to catch the essence of the problems at hand, but there are scant of no reports on the endless numbers of failures. actually no one is interested in a bunch of meaningless, junk results and we do not want to change this tradition. here we want just to emphasize that, except from very large and trivial bounds, we were not able to identify any simple rule for the choice of the parameters °, °, that up to now has proceeded in a case by case fashion. in our effort to establish the ability of simulating crack nucleation and propagation in 2d brittle solids by adopting a numerical model based on variational fracture, the first attempt has been to verify the capacity to reproduce the results of clfm in cases in which the transition to fracture occurs through stationary states of the system. such is the case of the propagation of a straight crack in mode i, into a strip of homogeneous, isotropic, linearly elastic material. the geometry of the problem and the main notation is reported in fig. 8. figure 8: plane strip with a straight crack in mode i, hard device. the boxed area is the square that is zoomed in figure. m http://dx.medra.org/10.3221/igf-esis.12.07&auth=true http://www.gruppofrattura.it m. angelillo et alii, frattura ed integrità strutturale, 12 (2010) 63-78; doi: 10.3221/igf-esis.12.07 70 in clfm it is assumed that the crack propagates along the line x2=0 when the given displacement u() reaches a critical value. this assumption, largely confirmed by a vast number of experimental results, makes in this case the question not “the how” but “the when”. in fig. 9 the outcome of an experimental test on an isotropic polycarbonate is reported into two photoelastic images, the first taken before and the second after the onset of the crack. (a) (b) figure 9: photoelastic images for a straight crack in mode i. fringe pattern before cracking (a) and after cracking (b). from al bin mousa [13]. in fig. 10b the quasi-static path of meta-stable states (local minima of the energy) followed by the system in the {c,u} plane, is represented with a solid line. the shaded line represents the part of the path that is made of stationary points of the energy that are not local minima. the values taken by the total energy and by the elastic energy along the stationary path are depicted in fig. 10a. in fig. 10c the total energy at increasing values of the given displacement u is reported as a function of c. the dots indicate the stationary points of . (a) (b) (c) figure 10: in (b) quasi static evolution of the system of fig.8 in the plane {c,u}. solid line: metastable states, shaded line: unstable states. in (a) total energy and elastic energy along the path of figure (b). in (c) total energy for increasing values of the given displacement u as a function of c. the computations have been performed by adopting the geometric and material constants reported in tab. 1, (for which ucr=0.0190 and ccrit = 10.1419). the specimen is discretized with a courant triangulation which includes the axis x1 within the skeleton of the mesh. in this way we already have the possible “new” interface along x1 . height length thickness young mod. poisson rat. thoughness h (cm) 5l (cm) t (cm) e (ncm-2)  gc (ncm-1) 1.0 15.0 1.0 3.0 105 0.0 1.0 table1: geometric and material constants. http://dx.medra.org/10.3221/igf-esis.12.07&auth=true http://www.gruppofrattura.it m. angelillo et alii, frattura ed integrità strutturale, 12 (2010) 63-78; doi: 10.3221/igf-esis.12.07 71 the qualitative results of our numerical simulation are reported in fig. 11, where 12 steps of the discretized evolution are shown. notice that these are stable equilibrium states of the system, that is local minima, reached through our descent minimization algorithm at twelve values of the imposed displacement (u=0.00,0.005,0.010,0.015,…,0.065). figure 11: evolution of the strip geometry and mesh for u=0.00, 0.005, 0.010, 0.015, 0.030, 0.035, 0.040, 0.045, 0.050, 0.055, 0.060, 0.065 (from left to right, from top to bottom). the maximum normal stress is reported in a grey scale. http://dx.medra.org/10.3221/igf-esis.12.07&auth=true http://www.gruppofrattura.it m. angelillo et alii, frattura ed integrità strutturale, 12 (2010) 63-78; doi: 10.3221/igf-esis.12.07 72 denoting m the total number of triangles in the mesh and n the total number of nodes, the energy to be minimized is a function of (2) 3 m nodal displacements u1(n), u2(n) (n=1,2,..,3m) and of 2 n nodal positions in the reference configuration x1(m), x2(m) (m=1,2,..,n). the energy is a complex, non convex function of its arguments with a lot of local minima. from fig. 11 we see that the fracture propagates at a critical value of the displacement whose value depends on the ratio °/h. in this example we focus on the tuning of the parameter °. in fig. 12 the values taken by the elastic energy at some steps of the discrete evolution are compared with the graph of fig. 10a. the two polylines a and b refer to two values of the parameter °: 246ncm-2 and 100ncm-2. for the first value the structures follows closely the exact energy path, even if with a sequence of snaps about the real trajectory. figure 12: elastic energy for increasing values of u. curve: exact elastic energy. polyline a: discrete trajectory with °=246 ncm-2. polyline b: discrete trajectory with °=100 ncm-2. nucleation in 2d. rupture of a stretched and sheared strip he strip of base b and length l=2b, represented in fig. 13 is considered. in (a) a topological representation of the original mesh is given: it is a structured mesh based on a uniform triangulation of the domain of mesh size h=l/20 2 . in grey the 100 physical triangles of the mesh and in white the 270 interface elements are reported. therefore the free node displacements, before considering the geometric constraints at the bases of the strip, are 2(3)100= 600 instead of the 2 (66)=132 of a classical fem mesh. the node positions in the reference configuration are also taken as variables. therefore there are 2(66)=132 more variables to be considered. the energy is a complex functions of these variables with a lot of local minima. (a) (b) (c) (d) figure 13: sheared and stretched strip. original mesh (a), starting state (b), deformed shape at convergence (c), final mesh at convergence (d). t http://dx.medra.org/10.3221/igf-esis.12.07&auth=true http://www.gruppofrattura.it m. angelillo et alii, frattura ed integrità strutturale, 12 (2010) 63-78; doi: 10.3221/igf-esis.12.07 73 such energy is minimized by fixing a given combination of stretch and shear at the constrained bases, and evolving an initial state compatible with this datum (the elastic solution, fig. 13b) through a descent algorithm (conjugate gradient). fig. 13a,b shows the final geometry of the strip and of the corresponding mesh in the original configuration, at the end of the minimization process. the result we show resemble the outcome of a number of fracture tests on concrete but we refrain the reader from being too excited by this. we must report indeed the rather frustrating results that one can obtain by just changing a little the starting state or the parameters (especially important is the interplay of ° and °). besides we must point out that the result we show in fig. 13 was obtained by fixing at the boundary a large displacement in a single step. any attempt to try to follow a sensible quasi-static trajectory has had always miserable results. we do not have a reasonable answer to this but feel that these difficulties may be remedied by introducing dynamics, that is by alternating a variational step and a dynamical step during the discretized evolution. propagation: kinking of a straight crack in mixed mode i&ii he propagation of a straight crack in a panel under mixed mode boundary conditions is considered. the geometries and boundary conditions considered are shown in fig. 1 and fig. 14, to which we refer for notations. propagation of the crack in clfm is still governed by the griffith’s criterion. consensus is breached when addressing how a path is selected by the crack. in particular, competing criteria have been proposed for the kinking of a straight crack. in an isotropic setting, a well regarded criterion is the principle of local symmetry, pls-criterion, [14] which states that the crack always propagates in mode i, that is with inplane tractions that remain perpendicular to the crack in a small neighborhood of the crack tip [15]. the maximum tangential stress, mts-criterion, (erdogan and sih [16], 1963) is the simplest criterion and it states that the direction of crack initiation coincides with the direction of the maximum tangential stress along a constant radius around the crack tip. another possible alternative is the gmax-criterion which states that the crack will kink along a direction that maximizes the release rate of its potential energy among all kinking angles. it was shown [17] that the three criteria generically yield different kinking angles. there is in truth scant evidence that would support one criterion over another, and even less so in anti-plane shear because the crack is in mode iii, so that the notion of mode i, or mode ii propagation is rendered meaningless. in very recent paper, [18 ], chambolle, franfort & marigo claim that the kinking of a straight crack is possible only if one admits discontinuity in time, that is the crack propagation is brutal. based on their theorem there are only two possibilities to propagate a straight crack: 1. the crack kinks and the system jumps dynamically from a local minimum to another local minimum. 2. crack branching is observed. in both cases clfm does not work since the griffith’s criterion does not apply in his classical form, whilst variational fracture does. figure 14: strip with a straight crack under mixed mode b.c. t http://dx.medra.org/10.3221/igf-esis.12.07&auth=true http://www.gruppofrattura.it m. angelillo et alii, frattura ed integrità strutturale, 12 (2010) 63-78; doi: 10.3221/igf-esis.12.07 74 photoelastic images of a strip, of the type of fig. 14, with a preexisting straight crack at =40°, are shown in fig. 15, where the interferometric fringes before and after crack propagation are reported. (a) (b) figure 15: photoelastic images for a straight crack in mixed mode i&ii. fringe pattern before cracking (a) and after kinking (b). from al bin mousa [13]. with the mts-criterion the angle of kinking, in terms of the stress intensity factor (sif) ratio =k2/k1, is given by              4 811 tan 2 arc (7) with the gmax-criterion the angle of kinking, in terms of the sif ratio =k2/k1, is given by         21 2 tan    arc (8) a plot of the kink angle as a function of the sif ratio is reported in fig. 16, where also a comparison with some experimental results, taken from the literature and collected by al bin mousa in [13], is shown. (a) (b) (c) figure 16: plots of the kinking angles versus the sif ratio (a), lower curve: gmax-criterion, upper curve: mts-criterion. comparisons of the theoretical curves with experimental results (b). the graph (b) is taken from al bib mousa [13] and “present work” in the legend (c) refers to [13]. the case represented in fig. 1, with h=b=l, sh=(1) and vh=(1), is then solved with our computer model. http://dx.medra.org/10.3221/igf-esis.12.07&auth=true http://www.gruppofrattura.it m. angelillo et alii, frattura ed integrità strutturale, 12 (2010) 63-78; doi: 10.3221/igf-esis.12.07 75 (a) (b) figure 17: kinking of a straight crack in mixed mode i & ii before kinking (a), after kinking (b). the elastic domain is discretized with a non-structured triangulation, as shown in fig. 17a where also the stress level is represented in a gray scale. the given displacement is discretized into 100 steps and the deformation at each step is determined by minimizing the energy with a descent algorithm. denoting m the total number of triangles in the mesh and n the total number of nodes, the energy to be minimized is a function of (2) 3 m nodal displacements u1(n), u2(n) (n=1,2,..,3m) and of 2 n nodal positions in the reference configuration x1(m), x2(m) (m=1,2,..,n). the energy is a complex, non convex function of its arguments with a lot of local minima. fig. 17a shows the deformation and stress at the onset of propagation. the propagation of the crack just before dynamical instabilization is shown in fig. 17b. the kink angle predicted by our model is 30.46°. from the deformed state of fig. 17 the sif’s k1, k2 can be derived approximately by computing the j-integral. the values obtained for k1, k2 are k1 = 1.3176, k2 = 0.4288 for these values the kink angle predicted by mts and gmax criteria can be computed from (7) and (8). in tab. 2 the theoretical and numerical values obtained in this case are compared. mts gmax numerical 30.84° 30.48° 30.46° table 2: kinking angle with mts, gmax criteria and from fem analysis. we see that our analysis reproduces closely the gmax-criterion. the last results we present are concerned with the convergence analysis relative to the kinking angle assessment. the problem is essentially the same of fig. 17, except for the signs of the given displacements: sh=(-1) and vh=(1). the “loading” history is again discretized into loading steps but the analysis is stopped as soon as the crack propagates. the domain  is discretized with structured meshes of decreasing mesh size h: h= l/12 2 , l/16 2 , l/20 2 , l/48 2 . the results of these three analysis are reported in figs. 18, 19, 20, 21. from these pictures we see that the kinking angle goes from 38.30° degrees for the coarser mesh to the value of 31.18° of the finest one. the value obtained converges toward the value predicted by gmax. notice that a star shaped region of different size, centered at the crack tip, is always created during the four analyses. such regions develop before crack propagation, that is in the elastic phase, and are formed by a fixed number of elongated triangles (6). a similar behaviour is detected also in the case of fig. 17, also if it is less evident. elongated triangles are usually hill-behaved in fem analysis, but the point here is that such shapes are chosen through minimization and are the best possible in order to approximate the large stress that develops around the crack tip. http://dx.medra.org/10.3221/igf-esis.12.07&auth=true http://www.gruppofrattura.it m. angelillo et alii, frattura ed integrità strutturale, 12 (2010) 63-78; doi: 10.3221/igf-esis.12.07 76 figure 18: kinking of a straight crack in mixed mode i & ii. mesh size: l/12 2 . minimal deformation and modified mesh at 8 time steps. crack kinking in the last snapshot. figure 19: kinking of a straight crack in mixed mode i & ii. mesh size: l/16 2 . minimal deformation and modified mesh at 8 time steps. crack kinking in the last snapshot. http://dx.medra.org/10.3221/igf-esis.12.07&auth=true http://www.gruppofrattura.it m. angelillo et alii, frattura ed integrità strutturale, 12 (2010) 63-78; doi: 10.3221/igf-esis.12.07 77 figure 20: kinking of a straight crack in mixed mode i & ii. mesh size: l/20 2 . minimal deformation and modified mesh at 8 time steps. crack kinking in the last snapshot. figure 21: kinking of a straight crack in mixed mode i & ii. refined mesh, mesh size: l/48 2 . minimal deformation and modified mesh at 8 time steps. crack kinking in the last snapshot. http://dx.medra.org/10.3221/igf-esis.12.07&auth=true http://www.gruppofrattura.it m. angelillo et alii, frattura ed integrità strutturale, 12 (2010) 63-78; doi: 10.3221/igf-esis.12.07 78 references [1] m. angelillo, e. babilio, a. fortunato, in: 2nd cancnsm, vancouver, canada. e. m. croitoro ed., (2002) 181. [2] m. angelillo, e. babilio, in: xiii aimeta congress, ancona (2009). [3] g.a. francfort, j.j. marigo, j. mech. phys. solids, 46(8) (1998) 1319. [4] b. bourdin, interfaces free bound., 9 (2007) 411. [5] g. del piero, g. lancioni,r. march, j. mech. phys. solids, 55 (2007) 2513. [6] l. ambrosio,v.m. tortorelli, comm. pure appl. math., 438 (1990) 999. [7] l. ambrosio,a. braides, in: homogenization and applications to material sciences (d. cioranescu, a. damlamian, p. donato eds.), gakuto, gakkotosho, tokio, (1997) 1. [8] e. de giorgi, free discontinuity problems in calculus of variations. frontiers in pure and applied mathematics, a collection of papers dedicated to j. l. lions on the occasions of his 60th birthday, r. dautray ed., amsterdam, (1991) 55. [9] a. griffith, phil. trans. roy. soc. london, ccxxi-a (1920) 163. [10] g. dal maso, r. toader, math. mod. meth. appl. sci., 12 (12) (2002) 1773. [11] c.j. larsen, epsilon-stable quasi-static brittle fracture evolution, preprint. [12] l. ambrosio, boll. un. mat. ital., 3–b (1989) 857. [13] j.h. al bin mousa, experimental and numerical analyses of mixed mode crack initiation angle, king fahd university of petroleum and minerals, thesis (2006). [14] r. v. goldstein, r. l. salganik, int. j. of fracture, 10 (1974) 507. [15] m. amestoy. propagation de fissures en élasticité plane. thèse de doctorat d'état, université pierre et marie curie, paris, (1987). [16] f. erdogan, g. c. shi, j. basic eng., 85 (1963) 519. [17] m. amestoy, j.-b. leblon, int. j. solids struct., 29(4) (1992) 465. [18] a. chambolle, g. a. francfort, j.j. marigo, umr cnrs, r.i. 654 (2009). http://dx.medra.org/10.3221/igf-esis.12.07&auth=true http://www.gruppofrattura.it microsoft word numero_49_art_31_2463 a. vedernikova et alii, frattura ed integrità strutturale, 49 (2019) 314-320; doi: 10.3221/igf-esis.49.31 314 focused on russian mechanics contributions for structural integrity the approach to fracture diagnosis by means of experimental measurements of the stored energy a. vedernikova, a. iziumova, a. vshivkov, o. plekhov institute of continuous media mechanics ub ras, 614013 perm, russia terekhina.a@icmm.ru abstract. energy dissipation in metals under irreversible deformation leads to intensive heat generation in strain localization zones. in this work, we focus on measuring heat source power using temperature data obtained by ir thermography. the calculated heat source power data were verified by analyzing the data recorded by the seebeck effect-based heat flux sensor developed in previous study. quasi-static tensile tests were conducted on titanium alloy grade 2 flat specimens. it is shown that the thermography data and the results obtained with the heat flux sensor are in good quantitative agreement. the dependence of the moment of fracture of metal specimens on the change in localized heat generation caused by irreversible deformation was determined. keywords. stored energy; thermography; heat flux sensor. citation: vedernikova, a., iziumova, a., vshivkov, a., plekhov, o., the approach to fracture diagnosis by means of experimental measurements of the stored energy, frattura ed integrità strutturale, 49 (2019) 314-320. received: 04.04.2019 accepted: 04.06.2019 published: 01.07.2019 copyright: © 2019 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. introduction oday the investigations of many authors [1-8] are aimed at creating theoretical models describing the behavior of materials under deformations process. these models include thermodynamic and structural parameters that determine the deformation process. the energy dissipation in metals during irreversible deformation and the change in the internal structure lead to intensive heat generation in strain localization zones. modern ir detectors allow studying the evolution of energy accumulation and dissipation and provide a deeper insight into plastic-deformation localization mechanisms [1-5]. in practice, researchers often differ in the quantitative estimation of the dissipation heat and the stored energy in a cold-worked material, which impedes the development of methods of damage assessment [6]. in this study, the dissipative properties of grade 2 titanium alloys were investigated in quasi-static tensile tests. the infrared thermography technique (irt) and the contact heat flux sensor used to study the evolution of heat sources and determine the critical state of materials. analysis of the results of investigation on the energy balance in the fracture zone obtained with the infrared techniques and heat flux sensor during the deformation of titanium alloy grade 2 lend confirm the validity of the proposed method. t http://www.gruppofrattura.it/va/49/2463.mp4 a. vedernikova et alii, frattura ed integrità strutturale, 49 (2019) 314-320; doi: 10.3221/igf-esis.49.31 315 experimental details he standard quasistatic tensile tests were performed on titanium alloy grade 2 flat specimens. the chemical composition of the material is presented in the tab. 1. specimens (gauge length of 120 mm and width of 20 mm) were made of a 3 mm thick sheet. mechanical tests were carried out using a 300 kn electromechanical testing machine shimadzu ag-x plus. the geometry of specimens and the deformation curve are shown in fig. 1. investigation of the heat source evolution was carried out using the temperature data obtained by an infrared camera flir sc 5000. ir camera has the following features: the spectral range of 3-5 μm, the maximum frame size is 320×256 pixels, the spatial resolution is 10-4 meters. the temperature sensitivity is in the range from 25 mk to 300 k. the surface of the specimens intended for infrared shooting was polished in several stages and coated by a thin layer of amorphous carbon to enhance the emissivity. a) b) figure 1: (a) geometry of specimens; (b) deformation curve. fe c si n ti o h other 0.25 0.07 0.1 0.04 99.24-99.7 0.2 0.01 0.3 table 1: the chemical composition of titanium alloy grade 2. to verify the heat source power obtained by the infrared technique, the contact heat flux sensor based on the seebeck effect [9] was directly attached to the specimen. to enhance the heat flow, a heat-conductive paste was applied between the sensor and the specimen. evaluation of the stored energy e calculate the heat source field by applying the heat conduction eqn. (1) to infrared thermography data:                 2 2 2 2 2 2 ( ) ( ) ( ) ( ) ( ) t x, y,z, t t x, y,z, t t x, y,z, t t x, y,z, t c q x, y,z, t k t x y z (1) where ( )t x, y,z, t is the temperature field,  is the material density (4505 kg/m3), c is the heat capacity (540 j/(kg·k)), k is the heat conductivity (16.2 w/(m·k)), ( )q x, y,z, t is the heat source field, x, y,z are the coordinates, and t is the time. the infrared camera allows registering the temperature distribution over the specimen surface but not across the specimen thickness. that is the reason why rather thin specimens are used in experimental investigations. it makes possible to assume that the temperature distribution through the specimen thickness is homogeneous. t w a. vedernikova et alii, frattura ed integrità strutturale, 49 (2019) 314-320; doi: 10.3221/igf-esis.49.31 316 the volume-averaged eqn. (1) is used for estimation of the integral power of the heat source. to this end, a standard averaging procedure was conducted. the difference between the averaged specimen temperature on volume t and the initial specimen temperature 0t in the thermal balance with the environment is defined as:            /2 /2 /2 0 0 /2 /2 /2 1 '( ) ( ( ) ) ( ) , a b h a b h t t x, y,z, t t dxdydz t t v (2) where a , b , h are the length, width and thickness of the specimen, respectively, and v is the volume. the boundary conditions are expressed as follows: 2 2 /2 0 /22 ( , , z, ) ( , , z, ) , ( , , z, ) ( ( , , z, ) ) , a a x x a x a x a t x y t t x y t x x gt x y t k t x y t t dxdydz x a                 (3) where xg means the heat exchange coefficient between the specimen and the environment on the corresponding edge of the specimen. therefore, integrating eqn. (1), considering expressions (2) and boundary conditions (3), we obtain relation (4) to estimate the heat source field caused by irreversible deformation:         0 ( ) ( ) ( ( ) ), t s t mc v t t t (4) where  is the average temperature of the examined surface, m is the mass of the representative volume where the average temperature is taken from, ( )s t is the heat source field (w), and  is the material parameter that determines heat losses associated with the heat exchange with the environment. the parameter  is determined by the additional experiment data from the tests in which the specimen was cooled after pulse point heating. fig. 2a presents the ir image, which was made during the pulse point heating experiment, and data of the average temperature of the heating area during the cooling process. to calculate the constant  , it is necessary to approximate the experimental data of the average specimen temperature after pulse point heating in terms of the solution of the averaged thermal conductivity eqn. (4) with a zero source (fig. 2b). the experimentally obtained value of parameter  is equal to 3.65·104. a) b) figure 2: (a) ir image of the specimen during pulse point heating; (b) approximation of the cooling curve of the specimen after its pulse point heating. a. vedernikova et alii, frattura ed integrità strutturale, 49 (2019) 314-320; doi: 10.3221/igf-esis.49.31 317 fig. 3 shows the infrared imaging of the specimen surface at the final stage of loading before its fracture and the timetemperature dependence during the test. at the beginning of the test, the average surface temperature decreases due to the thermoelastic effect, then the thermoplastic effect prevails, and the temperature of the specimen increases until the moment of necking and complete failure. figure 3: ir image of the specimen under quasistatic tensile conditions. according to eqn. (4), the time dependence of the heat source field was estimated based on the change of the specimen temperature during the mechanical test (fig. 4a). the calculated heat source power data were verified by analyzing the data recorded by the seebeck effect-based heat flux sensor. the heat source obtained by both methods do not coincide completely, which can be explained by different sensitivities of the devices, and errors of numerical processing of the infrared thermography data. nevertheless, these results suggest the possibility of using non-contact measurements to estimate the heat source distribution on the specimen surface. one part of the irreversible plastic work contributes to heat generation, and another is stored as the energy of crystal defects accompanying plastic deformation, known as the stored energy of cold work. for flat specimens, the plastic work spent on deformation of the specimen can be defined as a function of strain rate v and loading force  f t :    pw t f t v (5) the stored energy is determined as a difference between the plastic work spent on deformation and the integral heat dissipation. the time dependences of these values are presented in fig. 4b. analysis of the data in fig. 4b suggests that, when the material approaches fracture, the value of stored energy in the material reaches a critical value, and the rate of stored energy tends towards zero. in work [10], the algorithm allowing estimation of the heat transferred by convection, conduction and radiation:                                           2 4 4 cv ir ij ij cv n ir p v v s s v t d dv t dv t t ds t t ds c e dv t (6) where  is the thermal conductivity of the material,  is the heat transfer coefficient by convection,  is the surface emissivity,  is the density, c is the specific heat,  n is the stephan–boltzmann constant equal to 5.67·108 w/(m2 k4),  pe is the rate of variation of the stored energy, t is the room temperature, ( )t x, y,z, t is the time-dependent temperature field, and cvs , cds , irs are the three parts of the external surface of the control volume v through which the heat q is transferred by convection, conduction and radiation, respectively. a. vedernikova et alii, frattura ed integrità strutturale, 49 (2019) 314-320; doi: 10.3221/igf-esis.49.31 318 a) b) figure 4: (a) infrared thermography data vs heat flux sensor data; (b) time dependence of heat dissipation and stored energy (eqn. 4). the parameters q and  pe can be derived via eqn. (6) using the experimental surface temperature measurements and the room temperature data, provided that the heat transfer coefficient  and the surface emissivities  are known. in our case, the specimen surface was coated with a thin layer of amorphous carbon, and the emissivity coefficient was equal to 0.92. the following three different formulae were used in order to evaluate the heat transfer coefficient in the case of natural convection [11]:   2 1/6 8/279/16 1/4 4 1/2 1/4 1/4 0.387 0.825 , 0.492 1 , , 2.43478 4.884 4.95283 0.667 , 0.952 , a ra nu pr pr nu a gr pr a pr pr pr nu ra pr l nu                                          (7) where gr , nu , pr , ra are the non-dimensional grashof, nusselt, prandtl and rayleigh numbers, l is the length of the examined part of the specimen, and a is the thermal conductivity of the air [w/(m k)]. it has been established that these formulae give very similar results and the mean value of heat transfer coefficient   3.7 w/(m2 k). based on the obtained results, we can conclude that conduction is the predominant heat transfer mechanism for titanium alloy grade 2 specimens (fig. 5a). the curve describing stored energy evolution during the mechanical test is presented in fig. 5b. this plot coincides with the curve obtained according to eqn. (4), which confirms the possibility of using the stored energy value as a reliable parameter for diagnosis of fracture. conclusion volution of irreversible deformation in the material is accompanied by the processes of energy accumulation and dissipation. in this work, we analyzed the energy balance of the material during the deformation process by two methods: infrared thermography technique and the method which uses the heat flux sensor. the infrared scanning e a. vedernikova et alii, frattura ed integrità strutturale, 49 (2019) 314-320; doi: 10.3221/igf-esis.49.31 319 method was found to be efficient for estimating the accumulated energy in the titanium alloy grade 2. it was established that conduction is the predominant heat transfer mechanism for the examined material. the value of stored energy reaches a critical value and stored energy rate tends towards zero at the end of deformation process. this indicates that most of the plastic work is converted into heat, and the material is close to being fractured. hence, it can be concluded that the analysis of the energy stored in the material can provide an adequate description of damage evolution in metals under deformation. a) b) figure 5: (a) the different contributions of conduction, convection and radiation to the total energy dissipation; (b) time dependence of heat dissipation and stored energy (eqn. 5). acknowledgments his work was supported by the grants rfbr №18-31-00293 and №16-51-48003. references [1] rosakis, p., rosakis, a.j., ravichandran, g., hodowany j. (2000). a thermodynamic internal variable model for the partition of plastic work into heat and stored energy in metals, j. mech. phys. solids, 48, pp. 581-607. [2] la rosa, g., risitano, a. (2000). thermographic methodology for rapid determination of the fatigue limit of materials and mechanical components, // int. j. fatigue, 22, pp. 65–73. doi: 10.1016/s0142-1123(99)00088-2. [3] oliferuk, w., maj, m., raniecki b. (2004). experimental analysis of energy storage rate components during tensile deformation of polycrystals, mater. sci. eng., 374, pp. 77-81. doi: 10.1016/j.msea.2003.12.056. [4] benaarbiaa, a., chrysochoos, a., gilles r. (2014). kinetics of stored and dissipated energies [5] risitano a., risitano g. (2010). cumulative damage evaluation of steel using infrared thermography, theor. appl. fract. mec., 54(2), pp. 82-90. doi: 10.1016/j.tafmec.2010.10.002. [6] plekhov, o.a., saintier, n., naimark, о.b. (2007). experimental study of energy accumulation and dissipation in iron in an elastic-plastic transition, tech. phys. lett., 52(9), pp. 1236-1238. doi: 10.1134/s106378420709023x. [7] fedorova, a., bannikov, m., terekhina, a., plekhov, o. (2014). heat dissipation energy under fatigue based on infrared data processing, quant infrared thermogr j., 11(1), pp. 2-9. doi: 10.1080/17686733.2013.852416. [8] iziumova, a.yu., vshivkov, a.n., prokhorov, a.e., plekhov, o.a., venkatraman, b. (2016). study of heat source evolution during elastic-plastic deformation of titanium alloy ti-0.8al-0.8mn based on contact and non-contact measurements, pnrpu mechanics bulletin, 1, pp. 68–81. doi: 10.15593/perm.mech/2016.1.05. [9] iziumova, a.yu., plekhov, o.a., vshivkov, a.n., prokhorov, a.a., uvarov, s.v. (2014). studying the rate of heat t a. vedernikova et alii, frattura ed integrità strutturale, 49 (2019) 314-320; doi: 10.3221/igf-esis.49.31 320 dissipation at the vertex of a fatigue crack, tech. phys. lett., 40, pp. 830-832. doi: 10.1134/s1063785014090211. [10] meneghetti, g. (2007). analysis of the fatigue strength of a stainless steel based on the energy dissipation, int j fatigue, 29, pp. 81-94. doi:10.1016/j.ijfatigue.2006.02.043 [11] bonacina, c, cavallini, a, mattarolo, l. 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can be opened with acrobat and adobe reader 5.0 and later.) >> /namespace [ (adobe) (common) (1.0) ] /othernamespaces [ << /asreaderspreads false /cropimagestoframes true /errorcontrol /warnandcontinue /flattenerignorespreadoverrides false /includeguidesgrids false /includenonprinting false /includeslug false /namespace [ (adobe) (indesign) (4.0) ] /omitplacedbitmaps false /omitplacedeps false /omitplacedpdf false /simulateoverprint /legacy >> << /addbleedmarks false /addcolorbars false /addcropmarks false /addpageinfo false /addregmarks false /convertcolors /converttocmyk /destinationprofilename () /destinationprofileselector /documentcmyk /downsample16bitimages true /flattenerpreset << /presetselector /mediumresolution >> /formelements false /generatestructure false /includebookmarks false /includehyperlinks false /includeinteractive false /includelayers false /includeprofiles false /multimediahandling /useobjectsettings /namespace [ (adobe) (creativesuite) (2.0) ] /pdfxoutputintentprofileselector /documentcmyk /preserveediting true /untaggedcmykhandling /leaveuntagged /untaggedrgbhandling /usedocumentprofile /usedocumentbleed false >> ] >> setdistillerparams << /hwresolution [2400 2400] /pagesize [612.000 792.000] >> setpagedevice microsoft word numero 24 articolo 7 ig. s. konovalenko et alii, frattura ed integrità strutturale, 24 (2013) 75-80; doi: 10.3221/igf-esis.24.07 75 special issue: russian fracture mechanics school multiscale approach to description of deformation and fracture of brittle media with hierarchical porous structure on the basis of movable cellular automaton method ig. s. konovalenko institute of strength physics and materials science sb ras, 2/4 akademicheskii pr., tomsk, 634021, russia igkon@ispms.tsc.ru a. yu. smolin, s. g. psakhie institute of strength physics and materials science sb ras, 2/4 akademicheskii pr., tomsk, 634021, russia tomsk state university, 36 lenin pr., tomsk, 634050, russia abstract. an approach to multiscale description of deformation and fracture of brittle porous materials on the basis of movable cellular automaton method was proposed. the material characterized by pore size distribution function having two maxima was considered. the core of the proposed approach consists in finding the automaton effective response function by means of direct numerical simulation of representative volume of the porous material. a hierarchical two-scale model of mechanical behavior of ceramics under compression and shear loading was developed. zirconia based ceramics with pore size greater than the average grain size was considered. at the first scale of the model only small pores (corresponding to the first maximum of the pore size distribution function) were taking into account explicitly (by removing automata from the initial structure). the representative volume and effective elastic properties of the porous material at this scale were evaluated. at the second scale of the model, big pores were taking into account explicitly, the parameters of the matrix corresponded to the ones determined at the first scale. simulation results showed that the proposed multiscale model allows qualitatively and quantitatively correct describing of deformation and fracture of brittle material with hierarchical porous structure. keywords. deformation and fracture; brittle materials; porous ceramics; 2d modeling; particle-based approach, movable cellular automaton method. introduction t is well known that real porous materials are characterized by hierarchical pore structure and complex mechanical behavior, including fracture [1-3]. to study and describe these materials the information about the relationship of their structure and mechanical properties at various scales is needed. one of the ways of getting this information is numerical simulation. in the framework of one-scale approach direct taking into account all peculiarities of structure and mechanical behavior of a material at each scale seems to be impossible. therefore the goal of this paper is development of the multiscale approach, represented in [4], and construction of the corresponding hierarchical model for describing deformation and fracture of nanostructured porous ceramics under compression and shear on the basis of movable cellular automaton method (mca). detailed description of the mca method can be found in paper [5] published in this issue of the journal. note, that this method have been chosen because it has successfully proved itself in studying i http://dx.medra.org/10.3221/igf-esis.24.07&auth=true http://www.gruppofrattura.it ig. s. konovalenko et alii, frattura ed integrità strutturale, 24 (2013) 75-80; doi: 10.3221/igf-esis.24.07 76 mechanical behavior of brittle porous materials from initiation of the first damages till cracks propagation and complete failure [6-9]. the calculations were carried out for a model material having mechanical properties of nanocrystalline zro2(y2o3) (yttria-stabilized zirconia) with the average pore size greater than the average grain size and two maxima in its pore size distribution function [2, 3]. the hierarchical model of the material with properties of the ceramics under consideration was constructed in several stages. at the first stage, the response of the ceramic material at the microscale (20÷250 μm) was simulated with explicit taking into account the porous structure of the material under various types of mechanical loading and the representative volume of this scale was determined. the result of the first stage was determination of the response function parameters of macroscale movable automata, corresponding to representative volume of the microscale. at the second stage, similar calculations were carried out at the macroscale with explicit taking into account of the porous structure of this scale. data on the porous structure of lower scale were allowed for in the effective automata response functions defined at the first stage. at the final third stage, qualitative and quantitative verification of the developed model at the macroscale was made including comparison of simulation and experimental data. determining the representative volume of the microscale and the macroscale effective response function t the microscale of the proposed model, the representative volume is determined by analyzing the convergence of elastic and strength characteristics of porous model specimens with an increase in their dimension. modeling of six groups of porous ceramics specimens under uniaxial compression and simple shear was performed. all the specimens in each group had the same dimension, but different pore distribution in space. each group was consisted of six plane square specimens. specimens under consideration had dimension (square side) of 20, 60, 100, 150, 200 and 250 μm according to the groups. it was supposed that all pores in the ceramics under investigation, as well as the model material, were equiaxed. the pore size of the model material, according to the maximum of the ceramics pore size distribution function, was equal to 3 μm [2, 3]. diameter of the movable cellular automata, according to the average grain size, was equal to 1 μm [2, 3]. the pore structure of the specimens was specified by randomly removing individual automata and their six nearest neighbors. the total porosity for all the specimens was equal to 7% [2, 3]. typical initial structure of one of the model specimens is shown in fig. 1. (a) (b) (c) figure 1: initial structure of a model specimen with a size of h = 60 μm and scheme of loading for shear (a) and uniaxial compression (b); the plot of velocity vs time for the upper automaton layer of the specimen (c). the shear loading was simulated by setting up one and the same horizontal velocity to all automata in the upper layer with automata of the lower layer being rigidly fixed (fig. 1,a,c). at the initial stage, the velocity of automata of the upper layer was increased by the sinusoidal law from 0 to 1 m/s and then was assumed to be constant. this scheme ensured a quasisteady regime of loading and allowed dynamic effects to be eliminated until the first damage appeared. duration of the loading velocity increase depended on the size of the specimen and was determined by preliminary calculations. all the samples had periodic boundary conditions in the direction of shear loading. the uniaxial compression loading was simulated by setting up one and the same velocity in vertical direction (up to 1 m/s) to all automata in the upper layer (fig. 1,b,c). the vertical velocity of automata in the lower layer were set to zero. displacements in horizontal direction were allowed for automata in the both lower and upper layers. the lateral surfaces of the specimen were free. the problem was solved under plane strain conditions. the response function of automata corresponded to the loading a http://dx.medra.org/10.3221/igf-esis.24.07&auth=true http://www.gruppofrattura.it ig. s. konovalenko et alii, frattura ed integrità strutturale, 24 (2013) 75-80; doi: 10.3221/igf-esis.24.07 77 diagram for nanocrystalline zro2(y2o3) with total porosity of 2% and an average pore size to be equal about the grain size [2, 3]. shear modulus g and poisson ratio ν of the movable cellular automaton were equal to 59.2 gpa and 0.3 correspondingly. inter-automaton bond rupture criterion used in calculations was formulated as a threshold value for intensity of shear stresses [10]. (a) (b) (c) (d) figure 2: relative deviation of compression modulus eeff, shear modulus geff, compression strength σc and shear strength τc of the model specimens from the corresponding mean values <eeff>, <geff>, <σc>, <τc> under uniaxial compression (a, b) and shear (c, d). convergence analysis of mechanical properties for the porous model specimens with increase of their size was performed in terms of estimated deviation of effective elastic and strength properties of the specimens (modulus of compression eeff, shear modulus geff, compression strength σc and shear strength τc obtained from simulated loading diagram) from the corresponding mean values in the groups <eeff>, <geff>, <σc> and <τc>. the specimen size for which the deviation did not exceed 3% for eeff, geff and 15% for σc, τc was accepted as the size of representative volume. the results of simulation (fig. 2) showed nonlinear convergence of strength and elastic properties of the model specimens. for the model specimens with the side of 150 μm relative deviations of eeff , geff, σc and τc from the corresponding group average values were 0.51, 0.38, 6.0 and 7.6% correspondingly. these values did not exceed the prescribed limits. thus, it proved that the porous specimens with dimension of 150 μm are representative volumes of the model material under consideration. the values of <eeff> and <σc> were taken as the parameters of response function of automata at macroscopic scale. slight deviations of these values (−9.5 % and 36.0 %) from ones evaluated experimentally are related with two-dimensional formulation of the problem and incomplete correspondence of the model pore morphology with the one of real ceramics. therefore the corresponding characteristics of response function were corrected by means of the correction ratio. the conversion from the elastic modulus determined from the loading diagram under plane strain conditions epss to the young's modulus was based on the ratio )1( 2 pssee [11]. simulations at macroscale t macroscale the calculations were carried out for nine square porous specimens with the dimension of 22.5 mm. according to the representative volume determined at the previous stage the diameter of movable cellular automata at this scale was equal to 150 μm. the information about structure and strength properties of the a http://dx.medra.org/10.3221/igf-esis.24.07&auth=true http://www.gruppofrattura.it ig. s. konovalenko et alii, frattura ed integrità strutturale, 24 (2013) 75-80; doi: 10.3221/igf-esis.24.07 78 material was transferred from microto macroscale by means of the response function with the parameter values corresponding to the loading diagrams of the representative volume of the material at microscale. the response function of automata was chosen to be a linear one and characterized by two parameters: the maximal value of specific resistance force (corresponded to strength limit) and the elastic parameter (corresponded to young’s modulus). the values of these parameters determined at the first stage were found to be equal to 846 mpa and 112 gpa correspondingly. explicit setting up of pore structure of the material at macroscale scale, loading conditions and assumption about stress state were similar with that of the first stage. according to the pore size distribution function the explicit porosity of the macroscale specimens was equal to 28% and the pore size was equal to 450 μm [2, 3]. verification of the model et us assume the model to be successfully verified (i.e. the model represents the main features of the ceramics under investigation) if the simulation results satisfy the following criteria: 1) the loading diagram of the modeled specimen is linear in elastic region and contains horizontal section corresponding to quasi-ductile fracture for porosity greater than 20 %; 2) qualitative correspondence of the fracture patterns of the modeled specimens to real ceramics; 3) strength properties of the modeled specimens belong to a certain value interval found from experimental data. the loading diagrams which are typical for all the model specimens in case of different types of mechanical loading are presented in fig. 3. on these diagrams one can see several parts. the first linear part, corresponding to elastic deformation of the specimen, is typical for brittle materials with any value of porosity. the next part is still ascending but insignificantly, it also contains multiple stress “oscillations” (only under uniaxial compression, fig. 3, a). this part corresponds to repetitive processes of damage generation, local cracking and subsequent elastic deformation of the material all over the entire specimen. the last part of the diagram is descending. it corresponds to macrocrack propagation as well as generation of separate multiple damages. in shear loading (fig. 3, b) one can see another ascending sections of the curve with breakdowns and subsequent drop-down on the plotted diagram after the above mentioned parts. under constrained deformation conditions, it is to these portions of the diagram that the development of a system of macrocracks in the specimen corresponds, and the first descending portion corresponds to nonrecurring generation of damages throughout the entire specimen and their development without the formation of a system of macrocracks. (a) (b) figure 3: loading diagrams of the model specimen with dimension of 22.5 mm under uniaxial compression (a) and shear loading (b). it should be noted, that the horizontal plateau on the compression diagram of the brittle specimens (fig. 3, a) reveals their quasi-ductile fracture, which occurs only when porosity of the specimen is greater than 20% [9]. the extent to which these properties show up is proportional to the length of the given portion (plateau) and is different for different model specimens. a decrease in the length of this diagram portion points to the proximity of fracture to brittle fracture. it would appear reasonable that both the transition to quasi-ductile fracture and the extent to which it develops are determined by certain critical local porosity of the specimens. the critical local porosity is associated, in particular, with the total specimen porosity and with the pore shape and size. it is worthy of note that quasi-ductile fracture in this case is completely determined by the geometric factor, because the model takes into account neither phase transitions, nor rearrangement of the material lattice. l http://dx.medra.org/10.3221/igf-esis.24.07&auth=true http://www.gruppofrattura.it ig. s. konovalenko et alii, frattura ed integrità strutturale, 24 (2013) 75-80; doi: 10.3221/igf-esis.24.07 79 typical loading diagrams of brittle porous solids under shear and uniaxial compression are presented in fig. 4 [2, 9]. comparison of the diagrams in fig. 3 with corresponding diagrams of brittle porous solids in shear and uniaxial compression [2, 9] shows their good qualitative agreement. thus, the first macroscale criterion of model verification, which is in the loading diagram correlation, is fulfilled. typical fracture pattern of the model specimens, represented as inter-automaton bond net at the time of first macrocrack propagation, are shown in fig. 5. under uniaxial compression the specimen failure occurred due to generating therein the asymmetrical system of macrocracks with complex propagation path. in addition, generation of multiple separated fracture regions took place near the macrocracks. (a) (b) (c) figure 4: experimental loading diagrams of zro2 ceramic specimen with different value of porosity under uniaxial compression (a) [2] and corresponding diagrams obtained from numerical simulation (b and c) [9]. (a) (b) figure 5: fracture patterns of the model specimen with the porosity of 28 % at the moment of the first macrocrack propagation under uniaxial compression (a) and shear loading (b). http://dx.medra.org/10.3221/igf-esis.24.07&auth=true http://www.gruppofrattura.it ig. s. konovalenko et alii, frattura ed integrità strutturale, 24 (2013) 75-80; doi: 10.3221/igf-esis.24.07 80 in the case of quasi-ductile fracture (fig. 3, a) damage generation and crack growth occurred locally, in several regions of the sample, characterized by the highest value of local porosity (and the least thickness of web between isolated pores). until a certain moment, some cracks were not merged into main crack, the stage of its growth were somehow elongated. it led to extensive local cracking of the material without losing the integrity of the sample and, consequently, to a substantial dissipation of elastic energy and decreasing of the effective elastic properties of the material (of the whole specimen). thus, the second criterion of the constructed model verification is fulfilled. to verify the third criterion of the model verification the average value of the effective elastic modulus (<eeff>) and maximum specific resistance force to loading under uniaxial compression were calculated. then they were compared with the corresponding values found from real experiments. it was shown that the deviation of <σs_eff> and <eeff> for the model samples from the experimental data did not exceed 30 % and 12 %, respectively. it is a rather good accuracy for simulating highly porous media in plane approximation. this indicates to a good quantitative agreement of the calculations and the experiment and means that the third criterion of the model verification is fulfilled. thus, a two-scale model of porous ceramics with bimodal pore size distribution function was constructed herein based on a multiscale approach to numerical simulation and validated against available experimental data. conclusions multiscale approach to numerical simulation of porous materials is developed on the basis of movable cellular automaton method. the hierarchical two-scale model constructed using the proposed approach can adequately describe deformation and fracture of the porous zirconia ceramics under mechanical loading. since the proposed approach is sufficiently general, then, if it is necessary, a heterogeneous material containing more than two structural scales can be also simulated on the basis of this approach. acknowledgements his study was supported by the russian foundation for basic research, project no. 12-08-00379-а. references [1] global roadmap for ceramics: proceedings of 2nd international congress on ceramics (icc2). alida belosi and gian nicola babini (eds.). institute of science and technology for ceramics, national research council, verona (italy), (2008). [2] s.p. buyakova, han wei, li dunmy et al., tech. phys. lett., 25(9) (1999) 695. [3] s.n. kulkov, s.p. buyakova, v.i. maslovskii, vestnik tgu, 13 (2003) 34 [in russian] [4] ig.s. konovalenko, a.yu. smolin, s.g. psakhie, phys. mesomech., 13(1–2) (2010) 47. [5] s. psakhie, e. shilko, a. smolin, s. astafurov, v. ovcharenko, frattura ed integrità strutturale, 24 (2013) 26. [6] ig.s. konovalenko, a.yu. smolin, in: proc. of the xxxvi summer school “advanced problems in mechanics (apm’ 2008)” d. a. indeitsev, a. m. krivtsov (eds.), institute for problems in mechanical engineering, st. petersburg, (2008) 352. [7] a.yu. smolin, ig.s. konovalenko, s.n. kul’kov, s.g. psakhie, tech. phys. lett., 32(9) (2006) 738. [8] a.yu. smolin, ig.s. konovalenko, s.n. kulkov, s.g. psakhie, izv. vuzov fizika, 49(3) (2006) 70 [in russian]. [9] ig.s. konovalenko, theoretical study of deformation and fracture of porous materials for medicine and biomechanical structures, cand. degree thesis (phys&math), ifpm so ran, tomsk, (2007) [in russian]. [10] l.m. kachanov, the foundations of fracture mechanics, nauka, moscow, (1974) [in russian] [11] l.i. sedov, a course in continuum mechanics, wolters-noordhoff, groningen, (1971). a t http://dx.medra.org/10.3221/igf-esis.24.07&auth=true http://www.gruppofrattura.it microsoft word numero_45_art_13 p. jinchang et alii, frattura ed integrità strutturale, 45 (2018) 156-163; doi: 10.3221/igf-esis.45.13 156 graphene oxide on the microstructure and mechanical properties of cement based composite material pang jinchang, wang yeming college of architecture and civil engineering, nantong institute of technology, nantong, jiangsu, 226000, china pjcpangjc@163.com abstract. to investigate the mixing amount of graphene oxide and water cement ratio on the microstructure and mechanical properties of graphene oxide reinforced cement based composite material, graphene oxide suspension was developed using improved hummers method, and the structure, size and morphology of graphene oxide were represented using fourier transform infrared spectroscopy (ftir), x-ray diffraction (xrd) and afm. the results demonstrated that the bending and compressive strength of graphene oxide reinforced cement based composite material improved firstly and then declined with the increase of the mixing amount of graphene oxide, and moreover the improvement of the bending strength was obvious than that of the compressive strength. when the content of graphene oxide was 0.03%, the bending strength reached the maximum, 13.73 mpa. under a high water cement ratio, the addition of graphene oxide was more effective in enhancing the strength of cement mortar. the representation of the microstructure of cement based composite material with scanning electron microscope (sem) suggested that graphene oxide could optimize the microstructure of cement hydration products, improve the pore structure of set cement, reduce the volume of micropore in set cement, and increase the compactness of set cement, i.e. apparently strengthen the toughening effect of set cement. the research achievements are useful to improve the mechanical properties of cement based composite materials. keywords. graphene oxide; cement based composite material; mechanical properties. citation: jinchang, p., yeming, w., graphene oxide on the microstructure and mechanical properties of cement based composite material, frattura ed integrità strutturale, 45 (2018) 156-163. received: 25.03.2018 accepted: 02.06.2018 published: 01.07.2018 copyright: © 2018 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. introduction oncrete is the most extensively applied cement based composite material [1, 2] which is composed of cement, dinas, rebars and reinforced fibers. concrete has been extensively applied in the construction of buildings, roads, bridges and dams for its advantages of extensive source of raw materials, low cost, simple preparation techniques and high strength [3-6]. with the development of the construction field, concrete which was a traditional structural material with high bearing capacity has developed to be more functional and environmental-friendly. currently, high performance concrete (hpc), an important development direction of concrete, is a cement based composite material with high strength, durability c http://www.gruppofrattura.it/va/45/16.mp4 p. jinchang et alii, frattura ed integrità strutturale, 45 (2018) 156-163; doi: 10.3221/igf-esis.45.13 157 and workability [7, 8]. the cement composites have a noticeable feature of relatively high compressive strength and low tensile and flexural strength, which belong to brittle materials. new carbon materials such as carbon fibers and carbon nanotubes were used to enhance the strength of cement composites or provide the cement composites with improved thermal performance. nevertheless, the reinforcing materials such as carbon fibers and carbon nanotubes only play a physical role in the cement composites and take no participation in the hydration and microstructural modification of the cement, especially the pore structure and crystalline structure of cement paste. the dispersion of carbon fibers and carbon nanotubes in the cement matrix is also challenging because of the hydrophobic surface of these reinforcing materials [9-11]. therefore, it is urgent to find a new material which cannot only disperse uniformly in the aqueous system of hydrated cement, but also improve the toughness of hardened cement paste by microstructural modifications. graphene oxide is an intermediate product in graphene preparation, which has many advantages as a reinforcing material such as excellent mechanical, electrical and thermal properties [12-14]. it is easy to disperse uniformly in cements, which is beneficial to the reinforcing effect. but the study on modifying traditional cement with graphene oxide is just getting started. some scholars have investigated the modification of cement based composite material with graphene oxide. cao et al. [9] added the modified graphene into cement and found that the addition of graphene could produce promotion and template effects on the formation of hydrate crystal product to improve the strength and tenacity of cement-based materials. babak et al. [15] studied the mechanical properties of graphene oxide reinforced cement based composite material and found that the tensile strength had an improvement of 48% when the weight proportion of graphene oxide was 1.5%. in the study of liang et al. [16], graphite oxide was dispersed to water via ultrasound and blended with polyvinyl alcohol solution. then polyvinyl alcohol/graphene oxide composite was prepared by volatilizing solvent via solution casting. when 0.7wt% of graphene oxide was added, the tensile strength and young's modulus of the composite was improved76% and 62% respectively compared to pure polyving alcohol, and moreover the thermal decomposition of the composite was also improved. in this study, graphene oxide was prepared using oxidation reduction to study the effects of different mixing amount of graphene oxide and water cement ratio on the mechanical properties (bending and compressive strength) and microstructure of cement based composite material and analyze the variation rules. this work aims to figure out the influencing mechanism of the mixing amount of graphene oxide and water cement ratio on graphene oxide reinforced cement based composite material to lay a basis for the application of graphene oxide in cement based material. experimental scheme experimental materials aterials included graphite powder (granularity ≤ 30 μm, sinopharm chemical reagent co., ltd., china), concentrated sulfuric acid (h2so4, 98% mass fraction), potassium permanganate (kmno4, mass fraction ≥ 99.5%), concentrated phosphoric acid (hpo3, mass fraction ≥ 85%), hydrogen peroxide (h2o2, 30% mass fraction), polycarboxylate superplasticizer, ordinary portland cement p.o.42.5 and iso standard sand. preparation of graphene oxide 1 g of graphite powder and 46 ml of concentrated sulfuric acid were added into a conical flask. the temperature was kept below 3 °c. then 6 g of kmno4 was slowly added during stirring for 2 h of reaction at 15 °c and 10 h (20 h/30 h/40 h) of reaction at 35 °c; the reactant turned to be green. then 100 ml of deionized water was slowly added for 30 min of reaction at 80 °c. after the addition of 15 ml of 30% hydrogen peroxide, the reactant turned to be golden yellow; the reaction continued for 30 min. next centrifugation and washing with deionized water were performed until there was no 2 4so in the washing liquid. the value of ph was adjusted to 7.0. it was processed by ultrasonic wave under 500 w for 30 min to obtain graphene oxide dispersion liquid after the addition of polycarboxylate superplasticizer. its mass fraction was controlled at 0.2%. representation of graphene oxide the x-ray diffraction (xrd) of graphite and graphite oxide were detected using d/max 2200 pc x-ray diffractometer (rigaku, japn). cu kα was x-ray source. the test was performed under 40 kv and 40 ma, and the angle was between 2° and 70°. irprestige-21 fourier transform infrared spectrometer was used to represent the molecular structure and functional group of graphene oxide and identify the category of the functional group. specimens used for fourier transform infrared spectroscopy (ftir) was dried using a dryer and ground into powder. kbr pellet pressing method was used. m p. jinchang et alii, frattura ed integrità strutturale, 45 (2018) 156-163; doi: 10.3221/igf-esis.45.13 158 the size of graphene oxide nanosheets was detected using spi3800n/spa400 atomic force microscope (nsk, japan). 0.5 % graphene oxide was diluted to 1500 times, and one drop was taken and dried on a monocrystalline silicon piece (10 mm × 10 mm) at 25 °c. preparation of graphene oxide reinforced cement based composite material it has been found that the addition of a small amount of nanometer material can significantly improve various performances of composite materials [17, 18]. in this study, the mass fraction of graphene oxide was set as 0%, 0.01%, 0.03%, 0.05% and 0.07% to study the effects of the mixing amount of graphene oxide on the mechanical properties of test specimens. water cement ratio is an important parameter determining the strength, working performance and durability of cement based composite material [19]. water cement ratio was set as 0.35, 0.4, 0.45 and 0.5 to investigate the variation rules of the mechanical strength of specimens under the same mixing amount of graphene oxide and different water cement ratio. 0.2% polycarboxylate superplasticizer was added to all the specimens to solve the problem of reduced fluidity caused by the addition of graphene oxide [20]. according to the preparation techniques described in method of testing cements determination of strength (gb176711999), cement mortar was put into a mould in a size of 40 mm ×40 mm × 160 mm for curing. then the test specimens were developed as per the mix proportion shown in tab. 1 for the compressive and bending strength tests. all the specimens were demoulded after 24 h of maintenance and then maintained in water under standard conditions, i.e. 20 °c and 90% relative humidity, before test. no. of specimen cement/g water cement ratio standard sand/g graphene oxide/wt% polycarboxylate superplasticizer/wt % 1 450 0.35 1350 0 0.2 2 0.35 0.01 3 0.35 0.03 4 0.35 0.05 5 0.4 0 6 0.4 0.03 7 0.45 0 8 0.45 0.03 9 0.5 0 10 0.5 0.03 table 1: the mix proportion of cement mortar specimens. test on the mechanical properties of cement mortar the test specimens were taken out from water and dried, and then the bending and compressive strength of the specimens were detected under 50 n/s and 2400 n/s following gb17671-1999. in each group, three test specimens were tested, and the average value was taken as the final result. samples were collected from the crashed fracture surface of the test specimens and immersed in absolute ethyl alcohol to stop hydration, and finally preserved in a vacuum drier. energy spectrum was analyzed using an american jsm-6360lv scanning electron microscope (sem) and a spectrometer. test results and analysis analysis of representation of graphene oxide he xrd spectra of graphite powder and graphite oxide sample are shown in fig. 1. the peak in the curve (a) of fig. 1 was the characteristic peak of graphite, and the peak in the curve (b) was the characteristic peak of graphene oxide. the results demonstrated that the interlayer spacing of graphene oxide increased from 0.33855 nm to 0.83859 nm, which contributed to the introduction of oxygen-containing groups in graphite nanosheets under oxidation. oxygen connected with graphene in the form of a covalent bond, leading to the changes of laminated structure and diffraction peak deviation of graphene oxide. t p. jinchang et alii, frattura ed integrità strutturale, 45 (2018) 156-163; doi: 10.3221/igf-esis.45.13 159 figure 1: the xrd spectra of graphite and graphite oxide. the ftir spectrum of graphite oxide is shown in fig. 2. as shown in fig. 2, the stretching vibration and bending vibration peaks of -oh in water molecule were at 3394 cm-1 and 1622 cm-1 respectively, the the stretching vibration and bending vibration peaks of -oh in hydroxyl group were at 3141 cm-1 and 1401 cm-1 respectively, the stretching vibration peak of c=o in carboxyl group and carbonyl group at the edge of graphite oxide nanosheets was at 1727cm-1 , and the stretching vibration peaks of c-o-c/-c-o were at 1116 cm-1 and 1075 cm-1. the existence of those characteristic peaks suggested that oxygen-containing groups such as carboxyl group, epoxy group and carbanyl group were introduced in the preparation of graphite oxide, i.e. graphite has been successfully oxidized. figure 2: the ftir spectrum of graphite oxide. figure 3. afm image of graphene oxide nanosheets. afm image of graphite oxide is shown in fig. 3. it can be seen from fig. 3 that the size and thickness of graphite oxide sheet were 100-1000 and 0.7 nm, respectively, indicating that graphite oxide is one or two atom thick layers. it suggested that the prepared graphite oxide with oxygen-containing functional group on the surface had favorable dispersion and peeling. effects of the mixing amount of graphene oxide on the mechanical properties of the test specimens the bending and compressive strength of the prepared graphene oxide reinforced cement based composite material were tested, as the results are shown in tab. 2 and 3. p. jinchang et alii, frattura ed integrità strutturale, 45 (2018) 156-163; doi: 10.3221/igf-esis.45.13 160 no. of test specimen water cement ratio mixing amount of graphene oxide/(%) bending strength/ mpa growth rate of bending strength/(%) compressive strength/mpa growth rate of compressive strength/(%) 1 0.35 0 11.07 65.66 2 0.35 0.01 11.12 0.28 68.07 3.66 3 0.35 0.03 13.73 23.82 72.78 10.86 4 0.35 0.05 9.96 -10.21 55.42 -15.61 table 2: the basic mechanical properties of cement mortar under different mixing amount of graphene oxide. no. of test specimen water cement ratio mixing amount of graphene oxide/(%) bending strength/ mpa growth rate of bending strength/(%) compressive strength/mpa growth rate of compressive strength/(%) 1 0.35 0 11.07 65.66 3 0.35 0.03 11.13 23.82 72.78 10.86 5 0.4 0 10.41 63.84 6 0.4 0.03 11.85 10.49 67.95 6.42 7 0.45 0 9.32 60.44 8 0.45 0.03 10.94 17.41 65.66 8.60 9 0.5 0 5.77 30.57 10 0.5 0.03 9.98 73.10 52.66 72.36 table 3: the basic mechanical properties of cement mortar under different water cement ratios. figure 4: the variation of the bending and compressive strength of graphene oxide reinforced cement based composite material with the changes of the mixing amount and water-cement ratio of graphene oxide. fig. 4(a) described the variation rules of the mechanical properties of graphene oxide reinforced cement based composite material with the variation of the mixing amount of graphene oxide when the water-cement ratio was 0.35. as shown in the figure, the influence of the mixing amount of graphene oxide on the compressive and bending strength of the test specimens was consistent, i.e. increase firstly and then decrease; the compressive and bending strength was maximum when the mixing amount of graphene oxide was 0.03%, and there was a growth rate of 23.83% and 10.85%, indicating that the improvement of the bending strength was more obvious when the mixing amount of graphene oxide was within a certain range; when the mixing amount exceeded 0.03%, the bending and compressive strength had significant decline and even became lower than that of the blank samples. the first reason might be water demand significantly improved after the addition of cementbased materials because of the extremely large surface energy and specific surface area of graphene oxide. zhu [21] found that the slump of cement paste which contained 0.05% graphene oxide reduced by 41.7%, which revealed that water demand sharply increased with the increase of the content of graphene oxide. the second reason might be graphene oxide was prone to gather because of van der waals attraction when the content of graphene oxide was high. moreover, many water molecules around were absorbed, leading to inconsistent water-cement ratio and uneven hydrate formation. fig. 4(b) shows the variation rules of the mechanical properties of compound cement mortar under different water cement ratio. the mechanical performance of the test specimens which were mixed with graphene oxide was superior to that of the specimens which were not mixed with graphene oxide, and the larger the water-cement ratio, the lower the strength of the p. jinchang et alii, frattura ed integrità strutturale, 45 (2018) 156-163; doi: 10.3221/igf-esis.45.13 161 test specimens. but when the water-cement ratio increased from 0.45 to 0.5, the strength of the test specimens which were not mixed with graphene oxide significantly declined, and the bending and compressive strength changed more gently. when the water-cement ratio was 0.5, the growth rates of the bending and compressive strength of the test specimens which were not mixed with graphene oxide were maximum, 73.09% and 72.35% respectively. on one hand, residual water evaporated during setting and hardening of cement paste, leading to the generation of large pores; on the other hand, graphene oxide was prone to fill in the micro-pores of the cement paste to improve the structure under a high water cement ratio. but graphene oxide as a nanometer material cannot fill in the large pores left after evaporation of water; therefore, the overall decrease tendency of the strength did not change with the variation of the water cement ratio. effects of graphene oxide on the microstructure of graphene oxide reinforced cement-based composite material fig. 5 exhibits the sem images of the test specimens under different mixing amount of graphene oxide (0, 0.01%, 0.03% and 0.05%). the calcium silicate hydrate (csh) gel and calcium hydroxide (ch) grew in the test specimens which were not mixed with graphene oxide. there were many pores in the hardened cement paste, and the insufficient ettringite inside the pores led to loose connection. but a large amount of ettringite scattering on the surface failed to play the roles of filling and connection, which was not beneficial to the structure of cement mortar. with the addition of graphene oxide, tiny csh gels in a size of 1 μm distributed on the surface of cement particles like a roll leaf (fig. 5(b)). when the content of graphene oxide was 0.03%, the structure of the hardened cement paste was significantly improved, no isolated hydration products were observed, and csh structure in the shape of roll leaf which became more even and compact covered on the surface of other crystals and cement particles (fig. 5(c)). when the content of graphene oxide was 0.05%, a compact and even structure which was composed of various hydrates was observed, but large pores and cracks appeared in the surrounding and flocculent csh gel scattered on the surface (fig. 5(d)). (a) the content of graphene oxide was 0. (b) the content of graphene oxide was 0.01%. (c) the content of graphene oxide was 0.03%. (d) the content of graphene oxide was 0.05%. figure 5: the test specimens under different mixing amount of graphene oxide under scanning electron microscope. p. jinchang et alii, frattura ed integrità strutturale, 45 (2018) 156-163; doi: 10.3221/igf-esis.45.13 162 conclusions raphene oxide solution was prepared using the improved hummers method and mixed with cement mortar to form cement-based composite material to investigate the effects of different mix proportion on the mechanical properties and microstructure of graphene oxide reinforced cement based composite material. the following conclusions were obtained. (1) when the water cement ratio was fixed. the mechanical strength of cement mortar increased with the increase of the content of graphene oxide and reached the maximum when the content of graphene oxide was 0.03%; the increase of the bending strength (23.83%) was the most obvious. those findings suggested the addition of graphene oxide could greatly improve the toughness of cement. (2) when the content of graphene oxide was 0.03%, cement mortar was the same with the traditional cement; the larger the water cement ratio, the lower the strength. but the specimens which were added with graphene oxide effectively slowed the decline of the strength of the specimens with high water cement ratio (w/c=0.5). compared to the blank specimens, the bending and compressive strength of the specimens which was mixed with graphene oxide had an improvement of 73.09% and 72.35%. (3) the analysis of the microstructure suggested that the addition of graphene oxide could affect the growth form and number distribution of cement hydration products. the filling effect, hydration effect and nucleation effect of graphene oxide was notable when the content of graphene oxide was within a certain range. graphene oxide became the zone for various hydration reactions because of its large specific surface area, which provided a better growth space for hydration products. it could reduce the porosity of the hardened cement paste and make the structure of cement mortar tighter; leading to the improved strength and ductibility. the above research results which were similar to the research results of xu et al. [22] were meaningful to improve the bending strength and crack resistance of cement-based materials and extend their service life, which can provide a reference for the future studies. acknowledgments his study was supported by the key laboratory of architectural structure (project no. cp12015005). references [1] boulekbache, b., hamrat, m. and chemrouk, m., et al., (2012). influence of yield stress and compressive strength on direct shear behaviour of steel fibre-reinforced concrete, construction and building materials, 27(1), pp. 6-14. [2] wille, k., naaman, a.e. and parra-montesinos, g.j. (2012). ultra-high performance concrete and fiber reinforced concrete: achieving strength and ductility without heat curing, materials and constructure, 3, pp. 1-16. [3] han, y. (2015). study on properties of cement based composites based on grapheme, low temperature architecture technology, 2, pp. 4-6. [4] nobili, a., lanzoni, l. and tarantino, a.m. (2013). experimental investigation and monitoring of a polypropylenebased fiber reinforced concrete road pavement, construction and building materials, 47, pp. 888-895. [5] liu, x.h., duan, y., zhou, w., et al. (2013). modeling the piped water cooling of a concrete dam using the heat-fluid coupling method, journal of engineering mechanics, 139(9), pp. 1278-1289. [6] freyne, s., ramseyer, c. and giebler, j. (2012). high-performance concrete designed to enhance durability of bridge decks: oklahoma experience, journal of materials in civil engineering, 24(7), pp. 933-936. [7] yu, h.y., zhao, r.x. and zou, h.f. (2005). development and prospect of cement-based composite materials. henan building materials, 3, pp. 21-19. [8] feng, n.q. (2003). development and application of high performance concrete, construction technology, 32(4), pp. 1-6. [9] cao, m.l. (2015). effect of graphene on mechanical properties and microstructure of cement paste, journal of harbin institute of technology, 47, pp. 26-30. g t p. jinchang et alii, frattura ed integrità strutturale, 45 (2018) 156-163; doi: 10.3221/igf-esis.45.13 163 [10] li, g.y. and wang, p.m. (2005). microstructure and mechanical properties of carbon nanotubes cement matrix composites, journal of the chinese ceramic society, 33(1), pp. 105-108. [11] lao, y.s., zhang, l., wang, x.p., et al. (2014). research progress in effect of nanoparticles on the performance of cement-based materials, materials review, 28(3), pp. 93-96. [12] yang, q.h. (2011). dreams may come: from fullerene, carbon nanotube to grapheme, new carbon material, 26(1), pp. 1-4. [13] du, h.j., pang, s.d. (2015). transport of water and chloride ion in cement composites modified with graphene nanoplatelet, key engineering materials, 629-630(1), pp. 162-167. [14] yang, y.g., chen, c.m., wen, y.f., et al. (2008). oxidized graphene and graphene based polymer composites, new carbon materials, 23(3), pp. 193-200. [15] babak, f., abolfazl, h., alimorad, r., et al. (2014). preparation and mechanical properties of graphene oxide: cement nanocomposites, the scientific world journal, 1, pp. 1-10. [16] liang, j.j., huang, y., zhang, l., et al, (2009). molecular-level dispersion of graphene into poly(vinyl alcohol) and effective reinforcement of their nanocomposites, advanced functional materials, 19, pp. 2297-2302. [17] morsy, m.s., alsayed, s.h. and aqel, m. (2011). hybrid effect of carbon nanotube and nano-clay on phsico-mechanical properties of cement mortar, construction & building materials, 25, pp. 145-149. [18] cwirzen, a., habermehl-cwirenzen, k. and penttala, v. (2008). surface decoration of carbon nanotubes and mechanical properties of cement/carbon nanotubes composites, advances in cement research, 20(2), pp. 65-73. [19] makar, j.m., margeson, j.c. and luh, j. (2005). carbon nanotube/cement composites-early results and potential applications, nrc publications record, pp. 1-10. [20] yu, s., dong, z., et al. (2015). effect of grapheme oxide on the rheological properties of cement pastes, construction & building materials, 96, pp. 20-28. [21] zhu, p., li, h., et al. (2015). mechanical properties and microstructure of a grapheme oxide-cement composite, cement & concrete composites, 58, pp. 140-147. [22] xu, y.d., zeng, j.q., chen, w., et al. 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can be opened with acrobat and adobe reader 5.0 and later.) >> /namespace [ (adobe) (common) (1.0) ] /othernamespaces [ << /asreaderspreads false /cropimagestoframes true /errorcontrol /warnandcontinue /flattenerignorespreadoverrides false /includeguidesgrids false /includenonprinting false /includeslug false /namespace [ (adobe) (indesign) (4.0) ] /omitplacedbitmaps false /omitplacedeps false /omitplacedpdf false /simulateoverprint /legacy >> << /addbleedmarks false /addcolorbars false /addcropmarks false /addpageinfo false /addregmarks false /convertcolors /converttocmyk /destinationprofilename () /destinationprofileselector /documentcmyk /downsample16bitimages true /flattenerpreset << /presetselector /mediumresolution >> /formelements false /generatestructure false /includebookmarks false /includehyperlinks false /includeinteractive false /includelayers false /includeprofiles false /multimediahandling /useobjectsettings /namespace [ (adobe) (creativesuite) (2.0) ] /pdfxoutputintentprofileselector /documentcmyk /preserveediting true /untaggedcmykhandling /leaveuntagged /untaggedrgbhandling /usedocumentprofile /usedocumentbleed false >> ] >> setdistillerparams << /hwresolution [2400 2400] /pagesize [612.000 792.000] >> setpagedevice microsoft word 2242 v. rizov, frattura ed integrità strutturale, (2047) 468-481; doi: 10.3221/igf-esis.47.37 468 influence of material inhomogeneity and non-linear mechanical behavior of the material on delamination in multilayered beams victor rizov department of technical mechanics, university of architecture, civil engineering and geodesy, 1 chr. smirnensky blvd., 1046 – sofia, bulgaria v_rizov_fhe@uacg.bg abstract. the delamination fracture in four-point bending beams made of adhesively bonded lengthwise vertical layers is studied assuming that each layer exhibits smooth material inhomogeneity along the width and length of the layer. the study aims at determining the strain energy release rate with applying the ramberg-osgood equation for modeling the non-linear mechanical behavior of the material in each layer. cosine laws are used to describe the continuous variation of the modulus of elasticity in width and length directions of layers. beams made of an arbitrary number of vertical layers which have individual widths and material properties are considered. besides, the delamination crack is located arbitrary between layers, i.e. the two crack arms have different widths. the j-integral is applied for verification of the non-linear solution to the strain energy release rate derived in the present paper. the solution is used to investigate the influence of material inhomogeneity in width and length directions of layers, the crack location along the beam width, the non-linear mechanical behavior of the material and the crack length on the delamination fracture behavior. the approach developed is expected to be useful in structural design of multilayered inhomogeneous beams with considering the delamination fracture behavior. keywords. multilayered beam; material inhomogeneity; delamination fracture; non-linear mechanical behavior of the material. citation: rizov, v., influence of material inhomogeneity and non-linear mechanical behavior of the material on delamination in multilayered beams, frattura ed integrità strutturale, 47 (2019) 468-481. received: 31.10.2018 accepted: 17.12.2018 published: 01.01.2019 copyright: © 2017 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. introduction tructural members and components made of adhesively bonded layers of dissimilar materials are extensively used in various applications in aerospace and civil engineering mainly when high performance is required [1-3]. various studies of adhesively bonded joints of fiber reinforced composites and sandwich structures have been reviewed in [1]. the influence of different factors such as joint configuration, adhesive properties, preparation of surfaces and environment factors on the joint behavior has been evaluated and discussed thoroughly. methods and approaches for predicting the failure behavior have been presented too. the application of fracture mechanics for analyzing of adhesively s http://www.gruppofrattura.it/va/47/2242.mp4 v. rizov, frattura ed integrità strutturale, (2047) 468-481; doi: 10.3221/igf-esis.47.37 469 bonded joints has also been considered. it has been shown the importance of using of reliable failure criteria for widening the application of adhesively bonded joints in load-bearing composite and sandwich structural members and components in different industries [1]. a through review of recent publications on failure behaviour of different type of fiber reinforced composite materials has been presented in [2]. various aspects of fatigue and life prediction of fiber reinforced composites have been discussed in detail. the effects of inherent and environmental factors such as temperature, moisture and corrosion on fatigue and failure of composites have been analyzed. a summary of commonly used failure criteria for life prediction of composite structures subjected to static and fatigue load conditions has been reported. a progressive fatigue model has also been considered in the review. models for prediction of residual mechanical properties of composites under different loading conditions have been described and discussed [2]. the thermomechanical behaviour of a carbon fiber composite laminated sheet that is irradiated by using a continuous wave chemical oxygen iodine laser has been analyzed in [3]. a potential delamination of the composite sheet makes the analysis of the influence of the laser an important practical task. the temperature distribution in the composite has been studied. the peak temperature of irradiated region has been evaluated. it has been found that the model developed is suitable for simulating of laser ablation of carbon fiber epoxy composite materials. the study has indicated that the laser beam machining is an appropriate process for manufacturing of fiber reinforced composite materials [3]. however, multilayered materials and structures have low interlaminar strength which is a premise for development of delamination cracks [4, 5]. delamination fracture or separation of layers is the predominant failure mode of multilayered structures. the service lifetime of laminated composite structural members and components is limited by their delamination fracture behavior under certain loading conditions [4]. delamination fracture of multilayered material systems under mode ii crack loading conditions with considering of the creep behavior has been studied in [4]. for this purpose, the methods of linear elastic fracture mechanics have been applied. an elevated temperature has been used to accelerate the delamination fracture under constant external loads. delamination behavior of a double cantilever beam configuration has been analyzed. by using of the paris power law, a methodology for predicting the service lifetime of multilayered beam structures in terms of service load, temperature and initial delamination crack length has been developed [4]. a review of techniques for modeling and analysis of functionally graded single layers and sandwich beam configurations has been presented in [5]. various solutions which are based on the assumption for linear-elastic behavior of the functionally graded material have been presented and discussed. analyses of beam structures under both static and dynamic loading conditions have been considered. free and forced vibrations of functionally graded sandwich constructions have been studied. investigations of functionally graded sandwich beams resting on two-parameter elastic foundation have been reported. studies of buckling behaviour of sandwich beams have been reviewed too. various analyses of bending behaviour of viscoelastic sandwich structures have been discussed. works dealing with static analyses of functionally graded sandwich beams resting on a pasternak elastic foundation have also been presented. solutions of linear-elastic beams made of functionally graded materials under tension and bending have been considered [5]. the main goal of the present paper is to derive the strain energy release rate for a delamination crack in multilayered fourpoint bending beam configurations assuming that each layer exhibits smooth material inhomogeneity in width and length directions. the beam under consideration is made of an arbitrary number of adhesively bonded lengthwise vertical layers which have non-linear mechanical behavior of the material that is treated by applying the ramberg-osgood equation. it should be mentioned that in his previous works, the author has studied delamination fracture behavior of various multilayered beam structures made by lengthwise vertical inhomogeneous layers usually by applying power law stress-stain relations for modeling the non-linear mechanical behavior of the material [6, 7]. the solution to the strain energy release rate derived in the present paper can be applied in fracture mechanics based structural design of multilayered beams made of inhomogeneous materials such as functionally graded materials which have been widely used in recent years as advanced structural materials in many engineering applications [8, 9, 10, 11, 12, 13, 14, 15]. determination of the strain energy release rate multilayered four-point bending beam configuration containing a delamination crack of length, 2a , is shown schematically in fig. 1. the external loading consists of two vertical forces, f , applied at the two ends of the beam. the beam crosssection is a rectangle of width, b , and height, h . the length of the beam is  1 22 l l . it is assumed that the beam is made a v. rizov, frattura ed integrità strutturale, (2047) 468-481; doi: 10.3221/igf-esis.47.37 470 of adhesively bonded lengthwise vertical layers which exhibit material inhomogeneity in both width and length directions. the number of layers is arbitrary. each layer has individual width and material properties. besides, each layer exhibits nonlinear mechanical behavior of the material which is treated by applying the ramberg-osgood equation. a notch of depth, 2b , is introduced in the right-hand lateral surface of the beam in order to generate conditions for delamination fracture. the delamination crack is located symmetrically with respect to the mid-span. besides, the delamination crack is located arbitrary between vertical layers. therefore, the cross-sections of the two crack arms have different widths denoted by 1b and 2b for the left-hand and right-hand crack arms, respectively. the notch divides the right-hand crack arm in two symmetric segments of length, a , each. apparently, the two segments of the right-hand crack arm are free of stresses. it should also be mentioned that the delamination crack is located in the beam portion, 2 4b b , which is loaded in pure bending (fig. 1). due to the symmetry, only half of the beam,  1 2 3 1 22l l x l l    , is considered in the present fracture analysis. figure 1: loading and geometry of the multilayered four-point bending beam configuration. the delamination fracture behavior is studied in terms of the strain energy release rate, g . for this purpose, the strain energy release rate is written as [16] *du g da  (1) where *du is an elementary change of the complementary strain energy, da is an elementary increase of the delamination crack area. since da hda (2) formula (1) takes the form *du g hda  (3) v. rizov, frattura ed integrità strutturale, (2047) 468-481; doi: 10.3221/igf-esis.47.37 471 where da is an elementary increase of the delamination crack length. figure 2: cross-section of the left-hand crack arm in the beam mid-span. since the delamination crack is located in beam portion, 2 4b b , the complementary strain energy cumulated in the beam portions, 1 2b b and 4 5b b , does not depend on the delamination crack length (fig. 1). thus, it is enough to calculate the complementary strain energy cumulated in beam portion, 3 4b b , only. since the two segments of the right-hand crack arm are free of stresses, the complementary strain energy, *u , is written as * * * l ru u u  (4) where *lu and * ru are the complementary strain energies cumulated in the left-hand crack arm and the un-cracked beam portion, 1 2 3 1 22l l a x l l     . the complementary strain energy cumulated in the left-hand crack arm is expressed as 1 1 1 2 * * 0 1 1 1 1 0 2 il i i h yai n l l i hy u u dx dy dz         (5) where ln is the number of layers in the left-hand crack arm, 1iy and 1 1iy  are the coordinates, respectively, of the lefthand and right-hand lateral surfaces of the i-th layer, *0 ilu is complementary strain energy density in the same layer, the axes, 1x , 1y and 1z , are shown in fig. 2. the ramberg-osgood stress-strain relation which is used to model the material non-linearity is written as 1 imi i i ie h            (6) where  is the distribution of the lengthwise strains in the cross-section of the left-hand crack arm, i is the distribution of the normal stresses in the cross-section of the i-th layer, ie is the modulus of elasticity in the same layer, ih and im are v. rizov, frattura ed integrità strutturale, (2047) 468-481; doi: 10.3221/igf-esis.47.37 472 material properties which describe the hardening behavior of the material (actually, the second term of the right-hand side of (6) models the material non-linearity). each layer exhibits smooth material inhomogeneity along the width and length of the layer. thus, it is assumed that the modulus of elasticity in the i-th layer varies continuously along the width according to following cosine law: 1 1 1 1 1 cos 2i i i i d f i i y y e e e y y           (7) where 1 1 1 1i iy y y   . (8) in (7), id e is the value of the modulus of elasticity at the right-hand lateral surface of the layer, if e is a material property which governs the material gradient along the width. apparently, the value of the modulus of elasticity at the left-hand lateral surface of the layer is i id f e e . the continuous variation of id e in the length direction of the i-th layer is written as 1 2 3 1 2 cos 2i i i d g r l l x e e e l l          (9) where  3 1 20 2x l l   (10) the 3x -axis is shown in fig. 1. in (9), ige is the value of ide at the two end sections, 3 0x  and  3 1 22x l l  , of the beam, ir e is a material property which governs the material gradient in the length direction. it is obvious that the value of id e in the mid-span is i ig r e e . for the ramberg-osgood stress-strain relation, *0 ilu which is needed in order to calculate * lu by (5) can be written as [17, 18]   1 2 * 0 12 1 i i i i m m i i i l i m i i m u e m h       (11) by substituting of (7) in (11), one arrives at   1 2 * 0 1 1 1 1 1 1 2 cos 1 2 i i i i i i m m i i i l i m d f i i i i m u y y e e m h y y                 (12) in order to perform the integration in (5), id e in (12) should be expressed as a function of 1x . for this purpose, (9) is rewritten as 1 1 2 ( ) cos 2i i i d g r x e e e l l         (13) v. rizov, frattura ed integrità strutturale, (2047) 468-481; doi: 10.3221/igf-esis.47.37 473 the complementary strain energy cumulated in portion, 1 2 3 1 22l l a x l l     , of the un-cracked part of the beam is written as 2 12 2 2 * * 0 1 2 2 1 2 i i i h yli n r r i ha y u u dx dy dz         (14) where n is the number of layers in the un-cracked beam portion, 2iy and 2 1iy  are the coordinates, respectively, of the left-hand and right-hand lateral surfaces of the i-th layer, *0 iru is the complementary strain energy density in the same layer, 2y and 2z , are the centroidal axes of the cross-section of the un-cracked portion of the beam. the complementary strain energy density in the i-th layer of the un-cracked beam portion can be obtained by (12). for this purpose, i , 1y , 1iy and 1 1iy  have to be replaced, respectively, with ir , 2y , 2iy and 2 1iy  where ir is the distribution of the normal stresses in the cross-section of the i-th layer of the un-cracked beam portion. in order to perform the integration in (5), i has to be presented as a function of 1y and 1z . it is obvious that i can not be determined explicitly from eq. (6). therefore, i is expanded in series of taylor by keeping the first six members             2 2 1 1 1 1 12 1 1 1 2 2 2 1 1 12 1 1 1 , 0 , 0 , 0 ( , ) ( , 0) ( ) 2! , 0 , 0 ( ) 2! i ai i ai i ai i i ai ai ai i ai i ai ai y y y y z y y y z y y y z y y y y y z z y z z                             (15) where  1 1 1 / 2ai i iy y y   , 1 1 1 1i iy y y   and 1/ 2 / 2h z h   (fig. 2). formula (15) is re-written as 2 2 1 1 1 2 1 3 1 4 1 5 1 1 6 1( , ) ( ) ( ) ( )i i i ai i i ai i ai iy z y y z y y y y z z               (16) where the coefficients, 1i , 2i , 3i , 4 i , 5i and 6i , are determined in the following manner. first, the distribution of lengthwise strains in the cross-section of the left-hand crack arm is written as 1 1z  (17) where 1 is the curvature the left-hand crack arm. it should be noted that formula (17) follows from the fact that validity of the bernoulli’s hypothesis for plane sections is assumed in the present paper since the span to height ratio of the beam under consideration is large. concerning the application of the bernoulli’s hypothesis for plane sections, it should also be mentioned that since the beam portion, 2 4b b , in which the delamination crack is located, is loaded in pure bending (fig. 1), the only non-zero strains are the lengthwise strains. thus, according to the small strains compatibility equations, the lengthwise strains are distributed linearly along the cross-section height. by substituting of (7), (16) and (17) in (6), one arrives at   2 2 1 2 1 3 1 4 1 5 1 1 6 1 1 1 1 1 1 1 1 1 2 2 1 2 1 3 1 4 1 5 1 1 6 1 1 ( ) ( ) ( ) cos 2 ( ) ( ) ( ) i i i i i i ai i i ai i ai i i d f i i mi i ai i i ai i ai i m i y y z y y y y z z z y y e e y y y y z y y y y z z h                                         (18) v. rizov, frattura ed integrità strutturale, (2047) 468-481; doi: 10.3221/igf-esis.47.37 474 by substituting of 1 aiy y and 1 0z  in (18), one obtains   1 1 1cos 0 im i i i ai i i iy           (19) where 1 i i d i m i e h   (20) 1 i i f i m i e h   (21)  1 1 12 i i iy y      (22)   1 1 1 12 i i i i y y y      (23) further, by substituting of 1 aiy y and 1 0z  in the first derivative of (18) with respect to 1y , one arrives at   11 2 1 1 2 1 sin( ) cos 0 i i i m m m i i i ai i i i i i ai i i i i i y y m                      (24) similarly, by substituting of 1 aiy y and 1 0z  in the first derivative of (18) with respect to 1z , one obtains   1 1 1 3 1 3 1 cos( ) cos i i i m m di f ai i i i i i ai i i i i i e e y y m                     (25) further, by substituting of 1 aiy y and 1 0z  in the second derivatives of (18) with respect to 1y , 1y and 1z , and 1z , one arrives at     1 11 2 4 1 1 2 1 1 2 1 1 2 2 1 42 1 1 2 cos( ) sin( ) sin( ) 1 1 cos 2 cos 0 i i i i i i i i i m m m m m i i i ai i i i i i ai i i i i i i ai i i i i i m m m mi i i ai i i i i i i i ai i i i i ii y y y m m m y y mm                                                            (26)   1 1 5 1 3 1 2 1 1 3 2 1 5 1 sin( ) sin( ) 1 1 cos i i i i i i i m m f i ai i i i i i ai i i i i i m m m mi i i ai i i i i i i i i i e y y m m y m m                                        , (27) v. rizov, frattura ed integrità strutturale, (2047) 468-481; doi: 10.3221/igf-esis.47.37 475   11 2 2 6 1 3 1 62 1 2 2 cos 0 ii i i mm m mi i i i ai i i i i i i ii m y mm                       (28) eqns. (19), (24) – (28) can be written for each layer of the left-hand crack arm. in this way, 6 ln equations with 6 1ln  unknowns, 1i , 2i , 3i , 4 i , 5i , 6i and 1 , where 1, 2, ..., li n , can be constructed. another equation can be written by considering the equilibrium of the elementary forces in the left-hand crack arm cross-section 1 1 1 2 1 1 1 1 2 il i h yi n i i hy m z dy dz        (29) where m is the bending moment in the left-hand crack arm. it is obvious that (fig. 1) 1m fl (30) by substituting of (16) in (29), one derives       3 3 2 2 3 1 1 1 5 1 1 1 1 12 24 li n i i i i i ai i ai i h h m y y y y y y                  (31) eqns. (19), (24) – (28) and (31) should be solved with respect to 1i , 2i , 3i , 4 i , 5i , 6i and 1 by using the matlab computer program. formula (16) is applied also to present ir  as a function of 2y and 2z . for this purpose, 1i , 2i , 3i , 4 i , 5i , 6i , 1y and 1z are replaced with 1ri , 2ri , 3ri , 4 ri , 5ri , 6ri , 2y and 2z , respectively. it should be noted that eqs. (19), (24) – (28) and (31) can be used also to determine 1ri , 2ri , 3ri , 4 ri , 5ri , 6ri and 2 where 2 is the curvature of the portion, 1 2 3 1 22l l a x l l     , of the un-cracked part of the beam. for this purpose, ln , 1iy , 1 1iy  , 1i , 2i , 3i , 4 i , 5i , 6i and 1 are replaced, respectively, with n , 2iy , 2 1iy  , 1ri , 2ri , 3ri , 4 ri , 5ri , 6ri and 2 in (19), (22) – (28) and (31). by substituting of (4), (5) and (14) in (3), one arrives at 1 1 2 1 1 2 2 2 * * 0 1 1 0 2 2 1 1 2 2 1 1 2 i il i i i i h h y yi n i n l r i ih hy y g u dy dx u dy dz h h                        (32) where *0 ilu and * 0 ir u are obtained by (12), (13), (16), (19), (20), (23), (25) – (28) and (31) at 1x a . it should be noted that the term in the brackets in (32) is doubled in view of the symmetry (fig. 1). the integration in (32) should be carried-out by using the matlab computer program. the delamination fracture behavior is analyzed also by applying the j-integral approach [19] in order to verify the solution to the strain energy release rate (32). the integration of the j-integral is performed along the integration contour,  , showed by a dashed line in fig. 1. since the right-hand crack arm is free of stresses, the solution of the j-integral is written as   1 2 2j j j   (33) where 1 j and 2j are the values of the j-integral, respectively, in segments, 1 and 2 , of the integration contour (segments, 1 and 2 , coincide with the cross-section of the left-hand crack arm and un-cracked beam portion, respectively). the term in brackets in (33) is doubled because of the symmetry. v. rizov, frattura ed integrità strutturale, (2047) 468-481; doi: 10.3221/igf-esis.47.37 476 the j-integral in segment, 1 , is written as 1 1 1 1 0 1 cos il i i yi n l xi yi i y u v j u p p ds x x                  (34) where 0 ilu is the strain energy density in the i-th layer of the left-hand crack arm, α is the angle between the outwards normal vector to the contour of integration and the crack direction, xip and yip are the components of stress vector in the i-th layer of the left-hand crack arm, u and v are the components of displacement vector with respect to the crack tip coordinate system xy (x is directed along the delamination crack), ds is a differential element along the contour of integration. the strain energy density in the i-th layer of the left-hand crack arm is obtained by applying the following formula [17, 18]:   1 2 0 12 1 i i i i m m i i l i m i i u e m h       (35) by substituting of (7) in (35), one obtains   1 2 0 1 1 1 1 1 1 2 cos 1 2 i i i i i i m m i i l i m d f i i i i u y y e e m h y y                 . (36) the other components of the j-integral in segment, 1 , are written as xi ip   (37) 0yip  (38) 1ds dy (39) cos 1   (40) it should be noted that formula (16) is used to obtain the stress, i , in (37). the partial derivative, /u x  , that is involved in (34) is expressed as 1 1 u z x       . (41) the j-integral is segment, 2 , is written as 2 1 2 2 0 1 cos i i i yi n r r xri yri r i r ry u v j u p p ds x x                    (42) where the strain energy density, 0 iru , in the i-th layer of the un-cracked beam portion is obtained by formula (36). for this purpose, i , 1y , 1iy and 1 1iy  are replaced, respectively, with ir , 2y , 2iy and 2 1iy  . the other components of 2j are written as v. rizov, frattura ed integrità strutturale, (2047) 468-481; doi: 10.3221/igf-esis.47.37 477 ixri r p  (43) 0yrip  (44) 2rds dy  (45) cos 1r  (46) 2 2 r u z x     (47) formula (16) is applied to calculate the stress, ir  , in (43). for this purpose, 1i , 2i , 3i , 4 i , 5i , 6i , 1y and 1z are replaced with 1ri , 2ri , 3ri , 4 ri , 5ri , 6ri , 2y and 2z , respectively. the average value of the j-integral along the delamination crack front is written as 2 1 2 1 h av h j j dz h    (48) by substituting of (33), (34) and (42) in (48), one arrives at 1 1 1 2 1 2 2 0 1 2 2 0 1 2 2 cos cos il i i i i i h yi n av l xi yi i h y h yi n r r xri yri r i h r ry u v j u p p ds h x x u v u p p ds x x                                               (49) where 0 ilu , 0 iru , xip and xrip are obtained by (16), (19), (20), (23), (25) – (28), (31), (36), (37) and (43) at 1x a . the integration in (49) should be carried-out by the matlab computer program. the j-integral value obtained by (49) matches exactly the strain energy release rate determined by (32). this fact is a verification of the delamination fracture analysis developed in the present paper. it should be mentioned that the delamination fracture is analyzed also by keeping more than six members in the in series of taylor (15). the results obtained are very close to these derived by keeping six members (the difference is less than 2 %). parametric study ffects of material inhomogeneity in width and length directions, crack location along the beam width, non-linear mechanical behavior of the material and crack length on the delamination fracture in the multilayered four-point bending beam are investigated by applying the solution to the strain energy release rate (32). the results obtained are presented in non-dimensional form by using the formula   1 /n gg g e b . two three-layered four-point bending beam configurations are considered in order to evaluate the influence of the delamination crack location along the beam width on the fracture behavior (fig. 3). a beam configuration with a delamination crack located between layers 2 and 3 is shown in fig. 3a. a beam with a delamination crack between layers 1 and 2 is also considered (fig. 3b). the width of each layer is t . it is assumed that 0.004t  m, 0.016h  m, 1 0.100l  m, 2 0.150l  m and 15f  n. e v. rizov, frattura ed integrità strutturale, (2047) 468-481; doi: 10.3221/igf-esis.47.37 478 the strain energy release rate in non-dimensional form is presented as a function of 2 1/h h ratio in fig. 4 for the two beam configurations shown in fig. 3 at 2/ 0.75a l  , 2 1/ 0.6g ge e  , 3 1/ 0.5g ge e  , 1 1/ 0.4r ge e  , 2 1/ 0.6r re e  , 3 1 / 0.8r re e  , 1 1/ 0.6f ge e  , 2 1/ 0.7f fe e  , 3 1/ 1.1f fe e  , 11 / 0.6gh e  , 3 1/ 0.7h h  and 1 2 3 0.7m m m   . figure 3: two three-layered four-point bending beam configurations with delamination crack located between (a) layers 2 and 3 and (b) layers 1 and 2. the curves in fig. 4 indicate that the strain energy release rate decreases with increasing of 2 1/h h ratio. besides, it can be observed in fig. 4 that the strain energy release rate is higher when the delamination crack is located between layers 1 and 2. this behavior is due to the fact that when the delamination crack is located between layers 1 and 2, the stiffness of lefthand crack arm is lower. the influence of the 2 1 /g ge e ratio on the delamination fracture is investigated too. for this purpose, the strain energy release rate in non-dimensional form is presented as a function 2 1 /g ge e ratio in fig. 5. the three-layered four-point bending beam configuration with a delamination crack located between layers 1 and 2 is analyzed (fig. 3b). it can be observed in fig. 5 that the strain energy release rate decreases with increasing of 2 1 /g ge e ratio. the effect of the non-linear mechanical behavior of the material is elucidated also. for this purpose, the strain energy release rate obtained assuming linear-elastic behavior of the inhomogeneous material in each layer is presented also in fig. 5 for comparison with the non-linear solution. the linear-elastic solution is derived by substituting of ih   in formulae (12), (19), (20) and (32) since at ih   the ramberg-osgood stress-strain relation (6) transforms in the hooke’s law. one can observe that the non-linear behavior of the material leads to increase of the strain energy release rate (fig. 5). v. rizov, frattura ed integrità strutturale, (2047) 468-481; doi: 10.3221/igf-esis.47.37 479 figure 4: the strain energy release rate in non-dimensional form presented as a function of 2 1/h h ratio (curve 1 – for the beam configuration with delamination located between layers 2 and 3 (refer to fig. 3a), curve 2 – for the beam configuration with delamination located between layers 1 and 2 (refer to fig. 3b)). the effect of material inhomogeneity along the width of layer 1 on the delamination fracture is analyzed (the beam configuration shown in fig. 3b is considered). for this purpose, the strain energy release rate in non-dimensional form is presented as a function of 1 1 /f de e ratio in fig. 6 at two 11 / dh e ratios. it can be observed in fig. 6 that the strain energy release rate decreases with increasing of 1 1 /f de e and 11 / dh e ratios. figure 5: the strain energy release rate in non-dimensional form presented as a function of 2 1 /g ge e ratio (curve 1 – at non-linear mechanical behavior of the material, curve 2 – at linear-elastic behavior). the influences of the material inhomogeneity in the beam length direction and the delamination crack length on the fracture behavior are studied. for this purpose, the strain energy release rate in non-dimensional form is presented as a function of 1 1 /r ge e in fig. 7 at three 2/a l ratios for the three-layered beam configuration shown in fig. 3b. the curves in fig. 7 indicate that the strain energy release rate decreases with increasing of 1 1 /r ge e ratio. one can observe also in fig. 7 that the strain energy release rate increases with increasing of 2/a l ratio (this founding is attributed to the fact that the modulus of elasticity in the beam cross-section in which the delamination crack front is located decreases with increasing of the crack length). v. rizov, frattura ed integrità strutturale, (2047) 468-481; doi: 10.3221/igf-esis.47.37 480 figure 6: the strain energy release rate in non-dimensional form presented as a function of 1 1 /f de e ratio (curve 1 at 1 1/ 0.5dh e  curve 2 at 1 1/ 4dh e  ). figure 7: the strain energy release rate in non-dimensional form presented as a function of 1 1 /r ge e ratio (curve 1 at 2/ 0.25a l  , curve 2 at 2/ 0.5a l  and curve 3 at 2/ 0.75a l  ). conclusions solution to the strain energy release rate for a delamination crack in multilayered four-point bending beam configurations is derived assuming that each layer exhibits smooth material inhomogeneity in both width and length directions. the solution is intended for brittle materials. cosine laws are adopted in order to describe the continuous variation of the modulus of elasticity along the width and length of layers. the beam is made by adhesively bonded lengthwise vertical layers which have individual widths and material properties. the number of layers is arbitrary. the material in each layer exhibits non-linear mechanical behavior that is modeled by applying the ramberg-osgood equation. the solution derived holds for a delamination crack that is located arbitrary between layers. the delamination fracture is analyzed also by applying the j-integral approach in order to verify the solution to the strain energy release rate. it should be mentioned that the delamination fracture analysis developed in the present paper is valid for non-linear elastic behavior of the material. however, the analysis can also be applied for elastic-plastic behavior if the multilayered beam a v. rizov, frattura ed integrità strutturale, (2047) 468-481; doi: 10.3221/igf-esis.47.37 481 under consideration undergoes active deformation, i.e. if the external loading increases only [20, 21]. the influence of material inhomogeneity along the width and length of layers is elucidated. it is found that the strain energy release rate decreases with increasing of 1 1 /f de e and 1 1/r ge e ratios. the effect of crack location along the beam width is evaluated too. the analysis reveals that the strain energy release rate decreases with increasing of the width of the left-hand crack arm. concerning the influence of the delamination crack length on the fracture behavior, it is found that the strain energy release rate increases with increasing of the crack length. the approach developed in the present paper can be useful for evaluation of the effects of material inhomogeneity and non-linear mechanical behavior of the material on delamination fracture in design of multilayered beam structures. references [1] banea, m.d., da silva, l.f.m. (2016). adhesively bonded joints in composite materials: an overview, proceedings of the institution of mechanical engineers, part l: journal of materials: design and applications, 223, pp. 1-18. [2] wicaksono, s., chai, g.b. (2012). a review of advances in fatigue and life prediction of fiber-reinforced composites, proceedings of the institution of mechanical engineers, part l: journal of materials: design and applications, 227, pp. 179-195. [3] long, l., huang, y., zhang, j. (2015). experimental investigation and numerical simulation on continuous wave laser ablation of multilayer carbon fiber composite, proceedings of the institution of mechanical engineers, part l: journal of materials: design and applications, 231, pp. 674-682. [4] al-khanbashi, a., hamdy, a.e. (2004). fracture mechanics approach to predict delamination lifetime in mode ii under constant loads, journal of adhesion science and technology, 18, pp. 227-242. [5] sayyad, a.s., ghugal, y.m. (2018). modeling and analysis of functionally graded sandwich beams: a review, mechanics of advanced materials and structures, 1, pp. 1-20. [6] rizov, v.i., (2017). delamination of multilayered functionally graded beams with material nonlinearity, international journal of structural stability and dynamics, 18(4), 1850051. doi: 10.1142/s0219455418500517. [7] rizov, v.i., (2017). non-linear elastic delamination of multilayered functionally graded beam, multidiscipline modeling in materials and structures, 13, pp. 434-447. [8] mortensen, a., suresh, s. (1995). functionally graded metals and metal-ceramic composites: part 1 processing, international materials review, 40, pp. 239-265. [9] gasik, m.m. (1995). functionally graded materials: bulk processing techniques, international journal of materials and product technology, 39, pp. 20-29. [10] neubrand, a., rödel, j. (1997). gradient materials: an overview of a novel concept, zeit f met, 88, pp. 358-371. [11] suresh, s., mortensen, a. (1998). fundamentals of functionally graded materials, iom communications ltd, london . [12] hirai, t., chen, l. (1999). recent and prospective development of functionally graded materials in japan, material science forum, 308-311, pp. 509-514. [13] butcher, r.j., rousseau, c.e., tippur, h.v. (1999). a functionally graded particulate composite: measurements and failure analysis, acta matererialia, 47, pp. 259-268. [14] nemat-allal, m.m., ata, m.h., bayoumi, m.r., khair-eldeen, w. (2011). powder metallurgical fabrication and microstructural investigations of aluminum/steel functionally graded material, materials sciences and applications, 2, pp. 1708-1718. [15] bohidar, s.k., sharma, r., mishra, p.r., (2014). functionally graded materials: a critical review, international journal of research, 1, pp. 289-301. [16] rizov, v.i., (2017). analysis of longitudinal cracked two-dimensional functionally graded beams exhibiting material non-linearity, frattura ed integrità strutturale, 41, pp. 498-510. [17] rizov, v.i. (2017). delamination analysis of a layered elastic-plastic beam, international journal of structural integrity, 4, pp. 516-529. [18] rizov, v.i. (2018). lengthwise fracture analyses of functionally graded beams by the ramberg-osgood equation, engineering review, 38, pp. 309-320. [19] broek, d. (1986). elementary engineering fracture mechanics, springer. [20] lubliner, j. (2006). plasticity theory (revised edition), university of california, berkeley, ca . [21] chakrabarty, j. 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/pdfxoutputintentprofileselector /documentcmyk /preserveediting true /untaggedcmykhandling /leaveuntagged /untaggedrgbhandling /usedocumentprofile /usedocumentbleed false >> ] >> setdistillerparams << /hwresolution [2400 2400] /pagesize [612.000 792.000] >> setpagedevice microsoft word numero_49_art_51_2059 b. el-hadi et alii, frattura ed integrità strutturale, 49 (2019) 547-556; doi: 10.3221/igf-esis.49.51 547 a 3d analysis of crack-front shape of asymmetric repaired aluminum panels with composite patches el hadj besseghier, abdelkader djebli, mostefa bendouba, abdelghani baltach, abdelkrim aid. laboratory of quantum physics of matter and mathematical modeling (lpq3m), university of mascara, mascara 29000, algeria. besseghier.hadj@outlook.fr, djebliabdelkader@univ-mascara.dz, bendoubamos@yahoo.fr, baltachabdelghani@yahoo.fr, aid_abdelkrim@gmail.com. abstract. through this study, a numerical simulation based on 3d in order to investigate the effect of crack-front shape on the stress intensity factor and fatigue crack growth behavior of center cracked aluminum plate repaired asymmetrically with bonded composite patch. consequently, skew degree it is a significant effect on stress intensity factor (sif) distribution along the crack front in thick panels more than in thin panels. moreover, fatigue life was calculated using different averaged stress intensity factor of patched panel determined from uniform crack front model and skew crack front model obtained from fem and when comparing fatigue life values obtained from the finite element model with experimental values were shown a good agreement. keywords. patch repair; stress intensity factor; aluminum alloy; fatigue; crack front. citation: besseghier, e.h., djebli, a., bendouba, m., baltach, a., aid, a., a 3d analysis of crack-front shape of asymmetric repaired aluminum panels with composite patches, frattura ed integrità strutturale, 49 (2019) 547-556. received: 26.02.2019 accepted: 05.05.2019 published: 01.07.2019 copyright: © 2019 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. introduction mong the methods of repairing damaged structures, bonding a composite patch is currently the most used. in particular, composite patch repair has shown its effectiveness in the field of aeronautics and maritime structures [1-2]. according to research, most studies address the problem of shape optimization, i.e the surface and the thickness of the patch [3-10]. without omitting the effect of the parameters related to the adhesive such as the thickness and the type of the glue that have provoked several searches as for example in [11-15]. allan baker initially developed the technique of bonding a composite patch in a cracked structure in the late 1970s. this technique appeared to be an advantageous alternative to the more conventional techniques of repair, by riveting or welding metallic structures. indeed, the bonding of a composite patch to the damaged structure significantly reduces the stress field on the damaged area. that leads to improve the structural strength and the extension of the lifetime of the structure under stress [16-17], without a http://www.gruppofrattura.it/va/49/2059.mp4 b. el-hadi et alii, frattura ed integrità strutturale, 49 (2019) 547-556; doi: 10.3221/igf-esis.49.51 548 introducing a new hole or changing the microstructure of the material. in fact, there are two patch repair techniques, namely, simple patch repair (asymmetric repair) and double side patch repair (symmetric repair) [16-19]. generally, it is the double patch that is preferable, because of the deflection effects that the simple patch introduces into the charged structure [20]. regardless of the type of repair (symmetrical or asymmetrical), parameters such as thickness, surface area, number of layers, fiber orientation and patch shape remain the most studied for their interdependent influence on repair efficiency. in this context, ramji & all carried out a comparative study in [16]. these authors studied several forms of patch and concluded that an extended octagonal patch has better performance for stress intensity factor reduction. recently, bachir bouiadjra & all concluded in [7] that a trapezoidal form is more powerful than a rectangular form. furthermore, in [10], it was concluded that a butterfly shape with a suitable dimensions is more efficient than the rectangular shape. for the number of layer and the thickness of the patch, h. hosseini and colleagues in [21] concluded that the performance of the patch is proportionately improved by increasing the number of layers and reducing the thickness of the plate. furthermore, [22] established that increasing the life of the repaired plate is related to increasing the thickness of the patch. also for the type of composite used in the repair, h. hosseini and co-workers in [23] found that, for a 45° inclined crack in a thick aluminum panel repaired by an asymmetric glass / epoxy patch, the lifetime during the crack propagation is significantly improved. among the positive effects on the repair, [24] studied the effect of overload during the fatigue test. as a result, it was found that overloading extends the service life of the repaired structure. despite a large number of published researches on this topic, to our knowledge, few of them consider the value of the stress intensity factor to be used for estimating the lifetime of repaired structures. indeed, d. c. seo and j. j. lee in [25] experimentally proved that the crack front is not always a straight line when the crack is propagated. these latter concluded that the stress intensity factor of thick specimen showed a large variation through thickness direction. moreover, woo-yong lee and jung-ju lee in [26] stated that the stress intensity factor (sif) calculated at the crack tip is much influenced by crack front shape. consequently, they proposed to predict the actual crack front shape evolution and take it into account for the accurate analysis of fatigue behavior. this was confirmed later by h. hosseini et al. in [27] and recently in [28], where it was noted that the crack growths non-uniformly from its initial location through the thickness of the repaired panel and the maximum crack length occur at un-patched surface of the panels. in this study, for the accurate investigation of fatigue crack growth behavior, a consideration is taken for the crack front inclined in its plan from the patched toward un-patched side by various angles. this is done to simulate the experimental fatigue crack-growth behavior in mode-i failure and examine the sif’s distribution along the crack front within centrally cracked aluminum panels. moreover, trying to understand the physic of the crack growth difference between patched and un-patched side in two different panels thick and thin. figure 1 geometrical model of the repaired central cracked specimen. geometries and mechanical properties of the model ig. 1 shows the basic geometry of the cracked structure considered in this study. this model is adapted from that proposed in [21]. the aluminum alloy plate 2014-t3 has dimensions of 100 x 50 mm2 with two different thicknesses, namely 2.29 and 6.35 mm. the plates contain an initial crack length of 2a = 10 mm and perpendicular to the loading axis (fig. 1). table 1 summarizes the dimensions of the plate, the patch and the adhesive. mechanical f b. el-hadi et alii, frattura ed integrità strutturale, 49 (2019) 547-556; doi: 10.3221/igf-esis.49.51 549 properties of the 2024-t3 aluminum alloy plate, the glass/epoxy composite patch and the fm-77 adhesive are given in table 2. material aluminum panel patch adhesive l (mm) 100 40 40 w (mm) 50 35 35 t (mm) 2.29 and 6.35 1.44 0.1 table 1: dimensions of the panel, adhesive layer and patch. material e1 (gpa) e2, e3 (gpa) ν12, ν13,ν23 g12, g13 (gpa) g23 (gpa) aluminum (2014-t3) 71.3 0.33 glass/epoxy 50 14.5 0.33 2.56 2.24 adhesive(fm77) 1.89 0.33 table 2: materials properties. the objective of this work is to analyze the effect of the inclination of the crack front in its plane. for this purpose, the crack line is inclined from the patched side toward the un-patched side by different angles ө = 0°, 15°, 30°, 45° and 60° respectively (fig. 2.a). fig. 2.b shows the different inclinations of the crack front, where the mesh refinment indicates the front of the crack and the immediate adjacent region in the plane of the thickness. then to compare the stress intensity distribution between two different thickness panels, i.e. thin (2.29mm) and thick (6.35mm). figure 2 (a) skew crack front. (b) finite element model showing the crack front configuration numerical modeling and boundary conditions he model was solicited by applying a cyclic load to the upper edge in the y-direction with a lower edge embedding. so, the plate is subjected to a maximum stress σ=118 mpa with a load ratio of r = 0.05. the analysis was carried out using abaqus 6.13 software. a three-dimensional finite element method with automatic meshing was carried out on the structure using 8-nodes brick elements and refinement of the mesh was created in the vicinity of the crack tips as shown in figures 3.c. the composite patches ply orientation is parallel to the loading axis. so, as geometry and loading conditions are symmetrical, only one quarter of the specimens were simulated. due to its simplicity, paris law is usually used to predict the fatigue life, which can be expressed as [21]:  m da c k dn   (1) t b. el-hadi et alii, frattura ed integrità strutturale, 49 (2019) 547-556; doi: 10.3221/igf-esis.49.51 550 where c and m are properties constant for a material regrouped in tab.3, δk=kmax-kmin is the sif range, n is number of cycles, a is crack length and da is change in crack length. figure 3 finite element model mesh of the repaired plate. (a) t=2.29 mm, (b) t=6.35 mm and (c) near crack mesh refinement. plate thickness 2.29 (mm) plate thickness 6.35 (mm) m=3.2828 m=4.224 c=3.63e-13 c=1.51e-15 table 3: material constants in paris law for aluminum plates [21]. the adopted method was to evaluate sifs with abaqus using j-integral. the energy approach states that fracture will occur when the energy release rate, reaches a critical value gc, and is consistent with the idea that failure occurs when the sif in mode i, ki, reaches a critical value, called the fracture toughness (kic). for linear elastic material, j (equivalent to g) is related to the sif by [29]:  2 2 2* * 1 1 2 j g g g k k k e g            (2) where i, ii and iii denotes the modes of fracture, and e*=e / (1-2) for plane strain case (3d configuration). the jintegral in pure mode i loading condition, can then be correlated to ki using the relation: 21 i ej k v   (3) where e is young’s modulus and  is the poisson’s ratio. if an arbitrary contour is considered as illustrated in fig.4, the j-integral is given by: i i u j wdy t ds x     (4) where w is the strain energy density, ti are components of the traction vector, ui are the displacement vector components, and ds is a length increment along the contour γ. the strain energy is defined as: b. el-hadi et alii, frattura ed integrità strutturale, 49 (2019) 547-556; doi: 10.3221/igf-esis.49.51 551 0 ij ij ijw d     (5) where, σij and εij are the stress and strain tensors, respectively. the traction is a stress vector normal to the contour. to evaluate these integrals, abaqus defines the domain in terms of rings of elements surrounding the crack tip. figure 4: definition of the j-integral: a contour integral along the path γ [y]. the von-mises stress used in the analysis of stress distribution along the crack front can be written in terms of stress components as [30]:        2 2 2 2 2 26 2 xx yy yy zz zz xx xy yz zx vm                   (6) where, xx , yy and zz are the normal stresses according to x, y and z direction respectively and xy , yz and zx are shear stresses in the yz, xz and xy planes respectively (fig. 5). figure 5: stresses on a cubical element in equilibrium validation of the model he validation of the present model is presented in fig.6.a and 6.b, where a comparison with the results of hossieni & all [21] is made. the figures show a comparison of the fatigue life of thin and thick panels respectively. moreover, it can be seen from the figures that present results are in good agreement with the literature. figure gives the fatigue life of plate after repair. t b. el-hadi et alii, frattura ed integrità strutturale, 49 (2019) 547-556; doi: 10.3221/igf-esis.49.51 552 figure 6: comparisons of finite element results with experimental data for the fatigue life of repaired panels. (a) t =2.29mm (b) t=6.35mm. results and discussion igs 7.a and 7.b present the distribution of von-mises stresses in thin and thick repaired aluminum plates respectively. the crack length is taken to be 2a=10 mm. from fig 7.a, a non uniform distribution along the crack front can be observed. in fact, the stress transfer between the repaired plate and the patches mainly occurs in the patched side of the plate. the stress at the crack tip in the patched side of the plate is much smaller than that in the unpatched side of the plate, which accounts for sif variation in thickness direction of the aluminum plate. moreover, comparing the crack tip stresses distribution between figs7.a and 7.b, one can also observe that with the help of the patches, the stress at the crack tip in thin repaired plate is much smaller than that in the thicker one. this accounts for the significant sif's difference between thin and thick plates. figure 7: distribution of the von-mises stresses across the crack front for the repaired plate. (a) t=2.29mm; (b) t=6.35mm. fig.8 shows that the change in maximum values of von-mises stresses (red zone in fig) is with growth of the crack where this value is shifted from the free side toward the patched side and this applies to all panels, whether thin or thick. accordingly, this finding will be highlighted, hereinafter by the stress intensity factor results in fig 9.a and 9.b. figures 9.a and 9.b shows the distribution of stress intensity factor along the crack front. it is noted through the curves trend that the maximum value of sif is shifted from the free side of the plate towards the patched side. this suggests a cascade growth of the crack, obviously starting from the free surface going toward the patched surface. a differed of this behavior can be noted between the thin and the thick plates. effectively, the maximum value in fig 8.a is resulted for the angle ө=0° curve and the last point in crack front in the free side of the plate. this maximum value is in no case f b. el-hadi et alii, frattura ed integrità strutturale, 49 (2019) 547-556; doi: 10.3221/igf-esis.49.51 553 exceeded for other configurations (fig. 8.a). on the other side, fig. 8.b shows that the maximum value of the stress intensity factor increases with the growth of the angle and is located inside the front of the crack. figure 8: distribution of the von-mises stresses (mpa) in skew crack front. figure 9: stress intensity factors along skewed crack front for different thickness. (a) t=2.29mm (b) t=6.35mm. consequently, this explains the crack shape in the fig 10.a where it is clearly shown that the maximum length of the crack appears in last point crack front of the free side of the panel and this makes it compatible with stress intensity factor distribution results. figure 10 (a) crack-front shape obtained from fatigue crack propagation of repaired plates (b) comparison of normalized crack-front shapes between repaired panels with 2.29 mm and 6.35 mm thickness [27]. fig. 9 shows the distribution of the stress intensity along the crack front for the thick panels where it can be observed a shifted of maximum value from the free side of the plate towards the patched side. accordingly, the maximum value is b. el-hadi et alii, frattura ed integrità strutturale, 49 (2019) 547-556; doi: 10.3221/igf-esis.49.51 554 obtained for the angle ө=60° and located at approximately 60% (fig. 9.b) of the thickness from the patched side to the free side and this also makes it compatible with the shape of the crack in fig10.a. fig. 10.a also shows the maximum length of crack whose position exactly corresponds to the position for the maximum value of stress intensity factor. fig.10.b compares the normalized crack-front shapes between repaired plates with 2.29 mm and 6.35 mm thickness. as can be seen in the figure, the difference between the maximum length crack positions confirms the current results. thus, it is useful to give a precise prediction of the crack behavior and to identify the adequate value of the stress intensity factor for an accurate estimate of the lifetime of the patch-repaired structure and this for the two thicknesses studied in this work. in this respect, fig.11 shows a comparison between average of the stress intensity factors versus the crack front inclination for thin and thick panels. incontestably, the obtained results indicate horizontal monotony of the average stress intensity factors for a thin panel. accordingly, one can suggest that the ideal choice for the calculation of the crack propagation is the average of the sif's values along the crack front. this will be confirmed, hereinafter through the analyzed fatigue life results. conversely, the curve of the thick panel (t=6.35 mm) shows a change of the average stress intensity factor when the skew changed. here, the averaged sif icreases with the increase of the skew angle.   figure 11: average stress intensity factors versus angle inclination in the crack plane for different thickness figs. 12.a and 12.b show the comparison of fatigue life between experimental results and fem results obtained from using different averaged stress intensity factor, namelly maximum value in the thickness direction (k.max), average all values in the thickness direction (avg-all), mid-point value in the thickness direction (k.mid) , root mean square value of all values (avg-k.rms), average all values from patched side to mid-point (avg-h.p.s), average all values from unpatched side to mid-point (avg-h.un-p.s), average all values except the values of both side element in the thickness direction (avg9.mid). figure 12: comparison of fatigue life between experimental results and predicted values using averaged fem results: (a) t=2.29mm (b) t=6.35 mm. b. el-hadi et alii, frattura ed integrità strutturale, 49 (2019) 547-556; doi: 10.3221/igf-esis.49.51 555 as expected above by analyzing the distribution of stress intensity factors, fig. 12.a shows that the fatigue lifetime obtained from using of the stress intensity factor (avg-all) and to a lesser extent the results obtained from using the (avg9.mid) , (k.mid) and (avg-k.rms) respectively, gives a precise results for the case of thin repaired plates .this is evident through a good agreement of fem curve results obtained from (avg-all) with experimental curve. on another side, fig.12.b shows that the values obtained from the root mean square stress intensity factor (avg-k.rms) and to a lesser extent obtained from the (k.mid), (avg-9 .mid) and (avg-all), respectively gives precise results for the case of the thick repaired plates. this is evidenced by the good agreement of the numerically obtained lifetimes with those obtained experimentally.     conclusion his study focused on the fatigue crack growth behavior of center cracked aluminum plate repaired asymmetrically with bonded composite patch .the analysis led to the following conclusions: the stress at the crack tip in the patched side of the plate is much smaller than that in the un-patched side of the plate. the maximum length of crack whose position exactly corresponds to the position for the maximum value of stress intensity factor. the crack front shape differs between the thin and thick plates. reliance on the stress average all (avg-all) in the calculate the fatigue life of the thin plates repaired asymmetrically. showed excellent accuracy compared with experimentally reverse thick plates which the stress root mean square (k.rms). references [1] baker, a.a., rose, l.r.f., jones, r. (2002). advances in the bonded composite repair of metallic aircraft structure, killington, elsevier publications. [2] bianchi, r. w., kwon, y. w., alley, e. s. (2019). composite patch repair for underwater aluminum structures, journal of offshore mechanics and arctic engineering, 141(6), p. 064501. doi: 10.1115/1.4042940. [3] umamaheswar, t.v.r.s., ripudaman, s. (1999). modelling of a patch repair to a thin cracked sheet, eng fract mech., 62(2-3), pp. 267-289. doi: org/10.1016/s0013-7944(98)00088-5. [4] mahadesh, k.a., hakeem, s.a. (2000). optimum design of symmetric composite patch repair to center cracked metallic sheet, compos struct. 49(3), pp. 285–292. doi:org/10.1016/s0263-8223(00)00005-2. [5] brighenti, r. (2007). patch repair design optimization for fracture and fatigue improvements of cracked plates. solids struct. 44(3-4), pp. 1115–1131. doi: org/10.1016/j.ijsolstr.2006.06.006. [6] rachid, m., serier, b., bachir bouiadjra, b., belhouari, m. (2012). numerical analysis of the patch shape effects on the performances of bonded composite repair in aircraft structures, compos b: eng. 43(2), pp. 391–397. doi: org/10.1016/j.compositesb.2011.08.047. [7] bachir bouiadjra, b., fari bouanani, m., albedah, a., benyahia, f., es-saheb m., (2011). comparison between rectangular and trapezoidal bonded composite repairs in aircraft structures: a numerical analysis, mater des. 32(6), pp. 3161–3166. doi: org/10.1016/j.matdes.2011.02.053. [8] kashfuddoja, m., ramji, m. (2014). design of optimum patch shape and size for bonded repair on damaged carbon fibre reinforced polymer panels, mater des. 54, pp. 174-183. doi: org/10.1016/j.matdes.2013.08.043. [9] soutis, c., hu, f.z. (1997). design and performance of bonded patch repairs of composite structures, proc inst mech eng g: aerospace eng. 211(4), pp. 263–271. doi:org/10.1243/0954410971532668. [10] besseghier, e.h., djebli, a., bendouba, m., aid, a. (2017). effect of patch shape on the repair efficiency of a cracked aluminum panel, materials and engineering structures, 4, pp. 225–233. [11] shiuh-chuan, h., chao, m.n. (2011). adhesively bonded patch repair of composite laminates, adhes sci technol. 25(18), pp. 2569–2585. doi: org/10.1163/016942411x580234. [12] turaga, v.r.s., ripudiman, (1999). modeling of patch repairs to a thin cracked sheet. engn. fract. mec. 74, pp. 431443. [13] cheng, p., xiao-jing, g., hearn, d., aivazzadeh, s. (2011). tensile behaviour of patchrepaired cfrp laminates, compos struct. 93(2), pp. 582–589. doi: org/10.1016/j.compstruct.2010.08.021. t b. el-hadi et alii, frattura ed integrità strutturale, 49 (2019) 547-556; doi: 10.3221/igf-esis.49.51 556 [14] liu, x., wang, g. (2007). progressive failure analysis of bonded composite repairs. compos struct. 81(3), pp. 331340. doi: org/10.1016/j.compstruct.2006.08.024 [15] albedah, a., bouiadjra, b. b., benyahia, f., mohammed, s. m. k. (2018). effects of adhesive disbond and thermal residual stresses on the fatigue life of cracked 2024-t3 aluminum panels repaired with a composite patch. international journal of adhesion and adhesives, 87, pp. 22-30. doi: 10.1016/j.ijadhadh.2018.09.004 [16] ramji, m., srilakshmi, r., bhanu prakash, m. (2013), towards optimization of patch shape on the performance of bonded composite repair using fem. composites: part b. 45(1), pp. 710-720. doi: 10.1016/j.compositesb.2012.07.049. [17] belhouari, m., bachir bouiadjra, b., megueni, a., kaddouri, k. (2004). comparison of double and single bonded repairs to symmetric composite structures: a numerical analysis, composite structures. 65(1), pp. 47-53. doi: 10.1016/j.compstruct.2003.10.005. [18] baltach, a., aid, a., djebli, a., bouiedjra, b. b., benhamena, a. (2017). numerical analysis of asymmetrically bonded composite patch repair and effect of in-plane skewed crack front on the sif. int. j. eng. res. afr. 30, pp.11-22. doi: 10.4028/www.scientific.net/jera.30.11 [19] makwana, a., shaikh, a. a., bakare, a. k., saikrishna, c. (2018). 3d numerical investigation of aluminum 2024-t3 plate repaired with asymmetric and symmetric composite patch. materials today: proceedings, 5(11), pp. 2363823647. doi: 10.1016/j.matpr.2018.10.153. [20] duong, c.n., wang, c.h. (2007). composite repair, theory and design. amsterdam, elsevier publications. [21] hosseini-toudeshky, h., mohammadi, b., sadeghi, g, daghyani, h.r. (2007). numerical and experimental fatigue crack growth analysis in mode-i for repaired aluminum panels using composite material. composites: part a. 38(4), pp. 1141-1148. doi: 10.1016/j.compositesa.2006.06.003. [22] hosseini-toudeshky, h., ghaffari, m.a., mohammadi, b. (2012). finite element fatigue propagation of induced cracks by stiffeners in repaired panels with composite patches, compos struct. 94(5), pp. 1771-1780. doi: 10.1016/j.compstruct.2012.01.002. [23] hosseini-toudeshky, h., bakhshaneh, s. mohammadi, b. daghyani, h.r. (2006). experimental investigations on fatigue crack growth of repaired thick aluminum panels in mixed-mode conditions, composite structures 75(1-4), pp. 437-443. doi: 10.1016/j.compstruct.2006.04.021. [24] seriari, f. z., benachour, m., benguediab, m. (2018). fatigue crack growth of composite patch repaired al-alloy plates under variable amplitude loading, frattura ed integrità strutturale, 12(43), pp. 43-56. doi: 10.3221/igf-esis.43.03. [25] seo, d. c., lee, j. j. (2002). fatigue crack growth behavior of cracked aluminum plate repaired with composite patch, composite structures, 57(1-4), pp. 323-330. doi: 10.1016/s0263-8223(02)00095-8. [26] lee, w.y., lee, j. j. (2004). successive 3d fe analysis technique for characterization of fatigue crack growth behavior in composite repaired aluminum plate, composite structures, 66(1-4), pp. 513-520. doi: 10.1016/j.compstruct.2004.04.074. [27] hosseini-toudeshky, h., sadeghi, g., daghyani, h.r. (2005). experimental fatigue crack growth and crack-front shape analysis of asymmetric repaired aluminium panels with glass/epoxy composite patches, composite structures 71, pp. 401–406. doi: 10.1016/j.compstruct.2005.09.032. [28] hosseini-toudeshky, h., ghaffari, m.a., mohammadi, b. (2011). fatigue propagation of induced cracks by stiffeners in repaired panels with composite patches, procedia engineering, 10, pp. 3285-3290. doi: 10.1016/j.proeng.2011.04.542. [29] duó, p., nowell, d. (2003). the use of abaqus for stress intensity factors evaluation: comparison with the distributed dislocation method and other numerical approaches. uk abaqus user group conference. [30] nies, a. 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can be opened with acrobat and adobe reader 5.0 and later.) >> /namespace [ (adobe) (common) (1.0) ] /othernamespaces [ << /asreaderspreads false /cropimagestoframes true /errorcontrol /warnandcontinue /flattenerignorespreadoverrides false /includeguidesgrids false /includenonprinting false /includeslug false /namespace [ (adobe) (indesign) (4.0) ] /omitplacedbitmaps false /omitplacedeps false /omitplacedpdf false /simulateoverprint /legacy >> << /addbleedmarks false /addcolorbars false /addcropmarks false /addpageinfo false /addregmarks false /convertcolors /converttocmyk /destinationprofilename () /destinationprofileselector /documentcmyk /downsample16bitimages true /flattenerpreset << /presetselector /mediumresolution >> /formelements false /generatestructure false /includebookmarks false /includehyperlinks false /includeinteractive false /includelayers false /includeprofiles false /multimediahandling /useobjectsettings /namespace [ (adobe) (creativesuite) (2.0) ] /pdfxoutputintentprofileselector /documentcmyk /preserveediting true /untaggedcmykhandling /leaveuntagged /untaggedrgbhandling /usedocumentprofile /usedocumentbleed false >> ] >> setdistillerparams << /hwresolution [2400 2400] /pagesize [612.000 792.000] >> setpagedevice microsoft word 2219 r. brighenti et alii, frattura ed integrità strutturale, 48 (2019) 1-9; doi: 10.3221/igf-esis.48.01 1 focussed on “crack paths” crack paths in soft thin sheets roberto brighenti, andrea carpinteri, federico artoni department of engineering and architecture, university of parma, viale usberti 181/a, 43124 parma, italy brigh@unipr.it ,https://orcid.org/0000-0002-9273-0822 andrea.carpinteri@unipr.it, https://orcid.org/0000-0002-8489-6005 federico.artoni@studenti.unipr.it, https://orcid.org/0000-0001-9032-2959 abstract. highly deformable materials (elastomers, gels, biological tissues, etc.) are ubiquitous in nature as well as in technology. the understanding of their flaw sensitivity is crucial to ensure a desired safety level. fracture failure in soft materials usually occurs after the development of an uncommon crack path because of the non-classical near-tip stress field and the viscous effects. in a neo-hookean material, the true opening stress singularity along the crack path (evaluated normal to the crack line) is of the order 2r  , while it is of the order 1/2s  ahead of the crack tip, promoting the appearance of a crack tip splitting leading to a tortuous crack. in the present paper, experimental tests concerning the fracture behavior of highly deformable thin sheets under tension are discussed, and the observed crack paths are interpreted according to the crack tip stress field arising for large deformations. the study reveals that higher strain rates facilitate the development of a simple mode i crack path, while lower strain rates induce a mixed mode in the first crack propagation stage, leading to the formation of new crack tips. the above described behavior seems to not be affected by the initial crack size. keywords. rubber; highly deformable materials; crack path; strain rate; crack tip splitting. citation: brighenti, r., carpinteri, a., artoni, f., crack paths in soft thin sheets, frattura ed integrità strutturale, 48 (2019) 1 -9. received: 15.10.2018 accepted: 06.01.2019 published: 01.04.2019 copyright: © 2019 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. introduction oft materials such as rubbers, elastomers, gels, foams, granular and many biological materials are usually prone to easily deform, leading to a highly nonlinear response under mechanical actions [1, 2]. on the other hand, the capability to modulate their toughness or viscosity has promoted a wide attention in advanced applications (from materials science to bioengineering) where such materials can be conveniently exploited to get smart and functional materials such as artificial muscles, active and self-morphing materials [3, 4]. furthermore, highly deformable materials often exhibit a rate-dependent response [5, 6], and in some cases (such as for natural rubbers) when sufficiently stretched at room temperature, show a strain-induced crystallization inducing a change s http://www.gruppofrattura.it/va/48/2219.mp4 r. brighenti et alii, frattura ed integrità strutturale, 48 (2019) 1-9; doi: 10.3221/igf-esis.48.01 2 from an amorphous into a semicrystalline-like microstructural configuration due to the appearance of a highly oriented microstructure developing along the tensile direction [7]. the microstructure of polymer materials is fully amorphous and, at the molecular level, is formed by a three-dimensional network of polymer chains linked at several discrete points (cross-links). the mechanics of these materials depends on the relative interaction and motion of the entangled linear macromolecules; the physical-chemistry basis of such a class of materials has been firstly established by paul j. flory, p.g. de gennes and l.r.g. treloar [8-10], through their fundamental theoretical and experimental research work. another key aspect of soft materials is their ability to withstand defects (such as cracks and notches) in presence of mechanical actions, without showing brittle failure [11, 12]; in the near tip region of a crack, the local large deformation induces a microstructure rearrangement (chains alignment) and promotes a change in the macroscopic shape of the defect. these mechanisms enhance a material strengthening-like mechanism, leading to a noticeable defect tolerance capability. in the present study, we consider the fracture behavior of highly deformable thin cracked sheets under tension. experimental tests performed at various strain rates on pre-cracked soft rubber specimens are presented, and the experimentally observed crack paths are interpreted according to the crack tip stress field arising in the case of large deformations. the experimental outcomes show that, for cracks tested in mode i, higher strain rates facilitate the development of a simple mode i crack path, while lower strain rates can induce a mixed mode in the first stage of the crack propagation. moreover, during the loading process the appearance of new crack tips due to the mode mixity has been observed as a consequence of the nonclassical stress field existing around the crack tip. tests have confirmed that the above described mechanical response in terms of crack path is not influenced by the initial crack size. crack tip stress field in highly deformable materials typical way to measure the flaw tolerance of materials is through the determination of the fracture energy; experiments conducted on soft polymers indicated a strong rate and temperature dependency for such a fracture property because of the energy dissipation produced by viscoelasticity [13]. some different approaches to explain the failure in rubber-like materials have been proposed; among them the so-called cavitation criterion assumes the presence of intrinsic small defects that lead to failure under a sufficiently large hydrostatic stress state provoking void expansion and coalescence [14]. on the other hand, within the classical fracture mechanics approach, the near crack tip stress field governs the local failure of the material in terms of chains failure and growth of small existing microdefects and voids. because of the high deformation capability of this class of materials, the classical linear elastic fracture mechanics (lefm) approach valid for infinitesimal strains is not applicable anymore, and the large displacement effects must be accounted for instead. further, the isochoric (incompressible) deformation process, typically shown by polymers, must be also considered in the determination of the singular stress field induced by a crack [15, 16]. in fig. 1 the geometry of the considered cracked plate is shown; the global reference coordinate system ,x y and the crack tip reference coordinates 1 2,x x are depicted in fig. 1a, while the current (deformed) crack tip coordinates are indicated with 1 2,y y (fig. 1b). note that the crack tip moves from the initial position o to the current one 'o . formulation of the problem in large deformation in the reference coordinate system 1 2,x x , the equilibrium equations in absence of body forces and the traction-free boundary conditions are /   0ij jp x   , , 1, 2 i j  , 22 12( 0, π) ( 0, π) 0p r p r         (1) where the nominal stress tensor p (piola stress) has been used, while the true stress referred to the current deformed configuration (cauchy stress σ ) is related to the nominal piola stress through the relationship 1 tj σ pf , /ij ij i jf u x    f being the deformation gradient tensor of the displacement iu and detj  f being the volume variation which, for an incompressible material, must be equal to 1. a r. brighenti et alii, frattura ed integrità strutturale, 48 (2019) 1-9; doi: 10.3221/igf-esis.48.01 3 figure 1: cracked plate: main geometrical sizes and reference systems in the (a) undeformed and (b) deformed configuration. constitutive models constitutive models for polymers are usually defined in terms of the strain energy function ̂ ; several models suitable for rubber-like materials have been proposed in the literature. among them, the well-known neo-hookean, gent and ogden models can be mentioned [17]. in particular, the following energy expression  r for the deformation of a single chain is assumed by the neo-hookean model, and the strain energy density follows the gent model, respectively:    2 112 3 ,        ln 1ˆ 62 b m m k t je r r j j jnb            (2) where bk is the boltzmann constant and t the absolute temperature. further, n is the number of kuhn’s segments in a single polymer chain and b is their length, whereas e is the small strain young modulus, 1 1 3j i  is a stretch invariant, and mj is the limit value of 1j . the energy per unit volume of the material  can be obtained from the following relationship:     ω ωˆ d    r r (3) r. brighenti et alii, frattura ed integrità strutturale, 48 (2019) 1-9; doi: 10.3221/igf-esis.48.01 4 where  3ω  r indicates the chain configuration space and   r is the chains’ end-to-end distance distribution function, i.e. it provides the number of chains per unit volume whose end-to-end distance is comprised between r and dr r . once the energy function is known, the nominal stress tensor can be obtained from the strain energy as       ω ω ˆ tr r d p t j          p ff f (4) where  p is the hydrostatic pressure, introduced as a lagrange multiplier to enforce the incompressibility condition herein assumed for the polymer as usually observed for this class of materials, being det 1j  f . the above expression(3), in the case of the standard gaussian distribution  r of r (typically adopted in rubber elasticity), leads to  1 3 / 2i   , where 2 2 21 1 2 3i      , is the first invariant of the right cauchy-green deformation tensor tc f f ,  is the small strain shear modulus and 1 2 3, ,   are the three stretches along the cartesian directions. an energy expression valid for large strains of a single chain is the one proposed by kuhn, namely   ln sinh br nk t r bn             , where 1 1 r bn n                  , 1 is the inverse langevin function, while b , n and  are the kuhn’s segment length, the number of segments per chain and the chain stretch, respectively. crack tip stress field it is well-known that, in a 2d problem, the mode i crack tip stress field within the lefm hypothesis is expressed by:  i . . . 2π ij ij ij k p f h o t r     , , 1, 2i j  (5) where  ijf  is an angular function, ik is the mode i stress-intensity factor (sif) and, thanks to the small deformation hypothesis, the nominal ( ijp ) and true stress ( ij ) tensor components are identical. within the lefm, the stresses are linear function of strain, and can be superimposed. further, all the stress components have the same inverse square root singularity for the three deformation modes (mode i, mode ii and mode iii). within the large displacement field context, knowles and sternberg [18] performed the crack-tip asymptotic analysis through a series expansion of the deformed coordinates, consisting of separable functions of the polar coordinates ( ,r  ) in the undeformed material, in a way similar to the william’s expansion approach in lefm [19]. the crack tip stress field under large deformation results to be quite different from the one valid in the lefm hypothesis and depends upon the constitutive model in turn; such a problem has been solved applying the asymptotic analysis method [20] by writing the crack tip deformed coordinates, 1 2,y y , with respect to the undeformed material coordinate system, 1 2,x x , through a series of separable functions of the polar coordinates ,r  (fig. 1). it can be shown that, under large deformation the true (cauchy) stress components for a neo-hookean incompressible material are given by    2 1/2 2 111 12 21 22,    , sin  ,    , 2 2 4 c r acr r a r                (6) where ,a c are unknown positive amplitudes depending on loading and geometry of the configuration being examined, and the pressure field required to enforce the incompressibility condition (usually assumed for polymeric materials since they can undergo only isochoric deformations) turns out to be 1 1/22 cos 2 p ca r     . the stress field is thus governed by these two parameters instead of the only one (the sif, ik ) needed in the lefm. from eq. (6) it is evident that, differently from the lefm case, the singularity of the opening stress component 22 is different from the singularity of the shear stress component 12 as r approaches the crack tip. r. brighenti et alii, frattura ed integrità strutturale, 48 (2019) 1-9; doi: 10.3221/igf-esis.48.01 5 the knowledge of the kinematic relationship between deformed and reference configuration, 1 2cos ,  sin / 2y cr y a r   [20], allows to express the true stress components in terms of the polar coordinates ( ,  ) in the deformed (current) configuration (fig. 1b, fig. 2). along the deformed upper parabolic crack profile, the true stress components are: 2 2 1 4 2 11 12 21 22 π π ,   , ,  , ,   0 2 4 2 8 c a c a                                 (7) where only the singular terms have been reported and the relationship / 2  has been considered due to the fact that the deformed crack profile at the crack tip becomes parallel to the vertical axis (the tangent to the parabolic profile is vertical) [20]. (a) (b) figure 2: (a) undeformed cracked plate and deformed configuration with the related reference systems. (b) crack tip detail of the stress field. in large deformation, the singularity of the true stress 22 is sharper along the 2y axis than along the 1y axis. expected crack path in large deformation from eqs (6),(7) it can be remarked that the stress component 22 along the deformed parabolic crack profile ( π / 2  ) has a singularity -2 (i.e. 2 ), while the same stress component has a singularity -1 (i.e. 1r  ) ahead of the crack tip ( 0  ). this different singularity can trigger the appearance of a secondary crack, departing from the blunted deformed one (crack tip splitting), leading to a tortuous crack path or to a rough crack profile. in other words, the singularity of the true stress 22 is sharper along the 2y axis than along the 1y one (see fig. 2); thus the material tends easily to break apart close to the crack tip along 2y , leading to the appearance of secondary cracks, responsible for curved crack paths. r. brighenti et alii, frattura ed integrità strutturale, 48 (2019) 1-9; doi: 10.3221/igf-esis.48.01 6 finally, the rate-dependence of failure in elastomers is a well-known phenomenon and has been explained through the internal energy dissipation mechanism by assuming that the chains bond lifetime depends on the applied stress level  [21]. a slower strain rate allows the material to easily flow in time, while a faster rate entails a more elastic behavior. the experimental outcomes have shown that the crack branching easily occurs for slower strain rates. experimental tests he mechanical response under tension of a pre-cracked elastomeric sheet, made of a common silicone polymer, has been experimentally investigated. the evolution of the deformation and of the crack path have been controlled and monitored through the “contact-free” digital image correlation (dic) measurement technique. the specimens, having width equal to w = 112 mm, are characterized by an initial elastic modulus of about 1.12 mpae  and poisson’s ratio 0.42  , whereas samples’ geometric characteristics are shown in tab.1. the ratio 2 /l w is assumed to be sufficiently high to ensure a uniaxial stress state in the central part of the sample, by limiting the boundary effects. the dimensionless small deformation stress intensity factors  *i i ,0/ π  yk k a are also reported in tab. 1. the tests have been conducted by applying a controlled displacement to the edge of the plate placed at y l  , while the other has been kept fixed; three different strain rates have been adopted, namely: 3 11 9.615 10  s    , 3 12 5.769 10  s    and 4 1 3 1.603 10  s    (  / 2d l   , d being the applied displacement rate), in order to investigate the effect of the deformation velocity on the mechanical response of the cracked plates. spec. no. 2a (mm) t (mm) 2 /a w (---) * ik (---) c2a 20 2.75 0.179 1.019 c2b 20 2.85 0.179 1.019 c2c 20 2.75 0.179 1.019 c3a 30 3.00 0.268 1.045 c3b 30 3.00 0.268 1.045 c3c 30 2.60 0.268 1.045 c4a 40 2.75 0.357 1.084 c4b 40 1.80 0.357 1.084 c4c 40 2.00 0.357 1.084 table 1: geometric characteristics of the tested specimens and related dimensionless sif, *ik . the symbol cnα (n = 2, 3, 4, 5; α = a, b, c) refers to plates with different crack lengths tested at strain rates: α = a, strain rate 1 ; α = b, strain rate 2 ; α = c, strain rate 3 . the true stress vs stretch behavior of the examined material under tension is reported in fig. 3a; the true stress has been obtained from the nominal stress by exploiting the incompressibility assumption. both the neo-hookean model and the gent model are also reported to underline which is the best fitting theoretical model. in fig. 3b, the variation of the poisson’s ratio measured experimentally vs the stretch value and the corresponding curve for a perfectly incompressible material are displayed; in particular, the theoretical poisson’s ratio vs stretch for an isochoric deformation is expressed as    1 21 / 1      [22]. from the above-mentioned mechanical tests, it can be concluded that the material behaves very close to the predictions deduced according to the gent model, and is nearly incompressible. from the tested material, the mechanical parameters have been found to be 1.5 mpae  and 2.35mj  . t r. brighenti et alii, frattura ed integrità strutturale, 48 (2019) 1-9; doi: 10.3221/igf-esis.48.01 7 figure 3: (a) true stress vs stretch for the examined material. (b) variation of the poisson’s ratio with the deformation. experimental and theoretical values are reported. in fig. 4 the crack tip splitting phenomenon is shown at the incipient failure for the specimens c2b, c3b and c4b, while the whole crack paths after failure are depicted in fig. 4 for the three strain rates adopted, 1 , 2 , 3 . (a) (b) (c) figure 4: crack tip splitting at the incipient failure for specimens (a) c2b, (b) c3b and (c) c4b. (a) 1 (b) 2 (c) 3 (d) 1 (e) 2 (f) 3 (g) 1 (h) 2 (i) 3 figure 5: crack paths for specimens (a) c2a, (b) c2b, (c) c2c, (d) c3a, (e) c3b, (f) c3c, (g) c4a, (h) c4b and (i) c4c (only half of each specimen corresponding to 0y  , see fig. 1, is shown). the initial crack (blue straight line) grows as is indicated by the red line. a=15 mm a=20 mm a=10 mm r. brighenti et alii, frattura ed integrità strutturale, 48 (2019) 1-9; doi: 10.3221/igf-esis.48.01 8 fig. 5 shows the crack paths obtained for the different cracked samples by changing the initial crack length 2 20, 30, 40 mma  and the applied strain rate (only half of the specimen is shown). it can be appreciated that the resulting crack paths, observed after the final failure of the specimen, are only slightly influenced by the initial crack size, while the strain rate plays a crucial role. it’s worth noting that, because of the testing imperfections, the final failure pattern in the specimens usually appeared to be symmetric with respect to the y axis, while in some cases the crack propagated only in one side of the sheet. in these latter cases, only the cracks half of the specimens have been shown (fig. 5). the observed results allow us to obtain a physical interpretation to the way how the crack behaves: under a fast deformation, the material behaves in an elastic way, so that the theoretical stress singularities shown in eq. (6) are fulfilled. on the other hand, a low strain rate allows the material to damage locally in preferential directions, according to the severity of the stress component singularity, leading to a more marked crack kinking. in this case, the crack initially tends to propagate practically in almost pure mode ii, i.e. in a direction normal to the crack line. from the crack tip stress field viewpoint (see eqs (6), (7) ), when the material deforms elastically – such as in the small deformation regime – the stress component 22 along the deformed parabolic crack profile ( π / 2  ) is more singular ( 2 ) than along the crack symmetry axis ( 0  , 1r  ). this fact justifies the crack tip split taking place at the crack tip at the very early stage of the deformation process. the numerical analysis reported in krishnan et al. [23] shows that a concentration of shear deformation exists near the crack tips, especially when the material display a less pronounced strain hardening behavior, such as happens in the case of low strain rates. this justifies the more evident persistence of the mode ii deformation in cases where the material is subjected to low strain rates (fig. 5c, f, i) with respect to the cases characterized by high strain rates (fig. 5a, d, g). conclusions n the present paper, the crack behavior of soft cracked plates has been examined. the crack tip stress field under large displacements as well as the rate-dependent behavior have been considered. the remarkable result from the literature that the singularity of the true stress in large deformation is quite different from the one according to the lefm theory has been adopted. moreover, the different order of singularity of the stress components in large deformation gives rise to crack tip splitting and, consequently, curved crack paths develop even under remote pure mode i loading. this behavior is enhanced at slow strain rates (see the curved crack paths in fig. 3c, f, i), while faster strain rates have a lower effect in terms of promoting such a weird crack growth (see fig. 3a, d, g). in fact, because of the existence of the strain rate effect that typically arises in this class of materials, the purely linear behavior is recovered only when the strain rate is sufficiently small, while a more severe crack tilting is observed (with a consequent curved crack path) thanks to the more pronounced damage arising locally in preferential directions according to the severity of the stress component singularity. in the latter case, the crack tends to propagate seemingly in pure mode ii, i.e. in a direction almost normal to the crack line. moreover, the observed crack paths deviate from the pure mode i propagation irrespective of the initial crack length. the experimental results have shown that the crack tip singular stress field arising in highly deformable materials can lead to complex curved crack paths which cannot be predicted by using the standard lefm approach. references [1] treloar, l.r.g. (1975). physics of rubber elasticity, oxford university press . [2] doi, m. (2013). soft matter physics. oxford: oxford univ. press. [3] chen, d., yoon, j., chandra, d., crosby, a.j., hayward, r.c. (2014). stimuli-responsive buckling mechanics of polymer films. j. polym. sci., part b: pol. phys, 52, pp. 1441–1461. doi: 10.1002/polb.23590. [4] roland, c.m. (2006). mechanical behavior of rubber at high strain rates. rubber chem. tech., 79(3), pp. 429–459. doi: 10.5254/1.3547945. [5] bergström, j.s., boyce, m.c. (2016). constitutive modelling of the large strain time-dependent behaviour of elastomers. j. mech. phys. sol., 46, pp. 931–954. doi: 10.1016/s0022-5096(97)00075-6. [6] brighenti, r., vernerey, f.j., artoni, f. (2017). rate-dependent failure mechanism of elastomers. j. mech. sci., 130, pp. 448–457. doi: 10.1016/j.ijmecsci.2017.05.033. [7] candau, n., laghmach, r., chazeau, l., chenal, j-m., gauthier, c., biben, t., munch, e. (2014). strain-induced crystallization of natural rubber and cross-link densities heterogeneities. macromolecules, 47(16), pp. 5815–5824. doi:10.1021/ma5006843. i r. brighenti et alii, frattura ed integrità strutturale, 48 (2019) 1-9; doi: 10.3221/igf-esis.48.01 9 [8] flory, p.j. (1989). statistical mechanics of chain molecules. cincinnati (ohio): hanser-gardner. [9] de gennes, p.g. (1971). reptation of a polymer chain in presence of fixed obstacles. j. chem. physics, 55, pp. 572– 579. doi: 10.1063/1.1675789. [10] treloar, l.r. (1973). the elasticity and related properties of rubbers. rep. prog. phys., 36, pp. 755–826. doi: 10.1088/0034-4885/36/7/001. [11] trapper, p., volokh, k.y. (2008). cracks in rubber. j. sol. struct., 45, pp. 6034–6044. doi: 10.1016/j.ijsolstr.2008.07.016. [12] brighenti, r., carpinteri, a., artoni, f. (2017). defect sensitivity to failure of highly deformable polymeric materials. theor. appl. fract. mech., 88, pp. 107–116. doi: 10.1016/j.tafmec.2016.12.005. [13] gent, a.n. (1996). adhesion and strength of viscoelastic solids. is there a relationship between adhesion and bulk properties?, langmuir 12, pp. 4492–4496. doi: 10.1021/la950887q. [14] lev, y., volokh k.y. (2016). on cavitation in rubberlike materials. j. app. mech. 83(4), 0044501-1–4. doi: 10.1115/1.4032377. [15] knowles, j.k., sternberg, e. (1973). an asymptotic finite deformation analysis of the elastostatic field near the tip of a crack. j. elast., 3, pp. 67–107. doi: 10.1007/bf00049265. [16] gao, y.c., jin, m., dui, g.s. (2008). stresses, singularities, and a complementary energy principle for large strain elasticity, appl. mech. rev. 61, 030801. doi: 10.1115/1.2909715. [17] boyce, m.c., arruda, e.m. (2000). constitutive models of rubber elasticity: a review, rubber chemistry and technology, 73, pp. 504-523. doi: 10.5254/1.3547602. [18] knowles, j.k., sternberg, e. (1973). an asymptotic finite deformation analysis of the elastostatic field near the tip of a crack, j. elast., 3, pp. 67–107. doi: 10.1007/bf00045816. [19] williams, m. (1957). on the stress distribution at the base of a stationary crack. j. appl. mech., 24, pp. 109–114. doi: 10.1115/1.3640470. [20] long, r., krishnan, v.r., hui, c.y. (2011). finite strain analysis of crack tip fields in incompressible hyperelastic solids loaded in plane stress. mech. phys. sol., 59, pp. 672–695. doi: 10.1016/j.jmps.2010.12.005. [21] hui, c-y., tang, t., lin, y-y, chaudhury, m.k. (2004). failure of elastomeric polymers due to rate dependent bond rupture. langmuir, 20, pp. 6052-6064. doi: 10.1021/la0356607. [22] beatty, m. f., stalnaker, d. o. (1986). the poisson function of finite elasticity. journal of applied mechanics, 53(4), pp. 807-813. doi: 10.1115/1.3171862. [23] krishnan, v.r., hui, c-y., long, r., (2008). finite strain crack tip fields in soft incompressible elastic solids. langmuir, 24(24), pp. 14245-14253. doi: 10.1021/la802795e. << /ascii85encodepages false /allowtransparency false /autopositionepsfiles true /autorotatepages /none /binding /left /calgrayprofile (dot gain 20%) /calrgbprofile (srgb iec61966-2.1) /calcmykprofile (u.s. web coated \050swop\051 v2) /srgbprofile (srgb iec61966-2.1) /cannotembedfontpolicy /error /compatibilitylevel 1.4 /compressobjects /tags /compresspages true /convertimagestoindexed true /passthroughjpegimages true /createjobticket false /defaultrenderingintent /default /detectblends true /detectcurves 0.0000 /colorconversionstrategy /cmyk /dothumbnails false /embedallfonts true /embedopentype false /parseiccprofilesincomments true /embedjoboptions true /dscreportinglevel 0 /emitdscwarnings false /endpage -1 /imagememory 1048576 /lockdistillerparams false /maxsubsetpct 100 /optimize true /opm 1 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/hrv (za stvaranje adobe pdf dokumenata najpogodnijih za visokokvalitetni ispis prije tiskanja koristite ove postavke. stvoreni pdf dokumenti mogu se otvoriti acrobat i adobe reader 5.0 i kasnijim verzijama.) /hun 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can be opened with acrobat and adobe reader 5.0 and later.) >> /namespace [ (adobe) (common) (1.0) ] /othernamespaces [ << /asreaderspreads false /cropimagestoframes true /errorcontrol /warnandcontinue /flattenerignorespreadoverrides false /includeguidesgrids false /includenonprinting false /includeslug false /namespace [ (adobe) (indesign) (4.0) ] /omitplacedbitmaps false /omitplacedeps false /omitplacedpdf false /simulateoverprint /legacy >> << /addbleedmarks false /addcolorbars false /addcropmarks false /addpageinfo false /addregmarks false /convertcolors /converttocmyk /destinationprofilename () /destinationprofileselector /documentcmyk /downsample16bitimages true /flattenerpreset << /presetselector /mediumresolution >> /formelements false /generatestructure false /includebookmarks false /includehyperlinks false /includeinteractive false /includelayers false /includeprofiles false /multimediahandling /useobjectsettings /namespace [ (adobe) (creativesuite) (2.0) ] /pdfxoutputintentprofileselector /documentcmyk /preserveediting true /untaggedcmykhandling /leaveuntagged /untaggedrgbhandling /usedocumentprofile /usedocumentbleed false >> ] >> setdistillerparams << /hwresolution [2400 2400] /pagesize [612.000 792.000] >> setpagedevice shot peening processes to obtain nanocrystalline surfaces in metal alloys: j. kasivitamnuay et alii, frattura ed integrità strutturale, 52 (2020) 163-180; doi: 10.3221/igf-esis.52.14 163 object-oriented software for fitness-for-service assessment of cracked cylinder based on api rp 579 jirapong kasivitamnuay, pairod singhatanadgid chulalongkorn university, thailand jirapong.k@chula.co.th, http://orcid.org/0000-0002-9933-7652 pairod.s@chula.ac.th, http://orcid.org/0000-0002-4972-753x abstract. fitness-for-service assessment of a cracked component intends to evaluate its remaining strength and remaining life to support the implementation of a maintenance plan. this research aims to develop a fitness-for-service assessment software to facilitate the task. the software development process included identifying the software specifications, designing the software structure, manipulating the information in the standard for programming, the graphical user interface design, and finally verification. the assessment procedure employed in this study was the third edition of the standard api rp 579. the software structure was designed using an objectoriented concept. the software can perform integrity assessment levels 1, 2, and 3 option b, leak-before-break assessment, and remaining life assessment for a cracked cylinder that has a through-thickness crack or semi-elliptical surface crack oriented in an axial or circumferential direction. the applied loads could be a nominal axial force, bending moment, and internal pressure, as well as stress profiles perpendicular to the crack plane due to mechanical, thermal, and residual stresses. accuracy of the software was demonstrated by applying it to example problems. some aspects of the software extensibility were conceptually discussed. keywords. api 579; fitness-for-service; fracture mechanics; objectoriented programming; pressure vessel. citation: kasivitamnuay, j., singhatanadgid, p., object-oriented software for fitness-forservice assessment of cracked cylinder based on api rp 579, frattura ed integrità strutturale, 52 (2020) 163-180. received: 25.12.2019 accepted: 04.02.2020 published: 01.04.2020 copyright: © 2020 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. introduction crack-like flaw is one of the major service degradation mechanisms for pressure vessels and piping. fitness-forservice (ffs) assessments are conducted on these cracked components to quantitatively evaluate their suitability for operation and to determine the remaining service life. numerous professional ffs assessment procedures have been developed worldwide, as reviewed by hasegawa [1]. to enhance ffs assessment activities, filiou et al. [2] suggested the development of ffs software. researchers from universities, organizations, and companies have attempted to develop these software packages [3-14]. the computational basis within these packages may refer to a single specific ffs standard [3, 6, 9, 11, 14], an integration of several ffs standards [12, 13], or a direct implementation of a fracture mechanics methodology without referring to any standard [4, 5, 7, 8, 10]. a https://youtu.be/flqlcpj7sgc j. kasivitamnuay et alii, frattura ed integrità strutturale, 52 (2020) 163-180; doi: 10.3221/igf-esis.52.14 164 the api 579 standard [15] is a well-known assessment standard, especially in the petrochemical industry since it covers the major damage mechanisms found in this area of application. since the first edition was first released in 2000, the code has been continually revised, with the most recent third edition of the code published in 2016. for the crack-like flaw assessment module, the code provides necessary assessment information similar to other well-accepted codes, such as bs 7910, r6, and fitnet procedures. the stress intensity factor (sif) solutions in the api 579 standard support the broadest range of cylindrical components and allow the calculation of sif due to an arbitrary stress distribution profile [16]. the latest edition of standard revised a number of elements, for example, the reference temperature for a level 1 assessment, the recommended residual stress profiles, and the method to determine the plasticity correction factor. the ffs software developed based on the api 579 standard is rarely found in the literature [9, 11, 12]. furthermore, the available software can assess up to level 2 and do not support the latest edition of this standard. in the development of the ffs software, the extensibility of the software is a necessary concern. object-oriented (oo) programming is one of the proper approaches that can support the software structure design to satisfy such requirements [17]. a few applications of the oo concept in ffs software for a cracked component were found in the literature [3, 4, 8]. furthermore, to the authors’ knowledge, the oo concept has not yet been applied in the development of a ffs software based on the api 579 standard. the present paper aims to apply the oo concept to develop the ffs software for a cracked cylinder, based on the latest edition of the api 579 standard. the major concern is to develop a class hierarchy diagram to support the extensibility of the software. the paper is composed of a review of the api 579 standard, the software design process, and an application of the software with example problems. api 579 standard he api 579 standard provides three levels of integrity assessment. the higher level of assessment requires more detailed information and analysis, although more precise assessment results can be obtained. fig. 1 provides an overview of the integrity assessment recommended by the standard. the assessment always starts from level 1 if this level’s applicability criteria are satisfied. the higher level of the assessment should be performed if the lower level assessment predicts a component failure. however, if it is decided not to conduct the higher assessment level, the component must be repaired or replaced as suggested by the standard. an assessment of component acceptability must also consider the potential for future component degradation under continued service conditions, based on the potential for crack growth due to fatigue or corrosion. if there is a potential of crack growth, it is necessary to evaluate its remaining life. the background of the integrity assessment for each level and the remaining life evaluation can be summarized as follows. a level 1 assessment adopts a screening curve approach to determine a permissible crack length in a component. the standard prepares several screening curves according to component geometries (i.e., plate, cylinder, sphere), a crack depth relative to the thickness of the component, and the crack location (i.e., base metal, heat-affected zone, weld). fig. 2 schematically represents this curve for a particular case. the horizontal axis is t – tref + 56 (in oc), where t is the component service temperature, and tref is a reference temperature of the material. the tref can be set as a nil-ductilitytransition temperature, rtndt, or estimated from the specified minimum yield strength (smys) and the exemption curve of a material. from knowing the t, tref, crack depth, crack location, and component wall thickness, the allowable crack length can be determined from this curve. if the allowable crack length is shorter than that from the inspection, the component is predicted to be unsafe. level 2 and 3 assessments adopt a failure assessment diagram (fad) approach. fig. 3 schematically represents the diagram. the horizontal axis of the fad is a load ratio based on primary stress, lr,p, while the vertical axis is a toughness ratio, kr. the current status of a cracked component is represented by an assessment point (lr,p, kr). the component is predicted to be safe (or acceptable) only if the assessment point lies on or below the failure assessment curve (fac). parameter lr,p is defined as:   = , , ref p r p y l (1) where ref,p is the reference stress based on the primary stress, and y is the yield strength. equations used to determine the reference stress of a specific cracked component are written in terms of linearized stress components, i.e. the membrane and bending components. t j. kasivitamnuay et alii, frattura ed integrità strutturale, 52 (2020) 163-180; doi: 10.3221/igf-esis.52.14 165 obtain component data and preliminary inspection data characterize the shape and size of the crack is component acceptable? perform a level 2 assessment is component acceptable? rerate component perform a level 3 assessment no yes no no rerate component is component acceptable? yes no perform rerate per level 2 criteria to modify pressure and/or temperature yes perform rerate per level 3 criteria to modify pressure and/or temperature yes is crack has potential to grow in-service? return component to service yes repair or replace component no no no yes no perform crack growth analysis yes yes is level 1 assessment applicable? yes no perform a level 1 assessment figure 1: overview of a cracked component assessment based on the api 579 standard. j. kasivitamnuay et alii, frattura ed integrità strutturale, 52 (2020) 163-180; doi: 10.3221/igf-esis.52.14 166 p e rm is si b le c ra c k l e n g th t – tref + 56 (oc) figure 2: schematic illustration of a screening curve. 1 failure assessment curve (fac) assessment point safe unsafe load ratio, lr,p t o u g h n e ss r at io , k r lr,p(max) figure 3: schematic illustration of a failure assessment diagram (fad). parameter kr is defined as: +  = i, ,p i sr r mat k k k k (2) where ki,p and ki,sr are mode-i stress intensity factors due to primary and secondary stresses, respectively, kmat is fracture toughness of the component’s material, and  is the plasticity correction factor. the sif of specific cracked component geometry and applied loads can be determined from formulas in the standard. the sif solutions may be expressed in terms of nominal loads, linearized stress components, or influence coefficients. the last form of the sif solution is appropriate to evaluate the sif due to a stress profile acting normal to the crack plane, e.g. thermal and residual stress profiles. the standard employs an approximation of the actual stress profile with the following 4th order polynomial function:             = +  +  +  +             2 3 4 0 1 2 3 4 ( ) x x x x x t t t t (3) where 0, 1, 2, 3 and 4 are best-fit coefficients, t is the nominal thickness corrected with uniform corrosion, and x is the local coordinate pointed along the thickness direction. a level 2 fac is a general curve, which means it is independent of the materials and component geometries. this general curve is expressed by: j. kasivitamnuay et alii, frattura ed integrità strutturale, 52 (2020) 163-180; doi: 10.3221/igf-esis.52.14 167 ( ) ( )    = − + −       2 6 , , 1 0.14 0.3 0.7 exp 0.65 r r p r p k l l (4) a level 3 fac depends on an analysis option. for option b which is implemented in this software, the fac is expressed by: ( )    −    = +     1 3 2 , , 2 r p yref r r p y ref le k l e (5) where e and ref are young’s modulus and reference strain, respectively. it should be noted that the fac depends on the material properties, so it can be called a material-specific fac. the extent of the fac on the lr,p axis is dependent on a material’s deformation behavior. for materials with a yield point plateau (where the strain hardening exponent is greater than 15) or materials with unknown strain-hardening characteristics, the lr,p(max) is set to 1. for specific material types or classes such as astm a508 steel, c-mn steels, and austenitic stainless steels, the recommended values of lr,p(max) are 1.15, 1.25, and 1.80, respectively. for materials with a typical strain hardening characteristic, the lr,p(max) is determined from the following equation: , (max) f r p y l   = (6) where f is the flow stress which is typically an average of the yield and ultimate strength of a material. if the component is predicted to be safe per level 3 assessment, then the assessment can proceed to evaluate the remaining life of the cracked component. to determine the remaining life, processes of updating the crack size and assessing the integrity of the structure are alternately conducted until the assessment point lies above the fac, where the component is predicted to be unsafe. the summation of a number of cycles (or time) during each step of crack increment is the remaining life. for the case of a component with a surface crack, both crack length and crack depth are continually evaluated. the surface crack will be recategorized as a through-wall crack when its depth reaches 80% of the wall thickness, as illustrated in fig. 4. the length of a through-wall crack after recategorized is given by 2c = 2cs + 2(t − as), where 2cs and as are the length and depth of a surface crack when the crack size meets the recategorization criteria. the component with this through-wall crack is then reassessed. if it is predicted to be safe, the processes of crack growth analysis and integrity assessment will proceed as previously described. thus, the remaining life of a component with a surface crack might be a combination of the surface crack growth period and the through-wall crack growth period. 2cs as 2c = 2cs +2(t as) t when as/t > 0.8 figure 4: surface crack recategorized as a through-wall crack. software design his section describes the software design processes, beginning with a description of the software specifications, followed by highlighting some calculation issues. in this study, the information from the standard which is presented in graphical and tabular forms are transformed into other forms to make them more convenient to handle during the programming process. other issues including calculating the sif and fatigue crack growth analysis are also addressed. next, the class hierarchy diagram of the program is presented. finally, the user interface is demonstrated. t j. kasivitamnuay et alii, frattura ed integrità strutturale, 52 (2020) 163-180; doi: 10.3221/igf-esis.52.14 168 specifications the software specifications are related to the types and levels of assessments, cracked component geometries, and types of applied loads. the software was specified to perform integrity, leak-before-break (lbb), and remaining life assessments of a cracked cylinder. four types of cracked cylinder (namely ctcl, ctcc, cscle, and cscce) were considered, as illustrated in fig. 5. for cscle and cscce, both the inner-wall and outer-wall cracks were included in the study. the treatments of crack interaction and weld strength mismatch were not included. the si unit system was adopted. the integrity assessment covered levels 1, 2, and 3 option b. the lbb assessment was permitted for the level 2 and 3 assessments, whereas the remaining life assessment permitted only a level 3 assessment. for the lbb assessment, the user must provide the length of a through-wall crack at a detectable leak rate. the remaining life assessment covered only the crack growth mechanism by fatigue. furthermore, only cyclically nominal loads with a constant amplitude were considered. the analysis was performed at two representative locations on the crack front. the applied loads on the cylinder could be nominal loads, i.e. internal pressure, axial force, and bending moment, as well as through-thickness mechanical, thermal, and residual stress distribution perpendicular to the crack plane. these stress profiles are expressed in the form of eqn. (3), where the coefficients in the equation are specified for given types and directions of stresses. the coefficients of thermal stress profiles were provided by the user. meanwhile, for residual stress, the user has a choice of whether to use the recommended profiles in the standard. 2c x ri t 2c t 2q ri x 2c x ri t 2c x ri t a a x 2c a x 2c a t ri t ri (a) (b) (c) (d) (e) (f) figure 5: types of cracked cylinder included in the software: (a) ctcl; (b) ctcc; (c) cscle (inner-wall crack); (d) cscle (outerwall crack); (e) cscce (inner-wall crack); and (f) cscce (outer-wall crack). the software incorporated a text file containing a material information of some pressure vessel steels. the information includes material specifications, specified minimum yield strength (smys), and specified minimum ultimate strength (smts). however, the software allowed the user to input actual material information. the constitutive equation incorporated in the software was only the ramberg-osgood (r-o) model. the parameters of the r-o model can be userdefined input or estimated by the formulas in the standard. the fracture toughness could be the custom input value or estimation from various methodologies in tab. 1. the supported fatigue crack growth rate (fcgr) models were paris and walker models, with the material parameters being user provided. j. kasivitamnuay et alii, frattura ed integrità strutturale, 52 (2020) 163-180; doi: 10.3221/igf-esis.52.14 169 methodology region model reference temperature lower bound transition asme section xi nil-ductility transition temperature, rtndt asme section viii estimate from charpy transition curve and asme exemption curve charpy impact transition charpy v-notch transition curve upper shelf rolfe-novak correlation wallin j-integral correlation master curve transition master curve index temperature, t0 table 1: fracture toughness estimation methodologies adopted in software development. calculation issues the standard provides definite steps to manipulate the input information for each type and level of assessment. yet some issues require preparation and consideration before coding. the first issue was information preparation in the standard which appears as a graph (e.g., screening curve) or table and converting that into a suitable format for programming. the next issue was the sif calculation when the origin of the local coordinate on the thickness direction of a cracked cylinder differs from the recommended residual stress profile, or from after crack recategorization. the final issue was related to fatigue crack growth analysis. each screening curve was digitized and the coordinates obtained were stored in a text file. an array-type variable was prepared to store the data read from the opened text file while the program was running. a one-dimensional linear interpolation algorithm was used to determine a permissible crack length at an intermediate value of the independent variable, i.e. t –tref + 56. the information from each table was stored in a text file. a one or three-dimensional linear interpolation algorithm was employed depending on the number of independent variables. the next issue was sif calculation. considering the cscle and cscce cracked cylinders with an external surface crack, shown respectively in figs. 5(d) and 5(f), the origin of the local coordinate x was defined at the outer wall, whereas the recommended residual stress profiles were typically defined at the inner wall. therefore, before computing the sif of these two cracked cylinder geometries, the recommended residual stress profiles must be rewritten in the form of: 2 3 4 0 1 2 3 4 ( ) 1 1 1 1 x x x x x t t t t               = +  − +  − +  − +  −                (7) where 0, 1, 2, 3 and 4 are recommended coefficients given in the standard. a similar situation occurs when the cscle and cscce cracked cylinders with an external surface crack (figs. 5(d) and 5(f)), are respectively recategorized as the ctcl (fig. 5(a)) and ctcc (fig. 5(b)) cracked cylinders. the user-defined stress profiles of any type (i.e. mechanical, thermal and residual) for the cases of cscle and cscce must be rewritten in the form of eqn. (7) before computing the sif for the ctcl and ctcc cases. for fatigue crack growth analysis, the standard does not provide guidance to incorporate the influence of residual stress on the fcgr. this software considered the residual stress as mean stress, thus the stress ratio, r in the walker fcgr model was given by: min max res res k k r k k + = + (8) where kmin and kmax are the minimum and maximum of mode-i sif due to a cyclic nominal load, respectively. kres is mode-i sif due to residual stress. a further consideration for crack growth analysis is the calculation of the remaining life of a cracked cylinder. as a compromise between accuracy and computational time, fcgr was calculated only at the representative locations on the crack front. in addition, the crack size was updated every allowable number of loading cycles, i.e. the fcgr was supposed to be constant during this interval. herein, the allowable number of loading cycles was set to the number of cycles required to grow the crack by 1% of its previous dimensions. for a through-thickness crack, fcgrs were calculated at the inner and outer points on the crack front. the allowable number of loading cycles nallow was determined from: j. kasivitamnuay et alii, frattura ed integrità strutturale, 52 (2020) 163-180; doi: 10.3221/igf-esis.52.14 170 ( ) ( ) floor max , allow allow in out c n dc dn dc dn     =      (9) where callow is the allowable increment of half crack length (i.e. 0.01c), and (dc/dn)in and (dc/dn)out are the fcgrs at the inner and outer points, respectively. note that eqn. (9) yields a conservative value of nallow since the maximum between fcgrs at two locations and the floor function were used. the increments of a half crack length at the inner point cin and the outer point cout under a cyclic load of nallow cycles are cin = nallow·(dc/dn)in and cout = nallow·(dc/dn)out, respectively. since cin is typically unequal to cout (fig. 6), the maximum between both values was chosen to be the half crack length increment c, i.e. c = max(cin , cout ). for a semi-elliptical surface crack, fcgrs at the surface and deepest points were calculated. the conservative allowable number of loading cycles nallow was determined from: ( ) ( ) min , floor max , allow allow allow c a n dc dn da dn     =      (10) where callow is the allowable increment of half crack length (i.e. 0.01c), aallow is the allowable increment of crack depth (i.e. 0.01a); dc/dn and da/dn are fcgrs at the surface and deepest points, respectively. the increments of half crack length c and the increment of crack depth a after nallow loading cycles were respectively expressed as: allow c n dc dn =   , and allowa n da dn =   (11) class hierarchy diagram this section explains the class hierarchy diagram development process. this process involved identifying appropriate classes and assigning class relationships. this research identified the classes from nouns and noun phrases in the problem description. the following paragraph presents the problem description and the candidate classes are underlined. in-servicing cylindrical vessel has been degraded by uniform corrosion and crack. to perform an assessment, engineers gather information which is a fabrication (e.g., weldment and residual stress), material (e.g., general information, tensile properties, fracture toughness, fatigue crack growth rate), environment, nominal loads, and stresses on the crack plane. for convenience, these identified classes are renamed and listed (in the same order as those appearing in the problem description) as cylinder, uniformcorrosion, crack, assessment, weldment, residualstress, material, generalinfo, tensile, toughness, fcg, environment, nominalload, and stress classes. 2c cin cout cin cout 2[c + max(cin , cout )] update figure 6: crack length updated for through-wall crack growth analysis. the class hierarchy was developed by applying the concepts of association, inheritance (the “is a” relationship), and composition (the “has a” relationship). the concept of inheritance might introduce generalized classes. the class diagram obtained from these considerations is shown in fig. 7. brief explanations of the diagram are given as follows: • the generalinfo, environment, and nominalload classes were changed to be the property (also called attribute) of the material, structure, and cylinder classes, respectively. they are therefore not included in the diagram. • the uniformcorrosion and crack classes are derived from the same base class (the defect class) since both uniform corrosion and crack are specific types of defects. j. kasivitamnuay et alii, frattura ed integrità strutturale, 52 (2020) 163-180; doi: 10.3221/igf-esis.52.14 171 • the cylinder class is derived from a more generalized class (the structure class) since a cylinder is a specific type of structure. this class had a specific method to calculate the stresses due to nominal loads. • the structure class is an aggregation of the weldment and defect classes because weldment and defect might exist in a structure. this class was also composed of the material and stress classes since a structure is made of a specific type of material and is always under stress. • the residualstress class is derived from the stress class because residual stress is a specific type of stress. the stress class had a method to determine linearized stress components. • the weldment class is composed of the material and residualstress classes because weldment is made of a specific type of material and always introduces residual stress in a structure. • the fcg class is derived from the crackgrowth class since fatigue crack growth is a specific type of crack growth mechanism. • the material class is composed of the tensile, toughness, and crackgrowth classes. • the assessment class is associated with the structure class because assessment requires information of structure to perform calculations. by considering the software specifications and its extensibility, modifications were made to the structure, stress, tensile, toughness, crackgrowth, and assessment classes, as shown respectively in figs. 8(a) – 8(f), where the new classes are presented in shaded rectangles. descriptions of these modifications, important properties, and methods of the classes are summarized below: • in fig. 8(a), the crackcylinder class is derived from the cylinder class. the important properties of the crackcylinder class were crack information, sif and reference stress. the crackcylinder class also used the properties of the ancestor classes (i.e. cylinder and structure classes) such as cylinder dimensions and the amount of uniform metal loss. this class is a base class of the ctcl, ctcc, cscle, and cscce classes, where each subclass has specific methods to calculate sif and reference stress. • the class hierarchies in figs. 8(b) to 8(d) are the player-role pattern in oo design. the player classes residualstress, tensile, and toughness are composed of the role classes residualmodel, constitutive, and kicestmodel, respectively. various subclasses of the role class allow behaviors of a role class’s object to vary according to the subclass’s object being created. • in fig. 8(b), the residualmodel class had the coefficients of residual stress profile as a property. the derived class, i.e. resstrcylinder, had a specific method to determine these coefficients of a cylinder from the weld information. • in fig. 8(c), the abstract class constitutive had only a name of the stress-strain relation as a property. the derived class rambergosgood had material parameters of the r-o model as a property and the class had a method to compute a strain from a given stress. the derived class rambergosgoodest added a specific method to estimate the material parameters of the r-o model from specified tensile strengths. structure cylinder defect uniformcorrosion crack weldment material tensile toughness crackgrowth fcg stress assessment residualstress symbol relationship association inheritance aggregation composition figure 7: preliminary class diagram derived from candidate classes. • in fig. 8(d), the toughness class had kmat as a property. each of the derived classes asme, charpy, and mastercurve had a method to estimate a kmat according to asme section xi lower bound curve, charpy impact transition curve or charpy impact energy, and master curve methodologies, respectively. • in fig. 8(e), the abstract class fcg has two subclasses named paris and walker. each subclass had parameters in fcgr model as a property and was able to calculate the fatigue crack growth rate. j. kasivitamnuay et alii, frattura ed integrità strutturale, 52 (2020) 163-180; doi: 10.3221/igf-esis.52.14 172 • in fig. 8(f), the assesscrack class is derived from the abstract class assessment. this class had a method to perform an assessment of a cracked cylinder according to the specified type and level of assessment. the object created by the abstract class level behaves according to the object of the subclass being created, i.e. the level1 or level2 class. the level1 class had a method to determine a permissible crack length from a screening curve. the level2 class had a method to determine an assessment point and the fac. the level3 class inherits the method to determine an assessment point from the level2 class and overrides the method to determine the fac. structure cylinder crackcylinder ctcl ctcc cscle cscce stress residualstress residualmodel resstrcylinder tensile constitutive rambergosgood rambergosgoodest toughness kicestmodel asme charpy mastercurve crackgrowth fcg paris walker assessment assesscrack level level1 level2 level3b (a) (b) (c) (d) (e) (f) figure 8: class refinement in the preliminary class diagram (fig. 7). the additional classes are shown in shaded rectangles: (a) structure class; (b) stress class; (c) tensile class; (d) toughness class; (e) crackgrowth class; and (f) assessment class. all classes shown in figs. 7 and 8 are classified as the application classes. to complete the software design, it is necessary to create the graphical user interface (gui) classes. the gui classes have the purpose of receiving input information and creating and managing the application objects. the designed gui class hierarchy and its communications with the application classes (partially presented) are illustrated in fig. 9. all the gui classes in this figure have a name starting with the letters “frm”. the frmmain class creates the application objects of the structure and material classes. after that, it creates the gui object (or windows) of the frmcrackcylinder class to acquire information about cylinder geometry, welding, crack, and applied loads, and it also creates the gui object of the frmmaterial class to acquire information about materials. the acquired information is then assigned to the corresponding application objects. finally, the frmmain class creates the object of the assessment class to assess the object(s) of the structure class. at this stage, the present class diagram can fulfill the software specifications. however, it may be useful to reexamine the present class diagram for its extensibility. the following paragraph conceptually discusses an extension of the software if it is required to include the other types of a cracked component. fig. 10 shows an extension of the class diagram to incorporate the other cracked component types, e.g. a cracked plate. the plate and resstrplate classes are derived from the structure and residualmodel classes, respectively. the plate class has the plate dimensions (e.g., width and thickness) as properties and has a method to calculate for calculating nominal stress. the crackplate class which is derived from the plate class has the sif and reference stress as properties. additional classes for a specific type of cracked plate can be derived from the crackplate class. each of the inherited classes has a specific method to calculate sif and reference stress. the derived class resstrplate has a specific method to determine the residual j. kasivitamnuay et alii, frattura ed integrità strutturale, 52 (2020) 163-180; doi: 10.3221/igf-esis.52.14 173 stress profile of a plate from the weld information. in summary, the present class diagram has sufficient flexibility for further additional functions and improvements. frmmain frmmaterialfrmstructure frmcylinder frmcrackcylinder structure materialassessment gui classes operation classes figure 9: class diagram of the graphical user interface (gui) classes and their association with the application classes. user interface the implementation of gui design and programming was accomplished by using the integrated development environment (ide) of delphi 10.2.3 community edition from embarcadero technologies. the information for the assessment was organized into three windows: main window (fig. 11); cracked cylinder window (figs. 12 and 13); and material window (fig. 14). note that the displayed information in all of these figures is for the level 3 option b assessment. for the lower assessment level, unnecessary information will be hidden or disabled. instructions for using the software are described as follows. first, the defect type and assessment level in option tab of main window (fig. 11(a)) are specified. if a level 2 or 3 option b assessment is selected, the additional options for assessment will be enabled. for the lbb assessment, the user must input the crack length at the detectable leak rate. the remaining life assessment is enabled for the level 3 option b assessment and the user must specify the crack growth mechanism. structure cylinder crackcylinder ctcl ctcc cscle cscce plate crackplate ... ... ... stress residualstress residualmodel resstrcylinder resstrplate figure 10: extension of the application classes to incorporate a cracked plate assessment. next, it proceeds to the information tab of the main window (fig. 11(b)) where the user is asked for specifying equipment details and material data source. the user then opens the cracked cylinder window (figs. 12 and 13) and material window (fig. 14) to specify detailed information of the cracked cylinder and material properties, respectively. the cracked cylinder window organizes information into dimension, weldment, defect, and operation tabs, as shown in figs. 12(a) to 12(d), respectively. the operation tab covers information about design, service, and maintenance of the cylinder. additional details of the service conditions are illustrated in fig. 13. for the mechanical load tab shown in fig. 13(a), the user can specify the applied nominal loads or coefficients of a stress profile. the thermal stress tab is similar to the j. kasivitamnuay et alii, frattura ed integrità strutturale, 52 (2020) 163-180; doi: 10.3221/igf-esis.52.14 174 mechanical load tab so it is not presented. for the residual stress tab shown in fig. 13(b), the user can enter the coefficients of a residual stress profile or allow the software to select the recommended profile in the standard. the material window has two main tabs to specify properties of base material and weld material (if weldment exists). both tabs contain almost similar information, so only base material tab is presented (fig. 14). the mechanical properties are organized into tabs of tensile, fracture toughness, and crack growth, with details of each tab shown in fig. 14(a) (c), respectively. the user can perform an assessment after completing the information and analysis options. the result of each assessment type or level is separately saved in a text file that can be displayed in the result tab of the main window (fig. 11(c)). (a) (b) (c) figure 11: main window: (a) option tab; (b) information tab; and (c) result tab. (a) (b) figure 12: cracked cylinder window: (a) dimension tab; (b) weldment tab; (c) defect tab; and (d) operation tab. j. kasivitamnuay et alii, frattura ed integrità strutturale, 52 (2020) 163-180; doi: 10.3221/igf-esis.52.14 175 (c) (d) figure 12 (continued): cracked cylinder window: (a) dimension tab; (b) weldment tab; (c) defect tab; and (d) operation tab. (a) (b) figure 13: service load (or stress): (a) mechanical load tab and (b) residual stress tab. j. kasivitamnuay et alii, frattura ed integrità strutturale, 52 (2020) 163-180; doi: 10.3221/igf-esis.52.14 176 (a) (b) (c) figure 14: material window: (a) material information and tensile tab; (b) fracture toughness tab; and (c) crack growth tab. j. kasivitamnuay et alii, frattura ed integrità strutturale, 52 (2020) 163-180; doi: 10.3221/igf-esis.52.14 177 verifications his section presents an application of the software to two example problems. the accuracy of the results were investigated by comparing them with results calculated by mathcad prime 4 software which performed the same calculation steps. tab. 2 lists the options of input information for these examples. descriptions of the examples are given in the following sections. input information selected options example 1 example 2 weldment (fig. 12(b)) heat input data source custom api 579 residual stress (fig. 13(b)) data source api 579 (2016) custom tensile (fig. 14(a)) strength option minimum specified minimum specified material parameters estimate estimate fracture toughness (fig. 14b) option estimate actual estimate model asme section xi reference temperature exemption curve crack growth (fig. 14c) model paris paris table 2: input information options in the software to solve the example problems. example 1 the cylindrical vessel constructed according to the asme b&pv code, section viii division 1 had a longitudinal semielliptical surface crack in the longitudinal seam on the inner wall (i.e. case in fig. 5(c)). uniform corrosion was not detected on either the inner or outer walls. the vessel was made of sa-516 grade 70 steel with a specified minimum yield strength and ultimate strength of 260 mpa and 485 mpa, respectively. the material’s exemption curve was assigned as a b-curve. the weld seam was a double v-groove 10 mm wide, produced by a shield metal arc weld (smaw) process with a linear heat input of 1,500 j/mm and was not subjected to a post-weld heat treatment. the nominal inside diameter and thickness of the vessel were 3,050 mm and 25 mm, respectively. the vessel operated at an internal pressure of 0.7 mpa at 5 oc. an 80 mm long and 5 mm deep crack was detected by ultrasonic and magnetic particle techniques, respectively. the nearest major discontinuity was 800 mm from the crack. the vessel was also subjected to cyclic pressure with a maximum value of 0.7 mpa and a minimum value of 0 mpa. thus, crack propagation by fatigue was possible. the fcgr is given by da/dn = 2.910-8k3, where da/dn is the fatigue crack growth rate (in mm/cycle) and k is the stress intensity factor range (in mpa·m1/2). in the level 1 integrity assessment, the software used information about the crack size, crack orientation, weld orientation, material’s exemption curve, smys, and the service temperature. the permissible crack length in the cylinder was determined to be 8.3 mm, smaller than the 80 mm long crack found during the inspection, so the cylinder was predicted to be unsafe. for the level 2 and 3 option b integrity assessments, the software reported important parameters which are shown in column 2 of tab. 3, and predicted that the cylinder was safe. for the remaining life evaluation, the fatigue crack growth rate was the additional input data. the fcgr model selected was paris’s model. the surface crack was recategorized as a through-wall crack that was 99.841 mm long at cycle number 583,672. the cylinder with this through-wall crack was assessed and the software predicted the component was unsafe. thus, the remaining life reported was 583,672 cycles and a critical crack length and depth were 19.932 and 89.706 mm, respectively, which is the crack size just before recategorization. the remaining life was determined in less than one second of computational time. both the integrity and remaining life assessment results from this software matched those computed by the mathcad worksheet. example 2 the cylindrical vessel constructed according to the asme b&pv code, section viii division 1 had a circumferential semi-elliptical surface crack in the circumferential seam on the outer wall (see the case in fig. 5(f)). uniform corrosion was not detected on either the inner or outer walls. the vessel was made of sa-106 grade b steel with a specified minimum t j. kasivitamnuay et alii, frattura ed integrità strutturale, 52 (2020) 163-180; doi: 10.3221/igf-esis.52.14 178 yield strength of 240 mpa and an ultimate strength of 415 mpa, while the fracture toughness was 100 mpa·m1/2. the weld seam was a single v-groove 10 mm wide produced by a shield metal arc weld (smaw) process and was not subjected to a post-weld heat treatment. the through-thickness residual stress profile is expressed by eqn. (3) with coefficients of 0 = 231.16 mpa, 1 = –613.8 mpa, 2 = –2756.2 mpa, 3 = 8356.2 mpa, and 4 = –5006.3 mpa. the vessel’s nominal inside diameter and thickness were 490 mm and 10 mm, respectively. the vessel was subjected to an internal pressure of 6.5 mpa, a nominal bending moment of 55 kn-m, and a temperature of 20 oc. a 15 mm long, 4 mm deep crack was detected by ultrasonic and magnetic particle techniques, respectively. the nearest major discontinuity was 1,000 mm from the crack. the cyclic load applied to the vessel fluctuated between zero and the maximum operating load. the fcgr is given by da/dn = 3.810-8k3, where da/dn is the fatigue crack growth rate (in mm/cycle), and k is the stress intensity factor range (in mpa·m1/2). a level 1 assessment was not applicable in this case since the supplemental load (i.e. bending moment) exists. for the level 2 and 3 option b assessment, the important parameters calculated by the software are shown in column 3 of tab. 3. the cylinder was predicted to be safe. for the remaining life analysis, the results from the software and from the mathcad worksheet are summarized in tab. 4. the remaining life predicted by the software was 58,246 cycles, which were the summation of a surface crack growth period of 43,848 cycles, and a through-wall crack growth period of 14,398 cycles. the surface crack was recategorized as a through-wall crack with a length and depth of 23.285 mm and 7.949 mm, respectively. the critical crack length was 71.672 mm. by comparing these results with those obtained by mathcad as listed in column 4 of tab. 4, it can be concluded that the present ffs software was accurate. parameters results by present software example 1 example 2 fracture toughness, kmat (mpa·m1/2) 63.90 100 sif (mpa·m1/2) primary load, ki,p surface point 2.22 9.87 deepest point 6.37 11.40 secondary stress, ki,sr surface point 17.37 16.20 deepest point 20.45 3.97 reference stress based on primary stress, ref,p (mpa) 43.94 103.90 toughness ratio, kr surface point 0.33 0.28 deepest point 0.44 0.16 load ratio based on primary stress, lr,p 0.17 0.43 maximum permitted value of load ratio, lr,p(max) 1.43 1.36 maximum permitted value of toughness ratio, krc level 2 0.996 0.971 level 3 option b 0.993 0.947 integrity status level 2 safe safe level 3 option b safe safe table 3: integrity assessment results of the example problems. result analysis tools present software mathcad remaining life (cycles) surface crack growth period 43,848 43,841 through-wall crack growth period 14,398 14,402 total 58,246 58,243 crack size just before recategorization (mm) length 23.285 23.266 depth 7.949 7.944 crack length just after recategorized (mm) 27.388 27.378 critical crack length (mm) 71.672 71.644 table 4: remaining life analysis results of the cscce cracked cylinder in example 2. j. kasivitamnuay et alii, frattura ed integrità strutturale, 52 (2020) 163-180; doi: 10.3221/igf-esis.52.14 179 conclusions he object-oriented software for fitness-for-service assessment of a cracked cylinder based on the current edition of the api 579 standard has been developed. the software development process was described and a unique class diagram was developed. extension of the class diagram to include another type of cracked component (e.g. a cracked plate) was conceptually demonstrated. programming issues were discussed, for example the preparation of information in the standard for coding, handling of a changing of a local coordinate in sif calculation, crack size updating in fatigue crack growth analysis, and incorporating the effect of residual stress on the fatigue crack growth rate. the software’s source code was written in the delphi programming language. the software is able to perform brittle fracture assessment at levels 1, 2 and 3 option b, leak-before-break assessment, and remaining life assessment of a cracked cylinder subjected to axial force, bending moment, and internal pressure, in addition to stress profiles perpendicular to the crack plane due to mechanical, thermal and residual stresses. the cracked cylinders included in the software had either a through-thickness crack or a semi-elliptical surface crack oriented in axial or circumferential directions. the software incorporated a material database and methods to estimate the fracture toughness and material parameters in the r-o model when the user does not have this data. the software was found to accurately and rapidly perform the assessments. acknowledgments unding for this research was provided by chulalongkorn university research, grant no. cu-gfi_60_01_21_01. references [1] hasegawa, k. (2007). summary and comparison of fitness-for-service rules for structural component in the world, weld. world, 51(5-6), pp. 76-84. [2] filiou, c., taylor, n., lejuste, p. and houghton, r. (2003). survey of current application and future requirements for european fitness-for-service technology. available at: http://www.eurofitnet.org/report_tr2-03.pdf. [3] kobayashi, h., sakai, s., asano, m., miyazaki, k., nagasaki, t. and takahashi, y. (2000). development of a flaw evaluation handbook of the high pressure institute of japan, int. j. press. ves. pip., 77(14-15), pp. 929-936. [4] jovanovic, a., maile, k., wagemann, g., le mat-hamata, n., gampe, u., andersson, p., segle, p. and gelineau, o. (2001). assessment of cracks in power plant components by means of the hida knowledge-based system (kbs), int. j. press. ves. pip., 78(11-12), pp. 1053-1069. [5] kim, y.j., choi, j.b., lee, j.s., jun, h.k. and park, y.w. (2003). development of an integrity evaluation system for nuclear power plants, jsme int. j. ser. c, 46(4), pp. 1464-1472. [6] gubeljak, n., koçak, m., huther, m. and valh, t. (2008). fitnet fitness-for-service fracture module software, fme transaction, 36(1), pp. 39-44. [7] machida, h., arakawa, m., yamashita, n. and yoshimura, s. (2009). development of probabilistic mechanics analysis code for pipes with stress corrosion cracks, journal of power and energy systems, 3(1), pp. 103-113. [8] murthy, a.r.c., palani, g.s. and iyer, n.r. (2011). object-oriented programming paradigm for damage tolerant evaluation of engineering structural components, adv. eng. softw., 42(1-2), pp. 12-24. [9] zhou, x.j., duan, q.q., zhang, h., zhao, l. and wu, x.y. (2015). crack-like flaws pressure vessel fitness-for-service assessment and software programming based on api rp 579, procedia engineering, 130, pp. 1359-1370. [10] bass, b.r., williams, p.t., dickson, t.l. and klasky, h.b. (2017). favor version 16.1 – a computer code for fracture mechanics analyses of nuclear reactor pressure vessels. proc asme 2017 pressure vessels and piping conference pvp, waikoloa, hawaii, us., 16-20 july. [11] integriwisetm api 579 fitness-for-service software. available at: http://www.twisoftware.com/software/integritymanagement-software/integriwise/integriwise_eflyer_2-10.pdf. [12] signaltm fitness-for-service software. available at: https://www.questintegrity.com/assets/pdfs/flyers-newbrand/signal-fitness-for-service-flyer-ltr-rev.07-16-web.pdf. [13] iwm verb. available at: https://www.iwm-verb.de/en/scope.html. t f j. kasivitamnuay et alii, frattura ed integrità strutturale, 52 (2020) 163-180; doi: 10.3221/igf-esis.52.14 180 [14] vindio. available at: http://inescoingenieros.com/en/services/software-solutions/. [15] api 579/asme ffs-1. (2016). recommended practice for fitness-for-service, washington, api. [16] larrosa, n.o. and ainsworth, r.a. (2016). comparisons of the solutions of common ffs standard procedures to benchmark problems, int. j. press. ves. pip., 139-140, pp. 36-46. [17] dathan, b. and ramnath, s. (2011). object-oriented analysis and design, springer. microsoft word numero_30_art_49 g. zucca et alii, frattura ed integrità strutturale, 30 (2014) 409-416; doi: 10.3221/igf-esis.30.49 409 focussed on: fracture and structural integrity related issues failure of cargo aileron’s actuator g. zucca, m. amura, l. allegrucci, m. bernabei italian air force, flight test centre, chemistry department, military airport m. de bernardi, via pratica di mare, pomezia (rm), 00040, italy guido.zucca@aeronautica.difesa.it, mikael.amura@aeronautica.difesa.it, laura.allegrucci@aeronautica.difesa.it, manuele.bernabei@aeronautica.difesa.it abstract. during a ferry flight, in a standard operation condition and at cruising level, a military cargo experienced a double hydraulic system failure due to a structural damage of the dual booster actuator. the booster actuator is the main component in mechanism of aileron’s deflection. the crew was able to arrange an emergency landing thanks to the spare oil onboard: load specialists refilled the hydraulic reservoirs. due to safety concerns and in order to prevent the possibility of other similar incidents, a technical investigation took place. the study aimed to carry out the analysis of root causes of the actuator failure. the booster actuator is composed mainly by the piston rod and its aluminum external case (aa7049). the assembly has two bronze caps on both ends. these are fixed in position by means of two retainers. at one end of the actuator case is placed a trunnion: a cylindrical protrusion used as a pivoting point on the aircraft. the fracture was located at one end of the case, on the trunnion side, in correspondence to the cap and over the retainer. one of the two fracture surfaces was found separated to the case and with the cap entangled inside. the fracture surfaces of the external case indicated fatigue crack growth followed by ductile separation. the failure analysis was performed by means of optical, metallographic, digital and electronic microscopy. the collected evidences showed a multiple initiation fracture mechanism. moreover, 3d scanner reconstruction and numerical simulation demonstrated that dimensional non conformances and thermal loads caused an abnormal stress concentration. stress concentration was located along the case assy outer surface where the fatigue crack originated. the progressive rupture mechanism grew under cyclical axial load due to the normal operations. recommendations were issued in order to improve dimensional controls and assembly procedures during production and overhaul activities. keywords. ailerons actuator; aa7049; multiple initiation sites fatigue; thermal load; dimensional non conformances. introduction military cargo airplane during a ferry flight in standard operation conditions, experienced a double failure of both the hydraulic systems on board. as a consequence, the pressure of the servo-actuators relevant to the flight controls suddenly dropped. although the cloche became stiff, the well trained crew managed to land safely by using the spare hydraulic fluid on board to refill the reservoirs. the subsequent inspection highlighted a rupture on the dual booster actuator (dba). a g. zucca et alii, frattura ed integrità strutturale, 30 (2014) 409-416; doi: 10.3221/igf-esis.30.49 410 this component function is the ailerons deflection. being a primary importance actuator for the aircraft controllability, it is connected to both the hydraulic systems for safety reasons. the main parts of the dba are the piston rod and the external case. two bronze caps are placed at both ends, and they are fixed in position by means of two retainers. the dba is hinged to the aircraft by a cylindrical support fixed at one end of the actuator case, named trunnion. the fracture surface was located at the actuator case end on the trunnion side, over the retainer (fig. 1). this paper illustrates the failure analysis of the aforementioned actuator. figure 1: rupture position. instruments ptical examination was carried out using a leica m 205 c microscope. microfractographical evidences were acquired by a gemini ultra plus field emission scanning electron microscope (fesem) equipped with an incax-sight oxford instruments xray energy dispersive spectroscopy (eds) to perform a semi-quantitative microanalysis exam. microstructural examination was made using a leica ctr 6000 metallographic microscope, whereas a panalytical axios max to perform x-ray fluorescence spectroscopy was used to determine the chemical composition of the forging. hardness measurements were carried out with a200 hardness rockwell tester officine galileo and leica vmht auto. metrologic measurements were performed using konica minolta range 7 3d scanner. fea was carried out by ansys 14.0 software program. results visual and optical observation. he cap was found entangled inside the detached fracture surface and some force was needed to remove it (fig. 2). however, no damages were produced in this operation. the two fracture surfaces showed the same features. the fracture started from the external surface, and propagated toward the internal one. the fracture surface was divided in two zones, named a and b (fig. 3). zone a was rough, dull, characterized by coarse grains and it was oriented at about 45° to the transversal section. moreover, a plastic deformation, associated to the final phase of the failure, was o t g. zucca et alii, frattura ed integrità strutturale, 30 (2014) 409-416; doi: 10.3221/igf-esis.30.49 411 observed. therefore, zone a was the region of the final, unstable fracture. zone b was characterized by a fracture surface flat, smooth and bright with beach marks typical of fatigue crack growth. (fig. 4). on the external surface’s edge there were ratchet marks, showed by black arrows in fig. 4. however, also in the 45° orientation areas, there was a small flat area running all around on the external side (black arrow in fig. 5) showing ratchet marks. zone a zone b figure 2: cap entangled inside the fracture surface. figure 3: fracture surface. figure 4: beach marks and ratchet marks on the surface’s edge. figure 5: fracture detail. electronic microscopy fesem observations of the zone b of fracture surface confirmed the presence of the fatigue crack mechanism fig. 6 and fig. 7. multiple initiation sites of the fatigue crack are all around the external edge of the fracture surface. zone a showed dimples and microvoid, these are evidences of unstable fatigue crack propagation (fig. 8) [1]. g. zucca et alii, frattura ed integrità strutturale, 30 (2014) 409-416; doi: 10.3221/igf-esis.30.49 412 figure 6: area of fatigue crack propagation. figure 7: area of fatigue crack propagation. figure 8: dimples and microvoid. figure 9: striation spacing. in zone b in the stable propagation phase of the fatigue phenomenon the striations spacing was about 60 nm (fig. 9) [2] [3]. 3d reconstruction and metrologic measurement. actuator case and cap geometry were acquired using a 3d scanner fig. 10 e fig. 11, the diameters were measured in 8 points as showed in fig. 12 e fig. 13. figure 10: actuator case, digital geometry. figure 11: cap, digital geometry. g. zucca et alii, frattura ed integrità strutturale, 30 (2014) 409-416; doi: 10.3221/igf-esis.30.49 413 figure 12: actuator case internal diameter measurements. figure 13: cap external diameter measurements. results are showed in tab. 1. the two parts have an average mechanical interference of 25 µm. this was the reason of the tight fit observed during disassembly operations between external case and cap. mean diameter [mm] mean coupling [mm] cap 50.8843±0.1498 -0.025 actuator case 50.8587±0.0565 table 1: results of measurement. design drawing values are: diameter of actuator case 2.000 – 2.002 inches (50.8000 50.8508 mm) diameter of cap 1.998 – 1.999 inches (50.7492 50.7746 mm) table 2: drawing requirements. therefore, the required gap should be comprised between 25.4 to 101.6 µm. microstructural analysis. a microstructural examination, were performed on two sections of actuator case made orthogonally and parallel to its axis. the examination, revealed the joint zone between the two halves of the actuator case, showing two different microstructures [4]. transition is showed in fig. 14. hardness test will evaluate mechanical consequences of this anomaly. another section, near the oil chamfer was analyzed, in order to evaluate the shot peening treatment required by design. chemical analisys and conductivity test. x-ray fluorescence (xrf) showed that the actuator case samples were in accordance with the specification for a 7049 [5] [6] aluminum alloy. alloy homogeneity was confirmed by eds mapping on the outer edge of the actuator case. g. zucca et alii, frattura ed integrità strutturale, 30 (2014) 409-416; doi: 10.3221/igf-esis.30.49 414 figure 14: transition between two halves of the actuator case. hardness test hardness test (tab. 3) was performed on the actuator internal and external surface in accordance to hrb. moreover, mhv method was used across the thickness in order to evaluate the shot peening effect. location hardness mean std. dev. internal surface (hrb) 86.3 0.9 external surface (hrb) 82 1.6 on the section (from outside to inside) (mhv) 175.7 3.5 table 3: hardness results. the results confirm a t73 heat treatment [5] [6], while the values taken across the thickness highlight an increase in hardness where the shot peening should have been applied, confirming the correct procedure was applied during production. finite element analysis a fea model was performed in order to evaluate the effect of forced coupling between the actuator case and the cap. the geometric 3d model of dba was reproduced by the design drawings fig. 15. 4768 hexahedrons [7] elements were applied to provide the mesh for mathematical model fig. 15. being impossible to reproduce exactly the geometry of the interference, it was assumed as a conservative hypothesis the perfect fit between the two parts: no gap and no interference. the hydraulic system oil works oil within a range of 60°c 90°c, while the pressurized cabin compartment where the dba is placed is at about 20° c. this implies a thermal variation of δt= 40 – 70 ° c that becomes a thermal load to the structure due to the different thermal expansion coefficient of the case assy and the cap. indeed, the cap is made of copper alloy ams 4631, while the case assy is aa7049. therefore an average δt= 55° c was applied. pressure and inertial loads were not simulated because no findings during the failure analysis suggested they could have been abnormal. g. zucca et alii, frattura ed integrità strutturale, 30 (2014) 409-416; doi: 10.3221/igf-esis.30.49 415 figure 15: cad geometry (left), mathematical model (right). numerical results showed how just the perfect fit was enough to increase the stress value of about 60 mpa. in the real condition of forced coupling (about 25 µm interference) the stress increase would be higher. stress map fig. 16 shows how the maximum stress is reached on the outer edge of the case assy. a parametrical simulation was carried out increasing the gap between the actuator case and the cap. results showed that the stress became null at about 50 µm of gap (fig. 17). figure 16: stress map. g. zucca et alii, frattura ed integrità strutturale, 30 (2014) 409-416; doi: 10.3221/igf-esis.30.49 416 figure 17: transition between two halves of the actuator case. discussion he examination of fracture surface showed a multisite fatigue phenomenon started from the external edge of actuator case. chemical analysis and hardness measurement indicated that no unusual features were found in the material and his heat treatment. metrological checks showed interference between the cap and the actuator case. the gap between the actuator and the cap has to be between 25.4 and 101.6 µm as design requirements. tolerance between cap and actuator case is established taking in account thermal expansion. fem analysis showed that less than 50 µm of gap between the two parts would induce abnormal stresses on the outer edge of the case assy due to the normal thermal conditions. these, in addition to the other normal operative loads, such as the actuation pressure, started the multiple initiation site fatigue the evaluation of striations spacing features an high-cycle fatigue, compatible with vibration during flight [8] [3]. conclusions he dual booster actuator failed because of a high-cycle multiple initiation sites fatigue mechanism. this was due to stress intensification caused by dimensional non conformances. recommendations were issued in order to improve dimensional controls. references [1] oddone, g., guida alle interpretazioni delle caratteristiche morfologiche delle superfici di frattura al microscopio elettronico a scansione, ragno editore, (1981). [2] amura, m., allegrucci, l., de paolis, f., bernabei, m., fatigue fracture of an amx aircraft main weel, engineering failure analysis, 27 (2012)194-202. [3] cameron, d., fatigue properties in engineering. fatigue and fracture., asm handbook, (1996). [4] handbook, metallography and microstructure, george f. vander voort, 9 (2004). [5] handbook, properties and selection nonferrous alloys and special-purpose materials, (1990). [6] matweb, www.matweb.com (2014). [7] taylor, r., zienkiewicz, o.c., the finite element method, 5th ed., 2 (2000). [8] gugliotta, a., introduzione alla meccanica della frattura lineare elastica., levrotto & bella, (2002). t t microsoft word 2176 v. alecci et alii, frattura ed integrità strutturale, 47 (2019) 161-167; doi: 10.3221/igf-esis.47.13 161 design of civil environmental engineering building irregularity issues and architectural design in seismic areas valerio alecci, mario de stefano university of florence, italy valerio.alecci@unifi.it, http://orcid.org/0000-0002-8143-7102 mario.destefano@unifi.it, http://orcid.org/0000-0001-6077-3732 abstract. when designing buildings in seismic areas, choices of the architectural designer heavily influences seismic structural performances. namely, building morphology may lead to complex seismic responses as it occurs when building plan and elevation become irregular. typical irregularities are due to architectural, functional and distribution constraints, thus leading to plan or vertical or combined plan/vertical irregularities. a frequent plan-wise irregularity arises when earthquake resistant structures, such as cores and shear walls, are concentrated on one side of the building plan, while vertical irregularity often arises from the presence of soft stories especially located at the ground level or, less frequently, at an intermediate level. in the last decades, some trends in architectural design, such as deconstructivism and other contemporary theories, worked in pursuing architectural solutions based on the concept of “deconstruction” in place of “construction”, favoring non-rigid schemes, non-regular shapes and, more generally, avoiding geometric rules and classical canons of symmetry and regularity. in this paper the above issues are investigated with the goal of assessing effects of irregularity conditions, introduced by the architectural design, on the building seismic performances with the aim at not forbidding the designer ambitions but at making him aware of the effects of his architectural choices. keywords. architectural design; seismic areas; building irregularity. citation: alecci, v., de stefano, m., building irregularity issues and architectural design in seismic areas, frattura ed integrità strutturale, 47 (2019) 161-168. received: 22.08.2018 accepted: 20.11.2018 published: 01.01.2019 copyright: © 2019 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. introduction eismic events of recent decades showed the high vulnerability of irregular buildings. perfect regularity is an idealization that rarely occurs in new as well as in existing buildings; in turn, the concept of irregularity itself is a “fuzzy” one. structural irregularities may vary dramatically in their nature and, in principle, are very difficult to define. definition by codes refers to the distribution of mass, strength and stiffness, both in plan and in elevation. s http://www.gruppofrattura.it/va/47/2176.mp4 v. alecci et alii, frattura ed integrità strutturale, 47 (2019) 161-167; doi: 10.3221/igf-esis.47.13 162 plan irregularity is characterized by uneven plan distribution of earthquake-resistant structures or masses; vertical irregularity is due to mass, stiffness or strength discontinuities along the building height. plan and vertical irregularities result in seismic over-demand into specific structures/elements which can lead to their early collapse, while not allowing the entire building structure to exploit its full seismic capacity. in fact, irregularity is one of the most frequent sources of severe damage during earthquake [1]. in 1985, during the earthquake of mexico city, 42% of damaged or collapsed structures were corner buildings. furthermore, many buildings failed in torsion due to asymmetric layout of masonry walls [2]. in the last decades, several studies on the design eccentricity were carried out [3-13]. building irregularity unknown concept in the classical and post-classical architecture became a particularly widespread condition in postmodern and rational architecture. in fact, the famous "five points" of le corbusier’s architecture generated, for many decades, highly irregular buildings, characterized by free facades, soft stories with slim columns (pilotis), alternating to fully closed or/and opened floor plans, long strips of ribbon windows (and consequent short columns), etc. otherwise, in the more remote past, wonderful "regular" buildings were built, based on obvious structural and constructive assumptions. in that period, architect and engineer coexisted and their contribution to the final project was perfectly integrated. in fact, in the past, a unique technician, combining creativity and structural knowledge, designed buildings with structural rigor but also expressing his own stylistic will. this condition, which allow architectural and structural issues to be perfectly integrated, played a crucial role for optimizing the final project. this kind of architecture/structure integration, desirable for the success of the project, is strictly necessary when designing in seismic zone, where the lack of architecture/structure integration can involve heavy losses in terms of human lives. in the last decades, the apparent rigor (more from an architectural than structural point of view, as we highlighted above) of postmodernist movements involved a sort of compositional anarchy that rob krier defined “the confusion in today’s art of building” and whose deconstructivist architecture is the maximum expression. deconstructivism worked in pursuing architectural solutions based on the concept of “deconstruction” in place of “construction”, favoring non-rigid schemes, non-regular shapes and, more generally, avoiding geometric rules and classical canons of symmetry and regularity. the result of this philosophy is the growing proliferation of aesthetically spectacular buildings, with audacious shapes and impressive dimensions, supported by a clear propensity of contractors and funders to design and realize buildings outside the traditional and classical rules, gaining a “status symbol function” and getting a positive impact on their brand image. in this contest, it is not possible (and really desirable) to prevent the design of irregular buildings while it has to be pursued that designers know the consequences of their architectural design on a seismic and, more generally, structural field. the architectural designer would achieve a "seismic" training, with the aim at not forbidding his ambitions but at making him aware of the effects of his architectural choices. figure 1: causes of structural irregularity. structural irregularity he seismic vulnerabilities of a building depend on the morphological and structural condition and on the constructive details. the morphological irregularity is prodromal of structural irregularity and it is due to three main factors: economical, functional and aesthetical-formal (fig. 1). an economical factor exists because, especially in densely populated urban areas, contractors try to fully exploit the available space in order to obtain the t v. alecci et alii, frattura ed integrità strutturale, 47 (2019) 161-167; doi: 10.3221/igf-esis.47.13 163 maximum economical return; a functional factor exists because the buildings are often organized to have parts with a particular orientation also for better enlighten the different spaces; finally, the aesthetical-formal factor depends on the new architectural trends (as better described in the next paragraph). plan irregularity is characterized by uneven plan distribution of earthquake resistant vertical structures and/or of masses; it results in a dangerous torsional behavior consisting of large floor rotations. a close relationship between mass and stiffness plan distribution reduces eccentricity between mass center cm and rigidity center cr, thus resulting in a regular, mainly translational behavior of the building (fig. 2). figure 2: plan irregularity (on the left) and regularity (on the right). plan irregularity is due to a non-symmetrical plan, resulting from a particular functional distribution of the spaces which leads to concentrate stiffness and/or strength on one side of the building plan (stiff side) compared to the other side (flexible side). it may also be due to mass concentration on one side of the building, which becomes the flexible side. in case of seismic actions, building response is characterized by floor rotations (torsional behavior) with increase ductility demands on structural elements often leading to very severe damage or collapse. vertical irregularity is due to sudden variations in mass, stiffness (and strength) along the building height, which result in formation of soft/weak storeys where an earlier collapse can develop due to concentration in member forces and ductility demands (fig. 3). it can be very common, in contemporary buildings, that layouts of different levels develop as distinct entities in which even structural elements can change in size, consistency, position. this can occur because of changes in the use of a single level or due to the will of the designer to formally differentiate the façade (facades with large openings alternate to fully “closed” portions). both plan and vertical irregularities (figg. 4-5) do not allow uniform damage distribution and, therefore, strength and ductility resources of the entire structure cannot be fully exploited. building codes, such as eurocodes and the italian ntc, penalize design of buildings classified as irregular by prescribing larger design forces. figure 3: vertically irregular (above) and regular (below) configurations. v. alecci et alii, frattura ed integrità strutturale, 47 (2019) 161-167; doi: 10.3221/igf-esis.47.13 164 figure 4: plan irregularity (kokaeli, turkey, 1999). figure 5: vertical irregularity (sichuan, china, 2008). decontructivist trends in contemporary architecture he term "deconstructivist architecture" appears for the first time in 1988, at the exhibition organized by philip johnson and mark wigley at the museum of modern art (moma) in new york. deconstructivism immediately appeared as opposite to the rationality of postmodernism, functionalism, structuralism and also eclecticism (in fact, eclectism is the combination of different materials and styles, but maintaining an architectural scheme still strongly dependent on structural requirements). deconstructivist architecture represents the overcoming of highly celebrated theories based on expressions like “form follows function”, “purity of form”, “truth to material”, etc. and of the philosophy of architects like le corbusier, wright, mies van der rohe, michelucci. deconstructivism is characterized by an absence of harmony, continuity, or symmetry. deconstructivist architectures have an unstable geometry, sudden cuts in architectural and structural continuity, deformed volumes, asymmetry, unrecognizability of structural elements. theoretical base of deconstructivist architecture is the philosophy of the french philosopher jacques derrida and, in particular, his concept of “différance”. extending the heidegger's theory of the difficulty of being, derrida recognizes the indefinability of the identity of being as it preserves an intrinsic “différance”. derrida had a significant influence upon the humanities and social sciences, including literature, law, anthropology, historiography, applied linguistics, psychoanalysis, political theory, ethics, aesthetics, hermeneutics, architecture (in the form of deconstructivism), music. derrida’s philosophy influenced the deconstructivism’s fathers who exhibited their projects at the moma in 1988: daniel libeskind, zaha hadid, frank o. gehry, rem koolhaas, peter eisenman, bernard tschumi. they designed always rejecting the principles of vitruvian geometry and harmony which perroult transformed into firmitas, utilitas venustas triad. in the first book of vitruvius’ treatise “de architectura”, is reported: “all buildings must have solidity, utility and beauty. they will have solidity when the foundations, constructed with materials chosen with care and without greed, will rest deeply and firmly on the ground; utility when the distribution of the interior space of each building will be correct and of practical use; beauty, when the aspect of the work will be pleasant for the harmonious proportion of the parts obtained with the accurately calculated symmetry”. conversely, in the book “line of fire” of daniel libeskind [14] is reported: "(the vitruvian principles) were extended beyond the roman world, beyond the west, to the islamic and indian architecture and, through the european renaissance, they come to modernity and to the contemporary and globalized world. with their deference to the right angle and the correct way to build, with their care for the geometric order, the symmetry and the rigid proportions, the ten books became a sort of emblem of what was codified and institutionalized with the name of architecture”. libeskind reflects on "the liberation of architecture from vitruvio's diktat", proposing a new architecture not depending on geometric rules but on music, astronomy, graphology, theater and art. this philosophy is the crucial base of his projects and buildings: the berlin jewish museum (fig. 6) inspired by the music of arnold schönberg, the new ground zero and the warsaw tower drawn up following the sun's motion trajectory, the las vegas city center (fig. 7) inspired t v. alecci et alii, frattura ed integrità strutturale, 47 (2019) 161-167; doi: 10.3221/igf-esis.47.13 165 by xenomorphic crystals, the jewish museum of san francisco drawn following the jewish letters, the piazza italia for the expo of milan inspired by the paintings by giuseppe arcimboldo. figure 6: berlin jewish museum figure 7: las vegas city center “the classicist architect” is reported in the monograph on zaha hadid directed by bruno zevi [15] – “does not put any of his own inspiration when designing, he only applies pre-established codes. conversely, the “différance” and the deconstruction, are “iconoclasts”: no rigid codes can regulate it. “deconstruction” doesn’t generate anonymous buildings, where the designer replicates geometric and structural code requirements and historicized typological schemes. it generates indefinite, confused, transformable spaces”. the historian davide de sessa defines the hadid’s buildings as "medieval agglomerations made of additions, [...] contrasts between the different levels, anti-geometries” (fig. 8). zaha hadid, like other contemporary architects, “has no truck with typologies, applied orders, implied assumptions of gravity [….], she aims at being liberated from the past and from the constraints of physical laws” [16]. then, vitruvian triad is transformed into a sort of “deconstructivist triad”, based on the immateriality of the walls, on the anti-gravitational and anti-cartesian will, on the manipulation of structures. the complex joints in peter eisenman's projects, the confusion of the signs in bernard tschumi’s architecture, the cubist philosophy of frank o. gehry, fully embody these concepts. figure 8: antwerp port authority. in all of their projects, the manipulation of the building structure is evident. the structural mesh is not detectable, it appears like a part no longer necessary for supporting the construction, a simple figurative game useful to make spaces more enjoyable. “gehry's architecture is a challenge to common sense”, is reported in a monograph of mildred friedman [17] dedicated to the gehry’s projects. gehry’s buildings would be defined like “architectural sculptures” than simply like “buildings”: guggenheim museum of bilbao (fig. 9) or the nationale-nederlanden building of prague (fig. 10), are today considered great "sculptures" more than architectural buildings. v. alecci et alii, frattura ed integrità strutturale, 47 (2019) 161-167; doi: 10.3221/igf-esis.47.13 166 figure 9: guggenheim museum, bilbao figure 10: nationale-nederlanden building, prague nowadays, structural architects are increasingly becoming architects/artists who reject the written rules and the structural grids, giving space to creativity, dreams, free inspiration. this cultural trend inevitably influences the new master architects, the young generation of architects, the architectural schools and associations which enhance the expressiveness of architectural and structural designers but, at the same time, represents a sort of challenge that architectural designers can overcome if equipped with a solid structural and seismic background. they must know irregularity conditions, their relations with seismic loads and how to mitigate their effects. they must have a threedimensional view of the structural and seismic issues (and not just plane) evaluating the opportunity to apply the simplifications that several calculation methods assume (rigid diaphragm, uniform seismic action, etc.), also performing an additional evaluation in the design stage of some effects which usually are secondary in ordinary buildings, such as torsional moments on individual structural elements, p-delta effects, etc. analysis methods of irregular structures eismic behavior of irregular structures is usually investigated by single-storey models. although single-storey models represent the most extreme idealization of plan irregular buildings, they still attract many researchers, as they remain adequate to obtain general information on torsional behavior of asymmetric buildings, particularly from a qualitative point of view. they have been widely used in the past also due to their capability of clarifying the influence of the governing parameters and derive effective design criteria. however, in recent years multi-storey building models have been used to study more realistically inelastic earthquake response of asymmetric buildings due, firstly, to the shortcomings of one-storey models in predicting torsional behavior of real structures and, secondly, for the development of powerful computational tools able to make extensive and refined numerical analyses of 3d multi-storey building structures. an accurate prediction of seismic behavior of irregular structures cannot be done by applying a standard non-linear static procedure (nsp) because, in virtue of an uneven plan displacement demand, one target displacement is not sufficient and an evaluation of the amplification of displacement demand due to torsional effect is necessary. furthermore, no allowances are considered for dynamic effects of lateral-torsional coupling and large uncertainties remain when results obtained from independent pushover analysis in the two horizontal directions are combined. nowadays, the main approach available in literature to adapt standard nsps for plan-irregular structures is represented by different displacement amplification methods. one such method, proposed by fajfar et al. [18], considers to properly including torsional effects combining the results obtained by pushover analysis of a 3d structural model, based on the n2 method, with the results from a linear dynamic (spectral) analysis. the n2 method controls the target displacements and distribution of deformations along the height of the building, whereas the linear dynamic analysis is used to define the s v. alecci et alii, frattura ed integrità strutturale, 47 (2019) 161-167; doi: 10.3221/igf-esis.47.13 167 torsional amplifications of lateral displacements. the elastic amplifications of lateral displacements obtained by modal analysis are conservative with respect to the inelastic ones. tests on case study buildings gave promising results [19-20]. the assumption of the conservativeness of the elastic envelope appears to be valid for torsionally flexible and moderately torsionally stiff (framed) building structures. on the contrary, it does not hold true for very torsionally stiff structures, such as shear-walled buildings [21]. another method, proposed by ghersi et al., [22], is based on modal analysis involving the definition of corrective eccentricities used to determine the application points of the load vectors, on either sides of the cm so as to obtain an envelope of plan distribution of maximum displacements. corrective eccentricities have been calibrated from response of a one-storey building while their application to multistory buildings requires complex parameters definition. final considerations rchitectural design in seismic areas is the first and fundamental step to guarantee good seismic performance. architectural designer must be aware that his choices of building morphology, plan and vertical layout of resisting structures, member tentative dimensions, have a profound impact on the behavior under seismic actions. this paper has focused on the effects of irregularity conditions resulting from architectural design. it is demonstrated that irregularities, arising from economical, functional and aesthetical/formal requirements, cannot be prohibited; however, architectural designer must know irregularity conditions, their outcome on seismic response and how to mitigate their effects. acknowledgements he financial support of reluis through the progetto esecutivo convenzione dpc/reluis 2017 – pr2 strutture in cemento armato – is gratefully acknowledged. references [1] de stefano, m. and pintucchi, b. (2008). a review of research on seismic behavior of irregular building structures since 2002, bulletin of earthquake engineering, 6(2), pp. 285-308. [2] rosenlueth, e. and meli, r. (1986). the 1985 earthquake: causes and effects in mexico city, concrete international, 8(5), pp. 23–34. [3] tso, w. k. (1990). static eccentricity concept for torsional moment estimations, journal of structural engineering, 116(5) pp. 1199–1212. [4] chopra, a. k. and goel, r. k. (1991). evaluation of torsional provisions in seismic codes, journal of structural engineering, 117(12), pp. 3762–3782. [5] de stefano, m. faella, g. and ramasco, r. (1993). inelastic response and design criteria of plan-wise asymmetric systems, earthquake engineering and structural dynamics, 22(3), pp. 245-259. [6] chandler, a. correnza, j. c. and huchinson, g. l. (1995). influence of accidental eccentricity on inelastic seismic torsional effects in buildings, engineering structures, 17(3), pp. 167-178. [7] de stefano, m. and rutenberg, a. (1997). a comparison of the present seaoc/ubc torsional provisions with the old ones, engineering structures, 19(8), pp. 655-664. [8] foraboschi, p. (2016). the central role played by structural design in enabling the construction of buildings that advanced and revolutionized architecture. construction and building materials, 114, pp. 956-976. [9] foraboschi, p. (2016). versatility of steel in correcting construction deficiencies and in seismic retrofitting of rc buildings. journal of building engineering, 8, pp. 107-122. [10] foraboschi, p. 2016. structural layout that takes full advantage of the capabilities and opportunities afforded by twoway rc floors, coupled with the selection of the best technique, to avoid serviceability failures. engineering failure analysis, 70, pp. 387-418. [11] sassu, m. puppio, m. l. mannari, e. (2017). seismic reinforcement of a r.c. school structure with strength irregularities throughout external bracing walls, buildings, 7(58). doi:10.3390/buildings7030058. mdpi. a t v. alecci et alii, frattura ed integrità strutturale, 47 (2019) 161-167; doi: 10.3221/igf-esis.47.13 168 [12] puppio, m. l. pellegrino, m. giresini, l. sassu, m. (2017). effect of material variability and mechanical eccentricity on the seismic vulnerability assessment of reinforced concrete buildings, buildings, 7(66). doi:10.3390/buildings7030066. mdpi. [13] bonannini e., cinotti, m. puppio, m. l. sassu, m. (2017). seismic response of a stock of social housings in italy with r.c. and masonry materials, advances in engineering research (aer), second international conference on mechanics, materials and structural engineering (icmmse 2017). atlantis press (102 – 285). [14] libeskind, d. (2014). la linea del fuoco – scritti, disegni, machine, macerata, quodlibet s.r.l. [15] zevi, b. and de sessa, d. (1996). zaha hadid – eleganze dissonanti (1st ed.), torino, testo e immagine s.r.l. [16] betsky, a. (1998). zaha hadid the complete buildings and projects, london, thames and hudson. [17] friedman, m. (2000). frank o. gehry – architettura + sviluppo, new york, rizzoli international publication inc. [18] fajfar, p. marusic, d. and perus, i. (2005). the extension of the n2 method to asymmetric buildings, proceedings of the 4th european workshop on the seismic behavior of irregular and complex structures, cd-rom, thessaloniki, greece. [19] bhatt, c. and bento, r. (2012). comparison of nonlinear static methods for the seismic assessment of plan irregular frame buildings with non seismic details, journal of earthquake engineering, 16, pp. 15-39. [20] bosco, m. ghersi, a. marino, e.m. and rossi, p.p. (2013). comparison of nonlinear static methods for the assessment of asymmetric buildings, bulletin of earthquake engineering, 11(6), pp. 2287–2308. [21] de stefano, m. and pintucchi, b. (2010). predicting torsion-induced lateral displacements for pushover analysis: influence of torsional system characteristics, earthquake engineering and structural dynamics, 39(12), pp. 13691394. [22] ghersi, a. marino, e.m. and rossi, p.p. 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can be opened with acrobat and adobe reader 5.0 and later.) >> /namespace [ (adobe) (common) (1.0) ] /othernamespaces [ << /asreaderspreads false /cropimagestoframes true /errorcontrol /warnandcontinue /flattenerignorespreadoverrides false /includeguidesgrids false /includenonprinting false /includeslug false /namespace [ (adobe) (indesign) (4.0) ] /omitplacedbitmaps false /omitplacedeps false /omitplacedpdf false /simulateoverprint /legacy >> << /addbleedmarks false /addcolorbars false /addcropmarks false /addpageinfo false /addregmarks false /convertcolors /converttocmyk /destinationprofilename () /destinationprofileselector /documentcmyk /downsample16bitimages true /flattenerpreset << /presetselector /mediumresolution >> /formelements false /generatestructure false /includebookmarks false /includehyperlinks false /includeinteractive false /includelayers false /includeprofiles false /multimediahandling /useobjectsettings /namespace [ (adobe) (creativesuite) (2.0) ] /pdfxoutputintentprofileselector /documentcmyk /preserveediting true /untaggedcmykhandling /leaveuntagged /untaggedrgbhandling /usedocumentprofile /usedocumentbleed false >> ] >> setdistillerparams << /hwresolution [2400 2400] /pagesize [612.000 792.000] >> setpagedevice shot peening processes to obtain nanocrystalline surfaces in metal alloys: j. liu et alii, frattura ed integrità strutturale, 48 (2019) 161-173; doi: 10.3221/igf-esis.48.19 161 a new method for testing the interfacial shear properties between rock and early-aged shotcrete jian-guo liu, xiao-jun zhou, wei zhao, yu-sheng shen, qing-hua xiao key laboratory of transportation tunnel engineering, ministry of education, school of civil engineering, southwest jiaotong university, chengdu 610031, china xqhbp@home.swjtu.edu.cn abstract. a new method for testing the interfacial shear properties between early-aged shotcrete and rock was developed in the present study, which was proposed following a new test principle. a new set of mould was also designed and described in detail, as well as the test procedures. the main advantages of the new method were that, the shock and vibration could be eliminated compared with the traditional ones, and made the evaluation on the shear properties of the very early-aged rock-shotcrete interface possible. with the newly developed method, the time-dependent rock-shotcrete interfacial shear properties were addressed. it was found that, the time-dependent shear behaviors of the interface could be regressed by a 3-parameter exponential function with high accuracy. in general, the presented research focused on the description and verification of the new test method, which could provide a new way to evaluate the interfacial shear properties between very early-aged shotcrete and rock for numerical simulations and other uses. keywords. shotcrete-rock interface; new test method; direct shear test; time-dependent behaviors; interfacial shear properties. citation: liu, j., zhou, x., zhao, w., shen, y., xiao, q., a new method for testing the interfacial shear properties between rock and early-aged shotcrete, frattura ed integrità strutturale, 48 (2019) 161-173. received: 20.11.2018 accepted: 23.01.2019 published: 01.04.2019 copyright: © 2019 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. introduction hotcrete is widely used as the primary support in underground openings, which can form a skin on the rock surface immediately to protect the rock mass, and thus the host rock can support itself [1]. to form a strong primary support alone or with steel arch, mesh and rock bolt, the interfacial properties between rock and shotcrete are quite important, on which the adhesion and load transferring are dependent [1-4]. previous studies have revealed that the interaction between rock and shotcrete liner were dependent not only on the properties of rock and shotcrete but also on the interface between them [2, 5-6]. ansell highlighted the need of accurate interfacial bond strength for numerical analysis [7-8], and various test methods have been developed for reliable and accurate evaluation of the bond strength of rock-shotcrete interface [4, 9-12]. on the other hand, the shear properties of s http://www.gruppofrattura.it/va/48/2265.mp4 j. liu et alii, frattura ed integrità strutturale, 48 (2019) 161-173; doi: 10.3221/igf-esis.48.19 162 rock-shotcrete interface have not attracted so much attention, and only a few tests were performed [13-15], including the interfacial shear strength between shotcrete and different types of rock substrate [13], shear strength and stiffness with different surface profiles of rock substrate [14] and time-dependent variations of the shear properties [15]. it was found that, the samples for direct shear test was quite difficult to be obtained from tunnel site due to rock fractures, shock and vibration during boring, especially for early-aged samples [15]. to assess the interfacial shear properties between rock and early-aged shotcrete, the bond interfaces of the samples should be prepared without being damaged, and making individual samples might be the possible way, like the direct shear tests on rock-concrete interface [16-19]. given this comprehension, a new direct shear test method was developed through making individual samples, without coring process after shotcreting. a new set of mould was also designed for sample preparation and described in detail, as well as the test procedures. with the newly developed test method, a series of direct shear tests were performed and the interfacial shear properties between early-aged shotcrete and rock substrate were investigated. then, the time-dependent interfacial shear properties of rock-shotcrete interface were evaluated and regressed with different equations. the failure modes of bond interfaces were discussed, as well as the deficiency of the newly developed test method. the obtained interfacial shear properties could be useful for numerical simulations and other purposes. improved test method irect shear test has always been used as the evaluation method for the shear properties of the interface formed by shotcrete and rock. the procedures could be summarized as sample preparation and direct shear test in sequence. in general, the two kinds of rock-shotcrete samples have been used in the previous studies, and the main difference between them was in the sample preparation process. one kind of the previous rock-shotcrete samples were drilled from tunnel sites with a certain period of curing time after the shotcrete was placed [15], while samples in the other kind were drilled in laboratory after pre-processed rock was placed in mould and the shotcrete was sprayed onto the rock surface [14]. it is obvious that the vibration and shock effects on the rock-shotcrete bond interface could not be avoided, which would cause damage to the bond interface, especially when the shotcrete was early-aged. to overcome the limitation of the methods adopted in the previous studies, a new test method for the evaluation of rockshotcrete interfacial shear properties was proposed, with a main improvement of eliminating the drilling process in the sample preparation. the main principle of the newly developed method was to make individual samples with individual rock cores directly. a new set of mould was used to position rock core and house shotcrete in this method. the individual samples then were arrayed on a special wooden plate for shotcreting (fig. 1a). after a period of curing time, the sample cells could be disassembled for direct shear test (fig. 1b). (a) (b) figure 1: (a) sample cells prepared on a wooden plate; (b) special designed wooden plate with a sample cell attached on. new test apparatus for sampling the mould was the core apparatus for sample preparation, which was made of perspex and consisted of three main parts: rock core positioning assembly (rcpa), gap ensuring cushion plates (gecp) and shotcrete housing dock (shd), and the details of the mould are illustrated in fig. 2a. the heights of the rcpa and shd were 30 mm and 43 mm, respectively. the rcpa was used to position the rock core with a 100mm-diameter cylindrical hole in the center. as shown in fig. 2b (a-a section from fig. 1b), the bottom surface of rock was a little lower than that of the rcpa (i.e. 1 mm). below the d j. liu et alii, frattura ed integrità strutturale, 48 (2019) 161-173; doi: 10.3221/igf-esis.48.19 163 rcpa was the gap ensuring cushion plates (gecp), which was used to form a gap between rcpa and shd, between which the bond interface was generated. the thickness of gecp was 3 mm, with a φ100 mm hole designed at the center of it, and the gecp was cut into 2 halves. the shd was used to house shotcrete spayed onto the bottom surface of rock core, with a main cubic space of 120 mm×120 mm×40 mm at the bottom as well as a cylindrical space of φ100 mm×3 mm on the top. when shotcrete was spayed into the space form by shd, gecps and rock core, the bond interface was formed just between the gap occupied by gecp temporarily, and the gecp would be removed before direct shear test. the outer size of the prepared sample with the mould was 150 mm×150 mm×90 mm. (a) (b) figure 2: (a) the assemblies of the mould; (b) concept map of an individual sample materials and test procedures limestone was used as the rock core in the tests, and the uniaxial compressive strength was above 50 mpa. the rock core was a 99.5-mm-diameter cylinder with a height of about 45 mm, which was collected from a tunnel site. as has been noted that, the surface roughness of the rock substrate had remarkable influence on the shear behaviors of the interface formed by rock and support material [3, 20], and thus the bottom surface of the rock core used for interface generation purpose was polished through grinding machine, and the surface profiles were controlled to a joint roughness coefficient (jrc) value of 0~1. the polishing process is illustrated in fig. 3. figure 3: surface polishing through grinding machine after the bottom surface was polished, the rock core was placed into the rcpa. to ensure that the bottom surface was just 1 mm lower than the bottom surface of rcpa, two 1-mm-thick plates were used as the temporary cushion plate (tcp) which contained a hole with a diameter slightly larger than that of the rock core, and the rock then was fixed in the rcpa by hot-melt adhesive and risen on a flat working table as show in fig. 4 and fig. 5a,b. hot-melt adhesive was smeared around the rock core, and resin adhesive of low viscosity was injected into the tiny gap between rock core and rcpa (fig. 5a, b), so that the rock core could not move or rotate in the following steps. j. liu et alii, frattura ed integrità strutturale, 48 (2019) 161-173; doi: 10.3221/igf-esis.48.19 164 figure 4: sketch map of rock core positioning (a) (b) figure 5: (a) rock core fixed in rcpa with hot-melt adhesive; (b) resin injected into the side gap when rock core was positioned and fixed, the next step was to assemble a sample cell by fastening the rcpa, gecp and shd together with bolts. four bolts were used for each sample cell at the four corners, with two just to fasten the mould assemble and the other two to fasten the mould on a special wooden plate. 20 sample cells were arrayed on each plate for shotcreting (fig. 1a). when fastening the bolts, an electro drill was used and the moment applied was about 1 n•m. besides, a bit of vaseline was smeared on both sides of the gecp for lubrication. shotcrete used in this study was a typical wet mixture for underground primary support purpose, which was designed as c20 type, and its composition used is listed in tab. 1. p.o. 42.5 r portland cement was used in the tests, which is a typical cement for underground use. the maximum aggregate size was restricted to 8 mm, which is usually for standard wet-mix shotcrete. alkali-free accelerator was added at the nozzle during spraying. the wooden plates with sample cells were placed vertically at the foot of an underground opening for shotcreting as shown in fig. 6a. composition weight cement content (kg/m3) 460 water content (kg/m3) 238 accelerator (hx-10) (kg/m3) 10.2 aggregates (kg/m3) 0~2mm 887 aggregates (kg/m3) 0~8mm 732 density (kg/m3) 2321.2 table 1: composition of shotcrete used in the tests since the bottom surfaces of the samples were not regular and flat after shotcreting, which may cause uneven normal load during testing. so, the surface was flattened immediately after shotcreting. once the bottom surfaces became even, the samples were moved to an environment of 20℃ and 32% rh for curing. before direct shear tests, the sample cells were remained on the wooden plates. the samples were disassembled from the wooden plates after different curing hours, which were 8 h, 16 h, 24 h, 36 h, 2 d, 3 d, 5 d, 7 d and 14 d after shotcreting. for each curing time, 8 samples were tested with different normal load. before testing, the sample cells were disassembled from the wooden plates by loosening the 2 bolts that fixing the cells on the plates, and then the other 2 bolts were loosened so that the gap ensuring cushion plates (gecp) were not fixed in the j. liu et alii, frattura ed integrità strutturale, 48 (2019) 161-173; doi: 10.3221/igf-esis.48.19 165 mould any more, and could be removed with a screwdriver in the direction perpendicular to the axis of rock core. the gecp removing process and test-ready sample are shown in fig. 7a, b. figure 6: shotcreting on wooden plates for sampling at tunnel site (a) (b) figure 7: (a) gecp removed in the lateral direction; (b) sample ready for test (a) (b) figure 8: (a) shear test diagram; (b) sample loaded in the test machine and ready for test the direct shear test with the newly developed apparatus is schematically described in fig. 8a. normal load as applied on the top surface of rock core through a steel load transfer plate (ltp). shear load was applied on the right outer side of shd by the test machine. since shotcrete was enwrapped in the shd, and shear load on the right boundary was the only lateral force applied on shd, the shear load during test could be transferred to shotcrete body and to the bond interface in sequence. the main difference between the new test method and the previous ones was that, some parts of the mould in the sampling process were remained during the test [5, 14-15]. as the mould was made of perspex, and the strain of the mould could not be neglected when subjected to shear load, which could lead to inaccurate evaluation on the shear j. liu et alii, frattura ed integrità strutturale, 48 (2019) 161-173; doi: 10.3221/igf-esis.48.19 166 properties of the bond interface, especially for the shear stiffness. a load transfer assembly (lta) made of steel was installed in the gap of the rcpa to bear the shear load from the shear test machine and to transfer the load to the lateral surface of rock core. shear load was applied on the right side of the perspex mould. besides, a steel load transfer plate (ltp) was placed on the top of rock core to make sure that the normal load could be applied evenly (fig. 8b). the samples were tested on the typical rock shear test machine that had shear and normal load capacities of 500 kn and 300 kn, respectively, with a resolution of 0.01 kn. the shear speed and data sampling interval were set at 0.1 kn/s and 10 ms, respectively. the servo controlled hydraulic test machine, presented in fig. 9, had four lvdts to monitor the vertical displacement and two lvdts for the shear displacement. figure 9: yds-2 type rock shear testing machine results and discussion he shear properties were presented in following with failure modes of the interfaces, and the time-dependent shear cohesion and frictional angle of the interface as well as the shear stiffness were discussed in detail. as the compressive strength of early-aged shotcrete was quite small, the average normal loads in the tests for different curing time were different. 0.0 0.5 1.0 1.5 2.0 2.5 3.0 0.00 0.05 0.10 0.15 0.20 0.25 0.30 1 k s s h e a r st re ss ,  ( m p a ) shear displacement, u (mm)  n =0.15mpa, t =8h 0.0 0.5 1.0 1.5 2.0 2.5 0.0 0.1 0.2 0.3 0.4 0.5 0.6 1 k s shear displacement, u (mm) s h e a r st re ss ,  ( m p a )  n =0.3mpa, t =16h (a) (b) figure 10: (a) the test results of very early-aged samples; (b) the results of samples with longer curing time during the shear tests, two typical shear behaviors were observed (fig. 10a, b). for the samples with very short curing time (e.g. 8 h), the bond interface showed gradual failure, and the shear stress reduced gradually after the peak value; while for the samples with longer curing time (e.g. 16 h and above), the curves showed sudden drops after the peak shear stress. the difference might be attributed to brittleness of shotcrete after a longer period of curing time, and it was also a kind of fundamental property of the bond interface. t j. liu et alii, frattura ed integrità strutturale, 48 (2019) 161-173; doi: 10.3221/igf-esis.48.19 167 time-dependent shear strength of bond interface the relationships between peak shear stress and normal stress from the experimental results for different curing time were illustrated in fig. 11 through linear fitting. the shear cohesion and friction angle of the interfaces of different ages were obtained, when the mohr-coulomb failure criterion was applied. to regress the time-dependent behaviors of the interfacial shear properties, different equations were attempted for curve fitting as presented in fig. 12 and fig. 13. 0.10 0.15 0.20 0.25 0.30 0.35 0.40 0.45 0.26 0.28 0.30 0.32 0.34 0.36 0.38 0.40 0.42 a: curing time 8h liner fitting experimental results τ max =0.509*σ n +0.210 (r 2 =0.977) 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 0.45 0.50 0.55 0.60 0.65 0.70 0.75 0.80 0.85 b: curing time 16h liner fitting experimental results τ max =0.616*σ n +0.354 (r 2 =0.971) 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2 0.8 0.9 1.0 1.1 1.2 1.3 1.4 c: curing time 24h liner fitting experimental results τ max =0.737*σ n +0.537 (r 2 =0.974) 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0 1.0 1.2 1.4 1.6 1.8 2.0 2.2 2.4 d: curing time 36h liner fitting experimental results τ max =0.837*σ n +0.723 (r 2 =0.998) p e a k s h e a r st re ss , τ m a x ( m p a ) 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 1.2 1.4 1.6 1.8 2.0 2.2 2.4 e: curing time 48h liner fitting experimental results τ max =0.910*σ n +0.841 (r 2 =0.998) 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0 1.4 1.6 1.8 2.0 2.2 2.4 2.6 2.8 f: curing time 72h liner fitting experimental results τ max =0.956*σ n +1.063 (r 2 =0.981) 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0 1.4 1.6 1.8 2.0 2.2 2.4 2.6 2.8 3.0 g: curing time 120h liner fitting experimental results τ max =0.901*σ n +1.325 (r 2 =0.969) 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0 1.6 1.8 2.0 2.2 2.4 2.6 2.8 3.0 3.2 h: curing time 168h liner fitting experimental results τ max =1.104*σ n +1.181 (r 2 =0.980) normal stress, σ n (mpa) 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 1.6 1.8 2.0 2.2 2.4 2.6 2.8 3.0 3.2 i: curing time 336h liner fitting experimental results τ max =1.069*σ n +1.310 (r 2 =0.997) figure 11: relationship between peak shear stress and normal stress of interfaces at different curing time 0 50 100 150 200 250 300 350 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 c o h e si o n o f th e i n te rf a c e , c ( m p a ) curing time, t (h) experimental results c=1.308(1-e -0.022t ) (r 2 =0.983) c=-0.327+0.304ln(t-2.928) (r 2 =0.936) c=-1.300e -0.024t +1.346 (r 2 =0.984) 4 6 8 10 12 14 16 18 0.4 0.6 0.8 1.0 1.2 1.4 compressive strength, f c (mpa) c o h e si o n o f th e i n te rf a c e , c ( m p a ) experimental results c=-2.604e -0.239f c+1.346 (r 2 =0.916) c=-0.677(f c -4.438) 0.267 (r 2 =0.922) (a) (b) figure 12: (a)time-dependent shear cohesion of interface; (b) compressive strength vs. shear cohesion of interface j. liu et alii, frattura ed integrità strutturale, 48 (2019) 161-173; doi: 10.3221/igf-esis.48.19 168 0 50 100 150 200 250 300 350 25 30 35 40 45 50 f ri c ti o n a l a n g le o f th e i n te rf a c e , φ ( °) curing time, t (h) experimental results φ=44.019(1-e -0.089t ) (r 2 =0.935) φ=24.932+4.107ln(t-6.467) (r 2 =0.927) φ=-25.890e -0.041t +45.681 (r 2 =0.949) 4 6 8 10 12 14 16 18 35 40 45 50 f ri c ti o n a l a n g le o f th e i n te rf a c e , φ ( °) compressive strength, f c (mpa) experimental results φ=-26.297e -0.187f c+47.865 (r 2 =0.852) φ=38.030(f c -4.223) 0.081 (r 2 =0.875) (a) (b) figure 13: (a)time-dependent shear fraction of interface; (b) compressive strength vs. shear friction of interface as shotcrete hardened, both the cohesion and frictional angle of rock-shotcrete interface showed strong time-dependent behaviors and rapid growth in the early ages (e.g. before 120 h). after 120 h, both cohesion c and frictional angle  grew smoothly which was similar to the mechanical properties of shotcrete [21-22]. oreste [23] suggested that, the timedependent properties of shotcrete could be simulated by eq.(1). 0 (1 ) t tm m e  = − (1) where tm is a mechanical property at curing time of t, 0m is the final property for t =  , and  is a time constant for different mechanical properties. two other types of curve fitting were carried out for the time-dependent behaviors of cohesion and frictional angle, which were suggested by the following two equations. ( )lntm a b t c= + + (2) ct tm a be − = + (3) both the time-dependent behaviors of cohesion and frictional angle of the interface at different curing time could not be regressed by eq.(2) very well as shown in fig. 12a and fig. 13a, when compared with the results from eq.(1). although eq. (2) was suggested by bae et al. [15] to simulate the uniaxial compressive strength of shotcrete of a certain period (between 1 day and 30 days), the regressions of time dependent behaviors of cohesion and frictional angle of the interface by eq.(2) seem to be not very well, and the increase after 336 h predicted by eq.(2) could not be neglected. for more reasonable simulation of the time-dependent interfacial cohesion and frictional angle, eq.(3) was modified based on eq.(1) and adopted for curve fitting. the results showed that, both the cohesion and frictional angle of the bond interface followed the regression by eq.(3) at a good level. since interfacial shear properties between shotcrete and rock substrate were time-dependent, as well as the compressive strength of shotcrete, there might be some relationships between them. during the direct shear test, the compressive strength of shotcrete at curing time of 24 h, 36 h, 2 d, 3 d, 5 d, 7 d and 14 d was tested, since the shotcrete cubes younger than 24 h was hard to demold. the time-dependent development of compressive strength could be regressed by eq.(1) at a reasonable level, as presented in fig. 14. the relationships between interfacial shear strength and compressive strength of shotcrete were regressed and demonstrated in fig. 12b and fig. 13b. it seems that, the proposed eq.(3) could regress the relationships at an acceptable level, and the equation determined by eq.(1) and eq.(3) seems to better for such regressions. by regressing the relationship between interfacial shear strength and compressive strength of shotcrete, the interfacial shear strength could easily obtain in practical use like numerical models and analytical solutions. time-dependent shear stiffness of bond interface the shear stiffness of bond interface is affected by shotcrete mechanical properties, rock type, curing time [15] and surface roughness of rock [19]. to reveal the relationship between shear stiffness and curing time, all the factors excluding curing time of shotcrete were nearly the same in this study. interfacial shear stiffness for all the samples were calculated as j. liu et alii, frattura ed integrità strutturale, 48 (2019) 161-173; doi: 10.3221/igf-esis.48.19 169 the slopes of the sections where shear stress increases almost linearly with respect to shear displacement in u − curves, as the blue dash line demonstrated in fig. 10, and the relationship is presented in fig. 15a. 0 50 100 150 200 250 300 350 4 6 8 10 12 14 16 18 experimental results k s =17.837(1-e -0.0107t ) (r 2 =0.957) c o m p re ss v ie s tr e n g th , f c ( m p a ) curing time, t (h) figure 14: time-dependent compressive strength of shotcrete. 0 50 100 150 200 250 300 350 0 1 2 3 4 5 6 7 8 experimental results k s =7.298(1-e -0.027t ) (r 2 =0.946) k s =-0.151+1.41ln(t-6.453) (r 2 =0.904) k s =7.129-8.700e -0.036t (r 2 =0.966) s h e a r st if fn e ss o f in te rf a c e , k s (g p a /m ) curing time, t (h) 4 6 8 10 12 14 16 18 3 4 5 6 7 experiment results k s =6.832-20.779e -0.391f c (r 2 =0.967) k s =4.917(f c -4.782) 0.143 (r 2 =0.961) s h e a r st if fn e ss o f in te rf a c e , k s ( g p a /m ) compressvie strength, f c (mpa) (a) (b) figure 15: (a)time-dependent shear stiffness of interface; (b)compressive strength vs. shear stiffness of interface the shear stiffness of the interface was found to grow quickly during the first 72 h, while after 120 h, the shear stiffness seemed to grow very little (fig. 15a), which was similar to the behaviors of shear strength. three types of curve fitting were carried out suggested by eq.(1)~(3), and it’s found that, the logarithm equation was not suitable for simulating the time-dependent behaviors of shear stiffness, since the stiffness of the samples younger than 8 h could not be regressed. when the exponential functions were applied, it could well be regressed. besides, the 3-parameter exponential function provided a better regression than the 2-parameter one. based on the comparison of the 3 functions in the curve fitting for shear strength and shear stiffness, the 3-parameter exponential function was found to be more suitable and accurate for simulating the time-dependent behaviors of shear strength and stiffness, especial for the early-aged samples compared with the 2-parameter one. interfacial shear stiffness could be represented by compressive strength of shotcrete with certain regressions. two equations were used to regress to relationship between shear stiffness and compressive strength, eq. (3) and a combination of eq. (1) and (3) in detail (fig. 15b). it could be seen that, the regression by eq. (3) was a little better than that by the combination of eq. (1) and (3), which is different from the regression case of interfacial shear strength. shear failure modes of the bond interface during the direct shear tests, two failure types were observed. full shear bond failures were observed for about 89.6% (60 out of 67) of the samples, and for the other samples, part of shotcrete failed and remained on the rock substrate. the percentages of failure modes for different aged samples were summarized in fig. 16. for samples aged between 72 h and 168 h, shotcrete failure was observed at each age, while for samples at other ages, only shear failure along the interface occurred. j. liu et alii, frattura ed integrità strutturale, 48 (2019) 161-173; doi: 10.3221/igf-esis.48.19 170 8 16 24 36 48 72 120 168 336 0% 20% 40% 60% 80% 100% curing time, t (h) shear bond failure(2) shear bond & shotcrete failure figure 16: failure modes of different aged samples the area ratios of failed shotcrete were calculated as illustrated in fig. 17, and the ratio of shotcrete remained on rock substrate exceeded 17.3% for no samples. the failure zone of shotcrete was near the edge toward to the shear direction. figure 17: shear failure modes of shotcrete at interface. it’s clear in fig. 17 that, the failure of interface could be described as three kinds of zones, and the main one should be the intact zone, which means no shotcrete were remained on the rock substrate and the failure of the bond interface was along the interface. the second kind one should be the surface failure zone, which means some shotcrete were remained on the rock substrate. the third one should be the cracked zone, which means the shotcrete was cracked with certain depth and even to the other surface. from the three kind of failure zones, it could be inferred that, the failure of rockshotcrete bond interface in shear direction is a very complicated process, which involves in not only the properties of bond interface, but also the failure mechanism of materials. discussion on the newly developed test method the newly developed test method for rock-shotcrete interfacial shear properties is reliable and suitable for use in laboratory environments. the method focused on the accuracy during the sample preparation process, especially with drilling rock substrate before shotcreting and making individual sample cells. the main advantage of the method is that, the samples of early age would not be subjected to shock and vibration in the drilling or sawing process which could cause damages to the bond interface. another feature of the method is that, the position of the interface can be accurately guaranteed, so that the shear failure could occur just at the interface and the “real” shear properties of the interface can be evaluated. besides, the inner size of shotcrete housing dock was designed bigger than that of the rock core, so that the two materials could be fully bonded at the interface. j. liu et alii, frattura ed integrità strutturale, 48 (2019) 161-173; doi: 10.3221/igf-esis.48.19 171 the assembly of rcpa and shd were remained around the sample, which made it easier for shear test, without demoulding process. however, the load was not applied on shotcrete directly, but on the right side of the perspex mould (fig. 8a), which could cause strain in the mould. as the interfacial shear stiffness was defined as the ratio of shear stress to shear displacement, the strain in the mould would affect the obtained interfacial shear stiffness. the strain can be described with eq.(4): /sf ea = (4) where  is the strain in the part of mould where the shear load applied, sf is the peak shear load, the elastic modulus of perspex e =2.9 gpa, and the area of the mould contacting with shear machine a =4000 mm2. the deformation of the mould during shearing could be calculated by using eq.(5). /sl l lf ea = = (5) where l is the change in length of the mould and l =15 mm is the original length. when testing the early-aged samples, the shear load was rather low, and thus the deformation of the mould was quite small compared with the whole shear displacement. for example, for the sample tested at 16 h and 0.8 mpa of normal load, the maximum shear stress max =0.82 mpa, and the corresponding deformation of the mould was 0.008 mm, just 1.3% of the total shear displacement. while for the sample tested at 336 h and 1.65 mpa of normal load, the overestimated shear displacement was 0.031 mm, about 4.5% of the total shear displacement, and thus the shear stiffness of the hardened samples might be underestimated a bit. in addition, some energies were gathered in the mould during the tests, and the shear displacement on the interface increased too quickly than expected after failure due to energy released from the mould. for this reason, no residual friction were obtained as the shear behaviors was not quasi-static any more. to eliminate the underestimation of shear stiffness and to evaluate the residual friction of the rock-shotcrete interface, the right part of shd could be replaced by other much stiffer materials like steel or iron, which could be the main improvement to be made in the following research. conclusions new test method for the evaluation of the rock-shotcrete interfacial shear properties was developed in this paper, in which the shock and vibration effects were eliminated compared with the previous methods, and thus the shear properties could be tested more accurately, especially for the bond interface formed by early-aged shotcrete and rock. based on the method described above and test results presented, the following conclusions can be drawn: (1) the newly developed method for testing the rock-shotcrete interfacial shear properties was based on a new principle that the rock used for substrate was prepared before shotcreting and the test samples were made as individual cells. this method was proved to be an easy and stable way to evaluate the properties compared with the previous ones. (2) the new set of mould that following the new test principle was designed with simple assemblies and made of perspex with low costs, which made it possible for wide usage. with the newly designed mould, unlimited samples could be made at the same time for testing. the set of mould, however, was just an example designed for a special test machine, and could be modified for other shear test machines easily. (3) with the newly developed test method and mould, the very early-aged (8 h) rock-shotcrete interfacial shear properties were successfully tested. the time-dependent shear properties of rock-shotcrete interface were revealed and regressed by using different functions. the regression results showed that, the time-dependent behaviors of interfacial shear strength and stiffness could be simulated by the same type of function with different parameters. and both the interfacial shear strength and stiffness could be represented by compressive strength of shotcrete through simple equations, which could offered an easy way for practical use of the interfacial properties. (4) as the shear load was applied to shotcrete through the mould on the right side, the deformation of the mould could not be neglected, which could lead to underestimation of the interfacial shear stiffness. in addition, the energies gathered in the mould could destroy the quasi-static shear behaviors after peak shear stress, and thus no residual friction coefficient was obtained. however, the deficiency of the mould could be avoided by replacing part of the shd with steel, so that the deformation of the mould and energies gathered in the mould could be eliminated, which could be the direction of further researches of this method. a j. liu et alii, frattura ed integrità strutturale, 48 (2019) 161-173; doi: 10.3221/igf-esis.48.19 172 acknowledgments his work was sponsored by the national natural science foundation of china (no. 51378436, no. 51678501, and no. 51778540) and the national key research and development program of china (2016yfb1200401). references [1] guan, b.s. (2009). shotcrete technology for tunneling and underground engineering. beijing, china communications press. [2] malmgren, l. and nordlund, e. (2008). interaction of shotcrete with rock and rock bolts a numerical study, international journal of rock mechanics and mining sciences, 45(4), pp. 538-553. [3] nwoji, c.u., onah, h.n., mama, b.o. and ike c.c. (2018). ritz variational method for bending of rectangular kirchhoff plate under transverse hydrostatic load distribution, mathematical modelling of engineering problems, 5(1), pp. 1-10. [4] bryne, l.e., ansell, a. and holmgren, j. (2014). laboratory testing of early age bond strength of shotcrete on hard rock, tunnelling and underground space technology incorporating trenchless technology research, 41, pp. 113119. [5] tian, h., chen, w., yang, d., wu, g. and tan, x. (2016) numerical analysis on the interaction of shotcrete liner with rock for yielding supports, tunnelling and underground space technology, 54, pp. 20-28. [6] lee, s.d. (2010). numerical analysis for irregular shotcrete on uneven tunnel perimeter, international journal of rock mechanics and mining sciences, 47(3), pp.488-495. [7] ansell, a. (2005). recommendations for shotcrete on rock subjected to blasting vibrations, based on finite element dynamic analysis, magazine of concrete research, 57(3), pp. 123-133. [8] ansell, a. (2007). dynamic finite element analysis of young shotcrete in rock tunnels, aci structural journal, 104(1), pp. 84-92. [9] bryne, l. e., ansell, a. and holmgren, j. (2014). laboratory testing of early age bond strength between concrete for shotcrete use and rock, nordic concrete research, pp. 81-100. [10] malmgren, l., nordlund, e. and rolund, s. (2005) adhesion strength and shrinkage of shotcrete, tunnelling and underground space technology incorporating trenchless technology research, 20(1), pp. 33-48. [11] efnarc. (1996). european specification for sprayed concrete. [12] bernard, e.s. (2008). early-age load resistance of fibre reinforced shotcrete linings, tunnelling and underground space technology incorporating trenchless technology research, 23(4), pp. 451-460. [13] thomas, a. (2009). spayed concrete lined tunnel, london and new york, taylor and francis group. [14] saiang, d., malmgren, l. and nordlund, e. (2005). laboratory tests on shotcrete-rock joints in direct shear, tension and compression, rock mechanics and rock engineering, 38(4), pp. 275-297. [15] bae, g.j., chang, s. h., lee, s.w. and park, h.g. (2004). evaluation of interfacial properties between rock mass and shotcrete, international journal of rock mechanics and mining sciences, 41(3), pp. 106-112. [16] sadki, a., younes, r., bradai, m.a., hattali, m.l. and mesrati, n. (2016). microstructure and interfacial strength of stainless steel coatings obtained by thermal spray process, annales de chimie: science des materiaux, 40(3-4), pp. 131-142. [17] li, x., tang, c., wang, q., li, x.p. and hao j. (2017). molecular simulation research on the micro effect mechanism of interfacial properties of nano sio2/meta-aramid fiber, international journal of heat and technology, 35(1), pp. 123-129. [18] wang, j.l., zhang, s.h., peng, f.f. (2018). influence mechanism of hard brittle grits on the drilling performance of diamond bit, annales de chimie science des matériaux, 42(2), 209-220. [19] meng, h., wei, j., xing, l.x. (2018). permeability and mechanical properties of basalt fiber-reinforced concrete under magnesium sulfate corrosion, revue des composites et des matériaux avancés, 28(3), 333-343. [20] qiao, q., nemcik, j., porter, i. and baafi, e. (2015). laboratory tests on thin spray-on liner penetrated rock joints in direct shear, rock mechanics and rock engineering, 48, pp. 2173-2177. [21] chang, y. (1992). the influences of the early age properties of shotcrete on tunnel lining, journal of yangtze river scientific research institute, 9(3), pp. 8-16. t j. liu et alii, frattura ed integrità strutturale, 48 (2019) 161-173; doi: 10.3221/igf-esis.48.19 173 [22] hellmich, c., ulm, f.j., mang, h.a. (1999). multisurface chemoplasticity. i: material model for shotcrete, journal of engineering mechanics, 125(6), 692-701. [23] oreste, p.p. (2003). a procedure for determining the reaction curve of shotcrete lining considering transient conditions, rock mechanics and rock engineering, 36(3), pp. 209-236. [24] gao, s.y. and tang, x.n. (2018). impact mechanism of marine biofilm on concrete durability, chemical engineering transactions, 64, 613-618. shot peening processes to obtain nanocrystalline surfaces in metal alloys: y. mizuno et alii, frattura ed integrità strutturale, 47 (2019) 209-220; doi: 10.3221/igf-esis.47.16 209 design of civil environmental engineering structural form of bridges reflecting construction processes yusuke mizuno nippon engineering consultants co., ltd., japan mizuno@ne-con.co.jp yoshiaki kubota university of toyama, japan kubota@sus.u-toyama.ac.jp abstract. the structural form of a bridge during construction is strongly affects its structural form after completion, with innovative construction processes sometimes leading to innovative bridge designs. it is thus important to consider the construction process during bridge design methods. this approach could be applied not only to new construction but also to replacements, reconstructions, or reinforcements. one of the authors has previously systematized the structural forms of bridges and clarified the principles. this study aims to extend these principles to construction systems. changes in the structural systems of the construction processes and systematization of the relationship between a completed bridge and construction process in a design are illustrated. three types of structural systems (suspension, beam, and arch systems) were analysed in terms of material efficiency and time efficiency for corresponding construction states of construction, completed, retrofitted, and retrofitting. each system exhibited different levels of efficiency at different levels of efficiency at different states of construction. this systematization enables the application of a variety of conventional construction methods in a system. this would be helpful in developing new construction methods and designs for bridges. keywords. systematization; construction process; innovative bridge design. citation: mizuno, y., n., kubota, y., n., structural form of bridges reflecting construction processes, frattura ed integrità strutturale, 47 (2019) 209-220. received: 29.07.2018 accepted: 29.11.2018 published: 01.01.2019 copyright: © 2019 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. introduction he structural form of a completed bridge is strongly affected by its structural form during construction. as such, innovative construction processes sometimes produce innovative bridge designs. it is important to consider the construction process in conjunction with bridge design methods. for example, kingsgate bridge (fig. 1) in durham, t http://www.gruppofrattura.it/va/47/2153.mp4 y. mizuno et alii, frattura ed integrità strutturale, 47 (2019) 209-220; doi: 10.3221/igf-esis.47.16 210 the uk, which was designed by sir ove nyquist arup, elegantly represents the construction process of the bridge in the completed form. during the construction of this bridge, bents and scaffoldings were not used in order to protect the river ecosystem. instead, each half of the bridge, which comprised a concrete v-shaped rigid frame pier and beam, was constructed at each bank of the river on a cylindrical foundation parallel to the river. the parts were then rotated by 90º to form the complete bridge. this is an example of an outstanding design approach where the construction process led to the invention of a new construction method that solved a specific problem at the site. furthermore, the resulting bridge is a fine-looking structure. in this manner, the design approach, which also considers the construction process, could be applied not only to new constructions but also to replacements, reconstructions, or reinforcements. figure 1: king’s gate bridge [1]. background and purpose of research esearchers such as frei otto, mike schlaich, and others have advanced the systematization of structures. frei otto [2] organized a lightweight structure in a book titled “form and structure”. mike schlaich [3], organized a lightweight structure in a book titled “shape and structure”. one of the authors of this paper, kubota [4], has systematized the structural forms of bridges and clarified their underlying principles on the basis of the types of forces acting on bridge members. to date, research has mainly focused on the structural forms of completed bridges. this study aims to extend kubota’s method to include the construction systems. in this research, changes in the structural systems during the construction processes and systematization of the relationship between a completed bridge and construction process in a design are illustrated. table 1: dimensions of acting forces, structural systems, and fundamental bridge types [5]. r y. mizuno et alii, frattura ed integrità strutturale, 47 (2019) 209-220; doi: 10.3221/igf-esis.47.16 211 basic theory his work relies on kubota’s [4] previous research, which describes the form of fundamental bridge types and force acting upon them. a new method is developed to elucidate the transition of structural forms in the construction process. relationship between force and form of fundamental bridge types enerally, five types of forces can be imposed on a bridge. these can be classified as follows according to the dimensions of the space where they can exist: axial force, that is, tension and compression, for one dimension; bending moment and shearing force for two dimensions; and torsional moment for three dimensions. tab. 1. shows the forces acting on a bridge, dimensions that the forces that can exist within, typical structural systems that resist these forces, and corresponding fundamental bridge types. as ordinary bridges are usually constructed to cross at a right angle to obstacles, such as rivers, roads, or railways, and cross straight to the other side, torsional moment seldom becomes a major factor when selecting the bridge type. thus, torsional moment does not correspond to any of the structural systems and bridge types in this table. in practical applications, there are obviously more bridge types. in addition, the forces acting on a real bridge are more complicated as several types of forces often act simultaneously on a member. however, it is important to understand that the dominant force imposed on a structure has a great influence on the form of the bridge. therefore, this analysis pairs four bridge types (suspension, arch, girder, and truss) with their corresponding forces. the abovementioned four fundamental bridge types are related to each other, and the relationships are illustrated in fig. 2. there are six combinations of two bridge types. figure 2: continuous relationships between fundamental bridges [5]. figure 3: interrelationships among four fundamental bridge types [5]. in this figure, the relationship between the suspension bridge and arch bridge is expressed as continuity. however, it could also be expressed as symmetry. fig. 3 illustrates the interrelationships among the four fundamental bridge types related to t g y. mizuno et alii, frattura ed integrità strutturale, 47 (2019) 209-220; doi: 10.3221/igf-esis.47.16 212 the acting forces. in this figure, the relationships between the four fundamental bridge types are integrated into a diagram with six arrows indicating the continuity or symmetry in structure and form among them. this figure also shows three classifications of structural systems: a suspension system, beam systems, and an arch system. we can consider not only the linear relationships shown in fig. 3, but also more complex relationships among the various bridges. the relationships shown in fig. 3 are altered to obtain two (upper and lower) triangular coordinate systems with bilateral symmetry in fig. 4. furthermore, the vertical position of the main structure and the floor system is illustrated in the depth direction of the figure. a bridge consisting of a suspension system, a web system, and a diagonal system is shown in the upper half of the figure (triangular prism s1g1t1-s3g3t3), while a bridge consisting of an arch system, a web system, and a diagonal system is shown in the lower half of the figure (triangular prism a1t1g1-a3t3g3). bridges that have a symmetrical relationship in structure and form would be placed at symmetrical points with respect to the central plane (g1t1t3g3), as shown in fig. 4. figure 4: correlation chart expressed by triangular coordinate systems [5]. transition of structural form he structural form changes during the life cycle of a bridge (fig. 5). in this study, the states are separated into three parts: construction state, completed state, and retrofitted state. furthermore, retrofitting is defined as a new structural system applied to an existing structure. figure 5: transition of structural form in a typical life cycle of a bridge. t y. mizuno et alii, frattura ed integrità strutturale, 47 (2019) 209-220; doi: 10.3221/igf-esis.47.16 213 classification of elements of transition of structural form coordinate system for a bridge incorporates movement, which occurs during the construction of the bridge. this is described by a combination of six degrees of freedom in three-dimensional space (fig. 6). the x-axis is the bridge’s axial direction, the y-axis is the direction in a horizontal plane at right angles to the x-axis, and the z-axis is the vertical direction. the coordinate origin is set at the point where the rotation of the structural system is the simplest on the x-axis. rot-x can support small rotations such as when the structure supports a dead load, but this ability decreases drastically as the rotation angle becomes large. rot-y is effective in beam systems, but it cannot achieve the cantilever status in spanning system (suspension and arch). therefore, its support base, such as suspension tower and bearing, moves vertically. rot-z can occur only in a beam system (diagonal system structure and web system structure) because it can become a cantilever system. figure 6: movement and rotation of the bridges. the element variations of structures include four typical structural systems are shown in tab. 2. first, the structural condition of bridges is classified into the “spanning system” and “cantilever system” (tab. 2). then, the “spanning system” is classified into the free rotation condition (rot) and fixed rotation condition (fix) of the end point in the y-z plane. this classification can describe typical structural conditions of bridges, such as simple structure, consecutive structure, bothends-fixed structure, and cantilever structure. thus, all structural conditions can be described in the area enclosed by a heavy line in tab. 2. basic transitions of structural form in the construction process can be explained as a combination of them. table 2: adaptability to spanning/cantilever systems and movement within six degrees of freedom. a y. mizuno et alii, frattura ed integrità strutturale, 47 (2019) 209-220; doi: 10.3221/igf-esis.47.16 214 analysis of examples illustration method of transition of structure he four coloured shapes from the triangular coordinate system correspond to four types of life cycle states. members in the construction, completed, retrofitted, and retrofitting states are shown in light blue, magenta, orange, and purple, respectively. the construction process proceeds from left to right. we examined six examples of construction processes illustrated below. figure 7: construction states (g, s, t, a mean girder, suspension, truss, arch). single-operation method of the suspension bridge (fig. 8) this construction method involves an innovative idea in the construction process. when hung up, temporary compression diagonal members enable the structure to function as a cantilever truss balanced at both endpoints. after it is set, the cables, which are left at both the endpoints, are fixed at the anchor while the structure is hung up. as the temporary diagonal members are removed, the structural system becomes the suspension system. thus, the structure supporting the dead load changes from the cantilever system to the suspension system. this bridge needs few temporary diagonal members to function as it is made of fibre reinforced plastic. thus, this method is an example of a simple, single-operation method for small and medium sized bridges using only one crane. furthermore, the design is innovative and aesthetic. this design hides the pylons in the trees and vegetation such that drivers under the bridge can see only the slender bridge girder. figure 8: single-operation method of the suspension bridge (halgavor footbridge [6]). construction of the dischinger-type bridge (fig. 9) at first, cable-stayed bridges are constructed to overhang from the pylons. the bridge is designed as a diagonal system, the truss system. then, the pylons for making the cable-stayed bridge are used for the exact purpose as for suspension cables. t y. mizuno et alii, frattura ed integrità strutturale, 47 (2019) 209-220; doi: 10.3221/igf-esis.47.16 215 in this manner, live load and dead load of the floor construction beam are supported by the combination of a cable-stayed system as one of the truss systems and a suspension system. in this method, there are no large temporary support structures. thus, this method is efficient because of material efficiency and is suitable for long bridges. this dischinger method is currently the best method for constructing long span bridges. although the cables visually clash with each other and appear complicated at the spot where both structural systems overlap, the completed bridge appears light because many cables are used in the cable-stayed system and suspension system. figure 9: construction method of the dischinger-type bridge (the yavuz sultan bridge [7]). lowering method (fig. 10) in the lowering method, precast arch rib members are rotated on hinges installed on both banks, which eventually make up the arch system. in the rotation process, cables receive reaction force from outside the system and arch rib members constitute a cantilever truss system, which resemble triangles. the truss system changes its stress state during the rotation process. finally, the arch rib members are closed and function as an arch system. this method features good the material efficiency because no huge temporary support structure is used during construction. however, the axial force occurring in the arch rib members during the rotation process is converted into the bending moment because their shape bends in relation to the arch structure. thus, this method is not suitable for very long bridges because the truss system is not structurally efficient. almost nothing from the rotation process remains in the construction state. nevertheless, stress analysis is necessary for every angle because internal stress changes along with the form change of the truss structure. figure 10: lowering method [8]. y. mizuno et alii, frattura ed integrità strutturale, 47 (2019) 209-220; doi: 10.3221/igf-esis.47.16 216 horizontal rotation method (fig. 11) kingsgate bridge is a pedestrian bridge over the river wear that ove arup regarded as his life’s masterpiece. as explain earlier, v-shaped half parts, rigid frame pier and beam, were constructed on cylindrical foundations parallel to the river. the parts were then rotated by 90° and connected. during construction, the two v-shaped structures functioned as a cantilever truss system. then, the final structural form took shape through rotation-z on the cylindrical foundation. the extremely slender v-shaped pier gives the bridge an elegant and delicate appearance. figure 11: horizontal rotation method (kingsgate bridge [1]). vertical cable erection method (fig. 12) in this method, two types of suspension cables are employed in the construction state. carrier cables transport blocks of bridge members and main cables hang vertically. after the truss bridge (the final structure) is completed, hanger ropes are removed and the dead load is transferred from a suspension system to a diagonal system––the truss system. this method requires many temporary structures, such as pylons, carrier cables, and main cables; however, there are many variations of structural forms in the completed state because the main cables work as falsework, taking all loads. figure 12: vertical cable erection method [9]. reinforcement by retrofitting the middle hinge pc bridge with string beam structure (fig. 13) the rigid-frame middle hinge bridges, which were constructed frequently during the period of high economic growth in japan, has a striking deflection at the hinge located in middle of the span. therefore, this method was used for restoring it. the bending moment at the hinge point is zero and the floor construction beam overhangs both endpoints beyond the y. mizuno et alii, frattura ed integrità strutturale, 47 (2019) 209-220; doi: 10.3221/igf-esis.47.16 217 post. therefore, the span, which includes the repair part, is regarded as two cantilever girders butted against each other. thus, the final structure system is a retrofitted cantilever girder with the spanning system. figure 13: reinforcement by retrofitting the middle hinge of a pc bridge with string beam structure (kireuriwari bridge [10]). evaluation of the applicability and efficiency of structural systems he lifecycle of brides involve many construction types, including new construction, reinforcement, repair, and removal. new construction is a basic construction type used to consider all other types. structural changes that occur in new constructions are shown in tab. 4 and tab. 5. (note: tab. 4 and tab. 5 are presented separately to avoid spacing issues). we analysed the “applicability of structural system”, which indicates the likelihood that a structural system will change to another system and “efficiency of material and time” for tab. 4 and tab. 5. applicability of structural system the vertical cable erection method, which uses a suspension system, can be used to construct almost all types of bridges. the diagonal cable erection method or overhanging erection method, which use a diagonal system, can be applied to many types of bridges, such as arch bridges, cable-stayed bridges, and truss bridges. using the special construction methods of the “halgavor footbridge” suspension bridges can also be constructed with a diagonal system. in this respect, a suspension system and a diagonal system have high potential for constructing various types of bridges. on the other hand, while a web system can be used in the launching method as a beam system, the applicability of that structural system is comparatively low. an arch system is rarely used in the construction state. however, the applicability of a suspension system and a diagonal system in the construction state is particularly high. material efficiency bridges that do not undergo changes in their structural system from the construction to the completed state throughout the cycle, such as a suspension bridge or a cable-stayed bridge, have high material efficiency because they do not require massive temporary structures. time efficiency bridges using a beam system have high time efficiency because they can be placed using parallel translation such as the launching-type erection method. in addition, a beam system can be hung up by a small number of cranes. however, these methods generally require many temporary structures in the construction state. accordingly, material efficiency tends to be low. nevertheless, attempts can be made to improve material efficiency by using temporary structures several times. t y. mizuno et alii, frattura ed integrità strutturale, 47 (2019) 209-220; doi: 10.3221/igf-esis.47.16 218 table 4: structural change list no.1 for newly constructed bridges. efficiency under different conditions ab. 6 compares the efficiency between three types of structural systems, including a suspension system, a beam system, and an arch system, with corresponding construction states of construction, completed, retrofitted and retrofitting. the suspension system generally exhibits good material efficiency, but the efficiency is low in the retrofitted state, because of the difficulty of reinforcement. it is difficult to maintain the cable as a series of elements in order to conduct the reinforcement in such a manner that the tension force is not interrupted but flows to the end portion. the beam system has better material efficiency because it requires a small number of temporary structures for the advantage of cantilevering. in addition, time efficiency can be improved by using the launching-type erection method. it functions well in the construction state, and it is efficient in the retrofitting state if a diagonal system is used for stiffening. the arch system is not efficient in the construction state because it is not easy to build without support from another system. however, in the retrofitting state, it is efficient for reinforcing existing structures. the arch system can accept various types of reinforcement in the retrofitted state because countermeasures, such as rolling up reinforcement, can be easily taken afterwards. material time suspension bridge ◎ ○ vertical cable erection method × △ single-operation method of the suspension bridge ○ ◎ cable-stayed bridge ◎ × dischinger-type bridge ◎ × vetrical rotation method ◎ ○ pylon method × △ diagonal cable erection method × △ construction method / names of completed bridge efficiency （dimensionless） transition construction process / life cycle t y. mizuno et alii, frattura ed integrità strutturale, 47 (2019) 209-220; doi: 10.3221/igf-esis.47.16 219 table 5: structural change list no. 2 for newly constructed bridges. table 6: effectiveness in each structure system. material time lowering method ○ △ overhanging arch erection method with truss ○ × arch center method × ○ balanced cantilever method ◎ △ launching erection method △ ◎ span by span construction method × ◎ single‐operation method with floating crane or pontoon × ◎ fixed timbering erection method × ◎ construction method / names of completed bridge efficiency （dimensionless） transitionconstruction process constructed completed retrofitted retrofitting efficient because of the material efficiency more efficient because of the material efficiency low efficiency efficient because of the material efficiency web system (beam system) diagonal system (beam system) efficient at both time and material because of being used as a cantilever efficient because of the material efficiency efficient efficient if being used as a diagonal system low efficiency more efficient because of the material efficiency efficient efficient for supporting exisiting spanning systems triangular coordinate system suspension system (spanning system) arch system (spanning system) y. mizuno et alii, frattura ed integrità strutturale, 47 (2019) 209-220; doi: 10.3221/igf-esis.47.16 220 thus, in the construction state, the suspension system is the most efficient system and the arch system is the most inefficient system from the aspect of material quantity. in contrast, in the retrofitted state, the suspension system is the most inefficient system and the arch system is the most efficient system from the aspect of material property. the superiority of each structural system is dependent upon whether it is a new construction or reinforced structure. conclusion n this study, we established an analysis method based on a “structural form correlation chart”, which showed the change of structural form throughout the life cycle of bridges including construction processes. we then systematized the relationships between the structural forms in the completed state and construction processes including retrofitting existing bridges. in addition, we revealed the peculiarities of four fundamental structural systems such as the applicability of structural systems and the efficiency of material and time corresponding to the three states of construction, completed, and retrofitted. we will improve this theory in future studies to develop innovative construction processes and bridge designs while focusing on more example analyses in a quantitative manner. references [1] mikami, y. (1996). kenchiku shiryo kenkyusha co., ltd., zokei in japanese, pp. 74–81. [2] frei, o. (1976). form and structure. harper collins distribution services. [3] schlaich, m. (2006). challenges in education–conceptual and structural design iabse symposium report, iabse symposium, budapest 2006: responding to tomorrow's challenges in structural engineering, pp. 20–26. [4] kubota, y. (2009). fundamental study on the method used for the operations on the structure and form of a bridge, j. japan soc. civ. eng., 65(1), pp. 64–76. [5] kubota, y. (2010). systematization of structures and forms of truss systems, 34th international symposium on bridge and structural engineering, pp. 1–5. [6] firth, i. and cooper, d. (2018). new materials for new bridges––halgavor bridge, uk, struct. eng. int., 12(2), pp. 80–83. [7] iabse (2016). the yavuz sultan selim bridge, turkey. available at: [8] https://www.iabse.org/iabse/association/award_files/outstanding_structure_award/yssb_turkey.aspx [9] sato, t., kaneko, k., and kajima k. (2013). adoption of the lowering construction method of raise type rc fixed arch bridge takatakinozawa bridge in japanese, the 57th hokkaido development technology research presentation. [10] otsuka, s., minami, d., yoshida, m., kondo, h., miyama, y., and shibuya, d. (2017). design and construction of make more rationalized truss by sandwich composite slab: nagatani bridge, bridge and foundation engineering, 51(3), pp. 25–30. [11] suzuki, t., wakatsuki, k., and manabe, h., nishi, h. (2004). reinforcement design and construction of kireuriwari viaduct––confirmation of reinforcement effect of hinge ramen bridge using lower string cables in japanese, proceedings of symposium on the development of prestressed concrete 13, pp.45–54. i microsoft word numero_59_art_08_3254.docx j.l. gonzález -velázquez et alii, frattura ed integrità strutturale, 59 (2022) 105-114; doi: 10.3221/igf-esis.59.08 105 focussed on fracture and structural integrity on the assessment of non-metallic inclusions by part 13 of api 579 -1/asme ffs-1 2016 jorge luis gonzález-velázquez, ehsan entezari department of metallurgy and materials, escuela superior de ingeniería química e industrias extractivas, instituto politécnico nacional, mexico jlgonzalezv@ipn.mx, https://orcid.org/0000-0001-6914-4449 ehsan.entezari2014@gmail.com, https://orcid.org/0000-0003-3379-1761 jerzy a. szpunar department of mechanical engineering, university of saskatchewan, canada jerzy.szpunar@usask.ca, https://orcid.org/0000-0002-1291-8375 abstract. improvement of non-destructive inspection techniques has allowed more frequent detection of closely spaced zones of non-metallic inclusions in pressure vessels made of low carbon steel. in the present study, closely spaced inclusions in an in-service cylindrical horizontal pressure vessel were detected by scan-c ultrasonic inspection and considered as laminations to be assessed by part 13 of the api 579-1/asme ffs-1 2016 standard. the outcoming results were considered as a rejection for level 1 assessment, and a repair or replacement of the component was required, even though it retained a significant remaining strength. thus, an alternative procedure to assess the mechanical integrity of pressure vessels containing zones of nonmetallic inclusions is proposed by adopting some criteria of the api 5791/asme ffs-1 part 13 standard procedure and taking into consideration the dimensions and grouping characteristics of the inclusion zones. keywords. structural integrity assessment; non-metallic inclusions ultrasonic inspection; pressure vessel. citation: gonzález-velázquez, j.l., entezari, e., szpunar, j.a., assessment of non-metallic inclusions by part 13 of api 579 -1/asme ffs-1 2016, frattura ed integrità strutturale, 59 (2022) 105-114. received: 28.08.2021 accepted: 15.10.2021 published: 01.01.2022 copyright: © 2022 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. introduction he presence of non-metallic inclusions (nmis) in the shell and heads of pressure vessels made of low carbon steel exposed to sour environments in the oil and gas industries is one of the main factors to increase the susceptibility of hydrogen-induced cracking (hic). according to gonzalez-velazquez [1], the interface between the nmis and the steel matrix is the preferred site for hydrogen trapping and nucleate hic. accordingly, the hydrogen originated from hydrogen sulfide (h2s) and atmospheric moisture traps at the interface between steel matrix and nmis, increasing molecular hydrogen pressure [2-4]. high molecular hydrogen pressure separates the metallic matrix and inclusions, causing propagation t https://youtu.be/un6auk1uhiq j.l. gonzález -velázquez et alii, frattura ed integrità strutturale, 59 (2022) 105-114; doi: 10.3221/igf-esis.59.08 106 of hic parallel to the pipe wall [5]. liu et al. [6] and dong et al. [7] showed that the hic is commonly associated with clusters of si, al, mn, and ca-based nmis in steel plates, where the shape, size, and distance between inclusions affect the hic. most researchers showed that large inclusions are prone to trap more hydrogen, increasing hic susceptibility, and concluded that the shape, size, and separation between nmis are critical factors for hic propagation [8,9,10]. the connection between hic and nmis has been of great concern for pressure vessel users in the oil and gas industry, leading to the need to assess the impact of nmis on the fitness-for-service (ffs) of pressure vessels. however, because of the absence of a specific assessment procedure, nmis are usually evaluated as laminations. laminations are made by the plane with weaker texture parallel to the rolling plane and have a higher risk of cracking at high hydrogen pressure [11]. molecular hydrogen pressure in lamination zones is higher than in other areas, leading to the stress fields at plastic zones of crack tips which trigger the hic propagation [12]. moussa et al. [13] reported that high hydrogen pressure between 2 laminations increased the stress intensity factor for hic, causing crack growth at the critical pressure. the detection of zones of closely spaced nmis in pressure vessels is typically done by conventional straight beam ultrasonic inspection in scan-c mode. it is a common practice by the inspectors to report them as laminations. gomera et al. [14] observed that signs of continuous laminations are associated with the accumulation of nmis in hot rolled carbon steel plates. gonzález et al. [15] analyzed the mechanical behavior of non-coplanar pressurized laminations in carbon steel pipes. they observed that the laminations might be interconnected by plastic deformation and then create a larger damaged area. the ffs assessment of pressure vessels containing laminations is done by part 13 of standard api 579 -1/asme ffs-1 2016 [16]. this standard illustrates 3 assessment levels. level 1 assessment is the most conservative method, evaluating lamination zones from the perspective of metal loss with a minimum amount of inspection. level 1 assessment commonly proposes a reduction of internal pressure of pressure vessels for maintaining safety. [17,18]. in the level 2 assessment, lamination zones are considered as local thinner areas or a crack-like flaw and evaluated by criteria such as remaining strength factor (rsf) and failure assessment diagram (fad) [19]. the level 3 assessment also is done using the finite element method (fem) for explicit modeling and the most accurate stress analysis of lamination zones, considering defects geometry and loading conditions [17, 20]. the equipment’s owners/users often question the assessment criteria of api 579 and request ffs engineers to provide technical advice for modifying the system due to the high financial cost. thus, the ffs assessment of zones containing groups of nmis can be done by methods similar to those used for laminations but with less strict assessment criteria. the present research aims to adapt the ffs assessment procedure and criteria presented in part 13 of the api 579-1/asme ffs-1 standard to assess zones of non-metallic inclusions in pressure vessel shells made of low carbon steel. theoretical overview: scope and assessment criteria of non-metallic inclusions by part 13 of api 579-1/asme ffs-1 standard definition and applicability criteria of non-metallic inclusion zone he nmis are not considered as defects by any code, standard, or technical specification of mechanical integrity or ffs. nonetheless, as nmis are parallel to the shell wall in non-destructive inspections, they are considered as laminations for assessment purposes by structural integrity engineers. the dimensioning of zones of nmis is based on the guidelines of api 579, as indicated in fig. 1. the non-destructive inspection of zones of nmis is typically done by industrial ultrasonic testing, using a straight beam or phased array [16]. definition and applicability criteria of laminations paragraph 13.1.2 of the api 579 standard defines laminations as non-fusion planes inside a steel plate produced in the fabrication process, and they may exist in one or more planes in the plate. laminations are planar defects, so they do not produce bulging on the metal surface, have no cracking in the direction of the thickness, and are not interconnected [16]. according to paragraph 13.4.2.1 of api 579 part 13, the level 1 assessment procedure of laminations in a type a component, a component with a specific design code, subjected to internal pressure is the following [16]: step 1. obtain the significant dimensions of the lamination (see fig. 1). step 2. determine tc= trd – fca step 3. if there are two or more laminations in the same plane and it is met that ls<2tc, they must be combined as a single lamination with longitudinal (s) and circumferential (c) dimensions adjusted to the total size of the zone containing the laminations. step 4. verify if the edge of the lamination closest to a major structural discontinuity is at a distance t j.l. gonzález -velázquez et alii, frattura ed integrità strutturale, 59 (2022) 105-114; doi: 10.3221/igf-esis.59.08 107 lmsd ≥1.8 dtc. step 5. verify if the vertical separation between the edge of multiple laminations weld meets lh ≤ 0.09 max s, c , and lh ≤ min tc/3 ,0.5 in . step 6. verify that there is no cracking through the thickness and the lamination is not surface breaking, according to tmm ≥ 0.01 tc. step 7. verify if the distance between the edge of the lamination and the nearest weld satisfies lw ≥ max 2tc, 25 mm 0.1 in . step 8. if the lamination is in a hydrogen charging environment, the lamination dimensions must satisfy s, c ≤0.6 dtc. step 9. if the conditionals of steps 4 to 8 are met, the lamination is acceptable by the level 1 assessment, and consequently, no corrective action is required. otherwise, the component is rejected, a level 2 assessment is recommended. step 10. determine the mawpr using tc from step 2 (equations are provided in annex 2c of api 579 standard). figure 1: significant dimensions for assessing laminations as established in figs 13.2 and 13.3 of api 579-1/asme ffs-1 2016. the level 2 assessment procedure considers the lamination as a local thin area with a remaining thickness equal to the maximum value of [tc  lh  tmm], or tmm. in this case, the zones containing laminations are evaluated by part 5 of the api 579. however, if the lh criterion of step 5 above is not satisfied, the lamination is evaluated as a crack-like flaw using level 2 methodology of part 9 of api 579, where the crack depth 2a = lh. obviously, the above criteria lead to overconservative assessments, and even innocuous zones of nmis (regarded as laminations) with a few inches in length are rejected. ffs assessment of zones of non-metallic inclusions n order to analyze the ffs assessment procedure of a pressure vessel with zones of nmis, a real-life case was used. fig. 2 shows a photograph of the pressure vessel containing zones of nmis, as installed and operated in an oil i j.l. gonzález -velázquez et alii, frattura ed integrità strutturale, 59 (2022) 105-114; doi: 10.3221/igf-esis.59.08 108 production offshore facility. this case was of critical importance to the owner due to the high costs of repair and the extreme consequences of failure. figure 2: photograph of the assessed pressure vessel installed and operated in an oil production offshore facility. type of component cylindrical horizontal, torispherical heads, welded service sour gas/condensate separator design code asme sec. viii, div. 1 material specification sa 516 gr. 70 operating pressure 14.2 psi maximum allowable working pressure (mawp) 42.6 psi service temperature 95 f external diameter (d) 122 in nominal thickness (tnom) 1 in minimum required wall thickness (tmin) 0.130 in future corrosion allowance (fca) 0.125 in table 1: technical data of the pressure vessel. figure 3: the typical distribution of non-metallic inclusions in the vessel shell. as-polished sample and bright-field metallographic microscope. j.l. gonzález -velázquez et alii, frattura ed integrità strutturale, 59 (2022) 105-114; doi: 10.3221/igf-esis.59.08 109 tab. 1 summarizes the main technical data of the assessed pressure vessel. the appearance of the nmis was determined by the metallography of a coupon extracted from a previous repair and is shown in fig. 3. the inclusions were identified as type a, thick series, according to the astm e45 standard [21]. fig. 4 shows a drawing of the pressure vessel. the inclusion zones were detected in the shell plates env-2 and env-3 and the heads tp-1 and tp-2. figure 4: pressure vessel design drawing, indicating the identification tags of the shell plates. the zones of nmis were detected by phased array ultrasonic testing (paut) in scan-c mode. fig. 5 shows detected zones of nmis, along with the corresponding paut screen record. of the 5 zones of nmis detected, one is close to a weld joint (env-3.2), and the other is isolated (tp-1.6). it is noted that the zones are planar and not interconnected and also spread across a significant portion of the thickness. j.l. gonzález -velázquez et alii, frattura ed integrità strutturale, 59 (2022) 105-114; doi: 10.3221/igf-esis.59.08 110 figure 5: photographic records of zones of non-metallic inclusions detected by paut in the pressure vessel. tab. 2 shows the dimensions of the zones of nmis detected by the non-destructive inspection in the pressure vessel. defect id wall thickness away of lamination (trd) long. dimension (s) circ. dimension (c) minimum measured thickness (tmm) lamination height (lh) lamination to lamination spacing (ls) spacing to a nearest major discontinuity (lmsd) spacing to nearest weld joint (lw) env-3.2 1.046 16.00 14.00 0.296 0.630 40 35.83 0.5 env-2.4 1.014 13.00 10.00 0.582 0.242 40 13.78 14.0 tp-1.6 1.098 7.50 6.50 0.296 0.720 22.5 16.50 30.0 tp-2.23 1.112 14.00 16.50 0.287 0.552 16.5 3.00 34.0 tp-2.24 1.112 12.50 22.00 0.278 0.616 16.5 6.00 17.5 table 2: dimensions of the zones of non-metallic inclusions detected in the pressure vessel (all dimensions in inches). ffs assessment of inclusion zones by part 13 of api 579 ab. 3 presents the results of part 13 of api 579 level 1 assessment of the zones of non-metallic inclusions listed in tab. 2, regarding them as laminations, and evaluated according to the procedure described in section 2.2 of this paper. the sequence of steps was modified to display the calculations in a rational order. t j.l. gonzález -velázquez et alii, frattura ed integrità strutturale, 59 (2022) 105-114; doi: 10.3221/igf-esis.59.08 111 step/criterion env-3.2 env-2.4 tp-1.6 tp-2.23 tp-2.24 tc= trd – fca 0.921 0.899 0.973 0.987 0.987 1.8 dtc 19.080 18.850 19.611 19.752 19.752 0.01 tc 0.009 0.009 0.010 0.010 0.010 2tc 1.842 1.798 1.946 1.974 1.974 ls<2tc yes yes yes yes yes lmsd ≥1.8 dtc yes no no no no tmm ≥ 0.01 tc yes yes yes yes yes lw ≥ max 2tc , 0.1 in no yes yes yes yes 0.09 max s, c 1.440 1.170 0.675 1.485 1.98 lh ≤ 0.09 max s, c yes yes no yes yes tc/3 0.307 0.210 0.324 0.239 0.239 lh ≤ min tc/3,0.5 in no no no no no 0.6 dtc 4.497 4.443 4.623 4.656 4.656 s, c ≤0.6 dtc no no no no no mawpr 299 psi 292 psi 207 psi 206 206 result rejected rejected rejected rejected rejected table 3: level 1 assessment of the zones of non-metallic inclusions by part 13 of api 579 in the pressure vessel. (all dimensions in inches). tab. 4 shows the results of the level 2 assessment. since the lh  min [tc/3, 0.5 in] criterion was not satisfied, zones of nmis were assessed as a crack-like flaw using level 2 methodology of part 9 of api 579. for this aim, 2a = lh and 2c = max [s, c], the ligament length d = tmm, and the thickness was trd, as listed in tab. 2. the level 2 assessment also was done by a commercial fracture mechanics application software. further, the mechanical properties of the sa 516 gr.70 steel were taken at the nominal values ys = 38 ksi and uts = 70 ksi and assuming a kic = 100 ksi √𝑖𝑛. the reference stresses were inferred from the internal pressure. step/criterion env-3.2 env-2.4 tp-1.6 tp-2.23 tp-2.24 kr 0.621 0.063 0.015 0.012 0.014 lr 0.126 0.078 0.061 0.057 0.278 location of assessment point in the fad envelope inside inside inside inside inside rsf 1.57 15.7 19.1 22.7 20 result accepted accepted accepted accepted accepted table 4: level 2 assessment of the zones of non-metallic inclusions by part 9 of api 579 in the pressure vessel. results and discussion s expected, the level 1 assessment by part 13 of api 579 rejected all five defects, failing three out of seven criteria. nonetheless, the mawpr calculated with the reduced thickness was much higher than the mawp. the criteria that caused rejection in all cases were the lamination height (lh) which ratio lh/ trd variated from 0.6 to 0.5, and the lamination size (s, c), where the allowable size ranged from 4.443 to 4.656 in, while the maximum length of the zones of nmis was from 22 in to 7.5 in. the next most important factors were the spacing to a major structural discontinuity (lmsd) and the distance to the nearest weld joint (lw); a combination of these two factors was a cause of rejection. a j.l. gonzález -velázquez et alii, frattura ed integrità strutturale, 59 (2022) 105-114; doi: 10.3221/igf-esis.59.08 112 in the level 2 assessment, however, all five defects were acceptable and more important; the assessment points were in the lower right corner of the fad, indicating that the severity of the defects is quite low, even though they were assessed as crack-like defects. the only defect that was more far away from the origin of the fad was env-3.2, a defect zone in the vicinity of weld metal with rsf of 1.57. although the defect env-3.2 has similar dimensions and a similar lh/trd ratio with the defect tp-2.23, the rsf of defect env-3.2 is much lower than that of defect tp-2.23, as shown in fig. 6. thus, the proximity of the defect env-3.2 to a weld metal is the main factor that decreased the rsf. further, the rest of the defects have rsf greater than 15, which indicates that the pressure vessel containing laminations as large as 16 in long and occupying as much as 60% of the thickness still retain sufficient strength to remain in service. figure 6: variation of remaining strength factor with spacing to the nearest weld joint. based on the above observations, the following rules can be adopted to perform ffs assessments of zones of nmis inclusions in pressure vessels made of low carbon steel, based on the procedure of part 13 of api 579: 1. the most important dimensions for the assessment are the lamination size (s, c), and the spacing to the nearest weld joint (lw). 2. the lamination height (lh) can be disregarded since it may cause unnecessary rejections and additionally has a minor effect on the rsf when the nmis zone is evaluated as a crack-like defect. this is due to the fact that nmis are discontinuous and disperse across the thickness, so they do not introduce a significant reduction of the effective cross-section area, nor are significant stress concentrators. 3. the criterion s, c ≤ 0.6 dtc can be disregarded because of the discontinuous and disperse nature of the nmis. therefore, longitudinal and circumferential dimensions of nmis do not affect the remaining strength. 4. if possible, it is advisable to leave out the level 1 assessment and directly perform the level 2 assessment since it provides a less conservative assessment when the nmis zone is evaluated as a crack-like defect. conclusion he fitness-for-service assessment of pressure vessels containing zones of closely spaced non-metallic inclusions can be effectively performed, assuming that the defect is considered as lamination and evaluated by part 13 of the api 579 standard. for level 1 assessments, the most important dimensions are the lamination size (s, c), and the spacing to the nearest weld joint (lw), while the lamination height (lh) and the s, c < 0.6(d tc) criteria can be disregarded since it is very likely that the defect will be rejected because of these, and the discontinuity and dispersion of non-metallic inclusions across the thickness do not introduce significant reduction of the effective cross-section area, nor are relevant stress concentrators. finally, if possible, it is advisable to skip the level 1 assessment and directly perform the level 2 t j.l. gonzález -velázquez et alii, frattura ed integrità strutturale, 59 (2022) 105-114; doi: 10.3221/igf-esis.59.08 113 assessment considering the non-metallic inclusion as a buried crack-like defect since it provides less conservative assessments. acknowledgments he authors would like to acknowledge the national polytechnic institute (ipn), the national council of science and technology (conacyt), and the grupo de análisis de integridad de ductos (group of pipeline integrity analysis) of the instituto politécnico nacional (ipn) for the support to carry out this research. references [1] gonzález-velázquez, j.l. (2021). fatigue and environmentally assisted crack propagation. a practical approach to fracture mechanics. doi: 10.1016/b978-0-12-823020-6.00006-2. [2] mohtadi-bonab, m.a., eskandari, m., karimdadashi, r., szpunar, j.a. (2017). effect of different microstructural parameters on hydrogen-induced cracking in an api x70 pipeline steel, met. mater. int., 23(4), doi: 10.1007/s12540-017-6691-z. [3] mohtadi-bonab, m.a., eskandari, m. (2017). a focus on different factors affecting hydrogen-induced cracking in oil and natural gas pipeline steel, eng. fail. anal., 79, doi: 10.1016/j.engfailanal.2017.05.022. [4] pedeferri, p. (2018). hydrogen-induced damage. corrosion science and engineering, springer, pp. 275–295. doi: 10.1007/978-3-319-97625-9. [5] wasim, m., djukic, m.b. (2020). hydrogen embrittlement of low carbon structural steel at macro-, micro-and nanolevels, int. j. hydrogen energy, 45(3), pp. 2145–2156. doi: 10.1016/j.ijhydene.2019.11.070. [6] liu, z.y., wang, x.z., du, c.w., li, j.k., li, x.g. (2016). effect of hydrogen-induced plasticity on the stress corrosion cracking of x70 pipeline steel in simulated soil environments, mater. sci. eng. a, 658, doi: 10.1016/j.msea.2016.02.019. [7] dong, c.f., liu, z.y., li, x.g., cheng, y.f. (2009). effects of hydrogen-charging on the susceptibility of x100 pipeline steel to hydrogen-induced cracking, int. j. hydrogen energy, 34(24), doi: 10.1016/j.ijhydene.2009.09.090 [8] peng, z., liu, j., huang, f., hu, q., cao, c., hou, s. (2020). comparative study of non-metallic inclusions on the critical size for hic initiation and its influence on hydrogen trapping, int. j. hydrogen energy, 45(22), doi: 10.1016/j.ijhydene.2020.02.131. [9] kim, w.k., koh, s.u., yang, b.y., kim, k.y. (2008). effect of environmental and metallurgical factors on hydrogen-induced cracking of hsla steels, corros. sci., 50(12), pp. 3336–3342. doi: 10.1016/j.corsci.2008.09.030. [10] rahman, k.m.m., mohtadi-bonab, m.a., ouellet, r., szpunar, j., zhu, n. (2019). effect of electrochemical hydrogen charging on an api x70 pipeline steel with focus on characterization of inclusions, int. j. press. vessel. pip., 173, pp. 147–155. doi: 10.1016/j.ijpvp.2019.05.006. [11] gonzalez, j.l., ramirez, r., hallen, j.m., guzman, r.a. (1997). hydrogen-induced crack growth rate in steel plates exposed to sour environments, corros., 53(12), doi: 10.5006/1.3290278. doi: 10.5006/1.3290278. [12] servin, a., gonzález, j.l., morales, a. (2009). behavior of coplanar and non-coplanar laminations in api5l x52 steel simulated by finite elements, inf. tecnológica, pp. 97–106. doi: 10.1612/inf.tecnol.4113it.08. [13] moussa, w.a., bell, r., tan, c.l. (1999). the interaction of two parallel semi-elliptical surface cracks under tension and bending, j. press. vessel technol. trans. asme, 121(3), doi: 10.1115/1.2883710. [14] gomera, v.p., sokolov, v., fedorov, v., okhotnikov, a.a. and saykova, m.s. (2010). use of ae method for detection of steel lamination in the industrial pressure vessel, j. acoust. emiss., 28, pp. 234–245. [15] gonzalez, j.l., morales, a. (2006). analysis of non-coplanar the pressurized laminations in x52 steel pipes by nonlinear by finite element. international pipeline conference, vol. 42622, pp. 791–8. doi: 10.1115/ipc2006-10514. [16] a.p.i. (2016). fitness-for-service: api 579-1/asme ffs-1, american petroleum institute. [17] anderson, t.l., osage, d.a. (2000). api 579: a comprehensive fitness-for-service guide, int. j. press. vessel. pip., 77(14–15), doi: 10.1016/s0308-0161(01)00018-7. t j.l. gonzález -velázquez et alii, frattura ed integrità strutturale, 59 (2022) 105-114; doi: 10.3221/igf-esis.59.08 114 [18] purnana, p., ibrahim, s. (2019). fitness for service assessment of cross-country oil pipelines based on api 579 (application of api 579 on asme b 31.4). asme 2019 india oil and gas pipeline conference, iogpc 2019. doi: 10.1115/iogpc2019-4555. [19] jaske, c.e., rubal, m.j. (2010). fitness for service document comparison: api 579 vs. pdam. proceedings of the biennial international pipeline conference, ipc, 1. doi: 10.1115/ipc2010-31552. [20] fernández-cueto, m.j., capula-colindres, s., angeles-herrera, d., velázquez, j.c., méndez, g.t. (2018). analysis of 3d planar laminations in a welded section of api 5l x52 applying the finite element method, soldag. e insp., 23(1), doi: 10.1590/0104-9224/si2301.03. [21] astm. (2018). e 45-18a standard test methods for determining the inclusion content of steel, astm int. conshohocken, pa, www.astm.org, (c). nomenclature c lamination dimension in the circumferential direction d inside diameter of the component fca future corrosion allowance fad failure assessment diagram lh depth of the defects to the external surface lmsd spacing to the nearest major structural discontinuity ls lamination-to-lamination spacing lw spacing to the nearest weld joint mawp maximum allowable working pressure mawp reduced maximum allowable working pressure nmis non-metallic inclusions rsf remaining strength factor s lamination dimension in the longitudinal direction tc corroded wall thickness tmin thickness required to support the internal pressure in the pressure vessel tmm minimum measured thickness tnom nominal thickness of the component trd wall thickness away of lamination microsoft word numero_35_art_10 s. morita et alii, frattura ed integrità strutturale, 35 (2016) 82-87; doi: 10.3221/igf-esis.35.10 82 focussed on crack paths microstructure dependence of fatigue crack propagation behavior in wrought magnesium alloy s. morita, s. fujiwara, t. hori, n. hattori department of mechanical engineering, saga university, 1 honjo, saga 840-8502, japan morita@me.saga-u.ac.jp h. somekawa national institute of materials science, somekawa.hidetoshi@nims.go.jp t. mayama kumamoto university, mayama@kumamoto-u.ac.jp abstract. this paper deals with the fatigue crack propagation behavior of rolled az31b magnesium alloy (grain size: approximately 40 m). fatigue crack propagation tests were performed on single edge notched tension specimens at a stress ratio of r = 0.1 and a frequency of 10 hz at room temperature. loading axes were parallel to the rolling direction; fatigue cracks propagated parallel to the transverse direction (l-t specimen), parallel to the short transverse direction (l-s specimen). loading axis was perpendicular to the rolling direction; fatigue cracks propagated parallel to the transverse direction (s-t specimen). the crack growth rate (da/dn) of the l-s specimen was several times lower than that of the l-t specimen in the examined stress intensity factor range (k). fracture surfaces of the l-t and l-s specimens showed many steps parallel and perpendicular, respectively, to the macroscopic crack growth direction. the da/dn of the s-t specimen was higher than that of the l-t and l-s specimens in the examined k. the fracture surface was covered by quasi-cleavage facets independent of macroscopic crack growth direction, and the fracture surface roughness at low k was larger than that at high k. keywords. fatigue crack; texture; magnesium. introduction agnesium alloys are the lightest structural material with high specific strength and stiffness. these features make magnesium alloys attractive for applications in the automotive industry [1]. wrought mg-al-zn system alloys, especially rolled and extruded magnesium alloys, are the candidates for structural parts. it is necessary to investigate the fatigue crack initiation and propagation behavior of the material used for structural parts. m s. morita et alii, frattura ed integrità strutturale, 35 (2016) 82-87; doi: 10.3221/igf-esis.35.10 83 it is well known that magnesium alloys have a hexagonal close-packed (hcp) structure, and strong textures are formed by rolling. in such textured magnesium alloys, basal planes are aligned parallel to the rolling direction by rolling. depending on their texture, rolled magnesium alloys show unique deformation behavior such as mechanical anisotropy [2-4], pseudoelasticity in cyclic loading-unloading [4-8], and asymmetricity of stress-strain hysteresis loops in strain controlled low-cycle fatigue tests [9-14] and even in load controlled high-cycle fatigue tests [3, 9], etc. the orientation dependence of fatigue crack propagation behavior of magnesium single crystals [15-17], and the effect of grain size [18-21] and texture [22-25] on fatigue properties of polycrystalline magnesium alloys have been reported in previous works. however, the effect of texture on the fatigue crack propagation behavior of magnesium alloy is still poorly understood. in the present study, the crystallographic orientation dependence of the fatigue crack propagation behavior of rolled az31b magnesium alloy is investigated. experimental procedure ommercial rolled az31b magnesium alloy plate with a thickness of 60 mm was used in the present study. chemical composition of the alloy is listed in tab. 1. the alloy has equiaxed grains, and the average grain size was approximately 40 m. the alloy showed typical texture as shown in fig.1 and fig.2; basal planes were aligned parallel to the rolling direction. three types of tensile and compressive specimens were machined with the loading axis parallel (l-specimen), perpendicular (t-specimen) and normal (s-specimen) to rolling direction. compressive and tensile mechanical properties of the alloy is summarized in tab. 2. al zn mn fe si cu ni mg 3.1 0.929 0.41 0.003 0.037 0.004 0.001 bal. table 1: chemical composition. (mass%) specimen compressive 0.2% proof stress, 0.2comp [mpa] tensile 0.2% proof stress, 0.2tens [mpa] tensile strength, b [mpa] tensile fracture strain, el [%] l-specimen 78 129 240 10 t-specimen 73 94 240 12 s-specimen 85 53 255 15 table 2: mechanical properties. figure 1: (0001) and (10-10) pole figures. c s. morita et alii, frattura ed integrità strutturale, 35 (2016) 82-87; doi: 10.3221/igf-esis.35.10 84 figure 2: ipf map. single edge notched tension specimens with a width (w) of 12 mm, a thickness (b) of 4 mm, a initial crack length (a) of 1 mm, and a length (l) of 50 mm were machined from a rolled as shown in fig.3. loading axes were parallel to the rolling direction; fatigue crack propagated parallel to the transverse direction (l-t specimen), parallel to the short transverse direction (l-s specimen). on the other hand, loading axis was normal to the rolling direction; fatigue cracks propagated parallel to the transverse direction (s-t specimen). fatigue crack propagation tests were performed on an electro-hydraulic testing machine (capacity: 9.8 kn) at a stress ratio of r = pmin/pmax = 0.1 (tension-tension) and a frequency of 10 hz at room temperature in air. here, pmax and pmin are the maximum and minimum applied load, respectively. the fatigue crack length was determined using a microscope. the stress intensity factor range (k) was calculated using the following equation: 32 tan 2 0.752 2.02 0.37 1 sin 2 cos 2                              a p a awk a w wb w w (1) where p is the applied load, and w, b and a are the width, thickness, and crack length, respectively. the fracture surface of the fatigue tested specimens were observed by sem. figure 3: shape and dimensions of sent specimen (in mm). 300μm s. morita et alii, frattura ed integrità strutturale, 35 (2016) 82-87; doi: 10.3221/igf-esis.35.10 85 results and discussion he relationship between the crack growth rate (da/dn) and the k is shown in fig.4. the figure shows that the da/dn of the l-s specimen was several times lower than that of the l-t and s-t specimens in the examined k. the da/dn of the s-t specimen was higher than that of the l-t and l-s specimens in the examined k. fig. 5 shows the typical sem images of the fatigue tested l-t, l-s, and s-t specimens. many straight lines or steps were observed over several grains along with the macroscopic direction of fatigue crack growth in the l-t specimen (fig.5(a) and (b)). in contrast, in the l-s specimen, many lines or steps perpendicular to the macroscopic direction of fatigue crack growth were observed (fig.5(c) and (d)). the fracture surface of the l-t and l-s specimens had a similar morphology and did not depend on k. on the other hand, various quasi-cleavage facets independent of the macroscopic direction of fatigue crack growth were observed in the s-t specimen (figs.5(e) and (f)). moreover, the fracture surface roughness at low k, up to k = 7 mpa·m1/2, was larger than that at high k, above k > 7 mpa·m1/2. the macroscopic fatigue crack propagation is parallel to the a-axis (perpendicular to basal plane) of each grain for the l-t specimen, and parallel to the c-axis (perpendicular to basal plane) of each grain for the l-s specimen. therefore, it is inferred that the c-axis direction is unfavorable for the fatigue crack propagation in rolled az31b magnesium alloy. it is also found that the macroscopic fatigue crack propagation is various directions to the a-axis (parallel to basal plane) of each grain in the s-t specimen. thus, it appears that the fatigue crack propagated easily in a direction parallel to the a-axis (parallel to basal plane) of each grain in the s-t specimen. in addition, the deformation twinning of polycrystalline magnesium alloys plays an important role in the deformation process because of the limitation of slip system. when the specimens were subjected to a stress higher than the compressive and tensile yield stress in the load-controlled fatigue test, deformation twins were observed in the extruded magnesium alloys [3, 4, 26]. in contrast, free deformation twins are observed around the fatigue crack path (within the plastic zone) in the l-t and l-s specimens. it appears that the fatigue crack growth is not controlled by the deformation twinning at a crack tip in textured polycrystalline magnesium alloys. figure 4: relationship between crack growth rate and stress intensity factor range. conclusions he fatigue crack propagation behaviors of three types of specimens of textured polycrystalline magnesium alloy, in which the macroscopic fatigue crack propagated perpendicular to and parallel to the basal plane of each grain, has been investigated. it is found that the a-axis direction is favorable for the fatigue crack propagation in textured t t s. morita et alii, frattura ed integrità strutturale, 35 (2016) 82-87; doi: 10.3221/igf-esis.35.10 86 polycrystalline magnesium alloy. figure 5: fracture surfaces of fatigue tested (a) l-t specimen at k = 6.8 mpa·m1/2, da/dn = 10-7 m/cycle; (b) l-t specimen at k = 13 mpa·m1/2, da/dn = 10-6 m/cycle; (c) l-s specimen at k = 6.4 mpa·m1/2, da/dn = 10-8 m/cycle; (d) l-s specimen at k = 13 mpa·m1/2, da/dn = 10-6 m/cycle; (e) s-t specimen at k = 6.2 mpa·m1/2, da/dn = 10-7 m/cycle; and (f) s-t specimen at k = 7 mpa·m1/2, da/dn = 10-6 m/cycle. acknowledgment his work was supported by jsps kakenhi grant numbers 24760578, 26820318. references [1] ebert, t., mordike, b.l., magnesium properties – applications – potential, mater. sci. eng. a, 302 (2001) 37–45. [2] yukutake, e., kaneko, j., sugamata, m., anisotropy and non-uniformity in plastic behavior of az31 magnesium alloy plates, mater. trans., 44 (2003) 452–457. [3] somekawa, h., maruyama, n., hiromoto, s., yamamoto, a., mukai, t., fatigue behaviors and microstructures in an extruded mg-al-zn alloy, mater. trans., 49 (2008) 681–684. [4] morita, s., tanaka, s., ohno, n., kawakami, y., enjoji, t., cyclic deformation and fatigue crack behavior of extruded az31b magnesium alloy, mater. sci. forum, 638-642 (2010) 3056–3061. [5] cáceres, c.h., sumitomo, t., veridt, m., pseudoelastic behaviour of cast magnesium az91 alloy under cyclic loading–unloading, acta mater., 51 (2003) 6211–6218. [6] li, y., enoki, m., evaluation of the twinning behavior of polycrystalline magnesium at room temperature by acoustic emission, mater. trans., 48 (2007) 1215–1220. t crack growth direction (a) (b) (c) (d) (e) (f) s. morita et alii, frattura ed integrità strutturale, 35 (2016) 82-87; doi: 10.3221/igf-esis.35.10 87 [7] li, y., enoki, m., deformation and anelastic recovery of pure magnesium and az31b alloy investigated by ae, mater. trans., 48 (2007) 2343–2348. [8] li, y., and enoki, m., recovery behaviour of pure magnesium in cyclic compression-quick unloading-recovery process at room temperature investigated by ae, mater. trans., 49 (2008) 1800–1805. [9] hasegawa, s., tuchida, y., yano, h., matsui, m., evaluation of low cycle fatigue life in az31 magnesium alloy, int. j. fatigue, 26 (2007) 1839–1845. [10] lin, x.z., chen, d.l., strain controlled cyclic deformation behavior of an extruded magnesium alloy, mater. sci. eng. a, 496 (2008) 106–113. [11] matsuzuki, m., horibe, s., analysis of fatigue damage process in magnesium alloy az31, mater. sci. eng. a, 504 (2009) 169–74. [12] begum, s., chen, d.l., xu, s., luo, alan a., effect of strain ratio and strain rate on low cycle fatigue behavior of az31 wrought magnesium alloy, mater. sci. eng. a, 517 (2009) 334–343. [13] lv, f., yang, f., duan, q.q., luo, t.j., yang, y.s., li, s.x., zhang, z.f., tensile and low-cycle fatigue properties of mg–2.8% al–1.1% zn–0.4% mn alloy along the transverse and rolling directions, scripta mater., 61 (2009) 887–890. [14] park, s.h., hong, s.g., bang, w., lee, c.s., effect of anisotropy on the low-cycle fatigue behavior of rolled az31 magnesium alloy, mater. sci. eng. a, 527 (2010) 417–423. [15] ando, s., iwamoto, n., hori, t., tonda, h., fatigue crack propagation in magnesium crystals, j. japan inst. metals, 65 (2001) 187–190. [16] ando, s., saruwatari, k., hori, t., tonda, h., fatigue crack propagation behavior in magnesium single crystals, j. japan inst. metals, 67 (2003) 247–251. [17] ando, s., ikejiri, y., iida, n., tsushida, m., tonda, h., orientation dependence of fatigue crack propagation in magnesium single crystals, j. japan inst. metals, 70 (2006) 634–637. [18] kim, h.-k., lee, y.-i., chung, c.-s., fatigue properties of a fine-grained magnesium alloy produced by equal channel angular pressing, scripta mater., 52 (2005) 473–477. [19] uematsu, y., tokaji, k., kamakura, m., uchida, k., shibata, h., bekku, n., effect of extrusion conditions on grain refinement and fatigue behaviour in magnesium alloys, mater. sci. eng. a, 434 (2006) 131–140. [20] ochi, y., masaki, k., hirasawa, t., wu, x., matsumura, t., takigawa, y., higashi, k., high cycle fatigue property and micro crack propagation behavior in extruded az31 magnesium alloys, mater. trans., 47 (2006) 989–994. [21] tsushida, m., shikada, k., kitahara, h., ando, s., tonoda, h., relationship between fatigue strength and grain size in az31 magnesium alloys, mater. trans., 49 (2008) 1157–1161. [22] sajuri, z.b., miyashita, y., hosokai, y., mutoh, y., effects of mn content and texture on fatigue properties of as-cast and extruded az61 magnesium alloys, int. j. mech. sci., 48 (2006) 198–209. [23] ishihara, s., nan, z., goshima, t., effect of microstructure on fatigue behavior of az31 magnesium alloy, mater. sci. eng. a, 468-470 (2007) 214–222. [24] zeng, r.c., xu, y.b., ke, w., han, e.h., fatigue crack propagation behavior of as-extruded magnesium alloy az80, mater. sci. eng. a, 509 (2009) 1–7. [25] zeng, r., han, e., ke, w., dietzel, w., kainer, k.u., atrens, a., influence of microstructure on tensile properties and fatigue crack growth in extruded magnesium alloy am60, int. j. fatigue, 32 (2010) 411–419. [26] yang, f., yin, s.m., li, s.x., zhang, z.f., crack initiation mechanism of extruded az31 magnesium alloy in the very high cycle fatigue regime, mater. sci. eng. a, 491 (2008) 131–136. << /ascii85encodepages false /allowtransparency false /autopositionepsfiles true /autorotatepages /none /binding /left /calgrayprofile (dot gain 20%) /calrgbprofile (srgb iec61966-2.1) /calcmykprofile (u.s. web coated \050swop\051 v2) /srgbprofile (srgb iec61966-2.1) /cannotembedfontpolicy /error /compatibilitylevel 1.4 /compressobjects /tags /compresspages true /convertimagestoindexed true /passthroughjpegimages true /createjobticket false /defaultrenderingintent /default /detectblends true /detectcurves 0.0000 /colorconversionstrategy /cmyk /dothumbnails false /embedallfonts true /embedopentype false /parseiccprofilesincomments true /embedjoboptions true /dscreportinglevel 0 /emitdscwarnings false /endpage -1 /imagememory 1048576 /lockdistillerparams false /maxsubsetpct 100 /optimize true /opm 1 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can be opened with acrobat and adobe reader 5.0 and later.) >> /namespace [ (adobe) (common) (1.0) ] /othernamespaces [ << /asreaderspreads false /cropimagestoframes true /errorcontrol /warnandcontinue /flattenerignorespreadoverrides false /includeguidesgrids false /includenonprinting false /includeslug false /namespace [ (adobe) (indesign) (4.0) ] /omitplacedbitmaps false /omitplacedeps false /omitplacedpdf false /simulateoverprint /legacy >> << /addbleedmarks false /addcolorbars false /addcropmarks false /addpageinfo false /addregmarks false /convertcolors /converttocmyk /destinationprofilename () /destinationprofileselector /documentcmyk /downsample16bitimages true /flattenerpreset << /presetselector /mediumresolution >> /formelements false /generatestructure false /includebookmarks false /includehyperlinks false /includeinteractive false /includelayers false /includeprofiles false /multimediahandling /useobjectsettings /namespace [ (adobe) (creativesuite) (2.0) ] /pdfxoutputintentprofileselector /documentcmyk /preserveediting true /untaggedcmykhandling /leaveuntagged /untaggedrgbhandling /usedocumentprofile /usedocumentbleed false >> ] >> setdistillerparams << /hwresolution [2400 2400] /pagesize [612.000 792.000] >> setpagedevice microsoft word numero_30_art_33 v. veselý et alii, frattura ed integrità strutturale, 30 (2014) 263-272; doi: 10.3221/igf-esis.30.33 263 focussed on: fracture and structural integrity related issues electrical resistivity and ultrasonic measurements during sequential fracture test of cementitious composite v. veselý, p. konečný, p. lehner, d. pieszka, l. žídek všb-technical university of ostrava, faculty of civil engineering, department of structural mechanics, ostrava, czech republic vesely.v1@fce.vutbr.cz, petr.konecny@vsb.cz, petrlehner@gmail.com, daniel.pieszka@ips-konstrukt.cz, libor.zidek@vsb.cz abstract. cracks in cover of reinforced and pre-stressed concrete structures significantly influence the ingress of deleterious species causing decrease in durability of these structures. the paper is focused on the effect of fracture process on two selected physical parameters of concrete – the electrical resistivity and the ultrasonic pulse passing time – which might be employed as the quality indicator of concrete cover within (nondestructive) procedure(s) of assessment of the structural durability. the concrete electrical resistivity and ultrasonic passing time were investigated here with respect to two variants of treatment of the test specimens’ surface (the pre-dried surface and the wet surface). test configuration of three-point bending of notched beam was utilized to control the crack propagation; the fracture process passed through several loading–unloading sequences between which the electrical resistivity and ultrasonic passing time readings over the fractured region were performed. equivalent elastic crack model was used for estimation of the fracture advance (described via the effective crack length) at the loading stages corresponding to the resistivity and ultrasonic measurements. relationships between changes of both the concrete resistivity and ultrasonic pulse passing time and the effective crack length is determined and discussed. keywords. cementitious composite; three-point bending test; electrical resistivity; ultrasound pulse passing time; effective crack length; moisture. introduction and motivation he paper is aimed at durability issues of reinforced and pre-stressed concrete civil engineering structures. service life of such structures is closely connected with the level of their damage caused by initiation and propagation of cracks [1-3]. the manner of their fracture behaviour is referred to as the quasi-brittle one, e.g. [4-6], i.e. there exists a large nonlinear zone around the propagating crack tip where the material is being damaged via numerous failure mechanisms like micro-cracks growth, their coalescence, bending and branching etc., resulting in an increase of porosity of the material in that zone. aggressive agents (e.g. ice-melting salts, see water etc.) can penetrate to the level of steel reinforcement through the damaged concrete cover more easily. preferential pathways for the ingress of deleterious species cause decrease in durability of the structures in question which has a considerable economical impact. in recent years, numerical models taking into account the effect of concrete cracking on the aggressive agents’ penetration have been proposed both from the numerical [7,8] and analytical [9,10] standpoint. these models are typically based on t v. veselý et alii, frattura ed integrità strutturale, 30 (2014) 263-272; doi: 10.3221/igf-esis.30.33 264 rather significant simplifications concerning description of the physics behind these complex phenomena. thus, exploring of the effects of cracking on the aggressive agents ingress in more depth seems as very reasonable research issue. one of procedures for the estimation of concrete ability to resist aggressive agents expressed via diffusion coefficient proposed in literature [11,12] is evaluated through electrical resistivity measurements of concrete. the correlation between the level of concrete cracking and the (change in) electrical resistivity of the material is selected herein as qualitative indicator. conducted experiments, whose selected results are presented in this paper, investigate phenomena related to the introduced problem. evaluation of concrete electrical resistivity complemented with ultrasonic measurements serves as the indicator of the material’s ability to resist the penetration of aggressive agent through the material. observations are performed on both uncracked and cracked specimen regions. particularly, it is investigated how the aggressive agent ingress can be related to the level of tensile damage of the covering material. in other words, a question relevant for practical interest may sound: how the aggressive agent ingress’ increase due to cracking can be estimated (for instance on surfaces of the structural parts under tensile stresses) e.g. even if the damage is not visible by naked eye. sequential three-point bending tests of single edge notched concrete beams (sen-tpb geometry) were performed accompanied with measurement of both the change in electrical resistivity and the decrease of ultrasound pulse velocity in the damaged area. the level of the material damage (the degree of decrease of the material structure’s integrity) in the cracked part of test specimens is investigated using ultrasound measurements; changes in electrical resistivity in that part can reveal relationship between the coefficient of diffusion of an aggressive agent (chloride) ions and the extent of the concrete fracture. both these non-destructive methods are used here with the ambition to employ them for quick assessment of quality of concrete in the tensioned structural regions. this is important with respect to ascertain/eliminate a premature degradation of reinforced and pre-stressed concrete civil engineering structures. parts of the study devoted to either the electrical resistivity or ultrasonic measurements were already published by the authors in [13] and [14], respectively; this paper adds new results originating from supplementary tests conducted under different moisture conditions. experimental study material and specimens ommon concrete mix provided by a local commercial concrete mixing plant was used to produce the test specimens. c 30/37 xf4 ought to be the designed strength class of the used normal concrete. specimens were casted into steel moulds from one batch of fresh concrete and properly vibrated (for cca 30–60 s). apart from the standard beams of dimensions 100 × 100 × 400 mm3 whose test results are reported in this paper also cubes of and cylinders for standard tests on compressive strength, splitting tensile strength and modulus of elasticity (both static and dynamic) were produced. all specimens were submerged in a tank with water at laboratory temperature. before fracture tests the beams were cut into three slices (along the longitudinal axe of the beam, in planes perpendicular to the casting direction) by diamond saw. the two cover layers created on the specimens by the bottom of the mould and the upper open surface were also cut off (in a layer of several millimetres) in order to diminish the surface effect (due to the aggregate arrangement and the cement paste layer at the specimen surfaces). thus, three specimens, marked with letters a, b, c, were prepared from each standard beam, see fig. 1a). nominal dimensions of the specimens, w × b × l (i.e. width × breadth × length), were equal to 100 × 30 × 400 mm3. specimens were then provided with notches, again using the diamond saw. the tests were conducted in several series, two of which, differing in the moisture treatment of the specimen surfaces, are presented in the paper. the first set of three standard beams, i.e. nine test specimens, was taken out from the curing position in water bath one day before testing. after dividing them into three parts and providing the notches (by diamond saw as well) the surface of the specimens was left at air to dry-out. this specimen set is marked as that with pre-dried surface and consisted of beams marked as t1, t63, and t69. three slices of each beam, i.e. the test specimens a, b, and c, were provided with notches of relative lengths, 0, approximately equal to 0.1, 0.3, and 0.5, respectively. the pre-dried surface set was tested at the age of 224 days. the second set comprising of four standard beams, i.e. twelve test specimens, was cut and notched one day before testing as well and then returned back in the curing bath. testing was conducted subsequently after taking them out from the bath and letting drip off the water from their surface. however, the surfaces were kept wet during the whole testing procedure treating them by wet sponge. this specimen set is referred to as the wet surface one and consisted of beams c v. veselý et alii, frattura ed integrità strutturale, 30 (2014) 263-272; doi: 10.3221/igf-esis.30.33 265 marked as t31, t39, t86, and t88. the test specimens a, b, and c were provided with notches of relative lengths, 0, approximately equal to 0.251, 0.33 and 0.50 respectively. the pre-dried surface set was tested at the age of 1 year. the loading span, s, of the three-point bending testing configuration was set to 380 mm. individual dimensions of the tested specimens, their weight and moisture content are given in tab. 1. # part w [mm] b [mm] s [mm] l [mm] a0 [mm]  = a0/w m [kg] [%wt.] pre-dried surface specimens t1 a 100.09 26.54 380 400.77 9.52 0.095 2.756 8.16 b 100.14 27.77 380 400.67 29.70 0.297 2.493 6.47 c 100.21 30.82 380 400.63 50.48 0.504 2.756 5.80 t63 a 100.15 24.69 380 400.39 9.80 0.098 2.268 5.80 b 100.10 24.62 380 400.46 30.12 0.301 2.184 6.98 c 100.04 24.89 380 400.50 49.38 0.494 2.141 7.24 t69 a 100.06 26.33 380 400.01 8.41 0.084 2.332 6.70 b 99.89 26.44 380 399.93 28.88 0.289 2.369 6.57 c 99.83 29.17 380 399.93 50.00 0.501 2.597 5.77 wet surface specimens t31 a 100.09 29.55 380 400.47 25.62 0.256 2.579 8.95 b 100.11 29.81 380 400.31 32.07 0.320 2.68 7.50 c 100.25 32.96 380 400.20 48.85 0.487 2.987 7.10 t39 a 99.62 99.62 380 400.15 25.44 0.255 2.702 8.73 b 99.54 29.77 380 400.10 31.05 0.312 2.643 7.73 c 99.57 31.46 380 400.01 47.72 0.479 2.807 7.56 t86 a 100.14 25.74 380 399.79 24.86 0.248 2.324 *4.57 b 100.21 27.90 380 400.03 32.84 0.328 2.563 *4.06 c 100.20 26.52 380 400.05 49.84 0.497 2.384 *4.01 t88 a 100.22 29.30 380 400.78 24.44 0.244 2.599 8.26 b 100.29 29.02 380 401.44 33.09 0.330 2.629 7.06 c 100.21 32.21 380 401.62 49.44 0.493 2.967 6.76 table 1: specimen dimensions, values of relative crack length, mass and moisture. fracture testing specimens were loaded under control of displacement of the upper jaw at the rate of 0.5 mm/min using heckert fp 10/1 testing machine. the loading force and the doubled mid-span deflection were recorded using the fixture enabling the pure beam deflection reading, see fig. 1b). 1 it was observed during the fracture testing of the first set that the behaviour of specimens with the shortest notches was accompanied with a part of a fast unstable regime where the structural response was not recorded. these parts of the load–deflection diagrams were then reconstructed/approximated. this observed phenomenon is linked to the insufficiently low stiffness of the used testing device. therefore, deeper notches (causing lower stiffness of the specimens) were used in the second set. v. veselý et alii, frattura ed integrità strutturale, 30 (2014) 263-272; doi: 10.3221/igf-esis.30.33 266 a) b) figure 1: a) preparation of notched specimens for bending test from standard beams, b) employed fracture test geometry – three-point bending of notched beam – with a depiction of the measuring fixture enabling recording of pure beam deflection. several loading−unloading cycles were accomplished during the test on each specimen. unloading was performed on the beginning of the descending branch of the recorded load−deflection (p−d) curve (at a value of approx. 80% of the peak load from the corresponding loading cycle). the unloading was performed manually by switching the regime of the used electro-mechanical testing machine. manual switching didn’t allow precise attaining of the desired unloading level, especially in the cases of specimens with the shortest notches (particularly in the pre-dried sample set with 0 = 0.1, see the footnote above). a dynamic onset of fracture (a fast release of energy accumulated in the insufficiently stiff loading system) was observed during the tests of these specimens. this dynamic event was indicated by sparse occurrence of points on a relatively long section of the descending branch of the plotted p−d diagram. the specimens were removed from the testing machine after full unloading of each cycle. the ultrasound as well as resistivity measurements were conducted (see the subsections bellow) and then the specimens were returned back to the loading machine for the next cycle. the number of cycles varied from two to five depending on the above-mentioned stability of the test (from the perspective of the ability to record the descending branch of the loading curve). typical examples of p−d diagrams corresponding to tests with the quasi-static (desired) and dynamic (undesired) fracture are shown in fig. 2 (the abovementioned partial approximations of the descending branch of the p−d curve can be seen in the latter case). the individual loading−unloading cycles are distinguished with colours and marked with arabic numerals after dash. electrical resistivity measurements measurements of electrical resistivity,  [kcm], were conducted on the specimens before starting of the sen-tpb test and after its individual subsequent unloading stage – the specimens were removed from the loading machine and investigated using the resi resistivity meter (proceq). the measurement is conducted via a beam-shaped probe using this apparatus; there are four electrodes placed along the probe (usually referred to as the wenner probe) perpendicularly to its longitudinal axe. wet sponges assured the contact between the electrodes of the measuring probe and concrete of the a) b) figure 2: example of recorded load vs. mid-span deflection curves (p–d diagrams); a) with quasi-static fracture propagation (specimen t69b), b) with a dynamic event on the descending branch of the first loading cycle (specimen t1a). 0 250 500 750 1000 1250 0 0.2 0.4 0.6 0.8 lo a d in g f o rc e p [n ] mid-span deflection d [mm] t69b-1 t69b-2 t69b-3 t69b-4 0 500 1000 1500 2000 0 0.2 0.4 0.6 0.8 lo a d in g f o rc e p [n ] mid-span deflection d [mm] t1a-1 t1a-2 t1a-3 t1a-1-approx v. veselý et alii, frattura ed integrità strutturale, 30 (2014) 263-272; doi: 10.3221/igf-esis.30.33 267 specimen. the resistivity was measured in three areas along the specimen length − in the left (marked as l), middle (m, i.e. across the fractured cross-section) and right (r) part, respectively2. three readings were made also along the specimen width − near the upper surface of the specimen (the ligament, marked as l), in the middle (m) and near the bottom surface provided with the notch (n)3. all these readings were made from either flat side surface of the specimen. the placement of the four electrodes (with wet sponges) of the probe on the specimen surfaces is depicted in fig. 3a) using circles, the measuring position (m-n) on the front surface is indicated by red colour. ultrasonic measurements similarly to the resistivity measurements described above, the concrete specimens were subjected to ultrasonic measurements before each sequence of loading cycle. the tico ultrasonic instrument (proceq) was used; this device is able to record the time needed for ultrasound pulse to pass through the defined portion of the concrete test specimen or, inversely, the speed of the ultrasound wave propagation. there are two probes applied on the surface of the test (in our case notched/cracked) specimen, first of which emits and the second receives the ultrasound waves. the specimens were laid down on a rubber pad in a precisely determined position in order to hold uniformity of placements of the measuring probes at the determined points on the specimen surfaces for measurement of each test specimen. four points on each side surface, i.e. eight points on both sides, determined the position of the probes for the measurement4; see the circles in fig. 3b). thus, the pair of measuring probes was placed on two locations on either side of the specimen, at the notch (n) and ligament (l) area (i.e. positions 1, 3 and 2, 4, respectively) then, the time for the acoustic pulse to pass the sample, t [s], was measured. processing of recorded data, used methods and models estimation of current crack length – effective crack model he crack length at the stages of test corresponding to the electrical resistivity and ultrasonic measurements were calculated using equivalent elastic crack approach. according to this approach the nonlinear fracture of quasibrittle material is simulated by replacing the real body containing a crack of a certain length and a fracture process zone ahead of it with a brittle body with an effective crack (longer than the initial one). both bodies are forced to exhibit the same stiffness parameters (for more details see e.g. [4-6]). 2 by coincidence, the wenner probe of the used resi apparatus was roughly of the same length as one half of the test specimen, so (l) and (r) measurements took place just (centred) at the left and right halves of the specimen, and the (m) measurement over the inner two quarters (the centre of the specimen). 3 resistivity measurement locations were distributed along the specimen width, w, as follows: the (n) reading was made at 1/6 of w from the bottom, the (m) one in the middle, and the (l) one at 5/6 of w from the bottom. 4 the probes of the used tico instrument are of cylinder shape, cca 50 mm in diameter. the individual probes of the measuring pair were placed at distances 1/4 and 3/4 of the specimen length, l, respectively; (n) measurement level was at 1/4 of w from bottom, the (l) one 3/4 of w from bottom. a) b) figure 3: illustration of positioning of probes of the measuring devices on the test specimen in the case of electrical resistivity measurements (a) and the ultrasonic measurements (b). t v. veselý et alii, frattura ed integrità strutturale, 30 (2014) 263-272; doi: 10.3221/igf-esis.30.33 268 a modification of the effective crack model by nallathambi and karihaloo [4] was adopted in order to determine the equivalent elastic crack length at the stages of the unloading−reloading cycles. the crack length was calculated by iteration process using the formula for compliance of the three-point bend beam with a central crack. in this formula the crack length is presented as the upper limit of integral of a certain multiplication of (usually polynomial) function of geometry. the procedure was implemented in mathcad mathematical package. several compliance values were taken from the unloading−reloading branches of the recorded p−d diagrams, namely the secant, unloading, reloading, and some kind of “mean” value of the latter two ones. the mean compliance was obtained as a line going through the intersections of the unloading and reloading branches of the p−d curve. interpretation of the secant, unloading and reloading compliance and construction of the mean compliance is illustrated in fig 4. values of the effective crack length presented further in this paper were computed based on the mean compliance. this approach is closest to the variant according to jenq-shah [5]. if the pure nalathambi-karihaloo model [4] based on the secant compliance was used, the effective crack lengths would be much larger than those determined from the mean compliance (and the reloading and unloading ones too). investigation of changes in electrical resistivity during fracture process selected results from the evaluated concrete electrical resistivity measurements are presented herein. the measurements of resistivity were conducted before loading and after each unloading cycle until the sample broke. there was observed a gradual reduction of concrete resistivity as the loading–unloading cycles went by in the case of the specimens set with pre-dried surface (which was conducted first). even the resistivity in the same measuring locations of the sample’s intact parts was generally decreasing from cycle to cycle. moreover, an effect of increasing wetting of the concrete surface around the wenner probe contacts areas was observed. it is believed that the reduction of resistivity was caused by the measuring instrument repetitive wet sponge-maintained contacts with the pre-dried concrete. therefore, the resistivity difference, , between the crack affected and unaffected areas (and not the absolute resistivity values, ) was selected in order to overcome the influence of gradual probe contact areas wetting. in the second testing set, the samples were kept in bath until the test started in order to mitigate the effect of the gradual surface wetting. the notched (n) area in the middle (m) of the sample (marking is indicated in fig. 3a), was selected in order to study effect of the fracture propagation on the changes of electrical resistivity of the material. the average value from the left (l-n) and right (r-n) measurements in the notched area were used as a reference. resulting parameter  represents the resistivity reading in the middle notched area (m-n) minus the average of the intact reference areas (mean value of (l-n) and (r-n)). the relationship between the  value and the computed effective crack length, aeff, is given in figs. 5a) and 5b) for the pre-dried and wet surface specimen sets, respectively. investigation of changes in ultrasound pulse passing time during fracture process the measurements of ultrasound pulse passing time, t, were conducted before the loading begins and after each of unloading cycles similarly to the resistivity readings. the notch area (n) was of the interest herein as well. thus, readings from the same vertical location of the specimen from its both sides were averaged (location 1 with location 3, see fig. 3b). the time for the ultrasound wave to pass the zone affected by cracking had increasing tendency as the fracture propagated, see figs. 6a) and 6b). figure 4: variants of estimation of the specimen compliances considered for the determination of the effective crack length. 0 250 500 750 1000 1250 0 0.1 0.2 0.3 0.4 lo a d in g f o rc e p [n ] mid-span deflection d [mm] specimen t1b cycle 1 cycle 2 cycle 3 unloading compliance reloading compliance "mean" compliance secant compliance 0 200 400 600 0.05 0.1 0.15 lo a d in g f o rc e p [n ] mid-span deflection d [mm] specimen t1b cycle 1 cycle 2 unloading compliance reloading (elastic) compliance "mean" compliance secant compliance v. veselý et alii, frattura ed integrità strutturale, 30 (2014) 263-272; doi: 10.3221/igf-esis.30.33 269 a) b) figure 5: relationship between the concrete electrical resistivity difference, , and the relative effective crack length, eff, for the pre-dried (a) and the wet surface (b) samples evaluated at the notch (n) level. a) b) figure 6: relationship between the ultrasound pulse passing time, t, and the relative effective crack length, eff, for the pre-dried (a) and the wet surface (b) samples evaluated at the notch (n) level. discussion of results here were two sets of samples subjected to testing in order to indicate the difference between the dried and wet surface on the results of concrete electrical resistivity as well as ultrasound pulse passing time. as was mentioned above, the samples have been cured by saturation in lime water. the pre-dried samples have been removed from the curing tank one day before testing in order to let the surface dry out. wet samples were stored in lime-water tank until the experiment took place. these samples have been kept wet between the subsequent testing cycles by treating the surfaces with wet sponge. both test series were conducted at different ages of the concrete specimens. thus, differences in conditions between the tests on the two specimen sets went from three sources: i) the time period between the specimen removal from the storage tank and the testing, ii) the existence of the wet sponge-based treatment of sample surfaces before the (resistivity) test, and iii) the age of concrete specimens. however, based on the nature of results of the conducted tests, it is not possible to precisely distinguish the effect of the individual source. thus, the analysis is limited to the overall difference between the two specimen sets. electrical resistivity measurements fig. 5a) illustrates the overall pre-dried samples performance in terms of the difference between the resistivity value in the central (cracked) part of the specimen and the average of its values in its side (intact) parts, , versus the relative effective -10 10 30 50 0.00 0.20 0.40 0.60 0.80 1.00 e l. r e si st iv it y d if fe re n ce   [k  cm ] relative effective crack length eff [-] pre-dried surface samples t1a t1b t1c t63a t63b t63c t69a t69b t69c -10 10 30 50 0.00 0.20 0.40 0.60 0.80 1.00 e l. r e si st iv it y d if fe re n ce   [k  cm ] relative effective crack length eff [-] wet surface samples t31a t31b t31c t39a t39b t39c t86a t86b t86c t88a t88b t88c 0 40 80 120 160 0.00 0.20 0.40 0.60 0.80 1.00 u lt ra so u n d p a ss in g t im e t [ s] relative effective crack length eff [-] pre-dried surface samples t1a t1b t1c t63a t63b t63c t69a t69b t69c 0 40 80 120 160 0.00 0.20 0.40 0.60 0.80 1.00 u ltr a so u n d p a ss in g t im e t [ s] relative effective crack length eff [-] wet surface samples t31a t31b t31c t39a t39b t39c t86a t86b t86c t88a t88b t88c t v. veselý et alii, frattura ed integrità strutturale, 30 (2014) 263-272; doi: 10.3221/igf-esis.30.33 270 crack length, eff. note that results from measurements in the notch level (n) are displayed. a rather disordered relationship with a large scatter was observed; however, a general trend is visible – the longer was the notch the higher was the electrical resistivity difference at the affected area, moreover, the  value increases (in average) with increasing relative effective crack length. it is believed that the crack development created higher porosity (voids, (empty) microcracks) in the fracture process zone thus creating a stronger barrier for electric current to flow. it was expected that the response of the wet specimens would be opposite to the pre-dried surface cases because microcracks that are created during the fracture process (expected to be filled with water) may open a path for ionic movement and thus decrease the resistivity. however, no significant relation between the resistivity difference and effective crack length was observed in the case of wet specimens; the  values remain close to constant with the increase of the crack length. the graph is shown on the fig. 5b). this phenomenon was observed probably due to too narrow (micro-)cracks in the fracture process zone to influence the electrical characteristics of the investigated concrete. however, the  values of the wet surface samples were sensitive to the length of the initial notch, a0; the resistivity difference values corresponding to different notch lengths, as well as their scatter, increased with the increase of relative notch length 0. in spite of the fact that the difference in electrical response between the pre-dried and the wet surface specimens was rather obvious, the values of moisture content determined after testing via standard technique (from difference of current weight and weight after drying at 110°c) were almost the same, see the last column in tab. 1. mean value of moisture content for the pre-dried and the wet surface samples was 6.61% and 7.74%, respectively5. note that more considerable difference was expected. ultrasonic measurements the ultrasound pulse passing time, t, contrary to the above-mentioned analysis on , is showing notable correlation with the effective crack length, eff, on the pre-dried as well as the wet samples; an increasing trend is obvious, see figs. 6a) and 6b) respectively. the distinction in t values for different notch lengths, a0, has not been observed clearly compared to e.g. the resistivity difference of wet surface sample case (fig. 5b)). however, again, the scatter in measured values increased with increasing notch length. summarizing remarks it is worth emphasizing the following interesting findings: – a rather significant correlation of the resistivity measurements and the effective crack length was observed only in the case of pre-dried surface specimens and not in the case of the wet surface ones. – the relationship between the notch size and resistivity differences was observed both in the case of pre-dried as well as wet surface specimens. – in contrast, the ultrasonic passing time has correlated significantly with crack propagation in both cases. thus, the decrease in the velocity of waves originated by the ultrasound pulse well indicated the ongoing fracture. – the reason for no correlation of the resistivity difference and the crack length in the case of wet surface samples may be related to too small width of the propagating crack. it is proved that only cracks wider than 30 m allow chlorides to penetrate faster through concrete [15]. similar phenomenon might have been present for water in voids and micro-cracks in these tests. alternatively to the graphs in figs. 5 and 6, it might be convenient (e.g. in future physical analyses) to display the dependences of the measured physical properties as functions of the transverse distance between the current effective crack tip and the measuring position. this distance is marked as lm here (see fig. 3). its relative value, m, i.e. lm/w, is used on horizontal axis in alternative interpretations of findings shown above. in this interpretation the dependences get opposite trends, compare fig. 7 and fig. 5b) or fig. 8 and fig. 6a). conclusions and outlooks he paper presents results of sequential fracture tests rather uniquely complemented with nondestructive measurements allowing studying the effect of crack growth on the concrete electrical resistivity and ultrasonic pulse passing time. the (changes in) resistivity values were considered as a measure for the ability of concrete to 5 omitting far-off measurements for specimen t86 marked with asterisk in tab. 1. t v. veselý et alii, frattura ed integrità strutturale, 30 (2014) 263-272; doi: 10.3221/igf-esis.30.33 271 resist penetration of aggressive species. the ultrasonic passing time values were considered as measure of damage in the area of interest. figure 7: relationship between the electrical resistivity difference, , and the relative transverse distance between the effective crack tip and the measuring location, m, for the wet surface samples evaluated at the notch (n) level. figure 8: a) relationship between the ultrasound pulse passing time, t, and the relative transverse distance between the effective crack tip and the measuring location, m, for the pre-dried surface samples evaluated at the notch (n) level. the study showed that the ultrasound passing time increased with the crack growth, which indicated the escalation of damage in the fracture process zone. the results of ultrasonic measurements were consistent regardless to moisture treatment of the specimen surfaces (wet or pre-dried). the studied effect of the notch length was not captured in this measurement too. on the other hand, the results of concrete resistivity depended on the moisture treatment of the specimen surface, at least partially. the length of the effective crack seems to affect resistivity only in the case of the pre-dried surface specimens. the longer was the crack the larger was the difference between resistances in the cracked and uncracked areas. the crack length had no influence on the change of the concrete resistivity when the wet surface specimens were tested. a hypothesis is made that the concrete resistivity of wet surface samples can be influenced only with cracks of some minimal width, in the similar manner as diffusion of chlorides through crack is influenced by its opening. the next part of the ongoing experimental campaign shall consider both cases of the surface treatment (pre-dried as well as wet surface) to validate the presented results and the suggested hypothesis. thus, the crack width shall be more precisely investigated during the subsequent loading−unloading cycles of the fracture test. since the crack width is the crucial parameter for validating the hypothesis, it will be useful to have its numerical estimation as well. linear elastic fracture mechanics will be employed for estimation of the effective crack width in the first step, then possibly some nonlinear approaches might be used. deeper analysis taking into account also the other considered representations of the crack length (calculated from the unloading, reloading and secant compliance) as well as the measured data from the other than only the notch (n) level of the specimens is planned. acknowledgements inancial support from všb-technical university of ostrava by means of the czech ministry of education, youth and sports through the institutional support for conceptual development of science, research and innovations for the year 2014 is gratefully acknowledged. references [1] lindquist, w.d., darwin, d., browning j, miller, g.g., effect of cracking on chloride content in concrete bridge decks, aci mater j, 103(6) (2006) 467–473. -10 10 30 50 -0.90 -0.70 -0.50 -0.30 -0.10 0.10 e l. re si st iv ity d if fe re n ce   [k  cm ] relative part of ligament m [-] wet surface samples t31a t31b t31c t39a t39b t39c t86a t86b t86c t88a t88b t88c f v. veselý et alii, frattura ed integrità strutturale, 30 (2014) 263-272; doi: 10.3221/igf-esis.30.33 272 [2] fanous, f., wu, h., performance of coated reinforcing bars in cracked bridge decks, j bridge eng, 10(3) (2005) 255– 261, doi: 10.1061/(asce)1084-0702(2005)10:3(255). [3] seitl, s., knésl, z, šimonová, h., keršner, z., fatigue crack growth in cement based composites: experimental aspects, in: proceedings of the 3rd international symposium on life-cycle civil engineering – life-cycle and sustainability of civil infrastructure systems, ialcce (2012) 1314–1317. [4] karihaloo, b.l., fracture mechanics and structural concrete, longman, new york, (1995). [5] shah, s.p., swartz, s.e., ouyang, c., fracture mechanics of structural concrete: applications of fracture mechanics to concrete, rock, and other quasi-brittle materials, wiley, new york (1995). [6] bažant, z.p., planas, j., fracture and size effect in concrete and other quasibrittle materials, crc press, boca raton (1998). [7] konečný, p., tikalsky, p.j., tepke, d.g., performance evaluation of concrete bridge deck affected by chloride ingress, transportation research record, 2028 (2007) 3–8, doi: 10.3141/2028-01. [8] bentz, d.p.,garboczi, e.j., lu, y., martys, n., sakulich, a.r., weiss, w.j., modeling of the influence of transverse cracking on chloride penetration into concrete, cement & concrete composites, 38 (2013) 65–74. [9] bentz, d.p., clifton, j.r., snyder, k.a., predicting service life of chloride-exposed steel-reinforced concrete, concr int, 18(12) (1996) 41–47. [10] vořechovská, d., teplý, b., chromá, m., probabilistic assessment of concrete structure durability under reinforcement corrosion attack, j perform constr facil, 24(6) (2010) 571–579. [11] morris, w., moreno, e.i. sagues, a.a., practical evaluation of resistivity of concrete in test cylinders using a wenner array probe, cement and concrete research, 26(12) (1996) 1779–1787. [12] ghosh, p., hammond, a., tikalsky, p.j., prediction of equivalent steady state chloride diffusion coefficients, aci mater j, 108(1) (2011) 88–94. [13] veselý, v., konečný, p., lehner, p., pařenica, p., hurta, j., žídek, l., investigation of fracture and electrical resistivity parameters of cementitious composite for their utilization in deterioration models, key eng mat, vols. 577–578 (2014) 265–268, doi:10.4028/www.scientific.net/kem.577-578.265. [14] konečný, p., veselý, v., lehner, p., pieszka, d., žídek, l., investigation of selected physical parameters of cementitious composite during sequential fracture test, advanced materials research, 969 (2014) 228–233, doi:10.4028/www.scientific.net/amr.969.228. [15] djerbi, a., bonnet, s., khelidj, a., baroghel-bouny, v., influence of traversing crack on chloride diffusion into concrete, cement and concrete research, 38(6) (2008) 877–883. shot peening processes to obtain nanocrystalline surfaces in metal alloys: j. toribio et alii, frattura ed integrità strutturale, 41 (2017) 139-142; doi: 10.3221/igf-esis.41.19 139 focused on crack tip fields crack tip field in circumferentially-cracked round bar (ccrb) in tension affected by loss of axial symmetry j. toribio, b. gonzález, j.c. matos fracture and structural integrity research group (fsirg), university of salamanca (usal) e.p.s., campus viriato, avda. requejo 33, 49022 zamora, spain toribio@usal.es, bgonzalez@usal.es, jcmatos@usal.es abstract. in this paper, the stress intensity factor (sif) is computed in a circumferentially-cracked round bar (ccrb) subjected to tensile loading, considering that the resistant ligament is circular and exhibits certain eccentricity in relation to the cylinder axis. the computation was performed by means of the finite element method (fem) using a three dimensional (3d) model and the j-integral, the analyzed variable being the eccentricity of the circular ligament. results show that the sif is higher at the deepest point of the crack and that an increase of eccentricity (in relation to the bar axis) raises the difference between the sif values along the crack front. from a certain value of the misalignment a bending effect appears, so that the crack remains closed in the area near the point of lower depth. keywords. stress intensity factor; finite element method; j-integral; circumferentially-cracked round bar; eccentricity of circular ligament. citation: toribio, j., gonzález, b., matos, j.c., crack tip field in circumferentiallycracked round bar (ccrb) in tension affected by loss of axial symmetry, frattura ed integrità strutturale, 41 (2017) 139-142. received: 28.02.2017 accepted: 15.04.2017 published: 01.07.2017 copyright: © 2017 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. introduction ylindrical samples with annular cracks exhibit numerous advantages when compared to the standard specimens recommended by the astm e399 standard [1]: (i) they are easy to machine and thus cheaper; (ii) they need less amount of material to guarantee the plane strain condition because their circular geometry increases the constraint, thereby assuring a plane strain state with independence of their size; (iii); the annular crack does not end in a plane stress region. these specimens also exhibit some disadvantages such as the frequent appearance of non-symmetric crack advance [2], thus producing eccentricity of the circular ligament in relation to the bar axis. this phenomenon may be caused by slight non-symmetries regarding the sample, the grips or the testing machine, as well as non-uniform material properties [3], residual stress effects, etc. diverse sif solutions were published in the matter of a circumferentially-cracked round bar (ccrb) subjected to tensile loading, for both symmetric [4-6] and non-symmetric cracks [3,7] where the ligament eccentricity produces additional bending stresses. these specimens have been successfully used to obtain the fracture toughness of different materials [2,3,8,9] where the eccentricity increases the scattering of the measurements [3]. they have been used to evaluate fatigue c j. toribio et alii, frattura ed integrità strutturale, 41 (2017) 139-142; doi: 10.3221/igf-esis.41.19 140 crack propagation [9] and stress corrosion cracking (scc) phenomena [10]. with regard to fatigue, the eccentricity reduces the time to reach the critical situation [11,12] and increasing the instability [13]. in spite of the afore-said references, there is a lack of information in the scientific literature regarding sif values in points of the crack different from the central one. this paper tries to fill this gap by providing solutions along the crack front. numerical modeling he finite element method (fem) together with the msc.marc code was employed to obtain the sif in cylindrical bars with a non-symmetric external annular crack under tensile loading. the resistant ligament, characterized as a circle, is not centered in relation to the bar axis, so a quarter of the solid was modeled (fig. 1) with the adequate boundary conditions. figure 1: 3d mesh of the bar with a non-symmetric annular crack. isoparametric hexahedral elements with 20 nodes were used in the computations, and the middle nodes of the first core surrounding the crack tip were shifted to the quarter-point position to reproduce the r–1/2 singularity. in addition, a mesh sensitivity analysis was performed. figure 2: detail of the finite element mesh in the vicinity of the crack tip. the mode i (opening) sif ki was computed from the j integral by using the expression (for plane strain conditions), i ν = − 21 ej k (1) where e is the young’s modulus of the material and ν the poisson coefficient. the geometry of the cracked bar was characterized my means of the following parameters: bar diameter d, maximum crack depth amax, minimum crack depth amin, ligament diameter d, = − −max mind d a a (2) and eccentricity, ε, ε − = max min 2 a a (3) t j. toribio et alii, frattura ed integrità strutturale, 41 (2017) 139-142; doi: 10.3221/igf-esis.41.19 141 the point a on the crack front is associated with the maximum crack depth amax and the point b with the minimum crack depth amin (fig. 3). figure 3: cracked surface. numerical results ig. 4 shows the dimensionless sif ki/σ(πd)1/2 along the crack front (characterizing its points by means of the angle θ) for d/d=0.4 and for ε/d from 0 (symmetric case) to 0.200 with increments of 0.025 and fig. 5 the axial displacement uz on the deformed profile (showing the initial profile in black color). 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 0 30 60 90 120 150 180 θ (º)a b k i/σ (π d )1 /2 ε/d figure 4: dimensionless sif along the crack front for d/d=0.4 and ε/d from 0 to 0.200 with increments of 0.025. (a) (b) (c) (d) figure 5: displacement uz for d/d=0.4: (a) ε/d=0; (b) ε/d=0.025; (c) ε/d=0.050; (d) ε/d=0.125. d d amin a b amax f a b θ j. toribio et alii, frattura ed integrità strutturale, 41 (2017) 139-142; doi: 10.3221/igf-esis.41.19 142 for non-symmetric cracks, the eccentricity of the resistant ligament makes the sif vary along the crack front, increasing from point b to point a. the increase of eccentricity raises the differences between sifs at different points of the crack, thereby increasing even more the eccentricity itself when the cracks propagate by fatigue or scc. the tensile loading applied at the bar ends generates a bending stress caused by the eccentricity of the ligament, thus provoking a rotation in the sample. from ε/d=0.050 (fig. 5c) partial contact appears between the crack faces, thereby reducing the trend of sif increment with the eccentricity and for ε/d=0.125 (fig. 5d) full contact takes place, so that the crack remains fully closed in the zone associated with the tip b (where the sif is equal to zero). conclusions s the eccentricity of the ligament increases, so does the difference between the sif values along the crack front. from a certain value of the misalignment, as a consequence of the bending effect, the crack remains closed in the area near the point of lower depth b at which the sif is equal to zero. acknowledgements he authors wish to acknowledge the financial support provided by the following spanish institutions: micyt (grant mat2002-01831), mec (grant bia2005-08965), micinn (grant bia2008-06810), mineco (grant bia2011-27870) and jcyl (grants sa067a05, sa111a07 and sa039a08). references [1] standard test method for linear-elastic plane-strain fracture toughness kic of metallic materials (astm e399), astm international, west conshohocken, (2012). [2] stark, h.l., ibrahim, r.n., estimating fracture toughness from small specimens, eng. fract. mech., 25 (1986) 395– 401. doi: 10.1016/0013-7944(86)90253-5. [3] ibrahim, r.n., kotousov, a., eccentricity correction for the evaluation of fracture toughness from cylindrical notched test small specimens, eng. fract. mech., 64 (1999) 49–58. doi: 10.1016/s0013-7944(99)00056-9. [4] benthem, j.p., koiter, w.t., asymptotic approximations to crack problems, in: g.c. sih (ed.), method of analysis and solutions of crack problems, noordhoft international publishing, croningen, (1973) 131–178. [5] gray, t.g.f., convenient closed form stress intensity factors for common crack configurations, int. j. fract., 13 (1977) 65–75. doi: 10.1007/bf00040876. [6] dieter, g.e., mechanical metallurgy si edition, mcgraw-hill, singapore, (1988). [7] mattheck, c., morawietz, p., munz, d., stress intensity factors of sickle-shaped cracks in cylindrical bars, int. j. fatigue, 7 (1985) 45–47. doi: 10.1016/0142-1123(85)90007-6. [8] ibrahim, r.n., stark, h.l., establishing k1c from eccentrically fatigue cracked small circumferentially grooved cylindrical specimens, int. j. fract., 44 (1990) 179–188. doi: 10.1007/bf00035515. [9] neelakantha, v.l., jayaraju, t., naik, p., kumar, d., rajashekar, c.r., kumar, m., determination of fracture toughness and fatigue crack growth rate using circumferentially cracked round bar specimens of al2014t651, aerosp. sci. tech., 47 (2015) 92–97. doi: 10.1016/j.ast.2015.09.023. [10] rihan, r., singh raman, r.k., ibrahim, r.n., determination of crack growth rate and threshold for caustic cracking (kiscc) of a cast iron using small circumferential notched tensile (cnt) specimens, mater. sci. eng. a, 425 (2006) 272– 277. doi: 10.1016/j.msea.2006.03.095. [11] zhao, y., kim, i., choi, b.-h., lee, j.-m., variation of the fatigue lifetime with the initial notch geometry of circular notched bar specimens, int. j. fract., 167 (2011) 127–134. doi: 10.1007/s10704-010-9532-3. [12] kim, i., zhao, y., choi, b.-h., lee, j.m., lee, k.-s., lee, j.-m., numerical analysis of asymmetric fatigue crack growth behaviors of circular notched bar specimen resulting from various geometric misalignments, eng. fract. mech., 108 (2013) 50–64. doi: 10.1016/j.engfracmech.2013.04.015. [13] yngvesson, m., eccentric circumferential cracks in cylindrical specimens, int. j. fract., 102 (2000) l9–l14. doi: 10.1023/a:1007623622121. a t microsoft word numero_50_art_43_2618 g.v. seretis et alii, frattura ed integrità strutturale, 50 (2019) 517-525; doi: 10.3221/igf-esis.50.43 517 focused on the research activities of the greek society of experimental mechanics of materials multi-parameter analysis of curing cycle for gnps/glass fabric/ epoxy laminated nanocomposites georgios v. seretis national technical university of athens, school of mechanical engineering, 15780 zografou, athens, greece elvalhalcor s.a., copper tubes division (halcor), 32011, oinofyta, viotia, greece gio.seretis@yahoo.com / gseretis@halcor.com, http://orcid.org/0000-0003-2824-3576 aikaterini k. polyzou, dimitrios e. manolakos, christopher g. provatidis national technical university of athens, school of mechanical engineering, 15780 zografou, athens, greece k.polyzou@gmail.com; manolako@central.ntua.gr; cprovat@central.ntua.gr abstract. in this study, a multi-parameter analysis, using taguchi method for design of experiments, has been conducted to investigate the optimum curing conditions for gnps/e-glass fabric/epoxy laminated nanocomposites. the independent variables in the l25 taguchi orthogonal array were heating rate, curing temperature and curing time, addressing five levels each. tensile and 3-point bending tests were performed for each experiment number (run number) of the taguchi l25. the analysis shown that the most significant parameter for tensile strength is the time and for flexural strength is the temperature. also, it shown that the optimum performance was obtained for temperature values greater than the glass transition temperature tg. keywords. polymer-matrix composites; nanocomposites; graphene nanoplatelets; curing; mechanical testing; multi-parameter analysis. citation: seretis, g.v., polyzou, a.k., manolakos, d.e., provatidis, c.g., multi-parameter analysis of curing cycle for gnps/glass fabric/ epoxy laminated nanocomposites, frattura ed integrità strutturale, 50 (2019) 517-525. received: 19.01.2019 accepted: 22.05.2019 published: 01.10.2019 copyright: © 2019 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. introduction omposites of epoxy matrix are of the most commonly used polymer matrix composites. for this kind of composites several different types of reinforcement have been tested. however, the reinforcing material is not the only significant factor for the final properties of the produced epoxy matrix composites. the curing process, due to the great number of properties it affects or controls [1,2], also plays a key role. for this reason, to accurately control the results of a curing process, it is necessary to understand the effects of all the affecting parameters. therefore, the parameters which are known to affect a curing process, such as curing temperature and time, have been widely investigated [3-10]. for example, the relation between the curing temperature (tcure) and the glass transition temperature (tg) has been found to controls the applied curing mechanism and, therefore, it is of great importance [11]. also, related research works have been focused on alternative curing processes [12-14], such as curing using microwaves. c http://www.gruppofrattura.it/va/50/2618.mp4 g.v. seretis et alii, frattura ed integrità strutturale, 50 (2019) 517-525; doi: 10.3221/igf-esis.50.43 518 taguchi analysis is widely used in the research of composite materials. for example, it is used to investigate the influence of surface treatment on the composites’ performance [15] and the importance of v-ring indenter parameters [16], to determine the optimum machining conditions leading to minimum surface roughness in drilling of gfrp composite [17], to develop multiphase hybrid epoxy matrix composites reinforced with glass-fiber and filled with rice husk particulates [18], etc. analysis of variance (anova) and regression or multiple regression models regularly follow the taguchi method to create an effective prediction model. the commonly used multiple regression models [16,17] are not always able to achieve high accuracy in prediction. therefore, researchers started working on more accurate multiple regression models [19,20]. in this study, a multi-parameter analysis, using taguchi method for design of experiments, has been conducted to investigate the optimum curing conditions for gnps/e-glass fabric/epoxy laminated nanocomposites. the independent variables in the l25 taguchi orthogonal array were heating rate, curing temperature and curing time, addressing five levels each. tensile and 3-point bending tests were performed for each experiment number (run number) of the taguchi l25. according to the analysis of variance, the significant parameter for tensile performance was the curing time and for flexural performance was the curing temperature, at a 95% confidence level. the full quadratic regression model was used to predict the tensile response of the nanocomposites, since the respective main effects plots were more linear or shown clear trends. on the other hand, for the flexural performance, where the respective main effects plots neither were linear nor shown clear trends, the poisson regression model was used to achieve high accuracy in prediction. the r2 of the regression models used was greater than 90% for the prediction of both tensile and flexural values. experimental protocol materials he matrix material used for the nanocomposite specimens was the low-viscosity araldite gy 783 epoxy resin together with the low-viscosity, phenol free, modified cycloaliphatic polyamine hardener. the glass transition temperature (tg) was 100°c and the gel time for the specific matrix composition at 20°c and 65% relative humidity (rh), conditioning requirements which were obeyed during the preparation of the nanocomposites laminates, was 35 min. woven e-glass fabric of 282 g/m2 density was used for matrix reinforcement, as presented in fig.1. table 1 presents the characteristics of the fabric used. the warp direction is the enhanced one, as can be seen in, and therefore it was the main weave direction. thus, the laminae orientations in the stacking sequence of the composites will be based on the warp direction. graphene nanoplatelets (gnps) by alfa aesar of surface area (s.a.) 500 m2/g were also used as filler material. figure 1: the woven e-glass fabric used in positioning angle (layer orientation) 0º. characteristics warp weft fiber description glass ec11 204 fiber glass ec11 204 fiber thread count (ends/cm) 8 6 weight distribution (%) 57 43 table 1: e-glass fabric’s characteristics. preparation of e-glass fabric/epoxy laminated composites to prepare the gnps-reinforced matrix, weighed amount of pre-dried graphene nanoplatelets were stirred gently into the epoxy resin using a laboratory mixer for mechanical stirring for a process time of 25 min at 200 rpm, to ensure homogeneity of the suspension [22]. weighed amount of hardener was added into the gnps reinforced epoxy resin mixture at the manut g.v. seretis et alii, frattura ed integrità strutturale, 50 (2019) 517-525; doi: 10.3221/igf-esis.50.43 519 facturer recommended resin/hardener proportion, which was a 100:50 by weight ratio, and stirred gently using a laboratory mixer for mechanical stirring for a process time of 5 min at 200 rpm. subsequently, the matrix mixture was coated and handrolled on e-glass fabrics in layer sequence under constant stirring [22-25]. for each hand lay-up procedure, four layers of e-glass fabric were employed in [0˚/45˚/-45˚/0˚]t sequence. the gnps w.t. contents used for ud laminates reinforcement were 5%. the selection of the gnps content was made based on literature on the content that provides the best performance of the specific nanocomposites [22]. before the first layer coating, the surface on which the specimens were produced was covered by release paste wax. the hand lay-up procedure applied is well-known and has been presented in explosive view mode in other published works [22,23]. to achieve a 40±1% by volume epoxy proportion in all specimens, both the fabric and the matrix mixture used for coating were weighed before each hand lay-up process and after solidification. curing cycle all specimens left in ambient temperature for 6 hours before the curing conditions of the taguchi design of experiments were applied. therefore, the complete curing cycle applied is presented in fig.2, where parameter a, t1 and h1 represent the heating rate [°c/min], the temperature of the first curing step [°c] and the duration of the first curing step [h], respectively. the selected values for each parameter under study (i.e. the design of experiment levels) can be found in table 2. figure 2: the curing cycle applied with the parameters of the taguchi design of experiments noted. control factor level 1 2 3 4 5 a: heating rate [oc/min] 1 2 3 4 5 b: temperature [oc] 50 80 100 120 140 c: time [h] 2 4 6 8 10 table 2: design of experiments (doe) factors and their levels. the curing temperature (tcure) can be either higher or lower of the glass transition temperature (tg) [3-5,22-25]. when tcure>tg, the reaction proceeds rapidly at a rate driven by chemical kinetics. when tcure=tg, vitrification takes place (i.e., material solidifies). finally, when tcure<tg, the reaction rate decelerates and becomes diffusion-controlled. to include all these mechanisms in the taguchi design of experiments, apart from the tg temperature, two different temperatures both under and over tg were selected as presented in table 2. the dimensions of each specimen which underwent 3-point bending tests were 93.6 × 12.7 ×1.1 mm, according to the astm d790-03 test method. the specimens which underwent tensile test had a total size of 102 × 6 × 1.1 mm in accordance with astm d3039/3039m. all specimens were cut at their testing dimensions using a struers discotom-2 along with a 40a25 cut-off wheel. to evaluate if tabs were needed on the holding regions of the specimens, the theoretical tab limits were marked on the specimens, as indicated from the above astm standard method [22,23]. since the failure occurred into the theoretical control region no tabs are recommended by the astm standard used. for each experiment number (run number) of the taguchi design of experiments, five specimens were prepared and underwent each test (five specimens for each tensile and five for each flexural test). experimental set-up and tests an instron 4482 test machine of 100 kn capacity was used for the both tensile and 3-point bending tests. in accordance with the astm standard methods d790-03 and d3039/3039m, all tests were performed in a standard laboratory atmo g.v. seretis et alii, frattura ed integrità strutturale, 50 (2019) 517-525; doi: 10.3221/igf-esis.50.43 520 sphere (23±1˚c and 50±5% relative humidity). test conditioning was kept constant for 6 hours before each test. to meet the test method’s span-to-depth specification, the support span was set at 52 mm for the flexural tests. the recommended from the astm methods test speed of 2 mm/min was applied on both tensile and 3-point bending tests. taguchi design of experiments taguchi’s method uses a special design of orthogonal arrays to study the entire process parameter space with just a small number of experiments. using taguchi’s method the number of experiments to evaluate the influence of control parameters on certain quality properties or characteristics is considerably reduced as compared to a full factorial approach [23,24]. there are three ways of transformation to calculate the loss function, depending on the desired characteristic of the measured value. the characteristic of the desired value can either be the-lower-the-better, the-higher-the-better or thenominal-the better. the loss function of the ‘‘the-higher-the-better’’ quality characteristic (yk), which was used for this study, with m as the mean of the target quality parameter is calculated as shown in eq.(1) where lij is the loss function of the ith performance characteristic in the jth experiment [23,24]. 𝐿 ∑ (1) in the taguchi method, the s/n ratio nij for the ith performance characteristic in the jth experiment, which can be calculated using eq.(2), is used to determine the deviation of the performance characteristic from the desired [23,24]: 𝑛 10log 𝐿 (2) regardless of the category of the performance characteristic, a larger s/n ratio indicates a performance of a better quality. therefore, the optimal level of the process parameters is the level with the highest s/n ratio. the selection of control factors is the most important step in a design of experiments. it is known that heating rate (a), temperature (t1), time (t1) are three factors which affect the mechanical behavior of an epoxy matrix and, consequently, of a laminated composite [23,24]. therefore, it is expected that these three factors also affect the mechanical behavior in the case of epoxy matrix nanocomposites. in this work, the impact of these three factors on tensile and flexural strength of gnps/glass fabric/epoxy laminated nanocomposites is studied using an l25 orthogonal array design. the selected levels of the three control factors are presented in table 2. analysis of variance (anova) nalysis of variance (anova) is a statistical tool which examines the hypothesis that the means of two or more populations are equal and, subsequently, it evaluates the significance of one or more factors, by comparing the response variable means at the different factor levels. the significant factors for both tensile and flexural performance were temperature and time in this study, at 95% confidence level (see tables 3 and 4). specifically, the tensile performance is mostly affected by curing time (31.18%). on the other hand, the flexural performance is mostly affected by curing temperature (32.67%) and secondarily by curing time (18.32%). the main effects plot for the main effect terms in ultimate tensile strength (uts) and flexural strength for factors a, t1, and t1 are shown in figs.3 and 4, respectively. additional tests were conducted to confirm the results of the above analysis (see tables 5 and 6). the error achieved was lower than 1% in both cases. the optimal values can be predicted using eq.(3) [23,24]. 𝑛 𝑛 ∑ 𝑛 𝑛 (3) where: nm is the total mean of the response (uts and flexural strength, respectively) and characteristic under consideration; ni is the mean values at the optimum level and q is the number of control factors that significantly affects curing process of composite. results and discussion the main effects plot for the main effect terms in uts for factors a, t1, h1 are shown in fig.3. from the main effect plots, it has been observed that the uts of the composite significantly increase for temperature increase from 50 °c to 80 °c. temperature increase up to 120°c does not cause any change in the tensile performance, while further increase again increases a g.v. seretis et alii, frattura ed integrità strutturale, 50 (2019) 517-525; doi: 10.3221/igf-esis.50.43 521 figure 3: main effect plots for uts for a, t1 and h1 factors. figure 4: main effect plots for flexural strength for a, t1 and h1 factors. source df sum of squares mean square f-value p value c (%) a: heating rate [oc/min] 4 661.7 165.4 0.51 0.73 9.23 b: temperature [oc] 4 423,2 105,8 0.31 0.865 5.9 c: time [h] 4 2235 558.6 2.26 0.098 31.18 table 3: anova results for tensile tests without interaction, * significant at 95% confidence level. source df sum of squares mean square f-value p value c (%) a: heating rate [oc/min] 4 2644 661 0.54 0.711 9.68 b: temperature [oc] 4 8925 2231.2 2.43 0.082 32.67 c: time [h] 4 5004 1251 1.12 0.374 18.32 table 4: anova results for flexural tests without interaction, * significant at 95% confidence level. parameter optimal parameters a3b5c1 experimental predicted uts (mpa) 214.65 218.848 error % 1.95 % table 5: confirmation table for optimum tensile performance. g.v. seretis et alii, frattura ed integrità strutturale, 50 (2019) 517-525; doi: 10.3221/igf-esis.50.43 522 parameter optimal parameters a2b5c1 experimental predicted flexural strength (mpa) 285 278.007 error % 2.45 % table 6: confirmation table for optimum flexural performance. the tensile performance of the nanocomposites. it seems that the nanofillers act like cooling points within the epoxy matrix, negating in this manner the previously reported negative effect of temperature increase on e-glass fabric/ epoxy composite specimens’ performance. the heating rate, when it increases from 1°c/min to 2°c/min, results in a slight tensile increase, while greater increase of its value tend to decrease the tensile performance of the material. specifically, for heating rate values ranging from 2°c/min to 3°c/min a significant performance drop can be observed. subsequently, for heating rate value increase up to 4°c/min the tensile performance slightly increases and for further increase of a it decreases again. overall, for heating rate values greater than 2οc/min the uts values are considerably low. the curing time increase up to 6 hours leads to a consequent significant performance drop. however, for further curing time increase, up to 10 hours, the tensile performance increases again, overpassing the performance that corresponds to a curing time equal to 2 hours. the main effects plot for the main effect terms in flexural strength for factors a, t1, and h1 are shown in fig.4. the heating rate increase leads to an initial flexural performance increase, for heating rate value increase from 1°c/min to 2°c/min, and subsequently, for further increase of the heating rate value, to a flexural performance drop. slight curing temperature increase, i.e. from 50°c to 80°c, dramatically decrease the flexural strength of the material. further temperature increase causes a consequent increase in flexural performance. a progressive increase of the curing time significantly decreases the flexural strength of the material. multiple regression analysis he above analysis was followed by a regression analysis, which was applied to create a model for prediction of the performance of the nanocomposites as regards both tensile and flexural performance. the commonly used full quadratic regression model, involving only the main factors as they occurred from the anova analysis, achieved significantly low prediction accuracy in the case of the nanocomposite materials (about 62%). due to the low accuracy of this regression model led to the necessity for a more leviable and accurate regression model. therefore, a poisson regression model was used to improve the prediction accuracy for the flexural performance and the full quadratic regression model enhanced with the interaction between the second order terms (modified full quadratic model) was used for tensile performance prediction. the accuracy of these models was 94.9% and 90.99%, respectively. the backwards elimination method was applied again on all the parameters included in the regression. the fout factor for terms removal was selected equal to 4. all three curing process parameters selected were considered as independent variables. therefore, two different regression models were created, i.e. a poisson regression model for the flexural performance prediction and a modified full quadratic regression model for the tensile performance prediction of the nanocomposites. these two regression models are presented in eqs.(4) and (5), respectively. 𝐹𝑙𝑒𝑥𝑢𝑟𝑎𝑙 𝑆𝑡𝑟𝑒𝑛𝑔𝑡ℎ 𝑒 (4) where 𝑌 6.09 4.10 𝑎 0.0054 𝑇 4.703 ℎ 1.105 𝑎 0.001897 𝑇 0.12 ℎ 0.063 𝑎 𝑇 0.841 𝑎 ℎ 0.03293 𝑇 ℎ 0.33 𝑎 0.00001 𝑇 0.0401 ℎ 0.0914 𝑎 ℎ 0.0001 𝑎 𝑇 0.001283 𝑎 ℎ 𝑇 0.01888 𝑎 0.001775 ℎ 0.01132 𝑎 ℎ 𝑇𝑒𝑛𝑠𝑖𝑙𝑒 𝑆𝑡𝑟𝑒𝑛𝑔𝑡ℎ 𝑌 (5) where t g.v. seretis et alii, frattura ed integrità strutturale, 50 (2019) 517-525; doi: 10.3221/igf-esis.50.43 523 𝑌 407 166 𝑎 10.29 𝑇 2.4 ℎ 55.8 𝑎 0.0491 𝑇 19.22 ℎ 11.77 𝑎 𝑇 84.7 𝑎 ℎ 1.399 𝑇 ℎ 2.403 𝑎 𝑇 18.51 𝑎 ℎ 0.0654 𝑎 𝑇 9.31 𝑎 ℎ 0.01051 𝑎 𝑇 1.597 𝑎 ℎ results and discussion fig.5 presents the performance of the modified full quadratic regression model used for the tensile performance prediction. fig.6 presents the performance of the poisson regression model used for the flexural performance prediction. the above results when compared to the respective ones for laminated composites without gnps reinforcement [23], lead to the conclusion that the gnps reinforcement does not affect which is the most significant parameter for both tensile and flexural performance. thus, for the tensile performance of the specific composites, with and without gnps reinforcement, the most significant parameter is the curing time and for the flexural performance the curing temperature. however, in the case of gnps reinforced nanocomposites, the less significant parameter for the tensile performance is temperature, when the respective one for the composites without gnps reinforcement is heating rate [23]. this may be related to the significantly different thermal expansion coefficient between matrix, fibers and graphene nanoparticles [25]. figure 5: experimental and theoretical values of tensile strength (calculated using the modified full quadratic regression model). figure 6: experimental and theoretical values of flexural strength (calculated using the poisson regression model). conclusions nps/woven e-glass fabric/epoxy laminated nanocomposites were produced using a hand lay-up process and underwent tensile and flexural testing according to a l25 taguchi design of experiments. based on the experimental results as well as the subsequent statistical analysis, the following remarks may be drawn: g g.v. seretis et alii, frattura ed integrità strutturale, 50 (2019) 517-525; doi: 10.3221/igf-esis.50.43 524 (a) the most significant parameter for tensile strength is the time and for flexural strength is the temperature. therefore, for slow temperature increase values, i.e. 1-5 °c/min, the effect of the heating rate on both the tensile and the flexural performance of the cured laminated nanocomposites is not considerable. (b) the optimum performance was obtained for temperature values greater than the glass transition temperature tg. it is known that when tcure˃tg, the reaction proceeds rapidly at a rate driven by chemical kinetics. therefore, it is obvious that both tensile and flexural performance of the epoxy matrix laminated nanocomposites is mainly controlled by the chemical kinetics. (c) the full quadratic regression model was used to predict the tensile response of the nanocomposites, since the respective main effects plots were more linear or shown clear trends. on the other hand, for the flexural performance, where the respective main effects plots neither were linear nor shown clear trends, the poisson regression model was used to achieve high accuracy in prediction. references [1] gao, l., zhang, q., guo, j., li, h., wu, j., yang, x., sui, g. (2016). effects of the amine/epoxy stoichiometry on the curing behavior and glass transition temperature of mwcnts-nh2/epoxy nanocomposites, thermochim acta, 639, pp. 98-107. [2] fu, y., zhong, w.h. (2011). cure kinetics behavior of a functionalized graphitic nanofiber modified epoxy resin, thermochim acta, 516, pp. 58–63. [3] ellis, b. (1993). chemistry and technology of epoxy resins, london, new york: blackie academic & professional, an imprint of chapman & hall. [4] wisanrakkit, g., gillham, j.k. (1990). glass transition temperature (tg) as an index of chemical conversion for hightg amine/epoxy system: chemical and diffusion controlled reaction kinetics, j. appl. polymer sci., 41(11-12), pp. 2885–2929. [5] moussa, o., vassilopoulos, a.p., castro, j., keller, t. (2012). time temperature dependence of thermomechanical recovery of cold-curing structural adhesives, int. j. adhes. adhes.,35, pp. 94–101. [6] maljaee, h., ghiassi, b., lourenço, p.b. (2017). effect of synergistic environmental conditions on thermal properties of a cold curing epoxy resin, compos. part b-eng., 113, pp. 152-163. [7] chang, c.y., houang, l.w., chou, t.y. (2006). effect of process variables on the quality of compression resin transfer molding, j. reinf. plast. and comp., 25, pp. 1027-1037. [8] oh, j.h., lee, d.g. (2002). cure cycle for thick glass/epoxy composite laminates, j. comp. mat., 36, pp. 19-44. [9] rai, n., pitchumani, r. (1997). optimal cure cycles for the fabrication of thermosetting matrix composites, polym. compos. 18(4), pp. 566–81. [10] li, m., zhu, q., geubelle, p.h., tucker iii, c.l. (2001). optimal curing for thermoset matrix composites: thermochemical considerations, polym. compos., 22(1), pp. 118–31. [11] moussa, o., vassilopoulos, a.p., keller, t. (2012). effects of low-temperature curing on physical behavior of coldcuring epoxy adhesives in bridge construction, int. j, adhes. adhes. 32, pp. 15–22. [12] mijovic, j., fishbain, a., wijaya, j. (1992). mechanistic modeling of epoxy amine kinetics. 2. comparison of kinetics in thermal and microwave fields, macromolecules, 25, pp. 986–989. [13] kwak, m., robinson, p., bismarck, a., wise, r. (2015). microwave curing of carbon–epoxy composites: penetration depth and material characterization, compos. part a-appl. s., 75, pp. 18–27. [14] johnston, k., pavuluri, s.k., leonard, m.t., desmulliez, m.p.y., arrighi, v. (2015). microwave and thermal curing of an epoxy resin for microelectronic applications, thermochim acta, 616, pp. 100–109. [15] barbosa, a.q., da silva, l.f.m., abenojar, j., figueiredo, m., ochsner, a. (2017). toughness of a brittle epoxy resin reinforced with micro cork particles: effect of size, amount and surface treatment, compos. part b-eng., 114, pp. 299-310. [16] thipprakmas, s. (2010). application of taguchi technique to investigation of geometry and position of v-ring indenter in fine-blanking process, mater. des., 31, pp. 2496-2500. [17] parida, a.k., routara, b.c., bhuyan, r.k. (2015). surface roughness model and parametric optimization in machining of gfrp composite: taguchi and response surface methodology approach, materials today: proceedings, 2, pp. 30653074. [18] rout, a.k., satapathy, a. (2012). study on mechanical and tribo-performance of rice-husk filled glass–epoxy hybrid composites, mater. des. 41, pp. 131-141. g.v. seretis et alii, frattura ed integrità strutturale, 50 (2019) 517-525; doi: 10.3221/igf-esis.50.43 525 [19] guo, h., wang, x., gao, z. (2017). uncertain linear regression model and its application, j. intell. manuf., 28, pp. 559. doi: 10.1007/s10845-014-1022-4 [20] tangjitsitcharoen, s., thesniyom, p., ratanakuakangwan, s. (2017). prediction of surface roughness in ball-end milling process by utilizing dynamic cutting force ratio, j. intell. manuf., 28, pp.13. doi: 10.1007/s10845-014-0958-8 [21] li, h., wang, y., zhao, p., zhang, x., zhou, p. (2015). cutting tool operational reliability prediction based on acoustic emission and logistic regression model, j. intell. manuf. 26(5), pp. 923-931. doi: 10.1007/s10845-014-0941-4 [22] seretis, g.v., kouzilos, g., manolakos, d.e., provatidis, c.g. (2017). on the graphene nanoplatelets reinforcement of hand lay-up glass fabric/epoxy laminated composites, compos. part b-eng. 118, pp. 26-32. [23] seretis, g.v., kouzilos, g., manolakos, d.e., provatidis, c.g. (2018). multi-objective curing cycle optimization for glass fabric/epoxy composites using poisson regression and genetic algorithm, mater. research, doi: 10.1590/1980-5373-mr-2017-0815 [24] seretis, g.v., kouzilos, g., manolakos, d.e., provatidis, c.g. (2018). multi-objective optimization of post-curing process for gnps reinforced glass fabric/epoxy nanocomposite laminae. polym. compos.. doi: 10.1002/pc.24777 [25] seretis, g.v., nitodas, s.f., mimigianni, p.d., kouzilos, g., manolakos, d.e., provatidis, c.g. 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<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> /enu (use these settings to create adobe pdf documents best suited for high-quality prepress printing. created pdf documents can be opened with acrobat and adobe reader 5.0 and later.) >> /namespace [ (adobe) (common) (1.0) ] /othernamespaces [ << /asreaderspreads false /cropimagestoframes true /errorcontrol /warnandcontinue /flattenerignorespreadoverrides false /includeguidesgrids false /includenonprinting false /includeslug false /namespace [ (adobe) (indesign) (4.0) ] /omitplacedbitmaps false /omitplacedeps false /omitplacedpdf false /simulateoverprint /legacy >> << /addbleedmarks false /addcolorbars false /addcropmarks false /addpageinfo false /addregmarks false /convertcolors /converttocmyk /destinationprofilename () /destinationprofileselector /documentcmyk /downsample16bitimages true /flattenerpreset << /presetselector /mediumresolution >> /formelements false /generatestructure false /includebookmarks false /includehyperlinks false /includeinteractive false /includelayers false /includeprofiles false /multimediahandling /useobjectsettings /namespace [ (adobe) (creativesuite) (2.0) ] /pdfxoutputintentprofileselector /documentcmyk /preserveediting true /untaggedcmykhandling /leaveuntagged /untaggedrgbhandling /usedocumentprofile /usedocumentbleed false >> ] >> setdistillerparams << /hwresolution [2400 2400] /pagesize [612.000 792.000] >> setpagedevice microsoft word numero_34_art_63 x. zhengbing et alii, frattura ed integrità strutturale, 34 (2015) 574-579; doi: 10.3221/igf-esis.34.63 574 a comparative study on dynamic mechanical performance of concrete and rock xia zhengbing, zhang kefeng, deng yanfeng, ge fuwen college of architecture and civil engineering, jiangsu city vocational college nantong campus, nantong, jiangsu, 226000, china zhengbxia@163.com abstract. recently, engineering blasting is widely applied in projects such as rock mineral mining, construction of underground cavities and field-leveling excavation. dynamic mechanical performance of rocks has been gradually attached importance both in china and abroad. concrete and rock are two kinds of the most frequently used engineering materials and also frequently used as experimental objects currently. to compare dynamic mechanical performance of these two materials, this study performed dynamic compression test with five different strain rates on concrete and rock using split hopkinson pressure bar (shpb) to obtain basic dynamic mechanical parameters of them and then summarized the relationship of dynamic compressive strength, peak strain and strain rate of two materials. moreover, specific energy absorption is introduced to confirm dynamic damage mechanisms of concrete and rock materials. this work can not only help to improve working efficiency to the largest extent but also ensure the smooth development of engineering, providing rich theoretical guidance for development of related engineering in the future. keywords. concrete; rock; dynamic mechanical performance; shpb. introduction tudies focusing on dynamic mechanical performance of rock materials, a relatively basic branch in rock mechanics, originate from researches on safety protection of atomic energy plant and earthquake engineering [1]. as engineering construction frequently involves rock materials in the last few years, to be specific, national large-scale energy engineering including water and electricity and nuclear power project, transportation including national railway and highway, engineering including blasting excavation and fixed point blasting or facilities establishment including high-level building, bridge, airport pavement and dam all involves dynamic mechanical performance of rock materials under the impact of medium and high strain-load [2], more and more experts and scholars devote themselves to deep study of dynamic mechanical properties of rock materials. compared to statics of rock materials, difficulties encountered by works on dynamics are tougher. in the perspective of mechanical analysis alone, knowledge theories of physics and mathematics are more complicated [3]. consequently, research on mechanics of rock materials has still remained at immature stage, and what is worse, some related areas are just started. concrete and rock are two kinds of the most commonly seen materials among rock materials which are usually combined used in engineering practice, such as airport pavement engineering, ground foundation engineering and mine resource s x. zhengbing et alii, frattura ed integrità strutturale, 34 (2015) 574-579; doi: 10.3221/igf-esis.34.63 575 exploitation. thus to meet the demand of engineering more effectively, the key point lies on the comparative study of mechanical performance of concrete and rock [4]. but scholars tend to focus more on static characteristics of concrete and rock [5, 6] rather than dynamic mechanical performance of them. furthermore, literatures about comparison of mechanical performance of them together are seldom reported though many scholars have carried out related researches. through comparing mechanical performance of concrete and rock under impact load, this study further analyzed their damage mechanism, aiming to offer more theoretical reference for dynamic load carrying of practical structural engineering. overview of mechanical characteristics of rock materials tudy of dynamic mechanical characteristics of rock materials mainly includes three aspects, i.e., dynamic input, analysis of dynamic mechanical characteristics of materials and dynamic respond analysis of structure of rocks [7]. study of structural dynamics has acquired substantial breakthrough, because only one experiment is enough to effectively stimulate all influence factors to reflect actual situation of structure, benefiting from the innovation of experimental instruments and test technology, enhancement of dynamic theory and remarkable results of structural mechanical model experiment. relatively speaking, analysis dynamic input and dynamic mechanical characteristics is weak, as related research is not deep enough and many basic issues are still being explored. an important research direction exists in study of dynamic mechanical performance of rock materials, i.e., correlation rule of strain rate of dynamic performance of materials. a large amount of previous comparative analysis of dynamic and static experimental results of rock materials [8] suggest that, strain rate is closely correlated with performance of materials, and the correlation has recognized by most experts and scholars. however, issues concerning how strain rate impacts performance of materials and what is the rule have not been unified in academic field, and moreover, related research is still remained at impact of material strength, such as impact on dynamic fracture character and deformation characteristics and sensitivity of micro-structure dynamic characteristics of different materials to strain rate. comparative experiment of dynamic mechanical performance of concrete and rock experimental materials oncrete used is ordinary silicate concrete composing of water, ordinary portland cement, coal ash, silica fume, macadam, sand and water reducing agent. detailed proportion is shown in tab. 1. water cement coal ash silica fume macadam sand water reducing agent 180 375 125 25 690 1030 5 table 1: proportion of different components of ordinary silicate concrete (kg/m3). rock used is unweathered natural sandstone taken from qinling mountains with field sampling method. it is mainly composed of quartz and calcite and shows up white color. detailed components are presented in tab. 2. components quartz calcite plagioclase potassium feldspar montmorillonite chlorite illite dolomite content (%) 52 27 8 6 1 2 3 1 table 2: component of sandstone. experimental equipment and method split hopkinson pressure bar (shpb) (diameter 100 mm) made up of three parts, main equipment, energy system and test system is the main equipment for dynamic compression test [9]. sample of concrete and rock is obtained through several professional procedures. first, samples are taken using zs-100 upright core drilling machine, then cut by dq-1 cutting machine. (the machine can be applied in fields like petroleum, geology, metallurgy, coal and exploration; diameter of blade: 450 mm or 500 mm; cutting scope: single blade (diameter 500 mm) can cut cylindrical rock core with a diameter of s c x. zhengbing et alii, frattura ed integrità strutturale, 34 (2015) 574-579; doi: 10.3221/igf-esis.34.63 576 25~180 mm as well as original rock with a size of 180 mm×180 mm×350 mm, while double blade (diameter 450 mm) can cut square (50 mm×50 mm) or rectangle (50 mm×120 mm); power of main motor: 2.2 kilowatt; power of longitudinal motor: 0.75 kilowatt) and finally polished by shm-200 double-end face stone mill. after sampling, a cylinder (diameter 100 mm×50 mm, length-diameter ratio 1:2) is used for experiment combining with literatures related to dynamic compression test performed with shpb. five different levels of impact load are designed for two materials. every impact load is corresponding to one strain rate and every experiment is repeated thrice under the same strain rate. the most reasonable group of data is selected for analysis after comparing experimental data in every group. experimental results tab. 3 and 4 are impact test results of concrete and sandstone obtained under five different strain rates respectively. dynamic damage forms corresponding to two materials is shown in fig. 1 and 2 respectively and they rank based on the strain ratio from low to high. number of samples diameter of reshaper (mm) blow speed (m/s) strain rate  , s-1 dynamic compressive strength ,c df mpa peak strain p ,10-3 specific energy absorption (kj/m3) damage form of sample a1 20 5.29 40.95 76.60 6.30 555.89 blocky fragmentation b1 22 6.40 60.79 84.08 6.45 827.55 blocky fragmentation c1 25 7.53 86.42 95.82 7.14 1174.38 severe fragmentation d1 27 8.29 95.01 107.57 7.21 1344.52 severe fragmentation e1 30 9.99 125.70 130.75 8.60 1558.67 severe fragmentation table 3: shpb test results of concrete. number of samples diameter of reshaper (mm) blow speed (m/s) strain rate  , s-1 dynamic compressive strength ,c df mpa peak strain p , 10-3 specific energy absorption (kj/m3) damage form of sample a2 30 11.0 93.1 173.5 18.32 1059.87 large block b2 33 12.58 123.5 179.4 19.02 2490.25 medium block c2 35 13.49 135.2 203.7 19.48 2830.33 small block d2 40 14.39 154.9 218.9 20.37 3050.47 blocky fragmentation e2 45 15.53 166.0 226.8 21.70 3320.12 severe fragmentation table 4: shpb experiment results of sandstone.   (a1) (b1) (c1) (d1) (e1) figure 1: damage form of concrete samples. x. zhengbing et alii, frattura ed integrità strutturale, 34 (2015) 574-579; doi: 10.3221/igf-esis.34.63 577   (a2) (b2) (c2) (d2) (e2) figure 2: damage form of sandstone samples result analysis it can be seen from fig. 3 described based on tab. 3 and 4 that, dynamic mechanical performance of two materials is closely correlated to strain rate. to be specific, dynamic compressive strength of two materials increases linearly with strain rate; dynamic compressive strength of concrete is lower than sandstone. through linear regression, we can conclude a formula of the relationship of dynamic compressive strength and strain rate of two materials (c stands for concrete, s stands for sandstone and r2 stands for correlation coefficient). 2 , 2 , ( ) 46.40 0.64 0.95067 ( ) 94.56 0.79 0.87914 c d c d f c r f s r             (1) comparing the formula, we can conclude that, dynamic compressive strength of rock varies more obvious as strain rate changes. 240 220 180 140 100 60 40 60 80 100 120 140 160 180 concrete rock strain rate/s-1 80 120 160 200 figure 3: correlation between dynamic compressive strength and strain rate. fig. 4 shows the correlation between peak strain and strain rate of concrete and sandstone under the effect of impact load. it can be observed from the figure that, peak strain of two materials tends to be higher as strain rate increases and moreover, this corresponding relationship is quadratic. formula regarding to the correlation between strain rate and peak strain of two materials can be obtained after linear regression, as follows (c stands for concrete, s stands for sandstone and r2 stands for correlation coefficient). 4 2 2 4 2 2 ( ) 6.60 0.019 2.76 10 0.99756 ( ) 23.37 0.108 5.87 10 0.96554 p p c r s r                         (2) it can be known that, under the effect of impact load, both concrete and rock changes their forms, and the variation degree is positively correlated to strain rate, i.e., peak value increases with the increase of strain rate. x. zhengbing et alii, frattura ed integrità strutturale, 34 (2015) 574-579; doi: 10.3221/igf-esis.34.63 578 figure 4: correlation between peak strain and strain rate. analysis of dynamic damage mechanism t has been found from fig. 1 and 2 that, two materials obviously change their forms under the effect of impact load, and concrete is broken to even blocks no matter strain rate is high or low, while sandstone changes into different forms under impact load with different strain rate, relatively large block under low strain rate and relatively small and powdered block under high strain rate [10]. to present dynamic damage mechanism of two materials more clearly, we use specific energy absorption to describe toughness of materials. in the view of physics, it means the stress wave energy absorbed by sample material in unit volume. fig. 5 demonstrates the correlation between specific energy absorption and strain rate of concrete and sandstone. s p ec if ic e ne rg y a b so rp ti o n /( k j/ m 3 ) figure 5: correlation between specific energy absorption and strain rate. the figure above showed that specific energy absorption increases linearly with the increase of strain rate and the fitted formula is as follows: 2 2 ( ) 94.28 12.20 0.96849 ( ) 1473.45 29.91 0.88962 sea c r sea s r              (3) energy absorption ability of sandstone is more significant than concrete. when strain rate becomes higher, specific energy absorption of sandstone varies more obviously. taking dynamic damage forms of two materials into account, we can summarize that, dynamic forms of materials is correlated to specific energy absorption value. to be specific, dynamic i x. zhengbing et alii, frattura ed integrità strutturale, 34 (2015) 574-579; doi: 10.3221/igf-esis.34.63 579 damage materials varies more significant, leading to smaller pieces, when specific absorption value becomes higher. hence we confirm that, the dynamic damage mechanism of concrete and rock materials is that, two materials are in a dynamic instability state when carrying impact load; large energy absorbed by unit volume of material will result in severe damage. as energy absorption ability is determined by properties and strain rate of material, sandstone has a stronger energy absorption ability than concrete. conclusions hree points can be summarized from the test results. firstly, dynamic mechanical performance of concrete and sandstone is in a close correlation with strain rate and dynamic compressive strength and peak strain is positively correlated to strain rate, i.e., the former increase with the increase of the latter. secondly, dynamic compressive strength of two materials is approximately in linear correlation with strain rate, and peak strain and strain rate has a second order correlation, concrete is more obvious than rock. the last point is that, dynamic damage mechanism of two materials is actually a dynamic instability process produced after absorbed impact load and damage becomes severer as energy increases; the ability of energy absorption is usually determined by characteristics and strain rate of materials. we conclude from the above three points that, concrete is more suitable to be used as building material than rock materials. however, selection of material is affected by multiple factors in the process of engineering construction; therefore, construction material should be chosen according to local conditions. references [1] huang, l.x., development and new achievements of rock dynamics in china, rock and soil mechanics, 2(10) (2011) 2889-2900. [2] hong, l., li, x.b., ma, c.d., yin, s.b., ye, z.y., liao, g.y., study on size effect of rock dynamic strength and strain rate sensitivity, chinese journal of rock mechanics and engineering, 27(3) (2008) 526-533. [3] xu, j.y., li, w.m., fan, f.l., bai, e.l., experimental study on impact properties of carbon fiber reinforced geopolymeric concrete using a shpb, journal of building materials, 13(4) (2010) 66-69. [4] wu. j.h., yu, h.y., li, q., jiang, y.d., experimental study on axial property for concrete with constant surrounding pressure ratio, journal of experimental mechanics, 22(2) (2007) 142-148. [5] zhi, l.p., xu, j.y., liu, j.z., liu, s., study on dynamic mechanical properties of two rocks under shpb experiment. building science research of sichuan, 38(4) (2012) 111-114. [6] jiao, c.j., sun, w., gao, p.z., study of steel fiber reinforced high strength concrete subject to blast loading, engineering mechanics, 25(3) (2008) 158-166. [7] xu, j.y., liu, s., fractal features of marble pieces in impact loading test, rock and soil mechanics, 3(11) (2012) 32253229. [8] shao, m.s., li, l., li, z.x., elastic wave velocity and mechanical properties of sandstone under different water content at longyou grottoes, 29(supplement) (2010) 3514-3518. [9] huang, z.p., tang, c.a., zhao, w., numerical simulation of rockburst failure induced transient unloading under different axial stress, journal of northeastern university, 32(6) (2011) 859-863. [10] li, s.j., geological natural of rock and its deduction for rock mechanics, chinese journal of mechanics and engineering, 28(3) (2009) 433-450. t microsoft word 2202 318 l. reis et alii, frattura ed integrità strutturale, 48 (2019) 318-331; doi: 10.3221/igf-esis.48.31 focused on the “portuguese contributions for structural integrity” damage evaluation under complex fatigue loading conditions l. reis idmec, instituto superior técnico, universidade de lisboa, av. rovisco pais, 1, 1049-001 lisbon, portugal luis.g.reis@tecnico.ulisboa.pt; http://orcid.org/0000-0001-9848-9569 j. caxias, h. soares, p. r. costa instituto superior técnico, universidade de lisboa, av. rovisco pais, 1, 1049-001 lisbon, portugal joaohcaxias@gmail.com, soares.hn@gmail.com, pedro.r.costa@ist.utl.pt v. anes instituto superior de engenharia de lisboa, instituto politécnico de lisboa, rua conselheiro emídio navarro, 1, 19559-007, lisbon, portugal vanes@dem.isel.pt m. freitas idmec, instituto superior técnico, universidade de lisboa, av. rovisco pais, 1, 1049-001 lisbon, portugal manuel.freitas@tecnico.ulisboa.pt abstract. fatigue damage and life assessment of multiaxial loadings is still an issue yet to resolve. many methods have been proposed with promising agreements with the experimental results. however, the performance of such methods is, more than often, purely based on fatigue tests with simple loading conditions. in this work the stress scale factor (ssf) criterion and the virtual cycle counting (vcc) method are used to estimate fatigue life and damage accumulation with two damage accumulation rules. fatigue tests were carried out with three different variable amplitude random loadings, applied to several specimens made from a 42crmo4 high-strength steel. fatigue crack plane measurements were compared with predictions from several critical plane models. the applied methods provided very acceptable results making the ssf package (ssf equivalent stress and virtual cycle counting method) a good method to estimate fatigue life and assessment of the damage accumulation in random fatigue loadings. keywords. multiaxial fatigue; fatigue life; damage accumulation; ssf; critical plane models. citation: reis, l., caxias, j., soares, h., costa, p. r., anes, v., de freitas, m., damage evaluation under complex fatigue loading conditions, frattura ed integrità strutturale, 48 (2019) 318-331. received: 26.09.2018 accepted: 28.11.2018 published: 01.04.2019 copyright: © 2019 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. http://www.gruppofrattura.it/va/48/2202.mp4 l. reis et alii, frattura ed integrità strutturale, 48 (2019) 318-331; doi: 10.3221/igf-esis.48.31 319 introduction n general, fatigue occurs in materials that are subjected to cyclic loadings. the consecutive loading and unloading cycles applied to the component, with amplitudes below the material’s yield stress, will damage the component. cycle by cycle the damage done to the material will accumulate, promoting fatigue crack’s nucleation and growth, degradation of material properties and, ultimately, fracture [1]. unlike static fracture, that occurs with visible plastic deformation, fatigue fracture will occur without warning, except for the cases where a crack is detected and its growth monitored before fracture. depending on the role of a component in a mechanical structure, fatigue failure might have huge consequences, which can include life losses and great financial costs. one example, where mechanical fatigue failure is a major cause of incidents, is the aviation industry where, between 1927 and 1984, more than half of the documented incidents were due to fatigue failure [2]. the damage mechanism in uniaxial fatigue is well understood, and fatigue life is reasonably estimated. however, for multiaxial fatigue, which consists in the combination of stresses acting in two or more axes, is yet to be fully understood. damage mechanisms depending on stress combinations, loading interaction effects, sequence effects, and cyclic plasticity are some of the many variables needed to be considered to assess fatigue damage in multiaxial loading conditions. several studies were already conducted for the referenced parameters and many others related to multiaxial fatigue behavior [3-7]. along the last decades, a great effort was made to correctly model the damage mechanism of multiaxial fatigue. however, most of the proposed criteria found in the literature has serious limitations to its usage. most of the criteria proposed in the literature use parameters based in uniaxial testing data, or parameters that require extensive testing to determine them. moreover, most of these criteria are evaluated using simple block loadings. however, when applied to complex nonproportional loadings, or random loadings, with variable stress amplitude, these models give poor or inconsistent results. when a new criterion is proposed, it should be validated with the most challenging task, which is to estimate fatigue life with non-proportional random loadings with variable stress amplitude. many important authors in the multiaxial fatigue area of research have compared experimental results with many of the created models and with new and improved ones by themselves relating to the parameter of study [8-13]. this work aims to validate the stress scale factor model (ssf) recently proposed and developed by anes et al. [14] under those loading conditions. theoretical background ssf criterion nes et al. [10] proposed a multiaxial fatigue criterion in a form of an equivalent shear stress. this criterion uses a new approach to calculate the stress scale factor. the stress scale factor (ssf) is often used in multiaxial fatigue criterions to convert an axial damage into shear’s damage scale, or conversely. for example, in the von mises criterion, the shear damage is updated into the axial damage scale, by multiplying the shear stress by a factor of √3. in previous works, the authors found that the loading path, the stress amplitude ratio and the stress level, all have influence in fatigue life. therefore, using a constant ssf can lead to poor estimations. using six different loading paths, where five were proportional and one was nonproportional, the authors obtained, through regression of fatigue data, a polynomial function, as shown in eq. (1). 𝑠𝑠𝑓 𝜆, 𝜎 𝑎 𝑏 ∙ 𝜎 𝑐 ∙ 𝜎 𝑑 ∙ 𝜎 𝑓 ∙ 𝜆 𝑔 ∙ 𝜆 ℎ ∙ 𝜆 𝑖 ∙ 𝜆 (1) where a, b, c, d, f, g and h are the polynomial fitting constants and are material dependent. therefore, they need to be estimated with experimental fatigue data from the referenced six different loadings paths and stress levels. the fatigue results will give the s-n trendline for each applied loading path and thought them a corresponding sff value can be calculated. it is using the different sff values for each loading path that the polynomial constants of eq. (1) can be calculated. λ represents the stress amplitude ratio, and it is given by eq. (2). 𝜆 tan (2) where τa and σa are the shear stress amplitude and the axial stress amplitude, respectively. this polynomial function can estimate the ssf for all stress amplitude ratios and stress levels for a given material. i a l. reis et alii, frattura ed integrità strutturale, 48 (2019) 318-331; doi: 10.3221/igf-esis.48.31 320 the ssf equivalent shear stress is given by eq. (3). 𝜏 𝜏 𝑠𝑠𝑓 𝜆, 𝜎 ∙ 𝜎 (3) to estimate fatigue life, the criterion uses the maximum equivalent shear stress as the damage parameter and uses the s-n trend line in pure shear loading conditions, as shown in eq. (4). 𝜏 𝑚𝑎𝑥 𝐴 𝑁 (4) where a and b are the trend line parameters of the s-n curve, obtained in pure shear loading conditions. for variable amplitude loading conditions, anes et al. proposed a block extraction method. in this method, illustrated in fig. 1, every time a τeqv peak greater than the previous peak is identified, a block is defined and a new block starts. this new maximum value of τeqv is the reference equivalent shear stress for the next loading block. the method is applied until all blocks have been identified. figure 1: block extraction method [15]. the number of cycles to failure, for each extracted block, is then calculated, as formulated in eq. (5). 𝜏 , 𝐴 𝑁 , (5) to calculate fatigue life, a cycle counting method must be used to count cycles in each extracted block. then, the damage for each reversal can be determined by the ratio 𝑛 𝑁⁄ and summed with a damage accumulation rule. critical plane models findley findley [16] proposed a stress-based critical plane criterion that determines the critical plane as the one with the maximum damage parameter. its formulation is given by eq. (6). min 𝜏 𝑘𝜎 , (6) where, for each plane θ, τa is the shear stress amplitude, σa,max is the maximum normal stress amplitude, and k is a stress scale factor, that must be determined experimentally. the k parameter varies between 0.2 and 0.3 for ductile materials. brown-miller after an extensive review brown and miller (b-m) concluded that both the octahedral shear strain and the maximum shear strain criteria fail to correctly describe the low-cycle fatigue behaviour. after combined tension and torsion fatigue testing, l. reis et alii, frattura ed integrità strutturale, 48 (2019) 318-331; doi: 10.3221/igf-esis.48.31 321 the authors proposed a strain-based criterion [17], with two strain parameters, depending on the type of fatigue crack nucleation and growth, given in eq. (7) and eq. (8). for a type cracks: ∆ 1 (7) for b type cracks: ∆ 𝑐𝑜𝑛𝑠𝑡. (8) where ∆γ is the shear strain range and g, h and j are material properties that must be determined experimentally. the same authors proposed a simplified formulation for a type cracks, which is given in eq. (9). ∆ 𝑆 ∙ ∆𝜀 (9) where ∆γmax is the maximum shear strain range in a plane θ, ∆εn is the normal strain, in the plane of maximum shear strain, and s is the normal strain effect coefficient and is a material parameter. fatemi-socie fatemi and socie [18] (f-s) prosed a critical plane criterion that, compared to brown-miller’s model, uses a normal strain parameter instead of the normal strain. the damage parameter is calculated using eq. (10). ∆ ∙ 1 𝑘 ∙ , (10) where σn,max is the maximum normal stress in the plane of maximum shear strain amplitude, σy is the monotonic yield stress and k is a sensitivity parameter, that depends on the stress level. when a loading has mean stress, the damage parameter is calculated as shown in eq. (11). max ∆ ∙ 1 𝑘 ∙ (11) where 𝜎 is the normal stress amplitude and 𝜎 is the normal mean stress, both calculated in the plane with the maximum shear strain amplitude. smith-watson-topper smith et al. [19] developed a model, usually referred as the swt model, to account the mean stress effect in uniaxial fatigue loading conditions. later on, socie [20] used a critical plane approach to extend the usage of this model in multiaxial loading conditions. in these conditions, the damage parameter is given by eq. (12). max 𝜎 ∙ ∆ (12) where 𝜎 is the normal stress on a plane θ and ∆𝜀 is the principal strain range in that plane. l. reis et alii, frattura ed integrità strutturale, 48 (2019) 318-331; doi: 10.3221/igf-esis.48.31 322 liu liu’s proposal [21] consists in an energy-based model with two different formulations, depending on fatigue failure’s mode. for tensile failure mode the damage parameter, ∆𝑊 is given by eq. (13), and by eq. (14) for shear failure mode, ∆𝑊 . ∆𝑊 max ∆𝜎 ∙ ∆𝜀 ∆𝜏 ∙ ∆𝛾 (13) where ∆𝜎 is the normal stress range, ∆𝜀 is the normal strain range. ∆τ and ∆γ are the shear stress range and the shear strain range, respectively. ∆𝑊 ∆𝜎 ∙ ∆𝜀 max ∆𝜏 ∙ ∆𝛾 (14) this method uses a virtual strain energy (strain multiplied by stress) concept (vse). the plane θ with the higher vse will be the critical plane. cycle counting as it was described, when a part or material sample is subjected with variable fatigue damage due to variable amplitude loading conditions, it is essential to design a model that can count the cycles in order to estimate the damage output in to the material. in this work three different counting methods were applied, the rainflow, virtual cycle counting and the wang-brown method. they are now briefly described. rainflow counting method matsuiski and endo proposed cycle counting method based on the concept of a raindrop falling from a pagoda roof. the method identifies closed hysteresis loops, in a stress-strain plot, as cycles. a series of rules must be followed to extract cycles from a strain-time or stress-time history [22]. virtual cycle counting (vcc) anes et al. [23] proposed a cycle counting method for variable amplitude multiaxial loadings, based on the ssf equivalent shear stress time evolution. in ssf equivalent shear stress history, the number of virtual cycles is given by adding the maximum absolute value of the peaks and valleys found between two zero stress points. this sum is then divided by the double of the maximum equivalent shear stress in the considered loading block. this method is formulated in eq. (15). 𝑣𝑐𝑐 ∑ ∑ ∙ , (15) the formulation in eq. (15) assumes that the block extraction method was applied. otherwise, the denominator would be the maximum equivalent shear stress in the entire loading spectrum. wang-brown wang and brown [24] proposed a method to estimate fatigue life in variable amplitude loading conditions. in this method, it was proposed a new procedure to count cycles. given a multiaxial strain history, the von mises equivalent strain is calculated, as shown in eq. (16). 𝜀 √ ⎩ ⎨ ⎧ 𝜀 𝜀 𝜀 𝜀 𝜀 𝜀 𝛾 𝛾 𝛾 ⎭ ⎬ ⎫ (16) l. reis et alii, frattura ed integrità strutturale, 48 (2019) 318-331; doi: 10.3221/igf-esis.48.31 323 once the equivalent strain history is obtained, it is identified the maximum peak of the equivalent strain history, 𝜀 , which will be the reference strain. all points prior to the time instant of 𝜀 , 𝑡 , are moved to the end of the history and the equivalent relative strain is then calculated, as shown in eq. (17), resulting in a new strain history, where the first half-cycle goes from 0 to 2. 𝜀 𝑡 𝜀 𝜀 𝑡 𝜀 𝑡 (17) after obtaining the relative strain history, it is performed the extraction of reversals. the extraction of a reversal starts at t0, which once was ta, and stops whenever a descending path is found. when this occurs the extraction of that reversal is resumed after an ascending path, with a higher relative strain, is found. this procedure goes on until the end of the relative strain history. once a reversal is extracted, the equivalent shear strain data points, from this reversal, are removed from the original strain history, and the relative strain is again computed, followed by the extraction method. this procedure is conducted until there are no more reversals to extract. finally, the wang-brown’s damage parameter is calculated for each reversal, as formulated in eq. (18). 𝜀̂ ≡ . ∆ (18) where ∆𝛾 is the maximum shear strain range, found in all the planes of projection, and 𝛿𝜀 is the normal strain excursion calculated between the time interval of ∆𝛾 and in the same plane of ∆𝛾 . 𝜈 is the effective poisson coefficient and 𝑆 is a material constant. the number of reversals to failure, 2𝑁 , is then calculated for every reversal, as formulated in eq. (19). 𝜀̂ ∙ , ∙ 2𝑁 𝜀 ∙ 2𝑁 (19) where 𝜎 and 𝜀 are the fatigue resistance coefficient and the fatigue ductility coefficient, respectively. 𝑏 and 𝑐 refer to the fatigue strength exponent and the fatigue ductility exponent. the damage of a loading block is calculated using a linear damage accumulation rule, as shown in eq. (20). fatigue life, in blocks, is estimated as formulated in eq. (21). 𝐷 ∑# (20) 𝑁 (21) damage accumulation rules in this work, two non-linear damage accumulation models were calculated for comparison, the palmgren-miner’s rule and the morrow’s rule [25]. palmgren proposed damage concept defined by the ratio between the number of cycles performed and the number of cycles to failure at a given load level. using this concept, miner proposed the so called palmgren-miner’s rule. this damage accumulation rule computes fatigue damage block by block and adds the damage linearly, as shown in eq. (22). 𝐷 ∑ (22) where 𝑛 and 𝑁 are the number of cycles in a block and the number of cycles to failure of the ith block, respectively, at a given stress level. 𝑘 is the number of stress levels present in the loading history. the rule states that the damage at failure moment is equal to 1. morrow proposed a nonlinear damage accumulation rule that accounts for load interaction effects in variable amplitude loadings. this rule updates the miner’s damage by a parameter that is computed by the ratio between the maximum stress amplitude at the ith stress level and the maximum normal stress of the loading spectrum, as shown in eq. (23). l. reis et alii, frattura ed integrità strutturale, 48 (2019) 318-331; doi: 10.3221/igf-esis.48.31 324 𝐷 ∑ ∙ (23) where 𝑑 is the materials sensitivity to a variable amplitude loading history. this parameter is determined with cyclic properties of the material [26]. experimental procedure material ollowing up on previous works from other authors, the 42crmo4 steel was selected for analysis. the low alloy steel din 42crmo4 (aisi4140) is typically heat-treated quenching, and tempering. the chromium and molybdenum presence in the 42crmo4 steel makes this alloy particularly suitable to get a variety of strength and ductility combinations, being widely used in automotive components such as crankshafts, front vehicle axles, steering components and hot forging components. in tab. 1 it is shown the chemical composition of the steel and, in tab. 2, it is summarized the monotonic and cyclic properties of the 42crmo4 steel. element c si mn p s cr ni mo cu weigth (%) 0.39 0.17 0.77 0.025 0.020 1.10 0.3 0.16 0.21 table 1: chemical composition of the 42crmo4 steel [26]. propriety abbreviation value yield’s strength, mpa 𝜎 980 young’s modulus, gpa 𝐸 206 ultimate tensile strength, mpa 𝜎 1100 ultimate tensile deformation 𝜀 0.16 hardness hv 362 cyclic yield strength, mpa 𝜎′ 640 strain hardening exponent 𝑛′ 0.12 fatigue strength coefficient, mpa 𝜎′ 1154 fatigue strength exponent b -0.061 fatigue ductility coefficient 𝜀′ 0.18 fatigue ductility exponent c -0.529 table 2: monotonic and cyclic properties of the 42crmo4 steel [26]. specimens several 42crmo4 specimens were fabricated from 25mm diameter rod. the raw material was cut and machined into several specimens, with the dimensions shown in fig. 2. figure 2: dimensions of the specimens (mm). f l. reis et alii, frattura ed integrità strutturale, 48 (2019) 318-331; doi: 10.3221/igf-esis.48.31 325 loading sequences to assess the performance of the ssf criterion with random loadings, two different loading paths where generated. these loading paths’ plots, in the von mises stress space, are illustrated in fig. 3. figure 3: loading spectra with variable amplitude loading, (a) loading case er, (b) loading case fsm. the loading path er (fig. 3(a)) contains 4 branches, separated by 45º, and each branch is a full reversal. to make this loading path a random loading, the sequence in which each branch is applied must be random. two random sequences, er1 and er2, were generated from this loading path. both sequences were generated with the commercial software matlab [27] with the randi() function, resulting in two distinct loading sequences, each one with 100 branches, which are repeated until fracture. the number of times each branch occurs in a sequence is shown in fig. 4. each angle represents a different stress amplitude ratio. figure 4: number of branches per angle. the non-random version of this loading path is designated as enr. fatigue data from random loadings is compared with the non-random results, retrieved from the work of anes et al. [28]. fig. 3(b) depicts the loading case fsm. this loading path is a variable amplitude loading that activates several loading phenomena such as proportionality and non-proportionality. the loading spectrum is a modified version of the well-known falstaff loading spectrum, which has been obtained from the afgrow fracture analysis software [29]. falstaff, which stands for fighter aircraft loading standard for fatigue, released in 1975 [30], represents the load spectrum of the lower wing root panel from a combat aircraft, and contains data from about 200 flights with around 36,000 cycles. a portion of the spectrum was randomly selected, and then modified to fit the purpose of this work. from the retrieved portion of the original spectrum, all points between -0.4 and 0.4 are removed, and a factor of 1.2 is applied to all points, and those which result in an absolute value greater than 1.0 are removed. lastly all points between 0.6 and 0.8 (in absolute value) are again increased by a factor of 1.2; this modification is needed to increase the damage in the specimen. the resulting spectrum, with 1500 data points, is applied to the axial component and, in reversed order, to the torsional component. fractography analysis after failure, specimen’s surfaces were inspected. with the aid of an electronic microscope, the initiation point of the fatigue crack was identified. measured angles were compared with predictions from referenced critical plane models. 0 10 20 30 40 0 π/4 π/2 3π/4n um b er o f o co rr en ce s angle (radians) number of branches/angle er1 er2 l. reis et alii, frattura ed integrità strutturale, 48 (2019) 318-331; doi: 10.3221/igf-esis.48.31 326 damage accumulation ab. 3 summarizes the experimental data for all loading cases. in the first column, it is specified the loading case. in the second column corresponds to que specimen designation. the third and fourth columns contain the maximum value of axial stress and shear stress, respectively, for each specimen. fatigue life is given in blocks in the fifth column, where a block is defined as the spectrum history of the loading sequence. case specimen designation axial [mpa] shear [mpa] nf er1 er1-501 501 290 1243 er1-523 523 303 748 er1-529 529 325 528 er1-546 546 323 626 er2 er2-498 498 288 1425 er2-505 505 292 2986 er2-521 521 301 1232 er2-530 530 307 706 enr* enr-490 490 283 16458 enr-520 520 300 7823 enr-540 540 312 5525 enr-552 552 319 1040 fsm fsm-463 463 267 1955 fsm-488 488 282 1085 fsm-496 496 286 659 fsm-517 517 299 542 fsm-520 520 300 338 fsm-541 541 312 283 fsm-546 546 315 202 table 3: experimental fatigue data for all loading cases. *fatigue data retrieved from the work of anes et al. [28]. fig. 5 shows fatigue life correlation for all the loading cases considered. fatigue life boundary factors of 2 and 3 are plotted with a dashed line and a solid line, respectively. fatigue life was estimated in fig. 5 with the full ssf package (damage criterion, block extraction method, cycle counting method of vcc and miner’s linear damage accumulation rule). figure 5: fatigue life correlation with the ssf method applied with the vcc and miner’s rule (experimental vs estimated). 1e2 1e3 1e4 1e5 1e2 1e3 1e4 1e5 n um b er o f e st im at ed li fe b lo ck s (s sf ) number of experimental life blocks fatigue life ssf (vcc and mner's rule) er1 er2 enr (rept. 25) fsm t l. reis et alii, frattura ed integrità strutturale, 48 (2019) 318-331; doi: 10.3221/igf-esis.48.31 327 in fig. 5 each point corresponds to a specific stress level. all points are within the outer bounds and only 5 points are outside from the inner boundaries. it seems to be an underestimation behaviour of the ssf model that resulted in fatigue life estimates higher than the experimental ones, which is deducted from the higher density of points above the dotted line. in fig. 6 the same sff package was applied but with the rainflow cycle counting method instead of the vcc method. the results show an underestimation within the 2 and 3 boundary factors, having only satisfactory results for the er1 and er2. figure 6: fatigue life correlation with the ssf method applied with the vcc and miner’s rule (experimental vs estimated). in fig. 7 it is shown the fatigue life correlation, obtained for the w-b method. fatigue life, which is presented in blocks, is calculated using eq. (21). figure 7: fatigue life correlation with the w-b method. the fatigue life estimates obtained with the w-b show a big scatter, where most of the estimations of the er1 and er2 loading sequences are above the upper life factor 3 boundary. this shows that the accumulated damage is lower than it 1e1 1e2 1e3 1e4 1e5 1e1 1e2 1e3 1e4 1e5 n um b er o f e st im at ed li fe b lo ck s number of experimental life blocks fatigue life sff (rainflow and miner's rule) er1 1e2 1e3 1e4 1e5 1e2 1e3 1e4 1e5 n um b er o f e st im at ed li fe b lo ck s number of experimental life blocks wang-brown (s = 1.03) er1 er2 enr fsm l. reis et alii, frattura ed integrità strutturale, 48 (2019) 318-331; doi: 10.3221/igf-esis.48.31 328 should for these loadings. an opposite behaviour was shown with the fsm loading, where the accumulated damage was higher than it should be, leading to an underestimation of the fatigue life. the damage accumulation approach was evaluated for w-b and sff with both cycle counting methods vcc and rainflow. fig. 8 and fig.9 present the accumulated damage, estimated at the time of fracture, using the w-b method and the ssf (vcc) method, where for the latter the miner’s and the morrow’s rules were applied. fig 10 is also introduced in order to compare the estimated accumulated damage through the sff rainflow cycle counting method. figure 8: accumulated damage at the time of fracture, for the er1, er2 and enr loadings. figure 9: accumulated damage at the time of fracture, for the fsm loading. as seen in fig. 8, the accumulated damage, for all the loadings and all stress levels, is too low with the w-b model. with ssf model the accumulated damage is much higher. however, in most of the stress levels of the er1 and er2 loadings the damage is almost half of what it should be. for the fsm loading estimates, shown in fig. 9, the accumulated damage 0,0 0,5 1,0 1,5 2,0 2,5 e r 150 1 e r 152 3 e r 152 9 e r 154 6 e r 249 8 e r 250 5 e r 252 1 e r 253 0 e n r -4 82 e n r -4 90 e n r -5 10 e n r -5 20 er1 er2 enr a cc um ul at ed d am ag e w-b vs ssf (vcc) w-b ssf (miner) ssf (morrow) 0,0 0,5 1,0 1,5 2,0 2,5 3,0 3,5 4,0 4,5 5,0 fsm-463 fsm-488 fsm-496 fsm-517 fsm-520 fsm-541 fsm-546 fsm a cc um ul at ed d am ag e w-b vs ssf (vcc) w-b ssf (miner) ssf (morrow) l. reis et alii, frattura ed integrità strutturale, 48 (2019) 318-331; doi: 10.3221/igf-esis.48.31 329 estimated with the w-b method was too high, as expected from the correlation shown previously in fig. 7. however, the extra damage will lower as the stress level increases. the ssf results for the fsm loading case are much better, with most of the stress levels being near the unitary damage line. as seen in fig. 8 and fig. 9, there is not much difference between the use of the morrow’s rule and the miner’s rule. this is explained by the fact that the block extraction method only extracted a few blocks, due to the low variation of the ssf’s eq. shear stress amplitude. through fig. 10 it is observed that the estimation of accumulated damage with the rainflow cycle counting showed very high values. this is due to the significant increase number of accounted cycles per bloc for all the applied loading sequences. the increase is more significant in the fsm loading sequence where the number of cycles withdrawn from the spectrum is three times higher than the considered by the vcc method. only in er1 and er2 the results are satisfactory. figure 10: accumulated damage at the time of fracture, for the four loading sequences it is also relevant to compare the estimate crack plane and the measured in all the tested specimens for each of the four loading cases. one angle measurement and initiation point of fracture for each of the loading sequence obtained in the random loading sequences is presented in the fig. 11. with tab. 4 a comparison is easily visible between the measured crack plane angles and the crack plane estimates, obtained with different critical plane models. figure 11: example photographs of angles and initiation points of fracture obtained in (a) er1 (b) fsm (c) er2 0,0 0,5 1,0 1,5 2,0 2,5 3,0 3,5 e r 150 1 e r 152 3 e r 152 9 e r 154 6 e r 249 8 e r 250 5 e r 252 1 e r 253 0 e n r -4 82 e n r -4 90 e n r -5 10 e n r -5 20 f sm -4 63 f sm -4 88 f sm -4 96 f sm -5 17 f sm -5 20 f sm -5 41 f sm -5 46a cc um ul at ed d am ag e ssf (rainflow) miner morrow l. reis et alii, frattura ed integrità strutturale, 48 (2019) 318-331; doi: 10.3221/igf-esis.48.31 330 er1 er2 enr fsm findley 0º 0º 0º 21º b-m 0º 0º 0º 21º s-w-t 0º 0º 0º 24º f-s 0º 0º 0º 20º liu i 0º 0º 0º 20º liu ii 90º/0º/+90º 90º/0º/+90º 90º/0º/+90º -70º/+20º measured 0º -22º/0º/5º 0º 0º table 4: comparison of the measured crack plane angle with estimates. for the er1 and enr loading cases, all models correctly predicted the crack plane for all stress levels. for the er2 sequence, two of the specimens showed distinct crack plane angles. in all the criteria, in each plane, the damage parameter showed the same value for loadings er1, er2 and enr, which share the same loading path. this behaviour shows that critical plane models do not consider the load sequence. for the fsm loading case, all the specimens fractured at 0º, and none of the selected criteria was able to predict that crack plane angle. conclusions n this work, one non-random and three random sequences were applied to specimens of the 42crmo4 steel under different stress levels. fatigue life from the er1 and the er2 loading sequences were considerably shorter than the lives obtained with the non-random equivalent loading sequence, enr. the randomness introduced in the loading path, shared by these three loading sequences, significantly reduced fatigue life. for all the loading cases fatigue life was estimated by the ssf model using miner and morrows damage accumulation rule and using as cycle counting methods the rainflow rule and vcc method. the difference between miner and morrow’s rules is negligible in comparison with wangbrown in all loading cases. there is only a big difference between the sff models when the cycle counting method is changed, having almost opposite behaviors, the rainflow tends underestimate life and vcc tends to overestimate, but both are able to predict fatigue life under the boundary life factor 3, which is commonly used in fatigue life correlation. damage accumulation, at time of fracture, was not only estimated with the ssf model but also with wang-brown’s model (w-b). wang-brown’s underestimated the damage of the enr, er1 and er2 loading sequences, as oppose the damage overestimation shown in the fsm loading. the ssf model also showed a tendency to underestimate damage, although, in a smaller scale, compared to w-b. even though the ssf criterion, at its present state, can’t account the mean stress effect, it showed good results when estimating fatigue life with non-proportional random loadings with variable stress amplitudes and mean stress, performing better than the w-b model. however, additional studies are needed to confirm, or not, the verified trend according to which the ssf equivalent stress tends to be lower than the value it should be under random loadings with variable amplitude. acknowledgements this work was supported by fct, through idmec, under laeta, project uid/ems/50022/2019. references [1] cui, w. (2002). a state-of-the-art review on fatigue life prediction methods for metal structures, journal of marine science and technology, 7(1), pp. 43-56. doi: 10.1007/s007730200012. [2] campbell, g. s., lahey, r. (1984). a survey of serious aircraft accidents involving fatigue fracture, international journal of fatigue, 6(1), pp. 25-30. doi: 10.1016/0142-1123(84)90005-7. [3] gates, n., fatemi, a. (2016). multiaxial variable amplitude fatigue life analysis including notch effects, international journal of fatigue, 91(2), pp. 337-351. doi: 10.1016/j.ijfatigue.2015.12.011. [4] freitas, m., reis, l., meggiolaro, m. a., de castro, j.t.p. (2016). comparison between ssf and critical-plane models to predict fatigue lives under multiaxial proportional load histories, frattura ed integrità strutturale, 38, pp. 121-127. doi: 10.3221/igf-esis.38.16. i l. reis et alii, frattura ed integrità strutturale, 48 (2019) 318-331; doi: 10.3221/igf-esis.48.31 331 [5] reis, l., li, b., de freitas, m. (2009). crack initiation and growth path under multiaxial fatigue loading in structural steels, international journal of fatigue, 31, pp. 1660-1668. doi: 10.1016/j.ijfatigue.2009.01.013. [6] papadopoulos, i. v. (2002). critical plane approaches in high-cycle fatigue: on the definition of the amplitude and mean value of the shear stress acting on the critical plane, fatigue & fracture of engineering materials & structures, 21(3), pp. 269-285. doi: 10.1046/j.1460-2695.1998.00459.x. [7] manuel de freitas, luis reis, and bin li (2006). comparative study on biaxial low-cycle fatigue behaviour of three structural steels, fatigue & fracture of engineering materials & structures, 29(12), pp. 992-999. doi: 10.1111/j.1460-2695.2006.01061.x. [8] xia, t., yao, w. (2013). comparative research on the accumulative damage rules under multiaxial block loading spectrum for 2024-t4 aluminium alloy, international journal of fatigue, 48, pp. 257-265. doi: 10.1016/j.ijfatigue.2012.11.004. [9] palin-luc, t., lasserre, s. (1998). an energy based criterion for high cycle multiaxial fatigue, european journal of mechanics, 17(2), pp. 237-251. doi: 10.1016/s0997-7538(98)80084-3. [10] morel, f., morel, a., nadot, y. (2009). comparison between defects and micro-notches in multiaxial fatigue – the size effect and the gradient effect, international journal of fatigue, 31(2), pp. 263-275. doi: 10.1016/j.ijfatigue.2008.09.005. [11] v. anes, l. reis, b. li, m. freitas, and c.m. sonsino (2014). minimum circumscribed ellipse (mce) and stress scale factor (ssf) criteria for multiaxial fatigue life assessment, theoretical and applied fracture mechanics, 73, pp. 109119. doi: 10.1016/j.tafmec.2014.08.008. [12] hertel, o., vormwald, m. (2014). multiaxial fatigue assessment based on a short crack growth concept, theoretical and applied fracture mechanics, 73, pp. 17-26. doi: 10.1016/j.tafmec.2014.06.010. [13] louks, r., gerin, b., draper, j., askes, h., susmel, l. (2014). on the multiaxial fatigue assessment of complex threedimensional stress concentrators, international journal of fatigue, 63, pp. 12-24. doi: 10.1016/j.ijfatigue.2014.01.001. [14] anes, v., reis, l., li, b., fonte, m., de freitas, m. (2014). new approach for analysis of complex multiaxial loading paths, international journal of fatigue, 62, pp. 21-33. doi: 10.1016/j.ijfatigue.2013.05.004. [15] anes, v. (2015). damage analysis of complex loading paths, universidade de lisboa, instituto superior técnico, doctoral dissertation. [16] findley, w. n. (1958). a theory for the effect of mean stress on fatigue of metals under combined torsion and axial load or bending, engineering materials research laboratory, division of engineering, brown university. [17] brown, m. w., miller, k. j. (1973). a theory for fatigue failure under multiaxial stress-strain conditions, proceedings of the institute of mechanical engineers, 187(1), pp. 745-755. doi: 10.1243/pime_proc_1973_187_069_02. [18] fatemi, a., socie, d.f. (1988). a critical plane approach to multiaxial fatigue damage including out-of-phase loading, fatigue and fracture of engineering materials and structures, 11(3), pp. 149-165. doi: 10.1111/j.1460-2695.1988.tb01169.x [19] smith, k. n., watson, p., topper, t. h. (1970). a stress-strain function for the fatigue of metals, journal of materials, 5(4), pp. 767-778. [20] socie, d. f., marquis, g. b. (2000). multiaxial fatigue. society of automotive engineers, warrendale, pa, eua. [21] kc liu. (1993). a method based on virtual strain-energy parameters for multiaxial fatigue life prediction, astm special technical publication, 1191, pp. 67–67. doi: 10.1520/stp24796s [22] astm e1049, standard practices for cycle counting in fatigue analysis, astm international, 2011. [23] anes, v., reis, l., li, b., de freitas, m. (2014). new cycle counting method for multiaxial fatigue, international journal of fatigue, 67, pp. 78-94. doi: 10.1016/j.ijfatigue.2014.02.010 [24] wang, c. h., brown, m. w. (1996). life prediction techniques for variable amplitude multiaxial fatigue – part 1: theories, asme journal of engineering and materials technology, 118, pp. 367–370. doi: 10.1115/1.2806821. [25] lv, z., huang, h-z., zhu, s-p., gao, h., zuo, f. (2015). a modified nonlinear fatigue damage accumulation model, international journal of damage mechanics, 24, pp. 168-181. doi: 10.1016/j.ijmecsci.2015.06.016. [26] reis, l. (2004). comportamento mecânico de aços em fadiga multiaxial a amplitude de carga constante e síncrona, universidade técnica de lisboa, instituto superior técnico, doctoral dissertation. [27] matlab release 2015a, the mathworks, inc., natick, massachusetts, united states. [28] anes, v., caxias, j., freitas, m., reis, l. (2017). fatigue damage assessment under random and variable amplitude multiaxial loading conditions in structural steels, international journal of fatigue, 100, pp. 591-601. doi: 10.1016/j.ijfatigue.2016.12.009 [29] afgrow v5.2.5.19, lextech, inc., centerville, ohio, united states. [30] aircher, w., branger, j., van dijk, g. m., ertelt, j., hück, m., de jonge, j. b. (1976). description of a fighter aircraft loading for standard for fatigue evaluation. falstaff, common report of fcw emmen, lbf, nrl, iabg. << /ascii85encodepages false /allowtransparency false /autopositionepsfiles true /autorotatepages /none /binding /left /calgrayprofile (dot gain 20%) /calrgbprofile (srgb iec61966-2.1) /calcmykprofile (u.s. web coated \050swop\051 v2) /srgbprofile (srgb iec61966-2.1) /cannotembedfontpolicy /error /compatibilitylevel 1.4 /compressobjects /tags /compresspages true /convertimagestoindexed true /passthroughjpegimages true /createjobticket false /defaultrenderingintent /default /detectblends true /detectcurves 0.0000 /colorconversionstrategy /cmyk /dothumbnails false /embedallfonts true /embedopentype false /parseiccprofilesincomments true /embedjoboptions true /dscreportinglevel 0 /emitdscwarnings false /endpage -1 /imagememory 1048576 /lockdistillerparams false /maxsubsetpct 100 /optimize true /opm 1 /parsedsccomments true /parsedsccommentsfordocinfo 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/hrv (za stvaranje adobe pdf dokumenata najpogodnijih za visokokvalitetni ispis prije tiskanja koristite ove postavke. stvoreni pdf dokumenti mogu se otvoriti acrobat i adobe reader 5.0 i kasnijim verzijama.) /hun 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can be opened with acrobat and adobe reader 5.0 and later.) >> /namespace [ (adobe) (common) (1.0) ] /othernamespaces [ << /asreaderspreads false /cropimagestoframes true /errorcontrol /warnandcontinue /flattenerignorespreadoverrides false /includeguidesgrids false /includenonprinting false /includeslug false /namespace [ (adobe) (indesign) (4.0) ] /omitplacedbitmaps false /omitplacedeps false /omitplacedpdf false /simulateoverprint /legacy >> << /addbleedmarks false /addcolorbars false /addcropmarks false /addpageinfo false /addregmarks false /convertcolors /converttocmyk /destinationprofilename () /destinationprofileselector /documentcmyk /downsample16bitimages true /flattenerpreset << /presetselector /mediumresolution >> /formelements false /generatestructure false /includebookmarks false /includehyperlinks false /includeinteractive false /includelayers false /includeprofiles false /multimediahandling /useobjectsettings /namespace [ (adobe) (creativesuite) (2.0) ] /pdfxoutputintentprofileselector /documentcmyk /preserveediting true /untaggedcmykhandling /leaveuntagged /untaggedrgbhandling /usedocumentprofile /usedocumentbleed false >> ] >> setdistillerparams << /hwresolution [2400 2400] /pagesize [612.000 792.000] >> setpagedevice microsoft word numero_31_art_2 j. xavier et alii, frattura ed integrità strutturale, 31 (2015) 13-22; doi: 10.3221/igf-esis.31.02 13 determining mode i cohesive law of pinus pinaster by coupling double cantilever beam test with digital image correlation j. xavier centre for the research and technology of agro-environmental and biological sciences, citab, university of trás-os-montes and alto douro, utad, quinta de prados, 5000-801 vila real, portugal. inegi, feup, university of porto, rua dr. roberto frias, 4200-465 porto, portugal. jxavier@inegi.up.pt m. oliveira centre for the research and technology of agro-environmental and biological sciences, citab, university of trás-os-montes and alto douro, utad, quinta de prados, 5000-801 vila real, portugal. instituto superior politécnico de viseu, departamento de engenharia de madeiras, viseu, portugal j.j.l. morais centre for the research and technology of agro-environmental and biological sciences, citab, university of trás-os-montes and alto douro, utad, quinta de prados, 5000-801 vila real, portugal. m.f.s.f. de moura inegi, feup, university of porto, rua dr. roberto frias, 4200-465 porto, portugal. abstract. the direct identification of the cohesive law in pure mode i of pinus pinaster is addressed. the approach couples the double cantilever beam (dcb) test with digital image correlation (dic). wooden beam specimens loaded in the radial-longitudinal (rl) fracture propagation system are used. the strain energy release rate in mode i ( ig ) is uniquely determined from the load-displacement ( p  ) curve by means of the compliance-based beam method (cbbm). this method relies on the concept of equivalent elastic crack length ( eqa ) and therefore does not require the monitoring of crack propagation during test. the crack tip opening displacement in mode i  iw is determined from the displacement field at the initial crack tip. the cohesive law in mode i i i( )w  is then identified by numerical differentiation of the i ig w relationship. moreover, the proposed procedure is validated by finite element analyses including cohesive zone modelling. it is concluded that the proposed data reduction scheme is adequate for assessing the cohesive law in pure mode i of p. pinaster. keywords. wood; mode i fracture mechanics; double cantilever beam test; cohesive law; digital image correlation. j. xavier et alii, frattura ed integrità strutturale, 31 (2015) 13-22; doi: 10.3221/igf-esis.31.02 14 introduction ood is a hierarchical, anisotropic and heterogeneous composite material formed by trees. recently, green composites based on lignocellulosic fibres and forest-based resources have attracted increasing interest in both research and market [1, 2]. moreover, in a policy of sustainability, wood and wood products are increasingly used nowadays, for instance, in structural and semi-structural applications [3]. however, for a better and efficient utilisation of wood material, several issues must be further investigated. one fundamental aspect concerns the fracture mechanical behaviour of wood. relatively extensive fracture process zones (fpz) are observed in wood due to fibre bridging and micro-cracking ahead of the crack tip [4]. however, the microstructural mechanisms in wood fracture are usually confined to a region of reduced thickness [5]. therefore, at the macroscopic scale, the wood behaviour in the fpz can be conveniently described through a phenomenological constitutive cohesive law [6, 7]. in order to obtain the cohesive law, one approach consists in minimising an objective function quantifying the difference between numerical and experimental load-displacement ( p  ) curves by inverse analysis, assuming a given shape of the softening law. this approach, however, is semi-empirical and does not guarantee the uniqueness of the solution. notwithstanding, it has been shown that the inverse identification of cohesive laws provide good agreement between experimental and numerical finite element simulations [7, 8]. instead, a direct method for evaluating the cohesive law can be proposed based on independent determination of strain energy release rate and crack tip opening displacement (ctod) [9]. the advantages of this approach are: (i) the shape of the cohesive law does not need to be assumed a priori; (ii) the cohesive law is determined based on local measurements. in this work, a direct identification of the cohesive law in mode i of p. pinaster was investigated by coupling the double cantilever beam (dcb) test with digital image correlation (dic). specimens oriented in the radial-longitudinal (rl) propagation system were used. the strain energy release rate in mode i ( ig ) was explicitly determined from the p  curve by means of the compliance-based beam method (cbbm). this data reduction scheme is based on the concept of equivalent elastic crack length ( eqa ) and, therefore, does not require the measurement of the crack length during test. an independent evaluation of ctod in mode i ( iw ) was determined from displacement fields at the initial crack tip. the direct differentiation of the i ig w curve and the reconstruction of the i iw  cohesive law, by means of least-squares regression using a continuous approximation function, were addressed. the proposed procedure was also validated by finite element simulations including cohesive zone modelling. figure 1: schematic representation of the dcb test ( 2h = 20 mm, 1l = 300 mm, l = 280 mm, b = 20 mm and 0a = 100 mm). data reduction he dcb test is schematically shown in fig. 1. the specimen is a 1 2l h b  mm3 rectangular beam. the resistance curve (r–curve) can then be determined from the irwin-kies equation 2 i d 2 d p c g b a  (1) w t j. xavier et alii, frattura ed integrità strutturale, 31 (2015) 13-22; doi: 10.3221/igf-esis.31.02 15 in which /c p is the compliance. from the timoshenko beam theory and castigliano theorem an expression for the compliance of the dcb specimen can be obtained. this equation can be solved for the flexural modulus ( fe ) using an initial compliance 0( )c and the corrected initial crack length 0( )a   as [4]     1 3 0 0 0 3 lr 12 8 5 f a a e c bhg bh            (2) where  accounts for root rotation effects and can be determined from finite element analysis [4], and glr is the shear moduli of the material. the cbbm is based on eqa , which is considered to account for the fpz effect at the crack tip as given by: eq fpza a a     [7, 10]. finally, the application of cbbm to the dcb test yield the following expression for the strain energy release rate in mode i (resistance or r–curve) [4] 22 eq i 2 2 lr 26 1 5f ap g b h e h g         (3) it is worth noting that this procedure is less sensitive to experimental errors. this is supported by the fact that the measurement of the crack length during the fracture test is not required. besides, the inherent elastic properties variability among specimens is taken into account by computing a flexural modulus for each p  curve eq. (2). in mode i loading, strain energy release rate ( ig ) and ctod ( iw ) can be related by the following expression [9] i i i i i( )d w o g w w  (4) the cohesive law ( i if ( )w  ) can then be directly obtained by differentiating the above equation ii i i ( ) g w w     (5) this data reduction scheme, however, requires the accurate evaluation of the i if ( )g w relationship. moreover, a suitable differentiation algorithm must be used to avoid noise amplification in the reconstruction of the constitutive cohesive law. in order to solve eq. (5), it is proposed here to fit the i ig w data by a continuous function described by the following expression (logistic function) 1 2i 2 i i,01 ( / ) p a a g a w w     (6) where 1a , 2a , p and i, 0w are constants to be determined in least-square sense. in this function, the 2a parameter must provide an estimation of the critical strain energy release rate: i 2 i iclim w a g g    . figure 2: finite element model of the dcb test (cohesive law, mesh and boundary conditions). j. xavier et alii, frattura ed integrità strutturale, 31 (2015) 13-22; doi: 10.3221/igf-esis.31.02 16 in the literature, several analytical expressions for the cohesive law in mode i have been proposed. among them, there is the xu and needleman exponential law [11] ic i ii iu iu iu exp g w w w w w               (7) in which iuw is the crack tip opening displacement at maximum stress ( iu ) (see cohesive law in fig. 2). the logistic (eq. 6) and exponential (eq. 7) cohesive laws are then compared and discussed during the analysis. digital image correlation ull-field optical techniques have become very important tools in experimental solid mechanics. among them, dic has become widely used, following the development of digital cameras and automatic digital image processing techniques [12]. this computer vision technique has the advantages of a simple principle and experimental set-up, which can switch from large down to small scales of observation. in dic-2d, a planar object is imaged by a single camera-lens optical system connected to a computer for real-time visualisation. it is assumed that the surface of interest has a local random textured pattern uniquely characterising the material surface. a matching process is then carried out between images taken before and after deformation. typically, the reference (undeformed) image is divided into subsets, whose number of pixels defines the displacement spatial resolution (i.e., the smaller distance separating two independent displacement measurements). the selection of these measuring parameters, together with the quality of the speckle pattern, are key issues for determining the spatial resolution and accuracy associated to dic measurements. therefore, they should be carefully chosen in a compromise between correlation (small subsets) and interpolation (large subsets) errors. crack tip opening displacement the ctod in mode i i( )w was determined by processing the displacements provided by dic. for a complex material such as wood, this technique can be advantageous with regard to standard monitoring methods. as a procedure, the initial crack length is firstly identified in the reference (undeformed) image. a suitable pair of subsets near the crack tip is then selected. during the test, the relative displacement of these points is evaluated. the iw can then be determined by [13, 14] i i iw w w    (8) where iw  and iw  are the components of the displacement in the direction perpendicular to the crack propagation associated, respectively, to the upper and the lower cracked surface and . represent the euclidean norm. mechanical properties fracture properties (mode i, trilinear cohesive law) le (gpa) re (gpa) lr (-) lrg (gpa) icg (n/mm) iu (mpa) ib (mpa) ibw (mm) 7.7 1.91 0.47 1.12 0.26 5.34 0.49 0.076 table 1: mechanical and fracture properties of p. pinaster used in the finite element analyses of the dcb test. finite element simulation wo-dimensional finite element analyses (fea) of the dcb test under plane strain state, including cohesive zone modelling, were performed in order to validate the proposed procedure using cbbm. nominal dimensions of the dcb specimen were (fig. 1): 2h = 20 mm, 1l = 300 mm, l = 280 mm, b = 20 mm and 0a = 100 mm. f t j. xavier et alii, frattura ed integrità strutturale, 31 (2015) 13-22; doi: 10.3221/igf-esis.31.02 17 isoparametric 8-node planar solid finite elements were used for the bulk material, whilst 6-node cohesive elements were applied along the fpz, which in this case was confined to a line at mid-height of the specimen (fig. 2). wood was modelled as an orthotropic linear elastic material with properties summarised in tab. 1 [7, 15-17]. experimental work pecimens for the dcb test were cut from a single p. pinaster tree. specimens were selected in the mature region within the stem at a given location to minimise material variability. twelve specimens were prepared with axes oriented along the rl propagation system. the nominal dimensions of the dcb specimens were those already used in the numerical simulation (fig. 1). the crack was generated by using a band saw of 1 mm thickness followed by an impacted blade to guarantee a sharp initial crack surface. the fracture tests were performed in an instron 1125 universal testing machine, with a controlled crosshead displacement rate of 3 mm/min. the load was measured by means of a 5 kn load cell, setting the gain at 50 n/v. specimens were tested after stabilisation at laboratory conditions of 60-65% relative humidity and temperature of 20-25 ºc. the aramis dic-2d system was used in this work [18-20]. the speckled pattern required in the dic method was painted over the region of interest by means of an airbrush to guarantee suitable granulometry, contrast and isotropy at the scale of magnification. for dic analyses, a subset size of 15×15 pixel2 (0.270×0.270 mm2) and a subset step of 13×13 pixel2 (0.234×0.234 mm2) were selected for enhancing spatial resolution [19]. a resolution in displacement of 1–2×10−2 pixel (0.18–0.36 μm) was obtained. for measuring ctod i( )w , the coordinates of the initial crack tip were firstly identified in the reference image. the iw was then determined by post-processing the displacement of subsets chosen upper and lower the crack tip during the test (eq. 8). the base distance between the two subsets was 0.468 mm figure 3: dcb test: (a) curves and macroscopic visualization of the crack propagation; (b) r–curve obtained by cbbm; (c) r–curve obtained by irwin-kies equation s j. xavier et alii, frattura ed integrità strutturale, 31 (2015) 13-22; doi: 10.3221/igf-esis.31.02 18 results and discussion he crack length propagation during the fracture test was determined based on dic measurements: dic 0( ) ( )a a a    . the algorithm proposed for this evaluation together with a further comparison between eqa and dica as a function of the applied displacement in the dcb test is described in detailed in ref. [10]. hereafter, a systematic evaluation of mode i fracture properties (r – curve and cohesive law) obtained from both cbbm and irwinkies equations is addressed. to start with, the r–curves determined from both irwin–kies equation and cbbm (eq. 3) were analysed. the compliance versus crack length ( dica ) function was fitted in the least-square sense by a cubic function of the form: 3c ma n  . the analytical differentiation of this function was then used in order to compute ig . fig. 3a shows the p  curves obtained experimentally together with the numerical one resulting from fea using the trilinear cohesive law (fig. 2). this law was defined using the average values of icg and iu in order to outline the area circumscribed by the law and the peak stress value, respectively. the coordinates of the inflection point ( ibw = 0.04 mm, ib = 2.0 mpa) were taken from the experimental cohesive laws, considering the issuing average values. the scatter on the initial compliance among the curves ( 0 0.072 0.0076c   mm/n) is expected due to the inherent variability of the material. moreover, qualitatively, the numerical prediction of the p  curve was in good agreement with the experimental ones. in fig. 3a it is also shown a macroscopic visualisation of crack propagation. as it can be seen, microcracking and fibre bridging can be identified. this confirms the difficulties in measuring accurately the crack length using conventional monitoring techniques. some authors (e.g., [21]) report that the main mechanism of mode i fracture is fibre bridging. however, these observations suggest that both micro-cracking and fibre bridging contribute significantly for the energy dissipation in the fpz. the r–curves in mode i obtained from the dcb test by both cbbm and irwin-kies equations are shown in fig. 3b and 3c, respectively, together with the numerical resistance curve. the wide dispersion of the experimental curves is most likely a reflection of the local variability of wood microstructure at the initial crack tip (e.g., earlywood and latewood constituents). specimens cbbm ik  fe iig icg iig icg (g/cm3) (n/mm2) (n/mm) (n/mm) (n/mm) (n/mm) 1 0.539 9888 0.22 0.41 0.18 0.34 2 0.566 7279 0.14 0.28 0.10 0.21 3 0.529 8890 0.10 0.18 0.15 0.25 4 0.545 7423 0.14 0.41 0.14 0.40 5 0.548 8585 0.20 0.30 0.18 0.27 6 0.550 9833 0.17 0.29 0.15 0.27 7 0.535 7585 0.13 0.21 0.12 0.19 8 0.496 8473 0.20 0.37 0.16 0.30 9 0.566 8043 0.25 0.34 0.20 0.27 10 0.553 10105 0.17 0.27 0.15 0.25 mean 0.543 8610 0.17 0.31 0.15 0.27 c.v.(%) 3.8 12.2 26.3 25.4 18.6 22.1 table 2: density (  ), flexural modulus ( fe ), initial ( iig ) and critical ( icg ) strain energy release rates in mode i obtained from the dcb tests by cbbm and irwin-kies (ik) equation. from the r–curves, the evaluation of the strain energy release rate in mode i was carried out at two distinct stages. the first corresponds to the starting point of the non-linearity in the p  curve and therefore the initialisation of the fpz ( iig ), whilst the second is defined at the maximum loading ( img ). due to the fact that some of the r–curves do not reveal a clear plateau identifying the critical strain energy release rate, it was assumed that: im icg g . this value is then related to the complete development of the fpz and initial steady-state crack propagation [7,10]. the iig and icg values for both cbbm and irwin-kies equations are reported in tab. 2, together with density and flexural modulus (eq. 2). t j. xavier et alii, frattura ed integrità strutturale, 31 (2015) 13-22; doi: 10.3221/igf-esis.31.02 19 these results point out that an underestimation of ig can be obtained if the actual crack length is used (eq. 1) because a fraction of fracture energy dissipation at the fpz is not properly taken into account. it should be noted that the density values among specimens have a coefficient of variation (c.v.) lower than 4%. consequently, it is not surprising that scatter of iig and icg was not statistically correlated with density. indeed, as already pointed out, this scatter is likely due to natural variability of wood cellular structure at the crack tip among specimens. as can be concluded, the evaluation of the strain energy release rate in mode i by the irwin-kies equation is slightly lower than the one from cbmm. this difference is of 11.8% and 12.9% for iig and icg respectively, which is lower than the coefficients of variation among the tested specimens. the higher scatter observed in the r-curves resulting from cbbm relative to irwin-kies is explained by the scatter on elastic properties. in fact, since cbbm is based on specimen compliance it becomes more susceptible to material variability. from the dic measurements both normal and transverse ctod, with regard to the crack plane, were determined during the dcb test. as expected, ctod in mode ii ( iiw ) was negligible. characteristic r–curves in mode i i i( )g w were then obtained as shown in fig. 4a and fig. 5a for the cbbm and irwin-kies equations, respectively. the numerical characteristic r–curve obtained by fea of the dcb test was generically in relative good agreement with the experimental ones. for determining the cohesive law (eq. 5), a logistic function (eq. 6) was firstly fitted to the experimental data as shown in figs. 4b (cbbm) and 5b (irwin-kies). for this analysis, only the data points just before initial crack propagation, where the fpz is assumed to be completely developed were considered. as it can be seen, a relatively good approximation was obtained in both cases. this procedure allows filtering experimental data and provides a basis for analytical differentiation, which is less prone to noise amplification. the cohesive laws in mode i obtained from the dcb test are shown in figs. 4c (cbbm) and 5c (irwin-kies), together with the numerical curve. figure 4: dcb test processed by cbbm: (a) characteristic r–curves; (b) least-square regression with the logistic function; (c) cohesive laws in mode i; (d) comparison between logistic and exponential mean cohesive laws. the parameters ( 1a , 2a , p and i, 0w ) of the logistic function (eq. 6) obtained from this study are reported in tab. 3 (cbbm) and 4 (irwin-kies), together with the characteristic values of maximum stress ( iu ) and relative displacements ( iuw , icw in fig. 2) in mode i. the mean value of 2a (tab. 3 and 4) represents an estimation of icg . in this case, a systematic lower evaluation was obtained from this fitting with regard to the independent measurements based on the r– j. xavier et alii, frattura ed integrità strutturale, 31 (2015) 13-22; doi: 10.3221/igf-esis.31.02 20 curves (tab. 2). it is interesting to notice that iu (tab. 3, 4) is of the same order of magnitude as the radial tensile strength (7.93 mpa) measured from tensile tests on p. pinaster (with density of 0.7 g/cm3) in [22]. the mean cohesive law in mode i for p. pinaster was determined from the mean values of the parameters governing the logistic function, as shown in figs. 4d (cbbm) and 5d (irwin-kies). for comparison purposes, the exponential (eq. 7) cohesive law is also plotted in figs. 4d (cbbm) and 5d (irwin-kies), determined from mean values of the fitting parameters. qualitatively both laws have a similar behaviour as summarised in tab. 3 and 4. figure 5: dcb test processed by irwin-kies equation: (a) characteristic r–curves i i( )g w ; (b) least-square regression with the logistic function; (c) cohesive laws in mode i i i( )w  ; (d) comparison between logistic and exponential mean cohesive laws. specimens 1a 2a p i,0w iuw icw iu logistic exponential (n/mm) (n/mm) (-) (mm) (mm) (mm) (mpa) (mpa) 1 0.016 0.35 2.45 0.026 0.018 0.12 9.19 9.16 2 0.011 0.29 2.05 0.017 0.010 0.12 10.5 9.90 3 0.016 0.18 3.09 0.020 0.016 0.08 7.14 5.49 4 0.005 0.28 2.43 0.027 0.019 0.13 7.31 6.37 5 0.016 0.30 2.21 0.027 0.017 0.15 7.16 6.52 6 0.004 0.29 1.81 0.016 0.008 0.12 11.3 11.2 7 0.006 0.21 2.40 0.015 0.010 0.08 9.44 8.32 8 0.013 0.31 1.99 0.032 0.019 0.19 6.02 5.71 9 0.019 0.35 2.81 0.037 0.029 0.16 7.04 5.60 10 0.004 0.25 2.24 0.024 0.015 0.13 7.30 6.61 mean 0.011 0.28 2.35 0.024 0.016 0.13 8.24 7.48 coefficient of variation c.v (%) 51.5 19.5 16.2 30.1 36.4 25.2 21.1 26.9 table 3: parameters of the logistic function ( 1a , 2a , p and i,0w ), and characteristic values of maximum stress ( iu ) and relative displacements ( iuw , icw , see fig. 2) determined by cbbm. j. xavier et alii, frattura ed integrità strutturale, 31 (2015) 13-22; doi: 10.3221/igf-esis.31.02 21 specimens 1a 2a p i,0w iuw icw iu logistic exponential (n/mm) (n/mm) (-) (mm) (mm) (mm) (mpa) (mpa) 1 0.001 0.32 1.51 0.014 0.005 0.14 9.19 9.81 2 0.002 0.23 1.60 0.019 0.008 0.14 7.20 7.45 3 0.023 0.26 3.15 0.019 0.016 0.08 10.5 8.00 4 0.005 0.25 2.48 0.026 0.019 0.13 6.95 6.01 5 0.013 0.26 2.14 0.027 0.017 0.15 6.15 5.69 6 0.004 0.26 1.82 0.016 0.008 0.12 10.2 10.0 7 0.005 0.18 2.37 0.015 0.010 0.08 8.28 7.35 8 0.009 0.25 1.86 0.033 0.018 0.18 4.58 4.38 9 0.013 0.27 2.64 0.038 0.028 0.16 5.33 4.38 10 0.004 0.23 2.24 0.024 0.014 0.13 6.70 6.06 mean 0.008 0.25 2.18 0.023 0.014 0.13 7.51 6.93 coefficient of variation c.v.(%) 87.2 13.8 23.1 34.3 47.2 22.9 26.6 28.5 table 4: parameters of the logistic function ( 1a , 2a , p and i,0w ), and characteristic values of maximum stress ( iu ) and relative displacements ( iuw , icw , see fig. 2) determined by the irwin-kies equation. conclusions he resistance curves in mode i of p. pinaster were determined by applying the cbbm and irwin-kies equations to the dcb fracture test. initial and critical strain energy release rates in mode i were then determined. by combining these strain energy release rate values, determined from both cbbm and irwin-kies equations, with ctod in mode i provided by dic, characteristic r–curves and cohesive laws in mode i for p. pinaster were evaluated by the direct method. results were consistent with literature values. moreover, the proposed procedure was validated by finite element simulations using a cohesive zone model with a bilinear softening law that was adjusted to the experimental ones. the good agreement observed between numerical and experimental results demonstrates the adequacy of the proposed procedure in the determination of the wood cohesive law under mode i fracture. acknowledgement his work is supported by european union funds (feder/compete operational competitiveness programme) and by national funds (fct portuguese foundation for science and technology) under the project fcomp-01-0124-287 feder-022692. the authors would like to acknowledge the support of fct under the project ptdc/eme-pme/114443/2009 and ciência 2008 program. references [1] satyanarayana, k., arizaga, g.g.c., wypych, f., biodegradable composites based on lignocellulosic fibers – an overview, prog polym sci, 34 (2009) 982–1021. [2] xavier, j., belini, u., pierron, f., morais, j., lousada, j., tomazello, m., characterisation of the bending stiffness components of mdf panels from full-field slope measurements, wood sci technol, 47 (2013) 423–441 [3] fao, state of the world's forests 2009 report. part 2 adapting for the future. un food and agriculture organization (2009). t t j. xavier et alii, frattura ed integrità strutturale, 31 (2015) 13-22; doi: 10.3221/igf-esis.31.02 22 [4] de moura, m.f.s.f., silva, m.a.l., de morais, a.b., morais, j.j.l., equivalent crack based mode ii fracture characterization of wood, eng fract mech, 73 (2006) 978–993. [5] vasic, s., smith, i., bridging crack model for fracture of spruce, eng fract mech, 69 (2002) 745–760. [6] de borst, r., numerical aspects of cohesive-zone models, eng fract mech, 70 (2003) 1743–1757. [7] de moura, m.f.s.f., morais, j.j.l., dourado, n., a new data reduction scheme for mode i wood fracture characterization using the double cantilever beam test, eng fract mech, 75 (2008) 3852–3865. [8] silva, f., xavier, j., pereira, f.a.m., morais, j., dourado, n., de moura, m.f.s.f., determination of cohesive laws in wood bonded joints under mode i loading using the dcb test, holzforschung, 67 (2013) 913-922. [9] fernberg, s.p., berglund, l.a., bridging law and toughness characterisation of csm and smc composites, compos sci technol, 61 (2001) 2445–2454. [10] xavier, j., oliveira, j., monteiro, p., morais, j.j.l., de moura, m.f.s.f., direct evaluation of cohesive law in mode i of pinus pinaster by digital image correlation, experimental mechanics, 54(5) (2014) 829-840. [11] van den bosch, m.j., schreurs, p.j.g., geers, m.g.d., an improved description of the exponential xu and needleman cohesive zone law for mixed-mode decohesion, eng fract mech, 73 (2006) 1220–1234. [12] sutton, m., orteu, j.-j., schreier, h., image correlation for shape, motion and deformation measurements: basic concepts, theory and applications, springer (2009). [13] sousa, a.m.r., xavier, j., morais, j.j.l., filipe, v.m.j., vaz, m., processing discontinuous displacement fields by a spatio-temporal derivative technique, opt laser eng, 49 (2011) 1402–1412. [14] xavier, j., sousa, a.m.r., morais, j.j.l., filipe, v.m.j., vaz, m., measuring displacement fields by cross-correlation and a differential technique: experimental validation, opt eng, 51 (2012) 043602. [15] xavier, j.c., garrido, n.m., oliveira, m., morais, j.l., camanho, p.p., pierron, f., a comparison between the iosipescu and off-axis shear test methods for the characterization of pinus pinaster ait, compos part a-appl, s 35 (2004) 827–840. [16] xavier, j., avril, s., pierron, f., morais, j., novel experimental approach for longitudinal-radial stiffness characterisation of clear wood by a single test, holzforschung, 61 (2007) 573–581. [17] xavier, j., oliveira, m., morais, j., pinto, j., measurement of the shear properties of clear wood by the arcan test. holzforschung, 63 (2009) 217–225. [18] gom mbh. aramis commercial software, aramis 6.0.2 (2007). [19] xavier, j,, de jesus, a.m.p., morais, j.j.l., pinto, j.m.t., stereovision measurements on evaluating the modulus of elasticity of wood by compression tests parallel to the grain, constr build mater, 26 (2012) 207–215. [20] sousa, a.m.r.; xavier, j.; vaz, m.; morais, j.j.l.; filipe, v.m.j., cross-correlation and differential technique combination to determine displacement fields. strain 47 (2) (2011) 87-98. [21] vasic, s., smith, i., bridging crack model for fracture of spruce, eng fract mech, 69 (2002) 745–760. [22] pereira, j.l.e. comportamento mecânico da madeira em tracção nas direcções de simetria material. msc thesis, university of trás-os-montes a alto douro, vila real (2005). microsoft word numero_30_art_60 g. jingran et alii, frattura ed integrità strutturale, 30 (2014) 495-501; doi: 10.3221/igf-esis.30.60 495 degradation assessment of waterlogged wood at haimenkou site gao jingran, li jian northeast forestry university material science and engineering institute, ha’erbin, heilongjiang 150040 e-mail:48682171@qq.com qiu jian southwest forestry university school of materials engineering, kunming, yunnan 650024 e-mail:qiujianswfu@foxmail.com guo menglin iowa state university, iowa, u.s.a) abstract. haimenkou site is the largest railing-enclosed wooden architecture settlement site on the waterfront in current china. this research conducts degradation assessment of waterlogged wood at haimenkou site with various methods, including maximum moisture content analysis, basic density analysis, shrinkage measurement, swelling analysis, chemical composition analysis, measurement of compression strength parallel to grain, sem microstructure analysis and measurement of crystallinity, providing scientific guidance for the subsequent formulation of proper methods of reinforcement. keywords. haimenkou site; waterlogged wood; degradation assessment. introduction aimenkou site locates at 1 km northwest to haimenkou village in diannan, jianchuan, dali, yunnan province, whose gps coordinates are 99°33´~100°33´ e and 26°12´~26°41´ n, adjoining the northwest bank of haiwei river at the southwest outfall of jian lake. during the archaeological excavation, a huge area of wooden architecture relics and abundant cultural relics such as pottery, bronze ware, stoneware and ironware were discovered. c14 analysis shows they could be dated back to 5300~2500 years ago, counted as a neolithic or bronze-age settlement site. since 1957 the site has been unearthed for three times, the third one in 2008 excavating more than 4000 timber piles in an excavation unit of 1395 square meters. meanwhile, the site area was measured to be 140000 m2, and the concentration area of timber piles was measured as 20000-25000 m2, making it the largest railing-enclosed wooden architecture settlement site on the waterfront in current china. its rareness on earth provides a precious case for analyzing types of chinese prehistoric settlements, and is of great value on the study of social development history and ethnic history of yunnan province. professor qiujian from southwest forestry university has conducted random sampling test on unearthed wood piles, finding most of the tree belonged to pinus yunnanensis. therefore this research chooses waterlogged wood pinus yunnanensis as samples to develop degradation assessment, trying to provide scientific guidance for the subsequent formulation of proper methods of reinforcement. h g. jingran et alii, frattura ed integrità strutturale, 30 (2014) 495-501; doi: 10.3221/igf-esis.30.60 496 materials and methods specimen source aterlogged wood is collected from test pit at2001 of haimenkou site with a diameter of 12.7cm, length of 62cm and weight of 7.9kg. it belongs to the middle period, and the species belongs to pinus yunnanensis (pinus yunnanensis). due to the severe degradation, the waterlogged wood is as soft as sponges, which requires the pegembedding before sawing the specifications sample. the preparation method was the following: soak the ancient wood in peg2000 at 60°c. after 15 days, when the ancient wood is totally immersed in peg; dry it in the air and leave it to harden; saw the specimen into needed sizes, and put it in water to draw out peg for 10 days (each day replace clean water). the contrast sample, pinus yunnanensis (pinus yunnanensis) healthy wood, is collected from puer, yunnan. experimental methods: maximum moisture content and basic density maximum moisture content is measured according to gb/t1931-2009 method for determination of the moisture content of wood. to ensure the maximum moisture content of wood during measurement, the saturation of wood with water is needed: put the sample into a vessel with distilled water; immerse it totally into water by a stainless steel wire mesh; leave the vessel to a vacuum drying oven for 1 hour to vacuumize with the vacuum degree of -0.09 mpa; release the vacuum and still the sample; conduct measurement after the sample weight becomes stable. basic density is tested according to gb/t1933-2009 method for determination of the density of wood, chapter 7. experimental methods: shrinkage, swelling and water absorption shrinkage is measured according to gb/t1932-2009 method for determination of the shrinkage of wood; swelling is determined according to gb/t1934.2-2009 method for determination of the swelling of wood; water absorption is determined according to gb/t1934.1-2009 method for determination of the water absorption. experimental methods: compressive strength parallel to grain of wood the compressive strength parallel to grain of wood is measured according to gb/t1935-2009 method of testing in compressive strength parallel to grain of wood. experimental methods: chemical composition analysis the content of solvent extractives is measured according to gb/t2677.6-94 fibrous raw material—determination of solvent extractives. the content of acid-insoluble lignin is measured according to fibrous raw material—determination of acid-insoluble lignin. the content of holocellulose is measured according to gb/t2677.10-94 fibrous raw materialdetermination of holocellulose. the content of pentosan is measured according to gb/t2677.9-94 fibrous raw material—determination of pentosan. experimental methods: scanning electron microscope (sem) examination the scanning electron microscope is hitachi s-3000n, whose accelerating voltage is 15.0kv. the sample is cut by hand from horizontal, radial and chordwise sections using germany leica specialized microtome blade. results and discussion maximum moisture content and basic density s is shown in tab. 1, maximum moisture content and basic density are two scientific and relatively more easilyoperated indicators for the degradation degree of waterlogged wood [1]. waterlogged wood is usually divided into 3 categories according to its preservation states: category i, maximum moisture content ≥400%, severe degradation; w a g. jingran et alii, frattura ed integrità strutturale, 30 (2014) 495-501; doi: 10.3221/igf-esis.30.60 497 category ii, 400% > maximum moisture content >185%, moderate degradation; category iii, maximum moisture content ≤185%, mild degradation [2]. within the same species, the further the waterlogged wood basic density is away from that of healthy wood, the more severe its degradation is. during the reinforcement, if there appears an obvious tendency of cell collapse and dimension shrinkage [3], then milder methods is supposed to be chosen in the later drying process. as is shown in tab. 1, the maximum moisture content of ancient wood is 578.68%, 4.14 times of the healthy wood (139.64%), while the basic density of waterlogged wood (0.16 g/cm3) is only one-third of that of healthy wood (0.48 g/cm3), indicating that haimenkou site waterlogged wood has a severe degradation. sample size mean/% max/% min/% standard deviation variable coefficient/% basic density g/cm3 ancient wood 60 0.16 0.22 0.13 0.02 14.51 modern healthy wood 60 0.48 0.58 0.36 0.06 12.24 maximum saturation moisture content % ancient wood 60 578.68 705.92 373.52 66.58 11.51 modern healthy wood 60 139.64 190.75 102.08 24.91 17.84 table 1: maximum moisture content, basic density and oven dry porosity of pinus yunnanensisancient wood and healthy wood. shrinkage, swelling and water absorption the rules of shrinkage and swelling of waterlogged wood are different from healthy wood. tab. 2 shows the following conclusions: 1) the shrinkage rate of waterlogged wood from waterlogged state to full hardness (radial direction 8.16%, chordwise 24.74%) is obviously higher than healthy wood (radial direction 4.46%, chordwise7.76%), indicating that haimenkou site ancient wood has severe shrinkage. in the drying process during late reinforcement, the removal of solvent should slow down, preventing the deformation and craze of the ancient wood caused by cell collapse. 2) the swelling of waterlogged wood from full hardness to waterlogged state (radial direction 4.12%, chordwise11.28%) is slightly higher than healthy wood (radial direction 4.46%, chordwise8.50%). besides, the swelling of waterlogged wood is much lower than its shrinkage, meaning that the re-absorption of water after drying process cannot return to the original size, though it can swell to a certain extent. according to previous studies, the more severe degradation of waterlogged wood is, the larger disparity there will be. repeated drying and swelling of ancient wood will lead to larger and larger disparity [4]. the reason lies in the degradation of polysaccharide substances in ancient wood, which produces large amount of hydroxyl and increases porosity of wood, leading to the increase of ancient wood maximum saturation moisture content. in the drying process, as water is drawing out, cellulose chains are growing closer, allowing hydroxyl to form hydrogen bond. when the ancient wood after oven dry reabsorbs water, the newly formed hydrogen bonds can no more accept water molecules, making the swelling unable to return to original size. 3) the shrinkage of healthy wood chordwise is 1.74 times that of radial direction, while the shrinkage of waterlogged wood chordwise is 3.03 times that of radial direction. the result demonstrates that compared with healthy wood, there is a larger gap between the shrinkage of waterlogged wood from chordwise and radial direction. the main reason lies in the containment of wood ray, which is the major difference between the woods from radial direction and chordwise. for waterlogged wood whose cytoderm is severely degraded, the containment of wood ray is more obvious. 4) water absorption of full hardness waterlogged wood (454.29%) is much higher than that of healthy wood (144.97%). compression strength parallel to grain as tab. 3 shows, the compression strength parallel to grain of pinus yunnanensis healthy wood is 59.28 mpa while that of pinus yunnanensis ancient wood is only 3.67 mpa, indicating the mechanical strength of ancient wood in haimeikou site g. jingran et alii, frattura ed integrità strutturale, 30 (2014) 495-501; doi: 10.3221/igf-esis.30.60 498 is unable to support its exhibition, storage and transport as wood relics. therefore the timely reinforcement is needed. besides, the maximum indenter displacement of cracking load of ancient wood (1.30 mm) is lower than that of healthy wood (1.52 mm), showing that elasticity of ancient wood after air-seasoning is lower than healthy wood, indicating higher brittleness which is adverse to the preservation of ancient wood. analysis of causes for the heavy decrease of compression strength parallel to grain of haimenkou site waterlogged wood can be summarized as follows: 1) from macro-perspective, severe degradation leads to the shrinkage distortion of ancient wood in the process of airseasoning. shrinkage cracks appear in part of the wood, some of which has a sharp fall of the compression strength parallel to grain, one of the reasons for the significant excess of ancient wood variable coefficient than healthy wood. 2) from micro-perspective, degradation of three major chemical dispositions in wood causes destruction of cytoderm, increase of porosity and decrease of crystallinity, which all contribute to the fall of compression strength parallel to grain in ancient wood. 3) from molecule perspective, degradation and breakage of cellulose chain impairs its original rigidity. degradation of hemicelluloses and lignin reduces the closeness between cytoderm matrix substances. sample size mean/% max/% min/% standard deviation variable coefficient/% shrinkage from saturation to full hardness /% radial direction waterlogged wood 60 8.16 13.41 3.84 2.19 26.88 modern healthy wood 60 4.46 6.90 2.56 1.20 26.98 chordwise waterlogged wood 60 24.74 32.16 7.20 6.13 24.78 modern healthy wood 60 7.76 9.57 5.66 1.12 14.44 swelling from full hardness to saturation /% radial direction waterlogged wood 60 4.12 6.01 2.06 1.06 25.79 modern healthy wood 60 4.46 6.69 2.59 1.14 25.51 chordwise waterlogged wood 60 11.28 16.91 6.65 2.58 22.89 modern healthy wood 60 8.50 10.75 6.24 1.32 15.59 water absorption from full hardness to saturation /% waterlogged wood 60 454.29 584.63 337.96 60.00 13.21 modern healthy wood 60 144.97 212.74 104.94 27.24 18.79 table 2: shrinkage, swelling and water absorption of pinus yunnanensis ancient wood and healthy wood. g. jingran et alii, frattura ed integrità strutturale, 30 (2014) 495-501; doi: 10.3221/igf-esis.30.60 499 table 3: compression strength parallel to grain of pinus yunnanensis ancient wood and healthy wood. chemical components of waterlogged wood for ancient wood, the content of extractions can to some extent demonstrate its environment and degradation degree. as is shown in tab. 4, the content of 1%naoh extraction of waterlogged wood (12.85%) is much higher than modern healthy wood (7.38%). it’s because haimenkou site ancient wood has been buried under oxygen-deficient and high temperature environment all year round, under which ancient wood is mainly corrupted by anaerobic bacteria. most of the compositions degraded by anaerobic bacteria are celluloses and hemicelluloses. hemicelluloses in ancient wood are degraded into glycosyl units such as hexose and pentosan with the impact of light, heat, oxidation and microorganism. the glycosyl units can be extracted by 1%naoh solution, causing the content of 1%naoh extraction in ancient wood higher than healthy wood. the research shows a positive correlation between severities of degradation of ancient wood and the relative extraction content of 1%naoh solution in ancient wood compared with healthy wood [5]. the content of holocellulose can relatively be more accurate in reflecting the rotten degree of waterlogged wood [6-8]. the white rot fungi, which can degrade lignin, belong to aerobic fungi. therefore in oxygen-deficient environment the lignin cannot easily be degraded. according to previous studies, the degradation of ancient wood mainly includes the degradation of celluloses and hemicelluloses. as is shown in tab. 4, the content of holocellulose in ancient wood is 42.94%, taking up only 55% of that in healthy wood (78.38%). the low content of holocellulose indicates that celluloses and hemicelluloses have been severely degraded. the content of pentosan in ancient wood is 2.91%, only 22% that of healthy wood (13.23%), showing that the degradation of hemicelluloses is more serious than celluloses. the reason is that although celluloses and hemicelluloses are both high-molecular polymer made up by glycosyl units, celluloses have no branched chain, and possess only one kind of glycosyl, while hemicelluloses are made up by various kinds of glycosyl and have many short branched chains[9], making it easier for hemicelluloses to be degraded. as is shown in tab. 4, the content of lignin in ancient wood is 57.99%, while in healthy wood the figure is 30.48%. superficially the lignin content has increased, but it is a relative increase caused by a larger decrease of celluloses and hemicelluloses. table 4: chemical compositions of pinus yunnanensis ancient wood and healthy wood. sample size moisture content/% mean max min standard deviation variable coefficient/% moisture content is 12% /mpa waterlogged wood 26 12.09 3.67 4.93 1.98 0.76 20.73 modern healthy wood 26 10.99 59.28 68.85 49.57 5.42 9.15 the maximum indenter displacement of cracking load /mm waterlogged wood 26 12.09 1.30 2.03 0.96 0.26 19.94 modern healthy wood 26 10.99 1.52 2.23 1.21 0.25 16.38 alcohol-benzene extract /% 1%naoh extract/% acid accumulator insoluble lignin /% holocellulose /% pentosan /% waterlogged wood 2.16 12.85 57.99 42.94 2.91 healthy wood 2.35 7.38 30.48 78.38 13.23 g. jingran et alii, frattura ed integrità strutturale, 30 (2014) 495-501; doi: 10.3221/igf-esis.30.60 500 scanning electron microscope (sem) examination of ancient wood seen from fig. 1(a), the cytoderm of early wood cells on cross section of waterlogged wood at haimenkou cannot keep original forms due to the degradation of chemical compositions such as celluloses. fig. 1 (b) shows that the latewood secondary wall of ancient wood cross section is seriously degraded and shrank, breaking away from the relatively wellpreserved middle lamella. sem samples of ancient wood are selected from natural drying waterlogged wood. natural drying can cause serious shrinkage and deformation of ancient wood cells, demonstrating that the wood cells must be padded and consolidated with reagent to maintain the state of ancient wood before dehydration. fig. 1 (c) shows that the diameter of cytoderm pit on radial section of ancient wood is long and in large quantity, whose pit membrane has been destroyed. the permeability of wood is closely related to the number and radius of pit membrane micropores, which offers a favorable condition for the entry of reinforcement reagent inside the cytoderm of ancient wood cells. it is predicted that no inflating or vacuum is needed during the reinforcement process but ordinary pressure. in this way it not only prevents fragile wood cells from high pressure, but also reduces the cost and time. (a) 500×waterlogged wood sem microstructure of early wood cells on cross section (b) 500×waterlogged wood sem microstructure of late wood on cross section (c) sem microstructure on radial section of 500×waterlogged wood. figure 1: waterlogged wood sem microstructure. g. jingran et alii, frattura ed integrità strutturale, 30 (2014) 495-501; doi: 10.3221/igf-esis.30.60 501 conclusion 1) the maximum moisture content of unearthed waterlogged wood at haimenkou site is 578.68%, its basic density is 0.16g/cm3, full hardness shrinkage on radial direction is 8.16% and chordwise 24.74%, largely different from healthy wood. 2) the compression strength parallel to grain is 3.67 mpa, only 6.19% of the healthy wood, unable to support the sequent exhibition and preservation. the timely reinforcement is needed. 3) the degradation of celluloses and hemicelluloses in waterlogged wood at haimenkou site is serious, which is the major cause for the degradation of ancient wood’s physical and mechanical performance. 4) according to the analysis on full hardness shrinkage and sem microstructure, the waterlogged wood cells endure severe shrinkage and deformation in the natural drying process, which further leads to the cracking of the wood. therefore special attention should be paid to adopting mild drying methods in drying and reinforcement process. references [1] jinping, z., rui, z., the physical index on the degradation of archaeological wood, sciences of conservation and archaeology, 19(2) (2007) 34-37. [2] hongyin, z., jingwu, w., guotu, c., physical and chemical properties of microstructure of water-rich wooden relics, southeast colture, 4 (20089 89-92. [3] kaye, b, consernation of waterlogged archaeological wood, chemaical society reviews, (1995) 35-43. [4] ling, l., unearthed archeological wooden relics: generation, reply and permanent fixture, sicentific research of china’s cultural relics, 2 (2009) 53-55. [5] zhengjun, z., research on processing unearthed ancient water-rich wood using lactitol, nanjing, nanjing forestry university, wood science and technology (2006). [6] giachi, g., bettazzi, f., chimichi, s., staccioli, g., chemical characterisation of degraded wood in ships discovered in a recent excavation of the etruscan and roman harbour of pisa, journal of cultural heritage, 4(2) (2003) 75–83. [7] passialis, c.n., physico-chemical characteristics of waterlogged archaeological wood, holzforschung, 51(2) (1997) 111-113. [8] ucar, g., yillgor, n., chemical and technological properties of 300 years waterlogged wood, holz als rohund werkstoff, 53(2) (1995) 129-132. [9] yixing, l., guangjie z., wood resource materials, beijing, china forest publishing, (2003). microsoft word numero_30_art_55 v. di cocco et alii, frattura ed integrità strutturale, 30 (2014) 454-461; doi: 10.3221/igf-esis.30.55 454 focussed on: fracture and structural integrity related issues fatigue crack behavior on a cu-zn-al sma v. di cocco, f. iacoviello università di cassino e del lazio meridionale, dicem, via g. di biasio, 43, 03043, cassino (fr), italy v.dicocco@unicas.it s. natali, v. volpe university of rome “sapienza”, dicma, via eudossiana 18, rome, italy stefano.natali@uniroma1.it abstract. in recent years, mechanical property of many sma has improved in order to introduce these alloys in specific field of industry. main examples of these alloys are the niti, cu-zn-al and cu-al-ni which are used in many fields of engineering such as aerospace or mechanical systems. cu-zn-al alloys are characterized by good shape memory properties due to a bcc disordered structure stable at high temperature called β-phase, which is able to change by means of a reversible transition to a b2 structure after appropriate cooling, and reversible transition from b2 secondary to do3 order, under other types of cooling. in β-cu-zn-al shape memory alloys, the martensitic transformation is not in equilibrium at room temperature. it is therefore often necessary to obtain the martensitic structure, using a thermal treatment at high temperature followed by quenching. the martensitic phases can be either thermally-induced spontaneous transformation, or stressinduced, or cooling, or stressing the βphase. direct quenching from high temperatures to the martensite phase is the most effective because of the non-diffusive character of the transformation. the martensite inherits the atomic order from the β-phase. precipitation of many kinds of intermetallic phases is the main problem of treatment on cu-based shape memory alloy. for instance, a precipitation of α-phase occurs in many low aluminum copper based sma alloy and presence of α-phase implies a strong degradation of shape recovery. however, cu-zn-al sma alloys characterized by aluminum contents less than 5% cover a good cold machining and cost is lower than traditional niti sma alloys. in order to improve the sma performance, it is always necessary to identify the microstructural changing in mechanical and thermal conditions, using x-ray analyses. in this work a cu-zn-al sma alloy obtained in laboratory has been microstructurally and metallographically characterized by means of x-ray diffraction and light optical microscope (lom) observations. furthermore a fatigue crack propagation and fracture surface scanning electron microscope (sem) observations have been performed in order to evaluate the crack path and the main crack micromechanisms. keywords. sma; cu alloys; structure; fatigue crack propagation. introduction ince the discovery of the first shape memory alloy (au-cd, in 1938), many alloys characterized by memory property have been studied. often, the chemical composition was characterized by the presence of rare metals with low mechanical properties and sma effects that did not allow an industrial development on a large scale. in recent s v. di cocco et alii, frattura ed integrità strutturale, 30 (2014) 454-461; doi: 10.3221/igf-esis.30.55 455 years, mechanical properties of many sma have improved, allowing to introduce these alloys in specific field of industry. main examples of these alloys are the niti, cu-zn-al and cu-al-ni which are used in many fields of engineering such as aerospace or mechanical systems [1]. many scientific papers are published mainly on niti alloy (nitinol), analyzing both the microstructure peculiarities and the thermo-mechanical properties [2]. however, this alloy is characterized by some processing difficulties that imply an increase of costs. the main difficulty is due to presence of titanium that makes it readily oxidisable and, because of its good mechanical properties, it must be hot worked. in the last decades, different shape memory alloys have been optimized, such as the copper-zinc-aluminum (zncual), copper-aluminum-nickel (cualni), nickel-manganese-gallium (nimnga), nickel-titanium (niti), and other smas obtained alloying zinc, copper, gold, iron, etc.. however, the near equiatomic niti binary system shows the most interesting properties and it is currently used in an increasing number of applications in many fields of engineering, for the realization of smart sensors and actuators, joining devices, hydraulic and pneumatic valves, release/separation systems, consumer applications and commercial gadgets [1, 2]. due to their good biocompatibility, another important field of sma application is medicine, where the pseudo-elasticity is mainly exploited for the realization of several components such as cardiovascular stent, embolic protection filters, orthopedic components, orthodontic wires, micro surgical and endoscopic devices [3]. from the microstructural point of view, shape memory and pseudo-elastic effects are due to a reversible solid state microstructural transition from austenite to martensite, which can be activated by mechanical and/or thermal loads [4]. copper-based shape-memory alloys are very sensitive to thermal effects, and it is possible that in thermal cycles its properties change (e.g., shape-recovery ratio, transformation temperatures, crystal structures, hysteresis and mechanical behavior). cu-zn-al alloys are characterized by good shape memory properties due to a bcc disordered structure stable at high temperature called β-phase, which is able to change by means of a reversible transition to a b2 structure after appropriate cooling, and reversible transition from b2 secondary to do3 order, under other types of cooling. in β-cu-zn-al shape memory alloys, the martensitic transformation is not in equilibrium at room temperature. it is therefore often necessary to obtain the martensitic structure, using a thermal treatment at high temperature followed by quenching. the martensitic phases can be either thermally-induced spontaneous transformation, or stress-induced, or cooling, or stressing the β phase. direct quenching from high temperatures to the martensite phase is the most effective because of the nondiffusive character of the transformation. the martensite inherits the atomic order from the β-phase [5]. precipitation of many kinds of intermetallic phases is the main problem of treatment on cu-based shape memory alloy. for instance, a precipitation of α-phase occurs in many low aluminum copper based sma alloy and presence of α-phase implies a strong degradation of shape recovery [6]. however, cu-zn-al sma alloys characterized by aluminum contents less than 5% cover a good cold machining and cost is lower than traditional niti sma alloys. other investigations carried out on cuznal alloys, showed a strain influence on the macroscopic behavior and on martensite morphology. martensitic transformation occurs initially in deformed material and the manufact shape follows the transformation [7]. larger grains dimensions allow an easier transformation process, allowing the growth of 18r martensite [8]. in this work a cu-zn-al sma alloy obtained in laboratory has been microstructurally and metallographically characterized by means of x-ray diffraction and light optical microscope (lom) observations. these analyses have performed under load conditions in order to identify the behavior of alloy. furthermore fatigue crack propagation and fatigue crack paths were investigated by means of a scanning electron microscope (sem). material and procedures n this work, a cuznal pseudo-elastic alloy, made in laboratory by using controlled atmosphere furnace and characterized by chemical composition shown in tab. 1, has been investigated focusing the fatigue crack propagation paths. cu zn al other 73.00 21.80 5.04 0.16 table 1: chemical composition of cu-zn-al investigated alloy. i v. di cocco et alii, frattura ed integrità strutturale, 30 (2014) 454-461; doi: 10.3221/igf-esis.30.55 456 prior to evaluate mechanical properties, crono-amperometric tests have been performed in order to evaluate the homogeneity of material and its electrochemical behaviours, using a 0.1 mol nacl solution at -50mv/sce for 1800s [9]. in order to evaluate the structure transformation, a customized testing machine equipped with a removable loading frame was used to perform x-ray analyses at fixed values of applied load and/or deformations. xrd measurements were carried out by using a philips x-pert pro diffractometer equipped with vertical bragg-brentano powder goniometer. a step-scan mode was used in the 2θ range from 25° to 90° with a step width of 0.02° and a counting time of 3 s per step, and receiving slit 0.02 mm. the employed radiation was monochromated cu kα (40kv – 40 ma). fatigue crack propagation tests were performed by using ct specimens obtained by machining the cast ingots according to astm e 647 prescriptions. both lateral surfaces have been metallographically prepared to scanning electron microscope (sem) observations. a servohydraulic testing machine has been used in order to evaluate fatigue crack propagation using the astm e 647 testing conditions. fatigue cracks propagation tests are performed by using the following conditions: 1) p = const. 2) r = pmin/pmax = 0.1 and 0.5. 3) load: sinusoidal waveform. 4) load frequency = 30hz. 5) lab conditions. finally, fracture paths have been analysed by means of a sem in order to evaluate the loading conditions influence. results and comments om observations show a traditional structure whose grain diameter mean value is about 700 m. alloy microstructure is not completely homogeneous and grains are characterized by a needle like morphology as shown in fig. 1. figure 1: etched surface of the investigated material. needles microstructure is oriented: needles only partially cover the diameter of the prior austenitic grains. no subgrains are observed. the alloy inhomogeneities have been highlighted by crono-amperometric tests which the results are shown in fig. 2a [9]. the electrochemical behaviour is characterized by a decrease of current due to presence of corrosion products on the etched surface and to the consequent lower passive property. corrosion products are not homogenous due to the microstructure differences between grains bulk and boundary. l v. di cocco et alii, frattura ed integrità strutturale, 30 (2014) 454-461; doi: 10.3221/igf-esis.30.55 457 4.e‐03 5.e‐03 6.e‐03 7.e‐03 8.e‐03 9.e‐03 1.e‐02 0 200 400 600 800 1000 1200 1400 1600 1800 2000 c u rr e n t  d e n si ty  [ a /c m 2 ] time [s] a) b) figure 2: electrochemical behavior and microstructure etched of material: a) polarization curve, b) microstructure of boundary grain. “acicular like” zones near grains boundaries are shown in fig. 2b. evidence of microstructure transitions are in fig. 3, where two diffractograms show respectively the undeformed and the deformed at eng = 5% specimen. 0 200 400 600 800 1000 1200 1400 40 50 60 70 80 90 in te n si ty 2θ [°] serie1 eng. epsilon 5% εeng = 0% εeng = 5% figure 3: diffraction spectra. the undeformed specimen spectrum shows four peaks corresponding to 42.35°, 43.71°, 70.39°, 80.23° that correspond to two different phases [10]: cubic b2 phase (like cscl lattice), sometimes named as β2 that take place at 550°c, but measured peaks are not sufficient to evaluate the cell parameter; cubic l21 phase (like cu2mnal), sometimes named as β3 that take place at 320°c, characterized by cell parameter about a=5.8707 ǻ. the eng = 5% deformed specimen shows also four peaks but corresponding to different diffraction angles (42.27°, 43.43°, 43.85° and 85.71°). presence of these peaks are compatible with presence of two phases [11, 12]: austenite β3 (l21 structure not stress induced transformed), characterized by cell parameter about a=5.8707 ǻ as in the undeformed state.; martensite m18r structure, characterized by a=4.4189 ǻ, b=5.332 ǻ, c=38.8 ǻ and angle β=89.7°. peaks modifications (considering both angles and intensity) show the mechanical deformation influence on the microstructure modifications. fatigue crack propagation results (da/dn-k) at r=0.1 and r=0.5 are shown in fig. 4a. v. di cocco et alii, frattura ed integrità strutturale, 30 (2014) 454-461; doi: 10.3221/igf-esis.30.55 458 focusing the r=0.1 results, five different stages can be observed (fig. 4b). considering the increase of the crack tip plastic zone radious with the increase of the applied k, a possible crack propagation micromechanism is proposed (to be confirmed by further experimental and numerical analyses): stages 1 and 2: the specimen is almost completely austenitic, with the exception of the crack tip plastic zone, but, considering the applied k values, its radious be considered as negligible; corresponding to kmin values, considering the typical sma stress-strain behaviour (fig. 5), almost all the crack tip plastic zone reverts from martensite to austenite (point a). stage 3: transition stages 4 and 5: the higher applied k values imply an increase of the radious of the crack tip plastic zone (martensitic!). corresponding to kmin values, the radious of the crack tip plastic zone that does not reverts its microstructure is larger than the one observed in stage 1 and 2 (fig. 5, point b). in this zone, the stress induced martensite (obtained corresponding to kmax) remains unchanged. 4.0e‐09 4.0e‐08 4.0e‐07 3 30 d a /d n  [ m /c y le ] δk [mpa√m] r=0.1 r=0.5 4.0e‐09 4.0e‐08 4.0e‐07 3 30 d a /d n  [ m /c y le ] δk [mpa√m] r=0.1 r=0.5 stage 1 stage 2 stage 3 stage 4 stage 5 stage 1 stage 2 stage 3 a) b) figure 4: fatigue crack propagation results: a) da/dn behavior, b) stages. for r=0.5, only three “traditional” stages are observed. this is probably due to the higher kmin values and to the larger extent of the crack tip plastic zone, also corresponding to lower k values, if compared to r = 0.1: martensite obtained corresponding to kmax at the crack tip remains unchanged also corresponding to kmin.   martensite austenite &  martensite  austenite ε σ   b  a  figure 5: scheme of σ-ε curve of sma materials with structure transitions. v. di cocco et alii, frattura ed integrità strutturale, 30 (2014) 454-461; doi: 10.3221/igf-esis.30.55 459 a) b) c) d) figure 6: fatigue crack path at r=0.1: a) and b) two different values of crack extension, c) main and secondary path corresponding to boundary grains, d) high magnification in a zone in the front of conventional crack tip. for r = 0.1, the crack path is characterized both by the presence of linear paths (fig. 6a) and by the presence of a sort of “zig-zag” propagation paths (fig. 6b), with secondary paths that after some hundreds of microns join again the main crack. presence of “zig-zag” paths are probably due to presence of inhomogeneities boundary grains (brittle precipitates) as shown in fig. 2b. secondary crack paths are due to a different interaction of main path to boundary grains, as shown in fig. 6c. in this case, the main crack is almost to 90° respect the boundary grain and the brittle precipitates deviate the path with an angle that that is analogous to the precipitates angle observed in fig. 2b. finally, short microcracks are observed ahead of the crack tip under loading conditions (fig. 6d), probably due to the stress field around the crack and the consequent microstructure stress-induced transformation. considering r=0.5, analogously to the results obtained for r = 0.1, crack paths (fig. 7a and b) are characterized by the presence of the “zig-zag” path propagation and by the presence of secondary cracks that can be observed at boundary grains (fig. 7c). the main differences can be summarized as follows: microcracks are not observed ahead of the crack tip. this is probably due to the absence of stage 4 and the crack tip stress field generate a transformed structure characterized by a homogenous behaviour; secondary cracks do not join again the main crack (fig. 7d). v. di cocco et alii, frattura ed integrità strutturale, 30 (2014) 454-461; doi: 10.3221/igf-esis.30.55 460 a) b) c) d) figure 7: fatigue crack path at r=0.5: a) and b) two different values of crack extension, c) a zone in the front of conventional crack tip, d) damaged zone near the main crack path. conclusions n this work, the fatigue crack propagation in a cu-zn-al shape memory alloy, obtained in laboratory, has been evaluated in correlation to main crack micromechanisms by using scanning electron microscopy. fatigue crack propagation has been carried out by means of traditional hydraulic fatigue crack machine tests and ct specimens, at δp=constant, r=0.1 and r=0.5 in lab conditions (astm e 647). for r=0.1, the ability for material to change its structure under load generates a particular fatigue crack propagation behavior characterized by five different stages. corresponding to the third stage, microstructure transformation takes place. considering the crack paths, the following conclusions can be summarized: 1) da/dn-k results are strongly influenced by the r value, probably due to peculiar mechanical behavior of the investigated alloy, with a possible reversion of the stress induced martensite (obtained for kmax) to austenite, depending on the loading conditions (r and k values) 2) main crack path is characterized by the presence of a “zig-zag” path, probably due to the presence of brittle inhomogeneities at boundary grains; the angle between main crack and boundary grains determine the initiation of secondary cracks; i v. di cocco et alii, frattura ed integrità strutturale, 30 (2014) 454-461; doi: 10.3221/igf-esis.30.55 461 3) for r = 0.1, corresponding to “stage 4”, a stress induced microstructure modification is obtained as a consequence of the crack tip stress field, with the consequent initiation of very short microcracks; 4) for r=0.5, no microcracks are observed ahead of the crack tip; 5) for r=0.5, secondary cracks do not join again the main crack. references [1] dong, y., boming, z., jun, l., a changeable aerofoil actuated by shape memory alloy springs, materials science and engineering a, 485 (2008) 243–250. [2] otsuka, k., ren, x., physical metallurgy of ti–ni-based shape memory alloys, progress in materials science (2005) 511. [3] chen, b., liang, c., fu, d., pitting corrosion of cu-zn-al shape memory alloy in simulated uterine fluid, j. mater. sci. technology, 21(2) (2005) 226-230.3 [4] liu, y., tan, g.s., formation of interfacial voids in cast and micro-grained γ′-ni3al during high temperature oxidation, intermetallics (2000) 8 1385-1391.4 [5] suzuki, t., kojima, r., fujii, y., nagasawa, a., acta metall., 37 (1) (1989) 163–168.3 [6] asanovic, v., delijic, k., jaukovic, n., a study of transformation of β-phase in cu-zn –al shape memory alloys, scripta materialia, 58 (2008) 599-601.7 [7] kayali, n., ozgen, s., adiguzel, o., strain effects on the macroscopic behaviour and martensite morphology in shape-memory cuznal alloys, journal of materials processing technology, 101 (2000) 245-249.6 [8] zhang, j.x., zheng, y.f., zhao, l.c., the structure and mobility of intervariant boundaries in 18r martensite in a cu-zn-al alloy, acta mater., 47(7) (1999) 2125-2141. [9] di cocco, v., iacoviello, f., tomassi, l., rossi, a., natali, s.,volpe, v., crack path in a zn-cu-al pe alloy under uniaxial load, convegno nazionale igf xxii, roma, italia, 1-3 luglio 2013, 255-261, acta fracturae issn 22811443. [10] rapacioli, r., ahlers, m., ordering in ternary β cuznal alloys, scripta met., 11 (1977) 1147-1150. [11] chandrasekaran, m., cooreman, l., yan humbeek, j., delaey, l., martensitic transformation in cu-zn-al: changer in transformation entropy due to post-quench ageing in the β or martensitic condition, scripta met., 23 (1989) 237-239. [12] wang, t.m., wang, b.y., feng, b.x., liu, c.l., jiang, b.h., xu, z.y., the recovery behavior of quenched-in vacancies in cu-zn-al alloy, phys. stat. sol., 114 (1989) 451. microsoft word numero 12 art 8 r. tovo et alii, frattura ed integrità strutturale, 12 (2010) 79-87; doi: 10.3221/igf-esis.12.08 79 previsione della resistenza a fatica in saldature per punti attraverso modellazione solida r. tovo, p. livieri, s. capetta università di ferrara, dipartimento di ingegneria, via saragat 1, 44122 ferrara roberto.tovo@unife.it; paolo.livieri@unife.it; simone.capetta@unife.it riassunto. nel presente lavoro vengono messi a confronto due metodi idonei per la verifica di giunzioni saldate per punti: il metodo del raggio di raccordo fittizio ed il metodo del gradiente implicito. il primo impone un raggio di raccordo diverso da zero al piede o alla radice del cordone di saldatura, il secondo, invece, considera più semplicemente la saldatura come un intaglio acuto. il confronto è fatto sulla capacità di prevedere l’affidabilità di giunti saldati per punti in acciaio aventi spessore variabile da 0.8 a 1.5 mm. tali giunti sono sollecitati a taglio (giunti a semplice sovrapposizione) o a trazione (giunti a tazza). infine, è discussa la condizione di convergenza delle analisi numeriche necessarie, in entrambi i metodi, per il calcolo di una tensione equivalente da porre a confronto direttamente con la di resistenza a fatica del materiale. abstract. in this research paper we compare two different methods to estimate the fatigue life of spot welded joints: the method of fiction notch radius and the implicit gradient approach. the first requires a radius of curvature at the weld toe or at the weld root that is different from zero, the second simply considers the weld as a sharp notch. the comparison is made on the ability to predict the reliability of spot welded joints made of steel with a thickness ranging from 0.8 to 1.5 mm. these joints are subjected to shear loading (lap joints) or to tensile loading (circular cup joints). finally, we discuss the convergence condition of the numerical analysis needed, in both methods, for the calculation of equivalent stress to be used in the fatigue analysis. parole chiave. saldature per punti; gradiente implicito; metodi numerici. introduzione elle strutture saldate l’effetto d’intaglio dovuto al cordone di saldatura gioca un ruolo fondamentale nella previsione della resistenza a fatica. come ben noto, le normative [1, 2] o le procedure di riferimento internazionali [3] propongono le curve di progetto dei più comuni particolari saldati in funzione della tensione nominale. tuttavia, nei casi assai frequenti in cui la geometria del giunto non rientrasse nelle classi di resistenza prescritte dalle normative, risulta problematica per il progettista la determinazione della curva di wöhler del dettaglio strutturale, e di conseguenza, anche il calcolo di un indice di affidabilità del componente saldato risulterebbe di difficile valutazione. è comunque ampiamente riconosciuto in letteratura che per affrontare il problema dell’effetto d’intaglio nelle saldature si debba far ricorso ad una procedura di tipo locale che ritenga pericoloso, ai fini della resistenza a fatica, il campo di tensione nelle immediate vicinanze del cordone di saldatura anziché la sola tensione nominale a monte del cordone (si veda ad esempio la trattazione sui metodi locali presentata da radaj et al. [4]). nel presente lavoro verranno presi in esame due metodi ritenuti capaci di integrarsi con la moderna progettazione assistita dal calcolatore. il primo è il metodo del raggio di raccordo originariamente proposto da neuber e successivamente applicato da radaj alle saldature di grosso n http://dx.medra.org/10.3221/igf-esis.12.08&auth=true http://www.gruppofrattura.it r. tovo et alii, frattura ed integrità strutturale, 12 (2010) 79-87; doi: 10.3221/igf-esis.12.08 80 spessore [5] ed il secondo è il metodo del gradiente implicito di recente sviluppo [6, 7]. tali metodi, sono entrambi in grado di fornire un indice sulla affidabilità strutturale basato sui risultati di analisi numeriche agli elementi finiti di tipo lineare elastico. ovviamente, per la costruzione del modello tridimensionale, entrambi gli approcci si possono avvalere di moderni modellatori 3d di tipo commerciale. tuttavia, mentre con il metodo del gradiente implicito le saldature sono considerate come intagli acuti a spigolo vivo indipendentemente dallo spessore delle lamiere, il metodo del raggio fittizio impone, in primis, una variazione del modello geometrico (introduzione del raggio di raccordo al piede o alla radice del cordone di saldatura) e in secondo luogo, sulla base di una recente proposta presentata in [8], il valore del raggio di raccordo dipende anche dallo spessore del giunto. la presente memoria metterà in luce alcune problematiche nell’impiego di modelli tridimensionali per la valutazione della resistenza a fatica in giunti di piccolo spessore. verranno esaminate alcune serie di giunzioni saldate per punti aventi spessore variabile da 0.8 a 1.5 mm. i dati sperimentali sono tratti dalla letteratura e fanno riferimento a giunzioni in acciaio. inquadramento teorico del metodo del gradiente implicito applicato alle giunzioni saldate ei corpi con intagli a spigolo vivo l’ipotesi di materiale lineare elastico, come ben noto, porta ad avere campi di tensione singolari in corrispondenza dell’apice intaglio [9]. il metodo del gradiente implicito, applicato di recente alla progettazione meccanica [6] e [7], è capace di trasformare un campo tensionale preso a riferimento (tensione equivalente locale) in un campo di tensione continuo (tensione equivalente non-locale) in modo da rendere possibile l’applicazione dei criteri di resistenza che necessitano di un campo di tensione regolare. in questo paragrafo si richiamano le equazioni fondamentali alla base del metodo del gradiente implicito. assegnato un corpo di volume v, la tensione non locale   x nel punto  1 2 3x x , x , x di v può essere ottenuta dalla media pesata del tensore degli sforzi locale  x attraverso l’espressione:         vr 1 x x, y y d y v x     (1) nell’equazione (1) il simbolo  x, y indica un valore scalare della funzione peso che dipende dalla distanza euclidea x y tra il punto x ed ogni punto  1 2 3y y , y , y di v. inoltre, il volume di riferimento  rv x può essere calcolato per mezzo della condizione di normalizzazione della funzione peso sul dominio v:    r v v x x, y d y  (2)  rv x è quindi l’integrale della funzione peso  x, y esteso a tutto il volume del corpo. senza entrare nel dettaglio della trattazione matematica dei modelli non locali, il problema del calcolo della tensione equivalente non locale   x può essere trasferito alla risoluzione di una equazione differenziale del secondo ordine [10]. indicata con eff la tensione efficace ai fini della resistenza a fatica, la (1) equivale a risolvere la seguente equazione differenziale:      2 2eff eff eqx c x x      (3) eff n 0   (4) dove c è una dimensione intrinseca legata al materiale in esame, 2 è l’operatore di laplace e eq è la tensione equivalente locale ritenuta responsabile del danno a fatica (per una trattazione più approfondita del problema si rimanda ai riferimenti bibliografici [6,7]). il parametro c è legato in modo univoco alla lunghezza intrinseca a0 di el haddad et al. [11]; nel caso di tensione efficace ottenuta dalla tensione principale massima e imponendo come condizioni al bordo le n http://dx.medra.org/10.3221/igf-esis.12.08&auth=true http://www.gruppofrattura.it r. tovo et alii, frattura ed integrità strutturale, 12 (2010) 79-87; doi: 10.3221/igf-esis.12.08 81 condizioni di neumann ( eff n 0   su tutto v ) vale la relazione: c = 0.54·a0 [12]. nella memoria [6] e’ stata messa a punto una procedura di carattere numerico capace di risolvere il problema (3) della non-località della tensione su un dominio tridimensionale anche nel caso di modelli con geometrie complesse con campi di tensione singolari. con queste ipotesi, utilizzando diverse serie di dati sperimentali prese dalla letteratura, è stato possibile tracciare una banda di dispersione per le saldature di grosso spessore nel campo della vita a termine fra 104 e 5106 cicli. la banda di dispersione è espressa in termini di variazione della tensione equivalente non locale massima max,eff calcolata in prossimità del punto di innesco della cricca. gli spessori del piatto principale e degli irrigidimenti, dei giunti usati per tracciare la curva di riferimento, variavano da 3 a 100 mm. il valore della pendenza della curva di woehler risulta pari a 3 ed il valore di riferimento a 2106 cicli al 97.7% di probabilità di sopravvivenza è di 212 mpa. la banda di dispersione è stata identificata dopo aver calcolato che per le saldature in acciaio c assume un valore di 0.2 mm [6]. il metodo del raggio fittizio applicato alle giunzioni saldate l metodo del raggio fittizio, inizialmente proposto da neuber, è basato sull’assunzione che una tensione mediata su una lunghezza microstrutturale caratteristica del materiale potesse essere utilizzata per descrivere la gravosità dello stato tensionale in presenza di intagli con raggio di raccordo ridotto. nel riferimento bibliografico [5] radaj propose di utilizzare tale metodo nello studio della resistenza a fatica delle giunzioni saldate dove, l’effetto d’intaglio, viene studiato introducendo un raggio fittizio ρf pari alla somma del raggio ρ di raccordo reale ed il prodotto s·ρ*, dove ρ* è un parametro dipendente dal solo materiale, mentre, s è definito come il coefficiente di multiassialità dipendente dal criterio di cedimento assunto per il materiale. l’espressione del raggio fittizio è data da: * f s    (5) utilizzando l’espressione (5), la resistenza a fatica di un intaglio viene relegata al calcolo del solo picco di tensione in prossimità del raggio di raccordo. nel caso delle saldature ρ è assunto pari a zero (ipotesi in vantaggio di sicurezza e coerente con il metodo del gradiente implicito) mentre il prodotto s·ρ* per acciai assume un valore unitario, perciò si ottiene: ρf≈1mm. tale approccio è applicabile ai giunti di grosso spessore (t≥5mm [8, 13]) per i quali è data la curva di progetto in termini di tensione di picco. tuttavia, quando lo spessore del giunto è ridotto (t<5mm) l’introduzione di un raggio fittizio pari ad 1 mm potrebbe risultare eccessivo comportando delle variazioni geometriche non più trascurabili. in tal caso è stato proposto di recente da karakas et al. [8] una variante del metodo originariamente presentato da radaj. il valore del raggio fittizio di raccordo viene ridotto da 1 mm a 0.05 mm. tale modifica, tuttavia, comporta una notevole complicazione dal punto di vista del calcolo del picco di tensione da porre a confronto con la curva di riferimento. come si vedrà nel seguito, la condizione di convergenza della soluzione lineare elastica in prossimità del raggio di raccordo richiede un numero elevato di elementi con un costo, in termini computazionali, notevole anche per particolari saldati di piccole dimensioni. (a) (b) figura 1: geometrie analizzate: a) giunto a tazza assialsimmetrico [14]; b) giunto a semplice sovrapposizione [15]. i http://dx.medra.org/10.3221/igf-esis.12.08&auth=true http://www.gruppofrattura.it r. tovo et alii, frattura ed integrità strutturale, 12 (2010) 79-87; doi: 10.3221/igf-esis.12.08 82 geometrie analizzate l confronto proposto in questo lavoro fra il metodo del raggio fittizio ed il metodo del gradiente implicito è sviluppato su due tipologie di giunti saldati di piccolo spessore tratti dalla letteratura. la fig. 1a mostra la geometria di una giunzione a tazza in cui il punto di saldatura è sollecitato a sola trazione [14]. la fig. 1b, invece, riporta la geometria di un classico giunto a semplice sovrapposizione ottenuto con un solo punto di saldatura [15]. in questo caso la saldatura è sollecitata a taglio e a flessione qualora nel piatto principale sia applicata una tensione nominale di trazione. tutte le analisi fem sono state eseguite in ipotesi di piccoli spostamenti mantenendo un comportamento lineare elastico del materiale indipendentemente dal livello di carico raggiunto nella sezione nominale. saranno esaminate quattro serie di dati sperimentali: tre relative ai giunti a tazza aventi spessore variabile da 0.8 mm a 1.5 mm e una serie relativa a giunti a sovrapposizione aventi spessore di 1 mm. tutti i giunti sono sollecitati da un carico nominale di trazione. analisi numeriche sintesi dei risultati numerici con il metodo del gradiente implicito giunti saldati illustrati al paragrafo precedente possono essere esaminati con il metodo del gradiente implicito applicando esattamente la stessa metodologia descritta per i giunti di grosso spessore, in particolare, senza variare i parametri legati alla resistenza del materiale (si mantiene costante c anche per giunti di piccolo spessore). assunta la tensione principale come parametro responsabile del danneggiamento a fatica, risolvendo l’eq. (3), in ogni punto del giunto saldato si calcola la tensione efficace eff da porre a confronto con la curva di wöhler del materiale. le mesh tipicamente usate nell’analisi delle quattro serie sono mostrate nelle fig. 2a e 3a, mentre le curve di livello della eff è evidenziato nelle fig. 2b e 3b. le zone evidenziate in rosso sono quelle in cui la tensione efficace eff raggiunge il valore massimo ed esattamente laddove si ha la enucleazione della cricca per fatica. (a) (b) figura 2: a) esempio di mesh usata per il calcolo di eff con il metodo del gradiente implicito; b) tensione efficace eff per il giunto a sovrapposizione (tensione nominale di 1 mpa). (a) (b) figura 3: a) esempio di mesh usata per il calcolo della tensione efficace eff con il metodo del gradiente implicito; b) tensione efficace eff per il giunto a sovrapposizione (tensione nominale di 1 mpa sul collare). i i http://dx.medra.org/10.3221/igf-esis.12.08&auth=true http://www.gruppofrattura.it r. tovo et alii, frattura ed integrità strutturale, 12 (2010) 79-87; doi: 10.3221/igf-esis.12.08 83 la fig. 4 riporta i valori massimi max,eff della tensione efficace al variare della dimensione dell’elemento più piccolo usato nell’analisi fem tridimensionale (l’adimensionalizzazione è fatta rispetto al valore limite , max limeff ottenuto quando la dimensione dell’elemento più piccolo della mesh tende a zero). il metodo si dimostra numericamente stabile anche con discretizzazioni che impiegano un solo elemento nello spessore (in questo caso la differenza è inferiore al 5% rispetto a mesh molto accurate). la fig. 5 analizza la resistenza a fatica delle quattro serie di dati sperimentali in termini di valore massimo del range di max,eff . la banda tracciata è relativa alle connesioni di grosso spessore [6] mentre i simboli fanno riferimento ai giunti saldati per punti aventi spessore variabile da 0.8 a 1.5 mm. figura 4: picco di tensione efficace normalizzato rispetto al valore limite al variare delle dimensioni della mesh , max, 1 , 1 , maxlim lim ,         effloc s loc s eff . figura 5: previsione della resistenza a fatica di giunzioni saldate per punti fra 104 e 5·106 cicli con il metodo del gradiente implicito. la banda di dispersione è quella dei giunti saldati ad arco in acciaio di grosso spessore relativa al valore medio 2 deviazioni standard. http://dx.medra.org/10.3221/igf-esis.12.08&auth=true http://www.gruppofrattura.it r. tovo et alii, frattura ed integrità strutturale, 12 (2010) 79-87; doi: 10.3221/igf-esis.12.08 84 sintesi dei risultati numerici con il metodo del raggio fittizzio rf = 0.05 mm l’analisi dei giunti di fig. 1 con il metodo del raggio fittizio di raccordo deve necessariamente prevedere l’adozione di un raggio di raccordo inferiore ad 1 mm per non alterare completamente la geometria del giunto in quanto risulterebbe non compatibile con lo spessore del giunto stesso (ρ>t). poiché lo spessore del giunto è minore di 5 mm il raggio di raccordo dell’apice del punto di saldatura è stato posto pari a 0.05 mm come indicato in [8]. le fig. 6a e 7a mostrano due tipiche mesh impiegate nell’analisi fem, mentre le fig. 6b e 7b evidenziano la dimensione degli elementi in prossimità del raggio di raccordo. le dimensione degli elementi più piccoli risultano inferiori al centesimo di millimetro. le fig. 8 e 9 riportano i risultati, a curve di livello, del valore raggiunto dalla tensione principale massima. (a) (b) figura 6: a) esempio di mesh usata per il calcolo della tensione di picco; b) zoom nella zona di raccordo. (a) (b) figura 7: a) esempio di mesh usata per il calcolo della tensione di picco; b) zoom nella zona di raccordo. l’analisi di convergenza è riassunta nella fig. 4 e 10. il picco della tensione principale massima normalizzata è riportato in funzione del numero totale di nodi usato per discretizzare il giunto. per il giunto a tazza di fig. 10 quando il numero di elementi nello spessore è pari a due la differenza rispetto ad un modello molto accurato è del 12%, mentre con il metodo del gradiente implicito l’errore è inferiore al 4% quando si adotta un solo elemento nello spessore (vedi fig. 4). relativamente al giunto a sovrapposizione, la differenza fra una mesh rada e una mesh fitta è considerevole. con il metodo del raggio fittizio, utilizzando due elementi nello spessore, l’errore è del 76%, mentre, con il gradiente implicito usando uno o due elementi nello spessore l’errore è del 5% e scende al di sotto del 2% con 4 elementi nello spessore. infine, per quanto riguarda la previsione della resistenza a fatica in termini di tensione principale massima o di tensione di von mises, le figure, rispettivamente 11 e 12, riportano le variazioni del picco di tensione valutate per le due geometrie di fig. 1. ad alto numero di cicli i punti sperimentali tendono a posizionarsi al di fuori della banda la cui dispersione è stata assunta pari a quella dei giunti di grosso spessore [13]. http://dx.medra.org/10.3221/igf-esis.12.08&auth=true http://www.gruppofrattura.it r. tovo et alii, frattura ed integrità strutturale, 12 (2010) 79-87; doi: 10.3221/igf-esis.12.08 85 figura 8: tensione principale massima per il giunto a tazza di fig. 1a (tensione nominale di 1 mpa sul collare). figura 9: tensione principale massima per il giunto a sovrapposizione di fig. 1b (tensione nominale di 1 mpa). figura 10: picco di tensione principale massima normalizzato rispetto al valore limite al variare delle dimensioni della mesh , max, 1 , 1 , maxlim lim ,         effloc s loc s eff . conclusioni e analisi numeriche sulla previsione della vita a fatica di giunzioni di piccolo spessore eseguite con il metodo del gradiente implicito o con il metodo del raggio di raccordo fittizio ha portato alle seguenti conclusioni: o adottando il metodo del gradiente implicito è possibile affrontare lo studio delle strutture saldate senza apportare esemplificazioni di tipo geometrico. o l’effetto scala con il metodo del gradiente implicito è pienamente considerato. infatti, i punti sperimentali relativi al comportamento a fatica di giunti di piccolo spessore vanno a cadere all’interno della banda di dispersione proposta in precedenza per i giunti di grosso spessore. o dal punto di vista concettuale il metodo del raggio di raccordo è semplice da applicare ma impone di usare un raggio di raccordo relativamente piccolo rispetto allo spessore. ciò consegue che le mesh devono risultare sufficientemente accurate in corrispondenza del raggio di raccordo. l http://dx.medra.org/10.3221/igf-esis.12.08&auth=true http://www.gruppofrattura.it r. tovo et alii, frattura ed integrità strutturale, 12 (2010) 79-87; doi: 10.3221/igf-esis.12.08 86 o la condizione di convergenza sul metodo del gradiente implicito è ottenuta rapidamente all’aumentare del numero di elementi sebbene le saldature siano considerate come intagli acuti a v. figura 11: range della tensione principale massima di picco in funzione della resistenza a fatica. figura 12: range della tensione di von mises di picco in funzione della resistenza a fatica. bibliografia [1] eurocode 3: design of steel structures; general rules. (1993) 1-1. [2] british standard published document, code of practice for fatigue design and assessment of steel structures, bs 7608 (1993). [3] a. hobbacher. recommendation on fatigue of welded components, iiw document xiii-1539-95/ xv-845-95 (1995). [4] d. radaj, cm sonsino, w. fricke. fatigue assessment of welded joints by local, approaches. 2nd ed. cambridge: woodhead publishing and boca raton fla: crc press (2006). http://dx.medra.org/10.3221/igf-esis.12.08&auth=true http://www.gruppofrattura.it r. tovo et alii, frattura ed integrità strutturale, 12 (2010) 79-87; doi: 10.3221/igf-esis.12.08 87 [5] d. radaj, design and analysis of fatigue resistant welded structures, abington publishing, abington, cambridge (1990). [6] r. tovo, p. livieri, engineering fracture mechanics, 74 (2007) 515. [7] r. tovo, p. livieri, engineering fracture mechanics, 75 (7) (2008) 1804. [8] ö. karakas, c. morgenstern, c.m. sonsino, international journal of fatigue, 30(12) (2008) 2210. [9] m.l. williams, asme journal of applied mechanics, 19 (1952) 526. [10] r.h.j. peerlings, r. de borst, w.a.m. brekelmans, j.h.p. de vree, international journal of numerical methods in engineering, 39 (1996) 3391. [11] m. h. el haddad, t.h. topper, k. n. smith, asme, journal of engineering material and technology, 101 (1979) 42. [12] r. tovo, p. livieri, e. benvenuti, international journal of fracture, 141(3) (2006) 497. [13] c.m. sonsino, t. bruder, j. baumgartner, sn-curves for welded thin jointssuggested slopes and fat-values for applying the notch stress concept with various reference radii. iiw-doc. no. xiii-2280 (2009)/xv-1325 (2009). [14] o. hahn, j. r. kurzok, a. rohde (in german: investigation of the transferability of characteristic values determined on a single-spot-weld specimen to multi-spot-welded specimens or structures). 1998, fat schriften reihe 142 reported in: g. zhang , b. richter, fatigue fract. engng. mater. struct., 23 (2000) 499. [15] j. a. newman, n. e. dowling, fatigue & fracture of engineering materials & structures, 21 (1998) 1123. http://dx.medra.org/10.3221/igf-esis.12.08&auth=true http://www.gruppofrattura.it microsoft word numero_52_art_13_2691 a. ayadi et alii, frattura ed integrità strutturale, 52 (2020) 148-162; doi: 10.3221/igf-esis.52.13 148 elastoplastic analysis of plane structures using improved membrane finite element with rotational dofs ayadi ayoub, meftah kamel university of biskra, laboratoire de génie energétique et matériaux, lgem, faculty of sciences and technology, biskra, 07000, algeria a.ayadi@univ-biskra.dz k.meftah@univ-biskra.dz, http://orcid.org/0000-0002-5671-602x sedira lakhdar university of biskra, laboratoire de génie mécanique, lgm, faculty of sciences and technology, biskra, 07000, algeria l.sedira@univ-biskra.dz, http://orcid.org/0000-0003-1735-2195 abstract. in this work, the small-strain elastoplastic behavior of structures is analyzed using an improved nonlinear finite element formulation. in this framework, an eight-node quadrilateral finite element denoted pfr8 (plane fiber rotation) that belongs to the set of elements with rotational degrees of freedom is developed. its formulation stems from the plane adaptation of the space fiber rotation (sfr) concept that considers virtual rotations of nodal fiber within the element. this approach results in an enhancement of the displacement vector approximation. von-mises yield criteria have been applied for yielding of the materials along with the associated flow rule. newton-raphson method has been used to solve the nonlinear equations. to assess the performance of the proposed element, benchmark problems are addressed and the results are compared with some analytical and numerical solutions from the literature. keywords. elasto-plasticity; nonlinear analysis; membrane finite element; plane fiber rotation; rotational dofs. citation: ayadi, a., meftah, k., sedira, l., elastoplastic analysis of plane structures using improved membrane finite element with rotational dofs, frattura ed integrità strutturale, 52 (2020) 148-162. received: 22.11.2019 accepted: 03.02.2020 published: 01.04.2020 copyright: © 2020 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. introduction onlinear problems arise in almost all disciplines of science and engineering practice. in structural mechanics, nonlinear analysis has emerged as a powerful platform for evaluation the performance of structural systems at the life safety and collapse prevention levels [1]. the literature on nonlinear structural behavior has highlighted several types of nonlinearities including geometric, material, kinematic and force nonlinearities [2]. in recent years, a large n https://youtu.be/bn-cfiy7cqq a. ayadi et alii, frattura ed integrità strutturale, 52 (2020) 148-162; doi: 10.3221/igf-esis.52.13 149 and growing body of literature has investigated the nonlinear elastoplastic behavior of structures as it appears in a wide range of applications and industrial processes. for instance, crashworthy structures show a complex combination of structural nonlinearities in which plastic deformation is expected to contribute to the energy absorption [3]. another example is drop test of some mobile devices such as mobile phones, personal digital assistants and laptops which end up generally with permanent deformation [4]. due to complexity of geometry, boundary and loading conditions, there are limited practical problems in plasticity where analytical solution is available. therefore, numerical analysis, and in particular, the finite element method has emerged as a viable alternative in addressing this kind of problems. within this framework, accuracy and efficiency of finite elements have gained fresh prominence. to avoid the problem of singularity in the stiffness matrix and also to improve the accuracy of numerical results, there has been renewed interests in finite element with in-plane rotational degrees of freedom called also drilling rotations [5]. since the first successful element with drilling variables proposed by allman [6], a considerable amount of literature has been published on this subject [7–13]. working along similar lines, many three-dimensional solid element formulations with rotational dofs have been also proposed [14–24]. ayad et al.[24], developed two eight-node hexahedral elements sfr8 and sfr8i based on the so-called space fiber rotation concept (sfr). this approach, firstly introduced by ayad [25], considers 3d virtual rotations of a nodal space fiber within the finite element that improves the displacement vector approximation. similarly, many authors implemented this concept in different area of research [16, 17, 23–25, 27]. despite the abundance of literature on the finite elements with rotational dofs, only a few have been proposed to account for material and geometric nonlinear problems. these includes the works of gruttmann et al. [28], ibrahimbegovic et al. [29–31], rebiai et al. [13] and zouari et al. [32]. in the work of zouari et al. [32], this approach has been successfully adopted to develop two four-node membrane elements, named pfr4 and pfr4i, to analyze linear and nonlinear geometric plane problems. this paper presents a new eight-node membrane finite element pfr8 in order to analyze elastoplastic nonlinear problems. the element’s formulation is based on a planar adaptation of the sfr concept which results in a simpler and more concise formulation than the previous developed membrane elements with rotational dofs. the remaining part of the paper proceeds as follows. in section 2, the formulation behind the proposed quadrilateral element is detailed. in section 3, the model is framed within the nonlinear analysis through the small strain elastoplastic constitutive model. finally, and before highlighting the concluding remarks, numerical results relative to a series of benchmarks are presented. basic constitutive equations of continuum elastoplasticity fter initial yielding the material behavior will be partly elastic and partly plastic. the phenomenon is characterized by an irreversible deformation where the total strain can be expressed:    e pij ij ij     (1) where  eij and   p ij are the elastic and plastic components of the total strain respectively. the elastoplastic behavior is governed by a scalar function called yield function of the form:  , 0ij   (2) where ij denotes the indicial form of the stress tensor and  represents hardening parameters. as shown in fig. 1, the yield condition can be visualized as a surface in the stress space where the size of the surface depends on the value of the parameter  . in this paper, the elastoplastic model based on the von-mises associated yield criterion is adopted. thus, the above yield condition can be expressed as:  , 0pe y       (3) where e is the von-mises effective stress and y is the yield stress. a a. ayadi et alii, frattura ed integrità strutturale, 52 (2020) 148-162; doi: 10.3221/igf-esis.52.13 150 using the classical associative plastic flow rule, the plastic strain rate is assumed to be given by: figure 1: yield surface and normality rule in 2d stress space.[33][34] p ij ij            (4) where  and p represent the plastic multiplier and the plastic flow direction, respectively. the elastic part of strain field is linked to stress field through the relation:    -e p eij ijkl kl kl ijkl klc c       (5) where eijklc is the tensor of elastic constants which for an isotropic material may be given as: 2 1 2 e ijkl ij kl ik jl il jkc g                (6) in which g is the shear modulus;  is poisson’s ratio and ij represents the kronecker delta. using the consistency condition 0  , the plastic multiplier in eq. (4) can be expressed as:       e ij ijkl ij e rs rstu tu c c                 (7) finally, by substituting the expression of the plastic multiplier into eq. (5), the elastoplastic tangent modulus is derived as:        e e ijmn mn pq pqklep e ijkl ijkl e rs rstu tu c c c c c                  (8) where 1  for strict plastic loading and 0  for elastic loading/unloading. therefore, the elastoplastic stress-strain relation can be expressed: ep ij ijkl klc  (9) a. ayadi et alii, frattura ed integrità strutturale, 52 (2020) 148-162; doi: 10.3221/igf-esis.52.13 151 finite element procedure onsider a body of a domain  , in which the internal stresses   , boundary tractions t , and the distributed loads/unit volume vf form an equilibrium field; to undergo an arbitrary admissible displacement u . therefore, the virtual work principle requires that:             0 t t t v s d u f d u t da             (10) where   is the vector of associated virtual strains and s is the boundary on which tractions are applied. the virtual linearized strain tensor  can be expressed in terms of the displacement vector as:     ¨1 grad grad2 t u u    (11) kinematics of the pfr8 finite element the plane fiber rotation (pfr) formulation stems from the space fiber rotational (sfr) concept. this concept, firstly introduced by ayad [25], considers a 3d virtual rotations of nodal space fiber within the element that enhances the displacement vector approximation. despite some differences (geometry, interpolation functions…), the pfr and sfr formulations proceed very much in the same way. (a) (b) figure 2: the pfr approach: (a) out of plane rotation of the virtual fiber iq inducing an additional displacement i z iq  . (b) the eight-node membrane element pfr8 with its nodal dofs. in this section, the plane fiber rotation approach is used to formulate an eight-node quadrilateral finite element called pfr8. as shown in fig. 2, the pfr approach considers the rotation of the out of plane virtual nodal fiber iq within the element. this results in an enhancement in the displacement vector approximation. the pfr approximation of the displacement vector of a point q of the element takes the following form:   8 1 ,i i i i uq n u f iq      (12) c a. ayadi et alii, frattura ed integrità strutturale, 52 (2020) 148-162; doi: 10.3221/igf-esis.52.13 152 where  ,if iq is the additional displacement, iu is the vector of nodal displacements, and in are the classical shape functions associated with the serendipity eight-node quadrilateral element. the additional displacements vector is given by:     8 1 , ; i i ii ii x x f iq n z iq iq y y              (13) therefore:       8 8 , i i ii i i ii u u y y n v v x x                      (14) where x and y are the cartesian coordinates of q, ix and iy 1, 8i  are the nodal coordinates, iu , iv and i , 1, 8i  are the nodal dofs (two displacements and one virtual rotation per node). in the matrix form, the approximation can be rewritten as:     , uen v u n n u n v n             (15) where     0 1, 8 0 1, 8 u i i i v i i i n n n y y i n n n x x i            (16) and    1, 8 ten i i iu u v i   (17) is nodal dofs vector of the pfr8 containing the mechanical displacements and rotations. the finite element discretization leads to write strains in the element level as:     enb u  (18) where  b is the discrete symmetric gradient which has the format:   , , , , u x v y u y v x n b n n n            (19) since the shape function derivatives are expressed in terms of natural coordinates  ,  , a transformation to the physical domain  ,x y should be performed. accordingly, the shape function derivatives in terms of the physical domain coordinates  ,x y are given by: a. ayadi et alii, frattura ed integrità strutturale, 52 (2020) 148-162; doi: 10.3221/igf-esis.52.13 153 , 11 , 12 , , 21 , 22 , x y n j n j n n j n j n               (20) where lkj are the terms of inverse jacobian matrix. based on eqns. (9), (10), and (18), the virtual potential energy expression can be conveniently rearranged as:                 0t t t te e ep en n v s u b c b d u n f d n t da                          (21) this equation results to the following expression:    e e et n extk u f    (22) where etk is the (24 × 24)-sized element stiffness matrix and e extf is the external force vector. in this work, this system (eq. 20) is solved by the classical frontal method [35, 36]. numerical solution for elastoplastic problems n order to solve elastoplastic problems, an algorithm based on the return mapping scheme [37, 38] is adopted. this algorithm relies basically on a two-step procedure: perform a predictor step in which we assume that the step  1,n nt t  is elastic. accordingly: 1 trial e n n      (23) the corresponding trial stress is given by:  1 1trail pn n nd     (24) evaluation of the yield function: if  1 , 0trialn   , the stress relies within the yield surface and the trial state represents the actual final state of material. thus:    1 1 trial n n     (25) if  1 , 0,trialn   the elastic trial state is not plastically admissible and the consistency condition is violated. therefore, a plastic corrector step (or return mapping algorithm) is required. accordingly: c : p trial trial t t t t trial t t t t t trial e t t t p                       (26) the flowchart in fig. 3 presents an overall summary of the procedure. i a. ayadi et alii, frattura ed integrità strutturale, 52 (2020) 148-162; doi: 10.3221/igf-esis.52.13 154 figure 3: flowchart of the numerical procedure. numerical examples n order to evaluate the accuracy, efficiency, and robustness of the proposed eight-node quadrilateral element pfr8, the element’s formulation is implemented in the fortran finite element code hyplas [39] to account for elastic and elastoplastic problems. in this section, representative benchmark problems are addressed. the obtained results are compared with the following reference elements:  q8: the standard 8-node quadrilateral element with full numerical integration scheme.  hwq8d: 8-node mixed quadrilateral element based on the hu-washizu functional [40].  cps8: the plane stress eight-node quadrilateral abaqus element with a full numerical integration scheme [41].  cps8r: the plane stress eight-node quadrilateral abaqus element with a reduced numerical integration scheme [41].  q4: the standard 4-node quadrilateral element with full numerical integration scheme.  pfr4: 4-node quadrilateral element based on the concept of ‘plane fiber rotation’ [32].  q4ps: 4-node quadrilateral hybrid element [42].  q4wt: 4-node quadrilateral non-conforming element [43, 44].  allman : 4-node quadrilateral element with drilling dofs [45]. for each elastoplastic problem, the von-mises plasticity model is adopted where the newton raphson tangential stiffness method is used to solve the nonlinear resulting systems. i a. ayadi et alii, frattura ed integrità strutturale, 52 (2020) 148-162; doi: 10.3221/igf-esis.52.13 155 cantilever beam under in-plane bending load the first analyzed problem is a cantilever beam under pure plane bending. this example is a popular benchmark that has been studied by several authors [24, 43, 46] to evaluate the convergence rate and sensitivity to mesh distortion of the proposed elements. geometry and material properties are shown in fig. 4. as illustrated in fig. 5, the beam is modeled with six different meshes: three structured and three distorted meshes. the maximum vertical displacement of point c, belonging to the right end side of the beam, can be obtained analytically by using the timoshenko beam theory: 3 6 4.03 3 5 y yref c p l p l v ei ga    (27) the normalized vertical displacement of point c is then determined and the obtained results are plotted in fig. 6. for structured meshes, the pfr8 element has the best convergence rate when comparing to the other reference elements. on the other hand, the element exhibits very good performance for distorted meshes and it turns out to be less sensitive to mesh distortion. figure 4: plane bending of a cantilever beam: geometry and material properties. figure 5: plane bending of a cantilever beam: structured and distorted meshes. (a) (b) figure 6: plane bending of a cantilever beam: normalized vertical displacement of point c. (a) structured meshes; (b) distorted meshes. a. ayadi et alii, frattura ed integrità strutturale, 52 (2020) 148-162; doi: 10.3221/igf-esis.52.13 156 cook’s membrane this is a popular benchmark to evaluate the element’s performance in bending dominated applications [7, 47]. it consists of a trapezoidal cantilever plate completely constrained at the left-end and subjected to a uniform tangential load at the right free edge as shown in fig. 7. the analysis is performed on the basis of six different structured meshes of 2 2 elements, with 𝑛 1,…,6. material properties, boundary conditions and finite element mesh for 𝑛 1 are illustrated in fig. 7. the reference solution of the vertical displacement of point a is reported by bergan and felippa in [7] and it is taken to be: 23.9refav  . the results of pfr8 element are compared with some reference elements in tab. 1 where the convergence curves are depicted in fig. 8. the findings demonstrate that the proposed pfr8 element for a given mesh density is better than the q4 and q8 elements and can be competitive when compared to the other reference elements. figure 7: cook’s membrane: geometry and material properties this example is also a well-known benchmark to evaluate the effectiveness of the finite element formulation in elastoplastic behavior [40, 48, 49]. material properties adopted are: poisson’s ration 0.2  , young modulus 70000e  , yield stress 0 243y  and the isotropic hardening modulus 1000h  . a total load 1600f  is applied via an incremental scheme of 11 time steps where a mesh of (4 × 4) elements is adopted. fig. 9 provides a comparison of the load-displacement curves of different elements. as can be seen, the pfr8 element results agree very well with the other reference solutions. n pfr8 hwq8d q8 allman hs-a7 q4 1 23.064 22.833 22.141 20.267 22.550 11.748 2 23.469 23.669 23.275 22.776 23.440 18.262 3 23.578 23.813 23.521 23.565 23.790 22.030 4 23.612 23.914 23.593 23.900 23.382 5 23.625 23.914 23.618 23.770 6 23.629 23.928 23.620 23.827 table 1: cook’s membrane: vertical displacement of point a  23.9refav  . a. ayadi et alii, frattura ed integrità strutturale, 52 (2020) 148-162; doi: 10.3221/igf-esis.52.13 157 figure 8: cook’s membrane: convergence of the normalized vertical displacement of point a. figure 9: elastoplastic cook’s membrane: load-displacement curve. cantilever beam in this example, an elastoplastic cantilever beam with rectangular cross section is analyzed. as shown in fig. 10, this beam is subjected to an in-plane load f at point c. geometric as well as material properties are set out in tab. 1. the material is assumed to be perfectly plastic where the von-mises model is implemented in the plane stress conditions. the cantilever is discretized into (2 × 50) regular quadrilateral finite elements. in this example, two cases of boundary conditions are studied as shown in fig. 10. for case (a), the analytical limit load is given by lubliner [50]: 2 lim 30 4 y th f kn l    (28) fig. 11 shows the load displacement curve at point c for both cases of boundary conditions. the results of pfr8 element are compared with some reference solutions. for both cases, the present results agree very well with the reference curves. the limit load obtained in the present solution for case (a) is 8lim 29, 6388 pfrf kn . the evolution of the equivalent plastic strain for case (a) and (b) are depicted in fig. 12 and fig. 13. for case (a), it can be clearly seen that the plastic a. ayadi et alii, frattura ed integrità strutturale, 52 (2020) 148-162; doi: 10.3221/igf-esis.52.13 158 deformation starts at the node where the pinned boundary condition is applied and extends along the edge. on the other hand, the clamped edge doesn’t show plastic deformation in case (b). geometric properties material properties length 1000l mm young modulus 210e gpa width 100h mm poisson’s ratio 0.3  thickness 50t mm yield stress 0.24y gpa  table 2: cantilever beam: geometric and material properties. (a) (b) figure 10: cantilever beam: (a) geometry and boundary conditions for case (a); (b) geometry and boundary conditions for case (b) thick cylinder this example considers an infinitely long thick cylinder subjected to a gradually increasing internal pressure. this benchmark has been studied by several authors [39, 51] and a reference solution was derived by hill [52] where the limit pressure is expressed as: 2 lim 1 2 ln 3 y r p r         (29) (a) (b) figure 11: cantilever beam: (a) load displacement curve for case (a); (b) load displacement curve for case (b). a. ayadi et alii, frattura ed integrità strutturale, 52 (2020) 148-162; doi: 10.3221/igf-esis.52.13 159 figure 12: cantilever beam: evolution of plastic strain case (a). figure 13: cantilever beam: evolution of plastic strain case (b). the geometry of the problem as well as the adopted finite element mesh are shown in fig. 13. the limit pressure for the present properties becomes: lim 0.19209p gpa (30) owing to the symmetry of the problem, only a 30° segment of the cylinder is discretized assuming plane strain conditions along the axis of the cylinder. material as well as geometric properties are summarized in tab. 3. the radial displacement at point b is plotted against the applied pressure in fig. 14. the pfr8 results are compared to the q8 standard element and the hill’s solution and a good correlation among the three set of results is obtained. in this example, yielding starts at the inner face of the cylinder and extends along the radius toward the outer face as depicted in fig. 15. (a) (b) figure 13: thick cylinder: (a) geometry (b) finite element meshes. geometric properties material properties internal radius 1 100r mm young modulus 210e gpa external radius 2 200r mm poisson’s ratio 0.3  yield stress 0.24y gpa  table 3: thick cylinder: geometric and material properties. a. ayadi et alii, frattura ed integrità strutturale, 52 (2020) 148-162; doi: 10.3221/igf-esis.52.13 160 figure 14: thick cylinder: pressure-displacement curve. figure 15: thick cylinder: evolution of plastic deformation. conclusion n this paper, an eight-node quadrilateral element denoted pfr8 has been developed to account for elastic and elastoplastic problems. the element formulation relies on the plane adaptation of the space fiber rotation (sfr) concept that considers an out of plane virtual rotation of a nodal fiber within the element which results in an enhancement in the displacement vector approximation. the present analysis focuses on small strain applications using the associative von-mises plasticity model. the proposed quadrilateral plane element pfr8 was implemented in hyplas, a fortran finite element code developed by de souza neto et al. [39]. the element performance was evaluated through plane strain/stress benchmark examples. for all examples, the numerical results obtained with the pfr8 element showed good agreement with the reference solutions. references [1] krawinkler, h. (2006). importance of good nonlinear analysis, struct. des. tall spec. build., 15(5), pp. 515–531, doi: 10.1002/tal.379. [2] kim, n.-h. (2014). introduction to nonlinear finite element analysis, springer science & business media. [3] fang, j., sun, g., qiu, n., kim, n.h., li, q. (2017). on design optimization for structural crashworthiness and its state of the art, struct. multidiscip. optim., 55(3), pp. 1091–119, doi: 10.1007/s00158-016-1579-y. [4] che, f.x., pang, j.h.l. (2015). study on board-level drop impact reliability of sn–ag–cu solder joint by i a. ayadi et alii, frattura ed integrità strutturale, 52 (2020) 148-162; doi: 10.3221/igf-esis.52.13 161 considering strain rate dependent properties of solder, ieee trans. device mater. reliab., 15(2), pp. 181–190. [5] iura, m., atluri, s.n. (1992). formulation of a membrane finite element with drilling degrees of freedom, comput. mech., 9(6), pp. 417–428, doi: 10.1007/bf00364007. [6] allman, d.j. (1984). a compatible triangular element including vertex rotations for plane elasticity analysis, comput. struct., 19(1–2), pp. 1–8, doi: 10.1016/0045-7949(84)90197-4. [7] bergan, p.g., felippa, c.a. (1985). a triangular membrane element with rotational degrees of freedom, comput. methods appl. mech. eng., 50(1), pp. 25–69, doi: 10.1016/0045-7825(85)90113-6 [8] ibrahimbegovic, a., taylor, r.l., wilson, e.l. (1990). a robust quadrilateral membrane finite element with drilling degrees of freedom, int. j. numer. methods eng., 30(3), pp. 445–457, doi: 10.1002/nme.1620300305. [9] yang, h.t.y., saigal, s., masud, a., kapania, r.k. (2000). a survey of recent shell finite elements, int. j. numer. methods eng., 47(1‐3), pp. 101–127, doi: 10.1002/(sici)1097-0207(20000110/30)47:1/3<101::aid-nme763>3.0.co;2-c. [10] geyer, s., groenwold, a.a. (2003). on reduced integration and locking of flat shell finite elements with drilling rotations, commun. numer. methods eng., 19(2), pp. 85–97, doi: 10.1002/cnm.567 [11] choi, n., choo, y.s., lee, b.c. (2006). a hybrid trefftz plane elasticity element with drilling degrees of freedom, comput. methods appl. mech. eng., 195(33–36), pp. 4095–4105, doi: 10.1016/j.cma.2005.07.016. [12] boutagouga, d., gouasmia, a., djeghaba, k. (2010). geometrically nonlinear analysis of thin shell by a quadrilateral finite element with in-plane rotational degrees of freedom, eur. j. comput. mech. eur. mécanique numérique, 19(8), pp. 707–724, doi: 10.3166/ejcm.19.707-724. [13] rebiai, c., belounar, l. (2013). a new strain based rectangular finite element with drilling rotation for linear and nonlinear analysis, arch. civ. mech. eng., 13(1), pp. 72–81, doi: 10.1016/j.acme.2012.10.001. [14] yunus, s.m., pawlak, t.p., cook, r.d. (1991). solid elements with rotational degrees of freedom: part 1— hexahedron elements, int. j. numer. methods eng., 31(3), pp. 573–592, doi: 10.1002/nme.1620310310. [15] ibrahimbegovic, a., wilson, e.l. (1991). thick shell and solid finite elements with independent rotation fields, int. j. numer. methods eng., 31(7), pp. 1393–1414, doi: 10.1002/nme.1620310711. [16] zouari, w., assarar, m., ayad, r. (2015). free vibration analysis of homogeneous piezoelectric structures using specific hexahedral elements with rotational dofs, 226(6), pp. 1737–1756, doi: 10.1007/s00707-014-1274-2. [17] ghomari, t., meftah, k., ayad, r., talbi, n. (2015). a space fibre as added value in finite element modelling for optimal analysis of problems involving contact, eur. j. comput. mech., 7179(october), doi: 10.1080/17797179.2012.702435. [18] pawlak, t.p., yunus, s.m., cook, r.d. (1991). solid elements with rotational degrees of freedom: part ii— tetrahedron elements, int. j. numer. methods eng., 31(3), pp. 593–610, doi: 10.1002/nme.1620310311 [19] sze, k.y., ghali, a. (1993). a hybrid brick element with rotational degrees of freedom, comput. mech., 12(3), pp. 147–163, doi: 10.1007/bf00371990 [20] sze, k.y., pan, y.s. (2000). hybrid stress tetrahedral elements with allman’s rotational dofs, int. j. numer. methods eng., 48(7), pp. 1055–70, doi: 10.1002/(sici)1097-0207(20000710)48:7<1055::aid-nme916>3.0.co;2-p [21] ayad, r. (2003).un elément fini solide 3d à 8 nœuds basé sur le modèle sfr (space fiber rotation), 16ème congrés français de mécanique. [22] tian, r., yagawa, g. (2005). generalized nodes and high‐performance elements, int. j. numer. methods eng., 64(15), pp. 2039–2071, doi: 10.1002/nme.1436. [23] meftah, k., ayad, r., hecini, m. (2012). a new 3d 6-node solid finite element based upon the “space fibre rotation” concept, eur. j. comput. mech., (10 sep 2012), pp. 37–41, doi: 10.1080/17797179.2012.721502 [24] ayad, r., zouari, w., meftah, k., zineb, t. ben. (2013). enrichment of linear hexahedral finite elements using rotations of a virtual space fiber, int. j. numer. methods eng., (may), pp. 46–70, doi: 10.1002/nme. [25] meftah, k., sedira, l., zouari, w., ayad, r., hecini, m. (2015). a multilayered 3d hexahedral finite element with rotational dofs a multilayered 3d hexahedral finite element with rotational dofs, eur. j. comput. mech. issn, 7179(november), doi: 10.1080/17797179.2015.1089462. [26] ayad, r. (2002). contribution to the numerical modeling of solids and structures and the non-newtonian fluids forming process. application to packaging materials, habilit. to conduct res. univ. reims, ,. [27] meftah, k., zouari, w., sedira, l., ayad, r. (2016). geometric non-linear hexahedral elements with rotational dofs, comput. mech., 57(1), pp. 37–53, doi: 10.1007/s00466-015-1220-8. [28] gruttmann, f., wagner, w., wriggers, p. (1992). a nonlinear quadrilateral shell element with drilling degrees of freedom, arch. appl. mech., 62(7), pp. 474–486, doi: 10.1007/bf00810238. a. ayadi et alii, frattura ed integrità strutturale, 52 (2020) 148-162; doi: 10.3221/igf-esis.52.13 162 [29] ibrahimbegović, a. (1994). stress resultant geometrically nonlinear shell theory with drilling rotations—part i. a consistent formulation, comput. methods appl. mech. eng., 118(3–4), pp. 265–284, doi: 10.1016/0045-7825(94)90003-5 [30] ibrahimbegović, a., frey, f. (1994). stress resultant geometrically non‐linear shell theory with drilling rotations. part iii: linearized kinematics, int. j. numer. methods eng., 37(21), pp. 3659–3683, doi: 10.1002/nme.1620372106. [31] ibrahimbegović, a., frey, f. (1994). stress resultant geometrically nonlinear shell theory with drilling rotations— part ii. computational aspects, comput. methods appl. mech. eng., 118(3–4), pp. 285–308, doi: 10.1016/0045-7825(94)90004-3 [32] zouari, w., hammadi, f., ayad, r. (2016). quadrilateral membrane finite elements with rotational dofs for the analysis of geometrically linear and nonlinear plane problems, comput. struct., 173, pp. 139–149, doi: 10.1016/j.compstruc.2016.06.004. [33] meftah, k., sedira, l. (2019). a nonlinear elasto-plastic analysis of reissner-mindlin plates by finite element method, frat. ed integrità strutt., 13(50), pp. 276–285, doi: 10.3221/igf-esis.50.23 [34] zienkiewicz, o.c., taylor, r.l. (2005). the finite element method for solid and structural mechanics, elsevier. [35] hinton, e., owen, d.p. (1977). finite element programming, ,. [36] irons, b.m. (1970). a frontal solution program for finite element analysis, int. j. numer. methods eng., 2(1), pp. 5–32, doi: 10.1002/nme.1620020104. [37] simo, j.c., taylor, r.l. (1985). consistent tangent operators for rate-independent elastoplasticity, comput. methods appl. mech. eng., 48(1), pp. 101–18, doi: 10.1016/0045-7825(85)90070-2. [38] simo, j.c., taylor, r.l. (1986). a return mapping algorithm for plane stress elastoplasticity, int. j. numer. methods eng., 22(3), pp. 649–70, doi: 10.1002/nme.1620220310. [39] de souza neto, e.a., peric, d., owen, d.r.j. (2011). computational methods for plasticity: theory and applications, john wiley & sons. [40] nodargi, n.a., bisegna, p. (2017). a novel high-performance mixed membrane finite element for the analysis of inelastic structures, comput. struct., 182, pp. 337–353, doi: 10.1016/j.compstruc.2016.10.002. [41] systèmes, d. (2012). abaqus analysis user’s manual, version 6.12, dassault systèmes, provid. ri,. [42] pian, t.h.h., sumihara, k. (1984). rational approach for assumed stress finite elements, int. j. numer. methods eng., 20(9), pp. 1685–1695, doi: 10.1002/nme.1620200911. [43] wilson, e.l., taylor, r.l., doherty, w.p., ghaboussi, j. (1973).incompatible displacement models. numerical and computer methods in structural mechanics, elsevier, pp. 43–57, doi: 10.1016/b978-0-12-253250-4.50008-7. [44] taylor, r.l., beresford, p.j., wilson, e.l. (1976). a non‐conforming element for stress analysis, int. j. numer. methods eng., 10(6), pp. 1211–1219, doi: 10.1002/nme.1620100602. [45] allman, d.j. (1988). a quadrilateral finite element including vertex rotations for plane elasticity analysis, int. j. numer. methods eng., 26(3), pp. 717–730, doi: 10.1002/nme.1620260314. [46] batoz, j.-l., dhatt, g. (1990). modélisation des structures par éléments finis: solides élastiques, presses université laval. [47] cook, r.d. (2007). concepts and applications of finite element analysis, john wiley & sons. [48] bilotta, a., leonetti, l., garcea, g. (2011). three field finite elements for the elastoplastic analysis of 2d continua, finite elem. anal. des., 47(10), pp. 1119–1130, doi: 10.1016/j.finel.2011.05.002. [49] moharrami, h., mahini, m.r., cocchetti, g. (2015). elastoplastic analysis of plane stress/strain structures via restricted basis linear programming, comput. struct., 146, pp. 1–11, doi: 10.1016/j.compstruc.2014.08.007. [50] lubliner, j. (n.d.). 1990, plasticity theory. macmillan publishing company, new york. [51] nayak, c. (1972). elasto-plastic stress analysis. a generalization for various constitutive relations including strain softening, int. j. numer. methods eng., 5, pp. 113–135, doi: 10.1002/nme.1620050111 [52] hill, r. 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/pdfxoutputintentprofileselector /documentcmyk /preserveediting true /untaggedcmykhandling /leaveuntagged /untaggedrgbhandling /usedocumentprofile /usedocumentbleed false >> ] >> setdistillerparams << /hwresolution [2400 2400] /pagesize [612.000 792.000] >> setpagedevice microsoft word numero_59_art_xx_3290.docx r. fincato et alii, frattura ed integrità strutturale, 59 (2022) 1-17; doi: 10.3221/igf-esis.59.01 1 ductile fracture modeling of metallic materials: a short review riccardo fincato, seiichiro tsutsumi university of osaka, jwri, japan fincato@jwri.osaka-u.ac.jp, http://orcid.org/ 0000-0003-4058-0460 tsutsumi@jwri.osaka-u.ac.jp, http://orcid.org/ 0000-0002-9279-0657 abstract. since the end of the last century a lot of research on ductile damage and fracture process has been carried out. the interest and the attention on the topic are due to several aspects. the margin to reduce the costs of production or maintenance can be still improved by a better knowledge of the ductile failure, leading to the necessity to overcome traditional approaches. new materials or technologies introduced in the industrial market require new strategies and approaches to model the metal behavior. in particular, the increase of the computational power together with the use of finite elements (fe), extended finite elements (x-fe), discrete elements (de) methods need the formulation of constitutive models capable of describing accurately the physical phenomenon of the damaging process. therefore, the recent development of novel constitutive models and damage criteria. this work offers an overview on the current state of the art in nonlinear deformation and damaging process reviewing the main constitutive models and their numerical applications. keywords. ductile damage; finite element method; experimental characterization; numerical modeling. citation: fincato, r., tsutsumi, s., ductile fracture modelling of metallic materials: a short review, frattura ed integrità strutturale, 59 (2022) 1-17. received: 04.10.2021 accepted: 09.10.2021 published: 01.01.2022 copyright: © 2022 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. introduction he generation of large inelastic deformations accompanied by the progressive degradation of mechanical properties, and finally by the material failure, is a relevant topic in many competitive industrial sectors (automotive, construction, naval, etc.). an underestimation of the material capability of bearing loads, or an incorrect design of components can lead to a catastrophic outcome with severe consequences in terms of lives or economic impact. the understanding of the damaging process has a key role under several aspects. firstly, the prediction of the failure mechanism can lead to a better design of components and structure, with a consistent reduction in the costs production and, more importantly, in maintenance costs. it can help the development and use of new materials and technologies, especially in applications linked to emerging industrial sectors such as biomedical, robotics, and aerospace. lastly, recent experimental investigations on non-linear deformations and rapture under various loading/boundary conditions provide useful information for the development of constitutive models or empirical formulas for the description of the damage processes. t https://youtu.be/oy5pl_pjvrs r. fincato et alii, frattura ed integrità strutturale, 59 (2022) 1-17; doi: 10.3221/igf-esis.59.01 2 in particular, the increase of the computational power incentivized the theoretical research on mechanical models on ductile damage thanks to their implementation in in-house or commercial software based on the finite element (fe) or discrete elements (de) methods. the great interest around numerical simulations derives from the possibility of conducting parametric studies on components, varying geometrical features, or loading conditions without additional experimental costs. numerical codes can be applied for the simulation of the service life of large structures such as bridges, skyscrapers, ships, for which full-scale experimental approaches would be unfeasible or too costly. moreover, experimental campaigns on cyclic loading or low cycle fatigue (lcf) problems can require a considerable time, especially if the investigations are applied to several specimens. fe or de simulations can speed up the computation process and can be applied on several problems [1–4]. the continuous development of robust damage and fracture models represented, and still represents, an essential point to obtain a more realistic description of the material behavior. on the other hand, since the pioneering works on ductile damage in the second half of the last century, several researchers developed alternative theories for the description of the phenomenon. the present work aims to offer an overview on the current state of the art, pointing out the different aspects that characterize the main constitutive models. the reader should keep in mind that a detailed description of all the existing models is unrealistic since the literature on the topic is quite vast. for the same reason the authors did not report the constitutive equations of the models discussed, the reader is referred to the referenced literature for a in depth description of single theories. the paper is organized as follows. initially, a brief introduction deals with the definition of the nature of the damage. the experimental characterization of the damaging process is discussed, describing some of the current measuring techniques. subsequently, an overview of the available models for the damage description, and a discussion of the main aspects of each theory, is offered together with references of recent applications. finally, some computational aspects are presented. damage definitions efore dealing with the experimental characterization and the numerical modeling of the damage phenomenon it is necessary to point out some different mechanisms that lead to the formation of macro cracks. in fact, even if the outcome of the process is the material failure, the causes for initiation and the evolution of the phenomena are quite different depending on the loading and boundary conditions. here, a brief description of the fracture processes is given, the reader is referred to [5,6] for an in-depth discussion. in summary, fracture can be distinguished in three mechanisms:  ductile fracture. this type of fracture is accompanied by a large amount of irreversible deformations that alter the geometry or shape of the components (i.e. necking, shear bands, etc.). the process is generally triggered by the presence of internal material defects (voids, inclusions) around which a stress localization induces crystallographic slips and the progressive decohesion at the interface between the inclusion and the matrix. alternatively, the inclusion can break under the effect of the surrounding stress fields. ductile fracture is characterized by internal micro-cracks formation, driven by high stress triaxialities (see fig. 1a). the progressive application of the load increases the number and volume of voids and decohesion around defects until their coalescence into a macroscopic crack that quickly propagates until the material failure. in case of low stress triaxiality three failure mechanisms can be observed. in the first, the void nucleation tends to take place in a shear band (see fig. 1b). the subsequent elongation of the voids induced by shear strain leads to their coalescence and finally to the macroscopic rapture. the second one is named ‘void sheeting’ where the void nucleation takes place in multiple shear plane that coalesce under shear straining (see fig. 1c). finally, the socalled orowan alternating slip mechanism (oas). the void nucleation and subsequent coalescence takes place into two intersecting shear bands forming a prismatic cavity at the core of the material (see fig. 1d). an exhaustive explanation of the different mechanisms is offered in [7]. ductile rapture is typical of loading conditions that induce a non-negligible amount of plastic deformations, including cyclic mobility and low cycle fatigue (lcf) problems [8–10].  low ductility fracture (often referred as brittle fracture). the type of fracture that belongs to this category is characterized by the formation of cavities between grain boundaries. the cause for these micro-cracks formation can be due to accumulation of dislocation, low melting-point impurity phases or concentration of impurity elements (e.g. v-group elements in steels, bi and pb in coppers). in particular the presence of impurities is known to promote embrittlement [11,12]. the number and size of cavities increase under the effect of the load on the structure or component and the effect of the temperature. the coalescence of the cavities leads to break some grain boundaries, causing a brittle fracture which can propagates or influence the macro-crack formation and material failure (see fig. b r. fincato et alii, frattura ed integrità strutturale, 59 (2022) 1-17; doi: 10.3221/igf-esis.59.01 3 2). detailed information and few examples on numerical modeling of the low ductility fracture can be found in [13– 15].  progressive fracture mechanisms (fatigue or creep). in case of fatigue mechanism, it has to be excluded the scenario where the metallic material fails under cyclic loading conditions after the generation of large plastic deformation (for instance in very low/ low cycle fatigue). in fact, in this case, the fracture mechanism belongs to the aforementioned ductile fracture. fatigue fracture is characterized by three stages. firstly, the crack nucleation takes place in persistent slip bands, close or at the free surface, with an inclination of 45° compared to the loading direction, along the crystallographic slip planes [16]. during the second stage the crack propagates along a plane, more or less, perpendicular to the pulling direction up to a point that the cross section cannot withstand the applied cyclic loading (see fig. 3). finally, the third stage consists in the ultimate crack propagation the rate of which is roughly half of the speed of sound in the material [17]. recent works on fatigue fracture with some numerical applications can be found in [18–22]. creep fracture is particularly relevant in components that operate at high temperatures (e.g., turbine, petrochemical or nuclear plants, etc.). in this case, creep progressively developed from nucleated intergranular void depending on the loading and heating conditions in the form of irreversible deformations. the evolution of plastic deformation is associated with the enlargement of the voids and their coalescence following three stages: primary, secondary and tertiary creep. after an initial increase of the creep rate during the primary stage a constant creep rate is reached and is kept throughout the second stage. during the tertiary creep a consistent increase of the creep rate is registered until failure. few works on the topic of creep fracture are reported in [23–28]. the present paper focuses the attention in reviewing the first fracture process. in the following sections we will refer to a damage variable associated with the ductile fracture mechanism. in particular, it is important to point out that the characteristics that define the damage are substantially different from the ones proper of the deformation process. damage itself consists in the rapture of bonds (atomic bonds between the matrix and defects, atomic bonds between atoms of the defects or the matrix), while elastic deformations are reversible variations of the atomic distances and plastic deformations account for the accumulation or movements of dislocations. therefore, a new variable must be introduced to describe the damaging process, in addition to the standard variables (i.e., stress, elastic strain, plastic strain, etc.). this aspect will be discussed from a theoretical in the following section ‘theoretical damage characterization’. in the next section a more practical approach is introduced, giving some information about the experimental characterization of the damaging process. figure 1: typical ductile fracture mechanism (simplified and redrawn version of fig. 2 in [7]). r. fincato et alii, frattura ed integrità strutturale, 59 (2022) 1-17; doi: 10.3221/igf-esis.59.01 4 figure 2: typical low ductility fracture. figure 3: typical fatigue fracture. experimental damage characterization he measurement of the ductile damage in the ongoing of an experiment is a challenging aspect since the damage variable can hardly be measured directly such as other variables (i.e., total force, displacements, strain, geometrical variations, etc.). as mentioned before the damage variable gives an indication about the void formation and growth during the loading and, therefore, it is intrinsically associated with the development of internal cracks. currently, there are several techniques that allow a more or less accurate measurement of the damage evolution. a very simple, however time-consuming technique, consists in cutting part of the sample to have a direct observation of the state of void formation. as it can be imagined, the damage evolution can be estimated by a series of tests, performed under the same conditions, where the cut and void observation is done at predefined stages of the loading sequence. a valid alternative is represented by hardness evaluation by means of indentation. this method consists in recording, throughout the experiment, the magnitude of the applied load and the indentation depth. by the technique proposed by oliver and pharr [29], the indentation measure can be correlated to the decrease of the elastic modulus and therefore to the measure of the damage evolution. this expedient can return very accurate values of the local damage and it can be used to evaluate the degradation in strain localization areas (i.e. necking, shear bands, etc.) [30,31]. the electrical resistance of the material can also be used to evaluate the resisting area and therefore to measure the level of damage in the material. the changes in electrical resistance measured during the material loading are mainly due to the generation of plastic deformations and damage. as shown in [30], it is possible to obtain a formula that relates the change in resistance with the evolution of the damage. the damage evaluation seems to be quite good and able to predict a realistic evolution. this last method was proposed by lemaitre and dufally [32] and used for the first time by kumar et al. [33]. t r. fincato et alii, frattura ed integrità strutturale, 59 (2022) 1-17; doi: 10.3221/igf-esis.59.01 5 micrographic sem pictures were mentioned by lemaitre and dufally [32] as a method to obtain the damage by the comparison of the area fraction that corresponds to voids to the total area observed. sem picture can be used a posteriori to investigate the nature of the rapture (brittle, ductile, fatigue) [34] giving high resolution images of the damaged area. a recent work by hutiu et al. [35] proposed the use of optical coherence tomography (otc) to perform fracture analyses as a valid alternative to sem pictures. even though the images obtained with the otc method are characterized by a much lower resolution of the sem, the otc low costs and portability of the equipment make this approach particularly suitable for in situ investigations. recently transmission electron microscopy (tem) has been used to investigate the deformation and fracture mechanisms of materials [36–38]. thanks to the high-resolution and real-time imaging of this technique it was possible to observe several micro-scale and atomic-scale phenomena leading to the material failure (e.g., dislocation-dominated, twinning-dominated, mechanical annealing, phase transformation). zhang et al. [39] proposed a methodology that adopts a microelectromechanical systems-based thermomechanical testing apparatus that enabled to observe the atomic-scale ductile mechanism in single crystal tungsten at high temperatures. this type of material is characterized by a brittle type of fracture at room temperature, but the failure mechanism shifts to ductile fracture with the increase of the temperature. the development of a custom-designed transmission electron microscope showed direct evidence of strain induced phase transformation at the crack tip that prevents the brittle fracture improving the ductility. x-ray micro-tomography can be also used to obtain the volume of the void [40]. one of the advantages of the use of the micro-tomography is the possibility to monitor the whole process from the micro-cracks formation, their growth, coalescence and final macro crack formation. in particular, several authors recurred to this technique for the estimation of the material parameters in numerical simulations. on the other side, micro-tomography requires specialized technicians for its application and it is characterized by high costs compared to other strategies [41–43]. another technique, often referred in the literature as ultrasonic testing (ut) technique, consists in observing the response of the material to ultrasonic pulses, in order to evaluate the density of voids and internal defects. the difference of the ultrasonic pulse velocity of the sample before and during the experiment can be correlated to the damage evolution [44]. an interesting work by chiantoni et al. [45] provides an interesting comparison between the micro-tomography and the ut methods for the assessment of the damage evolution in p91 steel at high temperature. it is concluded that both techniques are in good agreement in catching the damage evolution. however, micro-tomography can offer detailed pictures of the actual distribution of voids in the damage localized area, while ut gives an overall evolution of the damage variable in the sample. the lack of resolution of the ut is somehow compensated by the low costs and easy use of the ultrasonic equipment. the most common technique for the evaluation of the damage is the stiffness or elastic modulus reduction measurement as largely developed and adopted by lemaitre and dufally [32] and bonora et al. [46]. its application is quite simple, and it consists of a series of measurements of the effective elastic modulus during partial unloading of the sample. the decrease of the modulus can be associated with the progressive loss in the load-carrying capacity of the material caused by the void formation. this technique is quite easy to actuate, and it does not require the use of sophisticated equipment (i.e., sem pictures, x-ray micro-tomography, ultrasonic pulse). theoretical damage characterization damage preliminaries and characterization of the stress state o describe the process that leads to the progressive degradation of the mechanical properties, it is important to understand the factors that influence the nucleation, growth, and coalescence of micro-voids in metallic materials. firstly, it is worth mentioning that the growth of the cavities, defects, decohesion inside the material tends to be oriented by the macroscopic load that created them. this means that the variable that should be selected for the description of the process should have a tensorial nature (first, second or even fourth order tensors) or, at least, it should be able to take into account the shape and the orientations of the voids. however, for metallic materials, and in most of industrial applications, the adoption of an isotropic scalar variable can give satisfactory results. for sake of completeness, the reader is referred to [47,48] for examples of tensorial damage variables. usually, the process discussed in the ‘ductile fracture’ bullet point of the previous section can be described by the addition of one, or more, internal variables in elastoplastic constitutive theories. this new variable, or variables, are responsible for describing the formation and progression of cracks until the complete failure of the material. although the material degradation description depends on the selected constitutive model, a common aspect among several approaches is to t r. fincato et alii, frattura ed integrità strutturale, 59 (2022) 1-17; doi: 10.3221/igf-esis.59.01 6 consider a variable (or variables) limited between two extremes (a scalar variable is assumed in eq. (1) and generically indicated with d):    0 1 d non damaged material d material failure (1) a d = 0 condition implies an undamaged material, without voids. a d = 1 condition characterizes the material failure. often, in finite element analyses, a threshold value cd < 1 is used (e.g., [49–51]) to indicate the formation of a crack, or the material failure, in order to avoid numerical problems such as damage localization or convergence issues. these aspects are discussed later. figure 4: typical dependency of the equivalent strain to fracture on the stress triaxiality. an important aspect in the numerical modeling of the damaging process consisted, and still consists, in formulating a constitutive law for the description of the evolution of the d variable, from the non-damaged state until the final failure. in particular, the challenge is represented by formulating the simplest law that includes the main factors governing the void nucleation, growth and coalescence. the extensive experimental campaign conducted in the second half of the last century [52–58] pointed out the dependency of the damage process on a dimensionless stress parameters: the stress triaxiality  (e.g.,[59–63]). in fact, for metallic materials was found that the ductile fracture mechanism and final deformation to fracture (i.e., equivalent strain to fracture  f ) are strongly related to the magnitude of the stress triaxiality (fig. 4). while the effect of the stress triaxiality has been initially incorporated in most of the constitutive models for the description of metal failure, the role of the lode angle [59]  became evident later, when experiments under different loading conditions showed that the equivalent strain to fracture changes for different values of the lode angle under the same stress triaxiality. the effect of the lode angle is often taken into account by introducing the lode angle parameter  (e.g., [59–66]), a dimensionless scalar variable that assumes values between -1 and +1 (-1 in case of compression, 0 in case of shear or plane stress condition and +1 for tension), see fig. 5. most of the recent constitutive models account for damage evolution laws that consider the effects of both stress triaxiality and lode angle parameters. ductile damage models the ductile damage evolution and fracture prediction represent the central points for the scientific and engineering community in the framework of material failure. several works have been carried out developing various theories for the description of the damage. in the literature they can be divided into three main categories:  group i: empirical failure criteria.  group ii: phenomenological models. r. fincato et alii, frattura ed integrità strutturale, 59 (2022) 1-17; doi: 10.3221/igf-esis.59.01 7  group iii: micromechanics-based models. it should be mentioned that the classification of the theories is not unique. in this work, the classification proposed by de souza neto et al. [67], besson [68] and others [6,69] is followed. sometimes, group ii is referred as continuum damage mechanics (cdm) models (e.g. [70,71]). in this work it is considered that both group ii and group iii belong to the cdm framework since they both offer a continuous description of the damage. figure 5: typical dependency of the equivalent strain to fracture on the lode angle parameter. group i. to this first category belong the models that consider the damaging process as independent form the plastic behavior of the material. often in the literature this approach is referred as ‘uncoupled´ meaning that the damage internal variable has no influence on the other plastic internal variables nor the elastic properties of the material and vice versa. therefore, the variable d is merely indicator of the state of the material without an actual contribution on the degradation of the mechanical properties. due to their simplicity, the empirical failure criteria spread widely, especially for industrial applications [72]. the cockcroft-latham criterion [73] and its subsequent modification into the cockcroft-latham-oh [74] represent a widely used criteria for the prediction of the rapture. in the last decade, several papers and technical reports adopted this approach due to its simplicity and the extremely low number of parameters required. on the other side, due to their simple form, they do not consider the effect of the lode angle and returns qualitative results in case of significant variation of the stress state. wilkins et al. [54] tried to consider the effect of the stress triaxiality together with the lode angle, where the lode angle was considered by a scalar factor a that describes the stress asymmetry of the principal stress deviators. a good description of the rapture under different stress states can be obtained if the material does not show a pronounced lode angle sensitivity. johnson and cook [53] developed a material constitutive model that is still widely used. in particular, even if the lode angle effect is still neglected, this approach includes the effect of the strain rate and temperature beside the stress triaxiality. its calibration requires the definition of a total of 8 material parameters, which can be reduced to 3 in case of quasi-static and isothermal conditions. the j-c criteria is particularly suitable to predict failure at impact or high rate loading conditions [75]. recently, bai and wierzbicki [60] proposed a modified mohr-coulomb criterion (mmc) for the prediction of ductile fracture. the mmc can take into consideration the effect of the stress triaxiality and lode angle and it requires a total of 8 material parameters in its general form, or 4 material parameters in case a von mises yield function is assumed. this last criterion seems to predict quite accurately the ductile failure and it has found a large application in the recent literature. a comparative study on failure criteria is offered in [76]. an interesting work by bao and wierzbicki [77] pointed out that all the aforementioned criteria are not able to describe the material failure under a wide range of stress triaxiality. modifications of the criteria are needed in case of low or negative values of the stress triaxiality. moreover, it should be also pointed out that the construction of the failure envelope (i.e., locus of the final strain to fracture as a function of the stress triaxiality and/or lode angle parameter) is valid only for proportional loading paths. exceptions are represented by the use of empirical criteria coupled with plastic internal variables [64,78–80]. a recent interesting work from ganjiani and homayounfard [81] presented a ductile failure criterion based on an analytical definition of the plastic strain onset of the fracture capable to account for proportional and non-proportional loading conditions. the coupled elastoplastic and damage model in [81] can consider plastic anisotropy by means of the hill48 yield criterion [82] and resulted in a good prediction r. fincato et alii, frattura ed integrità strutturale, 59 (2022) 1-17; doi: 10.3221/igf-esis.59.01 8 of the failure mechanism of several materials (i.e., al6012-t6 and al2024-t351 aluminums, a533b and 1045 steels). the work of wang et al. [83] proposed a novel criterion for metal failure under cyclic loading coupled with an innovative elastoplastic model. the advantages of this theory consist of a simple numerical procedure and the possibility to predict cracks formation at low and high cycle fatigue. a recent uncoupled ductile fracture criterion has been proposed by quanch et al. [84] focusing the attention on the micro-mechanism of void nucleation, growth and coalescence. moreover, their work investigated the material failure considering the anisotropic behavior of 6016-ac200 aluminum under a wide range of stress states. group ii. the phenomenological models describe the damaging process from a macroscopic point of view. this class of theories developed from the initial work of kachanov [85] and rabotnov [86], who tried to give a first physical characterization of the damage as the reduction of the resisting area in the material. the damage concept was later consolidated in a consistent thermodynamic framework by lemaitre [87,88]. lemaitre’s model is based on two assumptions:  effective stress tensor ‘as the stress to be apply to a non-damaged element of material so it deforms as damage element under the actual current stress’ [68].  strain equivalence as ‘the strain behavior of a damage material is represented by the constitutive equation of the non-damaged material, using the effective stress’. alternatively, saanouni et al. [89] proposed the hypothesis of energy equivalence to define the constitutive variables governing the damaging process. in case of material anisotropy the energy equivalence should be adopted [6,90]). from the lemaitre’s initial formulation several theories were developed. all of them can be considered as phenomenological since the micro-cracks or voids inside the material are not considered individually but they are ‘smeared’ in the media. in this sense the constitutive equations describe the overall macroscopic response of the damaged material. as mentioned before, group ii models are derived from a consistent thermodynamic framework which allows different type of couplings between the damage and the elasto-plastic internal variables depending on the free energy definition [6]. it also allows the definition of several types of non-negative dissipation potential and yield functions. the lemaitre’s formulation [87,88] considered uniquely the effect of the stress triaxiality. recent developments of the theory formulated the damage evolution as a function of the lode angle parameter [66,91–95]. phenomenological models were also developed in a finite strain framework accounting for material anisotropy [47,96–98] improving the material description in several industrial processes with large plastic straining. as for the empirical failure criteria, the calibration of the material parameter should be carried out carefully. nonetheless, depending on the material, it can be still difficult to characterize the failure behavior under a wide range of the stress triaxiality and lode angle parameter. moreover, group ii models usually need the calibration of several material parameters. group iii. the pioneering work in this category was undertaken by mcclintock [99] and rice and tracey [62] who formulated the first two damage criteria based on geometrical observations on a defect inside a material matrix. these two initial works laid the foundations for the damage criterion which considered the material failure whenever the normalized void radius reached a critical value. gurson [100] was the first to consider the interaction between the voids and the their growth and the material response in terms of stress and strain. he re-formulated the yield criterion adding the contribution of the volume of the voids and, in detail, he associated the damage evolution with the porosity f, or void volume fraction. the influence of the damage on the plastic flow was therefore included in the porosity that progressively shrinks the plastic potential. the failure is assumed for f = 1, similarly to the concept expressed in eq. (1). further development of the model led to the well-known gurson-tvergaard-needleman (gtn) model. the improvement consisted in a better description of the void nucleation, growth, and coalescence mechanism with a more realistic description of the material failure. it should be pointed out that micromechanics-based models are not derived from a consistent thermodynamical framework (with the exception of the hybrid model proposed by rousselier [63], even though it should be considered in a group of its own), where the damage evolution is not associated with a dissipative mechanism. the gtn approach and its subsequent developments proved to have a high predictive capability at high stress triaxiality. unfortunately, the model does not perform well at low stress triaxiality and in case of pure shear, where no void growth is generated. to overcome these drawbacks, recent modifications of the original gtn model were carried out. [101–106], however, with an increase of material parameters. moreover, the inclusion of the effect of the third invariant with the introduction of the lode angle parameter was carried out on a phenomenological approach and micro-mechanical justification was not given. the motivation for the poor performance of the gtn model at low stress triaxiality lies on the assumption that spherical voids remain spherical, which does not seem to be accurate. therefore, jiang et al. [107] proposed a model based on a duplex mechanism, one for the void growth and one for void shear. their results seem to be in good agreement with experimental data for a wide range of stress triaxiality and lode angles. r. fincato et alii, frattura ed integrità strutturale, 59 (2022) 1-17; doi: 10.3221/igf-esis.59.01 9 even in case of micromechanics-based constitutive models the number of material parameters to be calibrated can be considerable, especially in the recent development of the gtn model. moreover, some of the material parameters should be characterized by micromechanical analyses and cannot be identified by conventional mechanical tests. models comparison and computational aspects ven though the choice of the best model or criteria for the description of the ductile behavior depends on the single model itself, in the present section a general comparison among the group i, group ii, and group iii models is given. the main aspects will be presented in the following bullet points.  elastic behavior. among the three groups, the damage plays an important role on the elastic stiffness only in the models derived by the lemaitre’s concept. the damage internal variable can be coupled with the elastic free energy for the definition of the elasto-damage behavior. however, it is also possible to couple the damage variable uniquely with the plastic variables, or to regulate the effect on the material stiffness as suggested by xue [108]. moreover, to diversify the model elastic response in tension or compression it is possible to simulate the crack closure effect with the addition of one scalar material parameter [109]. uncouples models of group i, clearly do not consider the effect of the damage on the elastic behavior. in general, the models derived by the gtn concept do not consider the mechanical degradation of the elastic properties. experimental evidence showed that the effect of the damage on the elastic properties is limited, it can become more visible in case of cyclic loading upon failure.  plastic volume change. models of group i or ii, in general, do not consider the plastic volume changes. the firsts since there is no coupling with the damage. the seconds because only the stress deviator or the effective stress deviator is used in the formulation of the yield potential. consequently, micromechanics-based models are the only one to fulfill the mass conservation, since the damage evolution law is directly based on the evolution of the void volume fraction. it should be pointed out that few attempts have been made to include the effect of the porosity in phenomenological models such as the work of hammi and horstemeyer [110] even though the volume change is not actually accounted for. santaoja [111] recently published a paper presenting a phenomenological model where the damage variable was redefined to take into account the void volume fraction. however, this model considers an elastic matrix response with spherical microvoids only.  strain induced anisotropy. strain induced anisotropy can be easily taken into account in uncoupled or lemaitre’s type models, since the implementation of kinematic hardening laws is straightforward. the initial gtn model does not consider the effect of kinematic hardening and it was based on isotropic hardening only. recent versions of the gtn model overcame this drawback and can consider the contribution of the kinematic hardening (e.g., [112]).  plastic anisotropy and anisotropic ductile damage. while it is possible to consider plastic anisotropic by means of anisotropic yield criteria [82,113–115], an anisotropic damage variable has been described by several approaches in group ii. a first strategy consists in describing the damage by means of set of vectors associated with predefined directions [116,117]. alternatively, the damage can be described by second-order tensors [48,118,119] even though a second-order damage tensor itself can not properly describe the damage induced anisotropy in the fourth order elastic tensor. lastly, the damage can be described by a fourth-order tensor which is derived consistently from the effective stress concept, and it has been widely adopted in the literature [97,120–122]. however, recent works showed the possibility to use a scalar damage variable to model an anisotropic damaging process [51,123]. these approaches, even if not representative of the true nature of an anisotropic damage variable, can be still useful in several engineering applications. in gtn-type models the anisotropic evolution of the void (and therefore of the damage) can be considered by adopting ad hoc laws with shape factors [124,125] that describes the volume and shape changes of the voids as well as their rotation during the loading process. the consideration of the void shape changes and reorientation complicates the formulation of group iii models and their validation on three dimensional problems with complex loading conditions remains challenging.  rate and temperature dependencies. from experimental observations, metals seems to show an increase in ductility with the strain rate (found in steel, aluminum, copper, titanium etc.) [126]. the formulation of group i models with deformation rate dependency or temperature dependency can be easily done by adding ad-hoc terms to the failure criteria. in coupled models the effect of the rate-sensitivity and temperature should be taken into account both in the deformation and damaging processes. the development of rate-dependent and temperature dependent lemaitre’s type models is quite straightforward [108,127,128] and it requires simple modification with the addition of few material e r. fincato et alii, frattura ed integrità strutturale, 59 (2022) 1-17; doi: 10.3221/igf-esis.59.01 10 parameters. on the other side, micromechanical investigation for the formulation of the rate-dependency and temperature dependency gtn-type models seems more complex.  mesh sensitivity. due to the uncoupled nature of the constitutive equations, models in group i are less influenced by the mesh size but can however suffer from strain localizations problems. on the contrary, due to the material softening induced by the damage evolution, mesh sensitivity is an important issue for models of group ii and iii [129]. from a theoretical point of view, the boundary problem becomes ill-posed once the deformation and damage accumulates in few elements. to prevent this problem several methods were proposed (i.e., viscoplastic regularization, non-local theories, gradient-like definition of the internal variables). most commonly, a spatial averaging term is adopted, where it is assumed that the value of the state variables (damage, plastic deformations) in a local point depends on the values of the state variables in the neighborhood of the point. this concept adopts a characteristic length to define a domain (area or volume) used to average the damage variable and avoid the localization and consequent softening in single elements [130,131]. unfortunately, in commercial software it is difficult to implement such strategy even with the use of user-subroutines. another solution is represented by models adopting the definition of gradient-like formulation of the internal variables [132–134]. alternatively, a common and easy solution is to set a value of the critical damage dc small enough (0.2~0.3) to avoid localization. this strategy has also the benefit of avoiding an excessive loss of stiffness which leads to the loss of quadratic rate of convergence if an implicit numerical scheme is used for the integration of the constitutive equations [67].  proportional, non-proportional loading conditions. the use of empirical criteria for the description of the damage evolution should be limited to proportional loading only. however, the use of empirical criteria where the damage and plastic variables are coupled showed good agreement with experimental data on material failure under nonproportional loading paths [79,81,135,136]. example of the applications of the lemaitre-type and gtn-type models to non-proportional loading can be found in [137,138].  calibration of the mechanical parameters. a common practice for the calibration of the material constants of the models in all groups is to conduct inverse and parametric studies to fit the experimental curves. in detail, knowing the force-displacement curve for a sample together with the final elongation to fracture, the calibration is conducted to identify the set of parameters, within their ranges of existence, that minimizes the differences between the experimental and numerical curves. the uncoupled nature of the models in group i allows to distinguish between the calibration of the elastoplastic constants and the parameters for the damage evolution law, leaving to the firsts the fitting of the experimental force-displacement trend and to the seconds the description of the final elongation to fracture. on the other hand, the coupled nature of models in group ii and iii requires the elastoplastic and damage parameters to be identified simultaneously. from a theoretical point of view, the constants for models in group iii should be based on micro-mechanicals investigations. however, often the parameters for the gtn-type models are obtained from macroscopic mechanical tests due to costs of ad hoc experimental investigations and due to the phenomenological formulation of some laws, for instance the lode angle dependency. recently, several authors combined the use of finite element modeling and artificial intelligence (ai) for the numerical characterization of ductile failure. this methodology seems promising and gave accurate predictions, however, it still relies on the size and quality of the experimental database to train the ai algorithm. baltic et al. [139] combined fe and artificial neural network (ann) to calibrate a gtn-type model on a single sample. the main advantage is the possibility of extracting the model parameters from a single sample as opposed to the many geometries usually necessary to define the locus of the strain to failure. moreover, the ann algorithm showed a good performance in calibration even with limited data available for the training and learning. quan et al. [140] adopted ann to identify the damage parameters of the shear modified gtn model [141] in a small punch test. the numerical simulations reproduced accurately the experimental tests. the following tab. 1 offers a list of the advantages and shortcomings of the different approaches for modeling the metallic material failure. conclusions he present work aims to offer useful information for the characterization of the ductile damaging phenomenon. initial considerations were described to distinguish the different damaging mechanisms that might take place in metallic materials. among them, ductile fracture has relevant role in many industrial applications and therefore it t r. fincato et alii, frattura ed integrità strutturale, 59 (2022) 1-17; doi: 10.3221/igf-esis.59.01 11 has been widely investigated leading to the generation of predictive models with the intent of improving the design and service life of components/structures. experimental characterization of the damage is another fundamental aspect to reach a reliable numerical modeling of the phenomena, and at the same time to offer a tool for the maintenance of existing structures. several techniques have been described and reported. lastly, three different classes of numerical approaches have been introduced, giving a brief summary of their main features. in detail, the previous section discussed the strong and weak points of each theory. the reader should be reminded that the choice of the computational model should depends on the specific case to analyze and the possibility to characterize the material parameters. clearly the choice of a particular constitutive model should be balanced between its simplicity and the predictive capability in relation to the problem to solve. a judgment on the best model based on the constitutive equations themselves cannot be objective. the authors tried to report the most recent relevant literature in order to offer a view on the state of the art in metal ductility and failure. advantages disadvantages group i  simple application in fe;  negligible mesh dependency;  stress triaxiality and lode angle;  plastic anisotropy of the material matrix.  application on proportional loadings only (except for models with coupled damage and plastic variables);  lack of physical meaning;  different functions to predict failure at different triaxialities;  no influence of the damage on the plastic variables and vice versa (except for models with coupled damage and plastic variables). group ii  thermodynamically consistent;  coupling damage and elasticity;  easy implementation of kinematic hardening;  stress triaxiality and lode angle dependency;  proportional and non-proportional loading path;  anisotropy of the material matrix.  mesh dependency;  does not fulfil mass conservation;  no physical parameters involved;  requires to include lode angle parameter for shear failure. group iii  fulfilment of mass conservation  stress triaxiality and lode angle dependency;  proportional and non-proportional loading paths.  mesh dependency;  coupling damage and elasticity requires an ad hoc formulation;  requires ad hoc formulation of kinematic hardening;  lode angle dependency does not have micromechanical justification;  requires a lot of material parameters;  material parameters calibration requires micromechanical tests;  requires ‘phenomenological’ modification to model low stress triaxiality damaging. table 1: summary of the features of the group i, ii and iii models. references [1] takazawa, h., iwamatsu, f., miyazaki, k. (2013). os1428 evaluation of ductile fracture using gtn model in commercial fea code, proc. mater. mech. conf., 2013, pp. _os1428-1_-_os1428-3_ doi: 10.1299/jsmemm.2013._os1428-1_. r. fincato et alii, frattura ed integrità strutturale, 59 (2022) 1-17; doi: 10.3221/igf-esis.59.01 12 [2] ikushima, k., yano, t., natsume, r., shibahara, m., ohata, m. (2017). study on fracture mode of spot weld joint using continuum damage mechanics model, q. j. japan weld. soc., 35(2), pp. 28s-32s, doi: 10.2207/qjjws.35.28s. [3] watanabe, i. (2015). multiscale modeling of ductile fracture in continuum mechanics, tetsu-to-hagane, 101(9), pp. 465–470, doi: 10.2355/tetsutohagane.tetsu-2015-022. [4] sugiyama, h., matsui, k., endo, t., yamada, t. (2014). propagation of discontinuities with damage model, proc. comput. mech. conf., 2014.27, pp. 473–474, doi: 10.1299/jsmecmd.2014.27.473. [5] pantazopoulos, g. (2019). a short review on fracture mechanisms of mechanical components operated under industrial process conditions: fractographic analysis and selected prevention strategies, metals (basel)., 9(2), pp. 148, doi: 10.3390/met9020148. [6] besson, j., forest, s., cailletaud, g., blétry, m., chaboche, j.l. (2010). non-linear mechanics of materials, solid mech. its appl., doi: 10.1007/978-90-481-3356-7_1. [7] noell, p.j., carroll, j.d., boyce, b.l. (2018). the mechanisms of ductile rupture, acta mater., 161, pp. 83–98, doi: 10.1016/j.actamat.2018.09.006. [8] wada, y., ueda, k. (2019). evaluation of equivalent plastic strain and stress triaxiality and δj for proposing a crack growth formula under extremely low cycle fatigue, proc. comput. mech. conf., 2019.32, pp. 092, doi: 10.1299/jsmecmd.2019.32.092. [9] sawamoto, y., kubota, j., ohsaki, m. (2020). evaluation on plastic deformation capacity of steel beam ends with local buckling andfracture under cyclicloading using fe analysis, j. struct. constr. eng. (transactions aij), 85(767), pp. 105– 115, doi: 10.3130/aijs.85.105. [10] kimura, k., tomioka, n., okabe, a. (2019). high cycle fatigue damage of steel sheet used in vehicle body, proc. mater. mech. conf., 2019, pp. gs14, doi: 10.1299/jsmemm.2019.gs14. [11] pantazopoulos, g. (2002). leaded brass rods c 38500 for automating machining operations: a technical report, j. mater. eng. perform., 11(4), pp. 402–407, doi: 10.1361/105994902770343926. [12] lynch, s.p., moutsos, s. (2006). a brief history of fractography, j. fail. anal. prev., doi: 10.1361/154770206x156231. [13] lu, m., wang, f., zeng, x., chen, w., zhang, j. (2020). cohesive zone modeling for crack propagation in polycrystalline niti alloys using molecular dynamics, theor. appl. fract. mech., 105, pp. 102402, doi: 10.1016/j.tafmec.2019.102402. [14] margolin, b., karzov, g., shvetsova, v., kostylev, v. (2002). modelling for transcrystalline and intercrystalline fracture by void nucleation and growth, fatigue fract. eng. mater. struct., 21(2), pp. 123–137, doi: 10.1046/j.1460-2695.1998.00474.x. [15] sun, z., benabou, l., xue, h. (2016). numerical modeling and simulation of intergranular fracture due to dynamic embrittlement for a cunisi alloy, mech. res. commun., 75, pp. 81–88, doi: 10.1016/j.mechrescom.2016.06.003. [16] ikeya, h., umezawa, o., fukutomi, h. (2019). crystal lattice rotation and fatigue crack generation in aluminum wire under cyclic bending deformation, j. japan inst. light met., 69(6), pp. 302–208, doi: 10.2464/jilm.69.302. [17] alderliesten, r. (2017).fatigue crack propagation. solid mechanics and its applications. [18] he, l., akebono, h., sugeta, a., hayashi, y. (2020). cumulative fatigue damage of stress below the fatigue limit in weldment steel under block loading, fatigue fract. eng. mater. struct., 43(7), pp. 1419–1432, doi: 10.1111/ffe.13204. [19] sakai, t. (2009). review and prospects for current studies on very high cycle fatigue of metallic materials for machine structural use, j. solid mech. mater. eng., 3(3), pp. 425–39, doi: 10.1299/jmmp.3.425. [20] tang, l., ince, a., zheng, j. (2020). numerical modeling of residual stresses and fatigue damage assessment of ultrasonic impact treated 304l stainless steel welded joints, eng. fail. anal., 108, pp. 104277, doi: 10.1016/j.engfailanal.2019.104277. [21] borges, m.f., neto, d.m., antunes, f.v. (2020). numerical simulation of fatigue crack growth based on accumulated plastic strain, theor. appl. fract. mech., 108, pp. 102676, doi: 10.1016/j.tafmec.2020.102676. [22] tanaka, n., saitou, y., matsumura, t. (2019). very high cycle fatigue properties and damage mechanism of cast aluminum alloy, proc. mater. mech. conf., pp. os0905, doi: 10.1299/jsmemm.2019.os0905. [23] nowak, k. (2020). application of a nonlocal grid model for analysis of the creep damage of metals, int. j. damage mech., 29(5), pp. 780–797, doi: 10.1177/1056789519883668. [24] meng, q., wang, z. (2019). creep damage models and their applications for crack growth analysis in pipes: a review, eng. fract. mech., 205, pp. 547–576, doi: 10.1016/j.engfracmech.2015.09.055. [25] liu, y., murakami, s. (1998). damage localization of conventional creep damage models and proposition of a new model for creep damage analysis., jsme int. j. ser. a, 41(1), pp. 57–65, doi: 10.1299/jsmea.41.57. [26] zheng, x., xu, q., lu, z., wang, x., feng, x. (2020). the development of creep damage constitutive equations for high cr steel, mater. high temp., 37(2), pp. 129–138, doi: 10.1080/09603409.2020.1716145. [27] yamazaki, n., nomura, k., kubushiro, k. (2020). creep-fatigue damage for boiler header stub mock-up specimen r. fincato et alii, frattura ed integrità strutturale, 59 (2022) 1-17; doi: 10.3221/igf-esis.59.01 13 of 47ni–23cr–23fe–7w alloy, mater. trans., 61(6), pp. 1109–1114, doi: 10.2320/matertrans.z-m2020813. [28] koiwa, k., tabuchi, m., demura, m., yamazaki, m., watanabe, m. (2019). prediction of creep rupture time using constitutive laws and damage rules in 9cr–1mo–v–nb steel welds, mater. trans., 60(2), pp. 213–221, doi: 10.2320/matertrans.me201703. [29] oliver, w.c., pharr, g.m. (1992). an improved technique for determining hardness and elastic modulus using load and displacement sensing indentation experiments, j. mater. res., 7(06), pp. 1564–1583, doi: 10.1557/jmr.1992.1564. [30] zhang, s., xia, q., li, w., zhou, x. (2014). ductile damage measurement and necking analysis of metal sheets based on digital image correlation and direct current potential drop methods, int. j. damage mech., 23(8), pp. 1133–1149, doi: 10.1177/1056789514527978. [31] mastrone, m.n., fraccaroli, l., concli, f. (2021). ductile damage model of an alluminum alloy: experimental and numerical validation on a punch test, int. j. comput. methods exp. meas., 9(3), pp. 249–260, doi: 10.2495/cmem-v9-n3-249-260. [32] lemaitre, j., dufailly, j. (1987). damage measurements, eng. fract. mech., 28(5–6), pp. 643–661, doi: 10.1016/0013-7944(87)90059-2. [33] kumar, j., padma, s., srivathsa, b., rao, n.v., kumar, v. (2009). evolution of damage in near α imi-834 titanium alloy under monotonic loading condition: a continuum damage mechanics approach, j. eng. mater. technol., 131(3), pp. 031012, doi: 10.1115/1.3086384. [34] goldstein, j.i., newbury, d.e., michael, j.r., ritchie, n.w.m., scott, j.h.j., joy, d.c. (2017). scanning electron microscopy and x-ray microanalysis. [35] hutiu, g., duma, v.-f., demian, d., bradu, a., podoleanu, a. (2018). assessment of ductile, brittle, and fatigue fractures of metals using optical coherence tomography, metals (basel)., 8(2), pp. 117, doi: 10.3390/met8020117. [36] shan, z.w., mishra, r.k., syed asif, s.a., warren, o.l., minor, a.m. (2008). mechanical annealing and source-limited deformation in submicrometre-diameter ni crystals, nat. mater., 7(2), pp. 115–119, doi: 10.1038/nmat2085. [37] ly, t.h., zhao, j., cichocka, m.o., li, l.-j., lee, y.h. (2017). dynamical observations on the crack tip zone and stress corrosion of two-dimensional mos2, nat. commun., 8(1), pp. 14116, doi: 10.1038/ncomms14116. [38] wang, l., teng, j., sha, x., zou, j., zhang, z., han, x. (2017). plastic deformation through dislocation saturation in ultrasmall pt nanocrystals and its in situ atomistic mechanisms, nano lett., 17(8), pp. 4733–4739, doi: 10.1021/acs.nanolett.7b01416. [39] zhang, j., li, y., li, x., zhai, y., zhang, q., ma, d., mao, s., deng, q., li, z., li, x., wang, x., liu, y., zhang, z., han, x. (2021). timely and atomic-resolved high-temperature mechanical investigation of ductile fracture and atomistic mechanisms of tungsten, nat. commun., 12(1), pp. 2218, doi: 10.1038/s41467-021-22447-y. [40] cao, t.-s., maire, e., verdu, c., bobadilla, c., lasne, p., montmitonnet, p., bouchard, p.-o. (2014). characterization of ductile damage for a high carbon steel using 3d x-ray micro-tomography and mechanical tests – application to the identification of a shear modified gtn model, comput. mater. sci., 84, pp. 175–187, doi: 10.1016/j.commatsci.2013.12.006. [41] maire, e., bouaziz, o., di michiel, m., verdu, c. (2008). initiation and growth of damage in a dual-phase steel observed by x-ray microtomography, acta mater., 56(18), pp. 4954–4964, doi: 10.1016/j.actamat.2008.06.015. [42] weck, a., wilkinson, d.s., maire, e., toda, h. (2008). visualization by x-ray tomography of void growth and coalescence leading to fracture in model materials, acta mater., 56(12), pp. 2919–2928, doi: 10.1016/j.actamat.2008.02.027. [43] cao, t.-s., maire, e., verdu, c., bobadilla, c., lasne, p., montmitonnet, p., bouchard, p.-o. (2014). characterization of ductile damage for a high carbon steel using 3d x-ray micro-tomography and mechanical tests – application to the identification of a shear modified gtn model, comput. mater. sci., 84, pp. 175–187, doi: 10.1016/j.commatsci.2013.12.006. [44] boccaccini, d.n., boccaccini, a.r. (1997). dependence of ultrasonic velocity on porosity and pore shape in sintered materials, j. nondestruct. eval., 16(4), pp. 187–192, doi: 10.1023/a:1021891813782. [45] chiantoni, g., comi, c., mariani, s., bonora, n. (2014). experimental assessment of ductile damage in p91 steel at high temperature, int. j. damage mech., 23(4), pp. 567–587, doi: 10.1177/1056789513503972. [46] bonora, n., ruggiero, a., gentile, d., de meo, s. (2011). practical applicability and limitations of the elastic modulus degradation technique for damage measurements in ductile metals, strain, 47(3), pp. 241–254, doi: 10.1111/j.1475-1305.2009.00678.x. [47] rajhi, w., saanouni, k., sidhom, h. (2014). anisotropic ductile damage fully coupled with anisotropic plastic flow: modeling, experimental validation, and application to metal forming simulation, int. j. damage mech., 23(8), pp. 1211– 1256, doi: 10.1177/1056789514524076. r. fincato et alii, frattura ed integrità strutturale, 59 (2022) 1-17; doi: 10.3221/igf-esis.59.01 14 [48] reese, s., brepols, t., fassin, m., poggenpohl, l., wulfinghoff, s. (2021). using structural tensors for inelastic material modeling in the finite strain regime – a novel approach to anisotropic damage, j. mech. phys. solids, 146, pp. 104174, doi: 10.1016/j.jmps.2020.104174. [49] javani, h.r., peerlings, r.h.j., geers, m.g.d. (2016). three-dimensional finite element modeling of ductile crack initiation and propagation, adv. model. simul. eng. sci., 3(1), pp. 19, doi: 10.1186/s40323-016-0071-y. [50] yang, f., veljkovic, m., liu, y. (2020). ductile damage model calibration for high-strength structural steels, constr. build. mater., 263, pp. 120632, doi: 10.1016/j.conbuildmat.2020.120632. [51] zhang, h., zhang, h., li, f., cao, j. (2019). a novel damage model to predict ductile fracture behavior for anisotropic sheet metal, metals (basel)., 9(5), pp. 595, doi: 10.3390/met9050595. [52] hancock, j.w., mackenzie, a.c. (1976). on the mechanisms of ductile failure in high-strength steels subjected to multiaxial stress-states, j. mech. phys. solids, 24(2–3), pp. 147–160, doi: 10.1016/0022-5096(76)90024-7. [53] johnson, g.r., cook, w.h. (1985). fracture characteristics of three metals subjected to various strains, strain rates, temperatures and pressures, eng. fract. mech., 21(1), pp. 31–48, doi: 10.1016/0013-7944(85)90052-9. [54] wilkins, m.l., streit, r.d., reaugh, j.e. (1980). cumulative-strain-damage model of ductile fracture: simulation and prediction of engineering fracture tests, livermore, ca. [55] clausing, d.p. (1970). effect of plastic strain state on ductility and toughness, int. j. fract. mech., 6(1), doi: 10.1007/bf00183662. [56] bridgman, p.w. (1952). studies in large plastic flow and fracture: with special emphasis on the effects of hydrostatic pressure, cambridge, ma, harvard university press. [57] mcclintock, f.a. (1971).plasticity aspects of fractures, chapter 2. engineering fundamentals and environmental effects, pp. 47–225. [58] toda, h., tsuruta, h., horikawa, k., uesugi, k., takeuchi, a., suzuki, y., kobayashi, m. (2014). effects of stress triaxiality on damage evolution from pre-existing hydrogen pores in aluminum alloy, mater. trans., 55(2), pp. 383– 386, doi: 10.2320/matertrans.l-m2013841. [59] lode, w. (1926). versuche uber den einfluss der mittleren hauptspannung auf das fliess en der metalle eisen, kupfer und nickel, zeitschrift fur phys., 36(11–12), pp. 913–939, doi: 10.1007/bf01400222. [60] bai, y., wierzbicki, t. (2010). application of extended mohr–coulomb criterion to ductile fracture, int. j. fract., 161(1), pp. 1–20, doi: 10.1007/s10704-009-9422-8. [61] bonora, n. (1997). a nonlinear cdm model for ductile failure, eng. fract. mech., 58(1–2), pp. 11–28, doi: 10.1016/s0013-7944(97)00074-x. [62] rice, j.r., tracey, d.m. (1969). on the ductile enlargement of voids in triaxial stress fields, j. mech. phys. solids, 17(3), pp. 201–217, doi: 10.1016/0022-5096(69)90033-7. [63] rousselier, g. (1987). ductile fracture models and their potential in local approach of fracture, nucl. eng. des., 105(1), pp. 97–111, doi: 10.1016/0029-5493(87)90234-2. [64] tsutsumi, s., kitamura, t., fincato, r. (2020). ductile behaviour of carbon steel for welded structures: experiments and numerical simulations, j. constr. steel res., 172, doi: 10.1016/j.jcsr.2020.106185. [65] cheng, l., monchiet, v., morin, l., de saxcé, g., kondo, d. (2015). an analytical lode angle dependent damage model for ductile porous materials, eng. fract. mech., 149, pp. 119–133, doi: 10.1016/j.engfracmech.2015.09.038. [66] cao, t.s., gachet, j.m., montmitonnet, p., bouchard, p.o. (2014). a lode-dependent enhanced lemaitre model for ductile fracture prediction at low stress triaxiality, eng. fract. mech., 124–125, pp. 80–96, doi: 10.1016/j.engfracmech.2014.03.021. [67] de souza neto, e.a., peric, d., owen, d.r.j. (2008). computational methods for plasticity, 55. [68] besson, j. (2010). continuum models of ductile fracture: a review, int. j. damage mech., 19(1), pp. 3–52, doi: 10.1177/1056789509103482. [69] malcher, l., andrade pires, f.m., césar de sá, j.m.a. (2012). an assessment of isotropic constitutive models for ductile fracture under high and low stress triaxiality, int. j. plast., 30–31, pp. 81–115, doi: 10.1016/j.ijplas.2011.10.005. [70] cao, t.s. (2017). models for ductile damage and fracture prediction in cold bulk metal forming processes: a review, int. j. mater. form., 10(2), pp. 139–171, doi: 10.1007/s12289-015-1262-7. [71] broggiato, g.b., campana, f., cortese, l. (2007). identification of material damage model parameters: an inverse approach using digital image processing, meccanica, 42(1), pp. 9–17, doi: 10.1007/s11012-006-9019-5. [72] yamada, t., ohata, m. (2020). prediction of ductile crack growth resistance using mechanical properties of material, q. j. japan weld. soc., 38(2), pp. 85–94, doi: 10.2207/qjjws.38.85. [73] cockcroft, m.g., latham, d.j. (1968). ductility and the workability of metals, j inst met. inst. met. [74] oh, s.i., chen, c.c., kobayashi, s. (1979). ductile fracture in axisymmetric extrusion and drawing—part 2: r. fincato et alii, frattura ed integrità strutturale, 59 (2022) 1-17; doi: 10.3221/igf-esis.59.01 15 workability in extrusion and drawing, j. eng. ind., 101(1), pp. 36–44, doi: 10.1115/1.3439471. [75] rodriguez-millan, m., garcia-gonzalez, d., rusinek, a., arias, a. (2018). influence of stress state on the mechanical impact and deformation behaviors of aluminum alloys, metals (basel)., 8(7), pp. 520, doi: 10.3390/met8070520. [76] lou, y., huh, h. (2013). evaluation of ductile fracture criteria in a general three-dimensional stress state considering the stress triaxiality and the lode parameter, acta mech. solida sin., 26(6), pp. 642–658, doi: 10.1016/s0894-9166(14)60008-2. [77] bao, y., wierzbicki, t. (2004). on fracture locus in the equivalent strain and stress triaxiality space, int. j. mech. sci., 46(1), pp. 81–98, doi: 10.1016/j.ijmecsci.2004.02.006. [78] wu, b., li, x., di, y., brinnel, v., lian, j., münstermann, s. (2017). extension of the modified bai-wierzbicki model for predicting ductile fracture under complex loading conditions, fatigue fract. eng. mater. struct., 40(12), pp. 2152– 68, doi: 10.1111/ffe.12645. [79] fincato, r., tsutsumi, s. (2019). numerical modeling of the evolution of ductile damage under proportional and nonproportional loading, int. j. solids struct., 160, pp. 247–264, doi: 10.1016/j.ijsolstr.2018.10.028. [80] erice, b., gálvez, f. (2014). a coupled elastoplastic-damage constitutive model with lode angle dependent failure criterion, int. j. solids struct., 51(1), pp. 93–110, doi: 10.1016/j.ijsolstr.2013.09.015. [81] ganjiani, m., homayounfard, m. (2021). development of a ductile failure model sensitive to stress triaxiality and lode angle, int. j. solids struct., 225, pp. 111066, doi: 10.1016/j.ijsolstr.2021.111066. [82] hill, r. (1948). a theory of the yielding and plastic flow of anisotropic metals, proc. r. soc. london. ser. a. math. phys. sci., 193(1033), pp. 281–297, doi: 10.1098/rspa.1948.0045. [83] wang, s., zhan, l., bruhns, o.t., xiao, h. (2021). metal failure effects predicted accurately with a unified and explicit criterion, zamm j. appl. math. mech. / zeitschrift für angew. math. und mech., doi: 10.1002/zamm.202100140. [84] quach, h., kim, j.j., sung, j.h., kim, y.s. (2020). a novel uncoupled ductile fracture criterion for prediction of failure in sheet metal forming, iop conf. ser. mater. sci. eng., 967, pp. 012032, doi: 10.1088/1757-899x/967/1/012032. [85] kachanov, l.m. (1958). time of the rupture process under creep conditions, izv akad nauk s s r otd tech nauk, 8, pp. 26–31, doi: citeulike-article-id:5466815. [86] rabotnov, y.n. (1963). paper 68: on the equation of state of creep, proc. inst. mech. eng. conf. proc., 178(1), pp. 2-117-2–122, doi: 10.1243/pime_conf_1963_178_030_02. [87] lemaitre, j. (1985). coupled elasto-plasticity and damage constitutive equations, comput. methods appl. mech. eng., 51(1–3), pp. 31–49, doi: 10.1016/0045-7825(85)90026-x. [88] lemaitre, j. (1985). a continuous damage mechanics model for ductile fracture, j. eng. mater. technol., 107(1), pp. 83, doi: 10.1115/1.3225775. [89] saanouni, k., forster, c., hatira, f. ben. (1994). on the anelastic flow with damage, int. j. damage mech., 3(2), pp. 140–169, doi: 10.1177/105678959400300203. [90] grammenoudis, p., reckwerth, d., tsakmakis, c. (2009). continuum damage models based on energy equivalence: part i — isotropic material response, int. j. damage mech., 18(1), pp. 31–63, doi: 10.1177/1056789508090466. [91] zhang, k., badreddine, h., saanouni, k. (2020). ductile fracture prediction using enhanced cdm model with lode angle-dependency for titanium alloy ti-6al-4v at room temperature, j. mater. process. technol., 277, pp. 116462, doi: 10.1016/j.jmatprotec.2019.116462. [92] shinozuka, j., goto, k. (2015). 10501 a fem simulation of the serrated type of chip formation employing lemaitre’s damage model, proc. conf. kanto branch, 2015.21, pp. _10501-1_-_10501-2_ doi: 10.1299/jsmekanto.2015.21._10501-1_. [93] fincato, r., tsutsumi, s. (2017). effect of the stress triaxiality and lode angle on the ductile damage evolution, q. j. japan weld. soc., 35(2), pp. 185s-189s. [94] bonora, n., testa, g., ruggiero, a., iannitti, g., gentile, d. (2018). modification of the bonora damage model for shear failure, frat. ed integrità strutt., 12(44), pp. 140–150, doi: 10.3221/igf-esis.44.11. [95] bonora, n., testa, g., iannitti, g., ruggiero, a., gentile, d. (2018). prediction of the formability limit using damage mechanics, j. phys. conf. ser., 1063, pp. 012066, doi: 10.1088/1742-6596/1063/1/012066. [96] benallal, a., billardon, r., lemaitre, j. (1991). continuum damage mechanics and local approach to fracture: numerical procedures, comput. methods appl. mech. eng., 92(2), pp. 141–155, doi: 10.1016/0045-7825(91)90236-y. [97] badreddine, h., saanouni, k. (2017). on the full coupling of plastic anisotropy and anisotropic ductile damage under finite strains, int. j. damage mech., 26(7), pp. 1080–1123, doi: 10.1177/1056789516635729. [98] badreddine, h., yue, z.m., saanouni, k. (2017). modeling of the induced plastic anisotropy fully coupled with ductile damage under finite strains, int. j. solids struct., 108, pp. 49–62, doi: 10.1016/j.ijsolstr.2016.10.028. [99] mcclintock, f.a. (1968). a criterion for ductile fracture by the growth of holes, j. appl. mech., 35(2), pp. 363, r. fincato et alii, frattura ed integrità strutturale, 59 (2022) 1-17; doi: 10.3221/igf-esis.59.01 16 doi: 10.1115/1.3601204. [100] gurson, a.l. (1977). continuum theory of ductile rupture by void nucleation and growth: part i—yield criteria and flow rules for porous ductile media, j. eng. mater. technol., 99(1), pp. 2, doi: 10.1115/1.3443401. [101] ying, l., wang, d., liu, w., wu, y., hu, p. (2018). on the numerical implementation of a shear modified gtn damage model and its application to small punch test, int. j. mater. form., 11(4), pp. 527–539, doi: 10.1007/s12289-017-1362-7. [102] zhou, j., gao, x., sobotka, j.c., webler, b.a., cockeram, b. v. (2014). on the extension of the gurson-type porous plasticity models for prediction of ductile fracture under shear-dominated conditions, int. j. solids struct., 51(18), pp. 3273–3291, doi: 10.1016/j.ijsolstr.2014.05.028. [103] he, z., zhu, h., hu, y. (2021). an improved shear modified gtn model for ductile fracture of aluminium alloys under different stress states and its parameters identification, int. j. mech. sci., 192, pp. 106081, doi: 10.1016/j.ijmecsci.2020.106081. [104] ohata, m., fukahori, t., minami, f. (2010). damage model for predicting the effect of steel properties on ductile crack growth resistance, int. j. damage mech., 19(4), pp. 441–459, doi: 10.1177/1056789509103704. [105] fukahori, t., ohata, m., minami, f., kayamori, y., inoue, t. (2008). damage model for simulating the effect of material properties on ductile crack growth resistance-simulation of ductile crack growth-, tetsu-to-hagane, 94(6), pp. 222–230, doi: 10.2355/tetsutohagane.94.222. [106] ishiguro, t., yoshida, y., yukawa, n., ishikawa, t. (2009). deformation analysis of shearing process using results of notched round bar tension test, mater. trans., 50(7), pp. 1671–1677, doi: 10.2320/matertrans.mf200903. [107] jiang, w., li, y., su, j. (2016). modified gtn model for a broad range of stress states and application to ductile fracture, eur. j. mech. a/solids, 57, pp. 132–148, doi: 10.1016/j.euromechsol.2015.12.009. [108] gao, l., zhao, j., quan, g., xiong, w., an, c. (2019). study on the evolution of damage degradation at different temperatures and strain rates for ti-6al-4v alloy, high temp. mater. process., 38(2019), pp. 332–341, doi: 10.1515/htmp-2018-0091. [109] bouchard, p.-o., bourgeon, l., fayolle, s., mocellin, k. (2011). an enhanced lemaitre model formulation for materials processing damage computation, int. j. mater. form., 4(3), pp. 299–315, doi: 10.1007/s12289-010-0996-5. [110] hammi, y., horstemeyer, m.f. (2007). a physically motivated anisotropic tensorial representation of damage with separate functions for void nucleation, growth, and coalescence, int. j. plast., 23(10–11), pp. 1641–1678, doi: 10.1016/j.ijplas.2007.03.010. [111] santaoja, k.j. (2019). on continuum damage mechanics, raken. mek., 52(3), pp. 125–147, doi: 10.23998/rm.76025. [112] besson, j., guillemer-neel, c. (2003). an extension of the green and gurson models to kinematic hardening, mech. mater., 35(1–2), pp. 1–18, doi: 10.1016/s0167-6636(02)00169-2. [113] barlat, f., brem, j.c., yoon, j.w., chung, k., dick, r.e., lege, d.j., pourboghrat, f., choi, s.-h., chu, e. (2003). plane stress yield function for aluminum alloy sheets—part 1: theory, int. j. plast., 19(9), pp. 1297–1319, doi: 10.1016/s0749-6419(02)00019-0. [114] cazacu, o. (2018). new yield criteria for isotropic and textured metallic materials, int. j. solids struct., 139–140, pp. 200–210, doi: 10.1016/j.ijsolstr.2018.01.036. [115] cazacu, o., plunkett, b., barlat, f. (2006). orthotropic yield criterion for hexagonal closed packed metals, int. j. plast., 22(7), pp. 1171–1194, doi: 10.1016/j.ijplas.2005.06.001. [116] costin, l.s. (1985). damage mechanics in the post-failure regime, mech. mater., 4(2), pp. 149–160, doi: 10.1016/0167-6636(85)90013-4. [117] rabotnov, y.n. (1969).creep rupture. applied mechanics, berlin, heidelberg, springer berlin heidelberg, pp. 342– 349. [118] wulfinghoff, s., reese, s. (2015). on anisotropic damage theories based on 2nd order damage tensors, pamm, 15(1), pp. 165–166, doi: 10.1002/pamm.201510073. [119] voyiadjis, g.z., kattan, p.i. (1999).damage and plasticity in metals. advances in damage mechanics: metals and metal matrix composites, elsevier, pp. 109–157. [120] olsen-kettle, l. (2019). bridging the macro to mesoscale: evaluating the fourth-order anisotropic damage tensor parameters from ultrasonic measurements of an isotropic solid under triaxial stress loading, int. j. damage mech., 28(2), pp. 219–232, doi: 10.1177/1056789518757293. [121] desmorat, r., desmorat, b., olive, m., kolev, b. (2018). micromechanics based framework with second-order damage tensors, eur. j. mech. a/solids, 69, pp. 88–98, doi: 10.1016/j.euromechsol.2017.11.014. [122] badreddine, h., saanouni, k., nguyen, t.d. (2015). damage anisotropy and its effect on the plastic anisotropy r. fincato et alii, frattura ed integrità strutturale, 59 (2022) 1-17; doi: 10.3221/igf-esis.59.01 17 evolution under finite strains, int. j. solids struct., 63, pp. 11–31, doi: 10.1016/j.ijsolstr.2015.02.009. [123] fincato, r., tsutsumi, s. (2021). coupled elasto-viscoplastic and damage model accounting for plastic anisotropy and damage evolution dependent on loading conditions, comput. methods appl. mech. eng., 387, pp. 114165, doi: 10.1016/j.cma.2021.114165. [124] nagaki, s., saboi, d., muroi, k., iizuka, m., oshita, k. (2016). anisotropic damage evolution for perforated sheet under tensile deformation, key eng. mater., 725, pp. 489–494, doi: 10.4028/www.scientific.net/kem.725.489. [125] shahzamanian, m.m. (2018). anisotropic gurson-tvergaard-needleman plasticity and damage model for finite element analysis of elastic-plastic problems, int. j. numer. methods eng., 115(13), pp. 1527–1551, doi: 10.1002/nme.5906. [126] takazawa, h., iwamatsu, f., miyazaki, k., yamada, h., ogasawara, n. (2019). effect of strain rate on crack propagation of ductile fracture behavior using damage mechanics model, proc. comput. mech. conf., 2019.32, pp. 099, doi: 10.1299/jsmecmd.2019.32.099. [127] tang, b., li, c., xiao, g., zhao, w., li, h. (2017). numerical modeling and experimental verification of ductile damage in boron steel hot stamping process, procedia eng., 207, pp. 675–680, doi: 10.1016/j.proeng.2017.10.1040. [128] kumar, m., gautam, s.s., dixit, p.m. (2019). a non-linear ductile damage growth law at elevated temperature, sādhanā, 44(6), pp. 145, doi: 10.1007/s12046-019-1119-8. [129] hirose, s., toi, y. (2017). investigation of continuum damage mechanics model without element size sensitivity, trans. jsme (in japanese), 83(852), pp. 17-00130-17–00130, doi: 10.1299/transjsme.17-00130. [130] huang, l., yao, y. (2021). a thermodynamically nonlocal damage model using a surface-residual-based nonlocal stress, j. mech., 37, pp. 484–495, doi: 10.1093/jom/ufab017. [131] andrade, f.x.c., césar de sá, j.m.a., andrade pires, f.m. (2011). a ductile damage nonlocal model of integraltype at finite strains: formulation and numerical issues, int. j. damage mech., 20(4), pp. 515–557, doi: 10.1177/1056789510386850. [132] sprave, l., menzel, a. (2020). a large strain gradient-enhanced ductile damage model: finite element formulation, experiment and parameter identification, acta mech., 231(12), pp. 5159–5192, doi: 10.1007/s00707-020-02786-5. [133] brepols, t., wulfinghoff, s., reese, s. (2017). gradient-extended two-surface damage-plasticity: micromorphic formulation and numerical aspects, int. j. plast., 97, pp. 64–106, doi: 10.1016/j.ijplas.2017.05.010. [134] enakoutsa, k. (2014). an improved nonlocal gurson model for plastic porous solids, with an application to the simulation of ductile rupture tests, appl. math. model., 38(11–12), pp. 2791–2799, doi: 10.1016/j.apm.2013.11.007. [135] cortese, l., nalli, f., rossi, m. (2016). a nonlinear model for ductile damage accumulation under multiaxial nonproportional loading conditions, int. j. plast., 85, pp. 77–92, doi: 10.1016/j.ijplas.2016.07.003. [136] papasidero, j., doquet, v., mohr, d. (2015). ductile fracture of aluminum 2024-t351 under proportional and nonproportional multi-axial loading: bao–wierzbicki results revisited, int. j. solids struct., 69–70, pp. 459–474, doi: 10.1016/j.ijsolstr.2015.05.006. [137] zhang, k., badreddine, h., saanouni, k. (2018). thermomechanical modeling of distortional hardening fully coupled with ductile damage under non-proportional loading paths, int. j. solids struct., 144–145, pp. 123–136, doi: 10.1016/j.ijsolstr.2018.04.018. [138] neves, r.s., ferreira, g.v., malcher, l. (2020). gurson-based incremental damage in fatigue life estimate under proportional and non-proportional loading: constant amplitude and low cycle regime applications, theor. appl. fract. mech., 108, pp. 102678, doi: 10.1016/j.tafmec.2020.102678. [139] baltic, s., asadzadeh, m.z., hammer, p., magnien, j., gänser, h.-p., antretter, t., hammer, r. (2021). machine learning assisted calibration of a ductile fracture locus model, mater. des., 203, pp. 109604, doi: 10.1016/j.matdes.2021.109604. [140] sun, q., lu, y., chen, j. (2020). identification of material parameters of a shear modified gtn damage model by small punch test, int. j. fract., 222(1–2), pp. 25–35, doi: 10.1007/s10704-020-00428-4. [141] nahshon, k., hutchinson, j.w. (2008). modification of the gurson model for shear failure, eur. j. mech. a/solids, 27(1), pp. 1–17, doi: 10.1016/j.euromechsol.2007.08.002. shot peening processes to obtain nanocrystalline surfaces in metal alloys: d. yang et alii, frattura ed integrità strutturale, 45 (2018) 45-52; doi: 10.3221/igf-esis.45.04 45 effects of weld size on stress concentration factors of chs-cfshs joints delei yang department of architectural and civil engineering, university of huanghuai, zhumadian 463000, china department of civil engineering, university of ottawa, east ottawa, on k1n 6n5, canada dyang2@uottawa.ca lewei tong department of building engineering, tongji university, shanghai 200092, china tonglw@tongji.edu.cn abstract. this paper aims to disclose the effects of weld size on hot spot stress in the calculation of fatigue performance of the joints. for this purpose, the author explored the hot spot stress of chs-cfshs t-joints, which consists of circular hollow section (chs) braces and concrete-filled square hollow section (cfshs) chords. after reviewing the previous studies and the relevant specifications on weld size, the author probes into the effects of weld size on the stress concentration factor (scf) of chs-cfshs joints via finiteelement analysis. the analysis show that the weld size directly affected the hot spot stress in both conditions, and the influence laws were largely the same; with the increase of weld size, the brace-side scf plunged when the chordsize weld size remained the same, but the chord-side scf changed slightly when the brace-side weld size was constant; the brace-side and chord-side scf declined when the brace-side and chord-side weld sizes increased by the same amount. this research successfully determined the weld sizes that are consistent with the relevant specifications, and safe and simple to apply in actual engineering. keywords. weld size; stress concentration factors (scf); finite-element analysis; circular hollow section (chs); concrete-filled square hollow section (cfshs); welded joints. citation: yang, d., tong, l., effects of weld size on stress concentration factors of chscfshs joints, frattura ed integrità strutturale, 45 (2018) 45-52. received: 07.05.2018 accepted: 29.05.2018 published: 01.07.2018 copyright: © 2018 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. introduction he concrete-filled steel tube (cfst) is a composite member consisting of a steel tube infilled with concrete. with high bearing capacity, good seismic property, strong fire resistance and short construction period, this new structure can satisfy the various needs of modern engineering structures, such as large-span, high altitude, t http://www.gruppofrattura.it/va/45/27.mp4 d. yang et alii, frattura ed integrità strutturale, 45 (2018) 45-52; doi: 10.3221/igf-esis.45.04 46 overloading and industrialized construction [1, 2]. as a result, the cfst has been extensively applied to build complex structures like industrial plants, high-rise buildings and large-span bridges. the superiority of the cfst is partially attributable to its welded joints. compared to other types of joints, the cfst’s welded joints have a simple and neat appearance, with no protruding node, a clear force transmission line, a simple and easy-to-maintain structure. the static strength, stiffness, seismic property and fatigue performance of the welded joints are critical to the overall state of the cfst. for instance, the fatigue performance of the joints directly bears on the structural safety of bridges and offshore platforms, which are subjected to long-term alternating loads, and the service life of highrises and other structures under long-term wind loads. over the years, various methods have been developed to evaluate the fatigue performance of steel tube joints. among them, hot spot stress stands out as the most popular and successful strategy for fatigue calculated of welded tube joints [315]. nevertheless, there is not yet a consensus on the effects of weld size on hot spot stress in the calculation of fatigue performance of the joints. to solve the problem, this paper explores the hot spot stress of chs-cfshs t-joints, which consists of circular hollow section (chs) braces and concrete-filled square hollow section (cfshs) chords. the t-joint is commonly used in engineering practice. it is the building block of complex 2d and 3d joints. after reviewing the previous studies and the relevant specifications on weld size, the author probes into the effects of weld size on the stress concentration factors (scf) of chs-cfshs joints via finite-element analysis. literature review o far, there is no agreement on the impacts of weld size on the scf of welded joints. some hold that the extrapolated scf is not affected by weld size, because the extrapolation region is far enough from the weld toe. this view is reflected in the scf formula for pure chs joints in reference [6], which does not consider the impact of weld size. some believe that the weld size has a certain effect on the scf of the welded joint, as evidenced by the scf formula in reference [3]. below are two representative studies concerning the effect of weld size on the scf of welded joints. wingerde conducted a finite-element modeling of fillet weld and full penetration butt weld of different sizes, aiming to disclose the effects of weld size on the scf of shs joints (fig. 1). the modeling reveals that the brace-side scf of fillet weld was 1.4 times that of the butt weld, while the chord-side scf of the two types of weld was almost the same. (a) fillet weld (b) full penetration weld figure 1: finite-element model of wingerde. through finite-element analysis, zheng hongzhi examined the scf of chs-shs joints under the different sizes of fillet weld, partial penetration butt weld, and full penetration butt weld [16]. to obtain the brace-side scf of the joints with full or partial penetration weld, the weld size-brace wall thickness ratio was taken as a dimensionless factor in the finiteelement model, while brace-side weld size was maintained equal to the chord-side weld and subjected to four changes on four levels (fig. 2(a)). to acquire the chord-side scf of the joints with full or partial penetration weld, the weld size was set to the same level as that in the model of wingerde for full penetration butt weld (fig. 1(b)). the scf of the joints with fillet weld was computed by the finite-element model in fig. 2(b), where both brace-side and chord-side sizes of the fillet weld were 1.2tl. the theoretical scfs obtained by zheng were the upper limits of the corresponding joint. nevertheless, the weld size-brace wall thickness ratio must be considered before computing the brace-side scf of the joints with full or partial penetration weld. this complicates the computing process and adds to the difficulty of engineering application. s d. yang et alii, frattura ed integrità strutturale, 45 (2018) 45-52; doi: 10.3221/igf-esis.45.04 47 (a) (b) figure 2: finite-element model of zheng hongzhi. relevant specifications he current calculation method for hot spot stress adopts the minimum distance between the extrapolation region and the weld toe, seeking to eliminate the impact of the local shape of the weld. mechanically speaking, the weld size has a positive correlation with the distance between the extrapolation region and the intersection area, the most obvious variation place of stiffness. in other words, the scf tends to decline with the increase in the weld size. hence, it is assumed here that the weld size does have an impact on the scf. the range of weld size must be determined before studying the effect of weld size on the scf of welded joints. below is a review of the relevant specifications on weld size. (1) for welded joints directly under fatigue load, the technical specification for structures with steel hollow sections (cecs 280:2010) [17] stipulates that the partial or full penetration weld should be adopted if the brace wall thickness t is greater than 8mm; the fillet weld can be used if the brace wall thickness is smaller than or equal to 8mm (article 8.28). (2) for tubular t-joints with full penetration weld, the technical specification for welding of steel structure of building (jgj 81-2002) [18] stipulates that the minimum weld size should be w0=0.5t1 at the chord-side and w1=6mm+0.767t1 at the brace-side (article 4.3.6-1), where t1 is the brace wall thickness. that is, the minimum weld size-brace wall thickness ratio remains at 0.5 at the chord-size, and changes at the brace-side with brace wall thicknesses. moreover, the ratio of weld-size to brace wall thickness should fall in 1.14~2.27 if the brace wall thickness varies between 4mm and 16mm (the brace wall thickness should not exceed 16mm) (article 4.3.6-1). (3) for tubular t-joints with fillet weld, the technical specification for structures with steel hollow sections (cecs 280:2010)[17] stipulates that the weld thickness should not be smaller than brace wall thickness t1 (article 8.2.8) and should not exceed twice the brace wall thickness (article 7.1.1-4); the code for design of steel structures (gb 500172013)[19] stipulates that the ratio of brace-side weld size to chord-side weld size can be 1: 1 (article 8.2.8). in the rightangle fillet weld, the fillet weld size should be about 1.4 times of the weld thickness. in other words, the fillet weld size should not be smaller than 1.4t1, should not be greater than 2t1, and must not be greater than 2.8t1, where t1 is the brace wall thickness. (4) for tubular t-joints with partial penetration weld, the technical specification for structures with steel hollow sections (cecs 280:2010) [17] stipulates that the fatigue performance of the weld should be the same as that of fillet weld, that is, the weld size should not be smaller than 0.5t1 at the chord-side or smaller than 1.73t1 at the brace-side, where t1 is the brace wall thickness. finite-element analysis finite-element model eld configuration. fig. 3 presents the three possible welds for the brace and chord of welded tube joints, namely, full penetration weld, partial penetration weld and fillet weld. wingerde examined the weld configuration by finite-element method, suggesting that the effect of different weld configurations on the scf is negligible [3]. zheng hongzhi also applied finite-element method to examine the impacts of different weld configurations on the scf and concluded that the scf of full penetration weld is less than 10% greater than that of the other two configurations under the same weld size and dimensionless parameters [16]. for reliability and accuracy, the three types of welds are all modeled according to the configuration of full penetration weld in this research (fig. 3(a)). t w d. yang et alii, frattura ed integrità strutturale, 45 (2018) 45-52; doi: 10.3221/igf-esis.45.04 48 (a) full penetration weld (b) partial penetration weld (c)fillet weld figure 3: weld configuration calculation parameters and working condition. a total of six finite-element models (wt1~wt6) were established with b0=200, d1=80, t0=10, t1=5, β=0.4, 2γ=20 and τ=0.5, according to the relevant specifications on weld size of tube joints and the empirical range of influencing parameters of steel tubular joints β=d1/b0, 2γ=b0/t0 and τ=t1/t0. in wt1 and wt2, w0/t1 was set to 0.5 and w1/t1 was set to 1.2~2.0; in wt3 and wt4, w0=w1, and w1/t1 was set to 1.2~1.8; in wt5 and wt6, w1/t1 was set to 1.8 and w0/t1 was set to 0.5~1.0. fig. 4 and fig. 5 respectively explain the meanings of β, 2γ and τ, and the calculated scf positions, where w0 is the chord-side weld size and w1 was the brace-side weld size. d1 chord brace concrete β = d1/b0 2γ = b0/t0 τ = t1/t0 c0 c45 c60 c90 c180b0 b45 b60 b90 figure 4: schematic diagram of chs-cfshs t-joint. figure 5: calculated scf positions given the symmetry of joints, a half finite-element model was constructed on the finite-element software abaqus [20]. the steel tube was meshed into incompatible mode eight-node brick elements (c3d8i) and the concrete into eight-node brick elements with reduced integration (c3d8r). the face-to-face discrete method was employed to simulate the contact between steel tube and concrete. the normal contact was simulated as hard contact, and the tangential bond and slip were modeled with the kulun friction model whose friction coefficient was set to 0.35. our purpose is to acquire the scf of cfst joints under the normal working condition, rather than the bearing capacity of these joints. thus, the monotonic constitutive relation of concrete is not considered here. the elastic modulus was set to e＝2.05×105mpa (steel tube) and 3.45×104mpa (concrete), and the poisson’s ratio was set to ν＝0.3 (steel tube) and 0.2 (concrete). to disclose of the effect of the weld size, the two ends of all models were constrained by the same hinged connection; the steel grade was set to q345; the strength of the filled concrete was set to c50; the friction properties were the same between steel tube and concrete. for accuracy and efficiency, the grid size of finite-element modeling was determined in light of the previous studies (fig. 6). the braces of all models were subjected to axial tension and in-plane bending moment (figs. 7 and 8). the joints were in elastic phase throughout the simulation according to the rule of fatigue failure. d. yang et alii, frattura ed integrità strutturale, 45 (2018) 45-52; doi: 10.3221/igf-esis.45.04 49 concrete c3d8r steel tube c3d8i extrapolation points “hard contact” with coulomb friction weld figure 6: finite-element grids of a chs-cfshs t-joint (partial). brace 0°180° 45° 60°90° 270° chord at 0°180° 45° 60°90° 270° chord t e n s il e c o m p re s si v e brace ipb figure 7: condition of axial tension. figure 8: condition of in-plane bending moment. results and analysis tabs. 1 and 2 show the sfc results in conditions 1 and 2 respectively, according to the scf calculation method in the existing achievements [16, 21]. the following conclusions were drawn from the scf results. joints w0/t1 w1/t1 brace-side scf chord-side scf 0° 60° 90° 0° 60° 90° wt1 0.5 1.2 3.61 5.82 6.70 5.48 7.96 9.05 wt2 0.5 2.0 1.70 3.82 4.48 5.60 8.34 9.29 wt3 1.2 1.2 4.19 6.66 7.56 5.06 7.06 7.76 wt4 1.8 1.8 3.29 5.76 6.63 4.87 6.46 6.95 wt5 0.5 1.8 2.14 4.20 4.88 5.71 8.27 8.93 wt6 1.0 1.8 2.83 5.25 6.03 5.34 7.61 8.41 table 1: scf in condition 1. d. yang et alii, frattura ed integrità strutturale, 45 (2018) 45-52; doi: 10.3221/igf-esis.45.04 50 joints w0/t1 w1/t1 brace-side scf chord-side scf 0° 135° 180° 135° 180° wt1 0.5 1.2 2.19 1.75 1.82 2.54 2.68 wt2 0.5 2.0 1.78 1.23 1.18 2.59 2.72 wt3 1.2 1.2 2.35 1.96 2.05 2.27 2.35 wt4 1.8 1.8 2.25 1.77 1.83 2.08 2.11 wt5 0.5 1.8 1.88 1.34 1.33 2.60 2.83 wt6 1.0 1.8 2.13 1.63 1.64 2.41 2.47 table 2: scf in condition 2. (a) effect of only size change of brace-side weld. (b) effect of equal proportionally change of weld size (c) effect of only size change of chord-side weld figure. 9: effects of weld size on the scf. first, the weld size directly affected the hot spot stress in both conditions, and the influence laws were largely the same. second, the chord-side weld size was all 0.5t1, while the brace-side weld size was 1.2t1, 1.8t1 and 2.0t1, respectively, in wt1, wt5 and wt2. in both conditions, the brace-side scf plunged with the increase of brace-side weld size, while the chord-side scf changed slightly less than 5%. fig. 9(a) illustrates the effect of weld size on the scf in condition 1. the effect of weld size in condition 2 was similar to that in condition 1. this is because the increase in brace-side weld size pushed the brace-side extrapolation region away from the stress hotspot, leading to reduced hot spot stress obtained by extrapolation. third, the weld size in wt3 was 1.2t1 at both brace-side and chord-side, and that in wt4 was 1.8t1 at both brace-side and chord-side. in both conditions, the scf in wt3 surpassed that in wt4 at both brace-side and chord-side. fig. 9(b) depicts the effect of fillet weld size on the scf in condition 1. the effect of fillet weld size in condition 2 was similar to d. yang et alii, frattura ed integrità strutturale, 45 (2018) 45-52; doi: 10.3221/igf-esis.45.04 51 that in condition 1. the results demonstrate that the brace-side and chord-side scfs declined when the brace-side and chord-side weld sizes increased by the same amount. fourth, wt5 and wt6 shared the same weld size at the brace-side, but wt5 had half the weld size of wt6 at the chordsize. in both conditions, the scf decreased slightly with the increase of weld size at the chord-size, and increased at the brace-side. fig. 9(c) describes the effect of fillet weld size on the scf in condition 1. the effect of fillet weld size in condition 2 was similar to that in condition 1. the effects can be explained as follows: with the growth in chord-side weld size, the angle between weld surface and brace wall expanded, adding to the slope of the transition area between the weld and the wall. recommended weld sizes hrough the simulation of six models, it is clear that the joint scf is indeed affected by weld size. this section attempts to recommend rational weld sizes for engineering practice. the idea of wingerde fails to ensure the safety of brace-side scf for full penetration butt weld, while the idea of zheng hongzhi complicates the scf calculation with the consideration of brace-side minimize weld size. considering the relevant specifications, the author recommended the following weld sizes which are easy to compute and implement. first, the chord-side scf of full or partial penetration weld joints increased significantly with the decrease of chord-side weld size, but insensitive to the variations in brace-side weld size. in actual projects, the weld size should be minimized at chord-side and set to a common size at brace-side (fig. 10(a)). the chord-side scf calculated of our finite-element model is the upper limit of the actual chord-side joint scf. thus, it is safe for engineering application. second, the brace-side scf of full or partial penetration weld joints was almost the same as that at chord-side, because the joint scf increased with the decrease of weld size. thus, both brace-side and chord-side weld sizes were 1.2t1 (fig. 10(b)). the brace-side scf calculated of our finite-element model is the upper limit of the actual brace-side joint scf. thus, it is safe for engineering application. third, the fillet weld size was set to 1.2t1 for simplicity and applicability, because the scf of fillet weld joints grew with the decrease of weld size. the size was the same as that for computing the brace-side scf of joints connected by full or partial penetration weld (fig. 10 (c)). the scf calculated from our finite-element model is the upper limit of the actual fillet weld joint scf. thus, it is safe for engineering application. (a) (b) figure 10: recommended weld sizes in finite-element calculation. conclusions inite-element analysis reveals that the weld size directly affected the hot spot stress in both conditions, and the influence laws were largely the same. with the increase of weld size, the brace-side scf plunged when the chordsize weld size remained the same, but the chord-side scf changed slightly when the brace-side weld size was constant. brace-side and chord-side scf declined when the brace-side and chord-side weld sizes increased by the same amount. the recommended weld sizes are consistent with the relevant specifications and safe and simple to apply in actual engineering. t f d. yang et alii, frattura ed integrità strutturale, 45 (2018) 45-52; doi: 10.3221/igf-esis.45.04 52 acknowledgments he authors wish to thank the natural science foundation of china for financially supporting the research in the paper through the grant no.51478334 and henan science and technology department supporting the research in the paper through the grant no.122102210087 and no.182102310918. references [1] han, l. h. and yang, y. f. (2007). modern technology of concrete-filled steel tubular structures, 2nd ed. beijing, pr china: china architecture & building press. [2] han, l. h., li, w. and bjorhovde, r. (2014). developments and advanced applications of concrete-filled steel tubular (cfst) structures: members, journal of constructional steel research, 100, pp. 211-228. [3] wingerde, a. m. v., packer, j. a. and wardenier, j. (1995). criteria for the fatigue assessment of hollow structural section connections, journal of constructional steel research, 35, pp. 71-115. [4] recommended practice for fatigue strength analysis of offshore steel structures, dnv rp-c203, (2001). [5] zhao x. l., herion, s. and packer, j. a. (2001). design guide for circular and rectangular hollow section welded joints under fatigue loading, cidect and tuv-verlag, german. [6] hobbacher, a. f. (2008). recommendations for fatigue design of welding joints and components, international institute of welding, doc. xiii-2151-07/xv-1254-07. [7] aws d1.1-2008. structure welding code-steel, the american national standards institute, american welding society, (2008). [8] packer, j. a., mashiri, f. r., zhao, x. l. and willibald, s. (2007). static and fatigue design of chs-to-rhs welded connections using a branch conversion method, journal of constructional steel research, 63, pp. 82-95. [9] mashiri, f. r. and zhao, x. l. (2010). square hollow section (shs) t-joints with concrete-filled chords subjected to in-plane fatigue loading in the brace, thin-walled structures, 48, pp. 150-158. [10] mashiri, f. r., zhao, x. l. and tong, l. w. (2013). fatigue tests and design of thin chs–shs t-joints under cyclic in-plane bending, j civil struct health monit., 3, pp. 129-140. [11] wang, k., tong, l. w., zhu, j., zhao, x. l. and mashiri, f. r. (2013). fatigue behavior of welded t-joints with a chs brace and cfchs chord under axial loading in the brace, journal of bridge engineering., 18, pp. 142-152. [12] kim, i. g., chung, c. h., shim, c. s. and kim, y. j. (2014). stress concentration factors of n-joints of concrete-filled tubes subjected to axial loads, int j steel struct., 14, pp. 1-11. [13] qian, x. d., jitpairod, k., marshall, p. and swaddiwudhipong, s., ou, z. y., zhang, y., pradana, m. r. (2014). fatigue and residual strength of concrete-filled tubular x-joints with full capacity welds, journal of constructional steel research, 100, pp. 21-35. [14] tong, l. w., xu, g. w., liu, y. q., yan, d. q. and zhao, x. l. (2015). finite element analysis and formulae for stress concentration factors of diamond bird-beak shs t-joints, thin-walled structures, 86, pp. 108-120. [15] tong, l. w., xu, g. w., yan, d. q. and zhao, x. l. (2016). fatigue tests and design of diamond bird-beak shs tjoints under axial loading in brace, journal of constructional steel research, 118, pp. 49-59. [16] tong, l. w., zheng, h. z., mashiri, f. r. and zhao, x. l. (2013). stress-concentration factors in circular hollow section and square hollow section t-connections: experiments, finite-element analysis, and formulas, journal of structural engineering, 139, pp. 66-81. [17] technical specification for structures with steel hollow sections (cecs 280:2010), beijing, china; china plan press., (2010). [18] technical specification for welding of steel structure of building (jgj 81-2002), beijing, china; china construction industry press., (2002). [19] code for design of steel structures (gb 50017-2013), beijing, china; china standard press., (2010). [20] simulia. abaqus 6.12. analysis user’s manual, (2013). [21] tong, l. w., yang, d. l. and zhao, x. l. (2013). experimental study on fatigue behaviour of welded chs-toconcrete filled shs t-joints. journal of variation and shock, 2, pp. 99-105. t microsoft word numero_51_art_33_2666 m. cauwels et alii, frattura ed integrità strutturale, 51 (2020) 449-458; doi: 10.3221/igf-esis.51.33 449 focussed on the 1st benelux network meeting and workshop on damage and fracture mechanics the hydrogen embrittlement sensitivity of duplex stainless steel with different phase fractions evaluated by in-situ mechanical testing margo cauwels, lisa claeys, tom depover, kim verbeken ghent university, department of materials, textiles and chemical engineering, technologiepark 46, 9052 zwijnaarde, belgium margo.cauwels@ugent.be lisa.claeys@ugent.be tom.depover@ugent.be, http://orcid.org/0000-0002-8856-1122 kim.verbeken@ugent.be, http://orcid.org/0000-0002-5190-016x abstract. the influence of the austenite (γ) phase fraction on the hydrogen embrittlement of duplex stainless steel is investigated. heat treatments are performed to create two duplex stainless steel specimens, containing 50% and 44% of austenite, respectively. mechanical testing with and without hydrogen charging reveals that significant embrittlement occurs regardless of the austenite fraction. a higher austenite fraction results in a reduced ductility loss under the presence of hydrogen. samples with a higher ferrite fraction are embrittled more due to their higher hydrogen diffusivity. in-situ tensile tests, interrupted at the ultimate tensile strength, show hydrogen-assisted cracks on the specimen surface both in austenite and ferrite and across the α/γ interface. keywords. hydrogen embrittlement; duplex stainless steel; in-situ mechanical testing citation: cauwels, m., claeys, l., depover, t., verbeken, k., the hydrogen embrittlement sensitivity of duplex stainless steel with different phase fractions evaluated by in-situ mechanical testing, frattura ed integrità strutturale, 51 (2020) 449-458. received: 31.10.2019 accepted: 03.12.2019 published: 01.01.2020 copyright: © 2019 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. introduction uplex stainless steels (dss) are a family of stainless steel grades characterised by a mixed microstructure of austenite (γ, fcc crystal structure) and ferrite (α, bcc crystal structure). they combine high mechanical strength with excellent corrosion resistance. dss are therefore attractive materials for application in a diverse range of industries, such as energy, marine, petrochemical, paper and oil & gas industry. their use has largely increased during the last decade. however, dss have an important drawback: they are vulnerable to hydrogen embrittlement (he) and hydrogen induced stress cracking (hisc) [1, 2]. hydrogen embrittlement is used to refer to a degradation of mechanical properties due to the presence of hydrogen. this phenomenon is mostly reported as a decrease in material ductility and toughness, which can lead to unexpected and premature failure. hydrogen can enter the dss during production and processing, for example during welding, or during in-service conditions, such as for cathodically over-protected offshore structures or because of general corrosion that can be aggravated in environments where h2s is present [3–5]. d http://www.gruppofrattura.it/va/51/2666.mp4 m. cauwels et alii, frattura ed integrità strutturale, 51 (2020) 449-458; doi: 10.3221/igf-esis.51.33 450 several possible theories for hydrogen embrittlement have been proposed, with the operational mechanism depending on the material, the hydrogen charging condition and the load type [6, 7]. no single mechanism can comprehensively describe the he phenomena and different combinations of mechanisms have also been described [8]. for non-hydride forming materials, hydrogen enhanced decohesion (hede), hydrogen enhanced localised plasticity (help) and hydrogen enhanced strain-induced vacancies (hesiv) are most commonly cited. hede is the oldest proposed mechanism and proposes hydrogen induced weakening of interatomic bonds, as such promoting decohesion in the lattice [9–11]. the help model is based on atomic hydrogen enhancing dislocation mobility through an elastic shielding effect. this locally reduces the shear strength, leading to premature fracture [12–14]. finally, according to the hesiv theory, hydrogen stabilises vacancies and reduces their mobility, increasing the strain-induced creation of vacancies and reducing the material ductility [15, 16]. hydrogen induced ductility loss of dss under cathodic protection in artificial seawater or nacl-containing solutions has been reported in several studies [4,17–21]. the hydrogen susceptibility was found to be more pronounced for welded dss because of microstructural changes and a higher ferrite content in the heat affected zone as compared to the base metal [22]. the hydrogen properties of the two phases in dss are very different. in ferrite, the hydrogen diffusion is relatively high but the hydrogen solubility is low, while for austenite the reverse is true [23]. usually, α and γ are present in equal fractions in commercial dss to obtain an optimal combination of mechanical properties. an austenite phase fraction that differs from this ideal 50% is relevant for example in the heat affected zone of welded dss structures. this work aims to study the influence of the austenite phase fraction on the hydrogen embrittlement sensitivity of dss. first, two heat treatments were devised in order to create dss samples with a different austenite phase fraction. thereafter, tensile tests were performed both with and without the presence of hydrogen. the tests without hydrogen were performed in air and tests with hydrogen were performed in-situ, i.e. with continuous electrochemical hydrogen charging during the tensile test, using pre-charged specimens. materials and experimental procedure he material used was uns s32205 duplex stainless steel, hot rolled to plates of 0.8 mm thickness. the chemical composition is given in tab. 1. the as-received material contained 53% ferrite as determined via magnetic measurements (feritscope® fmp30). the steel was subjected to two different heat treatments in order to create materials with a differing austenite fraction: one with equal fractions of ferrite and austenite, and another with approximately 40% austenite. the samples were heated to a temperature were the desired phase balance was present, followed by quenching in a brine solution (7 wt% nacl). the required annealing temperatures were chosen based on thermocalc® calculations as 1190 °c and 1110 °c for the 40% γ and 50% γ samples, respectively. annealing times were selected to ensure similar grain sizes in both heat treated materials, since grain size influences both the hydrogen behaviour of a material, as well as its mechanical properties. 10 min was selected for the samples annealed at 1190 °c and 30 min was chosen for the samples annealed at 1110 °c. the resulting two heat treated materials will be referred to as ht 1190 and ht 1110 in the following sections. wt% c cr ni mo mn si other uns s32205 0.022 22.850 5.500 3.070 1.810 0.320 cu 0.200, p 0.027, co 0.162, n 0.173, al 0.022 table 1: chemical composition of uns s32205 the heat treated materials were etched with carpenter stainless steel etchant (8.5 g ferric chloride, 2.4 g cupric chloride, 122 ml ethanol, 122 ml hydrochloric acid and 6 ml nitric acid) and investigated using light optical microscopy (keyence vhx-2000), scanning electron microscopy (quanta feg 450, accelerating voltage 20 kv, spot size 5 nm) in combination with energy-dispersive x-ray analysis (edx), and electron backscatter diffraction (ebsd). phase fractions were determined using a feritscope® fmp30. tensile tests were performed on non-notched samples. the sample geometry is given in fig. 1. samples were heat treated in a resistance furnace (nabertherm®) and subsequently ground and polished to remove oxides. both materials were tested in uncharged condition in air, as well as in hydrogen charged condition, to evaluate the impact of hydrogen on the mechanical properties. the hydrogen charged condition consisted of pre-charging for one day followed by in-situ charging during the tensile test. hydrogen charging was done electrochemically in a 0.5 m h2so4 solution containing 1g/l thiourea with an applied constant current density of 0.8 ma/cm2. continuous in-situ hydrogen charging ensured that hydrogen did not t m. cauwels et alii, frattura ed integrità strutturale, 51 (2020) 449-458; doi: 10.3221/igf-esis.51.33 451 diffuse out of the sample during testing. the tests were performed at a constant cross-head displacement speed of 0.6 mm/min, which corresponded to a strain rate of 1·10-3 s-1. fracture surfaces were investigated using sem. tensile tests were also interrupted before fracture (stopped at an elongation where the ultimate tensile strength (uts) was just reached) to study hydrogen-assisted cracking on the sample surfaces. figure 1: geometry of tensile samples results and discussion material characterization ptical microscopy (fig. 2) revealed a strongly oriented microstructure as a result of hot rolling. on the longitudinal section (td plane) elongated austenite ‘rods’ (light coloured phase on fig. 2) were observed parallel with the rolling direction, embedded in a ferrite ‘matrix’ (darker coloured phase on fig. 2). the samples were free of intermetallic sigma phase, which may precipitate during heat treatment of dss [24]. the average grain diameter on the td plane was determined using the linear intercept method until a relative accuracy (%ra) lower than 10 % at a confidence level of 95% was reached. this resulted in 5.18 ± 0.51 μm for ht 1190 and 4.42 ± 0.34 μm for ht 1110. the phase balance in both heat treated samples, determined by ebsd and feritscope® measurements, is given in tab. 2. magnetic measurements (feritscope®) were considered to be more reliable since they analyze a relatively large volume of material compared to ebsd, which is a local 2d technique and might therefore not be representative for the entire sample. the ht 1110 sample had an austenite phase fraction close to the intended 50%, while the ht 1190 sample had an austenite content close to 44%. γ% ht 1190 ht 1110 ebsd 39.20 ± 2.40 46.10 ± 1.09 feritscope® 43.91 ± 1.15 49.83 ± 0.95 table 2: average austenite fraction γ% for the different heat treatments, as determined by ebsd and feritscope®. figure 2: optical microscopy images of the td plane of (a) ht 1190 and (b) ht 1110. o m. cauwels et alii, frattura ed integrità strutturale, 51 (2020) 449-458; doi: 10.3221/igf-esis.51.33 452 hydrogen induced mechanical degradation fig. 3 shows the engineering stress-strain curves for the samples tested in air (full lines) and for those tested in hydrogen charged condition (dotted lines). although some experimental variation can be detected on the mechanical data, trends are still reproducible and valid for further evaluation. a possible explanation for the experimental spread is the microstructural nature of heat treated dss material, while the tested samples were only between 0.600 and 0.700 mm thick, increasing the possibility of having different amounts of austenite at the edges where hydrogen is entering the material. additionally, because of the quenching procedure after the heat treatment, the tensile specimens were geometrically distorted, influencing the reproducibility of the results. nevertheless, the averaged results are still reliable with clear differences between both material conditions. figure 3: stress-strain curves of samples tested in air (full lines) and with in-situ hydrogen charging after 1 day of hydrogen pre-charging (dotted line) for both heat treated materials (ht 1190 and ht 1110) for the tensile tests performed in air, the elongation at fracture increased with an increased austenite phase fraction. this is to be expected since austenite is more ductile compared to ferrite. the ultimate tensile strength of both heat treated materials was similar. hydrogen charging has a clear effect on the tensile behaviour of the material. for both heat treatments, there is an evident loss of ductility, seen in the reduction of the total elongation at fracture. based on the elongation at fracture in air and in hydrogen charged condition, an embrittlement index (ei) was calculated according to the following formula [25]: elongation in air - elongation when charged ei =  elongation in air (1) this resulted in a value of 43.3% for ht 1190 and 36.5% for ht 1110. this is in agreement with other findings in literature since ferrite is considered more susceptible to hydrogen embrittlement than austenite [18,26–28]. moreover, örnek et al. [29] found that dss microstructures with a large austenite spacing were more sensitive to he. the spacing of the austenite ribbons was larger in the ht 1990 sample, both on account of it having a lower austenite fraction and a slightly larger grain size, as mentioned in the previous section and as seen in fig. 2. ht 1190 also had a higher hydrogen content than ht 1110 after one day of hydrogen charging and zakrocymski et al. [26] found that the severity of he in dss increased with higher hydrogen concentrations. additionally, the diffusion of hydrogen was faster in ht 1190 samples which contributed to its higher sensitivity to hydrogen [30]. the decrease in ductility is significant, even though the sample was not saturated with hydrogen after one day of hydrogen pre-charging and thus hydrogen is not present throughout the entire thickness of the specimen. additionally, the yield stress of the material increased in hydrogen charged condition. this effect was more pronounced for ht 1190. the increase of the yield strength after hydrogen charging was also observed in other works, such as in [26, 31] for dss, and in [32, 33] for austenitic stainless steels. the strengthening effect of hydrogen can be attributed m. cauwels et alii, frattura ed integrità strutturale, 51 (2020) 449-458; doi: 10.3221/igf-esis.51.33 453 to a combination of effects. first, the pinning of dislocations by hydrogen, impeding cross-slip and dislocation movement, leading to solid solution strengthening [34]. secondly, barnoush et al. [35] found that when the hydrogen concentration is high enough, the shear modulus of the austenite is reduced locally. dislocation sources such as frank-read sources, that were previously inactive will then generate new dislocations under the high internal stresses inherently present in the dss due to the differing thermal expansion coefficients of ferrite and austenite. the generation of new dislocations increases the dislocation density, which in turn increases the stress required to move dislocations, and thus increases the yield strength. both effects may be increased in the ht 1190 samples compared to the ht 1110 samples due to the higher hydrogen content in those samples. evaluation of the fractography and hydrogen-assisted cracks by sem the fracture surface of both materials tested in air showed dimples. a lot of necking occurred for both samples, resulting in a very thin fracture surface due to the large reduction in area. fig. 4a shows the fracture surface delineated by white lines. the fractured specimens also had a cup-and-cone-like appearance. this, as well as the presence of dimples on the fracture surface indicates a ductile fracture behaviour in air. figure 4: fracture surface for a ht 1190 sample tested (a) in air, (b) and (c) in hydrogen charged condition. (c) shows the depth of the brittle zone (white dotted line) and the direction of hydrogen entry (white arrows). figure 5: sem images of the embrittled zone in sample (a) ht 1190 and (b) ht 1110. arrows indicate examples of river markings. m. cauwels et alii, frattura ed integrità strutturale, 51 (2020) 449-458; doi: 10.3221/igf-esis.51.33 454 in the presence of hydrogen (fig. 4b), the appearance of the fracture surface is clearly different. near the edges of the sample, brittle fracture features were observed. in the centre, still ductile fracture features such as dimples were observed. in between, a transition shear zone was observed. on fig. 4c, the dashed line indicates the size of the brittle zone. this distinct fracture surface is a consequence of hydrogen not being present throughout the entire thickness of the sample after one day of pre-charging, considering the relatively slow diffusion of hydrogen in dss. the side (nd) surfaces of the hydrogen charged samples showed secondary cracks which were not present when specimens were tested in uncharged condition. fig. 5 shows the embrittled zone in detail for both heat treatments. these images show a combination of (quasi-)cleavage and intergranular fracture features. quasi-cleavage is used to refer to features on a fracture surface that exhibits characteristics of both plastic deformation and cleavage. for quasi-cleavage, the fracture surface has the appearance of a cleavage fracture, but is not along a known cleavage plane [36, 37]. this is an often observed feature for fracture of ferrous alloys which are susceptible to he [38]. quasi cleavage is often characterised by fine lines that follow the crack propagation direction called ‘river markings’ (fig. 5a). a smaller part of the brittle features for both heat treated samples was intergranular. there was some indication that intergranular fracture was more common for the ht 1110 sample than the ht 1190 sample. after one day of hydrogen pre-charging, the samples are not saturated with hydrogen. the depth of the area affected by hydrogen was measured on several sem images and averaged out resulting in a depth of embrittlement of 66.78 ± 1.8 μm for ht 1190 and 56.43 ± 0.8 μm for ht 1110. the hydrogen concentration ch throughout the sample can be modelled by solving fick’s second law for uniaxial diffusion in a thin plate [23]. a qualitative representation of the hydrogen profiles in ht 1190 and ht 1110 tensile samples with a thickness of 0.650 mm after one day of hydrogen charging is given in fig. 6. as ht 1190 has a higher ferrite fraction, hydrogen can diffuse further into the material due to a higher average diffusion coefficient [39]. the average diffusion coefficient of hydrogen in dss depends on austenite fraction, as well as the shape, size and spacing of the austenite and its orientation in relation to the direction of hydrogen entry into the material. the lower austenite fraction and larger grain size of the ht 1190 sample contribute to a less tortuous path for hydrogen diffusion and less opportunity for hydrogen to get trapped at the α/γ interface. the diffusion coefficients used for this calculation were 1.14·10-14 m2·s-1 for ht 1190 and 3.37·10-15 m2·s-1 for ht 1110 these coefficients were determined by fitting fick’s diffusion law to a saturation curve for each respective material following the procedure established by claeys et al. in [40]. also based on fick’s diffusion law, the distance x hydrogen can theoretically diffuse into the material in a given time t is given by the formula: x =  dt (2) fick’s laws for diffusion, however, assume a homogeneous microstructure, which is certainly not the case for dss. application of eqn. (2) using the experimentally determined diffusion coefficients mentioned above, results in 31.4 μm and 17.07 μm for ht 1190 and ht 1110, respectively. this is a considerable underestimation of the diffusion depth compared to the values measured on sem images. in dss, hydrogen will not be distributed uniformly over austenite and ferrite. since the diffusion coefficient of hydrogen in ferrite is much larger than the one in austenite, hydrogen will diffuse deeper into the material following ferrite ‘paths’, where diffusion is faster than the overall, effective diffusion speed, while diffusion in austenite contributes little to the overall hydrogen transport [39] figure 6: simulated normalised hydrogen concentration profile through the thickness of a tensile sample after one day of hydrogen charging for ht 1190 and ht 1110 m. cauwels et alii, frattura ed integrità strutturale, 51 (2020) 449-458; doi: 10.3221/igf-esis.51.33 455 secondary cracks on the nd surface were further examined on tensile samples that were stopped at an intermediate elongation at which ultimate tensile strength was just reached. these cracks were primarily transgranular. crack growth is reported to occur preferentially in ferrite [17, 18] and zheng and hardie [41] report that austenite acts as an obstacle to crack propagation since it is both more ductile and less susceptible to he. for both ht 1190 and ht 1110, cracks across the austenite-ferrite interface were often present (fig. 7a) as well as cracks that were seemingly unconnected to any ferrite grains (fig. 7b). oltra et al. [42] proposed a mechanism for hydrogen cracks in the austenitic phase of a dss that cross a phase boundary. cracking starts with brittle cleavage in ferrite, which induces a micro-crack in the adjacent austenite grain when it reaches the α/γ boundary. this allows a supply of hydrogen from the ferrite to the austenite at the crack tip, and particularly along slip planes. local hydrogen accumulation increases dislocation mobility, as per the help mechanism, leading to pile-ups ahead of the enhanced plasticity zone [43]. at a critical stress, a new crack is formed at the pile-up and the hydrogen crack can begin to propagate from the initial micro-crack. the sequence can then start again at the new crack, and this process can be expected to lead to regular changes in crack plane. the crack in fig. 7c, and some of the cracks in fig. 7b are examples of cracks that most likely propagated via this proposed mechanism. claeys [44] also noted that when charging in h2so4, probably there is sufficient hydrogen accumulation in austenite to initiate cracks as an alternative starting point for this mechanism in dss, and cleavage in ferrite is not strictly necessary. ‘zigzag’ cracks were also observed in austenite. an example of such a crack in an austenite grain in ht 1190 is indicated on fig. 8a with a white arrow. the shape of this crack can be a consequence of the micro-cracks alternating different slip planes while it propagates [42]. alternatively, koyama et al. [45] described hydrogen-assisted cracks in an austenitic steel occurring along primary and secondary twins also resulting in a zigzag pattern. finally, fig. 8b shows cracking around inclusions. the inclusions were identified as alumina by edx, which can originate from the desoxidation step in the steel production process, when al is added. laureys et al. [46] found that hydrogen-induced crack initiation was linked to alumina particles in ultra-low carbon steel, and a mechanism for this phenomenon was proposed by tiegel et al. [47]: as hydrogen accumulates at incoherent particle interfaces leading to interface debonding and vacancy stabilisation, leading to crack initiation. figure 7: secondary cracks on the nd surface of a ht 1110 tensile sample figure 8: secondary cracks on the nd surface of tensile samples: (a) zigzag crack (indicated by the white arrow) in an austenite grain in ht 1190 (b) hydrogen cracks around alumina inclusions in ht 1110 m. cauwels et alii, frattura ed integrità strutturale, 51 (2020) 449-458; doi: 10.3221/igf-esis.51.33 456 conclusion he influence of austenite phase fraction on the hydrogen sensitivity of duplex stainless steel was investigated in this work. heat treatments were performed to create dss with an austenite fraction of 50% and 44%. tensile tests in uncharged and hydrogen-charged condition were performed on these materials, based on which the following conclusions can be made: both heat treated samples suffered a considerable loss in ductility after hydrogen charging. for the sample with a 50% γ fraction, the elongation at fracture was reduced by 36.5%. for the specimens with 44% γ this was 43.3%. loss of ductility, as quantified by the embrittlement index, was larger for the sample with a higher ferrite content. the sample had a higher hydrogen content and a higher hydrogen diffusion coefficient, contributing to its increased sensitivity. fracture surfaces of specimens tested under the presence of hydrogen showed brittle fracture features on the edges. the depth of the zone with brittle features was related to the diffusion speed of hydrogen. the hydrogen distribution after one day of hydrogen pre-charging, simulated using the thin-plate solutions of fick’s second law, showed that hydrogen was not present throughout the thickness of the sample. the sample with 44% γ, which had a higher overall diffusion coefficient for hydrogen, had a larger embrittled zone since hydrogen could diffuse over a greater distance in the given pre-charging time. secondary cracking as hydrogen-assisted cracking was observed on the side surfaces of specimens tested with hydrogen and appeared to be primarily transgranular. tensile specimens tested in air did not show this secondary cracking. acknowledgements he authors acknowledge support from fwo (sb phd fellow via grant 1s16618n) for l. claeys, while t. depover holds a senior postdoctoral fellowship of the research foundation flanders (fwo) via grant 12zo420n. the authors also wish to thank the special research fund (bof), ugent (grant bof15/bas/062 and bof01p03516) and the research foundation flanders (fwo) via grant 3g056519. references [1] azevedo, c.r. de f., pereira, h.b., wolynec, s., padilha, a.f. (2019). an overview of the recurrent failures of duplex stainless steels, eng. fail. anal., 97, pp. 161–188, doi: 10.1016/j.engfailanal.2018.12.009. [2] johnsen, r. (2017).hydrogen induced stress cracking of stainless steel in seawater what do we know and what is still unknown? the annual congress of the european federation of corrosion, 20th international corrosion congress and process safety congress 2017, prague, czech republic. [3] popov, b.n., lee, j.w., djukic, m.b. (2018).hydrogen permeation and hydrogen-induced cracking. handbook of environmental degradation of materials third edition, elsevier inc., pp. 133–62. [4] francis, r., byrne, g., warburton, g.r. (1997). effects of cathodic protection on duplex stainless steels in seawater, corrosion, 53(3), pp. 234–240, doi: 10.5006/1.3280465. [5] campbell, h.s., francis, r. (1995). simulated service test for hydrogen embrittlement of cathodically protected subsea bolting materials, br. corros. j., 30(2), pp. 154–160, doi: 10.1179/000705995798114087. [6] depover, t., laureys, a., pérez escobar, d., van den eeckhout, e., wallaert, e., verbeken, k. (2018). understanding the interaction between a steel microstructure and hydrogen, materials (basel)., 11(5), pp. 698, doi: 10.3390/ma11050698. [7] robertson, i.m., sofronis, p., nagao, a., martin, m.l., wang, s., gross, d.w., nygren, k.e. (2015). hydrogen embrittlement understood, metall. mater. trans. a, 46(6), pp. 2323–2341, doi: 10.1007/s11661-015-2836-1. [8] djukic, m.b., bakic, g.m., sijacki zeravcic, v., sedmak, a., rajicic, b. (2019). the synergistic action and interplay of hydrogen embrittlement mechanisms in steels and iron: localized plasticity and decohesion, eng. fract. mech., 216, pp. 106528, doi: 10.1016/j.engfracmech.2019.106528. [9] zapffe, c.a., sims, c.e. (1941). hydrogen embrittlement, internal stress and defects in steels, trans. am. inst. min. metall. eng., 145, pp. 1–37. [10] troiano, a.r. (2016). the role of hydrogen and other interstitials in the mechanical behavior of metals (1959 edward t t m. cauwels et alii, frattura ed integrità strutturale, 51 (2020) 449-458; doi: 10.3221/igf-esis.51.33 457 de mille campbell memorial lecture), metallogr. microstruct. anal., 5(6), pp. 557–569, doi: 10.1007/s13632-016-0319-4. [11] oriani, r.a., josephic, p.h. (1974). equilibrium aspects of hydrogen-induced cracking of steels, acta metall., 22(9), pp. 1065–1074, doi: 10.1016/0001-6160(74)90061-3. [12] birnbaum, h.k., sofronis, p. (1994). hydrogen-enhanced localized plasticity a mechanism for hydrogen-related fracture, mater. sci. eng. a, 176, pp. 191–202. [13] beachem, c.d. (1972). a new model for hydrogen-assisted cracking ( hydrogen " embrittlement "), metall. trans., 3(february), pp. 437–451. [14] depover, t., verbeken, k. (2018). the detrimental effect of hydrogen at dislocations on the hydrogen embrittlement susceptibility of fe-c-x alloys: an experimental proof of the help mechanism, int. j. hydrogen energy, 43(5), pp. 3050–61, doi: 10.1016/j.ijhydene.2017.12.109. [15] nagumo, m. (2004). hydrogen related failure of steels a new aspect, mater. sci. technol., 20(8), pp. 940–950, doi: 10.1179/026708304225019687. [16] ortiz, m., cuitiño, a.m. (1996). ductile fracture by vacancy condensation in fcc. single crystals, acta mater., 44(2), pp. 427–436. [17] tsai, s.t., yen, k.p., shih, h.c. (1998). the embrittlement of duplex stainless steel in sulfide-containing 3.5 wt% nacl solution, corros. sci., 40(2–3), pp. 281–295, doi: 10.1016/s0010-938x(97)00135-2. [18] chou, s.l., tsai, w.t. (1999). hydrogen embrittlement of duplex stainless steel in concentrated sodium chloride solution, mater. chem. phys., 60(2), pp. 137–142, doi: 10.1016/s0254-0584(99)00077-2. [19] zucchi, f., grassi, v., monticelli, c., trabanelli, g. (2006). hydrogen embrittlement of duplex stainless steel under cathodic protection in acidic artificial sea water in the presence of sulphide ions, corros. sci., 48(2), pp. 522–530, doi: 10.1016/j.corsci.2005.01.004. [20] luo, h., dong, c.f., liu, z.y., maha, m.t.j., li, x.g. (2013). characterization of hydrogen charging of 2205 duplex stainless steel and its correlation with hydrogen-induced cracking, mater. corros., 64(1), pp. 26–33, doi: 10.1002/maco.201106146. [21] vaňová, p., sojka, j. (2014). hydrogen embrittlement of duplex steel tested using slow strain rate test, metalurgija, 53(2), pp. 163–136. [22] da silva, b.r.s., salvio, f., santos, d.s. (2012).hydrogen embrittlement of super duplex stainless steel tube uns s32750 under mechanical stress., pp. 245–253. [23] olden, v., thaulow, c., johnsen, r. (2008). modelling of hydrogen diffusion and hydrogen induced cracking in supermartensitic and duplex stainless steels, mater. des., 29(10), pp. 1934–1948, doi: 10.1016/j.matdes.2008.04.026. [24] pohl, m., storz, o. (2004). sigma-phase in duplex-stainless steels, zeitschrift für met., 95(7), pp. 631–638. [25] depover, t., escobar, d.m.p., wallaert, e., zermout, z., verbeken, k. (2014). effect of hydrogen charging on the mechanical properties of advanced high strength steels, int. j. hydrogen energy, 39(9), pp. 4647–4656, doi: 10.1016/j.ijhydene.2013.12.190. [26] zakroczymski, t., glowacka, a., swiatnicki, w. (2005). effect of hydrogen concentration on the embrittlement of a duplex stainless steel, corros. sci., 47(6), pp. 1403–1414, doi: 10.1016/j.corsci.2004.07.036. [27] chou, s.l., tsai, w.t. (1999). effect of grain size on the hydrogen-assisted cracking in duplex stainless steels, mater. sci. eng. a, 270(2), pp. 219–224, doi: 10.1016/s0921-5093(99)00174-4. [28] luu, w.c., liu, p.w., wu, j.k. (2002). hydrogen transport and degradation of a commercial duplex stainless steel, corros. sci., 44(8), pp. 1783–1791, doi: 10.1016/s0010-938x(01)00143-3. [29] örnek, c., reccagni, p., kivisäkk, u., bettini, e., engelberg, d.l., pan, j. (2018). hydrogen embrittlement of super duplex stainless steel – towards understanding the effects of microstructure and strain, int. j. hydrogen energy, 43(27), pp. 12543–12555, doi: 10.1016/j.ijhydene.2018.05.028. [30] depover, t., wallaert, e., verbeken, k. (2016). on the synergy of diffusible hydrogen content and hydrogen diffusivity in the mechanical degradation of laboratory cast fe-c alloys, mater. sci. eng. a, 664, pp. 195–205, doi: 10.1016/j.msea.2016.03.107. [31] claeys, l., depover, t., de graeve, i., verbeken, k. (2019). first observation by ebsd of martensitic transformations due to hydrogen presence during straining of duplex stainless steel, mater. charact., 156, pp. 109843, doi: 10.1016/j.matchar.2019.109843. [32] abraham, d.p., altstetter, c.j. (1995). the effect of hydrogen on the yield and flow stress of an austenitic stainless steel, metall. mater. trans. a, 26(11), pp. 2849–2858, doi: 10.1007/bf02669643. [33] takakuwa, o., mano, y., soyama, h. (2014). increase in the local yield stress near surface of austenitic stainless steel due to invasion by hydrogen, int. j. hydrogen energy, 39(11), pp. 6095–6103, doi: 10.1016/j.ijhydene.2014.01.190. m. cauwels et alii, frattura ed integrità strutturale, 51 (2020) 449-458; doi: 10.3221/igf-esis.51.33 458 [34] kheradmand, n., johnsen, r., olsen, j.s., barnoush, a. (2016). effect of hydrogen on the hardness of different phases in super duplex stainless steel, int. j. hydrogen energy, 41(1), pp. 704–712, doi: 10.1016/j.ijhydene.2015.10.106. [35] barnoush, a., zamanzade, m., vehoff, h. (2010). direct observation of hydrogen-enhanced plasticity in super duplex stainless steel by means of in situ electrochemical methods, scr. mater., 62(5), pp. 242–245, doi: 10.1016/j.scriptamat.2009.11.007. [36] martin, m.l., fenske, j.a., liu, g.s., sofronis, p., robertson, i.m. (2011). on the formation and nature of quasicleavage fracture surfaces in hydrogen embrittled steels, acta mater., 59(4), pp. 1601–6, doi: 10.1016/j.actamat.2010.11.024. [37] kerlins, v. (1998).modes of fracture. asm handbook volume 12: fractography, asm international, p. 857. [38] lynch, s.p. (1984). a fractographic study of gaseous hydrogen embrittlement and liquid-metal embrittlement in a tempered-martensitic steel, acta metall., 32(1), pp. 79–90, doi: 10.1016/0001-6160(84)90204-9. [39] turnbull, a., hutchings, r.b. (1994). analysis of hydrogen atom transport in a two-phase alloy, mater. sci. eng. a, 177(1–2), pp. 161–171, doi: 10.1016/0921-5093(94)90488-x. [40] claeys, l., depover, t., de graeve, i., verbeken, k. (2019). electrochemical hydrogen charging of duplex stainless steel, corrosion, 75(8), pp. 880–887, doi: 10.5006/2959. [41] zheng, w., hardie, d. (1991). effect of structural orientation on the susceptibility of commercial duplex stainless steels to hydrogen embrittlement, corrosion, 47(10), pp. 792–799, doi: 10.5006/1.3585190. [42] oltra, r., bouillot, c., magnin, t. (1996). localized hydrogen cracking in the austenitic phase of a duplex stainless steel, scr. mater., 35(9), pp. 1101–1105, doi: 10.1016/1359-6462(96)00293-x. [43] magnin, t., chambreuil, a., bayle, b. (1996). the corrosion-enhanced plasticity model for stress corrosion cracking in ductile fcc alloys, acta mater., 44(4), pp. 1457–1470, doi: 10.1016/1359-6454(95)00301-0. [44] claeys, l., depover, t., de graeve, i., verbeken, k. (2019). hydrogen-assisted cracking in 2205 duplex stainless steel: initiation, propagation and interaction with deformation-induced martensite, mater. sci. eng. a, under review. [45] koyama, m., akiyama, e., sawaguchi, t., raabe, d., tsuzaki, k. (2012). hydrogen-induced cracking at grain and twin boundaries in an fe-mn-c austenitic steel, scr. mater., 66(7), pp. 459–462, doi: 10.1016/j.scriptamat.2011.12.015. [46] laureys, a., van den eeckhout, e., petrov, r., verbeken, k. (2017). effect of deformation and charging conditions on crack and blister formation during electrochemical hydrogen charging, acta mater., 127, pp. 192–202, doi: 10.1016/j.actamat.2017.01.013. [47] tiegel, m.c., martin, m.l., lehmberg, a.k., deutges, m., borchers, c., kirchheim, r. 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/hrv (za stvaranje adobe pdf dokumenata najpogodnijih za visokokvalitetni ispis prije tiskanja koristite ove postavke. stvoreni pdf dokumenti mogu se otvoriti acrobat i adobe reader 5.0 i kasnijim verzijama.) /hun 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/pdfxoutputintentprofileselector /documentcmyk /preserveediting true /untaggedcmykhandling /leaveuntagged /untaggedrgbhandling /usedocumentprofile /usedocumentbleed false >> ] >> setdistillerparams << /hwresolution [2400 2400] /pagesize [612.000 792.000] >> setpagedevice microsoft word numero_49_art_18_2465 m. semin et alii, frattura ed integrità strutturale, 49 (2019) 167-176; doi: 10.3221/igf-esis.49.18 167 focused on russian mechanics contributions for structural integrity numerical simulation of frozen wall formation in water-saturated rock mass by solving the darcy-stefan problem mikhail semin, lev levin mining institute of the ural branch of the russian academy of sciences seminma@outlook.com, https://orcid.org/0000-0001-5200-7931 aerolog_lev@mail.ru, http://orcid.org/0000-0003-0767-9207 abstract. artificial ground freezing (agf) is a common technology of shaft sinking through water-bearing strata. the agf technique is used to create a frozen wall preventing shaft flooding. an additional factor that makes shaft sinking more complicated is associated with external groundwater flows occurred due to hydrostatic pressure gradients. in this paper, we study the influence of groundwater seepage on the frozen wall formation in fluidsaturated rock mass in the framework of the two-dimensional two-phase darcy-stefan problem. the results of numerical simulation of the thermal and hydraulic properties of the sandstone layer at the site of petrikov mining and processing plant are presented. it has been found that the external groundwater flow has a significant effect on the growth of a frozen wall in the case when the groundwater velocity magnitude is greater than or equal to 50 mm/day. this critical seepage velocity strongly depends on how quickly the water content and rock mass permeability decrease with decreasing temperature, or on the parameters of the rock mass freezing characteristic curve and permeability versus temperature curve. the proper setting of these parameters is a sine qua non for creating adequate mathematical models of heat and mass processes in the artificially frozen water-saturated rock mass. keywords. frozen wall, numerical simulation; darcy-stefan problem; mine shaft; artificial ground freezing. citation: semin, m., levin, l.., numerical simulation of frozen wall formation in watersaturated rock mass by solving the darcystefan problem, frattura ed integrità strutturale, 49 (2019) 167-176. received: 08.04.2019 accepted: 21.05.2019 published: xx.yy.zzzz copyright: © 2019 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. introduction haft sinking through water-bearing strata requires special methods to prevent the flow of water in the excavation. artificial ground freezing (agf) is the most widely used and highly efficient method of ground water control. the ground freezing process involves drilling and installing a series of relatively closely spaced pipes around the future shaft and circulating a coolant through these pipes (see fig. 1). this method is used when other conventional methods such as dewatering, shoring and grouting are not feasible [1]. s http://www.gruppofrattura.it/va/49/2465.mp4 m. semin et alii, frattura ed integrità strutturale, 49 (2019) 167-176; doi: 10.3221/igf-esis.49.18 168 freezing continues until a frozen cylinder of sufficient strength to withstand the hydrostatic pressure is formed. the frozen cylinder is also known as the frozen wall or the ice wall [2, 3]. when the required thickness of the frozen wall is reached, the procedure of shaft sinking begins. figure 1: circular contour of freezing pipes and formation of the frozen wall. the time at which the frozen wall reaches the required thickness can be determined by both experimental monitoring [4, 5] and mathematical modeling [6, 7]. due to the high velocity of groundwater in a porous rock mass, the correct mathematical prediction of the temperature field in the water-saturated rock mass is possible only in the framework of a coupled thermohydraulic problem, also known as a darcy-stefan problem [8 – 10]. literature review shows that there are many works devoted to the darcy-stefan problem, in which the freezing and thawing processes arising in soils and rocks in various natural and technical systems are studied. in [11, 12], the heat and mass transfer processes in partially frozen porous media are considered in relation to permafrost thaw. numerical analysis of heat and mass transfer in artificially frozen rocks during the construction of tunnels and mine shafts was carried out in [10, 13 – 15]. in [13], the authors investigated the influence of coolant temperature, freeze pipe spacing and seepage temperature on the closure time and shape of the frozen wall. in [10], a thermo-hydraulic model of fluid-saturated rock mass was used to analyze how the heterogeneity of rock mass properties affects the formation of a frozen wall. in (15], a coupled thermo-hydromechanical mathematical model is proposed for studying the frozen wall formation during tunnel excavation. in [14], the unsteady salinity distribution near the phase transition zone was considered. the seepage of groundwater is often neglected in the calculation of temperature fields in artificially frozen rocks and soils [6, 16 – 18]. the reason is that the effect of groundwater seepage is negligible in most practical cases when the content of groundwater is low, or the groundwater is stagnant. there is nevertheless a need to determine the right conditions for simulation of the frozen wall formation without consideration of groundwater seepage, and it is the purpose of this paper to find such conditions. to this end, we have formulated a two-dimensional two-phase darcy-stefan problem for the horizontal layer of water-saturated rock mass and developed an algorithm for a numerical solution of the stated problem of artificial ground freezing using the finite difference method. mathematical model he problem of artificial freezing of the water-saturated rock mass is considered. it is assumed that the physical processes occurred in the rock mass and having a strong impact on temperature distribution are as follows:  groundwater seepage;  diffusion and convection heat transport; t m. semin et alii, frattura ed integrità strutturale, 49 (2019) 167-176; doi: 10.3221/igf-esis.49.18 169  phase transition of groundwater from liquid to solid state;  heat exchange between the rock mass and the coolant circulating through freezing pipes. we make the following assumptions in order to develop the model: 1. the rock mass is isotropic and fully water saturated. 2. the initial temperature field in the rock mass is homogeneous. 3. heat and mass transfer in the vertical direction is negligible compared to that in the horizontal direction. 4. filtration of groundwater occurs under the action of a horizontal pressure gradient. 5. ground water and ice are incompressible. 6. freezing pipes have deviations from the vertical position due to the error in determining the direction of drilling. it should be noted that the validity of the second assumption was verified by analyzing the conditions at the site of petrikov deposit of potash salt in belarus. the 3d numerical simulations of the frozen wall formation have shown that this assumption is valid when the simulation time of artificial freezing is less than 200 days and the thickness of the considered rock mass layer is more than 5 m [19]. the assumptions listed above make it possible to reduce the dimensions to 2d for the horizontal layer of the rock mass. the computational domain of this problem is shown in fig. 2. the equations of mass and energy balance in the horizontal layer of the rock mass can be written as                  1 0 il l l w nwn t t v (1)   tot l l h h w t t         v (2) where l is the groundwater density, kg/m3; w is the unfrozen water content; n is the porosity; i is the ice density, kg/m3; lv is the vector of groundwater velocity, m/s; toth is the total specific enthalpy of the water-saturated rock mass (including water and ice in pores), j/(kg°c); lh is the specific enthalpy of the groundwater, j/(kg°c);  is the thermal conductivity of water-saturated rock mass, w/(m°с); t is the temperature of water-saturated rock mass, °с; t is time, s. figure 2: two-dimensional geometric model of the water-saturated rock mass: 1 – frozen zone, 2 – unfrozen zone. the thermal conductivity of the water-saturated rock mass depends on the unfrozen water content according to the following law:    1 2 1w w w     (3) m. semin et alii, frattura ed integrità strutturale, 49 (2019) 167-176; doi: 10.3221/igf-esis.49.18 170 where 1 is the thermal conductivity of the frozen rock mass, w/(m°с); 2 is the thermal conductivity of the unfrozen rock mass, w/(m°с). the groundwater velocity is calculated from the darcy’s law: r l l l k k p     v (4) where rk is the water relative permeability; k is the absolute permeability of rock mass, m2; l is the dynamic viscosity of groundwater, pas; lp is the hydrostatic pressure in the pore space, pa. the dependence of the total specific enthalpy toth on the temperature t of the water-saturated rock mass is expressed by the formula: 2 2 1 1 ( ) , ( ) ( ) ( ) , sc l sc tot sс l sc c t t nl t t h t c t t nw t l t t             (5) where 1 is the density of the frozen rock mass, kg/m3; 2 is the density of the unfrozen rock mass, kg/m3; 1c is the specific heat capacity of the frozen rock mass, j/(kg°c); 2c is the specific heat capacity of the unfrozen rock mass, j/(kg°c); l is the specific heat of groundwater phase transition, j/kg; sct is the temperature when the groundwater freezing begins, °c. the specific enthalpy lh can be represented as the function of temperature t : ( ) , ( ) ( ) , l l sc l sc l l sc c n t t nl t t h t nw t l t t          (6) as follows from (6), when the unfrozen water content w is equal to zero, the specific enthalpy lh of water in the pores is also assumed to be zero, since there is no unfrozen water in the pores at such temperatures. the dependence of the unfrozen groundwater content w on the temperature t (or the soil freezing characteristic curve) can be written in the form:   1, ( ) exp , sc scsc t t w t t tb t t         (7) where b is the empirical parameter, which characterizes the reduction of the water content with decreasing temperature. it is assumed that the relative permeability of the water in pores is a temperature-dependent parameter. hence we can write   1, ( ) exp , sc r scsc t t k t t tm t t         (8) where m is the empirical parameter, which characterizes the reduction of the water relative permeability with decreasing temperature. the problem (1) — (8) is supplemented with boundary and initial conditions: 0 out t t   (9)    ( ) 0 fr fr t t t t t n          (10) m. semin et alii, frattura ed integrità strutturale, 49 (2019) 167-176; doi: 10.3221/igf-esis.49.18 171 0 out l  v v (11) 00t t t   (12) 00l t  v v (13) where 0 sct t is the initial temperature of water-saturated rock mass, °с; 0v is the initial value of groundwater velocity vector, m/s; is the heat exchange coefficient between the rock mass and the coolant in the freezing pipe, w/(m2°с); ( )frt t is the temperature of coolant, °с; out is the outer boundary of the domain; fr is the boundary of the freezing pipes. numerical simulation numerical simulation of the problem (1) — (13) was undertaken using the finite difference method. an explicit scheme with first-order accuracy in time and second-order accuracy in space was applied. for the discretization of the system of eqns. (1) — (13), we used a non-uniform rectangular grid. the grid sizes at the outer boundary out and at the boundary fr of the freezing pipes were selected by performing preliminary calculations to determine the temperature distribution independent of the grid parameters. at the boundary fr , the heat flow was calculated using the effective heat exchange area effs , which is formed by the faces of the cells intersecting with the freezing pipe circle (see fig. 3). the inequality of the physical and effective heat exchange areas is cancelled out by means of a reduction factor r , which is equal to the ratio of the physical and effective heat exchange areas. figure 3: discretization of the domain (a) and grid refinement near freezing pipe (b). the finite difference scheme is implemented in c # programming language. the calculation was carried out for the conditions at the site of petrikov mining and processing plant. the sandstone layer at the depth interval 136-146 m was considered. the necessary input data for numerical calculation is given in tab. 1. the deviation of the position of a freezing pipe with increasing depth was obtained from the inclinometry data at the site. the maximum deviation of the freezing pipes at a depth of 146 m from the design position is 1.85 m, whereas the minimum deviation is 0.7 m (see fig. 2). the diagram given in fig.4 shows the coolant temperature as a function of time. a m. semin et alii, frattura ed integrità strutturale, 49 (2019) 167-176; doi: 10.3221/igf-esis.49.18 172 parameter value thermal conductivity of the frozen rock mass, w/(m°с) 3.84 thermal conductivity of the unfrozen rock mass, w/(m°с) 2.37 specific heat capacity of the frozen rock mass, j/(kg°c) 1223 specific heat capacity of the unfrozen rock mass, j/(kg°c) 1958 density of the frozen and unfrozen rock mass, kg/m3 2580 porosity 0.35 density of the groundwater, kg/m3 998 specific heat capacity of the groundwater, j/(kg°c) 4200 specific heat of groundwater phase transition, j/kg 333000 absolute permeability of rock mass, m2 6.510-12 groundwater density, kg/m3 998 temperature when freezing begins, °с 0 initial temperature of rock mass, °с 10 heat exchange coefficient between the rock mass and the coolant in the freezing pipe, w/(m2°с) 25 number of freezing pipes 41 freezing pipe radius, m 0.073 freezing contour radius, m 8.2 domain width (length), m 35 coefficient м 0.33 coefficient b 1.8 table 1: input data for numerical calculation. figure 4: coolant temperature vs time m. semin et alii, frattura ed integrità strutturale, 49 (2019) 167-176; doi: 10.3221/igf-esis.49.18 173 the results of the numerical solution of the darcy-stefan problem are presented in fig. 5 – 7. temperature distributions are shown in fig. 5. fig. 6 demonstrates the distribution of the relative velocity after 60 days of freezing. different values of the external seepage velocity are considered. the relative velocity is the ratio of the seepage velocity magnitude to the constant external seepage velocity magnitude:     0 , , t v t  v r r v (14) where r is the radius vector of the point, m; t is time, s. it is seen that the relative seepage velocity is equal to 1 at the outer boundary. the groundwater flow has a significant impact on the formation of the frozen wall when the external seepage velocity is greater than or equal to 50 mm/day. in this sense, 50 mm / day is the critical seepage velocity for the considered thermal properties of the rock mass. the significant impact means that the time of closed-loop frozen wall formation (or frozen wall closure time) changes by more than 5% due to the presence of groundwater seepage. qualitatively, this fact corresponds to the results obtained by the authors of the study [19] for the rock mass layer with similar thermal properties. the quantitative analysis shows that the results obtained in [19] give the critical seepage velocity 1.5 — 2 times lower than that obtained in our calculations. this is due to the fact that another function ( )rk t was used in this study (heaviside step function). figure 5: temperature distribution in the horizontal layer of the rock mass after 60 days of freezing for different external seepage velocities: (a) – 10 mm / day, (b) – 50 mm / day, (c) – 100 mm / day, (g) – 150 mm / day m. semin et alii, frattura ed integrità strutturale, 49 (2019) 167-176; doi: 10.3221/igf-esis.49.18 174 figure 6: relative velocity distribution in the horizontal layer of the rock mass after 60 days of freezing for different external seepage velocities: (a) – 10 mm / day, (b) – 50 mm / day, (c) – 100 mm / day, (g) – 150 mm / day figure 7: frozen wall closure time as a function of the m and b parameters m. semin et alii, frattura ed integrità strutturale, 49 (2019) 167-176; doi: 10.3221/igf-esis.49.18 175 the performed numerical simulation showed that the critical seepage velocity strongly depends on the empirical parameters m and b in formulas (7) — (8). fig. 7 shows the frozen wall closure time as a function of the parameters m and b. these results were determined for the external seepage velocity 150 mm/day. the closure of the frozen wall is assumed to occur when the water relative permeability value becomes equal or less than 0.02. as shown in fig. 7, the dependence of the frozen wall closure time on the parameter m has a pronounced hyperbolic character. in the interval 0.2 0.3m  , all three curves in the graph have asymptotes. this means that, for sufficiently low values of m, the closure of the frozen wall does not occur. when the parameter m increases from 0.3 to 2.0, the closure time decreases more than fourfold. for large values of m, when the water relative permeability falls to zero almost immediately after the temperature reaches the value sct , the effect of parameter b on the frozen wall closure time is minimal. conclusions n this paper, the two-dimensional two-phase darcy-stefan problem is formulated and applied to the problem of frozen wall growth simulation in the presence of external groundwater flow. a numerical algorithm for solving this problem is described. the results of a multiparameter numerical simulation of the frozen wall formation obtained in the study of the thermal and hydraulic properties of the sandstone layer at the site of petrikov mining and processing plant are presented. it was found that the external groundwater flow has a significant effect on the frozen wall growth when its velocity magnitude is greater than or equal to 50 mm/day. this critical seepage velocity depends on the thermal and hydraulic properties of the layer. specifically, it strongly depends on how quickly the water content and rock mass permeability decrease with decreasing temperature, or on the parameters of the rock mass freezing characteristic curve and permeability versus temperature curve. therefore, the development of an adequate mathematical model of heat and mass transfer in the artificially frozen water-saturated rock mass requires effective identification of these parameters on the basis of the laboratory test results. acknowledgements his work was supported by the russian science foundation (project 17-11-01204). references [1] sopko, j. (2017). coupled heat transfer and groundwater flow models for ground freezing design and analysis in construction, geotechnical frontiers, 11 p. doi: 10.1061/9780784480472.076. [2] levin, l.y., semin, m.a., parshakov, o.s. (2017). mathematical prediction of frozen wall thickness in shaft sinking, j. min. sci, 53(5), pp. 938–944. doi: 10.1134/s1062739117052970. [3] schmall, p. c., maishman, d. (2007). ground freezing a proven technology in mine shaft sinking, tunnels and underground construction magazine, 59 (6), pp. 25–30. [4] pimentel, e., papakonstantinou, s., anagnostou, g. (2012). numerical interpretation of temperature distributions from three ground freezing applications in urban tunneling, tunn. undergr. sp. tech., 28(1), pp. 57–69. doi: 10.1016/j.tust.2011.09.005. [5] hentrich, n., franz, j. (2015). about the application of conventional and advanced freeze circle design methods for the ust-jaiwa freeze shaft project. vertical and decline shaft sinking: good practices in technique and technology, international mining forum, pp. 89–104. [6] kim, y.s., kang, j.-m., lee, j., hong, s.-s., kim, k.-j. (2012). finite element modeling and analysis for artificial ground freezing in egress shafts, ksce j. civ. eng., 16(6), pp. 925–932. doi: 10.1007/s12205-012-1252-y. [7] khokholov, y.a., kurilko, a.s., solov’ev, d.e. (2016). temperature field analysis in salty rocks at shaft mouth under operation of a freezing system., j. min. sci., 52(3), pp. 593-600. doi: 10.1134/s1062739116030862. [8] rodrigues, j.f., urbano, j.m. (1999). on a darcy-stefan problem arising in freezing and thawing of saturated porous media, continuum mech. therm., 11(3), pp. 181-191. doi: 10.1007/s001610050110. i t m. semin et alii, frattura ed integrità strutturale, 49 (2019) 167-176; doi: 10.3221/igf-esis.49.18 176 [9] sazhenkov, s.a. (2008). studying the darcy-stefan problem on phase transition in a saturated porous soil, j. appl. mech. tech. phys, 49(4), pp. 587-597. doi: 10.1007/s10808-008-0076-5. [10] vitel, m., rouabhi, a., tijani, m., guérin, f. (2016). thermo-hydraulic modeling of artificial ground freezing: application to an underground mine in fractured sandstone, comput. geotech., 75, pp. 80–92. doi: 10.1016/j.compgeo.2016.01.024. [11] frampton, a., painter, s., lyon, s.w., destouni, g. (2011). non-isothermal, three-phase simulations of near-surface flows in a model permafrost system under seasonal variability and climate change, j. hydrol., 403(3-4), pp. 352–359. doi: 10.1016/j.jhydrol.2011.04.010 [12] kurylyk, b.l., macquarrie, k.t.b., mckenzie, j.m. (2014). climate change impacts on groundwater and soil temperatures in cold and temperate regions: implications, mathematical theory, and emerging simulation tools, earth science rev., 138, pp. 313-334. doi: 10.1016/j.earscirev.2014.06.006 [13] alzoubi, m.a., madiseh, a., hassani, f.p. (2019). heat transfer analysis in artificial ground freezing under high seepage: validation and heatlines visualization, int. j. therm. sci., 139, pp. 232–245. doi: 10.1016/j.ijthermalsci.2019.02.005. [14] rouabhi, a., jahangir, e., tounsi, h. (2018). modeling heat and mass transfer during ground freezing taking into account the salinity of the saturating fluid, int. j. heat mass transf. 120, pp. 523–533. doi: 10.1016/j.ijheatmasstransfer.2017.12.065. [15] zhou, m.m., meschke, g. (2013) a three-phase thermo-hydro-mechanical finite element model for freezing soils, int. j. numer. anal. met., 37(18), pp. 3173–3193. doi: 10.1002/nag.2184. [16] brovka, g.p., ivanov, s.n. (2004). calculation of temperature fields in the ground with water-ice phase transitions in the temperature spectrum, j. eng. phys. thermophys., 77 (6), pp. 1192–1200. doi: 10.1007/s10891-005-0014-9. [17] hu, j., liu, y., wei, h., yao, k., wang, w. (2017). finite-element analysis of heat transfer of horizontal ground-freezing method in shield-driven tunneling, int. j. geomech., 17(10), 04017080. doi: 10.1061/(asce)gm.1943-5622.0000978. [18] levin, l.y., semin, m.a., zaitsev, a.v. (2018). solution of an inverse stefan problem in analyzing the freezing of groundwater in a rock mass, j. eng. phys. thermophys., 91(3), pp. 611–618. doi: 10.1007/s10891-018-1782-3. [19] panteleev, i., kostina, a., zhelnin, m., plekhov, o., levin, l. (2018). numerical model of fluid-saturated rock mass with phase transitions as a theoretical basis for artificial ground freezing control system, geomechanics and geodynamics of rock masses: proceedings of the 2018 european rock mechanics symposium, 1, pp. 1273–1279. doi: 10.3724/sp.j. << /ascii85encodepages false /allowtransparency false /autopositionepsfiles true /autorotatepages /none /binding /left /calgrayprofile (dot gain 20%) /calrgbprofile (srgb iec61966-2.1) /calcmykprofile (u.s. web coated \050swop\051 v2) /srgbprofile (srgb iec61966-2.1) /cannotembedfontpolicy /error /compatibilitylevel 1.4 /compressobjects /tags /compresspages true /convertimagestoindexed true /passthroughjpegimages true /createjobticket false /defaultrenderingintent /default /detectblends true /detectcurves 0.0000 /colorconversionstrategy /cmyk /dothumbnails false /embedallfonts true /embedopentype false /parseiccprofilesincomments true /embedjoboptions true /dscreportinglevel 0 /emitdscwarnings false 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can be opened with acrobat and adobe reader 5.0 and later.) >> /namespace [ (adobe) (common) (1.0) ] /othernamespaces [ << /asreaderspreads false /cropimagestoframes true /errorcontrol /warnandcontinue /flattenerignorespreadoverrides false /includeguidesgrids false /includenonprinting false /includeslug false /namespace [ (adobe) (indesign) (4.0) ] /omitplacedbitmaps false /omitplacedeps false /omitplacedpdf false /simulateoverprint /legacy >> << /addbleedmarks false /addcolorbars false /addcropmarks false /addpageinfo false /addregmarks false /convertcolors /converttocmyk /destinationprofilename () /destinationprofileselector /documentcmyk /downsample16bitimages true /flattenerpreset << /presetselector /mediumresolution >> /formelements false /generatestructure false /includebookmarks false /includehyperlinks false /includeinteractive false /includelayers false /includeprofiles false /multimediahandling /useobjectsettings /namespace [ (adobe) (creativesuite) (2.0) ] /pdfxoutputintentprofileselector /documentcmyk /preserveediting true /untaggedcmykhandling /leaveuntagged /untaggedrgbhandling /usedocumentprofile /usedocumentbleed false >> ] >> setdistillerparams << /hwresolution [2400 2400] /pagesize [612.000 792.000] >> setpagedevice microsoft word numero_30_art_50 d.s. paolino et alii, frattura ed integrità strutturale, 30 (2014) 417-423; doi: 10.3221/igf-esis.30.50 417 focussed on: fracture and structural integrity related issues duplex s-n fatigue curves: statistical distribution of the transition fatigue life d.s. paolino, a. tridello, h.s. geng, g. chiandussi, m. rossetto department of mechanical and aerospace engineering, politecnico di torino, turin, italy davide.paolino@polito.it, andrea.tridello@polito.it, hanze.s.geng@gmail.com, giorgio.chiandussi@polito.it, massimo.rossetto@polito.it abstract. in recent years, very-high-cycle fatigue (vhcf) behavior of metallic materials has become a major point of interest for researchers and industries. the needs of specific industrial fields (aerospace, mechanical and energy industry) for structural components with increasingly large fatigue lives, up to 1010 cycles (gigacycle fatigue), requested for a more detailed investigation on the experimental properties of materials in the vhcf regime. gigacycle fatigue tests are commonly performed using resonance fatigue testing machines with a loading frequency of 20 khz (ultrasonic tests). experimental results showed that failure is due to cracks which nucleate at the specimen surface if the stress amplitude is above the conventional fatigue limit (surface nucleation) and that failure is generally due to cracks which nucleate from inclusions or internal defects (internal nucleation) when specimens are subjected to stress amplitudes below the conventional fatigue limit. following the experimental evidence, the authors recently proposed a new statistical model for the complete description of sn curves both in the high-cycle-fatigue (hcf) and in the vhcf fatigue regions (duplex s-n curves). the model differentiates between the two failure modes (surface and internal nucleation), according to the estimated distribution of the random transition stress (corresponding to the conventional fatigue limit). no assumption is made about the statistical distribution of the number of cycles at which the transition between surface and internal nucleation occurs (i.e., the transition fatigue life). in the present paper, the statistical distribution of the transition fatigue life is obtained, according to the statistical model proposed. the resulting distribution depends on the distance between the hcf and the vhcf regions and on the distribution of the random transition stress. the estimated distribution can be effectively used to predict, with a specified confidence level, the number of cycles for which an internal nucleation may probabilistically occur in a vhcf test and it is also informative for properly choosing the end of hcf tests in terms of number of cycles. a numerical example, based on experimental datasets taken from the literature, is provided. keywords. ultra-high-cycle; gigacycle; random transition-stress; random transition fatigue-life; random fatigue limit. introduction n recent years, very-high-cycle-fatigue (vhcf) test results showed that specimens may also fail at stress amplitudes below the conventional fatigue limit and, therefore, drastically affected the way of modelling fatigue data and designing machine components under vhcf loading conditions [1]. i d.s. paolino et alii, frattura ed integrità strutturale, 30 (2014) 417-423; doi: 10.3221/igf-esis.30.50 418 two distinct failure mechanisms are generally visible in vhcf data plots and, at a stress value near the conventional fatigue limit, plots show a plateau separating the two failure modes. for this reason, the conventional fatigue limit can be considered as a transition stress that differentiates between the two failure modes [2]. in particular, the plateau separating different failure mechanisms represent a transition stress, while the plateau separating finite lives from infinite lives can be considered as a real fatigue limit, if it exists [3, 4]. following the experimental evidence, new fatigue life models [2, 5-7] were proposed in the literature for the description of s-n curves characterized by two failure modes. a novel general statistical model, which can take into consideration the two failure modes (duplex s-n curve) and the possible presence of a fatigue limit is described in [8]. the model differentiates between the two failure modes (surface and internal nucleation) according to the estimated distribution of the random transition stress (corresponding to the conventional fatigue limit). no assumption is made about the statistical distribution of the number of cycles at which the transition between surface and internal nucleation occurs (i.e., the transition fatigue life). in the present paper, the statistical distribution of the transition fatigue life is obtained, according to the statistical model proposed in [8]. a numerical example, based on experimental datasets taken from the literature, is provided. the paper shows results obtained in case of a duplex s-n curve with fatigue limit. methods n [8], a unified statistical model for various types of s-n curve was defined. in subsection duplex s-n curves: statistical model, the particular case of duplex s-n curves is recalled. the model is able to take into account the possible presence of a fatigue limit. in subsection ‘transition life: statistical distribution’ a procedure for the estimation of the statistical distribution of the transition life is presented. duplex s-n curves: statistical model in case of duplex s-n curve with fatigue limit, the cumulative distribution function (cdf) of the fatigue life y (i.e., logarithm of the number of cycles to failure) can be expressed as [8]:  1 t l ty x x xy surf y int f f f f f f   (1) where y surf f is the cdf of the fatigue life if crack nucleates superficially (i.e., of the random variable (rv) )y surf , y intf is the cdf of the fatigue life if crack nucleates internally (i.e., of the rv y int ), tx f is the cdf of the logarithm of the transition stress (i.e., of the rv tx ), lx f is the cdf of the logarithm of the fatigue limit (i.e., of the rv lx ). yf given in eq. (1) depends on the cdfs of the continuous rvs lx , tx , y int and y surf . according to what proposed in the literature [9-12] for the fatigue strength, both lx and tx can be assumed as normal distributed (i.e., the fatigue limit and the transition stress are log-normal distributed). in particular, let lx have mean value lx and standard deviation lx  , and tx have mean value tx and standard deviation tx , then: φ l l l x x x x f           (2) and φ t t t x x x x f           (3) where φ is the standardized normal cdf, x denotes the logarithm of the applied stress amplitude. i d.s. paolino et alii, frattura ed integrità strutturale, 30 (2014) 417-423; doi: 10.3221/igf-esis.30.50 419 in the literature [9-11], different types of continuous distribution have been proposed for the number of cycles to failure. usually, either a 2-parameter weibull distribution or a log-normal distribution are used for the cycles to failure rv. without loss of generality, the conditional fatigue life is supposed to be normal distributed (i.e., the conditional number of cycles to failure is log-normal distributed). therefore, suppose that the mean values of y int and y surf follow the basquin’s law and that the standard deviations are constant for any value of x , then:   φ y int y int y int y int y a x b f            (4) and   φ y surf y surf y surf y surf y a x b f            (5) where y inta , y intb , y surfa and y surfb are four constant coefficients related to the basquin’s law and y int and y surf denote the standard deviations of y int and y surf , respectively. fig. 1 shows a schematic of a duplex s-n curve together with the statistical distributions assumed in each characteristic region: the surface-nucleation and the internal-nucleation regions are described by a randomly variable fatigue life (eqs. 4 and 5), while the transition and fatigue-limit regions are described by a randomly variable stress amplitude (eqs. 2 and 3). figure 1: schematic of a statistical duplex s-n curve with fatigue limit. by taking into account eqs. 2-5, yf finally becomes:     φ φ φ φ 1 φt l t t l t y surf y surf y int y intx x x y x x xy surf y int y a x b y a x bx x x f                                                          (6) with a number of parameters equal to 10. transition life: statistical distribution statistical estimation of the parameters permits to compute the s-n curves corresponding to different probabilities of failure (quantile s-n curves). eq. (6) can be exploited for the estimation of the  -th quantile s-n curve: if yf  and d.s. paolino et alii, frattura ed integrità strutturale, 30 (2014) 417-423; doi: 10.3221/igf-esis.30.50 420 the 10 parameters are substituted with their estimates, eq. (6) provides the relationship between x and y when the probability of failure equals  , which is the definition of the  -th quantile s-n curve. transition stress may vary from one specimen to another and, in a statistical framework, each specimen can be considered as representative of a particular quantile of the transition stress distribution. similarly, a particular quantile s-n curve hides out each specimen. therefore, for a given specimen, both the quantile s-n curve and the quantile of the transition stress distribution are uniquely determined. in particular, let the specimen be representative of the  -th quantile s-n curve (i.e., yf  ) and of the  -th quantile of the transition stress distribution (i.e., ,t tx x  ). if the stress amplitude equals the transition stress of the specimen (i.e., if ,tx x  ), then the fatigue life of the specimen corresponds to the transition life of the specimen (i.e., then ,ty y  ). thus, eq. (6) becomes:       , , , , , φ φ φ 1l l t t t ty surf y surf y int y int t x xy surf y int y a x b y a x b x                                             (7) where  denotes a parameter estimate, ,ty  is the  -th quantile of the transition life distribution, ,tx  is the  -th quantile of the transition stress distribution. it must be noted that the term , φ l l t x x x           in eq. (7) is almost equal to one since, according to the hypotheses stated in the definition of the unified statistical model [8], tx must be larger than lx (i.e., , lt xx   ). by taking into account that , φ 1l l t x x x           , eq. (7) can be reformulated as follows:       , , , , , , φ 1 φ φ t ty int y int y int t t t ty int y int y surf y surf y int y surf y a x b y a x b y a x b                                                  (8) eq. (8) provides an implicit relationship between ,ty  and  and, consequently, permits the numerical computation of the statistical distribution of the transition life. numerical example n experimental dataset taken from the literature [13] is analyzed in order to show main characteristics of the statistical distribution of the transition life. the selected experimental data [13] are obtained by testing ti-6al-4v titanium alloy specimens and are shown in fig. 2. estimates of the parameter involved in the model given in eq. (6) can be computed by applying the maximum likelihood principle to the experimental data. results, obtained with a code developed in matlab®, are given in the following list: 100.20 33.26 0.4639 40.36 11.67 0.3280 2.8192 0.0023 2.7200 0.0059 t t l l y surf y surf y surf y int y int y int x x x x a b a b                                 (9) a d.s. paolino et alii, frattura ed integrità strutturale, 30 (2014) 417-423; doi: 10.3221/igf-esis.30.50 421 figure 2: experimental fatigue data plot [13]. quantile s-n curves parameter estimates given in eq. (9) can be used for computing quantile s-n curves. in particular, if the  -th quantile sn curve is of interest, the following equation:     φ φ φ φ 1 φt l t t l t y surf y surf y int y intx x x x x xy surf y int y a x b y a x bx x x                                                                    (10) must be solved with respect to y for different values of x . fig. 3 shows the s-n plot together with the 10%, 50% and 90% quantile s-n curves. figure 3: quantile s-n curves. as shown in fig. 3 the region between the 10% and 90% quantile s-n curves includes about the 86% (which is close to the expected 80%) of the failure data; while the 50% quantile s-n curve is almost median between failure data at each stress amplitude. statistical distribution of the transition life if parameters are substituted by their estimates, eq. (8) can be used for numerically computing the statistical distribution of the transition life. to this aim, eq. (8) must be solved with respect to ,ty  for different values of  ranging from zero to one. it is worth noting that for a given value of  , ,tx  in eq. (8) is a known quantity and is equal to t tx xz   , being z the  -th quantile of a standardized normal distribution. fig. 4 shows the computed statistical distribution of the transition life. d.s. paolino et alii, frattura ed integrità strutturale, 30 (2014) 417-423; doi: 10.3221/igf-esis.30.50 422 figure 4: statistical distribution of the transition life together with the probable fatigue regions. as shown in fig. 4, the median of the transition life can be usefully considered to discriminate between the two fatigue regions of hcf and vhcf: failures that occur at a number of cycles smaller than the median more probabilistically belong to the hcf region; while failures that occur at a number of cycles larger than the median more probabilistically belong to the vhcf region. for the analyzed case, the median of the transition life is equal to 7.035 , which results in a median transition cycle equal to 71.08 10 . as visible in fig. 5, the median value properly differentiates between the two fatigue regions: each internally nucleated failure is above the median value, while each superficially nucleated failure is below the median value. figure 5: experimental data and probable fatigue regions as discriminated by the median value of the transition life. conclusions procedure for the estimation of the statistical distribution of the transition life in a duplex s-n curve was shown. the statistical distribution was estimated by numerically solving an equation which correlates the cumulative distribution function to the quantile of the distribution. as shown with a numerical example taken from the literature, the resulting distribution depends on the distance between the hcf and the vhcf regions and on the distribution of the random transition stress. the estimated distribution can be effectively used to predict, with a specified confidence level, the number of cycles for which an internal nucleation may probabilistically occur in a vhcf test and it is also informative for properly choosing the end of hcf tests in terms of number of cycles. a d.s. paolino et alii, frattura ed integrità strutturale, 30 (2014) 417-423; doi: 10.3221/igf-esis.30.50 423 acknowledgements he authors gratefully acknowledge financial support from the piedmont region industrial research project ngp bando misura ii.3. references [1] bathias, c., paris, p.c., gigacycle fatigue in mechanical practice, crc dekker, new york, (2005). [2] harlow, d.g., statistical characterization of bimodal behavior, acta mater., 59 (2011) 5048–5053. [3] bathias, c., there is no infinite fatigue life in metallic materials, fatigue fract. engng. mater. struct., 22 (1999) 559– 565. [4] pyttel, b., schwerdt, d., berger, c., very high cycle fatigue – is there a fatigue limit?, int. j. fatigue, 33 (2011) 49–58. [5] cashman, g.t., a statistical methodology for the preparation of a competing modes fatigue design curve. j. engng. mater. technol., 129 (2007) 159–168. [6] sakai, t., lian, b., takeda, m., shiozawa, k., oguma, n., ochi, y., nakajima, m., nakamura, t., statistical duplex sn characteristics of high carbon chromium bearing steel in rotating bending in very high cycle regime, int. j. fatigue, 32 (2010) 497–504. [7] bomas, h., burkart, k., zoch, h.w., evaluation of s-n curves with more than one failure mode, int. j. fatigue, 33 (2011) 19–22. [8] paolino, d.s., chiandussi, g., rossetto, m., a unified statistical model for s-n fatigue curves: probabilistic definition, fatigue fract. eng. mater. struct., 36 (2013) 187–201. [9] nelson, w., accelerated testing: statistical models, test plans, and data analyses. john wiley & sons, new york, (1990). [10] pascual, f.g., meeker, w.q., estimating fatigue curves with the random fatigue-limit model, technometrics, 41 (1999) 277–290. [11] lorén, s., fatigue limit estimated using finite lives. fatigue fract. engng. mater. struct., 26 (2003) 757–766. [12] hanaki, s., yamashita, m., uchida, h., zako, m., on stochastic evaluation of s-n data based on fatigue strength distribution. int. j. fatigue, 32 (2010) 605–609. [13] nims fatigue data sheet no. 98, data sheet on giga-cycle fatigue properties of ti-6al-4v (1100 mpa class) titanium alloy, national institute for materials science, tokyo, (2005). t microsoft word numero_41_art_55.docx s.m.j. razavi et alii, frattura ed integrità strutturale, 41 (2017) 440-446; doi: 10.3221/igf-esis.41.55 440 40crmov13.9 notched specimens under multiaxial fatigue: an overview of recent results s.m.j. razavi, m. peron, j. torgersen, f. berto, t. welo department of mechanical and industrial engineering, norwegian university of science and technology (ntnu), norway javad.razavi@ntnu.no, mirco.peron@ntnu.no, jan.torgersen@ntnu.no, filippo.berto@ntnu.no abstract. the multiaxial fatigue strength of circumferentially v-notched and semicircular notched specimens made of 40crmov13.9 has been investigated in this paper. the multiaxial load were applied using combined tension and torsion loading, both in-phase and out-of-phase. the axissymmetric v-notched specimens were characterized by a blunt notch tip (radius: 1 mm) and notch opening angle of 90o and the semicircular specimens were characterized by a constant notch tip radius. the net sectional area of both cases was equal with a diameter of 12 mm. the notched specimens were tested under pure mode i (tension), mixed mode i/iii and pure mode iii (torsion). more than 120 fatigue test data are used in this paper to evaluate the fatigue behaviour of 40crmov13.9 alloy. all fatigue data are analysed using the average strain energy density (ased) criterion which employs the mean value of the strain energy density evaluated over a finite size semicircular sector surrounding the tip of the notch to predict the fatigue life of the tested specimens. keywords. multiaxial fatigue; sed criterion; notched components; mixed mode i/iii. citation: razavi, s.m.j., peron, m., torgersen, j., berto, f., welo, t., 40crmov13.9 notched specimens under multiaxial fatigue: an overview of recent results, frattura ed integrità strutturale, 41 (2017) 440-446. received: 18.05.2017 accepted: 27.05.2017 published: 01.07.2017 copyright: © 2017 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. introduction he majority of engineering components are subjected to complex multiaxial loading histories. this makes it especially important to be able to accurately estimate fatigue damage under multiaxial loading. to this end, considerable effort in the past decades has been put into developing damage parameters which reflect the actual damage mechanisms of the multiaxial fatigue failure process [1-6]. numerous predictive methods have been proposed in the literature for the cracked and notched components under multiaxial loading including the critical plane [7,8], energetic criterion [9] and thermodynamics based method [10]. nieslony and sonsino [11] conducted a comparison among different available failure criteria considering a large bulk of experimental data from notched specimens. ayatollahi et al. [12] proposed a local numerical method in order to predict the fatigue crack initiation and propagation in the cracked and t s.m.j. razavi et alii, frattura ed integrità strutturale, 41 (2017) 440-446; doi: 10.3221/igf-esis.41.55 441 notched components. this method was then enhanced by other scholars to consider different parameters which affect the fatigue crack growth behaviour in different materials [13-19]. prediction of the branch crack threshold condition under mixed mode (i+iii) was suggested by pook and sharples [20] through the analysis of the main crack tip stress field. pook [21] revealed that there are different thresholds for the initiation of crack growth, crack arrest and specimen failure under multiaxial fatigue loading. additionally, definition of a fatigue threshold δkth under poly-modal loading is difficult because under torsion loading an extensive plastic zone is developed at the vicinity of the crack [22]. the presence of plastic deformation around the crack tip in conjunction with the dissipative phenomena due to the possible contact of the crack surfaces result in a strong influence of the specimen geometry on the test data. christopher et al. [23] developed a novel mathematical model of the stress fields around the crack tip under fatigue loading, taking into account the effects of plasticity through an analysis of their shielding effects on the applied elastic field. lin et al. [24] studied the complex initiation of crack growth under a combination of opening and out of plane shearing mode loading showing that the cracks do not grow through a continuous evolution of the crack surface but rather by means of an abrupt fragmentation or segmentation of the crack front. in the last years the ased approach which is based on the average value of strain energy density over a control volume has been extended for various brittle and quasi-brittle materials under tensile loading and a wide range of materials under fatigue loading. in particular, this method was used to assess the fatigue behaviour of axisymmetric specimens made of a medium carbon steel (c40) [25] and a 39nicrmo3 [26] steel subjected to uniaxial and multiaxial loading. in addition, the dissipative phenomena and non-propagating cracks in the run-out specimens were studied by berto et al. [27] and [28]. they reported that the control volume radius was found to be strongly influenced by extrinsic shielding mechanisms under mode iii loading conditions. in the current paper, the multiaxial fatigue strength of circumferentially v-notched and semicircular notched specimens made of 40crmov13.9 were investigated under combined tension and torsion loading. the ased criterion is used in order to predict the fatigue strength of notched components subjected to uniaxial and multiaxial loading. for 40crmov13.9 alloy which is a high strength steel the ased approach is essentially able to overcome the complexity of non-proportional loading using a single control volume which was used independent of the loading mode. material and geometry of the specimens ll the specimens were made of 40crmov13.9 steel. static tensile tests were carried out to evaluate the elastic and the strength properties of the material; the relevant mean values are listed in tab. 1, while the chemical composition of the material is reported in tab. 2. ultimate tensile strength (mpa) yield stress (mpa) elongation to fracture (%) brinell hardness 1355 1127 15.2 393-415 table 1: mechanical properties of 40crmov13.9. c mn si s p cr ni mo v al w 0.38 0.5 0.27 0.006 0.003 3.05 0.24 1.04 0.24 0.013 0.005 table 2: chemical composition wt.%, balance fe. the geometries of the specimens tested in the present investigation are shown in fig. 1. the v-notch depth d was equal to 4 mm for both cases. the axis-symmetric v-notched specimens were characterized by a constant notch tip radius (1 mm) and a v-notch opening angle equal to 90o. the geometry of semicircular specimens instead was characterized by a constant notch tip radius equal to 4 mm. a s.m.j. razavi et alii, frattura ed integrità strutturale, 41 (2017) 440-446; doi: 10.3221/igf-esis.41.55 442 d = 4 mm=1.0 mm 20 90° d = 4 mm=4.0 mm 20 figure 1: geometry of v-notched specimens and semicircular specimens. the specimens were tested under pure tension, pure torsion and multiaxial tension-torsion loading with different biaxiality ratios (λ = τa/σa =0.6 and 1.0). in particular, ten fatigue test series were conducted, according to the following subdivision: 1) two series of tests on notched specimens (v and semicircular notches) under pure torsion fatigue loading (nominal load ratio r = -1); 2) one series of tests on v-notched specimens under pure tension fatigue loading (nominal load ratio r = -1). 3) two series of tests on v-notched specimens under combined tension-torsion fatigue loading, under constant biaxiality ratio λ = 1, load ratio r = -1, load phase angle φ= 0° or φ= 90°; 4) two series of tests on v-notched specimens under combined tension-torsion fatigue loading, under constant biaxiality ratio λ = 0.6, load ratio r = -1, load phase angle φ= 0° or φ= 90°; 5) two series of tests on semicircular specimens under combined tension-torsion fatigue loading, under constant biaxiality ratio λ = 1, load ratio r = -1, load phase angle φ= 0° or φ= 90°; 6) one series of tests on semicircular specimens under combined tension-torsion fatigue loading, under constant biaxiality ratio λ = 0.6, load ratio r = -1, load phase angle φ= 0°. fatigue test data on v-notched and semicircular specimens efore being tested, all specimens have been polished in order to both eliminate surface scratches or machining marks and to make the observation of the fatigue crack path easier. fatigue tests have been carried out on a mts 809 servo-hydraulic biaxial machine with a 100 kn axial load cell and a torsion load cell of 1100 n.m. all tests have been performed under load control, with a frequency ranging from 1 and 10 hz, as a function of the geometry and load level. at the end of the fatigue tests, the notch root and the fracture surfaces were examined using optical and electronic microscopy. some examples of fracture surfaces are visible in fig. 2a and 2b for in phase and out of phase multiaxial loading. the results of statistical analyses carried out by assuming a log-normal distribution are summarised in tab. 3. in particular, it is summarised the mean values of the nominal stress amplitudes at different number of cycles, the inverse slope k of the wöhler curves and the scatter index t, which quantifies the width of the scatterband included between 10 and 90% probability of survival curves. all failures from 104 to 5x106 have been processed in the statistical analysis whereas the run-outs were excluded. fig. 3 depicts fatigue data from v-notched specimens tested under tension, torsion and combined tension and torsion with different load phases. in this case the biaxiality ratio is equal to 1. it is visible from the figure that the out of phase loading causes a detrimental effect on the fatigue life of the v-notched specimens. this effect is not observed in the case of semicircular notches where the most damaging case is the in-phase loading. by changing the biaxiality ratio from 1 to 0.6 on v notched specimens tests, the effect of out of phase is again present. summarising this aspect it seems that the phase displacement could increase or vice versa decrease the fatigue life of the component as a function of the notch geometry. b s.m.j. razavi et alii, frattura ed integrità strutturale, 41 (2017) 440-446; doi: 10.3221/igf-esis.41.55 443 figure 2: fracture surfaces of (a) in phase and (b) out of phase multiaxial loading. table 3: results from fatigue tests. mean values, ps=50%. stresses referred to the net area. a synthesis in terms of linear elastic sed averaged over a control volume he averaged strain energy density criterion (sed) states that brittle failure occurs when the mean value of the strain energy density over a given control volume is equal to a critical value wc. this critical value varies from material to material but does not depend on the notch geometry and sharpness. in the particular case of 40crmov13.9 steel the radius of the control volume (rc) has been found to be equal to 0.05 mm. dealing with v-shaped notches the control volume is defined as is visible in fig. 4a, the volume assumes a crescent shape and it is centred at a distance equal to r0 from the notch tip. the distance r0 depends on the radius of the notch ρ and on the notch opening angle 2α. series load n k tσ or tτ σa or τa 106 2 106 5 106 1 torsion r = -1 16 τ 13.33 1.144 281.16 266.91 249.18 2 multiaxial r = -1, φ= 0°, λ = 1.0 14 σ 9.39 1.176 182.6 169.91 153.84 3 multiaxial r = -1, φ= 90°, λ = 1.0 13 σ 7.67 1.428 145.83 133.23 118.23 4 tension r = -1 12 σ 8.42 1.335 253.69 233.64 209.55 5 multiaxial r = -1, φ = 0°, λ = 0.6 12 σ 9.9 1.202 214.61 200.10 182.41 τ 128.77 120.06 109.45 6 multiaxial r = -1, φ = 90°, λ = 0.6 13 σ 7.63 1.485 187.45 171.17 151.8 τ 112.47 102.7 91.08 7 torsion r = -1 semicircular 11 τ 14.27 1.160 367.17 349.76 328.01 8 multiaxial r = -1, φ = 0°, λ = 1.0 semicircular 15 σ 7.68 1.268 239.57 218.9 194.28 9 multiaxial r = -1, φ = 90°, λ = 1.0 semicircular 17 σ 10.79 1.260 263.82 247.4 227.26 10 multiaxial r = -1, φ = 0°, λ = 0.6 semicircular 12 σ 11.45 1.307 332.64 313.10 289.02 τ 199.58 187.86 173.41 t s.m.j. razavi et alii, frattura ed integrità strutturale, 41 (2017) 440-446; doi: 10.3221/igf-esis.41.55 444 2 2 q      (1) 0 1q r q    (2) for semicircular notches under mode i and iii loadings, the volume assumes the crescent shape shown in fig. 4b, where rc is the depth measured along the notch bisector line. the outer radius of the crescent shape is equal to rc+ρ/2, being ρ/2 the distance between the notch tip and the origin of the local coordinate system. 60 600 1.00e+04 1.00e+05 1.00e+06 1.00e+07 n o m in al s tr es s am p li tu d e [m p a] number of cycles to failure, n torsion r=-1 tension r=-1 multiaxial r=-1 =1 =0° multiaxial r=-1 =1 =90° figure 3: data from multiaxial tests from v-notched specimens. rc+r0  rc r0 (a) 2  rc /2  (b) figure 4: critical volume for (a) v-shaped notches and (b) semicircular notches. the value of the sed averaged over the control volume carefully defined as presented above, has been calculated numerically by using the fe code ansys 12.0® both for v-notched and semicircular notched specimens. fig. 5 shows the synthesis based on local sed. by comparing fig. 5 with fig. 3 it is evident that a single narrow scatterband has been obtained by means of the local energy. conclusions large bulk of results from multiaxial tests on v-notched and semicircular notched specimens made of 40crmov13.9 steel are discussed together with those obtained under pure tension and pure torsion loading from notched specimens with the same geometry. altogether more than 120 new fatigue data (10 fatigue curves) are a s.m.j. razavi et alii, frattura ed integrità strutturale, 41 (2017) 440-446; doi: 10.3221/igf-esis.41.55 445 summarised in the present work. all fatigue data are present first in terms of nominal stress amplitudes and then re analysed in terms of the mean value of the strain energy density evaluated over a finite size semicircular sector surrounding the tip of the notch. the synthesis permits to obtain a very narrow band characterised by a scatter index equal to 1.96. the synthesis has been carried out with a constant radius independent on the loading conditions. figure 5: synthesis by means of local sed of multiaxial series data. references [1] gates, n.r., fatemi, a., interaction of shear and normal stresses in multiaxial fatigue damage analysis, frattura ed integrita strutturale, 10(37) (2016) 160-165. [2] anes, v., reis, l., de freitas, m., on the assessment of multiaxial fatigue damage under variable amplitude loading, frattura ed integrita strutturale, 10(37) (2016) 124-130. [3] albinmousa, j., investigation on parametric representation of proportional and nonproportional multiaxial fatigue responses, frattura ed integrita strutturale, 10(37) (2016) 94-100. [4] mazanova, v., polak, j., skorik, v., kruml, t., multiaxial elastoplastic cyclic loading of austenitic 316l steel, frattura ed integrita strutturale, 11(40) (2017) 162-169. [5] pook, l.p., berto, f., campagnolo, a., lazzarin, p., coupled fracture mode of a cracked disc under anti-plane loading, eng. fract. mech., 128 (2014) 22-36. [6] kotousov, a., berto, f., lazzarin, p., pegorin, f., three dimensional finite element mixed fracture mode under antiplane loading of a crack, theor. appl. fract. mech., 62(1) (2012) 26-33. [7] carpinteri, a., spagnoli, a., multiaxial high-cycle fatigue criterion for hard metals, int. j. fatigue, 23 (2001) 135-145. [8] carpinteri, a., spagnoli, a., vantadori, s., multiaxial fatigue life estimation in welded joints using the critical plane approach, int. j. fatigue, 31 (2009) 188-196. [9] łagoda, t., macha, e., bedkowski, w., a critical plane approach based on energy concepts: application to biaxial random tension-compression high-cycle fatigue regime, int. j. fatigue, 21 (1999) 431-443. [10] ye, d., hertel, o., vormwald, m., a unified expression of elastic–plastic notch stress–strain calculation in bodies subjected to multiaxial cyclic loading, int. j. solids struct., 45 (2008) 6177-6189. [11] nieslony, a., sonsino, c.m., comparison of some selected multiaxial fatigue assessment criteria, lbf report no. fb234 (2008). s.m.j. razavi et alii, frattura ed integrità strutturale, 41 (2017) 440-446; doi: 10.3221/igf-esis.41.55 446 [12] ayatollahi, m.r., razavi, s.m.j., yahya, m.y., mixed mode fatigue crack initiation and growth in a ct specimen repaired by stop hole technique, eng. fract. mech. 145 (2015) 115-127. [13] ayatollahi, m.r., razavi, s.m.j., chamani, h.r., fatigue life extension by crack repair using stop-hole technique under pure mode-i and pure mode-ii loading conditions, procedia eng., 74 (2014) 18–21. [14] ayatollahi, m.r., razavi, s.m.j., chamani, h.r., a numerical study on the effect of symmetric crack flank holes on fatigue life extension of a sent specimen, fatigue fract. eng. mater. struct., 37(10) (2014) 1153-1164. [15] ayatollahi, m.r., razavi, s.m.j., rashidi moghaddam, m., berto, f., mode i fracture analysis of polymethylmetacrylate using modified energy—based models, phys. mesomech. 18(5) (2015) 53-62. [16] ayatollahi, m.r., rashidi moghaddam, m., razavi, s.m.j., berto, f., geometry effects on fracture trajectory of pmma samples under pure mode-i loading, eng. fract. mech., 163 (2016) 449–461. [17] ayatollahi, m.r., razavi, s.m.j., sommitsch, c., moser, c., fatigue life extension by crack repair using double stophole technique, mater. sci. forum 879 (2017) 3-8. [18] rashidi moghaddam, m., ayatollahi, m.r., razavi, s.m.j., berto, f., mode ii brittle fracture assessment using an energy based criterion, phys. mesomech. (in press). [19] razavi, s.m.j., ayatollahi, m.r., sommitsch, c., moser, c., retardation of fatigue crack growth in high strength steel s690 using a modified stop-hole technique, eng. fract. mech. 169 (2017) 226–237. [20] pook, l.p., sharples, j.k., the mode iii fatigue crack growth threshold for mild steel, int. j. fract., 15 (1979) r223r226. [21] pook, l.p., the fatigue crack direction and threshold behaviour of mild steel under mixed mode i and iii loading, int. j. fatigue, 7 (1985) 21-30. [22] tong, j., yates, j.r., brown, m.w., some aspects of fatigue thresholds under mode iii and mixed mode and i loadings, int. j. fatigue, 18 (1986) 279-285. [23] christopher, c.j., james, m.n., patterson, e.a., tee, k.f., towards a new model of crack tip stress fields, int. j. fract. 148 (2007) 361–371. [24] lin, b., mear, m.e., ravi-chandar, k., criterion for initiation of cracks under mixed-mode i + iii loading, int. j. fract. 165 (2010) 175-188. [25] atzori, b., berto, f., lazzarin, p., quaresimin, m., multiaxial fatigue behaviour of a severely notched carbon steel, int. j. fatigue, 28 (2006) 485-493. [26] berto, f., lazzarin, p., yates, j., multiaxial fatigue of v-notched steel specimens: a non-conventional application of the local energy method, fatigue fract. eng. mater. struct. 34 (2011) 921–943. [27] berto, f., lazzarin, p., fatigue strength of structural components under multi-axial loading in terms of local energy density averaged on a control volume, int. j. fatigue, 33 (2011) 1055-1065. [28] gallo, p., berto, f., glinka, g generalized approach to estimation of strains and stresses at blunt v-notches under non-localized creep, fatigue fract. eng. mater. struct, 39 (2016) 292-306. << /ascii85encodepages false /allowtransparency false /autopositionepsfiles true /autorotatepages /none /binding /left /calgrayprofile (dot gain 20%) /calrgbprofile (srgb iec61966-2.1) /calcmykprofile (u.s. web coated \050swop\051 v2) /srgbprofile (srgb iec61966-2.1) /cannotembedfontpolicy /error /compatibilitylevel 1.4 /compressobjects /tags /compresspages true /convertimagestoindexed true /passthroughjpegimages true /createjobticket false /defaultrenderingintent /default /detectblends true /detectcurves 0.0000 /colorconversionstrategy /cmyk /dothumbnails false /embedallfonts true /embedopentype false /parseiccprofilesincomments true /embedjoboptions true /dscreportinglevel 0 /emitdscwarnings false /endpage -1 /imagememory 1048576 /lockdistillerparams false /maxsubsetpct 100 /optimize true 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can be opened with acrobat and adobe reader 5.0 and later.) >> /namespace [ (adobe) (common) (1.0) ] /othernamespaces [ << /asreaderspreads false /cropimagestoframes true /errorcontrol /warnandcontinue /flattenerignorespreadoverrides false /includeguidesgrids false /includenonprinting false /includeslug false /namespace [ (adobe) (indesign) (4.0) ] /omitplacedbitmaps false /omitplacedeps false /omitplacedpdf false /simulateoverprint /legacy >> << /addbleedmarks false /addcolorbars false /addcropmarks false /addpageinfo false /addregmarks false /convertcolors /converttocmyk /destinationprofilename () /destinationprofileselector /documentcmyk /downsample16bitimages true /flattenerpreset << /presetselector /mediumresolution >> /formelements false /generatestructure false /includebookmarks false /includehyperlinks false /includeinteractive false /includelayers false /includeprofiles false /multimediahandling /useobjectsettings /namespace [ (adobe) (creativesuite) (2.0) ] /pdfxoutputintentprofileselector /documentcmyk /preserveediting true /untaggedcmykhandling /leaveuntagged /untaggedrgbhandling /usedocumentprofile /usedocumentbleed false >> ] >> setdistillerparams << /hwresolution [2400 2400] /pagesize [612.000 792.000] >> setpagedevice microsoft word numero 25 art 5 d. a. hills et aliii, frattura ed integrità strutturale, 25 (2013) 27-35; doi: 10.3221/igf-esis.25.05 27 special issue: characterization of crack tip stress field sharp contact corners, fretting and cracks d. a. hills, r. c. flicek department of engineering science, university of oxford, parks road, oxford, ox1 3pj, uk d. dini department of mechanical engineering, imperial college london, south kensington campus, exhibition road, london, sw7 2az, uk abstract. contacts with sharp edges subject to oscillatory loading are likely to nucleate cracks from the corners, if the loading is sufficiently severe. to a first approximation, the corners behave like notches, where the local elastic behaviour is relieved by plasticity, and which in turn causes irreversibilities that give rise to crack nucleation, but also by frictional slip. one question we aim to answer here is; when is the frictional slip enveloped by plastic slip, so that the corner is effectively a notch in a monolithic material? we do this by employing the classical williams asymptotic solution to model the contact corner, and, in doing so, we render the solution completely general in the sense that it is independent of the overall geometry of the components. we then re-define the independent parameters describing the properties of the williams solution by using the inherent length scale, a procedure that was described at the first ijfatigue and ffems joint workshop [1]. by proceeding in this way, we can provide a self-contained solution that can be ‘pasted in’ to any complete contact problem, and hence the likelihood of crack nucleation, and the circumstances under which it might occur, can be classified. further, this reformulation of williams' solution provides a clear means of obtaining the strength (defined by crack nucleation conditions) of a material pair with a particular contact angle. this means that the results from a test carried out using a laboratory specimen may easily be carried over to any complicated contact problem found in engineering practice, and a mechanical test of the prototypical geometry, which may often be quite difficult, is avoided. keywords. asymptotic approaches; complete contacts; fretting fatigue; mode mixity; sharp notches; small scale yielding; williams solution introduction ur aim is to provide a framework for the understanding of fretting fatigue for complete contacts, when the geometry of the contact itself and both the type and history of loading are completely general. we do this by studying only the extreme corners of the contact, and which we assume, for now, are both closed and adhered. the form of the contact and the loading then enter the solution only through the generalised stress intensity factors, ik , iik , defining the loading on a monolithic semi-infinite wedge. so, we begin by stating williams' solution [2] for the stress at the tip of a semi-infinite sharp notch, of included angle in the solid of 2 , which shows that the state of stress may be written in the form      1  1 , i iii iiij i ij ii ijr k r f k r f        , (1) where  , ,i j r  , and, assuming plane strain, o http://www.gruppofrattura.it http://dx.medra.org/10.3221/igf-esis.25.05&auth=true d. a. hills et alii, frattura ed integrità strutturale, 25 (2013) 27-35; doi: 10.3221/igf-esis.25.05 28      , ( , , )zz rrr r r        (2) where r is the radial distance from the notch tip, the angle  is measured from the notch bisector and taken to be positive in the counter-clockwise direction, the eigenvalues i ,   ii , are the lowest roots of the equations sin 2 sin 2 0i i    (3) sin 2 sin 2 0ii ii    (4) and the generalised stress intensity factors are defined along the bisector of the ‘notch’  0  as   1 0   lim , 0 ii r k r r     (5)   1 0 lim , 0 iiii r r k r r     (6) williams' solution may be written in an alternative form that is more suitable for frictional contacts. the punch has an included angle  , and is in contact with a half-plane, as shown in fig. 1, so that the total included angle is 2    . the contact interface lies along the line   / 2    , and is denoted int , while the distance from the notch tip along the interface line is x . the direct  p x , and shearing  q x , interfacial tractions may therefore be written as        1  1  0 1  0 1 , i ii i iii iiint i int ii int i iip x x k x f k x f k x k x                 (7)        1  1  0 1  0 1 , i ii i iii ii i iir int i r int ii r int i r ii rq x x k x f k x f k x g k x g                  (8) where compression is taken to be positive, and the generalised stress intensity factors calibrated along the interface line are denoted 0nk , where  ,n i ii , and are found from  0 ii i intk k f  ,  0 iiii ii intk k f  (9) where         i r inti r i int f g f       ,       ii r intii r ii int f g f       (10) figure 1: a diagram of the idealised geometry considered, including the coordinate system. edge separation illiams’ solution displays a power law variation of the stress field with radial distance from the notch tip and expresses this as a series expansion, of which we consider only the first two terms; ik and iik . because each term in the series is raised to a different power (except in the case of an edge crack when   ), the relative   x r int half-plane punch w http://www.gruppofrattura.it http://dx.medra.org/10.3221/igf-esis.25.05&auth=true d. a. hills et aliii, frattura ed integrità strutturale, 25 (2013) 27-35; doi: 10.3221/igf-esis.25.05 29 strengths of the two competing terms vary with radial distance from the notch tip, which creates an intrinsic length scale in the solution; the mode i term is more strongly singular and dictates contact edge behaviour, whilst the mode ii term less strongly singular (or for punch angles less than 77.4 the mode ii term is bounded) and controls the stress field slightly further from the sharp corner. this length scale can be emphasised by replacing the two parameters   ik and iik in williams' solution with two new composite parameters 0d and 0g . the definition of these quantities involves raising the generalised stress intensity factors ik and iik , to fractional powers, and for this reason, we modify the definition depending on whether the remote loads excite positive or negative values of ik and ,iik in order to avoid imaginary solutions. for simplicity, let us first consider the case when the remote loads excite positive values of the generalised stress intensity factors ik and iik . in this case, 0d and 0g are defined as 1 0     i iiii i k d k         , 1 1 0     ii i ii i i ii i iig k k           (11) where it is now clear that 0  d has the physical significance of representing the boundary, in some way, between mode i domination and mode ii domination of the stress field, whilst 0  g represents the magnitude of loading. eq. (1) can now be re-written as       1  1  0 0 0 , i iiij i ii ij ij r r r f f g d d                     . (12) we now, as in eq. (7) and (8), write out the direct  p x , and shearing  q x , tractions, but this time with the alternative formulation of the stress field, and we also, for compactness, use the shorthand  n nij ij intf f  , as     1  1  0 0 0 0 , i iiint i iirp x x xf f g g d d                        (13)     1  1  0 0 0 0 , i iir int i ii r r rq x x x f f g g d d                        . (14) when the remote loads are such that the generalised stress intensity factors ik and iik , are of the same sign (either both positive or both negative), williams' solution implies that the direct traction  p x , is of a different sign in the mode i and mode ii dominated regions of the stress field. when ik and iik are both positive, there is implied separation at the edge of contact, but closure is implied further away from the contact edge. conversely, when ik and iik are both negative, closure is implied at the edge of contact, but separation is implied to extend from the interior. it is particularly important in the latter case, to appreciate that a state of separation may not actually arise because, by the time the mode ii solution dominates the mode i solution, the next term in the series, which has not been found, may be important . in any case, when the generalised stress intensity factors take on similar signs, the length along the interface at which williams' solution implies that the boundary between separation and closure lies, based on violations of the condition   0p x  , is denoted 0x , and is given simply by setting   0p x  , and solving for the value of 0/x d at which this condition is met, which gives 1 0 0 i ii ii i x f d f            (15) note that, perhaps surprisingly, when represented in this way, the strength of the remote loading 0g , does not influence the position of the boundary between separation and closure 0x , if normalised by 0d . also, note that, for remote loading that results in ik and iik taking on opposing signs, williams' solution implies no change in sign of the direct traction http://www.gruppofrattura.it http://dx.medra.org/10.3221/igf-esis.25.05&auth=true d. a. hills et alii, frattura ed integrità strutturale, 25 (2013) 27-35; doi: 10.3221/igf-esis.25.05 30  p x . thus, when ik is negative and iik is positive, closure is implied in both mode i and mode ii regions. conversely, when ik is positive and iik is negative, williams' solution implies separation throughout the whole of the region controlled by the asymptote. this implication of gross separation means that williams' solution cannot yield any further characterisation of contact edge behaviour, therefore we do not consider this case in the subsequent analysis. regions of frictional slip o estimate the implied extent of slip, based on violations of the slip condition, the adhered interfacial tractions must be substituted into the slip condition    q x fp x  , where f is the coefficient of friction. this calculation reveals the position of all the implied boundaries between stick and slip within the edge region controlled by the asymptote, where we denote the distance from the corner to any point at which slip condition is just met as sx . for simplicity, we begin by considering the case when ik and iik are both positive, such that a small region of edge separation is implied, with an adjacent slip region. explicitly, the slip extent, 0/x d , is given by 1 0 i ii ii ii s r i i r x f f f d f f f                (16) plots of the implied slip extent (from eq. (16)) as well as a line showing the implied separated region (from eq. (15)), for the case when ik and iik are both positive, are shown in fig. 2, for three sample punch angles  60 , 90 ,120     . figure 2: plots of the implied regions of slip, stick, and separation, when both ik and iik are positive, for punch angles of  60 , 90 , 120     , where the black line denotes the boundary between closure and separation, the red line the position at which the     q x fp x  condition is met, and the blue line the position at which the     q x fp x  condition is met. for the case when the remote loads excite stresses that result in a negative ik and a positive iik , the parameters 0d and 0g must be defined differently from eq. (11), to avoid raising a negative number to a fractional power. thus, we define a new parameter n nk k  , and substitute it in place of the negative stress intensity factor, so that, for example when ik is negative and iik is positive we have stick slip + slip separation 60° punch ki ,  kii 0.5 1.0 1.5 2.0 2.5 3.0 3.5 xs d0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 f 90° punch stick + slip separation ki ,  kii 1 2 3 4 xs d0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 f 120° punch ki ,  kii + slipseparation 0.5 1.0 1.5 2.0 2.5 xs d0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 f t http://www.gruppofrattura.it http://dx.medra.org/10.3221/igf-esis.25.05&auth=true d. a. hills et aliii, frattura ed integrità strutturale, 25 (2013) 27-35; doi: 10.3221/igf-esis.25.05 31 1 0     i iiii i k d k         , 1 1 0     ii i ii i i ii i iig k k           (17) for this case, the stresses, instead of being given by eq. (12), are instead given by       1  1  0 0 0 , i iiij i ii ij ij r r r f f g d d                      (18) so that the direct  p x , and shearing  q x , are given by     1  1  0 0 0 0 , i iiint i iirp x x xf f g g d d                         (19)     1  1  0 0 0 0 , i iir int i ii r r rq x x x f f g g d d                         (20) when ik is negative and iik is positive, closure is implied through the asymptotic region. however, depending on the punch angle,  , and the coefficient of friction, f , various slip regions are implied at the edge and/or interior of the contact. to compute the implied slip extents we substitute eq. (19) and (20) into the slip condition    q x fp x  , and solve for 0/x d , again, denoting any boundary between stick and slip as sx , which gives 1 0 i ii ii ii s r i i r x f f f d f f f                (21) figure 3: plots of the implied regions of slip and stick, when ik is negative and iik is positive, for punch angles of  60 , 90 , 120     , where the red line denotes the position at which the     q x fp x  condition is met, and the blue line the position at which the     q x fp x  condition is met. 60° punch stick slip ki ,  kii 0 1 2 3 4 xs d0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 f 90° punch  ki ,  kii stickslip 0 1 2 3 4 5 xs d0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 f 120° punch  ki ,  kii stick + slip slip 0 1 2 3 4 5 6 xs d0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 f http://www.gruppofrattura.it http://dx.medra.org/10.3221/igf-esis.25.05&auth=true d. a. hills et alii, frattura ed integrità strutturale, 25 (2013) 27-35; doi: 10.3221/igf-esis.25.05 32 plots of the implied slip regions (from eq. (21)) as a function of the coefficient of friction f , for the case when ik is negative and iik is positive, are shown in fig. 3, for three sample punch angles  60 , 90 ,120     . finally, for cases in which both ik and iik are negative, separation is implied to extend from the interior of the contact, with closure and a slip region at the edge of contact whose extent is controlled by the next term in a series expansion. we do not consider this possibility here or in any subsequent analysis. the plastic zone he implied elastic state of stress near a sharp feature is singular, but in practice the singular behaviour is truncated by the presence of a plastic zone incorporating a process region, and whose extent is determined by the strength of the applied load and the yield strength of the material. in order to determine the size of the plastic zone, implied by violations of the yield condition, we use the second invariant of deviatoric stress  2 2 2 22 3rr zz rr zz zz rr rj                    (22) and note that, with this scaling von mises yield condition is 2 2 3j k (23) where k is the yield stress of the material in pure shear. we then modify eq. (12) to be specifically along the interface of the contact, i.e.       1  1  0 0 0 , i iiij int i ii ij int ij int x x x f f g d d                     (24) and use this expression (eq. (24)) together with eq. (22), and then simplify the result, to give             2 1   2 1   2   2 2 0 0 0 0 i ii i ii i int ii int i ii int x x x j g p p p d d d                                      (25) where  i intp  ,  ii intp  , and  i ii intp  represent the  -dependence of the mode i , mode ii , and mixed mode terms in the solution, respectively. we now impose the yield condition given in eq. (23), denote the size of the plastic zone along the interface line px , and solve for 0 /g k , which gives             1   2 1   2 1   2   2 0 0 0 0 3 i ii i ii p p p i int ii int i ii int x x xg p p p k d d d                                      (25) if the punch angle  , is specified, eq. (25) can be used to determine the size of the plastic zone 0/px d , as a function of strength of the applied load 0 /g k , and this is plotted for punch angles of  60 , 90 ,120     in fig. 4. this figure illustrates the perhaps surprising property that the relationship between the strength of the applied load 0 /g k , and the normalised size of the plastic zone specified along the interface line 0/px d , is not monotonically increasing. this is because, as described in hills et al. [1], as strength of the remote load is increased, the plastic front rotates and changes from being very mode i like when loaded lightly to being very mode ii like in character when loaded heavily. therefore, although the maximum radius of the plastic zone does increase monotonically in size with stronger loading, when specified along the interface line, the plastic radius takes on its maximum value when the remote loading causes the maximum plastic radius to coincide with the interface line. the plastic length along the interface then decreases for stronger loads, because the maximum plastic radius rotates away from the line corresponding to the frictional interface. t http://www.gruppofrattura.it http://dx.medra.org/10.3221/igf-esis.25.05&auth=true d. a. hills et aliii, frattura ed integrità strutturale, 25 (2013) 27-35; doi: 10.3221/igf-esis.25.05 33 figure 4: a plot showing the size of the plastic zone p 0x / d , as a function of strength of the applied load 0g / k , for example punch angles of  60 , 90 , 120     , shown in red, black, and blue, respectively. determination of the dominant slip process: plastic vs. frictional e have described how to calculate the relative sizes of the implied regions of adhesion, slip, and separation, and also how the size of the plastic zone specified along the interface line scales with remote load, so we are in a position to address the question that motivated this analysis; "when is the frictional slip enveloped by plastic slip, so that the corner is effectively a notch in a monolithic material?" the first thing to be said on this issue is that, if frictional slip is implied to extend out past the mode ii region of the solution and into the region where bounded terms control the behaviour of the contact, then whether or not the plastic zone fully envelops the zone of frictional slip at the edge of contact cannot be determined through examination of the implications williams' asymptotic solution. to find out when this condition obtains we consider the value of the implied traction ratio in the mode ii region, which, for the example punch angles of  60 , 90 ,120     , is  0.3224,  0.2189,   0.8500iirg     , respectively. thus, if the coefficient of friction is less than the absolute value of this implied traction ratio, i.e. if iirf g  , then the question of whether or not the frictional slip zone is enveloped by plasticity cannot be determined by consideration of williams' asymptote. if, however, slip is not implied to extend past the mode ii region of the solution, and is contained within the asymptote, i.e. if iirf g  , then further examination of the implications of williams' solution is merited. for cases when ii rf g  and thus adhesion is implied in the mode ii region of the solution, we can calculate the strength of load required to imply a plastic zone of equal size to the implied zone of frictional slip. this is achieved by setting    0 0/ /p sx d x d in eq. (25), and solving for the value of 0 /g k . the result of this calculation is plotted against the coefficient of friction f , for punch angles of  60 , 90 ,120     , in fig. 5. also plotted in fig. 5, are three horizontal dashed lines showing the values of iirg  for the three punch angles considered. this information is added because, as stated above, if the coefficient of friction is less than this value, i.e. if iirf g  , then slip is implied to extend outside the region controlled by the asymptote, and the magnitude of load required to imply a process zone of equal size to the frictional slip zone cannot be calculated within the asymptote. the solid lines in fig. 5 plot the magnitude of load 0 /g k , that results in the conditions    0 0/ /p sx d x d and iirf g  both being met, while the dotted lines plot the value of 0 /g k that result in only the first condition being satisfied. so, for loads greater in strength than the solid line in fig. 5, slip is implied only in the mode i dominated region (because iirf g  ), and the process zone is implied to be larger than the slip zone in this region. thus, in this case the contact is expected to behave like a notch. for loads greater than the dotted lines in fig. 5, which 60° 90° 120° 1 2 3 4 5 xp d0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 g0 k w http://www.gruppofrattura.it http://dx.medra.org/10.3221/igf-esis.25.05&auth=true d. a. hills et alii, frattura ed integrità strutturale, 25 (2013) 27-35; doi: 10.3221/igf-esis.25.05 34 are in the range iirf g  , the process zone is implied to be as large as the slip zone in the mode i dominated region, but a second slip zone is implied to extend past the mode ii dominated region. these dotted lines are included in the figure to distinguish between cases in which the slip zone in the mode i dominated region is fully enveloped by plasticity at a coefficient of friction below iirg  , which implies that for coefficients of friction greater than ii rg  there will be no slip, from the cases in which the magnitude of load required to envelop the slip zone in the mode i dominated region does not appear on the plot, which implies that, for the range of load shown in the figure, the slip zone is larger than the process zone and that the contact will slip. the curves in fig. 5 corresponding to the case 120   (shown in blue) illustrate these two distinct possibilities; when ik and iik are both positive (left) neither dotted nor solid lines appear on the plot and the slip zone is implied to be larger than the plastic zone in the range of f and 0g / k shown in the figure, but when ik is negative and iik is positive (right) a dotted line appears on the plot and thus if ii rθf g no slip is implied. figure 5: plots showing the strength of load 0 /g k , above which the process zone and frictional slip zone at the edge of contact are implied to be of equal size when iirf g  (solid lines), and when ii rf g  (dotted lines), for punch angles of  60 , 90 , 120     , plotted in red, black, blue, respectively. this is done for the case when both ik and iik are positive (left) and when ik is negative and iik is positive (right). also shown are the values of ii rg  for each punch angle (horizontal dotted lines), using the same colour scheme as for the other lines. conclusions his paper develops further our physical understanding of the physical implications of the asymptotic form given by williams, allowing not only mode mixity but also the competing effects of frictional and plastic slip to be treated; the former, but not the latter, is independent of the magnitude of the load. the ‘output’ of this paper is therefore a specific answer to the question ‘when is a sharp contact corner rigorously notch-like?’ and equally ‘when is frictional slip likely to be important?’. space limitations preclude the application of the results to real problems, which requires calibrations for ik and iik in terms of the applied loads. this last step then permits these results to be applied directly to any complete fretting (or potentially fretting) contact, by simply ‘pasting in’ this asymptotic form. acknowledgements . c. flicek thanks rolls royce plc for financial support for his studentship and david hills thanks the zilkha trust for the award of a travel grant permitting these results to be presented. 60°90° 121° gr� ii 60° gr� ii 90° gr� ii ki ,  kii 0.0 0.2 0.4 0.6 0.8 1.0 1.2 g0 k 0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 f 60° 90° 120° 121° gr � ii 60° gr � ii 90° gr � ii k i ,  kii 0.0 0.2 0.4 0.6 0.8 1.0 1.2 g0 k 0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 f t r http://www.gruppofrattura.it http://dx.medra.org/10.3221/igf-esis.25.05&auth=true d. a. hills et aliii, frattura ed integrità strutturale, 25 (2013) 27-35; doi: 10.3221/igf-esis.25.05 35 references [1] hills, d.a., dini, d., characteristics of the process zone at sharp notch roots, int. j. solid struct., 48 (2011), 2177– 2183. [2] williams, m. l., stress singularities resulting from various boundary conditions in angular plates in extension. j. appl. mech., 19 (1952), 526–528. http://www.gruppofrattura.it http://dx.medra.org/10.3221/igf-esis.25.05&auth=true microsoft word numero 25 art 21 b. moreno et alii, frattura ed integrità strutturale, 25 (2013) 145-152; doi: 10.3221/igf-esis.25.21 145 special issue: characterization of crack tip stress field high magnification crack-tip field characterisation under biaxial conditions b. moreno, p. lopez-crespo, j. zapatero department of civil and materials engineering, university of malaga, malaga (spain) abstract. this work presents a novel methodology for characterising fatigue cracks under biaxial conditions. the methodology uses high magnification digital image correlation (dic) technique for measuring displacement and strain crack-tip fields. by applying micro-speckle pattern on the metal surface it is possible to achieve high magnification for dic technique. the speckles were created by electro-spray technique. the validity of this novel technique is demonstrated by direct comparison with standard extensometer measurements, under tension-compression and torsion conditions. in order to image the correct region, the notch effect on the fatigue life was also evaluated. keywords. biaxial fatigue; digital image correlation; crack-tip strain field; electro-spray. introduction umerous engineering components and structures are subjected to biaxial loading conditions. in these cases two principal stresses and strains change in time, both in magnitude and directions. however, due to biaxial experimental tests being difficult, expensive and time-consuming, the number of experimental data available in the literature is much limited than that for uniaxial fatigue. the aim of this work is to develop a methodology capable of characterising crack-tip fields under biaxial conditions. a procedure to enforce the crack initiation at a specific location without changing the fatigue life is explained. then a new method for measuring displacement and strain crack-tip fields on fatigue cracks grown following the previous procedure is shown. this method is based on high-magnification digital image correlation (dic) technique. surface finish required by dic was achieved by electro-spray technique. materials and methods he material investigates was st-52-3n steel with the chemical composition shown in tab. 1. this is a low carbon steel often employed in structural applications. alloy c si mn p s cr ni mo st-52-3n 0.17 0.225 1.235 0.010 0.0006 0.072 0.058 0.16 table 1: chemical composition in weight % of st-52-3n steel. the balance is fe. tubular hollow specimens with the dimensions described in fig. 1 (rhs) were used in this work. all experiments were conducted with mts 809 servo-hydraulic loading rig, allowing applying tension-compression-torsion load. biaxial n t http://www.gruppofrattura.it http://dx.medra.org/10.3221/igf-esis.25.21&auth=true b. moreno et alii, frattura ed integrità strutturale, 25 (2013) 145-152; doi: 10.3221/igf-esis.25.21 146 extensometer epsilon 3550 was employed for axial and angular strain measurement. the experimental setup employed in this work is shown in fig. 1. figure 1: (lhs) experimental setup and (rhs) geometry of the specimen employed in the experiments. dimensions are in mm. methodology to study crack initiation rack initiation stage was studied under combined tension-compression and torsion tests. strain control mode was used during the experiments with cyclic sinus signal where the mean strain was zero (r = -1). at this stage proportional loading with amplitudes εa = 0.0015 and γa = 0.0032 was applied. the objective is to measure the initiation and growth of cracks with size ranging from a few hundreds microns up to 2 mm. this was done by means of a long distance microscope capable of imaging field of view of 2 × 1.5 mm2. however, it is very complicated to know a priori the exact spot where the crack will nucleate, given the cylindrical shape of the specimens. moreover, current biaxial extensometers hide a large portion of the sample, making it extremely difficult to find the nucleation point with the long distance microscope. therefore the geometry of the specimen needs to be modified so as to force the initiation of the crack at a particular spot and focus the microscope right there. different possibilities were explored. the first option was to use cylindrical specimens where the thickness was minimum at the central section, similarly to hour glass specimens [1]. however this option would not solve the problem, since although the crack would initiate at a particular section (that of minimum thickness), it could appear anywhere around the circumference. moreover this geometry would condition the crack to grow in specific orientations. this could be avoided by introducing a very small stress concentrator. by making the concentrator of circular shape, it will not condition the direction of initiation of the crack. thus, the second option investigated was to insert an indentation with a hardness testing facility. the main advantages of this option are the experimental simplicity and the repeatability that can be achieved by employing the same load and the same penetrator. three indentations were introduced in a sample with a conical penetrator. the diameter of the mark left by the penetrator was smaller than 200 µm. however, it was observed that after applying 40000 cycles not only the specimen did not fail from any of these indentations, but also no single crack nucleated around the indentations. this is explained by the fact that the material work hardens around the indentation, thus being more resistant to fatigue growth in these spots. the third option explored consisted of drilling a very small hole. the hole should be large enough to force the crack nucleation around it, but small enough to induce a damage equivalent to that of the defects existing already in the material. the effect of holes of different diameter was thus analysed. the fatigue life of different samples with holes of diameters 1.25, 1, 0.6, 0.2 and 0.15 mm and no hole were studied, following murakami’s ideas [2]. the depth of the hole in all cases was approximately the same dimension as the diameter. the results are shown in fig. 1. all the experiments were stopped when the axial load or torque dropped 20%. the crack length at the end of each experiment was approximately 20 mm. a crack nucleated around the hole in the sample with 0.15 mm drilled hole and fatigue life of 43500 cycles. however that crack did not propagate and instead the dominant crack did not originate at the hole. the results from fig. 1 show that the fatigue life is reduced as the size of the hole is increased. for the largest hole tested, the fatigue life was reduced by 90% approximately. the fatigue life increases c http://www.gruppofrattura.it http://dx.medra.org/10.3221/igf-esis.25.21&auth=true b. moreno et alii, frattura ed integrità strutturale, 25 (2013) 145-152; doi: 10.3221/igf-esis.25.21 147 approximately in a linear way as the size of the hole is reduced, up to a size of approximately 0.15 mm. by reducing further the size of the hole below 0.15 mm no change in the fatigue life is observed. a similar behaviour was previously found on other steels [2]. hence holes of size 0.15 mm and smaller would not be expected to be detrimental to fatigue life. this is also supported by the fact that one of the samples with 0.15 mm hole did not fail at the hole and instead it failed from a crack nucleated elsewhere. accordingly, drilling a hole of 0.15 mm diameter was chosen to force the crack to nucleate at a particular spot without affecting the fatigue properties of the material. 0 10000 20000 30000 40000 50000 0 0.5 1 1.5 hole diame te r (mm) f a ti g u e l if e ( c y c le s ) figure 2: fatigue lives for the different sizes of holes drilled investigated. digital image correlation technique igital image correlation (dic) allows experimental measurement of displacement and strain fields in mechanical components. important progress in the last decade in the field of digital photography gave rise to a more robust and accurate technique, in particular in the fields of fatigue and fracture [3, 4]. dic equipment is relative simple and consists of a digital camera, a computer and specific software to process the images. the technique works by comparing digital images with different strain levels. each image is subdivided in interrogation windows or subsets, so that the change in position of each of these interrogation windows is identified by comparison with a reference image. the displacement of each interrogation window is determined by minimising a cross-correlation function. accurate results can be achieved by imaging non-uniform surfaces, so that each interrogation window can be identified uniquely in the deformed image. this non-uniform finish is normally obtained by slightly spray painting the surface with black and white [3-6], although other alternatives have also been developed [7]. in this work dic technique has been employed to measure experimentally displacement and strain fields in cylindrical hollow specimens such as those described in the previous section, subjected to tension-torsion loads. dic commercial package vic-2d was employed for data processing. images were captured with a long-distance microscope (questar qm100) and a 5 mega-pixel digital camera with 8 bit dynamic range. due to the high level of magnification achieved with the microscope, the speckle pattern has to be extremely fine. this cannot be achieved by conventional spray-painting. it is thus the aim of this work to develop a technique capable of producing a pattern with ultra-fine speckles. the possibility of electro-hydrodynamic atomisation by means of electro-spray technique will be studied for this purpose. first, the methodology for generating the micro-speckle pattern is presented. the validity of the methodology is then studied by comparison with standard extensometer measurements. finally the new procedure is used to characterise crack-tip displacement and strain fields under biaxial conditions (tension and/or torsion). micro-speckle generation by means of electro-spray technique lectro-spray technique consists of extruding a liquid through a needle subjected to an electric field. by introducing solid particles in the liquid, the very fine jet coming out of the needle produces very small drops which get attached to the surface. once the liquid is evaporated, the drops will give rise to micro or nanospeckles [8]. the most common electro-spray setup consists of a capillary with sharp ending through which a pumped liquid flows. a high voltage is then applied between the sharp edge of the capillary and a collector electrode. the collector electrode can have either zero voltage or the negative voltage of the capillary (see fig. 3 lhs). d e http://www.gruppofrattura.it http://dx.medra.org/10.3221/igf-esis.25.21&auth=true b. moreno et alii, frattura ed integrità strutturale, 25 (2013) 145-152; doi: 10.3221/igf-esis.25.21 148 figure 3: (lhs) schematic of the setup used for electro-spray technique. (rhs) speckle pattern produced by electro-spray. the diameter of the centre hole is 0.5 mm. the free charges of the liquid transform the shape of the liquid located at the ending of the capillary from spherical shape to conical shape. the thereby created cone is called taylor cone [8]. the high charge of the drops induces repulsion forces between them. the smaller drops appear in the outer area of the cone and the heavier and larger drops tend to fall in the central axis of the spray [9]. there are two main parameters governing the electro-spray process: (i) the electric current flowing through the cone and (ii) the size of the spray drops. the diameter of the drops ranges between dozens of nanometres to hundreds of microns. both parameters can be controlled by the flow rate and the properties of the fluid, namely electric conductivity, surface tension, viscosity, density and electric permittivity [10, 11]. to a first approximation, the fluid conductivity allows controlling the order of magnitude of the drop diameter. the flow rate allows a smaller range once the conductivity is fixed. the size of the drops should be small enough so that each of the interrogation windows in which the image is divided can be indentified uniquely by the cross-correlation algorithm. drop sizes of 3 × 3 pixels are typically recommended to obtain good results. for the magnification level employed with the current long-distance microscope, the resolution is approximately 1 µm/pixel. accordingly, the size of the drops should be around 3µm. black and white inks were chosen for better contrast. the black ink of was made of dimethylformamide (dmf), vulcan carbon with xylene and polyethylene vinyl acetate (peva). the addition of peva improved the adhesiveness of the ink to the metal surface. this adhesiveness is much required since once the speckle is applied onto the surface, the paint can be detached during the handling of the specimen. this includes the drilling of the hole, placing the specimen in the grips of the loading rig and placing the extensometer in the sample. in order to increase the conductivity of the solution, antistatic agent stadis was also added. this was the black solution that was used as background on the metal surface. white speckles were created with a solution made of methylene chloride and methanol with titanium oxide (tio2). the solvent was chosen so that flow rates between 0.04 and 2 ml/hour and voltage of 60 kv can be used. the flow rate and voltage values were given by the pump and the voltage source respectively. an example of the speckle pattern generated is shown in fig. 3 rhs. strain results in un-cracked specimens n order to validate the experimental setup described in the previous sections, dic strain data were compared with strain information measured with a biaxial extensometer. cylindrical shaped hollow un-cracked specimens were used. these were subjected firstly to uniaxial tension-compression cyclic load and secondly to biaxial tensioncompression-torsion in-phase cyclic load. tests were made with load and torque control mode on the loading rig at a 0.2 hz frequency. this frequency allowed the acquisition of 65 images by the digital camera, providing enough information to describe a cycle. the reference image for dic was the one giving zero strain with the extensometer. since no stress concentrator was introduced in these specimens, the displacements both in the axial and the angular direction were linearly proportional to the distance from the grips. therefore, uniform distribution in axial and angular strain fields is expected in the calibrated length of the specimen. fig. 4 lhs shows a comparison of the axial strain measured by both dic technique and extensometer. these were obtained under tension-compression uniaxial test with loads ranging between ± 15 kn. fig. 4 rhs shows a comparison of the angular strain measured by both dic technique and extensometer. tension-compression-torsion loads were applied during the test shown in fig. 4 rhs, with axial loads being ± 15 kn and torsion torque ± 70 nm. similar agreement between dic and extensometer were obtained in biaxial i http://www.gruppofrattura.it http://dx.medra.org/10.3221/igf-esis.25.21&auth=true b. moreno et alii, frattura ed integrità strutturale, 25 (2013) 145-152; doi: 10.3221/igf-esis.25.21 149 test in both axial and torsion components. the very good agreement observed in fig. 4 between dic and extensometer data demonstrate the validity of the experimental proposed method. figure 4: (lhs) axial strain and (rhs) angular strain evolutions along 5 cycles measured by dic and biaxial extensometer. strain results in cracked specimens n-cracked specimens were used to validate the methodology combining dic and long-distance microscope on biaxial samples. once the methodology was validated, it is applied to study the crack-tip field around fatigue cracks. a 0.15 mm diameter hole was drilled in a sample. the sample was then subjected to ± 15 kn axial load and ± 70 nm torsion torque at a 3 hz frequency. axial load and torsion torque were in-phase. however, due to the small stress concentrator effect of the 0.15 mm diameter hole, the crack was initiated in a region far from the hole and thus it could not be detected nor measured with dic. it was then decided to drill a larger hole (0.5 mm diameter) to enforce the crack initiation from the hole (see fig. 3 rhs). every 2500 cycles, the frequency was decreased from 3 to 0.2 hz so that each cycle could be studied with sufficient number of images (65 images per cycle). 5 complete cycles were captured by acquiring images for 30 seconds. subsequently, the frequently was set to 3 hz again and 2500 cycles were applied before the following measurement. fig. 5 shows the vertical displacement field, as well as a displacement profile along a vertical line after 100 cycles were applied on the specimen. no crack was detected in fig. 5. a linear displacement distribution along the vertical direction is also observed in fig. 5. very similar results were obtained in un-drilled samples, thus suggesting the little stress concentrator effect of such hole. figs. 6 lhs and rhs show the strain field after applying 27500 and 30000 cycles respectively. the stress concentrator effect can be easily appreciated in figs. 6 in two diametrically opposite regions around the hole. the growth direction of the crack can be estimated from fig. 6 to be approximately 30º with respect the longitudinal (vertical) axis of the specimen. by carefully examining the hole, the crack can be only appreciated on the top right area and bottom left area of the hole. however, it is not possible to distinguish the crack in the speckle-painted surface. nevertheless, the strain maps in figs. 6 clearly show evidence of a crack. figure 5: (lhs) vertical displacement field and (rhs) displacement profile along a vertical line (shown in white) after applying 100 cycles on the specimen. u http://www.gruppofrattura.it http://dx.medra.org/10.3221/igf-esis.25.21&auth=true b. moreno et alii, frattura ed integrità strutturale, 25 (2013) 145-152; doi: 10.3221/igf-esis.25.21 150 figure 6: strain strain field after applying (lhs) 27500 and (rhs) 30000 cycles. fig. 7 shows the vertical displacement map as well as a vertical displacement profile along crack opening direction. fig. 7 was obtained by rotating the camera some 60º clockwise so that the crack appears horizontal in the image. a drastic change due to the existence of a discontinuity is observed in the displacement profile (rhs in fig. 7). therefore, after applying 33500 cycles (fig. 7) it is possible to distinguish the crack. at this stage, the crack can be distinguished as a discontinuity in the vertical displacement field (rhs in fig. 7). the crack is also visible by looking at the painted surface because of the paint being cracked around the fatigue crack mouth. rotation of the camera also allows easier identification of the crack as a mode i (opening mode) crack. due to the discontinuity introduced by the crack, the algorithm is not able to provide displacement information just above and below the crack plane, since displacements in these positions are very different. this behaviour is most probably due to the fact that the crack in the metal is longer than that in the paint. when the crack is very short (up to approximately 30000 cycles in the current specimen), the paint is elastically deformed without being cracked. for longer crack lengths (from 33500 cycles onwards) the crack opening displacement in the metal is so large that elastic deformation of the paint is not enough to accommodate such large displacement. this causes the paint to break around the region close to the metal crack mouth. the fact that the crack length shown by the paint is smaller than the real crack length in the metal is studied in fig. 8. fig. 8 shows a superposition of the metal surface after being cleaned (i.e. with no paint) and vertical strain fields calculated by dic. comparison between figs. 7 and 8 makes clear that actual crack length in the metal (approximately 3.2 mm) is much longer than that in the paint (approximately 0.86 mm). therefore, with the current arrangement, it is not possible to directly measure the correct crack length in the speckled surface. figure 7: (lhs) vertical displacement field and (rhs) displacement profile along a vertical line (shown in white) after applying 33500 cycles on the specimen http://www.gruppofrattura.it http://dx.medra.org/10.3221/igf-esis.25.21&auth=true b. moreno et alii, frattura ed integrità strutturale, 25 (2013) 145-152; doi: 10.3221/igf-esis.25.21 151 figure 8: superposition of the metal surface after being cleaned (i.e. with no paint) and vertical strain fields calculated by dic after applying 33500 cycles. concluding remarks rom the results obtained, the following conclusions can be drawn: a new procedure based on murakami’s ideas for enforcing the crack initiation at a specific location was successfully developed. electro-spray technique was effectively employed for producing a micro-speckle pattern that can be used by dic technique combined with long-distance microscope to evaluate crack-tip displacement and strain fields. electro-spray technique for creating the speckle pattern required by dic did not allow the monitoring of the crack length, since it obscures the crack. better results could be obtained when monitoring the crack length by making the speckle paint film not continuous. however this would also imply a lower contrast and so further experiments are required to find a solution. acknowledgements inancial support of spanish ministerio de economía y competitividad through grant reference dpi2012-33382 is greatly acknowledged. experimental help by mr f sabarit is also much appreciated. references [1] astm e606 / e606m 12 standard test method for strain-controlled fatigue testing. (2012). [2] murakami, y., metal fatigue: effects of small defects and non metallic inclusions oxford, uk: elsevier, (2002) 35-56. [3] sutton, m. a., mcneill, s. r., helm, j. d., chao, y. j., advances in two-dimensional and three-dimensional computer vision. in: photomechanics, topics in applied physics, rastogi pk, editor., 77 (2000) 323-372. [4] fonseca, j. qd., mummery,p. m. , withers, p. j., full-field strain mapping by optical correlation of micrographs acquired during deformation, journal of microscopy, 218(1) (2005) 9-21. [5] yoneyama, s., ogawa, t., kobayashi, y., evaluating mixed-mode stress intensity factors from full-field displacement fields obtained by optical methods, engineering fracture mechanics, 74 (2007) 1399-1412. [6] roux, s., hild, f., stress intensity factor measurements from digital image correlation: post-processing and integrated approaches, international journal of fracture, 140 (2006) 141-157. [7] lopez-crespo, p., shterenlikht, a., patterson, e. a., withers, p. j., yates, j. r., the stress intensity of mixed mode cracks determined by digital image correlation, journal of strain analysis for engineering design, (2008) 43. [8] taylor, g. i., disintegration of water drops in an electric field. proceedings of the royal society – a, 280 (1964) 383397. [9] deng, w., gomez, a., influence of space charge on the scale-up of multiplexed electrosprays, journal of aerosol science, 38 (2007) 1062-1078. f f http://www.gruppofrattura.it http://dx.medra.org/10.3221/igf-esis.25.21&auth=true b. moreno et alii, frattura ed integrità strutturale, 25 (2013) 145-152; doi: 10.3221/igf-esis.25.21 152 [10] mora, j. fdl., loscertales, i. gj., the current emitted by highly conducting taylor cones, fluid mechanics, 260 (1994) 155-158. [11] gañán-calvo, a., dávila, j., barrero, a., current and droplet size in the electrospraying of liquids scaling laws, journal of aerosol science, 2 (1997) 249-275. http://www.gruppofrattura.it http://dx.medra.org/10.3221/igf-esis.25.21&auth=true microsoft word numero_30_art_67 p. livieri, frattura ed integrità strutturale, 30 (2014) 558-568; doi: 10.3221/igf-esis.30.67 558 focussed on: fracture and structural integrity related issues on the notch sensitivity of cast iron under multi-axial fatigue loading p. livieri, e. maggiolini, r. tovo university of ferrara, italy paolo.livieri@unife.it, enrico.maggiolini@unife.it, roberto.tovo@unife.it abstract. this work deals with the notch sensitivity of sharp notches under multi-axial fatigue loading. the main discussion concerns the differences in notch sensitivity at high cycle fatigue regime, between tensile, torsional and combined loading. for this comparison, this paper considers a large set of fatigue experimental tests and several computing simulations analyzed with several notch theories for predicting fatigue life of a component. the considered experimental data, taken from literature, deal with the fatigue behavior of cast iron circumferentially v-notched specimens under tension, torsion, and combined loading mode. this paper tries to apply several techniques for theoretical strength assessment and to compare different procedures. the examined procedures need the computation of many parameters, focusing on the importance of using the tensile resistance to set these parameters or using both tensile and torsion resistances. however, the improvements obtained by means of the more complex procedures are not noteworthy, compared to the overall scatter. in author’s opinion, the differences in notch sensitivity under tensile and torsional loading remain questionable. keywords. notch; fatigue; tensile; torsion; combined load. introduction he well-known problem of estimating the fatigue life of severely notched components, in the literature, is comprehensively studied, regardless of the material: for example carbon steel [1], titanium alloy [2] or polycrystals [3]. since neuber [4], the fatigue strength of notched components has been related not strictly to the peak stress at the notch tip, but to an effective stress defined as an average value over a small volume of material of depth “q”, depending on material. the difference between the increment of the peak stress and the actual reduction of strength at notches is usually called “notch sensitivity”. successively, for the “notch sensitivity” modelling, peterson [5] largely confirmed the need of introducing at least one length, material dependent, to be compared with the notch tip radius. another way, to predict fatigue life of notched components, is obviously to perform several tests to build, for example, the sn diagram, but this strategy needs a lot of time and money. multi-axial fatigue tests on notched specimen has been performed and reported in different papers and conferences: in the presence of blunt circumferential notch [6], near holes [7], considering the crack behavior [8], under proportional/nonproportional loading [9]. it is possible to note the difference in the fatigue resistance by changing the loading mode, in the presence of geometrical irregularities. it was demonstrated by the modified wohler curve method the important role of t p. livieri, frattura ed integrità strutturale, 30 (2014) 558-568; doi: 10.3221/igf-esis.30.67 559 the shear stress in the stage i fatigue cracks [10] and of the normal stress that open and close the micro cracks influencing the propagation of themselves [11]. anyway, even if the multi-axial notch sensitivity is a well-known global problem, its actual relationship with the load case is not definitely clear. by taking advantage from the numerical tools, a simple strategy would be to investigate how the stress field is setup around the notch tip and to compute, by a fem software or formulas, the fatigue strength according to the overall stress field at the notch tip and in the surrounding zone. many procedures in the last years came up to provide for this problem (implicit gradient [12], critical distance [13], strain energy density [14] for instance) and many researchers are studying the way to predict the resistance of a notched component without specific experimental tests. one or more characteristic lengths lead all these theories. these lengths are calibrated on reference cases: for instance, the pure tensile and torsion tests; but, is it necessary to study all the different cases? what about the load ratio? is the combined in phase/out-of-phase test influenced by the pure torsion sensitivity or tensile strength knowledge is sufficient? from applicative point of view, every current influencing factor requires a model and usually the introduction of a specific coefficient to be evaluated; at least one further undetermined coefficient should be fitted for every influencing factor introduced. the paper investigates whether the loading mode is an actual influencing factor for the notch sensitivity of metals, i.e. if and how much it is necessary to change or modify the notch sensitivity assessment when uniaxial, or biaxial stress are applied to a notch. in this paper, the investigation focuses on cast iron. cast iron are expected to be more used in the next years, the production mechanism is improving the quality and cast iron has, by now, a good mechanical and technological properties. many studies made on wind turbine [15-18] demonstrate the importance of casting thickness and microstructure in the fatigue mechanism. metallurgical defects are inevitable and defects are very common especially on this kind of materials: cavities, porosity, graphite degenerated and so on; all of these imperfections influence the resistance of cast iron because this kind of defect could be compared to cracks [19]. tests on sharp notches are particularly suitable because notches give to the designer the same problems of cracks, so tests on notches provide information concerning both notch sensitivity and defect tolerance of a material. the aim of this paper is to understand the difference between setting the characteristic length only on the pure tensile test and setting on the pure tensile and on torsion resistance. for this purpose, the paper takes the fatigue strength of cast iron specimens under tensile, torsion and mixed in-phase and out-of-phase combined load from [20] and it compares the possible expectations computed by means of different theories. theoretical overview of notch strength theories n the literature, it is simple to find out that, traditionally, almost all the theories usually are set up in pure tensile load case because tensile loading is the most common applied load, tensile is the most representative resistance and it is the most simple load to apply by testing devices. one of these approaches, for instance, is the implicit gradient. implicit gradient (ig) this method, as proposed in [21], is particularly suitable for a numerical estimation of the component fatigue life dependent on its geometry; the idea is very simple and it enables the application of the average damage originally formulated in the 1930s by neuber [4]. ig method is based on the assumption that the damage should be related to the average of the stress components occurring on the body, where the values near to the critical point are more important than the far away field. the influence zone dimension is regulated simply by the material properties and is indicated by the length c. in a body of volume v, it is possible to define a non-local effective tension σeff in a generic point x as an integral average of an equivalent local tension σeq, weighted by a gaussian function ψ (x,y) depending on the distance between points x and y of the body: σeff,int (x) =    eq 1   ψ x,y  dy r(x) v y v      eqψ x,y σ (y)d   ψ x,y v v v dv    in v (1) where i p. livieri, frattura ed integrità strutturale, 30 (2014) 558-568; doi: 10.3221/igf-esis.30.67 560 ψ = 2 2 |x y| 2 l 2 e 2l   [mm-2] l=c 2 [mm] (2) by approximating eq. (1), it is possible to define an effective stress σeff by the helmholtz equation [22] using neumann boundary conditions ( eff n 0   ) [4]. 22eff,ig eff,ig eqc   in v (3)   where eq is the first principal stress (for example) and c is a material coefficient (for instance, it is 0.2 mm for weldable construction steel). theory of critical distance (tcd) another simple approach is the critical distance approach. in its original formulation the critical length is simply defined as a material characteristic length l, computed according to tensile properties of material: i,th 1 l = a k         (4) the effective value of the stress is obtained by considering the elastic field around the notch tip. in particular the remarkable elastic stress field around the notch is obtained plotting the stress (i.e. the maximum principal stress) depending by the distance from the notch tip in a defined direction. figure 1: stress distribution from a notch tip and effective values of cd and ig approaches. specifically, the point method states that the effective stress is the stress evaluated at one half of the critical length: σeff,cd = σeq(l/2) (5) having l given by material, the σeff can be easily found by the formulas or graphs similar to fig. 1. differently from the original formulation, in the case of combined loading, in the multi-axial fatigue[23, 24] a more general approach is proposed by suggesting a critical length linearly dependent from the biaxiality ratio ρ. the biaxiality ratio is defined by: p. livieri, frattura ed integrità strutturale, 30 (2014) 558-568; doi: 10.3221/igf-esis.30.67 561 ρ = 3 1     (6) and consequently the critical length l depends from the biaxiality ratio according to: l = a ρ + b (7) in the above linear relationship, a and b are material constants to be determined by the critical distance value generated under two different ρ ratios: for instance, eq. (7) could be easily calibrated by considering the material characteristic length generated both under plane stress mode i loading (ρ = 0) and under mode iii loading (ρ = 1). we will call this linear variability of the critical length: “bi-parametric approach”, since its definition requires the calibration of the two values under separated loading conditions bi-parametric extension of the implicit gradient (ig) it is quite easy to provide a bi-parametric version of the implicit gradient approach too and such extension is here proposed. by using the same linear dependence of eq. (7), even the constant c of eq. (3) can change according to the biaxiality ratio. hence, in a bi-parametric version of the implicit gradient approach, c will be computed according to: c = a’ ρ + b’ (8) where, similarly to the critical distance approach, a’ and b’ will be calibrated by means of two experimental values obtained under different biaxiality ratios. strain energy density (sed) the energy stored in a body due to the deformation is called strain energy. the strain energy per volume unit is the sed, that is the area underneath the stress-strain curve up to the point of deformation. it is obvious that any strain energy density approach strictly speaking cannot be used at the tip of a sharp v-shaped notch since not only do stresses tend toward infinite (both in the case in which they obey the linear elasticity, and when they obey a power-hardening law), but so does the strain energy density. on the contrary, in a small but finite volume of material close to the notch, whichever its characteristics (blunt notch, severe notch, re-entrant corner, crack), the energy always has a finite value and the main question is rather that of estimating the size of this volume. to calculate the sed in a finite volume around the focus point it needs:  mode x eigenvalues, according to the williams’ solution λx  non dimensional shape factors in the nsif expressions k1,3  v-notch depth d’=(d/2)-d  parameters for the energy density evaluation e1,3  poisson ratio υ  young module e  weight function cw the reference [20] demonstrates how to calculate the sed, at sharp notches, in a multi-axial case and for the specific experimental data considered in the following. the first point is the evaluation of the notch sif: 1(1 λ )1 1 nomk k d' σ    (9) 3'(1 λ )3 3 nomk k d τ    (10) then, the radius of integration shall be evaluated, by obtaining two different values for tensile and torsional loading, i.e. mode i and iii respectively. 1 1 1 λ1a 1 1 1a k r 2e   σ       (11) 3 1 1 λ3 3a 3 3a e k r   1 ν σ        (12) p. livieri, frattura ed integrità strutturale, 30 (2014) 558-568; doi: 10.3221/igf-esis.30.67 562 finally, the effective strain energy density shall be evaluated, by computing the average energy and by introducing an appropriate correction cw due to the load ratio. 1 3 22 31 1 32(1 λ ) 2(1 λ ) 1 3 kk1 w e  + e e r r          (13)     2 2 2 2 1+           1 0 1-r 1           0 1        0 1 1-r w r for r c for r r for r              (14) wsed c w  (15) note that, since the integration fields are different under tensile and torsional loading and the two strengths shall be known for the sed evaluation, the proposed approach is actually a bi-parametric one. a mono-parametric version of such theory can be easily obtained by using only the parameters evaluated under tensile loading; i.e. using only r1 and assuming, for a sake of simplicity, r3 equal to r1. this choice is not suggested in [20], but it is here introduced just for this specific investigation. experimental data from the literature or a discussion on real data, experimental tests taken from literature are here considered. data are taken from the recent paper [20] previously cited and such experimental data concern the fatigue tests on sharp notches, made of ductile cast iron, under multi-axial loading. cylindrical specimens are made of en-gjs400 cast iron with a circumferential v-notch. according to [20], the mechanical properties of the parent material are: ys = 267 mpa, uts = 378 mpa and the elongation to fracture equal to 11.5%. the reference fatigue strength of the parent material, under fully reversed, tensile and under torsional loading, are σa = 150.4 mpa, τa = 145.6 mpa. the notched specimens were tested under tensile, torsion, mixed in phase and out-of-phase fatigue loading. the main results are in tab. 2. tab. 2 shows the following parameters: r = stress ratio; λ = nominal biaxiality ratio; φ= phase shift angle under combined loading. the tab. 2 provides, as an index of the obtained results, the values σa and τa, i.e. the average strength at 2 millions of cycles to failure for the considered case. figure 2: geometry of experimental specimens [20]. b [mm] d [mm] d[mm] α [°] r [mm] 200 20 6 90 0.1 tab. 1: specimens size. f p. livieri, frattura ed integrità strutturale, 30 (2014) 558-568; doi: 10.3221/igf-esis.30.67 563 data set r load case phase shift angle φ biaxiality ratio λ σa [mpa] τa [mpa] a -1 tension 89.9 b -1 torsion 151.9 c -1 combined 0 1 74.0 74.0 d -1 combined 90 1 82.6 82.6 e -1 combined 90 0.6 85.9 51.5 f -1 combined 0 0.6 99.7 59.8 g 0 tension 57.5 h 0 torsion 109.5 i 0 combined 0 1 56.4 56.4 j 0 combined 90 1 53.3 53.3 table 2: results taken from [20]. numerical simulations he proposed approaches are based on the linear elastic stress field. several fe tools can easily compute the linear elastic stress filed. in the following, comsol multiphysics fe software has been used because it is the easiest way to solve the helmholtz equation eq. (3), necessary for ig, due to the built-in pd equation solver. authors developed another way to solve the ig with others fe software [25], but it turns out approximate and a direct solution is more accurate. tcd and sed do not need any specific software to be solved. a free mesh was applied on the most part of the geometry; a mapped mesh was used in the proximity of the notch tip. the investigated geometry has a tensile stress concentration factor kt,σ and the torsional stress concentration factor kt,τ respectively equal to kt,σ = 7.467 and kt,τ = 3.178. figure 3: mapped mesh on the notch tip (element size=r/6.25). application of effective stress theories or the actual computation of the effective values, according to presented theories, some further descriptions are necessary. first, an equivalent stress value shall be chosen for ig and cd approaches, see eq. (3) and (5). t f p. livieri, frattura ed integrità strutturale, 30 (2014) 558-568; doi: 10.3221/igf-esis.30.67 564 in [26], a large investigation has been carried out on a similar ductile cast iron. the main principal stress amplitude σ1,a turned out to be a proper choice for the equivalent stress under multi-axial fatigue loading. this choice will be adopted in the following. moreover, [26] demonstrated a large sensitivity to the mean principal stress value. in that case, a proper correction for the loading conditions with mean value different from zero, was the following: σeq,a = σ1,a + 0.5 σ1,m (16) where σ1,m is the mean value of the main principal stress. to characterize the length useful to calculate the effective stress, by using both tensile and torsion, we use the formula (7) for all the proposed techniques. the biaxility index ρ is calculated with the nominal principal stresses values. ig according to previous equations and the given experimental data, the parameter “c” for the ig approach have been fitted on the pure tensile and torsional reverse loading: data set a and b of tab. 2. they turn out to be cσ = 0.3985 and cτ = 0.5684. in a simple mono-parametric investigation “c” of eq. (3) will be constant and equal to cσ. in the case of a bi-parametric study, the characteristic length is a combination of tensile and torsion; according to the linear assumption of eq. (7), it turns out to be: c=( cτ cσ)*ρ+cσ (17) obtained results are shown in tab. 3. note that, a perfect agreement of the proposed approach is obtained when the effective stress of the considered case is equal to the reference strength of the parent material under tensile loading, σa = 150.4 mpa. r load case σnom τnom σeff,gi mono-par. σeff,gi bi-par. -1 tensile 89.9 0.0 149.5 149.5 -1 torsion 0.0 151.9 169.2 144.5 -1 φ=0° λ=1 74.0 74.0 174.9 163.2 -1 φ =0° λ =0.6 99.7 59.8 198.0 190.0 -1 φ =90° λ =1 82.6 82.6 125.8 128.0 -1 φ =90° λ =0.6 85.8 51.5 130.8 125.2 0 tensile 57.6 0.0 143.7 143.7 0 torsion 0.0 109.6 183.1 156.4 0 φ =0° λ =1 56.4 56.4 200.0 186.6 0 φ =90° λ =1 53.3 53.3 152.1 141.9 table 3: effective stress values provided by the ig approach. tcd similarly, to the ig approach, in the tcd methods, the critical length value have been fitted on tensile and torsional loading cases. the obtained values are: l(σ) = 0.540 mm and l(τ) = 0.968 mm. for the dependence of l by combined tensile and torsion the eq. (7) is used with a=0.428 and b=0.540. results are shown in tab. 4 p. livieri, frattura ed integrità strutturale, 30 (2014) 558-568; doi: 10.3221/igf-esis.30.67 565 r load case σnom τnom σeff,cd mono-par. σeff,cd bi-par. -1 tensile 89.9 0.0 149.9 149.9 -1 torsion 0.0 151.9 190.9 150.2 -1 φ=0° λ=1 73.99 73.99 192.5 171.8 -1 φ =0° λ =0.6 99.70 59.82 212.8 198.4 -1 φ =90° λ =1 82.57 82.57 137.7 122.0 -1 φ =90° λ =0.6 85.83 51.50 143.1 133.4 0 tensile 57.60 0.00 144.0 144.1 0 torsion 0.00 109.60 206.7 162.5 0 φ =0° λ =1 56.40 56.40 220.2 196.4 0 φ =90° λ =1 53.30 53.30 176.7 143.5 table 4: effective stress values provided by the cd approach. sed in order to apply the sed approach and to calculate the reference strength ak necessary for eq. (11, 12), a possibility is to use the same reference tensile and torsional strength previously reported and used for the other approaches. from eq. (11, 12) the integration field dimensions resulted respectively r1 = 0.48 mm and r3=1.18 mm. these results were one of the possibilities given by [20]; anyway, it is necessary to remark that the authors in [20] suggested even a slightly different choice by obtaining a lower r1 radius equal to 0.33 mm. in the following, we will used the final value suggested by the authors of [20]. however, this choice affects the absolute value of the results; but, in the following, the absolute comparison between different approaches could be questionable in any case and the main target of the following discussion will not be the absolute comparison of the proposed methods, but only the relative effect of the introduction of the bi-parametric sensitivity. so, at this stage, the actual r1 used is not critical, if the choice is among the values proposed by the authors of [20]. in order to consider the characteristic length only depending by the tensile loading, i.e. the mono-parametric approach instead of the bi-parametric one, it is sufficient to set r3 = r1 = 0.33 mm. having these data, it is simple to calculate sed and results are given in tab. 5. r load case δσnom 1 δσnom 3 sed mono-par. sed bi-par. -1 tensile 179.8 0.0 0.152 0.152 -1 torsion 0.0 303.8 0.669 0.370 -1 φ=0° λ=1 148.0 148.0 0.262 0.191 -1 φ =0° λ =0.6 199.4 119.6 0.291 0.244 -1 φ =90° λ =1 165.1 165.1 0.326 0.237 -1 φ =90° λ =0.6 171.7 103.0 0.215 0.181 0 tensile 115.2 0.0 0.125 0.125 0 torsion 0.0 219.2 0.697 0.385 0 φ =0° λ =1 112.8 112.8 0.304 0.221 0 φ =90° λ =1 106.6 106.6 0.272 0.198 table 5: sed values for the considered tests. p. livieri, frattura ed integrità strutturale, 30 (2014) 558-568; doi: 10.3221/igf-esis.30.67 566 discussion first check of the obtained results could be a general overview of the overall accuracy. as previously stated, a good assessment is obtained when the effective stress values (or the sed), calculated at the reference strength (i.e. the values given in the previous tables) are the same for all the considered experimental test data. in this case, considered approaches have been fitted mainly on the tensile fully reversed loading test, hence the referring case is the set a of tab. 2: tensile loading at r = -1. for the considered approaches, this optimal condition is not completely satisfied. the scatter of the effective values is much lower than the nominal or peak values, but it is important. the combined loading conditions seem the most critical; there is an under estimation of the fatigue strength for the in-phase loading (because the effective values at the experimental strength value are higher than expected) and an over estimation of the fatigue strength for the out-of-phase loading, independently from the load ratio r. for a quantitative comparison, the relative errors are defined as the effective value minus the referring tensile case (i.e. 150.4 mpa for stress) divided by the same strength. for the sed approach, errors have been computed on the squared roots of the obtained values, because sed is an energy and not a stress; elsewhere errors of the sed approach should be incorrectly too high compared to errors defined on stress values. a diagram of the obtained values is given in fig. 4. ‐40.00% ‐20.00% 0.00% 20.00% 40.00% 60.00% 80.00% 100.00% 120.00% i g  1 ‐ p a r i g  2 ‐ p a r se d  1‐ p a r se d  2‐ p a r c d  1‐ p a r cd  2‐ p a r a b c d e f g h i j figure 4: relative errors of obtained results. a “box and whisker plot” can give a more appropriate representation of the scatter of the obtained results. fig 5 shows the results. as usual, in this “boxplot” the bottom and the top of the boxes are the first and third quartiles, and the band inside the boxes is the second quartile (the median); the ends of the whiskers are the minimum and maximum of all of the data. ‐60.00% ‐40.00% ‐20.00% 0.00% 20.00% 40.00% 60.00% 80.00% 100.00% 120.00% ig 1‐par ig 2‐par sed 1‐par sed 2‐par cd 1‐par cd 2‐par figure 5: box-plot of relative errors. a p. livieri, frattura ed integrità strutturale, 30 (2014) 558-568; doi: 10.3221/igf-esis.30.67 567 apparently, mono-parametrical sed has a higher scatter; but it is not here proposed as an actual prediction procedure, it is simply here computed for the specific target of this paper. in this discussion, the main question does not deal with a comparison among the different approaches, but we want to comment the differences between the mono-parametric and the bi-parametric version of each approach. it is clear that the median and the mean value of the bi-parametric approaches are better. in addition, the overall scatters are smaller; hence, we can say that the bi-parametric approaches are somehow better than the mono-parametric ones. on the other hand, we can also say that this evidence is trivial, because bi-parametric approaches are fitted on two set of data, hence they shall necessary have a better outcome than the approaches fitted on just one set of data. in our opinion, the problem turns out to be: is the obtained improvement actually significant compared to the overall scatter of the results? the analysis of variance (anova) can address this problem. the hypothesis to be verified is the equality of the mean response of the bi-parametric and the mono-parametric estimations, for each approach separately. the “null hypothesis” is the equality of the means; hence, the null hypothesis is that mono and bi-parametric estimations have equal mean values. conversely, if we prove the inconsistency of the null hypothesis, we can say that the two estimations have actually different mean values and so they are substantially different. by using the anova, we make some questionable assumption; for instance, we accept that each estimation can be assumed as a random independent observation. tab. 6 gives the obtained values of the inconsistency of probability of the null hypothesis. ig sed cd 62.3% 88.9% 86.8% table 6: probability of inconsistency of the means equality obtained by the anova. such probabilities of inconsistency of the null hypothesis are usually compared with an assumed confidence probability level, conventionally 95%, sometimes 90%. each obtained value is lower than any usual confidence level; we have to conclude that, in the considered experimental data, the null hypothesis cannot be rejected. from a statistical point of view, it is not possible to state that means are actually different. from an engineering point of view, we argue that the improvement of the bi-parametric approaches compared to the mono-parametric ones is not so substantial compared to the intrinsic scatter of the problem. conclusions hree separate approaches for fatigue strength assessment of notches have been considered. for each approach, two versions have been proposed: a first one, called mono-parametric, is defined by assuming the same notch sensitivity under tensile and torsion loading. in a second version, called bi-parametric, the notch sensitivity is different by changing the loading mode and the sensitivities under tensile and torsional loading are consequently different. the obtained approaches have been tested on experimental data taken from the literature and dealing with the fatigue strength of sharp notches on a ductile cast iron. the results have been statistically investigated by means of anova too. the main evidence is that the advantage of using bi-parametric approaches is not so convenient compared to the scatter of the problem, hence the different notch sensitivity under torsional loading is not clear and it is dependent on the chosen effective stress definition. references [1] atzori, b., berto, f., lazzarin, p., quaresimin, m., multi-axial fatigue behaviour of a severely notched carbon steel, international journal of fatigue, 28 (2006) 485–493. t p. livieri, frattura ed integrità strutturale, 30 (2014) 558-568; doi: 10.3221/igf-esis.30.67 568 [2] wang, x.m., cao, w., deng, c.h., liu, h., pfetzing-micklich, j., yue, z.f., the effect of notches on the fatigue behavior in niti shape memory alloys, materials science and engineering a, 610 (2014) 188–196. [3] wan, v.v.c., maclachlan, d.w., dunne, f.p.e., a stored energy criterion for fatigue crack nucleation in polycrystals, international journal of fatigue, 68 (2014) 90-102. [4] neuber, h., uber die berucksichtigung der spannungskonzentration bei festigkeitsberechnungen. konstruktion, 20 (7) (1968) 245-251. [5] peterson, r.e., notch sensitivity, in: metal fatigue (edited by g. sines and j.l. waisman), mcgraw hill, new york, (1959) 293-306. [6] berto, f., lazzarin, p., marangon, c., fatigue strength of notched specimens made of 40crmov13.9 under multiaxial loading”, materials and design, 54 (2014) 57–66. [7] gates, n., fatemi, a., notched fatigue behavior and stress analysis under multiaxial states of stress, international journal of fatigue, 67 (2014) 2–14. [8] matsubara, g., nishio, k., multiaxial high-cycle fatigue criterion for notches and superficial small holes from considerations of crack initiation and non-propagation, international journal of fatigue, 67 (2014) 28–37. [9] chen, h., shang, d.-g., tian, y.-j., xu, g.-w, multiaxial fatigue life prediction for notched components under proportional and non-proportional cyclic loading, applied mechanics and materials, 197 (2012) 585-589. [10] susmel, l., multiaxial notch fatigue from nominal to local stress-strain quantities., cambridge, uk woodhead & crc; (2009). [11] kanazawa, k., miller, k.j., brown, m.w., low-cycle fatigue under out-of-phase loading conditions., trans asme, j eng mater. technol., (1977) 222–228. [12] [1]tovo, r., livieri, p., an implicit gradient application to fatigue of sharp notches and weldments, engineering fracture mechanics, 74(4) (2007) 515-526. [13] susmel, l., taylor, d., the theory of critical distances to estimate lifetime of notched components subjected to variable amplitude uniaxial fatigue loading, international journal of fatigue, 33(7) (2011) 900-911. [14] lazzarin, p., zambardi, r., a finite-volume-energy based approach to predict the static and fatigue behavior of components with sharp v-shaped notches, international journal of fracture, 112(3) (2001) 275-298. [15] shirani, m., härkegård, g., casting defects and fatigue behaviour of ductile cast iron for wind turbine components: a comprehensive study, materialwissenschaft-und-werkstofftechnik (2011). [16] shirani, m., härkegård, g., large scale axial fatigue testing of ductile cast iron for heavy section wind turbine components, engineering failure analysis, 18 (2011) 1496–1510. [17] roedter, h., gagne, m., ductile iron for heavy section wind mill castings a european experience., in: proceedings of the 2003 keith d. millis world symposium on ductile iron, south carolina, (2003) 11. [18] shirani, m., härkegård, g., fatigue life distribution and size effect in ductile cast iron for wind turbine components., eng fail anal, 18(1) (2011) 12-24. [19] zambrano, h. r., harkegard g., stark, k. f., fracture toughness and growth of short and long fatigue cracks in ductile cast iron en-gjs-400-18-lt , fatigue and fracture of engineering materials & structures, 35(4) (2012) 374388 [20] berto, f., lazzarin, p., tovo, r., multiaxial fatigue strength of severely notched cast iron specimens, international journal of fatigue, 67 (2014) 15–27. [21] maggiolini, e., livieri, p., tovo, r., on numerical integration for effective stress assessment at notches, frattura ed integrità strutturale, 25 (2013) 117-123; doi: 10.3221/igf-esis.25.17. [22] peerlings, r.h.j., de borst, r., brekelmans, w.a.m., de vree, j.h.p., gradient enhanced damage for quasi brittle material, international journal of numerical methods in engineering, 39 (1996) 3391–3403. [23] susmel, l., taylor, d., the theory of critical distances to estimate the static strength of notched samples of al6082 loaded in combined tension and torsion. part i material cracking behaviour, engineering fracture mechanics, 77 (2010) 452–469. [24] susmel, l., taylor, d., the theory of critical distances to predict static strength of notched brittle components subjected to mixed-mode loading, engineering fracture mechanics, 75 (2008) 534–550. [25] maggiolini, e., livieri, p., tovo, r., implicit gradient and integral average effective stresses relationships and numerical approximations, fatigue and fracture of engineering materials & structures, in press, doi: 10.1111/ffe.12216. [26] tovo, r., lazzarin, p., berto, f., cova, m., , e., experimental investigation of the multiaxial fatigue strength of ductile cast iron, theoretical and applied fracture mechanics, in press, doi: 10.1016/j.tafmec.2014.07.003. microsoft word numero 25 art 22 p. lopez-crespo et alii, frattura ed integrità strutturale, 25 (2013) 153-160; doi: 10.3221/igf-esis.25.22 153 special issue: characterization of crack tip stress field study of overload effects in bainitic steel by synchrotron x-ray diffraction p. lopez-crespo department of civil and materials engineering, university de malaga, c/dr ortiz ramos, s/n, 29071 malaga, spain p.j. withers, j. r. yates school of materials, university of manchester, grosvenor st, manchester, m13 9pl, uk a. steuwer max iv laboratory, lund university, box 118 se-221 00 lund, sweden t. buslaps esrf, 6 rue j horowitz, 38000 grenoble, france y. h. tai rolls-royce plc, po box 31, derby, de24 8bj, uk abstract. this work presents an in-situ characterisation of crack-tip strain fields following an overload by means of synchrotron x-ray diffraction. the study is made on very fine grained bainitic steel, thus allowing a very high resolution so that small changes occurring around the crack-tip were captured along the crack plane at the mid-thickness of the specimen. we have followed the crack as it grew through the overload location. once the crack-tip has progressed past the overload event there is strong evidence that the crack faces contact in the region of the overload event (though not in the immediate vicinity of the current locations of the crack tip) at kmin even when the crack has travelled 1mm beyond the overload location. it was also found that at kmax the peak tensile strain ahead of the crack-tip decreases soon after the overload is applied and then gradually recovers as the crack grows past the compressive region created by the overload. keywords. crack-tip strain field, overload effect, x-ray diffraction, bainitic steel. introduction he concept of crack closure has been used to explain many crack retardation effects in fatigue of materials. closure is associated with effects that cause the crack faces to close early during unloading so that the crack-tip does not experience the full crack-opening fatigue cycle. plasticity induced crack closure is one of the most important mechanisms of crack closure, but is still a hotly debated subject. some different researchers have suggested that closure does not occur at all [1] while others believe that it can only occur under plane stress [2]. to date, experimental measurements of crack closure have been inconclusive and have relied on either (i) measuring some secondary property of t http://www.gruppofrattura.it http://dx.medra.org/10.3221/igf-esis.25.22&auth=true p. lopez-crespo et alii, frattura ed integrità strutturale, 25 (2013) 153-160; doi: 10.3221/igf-esis.25.22 154 the cracked body such as compliance or electrical resistance or (ii) measurement of crack-opening displacements on the surface of the cracked body. third generation synchrotron x-ray facilities allow experimental measurement of the strain at the interior of the specimen. recent works have shown that it is possible to map in 2d the strain fields around the crack tip [3-5]. however, our highest spatial resolution measurements (25m) were made on a very fine grained al-li alloy, with low fracture toughness such that the plastic zone was very small. nevertheless it was possible to extract accurate measures of the crack tip stress intensity factor at minimum, maximum and overload stresses, kmin, kmax and kol. more recent experiments allowed the measurement of crack-tip strains under plane stress conditions with characteristically larger plastic zones [6, 7]. overload events were studied, both at the surface via digital image correlation and in the interior, via synchrotron x-ray diffraction. however, the large grain size (~50m) did not allow sufficiently high resolution strain mapping to resolve the changes occurring immediately local to the crack-tip. the current work aims to examine the effect of overload in a bainitic material having large plastic-zone and very fine grain size, thus achieving excellent resolution in mapping the strain fields around the plastic one of a crack-tip. material and specimen compact tension (ct) fatigue specimen was machined from quenched and tempered steel similar to q1n (hy80) [8]. its chemical composition is summarised in tab. 1. the tensile properties are as follows: yield stress = 570 mpa and ultimate tensile stress = 663 mpa. the ct specimen had a width (w) of 60 mm and thickness (b) of 12 mm. the steel has an acicular microstructure as shown in fig. 1 with an approximate grain size of 5 µm. alloy c si mn p s cr ni mo cu q1n 0.16 0.25 0.31 0.010 0.008 1.42 2.71 0.41 0.10 table 1: chemical composition in weight % of q1n steel. the balance is fe. figure 1: optical micrograph of the bainitic steel used in the current work. the micrograph was obtained at 1000x magnification. x-ray diffraction experimental setup he crack-tip elastic strain fields were measured on the id15 beamline at the european synchrotron radiation facility (esrf), using the same arrangement as that described in [4] shown schematically in fig. 2. the incident beam slits were opened to 60 × 60 µm giving a lateral resolution (x,y) of 60�m and a nominal gauge length a t http://www.gruppofrattura.it http://dx.medra.org/10.3221/igf-esis.25.22&auth=true p. lopez-crespo et alii, frattura ed integrità strutturale, 25 (2013) 153-160; doi: 10.3221/igf-esis.25.22 155 through-thickness (z) of around 1.4 mm. this allowed a 10 times greater resolution than in previous plastic zone mapping experiments [7]. such a good resolution was possible because of the very small grain size of the bainitic steel used here. figure 2: schematic of the diffraction geometry showing a ct specimen with the crack plane horizontal, and the two detectors measuring two directions of strain; note the coordinate system for εxx and εyy adopted after [4]. for very low  these strains can be taken as representative of those in the loading (y) and crack growth (x) directions. fatigue experiment he specimen was fatigue pre-cracked for 43000 cycles at a frequency of 10hz, stress intensity range δk = 28 mpa√m and load ratio kmin/kmax = 0.05. plane strain conditions were met at the mid plane through the thickness for all loads applied during the experiment [9]. the crack length was measured perpendicularly to the loading direction from the centre of the loading holes [10]. once the fatigue crack had grown to a length of 12.75 mm, a 100% overload (ol) was applied. strain measurements were made at a number of fatigue stages, namely during the cycle just before the overload (ol-1), during the overload (ol), and for the cycles just after the overload (ol+1), 20 cycles after the overload (ol+20), 1000 cycles after the overload (ol+1000), 11000 cycles after the overload (ol+11000) and 21000 cycles after the overload (ol+21000). by measuring around 50 strain points along the crack plane (y=0), a profile of the strain evolution behind and ahead of the crack-tip was produced for each of the fatigue stages studied. results and discussion he traditional crack closure approach defines a nominal stress intensity factor at which the crack faces touch represented by kcl. this is often identified by a knee in the crack compliance during unloading from kmax, as recorded by a back-face strain gauge, for example [11]. to investigate the manner in which the crack-tip strain field varies with unloading a series of measurements were made during an unloading cycle (kmax, 0.7kmax, 0.2kmax, kmin) and the results are shown in fig. 3. from these measurements it is clear that the reverse plastic zone has started to develop by the time 0.2kmax has been reached. indeed the reverse plastic zone appears to increase only marginally with further unloading to kmin although the peak tensile stress ahead of the crack at the edge of the plastic zone continues to fall to a value of around 400x10-6 at kmin. t t http://www.gruppofrattura.it http://dx.medra.org/10.3221/igf-esis.25.22&auth=true p. lopez-crespo et alii, frattura ed integrità strutturale, 25 (2013) 153-160; doi: 10.3221/igf-esis.25.22 156 figure 3: the variation in the crack opening elastic strain measured mid-thickness (z=0) along the crack plane (y=0) as the samples was unloaded from kmax to kmin at ol-1. fig. 4 shows the evolution in the strain field in the crack opening direction along the crack plane at mid-thickness both at maximum and minimum loading as the sample undergoes the overload event and then as the crack grows through the plastic zone created by the overload event. it is clear that the crack growth is very small after 20 and 1000 cycles. after 10,000 additional cycles the crack has progressed around 300m while after an additional 20,000 cycles the crack has progressed 1070m beyond the overload event. it should be noted that during the loading event the ct sample moves slightly in response to the applied load, however we have tried to correct for movement in both the crack growth direction (x) and perpendicular to it (y). it is interesting to note that the compressive regions near the crack tip are not so sharp, or deep for the baseline fatigue response (ol-1) or immediately after overload (ol) as compared to those after 20 or 1000 additional fatigue cycles, although this could be due to the fact that the linescan has missed the peak value in the 2d (x,y) strain field. closer comparison of the shapes and magnitudes of the strains local to the crack-tip can be obtained by examination of figs. 5a) and b). these show the strain evolution for the maximum and minimum loads respectively shifted so that each curve has the current position of the crack-tip (defined as the point of zero strain at kmax) coincident with the others. it is clear from these curves that the peak tensile strain at kmax falls immediately after overload and this rises towards the baseline fatigue level as the crack advances. this is in agreement with our previous paper on austenitic steel [12]. there it was shown that this is due to the compressive residual stress in the near crack tip zone after overload through which the crack must grow. that this is due to the effect of climbing out of the compressive residually stressed zone is confirmed by the fact that when the difference in strain between kmax and kmin is plotted in fig. 6 the elastic stress changes each cycle are almost identical for ol-1, ol+20 and ol+1000. it is clear from fig 5a that considerable plastic deformation has been induced in the crack-tip region by the overload event since the tensile peak at overload (ol) is only slightly higher than prior to overload (ol-1) but the tensile region is broader. fig. 5b) shows the curves at minimum load relative to the position of the crack tip at that instant. the fact that for most of the points behind the crack the strains lie slightly below zero (~-400x10-6) might be suggestive of a slight error in the strain free lattice spacing as one would certainly expect there to be no contact at kmax (fig. 5a) across the crack faces yet the strains are similarly compressive. however, it should be noted that towards the back face the strains do appear to approach zero suggesting that we do indeed have a representative value. alternatively it could be that the stress is zero across the crack, but the strain is not. crack face closure forces would be evident as compressive strains behind the cracktip, while compressive residual stresses arising from the plastic zone would lie ahead of the current crack-tip position. http://www.gruppofrattura.it http://dx.medra.org/10.3221/igf-esis.25.22&auth=true p. lopez-crespo et alii, frattura ed integrità strutturale, 25 (2013) 153-160; doi: 10.3221/igf-esis.25.22 157 figure 4: strain evolution at mid-thickness (z=0) along the crack plane (y=0) for all fatigue stages analysed. kmax data is represented by the solid line and kmin data by the broken line. ol-1 ol ol+20 ol+1000 ol+11000 ol+21000 http://www.gruppofrattura.it http://dx.medra.org/10.3221/igf-esis.25.22&auth=true p. lopez-crespo et alii, frattura ed integrità strutturale, 25 (2013) 153-160; doi: 10.3221/igf-esis.25.22 158 careful examination of fig. 5b would appear to show a compressive trough centred on the crack position for ol-1. similarly the overload event is accompanied by a compressive strain dip on either side of the crack-tip location. by contrast for a low numbers of cycles (ol+20 and ol+1000) the compressive stress at kmin appears to be sharper and associated only with plasticity ahead of the crack tip. this may be because of in the absence of crack face contact the crack is no longer wedged open allowing a larger compressive zone in the plastic zone to develop. while great care was taken to ensure that the crack tip was lying exactly on the line of the scan, 2d maps are currently being acquired [13] to find out whether this effect is instead merely due to scanning slightly off the line of the compressive maximum with some of the linescans. with further cycling and crack growth (ol+11000 & ol+21000) fig. 5b appears to show a distinct compressive contact stress in the region of the overload cycle. this compressive stress in the region of the overload at kmin is even more clearly evident in fig. 6 as positive peaks in the kmax-kmin curves for ol+10000 and ol+21000 at the location of the plastic zone generated by the overload. (a) (b) figure 5: strain evolution mid-thickness along the crack plane at a) kmax and b) kmin for all the stages of fatigue crack growth analysed. the coordinate along the crack plane (horizontal axis) has been corrected so that the crack-tip position coincides for all cases. figure 6: plots showing the change in elastic strain between kmax and kmin as a function of number of cycles. the arrow shows the location of the extensive plastic deformation from the overload event. it is also noteworthy that for all the crack locations the tensile peak ahead of the crack at kmin is approximately constant (~500x10-6) and located around 400-500m ahead of the crack (fig. 5b). http://www.gruppofrattura.it http://dx.medra.org/10.3221/igf-esis.25.22&auth=true p. lopez-crespo et alii, frattura ed integrità strutturale, 25 (2013) 153-160; doi: 10.3221/igf-esis.25.22 159 conclusions sing very high spatial resolution (60m laterally) we have been able to explore the crack opening elastic strains in the vicinity of a fatigue crack before and after an overload event. we have followed the crack until it is 1mm beyond the overload location. it is clear that the peak tensile strain drops dramatically and slowly recovers as the fatigue crack works its way through the compressively stressed plastic zone caused by the overload event. that this is an elastic effect is demonstrated by the similarity of the elastic strain changes before and just after overload between kmax and kmin. by superimposing the crack tip strain fields for the crack tip at different stages of growth there is a suggestion that for baseline fatigue there is both a compressive stress just ahead of the crack due to plasticity and behind the crack due to crack face closure. there is no evidence of the later after a small number of cycles in agreement with surface digital image correlation measurements that indicate no closure in this regime. once the crack-tip has progressed significantly past the overload event there is strong evidence that the crack faces contact in the region of the overload event (though not in the immediate vicinity of the current locations of the crack tip) even when the crack has travelled 1mm beyond the overload location. of course it is extremely difficult to scan a 60m beam along the crack plane, experiments are now being undertaken to provide full 2d maps of the crack tip stress field to provide more definitive evidence. acknowledgements e acknowledge esrf for the use of facilities and the epsrc for funding through grant ep/f028431/1.  references [1] sadananda, k., vasudevan, a.k., holtz, r.l., lee, e.u., analysis of overload effects and related phenomena. international journal of fatigue, 21 (1999) s233-s246. [2] alizadeh, h., hills, d.a., de-matos, p.f.p., nowell, d., pavier, m.j., paynter, r.j., smith, d.j., simandjuntak, s., a comparison of two and three-dimensional analyses of fatigue crack closure, international journal of fatigue29 (2007) 222-231. [3] steuwer, a., edwards, l., pratihar, s., ganguly, s., peel, m, fitzpatrick, m.e., marrow, t.j., withers, p.j., sinclair, i., singh, k.d., gao, n., buslaps, t., buffière, j.-y., in situ analysis of cracks in structural materials using synchrotron x-ray tomography and diffraction, nuclear instruments and methods in physics research, b 246 (2006) 217-225. [4] steuwer, a., rahman, m., shterenlikht, a., fitzpatrick, m.e., edwards, l., withers, p.j., the evolution of crack-tip stresses during a fatigue overload event, acta materialia, 58 (2010) 4039-4052. [5] croft, m., shukla, v., jisrawi, n.m., zhong z., sadangi, r.k., holtz, r.l., pao, p.s., horvath, k., sadananda, k., ignatov, a., skaritka, j., tsakalakos, t., mapping and load response of overload strain fields: synchrotron x-ray measurements. international journal of fatigue, 31 (2009) 1669–1677. [6] kelleher, j.f., lopez-crespo, p., yusof, f., withers, p.j., the use of diffraction to study fatigue crack tip mechanics. materials science forum, 652 (2010) 216-221. [7] lopez-crespo, p., withers, p.j., yusof, f., dai, h., steuwer, a., kelleher, j.f., buslaps, t., overload effects on fatigue crack-tip fields under plane stress conditions: surface and bulk analysis, fatigue and fracture of engineering materials and structures, 36 (2013)75-84. [8] robertson, i.m., measurement of the effects of stress ratio and changes of stress ratio on fatigue crack growth rate in a quenched and tempered steel. international journal of fatigue, 16 (1994) 216-220. [9] anderson, t.l., fracture mechanics, fundamentals and applications, (2005). [10] murakami, y., stress intensity factors handbook. oxford: pergamon press, (1987). [11] stoychev, s., kujawski, d., methods for crack opening load and crack tip shielding determination: a review. fatigue and fracture of engineering materials and structures, 26 (2003) 1053-1067. u w http://www.gruppofrattura.it http://dx.medra.org/10.3221/igf-esis.25.22&auth=true p. lopez-crespo et alii, frattura ed integrità strutturale, 25 (2013) 153-160; doi: 10.3221/igf-esis.25.22 160 [12] lopez-crespo, p., withers, p.j., yusof, f., dai, h., steuwer, a., kelleher, j.f., buslaps, t., overload effects on fatigue crack-tip fields under plane stress conditions: surface and bulk analysis, fatigue and fracture of engineering materials and structures, (2013) 75-84. [13] withers, p.j., lopez-crespo, p., steuwer, a., buslaps, t., why do fatigue cracks slow after overload under plane strain? ma-1483 european synchrotron radiation facility internal report (2012). http://www.gruppofrattura.it http://dx.medra.org/10.3221/igf-esis.25.22&auth=true shot peening processes to obtain nanocrystalline surfaces in metal alloys: s.c. li et alii, frattura ed integrità strutturale, 47 (2019) 1-16; doi: 10.3221/igf-esis.47.01 1 numerical simulation method study of rock fracture based on strain energy density theory shuchen li, tengfei ma, luchen zhang, qian sun geotechnical and structural engineering research center, shandong university, jinan, shandong 250061, china 316159025@qq.com abstract. many numerical methods are carried out to study the nonlinear failure behaviors of the rock; however, the numerical simulation methods for the failed rock are still in the research stage. this paper establishes the damage constitutive equation by combining the bilinear strain softening constitutive model with energy dissipation principles, as well as the energy failure criterion of mesoscopic elements based on the strain energy density theory. when the strain energy stored by an element exceeds a fixed value, the element enters the damage state and the damage degree increases with increasing energy dissipation. simultaneously, the material properties of the damaged element change until it becomes an element with certain residual strength. as the load increases, the damage degree of an element increases. when the strain energy stored by an element exceeds the established value of the energy criterion, the element is defined to be failed. as the number of failed elements constantly increases, failed elements interconnect and form macrocracks. the rock fracture calculation program on the basis of the preceding algorithm is successfully applied to the fracture simulation process in brazilian splitting, tensile tests with build-in crack and tunnel excavation. keywords. strain energy density; energy dissipation; rock fracture; flac; numerical simulation; bilinear softening citation: li s.c., ma, t.f., zhang, l.c., sun, q., study on numerical simulation method based on strain energy density theory of rock fracture, frattura ed integrità strutturale, 47 (2019) 1-16. received: 22.07.2018 accepted: 24.11.2018 published: 01.01.2019 copyright: © 2019 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. introduction s a product of geological movements, the rock is a heterogeneous material with complex mechanical properties. the rock medium usually shows strong nonlinear characteristics [1] in the deformation process. physical and mechanical properties will be irreversible during the failure process, and this irreversible process will cause various forms of energy dissipation. according to the law of thermodynamics, energy conversion is the essential feature during the material physical process, and material failure is a kind of instability driven by energy. therefore, studying the energy change rules and establishing the relation between energy changes and strength as well as structural failure during the rock a http://www.gruppofrattura.it/va/47/2136.mp4 s.c. li et alii, frattura ed integrità strutturale, 47 (2019) 1-16; doi: 10.3221/igf-esis.47.01 2 failure process will be more conducive to reflecting strength changes and essential characteristics [2] of structural failure of the rock under the action of external load. since huber firstly introduced the potential energy concept to define material damage, many scholars at home and abroad have described rock deformation behaviors through energy analysis and achieved tremendous progress [3-8]. most work focused on tests and theoretical research and macroscopic failure behaviors of the rock were obtained through energy analysis. according to their studies, material failures are mainly caused by irreversible internal energy dissipation; meanwhile, the energy criterion is generally significant for determining the rock failure. the rock fracture is an entire process from damage, material progressive degradation, microcrack generation, expansion, and till penetration. therefore, studying rock fracture from the micromechanics perspective, analyzing the damage rules of tiny rock elements, and studying element failure through element energy dissipation and energy criterion can systematically show the entire rock fracture process. currently, the most representative strain energy failure criterion is distortional strain energy density theory (fourth strength theory) [9]. this is a better strength theory for plastic materials; however, it is applicable only to plastic materials with the same tension and compression properties rather than triaxial equivalent tension. therefore, besides the distortional strain energy, the volume deformation energy also needs to be considered [10]. the application of strain energy density theory [11] can comprehensively consider the preceding problems and take the strain energy density that is the sum of the volume deformation energy density and shape change energy density as the criterion of material failure. the advantage of this theory is that it can be well applied to complex geometry, loading conditions, and development situations of mixed cracks [12]. according to the preceding analysis, nonlinear failure behaviors of the rock are considered to simulate the rock partial failure and the entire process from microcrack generation, expansion, and complete fracture. in addition, the bilinear strain softening constitutive model is adopted by referring to document [13], and the energy criteria for the damage and failure of mesoscopic rock elements according to the strain energy density theory and energy dissipation principle. when the strain energy stored by an element exceeds a fixed value, the element enters the damage status. the damage degree of the element is determined based on the strain energy density and the material properties of the damaged element change until it becomes an element with certain residual strength. for rock elements entering the damage state, the energy failure criterion of strain energy density is used to determine whether the element is damaged. as the load increases, the number of failed elements gradually grows, and the failed elements interconnect and form macrocracks, causing the structural failure of the rock specimen. during the numerical simulation process, the elastic modulus reduction of damaged elements after reaching the stress extreme value is discretized. the preceding method completes the nonlinear calculation process with linear calculation, avoids singularity of numerical calculation in element fracture, and simulates the rock post-peak fracture behaviors. in this calculation method, the rock fracture calculation program is developed with fish language in the flac. it is successfully applied to the fracture simulation process in brazilian splitting, tensile tests with build-in crack and tunnel excavation, indicating the accuracy and feasibility of this method for simulating the rock fracture process. strain energy density theory he rock fracture mode is affected by many factors such as the loading type, geometry, and material properties. however, the strain energy density theory can comprehensively consider these factors. the rock is assumed to be a continuum composed of many tiny structural elements and each element contains per unit volume of the material. if the element deforms under the action of external force, strain energy will be stored inside the element. in this way, the energy stored by each element is called strain energy density ( / )dw dv . the strain energy density equation can be expressed as follows: 0 ( , ) ij ij ij dw d f t c dv   = +   (1) ij and ij are stress and strain components. t and c are the temperature and humidity variations, in general, when the temperature and humidity are basically constant, this part is negligible. so the strain energy density equation can be expressed as 0 / ij ij ijdw dv d   =  simply. for linear elastic loaded objects, the elastic strain energy is equal to the work done by the external force, and the strain energy stored in the material element depends only on the final value of the external force and the deformation, but has t s.c. li et alii, frattura ed integrità strutturale, 47 (2019) 1-16; doi: 10.3221/igf-esis.47.01 3 nothing to do with the loading sequence. therefore, in the case of linear elasticity, the relationship between each principal stress and the corresponding principal strain remains linear, so the strain energy density of the triaxial stress-state is as follows: 1 1 2 2 3 3 1 ( ) 2 dw dv      = + + (2) according to the general hooke's law: 1 1 2 3 2 2 3 1 3 3 1 2 1 [ ( )] 1 [ ( )] 1 [ ( )] v e v e v e              = − +    = − +   = − +  (3) substituting formula (3) into formula (2), we can get it: 2 2 2 1 2 3 1 2 2 3 3 1 1 [ 2 ( )] 2 dw dv e          = + + − + + (4) according to mohr stress circle theory of space state, the stress components on each surface are substituted into formula (4), in the case of linear elasticity, the general expression of strain energy density equation is as follows: 2 2 2 2 2 21 1 ( ) ( ) ( ) 2 x y z x y y z z x xy yz zx dw dv e e e               + = + + − + + + + + (5) therefore, in the case of plane stress state, the elastic strain energy density equation of the element body is expressed as follows: 2 2 21 1 ( ) 2 x y x y xy dw dv e e e        + = + − + (6) considering the stress-strain curves of materials under tensile conditions, as shown in the fig. 1, assuming that the stress continues to increase after reaching the yield stress y , plastic deformation occurs. if unloading at point p, the unloading path will be along line pm, and the new loading path will be along line mpf. in the process of unloading and reloading, energy represented by area oapm= ( / ) pdw dv is dissipated. therefore, the effective energy for crack propagation * ( / ) c dw dv can be expressed in oapm, or as the formula shows: * c c p dw dw dw dv dv dv       = −            (7) this formula represents the total energy required for unit volume when the material unit element fails. strain energy density theory is a good failure criterion for predicting nonlinear damage phenomena. the failure of materials is generally the process of stable crack development until the global instability of the structure. stable crack growth is a local or microstructural instability that can be predicted by the critical strain energy density ( / )cdw dv , the value can be obtained from the area under the complete stress-strain curve. no matter what stress the element bears, such as tension, compression, or shear stress, the strain energy density can comprehensively reflect the action of each stress component on the element. each element can store limited strain energy s.c. li et alii, frattura ed integrità strutturale, 47 (2019) 1-16; doi: 10.3221/igf-esis.47.01 4 at a specified time and the strain energy stored by the element varies with different parts of the material. therefore, the damage mode of the material can be evaluated based on the energy change process of the material from one element to another. figure 1: dissipative strain energy and recoverable strain energy under tensile condition determination of the strain energy density function considering strain softening according to the strain energy density theory, the strain energy density function of each element in the constant humidity and temperature condition can be expressed as: 0 ij ij ij dw d dv   =  (8) according to the preceding formula, the density of strain energy stored in an element is determined by its stress ij and the deformation history of strain increment ijd . this theory determines the yield failure of the material element based on strain energy density ( / )dw dv . limit value of strain energy density for failure of unit element, is determined by yielding test in uniaxial tension, and stipulate that, the total strain energy absorbed by the unit is equal to the energy absorbed ( / )cdw dv at fracture under uniaxial tension, the unit will yield failure. according to this theory, before the rock texture shows global instability under the action of load, partial failure and crack propagation already occur and seriously affect the macroscopic failure behaviors of the rock texture. the steady propagation of microcracks inside the rock will finally cause rock macroscopic fracture. the deformation process of each rock element is accompanied with energy dissipation that will cause material progressive damage, property deterioration, and strength loss [2]. the material mechanical damage can be described by strain softening. the bilinear strain softening constitutive model of the rock under uniaxial tension in document [13] is considered, that is, the uniaxial tension stress-strain relation of the rock is simplified, as shown in fig. 2. under the action of external force, the rock first shows elastic deformation and does not fail immediately after reaching the stress limit point u. instead, it enters the strain softening stage and the material starts to damage. as shown in the fig. 2, the density ( / )dw dv of strain energy absorbed by the material element at point a is area ouac surrounded by the stress-strain curve. if the element is unloaded at point a, the unloading path will be along line ab and the new loading path will be along line baf. in the process of unloading and reloading, energy represented by area ouab is dissipated. therefore, the density of strain energy absorbed by the material element is composed of the following two parts: ( ) ( )d e dw dw dw dv dv dv = + (9) in the preceding formula, ( / )ddw dv is the density of strain energy dissipated ouab while ( / )edw dv is the density of strain energy recoverable bac. strain a p f o m e f’ p dv dw       * c dv dw       y  stress s.c. li et alii, frattura ed integrità strutturale, 47 (2019) 1-16; doi: 10.3221/igf-esis.47.01 5 figure 2: bilinear strain softening stress-strain curve if point a is on line ou in the elastic stage, the unloading path will be along the loading path and the material will not damage. for the material element without damage, its critical strain energy density ( / )cdw dv is equal to area ouf. however, energy dissipation occurs after the material element damages. the residual critical strain energy density after damage *( / )cdw dv is the density of strain energy regained after the element is unloaded (that is area baf) and can be expressed as the following: * ( ) ( ) ( )c c d dw dw dw dv dv dv = − (10) the preceding formula indicates that a higher density of strain energy dissipated by the material element means more serious element damage and lower density of critical strain energy that can be borne. according to the preceding analysis, larger deformation of the material element under the action of external force means a higher density of strain energy absorbed ( / )dw dv and lower density of critical strain energy *( / )cdw dv . when * ( / ) ( / )cdw dv dw dv , cracks start to be generated. when ( / )dw dv is equal to the initial critical strain energy density ( / )cdw dv (that is, area ouf) of the material element, the element is completely fractured and cannot bear any load. the bilinear constitutive relation of the preceding rock element can be simply obtained through uniaxial tensile tests. the rock texture is usually under the action of complex external force and the internal rock elements are under the combined action of tension, compression, and shear stress. the strain energy density can be obtained based on the loading history of the rock element and it can comprehensively reflect the loading status of the element. the damage status of the rock element under complex stress conditions can be determined by comparing it with the strain energy density in different stages under uniaxial tension. energy dissipation and damage constitutive model according to energy opinions, after the rock shows inelastic deformation, the inelastic deformation energy the rock can bear has been significantly reduced, that is, the rock constitutive energy has decreased. this is also an expression of rock performance deterioration caused by the changes of rock microstructure [15]. after the rock element reaches the peak point of the tensile stress, it enters the strain softening stage and shows inelastic deformation and decreased material strength. the strength decrease of the material element is defined as the elastic modulus reduction and is expressed by equivalent elastic modulus *e . as shown in fig. 3, as the energy loses, the unloading peak strength decreases from point u to points g, h, i ... and the equivalent elastic modulus is * 1e , * 2e , * 3e , …and * ne respectively. for the sake of calculation, the equivalent elastic modulus is discretized into 20 different values: * ( 21 ) ( ) 20 n e n e − = (11) n=1, 2, ..., 20 s.c. li et alii, frattura ed integrità strutturale, 47 (2019) 1-16; doi: 10.3221/igf-esis.47.01 6 the following can be obtained according to the constitutive relation of continuous medium damage mechanics theory [16]: (1 )e d = − (12) e is the elastic modulus of the rock without damage. the damage parameter d of the rock element in this model is: * ( )e e n d e − = (13) figure 3: reduction of elastic modulus after energy dissipation n refers to the damage degree of the material element. for the discretization of the equivalent elastic modulus, a larger value of n means more accurate simulation results but remarkably lower calculation efficiency. n is set to 20 by taking both factors into consideration, which meets related requirements. according to the energy dissipation principle, energy dissipation is directly related to the damage and strength loss. the dissipation quantity reflects the reduction of the initial strength [2]. according to fig. 2 and formula (9), both the strain energy density and the energy dissipation increase after the rock element reaches the stress limit point. therefore, the strain energy density is used as the criterion to determine the rock element damage and failure. (1) when ( / ) ( / ) 1/ 2( )u u udw dv dw dv   = , the material element is in the elastic stage; no damage occurs; both the equivalent elastic modulus and critical strain energy density are the initial values of the element, that is, *e e= , * ( / ) ( / ) 1/ 2( )c c u fdw dv dw dv  = = . (2) when ( / ) ( / )udw dv dw dv= , the material element enters the damage stage. the discretized equivalent elastic modulus * ( )e n is regarded as the elastic modulus of the material element after damage. n refers to the damage degree of the material element ( 0 20)n  ) and its value is determined by the strain energy density. it also can be seen from fig. 2 that the critical strain energy density *( / )cdw dv decreases with increasing ( / )dw dv after the material element enters the damage stage. (3) when *( / ) ( / )cdw dv dw dv= , the element fails, marking the beginning of crack generation inside the material. (4) when ( / ) ( / ) 1/ 2( )c u fdw dv dw dv  = = , according to formula (13), the damage degree of the material element reaches the largest (n = 20); both the equivalent elastic modulus and critical strain energy density of the element change to zero; the element is completely fractured and loses the bearing capacity. to maintain the integrity of the entire structure calculation model and element continuity, the element completely fractured will be given a very small residual modulus * 0.05ce e= instead of removing the element. strain 1 * e 2 * e 3 * e u g h i ne * f stress s.c. li et alii, frattura ed integrità strutturale, 47 (2019) 1-16; doi: 10.3221/igf-esis.47.01 7 numerical implementation the flac2d finite difference numerical software is adopted to establish the rock element damage equation based on the preceding theory and develop a rock fracture calculation program with fish language. model loading adopts the load control stepwise loading method. in particular, equivalent tiny loads are accumulatively added to the model in turn. after calculation is balanced, the strain energy density of each element is calculated. then, the preceding strain energy density criterion is used to determine the element damage degree and failure. after the first loading step is performed, all elements are in the elastic stage due to the small load and the strain energy density of each element is: 2 2 2 21 [ 2 2 ( )] 2 x y xy x y xy dw v dv e      = + + − − (14) after loading step i is performed, the strain energy density of each element is: 1 1 ( 1) ( 1) 1 1 1 1 1 ( ) ( ) ( ) ( ) ( )( ) 2 1 1 ( )( ) ( )( ) 2 2 i i i i i i i x x x x i i i i i i i i y y y y xy xy xy xy dw dw dw dw dv dv dv dv             − − − − − − − − = +  = + + − + + − + + − (15) in the formula, i≥2 i x , i y , and i xy are the element stress in loading step i while 1i x − , 1i y − , and 1i xy − are the element stress in the last loading step. similarly, the strain has the same expression way. when the strain energy density of an element ( / ) ( / ) 1/ 2( )u u udw dv dw dv   = , the damage degree n is: ( / ) ( / ) 2( / ) 20 1 [ ( / ) ( / ) ] 20 u u u u f u u c u dw dv dw dv dw dv n dw dv dw dv       − − = = − − (16) n is set to the integer part of the calculation results on the right of the equation and ranges from 0 to 20. when 0n = , the element is still in the linear elastic stage and no damage occurs; when 20n = , the damage value is the maximum, indicating that the element is completely fractured and loses the bearing capacity. meanwhile, the element elastic modulus * e is obtained by using formula (11). the density of strain energy dissipated by the element is: 2 2 2 2 * 1 ( / ) ( / ) [ 2 2 ( )] 2 d x y xy x y xydw dv dw dv v e      = − + + − − (17) therefore, the critical strain energy density of the element is: * 2 2 2 2 * 1 ( / ) ( / ) ( / ) ( / ) 2 1 [ 2 2 ( )] 2 c c d u f x y xy x y xy dw dv dw dv dw dv dw dv v e         = − = − + + + − − (18) fig. 4 shows the calculation process of the damage constitutive calculation model based on strain energy density. s.c. li et alii, frattura ed integrità strutturale, 47 (2019) 1-16; doi: 10.3221/igf-esis.47.01 8 figure 4: numerical simulation flow of rock failure based on strain energy density theory numerical simulation of rock fracture brazilian splitting numerical simulation his case takes the brazilian splitting with lateral concentrated load in document [17] as an example. fig. 5 shows the calculation model. the disk diameter is 50mm and it is divided into 7860 elements. the model material adopts the marble in document [17] with the elastic modulus 66.8e gpa= , poisson's ratio 0.33v = , density 3 2620 /kg m = t no , yes/no mark element failure. no no no yes yes yes yes , yes/no give residual modulus to the element. does stepwise loading end? end calculation. start calculation. input model parameters. impose load and balance flac program calculation. , yes/no calculate the element damage degree n and reduce modulus accordingly. calculate the strain energy density of each element. s.c. li et alii, frattura ed integrità strutturale, 47 (2019) 1-16; doi: 10.3221/igf-esis.47.01 9 , element tension ultimate stress 20u mpa = , strain under ultimate stress 5 1.3 10u − =  , and strain when fracture occurs 4 1 10f − =  . the model top and bottom are imposed with load increased by 2kn in the negative y direction and positive y direction respectively. figure 5: numerical calculation model of brazil splitting after the first 2kn load is imposed, no damage occurs inside the disk; each element is in the linear elastic stage; fig. 5 shows the distribution of the stress inside the brazilian disk. the results of comparison of distribution rules and theoretical results of stress distribution inside the disk in document [17] show that the simulated stress distribution rules basically agree well with the theoretical distribution. simulated distribution theoretical distribution yy xx xy figure 6: comparison between theoretical and numerical results of stress distribution in brazil disc s.c. li et alii, frattura ed integrità strutturale, 47 (2019) 1-16; doi: 10.3221/igf-esis.47.01 10 as the load increases, the strain energy absorbed by each element gradually increases. the energy change process of elements in the middle of the disk top is recorded, as shown in fig. 6. the strain energy density absorbed by the element ( / )dw dv gradually increases from zero while the critical strain energy density *( / )cdw dv gradually decreases from ( / ) 1000cdw dv = . when they two intersect, the element fails. figure 7: curve of element strain energy density versus load change. it can be seen from fig. 7 that when calculation reaches the 7th loading step, that is, 14kn load is imposed, elements in the middle of the disk top have *( / ) ( / )cdw dv dw dv , indicating that elements at both ends of the disk start to fail. when calculation reaches the 15th loading step, that is, 30kn load is imposed, partial damage at both ends is suddenly developed into complete penetration in the middle of the specimen; meanwhile, there are partial failure areas on both ends of the disk. fig. 8 shows the failure of the specimen when it is loaded to loading step 7, 12, 14, and 15. step 7 step 12 step 14 step 15 figure 8: element failure process of brazil splitting under different loading steps fig. 9 shows the damage status of each element when the specimen fails. the damage value n is expressed by the built-in variable ex_5 of the element and ranges from 1 to 20. it can be seen from the damage cloud chart of the element that the damage value of each element at the penetration point in the middle of the disk reaches the maximum value 20, indicating that elements in the middle of the disk are completely fractured and lose the bearing capacity. elements on both ends of s.c. li et alii, frattura ed integrità strutturale, 47 (2019) 1-16; doi: 10.3221/igf-esis.47.01 11 the disk except a small number of elements are completely fractured, and surrounding elements also show different levels of damage. figure 9: element damage status in brazilian disc in numerical calculation documents [18-20] all conducted experimental studies on brazilian disk imposed with lateral load. the results show that both ends of the disk firstly fail due to the stress concentration caused at the loading point during the splitting process of the brittle rock. as the load continues to increase, penetration occurs in the middle of the disk and the failure pie section appears on the loading points at both ends of the disk. fig. 10 shows the sketch of splitting failure of the marble under different stepping bars in document [18]. comparison of fig. 8 and fig. 10 shows that simulated results of numerical calculation in this paper agree well with test results in the document, indicating the feasibility of this method for simulating the rock fracture. figure 10: test results of brazilian splitting for marble in document [18] numerical simulation of tensile test with built-in crack this case takes the tensile test with built-in crack in document [21] as an example. fig. 11 shows the calculation model. the specimen size is 50 100mm mm ; the length of the built-in crack is 20mm ; the specimen is divided into 9772 elements. the specimen material adopts the rock mortar with the elastic modulus 5.17e gpa= , poisson's ratio 0.192v = , density 32300 /kg m = , element ultimate tensile stress 2.7u mpa = , strain under ultimate stress 4 5.8 10u − =  , and strain when fracture occurs 4 7 10f − =  . the model top and bottom are imposed with uniform tensile load increased by 100n respectively. figure 11: numerical calculation model of uniaxial tensile test with built-in crack. s.c. li et alii, frattura ed integrità strutturale, 47 (2019) 1-16; doi: 10.3221/igf-esis.47.01 12 the following calculation results are obtained: under the action of tensile load, stress concentration occurs on the crack tip; elements at both ends of the crack start to fail when calculation reaches the fourth loading step, that is, 400n load. fig. 12 shows the strain energy density of the first element at the left end of the crack with changing load. figure 12: curve of element strain energy density versus load change when calculation reaches the fifth loading step, that is, 500n load, penetration occurs in the middle of the specimen in the crack direction. fig. 13 shows the failure status of the model when calculation reaches loading steps 4 and 5. step 4 step 5 figure 13: element failure process of uniaxial tensile test under different loading steps fig. 14 shows the damage status of each element when the specimen fails. it can be seen from the damage cloud chart of the element that each element surrounding the crack tip shows different levels of damage due to stress concentration and that the damage value of a series of elements from both ends of the crack to the model edge reaches 20, indicating that the specimen is completely fractured along the cross section of the crack. figure 14: element damage status in tensile test with built-in crack s.c. li et alii, frattura ed integrità strutturale, 47 (2019) 1-16; doi: 10.3221/igf-esis.47.01 13 document [21] conducted uniaxial tensile tests on mortar materials with different prefabricated crack dips on the rigidity servo testing machine. the test results show that when the tensile stress reaches a specific value, the prefabricated crack starts to initiate and then rapidly expands, causing the structural failure of the specimen. when the crack is horizontal (that is, crack dip 90 = ), wing crack is generated at the front edge of the crack and expanded in the direction of the original crack until the specimen is fractured. finally, the fracture trace is perpendicular to the axial tensile stress direction and the fracture surface is flat. fig. 15 shows the tensile failure of horizontal crack in document [21]. comparison of fig. 13 and fig. 15 shows that the simulated failure process and damage status in the built-in crack tensile tests of numerical calculation in this paper basically agrees with test results, indicating the accuracy and feasibility of this method in this paper for simulating the rock fracture. figure 15: test results of uniaxial tensile test in document [21] numerical simulation of tunnel excavation this case takes liangshui tunnel of lanzhou-chongqing line as an example to simulate the overloading process of its similar model test. the horizontal direction of tunnel cross-section is x-axis, the vertical direction is y-axis, and the excavation direction is z-axis. the calculation range is as follows: 60 60x m−   ; 67.5 52.5y m−   ; the thickness of z direction is 1m. the buried depth of the tunnel is 200 m and the lateral pressure coefficient is 0.54. the material parameters of surrounding rock are as follows: 2e gpa= , 0.35v = , 0.3c mpa= , 37 = , 1t mpa= , and 3 2620 /kg m = . the damage judgement parameters are: ultimate tensile stress of element 3u mpa = , strain under the ultimate stress 31 10u − =  , and strain when fracture occurs 2 1 10f − =  . fig. 16 shows the numerical calculation model. in order to simulate the tunnel buried depth of 200 meters, the vertical crustal stress at the buried depth of 147.5 meters and the corresponding horizontal stress are applied in the model. figure 16: numerical model of liangshui tunnel flac3d 3.00 itasca consulting group, inc. minneapolis, mn usa settings: model perspective 17:36:11 wed apr 27 2011 center: x: 0.000e+000 y: -7.500e+000 z: 5.000e-001 rotation: x: 90.000 y: 0.000 z: 0.000 dist: 3.918e+002 mag.: 1.25 ang.: 22.500 block group 1 2 3 4 s.c. li et alii, frattura ed integrità strutturale, 47 (2019) 1-16; doi: 10.3221/igf-esis.47.01 14 in the similar model test, overload test is carried out after tunnel excavation. keeping the coefficient of lateral pressure unchanged, increase the buried depth of tunnel step by step with the gradient of 50 m buried depth. that is to say, vertical loads at a specific buried depth are applied on the top of the tunnel and horizontal loads at corresponding horizontal insitu stress are applied on both sides of the tunnel to study the progressive failure characteristics of the tunnel. in the simulation calculation, the tunnel model is loaded in the same way. during the numerical simulation, the damage and failure of surrounding rock around the tunnel are as follows: (1) when loaded to 250 m buried depth, the damage and failure of surrounding rock is shown in fig. 17. it can be seen that at this time, the surrounding rock has not been destroyed, and the surrounding rock in the tunnel top and bottom within about 1 times the diameter of the tunnel begins to damage, and a small part of the elements at the distance of about 1 times the diameter of the tunnel on both sides of the side wall also occurs damage. the maximum damage value of the element is 2, and it occurs at the vault and the inverted arch. figure 17: damage and failure contour of surrounding rock. (2) when loaded at 350 m burial depth, the elements closest to the free surface of the vault and inverted arch begin to fail, and the damage value of the element is the largest, reaching 16. the damage scope of surrounding rock at the top and bottom of the tunnel has expanded by two times, and the damage of the elements in the range of about 0.8 times of the tunnel diameter on both sides has also occurred. fig. 18 shows the damage and failure of surrounding rock. figure 18: damage and failure contour of surrounding rock. (3) when loaded to the 600 m burial depth, the failure area of the vault and inverted arch continues to expand, extending to the tunnel spandrels, and some elements at the waist of the arch begin to fail. the damage value of the elements at the vault and inverted arch within about 1 times the diameter of the tunnel reaches the maximum value of 20, which indicates that they have completely broken and lost their bearing capacity, as shown in fig. 19. figure 19: damage and failure contour of surrounding rock. flac3d 3.00 itasca consulting group, inc. minneapolis, mn usa step 7230 model perspective 10:50:26 sat apr 30 2011 center: x: 0.000e+000 y: -7.500e+000 z: 5.000e-001 rotation: x: 90.000 y: 0.000 z: 0.000 dist: 3.918e+002 mag.: 3.05 ang.: 22.500 block contour of zone extra 2 0.0000e+000 to 1.0000e+000 1.0000e+000 to 2.0000e+000 2.0000e+000 to 2.0000e+000 interval = 1.0e+000 flac3d 3.00 itasca consulting group, inc. minneapolis, mn usa step 7230 model perspective 10:51:44 sat apr 30 2011 center: x: 0.000e+000 y: -7.500e+000 z: 5.000e-001 rotation: x: 90.000 y: 0.000 z: 0.000 dist: 3.918e+002 mag.: 3.05 ang.: 22.500 block group 4 flac3d 3.00 itasca consulting group, inc. minneapolis, mn usa step 19893 model perspective 21:05:41 wed mar 30 2011 center: x: 0.000e+000 y: -7.500e+000 z: 5.000e-001 rotation: x: 90.000 y: 0.000 z: 0.000 dist: 3.918e+002 mag.: 3.05 ang.: 22.500 block contour of zone extra 2 0.0000e+000 to 1.0000e+000 2.0000e+000 to 3.0000e+000 4.0000e+000 to 5.0000e+000 6.0000e+000 to 7.0000e+000 8.0000e+000 to 9.0000e+000 1.0000e+001 to 1.1000e+001 1.2000e+001 to 1.3000e+001 1.4000e+001 to 1.5000e+001 1.6000e+001 to 1.6000e+001 interval = 1.0e+000 flac3d 3.00 itasca consulting group, inc. minneapolis, mn usa step 19893 model perspective 21:03:44 wed mar 30 2011 center: x: 0.000e+000 y: -7.500e+000 z: 5.000e-001 rotation: x: 90.000 y: 0.000 z: 0.000 dist: 3.918e+002 mag.: 3.05 ang.: 22.500 block group 4 fail flac3d 3.00 itasca consulting group, inc. minneapolis, mn usa step 30381 model perspective 21:27:26 wed mar 30 2011 center: x: 0.000e+000 y: -7.500e+000 z: 5.000e-001 rotation: x: 90.000 y: 0.000 z: 0.000 dist: 3.918e+002 mag.: 3.05 ang.: 22.500 block contour of zone extra 2 0.0000e+000 to 1.0000e+000 2.0000e+000 to 3.0000e+000 4.0000e+000 to 5.0000e+000 6.0000e+000 to 7.0000e+000 8.0000e+000 to 9.0000e+000 1.0000e+001 to 1.1000e+001 1.2000e+001 to 1.3000e+001 1.4000e+001 to 1.5000e+001 1.6000e+001 to 1.7000e+001 1.8000e+001 to 1.9000e+001 2.0000e+001 to 2.0000e+001 interval = 1.0e+000 flac3d 3.00 itasca consulting group, inc. minneapolis, mn usa step 30381 model perspective 21:26:27 wed mar 30 2011 center: x: 0.000e+000 y: -7.500e+000 z: 5.000e-001 rotation: x: 90.000 y: 0.000 z: 0.000 dist: 3.918e+002 mag.: 3.05 ang.: 22.500 block group 4 fail s.c. li et alii, frattura ed integrità strutturale, 47 (2019) 1-16; doi: 10.3221/igf-esis.47.01 15 (4) when loaded to the 900 m burial depth, all the elements around the tunnel begin to fail, and the failed elements interconnect to form a whole region. especially in the position of the vault and the inverted arch, a large area of elements has failed. the damage value of the elements around the tunnel reaches the maximum value of 20 except for a small part of the elements at the side wall, as shown in fig. 20. figure 20. damage and failure contour of surrounding rock the loading test results of the scale model of liangshui tunnel are as follows: (1) when loaded to 350 m burial depth, the vault begins to crack and fall off. (2) when loaded to 600 m burial depth, the vault has larger deformation, and the side wall begins to crack gradually. (3) when loaded to 900 m burial depth, the vault material begins to peel off and collapse in large volume, the arch foot also appears obvious deformation, and the whole section of the tunnel has been seriously deformed. at this time, it is considered that the tunnel has been destabilized and destroyed. fig. 21 shows the failure in the model overload test. figure 21: failure in the model overload test. the results of tunnel overload test and numerical simulation are basically the same. the only difference is that the failure occurs below the inverted arch during numerical simulation while no corresponding phenomenon is observed in the model test. this is due to the side friction effect in the model test on the one hand, and the failure of the inverted arch under the condition of excavation cannot be clearly observed on the other hand. conclusions his numerical simulation method of rock fracture based on strain energy density theory completes the nonlinear calculation process with linear calculation, avoids singularity of numerical calculation in element fracture, and simulates the rock post-peak fracture behaviors. (1) the simple tensile bilinear strain softening constitutive model is adopted to analyze the energy and damage evolution process after the rock element reaches the stress limit point from the micromechanics perspective. in addition, the criterion is created to determine element failure based on strain energy density theory. this method can well simulate the entire process of rock damage. (2) the strain energy density of the rock element is obtained by accumulating the energy absorbed by the element after the load is imposed each time. meanwhile, the modulus reduction of the damaged element is discretized to complete nonlinear calculation with linear calculation. a very small residual modulus is given to elements (regarded to be completely fractured) with the maximum damage values. continuous calculation is used to implement discontinuous fracture behaviors of the rock to avoid singularity of numerical calculation in element fracture. flac3d 3.00 itasca consulting group, inc. minneapolis, mn usa step 38004 model perspective 21:23:49 wed mar 30 2011 center: x: 0.000e+000 y: -7.500e+000 z: 5.000e-001 rotation: x: 90.000 y: 0.000 z: 0.000 dist: 3.918e+002 mag.: 3.05 ang.: 22.500 block contour of zone extra 2 0.0000e+000 to 1.0000e+000 2.0000e+000 to 3.0000e+000 4.0000e+000 to 5.0000e+000 6.0000e+000 to 7.0000e+000 8.0000e+000 to 9.0000e+000 1.0000e+001 to 1.1000e+001 1.2000e+001 to 1.3000e+001 1.4000e+001 to 1.5000e+001 1.6000e+001 to 1.7000e+001 1.8000e+001 to 1.9000e+001 2.0000e+001 to 2.0000e+001 interval = 1.0e+000 flac3d 3.00 itasca consulting group, inc. minneapolis, mn usa step 38004 model perspective 21:22:57 wed mar 30 2011 center: x: 0.000e+000 y: -7.500e+000 z: 5.000e-001 rotation: x: 90.000 y: 0.000 z: 0.000 dist: 3.918e+002 mag.: 3.05 ang.: 22.500 block group 4 fail t s.c. li et alii, frattura ed integrità strutturale, 47 (2019) 1-16; doi: 10.3221/igf-esis.47.01 16 (3) numerical simulation of brazilian splitting, tensile tests with built-in crack and tunnel excavation shows that the preceding method can well simulate the entire process from partial failure to structural fracture of the rock and obtain the damage evolution process of each element during the failure process. (4) studying rock fracture from the energy perspective can comprehensively reflect the rock strength changes and essential characteristics of the structural failure. this paper develops a rock damage numerical calculation program with fish language in the flac. compared with the theory and analytic method, this program can directly resolve various complex problems and therefore has a wider application prospect. acknowledgments he authors would like to thank the support of the national basic research program of china (grant no. 2010cb732002), the national natural science foundation of china (grant no. 51179098、51379113), the specialized research fund for the doctoral program of higher education of china (grant no. 20120131110031). references [1] cai, m. (2002). rock mechanics and engineering, beijing: science press. [2] xie, h., ju, y. and li, l. (2005). criteria for strength and structural failure of rocks based on energy dissipation and energy release principles, chinese j. of rock mech. and eng., 24(17), pp. 3003-3010. [3] mikhalyuk, a.v. and zakharov, v.v. (1997). dissipation of dynamic-loading energy in quasi-elastic deformation processes in rocks, appl. mech. and tech. phys., 38(2), pp. 312-318. [4] steffler, e.d., epstein, j.s. and conley, e.g. (2003). energy partitioning for a crack under remote shear and compression, int. j. fracture, 120, pp. 563-580. [5] you, m., hua, a. (2012). energy analysis on failure process of rock specimens, chinese j. of rock mech. and eng., 21(6), pp.778-781. [6] xie, h., peng, r. and ju, y. (2014). energy dissipation of rock deformation and fracture, chinese j. of rock mech. and eng., 23(21), pp. 3565–3570. [7] yang, s., xu, w. and su c. (2006). study on the deformation failure and energy properties of rock specimen in uniaxial compression, acta mechanica solida sinica, 27(2), pp. 213-216. [8] carloni, c. and nobile, l. (2002). crack initiation behavior of orthotropic solids as predicted by the strain energy density theory, theoretical and applied fracture mechanics, (38), pp.109-119. [9] liu, h. (1999). mechanics of materials (i), beijing: high education press. [10] yu, x. (2012). the revision of the fourth strength theorem, j.of guangxi uni.(natural science), 27(supp.), pp.63-69. [11] li, q.m. (2011). strain energy density failure criterion, int. j. of solids and structures, (38), pp. 6997-7013. [12] gdoutos, e.e. (1984). problems of mixed mode crack propagation, martinus nijhoff publ, [13] wang, x., hai, l. and huang, m. (2014). inhomogeneity analysis of damage under uniaxial tension (i) basic theory, chinese j. of rock mech. and eng., 23(9), pp. 1446–1449. [14] jeong, d.y., orringer, o. and sih, g.c. (1994). strain energy density approach to stable crack extension under net section yielding of aircraft fuselage, theoretical and appl. fracture mech., 22(2), pp.127-137. [15] jin, f., jiang, m. and gao, x. (2014). defining damage variable based on energy dissipation, chinese j. of rock mech. and eng., 23(12), pp.1976–1980. [16] li, z. (2012). damage mechanics and its application, beijing: science press, pp.16–19. [17] ye, j., wu, f.q. and sun, j.z. (2013). estimation of the tensile elastic modulus using brazilian disc by applying diametrically opposed concentrated loads, int. j. of rock mech. & mining sci., 46, pp. 568-576. [18] yang, t., wang, b. and sun, l. (2012). effects of various spacer methods for rock split tests, site investigation sci. and tech., 1, pp.3-7. [19] hudson, j.a., brown, e.t. and rummel, f. (1972). the controlled failure of rock discs and rings loaded in diametral compression, int. j. rock mech. min. sci., 9, pp. 241–248. [20] markides, ch.f., pazis, d.n. and kourkoulis, s.k. (2010). closed full-field solutions for stresses and displacements in the brazilian disk under distributed radial load, int. j. of rock mech. & mining sci., 47, pp.227-237. [21] yang, l. (2012). experimental and numerical simulation study on the tensile fracture mechanism of threedimensional flaws in fractured rock mass [master thesis], ji nan: shandong university. t microsoft word numero_50_art_17_2533 m. godio et alii, frattura ed integrità strutturale, 50 (2019) 194-208; doi: 10.3221/igf-esis.50.17 194 focused on fracture and damage detection in masonry structures quantifying the out-of-plane response of unreinforced masonry walls subjected to relative support motion michele godio, katrin beyer laboratory of earthquake engineering and structural dynamics (eesd), school of architecture, civil and environmental engineering (enac), ecole polytechnique fédérale de lausanne (epfl), epfl enac iic eesd, gc b2 495, station 18, ch-1015 lausanne, switzerland michele.godio@epfl.ch, https://orcid.org/0000-0002-9586-8667 katrin.beyer@epfl.ch, https://orcid.org/0000-0002-6883-5157 abstract. the supports of out-of-plane loaded unreinforced masonry walls in buildings are subjected to a motion that is filtered and amplified by the building structure and, in some cases, can be significantly different from the ground motion. moreover, because these walls span one or several storeys, their top and bottom supports are subjected to motions that differ in phase and amplitude. in state-of-the-art assessment procedures for the out-of-plane stability of masonry walls any effect of a relative support motion is neglected. the objective of this paper is to study the effect of the relative support motion on the response of out-of-plane loaded vertically-spanning unreinforced masonry walls. the acceleration capacity of the walls is investigated by means of a discrete element model representative of different wall configurations. a set of ground motions covering a wide range of peak ground acceleration and peak ground displacement is used as input to the simulations. the relative motion between the wall supports is included in the model in a systematic way: firstly, through a motion that is non-synchronous but of equal amplitude; secondly, through a motion that is synchronous but of different amplitude. the effect of the relative support motion is studied on different wall configurations where the elastic modulus of masonry, the wall height-to-thickness ratio, the wall effective thickness and the overburden at the top wall are varied. the study shows that, because of the relative support motion, the acceleration capacity of the walls can drop by 20% and, in the cases where the overburden is high, by more than 50%. keywords. masonry; out-of-plane loading; discrete elements; incremental dynamic analysis; support motion; out-of-phase. citation: godio, m., beyer, k., quantifying the out-of-plane response of unreinforced masonry walls subjected to relative support motion, frattura ed integrità strutturale, 50 (2019) 194-208. received: 05.06.2019 accepted: 31.07.2019 published: 01.10.2019 copyright: © 2019 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. http://www.gruppofrattura.it/va/50/2533.mp4 m. godio et alii, frattura ed integrità strutturale, 50 (2019) 194-208; doi: 10.3221/igf-esis.50.17 195 introduction nreinforced masonry (urm) walls are very vulnerable to the out-of-plane actions, even more so at the higher levels of a building where the accelerations are large and the walls relatively slender [1]. the supports of out-of-plane loaded masonry walls in a building are subjected to a motion that is filtered and amplified by the building structure and, in some cases, can be significantly different from the ground motion. moreover, because these walls span one or several storeys, their top and bottom supports are subjected to motions that differ in phase and amplitude. relative support motion is reportedly due to two factors affecting the path of the seismic action from the ground to the walls located at the upper storeys of a building [2]: first, the diaphragm response, notably the in-plane or membrane flexibility of the diaphragm, see e.g. [3,4], and, second, the filtering and amplifying effect due to the building structure and, in particular, the shear walls. the performance of unreinforced masonry walls subjected to out-of-plane support motion including these two factors has been the topic of only few numerical studies so far. landi et al. [5] investigated the response of pinned-clamped walls undergoing vertical bending. the walls were modelled as assemblies of two axially-loaded rigid macro-blocks fully separated by a crack at a certain wall height and laterally restrained at the top by a spring. the wall motion was described by a lagrangian system of equations based on two degrees of freedom and integrated on a series of gaussian impulses and natural records. penner et al. [6] performed a parametric study on pinned-clamped vertically-spanning walls by using the software working model 2d [7]. the study extended the one by sharif et al. [8], who analysed two rigid macro-blocks subjected to equal input support motion, to two rigid macro-blocks subjected to relative support motion. this was achieved by connecting two lateral springs to the macro-block ends. the study included variations of the spring stiffnesses, wall thickness and slenderness and axial load magnitude and eccentricity. code-based records were used as input to the numerical model. derakhshan et al. [9] investigated the response of walls with pinned-pinned elastically-restrained supports. the wall response was captured by means of a tri-linear force-displacement model built upon a two-rigid-macro-block description. with respect to the two above-mentioned works [5,6], in this work the filtering action played by the structure was considered in the implementation of the input ground motions. as a result of the adopted filtering process, the input code-compatible records applied to the wall supports had a dominant period close to that of the building [9]. the out-of-plane response of urm walls was also studied by tondelli et al [10], who included as input to the out-of-plane wall support motion not only the effect of filtering due to the mixed unreinforced masonry – reinforced concrete wall structure but also the effect of rocking and therefore elongation of adjacent in-plane loaded urm walls on the top restraint of the out-of-plane loaded wall. both effects were experimentally observed [11] and simulated by means of the software udec 6.0 [12], where each brick row was modelled as a discrete rigid block. the above-mentioned numerical studies all show that urm walls appear to be more vulnerable when they are subjected to relative out-of-plane support motions [5,6,9,10]. providing some degree of flexibility to the wall supports by means of springs, which allows mimicking the situation in which the supports do not move simultaneously, leads in fact to a displacement demand that is higher than that of a wall with ‘fixed’ or highly stiff supports. while a wall with fixed supports collapses because of the excessive mid-height displacement [13–15], a wall with flexible supports can also collapse due to the excessive support displacement [9,16]. furthermore, the more the supports are flexible and have a different degree of flexibility, the higher can be the difference between the top and the bottom motions and the more vulnerable becomes the wall [6,16]. in the case of a very flexible top support, the upper macro-block behaves similarly to a parapet wall elastically restrained at the top and rocking on the lower macro-block, which, in turn, rocks on the fixed bottom support. in this situation, the support motion can give rise to a deformation pattern that is characterized by both macro-blocks rocking in the same direction, see e.g. [17]. this pattern is unfavourable when compared to the one experienced by a wall spanning vertically on fixed supports, since it results in a reduced wall force capacity [18] and displacement capacity [9]. the wall acceleration capacity consequently reduces. depending on the wall configurations, flexible supports were found to reduce the wall capacity by up to 1.3 times [6], but a systematic study quantifying the vulnerability of out-of-plane walls subjected to the relative support motion based on the input motion characteristics is missing. in the above-mentioned studies, the urm walls are modelled as vertical strips undergoing vertical one-way bending. such wall layout is simple yet representative of many wall configurations that are vulnerable to out-of-plane loading. during earthquakes, the effectiveness of wall side restraints, which would cause two-way bending, could in fact decrease, e.g. due to the weakening of the wall corners, which finally comes to trigger vertically-spanning overturning mechanisms. such wall configurations have also been tested on shake tables. among these tests, [15,16,19,20] include observations on the relative motion of the wall supports. when subjected to relative support motions the walls exhibit an acceleration profile varying piecewise linearly along the wall height [15]. furthermore, the motion of the top and bottom connections may not necessarily be in-phase [16,19,20]. these are certainly two sources of wall collapse that are, nonetheless, difficult to predict and quantify u m. godio et alii, frattura ed integrità strutturale, 50 (2019) 194-208; doi: 10.3221/igf-esis.50.17 196 [15]. moreover, test results [15] have shown a significant decrease in the initial lateral wall stiffness when cracking occurs. the stiffness also decreases through subsequent tests due to damage, that is, even if no new major cracks appear. the influence of the elastic modulus of masonry was, however, not included in previous numerical studies [5,6,9,10] and needs therefore to be investigated in a more systematic way. the objective of the here presented study is to quantify the vulnerability of walls subjected to the relative support motion by investigating the influence of the two fundamental input motion characteristics, which are (i) the relative amplitude and (ii) the phase shift between the top and bottom support motions. the numerical modelling of rocking masonry structures is a challenging task and many numerical modelling techniques based on e.g. finite element [21–23], discrete element [24– 28], applied element [29,30] and rigid-block models [31] have been put forward in the recent years. in this study, the urm walls are modelled by means of a discrete element model, which was already validated and employed in a previous work on walls with fixed support motions [32]. unlike the models used in previous numerical studies analysing urm walls under relative support motions [4,5,8] – except [10] – the here presented study makes no assumption on the height at which the macroscopic crack forms dividing the one-way spanning wall into a lower and an upper rocking body. this more versatile modelling approach allows some essential features of the out-of-plane behaviour of urm walls to be captured, namely, the opening/closure of the interfaces following the impacts and the change in height of the macroscopic crack during the shake due to the activation of ‘modes’ of rocking other than the two-macro-block mechanisms usually investigated [15]. relative support motions are generated from a suite of natural records. starting from these records, support motions are derived by changing, on the one hand, the phase shift, and, on the other hand, the relative amplitude. this is done by applying appropriate signal processing techniques. the strategy followed in this paper to produce records with relative amplitude formalises and extends the one already adapted by tondelli et al. [10]. in this paper, this strategy is applied for different wall configurations and, as a novelty, a strategy to produce out-of-phase motions is introduced. the resulting support motions are not necessary representative of the real floor motions, as these latter are usually amplified around the building frequency [2,9,33,34]. the reason of using synthetically-generated instead of experimentally-derived floor motions is that the former allows us examining a wide range of configurations controlling precisely the input motion characteristics. the vulnerability of the walls against relative support motions is quantified for different wall configurations through fragility curves. a parametric study investigates the acceleration capacity and the failure mechanisms of urm walls in which the masonry elastic modulus, wall height-to-thickness ratio, wall effective thickness and applied axial load (overburden) are varied. godio and beyer [32] carried out a parametric study on the same wall configurations and records, but for wall with identical support motions. response of urm walls under relative support motion bservations from shake table test show that uncracked urm walls undergo a uniform or a linearly varying acceleration profile along their height, depending on whether the input motions at the top and bottom of the wall are the same, i.e. have equivalent amplitude and are in-phase, or not [15]. when the walls are cracked, the acceleration profile becomes piece-wise linear between the cracks [15], and, for the general case in which the supports undergo relative motion, consists of three components (fig. 1): (a) a constant one, generated by the overall support motion; (b) a linear one, provided by the relative motion between the top and bottom supports, as a result, for instance, of the diaphragm flexibility; (c) a piece-wise linear one, engendered by the inertia of the macro-blocks separated by the cracked middle section undergoing rigid-body rocking motion. as illustrated by meisl et al. [15], the components (b) and (c) may not be necessarily in phase with the overall support acceleration (a), which can be a source for wall collapse [15]. the acceleration profile given by the support motion only is given by the sum of the components (a) and (b). the sum of these two components gives a trapezoidal acceleration profile. denoting with üt(t) and üb(t) respectively the top and bottom support accelerations, the overall support acceleration results in the average value: t bu (t ) u (t ) u(t ) 2     (1) the relative support acceleration, which is also a useful parameter in the present work, is defined as:    t bû(t ) u t u t    (2) o m. godio et alii, frattura ed integrità strutturale, 50 (2019) 194-208; doi: 10.3221/igf-esis.50.17 197 figure 1: acceleration profile components of cracked urm walls subjected to out-of-plane relative top and bottom support motion: (a) component generated by the overall support motion; (b) component provided by the relative motion between the top and bottom supports; (c) component engendered by the inertia forces of the two rocking macro-blocks. since in the experimental tests the out-of-plane walls are excited at their base, usually the overall support motion corresponds to the motion applied at the wall base and the diaphragm flexibility is concentrated at the wall top support. in that case, the trapezoidal acceleration profile of the support, i.e. the components (a)+(b) of the acceleration, can experience variation of the acceleration at the top of the wall only [15]. the urm walls tested in this study undergo generic out-of-plane relative support motions where both the top and the bottom supports can move. wall model he numerical model used in this study consists of a discrete element model of an urm wall of unitary length spanning vertically between the top and the bottom supports (fig. 2). the model is built by means of the commercial software udec 6.0 [12] and is the same model previously used and validated by godio and beyer [32]. in what follows, the model is briefly recalled. as a novelty, in this study the displacement histories applied to the wall top and bottom supports are different, as illustrated in fig. 2. the discrete element model falls within the class of simplified micro-models for masonry, according to which each masonry unit has an effective height hb that is equivalent to the nominal unit height plus the mortar joint thickness (fig. 2). the numerical model used in this study consists of a 2.8 m-high masonry wall made up of 14 units of effective height 0.2 m each, laying on a 0.6 x 0.3 m² discrete element representing the bottom wall support and in contact with a 0.5 x 0.1 m² discrete element representing the top wall support. this top block exerts a permanent, or dead, load of 0.88 kn. in addition, a vertical stress σv is applied to the top support. the axial force, or overburden, o is the resultant of the vertical stress plus the dead load. each masonry unit is modelled as an element of infinite stiffness and strength [12]. the wall deformation is therefore included in the constitutive law used for contact. as in [32], a coulomb slip model with integration over the contact area is adopted as joint material model [12]. the elastic joint stiffness coefficients are calculated as [10,32] w n b w ,e m ff e t k h t  ns k k 2(1 ν)   (3) where em is the elastic modulus of masonry and ν is its poisson’s ratio. the joints are also characterised by a tensile strength ft, a cohesion c, a friction angle φ, and a dilatation angle ψ. the masonry units have rounded corners [12]. contact between the units consequently occurs over an effective thickness tw,eff defined as w,eff w bt t 2r  (4) with rb the radius of the rounded corner of the units. contact is discretised in such a way that 10 contact points are placed across the effective wall thickness [32], which enables a realistic simulation of the contact forces exchanged by the blocks during the wall bending and rocking [35,36]. the parametric study carried out in this paper aims at studying the influence ut(t) ub(t) .. .. ut(t) ub(t) (a) (b) (c) t m. godio et alii, frattura ed integrità strutturale, 50 (2019) 194-208; doi: 10.3221/igf-esis.50.17 198 figure 2: discrete element model of a vertically-spanning urm wall with different top and bottom support motions used in the study. on the wall response of the elastic modulus of masonry, the wall height-to-thickness ratio, effective thickness and the vertical stress applied at the wall top. the parameters em, tw, rb and σv are therefore changed during the study, as explained later in the paper see tab. 2. the other parameters are defined as follows [32]: ν=0, ft=0 mpa, c=2 mpa, φ=35° and ψ=0°. a stiffness-proportional rayleigh damping model is used in the numerical simulations [12]. following the strategy validated in [32], the damping centred on the first flexural frequency of the wall, which is also reported in tab. 2, is obtained considering the wall as a double-clamped euler’s beam: 2 m w i w w w 1 4.730 e i f 2π h ρ t l       (5) with ρ the wall density and iw=1/12lwtw3 the moment of inertia of a generic cross-section of the wall. a damping ratio ζ of 20% operates at the above frequency [32]. time-history analyses are carried out through the numerical model by applying velocity histories in the out-of-plane direction of the wall. the velocity histories that are applied to the top and the bottom wall supports are different and are implemented following the strategies described in the next section. relative support motion generation ab. 1 contains the suite of records used in this study. the records are the same as those used by godio and beyer [32] and introduced by sorrentino et al. [37]. the set of selected records covers a wide window of peak ground acceleration (pga), velocity (pgv) and displacement (pgd), which is thought to diminish the record-to-record variability of the results obtained in the study. starting from these records, synthetic relative support motions are generated by introducing a phase shift and a relative amplitude. generation of support motions with phase shift the hilbert transform is a convenient method for generating signals that have the same amplitude but are phase-shifted, or asynchronous. the hilbert transform is the integral transform [39]: (6) in which s(t) is the original signal and pv is the cauchy principal value of the integral [39]. the hilbert transform operates on the signal as a filter and allows the analytical signal z(t) [40] to be generated starting from the original one: (7) in this study, the hilbert transform is used to introduce a phase shift between the input motions of the top and bottom wall supports. since the numerical model used in this study requires as input the velocity histories at the wall supports, the hilbert o tw hb rb tw,eff σv ut(t) ub(t) hw     1 s t τ s t pv dτ π τ            z t s t i s t   t m. godio et alii, frattura ed integrità strutturale, 50 (2019) 194-208; doi: 10.3221/igf-esis.50.17 199 earthquake year station label* mag. duration** (s) pga (g) pgv (cm/s) pgd (cm) kern county 1952 taft lincoln school taf111 7.36 20 0.18 19 9 san fernando 1971 pacoima dam (upp. left abut) pul164 6.61 12 1.22 114 39 friuli 1976 tolmezzo tmz000 6.5 10 0.36 23 5 imperial valley 1979 bonds corner bcr230 6.53 15 0.78 45 15 imperial valley 1979 el centro (array #7) e07230 6.53 15 0.47 113 47 nahanni 1985 site 1 s1280 6.76 10 1.2 41 10 loma prieta 1989 los gatos (lexington dam) lex000 6.93 10 0.44 86 17 northridge 1994 rinaldi (receiving stat.) rrs228 6.69 10 0.87 148 42 northridge 1994 sylmar (olive view med ff) syl360 6.69 10 0.84 129 32 kobe 1995 takatori tak000 6.9 15 0.62 121 40 *the records were downloaded from the peer-nga database [38] **the original records were shortened by cutting the parts preceding and succeeding the main shock table 1: natural records used in the parametric study. transform operates on the input velocities, which are expressed in the following form:           t 1 β 1 β u t u t u t 2 2                 b 1 β 1 β u t u t u t 2 2       (8) with u(t) the original input ground motion considered for the study and β a factor enabling to control the phase shift between the support motions. fig. 3 shows for one of the input ground motions used in this study the displacement histories and the lissajous diagrams of the top and bottom support displacements resulting from eqn. (8). in the figure, umax is calculated as max{u(t)}. lissajous is the name used in signal processing to designate diagrams where two signals are plotted on the two axes. this representation is very handy for comparing the two signals. if the signals have equal amplitude and frequency, as in the case of two sinusoidal signals, which are represented by dashed lines in the lissajous diagrams of fig. 3, the diagrams will take the shape of an ellipse. the shape and orientation of the ellipse will change according to the phase difference, or phase-shift, between the two signals. as apparent from these diagrams, by using eqn. (8) for β=0, the top and bottom support motions are identical and therefore of equal amplitude and in-phase; for non-zero values of β, the support motions have same amplitude but are out-of-phase with a phase shift that increases as β increases: in particular, for β=0.5 the phase shift amounts to 45°, whereas for β=1 the support motions are in quadrature, i.e. with a phase shift of 90°. for all values of β, the overall support velocity, i.e. the average velocity of the top and bottom supports, due to phase shift is (eqn. (1))      β u t u t u ( t ) 2      (9) and the relative velocity between the top and bottom supports is (eqn. (2))      βû (t ) β u t u t    (10) generation of support motions with relative amplitude a relative amplitude is introduced between the top and bottom wall support input motions as follows [10]: (11)      tu t 1 α u t        bu t 1 α u t   m. godio et alii, frattura ed integrità strutturale, 50 (2019) 194-208; doi: 10.3221/igf-esis.50.17 200 β=0 β=0.5 β=1 figure 3: displacement history (left-hand side) and lissajous diagrams (right-hand side) of top and bottom wall support motions with phase shift, eqn. (8) nahanni record (tab. 1). in dashed gray line: equal-amplitude sinusoidal motions shifted of 0° (top), 45° (center) and 90° (bottom). the input motions generated by the above expressions are synchronous but have unequal amplitude. starting from eqn. (11) it is easy to show that for any value of α, the overall support velocity is (eqn. (1))    αu t u t  (12) and the relative velocity between the top and bottom supports is (eqn. (2)):    αû t 2αu t  (13) the factor α controls therefore the difference between the amplitude of the top and bottom support motions. as illustrated in fig. 4, for α=0 the motion of the top and bottom supports are equal and therefore have all the same amplitude than the original input ground motion; for α=1 the bottom support is fixed and the top support moves with an amplitude that is twice the amplitude of the original input ground motion; intermediate values of α result in support motions with intermediate relative amplitude. -2 -1 0 1 2 -2 -1 0 1 2 -2 -1 0 1 2 -2 -1 0 1 2 -2 -1 0 1 2 -2 -1 0 1 2 m. godio et alii, frattura ed integrità strutturale, 50 (2019) 194-208; doi: 10.3221/igf-esis.50.17 201 α=0 α=0.5 α=1 figure 4: displacement history (left-hand side) and lissajous diagrams (right-hand side) of top and bottom wall support motions with relative amplitude, eqn. (11) nahanni record (tab. 1). parametric study parametric study is carried out on the 16 urm wall configurations already used in [32]. the wall configurations (tab. 2) are obtained starting from the reference configuration, denoted with c0, by changing at a time one of the following parameters: in c1-c4, the elastic modulus of masonry em; in c5-c8, the wall thickness tw, determining the height-to-thickness ratio of the wall; in c9-c12, the rounding of the masonry units rb, determining the effective thickness of the walls; in c13-c16, the vertical stress σv applied to the top support, giving a different overburden ratio o/w, where w is the wall body weight. in [32], 10 incremental dynamic analyses (ida) were run for each of the 16+1 configurations, by using the records of tab. 1. in the present study, 4 sets of (16+1) x 10 ida are run, resulting in 680 ida in total. two sets investigate the dynamic wall response when the top and the bottom support motions have the same amplitude but are phase-shifted; for these 2 sets, eqn. (8) is used for the generation of the input support motions, with β being set to 0.5 and 1. the other two sets investigate the wall response when the top and the bottom supports are in-phase but have different amplitude; in this case, the support motions are generated by using eqn. (11) setting α equal to 0.5 and 1. in the ida presented in [32], the input support motions were equal, which corresponds here to the case in which either β is set to 0 in eqn. (8) or α is set to 0 in eqn. (11) (c.f. fig. 3-fig. 4). -2 -1 0 1 2 -2 -1 0 1 2 -2 -1 0 1 2 -2 -1 0 1 2 -2 -1 0 1 2 -2 -1 0 1 2 a m. godio et alii, frattura ed integrità strutturale, 50 (2019) 194-208; doi: 10.3221/igf-esis.50.17 202 configuration wt  (mm) w wh /t  ( - ) br   w(%t ) w,eff wt /t  ( - ) me  (mpa) o/w ( - ) if  (hz) c0* 200 14 2 0.96 500 0.09 6.91 c1 200 14 2 0.96 125 0.09 9.77 c2 200 14 2 0.96 250 0.09 19.54 c3 200 14 2 0.96 1000 0.09 27.64 c4 200 14 2 0.96 2000 0.09 6.91 c5 100 28 2 0.96 500 0.18 13.82 c6 150 19 2 0.96 500 0.12 17.28 c7 250 11 2 0.96 500 0.07 20.73 c8 300 9 2 0.96 500 0.06 13.82 c9 200 14 0.5 0.99 500 0.09 13.82 c10 200 14 1 0.98 500 0.09 13.82 c11 200 14 1.5 0.97 500 0.09 13.82 c12 200 14 3 0.94 500 0.09 13.82 c13 200 14 2 0.96 500 1.40 13.82 c14 200 14 2 0.96 500 2.06 13.82 c15 200 14 2 0.96 500 4.03 13.82 c16 200 14 2 0.96 500 6.01 13.82 *reference configuration table 2: walls analysed in the parametric study. properties in bold are varied with respect to the reference configuration. results of the study results for support motions with phase shift fig. 5 shows the fragility curves for each of the configurations analysed in the parametric study and for support motions with different phase-shift, i.e. generated by eqn. (8) for β equal to 0, 0.5 and 1. the fragility curves are built from the results of the ida, as cumulative distributions of the limit pga, denoted here as pgalim. this latter corresponds to the pga of the time history in which the wall attains failure for the first time along the ida and it is defined from eqn. (9), as the average acceleration of the top and bottom supports:    t b lim β t t u t u t pga max max u 2       (14) the condition used for wall failure is that the wall undergoes a mid-height displacement d equal or larger than the limit displacement d0. the probability of wall failure is therefore p(|d|≥d0). this displacement is calculated as the maximum displacement that the wall attains under a uniformly distributed lateral load, assuming a failure mechanism similar to the one depicted in fig. 2, but with fixed wall supports. the expression for d0 is obtained in [41] and, for clarity, is reported here: w,ef 0 ft 2(1 ξ) d   (15) where ξ denotes the position of the middle masonry cracked joint, which can be calculated as: m. godio et alii, frattura ed integrità strutturale, 50 (2019) 194-208; doi: 10.3221/igf-esis.50.17 203 figure 5: fragility curves based on log-normal distributions obtained from the incremental dynamic analyses (ida) carried out on urm walls subjected to phase-shifted support motions. for β=0, in-phase motions; for β=0.5, motions with phase shift of 45°; for β=1: motions with phase shift of 90°. real discrete distributions based on the set of 10 ground motions are in dotted line and fitted lognormal distributions are in dashed, dashed-dotted or solid lines. pga values are in units of g. figure 6: median values of pgalim for all studied configurations and for different values of β. 0.0 1.0 2.0 0.0 0.3 0.5 0.8 1.0 0.0 1.0 2.0 0.0 0.3 0.5 0.8 1.0 0.0 1.0 2.0 0.0 0.3 0.5 0.8 1.0 0.0 1.0 2.0 0.0 0.3 0.5 0.8 1.0 0.0 1.0 2.0 0.0 0.3 0.5 0.8 1.0 0.0 1.0 2.0 0.0 0.3 0.5 0.8 1.0 0.0 1.0 2.0 0.0 0.3 0.5 0.8 1.0 0.0 1.0 2.0 0.0 0.3 0.5 0.8 1.0 0.0 1.0 2.0 0.0 0.3 0.5 0.8 1.0 0.0 1.0 2.0 0.0 0.3 0.5 0.8 1.0 0.0 1.0 2.0 0.0 0.3 0.5 0.8 1.0 0.0 1.0 2.0 0.0 0.3 0.5 0.8 1.0 0.0 1.0 2.0 3.0 0.0 0.3 0.5 0.8 1.0 0.0 1.0 2.0 3.0 0.0 0.3 0.5 0.8 1.0 0.0 1.0 2.0 3.0 0.0 0.3 0.5 0.8 1.0 0.0 1.0 2.0 3.0 0.0 0.3 0.5 0.8 1.0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 0 0.2 0.4 0.6 0.8 1 m. godio et alii, frattura ed integrità strutturale, 50 (2019) 194-208; doi: 10.3221/igf-esis.50.17 204 (16) cases of structural resurrection, i.e. cases where the wall can sustain levels of pga higher than those leading to collapse for the first time along the ida [42], have already been observed in rocking masonry structures [43], but are here neglected. as observed in [32], they may occur occasionally but it would be unsafe to consider them in the evaluation of the wall collapse, since from a practical point of view the first onset of failure is of interest. the figure shows both real distributions, in dotted line, and fitted log-normal distributions, using the line type indicated in the legend. comparing the curves obtained for all the studied configurations and for a given value of β, it can be noticed that increasing the wall thickness, which for a fixed wall height comes to decreasing the height-to-thickness ratio (c5-c8), the effective wall thickness over the nominal thickness (c9-c12) and the overburden ratio (c13-c16) increases the acceleration capacity of the wall. on the contrary, changes in the elastic modulus (c1-c4) have almost no effect on the acceleration capacity. an analogous outcome was obtained in [32] for walls subjected to identical support motion. comparing the wall capacity for a given configuration and for all values of β, it appears that increasing β from 0 to 1, i.e. increasing the phase-shift between the top and the bottom wall supports, the fragility curves shift to the left, leading to a decrease of limit pga for almost all probability levels and configurations. to better quantify the effect of a phase shift in the support motion, the median values pgalim(50) are plotted in fig. 6 for all configurations and all values of β. for the configurations c1 to c12, a phase-shift between the top and the bottom wall supports engenders a decrease of acceleration capacity of about 10% with respect to the in-phase case for β=0.5, which goes up to 20% when the phase-shift is maximum, i.e. for β=1. no significant difference between the configurations c1-c4 and c5-c12 is observed. for the configurations c13 to c16, the increase of overburden ratio at the wall top leads to a further reduction of the wall capacity. for the configuration c16, where o/w=6, the wall capacity is reduced to less than 40% of its initial value. the phase-shift of the support motions has therefore a detrimental effect on the wall acceleration capacity. this conclusion is supported by the observation of the wall failure mechanisms: even though the majority of the failure mechanisms is given by the formation of two macro-blocks spanning as illustrated in fig. 1, for the 34% and 31% of the studied configurations and records, deformation patterns corresponding to higher rocking ‘modes’, i.e. deformation patterns characterized by the formation of more than two macro-blocks, are activated for β=0.5 and β=1, respectively. unfavorable patterns as those discussed in [9], characterized by two macro-blocks rocking in the same direction, are observed for about the 0% and 3% of the cases, respectively. it appears, nonetheless, that the p-δ effect engendered by the relative support motion due to the phase-shift combined with a relatively high axial load creates the worst-case scenario for the wall. results for support motions with relative amplitude fig. 7 shows the fragility curves for each of the configurations analysed in the parametric study and for support motions with relative amplitude, i.e. generated for different values of α, namely 0, 0.5 and 1. the fragility curves are built as for fig. 5, as cumulative distributions of the limit pga obtained from the ida. fig. 8 sums up the results, by showing the median values of the obtained limit pga for all configurations and all values of α. overall, the figures show how introducing relative amplitudes in the wall support motions has a detrimental effect on the wall acceleration capacity. more specifically, for the configurations c1 to c12, the relative amplitude between the top and the bottom wall supports engenders a decrease in acceleration capacity with respect to the equal amplitude case of about 10% for α=0.5, and of about 20% for α=1. for the configurations c13 to c16, the decrease in acceleration is much more important and peaks at 85% for configuration c16 for α=1. from the comparison of these results with those obtained from the first two sets of simulations (fig. 6), it can be concluded that introducing relative amplitudes in the wall support motions has a detrimental effect on the wall acceleration capacity, which is comparable to the effect of introducing a phase-shift. it appears that the p-δ effect engendered by support motions of relative amplitudes combined a relatively high axial load creates the worst-case scenario for the wall. the failure mechanisms activated on the walls are for 16% and 19% of the cases, respectively for α=0.5 and =1, higher ‘rocking modes’ and for 1% and 15% of the cases unfavorable patterns. o(o w ) o ξ w    m. godio et alii, frattura ed integrità strutturale, 50 (2019) 194-208; doi: 10.3221/igf-esis.50.17 205 figure 7: fragility curves based on log-normal distributions obtained from the incremental dynamic analyses (ida) carried out on urm walls subjected to relative-amplitude support motions. for α=0, motions of same amplitude; for α=0.5, motions with relative amplitude equal to the original input motion; for α=1, motions with relative amplitude equal to two times the original input motion and with fixed bottom support. real discrete distributions based on the set of 10 ground motions are in dotted line and fitted log-normal distributions are in dashed, dashed-dotted or solid lines. pga values are in units of g. figure 8: median values of pgalim for all studied configurations and values of α. 0.0 1.0 2.0 0.0 0.3 0.5 0.8 1.0 0.0 1.0 2.0 0.0 0.3 0.5 0.8 1.0 0.0 1.0 2.0 0.0 0.3 0.5 0.8 1.0 0.0 1.0 2.0 0.0 0.3 0.5 0.8 1.0 0.0 1.0 2.0 0.0 0.3 0.5 0.8 1.0 0.0 1.0 2.0 0.0 0.3 0.5 0.8 1.0 0.0 1.0 2.0 0.0 0.3 0.5 0.8 1.0 0.0 1.0 2.0 0.0 0.3 0.5 0.8 1.0 0.0 1.0 2.0 0.0 0.3 0.5 0.8 1.0 0.0 1.0 2.0 0.0 0.3 0.5 0.8 1.0 0.0 1.0 2.0 0.0 0.3 0.5 0.8 1.0 0.0 1.0 2.0 0.0 0.3 0.5 0.8 1.0 0.0 1.0 2.0 3.0 0.0 0.3 0.5 0.8 1.0 0.0 1.0 2.0 3.0 0.0 0.3 0.5 0.8 1.0 0.0 1.0 2.0 3.0 0.0 0.3 0.5 0.8 1.0 0.0 1.0 2.0 3.0 0.0 0.3 0.5 0.8 1.0 m. godio et alii, frattura ed integrità strutturale, 50 (2019) 194-208; doi: 10.3221/igf-esis.50.17 206 conclusions his study shows by means of numerical simulations that the acceleration capacity of vertically-spanning urm walls decreases when the walls are subjected to a relative motion between the top and bottom supports. the study quantifies this in a systematic way, by looking at two fundamental input motion characteristics: firstly, by including motions that are phase-shifted, i.e. non-synchronous but of equal amplitude; secondly, through motions that are synchronous but of relative amplitude. the effect of the phase-shift and relative amplitude of the support motions have been studied for different wall configurations and by a model where the masonry components are modelled with infinite compressive strength and zero tensile strength. the effect of a limited compressive strength can be taken into account in the model by relating it to the effective wall thickness, see e.g. [10]. the assumption of zero tensile strength, which is not always verified in real situations, allows making a comparison with the results of a previous study [32]. as already observed in [32] for walls subjected to equal support motions, it appears here that for a given phase-shift or relative amplitude, variations in the masonry elastic modulus do not have a significant influence on the acceleration capacity of the urm walls. on the other hand, the wall height-to-thickness ratio, the wall effective thickness and, especially, the vertical stress, or overburden, applied at the wall top appear to be critical parameters that should be carefully evaluated because of their influence on the wall capacity [32]. as a novelty, the study further shows that, because of the relative support motion, the acceleration capacity of urm walls can drop by 10 to 20% for wall configurations with low to moderate overburden ratios and, in cases where the overburden ratio is high, it can drop by more than 50%. in conclusion, the strategies reported in this study allows quantifying the difference in shift and amplitude between the top and bottom wall support motions in efficient way. the support motions used in this study are nonetheless not yet representative of real building configurations as they do not contain any filtering effect due to the shear walls, which provide the wall supports with an input motion whose main period is close to the fundamental period of the structure [2,33,34]. further studies characterizing the input motion characteristics, i.e. phase shift and relative amplitude, of consecutive floor motions in urm buildings are necessary to put the present study into a real context and decide whether the extension of existing assessment methods to capture the effect of relative support motions is a step to be envisaged. reproducibility of the article content he content of this paper can be reproduced with the files provided at the following permanent repository: https://doi.org/10.5281/zenodo.3187536. the files include outputs of the numerical model, plus matlab scripts necessary to reproduce figs. 3-8 presented in the paper. acknowledgments he work presented in this paper was funded by the swiss federal office of the environment and the construction department of the canton basel-stadt. references [1] priestley, m.j.n. (1985). seismic behaviour of unreinforced masonry walls, bull. new zeal. natl. soc. earthq. eng., 18(2), pp. 191–205. [2] menon, a., magenes, g. (2011). definition of seismic input for out-of-plane response of masonry walls: i. parametric study, j. earthq. eng., 15(2), pp. 165–194, doi: 10.1080/13632460903494446. [3] giongo, i., dizhur, d., tomasi, r., ingham, j.m. (2015). field testing of flexible timber diaphragms in an existing vintage urm building, j. struct. eng., 141(1), pp. d4014009, doi: 10.1061/(asce)st.1943-541x.0001045. [4] brignola, a., pampanin, s., podestà, s. (2012). experimental evaluation of the in-plane stiffness of timber diaphragms, earthq. spectra, 28(4), pp. 1687–1709, doi: 10.1193/1.4000088. [5] landi, l., gabellieri, r., diotallevi, p.p. (2015). a model for the out-of-plane dynamic analysis of unreinforced masonry t t t m. godio et alii, frattura ed integrità strutturale, 50 (2019) 194-208; doi: 10.3221/igf-esis.50.17 207 walls in buildings with flexible diaphragms, soil dyn. earthq. eng., 79, pp. 211–222, doi: 10.1016/j.soildyn.2015.09.013. [6] penner, o., elwood, k.j. (2016). out-of-plane dynamic stability of unreinforced masonry walls in one-way bending: parametric study and assessment guidelines, earthq. spectra, 32(3), pp. 1699–1723, doi: 10.1193/011715eqs011m. [7] corporation, m.s. (2000). working model 2d. [8] sharif, i., meisl, c.s., elwood, k.j. (2007). assessment of asce 41 height-to-thickness ratio limits for urm walls, earthq. spectra, 23(4), pp. 893–908, doi: 10.1193/1.2790488. [9] derakhshan, h., griffith, m.c., ingham, j.m. (2015). out-of-plane seismic response of vertically spanning urm walls connected to flexible diaphragms, earthq. eng. struct. dyn., doi: 10.1002/eqe.2671. [10] tondelli, m., beyer, k., dejong, m. (2016). influence of boundary conditions on the out-of-plane response of brick masonry walls in buildings with rc slabs, earthq. eng. struct. dyn., 45(8), pp. 1337–1356, doi: 10.1002/eqe.2710. [11] beyer, k., tondelli, m., petry, s., peloso, s. (2015). dynamic testing of a four-storey building with reinforced concrete and unreinforced masonry walls: prediction, test results and data set, bull. earthq. eng., 13(10), pp. 3015–3064, doi: 10.1007/s10518-015-9752-z. [12] itasca consulting group. (2014). udec 6.0. [13] griffith, m.c., magenes, g., melis, g., picchi, l. (2003). evaluation of out-of-plane stability of unreinforced masonry walls subjected to seismic excitation, j. earthq. eng., 7(1), pp. 141–169, doi: 10.1080/13632460309350476. [14] griffith, m.c., lam, n.t.k., wilson, j.l., doherty, k. (2004). experimental investigation of unreinforced brick masonry walls in flexure, j. struct. eng., 130(3), pp. 423–432, doi: 10.1061/(asce)0733-9445(2004)130:3(423). [15] meisl, c.s., elwood, k.j., ventura, c.e. (2007). shake table tests on the out-of-plane response of unreinforced masonry walls, can. j. civ. eng., 34, pp. 1381–1392, doi: 10.1139/l07-059. [16] penner, o., elwood, k.j. (2016). out-of-plane dynamic stability of unreinforced masonry walls in one-way bending: shake table testing, earthq. spectra, 32(3), pp. 1675–1697, doi: 10.1193/011415eqs009m. [17] psycharis, i.n. (1990). dynamic behaviour of rocking two-block assemblies, earthq. eng. struct. dyn., 19(4), pp. 555– 575, doi: 10.1002/eqe.4290190407. [18] beyer, k., lucca, f. (2016).effect of static and kinematic boundary conditions on the out-of-plane response of brick masonry walls. in: modena, c., da porto, f., valluzzi, m.r., (eds.), proceedings of the 16th international brick and block masonry conference, padova, pp. 1439–1446. [19] erwing, r.d., johnson, a.w., kariotis, j.c. (1981). methodology for mitigation of seismic hazards in existing unreinforced masonry buildings: wall testing, out-of-plane. abk topical report 04, el segundo, california. [20] simsir, c., aschheim, m., abrams, d. (2004). out-of-plane dynamic response of unreinforced masonry bearing walls attached to flexible diaphragms, proc. 13th world conf. earthq. eng.. [21] avgenakis, e., psycharis, i.n. (2017). modeling of rocking elastic flexible bodies under static loading considering the nonlinear stress distribution at their base, j. struct. eng., 143(7), pp. 04017051, doi: 10.1061/(asce)st.1943-541x.0001783. [22] pitilakis, k., tsinidis, g., karafagka, s. (2017). analysis of the seismic behavior of classical multi-drum and monolithic columns, bull. earthq. eng., 15(12), pp. 5281–5307, doi: 10.1007/s10518-017-0160-4. [23] kalliontzis, d., sritharan, s. (2018). characterizing dynamic decay of motion of free-standing rocking members, earthq. spectra, 34(2), pp. 843–866, doi: 10.1193/011217eqs013m. [24] de felice, g. (2011). out-of-plane seismic capacity of masonry depending on wall section morphology, int. j. archit. herit., 5(4–5), pp. 466–482, doi: 10.1080/15583058.2010.530339. [25] stefanou, i., psycharis, i., georgopoulos, i.o. (2011). dynamic response of reinforced masonry columns in classical monuments, constr. build. mater., 25(12), pp. 4325–3437, doi: 10.1016/j.conbuildmat.2010.12.042. [26] dejong, m.j., vibert, c. (2012). seismic response of stone masonry spires: computational and experimental modeling, eng. struct., 40, pp. 566–574, doi: 10.1016/j.engstruct.2012.03.001. [27] çaktı, e., saygılı, ö., lemos, j. v., oliveira, c.s. (2016). discrete element modeling of a scaled masonry structure and its validation, eng. struct., 126, pp. 224–236, doi: 10.1016/j.engstruct.2016.07.044. [28] sarhosis, v., baraldi, d., lemos, j. v., milani, g. (2019). dynamic behaviour of ancient freestanding multi-drum and monolithic columns subjected to horizontal and vertical excitations, soil dyn. earthq. eng., 120(january), pp. 39–57, doi: 10.1016/j.soildyn.2019.01.024. [29] reuland, y., lestuzzi, p., smith, i.f.c. (2019). a model-based data-interpretation framework for post-earthquake building assessment with scarce measurement data, soil dyn. earthq. eng., 116(october 2018), pp. 253–263, doi: 10.1016/j.soildyn.2018.10.008. m. godio et alii, frattura ed integrità strutturale, 50 (2019) 194-208; doi: 10.3221/igf-esis.50.17 208 [30] malomo, d., pinho, r., penna, a. (2019). applied element modelling of the dynamic response of a full-scale clay brick masonry building specimen with flexible diaphragms, int. j. archit. herit., 0(0), pp. 1–18, doi: 10.1080/15583058.2019.1616004. [31] portioli, f., cascini, l. (2018). contact dynamics of masonry block structures using mathematical programming, j. earthq. eng., 22(1), pp. 94–125, doi: 10.1080/13632469.2016.1217801. [32] godio, m., beyer, k. (2019). evaluation of force-based and displacement-based out-of-plane seismic assessment methods for unreinforced masonry walls through refined model simulations, earthq. eng. struct. dyn., 48(4), pp. 454– 475, doi: 10.1002/eqe.3144. [33] menon, a., magenes, g. (2011). definition of seismic input for out-of-plane response of masonry walls: ii. formulation, j. earthq. eng., 15(2), pp. 195–213, doi: 10.1080/13632460903494446. [34] abbati, s.d., cattari, s., lagomarsino, s. (2019). seismic assessment of single-block rocking elements in masonry structures, mason. int., 31(2), pp. 39–48. [35] godio, m., stefanou, i., sab, k. (2018). effects of the dilatancy of joints and of the size of the building blocks on the mechanical behavior of masonry structures, meccanica, 53(7), pp. 1629–1643, doi: 10.1007/s11012-017-0688-z. [36] lemos, j. v. (2017). contact representation in rigid block models of masonry, int. j. mason. res. innov., 2(4), pp. 321– 334. [37] sorrentino, l., masiani, r., decanini, l.d. (2006). overturning of rocking rigid bodies under transient ground motions, struct. eng. mech., 22(3), pp. 293–310, doi: 10.12989/sem.2006.22.3.293. [38] pacific earthquake engineering research center. pacific earthquake engineering research center.(2017). peer ground motion database. available at: https://ngawest2.berkeley.edu. [accessed september 20, 2016]. [39] oppenheim, a. v., schafer, r.w. (1999). discrete time signal processing, new jersey, prentice-hall. [40] gabor, d. (1946). theory of communication. part 1: the analysis of information, j. inst. electr. eng. part iii radio commun. eng., 93(26), pp. 429–441, doi: 10.1049/ji-3-2.1946.0074. [41] godio, m., beyer, k. (2019). tri-linear model for the out-of-plane seismic assessment of vertically-spanning unreinforced masonry walls, j. struct. eng., accepted, pp. 1–9, doi: 10.1061/(asce)st.1943-541x.0002443. [42] vamvatsikos, d., allin cornell, c. (2002). incremental dynamic analysis, earthq. eng. struct. dyn., 31(3), pp. 491–514, doi: 10.1002/eqe.141. [43] psycharis, i.n. 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can be opened with acrobat and adobe reader 5.0 and later.) >> /namespace [ (adobe) (common) (1.0) ] /othernamespaces [ << /asreaderspreads false /cropimagestoframes true /errorcontrol /warnandcontinue /flattenerignorespreadoverrides false /includeguidesgrids false /includenonprinting false /includeslug false /namespace [ (adobe) (indesign) (4.0) ] /omitplacedbitmaps false /omitplacedeps false /omitplacedpdf false /simulateoverprint /legacy >> << /addbleedmarks false /addcolorbars false /addcropmarks false /addpageinfo false /addregmarks false /convertcolors /converttocmyk /destinationprofilename () /destinationprofileselector /documentcmyk /downsample16bitimages true /flattenerpreset << /presetselector /mediumresolution >> /formelements false /generatestructure false /includebookmarks false /includehyperlinks false /includeinteractive false /includelayers false /includeprofiles false /multimediahandling /useobjectsettings /namespace [ (adobe) (creativesuite) (2.0) ] /pdfxoutputintentprofileselector /documentcmyk /preserveediting true /untaggedcmykhandling /leaveuntagged /untaggedrgbhandling /usedocumentprofile /usedocumentbleed false >> ] >> setdistillerparams << /hwresolution [2400 2400] /pagesize [612.000 792.000] >> setpagedevice microsoft word numero_44_art_9 n.m. khansari et alii, frattura ed integrità strutturale, 44 (2018) 106-122; doi: 10.3221/igf-esis.44.09 106 development of an optimal process for friction stir welding based on ga-rsm hybrid algorithm nabi mehri khansari university of tehran, iran nabi_mehri@ut.ac.ir filippo berto norwegian university of science and technology (ntnu), norway filippo.berto@ntnu.no namdar karimi babol university of technology, iran namdarkarimi@gmail.com s.m.n. ghoreishi, mahdi fakoor university of tehran, iran mfakoor@ut.ac.ir, navid_ghoreishi@yahoo.com mozhgan mokari sharif university of technology, iran mozhgan.mokari@yahoo.com abstract. performance of friction stir welding (fsw) as a solid-state process is approved in several engineering applications, especially aluminum industries. identification of mechanical behavior of the associated welded zone is necessary due to these extensive applications of fsw. in this study, considering the effect of rotational and forward speed of welding tool on the mechanical properties of welded region, a hybrid optimization method based on combination of genetic algorithm (ga) and response surface method (rsm) named here as ga-rsm is proposed to achieve maximum tensile and ultimate strength. the results of ga-rsm are validated by per-forming necessary experimental tests on two wide-used 2024 and 5050 aluminum alloys. the results show that ga-rsm could be an effective approach to achieve optimized process for fsw with minimum cost. keywords. friction stir welding (fsw); optimized mechanical properties; genetic algorithm (ga); response surface methodology (rsm). citation: khansari, n.m., n., berto, f., karimi, n., ghoreishi, s.m.n., fakoor, m., mokari, m., development of an optimal process for friction stir welding based on garsm hybrid algorithm, frattura ed integrità strutturale, 44 (2018) 106-122. received: 16.02.2018 accepted: 02.03.2018 published: 01.04.2018 copyright: © 2018 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. n.m. khansari et alii, frattura ed integrità strutturale, 44 (2018) 106-122; doi: 10.3221/igf-esis.44.09 107 introduction pecial and attractive properties of aluminum alloys such as high strength to weight ratio, acceptable toughness and corrosion resistance has resulted in the impressive use of aluminum in various industries. considering different types of materials, which may employed for construction of a structure, several researches have been done to investigate the joining of aluminum alloys to the similar alloys or the other materials. some selected researches are reviewed in the following. habibnia et al. investigated the effects of rotation and forward speed of tool on the friction stir welding of 1100 al alloy to carbon steel [1]. uzun et al. investigated the joining of dissimilar al 6013-t4 alloy and x5crni18-10 stainless steel using fric-tion stir welding technique [2]. they also reported a good correlation between the hardness distribution and the welding zones of al 6013-t4 alloy and x5crni18-10 stainless steel joint. lee et al. studied the reaction layers of friction stir welded joints made from austenitic stainless steel and al alloy consisted of mixed layers of elongated, ultra-fine grains and the intermetallic compound layer [3]. zhu and chao, proposed a numerical simulation of transient temperature and residual stresses in friction stir welding of 304l stainless steel [4]. furthermore, effects of welding fusion, joint strength and welding microstructure were investigated and reported, experimentally [5-7]. moreover, the reports accent more difficulties in welding process of dissimilar alloys toward similar ones [1]. the main reason of the problem is due to the differences between their melting points, mechanical properties and welding method. on the other hand, in dissimilar welding process, the material with a lower melting point will melt quickly whereas; the other one remains solid and undesirable defects may appear in the welding zone. indeed, definition of an optimized method for dissimilar alloys due to difficulties is necessary. however, it has been proven practically that fsw, as a solid-state method is able to eliminate the formation of the intermetallic phase and to form uniform solid joints [8-9]. in addition, friction stir welding is a recent technique that utilizes a non-consumable rotating welding tool to generate frictional heat and plastic deformation at the welding location [10]. in fsw procedure, the desired plates are aligned with each other and clamped using fixtures. the tool rotates at high speed and moves along the weld centerline to generate connection between the work pieces. sharma has given a convenient overview of friction stir welding of aluminum to copper [11]. in this subject, three different zones can be observed in welded zones, including, heat affected zone (haz), thermo mechanically affected zone (tmaz) and fric-tion stir processed (fsp) zone [1]. the formation of the above regions is affected by the material flow behavior under the action of the mentioned rotating non-consumable tool. fsw has been studied from microstructural point of view in sever-al researches [12, 13]. in fsw method, it is essential to have a complete control over the relevant process to maximize the mechanical properties of the joint and to obtain desired strength. it is very important to select and control the welding process parameters for obtaining the maximum strength. various prediction methods can be employed to define the desired output variables. the relationship between fsw input parameters and output variables could be specified through developing mathematical models. in this regard, artificial neural network [14, 15], taguchi optimization technique [16, 17], genetic algorithm, fuzzy logic, and other optimization methods were applied [18, 19]. kumar and murugan employed fsw to maximize tensile strength and keep the mechanical properties in welding process of aluminum matrix composites. in this study, key parameters in fsw such as tool rotational speed, welding speed and axial force are used to develop regression models for prediction of the ultimate tensile strength and percent elongation [20]. qian et al. proposed an analytical approach for optimization of rotational and travel speed in fsw by trial and error [21]. recently, the response surface methodology (rsm) is introduced as a helpful approach in developing a suitable approximation for the true functional relationship be-tween the independent variables and the response variable that may characterize the nature of the joints. sometimes, response surface methodology is combined with other optimization methods like computer aided artificial neural network for more efficiency [22, 23]. as it can be found from the above literature, although, different researches have been done on various topics of fsw but presentation of optimum parameters for welding tool needs further development. therefore, in the present research, a hybrid optimization methodology is proposed based on combination of genetic algorithm (ga) and the response surface methodology (rsm) named here as ga-rsm to approximate the optimal tool’s rotational and forward speed in which maximum tensile strength could be achieved. then, presented optimization method based on empirical data is executed to obtain maximum tensile and ultimate strength of the welded region. in this regard, experimental tests are performed on two applicable 2024 and 5050 aluminum alloys in proposed optimized speeds. s n.m. khansari et alii, frattura ed integrità strutturale, 44 (2018) 106-122; doi: 10.3221/igf-esis.44.09 108 materials and method riction stir welding (fsw) is a solid-state joining process that utilizes a third body tool to join two facing surfaces. heat is generated between the tool and material that leads to a very soft region near the fsw tool. it then mechanically intermixes the two pieces of metal at the place of the joint, and then the softened metal due to the elevated temperature can be joined using mechanical pressure which is applied by the tool. fig. 1 illustrates both the friction stir welding tool and the relevant procedure parameters. figure 1: friction stir welding process, schematically in the present study, cold-rolled 2024 and 5050 aluminum alloy have been selected for friction stir welding process. chemical composition of aluminum alloy is listed in tab. 1 [1, 18]. elements mg cu v ni cr mn si ti zn al aa 5050 75.5 0.043 0.010 <0.005 0.010 0.224 0.120 0.018 <0.008 others aa 2024 1.57 4.15 0.001 <0.005 0.014 0.53 0.06 0.09 0.13 ≈93.4 table 1: chemical composition of aluminum alloy 2024 [1, 18]. furthermore, the sheets are cut in dimensions of 3 × 100 × 150 mm and are fixed in preferred fixture. in addition, hss and h13 have been utilized as welding tool. the chemical composition of fsw’s tools represents in tab. 2. elements fe si mn cu c ni cr v co w hss tool 75.5 0.32 0.25 0.109 0.88 0.163 3.57 1.90 0.09 7.32 h13 tool 91.7 1.07 0.47 0.06 0.30 0.04 4.37 0.95 0.45 0.08 table 2: chemical composition of hss and h13 tools [18]. figure 2: hss tool’s spin used in the present research f n.m. khansari et alii, frattura ed integrità strutturale, 44 (2018) 106-122; doi: 10.3221/igf-esis.44.09 109 the tool consists of 7.2 mm pins and 20 mm shoulder to transfer materials to the welding region. in addition, the shoulder set at angle of 6° to create convenience force whenever it passes through the weld-line. fig. 2 shows the tool that is employed for both 2024 and aa5050. welding process was performed in different rotational and forward speed. welding optimization algorithm genetic algorithm (ga) enetic algorithm is an iterative search procedure for optimization of an objective function, which describes the mechanics of natural genetics and natural selection [24]. although, ga has apparently simple method in computation, it is powerful in search. on the other hand, it does not need any specific properties of the problem. the application of ga needs to generate a population among candidate solutions to approximate the ideal populations, gradually. this procedure continues until satisfaction of specified criterion. in this regard, each chromosome of a population should be evaluated and compared with other one to achieve a better objective function. the individuals, who lead to a better objective function, have a greater chance for selection and pass their genes to next population. several stopping criteria are available to check in this step. response surface method (rsm) the response surface method (rsm) is employed to obtain an approximation for response function in terms of independent variables [25]. the most practical applications of rsm are in the empirical tests, particularly in situations where several input variables potentially influence in results. rsm is consisted of mathematical and statistical techniques that are based on the fit of the best empirical models on the extracted exploratory data from experimental tests. common form of the response is usually written as [25]:  1 2, ,..., ny f x x x   (1) where y is the estimated response, xi are independent variables, and ε is an error term. the function f is usually selected to be a polynomial. for a quadratic polynomial, f is written as [25]: 0 1 1 n n i i ij i j i i j f x x x          (2) where β represents as unknown coefficients and calculated by a linear multiple regressions based on the least square methods. the linear multiple regression models are rewritten in matrix form as follows [25]: y=xβ+ε (3) in which, y, x, β and ε are defined as: 1 11 12 1 0 1 2 21 22 2 1 2 1 2 1 1 y , x , β , ε 1 k k n n n nk k n y x x x y x x x and y x x x                                                                    (4) in general, y is a 1n  vector of the observations, x is a n k model matrix including the levels of the independent variables expanded to model form, β is a 1k  vector of the regression coefficients, and ε is a 1n  vector of random errors. the unbiased estimator b of the coefficient vector β is obtained using the least square error method as follows [26]:   1b x x x yt t (5) in which, the variance–covariance b matrix could be rephrased as function of error [26]: g n.m. khansari et alii, frattura ed integrità strutturale, 44 (2018) 106-122; doi: 10.3221/igf-esis.44.09 110     12ov , x xti j ijc b b c     (6) where σ is the error of y and can be obtained as follows: 2 y y b x y 1 t t t n k      (7) the adjusted coefficient of multiple determinations 2r (r-square-adjusted) is used to evaluate the performance of the approximation of the response surface and can be defined as [26]:     2 y y b x y 11 1 t t t yy n k r s n       (8) in which, syy is proposed as follows [26]: 2 1 y y n t yy i i s y n           (9) each coefficient of the response surface can be tested using the t-statistic. the statistic of the coefficient bj is [26]: 0 2 j jj b t c  (10) where cjj is the element of number j of the variance–covariance matrix of eq. (6). in the present research, coefficient 2r (eq. 8) has been calculated for validation of model’s goodness. hybrid optimization algorithm based on combination of genetic algorithm and the response surface methodology (ga-rsm) in the present study, a hybrid optimization methodology based on both genetic algorithm (ga) and the response surface methodology (rsm) named here as ga-rsm is proposed to obtain the optimum solution for a defined objective function. in this regards, in the genetic algorithm process, objective functions in each evaluation are calculated by response surface. fig. 3 illustrates flowchart of the developed hybrid optimization algorithm based on combination of genetic algorithm and the response surface methodology (i.e. ga-rsm). according to the proposed flowchart, the optimization algorithm starts by creating a random initial population. then, objective functions for each individual are evaluated from response surface, directly. then, according to the obtained objective functions, algorithm ranks of each individual part is evaluated. after that, a stochastic method is adopted for selection of two parents to create individuals for the next population. some genetic operators like mutation and crossover are also utilized in this step for production of new population. these processes will be iterated until stopping criterion is met. application of welding optimization procedure n this section, tensile strength of welded aa2024, also, tensile strength, and ultimate strength of welded aa5050 are optimized by ga-rsm. in this regard, at first, output parameters for all design points are determined with design of experiments. then, relationship between the output parameters and the independent variables is predicted by response function. in this paper, the latin hypercube sampling design (lhsd) technique has been applied for selecting a set of data points. the lhsd method is an advanced form of the monte carlo sampling that avoids clustering samples. in addition, the third order polynomial is employed as a function of response surface. i n.m. khansari et alii, frattura ed integrità strutturale, 44 (2018) 106-122; doi: 10.3221/igf-esis.44.09 111 start create initial population evaluate objective functions for each individual by response surface assign rank for each individual apply crossover among the best individuals (one point crossover) apply mutation on some individuals create new generation select individuals with stochastic universal sampling check convergence end no yes figure 3: flowchart of hybrid optimization methodology based on combination of genetic algorithm and response surface methodology (ga-rsm). figure 4: effects of forward and rotational speed on tensile strength of aa2024 using rsm. from literature and previous researches [21], in this study among many independent variables, forward and rotational speed have been selected as most influential parameters (independent variables). tensile strength was considered as objective function for aa2024 and tensile and ultimate strength were considered as objective functions for aa5050. lower and upper band of forward speed for both aa2024 and aa5050 are assumed as 25 and 95 mm/min, respectively. in addition, lower and upper band of rotational speed for both aa2024 and aa5050 are considered as 100 and 1300 rpm, respectively. mentioned parameters could be varied between lower and upper band continuously. it will be proven that n.m. khansari et alii, frattura ed integrità strutturale, 44 (2018) 106-122; doi: 10.3221/igf-esis.44.09 112 employing ga-rsm reduces the number of required experimental tests to find optimum point and acceptable optimum region, significantly. figs. 4 and 5 illustrate three dimensional response surface plots for the tensile strength of aa2024 and aa5050, respectively. three dimensional response surface plot for the ultimate strength of aa5050 has been shown in fig. 6. figure 5: effects of forward and rotational speed on the tensile strength of aa5050 using rsm. figure 6: effects of forward and rotational speed on ultimate strength of aa5050 using rsm. three dimensional response surface plots clearly show the effect of independent variables on output parameters. welding modality survey s it previously mentioned, the rotation and forward speed of tool are two significant parameters that can effect on final state of welding quality [21]. the aforementioned parameters effect on the amount of heat transferring in weld region. therefore, un-controlled tool speed can create defects such as cavity and flaw [18]. tensile and ultimate strength of welded aa2024 and aa5050 are assumed for optimization with ga-rsm. in the present research, various tool speeds were investigated around ga-rsm’s optimum suggested points on both aa2024 and aa5050. fig. 7 represents weld region of aa2024 and aa5050 for different rotation and forward speeds. as fig. 4 shows, different welding region quality has been achieved in various rotation and forward speeds. for more detail investigation of welding surface quality, microstructural metallography was performed. in this regard, specimens were pre-pared by cutting up aluminum sheet in transverse direction of weld-line and were polished by both sandpaper a n.m. khansari et alii, frattura ed integrità strutturale, 44 (2018) 106-122; doi: 10.3221/igf-esis.44.09 113 carbide (up to grade 5000) and alumina powder. furthermore, etching process performed by modified polton solution for 45 s. tunnel and groove defects are visible in specimens due to inadequacy in rotation and forward speed. microstructural metallography can show the tunnel and groove defects in specimens (fig. 8) in un-optimized rotation and forward speeds. aa2024 aa5050 figure 7: welded specimens in different rotation and forward speeds. as mentioned before, welded region usually consists of three different regions i.e. stir zone (sz), heat affected zone (haz) and thermo mechanically affected zone (tmaz). in the stirring zone as compared to the base metal, grains are extremely fine and homogeneous. this phenomenon is caused by recrystallization followed by severe plastic deformation that has occurred in this region. tmaz appears between the sz and the haz region. in addition, grains are similar to cold forming processes that has squeezed longitudinally in a particular direction. fig. 9 (a) and 6 (b) represent the 2024 and 5050 aluminum alloy microstructural grain at the center of stir zone. n.m. khansari et alii, frattura ed integrità strutturale, 44 (2018) 106-122; doi: 10.3221/igf-esis.44.09 114 figure 8: (a-1, a-2) and (b-1, b-2) represent cavity and tunnel defects for aa2024 and aa5050 specimens, respectively. (a) (b) figure 9: (a) and (b) 2024 and 5050 aluminum alloy microstructural grain at the center of sz. mechanical properties of welded joints ake into account of strength detection of welding, tensile and hardness tests were investigated. for this purpose, tensile test specimens prepared according to the astme8 (see fig. 10 (a)). also, vickers test was selected as hardness test (see fig. 10 (b)). in this regard, load of 100 gr in 15 seconds dropped at the welded region and for that, 5.1 mm deformation was measured. (a) (b) figure 10: (a) tension specimens according to astm e8 (b) vickers test. t n.m. khansari et alii, frattura ed integrità strutturale, 44 (2018) 106-122; doi: 10.3221/igf-esis.44.09 115 yield strength, ultimate strength, fracture zone, forward and rotational speed results of welded specimens for both aa5050 and aa2024 are evaluated experimentally. the results are listed in tab. 3 and tab. 4 for aa 5050 and aa 2024 respectively. specimen name fracture zone elongation% yield strength (mpa) ultimate strength (mpa) forward speed rotational speed (rpm) a nz 23.25 71.43 185.71 31.5 630 b nz 11.5 69.68 159.34 40 630 c haz 31.81 71.43 197.80 63 630 d bm 34.21 78.32 198.65 80 630 e nz 23.91 71.40 186.81 31.5 800 f tmaz 28.71 74.18 195.05 40 800 g nz 25.12 71.98 187.41 63 800 h nz 25.85 76.14 190.42 80 800 i nz 10.7 67.93 153.85 31.5 1000 j tmaz 27.56 75.4 192.3 40 1000 k nz 25.63 74.58 187.91 63 1000 l tmaz 26.05 77.08 189.06 80 1000 m nz 7.07 69.75 135.54 31.5 1250 n nz 9.63 71.66 142.54 40 1250 o nz 15.93 72.32 170.06 63 1250 p nz 18.02 73.08 177.07 80 1250 base metal 25.1 110.85 210 table 3: experimental evaluation and tool speed of aa 5050. specimen name fracture zone elongation% yield strength for 50 mm/min forward speed (mpa) ultimate strength in 90 mm/min forward speed (mpa) rotational speed (rpm) a nz 12 266.4 373.8 450 b nz 13 287.6 380.4 500 c haz 12.4 308.8 387 550 d bm 12.1 330 393.6 600 e nz 11.8 351.2 400.2 650 f tmaz 11.2 372.4 406.8 700 g nz 11 393.6 413.4 750 h nz 13.2 414.8 420 800 i nz 14.7 413.35 426.6 850 j tmaz 15.2 411.9 433.2 900 k nz 18.4 410.45 439.8 950 l tmaz 20.8 409 446.3 1000 m nz 17.8 388.77 442.9 1050 n nz 15.5 368.54 439.5 1100 o nz 11.9 348.31 436.1 1150 p nz 8.4 328.1 432.7 1200 base metal 210 table 4: experimental evaluation and tool speed of aa 2024. n.m. khansari et alii, frattura ed integrità strutturale, 44 (2018) 106-122; doi: 10.3221/igf-esis.44.09 116 as it shown in tab. 3 and tab. 4, the highest tensile strength for aa2024 and aa5050 reported as 446.3 (mpa) and 198.65 (mpa) at the 1000 and 630 rotational speeds (rpm), respectively. furthermore, fig. 11 indicates the fracture region of aa2024 and aa5050 specimens. as it can be found, initiation and propagation of crack in welded specimens begin from the tmaz and sz regions. figure 11: fracture region of aa2024 and aa5050 specimens. results and discussion n this study, presented hybrid optimization algorithm (ga-rsm) reduces the number of required experimental tests to find optimum point and acceptable optimum region, significantly. optimum region is an area which contains optimum point. on the other hand, experimental tests around the optimum points (or optimum region) confirmed the results of optimization processes (fig. 12). figure 12: optimum domain of tensile strength versus rotational speed. i n.m. khansari et alii, frattura ed integrità strutturale, 44 (2018) 106-122; doi: 10.3221/igf-esis.44.09 117 furthermore, coefficient (eq. 8) has been calculated for validation of model’s goodness. the parameter indicates matching of experimental and predicted values data based on the response surface method. figs. 13 and 14 represent the parameter for aa2024 and aa5050 welded specimens, respectively. figure 13: r2 parameter for aa2024 based on rsm of tensile strength. figure 14: r2 parameter for aa5050 based on rsm of tensile strength. in addition, r2 parameter is evaluated for ultimate strength of aa5050 in fig.15. figure 15: r2 parameter for aa5050 based on rsm of ultimate strength. as it shown in fig’s. 13-15, r2 is approximated to 1 (≈1). it means that, there is an adequate agreement between predicted values of the rsm and experimental data. moreover, for optimization the ga parameters such as elitist choice, mutation and crossover probability and convergence stability percentage were considered as 3%, 2%, 50%, and 0.01%. in addition, in order to obtain the best answer for objective function, three initial populations of ga were evaluated as 50, 75 and 100. n.m. khansari et alii, frattura ed integrità strutturale, 44 (2018) 106-122; doi: 10.3221/igf-esis.44.09 118 each initial population is created during a random process. the results of ga optimization for three different initial populations are presented in tab. 5, tab. 6 and tab. 7. the aforementioned tables are indicating that there are insignificant differences between the results for three different initial populations. initial population rotational speed (rpm) forward speed (mm/min) tensile strength (mpa) 50 1104.2 94.338 461.01 75 1096.8 94.573 462.23 100 1107.8 94.651 462.52 table 5: ga optimization of aa2024 for different initial populations. initial population rotational speed (rpm) forward speed (mm/min) tensile strength (mpa) 50 512.29 87.903 80.455 75 481.05 85.475 80.48 100 499.58 85.074 80.492 table 6: ga optimization of aa5050 for different initial populations. initial population rotational speed (rpm) forward speed (mm/min) ultimate strength (mpa) 50 466.9 72.725 216.33 75 509.12 71.087 217.36 100 490.87 70.296 217.56 table 7: ga optimization of aa5050 for different initial populations. furthermore, tensile and ultimate strength as an objective function versus number of evaluations for three different initial populations have been demonstrated as well in fig. 16 to fig. 18. figure 16: tensile strength of aa2024 versus number of evaluations for three different initial populations. as it shown in figs. 15 to 17, for all three distinct initial populations, tensile strength data for aa2024 and aa5050 obtained approximately as 462 and 80.5 mpa respectively. in addition, the evaluation reported for ultimate strength of aa5050 is 217 mpa. in the following, convergence stability versus the number of generations for three initial populations has been investigated (see fig. 19 and fig. 20). the convergence stability criterion is based on mean and standard deviation of the output parameters. it means that, for stable population, the optimization is converged. n.m. khansari et alii, frattura ed integrità strutturale, 44 (2018) 106-122; doi: 10.3221/igf-esis.44.09 119 figure 17: tensile strength of aa5050 versus number of evaluations for three different initial populations. figure 18: ultimate strength of aa5050 versus number of evaluations for three different initial populations. figure 19: convergence stability of aa2024 versus number of generations for three different initial populations. n.m. khansari et alii, frattura ed integrità strutturale, 44 (2018) 106-122; doi: 10.3221/igf-esis.44.09 120 figure 20: convergence stability of aa5050 versus number of generations for three different initial populations. it could be found that ga in combination with rsm has been converged after 17th, 9th and 11th generations for 50, 75 and 100 initial population, respectively. therefore, ga has been converged promptly with 75 and 100 initial populations for aa2024 and aa5050 in comparison with other populations, respectively. conclusions n optimized friction stir welding (fsw) process has been investigated in this research. critical mechanical properties of welded zone such as yield and ultimate strength of two kinds of aluminum alloys are targeted. tool’s rotational and forward speed are recognized as more effective parameters in fsw procedure on the mechanical properties of welded region. a hybrid optimization methodology based on both genetic algorithm (ga) and the response surface methodology (rsm) named here as ga-rsm was proposed for approximation of the crucial tool’s rotational and forward speed. in the aforementioned tool’s speeds, maximum tensile and ultimate strength of welded zone could be achieved. in this regard, experimental tests were performed on two useful aluminum alloys, i.e. aa2024 and aa5050. the results show that by employing the new presented hybrid optimization approach, more accuracy and reliability obtained for various tool’s speed in comparison to other techniques. references [1] habibnia, m., shakeri, m., nourouzi, s. and karimi, n., (2012). effect of tool rotation speed and feed rate on friction stir welding of 1100 aluminum alloy to carbon steel. in advanced materials research (vol. 445, pp. 741-746). trans tech publications. doi: 10.4028/www.scientific.net/amr.445.741. [2] uzun, h., dalle donne, c., argagnotto, a., ghidini, t. and gambaro, c., (2005). friction stir welding of dissimilar al 6013-t4 to x5crni18-10 stainless steel. materials & design, 26(1), pp.41-46. doi: 10.1016/j.matdes.2004.04.002. [3] lee, w.b., schmuecker, m., mercardo, u.a., biallas, g. and jung, s.b., (2006). interfacial reaction in steel–aluminum joints made by friction stir welding. scripta materialia, 55(4), pp.355-358. doi: 10.1016/j.scriptamat.2006.04.028 . [4] zhu, x.k. and chao, y.j., (2004). numerical simulation of transient temperature and residual stresses in friction stir welding of 304l stainless steel. journal of materials processing technology, 146(2), pp.263-272. doi: 10.1016/j.jmatprotec.2003.10.025. [5] geiger, m., micari, f., merklein, m., fratini, l., contorno, d., giera, a. and staud, d., (2008). friction stir knead welding of steel aluminium butt joints. international journal of machine tools and manufacture, 48(5), pp.515-521. doi: 10.1016/j.ijmachtools.2007.08.002. [6] jayaraj, r.k., malarvizhi, s. and balasubramanian, v., (2017). electrochemical corrosion behaviour of stir zone of friction stir welded dissimilar joints of aa6061 aluminium–az31b magnesium alloys. transactions of nonferrous metals society of china, 27(10), pp.2181-2192. doi: 10.1016/s1003-6326(17)60244-9. a n.m. khansari et alii, frattura ed integrità strutturale, 44 (2018) 106-122; doi: 10.3221/igf-esis.44.09 121 [7] tanaka, t., morishige, t. and hirata, t., (2009). comprehensive analysis of joint strength for dissimilar friction stir welds of mild steel to aluminum alloys. scripta materialia, 61(7), pp.756-759. doi: 10.1016/j.scriptamat.2009.06.022. [8] fujii, h., ueji, r., morisada, y. and tanigawa, h., (2014). high strength and ductility of friction-stir-welded steel joints due to mechanically stabilized metastable austenite. scripta materialia, 70, pp.39-42. doi: 10.1016/j.scriptamat.2013.09.012. [9] watanabe, t., takayama, h., kimapong, k. and hotta, n., (2003). joining of steel to aluminum alloy by interfaceactivated adhesion welding. in materials science forum, trans tech publications, 426, pp. 4129-4134. doi: 10.4028/www.scientific.net/msf.426-432.4129, [10] yong-jai, k.w.o.n., seong-beom, s. and dong-hwan, p.a.r.k., (2009). friction stir welding of 5052 aluminum alloy plates. transactions of nonferrous metals society of china, 19, pp. s23-s27. doi: 10.1016/s1003-6326(10)60239-7. [11] sharma, n. and siddiquee, a.n., (2017). friction stir welding of aluminum to copper—an overview. transactions of nonferrous metals society of china, 27(10), pp.2113-2136. doi: 10.1016/s1003-6326(17)60238-3. [12] zhang, q.z., gong, w.b. and wei, l.i.u., 2015. microstructure and mechanical properties of dissimilar al–cu joints by friction stir welding. transactions of nonferrous metals society of china, 25(6), pp.1779-1786. doi: 10.1016/s1003-6326(15)63783-9 [13] ilangovan, m., boopathy, s.r. and balasubramanian, v., (2015). microstructure and tensile properties of friction stir welded dissimilar aa6061–aa5086 aluminium alloy joints. transactions of nonferrous metals society of china, 25(4), pp.1080-1090. doi: 10.1016/s1003-6326(15)63701-3. [14] okuyucu, h., kurt, a. and arcaklioglu, e., (2007). artificial neural network application to the friction stir welding of aluminum plates. materials & design, 28(1), pp.78-84. doi: 10.1016/j.matdes.2005.06.003. [15] piccini, j.m. and svoboda, h.g., (2017). tool geometry optimization in friction stir spot welding of al-steel joints. journal of manufacturing processes, 26, pp.142-154. doi: 10.1016/j.jmapro.2017.02.004. [16] shojaeefard, m.h., khalkhali, a., akbari, m. and tahani, m., (2013). application of taguchi optimization technique in determining aluminum to brass friction stir welding parameters. materials & design (1980-2015), 52, pp.587-592. doi: 10.1016/j.matdes.2013.06.003. [17] lakshminarayanan, a.k. and balasubramanian, v., (2008). process parameters optimization for friction stir welding of rde-40 aluminium alloy using taguchi technique. transactions of nonferrous metals society of china, 18(3), pp.548-554. 10.1016/s1003-6326(08)60096-5. doi: 10.1016/s1003-6326(08)60096-5. [18] de vuyst, t., d’alvise, l., simar, a., de meester, b. and pierret, s., (2005). finite element modelling of friction stir welding of aluminium alloy plates-inverse analysis using a genetic algorithm. welding in the world, 49(3-4), pp.47-55. doi: 10.1007/bf03266475 [19] sankar, b.r. and umamaheswarrao, p., (2017). modelling and optimisation of friction stir welding on aa6061 alloy. materials today: proceedings, 4(8), pp.7448-7456. doi: 10.1016/j.matpr.2017.07.076. [20] kumar, b.a. and murugan, n., (2014). optimization of friction stir welding process parameters to maximize tensile strength of stir cast aa6061-t6/alnp composite. materials & design, 57, pp.383-393. doi: 10.1016/j.matdes.2013.12.065. [21] qian, j., li, j., sun, f., xiong, j., zhang, f. and lin, x., (2013). an analytical model to optimize rotation speed and travel speed of friction stir welding for defect-free joints. scripta materialia, 68(3-4), pp.175-178. doi: 10.1016/j.scriptamat.2012.10.008. [22] lakshminarayanan, a.k. and balasubramanian, v., (2009). comparison of rsm with ann in predicting tensile strength of friction stir welded aa7039 aluminium alloy joints. transactions of nonferrous metals society of china, 19(1), pp.9-18. doi: 10.1016/s1003-6326(08)60221-6. [23] jayaraman, m., sivasubramanian, r., balasubramanian, v. and lakshminarayanan, a.k., (2008). prediction of tensile strength of friction stir welded a356 cast aluminium alloy using response surface methodology and artificial neural network. journal for manufacturing science and production, 9(1-2), pp.45-60. doi: 10.1515/ijmsp.2008.9.1-2.45. [24] legrand, x., kelly, d., crosky, a. and crépin, d., (2006). optimisation of fibre steering in composite laminates using a genetic algorithm. composite structures, 75(1-4), pp.524-531. doi: 10.1016/j.compstruct.2006.04.067. [25] bezerra, m.a., santelli, r.e., oliveira, e.p., villar, l.s. and escaleira, l.a., (2008). response surface methodology (rsm) as a tool for optimization in analytical chemistry. talanta, 76(5), pp.965-977. doi: 10.1016/j.talanta.2008.05.019. 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can be opened with acrobat and adobe reader 5.0 and later.) >> /namespace [ (adobe) (common) (1.0) ] /othernamespaces [ << /asreaderspreads false /cropimagestoframes true /errorcontrol /warnandcontinue /flattenerignorespreadoverrides false /includeguidesgrids false /includenonprinting false /includeslug false /namespace [ (adobe) (indesign) (4.0) ] /omitplacedbitmaps false /omitplacedeps false /omitplacedpdf false /simulateoverprint /legacy >> << /addbleedmarks false /addcolorbars false /addcropmarks false /addpageinfo false /addregmarks false /convertcolors /converttocmyk /destinationprofilename () /destinationprofileselector /documentcmyk /downsample16bitimages true /flattenerpreset << /presetselector /mediumresolution >> /formelements false /generatestructure false /includebookmarks false /includehyperlinks false /includeinteractive false /includelayers false /includeprofiles false /multimediahandling /useobjectsettings /namespace [ (adobe) (creativesuite) (2.0) ] /pdfxoutputintentprofileselector /documentcmyk /preserveediting true /untaggedcmykhandling /leaveuntagged /untaggedrgbhandling /usedocumentprofile /usedocumentbleed false >> ] >> setdistillerparams << /hwresolution [2400 2400] /pagesize [612.000 792.000] >> setpagedevice shot peening processes to obtain nanocrystalline surfaces in metal alloys: d. yang et alii, frattura ed integrità strutturale, 48 (2019) 144-151; doi: 10.3221/igf-esis.48.17 144 damage evolution law on the surface field of argillaceous dolomite based on brazilian test and 3d digital image correlation delei yang department of architectural and civil engineering, university of huanghuai, zhumadian 463000, china department of civil engineering, university of ottawa, no.75 laurier avenue, n k1n 6n5, canada muyi20071001@126.com xiaochuan wang school of civil engineering, guizhou university, guiyang 550025, china abstract. this paper aims to disclose the damage evolution law of the surface field of argillaceous dolomite. for this purpose, the 3d digital image correlation was combined with the brazilian test into a new analysis method for the surface field damage evolution of the rock. first, the stress-strain curve of argillaceous dolomite was obtained in brazilian test, and the strain contours of the key points were acquired by 3d digital image correlation. then, the standard deviations of the x and y direction strains at the key points during the test were calculated using statistical methods. in addition, the dual damage factor was introduced to quantify the law of the strain statistics and plotted into a curve. finally, the strains in x and y directions on the horizontal axis ox in the disc center were obtained through elastic mechanical analysis and compared with those measured by 3d digital image correlation in the elastic phase. in this way, the following conclusions were drawn: the argillaceous dolomite exhibited obvious non-homogeneity in the surface field damage evolution. the different phases of the brazilian test can be determined accurately according to the turning points of the damage factor curve. the fluctuations of the damage factor curve also reveal the features of surface field damage evolution of argillaceous dolomite in brazilian test. this research shows that the traditional assumption of homogeneity cannot reflect the heterogeneity of the surface field damage evolution of argillaceous dolomite in brazilian test and provides a quantitative research method for rock damage evolution in that test. keywords. brazilian test; 3d digital image correlation; surface field; damage evolution. citation: yang, d.l., wang, x.c.., damage evolution law on the surface field of argillaceous dolomite based on brazilian test and 3d digital image correlation, frattura ed integrità strutturale, 48 (2019) 144-151. received: 07.11.2018 accepted: 02.02.2019 published: 01.04.2019 copyright: © 2019 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. http://www.gruppofrattura.it/va/48/2253.mp4 d. yang et alii, frattura ed integrità strutturale, 48 (2019) 144-151; doi: 10.3221/igf-esis.48.17 145 introduction here are many defects in natural rocks, such as microcracks and voids. under external loads, these defects will evolve continuously and coalesce into macrocracks, a precursor to rock damage and destruction. much theoretical research has been done on the initiation, propagation and coalescence laws of cracks in rocks, yielding fruitful results on the damage evolution mechanism of rocks [1, 2]. nevertheless, the existing theoretical models are not mature enough, making it necessary to perform experimental observations. in 1978, the international society for rock mechanics recommended the brazilian test as a method for measuring rock tensile strength [3]. in brazilian test, the rock failure is ultimately caused by tensile damage, for the tensile stress at the centre of the disc is 1/3 of the compressive stress [4] and compressive strength of the rock is generally 8~10 times the tensile strength [5]. the traditional procedure of brazilian test is as follows: paste a strain gauge at the centre of the disc vertically to the loading direction, measure the strain in the central tensile region, and compute the tensile modulus of the rock. there are several deficiencies with the traditional procedure [6~9]: first, the strain gauge must be pasted right at the centre and parallel to the tensile direction, and the length of the gauge should not exceed 1/10 of the disc diameter; otherwise, the measured strain will be less than the true strain at the centre of the disc. second, the rock is assumed to be homogenous, which is unlikely in reality. third, the traditional method may not always acquire enough data for further analysis. in fact, rock exists inhomogeneity, and damage and failure process under external force is difficult to predict. traditional methods study the damage evolution process of inhomogeneous rocks by measuring the stress-strain characteristics of individual points, which can not truly reflect the whole damage evolution process of inhomogeneous rocks. to solve these defects and to study accurately the law of rock damage evolution, we need to study the surface field of rock damage evolution process, the digital image correlation has been proposed and applied to examine the damage evolution and destruction of rocks under external loads [10]. for instance, ma shaopeng [11] described the damage evolution of rocks using digital image correlation. zhao cheng et al. [12] adopted the same method to study the deformation failure of pre-cracked rocks under uniaxial compression. dai shuhong et al. [13] put forward a test method to determine the crack tip location and stress intensity factor of grade i~ii rocks based on digital image correlation. ji weihong et al. [14] employed digital image correlation to ascertain the strain field of two different types of rock fractures, and determined the critical features and process length of the rock failures. zhang et al. [15~18] investigated the damage evolution mechanism and strain localization features of rock under cyclic and concentrated load by digital image correlation. gao yue [19] proposed a 3d digital image correlation approach, which overcomes the following problems of 2d digital image correlation: the axis of the camera must be vertical to the surface of the measured object, and the object surface must be flat and with no significant out-of-plane displacement. argillaceous dolomite is a rock with complex mineral components and fine grains. under external loads, microcracks may appear and propagate on argillaceous dolomite, and even penetrate through the rock. it is difficult to characterize the damage evolution of the rock by the traditional procedure of brazilian test. to disclose this process of inhomogeneous argillaceous dolomite, this paper combines the 3d digital image correlation and the brazilian test into a new analysis method for the surface field damage evolution of the rock. methodology ccording to the specification for rock tests in water conservancy and hydroelectric engineering (sl264-2001), the argillaceous dolomite with a diameter of 50mm and a height of 50mm was selected as the test specimen. the main mineral components of the specimen are sio2 (50%~70%) and al2o3 (15%~20%). in addition, the specimen also contains a small amount of fe2o3, feo and cao. the rmt-301 loading system developed by the institute of rock and soil mechanics, chinese academy of sciences was adopted for our test. the rmt-301, as the most advanced rock and concrete mechanics test system in china, is specially designed for mechanical properties test of engineering materials such as rock and concrete. the system has complete test functions, easy operation, high automation and high accuracy to meet the requirements of national indicators. the system consists of an axial displacement sensor (measuring range: 50mm; accuracy: 3‰), an axial force sensor (measuring range: 100kn; accuracy: 5‰) and a lateral displacement sensor (measuring range: 2.5mm; accuracy: 2‰). to simulate the entire process of crack initiation and propagation, the load was applied constantly at the rate of 0.01mm/s using displacement control. a 5 million-pixel industrial camera (focal length: 50mm; accuracy: 0.23μm) was employed to collect the test images of the specimen. in theory, the higher the pixels of industrial cameras, the higher the accuracy of the three-dimensional t a d. yang et alii, frattura ed integrità strutturale, 48 (2019) 144-151; doi: 10.3221/igf-esis.48.17 146 digital image correlation method. then, too high accuracy has little significance for the final calculation results. the industrial cameras with 5 million pixels used in this experiment have fully met the accuracy requirements of the experiment. the camera was controlled by software synchronous triggering, and the shooting frequency was set to 1frame/second, aiming to record the entire damage process of the specimen. in addition, a 15×13 calibration plate (pitch: 4mm) was adopted, considering the features of 3d digital image correlation. figure 1: stress-strain curve in brazilian test. figure 2: calculation area of the surface field. figure 3: damage evolution of surface strain field in brazilian test. results and analysis damage evolution law of surface field n the process of studying rock deformation and failure, scholars have deeply studied and analyzed the crack initiation, propagation law and damage evolution mechanism in rock from the angles of theory, model test and numerical analysis, and have achieved a lot of results[1,2,11,13]. based on previous research results and experimental data of this experiment, the stress-strain curve of the specimen was plotted along the loading direction in the brazilian test (fig. 1). -20 -15 -10 -5 0 5 10 15 20 y /m m -20 -15 -10 -5 0 5 10 15 20 y /m m 0 -1 -2 -3 -4 -5 ×10 -3 4 3 2 1 0 -1 -2 -3 ×10 -4(a)（εx） (a)（εy） 250 5 10 15 20-5-10-15-20-25 x/mm 250 5 10 15 20-5-10-15-20-25 x/mm -20 -15 -10 -5 0 5 10 15 20 y / m m -20 -15 -10 -5 0 5 10 15 20 y / m m -2 -4 -6 -8 -10 -12 -14 -16 -18 ×10 -3 2 1.5 1 0.5 ×10 -2(d)（εx） (d)（εy） 0 250 5 10 15 20-5-10-15-20-25 x/mm 250 5 10 15 20-5-10-15-20-25 x/mm -20 -15 -10 -5 0 5 10 15 20 y /m m -20 -15 -10 -5 0 5 10 15 20 y /m m 0 -2 -4 -6 -8 -10 -12 ×10 -3 3 2.5 2 1.5 0.5 0 ×10 -3(b)（εx） (b)（εy） 250 5 10 15 20-5-10-15-20-25 x/mm 250 5 10 15 20-5-10-15-20-25 x/mm -20 -15 -10 -5 0 5 10 15 20 y / m m -20 -15 -10 -5 0 5 10 15 20 y / m m 0 -2 -4 -6 -8 -10 -12 -14 -16 -18 -3 14 12 10 8 6 4 2 0 ×10 -3(c)（εx） (c)（εy） ×10 250 5 10 15 20-5-10-15-20-25 x/mm 250 5 10 15 20-5-10-15-20-25 x/mm -20 -15 -10 -5 0 5 10 15 20 y /m m -20 -15 -10 -5 0 5 10 15 20 y /m m 0 -0.5 -1 -1.5 -2 ×10 -2 -5 -4 -3 -2 -1 0 ×10 -2(e)（εx） (e)（εy） 250 5 10 15 20-5-10-15-20-25 x/mm 250 5 10 15 20-5-10-15-20-25 x/mm i d. yang et alii, frattura ed integrità strutturale, 48 (2019) 144-151; doi: 10.3221/igf-esis.48.17 147 referring to the previous research, points a~e were selected as the key points in the loading process. the calculation area of the surface field was determined before discussing the damage evolution of argillaceous dolomite throughout the test. previous studies have shown that the calculation area should be as large as possible, but should not reach the edge of specimen surface due to factors like lens distortion [20]. thus, the calculation area selected for our test is 50mm long along the x-axis and 40mm long along the y-axis (fig. 2). within this area, the strain contours in the x and y directions corresponding to the key points a~e were obtained by image correlation (fig. 3). during the calculation, the tensile strain was positive and the compressive strain was negative. as shown in figs. 1 and 3, the stress-strain curve of argillaceous dolomite in brazilian test falls into four distinct phases: the compaction phase (curve segment o~a), the elastic phase (curve segment a~b), the elastic-plastic phase (curve segment b~c), and the plastic phase (curve segment c~e). below is a detailed description of all four phases. in the first phase, the compression in the y direction caused the collapse of some large voids and the closure of some initial microcracks, while the tension in the x direction induced an increase in the number of voids and the further opening of the initial defects. this phase is marked by instability, jumping and fluctuation resulted from the uneven distribution of microcracks in argillaceous dolomite. according to the strain contours in the x and y directions (fig. 3a), all the strains in the y direction and most of those in the x direction were compressive, and some areas were stretched. these phenomena are closely related to the uneven distribution of voids and microcracks in the rock. in the second phase, the strains in the x and y directions were linearly correlated, despite the heterogeneity of the argillaceous dolomite. as shown in fig. 3b, the strains in the x direction shifted from the disordered state in the compaction phase to the ordered state in the elastic phase; the surface strain of the entire disc was relatively uniform, without large strain concentration. by contrast, the strains in the y direction were still disordered. the strain gradually decreased from the centre to the edge, forming an annular contour. the peak strain appeared at the top left of the centre, owing to the heterogenous distribution of internal defects. in the third phase, the initial microcracks propagated, new microcracks emerged, and internal damages began to appear. the strains further increased with the increase in load. despite the steady development of microcracks, there was no coalescence of macro or microcracks. near the end of this phase, a strain concentration area appeared at the bottom and expanded upwards. in the fourth phase, the macro and microcracks began to expand, leading to the unstable expansion of crack damage on the specimen [21]. from the strain contours of points d and e, it can be seen that the strain concentration area penetrated along the loading direction, forming a huge vertical macrocrack. thus, the argillaceous dolomite specimen broke into pieces. the above analysis shows that the argillaceous dolomite, as a soft rock, has a low tensile strength. the specimen exhibited obvious non-homogeneity in the surface field damage evolution through the brazilian test. the strain concentration in the x direction started from the bottom and gradually expanded along the loading direction, while that at the top of the rock appeared in the plastic phase. then, the top and bottom concentration areas moved towards each other and eventually converged into a band along the loading direction, pushing the stress to its peak value. in the y direction, the strain field was always nonhomogeneous and the strains were always disordered. strain statistics this subsection aims to further disclose the law of surface field damage evolution in the specimen. considering both computing accuracy and efficiency, the xand y direction strain fields of 20,588 scattered spots in each digital image acquired in brazilian test were statistically divided into an average of 20 groups. the strain statistics at points a~e are given in figs. 4 and 5, in which the x-axis shows the 20 statistical data for each group and the y-axis shows the mean value of each group. fig. 4 reveals a gradual increase of the tensile strains in the x direction, and a decrease in the proportion of stretched areas; this is because some areas were always compressed horizontally due to the complex voids and defects within the rock. with the increase of the load, the strains were relatively large in some areas and uniform in the other areas. as shown in fig. 5, the absolute value of the compressive strains in the y direction was gradually on the rise, the crack propagation was unstable after entering the elastic-plastic phase, and some areas seemed to be stretched. dual damage factors the dual damage factors k1 and k2 were introduced to quantify the law of the strain statistics in figs. 4 and 5. the factor can be expressed as: (1) 1 1 1 ( ) 1 n x i xi k n   = =  − − d. yang et alii, frattura ed integrità strutturale, 48 (2019) 144-151; doi: 10.3221/igf-esis.48.17 148 (2) where εxi and εyi are respectively the strain values in x and y directions at each point in the strain field. the mean values εx andεy can be expressed as: (3) (4) figure 4: horizontal strain statistics figure 5: vertical strain statistics the dual damage factors k1 and k2 are collectively referred to the damage factor k below. figure 6: damage factor curve. 2 1 1 ( ) 1 n y i yi k n   = =  − − 1 1 n x xiin   = =  1 1 n y yiin   = =  d. yang et alii, frattura ed integrità strutturale, 48 (2019) 144-151; doi: 10.3221/igf-esis.48.17 149 fig. 6 shows the variation in the damage factor over time. under the small tensile stress in the compaction phase, the strain field variation obeyed the random distribution in the x direction, showing no obvious strain concentration. hence, the dispersion in the x direction was relatively small and k was almost zero, while strain field variation increased steadily in the y direction. in the elastic phase, the strain field was relatively stable in the x direction, and the strain field variation still increased steadily in the y direction. this is because the strains in the y direction declined from the centre to both sides. at the end of the elastic phase, the slope of the standard deviations in the x and y directions began to increase, indicating a prominent damage evolution across the surface field. comparing fig. 1 and fig. 6, the stress-strain curve agrees well with the damage factor curve in different phases. thus, the different phases of the brazilian test can be determined accurately according to the turning points of the damage factor curve, rather than empirical judgement based on the stress-strain curve. the fluctuations of the damage factor curve also reveal the features of surface field damage evolution of argillaceous dolomite in brazilian test. comparison between analysis results and test results this subsection compares the test data with the results of the elastic mechanical analysis [22] on the surface strain of argillaceous dolomite. according to the elastic mechanical analysis of the plane stress problem, the stress-strain relationship at any point on the x-axis vertical to the loading direction in the disc plane can be obtained by: (5) (6) where -0.5d≦x≦0.5d; d is disc diameter. figure 7: the analytic strains in x and y directions on the horizontal axis ox in the disc centre. figure 8: measured strains in x and y directions on the horizontal axis ox in the disc centre. according to elastic mechanics, the strains at any point of x in (x, 0) x and y directions are as follows: (7) 2 2 2 2 2 2 16 [ 1] (4 ) x p d x dl x d   = − + 2 2 2 2 2 4 [ 1] (4 ) y p d x dl x d   = − + 2 2 2 2 2 2 2 2 2 2 . 16 4 1 [ 1] (4 ) (4 ) x y x p e dle d x d x x d x d      − = − = −    − − −   + +   d. yang et alii, frattura ed integrità strutturale, 48 (2019) 144-151; doi: 10.3221/igf-esis.48.17 150 (8) where e is the tensile modulus; p is the linear load; μ= 0.2 is the poisson’s ratio. the strains in x and y directions on the horizontal axis ox in the disc centre were obtained through elastic mechanical analysis and plotted in fig. 7. the same strains were measured by 3d digital image correlation in the elastic phase and recorded in fig. 8. as shown in the two figures, the curves shared a similar trend; however, a great difference between the measured and analytical strains was observed in the linear elastic phase at both ends of the a-axis. the difference is attributable to the end strains of the specimen induced by the compression of other parts during the test, which is, in turn, caused by the heterogeneity of the argillaceous dolomite. this contradicts the assumption of homogeneity in traditional procedure of the brazilian test. conclusions his paper explores the damage evolution law of surface field on argillaceous dolomite through 3d digital image correlation and brazilian test. for this purpose, the 3d digital image correlation was combined with the brazilian test into a new analysis method for the surface field damage evolution of the rock. first, the stress-strain curve of argillaceous dolomite was obtained in brazilian test, and the strain contours of the key points were acquired by 3d digital image correlation. then, the standard deviations of the x and y direction strains at the key points during the test were calculated using statistical methods. in addition, the dual damage factor was introduced to quantify the law of the strain statistics and plotted into a curve. finally, the strains in x and y directions on the horizontal axis ox in the disc center were obtained through elastic mechanical analysis and compared with those measured by 3d digital image correlation in the elastic phase. the main conclusions are as follows: (1) the argillaceous dolomite, as a soft rock with low tensile strength, exhibited obvious non-homogeneity in the surface field damage evolution. the strain concentration in the x direction started from the bottom and eventually formed a strain concentration band along the loading direction before the penetration of macrocracks. in the y direction, the strains were always disordered. (2) after statistically grouping the strain data of 3d digital image correlation, it is learned that the tensile strain increased gradually along the x direction throughout the brazilian test, but the proportion of stretched areas decreased; this is because some areas were always compressed horizontally due to the complex voids and defects within the rock. with the increase of the load, the strains were relatively large in some areas and uniform in the other areas. moreover, the absolute value of the compressive strains in the y direction was gradually on the rise, the crack propagation was unstable after entering the elastic-plastic phase, and some areas seemed to be stretched. (3) the different phases of the brazilian test can be determined accurately according to the turning points of the damage factor curve, rather than empirical judgement based on the stress-strain curve. the fluctuations of the damage factor curve also reveal the features of surface field damage evolution of argillaceous dolomite in brazilian test. (4) the strains in x and y directions on the horizontal axis ox in the disc centre were obtained through elastic mechanical analysis, and the same strains were measured by 3d digital image correlation in the elastic phase. comparison shows that the curves of the analytical and measured strains shared a similar trend; however, a great difference between the measured and analytical strains was observed in the linear elastic phase at both ends of the a-axis. the difference is attributable to the end strains of the specimen induced by the compression of other parts during the test, which is, in turn, caused by the heterogeneity of the argillaceous dolomite. this contradicts the assumption of homogeneity in traditional procedure of the brazilian test. acknowledgment he authors wish to thank the natural science foundation of china for financially supporting the research in the paper through the grant no.51478334 and henan science and technology department supporting the research in the paper through the grant no.182102310918. 2 2 2 2 2 2 2 2 2 2 . 16 16 [ 1] 1 (4 ) (4 ) y x y p e dle d x d x x d x d      − = =    − − −   + +    t t d. yang et alii, frattura ed integrità strutturale, 48 (2019) 144-151; doi: 10.3221/igf-esis.48.17 151 references [1] marcu, t., todea, m., maines, l., leordean, d., berce, p. popa, c. (2012). metallurgical and mechanical characterisation of titanium based materials for endosseous applications obtained by selective laser melting, powder metallurgy, 55(4), pp.309-314. [2] huang, c.s., zhang, z.f., dao, d.y. (2018). thermal stress restrained specimen test on fiber enhanced asphalt concrete and thermal stress calculation models, annales de chimie science des matériaux, 42(3), pp.387-403. [3] bieniawski, z. t., hawkes, i. (1978). suggested method for determining tensile strength of rock materials, international journal of rock mechanics and mining sciences and geo-mechanics abstracts, 15(3), pp.99-103. [4] hondros, g. (1959). the evaluation of poisson’s ratio and the modulus of materials of a low tensile resistance by the brazilian (indirect tensile) test with particular reference to concrete, australian journal of applied sciences, 10(3), pp.243-268. [5] gong, f. q., li, x. b., zhao, j. (2010). analytical algorithem to estmate tenile modulus in barazilan disk spliting tests, chinese journal of rock mechanics and engineering, 29(5), pp.881 -891. [6] zhao, j., li, h. b. (2000). experimental determination of dynamic tensile properties of granite, international journal of rock mechanics and mining sciences, 37(5), pp.861-866. [7] marino, c., nucara, a., pietrafesa, m. (2018). evaluation of the direct and diffused component of solar radiation starting from global radiation measurements: preliminary analysis, mathematical modelling of engineering problems, 5(4), pp.317-322. [8] tao, t.j., huang, p., wang, s.p., luo, y. (2018). safety evaluation of blasting fly-rock based on unascertained measurement model, instrumentation mesure métrologie, 17(1), pp.55-62. [9] liu, f. z. (1996). study of mechanical properties of rock in tension and tension-shear states, journal of yangtze riverentific research institute, 13(3), pp.35-39. [10] peters, w. h., ranson, w. f. (1982). digital imaging techniques in experimental stress analysis, optical engineering, 21(3), pp.427-431. [11] ma, s. p., zhou, h. (2006). study on the evolution characteristics of surface strain field during the process of rock failure, chinese journal of rock mechanics and engineering, 25(3), pp.590-595. [12] zhao, c., tian, j., matsuda, h., bao, c. (2015). crack propagation and damage of rock under uniaxial compression based on global strain field analysis, chinese journal of rock mechanics and engineering, 34(4), pp.763-769. [13] he, l.l., zhu h., gao, z.x. (2018). a novel asphalt pavement crack detection algorithm based on multi-feature test of cross-section image, traitement du signal, 35(3-4), pp.289-302. [14] ji, w., pan, p., miao, s., su, f. s., du, m. p. (2016). fracture characteristics of two types of rocks based on digital image correlation, rock and soil mechanics, 37(8), pp.2329-2305. [15] zhang, h., huang, g. y., song, h. p., kang, y. l. (2013). experimental characterization of strain localization in rock, geophysical journal international, 194, pp.1554-1558. [16] zhang, h., song, h. p., kang, y. l., huang, g. y., qu, c. y. (2012). experimental analysis on deformation evolution and crack propagation of rock under cyclic indentation, rock mechanics and rock engineering, 46, pp.1053-1059. [17] zhang, h., huang, g. y., song, h. p., kang, y. l. (2012). experimental investigation of deformation and failure mechanisms in rock under indentation by digital image correlation, engineering fracture mechanics, 9, pp.667-675. [18] zhang, h., fu, d. h., song, h. p., kang, y. l., huang, g. y., qi, g., li, j. y. (2014). damage and fracture investigation of three-point bending notched sandstone beams by dic and ae techniques, rock mechanics & rock engineering, 48(3), pp.1297-1303. [19] gao, y. (2014). research on key technologies and application of three-dimensional digital image correlation method, hefei: university of science and technology of china. [20] liu, x. y. (2012). digital image correlation method and its application on mechanical properties measurement or materials, changchun: jilin university. [21] cai, m. f. (2015). rock mechanics and engineering (second edition), beijing: science press. [22] xu, z. l. (1960). elasticity theory, beijing: people′s education press. microsoft word numero_41_art_20.docx d.-q. wang et alii, frattura ed integrità strutturale, 41 (2017) 143-148; doi: 10.3221/igf-esis.41.20 143 focused on crack tip fields crack tip strain evolution and crack closure during overload of a growing fatigue crack de-qiang wang, ming-liang zhu, fu-zhen xuan key laboratory of pressure systems and safety, moe; school of mechanical and power engineering, east china university of science & technology, shanghai 200237, china mlzhu@ecust.edu.cn jie tong mechanical behavior of materials laboratory, school of engineering, university of portsmouth, portsmouth po1 3dj, uk abstract. it is generally accepted that fatigue crack growth is retarded after an overload, which has been explained either by plasticity-induced crack closure or near-tip residual stress. however, any interpretation of overload effect is insufficient if strain evolution in front of crack tip is not properly considered. the current understanding of overload-induced retardation lacks the clarification of the relationship between crack closure at crack wake and strain evolution at crack tip. in this work, a material with low work hardening coefficient was used to study the effect of overload on crack tip strain evolution and crack closure by in-situ sem observation and digital image correlation technique. crack opening displacement (cod) and crack tip strain were measured before and after the overload. it was observed that the evolution of crack tip strain follows the crack opening behaviour behind the crack tip, indicating a smaller influence of overload on micro-mechanical behaviour of fatigue crack growth. after the overload, plastic strain accumulation was responsible for crack growth. the strain at a certain distance to crack tip was mapped, and it was found that the crack tip plastic zone size correlated well with crack growth rate during post-overload fatigue crack propagation. keywords. in-situ sem; overload; fatigue crack growth; digital image correlation. citation: wang, d.-q., zhu, m.-l., xuan, f.z., tong, j., crack tip strain evolution and crack closure during overload of a growing fatigue crack, frattura ed integrità strutturale, 41 (2017) 143-148. received: 28.02.2017 accepted: 15.04.2017 published: 01.07.2017 copyright: © 2017 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. introduction verloading behavior of a material has been widely investigated as variable amplitude loading is the load form that engineering structures and components often undergo. it is generally accepted that overloading of a fatigue crack often induces crack growth retardation and thus can influence fatigue life. to date, a variety of experimental and simulation work have focused on the influence of overload parameters, e.g. overload ratio, base stress intensity factor range, o d.-q. wang et alii, frattura ed integrità strutturale, 41 (2017) 143-148; doi: 10.3221/igf-esis.41.20 144 crack length, etc., on fatigue crack growth rates. although several mechanisms for the retardation have been proposed, including crack closure [1-4], crack tip hardening [5], crack branching [6], residual stresses [7] or combined effects [5, 8], the micro-mechanical behavior of the overload is still an open issue. the crack closure concept, though extensively applied with its roles recognized in the overload process, is actually physical only at crack wake; whereas the driving part of crack growth and associated cracking of materials is at crack front. it seems that any interpretation of overload effect is insufficient if crack closure at crack wake is not correlated with cracking process in front of crack tip. digital image correlation (dic) technique provides a good solution to strain measurement and has been widely applied in both engineering and laboratory scale researches. as for fatigue tests, the dic method was found to be very helpful to the determination of plastic zone size [9], crack closure level [3, 4, 10, 11], and microstructural scale strain localization [12]. the dic would be more powerful to resolve strain distribution if combined with high resolution images from sem. in this work, the dic technique combined with in situ sem was used to study the effect of overload on fatigue crack growth behavior. the strain evolution at crack tip as well as variation of crack opening displacement (cod) were measured and correlated with each other both before and after an overloaded growing fatigue crack. the driving force of fatigue crack growth in case of overload was also discussed. experimental methods material and specimen he material used in this work is 25cr2ni2mov, a type of rotor steel. the steel has been undergone quenching and tempering heat treatment, and a final tempering process was conducted at 560c for 40 hours. the chemical composition of the steel in wt.% mainly includes c (0.180.27), si (0.12), mn (0.120.28), p (0.015), s (0.015), ni (2.052.35), cr (2.152.45), mo (0.630.82), v (0.12), cu (0.17) and fe as the balance. the yield strength and ultimate strength of this steel are 793 mpa and 894 mpa, respectively. the material thus has a low work hardening coefficient. the microstructures are mainly tempered martensites. standard ct specimens with aw ratio of 0.5 and a thickness b of 16 mm were firstly prepared and then pre-cracked using high frequency fatigue testing machine. the stress intensity factor range k during the pre-cracking process was decreased from 15 mpam1/2 to 13.5 mpam1/2 for a first fatigue crack extension of 1.5 mm, followed by another 10% load decrease for another 1.5 mm extension. in total, the pre-crack length was 3 mm. several dog-bone shaped miniature specimens with a gauge cross-section of 0.54 mm2 and a gauge length of 10 mm were then cut from the ct specimen by electrical discharge machining (edm) technique. the specimen for in-situ sem fatigue test was thus prepared with a pre-crack length of 2.286 mm. the shape and dimensions of the standard ct specimen and a small size fatigue specimen is shown in fig. 1. figure 1: shape and dimensions of standard ct specimen and the machined small size tensile specimen in-situ fatigue test prior to in-situ fatigue test, the specimen was ground with sic papers, and polished and chemically etched to reveal the microstructures and then mounted onto a deben microtest tensile module with a load capacity of 5 kn equipped into a sem (zeiss, evo series). the loading scheme is shown in fig. 2. the base line k was 25 mpm1/2, and the overload ratio t d.-q. wang et alii, frattura ed integrità strutturale, 41 (2017) 143-148; doi: 10.3221/igf-esis.41.20 145 (olr) was set as 1.2. the cyclic loaded tests were interrupted every five cycles to take images, from which crack growth length and strain distribution were measured. sem images were taken at two magnifications, i.e., 500x for strain measurement and 5000x for crack length measurement. as shown in fig. 2, after 40 cycles of constant amplitude testing, an overload cycle was then exerted, followed by another 40 cycles of constant amplitude loading. special attention was paid to the overload cycle, and the cycle just before and after the overload, by taking more images at an increment of 5% of pmax. figure 2: the loading scheme of the experiment (the 40 cycles before and after the overload cycle is a loading block contains 8 subblock with 5 cycles for each of them) digital image correlation the in-plane displacement and strain were analyzed by commercial dic software (vic-2d 2009, correlated solutions). the un-deformed image at zero load was set as the reference image and the deformed images were target ones. in this work, the intrinsic microstructures of the steel with an average characteristic size of 10 m were regarded as speckles needed by dic for tracking in-plane deformation. suitable parameters such as subset size and step size were selected to be 31 pixels and 5 pixels, respectively. the strain measurement based on intrinsic microstructures as speckles was found with sufficient resolution in our previous work on a steel with similar microstructures [13]. results and discussion crack growth morphologies ig. 3 shows the crack growth morphologies during the overload process and strain distribution based on dic measurement. all the sem images shown here are taken at peak load. the fatigue crack is just at a grain boundary before the overload cycle, as observed in fig. 3a. the crack then gets across the grain boundary at the peak load of overloading and is branched (fig. 3b). fig. 3c shows the extension of branched cracks after overload cycle. figs. 3d, 3e and 3f denote the strain distribution before, at and after the overload. the strain distribution near crack tip is varied, and the shape of highly concentrated zone from which plastic zone size is determined is also changed with overload. it seems that the strain is localized at and around the grain boundary, indicating the potential of next cracking under constant amplitude loading. crack tip strain evolution the normal strains perpendicular to the crack plane ahead of the crack tip was extracted after correlation procedure. the reference image was taken at the minimum load at nol-1 cycle. the data points stands for the strain values with a distance of 50 m away from the crack tip. the strain evolution during the three full cycles is shown in fig. 4. strain loops are observed in the pre-overload and post-overload cycle, while the overload induces large residual strain at the crack tip. time 5 cycles r t0 t1 t8 40 cycles 5 cycles t1 t8 40 cycles overload r f d.-q. wang et alii, frattura ed integrità strutturale, 41 (2017) 143-148; doi: 10.3221/igf-esis.41.20 146 figure 3: crack growth morphologies during the overload process ((a), (b), and (c) are the crack tip before, at and after the overload, respectively; while (d), (e) and (f) are the corresponding strain distribution based on dic measurement). figure 4: the strain evolution at the crack tip at ol-1, ol and ol+1 cycles (data points are extracted from the strain distribution with a distance of 50 m in front of the crack tip) crack opening displacement evolution crack opening displacement (cod) values at crack wake was acquired by subtracting the vertical displacements of the top flank and bottom flank of the crack mouth, which varies as a function of distance behind the crack-tip [14]. in this study, the measurement point was 50 m behind the crack-tip. the cod loops for the three full cycles, as shown in fig. 5, have similar trend with that of crack tip strain in fig. 3. it seems the loading process at the crack wake follows the mechanical response at the crack tip under the stress level in this work. as observed from figs. 4 and 5, the crack closure varies little before and after the overload, probably due to the olr is not very high, and the material investigated here has a low hardening coefficient. crack growth rate and plastic zone size apart from crack closure, other parameters, i.e., fatigue crack growth rate, plastic zone size and strain increasing rate, are calculated based on the experimental measurement, and the results are illustrated in fig. 6. strain increasing rate was defined as the slope of fitting curve of max/0 –n relationship, while plastic zone size was defined as areas where normal strain yy is larger than 2%. here, max and 0 are the strain values at peak load and minimum load. it is observed that crack growth rate is decreased from 3.310-4 to 1.510-4 mm/cycle just after the overload, and then gradually restored to pre-overload 0.00 0.02 0.04 0.06 0.08 0.10 0 20 40 60 80 100 120 140 n ol -1 n ol n ol +1 p /p m a x (% ) crack tip strain d.-q. wang et alii, frattura ed integrità strutturale, 41 (2017) 143-148; doi: 10.3221/igf-esis.41.20 147 level. it seems that the plastic zone size as compared with strain increasing rate is a better parameter for correlating crack growth rate. figure 5: the evolution of cod at the crack wake at ol-1, ol and ol+1 cycles (data points are extracted from the measurement with a distance of 50 m behind the crack tip) figure 6: variations of crack growth rate, strain increasing rate and plastic zone size with number of cycles conclusions or the low hardening coefficient steel in this work, an in-situ fatigue test under an overload (olr =1.2) revealed little influence of overload on fatigue crack growth behavior. the measured crack tip strain and crack opening displacement behind crack tip have similar response to external loading. plastic zone size can correlate crack growth rate very well in case of overload. 0 5 10 15 20 25 0 20 40 60 80 100 120 140 n ol -1 n ol n ol +1 p /p m a x (% ) cod (pixel) 0 30 60 90 120 150 180 210 10-4 2x10-4 3x10-4 4x10-4 5x10-4 crack growth rate strain increasing rate plastic zone size (area) number of cycles n post-overload preoverload 2x10-2 4x10-2 6x10-2 8x10-2 m m /c yc le  m 2 overload,n=31 6x102 8x102 103 1.2x103 1.4x103 1.6x103 f d.-q. wang et alii, frattura ed integrità strutturale, 41 (2017) 143-148; doi: 10.3221/igf-esis.41.20 148 acknowledgements he authors are grateful for the supports provided by the national natural science foundation of china (nos. 51575182 and 51325504). references [1] lee, s.y., choo, h., liaw, p.k., an, k., hubbard, c.r., a study on fatigue crack growth behavior subjected to a single tensile overload: part ii. transfer of stress concentration and its role in overload-induced transient crack growth, acta. mater., 59 (2011) 495-502. [2] lee, s.y., liaw, p.k., choo, h., rogge, r.b., a study on fatigue crack growth behavior subjected to a single tensile overloadpart i. an overload-induced transient crack growth micromechanism, acta. mater., 59 (2011) 485-494. [3] nowell, d., de matos, p.f.p., application of digital image correlation to the investigation of crack closure following overloads, procedia engineering, 2 (2010) 1035-1043. [4] yusof, f., lopez-crespo, p., withers, p.j., effect of overload on crack closure in thick and thin specimens via digital image correlation, int. j. fatigue., 56 (2013) 17-24. [5] xiao, l., ye, d., chen, c., liu, j., zhang, l., instrumented indentation measurements of residual stresses around a crack tip under single tensile overloads, int. j. mech. sci., 78 (2014) 44-51. [6] suresh, s., further remarks on the micromechanisms of fatigue crack growth retardation following overloads, eng. fract. mech., 21 (1985) 1169-1170. [7] lopez-crespo, p., steuwer, a., buslaps, t., tai, y.h., lopez-moreno, a., yates, j.r., withers, p.j., measuring overload effects during fatigue crack growth in bainitic steel by synchrotron x-ray diffraction, int. j. fatigue., 71 (2015) 11-16. [8] sunder, r., andronik, a., biakov, a., eremin, a., panin, s., savkin, a., combined action of crack closure and residual stress under periodic overloads: a fractographic analysis, int. j. fatigue., 82 (2016) 667-675. [9] zhang, w., liu, y., plastic zone size estimation under cyclic loadings using in situ optical microscopy fatigue testing, fatigue. fract. eng. mater. struct., 34 (2011) 717-727. [10] carroll, j., efstathiou, c., lambros, j., sehitoglu, h., hauber, b., spottswood, s., chona, r., investigation of fatigue crack closure using multiscale image correlation experiments, eng. fract. mech., 76 (2009) 2384-2398. [11] nowell, d., kartal, m.e., de matos, p.f.p., digital image correlation measurement of near-tip fatigue crack displacement fields: constant amplitude loading and load history effects, fatigue. fract. eng. mater. struct., 36 (2013) 3-13. [12] stinville, j.c., vanderesse, n., bridier, f., bocher, p., pollock, t.m., high resolution mapping of strain localization near twin boundaries in a nickel-based superalloy, acta. mater., 98 (2015) 29-42. [13] wang, d.-q., zhu, m.-l., xuan, f.-z., correlation of local strain with microstructures around fusion zone of a cr-nimo-v steel welded joint, mater. sci. eng. a, 685 (2017) 205-212. [14] zhu, m.-l., xuan, f.-z., tu, s.-t., observation and modeling of physically short fatigue crack closure in terms of insitu sem fatigue test, mater. sci. eng. a, 618 (2014) 86-95. t << /ascii85encodepages false /allowtransparency false /autopositionepsfiles true /autorotatepages /none /binding /left /calgrayprofile (dot gain 20%) /calrgbprofile (srgb iec61966-2.1) /calcmykprofile (u.s. web coated \050swop\051 v2) /srgbprofile (srgb iec61966-2.1) /cannotembedfontpolicy /error /compatibilitylevel 1.4 /compressobjects /tags /compresspages true /convertimagestoindexed true /passthroughjpegimages true /createjobticket false /defaultrenderingintent /default /detectblends true /detectcurves 0.0000 /colorconversionstrategy /cmyk /dothumbnails false /embedallfonts true /embedopentype false /parseiccprofilesincomments true /embedjoboptions true /dscreportinglevel 0 /emitdscwarnings false /endpage -1 /imagememory 1048576 /lockdistillerparams false /maxsubsetpct 100 /optimize true /opm 1 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can be opened with acrobat and adobe reader 5.0 and later.) >> /namespace [ (adobe) (common) (1.0) ] /othernamespaces [ << /asreaderspreads false /cropimagestoframes true /errorcontrol /warnandcontinue /flattenerignorespreadoverrides false /includeguidesgrids false /includenonprinting false /includeslug false /namespace [ (adobe) (indesign) (4.0) ] /omitplacedbitmaps false /omitplacedeps false /omitplacedpdf false /simulateoverprint /legacy >> << /addbleedmarks false /addcolorbars false /addcropmarks false /addpageinfo false /addregmarks false /convertcolors /converttocmyk /destinationprofilename () /destinationprofileselector /documentcmyk /downsample16bitimages true /flattenerpreset << /presetselector /mediumresolution >> /formelements false /generatestructure false /includebookmarks false /includehyperlinks false /includeinteractive false /includelayers false /includeprofiles false /multimediahandling /useobjectsettings /namespace [ (adobe) (creativesuite) (2.0) ] /pdfxoutputintentprofileselector /documentcmyk /preserveediting true /untaggedcmykhandling /leaveuntagged /untaggedrgbhandling /usedocumentprofile /usedocumentbleed false >> ] >> setdistillerparams << /hwresolution [2400 2400] /pagesize [612.000 792.000] >> setpagedevice microsoft word numero_51_art_2_2570 a. chiozzi et alii, frattura ed integrità strutturale, 51 (2020) 9-23; doi: 10.3221/igf-esis.51.02 9 focussed on fracture and damage detection in masonry structures nurbs-based kinematic limit analysis of frp-reinforced masonry walls with out-of-plane loading andrea chiozzi university of ferrara, italy andrea.chiozzi@unife.it, http://orcid.org/0000-0003-4660-0637 nicola grillanda, gabriele milani technical university of milan, italy nicola.grillanda@polimi.it, gabriele.milani@polimi.it, http://orcid.org/0000-0001-5462-3420 antonio tralli university of ferrara, italy tra@unife.it abstract. a three-dimensional (3d) general upper-bound limit analysis procedure for the determination of the collapse load of out-of-plane loaded masonry walls with fiber reinforced polymer (frp) reinforcement strips is presented. the geometry of a given frp reinforced masonry wall of arbitrary shape is represented by its non-uniform rational b-spline (nurbs) description in the three-dimensional euclidean space. the nurbs parameter space is partitioned by means of a number of possible fracture lines and the original reinforced wall geometry is subdivided into an initial set of rigid elements, accordingly. an upper-bound limit analysis formulation, accounting for the main characteristics of both masonry material and frp reinforcement by means of homogenization techniques, is deduced. internal dissipation is allowed along element edges only and the effect of vertical loads and membrane stresses is considered as well. numerical experiments show that a good estimate of the load bearing capacity is obtained provided that the initial arrangement of yield lines is adjusted by means of a suitable genetic algorithm (ga). keywords. limit analysis; masonry; masonry walls; frp strips; nurbs; genetic algorithms. citation: chiozzi, a., grillanda, n., milani, g., tralli, a.., nurbs-based kinematic limit analysis of frp-reinforced masonry walls with out-of-plane loading, frattura ed integrità strutturale, 51 (2020) 9-23. received: 20.07.2019 accepted: 11.10.2019 published: 01.01.2020 copyright: © 2019 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. http://www.gruppofrattura.it/va/51/2570.mp4 a. chiozzi et alii, frattura ed integrità strutturale, 51 (2020) 9-23; doi: 10.3221/igf-esis.51.02 10 introduction asonry walls represent the commonest structural element encountered in masonry constructions, largely used both as principal members [1] and non-structural internal partitions and infill panels [2]. a relevant issue in the field of structural analysis of existing buildings is the assessment of the load bearing capacity of out-of-plane loaded masonry walls. in fact, out-of-plane failures are mostly a consequence of horizontal actions, especially seismic loads, against which they generally exhibit poor resistance. recent earthquakes in italy (l’aquila, 2009; emilia 2012; lazio 2016), demonstrated that out-of-plane failures stem from the lack of out-of-plane strength, especially for historical constructions [3–5]. for this reason, masonry walls in historical buildings often require external retrofitting interventions, in order to guarantee a sufficient level of out-of-plane strength. since conventional retrofitting solutions such as the use of steel plates and reinforced concrete plaster are often impractical and may add undesirable mass to the existing structure, the use of fiber reinforced polymer (frp) strips is acquiring good popularity in the scientific and professional community. frp retrofitting strips are characterized by durability, low invasiveness and good ultimate behavior. however, a limited body of work is available to date, addressing the numerical modeling of masonry walls reinforced with frp strips [6,7]. on the one hand, finite element analyses have been proposed as a viable tool for the prediction of the load bearing capacity of frp reinforced masonry walls [8]. however, finite element simulations are time expensive and require skilled users to correctly set the many material parameters required in order to provide reliable results. on the other hand, experimental tests carried out since the 70’s on masonry walls with out-of-plane loading, have shown that collapse occurs upon formation of a welldefined pattern of linear cracks [9,10]. this evidence inspired approximated solutions relying on both the fracture line theory [11] and the yield line theory [12,13], which in fact are applications of the upper-bound theorem of limit analysis. indeed, despite the well-established fact that masonry behaves very differently from a rigid-plastic material, limit analysis is among the most reliable tools for the assessment of the load bearing capacity of masonry walls [14]. after heyman’s assumption that masonry behaves as a no-tension material [15], several italian scientists, among which we recall como [14], di pasquale [16], angelillo [17], del piero [18], have proved that the load bearing capacity of masonry structures can be estimated within the scheme of classic limit analysis under the principles of the theory of plasticity. nevertheless, several mechanical features of masonry material are not accounted for by the no-tension model. first, masonry is a heterogeneous material with a nonisotropic behaviour, both in the elastic region and at collapse [19]. second, masonry tensile strength, even if usually very low, is quite variable and uncertain; moreover, the assumption of infinite compression strength is often too strict. third, experiments show that friction coefficient μ for masonry is relatively high [20]. therefore, a non-associative flow rule must be enforced and, as a consequence, limit analysis theorems cannot be applied anymore [21–23]. for such reasons, a number of computational methods for the limit analysis of out-of-plane loaded masonry walls, even in the presence of frp reinforcement, not based on the no-tension model, have been proposed in literature. for instance, we can recall several finite element methods (fem) based on homogenized limit analysis [24,25]. in the present paper, we propose a new nurbs-based adaptive scheme for the homogenized kinematic limit analysis of masonry walls with out of plane loading, in the presence of frp reinforcement. the approach, originally proposed by the authors for both unreinforced and reinforced masonry arches and vaults (see [26–34]), allows to easily assess the out-ofplane failure mechanism for an frp reinforced wall with openings of arbitrary geometry. homogenization concepts [35] are employed to obtain out-of-plane homogenized failure mechanical parameters. nurbs (i.e. non-rational uniform bispline) are the most common class of approximating basis functions employed in the field of 3d free form modeling [36]. an arbitrary frp reinforced masonry wall can be represented by a nurbs description of its mid-surface, which can be obtained within any commercial free form modeler, and providing information about the structural thickness at each point of the surface. frp reinforcement strips are modeled as nurbs surfaces as well. the nurbs parameter space is partitioned by means of a number of possible fracture lines and the original reinforced wall geometry is subdivided into an initial set of rigid elements, accordingly. a homogenized upper-bound limit analysis formulation, accounting for the main characteristics of both masonry material and frp reinforcement, is deduced. internal dissipation is allowed along element edges only and the effect of vertical loads and membrane stresses is considered as well. since the discretization makes use of a very limited number of rigid elements, the actual failure mechanism can be found provided that the discretization is suitably adjusted by means of a genetic algorithm (ga) with nonstandard optimization tools [37]. in the process, possible delamination at the frp/masonry interface is accounted for. even though delamination is a typically brittle phenomenon, and thus, strictly speaking, it limits the applicability of limit analysis theorems, an equivalent ultimate shear strength for frp/masonry interface is assumed in the framework of limit analysis, as suggested by the italian norm regulating of retrofit interventions with frp materials [38]. m a. chiozzi et alii, frattura ed integrità strutturale, 51 (2020) 9-23; doi: 10.3221/igf-esis.51.02 11 with respect to existing methods, the proposed procedure exploits the properties of the nurbs representation of a masonry panel in order to build a very coarse even though exact rigid element discretization. in addition, the knowledge of the actual failure mechanism is not required in advance and the problem is governed by a relatively low number of variables thanks to the use of a very coarse discretization. therefore, a high computational efficiency is attained. moreover, since nurbs functions are widespread in the field of free form modeling, the proposed method could easily be integrated within existing commercial cad software packages, which are popular among professional engineers and architects. the paper is organized as follows: section 2 treats the nurbs discretization of a generic masonry wall with openings of arbitrary shape. in section 3, the proposed upper bound limit analysis nurbs-based adaptive formulation is summarized, which allows to compute the collapse load for a set of given failure mechanisms also accounting for the presence of frp strips. finally, section 4 illustrates the proposed approach by means of numerical simulations. rigid elements discretization ny arbitrary frp reinforced masonry wall with openings, can be modeled as a set of nurbs surfaces within any commercial 3d modeling environment. nurbs basis functions stem from b-splines approximating functions, i.e. piecewise polynomial functions defined by a knot vector       1 2 1{ , ,..., }n p , whose elements,  [0,1]i , are points in a parametric space. let us denote by p the polynomial order and n the total number of basis functions. the coxde-boor recursion formula allows to compute the i-th b-spline basis function, ,i pn [36]. after defining a suitable set of weights iw , the nurbs basis functions, ,i pr , is given by:       , , , 1 ( ) ( ) . ( ) i p i i p n i p i i n w r n w (1) differently from b-spline basis functions, nurbs basis functions allow the exact representation of the geometry of a wide class of curves such as circles, ellipses, and parabolas [36], as well as the surfaces that can be generated by these curves. in analogy to nurbs curves, it is possible to define a nurbs surface of degree p in the u-direction and q in the v-direction as the three-dimensional parametric surface defined as:     , , 0 0 ( , ) ( , ) n m i j i j i j u v r u vs b (2) where { }ijb is a lattice of control points in the euclidean 3d space. again, it is necessary to set a suitable set of weights ,{ }i jw and two knot vectors in both u and v directions. most of the commercial three-dimensional surface modelers, such as rhinoceros® [39], make use of nurbs functions and their properties to generate and manipulate geometrical objects in the three-dimensional space. in the numerical simulations discussed in section 4, both masonry walls and frp reinforcement strips have been modeled within rhinoceros® as nurbs surfaces. the corresponding nurbs mathematical structure have been exported by means of the iges (initial graphics exchange specification) standard [40], so that a suitable (rigid) discretization of the frp reinforced masonry structure can be constructed in matlab®, by exploitation of the properties of nurbs functions. in the obtained mesh, each element is a nurbs surface itself and is assumed to be rigid and a thickness is assigned to the elements by offsetting the mid-surface of the desired quantity inward and outward with respect to the normal direction. in fact, the obtained discretization is an assembly of rigid blocks. in the simplest cases, assigned a given masonry wall which can be described by a single nurbs surface, the counter-image wi of its nurbs representation in the 2d parameters space u-v is the square [0,1] [0,1] . in general, the counter-image domain wi is bounded by nurbs two-dimensional curves, directly defined in the parameters space. the iges format stores all the information needed to reconstruct the parameters space of a given nurbs surface. subdividing the two-dimensional parameters space u-v, it is possible to construct a nurbs discretization of a given planar surface representing a masonry wall. more specifically, in the 2d parameter space it is possible to define a suitable lattice of nodes, which in fact are the counter-image of the nodes of the actual mesh. suitable curves in the parameters space, a a. chiozzi et alii, frattura ed integrità strutturale, 51 (2020) 9-23; doi: 10.3221/igf-esis.51.02 12 connecting the nodes define the edges of the elements in the three-dimensional euclidean space. an appropriate connectivity matrix for the 2d counter-image of the mesh in the parameters space can be assembled. figure 1: (a) nurbs model of a masonry wall. (b) counter-image iw of the nurbs surface in the parameters space u-v. (c) initial subdivision of the parameters space into four rectangular elements. (d) modified subdivision of the parameters space into four generic quadrilateral elements. fig. 1(a) depicts an example of a 3d nurbs surface used to model a rectangular masonry wall. fig. 1(b) shows the corresponding parameters space counter-image wi , coinciding with the parameters-space [0,1] [0,1] itself. fig. 1(c) and fig. 1(d) depict two possible four-element subdivisions of the parameters space. after the definition of a suitable lattice of nodes in the parameters space, it is possible to transition from the subdivision shown in fig. 1(c) to the one represented in fig. 1(d) by controlling the coordinates of the internal nodes. in the proposed approach this process will be suitably automated by means of a ga (see section 3). since masonry walls fail upon formation of a limited number of crack lines, the number of nodes belonging to the parameters space lattice can be relatively small [41]. in order to correctly treat openings, a simple algorithm is proposed to generate a robust mesh of the structure. this algorithm is illustrated and summarized in fig. 2 for a façade wall with two openings containing curved edges. fig. 2(a) shows the 3d nurbs representation of the wall, while its counter-image wi in the parameters space [0,1] [0,1] is depicted in fig. 2(b). on step one, an initial lattice subdivision of the square [0,1] [0,1] in the parameters space is performed, see fig. 2(c), independently from the presence of openings. then, the lattice nodes lying outside the actual counter-image of the original surface due to the presence of openings, are moved towards the closest bounding curve of the actual counterimage domain wi of the surface, along rectilinear trajectories parallel to axes u-v, as depicted in fig. 2(d) (step two). notable quantities to be computed are area of the surface and the center of mass of each element ie of the mesh. be ik the counter-image of element ie in the parameters space u-v. the surface area of ie can be determined by integration as:     i i i u ve k a ds du dvs s (3) where us and vs are the partial derivatives of surface ( , )u vs along u and v directions. on the other hand, the center of mass of ie may be computed as:     1 ( , ) i i u v e k i ds u v du dv a c x s s s (4) a. chiozzi et alii, frattura ed integrità strutturale, 51 (2020) 9-23; doi: 10.3221/igf-esis.51.02 13 figure 2: (a) nurbs model of masonry wall with openings. (b) counter-image iw of the nurbs surface in the parameters space u-v. (c) initial subdivision of the parameters space bounding region: step one. (d) initial subdivision of the counter-image wi of the nurbs surface: step two. (e) ga mesh adaptation in the parameters space bounding region: step one. (f) ga mesh adaptation in the actual parameter space: step two. figure 3: isoparametric linear mapping. integrals (3) and (4) on a generic rectangular domain can be approximated by gauss numerical cubature coupled with a suitable isoparametric approach, see fig. 3 and [26] for more details. a. chiozzi et alii, frattura ed integrità strutturale, 51 (2020) 9-23; doi: 10.3221/igf-esis.51.02 14 adaptive nurbs-based upper-bound limit analysis formulation rigid blocks kinematic limit analysis model iven the nurbs rigid blocks discretization model of the frp reinforced wall, an upper bound limit analysis formulation can be provided, where internal dissipation is allowed only at the element edges. this assumption has proven to be adequate for the general case of frp reinforced masonry shells with out-of-plane loading [25]. this section summarizes the proposed limit analysis formulation. be en the number of rigid elements composing the nurbs mesh of the frp reinforced masonry wall. the kinematics of each element is governed by the six generalized velocities   { , , , , , }i i i i i ix y z x y zu u u of its barycenter ig . both dead loads 0f and live loads γ act on the structure. the discretization involves three types of interfaces: masonry-masonry, frp-masonry and frp-frp interfaces. be     tot m m m f f fi i i in n n n the number of interfaces, the total internal dissipation rate intd is given by the sum of the power dissipated along each interface int jp . the total internal dissipation rate intd is also equal to the sum of the powers of external live ( 1 ) and dead ( 0f ) loads, respectively pγ and p 0f :    int int 1 in j j d p p p 0γ f (5)  is the multiplier of live loads. the linear programming (lp) problem associated to the upper-bound formulation of limit analysis requires the minimization of  under suitable constraints. the unknown of the problem are the set of elemental generalized velocities and plastic multipliers at the interfaces. geometrical constraints are imposed by prescribing the values of the generalized velocities at nodes belonging to the element free edges. therefore, the geometric constraints can be expressed in terms of the generalized velocities at the barycenter of the element containing those nodes, in the following equality form (see [26] for more details): , ,eq geom eq geoma x b (6) where ,eq geoma is the matrix of geometric constraints and ,eq geomb the corresponding vector of coefficients. with the aim of enforcing plastic compatibility along masonry-masonry interfaces, the edges of each interface have been subdivided into a given number ( 1)msdn of collocation points kp (see fig. 4), where a local reference system ( , , ) m m mn s t is defined, in which mn is the outward unit vector normal to the interface, ms is the longitudinal tangential unit vector and mt is the transversal tangential unit vector. on each point kp of a given interface, between two elements e and e , a compatibility relation must hold in the form:      f u λ σ (7) figure 4: masonry-masonry interface and local reference system. g a. chiozzi et alii, frattura ed integrità strutturale, 51 (2020) 9-23; doi: 10.3221/igf-esis.51.02 15 where   [ , , ]nn ns ntσ is the stress vector in the local reference system at kp , ( )f σ is a suitable yield function and λ is the (unknown) vector of plastic multipliers. in eqn. (7), u represents the relative velocities at points kp in the local reference system. the same quantity u in the global reference system is defined as:     i ip p u u u (8) being  ip u and  ip u are the velocity vectors at kp on the two sides of the interface. furthermore, the following relation must hold:   u r u (9) where r is a rotation matrix. the yield surface ( )f σ can be obtained by means of a homogenization technique based on the so-called method of cells (moc), first introduced in [42] for unidirectional composites and recently applied to inplane loaded masonry walls [43]. the reader is addressed to [26] for further details. be the m-th plane linearizing ( )f σ defined by the equation      1m nn m ns m nta b c . thus, eqn. (9) reduces to the equation:                                            1 1 1 [ ] pl pl pl n m m m m mk s n k m m k t m m mk n n m m m m m a u u b u c u (10) for each collocation point kp , where  m m m is the plastic multiplier corresponding to the m-th linearizing plane and m m pln is the total number of linearization planes. on each interface j, internal dissipation rate in the local reference system reads:    int, j m m j s p dsσ u (11) frp nurbs elements are assumed rigid, as well. therefore, dissipation is allowed along interfaces between adjacent elements only, and is related to longitudinal stresses in the fibers direction. again, with the aim of imposing plastic compatibility along frp-frp interfaces and correctly evaluating the internal dissipation rate, the mid-line of each interface has discretized into an assigned number ( 1)fsdn of collocation points kp (see fig. 5). figure 5: frp-masonry interface and local reference system. on each point kp , the local reference system ( , , ) f f fn s t is introduced, fn being the outward unit vector normal to the interface, fs is the longitudinal tangential unit vector and ft the transversal tangential unit vector. velocity jumps are 3 3 a. chiozzi et alii, frattura ed integrità strutturale, 51 (2020) 9-23; doi: 10.3221/igf-esis.51.02 16 allowed along direction fn only. typically, due to their negligible thickness, frp strips buckle when subjected to the lowest compression stresses. therefore, different tension and compression limit stresses are assigned, denoted as frpf (equal to fddf or ,fdd ridf according to [38]) and   0frpf respectively. the internal dissipation rate at the j-th frp-frp interface is computed as:            int, ( ) j j f f i frp i frp j frp k frp k l l p s dl s f f dlσ u (12) where s is the frp strip thickness, il the frp-frp interface mid-line and   i frp k and   i frp k are plastic multipliers at kp on the interface. delamination phenomenon depends on a large number of parameters related to materials with very different mechanical behavior (glue, brickwork, fibers). for the sake of simplicity, we adopt the provisions suggested by the italian technical norm [38]. more precisely, we account for delamination by means of a conventional approach, consisting in suitably limiting the longitudinal tensile stress in the frp strip – i.e. if the bond length lb is larger than optimal bond length le, the frp strip design traction strength ffdd is computed as:      21 frp fk fdd frpfd m e f t (13) whereas if lb le ffdd is computed as        , 2 b b fdd rid fdd e e l l f f l l (14) in eqn. (13) and (14), ffdd and ffdd,rid denote the design bond strength and the reduced design bond strength respectively, while efrp is the elasticity modulus of frp, tfrp is the thickness of frp strip, γfd is a safety factor equal to 1.20, γm is the masonry partial safety factor, assumed equal to 1.0, lb is the frp strips bond length and   2 frp frp e mtm e t l f is the optimal bond length. the quantity γfk in eqn. (13) represents the specific fracture energy of the frp reinforced masonry undergoing delamination. a sound estimation of the specific fracture energy is still an open research topic, since mechanical properties of masonry are widely viariable. nevertheless, as depicted in fig. 6, the italian norm prescribes the use of a bilinear τb-slip constitutive law, allowing the assessment of the limit shear stress bf , provided that ultimate slip is known (tipically assumed equal to 0.2 mm). as clearly pointed out in many studies, a damaging material model would be the optimal choice when studying failure of frp strips on masonry [44,45]. however, such model cannot be employed in the framework of limit analysis, which, as is well known, relies on the assumption of perfect plasticity. nevertheless, in agreement with suggestions contained in [38], limit analysis still remains the tool of choice in order to easily estimate the bearing capacity of a given masonry structure. this fact is also reflected in the provisions provided by both the italian building code [46] and the related explicative instructions [47]. moreover, a number of studies in the literature proved that limit analysis is still capable of reliably assess frp reinforced masonry structures, see e.g. [48,49]. finally, frp-masonry interfaces are nurbs surface belonging to the faces of the masonry wall. to account for dissipation along such third type of interface, a given number m fpn of collocation points on the interface are defined. at each point we introduce a local reference system ( , , )i i is t n so that the stress field    ( , , )s t nσ along the local axes is well defined. as before, with the aim of applying the limit analysis theorems, an associate flow rule on the frp-masonry interface must hold. again, the failure surface to be used on frp-masonry interfaces can be linearized as      1m nn m ns m nta b c ,  1, , m fplm n ( m f pln being the number of linearizing planes employed).  a. chiozzi et alii, frattura ed integrità strutturale, 51 (2020) 9-23; doi: 10.3221/igf-esis.51.02 17 figure 6: (a) τb-slip constitutive law; (b) σ-τs-τt failure surfaces for masonry-frp interfaces. in this case, flow rule (7) is specialized to:                                              1 1 1 [ ] m f pl m f pl m f pl n m f m m mk s n k m f k t m m mk n n m f m m m a u u b u c u (15) eqn. (15) represents further equality constraints to the lp problem, in which  m fm is the m-th plastic multiplier associated to the m-th linearizing plane. the italian design code for frp reinforcement suggest specific  - s - t failure surfaces for frp-masonry interfaces, as depicted in fig. 6(b), in which bf is the interface shear strength and mtf describes masonry tensile strength. for each point of each frp-masonry interface m fpln unknown plastic multipliers are introduced. therefore, the total number of unknown plastic multipliers for frp-masonry interfaces is equal to   m f m f m fpl p in n n . on each frp-masonry interface i , associated to the surface is , the internal dissipation rate is computed in the local reference system as:    int, j m f j s p dsσ u (16) moreover, the non-negativity of each plastic multipliers must be enforced by means of the additional constraint:   0.m (17) finally, we must impose a normality condition, requiring that the power dissipated by a unitary live load is equal to one, i.e.:  1 1p (18) therefore, the lp problem associated to the proposed upper-bound formulation reads: a. chiozzi et alii, frattura ed integrità strutturale, 51 (2020) 9-23; doi: 10.3221/igf-esis.51.02 18           int 1 min in j j p p 0f (19) under geometric constraints (6), compatibility constraints (10), (12) and (15), non-negativity of plastic multipliers constraints (17) and the normality condition (18). ga mesh adaptation scheme the mesh is adaptively adjusted by means of a ga, allowing the estimation of the minimum collapse multiplier, therefore determining the actual collapse mechanism. a ga is a metaheuristic algorithm for solving both constrained and unconstrained optimization problems, which mimics the process of natural selection and biological evolution [50]. the ga iteratively modifies a population of individual solutions. at each step, individuals are randomly selected from the current population and used as parents to produce next generation offspring, so that the population evolves toward an optimal solution. here, individuals are a set of parameters defining a mesh and the objective function is the collapse load multiplier. numerical examples n this section we apply the proposed ga-nurbs limit analysis procedure to the study of the ultimate behavior of out-of-plane loaded masonry walls reinforced with frp strips. the numerical simulations focuses on two frp reinforced masonry wall specimens subjected to two-way bending with and without openings, fixed at the bottom edge and simply supported along vertical edges. the geometry of the walls and the disposition of frp reinforcement strips is shown in fig. 7. in particular, the models reproduce specimens sb01 and sb02 of a set of experimental tests on five unreinforced solid clay bricks masonry panels (labeled from sb01 and sb05) carried out in [51]. all the panels of the experimental campaign have dimensions 5615x2475x102 mm. the panels were loaded in the out-of-plane direction by airbags inflated until failure with increasing pressure p. masonry parameters adopted in the simulations are taken from [51] and [52] (see tab. 1); no experimental data are available from the literature concerning such panels in presence of frp reinforcement. as for the reinforced case, two 100mm wide horizontal strips are disposed on the walls extrados, at the top and at the bottom, with the aim of preventing the opening of vertical and inclined cracks observed experimentally in the unreinforced panels. the initial nurbs discretization of the unreinforced panel is made of ten quadrangular elements, obtained by subdividing the parameters space starting from a 4x6 nodes lattice. while the four vertexes are kept fixed, the ga allows to evaluate the optimal position of the remaining fourteen free nodes, minimizing the collapse load multiplier and, thus, obtaining the actual failure mechanism. figure 7: (a-b) geometry of wall specimens sb01 and sb02; (c-d) frp reinforcement configuration for specimens sb01 and sb02. i a. chiozzi et alii, frattura ed integrità strutturale, 51 (2020) 9-23; doi: 10.3221/igf-esis.51.02 19 case study masonry material parameters masonry/fr p bond strength (fb) [mpa] compressive strength (fk) [mpa] tensile strength (ft) [mpa] shear strength (fvk0) [mpa] sb01, sb02 [25,51,52] 8.00 0.32 0.32 0.30 table 1: material parameters. every node position is controlled by two parameters, with the exception of one-parameter edge-nodes and the four fixed vertex-nodes. thus, also relying on the symmetry of the problem, the optimization problem is governed by fourteen parameters, which can be reduced to nine for to symmetry. a collapse load  2.69p kn/m2 has been coputed for the unreinforced case. fig. 8(a) and fig. 8(b) respectively depict the computed failure mechanism obtained by means of the proposed ga-nurbs approach and the homogenized fe limit analysis technique proposed in [25]. moreover, a good agreement can be found when comparing the obtained results from the proposed ga-nurbs approach with the outcomes of both original experiments and different numerical procedures found in the literature [27]. in particular, it can be seen that the proposed ga-nurbs approach slightly overestimates the actual collapse load. figure 8: sb01 masonry panel without openings tested in [51]. (a-c) unreinforced and reinforced case, respectively: collapse mechanism with the ga-nurbs approach; (b-d) unreinforced and reinforced case, respectively: collapse mechanism with the homogenized fe limit analysis proposed in [25]. a. chiozzi et alii, frattura ed integrità strutturale, 51 (2020) 9-23; doi: 10.3221/igf-esis.51.02 20 figure 9: dependence of the collapse load multiplier of reinforced panel sb01 on the frp-masonry bond strength fb. red dots: values computed by means of the proposed ga-nurbs approach; black line: values computed in [25]. figure 10: sb02 masonry panel with rectangular opening tested in [51]. (a-c) unreinforced and reinforced case, respectively: collapse mechanism with the ga-nurbs approach; (b-d) unreinforced and reinforced case, respectively: collapse mechanism with the homogenized fe limit analysis proposed in [25]. a. chiozzi et alii, frattura ed integrità strutturale, 51 (2020) 9-23; doi: 10.3221/igf-esis.51.02 21 on the other hand, fig. 8(c) and fig. 8(d) respectively represent the computed failure mechanism for the reinforced case, obtained by means of the proposed ga-nurbs approach and the homogenized fe limit analysis approach proposed in [25]. a collapse load p = 4.74 kn/m2 has been obtained for the reinforced case, which is in agreement with the collapse load found in [25], i.e. 4.58 kn/m2, as shown in fig. 9 (for  0.30bf mpa). fig. 9 also shows the variation in the collapse load multiplier due to a variation in the frp-masonry bond strength fb, compared with the values computed in [25]. figure 11: dependence of the collapse load multiplier of reinforced panel sb01 on the frp-masonry bond strength fb. red dots: values computed by means of the proposed ga-nurbs approach; black line: values computed in [25]. then, the unreinforced panel sb02 with a rectangular opening experimentally tested in [51] is analyzed. the initial nurbs discretization of the wall is made of sixteen quadrangular elements, after subdividing the parameters space from a 4x6 lattice of nodes. again the four vertex nodes are fixed. the ga allows to estimate the optimal position of the remaining twentyone nodes, by minimization of the collapse load multiplier, thus obtaining the actual failure mechanism. every node position is controlled by two parameters, except for the (one parameter) edge-nodes. finally, appealing to symmetry, the number of governing parameters is reduced to fourteen. a collapse load  2.19p kn/m2 has been computed with the proposed ganurbs scheme. fig. 10(a) and fig. 10(b) respectively represent the computed failure mechanism obtained through the proposed ga-nurbs approach and the homogenized fe limit analysis approach proposed in [25]. a good agreement is also found between the results from the proposed ga-nurbs approach with the outcomes from both original experiments and different numerical procedures found in the literature [27]. on the other hand, fig. 10(c) and fig. 10(d) represent the computed failure mechanism for the reinforced case, computed by means of the proposed ga-nurbs approach and the homogenized fe limit analysis approach proposed in [25], respectively. a collapse load p = 4.55 kn/m2 has been computed for the reinforced case, which is in agreement with the collapse load found in [25], i.e. 4.30 kn/m2, as shown in fig. 11 (for  0.30bf mpa). fig. 11 also shows the dependence of the collapse load multiplier on the frp-masonry bond strength fb, compared with the values computed in [25]. conclusions e presented a new ga-nurbs based approach for the upper-bound limit analysis of frp reinforced masonry walls with out-of-plane loading and arbitrary openings, in which the properties of nurbs functions are exploited to provide an efficient adaptive limit analysis scheme, allowing to easily evaluate both the collapse load multiplier and the failure mechanism of any given frp reinforced out-of-plane loaded masonry wall, building on its 3d nurbs model. the use of nurbs functions to construct a rigid blocks discretization, allows to easily port the proposed approach into any commercial modeling environment. moreover, differently from existing procedures implemented in commercial software packages, the ga-nurbs approach does not require an a-priori knowledge of the actual failure mechanism. by means of numerical simulations and comparisons with both experiments and numerical results from the literature, the approach has proved to be capable to accurately predict the ultimate capacity of any frp reinforced masonry wall with out of plane loading, by using very few elements, and, therefore, maximizing computational speed. w a. chiozzi et alii, frattura ed integrità strutturale, 51 (2020) 9-23; doi: 10.3221/igf-esis.51.02 22 references [1] huerta, s. (2011). the analysis of masonry architecture: a historical approach, archit. sci. rev., 51(4), pp. 297–328. [2] chiozzi, a., miranda, e. (2017). fragility functions for masonry infill walls with in-plane loading, earthq. eng. struct. dyn., 46(15), pp. 2831–2850, doi: 10.1002/eqe.2934. [3] giuffrè, a. (1993). safety and preservation of historical centers: the ortigia case, laterza (in italian). [4] spence, r., coburn, a. (1992). strengthening buildings of stone masonry to resist earthquakes, meccanica, 27(3), pp. 213–221, doi: 10.1007/bf00430046. [5] chiozzi, a., simoni, m., tralli, a. (2016). base isolation of heavy non-structural monolithic objects at the top of a masonry monumental construction, mater. struct. constr., 49(6), pp. 2113–2130, doi: 10.1617/s11527-015-0637-z. [6] korany, y., drysdale, r. (2007). load-displacement of masonry panels with unbonded and intermittently bonded frp. ii: analytical study, j. compos. constr., 11(1), pp. 24–32, doi: 10.1061/(asce)1090-0268(2007)11:1(24). [7] korany, y., drysdale, r. (2007). load-displacement of masonry panels with unbonded and intermittently bonded frp. i: analytical model, j. compos. constr., 11(1), pp. 15–23, doi: 10.1061/(asce)1090-0268(2007)11:1(15). [8] monaco, a., minafò, g., cucchiara, c., d’anna, j., la mendola, l. (2017). finite element analysis of the out-of-plane behavior of frp strengthened masonry panels, compos. part b eng., 115, pp. 188–202, doi: 10.1016/j.compositesb.2016.10.016. [9] de felice, g., giannini, r. (2001). out-of-plane seismic resistance of masonry walls, j. earthq. eng., 5(2), pp. 253– 271. [10] gazzola, e.a., drysdale, r.g., essawy, a.s. (1985). bending of concrete masonry walls at different angles to the bed joints, proc. third north amer. mas. conf., 27, doi: 10.1520/stp34544s. [11] sinha, b.p. (1978). a simplified ultimate load analysis of laterally loaded model orthotropic brickwork panels of low tensile strength, struct. eng., 56b(4), pp. 81–84. [12] losberg, a., johansson, s. (1969). sideways pressure on masonry walls of brickwork. cib symposium on bearing walls, warsaw, poland. [13] haseltine, b.a., west, h.w.h. (1977). design of walls to resist lateral loads, struct. eng., 55(10), pp. 422–430. [14] como, m. (2013). statics of historic masonry construction, springer-verlag berlin heidelberg. [15] heyman, j. (1966). the stone skeleton, int. j. solids struct., 2(2), pp. 249–79, doi: 10.1016/0020-7683(66)90018-7. [16] di pasquale, s. (1984). statica dei solidi murari: teoria ed esperienze, university of firenze. [17] angelillo, m. (1993). constitutive relations for no-tension materials, meccanica, 28(3), pp. 195–202, doi: 10.1007/bf00989121. [18] del piero, g. (1998). limit analysis and no-tension materials, int. j. plast., 14(1), pp. 259–271, doi: 10.1016/s0749-6419(97)00055-7. [19] dhanasekar, m., page, a.w., kleeman, p.w. (1985). the failure of brick masonry under biaxial stresses., proc. inst. civ. eng., 79(2), pp. 295–313, doi: 10.1680/iicep.1985.992. [20] vasconcelos, g., lourenço, p.b. (2006).assessment of the in-plane shear strength of stone masonry walls by simplified models. proceedings of the 5th international conference of structural analysis of historical construction, new delhi, india. [21] radenkovic. (1961). théorèmes limites pour un materiau de coulomb a dilatation non standardise, comptes rendue académie sci. paris, 252, pp. 4103–4104. [22] salençon j. (1977). application of the theory of plasticity in soil mechanics, john wiley & sons (usa). [23] orduña, a., lourenço, p.b. (2005). three-dimensional limit analysis of rigid blocks assemblages. part i: torsion failure on frictional interfaces and limit analysis formulation, int. j. solids struct., 42(18), pp. 5140–5160, doi: 10.1016/j.ijsolstr.2005.02.010. [24] grande, e., milani, g., sacco, e. (2008). modelling and analysis of frp-strengthened masonry panels, eng. struct., 30(7), pp. 1842–1860, doi: 10.1016/j.engstruct.2007.12.007. [25] milani, g. (2009). homogenized limit analysis of frp-reinforced masonry walls out-of-plane loaded, comput. mech., 43(5), pp. 617–639, doi: 10.1007/s00466-008-0334-7. [26] chiozzi, a., milani, g., tralli, a. (2017). a genetic algorithm nurbs-based new approach for fast kinematic limit analysis of masonry vaults, comput. struct., 182, pp. 187–204, doi: 10.1016/j.compstruc.2016.11.003. [27] chiozzi, a., milani, g., grillanda, n., tralli, a. (2017). a fast and general upper-bound limit analysis approach for outof-plane loaded masonry walls, meccanica, 53(7), pp. 1875–1898, doi: 10.1007/s11012-017-0637-x. [28] chiozzi, a., milani, g., tralli, a. (2017). fast kinematic limit analysis of frp-reinforced masonry vaults. i: a general a. chiozzi et alii, frattura ed integrità strutturale, 51 (2020) 9-23; doi: 10.3221/igf-esis.51.02 23 genetic algorithm nurbs-based formulation, j. eng. mech., 143(9), doi: 10.1061/(asce)em.1943-7889.0001267. [29] chiozzi, a., milani, g., tralli, a. (2017). fast kinematic limit analysis of frp-reinforced masonry vaults. ii: numerical simulations, j. eng. mech., 143(9), doi: 10.1061/(asce)em.1943-7889.0001268. [30] chiozzi, a., grillanda, n., milani, g., tralli, a. (2018). ub-almanac: an adaptive limit analysis nurbs-based program for the automatic assessment of partial failure mechanisms in masonry churches, eng. fail. anal., 85, pp. 201– 220, doi: 10.1016/j.engfailanal.2017.11.013. [31] chiozzi, a., milani, g., grillanda, n., tralli, a. (2016). an adaptive procedure for the limit analysis of frp reinforced masonry vaults and applications, am. j. eng. appl. sci., 9(3), pp. 735–745, doi: 10.3844/ajeassp.2016.735.745. [32] chiozzi, a., malagù, m., tralli, a., cazzani, a. (2016). archnurbs: nurbs-based tool for the structural safety assessment of masonry arches in matlab, j. comput. civ. eng., 30(2), doi: 10.1061/(asce)cp.1943-5487.0000481. [33] grillanda, n., chiozzi, a., bondi, f., tralli, a., manconi, f., stochino, f., cazzani, a. (2019). numerical insights on the structural assessment of historical masonry stellar vaults: the case of santa maria del monte in cagliari, contin. mech. thermodyn., in press, pp. 1–24, doi: 10.1007/s00161-019-00752-8. [34] grillanda, n., chiozzi, a., milani, g., tralli, a. (2019). collapse behavior of masonry domes under seismic loads: an adaptive nurbs kinematic limit analysis approach, eng. struct., accepted. [35] milani, g., taliercio, a. (2016). limit analysis of transversally loaded masonry walls using an innovative macroscopic strength criterion, int. j. solids struct., 81, pp. 274–293, doi: 10.1016/j.ijsolstr.2015.12.004. [36] cottrell, j.a., hughes, t.j.r., bazilevs, y. (2009). isogeometric analysis: toward integration of cad and fea, john wiley & sons. [37] milani, g., milani, f. (2008). genetic algorithm for the optimization of rubber insulated high voltage power cables production lines, comput. chem. eng., 32(12), pp. 3198–3212, doi: 10.1016/j.compchemeng.2008.05.010. [38] cnr-dt200. (2013). instructions for the design, execution and control of retrofit interventions on buildings by means of frp composites (in italian), italian research council. [39] mcneel, r. (2008). rhinoceros: nurbs modeling for windows, robert mcneel & associates. [40] uspro. (1996). initial graphics exchange specification, iges 5.3, u.s. product data association. [41] de felice, g., universi, r.g., studi, d., tre, r. (2001). out-of-plane seismic resistance of masonry walls, j. earthq. eng., 5(2), pp. 253–271. [42] aboudi, j. (2013). mechanics of composite materials: a unified micromechanical approach, elsevier. [43] milani, g., taliercio, a. (2015). in-plane failure surfaces for masonry with joints of finite thickness estimated by a method of cells-type approach, comput. struct., 150, pp. 34–51, doi: 10.1016/j.compstruc.2014.12.007. [44] luciano, r., sacco, e. (1998). damage of masonry panels reinforced by frp sheets, int. j. solids struct., 35(15), pp. 1723–41. [45] marfia, s., sacco, e. (2001). modeling of reinforced masonry elements, int. j. solids struct., 38(24–25), pp. 4177–4198, doi: 10.1016/s0020-7683(00)00297-3. [46] ntc2018. (2018). d.m. 17/01/2018 aggiornamento delle «norme tecniche per le costruzioni», s.o. alla g.u. n. 42 del 20/02/2018. [47] circ2009. (2009). instructions for the application of the new italian building code d.m. 14/01/2008 (in italian), g.u. n. 47 26/02/2009. [48] ascione, l., feo, l., fraternali, f. (2005). load carrying capacity of 2d frp/strengthened masonry structures, compos. part b eng., 36(8), pp. 619–626, doi: 10.1016/j.compositesb.2004.12.004. [49] caporale, a., luciano, r., rosati, l. (2006). limit analysis of masonry arches with externally bonded frp reinforcements, comput. methods appl. mech. eng., 196(1), pp. 247–260, doi: 10.1016/j.cma.2006.03.003. [50] haupt, r.l., haupt, s.e. (2004). practical genetic algorithms, john wiley & sons. [51] chong, v.l. (1993).the behavior of laterally loaded masonry panels with openings. university of plymouth, 1993. [52] milani, g., lourenço, p., tralli, a. (2006). homogenization approach for the limit analysis of out-of-plane loaded masonry walls, j. struct. eng., 132(10), pp. 1650–1663, doi: 10.1061/(asce)0733-9445(2006)132:10(1650). << /ascii85encodepages false /allowtransparency false /autopositionepsfiles true /autorotatepages /none /binding /left /calgrayprofile (dot gain 20%) /calrgbprofile (srgb iec61966-2.1) /calcmykprofile (u.s. web coated \050swop\051 v2) /srgbprofile (srgb iec61966-2.1) /cannotembedfontpolicy /error /compatibilitylevel 1.4 /compressobjects /tags /compresspages true /convertimagestoindexed true /passthroughjpegimages true /createjobticket false /defaultrenderingintent /default /detectblends true /detectcurves 0.0000 /colorconversionstrategy /cmyk /dothumbnails false /embedallfonts true /embedopentype false /parseiccprofilesincomments true /embedjoboptions true /dscreportinglevel 0 /emitdscwarnings false /endpage -1 /imagememory 1048576 /lockdistillerparams false /maxsubsetpct 100 /optimize true /opm 1 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/hrv (za stvaranje adobe pdf dokumenata najpogodnijih za visokokvalitetni ispis prije tiskanja koristite ove postavke. stvoreni pdf dokumenti mogu se otvoriti acrobat i adobe reader 5.0 i kasnijim verzijama.) /hun 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can be opened with acrobat and adobe reader 5.0 and later.) >> /namespace [ (adobe) (common) (1.0) ] /othernamespaces [ << /asreaderspreads false /cropimagestoframes true /errorcontrol /warnandcontinue /flattenerignorespreadoverrides false /includeguidesgrids false /includenonprinting false /includeslug false /namespace [ (adobe) (indesign) (4.0) ] /omitplacedbitmaps false /omitplacedeps false /omitplacedpdf false /simulateoverprint /legacy >> << /addbleedmarks false /addcolorbars false /addcropmarks false /addpageinfo false /addregmarks false /convertcolors /converttocmyk /destinationprofilename () /destinationprofileselector /documentcmyk /downsample16bitimages true /flattenerpreset << /presetselector /mediumresolution >> /formelements false /generatestructure false /includebookmarks false /includehyperlinks false /includeinteractive false /includelayers false /includeprofiles false /multimediahandling /useobjectsettings /namespace [ (adobe) (creativesuite) (2.0) ] /pdfxoutputintentprofileselector /documentcmyk /preserveediting true /untaggedcmykhandling /leaveuntagged /untaggedrgbhandling /usedocumentprofile /usedocumentbleed false >> ] >> setdistillerparams << /hwresolution [2400 2400] /pagesize [612.000 792.000] >> setpagedevice d. wang et alii, frattura ed integrità strutturale, 53 (2020) 236-251; doi: 10.3221/igf-esis.53.20 236 monitoring and analysis of reinforced concrete plate-column structures under room temperature and fire based on acoustic emission dongye wang huaqiao university, xiamen 361021, china xiamen city university, xiamen 361008, china wangdy2269@outlook.com yuli dong*, dashan zhang, weihua wang, xin lu huaqiao university, xiamen 361021, china dongyl@hqu.edu.cn, zhangds@hqu.edu.cn, whwang@hqu.edu.cn, 469316910@qq.com abstract. this paper attempts to disclose the damage mechanism of reinforced concrete plate-column structures under room temperature and fire. several tests were carried out to record the law of crack development on the plate surface under room temperature. the infrared detection technology was adopted to observe how cracks develop under fire. the acoustic emission (ae) signals at different positions of the specimen were monitored by the ae techniques. coupled with the macroscopic test phenomena, several characteristic parameters collected by the ae system, namely, cumulative number of events, event rate, energy rate and b-value, were analyzed in details. the results show that: the cumulative number of events was active in the loading, heating and cooling stages; the crack density and the change of internal forces could be derived from the trend of event rate; the local energy changes of the specimen could be deciphered from the curves of energy rate and b-value, making it possible to judge if a component has reached the failure state; the specimen suffered the most severe damage, when the ae parameters suddenly changed; ae monitoring enables the early warning of fire to reinforced concrete plate-column structure; infrared detection technology is suitable for real-time monitoring of crack development under high temperature. keywords. plate-column structure; acoustic emission (ae); fire test; cumulative number of events; event rate; energy rate; gutenberg-richter parameter (b-value). citation: wang, d.y., dong, y.l., zhang, d.s., wang, w.h., lu, x., monitoring and analysis of reinforced concrete plate-column structure under room temperature and fire based on acoustic emission, frattura ed integrità strutturale, 53 (2020) 236-251. received: 25.02.2020 accepted: 10.05.2020 published: 01.07.2020 copyright: © 2020 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. mailto:dongyl@hqu.edu.cn mailto:zhangds@hqu.edu.cn https://youtu.be/jdpiw4gaghg d. wang et alii, frattura ed integrità strutturale, 53 (2020) 236-251; doi: 10.3221/igf-esis.53.20 237 introduction coustic emission (ae) refers to the phenomenon that the local defects of materials or components release strain energy in the form of elastic wave, under external conditions like stress, temperature and magnetic field [1]. the ae sources could be generated by a variety of mechanisms, including impact, combustion, pressure leakage, phase change, plastic deformation, as well as crack formation and propagation in solid materials. each source generation mechanism produces a unique type of ae signals. whichever the mechanism, the ae is always a process in which a material is locally or partly destabilized under changing external conditions, and releases energy to reach a new equilibrium. ae signals and techniques have often been used to monitor dynamic processes, namely, how materials deform on the microscale under load, and how cracks emerge and develop. studies have shown that the ae signals (parameters) correspond to the material features and the mechanical changes in structures. based on the correspondence, the working state of structures can be monitored dynamically and evaluated easily at a fast speed. the application scope of ae techniques has widened from the detection of pressure vessels, metal fatigue and metal fractures to various industrial fields, such as initial detection of pressure vessels and metal fatigue and fracture to many industrial fields such as aerospace, railway, construction, shipbuilding, and electricity [2, 3]. in civil engineering, ae techniques have been successfully adopted to test mainstream materials like concrete and steel, triggering widespread interest in academia. on ae testing of concrete, most scholars focus on monitoring the static and dynamic damage of concrete structures. chen et al. [4] and kim et al. [5] investigated the features of ae signals from concrete under compression, and analyzed the correspondence between the degree of concrete damage and the features of ae signals. zhang et al. [6] elaborated that ae signals like cumulative signal strength and historical index can reflect the corrosion state of steel bars well, but cannot accurately quantify the degree of corrosion damage. patil et al. [7] applied ae and electrochemical techniques to examine the evolution of steel bar corrosion, and its impact on concrete cracking. calabrese et al. [8] conducted long-term corrosion monitoring of steel bars in concrete through cluster analysis and denoising. some scholars [9-12] employed the ae to monitor the mechanical performance of basic components, and probed deep into the ae features of reinforced concrete beams, plates and columns during the damage process. their studies mainly focus on band energy features, gutenberg-richter parameter (b-value), macro/micro evolution, and kaiser effect. men et al. [13] introduced the moment-tensor inversion in seismic engineering to quantify the damage of reinforced concrete components, and deduced the expressions for the moment-tensor inversion of cracking mechanism, providing a novel analytical tool based on ae signals. on ae testing of steel, some scholars [14-20] have conducted in-depth research on the ae features of traditional problems (e.g. steel damage at different tensile rates, and fatigue crack propagation of steel structures), and analyzed the relevant characteristic parameters. for example, prabhu et al. [21] monitored the creep fracture limit of stainless steel pipes in realtime online. taking q345r steel as an example, li et al. [22] designed a special fixture guided wave mechanism for creep ae, which breaks through the temperature limit of sensors, and carried out corresponding ae monitoring experiments. in recent years, scholars have made some interesting discussions on the acoustic emission test of concrete, rock, cement and other aspects [23-26]. currently, the ae techniques are mostly applied to reinforced concrete structures at room temperature. few have implemented ae techniques to predict the working performance and failure mode of building structures under fire and high temperature. guo et al. [27] tested the mechanical performance of post-fire concretes of different strength grades, and discussed the influence of high temperature on the ae in concrete damage process, laying the basis for safety evaluation of tunnel lining concrete structures under fire and high temperature. zhu [28, 29], yang [30] measured the ae features of two-way reinforced concrete plates in the overall structure, examined the changes in the number of ae events, energy rate and b-value of the plates under fire, and identified the correlation of each parameter with crack development, furnace temperature and vertical displacement of the plates. through their research, the ae techniques are successfully adopted to monitor the mechanical properties of two-way reinforced concrete plates under fire and high temperature, expanding the application scope of ae techniques. reinforced concrete plate-column structure is a common structural system. in the event of a fire, the structure may suffer from punch failure, even if it is not overloaded. in 2004, a car caught fire in an underground garage with slab-column structure, gretzenbach, northwestern switzerland. the nodes of the plate-column were penetrated and then collapsed continuously, killing 7 firefighters [31]. thus, firefighters and rescuers are very concerned about the safety of reinforced concrete plate-column structure under fire. this paper carries out tests on reinforced concrete plate-column structure under room temperature and fire , and places ae sensors on plate surfaces to collect ae signals from different parts. next, the ae features of reinforced concrete plate-column structure under fire were explored, in the light of the characteristic parameters (e.g. cumulative number of events, event rate, energy rate and b-value) and the macroscopic test phenomena. the research results lay the foundation for an ae-based early warning system for collapse room temperature and fire. a d. wang et alii, frattura ed integrità strutturale, 53 (2020) 236-251; doi: 10.3221/igf-esis.53.20 238 methodology specimen design hree specimens, denoted as s1-3, with the same size were designed according to the provisions of the relevant code [32]. the plate is 4.8 m in length (l1), 4 m in width (l2) and 0.2 m in thickness (h). the square column is 0.4 m in side length (a) and 1.6 m in height. beneath the column, there is a foundation with the side length of 1.4 m and thickness of 0.3 m. the vertical view and photo of a specimen are given in fig. 1(a) and fig. 1(b), respectively. (a): vertical view of the specimen. (b): photo of the specimen. figure 1: vertical view and photo of the specimen. the specimens were made with commercial concrete and cured for 221 days. for each specimen, three 150×150×150 mm standard concrete cubes were taken and cured under the same conditions as the specimens. on the test day, the mean compressive strength fcu of the concrete cubes was measured as 54.3 mpa, i.e., by using a microcomputer-controlled electrohydraulic servo universal testing machine [33]. hrb400 steel bars were selected and subjected to pull-out tests [34]. the standard values of the yield strength fyk and the ultimate strength fstk of the steel bars were measured through the tests. then, the mean design strength fy of the steel bars was derived as 412 mpa [32]. the plate was reinforced by two layers of bidirectional steel bars, with a diameter of 12 mm, a spacing of 150 mm and a 20 mm-thick protective layer. the column was reinforced by eight 20 mm-diameter longitudinal steel bars, and 8 mm-diameter stirrups, with a spacing of 100 mm. the foundation was reinforced at the bottom by bidirectional steel bars, with a diameter of 16 mm and a spacing of 200 mm. the reinforcement of each specimen is illustrated in figs. 2. (a): planar reinforcement of the specimen. (b): site pouring of the specimen (c): reinforcements of the column and the foundation. figure 2: reinforcement information and photos of specimen t d. wang et alii, frattura ed integrità strutturale, 53 (2020) 236-251; doi: 10.3221/igf-esis.53.20 239 fire test furnace the tests were performed in a combined horizontal fire furnace in the structural laboratory of huaqiao university. the net size of the furnace is 5.95m in length, 4.31 m in width and 1.5 m in height. three burners were installed on the long side of the furnace, and two on the short side. to correctly install and position specimens, a movable partition wall was added in the fire furnace. two burners were arranged in the middle of the wall, with a spacing of 2.8 m. fig. 3(a) shows the jet flame of the burners. on the unexposed surface of the wall, a 0.3 m-wide steel platform was set up for applying the fireproof cotton (fig. 3(b)). after the wall is fixed, the net distance from the edge of the exposed surface to the inner edge of the short side of the furnace is 3.7m. (a): jet flame of burners. (b): movable partition wall. (c): lifting and installation of specimen figure 3: fire furnace reconstruction and lifting and installation of specimen loading plan and fire plan before the test, the column and its foundation were covered by aluminum silicate fireproof cotton. as shown in fig. 3(c), each specimen was lifted into the horizontal fire furnace by the lifting equipment in the lab. once the specimen was in place, the plate surface is about 0.3 m taller than the movable partition wall. according to the provisions of reference [32], the punching bearing capacity of slab without stirrup under local load or concentrated reaction is fl≤0.7hftumh0 (1) h: the influence coefficient of section height h, when h ≤ 800mm, h = 1.0, when h ≥ 2000mm, h = 0.9, and the middle is taken as linear interpolation method; ft: design value of concrete tensile strength;  shall be calculated according to the following two equations, and the minimum value shall be taken: 1 1.2 =0.4+ s   (2a) 0 2 =0.5+ 4 s m h u   (2b) s: the ratio of the long side to the short side of the rectangular time in the local load or concentrated reaction area, and s should not be greater than 4. when s is less than 2, it is taken as 2; for the circular cutting surface, it is taken as 2. s is the influence coefficient of column position: middle column s = 40; side column s = 30; corner column s = 20. um: critical section perimeter, take the perimeter of the plate section at 0.5 h0 away from the column edge; h0: effective height of the plate. for the members in this paper, fcu can be used to calculate the average ft = 1.95n/mm2, h0=165 mm. after calculation, fl=509kn at room temperature. in the design of loading target value, the ratio of punching force and fl on the column is about 60-70%.the dead weight of the test piece plate is about 100kn, and the dead weight of the first level distribution beam (only one) and the second level distribution beams (there were two beams) in the loading device is about 25 kn. during the test, the target loading value is rounded and the final target loading value is determined to be 200 kn. d. wang et alii, frattura ed integrità strutturale, 53 (2020) 236-251; doi: 10.3221/igf-esis.53.20 240 to reach the target load of 200 kn, the load was applied by a jack with a measuring range of 1,000 kn, and transmitted to four loading points through two stages of distribution beams. there is one primary distribution beam and two secondary distribution beams. the total dead weight of these beams stood at 25 kn. the primary distribution beam, connected to the jack via a ball hinge, was placed right between the two secondary distribution beams. a steel roller (diameter: 45 mm) was added between the two stages of beams and cushioned with a 200 mm×350 mm baseplate. each secondary distribution beam was deployed close to the edge of the short side of plate surface. a steel roller (diameter: 45 mm) was added between the beam and the edge and cushioned with a 300 mm×300 mm baseplate. before the beam was in place, the outer edge of the baseplate was fixed at 0.4 m from the edge of the short side of plate surface. to prevent rollers from falling off under load, two 15 mm-diameter steel rods were welded to each baseplate. fig. 4(a) provides the details on the steel rollers and baseplates. fig. 4(b) shows both the specimen and the testing arrangement. (a) details of the roller. (b) relative position between test device and specimen. figure 4: details of the roller and relative position between test device and specimen. before the fire test, each specimen was loaded preliminarily in five stages at room temperature. the target loads of the five stages were 50, 100, 150, 175 and 200 kn, respectively. from the first to fourth stages, each target load was held for 10 min. on the fifth stage, the aluminum silicate fireproof cotton was applied after reaching the target load. specifically, the fireproof cotton was folded into l-shape: one side on the side of the reinforced concrete plate of the specimen, and the other side on the furnace wall or the upper edge of the partition wall, extending to the fixed steel beam outside the furnace wall or to the steel platform outside the wall. the fireproof cotton was kept in place by fire bricks (fig. 5). the pre-loading lasted 47 min for s1, 32 min for s2 and 65 min for s3. the duration of each fire test was 3 h. figure 5: application of fireproof cotton. infrared observation in the event of a fire, the crack development on plate surfaces can be recorded in real-time by infrared detection technology [35]. in our tests, the temperature field and crack development on the plate surface were observed by a fully digital dynamic infrared thermal monitoring device (fig. 6). d. wang et alii, frattura ed integrità strutturale, 53 (2020) 236-251; doi: 10.3221/igf-esis.53.20 241 figure 6: infrared monitoring device. deployment of ae system and sensors his paper adopts the micro-ii multi-channel digital ae system with a pci-e acquisition card. as shown in fig. 7a, fifteen ae sensors were deployed on the plate surface to record the ae signals at different positions, considering how plate cracking affects the generation and propagation of ae signals under fire. the working principle of ae is illustrated in fig. 7b. tab. 1 describes the setting of ae system and sensors. (a) ae mesuring points (b) working principle of ae figure 7: layout of ae measuring points and working principle of ae. sensor sampling frequency (khz) threshold (db) preamplifier (db) waveform setting number of sensors (each) r6-a resonance type 20~100 40 40 sampling rate (msps) length (number of points) 15 table 1: setting of ae system and sensors. plate damage phenomena macro phenomena rom 0 to 1 min at room temperature, as the load applied by the jack gradually reached 50 kn, there was no obvious cracking or deformation on the plate surface. from 14 to 15min, the load increased from 50 to 100 kn. during this process, five fine cracks appeared almost simultaneously on the plate surface on the east and west long sides, respectively. the cracks were symmetrically distributed about the central axis of the long sides, with a spacing of 15-18 cm. the cracking positions basically overlap those of steel bars on the plate surface. besides, cracks 1# on both east and west sides propagated to the center of the column. the crack width on the edge of the plate fell between 0.20 and 0.40 mm. from 26 to 28 min, the load further grew from 100 to 150 kn. during this process, two new cracks emerged on the east long side, and one on the west long side. at 30 min, two more cracks were observed on the east long side, and five on the west long side. the crack development was accompanied by a crisp sound similar to that of grains falling on the ground. t f d. wang et alii, frattura ed integrità strutturale, 53 (2020) 236-251; doi: 10.3221/igf-esis.53.20 242 the new cracks were 16-18 cm away from the original cracks. the cracks 1# and 3# on the east side and the cracks 2# and 3# on the west side propagated to the center of the column, while the original cracks became wider. on the edge of the plate, multiple cracks grew deeper into the plate. the crack width on the edge of the plate fell between 0.12 and 1.40 mm. from 38 to 39 min, the load climbed up from 150 to 175 kn. during this process, four new cracks emerged on the east long side, and four on the west long side. the new cracks were 16-22 cm away from the original cracks. the original cracks quickly widened and grew deeper into the plate, giving off a clear cracking sound. on the east and west sides, several cracks penetrated the edges of plate-column nodes. the areas of plate-column nodes were cracked and developed into a closed diamond shape with wide cracks. the crack width on the edge of the plate fell between 0.18 and 2.2 mm. from 49 to 50 min, the load continued to rose from 175 to 200 kn. during this process, two new cracks emerged on the east long side, and one on the west long side. in the areas of plate-column nodes, cracks developed quickly and became rather wide (10 mm). the original cracks widened quickly. the crack width on the edge of the plate fell between 0.38 and 2.8 mm. fig. 8 presents the crack development at room temperature. the furnace was ignited at 105 min. from 114 to 118 min, the furnace temperature was between 654 and 727 °c. six popping sounds were heard consecutively, due to concrete spalling. at 119 min, the furnace temperature increased to 736 °c. water stains started to appear simultaneously in the cracks on the north and south sides of the plate, and seeped to the short sides. meanwhile, two concrete spalling sounds were heard. at 121 min, the furnace temperature was 763 °c. four sounds of concrete spalling were heard; lots of water stains appeared in the cracks on plate surface, and seeped towards the short sides; water vapor escaped from the relatively width cracks (fig. 9). one concrete spalling sound was heard respectively at 131 and 133 min. at 140 min, the furnace temperature rose to 857 °c. the plate height was distorted at the top of the column. at 252 min, the furnace temperature was 1,078 °c, and the water stains on the plate surface were basically evaporated. at 315 min, the fire was turned off. fig. 10 displays the distribution of cracks in the thickness direction on the long sides of the plate. it can be seen that, in the thickness direction, longitudinal cracks developed and extended to 3/4 of plate thickness, without penetrating the plate. the spacing of the cracks was basically the same as the steel bars on the plate. after flameout, the cracks on the top of the plate radiated from the center to the edges (fig. 11). (a) s1 (b) s2 (c) s3 figure 8: the crack development at room temperature. figure 9: water stains and water vapor on the plate surface. d. wang et alii, frattura ed integrità strutturale, 53 (2020) 236-251; doi: 10.3221/igf-esis.53.20 243 figure 10: crack distribution in the thickness direction on the long sides of the plate. (a) s1 (b) s2 (c) s3 figure 11: crack distribution on the top of the plate. (a) 20min after ignition (b) 30min after ignition (c) 45min after ignition (d) 75min after ignition (e) 120min after ignition (f) 210min after ignition (flameout) figure 12: crack development on the top of the plate of s3 under fire. crack development on plate surface under fire in the fire test, the plate surface was covered by lots of water stains and water vapor, making it difficult to observe crack distribution and development with the naked eye. to overcome the difficulty, infrared detection technology was introduced to monitor the plate crack development. for the lack of space, this paper only provides the crack development of s3 in six stages after ignition, which was captured by our infrared thermal monitoring device (fig. 12). the crack development in plate-column was not captured, for the device was installed directly above the specimen (i.e. the central nodes were blocked by the loading beams and distribution beams). d. wang et alii, frattura ed integrità strutturale, 53 (2020) 236-251; doi: 10.3221/igf-esis.53.20 244 as shown in fig. 12, at 125 min (20 min after ignition), several hot spots formed in the longitudinal cracks near the center of the plate surface, indicating that the longitudinal cracks near the center were wider than those in other places. at 135 min (30 min after ignition), hot spots were clearly visible on several large longitudinal cracks and individual diagonal cracks. the radiating contour of cracks on the plate was faintly visible, and the cracks on the north and south sides developed in a uniform manner. at 150 min (45 min after ignition), there were lots of water stains on the plate surface. through our infrared thermal monitoring device, the hot spots were clearly visible on each crack, and the cracks were radiating from the center on the plate surface. moreover, the hot spots were plump and hot in the longitudinal cracks along the long sides. this means the longitudinal cracks are wide, and much heat is transmitted to the plate surface. by contrast, there were few low-temperature hot spots in diagonal cracks and transverse cracks, indicating that these cracks are relatively narrow. at 180 min (75 min after ignition), the hot spots in diagonal cracks were as plump as those in longitudinal cracks, and new short diagonal cracks formed at the corner of the plate. at 225 min (120 min after ignition), the temperature at other positions of the plate gradually approached the temperature in the cracks. at 315 min (flameout), the shape of the cracks of the plate surface was illegible. ae data analysis here are two major types of ae parameters: basic parameters and characteristic parameters. basic parameters refer to the frequency and time domain parameters directly measured by the ae device. basic parameters can be further divided into three categories: cumulative count parameters, statistical parameters, and rate of change (roc) parameters. the most common cumulative count parameters include the cumulative number of events, total energy, total ring count, and total amplitude count. typical examples of statistical parameters are amplitude distribution, frequency distribution, and duration distribution. the roc parameters demonstrate the change of an ae parameter per unit time. being quantities of states, popular roc parameters like event rate and energy rate are closely correlated with the internal change of materials. the ae parameters reflect the differences between various states or projects. there is no uniform standard for the selection of such parameters. instead, the ae parameters should be chosen to fully manifest the ae process and state, according to the scope and purpose of each research. the b-value is one of the most commonly chosen ae parameter. based on the macroscopic phenomena and ae signals, this paper selects such four parameters as cumulative number of events, event rate, energy rate and b-value to disclose the time-varying ae features. since the sensors are deployed symmetrically, the data collected by six (7#, 8#, 11#, 12#, 13# and 15#) out of the fifteen sensors (fig. 7a) were selected for further analysis. for the lack of space, specimen s3 was taken as an example in the following discussion. cumulative number of events the ae event is defined as a local change in the material that emits acoustic waves. the total count of all events in a process is called the cumulative number of events. this parameter reveals the time of crack emergence and the degree of crack development. the maximum cumulative number of events demonstrates the development and density of cracks at the measuring point, providing a yardstick of source activity. fig. 13 shows the variation in the cumulative number of events at each measuring point of s3 with time and furnace temperature. obviously, the entire process can be divided into the following three phases. the first phase is the staged loading at room temperature. in the first 72 min, the cumulative number of events surged up at each measuring point. the fastest growth rate (124 events/min) appeared at 8# at the center of the plate, with a cumulative number of events of 8,899. the cumulative number of events was relatively large (8,000) at 12#, 13# and 15#, which were arranged along the long side. the above results show that the central nodes of the plate were relatively active in the staged loading at room temperature, resulting in a high density of cracks. this agrees well with the macroscopic phenomenon that ring cracks continuously emerge in the area of these nodes. in addition, the nodes along the long side were more active than those along the short side, which is in line with the macroscopic phenomenon that longitudinal cracks mainly develop along the long sides. in the second phase, the fire was ignited and the furnace temperature started to rise. in this case, the cumulative number of events increased sharply and then stabilized. the sharp increase occurred between 106 and 143 min when the furnace temperature jumped from to 868 °c. in this phase, numerous diagonal cracks emerged, and the longitudinal cracks formed under room temperature continued to expand, causing the concrete at the bottom of the plate to spall. echoing with t d. wang et alii, frattura ed integrità strutturale, 53 (2020) 236-251; doi: 10.3221/igf-esis.53.20 245 macroscopic phenomena, the cumulative number of events at all measuring points rocketed up, with growth rates of 82.8, 98.2, 62.5, 65.0, 34.7, and 94.1 %, respectively. the growth rates at 8# and 15# both surpassed 90 %. hence, in the heating phase, the area of plate-column nodes was still more active and more severely damaged than the other places. the relatively large cumulative number of events at 7# signifies the generation of many diagonal cracks. in the third phase, the fire was turned off, and the furnace cooled down. in this case, the cumulative number of events rose rapidly for a while by less than 10 % and then stabilized. (a) 7-channel sensor (b) 8-channel sensor (c) 11-channel sensor (d) 12-channel sensor (e) 13-channel sensor (f) 15-channel sensor figure 13: variation in the cumulative number of events of s3 with time and furnace temperature. event rate, energy rate and b-value the event rate reflects the change of events measured per unit time, providing an indicator of crack density. the ae energy (unit: mv∙μs) is not an energy in the physical sense. this parameter is defined as the area under the envelope of the signal waveform, reflecting the signal intensity. generally, the square of the amplitude and duration of ae signals can both serve as energy parameters. the internal damage or surface cracking that emit acoustic waves are often accompanied by energy generation. the change of energy measured per unit time, i.e. energy rate, can reflect the degree of cracking and internal damage of the concrete. the b-value, an important parameter in seismic analysis, was originally used to characterize the relationship between seismic frequency and magnitude. with the proliferation of ae techniques, b-value has been adopted to analyze the ae signals of building structures under fire. the relationship between the number of events n and the amplitude a can be expressed as: 0 100 200 300 400 500 600 0 2000 4000 6000 8000 10000 12000 14000 cumulative number of events mean furnace temperature ignition 105min flameout 315min c u m u la ti v e n u m b e r o f e v e n ts ( e a c h ) time (min) t e m p e ra tu re ( ℃ ) 0 100 200 300 400 500 600 700 800 900 1000 1100 1200 0 100 200 300 400 500 600 0 2000 4000 6000 8000 10000 12000 14000 16000 18000 20000 22000 105min 315min c u m u la ti v e n u m b e r o f e v e n ts ( e a c h ) ignition flameout cumulative number of events mean furnace temperature time (min) t e m p e ra tu re ( ℃ ) 0 100 200 300 400 500 600 700 800 900 1000 1100 1200 0 100 200 300 400 500 600 0 2000 4000 6000 8000 10000 12000 105min 315min c u m u la ti v e n u m b e r o f e v e n ts ( e a c h ) ignition flameout cumulative number of events mean furnace temperature time (min) t e m p e ra tu re ( ℃ ) 0 100 200 300 400 500 600 700 800 900 1000 1100 1200 0 100 200 300 400 500 600 0 2000 4000 6000 8000 10000 12000 14000 16000 18000 20000 105min 315min c u m u la ti v e n u m b e r o f e v e n ts ( e a c h ) flameout ignition cumulative number of events mean furnace temperature t e m p e ra tu re ( ℃ ) time (min) 0 100 200 300 400 500 600 700 800 900 1000 1100 1200 0 100 200 300 400 500 600 0 2000 4000 6000 8000 10000 12000 14000 105min 315min c u m u la ti v e n u m b e r o f e v e n ts ( e a c h ) flameout ignition cumulative number of events mean furnace temperature t e m p e ra tu re ( ℃ ) time (min) 0 100 200 300 400 500 600 700 800 900 1000 1100 1200 0 100 200 300 400 500 600 0 2000 4000 6000 8000 10000 12000 14000 16000 18000 20000 22000 105min 315min c u m u la ti v e n u m b e r o f e v e n ts ( e a c h ) flameout ignition cumulative number of events mean furnace temperature t e m p e ra tu re ( ℃ ) time (min) 0 100 200 300 400 500 600 700 800 900 1000 1100 1200 d. wang et alii, frattura ed integrità strutturale, 53 (2020) 236-251; doi: 10.3221/igf-esis.53.20 246 logn=a-bloga (3) where, a is a constant. there are many different definitions on the b-value of concrete. here, the physical meaning of b-value [36] is defined as the degree of cracking on the plate surface under fire. the b-value is negatively correlated with the crack width and the proportion of large-amplitude signals in ae signals [citation suggested]. the b-value can be adopted to evaluate the degree of internal damage of concrete. under the effects of various small defects and errors, our specimens exhibited complex mechanical behaviors in the tests. as a result, there might be a certain degree of dispersion in the event rate, energy rate and b-value at each measuring point. it would be one-sided and incomprehensive to analyze only one parameter at a single measuring point. to correlate ae signals with macroscopic phenomena, this paper decides to jointly analyze all three characteristic factors: event rate, energy rate and b-value. the analysis shows that the variation in the three characteristic factors can be split into several stages. for convenience, the entire process of room temperature loading and fire test was divided into the following five stages: (1) room temperature stage i: the stage before any crack appeared on the specimen. this stage lasts from the start of the test to the completion of the first loading stage at room temperature. (2) room temperature stage ii: the stage of crack emergence and development. this stage lasts from the start of the second loading stage to the completion of the fifth loading stage at room temperature. (3) high temperature stage i: the stage of active ae signals. this stage lasts from the start of the fire test to 40min after ignition. (4) high temperature stage ii: the stage of stable ae signals. this stage lasts from the moment the furnace temperature surpassed 900 °c to the end of the fire test. (5) cooling stage: after the end of the fire test, the internal forces of the concrete plate were redistributed, and some sensors received ae signals. (a) 7-channel sensor (b) 8-channel sensor (c) 11-channel sensor (d) 12-channel sensor (e) 13-channel sensor (f) 15-channel sensor figure 14: variation in the event rate of s3 with time and furnace temperature. 0 50 100 150 200 250 300 350 400 450 500 550 -100 0 100 200 300 400 500 600 flameout 315min ignition 105min 0 100 200 300 400 500 600 700 800 900 1000 1100 1200 event rate mean furnace temperature t e m p e ra tu re ( °c ) time (min) e v e n t ra te ( e a c h /m in ) 0 50 100 150 200 250 300 350 400 450 500 550 -100 0 100 200 300 400 500 600 700 315min 105min 0 100 200 300 400 500 600 700 800 900 1000 1100 1200 e v e n t ra te ( e a c h /m in ) ignition flameout event rate mean furnace temperature t e m p e ra tu re ( °c ) time (min) 0 50 100 150 200 250 300 350 400 450 500 550 -100 0 100 200 300 400 500 315min 105min 0 100 200 300 400 500 600 700 800 900 1000 1100 1200 e v e n t ra te ( e a c h /m in ) ignition flameout event rate mean furnace temperature t e m p e ra tu re ( °c ) time (min) 0 50 100 150 200 250 300 350 400 450 500 550 -100 0 100 200 300 400 500 600 700 800 900 1000 1100 1200 315min 105min 0 100 200 300 400 500 600 700 800 900 1000 1100 1200 e v e n t ra te ( e a c h /m in ) ignition flameout event rate mean furnace temperature t e m p e ra tu re ( °c ) time (min) 0 50 100 150 200 250 300 350 400 450 500 550 -100 0 100 200 300 400 500 600 315min 105min 0 100 200 300 400 500 600 700 800 900 1000 1100 1200 e v e n t ra te ( e a c h /m in ) ignition flameout event rate mean furnace temperature t e m p e ra tu re ( °c ) time (min) 0 50 100 150 200 250 300 350 400 450 500 550 -100 0 100 200 300 400 500 600 700 800 315min 105min 0 100 200 300 400 500 600 700 800 900 1000 1100 1200 e v e n t ra te ( e a c h /m in ) ignition flameout event rate mean furnace temperature t e m p e ra tu re ( °c ) time (min) d. wang et alii, frattura ed integrità strutturale, 53 (2020) 236-251; doi: 10.3221/igf-esis.53.20 247 (a) 7-channel sensor (b) 8-channel sensor (c) 11-channel sensor (d) 12-channel sensor (e) 13-channel sensor (f) 15-channel sensor figure 15: variation in the energy rate of s3 with time and furnace temperature. (a) 7-channel sensor (b) 8-channel sensor (c) 11-channel sensor (d) 12-channel sensor (e) 13-channel sensor (f) 15-channel sensor figure 16: variation in the b-value of s3 with time and furnace temperature. figs. 14-16 show the variations in event rate, energy rate and b-value with time and furnace temperature, respectively. coupled with macroscopic phenomena, the change laws of the three characteristic parameters in each stage were analyzed based on the three figures: 0 50 100 150 200 250 300 350 400 450 500 550 -20000 0 20000 40000 60000 80000 100000 120000 140000 160000 180000 200000 flameout 315min ignition 105min 0 100 200 300 400 500 600 700 800 900 1000 1100 1200 energy rate mean furnace temperature t e m p e ra tu re ( ° c ) time (min) e n e rg y r a te ( m v * μ s/ m in ) 0 50 100 150 200 250 300 350 400 450 500 550 -20000 0 20000 40000 60000 80000 100000 120000 140000 160000 315min 105min 0 100 200 300 400 500 600 700 800 900 1000 1100 1200 e n e rg y r a te ( m v * μ s/ m in ) ignition flameout energy rate mean furnace temperature time (min) t e m p e ra tu re ( ° c ) 0 50 100 150 200 250 300 350 400 450 500 550 -20000 0 20000 40000 60000 80000 100000 120000 140000 160000 315min 105min e n e rg y r a te ( m v * μ s /m in ) ignition flameout energy rate mean furnace temperature time (min) t e m p e ra tu re ( ° c ) 0 100 200 300 400 500 600 700 800 900 1000 1100 1200 0 50 100 150 200 250 300 350 400 450 500 550 0 100000 200000 300000 400000 500000 600000 700000 800000 315min 105min e n e rg y r a te ( m v * μ s/ m in ) ignition flameout energy rate mean furnace temperature time (min) t e m p e ra tu re ( ° c ) 0 100 200 300 400 500 600 700 800 900 1000 1100 1200 0 50 100 150 200 250 300 350 400 450 500 550 -50000 0 50000 100000 150000 200000 250000 300000 350000 400000 450000 500000 550000 600000 315min 105min e n e rg y r a te ( m v * μ s/ m in ) ignition flameout energy rate mean furnace temperature time (min) t e m p e ra tu re ( ° c ) 0 100 200 300 400 500 600 700 800 900 1000 1100 1200 0 50 100 150 200 250 300 350 400 450 500 550 -20000 0 20000 40000 60000 80000 100000 120000 140000 160000 315min 105min e n e rg y r a te ( m v * μ s /m in ) ignition flameout energy rate mean furnace temperature time (min) t e m p e ra tu re ( ° c ) 0 100 200 300 400 500 600 700 800 900 1000 1100 1200 0 50 100 150 200 250 300 350 400 450 500 550 1.4 1.5 1.6 1.7 1.8 1.9 2.0 b-value mean furnace temperature t e m p e ra tu re ( °c ) time (min) b -v a lu e flameout 315min ignition 105min 0 100 200 300 400 500 600 700 800 900 1000 1100 1200 0 50 100 150 200 250 300 350 400 450 500 550 1.4 1.5 1.6 1.7 1.8 1.9 2.0 315min 105min b -v a lu e ignition flameout b-value mean furnace temperature time (min) t e m p e ra tu re ( °c ) 0 100 200 300 400 500 600 700 800 900 1000 1100 1200 0 50 100 150 200 250 300 350 400 450 500 550 1.4 1.5 1.6 1.7 1.8 1.9 2.0 315min 105min b -v a lu e ignition flameout b-value mean furnace temperature time (min) t e m p e ra tu re ( °c ) 0 100 200 300 400 500 600 700 800 900 1000 1100 1200 0 50 100 150 200 250 300 350 400 450 500 550 1.4 1.5 1.6 1.7 1.8 1.9 2.0 315min 105min b -v a lu e ignition flameout b-value mean furnace temperature time (min) t e m p e ra tu re ( °c ) 0 100 200 300 400 500 600 700 800 900 1000 1100 1200 0 50 100 150 200 250 300 350 400 450 500 550 1.4 1.5 1.6 1.7 1.8 1.9 2.0 315min 105min b -v a lu e ignition flameout b-value mean furnace temperature time (min) t e m p e ra tu re ( °c ) 0 100 200 300 400 500 600 700 800 900 1000 1100 1200 0 50 100 150 200 250 300 350 400 450 500 550 1.4 1.5 1.6 1.7 1.8 1.9 2.0 315min 105min b -v a lu e ignition flameout b-value mean furnace temperature time (min) t e m p e ra tu re ( °c ) 0 100 200 300 400 500 600 700 800 900 1000 1100 1200 d. wang et alii, frattura ed integrità strutturale, 53 (2020) 236-251; doi: 10.3221/igf-esis.53.20 248 (1) room temperature stage i from zero to one min at room temperature, as the load applied by the jack gradually reached 50 kn, there was no obvious cracking or deformation on the plate surface. as shown in fig. 14, the event rates of measuring points were around zero events/min, and the peak event rate, 53 events/min only, was captured by 13#, reflecting the rarity of cracks inside or on the plate. as shown in fig. 15, the energy rates of measuring points were rather low at about zero mv∙μs/min. thus, the cracks released a very small amount of energy. as shown in fig. 16, the first valley was observed for the b-values in all channels. the b-values at most measuring points were around 1.7-1.8, except that (1.55) at 13#. the values were much higher than those in the subsequent loading stages at room temperature. this means the crack width in this stage was much narrower than that in other stages. that is why the cracks were not observable in this stage. (2) room temperature stage ii from 14 to 15 min (second loading stage), the load increased from 50 to 100 kn. during the loading and holding, five fine cracks appeared in the east and west of the plate, respectively. from 26 to 28 min (third loading stage), the load further grew from 100 to 150 kn. during the loading and holding, four fine new cracks emerged in the east, and six on the west of the plate. from 38 to 39 min (fourth loading stage), the load increased from 150 to 175 kn. in this process, four fine new cracks emerged in the east and the west of the plate, respectively, and the first ring crack formed on the top of the column. from 49 to 50 min (fifth loading stage), the load continued to rose from 175 to 200 kn. during this process, two new cracks emerged in the east and one on the west of the plate. as shown in fig. 14, with the emergence of new cracks on the edges, the penetration of cracks and the appearance of ring crack on the top of the column, the event rates of the measuring points surged up to the peak values, and then plunged in the holding period, exhibiting as serrated curves. the event rates were uniformly distributed across the different loading stages. in the second loading stage, the peak event rate (541 events/min) was recorded at 7#; in the third loading stage, the peak event rate (591 events/min) was recorded at 8#. in the fourth loading stage, the peak event rate (456 events/min) was recorded at 8#; in the fifth loading stage, the peak event rate (409 events/min) was recorded at 12#. as shown in fig. 15, the energy rates at measuring points rose sharply to the peak values, and nosedived in the holding period, exhibiting as serrated curves. the peak energy rates differed greatly from measuring point to measuring point. relatively high peak values were observed at 12# and 13# through the five loading stages. in the second loading stage, the peak energy rate (568,205 mv∙μs/min) was recorded at 13#; in the third loading stage, the peak energy rate (754,844 mv∙μs/min) was recorded at 12#; in the fourth loading stage, the peak energy rate (302,332 mv∙μs/min) was recorded at 12#; in the fifth loading stage, the peak energy rate (189,839 mv∙μs /min) was recorded at 12#. as shown in fig. 16, the b-value at each measuring point hit the valley in each loading stage, and the valley values were close to each other, ranging from 1.45 to 1.50. therefore, the cracks developed rapidly in all loading stages. (3) high temperature stage i right after the ignition at 105 min, cracks appeared quickly along the short sides on the north and south of the plate, so did diagonal cracks. meanwhile, the cracks widened obviously at plate-column nodes. from 114 to 118 min, several popping sounds were heard consecutively, due to concrete spalling. as shown in fig. 14, the event rates at all measuring points reached the peaks again; all are far greater than the peaks at room temperature. the highest peak value was measured by 12#: 1,108 events/min. this means, with the rising furnace temperature, the specimen became more active in ae under the coupling of load and temperature. as shown in fig. 15, the energy rates at all measuring points returned to the peaks after ignition. the highest peak energy rate (165,293 mv∙μs/min) appeared at 12#. the results indicate that new energy was released by new cracks and concrete spalling. as shown in fig. 16, the b-values at all measuring points hit the valleys quickly after ignition. the valley values were between 1.40-1.45, lower than those under room temperature. next, the b-values gradually rebounded. it can be seen that cracks widened quickly and diagonal cracks emerged rapidly at the beginning of the fire; with the growing furnace temperature, it is increasingly difficult for new cracks to emerge and for old cracks to widen. (4) high temperature stage ii at 121min, the furnace temperature was 763 °c. four sounds of concrete spalling were heard; lots of water stains appeared in the cracks on plate surface, and seeped towards the short sides; water vapor escaped from the relatively width cracks. one concrete spalling sound was heard respectively at 131 and 133 min. at 140 min, the furnace temperature rose to 857 °c. the plate height was distorted at the top of the column. at 252 min, the furnace temperature was 1,078 °c, and the water stains on the plate surface were basically evaporated. at 315 min, the fire was turned off. d. wang et alii, frattura ed integrità strutturale, 53 (2020) 236-251; doi: 10.3221/igf-esis.53.20 249 as shown in fig. 14, the event rates at all measuring points declined sharply to the valleys at around zero events/min. this shows that no new cracks or concrete spalling occurred in this “quiet” stage. as shown in fig. 15, the energy rates at all measuring points dropped deep to the valleys at around zero mv∙μs/min. as shown in fig. 16, the b-values at all measuring points remained at a high value (2), exhibiting as serrated curves. this means, when the plate was under the same load, the crack width changed in a certain degree in the later period of heating, but the crack development was rather limited. (5) cooling stage after flameout, the data collection was stopped at 550 min. as shown in figs. 14 and 15, the event rates and energy rates at all measuring points surged up to the peak values between 326 and 329 min. the 3 min difference is due to multiple factors, such as the attenuation of acoustic waves in the propagation path. the peak event rate (137 events/min) was measured by 8#, while the peak energy rate (50,098 mv∙μs/min) was captured by 12#. these results indicate that, after flameout, the furnace temperature dropped sharply, and the heat was transferred from the bottom to the top of the specimen. the moisture in the plate continued to evaporate, creating temperature stress and internal stress, releasing some energy, and thus ae sources. after that, no new crack emerged, and no original crack widened. as a result, the event rates and energy rates at all measuring points dropped deeply to a low level, kicking off another “quiet” period. as shown in fig. 16, after flameout, the b-values of all measuring points started to decrease and reached the valleys (1.551.60) at around 326-329 min. it shows that in this stage, with the redistribution of internal forces, the internal cracks of concrete develop further. then, the b-values gradually picked up, and the number of ae sources decreased slowly in the specimen. conclusions his paper mainly carried out two works: one is to record the development law of slab cracks under normal temperature and fire; the other is to use acoustic emission technology to monitor the acoustic emission signals at different positions of the specimen, and to collect the accumulated events, event rate, energy rate, b value and other parameters analysis. the main conclusions are as follows: (1) before punch failure, the cracks mainly radiated from the center of the plate. among them, the diagonal cracks developed quickly under fire. the cracks under high temperature could be monitored in real-time by infrared detection technology. (2) the cumulative number of ae events can reflect the activity of the specimen. according to the test results, the cumulative number of events grew linearly in room temperature loading stages, high temperature stages and cooling stage. this means the specimen has been active in the entire process, and each stage has a “quiet” period. (3) throughout the test, the variation in event rate, energy rate and b-value can be split into several stages. upon load increase or ignition, the event rate and energy rate exhibited as serrated curves, while the b-value hit the valley. the specimen suffered the most severe damage when event rate and energy rate suddenly spiked and b-value suddenly dropped. in this case, the structure could have failed. by monitoring these three characteristic parameters, it is possible to provide early warning of fire to reinforced concrete plate-column structure. (4) the crack density and change in internal forces could be derived from the trends of event rate and energy rate. the local energy changes of the specimen could be deciphered from the curves of energy rate and b-value, making it possible to judge if a component has reached the failure state. this provides an important reference for preventing structural instability and internal damage. however, there are several limitations of this research. firstly, the ae testing for engineering structures under fire was only applied to reinforced concrete plate-column structure, due to the difficulty of full-scale testing. secondly, the authors only analyzed the features and trends of some typical ae parameters due to the limited amount of test data. the analysis cannot cover all possible problems. especially in the data collected from the acoustic emission test in this paper, there is almost no case that the number of events n is very small and the amplitude a is very large. therefore, the calculation formula of b value proposed in this paper is suitable for the test in this paper. however, in the process of unstable crack growth, there are not many possible crack events, and the energy (amplitude) is large. at this time, the b value calculated by the formula in this paper is likely to be too large, resulting in misjudgment. our attempt to apply ae techniques in fire safety of engineering structures has high universality and can be applied to various fields of civil engineering, such as health monitoring during the whole life of bridge engineering. to establish an ae-based early warning system for collapse of engineering structures under fire, more tests are needed to determine the failure thresholds of key ae parameters and realize the real-time online monitoring and damage assessment of engineering structures. t d. wang et alii, frattura ed integrità strutturale, 53 (2020) 236-251; doi: 10.3221/igf-esis.53.20 250 acknowledgements his project was supported by the national natural science foundation of china (grant no. 51778250), the education and scientific research project for young and middle-aged teachers in fujian province (grant no. jat191400). references [1] yang, x.j., yao, c.j., yuan, x.j., and long, x.h. (2016). material damage detection technology based on acoustic emission, beijing: beijing university of aeronautics and astronautics press. [2] ji, h.g. (2004). research and application of acoustic emission performance of concrete materials, beijing: coal industry press. [3] yuan, z.m., ma, y.k., and he, z.y. (1985). acoustic emission technology and its application, beijing: mechanical industry press. [4] chen, x.j., cai, y.q., cui, t.l. (2018). research on acoustic emission characteristics in the whole process of pressure test of concrete, highway and automotive technology, (1), pp. 134-138. doi: 10.3969/j.issn.1671-2668.2018.01.034 [5] kim, v.t., and nele, d.b. (2012). acoustic emission analysis for the quantification of autonomous crack healing in concrete, construction and building materials, 28(1), pp. 333-341. doi: 10.1016/j.conbuildmat.2011.08.079 [6] zhang, r., xu, g., and jiang, y., (2017). acoustic emission monitoring of rusty state of reinforced concrete structures, concrete, (1), pp. 34-43. [7] patil, s., karkare, b., and goyal, s. (2014). acoustic emission vis-a-vis electrochemical techniques for corrosion monitoring concrete element, construction and building materials, 68, pp. 326-332. doi: 10.1016/j.conbuildmat.2014.06.068 [8] calabrese, l., campanella, g., proverbio, e. (2012). noise removal by cluster analysis after long time ae corrosion monitoring of steel reinforcement in concrete, construction and building materials, 34, pp. 362-371. doi: 10.1016/j.conbuildmat.2012.02.046 [9] fan, y.h. (2017). research on bending damage of concrete specimens based on acoustic emission technology, beijing jiaotong university. [10] zhang, s., and wu, c. (2017). analysis of frequency band energy characteristics of emission signals of prestressed reinforced concrete beam damage process, journal of anhui jianke university, 25(4), pp. 9-13. doi: 10.11921/j.issn.2095-8382.20170403 [11] zitto, m.e., piotrkowski, r., gallego, a., sagasta, f., and benavent-climent, a. (2015). damage assessed by wavelet scale bands and b-value in dynamical tests of a reinforced concrete slab monitored with acoustic emission, mechanical systems and signal processing, 60, pp. 75-89. doi: 10.1016/j.ymssp.2015.02.006 [12] rao, t.e., krishna, g.r., kumar, m.v. (2019). investigation of microstructure and mechanical properties of mig welded mild steel plates, annales de chimie science des matériaux, 43(4), pp. 257-263. doi: 10.18280/acsm.430409. [13] men, j.j., zhao, q., zhu, l., and wang, x.d. (2017). moment-tensor-based acoustic emission detection method for reinforced concrete structure, journal of prevention and mitigation engineering, 37(5), pp. 822-841. doi: 10.13409/j.cnki.jdpme.2017.05.019 [14] peng, g.p., zhang, z.d., and lu, c. (2018). characterization and quantitative evaluation of acoustic emission characteristic parameters of q345r steel during tensile damage, pilot research, 40(1), pp. 50-54. doi: 10.11973/wsjc201801012 [15] long, x.j., li, q.f., he, c.h., wu, q., chen, g., and lu, c. (2017). acoustic emission monitoring and evaluation of steel damage at different tensile rates, journal of vibration and shock, 36(7), pp. 219-225. [16] song, j.b., song, r., xiong, z. (2018). acoustic radiation features and structural-acoustic sensitivity of channel beam, traitement du signal, 35(1), pp. 35-45. doi: 10.3166/ts.35.35-45. [17] bhuiyan, m.y., giurgiutiu, v. (2018). the signatures of acoustic emission waveforms from fatigue crack advancing in thin metallic plates, smart materials and structures, 27(1), 015019. doi: 10.1088/1361-665x/aa9bc2. [18] d’angela, d., ercolino, m., bellini, c., di cocco, v., iacoviello, f. (2020). characterisation of the damaging micromechanisms in a pearlitic ductile cast iron and damage assessment by acoustic emission testing, fatigue & fracture of engineering materials & structures. doi: 10.1111/ffe.13214. t d. wang et alii, frattura ed integrità strutturale, 53 (2020) 236-251; doi: 10.3221/igf-esis.53.20 251 [19] d’angela, d., ercolino, m. (2019). acoustic emission entropy as a fracture-sensitive feature for real-time assessment of metal plates under fatigue loading, procedia structural integrity, 18, pp. 570-576. doi: 10.1016/j.prostr.2019.08.201. [20] botvina, l.r., tyutin, m.r. (2019). new acoustic parameter characterizing loading history effects, engineering fracture mechanics, 210, pp. 358-366. doi: 10.1016/j.engfracmech.2018.06.020. [21] prabhu, n.m., gopal, k.a., murugan, s., haneef, t.k., mukhopadhyay, c.k., venugopal, s., and jayakumar, t. (2015). determining the feasibility of identifying creep rupture of stainless steel cladding tubes on-line using acoustic emission technique, international journal of structural integrity, 6(3), pp. 410-418. doi: 10.1108/ijsi-08-2014-0038 [22] li, b., zhang, y., wen, z.m., and cong, x.c. (2017). experimental study on the acoustic emission characteristics of q345r steel creep process, journal of experimental mechanics, 32(2), pp. 232-238. [23] kyriazopoulos, a. (2017). acoustic emissions and electric signal recordings, when cement mortar beams are subjected to three-point bending under various loading protocols, frattura ed integrità strutturale, 11(40), pp. 52-60. doi: 10.3221/igf-esis.40.05. [24] saliba, j., loukili, a., regoin, j.p., grégoire, d., verdon, l., pijaudier-cabot, g. (2015). experimental analysis of crack evolution in concrete by the acoustic emission technique, frattura ed integrità strutturale, 9(34), pp. 300-308. doi: 10.3221/igf-esis.34.32. [25] stavrakas, i. (2017). acoustic emissions and pressure stimulated currents experimental techniques used to verify kaiser effect during compression tests of dionysos marble, frattura ed integrità strutturale, 11(40), pp. 32-40. doi: 10.3221/igf-esis.40.03. [26] saltas, v., peraki, d., vallianatos, f. (2019). the use of acoustic emissions technique in the monitoring of fracturing in concrete using soundless chemical demolition agent, frattura ed integrità strutturale, 13(50), pp. 505-516. doi: 10.3221/igf-esis.50.42. [27] guo, q.h., xi, b.p., tian, j.b., li, z.w., and zheng, x.c. (2015). experimental research on mechanical property of tunnel concrete lining after high temperature of fire, chinese journal of underground space and engineering, 11(5), pp. 1316-1328. [28] zhu, c.j. (2012). research on the fire resistance performance of two-way plates with full-size reinforced concrete, harbin institute of technology. [29] zhu, c.j., dong, y.l., xie, q. (2016). real-time monitoring of the full-scale flate-plate floor subjected to fire by acoustic emission and energy rate analysis, transportation and environment, (31), pp. 229-234. doi: 10.2991/iccte-16.2016.38. [30] yang, z.n. (2012). study on the fire resistance of concrete two-way slab with different boundary constraints, harbin institute of technology. [31] muttoni, a., fürst, a., and hunkeler, f. (2005). deckeneinsturz der tiefgarage am staldenacker in gretzenbach, solothurn, switzerland. [32] national standard of the people's republic of china. (2011). gb50010 concrete structure design specification, beijing: china building industry press. [33] national standard of the people's republic of china. (2002). gb/t50081-2002(2003) standard for test method of mechanical properties on ordinary concrete, beijing: china architecture & building press. [34] national standard of the people's republic of china. (2010). gb/t228.1-2010(2010) metallic materials-tensile testingpart 1: method of test at room temperature, beijing: china standards press. [35] wang, y., wang, t.y., yuan, g.l., an, x.l., and dong, y.l. (2016). analysis of fire behavior of two-way concrete slabs based on different constitutive models, engineering mechanics, 33(11), pp. 208-219. doi: 10.6052/j.issn.1000-4750.2015.08.0690 [36] dong, y.l., xie, h.p., and li, y.s. (1995). acoustic emission characteristics and damage constitutive model of concrete under compression, mechanics and practice, 9(4), pp. 25-28. microsoft word numero_30_art_34 v. chaves et alii, frattura ed integrità strutturale, 30 (2014) 273-281; doi: 10.3221/igf-esis.30.34 273 focussed on: fracture and structural integrity related issues biaxial fatigue tests and crack paths for aisi 304l stainless steel v. chaves, c. madrigal, a. navarro university of sevilla, departamento de ingeniería mecánica y fabricación. escuela técnica superior de ingeniería. avenida camino de los descubrimientos s/n. 41092. sevilla, spain. chavesrv@us.es abstract. aisi 304l stainless steel specimens have been tested in fatigue. the tests were axial, torsional and in-phase biaxial, all of them under load control and r=-1. the s-n curves were built following the astm e739 standard and the method of maximum likelihood proposed by bettinelli. the fatigue limits of the biaxial tests were represented in axes σ-τ. the elliptical quadrant, appropriate for ductile materials, and the elliptical arc, appropriate for fragile materials, were included in the graph. the experimental values were better fitted with an elliptical quadrant, despite the ratio between the pure torsion and tension fatigue limits, τfl/σfl, is 0.91, close to 1, which is a typical value for fragile materials. the crack direction along the surface has been analyzed by using a microscope, with especial attention to the crack initiation zones. the crack direction during the stage i has been compared with theoretical models. keywords. multiaxial fatigue; s-n curve; crack direction; stage i. introduction he crack direction in the initiation zone (stage i) in planar specimens of ductile materials under fatigue is widely assumed to coincide with the maximum tangential stress direction (mode ii), and so is that for fragile materials with the maximum normal stress direction (mode i). a material is considered to be ductile under fatigue if its torsional-to-tensile fatigue limit ratio (τfl/σfl) is close to 0.5 and fragile if the ratio is near-unity. it is unclear whether a material with an intermediate ratio will behave as ductile or fragile and whether any stage i crack growth directions exist in between modes i and ii. in this work, we explored these possibilities. this paper reports the experimental results for crack growth in the initiation zone in cylindrical specimens of aisi 304l stainless steel as obtained in several series of tests under controlled uniaxial and biaxial loads. the experimental results were used to construct the s–n curves and the biaxial fatigue curve for the material. also, the direction of crack growth on the specimen surface for tests that lasted a large number of cycles (high cycle fatigue) was examined, focusing on the crack initiation zone, and compared with the predictions of various theoretical models. material and specimens he specimens used were round bars of commercially available austenitic stainless steel (aisi 304l). the chemical composition of the steel, in wt%, was as follows: 0.021 c, 0.029 p, 0.024 s, 0.34 si, 1.48 mn, 18.23 cr, 8.15 ni, 0.21 mo, 0.080 n and 0.39 cu. microstructurally, the material consisted of austenite grains of roughly equiaxial t t v. chaves et alii, frattura ed integrità strutturale, 30 (2014) 273-281; doi: 10.3221/igf-esis.30.34 274 geometry, in addition to a small amount of delta ferrite bands. the mean size of the austenite grains was 80 μm (see fig. 1). figure 1: microstructure of the stainless steel aisi 304l. the mechanical properties of the steel as determined from 5 tensile tests were as follows: tensile strength (σuts) = 654 mpa, yield stress 0.2% (σy) = 467 mpa and elongation = 56%. the material was subjected to various biaxial fatigue laboratory tests including tensile, torsional and in-phase tensile– torsional, all at r = –1. tests were conducted on specimens of cylindrical cross-section having a central diameter of 12.5 mm (see fig. 2). all specimens were carefully polished to an average surface roughness (ra) not exceeding 0.1 μm. also, all tests were performed on a biaxial fatigue hydraulic machine under controlled loading conditions, using a sine wave and a frequency of 6–8 hz. each test was finished when the crack grew several millimetres long (in some cases the specimen broke completely) or a number of 3.5×106 cycles (run-outs) was reached. r 110 60 57 60 ø 12,5 ø 20 f f t t figure 2: geometry of the cylindrical specimens tested in biaxial fatigue (in mm). s-n curves he results of the above-described tests were used to construct s–n curves in accordance with astm e 739-91 (2004) [1]. based on this standard, the variables stress and number of cycles to failure can be approximated by a linear logarithmic relationship, excluding run-outs. the fatigue limits were calculated using the maximum t v. chaves et alii, frattura ed integrità strutturale, 30 (2014) 273-281; doi: 10.3221/igf-esis.30.34 275 likelihood method proposed by betinelli [2]. this procedure, which uses both the failures and the run-outs, is an effective alternative to classical choices such as the staircase method and requires less experimental testing. the two straight lines were plotted in a single graph in order to obtain predictions throughout the entire life. fig. 3 and 4 show in a semi-logarithmic graph the experimental s–n curves for the monoaxial and biaxial tests, respectively. as can be seen, the curves were extremely horizontal. in fact, the difference between withstanding a few thousands of cycles only and not breaking was a few megapascals. this material exhibits a dual behaviour: either it exhibits a very short lifetime or does not break at all. it was therefore impossible to detect breaking points after around a million cycles since any specimens reaching those lifetimes failed to break beyond that point. also, having such a horizontal s–n curve had the advantage that fatigue limit calculations were subject to very little uncertainty. the tensile–compressive fatigue limit (r = –1) for the material as determined in cylindrical specimens and expressed in stress amplitude was σfl = 316 mpa and its torsional counterpart τfl = 288 mpa. 10 4 10 5 10 6 100 200 300 400 number of cycles, n s tr e s s  , m p a s-n curve: =366.7n-0.0126 fatigue limit: =316 mpa 10 4 10 5 10 6 100 200 300 400 number of cycles, n s tr e s s  , m p a s-n curve: =369.6n-0.0193 fatigue limit: =288 mpa a) b) figure 3: s-n curves for the monoaxial tests (r=-1): a) push-pull, b) torsion. 10 4 10 5 10 6 100 200 300 400 number of cycles, n s tr e s s  , m p a s-n curve: =346.5n-0.0172 fatigue limit: =283 mpa 10 4 10 5 10 6 100 200 300 400 number of cycles, n s tr e s s  , m p a s-n curve: =400.3n-0.0494 fatigue limit: =215 mpa a) b) 10 4 10 5 10 6 100 200 300 400 number of cycles, n s tr e s s  , m p a s-n curve: =517.3n-0.0557 fatigue limit: =250 mpa 10 4 10 5 10 6 100 200 300 400 number of cycles, n s tr e s s  , m p a s-n curve: =906.9n-0.113 fatigue limit: =283 mpa c) d) figure 4: s-n curves for the biaxial tests (r=-1): a) 0.5σ = τ, b) σ = τ, c) 2σ = τ, d) 4σ = τ. v. chaves et alii, frattura ed integrità strutturale, 30 (2014) 273-281; doi: 10.3221/igf-esis.30.34 276 biaxial fatigue curve he fatigue limits obtained from biaxial loading tests on cylindrical specimens can be used to construct σ–τ plots. as can be seen from fig. 5, our experimental values fitted an elliptical quadrant better than an elliptical arc. based on experimental results of gough et al. [3], fragile materials in fatigue are optimally approximated by an arc and ductile materials by a quadrant. aisi 304l steel has a near-unity σfl/τfl ratio (288/316 = 0.91); therefore, it behaves as a fragile material in fatigue. then, the present experimental results contradict experimental results of the previous authors for materials exhibiting a fragile behaviour under fatigue. but, certainly, the results of gough et al. corresponded to cast irons alone. 0 50 100 150 200 250 300 350 0 50 100 150 200 250 300 350  (mpa)  (m p a ) experimental ellipse quadrant ellipse arc figure 5: experimental fatigue limits for the biaxial tests. crack direction during stage i his section deals with crack direction across the first few grains (stage i) as determined experimentally or predicted with various models. the x axis ran across the specimen and the y axis along it (see fig. 6). determinations involved examining the crack at the specimen outer surface and measuring the angle, called α, from the x axis. a second angle, named θ, which is the angle that forms the crack with the direction that is normal to the first principal stress (σ1 direction) is defined for the comparison with the models. x y 1 di recti oncr ack dir ec tio n f f t t   figure 6: axes and angles for the study of the crack direction. t t v. chaves et alii, frattura ed integrità strutturale, 30 (2014) 273-281; doi: 10.3221/igf-esis.30.34 277 experimental results the experimental procedure was as follows: once the specimen broke completely or partly, a light microscope was used to photograph the surface containing the whole crack. with cylindrical specimens, this entails taking a large number of photographs and carefully assembling them with imaging software. the next step is examining the fracture surface. incompletely broken specimens are previously subjected to tensile stress until they break into two pieces; then, one of the pieces is examined under a light microscope to locate the origin of the fatigue crack, which will coincide with the merging point of “river lines”. the crack starts in a small zone of the specimen outer surface. some specimens develop several cracks at once but, invariably, one eventually prevails or all merge into a single, larger crack. some crack initiation zones are additionally examined under an electronic microscope. in any case, once the small zone where the crack starts is located in the photographs, the angle between the crack and the x axis in the specimen is measured. below is described the application of the above-described procedure to a cylindrical specimen under axial loading. the specimen was applied a cyclic load from –317 to 317 mpa, which caused it to break into two pieces after 145 850 cycles (see fig. 7). as can clearly be seen in the fracture surface picture, there was a smoother, fatigue zone and a rougher rapid fracture zone. the fatigue zone exhibited several lines radiating from the fatigue initiation zone, which fell on the specimen boundary (i.e., on the specimen outer surface) and was about 750 μm in size. the botton figure shows a magnified view of the crack on the outer surface and the location of the initiation zone. the angle between the crack at the initiation zone and the x axis was α = 12º and the zone was about 10 grains in size (i.e., at stage i of crack growth). 750 m view a initiation 750 minitiation 750 m =12º view a x y fracture surface detail of the initiation zone at the fracture surface figure 7: broken specimen subjected to axial loading (r=-1), n=145850 cycles. details of the fracture surface and the crack angle α during the stage i. v. chaves et alii, frattura ed integrità strutturale, 30 (2014) 273-281; doi: 10.3221/igf-esis.30.34 278 fig. 8 shows a specimen under in-phase biaxial loading, the photographic montage of the crack and a magnified view of the crack angle at stage i. the normal stress applied was twice the maximum tangential stress at the surface (i.e., 2σ = τ, r = –1). the test lasted 398,576 cycles, during which the crack grew 17 mm long (i.e., roughly one-half the specimen perimeter), but the specimen failed to break completely. usually, tests involving torsional loading are stopped before the specimen breaks completely in order to avoid the need for too wide a turn of the testing machine and facilitate monitoring of the crack direction and initiation zone. in addition, finishing tests before the specimen breaks prevents substantial deterioration of the fracture surface by effect of strong friction between the crack sides. as experimentally confirmed, a crack several millimetres long only requires about 100 further cycles —an insignificant number relative to a typical lifetime—for the specimen to break. therefore, both situations are identified with fracture. fig. 8 also shows the fracture surface and the location of the crack initiation zone, which was 1450 μm in size on the outer surface, as well as the angle between the stage i crack and the x axis (α = 37º). as can be seen, the crack was tilted in this zone but virtually horizontal in the crack propagation zone (stage ii). the latter was subject to heavy friction under torsion, hence its much darker colour. 1450 m detail of view a initiation initiation 1450 m view a 1450 m initiation x y x y =37º fracture surface view a figure 8: broken specimen subjected to in-phase biaxial loading 2σ = τ (r=-1), n=398576 cycles. details of the fracture surface and the crack angle α during the stage i. model-based predictions recently, chaves et al. [4] developed a method for predicting the growth direction in the initiation zone of a crack under high cycle fatigue. the method is based on the microstructural model of navarro et al. [5] for the fatigue limit under inphase biaxial loads. predictions are made from two properties of the material, namely: the axial fatigue limit (σfl) and the v. chaves et alii, frattura ed integrità strutturale, 30 (2014) 273-281; doi: 10.3221/igf-esis.30.34 279 torsional fatigue limit (τfl). the model calculates the angle θ between the crack initial direction and the normal to the maximum principal stress: 2 ( / )1 arccos 2 ( / ) fl fl fl fl             (1) based on the above-described experimental s–n curves, σfl and τfl for the studied material were calculated to be 316 and 288 mpa, respectively; therefore, the predicted angle was θ = 17º. models based on a critical plane are widely used in multiaxial fatigue studies. those of matake [6] and mcdiarmid [7] are especially useful at large numbers of cycles. according to these authors, the critical plane coincides with the direction of the maximum tangential stress (i.e., with θ = 45º). carpinteri and spagnoli [8] proposed the following equation to determine the crack initiation direction: 2 3 45 1 2 fl fl              (2) application of which to the studied material yielded θ =11º. tab. 1 shows the experimental and predicted crack directions in the stage i, expressed in absolute values of α (i.e., the angle with the x axis). the models used here allowed α to be easily calculated from θ and the specific type of load applied to the material. only the results for tests spanning more than 105 cycles were considered, however, in order to ensure applicability of the hypothesis of models for large numbers of cycles. as can be seen from tab. 1, the experimental angles were close to α = 0º in axial tests and increased with increasing torsional loading to a level near α = 45º in purely torsional tests. the best predictions were obtained with the model of carpinteri and spagnoli, followed by that of chaves et al. on the other hand, the models and matake and mcdiarmid gave much less accurate predictions. in fact, the experimental crack direction at the initiation stage was very close to the normal to the maximum principal stress i (i.e., to that of mode i). similar results in this respect were recently obtained by anes et al. [9] for 42crmo4 steel and az31 magnesium alloy. fig. 9 shows the crack direction at stage i in relation to the normal to the first principal stress, that is, θ, for all tests and the predictions of the models. the 20 experimental values of θ have been placed consecutively in this graph, in the same order as in tab. 1. an angle of θ = 0º corresponds to a mode i direction in stage i, and one of 45º to a mode ii direction. the average experimental angle (θ = 3.5º) was very close to 0º (i.e., it corresponded to mode i). the predicted angle obtained with the model of carpinteri and spagnoli, θ = 11.1º, was not very far. however, that obtained with the model of chaves et al. (θ = 17.0º) was somewhat more dissimilar, and that provided by the model of matake and mcdiarmid (θ = 45.0º) departed even further. in fact, the best prediction of crack direction at stage i was seemingly that corresponding to mode i. 0 5 10 15 20 0 5 10 15 20 25 30 35 40 45 50 number of test á n g le  ( º) axial biaxial 0.5= biaxial = biaxial 2= torsion experimental mean chaves et al. carpinteri-spagnoli matake/mcdiarmid figure 9: angle θ for the stage i obtained experimentally and predicted with some models for aisi 304l. v. chaves et alii, frattura ed integrità strutturale, 30 (2014) 273-281; doi: 10.3221/igf-esis.30.34 280 test cycles stage i direction, α (º) experimental chaves matake carpinteri axial 119185 4.0 17.0 45.0 11.1 248683 3.5 17.0 45.0 11.1 116413 10.5 17.0 45.0 11.1 145850 12.0 17.0 45.0 11.1 biaxial 490262 19.5 5.5 22.5 11.4 0.5σ = τ 230944 17.5 5.5 22.5 11.4 biaxial 424304 31.5 14.7 13.3 20.6 σ = τ 140828 32.0 14.7 13.3 20.6 254124 32.0 14.7 13.3 20.6 204955 32.0 14.7 13.3 20.6 biaxial 460657 37.0 21.0 7.0 26.9 2σ = τ 460663 40.0 21.0 7.0 26.9 376298 38.5 21.0 7.0 26.9 398576 37.0 21.0 7.0 26.9 278760 36.0 21.0 7.0 26.9 259028 38.0 21.0 7.0 26.9 torsion 337940 38.0 28.0 0.0 33.9 623200 43.0 28.0 0.0 33.9 134300 34.0 28.0 0.0 33.9 332011 41.0 28.0 0.0 33.9 table 1: experimental and predicted stage i crack directions for aisi 304l steel. in-phase tests (r=-1) summary and conclusions isi 304l stainless steel cylindrical specimens were subjected to biaxial loading fatigue tests in order to construct the s–n curves for the material. the in-phase biaxial loading curve was better fitted by an elliptical quadrant than by an elliptical arc. photographs of the cracks on the outer surface of broken specimens taken with a light microscope were used to measure the angle at the crack initiation zone (stage i), which was found to be close to the direction of mode i. a comparison of the measured angle with predicted values obtained by using the models of chaves et al., matake and mcdiarmid, and carpinteri and spagnoli, revealed that the last provided the best results in this respect. acknowledgements he authors would like to thank the spanish ministry of education for its financial support through grant dpi2011-27019. a t v. chaves et alii, frattura ed integrità strutturale, 30 (2014) 273-281; doi: 10.3221/igf-esis.30.34 281 references [1] astm international, standard practice for statistical analysis of linear or linearized stress-life (s-n) and strain-life (en) fatigue data, (2004). [2] bettinelli, s., sviluppo di metodologie innovative per l'analisi della resistenza a fatica dei materiali e dei componenti meccanici, tesi di laurea, università degli studi di padova, supervisor: prof. roberto tovo, (2006). [3] gough, h.j., pollard, h.v., clenshaw, w.j., some experiments on the resistance of metals to fatigue under combined stresses, ministry of supply, aeronautical research council reports and memoranda, london: his majesty's stationary office, (1951). [4] chaves, v., navarro, a., madrigal, c., vallellano, c., calculating crack initiation directions for in-phase biaxial fatigue loading, int j fatigue, 58 (2014) 166-171. [5] navarro, a., vallellano, c., chaves, v., madrigal, c., a microstructural model for biaxial fatigue conditions, int j fatigue, 33 (2011) 1048-54. [6] matake, t., an explanation on fatigue limit under combined stress, bull jsme 20 (1977) 257-63. [7] mcdiarmid, d.l., a general criterion for high cycle multiaxial fatigue failure, fatigue fract engng mater struct, 14 (1991) 429-53. [8] carpinteri, a., spagnoli, a., multiaxial high-cycle fatigue criterion for hard metals, int j fatigue, 23 (2001) 135-145. [9] anes, v., reis, l., li, b., freitas, m., crack path evaluation on hc and bcc microstructures under multiaxial cyclic loading, int j fatigue, 58 (2014) 102-113. microsoft word numero_34_art_65 z. jijun et alii, frattura ed integrità strutturale, 34 (2015) 590-598; doi: 10.3221/igf-esis.34.65 590 defect detection of wire rope for oil well based on adaptive angle zhang jijun, meng xiangqing southwest petroleum university, china 790100588@qq.com, 842676523@qq.com abstract. this paper uses a digital image processing method which is based on texture feature of steel cable to detect the fracture of steel wire. at first, it uses a modified homomorphic filtering method to eliminate environment heterogeneous shining. next, it obtains the body image of the steel line by using the method of edge detecting and section counting filtering to detect the bunch part of steel wire. by using an improved radon transformation method to indicate if those steel wire are in good condition or not. finally, by using bp neural network model it aims to judge the final result. test result shows that this method is easy to use and fulfill real time request. keywords. homomorphic filtering method; edge detection; integral projection; bp neural network. introduction s a flexible component, wire rope has been widely used in engineering. the common cableway, crane, hoister and elevator have all used wire rope, it occupies an important position in industrial sectors such as metallurgy, machinery, chemical industry, oil, transportation, tourism and construction industry, etc., therefore, it directly affects people’s daily life, even the development of the national economy [1]. wire rope is high in strength, good in tenacity, as well as strong in bearing capacity, which makes low noise and exert stability during work. however, as a bearing component in engineering, it will deform, be corroded, fracture or even suddenly break down due to the load and tensile force it bears for a long time. it affects the normal operation of the equipment, even threaten the life security of the public, great importance should be attached to its user’s safety. in the drilling platform of oil and gas in this paper, wire rope is supervised through naked-eye identification and regular replacement in order to extend the service life of wire rope and guarantee the safety of its application. however, erroneous judgment and negligence are inevitable in the check by naked eyes, and the regular replacement will also result in wasting, consuming unnecessary man power and material resource. hence, from the view of both economic benefit and social benefit, developing a new method to defect detection of wire rope is an inexorable trend [2-3]. in order to increase the degree of intelligentization of the nondestructive testing of wire rope, improve the objective & unscientific parts and low efficiency and provide more detailed and perfect information of fracture of wire, and evaluate the damage, this paper discusses a way of defect detection of wire rope for oil well based on adaptive angle by regarding the projection features of the images of wire rope as the basis of defect identification. a z. jijun et alii, frattura ed integrità strutturale, 34 (2015) 590-598; doi: 10.3221/igf-esis.34.65 591 detection method of broken wire rope image preprocessing based on the improved homomorphic filtering optimization algorithm s shown in fig. 1, the collected images all have relatively strong side light and serious degradation with uneven brightness since the experimental environment is very complex, bringing great difficulty to the following texture extraction. thus, the images should be dealt with filtering processing to different degrees. figure 1: original drawing of wire rope analysis shows that the background information of the image corresponds to the high-frequency part of the image, while the information of the object itself corresponds to the low-frequency part. for the image with uneven brightness, we need to weaken the low frequency component and strengthen high frequency component to reflect features of the object to the greatest extent and strengthen contrast ratio, and then conduct homomorphic filtering [4]. the classical homomorphic filtering algorithm is conducted in the frequency domain. firstly, fft exchanges will be made to the image, and different filter functions will be adopted for filtering according to the needs of image’s the low-frequency part and high-frequency part. ifft exchange will be conducted in the last period, and then turn the image back. there are several obvious disadvantages concerning the frequency domain algorithm. the first one is the failure to achieve the effect of local contrast enhancement; the second is that two times of fft will reduce the efficiency of operation due to the big calculation amount of fft. to solve these problems, conducting homomorphic filtering on spatial domain is taken into consideration. generally, it will firstly divide the original image into low-frequency part (incidence component) and highfrequency part (reflection component). next, conduct filtering to the images with gaussian lowpass filters to get the component of incident light. the original image subtracts the incident light to result in the reflection component. since the incident component and reflection component are separated by taking logarithm, the true image with enhancement can be obtained with antilog operation. in addition, the thought of template factoring has improved the gaussian lowpass filters and greatly reduced the space for operation and quickened the arithmetic speed, causing a satisfactory effect of homomorphic filtering. consequently, the paper adopts spatial homomorphic filtering algorithm [5-6], to correct the brightness of the image of wire rope, so as to eliminate the influence of the uneven illumination. the detailed steps are as follows: ( , )f x y , function of gray level of the image can be seen as the product of the incident light and reflected light, namely: ( , ) ( , ) ( , )f x y i x y r x y  ( , )i x y is incident light, and 0< ( , )i x y <∞, while ( , )r x y is the reflected light, and 0 ( , )i x y   . then take the logarithm of the image, that is assuming: ( , ) ln ( , ) ln ( , ) ln ( , )z x y f x y i x y r x y   in this way the incident light and reflected light can be separated. in that the low-frequency part of the image is the incident light and the high-frequency part is reflected light, the left will be the low-frequency part (incident light) when we conduct lowpass filtering to ( , )z x y , as shown below: a z. jijun et alii, frattura ed integrità strutturale, 34 (2015) 590-598; doi: 10.3221/igf-esis.34.65 592 ' ( , ) { ( , )} ln ( , )z x y lpf z x y i x y  thus, we can use the original image to subtract the image after lowpass filtering to get the image with increasing highfrequency part (reflected light): '( , ) ( , ) ( , ) ln ( , )s x y z x y z x y r x y   finally, we should conduct antilog operation to ( , )s x y to achieve correct results: ' ( , ) exp[ ( , )] ( , )s x y s x y r x y  however, it’s clear that if we just use the original image to subtract the image after lowpass filtering, it’s similar to conducting common lowpass filtering to the image, and we can get what we want. as a result, we consider conducting weighted approach on the lowpass filtering to get the expected effect of increasing high-frequency part and suppressing low-frequency part: '( , ) ( , ) ( , ) ln ( , ) (1 ) ln ( , )s x y z x y tz x y r x y t i x y     assume 1u t  , and the formula above will be: ( , ) ln ( , ) ln ( , )s x y r x y u i x y  u is the weighting variable, and 0 1u  , of which the meaning is the reserved weigh of low-frequency information in the image. next, to study the influence of value of u on the image, we will take 0.2 as step size, and conduct spatial homomorphic filtering to the original image. the results are as shown in fig. 2. (a) (b) (c) (d) (e) (f) figure 2: figs. a-f show the effects of homomorphic filtering under 0, 0.2, 0.4, 0.6, 0.8 and 1, respectively. from the analysis about a-f, we can infer that higher value of u indicates closer distance between the image and high-pass filtering, stressing the reflection of details, and resulting in loss of some necessary high-frequency information. lower z. jijun et alii, frattura ed integrità strutturale, 34 (2015) 590-598; doi: 10.3221/igf-esis.34.65 593 value of ( , )f i j means the uneven brightness of the image, and bigger the interference of the background information. therefore, we need to weigh in accordance with needs, and take weighting variables that are most suitable for effect of filtering. in this article, we take u as 0.6, and thus can get the ideal effect. fig. 3 tells us that the uneven brightness and shadowing are eliminated after spatial homomorphic filtering and the marginal information is strengthened. extraction of wire rope edge is the basic feature of the image. generally speaking, at the location of edge, the gray level will be different from that of the adjacent area, consequently it will draw the outline of the target object [7-9]. this article uses roberts operator to detect edge [10-11], and get the edge image. roberts uses the performance of the partial difference operator to find out the operator of the edge. it sets ( , )f i j as the input image and ( , )g i j as output image. roberts edge gradient is calculated by the formula below. 2 2( , ) {[ ( 1, 1) ( , )] [ ( , 1) ( 1, )] }g i j f i j f i j f i j f i j        figure 3: effect of holomorphic filtering. figure 4: roberts’s operator to calculate edge. it can be seen from the experiment that a certain quantity of noisy points have appeared during the edge detection of the image with roberts operator, as shown in fig. 4, which surely affecting the extraction of wire rope, conducting filtering is a necessity. it can be observed that the noise points are relatively separate and the quantity is small, resulting in a distinctive comparison with the wire rope itself at the vertical direction. this paper lists the statistical filtering to make statistics of the quantity of efficient points of each line of the image, and sets threshold value. then the wire rope itself and the blending points of the background will be differentiated based on the results of statistics and conduct filtering, as shown in fig. 5. in this way the extraction of the image of wire rope can be achieved, as shown in fig. 6. figure 5: denoised edge image. figure 6: a sketch after background subtraction. z. jijun et alii, frattura ed integrità strutturale, 34 (2015) 590-598; doi: 10.3221/igf-esis.34.65 594 extracting of the wire rope strand based on canny to judge whether there is any defect in the wire rope after separating it from its background, we need to extract the slant texture of the wire rope strand. if the wire rope is undamaged, the texture will be complete and regular, based on which, we firstly adopt the homomorphic filtering technique to filter the image by a high pass filter to strengthen the edge information of the wire rope strand as in fig. 7. the gray level change based on the reflected light image can strengthen the contrast of image. the process of grey level transformation is as below: ( , ) [ ( , )]g x y t f x y it turns the gray level, ( , )f x y , of each pixel, ( , )x y , in the input image into the gray level, ( , )g x y , in the output image. this article uses imadjust to transform the gray level, and the results are shown in fig. 8. figure 7: sketch after high-pass filtering. figure 8: sketch after gray level transformation. after we get the function of contrast enhancement, we need to position the edge point accurately on the pixel point that transformed to a higher grey level to restrain false edge to the best extent and reduce peripheral point. so we use canny operator[12] to conduct the extraction of wire rope strand. the procedure is as below: (1) smooth the image with gaussian filter. (2) calculate the gradient magnitude and direction with first-order partial finite difference. (3) restrain the gradient magnitude to the biggest extent. (4) detect and connect edges with dual threshold algorithm. the effect is shown as fig. 9. angle adaptive integral transformation the projection feature of image obtained by integral projection [13-15] has translation invariance and can well express the distribution pattern of pixels in the space. ijf is the gray level of the image at (i,j). the formulas to solve the horizontal integral projection, ipy , of image in [ 1 , mx x ] and the vertical integral projection, jpy , of the image in [ 1 , mx x ], are as below: 1 1 2 1 , , y , ..., y mx i ij n i x py f j y m    1 1 2 1 , , ,..., ny j ij m i y py f j x x x n    z. jijun et alii, frattura ed integrità strutturale, 34 (2015) 590-598; doi: 10.3221/igf-esis.34.65 595 after the edge of wire rope strand is extracted, the angle of the trend of strand cannot be accurately calculated, and because of which the project direction and the trend direction of the strand may not match if the line integral is conducted in a fixed angle. the corresponding result may also have errors in it. therefore, in this article, an improved horizontalprojection is adopted (by rotating the image with a fixed angular difference) to get all the projection integrals in one angle-domain. based on the judgment of all the results generated, the best integral angle can be chosen for the most suitable image with integral projection. figure 9: sketch of the extracted edge of the wire rope strand by canny operator. the thought to select the conditions for judgment is as below. when the integral position coincides with the edge of a wire rope strand, there will be a peak in the horizontal integral projection image, that is, the extreme point; and the strands under detection of each image under the same conditions are the same. from these angles, we can restrain the horizontal integral projection image as below. (1) restrain the scope of the quantity of the effective extreme points, ip , which should be two times of the quantity of strands of each picture, p , including the strands under detection, because each strand will have two extreme points. and, we can regard the 2p extreme points with the highest pulse are effective extreme points; (2) restrain the height of the extreme points in the image, ( )if p . when the sum of the heights of all the extreme points reaches to the peak, the direction of the integral is regarded as the same as the direction of strand. so, when the following conditions are met, the image with the best integral angle can be obtained. 1 1 1 2 ( ) [ ( )] n i n n i s i i i i p f p max f p             in the formula, 1, 2,i n  , which is the quantity of the extreme points of the current image, and 1, 2,s m  , which is the time of rotation in the angle domain. before conducting the angle adaptive integral transformation, a simple dilation operation shall be conducted to the image, because generally the strands of the wire rope are not absolute straight line, which may affect the effect of integral and lead to errors. so the combination of dilation operation and bold edge will achieve better effect. after the dilation operation on fig. 8 through steps above, the following angle adaptive integral projection will get the results as shown in fig. 10 and 11. it’s clear that we can identify where the fracture happens. in this way, not only can we judge whether the wire rope has superficial defect, but can also position the defect. the detection results meet the requirements. z. jijun et alii, frattura ed integrità strutturale, 34 (2015) 590-598; doi: 10.3221/igf-esis.34.65 596 figure 10: results of angle adaptive method. figure 11: horizontal integral projection. identify the defect of wire rope with neural network identify the superficial defect of the wire rope with bp neural network, sigmoid function as excitation function, and error signal back propagation algorithm [16-20] as training algorithm, parameters are as below: number of nodes at input layer is 4, and the input values are respectively quantity of effective pulse, width of pulse, sum of height of pulse and radius of wire rope under detection. we can identify whether the different kinds of wire ropes have defect. besides, the number of nodes at implicit strata is 6 and at output layer is 1. assume the transmission function and output of the j nerve cell at l-1 layer of the k training sample are respectively 1( )lju k  and 1( )ljz k  , then: 1 1 1 1 1 ( ) 2 ( ) 2 ( ) ( ) 2 ( ) ( ) lk i ij l l kl i ij k l l l i im ml k ij k l l i j k u ke e u k k z k k z k                                   in the formula, e is the overall error; ijl is weight; ( )i k is delta error. 1 1 1 1 1 1 ' 1 1 ( ) ( ) ( ) ( ) ( ) ( ( )) ( ) ( ( )) ( ) lm l m i l l l mi m i jk l l l m mj jl k ji m l l l j m mi m u ke e k u u k u k k f u k u k f u k k                                    the renewal process of weight is as below: 1 1 ( 1) ( ) ( ) ( ) ( ) ( 1) ( ) k l l l l ij ij i j k l l l ij ij ij t t k z k t t t                      z. jijun et alii, frattura ed integrità strutturale, 34 (2015) 590-598; doi: 10.3221/igf-esis.34.65 597 the last three items in the formula above are respectively gradient, temporal item and stochastic noise of the average error. in this paper, 30 images of normal wire rope and 30 images of wire rope with fractures are used for the training of the neural network model, taking learning rate,  , as 0.1, and instant constant,  , as 0.85. the output of the wire rope with defect is 1, or otherwise, 0. at the beginning, weight is selected as the random number to meet normal distribution. through the output results of the training set by statistics, the scope of the output threshold value can be identified. fig. 12 shows the structure of the three layers of bp neural network, and tab. 1 presents the results from the tests of the experimental groups. figure 12: structure of the three layers of bp neural network. no. state of wire rope output of neural network 1 surface damage 0.423 2 good 0.933 3 good 0.862 4 surface damage 0.699 5 good 0.914 6 good 0.872 7 surface damage 0.795 table 1: results from the tests of the experimental groups. based on the actual state of the wire rope, and the corresponding output results of the neural network, this paper sets the output threshold value for identifying of the neural network model at 0.85. results and analysis o verify the effectiveness of the neural network model, the collected 60 original pictures of wire rope are input as test samples into the neural network model to identify the existence of fracture. there are 30 pictures of good wire rope and 30 with defect. through the experimental analysis, the experimental results of wire rope test are shown in tab. 2. state of wire rope good wire rope wire rope with defect accuracy good surface 27 3 91% surface damage 2 28 93.3% table 2: detection results of wire rope. it can be seen from the results that the method proposed in this paper can reach a relatively high accuracy of the defect detection of surface of wire rope, yet some errors are inevitable. through the analysis, it indicates that the good wire rope t z. jijun et alii, frattura ed integrità strutturale, 34 (2015) 590-598; doi: 10.3221/igf-esis.34.65 598 will are often affected by oil contamination and other dirt on the surface, which will be mistakenly identified as defect; some of the damages on the surface of wire rope are not so obvious, therefore the wire will be identified as being in good condition. but the misjudgment rate is overall low, and the misjudgment rate of the wire rope with defect on the surface is lower than that of the wires with good surface. so this can replace the manpower to detect the wire ropes. conclusion he method of filtering realizes the separation of the texture and background of the wire ropes. the defect detection of wire rope for oil well based on angle adaptive can reach a relatively high accuracy and speed. it’s applicable for the online real-time detection of the wire rope. identifying the surface damage of wire ropes by the detection method proposed in this article can meet the needs of the actual detection. references [1] xv, j., the intelligent detection technique study for broken wires of the steel wire rope, wuhan university of technology, 2002. [2] shen, y., zhang, d., ge, s., effect of fretting amplitudes on fretting wear behavior of steel wires in coal mines, mining science and technology, 20 (2010) 803-808. [3] zhang, d., ge, s., xiong, d., fretting wear of steel wires in hoisting ropes , international journal of minerals metallurgy and materials, 9(2) (2002) 81-84. [4] wang, y., long, x., reduce non-uniform illumination with wavelet, optical technique, 5 (2005) 726-728. doi: 10.13741/j.cnki.11-1879/o4.2005.05.026 [5] wen, s., you, z., performance optimization homomorphic filtering algorithm, application research of computers, 3 (2000) 62-65. [6] bertalmío, m., caselles, v., provenzi, e., issues about retinex theory and contrast enhancement, international journal of computer vision, 83(1) (2009) 101-119. doi: 10.1007/s11263-009-0221-5 [7] ma, y., gu, x., wang, y., feature fusion method for edge detection of color images, journal of systems engineering and electronics, 20(2) (2009) 394-399. [8] li, j., huang, p., wang, x., pan, x., image edge detection based on beamlet transform, journal of systems engineering and electronics, 20(1) (2009) 1-5. [9] dou, z., shi, p., lin, y., a kind of edge detection algorithm with edge-preserving characteristics, journal of harbin institute of technology, 20(2) (2013) 86-89. [10] wang, b., using roberts operator for edge processing, gansu science and technology, 10 (2008) 18-20. [11] ma, y., zhang, z., comparison of several edge detection operator, industry and mine automation, 1 (2004) 54-56. [12] ding, l., goshtasby, a., on the canny edge detector, pattern recognition, 34(3) (2001) 721-725. doi: 10.1016/s0031-3203(00)00023-6. [13] feng, j., liu, w., yu, s., eyes location based on gray-level integration projection, computer simulation, 4 (2005) 7576,104. [14] jan, f., usman, i., agha, s., reliable iris localization using integral projection function and 2d-shape properties, chinese optics letters, 11 (2012) 111501(1)-111501(6). doi: 10.3788/col201210.111501 [15] kim, j., park, r., a fast feature-based block matching algorithm using integral projections, ieee journal on selected areas in communications, 10(5) (1992) 968-971. doi: 10.1109/49.139002 [16] mao, l., kong, f., et al., the wire rope surface defect detection based on image processing and neural network, measurement & control technology, 7 (2007) 23-25 [17] gao, h., yang, s., yang, k., et al., a neural network-based technique for quantitative wire rope inspection, ndt & e international, 26(1) (1993) 31-33. [18] fan, j., du, y., zhou, y., wang, y., edge detection of range images using genetic neural networks, journal of chongqing university of posts and telecommunications (natural science edition), 21(2) (2009) 272-275. [19] liu, x., deng, z., wang, t., real estate appraisal system based on gis and bp neural network, transactions of nonferrous metals society of china, 21 (2011) 626-630. doi: 10.1016/s1003-6326(12)61652-5. [20] zhang, l., zhao, j., zhang, x., zhang, e., study of a new improved pso-bp neural network algorithm, journal of harbin institute of technology, 20(5) (2013) 106-112. t microsoft word 2208 k. hachellaf et alii, frattura ed integrità strutturale, 47 (2019) 459-467; doi: 10.3221/igf-esis.47.36 459 mechanical behavior analysis of a friction stir welding (fsw) for welded joint applied to polymer materials hachellaf kaddour, meddah hadj miloud, ould chikh el bahri, lounis abdellah university of mascara, lste laboratory, 29000, mascara, algeria. kaddour.hachellaf@univ-mascara.dz, http://orcid.org/0000-0001-2345-6789 hmmeddah@yahoo.fr, http://orcid.org/0000-0002-2345-6790 b.ouldchikh@univ-mascara.dz, http://orcid.org/0000-0003-2345-6791 lounisabdallah@gmail.com, http://orcid.org/0000-0004-2345-6792 abstract. welding is a technique of fusion joining the material involving a process of inter-molecular diffusion adhesion. polymer welding is an assembly method among several known assembly techniques such as gluing. this welding process applies to thermoplastics; they have the rheological or softening characteristics during melting. this process is fast and controlled in order to obtain a solid and durable mechanical connection on the series parts. this study focuses on the weldability of high density polyethylene (hdpe) using the friction stir welding technique. a parametric choice was made to optimize the operating parameters namely the shape of the welding tool, the speed of rotation and the speed of advance of the tool. monotonic tensile tests were used to compare the mechanical characteristics between a hdpe test specimen and a specimen taken from an fsw weldment. it emerges from this study that the fsw welding introduces a weakening of the joints characterized by a clear decrease of the deformation at break. keywords. polymers; tensile tests; fsw; vickers hardness test. citation: hachellaf, k., meddah, h. m., ouldchikh, el. b, lounis, a., mechanical behavior analysis of a friction stir welding (fsw) for welded joint applied to polymer materials, frattura ed integrità strutturale, 47 (2018) 459-467. received: 02.10.2018 accepted: 14.12.2018 published: 01.01.2019 copyright: © 2018 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. introduction riction stir welding is a recent permanent assembly process considered as a major technology in the industry, this type of welding is applied to thermoplastic materials including polymers, its principle is based on the softening phenomenon following the melting caused by the heating of the material (fig. 1.a) assembled with a nonconsumable special rotating tool (fig. 1.b). the principle is to provide heat to the metal base by friction of the metal by a pin fixed on a base that rotates in the joint plane of the parts to be assembled. a metal layer in plastic and pasty form is formed under the base and around the pin. this process which performs the assembly at a temperature below the melting temperature of the metal to be bonded deforms less than the fusion processes. in addition, the mechanical characteristics of the welded materials remain close to the initial values of the base f http://www.gruppofrattura.it/va/47/2208.mp4 k. hachellaf et alii, frattura ed integrità strutturale, 47 (2019) 459-467; doi: 10.3221/igf-esis.47.36 460 materials. this process is well suited to alloys with a low melting point (aluminum, magnesium, copper) and found with these materials its main industrial applications: aeronautics, space, land transport, shipbuilding etc... during the welding operation the friction and the thermal field are factors that play an important role for the success of the fsw welding operation. the frictional heat of the shoulder of the tool and the heat of deformation of the tool spindle allow the material to soften without reaching the melting point. significant plastic deformation and flow of this plasticized material occur as the tool is translated along the welding direction. the material is transported from the front to the rear edge of the tool, where it is forged to form a joint [1]. panneerselvam and lenin [1,2] observed that in the fsw of nylon-6, a seal made with counter-clockwise rotation of the tool produced better material properties. hoseinlaghab et al. [1,3] studied the creep properties of fsw-welded polyethylene plate assemblies and reported that under controlled conditions, the creep resistance of welds may be better than that of the base [1]. fsw can be used to join sheets and aluminum plates, without filler wire or shielding gas. variety of materials ranging from aluminum alloys, copper, magnesium, lead, zinc and polymers and a material thickness ranging from 0.8 to 65 mm have been reported for successful welded joints at full penetration and without porosity and internal voids [4]. after the successful application of fsw on metals, adeel et al. found that, depending on their physical and rheological properties, the welding parameters differ from polymer to polymer. polymers with high melting temperature and viscosity require a higher speed of rotation and reach a sufficient heat and possibly a good resistance of the weld. in addition, to improve the welding force, the use of hot shoes or induction heating in situ showed good results [5]. olivier l. has shown that temperature plays a key role in the success of welding and thus the understanding and control of the flow of the material are related to the temperature field and are critical for the success of fsw welding [6]. in other sense the improvement of mechanical properties such as fatigue, zhou et al has confirmed through these tests on the service life is better in fsw (compared to other welding processes), higher service life for fsw welded joints (9 to 12 times higher) [7]. a) b) figure 1: fsw welding principle. a) fsw welding process, [8]. b) fsw welding tool, [9]. in this work we highlight the weldability of hdpe polymer by friction stir welding technique (fsw), the hdpe material is used in the drinking water networks and thus the city gas networks. three welding parameters, the speed of rotation, the speed of advance and the geometrical shape of the tools, were studied. mechanical behavior tests were carried out to evaluate and optimize the necessary parameters involved in achieving a good weld. experimental procedure he material used is high density polyethylene (hdpe) is a thermoplastic polymer of high diffusion. it is part of the family of polyolefins, in the same way as low or medium density polyethylenes, used in the manufacture of pipes reserved for the supply and distribution of drinking water in accordance with algerian standards na7700-2 manufactured by the group chiali sidi bel-abbes (algeria), molar mass is of the order of 500 kg / mol and glass transition temperatures and melting are respectively (-125 ° c and 135 ° c) [10]. tabs. 1 and 2 below show the mechanical and physical properties of hdpe (pe100). the tensile test carried out taken from a drinking water pipe made of hdpe (dumbbell type) in fig. 2 according to the iso 3167 standard [12]. then perform the monotonic tensile operation to complete the main mechanical properties of a material (fig. 3), such as yield strength, breaking strength and elongation. t k. hachellaf et alii, frattura ed integrità strutturale, 47 (2019) 459-467; doi: 10.3221/igf-esis.47.36 461 resin's designation minimal stress required msr (mpa) long-term hydrostatic stress σ (mpa) pe100 10 8 pe 80 8 6.3 table 1: resin’s used for hdpe tubes [42]. characteristics units pe80 pe100 density kg/m3 949-956 956-961 melt flow index( mfi (190 °c ; 5kg) g/10 mn 0.7-1 0.2-0.5 resistance at the yield point mpa ≥15 ≥19 elongation at break % >600 >600 elasticity modulus mpa 800 1000 fragility temperature 0c <-100 <-100 linear expansion k-1 24.104 24.104 electrical resistance ω/cm ≥1012 ≥1012 table 2: physical characteristics of hdpe [10]. figure 2: no welded test specimen [12]. figure 3: stress-strain curve (non-welded test specimen) in the strain rate. for the investigation, samples of size 300 mm x 60 mm x 4 mm were used fig. 4. butt welding was done. the tools used are prepared by steel commonly used to ensure good mixing and good softening of the material entrained fig. 5. figure 4: fsw welding sample. k. hachellaf et alii, frattura ed integrità strutturale, 47 (2019) 459-467; doi: 10.3221/igf-esis.47.36 462 figure 5: geometry of the tools. tool type process parameters welding quality welded cord pin profile: cylindrical (t1) rotation speed n (rpm) advance speed a (mm/min) test n° 1 875 24 welding correct 2 40 regular cord 3 1750 24 bad welding 4 40 cracked cord 5 720 24 bad welding 6 40 bad welding table 3a: welding process parameters the material used for welding tools is ordinary steel. these tools are suitable for friction welding fsw of hdpe plates. they are able to perform the three main welding functions [13, 14]: heat the parts by friction and by plastic deformation, k. hachellaf et alii, frattura ed integrità strutturale, 47 (2019) 459-467; doi: 10.3221/igf-esis.47.36 463 mix the materials to form the joint contain the flow of material under the shoulder and around the pin. the shoulder serves to bring heat by friction and to confine the kneaded material under the tool. tool type: pin profile : conical (t2) process parameters welding quality welded cord rotation speed n (rpm) advance speed a (mm/min) test n° 1 875 24 welding correct 2 875 40 welding correct 3 1750 24 bad welding 4 1750 40 bad welding 5 720 24 no welding 6 720 40 cracked cord table 3b: welding process parameters. results and discussions he experiment was successfully carried out on hdpe plates with a thickness of 4 mm with all the parameters selected. examination of these welded samples by both types of tools gives some good results for welding quality. the samples relating to the welding by the two tools t1 and t2 for rotation speed of 875 rpm and advance speed of 24 and 40 mm/min have a satisfactory appearance. for other cutting parameters, we notice a bad quality of welding. we also noticed that with a cylindrical pin, the kneading zone of the welded sample had a good surface state, which proves the effectiveness of the tool for kneading the softened polymeric material (tab. 3). when the linear welding operation is finished sample preparation is carried out for tensile tests (fig. 6), tensile test specimens made of dumbbell form according to iso 3167. tensile tests are carried out under room temperature. t k. hachellaf et alii, frattura ed integrità strutturale, 47 (2019) 459-467; doi: 10.3221/igf-esis.47.36 464 figure 6: welded test specimen [12]. fig. 7 shows a typical aspect of the weld on welded plates with a rotation speed of 875 rpm and advance speed of 24 and 40 mm/min shown in tab. 3. figure 7: law behavior of welded specimens table 4: tensile strength values and their effectiveness on the welded bead. tool type : rotation speed (rpm) advance speed a (mm/min) max stress of tensile test rm max (mpa) elasticity module e (mpa) average (x) standard deviation () efficiency rate the stress of the welded joint (%) conical profile (t1) test n° 1 875 24 22.60 1320 23.257 0.927 5.56 2 40 23.11 2102 7.94 cylindrical profile (t2) 3 875 24 24.61 1500 14.94 4 40 22.71 1433 6.07 no welded sample test 21.41 920 / / / k. hachellaf et alii, frattura ed integrità strutturale, 47 (2019) 459-467; doi: 10.3221/igf-esis.47.36 465 tab. 4 shows the tensile strength values and their effectiveness on the weld bead for different parameters and for the two tools with cylindrical and conical pins. the cylindrical pin tool achieves maximum efficiency of the joint strength respectively 14.94% and 6.07% for advanced speed 24 mm/min and 40 mm/min and in parallel for the conical tool profile has a value of 13.12% for a speed of 24 mm/min. the experimental results shown in fig. 7 (stress-strain curves) for tensile tests with a strain rate of 0.01s-1 at room temperature are compared to those of the no welded test specimen. according to these results of the fsw welding on hdpe, it can be seen that these results are very satisfactory, especially the tools t1 and t2 for the two advanced speed 24 and 40 mm/min, where a remarkable improvement is observed caused by the temperature welding effect on the material that is triggered at the beginning of the tensile stress on the elastic zone (fig. 7). from fig. 7, we remarked also that the maximum stress rm = 24.3 mpa became important, an improvement of the modulus of elasticity with respect to that of the no welded specimen which was of value rm = 20.41 mpa, at the same time or we have a reduced plastic part noticing on the curves where the plasticity domain of the material (plastic side on the tensile curve) was lost, therefore the material has become rigid, the latter linked to several phenomena and several parameters influenced by the fsw welding operation and even the material as there are other parameters that play an important role, all due to the influence of the machined weld joint that changes the mechanical behavior of the fsw welded material. these experimental results obtained allowed us to better understand certain phenomena resulting for example the flow of the material around the tool. micro hardness test he vickers micro-hardness test is done on a very sophisticated automatic ft-ars 9000 laboratory mechanical engineering tester with a load of 500 gf for 10 seconds at room temperature [15]. the determination of the hardness value of the weld seams for comparing the results to those of the non-welded material, the micro-hardness was measured on the mid-thickness of the welded joints perpendicular to the welding axis are made (fig. 8) with a step of 1 mm between the points measured, where the measurements are carried out symmetrically with respect to the main axis of welding. figure 8: profile of welded joint on half thickness. the results of the vickers micro-hardness (hv) shown in (fig. 9), made on the average thickness of two welded plates (lateral side) of the welded bead (fig. 8 ) with a spacing of 1 mm ,within a limited range of (-15 to +15 mm) from the center of the weld, variable hardness applies over 4 main thermal zones, the core zone (or nugget zone nz), thermomechanical affected zone (tmaz), heat affected zone ( haz) and base material (bm) which is not affected by the fsw welding process. the mechanical properties vary between deferent component zones of the welding. the micro-hardness profile exhibits an increase in all cases which reaches a maximum value at the core zone (nz) which is the equi-axed zone is harder than the other zones, the curve is fairly symmetrically to the axis, ie the core zone is very hard relative to the base material zone bm. the micro-hardness decreases towards the less hard zone, the latter represents the normal state of the non-welded material, this zone is located outside the thermal deformation during welding, so it retains its original granular structure without change. according to [16, 17] the hardness value in the nz zone should be higher than the other zones because of its structure. the distribution of microhardness is almost symmetrical with respect to the median weld line because the field plastic flow on both sides of the weld center is uniform [16, 18]. t k. hachellaf et alii, frattura ed integrità strutturale, 47 (2019) 459-467; doi: 10.3221/igf-esis.47.36 466 fig. 9.: variation of micro-hardness vickers hv. conclusions he characterization of the mechanical behavior of the materials through the various tests carried out, the results obtained show the complex relationship between material and tool which contributes to the physicochemical change modified by several welding parameters such as the advance speed, the rotation speed and tool geometry. this study, we concluded that the behavior of the welded joint fsw strongly depends on the geometry of the tool which plays an important role with the chosen parameters. the union of all these parameters proves that fsw welding of hdpe gives very satisfactory and important results. it should be noted that the analysis of the results made it possible to understand the influence of the tool geometry and cutting parameters used in fsw. according to the results obtained, it is observed that the best results were obtained by the cylindrical profiled tool t2 which have a maximum efficiency of the weld of 14.94% compared to the base material, better than the tool t1 with a conical profile which reaches a efficiency of 7.94%, the cylindrical profile with a dynamic volume ratio produces better results than the conical profile are suitable to obtain a good quality of welding of thermoplastic materials such as hdpe. this work is a real experimental challenge. to do this, we have developed a technique for welding hdpe. with regard to the influence of tool geometry on fsw welding, tools t1 and t2 are suitable for obtaining good welding quality. reference [1] vijendra, b., sharma, a. (2015). induction heated tool assisted friction-stir welding (i-fsw): a novel hybrid process for joining of thermoplastics, j. man. proces. 20, pp. 234-244. doi:10.1016/j.jmapro.2015.07.005. [2] panneerselvam, k., lenin, k. (2014). joining of nylon 6 plate by friction stir welding process using threaded pin profile, j. mater. design, 53, pp. 302–307. doi: 10.1016/j.matdes.2013.07.017. [3] hoseinlaghab, s., mirjavadi, s.s., sadeghian, n., jalili, i., azarbarmas, m., givi, (2015). influences of welding parameters on the quality and creep properties of friction stir welded polyethylene plates, j. mater design, 67, pp. 369–378. [4] patel, a. r., dalwadi, c.g. (2016). a review: dissimilar material joining of metal to polymer using friction stir welding (fsw). inter j. sci. technology & engineering, 2(10), pp. 702-706. [5] zafar, m., awang, m., raza khan, s. (2017). friction stir welding of polymers. 2nd international conference on mechanical, manufacturing and process plant engineering, lecture notes in mechanical engineering, pp. 19-36. doi 10.1007/978-981-10-4232-4_2. [6] lorrain o., ed., (2010). analyses expérimentale et numérique du procédé de soudage par friction malaxage fsw, paris tech, thèse de doctorat, l’ecole nationale supérieure d'arts et métiers, paris tech. [7] zhou, c., yan, x., luan, g. (2005). fatigue properties on friction stir welding in al 5083, j. scripta materialia, 53(10), pp.1187-1191. doi 10.1016/j.scriptamat.2005.07.028. t k. hachellaf et alii, frattura ed integrità strutturale, 47 (2019) 459-467; doi: 10.3221/igf-esis.47.36 467 [8] hamilton, c., dymek, s., bucharski, m., (2008). friction stir welding of aluminum 7136-t 76s11 extrusions. j. sci. and technology of welding and joining, 13(8), pp. 714-720. [9] mishra, r.s., ma, z.y. (2005). friction stir welding and processing, j. mat. sci. and engineering , 50, pp. 1-78. [10] catalogue technique pour tubes en polyéthylènepe, groupe chiali de sidi bel-abbesalgeria, available at (2017): http:/www.groupe-chiali.com. [11] catalogue société conceptcuve société de chaudronnerie plastique de france ; contact@conceptcuve.com; france, available at (2017): https://www.conceptcuve.com/polyethylene-pehd.htm. [12] astm d 638 standard test method for tensile properties of plastics. (2017). [13] thomas, w.m., (1991). friction stir welding, j. inter. patent appl. no.pct/gb92/02203 and gb patent application no. 9125978.8, us. patent no. 5,460, 317. [14] shigeki, h., harsha, b., kazutaka, o., toshio, t., tsuyoshi, k., (2010). analysis of effect of tool geometry on plastic flow during friction stir spot welding using particle method, j.of mat. proc. tech., 210, pp. 1455–1463. [15] hardness tester fully-automatic micro/vickers hardness. fv-ars 9000, avaible at (2017): www.ft-hardness.com [16] chen, z., shengxi, li. lloyd, h. (2015). microstructure, mechanical properties and corrosion of friction stir welded 6061 aluminum alloy, hawaii corrosion laboratory, department of mechanical engineering, university of hawaii at manoa, honolulu, hi 96822, usa, pp.1-25. [17] jeong, d. h., erb, u., aust, k. t., palumbo g., (2003). the relationship between hardness and abrasive wear resistance of electrodeposited nanocrystalline ni–p coatings, j. scripta materialia, 48 (2003), pp. 1067-1072 [18] xu, w., liu, j., luan, g., dong, c. (2009). microstructure and mechanical properties of friction stir welded joints in 2219-t6 aluminum alloy, j. materials & design, 30, pp. 3460-3467. << /ascii85encodepages false /allowtransparency false /autopositionepsfiles true /autorotatepages /none /binding /left /calgrayprofile (dot gain 20%) /calrgbprofile (srgb iec61966-2.1) /calcmykprofile (u.s. web coated \050swop\051 v2) /srgbprofile (srgb iec61966-2.1) /cannotembedfontpolicy /error /compatibilitylevel 1.4 /compressobjects /tags /compresspages true /convertimagestoindexed true /passthroughjpegimages true /createjobticket false /defaultrenderingintent /default /detectblends true /detectcurves 0.0000 /colorconversionstrategy /cmyk /dothumbnails false /embedallfonts true /embedopentype false /parseiccprofilesincomments true /embedjoboptions true /dscreportinglevel 0 /emitdscwarnings false /endpage -1 /imagememory 1048576 /lockdistillerparams false /maxsubsetpct 100 /optimize true /opm 1 /parsedsccomments true 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can be opened with acrobat and adobe reader 5.0 and later.) >> /namespace [ (adobe) (common) (1.0) ] /othernamespaces [ << /asreaderspreads false /cropimagestoframes true /errorcontrol /warnandcontinue /flattenerignorespreadoverrides false /includeguidesgrids false /includenonprinting false /includeslug false /namespace [ (adobe) (indesign) (4.0) ] /omitplacedbitmaps false /omitplacedeps false /omitplacedpdf false /simulateoverprint /legacy >> << /addbleedmarks false /addcolorbars false /addcropmarks false /addpageinfo false /addregmarks false /convertcolors /converttocmyk /destinationprofilename () /destinationprofileselector /documentcmyk /downsample16bitimages true /flattenerpreset << /presetselector /mediumresolution >> /formelements false /generatestructure false /includebookmarks false /includehyperlinks false /includeinteractive false /includelayers false /includeprofiles false /multimediahandling /useobjectsettings /namespace [ (adobe) (creativesuite) (2.0) ] /pdfxoutputintentprofileselector /documentcmyk /preserveediting true /untaggedcmykhandling /leaveuntagged /untaggedrgbhandling /usedocumentprofile /usedocumentbleed false >> ] >> setdistillerparams << /hwresolution [2400 2400] /pagesize [612.000 792.000] >> setpagedevice microsoft word numero_50_art_24_2571 h. saidi et alii, frattura ed integrità strutturale, 50 (2019) 286-299; doi: 10.3221/igf-esis.50.24 286 vibration analysis of functionally graded plates with porosity composed of a mixture of aluminum (al) and alumina (al2o3) embedded in an elastic medium saidi hayat, sahla meriem civil engineering department, faculty of technology, university of sidi bel abbes, laboratory of materials and hydrology (lmh), algeria. hayatsaidi2019@yahoo.fr, meriemsahla@gmail.com abstract in this scientific work, a new shear deformation theory for free vibration analysis of simply supported rectangular functionally graded plate embedded in an elastic medium is presented. due to technical problems during the fabrication, porosities can be created in side fgm plate which may lead to reduction in strength of materials. in this investigation the fgm plate are assumed to have a new distribution of porosities according to the thickness of the plate. the elastic medium is modeled as winkler-pasternak two parameter models to express the interaction between the fgm plate and elastic foundation. the four unknown shear deformation theory is employed to deduce the equations of motion. the hamilton’s principle is used to derive the governing equations of motion. the accuracy of this theory is verified by compared the developed results with those obtained using others plate theory. some examples are performed to demonstrate the effect of changing gradient material, elastic parameters, porosity index, and length to thickness ratios on the fundamental frequency of functionally graded plate. keywords. shear deformation theory; vibration; functionally graded plate; porosity; frequency. citation: saidi, h., sahla, m., vibration analysis of functionally graded plates with porosity composed of a mixture of aluminum (al) and alumina (al2o3) embedded in an elastic medium, frattura ed integrità strutturale, 50 (2019) 286-299. received: 20.07.2019 accepted: 19.08.2019 published: 01.10.2019 copyright: © 2019 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. introduction unctionally graded materials (fgms) are a type of heterogeneous composite materials that exhibits a continuous variation of mechanical properties from one point to another. the concept of functionally graded material was first considered in japan in 1984 during a space plane project. such kind material is produced by mixing two or more materials by a graded distribution of the volume fractions of the constituents [1], the fgm is thus suitable for diverse applications, such as thermal coatings of barrier for ceramic engines, electrical devices, energy transformation, biomedical engineering, optics, etc [2-11]. f http://www.gruppofrattura.it/va/50/2571.mp4 h. saidi et alii, frattura ed integrità strutturale, 50 (2019) 286-299; doi: 10.3221/igf-esis.50.24 287 however, in fgm fabrication, micro voids or porosities can occur within the materials during the process of sintering. this is because of the large difference in solidification temperatures between material constituents [12]. wattanasakulpong [13], also gave the discussion on porosities happening inside fgm samples fabricated by a multi-step sequential infiltration technique. therefore, it is important to take into account the porosity effect when designing fgm structures subjected to dynamic loadings [14]. currently, many functionally graded (fg) plate structures which have been employed for engineering fields led to the development of various plate models to study the static, buckling and vibration responses of fg structures [15-19]. the classical plate theory (cpt) is based on the supposition that straight lines which are normal to the neutral surface before deformation remain straight and normal to the neutral surface after deformation. since the transverse shear deformation is neglected [20-23], it cannot be suitable for the investigating of moderately thick or thick plates in which transverse shear deformation effects are more important. for fg thick and moderately thick plates; the first-order shear deformation theory (fsdt) has been employed [24-27]. in such formulation, the displacements are linearly varied within the thickness and need a shear correction coefficient to correct the unrealistic distribution of the transverse shear stresses and shear strains across the thickness. to avoid the use of the shear correction coefficient, higher-order shear deformation plate theories (hsdts) have been developed [28-40]. the purpose of this work to propose a new higher-order shears deformation theory for free vibration response of fg plates with porosity embedded in elastic medium. in this investigation the fgm plate are assumed to have a new distribution of porosity according to the thickness of the plate. the elastic medium is modeled as winkler-pasternak two parameter models to express the interaction between the fgm plate and elastic foundation. the four unknown shear deformation theory is employed to deduce the equations of motion from hamilton’s principle. the hamilton’s principle is used to derive the governing equations of motion. the accuracy of this theory is verified by compared the developed results with those obtained using others plate theory. some examples are performed to demonstrate the effect of changing gradient material, elastic parameters, porosity index, and length to thickness ratios on the fundamental frequency of functionally graded plate. figure 1: schematic representation of a rectangular fg plate resting on elastic foundation. mathematical formulation n the current work, a fg simply supported rectangular plate with length, width and uniform thickness equal to a, b and h respectively is considered. the geometry of the plate and coordinate system are illustrated in fig. 1. the material characteristics of fg plate are considered to vary continuously within the thickness of the plate in according to the power law distribution as follows     ( /2 )1( ) 1 2 k m c m c m z e z e e e e e e h            (1a)     ( /2 )1( ) (1 ) 2 k m c m c m z z e e e h                (1b) i h. saidi et alii, frattura ed integrità strutturale, 50 (2019) 286-299; doi: 10.3221/igf-esis.50.24 288 where the subscripts m and c denote the metallic and ceramic components, respectively; and p is the power law exponent. the value of k equal to zero indicates a fully ceramic plate, whereas infinite p represents a fully metallic plate. since the influences of the variation of poisson's ratio  on the behavior of fg plates are very small [37], it is supposed to be constant for convenience. 𝜉 is the factor of the distribution of the porosity according to the thickness of the plate [41]. kinematics and strains n this investigation, further simplifying supposition are made to the conventional higher shear deformation theory (hsdt) so that the number of unknowns is reduced. the displacement field of the conventional hsdt is expressed by saidi et al [40]. 0 0( , , , ) ( , , ) ( ) ( , , )x w u x y z t u x y t z f z x y t x       (2a) 0 0( , , , ) ( , , ) ( ) ( , , )y w v x y z t v x y t z f z x y t y       (2b) 0( , , , ) ( , , )w x y z t w x y t (2c) where the shape function ( )f z is chosen according to mahi et al [42]: 3 2 2 4 ( ) tanh 2 2 3 cosh (1) z zh f z h h            (3) clearly, the displacement field in eq. (2) considers only four unknowns ( 0u , 0v , 0w and  ). the nonzero strains associated with the displacement field in eq. (2) are: 0 0 0 ( ) b s x x xx b s y y y y b s xy xy xy xy k k z k f z k k k                                                         , 0 0 ( ) yz yz xz xz g z                   (4) where 0 0 0 0 0 0 0 x y xy u x v x u v y x                                   , 2 0 2 2 0 2 2 02 b x b y b xy w xk w k y k w x y                                    , 2 2 2 2 2 2 s x s y s xy xk k y k x y                                       , 0 0 yz xz y x                          (5a) and ( ) ( ) df z g z dz   (5b) i h. saidi et alii, frattura ed integrità strutturale, 50 (2019) 286-299; doi: 10.3221/igf-esis.50.24 289 for elastic and isotropic fgms, the constitutive relations can be expressed as: 11 12 12 22 66 44 55 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 x x y y xy xy yz yz xz xz c c c c c c c                                                    (6) where ( x , y , xy , yz , xz ) and ( x , y , xy , yz , xz ) are the stress and strain components, respectively. using the material properties defined in eq. (1), stiffness coefficients, ijc , can be written as 11 22 2 ( ) , 1 e z c c     12 2 ( ) , 1 e z c      44 55 66 ( ) 2 1 e z c c c      (7) equation of motion amilton’s principle is herein employed to determine the equations of motion: (8) where u is the variation of strain energy; v is the variation of work done; and k is the variation of kinetic energy. the variation of strain energy of the plate is computed by 0 0 0 0 0 0 x x y y xy xy yz yz xz xz v b b b b b b x x y y xy xy x x y y xy xy a s s s s s s s s x x y y xy xy yz yz xz xz u dv n n n m k m k m k m k m k m k s s da                                                      (9) where a is the top surface and the stress resultants n , m , and s are defined by     /2 /2 , , 1, , h b s i i i i h n m m z f dz    ,  , ,i x y xy and     /2 /2 , , h s s xz yz xz yz h s s g dz     (10) the variation of the potential energy of elastic foundation can be calculated by 0 e a v f w da   (11) where ef is the density of reaction force of foundation. for the pasternak foundation model [43-53]. (12) h 2 2 22 2 1 y w k x w kwkf sswe       0 0 ( ) t u v k dt     h. saidi et alii, frattura ed integrità strutturale, 50 (2019) 286-299; doi: 10.3221/igf-esis.50.24 290 where wk is the modulus of subgrade reaction (elastic coefficient of the foundation) and 1sk and 2sk are the shear moduli of the subgrade (shear layer foundation stiffness). if foundation is homogeneous and isotropic, we will get 1 2s s sk k k  . if the shear layer foundation stiffness is neglected, pasternak foundation becomes a winkler foundation. the variation of kinetic energy of the plate can be expressed as: (13) where dot-superscript convention indicates the differentiation with respect to the time variable t ; ( )z is the mass density given by eq. (1b); and ( ii , ij , ik ) are mass inertias expressed by     /2 2 0 1 2 /2 , , 1, , ( ) h h i i i z z z dz    (14a)     /2 2 1 2 2 /2 , , , , ( ) h h j j k f z f f z dz    (14b) substituting eqs. (9), (11), and (13) into eq. (8), integrating by parts, and collecting the coefficients of 0 u , 0v , 0w and   ; the following equations of motion are obtained: 0 0 0 0 1 1 0 0 0 0 1 1 2 22 2 20 0 0 0 0 1 2 0 22 2 22 2 : : : 2 : 2 xyx xy y b bb xy yx e s x nn w u i u i j x y x x n n w v i v i j x y y y m mm u v w f i w i i w j x y x yx y mm x                                                                   2 0 0 12 2 2 2 0 2 s s s s xy y xz yzm s s u v j x y x y x yy j w k                             (15) where 2 2 2 2 2/ /x y       is the laplacian operator in two-dimensional cartesian coordinate system.     0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 2 ( ) v a k u u v v w w z dv i u u v v w w w w w w i u u v v x x y y j u u v v x x y y w w w w i x x y y                                                                                                      2 0 0 0 0 2 k x x y y w w w w j da x x x x y y y y                                                                  h. saidi et alii, frattura ed integrità strutturale, 50 (2019) 286-299; doi: 10.3221/igf-esis.50.24 291 substituting eq. (4) into eq. (6) and the subsequent results into eqs. (10), the stress resultants are obtained in terms of strains as following compact form: s b s b s s s s s n a b b m b d d k m b d h k                            , ss a  , (16) in which  , , tx y xyn n n n ,  , , tb b b b x y xym m m m ,  , , ts s s s x y xym m m m , (17a)  0 0 0, , tx y xy    ,  , , tb b b b x y xyk k k k ,  , , ts s s s x y xyk k k k , (17b) 11 12 12 22 66 0 0 0 0 a a a a a a          , 11 12 12 22 66 0 0 0 0 b b b b b b          , 11 12 12 22 66 0 0 0 0 d d d d d d          , (17c) 11 12 12 22 66 0 0 0 0 s s s s s s b b b b b b             , 11 12 12 22 66 0 0 0 0 s s s s s s d d d d d d             , 11 12 12 22 66 0 0 0 0 s s s s s s h h h h h h             , (17d)  , ts sxz yzs s s ,  0 0, t xz yz   , 44 55 0 0 s s s a a a         , (17e) and stiffness components are given as:   11 11 11 11 11 11 /2 2 2 12 12 12 12 12 12 11 /2 66 66 66 66 66 66 1 1, , , ( ), ( ), ( ) 1 2 s s s h s s s hs s s a b d b d h a b d b d h c z z f z z f z f z dz a b d b d h                             , (18a)    22 22 22 22 22 22 11 11 11 11 11 11, , , , , , , , , ,s s s s s sa b d b d h a b d b d h , (18b)   /2 2 44 55 44 /2 ( ) , h s s h a a c g z dz     (18c) analytical solution for simply-supported fg plates ased on navier technique, the following expansions of generalized displacements are considered to automatically respect the simply supported boundary conditions: b h. saidi et alii, frattura ed integrità strutturale, 50 (2019) 286-299; doi: 10.3221/igf-esis.50.24 292 0 0 0 1 1 cos( )sin( ) sin( )cos( ) sin( )sin( ) sin( )sin( ) i t mn i t mn i t m n mn i t mn u e x yu v v e x y w w e x y x e x y                                           (19) where /m a  and /n b  ,  is the frequency of free vibration of the plate, 1i   the imaginary unit. substituting eqs. (19) into eq. (15) and collecting the displacements and acceleration for any values of m and n , the following problem is obtained: 11 12 13 14 11 13 14 12 22 23 24 22 23 242 13 23 33 34 13 23 33 34 14 24 34 44 14 24 34 44 0 0 0 0 0 0 mn mn mn mn s s s s m m m u s s s s m m m v s s s s m m m m w s s s s m m m m x                                                        (20) where 2 2 11 11 66s a a   ,  12 12 66s a a  ,  2 2 213 11 12 662s b b b       ,  2 2 214 11 12 662s s ss b b b       2 2 22 66 22s a a   ,  2 2 223 11 12 662s b b b       ,  2 2 224 11 12 662s s ss b b b       , (21) 4 2 2 4 2 2 33 11 12 66 222( 2 ) ( )w ss d d d d k k            , 4 2 2 4 34 11 12 66 222( 2 ) s s s ss d d d d       , 4 2 2 4 2 2 44 11 12 66 22 55 442( 2 ) s s s s s ss h h h h a a           11 22 0m m i  , 13 1m i  , 14 1m j  , 23 1m i  , 24 1m j  , 2 2 33 0 2 ( )m i i     , 2 234 2 ( )m j    , 2 2 44 2 ( )m k    (22) eq. (20) is a general form for buckling and free vibration analysis of fg plates resting on elastic foundations under inplane loads. the stability problem can be carried out by neglecting the mass matrix while the free vibration problem is achieved by omitting the in-plane loads. numerical examples and discussion n this section various numerical examples are examined to check the accuracy of the present formulation in predicting the free vibration behaviours of simply supported fg plates resting on elastic foundation. two types of fg plates of al/al2o3 are employed in this investigation. the material characteristics of fg plates are presented in tab. 1. for convenience, the following non-dimensional parameters are employed: ˆ /m mh e   proprieties aluminium (al) alumina (al2o3) young’s modulus (gpa) 70 380 poisson’s ratio 0.3 0.3 mass density kg/m3 2702 3800 table 1: material properties employed in the fg plates. in order to validate the present formulations that predict the vibration of fgm plates, various illustrative examples are presented. the present dimensionless frequency of the square fgm plate without a porosity are compared with those of i h. saidi et alii, frattura ed integrità strutturale, 50 (2019) 286-299; doi: 10.3221/igf-esis.50.24 293 thai and choi [54] as shown in tab.2. it can be observed that the results are in very good agreement with those predicted by thai and choi [54]. /a b /a h theory power law index ( k ) 0 0.5 1 2 5 10 0.5 5 ref (49) 11.3952 11.2331 11.1780 11.2018 11.3593 11.4558 present 11.3959 11.2335 11.1783 11.2019 11.3587 11.4557 10 ref (49) 11.7257 11.4992 11.4270 11.4530 11.6243 11.7093 present 11.7259 11.4993 11.4271 11.4529 11.6239 11.7092 20 ref (49) 11.8246 11.5780 11.5005 11.5273 11.7054 11.7886 present 11.8246 11.5781 11.5005 11.5272 11.7053 11.7885 1 5 ref (49) 15.3904 14.8757 14.6305 14.5004 14.5843 14.6636 present 15.3923 14.8768 14.6313 14.5006 14.5830 14.6635 10 ref (49) 16.1728 15.4895 15.1887 15.0455 15.1497 15.2045 present 16.1735 15.4898 15.1890 15.0455 15.1488 15.2043 20 ref (49) 16.4249 15.6851 15.3663 15.2209 15.3414 15.3929 present 16.4251 15.6852 15.3663 15.2209 15.3411 15.3928 2 5 ref (49) 28.6467 26.8009 25.7640 24.9077 24.5036 24.4352 present 28.6591 26.8086 25.7703 24.9109 24.4983 24.4367 10 ref (49) 32.3893 29.7133 28.3322 27.2931 26.8741 26.6994 present 32.3937 29.7163 28.3346 27.2932 26.8675 26.6951 20 ref (49) 33.8869 30.8606 29.3467 28.2628 27.9294 27.7426 present 33.8882 30.8614 29.3474 28.2627 27.9267 27.7419 table 2: dimensionless fundamental frequency  of rectangular plates ( 100)w sk k  , 2ˆ ( ) /m m a e h    in order to analyse the effect of porosity on the natural frequency of fgm plates, numerical results are presented in tabs. 2-6 and graphically plotted in figs. 2-4. a/h k ξ=0 ξ=0.1 ξ=0.2 ssdt present ssdt present ssdt present 5 0 0.4150 0.4152 0.4208 0.4210 0.4274 0.4276 0.5 0.3550 0.3552 0.3548 0.3550 0.3544 0.3546 1 0.3204 0.3206 0.3144 0.3146 0.3062 0.3062 2 0.2892 0.2895 0.2754 0.2756 0.2550 0.2554 5 0.2665 0.2674 0.2470 0.2480 0.2158 0.2170 10 0.2554 0.2563 0.2352 0.2364 0.2026 0.2042 10 0 0.1134 0.1134 0.1149 0.1149 0.1167 0.1167 0.5 0.0963 0.0963 0.09616 0.09616 0.09592 0.09598 1 0.0868 0.0868 0.08498 0.08504 0.08256 0.08256 2 0.0788 0.0788 0.07480 0.07480 0.06896 0.06896 5 0.07398 0.07410 0.06858 0.06870 0.05978 0.05988 10 0.07144 0.07150 0.06616 0.06628 0.05738 0.05754 20 0 0.02908 0.02908 0.02948 0.02948 0.02992 0.02992 0.5 0.02464 0.02464 0.02460 0.02460 0.02454 0.02454 1 0.02222 0.02222 0.02174 0.02174 0.02110 0.02110 2 0.02018 0.02018 0.01915 0.01915 0.01762 0.01763 5 0.01910 0.01910 0.01770 0.01771 0.01541 0.01542 10 0.01847 0.01848 0.01715 0.01715 0.01491 0.01492 table 3: the first non-dimensional frequencies 𝜔 of al/al2o3 square plate for various porosity parameters, power law indices and thickness ratios (a=10h, n=m=1, kw=ks=0) h. saidi et alii, frattura ed integrità strutturale, 50 (2019) 286-299; doi: 10.3221/igf-esis.50.24 294 a/h k ξ=0 ξ=0.1 ξ=0.2 ssdt present ssdt present ssdt present 5 0 0.4268 0.4270 0.4336 0.4338 0.4410 0.4412 0.5 0.3702 0.3704 0.3716 0.3716 0.3730 0.3730 1 0.3380 0.3382 0.3342 0.3342 0.3286 0.3286 2 0.3096 0.3098 0.2990 0.2992 0.2832 0.2834 5 0.2900 0.2908 0.2748 0.2758 0.2508 0.2518 10 0.2806 0.2814 0.2656 0.2664 0.2412 0.2426 10 0 0.1162 0.1162 0.1179 0.1180 0.1199 0.1200 0.5 0.09988 0.09988 0.1001 0.1001 0.1003 0.1003 1 0.09100 0.09100 0.08976 0.08976 0.08796 0.08802 2 0.08362 0.08368 0.08044 0.08044 0.07578 0.07578 5 0.07952 0.07958 0.07516 0.07528 0.06814 0.06820 10 0.07728 0.07734 0.07318 0.07324 0.06634 0.06646 20 0 0.02976 0.02976 0.03022 0.03022 0.03074 0.03074 0.5 0.02554 0.02554 0.02558 0.02558 0.02562 0.02564 1 0.02326 0.02326 0.02290 0.02290 0.02244 0.02244 2 0.02138 0.02140 0.02056 0.02056 0.01933 0.01933 5 0.02044 0.02044 0.01932 0.01933 0.01747 0.01748 10 0.01991 0.01991 0.01886 0.01887 0.01711 0.01712 table 4: the first non-dimensional frequencies ̂ of al/al2o3 square plate for various porosity parameters, power law indices and thickness ratios (a=10h, n=m=1, kw=100, ks=0). a/h k ξ=0 ξ=0.1 ξ=0.2 ssdt present ssdt present ssdt present 5 0 0.4382 0.4384 0.4456 0.4458 0.4540 0.4542 0.5 0.3844 0.3846 0.3872 0.3872 0.3900 0.3902 1 0.3544 0.3544 0.3522 0.3524 0.3490 0.3492 2 0.3282 0.3284 0.3204 0.3206 0.3082 0.3084 5 0.3110 0.3118 0.2996 0.3004 0.2808 0.2814 10 0.3032 0.3038 0.2920 0.2928 0.2736 0.2746 10 0 0.1188 0.1188 0.1208 0.1208 0.1230 0.1230 0.5 0.1033 0.1033 0.1039 0.1039 0.1045 0.1045 1 0.09492 0.09498 0.09412 0.09418 0.09294 0.09300 2 0.08814 0.08814 0.08560 0.08566 0.08188 0.08194 5 0.08448 0.08454 0.08106 0.08112 0.07536 0.07542 10 0.08256 0.08262 0.07938 0.07952 0.07404 0.07418 20 0 0.03042 0.03042 0.03092 0.03092 0.03148 0.03148 0.5 0.02638 0.02638 0.02652 0.02652 0.02664 0.02664 1 0.02422 0.02422 0.02400 0.02400 0.02368 0.02368 2 0.02250 0.02250 0.02184 0.02184 0.02084 0.02084 5 0.02168 0.02168 0.02078 0.02078 0.01927 0.01928 10 0.02120 0.02122 0.02040 0.02040 0.01901 0.01901 table 5: the first non-dimensional frequencies ̂ of al/al2o3 square plate for various porosity parameters, power law indices and thickness ratios (a=10h, n=m=1, kw=0, ks=10). h. saidi et alii, frattura ed integrità strutturale, 50 (2019) 286-299; doi: 10.3221/igf-esis.50.24 295 a/h k ξ=0 ξ=0.1 ξ=0.2 ssdt present ssdt present ssdt present 5 0 0.4494 0.4496 0.4576 0.4578 0.4668 0.4670 0.5 0.3984 0.3986 0.4024 0.4026 0.4068 0.4068 1 0.3702 0.3704 0.3700 0.3702 0.3688 0.3690 2 0.3464 0.3466 0.3408 0.3410 0.3318 0.3320 5 0.3314 0.3320 0.3230 0.3238 0.3084 0.3090 10 0.3246 0.3252 0.3170 0.3176 0.3084 0.3042 10 0 0.1214 0.1215 0.1236 0.1237 0.1260 0.1261 0.5 0.1067 0.1067 0.1076 0.1076 0.1085 0.1085 1 0.09884 0.09884 0.09846 0.09846 0.09778 0.09784 2 0.09250 0.09256 0.09064 0.09064 0.08772 0.08772 5 0.08932 0.08940 0.08672 0.08678 0.08212 0.08218 10 0.08766 0.08772 0.08536 0.08542 0.08120 0.08132 20 0 0.03108 0.03108 0.03164 0.03164 0.03224 0.03224 0.5 0.02722 0.02722 0.02742 0.02742 0.02766 0.02766 1 0.02518 0.02518 0.02508 0.02508 0.02488 0.02488 2 0.02360 0.02360 0.02308 0.02308 0.02230 0.02230 5 0.02288 0.02288 0.02218 0.02218 0.02096 0.02096 10 0.02246 0.02246 0.02186 0.02186 0.02078 0.02078 table 6: the first non-dimensional frequencies ̂ of al/al2o3 square plate for various porosity parameters, power law indices and thickness ratios (a=10h, n=m=1, kw=100, ks=10). tab. 3-6 present the natural frequencies of fgm plates resting on elastic foundation for different values of porosity parameter ( 0,   0.1,   0.2)      , and elastic foundation parameters. it can be seen that the results are in excellent agreement with those of sinusoidal plate theory given by zenkour, it is also concluded that the increase of porosity parameter leads to increase of natural frequency. it can be shown that the frequencies are increasing with the existence of (winkler and pasternak parameters). figure 2: variation of the natural frequency of the fgm plates according to the material power index k, mode1, a=b. figure 3: influence of thickness ratio on the frequency of the plate fgm, mode 2, ξ=0, ( 100)w sk k  . h. saidi et alii, frattura ed integrità strutturale, 50 (2019) 286-299; doi: 10.3221/igf-esis.50.24 296 as the material power index increases for fgm plates, the dimensionless frequency will decrease. the variation curves of the natural frequency of the first mode of various functionally graded plates as a function of material power index parameter ‘’k’’, for different values of porosity was presented in fig. 2. it can be seen that the increase of porosity parameter leads to an increase of the frequency of the first mode. fig. 3 shows the influence of thickness ratio, on the natural frequency of fgm plates (ξ=0), the elastic foundation parameters are taken equal to ( 100)w sk k  . it can be seen that the ratio (a/h) has a considerable effect on the frequency of the fgm plate, (the later decreases with the increase of this ratio). figure 4: effect of pasternak shear modulus parameter on dimensionless frequency of fgm plates, a/h=10, k=2. fig. 4 shows the effect of pasternak parameters on the variation of the dimensionless frequency of fgm plate for different values of porosity. the results show that the frequency increases with the increase of pasternak parameter and porosity index. conclusion his work proposes a new higher-order shears deformation theory for free vibration response of fg plates with porosity embedded in elastic medium. in this investigation the fgm plate are assumed to have a new distribution of porosity according to the thickness of the plate. the elastic medium is modeled as winkler-pasternak two parameter model to express the interaction between the fgm plate and elastic foundation. the four unknown shear deformation theory is employed to deduce the equations of motion from hamilton’s principle. the hamilton’s principle is used to derive the governing equations of motion. the accuracy of this theory is verified by compared the developed results with those obtained using others plate theory. some examples are performed to demonstrate the effect of changing gradient material, elastic parameters, porosity index, and length to thickness ratios on the fundamental frequency of functionally graded plate. it has been demonstrated that the present analytical formulation can accurately predict natural frequencies of fg plates with porosity resting on elastic foundation. also it can be concluded that the effect of volume fraction distributions, slenderness ratio and porosity on the non-dimensional frequency is significant. references [1] koizumi, m. (1997), fgm activities in japan, compos part b, 28, pp. 1–4. doi: 10.1016/s1359-8368(96)00016-9. [2] akbaş, ş. d. (2015), wave propagation of a functionally graded beam in thermal environments, steel and composite structures, 19(6), pp. 1421-1447. doi: 10.12989/scs.2015.19.6.1421. t h. saidi et alii, frattura ed integrità strutturale, 50 (2019) 286-299; doi: 10.3221/igf-esis.50.24 297 [3] bennai, r., ait atmane, h., tounsi, a. (2015), a new higher-order shear and normal deformation theory for functionally graded sandwich beams, steel and composite structures, 19(3), pp. 521 – 546. doi: 10.12989/scs.2015.19.3.521. [4] arefi, m. (2015), elastic solution of a curved beam made of functionally graded materials with different cross sections, steel and composite structures, 18(3), pp. 659 – 672. doi: 10.12989/scs.2015.18.3.659. [5] ait atmane, h., tounsi, a., bernard, f., mahmoud, s.r. (2015), a computational shear displacement model for vibrational analysis of functionally graded beams with porosities, steel and composite structures, 19(2), pp. 369-384. doi: 10.12989/scs.2015.19.2.369. [6] ebrahimi, f., dashti, s. (2015), free vibration analysis of a rotating non-uniform functionally graded beam, steel and composite structures, 19(5), pp. 1279 – 1298. doi: 10.12989/scs.2015.19.5.1279. [7] darılmaz, k., (2015), vibration analysis of functionally graded material (fgm) grid systems, steel and composite structures, 18(2), pp. 395 – 408. doi: 10.12989/scs.2015.18.2.395. [8] ebrahimi, f., habibi, s. (2016), deflection and vibration analysis of higher-order shear deformable compositionally graded porous plate, steel and composite structures, 20(1), pp. 205 225. doi: 10.12989/scs.2016.20.1.205. [9] kar, v.r., panda, s.k. (2016), nonlinear thermomechanical deformation behaviour of p-fgm shallow spherical shell panel, chinese journal of aeronautics, 29(1), pp. 173 – 183. doi: 10.1016/j.cja.2015.12.007. [10] moradi-dastjerdi, r. (2016), wave propagation in functionally graded composite cylinders reinforced by aggregated carbon nanotube, structural engineering and mechanics, 57(3), pp. 441 – 456. doi: 10.12989/sem.2016.57.3.441. [11] trinh, t.h., nguyen, d.k., gan, b.s., alexandrov, s. (2016), post-buckling responses of elastoplastic fgm beams on nonlinear elastic foundation, structural engineering and mechanics, 58(3), pp. 515 – 532. doi: 10.12989/sem.2016.58.3.515. [12] zhu, j., lai, z., yin, z., jeon, j. and lee, s. (2001), fabrication of zro2–nicr functionally graded material by powder metallurgy, mater. chem. phys., 68(1), pp. 130-135. doi: 10.1016/s0254-0584(00)00355-2. [13] wattanasakulpong, n., prusty, b.g., kelly, d.w. and hoffman, m. (2012), free vibration analysis of layered functionally graded beams with experimental validation, mater. des, 36, pp. 182-190. doi: 10.1016/j.matdes.2011.10.049. [14] daouadji, t.h., adim. b., and benferhat. b. (2018), bending analysis of an imperfect fgm plates under hygrothermo-mechanical loading with analytical validation, advances in materials research, 5(1), pp. 35-53. doi: 10.12989/amr.2016.5.1.035. [15] jha, d.k., kant, t., singh, r.k. (2013a), a critical review of recent research on functionally graded plates, compos. struct, 96, pp. 833–849. doi: 10.1016/j.compstruct.2012.09.001. [16] nguyen, k.t., thai, t.h., vo, t.p. (2015), a refined higher-order shear deformation theory for bending, vibration and buckling analysis of functionally graded sandwich plates, steel and composite structures, 18(1), pp. 91 – 120. doi: 10.12989/scs.2015.18.1.091. [17] pradhan, k. k., chakraverty, s. (2015), free vibration of functionally graded thin elliptic plates with various edge supports, structural engineering and mechanics, 53(2), pp.337 – 354. doi: 10.12989/sem.2015.53.2.337. [18] kar, v.r. and panda, s.k. (2015), nonlinear flexural vibration of shear deformable functionally graded spherical shell panel, steel compos. struct, 18(3), pp. 693-709. doi: 10.12989/scs.2015.18.3.693. [19] eltaher, m.a., khater, m.e., park, s., abdel-rahman, e., yavuz, m. (2016), on the static stability of nonlocal nanobeams using higher-order beam theories, advances in nano research, 4(1), pp. 51 – 64. doi: 10.12989/anr.2016.4.1.051. [20] feldman, e., aboudi, j. (1997), buckling analysis of functionally graded plates subjected to uniaxial loading, compos. struct, 38, pp. 29–36. doi: 10.1016/s0263-8223(97)00038-x. [21] mahdavian, m. (2009), buckling analysis of simply-supported functionally graded rectangular plates under nonuniform inplane compressive loading, j. solid mech, 1, pp. 213 – 225. [22] chen, c.s., chen, t.j., chien, r.d. (2006), nonlinear vibration of initially stressed functionally graded plates, thinwalled struct, 44(8), pp. 844–851. doi: 10.1016/j.tws.2006.08.007. [23] baferani, a.h., saidi, a.r., jomehzadeh, e. (2011a), an exact solution for free vibration of thin functionally graded rectangular plates, proc. inst. mech. eng. part c, 225, pp. 526 – 536. doi: 10.1243/09544062jmes2171. [24] praveen, g.n., reddy, j.n. (1998), nonlinear transient thermoelastic analysis of functionally graded ceramic-metal plates, int. j. solids struct., 35, pp. 4457–4476. doi: 10.1016/s0020-7683(97)00253-9. [25] croce, l.d., venini, p. (2004), finite elements for functionally graded reissner–mindlin plates. comput, methods appl. mech. eng, 193, pp. 705 – 725. doi: 10.1016/j.cma.2003.014. h. saidi et alii, frattura ed integrità strutturale, 50 (2019) 286-299; doi: 10.3221/igf-esis.50.24 298 [26] efraim, e., eisenberger, m. (2007), exact vibration analysis of variable thickness thick annular isotropic and fgm plates, j. sound vib. 299, pp. 720 – 738. doi: 10.1016/j.jsv.2006.06.068. [27] zhao, x., lee, y.y., liew, k.m. (2009), free vibration analysis of functionally graded plates using the element-free kp-ritz method, j. sound vib, 319, pp. 918 – 939. doi: 10.1016/j.jsv.2008.06.025. [28] reddy, j.n. (2000), analysis of functionally graded plates, int. j. numer. methods eng, 47, pp. 663 – 684. doi: 10.1002/(sici)1097-0207(20000110/30)47:1/3<663::aid-nme787>3.0.co;2-8. [29] pradyumna, s., bandyopadhyay, j.n. (2008), free vibration analysis of functionally graded curved panels using a higher-order finite element formulation, j. sound vib, 318, pp.176 – 192. doi: 10.1016/j.jsv.2008.03.056. [30] jha, d.k., kant, t., singh, r.k. (2013b), free vibration response of functionally graded thick plates with shear and normal deformations effects, compos. struct, 96, pp. 799 – 823. doi: 10.1016/j.compstruct.2012.09.034. [31] neves, a.m.a., ferreira, a.j.m., carrera, e., cinefra, m., roque, c.m.c., jorge, r.m.n., soares, c.m.m. (2013), static, free vibration and buckling analysis of isotropic and sandwich functionally graded plates using a quasi-3d higher-order shear deformation theory and a meshless technique, compos. part b, 44, pp. 657 – 674. doi: 10.1016/j.compositesb.2012.01.089. [32] reddy, j.n. (2011), a general nonlinear third-order theory of functionally graded plates, int. j. aerosp. lightweight struct, 1, pp. 1–21. doi: 10.3850/s201042861100002x. [33] talha, m., singh, b.n. (2010), static response and free vibration analysis of fgm plates using higher order shear deformation theory, appl. math. model, 34, pp. 3991 – 4011. doi: 10.1016/j.apm.2010.03.034. [34] chen, c., hsu, c., tzou, g. (2009), vibration and stability of functionally graded plates based on a higher-order deformation theory, j. reinf. plast. compos, 28, pp. 1215 – 1234. doi: 10.1177/0731684408088884. [35] mantari, j., soares, c.g. (2012), generalized hybrid quasi-3d shear deformation theory for the static analysis of advanced composite plates, compos. struct, 94(8), pp. 2561 – 2575. doi: 10.1016/j.compstruct.2012.02.019. [36] houari, m.s.a., tounsi, a., anwar bég, o. (2013), thermoelastic bending analysis of functionally graded sandwich plates using a new higher order shear and normal deformation theory, international journal of mechanical sciences, 76, pp. 102 – 111. doi: 10.1016/j.ijmecsci.2013.09.004. [37] saidi, h., houari, m.s.a., tounsi, a. and adda bedia, e.a. (2013), thermo-mechanical bending response with stretching effect of functionally graded sandwich plates using a novel shear deformation theory, steel compos. struct, 15, pp. 221 – 245. doi: 10.12989/scs.2013.15.2.221. [38] matsunaga, h. (2008), free vibration and stability of functionally graded plates according to a 2d higher-order deformation theory, compos. struct, 82, pp. 499 – 512. doi: 10.1016/j.compstruct.2007.07.006. [39] tounsi, a., houari, m.s.a., benyoucef, s., adda bedia, e.a. (2013), a refined trigonometric shear deformation theory for thermoelastic bending of functionally graded sandwich plates, aerospace science and technology, 24, pp. 209 – 220. doi: 10.1016/j.ast.2011.11.009. [40] saidi, h., tounsi, a., and bousahla, a.a. (2016), a simple hyperbolic shear deformation theory for vibration analysis of thick functionally graded rectangular plates resting on elastic foundations, geomechanics and engineering, an int'l journal, 11 (2), pp. 289 – 307. doi: 10.12989/gae.2016.11.2.289. [41] bennai, r., fourn, h, ait atmane, h., tounsi, a. and bessaim, a. (2018), a dynamic and wive propagation investigation of fgm plates with porosities using a four variable plate theory, wind and structures, 28 (1), pp. 49 – 62. doi: 10.12989/was.2019.28.1.049. [42] mahi, a., adda bedia, e.a., tounsi, a. (2015), a new hyperbolic shear deformation theory for bending and free vibration analysis of isotropic, functionally graded, sandwich and laminated composite plates, appl. math. modelling, 39, pp. 2489 – 2508. doi: 10.1016/j.apm.2014.10.045. [43] bounouara, f., benrahou, k.h., belkorissat, i., tounsi, a. (2016), a nonlocal zeroth-order shear deformation theory for free vibration of functionally graded nanoscale plates resting on elastic foundation, steel and composite structures, 20(2), pp. 227 – 249. doi: 10.12989/scs.2016.20.2.227. [44] abdelbari, s., a., fekrar, a., heireche, h., saidi, h., tounsi, a., adda bedia, e.a. (2016), an efficient and simple shear deformation theory for free vibration of functionally graded rectangular plates on winkler–pasternak elastic foundations, wind and structures, 22(3), pp. 329 – 348. doi: 10.12989/was.2016.22.3.329. [45] ait atmane, h., tounsi, a., bernard, f. (2016), effect of thickness stretching and porosity on mechanical response of a functionally graded beams resting on elastic foundations, international journal of mechanics and materials in design, (in press). doi: 10.1007/s10999-015-9318-x. [46] chikh, a., bakora, a., heireche, h., houari, m.s.a., tounsi, a., adda bedia, e.a. (2016), thermo-mechanical postbuckling of symmetric s-fgm plates resting on pasternak elastic foundations using hyperbolic shear deformation theory, structural engineering and mechanics, 57(4), pp. 617 – 639. doi: 10.12989/sem.2016.57.4.617. h. saidi et alii, frattura ed integrità strutturale, 50 (2019) 286-299; doi: 10.3221/igf-esis.50.24 299 [47] bakora, a., tounsi, a. (2015), thermo-mechanical post-buckling behavior of thick functionally graded plates resting on elastic foundations, structural engineering and mechanics, 56(1), pp.85 – 106. doi: 10.12989/sem.2015.56.1.085. [48] tebboune, w., benrahou, k.h., houari, m.s.a. and tounsi, a. (2015), thermal buckling analysis of fg plates resting on elastic foundation based on an efficient and simple trigonometric shear deformation theory, steel compos. struct, 18(2), pp. 443 – 465. doi: 10.12989/scs.2015.18.2.443. [49] meksi, a., benyoucef, s., houari, m.s.a., tounsi, a. (2015), a simple shear deformation theory based on neutral surface position for functionally graded plates resting on pasternak elastic foundations, structural engineering and mechanics, 53(6), pp. 1215 – 1240. doi: 10.12989/sem.2015.53.6.1215. [50] ait amar meziane, m., abdelaziz, h.h., tounsi, a. (2014), an efficient and simple refined theory for buckling and free vibration of exponentially graded sandwich plates under various boundary conditions, journal of sandwich structures and materials, 16(3), pp. 293 – 318. doi: 10.1177/1099636214526852. [51] zidi, m., tounsi, a., houari m.s.a., adda bedia, e. a., anwar bég, o. (2014), bending analysis of fgm plates under hygro-thermo-mechanical loading using a four variable refined plate theory, aerosp. sci. technol, 34, pp. 24 – 34. doi: 10.1016/j.ast.2014.02.001. [52] khalfi, y., houari, m.s.a. and tounsi, a. (2014), a refined and simple shear deformation theory for thermal buckling of solar functionally graded plates on elastic foundation, int. j. comput. meth, 11(5), 135007. doi: 10.1142/s0219876213500771. [53] bouderba, b., houari, m.s.a., tounsi, a. (2013), thermomechanical bending response of fgm thick plates resting on winkler–pasternak elastic foundations, steel and composite structures, 14(1), pp. 85 – 104. doi: 10.12989/scs.2013.14.1.085. [54] thai, h.t., choi, d.h. 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can be opened with acrobat and adobe reader 5.0 and later.) >> /namespace [ (adobe) (common) (1.0) ] /othernamespaces [ << /asreaderspreads false /cropimagestoframes true /errorcontrol /warnandcontinue /flattenerignorespreadoverrides false /includeguidesgrids false /includenonprinting false /includeslug false /namespace [ (adobe) (indesign) (4.0) ] /omitplacedbitmaps false /omitplacedeps false /omitplacedpdf false /simulateoverprint /legacy >> << /addbleedmarks false /addcolorbars false /addcropmarks false /addpageinfo false /addregmarks false /convertcolors /converttocmyk /destinationprofilename () /destinationprofileselector /documentcmyk /downsample16bitimages true /flattenerpreset << /presetselector /mediumresolution >> /formelements false /generatestructure false /includebookmarks false /includehyperlinks false /includeinteractive false /includelayers false /includeprofiles false /multimediahandling /useobjectsettings /namespace [ (adobe) (creativesuite) (2.0) ] /pdfxoutputintentprofileselector /documentcmyk /preserveediting true /untaggedcmykhandling /leaveuntagged /untaggedrgbhandling /usedocumentprofile /usedocumentbleed false >> ] >> setdistillerparams << /hwresolution [2400 2400] /pagesize [612.000 792.000] >> setpagedevice microsoft word numero_46_art_36 w. hao et alii, frattura ed integrità strutturale, 46 (2018) 391-399; doi: 10.3221/igf-esis.46.36 391 experimental study on the mechanical behavior of rpc filled square steel tube columns subjected to eccentric compression wenxiu hao*, xiao xu, zhiqiang niu hebei agricultural university, baoding 071001, china *hwxansys@126.com abstract. in order to study the mechanical behavior of reactive powder concrete (rpc) filled square steel tubular columns, this paper designs an eccentric compression experiment for 12 specimens of rpc filled square steel tubular columns and studies the effects of failure form, load-displacement curve, slenderness ratio, steel ratio and eccentricity ratio of an eccentrically loaded columns on its mechanical behavior. at the same time, it also compares the experiment results with the bearing capacity calculated with relevant specifications and uses abaqus to carry out numerical simulation of eccentrically loaded columns. the results show that, the failure form of the eccentrically loaded rpc filled square steel tubular column shows local buckling failure. before the ultimate load is reached, there is no significant change on the surface of the specimen, and the yield stage of the loaddisplacement curve is not obvious, either. the results of the bearing capacity calculation formula recommended in cecs28-2012 are close to the experiment results and relatively conservative, so it is more applicable to the bearing capacity design of eccentrically loaded rpc filled square steel tubular columns. the results of the numerical simulation analysis are in good agreement with the experimental results, which can provide theoretical support for engineering practice. keywords. square steel tube; reactive powder concrete; column; eccentric compression; mechanical behavior. citation: hao, w., xu, x., niu, z., n., experimental study on the mechanical behavior of rpc filled square steel tube columns subjected to eccentric compression, frattura ed integrità strutturale, 46 (2018) 391-399. received: 31.07.2018 accepted: 17.09.2018 published: 01.10.2018 copyright: © 2018 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. introduction he concrete filled square steel tubular structure has advantages such as simple structure, convenient connection, high bearing capacity and good seismic performance, making it widely used in industrial premises, high-rise buildings, bridges and other structures. the building space is often limited, but it can be well utilized if the slenderness ratios of the columns are large, which requires the concrete-filled steel tubular columns to have not only high bearing capacity, but also strong lateral stiffness. to achieve these two requirements, we not only have to increase the steel t http://www.gruppofrattura.it/va/46/36.mp4 w. hao et alii, frattura ed integrità strutturale, 46 (2018) 391-399; doi: 10.3221/igf-esis.46.36 392 ratios and improve the section forms of the columns, but also need to make sure they are filled with high-performance concrete. reactive powder concrete (rpc) is a new ultra-high-performance cement-based composite [1] with excellent mechanical properties such as ultra high strength, toughness and durability. compared with high-strength concrete (hsc), the 200mpalevel rpc has 2-4 times its compressive strength, 3-10 times its flexural strength and 200 times its fracture energy. the rpc filled steel tube can significantly improve the strength and deformation performance of the rpc as the steel tube can constrain its deformation. compared with ordinary concrete filled steel tubes, the rpc filled ones, have obvious mechanical advantages in reducing the cross-sectional dimensions of components and improving their bearing capacity and lateral stiffness. therefore, as a new type of composite structure, rpc filled square steel tube has a broad application prospect in civil engineering. at present, there are few researches on rpc filled square steel tubular columns at home and abroad. by carrying out an eccentric loading experiment on rpc filled square steel tubular columns, this paper attempts to study the mechanical behavior of eccentrically loaded rpc filled square steel tubular columns as well as their influencing factors. at the same time, it compares and analyzes the experimental results and the theoretical values of bearing capacity which were calculated with relevant specifications (or codes), and finds the calculation formula of bearing capacity suitable for rpc filled square steel tubular columns. in addition, this paper utilizes the finite element software abaqus to carry out numerical simulation of the eccentrically loaded rpc filled square steel tubular columns, which provides a theoretical basis for engineering practice. overview of the experiment preparing the specimens pc materials include p.o 42.5 ordinary portland cement (c), silica fume (sf), quartz sand (qu), super plasticizers (su), steel fiber (with a diameter of about 0.18~0.20mm and a length of 12~14mm) and water (w). by reference to relevant documents [2-3], the mix ratios are shown in tab. 1, where b=c+sf, the proportion of steel fiber is volume ratio, and the others are mass ratios. the mechanical properties of rpc are shown in tab. 2. cement c silica fume sf/c quartz sand qu/c super-plasticizers su/b water-binder ratio w/b steel fiber vs/v 1 0.21 1.8 0.035 0.23 1% table 1: mix ratios of rpc. strength type cube compressive strength fcu /n/mm2 axial compressive strength fc /n/mm2 splitting tensile strength fct /n/mm2 value 93.49 69.0 11.43 table 2: mechanical properties of rpc. the steel tubes are all straight-seam square steel tubes. the cross-section dimensions of all specimens are all 100mm×100mm. according to gb/t 228.1-2010 and gb/t 228-2002 metallic materials-tensile experimenting at ambient temperature, the mechanical properties of these specimens were experimented, as shown in tab. 3. nominal wall thickness t/mm measured wall thickness t/mm yield strength fy/n/mm2 tensile strength fst/n/mm2 modulus of elasticity es/n/mm2 3 2.63 390.3 429.9 2.17×105 4 3.70 383.7 423.6 2.20×105 5 4.71 354.9 396.6 2.44×105 table 3: mechanical properties of steel tube. by reference to relevant documents [4-7], 12 rpc filled square steel tubular column specimens were designed in this experiment, whose detailed parameters are shown in tab. 4. pressure-bearing cover plates were welded at both ends of the r w. hao et alii, frattura ed integrità strutturale, 46 (2018) 391-399; doi: 10.3221/igf-esis.46.36 393 specimens (a round hole was reserved in the cover plate at one end for pouring of rpc), and the prepared rpc was poured into the steel tubes, the experiment was carried out after natural curing for 28 days. fig. 1 is the specimen of square steel tube. specimen no. steel tube wall thickness t/mm eccentricity e/mm length of specimen l/mm slenderness ratio λ steel ratio α confinement coefficient ξ 1 3 20 300 10.39 0.11 0.65 2 3 20 600 20.78 0.11 0.65 3 3 20 800 27.71 0.11 0.65 4 3 20 1000 34.64 0.11 0.65 5 4 20 1000 34.64 0.17 0.92 6 5 20 1000 34.64 0.22 1.13 7 3 40 300 10.39 0.11 0.65 8 3 40 600 20.78 0.11 0.65 9 3 40 800 27.71 0.11 0.65 10 3 40 1000 34.64 0.11 0.65 11 4 40 1000 34.64 0.17 0.92 12 5 40 1000 34.64 0.22 1.13 table 4: parameters of the specimens. figure 1: specimen of the square steel tube. figure 2: experimental set. experimental equipment the experiment was carried out using a 500t hydraulic servo pressuretesting -machine to load pressure, a dh3818 static strain meter to collect experiment data, an electronic displacement meter to measure the lateral displacements of the specimens, and electronic strain gages pasted in the longitudinal and lateral positions at the mid-span of the specimens to measure the strains of the specimens. the experimental set is shown in fig. 2. experimental results failure forms of the specimens hrough experimental observations, it was found that the appearances of the rpc filled square steel tubular specimens did not change much until the ultimate load was reached. as the deformation of column gradually increased, the bearing capacity gradually decreased. when the bearing capacity of the column dropped to 95%-85% of the ultimate bearing capacity, the square steel tube showed obvious bending, and the lateral displacement in the mid-span t w. hao et alii, frattura ed integrità strutturale, 46 (2018) 391-399; doi: 10.3221/igf-esis.46.36 394 was also getting larger. before the specimen failed, usually it was the pressure side that showed bending first and the final failure form was the local bending deformation of the steel tube. the failure forms of the specimens are shown in fig. 3. figure 3: failure forms of specimens. when the slenderness ratios and eccentricities of the specimens were the same, if the steel ratios were different, the bent parts would also be different. for example, when the steel ratio α=0.11, the bent part of the rpc filled square steel tubular column was about 1/10 of the length from the top of the column; and when the steel ratio α=0.22, the bent part of the specimen was almost close to the mid-span of the specimen. this was because when the eccentrically loaded column was being compressed, the bending was extended from its two ends to the middle. the larger the steel ratio, the stronger the deformation resistance of the specimen is. load-displacement curves of specimens fig.4 shows the load-span lateral displacement curves of the specimens. it can be seen that the load-displacement curves of the rpc filled square steel tubular specimens can be roughly divided into three stages: the linear elastic stage, the elasticplastic stage and the descending stage. in the linear elastic stage, the load-displacement curve of the column is basically linear. the descending section of the curve is relatively flat, which shows that the specimen had good ductility and ability to maintain load in the later stage. as the slenderness ratio and eccentricity of the specimen increased, the ultimate bearing capacity of the column was gradually decreased, and the lateral displacement was increased gradually. when the eccentricity e=40mm, for a rpc filled square steel tubular column with a slenderness ratio of λ=10.39, 20.78, 27.71 and 34.64, the ultimate bearing capacity was 480kn, 450kn, 410kn and 382kn, respectively. when the eccentricity e=20mm, for a rpc filled square steel tubular column with a slenderness ratio of λ=10.39, 20.78, 27.71 and 34.64, the ultimate bearing capacity was 708kn, 694kn, 573kn and 588kn, respectively. the steel ratio and the confinement coefficient also had great effects on the ultimate bearing capacity and mid-span lateral displacement of the specimen. when the confinement coefficient ξ=0.65, 0.92 and 1.13, under the load with an eccentricity of e=40mm, the bearing capacity of the specimen was 382kn, w. hao et alii, frattura ed integrità strutturale, 46 (2018) 391-399; doi: 10.3221/igf-esis.46.36 395 464kn and 510kn, respectively. in the descending stage of load-displacement curve, for a specimen with a large confinement coefficient, the rate of load drop was small. for example, the descending speed of the curve of a specimen with a confinement coefficient of ξ=1.13 was smaller than that with a confinement coefficient of ξ=0.65. in summary, the rpc square steel tubular specimens exhibited good ductility, and had greater bearing capacities than ordinary concrete-filled ones. figure 4: load-span lateral displacement curves of the specimens. comparison of bearing capacity comparison with experimental results in [4] refs that were ordinary concrete-filled square steel tubular column were shown in tab. 5, their steel ratio is relatively close. when the eccentricity is 20 and 40, the bearing capacity of the specimen is increased by 172kn and 142kn respectively, increasing by 43% and 53% respectively. this shows that rpc filled square steel tubular column has obvious advantages. specimen no. steel tube wall thickness t/mm eccentricity e/mm length of specimen l/mm slenderness ratio λ steel ratio α bearing capacity nu/kn 3 2.63 20 800 27.71 0.11 573.0 [4] refs 2.72 20 800 27.70 0.12 401.0 9 2.63 40 800 27.71 0.11 410.0 [4] refs 2.72 40 800 27.71 0.12 268.0 table 5: comparison with experimental results in [4] refs. w. hao et alii, frattura ed integrità strutturale, 46 (2018) 391-399; doi: 10.3221/igf-esis.46.36 396 the bearing capacity of rpc filled square steel tubular column is an important indicator of engineering design, so an appropriate calculation formula for bearing capacity is very essential. according to the calculation formulas recommended in five commonly used bearing capacity calculation specifications (or codes) for ordinary concrete-filled steel tubes, namely aisc2005 [8], dbj13-51-2003 [9], gjb4142-2000 [10], cecs28-2012 [11] and gb50936-2014 [12], this paper calculates the eccentric compression capacities of the rpc filled square steel tubular specimens, with the results shown in tab. 6. it can be seen that, the ratio of bearing capacity nu/n between the experiment result and cecs28-2012 calculated results have a standard deviation of 0.069, a coefficient of variation of 0.066, and a mean value of 1.043. compared with the others specifications (or codes), the cecs28-2012 calculated results are quite close to the experiment results and also relatively conservative. therefore, the formula provided in cecs28-2012 is recommended for calculation of the bearing capacity of rpc filled square steel tubular column in engineering practice. specimen no. experiment nu/kn aisc2005 dbj13-51-2003 gjb4142-2000 cecs28-2012 gb50936-2014 n/kn nu/n n/kn nu/n n/kn nu/n n/kn nu/n n/kn nu/n 1 708 357 1.983 727 0.974 902 0.785 717 0.987 700 1.011 2 694 353 1.964 648 1.071 739 0.940 642 1.081 685 1.014 3 573 350 1.638 602 0.952 661 0.866 590 0.971 673 0.852 4 588 345 1.704 564 1.043 600 0.980 551 1.068 660 0.891 5 629 424 1.482 663 0.949 666 0.944 614 1.025 743 0.846 6 749 468 1.599 736 1.018 700 1.070 642 1.167 802 0.934 7 480 241 1.994 529 0.907 734 0.654 498 0.963 505 0.950 8 450 239 1.882 464 0.970 572 0.787 446 1.009 497 0.906 9 410 237 1.727 430 0.954 502 0.817 410 0.999 490 0.837 10 382 235 1.624 401 0.952 450 0.849 383 0.998 482 0.792 11 464 298 1.557 477 0.972 502 0.924 425 1.092 555 0.836 12 510 333 1.531 533 0.956 530 0.963 443 1.152 608 0.839 mean value / / 1.724 / 0.976 / 0.881 / 1.043 / 0.892 standard deviation / / 0.186 / 0.046 / 0.111 / 0.069 / 0.072 coefficient of variation / / 0.108 / 0.047 / 0.126 / 0.066 / 0.081 table 6: bearing capacity of the specimens. finite element analysis finite element model of columns his paper simulates the eccentrically loaded rpc filled square steel tubular column using the finite element software abaqus. the rpc filled square steel tubular column model consists of three parts, namely rpc, an outer steel tube and a loading cover. both the rpc and the loading cover are modelled with c3d8r brick elements (8-node 3d brick elements with reduced integration); and the steel tube is modelled with s4r shell element (4-node shell elements with reduced integration). the rpc stress-strain relationship [13] is as follows: the compressive stress-strain relationship of rpc is shown in formula (1): 4 5 2 1.3 0.4x 0.1x 0 1 1 6( 1) i cp c x x y x x x x x y f                 (1) where: εcp is the compressive strain when rpc reaches the peak compressive strength, which is set to be 4400×10-6; fc is the peak compressive strength of rpc, which is set to be 93.49n/mm2. t w. hao et alii, frattura ed integrità strutturale, 46 (2018) 391-399; doi: 10.3221/igf-esis.46.36 397 considering the crack resistance of steel fiber in rpc, the tensile stress-strain relationship of rpc is shown in formula (2): 2 3 1.7 1.1 0.8 0.9 0 1 1 2( 1) i ctp ct x x x x y x x x x x y f                 (2) where: εctp is the compressive strain when rpc reaches the peak tensile strength, which is set to be 400×10-6; fct is the peak tensile strength of rpc, which is set to be 11.43n/mm2. the stress-strain curve of steel [14] is divided into five stages: elastic, elastic-plastic, plastic, hardening and one-time plastic flow. figure 5: comparison of the experiment results and analysis results. comparison between the experiment results and the analysis results through the finite element simulation analysis of the rpc filled square steel tubular columns, the analysis results of the load-span lateral displacements of some specimens are compared with the experiment results, as shown in fig. 5. it can be seen that the experiment results are close to the simulation analysis results, indicating that the model is correct and reasonable and can provide theoretical reference for engineering practice. w. hao et alii, frattura ed integrità strutturale, 46 (2018) 391-399; doi: 10.3221/igf-esis.46.36 398 conclusions (1) through experimental observations, it was found that the appearances of the eccentrically loaded rpc filled square steel tubular columns did not change much until the ultimate load was reached. the final failure was caused by the local bending of the steel tube. the bent part gradually shifted from the two ends to the mid section of the specimen. (2) the load-displacement curve of an eccentrically loaded rpc filled square steel tubular column can be roughly divided into three stages: the linear elastic stage, the elastic-plastic stage and the descending stage. the descending section of the curve is relatively flat, which shows that the specimen had good ductility. as the increase of specimen slenderness ratio and eccentricity, the bearing capacity of specimens is gradually decreased, the increase of steel ratio and the confinement coefficient obviously improves the bearing capacity of specimens. (3) according to theoretical analysis, it is found that the results of bearing capacity test and cecs28-2012 calculation show that the average value of nu/n is 1.043. compared with other specifications (or codes), the calculated results are close to the test results and are conservative. therefore, the formula provided in cecs28-2012 is recommended for calculation of the bearing capacity of rpc filled square steel tubular column in engineering practice. (4) the simulation analysis results of abaqus are close to the experiment results, indicating that this finite element model is correct and reasonable and can provide theoretical reference for engineering practice. acknowledgments he research work was supported by science and technology research project of colleges and universities in hebei province (no. zd2018209) and key research and development project of hebei province (no. 18227209d). references [1] richard, p. and cheyrezy, m. (1995). composition of powder concretes, cement and concrete research, 25(7), pp. 1501-1511. [2] hao, w.x. and xu, x. (2012). experimental study on the mechanical properties of reactive powder concrete with steel fibre, architecture technology, 43(1), pp. 35-37. [3] hao, w.x. and xu, x. (2010). experimental study on the flexural behavior of reactive powder concrete with steel fibre, concrete, (10), pp. 53-55. [4] hu, n.d., du, x.k., liu, p. and niu, z. (2016). experimental study on mechanical behavior of recycled aggregate concrete-filled square steel tubular long columns under eccentric compression loading, journal of building structures, (s2), pp. 36-42. [5] chen, x.x. (2014). experimental study on mechanical behavior of recycled aggregate concrete-filled square steel tubular short columns, baoding: college of urban and rural construction, agricultural university of hebei. [6] lin, z.y., wu, y.h. and shen, z.y. (2005). research on behavior of rpc filled circular steel tube column subjected to axial compression, journal of building structures, 26(4), pp. 52-57. [7] song, j. and chen, f.y. (2015). calculation model for thermo-mechanical coupling and 3d numerical simulation for concrete tower of cable-stayed bridge, mathematical modelling of engineering problems, 2(1), pp. 9-12. [8] american institute of steel construction. (2005). aisc(2005) seismic provisions for structural steel buildings, chicago, il. [9] china association for standardization of engineering construction. (2012). cecs 28-2012 technical specification for concrete-filled steel tubular structures, beijing: china planning press. [10] china association for standardization of engineering construction. (2013). dbj13-51-2003 technical specification for concrete-filled steel tubular structures, beijing: china architecture and building press. [11] chinese national military standard. (2000). gjb4142-2000 technical specifications for early-strength model composite structure used for navy port emergency repair in wartime. beijing: the general logistics department of pla. [12] china association for standardization of engineering construction. (2013). gb50936-2014 technical code for concrete filled steel tubular structures, beijing: china architecture and building press. t w. hao et alii, frattura ed integrità strutturale, 46 (2018) 391-399; doi: 10.3221/igf-esis.46.36 399 [13] yan, z.g., ji, w.y. and an, m.z. (2009). experimental study and full-range analysis of reactive powder concrete tbeams, journal of beijing jiaotong university, 33(1), pp. 86-90. [14] zhong, s.t. 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<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> /enu (use these settings to create adobe pdf documents best suited for high-quality prepress printing. created pdf documents can be opened with acrobat and adobe reader 5.0 and later.) >> /namespace [ (adobe) (common) (1.0) ] /othernamespaces [ << /asreaderspreads false /cropimagestoframes true /errorcontrol /warnandcontinue /flattenerignorespreadoverrides false /includeguidesgrids false /includenonprinting false /includeslug false /namespace [ (adobe) (indesign) (4.0) ] /omitplacedbitmaps false /omitplacedeps false /omitplacedpdf false /simulateoverprint /legacy >> << /addbleedmarks false /addcolorbars false /addcropmarks false /addpageinfo false /addregmarks false /convertcolors /converttocmyk /destinationprofilename () /destinationprofileselector /documentcmyk /downsample16bitimages true /flattenerpreset << /presetselector /mediumresolution >> /formelements false /generatestructure false /includebookmarks false /includehyperlinks false /includeinteractive false /includelayers false /includeprofiles false /multimediahandling /useobjectsettings /namespace [ (adobe) (creativesuite) (2.0) ] /pdfxoutputintentprofileselector /documentcmyk /preserveediting true /untaggedcmykhandling /leaveuntagged /untaggedrgbhandling /usedocumentprofile /usedocumentbleed false >> ] >> setdistillerparams << /hwresolution [2400 2400] /pagesize [612.000 792.000] >> setpagedevice microsoft word numero_59_art_03_3255.docx a. behtani et alii, frattura ed integrità strutturale, 59 (2022) 35-48; doi: 10.3221/igf-esis.59.03 35 focussed on steels and composites for engineering structures residual force method for damage identification in a laminated composite plate with different boundary conditions amar behtani, samir tiachacht laboratory of mechanics, structure, and energetics, mouloud mammeri university of tizi-ouzou, algeria. amar.behtani@ummto.dz; https://orcid.org/0000-0003-4503-0409 samir.tiachacht@ummto.dz; https://orcid.org/0000-0002-3597-8725 tawfiq khatir department of technology, university centre of naama salhi ahmed, naama, algeria khatir_usto@yahoo.com; https://orcid.org/0000-0003-3009-8371 samir khatir, magd abdel wahab soete laboratory, faculty of engineering and architecture, ghent university, technologiepark zwijnaarde, zwijnaarde, belgium. khatir.samir@hotmail.fr; https://orcid.org/0000-0002-8101-3633 magd.abdelwahab@ugent.be; https://orcid.org/0000-0002-3610-865x brahim benaissa design engineering laboratory, toyota technological institute, nagoya, japan. benaissa@toyota-ti.ac.jp; https://orcid.org/0000-0002-9472-9331 mohand slimani laboratory of mechanics, structure, and energetics, mouloud mammeri university of tizi-ouzou, algeria. mohand.slimani@ummto.dz; https://orcid.org/0000-0003-4252-4892 abstract. the strongest point about damage identification based on the dynamic measurements, is the ability to perform structural health evaluation globally. researchers in the last few years payed more attention to damage indicators based on modal analysis using either frequencies, mode shapes, or frequency response functions (frfs). this paper presents a new application of damage identification in a cross-ply (0°/90°/0°) laminated composite plate based on force residual method (frm) damage indicator. considering single and multiple damages with different damage levels. as well as investigating the ssss and cccc boundary conditions effect on the estimation accuracy. moreover, a white gaussian noise is introduced to test the challenges of the technique. the results show that the suggested frm indicator provides accurate results under different boundary conditions, favouring the ssss boundary condition than the cccc for 3% noise. citation: behtani, a., tiachacht, s., khatir, t., hhatir, s., abdel wahab, m., benaissa, b., slimani, m., residual force method for damage identification in a laminated composite plate with different boundary conditions, frattura ed integrità strutturale, 59 (2022) 35-48. received: 28.08.2021 accepted: 02.10.2021 published: 01.01.2022 copyright: © 2022 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. https://youtu.be/23qmyy-ozd8 a. behtani et alii, frattura ed integrità strutturale, 59 (2022) 35-48; doi: 10.3221/igf-esis.59.03 36 keywords. damage quantification; rfm; noise; composite laminated plate. introduction omposite materials become a cornerstone of modern material and are being used in almost every engineering discipline, like civil, infrastructure, aerospace engineering to name a few, due to their outstanding strength compared to their weight. however, composite materials are not immune to damage, and when it happens, whether due to fatigue or accidents, it can reduce their rigidity significantly. therefore, researchers in the last decade developed new methods for damage identification dedicated to composite materials. in such methods, vibration-based structural responses are commonly used. doebling et al. [1] presented a review of these approaches. we mention in this paper some of the noticeable literature, such as the study made by khatri et al [2], in which the authors considered experimental analysis for damage identification in a complex structure, with an inverse problem formulation based on particle swarm optimization (pso). ghannadi et al. [3] presented an approach based on the multiverse optimizer (mvo). where two objective functions were used, namely the modal assurance criterion (mac) and the modified total modal assurance criterion (mtmac). wand et al. [4] suggested a neural network technique for damage identification refinement in the case of a suspension bridge. and providakis et al. [5] used impedance-type measurements and error statistics to present a new damage identification approach in composite structures. vahedian et al. [6] considered the case of multi-storey timber buildings and presented an improvement on the damage assessment by sfrp. and tiachacht et al. [7] investigated a new modified indicator based on cornwell indicator (ci). this indicator was tested in different structures and the results suggested better accuracy than the peer methods. the frequency change-based approach was used in the classification of vibration-based damage detection techniques [8, 9], a technique based on curvature mode shape [10], as well as another technique based on modal strain energy [11]. computational cost is often an issue in such methods. a quick damage identification method in the laminated composite plate using ci and machine learning based artificial neural network (ann) was presented in ref. [12]. the authors used isogeometric analysis (iga) combined with damage indicator for damage localization and ann for damage quantification. different indicators were combined with laminated composite beams and plates in refs. [13, 14]. nobahari et al. [15] suggested an approach with the name: “flexibility strain energy-based index (fsebi)”. for multiple damages identification, in both simple and complex cases. the efficiency of this method for multiple damage localization was shown in the results. flexibility matrix for damage identification was investigated by [16]. this technique is efficient for damaged detection. however, the provided technique is experimentally validated. ghannadi et al. [17] considered a variety of structures to investigate their new approach based on the grey wolf optimization (gwo) algorithm. using an objective function that combines the frequencies and mode shapes. the validation of the suggested methods is carried out in two experimental studies, namely a cantilever beam and a truss tower. different optimization techniques were investigated for damage identification problems [2, 12, 18-20], such as steel and composite plates, steel and composite beams, and complex structures. in this paper, a laminated composite plate with three layers (0°/90°/0°) is considered for damage identification, using the residual force method with fem. the structural response is studied under two kinds of boundary conditions, namely, fully simply supported (ssss) and fully clamped plates (cccc) to test the accuracy of frm. considering the measurement uncertainty up to 3% level, simulated by white gaussian noise. methodology finite element analysis of laminate plate his study is based on the first-order shear deformation theory (fsdt) [21]. in such a method, after material deformation, the effects of transverse shear strains cause the transverse to not remain perpendicular to the mid surface. w is not function of the thickness coordinate z because of the inextensibility of transverse normal. therefore, the displacement field of the fsdt function of time t is written in the following form: c t a. behtani et alii, frattura ed integrità strutturale, 59 (2022) 35-48; doi: 10.3221/igf-esis.59.03 37                           0 0 0 , , , , , , , , , , , , , , , , , , , x y u x y z t u x y t z x y t v x y z t v x y t z x y t w x y z t w x y t (1) where  0 0 0, ,u v w is the displacement vector of a point on the plane  0z , x is the rotations of a transverse normal around the x-axes and  y is the equivalent for the y-axes. figure 1: laminated plate organization of layers in the thickness direction. the strain energy is:             21 2 1 2 t t k t k t k t k m m m f f m f f a z t t k c c c a z u u b d b b d b b zd b b z d b dzuda u b d b dzuda (2) the components of the stiffness matrix include the membrane-bending coupling part, are written as follows:                e e e e e emm mf fm ff cck k k k k k (3) where emmk is the stiffness matrix of the membrane part, and e mfk , e fmk are the membrane-bending coupling components, e ffk represent the bending component and e cck represent the shear component. these matrices are detailed as follows:                                                       1 1 2 2 1 1 2 2 1 1 3 3 1 1 1 1 1 2 1 2 1 3 c c c c c n e t mm m k m k k k a n e t mf m k f k k k a n e t fm f k m k k k a n e t ff f k f k k k a n e t cc c c c k k k a k b d b z z da k b d b z z da k b d b z z da k b d b z z da k b d b z z da (4) here cn represents the number of layers across the z-axes. z layer 1 layer k zk+1 zk a. behtani et alii, frattura ed integrità strutturale, 59 (2022) 35-48; doi: 10.3221/igf-esis.59.03 38 there exist three b matrices (membrane, the bending and the shear components), corresponding to the strain-displacements. they are described in detail as follows:                                     , , , , , , , , , , 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 x m y y x x f y y x x c y n b n n n n b n n n n n b n n (5) where   , x n n x and   , y n n y in this paper, we consider the dynamic version of the principle of virtual displacements. the equations of motion for the free vibration of symmetric cross-ply laminated plates can be expressed as:                                                                      2 2 2 55 44 02 2 2 222 22 11 12 66 55 22 2 2 2 22 2 12 22 66 442 2 2 x x s y x s x y yx x s w w w k a a i x xx y t yw wxd d d k a i x y x y xx y t w d d d k a x y yy y x                    2 2 2 y y i t (6) here, 𝐼 and 𝐼 are the tensor components for the mass inertia, and they are defined as:    3 0 2; 12 h i h i (7) where  and h are, respectively, the density and the total thickness of the composite plate. 𝐴 and 𝐷 are the extensional and bending stiffnesses, and they are expressed as in the following equations:                     1 1 3 3 1 1 n k ij ij k k k n k ij ij k k k a q z z d q z z (8) where  kijq is the stress-reduced stiffness matrix for the transformed material plane in each layer k. in eqn. (8), the matrix can be obtained as follows: a. behtani et alii, frattura ed integrità strutturale, 59 (2022) 35-48; doi: 10.3221/igf-esis.59.03 39  tmq pq p (9) where p is the transformation matrix given by:                             2 2 2 2 2 2 2 2 0 0 0 0 0 0 0 0 0 0 0 0 p (10) where    cos ;    sin and   2 sin 2 and mq is the stress-reduced stiffness for the material plane                      1 12 2 12 2 2 23 13 12 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 m gq g g (11) here        1 1 12 211 e ; and        2 2 12 211 e , where 1e is young’s modulus for a layer parallel to fibres. and 2e is the equivalent young’s modulus for the layers that are perpendicular to fibres. on the other hand, 12 and 21 are poisson’s ratios. 23g is the shear modulus for planes 2−3, 13g is the equivalent shear modulus for planes 1−3, and 12g represent the shear modulus for planes 1−2. the variables w , x and  y can be expressed in the harmonic forms as follows:                           , , , , , , , , , i t i t x x i t y y w x y t x y e x y t x y e x y t x y e (12) and the equations of motion (6) become:                                                                                  2 2 2 55 44 02 2 2 222 2 11 12 66 55 22 2 2 22 2 12 22 66 442 2 2 x x s y yx s x x y yx x s y k a a i x xx y d d d k a i x y x y xx y d d d k a x y yy y x                2 2 yi (13) in which  is natural frequency. a. behtani et alii, frattura ed integrità strutturale, 59 (2022) 35-48; doi: 10.3221/igf-esis.59.03 40 residual forces in this section, we explore structural damage identification based on the residual forces, details about residual forces can be found in ref. [22]. in such approaches, the structure is divided into small elements via the finite element method, and the damage index of each element is expressed as the change of the rigidity i.e.:                  e e ee u d uii i i ik k k k (14) where    eu i k and    ed i k are the elementary matrices of the undamaged and damaged structures, respectively. in the above equation, eqn. (14),   eik is the difference in stiffness, and  is a value between 0 and 1, which indicates a loss of rigidity in each element. in other words, for undamaged elements,  is equal to 0, and to 1 in fully damaged elements. in this study, we assume that the damage does not affect the mass matrix of a damaged structure, therefore the rigidity matrix of the damaged element is expressed as follows:                  0 1, , ee u jj j m k k j m (15) and the modal residual force vector is expressed by this equation:                                                  1 2 1 2 e e ed i ii mi m r k f f f f f (16) as consequence, eqn. (16) can be represented in a matrix form by the following expression:      f r (17) the coefficient matrix  f is:        eeu d ij j ij f k (18) here,   ij f is the force vector in the actual node thi on the thj element, written in the global coordinates. the vector of residual force modal is expressed in this manner:           d dii ir k m (19) and eqn. (17) is rewritten in this manner:                                                                    111 12 1 1 221 22 2 2 1 2 m m mn n nm n f f f r f f f r f f f r (20) a. behtani et alii, frattura ed integrità strutturale, 59 (2022) 35-48; doi: 10.3221/igf-esis.59.03 41 here, n is the number of modes. and m is the number of elements. and the damage indicators are computed through the system of equations eqn. (20)                                                                     1 11 12 1 1 2 21 22 2 2 1 2 m m m n n nm n f f f r f f f r f f f r (21) numerical examples a square laminated (0°/90°/0°) plates o investigate the performance of the suggested method, we consider an example of square cross-ply laminated plates. in this study, we assume that all layers of the laminate have the same thickness and density, and made of linearly elastic composite material, with the following properties for each layer:   1 2 12 13 2/ 40, 0.6e e g g e ; 23 2 0.5g e ;  12 0.25 . subscripts 1 denote the direction parallel to fibre orientation in a layer and 2 represent the perpendicular direction to the fibre. considering that the measurement is performed clockwise, the ply angle is positive of each layer from the global x-axis to the fibre direction, and negative if measured anti-clockwise. we consider a mesh of 10 ×10 (100 elements) as shown in fig. 2. and to obtain the natural frequencies and mode shapes, the eigenproblem is solved using matlab. we compare our results to those published by ferreira and fasshauer [23] and [24], considering the same shear correction factors, as well as the nondimensionalized natural frequencies. figure 2: (a) a cross-ply (0°/90°/0°) square composite plate and (b) discretized square isotropic plate with two damage scenarios. the shear correction factor is considered as  2 / 12sk , and the dimensionless natural frequency is given by:      2 2 0b h d where    30 2 12 2112 1d e h . we also consider in this study, two damage scenarios, simulated by reducing the global stiffness of individual element in the following manner:      1 1 nele d e e k k (22) here, represents the damage ratio. dk is the global stiffness matrix representing the damaged structures. finally, ek is the stiffness matrix of the eth element. z x y lx ly 0° 90° 0° (a) 1 2 10 91 92 100 scenario 2 32 2928 8 lx= 1 m l y= 1 m scenario 1 x y scenario 4scenario 3 (b) 16 24 40 63 64 t a. behtani et alii, frattura ed integrità strutturale, 59 (2022) 35-48; doi: 10.3221/igf-esis.59.03 42 considering three-ply (0°/90°/0°) clamped cccc square, with laminated plates of thickness to span ratios  0.2t b and  1a b , tab. 2 shows the convergence results of dimensionless natural frequencies. to validate the proposed damage identification approach, we consider four damage scenarios. the first scenario has one damage, and two damages in the second scenario and two other scenarios has three and four damages, respectively. details of each damage case are shown in tab. 1. and the corresponding natural frequencies are shown in tab. 2. fig. 3 shows the first four mode shapes of the cross-ply (0°/90°/0°) square composite plate under ssss boundary conditions. scenario 1 scenario 2 scenario 3 scenario 4 element no 16 28 29 8 16 24 32 40 63 64 severity % 15 5 5 15 5 10 10 5 5 10 table 1: damage scenarios. mode 1 2 3 4 5 intact [23] 10 × 10 3.5479 5.8947 7.3163 8.6545 9.7538 [24] 3.5939 5.7691 7.3972 8.6876 9.1451 present 10 × 10 3.5479 5.8947 7.3163 8.6545 9.7538 damaged scenario 1 3.5425 5.8934 7.3093 8.6516 9.7514 scenario 2 3.5470 5.8933 7.3162 8.6541 9.7518 scenario 3 3.5410 5.8885 7.3048 8.6377 9.7461 scenario 4 3.5464 5.8905 7.3102 8.6455 9.7392 table 2: naturel frequencies of undamaged and damaged laminate plate structure ssss. figure 3: the first four mode shapes of the cross-ply (0°/90°/0°) fully simply supported square composite plate ssss. a. behtani et alii, frattura ed integrità strutturale, 59 (2022) 35-48; doi: 10.3221/igf-esis.59.03 43 (a) noise-free. (b) noise 3%. figure 4: damage index for all elements of the cross-ply (0°/90°/0°) square composite plate ssss – scenario 1. (a) noise-free. (b) noise 3%. figure 5: damage index for all elements of the cross-ply (0°/90°/0°) square composite plate ssss – scenario 2. (a) noise-free. (b) noise 3%. figure 6: damage index for all elements of the cross-ply (0°/90°/0°) square composite plate ssss – scenario 3. a. behtani et alii, frattura ed integrità strutturale, 59 (2022) 35-48; doi: 10.3221/igf-esis.59.03 44 (a) noise-free. (b) noise 3%. figure 7: damage index for all elements of the cross-ply (0°/90°/0°) square composite plate ssss – scenario 4. the presented results showed that frm predicts the location of damage correctly with higher accuracy in a laminated composite plate in the case of ssss boundary conditions. on the other hand, the indicator can support the noise of up to 3%. we note that prediction error under 3% noise correlates with the number of damages. the prediction error in the case of single and double damaged plates is very small, which is noticed when the number of damages is higher than three. fig. 8 shows the first four mode shapes, in the case of cross-ply (0°/90°/0°) square composite plate under cccc boundary conditions. and figs. 9-12 plot the results of each scenario in the presence and absence of measurement noise. the natural frequencies of each damage scenario are presented in tab. 3. mode 1 2 3 4 5 intact [23] 10 × 10 4.4145 6.8373 7.6291 9.2078 10.3964 [24] 4.4468 6.6419 7.6996 9.1852 9.7378 present 10 × 10 4.4145 6.8373 7.6291 9.2078 10.3964 damaged scenario 1 4.4069 6.8359 7.6198 9.2046 10.3939 scenario 2 4.4132 6.8347 7.6285 9.2060 10.3941 scenario 3 4.4060 6.8299 7.6169 9.1899 10.3885 scenario 4 4.4109 6.8282 7.6238 9.1976 10.3775 table 3: naturel frequencies of undamaged and damaged laminated plate structure cccc. under boundary condition cccc, the indicator can support the noise of up to 3%. however, the prediction error under noise is different in each scenario. the prediction error in the case of single and double damaged plates is higher than that of the cases of ssss. fig. 13 summarizes the obtained damage identification results for the laminated composite plate with and without noise and the accuracy in each damage scenario. these results suggest that the scenario of plates under ssss boundary condition correspond to the same accuracy in all cases where there is no noise. however, it has an advantage over cccc in the scenarios of 3% noise and three damages (case 3). cccc on the other hand presents an advantage in the small number of damages. a. behtani et alii, frattura ed integrità strutturale, 59 (2022) 35-48; doi: 10.3221/igf-esis.59.03 45 figure 8: the first four mode shapes of the cross-ply (0°/90°/0°) fully clamped square composite plate cccc. (a) noise-free. (b) noise 3%. figure 9: damage index for all elements of the cross-ply (0°/90°/0°) square composite plate cccc – scenario 1. a. behtani et alii, frattura ed integrità strutturale, 59 (2022) 35-48; doi: 10.3221/igf-esis.59.03 46 (a) noise-free. (b) noise 3%. figure 10: damage index for all elements of the cross-ply (0°/90°/0°) square composite plate cccc – scenario 2. (a) noise-free. (b) noise 3%. figure 11: damage index for all elements of the cross-ply (0°/90°/0°) square composite plate (cccc) – scenario 3. (a) noise-free. (b) noise 3%. figure 12: damage index for all elements of the cross-ply (0°/90°/0°) square composite plate (cccc) – scenario 4. a. behtani et alii, frattura ed integrità strutturale, 59 (2022) 35-48; doi: 10.3221/igf-esis.59.03 47 figure 13: comparison of obtained damage identification results for the laminated composite plat without noise and with noise. conclusion n this study, we present an application for damage identification based on force residual method (frm) in the case of a cross-ply (0°/90°/0°) laminated composite plate. we consider the cases of single and multiple damages, and different levels of damages. to test the accuracy of frm, different boundary conditions were applied to the composite plate. we found that the proposed approach is accurate for damage prediction, localization, and quantification in laminated composite plates. different levels of white gaussian noise are applied to the measured natural frequencies and used for damage prediction for ssss and cccc to test the effectiveness of frm for laminated composite. the results showed that ssss is more stable in cases of multiple damages than cccc, supporting noise level over 3%. acknowledgement he fourth author, samir khatir, acknowledges the funding of the postdoctoral fellowship bof20/pdo/045 provided by bijzonder onderzoeksfonds (bof), ghent university. references [1] doebling, s.w., farrar, c.r., prime, m.b. and shevitz, d.w. (1996). damage identification and health monitoring of structural and mechanical systems from changes in their vibration characteristics, a literature review. doi: 10.2172/249299. [2] khatir, s., dekemele, k., loccufier, m., khatir, t. and abdel wahab, m. (2018). crack identification method in beamlike structures using changes in experimentally measured frequencies and particle swarm optimization, comptes rendus mécanique, 346(2), pp. 110-120. doi: 10.1016/j.crme.2017.11.008. [3] ghannadi, p. and kourehli, s.s. (2020). multiverse optimizer for structural damage detection: numerical study and experimental validation, the structural design of tall and special buildings, 29(13), pp. e1777. doi: 10.1002/tal.1777. [4] wang, j. and ni, y. (2015). refinement of damage identification capability of neural network techniques in application to a suspension bridge, structural monitoring and maintenance, 2(1), pp. 77-93. doi: 10.12989/smm.2015.2.1.077. [5] providakis, c., tsistrakis, s., voutetaki, m., tsompanakis, y., stavroulaki, m., agadakos, j., kampianakis, e. and pentes, g. (2015). a new damage identification approach based on impedance-type measurements and 2d error statistics, structural monitoring and maintenance, 2(4), pp. 319-338. doi: 10.12989/smm.2015.2.4.319. case 1 16 element no. 0 5 10 15 20 actual cccc without noise cccc noise 3% ssss without noise ssss noise 3% case 2 28 29 element no. 0 5 10 actual cccc without noise cccc noise 3% ssss without noise ssss noise 3% case 3 8 16 24 element no. 0 5 10 15 20 actual cccc without noise cccc noise 3% ssss without noise ssss noise 3% case 4 32 40 63 65 element no. 0 5 10 15 actual cccc without noise cccc noise 3% ssss without noise ssss noise 3% i t a. behtani et alii, frattura ed integrità strutturale, 59 (2022) 35-48; doi: 10.3221/igf-esis.59.03 48 [6] vahedian, a., mahini, s.s. and glencross-grant, r. (2015). performance-based and damage assessment of sfrp retrofitted multi-storey timber buildings, structural monitoring and maintenance, 2(3), pp. 269-282. doi: 10.12989/smm.2015.2.3.269. [7] tiachacht, s., bouazzouni, a., khatir, s., abdel wahab, m., behtani, a. and capozucca, r. (2018). damage assessment in structures using combination of a modified cornwell indicator and genetic algorithm, engineering structures, 177, pp. 421-430. doi: 10.1016/j.engstruct.2018.09.070. [8] cawley, p. and adams, r.d. (1979). a vibration technique for non-destructive testing of fibre composite structures, journal of composite materials, 13(2), pp. 161-175. doi: 10.1177/002199837901300207. [9] kessler, s.s., spearing, s.m., atalla, m.j., cesnik, c.e.s. and soutis, c. (2002). damage detection in composite materials using frequency response methods, composites part b: engineering, 33(1), pp. 87-95. doi: 10.1016/s1359-8368(01)00050-6. [10] hamey, c.s., lestari, w., qiao, p. and song, g. (2004). experimental damage identification of carbon/epoxy composite beams using curvature mode shapes, structural health monitoring, 3(4), pp. 333-353. doi: 10.1177/1475921704047502. [11] kumar, m., shenoi, r.a. and cox, s.j. (2009). experimental validation of modal strain energies based damage identification method for a composite sandwich beam, composites science and technology, 69(10), pp. 1635-1643. doi: 10.1016/j.compscitech.2009.03.019. [12] khatir, s., tiachacht, s., thanh, c.-l., bui, t.q. and abdel wahab, m. (2019). damage assessment in composite laminates using ann-pso-iga and cornwell indicator, composite structures, 230, pp. 111509. doi: 10.1016/j.compstruct.2019.111509. [13] behtani, a., tiachacht, s., khatir, s., slimani, m., mansouri, l., bouazzouni, a. and abdel wahab, m. (2020), the sensitivity of modal strain energy for damage localization in composite stratified beam structures, proceedings of the 13th international conference on damage assessment of structures, singapore. [14] khatir, s., tiachacht, s., le thanh, c., khatir, t., capozucca, r. and abdel wahab, m. (2020), damage detection in laminated composite plates based on local frequency change ratio indicator, proceedings of the 13th international conference on damage assessment of structures, singapore. [15] nobahari, m. and seyedpoor, s.m. (2013). an efficient method for structural damage localization based on the concepts of flexibility matrix and strain energy of a structure, structural engineering and mechanics: an international journal, 46(2), pp. 231-244. doi: 10.12989/sem.2013.46.2.231. [16] pandey, a.k. and biswas, m. (1994). damage detection in structures using changes in flexibility, journal of sound and vibration, 169(1), pp. 3-17. doi: 10.1006/jsvi.1994.1002. [17] ghannadi, p., kourehli, s.s., noori, m. and altabey, w.a. (2020). efficiency of grey wolf optimization algorithm for damage detection of skeletal structures via expanded mode shapes, advances in structural engineering, 23(13), pp. 2850-2865. doi: 10.1177/1369433220921000. [18] khatir, s., abdel wahab, m., boutchicha, d. and khatir, t. (2019). structural health monitoring using modal strain energy damage indicator coupled with teaching-learning-based optimization algorithm and isogoemetric analysis, journal of sound and vibration, 448, pp. 230-246. doi: 10.1016/j.jsv.2019.02.017. [19] khatir, s. and abdel wahab, m. (2019). fast simulations for solving fracture mechanics inverse problems using podrbf xiga and jaya algorithm, engineering fracture mechanics, 205, pp. 285-300. doi: 10.1016/j.engfracmech.2018.09.032. [20] khatir, s., belaidi, i., serra, r., wahab, m.a. and khatir, t. (2015). damage detection and localization in composite beam structures based on vibration analysis, mechanics, 21(6), pp. 472-479. doi: 10.5755/j01.mech.21.6.12526. [21] reddy, j.n. (2003) mechanics of laminated composite plates and shells: theory and analysis. crc press. doi: 10.1201/b12409. [22] shen, j.y. and sharpe jr., l. (2000), damage detection using residual modal forces and modal sensitivity, proceeding of 14th asce engineering mechanics conference. [23] ferreira, a.j.m. and fasshauer, g.e. (2007). analysis of natural frequencies of composite plates by an rbfpseudospectral method, composite structures, 79(2), pp. 202-210. doi: 10.1016/j.compstruct.2005.12.004. [24] liew, k.m. (1996). solving the vibration of thick symmetric laminates by reissner/mindlin plate theory and the p-ritz method, journal of sound and vibration, 198(3), pp. 343-360. doi: 10.1006/jsvi.1996.0574. microsoft word 2266 e. maiorana, frattura ed integrità strutturale, 48 (2019) 459-472; doi: 10.3221/igf-esis.48.44 459 contribution of longitudinal stiffener rigidity and position to bridge girder integrity emanuele maiorana omba impianti & engineering spa, via della croce, 10 – 36040 torri di quartesolo (vi), italy emaior@libero.it, http://orcid.org/0000-0002-3574-1410 abstract. to increase the elastic critical load of a plate, such as i-shaped cross-welded section of bridge girders and upgrade bending and torsional stiffnesses, slenderness is usually reduced by dividing the web into subpanels, by means of transversal stiffeners and a longitudinal stiffener. the optimal solution is defined when the stiffener maximizes the buckling coefficient, with a minimal cross-section area. for this purpose, seven shapes of open and closed sections of longitudinal stiffeners, with different second moment of area, are examined in terms of buckling coefficients by theoretical solution and numerical computation, to compare their contribution in terms of weight per linear meter of beam. the optimum value of flexural stiffness is defined and a useful practical law is given to correlate the best position of a conventional flat stiffener with respect to variations of the stress gradient, from pure bending to pure compression, to maximize the benefits of its action and increase the stability of bridge girders. keywords. bridge stability; buckling coefficient; optimal stiffness; stiffener optimal positioning. citation: maiorana, e., contribution of longitudinal stiffener rigidity and position to bridge girder integrity, frattura ed integrità strutturale, 48 (2019) 459-472. received: 20.11.2018 accepted: 28.02.2019 published: 01.04.2019 copyright: © 2019 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. introduction lender elements are widely used in engineering, as the static inertial characteristics of their sections allow full use of materials by optimization of geometric shapes according also to the external loads to which they are subjected. generally, to increase the elastic critical load, see e.g. the bridge girders in fig. 1, slenderness  = h / t, i.e. the ratio between height h and thickness t of the web panel, is reduced by dividing the web into subpanels according to its stiffening system. a major difficulty encountered in the study of stiffened bridge webs subject to non-uniform compression, e.g., high beam web panels subject to bending-compressive loads, is to define a sufficient rigidity and accurate positioning of the longitudinal stiffener, since compression stresses vary linearly along the web. an optimal solution is represented by the solution in which the stiffener maximizes its effect for good web panel resistance at stability, with a minimal cross-section area. s http://www.gruppofrattura.it/va/48/2266.mp4 e. maiorana, frattura ed integrità strutturale, 48 (2019) 459-472; doi: 10.3221/igf-esis.48.44 460 although the analytical closed-form solution to determine buckling coefficient is only possible in a few simple cases of geometry and symmetry in loading (timoshenko and woinowsky-krieger 1959 [1]), the finite element method can be used to study many kinds of geometries, boundary conditions, and different configurations of loads, such as patch loading or local symmetrical loads, improving initial imperfections and covering a wide range of constitutive laws for materials in the non-linear range. figure 1: bridge web panel girders strengthened by a longitudinal stiffener. the increase in the elastic critical load through optimization of the stiffeners, by means of their shapes and positions, is examined in xie and chapman 2004 [2] and lee et al. 2002 [3] and that in plates subjected to shear loading in alinia 2005 [4]. the stability of longitudinally stiffened web plates under interactive shear and bending force is described in alinia and moosavi 2009 [5] and the influence of longitudinal stiffeners on the elastic stability of girder webs in maiorana et al. 2011 [6]. an improved design procedure for efficient design of stiffened plates, under combined compression and bending, and in detail the influence of the stiffener location on the stability of the structure, finding the optimum location of it, is proposed in bedair, 1997 [7]. the ultimate strength of longitudinally stiffened i-girder webs, subjected to combined patch loading and bending, is treated in graciano and casanova 2005 [8] and the shear strength of longitudinally stiffened panels with imperfections in pavlovčič et al. 2007 [9]. the beams examined in this work are reinforced with a longitudinal stiffener and some generalizations were made to improve stiffener design with regard to the rigidity and position, in order to maximize elastic stability. the longitudinal stiffener was connected to the plate at various positions h / h with respect to the compressed edge, so that the panel of length a at height h was divided into two subpanel: upper plate a with height h, and the lower plate b with height h. a finite element model was used according to the strand7 code (g+d computing 2005 [10]), with a static scheme consisting of a simple hinge bounded plate subjected to combination of bending moment and compression forces (fig. 2). a sensitivity analysis of the mesh, to define the shape and dimension of the elements was treated deeply in previous papers by the author of this paper. maiorana and pellegrino 2011 [11] compares k values obtained with the fe model and eurocode equations for square and rectangular panels of constant thickness subjected to axial force and bending moment, and pellegrino et al. 2009 [12] compares the results of the fe model with those of the literature, in the case of perforated steel plates under shear loading. the fe used for the mesh were plates with four nodes (quad4) and six degrees of freedom per node; the typical size of the elements being h / 20. boundary conditions were assumed to represent the plate as a web panel, see fig. 2: sides 1, 2, 3 and 4 displacements restrain uy = 0; side 2 and 4 uz = 0; and displacements ux were symmetric. the applied loads were in equilibrium and directly applied to the nodes on the two lateral vertical edges as a system of conservative forces which do not change direction during deformation, due to symmetry. e. maiorana, frattura ed integrità strutturale, 48 (2019) 459-472; doi: 10.3221/igf-esis.48.44 461 figure 2: static diagram of a plate divided into two subpanels a and b; a / h = 1.5. basic concept buckling coefficient heoretical buckling coefficients kth of simply supported plates subjected to uniform compression were analytically determined by solving the timoshenko’s equations based on equilibrium between external and internal forces, in a deformed configuration. the lower value of the compression force nx is obtained with n = 1, and the buckling coefficient is given by eqn. 1: kth = [(m b) / a + a / (m b)]2 (1) being stress gradient  = t / c the ratio between traction t and compression c stresses, in en 1993-1-5 2007 [13] the following k values are proposed: k = 4 for  = 1 k = 8.2 / (1.05 + ) for 1 >  > 0 k = 7.81 for  = 0 k = 7.81 – 6.29 + 9.7 2 for 0 >  > -1 k = 23.9 for  = -1 k = 5.98 (1  2) for -1 >  > -3 numerically, buckling coefficient knum was found by solving the corresponding eigenvalue problem. the lower eigenvalue refers to the critical elastic load and the eigenvector defines its deformed shape. stiffness matrix k was given by the conventional matrix in small deformations ke and the matrix ks, which takes into account the effect of stress  on the plate. the global stiffness matrix of the panel at stress level 0 may be written as follows: k (0) = ke + ks (0) (2) when the stress level reaches 0, the stiffness matrix becomes: t e. maiorana, frattura ed integrità strutturale, 48 (2019) 459-472; doi: 10.3221/igf-esis.48.44 462 k (0) = ke + ks (0) (3) the equation governing plate behavior is: df = [ke +  ks (0)] du (4) where du is the vector of displacement variations and df the vector of load variations. the determinant of the matrix becomes null at buckling, and an increase in displacement without a corresponding increase in load occurs: [ke +  ks (0)] du = 0 (5) the solution to this is an eigenvalue problem corresponding to the lower eigenvalue 1 related to critical elastic stress, at which buckling occurs: cr = 10 (6) optimal stiffness and best position on the base of relative bending stiffness, the behavior of the whole web panel-stiffener system can be divided into two categories, defined by the different mechanism of the loss of stability. the flexible stiffening system is characterized by the fact that the web panel and the stiffener reach instability together in a global way, whereas the rigid stiffening system has a local instability mode. in the first case, both web panel and stiffening have the same elastic critical load and the optimal position changes and must be determined numerically for a given relative flexural stiffness ratio for every value of eqn. 7 (dubas and gehri 1986 [14]). s = (e ist) / (d h) (7) where d in the flexural rigidity by eqn. 8 d = (e t 3) / [12 (1  2)] (8) in the second case, stiffening is sufficient against any loss of stability of the web panel, forming a nodal line, and the overall buckling load is the lower value, between that of the subpanels a and b. both deformation modes, flexible and rigid, occur together and interact closely in the typical buckling shapes of plates with semi-rigid stiffeners, classified as a transient stage. reaching optimal stiffness, these buckling shapes do not interact (alinia 2005 [4]) and stiffening remains straight until complete deformation has taken place. the optimal position of the stiffener is reached when the elastic critical load is the same in both subpanels and also depends on stress gradient  : for  < 0 bending dominates compression forces, whereas for  > 0 compression dominates the bending moment. thus, for a given value of stress gradient , the distribution of forces changes in subpanels a and b (fig. 1) and, accordingly, the optimal position changes. increasing , the optimal position of the stiffener moves to the centerline of the plate, regardless of relative stiffness (bedair 1997 [7]). in the design of open beams subject to pure bending forces, the american code (aashto 2018 [15]) recommends the longitudinal stiffener to be positioned at an average distance of h / h = 0.2 from the compressed edge. this position depends on the ratio between rigidities of stiffener and plate, and is not always exactly the same for each situation but changes according to relative flexural stiffness s. in fact, unlike the case of prevailing compression stresses, when the bending moment predominates, the optimal location for a longitudinal stiffener depends on the geometrical characteristics of the whole plate/stiffener relationship. in conclusion, reaching optimal stiffness with stiffener in its optimum position, maximal stability is reached, ensuring that the stiffener has a minimal cross-sectional area. effect of initial imperfection many national steel construction codes prescribe the maximum size/magnitude of the initial imperfection relating to panel height and width. generally standards take into account the influence of thickness, or refer to slenderness. european standard (en 1090-2 2018 [16]) refers to the slenderness, directly with b / t (local) or indirectly with l / 300 (global). e. maiorana, frattura ed integrità strutturale, 48 (2019) 459-472; doi: 10.3221/igf-esis.48.44 463 prescriptions are developed and used without any reference to the applied loads acting on the panels in question, so that the particular contexts of application are neglected. for the purposes of this study, the assumption is considering a perfect plane plate without out-of-plane eccentricities. the scope is to find buckling coefficients k from linear eigenbuckling analysis considering the loss of stability from 1st buckling mode. stiffener cross-section shape pen-section and closed-section longitudinal stiffeners are considered, each respecting the geometric relationships of dimensions according to en 1993-1-5 2007 [13]. for comparisons, seven cross-sections having an equal value of area but different second moments of area (table 1), i.e. three open cross-sections and four closed ones, have been examined. the choice was dictated by the need to consider the same contribution in terms of weight per linear meter of deck beam. fig. 3 compares solutions of linear buckling coefficients for non-stiffened plate us0 and stiffened plates with the seven types of stiffeners, with respect to the plate aspect ratios  = a / h (see fig. 2). cross-section cc6 appeared to be the best stiffener shape to stiffen the plate, for the usual range of web panel aspect ratios, i.e. 1.5 <   2. for  < 1.5, cross-section cr5 shows a greater value than cc6. ct4 makes the same contribution to stability varying . for the open-section stiffeners, the best characteristics were found in ot2 and ol3 that show higher second moments of area; of1 makes the lowest contribution to the increase of buckling coefficient k. with respect to open cross-sections, in cr5, cc6 and cz7, k decreases as  increases; local instabilities occur in closed cross-sections with greater slenderness. of1 ot2 ol3 ct4 cr5 cc6 cz7 t b s t b s f t b s f t b s f t b s f t b s f t b s fg flat cross section t-shaped cross section l-shaped cross section triangular cross section rectangular cross section circular cross section trapezoidal cross section t 10 10 10 10 10 10 10 b 150 100 100 112 100 95 86 s 15 15 15 7.5 7.5 7.5 7.5 f -50 50 200 100 300 200 g ------100 table 1: stiffeners: analysed cross-sectional shape and geometrical dimensions (mm). being equal the area ast, it is possible to improve stiffening performance by maximizing the second moment of area ist; a considerable increase in the linear buckling coefficient could be reached by using closed-section stiffeners rather than open types. fig. 4 compares solutions for the buckling coefficient of a stiffened plate with aspect ratio  = 1.5 and position of longitudinal stiffener h / h = 0.2. for the stiffened plate, the minimal value of buckling coefficient k is 5.73 for cross-section of1 and 8.26 for cc6. o e. maiorana, frattura ed integrità strutturale, 48 (2019) 459-472; doi: 10.3221/igf-esis.48.44 464 figure 3: buckling coefficient k vs. aspect ratio  for plate with and without stiffener. figure 4: comparison of solutions for k in plates under bending moment  = -1 for unstiffened plate us and with differing stiffener cross-section shapes, open o and closed c. correctly, the solution for the non-stiffened plate us0 has the lowest value of the group. in fig. 5 and fig. 6 a comparison of buckling coefficients according to differing cross-section shapes is proposed, varying aspect ratio , with range from 0.5 to 1.5; after  = 1.5, linear buckling coefficient values are constant. fig. 5 shows the solutions of k, comparing non-stiffened plates with open cross-section ones. fig. 6 shows the solutions of k, comparing non-stiffened plates with closed cross-section ones. for  < 1, cross-section cz7 is the best. tables 2-8 list the buckling coefficient values according to the theory (kth) and derived from numerical evaluation (knum). the difference between theoretical kth and numerical knum values is considerably large in many cases and numerical values are greater. this may be explained in two ways: 1) the numerical results show the restraining effect of each subpanel caused by the complementary one; 2) section area being equal, the second moment of area is not considered in theoretical calculations. 0 2 4 6 8 10 1 2 3 4 5 6 7 8 k us0 of1 ot2 ol3 ct4 cr5 cc6 cz7 e. maiorana, frattura ed integrità strutturale, 48 (2019) 459-472; doi: 10.3221/igf-esis.48.44 465 (a) (b) figure 5: buckling coefficient k vs. aspect ratio  with open section stiffening; subpanel a (a) and b (b). (a) (b) figure 6: buckling coefficient k vs. aspect ratio  with close section stiffening; subpanel a (a) and b (b). 4 5 6 7 0.5 0.7 0.9 1.1 1.3 1.5  k us0 of1 ot2 ol3 20 40 60 80 0.5 0.7 0.9 1.1 1.3 1.5  k us0 of1 ot2 ol3 4 6 8 10 12 0.5 0.7 0.9 1.1 1.3 1.5  k us0 ct4 cr5 cc6 cz7 10 30 50 70 90 110 0.5 0.7 0.9 1.1 1.3 1.5  k us0 ct4 cr5 cc6 cz7 e. maiorana, frattura ed integrità strutturale, 48 (2019) 459-472; doi: 10.3221/igf-esis.48.44 466  h' / h  = -1  = 0  = 1 kth knum kth knum kth knum 1.50 0.20 4.94 5.73 7.63 9.49 4.00 5.62 0.30 5.60 6.43 7.63 9.42 4.00 5.43 0.50 7.60 8.59 5.25 5.85 4.00 4.86 1.00 0.20 4.94 5.84 7.63 9.96 4.00 6.35 0.30 5.60 6.63 7.63 9.18 4.00 6.19 0.50 7.60 8.97 5.25 5.80 4.00 5.15 0.67 0.20 4.94 5.98 7.63 8.85 4.46 8.70 0.30 5.60 6.91 7.63 8.62 4.33 7.13 0.50 7.60 10.34 5.25 6.05 4.00 5.54 table 2: linear buckling coefficient for cross-section of1.  h' / h  = -1  = 0  = 1 kth knum kth knum kth knum 1.50 0.20 4.94 6.08 7.63 9.13 4.00 5.62 0.30 5.60 6.51 7.63 9.05 4.00 5.42 0.50 7.60 8.61 5.25 5.94 4.00 4.62 1.00 0.20 4.94 5.96 7.63 9.74 4.00 6.35 0.30 5.60 6.67 7.63 8.90 4.00 6.18 0.50 7.60 8.97 5.25 5.85 4.00 5.25 0.67 0.20 4.94 6.06 7.63 8.60 4.46 8.59 0.30 5.60 6.98 7.63 8.30 4.33 7.13 0.50 7.60 10.37 5.25 6.08 4.00 5.67 table 3: linear buckling coefficient for cross-section ot2.  h' / h  = -1  = 0  = 1 kth knum kth knum kth knum 1.50 0.20 4.94 6.10 7.63 8.96 4.00 5.62 0.30 5.60 6.60 7.63 8.90 4.00 5.43 0.50 7.60 8.54 5.25 6.05 4.00 5.02 1.00 0.20 4.94 6.04 7.63 9.67 4.00 6.27 0.30 5.60 6.74 7.603 8.84 4.00 6.12 0.50 7.60 9.05 5.25 5.97 4.00 5.34 0.67 0.20 4.94 6.12 7.63 8.47 4.46 8.08 0.30 5.60 7.11 7.63 8.18 4.33 7.13 0.50 7.60 10.52 5.25 6.14 4.00 5.80 table 4: linear buckling coefficient for cross-section ol3. e. maiorana, frattura ed integrità strutturale, 48 (2019) 459-472; doi: 10.3221/igf-esis.48.44 467  h' / h  = -1  = 0  = 1 kth knum kth knum kth knum 1.50 0.20 4.94 7.37 7.63 10.89 4.00 6.18 0.30 5.60 7.07 7.63 10.57 4.00 5.43 0.50 7.60 9.23 5.25 6.74 4.00 6.12 1.00 0.20 4.94 7.27 7.63 10.89 4.00 7.09 0.30 5.60 7.52 7.63 10.42 4.00 3.22 0.50 7.60 10.40 5.25 6.86 4.00 6.31 0.67 0.20 4.94 7.33 7.63 10.13 4.46 8.50 0.30 5.60 7.93 7.63 10.16 4.33 7.13 0.50 7.60 11.49 5.25 6.68 4.00 7.18 table 5: linear buckling coefficient for cross-section ct4.  h' / h  = -1  = 0  = 1 kth knum kth knum kth knum 1.50 0.20 4.94 7.36 7.63 11.56 4.00 6.51 0.30 5.60 8.75 7.63 11.26 4.00 6.63 0.50 7.60 9.80 5.25 7.23 4.00 6.89 1.00 0.20 4.94 9.93 7.63 11.56 4.00 7.42 0.30 5.60 8.84 7.63 11.32 4.00 7.38 0.50 7.60 10.30 5.25 7.25 4.00 7.28 0.67 0.20 4.94 9.93 7.63 10.33 4.46 8.66 0.30 5.60 9.06 7.63 10.58 4.33 7.95 0.50 7.60 11.78 5.25 7.12 4.00 7.83 table 6: linear buckling coefficient for cross-section cr5.  h' / h  = -1  = 0  = 1 kth knum kth knum kth knum 1.50 0.20 4.94 8.26 7.63 11.44 4.00 6.51 0.30 5.60 8.57 7.63 11.24 4.00 6.56 0.50 7.60 9.80 5.25 7.21 4.00 6.63 1.00 0.20 4.94 9.45 7.63 11.55 4.00 7.51 0.30 5.60 8.61 7.63 11.34 4.00 7.32 0.50 7.60 10.30 5.25 7.22 4.00 6.96 0.67 0.20 4.94 9.43 7.63 10.25 4.46 8.66 0.30 5.60 8.77 7.63 10.50 4.33 7.89 0.50 7.60 11.78 5.25 7.10 4.00 7.70 table 7: linear buckling coefficient for cross-section cc6. e. maiorana, frattura ed integrità strutturale, 48 (2019) 459-472; doi: 10.3221/igf-esis.48.44 468  h' / h  = -1  = 0  = 1 kth knum kth knum kth knum 1.50 0.20 4.94 7.18 7.63 11.92 4.00 6.68 0.30 5.60 9.19 7.63 13.22 4.00 6.75 0.50 7.60 9.94 5.25 7.51 4.00 6.89 1.00 0.20 4.94 9.60 7.63 11.88 4.00 7.59 0.30 5.60 9.29 7.63 11.64 4.00 7.45 0.50 7.60 10.55 5.25 7.46 4.00 7.12 0.67 0.20 4.94 10.80 7.63 10.78 4.46 8.74 0.30 5.60 9.46 7.63 11.12 4.33 8.08 0.50 7.60 11.88 5.25 7.34 4.00 7.95 table 8: linear buckling coefficient for cross-section cz7. stiffener positioning he optimal position of a stiffener with regard to web panel height is a function of the compressed subpanel (fig. 7). for  = 1, pure compression, the optimal position is h / h = 0.5, whereas for  = -1, pure bending, is h / h = 0.2 from the compressed edge. linear buckling analyses has been done for various positions of a longitudinal stiffener, from h / h = 0.14 to 0.5 with step 0.01, to cover the whole area of the compressed subpanel while  was set from -1 to 1 with step 0.25. a conventional flat stiffener was chosen, i.e. cross-section of1, the simplest section among those in tab. 1. figure 7: buckling coefficient k vs. stiffener position h / h for plate under pure bending moment. in order to analyse the variability of stiffeners geometric dimensions with respect to plate geometry, i.e., relative flexural stiffness, the relationship between stiffener thickness and width versus the elastic critical load of the plate was established. the resulting thickness/width groups were identified and four types were found (fig. 8). in case of1-i, the typical dimensions of the longitudinal stiffener were bst = 300 mm and tst = 10 mm, of1-ii bst = 100 mm and tst = 10 mm, of1-iii bst = 200 mm and tst = 20 mm, and of1-iv bst = 300 mm and tst = 30 mm. except of1-i (very flexible), the dimensions satisfy the relationship between width and thickness given by eqn. 9 12 355 y st st f b t (9) 0 4 8 12 16 0 0.2 0.4 0.6 0.8 1 h' / h k t e. maiorana, frattura ed integrità strutturale, 48 (2019) 459-472; doi: 10.3221/igf-esis.48.44 469 fig. 9 shows the relationship between the optimum value of stiffener position h / h and stress gradient  for the four groups. when   0, all the curves have enough h / h points in common; when  < 0, the positions of points h / h could be measured in each case. this is explained by the fact that, for   0, compression dominates bending, whereas for  < 0, bending dominates compression. in the latter case, stress distributions change in subpanels h and h ; accordingly, the optimal position differs in each load condition. increasing the value of  in the zone of positive abscissa, the optimal stiffener position moves toward the center-line of the plate, giving h / h = 0.5 in the case of pure compression stress,  = -1. (i) (ii) (iii) (iv) figure 8: plate a = 3 m, h = 1.5 m and t = 20 mm. out-of-plane displacements z from 1st buckling mode. figure 9: optimum value of stiffener position h / h vs. stress gradient  . looking at fig. 8, groups of1-i and of1-ii show marked deformation of the stiffener after the half-waves produced in the plate plan, reaching critical load; they were therefore classified as flexible types. group of1-iv shows a clear distinction 0.10 0.20 0.30 0.40 0.50 -1 -0.75 -0.5 -0.25 0 0.25 0.5 0.75 1  h' / h i ii iii iv -1 -0.75 -0.5 -0.25 0 0.25 0.5 0.75 1 -1 -0.75 -0.5 -0.25 0 0.25 0.5 0.75 1 -1 -0.75 -0.5 -0.25 0 0.25 0.5 0.75 1 -1 -0.75 -0.5 -0.25 0 0.25 0.5 0.75 1 -1 -0.75 -0.5 -0.25 0 0.25 0.5 0.75 1 -1 -0.75 -0.5 -0.25 0 0.25 0.5 0.75 1 -1 -0.75 -0.5 -0.25 0 0.25 0.5 0.75 1 e. maiorana, frattura ed integrità strutturale, 48 (2019) 459-472; doi: 10.3221/igf-esis.48.44 470 between the portions of plate divided by the stiffener; there are four half-waves instead of the three found in the other cases. group of1-iii shows behavior more similar to that of the first two groups, although there is less deformation as the value of the rigid stiffener in of1-iv is approached. therefore, an optimal cross-section stiffener in terms of relative flexural stiffness, corresponds to the curve described by group of1-iii and its interpolation equation, eqn.10, which shows that the optimal position on varying  is the following: h / h = ( 0.055  3  0.005  2 + 0.219  + 0.341) (10) with coefficient of determination r2 = 0.9991. alternately, the linear interpolation equation is: h / h = (0.179  + 0.339) (11) with coefficient of determination r2 = 0.9902. tab. 10 compares the results numerically, according to eqn.10 and eq.11, showing a good match. h / h  -1 -0.75 -0.5 -0.25 0 0.25 0.5 0.75 1 fem 0.17 0.20 0.24 0.28 0.34 0.40 0.44 0.48 0.50 [eq.10] 0.17 0.20 0.24 0.29 0.34 0.39 0.44 0.48 0.50 [eq.11] 0.16 0.20 0.25 0.29 0.34 0.38 0.43 0.47 0.52 table 10: results from numerical analyses, eq.10 and eq.11. fig. 10 shows the curve of the optimum value of stiffener position with respect to stress gradient  for optimal crosssection stiffener, in terms of relative flexural stiffness, together with results for the optimum location of stiffener determined according to an energy formulation and a sequential quadratic programming algorithm described in bedair 1997 [7]. figure 10: optimum value of h / h vs.  for optimal cross-section stiffener. comparison between results of eq.10 and results reported in bedair, 1997 . the comparison shows a good match considering the different approach and schematization of the beam web panel and stiffening. lastly, the following observations may be derived: for  < 0, the optimal position of the longitudinal stiffener depends on relative stiffness, and flexible and rigid stiffeners can be distinguished, particularly for  = -1; the best position y = -0.0549x 3 0.0048x 2 + 0.2192x + 0.3409 r 2 = 0.9991 0.10 0.20 0.30 0.40 0.50 0.60 -1 -0.75 -0.5 -0.25 0 0.25 0.5 0.75 1  h' / h e. maiorana, frattura ed integrità strutturale, 48 (2019) 459-472; doi: 10.3221/igf-esis.48.44 471 varies from 0.15h to 0.25h, depending on the relative rigidity of the system stiffener / plate (as confirmed in bedair 1997 [7]). for   0, the optimal position is independent of s and is a function of . conclusions hree open cross-sections (flat, t-shaped, l-shaped) and four closed ones (triangular, rectangular, circular, trapezoidal) longitudinal stiffeners, with equal area and differing second moment of area, were examined. through linear buckling analysis, buckling coefficient k was used to compare stiffeners contribution in terms of weight per linear meter. the following conclusions are reached:  for  < 1.5, rectangular cross-section shows the greater value while circular cross-section appeared to be the best shape to stiffen the plate for 1.5 <   2.  triangular cross-section makes the same contribution to stability with varying .  among the open-section stiffeners, the best characteristics were found in the profiles t-shaped and l-shaped crosssections, which show higher second moments of area.  flat cross-section makes the lowest contribution to the increase in buckling coefficient k.  respect to open cross-sections of equal area, with rectangular, circular and trapezoidal cross-sections, k decreases as  increases; local instabilities occur in closed cross-sections with greater slenderness.  with aspect ratio  = 1.5 and position of longitudinal stiffener h / h = 0.2, the minimal value of buckling coefficient k is for flat cross-section and maximum for circular.  comparing non-stiffened plates with closed cross-section ones, for the range  < 1, trapezoidal cross-section is the best. finally, longitudinal stiffeners, with optimal flexural stiffness,, set in various positions from the compressed edge were analysed and a useful practical law is given to correlate the best position with respect to variations in stress gradient . the results of numerical analyses were compared with those in the literature, to validate the proposed formulation, and a good match was obtained. references [1] timoshenko, s.p. and woinowsky-krieger, s. (1959). theory of plates and shells. mc-graw-hill book company. [2] xie, m. and chapman, j.c. (2004). design of web stiffeners: local panel bending effects. j. constr. steel res., 60(10), pp. 1425-1452. doi 10.1016/j.jcsr.2004.03.001. [3] lee, s.c., yoo, c.h. and yoon, d.y. (2002). behaviour of intermediate transverse stiffeners attached on web panels. j. struct. eng., asce, 128(3), pp. 337-345. [4] alinia, m.m. (2005). a study into optimization of stiffeners in plates subjected to shear loading. thin-walled struct., 43(5), pp. 845-860. doi 10.1016/j.tws.2004.10.008. [5] alinia, m.m. and moosavi, s.h. (2009). stability of longitudinally stiffened web plates under interactive shear and bending forces. thin-walled struct., 47(1), pp. 53-60. doi 10.1016/j.tws.2008.05.005. [6] maiorana, e., pellegrino, c. and modena, c. (2011). influence of longitudinal stiffeners on elastic stability of girder webs. j. constr. steel res., 67, pp. 51-64. doi 10.1016/j.jcsr.2010.07.005. [7] bedair, osama k. (1997). influence of stiffener location on the stability of stiffened plates under compression and inplane bending. int. j. mech. sci., 39(1) pp. 33-49. doi 10.1016/0020-7403(96)00017-3. [8] graciano, c. and casanova, e. (2005). ultimate strength of longitudinally stiffened i-girder webs subjected to combined patch loading and bending. j. constr. steel res., 61, pp. 93-111. doi 10.1016/j.jcsr.2004.07.006. [9] pavlovčič, l., detzel, a., kuhlmann, u. and beg, d. (2007). shear strength of longitudinally stiffened panels. part 1: tests and numerical analysis of imperfections. j. constr. steel res., 63, pp. 337-350. [10] g+d computing, (2005). strand7 user’s manual, sydney, australia. [11] maiorana, e. and pellegrino, c. (2011). linear buckling analysis of welded girder webs with variable thickness. steel and composite struct., 11(6), pp. 505-524. doi 10.12989/scs.2011.11.6.505. t e. maiorana, frattura ed integrità strutturale, 48 (2019) 459-472; doi: 10.3221/igf-esis.48.44 472 [12] pellegrino, c., maiorana, e. and modena, c. (2009). linear and non-linear behaviour of perforated steel plates with circular and rectangular holes under shear loading. tws, 47, pp. 607-616. doi 10.1016/j.tws.2008.11.001. [13] en 1993-1-5: 2007. eurocode 3. design of steel structures. part 1-5: stiffened plating subjected to in plane loading. cen european committee for standardization, brussels, belgium. [14] dubas, p. and gehri, e. (1986). behaviour and design of steel plated structures. 1st ed. institute of applied statics and steel structures ibs. swiss federal institute of technology eth zurich. eccs publication no. 44. [15] aashto (2018). lrfd bridge design specification. federal highway adm. washington d.c., usa. [16] en 1090-2: 2018. execution of steel structures and aluminium structures. part 2: technical requirements for steel structures. cen european committee for standardization, brussels, belgium. nomenclature a length of panel bst width of stiffener d flexural stiffness of plate h height of plate h  distance between stiffener center and edge subjected to compressive stress h  distance between stiffener center and edge subjected to tensile stress e young’s modulus ist second moment of area k buckling coefficient t thickness of plate tst thickness of stiffener x,y,z cartesian coordinates a aspect ratio s relative flexural stiffness  stress gradient  slenderness of plate σc compression stress σt traction stress  poisson’s ratio << /ascii85encodepages false /allowtransparency false /autopositionepsfiles true /autorotatepages /none /binding /left /calgrayprofile (dot gain 20%) /calrgbprofile (srgb iec61966-2.1) /calcmykprofile (u.s. web coated \050swop\051 v2) /srgbprofile (srgb 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can be opened with acrobat and adobe reader 5.0 and later.) >> /namespace [ (adobe) (common) (1.0) ] /othernamespaces [ << /asreaderspreads false /cropimagestoframes true /errorcontrol /warnandcontinue /flattenerignorespreadoverrides false /includeguidesgrids false /includenonprinting false /includeslug false /namespace [ (adobe) (indesign) (4.0) ] /omitplacedbitmaps false /omitplacedeps false /omitplacedpdf false /simulateoverprint /legacy >> << /addbleedmarks false /addcolorbars false /addcropmarks false /addpageinfo false /addregmarks false /convertcolors /converttocmyk /destinationprofilename () /destinationprofileselector /documentcmyk /downsample16bitimages true /flattenerpreset << /presetselector /mediumresolution >> /formelements false /generatestructure false /includebookmarks false /includehyperlinks false /includeinteractive false /includelayers false /includeprofiles false /multimediahandling /useobjectsettings /namespace [ (adobe) (creativesuite) (2.0) ] /pdfxoutputintentprofileselector /documentcmyk /preserveediting true /untaggedcmykhandling /leaveuntagged /untaggedrgbhandling /usedocumentprofile /usedocumentbleed false >> ] >> setdistillerparams << /hwresolution [2400 2400] /pagesize [612.000 792.000] >> setpagedevice microsoft word numero_30_art_57 g. belingardi et alii, frattura ed integrità strutturale, 30 (2014) 469-477; doi: 10.3221/igf-esis.30.57 469 focussed on: fracture and structural integrity related issues dynamic additional loads influencing the fatigue life of gears in an electric vehicle transmission g.belingardi, v. cuffaro, f. curà department of mechanical and aerospace engineering, politecnico di torino, torino (italy) giovanni.belingardi@polito.it, vincenzo.cuffaro@polito.it, francesca.cura@polito.it abstract. in recent years the implementation of the electric engine in the automotive industries has been increasingly marked. the speed of the electric motors is much higher than the combustion engine ones, bringing transmission gears to be subjected to high dynamic loads. for this reason the dynamic effects on fatigue life of these components have be taken into account in a more careful way respect to what is done with the usual gears. in the present work the overload effects due to both speed and meshing in a gear couple of an electric vehicle transmission have been analyzed. the electric vehicle is designed for urban people mobility and presents all the requirements to be certified as m1 vehicle (a weight less than 600 kg and a maximum speed more than 90 km/h). to investigate the overload effects of teeth in contact, the reference gear design standards (iso 6336) introduce a specific multiplicative factor to the applied load called internal dynamic factor (kv). aim of this work is to evaluate how dynamic overloads may influence the fatigue life of the above quoted gears in term of durability. to this goal, kv values have been calculated by means of the analytical equations (iso 6336 methods b and c) and then they have been compared with the results coming from multibody simulations, involving full rigid and rigid-flexible models. keywords. multibody simulations; electric vehicle; gear design. introduction n recent years, greater emphasis has been placed on the design of high-speed, lightweight, precision systems. both performance analysis and design of such systems can be greatly enhanced through transient dynamic simulations. the need for a better design has made necessary the insertion of many factors that have not been considered in the past. systems such as engines, robotics, machine tools and space structures may operate at high speeds and in very high temperature environments. in particular, the implementation of the electric engine in the automotive industries has been increasingly marked. the speed of the electric motors is much higher than the combustion engine ones, bringing transmission gears to be subjected to high dynamic loads. for this reason the dynamic effects on fatigue life of these components have be taken into account in a more careful way respect to what is done with the usual gears. i g. belingardi et alii, frattura ed integrità strutturale, 30 (2014) 469-477; doi: 10.3221/igf-esis.30.57 470 so, the behaviour of new automotive transmissions may be simulated with specific multibody programs, being these systems suitable to be described as a collection of subsystems called bodies and the motion of them is kinematically constrained. basic to any analysis of multibody mechanics is the understanding of the motion of subsystems (bodies or components). referring to this environment, a gear is a complex body with a specific geometry, as an example the modulus, the number of teeth, the face width and the contact ratio. once a gear is designed as a function of the power to be transmitted, it is necessary to analyse it from both kinematic and dynamic point of view [1]. some papers have been published about the numerical analysis of the dynamic meshing gears. most of them are based on lumped parameter models [2-5], where the teeth contact is represented by an equivalent mass, a stiffness and damping of the teeth. another way to address the contact analysis is related to fem simulations; this approach is helpful to determine the gear contact stiffness and the corresponding strain and stress distributions in the teeth. in particular the multibody kinematic approach uses a contact stiffness which depends on parameters that are not yet well understood [6]. in the present work the overload effects due to both speed and meshing in a gear couple of an electric vehicle transmission have been analyzed. the electric vehicle is designed for urban people mobility and presents all the requirements to be certified as m1 vehicle (a weight less than 600 kg and a maximum speed more than 90 km/h). the first aim of this research is to evaluate how the dynamic overloads may influence the fatigue life of the above quoted gears in term of durability. to this goal, a specific multiplicative factor to the applied load, called internal dynamic factor (kv), involved in iso 6336 standards [7-10] has been taken into account; kv values have been calculated by means of the related analytical equations (iso 6336 methods b and c [7]).then, the dynamic analysis of the above quoted two gears has been performed by means of the multibody software recurdyn (functionbay), in order to obtain the real response of the components. the model has been developed by tuning step by step the contact parameters of engaging pair of gears and by optimizing the integration parameters. forces values obtained by the simulations have been utilised to determine the dynamic factor kv involved in iso standard 6336 [7] for the calculation of gears load capacity. analytical results in terms of kv values have been compared with those coming from multibody simulations, involving full rigid and rigid-flexible models. gear model bject of this paper consists of two specific gears of a differential architecture for an electric vehicle. its design has been developed in order to keep as low as possible the transmission weight; in this work, a single speed stage gearbox has been chosen. transmission is constituted by an ordinary gear system and an epicyclical one named differential (see fig. 1). the ordinary gear system consists of four helical gears, the differential of four bevel gears (two pinions and two suns). from the dynamic point of view, only the ordinary gears system have to be taken into account; the transmitted torque passes directly to the wheel axes through the pinion and the vehicle has been analysed in a rectilinear motion condition. fig. 1 shows the complete transmission model that has been set up for the simulation. figure 1: complete transmission model. o g. belingardi et alii, frattura ed integrità strutturale, 30 (2014) 469-477; doi: 10.3221/igf-esis.30.57 471 the main design data of the four helical gears are reported in tab. 1 (engagement 1, gears 1 and 2; engagement 2, gears 3 and 4). all gears have been calculated according to iso 6336 standard [7-10]. in this work the engagement 2 has been considered (gears 3 and 4). gear 1 gear 2 gear 3 gear 4 pressure angle α 20 20 20° 20° helix angle β 30 (l.h.) 30 (r.h.) 30° (r.h.) 30° (l.h.) normal module mn 1.5 1.5 2 mm 2 mm number of teeth z 22 68 34 75 face width b 42 42 30 mm 30 mm table 1: main design dimensions of gear’s engagement 1 (input drive) and engagement 2 (final drive) multibody model he simulation of meshing gears has been analysed (see fig. 2). to obtain a correct simulation of this complex system, a lot of preliminary tests has been done in order to tune both kinematic and dynamic parameters. the final goal is to achieve a good matching between the multibody response and the corresponding theoretical one. in this paper two different type of contact have been realized; the first (fig. 2 on the left) consists of two rigid bodies in contact, the second (fig. 2 on the right) consists of two rigid-flexible bodies, simulating the gears web as a rigid body and the rim as flexible. since the system is very complex, the computational time is very high. so, it was necessary to properly calibrate the simulation before its starting. the best compromise between parameter’s calibration and the computational time has been searched. contact parameters have been changed from the default ones because the consequent increase in computation time is widely justified by the obtained improvement in the quality of the results. figure 2: multibody automotive transmission system, full-rigid on the left and rigid-flexible on the right. gears internal dynamic factor tandard design procedures compare the gears strength with a calculated stress value, in both bending and pitting cases. the most common approach used in calculation of these stress values, as widely described in iso standard 6336 part 1 [7], involves the use of influence factors, derived from results of research and field service. the influence factors may be distinguished between two categories, factors which are determined by gear geometry or which have been established by convention and factors which account for several influences and which are dealt with as independent of each other; in this last group is included the internal dynamic factor kv. as a matter of fact, even when the input torque and speed are constant, significant vibration of the gear masses and resultant dynamic tooth loads can exist. these loads result from the relative displacements between the mating gears as they vibrate in response to an excitation known as transmission error. t s g. belingardi et alii, frattura ed integrità strutturale, 30 (2014) 469-477; doi: 10.3221/igf-esis.30.57 472 the internal dynamic factor makes allowance for the effects of gear tooth accuracy grade as related to speed and load. high accuracy gearing requires less derating than low accuracy gearing.it is generally accepted that the internal dynamic load on the gear teeth is influenced by both design and manufacturing. “perfect” gears are defined as having zero quasi-static transmission error at the nominal transmitted (design)mesh torque. they can only exist for a single load and, with proper modifications, have zero dynamic effectszero transmission error (perfect conjugate action), zero excitation, no fluctuation at tooth mesh frequencyand no fluctuation at rotational frequencies. with zero excitation from the gears, there is zero response at any speed [7]. the internal dynamic factor kv takes into account the effects due to the rotating masses; iso 6336 part 1 [7] suggests three methods for calculating this factor. method a (kv-a) derives from the results of full scale load tests, precise measurements or comprehensive mathematical analysis of the transmission system and all gear and loading data shall be available, then this method, in this work, corresponds to the dynamic multibody analysis results. method a generally results the most sophisticated. method b (kv-b) is suited for all types of transmission, spur and helical gearing with any basic rack profile and any gear accuracy grade and, in principle, for all operating conditions. method c (kv-c) supplies average values which can be used for industrial transmissions and gear systems with similar requirements, with restriction in the application field. in the present paper methods b (kv-b) and c (kv-c) have been taken into account as the resolution of the corresponding equations described in detail in [7]. kv-b coefficient has been calculated on the basis of the different operating ranges (subcritical, main resonance, intermediate and supercritical ranges) related to the resonance ratio n of the mating gears [7]. firstly, the resonance running speed of the gear pair ne1 has been determined as a function of the reduced gear pair mass per unit face width, of the mesh stiffness and of the pinion number of teeth, as indicated in detail in [7]. then the resonance ratio n, where n=n1/ne1, has been calculated, being n1 is the rotational speed of the pinion in rpm. once the resonance ratio n has been obtained, the operating range has been determined as a function of the specific load ft· ka / b, according to [7],where ft is the tangential load, ka the application factor, b the gear face width and ns is the lower limit of the main resonance range. the dynamic factor kv-b has been computed for the different ranges, following the involved relationships indicated in [7]; non-dimensional parameters which take into account the effect of tooth deviations and profile modifications on the dynamic load are considered. in particular, it has been calculated for: subcritical range n ≤ ns (the majority of industrial gears operate in this range), main resonance range ns<n ≤ 1.15 (operation in this range should generally be avoided, especially for spur gears with unmodified tooth profile or helical gears of accuracy grade 6 or coarser, because the dynamic forces could be very high), supercritical range n ≥ 1.5 (most high precision gears used in turbine and other high speed transmissions operate in this range), intermediate range 1.15 <n< 1.5(the dynamic factor is calculated by linear interpolation between kv at n = 1.15 and kv at n = 1.5). according to method c [7], the dynamic factor kv-c has also been obtained as a function of the specific load (as kv-b), of the accuracy grades for spur and helical gears and of the tangential speed, without any attention to the operating ranges. result and discussion btained results are presented in this paper in terms of comparison between kv values related to the different calculation methods. for as concerns the methods biso 6336 [7], specific loads, resonance ratios, lower limits of main resonance range and corresponding kv-b values for each electric motor speed are reported in tab. 2; in particular, in column one is indicated the motor speed in rpm, in the second column is reported the specific loading of the gears, in the third one the resonance ration, in the fourth one the resonance ratio in the main resonance range and in the last one the internal dynamic factor of gear 4. for as concerns method c iso 6336[8], since the specific load is always lower than 100 n/mm for each class, the dynamic factor is a function of the tangential speed only. so, for the maximum tangential speed v = 12.02 m/s, kv is equal to 1.21. multibody simulation allows to determine contact forces involved in the calculation of dynamic parameters. the contact force components versus time of gear 4, obtained by the rigid simulation, are shown in fig. 3; the forces directions are referred to the ground system of the model. o g. belingardi et alii, frattura ed integrità strutturale, 30 (2014) 469-477; doi: 10.3221/igf-esis.30.57 473 the response of the elements (fig. 3) emphasizes an initial perturbation of the signal, but very quickly the behaviour of the system becomes stable and leads to the theoretical values. calculated averaged values are: force in x direction fx=157.18 n, force in y direction fy=-198.68 n and force in z direction fz=-134.69 n. electric motor rpm ft·ka/b n ns kv 500 71.85 0.02 0.80 1.01 1000 71.85 0.05 0.80 1.02 2000 71.85 0.09 0.80 1.05 3000 71.85 0.14 0.80 1.07 4000 65.32 0.19 0.78 1.10 5000 58.79 0.24 0.77 1.14 6000 45.72 0.30 0.74 1.20 7000 39.19 0.35 0.72 1.27 8000 35.93 0.41 0.71 1.33 9000 29.39 0.47 0.69 1.44 table 2: kv values in function of the electric motor speed. (a) (b) (c) figure 3: forces of the rigid simulation of gear 4, (a) contact force in x direction (radial force), (b) contact force in y direction (tangential force), (c) contact force in z direction (axial force). g. belingardi et alii, frattura ed integrità strutturale, 30 (2014) 469-477; doi: 10.3221/igf-esis.30.57 474 theoretical values of the above quoted forces may be calculated by the analytical combination of tangential, radial and axial components; these equilibrium equations are the following: x t rf f sinφ f cosφ    =157.18 [n] (1) y t rf f cosφ f sinφ     =-198.68 [n] (2) x af f  =-134.69 [n] (3) where tf , rf , af are respectively tangential, radial, axial forces and φ =15° is the misalignment angle of gears 3 and 4. from the analysis of fig. 3, it may be observed that numerical averaged forces well matches with the analytical ones. fig. 4 shows the internal dynamic factor (kv) trend of gear 4 during 6 second of the simulation. to calculate kv values, the following equation [7] has been used: static multibody fdynamic multibodytotal v static static static static ff ff k 1 1 f f f f       (4) where staticf is the static theoretical force of the meshing gears obtained by means of above quoted equations for gears 3 and 4, while dynamicf is the force trend obtained by means of the recurdyn simulation menus the static one. figure 4: dynamic factor of gear 4 for rigid simulation. by analysing the data reported in fig. 4, it is possible also to calculate the mean value of the dynamic factor (eq.(4)), that for gear 4 is equal to 1.125. this dynamic factor is very important to be determined already in the design phase because the fatigue strength of gears depends on it, as indicated in iso standard [7]. thanks to multibody simulations, however, it is possible to calculate a well defined value of kv as in experimental tests, even if a high computation time is required for the simulation of the complete model of the transmission (38 to 47 hours). the contact force components versus time of gear 4 obtained by the rigid-flexible simulation are shown in fig. 5; the forces directions are referred to the ground system of the model. averaged values are: force in x direction fx=157.2 n, force in y direction fy=-198.69 n force in z direction fz=-134.79 n. as it can be seen by fig. 5, the trend of the forces in the three directions, respect to the rigid simulation (fig. 3), is quite different, but the average values are practically the same. the difference is probably due to the flexibility of the teeth, as the rigid-flexible simulation results do not present the peaks emphasized in fig. 3. finally, the trend of kv factor (fig. 6) is proposed: the average value for gear 4 is 1.13, similar to that obtained by the rigid simulation. the trends of forces and of kv factor of the rigid-flexible simulation is slightly more accurate and do not present peaks respect to the rigid one, but a very high computational time has been required for this calculation (384 hours respect to a mean of 41 hours of the full rigid simulation). g. belingardi et alii, frattura ed integrità strutturale, 30 (2014) 469-477; doi: 10.3221/igf-esis.30.57 475 (a) (b) (c) figure 5: forces of the rigid-flexible simulation of gear 4, (a) contact force in x direction (radial force), (b) contact force in y direction (tangential force), (c) contact force in z direction (axial force). figure 6: dynamic factor of gear 4 for rigid-flexible simulation finally, tab. 3 resumes the mean values of the internal dynamic factor calculated respect to the iso standard [7] and by the multibody simulation respectively with rigid and rigid-flexible approaches: method internal dynamic factor (kv) iso standard method b 1.163 iso standard method c 1.210 multibody rigid simulation 1.125 multibody flexible-rigid simulation 1.130 table 3: kv values for gear 4. g. belingardi et alii, frattura ed integrità strutturale, 30 (2014) 469-477; doi: 10.3221/igf-esis.30.57 476 conclusions bject of the present paper is the simulation of the dynamic behaviour of an automotive transmission for electric vehicle by means a multibody approach, performed with the software recurdyn, so as to obtain some necessary information to be involved in the evaluation of the internal dynamic factor. the results obtained are very helpful in the evaluation of the dynamic loads. two different simulations have been done, the first has considered the two meshing gears as rigid bodies, the second one has been done with flexible rims and rigid webs. forces values have been compared to the corresponding theoretical ones and a very good agreement has been obtained. then, by processing force trends calculated with the multibody approach, the dynamic factor kv, involved in a fatigue study following the iso standard 6336 [10], has been determined for the gear 4. all obtained kv values match very well, emphasizing a similar dynamic behaviour of the system. it may be concluded that the multibody approach provides a satisfactory information about the dynamic response of the system in both instantaneous and averaged condition. however, on the basis of the obtained results, it may be observed that the more efficiency in calculation doesn’t justify the corresponding increasing in computational time by shifting from rigid (at maximum 47 hours) to flexible-rigid (384 hours) simulation, for as concerns the transmission considered in the present work. acknowledgements hanks to the regione piemonte for the financial support and bitron s.p.a. for the assistance. nomenclature α= pressure angle, °; β= helix angle, °; mn = normal module, mm; z = number of teeth; b = face width, mm; kv = internal dynamic factor; kv-a =internal dynamic factor calculating with method a of iso standard 6336-1 [7]; kv-b =internal dynamic factor calculating with method b of iso standard 6336-1 [7]; kv-c =internal dynamic factor calculating with method c of iso standard 6336-1 [7]; n = resonance ratio; ns = lower limit of the main resonance range; n1 = rotational speed of the pinion, rpm; ne1 = running speed of the gear pair, rpm; ft, fr, fa = tangential, radial, axial forces, n; ka = application factor; t af k / b = specific load, n/mm; fx ,fy, fz = forces in the main directions, n; v = maximum tangential speed, m/s. references [1] inc. functionbay. recurdyn/ solver theoretical manual, (2011). [2] kahraman, a., singh, r., non-linear dynamics of a spur gear pair, j. sound vib., 142 (1990) 49–75. o t g. belingardi et alii, frattura ed integrità strutturale, 30 (2014) 469-477; doi: 10.3221/igf-esis.30.57 477 [3] sato, k., yammamoto, s., kawakami, t., bifurcation sets and chaotic states of a gear system subjected to harmonic excitation, comput. mech., 7 (1991) 171–82. [4] blankenship, g.w., kahraman, a., steady state forced response of a mechanical oscillator with combined parametric excitation and clearance type non-linearity, j. sound vib., 185 (1995) 743–65. [5] rajendra, s., houser d.r., non-linear dynamic analysis of geared systems, cleveland: national aeronautics e space administration, (1990). [6] meagher, j., et al., a comparison of gear mesh stiffness modeling strategies, in: proc. of imac-xxviii (2010). [7] standard iso 6336-1, calculation of load capacity of spur and helical gears, part 1, international standard organization, geneva, (2006). [8] standard iso 6336-2, calculation of load capacity of spur and helical gears, part 2, international standard organization, geneva, (2006). [9] standard iso 6336-3, calculation of load capacity of spur and helical gears, part 6, international standard organization, geneva, (2006). [10] standard iso 6336-6, calculation of load capacity of spur and helical gears, part 1, international standard organization, geneva, (2006). microsoft word numero_50_art_44_2619 m. papachristoforou et alii, frattura ed integrità strutturale, 50 (2019) 526-536; doi: 10.3221/igf-esis.50.44 526 focused on the research activities of the greek society of experimental mechanics of materials use of by-products for partial replacement of 3d printed concrete constituents; rheology, strength and shrinkage performance michail papachristoforou, vasilios mitsopoulos, maria stefanidou laboratory of building materials, school of civil engineering, aristotle university of thessaloniki, greece papchr@civil.auth.gr, mitsopov@civil.auth.gr, stefan@civil.auth.gr abstract. in this paper, fly ash, ladle furnace slag and limestone filler were utilized in concrete used as material for additive manufacturing (3d printing). fly ash and ladle furnace slag were used as a replacement of cement (30% wt.) and limestone filler as a replacement of siliceous aggregates (50% wt.). workability of fresh concretes that contained these by-products was measured 0, 15 and 30 minutes after mixing. three different workability tests were conducted and compared: flow table, icar rheometer and an experimental method that measures the electric power consumption of the motor that rotates the screw extruder. workability parameters that were measured were evaluated regarding printability of mixtures. density, ultrasonic pulse velocity, compressive and flexural strength were measured on hardened concrete. additionally, relative likelihood of cracking of different concrete mixtures was estimated by performing restrained shrinkage test (astm c1581). results showed that use of fly ash or ladle furnace slag as binder, and limestone filler as aggregate decreases slightly the mechanical properties of concrete but improve its durability regarding cracking potential. monitoring of electric power consumption of screw extruder motor was found to be an effective method for measuring easily real-time workability and define if a mixture is printable or not. keywords. 3d printing, concrete; workability; astm c1581; shrinkage. citation: papachristoforou, m., mitsopoulos, v., stefanidou, m., use of by-products for partial replacement of 3d printed concrete constituents; rheology, strength and shrinkage performance, frattura ed integrità strutturale, 50 (2019) 526-536. received: 12.01.2019 accepted: 22.05.2019 published: 01.10.2019 copyright: © 2019 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. introduction -d printing technology is an additive manufacturing technique in which a structure is built layer by layer with various printing materials, based on a three dimensional (3d) model data. the first to introduce this technology in the construction industry using concrete as printing material was khoshnevis who invented the technique of contour crafting [1]. there has been a growing interest over the past decade upon 3d printing for civil engineering applications due to the advantages this method has compared to traditional concrete placing, such as the ability to construct freeform geometry without the need of formwork, construction speed and minimization of waste material and labour cost. today there are many research groups and industries working on the topic with successful applications (loughborough university [2], d-shape [3], 3 http://www.gruppofrattura.it/va/50/2619.mp4 m. papachristoforou et alii, frattura ed integrità strutturale, 50 (2019) 526-536; doi: 10.3221/igf-esis.50.44 527 apiscor [4], wasp [5], cybe constructions [6], winsun [7]), however daily practice still seems far away. this comes from the fact that construction industry is risk adverse and conservative in its practice but also because there are technical some challenges that need to be overcome to unlock and trigger all opportunities from 3d printing in building sector [8]. perhaps the greatest challenge of 3d printed concrete is to have a successful printing, meaning that the printed structure has the desired shape and material properties. printing system (type of printer, pump, printhead) and concrete fresh properties are the two factors that affect significantly printing quality. there are not any commercially available printers for concrete so researchers and industries have developed different types of prototype printers and printheads and properly configure mix design. focusing on the material, it must be flowable enough so that it can be extruded through the nozzle, meaning that the pump exerts enough stress to exceed the yield stress of concrete, causing it to flow and extrude through the nozzle. but once the layer is extruded, the concrete yield stress should be higher than the stress due to self weight in order to resist deformation. furthermore, the yield stress of the extruded concrete should increase even more in order to support the upcoming layers through thixotropy and cement hydration. therefore, concrete yield stress that can be measured using self compacting concrete (scc) tests becomes the most important parameter for mixture design and has an optimum range in which the material is both extrudable and buildable [9]. there are various research works studying fresh properties of 3d printed concrete using different tests. kazemian et al. [10] proposed a framework for accepting on not a mixture as printable. workability of a fresh printing mixture was tested using the flow table test and studied in terms of print quality and shape stability using measures of surface quality and dimensions of printed layers. perrot et al. [11] used a rotational rheometer to measure yield stress and compare the critical stress related to the plastic deformation with the vertical stress acting on the first printed layer. however, regardless the test adopted, testing procedure requires a sample of the material in order to be performed, meaning that printing procedure must be stopped for testing. for a given printing system, real time monitoring and active control of rheology during production by adding automatically chemical additives seems to be the most robust approach in order to address this challenge [8]. mixture proportions of concrete for 3d printing differ from ordinary one. regarding aggregates, in most cases only fine natural or crushed aggregate is used in order to allow the material to pass through the small pipes and nozzles at the printing head. while in ordinary concrete cement quantity is 270-350 kg/m³, concrete mixtures for 3d printing use higher amounts of cement (600-900 kg/m³) in order to improve consistency and strength [12]. however, increased cement content in combination with the absence of formwork that protects the freshly placed concrete against desiccation make the concrete volume more prone to shrinkage cracking compared to conventionally placed concrete. the use of supplementary cementitious materials (scm) such as fly ash, silica fume or slag as partially replacement of cement can improve crack resistance of concrete at early age [13]. chemical additives are also used to control workability and open time of fresh concrete for 3d printing which are related to printability and buildability [14]. printability can be defined as the capacity of concrete to pass through the small pipes and nozzles at the printing head and extrude continuously without blockage or fracture occurs, and buildability as the capacity to maintain its shape once deposited and not collapse under the load of subsequent layers [10]. the use of by-products in the production of 3d printed concrete has not been studied in the literature. the scope for using such alternative materials in concrete production is twofold; it can provide some technical improvements to the final product, but it is also expected to be beneficial from an environmental point of view [15]. this paper aims at developing effective and eco-friendly concrete mixtures for 3d printing by using by-products as binders and aggregates, measure fresh properties of these mixtures, correlate them with printability and buildability and finally, test mechanical properties and durability of hardened concretes in order to obtain the optimum materials and proportions. experimental program materials and printing system he industrial by-products that were used were high calcium (caofree content~10% wt.) fly ash (fa), ladle furnace slag (lfs) and limestone filler (lf). fa is produced in lignite fire power plants, lfs during steel production process and lf comes as a by-product from crushing of limestone. fa and lfs can be used as scms and increase durability of concrete [16,17,18], while lf is successfully used in self compacted concrete as filler material [19,20]. two sets of mixtures were produced in the laboratory, one with 500 kg/m³ and one with 830 kg/m³ total binder quantity. 10% of the binder was silica fume and 90% was cement type ii 52.5n. in some mixtures, 30% wt. of cement was replaced by fa or lfs passing from the 100μm sieve, while in others, lf replaced 50% wt. of siliceous river sand aggregates. the granulometry of lf, river sand and combination of both is given in fig.1. the proportions of all the mixtures produced are presented in tables 1 and 2, along with the type of by-products used in each mixture. from preliminary tests conducted, optimum superplasticizer and water quantities were obtained in order to have adequate and similar workability for all t m. papachristoforou et alii, frattura ed integrità strutturale, 50 (2019) 526-536; doi: 10.3221/igf-esis.50.44 528 mixtures. superplasticizer addition rate ranged from 2-3.4 % of binder and water to cement ratio 0.47-0.57 and 0.34-0.37 for the mixtures with 500 and 830 kg/m³ binder respectively. 0 25 50 75 100 0.01 0.1 1 p as si n g (% ) sieve (mm) limestone filler river sand composition figure 1: granulometry of aggregates used. materials (kg/m³) cl1 fl1 f1 ll1 l1 cement ii52,5n 450 350 350 350 350 silica fume 50 50 50 50 50 fly ash 100 100 ladle furnace slag 100 100 limestone filler 667 667 667 siliceous sand 667 667 1333 667 1333 water 289 280 242 280 237 superplasticizer 17 16 14 16 14 byproducts used binder fly ash fly ash lfs lfs aggregate limestone filler limestone filler limestone filler table 1: mixture proportions for 500 kg/m³ binder. materials (kg/m³) cl2 fl2 f2 ll2 l2 cement ii52,5n 747 582 582 582 582 silica fume 83 83 83 83 83 fly ash 165 165 ladle furnace slag 165 165 limestone filler 550 550 550 siliceous sand 550 550 1100 550 1100 water 308 308 281 308 281 superplasticizer 17 20 17 19 16 byproducts used binder fly ash fly ash lfs lfs aggregate limestone filler limestone filler limestone filler table 2: mixture proportions for 830 kg/m³ binder. m. papachristoforou et alii, frattura ed integrità strutturale, 50 (2019) 526-536; doi: 10.3221/igf-esis.50.44 529 a prototype printhead was introduced to extrude the mixtures. the diameter of the nozzle was 2 cm and a screw-kind extrusion system was selected for the extrusion process due to some of the advantages and easiness it offers in comparison to other extrusion methods (syringe extrusion) [21]. concrete tests fresh concrete properties were estimated using a rotational rheometer [22,23] and the flow table test according to en 1015-3 [24]. these tests were conducted 0, 15 and 30 min after mixing in order to determine the rate of which the workability is lost for the given 3d printing system and materials. however, performing of these tests requires extracting an adequate quantity of the material from the printing system and results are obtained after the test is completed. for this reason, a new method was implemented in order to estimate real-time workability of fresh concrete during printing by recording real time energy consumption of screw extruder motor. the method was calibrated with the rotational rheometer astm c1749 test [23] for measuring rheology characteristics of scc mixtures and the flow table test. the rotational rheometer test uses a rotating four-bladed vane. a strain gage measures deformation of the shaft rotating the vane and transforms it to torque and finally, yield stress. with the proposed method, the vane is substituted by the screw extruder and the complex strain gage recording apparatus fitted on the rotating shaft by a much simpler wattometer that records the watts of the motor that rotates the extruder. the same principle is used in ready-mix concrete plants where the power consumption of the mixer motor is recorded during mixing, making possible for the operator to adjust water quantity in order to obtain desired workability. by measuring real-time workability of mixture, it is possible to alter it manually or automatically by adding chemical additives in the print-head (superplasticizer, viscosity modifier, retarder etc.), using appropriate equipment as proposed by gosselin et al. [25]. the final workability parameters that were measured are presented in table 3. standard test apparatus parameter tested astm c 1749 rotational rheometer static yield stress (pa) en 1015-3:1999 flow table expansion (mm) real time monitoring of workability electric power consumption of electric motor rotating screw extruder (w) table 3: testes for measuring workability of 3d printing concrete. the threshold values of the above parameters were obtained in order to characterize the concrete mixture as printable, meaning that it can be extruded from the nozzle, and buildable. buildability was estimated by the number of layers of the printing specimen that can be achieved without collapse. malaeb et al. [26] proposed that 5 layers were considered to be the target and this was the method that was adopted. additionally, shape stability was another criterion for buildability and was estimated by measuring the dimensions of the first and fifth layer. the height ratio of the first layer versus fifth layer should be kept around 1 in order to accept the mixture as printable. final criteria for printability and buildability are given in table 4. characteristics of 3d printing concrete accepted not accepted printability 1. the mixture is extruded through the nozzle if 1 or 2 do not apply 2. good printing quality meaning no voids, no dimensional variations of extruded material buildability 3. five layers of printing material can be achieved without collapse if 3 or 4 do not apply 4. height of 1st layer versus height of 5th layer ~ 1 table 4: criteria for accepting concrete mixture as printable or not. regarding hardened concrete, compressive strength was measured on 40x40x40 mm cubes and 3-point flexural strength on 40x40x160 mm prisms after 28 days of curing in the humidity chamber. additionally, density and ultrasonic pulse velocity (upv) of concretes were also recorded. volume stability of mixtures, which is very important since shrinkage m. papachristoforou et alii, frattura ed integrità strutturale, 50 (2019) 526-536; doi: 10.3221/igf-esis.50.44 530 problems can be severe in 3d printing concrete due to high cement paste quantity, was also tested according to astm c1581-04 [27]. the procedure can be used to determine the effects of variations in the proportions and material properties of mortar or concrete on cracking due to both drying shrinkage and deformations caused by autogenous shrinkage and heat of hydration. the advantage of this test is that is more realistic since it measures concrete shrinkage under restrained conditions which occur in real applications. the apparatus consists of a steel ring with an outside diameter of 330 mm and height 152 mm and two strain gages at midheight locations on the interior surface of the steel ring along a diameter. the base, the outside steel ring surface and another outer ring with inner diameter 406 mm are used as a mould and concrete is poured. as concrete shrinks, it applies stress on the inner steel ring which is recorded in the form of deformation measured from the strain gages attached, until cracking occurs. results of the test are the age of concrete at cracking (days) and the stress rate at cracking ((mpa/day). in fig.2, a crack formed on concrete can be seen while fig.3 shows a typical diagram of age versus ring strain obtained from the measurements. figure 2: formation of crack on concrete due to restrained shrinkage. -60 -45 -30 -15 0 0 50 100 150 200 st ee l r in g st ra in x 1 06 specimen age (hours) figure 3: age versus steel ring stress obtained from the restrained shrinkage test. results results of workability 0, 15 and 30 minutes after mixing are given in tables 5 and 6. for the given printing system, it was soon realized that flow table expansion values, in order the mixture to be printable, should be between 18 and 24 cm. from the other tests, accurate threshold values could not be obtained. in figs.(4,5), flow table expansion versus the other parameters is given along with least squares regression lines and printable window (blue area with expansion 18-24 cm). for expansion less than 15 cm measured in some mixtures, no further testing was conducted since the mixtures were very stiff and could not be extruded. for the series of mixtures with low binder content (table 5), three out of five were considered as printable only for 0 minutes after mixing. after 15 minutes, all of the mixtures were considered as not printable. on the other hand, mixtures with high binder content (table 6) could be extruded but collapse 0 minutes after m. papachristoforou et alii, frattura ed integrità strutturale, 50 (2019) 526-536; doi: 10.3221/igf-esis.50.44 531 mixing, however printable mixtures were observed after 15 and even after 30 minutes. comparison of binder quantity with the workability parameters tested shows that when binder content increases, values of expansion and yield stress are increased. power consumption however is decreased and this can be attributed to the fact that higher quantity of cement renders to lower quantity of aggregate in a given volume of concrete and consequently, less friction induced by the aggregates in the moving parts of the screw extruder. mixtures with fa seem to lose more rapidly workability compared to mixtures with cement or cement and lfs as binder. no clear results were observed regarding the type of aggregates. cl1 fl1 f1 ll1 l1 expansion 0' 21 22 16.5 15.5 20.5 15' 16.5 17,5 17 30' 15,5 yield stress (pa) 0' 120 90 970 730 120 15' 1170 410 1170 30' 610 power consumption of screw extruder motor (w) 0' 732 680 741 812 694 15' 773 740 790 30' 784 table 5: workability results for mixtures with 500 kg/m³ binder. cl2 fl2 f2 ll2 l2 expansion 0' 30 28 29 22 23,5 15' 26 25 24 16,5 21 30' 23.5 18 19 15 18.5 yield stress (pa) 0' 90 0 0 30 90 15' 260 730 690 700 260 30' 440 1020 980 730 440 power consumption of screw extruder motor (w) 0' 615 605 605 651 643 15' 631 633 647 679 669 30' 647 684 665 698 683 table 6: workability results for mixtures with 830 kg/m³ binder. in fig.6, mixture f2 with river sand as aggregate and part of binder fa, can be seen 0 (left) and 15 minutes (right) after mixing. the mixture on the left, even though it fulfills criteria 1,2 and 3, does not meet criteria 4 regarding buildability, since height ratio of 1st layer versus 5th is 0.3, so it is characterized as not printable. on the other hand, the right specimen fulfills all 4 criteria and is characterized as printable. regarding hardened concrete properties, density of concretes with 500 and 830 kg/m³ binder was 2100 and 2225 kg/m³, respectively. compressive and flexural strength of mixtures is given in figs.(7,8). mixture with no scms as binder reached a compressive strength of 70 mpa. substituting 30% of cement with scms reduces compressive strength to 55 mpa and flexural strength from 12.1 to 8.7 mpa. similar strength development was observed for both fa and lfs mixtures. slightly lower strength was measured only in mixtures with fa, when limestone filler substituted 50% of natural sand. as expected, higher binder content showed increased strength. upv, a non destructive method to estimate strength, was also measured on specimens with the same moisture conditions and correlated with experimental results of compressive strength (fig.9). m. papachristoforou et alii, frattura ed integrità strutturale, 50 (2019) 526-536; doi: 10.3221/igf-esis.50.44 532 y = -0.0082x + 26.01 r² = 0.403 y = -0.0044x + 20.654 r² = 0.619 12 17 22 27 32 0 500 1000 1500 e xp an si on ( m m ) yield stress (pa) 830 kg/m3 500 kg/m3 figure 4: yield stress versus expansion along with printable window (blue area). y = -0.1528x + 121.82 r² = 0.9288 y = -0.0491x + 54.836 r² = 0.7645 12 17 22 27 32 580 680 780 880 e xp an si on ( m m ) power consumption (w) 830 kg/m3 500 kg/m3 figure 5: power consumption of screw extruder motor versus expansion along with printable window (blue area). figure 6: difference on printing quality due to different workability of the same mixture 0 (left) and 15 minutes (right)after mixing. m. papachristoforou et alii, frattura ed integrità strutturale, 50 (2019) 526-536; doi: 10.3221/igf-esis.50.44 533 results of the measurements of restrained shrinkage according to astm c1581 are given in figs.(10,11). mixtures with fa showed the best results since they lasted longer before crack formation occurs. for 830 kg/m³ binder, the mixture with fa cracked after 7.64 days while the mixture with no scms only after 4.88 days. mixtures with lfs had again better performance compared to one with no scms as binder, but not as good as fa based mixtures. use of lf as aggregate improves the time at cracking compared to mixtures with no lf. similar results were obtained from the stress rate calculation. mixtures with no scms induced higher stress to the ring compared to the other mixtures. 70.2 54.13 61.3 55.66 57.16 47.97 32.95 33.06 31.86 38.06 0 10 20 30 40 50 60 70 80 cement/lf cement/fa/lf cement/fa cement/lfs/lf cement/lfs 830 kg/m3 500 kg/m3 c om pr es si ve s tr en gt h (m p a) figure 7: compressive strength of mixtures with different binder content and materials used. 12.16 8.32 8.83 8.81 8.72 9.71 7.2 6.62 6.92 6.67 0 2 4 6 8 10 12 14 cement/lf cement/fa/lf cement/fa cement/lfs/lf cement/lfs 830 kg/m3 500 kg/m3 f le xu ra l s tr en gt h (m p a) figure 8: flexural strength of mixtures with different binder content and materials used. y = 0.0577x 199.55 0 30 60 90 3750 4000 4250 4500 4750 upv (m/s) c o m p re ss iv e st re n gt h (m p a) figure 9: ultrasonic pulse velocity versus compressive strength of mixtures. m. papachristoforou et alii, frattura ed integrità strutturale, 50 (2019) 526-536; doi: 10.3221/igf-esis.50.44 534 4.88 7.64 6.79 5.95 4.95 2.87 5.29 5.19 4.75 4.54 0.00 2.00 4.00 6.00 8.00 10.00 cement/lf cement/fa/lf cement/fa cement/lfs/lf cement/lfs 830 kg/m3 500 kg/m3 e la p se d tim e at c ra ck in g (d ay s) figure 10: time from molding to cracking for different mixtures. 0.00044 0.00024 0.00030 0.00030 0.00038 0.00068 0.00044 0.00042 0.00029 0.00028 0.0000 0.0002 0.0004 0.0006 0.0008 cement/lf cement/fa/lf cement/fa cement/lfs/lf cement/lfs 830 kg/m3 500 kg/m3 st re ss ra te (m p a/ da y) figure 11: stress rate at cracking for different mixtures. conclusions hree by-products, fly ash, ladle furnace slag and limestone filler, were used successfully in the production of concrete that can be applied with the 3d printing technique. workability and rheology of fresh concrete was measured by three different tests. the flow table expansion test described in the en 1015-3 was the most consistent one, and values of expansion between 18 and 24 cm were the optimum in order the mixture to be printed with the printing system used. electric power consumption of the motor that rotates the screw extruder was the method used for measuring real-time workability of the mixtures, making it possible to modify it on time in real scale applications by adding chemical additives during printing. regarding the type of materials used, mixtures with fa seem to lose more rapidly workability compared to mixtures with cement or cement and lfs as binder. however, this reduction of workability could possibly be addressed by using retarder admixtures. regarding hardened concrete, ultrasonic pulse velocity showed very good correlation with compressive strength measured experimentally, proving that it can be a reliable non-destructive testing of estimating strength of concrete on 3d printed concrete structures. however, for 3d concrete performance testing, the engineers must take into account the interface zone between layers. concerning the alternative binders used, when fa or lfs substituted 30% of cement, compressive strength dropped 20% and flexural strength 32%. natural sand substitution by lf had minimum effect on strength development. on the contrary, shrinkage of concrete under restrained conditions was lower for mixtures produced with fa, lfs and lf. fa showed the best results (57% improvement compared to mixture with no scms) followed by mixtures with lfs (22% improvement compared to mixture with no scms). utilization of lf again improved shrinkage behaviour, since time required for cracking increase by 12.5 to 20.5%. overall, lower cracking potential of the mixtures with the by-products can compensate lower strength performance, especially in case of 3d printing plain concrete, where there is no steel reinforcement to bear tensile loads induced under restrained concrete shrinkage and further research is suggested. t m. papachristoforou et alii, frattura ed integrità strutturale, 50 (2019) 526-536; doi: 10.3221/igf-esis.50.44 535 references [1] khoshnevis, b. (2004). automated construction by contour crafting-related robotics and information technologies. automation in construction, 13(1), pp. 5−19. doi: 10.1016/j.autcon.2003.08.012. [2] lim, s., et al. (2011). development of a viable concrete printing process. proc. 28th international symposium on automation and robotics in construction, (isarc2011), seoul, south korea, pp. 665−670. [3] cesaretti, g., dini, e., de kestelier, x., colla, v. and pambaguian, l. (2014). building components for an outpost on the lunar soil by means of a novel 3d printing technology. acta astronautica, 93, pp. 430−450. doi:10.1016/j. actaastro.2013.07.034. [4] website-6. (2019). apiscor | en. [online] available at: https://www.apis-cor.com/en [accessed 19 jan. 2019]. [5] 3dwasp.com. (2019). stampanti 3d | wasp | azienda leader nelsettoredellastampa 3d. [online] available at: https:// www.3dwasp.com. [6] cybe construction. (2019). cybe construction: redefining construction by enabeling 3d concrete printing by providing hardware, software, material, education, certification and business development. [online] available at: https://cybe.eu [7] winsun3d.com. (2019). contact usyingchuang building technique (shanghai) co.ltd. (winsun). [online] available at: http://www.winsun3d.com/en/contact/ [accessed 19 jan. 2019]. [8] schutter, g.d., lesage, k., mechtcherine, v., nerella, n.v., habert, g., agusti-juan, i. (2018). vision of 3d printing with concrete technical, economic and environmental potentials. cement and concrete research, 112, pp. 25−36. doi: 10.1016/j.cemconres.2018.06.001. [9] rahul, a.v., santhanam, m., meena, h., ghani, z. (2019). 3d printable concrete: mixture design and test methods. cement and concrete composites, 97, pp. 13–23. doi: 10.1016/j.cemconcomp.2018.12.014. [10] kazemian, a., yuan, x., cochran, e. and khoshnevis, b. (2017). cementitious materials for construction-scale 3d printing: laboratory testing of fresh printing mixture. construction and building materials, 145, pp. 639−647. doi: 10.1016/j.conbuildmat.2017.04.015. doi: 10.1016/j.conbuildmat.2017.04.015. [11] perrot, a., rangeard, d., pierre, a. (2016). structural built-up of cement-based materials used for 3d-printing extrusion techniques. materials and structures, 49, pp. 1213−1220. doi: 10.1617/s11527-015-0571-0. [12] le, t., austin, s., lim, s., buswell, r., gibb, a. and thorpe, t. (2012). mix design and fresh properties for high-performance printing concrete. materials and structures, 45(8), pp. 1221−1232. doi:10.1617/s11527-012-9828-z. [13] ma, l., zhao, y. and gong, j. (2018). restrained early-age shrinkage cracking properties of high-performance concrete containing fly ash and ground granulated blast-furnace slag. construction and building materials, 191, pp. 1−12. doi: 10.1016/j.conbuildmat.2018.09.154. [14] marchon, d., kawashima, s., bessaies-bey, h., mantellato, s. and ng, s. (2018). hydration and rheology control of concrete for digital fabrication: potential admixtures and cement chemistry. cement and concrete research, 112, pp. 96−110. doi: 10.1016/j.cemconres.2018.05.014. [15] anastasiou, e., liapis, a., papachristoforou, m. (2017). life cycle assessment of concrete products for special applications containing eaf slag, procedia environmental sciences, 38, pp. 469−476. doi: 10.1016/j.proenv.2017.03.138 [16] anastasiou, e., papayianni, i. (2012). use of calcareous fly ash in scc, conference: eurocoalash 2012 conference, thessaloniki, greece. [17] anastasiou, e., papayianni, i., papachristoforou, m. (2014). behaviour of self compacting concrete containing ladle furnace slag and steel fiber reinforcement, materials and design, 59, pp. 454−460. doi: 10.1016/j.matdes.2014.03.030. [18] sideris, k., tassos, ch., chatzopoulos, a., manita, p. (2018). mechanical characteristics and durability of self compacting concretes produced with ladle furnace slag. construction and building materials, 170, pp. 660−667. doi: 10. 1016/j.conbuildmat.2018.03.091. [19] shadkam, h.r., dadsetan, s., tadayon, m., sanchez, l.f.m., zakeri, j.a. (2017). an investigation of the effects of limestone powder and viscosity modifying agent in durability related parameters of self-consolidating concrete (scc), construction and building materials, 156, pp. 152−160. doi: 10.1016/j.conbuildmat.2017.08.165. [20] ling, s.k., kwan, a.k.h. (2016). adding limestone fines as cementitious paste replacement to lower carbon footprint of scc, construction and building materials, 111, pp. 326−336. doi: 10.1016/j.conbuildmat.2016.02.072. [21] li, w., ghazanfari, a., leu, m.c., landers, r.g. (2015). methods of extrusion on demand for high solids loading ceramic paste in freeform extrusion fabrication. proc. solid freeform fabrication symposium 2015, austin, tx, pp. 332−345. [22] koehler, e., fowler, d. (2004). [online] available at: https://repositories.lib.utexas.edu/handle/2152/35338. [23] en1015-3. (1999). methods of test for mortar for masonry, part 3: determination of consistence of fresh mortar (by flow table). m. papachristoforou et alii, frattura ed integrità strutturale, 50 (2019) 526-536; doi: 10.3221/igf-esis.50.44 536 [24] astm c1749-17a. (2017). standard guide for measurement of the rheological properties of hydraulic cementious paste using a rotational rheometer. doi: 10.1520/c1749-17a [25] gosselin, c., duballet, r., roux, ph., gaudillière, n., dirrenberger, j., morel, ph. (2016). large-scale 3d printing of ultra-high performance concrete a new processing route for architects and builders. materials and design, 100, pp. 102−109. doi: 10.1016/j.matdes.2016.03.097. [26] malaeb, z., hachem, h., tourbah, a., maalouf, t., el zarwi, n., hamzeh, f. (2015). 3d concrete printing: machine and mix design. international journal of civil engineering and technology, 6, pp. 14−22. 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can be opened with acrobat and adobe reader 5.0 and later.) >> /namespace [ (adobe) (common) (1.0) ] /othernamespaces [ << /asreaderspreads false /cropimagestoframes true /errorcontrol /warnandcontinue /flattenerignorespreadoverrides false /includeguidesgrids false /includenonprinting false /includeslug false /namespace [ (adobe) (indesign) (4.0) ] /omitplacedbitmaps false /omitplacedeps false /omitplacedpdf false /simulateoverprint /legacy >> << /addbleedmarks false /addcolorbars false /addcropmarks false /addpageinfo false /addregmarks false /convertcolors /converttocmyk /destinationprofilename () /destinationprofileselector /documentcmyk /downsample16bitimages true /flattenerpreset << /presetselector /mediumresolution >> /formelements false /generatestructure false /includebookmarks false /includehyperlinks false /includeinteractive false /includelayers false /includeprofiles false /multimediahandling /useobjectsettings /namespace [ (adobe) (creativesuite) (2.0) ] /pdfxoutputintentprofileselector /documentcmyk /preserveediting true /untaggedcmykhandling /leaveuntagged /untaggedrgbhandling /usedocumentprofile /usedocumentbleed false >> ] >> setdistillerparams << /hwresolution [2400 2400] /pagesize [612.000 792.000] >> setpagedevice microsoft word numero_30_art_52 p.n.b. reis et alii, frattura ed integrità strutturale, 30 (2014) 431-437; doi: 10.3221/igf-esis.30.52 431 focussed on: fracture and structural integrity related issues interlaminar fracture in woven carbon/epoxy laminates paulo n.b. reis department of electromechanical engineering, university of beira interior preis@ubi.pt josé a.m. ferreira, josé d.m. costa cemuc, department of mechanical engineering, university of coimbra martins.ferreira@dem.uc.pt, jose.domingos@dem.uc.pt antónio m. pereira estg/cdrsp, polytechnic institute of leiria mario.pereira@ipleiria.pt abstract. this paper describes an experimental study developed to characterize the mode i and mode ii fracture toughness of carbon/epoxy woven composites, using dcb and enf tests, respectively. the laminates were manufactured using an epoxy resin and twelve woven balanced bi-directional layers of carbon fibres, all of them with the same orientation (0/90º). significant instantaneous delaminations were observed particularly for the dcb specimen, which were responsible for an oscillatory behaviour of gi versus crack length. the maximum values obtained for gic and giic were 281 and 1800 j/m 2, respectively. keywords. carbon fibre reinforced composites; delamination; fracture toughness; mechanical testing. introduction mpacts at low velocity are the main cause of in-service delaminations, which are very dangerous because they are not easily detected visually [1, 2] and they can affect significantly the residual properties and structural integrity [3-8]. in this context, for design purpose it is very important to understand the interlaminar fracture toughness properties of fibre reinforced composite materials. if the double cantilever beam (dcb) test is one of the most popular to determine gic, because it presents simple specimen geometry and a stable crack growth in loading under displacement control, for mode ii the most popular tests are the end-notched flexure (enf), end-loaded split (els) and the four-point endnotched flexure (4enf) [9]. however, according to the morais and pereira [9], the enf specimen combined with the ecm (effective crack method) is the best solution for the characterization of mode ii fracture with some advantages like simplicity, negligible friction effects and low tendency for geometric non-linearity. for carbon fibre reinforced epoxies resins, it was found that the typical values of gic in stable propagation are around 260 j/m2 [10]. in order to improve the interlaminar toughness of the composites materials the bibliography suggests the application of the thermoplastic resins [10], due their high damage tolerance, or by insertion of ductile resin interleaf between each carbon fibre/epoxy layers [11]. an alternative to the toughened resins is the use of advanced textile technologies with substantially improved delamination resistance [12, 13]. it was demonstrated that gic values for the knitted composites are about 10 or 20 times higher than for the uniweave composite [6]. chen et al. [10] observed that the values of gic, in stable propagation, have a dropping tendency with increasing fibre content in the range 21-39% and i p.n.b. reis et alii, frattura ed integrità strutturale, 30 (2014) 431-437; doi: 10.3221/igf-esis.30.52 432 higher fibre bridging. the fibre direction was studied by miyagawa et al. [14] and they found that the lowest values were obtained with samples whose fibre direction was 90º. it is evident by the literature that the resistance to crack growth depends of the laminates, in terms of their constituents and set up. therefore, the present paper describes an experimental study developed to characterize mode i and mode ii fracture toughness using dcb and enf tests, respectively, in carbon/epoxy woven composites. experimental procedure omposite laminate sheets were manufactured using twelve woven, balanced, bi-directional, layers of carbon fibres (with 196 g/m2) all of them with the same orientation 0/90º, and an epoxy resin matrix. fibres and resin were hand placed in a mould. the mould was then put into a vacuum bag producing 0.1 mpa during 8 hours for curing at room temperature. the fibre volume fraction (vf) was 0.66 and the average plate thickness was 3 mm. details about the manufacture process of the composites laminates can be found in previous work of the authors [15]. a 100 m ptfe film was introduced into the plates during moulding of the laminates in order to generate the starter crack. fig. 1 shows the fibre distribution along the longitudinal direction. the fibre angle misalignment was determined using the designer 6.0 software and an average angle of 5.2º was obtained, with a standard deviation of 1.7º. figure 1: lateral view photo showing the fibre distribution along of the longitudinal direction of the specimen. a) b) figure 2: a) dcb specimen (mode i); b) enf specimen (mode ii). dimensions in mm. the experimental work involved double cantilever bean (dcb) and end-notched flexure (enf) tests. the specimens of composite material were cut by a diamond table saw from the original plates, 300 mm long and 100 mm wide, aligned with one fibre direction. the geometry and dimensions of the specimens are shown in fig. 2. dcb specimens were used with 180 mm length, 25 mm width and initial crack lengths (ao) of 30, 45 and 50 mm. two piano hinges were bonded to both surfaces of the specimen at the cracked end for load transmission. the piano hinges and the specimens were gritblasted with sandpaper before bonding and cleaned with alcohol impregnated soft paper. the adhesive used for bonding was an araldite 420 a/b bi-component. the dcb tests (fig. 2a) were performed in tension, according to astm d 5528c p.n.b. reis et alii, frattura ed integrità strutturale, 30 (2014) 431-437; doi: 10.3221/igf-esis.30.52 433 01 [16], using an electromechanical machine, shimadzu model ag-x, equipped with a 1kn load cell. the enf tests were carried out in the same machine in accordance with the literature [17, 18-19]. fig. 2b is a schematic view of the three point bending apparatus and the specimens’ dimensions with an initial crack (ao) of 30 mm. the load level, the displacement and the crack length were recorded during the tests. in order to obtain accurate results the crack length was measured using ccd camera, pco model pixelfly 270 xs, as shown in fig. 3. figure 3: dbc test apparatus with ccd camera video image. for each condition four samples was tested and the experiments carried out with the crosshead velocity of 0.5 mm/min for loading the samples [14]. in all samples one of the edges was painted with nail varnish and then several marks were made for determination of the crack length. results and discussion ig. 4a and 4b show the experimental load-displacement curves from the dcb and enf tests, respectively. relatively to dcb tests, fig. 4a, representative curves are presented for the initial cracks (ao) of 30, 45 and 50 mm. it is possible to observe that longer initial cracks produce curves with lower slopes. for the same displacement, the increase of initial crack length decreases the loads. all of them exhibit oscillatory behaviour, which is explained by the unstably crack propagation. in this case the load drops suddenly at a certain displacement and the crack propagates rapidly, increasing again the load with the displacement until a new drop occurs suddenly. according with several studies [11, 20-21] the unstable crack propagation is consequence of regions with different toughness. when the crack reaches the tougher region, it slows down until the rate of release of elastic stored energy is sufficient to propagate the crack through the tougher region. the release rate of stored energy is then higher than that required for stable growth. the crack then accelerates and unstable fracture occurs [20]. in fact it is possible to observe in fig. 1 regions with reduced amounts of resin, where the fibres practically contact, while other regions are rich in resin. therefore there are regions with different toughness which explain the unstable propagation observed. for mode ii specimens (enf), fig. 4b presents two experimental load-displacement curves for ao = 30 mm, which are reproducible and similar to other reported in literature [9, 14, 17]. an offset of 10 mm is represented between curves in order to obtain more details about their evolution. in this case unstably crack propagation was also observed but less significant. fig. 5 shows the interlaminar fracture toughness (gi) against the increment of the crack length (a). each value of gi is an average of four tests. according to the astm d 5528-01 standard [16], the mbt data reduction method was used because it promotes the most conservative values of gic. therefore, gic was calculated by the following equation: f p.n.b. reis et alii, frattura ed integrità strutturale, 30 (2014) 431-437; doi: 10.3221/igf-esis.30.52 434 )2.b.(a 3.p. i g δ δ   (1) where p is the load, δ is the load contact point displacement, b is the specimen width, a is the delamination length and δ is the modulus of a correction factor. this factor is obtained experimentally by generating a least squares plot of the cube root of the compliance c against the delamination length a (δ is the value for c1/3 equal to zero). it is possible to observe an initial stage, which is characterized by an increasing of the interlaminar fracture toughness (gi) with the crack length. after reaching a maximum value, or very close to it, is almost constant independently of crack length. this phenomenon agrees with fig. 4, where the load increases with the increase of the displacement and, after a peak load, unstable crack propagation can be observed promoting an oscillatory behaviour of gi. a) b) figure 4: typical load-displacement curves for: a) dcb tests, b) enf tests. gic values for the different initial crack lengths are presented in tab. 1. according to the astm d 5528-01 standard [16], three definitions for an initiation value of gic can be used. in the present study the gic values were determined using the load and deflection measured at the point at which the compliance has increased by 5 % or the load has reached a maximum value (5 %/max) [16]. however, the intersection of the load-deflection curve occurs after the maximum load point for all tests performed. therefore, the maximum load was used to calculate gic values according to the standard. figure 5: gi versus crack length. p.n.b. reis et alii, frattura ed integrità strutturale, 30 (2014) 431-437; doi: 10.3221/igf-esis.30.52 435 according with tab. 1, it is possible to observe that only a small decrease of the interlaminar fracture toughness occurs, around 7.5%, which means that the gic parameter is practically independent of the initial delamination length. therefore, for the present laminates, the average value of gic is around 281 j/m2. initial crack length (a0) 30 mm 45 mm 50 mm gic [j/m2] 292.3 279.6 270.4 sd [j/m2] 65.6 63.6 58.1 table 1: gic values versus delamination length. fig. 6 presents the energy release rate for mode ii specimens and the formulation used to obtain g can be found in the work of morais and pereira [9]. therefore, giic was calculated by the following equation: 3 1 2 2 e 2 .h.e16.b .a9.p ii g  (2) where p is the load, b is the specimen width, h is the specimen thickness, e1 is the flexural modulus ae is expressed by the eq. (3): 3 3 f 3 1 e 3 2.l.cb.h8.e . a   (3) where l is half of the spam length (50 mm) cf given by eq. (4): .b.h10. 3.l cc 13 f    (4) where 13is the shear moduli c the specimen compliance expressed by eq. (5): .b.h10 3.l .b.h8.e )3.(a2.l c 13 3 1 3 ii 3 .    (5) and, finally, for carbon fibers, δii is expressed by the following equation: 13 72. 1 e h. ii   (6) p.n.b. reis et alii, frattura ed integrità strutturale, 30 (2014) 431-437; doi: 10.3221/igf-esis.30.52 436 the giic results obtained with the enf specimen show a stable increase up to the peak value observed for an effective crack length of about 43 mm. the maximum values obtained for giic is around 1800 j/m2. figure 6: gii versus crack length. conclusions he delamination of carbon-epoxy laminated composites was studied using mode i dcb specimen and mode ii enf specimens. notched specimens were prepared, and tested under quasi-static loading, in order to obtain the load-displacement curves and energy release rate versus crack length. significant instantaneous delaminations were observed particularly for all the dcb specimen independently initial crack delamination length. the mode i critical energy release rate showed some oscillatory behaviour, explained by the instantaneous delaminations. the maximum values obtained for gic and giic were 281 and 1800 j/m2, respectively. references [1] adams, r.d., cawley, p.d., a review of defects types and non-destructive testing techniques for composites and bonded joints. ndt int., 21 (1998) 208-222. [2] amaro, a.m., reis, p.n.b., de moura, m.f.s.f., santos, j.b., damage detection on laminated composite materials using several ndt techniques. insight, 54 (2012) 14-20. [3] caprino, g., residual strength prediction of impacted cfrp laminates. j. compos. mater., 18 (1984) 508-518. [4] davies, g.a.o., hitchings, d., zhou, g., impact damage and residual strengths of woven fabric glass/polyester laminates. compos. part a-appl. s., 27 (1996) 1147-1156. [5] de moura, m.f.s.f., marques, a.t., prediction of low velocity impact damage in carbon-epoxy laminates. compos. part a-appl. s., 33 (2002) 361-368. [6] amaro, a.m., de moura, m.f.s.f., reis, p.n.b., residual strength after low velocity impact in carbon-epoxy laminates. mater. sci. forum, 514-516 (2006) 624-628. [7] amaro, a.m., reis, p.n.b., de mouram m.f.s.f., delamination effect on bending behaviour in carbon–epoxy composites. strain, 47 (2011) 203-208. [8] reis, p.n.b., ferreira, j.a.m., antunes, f.v., richardson, m.o.w., effect of interlayer delamination on mechanical behavior of carbon/epoxy laminates. j. compos. mater., 43 (2009) 26092621. t p.n.b. reis et alii, frattura ed integrità strutturale, 30 (2014) 431-437; doi: 10.3221/igf-esis.30.52 437 [9] morais, a.b., pereira, a.b., application of the effective crack method to mode i and mode ii interlaminar fracture of carbon/epoxy unidirectional laminates. compos. part a-appl. s., 38 (2007) 785-794. [10] chen, j.h., schulz, e., bohse, j., hinrichsen, g., effect of fibre content on the interlaminar fracture toughness of unidirectional glass-fibre/polyamide composite. compos. part a-appl. s., 30 (1999) 747-755. [11] matsuda, s., hojo, m., ochiai, s., murakami, a., akimoto, h., ando, m., effect of ionomer thickness on mode i interlaminar fracture toughness for ionomer toughened cfrp. compos. part a-appl. s., 30 (1999) 1311-1319. [12] kim, k.y., curiskis, j.i., ye, l., fu, s.y., mode i interlaminar fracture behaviour of weft-knitted fabric reinforced composites. compos. part a-appl. s., 36 (2005) 954-964. [13] mouritz, a.p., baini, c., herszberg, i., mode i interlaminar fracture toughness properties of advanced textile fiberglass composites. compos. part a-appl. s., 30 (1999) 859-870. [14] miyagawa, h., sato, c., ikegami, k., interlaminar fracture thoughness of cfrp in mode i and mode ii determined by raman spectroscopy. compos. part a-appl. s., 32 (2001) 477-486. [15] reis, p.n.b., ferreira, j.a.m., costa, j.d.m., richardson, m.o.w., fatigue life evaluation for carbon/epoxy laminate composites under constant and variable block loading. compos. sci. technol., 69 (2009) 154-160. [16] standard test method for mode i interlaminar fracture toughness of unidirectional fiber-reinforced polymer matrix composites, astm standard d 5528-01. philadelphia, pa: american society for testing and materials, 2001. [17] pereira, a.b., morais, a.b., mode ii interlaminar fracture of glass/epoxy multidirectional laminates. compos. part aappl. s., 35 (2004) 265-272. [18] davies, p., blackman, b.r.k., brunner, a.j., standard test methods for delamination resistance of composite materials: current status. appl. compos. mater., 5 (1998) 345-364. [19] davies, p., sims, g.d., blackman, b.r.k., brunner, a.j., kageyama, k., hojo, m., tanaka, k., murri, g., rousseau, c., gieseke, b., martin, r.h., comparison of test configurations for determination of mode ii interlaminar fracture toughness: results from international collaborative test programme. plast. rubber compos., 28 (1999) 432-437. [20] kotaki, m., hamada, h., effect of interfacial properties and weave structure on mode i interlaminar fracture behaviour of glass satin woven fabric composites. compos. part a-appl. s., 28 (1997) 257-266. [21] ozdil, f., carlsson, l.a., mode i interlaminar fracture of interleaved graphite/epoxy. j. comp. mater., 26 (1992) 433458. microsoft word numero 12 art 9 a. risitano et alii, frattura ed integrità strutturale, 12 (2010) 88-99; doi: 10.3221/igf-esis.12.09 88 analisi termica per la valutazione del comportamento a fatica di provini soggetti a successive serie di carichi antonino risitano università di catania, dipartimento d’ingegneria industriale e meccanica; viale a. doria 6, 95125 catania, italia arisitan@diim.unict.it giacomo risitano università degli studi guglielmo marconi, facoltà di scienze e tecnologie applicate; via plinio 44, 00193 roma, italia; g.risitano@unimarconi.it riassunto. partendo dalla osservazione che provini precedentemente danneggiati hanno un limite di fatica differente (vedi miner) viene esaminato il comportamento di un acciaio soggetto a serie di carichi affaticanti al fine di verificare la conseguente risposta termica. l’esame, mediante analisi termica, delle prove di fatica su provini di acciaio c40 danneggiati a diverso grado, da interessanti indicazioni sul ruolo dei carichi applicati in relazione alla possibilità di produrre danno nel materiale. viene messo in evidenza come la temperatura, conseguenza dell’energia consumata dal provino, possa essere elemento indicativo dello stato del materiale. vengono riportate le curve di fatica e le curve di temperatura di provini lisci sottoposti a storie di carico diverse. da esse si può evincere che mentre è valida la legge di linearità del danno (σini/ni= cost), la curva definita secondo la regola del miner-manson (σini/ni=1), che tiene solo conto del numero di volte in cui la tensione supera il limite di fatica del materiale (provini lisci), invece, non sempre rispecchia il reale stato di danno. questo specialmente quando si è in presenza di carichi prossimi al limite di fatica che, per la sequenza dell’applicazione, possono diventare carichi affaticanti. abstract. starting from the observation that previously damaged specimens have a fatigue limit differences (see miner), the behavior of a steel, subject to series of fatigue loads, was examined to verify the resulting thermal response. the review, by thermal analysis, fatigue tests on samples of steel c40 damaged in varying degrees, provides valuable insights on the role of loads applied in relation to the possibility of producing damage in the material. the temperature, therefore the energy consumed, is an element indicative of the state of the material. the fatigue curves and the curves of temperature of smooth specimens, subjected to different load histories have been reported. these are demonstrated that a valid law of linear damage (σini/ni= cost), but the curve defined under the rule of miner-manson (σini/ni=1), which takes into account only the number of times the stress exceeds the fatigue limit of the material (smooth specimens), however, does not always reflect the actual state of damage. especially when the loads are close to the fatigue limit, for the sequence of the application, loads can become fatiguing. parole chiave. termografia; limite di fatica; teoria del danno; miner. http://dx.medra.org/10.3221/igf-esis.12.09&auth=true http://www.gruppofrattura.it a. risitano et alii, frattura ed integrità strutturale, 12 (2010) 88-99; doi: 10.3221/igf-esis.12.09 89 introduzione noto che la rottura per fatica avviene quando nel materiale la sollecitazione a livello locale supera certi valori per cui si generano deformazioni irreversibili. durante questa fase come già osservato da taylor e quinney [1] la quasi totalità dell’energia è convertita in calore. in ogni caso, tale quantità di calore, e di conseguenza la temperatura, risulta funzione di un coefficiente β dipendente, nel caso più generale, da diversi fattori: la deformazione plastica, l’entropia, la densità di dislocazione. secondo mason et al. [2], per valori di tensione inferiori al limite di fatica (low stress region) l’energia del ciclo di isteresi è dovuta a meccanismi dissipativi “anelastici” che non procurano danni sul materiale. per valori superiori al limite di fatica (high stress region) l’energia di isteresi è quella dovuta a deformazioni plastiche. esiste una zona di transizione in cui l’energia del ciclo di isteresi si compone della parte anelastica e della parte plastica. questa zona di transizione si può pensare corrispondente alla banda di dispersione relativa al limite di fatica. constatato che per valori di tensione superiori al limite di fatica, l’energia in gioco dissipativa è quella corrispondente a deformazioni plastiche feltner e morrow [3] propongono un modello teorico per la valutazione del fenomeno e definiscono la legge che lega tensioni e numero di cicli. e’ stato messo in evidenza anche che la rottura di un provino avviene quando l’energia totale di deformazione plastica per unità di volume raggiunge un valore ec limite, costante caratteristico di ciascun materiale. nel caso di metalli, per valori sufficientemente elevati di deformazione locale rispetto a quella plastica a rottura (superiore a 0,15), il valore di tale coefficiente si può ritenere costante. ne consegue che, quando si sollecitano acciai con tensioni al di sopra del limite di fatica, la parte di calore sviluppato per ciclo, è proporzionale all’energia di deformazione plastica per ciclo epi, di conseguenza, per provini dello stesso materiale e della stessa forma, e per valori non eccessivamente elevati di temperatura raggiunti dal provino (minore di 200°c, in modo da poter trascurare l’effetto irraggiante), anche la temperatura si può porre proporzionale al lavoro di deformazione plastica epi (plastic work). dal punto di vista sperimentale è possibile notare che in prove di fatica, solo quando si è al di sopra del limite di fatica (quindi, in presenza di deformazioni plastiche locali) si notano sulla superficie del provino incrementi significativi della temperatura (dengel e harig [4] e kaleta et al. [5]). ciò è giustificato, come già detto, dal fatto che per sollecitazioni al di sotto del limite di fatica, l’effetto dovuto allo smorzamento interno della fase elastica del materiale e a tutti i fenomeni reversibili, è praticamente trascurabile in confronto a quello che si manifesta allorquando compaiono le prime deformazioni irreversibili. questa ultima osservazione ha permesso di sviluppare differenti metodologie per la ricerca del limite di fatica (risitano, luong, curti, blarasin, amiri, etc.). e’ stato visto sperimentalmente e dimostrato attraverso modelli teorici che in prove di fatica su acciai con sollecitazione al di sopra del limite di fatica, la temperatura superficiale del provino dopo un prima incremento iniziale (fatica a basso numero di cicli) si mantiene pressoché costante (fatica ad alto numero di cicli) fino a pochi cicli (circa 500) prima della completa rottura (fatica ad altissimo numero di cicli) del provino (fig. 1). figura 1: incremento qualitativo della temperature in funzione del numero di cicli per una tensione sopra il limite di fatica 0. applicando quanto prima detto al volume elementare relativo alla zona di rottura, per cui con sistemi a largo campo è possibile prima seguire e poi analizzate l’evoluzione della temperatura, si vede che la quantità totale di calore sviluppato durante tutta la prova, a meno di una costante dipendente dal coefficiente globale di trasmissione del calore (conduzione, convenzione, irraggiamento) del materiale e della geometria del provino, risulta praticamente proporzionale all’integrale della temperatura durante tutto il tempo di prova (fino alla rottura) φ=∫nitdni (fig. 2). dal punto di vista pratico, per la costanza della temperatura durante quasi tutta la prova (arig, risitano, etc.), se si opera a tensione massima costante, e parametri di prova costanti, essa si può scrivere come φ≈nixt facile anche da calcolare durante al fase di elaborazione è http://dx.medra.org/10.3221/igf-esis.12.09&auth=true http://www.gruppofrattura.it a. risitano et alii, frattura ed integrità strutturale, 12 (2010) 88-99; doi: 10.3221/igf-esis.12.09 90 delle acquisizioni. l’andamento della temperatura, evidenziato da kaleta e harig [5] e confermato da curti et al. [6,7], la rosa e risitano [8] e ultimamente adottato da m. amiri e m.m. khnsari [9], ha permesso di proporre metodi brevi per la determinazione del limite di fatica. l’osservazione sulla derivata nel tempo della temperatura già adottata da curti et al. [7] è stata ripresa ed adottata da m. amiri e m.m. khnsari in [9]. in tale lavoro e nel corrispondente brevetto, viene proposto anche un ulteriore metodo per la determinazione rapida del limite di fatica. la costanza del parametro φ=∫ni tdni è stata sperimentalmente sempre rilevata nella lunga attività di prove con acciai di diverso tipo e qualità da risitano e dalla sua scuola [10]. ciò conferma l’ipotesi di feltner e morrow sulla energia limite a rottura come caratterizzante il materiale e di taylor e quinney [1] sulla costanza per gli acciai del fattore β. un’osservazione importante derivante dalla ormai vasta letteratura sull’argomento è che in prove di fatica monoassiali sia la pendenza della curva temperatura con numero di cicli che la temperatura di stabilizzazione sono funzione della sollecitazione applicata al provino (fig. 3). figura 2: incremento qualitative di temperatura  and parametro energetico  = per tensioni sopra al limite di fatica  figura 3: incremento qualitativo delle temperature t per tensioni sopra al limite di fatica 0 123. come precedentemente detto, le diverse metodologie proposte per la ricerca del limite di fatica utilizzando il “terzo” parametro temperatura si basano sul fatto che l’incremento di temperatura è legato alla presenza di deformazioni plastiche permanenti che, con l’avanzare del numero di cicli, portano a rottura. il limite di fatica per un materiale integro coincide con quel valore di sollecitazione limite che è capace di produrre anche fenomeni locali di plasticizzazione (mason) per via dei quali, con il progredire del numero di cicli, si raggiungono i valori dell’energia limite caratterizzante il provino. se il materiale è danneggiato per una storia di carico precedente, il limite di fatica, inteso come quella tensione capace di produrre deformazioni plastiche locali che con il numero di cicli conducono alla rottura finale, risulta di valore più basso. in questo caso il fenomeno di deformazione plastica del provino è in parte iniziato e bastano valori di tensione minori per portare a rottura il provino, ovvero il limite di fatica risulta più basso. dal punto di vista dell’energia in gioco e quindi della temperatura superficiale, essendo il materiale in una nuova zona di transizione (mason), gli incrementi di temperatura superficiali sono limitati e difficili ancora da cogliere come incrementi significativi. se però si applicano carichi elevati fuori dalla normale fascia di dispersione tipica delle prove di fatica, l’energia consumata per ciclo aumenta (modello di feltener e morrow, deformazioni unitarie plastiche maggiori) ed il valore di temperatura che si può leggere sul provino è superiore a 0 nf tdn http://dx.medra.org/10.3221/igf-esis.12.09&auth=true http://www.gruppofrattura.it a. risitano et alii, frattura ed integrità strutturale, 12 (2010) 88-99; doi: 10.3221/igf-esis.12.09 91 quella che si avrebbe in un provino non danneggiato sollecitato alla stessa tensione. quanto detto prima si può riscontrare sperimentalmente facendo riferimento alle esperienze dei ricercatori che hanno proposto le varie metodologie per la ricerca rapida del limite di fatica (risitano, luong, curti, blarasin, amiri, etc.). infatti, si vede che nelle curve di temperatura in funzione della tensione applicata a cui si rifanno i vari metodi, al diminuire del limite di fatica, corrispondono curve traslate verso l’asse delle ascisse con incrementi maggiori di temperatura a parità di sollecitazione applicata (vedi ad esempio fig. 12 curva base e serie danneggiate). nel presente lavoro viene eseguita una verifica di quanto sopra detto e precisamente vengono rilevate le curve di temperatura per provini sollecitati a fatica con storie di carico diverse tali da produrre consumi di energia (deformazione plastica irreversibile) diversi. per successive serie di carico affaticanti, viene determinato di volta in volta il nuovo limite di fatica e le relative curve a tempo. procedura sperimentale e analisi dei risultati u provini in acciaio c40 sono state eseguite prove di fatica a frequenza di 10 hz per rapporto di carico r=-1. per la caratterizzazione statica dell’acciaio in esame, sono state eseguite prove di trazione e i valori caratteristici mediati su tre provini sono riportati in tab. 1. in fig. 4 sono riportate la forma e le dimensioni dei provini utilizzati per le prove di fatica. per tale acciaio si disponeva della curva di fatica definita in modo tradizionale da berto e lazzarin in [11]. ultimate strength r[mpa] yield strength s [mpa] fatigue limit 0 (r=-1) [mpa] 660.00 510.00 251.8 by [3] tabella 1: comportamento meccanico dell’acciaio c40. figura 4: dimensioni geometriche del provino (mm). la macchina di prova a fatica adottata è una instron® 8500 con cella di carico da 100 kn. i rilevamenti della temperatura della superficie dei provini (opportunamente rivestiti di vernice nera con emissività  pari a 0.92), sono stati eseguiti mediante il termografo agema thermovision 900 con thermovision 900 sw/te scanner, con cui sono state rilevate e registrate le temperature superficiali di ciascun provino. per ciascuna serie di prove, i provini usati erano in numero di tre. l’analisi della temperatura rilevata è stata eseguita alla fine di ciascuna prova ed i valori letti per ciascun provino sono stati fra di loro confrontati. per la rappresentazione finale, dopo la valutazione della differenza che non superava mai il 3% rispetto a quella media, per ragioni di chiarezza, si sono riportate solo le curve di temperatura a comportamento medio. la tab. 2 riporta i valori dei carichi e delle sollecitazioni massime corrispondenti per ciascun step di carico di ciascuna serie (i, ii, iii) a cui sono stati sottoposti i provini. il programma di prove prevedeva l’esecuzione delle stesse in due distinte fasi. nella fase 1 con rapporto di carico r=-1 e s http://dx.medra.org/10.3221/igf-esis.12.09&auth=true http://www.gruppofrattura.it a. risitano et alii, frattura ed integrità strutturale, 12 (2010) 88-99; doi: 10.3221/igf-esis.12.09 92 frequenza 10 hz, è stato caratterizzato (termo-meccanica-catatterizzazione) il materiale con carichi a scalino (10.000 cicli per scalino) fino alla rottura del provino (fig. 5) e rilevamento della temperatura superficiale per l’intero tempo di prova. l’analisi mediata dei dati (temperatura sul punto più caldo della superficie), su tre provini, permetteva la determinazione del limite di fatica e la valutazione del parametro energetico φ=∫nrtdn attraverso cui, (metodo risitano) veniva definita la curva di fatica del materiale integro. s [kn] [mpa] 14 155.5 17 188.9 20 222.2 23 255.5 26 288.9 28 311.1 tabella 2: valore dei carichi applicati. figura 5: incremento continuativo della tensione usato per la mappa mtc durante il primo stage di prove. figura 6: successione degli step di carico usati durante il secondo stage di prove. nella fase 2 (stesse condizioni di prova della fase 1), si sono applicate tre successive serie di carico simili a quelle usate per la caratterizzazione del materiale (fig. 6), senza arrivare a rottura, ma con carichi tali da produrre danno nel materiale. l’acquisizione della temperatura veniva eseguita per tutta la durata della prova. essendo i carichi di valore superiore al http://dx.medra.org/10.3221/igf-esis.12.09&auth=true http://www.gruppofrattura.it a. risitano et alii, frattura ed integrità strutturale, 12 (2010) 88-99; doi: 10.3221/igf-esis.12.09 93 limite di fatica del materiale, precedentemente determinato, essi erano idonei a generare microplasticizzazioni nel materiale con consumo di energia per deformazione plastica. alla fine della fase 2 si è stati in grado di avere l’andamento delle temperature per ciascun provino per le diverse serie di carico e, corrispondentemente, si è quantizzato il parametro energetico φ parziale (alla fine di ciascuna serie applicata) e totale (a rottura). con i dati acquisiti ed elaborati, alla fine di ciascuna serie, si è, quindi, determinato per ciascun provino il limite di fatica, la curva di wöhler ed il parametro φ=∫ni tdni, nonché il valore del parametro  i dati riportati, così come le curve, si riferiscono, per ciascuna tipologia di prova, sempre ai valori di uno dei tre provini, in quanto i valori di temperatura rilevati erano fra loro molto vicini (le differenze di temperatura non superavano mai il 3% ) e ai fini della elaborazione praticamente uguali. risultati e commenti elle figure da 7 a 14, per la frequenza di prova 10 hz, sono riportati gli andamenti delle temperature mediate in funzione dei carichi applicati ai provini della fase 1 (provini lisci). con i dati relativi alla fig. 7 è stato determinato il limite di fatica (fig. 8) che è risultato praticamente uguale a quello trovato da berto e lazzarin [11]. nella fig. 9, assieme alla curva di wöhler tradizionale di [11], sono riportati i punti della curva di wöhler definiti per il valore del parametro φ=nixt (circa pari all’integrale dell’area sottesa alla curva delle temperature) che è risultati pari a 110x104 cicli x °c. le figure da 8 a 14 si riferiscono ai risultati della fase 2 di prova. il post processing dei dati acquisiti ha evidenziato che il punto più caldo della superficie del provino non cambiava dopo l’applicazione delle successive serie di carico e fino alla rottura del provino. in fig. 10 è riportato l’andamento delle temperature per tutte le serie di carichi applicati ai provini. nella fig. 11, per meglio evidenziare il fenomeno, è riportato l’andamento delle temperature, a parità di carico applicato al provino, ma appartenente a serie di carico successive (i, ii, iii). l’esame delle figure evidenzia: 1) l’andamento della temperatura relativa alla prima serie di carichi, coincide nei limiti della normale dispersione, con quello di fig. 7 relativo ai provini integri, che, tuttavia, sono comunque diversi; 2) i valori di temperatura che si rilevano per sollecitazioni uguali, ma di serie successive diverse, sono sempre più elevati man mano che si passa dalla serie (i) alla seconda (ii) e alla terza (iii); 3) la differenza di temperatura, a parità di carico, per serie diverse è tanto più alto quanto più elevato è il valore del carico applicato. in fig. 12 sono riportate le temperature di stabilizzazione per ciascun valore di tensione applicata da cui secondo curti e risitano [7] si giunge alla determinazione del limite di fatica. nella fig. 13 sono riportate la curve di wöhler definite attraverso il parametro φ, calcolato per tutta la prova, e dei parametri φi parziale per ciascuna serie. in particolare le curve di wöhler successive (spostate in basso nella figura) sono state costruite facendo, di volta in volta, riferimento alla differenza fra il parametro φ totale e il parametro φi parziale precedente (energia “consumata”). in tab. 4 sono riportati i valori dei parametri φ parziali e totali. nella stessa fig. 13 è riportata anche la curva di wöhler definita da berto & lazzarin in [11]. i risultati, sintetizzati nelle figure sopra descritte, evidenziano ancora che il limite di fatica cambia man mano che al provino vengono applicate le serie successive di carichi. nella fig. 14, seguendo in parte quanto indicato da miner-manson, sono riportate le rette che uniscono i punti relativi ai limiti di fatica (ascisse n=2x106) dopo l’applicazione della i serie di carichi e della i e ii serie di carichi, con la tensione di snervamento del materiale. si può osservare come i punti determinati attraverso il parametro energetico φ siano allineati e posizionati su tali rette. f [hz] s0 [kn] 0 [mpa] 10 24.2 258.60 tabella 3: carichi corrispondenti al limite di fatica per l’acciaio c40 tramite tmc. [ciclix°c] r = -1 f = 10 hz  12.2*104  49.6*104  52.7*104  114.5*104 tabella 4: parametro energetico  n http://dx.medra.org/10.3221/igf-esis.12.09&auth=true http://www.gruppofrattura.it a. risitano et alii, frattura ed integrità strutturale, 12 (2010) 88-99; doi: 10.3221/igf-esis.12.09 94 indicazioni derivanti dall’analisi termica ome è noto, seguendo la regola del miner, il danno cumulativo è definito da dm = σini/ni, in cui, ni è il numero di cicli alla tensione σi, e ni è il numero di cicli a rottura per quella tensione. pertanto, nel nostro caso, dopo la prima serie di carichi risulta: dm n1/n1+n2/n2+n3/n3+n4/n4+n5/n5. figura 7: incrementi di temperature t in funzione dei numeri di cicli per l’acciaio c40 con frequenze di prova di 10 hz. figura 8: determinazione del limite di fatica 0=s0 /a con il metodo risitano. figura 9: curva di wöhler per provini lisci ricavata con metodo tradizionale e con quello termografico per frequenza di prova di 10 hz e rapporto di carico r=-1 . c http://dx.medra.org/10.3221/igf-esis.12.09&auth=true http://www.gruppofrattura.it a. risitano et alii, frattura ed integrità strutturale, 12 (2010) 88-99; doi: 10.3221/igf-esis.12.09 95 figura 10: incremento di temperatura t in funzione del numero di cicli per acciaio c40 (f=10 hz, r=-1) per differenti serie (i, ii, iii). figura 11: andamenti del t di temperature in funzione del numero di cicli (f=10 hz, r= -1) per differenti serie (i, ii, iii). c40 14 kn (10 hz) -1,0 -0,5 0,0 0,5 1,0 1,5 2,0 2,5 3,0 3,5 0 2 4 6 8 10 12 cycles x 1000  t l serie ll serie lll serie c40 17 kn (10 hz) -1,0 0,0 1,0 2,0 3,0 4,0 5,0 6,0 0 2 4 6 8 10 12 cycles x 1000  t l serie ll serie lll serie c40 20 kn (10 hz) 0,0 2,0 4,0 6,0 8,0 10,0 12,0 14,0 16,0 0 2 4 6 8 10 12 cycles x 1000  t l serie ll serie lll serie c40 23 kn (10 hz) 0,0 5,0 10,0 15,0 20,0 25,0 30,0 0 2 4 6 8 10 12 cycles x 1000  t l serie ll serie lll serie c40 26 kn (10 hz) 0,0 10,0 20,0 30,0 40,0 50,0 60,0 70,0 80,0 90,0 0 5 10 15 cycles x 1000  t l serie ll serie lll serie serie seri serie serie seri serie http://dx.medra.org/10.3221/igf-esis.12.09&auth=true http://www.gruppofrattura.it a. risitano et alii, frattura ed integrità strutturale, 12 (2010) 88-99; doi: 10.3221/igf-esis.12.09 96 figura 12: determinazione del limite di fatica 0=s0 /a con il metodo risitano. figura 13: curve di wöhler di provini lisci (base) e di provini sottoposti alla prime i e alla i e ii serie di carichi definite secondo il metodo risitano figura 14: curve di wöhler di provini lisci (base) e di provini sottoposti alle prime due serie di carichi secondo miner e risitano. facendo riferimento al metodo risitano e quindi al parametro energetico φ, il danno risulta: di=i/  σi(nit*i/niti) in cui t*i rappresenta la temperatura di stabilizzazione per una data tensione σi e ti la temperature per quella stessa tensione con cui il provino non danneggiato arriverebbe a rottura (tixni= cost). esplicitando, nel nostro caso si ha: di= i/  (n1t*1/n1t1+n2t*2/ n2t2+n3t*3/ n3t3+ n4t*4/ n4t4+ n5t*5/ n5t5 ) essendo, φ = costante e pari a n1t1 = n2t2 = n3t3…. (energia limite di deformazione plastica costante del materiale) essendo, come verificato sperimentalmente, i rapporti di temperatura, a parità di carico, per provini danneggiati e non, maggiori di 1, risulta che il danno valutato secondo la ipotesi del miner è inferiore a quello valutato sulla base dell’energia spesa per ciclo. tuttavia, nel caso in cui il provino già danneggiato, venisse portato a rottura con carichi di poco superiori al limite di fatica, i rapporti di temperatura sarebbero prossimi all’unità e l’ipotesi del miner coinciderebbe con quella derivante dal tener conto dell’effetto energetico (dm di). in casi diversi, ovvero, quando venissero applicati carichi elevati per arrivare a rottura, applicando l’ipotesi del miner, si avrebbero, sottostime del danno con errori anche http://dx.medra.org/10.3221/igf-esis.12.09&auth=true http://www.gruppofrattura.it a. risitano et alii, frattura ed integrità strutturale, 12 (2010) 88-99; doi: 10.3221/igf-esis.12.09 97 significativi. tale osservazione conferma quanto riportato da iqban rasool memon ed al. [12], per cui, se si inverte l’ampiezza di carichi affaticanti (superiori al limite di fatica) la regola del miner per la valutazione del danno non può essere usata. l’applicazione di quanto detto alla tipologia di carichi adottati nel lavoro di iqban rasool memon, porterebbe in un senso (carichi crescenti) ad un valore di danno pari a: dm= n1/n1+n2/n2 ed ad un valore, in termini energetici, pari a: di i/  n1t*1/n1t1+n2t*2/ n2t2 se l’ampiezza del primo carico fosse di poco superiore al limite di fatica ed il secondo fosse di parecchio più elevato, si avrebbe t*1= t1 ed, essendo stato il materiale poco danneggiato, t*2 t2 e quindi dm  di. applicando i carichi in senso opposto (carichi decrescenti) si avrebbe t*2= t2 ma una t*1 completamente diversa e maggiore da t1 (il materiale è stato danneggiato). di conseguenza sarebbe dm n2/n2 + n1/n1 pari a quello di prima (carichi crescenti) ma di i/  n2t*2/ n2t2 n1+t*1/n1t1 decisamente più alto. come già riferito in [49] vale la linearità del danno e la curva a tempo si può ottenere, una volta determinato il limite di fatica, tracciando nel diagramma semilogartmico (σ logn) la retta che congiunge il punto di coordinate σ0 e 2x106 cicli, con il punto di ascisse 0 e ordinata σs (tensione di snervamento). tale curva, tuttavia, non sempre coincide con quella tracciata secondo le indicazioni del miner, specialmente quando la storia di carico è tale che tensioni, apparentemente sotto il limite di fatica del materiale, diventano affaticanti per il danno prodotto da uno di essi (magari ad ampiezza elevata) applicato in precedenza. il diagramma di fig. 11, in cui sono stati riportati gli andamenti delle temperature a parità di tensione applicata nelle successive serie di carico, mette in evidenza questo aspetto. se si facesse riferimento al limite di fatica del materiale non danneggiato σ0= 251,8 n/mm2, in tutta la storia di carichi applicati solo con i carichi 23 e 26 kn si raggiungerebbero tensioni affaticanti (carico/area sezione provino) pari a 255,6 e 288,9 n/ in realtà, dopo l’applicazione della prima serie, che riporta un incremento di temperatura già per 17 kn e, di conseguenza, ad un limite di fatica differente (in fig. 12, la curva “base” è riferita alla curva relativa ai provini della fase 1), si avrebbero, per i carichi successivi (della stessa serie), gradi di danneggiamento sempre maggiori. questo è ancora più accentuato dai salti di temperatura, sempre più ampi a parità di tensione applicata per serie successive (fig. 11). in altre parole, con l’applicazione della successiva serie (ii serie di carichi), la riduzione del limite di fatica, anche per l’effetto della prima serie, amplifica il fenomeno termico. l’esame della figura evidenzia ancora come, all’applicazione della iii serie di carichi anche quei carichi, che in partenza erano inferiori al limite di fatica del materiale diventino affaticanti ed in grado di contribuire al consumo di energia plastica. i rapporti t*i/ti, derivanti dall’avere messo in gioco parametri energetici, permette di evidenziare e definire il danno cumulativo come rapporto della perdita di energia per ogni ciclo rispetto all’energia limite ec. quanto precedentemente detto è sintetizzato in fig. 14 in cui, assieme alla curva di wöhler tradizionale (per provini lisci), è stata riportata la retta (miner in figura) che si ottiene attraverso la regola del miner-manson dopo l’applicazione delle prime due serie di carichi. essa, per il fatto che praticamente solo due dei carichi applicati superano il limite di fatica del materiale, si dispone molto vicina alla curva base. nella stessa figura è riportata la curva di wöhler (risitano in figura) definita con il metodo risitano, ovvero, facendo riferimento al parametro energetico e quindi alla energia persa per ciclo per effetto di ciascuno dei carichi applicati (quelli della seconda serie a partire dal valore di 17 kn provocano danno ed il rapporto del ni/ni va corretto con i rapporti di temperatura t*i/ti). conclusioni engono messe in evidenza alcuni aspetti che hanno portato al lavoro degli autori [13] sulla valutazione del danno in materiali o componenti meccanici. utilizzando gli stessi dati sperimentali di [13] sono state fatte alcune considerazioni sulla possibilità della valutazione del danno sulla base di parametri che tengano conto della energia persa per ciclo. i risultati delle prove di fatica, effettuate su provini di acciaio c40 danneggiati con applicazioni di serie di carichi successive e per cui è stata costantemente rilevata la temperatura durante tutta la prova, hanno messo in evidenza quanto segue: 1) il limite di fatica del materiale, come è ovvio, varia con il grado del danno (energia spesa/energia limite) ed è facilmente rilevabile mediante l’analisi termica sotto carico; 2) la temperatura del punto più caldo della superficie del provino sollecitato a fatica varia per valori di carico uguali v http://dx.medra.org/10.3221/igf-esis.12.09&auth=true http://www.gruppofrattura.it a. risitano et alii, frattura ed integrità strutturale, 12 (2010) 88-99; doi: 10.3221/igf-esis.12.09 98 appartenenti a serie di carico successive; 3) durante l’applicazione delle successive serie di carico, il punto, in cui si rileva la massima temperatura, rimane lo stesso fino alla completa rottura del provino; 4) la legge lineare del danno, per la ricerca delle curve a tempo, può essere sempre applicata se si parte dalla valutazione esatta del nuovo limite di fatica; 5) viene confermata la legge lineare cumulativa del danno, ma la stessa legge scritta in termini di energia “consumata” per ciclo, evidenzia che la legge del miner in accordo con quanto segnalato da iqban rasool memon et al. [12] non sempre può essere applicata; 6) le variazioni di temperatura rilevate per tensioni di uguale entità, ma applicate dopo che il materiale è stato danneggiato “diversamente”, sono tanto più elevate quanto più è grande il grado di danno. le osservazioni sopra riportate, basate di fatto su considerazioni energetiche, insieme a quanto già riferito dagli autori in [13] e [14], permettono di eseguire in modo semplice valutazioni del danno nei materiali ed in componenti meccanici. gli autori considerano osservazioni preliminari quelle sui limiti di validità della legge del miner segnalati anche in [12] e si propongono di approfondirle con adeguate indagini che possano mettere in conto l’energia rilasciata per effetto del “danno”. bibliografia [1] g. i. taylor, h. quinney, in: proc. r. soc., a 134 (1934) 307. [2] j. j. mason, a. j. rosakis, g. ravichandra, mech. mat., 17 (1994) 135. [3] c.e. feltner, j.d. morrow, trans. asme, ser. d: j basic eng, 83 (1961) 15. [4] d. dengel, h. harig, fatigue fract eng mater struct, 3 (1980) 113. [5] j. kaleta, r. blotny, h. harig, j test eval, 19 (1990) 326. [6] g. curti, g. la rosa, m. orlando, a. risitano, in: 14th aias italian national conference, catania, italy, (1986) 211. [7] g. curti, a. geraci, a. risitano, ata ingegneria automotoristica, 10 (1989) 634. [8] g. la rosa, a. risitano, international journal of fatigue, 22 (2000) 65. [9] m. amiri, m.m. khonsari, international journal of fatigue, 32 (2010) 382. [10] g. fargione, a. geraci, g. la rosa, a. risitano, international journal of fatigue, 24 (2002) 11. [11] f. berto, p. lazzarin ,la metallurgia italiana, 3 (2005) 23. [12] iqbal rasool memon, xing zhang, deyu cui, international journal of fatigue, 24 (2002) 29. [13] a. risitano, g. risitano, in: workshop igf, forni di sopra (2010). [14] a. risitano, g. risitano; in: workshop igf, forni di sopra (2009) e pubblicato su “frattura ed integrità strutturale”, 9 (2009) 123. [15] g. c. sih, multiscale fatigue crack initiation and propagation of engineering materials, structural integrity and microstructural worthiness: solid mathematics and its applications, springer, 152 (2008). [16] a. palmgren, die lebensdauer von kugellagern, verfahrenstechinik, berlin, 68 (1924) 339. [17] m. a. miner, journal of applied mechanics, 67 (1945) a159. [17] l. locati, metall. it. al., 27 (1935) 188. [18] m. prot, misure et control, 13 (1948) 301. [19] m. prot, wadctr (1952) 53. [20] o. föppl, v.d.i.z., 70(39) (1926) 1291. [21] o. föppl, p. ludwik, v.d.i.z., 76(14) (1932) 683. [22] j f delorme, g sinicki, p. gobin, j. phys. d: appl. phys., 1 (1968) 1737. [23] t. catalbiano, a. geraci, m. orlando, il progettista industriale, (1984) 2. [24] a. geraci, g. la rosa, a. risitano, in: cres symposium, catania italy, 1984, pubblicato in ata ingegneria automotoristica 38 (1985) 8. [25] m.p. luong, mech. mater., 28 (1988) 155. [26] m.p. luong, spie, 1682 (1992) 222. [27] m.p. luong, k dang-van, in: atti della fondazione g. ronchi, il (1993) . [28] m.p. luong, nucl. eng. des., 158 (1995) 363. [29] a. blarasin, r. fracchia, m. pozzati, ata – ingegneria automotoristica, 51 (5) (1988) 255. [30] f. curà, g. curti, r. sesana, int. j. fatigue 27 (2005) 453. [31] f. walter , d.eifler, journal of solid mechanics and materials engineering, 2 (4), 2008. http://dx.medra.org/10.3221/igf-esis.12.09&auth=true http://www.gruppofrattura.it a. risitano et alii, frattura ed integrità strutturale, 12 (2010) 88-99; doi: 10.3221/igf-esis.12.09 99 [32] a. geraci, g. la rosa, a. risitano, in: 7th international conference on mechanical behaviour of material, the hague (1995). [33] r. blonty, kaleta, analysis of mathematical model of the fatigue energy hypothesis as seen by identification theory, phd thesis, inst. of material science and appl. mechanics , tu wroclaw, 199 (1978). [34] r. blonty, kaleta, international journal of fatigue, 1 (1986) 35. [35] r. blonty, kaleta, in: 7th international conference on fracture (icf-7), houston tex., pergamon press, oxford, (1989) 1195. [36] b. atzori, e. gasparini, g. meneghetti, in: proceedings of 30th aias national conference, (2001) 367. [37] b. atzori, g. meneghetti, lcf 5. in: proceedings of the 5th international conference on low cycle fatigue, p.d. portella, h. sehitoglu and k. hatanaka, editors, dvm, berlin (2003) 147. [38] g. meneghetti, international journal of fatigue, 29(1) (2007) 81. [39] o.a. plenkev, n. saintier, t. palinluc, s.v. uranov, naimark, material science and engineering, 462(1-2) (2007) 367. [40] n.w. klingbeil, int. j. fatigue, 25 (2003) 117. [41] t. boulanger, a. chrysochoos, c. mabru, a. galtier, int. j. fatigue, 26 (2004) 221. [42] n. ranc d. wagner, p.c. paris, study of thermal effects associated with crack propagation during very high cycle fatigue tests, acta materialia, 56(15) (2008) 4012. [43] m. selek, ö. s. şahin, ş. kahramanlı, in: eurocon 2007 the international conference on “computer as a tool” warsaw (2007). [44] p. lazzarin, p. livieri, f. berto, et alii, engineering fracture mechanics, 75(7) (2008) 1875. [45] a. chrysochoos, h. louche, international journal of engineering science, 38 (2000) 1759. [46] astm e 466-72 standard practice for conducting constant amplitude axial test of metallic materials. [47] j. hoodwany, g. ravichandran, a. j. rosakis, p. rosakis, experimental mechanics, 40(2) (2000). [48] a. chrysochoos, b.berthel, f. latourte, s. pagano, b wattrisse, b. weber, strain, 44 (2008) 327. [49] d. macduogall, experimental mechanics, 40 (3) (2000). [50] f. walter, d. eifler, journal of solid mechanics and material engineering, 2(4) (2008). http://dx.medra.org/10.3221/igf-esis.12.09&auth=true http://www.gruppofrattura.it microsoft word numero_46_art_21 l.u. argiento et alii, frattura ed integrità strutturale, 46 (2018) 226-239; doi: 10.3221/igf-esis.46.21 226 design of civil environmental engineering formulating the in-plane frictional resistances and collapse mechanisms for multi-storey masonry block walls l.u. argiento, a. maione, c. casapulla university of napoli federico ii, department of structures for engineering and architecture, italy lucaumberto.argiento@unina.it arch.maione@gmail.com casacla@unina.it abstract. in this paper a macro-block model accounting for frictional resistances is presented to assess the lateral strength of a multi-storey masonry block wall. the kinematic approach of limit analysis is used to define the load factor causing the onset of rocking-sliding mechanism under in-plane horizontal loading. a dry frictional contact condition is assumed at the rigid block interfaces, according to the coulomb's law with non-associated flow rule. the key aspect of the proposed approach is the introduction of a criterion to evaluate the contribution of the actual frictional resistances depending on the inclination angle of the crack line. an accurate assessment of the frictional resistances is also obtained by distinguishing two different contributions (the wall own weight and additional vertical loads) and their application points. hence, a sensitivity analysis is performed with respect to the overloading condition, the friction coefficient, and geometrical parameters such as the shape ratios of the wall and of the unit block and the number of rows. the analytical results of the proposed model are also validated against results from other existing macro and micro-block modelling approaches in terms of load factor. the comparison confirms the reliability of the proposed model that allows, with similar results, great simplification of the computational effort with respect to micro-block models. keywords. limit analysis; 3d macro-block model;  multi-storey masonry building; rocking-sliding failure; frictional resistances. citation: argiento, l.u, maione, a., casapulla, c., formulating the in-plane frictional resistances and collapse mechanisms for multi-storey masonry block walls, frattura ed integrità strutturale, 46 (2018) 226-239. received: 29.07.2018 accepted: 26.08.2018 published: 01.10.2018 copyright: © 2018 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. introduction he seismic damages suffered by unreinforced masonry block structures are often due to partial collapses with loss of equilibrium of walls or portions of them, while material failure rarely occurs. experimental tests carried out since ’80s of the last century on brickwork samples [1-3] have proved that the mechanical performance of such a t http://www.gruppofrattura.it/va/46/21.mp4 l.u. argiento et alii, frattura ed integrità strutturale, 46 (2018) 226-239; doi: 10.3221/igf-esis.46.21 227 material is characterized by a very high anisotropy, so that the direction of bedding surfaces and element shapes plays a central role in defining the type of failure. such experiments, further developed by other authors as ceradini [4], have stressed that in-plane failure in most of cases occurs by applying horizontal loads exceeding the friction coefficient, such to produce cracks along the joints without crashing of elements, while failure due to the overcoming of material strength (,) occurs for much higher applied loads. actually, the absence of tensile strength and the presence of weak mortar joints generally cause the development of cracks which transforms a masonry block structure into a system of rigid blocks which can exhibit sliding or rocking mechanisms as well as a combination of them. the geometry of these mechanisms can be quite easily identified in post seismic scenarios, since the crack pattern has been revealed, but when the attention is focused on the prevision of the expected behaviour of the structures the most likely collapse mechanisms have to be identified. to this aim, several combinations of material and structural models are possible, e.g. fem macro and micro-modelling [5], discrete element methods [6, 7], computational limit analysis procedure for rigid block assemblages [8, 9] or homogenization models [10]. a drawback for the use of these sophisticated models in the practical assessment of structures is the large amount of time needed for the structural model elaboration, for performing the non-linear analyses themselves and for reaching proper understanding of the results significance. conversely, the macro-block modelling in the framework of limit analysis with kinematic approach represents a more powerful tool because it allows an easy computation of the collapse load factor and the failure mode by means of minimization routines. the pioneering works of kooharian [11] and heyman [12], based on infinite frictional resistances, have largely been used to apply the plasticity theory to masonry block structures. according to this standard limit analysis, the application of the static theorem provides a lower-bound or safe solution of the collapse load factor, based on equilibrium equations, while the application of the kinematic theorem leads to an upper bound multiplier. the solution that satisfies the hypotheses of both theorems, equilibrium, compatibility and material conditions is the correct solution and provides the collapse load multiplier for the specific problem. however, the uniqueness of the solution is no longer guaranteed when non associated flow rules are involved, such as in case of coulomb’s friction at block interfaces [13, 14]. this means that a range of statically and kinematically admissible solutions can be identified and a safe solution can be represented by the minimum load multiplier computed by means of the kinematic approach [8]. crucial aspects are also the definition of the yield domains of dry or weak mortar joints able to dissipate seismic energy [15-17] or, as an alternative, the composition of units to enforce the capability of dissipating energy during motions of walls [18]. the macro-block modelling approach has been lately developed to investigate the local in-plane and out-of-plane failure modes in masonry buildings [19-22]. according to it, each block represents a portion of masonry which remains undamaged and is separated from others by a number of localized cracking where the frictional resistances can take place. when attention is paid to structural elements having a specific role in the overall building behaviour, special macroelements can simulate them to reduce computational and modelling efforts, e.g. architectonic elements in which the seismic behaviour is almost independent from the rest of the structure of masonry churches [23, 24] or masonry vaults typified by sets of equivalent trusses [25]. this modelling strategy could also be useful to further develop recent innovative research in the field of rocking rigid block dynamics [26, 27]. when applied to in-plane failure modes of masonry block structures with dry or weak mortar joints, generally characterized by a combined rocking-sliding mechanism, crucial to this approach is the assessment of the frictional resistances along the crack. in fact, it is not easy to identify the number of active sliding interfaces along the crack and the actual frictional resistance associated to the crack line could also be far from its maximum value. this issue has already been addressed with reference to a single-storey masonry block wall [22] and in this paper it is extended to a multi-storey wall. a proper evaluation of the in-plane frictional resistances, on the other hand, represents a relevant contribution also to the analysis of the out-of plane mechanisms; in fact these resistances can play an important role when the mechanism involves the façade wall with portions of side walls of a masonry building (complex rocking). thus, in the following sections, considering the masonry block wall as a single leaf wall arranged in a running bond pattern, the in-plane frictional resistances are firstly evaluated, also accounting for additional loads due to horizontal structures and live loads. the originality of this part can be recognized in the criterion to evaluate the contribution of the actual frictional resistances depending on the inclination angle of the crack line and the number of storeys, in addition to other geometrical and mechanical parameters. then, the “exact” ultimate load factor in case of rocking-sliding failure mode is computed by means of minimization routines, by taking into account variable positions of the conventional crack line. lastly, the validity and accuracy of the novel solution procedure are investigated through a sensitivity analysis and the comparison with results and benchmark examples existing in the literature. l.u. argiento et alii, frattura ed integrità strutturale, 46 (2018) 226-239; doi: 10.3221/igf-esis.46.21 228 in-plane frictional resistances of a multi-storey masonry wall he analysis of the rocking-sliding failure mode of a multi-storey wall is an extension of that referred to a singlestorey wall, based on a simple geometric and mechanical model. it is assumed, in fact, that the single-storey wall is made up of a single leaf of regular squared and rigid blocks, with geometric dimensions l × h × b (fig. 1a), placed with their longer side parallel to the wall length and overlapped with constant staggering length v, equal to half the block length (fig. 1b). the blocks interact through their bed joints according to the coulomb’s model of dry frictional contact [13]; no tensile strength, instead, is assumed against vertical loads which tend to detach overlapping layers. figure 1: a) masonry wall with dry assembled unit blocks; b) dimensions of the unit block. in this section the criterion developed and validated in previous works [21, 22] is applied to a multi-storey masonry wall to define the in-plane frictional resistances involved in the combined rocking-sliding mechanism. the adoption of macromodelling approach implies that the damage pattern is schematized by a single crack where the relative motions between the macro-blocks and frictional resistances develop. the difficulty of identifying the number of active sliding interfaces along the crack in a combined mechanism has been overcome by introducing a reduction criterion of the maximum value of the resultant frictional resistance based on the inclination of the crack. in fact, as highlighted in [22], this inclination tends to become vertical when pure sliding occurs and the resultant frictional resistance assume the maximum value; on the other hand, instead, the inclination tends to the staggering ratio when pure rocking occurs with no frictional resistances. among these two limit cases, a reliable evaluation of the resultant frictional resistance related to a combined mechanism can be found, as described in the following. according to the proposed approach, the maximum value of the resultant frictional resistance is firstly calculated assuming a pure sliding mechanism. hence, with reference to the generic multi-storey wall in fig. 2 with dimensions l × h and n storeys of heights hi (storey 1 is at the top wall), the following parameter is defined: tan pi n jj i l h     (1) which represents the shape ratio of the portion of the wall between the hinge position and the top storey i. it is worth noting that it is also tanp1 = tanp = l/h. the parameter hci, instead, represents the height of the portion of the wall related to the storey i, which is crossed by the crack line. in fact, depending on the position of the crack line, inclined of the angle c, hci can assume the following expressions: 1 1 1 a) b) tan c) 0 c pi ci i i n pi c pi ci j j ic c pi ci h h n h l h n h a h                      (2)   t l.u. argiento et alii, frattura ed integrità strutturale, 46 (2018) 226-239; doi: 10.3221/igf-esis.46.21 229 where ni is the number of rows related to the storey i (ni = hi/h, being h the height of the unit block). the parameter hci can also be expressed as a function of the number nci of rows crossed by the crack line at the storey i, i.e: ci cih n h (3) it is worth noting that the cases in eq. (2) cover all the possible configurations of the analyzed mechanism, and the geometric parameter hci, or the related nci, easily allows extending the relations defining the model of the single-storey wall to the multi-storey wall, as will be better shown later. the use of the relations defined for the single-storey wall in a previous work [22], instead, would have required a large number of conditions on the same relations, sharply increasing with the number of the stories. figure 2: macro-block model of a multi-storey wall with identification of the masonry panels involved in a rocking-sliding mechanism. the resultant of the frictional resistances is obtained as sum of two components in order to take into account the effect of their different points of application on the stabilizing moment. in particular, with reference to the storey i (fig. 3), the component fgi is due to the self-weight of the moving portion of the wall crossed by the crack and corresponds to a linear distribution along the height hci; the component fqi, instead, is due to the overloading and to the self-weight of the portion of the wall with height h – l/tanc and corresponds to a uniform distribution along the height hci. these components are here expressed by adopting the discrete formulation based on the number nci of rows crossed by the crack line at the storey i. thus, the frictional force sk at contact interface k is given by the weight wbi of the upper column of half-blocks, limited to the height of the crack line hci, multiplied by the friction coefficient f: ( 0,1,..., )k bi cis kf w k n  (4) where wbi = vhbi, bi is the thickness of the unit block related to the level i (it could also be different from those at different levels) and  is the specific weight of masonry. the two components fgi and fqi respectively are: l.u. argiento et alii, frattura ed integrità strutturale, 46 (2018) 226-239; doi: 10.3221/igf-esis.46.21 230   1 1 2 cin ci ci gi k i k n n f s vhb f     (5) 1 1 1 ( ) i i qi i ci i j j j ci j j f n n b h q n b h n vf                 (6) figure 3: frictional resistances related to a multi-storey wall. it is easy to verify [22] that fgi is applied at 2/3 from the top of the height hci since sk linearly increases from the top to the bottom, while fqi is applied at the half of the same height hci. hence, if a full activation of the frictional resistances occurs along the all the bed joints crossed by the crack line (pure sliding mechanism), their resultant assumes a maximum value given by: 1 1 n n gi qi i i f f f      (7) l.u. argiento et alii, frattura ed integrità strutturale, 46 (2018) 226-239; doi: 10.3221/igf-esis.46.21 231 if a combined rocking-sliding mechanism takes place, instead, this force is expected to be lower than the value provided by eq. (7); in this case, in fact, the rocking motion causes the uplift of a number of blocks and the reduction of the contact interfaces. in order to overcome the difficulty of identifying the real contact conditions, a criterion to assess the actual frictional resistances has been proposed and validated by casapulla et al. [21]. this criterion, as previously introduced, is based on the inclination of the crack line and provides a reliable estimation of the frictional resistances fw related to a combined mechanism. it is assumed in fact: 1 cw b f f          (8) where b = tan1(v/h) depends on the dimensions of the unit block (fig. 1b). hence, when the crack line is vertical (c = 0), all the contact interfaces along the crack are involved in sliding, so that the frictional resistances can be considered as activated on all courses crossed by the crack and their resultant attains its maximum value; in fact, it is fw = f, with f given by eq. (7). when c = b, instead, a pure rocking mechanism takes place with loss of contact over all the involved joints; as a consequence, the resultant frictional resistance can be considered null (fw = 0). when 0 < c < b, a combined rocking-sliding mechanism is expected with a resultant frictional resistance lower than its maximum value (0 < fw < f). it is worth noting that the case c > b it is excluded because unrealistic for dry joint masonry walls. finally, in order to better understand the proposed model, in tab. 1 the parameter hci and the components fgi and fqi defined in a compact form by eqs. (3), (5) and (6), respectively, are explicated with reference to a number of storey i = 3 and p2 < c < p3 (figs. 2 and 3). it is worth noting that hc1, fg1 and fq1 are all null because the crack line does not cross the wall at the storey 1. moreover, being p2 < c < p3, eqs. (2b) and (2c) are used to define hc2 and hc3, respectively. storey hci eq. (2) fgi eq. (5) fqi eq. (6) 1 2  2 3 tan c l n n h     2 2 2 1 2 c cn nvhb f   2 2 2 1 2 1 1 2( )c cn n b h q q n b h n vf     3 n3h  3 3 3 1 2 n n vhb f    1 2 3 1 1 2 2 3cq q q n b n b h n vf    table 1: expressions of the variables hci, fgi and fqi for a three-storey masonry wall, when p2 < c < p3. in-plane failure mode of masonry multi-storey walls and collapse load factors he analysis of the rocking-sliding failure mode of a multi-storey wall is an extension of that referred to a singlestorey wall, based on a simple geometric and mechanical model. the kinematic approach of the limit analysis is adopted to identify the geometry of the rocking-sliding mechanism (i.e. the inclination tanc of the crack line) which minimizes the load factor causing the onset of the mechanism. with reference to a generic multi-storey wall, fig. 4 represents the macro-block identified by the crack line with inclination c ≤ b and the actions (internal and external) involved in the mechanism at each level i. these actions are applied to the centre of gravity of each of the parts in which the moving macro-block has been geometrically divided; in particular, this partition takes into account the overlapping length v of the unit blocks as the width of the part a, marked in grey in fig. 4 and, as a consequence, the angle αc* is used instead of αc (figs. 3 and 4). the relation between the parameters tanc and tanc* is: *tan tanc c v nh    (9) t l.u. argiento et alii, frattura ed integrità strutturale, 46 (2018) 226-239; doi: 10.3221/igf-esis.46.21 232 the external loadings together with internal frictional resistances and the coordinates of the relative application points are reported in tab. 2. figure 4: representation of the external and internal actions involved in the rocking-sliding mechanism of a multi-storey masonry wall. thereafter, by applying the principle of virtual work to the system of virtual displacements derived by the rotation around the hinge o of the macro-block identified by the crack line, the following expression of the load factor is obtained (fig. 4): 1 1 1 1 1 1 1 1 1 1 1 1 n n n n n n n ai wai bi wbi ci wci di wdi i qi gi fgi qi fqi i i i i i i i r n n n n n ai wai bi wbi ci wci di wdi i qi i i i i i w x w x w x w x q x f y f y w y w y w y w y q y                                     (10) this load factor, accounting for eq. (9) is a function of the parameter tanc which defines the geometry of the mechanism; thus it can be minimized with respect to this parameter, with the following constraint: tan tanc b v n h    (11) it is worth noting that the minimization process has to take into account the circumstance that the position of the hinge can be located at the edge of each level of the multi-storey wall causing the onset of different mechanisms; thus the load factors related to all possible positions the of the hinge have to be compared in order to choose the minimum value l.u. argiento et alii, frattura ed integrità strutturale, 46 (2018) 226-239; doi: 10.3221/igf-esis.46.21 233 external actions horizontal lever arm (xj) vertical lever arm (yj) ai i iw n b hv 2 v 12 n i j j i n n h           ( ) ( )bi i ci iw n n l v hb     2 l v 12 n i ci j j i n n n h           * 2 1 tan n ci c ci i j j i w n h b n       * 1 tan 2 n c j j i h n v            12 n ci j j i n n h            2*tan 2 c ci di i n h w b    * * 1 tan tan 3 n c ci c j j i n h h n v       1 2 3 n ci j j i n n h           c pi i iq lq   tan n c pi i j c i j i q n h q       2c pi l  tan 2 n j c c pi j i n h       n j j i n h   internal actions horizontal lever arm (xj) vertical lever arm (yj)  1 2 ci ci gi i n n f vhb f   13 n ci j j i n n h           1 1 1 ( ) i i qi i ci i j j j ci j j f n n b h q n b h n vf                 12 n ci j j i n n h           table 2: analytical expressions of the external and internal actions together with their lever arms. . moreover, from the condition of translational equilibrium it is possible to define the load factor s related to the mechanism of pure sliding; it is: 1 1 1 1 1 1 1 n n gi qi i i s n n n n n ai bi ci di i i i i i i f f w w w w q                      (12) as already discussed in [22] it is always s ≥ f, resulting in particular s = f when tanc = tanb. this implies that the pure sliding failure rarely occurs, although the following parameters can increase the vulnerability to this kind of mechanism: the slenderness of the unit blocks together with the absence of overloading, a low number of rows or a low value of the friction coefficient [19, 28]. in these cases the entire wall is involved in the mechanism and the load factor tends to its maximum value coincident with the friction coefficient. this means that the friction coefficient represents an upper bound of the load factor and the condition s = f marks the transition from the mixed rocking-sliding to pure sliding mechanism. lastly, tab. 3 reports the expressions of the external actions for a three-storey masonry wall, when αp2 <c < p3. it can be derived from fig. 4 that the forces wc1 and wd1 at storey 1 and wb3 and wc3 at storey 3 are null. finally, being c greater both than p1 and p2, q1 and q2 assume the maximum value depending on the length l of the wall; q3, instead, depends on the inclination of the crack line c, being c ≤ p3. l.u. argiento et alii, frattura ed integrità strutturale, 46 (2018) 226-239; doi: 10.3221/igf-esis.46.21 234 storey wai wbi wci wdi qi 1 1 1n b hv 1 1( )n l v hb   lq1 2 2 2n b hv 2 2 2( ) ( )cn n l v hb    * 2 2 2 3tan c cn h b n   2* 2 2 tan 2 c cn h b   lq2 3 3 3n b hv  2* 3 3 tan 2 c cn h b   3 3tan cn h q table 3: expressions of the external actions for three-storey masonry wall, when p2 < c < p3. sensitivity analysis and validation of the proposed model sensitivity analysis numerical analysis is here reported in order to test the sensitivity of the results obtained from the proposed model with respect to the main geometrical parameters, the overloading and the friction coefficient. the dimensionless definition of such parameters is reported in tab. 4, together with their reference values. all the results of the numerical analysis of this and subsequent section have been obtained by using the solver tool from microsoft excel to calculate the minimum of eq. (10). parameter variable definition reference value wall shape ratio t h/l 1 unit shape ratio m h/l 1/3 number of rows o h/h 60 overloading ratio p q/(hb) 0 friction coefficient f f 0.6 table 4: non-dimensional parameters accounted by numerical analysis. the sensitivity analysis has been performed by varying only one parameter at a time, while keeping the others as reference values. for each parameter, three values are considered as representative of most recurrent cases. the analyzed model is a three-storey wall, with constant inter-storey height and equal overloading condition at each level. in tab. 5 the results in terms of load factor  and inclination angle c of the crack line are reported, highlighting the percentage variation of  for each set with respect to that corresponding to the reference value of the same parameter. this table also reports the c/b ratio for each set which is useful to indicate the prevalence of a mechanism over the other; in fact, according to eq. (8), when c/b → 1 fw → 0 and only rocking occurs, while when c/b → 0 fw → f and only sliding may take place. overall, a relevant trend of the position of the rotational hinge emerges from the analysis. in fact, for all the accounted combinations of parameters, except for set 4 only, the hinge is always located at the base vertex of the entire wall, defining a mechanism that always involves three levels. this also means that the load factor corresponding to such a position is always lower than those obtained if the hinge is located at the upper levels. set 4 is the only case with the hinge at the base of the top level. then, looking at the results related to set 1 and 2 in tab. 5, it arises that increasing friction coefficient implies the increment of the load factor and also of the inclination angle of the crack line with a bigger portion of the wall involved into the mechanism. the results related to the parameters p (sets 3 and 4) and o (sets 5 and 6), show that the variation of the overloading ratio and the number of rows are substantially irrelevant both on the load factor and the angle c. however, as previously mentioned, the only effect observed for set 4, corresponding to overloading ratio p = 8, is the shift of the position of the a l.u. argiento et alii, frattura ed integrità strutturale, 46 (2018) 226-239; doi: 10.3221/igf-esis.46.21 235 hinge from the base of the three-storey wall to the base of the top wall, even if the load multipliers corresponding to the three possible positions are very close to each other ( = 0.576, 0.578 and 0.582 from the top to the bottom, respectively). variable set value  %  var. c (deg) c/b f 1 0.4 0.519 -10.84% 35.51 0.63 ref 0.6 0.583 40.15 0.71 2 0.8 0.626 7.48% 43.34 0.77 p ref 0 0.583 40.15 0.71 3 2 0.578 -0.75% 40.11 0.71 4 8 0.576 -1.20% 40.12 0.71 o 5 36 0.513 -11.94% 37.42 0.66 6 45 0.585 0.46% 40.16 0.71 ref 60 0.583 40.15 0.71 t ref 1 0.583 40.15 0.71 7 2 0.406 -30.30% 55.64 0.99 8 3 0.290 -50.15% 56.31 1 m ref 1/3 0.583 40.15 0.71 9 1/2 0.451 -22.65% 35.12 0.78 10 1 0.252 -56.72% 26.57 1 table 5: results of sensitivity analysis. a significant influence on the load factor, instead, is due to the wall shape ratio t. in fact, increasing value of t implies increasing slenderness of the wall and decreasing load factors . in particular, assuming as a reference the load factor related to a square wall (t = 1),  decreases by about 30% when t = 2 (set 7) and by about 50% when t = 3 (set 8). moreover, it is worth noting that if the slenderness of the wall increases, the geometry of the mechanism changes significantly with respect to the case of square wall, because it results c > p, being in particular p2 < c < p3 and c > p3 for sets 7 and 8, respectively. this circumstance can justify the drastic variation of the load factor when going from t =1 to t =2, while from t =2 to t =3 the decrement of the load factor is lower. finally, sets 9 and 10 reveal that also the variation of the unit shape ratio m has a relevant effect both on the load factor and the angle c. in particular, with respect to the reference value related to m = 1/3, the load factor decreases by about 23% for m = 1/2 and by about 57% for m = 1. the same trend is also reported for the inclination angle of the crack line, that decreases with increasing values of m; in particular when m = 1, it is c = b = tan-1(1/2m) pointing out that in this case the frictional resistances are null and the mechanism involves only pure rocking. on the other hand, the increment of m implies the reduction of the overlapping length v of the unit blocks and as a consequence the reduction of the frictional resistances. validation of the proposed model in this section the results provided by the proposed approach to the analysis of the in-plane rocking-sliding mechanism of a multi-storey masonry wall are compared and validated throughout the comparison with other models available in the literature, such as the micro-block model developed by orduña [20] and the macro-block models proposed by buhan and de felice [29], orduña [20] and speranza [28]. the micro-block model, in particular, is here assumed as a reference to evaluate the macro-block models. the non-dimensional parameters accounted in the present analysis are those reported in tab. 4, except for the friction coefficient which is not included in the analysis and is kept as f = 0.75 for all the sets. the different sets of values assumed l.u. argiento et alii, frattura ed integrità strutturale, 46 (2018) 226-239; doi: 10.3221/igf-esis.46.21 236 for these parameters are reported in tab. 6 where the geometric ones have been chosen accounting for the condition c ≤ min(b, p). set wall t m o p 11 single-storey 0.5 1/3 12 12 single-storey 1.0 1/3 12 13 single-storey 1.0 1/2 12 14 single-storey 1.0 1 12 15 five-storey 1.0 1/3 150 16 five-storey 1.0 1/3 150 1 17 five-storey 1.0 1/3 150 8 table 6: sets of values assumed by the parameters of the comparative analysis. tab. 7 reports the comparison in terms of load factor between the proposed macro-block model and the micro-block model of orduña [20], highlighting the percentage difference; in tab. 8, instead, there are the load factors provided by the other macro-block models and the percentage difference with respect to the micro-block model of orduña [20]. in both cases, the comparison is possible only with reference to a single-storey wall (sets 11-14), accounted by all the models considered. multi-storey walls are, in fact, accounted only by the model developed by speranza [28] and the comparison with the proposed model is reported in tab. 9 with reference to a five-storey wall, having constant inter-storey height. looking at the results related to sets 11 and 12 in tabs. 7 and 8, it is possible to derive that when t ≤ 1, i.e. for stocky walls, the load factor is mostly not influenced by this parameter. besides, the load factors obtained from the proposed model (tab. 7) and the speranza’s model [28] (tab. 8) are very close to that of the micro-block model and by the safe side too. instead, the load factors of the other macro-block models (tab. 8) provide higher percentage differences with respect to the micro-block model, up to 23% for the model of de buhan and de felice [29]. set micro-block model [20] proposed macro-block model %  var. 11 0.69 0.65 -5.8 12 0.68 0.65 -4.4 13 0.49 0.49 ±0.0 14 0.26 0.26 ±0.0 table 7: micro-block model [20] vs. the proposed macro-block model. load factors and percentage differences. set orduña [20] %  var. de buhan and de felice [29] %  var. speranza [28] %  var. 11 0.75 +8.7 0.53 -23.2 0.67 -2.8 12 0.65 -4.4 0.53 -22.1 0.67 -1.5 13 0.50 +2.0 0.43 -12.2 0.52 +6.1 14 0.25 -3.8 0.31 +19.2 0.27 +3.8 table 8: load factors provided by literature macro-block models and percentage difference with the micro-block model. set proposed model speranza [28] %  var. 15 0.47 0.52 10.64 16 0.47 0.48 +2.13 17 0.47 0.37 -21.28 table 9: load factors provided by the proposed model and that of speranza [28] related to sets 15, 16 and 17. l.u. argiento et alii, frattura ed integrità strutturale, 46 (2018) 226-239; doi: 10.3221/igf-esis.46.21 237 moreover, for the proposed macro-block model, a doubled value of the unit shape ratio m, accounted by sets 13 and 14 (tab. 7), involves a reduction of the load factor to about half. the values obtained, on the other hand, exactly coincide with those obtained from the micro-block model. the macro-block models of orduña and speranza confirm the same trend with little percentage differences with respect to the micro-block model. the model of de buhan and de felice, instead, is less sensible to the parameter m and its percentage variation with respect to the micro-block model is more evident. all the models, however, highlight the same trend, i.e. the load factor decreases as the unit shape ratio m increases. this trend can be explained with the reduction of the frictional resistances due to reduction of the overlapping length of the unit blocks. thus, summarizing the mentioned results related to a single-storey wall, it arises that the proposed model together with the model of speranza [28] are more reliable with respect to the other accounted macro-block models, since they provide limited percentage differences with respect to the micro-block model of orduña [20], assumed as a reference. these results are also better displayed in fig. 5. figure 5: load factors provided by the literature vs. the proposed macro-block model. as previously anticipated, with reference to multi-storey walls the proposed model is comparable only with that developed by speranza [28], since the other macro-block models do not account for this case. thus, the results related to sets 15, 16, 17 are reported in tab. 9. it emerges that while the load factor of the proposed model is not influenced by the parameter p accounting for the overloading, that provided by speranza [28] decreases with increasing p. this trend of the latter model is mainly due to the absence of the contribution fq of the frictional resistance which therefore cannot counteract the overturning moment of the increasing overloading, as is possible with the proposed model. conclusions n this work, the mixed rocking-sliding mechanism of multi-storey walls due to in-plane horizontal actions has been analyzed; to this aim, a macro-block model has been adopted, schematizing the geometry of the mechanism through a single crack line where the frictional resistances and the relative displacements between the macro-blocks are concentrated. hence, the kinematic approach of limit analysis has been used to evaluate the inclination of the crack line and the position of the rotational hinge along the height of the wall, assuming that it is always located in correspondence of the floor levels. with such a purpose, a routine of minimization of the load factor related to each possible position has been implemented, comparing the results in order to choose the minimum value. the innovative aspect of the study is mainly related to the modelling of the resultant frictional resistance involved in a mixed mechanism with rocking and sliding; in fact, a criterion, based on the inclination angle of the crack line, is adopted, under the assumption of coulomb i l.u. argiento et alii, frattura ed integrità strutturale, 46 (2018) 226-239; doi: 10.3221/igf-esis.46.21 238 dry frictional contact with non-associated flow rule. this criterion, experimentally and numerically validated in previous works is now generalized to the analysis of a multi-storey masonry wall. a numerical analysis has been performed in order to test the sensitivity of the proposed model to the main geometrical parameters, as the shape ratios related to the wall and unit block and the number of rows; the overloading condition and the friction coefficient have been also taken into account. the analysis has highlighted that the overloading ratio and the number of rows are substantially irrelevant both on the load factor and the inclination angle c of the crack line; the unit shape ratio m, instead, influences both these parameters that result decreasing with increasing values of m. moreover, the wall shape ratio t, has a key role in the rocking-sliding mechanism of a slender multi-storey wall (t > 1) while it is quite irrelevant for squat walls (t <1). in the first case, in fact, increasing values of t imply increasing slenderness of the wall and decreasing load factors . this parameter, instead, results increasing with increasing values of the friction coefficient, as expected. lastly, the proposed model has been validated through the comparison against a micro-block and other macro-block models existing in the literature. the comparison has been performed in terms of both the load factor and the failure mode and with reference to key parameters as wall shape ratio, unit shape ratio, number of rows and overloading condition. it emerged that the proposed model provides results very close to the micro-block model, assumed as a reference, and can approach the “exact” solutions much better than the other compared macro-block models. these results can be very promising because can be obtained with lower computational effort than the micro-block modelling approaches, suggesting the possibility of using the proposed model also for extensive evaluations of the vulnerability of the ancient urban centres. acknowledgments he authors acknowledge the sponsorship of the italian civil protection, through the reluis project-line: masonry structures (2018). references [1] page, a.w. (1981). the biaxial compressive strength of brick masonry, p. i. civil eng. pt. 1, 71 (2), pp. 893-906. [2] mann, w. and muller, h. (1982). failure of shear-stressed masonry. an enlarged theory, tests and application to shear walls, p. brit. ceramic soc., 30, pp. 223-235. [3] dialer, c. (1991). some remarks on the strength and deformation behaviour of shear stressed masonry panels under static monotonic loading, proc. 9th international brick/block masonry conference, berlin (germany), pp. 276-283. [4] ceradini, v. (1992). models and experimental tests for the study of historical masonry, ph.d. thesis., university of roma la sapienza, roma, italy. [5] roca, p., cervera, m., gariup, g. and pelà, l. (2010). structural analysis of masonry historical constructions. classical and advanced approaches, arch. comput. methods eng., 17, pp. 299-325. doi: 10.1007/s11831-010-9046-1. [6] bui, t.t., limam, a., sarhosis, v. and hjiaj, m. (2017). discrete element modelling of the in plane and out of plane behaviour of dry joint masonry wall constructions, eng. struct., 136, pp. 277-94. doi: 10.1016/j.engstruct.2017.01.020. [7] cannizzaro, f., pantò, b., caddemi, s. and caliò, i. (2018). a discrete macro-element method (dmem) for the nonlinear structural assessment of masonry arches, eng. struct., 168, pp. 243-256. doi: 10.1016/j.engstruct.2018.04.006. [8] gilbert, m., casapulla, c. and ahmed, h.m. (2006). limit analysis of masonry block structures with non-associative frictional joints using linear programming, comput. struct., 84(13-14), pp. 873-87. doi: 10.1016/j.compstruc.2006.02.005. [9] mousavian, e. and mehdizadeh saradj, f. (2018). automated detailing and stability analysis of under-construction masonry vaults, j. archit. eng. asce 24(3), art. no. 04018014. doi: 10.1061/(asce)ae.1943-5568.0000314. [10] silva, l.c., lourenço, p.b. and milani, g. (2017). nonlinear discrete homogenized model for out-of-plane loaded masonry walls, j. struct. eng.-asce, 143(9), art. no. 04017099. doi: 10.1061/(asce)st.1943-541x.0001831. t l.u. argiento et alii, frattura ed integrità strutturale, 46 (2018) 226-239; doi: 10.3221/igf-esis.46.21 239 [11] kooharian, a. (1952). limit analysis of voussoir (segmental) and concrete arches, j. american concrete institute, 24(4), pp. 317-28. [12] heyman, j. (1966). the stone skeleton, int. j. solids struct., 2, pp. 249-79. [13] drucker, d.c. (1954). coulomb friction, plasticity and limit loads, j. app. mech., 21(1), pp. 71-4. [14] livesley, r.k. (1978). limit analysis of structures formed from rigid blocks, int. j. num. method eng., 12, pp. 185371. doi: 10.1002/nme.1620121207. [15] casapulla, c. and maione, a. (2016). formulating the torsion strength of dry-stacked stone blocks by comparing convex and concave contact formulations and experimental results, indian journal of science and technology, 9(46), 1-7.c doi: 10.17485/ijst/2016/v9i46/107346. [16] casapulla, c. and maione, a. (2018). modelling the dry-contact interface of rigid blocks under torsion and combined loading: concavity vs. convexity formulation, int. j. nonlin. mech., 99, pp. 86-96. doi: 10.1016/j.ijnonlinmec.2017.11.002. [17] sarhosis, v., garrity, s.w. and sheng, y. (2015). influence of brick–mortar interface on the mechanical behaviour of low bond strength masonry brickwork lintels, eng. struct., 88, pp.1–11. doi: 10.1016/j.engstruct.2014.12.014. [18] sassu, m., giresini, l., bonannini, e. and puppio m.l. (2016). on the use of vibro-compressed units with bionatural aggregate, buildings, 6(3), art. no. 40. doi: 10.3390/buildings6030040. [19] d’ayala, d. and speranza, e., 2003. definition of collapse mechanisms and seismic vulnerability of masonry structures, earthq. spectra, 19(3), 479-509. doi: 10.1193/1.1599896. [20] orduña, a. (2003). seismic assessment of ancient masonry structures by rigid blocks limit analysis, ph.d. thesis, university of minho, guimarães, portugal. [21] casapulla, c., maione, a., argiento, l.u. and speranza e. (2018). corner failure in masonry buildings: an updated macro-modeling approach with frictional resistances, eur. j. mech. a-solid, 70, pp. 213-225. doi: 10.1016/j.euromechsol.2018.03.003. [22] casapulla, c. and argiento, l.u. (2018). in-plane frictional resistances in dry block masonry walls and rocking-sliding failure modes revisited and experimentally validated, compos. part b-eng., 132, pp. 197-213. doi: 10.1016/j.compositesb.2017.09.013. [23] lagomarsino, s. and podestà, s. (2004). seismic vulnerability of ancient churches: i. damage assessment and emergency planning, earthq. spectra, 20(2), pp. 377-94. doi: 10.1193/1.1737735. [24] pantò, b., giresini, l., sassu, m. and caliò, i. (2017). non-linear modeling of masonry churches through a discrete macro-element approach, earthq. struct., 12(2), pp. 223-236. doi: 10.12989/eas.2017.12.2.223. [25] giresini, l., sassu, m., butenweg, c., alecci, v. and de stefano, m.d. (2017). vault macro-element with equivalent trusses in global seismic analyses, earthq. struct., 12(4), pp. 409-423. doi: 10.12989/eas.2017.12.4.409. [26] lagomarsino, s. (2015). seismic assessment of rocking masonry structures, b. earthq. eng., 13(1), pp. 97-128. doi: 10.1007/s10518-014-9609-x. [27] casapulla, c. and maione, a. (2017). critical response of free-standing rocking blocks to the intense phase of an earthquake, international review of civil engineering, 8(1), pp. 1-10. doi: 10.15866/irece.v8i1.11024. [28] speranza, e. (2003). an integrated method for the assessment of the seismic vulnerability of historic buildings, ph.d. thesis, university of bath, uk. [29] de buhan, p. and de felice, g. 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can be opened with acrobat and adobe reader 5.0 and later.) >> /namespace [ (adobe) (common) (1.0) ] /othernamespaces [ << /asreaderspreads false /cropimagestoframes true /errorcontrol /warnandcontinue /flattenerignorespreadoverrides false /includeguidesgrids false /includenonprinting false /includeslug false /namespace [ (adobe) (indesign) (4.0) ] /omitplacedbitmaps false /omitplacedeps false /omitplacedpdf false /simulateoverprint /legacy >> << /addbleedmarks false /addcolorbars false /addcropmarks false /addpageinfo false /addregmarks false /convertcolors /converttocmyk /destinationprofilename () /destinationprofileselector /documentcmyk /downsample16bitimages true /flattenerpreset << /presetselector /mediumresolution >> /formelements false /generatestructure false /includebookmarks false /includehyperlinks false /includeinteractive false /includelayers false /includeprofiles false /multimediahandling /useobjectsettings /namespace [ (adobe) (creativesuite) (2.0) ] /pdfxoutputintentprofileselector /documentcmyk /preserveediting true /untaggedcmykhandling /leaveuntagged /untaggedrgbhandling /usedocumentprofile /usedocumentbleed false >> ] >> setdistillerparams << /hwresolution [2400 2400] /pagesize [612.000 792.000] >> setpagedevice microsoft word numero 25 art 6 a. shanyavskiy, frattura ed integrità strutturale, 25 (2013) 36-43; doi: 10.3221/igf-esis.25.06 36 special issue: characterization of crack tip stress field subsurface metals fatigue cracking without and with crack tip andrey shanyavskiy state centre for flights safety, airport sheremetievo-1, po box 54, moscow region, chimkinskiy state, 141426, russia, shananta@mailfrom.ru abstract. very-high-cycle-fatigue regime for metals was considered and mechanisms of the subsurface crack origination were introduced. in many metals first step of crack origination takes place with specific area formation because of material pressing and rotation that directed to transition in any volume to material ultrahigh-plasticity with nano-structure appearing. then by the border of the nano-structure takes place volume rotation and fracture surface creates with spherical particles which usually named fine-granular-area. in another case there takes place first-smooth-facet occurring in area of origin due to whirls appearing by the one of the slip systems under discussed the same stress-state conditions. around fine-granular-area or firstsmooth-facet there plastic zone appeared and, then, subsurface cracking develops by the same manner as for through cracks. in was discussed quantum-mechanical nature of fatigue crack growth in accordance with yang’s modulus quantization for low level of deformations. new simply equation was considered for describing subsurface cracking in metals out of fine-granular-area or fist-smooth-facet. keywords. very-high-cycle-fatigue; subsurface; mechanisms; fine-granular-area; first-smooth-facet; ultrahigh-plasticity; quantum-mechanical; crack growth. introduction atigue crack growth for metals subsurface cracking in vhcf regime has been investigated in many cases [1-5]. main idea is about continuous (conventional) fatigue crack propagation process in spite of registered range of increments of crack in one cycle in two orders less than crystallographic lattice. it is physically clear that crack increment cannot be less than one lattice. that is why crack growth process in the considered case is not continuous. another basically idea is about subsurface cracking process that takes place in vacuum [6]. special tests in vacuum have been performed for steels and titanium alloys and it was demonstrated similarity in fracture surface patterns for through and subsurface cracks when through cracks did propagation in vacuum. moreover, it was discovered fine-granular-area (fga) for the first stage of through crack growth in vacuum. the idea about subsurface fatigue crack propagation in vacuum contradicted with test results of steels having different contents of hydrogen [7]. if hydrogen contents in metals has increasing, subsurface crack initiation has acceleration. clear that, if hydrogen influenced metals cracking, there is subsurface environment for developed fatigue cracks. in the center of a fish-eye area there has been discovered high level of oxygen [8, 9]. this is the same evidence that subsurface cracking can takes place in oxygen environment. in many cases studied of steels [10] and superalloy [8] subsurface cracking, there were very clear registered fatigue striations on the fracture surface which has been formed before crack evidence on the specimen surface. the fatigue striation formation process has been considered based on the knowledge about environment influence on this process. this consideration based on well-known investigation results which show that fatigue striations have not evidence in vacuum. consequently, the discussed investigation results demonstrate that subsurface cracking occurs in environment but not in vacuum. f http://www.gruppofrattura.it http://dx.medra.org/10.3221/igf-esis.25.06&auth=true a. shanyavskiy, frattura ed integrità strutturale, 25 (2013) 36-43; doi: 10.3221/igf-esis.25.06 37 it should be corrected knowledge about meaning of the word that used to such indication environment state as “vacuum”. usually considered: (1) low vacuum with gas pressure less than 100 pa; (2) middle pressure with 0.1<p <100pa; (3) high vacuum with 10-5 pa<p<0.1pa; (4) ultra-high-vacuum with p<10-5 pa. tests in vacuum performed under continual pumping with vacuum pumps to support needed level of low pressure in specimen chamber but not less that 10-5 pa. at the same time it should be clear that always in specimen chamber exist pressure of gases. this situation attests itself as dynamical vacuum. it means that inside of camera when tests perform exists low pressure always. that is why it should be corrected meaning of word “vacuum’: it is environment with low pressure of gases or other elements. the problem of subsurface crack initiation and propagation has been briefly discussed in the case of titanium alloy vt3-1 [11]. following by this consideration was clear that subsurface fatigue cracking performs not in vacuum but in low level pressure of rest cases existing in metals which are enough for environment influence consideration on this process. moreover, investigating of crack initiation processes, occurring and developing in chemically clean metals because of different types of defects formation, such as, for instance, pore’s, microcracks and etc., the theory of strength suggested that there inside of the defect volume has to be vacuum state. but it contradicted with physics of phase transformation [12]. from the diagram of phase transformation for each chemical element followed that solid phase cannot be in equilibrium state at the contact with vacuum. the solid body equilibrium state can be possible, if exist interaction effect between its own vapor or liquid in the triple point, t3, where simultaneously exist three phases. for example, if there exists in solid body spherical pore, it needs to be fill up of vapor or liquid metal. if volume of pores will be increased under external stressing, quantity of liquid and gas phases also will have increase. nevertheless, but it is clear that subsurface fatigue cracking in metals takes place not in vacuum but in specific environment having low value of rest gases or other elements pressure. at the surface layer atomic stress-state is not the same that subsurface. there is biaxial stress-state at the matrix by the surface and hydrostatic case takes place subsurface. that is why energy dissipation at the surface is more effective than subsurface. moreover, at the surface takes place disordering in atomic state. that is why there is more effective energy dissipation process under low level of deformation than subsurface. subsurface hydrostatic state influenced not only residual state because of non-elastic deformation but there metals can have transition in ultra-high-plasticity (uhp) state that has been discussed in the first part of our paper. also, there can be developed deformations not only during subsurface crack origination because of material volume rotations [11] but for crack propagation too. so, it should be considered metals critical state for crack origination and propagation by the three criteria: (1) non-elastic local deformation; (2) whirls formation under hydrostatic stress-state; (3) self-organized introducing in area of cracked metals own vapor or liquid because free surface can be creates only in environment conditions with some pressure. below will be discussed process of subsurface fatigue crack propagation in steels in gigacycle or ultra-high-cycle-fatigue (uhcf) regime based on the introduced above criteria. mechanism of fga forming e will discuss process of fga formation during crack propagation based on discovered fracture surface patterns for investigated steels [2, 13]. typical fracture surface patterns for all specimens are shown in fig.1. there are spherical and elliptically shaped particles and the same shape has roughed fracture surface in fga. it is not granules. it is nano-structure of metals that has been performed during cyclic loading. in some fga places there very clear seen “dimples” because several particles have been moved from their position during deformation process during crack propagation. size of particles is not more than 50nm. it is typical nano-structure for investigated metals. investigations subsurface layers in the depth direction for one and another part of fracture surfaces in fga discovered there the same ensemble of particles which structure has difference from matrix structure [2]. chemical composition investigations of the fga in steels performed by the fracture surface have shown that there is more percent of carbon than exists in metals composition [14]. following consideration of non-elastic diffusion in metals this effect can be clear explained. during metals plastic deformation in the case of hydrostatic pressure at the crack tip there takes place local matrix heating for propagating crack, carbides destruction, and, in another way, carbon from matrix has possibility to move inside of free area for occurred crack, and carbon moves there during crack propagation. this effect excluded ultra-high-vacuum state inside of the growing crack. because of hydrostatic stress-state the diffusion process can be considered based on the model that has been introduced for explanation subsurface crack occurring in the w http://www.gruppofrattura.it http://dx.medra.org/10.3221/igf-esis.25.06&auth=true a. shanyavskiy, frattura ed integrità strutturale, 25 (2013) 36-43; doi: 10.3221/igf-esis.25.06 38 case of rolling contact [15]. this case also related to hydrostatic pressing. for the introduced consideration in discussed case of external loading condition, the carbon diffusion in crack takes place because of carbides destruction. now it is clear that the carbon diffusion in area of crack is main process for steels that followed subsurface cracking. figure 1: view of fine-granular-area under high magnification [13]. spherical particles are dominant of the surface pattern. let be discussed metals composition in the depth direction in fga. it is clear that the same spheres or ellipsoids that have been discovered by the fracture surface followed metals subsurface cracking in the depth direction from the crack edges [2]. this type of nano-structures cannot be suddenly appeared in metals. it should be developed in time some process of their formation in the thin layer of fga where uhp has taken place. then in matrix develops specific process of fracture surface formation by the border of this structure. this fracture mechanism ought to be considered as the one of the step in nano-structure formation process based on earlier introduced consideration of spherical and elliptically shaped particles formation during fatigue crack propagation [16, 17]. earlier the same type of fracture surfaces patterns as ellipsoidal and spherical particles have been discovered in al-based alloys subjected to biaxial cyclic loading. the spherical or ellipsoidal particles had occurring because of specific process of metals deformation and destruction under local rotation when intensive pressing of material volume is occurred. in all cases of metal cracking under cyclic loads there has non-conventional manner of matrix fracture along the crack front. in the discussed case of fga formation for steels or other metals there is appearance of the same particles formation mechanism, fig2. figure 2: schema of the spherical particles formation in fga origin after ultra-high-plasticity in some metal’s volume after metals experienced uhp in area of the crack origination, inside of the plastically deformed volume there starts the rotation deformation process of local volumes inside the area of uhp. if critical density of defects is exceeded, by the border of rotated volumes appeared in homogeneity with spherical shape of fracture surface formation and with spherically or elliptically shaped particles too. during rotations in volume which will be in a further failed with fga formation, there takes place heating and inside of the volume can go carbon, rest gases and other elements of decomposed matrix. http://www.gruppofrattura.it http://dx.medra.org/10.3221/igf-esis.25.06&auth=true a. shanyavskiy, frattura ed integrità strutturale, 25 (2013) 36-43; doi: 10.3221/igf-esis.25.06 39 the discussed process of particles formation directed to crack growth retardation [16]. that is why cracking of metals during fga formation cannot be strongly expressed in term of crack growth rates now because it is not conventional process. it can be only say that the estimated crack growth in area out of fga is less than all period of subsurface metals cracking from the moment of start to form fga. based on the performed consideration, it can be summarized process of fga formation during metals subsurface fatigue cracking in the next manner: (1) in steels under cyclic loads there in the area of uhp takes place diffusion carbon with thin layers formation by the occurred free surface. the main role in fracture surface formation played matrix rotation instability that directed to for spherical particles and spherical in shape surface patterns. carbon is good seal for preventing crack edges interaction effect that is why its moves in area of the crack. hydrogen influenced this process being in matrix and trapped inclusions; (2) in titanium alloys there takes place diffusion of rest gases inside of the crack area and, also, some of the matrix chemical components can go in [11]. based on the considered sequence of fatigue crack growth events we can conclude that in all discussed cases of steels fatigue cracking there were four areas of different processes of fracture surface formation: (1) crack origination because of formation fga, fsf, or supergrain cracking; (2) smooth surface formation with or without bp that depended on the stress concentration around inclusions and cracked supergrain orientation in space according to acting external loading; (3) drastically change to increasing of fracture surface roughness because of metals cracking by grain boundary of by slip bands; (4) drastically change to fast fracture with dimpled surface formation. from considered sequence of formed fracture surface areas one can be conclude that it is not only one way for metals deformation and destruction processes to realize fatigue crack propagation mechanisms on the all discussed stages. there can be intensive cracking by the grain before fast fracture without influence of this mechanism on the crack origination in one matrix. in another metal crack origination has been performed with supergrain but fsf took place in the area of origin. consequently it can be conclude that in the case of subsurface crack origination there takes place some specific selforganized process of matrix destruction that has to be investigated further more precisely to discover regularities in this process. quantum-mechanical nature of propagated cracks n the case of subsurface fatigue cracking it was introduced paris-hertzberg equation for metals in the next form [1]: 1/2 3/ ( / [ ] )effda dn b k e b  (1) in eq.(1), e is young’s modulus, b – modulus of burger’s vector. earlier it was theoretically considered crack growth process in metals based on non-continuous approach [6]. it was introduced knowledge about minimum value of crack increment such as quant of metals cracking, aq, and this value has been calculated for steels [18] and al-based alloys [19, 20]. cascade of crack increments being more than aq –value was demonstrated and strongly expressed evidence of crack growth rate hierarchy was introduce in the next form: 1/1( / ) / ( / ) ( / ) q i i t tda dn da dn    (2) in eq. (2), t and t are theoretical shear and tension stress, respectively, q=1,2,4,8…. many experiments were done to confirm the relation (2) for al-based alloys [19, 21], fig.3. it was discovered constant values of crack growth rates in the crack growth direction with their hierarchy in accordance with eq. (2). following by physical approach to metal failure it is very easy to shown that for all metals cannot be realized crack increment in one cycle less than two lattice. for, example, one dislocation has in homogeneity in two lattices at its tip, fig.4. if sliding process is dominant ahead of a crack tip there will be interaction effect between two dislocations that directed to form inhomogeneities in the distance 4b (see fig.12b). values of aq were calculated and shown that for steels it is 0.5nm [18], but for al-based alloys it is 2nm [19], [21]. quantum-mechanical nature of subsurface crack growth can be seen based on test results under tension of wide range of metals in area of infinitesimal deformations. it was discovered quantum-mechanical nature for quantization of yang modulus [22]. in the range of stress levels for metals subsurface cracking realizes so small deformations that they ought to be considered as metals extension in area of infinitesimal deformation. in this case it was shown that knowledge about elastic modulus disappeared because in this area of deformation exists quantization of modulus by the order [22]: ( /2 ) ( /4 )2.06(1 )( 2 / 3) [1 / ( 2 )]s p me a t t    (3) i http://www.gruppofrattura.it http://dx.medra.org/10.3221/igf-esis.25.06&auth=true a. shanyavskiy, frattura ed integrità strutturale, 25 (2013) 36-43; doi: 10.3221/igf-esis.25.06 40 52.89 10a x mpa 1, 2, 3..., 0( 1)s p or  /2 /4(0) ( 2 / 3)s p a  (4) in eq.(3) tmtemperature of melting;  poisson factor; (0) shear modulus. figure 3: fatigue striation spacing against crack growth in the depth direction for semi-elliptic crack in a specimen of ak6 al-based alloy. numbers indicate spacing-values calculated in accordance with eq.2. a) b) figure 4: scheme of minimum inhomogeneity occurring (a) at the dislocation and (b) crack tip. it is very clear that subsurface cracking in uhcf regime takes place with level of deformation being the same which have to be classified as infinitesimal deformations. that is why quantum-mechanical approach for consideration crack increments quantization has fundamental nature. another way of consideration for quantum-mechanical approach to fatigue crack growth can be introduced based on wellknown relation for time dependent processes of solid body degradation [23]: 0 0exp( ) /u kt    (5) in eq.4 u0 – energy of activation for cracking process;  constant;  stress of external loading;  time for matrix cracking; 0 time for cracking start. let be considered crack growth rate in the form 0( / ) ( / ) exp( { } / )i ida dn da d c u e kt      (6) in the case of infinitesimal deformations between stress and strain takes place not uniformly expressed dependence because of (6). consequently, there will be cascade of crack growth rates constant values with constants energy levels 0( )iu e  , where i is local deformation at the crack tip. in the case of tests with high frequency measurements of crack increment can be realized now to register average value. that is why most of test results have not evidence of considered nature of crack growth. nevertheless, in one of the wellhttp://www.gruppofrattura.it http://dx.medra.org/10.3221/igf-esis.25.06&auth=true a. shanyavskiy, frattura ed integrità strutturale, 25 (2013) 36-43; doi: 10.3221/igf-esis.25.06 41 known tests this effect has been demonstrated [2]. horizontal line shows cascade of crack increments with constant value. indeed, it cannot be exactly calculated values on constant increments but they evidently exist. it needs to point out that during external stress level increasing there is in matrix process deformation with different value of elastic modulus for different areas in metals. that is why in matrix there will be different areas where plastic deformation will be realized. difference in value of local yield stress under the same external stress level, for instance, for polycrystalline aluminum can be more than 1.5 times at the moment of its start. under cyclic loading there will be difference in local stressing metals during uploading portion and unloading portion in each cycle because exist difference in elastic modulus for tension and compression too. moreover, the problem of specific environment low pressure for subsurface cracking shows that the (keff)e which has been used for crack growth rate calculation, ought to be diminished on the factor ce=(keff)e/(keff)se<1, where (keff)se is the stress intensity factor in environment with low pressure that at the one atmosphere. this consideration based on many test results that can be taken from review [21]. summarizing performed briefly discussion of non-conventional metals subsurface fatigue cracking it ought to introduce corrections in paris-hertzberg [1] equation in the next form: 1/2 3/ [ / ( ) ]q e eff qda dn a c k e a  (7) for metals it should be considered physically quant of fracture aq≥2b. parameter ce= (keff)e/(keff)se<1 has to be estimated for all metals applicably to results of fatigue cracking in vacuum and in environment. next point, that ought to be discussed, for process of subsurface matrix cracking is related to slope in paris-hertzberg equation (1). earlier it was shown that for low range of crack increments in one cycle being less than 10-7m/cycle, average value of crack growth rate can be considered under the load constant condition by the same manner that it is under constant deformation [21]. from this consideration follows that subsurface cracking takes place with slope in parishertzberg equation equals “2”. this value of slope has been discovered in steels based on fatigue striations measurements for subsurface crack propagation [8]. the striation spacing interval was in the range of (0.1-2.0)x10-6m. in this investigation has been discussed this situation and the discovered slope was equal “2” related to crack opening effect with cyclical plastic zone. from the performed above consideration of subsurface crack propagation follows that it can be considered paris equation in the next form: 2/ ( )o effda dn c k  (8) the value of aq has consideration at the threshold stress intensity factor, ( )eff thk . that is why c0 in eq. (8) can be considered as 20 / ( )q eff thс a k  . at the end we can conclude that 2/ ( /[ ] )q eff eff thda dn a k k   (9) in the case of circular subsurface crack growing [10] the stress intensity factor formula is: 1/2( 2 / ) [ ]k a     (10) substituting (10) in (9) we can obtain simply equation: 0/ ( / )q cda dn a a a (11) in eq.6, a0-value determines crack length at the fga border with crack increment aq, ac-value determines maximum length of subsurface crack. this equation can be considered for failure analyses because there is not need in special knowledge of stress level or environment effect during subsurface cracking. calculated number of cycles by the formula (11) will be always less than real subsurface cracking period because fga zone creation with spherical particles formation cannot be expressed in fracture mechanics terms. concluding remarks . new mechanism of fatigue crack subsurface origination was considered for metals with fine-granular-area forming. first, this pattern has result of material hydrostatic pressing and rotation that directed to appearance ultrahigh-plasticity in a local volume with nano-structure performing. second, fatigue cracking develops by the border of 1 http://www.gruppofrattura.it http://dx.medra.org/10.3221/igf-esis.25.06&auth=true a. shanyavskiy, frattura ed integrità strutturale, 25 (2013) 36-43; doi: 10.3221/igf-esis.25.06 42 nano-structure with their rotation and spherical particles forming. 2. it was considered quantum-mechanical nature of metals fatigue cracking on nano-scale level and shown that crack increments in loading cycle have to be strongly expressed in accordance with introduced expression. 3. simply equation was considered for subsurface cracking description and number of cycles’ estimation. it can be used in failure analyses of in-service cracked structures. references [1] bathias, c., paris, c.p., gigacycle fatigue in mechanical practice. marcel dekker, ny, usa, (2004). [2] sakai, t., li, w., lian, b., oguma, n., review and new analyses of fatigue crack initiation mechanisms of interior inclusion-induced fracture of high strength steels in very high cycle regime, in: c.berger and h.-j.christ (eds.), proc. of the int. conf. vhcf5, dvm, june 28-30, 2011, berlin, germany, (2011) 19-26. [3] j.e., jones, j.w., larsen, j.m., ritchie, r.o., proc. of fourth international conference on very high cycle fatigue, vhcf5, edited by allison, august 19-22, 2007. university of michigan, ann-arbour, michigan, usa, (2007). [4] shanyavskiy, a.a., modelling of metals fatigue cracking. synergetics in aviation. ufa, monograph, russia, (2007). [5] karsch, t., bomas, h., zoch, h.-w., influence of hydrogen and microstructure on the fatigue behavior of steel sae 52100 in the vhcf regime, in: c.berger and h.-j.christ (eds.), proc. of the int. conf. vhcf5, eds., dvm, june 2830, 2011, berlin, germany, (2011) 201-206. [6] nakamura, t., oguma, h., influence of environment on the formation unique morphology on fracture surface in subsurface fractures, in: c.berger and h.-j.christ (eds.), proc. of the int. conf. vhcf5, eds., dvm, june 28-30, 2011, berlin, germany, (2011) 257-263 [7] murakami, yu., metals fatigue: effects of small defects and nonmetallic inclusions. elsevier ltd, london, uk, (2002). [8] shanyavskiy, a.a., fatigue cracking of smooth and notched specimens of compacted superalloy ep741 np in high and very-high-cycle-fatigue regime, in: c.berger and h.-j.christ (eds.), proc. of the int. conf. vhcf5, eds., dvm, june 28-30, 2011, berlin, germany, (2011) 107-112. [9] carboni, m., annoni, m., ferraris, m., analyses of premature failure of some aluminum alloy sonotrodes for ultrasonic welding, in: c. berger and h.-j. christ (eds.), proc. of the int. conf. vhcf5, eds., dvm, june 28-30, 2011, berlin, germany, (2011) 589-594 [10] huang, z., wagner, d., bathias, c., paris, c.p., subsurface crack initiation and propagation mechanisms in gigacycle fatigue. acta materialia, 58 (2010) 6046-6054. [11] shanyavskiy, a., banov, m., the twisting mechanism of subsurface fatigue cracking in ti–6al–2sn–4zr–2mo–0.1si alloy. engineering fracture mechanics, 77 (2010) 1896–1906 [12] vasiliyev, l.s., at the theory of metals plastic deformation with melted grain boundaries. metals, 1 (2002) 112 – 122 (russia) [13] wang, c., nikitin, a., shanyavskiy, a., bathias, c., an understanding of crack growth in vhcf from an internal inclusion in high strength steel. in: andrea carpinteri, andrea spagnoli (eds), proceed. of the 4-th intern. conf. on “crack paths (cp 2012”), gaeta (italy), 19-21 september, (2012) 43. [14] shiozawa, k., lu, l., very high-cycle fatigue behaviour of shot-peened high-carbon chromium bearing steels. fatigue fract. engng. mater. struct., 25 (2002) 813-822 [15] karsch, t., bomas, h., zoch h.-w., influence of hydrogen and microstructure on the fatigue behaviour of steel sae 52100 in the vhcf regime. in: c.berger and h.-j.christ (eds.), proc. of the int. conf. vhcf5, eds., dvm, june 2830, 2011, berlin, germany, (2011) 201-206. [16] shanyavskiy, a.a., synergetical models of fatigue surface appearance in metals: the scale levels of self-organization the rotation effects, and density of fracture energy, in: g.n.frantziskonis (ed.) proc. nato “advanced research workshop on probamat-21st century”, tests, models and applications for the 21-st century, sept. 10-12 1997, kluwer academic publisher (1998) 11-44. [17] shanyavskiy, a.a., fatigue cracking simulation based on crack closure effects in al-based sheet materials subjected to biaxial cyclic loads. engineering fracture mechanics, special issue, multiaxial fatigue, (ed. by andrea carpinteri, les p.pook, andrea spagnoli), 78 (2011) 1516–1528 [18] gurevich, s.e., some aspects of fatigue fracture mechanics. in: ivanova, v.s. and gurevich, s.e. (eds), cyclical fracture toughness of metals and alloys, nauka, moscow, sssr, (1981) 19-38. http://www.gruppofrattura.it http://dx.medra.org/10.3221/igf-esis.25.06&auth=true a. shanyavskiy, frattura ed integrità strutturale, 25 (2013) 36-43; doi: 10.3221/igf-esis.25.06 43 [19] sasov, a.yu., shanyavsky, a.a., fourier-fractography foundation of quantum mechanical nature of cracks growth. acta stereol., 6/iii (1987) 825-830. [20] sasov a.yu., shanyavskiy, a.a., processing of scanning electron microscope images on basis of fast fouriertransformation. scann. microsc., 2 (1988) 827-834. [21] shanyavskiy, a.a., tolerance fatigue cracking of aircraft structures. synergetics in engineering applications. ufa, monograph, russia, (2003). [22] bell, d.f., mechanics of solids i, encyclopedia of solid, chief editor s.flugg, via/i, springer verlag, (1973). [23] jurkov, s.n., problems of solids strength. vest. akad. nauk ussr, 11 (1957) 78-82. http://www.gruppofrattura.it http://dx.medra.org/10.3221/igf-esis.25.06&auth=true microsoft word numero_31_art_3 c.l. dos santos et alii, frattura ed integrità strutturale, 31 (2015) 23-37; doi: 10.3221/igf-esis.31.03 23 mechanical behaviour of wood t-joints. experimental and numerical investigation c.l. dos santos, j.j.l. morais engineering department, school of science and technology, university of trás-os-montes e alto douro, quinta de prados, 5000801 vila real, portugal university of trás-os-montes e alto douro, citab, quinta de prados, 5000-801 vila real, portugal clsantos@utad.pt a.m.p. de jesus engineering department, school of science and technology, university of trás-os-montes e alto douro, quinta de prados, 5000801 vila real, portugal idmec, pólo-feup, rua dr. roberto frias, 4200-465 porto, portugal abstract. results of a double-shear single-dowel wood connection tested under monotonic quasi-static compression loading are presented and discussed in this paper. the wood used in this study was a pine wood, namely the pinus pinaster species, which is one of the most important portuguese species. each connection (specimen) consists of three wood members: a centre member, loaded in compression along the parallel-tograin direction and two simply supported side members, loaded along the perpendicular-to-grain direction (tconnection). the load transfer between wood members was assured by means of a steel dowel, which is representative of the most common joining technique applied for structural details in wooden structures. the complete load-slip behaviour of the joint is obtained until failure. in particular, the values of the stiffness, the ultimate loads and the ductility were evaluated. additionally, this investigation proposed non-linear 3d finite element models to simulate the t-joint behaviour. the interaction between the dowel and the wood members was simulated using contact finite elements. a plasticity model, based on hill’s criterion, was used to simulate the joint ductility and cohesive damage modelling was applied to simulate the brittle failure modes (splitting) observed in the side members of the joint. the simulation procedure allowed a satisfactory description of the non-linear behaviour of the t-joint including the collapse prediction. keywords. maritime pine wood (pinus pinaster ait.); dowel-type connections; t-connections; finite element analysis; hill plasticity model; cohesive damage models. introduction he connections are frequently the critical elements of timber structures, being responsible for the reduction of continuity and global structural strength, requiring oversized structural elements. about 80% of failures observed in timber structures are due to connections [1]. dowel-type timber connections are the most common t c.l. dos santos et alii, frattura ed integrità strutturale, 31 (2015) 23-37; doi: 10.3221/igf-esis.31.03 24 connections applied in timber structures. the singularity of this type of timber connections is associated to the combination of very distinct materials – wood and steel – and to the high anisotropy of wood. the knowledge of the mechanical behaviour of these dowel-type connections (e.g. load–slip relation, stress distribution, ultimate strength and failure modes) is of primordial importance for their rational application. this complex behaviour is governed by several geometric, material and load parameters (e.g. wood species, dowel diameter, end and edge distances, space between connectors, number of connectors, hole/dowel clearance, friction and load configuration). according to design codes of current practice [2, 3], the design of dowel-type timber connections has been based on the european yield model (eym) proposed by johansen [4]. according to the eym, the embedding strength of wood is a material parameter governing the failure of wood members. this model has an empirical basis and assumes an elasticperfectly plastic behaviour for both wood and dowel. it also considers that embedding strength is a material property, when in fact it is a combination of several geometric and material parameters. the eym only predicts the ultimate loads associated with ductile failure modes; brittle failure modes (e.g., shearing out, splitting perpendicular to grain) are not foreseen [5]. because the eym does not allow the simulation of brittle failure modes, design codes prescribe empiric minimum dimensions for connections (e.g., dowel holes to end member distances) to avoid the brittle failure modes. in addition to the minimum distances suggested by ec5 [3], the fastener slenderness may be controlled to allow ductile failure modes. generally, in order to verify the influence of parameters governing the mechanical behaviour of connections, a number of tests are required for assessing the embedding strength. these embedding tests are standardized such as in the en383 standard [6]. alternatively to the eym, 2d models have been proposed: non-linear beam on elastic foundation models [5, 7] and finite element (fe) models [5, 8-10]. however, these models do not predict the brittle failure modes. the finite element method has been used to simulate the non-linear behaviour of dowel-type wood connections involving different strategies, namely using constitutive models and failure criteria for specific failure modes [8-14], or using linear elastic fracture mechanics [15-17]. this paper presents experimental and numerical results from monotonic quasi-static compression tests of a double-shear single dowel wood connection, made of pinus pinaster wood, which is one of the species with large implantation in portugal. despite the abundance of this raw material, its use for structural applications has been disregarded due to several reasons, such as cultural and lack of data about the behaviour of this material. the experimental program included tests of single-doweled t-connections. the t-connection consists of three wood members: two simply supported side members loaded along the perpendicular-to-grain direction and a centre member loaded in compression along the parallel-to-grain direction, according to the recommendations of the en26891 standard [18]. the load–slip behaviour of the joint is determined until failure, including the characterization of the ultimate loads and the ductility. the connection configuration originated the occurrence of both ductile and brittle failure modes. for this reason, the numerical modelling included a plasticity model, to simulate the ductile behaviour observed essentially in the centre member, and a cohesive damage model implemented along with contact finite elements, to simulate the splitting occurred on side members. a three dimensional fe model of the wood connection is built using the commercial fe analysis code, ansys® [19]. the dowel is modelled as isotropic elastic material; wood is considered as orthotropic elastic-plastic material, following the hill’s criterion, in a similar approach applied by moses and prion [11-13]. cohesive elements were added to the side members at locations where brittle failures are likely to occur. the interaction between dowel and wood members is simulated using standard contact finite elements, namely surface-to-surface contact elements available in the ansys®. this approach involving mixed plasticity and cohesive damage modelling, is similar to the one followed by kaliske and resch [20, 21]. it should be noted that there is already experience documented in the literature about the fracture modelling of pine wood (the same species adopted in this study), using exclusively cohesive damage models [22, 23], but assuming the material in the elastic domain. the non-linear behaviour of the connection is evaluated and compared with the experimental data, allowing the calibration of the proposed models. experimental results and analysis he experimental program consisted of a series (10 tests) of a single-doweled t-connection. each specimen comprises three wood members: a centre member loaded in compression along the parallel-to-grain direction and two simply supported side members loaded along the perpendicular-to-grain direction (see fig. 1 and 2). the supports consisted of steel pipes with an inside diameter of 28 mm and an outside diameter of 34 mm. the distance t c.l. dos santos et alii, frattura ed integrità strutturale, 31 (2015) 23-37; doi: 10.3221/igf-esis.31.03 25 between the centres of the supports (span) was 426 mm. the load transfer between wood members was assured by means of a steel dowel, which is representative of the most common joining technique in wooden structures. wood members were cut aligned with the wood grain orientations, as illustrated in fig. 1. the thickness direction was chosen to correspond to the tangential direction of the wood. all tests were performed with a steel dowel with a nominal diameter, d = 14 mm. the nominal thickness of each wood member was 30 mm. figure 1: geometry and dimensions (in mm) of the single-doweled t-joint (d=14 mm): (a) centre member; (b) side members. figure 2: test apparatus adopted for the t-connections. tests were performed on an instron® machine, model 1125, rated to 100 kn, under crosshead displacement control. four linear variable differential transducers (lvdt) were used to measure the displacements (see fig. 2): two lvdts (1 and 2) were attached to the centre member to measure the displacement between a section of this member and the machine base; the other two lvdts (3 and 4) were directly connected to the dowel ends in order to measure the displacement between the dowel and the base of the machine. the lvdts used in the experimental program were from applied measurements® with the reference aml/eu ± 10-s10 (measurement range of ±10 mm). the data were acquired by means of a spider® 8-30 system. a loading–unloading-reloading procedure was adopted, as suggested in the en26891 standard [18]: firstly, specimens were loaded until 40% of the maximum estimated load (fest), and the crosshead position held for 30s; after this stage, specimens were unloaded until 0.1fest, and the crosshead position again maintained for 30s; finally, specimens were reloaded until failure. preliminary tests showed a maximum load of 16500 n. these strength values were the basis for planning the final tests, namely, for the definition of the initial loading cycles according to the procedures provided on the en26891 standard. the connection was tested with a displacement rate of 0.3 mm/min. wood densities were measured for each specimen member before testing. the average density was 612.8±30.7 kg/m3. wood members used in t-joint tests were placed in the laboratory several weeks before testing to allow the wood a) b) c.l. dos santos et alii, frattura ed integrità strutturale, 31 (2015) 23-37; doi: 10.3221/igf-esis.31.03 26 to stabilize with the laboratory environment. during the tests, the laboratory temperature was kept between 20 ºc and 25 ºc. the specimens used in the single-doweled t-connections were made of maritime pine wood (pinus pinaster ait.), that were manufactured from trees harvested in the region of viseu (portugal). trees with straight stems (absence of reaction wood) and diameters at breast height of approximately 400 mm were selected. three-meter-long logs were cut from the sample trees between three and six meters above the basal plane. the logs were live-sawn into thick boards that were kiln-dried to a moisture content between 10% and 12%. the specimens were cut from these boards by aligning the parallel-to-grain direction with the length of the specimens and the wood tangential direction with the thickness of the specimens, as depicted in fig. 3. wood with knots, resin pockets, or other type of defects was excluded to reduce the usual scatter observed in timber tests. figure 3: procedure for the extraction of specimens from a log of a tree (dimensions in mm). tab. 1 summarizes the main elastic properties of maritime pine wood, which have been assessed by xavier et al. [24, 25]. these authors performed their work using wood samples from trees harvested in the same region and with similar dimensions of trees used to extract the wood for this research. therefore, it is expected that the properties proposed by xavier et al. [24, 25] are representative of the wood samples used in this investigation. the elastic moduli (e) are given for the longitudinal (l), radial (r), and tangential (t) directions. in addition, the poisson ratios () and the shear moduli (g) are presented for the lr, rt, and tl planes. high anisotropic properties are verified for this wood species, which makes connections made of this material more susceptible to cracking due to perpendicular-to-grain tensile stresses. el = 15.1 gpa lr = 0.47 glr = 1283 mpa er = 1.91 gpa rt = 0.59 grt = 264 mpa et = 1.01 gpa tl = 0.05 gtl = 1117 mpa table 1: elastic properties of maritime pine [24, 25]. the load and displacements from four lvdts were recorded during the experimental tests of the t-connections. two types of direct displacement measurements were performed, namely, the displacement of a section of the middle wood member, located 60 mm from the loading plate (average displacements of lvdts 1 and 2), and the displacements of the dowel ends (average displacements of lvdts 3 and 4), both in relation to the machine base (see fig. 2). in addition to the previous displacement measurements – (1/2) and (3/4) displacements – the connection slip was computed as the difference between the previous displacements, (1/2)–(3/4). the difference in displacements represents the embedding of the middle member with respect to the dowel. the displacements and connection slip are presented in fig. 4. the analysis of fig. 4 shows that the displacements measured at the centre member ((1/2) displacement) are higher than the displacements measured directly on dowel ends ((3/4) displacement). on effect, lvdts 1 and 2 take into account the total deformation of the centre and lateral wood members; lvdts 3 and 4 only accounts for the deformation of the lateral members. the analysis of the load-(1/2) displacement results allows the assessment of the global ductility c.l. dos santos et alii, frattura ed integrità strutturale, 31 (2015) 23-37; doi: 10.3221/igf-esis.31.03 27 behaviour of the connection. with respect to this connection, 6 specimens failed at the side members and 4 failed at the centre member. fig. 5 illustrates the two referenced failure modes, with the final rupture characterized by cracks propagating in the rl system. when the rupture occurs in the centre member of the connection, it corresponds to a higher ductile behaviour because the crack is preceded by some embedding of the centre member in the dowel. the failure due to cracking of the lateral members corresponds to a global brittle behaviour, with the (3/4) displacement not exceeding 2 mm (see fig. 4b). (a) (b) (c) figure 4: experimental results: (a) load-(1/2) displacement; (b) load-(3/4) displacement; (c) load-(1/2)-(3/4) joint slip. tab. 2 summarizes the average strength and ductility values from the tests: ultimate load, fmax; maximum (1/2) displacement, d(1/2)max; maximum (3/4) displacement, d(3/4)max; stiffness from (1/2) displacement, k1; stiffness from (3/4) displacement, k2 and stiffness from (1/2)-(3/4) displacement, k3. experimental average ultimate loads were computed for each one of the two possible failure modes. it is interesting to note that the average ultimate loads are very close to each other, independently of the observed failure modes. however, the majority of the failures were observed on the side members, which may be justified by some size effect. the volume of material involved in the lateral members is twice the volume of the material of the centre member around the dowel; therefore failures are most likely to occur at the side member, for similar stress conditions leading to failure in both members. tab. 2 also includes estimates of the failure loads according to the ec5 [3]. according to this design code, the connection strength per shear plane and per fastener is obtained by the expression (1), for the side members: v ,r h ,1 1f f t d (1) and according expression (2), for the case of failure at the centre member: v ,r h ,2 20.5f f t d (2) where v ,rf is the load carrying capacity per shear plane and per fastener; h , if and it are, respectively, the embedment strength and the thickness of wood member i ( 1i  for side members; 2i  for centre member) and d is the dowel c.l. dos santos et alii, frattura ed integrità strutturale, 31 (2015) 23-37; doi: 10.3221/igf-esis.31.03 28 diameter. the previous relations consider that failure occurs due to embedding failure at the wood members. the required embedment strengths for previous formulae were obtained in the literature, specifically for the same wood species, using embedding tests with the same thicknesses ( 1 2 30 t t mm  ) and dowel diameter 14 d mm ( h ,1 h ,221.13.6 mpa; 46.44.2 mpa f f  ) [26, 27]. since the investigated connection shows one dowel and two shear planes, the strength values given by eq. (1) – (2) were multiplied by 2 to result the total failure loads. it is interesting to note that ec5 produced similar strength values to the experimental results. however, a slightly higher strength value is observed when the failure coincides with the embedment of the centre member. according to the ec5, the smallest strength value from all possible failure modes should be considered for the definition of the design failure load of the joint. in this case, the ec5 would suggest the failure mode corresponding to the embedment of the side members, which agrees with the experimental results that showed the majority of failures at the side members. despite showing apparent success in the prediction of the ultimate loads, the ec5 does not predict accurately the failure modes since it considers the embedding of the wood members as a failure mode when in the reality the situation is distinct, since crack initiation and propagation controls the ultimate loads (see fig. 5) and the ductility of the joint. experimental ec5 [3] fmax (n) side members 17213±1041 17724 centre member 17228±1868 19488 d(1/2)max (mm) 4.7±1.7 d(3/4)max (mm) 1.9±0.6 k1 (n/mm) 7416±1356 k2 (n/mm) 14445±3303 k3 (n/mm) 15546±2480 table 2: average strength and ductility of the t-joint. (a) (b) figure 5: failure modes of the t-connection: (a) failure at the centre member; (b) splitting at the side members. numerical modelling 3d fe model of the tested joint was built and simulation results are presented and discussed in this section. the commercial fe code ansys® was used for this purpose [19]. the ansys® parametric design language capabilities – apdl language – were used for this purpose. both wood members and steel dowel were accounted for in the model. they were modelled using hexahedra isoparametric 20-node elements (solid95) with full integration. the contact between the dowel and wood members was modelled applying the contact elements available in ansys®, using a surface-to-surface option. the contact between the central and side wood members was also simulated. the conta174 and targe170 elements were used to model, respectively, the contact and target surfaces, forming the socalled contact pairs. both surfaces of each contact pairs were assumed flexible. three contact pairs were considered: a c.l. dos santos et alii, frattura ed integrità strutturale, 31 (2015) 23-37; doi: 10.3221/igf-esis.31.03 29 i) between the dowel and the surface of the hole of the side member; ii) between the dowel and the surface of the hole of the centre member; iii) between the centre and side members (interface). the augmented lagrange contact algorithm was adopted in the analysis. with respect to this contact algorithm, two important numerical contact parameters need to be defined, namely the normal penalty stiffness factor, fkn, and normal penetration tolerance factor, ftoln [19]. for the proposed simulations, the following contact parameters were adopted: ftoln=0.1 and fkn={1.0,0.1,0.006}, the latter respectively for wood-wood contact, dowel-central wood member contact and dowel-side wood member contact. these contact parameters were calibrated by authors on previous elastic simulations of embedding tests along the longitudinal and radial directions, performed on similar wood members [27]. once the joint geometry admits two planes of symmetry, only 1/4 of the joint was modelled (1/2 of the side member and 1/4 of the centre member). the displacements of the nodes located at the planes of symmetry were restrained along the normal direction to these planes. fig. 6 shows the fe mesh built for the t-connection, where a mesh refinement around of the dowel is observed. the clearance between the dowel and the holes was assumed equal to 0.1mm which is an average value from experimental measurements. the friction coefficient was assumed equal to 0.5, which has been considered a typical value for steel/wood contact. figure 6: finite element mesh of the t-connection. with reference to the constitutive models used in the simulations, the steel dowel was modelled as a homogeneous and elastic material (e = 210 gpa;  = 0.3). with respect to the wood, several constitutive modelling alternative approaches were tested in this investigation. as a first approach, wood was simulated assuming a fully elastic behaviour with orthotropic elastic properties, as presented in tab. 1. however this first analysis revealed an unsatisfactory description of the experimental results since the observed experimental non-linear behaviour of the joint is not captured by the simulation. a literature review about numerical modelling of wood non-linear behaviour [11-13, 28] reveals plasticity constitutive models as a frequently adopted option. the ansys® code [19] offers a constitutive plasticity model for anisotropic materials, based on hill’s yield criterion. this model requires the definition of a reference non-linear uniaxial stress-strain curve and anisotropic stress ratios that allow the scaling of this reference curve in order to retrieve the material behaviour for each direction. the model does not distinguish tension from compression behaviours of wood. therefore, the model calibration requires a compromise between these two distinct wood behaviours, taking into account the dominant stresses applied on wood members. this plasticity model, based on hill’s yield criterion, was adopted to simulate the t-joint loaddisplacement behaviour. the material was assumed transversely isotropic and the reference curve was assumed perfectly plastic. therefore, the anisotropic stress ratios required for the model identification corresponded to ratios between anisotropic yield stresses. two alternative approaches were followed for the plastic analysis: i) the same plasticity model parameters were used for both wood members (see tab. 3). this approach is physically more consistent since the materials of each specimen members are the same. ii) distinct plasticity model parameters were used for each wood member (see tab. 4). this approach try to use independent plasticity parameters adjusted for each wood member of the joint (central and lateral members) in a tentative to produce better global predictions of the mechanical behaviour of the joint. c.l. dos santos et alii, frattura ed integrità strutturale, 31 (2015) 23-37; doi: 10.3221/igf-esis.31.03 30 tension/ compression shear l r / t lr rt lt experimental strength values [mpa] 40–98 4.2–9.4 14–16 2.4–4.5 14–16 adopted yield stresses [mpa] central member 80 6.1 12.8 3.6 12.8 side member table 3: experimental strength properties and adopted yield values for pine wood: same constants set used for both wood members [29]. tension/ compression shear l r / t lr rt lt experimental strength values [mpa] 40–98 4.2–9.4 14–16 2.4–4.5 14–16 adopted yield stresses [mpa] central member 90 5.3 12.8 4.1 14.4 side member 85 5.3 11.2 3.2 11.2 table 4: experimental strength properties and adopted yield values for pine wood: distinct constants used for each wood member [29]. even though the better description of non-linear response of joint, the elasto-plastic simulations are not able to simulate the initiation and propagation of cracks responsible for sudden load drop observed in the joint testing. therefore, the plasticity modelling strategy is important to describe the ductile behaviour characterizing the joint, but further enhancements are required to deal with brittle features of the failure modes. cohesive zone damage models can be used to simulate the brittle cracking occurring in the side members of the t-connection under investigation. in this paper, the use of both plasticity and cohesive zone damage models will be explored including their association. figure 7: strength – relative displacement relation for pure modes (adapted from [19]). the ansys® code [19] includes the possibility for cohesive zone damage modelling which can be used to simulate crack propagation at predefined interfaces that can experience decohesion. consequently, this approach requires the definition of interfaces which can be modelled using interface elements or contact elements. the implementation of the cohesive damage model was performed, in this study, using contact elements. the cohesive damage law adopted was the linear one as defined by alfano and crisfield [30]. the damage law for pure fracture modes (i and ii) is shown in fig. 7, where max ,i represents the onset damage stresses ( max ,i : maximum tensile stresses; max,ii : maximum shear stresses). the c.l. dos santos et alii, frattura ed integrità strutturale, 31 (2015) 23-37; doi: 10.3221/igf-esis.31.03 31 mixed mode damage propagation is simulated considering a linear energetic criterion, which takes into account the two fracture modes, according to: i ii ic iic 1 g g g g              (3) where ig and icg are, respectively, the energy release rate and the critical energy release rate ( i, iii  stands for fracture pure modes). the fracture properties required for the application of the cohesive damage model were extracted from experimental works performed on pine wood from the same population, and summarized in tab. 5 [31]. these fracture properties corresponded to the rl crack propagation system, which is one of the most important crack propagation systems for this wood species ( max ,i = r =maximum tensile radial stresses; max,ii = rl = maximum shear stresses in the rl plane). r(mpa) rl(mpa) gic(n/mm) giic(n/mm) 7.93 16 0.264 0.9 table 5: fracture properties for pine wood: rl propagation system [31]. tab. 6 presents an overview of simulations performed in this investigation. besides the fully elastic analysis, two elastoplastic analyses were performed using the sets of plastic constants given in tab. 3 (elastic-plastic (1)) and in tab. 4 (elastic-plastic (2)). these tables (tab. 3 and 4) present suggested yield stresses for tension/compression and shear loadings. using these yield stresses, the anisotropic ratios were defined taking into account an arbitrary reference curve. besides the yield stresses adopted for the plasticity model, strength properties extracted from experimental works performed on the same wood species and available in the literature [29], are also presented in the referred tables. these strength properties were used to estimate the yield stresses. the experimental strength properties were presented for both tension and compression longitudinal loading. for radial and tangential directions, only compression strengths were given in the tables (one value for each direction). concerning the shear strengths, a range of experimental values are given, which resulted from alternative shear testing [29]. constitutive modelling approach centre member side members fully elastic orthotropic elastic model with constants from tab. 1 elastic–plastic (1) orthotropic elastic model with constants from tab. 1 hill’s plasticity model with constants from tab. 3 elastic–plastic (2) orthotropic elastic model with constants from tab. 1 hill’s plasticity model with constants from tab. 4 elastic with cohesive orthotropic elastic model with constants from tab. 1 cohesive damage model with constants from tab. 5 elastic –plastic with cohesive (1) orthotropic elastic model with constants from tab. 1 hill’s plasticity model with constants from tab. 3 cohesive damage model with constants from tab. 5 elastic –plastic with cohesive (2) orthotropic elastic model with constants from tab. 1 hill’s plasticity model with constants from tab. 3 cohesive damage model with constants from tab. 5 table 6: different approaches for the constitutive modelling. a fully elastic model was also simulated with a cohesive interface on the side member (elastic with cohesive). the parameters of the cohesive damage model were given in tab. 5. the model was implemented by means of a contact pair c.l. dos santos et alii, frattura ed integrità strutturale, 31 (2015) 23-37; doi: 10.3221/igf-esis.31.03 32 placed in the side member along the horizontal lt plane containing the hole axis (see fig. 8). this interface was placed in the most likely position for the initiation and propagation of cracks in the side members. besides the simulation of the t-connection using standalone constitutive modelling approaches plasticity and cohesive damage modelling, two mixed constitutive modelling approaches were also investigated for the joint, as documented in tab. 6. firstly, the centre member was considered with elastic-plastic behaviour, through the implementation of the hill's plasticity model and the lateral member was considered elastic and showing a cohesive interface (elastic-plastic with cohesive (1)). this approach takes into account the higher embedding strength, experimentally verified in the centre member. finally, all wood members were assumed elastic-plastic and the cohesive interface on the side member was preserved (elastic-plastic with cohesive (2)). in both approaches, the hill´s plasticity model was applied, using the constants of the tab. 3. the cohesive damage model parameters from tab. 5 were maintained. figure 8: cohesive interface representation. results and discussion in this section, the results of numerical simulations, using the constitutive modelling approaches summarized in tab. 6, will be presented and compared with the experimental results, particularly the load-displacement curves obtained for the t-joint. fig. 9 compares the numerical responses from the simulations with plasticity models. the load-displacement curves shown in fig. 9 under the “elastic-plastic (1)” series were obtained using the same plasticity constants for both wood members. the consideration of distinct plasticity constants, for each wood member, resulted in an improved loaddisplacement curve, as demonstrated by the “elastic-plastic (2)” series (see fig. 9). figure 9: load-displacement curves: experimental vs. elastic-plastic analysis results. the experimental curves exhibit a non-linearity at the beginning of tests, which is due to some initial embedding between the steel dowel and wood, motivated from wood surface damage due to the drilling/cutting process, surface imperfections and small misalignments. the numerical models do not describe this behaviour; therefore numerical curves were subjected to a horizontal shift of 0.5 mm. in general, the numeric curves reproduced satisfactorily the initial part of the test results c.l. dos santos et alii, frattura ed integrità strutturale, 31 (2015) 23-37; doi: 10.3221/igf-esis.31.03 33 (elastic stiffness). in addition, the curve obtained with distinct plastic parameters calibrated for each direction (“elasticplastic (2)” series), showed better performance at the beginning of the yield region. the experimental analysis revealed that the t-connection exhibited two distinct failure modes: a dominant ductile failure mode, when it occurs at the centre member and a dominant brittle failure mode when it occurs at the side members. with respect to the stress distributions, it was observed (see fig. 10) that the maximum shear stresses, in the rl plane, occurred at the centre member and the maximum direct stresses, along the radial direction, occurred in the side members, in both cases at the vicinity of holes. the centre member shows a shear (rl plane) stress concentration above the hole, at locations where cracks were observed to initiated and propagated (see fig. 5). in the side member, significant radial tensile stresses was verified in the hole surface at the horizontal mid-plane. these tensile stresses can be related to the failure modes occurred in those members (see fig. 5). results illustrated in fig.10 were obtained for the elasto-plastic analysis with similar plastic constants for each wood member. however the previous discussion is also valid if distinct plastic constants were used for each wood member. (a) (b) figure 10: stress fields from elastic-plastic analysis, using constants from tab. 3: (a) centre member; (b) side member (f=14kn). figure 11: load-displacement curves: experimental vs. elastic-plastic and elastic with cohesive damage modelling. fig. 11 presents the experimental data with the numerical load-displacement curves resulting from the exclusive application of plasticity models and also resulting from the use of a full elastic model with a cohesive damage interface on the side member. the later numerical result exhibits a near linear behaviour until failure and slightly higher elastic stiffness than resulted from the application of the plasticity models. the cohesive damage model with elastic simulation did not provide any load reduction before the crack propagation onset; therefore a typical brittle behaviour is modelled. the cohesive damage model was able to prevent the unbounded load growing. the simulation was performed until a crack initiated and propagated under unstable conditions. thus, it is demonstrated the good performance of the cohesive model in predicting the ultimate load. in fig. 12, the nodal relative opening displacements of crack faces are quantified, confirming a corner crack, with a maximum crack opening of about 0.19 mm, at the unstable crack propagation onset. fig. 13b illustrates the resistance degradation (evolution of radial stresses) in the interface nodes located at the hole surface c.l. dos santos et alii, frattura ed integrità strutturale, 31 (2015) 23-37; doi: 10.3221/igf-esis.31.03 34 of lateral member (see fig. 13a). also, it is verified that most of nodes have suffered a total resistance degradation; only the pair of nodes farthest away from the interface between the two wood members, did not reached their total decohesion before unstable crack propagation. figure 12: crack opening displacement – elastic plus cohesive model results. (a) (b) figure 13: radial stress evolution at the nodes situated in the interface on the hole surface (elastic plus cohesive damage modelling): (a) nodes location; (b) stress-displacement relation. (a) (b) figure 14: load-displacement curves: experimental vs. numerical results: (a) side member with elastic behaviour and cohesive damage modelling and centre member with plastic behaviour; (b) members with elastic-plastic behaviour and cohesive damage modelling at side member. fig. 14a compares the load-displacement curves from previous simulations and the one resulted from an elastic-plastic behaviour for the centre member and an elastic simulation with cohesive interface for the side member (“elastic-plastic with cohesive (1)” series). in addition, fig. 14b presents the results obtained simulating all wood members with elastoplastic behaviour and using a cohesive interface in the side member (“elastic-plastic with cohesive (2)” series). the analysis c.l. dos santos et alii, frattura ed integrità strutturale, 31 (2015) 23-37; doi: 10.3221/igf-esis.31.03 35 of results shown in fig. 14 reveals a significant improvement in the numerical response, both in terms of ductility and ultimate loads prediction. the simulations assuming elastic-plastic behaviour in all wood members only produced a slight global strength reduction, confirming the little plastic deformation verified in the side members. however, the global response based in this simulation resulted in a better approximation with respect to the experimental data. a local peak was observed in the resulting p-d curves, which is due to the crack initiation. with respect to the crack configuration (see fig. 15a), the “elastic-plastic with cohesive (1)” approach resulted in a corner crack, similarly to the crack observed with the simulation presented in fig. 12, but lower opening displacement values were observed (fig.15b). the “elastic-plastic with cohesive (2)” resulted in an approximately central crack in the side member (see fig. 16a). in this case, the central nodes were the first ones to reach the rupture strength, starting the process zone at this location (see fig. 16b). for this case, the complete nodes separation was not verified before unstable crack growth. (a) (b) figure 15: elastic-plastic model in the centre member + elastic and cohesive damage model in the side member: (a) crack opening displacement; (b) stress-displacement relation at the nodes situated in the interface on the hole surface. (a) (b) figure 16: elastic-plastic model for both members + cohesive damage in the side member: (a) crack opening displacement; (b) stressdisplacement relation at the nodes situated in the interface on the hole surface. conclusions n experimental and numerical characterization of the mechanical behaviour of a type of doweled wood joints was investigated. in this particular case, the investigation was carried out over a t-joint with a central member loaded along the longitudinal or grain direction and the side member loaded perpendicularly to the grain direction. the tested t-joint exhibited both ductile and brittle failure modes. while the failure at side wood members corresponded to brittle failure modes, the failure at the central member corresponded to ductile failure modes. the application of ec5 rules allowed accurate predictions of the ultimate loads even considering that ec5 rules used for this calculation does not a c.l. dos santos et alii, frattura ed integrità strutturale, 31 (2015) 23-37; doi: 10.3221/igf-esis.31.03 36 account for brittle failure modes. however the ec5 procedures do not allow the prediction of the complete loaddisplacement behaviour of the joint. numerical simulations were performed considering distinct alternative constitutive modelling strategies. the t-joint simulation assuming elastic-plastic behaviour for both wood members allowed for a non-linear description of joint behaviour, but the ultimate loads related to the collapse of the connection were not accurately described. the use of cohesive damage models enables the simulation of failure modes and respective collapse loads. however, the exclusive use of cohesive damage models with elastic materials provides load-displacement curves without ductility. the simultaneous use of plasticity models with cohesive damage models, allowed the reproduction of both ductility and connection collapse. in the simulated example, the assumption of an elastic behaviour with cohesive damage, for the side member, also revealed satisfactory results, if the central member is simulated as a plastic material. the initial crack in the side member exhibits a shape change, from corner to almost centre crack, when the elastic-plastic behaviour was imposed to this member. this crack configuration needs experimental validation. references [1] itany, r.y., faherty, k.f., structural wood research, state-of-the-art and research needs, asce, new york, (1984) 210. [2] soltis, l.a., wilkinson, t.l., bolted-connection design, general technical report fpl-gtr-54, forest products laboratory – usda, madison, wi, (1987). [3] en1995-1-1 design of timber structures. part 1-1: general rules and rules for buildings, cen, brussels, (2004). [4] johansen, k.w., theory of timber connections, int assn bridge struct eng pub. 9, zurich, switzerland, (1949) 249– 311. [5] patton-mallory, m., pellicane, p.j., smith, f.w., modelling bolted connections in wood: review, j struct eng, 123 (1997) 1054–62. [6] en383: timber structures. test methods. determination of embedding strength and foundation values for doweltype fasteners, cen, brussels, (2007). [7] sawata, k., yasamura, m., estimation of yield and ultimate strengths of bolted timber joints by nonlinear analysis and yield theory, j wood sci, 49 (2003) 83–91. [8] chen, c.j., lee, t.l., jeng, d.s., finite element modelling for the mechanical behaviour of dowel-type timber joints, comput struct, 81 (2003) 2731–2739. [9] racher, p., bocquet, j.f., non-linear analysis of dowelled timber connections: a new approach for embedding modelling, electron j struct eng, 5 (2005) 1–9. [10] kharouf, n., mcclure, g., smith, i., elasto-plastic modelling of wood bolted connections, comput struct, 81 (2003) 747–54. [11] moses, d.m., prion, h.g.l., a three-dimensional model for bolted connections in wood”, can j civil eng, 30 (2003) 555-567. [12] moses, d.m., prion, h.g.l., stress and failure analysis of wood composites: a new model, compos part b-eng, 35 (2004) 251-261. [13] moses, d.m., prion, h.g.l., anisotropic plasticity and the notched wood shear block, forest prod j, 52 (2002) 4354. [14] patton-mallory, m., cramer, s.m., smith, f.w., pellicane, p.j., nonlinear material models for analysis of bolted wood connections, j struct eng, 123 (1997) 1063-1070. [15] yasumura, m., daudeville, l., fracture of multiply-bolted joints under lateral force perpendicular to wood grain, j wood sci, 46 (2000) 187-192. [16] ballerini, m., rizzi, m., 2007, numerical analyses for the prediction of the splitting strength of beams load perpendicular-to-grain by dowel-type connections, mater struct, 40(1) (2007) 139–149. [17] daudeville, l., yasumura, m., failure analysis of timber bolted joints by fracture mechanics, mater struct, 29 (1996) 418-425. [18] en26891-timber structures – joints made with mechanical fasteners – general principles for the determination of strength and deformation characteristics, (1991). [19] swanson analysis systems inc., ansys® version 12.0, houston, (2009). [20] resch, e.. kaliske, m., three-dimensional numerical analyses of load-bearing behavior and failure of multiple doubleshear dowel-type connections in timber engineering, comput struct, 88 (2012), 165-177. c.l. dos santos et alii, frattura ed integrità strutturale, 31 (2015) 23-37; doi: 10.3221/igf-esis.31.03 37 [21] resch, e., kaliske, m., numerical analysis and design of double-shear dowel-type connections of wood, eng struct, 41 (2012) 234–241. [22] dourado, n.m.m., de moura, m.f.s.f., morais, j.j.l., silva, a.l., estimate of resistance-curve in wood through the double cantilever beam test, holzforschung, 64 (2010) 119-126. [23] silva, m.a.l., morais, j.j.l., de moura, m.f.s.f., lousada, j.l., mode ii wood fracture characterization using the els test, eng fract mech, 74 (2008) 2133-2147. [24] xavier, j., garrido, n., oliveira, m., morais j.l., camanho, p.p., pierron, f., a comparison between the iosipescu and off-axis shear test methods for the characterization of pinus pinaster ait, compos part a, 35 (2004) 827–40. [25] xavier, j., oliveira, m., morais, j., pinto, t., , measurement of the shear properties of clear wood by the arcan test, holzforschung, 63 (2009) 217–25. [26] santos, c.l., de jesus, a.m.p., morais, j.j.l., lousada, j.l.p.c., quasi-static mechanical behaviour of a doubleshear single dowel wood connection, construction and building materials, 23 (2009) 171-182. [27] santos, c.l., de jesus, a.m.p., morais, j.j.l., lousada, j.l.p.c., a comparison between the en 383 and astm d5764 test methods for dowel-bearing strength assessment of wood, strain, 46 (2010) 159-174. [28] dias, a.m.p.g., van de kuilen, j.w.g., cruz, h.m.p., lopes, s.m.r., numerical modelling of the load-deformation behavior of doweled softwood and hardwood joints, wood fiber sci, 42 (2010) 480-489. [29] de jesus, a.m.p., pinto, j.m.t., morais, j.j.l., analysis of solid wood beams strengthened with cfrp laminates of distinct lengths, constr build mater, 35 (2012) 817–828. [30] alfano, g., crisfield, m.a., finite element interface models for the delamination analysis of laminated composites: mechanical and computational issues, int j numer meth eng, 50 (2001) 1701-1736. [31] oliveira, j.m.q., de moura, m.f.s.f., morais, j.j.l., 2009, application of the end loaded split and single-leg bending tests to the mixed-mode fracture characterization of wood, holzforschung, 63 (2009) 597–602. microsoft word numero_52_art_09_2668 b. paermentier et alii, frattura ed integrità strutturale, 52 (2020) 105-112; doi: 10.3221/igf-esis.52.09 105 focussed on the 1st benelux network meeting and workshop on damage and fracture mechanics numerical modelling of dynamic ductile fracture propagation in different lab-scale experiments using gtn damage model benoît paermentier*, dimitri debruyne, reza talemi department of materials engineering, ku leuven, belgium benoit.paermentier@kuleven.be abstract. initiation and propagation of ductile fractures are major consideration during the design of high-pressure pipelines. consequences of a pipeline failure can be catastrophic thus structural integrity must be ensured over several decades. traditional lab-scale experiments such as the charpy vnotch (cvn) and drop weight tear test (dwtt), impact experiments on a notched three-point bending sample, are widely used to measure the fracture toughness of a material. however, with increasing wall thickness and the transition to high-grade steels in the pipeline industry, the size-effect of the specimen and inverse fracture became prominent issues. a new testing methodology called the dynamic tensile tear test (dt3) is currently investigated as to address the issues presented by the current state of the art. in this study, a numerical investigation is conducted on the cvn, dwtt and dt3 experiments to compare the modelling of dynamic ductile fracture propagation in three different testing scales using the gurson-tvergaardneedleman (gtn) damage model. x70 and x100 pipeline steel grades are used to model material behaviour. for each considered lab-scale experiment, the dynamic ductile fracture behaviour was successfully reproduced using the gtn damage model. keywords. ductile fracture; high strength steel; fem; fracture toughness; gtn. citation: paermentier, b., debruyne, d., talemi, r., numerical modelling of dynamic ductile fracture propagation in different labscale experiments using gtn damage model, frattura ed integrità strutturale, 52 (2020) 105-112. received: 31.10.2019 accepted: 17.01.2020 published: 01.04.2020 copyright: © 2020 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. introduction igh-pressure pipelines are still considered as one of the most efficient means of transport for natural gas and other chemical products. due to the catastrophic consequences of pipeline failure, structural integrity must be ensured over several decades. therefore, ductile fracture control is a crucial consideration during the design phase. the high cost of the full-scaled experimental campaigns resulted in the development of more economical lab-scale tests such as the well-known charpy v-notch (cvn) impact test, drop weight tear test (dwtt) [1] and more recently the dynamic tensile tear test (dt3) [2, 3]. compared to modern pipelines with wall thickness reaching over 20 mm, the cvn has a relatively small standard specimen size with a 10 mm × 10 mm cross section [4]. extrapolation of the cvn test data has shown to result in dangerous nonh https://youtu.be/xinevx3wpt4 b. paermentier et alii, frattura ed integrità strutturale, 52 (2020) 105-112; doi: 10.3221/igf-esis.52.09 106 conservative predictions since the fracture toughness does not change in proportion to the increasing wall thickness, as has been reported in [5]. in contrast, the dwtt is able to test a full wall thickness specimen which avoided the need for extrapolation. the specimen height increased from 10 mm to 76.2 mm and the length increased from 55 mm to 305 mm. the main differences between the cvn and dwtt test are the larger impacting mass, the larger specimen geometry, and the different striker geometry of the latter. in general, materials are tested using the dwtt and the shear area (sa) criterion is applied to qualify for pipeline applications. however, with the transition to high-grade pipeline steels, issues such as inverse fracture were introduced [6]. inverse fracture is a phenomenon where a cleavage fracture is initiated in the region impacted by the striker. in the dt3, an even larger specimen with a height of 250 mm and length of 685 mm undergoes a tensile load similar to the in-service pipeline conditions. numerical modelling approaches are often applied to complement extensive testing campaigns. based on these correlations, damage models can be validated and/or calibrated in order to be implemented in more complex simulations. the gursontvergaard-needleman (gtn) model [7, 8] is a well-known and widely applied damage model to simulate dynamic ductile fracture propagation. due to the limited parameter set, it is often used in industry. throughout the development of lab-scale fracture toughness experiments, specimen sizes have been steadily increasing. in this paper the application of the gtn damage model for dynamic fracture propagation in different specimen scales is investigated. the fracture toughness simulations are applied on two high-strength pipeline materials, namely x70 and x100, with different plastic behaviour. the results of the numerical models are used to construct a force-displacement curve to compare experimental data with numerical predictions. gtn damage model he physical phenomenon of ductile damage can be described using the mechanisms of void nucleation, void growth, and void coalescence [7, 8]. due to the limited parameter set, the gtn model has become widely used to model ductile damage behaviour. based on these mechanisms, the strain based gtn model considers a weakening effect as the plastic deformation increases. the constitutive relations describes the plastic potential  as a function of the yield stress yld , and the effective porosity *f . 2 2 2 1 2 1 3 2 * cosh 1 * 0 2 eq hyd yld yld q f q q f                         (1) in which 1q , 2q and 3q are constitutive material parameters with 2 3 1q q , hyd is the hydrostatic stress, and eq is the equivalent stress. the effective porosity *f in the equation above is defined as:    * c f c c c c f f c f f f if f f f f f f f f if f f f f f f if f f             (2) in this definition, the effective void volume fraction *f , is a function of the void volume fraction f . the critical void volume fraction cf , indicates the onset of void coalescence and parameter ff represents the void volume fraction at final failure. constant 1 1 ff q is the maximum reachable value of the void volume fraction. the evolution of void volume fraction, f , can be considered as a combination of existing void growth, growthf , and nucleation of new voids, nucleationf . growth nucleationf f f    (3) t b. paermentier et alii, frattura ed integrità strutturale, 52 (2020) 105-112; doi: 10.3221/igf-esis.52.09 107 void growth can be written as a function of the rate of plastic volume change, plkk .  1 plgrowth kkf f    (4) void nucleation is defined in a strain-controlled nucleation function that considers a normal distribution for the nucleation strain. consequently, the void nucleation rate can be written as: 2 2 1 exp 2 pl pln n nucleation nn f f s s               π ε ε (5) where nf defines the void volume fraction of nucleated voids, n and ns indicate the mean value and standard deviation of the nucleation strain respectively, pl indicates the equivalent plastic strain, and pl defines the equivalent plastic strain rate. finally, the initial void volume fraction 0f indicates the presence of initial voids and is a measure for the relative density of the material. multiple studies have reported on the use of the gtn damage parameters for x70 and x100 grade pipeline steels [9, 10, 11, 12]. in this investigation, the gtn damage parameters, listed in tab. 1, were considered as typical material constants which were obtained from literature. material 𝑞 𝑞 𝑓 𝑓 𝑓 𝑓 𝑒 𝑠 x70 1.5 1.0 0.000401 0.001517 0.5 0.067143 0.8 0.1 x100 1.5 1.0 0.00015 0.02 0.18 0.005 0.3 0.1 table 1: gtn damage parameters for x70 and x100. figure 1: true stress-strain curve for x70 and x100 grade steels. material properties he mechanical properties of the investigated x70 and x100 grade steels were obtained from the literature [2, 3]. the flow curves – as presented in fig. 1 – describe the plasticity based on the true stress-strain relations. two different isotropic hardening laws were used to define the material behaviour in the post-necking region. for x70 grade steel, 0 200 400 600 800 1000 1200 0 0.2 0.4 0.6 0.8 1 t ru e st re ss [m p a] true plastic strain [-] x70 x100 t b. paermentier et alii, frattura ed integrità strutturale, 52 (2020) 105-112; doi: 10.3221/igf-esis.52.09 108 a simple power law relation is defined. in case of x100 grade steel, a more complex isotropic relation was applied [13] as given in tab. 2. strain rate dependency was taken into consideration using a norton law, the plastic strain rate pl is defined as:   n yldpl r k             (6) where k and n are referred to as the norton parameters which were obtained from literature [3, 10]. it should be noted that neither anisotropy nor adiabatic heating effects were taking into account throughout the numerical investigation. tab. 2 gives an overview of the mechanical properties for x70 and x100 grade steel that were used for the numerical investigations. x70 x100 young’s modulus e 210 gpa 210 gpa poisson’s ratio ν 0.3 0.3 isotropic hardening    0 0 nplr r  ε       1 20 1 21 1 1pl plk kr r q e q e        0 795r  mpa 0.13n  0 0.002ε 0 580r  mpa 1 0.367q  2 1.119q  1 46.48k  2 0.7411k  strain rate effect k n 55 mpa 1 ns 5 55 mpa 1 ns 5 table 2: mechanical material properties for x70 and x100 grade steels. numerical models or each lab-scale fracture toughness experiment (cvn, dwtt and dt3), a 3d solid finite element model was constructed using the abaqus software package. the abaqus/explicit solver which includes the standard gtn model referred to as “porous metal plasticity” was used in each model to simulate the dynamic fracture propagation. the geometry was created based on the standard specimen dimensions as previously discussed. in each model, the mesh was created using linear 8-node brick elements with reduced integration. the mesh size has a significant importance when the gtn damage model is implemented. a structured partitioning technique was applied using python scripting methodology as to keep the computational effort to an acceptable level. this meshing strategy was applied for each model and allowed for a uniform and fine mesh size in the region of crack propagation whilst larger elements could be used for the remainder. as reported in literature, the element size perpendicular to the crack propagation direction is dependent on the microstructure of the material and should range between 0.05 mm and 0.30 mm for ferritic steels [14, 15, 16]. in this study an element size of 0.2 mm was used. due to the large-scale geometry of the dt3, the mesh size in the crack region was increased to 0.7 mm to keep computational efforts acceptable. for both the cvn test and dwtt, the anvil and striker were modelled using rigid elements. an overview of the geometry of the constructed numerical models and their respective meshing strategy is presented in fig. 2. in the case of the cvn and dwtt models, a “hard” contact definition using a zero-penetration condition between hammer and specimen was implemented. also, friction was taken into consideration using a penalty function with friction coefficient 0.1. due to the impact loading in the cvn and dwtt, acceleration and consequently force measurements can show pronounced oscillations. therefore, velocity data was extracted and derived to obtain acceleration and force data. this method reduced the presence of oscillations and allowed to construct the forcedisplacement curves for each respective simulation. f b. paermentier et alii, frattura ed integrità strutturale, 52 (2020) 105-112; doi: 10.3221/igf-esis.52.09 109 figure 2: specimen geometry, notch geometry, boundary conditions, and meshing strategy for cvn specimen (a), dwtt specimen (b), and dt3 specimen (c). cvn model one half of a standard cvn specimen with a cross section of 10 mm × 10 mm and length of 27.5 mm was constructed. as to replicate the hammer impact on the specimen, an initial velocity of 5.5 m/s and a mass of 19.8 kg were assigned to the reference point of the hammer [17]. due to the geometry, symmetry conditions were applied on the y-z plane. for this model, x70 grade material properties were assigned to the specimen. dwtt model the geometry of the modelled specimen measures a cross section of 9.5 mm × 76.2 mm and a length of 152.5 mm. the larger dimensions resulted in a larger number of elements, thus an extra symmetry condition was applied. consequently, a total of two symmetry planes were defined on the x-y plane and on the y-z plane of the specimen, and only one quarter of a standard dwtt specimen was constructed. according to the performed dwtt experiments, an initial velocity of 6.5 m/s and a mass of 985 kg were assigned to the reference point of the striker. for the dwtt model, x70 material properties were assigned to the specimen. b. paermentier et alii, frattura ed integrità strutturale, 52 (2020) 105-112; doi: 10.3221/igf-esis.52.09 110 dt3 model the dt3 specimen has a significantly larger size than the previously discussed models with a cross section of 18.4 mm × 250 mm and length of 685 mm. furthermore, no symmetry conditions could be applied since the boundary conditions and loading conditions cannot be considered symmetrical. each side of the specimen is connected to a rail driven frame using a solid steel pin. one pin is assumed to be constrained in every translation direction whilst the other pin is able to move in the loading direction. each pin was modelled using rigid elements. the dt3 test procedure consists out of a quasi-static phase in which hydraulic cylinders apply a tensile load onto the specimen. during this loading phase, springs are compressed, and the potential energy is stored. once a crack initiates, the system becomes unstable and the springs release their potential energy. to simulate the quasi-static and dynamic phases, a velocity of 0.0001 m/s and 6 m/s was assigned to one of the pins, respectively. these pin velocities where calculated based on the experimental displacement-time measurements described by luu [3]. the instant transition from a quasi-static to dynamic velocity is physically not feasible. however, based on the obtained numerical results, the instant transition approximation can be considered satisfactory. due to the large time differences (180 s for the quasi-static phase and 10 ms for the dynamic phase), a different modelling approach was used. the simulation was split into two models: an implicit model simulating the quasi-static displacement of the hydraulic cylinders, and an explicit model simulating the crack propagation initiated by the springs. subsequently, the implicit model state was used to define the initial state for the following explicit simulation. in this case, x100 material properties were assigned to the specimen as well as the reinforcements. results and discussion he experimental load-displacement curve and the corresponding numerical prediction for each of the 3 tests are shown in fig. 3. for the cvn simulation shown in fig. 3 (a), a good correlation with the experimental data [17] was obtained. in the case of the dwtt, experimental data was obtained through tests on an instrumented dwtt experiment at room temperature. as can be seen in fig. 3 (b), the dwtt simulation also shows a good agreement with these experiments. however, a force peak is observed in the simulation at the moment of crack initiation. fig. 3 (c) shows the correlation of the dt3 simulation with experimental data. even though the mesh size was increased for the dt3 simulation, a very good correlation with experimental data was obtained, especially in the dynamic crack propagation phase. also, acceleration and force measurements showed considerably less oscillation than in the cvn and dwtt models. figure 3: experimental and numerical force-displacement curves for the cvn experiment (a), the dwtt experiment (b) and the dt3 experiment (c). fig. 4 gives an overview of the resulting fracture surfaces, mpa is used as a unit for the displayed stress distributions. comparing the cvn and dwtt fracture surface presented in fig. 4 (a) and fig. 4 (b) respectively, the same characteristic features can be observed. in both cases, thickness reduction appears at the initial notch and a thickness increase at the end of the fracture. besides these two similarities, the remainder of the fracture surface actually differs from each other. the central part of the observed dwtt fracture surface is more related to the dt3 fracture surface represented in fig. 4 (c). 0 5 10 15 20 0 5 10 15 20 experimental simulation force [kn] 0 100 200 300 400 0 20 40 60 experimental simulation force [kn] 0 500 1000 1500 2000 0 20 40 60 experimental simulation force [kn] displacement [mm] displacement [mm] displacement [mm] (a) (b) (c) t b. paermentier et alii, frattura ed integrità strutturale, 52 (2020) 105-112; doi: 10.3221/igf-esis.52.09 111 again, a thickness reduction at the initial notch and a thickness increase at the end of the fracture is observed in the dt3 specimen. in this case, the stress concentrations in the centre of the fracture are similar to the stress concentrations observed in the dwtt specimen. figure 4: fracture surfaces and corresponding stress distributions obtained through numerical simulations for the cvn specimen (a), the dwtt specimen (b), and the dt3 specimen (c). as can be observed in fig. 3, the peak force prediction of the cvn simulation and dwtt simulation is overestimated in comparison with the experimental data. in contrast, the dt3 peak force estimation does approximate the experimental data rather accurate. this observation suggests that the presence of impact loading in the numerical model increasingly complicates the acceleration and force calculations. as the impact conditions change during the simulation, the strain rate will also be adjusted continuously. consequently, the explicit integration and the constitutive material model will be affected. the dt3 test on the other hand, only uses a tensile force to introduce the crack propagation leading to an overall more stable simulation. furthermore, as to fulfil the gtn mesh size requirement, the element dimensions for the differently scaled cvn model and dwtt model were kept constant. this mesh size with respect to the total scale of the model will also influence the explicit solution scheme. moreover, relatively small elements are required for the gtn model, thus the computational effort significantly increases due to the fine meshing. therefore, the relatively larger geometry of the specimen does augment the issue regarding the contradictory role of the mesh size as material parameter as well as fe parameter. it is noteworthy that, even though the element size of the dt3 specimen was increased, the ductile fracture propagation does still present a good correlation with the experimental data. conclusions he main objective of this paper was to compare the numerical modelling of dynamic ductile fracture propagation on three different testing scales using the gtn damage model. based on the obtained data, following conclusions can be drawn:  in this study, the implemented gtn ductile damage model is able to describe ductile fracture propagation on a satisfactory level for the considered different lab-scale fracture tests using high-toughness grade pipeline steels with different mechanical properties.  the presence of impact loading does complicate the force prediction especially when the size of the considered specimen increases. even though, the test mechanism is similar and stress-strain conditions are the same, it is clear that the simulation of the dwtt is less stable than the smaller cvn test.  due to the large scale of the dt3 specimen, it currently is challenging to respect the mesh size requirements for the gtn damage model. the mesh size plays a contradictory role as a material property as well as a fundamental t b. paermentier et alii, frattura ed integrità strutturale, 52 (2020) 105-112; doi: 10.3221/igf-esis.52.09 112 finite element property. however, even without fulfilling the mesh size requirement, the dt3 simulation did approximate experimental data accurately. in future investigations, more advanced damage materials models will be implemented to improve the predictive performance of the numerical simulations. furthermore, the gtn relations only considers isotropic ductile damage conditions as well as the physical mechanisms of ductile damage evolution. in order to include brittle damage, multiple extensions of the gtn model have been proposed. some suggestions include a non-local probability approach; others are based on a clear brittle fracture criterion. however, these proposed models increase the calibration efforts considerably. therefore, in future research more advanced numerical models are required as to implement anisotropic behaviour as well as temperature dependency without overcomplicating the calibration procedures. acknowledgements he author gratefully acknowledges the support of the research foundation flanders (fwo) via phd fellowship grant 1sb6420n.. references [1] zhu, x. k. and leis, b. n. (2013). ductile fracture arrest methods for gas transmission pipelines using charpy impact energy or dwtt energy, journal of pipeline engineering, 3(12), pp. 259-272. [2] rivalin, f., pineau, a., di fant, m. and besson, j. (2001). ductile tearing of pipeline-steel wide plates i. dynamic and quasi-static experiments, engineering fracture mechanics, 68, pp. 329-345. [3] luu, t. t. (2006). déchirure ductile des aciers à haute résistance pour gazoducs (x100), école nationale supérieure des mines de paris, paris. [4] astm international, (2019). astm a370 -19e1, standard test methods and definitions for mechanical testing of steel products, west conshohocken, pa. [5] mannucci, g., demofonti, g. and di biagio, m. (2005). x100 fracture initiation and propagation. [6] zhu, x. k. (2015). state-of-the-art review of fracture control technology for modern and vintage gas transmission pipelines, engineering fracture mechanics, 148, pp. 260-280. [7] chu, c. c. and needleman, a. (1980). void nucleation effects in biaxially streched sheets, journal of engineering materials and technology, 3(102), pp. 249-256. [8] tvergaard, v. and needleman, a. (1984). analysis of the cup-cone fractured in a round tensile bar, acta metallurgica, 1(32), pp. 157-169. [9] maxey, w. a., kiefner, j. f., eiber, r. j. and duffy, a. r. (1971). ductile fracture initiation, propagation, and arrest in cylindrical vessels, in proceedings of the national symposium on fracture mechanics part ii. astm stp 514, illinois. [10] rivalin, f., besson, j., pineau, a. and di fant, m. (2001), ductile tearing of pipeline-steel wide plates ii. modeling of in-plane crack propagation, engineering fracture mechanics, no. 68, pp. 347-364. [11] nonn, a. and kalwa, c. (2012). simulation of ductile crack propagation in high-strength pipeline steel using damage models, in proceedings of the 9th international pipeline conference, calgary. [12] thibaux, p. and van den abeele, f. (2009). determination of crack initiation and propagation energy in instrumented charpy v-notch impact tests by finite element simulations, in pipeline technology conference, ostend. [13] besson, j.,cailletaud, g., chaboche, j.-l. and forest, s. (2001). mécanique non linéaire des matériaux, paris: hermes. [14] ruggieri, c., dodds, r. h. and panontin, t. l. (1996). numerical modeling of ductile crack growth in 3-d using computational cell elements, department of civil engineering, university of illinois, illinois. [15] chen, y. and lambert, s. (2003). analysis of ductile tearing of pipeline-steel in single edge notch tension specimen, international journal of fracture, 124, pp. 179-199. [16] scheider, i., nonn, a., völling, a., mondry, a.and kalwa, c. (2014). a damage mechanics based evaluation of dynamic fracture resistance in gas pipelines, procedia materials science, 3, pp. 1956-1964. [17] talemi, r., cooreman, s., mahgerefteh, h., martynov, s. and brown, s. (2019). a fully coupled fluid-structure interaction simulation of three-dimensional dynamic ductile fracture in a steel pipeline, theoretical and applied fracture mechanics, 101, pp. 224-235. t << /ascii85encodepages false /allowtransparency false /autopositionepsfiles true /autorotatepages /none /binding /left /calgrayprofile (dot gain 20%) /calrgbprofile (srgb iec61966-2.1) /calcmykprofile (u.s. web coated \050swop\051 v2) /srgbprofile (srgb iec61966-2.1) /cannotembedfontpolicy /error /compatibilitylevel 1.4 /compressobjects /tags /compresspages true /convertimagestoindexed true /passthroughjpegimages true /createjobticket false /defaultrenderingintent /default /detectblends true /detectcurves 0.0000 /colorconversionstrategy /cmyk /dothumbnails false /embedallfonts true /embedopentype false /parseiccprofilesincomments true /embedjoboptions true /dscreportinglevel 0 /emitdscwarnings false /endpage -1 /imagememory 1048576 /lockdistillerparams false /maxsubsetpct 100 /optimize true /opm 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/hrv (za stvaranje adobe pdf dokumenata najpogodnijih za visokokvalitetni ispis prije tiskanja koristite ove postavke. stvoreni pdf dokumenti mogu se otvoriti acrobat i adobe reader 5.0 i kasnijim verzijama.) /hun 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/pdfxoutputintentprofileselector /documentcmyk /preserveediting true /untaggedcmykhandling /leaveuntagged /untaggedrgbhandling /usedocumentprofile /usedocumentbleed false >> ] >> setdistillerparams << /hwresolution [2400 2400] /pagesize [612.000 792.000] >> setpagedevice microsoft word numero_53_art_06_2724 k. afaf et alii, frattura ed integrità strutturale, 53 (2020) 66-80; doi: 10.3221/igf-esis.53.06 66 experimental analysis of the physical degradation of polymers – the case of polymethyl methacrylate kaddouri afaf*, serier boualem, kaddouri khacem, belhouari mohamed university of djillali liabes, laboratory of mechanics physics of materials (lmpm laboratory), sidi bel abbes, algeria. kaddouri.af@gmail.com, serielem@yahoo.fr, kaddourikacem@yahoo.fr, belhouari@yahoo.com abstract. polymers are known to be sensitive to aging; their lifetime can be predicted through experimental tests. this paper displays an experimental study on the long-term performance of polymethyl methacrylate (pmma) exposed to solar (uv) radiations and artificial (uv) lamp radiations, drinking water and sea water. the performance of this polymer was analyzed in terms of strain variation; strain at break in tension, and young's modulus. the results obtained showed that the amount of absorbed water is independent of the nature of the solvent, and only the absorption kinetics may be regulated by the species contained in the medium. this seems to indicate that plastification of polymers is a reversible phenomenon. in addition, it was found that the tensile strength and elastic modulus drop with increasing immersion time. compared with seawater, the absorption of drinking tap water, after 36 months, leads to a non-linear behavior of the polymethyl methacrylate. exposition of pmma to artificial (uv) lamp radiations and solar (uv) radiations, for the same duration of exposure, resulted in greater performance degradation when the polymer was exposed to artificial (uv) lamp radiations. in addition, the results obtained after a 19 month exposure period that the artificial (uv) lamp radiations changes the behavior of this material from viscoelastic to viscoplastic. keywords. polymethyl methacrylate; aging; artificial (uv) lamp radiations and solar (uv) radiations; sea water; drinking water; mass gain. citation: afaf, k., serier, b., kaddouri, k., belhouari, m., experimental analysis of the physical degradation of polymers – the case of polymethyl methacrylate, frattura ed integrità strutturale, 53 (2020) 66-80. received: 08.01.2020 accepted: 06.05.2020 published: 01.07.2020 copyright: © 2020 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. introduction olymers offer remarkable technological solutions in many fields; they belong to a class of materials that are increasingly used in industries ranging from consumer goods to aerospace products, including healthcare items. polymer matrix nano-composites are widely employed materials as many researchers predict that they are entitled to a bright future and can be a solution to the more and more severe commissioning conditions. nowadays, these materials can seriously compete with traditional ones, like mineral materials, because of their low density; also, their thermomechanical properties are becoming more and more elaborate (functional polymers). furthermore, these materials p https://youtu.be/ungkyxqpfhg k. afaf et alii, frattura ed integrità strutturale, 53 (2020) 66-80; doi: 10.3221/igf-esis.53.06 67 have become attractive because they are recyclable, especially thermoplastics, and present excellent corrosion resistance. because of the attractive mechanical properties of polymethyl methacrylate (pmma) and its ability to be easily shaped, many research studies have focused on this polymer to improve its service strength. indeed, pmma can be used in nanotechnology, particularly in electronics, medicine, civil engineering, mechanical engineering, telecommunications (fiber optics), marine engineering, aeronautics, aerospace, consumer goods industries, etc. [1-7]. nevertheless, it has been shown that the exposure of this polymer to heat, sun radiation, humidity and some solvents may lead to the degradation of its mechanical properties. several research studies have been conducted on the aging behavior of polymethyl methacrylate when exposed to these media. indeed, while bokoi et al. [8] studied the cracking behavior of hydrated and stressed pmma, they found out that the water absorption process can help to determine the mode of crack propagation. dry pmma has excellent scratch resistance; it is often deposited on substrates as a coating to improve this resistance. for this purpose, moghbelli et al. [9] showed that water affects this resistance. in addition, in this same study, depending on the polarity and time of exposure, they showed that the presence of water acts as a harmless lubricator on the surface of the polymer, which can prevent the formation of scratches. after a period of 22 days of pmma in water heated to 60 °c, shen et al. [10] concluded that for a1% absorption content, this solvent leads to the plasticization of the polymer. for higher amounts of water, the polymer loses its transparency and significant changes occur during the deformations. the aging resistance of pmma can also be affected by other environmental media, including light, gamma radiation and heat. in this context, miller et al. [11] investigated the effects of ultraviolet (uv) light, temperature, and moisture on aging pmma materials using an aging test bench supplied with xenon lamps; they also compared the outdoor exposure test results for the purpose of predicting the service life of these materials. for their part, fu et al. [12], by analyzing the effect of temperature on the physical aging of high molecular weight pmma, showed that the aging process results in a decrease in the coefficient of permeability and an increase in selectivity. they also suggested that a modified three-parameter fit model can help predict the long-term physical aging behavior. these findings are in good agreement with the experiment results. on the other hand, cheng et al. [13] investigated the effect of thermal aging on the scratch resistance of pmma subjected to a normal progressive load; they reached the conclusion that a longer aging time can lead to a decrease in the critical load for triggering superficial cracks, which means that crack resistance of pmma drops with longer aging time. thominette and verdu [14] studied the case of pmma subjected to tensile stress and gamma radiation; they could show that either one of the two mechanisms could lead to a splitting of the primary macro-radical; this mechanism could be activated by the constraint. similarly, wenhua yin et al. [7] investigated the aging behavior of pmma in a liquid scintillator, at different temperatures and subjected to static tensile forces; they found out that an increase in the aging temperature engenders a rapid drop in the tensile strength of the pmma. in another study, karollyne gomes de castro monsores et al. [15] reported that the ultraviolet (uv) radiation can modify the rigidity of pmma, and causes a drop in its elongation at break and its tensile strength. on the other hand, mambaye n'diaye et al. [16] showed that pmma used as orthopedic cement in contact with the body fluids can swell after 24 hours if placed in distilled water. similarly, in order to improve the photovoltaic performance of pmma, myles p. et al. [17] exposed two types of polymethyl methacrylate to high intensity ultraviolet (uv) radiation and also to a concentrated xenon arc. these authors indicated that, compared to the xenon arc, exposure of this material to uv radiations leads to an increase in pmma photo-degradation that is three to six times higher. in addition, e. youssif et al. [18] reported that when the polymer is exposed to uv radiation, photo-degradation is the main cause of deterioration of aging resistance. for their part, a. ghasemi-kahrizsangi et al. [19] indicated that, depending on the nature of the polymer, exposure to uv radiation can lead to degradation of the surface of the material due mainly to the removal of the surface layers and also to the formation of pitting and microcracks. similarly, f. namouchia et al. [20] studied the effect of thermal aging on the electrical properties of polymethyl methacrylate (pmma) and found out that such aging promotes the phenomenon of oxidation of the polymer and can therefore cause an increase in the number of free radicals. this can lead to the polarization of the pmma and may give it a less insulating character. as for o.d. gonzales et al. [21], they deduced that the optical stress coefficient of pmma subjected to tensile stresses varies according to the water content. on the other hand, y. minhyuk et al. [22] examined the effect of physical aging on the thermomechanical properties of ps-pmma through the measurement of silicon microcantilever deflections; they found out that these polymers interact during the glass transition. similarly, t. šaraca et al. [23] investigated the effect of simultaneous aging, due to heat treatment and gamma irradiation, on the mechanical and physico-chemical properties of the industrial ethylene-propylenediene monomer (epdm). they suggested that the mechanical properties of this monomer, and in particular the ultimate tensile stress and elongation at break, are highly dependent on the radiation dose rate, the aging temperature and dose rate. furthermore, alenka vesel opens et al. [24] investigated the effect of oxygen plasma treatment on the aging of polymethyl methacrylate (pmma). in this case, the samples were aged in dry air and water at ambient temperature. a study of the effect of this type of treatment on the quality of the pmma / elastomer junction was conducted by suzhu yu k. afaf et alii, frattura ed integrità strutturale, 53 (2020) 66-80; doi: 10.3221/igf-esis.53.06 68 et al. [25] who highlighted the beneficial effect of this treatment not only on the mechanical strength of the pmmaelastomer interface but also on the degradation of its properties due to aging. for their part, jing zhao et al. [26] tried to elucidate, by the suspension polymerization process, how can microcapsules for thermal energy storage compensate for damage caused by ultraviolet (uv) light. these same authors demonstrated the beneficial impact of these microcapsules on the pmma lifetime. indeed, they found out that these microcapsules have a high thermal storage capacity, good reliability and thermal stability, and provide good protection against uv radiations. as for merdas et al. [27], they investigated the effect of the polymer polarity on the absorption of water. they succeeded in showing that the absorption of water increases with the polarity of the polymer; this absorption is more significant for interpenetrating polymer networks than for individual network components, and does not generally depend on the large-scale network structure. with regard to ángel serrano-aroca et al. [28], they carried out a dynamic mechanical analysis and investigated the sorption of water vapor in highly porous poly(methyl methacrylate) (pmma). they were able to show that sorption increases with the crosslinking agent of the cross-linker as a result of the higher number of polar coo groups; however, it decreases with increasing porosity due to the formation of water clusters, which prevents water molecules from occupying all the specific surface of the highly porous polymer. on the other hand, it has been revealed that freshwater sorption increases considerably in very porous pmma. research team of david miller et al. [29] reported that seawater has an impact on the behavior and performance of the vinylester epoxy composite and leads to decreased tensile strength, compression and fatigue. moreover, ryota imaizumi et al. [30] investigated the resistance of poly (n-methylmaleimide-altisobutene) and poly (disopropyl fumarate), as transparent polymer films, to uv and gamma radiations; they successfully demonstrated that uv irradiation leads to the cleavage of the pmi and pdipf side chain via the norrish i-type reaction and also due to the cross-linking resulting from the combination of radicals of the polymers formed, which leads to degradation of their optical and mechanical properties. indeed, it has been found that radiation induces significant changes in the mass of molecules and in the mechanical properties of polymers as well. similarly, s.i. senatova et al. [31] examined the effect of uv radiation on the structure and properties of pp nanocomposites. these same researchers argued that the most prevailing mechanism involved in the protection of pp composites is the absorption of uv radiations by zinc oxide (zno) nanoparticles. reducing the uv radiation intensity prevents the breakage of molecular chains within polypropylene (pp) and its oxidation. these nanoparticles may be recommended to protect polymers against uv radiation. in another study, t. lu et al. [32, 33, 34] and g. wypych [35] showed through an experimental study that long-term exposure of polymers to high uv radiation levels leads to faster degradation of their aging resistance. in addition, their immersion in water produces the same effects. xavier monnier [36] studied molecular dynamics in complex polymer systems: from anisotropy to confinement effects. it is shown that high cooling rates available by fsc allow to accelerate physical aging kinetics. it is shown that preferential orientation induced during electrospinning leads to the formation of mesophase, wich increase cooperativity, namely the intermolecular interactions. yamina hanafi [37] showed through her study the degradation of polyethersulfone / polyvinylpyrrolidone membranes by sodium hypochlorite that the pes-chain scission mechanism appeared to play the major role in the worsening of the membrane filtration performance. under the ageing conditions of this study it seems that neither the pes hydroxylation nor the pvp degradation play a significant role in the worsening of the membrane rejection properties. finally, the membrane structure was found to be substantially altered by the action of sodium hypochlorite, especially for membranes containing pvp. nadim ahmed haseg [38] have studied the molecular mobility of poly(methyl methacrylate) (pmma) during a physical ageing, at various temperatures. this study was carried out by means of two techniques, namely i) mechanical spectroscopy (ms) with scanning in temperature for 4 nearly simultaneous frequencies 0.33hz and 20hz, and ii) differential scanning calorimetry (dsc). concerning the experimental aspect, this study has allowed to find the two well known relaxation processes α and b and to highlight an additional signal induced by preliminary aging procedure. this peak due to structural relaxation strongly depends on the preliminary condition of annealing (temperature and time aging) and appears to be nearly non frequency dependent, as assesses by mechanical spectroscopy. géraldine rapp [39] studied a thermal aging of polyethylene used as cable insulation, shows that: the oxidation kinetics obey the arrhenius law for thermal ageing between 80°c and 110°c. the variations of mechanical properties can be linked to the evolution of the microstructure of each polymer and of their macromolecular architecture during thermo-oxidative ageing. the polymer (pmma) is a material that is predominantly used in industrial devices operating in cumulative immersion environments such as seawater, drinking water (tap water) and is generally exposed to ultraviolet (uv) and solar radiations. the main purpose of this study is to highlight by experimental analysis the effect of these environmental media on the long-term performance of the polymer (pmma), in terms of the tensile strength variations, strain at rupture variation and young's modulus variation. k. afaf et alii, frattura ed integrità strutturale, 53 (2020) 66-80; doi: 10.3221/igf-esis.53.06 69 experimental analysis he mechanical properties of the polymethyl methacrylate (pmma), of chemical formula (c5o2h8) n, are given in tab. 1. this is an amorphous transparent thermoplastic hard and rigid but fragile and notch-sensitive material. it is mainly used in an industrial device, namely the photobioreactor, which consists of two transparent pmma plates, assembled in a pvc frame (fig. 1). this device, containing seawater, is exposed simultaneously to natural lighting (solar (uv) radiations) and artificial lighting (artificial (uv) lamp radiations). the designer and user of this device are both especially interested in its long-term behavior, under the operating conditions mentioned above. then, the service life of this device, which consists of these two plates, immersed in water for 36 months and exposed to solar (uv) and artificial (uv) lamp radiations also for a length of 36 months, was examined in the long term. in order to be in the conditions of use of this device, pmma tensile specimens were prepared (fig. 2) by molding, then at room temperature (20°c) immersed separately in seawater and drinking water (tap water). they were then exposed to the solar (uv) radiations and artificial (uv) lamp radiations. these specimens were tested in uniaxial tension with a transverse displacement speed of 0.5 mm / min. a) production device b) prototype figure 1: photobioreactor made with pmma. modulus of elasticity (mpa) 3200 -4000 poisson’s ratio 0.35 -0.40 stress at rupture (break)(mpa) 70 80 strain at rupture (break) (%) 2.4 table 1: mechanical properties of pmma as given by the supplier. figure 2: tensile specimen made with pmma: iso 527-2. t k. afaf et alii, frattura ed integrità strutturale, 53 (2020) 66-80; doi: 10.3221/igf-esis.53.06 70 tests were carried out on a recent software-driven zwick machine with 25 kn resistance, equipped with a camera and a chamber that are required for the good conduct of the tests, at different temperatures (fig. 3). this machine is perfectly suited for polymer materials. for the reproducibility of the results, these tests were performed on a batch of six (6) samples non-aged and under various aging conditions. again, the tensile test was performed on a batch of six samples, and the average value was selected, as shown in fig. 4. after immersion in water brought to room temperature (20°c), the samples were dried with compressed air. figure 3: tensile testing machine. results and discussion o better understand the effects of aging, unaged (dry) pmma samples (six samples) were weighed with a very high precision scale (up to 10-6 g) and were then tested for uniaxial tension, as shown in fig. 4 which clearly exhibits the linear and brittle behavior of pmma. the average values of the modulus of elasticity (3750 mpa), tensile strength (69 mpa) and strain at break (2.31%) determined from this figure are comparable to those obtained by other authors [22]. figure 4: variation of stress as a function of strain for unaged dry polymethyl methacrylate (pmma) t k. afaf et alii, frattura ed integrità strutturale, 53 (2020) 66-80; doi: 10.3221/igf-esis.53.06 71 immersion in water ensile specimens were immersed separately, at room temperature and atmospheric pressure, in drinking water (tap water) and in seawater, for a period ranging from one to thirty-six months; they were than dried with compressed air and weighed and then tested in uniaxial tension. the absorption of water by pmma during aging was determined in terms of the mass gain rate, δm/m as a function of the square root of the immersion time “t1/2” (fig. 5). it has been shown that the penetration of water to the pmma obeys to the fick’s low and in this case the depth of water flow is proportional to “t1/2”. fig. 5 shows explicitly during the first months, immersion in drinking water (tap water) leads to the absorption of an amount of water (fig. 5a) larger than that in seawater (fig. 5b). thus, after a cumulative aging of eight months, the amount of absorbed water was found approximately twice as high (1.25%) in drinking water as in seawater (0.70%). after a 19-month immersion period in drinking water (tap water) and in seawater, separately, the maximum percentages of absorbed water were 1.58% and 1.51%, respectively. these proportions correspond to the saturation levels in water molecules absorbed by the polymer. the amount of water absorbed by the pmma seems to be insensitive to the immersion time, as can be seen in fig. 5 (a, b). a close examination of this figure clearly shows that the diffusion kinetics of seawater in pmma is much slower than that of drinking water (tap water) in the same polymer. indeed, the speed of water molecules is higher during the first moments of immersion, and then begins to slow down to reach its lowest level after 19 months of aging (fig. 5a). in seawater, as compared to drinking water (tap water), during the first five months of immersion, the speed of water molecules is relatively slow; it then begins to increase and stabilizes after a cumulative aging of 36 months (fig. 5b). this behavior explicitly shows that the activity of water strongly depends on its nature (tap water or seawater). therefore, it may be concluded that the diffusion kinetics of water molecules in the pmma is controlled by the species contained in water. longer immersion period, beyond 19 months, generates almost no weight gain (fig. 6). this seems to show that, under the current aging conditions, only water molecules are concerned with diffusion in pmma. the displacement of a water molecule in the intersites of this polymer is strongly slowed down by the elements contained in this solvent. this can be explained by the fact that water diffuses into the polymer and enters into the unoccupied intermolecular sites, which leads to the absorption of a large quantity of water. this behavior, which is observed during the first five-month immersion period, can be explained by the nature of the species contained in water. in addition to the fact that most elements in water consist essentially of hydrogen (h+) and hydroxide (oh-) ions, seawater also contains a high proportion (> 50%) of sodium ions (na +) and (> 30%) of chlorine ions (cl-). these two ions appear to have a decisive effect on the weight gain of pmma. indeed, these elements tend to slow down the activity of water within the pmma, which leads to a drop in the flow rate of water molecules inside this polymer. in fact, these molecules penetrate into the macromolecular networks, and this leads to the weakening, or even the breaking, of the secondary bonds between the chains that are responsible for the polymer cohesion. by destroying the secondary bonds of the polymer, water decreases the mechanical cohesion and increases the molecular mobility. it should be noted, however, that the diffusion of water within the pmma follows the fickian diffusion pattern below the glass transition temperature, because in this case water plays the role of a plasticizer. this would increase the chain mobility and allow a higher penetration of water, with a maximal percentage of about 2% of weight increase grinsted et al. [40]; nottrott [41]; mambaye n'diaye et al. [16]. in this study, the maximum level of drinking water absorbed by pmma was found corresponding to 1.95% weight increase; this is comparable to that obtained by the above mentioned authors. these findings suggest that pmma can absorb up to 2% of water. after 24 hours of immersion in distilled water, it was found that pmma can swell by absorbing a small amount of water mambaye n'diaye et al. [16]. in another analysis, in 2013, wayne nishio ayrea et al. [42] showed that the amount of absorbed water was around 2% of weight increase after immersion of the pmma in water for 30 days. the behavior of the polymer observed by these authors is consistent with the results obtained in this study. indeed, the absorption kinetics of water molecules turns faster as the solvent gets poorer in dissolved species. the proportions of 2% and 1.95%, found in this study, correspond to the maximum saturation levels in water molecules (fig. 6). in domain 1, plasticization is closely related to the nature of water, while in domain 2, it is independent. specimens were first placed in drinking water (tap water) and seawater (fig. 5) for a certain period of time. afterwards, they were weighed and tested in uniaxial tension a physical experiment which makes it possible to determine the behavior and to measure the degree of resistance to rupture of a material. the results thus obtained are represented in figs. 7 and 8. for the legibility of the behavior illustrated in these two figures, the value of the stress at rupture indicated represents the average value of six samples for condition of aging. these figures clearly show that the tensile stress at break and the modulus of elasticity of the pmma were affected by the amount of absorbed drinking water (tap water) and the quantity of absorbed seawater, respectively (fig. 6). this behavior is identical to that mentioned by c. ishiyama et al. [43]. note t k. afaf et alii, frattura ed integrità strutturale, 53 (2020) 66-80; doi: 10.3221/igf-esis.53.06 72 that the longer the immersion period (36 months), the more significant the degradation is. indeed, one may observe a premature tensile failure in the pmma due to the weakening of the intermolecular bonds, which engenders a drop in the cohesion energy of lennard jones. moreover, it is important to note that, regardless of the nature of water, young's modulus drops sharply during the first months of immersion, and then starts decreasing slowly during the last moments of aging (figs. 7 and 8). (a) (b) figure 5: effect of immersion time on weight gain (a): drinking water (tap water), (b) seawater. figure 6: the effects of the nature of solvent and the duration of immersion on the quantity of water absorbed by the pmma domain 1: the pmma mechanical properties are sensitive to the nature of water; domain 2: the pmma mechanical properties are insensitive to the nature of water. this behavior is essentially attributed to the amount of water absorbed by the pmma. indeed, because of their small size, the water molecules preferentially diffuse in the intermolecular sites, thus causing a plasticization of the polymer. the plasticization phenomenon causes a relaxation of the polymer chains and an increase in the intermolecular spaces [42]. it is useful to remember that the flow of water in this polymer obeys the fickian diffusion [42]. therefore, the penetration depth of the diffusing element is proportional to the square root of time. it is useful to note that the determination of the correlation between the pmma mechanical properties and fickian scattering is one of the objectives of this work. this justifies the variation of young's modulus and the weight gain as a function of the square root of time that is used in this study. on the other hand, the degradation of pmma resistance to aging, as a result of the variation in the mechanical characteristics like the tensile strength, strain at break and modulus of elasticity, can be explained by the fact that the water molecules could be attracted by the hydrophilic groups by destroying the hydrogen bonds or van der waals bonds in the macromolecular network, which can lead to an increase in the distance between the pmma chains, in addition to a k. afaf et alii, frattura ed integrità strutturale, 53 (2020) 66-80; doi: 10.3221/igf-esis.53.06 73 significant plasticization in comparison with that generated by the flow of seawater into the pmma (fig. 7 ). it is worth noting that this plasticization is responsible for the non-linearity of stress and strain observed during the first five-month period of immersion of the polymer in drinking water (fig. 8). the increase in the strain at break, in comparison with that obtained in dry pmma during this first aging period, is characteristic of this non-linear behavior. consequently, this immersion time leads to a transformation of the initially viscoelastic behavior (dry pmma) into viscoplastic (hydrated pmma). it is noted that, beyond that period, the longer the immersion duration, the less important the deformations are (fig. 9). the mechanical behavior observed in this case tends to become linear and brittle again. after 36 months of aging, the pmma exhibits a perfectly linear behavior. (a) (b) figure 7: effect of immersion time in seawater on the mechanical properties of pmma for (a) the stress at break, (b) the modulus of elasticity. for the same duration, and under the same aging conditions, the strain at break observed in samples aged in drinking water (tap water) is much larger than that noted in samples placed in seawater (fig. 9), which seems to explain the decline in the viscoelastic behavior of pmma. this behavior is consistent with that observed by schen et al. [10] and hamouda et al. [44]. the quantity of drinking water (1.30%) absorbed by the pmma during the first five months of aging is larger than that observed, during the same period, in the case of pmma immersed in seawater (0.27%). the close examination of these results shows that aging in drinking water (tap water) leads to greater plasticization. therefore, one may conclude that this process is responsible for the transformation of the initially linear viscoelastic behavior into the nonlinear and more ductile viscoplastic of the polymer, as shown in fig. 9a. in the case of aging in seawater, during the same period, the fragile behavior of pmma is preserved. compared with aging in sea water, the low values of tensile strength observed are characteristic of this pmma behavior (fig. 9a). in fact, a five-month time period of aging in drinking water (tap water) and in sea water respectively generates a degradation in tensile strength of pmma from 69 mpa to 27 mpa and from 69 mpa to 44mpa (fig. 9a). during the last five months of aging, the amount of water absorbed is independent of the nature of solvent; it corresponds to the average percentages of 1.58% in drinking water and 1.55% in sea water, respectively, as shown in fig. 6. this clearly indicates that during the last seventeen (17) months of immersion, the plastification is very insensitive to the nature of water used. the degradation rate of the tensile strength of pmma is approximately 69% in seawater and 71% in drinking water (tap water). moreover, its young's modulus does not depend on the nature of the aging water; it was found equal to about 77% and 78% in seawater and drinking water (tap water), respectively (figs. 9b and 10). these results are closely related to the amount of water absorbed by the pmma. compared to other studies [10, 44], it can be stated that the change in the pmma behavior (fragile-ductile-fragile) with the nature of aging water and the amount of absorbed water, observed in this study, constitute the originality of this work. compared to immersion in seawater, when pmma is in fresh water (tap water), its modulus of elasticity degrades more rapidly (fig. 10) during the first five months. the effect of the aging medium disappears after a 19-month period, which represents the saturation phase of this polymer in water. this can certainly be attributed to the amount of water absorbed during the aging period. k. afaf et alii, frattura ed integrità strutturale, 53 (2020) 66-80; doi: 10.3221/igf-esis.53.06 74 the results obtained in this study clearly suggest that during the first fifteen (15) months of immersion, the degradation kinetics of the mechanical properties (tensile strength and modulus of elasticity) largely depend on the nature of water used; whereas during the last months, it is practically independent. (a) (b) figure 8: effect of immersion time in drinking water (tap water) on the mechanical properties of pmma: (a) stress at break, (b) modulus of elasticity. (a) (b) figure 9: comparative analysis of the effect of the nature of aging medium on the mechanical behavior of pmma: (a) first five months of immersion, (b) last five months of immersion. figure 10: comparative analysis of young's modulus of pmma aged in seawater and in drinking water (tap water). k. afaf et alii, frattura ed integrità strutturale, 53 (2020) 66-80; doi: 10.3221/igf-esis.53.06 75 this study shows that the amount of water absorbed by the pmma is independent of the nature of the solvent used; this means that it is also independent of the species contained in this solvent. only the water absorption kinetics (diffusion) is strongly influenced by these species. this is one of the originalities of this work. to the best of our knowledge, no study has highlighted such a phenomenon. this behavior could mean that no mechanism of irreversible degradation (breaking of chemical bonds, hydrolysis, etc.) has occurred in the pmma during the absorption phase, either in drinking water (tap water) or in seawater. the plasticizing effect appears to be the main mechanism responsible for the degradation of resistance to aging, which is attributed to the deterioration of the mechanical properties of pmma after immersion in water. the reversibility of water absorption mechanism (hydration) can only be highlighted through a close examination of moisture desorption (dehydration) in pmma. this study is in progress. exposure to solar (uv) and artificial (uv) lamp radiations xposure of the polymer to solar (uv) and artificial (uv) lamp radiations was performed in accordance with the commissioning conditions of the industrial photobioreactor system shown in fig. 1. to do this, each side of the pmma specimens was exposed to solar (uv) and artificial (uv) lamp radiations for a period ranging from one (01) to thirty-six (36) months. they were then tested in uniaxial tension, as shown in figs. 11 and 12. these figures clearly indicate that a continuous exposure of 36 months to artificial (uv) lamp radiations leads to a drop in tensile strength at break, and a decrease in both the strain at break and the elastic modulus of the polymer. it should be noted, however, that, compared with solar (uv) radiations, exposure of the polymer to artificial (uv) lamp radiations engenders a significant degradation of its stress at break (figs. 11a, 12a) and its young's modulus as well (figs. 11b, 12b). the deterioration of the polymer mechanical properties is essentially assigned to the absorption of photons. these are potentially aggressive electromagnetic radiations that possess energies corresponding to those of certain chemical bonds. the absorption of photons can cause breaks in molecular chains, thus releasing free radicals and reducing the molecular weight of polymers. this should inevitably lead to degradation of the tensile strength at break, and deterioration of the strain at break, after a cumulative aging of 12 months, with a lower young's modulus [31, 45-48]. the results obtained in this study show that the artificial (uv) lamp radiations has a more significant effect on the degradation of the polymer mechanical properties. note that after a cumulative aging of thirty-six months, the solar (uv) radiation does not seem to affect the linear viscoelastic behavior of the polymethyl methacrylate (fig. 11). this behavior remains unchanged with regard to the exposure duration. this behavior is observed after an artificial (uv) lamp irradiation time of 3 to 12 months. a too long artificial (uv) lamp irradiation (36 months) leads not only to a considerable drop in tensile strength and young's modulus, but also to a greater strain at break than that observed in nonirradiated pmma (fig. 12a). in fact, it was noted that the tensile strength dropped by about half (fig. 12a) but the strain at break increased. this clearly indicates that a 36-month cumulative aging seems to lead to a change in the mechanical behavior of pmma from viscoelastic to viscoplastic. the observed nonlinear behavior is indicative of this transformation. understanding this change in behavior, which is a topical result, is required for the purpose of comprehending the degradation mechanisms involved in the aging resistance of pmma irradiated with uv light. this is one of the objectives of this work. fig. 13 summarizes the comparative analysis results of the effects of exposure of polymethyl methacrylate to solar (uv) radiations and artificial lamp radiations on its modulus of elasticity (fig. 13a) and tensile strength (fig. 13b). it is clearly illustrated in fig. 13a that regardless of the duration of aging, in comparison with exposure to solar (uv) radiations, the artificial (uv) lamp radiations causes a significant degradation of the pmma elastic modulus which drops sharply during the first six (06) months of irradiation, then starts decreasing slowly during the following six months (06); the degradation of this physical parameter is considerably slowed down during the last twenty-four (24) months of aging. it should be noted that the same behavior was observed in the case of pmma exposed to solar (uv) radiations. the behavior of the polymer illustrated in fig. 13b may be better interpreted by referring to fig. 14 which shows separately the effect of this exposure during the first nine months (fig. 14a) and during the last twenty-seven months (fig. 14b) of the exposure period. these figures suggest that the artificial (uv) lamp radiation leads to a slightly higher degradation of tensile strength and to lower strain at break. the initial linear viscoelastic behavior of pmma remained unchanged during the first twelve months of aging of the polymer exposed to artificial (uv) lamp and solar (uv) radiations (fig. 14a). after thirty-six months of artificial (uv) lamp radiation, a non-linear behavior was observed (fig. 14b) with a higher strain at break. it should be noted that this non-linearity in behavior was not observed in the case of pmma exposed to solar (uv) radiation, for the same period of exposure of 36 months. in addition, a 36-month cumulative aging after exposure of each side of the specimen to artificial (uv) lamp radiation, separately, resulted in a e k. afaf et alii, frattura ed integrità strutturale, 53 (2020) 66-80; doi: 10.3221/igf-esis.53.06 76 57% degradation of tensile strength, 10% increase in the strain at break, and 62% drop in young's modulus. for the same duration, exposure of pmma to solar (uv) radiation leads to a 50% drop in the stress at break and a 30% reduction in the strain at break, with a 47% drop in young's modulus. (a) (b) figure 11: effect of the duration of exposure to solar (uv) radiations on the mechanical properties of pmma: (a) stress at break, (b) modulus of elasticity. (a) (b) figure 12: effect of the duration of exposure to artificial (uv) lamp radiations on the mechanical properties of pmma: (a) stress at break, (b) modulus of elasticity. (a) (b) figure 13: comparing the effects of exposure time of pmma to solar (uv) radiations and artificial (uv) lamp radiations on its mechanical properties: (a) modulus of elasticity; (b) stress at break. k. afaf et alii, frattura ed integrità strutturale, 53 (2020) 66-80; doi: 10.3221/igf-esis.53.06 77 (a) (b) figure 14: comparative analysis of the effects of solar (uv) and artificial (uv) lamp radiations on the mechanical properties of pmma: (a) exposure duration: first 9 months; (b) exposure duration: last 27 months. conclusion he analysis of the experimental results obtained in this study, jointly with those reported in the literature, makes it possible to draw the following conclusions: aging in water: the amount of water (weight gain) absorbed by the pmma is closely related to the immersion time in both types of water (tap water and seawater). after a cumulative aging of thirty-six months, the average contents reached for seawater and tap water were 1.51% and 1.58%, respectively. the maximum values of these quantities correspond to the values of 1.87% and 1.95%, which are in fairly good agreement with those reported in the literature (2%). after twenty months of pmma hydration, the amount of water absorbed hardly changed with the increase in aging time; in the first five months of aging, the kinetics of water diffusion in pmma is closely linked to the nature of the immersion medium. it is greatly slowed down by the species contained in the water; after a nineteen months immersion time, and regardless of the nature of water, hydration reached a saturation point, beyond which the absorbed water content no longer evolves; during the first months of immersion (less than 19 months), the diffusion kinetics of water molecules in pmma was found to depend on the species contained in the solvent used. their presence considerably slows down the flow rate of water molecules inside the polymer. this rate turned out to be greater in drinking water (tap water) but slower in seawater. in the latter case, the diffusion was delayed and the water molecules took a longer time to reach the maximum amount of water absorbed by the pmma, after which the polymer reaches a state of saturation in water molecules, after a cumulative aging of 19 months. beyond this period, the amount of absorbed water becomes independent of the type of solvent used. only the diffusion kinetics of water molecules within the pmma depends on the nature of the solvent. on the other hand, the absorption of water leads to a degradation of aging resistance in terms of reduction of stiffness, tensile strength, and elongation at break of the polymethyl methacrylate (pmma). during the first five months of immersion in drinking water (tap water), the pmma changes from the initial linear viscoelastic behavior to the non-linear viscoplastic behavior. beyond this period, the polymer exhibits a reversible behavior. the pmma becomes viscoelastic again with a lower tensile strength. moreover, after nineteen months of immersion, the nature of water has practically no influence on the aging resistance of pmma. in this case, for the same aging time in drinking water (tap water) and in seawater, the attenuated values of tensile strength and elastic modulus are comparable. this could mean that during the absorption phase, whether in drinking water (tap water) or seawater, no mechanism of irreversible degradation occurs in pmma. after hydration, plastification seems to be the main mechanism responsible for the drop in resistance to aging. in addition, the reversibility of water absorption can only be proven by a moisture desorption analysis of the pmma. uv aging: exposure to solar (uv) and artificial (uv) lamp radiations leads to degradation of stiffness, tensile strength and strain at break of the polymer. an increase in irradiation time causes a drop in the aging resistance of the pmma. compared with exposure to solar (uv) radiation, and for the same duration of aging, artificial (uv) lamp radiation causes t k. afaf et alii, frattura ed integrità strutturale, 53 (2020) 66-80; doi: 10.3221/igf-esis.53.06 78 a greater degradation of mechanical characteristics. the breaking of the macromolecular chain is responsible for the deterioration of pmma properties; for longer ultraviolet radiation exposure times (beyond thirty-six months), the linear mechanical behavior of the nonirradiated pmma changes to a non-linear behavior, with greater deformations as compared to the non-irradiated polymer; the modulus of young of the pmma drops sharply during the first six months of exposure to artificial (uv) lamp radiation then starts decreasing slowly during the following six months. it is important to precise that the degradation of this physical parameter is significantly slowed down during the last twenty-four months of aging. a similar behavior is observed during exposure to solar (uv) radiation but with lower values, regardless of the aging time. references [1] kowalonek, j., kaczmarek, h., kurzawa, m. (2016). effect of uv-irradiation on fluorescence of poly (methyl methacrylate) films with photosensitive organic compounds, journal of photochemistry and photobiology a: chemistry. 319-320, pp.18-24. doi: 10.1016/j.jphotochem.2015.12.017 [2] münker, t.j.a.g., van de vijfeijken, s.e.c.m., mulder, c.s., vespasiano, v., becking, a.g., kleverlaan, c.j., and al. (2018). effects of sterilization on the mechanical properties of poly(methyl methacrylate) based personalized medical devices, journal of the mecchanical behavior of biomedical materials. 81, pp.168-172. doi: 10.1016/j.jmbbm.2018.01.033. [3] manjunatha, h.c. (2017). a study of gamma attenuation parameters in poly methyl methacrylate and kapton, journal of radiation physics and chemistry. 137, pp. 254-259. doi: 10.1016/j.radphyschem.2016.01.024 [4] zhong, z.w., wang, z.f., zirajutheen, b.m.p.( 2005). chemical mechanical polishing of polycarbonate and poly methyl methacrylate substrates, journal of microelectronic engineering. 81, pp. 117-124. doi: 10.1016/j.mee.2005.04.005. [5] bussi, y., golan, s., dosoretz, cg., eisen, ms. (2018). synthesis, characterization and performance of polystyrene/pmma blend membranes for potential water treatment, journal of desalination. 431, pp.35-46. doi: 10.1016/j.desal.2017.12.024. [6] ali, u., karim, k.j.b.a., buang, n.a. (2015). a review of the properties and applications of poly (methyl methacrylate) (pmma), journal of polymer reviews. 55, pp.678-705. doi.org/10.1080/15583724.2015.1031377. [7] wenhua, y., zeyu, x., yuming, y., jun, y., xiaodan, l., huiqin, w., shuang, w., yufang, x., yunong, y. (2019). aging behavior and lifetime prediction of pmma under tensile stress and liquid scintillator conditions, journal: advanced industrial and engineering polymer research. doi: 10.1016/j.aiepr.2019.04.002. [8] bokoi, y., ishiyama, c., shimojo, m., shiraishi, y., higo, y. (2000). effects of sorbed water on crack propagation in poly(methyl methacrylate) under static tensile stress, journal of materials science. 35, pp.5001-5011. doi: https://doi.org/10.1023/a:1004803030131 [9] ehsan, m., reid, b., hung, j.s. (2014). the effect of moisture exposure on scratch resistance of pmma, journal of tribology international. 69, pp.46–55. doi: 10.1016/j.triboint.2013.08. [10] shen, j., chen, c., sauer, j. (1985). effects of sorbed water on properties of low and high molecular weight pmma: 1. deformation and fracture behaviour, journal of polymer. 26, pp.511-518. doi: 10.1016/0032-3861(85)90150-8. [11] miller, d.c., carloni, j.d., johnson, d.k., pankow, j.w., gjersing, e.l., et al. (20.13). an investigation of the changes in poly (methyl methacrylate) specimens after exposure to ultra-violet light, heat, and humidity, solar energy, journal of materials and solar cells. 111, pp.165-180. [12] fu, y., hsiao, s., hu, c., lee, k., lai, j. (2008). prediction of long-term physical aging of poly(methyl methacrylate) membranes for gas separation, journal of desalination. 234, pp.51-57. doi: 10.1016/j.desal.2007.09.069. [13] cheng, q., jiang, c., zhang, j., yang, z., zhu, z., jiang, h. (2016). effect of thermal aging on the scratch behavior of poly (methyl methacrylate), journal of tribology international. 101: 110-114. doi: 10.1016/j.triboint.2016.04.013 [14] thominette, f., verdu, j. (1996). effect of a tensile stress on the radiolytic degradation of poly (methyl methacrylate), journal of polymer. 37, pp.1323-1327. doi: 10.1016/0032-3861(96)81128-1 [15] monsores, k. g. c., da silva, a. o., de sant’ana oliveira, s., rodrigues, j. g. p., pondé weber, r. (2019). influence of ultraviolet radiation on polymethylmethacrylate (pmma), journal of materials research and technology, 8, pp. 3713-3718. doi: 10.1016/j.jmrt.2019.06.023. [16] n’diaye, m., pascaretti-grizon, f., massin, p., baslé, m. f., chappard, d. (2012). water absorption of poly (methyl methacrylate) measured by vertical interference microscopy, gerom groupe etudes remodelage osseux et k. afaf et alii, frattura ed integrità strutturale, 53 (2020) 66-80; doi: 10.3221/igf-esis.53.06 79 biomatériaux−lhea, iris-ibs institut de biologie en santé, lunam université, chu d’angers, 49933 angers cedex, france, chirurgie orthopédique et traumatologie, hôpital bichat, 75018 paris, france, (pubs.acs.org/langmuir). doi: 10.1021/la302260a. [17] myles, p., murray., laura, s., bruckman., and roger, h, french. (2012). photodegradation in a stress and response framework: poly (methyl methacrylate) for solar mirrors and lens, journal of photonics for energy. 2. doi: 10.1117/1.jpe.2.022004. [18] yousif, e., haddad, r. (2013). photodegradation and photostabilization of polymers, especially polystyrene, journal of review, springerplus 2. 1, 398. doi: 10.1186/2193-1801-2-398. [19] ghasemi-kahrizsangi, a., shariatpanahi, h., neshati, j., akbarinezhad, e. (2015). degradation of modified carbon black/epoxy nanocomposite coatings under ultraviolet exposure, journal of applied surface science. 353, pp. 530539. doi: 10.1016/j.apsusc.2015.06.029 [20] namouchi, f., smaoui, h., fourati, n., zerrouki, c., h. guermazi, h., bonnet, jj. (2009). investigation on electrical properties of thermally aged pmma by combined use of ftir and impedance spectroscopies, journal of alloys and compounds. 469, pp.197–202. doi: 10.1016/j.jallcom.2008.01.148 [21] gonzales, o.d., nicassio, a., eliasson, v. (2016). evaluation of the effect of water content on the stress optical coefficient in pmma, journal of polymer testing. 50, pp.119–124. doi: 10.1016/j.polymertesting.2016.01.004. [22] minhyuk, y., namchul, j., changyong, y., sangmin j. (2011). nanomechanical thermal analysis of the effects of physical aging on glass transitions in ps/pmma blend and ps-pmma diblockcopolymers, journal of polymer, 18 (52): 4136-4140 doi: 10.1016/j.polymer.2011.06.051. [23] šaraca, t., devauxb, j., quiévyc, n., gusarova, a., konstantinovića, mj. (2017). the correlation between elongation at break and thermal decomposition of aged epdm cable polymer, journal of radiation physics and chemistry. 132, pp.8–12. doi: 10.1016/j.radphyschem.2016.10.017. [24] vesel opens, a., mozetic, m. (2012). surface modification and ageing of pmma polymer by oxygen plasma treatment, journal of vacuum. 6 (86), pp.634-637. doi: 10.1016/j.vacuum.2011.07.005. [25] suzhu, y., shu pei, n., zhenfeng, w., chu long t., yong chear, s. (2017). thermal bonding of thermoplastic elastomer film to pmma for microfluidic applications, journal of surface and coatings technology. 320, pp.437–440. doi: 10.1016/j.surfcoat.2016.11.102. [26] jing, z., yanyang, y., yu l., liang, z., hao, w., guolin s. (2017). microencapsulated phase change materials with tio2-doped pmma shell for thermal energy storage and uv-shielding, journal of solar energy materials and solar cells. 168, pp.62–68. doi: 10.1016/j.solmat.2017.04.014. [27] merdas, i., tcharkhtchi, a., thominette, f., verdu, j., dean, k., cook, w. (2002). water absorption by uncrosslinked polymers, networks and ipns having medium to high polarity, journal of polymer. 43, pp. 4619-4625. doi: 10.1016/s0032-3861(02)00267-7. [28] serrano-aroca, á., llorens-gámez, mar (2017). dynamic mechanical analysis and water vapour sorption of highly porous poly(methylmethacrylate), journal of polymer. 125, pp. 58-65. doi: 10.1016/j.polymer.2017.07.075. [29] miller, d., john, f. mandell, daniel, d., samborsky., b., hernandez-sanchezand, a., todd griffith, d. (2012). performance of composite materials subjected to salt water environments, aiaa sdm wind energy session. doi: 10.2514/6.2012-1575. [30] imaizumi, r., furuta, m., okamura, h., matsumoto, a. (2017). uv and y_ray resistance of poly(nmethylmaleimide_alt-isobutene) and poly(diisopropyl fumarate) as transparent polymer films, journal of physics and chemistry. 138, pp.22–28. doi: 10.1016/j.radphyschem.2017.04.018. [31] senatova, s.i., senatov, f.s., kuznetsov, d.v., stepashkin, a.a., issi, j.p. (2016). effect of uv-radiation on structure and properties of pp nanocomposites, journal of alloys and compounds. 707, pp.304-309. doi: 10.1016/j.jallcom.2016.11.170. [32] lu, t., solis-ramos, e., yun-bo yi., kumosa, m. (2016). synergistic environmental degradation of glass reinforced polymer composites, journal of polymer degradation and stability. 131, pp.1-8. doi: 10.1016/j.polymdegradstab.2016.06.025. [33] lu, t., solis-ramos, e., yi., y., kumosa, m. (2018). uv degradation model for polymers and polymer matrix composites, journal of polymer degradation and stability. 154, pp. 203-210. doi: 10.1016/j.polymdegradstab.2018.06.004. [34] lu, t., solis-ramos, e., yi, y., kumosa, m. (2017). particle removal mechanisms in synergistic aging of polymers and glass reinforced polymer composites under combined uv and water, journal of composites science and technology. 153, pp.273-281. doi: 10.1016/j.compscitech.2017.10.028. [35] wypych, g. (2011). handbook of uv degradation and stabilization, toronto. k. afaf et alii, frattura ed integrità strutturale, 53 (2020) 66-80; doi: 10.3221/igf-esis.53.06 80 [36] mounier, x. (2017). molecular dynamics in complex polymer systems: from anisotropy to confinement effects. university de rouen. [37] hanafi, y. (2017). study of the degradation of polyethersulfone/polyvinylpyrrolidone membranes by sodium hypochlorite. rennes doctoral school in matter,molecules and materials (le mans) in partnership with the university of brittany loire (comue) and the rennes institute of chemical sciences (laboratory). 1. [38] ahmed haseg, n. (2018). contribution to the study of the relaxation and ageing in amorphous polymers. [39] géraldine (2018). rapp, multi-scale analysis of the thermo-oxidative aging of a mixture of polyethylene reticles. clermont auvergne. [40] grinsted, r.a., clark, l., koenig, j.l. (1992). study of cyclic sorption–desorption into poly (methyl methacrylate) rods using nmr imaging, journal of macromolecules. 25 (4), pp.1235–1241. doi:.org/10.1021/ma00030a006. [41] nottrott, m. (2010). acrylic bone cements, journal of acta orthopaedica. 81 (s341), pp.1–27. doi: 10.3109/17453674.2010.487929. [42] ayrean, n., denyerb, s. p., evansa, s. l. (2014). ageing and moisture uptake in polymethyl methacrylate (pmma) bone cements wayne, journal of the mechanical behavior of biomedical materials. 32, pp.76–88. doi: 10.1016/j.jmbbm.2013.12.010. [43] ishiyama, c., higo, y. (2002). effects of humidity on young’s modulus in poly (methylmethacrylate), journal of polymer science part b. 40, pp.460–465 doi: 10.1002/polb.10107. [44] hamouda, a. (2002). the influence of humidity on the deformation and fracture behaviour of pmma, journal of materials processing technology. 124, pp.238–243. doi: 10.1016/s0924-0136(02)00096-1. [45] yan, l., chouw, n., jayaraman, k. (2015). effect of uv and water spraying on the mechanical properties of flax fabric reinforced polymer composites used for civil engineering applications, journal of materials and design. 71, pp.17–25. doi: 10.1016/j.matdes.2015.01.003. [46] kahlen, s., jerabek, m., wallner, g.m., lang, r.w. (2009). characterization of physical and chemical aging of polymeric solar materials by mechanical testing, journal of polymer testing. 29, pp.72–81. doi: 10.1016/j.polymertesting.2009.09.007. [47] cordelle, a., drissi-habti, m., aaron forster., joannie chin. (2013). effects of uv irradiation on the mechanical properties of polymer composite materials, journal of review of composites and advanced materials, lavoisier. 23 (2), pp.295-309. [48] colom, x., garcı ́a, t., suñol, j.j., saurina, j., carrasco, f. (2001). properties of pmma artificially aged, journal of non-crystalline solids. 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can be opened with acrobat and adobe reader 5.0 and later.) >> /namespace [ (adobe) (common) (1.0) ] /othernamespaces [ << /asreaderspreads false /cropimagestoframes true /errorcontrol /warnandcontinue /flattenerignorespreadoverrides false /includeguidesgrids false /includenonprinting false /includeslug false /namespace [ (adobe) (indesign) (4.0) ] /omitplacedbitmaps false /omitplacedeps false /omitplacedpdf false /simulateoverprint /legacy >> << /addbleedmarks false /addcolorbars false /addcropmarks false /addpageinfo false /addregmarks false /convertcolors /converttocmyk /destinationprofilename () /destinationprofileselector /documentcmyk /downsample16bitimages true /flattenerpreset << /presetselector /mediumresolution >> /formelements false /generatestructure false /includebookmarks false /includehyperlinks false /includeinteractive false /includelayers false /includeprofiles false /multimediahandling /useobjectsettings /namespace [ (adobe) (creativesuite) (2.0) ] /pdfxoutputintentprofileselector /documentcmyk /preserveediting true /untaggedcmykhandling /leaveuntagged /untaggedrgbhandling /usedocumentprofile /usedocumentbleed false >> ] >> setdistillerparams << /hwresolution [2400 2400] /pagesize [612.000 792.000] >> setpagedevice microsoft word numero_30_art_68 v. crupi et alii, frattura ed integrità strutturale, 30 (2014) 569-577; doi: 10.3221/igf-esis.30.68 569 focussed on: fracture and structural integrity related issues investigation of very high cycle fatigue by thermographyc method v. crupi, g. epasto, e. guglielmino, g. risitano university of messina, department of electronic engineering, chemistry and industrial engineering (diecii) crupi.vincenzo@unime.it; gabriella.epasto@unime.it; eguglie@unime.it; grisitano@unime.it abstract. nowadays, many components and structures are subjected to fatigue loading with a number of cycles higher than 107. in this scientific work, the behaviour of two kinds of tool steel was investigated in very high cycle fatigue regime. the fatigue tests were carried out at the frequency of 20 khz and in fully reversed tensioncompression mode (r = -1) by means of an ultrasonic fatigue testing equipment. the radiometric surface temperature was detected during all the test by means of an ir camera in order to extend the thermographic method and the energetic approach in very high cycle fatigue regime. the failure mechanism of the investigated steels was evaluated by means of several experimental techniques (scanning electron microscopy, energy dispersive x-ray spectroscopy and optical microscopy). keywords. very high cycle fatigue; thermographic method; energetic approach; failure analysis; microscopy. introduction ith the increasing progress of the technological development in structural applications of tool steels, the required fatigue life has increased, so it is very important to determine a safe fatigue strength for 109 cycles. nowadays, the very high cycle fatigue (vhcf) constitutes one of the main fatigue design criteria. many researches published important scientific works based on the results of ultrasonic fatigue testing. in 1999 bathias [1] experimentally proved that there is no infinite life in metallic materials and in 2007 sonsino [2] showed that a continuous decrease of fatigue strength occurs in the range of large cycle numbers. the fatigue crack initiation in the gigacycle regime seems to occur essentially inside the specimen [1] and not at the surface as it generally occurs in the low cycle fatigue (lcf) and high cycle fatigue (hcf) regime. this means that the effect of environment is quite small in the gigacycle regime as the initiation of short cracks is inside the specimen and the surface plays a minor role especially if it is smooth. the effect of internal hydrogen trapped by non-metallic inclusions on high cycle fatigue was first indicated by murakami et al. [3]. they observed that around the internal inclusion, from which the failure starts, an optical dark area (oda) can be seen by an optical microscope. the rule of a crack initiation located inside the specimen in vhcf regime is not rigid, but has several exceptions. according to bayraktar et al. [4], the crack initiation site in some automotive metallic alloys is not always in the interior of the specimen. moreover, the cause of the initiation site can be not only inclusions, but also the pores. sohar et al. [5] carried out ultrasonic fatigue testing on aisi d2 type wrought cold work tool steel, finding that crack growth behaviour can follow two mechanisms: the so-called fisheye (internal crack initiation) or half-of fish-eye (near-surface crack initiation), depending to the presence of primary carbides (clusters). moreover the temperature evolution during the fatigue tests in hcf [6 10] and lcf [11] regimes has been investigated by several researchers, but there are only few studies in vhcf regime. xue et al. [12] investigated fatigue damage w v. crupi et alii, frattura ed integrità strutturale, 30 (2014) 569-577; doi: 10.3221/igf-esis.30.68 570 progression of three kinds of alloy in the vhcf regime by thermographic analysis. blanche et al. [13] proposed a heat diffusion model to estimate dissipated energy during vhcf tests at high loading frequency (20 khz) and low stress. the authors of the present paper have a strong background in the infrared thermography (irt), which was proved to be effective in obtaining results in several fields: correlation between the values of stabilization of the temperature increments and the areas of the thermal hysteresis loops in lcf [11], fatigue assessment of mechanical components [14], relationship between the temperature evolution and the internal microstructural changes [15], correlation between internal damping and the temperature increment of metals subjected to fatigue loading [16], damage cumulative evaluation [17], analysis of sandwiches under impact loading [18]. in the present paper, the infrared (ir) thermography and an energetic approach were applied to investigate and compare a cold work tool steel (din en 115crv3) and a free-cutting steel (din en 60spb20+bi) in vhcf range. moreover, the failure mechanism was evaluated by means of several experimental techniques (scanning electron microscopy, energy dispersive x-ray spectroscopy and optical microscopy). the aim of the failure analysis was to assess if the nature of the microstructure and the metallurgical defects, in terms of inclusions and pores, can influence the crack initiation. material and methods he fatigue tests were performed without cooling at r= -1 and f= 20 khz by a piezoelectric fatigue machine (fig. 1a). the vibration of the specimen is included with a piezo-ceramic transducer, which generates acoustical waves to the specimen through a power concentrator (horn). the specimen geometry is represented in fig. 1b. the dynamic displacement amplitude of the specimen extremity is controlled in order to keep constant the stress during the test, through the computer control. the test is automatically stopped when the frequency falls down to 19.5 khz. the tests were carried out on specimens made of a high carbon cold work tool steel (din en 115crv3) and an unalloyed free-cutting high carbon steel with lead (din en 60spb20+bi). the chemical composition of the investigated specimens was derived from x-ray fluorescence analysis and the results are shown in tab. 1. (a) (b) figure 1: (a) experimental set-up and (b) geometry of the specimens (units: mm). t v. crupi et alii, frattura ed integrità strutturale, 30 (2014) 569-577; doi: 10.3221/igf-esis.30.68 571 grade din/en grade din/en 1.2210 115crv3 1.0758 60spb20+bi si mn s cr v pb fe si mn s cr mo pb fe % % % % % % % % % % % % % % 0.22 0.34 0.027 0.69 0.09 balance 0.25 1.34 0.39 0.24 0.024 0.27 balance table 1: chemical composition of the tested specimens by means of xrf analysis. during the fatigue tests, the radiometric surface temperature was measured by an uncooled long wave infrared (lwir) focal plane array camera with a resolution of 320x240 pixels and a measurement accuracy of ± 2 ºc (model flir systems a40m). the frame rate during the acquisition of thermal increment was of one frame per minute. moreover, fractographies were carried out by means of a scanning electron microscope (sem – jeol jsm5900lv) and an optical stereomicroscope (sm – leica m165c). results and discussion s-n curve he experimental results, obtained by the fatigue tests, are shown in fig. 2 in semi-logarithmic scale. according to the multistage fatigue life diagram [19, 20], the fatigue life diagram of 115crv3 can be divided into four regions. unlike the material 115crv3, the material 60spb20+bi presents a different behaviour with a continuous decrease of the fatigue life. the s-n curve has not the same slope, which has a significant decrease at a number of cycles equal to about 107, the slope decreases. figure 2: fatigue life diagrams. energetic approaches during hcf tests of common engineering metals and welded joints [6 10], the temperature evolution of the specimen, detected by means of an infrared camera, undergoes three separate phases. when a specimen is cyclically loaded above its fatigue limit, its superficial temperature usually rises quickly in the initial phase (phase 1), then reaches a stabilised asymptotic value (phase 2), and eventually this asymptote is left when plastic deformations become quite important, leading soon to failure after few cycles, with a very high further temperature increment (phase 3). the same trend was observed in lcf regime by crupi et al. [11]. this temperature evolution is closely related to the internal microstructural changes, as demonstrated in [15], and to crack initiation and propagation [21]. in the present study, the temperature evolution in vhcf regime was analysed using an ir thermography. the td – n, obtained applying the ir thermography in vhcf regime, shows a similar trend with the three stages. t v. crupi et alii, frattura ed integrità strutturale, 30 (2014) 569-577; doi: 10.3221/igf-esis.30.68 572 crupi [16] developed a theoretical model able to describe the temperature evolution during the phases 1 and 2 of the fatigue life:            n asd ett 1 (1) where  is a constant; if n is  then td is 0,63 tas and if n is 4 then td is 0,98 tas. the value of 4, applied successfully to conventional steel under hcf loading in [16], was considered also in the investigated vhcf tests. the td n data were interpolated by means of an exponential function according to eq. (1) and the convergence was achieved, as demonstrated in fig. 3 for 115crv3 and for 60spb20+bi. as can be seen, for both materials there is a strong correlation between the experimental data and the theoretical ones. figure 3: experimental and theoretical δtd n curves. fig. 4 shows the values of asymptotic temperature increment during fatigue test δtas (phase 2) as a function of the square of stress range applied δσ2 for the two investigated steels: 115crv3 and 60spb20+bi. the behaviour of the 60spb20+bi is a confirmation of the linear trend in vhcf tests, the same already observed in the hcf tests [6, 14, 15, 16]. however, it is interesting to note that the 115crv3 steel has a different trend, even if more tests should be necessary. figure 4: δtas vs δσ 2. v. crupi et alii, frattura ed integrità strutturale, 30 (2014) 569-577; doi: 10.3221/igf-esis.30.68 573 energetic approaches, based on ir analysis, has been applied by several researchers [17, 22, 23, 24] in hcf regime to obtain the s-n curve and to assess the residual fatigue life. the basic assumption of the so-called “energy approach” [22] is that the fatigue failure takes place when the absorbed energy reaches a certain threshold value ec characteristic for each structural detail. the limit energy ec is proportional to the integral of the td n curve:  fn dc dnnte 0 )( (2) where nf is the number of cycles to failure. it has been ascertained that the energy absorbed by a unit volume of material till failure is the same when load histories at different levels are applied, so the energy parameter is a material constant in hcf regime. the traditional energetic approach was developed by the authors in order to extend it in vhcf regime. the assessment of the integral  for the tests, carried out in a wide range of fatigue life, demonstrated that  is no longer constant for fatigue life higher than hcf zone (about 2·106), but increases by an order of magnitude with the increment of the number of cycles. fig. 5 reports the trend of integral  as a function of  for both materials. it's possible to note that the value of the integral  of 115crv3 decreases more steeply than the value of 60spb20+bi. figure 5: integral  as a function of δσ. failure analysis for 115crv3 steel, the thermal treatment made by the supplier produces a spheroidized structure, as evaluated by metallographic analyses. rockwell c hardness tests were carried out on some specimens after the fatigue tests and are reported in tab. 2. spheroidite can be considered a soft phase [25], thus the measured hardness values can be referred to a microstructure transformation occurred during the fatigue test. specimen 1 2 3 hrc 25.1 22.8 22.2 table 2: average rockwell c hardness values for some 115crv3 specimens. fracture surfaces of the investigated steel were observed after fatigue tests by sem and stereomicroscope. for 115crv3 steel, in the vhcf regime, the nucleation site of the crack is located sub-superficially at an average distance of about 100 μm from the external face. if we consider that a new phase has behaviour similar to an inclusion, its presence or a discontinuity in microstructure [26] at the initiation site is crucial for fatigue life. the microstructural transformation can have produced bainite, as confirmed by the calculated hardness and by the thermal history recorded during the test with v. crupi et alii, frattura ed integrità strutturale, 30 (2014) 569-577; doi: 10.3221/igf-esis.30.68 574 temperatures below approximately 350 or 400 °c. the lower bainite phase [27] can be the cause of no oda observed on the fracture surface [28, 29]. in very high cycle regime (beyond 107 cycles), for pb-added steel, the initiation sites were always found at inclusions located in the interior of the specimens. fig. 6 shows optical micrographs of the fracture surfaces. if we analyse carefully the center of the fish-eye, it is possible to find for many specimens a darker area around an inclusion, which is also the site of crack nucleation. this area is called the oda (optically dark area). it is interesting to underline that no oda is observed in the case of fractured specimens in the lcf regime (fig. 6d). for the analysed specimens in the fig. 6a and b, in the left column are reported the values of the areas of the inclusion (origin of the crack), of the so-called gbf (granular bright facet on the stage of crack propagation) and of the whole fish-eye. (a) m= 32x; = 568 mpa, nf= 3.3·108 cycles. m= 50x (b) m= 32x; = 610 mpa, nf= 7.6·106 cycles. m= 50x (c) m= 32x; = 650 mpa, nf= 1.1·106 cycles. (d) m= 25x; = 690 mpa, nf= 1.3·105 cycles. figure 6: fracture surfaces of some tested specimens. the observations at the stereomicroscope show that the gbf is more evident for the specimens that have a fatigue life over 106 cycles [30] and for which the area of the fish-eye increases with the fatigue life. a schematic representation of the 3 areas is shown in fig. 7. v. crupi et alii, frattura ed integrità strutturale, 30 (2014) 569-577; doi: 10.3221/igf-esis.30.68 575 figure 7: (a) scheme of the fracture surface morphology [30]; (b) fish-eye particular of the specimen tested at  = 568 mpa and failed at nf= 4.1·108 cycles. on the other hand, fatigue initiation occurred as in a sub-surface site as on the surface. as detected by bathias and paris [31], the investigated pb-added steel, for which there are no similar studies in the literature, shows a morphology of the fracture surface analogous to what is schematically reported in the fig. 8. figure 8: scheme of the fracture surface morphology related to the fatigue endurance [31]. conclusions ith the increasing progress of the technological development in structural applications of tool steels, the required fatigue life has increased, so it is very important to determine a safe fatigue strength for 109 cycles. in this paper, the behaviour of two kinds of tool steel was investigated in vhcf regime. the fatigue tests were carried out at the f = 20 khz and r = -1 by means of an ultrasonic fatigue testing equipment. the radiometric surface temperature was detected during the whole test by means of an ir camera. the traditional energetic approach was developed in order to extend it in vhcf regime. the failure analysis, based on experimental techniques (scanning electron microscopy, energy dispersive x-ray spectroscopy and optical microscopy), allowed the authors to assess that the microstructure of the analysed steels influences the crack initiation and its behaviour in the vhcf regime. nomenclature f = frequency [hz] ec = energy to failure per unit volume [jm-3] n = number of cycles nas = asymptotic number of cycles nf= = number of cycles to failure r = stress ratio tas = asymptotic temperature increment during fatigue test [k] td = surface temperature increment during fatigue test [k] = stress range [mpa] = fatigue limit [mpa] = thermal increment to failure per unit volume [km-3] w v. crupi et alii, frattura ed integrità strutturale, 30 (2014) 569-577; doi: 10.3221/igf-esis.30.68 576 references [1] bathias, c., there is no infinite fatigue life in metallic materials, fatigue fract. engng. mater. struct., 22 (1999) 559565. [2] sonsino, c.m., course of sn-curves especially in the high-cycle fatigue regime with regard to component design and safety, int. j. fatigue, 29 (2007) 2246-2258. [3] murakami, y., nomoto, t., ueda, t., factors influencing the mechanism of superlong fatigue failure in steels, fatigue fract. engng. mater. struct. 22 (1999) 581-590. [4] bayraktar, e., garcias, i.m., bathias, c., failure mechanisms of automotive metallic alloys in very high cycle fatigue range, int. j. fatigue 28 (2006) 1590–1602. [5] sohar, c.r., betzar-kotas, a., gierl, c. et al., fractographic evaluation of gigacycle fatigue crack nucleation and propagation of a high cr alloyed cold work tool steel, int. j. fatigue 30 (2008) 2191–2199. [6] la rosa, g., risitano, a., thermographic methodology for rapid determination of the fatigue limit of materials and mechanical components, int. j. fatigue, 22 (2000) 65–73. [7] amiri, m., khonsari, m.m., rapid determination of fatigue failure based on temperature evolution: fully reversed bending load, int. j. fatigue, 32 (2010) 382–389. [8] meneghetti, g., ricotta, m., atzori, b., a synthesis of the push-pull fatigue behaviour of plain and notched stainless steel specimens by using the specific heat loss, fatigue fract. engng. mater. struct., 36 (2013) 1306-1322. [9] curà, f., curti, g., sesana, r., a new iteration method for the thermographic determination of fatigue limit in steels. int. j. fatigue, 27 (2005) 453-459. [10] fan, j.l., guo, x.l., wu, c.w., zhao, y., guo, q., stress assessment and fatigue behavior evaluation of components with defects based on the finite element method and lock-in thermography, special issue “fatigue design and analysis in transportation engineering”, p. i. mech. eng. c. j. mech., (2014) doi:10.1177/0954406214541432. [11] crupi, v., chiofalo, g., guglielmino, e., infrared investigations for the analysis of low cycle fatigue processes in carbon steels. p. i. mech. eng. c. j. mech., 225 (2011) 833 – 842. [12] xue, h., wagner, d., ranc, n., bayraktar, e., thermographic analysis in ultrasonic fatigue tests, fatigue fract. engng. mater. struct., 29 (2006) 573-580. [13] blanche, a., chrysochoos, a., ranc, n., favier, v., dissipation assessments during dynamic very high cycle fatigue tests, exp. mech., (2014) doi: 10.1007/s11340-014-9857-3. [14] fargione, g., tringale, d., guglielmino, e., risitano, g., fatigue characterization of mechanical components in service, frat. integ. strut., 26 (2013) 143-155. [15] fan, j., guo, x., wu, c., crupi, v., guglielmino, e., using infrared thermography in effect evaluation of heat treatments on martensitic steel, exp. techniques, (2014) doi: 10.1111/ext.12019. [16] crupi, v., an unifying approach to assess the structural strength, int. j. fatigue, 30 (2008) 1150-1159. [17] risitano, a., risitano, g., cumulative damage evaluation in multiple cycle fatigue tests taking into account energy parameters, int. j. fatigue, 48 (2013) 214-222. [18] crupi, v., epasto, g., guglielmino, e., low-velocity impact strength of sandwich materials, j. sandw. struct. mater., 13 (2011) 409 426. [19] mughrabi, h., on ‘multi-stage’ fatigue life diagrams and the relevant life-controlling mechanisms in ultrahigh-cycle fatigue, fatigue fract. engng. mater. struct., 25 (2002) 755-764. [20] pyttel, b., schwerdt, d., berger, c., very high cycle fatigue – is there a fatigue limit?, int. j. fatigue, 33 (2011) 49-58. [21] plekhov, o.a., palin-luc, t., saintier, n., uvarov, s., naimark, o., fatigue crack initiation and growth in a 35crmo4 steel investigated by infrared thermography, fatigue fract. eng. m., 28 (2005) 169-178. [22] fargione, g., geraci, a., la rosa, g., risitano, a., rapid determination of the fatigue curve by the thermographic method, int. j. fatigue, 24 (2002) 11-19. [23] amiri, m., khonsari, m.m., life prediction of metals undergoing fatigue load based on temperature evolution, mat. sci. eng. a struct., 527 (2010) 1555-1559. [24] williams, p., liakat, m., khonsari, m.m., kabir, o.m., a thermographic method for remaining fatigue life prediction of welded joints, materials and design, 51 (2013) 916-923. [25] asm handbook, metals handbook: heat treatment, ninth ed., asm international, materials park, ohio (1981). [26] zhu, m.l., xuan, f.z., chen, j., influence of microstructure and microdefects on long-term fatigue behavior of a crmo-v steel, mat. sci. and eng. a, 546 (2012) 90–96. [27] asm handbook, metallography and microstructures, asm international, materials park, ohio (2004). v. crupi et alii, frattura ed integrità strutturale, 30 (2014) 569-577; doi: 10.3221/igf-esis.30.68 577 [28] murakami, y., nomoto, t., ueda, t., murakami, y., on the mechanism of fatigue failure in the superlong life regime (n>107 cycles). part i: influence of hydrogen trapped by inclusions, fatigue fract. engng. mater. struct., 23 (2000) 893-902. [29] murakami, y., toriyama, t., tsubota, k., furumura, k., what happens to the fatigue limit of bearing steel without nonmetallic inclusions?: fatigue strength of electron beam remelted super clean bearing steel, bearing steels, in: the 21st century, astm stp 1327, j. j. c. hoo, w. b. green (eds.), american society for testing and materials, philadelphia (1998) 87–105. [30] li, w., yuan, h., sun, z., zhang, z., surface vs. interior failure behaviors in a structural steel under gigacycle fatigue: failure analysis and life prediction”, int. j. of fatigue, 64 (2014) 42–53. [31] bathias, c., paris, p.c., gigacycle fatigue in mechanical practice, marcel dekker, new york (2005). microsoft word numero_35_art_12 p. bernardi et al, frattura ed integrità strutturale, 35 (2016) 98-107; doi: 10.3221/igf-esis.35.12 98 focussed on crack paths a non-linear procedure for the numerical analysis of crack development in beams failing in shear p. bernardi, r. cerioni, e. michelini, a. sirico dept. of civil, environmental, land management engineering and architecture, university of parma (italy) patrizia.bernardi@unipr.it, roberto.cerioni@unipr.it, elena.michelini@unipr.it, alice.sirico@studenti.unipr.it abstract. in this work, a consistent formulation for the representation of concrete behavior before and after cracking has been implemented into a non-linear model for the analysis of reinforced concrete structures, named 2d-parc. several researches have indeed pointed out that the adoption of an effective modeling for concrete, combined with an accurate failure criterion, is crucial for the correct prediction of the structural behavior, not only in terms of failure load, but also with reference to a realistic representation of crack initiation and development. this last aspect is particularly relevant at serviceability conditions in order to verify the fulfillment of structural requirements provided by design codes, which limit the maximum crack width due to appearance and durability issues. in more details, a constitutive model originally proposed by ottosen and based on non-linear elasticity has been here incorporated into 2d-parc in order to improve the numerical efficiency of the adopted algorithm, providing at the same time an accurate prediction of the structural response. the effectiveness of this procedure has been verified against significant experimental results available in the technical literature and relative to reinforced concrete beams without stirrups failing in shear, which represent a problem of great theoretical and practical importance in the field of structural engineering. numerical results have been compared to experimental evidences not only in terms of global structural response (i.e. applied load vs. midspan deflection), but also in terms of crack pattern evolution and maximum crack widths. keywords. reinforced concrete; constitutive modeling; biaxial stress state; cracking; fe analysis. introduction he analysis of the response up to failure of reinforced concrete (rc) structures through numerical techniques requires the adoption of effective material constitutive models, able to correctly represent the behavior of concrete and steel at the element level. this represents a quite complex task, since as loading increases, rc behavior is influenced by several non-linear mechanisms which often interact with each other, such as concrete cracking and crushing, aggregate interlock, bond-slip behavior, dowel action and yielding of reinforcement. therefore, realistic simulations of rc structural behavior require a correct description of each of these phenomena into the adopted material model, which can be subsequently implemented within the finite element (fe) framework. in this context, among the several constitutive laws proposed in the past within smeared crack formulations ([1-6], just to mention some), 2d-parc model [7] represents an effective tool to perform non-linear analyses up to failure of rc structures, since it is able to account for the most influencing aforementioned contributions. this model is structured in a modular framework, so that each mechanical phenomenon is indeed individually analyzed by using a proper constitutive law and then the corresponding contribution is inserted into a material stiffness matrix. in more detail, the present work focuses on the evaluation of concrete contribution before and after the development of cracking. as regards concrete modeling, the basic requirements concern the choice of an accurate failure criterion to be employed in conjunction with a proper non-linear stress-strain relationship. the seventies have seen the development of several t p. bernardi et al, frattura ed integrità strutturale, 35 (2016) 98-107; doi: 10.3221/igf-esis.35.12 99 failure criteria derived from different failure data (e.g., [8-11]), which have pointed out that concrete under a biaxial (or triaxial) state of stress exhibits different stiffness, strength and ductility than under uniaxial loading. consequently, the strength characteristics of concrete under a general multi-axial state of stress cannot be reproduced into a material model by directly using experimental uniaxial stress-strain curves. to represent the problem, several mathematical material models have been proposed, which can be substantially divided into orthotropic, non-linear elastic, plastic or endochronic ones [12]. with reference to orthotropic formulations, a fairly simple solution can be obtained by referring to the concept of equivalent uniaxial strain, as originally proposed by darwin and pecknold in [13] and implemented into 2d-parc model [7]. an interesting model based on non-linear elasticity was instead proposed by ottosen [14]. this formulation provides non-linear stress-strain relations for concrete by only properly changing the secant values of young modulus and poisson ratio. in this way, even if the model is able to realistically represent concrete behavior under a general stress state, its calibration is quite simple, only requiring experimental data obtained by standard uniaxial tests. for its flexibility and numerical feasibility, it has immediately appeared suitable for the implementation into fe programs, and applicable to the analysis up to failure of different types of rc structures [15, 16]. basing on the approach proposed by ottosen [14] and on the implementation performed by barzegar [16], concrete modeling into 2d-parc has been here revised. this modified formulation has been verified with reference to the analysis of rc beams without shear reinforcement [17, 18], where concrete modeling assumes particular relevance both before and after crack pattern development. furthermore, this represents a structural problem of significant theoretical and practical importance, subjected in the past to great experimental efforts [19, 20], since the comprehension of the mechanisms of shear transfer across cracks and failure in beams without shear reinforcement can improve the knowledge of concrete contribution on shear strength also in beams with web reinforcement. numerical model he behavior of reinforced concrete (rc) beams without shear reinforcement has been herein studied through a non-linear finite element (nlfe) procedure. in order to account for reinforced concrete mechanical non-linearity, a suitable constitutive model, named 2d-parc [7], has been adopted. this constitutive model is based on a smeared-fixed crack approach and its theoretical basis, which has been deduced for a rc membrane element subjected to general in-plane stresses, can be found in details in [7] and in [21, 22] with reference to its extension to the case of steelfiber reinforced concrete (sfrc) elements or to the 3d case. in the uncracked stage, concrete and steel are schematized like two material working in parallel, by assuming perfect bond between them. when the principal maximum stress violates the failure envelope in the cracking region, crack pattern is assumed to develop with a constant spacing am1. afterwards, a strain decomposition procedure is adopted, by subdividing the total strain into two components, respectively related to rc between cracks and to all the resistant mechanisms that develop after crack formation (i.e. aggregate bridging and interlock, tension stiffening and dowel action). these resistant contributions are expressed as a function of two main variables, namely crack width w1 and sliding v1, and included into the crack stiffness matrix [dcr1]. the behavior of rc between cracks is instead described by adopting the same approach used in the uncracked stage, even if a slight modification is operated on both concrete and steel stiffness matrices, [dc] and [ds], so as to account for the degradation induced by cracking. the cracked rc stiffness matrix is then expressed in the following form: 1 1 1 1 1                                                    c cr c sd d d i d d (1) where [i] is the identity matrix. this formulation has been successfully applied to the analysis of different types of structures (such as panels, beams, slabs, etc…), providing a good prediction of experimental evidences both in terms of load-deformation response up to the ultimate capacity of the considered element, and in terms of crack pattern evolution and failure mode (e.g. [7, 23, 24]). however, the proposed algorithm is quite complex and requires long calculation times, which are mainly related to the approach followed in the evaluation of concrete stiffness matrix [dc]. both in the uncracked and cracked stage, concrete is indeed modeled as an orthotropic, non-linear elastic material subjected to a biaxial state of stress, which is duplicated by means of two equivalent uniaxial curves, following darwin and pecknold approach [13]. these uniaxial curves for concrete in compression and in tension report the actual stress as a function of an equivalent uniaxial strain, which is in turn determined according to [25]. these curves are characterized by maximum strength values derived from an analytical t p. bernardi et al, frattura ed integrità strutturale, 35 (2016) 98-107; doi: 10.3221/igf-esis.35.12 100 biaxial strength envelope based on the one suggested by kupfer et al. [8] (see also [7] for further details), and by material secant moduli in the two orthotropic directions, to be inserted into the matrix [dc]. moreover, in the cracked stage the terms of matrix [dc] are adequately softened through an empirical damage coefficient  related to crack width w1, whose expression can be still found in [7]. the need of adopting a so refined model for the description of concrete behavior, instead of a simple linear-elastic matrix, is mainly aimed to a correct simulation of those elements made of plain concrete or reinforced in a single direction, such as, i.e., beams without shear reinforcement. in these cases, the structural behavior is indeed mainly governed by concrete performances, and consequently its correct constitutive modelling is mandatory for a realistic prediction of both element stiffness and strength. this work illustrates an alternative procedure that still allows a quite sophisticated representation of concrete behavior but requires a lower computational effort. its implementation into the 2d-parc model is also briefly discussed. modeling of concrete behavior in the uncracked stage the constitutive relation herein adopted for concrete modeling represents a specialized 2d form, according to barzegar [16, 26], of the 3d non-linear elastic model originally proposed by ottosen [14, 15]. the main advantages of this model lay on its simple definition, since the stress-strain relation is expressed as a function of only two parameters, i.e. the secant values of the young modulus ec and of the poisson coefficient , which are properly modified to account for material non-linearity. as a consequence, concrete stiffness matrix [dc] can be written as: 2 1 0 1 0 1 1 0 0 2                        c c e d (2) in the global x-y co-ordinate system. hence, with respect to the previous formulation implemented into 2d-parc relation, this model depends on a lower number of parameters and allows to bypass the evaluation of the two equivalent uniaxial strains, so reducing the required computational effort. moreover, this model is very flexible, since it can be used in conjunction with any failure criterion, by simply modifying a single parameter, the so-called “nonlinearity index”, as discussed in the following. similarly to the original approach of 2d-parc, the failure envelope proposed by kupfer et al. [8, 9] has been still considered, even if its analytical expression has been slightly modified according to [16] in the region corresponding to tension-compression, so as to avoid possible discontinuities in those points where the maximum principal tensile stress is close to zero. fig. 1 shows the adopted failure envelope and the analytical expressions describing each considered region (tension-tension, tension-compression and compression-compression); the bold line indicates the part of the curve effectively implemented into the 2d-parc model, according to its conventions (that is 1c ≥ 2c). concrete secant elastic modulus ec is computed using a parameter called “nonlinearity index”, , which depends on how far the current stress point is from failure and is then related to the amount of non-linearity in the stress-strain curves [14, 16]. in case of biaxial compression this parameter can be evaluated through the expression: 2 2     c fin (3) where 2c is the maximum principal compressive stress and 2fin represents its corresponding value on the failure envelope, determined by keeping fixed the other principal compressive stress 1c (being 1c ≥ 2c, and assuming compressive stresses as negative). thus,  < 1,  = 1 and  > 1 respectively correspond to stress states located inside, on, and outside the considered failure curve. when tensile stresses are present, the nonlinearity index is instead computed in terms of effective stresses. to this aim, the actual state of stress (1c, 2c), where at least 1c is a tensile stress, is properly turned into an “equivalent compressive case”, by superposing an hydrostatic pressure -1c to the existing stress field. in this way, a new state of stress ('1c, '2c) = (0, 2c 1c) is obtained and the nonlinearity index is evaluated as: p. bernardi et al, frattura ed integrità strutturale, 35 (2016) 98-107; doi: 10.3221/igf-esis.35.12 101 2 2 1 2 ' '        c c c fin cf (4) where fc is the uniaxial compressive strength of concrete. by following this procedure, the value of  is properly reduced when tensile stresses occur; thus,  < 1 always holds in this case. -1.4 -1 -0.6 -0.2 0.2 -1.4 -1 -0.6 -0.2 0.2  2c / | f c | 1c / |fc| 1c 2c tensio n-t ension 1 max1max2 max1       ctf tensio n-c om pression k k f ct 73.0 6.0 max2max1 max2         cct ffk k   73.0lim c om pressiontensio n   073.0 56.6699 8.12 max2max1 22 max2           k kkk k f c c om pressionc ompression   10 1 65.31 max2max1 2max2           cf c2 cc 21   figure 1: adopted failure envelope [16]. after having determined the nonlinearity index, concrete secant elastic modulus ec can be then calculated as:   2 2' ' ' 1 1 2 2 2 2                              ci ci ci ci c cf cf cf e e e e e e e e d (5) where eci is the initial value of concrete young modulus, d is a compressive post-peak nonlinearity parameter that determines the degree of strain softening when concrete crushing occurs (see [14, 16] for details), and e'cf is the secant modulus corresponding to peak stress. when a tensile stress is present, e'cf is simply evaluated as in case of uniaxial compression, i.e. e'cf = ecf = fc/c0, while for biaxial compression the following relation is adopted:   ' 1 4 1    cf cf e e a x , (6) a being the ratio between the initial value of concrete young modulus and the secant one corresponding to peak stress (eci/ecf), while the term x takes into account the dependence on the actual loading and is evaluated through the relation: 2 1 3        c f j x f . (7) the first addend of eq. 7 represents the failure value of the invariant 2 cj f . based on the definition of the nonlinearity index  (eq.3), the following expression can be found:  2 22 1 2 1 2 1 3      c fin c finj . (8) p. bernardi et al, frattura ed integrità strutturale, 35 (2016) 98-107; doi: 10.3221/igf-esis.35.12 102 similarly, 1 3 is the value of  2 c f j f for uniaxial compressive loading. as regards the evaluation of the secant value of poisson coefficient to be inserted into eq. 2, it has been experimentally observed that in presence of compressive stresses concrete tends first to compact, while after the appearance of microcracks it tends to dilate. as a consequence, its value should be properly adjusted during the analysis so as to correctly represent this behavior. following the procedure proposed in [14, 16], the poisson coefficient is kept fixed until  reaches a “limit value” a equal to 0.8, and afterwards it is updated by applying the following relation:   2 1 1                 a f f i a , (9) where i is the initial value of the poisson coefficient (assumed equal to 0.2) and f represents its secant value at peak (approximately equal to 0.36). the so obtained secant values of concrete elastic modulus and poisson coefficient have been inserted into the concrete stiffness matrix [dc] (eq. 2); in this way, only the constitutive relation adopted for concrete modeling has been modified, by keeping unchanged the global structure of 2d-parc algorithm. it should be observed that all the above described procedure is applied until either cracking or crushing occurs. cracking takes place when the current stress state reaches or violates the failure envelope in the cracking region, i.e. 1c ≥ 1max in tension-compression or simply 1c ≥ fct in case of tension-tension, being fct the tensile strength of concrete. in this case, the fixed-smeared crack approach previously described is applied (see [7] for further details), even if the modeling of concrete between cracks has been properly modified as described in the following subsection. on the contrary, when the stress state reaches or violates the failure envelope in the crushing region, i.e.  ≥ 1 in case of biaxial compression or 2c ≤ 2max in case of compression-tension, a very simplified procedure is applied herein. for the considered case studies, only small portions of the modeled structures can enter indeed in the post-crushing regime during the analysis (e.g. near concentrated loads or at supports) without affecting the global behavior, which is instead much more influenced by the appearance of tensile cracks. however, concrete crushing should be included in the model formulation so as to avoid numerical difficulties or wrong predictions of the ultimate failure load. to this aim, in 2d-parc model a reduced young modulus ec is simply considered, equal to 25% that of undeformed concrete, as suggested also in [27]. modeling of concrete behavior in the cracked stage the above described formulation has been applied also in the cracked stage for the evaluation of the stiffness matrix of concrete between cracks, [dc]. however, in order to include damaging due to the presence of cracks, a proper reduction in the concrete compressive strength and stiffness has been operated. to this aim, the biaxial concrete failure envelope shown in fig. 1 has been properly reduced, following the relation suggested in [26]: * *max 0 1 0.2 , 0.8                c c c c c c f f f f f , (10) where max is the current maximum principal tensile strain in cracked concrete and *cf is the modified value of the uniaxial compressive strength at peak. the corresponding modified strain *co can be in turn calculated as a function of the initial value of the strain c0 corresponding to peak stress in uniaxial compression, through the expression: * max1 0.1                co co co . (11) comparisons with experimental observations he capability of the proposed model to describe rc global behavior and crack pattern evolution has been verified against the results of two well-documented experimental programs concerning beams without shear reinforcement [17, 18]. among several research projects, the one carried out by vecchio and shim [17] has been selected owing t p. bernardi et al, frattura ed integrità strutturale, 35 (2016) 98-107; doi: 10.3221/igf-esis.35.12 103 to its effectiveness, being a duplicate of the well-known bresler and scordelis beam tests [20], always regarded as benchmark data. the choice of the experimental program undertaken by podgorniak-stanik [18] has instead been related to the availability of several experimental data monitored during test execution, mainly concerning the crack pattern evolution with increasing loads. description of experimental tests [17, 18] the attention has been initially focused on three beams without stirrups, named oa1, oa2, oa3, tested by vecchio and shim [17]. these specimens had the same rectangular cross section 305 mm wide and 552 mm deep and a net span respectively equal to 3660 mm, 4570 mm and 6400 mm, corresponding to an increasing amount of tension reinforcement, heavy enough to make the beams critical in shear. the main geometrical details of the considered specimens and their reinforcement arrangement are summarized in fig. 2a. the three beams were characterized by a progressively increasing concrete compressive strength fc (which was equal to 22.6, 25.9 and 43.5 mpa for specimen oa1, oa2 and oa3, respectively). the main characteristics of the adopted reinforcement, both in terms of geometrical details and steel properties, can be found in [17], to which reference is made. 305 55 2 oa1 oa2 oa3 64 64m30 m30 m25 m30 m30 50 85 85 85 85 85 300 50 0 m25 m20 m25 m20 m10 50 m15 300 25 0 bn50 bn50d bn25 bn25d 25 40 40 40 40 40 m15 #3 (a) (b) m25m25 sample span (mm) l (mm) longitudinal reinforcement oa1 3660 4100 2 m25b, 2 m30 oa2 4570 5010 2 m25a, 3 m30 oa3 6400 6840 2 m25b, 4 m30 sample span (mm) l (mm) longitudinal reinforcement bn25 1352 1502 3 m15 bn25d 1352 1502 3 m15, 10 #3 bn50 2700 3000 2 m20, 1 m25 bn50d 2700 3000 2 m20, 1 m25, 10m10 figure 2: geometric dimensions (in mm) and reinforcement arrangement of the analyzed beams: (a) oa [17] and (b) bn series [18]. all the tests were performed under loading control, with a central point load, until the approaching of the ultimate stage, when the procedure was switched to displacement control so to allow the evaluation of the post-peak behavior. as already mentioned, the purpose of this experimental program was to recreate, as much as possible, the bresler and scordelis tests [20], in terms of geometrical dimensions, reinforcement details, material strengths and loading. compared to these latter, the beams tested by vecchio and shim [17] exhibited indeed a very similar behavior, with only few minor differences; as a consequence, only the specimens described in [17] have been considered in the fe analyses reported herein. in addition to this series, other four beams (originally named bn25, bn25d, bn50, bn50d) belonging to the extensive experimental program carried out by podgorniak-stanik [18], have been numerically analyzed. series 25 and 50 differed from each other in terms of transverse cross-section dimensions, respectively equal to 300 mm x 250 mm and 300 mm x 500 mm, and in terms of net span, which was nearly doubled for the second one (fig. 2b). moreover, the two series were characterized by almost the same tension reinforcement ratio, which was equal on average to 0.85% for beams bn25 and bn50, and to 1.21% for beams bn25d and bn50d. these two last specimens contained indeed additional small longitudinal bars distributed along the web. more details about the geometric dimensions and reinforcement arrangement of the examined beams can be found in fig. 2b. all the beams were cast by using concrete with a cylindrical compressive strength equal to 37 mpa. mechanical properties of reinforcing steel and rebar details can be found in [18]. all the tests were performed under loading control, by applying a central point load in several steps. at the end of each step, the load was lowered to approximately 90% of its current peak value and then increased again. during all test execution, crack pattern evolution and crack width were monitored in detail. p. bernardi et al, frattura ed integrità strutturale, 35 (2016) 98-107; doi: 10.3221/igf-esis.35.12 104 numerical results vs. experimental observations numerical analyses have been carried out by implementing the above described 2d-parc model into a commercial fe code (abaqus, [28]). taking advantage of the symmetry of the problem, only one half of each beam has been simulated, by adopting a fe mesh constituted by quadratic, isoparametric 8-node membrane elements with reduced integration (4 gauss integration points). numerical analyses have been performed under displacement control, by applying an increasingly displacement at the loading point, in order to achieve a better numerical convergence and evaluate also the post-peak behavior. numerical and experimental results have been first compared by considering the global response, in terms of applied load vs midspan deflection, as can be seen from figs. 3, 4. in more details, figs. 3 and 4a-b refer to the three specimens tested by vecchio and shim [17]. on the same graphs, also the results obtained by bresler and scordelis [20] on nominally identical beams are reported. fig. 3 shows a comparison between the experimental data relative to specimen oa2 and the numerical results obtained by adopting the 2d-parc model, respectively implementing the non-linear constitutive relation described above or a simple linear elastic matrix for describing concrete behavior. these results highlight that the assumption of a constant value for concrete young modulus during the analysis – equal to its initial value (ec = eci) – obviously provides a stiffer response, which is more pronounced for higher values of the applied load, where the effect of mechanical non-linearity is more significant. moreover, the adoption of a linear elastic matrix for concrete leads in this case to a slight underestimation of the failure load. a more refined description of concrete behavior allows not only an improved modeling of the experimental response until failure, but also a much more stable solution, since the numerical analysis is characterized by a better convergence. on the contrary, both numerical analyses correctly predict the experimental shear failure mode and the corresponding final crack pattern. it should be here pointed out that the numerical response obtained through the original formulation of 2d-parc model described in [7] is almost superimposed to that provided by adopting the concrete modeling proposed in this work. for this reason, the corresponding curve has not been plotted, so as to allow a better comprehension of the graphs of fig. 3. in both cases, concrete is indeed treated as a non-linear elastic material subjected to a biaxial state of stress, but the here proposed approach is preferable since it requires a reduced computational effort and leads to an improved convergence of the algorithm. 0 50 100 150 200 250 300 350 400 0 3 6 9 12 15 18 vecchio-shim beam bresler-scordelis beam nlfea p [kn] δ [mm] oa2 nlfea, ec=eci figure 3: comparison between experimental [17] and numerical results in terms of applied load vs. midspan deflection for specimen oa2. numerical analyses have been repeated twice, by differently modeling concrete behavior. figs. 4a-b show similar comparisons for the other two specimens tested by vecchio and shim [17], namely oa1 and oa3 beams. in this case, experimental data have been only compared with the numerical response provided by the improved formulation of 2d-parc model proposed herein, so to better appreciate its effectiveness. the graphs highlight the good capability of the model to represent the global behavior both at serviceability (cracking load) and at ultimate limit state. the peak load is accurately predicted, as well as the brittle shear failure characterized by no ductility. an accurate simulation of the experimental behavior, both in terms of stiffness and failure load, has been also obtained for specimens tested by podgorniak-stanik [18], as shown in figs. 4c-d. the adopted fe model is also able to predict that beams bn25d and bn50d (containing an additional distributed reinforcement on element sides, in addition to the main flexural bottom rebars) fail for higher shear stresses than the corresponding specimens bn25 and bn50, as provided by test results. therefore, the satisfactory agreement between experimental and numerical responses proves that the proposed model is able to correctly describe the experimental behavior for different specimen geometries, as well as different reinforcement arrangements. p. bernardi et al, frattura ed integrità strutturale, 35 (2016) 98-107; doi: 10.3221/igf-esis.35.12 105      0 50 100 150 200 250 300 350 400 0 2 4 6 8 10 vecchio-shim beam bresler-scordelis beam nlfea p [kn] δ [mm] oa1 0 50 100 150 200 250 300 350 400 0 5 10 15 20 25 30 35 40 vecchio-shim beam bresler-scordelis beam nlfea p [kn] δ [mm] oa3 0 50 100 150 200 250 0 1 2 3 4 5 6 podgorniak-stanik beam nlfea p [kn] δ [mm] bn25 bn25d 0 50 100 150 200 250 300 350 0 1 2 3 4 5 6 7 8 9 pogdorniak-stanik beam nlfea p [kn] bn50 δ [mm] bn50d figure 4: comparison between experimental and numerical results in terms of applied load vs. midspan deflection for specimens (a), (b) of the oa series [17], and (c), (d) of the bn series [18].           wf-max = 0.40 mm wf-max = 0.43 mm wf-max = 0.30 mm wf-max = 0.47 mm wf-max = 0.35 mm wf-max = 0.49 mm oa1 oa2 oa3 w [mm] figure 5: experimental (left side, [17]) vs numerical (right side) crack patterns and crack widths at failure for specimens oa. further comparisons between numerical and experimental results are also provided in terms of cracking development and crack widths, as depicted in figs. 5 and 6. fig. 5 shows the crack pattern at failure for the three specimens tested by vecchio and shim [17]. as can be observed, the model exhibits a fine capability of reproducing the experimental diagonaltension crack, catching the very brittle and sudden failure typical of beams containing no shear reinforcement. furthermore, maximum crack widths, which represent one of the most difficult parameter to predict in numerical analyses, are substantially comparable to experimental ones. similar results have been also obtained for rc beams tested by podgorniak-stanik [18]. more attention has been here devoted to the analysis of crack pattern evolution for increasing p. bernardi et al, frattura ed integrità strutturale, 35 (2016) 98-107; doi: 10.3221/igf-esis.35.12 106 loads, in terms of crack distribution and widths. some of the obtained results have been reported in fig. 6 (for brevity, only for specimen bn50 [18]). as can be seen, crack patterns are reasonably well described during the entire loading history, highlighting that the proposed model can represent a powerful tool in the analysis of rc structures also at serviceability conditions, where crack control represents one of the fundamental issues to be checked. for the analyzed beam, the first numerical flexural crack occurred at approximately the same loading level registered during the experimental test. as proved by both numerical and experimental results, this first crack has been followed by the appearance of subsequent flexural cracks, until the attainment of the last loading stage, when a significant shear diagonal crack developed as extension of existing cracks.             wf-max = 0.10 mm wf-max = 0.21 mm wf-max = 0.15 mm wf-max = 0.37 mm wf-max = 0.20 mm wf-max = 0.41 mm wf-max = 0.05 mm wf-max = 0.05 mm wf-max = 0.10 mm wf-max = 0.30 mm wf-max = 0.20 mm wf-max = 0.41 mm ls1 ls3 ls5 ls2 ls4 ls6 bn50 ls1 → p=80 kn ls2 → p=100 kn ls3 → p=150 kn ls4 → p=180 kn ls5 → p=220 kn ls6 → p=250 kn lsf → failure → p=260 kn wf-max = 0.20 mm wf-max = 0.43 mm lsf w [mm] figure 6: numerical (left side) vs. experimental (right side, [18]) crack patterns and crack widths at different loading stages for specimen bn50. conclusions n this paper, a constitutive non-linear model for the analysis of reinforced concrete structures, named 2d-parc, has been modified so as to improve its computational efficiency, while maintaining its capability of providing correct predictions of the structural behavior. to this aim, the constitutive relation originally adopted in 2d-parc for the modeling of concrete, both before and after cracking, has been properly substituted by implementing the one proposed by ottosen, which is based on non-linear elasticity and is characterized by a high numerical feasibility. the accuracy of the proposed formulation has been tested through comparisons with experimental results on rc beams without stirrups failing in shear, which represent a quite difficult case study, particularly when modelled through two-dimensional membrane analysis. based on the obtained results, it has been generally proved that 2d-parc model is able to provide accurate predictions of strength, load-deformation response and failure mode. moreover, also crack pattern evolution, both in terms of crack distribution into the considered element and in terms of maximum crack width, can be satisfactorily evaluated. finally, it can be pointed out that the modular structure of 2d-parc model makes it an attractive and versatile alternative approach for the analysis of rc structures, since the representation of each single resistant contribution can be easily changed when more refined and/or efficient constitutive relations become available. i p. bernardi et al, frattura ed integrità strutturale, 35 (2016) 98-107; doi: 10.3221/igf-esis.35.12 107 references [1] vecchio. f.j., collins, m.p., the response of rc elements to in-plane shear and normal stresse, rep. 82-03, dept. of civ. eng., univ. of toronto, canada (1982) [2] rots, j. g., computational modelling of cracked concrete, phd thesis, dept. of civ. eng., delft univ. of technol., delft, the netherlands (1988) [3] hsu, h.t., schnobrich, w.c., nonlinear finite element analysis of reinforced concrete plates and shells under monotonic loading, comp. & struct, 38(5/6) (1991) 637-651 [4] vecchio, f.j., disturbed stress field model for reinforced concrete: formulation. asce j. struct. eng., 126(9) (2000) 1070–1077. [5] soltani, m., an, x., maekawa, k., computational model for post cracking analysis of rc membrane element based on local strain characteristics, engng struct, 25 (2003) 995-1007. [6] he w., wu, y.f., liew, k.m., wu, z., a 2d total strain based constitutive model for predicting the behaviors of concrete structures, int j engng science, 44 (2006) 1280-1303 [7] cerioni, r., iori, i., michelini, e., bernardi, p., multi-directional modeling of crack pattern in r/c members, eng. fract. mech., 75 (2008) 615-628. doi: 10.1016/j.engfracmech.2007.04.012 [8] kupfer, h., hilsdorf, h.k., rusch, h., behavior of concrete under biaxial stresses, proc. aci j., 66 (1969) 656–666. [9] kupfer, h., gerstle, k.h., behavior of concrete under biaxial stresses, asce j. eng. mech. div., 99 (1973) 853-866. [10] ottosen, n.s., a failure criterion for concrete, asce j. eng. mech. div., 103-em4 (1977) 527-535. [11] menétrey ph., willam, k.j., triaxial failure criterion for concrete and its generalization, aci struct. j., 92 (1995) 311318. [12] kwak, h.-g., filippou, f.c., finite element analysis of structures under monotonic loads, rep. ucb/semm-90/14, dept. of civ. eng., univ. of california, berkeley, california (1990). [13] darwin, d., pecknold, d.a., non-linear biaxial stress–strain law for concrete, j. engng. mech. div.: proc. asce, 103em2 (1977) 229–241. [14] ottosen, n.s., constitutive model for short-time loading of concrete, asce j. eng. mech. div., 105 (1979) 127-141. [15] ottosen, n.s., nonlinear finite element analysis of reinforced concrete structures, ph.d. thesis, technical university of denmark, (1980). [16] barzegar-jamshidi, f., nonlinear finite element analysis of reinforced concrete under short term loading, ph.d. thesis, university of illinois at urbana-champaign, (1986). [17] vecchio, f.j., shim, w., experimental and analytical reexamination of classic concrete beam test, j. struct. eng., 130 (2004) 460-469. [18] podgorniak-stanik, b.a., the influence of concrete strength, distribution of longitudinal reinforcement, amount of transverse reinforcement and member size on shear strength of reinforced concrete members, phd thesis, university of toronto, (1998). [19] leonhardt, f., walther, r., schubversuche an einfeldrigen stahlbetonbalken mit und ohne schubbewehrung, deutscher ausschuss für stahlbeton, h.151, ernst & sohn (1962). [20] bresler, b., scordelis, a.c., shear strength of reinforced concrete beams, j. am. concr. inst., 60 (1963) 51–72. [21] bernardi, p., cerioni, r., michelini, e., analysis of post-cracking stage in sfrc elements through a non-linear numerical approach, eng. fract. mech., 108 (2013) 238-250. doi: 10.1016/j.engfracmech.2013.02.024 [22] cerioni, r., bernardi, p., michelini, e., mordini, a., a general 3d approach for the analysis of multi-axial fracture behavior of reinforced concrete elements, eng. fract. mech., 78 (2011) 1784-1793. [23] bernardi, p., cerioni, r., michelini, e., numerical modelling of the behaviour of sfrc elements in presence of multiple cracks, in: j. barros et al. (eds.), proc. 8th rilem int. symposium on fibre reinforced concrete, guimarães, (2012) 219-220. [24] bernardi, p., cerioni, r., michelini, e., numerical modeling of bond in cracked reinforced concrete elements, in: j.w. cairns et al. (eds.), proc. of bond in concrete 2012: bond, anchorage, detailing, brescia (2012) 177-184. [25] elwi, a.a., murray, d.w., a 3d hypoelastic concrete constitutive relationship, j. engng. mech. div.: proc. asce, 105-em4 (1979) 623–641. [26] ramaswamy, a., barzegar, f., voyiadjis, g.z., postcracking formulation for analysis of rc structures based on secant stiffness, asce j. eng. mech., 120 (1994) 2621-2640. [27] sebastian, w.m., mcconnel, r.e., nonlinear fe analysis of steel-concrete composite structures, asce j. struct. eng., 126 (2000) 662-674. 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/pdfxoutputintentprofileselector /documentcmyk /preserveediting true /untaggedcmykhandling /leaveuntagged /untaggedrgbhandling /usedocumentprofile /usedocumentbleed false >> ] >> setdistillerparams << /hwresolution [2400 2400] /pagesize [612.000 792.000] >> setpagedevice microsoft word 2222 z.-y. han et alii, frattura ed integrità strutturale, 47 (2019) 74-81; doi: 10.3221/igf-esis.47.07 74 experimental study on shale fracturing assisted by low-temperature freezing zhong-ying han, yuan-fang cheng, xue-liang li, chuan-liang yan school of petroleum engineering, china university of petroleum (east china), qingdao, shandong 266580, china. hanzhying@.upc.edu.cn, yfcheng@upc.edu.cn abstract. under the cold impact of liquid nitrogen, the shale suffers from the significant freezing damage, which provides the possibility of liquid nitrogen fracturing. moreover, shale fracturing assisted by liquid nitrogen can effectively reduce reservoir pollution. in this paper, the hydraulic fracturing experiments of natural shale samples frozen by liquid nitrogen were carried out to investigate the factors affecting the crack propagation of shale after low temperature fracturing. the results show that a large number of cracks or macropores form inside the natural shale sample after freezing treatment by liquid nitrogen. the fracture pressure of the shale decreases with increasing impact time at the beginning of the immersion time, and remains substantially stable after an immersion of 2 hours. when the freezing time increases, the crack initiation time increases accordingly. after low temperature impact, the fracture pressure of shale decreases with the increase of stress difference, but the cracking times vary with the stress with obvious regularity. it is easier to form main fracture with larger displacement on the premise of well-developed shale bedding. keywords. liquid nitrogen; freezing; hydraulic fracture; fracture pressure; fracture initiation time. citation: han, z-y., cheng, y.f., li, x-l., yan, c-l.., experimental study on shale fracturing assisted by low-temperature freezing, frattura ed integrità strutturale, 47 (2019) 74-81 received: 18.10.2018 accepted: 14.11.2018 published: 01.01.2019 copyright: © 2019 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. introduction he freezing and fracturing of the shale shocked by liquid nitrogen on rock mainly follows two stages: cold shrinkage and frost heave. the huge temperature difference caused by the freezing of liquid nitrogen makes the pore structure of the shale shrink and deform, resulting in thermal stress. at the same time, when the pore water freezes into ice, it expands in volume and produces frost heave. under the combined action of thermal stress and frost heaving force, the pore structure of shale is destroyed and the cracks is generated [1-5]. shale fracturing assisted by lowtemperature freezing is to form a certain crack network by the freezing and breaking mechanism of liquid nitrogen, and then perform hydraulic fracturing to improve the shale conductivity and increase fracturing effect. low temperature fracturing technology in the petroleum industry has still been in the experimental stage of exploration. in 1983, king [6] used gelatinous liquid carbon dioxide as a modification liquid to improve the in-place production of t http://www.gruppofrattura.it/va/47/2222.mp4 z.-y. han et alii, frattura ed integrità strutturale, 47 (2019) 74-81; doi: 10.3221/igf-esis.47.07 75 tight sand layer, and achieved good results without experimental verification. mcdaniel et al. [7, 8] conducted a liquid nitrogen immersion test on coal rock in the laboratory. the results showed that low temperature fracturing might increase the production of coalbed methane and conduct field tests. because of the existed natural cracks and obvious layering, the damage mechanism of shale after low-temperature impact is more complicated. in fully understand the failure mechanism of shale after low-temperature impact, many experts and scholars have conducted a lot of basic experimental research [911]. cai et al. [12, 13] conducted an experimental study on the damage of shale pore structure under the action of liquid nitrogen. in recent years, to meet the needs of low-temperature fracturing technology, many scholars began to analyze the physical and mechanical properties of shale after liquid nitrogen treatment through indoor experiments, as well as considered the influence of shale bedding orientation [14-16]. in the physical simulation of hydraulic fracturing, the researchers [17, 18] used artificial cement samples to simulate low-temperature cracking of shale, but there were also some differences, such as randomly distributed natural cracks and bedding, between artificial and natural samples. in this paper, the crack propagation characteristics of shale after low-temperature fracturing are analyzed by the hydraulic fracturing experiment of natural shale samples, and the factors affecting crack propagation are discussed. experimental program he sample was taken from the outcrop shale of longmaxi formation in a certain area. the outcrop shale is a natural extension of the silurian longmaxi formation shale reservoir in the southeast of guizhou, china. the shale mineral composition analysis was carried out by an x-ray diffractometer, and the results are shown in fig. 1. the main component of the experimental sample is quartz, accounting for 52%, followed by clay minerals, accounting for 17%. among the clay minerals, illite is the main component, accounting for 60%. figure 1: shale mineral composition and its content. shale tensile strength test hydraulic fracturing is one of the prerequisites for the development of shale gas. the principle of shale hydraulic fracturing is to pump the fluid into the well by the ground high-pressure pump set with a displacement that greatly exceeds the absorption capacity of the formation, and then cause the high pressure near the bottom of the well. when the pressure is greater than the in-situ stress near the borehole wall and the tensile strength of the shale, cracks forms in the formation near the bottom of the well. the tensile strength of the shale characterizes the ultimate bearing capacity of the shale during tensile failure. the tensile strengths of the shale before and after freezing were determined before the hydraulic fracturing experiment. the results are listed in fig. 2. it can be seen that the tensile strength of shale decreases by about 20% before and after freezing of liquid nitrogen, and the reduction of tensile strength is more conducive to the formation of cracks during fracturing. shale fracturing experiment assisted by liquid nitrogen a true triaxial experimental system was used for liquid nitrogen fracturing test. it mainly includes liquid nitrogen selfpressurizing system, intermediate container, and true triaxial experimental equipment, as shown in fig. 3. the experimental sample was cut from a cuboid shale rock to a dimension of 100mm100mm100mm, with the surfaces smoothed by grinding. the length of the open hole of simulated wellbore was 30 mm, as shown in fig. 4. t z.-y. han et alii, frattura ed integrità strutturale, 47 (2019) 74-81; doi: 10.3221/igf-esis.47.07 76 the factors affecting fracturing efficiency of shale after liquid nitrogen cold impact treatment, such as the complexity of natural cracks, the displacement of fracturing fluid and the difference of ground stress, were mainly discussed. a comparison table of control variables was used to develop an experimental program, as shown in tab. 1, where σv is the vertical stress, mpa, σh is the maximum horizontal principal stress, mpa, and σh is the minimum horizontal principal stress, mpa. to achieve the goal of fully extending of crack, the pre-freezing displacement is set to an intermediate value of 40 ml/min, and the order from low to high after freezing is 20 ml/min, 40 ml/min and 60 ml/min. the liquid nitrogen treatment times are set as 1h, 2h and 3h, respectively. figure 2: change law of tensile strength before and after shale freezing. figure 3: true triaxial experimental system for liquid nitrogen fracturing. figure 4: sample basic model diagram. 0 1 2 3 4 5 6 7 8 0 2 4 6 8 10 t en si le s tr en g th /m p a core data points before freezing after freezing face a face b face c face d face e face f z.-y. han et alii, frattura ed integrità strutturale, 47 (2019) 74-81; doi: 10.3221/igf-esis.47.07 77 experiment number σv /mpa σh /mpa σh /mpa stress difference /mpa freezing time /h displacement /ml/min s-6 10 8 3 5 0 40 sl-1 10 8 3 5 1 40 sl-2 10 8 3 5 2 40 sl-3 10 8 3 5 3 40 sl-4 10 5 3 2 3 40 sl-5 12 11 3 8 3 40 sl-6 10 8 3 5 3 20 sl-7 10 8 3 5 3 60 table 1: shale fracturing test after liquid nitrogen freeze-thaw. the main steps of the fracturing simulation experiment under liquid nitrogen freezing are as follows: (1) seven standard samples as shown in fig. 4 were prepared according to the standard and labeled separately. a silica gel solution with a mass fraction of 4% was used as a fracturing fluid, and an appropriate amount of tracer was added. (2) the sample was placed in a heat preservation container, and the liquid nitrogen was continuously injected into the sample simulation wellbore through the low-temperature pipeline by using the liquid nitrogen self-pressurization system, and the duration varied from 1h to 3h according to the experimental requirements. (3) the sample had been placed at rest for a period of time after taken out from container, and then was placed in the main pressure-bearing cavity. two steel blocks were placed on both face a and face b to adjust the height, and the upper cover of the experimenter was sealed and fasten with bolts. (4) an air compressor and a pneumatic control valve were used to apply the in-situ stress. the pressure was maintained at 0.8 mpa by the air compressor. the gas boosting device and the hydraulic pump were used to apply stress to the sample in three directions to a predetermined value. the load was applied smoothly to prevent pressure fluctuations during the whole process. (5) after the three-direction stresses applied to the presupposed values and kept stably, a pipeline was connected to the reserved hole above the sample. the silica gel solution with a mass fraction of 4% was injected in by a displacement pump controlled by the servo motor, to simulate the pressure variation during the whole fracturing process. the real-time pressure information of the injected fluid was synchronously recorded by the computer. (6) the pump was stopped when the experiment was finished. the wellbore pressure and the stress acting on the sample were unloaded in turn. the pressure in the hydraulic bladder was slowly released to zero to prevent damage to the equipment from instantaneous depressurization. (7) after the sample was taken out from the autoclave, and the crack morphology after fracturing was observed in detail and the fracturing mechanism was discussed. experimental results acoustic wave results total of 7 samples were involved in the experiment. according to the experimental procedure, each sample was initially frozen by liquid nitrogen. from the experimental phenomena, the original bedding and natural cracks on the surface, especially on face a, of the shale developed well after cold treatment by liquid nitrogen. the fractures showed a radial distribution along the simulated wellbore, and the natural fracture network was perfect. to detect the formation of cracks in detail, five points were randomly selected on face c and face d, as shown in fig. 5. the acoustic wave variations of the sample before and after the liquid nitrogen treatment on both sides of face c and face d were determined. taking the sample sl-1 as an example, as shown in fig. 6, the acoustic wave values of each monitoring point have decreased to some extent after liquid nitrogen cooling treatment, indicating that a large number of cracks or macropores have generated inside the sample after cold treatment. a z.-y. han et alii, frattura ed integrità strutturale, 47 (2019) 74-81; doi: 10.3221/igf-esis.47.07 78 from the results of fracturing, main hydraulic cracks form near simulated wellbore, and extend along the direction perpendicular to the minimum horizontal principal stress, finally form a vertical fracture surface. micro-cracks form on each face, and most of them extend in the direction of natural cracks and then cross each other to form a crack network. from the dissection of the sample after fracturing, the traces of the white tracer are clearly, indicating that liquid nitrogen enhances its permeability of shale. figure 5: schematic diagram of acoustic wave test points. figure 6: acoustic wave results before and after freezing of face c and face d on sl-1 sample. effect of liquid nitrogen cold treatment time the hydraulic fracturing simulations were carried out to study the effect of cold treatment time on fracturing effect. the fracturing construction curve of sample sl-1, sl-2 and sl-3, by changing the length of liquid nitrogen action time while maintaining the stress difference and displacement, are shown in fig. 7. it can be seen that the fracture pressure is the highest after immersion for 1 hour in liquid nitrogen, about 21 mpa. after immersing for 2 hours and 3 hours, the fracture pressure remains basically unchanged as 10.8 mpa and 10.5 mpa, respectively. this phenomenon shows that the fracture pressure decreases with the increase of impact time within a certain period of time. but this change is limited by a time effect. after immersion of 2 hours, the effect of the low temperature on the physical and mechanical properties of the sample did not change much as the treatment time prolonged. the cracking time reflects that the pre-impact of liquid nitrogen mainly enhances the brittleness of shale. however, the late impact reduces the brittleness of shale and increases the plasticity, and it is not easy for cracking, and the cracking time is greatly increased by about 5 times. the crack gradually forms a cross-sewed network from the general macro-crack, and the fracturing effect is better at about 2h. influence of stress difference the comparative experimental results of sample sl-3, sl-4 and sl-5 show that the fracture pressure of the sample decreases with the increase of the stress difference, under the condition of only changing the magnitude of the stress difference, as shown in fig. 8. however, there is no obvious regularity about the initiation time affected by the stress difference. at the same time, the fracture-making ability increases gradually with the increase of the stress difference because the cross-sewed network gradually forms from the general macro-crack. p1 p1' p2p2' p3 p4 p5 p3' p4' p5' face c face d 4250 4300 4350 4400 4450 4500 4550 4600 4650 1 2 3 4 5 w av e sp ee d m /s measuring point before freezing after freezing z.-y. han et alii, frattura ed integrità strutturale, 47 (2019) 74-81; doi: 10.3221/igf-esis.47.07 79 a) sl-1 b) sl-2 c) sl-3 figure 7: rock sample fracturing curve. figure 8: curve of fracture pressure with stress difference. influence of fracturing fluid displacement in comparisons of the experimental results of sample sl-3, sl-6, and sl-7, the following conclusion can be drawn that the fracture pressure increases as the displacement of the fracturing fluid increases, by changing the pumping displacement of the fracturing fluid while keeping other reference factors constant, as shown in fig. 9. similarly, there is no regularity in the initiation time with the change of displacement. from the point of view of fracture-forming ability, it is easier to form main fractures with larger displacement on the premise of well-developed shale bedding, as shown in fig. 10. however, the effect of crack propagation in the formation of secondary seams under large displacement is not good. 13,44 10,5 8,6 0 2 4 6 8 10 12 14 16 0 2 4 6 8 10 f ra ct u re p re ss u re /m p a stress difference/mpa z.-y. han et alii, frattura ed integrità strutturale, 47 (2019) 74-81; doi: 10.3221/igf-esis.47.07 80 therefore, to get a better fracturing effect, it is suggested that the larger displacement fracturing be adopted firstly to produce the main fracture, and then the lower displacement fracturing be used to develop the fracture network. figure 9: curve of fracture pressure with displacement. a) before fracturing (face a) b) after fracturing (face a) c) before fracturing (face c) d) after fracturing (face c) figure10: morphology of the sl-7 sample before and after fracturing. conclusion (1) the original bedding and natural cracks on the surface of the natural shale sample were further developed after the cold treatment by liquid nitrogen. the sound wave test results showed that a large number of cracks or large pores had generated inside the sample. (2) the fracture pressure of the shale decreased with the increase of the impact time when the immersion time was short, and remained stable after immersion of 2 hours. when the freezing time extended, the crack initiation time increased accordingly. (3) after low temperature impact, the fracture pressure of shale decreased with the increase of stress difference, but the effect of stress difference on initiation time was not obvious. (4) from the perspective of crack-forming ability, under the premise of good developed bedding, the larger displacement was more likely to form the main crack inside the shale, while the effect of forming the secondary crack was not good. 9,3 10,5 21 0 5 10 15 20 25 0 20 40 60 80 f ra ct u re p re ss u re /m p a displacement/ml/min z.-y. han et alii, frattura ed integrità strutturale, 47 (2019) 74-81; doi: 10.3221/igf-esis.47.07 81 funding his research was financially supported by the national natural science foundation of china (no. 51504280), the fundamental research funds for the central universities (no. 16cx02022a), and the funds of china university of petroleum talents introduction (no. yj201601094). acknoledgements his work should be thankful for the help from rock mechanics laboratory in china university of petroleum (east china). references [1] inada, y., and yokota k. (1984). some studies of low temperature rock strength. international journal of rock mechanics & mining sciences & geomechanics abstracts, 21(3), pp.145-153. doi: 10.1016/0148-9062(84)91532-8. [2] matsuoka, k. (1988). a laboratory simulation of rock breakdown due to freeze-thaw in a maritime antarctic environment. earth surface processes and landforms, 13, pp. 369-382. doi: 10.1002/esp.3290130408. [3] bellanger, m., homand f., and remy, j.m. (1993). water behavior in limestones as a function of pores structure: application to frost resistance of some lorraine limestones. engineering geology, 36(1-2), pp. 99-108. doi: 10.1016/0013-7952(93)90022-5. [4] chen, t. c., yeung, m. r., and mori, n. (2004). effect of water saturation on deterioration of welded tuff due to freeze-thaw action. cold regions science and technology, 38(2), pp.127-136. doi: 10.1016/j.coldregions.2003.10.001. [5] ren, s.r., fan z.k., zhang l., et al. (2013). mechanisms and experimental study of thermal-shock effect on coal rock using liquid nitrogen. chinese journal of rock mechanics and engineering, (z2), pp. 3790-3794. (in chinese) [6] king, s. r. (1983). liquid co2 for the stimulation of low-permeability reservoirs. soc. pet. eng., 11616, pp.145-151. [7] mcdaniel, b.w., grundmann, s., kendrick, w., et al. (1997). field applications of cryogenic nitrogen as a hydraulic fracturing fluid. journal of petroleum technology, 50(3), pp.38-39. [8] grundmann, s.r., rodvelt, g.d., dials, g.a., allen, r.e. (1998). cryogenic nitrogen as a hydraulic fracturing fluid in the devonian shale. spe eastern regional meeting. society of petroleum engineers, pittsburgh, pennsylvania. gupta. [9] hall, k. (2010). a laboratory simulation of rock breakdown due to freeze-thaw in a maritime antarctic environment. earth surface processes and landforms, 13(4), pp.369-382. doi: 10.1002/esp.3290130408. [10] nicholson d.t., and nicholson, f. h. (2000). physical deterioration of sedimentary rocks subjected to experimental freeze–thaw weathering. earth surface processes and landforms, 25(12), pp.1295-1307. doi: 10.1002/1096-9837. [11] kim, k. m., and kemeny, j. (2009). effect of thermal shock and rapid unloading on mechanical rock properties. 43rd u.s. rock mechanics symposium and 4th u.s.-canada rock mechanics symposium. [12] cai, c., li, g., et al. (2014) experiment study of rock porous structure damage under cryogenic nitrogen freezing. rock and soil mechanics, 35(4), pp. 965-971. (in chinese) [13] cai, c., li, g., et al. (2014). experimental study on effect of liquid nitrogen on rock failure during cryogenic nitrogen fracturing. journal of china university of petroleum, 38(4), pp. 98-103. (in chinese) [14] jiang, l., cheng, y.f., han, z.y., et al. (2018). effect of liquid nitrogen cooling on the permeability and mechanical characteristics of anisotropic shale. journal of petroleum exploration and production technology, (on line). doi: 10.1007/s13202-018-0509-5. [15] han, s.c., cheng, y.f., gao, q., et al. (2018). experimental study of the effect of liquid nitrogen on shale physical/mechanical properties. arma, pp.18–273. [16] shi, x., zhang, l., cheng, y.f., et al. (2017). pore structure and mechanical property change of different rocks under nitrogen freezing. arma, pp.17–212. [17] cha, m.s., yin, x.l., kneafsey, t., et al. (2013). cryogenic fracturing for reservoir stimulation-laboratory studies. journal of petroleum science and engineering, 124, pp. 436-450. doi: 10.1016/j.petrol.2014.09.003. [18] wang, l., yao, b.w., cha, m.s., et al. 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can be opened with acrobat and adobe reader 5.0 and later.) >> /namespace [ (adobe) (common) (1.0) ] /othernamespaces [ << /asreaderspreads false /cropimagestoframes true /errorcontrol /warnandcontinue /flattenerignorespreadoverrides false /includeguidesgrids false /includenonprinting false /includeslug false /namespace [ (adobe) (indesign) (4.0) ] /omitplacedbitmaps false /omitplacedeps false /omitplacedpdf false /simulateoverprint /legacy >> << /addbleedmarks false /addcolorbars false /addcropmarks false /addpageinfo false /addregmarks false /convertcolors /converttocmyk /destinationprofilename () /destinationprofileselector /documentcmyk /downsample16bitimages true /flattenerpreset << /presetselector /mediumresolution >> /formelements false /generatestructure false /includebookmarks false /includehyperlinks false /includeinteractive false /includelayers false /includeprofiles false /multimediahandling /useobjectsettings /namespace [ (adobe) (creativesuite) (2.0) ] /pdfxoutputintentprofileselector /documentcmyk /preserveediting true /untaggedcmykhandling /leaveuntagged /untaggedrgbhandling /usedocumentprofile /usedocumentbleed false >> ] >> setdistillerparams << /hwresolution [2400 2400] /pagesize [612.000 792.000] >> setpagedevice microsoft word numero_52_art_12_2694 s. budhe et alii, frattura ed integrità strutturale, 52 (2020) 137-147; doi: 10.3221/igf-esis.52.12 137 prediction of the burst pressure for defective pipelines using different semi-empirical models s. budhe, m.d. banea federal center of technological education in rio de janeiro – cefet/rj, rio de janeiro/rj, brazil sandipiit@gmail.com, http://orcid.org/0000-0002-3235-9232 mdbanea@gmail.com, http://orcid.org/0000-0002-8378-2292 s. de barros federal center of technological education in rio de janeiro – cefet/rj, rio de janeiro/rj, brazil gem institute, umr 6183 cnrs, cesi, saint-nazaire, france silvio.debarros@gmail.com, http://orcid.org/0000-0002-2520-569x abstract.the main aim of this work is to predict the theoretical burst pressure of defective pipelines using different semi-empirical models and compare them with the hydrostatic test results. a new methodology was formulated with accounting for a minimum thickness (weakest section of the pipe) over the length of the pipe to predict the most conservative burst pressure. with a simple analytical expression, a reasonable accuracy and more conservative burst pressure can be obtained for any arbitrary defect shapes. a variation of burst pressure was found between theoretical prediction and hydrostatic burst test results with respect to the different semi-empirical models even for the same corroded defects. different defect geometry shape and pipe material conditions are the possible causes for variation in the burst pressure between the semi-empirical models, so a careful selection of these parameters is necessary. the proposed methodology predicted a more conservative burst pressure for all arbitrary defects shapes and can predict reasonably accurate values if it accounts for the axial stress. keywords. burst pressure; metallic pipelines; remaining strength; pipeline corrosion; empirical model; corroded pipeline. citation: budhe, s., banea, m. d., de barros, s., prediction of the burst pressure for defective pipelines using different semiempirical models, frattura ed integrità strutturale, 52 (2020) 137-147. received: 28.11.2019 accepted: 28.01.2020 published: 01.04.2020 copyright: © 2020 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. introduction etallic pipelines are extensively used to transport fluids (oil, gas, water) over a long distance, especially in the oil, gas and petroleum industries. pipelines are exposed to harsh environmental conditions which lead to defects, such as metal-loss corrosion, gouges and stress corrosion cracking, etc. [1-4]. however, natural corrosion is the m https://youtu.be/vmkkdmanltu s. budhe et alii, frattura ed integrità strutturale, 52 (2020) 137-147; doi: 10.3221/igf-esis.52.12 138 main source of damage in metallic pipelines and this process causes metal loss of the pipe. both internal and external corrosion processes cause material reduction of the pipe and consequently decrease its strength capacity. if the strength capacity of a damaged pipe can sustain the designed burst pressure, then it can avoid incurring the cost of maintenance and repair [5]. hence, an accurate and conservative theoretical prediction of burst pressure is an important issue, which would help to make a final call on whether the repair and maintenance can be postponed. theoretical prediction of the burst pressure of a corroded pipeline is of significant relevance to the gas and pipeline industry. already, many semi-empirical models have been developed to predict the burst capacity of damage pipelines. there are many semi-empirical models which include: asme b31g, modified asme b31g, rstreng 0.85, shell92, dnv, pcorrc, chell limit, sims pressure and ritchie, etc. to assess the durability condition of corroded pipelines [611]. the basic assumption of an empirical model is that the reduction of strength due to corrosion is corresponding to the amount of material loss measured along the length of the pipe. generally, the defect region of the pipe is represented through a rectangle, elliptical, parabolic or mixed defect shape which is machined with depth interrelated to the greater corrosion depth measured along the pipe [12-17]. hydrostatic burst tests are generally carried out on different metal wall loss defect geometries for assessing the structural integrity of these pipelines. many researchers found a variation of theoretical prediction of burst pressure with respect to the different semi-empirical models even for the same defect area [11, 17-22]. pipe material condition and empirical equation of remaining strength factor (defect geometry) are different in each model, which leads to a difference in theoretical burst pressure. still there is difference in the theoretical prediction and experimental burst pressure and this is due to certain assumptions while deriving the analytical model. for example, in a burst test, there is an axial stress induced as both the ends of the cylindrical tube are closed, however in the analysis it is neglected [18, 23]. in most of the semi-empirical model, defect width is not accounting in the analysis, but it effects on the prediction of burst pressure [24]. real pipelines are long and the effect of axial stresses in straight lines is almost negligible (all criteria for corroded pipelines mentioned before neglect the effect of axial stresses), but that is not the case of the specimens for hydrostatic testing. a pipe specimen has a machined defect region with reduced wall thickness for a hydrostatic burst test and this makes a small variation between the actual corroded geometry region and the machined defect geometry of the test specimen. this assumption should be accounted for in the analysis for a better prediction of the burst pressure of a corroded pipeline. the study of the burst pressure of corroded pipes is reasonably well developed, but still a very active area, as there is scope to refine the model with certain conditions. in the first part of this paper, validate the theoretical burst pressure obtained through different semi-empirical model with the hydrostatic burst pressure. in addition to that, this paper presents a methodology to estimate the burst pressure of pipelines with an arbitrary localized damage without accounting for the remaining strength factor. the minimum thickness of the pipe in its weakest part (corroded damage section) is considered in the analysis. thus, it is expected to obtain a lower limit for the burst pressure of a metallic pipeline with an arbitrary localized corrosion defect. a total of 35 experimental burst tests carried out in different laboratories are compared with the proposed theoretical method for an assurance on the proposed model. burst pressure defect free pipelines he integrity of a pipeline is generally determined by the ability of the pipe to sustain the fluid pressure within the pipe. a pipe fails when the stress in the pipe material exceeds its limit with the internal pressure increases and generally it comes into the plastic collapse stage (plastic deformation). the burst pressure of a defect free pipe is determined based on yield failure criteria such as von mises, tresca or assy (average shear stress yield). the general form of the burst pressure can be expressed as follows [25, 26]: 1 4 2 n b ult k t p d         (1) where, n is the strain hardening exponent which is material dependent and kis the material constant that depends on the yielding criterion as follows [25]. t s. budhe et alii, frattura ed integrità strutturale, 52 (2020) 137-147; doi: 10.3221/igf-esis.52.12 139 1      2   ,    3 1 1  ,    . 2 2 tresca k von mises assy           the strain hardening exponent is determined based on the hollomon (power-law) model [27] and the ramberg-osgood model [28] for failure analysis of pipeline. corroded pipelines the basic model of the pipe to determine the theoretical burst pressure is extended to the corroded (damage/defect) metallic pipeline. the general equation of the burst pressure for a pipeline with a corrosion defect is as follows: th max flow i t p r    (2) where the flow stress ( flow ) represents the flow stress of the pipe material and  is a remaining strength function (i.e. damage factor) which represents the strength reduction of the pipelines due to the corrosion. there are many semi-empirical models available in the literature however a careful selection of the model is very important as both flow stress and remaining strength values differ with respect to the model. remaining strength of corroded pipelines n accurate representation of defect geometry and defect shape of the damaged pipeline is useful for a better prediction of the remaining strength capacity of the pipe. natural corrosion is the main source of localized damage of metallic pipelines, hence, defect size and shape is quite different from case to case. generally, a nonuniform nature of corrosion occurs as shown in fig 1(a) and to represent the actual defect shape for analysis is quite difficult. in most of the semi-empirical models (tab. 1), the defect shapes are idealized as rectangular, parabolic, elliptical, mixed or effective area shape. researchers often used a controlled metal wall loss using a machined process on a metal tube to replicate the actual corrosion defect and one such example is rectangular defect as shown in fig 1(b) [12]. figure 1: metallic pipeline (a) with actual corroded defect [27] (b) machined defect to represent corroded damage [12]. metal wall loss defects (rectangular, parabolic, etc.) in metallic pipelines are taken into account by the remaining strength factor ( ) for prediction of strength capacity of a corroded pipe. the general form of strength prediction of defective pipelines is as: i undamaged p r t          (3) a s. budhe et alii, frattura ed integrità strutturale, 52 (2020) 137-147; doi: 10.3221/igf-esis.52.12 140 th max flow i t p r     (4) sr. no criteria damage factor/remaining strength bulging/folias factor flow stress defect shape 1 asme b31g [6] 2 4,     2 1 3 1 2 1 3 f f ifa d t a d t                4 ,    f t ifa t d    0.893 f l a d t       1.1flow y  parabolic 2 rstren g 0.85 (modified asme b31g) [9] 1 1 0.85 1 0.85 t d t m d t                 22 2 1 0.275 0.00375t l l m d t d t                2 3.3 0.032t l m d t         69flow y   effective area/length mixed 3 dnv [8] 1 1 1 d t q d t                      2 1 0.31 l q d t         flow ult  rectan. 4 ritchie and last criterion [11] 1 1 1 1 t d t m d t                2 1 0.8t l m d t         0.9 flow ult  rectan. 5 prc battelle [11]   1 1 1 0.157 d l exp t r t d                    flow ult  elliptical table 1: damage factor (remaining strength) and flow stress equation of different criteria/model there are many existing semi-empirical models available in the literature and the most widely used are listed in tab.1 da mattos et al. [11] found that the remaining strength factor value differs almost 50-80% with respect to different semiempirical models for the same defect size on metallic pipelines. this is a large variation in the remaining strength factor value found for the same defect geometry and hence proper selection of the model is necessary, as per the area of application. similarly, the flow stress value also differs with respect to the selection of the model (tab. 1). however the flow stress value should be less than the ultimate strength of the pipe material (𝜎𝑓𝑙𝑜𝑤≤𝜎𝑢𝑙𝑡) for safe design. on the contrary, the flow stress exceeds the ultimate strength as per rstreng 0.85 criterion due to the high strength pipe metal having a very small difference in yield and ultimate strength [19]. therefore, for a high strength metal pipe, it would be better to take the ultimate stress as the flow stress. in summary, the remaining strength factor and flow stress factor play an important role for predicting the burst pressure. s. budhe et alii, frattura ed integrità strutturale, 52 (2020) 137-147; doi: 10.3221/igf-esis.52.12 141 tab. 2 summarizes the test results of 35 burst tests data using pipe specimens with machined different artificial metal losses (defects) [11, 19, 20, 24, 30-33] to demonstrate the suitability of the semi-empirical model for a better prediction of the strength capacity of defect pipe. sr. no (ref.) material grade y  (mpa) ult (mpa) d (mm) t(mm) d (mm) l (mm) exp maxp (mpa) 1 [19] x80 589 731 459 7.9 3 40 24.2 2 [19] x80 601 684 457 7.9 4 40 22.7 3 [19] x60 452 542 324 9.5 6.67 256 14.4 4 [19] x46 391 458 76.2 2.04 1.4 75 9.4 5 [19] a25 260 309 76.2 2 1.4 75 5.45 6 [19] x60 452 542 324 9.5 6.67 306 14.07 7 [19] x60 452 542 324 9.5 6.67 350 13.58 8 [19] x60 452 542 324 9.5 6.67 395 12.84 9 [19] x60 452 542 324 9.5 6.67 433 12.13 10 [19] x60 452 542 324 9.5 6.67 467 11.92 11 [19] x60 452 542 324 9.5 6.67 484 11.91 12 [19] x60 452 542 324 9.5 6.67 500 11.99 13 [19] x60 452 542 324 9.5 6.67 528 11.3 14 [30] x80 601 684 458.8 8.1 5.39 39.6 22.68 15 [30] x80 589 731 459.4 8.1 3.75 40.05 24.2 16 [20] x42 380 528.5 273.8 5.30 2.52 1000 15.53 17 [20] x42 380 528.5 273.7 5.24 2.04 1000 15.34 18 [20] x46 357.9 458.2 456.5 6.56 3.32 2750 10.34 19 [20] x46 355.7 539.2 457.7 6.23 3.27 2750 12.06 20 [20] x46 362.3 557.3 457.1 6.09 2.8 2750 12.63 21 [20] x46 285.1 428.5 457.7 6.04 2.71 2750 10.13 22 [20] x46 345.4 568.2 457.7 6.03 2.79 2750 13.04 23 [31] x65 495 565 762.0 17.50 8.75 50 27.50 24 [31] x65 495 565 762.0 17.50 8.75 100 24.30 25 [31] x65 495 565 762.0 17.50 8.75 200 21.80 26 [31] x65 495 565 762.0 17.50 8.75 300 19.80 27 [31] x65 495 565 762.0 17.50 8.75 600 18.50 28 [31] x65 495 565 762.0 17.50 8.75 900 15.00 29 [32] x70 532.2 628.8 762 15.9 7.95 300 21.2 30 [33] steel 20 305 585 219 6 3.6 133 13.8 31 [11] x60 478 542 527 14.3 10 500 11.6 32 [24] x42 284 464 60 5.80 4.1 49.7 54 33 [24] x42 284 464 60 5.60 3.5 49.8 61 34 [24] x42 284 464 60 5.55 4 69.7 46 35 [24] x42 284 464 60 5.62 4.5 50 44 table 2: burst tests data burst pressure prediction using semi-empirical models igs. 2 and 3 present the ratio between the predicted burst pressure and the experimental burst pressure (ptheoretical/pexperimental) using the different semi-empirical models. the results shows a mixed trend (conservative/non conservative/accurate) of burst pressure values between predicted and experimental with respect to the different semi empirical models. some models show conservative predictions of burst pressure, while others f s. budhe et alii, frattura ed integrità strutturale, 52 (2020) 137-147; doi: 10.3221/igf-esis.52.12 142 show more accurate predictions of the burst pressure. there is quite a significant variation of the theoretical burst pressure between the different semi-empirical models for the same test specimen. this is related to the assumptions of remaining strength function (𝛼𝜃) and flow stress material (𝜎𝑓𝑙𝑜𝑤), which leads to a variation in burst pressure even for the same defect pipe.in most of the semi empirical model the defect width in pipeline is not accounted, however some results found the influence of width on final burst pressure [9, 24,34]. in addition to that the complicated geometry of corroded region to represent in analysis is quite complicated and leads in the variation in experimental and theoretical results. hence, defect geometry shape, size and other dimensions of pipeline need to be accounted when the semi-empirical model is selected. figure2: (ptheoretical/pexperimental) per test with conservative and non-conservative burst pressure using selected semi-empirical model. figure 3: (ptheoretical/pexperimental) per test with accurate burst pressure using selected semi-empirical model. the asme b31g and ritchie models give more conservative predictions of burst pressure in all 35 hydrostatic tests, however rstreng model gives mixed predictions some tests predictions are conservative and some are more nonconservative as shown in fig.2. however,the dnv and battele models give more accurate predictions which is closer to the experimental burst pressure except in some burst tests (fig.3). the dnv and battele models show good predictions, s. budhe et alii, frattura ed integrità strutturale, 52 (2020) 137-147; doi: 10.3221/igf-esis.52.12 143 but the burst pressures are higher than the measured ones in a few experiments (test number 5 and 6) where the  flow ult  condition is met [19]. as already mentioned in the previous section, the material with close values of yield strength and ultimate strength violate the flow stress condition under these criteria, which leads to an over-predicted pressure. thus, special attention should be given to the material properties before selection of the criterion for the prediction of the burst pressure in order to avoid over-prediction. semi-empirical model selection should be based on the requirement of the level of accuracy and conservativeness for a particular area of application. new methodology for prediction of the burst pressure t is difficult to represent the actual corroded area in the analysis, as the natural corrosion process is non-uniform in nature, which leads to questionable prediction of the burst pressure of the pipe. a large variation of the remaining strength value with respect to the model has an impact on the final theoretical burst pressure, as it is difficult to represent the actual defect area. in this section the author proposed a methodology to evaluate the conservative burst pressure. this methodology is formulated with accounting for the minimum thickness (weakest section of the pipe) over the length of the pipe for evaluating the conservative burst pressure (fig.4). this formulation can be used for any type (arbitrary) of defect shapes and sizes, as it does not depend on the defect area and requires only the pipe’s geometry and elastic properties. most conservative theoretical predictions of the burst pressure can be calculated considering the weakest section of the metallic pipeline which is normally the defect section. assuming, the weakest section thickness (e-d) as the pipe thickness and estimating the burst pressure in two cases: openended and closed-ended cylinder. ( ) *th uts max i t d p r   open ended cylinder (5) 2 * ( ) * 3 * th uts max i t d p r   closed ended cylinder (6) figure 4: metal loss in the pipe (a) pipe geometry with defect (b) pipe geometry with minimum thickness for new model fig. 5 shows the comparison between the predicted burst pressure and the experimental burst pressure. it is clearly observed that the experimental burst pressure (35 burst tests) is higher than the predicted burst pressure using the proposed methodology. this methodology can be implemented to any arbitrary corroded specimen and estimate the most conservative burst pressure, as it is considered the thinnest (weakest) section of the pipe for the calculation of the burst pressure. on the other hand, an accurate pressure can be obtained with the same methodology with accounting the axial stress which is realistic to the hydrostatic burst tests. actual testing scenario and assumptions during the analysis, makes a difference in the predicted and experimental burst pressure. fig. 6 shows the predicted burst pressure with accounting the axial stress which gives more accurate results compared to without accounting axial stress. the predicted pressure with accounting axial stress in the analysis is validating the concept for accurate results suggested by many researchers [35-37]. the predicted burst pressure is 1.15 times higher when axial stress is accounted in the analysis. besides the axial stress, radial stress and elasto-plastic behavior far from defect can be accounted in the analysis for a more accurate prediction of the burst pressure. it is possible to extend the study to account radial stress and elasto-plastic behavior; however the resulting expression can be more complex and require additional material properties. i s. budhe et alii, frattura ed integrità strutturale, 52 (2020) 137-147; doi: 10.3221/igf-esis.52.12 144 figure 5: comparison between predicted and experimental burst pressure using the proposed model figure 6: (ptheoretical/pexperimental) per test using proposed methodology with and without account axial stress conclusions his study presents an assessment of the theoretical burst pressure of metallic pipelines with wall loss defects using different semi-empirical models and validated with the experimental results of 35 hydrostatic burst tests obtained in different laboratories. there is quite a variation of burst pressure between the theoretical and experimental results with respect to the different semi-empirical models. most of the models predict very conservative burst pressures with respect to the experimental burst pressure. the higher conservativeness is due to neglecting the axial stress and width of the defect section in the analytical model. a mixed prediction of the burst pressure (over predicted/ conservative/accurate) for different tests under the same model is due to the different corroded geometry, shape and material properties of the pipeline. the selection of the empirical model is an open question as it gives dispersed values of burst pressure, so it is needed to be t s. budhe et alii, frattura ed integrità strutturale, 52 (2020) 137-147; doi: 10.3221/igf-esis.52.12 145 careful about pipe geometry and material properties of the pipe while selecting the model. selection of criterion should be based on the requirement of the level of accuracy and/or conservativeness for a particular area of application. the new methodology is applicable for any type of arbitrary defect in a pipeline considering the weakest section of a damaged pipeline predicts the most conservative burst pressure. this methodology can predict accurate burst pressure if the axial stress is accounted for in the analysis. the proposed methodology aims to provide a lower limit of theoretical burst pressure (conservative) for safe operation in a critical area of application. acknowledgements he authors would like to acknowledge the support of the brazilian research agencies cnpq, capes and faperj. references [1] frankel, g.s., (1998). pitting corrosion of metals a review of the critical factors. j. electrochem. soc., 145(6), pp. 2186-2198. [2] budhe, s., banea, m.d., de barros, s. (2019).composite repair system for corroded pipelines: an overview of recent developments and modelling. j. mar. sci. technol., (2019). https://doi.org/10.1007/s00773-019-00696-3. [3] francis, r., (1984). galvanic corrosion of high alloy stainless steel in sea water. br. corros. j., 29(1), pp. 53-57. [4] de barros, s., budhe, s., banea, m.d., rohem, n.r.f., sampaio, e.m., perrut, v.a. and lana, l.d.m. (2018). an assessment of composite repair system in offshore platform for corroded circumferential welds in super duplex steel pipe. frattura ed integrità strutturale, 44, pp. 151-160. [5] koch, g.h., brongers, m.p.h., thompson, n.g., virmani, y.p., payer, j.h., (2002). corrosion cost and preventive strategies in the united states. national technical report library u.s. department of commerce. [6] asme b31g (1991): manual for determining the remaining strength of corroded pipelines, a supplement to asmeb31 code for pressure piping. american society of mechanical engineers, new york. [7] stephens, d. r. and leis, b. n. (2000). development of alternative criterion for residual strength of corrosion defects in moderate-to-high-toughness pipe. international pipeline conference, calgary, alberta, canada, 1-5 october. [8] det norske veritas, dnv-rp-f101 (2004): recommended practice for corroded pipelines. [9] budhe, s., banea, m. d., de barros, s. and rohem, n. r. f. (2018). assessment of failure pressure of a gfrp composite repair system for wall loss defect in metallic pipelines. materialwiss werkstofftech. 49, pp.1-10. [10] cai, j., jiang, x., lodewijks, g., (2017). residual ultimate strength of offshore metallic pipelines with structural damage a literature review. ships offshore struc. 12(8), pp.1037-1055. [11] da silva, m.l. and da costa mattos, h.s. (2013). prediction of the bust pressure for metallic pipelines with localized corrosion defects. proc. international symposium on solid mechanics. porte alegre, brazil, 18-19 april. [12] rohem, n.r.f., pacheco, l.j., budhe, s., banea, m.d., sampaio, e.m. and de barros, s. (2016). development and qualification of a new polymeric matrix laminated composite for pipe repair. compos struct. 152, pp.737-745. [13] andrade, e.q. and benjamin, a.c. (2004). structural evaluation of corrosion defects in pipelines: comparison of fe analyses and assessment methods. in proceedings of the fourteenth international offshore and polar engineering conference, toulon, france, 23-28 may. [14] budhe, s. banea, m.d., rohem, n.r.f. rohem, sampaio, e.m. and de barros, s. (2017). failure pressure analysis of composite repair system for wall loss defect of metallic pipelines. compos. struct. 176, pp.1013-1019. [15] kaptan, a. and kisioglu, y. (2007). determination of burst pressures and failure locations of vehicle lpg cylinders. int. j. press. vess. pip., 84(7), pp.451-459. [16] cronin, d.s. and pick, r.j. (2002). prediction of the failure pressure for complex corrosion defects. int. j. pres. ves. pip. 79(4), pp.279-287. [17] freire, j. l. f.,vieira, r. d.,castro, j. t. p. andbenjamin, a. c. (2007). applications of experimental techniques in the field of pipeline integrity series — part 5: rupture tests of pipeline containing complex-shaped metal loss defects exp. tech.,31(2), pp. 57-62 [18] da costa mattos, h.s., reis, j.m.l., paim, l.m., da silva, m. l., lopes junior, r., perrut, v.a., (2016). failure analysis of corroded pipelines reinforced with composite repair systems. eng. fail. anal., 59, pp.223-236. t s. budhe et alii, frattura ed integrità strutturale, 52 (2020) 137-147; doi: 10.3221/igf-esis.52.12 146 [19] freire, j.l.f., vieira, r. d., castro, j. t. p., benjamin, a. c. b., (2007). applications of experimental techniques in the field of pipeline integrity series — part 3: burst tests of pipeline with extensive longitudinal metal loss. exp. tech., 30(6), pp. 60-65. [20] souza, r.d., benjamin, a.c., vieira, r.d., freire, j.l.f., castro, j.t.p., (2007). applications of experimental techniques in the field of pipeline integrity series — part 4: rupture tests of pipeline segments containing long real corrosion defects exp. tech., 31(1), pp. 46-51. [21] motta, r. s., cabral, h. l. d., afonso, s. m. b., willmersdorf, r. b., bouchonneau, n., lyra, p. r. m. and de andrade, e. q. (2017). comparative studies for failure pressure prediction of corroded pipelines, eng. fail. anal., 81, pp. 178-192. [22] majid, f. and elghorba, m. (2018). continuum damage modeling through theoretical and experimental pressure limit formulas, fratturaedintegritàstrutturale, 43, pp. 79-89. [23] freire, j. l. f., vieira, r. d. and benjamin, a. c. (2006). experimental strain analysis of metal loss defects in pipeline. exp. tech., 30(5), pp. 42-47. [24] alang, n. a., razak, n. a., shafie, k. a. and sulaiman a. (2013). finite element analysis on burst pressure of steel pipes with corrosion defects. 13th international conference on fracture. beijing, china, 16-21 june. [25] zhu x. k., leis b. n. (2006). average shear stress yield criterion and its application to plastic collapse analysis of pipelines. int. j. press. vessel. pip. 83(9), pp.663-671. [26] amaya-gomeza r, sanchez-silva m, bastidas-arteaga e, schoefsc f, munoz f. (2019). reliability assessments of corroded pipelines based on internal pressure – a review. eng. fail. anal. 98, pp. 190-214. [27] andreas, l., gerhard, k. and steffen, z. (2007). strain based design -what the contribution of a pipe manufacturer can be. the seventeenth international offshore and polar engineering conference, lisbon, portugal, 1-6 july. [28] skelton, r.p., maier, h.j., christ, h.j., (1997). the baushinger effect, masing model and the ramberg–osgood relation for cyclic deformation in metals. mater. sci. eng. a., 238, pp. 377-390. [29] yeom, k. j., woo sik kim, w. s., oh, k.w., (2016). integrity assessment of api x70 pipe with corroded girth and seam welds via numerical simulation and burst test experiments. eng. fail. anal., 70, pp. 375-386. [30] benjamin, a.c., freire, j.l.f., vieira, r.d., (2007). part 6: analysis of pipeline containing interacting corrosion defects. exp. tech., 31 (3), pp. 74-82. [31] kim, y.p., kim, w.s., lee, y.k., oh, k.h., (2004). the evaluation of failure pressure for corrosion defects within girth or seam weld in transmission pipelines. in: 2004 international pipeline conference. asme, pp. 1847-1855. [32] yeom, k. j., lee, y-k., oh, k. h., kim, w. s., (2015) integrity assessment of a corroded api x70 pipe with a single defect by burst pressure analysis. eng. fail. anal., 57, pp. 553-561. [33] mazurkiewicz, l., tomaszewski, m., malachowski, j., sybilski k., chebakov, m., witek, m., yukhymets, p., dmitrienko, r., (2017) experimental and numerical study of steel pipe with part-wall defect reinforced with fibre glass sleeve. int. j. pres. ves. pip., 149, pp. 108-119. [34] berrekia, h., benzerga, d. and haddi, a. (2019). behavior and damage of a pipe in the presence of a corrosion defect depth of 10% of its thickness and highlighting the weaknesses of the asme / b31g method. frattura ed integrità strutturale, 49, pp. 643-654. [35] da costa mattos, h.s., reis, j. m. l., paim, l. m., da silva, m.l., amorim, f. c. and perrut, v.a. (2014). analysis of a glass fibre reinforced polyurethane composite repair system for corroded pipelines at elevated temperatures, compos. struct., 114, pp.117-123. [36] budhe, s., banea, m.d. and de barros, s. (2019). prediction of failure pressure for defective pipelines reinforced with composite system, accounting for pipe extremities. j fail. anal. andpreven. 19 (6), pp. 18321843. [37] da costa mattos, h. s., paim, l. m., and j. m. l. reis. 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can be opened with acrobat and adobe reader 5.0 and later.) >> /namespace [ (adobe) (common) (1.0) ] /othernamespaces [ << /asreaderspreads false /cropimagestoframes true /errorcontrol /warnandcontinue /flattenerignorespreadoverrides false /includeguidesgrids false /includenonprinting false /includeslug false /namespace [ (adobe) (indesign) (4.0) ] /omitplacedbitmaps false /omitplacedeps false /omitplacedpdf false /simulateoverprint /legacy >> << /addbleedmarks false /addcolorbars false /addcropmarks false /addpageinfo false /addregmarks false /convertcolors /converttocmyk /destinationprofilename () /destinationprofileselector /documentcmyk /downsample16bitimages true /flattenerpreset << /presetselector /mediumresolution >> /formelements false /generatestructure false /includebookmarks false /includehyperlinks false /includeinteractive false /includelayers false /includeprofiles false /multimediahandling /useobjectsettings /namespace [ (adobe) (creativesuite) (2.0) ] /pdfxoutputintentprofileselector /documentcmyk /preserveediting true /untaggedcmykhandling /leaveuntagged /untaggedrgbhandling /usedocumentprofile /usedocumentbleed false >> ] >> setdistillerparams << /hwresolution [2400 2400] /pagesize [612.000 792.000] >> setpagedevice microsoft word numero_60_art_28_3293.docx d.-e. semsoum et alii, frattura ed integrità strutturale, 60 (2022) 407-415; doi: 10.3221/igf-esis.60.28 407 the proposition of analytical expression hm–(√p/s) in microindentation pile-up deformation mode d.-e. semsoum lgidd, department of mechanical engineering, mustapha stambouli university of mascara, 29000, algeria. djameleddine.semsoum@univ-mascara.dz s. habibi* laboratory of industrial engineering and sustainable development (lgidd, department of mechanical engineering, ahmed zabana university of relizane, 48000, algeria. habibismr@yahoo.com s. benaissa, h. merzouk lgidd, department of mechanical engineering, mustapha stambouli university of mascara, 29000, algeria. soufiane.benaissa@univ-mascara.dz, hassen.merzouk@univ-mascara.dz abstract. in this article, the characteristic curves of microindentation measured on cu99 were analyzed on the basis of the analytical expression proposed by habibi et al. (j. mater. res, 2021, 36 (15): 3074-3085). the ratio of applied load to square displacement, p/(h+h0)2, was discovered to be nonconstant during the loading segment of the microindentation test. an empirical expression for the determination of martens hardness as a function of indentation load, contact stiffness, and reduced modulus of elasticity by analyzing indentation load curves has been proposed for pile-up mode strain with the corrections imposed by the tip defect, the compliance of the instrument, and the axial axisymmetry coefficient of the vickers indenter. the results from microindentation tests on this examined ductile material show excellent agreement. keywords. microindentation; martens hardness; pile-up; empirical; cu99. citation: semsoum, d.-e., habibi, s., benaissa, s., merzouk, the proposition of analytical expression hm–(√p/s) in microindentation pile-up deformation mode, frattura ed integrità strutturale, 60 (2022) 407-415. received: 05.10.2021 accepted: 05.03.2022 online first: 17.03.2022 published: 01.04.2022 copyright: © 2022 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. introduction any scientific investigations [1–5] reveal that the load curve derived from indentation experiments may be correctly characterized by the following power law: p=ʎh2 (1) m https://youtu.be/-gbwidlzzw0 d.-e. semsoum et alii, frattura ed integrità strutturale, 60 (2022) 407-415; doi: 10.3221/igf-esis.60.28 408 thus, the load p is equal to a constant ʎ times the square of the indentation depth h. this equation was developed by (hainsworth et al., 1996) [1] to refine a previous approach by loubet et al. [2], a three-dimensional finite element calculation (zeng and rowcliffe, 1996) [3], a dimensional analysis and finite element calculations (cheng and cheng, 1998) [4]. this relation (1) was used as a basis for the calibration of the indent radius and the calibration of the compliance (sun et al., 1999) [5]. the value of the constant ʎ depends on the geometry of the tip and the properties of the indented material. malzbender et al. [6] attempted to develop and refine a previous approach by hainsworth et al. [1] originally suggested to express p-h2, they derived eqn. (2) after analyzing indentation load-displacement curves measured on a wide range of different materials.             2 2 0 1 4 r r m r e h p e h h h ec (2) the authors [6] formulated the expression (2) of young's modulus (e) and of the hardness of the material (h) by indentation, for the mode of deformation in sink-in by indentation and they consider that the ratio p/(h+h0)2 is constant. however, the authors, habibi et al. [7] implemented a new analytical expression to predict the behavior of the material from h and e exclusively for the strain under the indenter in pile-up mode, taking into account the correction of the tip defect. this experimental relationship has been approved on the basis of a range of materials from different families. this expression is shown in eq. (3) as follows: where, e and h have been calculated via indentation, and the authors [6] consider that the ratio p/(h+h0)2 is a constant in sink-in deformation. as a result of the tip fault being corrected, the authors habibi et al. [7] devised a new analytical expression for predicting how the material from h and e will behave under strain in pile-up mode. a variety of materials from various families have been used to approve this experimental interaction. eq. (3) shows the following expression:              2 2 0 1 4 r r m r e h p e h h h ec (3) in eqn. (3), we see the emergence of the coefficient α which depends on the method of loubet et al [8-10], and the suppression of ε, a constant which depends on the geometry of the indenter in mode deformation in sink-in [11]. the coefficient c is equal to 24.5 tends to vary empirically for considerations related to the calculation of the projected contact area, and therefore the expression (3) will be slightly modified for more precision. the aims of this research are to: 1) convert the mechanical response expression to martens hardness in the pile-up mode; and 2) attempt to quantitatively express it as a function of the young's modulus and, load ratio on the contact stiffness, and, considering the identification of the pile-up deformation mode and the tip defect. the proposed model is then applied to a bulk metallic material exhibiting a pile-up deformation mode, namely copper (cu99). additionally, the classic martens hardness is always calculated by multiplying the applied load by the maximum depth of indentation. this explains why this hardness is insensitive to the types of deformation under the indenter and is independent of them (sink-in or pile-up). in contrast to contact hardness (or instrumented hardness), which is proportional to the contact depth. as a result, this research is attempting to develop a semi-empirical method for determining martens hardness that takes into account the plastic deformation of the material in pile-up mode. theoretical aspect he displacement of material under the indent is a function of the mechanical properties of the material, so the profile of the indent is often useful in determining which model to use. the total indentation depth, h, is seldom equal to the indentation contact depth, hc. the two main types of topography that can occur are: the pile-up is estimated by the methodology proposed by loubet et al. [8-10]. in the case where hc is greater than h, and the sink-in is calculated by the methodology of oliver and pharr [11] for hc less than h. the different physical parameters obtained from an instrumented microindentation test are presented in figure 1. because of displacement of material beneath the indent is a function of the material's mechanical properties, the indent profile is frequently important in selecting which model to use. the overall depth of the indentation, h, is rarely equal to the depth of the indentation contact, hc. there are two major sorts of topography that can occur: the pile-up is t d.-e. semsoum et alii, frattura ed integrità strutturale, 60 (2022) 407-415; doi: 10.3221/igf-esis.60.28 409 approximated using the loubet et al. [8-10] technique. when hc is larger than h, and when hc is less than h, the sink-in is determined using the methods of oliver and pharr [11]. the different physical parameters obtained from an instrumented microindentation test are presented in fig. 1. figure 1: an instrumented indentation test's force-displacement characteristic curve. pmax: maximum force, hmax = hm: maximum displacement, hf: residual depth, hr: plastic depth, s: stiffness hc: contact depth. the expression of the contact height by the model of loubet et al. [8-10] is as follows: hc = α (h – p/s) (4) to take into account the deformations around the indentation, we use the indentation hardness, h, which is defined as the ratio of the maximum applied force, pmax, to the projected contact surface area, ac, at a distance hc, which corresponds to the largest projected contact surface.  max c p h a (5) ac is proportional to the square of the contact depth hc when employing a vickers or berkovich indenter with perfect geometry and can be expressed as follows:  224, 5c ca h (6) we use the definition of hardness h expressed in eq. (5) to express hc: in eq. (5), we express hc using the concept of hardness h:  24, 5 c p h h (7) in that case, s should be calculated using the unloading curve between 40 and 98 percent of the maximum load, pmax. the following power law is frequently used: d.-e. semsoum et alii, frattura ed integrità strutturale, 60 (2022) 407-415; doi: 10.3221/igf-esis.60.28 410    mfp b h h (8) where b and m are smoothing parameters of the power law, and hf is the final depth after total unloading of the indenter. under these conditions, the slope s is found by taking the derivative of this function at its deepest point:        1 max m max f h h dp s mb h h dh (9) hence, the contact stiffness is expressed as follows:   4 r cs e a (10) where er is the reduced (mixed) young's modulus, given by:      2 21 11 i s r i se e e (11) with es and νs are respectively the young modulus and poisson's ratio of the indented sample and ei and νi are those of the penetrator. modeling of the analytical expression  /  mh p s specific to the pile-up ransformation of eqn. (3) according to the model of bull and page [12] gives:              2 2 0 1 2 m rm p h echh h (12) the classic martens hardness, hm, expresses the ratio of the ultimate indentation load to the maximum projected area with the imposed tip defect correction as follows:      2 026.43 m m m m p p h a h h (13) hence, we express the martens hardness as a function of the contact hardness and the reduced modulus for the pile-up mode by combining eqs. (12) and (13). we obtain:           2 1 1 26.43 2 m r h h ech (14) from joslin and oliver's relationship [13]:   2 24 m it r p h s e (15) the ratio of hardness to the square of the modulus is expressed as: t d.-e. semsoum et alii, frattura ed integrità strutturale, 60 (2022) 407-415; doi: 10.3221/igf-esis.60.28 411 2 it r h e =  2 4 mp s (16) finally, substituting er and hit by pm/s2 (see eq. (16)), eqn. (14) becomes as follows:                           2 1 1 26.43 2 m m m r p h sc p e s (17) this analytical expression is proposed in the present work for the calculation of martens hardness as a function of the maximum indentation load, the contact stiffness and the reduced modulus of elasticity as well as two empirical constants α and c. note that the designation λ corresponds to the mechanical response of the primitive function hm: λ=                          2 1 1 26.43 2 m m r p sc p e s (18) materials and experimental methods n this investigation, the specimen being studied is a commercial copper of 99% purity (cu99) and its poisson’s ratio =0.28. the terms in brackets are used in the following to refer to the samples. on the other hand, the objective of this work is not to deeply characterize the different tested materials from a mechanical point of view but to validate the model and the proposed methodology. that is why the authors think it is unnecessary to give more details on their microstructures to focus the readers’ attention on the model. the instrumented indentation experiments were performed on samples carefully prepared to limit both the roughness at the surface and the introduction of strain hardening due to polishing. subsequently, the specimen was grounded using sic papers of various grit sizes and a finished by, polishing by using a series of diamond pastes until the grit size of 1 µm. instrumented indentation tests have been performed employing a microhardness tester csm 2-107, equipped with a vickers indenter (for a diamond indenter, ei=1140 gpa and ʋi=0,07 [14]). the load resolution is given at 100 �n and the depth resolution of 0.3 nm, these values being provided by the csm instruments group. at selected indentation loads ranging from 0.2 to 20 n depending on the sample, around 24 exploitable indentation tests were performed. the values of the loading and unloading rates (expressed in mn/min) were set at twice the value of the maximum applied load according to the rule proposed by quinn et al.[15] and a dwell time of 15 s was imposed according to the standard indentation test procedure astm e92 and e384-10e2.before analyzing the load–depth curves related to given materials, the experimental system, including both the apparatus and the sample is systematically calibrated by determining the frame compliance, cf. indeed, fisher-cripps [16] has demonstrated that this term does not have a constant value. from a mathematical point of view, this correcting factor cf is obtained at the origin of the plot of the inverse of the total compliance as a function of the square root of the contact area. consequently, the experimental indentation depths are corrected, following the methodology proposed by fisher-cripps [16], suggesting that the corrected depth is then equal to the difference between the measured depth and the product of the frame compliance to the load (in this case, cf=0.071 nm/mn). i d.-e. semsoum et alii, frattura ed integrità strutturale, 60 (2022) 407-415; doi: 10.3221/igf-esis.60.28 412 results and analysis nstrumented indentation tests for a variety of representative ultimate loadings expressed in milli-newtons, namely 60, 125, 175, 200, 300, and 400 mn, have been produced. fig. 2 shows the p-h loading and unloading curves: figure 2: characteristic curves of cu99 at different indentation ultimate loadings. the p-h2 indentation characteristic curves of cu99 for various indentation loads are shown in fig. (2) which will be examined on the basis of the corrected depth, as shown in fig. (3b). for the purpose of expressing the pile-up analytic relation according to eq. (3) [7], we need to take into account an estimate of the tip defect, which is 150 nm in our case according to the fischer-cripps method [16].   figure 3: graphical representation of p/(h+h0)2 as a function of the corrected depth for six ultimate loads by indentation (with h0=150nm). the curve (3.a) shows the evolution of the charge at low indenter penetration values. the function p/(h+h0) resultant clearly shows a decreasing trend with h [150.3600] nm (see fig. (3.b)) and an increasing trend for shallow penetration depths ranging from 0 to 150 nm (see fig. (3.a)). this tendency to increase this ratio at low values of penetration depths is explained by the size effect in interpretation and was discussed in a previous publication [17]. hence, the ratio of charge to the square of the indentation depth is not constant as argued by the authors malzbender et al. [7] in their hypotheses. this upward trend in this ratio at low penetration depth values is explained by the indentation size effect (ise). note that the analysis and interpretation were discussed in a previous publication [17]. therefore, the ratio of indentation load to squared depth is not constant as mentioned by the authors malzbender et al. [7] in their hypotheses. 0 50 100 150 200 250 300 350 400 450 0 800 1600 2400 3200 4000 p  ( m n ) h (nm) pm = 60 mn pm = 125 mn pm = 175 mn pm = 200 mn pm = 300 mn pm = 400 mn 0 0,00001 0,00002 0,00003 0,00004 0,00005 0 30 60 90 120 150 p /( h + h 0 )  2  ( m n /n m 2 ) hcor (nm) (a) 0 0,000005 0,00001 0,000015 0,00002 0,000025 0,00003 0,000035 0,00004 0,000045 0,00005 0 900 1800 2700 3600 p /( h + h 0 )2  ( m n /n m 2 ) hcor (nm) (b) 60 mn 125 mn 175 mn 200 mn 300 mn 400 mn i d.-e. semsoum et alii, frattura ed integrità strutturale, 60 (2022) 407-415; doi: 10.3221/igf-esis.60.28 413 in order to confirm this idea, the hardness hm was calculated based on the indentation load p, and the stiffness based on eq. (17) using the values of p/(h+h0)2 given in fig. 4. the results presented in fig. 4, clearly show a significant dependence of the calculated hardness on the indentation load. the dependence of hardness on the measured load, ie ise, has been widely studied and some phenomenological explanations for the origin of ise have been proposed by the authors [18–19]. figure 4: graphical representation of the evolution of hm as a function of the ultimate indentation load. the graphic representation in fig. 4 shows a characteristic point cloud of martens hardness expressed in gpa relating to indentation tests at maximum loads. the trend of the curve is downward from 2.7gpa to an average value equal to approximately 1.5gpa. keep in mind that the hardness function on the ordinate is expressed in terms of the martens hardness definition that is calculated by eq. (14). in order to use eq. (17), it is necessary to identify the type of deformation mode under the indenter. from this, we calculate the ratio of the final penetration depth to the maximum depth, hf/hm. in our case study, the hf/hm ratio =0.95± 0.02, which shows that this ratio is greater than 0.83 (see details in the corresponding article [20]). therefore, the predominant deformation mode of cu99 is pile-up. this justifies the use of the expression (12) (see details in article [7]). on the other hand, in the case of the expression relating to hm compared to its response λ calculated as a function of the mixed modulus, the indentation load and the stiffness according to the expression proposed in this work, namely eq. (17). with the correction of the maximum indenter displacements which are likely to affect all characteristic points of indentation tests as has been shown in an earlier publication [7]. moreover, using the asymmetry correction β= 1.05 suggested by oliver and pharr [21]. figure 5: representation of the evolution of hm according to the joslin and oliver criterion expressed in the response λ (see eq. (23)). the linear regression shown in fig. 5 shows a very good collocation of the points and a good mathematical correlation with a reproducibility rate of 99.98% which tends towards the ideal case with only 0.02% deviation. so, as can be seen, a 1,2 1,7 2,2 2,7 0 400 800 1200 1600 h m ( g p a) pm (mn) d.-e. semsoum et alii, frattura ed integrità strutturale, 60 (2022) 407-415; doi: 10.3221/igf-esis.60.28 414 good linear relationship exists between the two parameters examined (the hardness function and its mechanical response), being in good agreement with the analytical expression proposed in the eqn. (18). conclusion n the basis of previous analysis, the following conclusion can be reached: 1. the hardness hm in eq. (17) cannot be considered a constant. as a result, the experimentally calculated p/(h+h0)2 significantly with displacement h and the corresponding indentation load. 2. we refined an analytical expression of martens hardness derived from a previously developed p-h2 expression relating to pile-up [7] as a function of the p1/2/s criterion used by joslin and oliver [13] for deformation in a mode pile-up in microindentation. martens hardness does not take into account the deformation modes under an indenter (sink-in, pile-up) which is its weak point compared to contact hardness. however, the proposed expression is a tool for predicting the variable hm function as a function of the load, the stiffness, and the reduced modulus taking into consideration the pile-up strain mode. 3. to use this proposed expression, you only need to figure out the hf/hm ratio first. this will help you figure out the pile-up deformation mode. 4. in perspective, this experimental modeling will be generalized to the two other modes of deformations, namely the sink-in and the limit of modal coexistence. acknowledgements his research was supported by the general directorate of scientific research and technological development of algeria (dgrsdt: under the authority of the ministry of higher education and scientific research in charge of scientific research). references [1] hainsworth, s. v., chandler, h. w., page, t. f. (1996). analysis of nanoindentation load-displacement loading curves, j. mater. res., 11, pp. 1987-1995. doi: 10.1557/jmr.1996.0250. [2] loubet, j. l., georges, j. m., meille, j. (1986). in microindentation techniques in materials science and engineering, edited by p. j. blau and b. r. lawn (american society for testing and materials, philadelphia), pp. 72–89. [3] zeng, k., rowcliffe, d. (1996). analysis of penetration curves produced by sharp indentations on ceramic materials, philosophical magazine a 74, pp. 1107-1116. doi: 10.1080/01418619608239711. [4] cheng, y.-t., cheng, c.-m. (1998). relationships between hardness, elastic modulus, and the work of indentation, appl. phys. lett., 73, p. 614. doi: 10.1063/1.121873. [5] sun,y., zheng, s., bell, t., smith, j. (1999). indenter tip radius and load frame compliance calibration using nanoindentation loading curves, philosophical magazine letters 79, pp. 649-658. doi: 10.1080/095008399176698 [6] malzbender, j., de with, g., den toonder, j. (2001). the p–h2 relationship in indentation, j. mater. res. 15, pp. 12091212. doi: 10.1557/jmr.2000.0171. [7] habibi, s., chicot, d., mejias, a., boutabout, b., zareb, e., semsoum, d.-e., benaissa, s., mezough, a., merzouk h. (2021). the p–h2 relationship on load–displacement curve considering pile-up deformation mode in instrumented indentation, journal of materials research, 36, pp. 3074–3085. doi: 10.1557/s43578-021-00286-3. [8] loubet, j.l., bauer, m., tonck, a., gauthier manuel, b. (1993). nanoindentation with a surface force apparatus, mechanical properties and deformation behaviour of materials having ultra-fine microstructures, kluwer academic publishers 233, pp. 429-447. [9] guillonneau, g. et al. (2012). determination of mechanical properties by nanoindentation independendly of indentation depth measurement. journal of materials research, 27, pp. 2551-2560. doi: 10.1557/jmr.2012.261 [10] bec, s., tonck, a., georges, j-m., georges, e., loubet, j.-l. (1996). improvements in the indentation method with a surface force apparatus, philos. mag., a 74, p. 1061. doi: 10.1080/01418619608239707. [11] oliver, w.c. and pharr, g.m. (1992). an improved technique for determining hardness and elastic modulus using load and displacement sensing indentation experiments, j. mater. res., 7, pp. 1564-1583. o t d.-e. semsoum et alii, frattura ed integrità strutturale, 60 (2022) 407-415; doi: 10.3221/igf-esis.60.28 415 doi: 10.1557/jmr.1992.1564. [12] bull, s. j., page, t. f., yoffe, e. h. (1989). an explanation of the identification size effect in ceramics, philos. mag. lett., 59, pp. 281–288. doi: 10.1080/09500838908206356. [13] joslin, d.l., oliver, w. c. (1990). a new method for analyzing data from continuous depth-sensing microindentation tests, j. mater. res., 5. doi: 10.1557/jmr.1990.0123. [14] field, j.-e., telling, r.-h. (1999). the young modulus and poisson ratio of diamond, research note cambridge, cavendish laboratory. [15] quinn, g.-d., patel, p.-l., loyd, i. (2002). effect of loading rate upon conventional ceramic microindentation hardness, j. res. natl. inst. stand. technol., 107, pp. 299–306. doi: 10.6028/2fjres.107.023. [16] fischer-cripps, a.-c. (2006). critical review of analysis and interpretation of nano-indentation test data. surf. coat. technol. 200, pp. 4153–65. doi: 10.1016/j.surfcoat.2005.03.018. [17] soufiane, b., habibi, s., semsoum, d.-e., merzouk, h., mezough, a., boutabout, b., montagne, a. (2021). exploitation of static and dynamic methods for the analysis of the mechanical nanoproperties of polymethylmetacrylate by indentation, frattura ed integrità strutturale, 56, pp. 46-55. doi: 10.3221/igf-esis.56.03. [18] fröhlich, f., grau, p., grellmann, w. (1977). performance and analysis of recording microhardness tests, phys. stat. sol. (a), 42, pp. 79–89. doi: 10.1002/pssa.2210420106. [19] li, h., bradt, rc. (1993). the microhardness indentation load/size effect in rutile and cassiterite single crystals, j. mater. sci., 28, pp. 917–926. doi: 10.1007/bf00400874. [20] yetna n’jock, m., chicot, d., ndjaka, j.-m., lesage, j., decoopman, x., roudet, f., and mejias, a. (2015). a criterion to identify sinking-in and piling-up in indentation of materials, int. j. mech. sci., 90, pp. 145-150. doi: 10.1016/j.ijmecsci.2014.11.008. [21] oliver, w.c., phar, g.m. (2004). measurement of hardness and elastic modulus by instrumented indentation: advanced in understanding and refinements to methodology, j. mat. res., 19, pp. 3-20. doi: 10.1557/jmr.2004.19.1.3. << /ascii85encodepages false /allowtransparency false /autopositionepsfiles true /autorotatepages /none /binding /left /calgrayprofile (dot gain 20%) /calrgbprofile (srgb iec61966-2.1) /calcmykprofile (u.s. web coated \050swop\051 v2) /srgbprofile (srgb iec61966-2.1) /cannotembedfontpolicy /error /compatibilitylevel 1.4 /compressobjects /tags /compresspages true /convertimagestoindexed true /passthroughjpegimages true /createjobticket false /defaultrenderingintent /default /detectblends true /detectcurves 0.0000 /colorconversionstrategy /cmyk /dothumbnails false /embedallfonts true /embedopentype false /parseiccprofilesincomments true /embedjoboptions true /dscreportinglevel 0 /emitdscwarnings false /endpage -1 /imagememory 1048576 /lockdistillerparams false /maxsubsetpct 100 /optimize true 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/hrv (za stvaranje adobe pdf dokumenata najpogodnijih za visokokvalitetni ispis prije tiskanja koristite ove postavke. stvoreni pdf dokumenti mogu se otvoriti acrobat i adobe reader 5.0 i kasnijim verzijama.) /hun 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can be opened with acrobat and adobe reader 5.0 and later.) >> /namespace [ (adobe) (common) (1.0) ] /othernamespaces [ << /asreaderspreads false /cropimagestoframes true /errorcontrol /warnandcontinue /flattenerignorespreadoverrides false /includeguidesgrids false /includenonprinting false /includeslug false /namespace [ (adobe) (indesign) (4.0) ] /omitplacedbitmaps false /omitplacedeps false /omitplacedpdf false /simulateoverprint /legacy >> << /addbleedmarks false /addcolorbars false /addcropmarks false /addpageinfo false /addregmarks false /convertcolors /converttocmyk /destinationprofilename () /destinationprofileselector /documentcmyk /downsample16bitimages true /flattenerpreset << /presetselector /mediumresolution >> /formelements false /generatestructure false /includebookmarks false /includehyperlinks false /includeinteractive false /includelayers false /includeprofiles false /multimediahandling /useobjectsettings /namespace [ (adobe) (creativesuite) (2.0) ] /pdfxoutputintentprofileselector /documentcmyk /preserveediting true /untaggedcmykhandling /leaveuntagged /untaggedrgbhandling /usedocumentprofile /usedocumentbleed false >> ] >> setdistillerparams << /hwresolution [2400 2400] /pagesize [612.000 792.000] >> setpagedevice microsoft word numero_46_art_10 w. song et alii, frattura ed integrità strutturale, 46 (2018) 94-101; doi: 10.3221/igf-esis.46.10 94 developments in the fracture and fatigue assessment of materials and structures high cycle fatigue assessment of steel load-carrying cruciform welded joints: an overview of recent results wei song, xuesong liu state key laboratory of advanced welding and joining, harbin institute of technology, harbin 150001, china. swingways@hotmail.com, liuxuesong@hit.edu.cn abstract. in this paper, high cycle fatigue failure behavior of steel loadcarrying cruciform welded joints (lcwj) is assessed by means of local approaches. different analytical solutions for weld toe and weld root are extended and applied to illustrate the effects of lcwj geometry under cycle tension and bending based on notch stress intensity factors (nsifs). the extended analytical solutions are validated by comparing finite element data from several simulations in terms of lcwj models, resulting in a good agreement. a bulk of experimental data taken from tests and the literature is calculated by the proposed solutions as the forms of sed, nsif and peak stress method (psm). the results show that the nsif-based analytical solutions for steel lcwj are effective for high cycle fatigue failure analyses. keywords. analytical solutions; strain energy density; load-carrying cruciform joints; tension and bending. citation: song, w., liu, x., high cycle fatigue assessment of steel load-carrying cruciform welded joints: an overview of recent results, frattura ed integrità strutturale, 46 (2018) 94101. received: 24.04.2018 accepted: 06.07.2018 published: 01.10.2018 copyright: © 2018 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. introduction s one of the most typical connection types in shipbuilding or ocean engineering structures, the load-carrying cruciform welded joints (lcwj) is widely used. numerous advanced local approaches have been proposed to characterize the fatigue life of welded joints, such as notch stress [1], hot spot stress [2], equivalent structural stress method [3], nsif method [4, 5], sed method [6-10], psm [11, 12], fracture mechanics method [13], and other method [14]. due to large numbers of complicated fe models are required to be created, it is cumbersome and time-consuming process for serving the needed results. to simplify this procedure of creating models, an analytical formulation based on nsifs is extended to calculate the fatigue life indicator of local approaches considering different joints geometry and cyclic loading modes. the fatigue life of the weld toe failure in lcwj tends to take longer than weld root failure due to the discrepancy of crack locations. zong et. al [15] discussed the effects of initial crack size and crack mode fatigue performance in lcwj by fracture mechanics approach. in addition, singh et. al [16] investigated the high cycle fatigue life variation of aisi 304l steel lcwj considering lack of penetration sizes. effective traction stress (ets) and equivalent effective traction stress (eets), which were based on structural mechanics theory, were employed to illustrate the weld toe and weld root failures as fillet a http://www.gruppofrattura.it/va/46/10.mp4 w. song et alii, frattura ed integrità strutturale, 46 (2018) 94-101; doi: 10.3221/igf-esis.46.10 95 weld size varies by xing [17]. from another perspective, nsifs are adequate to precisely assess the fatigue crack initiation at sharp corner notches or crack-liked notches [18]. however, the process is computationally expensive and highly impractical for complex component geometries and/or long loading histories. recently, qian et al. [19] and saiprasertkit et al. [20] provided explicit parametric expressions for non-load-carrying fillet welded joints and lcwj considering different loading conditions and material properties based on a fictitious notch rounding concept. hence, these analytical researches give us some inspiration to extend corresponding functions. sed values can be expressed as a function of relevant sifs, which are estimated readily by analytical equations. in this paper, the primary goal is to assess fatigue life of lcwj by extending an analytical formulation from the nsifs including weld toe and weld root in lcwj. then, sed and psm values are used to characterize the fatigue life from the related analytical equations. such simple analytical equations allow a direct estimation of nsif, sed and psm values at weld toe or weld root in lcwj by the available experimental data from fatigue tests and literature. notch mechanics theory he problem of singularity at sharp notch tip has been solved by williams solutions for mode i and mode ii loading. lately, these williams solutions were introduced into nsifs, to characterize quantitively the intensity of the asymptotic stress distributions close to a notch tip using a polar coordinate system (r, θ). nsifs related to mode i and ii can be expressed by the notch stress fields, which are defined as follow equations [21]: 11 1 0 2 lim ( , 0)n r k r r        (1) 21 2 0 2 lim ( , 0)n r r k r r        (2) where the stress components  and r have to be evaluated along the notch bisector (θ=0). since the mesh strategy limits the developing of the nsif method for complicated structures. we can obtain the notch intensity conveniently and avoid the disadvantage of nsif method that their units are not uniform for different notch angle. under plane strain conditions, the sed solutions containing mode i and mode ii can be expressed by eqn. (3) over a semicircular sector in fig. 1 [22]. 1 2 2 2 1 1 2 2 1 1 n n c c e k e k w e er r                  (3) where e is the young's modulus, and cr is the radius of the semicircular sector, which is dependent on the material properties. it is defined as c 0.28r mm for steel welded joints. the parameters 1e , 2e are dependent on the opening angle 2 and on the poisson’s ratio . lazzarin defined following convenient functions to assess the high cycle fatigue of welded joints for two fracture modes by simplifying the expression of nsifs: 11 1 1 n nk k t     (4) 21 2 2 n nk k t     (5) where n is the range of the nominal stress, t is the plate thickness and ik are non-dimensional coefficients, which are dependent on the overall joint geometry and on the kind of remote applied load (membrane or bending). therefore, the sed equation can be modified by extended analytical expression for notch specimens. furthermore, the sed equation is rewritten as the following form from eqn. 3: 1 22(1 ) 2(1 )2 2 2 1 1 2 2 0 0 n t tw e k e k e r r                       (6) t w. song et alii, frattura ed integrità strutturale, 46 (2018) 94-101; doi: 10.3221/igf-esis.46.10 96 it should be noted that the nrootk stands for the simplified form of mode i notch stress intensity factor. in order to calculate the nsifs and sed by efm method, meneghetti [20] connects the peak stress with these results to obtain closed-form expression of nsif and averaged sed values for different modes, which are written as follows: 1 1 1 , 0, 1.38 n fe peak k k d          (7) 2 2 1 , 0, 3.38 n fe r peak k k d          (8) where d is the mean finite element size. , 0, peak   and , 0,r peak   are the stress results under polar coordination from fe analysis. the nik values can be obtained from numerical results using very refined fe mesh patterns. finally, sed values can be deduced by the psm equation, which is shown as follows: 1 2 2 21 1 2 21 2 , 0, , 0, , 0 0 1 2 fe peak fe r peak eq peak e ed d w k k e r e r e                                                     (9) the equivalent peak stress can be obtained from the following equation: 2 2 2 2 , 1 , 0, 2 , 0,( )eq peak w w peak w r peakc f f            (10) where 1wf and 2wf are induced according to element size and the corresponding control volume for sed evaluation. it should be noted that the relationship between peak and ,eq peak for as-welded joints can be simplified by a correction parameter wf , which is shown as follows: ,w peak eq peakf     (11) for the notch opening angle 2 135   and the average fe size 0.5d mm , the parameter wf is obtained as 1.064. if the sed values are determined from nsif analytical solutions, the psm values can be calculated from eqn. 9. 2α t l h rc weld toe rc weld root 2 a tension bending θ figure 1: geometry of cruciform welded joints and corresponding sed geometry illustration. w. song et alii, frattura ed integrità strutturale, 46 (2018) 94-101; doi: 10.3221/igf-esis.46.10 97 the extended analytical equation based on sifs extension of analytical solutions onsidering the comprehensive effects of joints geometry on the non-dimensional parameters ik , we can deduce the analytical equations from these results via least square fitting methods. the non-dimensional parameters ik analytical solutions of nsifs at weld toe in non-load-carrying cruciform joints under pure tension were proposed by lazzarin et al. [5] and atzori et al. [23], which are shown as follows: 0.985( 2 / ) 1.12( 2 / ) 0.485( / ) 1 1.212 0.495 1.259 b t b t t tk e e      (12) 1.959( 2 / ) 1.126( 2 / ) 0.769( / ) 2 0.508 0.797 2.723 b t b t t tk e e      (13) similar to the expression of ik mentioned above, the equations of ik for lcwj considering the penetration effect under pure tension and bending loadings can be expressed as the following form: 2( ) ( ) ( )i i ih t h t p t i i i ik a b e c e          (19) the numerical analysis of lcwj under different loading conditions demonstrate local geometry imposes negligible effect on the strain energy density, as also reflects in eqn. 6, which cancel the effect of the attachment plate thickness (l), while incorporates the effects of weld length (h) and penetration length (p). finally, the ik equations of weld toe and weld root under different loading conditions from the eqn. 14 becomes: for weld toe: tension: 1 3.691( ) 3.177( ) 4.707( )toe, tension 1.204 1.284 6.8h t h t p tk e e       (15) bending: 1 toe,bending 4.892( ) 7.763( ) 22.41( )0.8681 0.6158 2.563h t h t p tk e e       (16) for weld root: tension: 1.414( ) 1.414( ) 0.3516( ),1 0.2553 7.732 9.287 h t h t p troot tensionk e e       (17) bending: 1 , 1.762( ) 4.556( ) 7.304( )0.056+0.2706 0.6201root bending h t h t p tk e e      (18) based on these extension equations, the nsif and sed values at weld toe and weld root in lcwj can be simply estimated without some fe analysis. experimental verification n this section, the experiments data were used to verify the proposed analytical solutions. high cycle fatigue experiments of load-carrying cruciform welded joints were performed on a 250kn electro-hydraulic servo testing system mts 809 with a loading-control condition. fig. 3 illustrates the procedure of specimens processing and fatigue tests. two panels of 10crni3mov steel were fabricated in fig. 3(a). each panel was cut up into lcwj specimens of 35mm width by wire-electrode method, as shown in fig. 3(b). this steel yield stress is about 693mpa. the nominal stress range of 100-200 mpa was tested with a stress ratio (r=0.1) and loading frequency between 5 and 15hz. more test details are described in ref. [10]. c i w. song et alii, frattura ed integrità strutturale, 46 (2018) 94-101; doi: 10.3221/igf-esis.46.10 98 figure 3: load-carrying cruciform plate/joints specimen sizes and fatigue tests[10]. specimens stress range (mpa) fatigue life fracture location specimens stress range (mpa) fatigue life fracture location sp1 400 21500 weld toe sp13 120 429300 weld toe sp2 360 37800 weld toe sp14 160 157400 weld toe sp3 320 46800 weld toe sp15 300 118800 weld toe sp4 280 56580 weld toe sp16 320 73200 weld toe sp5 240 129600 weld toe sp17 305 28700 weld toe sp6 200 224700 weld toe sp18 305 53500 weld toe sp7 240 327400 weld toe sp19 100 320500 weld root sp8 400 15200 weld toe sp20 120 184500 weld root sp9 360 47000 weld toe sp21 120 156900 weld root sp10 280 160700 weld toe sp22 150 41400 weld root sp11 180 95000 weld toe sp23 150 54190 weld root sp12 150 204100 weld toe sp24 180 75450 weld root specimens stress range (mpa) fatigue life fracture location specimens stress range (mpa) fatigue life fracture location q345-sp1 130 214500 weld toe q345-sp14 90 608738 weld toe q345-sp2 130 612100 weld root q345-sp15 90 538695 weld toe q345-sp3 130 206234 weld root q345-sp16 80 256961 weld root q345-sp4 120 602991 weld toe q345-sp17 80 328896 weld toe q345-sp5 120 460568 weld toe q345-sp18 80 294796 weld root q345-sp6 120 323194 weld toe q345-sp19 80 810030 weld toe q345-sp7 120 343144 weld root q345-sp20 80 552986 weld toe q345-sp8 110 482628 weld root q345-sp21 70 962772 weld toe q345-sp9 110 523176 weld toe q345-sp22 70 1488320 weld toe q345-sp10 110 602503 weld toe q345-sp23 70 1088900 weld root q345-sp11 100 548100 weld root q345-sp24 60 677008 weld root q345-sp12 100 674549 weld root q345-sp25 60 2296250 weld root q345-sp13 90 632400 weld root q345-sp26 60 2085860 weld root specimens stress range (mpa) fatigue life fracture location specimens stress range (mpa) fatigue life fracture location aisi 304l-sp1 260 438000 weld root aisi 304l-sp8 170 315000 weld root aisi 304l-sp2 230 744000 weld root aisi 304l-sp9 150 1100000 weld root aisi 304l-sp3 210 1090000 weld root aisi 304l-sp10 130 1980000 weld root aisi 304l-sp4 210 240000 weld root aisi 304l-sp11 150 116000 weld root aisi 304l-sp5 170 1260000 weld root aisi 304l-sp12 130 2510000 weld root aisi 304l-sp6 150 1840000 weld root aisi 304l-sp13 110 983000 weld root aisi 304l-sp7 190 227000 weld root table 1: fatigue test results of 10crni3mov[10], q345qd [15] and aisi 304l [16] steel lcwj. before fatigue tests, the lcwj geometrical profile obtained by image scanner were measured by cad software. 24 specimens in total were measured and tested. the specimens with zero penetration at weld root is processed by wireelectrode method. the fatigue test data and fatigue failure locations were summarized in tab. 1. due to the difference of weld penetration in lcwj, the fatigue failure modes were different. on the other hand, the fatigue test data of q345qd and aisi 304l steel lcwj from [15,16] has been collected for the analysis in this study, which are shown in tab. 1. w. song et alii, frattura ed integrità strutturale, 46 (2018) 94-101; doi: 10.3221/igf-esis.46.10 99 all the fatigue data are plotted in fig. 4 in the form of nominal stress ranges ( nom ). in iiw standard, the fat of weld toe and weld root in lcwj are given as 63 and 36, respectively. the slope of these lines is fixed as 3 in terms of steel. for the 10crni3mov steel, the results agree well with the fat63 and fat36 for the weld toe and weld root, respectively. however, the q345qd lcwj fatigue data in ref. 15 show lower fatigue strength for weld toe failure. it demonstrates that the lcwjs of q345qd steel are undergrad. additionally, the lcwj made by aisi 304 stainless steel were all failure at weld root. meanwhile, fig. 4 compares the experimental data relevant to lcwj made of 10crni3mov steel with the scatter band suggested to design steel welded joints against fatigue. on the other hand, the proposal fatigue design standards based on sed approaches for uniaxial loading by lazzarin [25] was adopted here. this design scatter bond was proposed by fitting approximately 200 experimental data taken from literatures. fig. 5 shows the nsifs against fatigue life, and the results demonstrate that most of the experimental data are agreed with the nsif design scatter bonds [6] for weld toe and weld root respectively. however, it cannot combine these data into a same scatter bond due to the unit’s inconsistency of nsifs for weld toe and weld root failure. fig. 6 shows fatigue life assessment by sed for these experimental data. the fatigue strength expressed by averaged strain energy density is ∆w50%=0.015 n mm/mm3, and the inverse slope of the design scatter band is 1.5. a good agreement between theoretical estimations based on sed extended analytical solutions has been obtained for weld toe and weld root failure. similarly, most of these data are located in the design scatter band. regards of the fatigue failure criterion from sed method, it shows clearly that the sed criterion boundary can be used to separate the failure mode from the weld geometry in lcwj, see fig. 6. these results are compared with the scatter band proposed for steel welded joints, as shown in fig. 6 and fig. 7. these design scatter bands reported in fig. 7 based on psm has been defined by taking the endurable stress range at 5 million and 2 million cycles. a good agreement between theoretical estimations for psm ( peak ) and experimental data has been obtained for most fatigue test data under tension loading. p l t h 104 105 106 107 10 20 30 40 50 60 70 80 90 100 200 300 400 500 600 700 800 900 1000 fat 63 fat 36 weld toe failure [10] weld root failure [10] weld toe failure [15] weld root failure [15] weld root failure [16] n o rm a l s tr e s s r a n g e   ( m p a ) life (n) n = 2 1 0 6 tension figure 4: fatigue test results of 10crni3mov lcwj expressed in terms of nominal stress range. figure 5: fatigue test results of 10crni3mov lcwj according to notch stress intensity factors. p l t h 104 105 106 107 100 1000 10000 weld root failure [10] weld root failure [15] weld root failure [16] 1 th=180mpaꞏmm 0.5 (radaj 1990) 126 180 n s if -k 1 ( m p a ꞏm m 0 .5 ) cycles to failure, n 256 3.2 tension w. song et alii, frattura ed integrità strutturale, 46 (2018) 94-101; doi: 10.3221/igf-esis.46.10 100 figure 6: fatigue test results of 10crni3mov lcwj according to averaged strain energy density ∆w. p l t h 104 105 106 107 100 1000 p e a k s tr e s s f w   p e a k ( m p a ) slope k=3 296 214 5000 weld toe failure [10] weld root failure [10] weld toe failure [15] weld root failure [15] weld root failure [16] 2000 500 50 cycles to failure, n 200 156 figure 7: fatigue test results of 10crni3mov and lcwj according to peak stress methods. conclusion he analytical equations at weld toe and weld root under tension and bending loading in lcwj were extended to estimate the sed values on the basis of nsifs. the different geometric factors of lcwj including incomplete penetration length were incorporated into these analytical formulations. these analytical solutions were verified by the classical notch stress intensity factors from the finite element results. for the sake of extended analytical solutions, the fatigue life assessment of the investigated outcomes of 10crni3mov, q345qd and aisi 304l steel lcwjs was conducted and it further validates the feasibility of these analytical solutions by local approaches, such as nsifs, sed, and psm. all fatigue data is recalculated by the parameters of notch stress intensity factors and peak stress according to extended analytical solutions for weld toe and weld root failure in lcwj. this synthesis was verified in the corresponding design scatter bands. references [1] radaj, d. (1996). review of fatigue strength assessment of nonwelded and welded structures based on local parameters, int. j. fatigue 18, pp.153-170. [2] hobbacher, a.f. (2016). fatigue design of welded joints and components(second edition), iiw document iiw2259-2215. [3] dong, p. (2001). a structural stress definition and numerical implementation for fatigue analysis of welded joints, int. j. fatigue 23, pp. 865-876. t p l t h 104 105 106 107 0.01 0.1 1 10 weld toe failure [10] weld root failure [10] weld toe failure [15] weld root failure [15] weld root failure [16] 0.058 0.105  w a n a ly ti c a l [ n m m /m m 3 ] cycles to failure, n 0.192 inverse slope k=1.5 tension w. song et alii, frattura ed integrità strutturale, 46 (2018) 94-101; doi: 10.3221/igf-esis.46.10 101 [4] atzori, b., lazzarin, p. and meneghetti, g. (2008). fatigue strength assessment of welded joints: from the integration of paris' law to a synthesis based on the notch stress intensity factors of the uncracked geometries, eng. fract. mech., 75, pp. 364-378. [5] lazzarin, p. and tovo, r. (1998). a notch intensity factor approach to the stress analysis of welds, fatigue fract. eng. mater. struct. 21, pp. 1089-1103. [6] lazzarin, p., berto, f., gomez, f.j. and zappalorto, m. (2008). some advantages derived from the use of the strain energy density over a control volume in fatigue strength assessments of welded joints, int. j. fatigue 30, pp. 1345-1357. [7] lazzarin, p., berto, f. and zappalorto, m. (2010). rapid calculations of notch stress intensity factors based on averaged strain energy density from coarse meshes: theoretical bases and applications, int. j. fatigue 32, pp. 1559-1567. [8] lazzarin, p., berto, f. and atzori, b., (2013). a synthesis of data from steel spot welded joints of reduced thickness by means of local sed. theor appl fract mech., 63, pp. 32-39. [9] razavi, s.m.j, ferro, p., berto, f. and torgersen, j. (2017). fatigue strength of blunt v-notched specimens produced by selective laser melting of ti-6al-4v, theoretical and applied fracture mechanics 87. [10] song, w. and liu, x. (2018). fatigue assessment of steel load-carrying cruciform welded joints by means of local approaches. fatigue fract. eng. mater. struct, 41. [11] meneghetti, g. (2008). the peak stress method applied to fatigue assessments of steel and aluminium fillet-welded joints subjected to mode i loading, fatigue fract. eng. mater. struct. 31, pp. 346-369. [12] meneghetti, g., marchi, a. de and campagnolo, a. (2016). assessment of root failures in tube-to-flange steel welded joints under torsional loading according to the peak stress method, theor. appl. fract. mech. 83, pp. 19-30. [13] nykänen, t., li, x., björk, t. and marquis, g., (2005). a parametric fracture mechanics study of welded joints with toe cracks and lack of penetration, eng. fract. mech. 72, pp. 1580-1609. [14] liu, g., liu, y. and huang, y. (2014). a novel structural stress approach for multiaxial fatigue strength assessment of welded joints, int. j. fatigue 63, pp. 171-182. [15] zong, l., shi, g., wang, y.-q., yan, j.-b. and ding y. (2017). investigation on fatigue behaviour of load-carrying fillet welded joints based on mix-mode crack propagation analysis, archives of civil and mechanical engineering 17, pp. 677-686. [16] singh, p. j., achar, d. r. g., guha, b. and nordberg, h. (2003). fatigue life prediction of gas tungsten arc welded aisi 304l cruciform joints with different lop sizes, international journal of fatigue, 25, pp. 1-7. [17] xing, s., dong, p. and threstha, a. (2016). analysis of fatigue failure mode transition in load-carrying fillet-welded connections, marine structures, 46, pp. 102-126. [18] lazzarin, p., berto, f., zappalorto, m. and meneghetti, g. (2009). practical application of the n-sif approach in fatigue strength assessment of welded joints, welding in the world, 53. [19] feng, l. and qian x. (2017). a hot-spot energy indicator for welded plate connections under cyclic axial loading and bending, eng. struct. 147, pp. 598-612. [20] saiprasertkit, k., hanji, t. and miki, c. (2012). fatigue strength assessment of load-carrying cruciform joints with material mismatching in lowand high-cycle fatigue regions based on the effective notch concept, int. j. fatigue 40, pp. 120-128. [21] gross, b. and mendelson, a. (1972). plane elastostatic analysis of v-notched plates, int. j. fract.mech. 8, pp. 267-276. [22] lazzarin, p. and zambardi, r. (2001). a finite-volume-energy based approach to predict the static and fatigue behavior of components with sharp v-shaped notches, int. j. fract. 112, pp. 275-298. [23] meneghetti, g., marini, d. and babini, v. (2016). fatigue assessment of weld toe and weld root failures in steel welded joints according to the peak stress method, welding in the world, 60, pp. 559-572. [24] atzori, b., lazzarin, p. and, tovo r. (1999). stress field parameters to predict the fatigue strength of notched components, j. strain anal. eng. des. 34, pp. 437-453. [25] lazzarin p., livieri p., berto f. and zappalorto, m. 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can be opened with acrobat and adobe reader 5.0 and later.) >> /namespace [ (adobe) (common) (1.0) ] /othernamespaces [ << /asreaderspreads false /cropimagestoframes true /errorcontrol /warnandcontinue /flattenerignorespreadoverrides false /includeguidesgrids false /includenonprinting false /includeslug false /namespace [ (adobe) (indesign) (4.0) ] /omitplacedbitmaps false /omitplacedeps false /omitplacedpdf false /simulateoverprint /legacy >> << /addbleedmarks false /addcolorbars false /addcropmarks false /addpageinfo false /addregmarks false /convertcolors /converttocmyk /destinationprofilename () /destinationprofileselector /documentcmyk /downsample16bitimages true /flattenerpreset << /presetselector /mediumresolution >> /formelements false /generatestructure false /includebookmarks false /includehyperlinks false /includeinteractive false /includelayers false /includeprofiles false /multimediahandling /useobjectsettings /namespace [ (adobe) (creativesuite) (2.0) ] /pdfxoutputintentprofileselector /documentcmyk /preserveediting true /untaggedcmykhandling /leaveuntagged /untaggedrgbhandling /usedocumentprofile /usedocumentbleed false >> ] >> setdistillerparams << /hwresolution [2400 2400] /pagesize [612.000 792.000] >> setpagedevice microsoft word numero_41_art_56.docx f. chebat et alii, frattura ed integrità strutturale, 41 (2017) 447-455; doi: 10.3221/igf-esis.41.56 447 fatigue assessment of steel rollers by means of the local energy f. chebat, m. cincera rulli rulmeca s.p.a., via a. toscanini, 1, i-24011 alme’ (bergamo) – italy s.m.j. razavi, f. berto, t. welo department of mechanical and industrial engineering, norwegian university of science and technology (ntnu), norway javad.razavi@ntnu.no, filippo.berto@ntnu.no abstract. this paper aims to analyses the fatigue behavior of steel rollers using the average strain energy density (sed) criterion. considering the variability of the v-notch opening angle, a simple scalar quantity, i.e. the value of the strain energy density averaged in a control volume surrounding the notch tip, has been introduced to overcome the complexities in failure assessment of this component. the strain energy is obtained using close form solutions based on the relevant notch stress intensity factors (nsif) for modes i, ii and iii. referring to the conventional arc welding processes, the radius of the control volume is carefully identified with reference to conventional arc welding processes being equal to 0.28 mm for welded joints made of steel. in this paper firstly the employed methodology for the fatigue assessment is described and then the first synthesis of fatigue data by means of local sed for a specific geometry is shown. keywords. notch stress intensity factor; welded joints; strain energy density; fatigue strength. citation: chebat, f., cincera, m. razavi, s.m.j., berto, f., welo, t., fatigue assessment of steel rollers by means of the local energy, frattura ed integrità strutturale, 41 (2017) 447-455. received: 12.05.2017 accepted: 24.05.2017 published: 01.07.2017 copyright: © 2017 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. introduction he geometry of weld fillet cannot be exactly defined due to variation of different parameters such as length of lack of penetration, root radius, toe radius and bead shape from joint to joint even in well-performed operations [1-5]. the weld toe radius decreases in presence of the local heat concentration during the welding process and it is considerably small for automated high-power processes such as laser beam welding. according to the small values of toe radius in conventional arc welding [6], the weld toe is considered as a sharp notch and using the nsif approach the local stress can be obtained [6,7]. considering the large opening angles of the weld toe, the stress component regarding to mode ii is non-singular and the fatigue behaviour can be assessed only by use of mode i nsif [7]. based on the relevant theoretical stress concentration factors an evaluation of different steel welded joints can be conducted considering a fictitious notch t f. chebat et alii, frattura ed integrità strutturale, 41 (2017) 447-455; doi: 10.3221/igf-esis.41.56 448 radius ρf =1.0 mm if the weld toe and root radius be considered as zero [8]. fatigue failure is generally characterized by the nucleation and growth of cracks [9-13]. the difference between two stages of nucleation and growth of fatigue crack is “qualitatively distinguishable but quantitatively ambiguous” [14]. in this regard, nsifs were used for prediction of crack nucleation and also the total fatigue life [15-19]. prediction of the total fatigue life using nsifs is only limited for the cases in which a large amount of fatigue life is consumed at short crack depth, within the zone governed by the notch singularity at the weld toe or root. lassen [20] reported that up to 40 percent of fatigue life of transverse non-load-carrying fillet welded joints was related to nucleation of a microcrack with a length of 0.1 mm. singh et al. [21,22] showed that 70 percent of the total fatigue life of fillet joints in aisi 304l was related to crack nucleation up to a size of 0.5 mm. according to the theoretical formulations related to the nsif approach, this method cannot be employed for the joints characterized by weld flank angles very different from 135 degrees or for comparing failures at the weld root (2α =0°) or weld toe (2 α =135°). that is due to the units which are used for mode i nsif as mpa(m)β, where the exponent β depends on the v-notch angle, according to the expression β = 1-λ1, λ1 being williams’ eigenvalue (williams 1952). this problem was solved later by using the average strain energy density range present in a critical volume of radius rc surrounding the weld toe or the weld root. using some closed form formulations, the strain energy density range was defined as a function of the relevant nsifs. the nsif approach was later extended to welded joints under multiaxial loading [23]. the simple volume is approximately similar to that of proposed by sheppard [24], while proposing a volume criterion based on local stresses to predict fatigue limits of notched components. sonsino [25] proposed the highly stressed volume (the region where 90% of the maximum notch stress is exceeded) to predict the high cycle strength of welded joints. the same methodology based on strain energy is employed in this paper for fatigue analysis of streel rollers made by rulmeca [26] with failure occurring at the weld root. the rollers studied in the present paper belong to the category psv which is mainly suitable for conveyors that operate in very difficult conditions with high level of working loads where large lump size material is conveyed; and yet, despite these characteristics, they require minimal maintenance. the bearing housings of the psv series are welded to the tube body using autocentralising automatic welding machines utilizing a continuous wire feed. considering the fatigue behavior of the component, the weakest point of the entire structure is the lack of penetration of the weld root. hence, if the roller is loaded well above its declared nominal admitted load [26] it would experience fatigue failure starting at the level of the weld root. the current paper aims to describe the modelling method of the roller by using the finite element method combined with three-dimensional analyses (the procedure is described in more detail in [27] and implementation of the sed method in a control volume for two different tested geometries belonging to the family of rollers called psv4 and characterized by a different lengths. approach based on the local sed: analytical preliminaries he degree of singularity of the stress fields due to re-entrant corners was established by williams both for mode i and mode ii loading [28]. when the weld toe radius ρ is set to zero, nsifs quantify the intensity of the asymptotic stress distributions in the close neighbourhood of the notch tip. by using a polar coordinate system (r, θ) having its origin located at the sharp notch tip, the nsifs related to mode i and mode ii stress distribution are [29]: 11 1 0 2 lim ( , 0)n r k r r        (1) 21 2 0 2 lim ( , 0 )n r r k r r        (2) where the stress components σθθ and τrθ have to be evaluated along the notch bisector (θ = 0). dealing with mode iii loading an extension of the definition proposed by gross and mendelson [29] has been carried out in [30,31]: 31 3 0 2 lim ( , 0 )n z r k r r        (3) by means of eqs. (1,2), it is possible to present williams’ formulae for stress components as explicit functions of the nsifs. then, mode i stress distribution is [32]: t f. chebat et alii, frattura ed integrità strutturale, 41 (2017) 447-455; doi: 10.3221/igf-esis.41.56 449                         1 1 1 11 1 1 1 1 1 1 1 1 1 1 1 10 1 cos 1 cos 1 1 3 cos 1 1 cos 1 1 12 1 sin 1 sin 1 n rr r r k                                                                          (4) mode ii stress distribution is:                         2 2 2 21 2 2 2 2 2 2 2 2 2 2 2 20 1 sin 1 sin 1 1 3 sin 1 1 sin 1 1 12 1 cos 1 cos 1 n rr r r k                                                                            (5) mode iii stress distribution is:     3 3 13 3 13 3 sin 2 cos 2 n zr n z k τ r k τ r              (6) all stress and strain components in the highly stressed region are correlated to mode i, mode ii and mode iii nsifs. under plane strain hypothesis, the strain energy included in a semicircular sector is [33,34]: 31 2 2 2 2 3 31 1 2 2 11 1 nn n c c c e ke k e k w e r e r e r                           (7) where rc is the radius of the semicircular sector and e1, e2 are functions that depend on the opening angle 2α and on the poisson’s ratio ν, while e3 depends only on the notch opening angle. a rapid calculation, with ν = 0.3, can be made for e1 and e2 by using the following expressions [33]: 6 42 1 5.373 10 (2 ) 6.151 10 (2 ) 0.1330e         (8) 6 2 3 2 4.809 10 (2 ) 2.346 10 (2 ) 0.3400e         (9) where 2α is in degrees. dealing with failures originated at the crack tip (i.e. weld root) eq. (7) can be simplified as follows: 2 2 2 1 1 2 2 3 3 1 c w e k e k e k er          (10) the material parameter rc can be estimated by using the fatigue strength δσa of the butt ground welded joints (in order to quantify the influence of the welding process, in the absence of any stress concentration effect) and the nsif-based fatigue f. chebat et alii, frattura ed integrità strutturale, 41 (2017) 447-455; doi: 10.3221/igf-esis.41.56 450 strength of welded joints having a v-notch angle at the weld toe constant and large enough to ensure the non singularity of mode ii stress distributions. a convenient expression is [33]: 1 1 1 1 12 n a c a e k r          (11) where both λ1 and e1 depend on the v-notch angle. eq. (11) will be applied in the next sections of the paper taking into account the experimental value 1 n ak at 5 million cycles related to transverse non-load carrying fillet welded joints with 2α = 135 degrees at the weld toe. the hypothesis of constancy of rc under mixed mode loads had been validated by lazzarin and zambardi [33] by using experimental data mainly provided by seweryn et al. [35] and kihara and yoshii [36]. from a theoretical point of view the material properties in the vicinity of the weld toes and the weld roots depend on a number of parameters as residual stresses and distortions, heterogeneous metallurgical micro-structures, weld thermal cycles, heat source characteristics, load histories and so on. to device a model capable of predicting rc and the fatigue life of welded components on the basis of all these parameters is really a task too complex. thus, the spirit of this approach is to give a simplified method able to summarise the fatigue life of components only on the basis of geometrical information, treating all other effects only in statistical terms, with reference to a well-defined group of welded materials and, for the time being, to arc welding processes. eq. (11) makes it possible to estimate the rc value as soon as 1 n ak and δσa are known. at na = 5106 cycles and in the presence of a nominal load ratio r equal to zero, a mean value 1 n ak equal to 211 mpa.mm 0.326 can be assumed [37]. for butt ground welds made of ferritic steels atzori and dattoma [38] found a mean value δσa = 155 mpa (at na= 5×106 cycles, with r=0). that value is in very good agreement with δσa =153 mpa recently obtained by taylor at al. [5] by testing butt ground welds fabricated of a low carbon steel. then, by introducing the above mentioned value into eq. (11), one obtains for steel welded joints with failures from the weld toe rc =0.28 mm. the choice of 5 million cycles as a reference value is due mainly to the fact that, according to eurocode 3, nominal stress ranges corresponding to 5 million cycles can be considered as fatigue limits under constant amplitude load histories. it is worth noting that the simplified hypothesis of a semicircular core of radius rc led to the assessment of a fatigue scatter band that exactly agreed with that of haibach’s normalised s-n band [39]. in the case 2α= 0 and fatigue crack initiation at the weld root eq. (11) gives rc = 0.36 mm, by neglecting the mode ii contribution and using e1 = 0.133, eq. (8), 1 n ak = 180 mpa mm 0.5 and, once again, δσa = 155 mpa. there is a small difference with respect to the value previously determined, rc = 0.28 mm. however, in the safe direction, the proposal is to use rc = 0.28 mm also for the welded joints with failures from the weld roots which is the case considered in the present manuscript. as opposed to the direct evaluation of the nsifs, which needs very refined meshes, the mean value of the elastic sed on the control volume can be determined with high accuracy by using coarse meshes [40-43]. modelling of the rollers and evaluation of the local sed he rollers considered in the present investigation belong to the series psv which offer the highest quality and the maximum load capacity of rulmeca’s production (see fig. 1) [26]. rollers psv are particularly suited to conveyors that operate in very difficult conditions, where working loads are high, and large lump size material is conveyed; and yet, despite these characteristics, they require minimal maintenance. typical types of application are: mines, caves, cement works, coal-fired electric utilities and dock installations. the effectiveness of the psv roller sealing system provides the solution to the environmental challenges of dust, dirt, water, low and high temperatures. roller is made of the following main components: a mantel, constituted by a tube cut and machined using automatic numerically controlled machines, which guarantee and maintain the tolerances and the precision of the square cut. two bearing housing made by a steel monolithic structure (in agreement with uni en 10111 characterized by a yield strength 170<σy<330 mpa), deep drawn and sized to a forced fixed tolerance (iso m7) at the bearing position. the thickness of the housings is proportional to the spindle diameter and to the bearing type, with thicknesses that are up to 5 mm, to guarantee the maximum strength for each application, including the heaviest. t f. chebat et alii, frattura ed integrità strutturale, 41 (2017) 447-455; doi: 10.3221/igf-esis.41.56 451 a spindle which sustains the roller when it is assembled into the troughing set supports. it is made from drawn steel, cut and machined by automatic numerically controlled machines. the spindle is ground to a precision tolerance, to guarantee a perfect match of bearings, seals. spindle tolerance, together with bearing housing tolerances, functionally guarantees the autoalignment of the internal and outer bearing rings of the ball race resulting in a good performance even when the spindle deflection is extreme due to overloading. the seals components, which are meant to protect the bearing from harmful elements that may impinge from the outside or the inside of the roller, made of three main sections: figure 1: scheme showing the main geometrical parameters at the weld root and an example of lack of penetration. two bearing housing made by a steel monolithic structure (in agreement with uni en 10111 characterized by a yield strength 170<σy<330 mpa), deep drawn and sized to a forced fixed tolerance (iso m7) at the bearing position. the thickness of the housings is proportional to the spindle diameter and to the bearing type, with thicknesses that are up to 5 mm, to guarantee the maximum strength for each application, including the heaviest. a spindle which sustains the roller when it is assembled into the troughing set supports. it is made from drawn steel, cut and machined by automatic numerically controlled machines. the spindle is ground to a precision tolerance, to guarantee a perfect match of bearings, seals. spindle tolerance, together with bearing housing tolerances, functionally guarantees the autoalignment of the internal and outer bearing rings of the ball race resulting in a good performance even when the spindle deflection is extreme due to overloading. the seals components, which are meant to protect the bearing from harmful elements that may impinge from the outside or the inside of the roller, made of three main sections: 1. external section: made of an external stone guard, a lip ring made from soft anti-abrasive rubber with a large contact surface onto a metal cover cap; that forms a self-cleaning stage of seal in that it centrifugally repels water and dust naturally towards the outside; 2. outward bearing protection: triple lip labyrinth in nylon pa6 greased to give further bearing protection; 3. inward bearing protection, made of a sealing ring in nylon pa6 is positioned that provides an ample grease reservoir and also retains the grease near to the bearing even when there is a depression due to an abrupt change in temperature (pumping effect). locking system: provided by means of the correctly located cir-clip, which is the most effective and the strongest system implemented in heavy rollers for belt conveyors. the feature under investigation in this paper is the joint between tube and bearing housing. the bearing housings of the psv rollers are welded to the tube body using autocentralising automatic welding machines utilising a continuous wire feed. tube and bearing housing form a monolithic structure of exceptional strength which itself reduces to the minimum any imbalance in the roller. this guarantees the alignment and concentricity with respect to the external diameter of the component parts of the sealing system. the optimum balance and concentricity thus obtained allows these rollers to be used at the highest speeds, eliminating harmful vibration to the conveyor structure and the “hammer effect” on the bearings of the rollers. from the point of view of the fatigue behavior under loading, the weakest point of the entire structure is the lack of penetration of the weld root. therefore, if the roller is loaded well above its declared nominal admitted load [26] it would experience fatigue failure starting at the level of the weld root. a detail of the weld root is shown in fig. 1, where the lack f. chebat et alii, frattura ed integrità strutturale, 41 (2017) 447-455; doi: 10.3221/igf-esis.41.56 452 of penetration length is indicated as c. the load on top of the roller is modelled typically as a uniformly distributed load on the longitudinal line of the roller. (a) (b) figure 2: geometry of the rollers: psv4 133 315 (a) psv4 159 530 (b). two geometries have been considered here and the details of the geometrical parameters are reported in fig. 2a and 2b for the two cases, named in the following as psv4 133 315 and psv4 159 530. for sake of brevity the modeling will be shortly described only for the first geometry. further details are reported in [27]. the analysis of the stress fields in these welded details needed 3d models, because of their variability along the circular path described by the weld root. the two considered geometries reported in fig. 2 have been modelled by means of 20-node 3d finite elements implemented in the fe code ansys. due to the symmetry of geometry and loading only one quarter of the geometry has been considered. the bearing has been considered of infinite stiffness and all the nodes of the bearing housing have been connected by means of rigid elements (links) to a master node. this special node has been placed on the symmetrical longitudinal axis of the roller in correspondence of the instantaneous rotation centre of the bearing. the rotation about the axis z (rotz) and the longitudinal displacement (uy, see fig. 1) have been left unconstrained, while all other displacements and rotations of the master node have been constrained. the load has been distributed along the longitudinal line. for each geometry two models were created: the first was mainly oriented to the determination of the point where the maximum principal stress and the maximum value of the strain energy density were located. due to the complex geometry of the bearing housing in fact the point varies as a function of the geometry. in this case a regular fine mesh has been used with the aim also to determine the sifs at the weld root. the second model was characterized by a coarse mesh but by an accurate definition of the control volume where the strain energy density should be averaged. as just stated the mesh used in that case was coarse with a regular increasing spacing ratio in the direction of the position of the control volume mainly aimed to a correct positioning of the volume itself in the most critical region. all fe analyses have been carried out by means of 20-node finite elements under linear-elastic hypotheses. f. chebat et alii, frattura ed integrità strutturale, 41 (2017) 447-455; doi: 10.3221/igf-esis.41.56 453 fatigue strength in terms of strain energy density averaged in a finite size volume y using the first model with a regular and very fine mesh the sed has been evaluated circumferentially all around the roller in the zone surrounding the weld root. the maximum sed value occurs outside the line of the application of the load. the angle of rotation is strongly dependent on the geometry of the bearing housing. in the case of the roller psv 133 315 the maximum sed occurs at about 30 degrees from the line of load application. in that point all the modes of failure are contemporary present as will be discussed in the following. for this specific model an analysis of sensitivity of sed as a function of the length of the lack of penetration c has been carried out [27]. from a micrographic analysis conducted on a large amount of welded rollers c has been found to vary in the range between 0.6 and 1.0 mm. a typical image of the weld root is shown in fig. 1b. the sensitivity analysis has been made varying the length of the lack of penetration and evaluating the sed in a control volume of radius rc = 0.28 mm. the variation of the sed is very limited in the range of c considered. the sed varies from 0.31 mj/m3 to 0.35 mj/m3 for a value of c corresponding to 0.6 and 1.0 mm, respectively. considering the low variation of the sed as a function of the initial lack of penetration, the length c = 1 mm has been set in all fe analyses. this choice is in the safe direction because the worst configuration has been considered. some fatigue tests have been conducted on the two rollers shown in fig. 2 [27]. a test system has been created for reproducing the service conditions on the roller. the load has been applied by means of an external counter-roll which press with a constant pressure the tested roller which rotates with a regular speed. altogether 22 new tests have been carried out considering the two investigated geometries. the new results reconverted in terms of the local sed have been compared with the scatterband proposed for structural welded steels [36]. that band is shown in fig. 3 together with the new data. it is evident that the previous scatter band can be satisfactorily applied also to the new data from failure at the weld root of rollers tested at different load levels. figure 3: synthesis of new data in terms of local sed and comparison with the scatterband by lazzarin and co-authors. conclusions he present paper deals with a local energy based approach employed for the fatigue assessment of rollers with failure occurring at the weld root. the rollers considered in the present investigation are particularly suited to conveyors that operate in very difficult conditions, where working loads are high, and large lump size material is conveyed; and yet, despite these characteristics, they require minimal maintenance. the bearing housings are welded to the tube body using autocentralising automatic welding machines utilizing a continuous wire feed. from the point of view of the fatigue behavior under loading, the weakest point of the entire structure is the lack of penetration of the weld root. therefore, if the roller is loaded well above its declared nominal admitted load [26], it would b t f. chebat et alii, frattura ed integrità strutturale, 41 (2017) 447-455; doi: 10.3221/igf-esis.41.56 454 experience fatigue failure starting at the level of the weld root. a detail of the weld root is shown in fig. 1b, where the lack of penetration length is indicated as c. the rollers have been modelled by using the finite element method combined with three-dimensional analyses. the procedure for evaluating the local parameters in the zone close to the lack of penetration at the weld root has been described in the paper showing the low sensitivity of the model to the length of the lack of penetration. the detailed procedure for evaluating the sed in the control volume surrounding the crack tip in the weakest point of the roller has been summarised [27]. some fatigue tests from two different geometries belonging to the family of rollers called psv4 from rulmeca production have been carried out and summarised here by means of local sed. it has been proved that the scatter band δw-n (strain energy range – number of cycles to failure), summarising about 1200 fatigue data from welded joints with the majority of failures originated from the weld toes, can be successfully applied also to welded joints with failures from the weld roots and in particular to the considered rollers geometry. references [1] zou, l., yang, x., tan, j., sun, y., s-n curve modeling method of aluminum alloy welded joints based on the fatigue characteristics domain, frattura ed integrita strutturale, 11(40) (2017) 137-148. [2] abe, t., akebono, h., kato, m., sugeta, a., fatigue properties and fracture mechanism of load carrying type fillet joints with one-sided welding, frattura ed integrita strutturale, 10(35) (2016) 196-205. [3] tsutsumi, s., morita, k., fincato, r., momii, h., fatigue life assessment of a non-load carrying fillet joint considering the effects of a cyclic plasticity and weld bead shape, frattura ed integrita strutturale, 10(38) (2016) 244-250. [4] radaj, d., design and analysis of fatigue resistant welded structures, abington publishing, cambridge (1990). [5] taylor, d., barrett, n., lucano, g., some new recent methods for predicting fatigue in welded joints, int. j. fatigue, 24 (2002) 509-518. [6] yakubovskii, v.v., valteris, i.i., geometrical parameters of butt and fillet welds and their influence on the welded joints fatigue life, international institute of welding, document xiii-1326-89 (1989). [7] dunn, m.l., suwito, w., cunningham, s., fracture initiation at sharp notches: correlation using critical stress intensities, int. j. solids struct., 34 (1997) 3873-3883. [8] lazzarin, p., tovo, r., a notch intensity approach to the stress analysis of welds, fatigue fract. eng. mater. struct. 21 (1998) 1089-1104. [9] ayatollahi, m.r., razavi, s.m.j., chamani, h.r., fatigue life extension by crack repair using stop-hole technique under pure mode-i and pure mode-ii loading conditions, procedia eng., 74 (2014) 18–21. [10] ayatollahi, m.r., razavi, s.m.j., chamani, h.r., a numerical study on the effect of symmetric crack flank holes on fatigue life extension of a sent specimen, fatigue fract. eng. mater. struct. 37(10) (2014) 1153-1164. [11] ayatollahi, m.r., razavi, s.m.j., yahya, m.y., mixed mode fatigue crack initiation and growth in a ct specimen repaired by stop hole technique, eng. fract. mech. 145 (2015) 115-127. [12] ayatollahi, m.r., razavi, s.m.j., sommitsch, c., moser, c., fatigue life extension by crack repair using double stop-hole technique, mater. sci. forum, 879 (2017) 3-8. [13] razavi, s.m.j., ayatollahi, m.r., sommitsch, c., moser, c., retardation of fatigue crack growth in high strength steel s690 using a modified stop-hole technique, eng. fract. mech., 169 (2017) 226–237. [14] jiang, y., feng, m., modeling of fatigue crack propagation, j. eng. mater. technol., 126 (2004) 77-86. [15] berto, f., lazzarin, p., recent developments in brittle and quasi-brittle failure assessment of engineering materials by means of local approaches, mater. sci. eng. r, 75 (2014) 1–48. [16] ferro, p., the local strain energy density approach applied to pre-stressed components subjected to cyclic load, fatigue fract. eng. mater. struct. 37 (2014) 1268–1280. [17] radaj, d., state-of-the-art review on the local strain energy density concept and its relation to the j-integral and peak stress method, fatigue fract. eng. mater. struct., 38 (2015) 2–28. [18] radaj, d., berto, f., lazzarin, p., local fatigue strength parameters for welded joints based on strain energy density with inclusion of small-size notches, eng. fract. mech., 76 (8) (2009) 1109-1130. [19] lazzarin, p., campagnolo, a., berto, f., a comparison among some recent energyand stress-based criteria for the fracture assessment of sharp v-notched components under mode i loading, theor. appl. fract. mech., 71 (2014) 2130. [20] lassen, t., the effect of the welding process on the fatigue crack growth. welding j. 69, research supplement, (1990) 75s-81s. f. chebat et alii, frattura ed integrità strutturale, 41 (2017) 447-455; doi: 10.3221/igf-esis.41.56 455 [21] singh, p.j., achar, d.r.g., guha, b., nordberg h., fatigue life prediction of gas tungsten arc welded aisi 304l cruciform joints different lop sizes, int. j. fatigue, 25 (2003) 1-7. [22] singh, p.j., guha, b., achar, d.r.g., nordberg, h., fatigue life prediction improvement of aisi 304l cruciform welded joints by cryogenic treatment, eng. fail. anal. 10 (2003) 1-12. [23] lazzarin, p., sonsino, c.m., zambardi, r., a notch stress intensity approach to predict the fatigue behaviour of t butt welds between tube and flange when subjected to in–phase bending and torsion loading, fatigue fract. eng. mater. struct. 27 (2004) 127-141. [24] sheppard, s.d., field effects in fatigue crack initiation: long life fatigue strength. trans. asme, j. mech. design 113 (1991) 188-194. [25] sonsino, c.m., multiaxial fatigue of welded joints under in-phase and out-of-phase local strains and stresses, int. j. fatigue 17 (1995) 55-70. [26] rulmeca bulk catalogue, 2014 [27] berto, f., campagnolo, a., chebat, f., cincera, m., santini, m., fatigue strength of steel rollers with failure occurring at the weld root based on the local strain energy values: modelling and fatigue assessment, int. j. fatigue, 82 (2016) 643–657. [28] williams, m.l., stress singularities resulting from various boundary conditions in angular corners of plates in extension, j. appl. mech. 19 (1952) 526-528. [29] gross, r., mendelson, a., plane elastostatic analysis of v-notched plates, int. j. fract. 8 (1972) 267-276. [30] qian, j., hasebe, n., property of eigenvalues and eigenfunctions for an interface v-notch in antiplane elasticity, eng. fract. mech. 56 (1997) 729–734. [31] zappalorto, m., lazzarin, p., yates, j.r., elastic stress distributions resulting from hyperbolic and parabolic notches in round shafts under torsion and uniform antiplane shear loadings, int. j. solid. struct., 45 (2008) 4879-4901. [32] lazzarin, p., tovo r., a unified approach to the evaluation of linear elastic fields in the neighbourhood of cracks and notches, int. j. fract., 78 (1996) 3-19. [33] lazzarin, p., zambardi, r., a finite-volume-energy based approach to predict the static and fatigue behaviour of components with sharp v-shaped notches, int. j. fract. 112 (2001) 275-298. [34] berto, f., campagnolo, a., lazzarin, p., fatigue strength of severely notched specimens made of ti–6al–4v under multiaxial loading, fatigue fract. eng. mater. struct. 38 (2015) 503–517. [35] seweryn, a., poskrobko, s., mróz, z., brittle fracture in plane elements with sharp notches under mixed-mode loading, j. eng. mech. 123 (1997) 535-543. [36] kihara, s., yoshii, a., a strength evaluation method of a sharply notched structure by a new parameter, “the equivalent stress intensity factor”. jsme int. j., 34 (1991) 70-75. [37] livieri, p., lazzarin, p., notch stress intensity factors and fatigue strength of aluminium and steel welded joints, int. j. fract. 133 (2005) 247-276. [38] atzori, b., dattoma, v., a comparison of the fatigue behaviour of welded joints in steels and in aluminium alloys, iiw doc xxxiii (1983) 1089-1983. [39] haibach, e., service fatigue-strength – methods and data for structural analysis. dusseldorf, vdi (1989). [40] lazzarin, p., berto, f., gomez, f.j., zappalorto, m., some advantages derived from the use of the strain energy density over a control volume in fatigue strength assessments of welded joints, int. j. fatigue, 30 (2008) 1345-1357. [41] lazzarin, p., berto, f., zappalorto, m., rapid calculations of notch stress intensity factors based on averaged strain energy density from coarse meshes: theoretical bases and applications, int. j. fatigue, 32 (2010) 1559–1567. [42] meneghetti, g., campagnolo, a., berto, f., atzori, b., averaged strain energy density evaluated rapidly from the singular peak stresses by fem: cracked components under mixed-mode (i+ii) loading, theor. appl. fract. mech., 79 (2015) 113–124. 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can be opened with acrobat and adobe reader 5.0 and later.) >> /namespace [ (adobe) (common) (1.0) ] /othernamespaces [ << /asreaderspreads false /cropimagestoframes true /errorcontrol /warnandcontinue /flattenerignorespreadoverrides false /includeguidesgrids false /includenonprinting false /includeslug false /namespace [ (adobe) (indesign) (4.0) ] /omitplacedbitmaps false /omitplacedeps false /omitplacedpdf false /simulateoverprint /legacy >> << /addbleedmarks false /addcolorbars false /addcropmarks false /addpageinfo false /addregmarks false /convertcolors /converttocmyk /destinationprofilename () /destinationprofileselector /documentcmyk /downsample16bitimages true /flattenerpreset << /presetselector /mediumresolution >> /formelements false /generatestructure false /includebookmarks false /includehyperlinks false /includeinteractive false /includelayers false /includeprofiles false /multimediahandling /useobjectsettings /namespace [ (adobe) (creativesuite) (2.0) ] /pdfxoutputintentprofileselector /documentcmyk /preserveediting true /untaggedcmykhandling /leaveuntagged /untaggedrgbhandling /usedocumentprofile /usedocumentbleed false >> ] >> setdistillerparams << /hwresolution [2400 2400] /pagesize [612.000 792.000] >> setpagedevice microsoft word numero_49_art_1_2466 y. chang et alii, frattura ed integrità strutturale, 49 (2019) 1-11; doi: 10.3221/igf-esis.49.01 1 focused on crack tip fields further investigation on microstructure refinement of internal crack initiation region in vhcf regime of high-strength steels yukun chang lnm, institute of mechanics, chinese academy of sciences, beijing 100190, china school of science, harbin institute of technology, shenzhen 518055, china yukunchang@foxmail.com liang zheng school of science, harbin institute of technology, shenzhen 518055, china icon_lzheng@hit.edu.cn xiangnan pan, youshi hong* lnm, institute of mechanics, chinese academy of sciences, beijing 100190, china school of engineering science, university of chinese academy of sciences, beijing 100049, china panxiangnan@lnm.imech.ac.cn, hongys@imech.ac.cn abstract. the profile samples prepared by focused ion beam (fib) in crack initiation region (cir) and fish-eye (fie) region of failed specimens subjected to rotary bending (rb) and ultrasonic axial (ul) fatigue testing with various stress ratios (r) were observed by transmission electron microscopy (tem) with selected area electron diffraction (sad) detection for two high-strength steels. the grain size and the thickness of nanograin layer along the crack growth path in cir underneath fine-granular-area (fga) were measured for the cases of r < 0, and a normalized quantity d* based on the detected sad patterns was introduced to quantitatively demonstrate the variation of the grain size. the results showed that the nanograin size near the origin (an inclusion) of crack initiation is smaller than that away from the inclusion. nevertheless, there was no evidence of grain refinement in cir for the cases of r > 0 and the fie region outside cir for either negative or positive stress ratio cases, which suggests that the formation of nanograin layer in the fga region is due to the numerous cyclic pressing (ncp) process and the plastic deformation ahead of the crack tip may cause certain extent of microstructure deformation but is insufficient to form nanograin layer on crack surfaces. keywords. very-high-cycle fatigue; nanograins; microstructure refinement; crack initiation; fga; high-strength steels. citation: chang y.k., pan x.n., zheng l., hong y.s., further investigation on microstructure refinement of internal crack initiation region in very-high-cycle fatigue regime of high strength steels, frattura ed integrità strutturale, 49 (2019) 1-11. received: 08.04.2019 accepted: 23.04.2019 published: 01.07.2019 copyright: © 2019 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. http://www.gruppofrattura.it/va/49/2466.mp4 y. chang et alii, frattura ed integrità strutturale, 49 (2019) 1-11; doi: 10.3221/igf-esis.49.01 2 introduction atigue failure of engineering materials and structures bearing cyclic loading beyond 107 cycles, i.e. very-high-cycle fatigue (vhcf), may still happen in practical industrial applications [1-4]. vhcf behavior has attracted the attention of researchers in recent decades due to increasingly realistic requirements and scientific interests [5-9]. at present, it has been known that the typical morphology of the internal crack initiation region (cir) for vhcf of highstrength steels is a fish-eye (fie) containing a relatively rough region of fine-granular area (fga), and it surrounds an inclusion which is considered as the origin of the crack initiation [10-13]. in general, fga is regarded as the characteristic region of the internal crack initiation of vhcf due to its stable value of related stress intensity factor range and the consumption of the majority of total fatigue life [10,11,14]. as one of the most popular and challenging problems in vhcf, the formation mechanism of fga has been investigated widely and deeply in last two decades [15-21]. sakai et al. [18] examined the microstructure beneath the fga by transmission electron microscopy (tem). the tem sample was prepared by focused ion beam (fib) technique, and their results showed that the fine granular layer was observed in fga region, whereas the fine polygonization was not observed in the location away from the fga surface. based on this observation, they proposed the model of “formation and debonding of fine granular layer” [22]. similarly, an investigation by grad et al. [15] reported that an average grain size of about 70 nm was observed in fga for a high-strength steel and proposed an fga formation mechanism called “local grain refinement at the crack tip”. this model was extended very recently by spriestersbach and kerscher [23]. the most recent investigations by chai et al. [24,25] also believed that localized plastic deformation would promote the formation of fga. it should be noted that only the fully reversed cyclic loading was considered in all above-mentioned investigations, meaning the stress ratio of r = ‒1. in order to investigate the formation mechanism of fga more deeply and comprehensively, hong et al. [16] first performed fatigue tests under different stress ratios via rotary bending (rb) and ultrasonic axial (ul) loading for two high-strength steels, then the profile samples were prepared by fib at the characteristic region of crack initiation of failed specimens, and subsequently the microstructure of the samples were examined by tem. their observations revealed the existence of the thin nanograin layer of fga under negative stress ratios, whereas the morphology of fga was diminishing or even extinguishing under positive stress ratios without the evidence of nanograin feature. based on such experimental results, a new model named “numerous cyclic pressing (ncp)” was proposed to describe the formation processes of fga. subsequently, some results obtained by our group on structural steels [26] and titanium alloys [27,28] have confirmed the ncp model. most recently, numerical and experimental results reported by ritz et al. [29] also validated the ncp model. despite the formation mechanism of fga has been investigated widely by researchers, the effect of the plastic deformation ahead of the crack tip during crack initiation process on the microstructure refinement, and the more detailed characteristics of microstructure in cir and fie regions, are still not clear at the present time. therefore, in this paper, further investigation was carried out on the microstructure features in the cir and fie regions for high-strength steels bearing fatigue loading up to very-high-cycle regime. several profile samples prepared by fib in cir and fie regions were examined by tem with selected area electron diffraction (sad) detection. the detailed observations indicate that the nanograin size near the origin of crack initiation is smaller than that away from the origin for the cases of r < 0, and higher compressive stress and longer loading cycles promote the microstructure refinement. nevertheless, there was no evident grain refinement in cir for the cases of r > 0 and the fie region outside cir for either negative or positive r cases, suggesting that the formation of nanograins in the fga region is due to the ncp process and the plastic deformation ahead of crack tip may cause certain extent of microstructure deformation but is insufficient to form nanograin layer on crack surfaces. test materials and experimental procedure test materials he test materials utilized in this research were two high-strength steels. for convenience, they were marked as material a and material b, respectively. the corresponding chemical compositions are listed in tab. 1. two heattreatment processes were performed: austenization at 845 ℃ for 2 h in vacuum, oil-quenched then tempered for 2 h in vacuum at 180 ℃ for the specimens of material a, and austenization at 845 ℃ for 1 h in vacuum, oil-quenched then tempered for 2 h in vacuum at 180 ℃ for the specimens of material b. after such heat-treatment processes, identical f t y. chang et alii, frattura ed integrità strutturale, 49 (2019) 1-11; doi: 10.3221/igf-esis.49.01 3 microstructure of tempered martensite was obtained. results of monotonic quasi-static tensile and micro-hardness tests exhibited their high strength and hardness with the ultimate tensile strength of 1849 mpa and the micro-hardness of 753 hv (kgf/mm2) for material a, and the ultimate tensile strength of 1896 mpa and the micro-hardness of 760 hv (kgf/mm2) for material b. material c cr mn si s p fe a 1.06 1.04 0.88 0.34 0.005 0.027 balance b 1.04 1.51 0.29 0.24 0.003 0.0058 balance table 1: chemical compositions (wt. %) of two materials. experimental procedure rotary bending and ultrasonic axial loading are commonly used in the vhcf tests of materials. in the previous research developed in our group, material a was tested on a rotary bending machine with r = ‒1, and material b was tested on an ultrasonic machine (equipped with a tensile facility to superimpose required mean stress) running at the resonant frequency of 20 khz with the stress ratios of r = ‒1, ‒0.5, 0.1 and 0.3. more detailed information concerning the fatigue tests was described in [16]. then the morphology of the fracture surface was observed by scanning electron microscopy (sem), and it was noticed that the failure of every specimen was due to internal cracking originated from an inclusion [16]. in addition, for the purpose of investigating the characteristics of microstructure for fga and fie on the fracture surface, several specimens under various loading conditions were cut by fib to obtain the profile samples, and their relevant data were listed in tab. 2. subsequently these samples were carefully examined by tem, especially near the fracture surfaces, and the microstructure details were detected by sad with an aperture diameter of 200 nm. sample loading condition σa/mpa σmax/mpa σmin/mpa nf/cycles sampling location a1 rb, r = ‒1 775 775 ‒775 2.40×107 cir a2 rb, r = ‒1 750 750 ‒750 5.08×107 fie b1 ul, r = ‒1 989 989 ‒989 1.11×108 cir b2 ul, r = ‒0.5 633 844 ‒422 4.81×108 cir b3 ul, r = 0.1 534 1187 119 1.84×107 cir b4 ul, r = 0.3 430 1229 368 8.70×108 cir b5 ul, r = 0.3 430 1229 368 8.70×108 fie table 2: loading conditions and sampling locations of several failed specimens. results and discussion microstructural features in cir for negative stress ratio cases t can be seen from tab. 2 that a1, b1 and b2 samples were cut from cir of the failed specimens bearing fatigue loading with negative stress ratios in vhcf regime. fig. 1 illustrates the microstructural features of sample a1. it is seen from fig. 1a that the crack initiated from a spherical inclusion then to form an fga region. the small dashed yellow rectangle in fig. 1a represents the sampling location in the fga region, and fig. 1b illustrates the bright field imaging (bfi) of sample a1. figs. 1c and 1d show the sad patterns at the locations just underneath the fga surface with discontinuous diffraction rings of polycrystals, which suggests that there are several grains within the diffraction area of 200 nm in diameter. figs. 1e and 1f are dark field images (dfi) of the left and right dashed green boxes marked in fig. 1b, and the fine granular layer can be clearly observed in both figures. fig. 2 illustrates the microstructural features of sample b1. similar to the above situation of sample a1, in the failed specimen associated with sample b1, the crack also originated from an inclusion to form an fga region. bfi and dfi of the sample, displayed as a small dashed yellow rectangle in fig. 2a, are presented in figs. 2b and 2c, respectively. both bfi i y. chang et alii, frattura ed integrità strutturale, 49 (2019) 1-11; doi: 10.3221/igf-esis.49.01 4 and dfi showed that there are many fine grains near the fracture surface. sad patterns of the left, middle and right dashed yellow circles marked in fig. 2b are illustrated in figs. 2d-f. all of these three patterns are discontinuous diffraction circles, suggesting several grains existing at these different locations. similar results were obtained for sample b2 (as shown in fig. 3). figure 1: microstructural features of sample a1 (rb, r = ‒1, σa = 775 mpa, nf = 2.40╳107), (a) sem image of cir showing the sampling location by a marked dashed yellow rectangle; (b) bfi; (c,d) sad patterns of the left and right dashed yellow circles in (b); (e,f) dfi of the left and right dashed green boxes in (b). figure 2: microstructural features of sample b1 (ul, r = ‒1, σa = 989 mpa, nf = 1.11╳108), (a) origin of crack initiation showing clear fga feature; (b) bfi; (c) dfi; (d-f) sad patterns of the left, middle and right dashed yellow circles in (b). y. chang et alii, frattura ed integrità strutturale, 49 (2019) 1-11; doi: 10.3221/igf-esis.49.01 5 figure 3: microstructural features of sample b2 (ul, r = ‒0.5, σa = 633 mpa, nf = 4.81╳108), (a) sem image showing crack origin; (b) bfi; (c,d) dfi of the left and right dashed green boxes in (b); (e-g) sad patterns of the left, middle and right dashed yellow circles in (b). the above experimental results indicate the existence of nanograins in cir underneath fga surface for the cases of r = ‒1 and ‒0.5 under rb and ul loading conditions, confirming that the nature of fga is a nanograin layer [16]. for the detail investigation of the relationship between the grain size and loading conditions, the distribution of grain size in cir underneath fga surface for samples a1, b1 and b2 was measured and the results are illustrated in fig. 4. it is seen from fig. 4 that the grain size ranges from 20 nm to 130 nm, and the average equivalent diameters are 54 nm, 48 nm and 73 nm for a1, b1 and b2, respectively. similarly, the distribution of thickness for these nanograin layers along the crack growth path was shown in fig. 5, indicating that the average values of thickness are 315 nm, 435 nm and 386 nm for a1, b1 and b2, respectively. note that the data in figs. 4 and 5 are largely discrete, which suggests that the grain size and the thickness of nanograin layer are affected by cyclic loading condition and the microstructure of the material. as an effective method for analyzing the microstructure of materials, sad technique can be utilized to reveal the essential characteristics of the microstructure more objectively. according to the diffraction principle [30], sad patterns will appear as a series of rings if it contains many grains with different orientations within the selected area, and with the increase of the number of grains, namely more fine grains, diffraction rings will become more continuous. therefore, for the purpose of quantitatively describing the distribution of grain size under different loading conditions, a normalized quantity d* is introduced and expressed as:  0 * l d l (1) where l0 presents the perimeter of a completely continuous diffraction ring associated with a given crystal plane family, and l presents total lengths of the ring measured in experiments. for this purpose, a number of discontinuous diffraction rings associated with {110} planes for samples a1, b1 and b2 were measured, and the results described by d* are illustrated in fig. 6. the value of d* notably decreases along the crack growth path, implying that the size of nanograins gradually increases with the propagation of the crack, which may be due to gradually-reduced pressing actions. moreover, the datum points of b1 are evidently higher than those of a1 and b2, suggesting that the greater compressive stress and the longer loading cycles may promote the grain refinement. y. chang et alii, frattura ed integrità strutturale, 49 (2019) 1-11; doi: 10.3221/igf-esis.49.01 6 figure 4: distribution of grain size underneath fga surface for samples a1, b1 and b2. figure 5: thickness of nanograin layer along crack growth path underneath fga surface for samples a1, b1 and b2. figure 6: distribution of normalized quantity d* versus crack growth path for samples a1, b1 and b2. 0 20 40 60 80 100 120 140 160 0 10 20 30 40 50 60 f re q u en cy , % grain size, nm a1, d = 54 nm b1, d = 48 nm b2, d = 73 nm 0 2 4 6 8 10 0 200 400 600 800 1000 a1, t = 315 nm b1, t = 435 nm b2, t = 386 nm t h ic k n es s of n an o gr ai n l ay er , n m distance along crack growth path, μm 4 6 8 10 12 14 16 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 a1, rb, r =1 b1, ul, r =1 b2, ul, r =0.5 d * , n o rm al iz ed q u an ti ty distance along crack growth path, μm y. chang et alii, frattura ed integrità strutturale, 49 (2019) 1-11; doi: 10.3221/igf-esis.49.01 7 microstructural features in cir for positive stress ratio cases the above results indicate that the features of nanograins clearly prevailed underneath the fracture surface in the fga region for the cases with negative stress ratios, whereas the microstructural features were not clear for the cases with positive stress ratios. it is well known that the plastic deformation occurs at crack tip. based on the equation proposed by murakami et al. [31]:    1/2max max=k c area (2) and the plastic zone size (rp) at crack tip under plane strain condition [32]:          2 max p y 1 6 k r (3) the value of kmax increases with the raise of σmax and crack size, causing the expansion of the plastic zone near the crack tip. in order to investigate the effect of the plastic deformation at the crack tip on the microstructure of high-strength steels, two profile samples cut in cir (b3 and b4) with positive stress ratios and two samples cut in fie (a2 and b5) were prepared. the results of the samples cut in cir are presented in this section, and the results of samples cut in fie will be presented in next section. fig. 7 illustrates the microstructural features of sample b3 (r = 0.1), and the sampling location is denoted by a small dashed yellow rectangle shown in fig. 7a, from which a cluster of inclusions as the origin of crack initiation and the diminishing fga feature can be clearly observed. fig. 7b presents the whole bfi of sample b3, and the dfi of its local location (dashed green box) is illustrated in fig. 7c, showing that any position on the profile is original martensite microstructure, meaning no sign of grain refinement. fig. 7d shows the sad pattern of slightly elongated diffraction spots, which is the result of localized plastic deformation. fig. 7e shows the sad pattern with typical isolated spots, which are the normal diffraction of a single crystal, i.e., the original coarse martensite microstructure. similar observations of sample b4 (r = 0.3) are obtained as shown in fig. 8. figure 7: microstructural features of sample b3 (ul, r = 0.1, σa = 534 mpa, nf = 1.84╳107), (a) sem image showing crack origin; (b) bfi; (c) dfi of the dashed green box in (b); (d,e) sad patterns of the left and right dashed yellow circles in (b). y. chang et alii, frattura ed integrità strutturale, 49 (2019) 1-11; doi: 10.3221/igf-esis.49.01 8 figure 8: microstructural features of sample b4 (ul, r = 0.3, σa = 989 mpa, nf = 8.70╳108), (a) sem image showing crack origin; (b) bfi; (c) dfi; (d,e) sad patterns of the left and right dashed yellow circles in (b). microstructural features in fie fish-eye is a typical morphology of vhcf for metallic materials, but the microstructural features in the fie region were not very clear so far. for the purpose of further examination for the microstructure features in fie, two profile samples (a2 and b5) were prepared by fib cut from the fie region of failed specimens in vhcf regime under r = ‒1 and 0.3. the loading conditions of these two specimens are also listed in tab. 2. fig. 9 illustrates the microstructural features of sample a2, for which the sampling location (quadrate rabbet) is close to the outer boundary of the fie (fig. 9a). fig. 9b presents the whole bfi of a2 and fig. 9c illustrates the dfi of its local field, showing any position on the profile is original martensite microstructure. fig. 9d shows the sad pattern with slightly elongated spots, which is the result of localized plastic deformation. fig. 9e shows isolated spot pattern indicating only one grain within the diffraction area of 200 nm in diameter. in brief, the result of fig. 9 shows that the microstructure underneath the fracture surface in the fie region does not undergo grain refinement, which may be related to insufficient pressing during cycling because of the relatively faster crack growth rate in the fie region. fig. 10 illustrates the microstructural features of sample b5 (also cut from fie region), similar to the results shown in fig. 9. there is no evidence of microstructure refinement in spite of the high maximum stress (σmax), suggesting that plastic deformation ahead of crack tip cannot cause the formation of nanograins. conclusions n this paper, a series of profile samples from two high-strength steels were prepared by fib in cir and fie regions of failed specimens subjected to rotary bending and ultrasonic axial cycling up to vhcf regime with various stress ratios. then such samples were observed by tem with sad detection. based on the experimental investigations, the following conclusions were obtained: i y. chang et alii, frattura ed integrità strutturale, 49 (2019) 1-11; doi: 10.3221/igf-esis.49.01 9 figure 9: microstructural feature of sample a2 (rb, r = ‒1, σa = 750 mpa, nf = 5.08╳107), (a) sem image showing sampling location (quadrate rabbet); (b) bfi; (c) dfi of dashed green box in (b); (d,e) sad patterns of the left and right dashed yellow circles in (b). figure 10: microstructural feature of sample b5 (ul, r = 0.3, σa = 430 mpa, nf = 8.70╳108), (a) sem image showing sampling location (quadrate rabbet); (b) bfi; (c) dfi of dashed green box in (b); (d,e) sad patterns of the left and right dashed circles in (b). y. chang et alii, frattura ed integrità strutturale, 49 (2019) 1-11; doi: 10.3221/igf-esis.49.01 10 (1) the ncp process dominates the formation of nanograin layer in cir underneath fga surface. large compressive stress with sufficient pressing results in the formation of nanograins and consequently the nanograin layer. (2) the plastic deformation at crack tip can only cause certain extent of deformation in microstructure of high-strength steels, but is insufficient to produce nanograins. (3) there is no microstructure refinement in the fie region no matter the sample was in the cases of negative or positive stress ratios, which may be due to the lack of crack surface contacting during cycling in the fie region. acknowledgements he financial supports from the national natural science foundation of china (11572325) and from the strategic priority research program of the chinese academy of sciences (xdb22040503, xdb22020201) are greatly appreciated. references [1] hong, y. and sun, c. (2017). the nature and the mechanism of crack initiation and early growth for very-high-cycle fatigue of metallic materials an overview, theoretical and applied fracture mechanics, 92, pp. 331-350. doi: 0.1016/j.tafmec.2017.05.002. [2] marines, i., bin, x., bathias, c. (2003). an understanding of very high cycle fatigue of metals, international journal of fatigue, 25(9-11), pp. 1101-1107. doi: 0.1016/s0142-1123(03)00147-6. [3] mayer, h. (2016). recent developments in ultrasonic fatigue, fatigue and fracture of engineering materials and structures, 39(1), pp. 3-29. doi: 10.1111/ffe.12365. [4] jeddi, d., palin-luc, t. (2018) a review about the effects of structural and operational factors on the gigacycle fatigue of steels. fatigue and fracture of engineering materials and structures, 41(5), pp. 969-990. doi: 10.1111/ffe.12779 [5] krupp, u., giertler, a., koschella, k. (2017). microscopic damage evolution during very-high-cycle fatigue (vhcf) of tempered martensitic steel, fatigue and fracture of engineering materials and structures, 40(11), pp. 1731-1740. doi: 10.1111/ffe.12685. [6] hu, y., sun, c., hong, y. (2018) crack growth rates and microstructure feature of initiation region for very‐high‐ cycle fatigue of a high-strength steel. fatigue and fracture of engineering materials and structures, 41(8), 1717-1732. doi: 10.1111/ffe.12811 [7] liu, x., sun, c., hong, y. (2015). effects of stress ratio on high-cycle and very-high-cycle fatigue behavior of a ti6al-4v alloy, materials science and engineering, a: structural materials: properties, microstructure and processing, 622, pp. 228-235. doi: 10.1016/j.msea.2014.09.115. [8] pineau, a. and forest, s. (2017). effects of inclusions on the very high cycle fatigue behaviour of steels, fatigue and fracture of engineering materials and structures, 40(11), pp. 1694-1707. doi: 10.1111/ffe.12649. [9] shiozawa, k. and lu, l. (2002). very high-cycle fatigue behaviour of shot-peened high-carbon-chromium bearing steel, fatigue and fracture of engineering materials and structures, 25, pp. 813-822. [10] hong, y., lei, z., sun, c., zhao, a. (2014). propensities of crack interior initiation and early growth for very-highcycle fatigue of high strength steels, international journal of fatigue, 58, pp. 144-151. doi: 10.1016/j.ijfatigue.2013.02.023. [11] lei, z., xie, j., sun, c., hong, y. (2014). effects of loading condition on very-high-cycle fatigue behaviour and dominant variable analysis, science china-physics mechanics and astronomy, 57(1), pp. 74-82. doi: 10.1007/s11433-013-5332-x. [12] shyam, a., blau, p., jordan, t., yang, n. (2014). effect of submillimeter size holes on the fatigue limit of a high strength tool steel, fatigue and fracture of engineering materials and structures, 37(4), pp. 368-379. doi: 10.1111/ffe.12119. [13] stanzl-tschegg, s.e. (2017). fracture mechanical characterization of the initiation and growth of interior fatigue cracks, fatigue and fracture of engineering materials and structures, 40(11), pp. 1741-1751. doi: 10.1111/ffe.12622. [14] marines-garcia, i., paris, p. c., tada, h., bathias, c. (2007). fatigue crack growth from small to long cracks in veryhigh-cycle fatigue with surface and internal "fish-eye" failures for ferrite-perlitic low carbon steel sae 8620, materials science and engineering a-structural materials properties microstructure and processing, 468, pp. 120-128. doi: 10.1016/j.msea.2006.08.131. t y. chang et alii, frattura ed integrità strutturale, 49 (2019) 1-11; doi: 10.3221/igf-esis.49.01 11 [15] grad, p., reuscher, b., brodyanski, a., kopnarski, m., kerscher, e. (2012). mechanism of fatigue crack initiation and propagation in the very high cycle fatigue regime of high-strength steels, scripta materialia, 67(10), pp. 838-841. doi: 10.1016/j.scriptamat.2012.07.049. [16] hong, y., liu, x., lei, z., sun, c. (2016). the formation mechanism of characteristic region at crack initiation for very-high-cycle fatigue of high-strength steels, international journal of fatigue, 89, pp. 108-118. doi: 10.1016/j.ijfatigue.2015.11.029. [17] murakami, y., nomoto, t., ueda, t. (1999). factors influencing the mechanism of superlong fatigue failure in steels, fatigue and fracture of engineering materials and structures, 22, pp. 581-590. [18] sakai, t., harada, h., oguma, n. (2006). crack initiation mechanism of bearing steel in very high cycle fatigue, proceedings of ecf-16, cd-rom. [19] shiozawa, k., morii, y., nishino, s., lu l. (2006). subsurface crack initiation and propagation mechanism in highstrength steel in a very high cycle fatigue regime, international journal of fatigue, 28(11), pp. 1521-1532. doi: 10.1016/j.ijfatigue.2005.08.015. [20] shanyavskiy, a.a. (2013). very-high-cycle-fatigue of in-service air-engine blades, compressor and turbine, science china physics, mechanics and astronomy, 57(1), pp. 19-29. doi: 10.1007/s11433-013-5364-2. [21] gerbe, s., krupp, u., michels, w. (2019). influence of secondary dendrite arm spacing (sdas) on the fatigue properties of different conventional automotive aluminum cast alloys, frattura ed integrità strutturale, 48, pp. 105115. doi: 10.3221/igf-esis.48.13 [22] sakai, t. (2009). review and prospects for current studies on very high cycle fatigue of metallic materials for machine structural use, journal of solid mechanics and materials engineering, 3, pp. 425-439. doi: 10.1299/jmmp.3.425. [23] spriestersbach, d. and kerscher, e. (2018). the role of local plasticity during very high cycle fatigue crack initiation in high-strength steels, international journal of fatigue, 111, pp. 93-100. doi: 10.1016/j.ijfatigue.2018.02.008. [24] chai, g., forsman, t., gustavsson, f. (2016). microscopic and nanoscopic study on subsurface damage and fatigue crack initiation during very high cycle fatigue, international journal of fatigue, 83, pp. 288-292. doi: 10.1016/j.ijfatigue.2015.10.024. [25] chai, g., forsman, t., gustavsson, f., wang, c. (2015). formation of fine grained area in martensitic steel during very high cycle fatigue, fatigue and fracture of engineering materials and structures, 38(11), pp. 1315-1323. doi: 10.1111/ffe.12345. [26] jiang, q., sun, c., liu, x., hong, y. (2016). very-high-cycle fatigue behavior of a structural steel with and without induced surface defects, international journal of fatigue, 93, pp. 352-362. doi:10.1016/j.ijfatigue.2016.05.032. [27] pan, x., su, h., sun, c., hong, y. (2018). the behavior of crack initiation and early growth in high-cycle and veryhigh-cycle fatigue regimes for a titanium alloy, international journal of fatigue, 115, pp. 67-78. doi: 10.1016/j.ijfatigue.2018.03.021. [28] su, h., liu, x., sun, c., hong, y. (2017). nanograin layer formation at crack initiation region for very-high-cycle fatigue of a ti-6al-4v alloy, fatigue and fracture of engineering materials and structures, 40(6), pp. 979-993. doi: 10.1111/ffe.12562. [29] ritz, f., stäcker, c., beck, t., sander, m. (2018). fga formation mechanism for x10crnimov12-2-2 and 34crnimo6 for constant and variable amplitude tests under the influence of applied mean loads, fatigue and fracture of engineering materials and structures, 41(7), pp. 1576-1587. doi: 10.1111/ffe.12797. [30] williams, d.b., carter, c.b. (2009), transmission electron microscopy: a textbook for materials science, second edition, springer. [31] murakami, y., kodama, s., konuma, s. (1989). quantitative evaluation of effects of non-metallicinclusions on fatigue strength of high strength steels. i: basic fatigue mechanism and evaluation of correlation between the fatigue fracture stress, international journal of fatigue, 11(5), pp. 291-298. [32] zhao, a., xie, j., sun, c., lei, z., hong, y. 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/hrv (za stvaranje adobe pdf dokumenata najpogodnijih za visokokvalitetni ispis prije tiskanja koristite ove postavke. stvoreni pdf dokumenti mogu se otvoriti acrobat i adobe reader 5.0 i kasnijim verzijama.) /hun 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can be opened with acrobat and adobe reader 5.0 and later.) >> /namespace [ (adobe) (common) (1.0) ] /othernamespaces [ << /asreaderspreads false /cropimagestoframes true /errorcontrol /warnandcontinue /flattenerignorespreadoverrides false /includeguidesgrids false /includenonprinting false /includeslug false /namespace [ (adobe) (indesign) (4.0) ] /omitplacedbitmaps false /omitplacedeps false /omitplacedpdf false /simulateoverprint /legacy >> << /addbleedmarks false /addcolorbars false /addcropmarks false /addpageinfo false /addregmarks false /convertcolors /converttocmyk /destinationprofilename () /destinationprofileselector /documentcmyk /downsample16bitimages true /flattenerpreset << /presetselector /mediumresolution >> /formelements false /generatestructure false /includebookmarks false /includehyperlinks false /includeinteractive false /includelayers false /includeprofiles false /multimediahandling /useobjectsettings /namespace [ (adobe) (creativesuite) (2.0) ] /pdfxoutputintentprofileselector /documentcmyk /preserveediting true /untaggedcmykhandling /leaveuntagged /untaggedrgbhandling /usedocumentprofile /usedocumentbleed false >> ] >> setdistillerparams << /hwresolution [2400 2400] /pagesize [612.000 792.000] >> setpagedevice microsoft word numero_34_art_66 y. li et alii, frattura ed integrità strutturale, 34 (2015) 599-607; doi: 10.3221/igf-esis.34.66 599 on the decay of strength in guilin red clay with cracks yi li, keneng zhang school of geosciences and info-physics, central south university, changsha, 410083, china 349613828@qq.com baochen liu college of civil engineering and architecture, guilin university of technology, guilin, 541004, china 979811051@qq.com zongyuan pan institute of karst geology, cags, guilin, 541004, china 65709162@qq.com abstract. in order to research the effect of cracks in red clay on shear strength through dry-wet cycle test, the experimenters used imaging software and a mathematical model to determine fractal dimension and crack ratio of surface cracks in red clay in guilin, china. after each dry-wet cycle, direct shear tests were carried out on the sample, and such variables as matrix suction on the crack propagation process of red clay were analyzed. the mechanics model was established and obtained the critical condition of soil cracks. the results show that with the increase in the number of dry-wet cycles the shear strength of the samples would decrease. but the rule of shear strength of sample 3 is slightly different from samples 1 and 2. the shear strength of red clay has a good correlation with fractal dimension and crack ratio, which could be an identification index of the strength of red clay. keywords. red clay; dry-wet cycle; fractal dimension; crack ratio; shear strength. introduction uilin is located in the northeast of guangxi province, at a low latitude, with a subtropical monsoon climate. it is variably rainy throughout the year, with the rainy season coinciding with high temperatures. the climate easily causes the development of soil fissure of guilin red clay resulting in a decline in the ultimate strength of the clay. we should pay attention to the influence of red clay cracks on the stability in the area of slope and foundation excavation, as it may lead to free face collapse, ground subsidence and other geological mishaps. therefore, researching the influence of cracks on the shear strength of red clay will help us to improve the safety of the geo-body. cracks in soil have been a concern for a long time, however, the research on geotechnical engineering is still relatively insufficient. until the 1980s, only a few scholars have started the research on the soil cracks [1-6]. a new kind of constitutive model capable of describing the damage of soil structure has been proposed and crack evolution in clay during dry and wet cycles has been simulated [7,8]. the effects of cyclic dry-wet process on the fatigue g y. li et alii, frattura ed integrità strutturale, 34 (2015) 599-607; doi: 10.3221/igf-esis.34.66 600 strength of the cement silt clay and the cement silt were researched by cyclic triaxial tests [9]. high liquid limit undisturbed clay quick shear tests with different moisture were carried out through different dry-wet cycle paths, including the process of humidification and dehumidification of the dry-wet cycle[10]. the relationship between particle mesoscopic and macroscopic mechanical parameters of cohesive materials were studied [11]. but there is little research on shear strength of red clay based on dry-wet cycle. experiments have been conducted on the strength characteristics of unsaturated red clay and expansive soil, which are different from those of common clay soil [12]. the relationships among mechanical indexes, swelling-shrinkage properties, pore size distributions and moisture content of lateritic clay in guigang of guangxi zhuang autonomous region were discussed [13]. the red clay soil and the expansive soil were analyzed regarding the relationships between shear strength index and temperature [14]. it has been determined that high and low confining pressures have different effects on the deformational properties and mechanical index of frozen soil [15]. in addition, the above results show the various impact factors of study on intensity variability of the clay. however, the cracks’ effect on the shear strength of red clay has been limited. in order to observe development of red clay fractures, we simulated red clay in dry-wet cycles under natural conditions combined with computer image processing technology. it was concluded that reticular cracks will form in the red clay under certain circumstances, then a direct shear apparatus was used to test this sample. the test considered multiple factors in controling the cutting ring size and humidification method to determine the fractal dimension and crack ratio of three samples under different conditions. after each dry-wet cycle, direct shear tests were conducted on samples to study the effects of red clay cracks on cohesive force and internal friction angle. testing methods samples he red clay samples were taken from the guilin yan mountain. the red clay samples were dried then crushed, and a fine sieve 2.0mm was used to sieve samples. finally, these samples were stored. the physical and mechanical parameters of the red clay are shown in the tab. 1. w/% ρ(g/cm3) e ip/% il c/kpa φ /° av1-2/mpa-1 51.20 1.81 1.42 26.10 0.76 19.00 13.20 0.60 table 1: physical and mechanical indexes of red clay. factors value class number artificial humidification times of dry-wet cycle: 1, 2, 3, 4, 5; moisture content: 35%; dry density: 1.5 g/cm3; small cutting ring: diameter is 61.8mm, height is 20mm; large cutting ring: diameter is 150mm, height is 50mm. small cutting ring: 12 group large cutting ring: 12 group vacuum saturation times of dry-wet cycle: 1, 2, 3, 4, 5; moisture content: 35%; dry density: 1.5 g/cm3; small cutting ring: diameter is 61.8mm, height is 20mm. small cutting ring: 12 group table 2: test project. test project this test mainly considered the sample size and the influence of different humidification methods on the mechanical properties of red clay. study on the attenuation law of shear strength of samples after five dry-wet cycles shows that shear t y. li et alii, frattura ed integrità strutturale, 34 (2015) 599-607; doi: 10.3221/igf-esis.34.66 601 strength is related to fractal dimension and crack rate, according to the design scheme carried out by the direct shear test. one type of the sample’s diameter is 61.8mm and the height is 20mm, another sample’s diameter is 150mm and the height is 50mm. a drying cabinet set at 60°c was used to dehydrate all of these samples for 12h. the wet mode was divided into two methods; artificial humidification (using a watering can to spray distilled water onto the surfaces of the obtained samples for 10 minutes, then putting the samples in cylinder seals for 24h) and vacuum saturation (pumping gas saturation for 1h, then soaking the samples in water for 10h). the specific plan is shown in the tab. 2. fracture development mechanism analysis fracture characterization analysis his paper selects the artificial humidification using a small cutting ring (sample 1) and a large cutting ring (sample 2) and vacuum saturated (sample 3) for each group, respectively. the article determines fractal dimension and crack ratio of three groups of samples in five dry-wet cycles (see tab. 3). the crack ratio is determined by the use of matlab to select and count black and white pixels of the image, then is compared with the amount of black pixels in general pixels by the following formula, fracture area black pixels 100% 100% surface area general pixels      (1) the fractal dimension of the crack is measured by determining the box dimension. the box dimension is defined as coordinates net δ of rn: [m1 ,(m1+1)]×…×[mn ,(mn+1)], [mi ,(mi+1)] is the side of coordinates net δ, m1,…,mn are integers. suppose f is a limited non-zero collection on rn, nδ(f) stands for diameter, the maximum δ can cover a minimum set number, the box dimension for f is defined as: δb δ 0 logn (f) dim f lim logδ   (2) δb δ 0 logn (f) dim f lim logδ   (3) when the dimensions of the upper box and the lower box are equal, f is called the box dimension, indicated as: δb δ 0 logn (f) dim f lim logδ   (4) when calculating the box dimension for f, the length of δ intersects f, and the number of the intersectional points is the box dimension nδ(f). when δ approaches zero, this means adding logarithmic speed of nδ(f), or the negative values of the slopes of log δ and lognδ(f) is the box dimension. the box dimension of the red clay crack can be determined as follows: in order to calculate its box dimension, the images of cracks are regard as a set f. we can draw a square grid of coordinate δ in the image to calculate f and grid square intersect number nδ(f), take the value of δ (for example, n=1/ 2n, n=1, 2,... ), then confirm the different nδ(f). in this region, by using the least square method we can get the regression linear equation:   1δgn f = a(lgδ ) b   (5) the slope of the linear can be regarded as approximate value of box dimension f, based on the box-counting dimension, the box dimension of crack image under various δ can be obtained: n n δ b δ 1 n lgn (f) dim f lgδ  (6) t y. li et alii, frattura ed integrità strutturale, 34 (2015) 599-607; doi: 10.3221/igf-esis.34.66 602 number of dry-wet cycles: 1 2 3 4 5 sample 1 crack ratio 0 1.65% 2.57% 3.27% 3.63% fractal dimension 0 0.632 0.783 1.012 1.133 sample 2 crack ratio 2.25% 2.77% 3.86% 6.55% 8.03% fractal dimension 0.688 0.853 1.016 1.193 1.417 sample 3 crack ratio 0 2.14% 2.92% 3.37% 3.77% fractal dimension 0 0.963 1.076 1.167 1.257 table 3: number of dry-wet cycles as related to crack ratio and fractal dimension. tab. 3 shows that sample 1 and sample 3 had no fissures after the first wet-dry cycle, but the crack ratio and fractal dimension were 2.25% and 0.688, respectively. comparing three groups of crack samples after five dry-wet cycles, the fissure of sample 2 developed earlier and more was more substantial than that of samples 1 and 3. this is because sample 2 was obtained by the large ring sampler while samples 1 and 3 used the small ring. in addition, the fissure ratio and fractal dimension of sample 3 was slightly larger than that of sample 1 due to different humidification methods. fracture mechanical analysis the red clay is the unsaturated soil under normal circumstances. this soil has the characteristics of shrinkage and the rate of water loss in soil on the surface is greater than internally. after water loss and the matric suction increases, the soil is subjected to tensile stress at first. assuming that the soil is isotropic and linear elastic bodies, the following constitutive relations can be established:       x a a w x y z a y a a w y x z a z a a w z x y a σ u u uμ ε σ σ 2u e e h σ u u uμ ε σ σ 2u e e h σ u u uμ ε σ σ 2u e e h                         (7) where au pore air pressure wu pore water pressure e elastic modulus of soil  poisson ratio h elastic modulus associated with a wu u , x horizontal strain y longitudinal strain z vertical strain x horizontal stress y longitudinal stress z vertical stress. taking the horizontal as the object of study, and there are no cracks in the soil: 0x  (8) the first combination of the constitutive relation:       a w x a z a u u eμ σ u σ u 1 u h 1 u        (9) y. li et alii, frattura ed integrità strutturale, 34 (2015) 599-607; doi: 10.3221/igf-esis.34.66 603 when the matrix suction is zero, the soil pressure formula is expressed as a saturated state. in the unsaturated soil, the matrix suction can decrease the horizontal stress, and even with a negative matrix suction it will form tension stress. when tensile stress is greater than the ultimate strength of soil, cracks will appear on the surface. the maximum tensile strength of soil is f , criterion condition as follows:       a w x a z a f u u eμ σ u σ u σ 1 u h 1 u          (10) at the initial stages of fracture, without considering au , we can assume 0z au   , 0a wu u s  , 0s is matric suction:     a w f u u e σ h 1 u    (11) before cracking matric suction is as follows:    ff 0 a w σ h 1 μ s u u e     (12) in the isotropic linear elastic soil,  / 1 2e h   , by the following formula:     ff 0 σ 1 μ s 1 2μ    (13) the critical condition of soil crack:     ff 0 0 σ 1 μ s s 1 2μ     (14) results the relationship between shear strength and wet-dry cycle (1) the relationship between the number of dry-wet cycles and cohesive force is shown in tab. 4 and fig. 1. the cohesive force of samples 1 and 2 have essentially the same tendency for chang, and with the increase of the number of dry-wet cycles the cohesive force would decrease. after the first wet-dry cycle, the maximum cohesion of samples 1 and 2 are 39.38kpa and 38.57kpa, respectively. sample size has no effect on the trend of the cohesion of red clay, but the method of humidification has a significant impact on cohesion, meaning that after five wet-dry cycles, the cohesion of sample 3 decreases. (2) the relationship between the number of dry-wet cycles and internal friction angle is shown in tab. 4 and fig. 2. the internal friction angle and cohesion of samples 1 and 2 have essentially the same tendency for chang, but the internal friction angle of sample 2 is generally greater than that of sample 1, so sample size has significant effects on the internal friction angle. after two dry-wet cycles, the internal friction angle of sample 3 drops little, but after the third wet-dry cycle, the internal friction angle drops rapidly, the minimum value being 6.68°, so vacuum saturation has greater effect on the internal friction angle of samples than artificial humidification. the relationship between shear strength and crack ratio (1) the relationship between cohesive force and crack ratio is shown in tab. 5 and fig. 3. with crack ratio increasing the cohesive force of samples would decrease, but the reducing tendency shows little difference. when the crack y. li et alii, frattura ed integrità strutturale, 34 (2015) 599-607; doi: 10.3221/igf-esis.34.66 604 ratios of samples 1, 2 and 3 are over 1.65%、2.77% and 2.14% respectively, the cohesion drops rapidly, which indicates that there is a threshold quantity that makes the cohesion of red clay change. the cracks of sample 2 appears earlier than those of samples 1 3. after five dry-wet cycles, the cohesion of samples 1 and 2 are about 19kpa, but the cohesion of sample 3 is only 13.77kpa. (2) number of dry-wet cycles: 1 2 3 4 5 sample 1 cohesive force / kpa 39.38 38.21 36.14 29.57 19.05 internal friction angle /° 8.82 8.56 8.49 7.88 7.26 sample 2 cohesive force / kpa 38.57 37.89 34.77 30.09 18.66 internal friction angle /° 9.76 9.29 9.03 8.56 7.12 sample 3 cohesive force / kpa 38.04 33.05 27.39 19.33 13.77 internal friction angle /° 9.06 8.66 7.69 7.13 6.68 table 4: the relationship between the number of dry-wet cycles and shear strength of test results. figure 1: the relationship between the number of dry-wet cycles and cohesive force. figure 2: the relationship between the number of dry-wet cycles and internal friction angle. (2) the relationship between the crack ratio and the internal friction angle is shown in tab. 5 and fig. 4. changes in the internal friction angle in different crack ratios are familiar to cohesive force, both having a threshold quantity. after two dry-wet cycles, the internal friction angle of sample 3 is slightly higher than that of sample 1, but after the forth wet-dry y. li et alii, frattura ed integrità strutturale, 34 (2015) 599-607; doi: 10.3221/igf-esis.34.66 605 cycle, the law reverses. after the first dry-wet cycle, the internal friction angle of sample 2 is 9.76°, the largest of the three samples. number of dry-wet cycles: 1 2 3 4 5 sample 1 crack ratio 0 1.65% 2.57% 3.27% 3.63% fractal dimension 0 0.632 0.783 1.012 1.133 cohesive force / kpa 39.38 38.21 36.14 29.57 19.05 internal friction angle /° 8.82 8.56 8.49 7.88 7.26 sample 2 crack ratio 2.25% 2.77% 3.86% 6.55% 8.03% fractal dimension 0.688 0.853 1.016 1.193 1.417 cohesive force / kpa 38.57 37.89 34.77 30.09 18.66 internal friction angle /° 9.76 9.29 9.03 8.56 7.12 sample 3 crack ratio 0 2.14% 2.92% 3.37% 3.77% fractal dimension 0 0.963 1.076 1.167 1.257 cohesive force / kpa 38.04 33.05 27.39 19.33 13.77 internal friction angle /° 9.06 8.66 7.69 7.13 6.68 table 5: test results of the relationship between crack ratio, fractal dimension and shear strength. figure 3: the relationship between crack ratio and cohesive force. figure 4: the relationship between crack ratio and internal friction angle. y. li et alii, frattura ed integrità strutturale, 34 (2015) 599-607; doi: 10.3221/igf-esis.34.66 606 the relationship between shear strength and fractal dimension (1) the relationship between fractal dimension and the cohesive force is shown in tab. 5 and fig. 5. with fractal dimension increasing, the cohesive force would decrease. when the fractal dimensions of samples 1, 2 and 3 are over 0.5, 0.85 and 0.963 respectively, the cohesion drops rapidly, and changes of cohesion in different fractal dimensions are familiar to crack ratio. but even though the mutation of the fracture in sample 3 is apparent, it cannot be observed when the fractal dimension is less than 0.963, so it is considered to have no impact on crack ratio in this situation. (2) the relationship between the fractal dimension and the internal friction angle is shown in tab. 5 and fig. 6. changes in the internal friction angle in different fractal dimensions are familiar to cohesive force, and they both have a threshold quantity. after the first wet-dry cycle, the crack of samples 1 and 3 do not appear, the fractal dimension is 0, the internal friction angle is 8.82°and 9.06°respectively. after the second wet-dry cycle, because of the different method of humidification, the fractal dimension and internal friction angle of samples 1 and 3 have different trends. due to the relatively large size, sample 2 would form the earlier fracture, with the fractal dimension having a great effect on the internal friction angle. figure 5: the relationship between fractal dimension and cohesive force. figure 6: the relationship between fractal dimension and internal friction angle. conclusion y changing the sample size and humidification method to study the effects of cracks on shear strength of red clay, this study analyzed the mechanics of red clay cracking, and the main conclusions are as follows: 1. to analyze variables such as the matrix suction in the process of fracture development in red clay, we established the mechanics model, determined the state equation of the soil cracking critical conditions, so that study of the images of soil fissures would become an analysis of the specific formula. 2. with the increase of the number of dry-wet cycles, shear strength of samples 1 and 2 would decrease. after the first dry-wet cycle, the intensity index was at its maximum. with the increase of the number of dry-wet cycles, the cohesive force of sample 3 continued to decline. 3. there is a strong correlation between the shear strength of red clay and the crack ratio. with an increase in the crack ratio, the strength curve of samples 1 and 3 are both similar to a parabola, and the change rule of the curve of sample 2 is slightly different. 4. with an increase in the fractal dimension, the intensity index will decrease, as the influence of the crack ratio on the strength index shows that the fractal dimension can be used as one of the indicators in discrimination of the crack influence on the strength of red clay. references [1] yingwen, z., lingwei, k., aiguo, g., et al., mechanical behaviors and water-sensitive properties of intact guangxi laterite, rock and soil mechanics, 04 (2003) 568-572. b y. li et alii, frattura ed integrità strutturale, 34 (2015) 599-607; doi: 10.3221/igf-esis.34.66 607 [2] zhihong, h., lijun, z., yiling, l., et al., study on mechanical properties of red clay fracture, geotechnical investigation and surveying, 4 (2004) 9-12. [3] zhiwei, w., gengsun, w., flac simulation for progressive failure of fissured clay slope, rock and soil mechanics, 10 (2005) 116-119. [4] morris, p.h., graham, j., williams, d.j., cracking in drying soils, can geotech. j., 29 (1992) 264-277. [5] konrad, j.m., ayad, r., desiccation of a sensitive clay: field experiment observations, can geotech.j., 34 (1997) 929942. [6] preston, s., griffiths, b.s., young, i.m., an investigation into sources of soil crack heterogeneity using fractal geometry, european journal of soil science, 48 (1997) 31-37. [7] zhujiang, s., a masonry model for structured clays, rock and soil mechanics, 01 (2000) 1-4. [8] zhujiang, s., gang, d., numerical simulation of crack evolution in clay during drying and wetting cycle, rock and soil mechanics, s2 (2004) 1-6. [9] minglong, z., jianhua, w., aihua, l., test study on the effect of cyclic dry—wet process on the fatigue strength of cement-soil, china railway science, 02 (2005) 28-31. [10] jinlai, y., tian, h., jian, z., et al., change of high liquid limit clay intensity during humidification and dehumidification process of the dry-wet cycle, journal of changsha university of science and technology (natural science), 03 ( 2011) 39-43. [11] bo, z., huabin, w., wenfeng, z., et al., analysis of relationship between particle mesoscopic and macroscopic mechanical parameters of cohesive materials. rock and soil mechanics, 10 (2012) 3171-3175. [12] qing, y., jie, h., maotian, l., comparative study on shear strength of unsaturated red clay and expansive soils, rock and soil mechanics, 01 (2003) 13-16. [13] yingwen, z., ling-wei, k., aiguo, g., et al., strength properties and swelling-shrinkage behaviors of compacted lateritic clay in guangxi, rock and soil mechanics, 03 (2004) 369-373. [14] xiaoduo, o., heng, w., dong, z., comparative study on thermodynamics characteristics of red clay and expansive soils in guangxi, rock and soil mechanics, 07 (2005) 1068-1072. [15] xinglian, s., ren, w., mingjian, h., et al., triaxial strength and deformation properties of frozen silty clay under low confining pressure, rock and soil mechanics, 10 (2005) 102-106. numero_45_art_5 l. zou et alii, frattura ed integrità strutturale, 45 (2018) 53-66; doi: 10.3221/igf-esis.45.05 53 fatigue life prediction of 5083 and 5a06 aluminum alloy t-welded joints based on the fatigue characteristics domain li zou, xinhua yang dalian key laboratory of welded structures and its intelligent manufacturing technology (imt) of rail transportation equipment, dalian jiaotong university, china; sichuan provincial key lab of process equipment and control, china lizou@djtu.edu.cn, yangxhdl@foxmail.com jianrong tan department of mechanical engineering and automation, zhejiang university, china tjr@cad.zju.edu.cn hongji xu, yibo sun dalian key laboratory of welded structures and its intelligent manufacturing technology (imt) of rail transportation equipment, dalian jiaotong university, china xuhongji@djtu.edu.cn, yibo_sun@126.com abstract. three-point bending fatigue test of 5083 and 5a06 aluminum alloy t-welded joints is carried out, and the fatigue life of the specimens with different influencing factors are obtained. finite element model of the twelded joint is established and the nodal force based structural stress is calculated. neighborhood rough set theory is used for analysis of the factors which influence the fatigue life of the aluminum alloy welded joints. key influencing factors are studied and the fatigue characteristic domains are determined. the master s-n curve characterized by the nodal force based structural stress range and cycles to failure on bi-logarithmic coordinate as well as s-n curves corresponding to the fatigue characteristic domain are fitted. a case study of fatigue life prediction of 5a06 aluminum alloy welded joint indicates the effectiveness of the fatigue life prediction method based on the fatigue characteristic domain. keywords. fatigue life; welded joints; fatigue characteristic domain. citation: zou, l., yang, x., tan, j., xu, h., sun, y., fatigue life prediction of 5083 and 5a06 aluminum alloy t-welded joints based on the fatigue characteristic domain, 45 (2018) 53-66. received: 10.02.2018 accepted: 06.04.2018 published: 01.07.2018 copyright: © 2018 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. introduction aster s-n curve method, also called equivalent structural stress method or nodal force based structural stress method is a new type of fatigue life prediction technology for welded structures proposed by dong etc. [1, 2] at the beginning of this century. the structural stress calculated in the master s-n curve method is mesh-m http://www.gruppofrattura.it/va/45/5.mp4 l. zou et alii, frattura ed integrità strutturale, 45 (2018) 53-66; doi: 10.3221/igf-esis.45.05 54 insensitive, so it is intrinsic to a given joint geometry and loading mode [3]. due to the mesh-insensitive structural stress calculation, its high precision and widely applicability, the master s-n curve method is one of the most attractive fatigue analysis engineering technologies for welded structures in the world. for example, master s-n curve in asme code is used for life evaluation for plane steel gate [4]. hong and cox [5] proposed a procedure for fatigue behavior of welded joints with multi-axial stress states by using an effective equivalent structural stress range parameter combined normal and in-plane shear equivalent structural stress ranges. they suggested that it could be generally applicable to predict the failure location and the fatigue life at welds of interest. the application of the master s-n curve approach for fatigue analysis of breathing webs through fe simulation of multiple plate girders is illustrated and the effect of initial out-of-plane displacement as an important geometrical parameter in the girders' fatigue behavior is investigated by mojgan [6]. a simplified version of master s-n curve method, which needs even less experimental input, using an assumption of constant s-n curve slope is presented by atul [7]. dong etc. have carried on the reprocessing of thousands of fatigue test results data of steel structure welded joint in the last 50 years. the master s-n curve for fatigue design based on equivalent structural stress range is determined by linear regression analysis. statistical results show that the scatter level of all s-n samples represented by standard deviations is about 0.25 [8]. in order to further reduce the scatter degree of s-n curves and to improve the fatigue life prediction accuracy, rough set theory is used for analysis of the factors which influence the fatigue life of the aluminum alloy welded joints. rough set theory (rst) [9], proposed by pawlak, has been successfully used as a new feature reduction tool to discover data dependencies and reduce the number of features contained in a dataset. the traditional rst-based feature reduction algorithms are established on the equivalence relation and only compatible for categorical datasets. discretization should be conduct when processing continuous numerical data, which would lead to losing of information [10, 11]. to overcome this drawback, many extensions of rst have been proposed, such as fuzzy rough sets [12, 13], tolerance approximate models [14, 15], covering approximate model [16, 17] and neighborhood granular model [18, 19]. among all the extensions, neighborhood rough set model can process both numerical and categorical data set via the -neighborhood set, which will not break the neighborhood and order structure of dataset in real spaces [20]. to reduce information loss, neighborhood rough set theory is used here to determine the fatigue characteristics domain. three-point bending fatigue test of 5083 and 5a06 aluminum alloy t-welded joints is carried out in this work to further demonstrate the applicability and validity of the s-n curve modeling method based on the fatigue characteristics domain. fatigue characteristic domains are determined and a set of s-n curves correspond to the different fatigue characteristic domain are obtained. statistical analysis is carried out and a case study of fatigue life prediction of 5083 aluminum alloy twelded joint is conducted. the results of case study show that the predicted result is in good agreement with the test result. methodology basic principle of the master s-n curve approach he nodal force based structural stress method is based on equilibrium-equivalent decomposition of an arbitrary stress state at a location of interest such as at weld toe (fig. 1) into an equilibrium-equivalent structural stress part and a self-equilibrating notch-stress part [3]. the equivalent structural stress is described as s m b   = + (1) figure 1: stress distribution at the weld toe.  t + = + weld toe τ ( z ) t fy mx y x z σ z =（σ b + σ m） + σ n s m b  = + l. zou et alii, frattura ed integrità strutturale, 45 (2018) 53-66; doi: 10.3221/igf-esis.45.05 55 suppose l represents the length of the weld toe line, the plate thickness is t, the force vertical to the welding toe is fy, the bending moment around the welding toe is mx, fy is line force and mx is line moment, according to the mechanical formula of the material as shown in eqn. (2), the structural stress can be calculated as eqn. (3) and (4). , 1 2 6 m mfy fy x x m ba l t w l t  = = = =    (2) = / , = /f fy l m m l y x x (3) 6 2 f my x s m b t t   = + = + (4) an equivalent structural stress range parameter can be defined as: 2 1 ( )2 s s s m t i rm m   = −  (5) where s  represents the structural stress range calculated, ( )i r is a dimensionless parameter derived by fracture mechanics considerations, and m is the crack propagation exponent in the conventional paris law, taking on a value of about 3.6 [21]. it could be seen that the equivalent structural stress parameter described in eqn. (5) can capture the effects of stress concentration, plate thickness and loading mode effects on fatigue behavior of welded components. the formula for fatigue life calculation of welded joints using the equivalent structural stress s s  can be expressed as h s cn s  = (6) where n is the number of cycles which indicate the fatigue life of the structure, c is material constant and h represents the negative slope of the master s-n curve. by performing regression analysis with respect to the cycles to failure, tab. 1. summarizes the statistical parameters of the master s-n curve in terms of the mean, 1 , 2 , 3 [21]. statistical basis ferritic and stainless steels aluminum c h c h mean 19930.2 -0.32 3495.13 -0.28 +1σ (upper 68%) 23885.8 4293.19 -1σ (lower 68%) 16629.7 2845.42 +2σ (upper 95%) 28626.5 5273.48 -2σ (lower 95%) 13875.7 2316.48 +3σ (upper 99%) 34308.1 6477.60 -3σ (lower 99%) 11577.9 1885.87 table1: coefficients of master s-n curve. fatigue characteristics domain rough set theory can objectively obtain the key fatigue life influencing factors set of welded joints from the data of fatigue test specimens of welded joints. the fatigue samples with the same value of the key fatigue life influencing factors of the welded joints are distributed in a relatively independent area, which is called fatigue characteristics domain. the calculation l. zou et alii, frattura ed integrità strutturale, 45 (2018) 53-66; doi: 10.3221/igf-esis.45.05 56 of weights is a quantitative description of the extent to which various key influencing factors affect fatigue life. if there are too many key fatigue life influencing factors in the neighborhood rough set attributes reduction results, the number of the key factors could be appropriately reduced by increasing the criticality threshold of the influencing factors so as to reduce the number of the fatigue characteristics domains. the basic process for determine of the fatigue characteristics domains is shown in fig. 2. figure 2: process of determining of the fatigue characteristics domain. among all the steps in the process of determining the fatigue characteristics domain, the neighborhood attributes reduction step is the most important. a forward greedy algorithm is used for attributes reduction as described in [21]. the forward greedy algorithm includes the following 7 steps. step 1: input the fatigue decision system <u, c, d,  > and the attribute importance threshold ε. where u={x1,x2, ...xn} is a nonempty finite set of objects called the universe, c is the condition features set, c={a1,a2,...,an}, d is the set of decision features, and  is the neighborhood parameter( 0 1  ). for the fatigue decision system here, u is the set of all the fatigue specimens, c is the set of the fatigue life influencing factors of the welded joints, d is the fatigue life of the welded joints. step 2: for each condition attribute ia c , compute the neighborhood radius ( ) ( ) /i ia std a = , where std(ai) represents the average value of the attribute ai, and λ is a neighborhood radius calculation parameter, its value is usually between 2~4. step 3: let red → . step 4: for each eia c r d − compute the significance of ai, re re( , re , ) ( ) ( )i d ai dsig a d d d d = − where re re | | ( ) | | d d n d d u  = is attribute dependence, re re{ | ( ) , }i i id dn d x x d x u=   is the lower approximate set, ( ) { , ( , ) }ix x u x xi =    , ( , )x y is a distance function, which satisfies (1) ( , ) 0x y  ; (2) ( , ) 0x y = , if and only if x=y; (3) ( , ) ( , )x y y x =  ; (4) ( , ) ( , ) ( , )x y y z x z +    . step 5: select the attribute ak with the maximum significance value in the conditional attribute sets. step 6: determine whether the significance value of the attribute ak is greater than the given threshold value, if it is true then go to step 4, otherwise go to step 7. step 7: return the reduction results red, exit. begin data preprocessing fatigue decision system of the welded joints neighborhood attributes reduction fatigue characteristics domains key influencing factors of fatigue life fatigue database of the welded joints weights calculation end l. zou et alii, frattura ed integrità strutturale, 45 (2018) 53-66; doi: 10.3221/igf-esis.45.05 57 experiment hree-point bending fatigue experiment is carried out to test the fatigue life of specimens. first of all, material of the specimens and welding technology are introduced, then the three-point bending fatigue test of aluminum alloy t-welded joints is described, after that finite element model of t-joint is established, hot spot stress is calculated and equivalent structural stress transformation is accomplished. master s-n curve for design together with the s-n curves cluster according to the fatigue characteristic domain are fitted. finally, the s-n curve cluster and the master s-n curve are compared and a case study is analyzed. material of the specimens materials of the specimens used in the experiment are 5083 and 5a06 aluminum alloy. these two kinds of aluminum alloy belong to non-heat treatment aluminum alloy material in al-mg alloy. the chemical composition and mechanical properties of the materials are shown in tab. 2 and tab. 3 respectively. the welding material is 5183 aluminum alloy welding wire and the diameter of the welding wire is 1.2 mm. the chemical composition of deposited metal is shown in tab. 4, and the protective gas used is ar. material brand si fe cu mn mg cr zn ti al 5083 measured 0.1 0.25 0.04 0.62 4.68 0.11 0.02 0.10 other standard ≤0.40 ≤0.40 ≤0.10 0.40~1.0 4.0~4.9 0.05~0.25 ≤0.25 ≤0.15 other 5a06 measured 0.15 0.25 0.05 0.62 6.54 / 0.02 0.04 other standard ≤0.40 ≤0.40 ≤0.10 0.50~0.80 5.8~6.8 / ≤0.20 0.02~0.10 other table 2: chemical composition of test materials (%). material brand thickness /mm tensile test bend test hardness hb rm /mpa rp0.2 /mpa a /% bend diameter /mm bend angle /° result 5083 6 350 220 17.5 36 180 no cracks 84.4 345 220 15.5 no cracks 10 320 192 19.5 60 180 no cracks 79.1 320 195 19.0 no cracks 5a06 6 345 177 24.5 36 180 no cracks 84.9 345 184 18.5 no cracks 12 350 166 26.0 72 180 no cracks 83.9 350 168 27.0 no cracks 16 345 154 28.0 96 180 no cracks 83.9 345 154 29.5 no cracks table 3: mechanical properties of test materials. material name si cu mn mg cr zn al 5183 0.4 0.10 0.5~1.0 4.3~5.2 0.05~0.25 0.25 other table 4: chemical composition of 5183 aluminum alloy welding wire. t l. zou et alii, frattura ed integrità strutturale, 45 (2018) 53-66; doi: 10.3221/igf-esis.45.05 58 welding process mig welding method with the austria fronius welding machine is used in the experiment here. the t-welded joints specimen has k type groove, the groove angle is 55°, without leaving blunt edge, the interval is 1-2mm, tests of the tjoints made of 5083 and 5a06 aluminum alloy with different thickness are carried out respectively. x ray flaw detection is carried out after welding, and three-point bending fatigue experiment of 5a06+5083 t-joint and 5a06+5a06 t-joint are made. the relevant welding parameters of the t-joints are shown in tab.5. material thickness /mm groove form layers welding current /a welding voltage /v welding speed /mm/s gas flow /l/min x ray flaw detection rating 5a06+ 5083 16+10 k 1 210 24.2 7.0 20 ⅱ 2 240 24.8 7.45 20 3 220 26.6 4.61 20 4 220 26.6 4.56 20 5a06+ 5a06 35+16 k 1 220 26.6 7.29 20 ⅰ 2 236 24.8 7.78 20 3 220 26.6 5.93 20 4 220 26.6 5.30 20 5 220 27.4 5.30 20 6 220 27.4 4.86 20 table 5: welding parameters of t-welded joints. three-point bending fatigue test of t-joint the experiment is carried out in accordance with jb/t7716-95. size and shape of the specimen in the three-point bending fatigue test are shown in fig. 3. the thickness of the t-welded joint expressed as in fig. 3. in this work, the nominal value of is 8.6mm for the 5a06+5083 t-joint and it is 14.9mm for the 5a06+5a06 t-joint. plg-100 microcomputer controlled high frequency fatigue testing machine is used for the three-point bending fatigue test of t-joint. other technical specifications in the test are: the precision of the static load is ±1%, the average fluctuation of dynamic load is ±1%, the amplitude fluctuation of dynamic load is ±2%. the loading mode of the three-point bending fatigue test is shown in fig. 4. span of fulcrum of the 5a06+5a06 t-joint is 100mm, and that of the 5a06+5083 t-joint is 60 mm. vibration frequency for 5a06+5a06 t-joint is 170hz, and for 5a06+5083 t-joint, it is 160hz. during the test, when the crack size at the weld toe is large enough causing the load not to go up, automatically unload and stop vibration, then record the cycle times. the cyclic stress ratio used in the test is r=0.1, and the designated cycle life is 1×107. ten 5a06+5a06 and ten 5a06+5083 t-joints specimens are used in the three-point bending fatigue test. fatigue life data of the specimens obtained in the test are shown in tab. 6. figure 3: size and shape of the three-point bending fatigue specimen. a a l. zou et alii, frattura ed integrità strutturale, 45 (2018) 53-66; doi: 10.3221/igf-esis.45.05 59 figure 4: loading mode of t-joint specimen. material specimen number load frequency （hz） max mpa cycle numbers when crack （×106） fracture location note 5a06+5083 1-1 163 75.0 0.4521 weld toe 1-2 174 70.0 0.9885 weld toe clip holding problem 1-3 171 80.0 0.2257 weld toe 1-4 151 60.0 ＞10 without fracture 1-5 150 70.0 2.08 weld toe 1-6 159 60.0 3.3749 weld toe 1-7 163 55.0 ＞10 without fracture 1-8 162 60.0 4.3542 weld toe 1-9 159 55.0 ＞10 without fracture 1-10 171 60.1 5.7485 weld toe 5a06+5a06 2-1 158 80.0 0.2729 weld toe 2-2 158 70.0 0.7759 weld toe 2-3 159 40.0 8.7281 weld toe 2-4 164 35 ＞10 without fracture 2-5 170 37.5 ＞10 without fracture weld toe is not fused 2-6 172 40.0 4.3287 weld toe 2-7 172 37.5 9.3184 weld toe there is a scratch 2 mm around the weld toe 2-8 170 35 ＞10 without fracture 2-9 170 37.5 ＞10 without fracture 2-10 170 40.0 6.3685 weld toe table 6: three-point bending fatigue test data of t-joints. where max is computed through eqn. (7)~(9), which is the maximum bending fatigue stress, m is the maximum bending moment,  is the anti-bending section coefficient, f is the load applied, ls is the distance between pivots, b is the width of the specimen, h is the thickness of the specimen. max m   = (7) 4 fls m = (8) l. zou et alii, frattura ed integrità strutturale, 45 (2018) 53-66; doi: 10.3221/igf-esis.45.05 60 2 6 bh  = (9) finite element model of t-joints material properties used in the fe analysis are shown in tab.7 and the finite element type is c3d8r. the size of the mesh refinement will not influence the calculation result of the nodal force based structural stress and the element size is not unified here. according to the size of the specimens of 5a06+5083 t-joint and 5a06+5a06 t-joint, the corresponding finite element model is established as shown in fig. 5 and fig. 6. position of the fulcrum in the test is determined according to jbt 7716-1995. for the 5a06+5083 t-joints, the span of fulcrum is 60 mm, and for the 5a06+5a06 tjoints, the span of fulcrum is 100mm. the loading mode of the 5a06+5083 t-joint is shown in fig. 7. material density (kg/mm3) young modulus (mpa) poisson ratio 5a06 2.7e-9 71000 0.33 5083 2.72e-9 71016 0.33 5183 2.66e-9 70327 0.33 table 7: material properties. figure 5: finite element model of 5a06+5083 t-joint. figure 6: finite element model of 5a06+5a06 t-joint. figure 7: loading position of 5a06+5083 t-joint. structural stress computation abaqus software is used to simulate the 5a06+5083 t-joint and the 5a06+5a06 t-joint so that the nodal force at weld toe is computed. the detailed calculation process of structural stress and equivalent structural stress could be found in reference [1,2]. for example, the nodal force computation result of 5a06+5083 t-joint when 70max mpa = and the nodal force computation result of 5a06+5083 t-joint when 80max mpa = are shown as in fig. 8 and fig. 9. the thickness of the 5a06+5083 t-joint shown as a in fig. 3 is 8.6 mm and it is 14.9 mm for the 5a06+5a06 tjoint. l. zou et alii, frattura ed integrità strutturale, 45 (2018) 53-66; doi: 10.3221/igf-esis.45.05 61 figure 8: stress results of 5a06+5083 t-joint. figure 9: stress results of 5a06+5a06 t-joint. according to the results of nodal force, verity module in the fe-safe software is used for structural stress computation and equivalent structural stress transformation at weld toe. computation results of the 5a06+5083 t-joint and 5a06+5a06 t-joint are obtained as shown in tab.8. material specimen number max mpa structural stress (mpa) equivalent structural stress range (mpa) cycle numbers when crack （×106） 5a06+5083 1-1 75 51.99 81.19 0.4521 1-3 80 55.45 86.61 0.2257 1-5 70 48.52 75.78 2.08 1-7 60 41.59 64.95 4.3542 1-9 60 41.59 64.95 3.7642 1-11 60.1 42.28 66.04 5.7485 5a06+5a06 2-1 80 74.75 129.69 0.2729 2-2 60 56.06 97.27 1.3366 2-3 50 46.72 81.06 2.3358 2-4 40 37.38 64.85 8.7281 2-7 40 37.38 64.85 4.3287 2-11 40 37.38 64.85 6.3685 table 8: computation results of structural stress and equivalent structural stress range. results master s-n curve for fatigue design ccording to the results of three-point bending fatigue test and the data collected from related literatures [22-25], fatigue database of aluminum alloy welded joints is established. some of the data in the database are shown in the following tab.9. there are 76 samples in the database including 7 types of materials, 4 kinds of welding methods, 6 types of plate thickness whose range is from 2.5mm to 16mm, three cases of stress ratio including 0, 0.1 and 0.5, 3 kinds of loading type including tensile(t), four point bending (4b) and three-point bending(3b), 3 kinds of joint type including t-joints, lap joints and butt joints. the fatigue test data of aluminum alloy welded joints is analyzed by using matlab software, and s-n curve is expressed in the form of . on bi-logarithmic coordinate, mean s-n curve of the test samples based on lg lgs a b n= + a l. zou et alii, frattura ed integrità strutturale, 45 (2018) 53-66; doi: 10.3221/igf-esis.45.05 62 equivalent structural stress range is fitted by using least square method as mean1 in fig. 10. mean of the master s-n curve defined in tab. 1 is shown as mean2 in fig. 10. goodness-of-fit statistics of master s-n curve by using eq.ss range is shown in tab.10. for more detailed about the definition of sse, r-square, adjusted r-square and rmse, please see reference [26]. figure 10: master s-n curve based on eq. ss range. material type welding method thickness (mm) ratio loading type joint type equivalent structural stress range(mpa) life cycles 5083 h11 mig 10 0.1 4b tj:p 187.6994 29250 5083 h11 mig 10 0.1 4b tj:p 160.8852 55000 almg4mncr gmaw 2.5 0.1 t lj_ss:p 154.7135 20540 almg4mncr gmaw 2.5 0.1 t lj_ss:p 85.0924 121730 almgsi1 (6082) tig 3 0 t lj_ds:p 294.1392 13250 almgsi1 (6082) tig 3 0 t lj_ds:p 159.7613 85920 np5/6 manual arc 4.76 0 t sj_ds:p 154.9481 90000 hp30 manual arc 4.76 0 t sj_ds:p 116.2111 188000 5a06+5083 mig 10 0.1 3b t 81.19 452100 5a06+5a06 mig 16 0.1 3b t 129.69 272900 table 9: fatigue data of aluminum alloy welded joints. mean value sse 0.4389 r-square 0.7929 adjusted r-square 0.7901 rmse 0.0770 table 10: goodness-of-fit statistics of master s-n curve by using eq.ss range. expression of the mean s-n curve of aluminum alloy welded joint based on the eq.ss range obtained in the experiment is shown as the following eqn.(10). l. zou et alii, frattura ed integrità strutturale, 45 (2018) 53-66; doi: 10.3221/igf-esis.45.05 63 lg 3.144 0.2018 lgs n = − (10) s-n curves cluster based on fatigue characteristic domain neighborhood fatigue decision system is constructed according to the established fatigue database of aluminum alloy welded joints. feature reduction of this neighborhood fatigue decision system is accomplished by using the forward greedy algorithm. the reduction result we get in the experiment is {material type, ratio, equivalent structural stress range}. accordingly, fatigue characteristic domain is divided based on the reduction result and we get the 8 fatigue characteristic domains from s1 to s8. in domain s1, material type is 5083h11 and ratio is 0.1. in domain s2, material type is 5083h11 and ratio is 0.5. in domain s3, material type is almg4mncr and ratio is 0.1. in domain s4, material type is almgsi1(6082) and ratio is 0. in domain s5, material type is np5/6 and ratio is 0. in domain s6, material type is hp30 and ratio is 0. in domain s7, material type is 5a06+5083 and ratio is 0.1. in domain s8, material type is 5a06 and ratio is 0.1. sn curves are fitted in each fatigue characteristic domain, and the s-n curves cluster we get in the experiment are shown in fig. 11. where mean7 and mean8 corresponds to the 5a06+5083 and the 5a06+5a06 t-joints respectively. goodness-offit statistics of mean7 and mean8 are shown in tab. 11. figure 11: s-n curve cluster based on the fatigue characteristic domain. mean7 mean8 sse 0.0012 0.0029 r-square 0.9202 0.9555 adjusted r-square 0.9002 0.9406 rmse 0.0173 0.0311 table 11: goodness-of-fit statistics of mean7-mean8. the s-n curve equation of mean7 and mean8 are shown as the following (11) and (12). (11) (12) from the process of the determination of the fatigue characteristic domains we could see that neighborhood rough set reduction result is the foundation of determination of fatigue characteristic domains. by using neighborhood rough set theory, we don’t depend on any prior knowledge to achieve the classification of the welded joint fatigue samples. each lg 2.426 0.0907 lgs n = − lg 3.302 0.2183lgs n = − l. zou et alii, frattura ed integrità strutturale, 45 (2018) 53-66; doi: 10.3221/igf-esis.45.05 64 class of welded joint fatigue test samples forms a relatively independent sample space, which is called fatigue characteristic domain. s-n curve cluster could be obtained by fitting the s-n curve in each fatigue characteristic domain. the fatigue life of welded joints is evaluated based on the fitted s-n curve cluster, which can further reduce the dispersion degree of fatigue test samples and improve the prediction accuracy of fatigue life of welded joints. it could be seen from fig. 11, under semi-log coordination, fatigue test samples of aluminum alloy welded joints with different types of materials, under different stress ratio distributed in a relatively independent space, which is called the fatigue characteristic domain. s-n curve cluster is obtained by fitting the s-n curve in each fatigue characteristic domain, mean1~mean8. from tab.10 and tab. 11, we could find that sse and rmse of mean7 and mean8 are both smaller than that of the mean, while r-square and adjusted r-square of mean7 and mean8 are both closer to 1 than that of the mean. smaller sse and rmse, bigger r-square and adjusted r-squares indicate that s-n curves fitted based on the characteristic domain have better performance and higher prediction accuracy. case study to further verify the effectiveness of the fatigue life prediction method based on the fatigue characteristics domain, under the same experiment conditions, take one 5a06+5a06 t-joint specimen as example. the three-point bending fatigue test of the welded joint is carried out. fatigue life prediction of the t-joint by using master s-n curve is compared with the prediction value by using s-n curve mean8 based on the fatigue characteristic domain and the actual value obtained in the fatigue test. the number of cycles to failure of the specimen is 249363 according to eqn. (10) and it is 516050 by using eqn. (12). comparison result show that fatigue life prediction value of the t-joint by using s-n curve mean8 is in better agreement with the experiment results than by using the master s-n curve. actual fatigue life of the test case is shown in tab. 12. material type welding method thickness (mm) ratio loading type joint type equivalent structural stress range (mpa) life cycles 5a06+5a06 mig 16 0.1 3b t 113.48 775900 table 12: fatigue test data of aluminum alloy t-welded joints. discussion and conclusion hree-point bending fatigue test of aluminum alloy t-welded joint of 5083 and 5a06 is carried out. the finite element model of t-joints is established, and the equivalent structural stress is calculated. the master s-n curve for fatigue design and the s-n curves cluster in different fatigue characteristic domains are fitted according to the experimental fatigue data and the data collected from the literatures. goodness-of-fit statistics results indicate that the s-n curve cluster has higher prediction accuracy than the master s-n curve. the case study of fatigue life prediction of 5a06+5a06 aluminum alloy t-welded joint specimen show fatigue life prediction by using the s-n curves cluster is in better agreement with the experimental results. neighborhood rough set theory could find the core factors which influence the fatigue life of the aluminum alloy twelded joints from the data itself without any prior experience. fatigue characteristics domain of aluminum alloy twelded joints could be determined based on reduction results of the neighborhood rough set theory. the result of the case study show that the dispersion level of fatigue samples is further reduced and the fatigue life prediction accuracy is further improved. future work will be concentrated on the further validation of the fatigue life prediction method based on the fatigue characteristics domain in the practical engineering. acknowledgements he authors would like to thank all the reviewers for their constructive comments. this research was supported by national science foundation of liaoning province (2015020169) and liaoning provincial education department project(jdl2017025). and the open project program of sichuan provincial key lab of process equipment and control(gk201815). t t l. zou et alii, frattura ed integrità strutturale, 45 (2018) 53-66; doi: 10.3221/igf-esis.45.05 65 references [1] dong, p., hong j. k., osage d. et al. (2013). assessment of asme’s fsrf rules for vessel and piping welds using a new structural stress method, welding in the world, 47, pp. 31-43.doi:10.1007/bf03266376. [2] dong, p. (2001). a structural stress definition and numerical implementation for fatigue analysis of welded joints, international journal of fatigue, 23 865-876. doi:10.1016/s0142-1123(01)00055-x. [3] dong, p. and hong j. k. (2013). the master s-n curve approach to fatigue of piping and vessel welds, welding in the world, 48, pp. 28-36. doi:10.1007/bf03266411. [4] guo, h. g., zhang, j., zhang, y. et al. (2013). structural stress based fatigue analysis method for plane steel gate, advanced materials research, 838-841, pp. 314-318. doi:10.4028/www.scientific.net/amr.838-841.314. [5] hong, j. k. and cox, a. (2017). application of weld fatigue evaluation procedure for considering multi -axial stress states using the battelle structural stress method, proceedings of the sae world congress experience, wcx™ 17: sae world congress experience. doi:10.4271/2017-01-0338. [6] yaghoubshahi, m., alinia, m. m. and milani, a. s. (2017). master s-n curve approach to fatigue prediction of breathing web panels, journal of constructional steel research, 128, pp.789-799. doi: 10.1016/j.jcsr.2016.10.015. [7] jain, a., paepegem, w. v., verpoest, i. and lomov, s. v. (2016). a feasibility study of the master sn curve approach for short fiber reinforced composites, international journal of fatigue, 91, pp. 264-274. doi:10.1016/j.ijfatigue.2016.06.015. [8] dong, p., prager, m. and osage, d. (2013). the design master s-n curve in asme div 2 rewrite and its validations, welding in the world, 51, pp. 53-63. doi: 10.1007/bf03266573. [9] pawlak, z. (1984). rough classification, international journal of man-machine studies, 51, pp. 469-483. doi:10.1006/ijhc.1983.0315. [10] wen, l. y., min, f. and wang, s. y. (2017). a two-stage discretization algorithm based on information entropy, applied intelligence, 47, pp. 1-17. doi:10.1007/s10489-017-0941-0. [11] luo, j., xue, q. and tang, z. w. (2013). research on attribute discretization for combat simulation data, computer simulation, 30, pp. 26-13. (in chinese) [12] feng, t., fan, h. t. and mi, j. s. (2017). uncertainty and reduction of variable precision multigranulation fuzzy rough sets based on three-way decisions, international journal of approximate reasoning, 85, pp. 36-58. doi: 10.1016/j.ijar.2017.03.002. [13] feng, t. and mi, j. s. (2016). variable precision multigranulation decision-theoretic fuzzy rough sets, knowledgebased systems, 91, pp. 93-101. doi:10.1016/j.knosys.2015.10.007. [14] rahimi, a., benini, l. and gupta, r. k. (2017). from variability tolerance to approximate computing in parallel integrated architectures and accelerators, springer, switzerland. [15] kiapour, a., naghizadeh and qomi m. (2017), an approximate tolerance interval for the size-biased poissonlindley random variable, 10, pp. 299-316. doi:10.18869/acadpub.jss.10.2.299. [16] tripathy, b. k. and parida, s. k. (2017). covering based pessimistic multigranular approximate rough equivalences and approximate reasoning, first international conference on sci 2016. doi: 10.1007/978-981-10-5544-7_30. [17] lin, g. and li, j. (2011). a covering-based pessimistic multigranulation rough set. 7th international conference on intelligent computing, pp. 673-680. doi: 10.1007/978-3-642-24553-4_89. [18] zhang, j., li t., da r. and liu d. (2012). neighborhood rough sets for dynamic data mining, international journal of intelligent systems, 27, pp. 317-342. doi:10.1002/int.21523. [19] shakiba, a. and hooshmandasl, m. r. (2015). neighborhood system s -approximation spaces and applications, knowledge & information systems, 49, pp. 749-794. doi:10.1007/s10115-015-0913-9. [20] hu, q., yu d., liu j. and wu c. (2008). neighborhood rough set based heterogeneous feature subset selection, information sciences, 178(18), pp. 3577-3594. doi:10.1016/j.ins.2008.05.024. [21] dong, p., osage, d. a., prager, m. (2002). master s-n curve method for fatigue evaluation of welded components, welding research council bulletin, 47, pp. 41-44. [22] cruz, j. a. m. p. d., costa, j. d. m., borrego, l. f. p. and ferreira j. a. m. (2000). fatigue life prediction in almgsi1 lap joint weldments, international journal of fatigue, 22 , pp. 601-610. doi:10.1016/s01421123(00)00023-2. [23] beretta, s. and sala, g. (2004). a model for fatigue strength of welded lap joints, fatigue & fracture of engineering materials & structures, 28, pp. 257-264. doi:10.1111/j.1460-2695.2004.00849. l. zou et alii, frattura ed integrità strutturale, 45 (2018) 53-66; doi: 10.3221/igf-esis.45.05 66 [24] sidhom, n., laamouri, a., fathallah, r., braham, c. and lieurade, h. p. (2005). fatigue strength improvement of 5083 h11 al-alloy t-welded joints by shot peening: experimental characterization and predictive approach, international journal of fatigue, 27, pp. 729-745. doi:10.1016/j.ijfatigue.2005.02.00. [25] sidhom, n., braham, c. and lieurade, h. p. (2007). fatigue life evaluation of shot peened al-alloys 5083 h11 t-welded joints by experimental and numerical approaches, welding in the world, 51 , pp. 50-57. doi:10.1007/bf03266548. [26] zou, l., yang, x., tan, j. et al. (2017). s-n curve modeling method of aluminum alloy welded joints based on the fatigue characteristics domain, frattura ed integrità strutturale, 40, pp. 137-148. doi:10.3221/igf-esis.40.12. microsoft word numero_41_art_21.docx f.v. antunes et alii, frattura ed integrità strutturale, 41 (2017) 149-156; doi: 10.3221/igf-esis.41.21 149 focused on crack tip fields effect of numerical parameters on plastic ctod f.v. antunes, r. simões, r. branco, p. prates university of coimbra, portugal fernando.ventura@dem.uc.pt, http://orcid.org/0000-0002-0336-4729 www_rafael_inc@hotmail.com ricardo.branco@dem.uc.pt, http://orcid.org/0000-0003-2471-1125 pedro.prates@dem.uc.pt, http:// orcid.org/0000-0001-7650-9362 abstract. fatigue crack growth (fcg) is associated with irreversible and non-linear processes happening at the crack tip. this explains different problems observed in the use of da/dn-k curves, namely the inability to explain stress ratio and load history effects. the replacement of k by nonlinear crack tip parameters, namely the crack tip opening displacement (ctod) is an interesting alternative. however, the determination of ctod, using the finite element method, depends on different numerical parameters, not sufficiently studied so far. the objective here is to study the effect of these parameters on plastic ctod, and therefore on da/dn-ctodp curves. a transient behaviour was found at the beginning of numerical crack propagation which is linked to the formation of residual plastic wake. therefore, a minimum number of crack increments is required to obtain stabilized values. on the other hand, the predicted ctodp decreases with the distance to crack tip. close to the crack tip, sensitivity to the measured values is much higher, but it also exists at remote positions. in addition, the mesh has a relatively low influence on ctodp. finally, the effect of the number of load cycles between crack increments greatly depends on material properties. keywords. crack tip opening displacement (ctod); plastic ctod; finite element method; numerical parameters. citation: antunes, f.v., simões, r., branco, r., prates, p., effect of numerical parameters on plastic ctod, frattura ed integrità strutturale, 41 (2017) 149-156. received: 28.02.2017 accepted: 15.04.2017 published: 01.07.2017 copyright: © 2017 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. introduction he analysis of fatigue crack propagation is usually conducted by relating the crack advance per unit cycle, da/dn, to the stress intensity factor range, k. nevertheless, da/dn-k relations have several limitations, namely: (i) such curves are completely phenomenological, not derived from physics, and the fitting parameters have units with no physical justification; (ii) such curves are only valid in the small-scale yielding range; (iii) and da/dn depends on t f.v. antunes et alii, frattura ed integrità strutturale, 41 (2017) 149-156; doi: 10.3221/igf-esis.41.21 150 other parameters, including the stress ratio and the load history. in order to overcome the difficulties related to the application of k to the analysis of fatigue crack growth, several concepts have been proposed, namely crack closure, partial crack closure, t-stress or the cjp model. in authors’ opinion, the linear elastic k parameter must be replaced by non-linear crack tip parameters, because fatigue crack growth is effectively linked to non-linear processes happening at the crack tip. different parameters have been proposed to quantify crack tip plastic deformation, namely the plastic strain range, the energy dissipated around the crack tip and the crack opening displacement (cod) 1. the crack opening displacement (cod) is a classical parameter in elastic-plastic fracture mechanics, still widely used nowadays [2]. it has also great importance for fatigue analysis. crack tip blunting under maximum load and re-sharpening of the crack-tip under minimum load were used to explain fatigue crack growth under cyclic loading [3]. additionally, it was shown by various authors that there is a relationship between the striation spacing (related to the amplitude of crack tip blunting over a full fatigue cycle) and the crack growth rate [4]. the experimental measurement of cod is usually made remotely to crack tip. in ct specimens an extensometer with blades is used to measure the opening of the specimen at the edge, usually called crack mouth opening displacement (cmod). in the m(t) specimen a pin extensometer is placed at the center of the specimen, fixed in two small holes to avoid sliding. however, optical techniques have been gaining increased relevance. nevertheless, the crack tip opening displacement, ctod, has only been measured numerically or analytically. in the finite element analysis, the displacement of the first node behind the crack tip is generally used as an operational ctod [5]. the crack profiles also express the crack opening displacements, and are interesting to analyze the effect of load history. in a previous work [6], da/dn was related with the range of plastic ctod, ctodp, for the 7050-t6 aluminum alloy. it was found to be a viable and interesting alternative to k, since it is a local parameter that quantifies crack tip plastic deformation, which is expected to control fatigue crack growth. additionally, it includes naturally the effect of crack closure and fatigue threshold. the relation between the numerical ctodp and the experimental da/dn values was used to predict fatigue crack growth rates for other loading conditions. the ctodp was predicted numerically at the first node behind crack tip, at a distance of 8 m from it. however, there are several numerical parameters which may affect by the magnitude of plastic ctod, and therefore of da/dn versus ctodp relations. the objective here is to study the effect of these parameters on ctodp, namely the measurement node behind crack tip, the crack propagation, the finite element mesh, and the number of load cycles between crack increments. numerical model he specimen geometry studied was a middle-tension specimen, having w=60 mm, and a small thickness (t=0.2 mm) in order to obtain a plane stress state. a straight crack was modeled, with an initial size, ao, of 5 mm (ao/w=0.083). since the specimen is symmetric about three orthogonal planes, only 1/8 was simulated considering proper boundary conditions. pure plane strain state was also modeled constraining out-of-plane deformation. the materials considered in this research were the 6016-t4 (ys=124 mpa) and 6082-t6 (ys=238 mpa) aluminum alloys. the mechanical behaviour was represented using an isotropic hardening model described by a voce type equation:     p ys (1 ) nv saty r e (1) combined with a non-linear kinematic hardening model described by a saturation law:               p , 0x satc x σ x x x x 0 (2) in the previous equations, y is the flow stress,  p is the equivalent plastic strain, ys is the initial yield stress, rsat is the saturation stress, n, cx and xsat are material constants, σ is the deviatoric stress tensor, x is the back stress tensor, and  p is the equivalent plastic strain rate. an anisotropic yield criterion, defined by a quadratic function, was considered:                        2 2 2 2 2 2 22 2 2yy zz zz xx xx yy yz zx xyf g h l m n (3) t f.v. antunes et alii, frattura ed integrità strutturale, 41 (2017) 149-156; doi: 10.3221/igf-esis.41.21 151 where xx ,  yy , zz , xy , xz and  yz are the components of the effective stress tensor (  σ σ x ) defined in the orthotropic frame; and f=0.5998, g=0.5862, h=0.4138, l=1.2654, m=1.2654, and n=1.2654 are the coefficients that characterize the material orthotropic behaviour. the material constants, determined for 6016-t4 aluminium alloy, are: ys =124 mpa, rsat=291 mpa, n= 9.5, cx= 146.5 and xsat= 34.90 mpa. for the 6082-t6 aluminium alloy, the material constants obtained were 0 = 238.15 , = 249.37 , n= 0.01, = 244.44, and = 83.18 . the finite element model of the m(t) specimen had a total number of 6639 linear isoparametric elements and 13586 nodes. the finite element mesh was refined near the crack tip, having 88 m2 elements there. only one layer of elements was considered along the thickness. crack propagation was simulated by successive debonding of nodes at minimum load. each crack increment corresponded to one finite element and two load cycles were applied between increments. in each cycle, the crack propagated uniformly over the thickness by releasing both current crack front nodes. a total number of 320 load cycles were applied, corresponding to a total crack propagation of a=(160-1)8 m=1272 m. note that the first two load cycles were applied without crack increment, i.e., at a=5 mm. a wide range of constant amplitude tests was considered. the remote stresses can be obtained by dividing the loads by the area of cross section, i.e., =f/a, being a=300.1 mm2. the numerical simulations were performed with the three-dimensional elasto-plastic finite element program (dd3imp). this software was originally developed to model deep drawing, and was adapted to study picc due to its great competence in the modeling of plastic deformation. the ctod was measured at the first node behind crack tip, i.e., 8 m from crack tip. further details of the numerical procedure may be found in previous publications of the authors 1,6. numerical results effect of measurement point ig. 1a presents typical results of ctod versus load. the ctod was measured after 160 crack propagations (a=1.272 mm), at nodes 1 and 5 behind crack tip. the load is quantified by the remote stress. the first node behind crack tip (node 1) is closed at minimum load (a) and only opens when the load reaches point b, which is the crack opening load. after opening, ctod increases linearly with load, but after point c, there is some deviation from linearity, which indicates the occurrence of plastic deformation. the maximum ctod occurs at point d, which corresponds to the maximum applied load. the fifth node behind crack tip (node 5) has higher levels of ctod as could be expected. the crack opens at point e, at a load lower than observed for node 1. in fact, the crack opens progressively, therefore node 1 is the last node to open. in the region e-f, the crack opens progressively from node 5 to node 1, and only after point e it is totally open. after the opening of node 1 there is a second linear region, but with a slope higher than in region ef, which indicates a lower rigidity. the plastic deformation starts at point g, increasing progressively up to the maximum load (h). after the maximum load, there is also a linear variation of ctod with load decrease. with subsequent load decrease, reversed plastic deformation starts and the crack closes again. matos and nowell 7 studied nodes 1 and 2 behind crack tip. the displacements obtained at node 2 were higher than those obtained with node 1, as could be expected. the same global aspect was observed, however the plastic deformation obtained by them is significantly higher, since the elastic regimes are relatively short. they studied the ti-6al-4v titanium alloy, assuming an elastic perfect plastic behaviour, and used 5 or 10 m elements near the crack tip. however, only the plastic variation of ctod is relevant for the study of fatigue crack propagation, since this phenomenon is linked to irreversible mechanisms. fig. 1b plots the variation of ctodp for different nodes behind crack tip. for each node, there is a progressive increase of plastic ctod up to the maximum load. the maximum ctodp decreases with the departure of measurement point from crack tip. the load corresponding to the onset of plastic deformation can be used to calculate the fatigue threshold. as can be seen in fig. 1b, the same fatigue threshold is obtained at different measurement points behind crack tip. fig. 2 presents the variation of plastic ctod range with distance to crack tip, d. there is a sharp decrease of ctodp immediately behind crack tip. this variation is particularly relevant up to a distance of 100 m behind crack tip. the increase of d reduces the rate of variation, however, a slight decrease is always observed, at least for the range of d values studied. note also that there is a great difference between the first value, obtained at a distance of 8 m behind crack tip (ctodp=0.35 m), and the value measured at a distance of 640 m behind crack tip (ctodp=0.086 m). in other words, and predictably, the numerical predictions of ctodp are quite sensitive to the position of measurement point relatively to the crack tip. f f.v. antunes et alii, frattura ed integrità strutturale, 41 (2017) 149-156; doi: 10.3221/igf-esis.41.21 152 figure 1: (a) ctod versus load. (b) plastic ctod versus load (6082-t6 aa; plane stress). an additional measurement was made at the center of the m(t) specimen, which replicates the experimental measurement made with a pin extensometer. the measurement point has coordinates: x=0, y= 1.75 mm. therefore, it is at a distance of 6.5 mm from the crack tip (x=6.272 mm, y=0). the corresponding values of ctodp are significantly lower than those obtained at a distance less than 1 mm from crack tip. this seems to indicate that sensitivity relatively to the measurement point always decrease with distance d. anyway, the measurement at a quite remote position is able to capture some plastic deformation, which is remarkable. similar trends were obtained for all the other loads and materials studied. the same trend was also obtained for plane strain state. note that the values of ctodp presented are relatively small, lower than 1 m. this is certainly a challenge for the experimental determination of plastic ctod. effect of crack propagation in the numerical simulation of fcg, there is a transient behaviour at the beginning of crack propagation. in fact, some crack propagation is required to stabilize the plastic deformation at the crack tip. fig. 3a presents the variation of ctodp with crack increment, a. the first values are relatively high, which can be explained by the low hardening of the material and by the relatively low values of crack closure. initially the material is virgin in terms of plastic deformation, and, as could be expected, predictions tend to stabilize, as the crack propagates. as can be seen in fig. 3a, a propagation a=552 m, which corresponds to 70 crack increments of 8 m, is enough to stabilize the predictions of ctodp. after stabilization there is a progressive increase of plastic ctod with crack propagation, because since the tests are made at constant load, there is a progressive increase of k at the crack tip. for all load cases studied, 100 crack increments were found enough to stabilize the values, however 160 propagations were considered. the distance for stabilization increases with load range. fig. 3b shows, in the 7050-t6 aluminum alloy, the effect of stress state on ctodp versus a plots. the general behavior is similar for plane stress and plane strain states. in both cases there is an initial decrease, which is more relevant for the plane stress state. the stabilization is relatively fast, compared with that observed in fig. 3a for the aa6082-t6. after stabilization, there is a relatively fast increase of ctodp with a, particularly for plane strain state. the comparison between figs. 3a and 3b shows the importance of material behavior on the crack tip plastic deformation, here quantified by the plastic ctod. the analysis of the ctod versus load plots showed that the 7050-t6 aluminum alloy has no crack closure. effect of finite element mesh the finite element mesh is a main parameter in finite element analyses. fig. 4 shows the effect of the size of crack tip elements on the predictions of plastic ctod. there is a relatively low influence of finite element mesh on plastic ctod. this difference vanishes when the measurement point is relatively far from crack tip. this seems to indicate that the 0.0 0.5 1.0 1.5 2.0 2.5 0 20 40 60 80 100 c t o d [ m ]  [mpa] node 5 node 1 aa e g h f b c d 0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0 20 40 60 80 100 c t o d p [ m ]  [mpa] node 1 node 3 node 5 node 10 (a) (b) f.v. antunes et alii, frattura ed integrità strutturale, 41 (2017) 149-156; doi: 10.3221/igf-esis.41.21 153 predictions are robust relatively to the finite element mesh. anyway, if the ctodp is measured at the first node behind crack tip, the value measured using a mesh of 32 m is lower than that predicted with 8 m, simply because the first node is more distant. figure 2: plastic ctod range versus distance behind crack tip, d (mt specimen; a=6.272 mm; 6082-t6 aa; mesh m8; contact; plane stress; fmin=-40 n, fmax=240 n). figure 3: (a) effect of crack propagation on ctodp (aa6082-t6; node 1; plane stress; fmin=0 n, fmax=360 n). (b) effect of stress state (aa7050-t6 fmin=165 n, fmax=552 n). effect of the number of load cycles between crack increments the number of load cycles between crack increments (nlc) is another major parameter. the application of five load cycles between crack increments is closer to real fatigue crack growth rates than when are used two load cycles. figs. 5a and 5b present results for the 6082-t6 and 6016-t4, respectively. as can be seen, there is a great difference of behaviour, which indicates that material properties play a major role when the number of load cycles is being studied. in the 6016-t4 the increase of the number of load cycles decreases the values of ctodp. 0 0.1 0.2 0.3 0.4 0 200 400 600 800  c t o d p (µ m ) d (µm) a d a x y 0 0.4 0.8 1.2 1.6 0 500 1000 1500  c t o d p (µ m ) a (µm) plane strain plane tress 0 0.5 1 1.5 2 2.5 3 0 400 800 1200  c t o d p (µ m ) a (µm) ctodp ctod load f.v. antunes et alii, frattura ed integrità strutturale, 41 (2017) 149-156; doi: 10.3221/igf-esis.41.21 154 figure 4: effect of finite element mesh (aa6082-t6; plane stress; fmin=0 n, fmax=400 n). impact on da/dn predictions the effect of the measurement node on da/dn predictions was also studied. first, for the aa 7050-t6, two plots of da/dn versus ctodp were obtained using nodes 1 and 12 behind crack tip, at distances of 8 and 96 m, respectively. in addition, experimental values of da/dn in m(t) specimens were obtained, as described by antunes et al. 6. fig. 6a shows linear plots of the da/dn-ctodp values as well as models fitted to the results. node 12 gives lower values of plastic ctod, therefore the curves are on the left side of those obtained with node 1, since da/dn is the same. the models presented in fig. 6a were used to predict the effect of an overload. a numerical analysis was developed for constant amplitude loading with fmin=209 n and fmax=418 n. in a second analysis, an overload fol=627 n was applied after 80 crack increments. the plastic ctod was predicted numerically and was used to obtain the da/dn values using the models defined in fig. 6a. the results are presented in fig. 6b. the overload cycle produces a sudden increase of da/dn, followed by an important decrease to a minimum value, and, then, there is a progressive increase to the constant amplitude curves. the global aspect of these predictions are according experimental results 8. however, in sum, the node behind crack tip used to develop this study is relevant, since different results are obtained, particularly for constant amplitude tests. figure 5: effect of the number of load cycles (a) aa6082-t6; plane stress; fmin=0 n, fmax=360 n). (b) aa6016-t4; plane stress; fmin=0 n, fmax=140 n). 0 0.4 0.8 1.2 1.6 2 0 200 400 600 800  c t o d p (µ m ) d (µm) mesh m8 mesh m16 mesh m32 0 0.4 0.8 1.2 1.6 0 200 400 600 800  c t o d p (µ m ) d (µm) nlc=5 nlc=2 0 0.02 0.04 0.06 0.08 0.1 0 500 1000 1500  c t o d p (µ m ) a (µm) nlc=2 nlc=5 f.v. antunes et alii, frattura ed integrità strutturale, 41 (2017) 149-156; doi: 10.3221/igf-esis.41.21 155 figure 6: (a) effect of the node on da/dn-ctodp curves. (b) prediction of the effect of an overload. (aa7050-t6; plane strain; nlc=2; fmin=209 n, fmax=419 n; fol=627 n). conclusions he numerical predictions of ctodp are quite sensitive to the position of the measurement point relatively to the crack tip. at relatively short distances, there is a fast decrease of ctodp with departure from crack tip. at relatively large distances, there is a smooth but persistent decrease of predictions. anyway, the measurement at quite remote positions is able to capture some plastic deformation, which is remarkable. similar trends were obtained independently of load, material and stress state. the crack propagation, a, is also a major parameter. the first predictions, i.e. without significant propagation, are relatively high, which can be explained by the low hardening of the material, and by the relatively low values of crack closure. the propagation induces a relatively fast decrease of ctodp which is linked to material hardening, followed by stabilization as the residual plastic wake is formed. after stabilization, there is a progressive increase of plastic ctod with crack propagation, because there is a progressive increase of k at the crack tip. a relatively low effect of finite mesh was found, which indicates that the predictions of ctodp are robust relatively to this parameter. anyway, the increase of mesh size increases the distance of the first node behind crack tip and therefore reduces the predictions based on this node. the number of load cycles between crack increments affects the values of ctodp. however, the level of influence considerably depends on the material properties. for the 6016-t4 aluminum alloy, a strong effect was observed; while for the aa6082-t6, the influence was limited. further work is needed to understand the effect of material properties on crack tip plastic deformation, and on crack closure. aknowledgements his research is sponsored by feder funds through the program compete (under project t44950814400019113) and by national funds through fct – portuguese foundation for science and technology, under the project ptdc/ems-pro/1356/2014. one of the authors, p.a. prates, was supported by a grant for scientific research also from the portuguese foundation for science and technology (sfrh/bpd/101465/2014). all supports are gratefully acknowledged. the authors would also like to thank the dd3imp in-house code developer team for providing the code and all the support services. references [1] antunes, f.v., sousa, t., branco, r., correia, l. effect of crack closure on non-linear crack tip parameters, international journal of fatigue, 71 (2015) 53–63. t t 0.0 0.1 0.2 0.3 0.4 0 400 800 1 200 da /d n [ m /c yc le ] a[m] ol_node 1 ol_node 12 ca_node 1 ca_node 12 da/dn= 6.3445 x ctodp da/dn= 1.0608 ctodp 0.0 0.2 0.4 0.6 0.8 1.0 1.2 0.0 0.2 0.4 0.6 0.8 1.0 1.2 d a/ d n [ m /c yc le ] ctodp [m] node 12 node 1 f.v. antunes et alii, frattura ed integrità strutturale, 41 (2017) 149-156; doi: 10.3221/igf-esis.41.21 156 [2] kawabata, t., tagawa, t., sakimoto, t., kayamori, y., ohata, m., yamashita, y., tamura, e., yoshinari, h., aihara, s., minami, f., mimura, h., hagihara, y. proposal for a new ctod calculation formula, engineering fracture mechanics, 159 (2016) 16–34. [3] laird, c., smith, g.c. crack propagation in high stress fatigue, philos. mag., 8 (1962) 847–857. [4] pelloux, r.m. crack extension by alternating shear, engineering fracture mechanics, 1 (1970) 170-174. [5] wu, j., ellyin, f. a study of fatigue crack closure by elastic–plastic finite element for constant-amplitude loading. international journal of fracture, 82 (1996) 43–65. [6] antunes f.v., branco r., prates, p.a., borrego, l., fatigue crack growth modelling based on ctod for the 7050-t6 alloy, fatigue and fracture of engng materials structures, in press, doi: 10.1111/ffe.12582 [7] matos, p.f.p., nowell, d., on the accurate assessment of crack opening and closing stresses in plasticity-induced fatigue crack closure problems, eng. fract. mech., 74 (2007) 1579-1601. [8] borrego, l.p., ferreira, j.m., pinho da cruz, a. j.d.m. costa, evaluation of overload effects on fatigue crack growth and closure, eng. fract. mech., 70 (2003) 1379–1397. << /ascii85encodepages false /allowtransparency false /autopositionepsfiles true /autorotatepages /none /binding /left /calgrayprofile (dot gain 20%) /calrgbprofile (srgb iec61966-2.1) /calcmykprofile (u.s. web coated \050swop\051 v2) /srgbprofile (srgb iec61966-2.1) /cannotembedfontpolicy /error /compatibilitylevel 1.4 /compressobjects /tags /compresspages true /convertimagestoindexed true /passthroughjpegimages true /createjobticket false /defaultrenderingintent /default /detectblends true /detectcurves 0.0000 /colorconversionstrategy /cmyk /dothumbnails false /embedallfonts true /embedopentype false /parseiccprofilesincomments true /embedjoboptions true /dscreportinglevel 0 /emitdscwarnings false /endpage -1 /imagememory 1048576 /lockdistillerparams false /maxsubsetpct 100 /optimize true /opm 1 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can be opened with acrobat and adobe reader 5.0 and later.) >> /namespace [ (adobe) (common) (1.0) ] /othernamespaces [ << /asreaderspreads false /cropimagestoframes true /errorcontrol /warnandcontinue /flattenerignorespreadoverrides false /includeguidesgrids false /includenonprinting false /includeslug false /namespace [ (adobe) (indesign) (4.0) ] /omitplacedbitmaps false /omitplacedeps false /omitplacedpdf false /simulateoverprint /legacy >> << /addbleedmarks false /addcolorbars false /addcropmarks false /addpageinfo false /addregmarks false /convertcolors /converttocmyk /destinationprofilename () /destinationprofileselector /documentcmyk /downsample16bitimages true /flattenerpreset << /presetselector /mediumresolution >> /formelements false /generatestructure false /includebookmarks false /includehyperlinks false /includeinteractive false /includelayers false /includeprofiles false /multimediahandling /useobjectsettings /namespace [ (adobe) (creativesuite) (2.0) ] /pdfxoutputintentprofileselector /documentcmyk /preserveediting true /untaggedcmykhandling /leaveuntagged /untaggedrgbhandling /usedocumentprofile /usedocumentbleed false >> ] >> setdistillerparams << /hwresolution [2400 2400] /pagesize [612.000 792.000] >> setpagedevice microsoft word numero_45_art_16 o. reut et alii, frattura ed integrità strutturale, 45 (2018) 183-190; doi: 10.3221/igf-esis.45.16 183 the discontinuous solutions of lame’s equations for a conical defect o. reut, n. vaysfeld odessa mechnikov university, institute of mathematics, economics and mechanics, ukraine reut@onu.edu.ua, vaysfeld@onu.edu.ua abstract. in this article the discontinuous solutions of lame’s equations are constructed for the case of a conical defect. under a defect one considers a part of a surface (mathematical cut on the surface) when passing through which function and its normal derivative have discontinuities of continuity of the first kind. a discontinuous solution of a certain differential equation in the partial derivatives is a solution that satisfies this equation throughout the region of determining an unknown function, with the exception of the defect points. to construct such a solution the method of integral transformations is used with a generalized scheme. here this approach is applied to construct the discontinuous solution of helmholtz’s equation for a conical defect. on the base of it the discontinuous solutions of lame’s equations are derived for a case of steady state loading of a medium. keywords. conical defect; helmholtz’s equation; wave potential; integral transformation; lame’s equations. citation: reut, o., vaysfeld, n., the discontinuous solutions of lame’s equations for a conical defect, frattura ed integrità strutturale, 45 (2018) 183-190. received: 15.05.2018 accepted: 24.06.2018 published: 01.07.2018 copyright: © 2018 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. introduction he urgency of the problem of elastic waves diffraction is due to the need to take into account the presence of heterogeneities during the development of new composite materials, geophysical and seismological studies. these processes take place under dynamic loads of different nature. in order to facilitate engineering design, preliminary calculations are required on the basis of appropriate mathematical models that provide an opportunity to analyze the effects of such dynamic stress concentrators as inclusions, cavities, cracks, holes, etc. on the other hand, the problems of elastic wave diffraction are one of the classical problems of the mechanics of deformable bodies. the construction of their analytical solutions, analysis of wave fields in the vicinity of t defects constitute a broad class of problems whose decompositions require the involvement of complex mathematical apparatus. the development of this mathematical apparatus has been carried out by many scientists [1-14]. one of the powerful methods for solving problems of wave diffraction on defects of various forms is the method of discontinuous solutions. this method was created by g. ya. popov [15]. he gave a definition of a discontinuous solution of the differential equation in partial derivatives, namely: a discontinuous solution of a certain differential equation in partial derivatives is such a solution that satisfies this equation throughout the region of determining an unknown function, with the exception of the defect points, in the transition through which an unknown function has discontinuities with jumps of the unknown function itself and its normal derivative. t http://www.gruppofrattura.it/va/45/35.mp4 o. reut et alii, frattura ed integrità strutturale, 45 (2018) 183-190; doi: 10.3221/igf-esis.45.16 184 the jumps of the function and its normal derivative are given by the conditions of the original problem, both are established under certain conditions of the problem solving. under a defect one must understand a part of a surface (mathematical cut on the surface) when passing through which function and its normal derivative have discontinuities of continuity of the first kind. g.ya. popov proposed a method for constructing such solutions for defects and bodies, described in the orthogonal curvilinear coordinate systems. it is essential, corresponding to this method, to construct a discontinuous solution of a helmholtz’s equation (or the laplace equation in a static statement of a problem) and to further construct discontinuous solutions of the equations of motion (or equilibrium equations respectively). it is possible to realize this thanks to formulas connecting the wave potentials with the displacements and stress. in [15] the solutions of elasticity static problems were constructed for linear, circular, spherical and cylindrical defects. the method of discontinuous solutions was extended to the problem of wave diffraction in papers [16-18]. in [19] the method of discontinuous solutions is extended to the defect of an arbitrary form. the novelty of the proposed paper is in the construction of the discontinuous solutions of lame’s equations for a conical defect in the case of a steady state loading. as a first stage of the solution deriving, a discontinuous solution of the helmholtz equation for a case of a conical shape defect is constructed. the special scheme is proposed to find the unknown jumps of the displacements and stress. the derived formulae of lame’s equations discontinuous solutions can be applied for the solving of the boundary problems of elasticity for the different types of the conical defects, such as a crack, a thin inclusion adherent with a medium, partially adherent inclusion etc. for the case of an axisymmetric problem for a conical defect all obtained formulae are substantially simplified. statement of the problem et’s consider an acoustic medium containing a conical defect whose surface is described in a spherical coordinate system by the correspondences: , 0 ,a r b            (1) the steady-state oscillations of the media are described by the helmholtz equation        2 2 2' , , ' , , , , 0 i r r r r r c                   (2) here    , , , , , i tr t r e       , c is the wave’s speed in the acoustic medium. here it was agreed to disregard the designation "tilda" over a letter and to introduce the following new notations 2 2 2 2 i q c c         , where  is the frequency of the incident wave,     2 2 sin , , , , sin sin r r               , (here the point over the letter denotes a derivative with regard to a second variable). the aim is the deriving of the discontinuous solution of the eqn. (2) for the defect (1) located in acoustic medium. deriving of the discontinuous solution in the transformation domain he integral fourier transformation is applied to the equation with regard of variable     , , ,inn r e r d            (3) in the transformation’s domain (3) the eqn. (2) takes a form l t o. reut et alii, frattura ed integrità strutturale, 45 (2018) 183-190; doi: 10.3221/igf-esis.45.16 185       2 2 2' , ' , , 0n n n nr r r r q r           2 2 2 sin , , sin sin n n n rn r            (4) a change of variables x r q  was done in the eqn. (4). it was rewritten with the new variables in the following form 2 2' , ' , , 0n n n n x x x x x q q q                              (5) the kantorovich-lebedev integral transformation with regard to variable x is applied to the equality (5)     0 ,in n k x x dx qx                (6) in the transformations (6) domain the eqn. (5) can be reformulated as    2 1 0 4 n n n              (7) there is no possibility to apply the integral legendre transformation by the usual scheme to the eqn. (7) because there are discontinuities of the function  n  and its derivative when   . the jumps have the following form 0 0 , , , 0, , 0, , , , , , , x x x q q q x x q qx q                                                                     (8) the integral legendre’s transformation is applied to the eqn. (7) by the generalized scheme [15]     0 cos sinnn k n kp d          (9) it leads to the linear algebraic equation in the transformations (3), (6), (9) domain           22 cos1 / 2 sin cos n n k n k n k n dp k p d                             we will accept the designation    cos cosn nk kdp dp d d         in future. here o. reut et alii, frattura ed integrità strutturale, 45 (2018) 183-190; doi: 10.3221/igf-esis.45.16 186       0 , , , , n i in n x qk x e d dx x x q                                             finally, we derive the expression for the function’s transformation n k through the transformations of its jump and the jump of its normal derivative           22 sin cos cos 1/ 2 n n n k n k n k p p t k               (10) deriving the final formula he inverse legendre’s transformation is applied to (10)    cosnn kn k n k k n p         (11) where      1/ 2 ! ! kn k k n k n      then the inverse kantorovich-lebedev transformation is applied to the obtained expression       0 , in n k xx sh d q x                bearing in mind that the expressions for the transformations of the wave potential jumps and its normal derivative have the following form       0 , , n n i n n q k d q                                         in the fourier’s transformation domain, the wave potential has the following form               22 0 0 , sin cos 1/ 2 cos , cos , n i i n kn k k n n n k n k n sh k x kx p q xk p p d d q q                                                      the integral in the last formula is known [ 2.16.52(11), 20] t o. reut et alii, frattura ed integrità strutturale, 45 (2018) 183-190; doi: 10.3221/igf-esis.45.16 187         1 2 2 12 0 ( ) ( ),2 ( , ) , 1/ 2 2 ( ) ( ),1/ 2 i i k j q h xq xsh k x k i j x d k x j xq h q xk                                the discontinuous solution can be simplified 0 ( , ; , ) , sin ( , ( , ; , ) , ) , ,nn n n n g xx g x d x rq q q q q                                          (12) here    ( , ; , ) cos cos ( , )n nn kn k k k k n g x p p j x           . it was stated that the limit values of the wave potential near the branches of the defect (1) have the form 0 1 , 0 , 2 ( , ; , ) sin ( , , ( , ; , ) ) , , 0 0 n n n n n n x x q q g x g x d x rq q q q                                                           these formulas are derived by the use of the known facts of potential theory such as a discontinuity of a double layer’s potential and normal derivative of plane layer potential. the application of inverse integral fourier’s transformation to formula (12) completes the construction of discontinuous solution of helmholtz’s equation. construction of the discontinuous solutions of lame’s equations ccordingly to the discontinuous solution method [15] to derive the discontinuous solutions of lame’s equations, one must find the formulae expressing the jumps of the wave potentials and their derivatives through the jumps of the displacements and stress. the wave potential functions    , , , , , , 1, 2jr r j      satisfy the helmholtz’s eqns. (2) with the velocities 1 2,c c correspondently. well known formulas in the fourier’s transformation domain (3) are written in the form [11]: 1 2( , ) ( , ) ( , )n n n nu r r r r        , 1 12 1( , ) ( ( , ) ( ( , )) ) sin ( ) ( , )n n n nv r r r r r in r              , (13) 1 2 1( , ) ( sin ) ( ( , ) ( ( , )) ) ( , )n n n nw r in r r r r r            , here ( , ) ( , ), ( , ) ( , ), ( , ) ( , )n n nr n n nu r u r u r v r u r w r         . the stress transformations are expressed through the displacements and hence through the wave potentials as well. to use the discontinuous solution of the helmholtz’s eqn. (2) derived earlier, the jumps’ transformations of the wave functions    , , , , 1, 2n jnr r j    should be expressed through the jumps of the stress and displacements. this procedure is enough complicated, so here its scheme is shown. one must use such equalities 22 2 ( , ) ( , ),n n c nr l r     1( , ) ( , ),n n c nr l r     2 2 2 2( )cl y r y r c    . with regard of these formulas, it is possible to express the jumps of the mechanical characteristic through the jumps of the wave potentials: a o. reut et alii, frattura ed integrità strutturale, 45 (2018) 183-190; doi: 10.3221/igf-esis.45.16 188 2 1 2( , ) ( , ) ( , )n n c nu r r r l r       1 1 2 1( , ) ( ( , ) ( ( , ) ) ) sin ( , )n n n nv r r r r r in r              1 2 1( , ) ( sin ) ( ( , ) ( ( , ) ) ) ( , )n n n nw r in r r r r r            (14) 2 1 *( , ) 2 ( ( , ) ( ( , ) ( , ) )),n n n nr g q r r v r u r           1 1( , ) ( ( ( , ) ) ( , ) ),rn n nr g r r v r r u r        ( , ) ( ( , ) ( , ) cos ( , ) )n n n nr r g w r ctgw w r in ec v r         in the formulae (14) the jump ( , )nv r   should be excluded. the volume expansion’s transformation ( , )n r  is expressed through the displacements transformations to realize it. it is proved that the equality 2( , ) ( , )n nr q r    is true also. as a result, the jump ( , )nv r   is derived 2 1 2 1( , ) ( , ) ( ( , ) ) ( , ) sin ( , )n n n n nv r rq r r r u r ctg v r in w r              hence, from the formula for the normal stress jump (14), the jump of the scalar wave potential is expressed only through the given jumps of the stress and displacements 1 1 1 1 0 ( , ) ( 2 ) ( , ) ( , ) ( ( , ) ) ( sin ) ( , )n n n n nr g r r ctg v r r r u r in r w r                 the formula is constructed for the jump 1 ( , )n r  where it is expressed through the jumps of the displacements and stress only 2 1 1 1 ( , ) ( , ) 2 (sin ) ( , ) 2 ( , )c n n n nl r g r r in v r ctg w r            . (15) as it seen this formula is the differential equation with regard of unknown jump 1 ( , )n r  . to solve this equation a change of variable x r q  was done for eqn. (15) and integral transformation (6) was applied to both part of the equation. the unknown jump was written in the transformation’ domain   11 2 0 0 1 0 ( , ) ( , )1 ( ) ( ) 2 ( ) 1 4 ( , ) 2 (sin ) ( ) n n n i i n i w rs gs k d ctg k d v r in k d                                              (16) the inverse integral kantorovich-lebedev transformation is applied to the obtained expression (16), and final solution is derived in the form o. reut et alii, frattura ed integrità strutturale, 45 (2018) 183-190; doi: 10.3221/igf-esis.45.16 189 1 2 2 1 2 0 ( , ) ( , ) 2 ( , ) 2 (sin ) ( , ) ( , ) , n n n n k s r s s ctg w r in v r j rs s d s c g                                   (17) the jump of wave function 2 ( , )n r  is found by the analogical procedure 2 0 ( , ) ( ( , ) ( , ) ( , )n n n kr s r u r j rs s d            (18) the jumps of the wave functions derivatives are constructed using this scheme. for example, the expression for the derivative of wave potential jump 2 ( , )n r  has the form   12 1 0 ( , ) ( ( , ) sin ( , ) ) r n n nr r v in d             (19) as a result, all transformations of the wave functions and their derivatives jumps are expressed through the transformations of stress and displacements jumps. there are substituted to the corresponded formulae of the helmholtz’s equation discontinuous solution and inversion of the integrals transformations is done. the following substitution of these formulae to the expressions (13) finalizes the deriving of the discontinuous solutions of lame’s equations in a case of steady state oscillations for the defect (1). conclusions 1. the discontinuous solution of helmholtz’s equation is derived for a conical defect. 2. to construct the discontinuous solutions of lame’s equations for a conical defect one must express the jumps of wave functions and their derivatives through the displacements and stress jumps. the substitution of these formulas to the discontinuous solution of helmholtz’s equation leads to the discontinuous solutions of the lame’s equations. 3. in the case when a defect is a crack, the jumps of the stress are equal to zero, when a defect is a thin shell adherent to a medium the jumps of the displacements are equal to zero. so, the derived formulae can be used for the different types of the conical defects situated in a medium. 4. the derived formulae will be significantly simplified when the axisymmetrical problem is solved. in this case parameter n should be equal to zero in all final expressions. acknowledgments he authors are grateful to simon peter dyke for his attention and great help in the editing of the manuscript’s text. references [1] babeshko, v. a., babeshko, o. m. and evdokimova, o. v. (2010). on the method of block element, mechanics of solids, 45, pp. 437-444. doi: 10.3103/s0025654410030143. [2] grinchenko, v. t. and meleshko, v. v. (1981). harmonical oscillations and waves in elastic bodies (in russian), naukova dumka, kyiv. t o. reut et alii, frattura ed integrità strutturale, 45 (2018) 183-190; doi: 10.3221/igf-esis.45.16 190 [3] guz, a. n., kubenko, v. d. and cherevko, m. a. (1978). diffraction of elastic waves(in russian), naukova dumka, kyiv. [4] mykhas’kiv, v., stankevych, v., zhbadynskyi, i. and zhang, ch. (2009). 3-d dynamic interaction between a pennyshaped crack and a thin interlayer joining two elastic half-spaces, international journal of fracture, 159(2), pp. 137-149. [5] slepyan, l. i., mechanics of cracks (in russian), sudostroenie, leningrad (1990). [6] mnev, e. n. and perzev, a. k. (1970). hydroelasticity of shells (in russian), sudostroenie, leningrad. [7] vilde, m. v., kaplunov, yu. d. and kossovich, l. yu. (2010). boundary and interfacial resonance effects in elasticity bodies (in russian), fizmatgiz, moscow. [8] kit, g. s. and khay, m. v. (1989). method of potentials in three-dimensional problems for thermoelasticity bodies with cracks (in russian), naukova dumka, kyiv. [9] sladek, v. and sladek, j. (1984). transient elastodynamic three-dimensional problems in cracked bodies/applied mathematical modelling, 8(1), pp. 2-10. [10] guz, a.n., guz, i.a., men’shikov, a.v. and men’shikov, v.a. (2011). stress-intensity factors for materials with interface cracks under harmonic loading, int appl mech, 46, pp. 1093. doi: 10.1007/s10778-011-0401-1. [11] savruk, m. p., osiv, p. n. and prokopchuk, i. v. (1989). numerical analysis in plane problems of the crack’s theory (in russian), naukova dumka, kyiv. [12] di cocco, v. and iacoviello, f. (2017). ductile cast irons: microstructure influence on the damaging micromechanisms in overloaded fatigue cracks, engineering failure analysis, 82, pp. 340-349. [13] toribio, j., gonzàles, b. and matos, j.c. (2017). crack tip field in circumferentially-cracked round bar (ccrb) in tension affected by loss of axial symmetry, frattura ed integrità strutturale, 41, pp. 139-142. doi: 10.3221/igf-esis.41.19. [14] peron, m., razavi, s.m.j., berto, f. and torgersen, j. (2017). notch stress intensity factors under mixed mode loadings: an overview of recent advanced methods for rapid calculation, frattura ed integrità strutturale, 42, pp. 196-204. doi: 10.3221/igf-esis.42.21. [15] popov, g.ya. (1982). the elastic stress' concentration around dies, cuts, thin inclusions and reinforcements (in russian), nauka, moskow. [16] popov, v. g., (1995). the vertical oscillations of a boundary hard inclusion under harmonic loading, applied mechanics, 76(31), pp. 46-54. [17] vaisfel’d, n.d., (2005). time-dependent problems of the concentration of elastic stresses near a conical defect, journal of applied mathematics and mechanics, 69(3), pp. 427-437. [18] vaisfel’d, n.d. and popov, g.ya., (2001). the stress concentration around a semi-infinite cylindrical crack during the shock loading of an elastic medium by a centre of rotation, journal of applied mathematics and mechanics, 65(3), pp. 509-518. [19] reut, v. v., fesenko, h. o., vaysfel’d, n. and zhuravlova, z., (2017). orthogonal polynomials method and its generalization at some new problems of fracture mechanics/ june 2017, conference 14-th intern. conference on fracture (icf 14), rhodes, greece. 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can be opened with acrobat and adobe reader 5.0 and later.) >> /namespace [ (adobe) (common) (1.0) ] /othernamespaces [ << /asreaderspreads false /cropimagestoframes true /errorcontrol /warnandcontinue /flattenerignorespreadoverrides false /includeguidesgrids false /includenonprinting false /includeslug false /namespace [ (adobe) (indesign) (4.0) ] /omitplacedbitmaps false /omitplacedeps false /omitplacedpdf false /simulateoverprint /legacy >> << /addbleedmarks false /addcolorbars false /addcropmarks false /addpageinfo false /addregmarks false /convertcolors /converttocmyk /destinationprofilename () /destinationprofileselector /documentcmyk /downsample16bitimages true /flattenerpreset << /presetselector /mediumresolution >> /formelements false /generatestructure false /includebookmarks false /includehyperlinks false /includeinteractive false /includelayers false /includeprofiles false /multimediahandling /useobjectsettings /namespace [ (adobe) (creativesuite) (2.0) ] /pdfxoutputintentprofileselector /documentcmyk /preserveediting true /untaggedcmykhandling /leaveuntagged /untaggedrgbhandling /usedocumentprofile /usedocumentbleed false >> ] >> setdistillerparams << /hwresolution [2400 2400] /pagesize [612.000 792.000] >> setpagedevice microsoft word numero 13 articolo 3 a. finelli et alii, frattura ed integrità strutturale, 13 (2010) 24-30; doi: 10.3221/igf-esis.13.03 24 analysis of the influence of the anisotropy induced by cold rolling on duplex and super-austenitic stainless steels angelo finelli, martino labanti enea unità tecnica tecnologie dei materiali faenza riassunto. questo articolo contiene i risultati della caratterizzazione meccanica eseguita su due tipi di acciaio inossidabile (duplex 6%ni, 22%cr e super-austenitico 31%ni, 28%cr) utilizzati per la fabbricazione di tubi impiegati nella produzione di idrocarburi. l’attività è stata svolta con l’obiettivo primario di valutare l’effetto dell’anisotropia provocata sul manufatto dalla laminazione a freddo, considerando le caratteristiche meccaniche degli acciai misurate nelle tre direzioni principali. considerata la limitata sezione del manufatto, il metodo ed i campioni utilizzati per le prove non fanno riferimento a nessuna normativa. la procedura messa a punto ha previsto infatti l’utilizzo di estensimetri elettrici a resistenza, incollati sui campioni, per la misura della deformazione durante le prove. abstract. this report contains the results obtained from the mechanical characterization tests carried out on two different stainless steel (duplex 6%ni, 22%cr and super-austenitic 31%ni, 28%cr) used for the manufacturing of pipes which are employed in the oil production. the activity has been performed in order to evaluate the effects of anisotropy, induced by cold rolling, on the mechanical characteristics of the investigated steels, measured in the three main directions. considering the small size of the component, the method and the specimens used for the tests were not the standard one. the procedure carried out provided the strain measurement of the specimen during testing by means of resistive strain gages, bonded on the specimens. keywords. anisotropy; cold rolling; mechanical properties; strain gages. test aim he main goal of this activity is the evaluation the effects of the cold rolling process on the mechanical properties of two different stainless steels: a duplex stainless steel and a superaustenitic stainless steels. the main problem to be considered was the reduced specimens dimensions, for all the investigated testing directions: considering that no standards could be followed, it was necessary to optimize a customized testing procedure. t http://www.gruppofrattura.it http://dx.medra.org/10.3221/igf-esis.13.03&auth=true a. finelli et alii, frattura ed integrità strutturale, 13 (2010) 24-30; doi: 10.3221/igf-esis.13.03 25 investigated materials nvestigated steel are largely used in petrochemical industry (e.g., pipes manufacturing). the first investigated steel is a duplex stainless steel (chemical composition in tab 1). this tubular shaped material, sized 115x9 mm, has been subjected to the following processing cycle: hot extrusion. water cooling. annealing at 1050° c. water cooling. in order to obtain the final pipe dimensions (88.9x6.5 mm), a cold rolling treatment was performed. mat. c mn si s p ni cr mo cu v al n a1 0.038 1.37 0.40 0.001 0.013 5.54 21.93 3.00 0.035 0.040 0.045 0.140 a1l 0.038 1.37 0.40 0.001 0.013 5.54 21.93 3.00 0.035 0.040 0.045 0.140 5 0.018 1.81 1.01 0.002 0.017 32.60 26.47 3.55 1.01 0.098 4l 0.021 1.28 0.47 0.003 0.018 31.15 26.80 3.34 1.28 0.086 0.047 0.058 table 1: investigated steels chemical compositions. fig 1 and 2 show duplex stainless steel microstructure, considering longitudinal, transversal and radial sections, respectively before and after the cold rolling treatment (respectively named as “a1” and “a1l”). figure 1a: “a1” steel microstructure longitudinal section (x 200) figure 1b: “a1” steel microstructure – transversal section (x 200) figure 1c: “a1” steel microstructure – radial section (x 200) figure 2a: “a1l” steel microstructure longitudinal section (x 200). figure 2b: “a1l” steel microstructure transversal section (x 200). figure 2c: “a1l” steel microstructure – radial section (x 200). the second investigated steel is a super-austenitic stainless steel (chemical composition in tab 1). this tubular-shaped material, sized 121x8.25 mm, has been subjected to the following processing cycle: hot extrusion. water cooling. a stainless steel with a similar chemical composition was also investigated after a cold rolling treatment, obtaining a tubular-shaped material sized 88.9x6.5 mm). i http://www.gruppofrattura.it http://dx.medra.org/10.3221/igf-esis.13.03&auth=true a. finelli et alii, frattura ed integrità strutturale, 13 (2010) 24-30; doi: 10.3221/igf-esis.13.03 26 fig. 3 and 4 show super-austenitic stainless steel microstructure, considering longitudinal, transversal and radial sections, respectively before and after the cold rolling treatment (respectively named as “5” and “4l”). figure 3a: “5” steel microstructure longitudinal section (x 200). figure 3b: “5” steel microstructure transversal section (x 200). figure 3c: “5” steel microstructure radial section (x 200). figure 4a: “4l” steel microstructure longitudinal section (x 200). figure 4b: “4l” steel microstructure transversal section (x 200). figure 4c: “4l” steel microstructure – radial section (x 200). experimental procedure ue to pipes thickness, sampling according to standards requirements was impossible for the investigating directions t and r (longitudinal l, transversal t, radial r). it was only possible to manufacture l direction specimens according to the astm e8 standard (fig. 5) and they were named as sl specimens, for all the four investigated steels. figure 5: standard specimen (s) for tensile test. considering l and t directions, 5 mm gage length tensile specimens (named as “b”, fig. 6) were obtained for all the investigated materials. depending on the sampling direction, these specimens were named as “bl” or “bt”. d http://www.gruppofrattura.it http://dx.medra.org/10.3221/igf-esis.13.03&auth=true a. finelli et alii, frattura ed integrità strutturale, 13 (2010) 24-30; doi: 10.3221/igf-esis.13.03 27 figure 6: specimen short gage length (b) for tensile test. finally, for all the investigated directions (l, t and r) and the two cold rolled steels, compression specimens were obtained (fig. 7): they were named as “cl”, “ct” or “cr” depending on the sampling direction. figure 7: specimen for compression test (c). table 2 shows the test matrix. on the basis of the test results obtained in l direction using both standard specimens (s), short gage length specimens (b) and compression specimens (b), it is possible to evaluate the evolution of the mechanical properties in the other two directions, where it is impossible to obtain standard specimens. table 2: test matrix. figure 8: specimen (b) during tensile test. specimen steel standard (s) short gage length (b) compression (c) l l t l t r a1    a1l       5    4l       http://www.gruppofrattura.it http://dx.medra.org/10.3221/igf-esis.13.03&auth=true a. finelli et alii, frattura ed integrità strutturale, 13 (2010) 24-30; doi: 10.3221/igf-esis.13.03 28 both specimens “b” and “c” did not allow to use conventional extensometers; strain measurements were performed by means of resistive strain gages: these strain gages were able to detect strains up to 5% max. (fig. 8). all the tests were carried out in compliance with the astm a 370 standards according to the methods reported in astm e 8 and e 9 [1, 2]. at least, three tests were performed for all the investigated conditions. experimental results onsidering standard specimens (s), the following parameters were considered: ‐ yield strength at 0.2% (σs(0.2%)). ‐ ultimate tensile strength (σu). ‐ elongation measured on a base of 25 mm (a% 25 mm). mean values are shown in tab. 3. σs(0.2%) [mpa] σm [mpa] a(25) [%] a1sl 477 764 49 a1lsl 1046 1110 19 5sl 339 683 59 4lsl 833 925 19 table 3: tensile test average results of standard specimen (s) the same parameters were also considered with the "short gage length" (b) specimens, with a difference in the elongation measurement (a base of 12.5 mm instead of 25 mm) results are summarized in tab. 4. σs(0.2%) [mpa] σm [mpa] a(12.5) [%] a1bl 491 771 27 a1bt 507 772 25 a1lbl 971 1063 16 a1lbt 908 1111 13 5bl 308 669 36 5bt 337 696 34 4lbl 830 915 16 4lbt 749 916 16 table 4: tensile test average results of short gage length specimen (b). considering compression specimens (c), it was only possible to measure the yield strength value at 0.2%, since both the specimen geometry and the material ductility prevent the other parameters from being detected. mean values are shown in tab. 5. σs(0.2%) [mpa] a1lcl 860 a1lct 1081 a1lcr 1065 4lcl 714 4lct 938 4lcr 866 table 5: compression test average results (c). tab. 6 summarizes all the experimental results for all the investigated steels and all the considered specimens. c http://www.gruppofrattura.it http://dx.medra.org/10.3221/igf-esis.13.03&auth=true a. finelli et alii, frattura ed integrità strutturale, 13 (2010) 24-30; doi: 10.3221/igf-esis.13.03 29 specimen steel standard (s) short gage (b) compression (c) l l t l t r a1 477 491 508 σs(0.2%) [mpa] 765 770 770 σm [mpa] 49 27 25 a [%] a1l 1045 970 900 850 1100 1050 σs(0.2%) [mpa] 1110 1060 1110 σm [mpa] 19 16 14 a [%] 5 340 310 335 σs(0.2%) [mpa] 684 670 695 σm [mpa] 59 36 34 a [%] 4l 850 830 750 720 930 860 σs(0.2%) [mpa] 928 915 920 σm [mpa] 20 16 16 a [%] table 6: tests results. results analysis n the basis of microstructure analysis and of mechanical tests, the following remarks could be summarized: ‐ in the longitudinal section of material 5 (see fig. 4a), typical rolling texture is shown; it implies that the steel annealing was not complete. as a consequence, a slight difference between the results of specimens "5bl" and "5bt" (tab. 4) can be noticed; anyway, differences are not so evident to affect test results. ‐ considering both the sampling direction and the specimen geometry, tensile resistance of the heat-treated steels is therefore practically identical as regards. as a consequence, it is possible to suppose that such behaviour is also valid for the radial direction. the only difference is noticed in the measure of elongation between specimens "s" and "b" (tab. 6). this difference, which is about 100%, comes from the fact that the gage length of the two specimens is really different, hence the data cannot be compared. this measure is anyway appropriate between specimens with "b" geometry. ‐ the results of the tensile tests carried out on the cold worked materials indicate an increase by about 100% in the yield strength lengthwise and about 80% crosswise as regards the duplex stainless steel, as well as 150% lengthwise and 130% crosswise as regards the super-austenitic steel. on the contrary, the ultimate tensile strength values increase of about 40% and 35%, respectively. elongation values decrease of about 60 and 66% respectively, considering measurements performed with specimens "s" as a reference. ‐ compression tests results are characterized by a similar increase. ‐ the properties obtained from the specimens sampled in the radial direction are almost equal to the mean value, whilst the values obtained from the specimens sampled lengthwise and crosswise are divergent. such a difference, already detected in the tensile tests, is however marked by the fact that, in this case, the specimens sampled crosswise result in higher values. this fact can be explained by analyzing the cold worked steels microstructures (figs. 3 and 5). rolling produces a stressed stretching of grains and makes the structure similar to that of a plastic material reinforced by oriented fibres which have a resistance higher than that of the base material. these fibres reinforce the material in the direction they are arranged, if the material is subject to traction, whilst they have no influence if the material is subject to compression. the behaviour of the material, stressed radially, according to these considerations, should be similar, as it is, to the behaviour of the material stressed crosswise. ‐ tab. 7 contains the percentage changes of the yield strength of the cold-rolled steels, referred to the reference steels. it can be noticed that investigated steels show a non-homogeneity indicated by the different behaviour under tensile and o http://www.gruppofrattura.it http://dx.medra.org/10.3221/igf-esis.13.03&auth=true a. finelli et alii, frattura ed integrità strutturale, 13 (2010) 24-30; doi: 10.3221/igf-esis.13.03 30 compression or by specimens coming from the same sampling direction, beyond an anisotropy indicated by the difference between the values obtained from the longitudinal and transversal specimens. material tensile [%] compression [%] l t l t r a1l 100 80 75 125 115 4l 150 130 120 180 160 table 7: investigated steels yield strength vs specimen orientation and loading direction (deviation from annealed steels) conclusions onsidering the experimental results and the microstructure analysis, the following conclusions could be summarized: ‐ cold rolling process implies an increase in the yield strength and ultimate tensile strength values, higher for the yield strength, over 150% on the super-austenitic stainless steel, on the materials under test, whilst elongation values decrease significantly, over the 60%, ‐ the anisotropy caused on the materials by the rolling process, as seen on the microstructures, is such as to determine differences by about 20% on the increase of the tensile yield strength, higher in the rolling direction. on the contrary this change cannot be detected either on the ultimate strength or on the elongation. ‐ the test procedure set up enabled the determination of the tensile transverse strength by the short specimen “b” and to compare the yield strength in all three directions by the compression specimen “c”, ‐ the compression tests in the three directions, pointed out a considerable non-homogeneity of the cold-rolled materials, since the values of the yield strength, measured under tensile and compression stresses, in the two directions were found not symmetrical. references [1] standard methods of tension testing of metallic materials astm e 8. [2] standard methods of compression testing of metallic materials at room temperature astm e 9. c http://www.gruppofrattura.it http://dx.medra.org/10.3221/igf-esis.13.03&auth=true microsoft word numero_30_art_35 v. anes et alii, frattura ed integrità strutturale, 30 (2014) 282-292; doi: 10.3221/igf-esis.30.35 282 focussed on: fracture and structural integrity related issues evaluation of the az31 cyclic elastic-plastic behaviour under multiaxial loading conditions v. anes instituto superior técnico, university of lisbon 4140.fatigue@gmail.com l. reis, m. freitas idmec & icems, instituto superior técnico, university of lisbon, luis.g.reis@ist.utl.pt, mfreitas@dem.ist.utl.pt abstract. components and structures are designed based in their material’s mechanical properties such as young's modulus or yield stress among others. often those properties are obtained under monotonic mechanical tests but rarely under cyclic ones. it is assumed that those properties are maintained during the material fatigue life. however, under cyclic loadings, materials tend to change their mechanical properties, which can improve their strength (material hardening) or degrade their mechanical capabilities (material softening) or even a mix of both. this type of material behaviour is the so-called cyclic plasticity that is dependent of several factors such as the load type, load level, and microstructure. this subject is of most importance in design of structures and components against fatigue failures in particular in the case of magnesium alloys. magnesium alloys due to their hexagonal compact microstructure have only 3 slip planes plus 1 twining plane which results in a peculiar mechanical behaviour under cyclic loading conditions especially under multiaxial loadings. therefore, it is necessary to have a cyclic elastic-plastic model that allows estimating the material mechanical properties for a certain stress level and loading type. in this paper it is discussed several aspects of the magnesium alloys cyclic properties under uniaxial and multiaxial loading conditions at several stress levels taking into account experimental data. a series of fatigue tests under strain control were performed in hour glass specimens test made of a magnesium alloy, az31bf. the strain/stress relation for uniaxial loadings, axial and shear was experimentally obtained and compared with the estimations obtained from the theoretical elastic-plastic models found in the state-of-the-art. results show that the az31bf magnesium alloy has a peculiar mechanical behaviour, which is quite different from the steel one. moreover, the state of the art cyclic models do not capture in full this peculiar behaviour, especially the cyclic magnesium alloys anisotropy. further, an analysis is performed to identify the shortcomings inherent to the actual cyclic models in the capture of the magnesium alloys cyclic behaviour. several conclusions are drawn. keywords. magnesium alloys; az31b-f; cyclic elastic-plastic model; multiaxial loadings; experimental tests. v. anes et alii, frattura ed integrità strutturale, 30 (2014) 282-292; doi: 10.3221/igf-esis.30.35 283 introduction nowing the material stress state under any kind of loadings is of utmost importance since the interpretation of the mechanical behaviour is based in that stress state[1, 2]. in the design of mechanical components it is used the hooke’s law that relates linearly the stress and deformation. this law is only valid in elastic regimes and assumes that the relation between stress and deformation is always constant. however, even in elastic regimes, the material mechanical properties may change. this variation is related with the materials cyclic plasticity where the strength of the materials changes with the loading type and with the load level [2, 3]. also the material type has huge influence in the response to the load type. it was observed that the number of slip plans have an huge influence on the cyclic behaviour, for example, magnesium alloys have only 3 slip plans (or slip directions) against 12 found in steel alloys [4]. this is why these two types of materials have a cyclic mechanical behaviour so different. one way to interpret the variation of the cyclic mechanical properties is to analyse the hysteresis loop resulting from several loading paths at several stress levels. from these hysteresis loops can be inspected the yield stresses in tension and compression; in steels the yield stresses in tension and compression are the same or similar, but for other types of materials those stresses it may be quite different, which is the case of magnesium alloys. other important parameter that can be obtained from a hysteresis loop is the total strain for a certain stress level. as seen, in the aforementioned cyclic yield stress cases, also the total strain in tension and in compression may be different for the same stress level in tension and compression. this result indicates that the plastic strain in tension and compression are different as well as the elastic ones. the cyclic yield stresses are usually below the static ones, thus the aforementioned cyclic behaviours can occur with stresses below the static yield stress. thus a key question may be raised: what is the real stress state of the material under cyclic loading conditions? there is some way to know those stress states? the answer to these questions is of utmost importance because it is only possible to reach reliable conclusions about the material mechanical behaviour knowing the real relation between stress and strain in any loading condition. this relation depends on the stress level and of the load type. there are plenty of plasticity models in literature but the phenomenological ones covering the elastic-plastic behaviour under cyclic conditions are very few especially the ones that capture cyclic plasticity under multiaxial loading conditions. therefore, cyclic hardening/softening and cyclic creep under multiaxial loading conditions remains a subject that needs further research. this is so because elastic-plastic models must be made based in experimental tests. it is only possible know the material cyclic behaviour by testing them. it is required to perform a kind of mapping of the material cyclic behaviour under cyclic loadings, especially under multiaxial loading conditions. plasticity models usually have a yield function, a back stress function, and a kinematic function. these functions aim to capture the permanent deformation and change on the mechanical properties of the material. most of those plasticity models are strictly based in the static yield stress and assumes that the yield stress in tension and compression are equal. in other words, they assume that the difference between yield stresses in tension and compression is always maintained equal, trying to cover in that way the bauschinger effect. moreover, their yield stress is based in the von mises equivalent stress, which assumes that the relation between the deformation in axial and shear is given by √3, which is not true for certain materials under cyclic loading conditions[3, 5, 6]. therefore, that kind of plasticity models are not suitable to be used in cyclic analysis for materials with different yield stresses in tension and compression. in fact, commercial finite element packages do not have intrinsic cyclic plasticity models to modulate such type of materials. the only way to account the special cyclic behaviour, using commercial fea packages, is to implement an external routine that can update the material cyclic response. generally, the cyclic plasticity models are constitutive models that are modelled by numerical tools. they can be divided in six major groups, four groups based in yield surface [7-10], one based in overlapping models [11] and other one based in endochroic models[12]. models with one yield surface tend to be more robust than others that have two or more yield surfaces. one important issue in this subject is that all constitutive elastic-plastic models do not capture the materials anisotropy; they purely ignore this important material behaviour[4]. therefore, materials that have a cyclic anisotropic behaviour such as magnesium alloys will not be well modelled using these models. also, they do not capture the influence of the strain rate nor the temperature effect in the cyclic behaviour of the materials. moreover, the cyclic models available in literature do not cover an important aspect of mechanical components, which is the anisotropy from the manufacturing process. the anisotropy in the materials may result from several reasons; for instance, it is well known the directional dependence of the mechanical properties in a sheet of metal. that anisotropy is the result from the lamination process, also in an extruded rod, the longitudinal properties will be different from the transversal ones, and this difference is the result of the material alignment in the extrusion process. in this sense, it is quite difficult to find in the field, manufactured materials that have isotropic properties especially at surface. however, it is at surface where usually the fatigue phenomenon occurs; therefore k v. anes et alii, frattura ed integrità strutturale, 30 (2014) 282-292; doi: 10.3221/igf-esis.30.35 284 it is of utmost importance to know the local cyclic stress states of the material[16]. the isotropic hypothesis considered in the state of the art of the elastic-plastic models in reality is an approximation to the material stress state another type of anisotropy found in the materials is the one that results from the material response to the loading type. the rearrangements of the material microstructure have some preferable directions that are related with the loading type and the microstructure slip system. one example is the non-proportional hardening, which is the result of nonproportional loadings. in this type of loading all slip plans are activated however, the hardening effect it may be not equal in all directions [10, 13]. also within the non-proportional loadings there exist several non-proportionality levels, which also contribute to different anisotropy types. the research problem is that besides the actual cyclic elastic-plastic models do not cover the anisotropy that resulted from the manufacturing process also does not cover the anisotropy that results from the loading type. this is a huge shortcoming in these elastic-plastic models found in literature being not advisable their use in fatigue life assessment especially under multiaxial loading conditions. the objective of this work is to implement an elastic-plastic numerical model in order to modelling the materials cyclic elastoplasticity under complex multiaxial loadings. in order to do that, was selected the az31 magnesium alloy due to their peculiar mechanical behaviour and because it is a magnesium alloy used in the industry. also in this study it is presented methodologies to deal with this kind of materials i.e. hexagonal closed packed. the ultimate goal is to reach a numeric tool that can be used in generic hcp materials and used in synergy with a commercial finite element packages (external routine). results show that the numerical methodologies implemented allows modulating the az31 magnesium alloy mechanical behaviour under uniaxial loading conditions with acceptable accuracy; moreover under multiaxial conditions the achieved results are quite similar to the ones obtained with the jiang & sehitoglu plasticity model. however, additional multiaxial stress-strain experiments are needed to adjust and validate the considered multiaxial hypothesis. theoretical development he jiang & sehitoglu plasticity model is a non-linear kinematic hardening model that incorporates an armstrongfrederick type hardening rule, in order to capture the bauschinger effect on the cyclic plastic deformation. this model was implemented with the purpose of modulating the cyclic ratcheting phenomena that is a progressive and directional plastic deformation when a material is subjected to asymmetric loadings under stress-controlled regimens, which makes this model a good candidate to model the magnesium alloy elastic-plastic behaviour. one peculiarity associated with this model is related to the inclusion of a non-proportional hardening parameter, where the nonproportional hardening results in an additional resistance of the material to plastic deformation under non-proportional loading. also, it is introduced the memory concept on the material behaviour simulation in order to describe the strain range dependency in the cyclic hardening. the jiang & sehitoglu plasticity model also considers several others physical mechanisms, such as: yield function, which considers a combinations of stresses that will lead to plastic deformations; flow rule, creates a relationship between the stresses and plastic strains during plastic deformation; hardening rule, defines the yield criterion changes under plastic straining; stress relaxation and load redistribution in the stressed volume. the jiang & sehitoglu plasticity model routine used in this study has as input the strain loading paths and the az31b-f magnesium alloy mechanical properties; the analysis was performed under strain control conditions. this routine was implemented by considering the stress/strain tensor on an elemental cube, therefore it is not applied to a specimen test modelled in finite element. the mechanical properties considered as input in this program are: young’s modulus, cyclic strength coefficient, proportional cyclic strain hardening exponent, cyclic strength coefficient at 90 degrees, nonproportional cyclic strain hardening exponent at 90 degrees, poison coefficient and shear modulus. it is assumed that the cyclic hardening exponent is constant for proportional and non-proportional loads. the non-proportional cyclic strength at 90º is calculated considering the kanazawa non-proportional constant, with a value . in order to cover all the phenomena discussed in previous sections, it is used the experimental hysteresis loop data performed under cyclic strain control in pure axial loading and pure shear loading conditions. the objective is to achieve a numeric model capable to estimate the relation between stress-strain in uniaxial and biaxial loading conditions under a realistic strain range. the constraints aforementioned means that the numeric model only will modulate the applied strain if it belongs to the strain ranges established in the experimental tests. however, in this study the experimental tests were performed from elastic strains until reach total strains with high plasticity resulting in the specimen collapse at very few load cycles. thus, here a realistic stress-strain relation is covered. this does not mean that were made experimental tests for all total strain levels, instead were selected several total-strains that will allow to perform valid numeric regressions. these values were carefully selected and used in the experimental cyclic tests. from experiments, was found that the az31 magnesium alloy hysteresis loops can be approximated with very acceptable results using a third degree polynomial 0.1  t v. anes et alii, frattura ed integrità strutturale, 30 (2014) 282-292; doi: 10.3221/igf-esis.30.35 285 interpolation for any value of total-strain. in order to perform those interpolations it is considered several specific points on the hysteresis loop, thus for the compression polynomial branch, the points 1,2,3 and 4 shown on fig. 1 are used; for the tension polynomial branch, are used the points 4,5,6 and 1. these polynomials capture the twinning, de-twinning and slip effect at each total strain level. thus the hysteresis loop at specific total strain is given by the following equations for compression (eq. (1)) and tension (eq. (2)) respectively.        3 2 1total total total total total total totala b c d            (1)        3 2 1total total total total total total totale f g h            (2) from here, the problem is reduced to find the polynomial parameter values in compression and tension for any total strains within the experimental range. in order to do that, was considered the polyfit matlab routine to obtain these values; this routine has as arguments the stress-strain values inherent to the points 1,2,3 and 4 for compression and 4,5,6 and 1 for tension. from here the problem is reduced to find the function, which relates the arguments of the polyfit routine with the applied load i.e. the applied total strain. the referred points are related to the specific mechanical behaviour found under elastic-plastic regimes. the points 1 and 4 can be considered as values from an experimental yield function, where point 1 come from the tension /compression load direction and point 4 come from the compression/tension. moreover, the points 2 and 5 are the plastic strains, which can be related to the typical isotropic/kinematic hardening models found on constitutive plastic models. the points 3 and 6 can be related to the back-stress concept which is the stress needed to reduce plastic strains to zero. eq.(s) 3 and 4 presents de polyfit matlab function for the compression and tension loading branches, respectively.                 31 42, , , , , 0, , , 0 , ,total total total total total plastic totala b c d polyfit              (3)                 64 15, , , , , 0, , , 0 , ,total total total total total plastic totale f g h polyfit              (4) figure 1: third degree polynomial interpolation reference points, in tension and compression loading directions for two consecutive hysteresis loops. the core concept of the numeric model presented here is based on obtaining the functions relating the variation of the polynomial interpolation points with the total-strain variation. in this work, those values were determined by considering a third degree polynomial fitting equation for the branches in tension and compression, obtained from the experimental data hysteresis loop. with these experimental data, it was achieved the aforementioned functions by interpolation to estimate the variation of the polynomial regression arguments with the total strain variation. at the current state of the model, the biaxial elastic-plastic behaviour is estimated by considering separately the biaxial loading strains (axial and shear), which is a simplification. with this simplification, it is assumed that the axial stress and the shear stress do not contribute to each other in terms of cyclic plasticity. however, biaxial elastic-plastic experiments are in progress to be used in the upgrade of the current model. similarly to the jiang & sehitoglu plasticity model routine, the proposed approach also is related to an elemental cube; therefore, all conclusions made here are related to an infinitesimal material point. v. anes et alii, frattura ed integrità strutturale, 30 (2014) 282-292; doi: 10.3221/igf-esis.30.35 286 materials and methods he material used in this study was the magnesium alloy az31-b. this alloy was acquired in the form of rods with 26 mm of diameter and 1000 mm in length. the rods were extruded in a temperature range of 360 to 382 ºc with an extrusion speed of 50.8 mm/s. the applied extrusion ratio was about six, and after extrusion the alloy was air quenched. the tested specimens were machined in the extrusion/longitudinal direction and polished with decrease levels of sandpaper. an instron servo-hydraulic testing machine was used to perform the cyclic tests at strain control regime with r=-1 with a sinusoidal waveform. several total strain amplitudes were considered and obtained at the same strain rate. the strain rate considered in this study was about 0,003 [1/s], which is a value lower than the limit, from which the strain rate affects the cyclic strain behaviour of the magnesium alloys. the strain results were measured with a biaxial extensometer with a gauge length equal to 12.5 mm. the strain controlled tests were made considering the following total strains: 0.3%, 0.5%, 0.7%, 0.9%, 1.2% and 1,4%. each cyclic test was considered concluded at the occurrence of the specimen total separation. to evaluate the influence of the microstructure in the mechanical behaviour four biaxial loading paths were considered, please see fig. 2. the first loading case is a pure uniaxial tensile test, case pt; the second one is a pure shear loading, case ps. these loading paths were implemented in experiments and in the numerical analysis. the pp is a 45º proportional biaxial loading and the op case is a 90º out-of-phase loading path. these biaxial loading paths were implemented only in the numerical analysis. the experimental tests were performed at room temperature and ended when the specimens were totally separated. figure 2: loading paths: a) case pt, b) case ps, c) case pp and d) case op. results and discussion ig. 3 shows the variation of several variables inherent to the magnesium elastic-plastic mechanical behaviour in function of total strain values under cyclic loading conditions obtained from experimental tests. fig. 3a) and 3b) show the results for the axial loading case, can be seen that the compression and tension have a similar behaviour for total strains lower than 0.4% where the values of the back-stress are negligible. at total strains, with values between 0.4% and 0.6 %, the curves in tensile and compression have a cyclic hardening behaviour but with different hardening rates. this observation corroborates the results shown on fig. 3b) where the plastic strain increase is followed by an axial stress increase. moreover, from tensile stress curve and from the tensile plastic strain can be concluded that the plastic strain is increasing with a tensile stress decrease which indicates that the material softened for this total strain range i.e. between 0.6% and 1.4 %. in addition, it can be concluded that under compression, the material is always under a hardening regime. from here, can be concluded that the magnesium alloys harden, softens and have a mixed behaviour in axial loading regimes. from the axial results, fig. 3a), also can be concluded that the back-stress in compression is greater than the one found in tension for a total strain greater than 0.6%.for total-strains with values lower than 0.6%, the backstress in tension is greater than the one verified at compression. from here can be concluded that the back stresses in axial loading conditions operates differently in tension and compression. therefore, the plastic behaviour is dependent on the total strain amplitude. also the plastic strain in tension is always greater than the compressive one (see fig. 3).the pure shear results shown in fig. 3c) and 3d) indicate quasi-overlapping curves in the case of total-strains versus shear stresses. these results show that the shear-strain hysteresis loops are quasi symmetrical in any total shear strain. however, from the back-stress curves in shear, can be seen that the back stress has a different total shear stress evolution, indicating that the shear direction of the first cycle loading influences these results. this feature also can be observed in fig. 3c) where the total shear strain versus plastic strain curves are not overlapped as expected. despite the shear hysteresis loop be symmetrical the plastic strains are greater in one direction than in another. however, the curves have a similar shape, also t f a) b) c) d) v. anes et alii, frattura ed integrità strutturale, 30 (2014) 282-292; doi: 10.3221/igf-esis.30.35 287 leading to conclude that the first loading cycle has influence on the hysteresis inherent plasticity. this issue is related to the sequential effect on the elastic-plastic behaviour. this experimental evidence indicates one more variable to take into account in the numeric model only identified by experimental tests. however, this sequential effect identified for one shear direction it can be extrapolated for the other one, considering the same experimental data. figure 3: plastic strains and back stresses vs total strains under uniaxial loading conditions a) and b) axial loading case and c) and d) shear loading case. fig. 4 shows the experimental and numerical hysteresis loops for the uniaxial loading cases. fig. 4a) and 4b) show the experimental and numerical results of the pure axial loading path under several total strains. the pure shear results are shown in fig. 4c) and 4d). the total strain values selected to perform the numerical analyses were the same used in the experimental tests in order to analyse the accuracy of the numeric hysteresis loop estimation. since the numeric model here presented is based on the uniaxial experimental tests it is expected that the results be quite similar, if the assumptions made on the numeric model definition are true. nevertheless, the estimations are quite acceptable for the uniaxial loading cases, confirming that the hysteresis loops in pure axial and pure shear loading conditions can be approximated by a third degree polynomial function. in order to avoid confusion in the graphs interpretation was not considered here the representation of the hysteresis loops with total strains different of the experimental ones. however, the numerical model can estimate any hysteresis loop within the [0% to 1.4%] total strain range under uniaxial loading conditions. from the axial hysteresis loops can be identified the asymmetry inherent to the different mechanical behaviours found in tension and compression. moreover, the shear hysteresis loops are quasisymmetric. fig. 5a) and 5b) shows the numeric results for 0.4% of total axial strain and 0.23 % of total shear strain. fig. 5a) shows a comparison between the numerical model and the jiang plasticity model for the case of pure axial loading. from that comparison can be concluded that the jiang hysteresis loop is more open than the experimental one, indicating the existence of plastic strain and back stresses that in reality are not there. moreover, the stresses estimated by the jiang model at the maximum total strain in uniaxial axial loading, please see fig. 5b), are inferior to the ones obtained from the numerical model. considering the pure shear analysis, present in fig. 5b) the jiang model continues to estimate inferior stresses at the maximum total shear strains. the biaxial loading cases are shown in fig. 5c) and 5d). at the present work state, is not possible to compare the numerical estimates with the experimental results, however the numerical model implemented can be compared with the jiang plasticity model. for the pp loading case, can be concluded that the slope of the hysteresis loops and inherent orientations are different in both numeric models. the difference observed in the slope v. anes et alii, frattura ed integrità strutturale, 30 (2014) 282-292; doi: 10.3221/igf-esis.30.35 288 can result from the considered scale factor between axial and shear strains used in the jiang model. usually, the von mises stress scale factor is used but the jiang model uses 0.5 as stress scale factor against the 0.577 found in the von mises yield criterion. the numerical model presented here, considers the axial and shear total strain separately in order to estimate the mechanical behaviour as if they had been applied at the same time. the physical meaning of this simplification considers that the stress needed in shear and axial directions to make the same plastic strain is the same, which is not true for most metallic materials. this relation can only be found by performing biaxial stress-strain tests under an elastic-plastic regimen. fig. 5d) shows the results for the fully out-of-phase loading case; in this case, the estimations of both numerical models are quite similar. the jiang's model estimations are within of the numerical model results due to the fact that the jiang model calculates lower stresses, for the same total strain. however, in the stress space, both estimations for the loading path have a similar shape for the same total strain level presented in fig. 5d). figure 4: az31 experimental and numeric cyclic behavior a) axial experimental stress/strain evolution b) numeric results for axial stress/strain hysteresis loops c) shear experimental stress/strain evolution d) numeric estimation for shear stress/strain hysteresis loops. fig. 6 shows the numeric results for 0.8 % as total strain. the uniaxial results presented in fig. 6a) and 6b) indicate that the jiang's model continues to estimate a lower stress at maximum total strain in the compression region, but in tension the inherent stress is similar to the numerical model estimations. fig. 6 shows the very first hysteresis loop presented with a dashed line. for the pure axial loading case, the compressive plastic strain and back-stresses are quite similar in both models; however the plastic strains in the tension branch are very different. jiang's model gives values higher than the experimental results, please see fig. 6a) and 6d). in the pure shear loading case, the jiang's model has a hysteresis loop tighter than the experimental results presented here by the numerical simulation for this case. in these cases, the stresses inherent to the shear total strains in compression and tension obtained with the jiang’s model are very similar to the numeric model estimations; moreover the pure axial hysteresis loop is estimated as symmetric by the jiang model. for the pp loading case, please see fig. 6c) the jiang model also gives a symmetrical hysteresis loop. the numerical model displays asymmetrical hysteresis loop for the axial loading. the out-of-phase loading case, fig. 6d), shows a distorted circle for both numerical analyses; however, the distortion pattern has different directions. fig. 7 shows the numerical result for 1.2% of total strain. due to the high values of the plastic strains involved in this simulation (total strain equal to 1.2%) can be seen that the first hysteresis loop is quite different from the other ones in the v. anes et alii, frattura ed integrità strutturale, 30 (2014) 282-292; doi: 10.3221/igf-esis.30.35 289 developed numerical model, this indicates the adjustment of the material to the total strain level. the jiang model continues to estimate the hysteresis loops as symmetric in all loading cases considered here, although the biaxial loading experiments have not yet been made it is expected that the experimental biaxial hysteresis loops be asymmetric and not symmetric as reported by the jiang's model, once the uniaxial axial hysteresis loops are always asymmetrical. with the increase of the total strain, the inherent stresses estimated by the jiang's model also increases relatively to the experimental data. this indicates that the jiang's model does not capture well the total strain level effect on the hysteresis loops shapes. in this case of total strain, 1.2%, the two numerical estimations on the pure shear loading case are very similar having plastic strains and back stress values much alike. observing the numeric results for the loading cases pp and op, fig. 7c) and 7d) can be concluded that, for the first loading cycle, the numerical model and the jiang's model have a similar behaviour, diverging the results of both models in the subsequent loading cycles. fig. 8 presents the numeric results for the 1.4% of total strain, this is a very high strain level leading to the specimen test collapse in a few loading cycles. for all loading cases it can be seen that the jiang's hysteresis loops remain symmetric. figure 5: numeric cyclic behaviour comparison between the numeric model developed and the jiang &sehitoglu plasticity model for 0.4% as axial strain reference pt, ps, pp and op. a) b) c) d) under an extreme cyclic total strain the jiang's model presents same plastic strain and back stress values at tension and compression. which is far from the experimental data, where at the axial loading path the compression load induces high plastic strain and back stresses, moreover the plastic strain in tension is very small comparatively with the one found in compression. for the pure shear loading path, please see fig. 8d), the experimental hysteresis loop indicates different values for back stresses and plastic strains, which was not seen in lower total shear strains. from the axial loading case shown in fig. 8a), it can be seen that the yield stress in compression is much greater than the tension one for the same total strain in tension and compression, which confirms a softening behaviour in tension and a little hardening in compression. also can be concluded that the jiang's model is able to estimate well the hardening of the material but unable to deal with its softening. from here can be reinforced the idea which suggests that an experimental and numerical model is needed to establish the different physical phenomena encountered in materials with an hexagonal close packed microstructure (hcp), such as the magnesium alloys. v. anes et alii, frattura ed integrità strutturale, 30 (2014) 282-292; doi: 10.3221/igf-esis.30.35 290 figure 6: numeric cyclic behavior comparison between the numeric model developed and the jiang &sehitoglu plasticity model model for 0.8% as axial strain reference pt, ps, pp and op. a) b) c) d) figure 7: numeric cyclic behavior comparison between the numeric model developed and the jiang & sehitoglu plasticity model for 1.2% as axial strain reference pt, ps, pp and op. a) b) c) d) v. anes et alii, frattura ed integrità strutturale, 30 (2014) 282-292; doi: 10.3221/igf-esis.30.35 291 figure 8: numeric cyclic behavior comparison between the numeric model developed and the jiang & sehitoglu plasticity model for 1.4% as axial strain reference pt, ps, pp and op. a) b) c) d) conclusions n this paper was studied the elastic-plastic mechanical behaviour of a magnesium alloy (az31b-f) through experimental tests under uniaxial loading conditions. the particular mechanical behaviour inherent to these kinds of materials, hexagonal closed pack microstructures, leads to conclude that it is necessary to have a numeric elasticplastic model implemented through experimental data. in this context is presented here a first iteration for a numerical model, which modulates the several physical mechanisms inherent to the magnesium elastic-plastic behaviour in uniaxial loading conditions. in order to validate the work already done, numeric estimations were compared with the uniaxial data and with the jiang & sehitoglu plasticity model. the numeric results from the implemented model were acceptable; however the jiang & sehitoglu model shows some shortcomings on the magnesium hysteresis loop estimations. acknowledgements he authors gratefully acknowledge financial support from fct – fundação para a ciência e tecnologia (portuguese foundation for science and technology), through the project ptdc/eme-pme/104404/2008. references [1] sonsino, c.m., dieterich, k., fatigue design with cast magnesium alloys under constant and variable amplitude loading, international journal of fatigue, 28 (2006) 183–193. [2] anes, v., reis, l., li, b., fonte, m., de freitas, m., new approach for analysis of complex multiaxial loading paths, international journal of fatigue, 62 (2013) 21-33. i t v. anes et alii, frattura ed integrità strutturale, 30 (2014) 282-292; doi: 10.3221/igf-esis.30.35 292 [3] reis, l., anes, v., de freitas, m., az31 magnesium alloy multiaxial lcf behavior: theory, simulation and experiments, advanced materials research, 891 (2014) 1366-1371. [4] anes, v., l. reis, b. li, and m. freitas. "crack path evaluation on hc and bcc microstructures under multiaxial cyclic loading." international journal of fatigue 58 (2014): 102-113. [5] anes, v., reis, l., li, b., freitas, m., new approach to evaluate non-proportionality in multiaxial loading conditions, fatigue & fracture of engineering materials & structures, (2014). doi: 10.1111/ffe.12192 [6] armstrong, p.j., frederick, c.o., a mathematical representation of the multiaxial bauschinger effect, g. e. g. b., report rd/b/n, 731, (1966). [7] dafalias, y.f., popov, e.p., plastic internal variables formalism of cyclic plasticity, journal of applied mechanics, 43 (1976) 645–651. [8] kurtyka, t., parameter identification of a distortional model of subsequent yield surfaces, archives of mechanics, 40 (1988) 433–454. [9] valanis, k.c., a theory of viscoplasticity without a yield surface. iiapplication to mechanical behavior of metals(mechanical response of al and cu under complex strain histories conditions, using endochronic theory of viscoplasticity without yield surface), archiwum mechaniki stosowanej, 23 (1971) 535–551. [10] lee, m.g., kim, j.h., chung, k., kim, s.j., wagoner, r.h., kim, h.y., analytical springback model for lightweight hexagonal close-packed sheet metal, international journal of plasticity, 25 (2009) 399–419. [11] carpinteri, a., ronchei, c., spagnoli, a., vantadori, s., lifetime estimation in the low/medium-cycle regime using the carpinteri-spagnoli multiaxial fatigue criterion, theoretical and applied fracture mechanics, (2014). [12] carpinteri, a., spagnoli, a., vantadori, s., multiaxial fatigue assessment using a simplified critical plane-based criterion, international journal of fatigue, 33 (2011) 969–976. [13] carpinteri, a., spagnoli, a., vantadori, s., bagni, c., structural integrity assessment of metallic components under multiaxial fatigue: the c–s criterion and its evolution, fatigue & fracture of engineering materials & structures, 36 (2013) 870–883. microsoft word numero_49_art_66_2535 c. bellini et alii, frattura ed integrità strutturale, 49 (2019) 739-747; doi: 10.3221/igf-esis.49.66 739 experimental analysis of aluminium/carbon epoxy hybrid laminates under flexural load costanzo bellini, vittorio di cocco, francesco iacoviello, luca sorrentino department of civil and mechanical engineering, university of cassino and southern lazio, 03043 cassino, italy costanzo.bellini@unicas.it, http://orcid.org/0000-0003-4804-6588 vittorio.dicocco@unicas.it, http://orcid.org/0000-0002-1668-3729 francesco.iacoviello@unicas.it, http://orcid.org/0000-0002-9382-6092 luca.sorrentino@unicas.it, http://orcid.org/0000-0002-5278-7357 abstract. industry needs new materials that present very high structural characteristic, such as high strength, low weight and high damage tolerance. to obtain these characteristics a new class of materials has been introduced: fibre metal laminate (fml); they consist in metal sheets alternated to composite material layers: in such manner, the good characteristics of each constituent material confer the utmost properties to the fmls. however, the mechanical properties depend, among other factors, on the thickness and the numerousness of the layers constituting the fml, as well as the interface between metal and composite. therefore, in this paper, the influence of the abovementioned factors on the material answer to flexural load was investigated. in particular, different kinds of laminates were produced varying the layers adhesion and the layers thickness, but maintaining unaltered the metal/composite volume ratio and the total laminate thickness. then their structural behaviour was investigated through three-point bending test, and it was found that the flexural behaviour was affected by both the investigated factors; in fact, the maximum flexural load diminished incrementing the number of layers and inserting an adhesive layer at the metal/composite interface. keywords. fibre metal laminate; flexural load; structural behaviour. citation: bellini, c., di cocco, v, iacoviello, f., sorrentino, l., experimental analysis of aluminium carbon/epoxy hybrid laminates under flexural load, frattura ed integrità strutturale, 49 (2019) 739-747. received: 24.05.2019 accepted: 22.06.2019 published: 01.07.2019 copyright: © 2019 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. introduction everal industrial fields, like automotive, aeronautics and sports goods, need new materials presenting very high structural characteristics, such as high strength, low weight and high damage tolerance. these characteristics can be obtained by introducing a new class of materials: fibre metal laminate (fml); they consist of metal sheets alternated to composite material layers: in such manner, the good characteristics of each constituent material confer the utmost s http://www.gruppofrattura.it/va/49/2535.mp4 c. bellini et alii, frattura ed integrità strutturale, 49 (2019) 739-747; doi: 10.3221/igf-esis.49.66 740 properties to the fmls, such as high strength, high damage tolerance and low density [1]. these extraordinary structural properties are due to the particular characteristics of the materials the fmls are made of; in fact, the fmls made of aluminium and glass fibre composite, that are widespread in the aeronautical field, are less robust than those based on cfrp (carbon fibre reinforced polymer) [2]; in fact, carall (carbon fibre-reinforced aluminium laminates) are about 10% tougher than glare (glass fibre reinforced aluminium laminates) [3]. in general, carbon-based fmls present superior characteristics, as regards the ability to withstand crashes, energy absorption capacity, tensile modulus, yield strength and fatigue strength, in comparison with glass fibre or aramid-based fmls [4]. the fmls can be considered for ballistic applications too, together with aramid fibre composites [5]. usually, structural parts are subjected to flexural loads, that represents the most diffused, and consequently most studied failure mode. the elements an fml is made of have dissimilar properties, causing a complex damage behaviour; in fact, the composite layers are brittle, while metal layers are ductile. the most diffused failure mechanisms of flms are matrix cracking, metal layers plastic deformation, fibres fracture, composite layers delamination and debonding between metal and composite [6]. hu et al. [7] analysed the flexural properties of fmls made of carbon fibres reinforced pmr polyimide and titanium, finding a good structural strength at both room and high temperature. they also found that the micro roughness of the titanium surface layer improved the adhesion between composite material and titanium itself. lawcock et al. [8] found that the bending characteristics of carall depend on the adhesion between the composite laminate and the aluminium layers, while the tensile properties are not affected; in fact, a weak bonding can give rise to a decrement of about 10% for the interlaminar shear strength. they determined that the bonding strength did not influence the residual strength of notched specimen, even if a small decrease for a specimen with a stronger bonding was found. a similar result was stated by botelho et al. [9] that treated the aluminium surface with two different processes: sulphuric chromic acid etching and chromic acid anodization. they found that the latter method brought to better surface wetting, but the interlaminar shear strength of both glare and carall was not influenced. the effect of the metal sheet location along the laminate thickness was studied by dhaliwal and newaz [10], that produced and tested some carall specimens presenting carbon fibre laminate as outside layers. they compared the flexural properties of those laminates with that of common carall, that had aluminium layers outside, determining a superior strength for their material. they also made a comparison between carall and bulk aluminium specimens, determined a higher bending strength of the former ones. the effect of the aluminium sheet strength and the fibres directions on the in-plane flexural behaviour of caralls was analysed by xu et al. [2]. they discovered an increment of the flexural strength as both the amount of the longitudinal fibres and the metal strength were increased. as regards the progressive failure process, at first the aluminium sheets yield appeared, together with tension damage of fibre and resin in the section bottom and resin compression crushing in the section top; after, the delamination started in the laminate mid-span, caused by the unstable deformation. a work has been carried out aiming at analysing the behaviour of laminates with the same composite/metal volume fraction ratio and different layers thicknesses by wu et al. [11]. these authors studied the flexural behaviour of carbon fibre/magnesium fmls, discovering that the flexural modulus linearly decreased with the layer thicknesses, while no differences were observed for the flexural strength. however, the layer thickness decrease made the failure area shift from compression to tension region. moreover, the bonding behaviour is fundamental for composites and fmls [12,13]. the aim of the present work regards the analysis of the flexural behaviour of carall specimens, studying the influence of both layer thickness and the adhesion solution between cfrp laminate and aluminium sheet. in particular, the attention was paid not only to the maximum flexural strength reached by the specimens, but also to the stress-strain response after the first elastic phase and the first stress peak, that represents the maximum stress. in this manner, it is possible to determine also which parameter combination presents the highest toughness and the highest safety after the first peak stress. moreover, unidirectional reinforcements are usually employed in the design of fmls, while in this study a carbon fabric was considered as composite material reinforcement. the effect of the stacking characteristic on the laminate mechanical behaviour was studied by several researchers, even if they keep the composite laminate thickness [14,15] or metal sheet thickness [16,17] constant and focused the attention on the dynamic characterization. the layer thickness is a significant factor concerning the structural behaviour of fmls that should be taken into consideration for the product design, even if the study of this topic has been infrequently explored [11]. materials and methods n this work, the effects of layer thickness and of the layer adhesion were investigated both separately and combined. as reported in tab. 1, four different specimen types composed the full factorial plan of the experimental activity, that i c. bellini et alii, frattura ed integrità strutturale, 49 (2019) 739-747; doi: 10.3221/igf-esis.49.66 741 presented 2 levels for each factor. the analysis was carried out through three-point bending tests on the carall specimens with different stacking and dissimilar bonding strategy. specimen type number of metal sheet adhesive type a 1 yes type b 1 no type c 2 yes type d 2 no table 1: full factorial plan for factor influence analysis. as concerns the stacking sequence, two laminates with cfrp laminate as external layer were considered; in particular, one consisted of two layers of cfrp and one of aluminium, while the other one was formed by two layers of aluminium and three layers of carbon fibre. in order to maintain the laminate thickness and the cfrp/aluminium ratio constant, the aluminium sheet thickness of the former typology was equal to 0.6 mm and one composite laminate was composed by six prepreg plies, for a total of 12 plies, while the latter type presented two 0.3 mm thick aluminium foil and three cfrp layers consisting of four prepreg plies each. in such a manner, the obtained laminate thickness was 5 mm. in order to evaluate the influence of the adhesive interface between the composite material and the aluminium sheet on the mechanical performance of the hybrid laminates, both fmls with and without adhesive were produced and tested. in particular, for the former ones a structural adhesive, typically used in the aeronautical field, was adopted, while the bonding interface of the latter ones relied on the self-adhesive capacity of the resin being a part of the prepreg material. the different types of fml studied in the present work are reported in fig. 1. four specimens were tested for each set of parameters, so 16 flexure tests were carried out in total. a) b) c) d) figure 1: different kinds of fml considered in this work: a) one metal sheet with adhesive, b) one metal sheet without adhesive, c) two metal sheets with adhesive, d) two metal sheets without adhesive. the metal sheets considered for this work were made of aluminium al 1100, while the composite material was the se70/rc303t/1270/38%, a prepreg system made of se70 epoxy resin and a carbon twill style fabric. 2x2 twill is a weaving style that provides a diagonal pattern with one or more warp fibres woven in a regular manner above and below two or more weft fibres; the warp and weft are the sets of threads that together contribute to the creation of the fabric. the resin weight content was 38% and the fabric areal density was 303 g/m2. as concerns the bonding agent used in some specimens, c. bellini et alii, frattura ed integrità strutturale, 49 (2019) 739-747; doi: 10.3221/igf-esis.49.66 742 it was the af163-2k film adhesive. it had a thickness of about 0.24 mm and a carrier, made of glass fibres, was present inside it for resistance increment purpose. as regards the manufacturing process of the carall specimens, four laminates, one for each fml type considered in this work, were produced by the vacuum bag process. the mould consisted of a 10 mm thick steel plate, whose dimensions were 500 x 400 mm2, on which the four laminates were produced simultaneously, since the mould area was enough ample. in fact, it was decided to produce laminates with dimensions equal to 200 x 110 mm2, from which extract four specimens with dimensions of 160 x 20 mm2. the vacuum bag is a manufacturing process typically adopted in the aeronautical industries for composite material parts production. for the purpose of the present work, the mould surface was treated with marbocote, a release agent necessary to warrant a safe part removal at the end of the manufacturing process, without part damage or breakage. then, all the materials required for caralls manufacturing, that were the prepreg plies, the aluminium sheets and the adhesive plies, were cut into the right size and stacked as described in fig. 2. then, the four stacks were covered with a release film and a breather fabric: the latter was needed for evacuating air and gases out of the bag, while the former was used to separate the breather from the laminates. a caul plate was placed on the top prepreg layer to obtain a smooth surface finish on both laminate sides. finally, the mould was closed with the vacuum bag, closed with a butyl sealant tape, and the vacuum was applied and maintained until the thermal cycle end. after the mould preparation, the parts were polymerized in an autoclave following the thermal cycle suggested by the prepreg manufacturer, that was suitable for the adhesive cure too. in fact, the cure process is a very important step in polymeric material manufacturing [18,19]. this cycle scheduled a heating ramp with a rate of 2 °c/min and a temperature dwell of 100 min at 100 °c. at the end of the curing process, the laminates were taken from the mould and trimmed by a diamond disk saw, obtaining the desired specimens. the produced specimens for type a fml are visible in fig. 3. figure 2: prepreg plies and aluminium sheets after the stacking phase. figure 3: specimens cut from the fml plates. the bending tests carried out on the specimens to evaluate the flexural characteristic referred to the astm d790. this test method considered a three-point loading system applied to a simply supported beam. in particular, the test involved two cylindrical shape supports on which the rectangular cross-section specimen was laid, loaded by a cylindrical punch, halfway c. bellini et alii, frattura ed integrità strutturale, 49 (2019) 739-747; doi: 10.3221/igf-esis.49.66 743 between the two supports, as visible in fig. 4. the span between the support was set to 136 mm, while the loading rate to 6 mm/min. the specimens were loaded until the loading nose reached a stroke of 27 mm and then unloaded in order to evaluate the mechanical behaviour of the studied material, even after the maximum load, and so the maximum flexural strength, had been reached. figure 4: three-point bending test for type b specimen. results and discussion he influence of two factors, such as the number of layers and the presence of the adhesive, on the flexural properties of the carall was studied in this work. in particular, the attention was focused not only on the single factor but also on their combination, leading to a more accurate and deeper interpretation of the material behaviour. the threepoint bending test results concerned the flexural strength and they were analysed through inferential statistical techniques in order to ascertain the presence or absence of significant differences. for the purposes of the present paper, the assumption of equality of all population means was assumed as the null hypothesis, as commonly done for statistical analysis of data characterized by homoscedasticity, normal population distribution and independency of experimental runs. the observation of the p-value was chosen as criteria for null hypothesis rejection: if its value was below the significance level of 0.05, the generally adopted significance value, then the null hypothesis could be rejected and, consequently, the population means were effectively dissimilar and the influence of the studied factor could not be neglected. the flexural strength of the tested laminates, denoted as σf, was determined through the following relation, present in astm d790 standard and other papers in the literature [10,20,21]: (1) where p represents the load the specimen undergoes, l is the distance between the supports and h and b are the specimen thickness and width, respectively. as it can be noted in tab. 2 and fig. 5, the flexural strength ranged between 562.75 mpa and 641.86 mpa for the laminate with one aluminium sheet bonded with adhesive, while it oscillated between 644.25 mpa and 734.00 mpa for the same laminate without the adhesive, in which the composite material bonding on aluminium sheet was assured by the sole prepreg resin. as concerns the carall with two metal layers, the flexural strength interval went from 468.88 mpa to 553.30 mpa for the laminate with adhesive and from 498.38 to 641.38 for that one without adhesive. the cov (coefficient of variation) was low for all the carall types; in fact, it was equal to about 5-7%, and in only one 2 3    2      f p l b d   t c. bellini et alii, frattura ed integrità strutturale, 49 (2019) 739-747; doi: 10.3221/igf-esis.49.66 744 case it overcame 10%, even if only for a very small amount. it is worth to note that the results found in this experimental campaign are in accordance with other works on this class of material [10, 22, 23]. it can be noted from the experimental results that the highest strength value came from the laminate without the adhesive film and with only a metal sheet, while the lowest value to that one with two aluminium sheets and glued with adhesive. it can be stated that the presence of the adhesive film was detrimental for the material strength, whereas the decrease of metal sheets number was positive. as concerns the former conclusion, it seemed to be in contradiction with past literature; in fact, several researchers [8,24,25] discovered an improvement due to the presence of the adhesive, but it must be underlined that the enhancement was found only for lap shear and interlaminar shear tests, while the in-plane mechanical properties, as the tensile strength, showed a similar behaviour. only in the work of li et al. [25] the flexural behaviour was considered, but the same authors acknowledged their results to be highly depending on specimen and test geometry. run type a type b type c type d 1 562.75 658.22 497.84 542.37 2 641.86 644.25 468.88 498.45 3 602.50 655.68 534.33 641.38 4 621.18 734.00 553.30 563.26 mean 607.07 673.04 513.59 561.36 st. dev. 33.64 41.09 37.66 59.79 cv% 5.54% 6.11% 7.33% 10.65% table 2: flexural strength [mpa] for all the tested specimen. figure 5: comparison of flexural strength for the different type of carall. the results of the analysis of variance that was implemented on the experimental results are presented in tab. 3. it can be noted that the number of aluminium sheets was the most influencing factor, since it had a contribution of 53.41%, while the effect of the other factor, that is the presence of the adhesive, was far less important (16.42%). the contribution of the c. bellini et alii, frattura ed integrità strutturale, 49 (2019) 739-747; doi: 10.3221/igf-esis.49.66 745 interaction between factors was less than 0.5% and it can be neglected. however, for a more significant comparison the pvalue was calculated too for each factor; the analysis confirmed that both the considered factors had an effect on the material flexural strength, since their value was less than 0.05, the commonly chosen a-level, instead the interaction term p-value was 0.688 and so it can be disregarded. source df seq ss contribution adj ss adj ms f-value p-value n. sheets 1 42087.7 53.41% 42087.7 42087.7 21.55 0.001 adhesive 1 23937.6 16.42% 12937.6 12937.6 6.62 0.024 n. sheet * adhesive 1 330.9 0.42% 330.9 330.9 0.17 0.688 error 12 23439.7 29.75% 23439.7 1953.3 total 15 78795.9 100.00% table 3: anova analysis of experimental data. the flexural stress-strain curves of the tested specimens are reported in fig. 6; in particular, a representative curve is shown for each specimen type since the data scatter was quite limited. the mechanical behaviour of all the four specimens was quite similar; in fact, they presented a first stress increment, almost linear till the maximum stress value was reached, followed by a pseudo-ductile behaviour, with a fluctuating trend characterized by stress increment and decrement. however, there are substantial differences, especially in the second pseudo-ductile phase and, as abovementioned, the maximum stress level obtained. on the contrary, in the first elastic phase the slope of the stress-strain curve, that represents young’s modulus of the material, was quite the same for all the laminates, even if that slope was slightly steeper for the laminate without the adhesive. this conclusion can be justified by the fact that the adhesive is less stiff than the other materials and consequently it made the module of the whole laminate decrease. as concerns the post-first stress peak behaviour, the type a and type d laminates presented the highest stress drop, while for the type b and type c the drop was more reduced. in fact, the type a laminate lost about the 55% of its load capacity, while the type d about the 45%; this loss was equal to 20% for the type b and 2% for the type c specimen. after the stress drop there is a stress recovery for all the laminates, but the value of the second peak is quite different depending on the specimen type; in fact, for the type c the second peak value is quite similar to the first peak one, for the type b it corresponded to the 90% of the first peak while for the remaining laminates it was slightly higher than the drop value. these trends show that the type c laminate is the safest one, although it had the lowest flexural strength, since the stress drop after the first stress peak is low and the value of the second peak stress is like the first one. finally, it must be noted that the residual load capacity at the end of the test is negligible for the all the specimen except the type d. conclusions ml materials, that consist of composite layers alternated to metal sheets, are more and more adopted in several industrial fields due to their very high mechanical characteristics features. in this work, the mechanical behaviour of different types of fml was analysed, investigating the effect of the staking sequence and the adhesive presence at the interface between metal and composite material. in this study, aluminium was considered for the metal part of the fml, while the composite material consisted of an epoxy resin reinforced by carbon fabric. the flexural behaviour of the produced laminates was analysed, paying attention not only to the maximum strength but also to the post-peak stress behaviour. the produced laminates had the same thickness and the same metal/composite material ratio, but the material distribution along the thickness was dissimilar in order to obtain different layer thickness without changing the surface density of the panels. from the test results it can be concluded that the highest strength was reached by the laminate with a single metal sheet and without adhesive, while the worst condition was represented by that one with two metal sheets and the presence of the adhesive; in fact, passing from the latter to the former there is a strength increment of about 30%. as concerns the specimens f c. bellini et alii, frattura ed integrità strutturale, 49 (2019) 739-747; doi: 10.3221/igf-esis.49.66 746 behaviour after the maximum stress, various stress trends were noticed: an elevated stress drop characterized the type a and type d specimens, while for the other two laminates types it was reduced or quite absent. in the light of this analysis, it can be concluded that the specimen with two metal sheet and the adhesive was the safer one since it was able to sustain a load near to the maximum one for a long strain interval, even if it presented the lowest maximum stress. figure 6: flexural stress-strain curves of the tested specimens. references [1] vermeeren, c.a.j.r. (2003). an historic overview of the development of fibre metal laminates, appl. compos. mater., 10(4–5), pp. 189–205, doi: 10.1023/a:1025533701806. [2] xu, r., huang, y., lin, y., bai, b., huang, t. (2017). in-plane flexural behaviour and failure prediction of carbon fibrereinforced aluminium laminates, j. reinf. plast. compos., 36(18), pp. 1384–1399, doi: 10.1177/0731684417708871. [3] botelho, e.c., silva, r.a., pardini, l.c., rezende, m.c. (2006). a review on the development and properties of continuous fiber/epoxy/aluminum hybrid composites for aircraft structures, mater. res., 9(3), pp. 247–256, doi: 10.1002/ar.1092200206. [4] kim, j.g., kim, h.c., kwon, j.b., shin, d.k., lee, j.j., huh, h. (2015). tensile behavior of aluminum/carbon fiber reinforced polymer hybrid composites at intermediate strain rates, j. compos. mater., 49(10), pp. 1179–1193, doi: 10.1177/0021998314531310. [5] sorrentino, l., bellini, c., corrado, a., polini, w., aricò, r. (2015).ballistic performance evaluation of composite laminates in kevlar 29. procedia engineering, vol. 88, elsevier b.v., pp. 255–262. [6] frizzell, r.m., mccarthy, c.t., mccarthy, m.a. (2008). an experimental investigation into the progression of damage in pin-loaded fibre metal laminates, compos. part b eng., 39(6), pp. 907–925, doi: 10.1016/j.compositesb.2008.01.007. [7] hu, y.b., li, h.g., cai, l., zhu, j.p., pan, l., xu, j., tao, j. (2015). preparation and properties of fibre-metal laminates based on carbon fibre reinforced pmr polyimide, compos. part b eng., 69, pp. 587–591, doi: 10.1016/j.compositesb.2014.11.011. [8] lawcock, g., ye, l., mai, y.w., sun, c.t. (1997). the effect of adhesive bonding between aluminum and composite prepreg on the mechanical properties of carbon-fiber-reinforced metal laminates, compos. sci. technol., 57(1), pp. 35– 45, doi: 10.1016/s0266-3538(96)00107-8. [9] botelho, e.c., silva, r.a., pardini, l.c., rezende, m.c. (2004). evaluation of adhesion of continuous fiber-epoxy composite/aluminum laminates, j. adhes. sci. technol., 18(15–16), pp. 1799–1813, doi: 10.1163/1568561042708377. [10] dhaliwal, g.s., newaz, g.m. (2016). experimental and numerical investigation of flexural behavior of carbon fiber reinforced aluminum laminates, j. reinf. plast. compos., 35(12), pp. 945–956, doi: 10.1177/0731684416632606. [11] wu, x., pan, y., wu, g., huang, z., tian, r., sun, s. (2017). flexural behaviour of cfrp/mg hybrid laminates with different layers thickness, adv. compos. lett., 26(5), pp. 168–172. [12] sorrentino, l., polini, w., bellini, c., parodo, g. (2018). surface treatment of cfrp: influence on single lap joint c. bellini et alii, frattura ed integrità strutturale, 49 (2019) 739-747; doi: 10.3221/igf-esis.49.66 747 performances, int. j. adhes. adhes., 85, pp. 225–233, doi: 10.1016/j.ijadhadh.2018.06.008. [13] bellini, c., parodo, g., polini, w., sorrentino, l. (2018). influence of hydrothermal ageing on single lap bonded cfrp joints, frat. ed integrità strutt., 45, pp. 173–182, doi: 10.3221/igf-esis.45.15. [14] pärnänen, t., alderliesten, r., rans, c., brander, t., saarela, o. (2012). applicability of az31b-h24 magnesium in fibre metal laminates an experimental impact research, compos. part a appl. sci. manuf., 43(9), pp. 1578–1586, doi: 10.1016/j.compositesa.2012.04.008. [15] sadighi, m., pärnänen, t., alderliesten, r.c., sayeaftabi, m., benedictus, r. (2012). experimental and numerical investigation of metal type and thickness effects on the impact resistance of fiber metal laminates, appl. compos. mater., 19(3–4), pp. 545–559, doi: 10.1007/s10443-011-9235-6. [16] cortés, p., cantwell, w.j. (2005). the fracture properties of a fibre-metal laminate based on magnesium alloy, compos. part b eng., 37(2–3), pp. 163–170, doi: 10.1016/j.compositesb.2005.06.002. [17] ahmadi, h., sabouri, h., liaghat, g., bidkhori, e. (2011). experimental and numerical investigation on the high velocity impact response of glare with different thickness ratio, procedia eng., 10, pp. 869–784, doi: 10.1016/j.proeng.2011.04.143. [18] sorrentino, l., bellini, c., carrino, l., leone, a., mostarda, e., tersigni, l. (2009).cure process design to manufacture composite components with variable thickness by a closed die technology. 17th international conference on composite materials, edinburgh. [19] sorrentino, l., bellini, c. (2016). in-process monitoring of cure degree by coplanar plate sensors, int. j. adv. manuf. technol., 86(9–12), pp. 2851–2859, doi: 10.1007/s00170-016-8338-5. [20] sathyaseelan, p., logesh, k., venketasudhahar, m., dilip raja, n.. (2015). experimental and finite element analysis of fibre metal laminates (fml’s) subjected to tensile , flexural and impact loadings with different stacking sequence, int. j. mech. mechatronics eng., 15(03), pp. 23–27. [21] hamill, l., hofmann, d.c., nutt, s. (2018). galvanic corrosion and mechanical behavior of fiber metal laminates of metallic glass and carbon fiber composites, adv. eng. mater., 20(2), pp. 1–8, doi: 10.1002/adem.201700711. [22] pan, l., ali, a., wang, y., zheng, z., lv, y. (2017). characterization of effects of heat treated anodized film on the properties of hygrothermally aged aa5083-based fiber-metal laminates, compos. struct., 167, pp. 112–122, doi: 10.1016/j.compstruct.2017.01.066. [23] rajan, b.m.c., kumar, a.s. (2018). the influence of the thickness and areal density on the mechanical properties of carbon fibre reinforced aluminium laminates (caral), trans. indian inst. met., 71(9), pp. 2165–2171, doi: 10.1007/s12666-018-1348-2. [24] hamill, l., nutt, s. (2018). adhesion of metallic glass and epoxy in composite-metal bonding, compos. part b eng., 134, pp. 186–192, doi: 10.1016/j.compositesb.2017.09.044. [25] li, h., hu, y., fu, x., zheng, x., liu, h., tao, j. 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/hrv (za stvaranje adobe pdf dokumenata najpogodnijih za visokokvalitetni ispis prije tiskanja koristite ove postavke. stvoreni pdf dokumenti mogu se otvoriti acrobat i adobe reader 5.0 i kasnijim verzijama.) /hun 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can be opened with acrobat and adobe reader 5.0 and later.) >> /namespace [ (adobe) (common) (1.0) ] /othernamespaces [ << /asreaderspreads false /cropimagestoframes true /errorcontrol /warnandcontinue /flattenerignorespreadoverrides false /includeguidesgrids false /includenonprinting false /includeslug false /namespace [ (adobe) (indesign) (4.0) ] /omitplacedbitmaps false /omitplacedeps false /omitplacedpdf false /simulateoverprint /legacy >> << /addbleedmarks false /addcolorbars false /addcropmarks false /addpageinfo false /addregmarks false /convertcolors /converttocmyk /destinationprofilename () /destinationprofileselector /documentcmyk /downsample16bitimages true /flattenerpreset << /presetselector /mediumresolution >> /formelements false /generatestructure false /includebookmarks false /includehyperlinks false /includeinteractive false /includelayers false /includeprofiles false /multimediahandling /useobjectsettings /namespace [ (adobe) (creativesuite) (2.0) ] /pdfxoutputintentprofileselector /documentcmyk /preserveediting true /untaggedcmykhandling /leaveuntagged /untaggedrgbhandling /usedocumentprofile /usedocumentbleed false >> ] >> setdistillerparams << /hwresolution [2400 2400] /pagesize [612.000 792.000] >> setpagedevice shot peening processes to obtain nanocrystalline surfaces in metal alloys: c.y. liu et alii, frattura ed integrità strutturale, 49 (2019) 557-567; doi: 10.3221/igf-esis.49.52 557 rock brittleness evaluation method based on the complete stressstrain curve chenyang liu, yong wang, xiaopei zhang, lizhi du university of jilin, changchun 130012, china wyzrp613@jlu.edu.cn abstract. brittleness plays an important role in the brittle failure process of rocks, and is also one of the important mechanical properties of rocks and a key indicator in rock engineering such as hydraulic fracturing, tunnelling machine borehole drilling and rockburst prediction. therefore, aiming at the applicability of the brittleness index, this paper summarizes and analyzes the existing brittleness indices based on different experimental methods. through analysis, it is found that many of the existing methods have their limitations. on the other hand, the brittleness evaluation method based on the stress sstrain curve makes it easier to obtain key parameters and quantify them. therefore, this paper also adopts this practically widely used method. it proposes a brittleness index based on the post-peak stress drop rate of the rock stress-strain curve and the difficulty of brittle failure, verifies by the traditional triaxial surrounding rock pressure test the accuracy and superiority of bl and further explores the differences between the brittleness indices b8, b11, b12 and bl. finally, the brittleness index bl and b13 are further contrasted by the existing experimental data. keywords. rock mechanics; failure; brittleness; complete stress-strain curve. citation: liu, c.y., wang, y., zhang, x.p., du, l.z., rock brittleness evaluation method based on the complete stress-strain curve, frattura ed integrità strutturale, 49 (2019) 557-567. received: 07.11.2018 accepted: 19.02.2019 published: 01.04.2019 copyright: © 2019 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. introduction rittleness is a fundamental parameter of rock mechanics and plays an important role in rock failure engineering. for example, the brittleness of rocks is an important indicator to evaluate the risks of rockburst. for underground engineering, rockburst is the most important issue [1]; in tunnel engineering, the rock brittleness determines the excavation efficiency of the tbm shield tunnelling machine; it also determines the efficiency of shale gas and oil production and has a great impact on the hydraulic fracturing of horizontal wells [2-5]. in order to reduce or even prevent the adverse b http://www.gruppofrattura.it/va/49/2255.mp4 c.y. liu et alii, frattura ed integrità strutturale, 49 (2019) 557-567; doi: 10.3221/igf-esis.49.52 558 effects of disasters on underground engineering and improve mining efficiency, it is extremely important for scientific research to figure out how to accurately evaluate the brittleness of rocks. 𝐵1 = 𝜎𝑐 𝜎𝑡⁄ , 𝐵2 = (𝜎𝑐 − 𝜎𝑡 ) (𝜎𝑐 + 𝜎𝑡 ) ⁄ , 𝐵3 = 𝜎𝑐 𝜎𝑡 2⁄ ,𝐵4 = √𝐵3 𝜎𝑐 and 𝜎𝑡 are the ucs and the tensile strength, respectively. 𝐵5 = 𝐵5 ′ 𝐵5 " , 𝐵5 ′ = (𝜀𝐵𝑅𝐼𝑇 − 𝜀𝑛 )/(𝜀𝑚 − 𝜀𝑛 ), 𝐵5 " = 𝛼𝐶𝑆 + 𝛽𝐶𝑆 + 𝜂, cs = 𝜀𝑝(𝜎𝑝 − 𝜎𝑟 )/𝜎𝑝/ (𝜀𝑟 − 𝜀𝑝) ε𝐵𝑅𝐼𝑇 , ε𝑚, ε𝑛 are the peak strain, the peak strain maximum and the minimum value of sample rock specimen, respectively. 𝛼, 𝛽, 𝜂 are the standardized coefficients. 𝜎𝑝 and 𝜎𝑟 are the peak strength and the residual strength, respectively. 𝜀𝑝 and 𝜀𝑟 are the peak strain and the residual strain, respectively. 𝐵6 = (𝑀 − 𝐸)/𝑀,𝐵7 = 𝐸/𝑀 m and e are the post-peak modulus and the pro-peak elastic modulus, respectively. 𝐵8 = (𝜎𝑝 − 𝜎𝑟 )/𝜎𝑝, 𝐵9 = (𝜀𝑟 − 𝜀𝑝)/𝜀𝑝, 𝐵10 = 𝜀𝑅 /𝜀𝑃 𝜎𝑝 and 𝜎𝑟 are the peak strength and the residual strength, respectively. 𝜀𝑟 and 𝜀𝑃 are the peak strain and the residual strain, respectively, 𝜀𝑅 is the reversible strain of the stress-strain curve. 𝐵11 = 𝐵11 ′ 𝐵11 " , 𝐵11 ′ = (𝜎𝑝 − 𝜎𝑟 )/𝜎𝑝, 𝐵11 " = lg|𝑘𝑎𝑐 | /10 𝜎𝑝 and 𝜎𝑟 are the peak strength and the residual strength, respectively. 𝑘𝑎𝑐 is the post-peak stress drop rate. 𝐵12 = 𝐵12 ′ + 𝐵12 " , 𝐵12 ′ = (𝜎𝑝 − 𝜎𝑟 )/(𝜀𝑟 − 𝜀𝑝), 𝐵12 " = (𝜎𝑝 − 𝜎𝑟 )(𝜀𝑟 − 𝜀𝑝)/( 𝜎𝑝𝜀𝑝) 𝜎𝑝 and 𝜎𝑟 are the peak strength and the residual strength, respectively, 𝜀𝑝 and 𝜀𝑟 are the peak strain and the residual strain, respectively. 𝐵13 = 𝐵13 ′ + 𝐵13 ′′ , 𝐵13 ′ = 𝜀𝑝(𝜎p − 𝜎i) (𝜀𝑝 −⁄ 𝜀i)𝜎𝑝 ，𝐵13 ′′ = 𝜀𝑝(𝜎p − 𝜎r) 𝜎𝑝⁄ (𝜀𝑟 − 𝜀𝑝) 𝜎𝑝 and 𝜎𝑟 are the peak strength and the residual strength, respectively. 𝜀𝑝 and 𝜀𝑟 are the peak strain and the residual strain, respectively, 𝜎i and 𝜀i are the crack initiation stress and the crack initiation strain 𝐵14 = 𝑠𝑖𝑛𝛽, 𝐵15 = 45° + 𝛽/2 𝛽 is the inner friction angle determined from mohr’s envelope. 𝐵16 = 0.5𝐸𝑏𝑟𝑖𝑡 + 0.5𝜇𝑏𝑟𝑖𝑡 , 𝐸𝑏𝑟𝑖𝑡 = (𝐸 − 1)/(8 − 1) × 100,𝜇𝑏𝑟𝑖𝑡 = (0.4 − 1)/ (0.4 − 0.15) e and 𝜇 are the post-peak modulus and the elastic modulus, respectively. 𝐵17 = (𝐻𝜇 − 𝐻𝑚 )/𝑐 where hμ is the micro-indentation hardness, hm is the macro-indentation hardness, and c is the constant 𝐵18 = 𝐻𝑎 /𝐾𝑐 where ha is hardness and kc is fracture toughness. 𝐵19 = 𝐻𝑎 𝐸/𝐾𝑐 2 where ha and kc are same as those in b18, e is young’s modulus 𝐵19 = 𝑊𝑞𝑡𝑧 /(𝑊𝑞𝑡𝑧 + 𝑊𝑐𝑎𝑟𝑏 + 𝑊𝑐𝑙𝑎𝑦 ), wqtz, wcarb and wclay are the content of quartz, clay and carbonate minerals, respectively. table 1: formula meaning and explanation. c.y. liu et alii, frattura ed integrità strutturale, 49 (2019) 557-567; doi: 10.3221/igf-esis.49.52 559 however, there is currently no standard or widely accepted concept for the evaluation of the rock brittleness index. researchers hold different views for different research purposes. morley [6] and hetényi [7] argue that rock brittleness is characterized by low elongation or low strain value due to the lack of ductility or compressibility. ramasy [8] defines brittleness as the loss of cohesion in a rock as it deforms within the elastic range. similarly, obert and duaval [9] consider brittleness to be a phenomenon in which a material (such as cast iron or rock) breaks or only slightly exceeds the yield stress. tarasov and potvin [10] proposed that brittleness is the ability to self-maintain the macroscopic damage in the post-peak area under the compressive load due to the accumulation of elastic energy. with the development of rock mechanics, a lot of research has been done on the evaluation of rock brittleness, and the commonly used evaluation methods are shown in tab. 1. brittleness evaluation method based on the rock stress-strain curve in tab. 1, the brittleness indices b1-b4 are proposed based on the relationship between ucs (uniaxial compressive strength) and uniaxial tensile strength. according to the experimental results, kahraman [11] believed that the penetration rate of the rotary drill bit has a strong exponential relationship with the brittleness indices b1 and b2. altindag [12] proposed the brittleness indices b3-b4 based on the tensile-compressive strength curve to quantitatively evaluate the brittleness of rocks. these two indices are often used to predict the drillability of rocks. however, the brittleness indices b1-b4 based on ucs and uniaxial tensile strength is not applicable to the analysis of rock brittleness under complex stress conditions. according to the post-peak stress drop rate and peak strength, li qinghui et al [13] proposed the brittleness index b5, which is based on the three standard coefficients for the post-peak stress drop, but only applies to a certain type of rocks, and what is more, a lot of experiments need to be done to obtain an accurate value. at the same time, tarasov and potvin [14] proposed the brittleness indices b6-b7 based on the post-peak secant modulus and the pre-peak elastic modulus. xia yingjie believed that these two brittleness indices cannot effectively distinguish the brittle characteristics of different stress-strain curves [15]. r. altindag [16] proposed the brittleness indices b7 and b8 based on the peak stress-strain and residual stress-strain relations. hucka and das [17] proposed the brittleness indices b10 based on the ratio of recoverable strain to peak strain before the peak; however, these methods consider only a few mechanical parameters and cannot fully reflect the strain-strain process of the entire rock. therefore, these methods require further improvement. meng et al. [18] proposed the brittleness index b11 based on the relative magnitude and absolute rate of the post-peak stress drop, and further verified the accuracy of the index by doing comparison test on different types of rocks under different surrounding rock pressures, but this index does not represent the pre-peak mechanical characteristics. xia yingjie et al. proposed the brittleness index b12 based on the post-peak stress drop rate and the ratio of the elastic energy released by the instability failure to the total energy stored before the peak. chen guoqing et al. [19] proposed the rock brittleness index b13 based on the post-peak stress drop rate and the stress growth rate between the pre-peak initiation stress and the peak stress. the method uses the stress growth rate between the initiation stress and the peak stress to characterize the pre-peak brittle state. at present, there are two effective ways to determine the initiation stress, one being acoustic emission and the other based on the strain inflection point of the crack volume [20]. acoustic emission is often affected by noise, making it difficult to determine the moment of crack initiation. the second method, which determines the initiation stress through the strain inflection point of the crack volume, often depends on the mineral composition and particle size, so it is also difficult to determine an accurate value. in order to further verify the accuracy of the method proposed in this paper, the following section will make comparisons with the experimental data by chen guoqing et al. brittleness evaluation method based on internal friction angle hucka and das [21] proposed evaluating the brittleness indices b14 and b15 of rocks considering the internal friction angle. at the same time, tarasov and potvin [22] found through experiments that the brittleness index b13 is positively correlated with the rock fracture angle. however, the brittleness indices b14 and b15 only apply to the same type of rocks; and it is also difficult to obtain an accurate rock fracture angle. brittleness evaluation method based on elastic modulus and poisson's ratio rockman et al. [23] proposed the brittleness index b16 based on shale reservoir; however, the brittleness index b16 only takes into account the elastic modulus and poisson’s ratio, but ignores many important mechanical parameters. in order to obtain accurate parameters, mechanical experiments still need to be conducted on a lot of rock samples. all these factors limit the development of the brittleness index b16. c.y. liu et alii, frattura ed integrità strutturale, 49 (2019) 557-567; doi: 10.3221/igf-esis.49.52 560 brittleness evaluation method based on hardness hucka and das proposed a rock brittleness evaluation method based on the difference between rock micro-hardness and macro-hardness. lawn and marshall [24] established the brittleness index b18 for the ceramic engineering field. quinn and quninn [25] described an index b19 to measure the rock brittleness based on the ratio of the deformation energy per unit volume to the fracture surface energy per unit area. this brittleness evaluation index considers too few factors and is only applicable to the ceramic field, so its accuracy and applicability should be further considered in applications. rock brittleness index based on stress-strain drop and peak strain n the brittleness evaluation in hydraulic fracturing and rockburst prediction, the existing brittleness evaluation methods consider only a few mechanical parameters. what is more, many of them are only applicable to uniaxial load conditions, and not suitable for high surrounding rock pressure in deep tunnel construction. the stress-strain curve, on the other hand, reflects the whole process of the rock from deformation failure to the ultimate loss of bearing capacity under external load, and is applicable to the state analysis of rock failure under surrounding rock pressure. based on the stress-strain curve of the rock failure, quantitative brittleness parameters can be obtained. therefore, the post-peak stress-strain shape obtained in the laboratory is the main method for researchers to qualitatively understand the rock brittleness. based on the above, this paper proposes a brittleness evaluation method based on post-peak stress drop rate and pre-peak brittle failure. figure 1: simplified stress-strain curve in fig. 1, the polyline oabc is a simplified class i stress-strain curve. point a (𝜎𝑝, ε𝑝) corresponds to the peak point, and 𝜎𝑃 and ε𝑃 are the peak intensity and the peak strain, respectively; point b (𝜎𝑟 , ε𝑟 ) corresponds to the residual point, and 𝜎𝑟 and ε𝑟 are the residual stress and the residual strain, respectively. it is obvious in fig. 1 that the polyline oabc is divided by point a (𝜎𝑝, ε𝑝) and point b (𝜎𝑟 , ε𝑟 ), so that the corresponding mechanical parameters can be quantitatively obtained. the drawbacks of the brittleness indices b10-b11 are already discussed above. based on these two methods, this paper proposes a new method 𝐵l1, which considers both the stress drop b8 and the strain drop b9. at the same time, the faster the stress drop rate, the higher the brittleness, so the difference between the peak stress and the residual stress is proportional to the brittleness index and the difference between the peak strain and the residual strain is inversely proportional to the brittleness index. in addition, in order to emphasize the final increase of the post-peak strain, the residual strain is used to replace the peak strain in the denominator of the brittleness index b9. first, the post-peak brittleness index 𝐵l1 is: 𝐵l1 = σp−σr σp εr−εp εr (1) i c.y. liu et alii, frattura ed integrità strutturale, 49 (2019) 557-567; doi: 10.3221/igf-esis.49.52 561 where, εr and εp are the residual strain and the peak strain, respectively; σp and σr are the peak stress and the residual stress, respectively. peak strain can reflect the difficulty of brittle failure [23]. in addition, according to previous studies, as the peak strain increases, the rock tends to transition from being brittle to being ductile, i.e., the brittleness index will become lower. considering this factor, it is proposed that the pre-peak brittleness index bl2 should be the reciprocal of the peak strain. second, the index of the difficulty of pre-peak brittle failure is as follows: 𝐵l2 = 1 εp (2) based on this, the new rock brittleness index bl considers both the post-peak stress drop rate and the difficulty of pre-peak brittle failure. finally, the brittleness index bl is expressed as follows: 𝐵l = 𝐵l1𝐵l2 (3) in summary, the new rock brittleness evaluation method bl considers the post-peak stress drop rate and also introduces the residual strain to emphasize the final increase of post-peak strain. moreover, it incorporates the difficulty of brittle failure to characterize the pre-peak brittle characteristics. comparison and verification of brittleness indices onsidering the great impact of surrounding rock pressure on rock brittleness in underground engineering, this section will explore the variations of rock brittleness under different surrounding rock pressure conditions. in order to verify the accuracy of the brittleness index bl, tab. 2 determines the relevant mechanical parameters and calculates the brittleness index bl according to the stress-strain curve in fig. 4. at the same time, for comparison with other brittleness indices, the brittleness indices b6-b12 and b14 are selected from tab. 1 (as b13 needs initiation stress and initiation strain, it is not selected here for comparison. the following sections will use the data by chen guoqing et al. for further comparison). confining pressure /mpa σp/ (100mpa) εp/10 -3 σr/ (100mpa) εr/10 -3 εr/10 -3 rupture angle(°) b6 b7 b8 b9 b10 b11 b12 b14 bl 0 0.419 2.59 0.268 3.47 1.656 85 0.037 0.963 0.361 0.340 0.639 0.081 0.294 0.996 0.549 3 0.467 2.71 0.363 4.23 2.106 79 -1.549 2.549 0.223 0.561 0.777 0.041 0.194 0.982 0.229 9 0.586 3.39 0.484 4.5 2.799 75 -0.908 1.908 0.174 0.327 0.826 0.034 0.149 0.966 0.208 12 0.605 3.63 0.357 4.9 2.142 70 0.080 0.920 0.410 0.350 0.590 0.094 0.339 0.939 0.436 15 0.658 3.84 0.563 5.26 3.286 70 -1.793 2.793 0.144 0.370 0.856 0.026 0.120 0.939 0.139 18 0.7956 4.51 0.677 6.12 3.837 65 -1.657 2.657 0.149 0.357 0.851 0.028 0.127 0.906 0.126 25 0.982 5 0.8085 7.79 4.117 60 -2.292 3.292 0.177 0.558 0.823 0.032 0.161 0.866 0.099 table 2: conventional triaxial compression experimental data of rock specimens from phyllite preparation and experimental conditions of rock samples rock brittleness has a profound effect on the stability of deep buried tunnels. in order to accurately evaluate the brittleness of rocks, the effects of surrounding rock pressure must be considered. this paper takes the phyllite samples obtained from c c.y. liu et alii, frattura ed integrità strutturale, 49 (2019) 557-567; doi: 10.3221/igf-esis.49.52 562 a deep hole in a tunnel in southwest china as the object. considering the geostress conditions of the rock samples, the conventional triaxial compression test was carried out to verify the accuracy of the new brittleness index bl. this test was carried out using a mts 815 test machine under different surrounding rock pressures. considering the different depths at which the rock samples were taken, 6 surrounding rock pressures were set, which are namely 0, 3, 9, 12, 15, 18 and 25mpa. according to the regulations of the international society for rock mechanics, samples were processed into standard specimens with a height of 100mm and a diameter of 50mm. during the experiment, the axial and radial deformations of the sensor were connected to a computer. the surrounding rock pressure was loaded at a rate of 0.1mpa/s, and the axial force is subject to displacement control, with a loading rate of 0.002mm/s. comparison and verification of rock brittleness indices under different surrounding rock pressures the information on sample loading and deformation is collected and stored by the data acquisition system. the failure results and stress-strain curves of the rock samples are shown in fig. 2. fig. 2 shows the fracture characteristics of the rock samples under different surrounding rock pressures. the macroscopic forms of rock failure mainly include shear-sliding failure along the schistose structure, transverse failure along the schistose surface and composite failure sliding along the schistose surface. as the surrounding rock pressure increased, the fracture angle of the rock sample and the roughness of the fracture surface decreased significantly, and the failure mode of the rock also changed. and with the surrounding rock pressure increasing, the post-peak stress drop rate decreased significantly, and the rock tended to transition from being brittle to being ductile. the experimental results indicate that the brittleness index decreases as the surrounding rock pressure increases. in particular, the rock sample under a surrounding rock pressure of 12mpa had a very rough fracture surface. through observation of the rock sample after the test, it is found that it was due to the internal defects in this rock sample. fig. 3 shows the variations of different brittleness indices as the surrounding rock pressure increases according to the calculation results in tab. 2. based on the experimental results, the rock brittleness index should satisfy the following characteristics: (1) the brittleness anomaly caused by the internal defects of the core under a surrounding rock pressure of 12mpa; (2) the brittleness tends to decrease with the increase of the surrounding rock pressure. from fig. 5, it can be seen that the brittleness indices b8, b11, b12 and bl basically conform to these two characteristics. for the brittleness indices b6 and b7, as the surrounding rock pressure increases, they cannot reflect the transition of the rock from brittleness to ductility. this is because the brittleness index b6 only considers the post-peak elastic modulus and the pre-peak elastic modulus. for the brittleness index b9, it can be clearly seen from fig. 5 that it does not reflect the brittleness changes. this is because b9 only considers the effect of the strain state, but ignores the effect of stress on the brittleness index. b10 only considers the recoverable strain and peak strain before the peak, but ignores the post-peak brittle characteristics. figure 2: stress-strain curve of rock samples under different surrounding rock pressures. c.y. liu et alii, frattura ed integrità strutturale, 49 (2019) 557-567; doi: 10.3221/igf-esis.49.52 563 as shown in fig. 3, the brittleness index b14 cannot reflect the brittleness anomaly caused by the internal defects of the sample under a surrounding rock pressure of 12mpa. in addition, it is difficult to quantitatively obtain an accurate rock fracture angle, which may also limit the development of the brittleness index b13. brittleness indices b8, b11, b12 and bl can reflect the decrease trend of the brittleness index with the increasing surrounding rock pressure and the brittleness anomaly caused by the internal defects of rock samples under a surrounding rock pressure of 12mpa. the next section will further compare the brittleness indices b8, b11, b12 and bl based on the results of the experiment. figure 3: variations of the core brittleness indices bl, b14 and b6-b12 with the surrounding rock pressure from the above analysis, it can be seen that the brittleness index bl proposed in this paper is in good consistency with b8, b11 and b12. in order to further compare these brittleness indices, the failure characteristics are analyzed under the surrounding rock pressure of 0-12mpa and 12-25mpa. fig. 4 shows the test results of the core under the surrounding rock pressure of 0mpa and 12mpa, where the red lines represent the fracture surfaces. as can be seen from fig. 6, the fracture surface of core a is rougher than that of core b, with a larger fracture angle. in summary, core a is more brittle than core b. the brittleness indices b8, b11, b12 and bl are not consistent with the above analysis results. however, the brittleness index bl can better reflect the changes. fig. 5 shows the test results of cores c, d, and e under the surrounding rock pressure of 15, 18 and 25mpa, where the red lines represent the fracture surfaces. the fracture angels of core c, d and e are 70°, 65° and 60°, respectively. as can be seen from fig. 7, in the three groups of samples, the roughness of the fracture surface gradually decreases from core c to e, so does the penetration. the fracture surface of core c penetrates the entire core, but those of cores d and e do not penetrate c.y. liu et alii, frattura ed integrità strutturale, 49 (2019) 557-567; doi: 10.3221/igf-esis.49.52 564 them. in addition, the fracture angles of the cores are also gradually reduced. in summary, as the surrounding rock pressure increases, the core brittleness gradually decreases, but through the analysis of fig. 5, it is found that only the brittleness index bl satisfies this feature under a surrounding rock pressure range of 15mpa-25mpa. therefore, the brittleness index bl is an effective supplement to b8, b11 and b12. 0mpa 12mpa (a) (b) figure 4: mechanical test results of two groups of cores 15mpa 18mpa 25mpa (c) (d) (e) figure 5: mechanical test results of three groups of cores in addition, since it is difficult to obtain the accurate crack initiation stress and crack initiation strain during the test, the following section will use the experimental results of chen guoqing et al. to further compare and verify the brittleness indices bl and b13. further verification of the accuracy and applicability of the brittleness index bl under surrounding rock pressure his section will further verify the accuracy and applicability of the brittleness index bl based on the existing experimental data. tab. 3 shows the brittleness index bl calculated according to the experimental data of marble cores under different surrounding rock pressures obtained by chen guoqing et al.. at the same time, this paper draws the plots of the brittleness indices bl and b13 changing with the surrounding rock pressure in order to facilitate the comparison with the brittleness index b13, as shown in fig. 6. confining pressure/ mpa σi/mpa 𝜀𝑖 /10 −3 σp/mpa εp/10 −3 σr/mpa εr/10 −3 b13 bl 5 87.929 1.693 192.084 3.729 71.956 5.976 2.031 0.446 15 89.354 1.589 258.749 4.867 123.939 7.434 1.960 0.310 25 116.041 1.967 297.072 5.615 162.811 8.174 1.930 0.257 35 126.055 1.943 332.891 6.393 190.99 10.716 1.523 0.165 table 3: mechanical parameters of cores and calculation results of brittleness indices b13 and bl under surrounding rock pressure t c.y. liu et alii, frattura ed integrità strutturale, 49 (2019) 557-567; doi: 10.3221/igf-esis.49.52 565 figure 6: changes of the marble brittleness indices under different surrounding rock pressures the brittleness index bl meets the feature that the brittleness decreases as the surrounding rock pressure increases. in addition, as the surrounding rock pressure increases, the decrease of the brittleness index bl is more linear than b13, which is more in line with the actual test results. for b13, the variation interval is not large, making it difficult to quantitatively measure the changes of brittleness. on the contrary, bl changes more significantly, which is also more in line with the actual test results. in summary, the brittleness index bl can give a more accurate quantitative description of rock brittleness and more accurately reflect its variations. in order to further explore the applicability of the brittleness index bl to different types of rocks under surrounding rock pressure and compare it with b13, this paper calculates the brittleness index bl according to the experimental data of different rocks under the surrounding rock pressure of 30mpa obtained by chen guoqing et al., as listed in tab. 4, and draws the brittleness index variations of 5 types of rock samples under the tri-axial stress condition, as shown in fig. 7. rock sample type σi/mpa 𝜀𝑖 /10 −3 σp/mpa εp/10 −3 σr/mpa εr/10 −3 b13 bl marble 75.917 1.515 134.521 11.24 126.537 24.337 0.554 0.010 sandstone 106.045 3.596 245.677 11.382 144.481 21.565 1.291 0.079 limestone 248.161 9.669 286.085 12.767 198.059 18.385 1.245 0.077 coarse grain granite 120.904 3.79 291.095 11.226 133.415 20.598 1.531 0.106 fine grain granite 145.194 1.93 476.75 8.8 9.716 22.212 1.534 0.184 table 4: mechanical parameters and calculated brittleness indices b13 and bl of different rocks under surrounding rock pressure [18] figure 7: brittleness index variations of the 5 types of rocks under surrounding rock pressure c.y. liu et alii, frattura ed integrità strutturale, 49 (2019) 557-567; doi: 10.3221/igf-esis.49.52 566 as shown in fig. 7, the brittleness index bl satisfies the degree of brittleness: fine grain granite > coarse grain granite > sandstone > limestone > marble. the brittleness indices bl and b13 of marble are significantly lower than those of the other four types of rock samples, which is consistent with the experimental results. for the other four types of rocks, the differences of the brittleness index bl are more obvious, making it much easier to quantitatively measure the degree of brittleness and also better reflect the brittleness variation trends of different rock samples. section 4 further verifies the accuracy and applicability of the brittleness index bl by using the experimental results of the same type and different types of rocks under surrounding rock pressure. compared with the brittleness index b13, bl is applicable to the brittleness evaluation in both cases. conclusions ccurate evaluation of rock brittleness is of great importance in rock engineering, such as underground tunnel excavation and hydraulic fracturing and so on. this paper proposes a new brittleness index evaluation method bl and verifies its effectiveness with experimental results. in addition, it also verifies the accuracy and applicability of the method using the existing experimental data. through systematic discussion and analysis of rock brittleness, this paper finally obtains the following conclusions: 1. this paper proposes a new brittleness evaluation method bl based on the post-peak stress drop rate and the difficulty of the pre-peak brittle failure. it verifies the accuracy of this index using the experimental results of phyllite rock samples taken from a deep hole of a tunnel in southwest china. with the experimental results, this paper further compares bl with other brittleness indices b8, b11 and b12, and concludes that bl more accurately reflects the experimental results. 2. with the experimental results of different types of rocks under surrounding rock pressure, this paper compares the brittleness indices b13 and bl and finds that bl accurately reflects the true brittleness variation trend of different rocks under surrounding rock pressure; at the same time, it also explores the brittleness changes of the same type of rocks under different surrounding rock pressures and finds that bl can give a better quantitative description of the rock brittleness than b13. 3. by analyzing the core with a surrounding rock pressure of 12mpa, this paper finds that the internal defects of a rock have an important impact on the rock mechanics. in actual engineering, the internal defects of rocks should be used to the advantage of rock engineering, and attention should be paid to make sure these internal defects will not cause any serious engineering disaster. references [1] altindag, r. (2002). the evaluation of rock brittleness concept on rotary blast hold drills, journal of the southern african institute of mining and metallurgy, 102, pp. 61-66. [2] holt, r.m., fjær, e., stenebråten, j.f., nes, o.m. (2015). brittleness of shales: relevance to borehole collapse and hydraulic fracturing, journal of petroleum science and engineering, 131, pp. 200-209. doi: 10.1016/j.petrol.2015.04.006 [3] hajiabdolmajid, v., kaiser, p. (2003). brittleness of rock and stability assessment in hard rock tunneling, tunnelling and underground space technology, 18, pp. 35-48. [4] dursun, a.e., gokay, m.k. (2016.) cuttability assessment of selected rocks through different brittleness values, rock mechanics and rock engineering, 49, pp. 1173-1190. doi:10.1007/s00603-015-0810-2. [5] özfırat, m.k., yenice, h., şimşir, f., yaralı, o. (2016). a new approach to rock brittleness and its usability at prediction of drillability, journal of african earth sciences, 119, pp. 94-101. doi: 10.1016/j.jafrearsci.2016.03.017. [6] morley, a. (1944). strength of material, longman, green, london. [7] el-ebrashi, m.k., craig, r.g., peyton, f.a. (1969). experimental stress analysis of dental restorations. part iii. the concept of the geometry of proximal margins, journal of prosthetic dentistry, 22, pp. 333-345. [8] ramsay, j.g. (1967). folding and fracturing of rocks, mc graw hill book company, 568. [9] obert, l., duvall, w.i. (1967). rock mechanics and the design of structures in rock / leonard obert, wilbur i. duvall, wiley. [10] tarasov, b., potvin, y. (2013). universal criteria for rock brittleness estimation under triaxial compression, international a c.y. liu et alii, frattura ed integrità strutturale, 49 (2019) 557-567; doi: 10.3221/igf-esis.49.52 567 journal of rock mechanics & mining sciences, 59, pp. 57-69. doi: 10.1016/j.ijrmms.2012.12.011 [11] kahraman, s. (2003). corrigendum to: “correlation of tbm and drilling machine performances with rock brittleness, engineering geology, 67, pp. 269-283. doi: 10.1016/s0013-7952(01)00137-5 [12] altindag, r. (2002). the evaluation of rock brittleness concept on rotary blast hole drills, journalsouth african institute of mining and metallurgy, 102(1), pp. 61-66. [13] li, q.h., chen, m., jin, y., wang, f.p., hou, b. (2012). indoor evaluation method for shale brittleness and improvement, chinese journal of rock mechanics & engineering, 31 (8), pp. 1680-1685. [14] tarasov, b.g., potvin, y. (2012). absolute, relative and intrinsic rock brittleness at compression, mining technology, 121(4), pp. 218-225. [15] xia, y.j., li, l.c., tang, c.a., li, x.y., ma, s., li, m. (2017). a new method to evaluate rock mass brittleness based on stress–strain curves of class i, rock mechanics & rock engineering, 50(5), pp. 1-17. doi: 10.1007/s00603-017-1174-6. [16] altindag, r. (2009). assessment of some brittleness indexes in rock-drilling efficiency, rock mechanics & rock engineering, 43(3), pp. 361-370. [17] hucka, v., das, b. (1974). brittleness determination of rocks by different methods, international journal of rock mechanics & mining sciences & geomechanics abstracts, 11(10), pp. 389-392. doi: 10.1016/0148-9062(74)91109-7. [18] meng, f., zhou, h., zhang, c., xu, r., lu, j. (2015). evaluation methodology of brittleness of rock based on postpeak stress–strain curves, rock mechanics & rock engineering, 48(5), pp. 1787-1805. doi: 10.1007/s00603-014-0694-6. [19] chen, g., zhao, c., wei, t., wang, j. (2018). evaluation method of brittle characteristics of rock based on full stressstrain curve and crack initiation stress, chinese journal of rock mechanics & engineering. [20] wang, y., li, x., wu, y.f. (2014). research on relationship between crack initiation stress level and brittleness indices for brittle rocks, chinese journal of rock mechanics & engineering. [21] hucka, v., das, b. (1974). brittleness determination of rocks by different methods. international journal of rock mechanics & mining sciences & geomechanics abstracts, 11(10), pp. 389-392. [22] tarasov, b., potvin, y. universal criteria for rock brittleness estimation under triaxial compression. international journal of rock mechanics and mining sciences, 59, 57-69. [23] rickman, r., mullen, m.j., petre, j.e. (2008). a practical use of shale petrophysics for stimulation design optimization: all shale plays are not clones of the barnett shale; proceedings of the spe technical conference and exhibition. [24] lawn, b.r., marshall, d.b. (2010). hardness, toughness, and brittleness: an indentation analysis, journal of the american ceramic society, 62 (7-8), pp. 347-350. doi: 10.1111/j.1151-2916.1979.tb19075.x. [25] quinn, j.b., quinn, g.d. (1997). indentation brittleness of ceramics: a fresh approach, journal of materials science, 32, pp. 4331-4346. microsoft word 2232 e. grande et alii, frattura ed integrità strutturale, 47 (2019) 321-333; doi: 10.3221/igf-esis.47.24 321 fracture and structural integrity: ten years of ‘frattura ed integrità strutturale’ numerical simulation of the de-bonding phenomenon of frcm strengthening systems ernesto grande university guglielmo marconi, department of sustainability engineering, via plinio 44, 00193-roma, italy e.grande@unimarconi.it, http:// orcid.org/0000-0002-3651-1975 maura imbimbo, sonia marfia university of cassino and southern lazio, dep. of civil and mechanical engineering, via g. di biasio 43, cassino, italy mimbimbo@unicas.it, http://orcid.org/0000-0003-3163-3073 marfia@unicas.it, http://orcid.org/0000-0002-2166-9788 elio sacco university of naples federico ii, department of structures in engineering and architecture, via claudio 21, naples. italy elio.sacco@unina.it http:// orcid.org/0000-0002-3948-4781 abstract. aim of the paper is to present a one dimensional simple model for the study of the bond behavior of fabric reinforced cementitious matrix (frcm) strengthening systems externally applied to structural substrates. the equilibrium of an infinitesimal portion of the reinforcement and the mortar layers composing the strengthening systems allows to derive the governing equations. an analytical solution is determined solving the system of differential equations. in particular, in the first part of the paper a nonlinear shear-stress slip law characterized by a brittle post-peak behavior with a residual shear strength in the post peak phase is introduced for either the lower reinforcement-mortar interface (approach 1) or both the lower and the upper interface (approach 2). in the latter approach, a calibration of the shear strength of the upper interface is proposed in order to implicitly account for the effect of the damage of the mortar on the bond behavior. in the second part of the paper it is presented the solution of the problem in the case of softening behavior by approximating the shear-stress slip law throughout a step function. comparisons with experimental data, available in literature, are presented in order to assess the reliability of the proposed approach. keywords. frcm; de-bonding; analytical model; interface. citation: grande, e., imbimbo, m., marfia, s., sacco, e., numerical simulation of the debonding phenomenon of frcm strengthening systems, frattura ed integrità strutturale, 47 (2019) 321-333. received: 23.10.2018 accepted: 24.11.2018 published: 01.01.2019 copyright: © 2019 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. http://www.gruppofrattura.it/va/47/2232.mp4 e. grande et alii, frattura ed integrità strutturale, 47 (2019) 321-333; doi: 10.3221/igf-esis.47.24 322 introduction he reinforcement of existing structures has always been a relevant problem both in the technical and scientific civil engineering community. lately, the study and design of new reinforcement materials is a challenging issue. in particular, fabric reinforced cementitious matrix (frcm) is an emerging strengthening system obtained embedding a grid of the carbon, glass or aramid reinforcement in an inorganic matrix. in general, the matrix is applied as a double layer incorporating the reinforcement. nowadays, frcm systems are used in the current practice to reinforce concrete and masonry structures. some experimental investigations [1-7] and theoretical/numerical studies ([2, 3, 8-16] on frcm strengthening systems are available in the recent literature. they testify the efficacy and advantages of frcm systems together with the need to investigate aspects specifically characterizing the bond behavior of this new family of strengthening systems. the experimental investigations are mainly shear-lap tests that analyze the local bond behavior of frcms. from the experimental evidence different failure mechanisms can occur, such as a cohesive failure of the substrate, de-bonding at the reinforcement/substrate interface, de-bonding at the reinforcement/matrix interface, sliding of the reinforcement, tensile failure of the reinforcement in the un-bonded portion and tensile failure of the reinforcement within the mortar. the above mechanism occurrence depends on the characteristics of the strengthening system as well as of the support, such as the mechanical properties of the materials, the thickness of the mortar layers and the configuration of the reinforcement. these mechanisms particularly underline the role of additional phenomena to be necessarily considered for the study and the development of theoretical models/design formulas specific for frcms. regarding the theoretical and numerical studies, the approaches available in literature show particular interest to the derivation of simple laws able to simulate the de-bonding phenomenon and, moreover, models able to account for additional phenomena specific of frcms. in [2] the shear stress-slip law at the interface level was obtained throughout a procedure applied to steel and carbon frcm strengthening systems externally embedded on masonry supports. the procedure was carried out by directly considering the experimental data and in particular the strain gauge measurements. a procedure for the derivation of the shear stress-slip law for frcms based on the experimental data was also proposed in [3]. in particular, the authors firstly estimated the fracture energy by using the well-known formula derived by the theory of linear fracture mechanics and, subsequently, they performed numerical fe analyses to detect the optimal values of the parameters of the cohesive shear stress-slip law. in[4] the bond behavior of frcm-to-concrete was analytically examined by using a general approach applied to the case of frp-materials. the results emerged from this study particularly emphasized the role of the pronounced descending branch of the calibrated laws in leading to large values of the effective anchorage length. in addition, lower values of bond shear stresses on the concrete surface with respect to those typically characterizing frp strengthening systems were observed. a similar approach was also presented in [3] for the case of carbon-frcm materials externally applied on masonry supports. in [13] two approaches for numerically studying the bond behavior of masonry specimens strengthened with frcms were proposed. the first one, consisted of an analytical-numerical approach specifically accounting for the interaction between the reinforcement and the mortar; the second approach consisted of a full 3d-fem non-linear approach obtained as an extension of the procedure originally adopted in [13] and in [15]. a recent study presented in [9,16] was mainly devoted to investigate the influence of the upper mortar layer on the bond behavior of frcm-strengthening systems applied on structural supports. in particular, the authors carried out a theoretical modeling approach based on the solution of a system of differential equations obtained by introducing equilibrium considerations. from the study emerged interesting aspects concerning the role of the upper mortar layer on the debonding process of frcms. among these, it was observed that increasing the applied load after the occurrence of the de-bonding between the reinforcement and the upper interface it does not lead to further increases of the peak value of normal stresses of the upper mortar. on the other hand, after the occurrence of the first crack at the upper mortar, only the peak value of slips at the lower interface continues to increase whilst the peak value of slips at the upper interface does not significantly increase. in [10] it was proposed a simple approach for the study of the bond behavior of frcm applied to concrete supports able to enable the use of a common interface modeling strategy by implicitly introducing the effect of the damage of the matrix into the shear behavior of the reinforcement/mortar interface layer. in this paper a one dimensional simple model, based on the one presented in [9] and in [16], is proposed for the study of the bond behavior of frcm strengthening systems externally applied to masonry substrates. the model is mainly t e. grande et alii, frattura ed integrità strutturale, 47 (2019) 321-333; doi: 10.3221/igf-esis.47.24 323 characterized by the derivation of the explicit solution of a system of differential equations obtained by considering the equilibrium of an infinitesimal portion of the reinforcement and the mortar layers composing the strengthening systems. in order to model the slip between the reinforcement and the upper and lower mortar layers, two approaches are considered. the first approach (denoted in the following approach 1), considers a nonlinear behavior of the lower reinforcement/mortar interface only, by considering a shear stress-slip constitutive law characterized by a linear brittle behavior with a residual strength in the post-peak phase. on the other hand, the approach 2 assumes a nonlinear behavior for both the lower and the upper reinforcement/mortar interface, still considering a shear stress-slip constitutive law characterized by a linear fragile behavior with a residual strength in the post-peak phase. moreover, in the latter approach, a calibration of the shear strength of the upper interface is proposed in order to implicitly account for the effect of the damage of the mortar on the contribution of this component of the strengthening system. in addition to these approaches, in the second part of the paper is presented the analytical solution in case of a shear stress-slip law characterized by a linear softening behavior in the post-peak phase. in particular, a step function approximating the law together with the procedure carried out from the approach 2 are used in order to derive the analytical solution. the proposed approaches are validated in the paper by considering experimental results derived from the literature. moreover, the results are also compared with the ones obtained by the model recently proposed by [9,16], where, differently from the proposed approaches, the damage of the upper mortar was explicitly introduced in the model by assuming a nonlinear behavior in terms of normal stress-strain for the upper mortar layer. although this assumption allows to account for the phenomena generally observed, it leads to a computational effort significantly greater than the one characterized the two approaches proposed in this paper. accounted model and approaches he model here considered for the study of the bond behavior of frcm systems externally applied on masonry or concrete supports is based on the work in [9, 16]. indeed, considering the scheme shown in fig. 1, the main components characterizing the model are: a cohesive support, a lower mortar layer, a lower interface, the strengthening, an upper interface and an upper mortar layer. introducing a reference axis x in the direction of the reinforcement system and fixing the origin in correspondence of the unloaded section, the equilibrium of forces characterizing an infinitesimal portion of the reinforcement and the upper mortar layer (see fig. 1) leads to the following system of differential equations governing the problem of the bond behavior:       0 0 p e e i i p p p e e e ec p c p d b t s s b dx d b t s b dx                 (1) where p and e c are the normal stresses in the reinforcement and in the upper mortar, respectively; pt and e ct are the thicknesses of the reinforcement and the upper mortar, respectively; i and e are the shear stresses at lower and upper interfaces, respectively, both depending on the corresponding slips is and es ; pb is the width of the reinforcement. introducing the following hypotheses: the support and the lower mortar layer are assumed to be rigid; the (lower and upper) mortar/reinforcement interfaces are modeled as zero-thickness elements with only shear deformability; the upper mortar layer and the reinforcement are assumed deformable only axially. it is possible to write the displacements of both the reinforcement and the upper mortar layer (namely pu and e cu , respectively) as functions of the slip of the lower and upper interfaces: i p e i e c u s u s s    (2) t e. grande et alii, frattura ed integrità strutturale, 47 (2019) 321-333; doi: 10.3221/igf-esis.47.24 324 figure 1: schematic of an infinitesimal portion of the strengthening system and the upper mortar component used for performing the equilibrium of the involved forces. considering a linear-elastic behavior for both the reinforcement and the mortar: i p p p p e i e e c c c c du ds e e dx dx du ds ds e e dx dx dx             (3) the system of differential eqns. (1) becomes:       2 12 2 2 22 2 0 0 i e e i i i e e e d s k s s dx d s d s k s dx dx                   (4) where 1k and 2k are two constants equal to: 1 2 1 1 , e p p c c k k e t e t   (5) considering the system (4), the explicit solution is here derived by introducing different shear stress-slip laws characterizing the behavior of the reinforcement/mortar interface. approach 1: nonlinear behavior of the lower interface a preliminary approach is based on the assumption of a linear-fragile behavior with a residual shear strength in the postpeak stage only for the lower interface: 1( ) ( ) otherwise i i i i i i i i res s g s s s s         (6) where ires is the residual value of the shear strength in the post-peak stage, and ig is the shear stiffness of the lower interface in the pre-peak stage. differently, a linear-elastic behavior is assumed for the upper interface ( )e e e es g s  , where eg is the shear stiffness of the upper interface. p p pd p c cd c e e isupport lower interface strengthening upper interface upper mortar lower mortar x e. grande et alii, frattura ed integrità strutturale, 47 (2019) 321-333; doi: 10.3221/igf-esis.47.24 325 on the basis of these assumptions it is evident that, after the attainment of the slip threshold value at the lower interface, two different parts characterize the behavior of the specimen: part “1” where the upper mortar and the interfaces are both in the pre-peak stage and part “2” where the upper mortar and the upper interface are both in the pre-peak stage while the lower interface is de-bonded for a length a, representing an unknown of the problem. consequently, four differential equations govern the problem. the first two equations are derived by considering the equilibrium involving an infinitesimal portion of the strengthening system in the part “1”: 2 1 3 1 12 2 2 1 1 4 12 2 0 0 0 i e i i e e d s k s s dx x l a d s d s k s dx dx                   (7) where: 3 1 4 2, , i e e e g k k g k k g g    . the other two equations are obtained through the equilibrium involving an infinitesimal portion of the strengthening system of the part “2”: 2 2 3 22 2 2 2 2 4 22 2 0 0 i e i e e d s k s dx l a x l d s d s k s dx dx                   (8) where i res eg    . the system of differential eqns. (7) and (8) has an analytical solution that depends on eight constants of integration determined by introducing suitable boundary conditions. in particular, the following conditions are indeed enforced:                         1 1 2 1 2 1 2 1 2 1 2 1 1 0 0 0 0 0 p e e c c e e c c e e p p i i e e i l l a l a l a l a s l a s l a s l a s l a s l a s                         (9) the solution is graphically reported in fig. 2 by considering a length value of the part “2” equal to a=50 mm, a residual value of shear strength equal to zero and the data reported in tab. 1. approach 2: nonlinear behavior of both the interfaces as shown in [11,17], the damage of the upper mortar generally occurs before the slipping of the reinforcement/mortar interfaces by particularly influencing the shear stress transfer mechanism. this phenomenon is here simple introduced by considering an elastic-fragile behavior also for the upper interface and assuming for this component of the strengthening system a bond strength equal to the shear stress corresponding to the attainment of the tensile strength of the upper mortar layer. in other words, the effect of the damage of the upper mortar is implicitly introduced into the behavior of the upper interface. e. grande et alii, frattura ed integrità strutturale, 47 (2019) 321-333; doi: 10.3221/igf-esis.47.24 326 a) b) c) figure 2: approach 1: a) shear stress developing at the interfaces; b) slip of the interfaces; c) normal stresses at the upper mortar layer. symbol [unit] value young’s modulus of the reinforcement ep [mpa] 206000 young’s modulus of the mortar ec [mpa] 7000 equivalent thickness of the reinforcement tp [mm] 0.054 thickness of the mortar tc [mm] 4 width of the reinforcement bp [mm] 60 width of the mortar bc [mm] 60 bond length l [mm] 1000 table 1: data accounted for numerical analyses. considering this assumption, the system of equations governing the problem has to account for the development of three possible parts characterizing the behavior of the specimen: part “1”: 0<x<l-(a+b), where both the interfaces are in the pre-peak stage and normal stresses in the upper mortar are lower than the tensile strength; part “2”: l-(a+b)<x<l-b, where the upper interface is in the post-peak stage (the length of this zone is equal to a); part “3”: l-b<x<l, where both the interfaces are in the post-peak stage (the length of this zone is equal to b). in particular, while the equations characterizing the part “1” are the eqns. (7), the equations characterizing the part “2” are: 2 2 5 22 2 2 2 2 22 2 0 ( ) 0 i i i e e res d s k s dx l a b x l b d s d s k dx dx                      (10) and the equations characterizing the part 3 are: 2 3 12 2 2 3 3 22 2 0 0 i e i res res i e e res d s k dx l b x l d s d s k dx dx                    (11) where: e res ig    , 5 1 ik k g , a is the length of the part 2, b is the length of the part 3, eres and i res are the residual shear strength values are of the upper and lower interfaces respectively. the whole system of differential eqns. (7), (10) and (11) has an analytical solution that depends on twelve constants of integration determined by introducing suitable boundary conditions similar to the ones introduced for the approach 1. the solution is graphically reported in fig. 3 by considering a length value of the part “2” equal to a=50 mm, a length of e. grande et alii, frattura ed integrità strutturale, 47 (2019) 321-333; doi: 10.3221/igf-esis.47.24 327 the part “3” equal to b=50 mm, a shear strength of the lower mortar equal to 0.9 mpa, a shear strength of the upper mortar equal to 0.45 mpa, a residual value of shear strength equal to zero for both the interfaces and the data reported in tab. 1. a) b) c) figure 3: approach 2: a) shear stress developing at the interfaces; b) slip of the interfaces; c) normal stresses at the upper mortar layer. numerical applications for the approach 1 and the approach 2 in order to assess the capability of the proposed model in providing a reliable prediction of the bond behavior of frcm strengthening systems, some case studies derived from the current literature are considered ([4]). the case studies, here considered, consist of single lap shear tests of concrete blocks strengthened by a bidirectional unbalanced pbo fiber net with two mortar layers. in particular, in the present research the specimens are considered characterized by a bond length equal to 450 mm and two different values of the reinforcement width: bp=60 mm and bp=80 mm. these tests are of particular relevance since the experimental outcomes showed the damage of the upper mortar layer of tested specimens before the slipping at the interface level. regarding the application of the approach 1, a shear stress-slip law for the lower interface characterized by a shear strength equal to 0.9 mpa and a slip threshold equal to 1.2 mm is considered (see [4]). on the other hand, for the approach 2 a shear strength value of the upper interface corresponding to the attainment of the tensile strength of the upper mortar layer (fct=3.5 mpa) is considered. for both the approaches, a null value of the residual shear strength is assumed for both the interfaces. the obtained results are shown in fig. 4 in terms of applied load p versus the slip of the lower interface at the loaded section. in the same figure the envelop of the experimental curves (grey region) and the curve carried out in [4] are also reported. a) b) figure 4: comparison with experimental tests in terms of applied force vs. slip curves. 0 2 4 6 8 10 0 2 4 6 8 10 12 grande et al. 2018 approach 1 approach 2 slip si(x=l) [mm] a p p li e d lo a d p  [ k n ] d’antino et al. 2015 – bp=60mm 0 2 4 6 8 10 12 0 2 4 6 8 10 12 grande et al. 2018 approach 1 approach 2 slip si(x=l) [mm] a p p li e d lo a d p  [ k n ] d’antino et al. 2015 – bp=80mm e. grande et alii, frattura ed integrità strutturale, 47 (2019) 321-333; doi: 10.3221/igf-esis.47.24 328 from the plots clearly emerges the importance of introducing in the model the influence of the damage of mortar on the contribution of the upper interface. indeed, while the curves deduced from the approach 1 overestimate the experimental peak load, the curves derived by using the approach 2 provide a good approximation of the experimental outcomes. approximate solution in case of softening behavior n the previous section a solution of the de-bonding problem has been presented by introducing simplified shear stress-slip laws for the interfaces assumed with a perfect brittle post-peak behavior. this has allowed to obtain the analytical solution of the problem and to easily analyze different damage stages. the majority of studies available in the current literature are instead based on the use of constitutive laws where the softening governs the postpeak phase of the interface (cohesive models). the use of this type of laws at the interface level generally does not lead to computational problems when a finite element approach, or other types of numerical techniques, are used. on the contrary, it can present some drawbacks for the derivation of an analytical solution, particularly in the case of frcm systems where there are two interfaces interacting among them in the de-bonding process. for this reason, the analytical solution is here derived by approximating the linear descending post-peak branch of the shear stress-slip law throughout a step function, i.e. a piecewise constant function (fig. 5), and following the approach presented in the first part of the paper. moreover, taking into account the ‘approach 2’ presented in the first part of the paper, the softening behavior is only introduced for the lower interface, whilst a linear-brittle behavior is accounted for the upper interface by opportunely calibrating the corresponding bond strength. figure 5: scheme used for approximating the softening branch of the shear stress-slip law. also in this case, the system of equations governing the problem depends on the status of the two interfaces (see fig. 6). indeed, increasing the applied load p, the first phase is certainly characterized by the pre-peak stage of both the interfaces (fig. 6.a). in this case, the system of the two equations governing the problem is:       2 12 2 2 22 2 0 0 i e e i i i e e e d s k s s dx d s d s k s dx dx                   (12) where: ( ) ( ) i i i i e e e e s g s s g s     (13) s1 s2 s3 s4 1 2 3 4  s i e. grande et alii, frattura ed integrità strutturale, 47 (2019) 321-333; doi: 10.3221/igf-esis.47.24 329 a) b) c) figure 6: scheme used for approximating the softening branch of the shear stress-slip law: a) phase 1 *1 1; i es s s s  ; b) phase 2 zone 1: *1 1; i es s s s  ; zone 2 zone 3: *1 1; i es s s s  ; c) phase 3 zone 1: *1 1; i es s s s  ; zone 2 zone 3: *1 1; i es s s s  ; zone 4 zone 5: *1 1; i es s s s  . the analytical solution of this system depends on four constants of integration determined by introducing suitable boundary conditions. in particular, considering the attainment of the slip s1 at the lower interface (generally, the lower interface exhibits higher values of shear stresses than the upper interface), the following conditions are indeed enforced:         1 0 0 0 0 0 p e c e c i l s l s        (14) the subsequent phase is then characterized by the upper interface in the pre-peak stage and the lower interface in the post-peak stage (fig. 6.b). this phase ends when the upper interface attains the slip s1 at the loaded end. the occurrence of this condition identifies the number of steps approximating the descending branch of the shear stress-slip law of the lower interface involved in this phase. the number of equations governing the problem depends on the number of the zones in which the systems is divided and, thus, on the number of steps considered in the approximate descending branch of the interface constitutive law. for instance, considering the case of the fig. 6.b, it is supposed that there are three zones characterizing the behavior of the lower interface, which include two steps approximating the descending branch. consequently, the differential equations composing the system are the following: zone 1: 2 1 1 1 12 2 2 1 1 2 12 2 0 0 ( ) 0 i e e i i i e e e d s k g s g s dx x l a b d s d s k g s dx dx                  (15) zone 2: 2 2 1 2 22 2 2 2 2 2 22 2 0 ( ) 0 i e e i e e e d s k g s dx l a b x l b d s d s k g s dx dx                   (16) upper interface lowe interface (1) (2) (3) (1) (2) (3) (4) (5) e. grande et alii, frattura ed integrità strutturale, 47 (2019) 321-333; doi: 10.3221/igf-esis.47.24 330 zone 3: 2 3 1 3 32 2 2 3 3 2 32 2 0 0 i e e i e e e d s k g s dx l b x l d s d s k g s dx dx                 (17) where 2 and 3 are the shear stress values identified by the steps approximating the descending branch in the phase 2. in this case, it is necessary to introduce twelve boundary conditions. four boundary conditions concern the two end sections of the specimen where it is stated that: the stress is zero at the free end of the reinforcement; the stresses are zero at two ends of the upper mortar layer; the upper interface attains the slip *1s at the loaded end, i.e. the slip corresponding to the attainment of the tensile strength of the upper mortar layer, i.e.:         ,1 ,1 ,3 * 3 1 0 0 0 0 0 p e c e c e l s l s        (18) the other boundary conditions concern the continuity of normal stresses in the mortar layer and in the reinforcement, the continuity of the slip at the lower and upper layers at the section:                                         1 2 1 2 2 3 2 3 1 2 1 2 1 2 1 2 e e e e c c p p e e e e c c p p i i e e i i e e l a b l a b l a b l a b l b l b l b l b s l a b s l a b s l a b s l a b s l b s l b s l b s l b                                         (19) moreover, due to the introduction of the additional unknowns a and b, i.e. the length of the zone 2 and the zone 3 respectively, it is necessary to introduce the following two additional boundary conditions:     2 2 3 3 i i s l b s s l s    (20) where s2 and s3 are the slips identified by the two steps along the softening branch. the subsequent phase (fig. 6.c) is characterized by both the interfaces in the post-peak stage. an increase of the number of equations is still due to the steps discretizing the descending branch of the shear stress-slip law of the lower interface. moreover, some of the zones are also characterized by a null value of the shear stress at the upper interface. indeed, considering the example shown in fig. 6.c, the set of equations characterized by this condition are the ones related to the last two zones: zone 4:   2 4 1 42 2 2 4 4 2 2 0 0 i i e d s k dx l c d x l d d s d s dx dx               (21) e. grande et alii, frattura ed integrità strutturale, 47 (2019) 321-333; doi: 10.3221/igf-esis.47.24 331 zone 5: 2 5 1 52 2 2 5 5 2 2 0 0 i i e d s k dx l d x l d s d s dx dx             (22) the boundary conditions are the same of those accounted for the previous phases and, also in this case, it is necessary to introduce additional boundary conditions for deriving the length of the different zones. numerical applications for the case with softening considering the approach based on the step function approximation, numerical applications are performed with reference to the case studies presented in the first part of the paper ([4]). in particular, considering the shear stress-slip law proposed in [4], a bi-linear law has been derived (fig. 7.a). subsequently, this law has been approximated throughout a step function and assumed for the behavior of the lower interface (fig. 7.b). regarding the upper interface, a linear brittle shear stress-slip law has been considered by assuming a bond strength value equal to 0.9 mpa, which corresponds to the attainment of the tensile strength of the upper mortar layer (see the approach 2). a) b) figure 7: shear stress-slip law accounted for the lower interface in the case of the approach based on the step function approximation. a) b) figure 8: results in terms of applied load vs. slip: comparison between the approach 2 and the case with softening. 0 0.2 0.4 0.6 0.8 1 0 0.5 1 1.5 sh e a r  st re ss  [ m p a ] slip [mm] bi‐linear step‐function 0 2 4 6 8 0 1 2 3 4 a p p li e d  l o a d  p  [ k n ] slip si(x=l) [mm] d'antino et al., 2015 ‐ bp=60mm approach 2 softening 0 2 4 6 8 10 0 1 2 3 4 a p p li e d  l o a d  p  [ k n ] slip si(x=l) [mm] d'antino et al., 2015 ‐ bp=80mm approach 2 softening e. grande et alii, frattura ed integrità strutturale, 47 (2019) 321-333; doi: 10.3221/igf-esis.47.24 332 then, considering the equations at the basis of the problem and the boundary conditions, both presented in the previous section, the analytical solution has been derived and presented in fig. 8 in terms of applied load vs. the slip. in the same plot it is also reported the curve previously obtained by applying the approach 2 and then considering a linear-brittle behavior also for the lower interface. by examining the curves of the plot it emerges a similar value in terms of peak load and post-peak behavior. this outcome is due to the fact that the law assumed for the approach 2 and the one with softening are characterized by the same value of fracture energy: f=0.54 n/mm. on the other hand, the greater initial stiffness and the smoother post-peak branch of the case with softening are strictly related to the shape of the shear stressslip laws. in fig. 9, it is reported for the case with bp=60 mm the distributions along the bond length of shear stresses at the interfaces and normal stresses at the upper mortar layer for the load step corresponding to the attainment of the slip s1 at the lower interface. the plots underline the length of the four zones (a1=10mm; a2=28.5mm; a3=54mm; a4=25mm) characterizing the behavior of the lower interface. moreover, it also emerges that: the maximum value of normal stresses in the upper mortar layer remains equal to the tensile strength because of the assumption of a reduced bond strength for the upper mortar; after the zone a1, since shear stresses in the upper interface are equal to zero, also the normal stresses at the upper mortar layer are zero. a) b) c) figure 9: results in terms of distribution along the bond length of a) slips, b) shear stresses, c) normal stresses at the step corresponding to the attainment of the slip value si=sf=1.2 mm at the lower interface: case with softening. conclusive remarks n this paper a one-dimensional simplified model for studying the bond behavior of frcm strengthening systems externally applied to masonry structures is proposed. the model is based on the study of an infinitesimal portion of the strengthening system composed by the reinforcement and the mortar layers, computing the explicit solution of a system of equilibrium differential equations. interfaces are introduced between the reinforcement and the upper and lower mortar layers to model the possible slip phenomena. a nonlinear shear-stress slip laws, characterized by a brittle fracture with a residual strength in the post-peak stage, is adopted for the interfaces to derive the two approaches presented in the first part of the paper. these approaches differ only for the behavior of the upper interface: in the first one the upper interface is characterized by a linear behavior, while, in the second one by the proposed nonlinear response. both the approaches have been applied to two case studies available in the literature. from the results, approach 2 is able to better describe the experimental results, both in terms of peak load and post peak behavior, with respect to approach 1. in approach 2 the value of the peak shear stress in the upper interface is calibrated in order to take into account the damage occurring in the upper layer of mortar. the results are also compared with the ones obtained by the model proposed by [9,16]. from a computational point of view, the presented model results simpler than the one proposed in [9,16], as it doesn’t model directly the damage mechanism in the upper layer of mortar but it is able to take it into account by suitable setting the peak shear stress in the constitutive law of the upper interface. in the second part of the paper it has been presented the analytical solution in the case of softening behavior of the lower interface. in particular, a step function has been introduced in order to approximate the softening branch. also in this case the approach has been applied to the same case studies of literature. from the obtained results it is emerged a response similar to the one obtained in the approach 2 due to the important role played by the fracture energy, parameter common to the two models. i e. grande et alii, frattura ed integrità strutturale, 47 (2019) 321-333; doi: 10.3221/igf-esis.47.24 333 references [1] d’ambra, c., lignola, g.p., prota, a., sacco, e., fabbrocino, f. (2018). experimental performance of frcm retrofit on out-of-plane behaviour of clay brick walls, compos. part b eng., 148, pp. 198-206. doi: 10.1016/j.compositesb.2018.04.062. [2] d’ambrisi, a., feo, l., focacci, f. (2012). bond-slip relations for pbo-frcm materials externally bonded to concrete, compos. part b eng., 43(8), pp. 2938-2949. doi: 10.1016/j.compositesb.2012.06.002. [3] d’ambrisi, a., feo, l., focacci, f. (2013). experimental analysis on bond between pbo-frcm strengthening materials and concrete, compos. part b eng., 44, pp. 524-532. doi: 10.1016/j.compositesb.2012.03.011. [4] d’antino, t., sneed, l.h., carloni, c., pellegrino, c. (2015). influence of the substrate characteristics on the bond behavior of pbo frcm-concrete joints, constr. build. mater., 101(1), pp. 838-850. doi: 10.1016/j.conbuildmat.2015.10.045. [5] de felice, g., de santis, s., garmendia, l., ghiassi, b., larrinaga, p., lourenço, p.b., oliveira, d. v., paolacci, f., papanicolaou, c.g. (2014). mortar-based systems for externally bonded strengthening of masonry, mater. struct. constr., 47(2), pp. 2021-2037. doi: 10.1617/s11527-014-0360-1. [6] grande, e., imbimbo, m., sacco, e. (2015). investigation on the bond behavior of clay bricks reinforced with srp and srg strengthening systems, mater. struct. constr., 48(11), pp. 3755-3770. doi: 10.1617/s11527-014-0437-x. [7] marcari, g., basili, m., vestroni, f. (2017). experimental investigation of tuff masonry panels reinforced with surface bonded basalt textile-reinforced mortar, compos. part b eng., 108, pp. 131-142. doi: 10.1016/j.compositesb.2016.09.094. [8] grande, e., imbimbo, m., sacco, e. (2013). modeling and numerical analysis of the bond behavior of masonry elements strengthened with srp/srg, compos. part b eng., 55, pp. 128–38. [9] grande, e., imbimbo, m., sacco, e. (2017). local bond behavior of frcm strengthening systems: some considerations about modeling and response, 747 kem, pp. 101-107. [10] grande, e., milani, g. (2018). interface modeling approach for the study of the bond behavior of frcm strengthening systems, compos. part b eng., 141, pp. 221-233. doi: 10.1016/j.compositesb.2017.12.052. [11] carbone, i. (2010). delaminazione di compositi a matrice cementizia su supporti murari. università degli studi roma tre. [12] faella, c., martinelli, e., paciello, s., perri, f. (2009).composite materials for masonry structures: the adhesion issue. mechanics of masonry structures strengthened with composite materials, in: proc. of 3rd conf. on mechanics of masonry structures strengthened with composite materials: modeling, testing, design, control – murico3, venice (italy), pp. 266-273. [13] carozzi, f.g., milani, g., poggi, c. (2014). mechanical properties and numerical modeling of fabric reinforced cementitious matrix (frcm) systems for strengthening of masonry structures, compos. struct., 107, pp. 711-725. doi: 10.1016/j.compstruct.2013.08.026. [14] milani, g., lourenço, p.b. (2012). 3d non-linear behavior of masonry arch bridges, comput. struct., 110, pp. 133150. doi: 10.1016/j.compstruc.2012.07.008. [15] milani, g., tralli, a. (2012). a simple meso-macro model based on sqp for the non-linear analysis of masonry double curvature structures, int. j. solids struct., 49(5), pp. 808-834. doi: 10.1016/j.ijsolstr.2011.12.001. [16] grande, e., imbimbo, m., sacco, e. 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can be opened with acrobat and adobe reader 5.0 and later.) >> /namespace [ (adobe) (common) (1.0) ] /othernamespaces [ << /asreaderspreads false /cropimagestoframes true /errorcontrol /warnandcontinue /flattenerignorespreadoverrides false /includeguidesgrids false /includenonprinting false /includeslug false /namespace [ (adobe) (indesign) (4.0) ] /omitplacedbitmaps false /omitplacedeps false /omitplacedpdf false /simulateoverprint /legacy >> << /addbleedmarks false /addcolorbars false /addcropmarks false /addpageinfo false /addregmarks false /convertcolors /converttocmyk /destinationprofilename () /destinationprofileselector /documentcmyk /downsample16bitimages true /flattenerpreset << /presetselector /mediumresolution >> /formelements false /generatestructure false /includebookmarks false /includehyperlinks false /includeinteractive false /includelayers false /includeprofiles false /multimediahandling /useobjectsettings /namespace [ (adobe) (creativesuite) (2.0) ] /pdfxoutputintentprofileselector /documentcmyk /preserveediting true /untaggedcmykhandling /leaveuntagged /untaggedrgbhandling /usedocumentprofile /usedocumentbleed false >> ] >> setdistillerparams << /hwresolution [2400 2400] /pagesize [612.000 792.000] >> setpagedevice microsoft word numero_53_art_14_2760 g. giuliano et alii, frattura ed integrità strutturale, 53 (2020) 166-176; doi: 10.3221/igf-esis.53.14 166 uniformity of thickness of metal sheets by patchwork blanks: potential of adhesive bonding gillo giuliano, gianluca parodo, luca sorrentino department of civil and mechanical engineering, university of cassino and southern lazio, cassino (fr), italy giuliano@unicas.it, https://orcid.org/0000-0003-0018-0438 gianluca.parodo@unicas.it, http://orcid.org/0000-0001-7443-6518 sorrentino@unicas.it, http://orcid.org/0000-0002-5278-7357 abstract. the sheet metal forming operations generally involve the production of parts characterized by a non-uniform thickness distribution. however, in some cases, a product characterized by a distribution of thicknesses that is as uniform as possible may be desirable. this result can be obtained by using multiphase processes or by subtraction or addition of material from the blank. in this work, which deals with the method for adding material, an innovative methodology has been proposed as an alternative to the welding process. specifically, the methodology is based on the bonding of a patch (before the deformation process), on the base plate with a constant thickness, in the area that most suffers from the thinning caused by the forming process. in this way, it was possible to influence the deformation of the patchwork blank and its thicknesses distribution. through finite element analysis, it was possible to study the formability of a patchwork blank by varying the thickness and size of the patch, in order to produce an axially symmetric component by stretching through a hemispherical punch. preliminary experimental tests demonstrated the reliability of the bonding and the potential of this method to uniform the final thickness of the sheet. keywords. aa6060 aluminum alloy; forming process; finite element method; formability limit curve; adhesive bonding. citation: giuliano, g, parodo, g., sorentino, l., uniformity of thickness of metal sheets by patchwork blanks: potential of adhesive bonding, frattura ed integrità strutturale, 53 (2020) 166-176. received: 02.03.2020 accepted: 05.05.2020 published: 01.07.2020 copyright: © 2020 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. introduction o meet the growing needs of the automotive industry in terms of safety and comfort, the weight of cars has continuously increased over time. this is due both to the increase in the overall dimensions of the car and to the introduction of various electrical and electronic components [1]. t https://youtu.be/604qgvmouzs g. giuliano et alii, frattura ed integrità strutturale, 53 (2020) 166-176; doi: 10.3221/igf-esis.53.14 167 the weight of the car results into higher fuel consumption, which leads to an increase in the cost per kilometer as well as an increase in pollution. therefore, in order to deal with the increased weight of the cars due to the additional components, an attempt was made to reduce the weight of the body. generally, sheet metal forming processes are used for the production of automotive parts [2]. often, the sheet is made of aluminum alloy due to the high strength-to-weight ratio and the high corrosion resistance presented by these materials [3,4]. in addition, reinforced sheets are used where greater strength and stiffness is required [1]. in some cases, a different distribution of the thicknesses of the product obtained by forming may be necessary. this result can be achieved using multiphase processes by subtraction or addition of material from the initial semi-finished product. in [5,6], multi-phase hot forming processes were analyzed to produce components in aluminum alloy (aa2017) and pb-sn alloy. the subtraction processes of material from a semi-finished product are in developments by the authors. tailored blanks are blanks characterized by a local variation of the thickness of the sheet, by a local variation of the material, or by a local variation of the properties of the material. tailored blanks can be divided into: ‐ tailor welded blanks; ‐ tailor rolled blanks; ‐ tailor heat-treated blanks; ‐ patchwork blanks. tailor welded blanks are obtained by welding two or more sheets of different thickness in butt joint configuration [7,8]. welded sheets can be characterized by different thicknesses, coatings, and mechanical properties. the joining of the parts takes place by laser welding or mash seam welding [9]. the use of mash seam welding requires less precision in cutting the sheet metal and allows reaching high welding speeds [10]. on the contrary, laser welding produces a narrow weld seam reducing the heat-affected zone. laser welding allows reducing the weight of the welded product because it does not require overlapping of the material. in addition, curved welding lines can be made [7]. when non-weldable materials (such as aluminum) must be welded, friction stir welding is used because it does not require the melting of the material [11,12]. in [13], the possibility of reducing the body weight of the car by 25% was shown by using tailor welded blanks in high strength steel. the main disadvantages in the use of tailor-welded blanks are due to the complexity and high investment costs for carrying out the welding processes [14]. tailor rolled blanks [15] present a continuous transition between the thickest and thinnest part of the sheet. this produces a more homogeneous distribution of stress, which does not alter the material formability. however, production costs are high, as they require elaborate lamination processes. in [16,17], the optimal process parameters for adopting tailor rolled blanks in the automotive industry were examined. the goal of tailor heat-treated blanks is to increase the formability of the products, in particular for those materials (highstrength steels, aluminum alloys) that have a limited formability [18]. the mechanical properties are locally modified in order to optimize the subsequent forming operation [19]. the preparation of the patchwork blank partially allows reinforcing a base sheet by using patches [20]. this is done before subjecting the patchwork blank to a forming process [21–23]. for the coupling between the sheet base and the patch, spot welding, laser welding and adhesive bonding can be employed [21]. the preparation of patchwork by spot welding has already been used for the automotive industry [24]. the connection between the parts, using welding techniques, is an automatable operation as opposed to the connection by means of adhesive that requires a preparation of the surfaces to be bonded [25]. patchwork obtained by bonding technique is still under development. this work deals with a method by addition of material; in particular an innovative methodology has been proposed as an alternative to the welding process using patches. the methodology is based on the bonding of a patch on a constant thickness base sheet (before the deformation process), in the area that suffers more for the thinning caused by the forming process. preliminary tests were carried out to highlight the reliability and potential of bonded patchwork blanks, then the influence of the patch types and dimensions on the patchwork blank thickness was numerically analyzed. the numerical model, based on fem analyses, allowed to identify the most appropriate geometric dimensions of the patch to perform the forming process. materials and methods n this paragraph, the methods for manufacturing the bonded patchwork blanks and realizing the experimental tests are shown first; therefore, the methods adopted to investigate numerically the formability of the patchwork blank are illustrated. i g. giuliano et alii, frattura ed integrità strutturale, 53 (2020) 166-176; doi: 10.3221/igf-esis.53.14 168 experimental activity the process consists in stretching, by means of a hemispherical punch, a sheet positioned on a circular die and constrained, using a blank holder, to deform without sliding inside the die. the forming operations for manufacturing the patchwork blanks were carried out using five rectangular sheet samples (220x220 mm) with a thickness of 1 mm (fig. 1). the adopted patches have a circular shape with a radius of 30 mm and a thickness of 0.1 mm. they were obtained from the base sheet following a rolling process. subsequently, the patches were bonded on the base sheet. in a first phase, the surfaces of the sheet and the patch to be bended were subjected to a manual sanding treatment with a p100 abrasive paper to improve wettability. subsequently, in order to remove any possible contaminants, the sheets were subjected to degreasing treatment with acetone. the adhesive used for this activity was the loctite ea 9309.3na. it was a two-component paste adhesive, which cured at room temperature in five days [30]. the mechanical properties of the adhesive in the cured state are shown in tab. 1 [31]. properties value tensile strength 32.2 mpa tensile modulus 2303 mpa shear modulus 841 mpa poisson ratio 0.36 elongation at break 10% table 1: mechanical properties of ea 9309.3na adhesive. after five days the adhesive completed the polymerization, therefore it was possible to test the sheets with the bonded patches. in conclusion, five base sheet specimens and five patchwork blanks specimens were produced. the stretching process of the metal sheets was carried out using the machine present at the laboratory of technology and manufacturing system of the university of cassino and southern lazio, and proposed in [26]. the sheet was blocked between the die and the blank holder in circumferential direction and, therefore, subjected to the action of a hemispherical punch with a radius of 60 mm. the force-stroke curves of punch were obtained by interpreting the data from a load cell on the forming machine. details relating to the experimental equipment are reported in [26,32]. for the tests related to the patchwork blanks, a preliminary test of forming was carried out to estimate the punch stroke at failure. in this way, it has been possible to stop the patchwork blank forming tests before the failure for evaluate their thickness distribution. the measurements of the deformed patchwork blanks thicknesses were carried out using the non-contact measurements system faro laser scanarm platinum 6, characterized by an accuracy of ±35µm. after the thickness measurements, the tests were continued until failure. the stretching process was carried out in the absence of lubrication. it is known that friction affects the strain path and therefore indirectly on the formability limits of the sheet material. in [32,33], the influence of friction on the erichsen test results was demonstrated both by using aluminum alloy sheets (aa2017 and aa5083) and steel sheets (dc05). to evaluate the mechanical properties of the material (base sheet and patchwork) it was necessary to perform tensile tests using a galdabini sun 10 tensile machine. in this regard, five tensile specimens obtained from the base sheet and five tensile specimens with a bonded patch of 0.1mm thickness were manufactured. the tensile tests were carried out according to the standard uni en 10002-1:2004. numerical activity the commercial code of the msc.marc based on the finite element method (fem) was used to simulate the hemisphericalpunch stretch forming process. the numerical simulation considered the tools as rigid bodies while only the sheet was considered deformable. the sheet was discretized into finite elements using axisymmetric elements instead of threedimensional shell elements. in a previous work [26], it has been shown that the type of the used elements does not influence the results. the blank holder, which avoids the sliding of the sheet inside the die, was simulated by fixing the movement of the sheet nodes in the area where the blank holder was present. furthermore, the displacements of the sheet nodes on the symmetry axis have also been blocked, in order to satisfy the axial symmetry condition. g. giuliano et alii, frattura ed integrità strutturale, 53 (2020) 166-176; doi: 10.3221/igf-esis.53.14 169 the chemical composition by weight of the aluminum alloy used (aa6060) is shown in tab. 2. elements percentage si 0.6 fe 0.3 mn 0.1 mg 0.6 cu 0.1 zn 0.15 cr 0.05 ti 0.1 al rest table 2: chemical composition by weight of aa 6060. the mechanical properties of the base sheet material were determined by tensile tests conducted on specimens with a thickness of 1 mm. the mechanical properties of the material and the methods used for the tests are reported in [26]. the material followed a hardening law of the power type (hollomon or power law) characterized by a strength coefficient, k, and a strain hardening exponent index, n, and was of the type:   nk (1) where σ and ε represented respectively the equivalent stress and the equivalent strain. the area where the patch was present has been modelled as an equivalent material, whose mechanical properties have been obtained through specific technological tests, precisely tensile tests of specimens with bonded patch. the parameters for the modelling of the mechanical response of both the base sheet and the patchwork blank were therefore obtained. in the numerical simulations, the patch and the underlying base sheet were represented by elements that were characterized by material parameters (k and n) different from the only base sheet. friction between the sheet and the tools was simulated using the modified coulomb friction model [27], which is characterized by a relation between tangent and normal force of the type:             2 r t n sv v f f arctg r (2) in eq.(2), μ represents the friction coefficient, vr the relative sliding speed and rsv the speed below which ft = 0. during fem analyses, it was possible to assess the formability limit parameter (flp) [26]. it represents the ratio between the maximum deformation reached in a sheet metal node and the maximum limit deformation coming from a forming limit diagram (fld). the fld diagram represents a boundary line between safe and unsafe areas of deformability of the material. in this work, this boundary line was characterized by the boundary conditions introduced by hill [28] and swift [29]. instability in the material occurred when the flp parameter reaches a unit value in a node of the sheet. the validation of the model for the forming simulations of only the base sheet was made in another work of the authors [26]. for the case of the patchwork blanks forming simulations, the model was validated by comparison of thickness trends between experimental and numerical results related to a patch with a radius of 30 mm and a constant thickness of 0.1 mm. for the numerical analysis, three values friction coefficient has been considered (μ = 0, 0.1 and 0.2). further, an analysis of the principal factor of influence were carried out through fem simulations. specifically, the effect of patches with different radii and thicknesses was numerically investigated, as the influence of the friction coefficient. g. giuliano et alii, frattura ed integrità strutturale, 53 (2020) 166-176; doi: 10.3221/igf-esis.53.14 170 as stated before, the hemispherical-punch stretch forming process of the base sheet alone was simulated in three friction conditions: μ = 0, 0.1 and 0.2. in the same friction conditions, the stretching process was simulated using patchwork blanks. the patchwork blank was characterized by a circular patch with constant (0.1 mm, 0.2 mm, 0.3 mm, 0.5 mm, 0.7 mm) and variable (from 0 to 0.1 mm) thickness profile. the radius of the considered patches for the numerical analysis were equal to 10 mm and 30 mm. to clarify all the conditions, a plan of the numerical activity with all the analyzed factors is reported in tab. 3. furthermore, a schematic representation of the two types of patch adopted in this work was shown in fig. 2. factors # level levels friction condition (μ) 3 0 / 0.1 / 0.2 patch thickness [mm] 6 constant (0.1 / 0.2 / 0.3 / 0.5 / 0.7) linear (from 0 to 0.1) patch radius [mm] 2 10 / 30 table 3: plan of numerical tests. figure 1: dimensions related to the sheet samples, the process zone and the patches. figure 2: schematic representation of the two types of patch adopted in this work. results and discussion he experimental activity allowed verifying the tightness of the adhesive adopted to connect the patch to the base sheet. the patches were characterized by a thickness of 0.1 mm and a radius of 30 mm; for this test condition, five replications were made. a preliminary test of forming was carried out to estimate the punch stroke at failure, so the t g. giuliano et alii, frattura ed integrità strutturale, 53 (2020) 166-176; doi: 10.3221/igf-esis.53.14 171 subsequently tests were stopped before the failure for evaluate the thickness distribution of the patchwork. the failure appeared with a punch stroke of 18 mm, so all the experimental tests were stopped with a punch stroke of 15 mm. in this way, it was possible to compare the experimental thicknesses distribution with the numerical one. then the tests were continued until failure. the results of the experimental forming tests at failure are reported in tab. 4. specimen type base sheet patchwork blank average failure load [n] 13882.3 7954.1 st. dev. [n] 777.4 720.6 cv 5.6% 9.1% average failure stroke [mm] 29.6 18.2 st. dev. [mm] 2.3 1.3 cv 7.9% 7.1% table 4: experimental results of forming tests for base sheets and patchwork blanks. fig. 3 shows, for comparison, the average load-stroke response of the punch recorded during the test both using the patchwork blank and using only the base sheet. this comparison shows that failures (using a patchwork blank) were obtained for a stroke of the punch lower than that achievable in the stretching process of the base plate only. the minor formability of the patchwork is due to the stiffening produced by the operation of bonding the adhesive on the base sheet. this lower formability of the material is however balanced by the possibility of influence the distribution of thicknesses obtainable before reaching the failure conditions. fig. 4 shows the patchwork deformed at break: the failure occurred in the region of the base plate outside the patch. in addition, the adhesive showed a strong seal, without detaching from the base plate, despite the achievement of high loads (about 8000 n). in fact, the aim of this work consisted to evaluate the potentiality of using bonded patch for influence the distribution of thickness and without the debonding of the patch from the base sheet. obviously in the case of application of this methodology for a real case of study, the deformation must take place before the failure of the component; in fact, the ultimate goal is to obtain the desired deformation with a constant thickness. figure 3: experimental average force-stroke curves of the punch for base sheets and patchwork blanks characterized by a circular patch of 0.1 mm thickness and 30 mm radius. as stated in the previous paragraph, in the numerical simulations, the patch and the underlying base sheet were represented by elements that were characterized as equivalent material using material parameters (specifically k and n) different from g. giuliano et alii, frattura ed integrità strutturale, 53 (2020) 166-176; doi: 10.3221/igf-esis.53.14 172 the only base sheet. the values obtained from technological tensile tests for patchwork blanks were k = 128 mpa, and n = 0.08, while the values obtained for specimens without the bonded patch were k = 135 mpa and n = 0.12. to validate the numerical model, it was necessary to compare the distribution of the thicknesses obtained by fem and that measured experimentally at a predetermined stroke of the punch of 15 mm. this comparison, performed between the results of the fem simulations with a punch stroke of 15 mm in different friction conditions (μ = 0, 0.1 and 0.2) and the results of the experimental tests, as shown in fig. 5. considering the experimental variation of the results related to the thickness measurements of at least of 3%, it is possible to state that the numerical results showed a good correspondence. in fact, the maximum variation in the fem thicknesses, compared to the average values experimentally measured, was about 5% in the case of μ = 0, 3% in the case of μ = 0.1 and 2% in the case of μ = 0.2. figure 4: photo of a bonded patchwork blank sample deformed at failure. figure 5: numerical-experimental comparison of the distribution of the thicknesses after a stroke of the punch of 15 mm (patch radius equal to 30 mm). after the validation of the model, the numerical analyses descripted in the previous paragraph have been carried out. in fig. 6a, some stages of the stretching process were showed, with a particular for observe the mesh adopted for the base sheet. however, the thickness trend until the limit condition was not appreciable from a visual analysis of the mesh. furthermore, the patch with a thickness of 0.1 mm appeared very thin for a visual inspection (fig. 6b). fig. 7 shows the stroke of the punch reached at the beginning of the instability condition (when flp = 1) as a function of the thickness of the patch, related to a patch with a radius of 10 mm. the results obtained for the patch with a radius of 30 mm were quantitatively very similar with the results showed in fig.7. in fact, results obtained for the patch with a radius of 30 mm showed an average decrease in the stroke of the punch of about 3% compared to the results relating to a patch with a radius of 10 mm. the sheet formability (represented by the stroke of the punch corresponding to the condition flp = 1) increased as the thickness of the patch decreases. the same result can be achieved both by using a constant thickness patch and a linear thickness patch. in addition, the larger was the patch thickness, the more was the influence of the friction g. giuliano et alii, frattura ed integrità strutturale, 53 (2020) 166-176; doi: 10.3221/igf-esis.53.14 173 condition on the sheet formability. in conclusion, it is possible to state that the patch thickness that showed a lower influence on the friction condition and a higher sheet formability was the one with the thickness of 0.1 mm. once it was ascertained that the condition involving the greatest formability was related to the use of a patch with a thickness equal to 0.1 mm, the comparison between the results obtained for thicknesses of the patches thicker than 0.1 mm was considered superfluous and, therefore, was not been reported in the work. (a) (b) figure 6: phases of the fem simulation of the stretching process with hemispherical punch with particular of the mesh: (a) base sheet only (continuous frame); (b) patchwork blank (thickness equal to 0.1 mm, dotted frame). figure 7: numerical punch stroke patch thickness trend for flp = 1 (patch radius equal to 10 mm). fixed a certain stroke of the punch, fig. 8a shows the distribution of the thicknesses achieved using a 0.1 mm constant thickness patch patchwork with a patch radius of 10 mm and 30 mm and a for the only base sheet. it is possible to state that the most uniform distribution of the thicknesses was determined for a linear thickness patch with a radius of 30 mm in condition of perfect lubrications. patches with constant thickness showed a uniform trend until the transition region between the patch and the base sheet, where a drop in thickness has been observed numerically. however, this drop appeared of the same intensity independently from the friction conditions. probably the adoption of a tapered patch can make the uniform of thickness of the deformed patchwork blanks more consistent. in fact, linear thickness patch showed a more uniform distribution of thicknesses, in particular in case of perfect lubrication. however, in case of linear thickness patch, the dimension of the patch has more strongly influenced the uniformity of the thickness. in conclusion, it is possible g. giuliano et alii, frattura ed integrità strutturale, 53 (2020) 166-176; doi: 10.3221/igf-esis.53.14 174 to state that, among all the patches investigated, the linear patch with a radius of 30 mm it was the one that guaranteed the optimal distribution of the thicknesses (a) (b) figure 8: numerical distribution of the thicknesses between base sheets and patchwork blanks with radius of 10 mm and 30 mm: (a) constant thickness patch of 0.1 mm; (b) linear thickness patch. conclusions he aim of this work was to show the potential of using a bonded patchwork blank by means of a bonding process to obtain a product characterized by a distribution of thicknesses that is as uniform as possible. experimental tests showed the capability of bonded patch of influencing the thickness distributions during forming process, specifically to stretching process with a hemispherical punch. subsequently, a fem model was validated to investigate the effects of patch dimensions on the distribution of thickness in the patchwork blanks. in fact, through finite element analysis, it was possible to define the appropriate geometric characteristics of a patchwork blanks. therefore, in the case examined it was possible to establish the most appropriate thickness and radius values of the patch to produce a component of simple geometry. results showed a more uniform distribution of thickness for linear patch with a radius of 30 mm, while constant thickness patch showed a drop in thickness near the edges of the patch. further research developments will include the experimental investigations of the efficacy of linear thickness patches in case of more complex geometries and adopting other sheet materials. t g. giuliano et alii, frattura ed integrità strutturale, 53 (2020) 166-176; doi: 10.3221/igf-esis.53.14 175 references [1] merklein, m., johannes, m., lechner, m., kuppert, a. (2014). a review on tailored blanks production, applications and evaluation, j. mater. process. technol., 214(2), pp. 151–164, doi: 10.1016/j.jmatprotec.2013.08.015. [2] rong, h., hu, p., ying, l., hou, w., zhang, j. (2019). thermal forming limit diagram (tfld) of aa7075 aluminum alloy based on a modified continuum damage model: experimental and theoretical investigations, int. j. mech. sci., 156, pp. 59–73, doi: 10.1016/j.ijmecsci.2019.03.027. [3] tisza, m., czinege, i. (2018). comparative study of the application of steels and aluminium in lightweight production of automotive parts, int. j. light. mater. manuf., 1(4), pp. 229–238, doi: 10.1016/j.ijlmm.2018.09.001. [4] hirsch, j. (2014). recent development in aluminium for automotive applications, trans. nonferrous met. soc. china, 24(7), pp. 1995–2002, doi: 10.1016/s1003-6326(14)63305-7. [5] giuliano, g., corrado, a., polini, w. (2018). influence of multiphase forming approach on the thickness uniformity of components from superplastic pbsn60 alloy, manuf. lett., 18, pp. 16–19, doi: 10.1016/j.mfglet.2018.09.004. [6] giuliano, g. (2019). multiphase gas blow forming of aa2017, j. test. eval., 47(2), pp. 1236–1243, doi: 10.1520/jte20170086. [7] zadpoor, a.a. (2007). mechanics of tailor welded blanks: an overview, key eng. mater., 344, pp. 373–382, doi: 10.4028/www.scientific.net/kem.344.373. [8] kinsey, b.l., wu, x. (2011). tailor welded blanks for advanced manufacturing. [9] saunders, f.i., wagoner, r.h. (1996). forming of tailor-welded blanks, metall. mater. trans. a phys. metall. mater. sci., 27(9), pp. 2605–2616, doi: 10.1007/bf02652354. [10] miyazaki, y., sakiyama, t., kodama, s. (2007). welding techniques for tailored blanks, nippon steel tech. rep., (95), pp. 46–52. [11] buffa, g., fratini, l., merklein, m., staud, d. (2007). investigations on the mechanical properties and formability of friction stir welded tailored blanks, 344. [12] mishra, r.s., ma, z.y. (2005). friction stir welding and processing, mater. sci. eng. r reports, 50(1–2), pp. 1–78, doi: 10.1016/j.mser.2005.07.001. [13] ulsab. (2013). programme report. [14] mohrbacher, h. (2001).a critical review of laser welding technology for mass production of tailored blanks. proceedings of the 9th international conference on sheet metal, leuven, belgium, pp. 305–12. [15] kopp, r., wiedner, c., meyer, a. (2005). flexibly rolled sheet metal and its use in sheet metal forming, 6–8. [16] klinke, n., schumacher, a. (2016).finding the best thickness run parameterization for optimization of tailor rolled blanks. ls-dyna forum 2016. [17] han, s., hwang, t., oh, i., choi, m., moon, y.h. (2018). manufacturing of tailor-rolled blanks with thickness variations in both the longitudinal and latitudinal directions, j. mater. process. technol., 256, pp. 172–182, doi: 10.1016/j.jmatprotec.2018.02.013. [18] geiger, m., merklein, m. (2007). sheet metal forming a new kind of forge for the future, key eng. mater., 344, pp. 9–20, doi: 10.4028/www.scientific.net/kem.344.9. [19] kahrimanidis, a., lechner, m., degner, j., wortberg, d., merklein, m. (2015). process design of aluminum tailor heat treated blanks, materials (basel)., 8(12), pp. 8524–8538, doi: 10.3390/ma8125476. [20] lamprecht, k., geiger, m. (2005). experimental and numerical investigation of the formability of laser welded patchwork blanks, adv. mater. res., 6–8, pp. 689–696, doi: 10.4028/www.scientific.net/amr.6-8.689. [21] streitberger, h.-j., dossel, k.-f. (2008). automotive paints and coatings, weinheim, wiley-vch. [22] lei, c., xing, z., xu, w., hong, z., shan, d. (2017). hot stamping of patchwork blanks: modelling and experimental investigation, int. j. adv. manuf. technol., 92(5–8), pp. 2609–2617, doi: 10.1007/s00170-017-0351-9. [23] petitjean, p.-d., lescart, j.-c., sener, j.-y., delfanne, s. (2001). patchworks: from design to manufacture | patchworks: de la conception à l’industrialisation, rev. metall. cah. d’informations tech., 98(10), pp. 911–926, doi: 10.1051/metal:2001138. [24] magain, p., dawance, j., delfanne, s., chamont, b., fournet, a. (1998). the patchwork technique for proper material placement on panels: industrial application on the new peugeot 206, sae tech. pap., doi: 10.4271/982402. [25] sorrentino, l., polini, w., bellini, c., parodo, g. (2018). surface treatment of cfrp: influence on single lap joint performances, int. j. adhes. adhes., 85(may), pp. 225–233, doi: 10.1016/j.ijadhadh.2018.06.008. [26] giuliano, g., bellini, c., sorrentino, l., turchetta, s. (2018). forming process analysis of an aa6060 aluminum vessel, 45, pp. 164–172, doi: 10.3221/igf-esis.45.14. g. giuliano et alii, frattura ed integrità strutturale, 53 (2020) 166-176; doi: 10.3221/igf-esis.53.14 176 [27] bellini, c., giuliano, g., sorrentino, l. (2019). friction influence on the aa6060 aluminium alloy formability, frat. ed integrità strutt., 13(49), pp. 791–799, doi: 10.3221/igf-esis.49.70. [28] hill, r. (1948). a theory of the yielding and plastic flow of anisotropic metals, proc. r. soc. london. ser. a. math. phys. sci., 193(1033), pp. 281–297, doi: 10.1098/rspa.1948.0045. [29] swift, h.w. (1952). plastic instability under plane stress, j. mech. phys. solids, 1(1), pp. 1–18, doi: 10.1016/0022-5096(52)90002-1. [30] sorrentino, l., bellini, c., parodo, g., turchetta, s. (2019). increasing of enf bonded joints performance by design of laser surface texturing, key eng. mater., 813, pp. 346–351, doi: 10.4028/www.scientific.net/kem.813.346. [31] sorrentino, l., marfia, s., parodo, g., sacco, e. (2020). laser treatment surface: an innovative method to increase the adhesive bonding of enf joints in cfrp, compos. struct., 233(february 2020), pp. 111638, doi: 10.1016/j.compstruct.2019.111638. [32] giuliano, g. (2015). evaluation of the coulomb friction coefficient in dc05 sheet metal forming, j. mech. eng., 61(12), pp. 709–713, doi: 10.5545/sv-jme.2015.2733. [33] giuliano, g., samani, f. 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can be opened with acrobat and adobe reader 5.0 and later.) >> /namespace [ (adobe) (common) (1.0) ] /othernamespaces [ << /asreaderspreads false /cropimagestoframes true /errorcontrol /warnandcontinue /flattenerignorespreadoverrides false /includeguidesgrids false /includenonprinting false /includeslug false /namespace [ (adobe) (indesign) (4.0) ] /omitplacedbitmaps false /omitplacedeps false /omitplacedpdf false /simulateoverprint /legacy >> << /addbleedmarks false /addcolorbars false /addcropmarks false /addpageinfo false /addregmarks false /convertcolors /converttocmyk /destinationprofilename () /destinationprofileselector /documentcmyk /downsample16bitimages true /flattenerpreset << /presetselector /mediumresolution >> /formelements false /generatestructure false /includebookmarks false /includehyperlinks false /includeinteractive false /includelayers false /includeprofiles false /multimediahandling /useobjectsettings /namespace [ (adobe) (creativesuite) (2.0) ] /pdfxoutputintentprofileselector /documentcmyk /preserveediting true /untaggedcmykhandling /leaveuntagged /untaggedrgbhandling /usedocumentprofile /usedocumentbleed false >> ] >> setdistillerparams << /hwresolution [2400 2400] /pagesize [612.000 792.000] >> setpagedevice microsoft word numero_30_art_53 l. guerra rosa et alii, frattura ed integrità strutturale, 30 (2014) 438-445; doi: 10.3221/igf-esis.30.53 438 focussed on: fracture and structural integrity related issues integrated assessment procedure for determining the fracture strength of glass components in csp systems l. guerra rosa, j. cruz fernandes, b. li icems & dept. of mechanical engineering, instituto superior tecnico universidade de lisboa, av. rovisco pais, 1049-001 lisboa, portugal luisguerra@ist.utl.pt, cruz.fernandes@ist.utl.pt, bli@ist.utl.pt abstract. the structural integrity and reliability of glass components are key issues for concentrated solar power (csp) systems. for example, the glass windows in a solar furnace may suffer catastrophic fracture due to thermal and structural loadings, including reaction chamber pressure cycling. predicting design strength provides the basis for which the optical components and mounting assembly can be designed so that failure does not occur over the operational lifetime of a given csp system. the fracture strength of brittle materials is dependent on the size and distribution of cracks or surface flaws. due to the inherent brittleness of glass resulting in catastrophic failure, conservative design approaches are currently used for the development of optical components made of glass, which generally neglect the specific glass composition as well as subcritical crack growth, surface area under stress, and nature of the load – either static or cyclic – phenomena. in this paper, several methods to characterize the strength of glass are discussed to aid engineers in predicting a design strength for a given surface finish, glass type, and environment. based on the weibull statistical approach and experimental data available on testing silica glass rod specimens, a theoretical model is developed for estimating their fracture strength under typical loading conditions. then, an integrated assessment procedure for structural glass elements is further developed based on fracture mechanics and the theory of probability, which is based on the probabilistic modelling of the complex behaviour of glass fracture but avoids the complexity for calculation in applications. as an example, the design strength of a glass window suitable for a solar furnace reaction chamber is highlighted. keywords probabilistic model; fracture strength; structural glass; reliability; concentrated solar power (csp). introduction mprovements in production and refining technologies such as tempering and the production of laminated glass enabled glass to carry more substantial superimposed loads and therefore achieve a more ‘structural’ role [1]. especially, the glass components play important role in some new energy industries such as the concentrated solar power (csp) systems, etc. this gives impetus to studies on the mechanical behaviour of these materials and, in particular on their ability to resist fracture. i l. guerra rosa et alii, frattura ed integrità strutturale, 30 (2014) 438-445; doi: 10.3221/igf-esis.30.53 439 glass failure is the consequence of the growth of flaws, its behaviour strongly depends on the surface condition as well as on the environmental conditions and the thermal and mechanical loading history to which they are exposed to. due to the much more scatter in the data of glass materials, very large safety factors are often used in glass element design, up to 8 or more. these large safety factors are somewhat arbitrary and not satisfactory, because it is not very clear what the true factor of safety really is. in recent years, considerable research efforts have been paid to improve the understanding of the load-carrying behaviour of structural glass elements, and many new design approaches have been proposed to improve the safety and serviceability of the structural glasses [2-6]. in 1972, brown [7] proposed the “load duration theory” (ldt), which combined the static fatigue theory of charles & hillings [8] with the statistical failure probability function proposed by weibull [9]. in 1974, evans [10] developed the “crack growth model” (cgm) on the basis of the principles of linear elastic fracture mechanics. this method makes use of the empirical description of the sub-critical propagation of cracks (deduced from the experimental relationship between crack growth rate and stress intensity factor ki) together with the weibull failure probability under the hypotheses that a sub-critical crack growth takes place in all surface micro-cracks. fishercripps & collins [11] proposed a modified crack growth model, which is able to predict failure probabilities for both short and long term stresses [11]. fernandes & rosa [12, 13] presented a review on the “ring-on-ring” and “piston-on-3-ball” equibiaxial tests for ceramics and glasses, stress distributions in the test pieces were analysed, the importance of the effect of friction at the contact zones was discussed. based on the weibull statistics and experimental data obtained from testing silica glass rod specimens with diameters between 0.5 and 1 mm [14], a theoretical model was developed for estimating their fracture strength under different loading conditions [15]. by this method, the test results of strength from one testing type can be extrapolated to other test types, such as the uniaxial tension, 3-point bending, 4-point bending, etc. besides, rosa et al [16] studied the subcritical crack growth in three engineering ceramics under biaxial conditions, the results from the ring-onring tests were compared with 4-point bending tests. in 2001, porter [6] proposed the crack size design method (csd); and in 2006 haldimann [4] developed the lifetime prediction model (lpm) where he calculated directly the failure probability of a glass element starting from the probability distribution of its defects and from the deterministic knowledge of loading time-history [4]. recently, santarsiero and froli [2] formulated a new semi-probabilistic failure prediction method, called "design crack method” (dcm), defining a new quantity called design crack, which takes into account of the probability of failure and the surface damaging level. moreover, it is still a major concern to extrapolate the laboratory test results to applications for components under inservice conditions. a number of effects have to be considered, such as the size effect, the gradient effect or notch size effect, and multi-axial stress effect, etc. in ref. [17], the extension of the weakest-link model to multiaxial stress states was verified by comparing fracture stress distributions obtained in four-point bending and in a concentric ring-on-ring test, and it was discussed about how the selected failure criterion influences the predicted distribution of the fracture stress of a component. danzer et al [18] presented a new method for biaxial strength testing of brittle materials, the so-called ball on three balls (b3b) test method. a detailed analysis of the stress field in the specimens and of possible measuring errors were studied. the b3b-testing method has several advantages compared to common three or four-point bending tests and the ring-onring tests. from the above brief review of literature, it is shown that the mechanical behaviour of glass at breakage is very complex, more and more theoretical models as well as experimental methods have been developed. however, for engineering applications, the complexity of calculation procedures needs to be simplified reasonably. the motivation for this present work is to develop an integrated approach for analyzing the crack problem of the glass components in the csp industry, to incorporate the probabilistic modelling, the principles of fracture mechanics and the details of the specific design in question. mechanical characterization of glasses for use in strength forecasting he most commonly used mathematical representation of the relationship between applied stress and probability of survival for glasses is the two parameter weibull distribution as defined [19]: t l. guerra rosa et alii, frattura ed integrità strutturale, 30 (2014) 438-445; doi: 10.3221/igf-esis.30.53 440 (1) where σ is the applied stress; ps is the corresponding probability of survival; σ0 is the characteristic strength at which 63.2% of the test specimen will break; and m is the weibull modulus, which is a measure of the amount of scatter in the distribution (the shape parameter); small values of m imply wide variations in strength, whereas large values imply more consistent strength values. theoretical models were developed by rosa et al [13-16] for estimating the fracture strength of brittle materials (such as ceramics and glasses, etc) under different typical loading conditions. the probability of survival ps for glasses in a stressed volume v can be calculated as [12]: (2) the application of eq. (2) to uni-axial tension testing stress, t , yields: (3) the above eq. (3) can be expressed in the following linear equation, which facilitates to fit the weibull parameters from test results: (4) similarly, the application of eq. (2) for 4-point bending testing stress, 4p, yields: (5) the above eq. (5) can be expressed in the following linear equation, which facilitates to fit the weibull parameters from test results: (6) in the same way, the application of eq. (2) for 3-point bending testing stress, 3p, yields: (7) the above eq. (7) can be expressed in the following linear equation, which facilitates to fit the weibull parameters from experimental data: (8) the weibull effective volume or surface can be used to scale ceramic and glass strengths from one component size to another, or from one loading state to another. larger specimens or components are weaker, because of the bigger probability of containing larger and more critical flaws. the weibull weakest-link model leads to a strength dependency on component size [12]:                m sp 0 exp                   v m s dvp 0 exp                  m t s vp 0 exp    0lnlnln1lnln              t s mv p                      2 0 4 14 2 exp m mv p m p s       pms m m mv p 4 0 2 ln 14 2 ln1lnln                                         2 0 3 12 exp m v p m p s     pms m m v p 3 0 2 ln 12 ln1lnln                      l. guerra rosa et alii, frattura ed integrità strutturale, 30 (2014) 438-445; doi: 10.3221/igf-esis.30.53 441 (9) where 1 and 2 are the mean strengths of specimens of type 1 and 2 (which may have different sizes and stress distributions), ve1 and ve2 are the effective volumes, and m is the weibull modulus. similarly, the following relationships can be derived from eq. (4), (6) and (8): (10) (11) the above two eq. (10) and (11) confirmed that the bending strength is higher than the tension strength. if the weibull modulus m is equal to 10, the 3-point bending strength is 1.45 times the tension strength, and the 4-point bending strength is 1.73 times the tension strength. in view of the fact that the weibull modulus m is usually assumed to be a constant for a given material, only the characteristic strength 0 is needed to be extrapolated from laboratory specimen test data to components. for a component with a varying stress field , an effective surface area, aeff, may be computed using the following relationship: (12) then the characteristic strength σ0 for the component can be calculated from the data of specimen as: (13) in service, the components are generally subjected to multiaxial loading conditions, hence, we need to analyze the effect of multi-axial tensile stresses on flaws and determining one equivalent stress based on the selected multiaxial criterion. then, the equivalent stress can be assumed to be the applied stress σ in the above equations. glasses can demonstrate a loss of strength over time. this phenomenon is a kind of stress corrosion and it is known as static fatigue of glass. chemical attack by water vapour (or other media) permits a pre-existing flaw to grow to critical dimensions and cause spontaneous crack propagation as shown in the following fig. 1. figure 1: regions of a typical logv versus logk plot. m e e v v /1 1 2 2 1             m t p m /123 12      m t p m m /12 4 2 14            daa m eff         max  m component specimen specimen component a a /1 0 0            l. guerra rosa et alii, frattura ed integrità strutturale, 30 (2014) 438-445; doi: 10.3221/igf-esis.30.53 442 crack propagation velocity v is usually indicated in m/s. region i is of primary interest since it represents the main duration of stable crack growth, which may be expressed as a power law:  nv a k (14) where a and n are parameters which depend on the material and the stress-corrosion conditions, they can be determined from experimental data. integrated assessment procedure for structural glass component design ollowing the above process of characterizing the mechanical properties of glasses, one integrated analysis procedure is developed in this section for the component design of glasses, which consists of two major steps: step1: analyse the maximum tensile stresses in the component by the finite element method, taking into account the multiaxial loading conditions and the contact stresses between the glass component and the parts for mounting the glass. step 2: transform the weibull cdf (cumulative distribution function that was adjusted to data obtained from specimens´ testing) for predicting the survival probabilities for the application conditions with different load type, load duration, and surface area. the glass-mount contact can be approximated by hertzian contact of a cylinder on a flat glass surface. the contact halfwidth b can be expressed as [20]: * * 4pr b e  (15) where 122 * 11 gm m g vv e e e           is the effective modulus, 1 * 1 1 m g r r r          is the contact radius, young’s moduli em and eg ,and poisson ratios νm and νg are for the mounting part and the glass part, respectively. the stress distributions at the glass-mount contact area can be analysed using the equations derived in [20], compressive stresses occur in the zone just beneath the contact area, and the maximum tensile stress, t,max , occurs on the glass surface just outside the contact area, which can be derived as:   , 2 1 2 3 g t max v p b     (16) where p is the loading force, b is the contact half-width, vg is the poisson ratio of glass. since the maximum tensile stress (the first principal stress) is critical for brittle materials, it is assumed as the applied stress in the following evaluation procedure. from eq. (1) the stress at fracture ic can be calculated as: 1/ 0 1 ln m ic sp             (17) the initial stress-intensity kii at the crack tip may be estimated as: ii ic ic k k          (18) substituting eq. (17) into eq. (18) yields: f l. guerra rosa et alii, frattura ed integrità strutturale, 30 (2014) 438-445; doi: 10.3221/igf-esis.30.53 443 1 m ii ic 0 s σ 1 k k ln σ p           (19) in order to take into account the strength reduction of the glass material over time due to subcritical crack growth, analytical expressions had been derived from the v versus k data. the total time-to-failure, ts, of a component under a constant static stress with a known flaw was expressed as [5]: 2 2 2 ic ii k i s i k k t dk vy       (20) where kii is the initial stress intensity factor, and v is the crack velocity. if a power law for the crack velocity (region i of stable crack growth) is assumed, as shown in eq. (14), then the eq.(20) can be expressed as:    2 2 2 22 / 2n ns ii ict k k n a y       (21) therefore, one design strength diagram may be created from the above procedures and the time-to-failure versus equivalent stress curves as a function of the survivability probability (or reliability) can be shown in the diagram, which will be very helpful for the design processes as presented in the following section. design strength example ig. 2 shows some examples of glass components of csp systems used in the plataforma solar de almeria (psa). these glass windows are mounted inside a pressure vessel filled with argon gas at specified operating pressure, which may suffer catastrophic fracture due to thermal and structural loadings, including reaction chamber pressure cycling. we desire to accurately predict the state of stress created in the surface of the glass, and design the glass components for safety operation under severe thermal and mechanical loading conditions. (a) (b) figure 2: examples of glass components of csp systems at psa-ciemat. a) aspect of the solar concentrator and reaction chamber of sf-5 solar furnace; b) aspect of the minivac chamber installed at the focal spot of the new sf-40 solar furnace; a 45º inclined mirror above the minivac allows the sunrays to reflect vertically. during the operations, fracture problem occurred due to the severe thermal and mechanical loading conditions as shown in fig. 3 for one example, crack initiated from the zone close to glass-mount contact area, where the tensile stresses were generated. f l. guerra rosa et alii, frattura ed integrità strutturale, 30 (2014) 438-445; doi: 10.3221/igf-esis.30.53 444 fig. 4 shows the simulated deformation results of the glass component by ansys software, where the blue colour represents the deformed shape of the glass section due to the temperature and pressure loadings. it is shown that the zone near the glass-mount contact area had larger deformation, which explained why the crack initiated from there. based on the calculated maximum tensile stress in the glass component, the design strength diagram can be generated following the integrated assessment procedure as described in the above sections, which is shown in the fig. 5. the timeto-failure versus the maximum tensile stress curves as a function of the probability of survivability (or reliability) is shown in the diagram, which will be very helpful for the design improvement of the glass component. figure 3: one example of the fracture of glass component; crack initiated from the zone close to glass-mount contact area. figure 4: glass section deformation simulated by fem. figure 5: design strength diagram, the time-to-failure versus the maximum tensile stress curves as a function of the probability of survivability (or reliability) ps. conclusions ith the increasing applications of the glass and ceramic components in the new energy industries such as the csp systems, it is imperative to develop advanced design methods for the safety and reliability of these components, which are quite different from the metal components. the integrated assessment procedure 10 12 14 16 18 20 22 1,00 e-01 1,00 e+00 1,00 e+01 1,00 e+02 1,00 e+03 1,00 e+04 1,00 e+05 1,00 e+06 1,00 e+07 time to failure (hours) t e n s il e s tr e s s ( m p a ) ps=0,9999 ps=0,999 w l. guerra rosa et alii, frattura ed integrità strutturale, 30 (2014) 438-445; doi: 10.3221/igf-esis.30.53 445 proposed in this paper is based on the probabilistic modelling of the complex behaviour of glass fracture but avoids the complexity for calculation in applications. with demonstrative examples, it is shown that the procedure is effective for analyzing the fracture problem of the glass components and helpful for design improvement. acknowledgements he authors gratefully acknowledge the financial support from the eu integrated research programme in the field of concentrated solar power (csp) named “scientific and technological alliance for guaranteeing the european excellence in concentrating solar thermal energy (stage-ste)”. references [1] feldmann, m., kasper, r., guidance for european structural design of glass components, scientific and policy report by the joint research centre of the european commission, (2014). [2] santarsiero, m., froli, m., a contribution to the theoretical prediction of life-time in glass structures, journal of the international association for shell and spatial structures, 52(4) (2011) 225-231. [3] sutherland, k.k., an engineer’s guide to refined glass strength forecasting, aiaa 2009-2582, 50th aiaa/asme/asce/ahs/asc structures, structural dynamics, and materials conference, 4 7 may 2009, palm springs, california. [4] haldimann, m., fracture strength of structural glass elements–analytical and numerical modelling, testing and design, ph.d. thesis, epfl, lausanne, (2006). [5] doyle, k.b., kahan, m.a., design strength of optical glass, in: proceedings of spie, optomechanics 2003, san diego, california. international society for optical engineering (spie), bellingham, washington, (2003) 14-25. [6] porter, m., aspects of structural design with glass, ph.d thesis, university of oxford, (2001). [7] brown, w., a load duration theory for glass design, publications of national research council of canada, division of building research, nrcc 12354, ottawa, ontario, canada, (1972) 515-524. [8] charles, r., hilling, w., the kinetics of glass failure by stress corrosion, in: symposium on mechanical strength of glass and ways of improving it, belgium (1962). [9] weibull, w., a statistical distribution function of wide applicability, journal of applied mechanics, 18 (1951) 293-297. [10] evans, a.g., wiederhorn, s., proof testing of ceramic materials analytical basis for failure prediction, international journal of fracture, 10(3) (1974) 379-392. [11] fishchercripps, a., collins, r., architectural glazing: design standard and failure models, building and environment, 30 (1995) 29-40. [12] fernandes, j.j., silva, c.p., guerra rosa, l., estatística de weibull aplicada à resistência mecânica de materiais cerâmicos, in: actas "materiais 89"-iv encontro nacional da sociedade portuguesa de materiais, coimbra, i (1989) 55-66. [13] fernandes, j.j., guerra rosa, l., ensaios biaxiais de cerâmicos, in: actas do v encontro da s.p.m., materiais 91 1 (1991) 375-384. [14] santos moreira, j., guerra rosa, l., osório, a.m.b.a., avaliação da resistência mecânica de varetas e fibras de vidro de sílica, in: actas do v encontro da s.p.m., materiais 91, 2 (1991) 539-548. [15] santos moreira, j., guerra rosa, l., osório, a.m.b.a., ensaios de resistência mecânica de varetas de vidro de sílica – comparação entre a resistência mecânica medida por meio de ensaio de tracção e ensaios de flexão em 2, 3 e 4 pontos, in: actas das iv jornadas de fractura da s.p.m., lisboa, portugal, (1991) 1-12. [16] guerra rosa, l., cruz fernandes, j., alexandrino duarte, i., subcritical crack growth in three engineering ceramics under biaxial conditions, in: proceedings of ecf12 – fracture from defects, sheffield, uk, (1998) 509-514 [17] thiemeier, t., bruckner-foit, a., influence of the fracture criterion on the failure prediction of ceramics loaded in biaxial flexure, journal of american ceramics society, 74(1) (1991) 48-52. [18] danzer, r., harrer, w., supancic, p., lubea, t., wang, z., borger, a., the ball on three balls test-strength and failure analysis of different materials, journal of the european ceramic society, 27 (2007) 1481–1485. [19] weibull, w., a statistical theory for the strength of materials," technical report no. 151, swedish royal institute for engineering research, stockholm (1939). [20] johnson, k. l., contact mechanics, cambridge university press, cambridge, uk (1985). t microsoft word numero_59_art_06_3261.docx n. ekabote et alii, frattura ed integrità strutturale, 59 (2022) 78-88; doi: 10.3221/igf-esis.59.06 78 elastic-plastic fracture analysis of anisotropy effect on aa2050-t84 alloy at different temperatures: a numerical study nagaraj ekabote, krishnaraja g. kodancha, p. p. revankar school of mechanical engineering, kle technological university, hubballi, india ekabotenagaraj@gmail.com, krishnaraja@kletech.ac.in, pp_revankar@kletech.ac.in abstract. the third generation al-li alloy aa2050-t84 is widely used in aircraft applications due to its lightweight and significant mechanical properties. the anisotropic variations of tensile and compression properties of this alloy at various temperatures are substantial. in this work, the variations of the j-integral, ctod, and plastic zone size (pzs) due to anisotropy of a 4-inch thick aa2050-t84 plate at ambient and cryogenic temperatures were studied numerically by using compact tension (c(t)) specimen. the material anisotropy resulted in fracture and constraint parameter variation for mode-i constant load. numerical results indicated a decrease in crack driving parameters and a constraint parameter with the decrease in temperature at the plate surface and central location. plate surface locations appear to be isotropic for both temperatures under elastic-plastic fracture analyses as crack driving parameters were almost identical. the temperature effect is more on constraint as the normalized pzs values at ambient temperature have been twice that of cryogenic temperature. the isotropic behavior of a plate under sub-zero temperature makes the plate suitable for cryogenic temperature applications. keywords. aa2050-t84 al-li alloy; j-integral; ctod; constraint parameter; plastic zone size. citation: ekabote, n., kodancha, k. g., revenkar, p. p., elastic-plastic fracture analysis of anisotropy effect on aa2050-t84 alloy at different temperatures: a numerical study, frattura ed integrità strutturale, 59 (2022) 78-88. received: 02.09.2021 accepted: 30.09.2021 published: 01.01.2022 copyright: © 2022 this is an open-access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. introduction l-li alloys are popular in aircraft and space applications due to their significant mechanical properties and lightweight compared to conventional aluminum alloys [1]. aircraft applications have withdrawn use of 2nd generation al-li alloys owing to their anisotropic mechanical behavior, lower fracture toughness, and thermal instability induced lower toughness [1, 2, 3]. the high lithium weight percentage in al-li alloy has been the primary cause of these limitations. the innovative processing techniques of lithium addition to aluminum and restricting its proportion to less than 2% has led to emergence of 3rd generation al-li alloys. the commercial aircraft and space shuttle involve critical parts necessitating the use of aa2050-t84 alloy, a 3rd generation al-li alloy [3, 4]. aircraft wing components prone to fracture failure incorporate ‘damage tolerance criteria’ in their design. the critical material properties and loading patterns become essential in design to avoid fracture failure. the american society for testing and materials (astm) standards suggest procedure to obtain fracture toughness for mode-i loading [5, 6]. these a https://youtu.be/_4ebbmqnlys n. ekabote et alii, frattura ed integrità strutturale, 59 (2022) 78-88; doi: 10.3221/igf-esis.59.06 79 standards aim to obtain plane strain fracture toughness (kic or jic), assuring a minimum and conservative value at the high constraint. the fracture toughness depends on specimen geometry, load, and type of specimen, which coined the term constraint. constraint generated at the crack front is measured through well-defined constraint parameters under linear elastic fracture mechanics (lefm) and elastic-plastic fracture mechanics (epfm) [7, 8, 9, 10,11,12, 13, 14]. these constraint parameters are defined concerning either the stress field or the displacement field around the crack front. the variation of constraint parameters concerning crack length, specimen thickness, and load variations are well documented for different standard specimens. moreover, selecting standard methods and specimen types to obtain fracture toughness depends on the constraint present at the component level [15,16]. material anisotropy was the primary concern for the withdrawal of 2nd generation al-li alloys in aircraft applications. it was observed that anisotropy played a prominent role in the fracture toughness of aircraft components made of al-li alloys [1,4]. it also revealed that the aa2050-t84 plate of 4-inch exhibited variation in tensile, compression, and fracture toughness to a significant level [4]. researchers have opined that wing parts, such as spars and ribs fabricated from aa2050-t84 behave differently due to anisotropy under the same load. the constraint variation due to material anisotropy is scarcely reported in the literature, and is limited to specimen thickness, crack length, specimen type, and load conditions. hafley et al. [4] experimentally evaluated the 4-inch aa2050-t84 alloy plate performance and discussed its applicability to the cryogenic propellent tanks used for heavy-lift launch vehicles. the experimental comparison between aa2195-t8 and aa2050-t84 for tensile, compression, and fracture responses was investigated. the tensile behavior of the aa2050-t84 alloy at room and cryogenic temperatures exhibited anisotropic nature. however, the reported experimental fracture toughness tests as per astm test requirements at both temperatures were invalid. the likely reason for invalid fracture toughness experiments can be related to crack tip/front constraint variations, due to material anisotropy. chemin et al. [17] reported anisotropy through the valid fracture toughness tests on 2-inch aa2050-t84 plate at different orientation and temperatures. the anisotropic behavior was attributed to state of stress variation at crack influenced by grain properties. hence, anisotropy of 4-inch aa2050-t84 plate behavior needs numerical fracture constraint analyses based on tensile test results of hafley et al [4]. the experimentation needs high investment and more time, therefore researchers prefer numerical analysis. this work emphasizes on crack driving parameters like j-integral and crack tip opening displacement (ctod) analyzed for 4-inch aa2050-t84 plate. the through-thickness locations and orientations at ambient and cryogenic temperatures for a constant mode-i load were studied using abaqus software. the tensile properties for preprocess stage of simulation were adopted from hafley et al. [4]. plastic zone size (pzs) parameter was used to analyze the constraint variation at specified conditions. the suitability of 4-inch aa2050-t84 plate for cryogenic application was verified on the basis of anisotropy as a governing factor in crack driving and constraint parameter variations. nomenclature, specimen and material property ccording to astm e1820-20b, the fracture toughness depends on the orientation and location of the specimen extracted from the plate [6]. in the present analyses, the primary directions of the 4-inch aa2050-t84 alloy plate considered are rolling direction (l), transverse direction (t), and short transverse direction (s). the 4-inch aa2050-t84 alloy plate rolling direction is parallel to the l direction and possessed a larger dimension than the other two (t and s) directions. the different plate orientations for fracture study considered were l-t, t-l, and s-t, as shown in fig. 1. for instance, fracture specimen l-t orientation indicates loading in the l direction and crack propagation in the t direction. in the s-t plate orientation for 4-inch plate thickness, only one fracture specimen was possible with dimensions considered in line with experimental tests [4]. as indicated in fig. 1, t is the plate thickness (in this case 4-inch), making the t/2 at its center (2 inches), t/6 at outer plate surfaces. the various plate orientations and locations at ambient (240 c) and cryogenic (-1950 c) temperatures were considered for the fracture analyses. astm 182020b recommends two high constraint specimens viz. single edge bend (se(b)) and compact tension (c(t)) for the measurement of fracture toughness [6]. the c(t) specimen assures lower bound toughness value compared to se(b) and suited for primary structures of aircraft applications [1]. fig. 2 shows the c(t) specimen used for current fracture analyses adopting width (w) = 25.4 mm, crack length (a) = 12.7 mm and thickness (b) = 12.7 mm in compliance to astm 1820-20b [6]. a n. ekabote et alii, frattura ed integrità strutturale, 59 (2022) 78-88; doi: 10.3221/igf-esis.59.06 80 the material chemical composition constituted copper (3.3% to 3.4%) as the primary alloying element with lithium (less than 1%) added to introduce desirable properties [3]. the density reduction by almost 3% and rise in young’s modulus by 6% compared to conventional aluminum alloys were noticed [1, 3]. figure 1: various orientation and location of fracture specimens in a 4-inch aa2050-t84 plate. figure 2: c(t) specimen. the reported experimental tensile properties (shown in tab. 1) based on hafley et al. [4] were adopted for different orientations and locations of the plate at ambient (240 c) and cryogenic (-1950 c) temperatures for finite element (fe) analyses. tab. 1 shows the average tensile properties at various orientations and locations of the 4-inch aa2050-t84 plate [4]. diverse average tensile properties in different orientations and locations were reported for both ambient and cryogenic test temperature. anisotropic tensile behavior characterized by plate location and orientation at different temperatures becomes essential in designing spars and ribs. the damage tolerance criterion-based design accounts for anisotropy in the spars and ribs of the aircraft wing during the fracture analysis. temperature (0c) plate orientation specimen location σys (mpa) σut(mpa) e (gpa) 24 (ambient) l t/6 486.77 509.52 74.46 t/2 515.04 546.06 75.15 t t/6 478.5 521.93 75.15 t/2 468.84 515.73 75.84 s t/2 442.64 505.38 73.77 -195 (cryogenic) l t/6 561.92 612.25 82.05 t/2 592.26 659.82 84.11 t t/6 550.89 631.56 82.73 t/2 543.99 630.18 84.12 s t/2 504 601.91 82.05 table 1: tensile properties of 4-inch aa2050-t84 alloy plate [4] finite element analyses he current work emphasizes 3d elastic-plastic numerical fracture analysis on c(t) specimen for mode-i loading using abaqus 6.14. the stress and strain curves were adopted from the research work of hafley et al. [4] for the elastic-plastic fracture analysis. in this work, the material response has been considered to be a multi-linear kinematic hardening type. the material's plastic part's behavior was modelled by taking twenty divisions after the yielding point of the stress-strain curves along with elastic input viz., young’s modulus (e) and poisson’s ratio (ʋ). the material property input into the abaqus 6.14 for elastic-plastic fracture analysis is adopted as similar to the earlier work of kudari t n. ekabote et alii, frattura ed integrità strutturale, 59 (2022) 78-88; doi: 10.3221/igf-esis.59.06 81 et al. [14, 19]. the crack driving parameters such as j-integral and crack mouth opening displacement (cmod) were extracted directly from abaqus 6.14 post-processor [18]. the c(t) model being symmetric about y-axis was analyzed considering only one-half of it with a/w = b/w = 0.5, as shown in fig. 3. a quadratic 20-node hexahedral (brick) element with reduced integration (c3d20r) was used throughout the model for meshing. a similar kind of element was used in earlier work [19, 20]. the model contains 15910 elements with 71709 nodes. at the crack front, these nodes were collapsed at one end (near the crack tip side) for efficient replication of singularity. at the crack front, 1200 elements with 6013 nodes were created for better accuracy of results. figure 3: meshed model of c(t) specimen figure 4: fe model with boundary conditions in the model, along the area of the crack ligament (b), y-symmetry was imposed. a constant concentrated load corresponding to varying load ratio (papplied/pmax) between 0.1 and 1 with pmax of 16,000 n was applied at hole along ydirection for all numerical analyses. the applied stress (σapplied) is calculated for c(t) specimen by using the relation mentioned in the earlier work of a. h. priest [21]. the pmax of 16,000 n was selected to keep the stress ratio (σapplied/σys) in between the range 0.4 and 0.5. the wireframe model with boundary conditions shown in fig. 4 was used for all cases of numerical studies. however, the material properties were assigned as per the specimen's location, orientation, and operating temperature, as mentioned in tab. 1. results and discussion he numerical procedure for the determination of j-integral was validated through an experimental fracture toughness test performed according to astm e1820-20b. the current numerical elastic-plastic fracture analysis procedure was adopted and validated from the earlier work [14]. the experimental fracture toughness test resulted in jic of 11.589 n/mm at room temperature. the numerical analysis carried out for the same experimental load conditions resulted in the value of j-integral as 11.02 n/mm. the marginal difference (<5%) in values are served as motivation to extend the numerical procedure for further investigations. in the 3-d numerical analysis, the j-integral and cmod were extracted along the crack front (thickness direction) at room temperature as shown in figs. 5 and 6. fig. 5 indicates the variation of j-integral along the crack front at the ambient temperature of 240 c for various plate location and orientation conditions. the peak values of j-integral at crack front center were attributed to the crack tunneling effect [6]. a similar phenomenon of peak j-integral values at the crack front center was observed at a cryogenic temperature of -1950 c. as expected, the cmod values are constant along the crack front for all plate orientations. gentile et al. [13] have performed fe analysis to predict specimen response through crack driving parameters viz. computed j-integral with measured ctod. in the present work we have also attempted to study the behavior of variation of ctod on different orientation and locations. thus, the peak values of j-integral, and ctod at crack front center were taken up for further analysis at both temperatures. effect of plate location crack driving parameters characterized by j-integral and cmod were extracted in lt, tl, and st orientations at through-thickness locations of the plate. these parameters relative values provided insight into the behavioral aspects of t n. ekabote et alii, frattura ed integrità strutturale, 59 (2022) 78-88; doi: 10.3221/igf-esis.59.06 82 the plate under constant external load subjected to different plate orientations. figs. 7 and 8 depict them for varying load ratios. figure 5: j-integral along the crack front at ambient temperature. figure 6: cmod along the crack front at ambient temperature. figure 7: variation of j-integral for different plate orientation and location at 240 c figure 8: variation of cmod for different plate orientation and location at 240 c the non-linear nature of j-integral exhibited the increasing order lt-tl-st, with the highest value recorded for st orientation at a load ratio greater than 0.4. the j-integral differed by around 12% between lt and tl and around 30% between lt and st orientations with peak load ratio for unity. similarly, cmod value differed by about 8% at peak load ratio between lt and tl and around 23% between lt and st orientations. the value of j-integral and cmod for lt configuration was higher by 8-9% at plate center (t/2) against plate surface (t/6). however, it decreased by 2% in tl orientation at peak load ratio. figs. 9 and 10 depict j-integral and cmod variation for various load ratios at different orientations and locations of the plate for cryogenic temperature. the j-integral and cmod varied slightly (4% 8%) exhibiting gradual increase in the lttl-st sequence of plate orientations at peak load ratio. their values at cryogenic temperature increased by 2-4% from positions t/2 to t/6 for lt against less than 1% for tl orientations at peak load ratios. the anisotropy effect on crack driving parameters was less at cryogenic temperature, confirming with observed in tensile test results of hafley et al. [4]. ctod is another important fracture parameter based on displacement at the crack tip/front of the specimen. according to astm 1820-20b [6], ctod is calculated from j-integral value. figs. 11 and 12 show the ctod variation for different plate orientations and locations at ambient and cryogenic temperatures. these ctod variations follow a similar trend displayed by j-integral in figs. 5 and 7. plate surface (t/6) locations are isotropic for both temperatures under fracture analyses as crack driving parameters were almost identical. a similar observation was reported in the tensile behavior of hafley et al. [4]. the weaker intensities of deformation texture components were due to surface rolling associated with n. ekabote et alii, frattura ed integrità strutturale, 59 (2022) 78-88; doi: 10.3221/igf-esis.59.06 83 lower yield strength. the isotropic properties at t/6 location at both temperatures make it a congenial material for wing components like spars and ribs over the surface of the aa2050-t84 plate. figure 9: variation of j-integral for different plate orientation and location at -1950 c figure 10: variation of cmod for different plate orientation and location at -1950 c figure 11: variation of ctod for different plate orientation and location at 240 c figure 12: variation of ctod for different plate orientation and location at -1950 c the location in a plate was quite significant at both temperatures because of appreciable variations in crack driving parameters. however, the plate orientation had a substantial effect at ambient temperature compared to cryogenic temperature. aa2050-t84 plate showed inconsistent fracture behavior concerning locations and orientations at different temperatures being significant for designing aircraft primary wing components. chemin et al. [17] have observed that the plane strain fracture toughness (kic) of the 2-inch thick aa2050-t84 alloy material decreased with lt to tl orientation by almost 23% at ambient temperature. on the contrary, in the present epfm analyses, j-integral increased by nearly 11% from lt to tl orientation at a similar temperature. thus, the tl orientation is more susceptible to fracture failure than the lt under identical load at ambient temperature due to its lower kic value. effect of plate orientation the comparison of crack driving parameters at different temperatures was crucial to claim its suitability at cryogenic temperatures. this issue is prominent in the design of space shuttle tanks because of material extraction from different orientations. the variation of crack driving forces at these orientations at various operating temperatures was crucial also for aircraft component damage tolerance design. figs. 13 to 18 present the variation of j-integral, cmod and ctod at different plate locations dependent on plate temperature and orientations. n. ekabote et alii, frattura ed integrità strutturale, 59 (2022) 78-88; doi: 10.3221/igf-esis.59.06 84 figure 15: variation of cmod for different plate orientation at t/6 location figure 16: variation of cmod for different plate orientation at t/2 location figure 13: variation of j-integral for different plate orientation at t/6 location figure 14: variation of j-integral for different plate orientation at t/2 location figure 17: variation of ctod for different plate orientation at t/6 location figure 18: variation of ctod for different plate orientation at t/2 location n. ekabote et alii, frattura ed integrità strutturale, 59 (2022) 78-88; doi: 10.3221/igf-esis.59.06 85 the decrease in j-integral and cmod was noticed at a cryogenic temperature at both location and plate orientations. the temperature change from ambient to cryogenic leads to the decline by 22%, 32%, and 45% for j-integral values in lt, tl, and st orientations of t/2 locations for peak load ratio. similarly, 28% of the drop in j-integral at t/6 locations for both lt and tl orientations were observed for peak load ratio. in figs. 14 and 16, the specimen extracted at the plate surface (t/6) was less affected (<2%) by orientation at ambient and cryogenic temperatures. from figs. 13 and 15, the plate center (t/2) location show significant variations in j-integral and cmod values at ambient conditions only. the figs. 17 and 18 depict similar trend of ctod variations to establish a correlation with j-integral. the observed behavior was attributed to resistance for dislocation movement at cryogenic temperature, causing the material to dissipate lower energy [21]. fracture results at t/6 location of the plate exhibited isotropic behavior similar to tensile results hafley et al. [4] at both ambient and cryogenic temperatures. however, the plate center (t/2) location showed higher anisotropy at ambient temperature than cryogenic temperatures. the anisotropy was attributed to the strain gradients introduced during rolling, resulting in an increased strain in the vicinity of t/2 location [4]. these results strongly support use of aa2050-t84 plate for cryogenic applications. effect of anisotropy on pzs the modern-day fracture assessment criterion requires data on constraint variation near the crack front and crack driving parameters. constraint is defined as the restriction to plastic deformation at the crack front [22]. plasticity around the crack front is measured as plastic zone size and shape, which depend on the in-plane dimension (crack length) and out-ofplane dimension (specimen thickness) [14]. 3d crack front stress tri-axiality fields significantly affect the constraint measured by pzs [19, 23]. the plastic zone shape and size at the crack front are usually helpful to define plane stress and plane strain conditions. pzs is a suitable parameter to measure constraint near the crack under epfm. the pzs also significantly affects the standard specimen size required for experimental testing of fracture toughness [5, 6]. since the plastic zone is crucial in epfm analysis, the anisotropy role will be noteworthy in pzs variation. the present analysis attempts measurement of the constraint variation concerning anisotropy and temperature using normalized pzs (pzs/crack length = rp/a) at crack front. pzs measured as per kudari et al. [14] at the center of the crack front is shown in fig. 19, and the shape of pzs along the crack front is shown in fig. 20. figs. 21 and 22 show the variation of normalized pzs for plate orientation and location at ambient and cryogenic temperatures. at ambient temperature, normalized pzs for peak load ratio was almost 18% higher in lt orientation, t/6 location compared to t/2 location. pzs is inversely proportional to the square of the yield stress of the material [18]. normalized pzs increased with plate orientation in the order of lt-tl-st in agreement to observations made by hafley et al. [4] that reported a decrease in yield stress in the order of lt-tl-st at both locations of the plate. however, the constraint variation between lt and tl orientation for both temperatures was minimal (<5%) at t/6 location. the minimal difference of yield stress values can be visualized at t/6 locations from tab. 1 for both temperatures. unlike figs. 14 and 16, which showed minimal crack driving parameters at the t/2 location of the cryogenic temperature, the normalized pzs difference was substantial for different plate orientations. this trend indicated isotropic behavior at t/6 plate location for both temperatures, making the aa2050-t84 alloy plate surface suitable for ambient and cryogenic applications. from figs. 23 and 24, the effect of plate orientation on normalized pzs at t/6 location for cryogenic temperature was negligible. at cryogenic temperature, the variation of normalized pzs at t/2 location increased almost 35% between lt and tl or st orientations for peak load ratio, respectively. but, at t/6 location, the constraint variation was minimal (<5%) at cryogenic temperature. however, at ambient temperature, the normalized pzs variation was significant for plate location and orientation. at ambient temperature, the variation of normalized pzs at t/2 location increased almost 22% between lt to tl and 48% between lt and st orientations, respectively. similarly, at t/6 location the constraint variation was almost 4% between lt and tl orientations at ambient temperature. the temperature effect is remarkable on constraint as the normalized pzs values at ambient temperature were almost twice that of cryogenic temperature. the possible reason for lower values of normalized pzs is the brittle nature of the aa2050-t84 alloy at cryogenic temperature. the observations from crack driving parameters and constraint variation at cryogenic temperature strongly suggest that the plate orientation effect nullified and almost behaved as isotropic material at t/6 location (plate surface). n. ekabote et alii, frattura ed integrità strutturale, 59 (2022) 78-88; doi: 10.3221/igf-esis.59.06 86 figure 20: plastic zone shape along the crack front figure 19: pzs (rp) measurement at crack center figure 21: variation of normalized pzs for different plate orientation and location at 240 c figure 22: variation of normalized pzs for different plate orientation and location at -1950 c figure 23: variation of normalized pzs for various plate orientation at t/2 location figure 24: variation of normalized pzs for various plate orientation at t/6 location n. ekabote et alii, frattura ed integrità strutturale, 59 (2022) 78-88; doi: 10.3221/igf-esis.59.06 87 conclusion he computational investigations on the aa2050-t84 specimen revealed the following conclusive remarks. a 4inch aa2050-t84 alloy plate behavior under mode-i loading using c(t) specimen was analyzed in the present study. the effect of anisotropy on fracture and constraint parameters in j-integral, ctod, cmod and pzs was studied at ambient and cryogenic temperatures. on account of rolling, plate surface (t/6) location elongated more and had higher crack driving parameters than mid-plate location (t/2) under identical mode-i loading. plate orientation had a negligible effect on crack driving parameters at both ambient and cryogenic temperatures. however, the constraint parameter, pzs variation, was significant. both crack driving parameters and pzs increased in the order of lt-tl-st for ambient and cryogenic temperatures. the studies based on through-thickness variation indicated that crack driving parameters were maximum at plate surface (t/6) locations for both temperatures. the crack driving parameters were twice at the surface of the plate as compared to the mid-plate location. constraint parameter pzs was higher at plate surface (t/6) ambient temperature than mid-plate (t/2) location. however, the effect of plate location on constraint parameter pzs was minimal at cryogenic temperature. the crack driving parameters exhibited a falling trend with decreased test temperature. the effect of temperature on crack driving parameters and pzs was maximum at the plate surface compared to the mid-plate location. the plane strain fracture toughness (kic) of the aa2050-t84 alloy plate reduced with a decrease in temperature along lt orientation and was almost independent of orientation in tl [17]. the results obtained in the current work are helpful in deciding the location and orientation of the aircraft wing component extraction from aa2050-t84 alloy plate, as crack driving parameters and constraint variation were significant to anisotropic plate properties at different temperatures. the isotropic behavior at the t/6 location under sub-zero temperature made the plate surface suitable for cryogenic temperature applications. acknowledgments le technological university has partially supported this work under “capacity building project” grants. authors thank kle society and kle technological university, hubballi, for the funds and support. references [1] prasad, n. e., gokhale, a. and wanhill, r. j. h. (eds.). (2013). aluminum-lithium alloys: processing, properties, and applications, butterworth-heinemann. doi: 10.1016/c2012-0-00394-8. [2] lynch, s.p., muddle, b.c. and pasang, t., (2002). mechanisms of brittle intergranular fracture in al-li alloys and comparison with other alloys, philosophical magazine a, 82(17-18), pp. 3361-3373. doi: 10.1080/01418610208240447. [3] rioja, r. j. and liu, j. (2012). the evolution of al-li based products for aerospace and space applications, metallurgical and materials transactions a, 43(9), pp.3325-3337. doi: 10.1007/s11661-012-1155-z. [4] hafley, r. a., domack, m. s., hales, s. j. and shenoy, r. n. (2011). evaluation of aluminum alloy 2050-t84 microstructure and mechanical properties at ambient and cryogenic temperatures, nasa langley research center. report number: nasa/tm-2011-217163. [5] astm e399-20a, standard test method for linear-elastic plane-strain fracture toughness of metallic materials, astm international, west conshohocken, pa, 2020. doi: 10.1520/e0399-20a. [6] astm e1820-20b, standard test method for measurement of fracture toughness, astm international, west conshohocken, pa, 2020. doi: 10.1520/e1820-20b. [7] gupta, m., alderliesten, r. c. and benedictus, r. (2015). a review of t-stress and its effects in fracture mechanics, engineering fracture mechanics, 134, pp.218-241. doi:10.1016/j.engfracmech.2014.10.013. [8] moattari, m. and sattari-far, i. (2017). modification of fracture toughness master curve considering the crack-tip qconstraint, theoretical and applied fracture mechanics, 90, pp. 43-52. doi: 10.1016/j.tafmec.2017.02.012. t k n. ekabote et alii, frattura ed integrità strutturale, 59 (2022) 78-88; doi: 10.3221/igf-esis.59.06 88 [9] yang, j., wang, g. z., xuan, f. z. and tu, s. t. (2013). unified characterization of in-plane and out-of-plane constraint based on crack-tip equivalent plastic strain, fatigue & fracture of engineering materials & structures, 36(6), pp.504-514. doi: 10.1111/ffe.12019. [10] vasco-olmo, j. m., díaz, f. a., james, m. n., christopher, c. j. and patterson, e. a. (2017). experimental methodology for the quantification of crack tip plastic zone and shape from the analysis of displacement fields, frattura ed integrita strutturale, 11(41), pp.166-174. doi: 10.3221/igf-esis.41.23. [11] xu, j. y., wang, g. z., xuan, f. z. and tu, s. t. (2018). unified constraint parameter based on crack-tip opening displacement, engineering fracture mechanics, 200, pp.175-188. doi: 10.1016/j.engfracmech.2018.07.021. [12] matvienko, y., (2019). comparison of the constraint parameters in elastic-plastic fracture mechanics. frattura ed integrità strutturale, 13(49), pp.36-43. doi:10.3221/igf-esis.49.04. [13] gentile, d., persechino, i., bonora, n., iannitti, g. and carlucci, a. (2014). use of circumferentially cracked bar sample for ctod fracture toughness determination in the upper shelf regime. frattura ed integrità strutturale, 8(30), pp. 252-262. doi: 10.3221/igf-esis.30.32. [14] kudari, s. k., maiti, b. and ray, k. k. (2009). experimental investigation on possible dependence of plastic zone size on specimen geometry. frattura ed integrità strutturale, 3(7), pp. 57-64. doi: 10.3221/igf-esis.07.04. [15] chiesa, m., nyhus, b., skallerud, b. andthaulow, c. (2001). efficient fracture assessment of pipelines. a constraintcorrected sent specimen approach, engineering fracture mechanics, 68(5), pp.527-547. doi: 10.1016/s0013-7944(00)00129-6. [16] ekabote, n., kodancha, k.g. and kudari, s.k., (2021). suitability of standard fracture test specimens for low constraint conditions. iop conf. ser.: mater. sci. eng., 1123, 012033, doi: 10.1088/1757-899x/1123/1/012033. [17] chemin, a. e. a., afonso, c. m., pascoal, f. a., maciel, c. i. d. s., ruchert, c. o. f. t. and bose filho, w. w. (2019). characterization of phases, tensile properties, and fracture toughness in aircraft-grade aluminum alloys, material design & processing communications, 1(4), pp.1-13. doi:10.1002/mdp2.79. [18] abaqus 6.14-1. (2004) hibbitt, karlsson & sorensen, inc. [19] kudari, s. k. and kodancha, k. g. (2008). effect of specimen thickness on plastic zone. 17th european conference on fracture, brno, czeck republic. [20] moreira, p. m. g. p., pastrama, s. d. and de castro, p. m. s. t. (2009). three-dimensional stress intensity factor calibration for a stiffened cracked plate. engineering fracture mechanics, 76(14), pp. 2298-2308, doi: 10.1016/j.engfracmech.2009.07.003. [21] priest, a. h. (1975). experimental methods for fracture toughness measurement. journal of strain analysis, 10(4), pp. 225-232. doi: 10.1243/03093247v104225. [22] yuan, h. and brocks, w. (1998). quantification of constraint effects in elastic-plastic crack front fields, journal of the mechanics and physics of solids, 46(2), pp. 219-241. doi: 10.1016/s0022-5096(97)00068-9. [23] caputo, f., lamanna, g. and soprano, a. (2013). on the evaluation of the plastic zone size at the crack tip, engineering fracture mechanics, 103, pp. 162-173. doi: 10.1016/j.engfracmech.2012.09.030. microsoft word 2191 s. e. oliveira et alii, frattura ed integrità strutturale, 48 (2019y) 249-256; doi: 10.3221/igf-esis.48.26 249 focused on the “portuguese contributions for structural integrity” effect of machining parameters on the mechanical properties of high dosage short –carbonfiber reinforced composites s. e. oliveira, j.a.m. ferreira, j. da silva cemmpre, university of coimbra, department of mechanical engineering, portugal uc2014184149.seo@outlook.com, http://orcid.org/0000-0002-2749-2717 martins.ferreira@dem.uc.pt, http://orcid.org/0000-0002-0295-1841 joel.jesus@uc.pt, http://orcid.org/0000-0002-7133-2331 c. capela instituto politécnico de leiria, estg, department of mechanical engineering, portugal ccapela@ipleiria.pt, http://orcid.org/0000-0003-3334-4945 abstract. the machinability of polymer matrix composites with fibers strongly depends on the type of fiber and dosage in question, having a high influence on the selection of tools and cutting parameters. the cutting temperature depends of rotation speed and the feed cutting tools and is significantly influencing on the quality of the machined surfaces and tool life. this paper presents the results of a current study concerning the effect of the rotation-cutting speed on the cutting temperature, roughness and tensile strength of short carbon fiber reinforced epoxy composites, potentially used in automotive and aeronautic industries. composite plates were manufactured by compression molding, using short carbon fibers with 0.5 mm and 6 mm length. the increasing of the rotation-cutting speed increases significantly the temperature generated in the tool and slightly increases surface roughness. tensile strength and young´s modulus are little sensitive to drilling speed. however, above 3000 rpm it was observed significant loss of stiffness, associated with the developed temperature in the machining process. keywords. mechanical properties; short fiber composites; machinability of composites. citation: oliveira, s. e., ferreira, j.a.m., capela, c., da silva, j., effect of machining parameters on the mechanical properties of high dosage short –carbonfiber reinforced composites, frattura ed integrità strutturale, 48 (2019) 249-256. received: 14.09.2018 accepted: 24.10.2018 published: 01.01.2019 copyright: © 2019 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. introduction olymer matrix composites are widely used in the manufacture of components for engineering applications [1,2]. in particular, short-fiber reinforcement polymer (sfrp) composites are easy to manufacture, have low production costs and good mechanical properties. in general, the addition of short fibers in a polymer matrix aims to obtain p http://www.gruppofrattura.it/va/48/2191.mp4 s. e. oliveira et alii, frattura ed integrità strutturale, 48 (2019y) 249-256; doi: 10.3221/igf-esis.48.26 250 high performance composites, with the increase of the fiber fraction leading to an increase in modulus and strength of the processed material [3]. however, for a high dosage of reinforcing the homogeneous distribution of the fiber becomes very difficult and the porosity drastically increases, which justifies more detailed studies of this subject. machining of fiber-reinforced composites differs significantly in many aspects from the machining of conventional metals and their alloys. in the machining of fiber-reinforced composites the behavior of the material is not only inhomogeneous but it also depends on diverse fiber and matrix properties, fiber orientation, and the relative volume of matrix and fibers [4]. the cutting tool alternately cuts the matrix and the fibers which machining response may be entirely different [4]. in the manufacture of engineering components from composite material, it is sometimes necessary to perform drilling and milling operations. in the case of manufacturing components in a composite material with short fibers, milling operations may be performed to obtain the desired a local geometry of the components. the machinability of polymer matrix composites with fibers strongly depends on the type of fiber and composite dosage and their mechanical and physical (for instance, thermal) properties. however, the type of fiber used in processing of these materials has a major influence on the selection of tools and cutting parameters [5]. the cutting temperature is also a factor that has a significant influence on the quality of the machined surfaces and tool life. in turn, temperature around cutting point and the final surface roughness depend on rotation and feed cutting tools. during the milling of short-fibber-carbon-reinforced composites (scfc), the temperature on cutting point can cause damage or degradation to the composite’s surface. the surface roughness of the machined area greatly influences the mechanical performance of the dimensional precision and manufacturing costs [5]. therefore, surface roughness and degradation of the composite’s surface require study to ensure the use of an industrial process. this is the first step to study machinability involving a specific composite. milling in composite materials is a rather complex task due to its heterogeneity and the emergence of some problems such as surface delamination appearing during the machining process, associated with the characteristics of the material and cutting parameters. milling is the machining operation most frequently used in the manufacture of fiber-reinforced plastic parts, as a corrective operation to produce well-defined and high-quality surfaces that often require the removal of excess material to control tolerances. therefore, the ability to predict the cutting forces is essential to select process parameters which are necessary for an optimal machining. mechanical performance of scfc depends mainly on the capacity to obtain good fiber dispersion, usually evaluated by nondestructive methods such as ultrasonic c scanning and acoustic emission [6,7]. this paper studied the effect of cutting conditions during milling machining on roughness, cutting temperature and mechanical properties, with the purpose of contributing for a better understanding of the interdependence of these parameters, especially in the case of composites with high dosage. materials and samples or this investigation two composite batches were manufactured: a) a 6mm length fiber, and using biresin® cr120 as matrix, formulated by bisphenol a epichlorhydrin epoxy resin 1,4 bis (2,3-epoxypropoxy) butane, combined with the hardener ch120-3, with 40% (in volume fraction) of carbon fibers. b) 0.5 mm ± 0.15 in length and 7 µm ± 2 ø monofilaments, using biresin® cr83 matrix reinforced with 17.5% (in volume fraction) of carbon fibers. resins were supplied by sika, stuttgart, germany, while the company sigrafil, sgl group, germany, supplied the fibers. composite plates were manufactured by manual molding process, pressing the mold in a servo mechanical machine, mazzola w15. the compression was applied such as it is shown schematically in fig. 1, which also shows the mold and the positioning of the pressure transducer used to monitor inside pressure during the cure process. the desired amount of fibers previously subjected to the fiber separation treatment was added to the resin. then, the materials were mixed and placed in the mold cavity. afterwards, the mold was closed and placed in the mechanical compression load at 7600 dan, with corresponding pressure of about 50.7 bar. the processed plates were then subjected to cure and post cure processes. fig. 2a) shows the mold design and a final composite plate. from this plate, test specimens were later machined according to the scheme and dimensions indicated in fig. 2b). composite plates were subjected to a cure process done at room temperature for 20 hours in the mold, and a post cure was carried out at 70º c for 12 hours. the pressure during the curing process was monitored by the pressure transducer shown in fig. 1. as shown in fig. 2c) the pressure remains nearly constant for the entire duration of the cure process. f s. e. oliveira et alii, frattura ed integrità strutturale, 48 (2019y) 249-256; doi: 10.3221/igf-esis.48.26 251 the specimens were machined according to the geometry and dimensions indicated in fig. 2b) from the plates with dimensions 150x100x5 mm^3 using a computer numerical control (cnc) milling machine, hass mikron vce 500 and a sandvik carbide tool with a diameter of 20 mm, part number sandvik r390-11t308e-nl h13a. the machining parameters used are indicated in tab. 1. fig. 3 presents the most relevant details of track strategies for the plate machining to increasing cutting speed. spindle speed, (rpm) cutting speed, (mm/min) axial increment, (mm) inclination angle axis, (º) 750 50 1.0 0 1500 100 1.0 0 2250 150 1.0 0 3000 200 1.0 0 4500 300 1.0 0 table 1: cutting parameters used in the machining of composite plates. figure 1: scheme of molding apparatus: (a) composite plate. (b) rubber base. (c) pressure transducer. (d) steel upper die part. (e) steel lower die part. (f) aluminum base.   (a) steel upper die part (b) steel lower die part (c) composite plate a) b) figure 2: a) molding cavity; b) final specimen dimensions (units in mm); c) curing pressure. s. e. oliveira et alii, frattura ed integrità strutturale, 48 (2019y) 249-256; doi: 10.3221/igf-esis.48.26 252 figure 3: schematic view of the plate machining: (a) composite plate; (b) fittings; (c) double adhesive band; (d) plane-end mill set. experimental testing emperature profile is important to determine the limits for cutting speed. during the drilling process the temperature around the cutting tool was monitored using a thermographic camera, testo 875, as shown in exemplary fig. 4. figure 4: surface drilling and temperature measurement. sample manufactured with fiber length 6 mm and spindle speed 4500 rpm. surface roughness was quantified using the standardizing parameter rz, which is the arithmetic average of five distances values between the highest peak and lowest valley in each sampling length measures at 15 mm. roughness measurements were carried out using the equipment surface measuring instrument mitutoyo surftest sj-500. tensile tests for the characterization of the mechanical properties, tensile strength and young’s modulus were performed using a machining instron model 4206, monitoring the load and the displacement through an axial extensometer. fiber dispersion into composite was checked using optical equipment [8], the scanning electronic microscopy (sem) philips xl30. after carrying out tensile tests, the fracture surfaces in some specimens were gold sputtered and then observed in sem to understand the fiber adhesion failure mechanisms. fig. 5 shows a sem low magnification characteristic micrograph of the fracture of an external face of a specimen with 0.5 mm length fiber, in which a reasonable dispersion was observed, only with partial separation of the fibers. this kind of microscopic structure was observed in other specimens and cannot be classified as an isometric structure. t s. e. oliveira et alii, frattura ed integrità strutturale, 48 (2019y) 249-256; doi: 10.3221/igf-esis.48.26 253 results and discussion urface roughness was analyzed to verify the adequacy of the machined processing under development. fig. 6 shows the results obtained for both material batches: length fiber 0.5mm and 6mm, presenting the average values and the dispersion range of the experimental tests. the analysis of the figure shows that the experimental results are in good agreement with the usual values in the manufacturing industry, particularly to metallic materials. these results indicate that the parameter rz increases slightly with the drilling speed, in spite of the natural dispersion of the results. composites with lower fiber length and content exhibit much higher roughness rz, probably a consequence of the lower glass transition temperature, tg, of the polymer resin, and consequently in this case it is easier for the temperature on the surface of the tool to reach a value close to or greater than tg during the cutting operation. the analysis of the data indicated that the speed cutting up to 2250 rpm and feed 150 mm per minute presents smaller values of surface roughness. the temperature on the surface of the carbide tool during the cutting of the scfc plates was measured with an infrared thermograph camera, as shown in fig. 4. the values of the maximum observed temperature in the cutting tool during face machining are plotted against the rotation speed for both composites in fig. 7. in both cases, a significant increase of the temperature with the increase of cutting speed was observed. the temperature profile reveals that in some cases (above 3000 rpm) its values reach the glass transition temperature, tg, of the polymer matrices. for the 6mm fibers composites the tg of the resin (113 ºc [9]), while for biresin® cr83 resin, tg 84 ºc, according the manufacturer. figure 5: sem low magnification characteristic micrograph of the fracture surface. figure 6: surface roughness, rz, against drilling speed. the results of the tensile tests are summarized in figs. 8 and 9, which present the tensile strength and the young’s modulus, respectively, against drilling speed. tensile strength is the axial stress for the load peak of the load versus s s. e. oliveira et alii, frattura ed integrità strutturale, 48 (2019y) 249-256; doi: 10.3221/igf-esis.48.26 254 displacement curves. the stiffness modulus was calculated using the linear elastic hooke’s law in the linear region of load versus displacement plot. the collected values presented a correlation coefficient at least 0.99. contrary to the reported on scientific literature [3], a decreasing of the tensile strength with the increasing of both fiber content and length was observed. these results are justified by the poor fiber distribution, poor fiber/matrix adhesion and increasing porosity for higher fiber dosage composites. on the other side, and despite high dispersion of the results, rotation-cutting speed seems to play a reduced effect on composite tensile strength, for both materials. figure 7: maximum temperature around carbon tool against drilling speed. figure 8: tensile strength against rotation-cutting speed. the analysis of the stiffness modulus, shown in fig. 9, indicates that in this case the results are in accordance with the reported on literature [3], as it was observed an increasing of the stiffness with the increasing of both fiber content and length. the results mean that fibber distribution and porosity play a less significant role on composite stiffness than in tensile strength. the analysis of the figure also shows significant dispersion (with standard deviations from 0.25 to 2.65 gpa), but an important aspect must be stated for both materials: above 3000 rpm there is a significant loss of stiffness. this loss of rigidity may be associated with the temperature developed in the machining process and consequent degradation of the matrix. s. e. oliveira et alii, frattura ed integrità strutturale, 48 (2019y) 249-256; doi: 10.3221/igf-esis.48.26 255 failure surface of some samples was observed in the scanning electron microscope. fig. 10 shows a sem micrograph feature for 6mm length fiber composites fiber composites, which reveals a fair adhesion between resin matrix and fibers. it can also be observed some lack of polymers between the fiber and the fiber pullout, as reported in literature for high dosage composites [8, 10]. on the other hand, as shown in fig. 5, the composites with 0.5mm fiber length shows much better fiber dispersion and lower resin lacks. figure 9: stiffness modulus against drilling speed. figure 10: sem observations of fracture surfaces for 6mm fibers composites. conclusions his work studied the effect of rotation-cutting speed on the cutting temperature, roughness and tensile properties of two epoxy based composites reinforced with 17.5% and 40% in volume fraction short carbon fiber. the main conclusions drawn can be summarized as follows: the increasing of rotation-cutting speed significantly increases the temperature generated in the tool reaching the glass transition temperature, tg of the polymer matrices. the surface roughness (rz) only slightly increases with the drilling speed. t s. e. oliveira et alii, frattura ed integrità strutturale, 48 (2019y) 249-256; doi: 10.3221/igf-esis.48.26 256 mechanical properties such as tensile strength and young’s modulus are not very sensitive to drilling speed. nonetheless, the high dispersion of the results for rotation-cutting speed seems to play a reduced effect on composite tensile strength and stiffness for both materials. in any case, above 3000 rpm a significant loss of stiffness was observed, which may be associated with the temperature developed in the machining process, which reached values above the glass transition temperature (tg) of the resin. tensile stiffness increases significantly with the simultaneous increasing in the fiber content and length. in fact, tensile strength decreases with the increasing of the fiber content and length, in consequence of the poor fiber distribution and very high porosity for the too high fiber dosage composites. acknowledgments his research is sponsored by feder funds through the program compete – programa operacional factores de competitividade – and by national funds through fct – fundação para a ciência e a tecnologia –, under the project pest-c/eme/ui0285/2013. the authors thank the part of support to this investigation by the brazilian agency cnpq, conselho nacional de desenvolvimento ciêntifico e tecnológico, csf. references [1] shahrajabiana, h., hadia, m. and farahnakian, m. (2012). experimental investigation of machining parameters on machinability of carbon fiber/epoxy composites, int. j. of eng. and innov. tech. (ijeit), 2 (3), pp. 30-32. [2] agarwal, g., patnaik, a. and sharma, r. k. (2014). mechanical and thermo–mechanical properties of bi-directional and short carbon fiber reinforced epoxy composites. j. of eng. sci. and tech., school of engineering, 9(5), pp. 590 – 604. [3] fu, s. y., lauke, b, mäder, e., yue, c. y. and hu, x. (2000). tensile properties of short-glass-fiberand short-fibbercarbon-reinforced polypropylene composites, composites: part a 31, pp.1117-1125. doi: 10.1016/s1359-835x(00)00068-3. [4] komanduri, r. (1997). machining of fiber-reinforced composite. machining science and technology, 1 (1), pp. 113152. doi: 10.1080/10940349708945641. [5] davim, j. p. and reis, p. (2004). damage and dimensional precision on milling carbon fiber-reinforced plastics using design experiments. j. of mat. proc. tech. 160, pp. 160–167. doi: 10.1016/j.jmatprotec.2004.06.003. [6] park j.m., lee s.i., kim k.w. and yoon d.j. (2001). interfacial aspects of electrodeposited conductive fibers/epoxy composites using electro-micromechanical technique and nondestructive evaluation. j colloid interface sci., 237, pp. 80–90. doi: 10.1006/jcis.2001.7426. [7] xu x., zhou z., hei y., zhang b., bao j. and chen x. (2014). improving compression-afterimpact performance of carbon–fiber composites by cnts/thermoplastic hybrid film interlayer. compos sci technol, 95, pp. 75–81. [8] habib, s. and okada, a. (2016), influence of electrical discharge machining parameters on cutting parameters of carbon fiber-reinforced plastic. mach. sc. and tech., 20(1), pp. 99-114. doi: 10.1080/10910344.2015.1133914. [9] yashiro, t., ogawa, t. and sasahara, h. (2013). temperature measurement of cutting tool and machined surface layer in milling of cfrp. int. j. of machine tools & manufacture, 70, pp. 63–69. doi: 10.1016/j.ijmachtools.2013.03.009. [10] agarwal, h., amaranath, a., jamthe, y. and gururaja, s. (2015). an investigation of cutting mechanisms and strain fields during orthogonal cutting in cfrps. machining science and technology, 19 (3), pp. 416-439. doi: 10.1080/10910344.2015.1051539. t << /ascii85encodepages false /allowtransparency false /autopositionepsfiles true /autorotatepages /none /binding /left /calgrayprofile (dot gain 20%) /calrgbprofile (srgb iec61966-2.1) /calcmykprofile (u.s. web coated \050swop\051 v2) /srgbprofile (srgb iec61966-2.1) /cannotembedfontpolicy /error /compatibilitylevel 1.4 /compressobjects /tags /compresspages true /convertimagestoindexed true /passthroughjpegimages true /createjobticket false /defaultrenderingintent /default /detectblends true /detectcurves 0.0000 /colorconversionstrategy /cmyk /dothumbnails false /embedallfonts true /embedopentype false /parseiccprofilesincomments true /embedjoboptions true /dscreportinglevel 0 /emitdscwarnings false /endpage -1 /imagememory 1048576 /lockdistillerparams false /maxsubsetpct 100 /optimize true /opm 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can be opened with acrobat and adobe reader 5.0 and later.) >> /namespace [ (adobe) (common) (1.0) ] /othernamespaces [ << /asreaderspreads false /cropimagestoframes true /errorcontrol /warnandcontinue /flattenerignorespreadoverrides false /includeguidesgrids false /includenonprinting false /includeslug false /namespace [ (adobe) (indesign) (4.0) ] /omitplacedbitmaps false /omitplacedeps false /omitplacedpdf false /simulateoverprint /legacy >> << /addbleedmarks false /addcolorbars false /addcropmarks false /addpageinfo false /addregmarks false /convertcolors /converttocmyk /destinationprofilename () /destinationprofileselector /documentcmyk /downsample16bitimages true /flattenerpreset << /presetselector /mediumresolution >> /formelements false /generatestructure false /includebookmarks false /includehyperlinks false /includeinteractive false /includelayers false /includeprofiles false /multimediahandling /useobjectsettings /namespace [ (adobe) (creativesuite) (2.0) ] /pdfxoutputintentprofileselector /documentcmyk /preserveediting true /untaggedcmykhandling /leaveuntagged /untaggedrgbhandling /usedocumentprofile /usedocumentbleed false >> ] >> setdistillerparams << /hwresolution [2400 2400] /pagesize [612.000 792.000] >> setpagedevice microsoft word numero_50_art_26_2574 v. iasnii et alii, frattura ed integrità strutturale, 50 (2019) 310-318; doi: 10.3221/igf-esis.50.26 310 the effect of temperature on low-cycle fatigue of shape memory alloy v. iasnii, p. yasniy, d. baran faculty of engineering of machines, structures and technologies, ternopil ivan puluj national technical university, ternopil, ukraine v_iasnii@tntu.edu.ua, https://orcid.org/0000-0002-5768-5288 petroyasniy@gmail.com, https://orcid.org/0000-0002-1928-7035 jaturonkabat@gmail.com, https://orcid.org/0000-0002-2067-8164 a. rudawska faculty of mechanical engineering, lublin university of technology, lublin, poland a.rudawska@pollub.pl, https://orcid.org/0000-0003-3592-8047 abstract. the influence of temperature on the fatigue properties of pseudoelastic niti under low-cycle fatigue are investigated. tests were performed under the uniaxial tensile deformation (pull-pull) at 0°с and 20°с which is above the austenite finish temperature. experimental results indicate that the fatigue life of niti alloy increases with the decrease of test temperature from 20°с to 0°с in the case of presenting the results depending on the strain range and dissipated energy. regardless the test temperature, with the increase of number of cycles to failure, the stress and strain ranges, as well as the dissipation energy decrease, and the total dissipation energy and odqvist’s parameter increase. the slope of the fatigue curves of niti alloy is greater at the temperature of 0°с in comparison with the 20°с in the case of employing the stress range, strain range, odqvist’s parameter, and total dissipation energy as the failure criteria, and is less while employing the dissipation energy as the failure criterion. keywords. pseudoelsticity; niti alloy; low-cycle fatigue; odqvist’s parameter; dissipated energy. citation: iasnii, v., yasniy, p., baran, d., rudawska, a., the effect of temperature on low-cycle fatigue of shape memory alloy, frattura ed integrità strutturale, 50 (2019) 310-318. received: 26.07.2019 accepted: 19.08.2019 published: 01.10.2019 copyright: © 2019 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. introduction nlike traditional structural materials, shape memory alloys (sma) are characterized not only by mechanical and operational properties but also by functional ones. the functional properties of sma include shape memory effect and the pseudoelasticity. typical stress-strain curve of pseudoelastic smas above the austenite finish temperature shows a large hysteresis loop during loading and unloading. the hysteretic behaviour results in a high dissipation energy and stored strain energy which ensure high performance of sma as a material for damping and storing the energy. u http://www.gruppofrattura.it/va/50/2574.mp4 v. iasnii et alii, frattura ed integrità strutturale, 50 (2019) 310-318; doi: 10.3221/igf-esis.50.26 311 the application of smas depends on the phase transformation temperatures, mechanical and functional properties, type of loading (static, cyclic and thermo-mechanical). sma are increasingly used in machine parts, implants [1, 2]. due to the high ability to energy dissipation, sma are used in damping devices for civil engineering [3–6] or other structural elements [7, 8]. as they are subjected to intense cyclic loading during operation, it is important to ensure their reliability and lifetime under low-cycle fatigue [9]. defects, such as internal subsurface voids, surface scratches which lead to crack initiation, play significant role under lowcycle fatigue [10]. also, fatigue microcracks can initiate at the martensite–martensite or austenite–martensite interfaces [11]. the martensite– martensite or austenite–martensite interface motion causes the formation of defects in the grain, these defects becoming potential crack initiation areas. cracks can initiate at the grain boundaries [12]. the cyclical loading affects not only the ability of the material to resist structural fatigue, but also the functional properties. therefore, it is necessary to know how their functional and structural properties change in order to design reliably the devices and structural elements made of pseudoelastic sma which operate under fatigue loading. it is also important to take into account the balance between structural and functional fatigue. under a cyclic loading the residual strain [13] increases and the dissipation energy reduces, thus worsening the efficiency of the damping devices [14]. residual martensite plates increase with the number of cycles and are considered to be one of the causes of the formation of a residual strain during cyclic loading [15]. lifetime of sma can be predicted by stress[16, 10], strain[17-19] and energy based criteria [10] of fatigue failure. an overview of the structural fatigue of sma under mechanical and thermomechanical loading is presented, for instance in the paper [20]. for low cycle fatigue the strain amplitude and the number of cycles to failure could be represented by the empirical dependence fn    (1) where  and β represent εa in nf =1 and the slope of the logδε lognf curve, respectively. for niti wire of 0.5 mm in diameter under rotating-bending fatigue test the relationship between  and t is expressed by the following equation [21]: ( )10 sa t ms    (2) where t is test temperature; ms – martensite start temperature. based on the experimental results, the coefficients are determined as β = 0.28, αs= 0.248, a = 0.0032 k-1 [21]. for niti tube with outer diameter of 0.9 mm and inner 0.7 mm under rotating-bending fatigue test the dependence of α on t is expressed by the following equation [21]: 0 0( ) n m t t     (3) based on the experimental results, the coefficients are determined as β = 0.25, m = 0.065 kn, n = 0.4, t0 = 297 k, α0 = 0.057. a quasi-linear dependence of logδwdis on lognf for several values of the mean stress. it is, hence, interesting to approximate experimental results using the following curve [22]: 1 1dis fw n   (4) where δwdis – is dissipation energy per cycle; α and β are material parameters. numerical results are in good agreement with experimental data for α = 11 and β = −0.377. a damage based fatigue failure model by dividing the total damage sources into three parts, i.e., microcrack initiation, microcrack propagation and martensite transformation induced damage was proposed by song [23]. the damage variable as the ratio of the accumulated dissipation energy after a prescribed number of cycles to that obtained at the failure life was defined v. iasnii et alii, frattura ed integrità strutturale, 50 (2019) 310-318; doi: 10.3221/igf-esis.50.26 312 1 1 / f n n i ii i d w w      (5) where wi is the dissipation energy at i-th loading cycle. so it is important to study the influence of temperature, above the austenite finish temperature, on structural fatigue of pseudoelastic niti alloy. experimental setup and material he influence of temperature (at 0°c and 20°c) on structural fatigue was studied on pseudoelastic ni55.8ti44.2 alloy. characteristics of thermal transitions during sma phase transformations were investigated using differential scanning calorimetry (dsc) by dsc q1000 tai [24]. austenite finish temperature is af = – 38.7°с. material has the following mechanical properties at 0°с and 20°с: yield strength, 0.2 = 447 mpa and 523 mpa, ultimate tensile strength, uts = 869 mpa and 780 mpa [24, 25]. the chemical composition of the alloy according to the delivered certificate is as follows: 55.78% ni;0.005% co; 0.005% cu; 0.005% cr; 0.012% fe; 0.005% nb; 0.032% c; 0.001% h; 0.04% o; 0.001% n and 44.12% тi. cylindrical specimens with a diameter of 4 mm and gage length of 12.5 mm, machined from rod 8 mm in diameter, were tested under uniaxial cyclic loading at temperature 0°с and 20°с at stress ratio r = min/max = 0 (here min and max are the minimum and maximum stresses) on the servo-hydraulic machine stm-10 [26] with automated control and data acquisition system under sinusoidal load with a frequency of 0.5 hz. fatigue tests were carried out under displacement–controlled mode at 0°с. in this case, the maximum stress, except for the first twenty loading cycles, remains constant [24]. therefore, it can be assumed that the stress range was constant during the testing (the stress range was changed less than 3%). fatigue tests were carried out under stress–controlled mode at 20°с. longitudinal strain was measured by bi-06-308 extensometer produced by bangalore integrated system solutions (biss), maximum error did not exceed 0.1%. the crosshead displacement was determined by inductive bi-02-313 sensor with an error not more than 0.1%. the tests at 0°с were carried out in the chamber filled with ice and ice water. this provided the constant temperature of 0°c measured by chromel–alumel thermocouple mounted on the sample with an error not more than 0.5°c. a literature review [24] shows that water have not significant influence on fatigue behaviour of niti alloys [21, 27–29]. results and discussion he dependences of the stress range δσ on the number of cycles to failure nf for niti alloy in ice water at 0°с and at 20°с in the air are shown in fig. 1. stress range was determined at the number of half-cycles to failure. experimental data under low-cycle fatigue presented on fig. 1, are plotted according to the failure criterion of the specimen, and could be well-enough described by power function fn      (6) the parameters  and  in eqn. (6), that were determined by fitting of experimental data (fig. 1), are given in tab. 1. the increase of testing temperature from 0 to 20°с increases the fatigue lifetime under low-cycle fatigue at nf > 1000 cycles and decreases the angle of relationship between lgδσ and lgnf. a similar effect of testing temperature (323k, 333k) on the fatigue lifetime was found for ti 50.7at%ni alloy [30]. fig. 2 shows experimental fatigue curves in coordinates strain range versus number of cycles to failure of the specimen. the strain range values were determined at the number of half-cycles to failure, in the same way as stress range. the experimental data were fitted by means of eqn. (1) with the determined parameters, which are given in tab. 1. the linear behavior of the dependence of the strain amplitude on the number of cycles to failure under low-cycle fatigue at different ratios between the test temperature and the austenite finish temperature, is confirmed by the results obtained by the authors [31–33]. in contrast to the data presented in fig. 1, using strain range as a criterion of fatigue failure, fatigue lifetime of pseudoelastic ni55.8ti44.2 alloy at 20°с is significantly lower than at 0°с. moreover, the slope angle of both curves in logarithmic scales is t t v. iasnii et alii, frattura ed integrità strutturale, 50 (2019) 310-318; doi: 10.3221/igf-esis.50.26 313 approximately the same (parameter β in tab. 1). such effect of temperature on low-cycle fatigue lifetime are similar for niti wire of 0.5 mm in diameter and niti tube with outer diameter of 0.9 mm and inner 0.7 mm under rotating-bending fatigue test at temperatures 20°c 80°c [21]. fatigue lifetime increase with the decrease in temperature from 383 k to 293 k for 3 kinds of ti–ni base shape memory alloy wires with the compositions of ti– 50.0 at%ni, ti–50.5 at%ni and 50.85 at%ni, respectively under rotary bending fatigue tests [19]. this was observed for wires with diameter of 1.0 mm. figure 1: dependence of the stress range on the number of loading cycles in ice water at 0°с and at 20°с in the air. the fatigue life was estimated using the odqvist’s parameter, which characterizes the accumulated plastic strain p, and under uniaxial cyclic loading is determined by formula [34] 2 pn   (7) where n is the numbers of loading cycles. t, °с   r2   r2 a b r2 eq. (1) eq. (6) eq. (9) 0 8.754 ±1.339 0.14 ±0.026 0.868 943.7 ±53.84 0.0814 ±0.00898 0.933 2.472 0.0581 0.941 20 5.379 ±1.634 0.198 ±0.05 0.944 788.6 ±10.56 0.0396 ±0.00195 0.997 3.018 0.0205 0.999 table 1: equations parameters for ni55.8ti44.2 alloy replacing n in eqn. (7) on nf and taking into account that for the sma the plastic strain range can be replaced by the expansion of the elastic deformation δε, the formula (7) can be rewritten as follows: 2n   (8) in the eqn. (8), the strain range  was determined in the same way (at n=0.5 nf) as in the previous cases. according to the fig. 3, the odqvist's parameter increases linearly proportional to the number of loading cycles before the failure of the specimen and is well described by the dependence f fa b n    (9) v. iasnii et alii, frattura ed integrità strutturale, 50 (2019) 310-318; doi: 10.3221/igf-esis.50.26 314 the constant values (tab. 1) of the eqn. (9) were determined by the approximation of the experimental data using the least squares method. analysis of the experimental dependencies in fig. 3 shows that odqvist's parameter χf, before failure of material, increase with the decrease in temperature from 20 to 0°c. moreover, the odqvist's parameter at both temperatures 0°c and 20°c significantly increase with the increase in loading cycles. it implies from the analysis of experimental dependencies, presented on fig. 3, that the value of odqvist's parameter before the fatigue failure of material χf is increasing with the decrease of temperature from 20°с to 0°c. also, with the increase of number of loading cycles the ratio of odqvist's parameter at 0°с and 20 °с increases significantly. figure 2: dependence of the strain range on the number of loading cycles in ice water at 0°с and at 20°с in the air. figure 3: dependence of the odqvist’s parameter on the number of loading cycles in ice water at 0°с and at 20°с in the air. with the increasing of cycles to failure the dissipated energy per cycle decreases (fig. 4). experimental data in this case are well described by the logarithmic dependence w dis f ww n      (10) v. iasnii et alii, frattura ed integrità strutturale, 50 (2019) 310-318; doi: 10.3221/igf-esis.50.26 315 figure 4: dependence of the dissipated energy on the number of loading cycles in ice water at 0°с and at 20°с in the air. the constant values w and w of the eqn. (10) were determined by the approximation of the experimental data using the least squares method are presented in tab. 2. t, °с w w r2 aw bw r2 eq. (10) eq. (13) 0 9.974 ±1.604 0.3537 ±0.0351 0.950 142.6 0.663 0.709 20 2.478 ±1.253 0.3148 ±0.092 0.949 148.4 0.0925 0.924 table 2: equations parameters for ni55.8ti44.2 alloy. in the eqn. (10), the energy of dissipation was determined in the same way as in the previous cases at the number of halfcycles to failure. the fatigue life of the niti alloy increases with the decrease in test temperature when using the strain range (fig. 2), as well as dissipated energy (fig.4). the influence of testing temperature on accumulated dissipation energy before failure was analysed. the accumulated dissipation energy was determined by formula 1 , fn dis i i w w    (11) where wi is the dissipated energy for i-th loading cycle. as the first approximation, the change in the area of hysteresis loop during first cycles could be neglected. in this case, the formula (11) can be rewritten as follows: ,dis fdis nw w   (12) where wdis is the dissipated energy at mean lifetime nf. as in the case with odqvist's parameter, the experimental values of total dissipated energy could be described by a linearly proportional dependence on cycles to failure v. iasnii et alii, frattura ed integrità strutturale, 50 (2019) 310-318; doi: 10.3221/igf-esis.50.26 316 dis w w fw a b n   (13) the parameters (tab. 2) of the eqn. (13) were determined by the approximation of the experimental data using the least squares method. therefore (fig. 5), the total dissipation energy is not constant, but increases with the increasing number of loading cycles to specimen failure. figure 5: dependence of the total dissipation energy on the number of loading cycles in ice water at 0°с and at 20°с in the air. the fatigue life of niti alloy increases with the decrease in test temperature when using the strain range (fig. 2), as well as dissipated energy (fig. 4). conclusions 1. low-cycle fatigue of pseudoelastic ni55.8ti44.2 shape memory alloy was studied under the uniaxial tensile deformation at temperature of 0°с and 20°с, which is above the austenite finish temperature (af = – 38.7°с). fatigue tests were carried out on cylindrical specimens under displacement–controlled mode at 0°с and under stress–controlled mode at 20°с. the fatigue life was described by stress, strain and energy failure criteria. 2. the fatigue life of niti alloy increases with the decrease of test temperature from 20°с to 0°с in the case of presenting the results depending on the strain range and dissipated energy. nevertheless, in the case of employing the stress range, the odqvist’s parameter or the total dissipation energy, and the lifetime of niti alloy under the low temperature in the medium of distilled ice water is less comparing with the room temperature. 3. regardless the test temperature, with the increase of number of cycles to failure, the stress and strain ranges, as well as the dissipation energy decrease, and the total dissipation energy and odqvist’s parameter increase. 4. therefore, as in the case of traditional structural elements, the total dissipation energy of the low-cycle fatigue is not constant and increases proportionally to the increase of cycles number to failure. it is obvious, that if the energy of fatigue failure is constant, then the dissipation energy is wasted not only for the formation of fatigue damage, but also on the heating of specimen, as well as on the forward and reverse phase transformations during the cyclic loading. 5. the slope of the fatigue lifetime curves of niti alloy to the ox axis is greater at the temperature of 0°с in comparison with the 20°с in the case of employing the stress range, strain range, odqvist’s parameter and total dissipation energy as the failure criteria, and is less while employing the dissipation energy as the failure criterion. v. iasnii et alii, frattura ed integrità strutturale, 50 (2019) 310-318; doi: 10.3221/igf-esis.50.26 317 references [1] auricchio, f., boatti, e., conti, m. (2015). sma biomedical applications, shape mem. alloy eng., pp. 307–331. doi: 10.1016/b978-0-08-099920-3.00011-5. [2] morgan, n.b. (2004). medical shape memory alloy applications the market and its products, mater. sci. eng. a, 378(12 spec. iss.), pp. 16–23. doi: 10.1016/j.msea.2003.10.326. [3] ozbulut, o.e., hurlebaus, s., desroches, r. (2011). seismic response control using shape memory alloys: a review, j. intell. mater. syst. struct., 22(14), pp. 1531–1549. doi: 10.1177/1045389x11411220. [4] yasniy, p., kolisnyk, m., kononchuk, o., iasnii, v. (2017). calculation of constructive parameters of sma damper, sci. j. tntu, 88(4), pp. 7–15. [5] torra, v., auguet, c., carreras, g., dieng, l., lovey, f.c., terriault, p. (2012). the sma: an effective damper in civil engineering that smoothes oscillations, mater. sci. forum, 706–709(july 2015), pp. 2020–2025. doi: 10.4028/www.scientific.net/msf.706-709.2020. [6] isalgue, a., lovey, f.c., terriault, p., martorell., torra, f.r.m., torra, v. (2006). sma for dampers in civil engineering, mater. trans., 47(3), pp. 682–690. doi: 10.2320/matertrans.47.682. [7] menna, c., auricchio, f., asprone, d. (2015). applications of shape memory alloys in structural engineering, shape memory alloy engineering, elsevier. [8] mohd jani, j., leary, m., subic, a., gibson, m.a. (2014). a review of shape memory alloy research, applications and opportunities, mater. des., 56, pp. 1078–1113. doi: 10.1016/j.matdes.2013.11.084. [9] eggeler, g., hornbogen, e., yawny, a., heckmann, a., wagner, m. (2004). structural and functional fatigue of niti shape memory alloys, mater. sci. eng. a, 378(1-2 spec. iss.), pp. 24–33. doi: 10.1016/j.msea.2003.10.327. [10] predki, w., klönne, m., knopik, a. (2006). cyclic torsional loading of pseudoelastic niti shape memory alloys: damping and fatigue failure, mater. sci. eng. a, 417(1–2), pp. 182–189. doi: 10.1016/j.msea.2005.10.037. [11] miyazaki, s., imai, t., igo, y., otsuka, k. (1986). effect of cyclic deformation on the pseudoelasticity characteristics of ti-ni alloys, metall. trans. a, 17(1), pp. 1115–1120. doi: 10.1007/bf02644447. [12] gloanec, a.l., cerracchio, p., reynier, b., van herpen, a., riberty, p. (2010). fatigue crack initiation and propagation of a tini shape memory alloy, scr. mater., 62(10), pp. 786–789. doi: 10.1016/j.scriptamat.2010.02.001. [13] kan, q., yu, c., kang, g., li, j., yan, w. (2016). experimental observations on rate-dependent cyclic deformation of super-elastic niti shape memory alloy, mech. mater., 97, pp. 48–58. doi: 10.1016/j.mechmat.2016.02.011. [14] pan, q., cho, c. (2008). damping property of shape memory alloys, metal, pp. 1–5. [15] miyazaki, s., mizukoshi, k., ueki, t., sakuma, t., liu, y. (1999). fatigue life of ti–50 at.% ni and ti–40ni–10cu (at.%) shape memory alloy wires, mater. sci. eng. a, 273–275, pp. 658–663. doi: 10.1016/s0921-5093(99)00344-5. [16] scirè mammano, g., dragoni, e. (2012). functional fatigue of niti shape memory wires for a range of end loadings and constraints, frat. ed integrita strutt., 23, pp. 25–33. doi: 10.3221/igf-esis.23.03. [17] matsui, r., makino, y., tobushi, h., furuichi, y., yoshida, f. (2006). influence of strain ratio on bending fatigue life and fatigue crack growth in tini shape-memory alloy thin wires, mater. trans., 47(3), pp. 759–765. doi: 10.4028/www.scientific.net/kem.340-341.1193. [18] casciati, f., casciati, s., faravelli, l. (2007). fatigue characterization of a cu-based shape memory alloy, proc. est. acad. sci. – phys. math., 56(2), pp. 207–217. [19] kim, y. (2002). fatigue properties of the ti-ni base shape memory alloy wire, mater. trans., 43(7), pp. 1703–1706, doi: 10.2320/matertrans.43.1703. [20] kang, g., song, d. (2015). review on structural fatigue of niti shape memory alloys: pure mechanical and thermomechanical ones, theor. appl. mech. lett., 5(6), pp. 245–254. doi: 10.1016/j.taml.2015.11.004. [21] matsui, r., tobushi, h., furuichi, y., horikawa, h. (2004). tensile deformation and rotating-bending fatigue properties of a highelastic thin wire, a superelastic thin wire, and a superelastic thin tube of niti alloys, j. eng. mater. technol., 126(4), pp. 384–391. doi: 10.1115/1.1789952. [22] moumni, z., zaki, w., maitournam, h. (2009). cyclic behavior and energy approach to the fatigue of shape memory alloys, j. mech. mater. struct., 4(2), pp. 395–411. doi: 10.2140/jomms.2009.4.395. [23] song, d., kang, g., kan, q., yu, c., zhang, c. (2015). damage-based life prediction model for uniaxial low-cycle stress fatigue of super-elastic niti shape memory alloy microtubes, smart mater. struct., 24(8), pp. 085007. doi: 10.1088/0964-1726/24/8/085007. [24] iasnii, v., yasniy, p., lapusta, y., shnitsar, t. (2018). experimental study of pseudoelastic niti alloy under cyclic loading, sci. j. tntu, 92(4), pp. 7–12. v. iasnii et alii, frattura ed integrità strutturale, 50 (2019) 310-318; doi: 10.3221/igf-esis.50.26 318 [25] iasnii, v., junga, r. (2018). phase transformations and mechanical properties of the nitinol alloy with shape memory, mater. sci., 54(3), pp. 406–411. [26] yasniy, p. v., hlado, v.b., hutsaylyuk, v.b., vuherer, t. (2005). microcrack initiation and growth in heat-resistant 15kh2mfa steel under cyclic deformation, fatigue fract. eng. mater. struct., 28(4), pp. 391–397. doi: 10.1111/j.1460-2695.2005.00870.x. [27] tobushi, h., nakahara, t., shimeno, y., al., e. (2000). low cycle fatigue of tini shape memory alloy and formulation of fatigue life, j. eng. mater. technol. asme, 122(2), pp. 186–191. doi: 10.1115/1.482785. [28] cheung, g.s., shen, y., darvell, b.w. (2007). effect of environment on low-cycle fatigue of a nickel-titanium instrument, j endod, 33, pp. 1433–1437. [29] shen, y., qian, w., abtin, h., gao, y., haapasalo, m. (2012). effect of environment on fatigue failure of controlled memory wire nickel-titanium rotary instruments., j. endod., 38(3), pp. 376–380. doi: 10.1016/j.joen.2011.12.002. [30] van humbeeck, j. (1999). non-medical applications of shape memory alloys, mater. sci. eng. a, 273–275, pp. 134– 148. doi: 10.1016/s0921-5093(99)00293-2. [31] melton, k.., mercier, o. (1979). fatigue of niti thermoelastic martensites, acta metall., 27(1), pp. 137–144. doi: 10.1016/0001-6160(79)90065-8. [32] robertson, s.w., pelton, a.r., ritchie, r.o. (2012). mechanical fatigue and fracture of nitinol, int. mater. rev., 57(1), pp. 1–37. doi: 10.1179/1743280411y.0000000009. [33] melton, k.n., mercier, o. (1979). the effect of the martensitic phase transformation on the low cycle fatigue behaviour of polycrystalline ni-ti and cu-zn-al alloys, mater. sci. eng., 40(1), pp. 81–87. doi: 10.1016/0025-5416(79)90010-7. [34] yasnii, p.v., glad’o, v.b., gutsailyuk, v.b. (2003). the influence of elastoplastic deformation on the dislocation structure of 15kh2mfa steel, strength mater., 35(6), pp. 562–567. doi: 10.1023/b:stom.0000013606.21409.af. << /ascii85encodepages false /allowtransparency false /autopositionepsfiles true /autorotatepages /none /binding /left /calgrayprofile (dot gain 20%) /calrgbprofile (srgb iec61966-2.1) /calcmykprofile (u.s. web coated \050swop\051 v2) /srgbprofile (srgb iec61966-2.1) /cannotembedfontpolicy /error /compatibilitylevel 1.4 /compressobjects /tags /compresspages true /convertimagestoindexed true /passthroughjpegimages true /createjobticket false /defaultrenderingintent /default /detectblends true /detectcurves 0.0000 /colorconversionstrategy /cmyk /dothumbnails false /embedallfonts true /embedopentype false /parseiccprofilesincomments true /embedjoboptions true /dscreportinglevel 0 /emitdscwarnings false /endpage -1 /imagememory 1048576 /lockdistillerparams false /maxsubsetpct 100 /optimize true /opm 1 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/hrv (za stvaranje adobe pdf dokumenata najpogodnijih za visokokvalitetni ispis prije tiskanja koristite ove postavke. stvoreni pdf dokumenti mogu se otvoriti acrobat i adobe reader 5.0 i kasnijim verzijama.) /hun 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can be opened with acrobat and adobe reader 5.0 and later.) >> /namespace [ (adobe) (common) (1.0) ] /othernamespaces [ << /asreaderspreads false /cropimagestoframes true /errorcontrol /warnandcontinue /flattenerignorespreadoverrides false /includeguidesgrids false /includenonprinting false /includeslug false /namespace [ (adobe) (indesign) (4.0) ] /omitplacedbitmaps false /omitplacedeps false /omitplacedpdf false /simulateoverprint /legacy >> << /addbleedmarks false /addcolorbars false /addcropmarks false /addpageinfo false /addregmarks false /convertcolors /converttocmyk /destinationprofilename () /destinationprofileselector /documentcmyk /downsample16bitimages true /flattenerpreset << /presetselector /mediumresolution >> /formelements false /generatestructure false /includebookmarks false /includehyperlinks false /includeinteractive false /includelayers false /includeprofiles false /multimediahandling /useobjectsettings /namespace [ (adobe) (creativesuite) (2.0) ] /pdfxoutputintentprofileselector /documentcmyk /preserveediting true /untaggedcmykhandling /leaveuntagged /untaggedrgbhandling /usedocumentprofile /usedocumentbleed false >> ] >> setdistillerparams << /hwresolution [2400 2400] /pagesize [612.000 792.000] >> setpagedevice microsoft word 2268 j. christopher et alii, frattura ed integrità strutturale, 48 (2019) 554-562; doi: 10.3221/igf-esis.48.53 554 focused on “showcasing structural integrity research in india” comparative evaluation of two physically based models for the description of stress-relaxation behaviour of 9% chromium containing steel j. christopher*, c. praveen, b.k. choudhary materials development and technology division, hbni, indira gandhi centre for atomic research, kalpakkam, tamil nadu, 603102, india, e-mail: jchris@igcar.gov.in abstract. an attempt has been made to evaluate the applicability of two constitutive models related to the dislocation-obstacle interactions for the description of stress-relaxation behaviour of e911 tempered martensitic steel. the first one is feltham model (model-i) and the second model proposed by christopher and choudhary (model-ii) is based on the sine hyperbolic kinetic rate formulation coupled with the evolution of internal stress. the physical constants associated with these models have been determined by the minimization of errors between experimental and predicted relaxation stress vs. hold time data for two different strain hold levels of 1.3 and 2.5% at 873 k for e911 steel. model-ii provides better prediction of stress-relaxation behaviour of the steel as compared to model-i. in addition to prediction of relaxation stress vs. hold time data, model-ii describes the evolution of internal stress, inter-barrier spacing and activation volume with the hold time. the predicted increase in inter-barrier spacing and activation volume with hold time indicated that substructural coarsening remains dominant in e911 steel under stress-relaxation conditions. keywords. feltham model; sine hyperbolic kinetic rate; e911 steel; stressrelaxation behaviour citation: christopher, j., praveen, c., choudhary, b.k, comparative evaluation of two physically based models for the description of stress-relaxation behaviour of 9% chromium containing steel, frattura ed integrità strutturale, 48 (2019) 554-562. received: 22.11.2018 accepted: 28.02.2019 published: 01.04.2019 copyright: © 2019 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. introduction % chromium tempered martensitic steels are favoured structural materials for high temperature heat exchanger applications in power generating industries. among 9% cr steels, e911 steel offers good combination of high creep strength and ductility, and microstructural stability over long exposures at elevated temperatures [1]. understanding and modelling of inelastic deformation behavior of structural materials at elevated temperatures attract continued scientific and technological interest in view of improving the appropriate conditions for material processing and for reliable prediction of the performance of the components during service. stress-relaxation testing is one of the potential techniques for understanding the high temperature inelastic deformation behaviour of materials [2]. during stressrelaxation testing, the externally imposed constraint i.e. total applied strain (t), is kept constant. since the total strain rate is related to the sum of elastic (e) and inelastic (in) strain components, the total applied strain rate is equal to zero and it is represented as 9 http://www.gruppofrattura.it/va/48/2268.mp4 j. christopher et alii, frattura ed integrità strutturale, 48 (2019) 554-562; doi: 10.3221/igf-esis.48.53 555 0t e in       (1) further, the elastic strain rate ( e ) given in eqn. (1) is written as r e c      (2) the interrelationship between stress-relaxation rate and inelastic strain rate can be obtained from eqn. (1) and eqn. (2) as r in e c         (3) eqn. (3) indicates that the decrease in elastic strain is exactly balanced by an increase in inelastic strain during relaxation. this leads to the decrease in stress values with hold time. eqn. (3) represents a generalised relationship for the description of stress-relaxation behaviour for any materials. in common, developed models for stress-relaxation mainly focus on the interrelationship between inelastic strain rate and relaxation stress. the inelastic strain rate given in eqn. (3) captures only the creep strain developed during stress relaxation. time independent part of inelastic strain (i.e. plastic strain) has been assumed to be insignificant in the present investigation. between the existing models [3], the model proposed by feltham [4] is widely used to describe the stress-relaxation behaviour of different metals and alloys [4-7]. in this study, in addition to the feltham model, the relationship recently proposed by christopher and choudhary [8] based on the sine hyperbolic kinetic rate formulation coupled with the evolution of internal stress has been employed to describe the stress-relaxation behaviour of materials. the physical constants associated with these models have been determined by the minimization of errors between experimental and predicted relaxation stress vs. hold time data for two different strain hold levels of 1.3 and 2.5% at 873 k for e911 steel. among these two models, the appropriate relationship applicable for the e911 steel has also been identified in this study. modelling framework feltham relationship for stress-relaxation behaviour (model-i) ased on kinetic theory of dislocation-local obstacle interaction, feltham [4] proposed the inelastic strain rate relationship to describe the stress-relaxation behaviour and it is given as    0 exp r i in m q v kt                   (4) where 0 is the characteristic strain rate that includes a frequency factor, the area swept out by an activated dislocation and the burgers vector (b) and r  i is equal to the effective stress (e). according to feltham [4], the parameters such as characteristic strain rate ( 0 ), mobile dislocation density (m) and activation volume (v) are unaltered during deformation under stress-relaxation and the internal stress i is assumed as a constant. eqn. (4) is substituted in eqn. (3) and integration of eqn. (3) with appropriate boundary conditions is represented as    0 0 0 exp r r t r i r m q v d c dt kt                     (5) where r0 is the relaxation stress at t = 0. eqn. (5) yields 0 0 ln 1r r kt t v t            (6) b j. christopher et alii, frattura ed integrità strutturale, 48 (2019) 554-562; doi: 10.3221/igf-esis.48.53 556 where   00 0 1 exp r im q vc v t kt kt                with t0 is treated as a constant. eqn. (6) is employed for the description of relaxation behaviour of different materials. in common, the simplified form of eqn. (6) is represented as  0 ln 1r r s t     (7) where s and  are constants and s = kt/v;  =1/t0. sine hyperbolic rate model for stress-relaxation behaviour (model-ii) n addition to feltham model (model-i) [4], recently developed constitutive model for the description of stressrelaxation behavior of p91 steel has also been used to examine the stress-relaxation behaviour of the steel [8]. the model is based on the incorporation of stress dependent activation volume and average dislocation segment length into the kinetic rate theories [8,9]. the final relationship defining the inelastic strain rate in terms of internal stress (i) is represented by           1/32 2 3 2 1/32 exp sinh m d r i i r i r i in i r i b v q b rt mktm                                    (8) the rate equation for the evolution of internal stress with time is derived based on the power law relationship proposed by argon and takeuchi [10] and it is given as m r i i r r r r h m m                       (9) the coupled differential equations i.e. eqn.(3), eqn. (8) and (9) have been used to describe the stress-relaxation beahviour of the materials. there are three unknown constants such as initial relaxation stress (r0), initial internal stress (i0) and power law exponent (m) related to internal stress. the power law coefficient (h) given in eqn. 9 can be obtained as 0 0 i m r h    . experimenal data he relaxation stress vs. hold time data obtained for e911 steel in normalised and tempered condition has been used in the present investigation. the chemical composition (wt. %) of e911 ferritic-martensitic steel was as follow as: fe-0.105c-9.16cr-1.01mo-1.0w-0.07ni-0.20si-0.35mn-0.23v-0.068nb-0.007p-0.003s-0.072n. normalizing treatment involved austenitizing at 1323 k for 30 min followed by air cooling and tempering treatment was performed by soaking at 1023 k for 1 h followed by air cooling. tem microstructure of e911 steel shows the tempered martensitic lath structure accompanied with dense dislocations as depicted in fig. 1. cylindrical specimens of 32.5 mm gauge length and 6.4 mm gauge diameter were machined from the normalised and tempered specimen blanks. test specimen dimensions are shown in fig. 2. stress-relaxation tests were carried out in air environment (i.e. ambient condition without controlled atmosphere and possibility of air ingress into the furnace environment) at 873 k in a servohydraulic universal testing system equipped with three-zone-resistance heating furnace and proportional-integral-derivative temperature controller. three-zone-resistance heating furnace provides much larger uniform temperature zone than the specimen dimension. calibrated thermocouples were used in conjunction with the appropriate temperature indicating devices and the test temperature was controlled well within ± 2 k. tests were performed by employing nominal loading strain rate of 1  104 s–1 to the desired total applied strain levels of 1.3 and 2.5%. after 24 hours of hold duration, the i t j. christopher et alii, frattura ed integrità strutturale, 48 (2019) 554-562; doi: 10.3221/igf-esis.48.53 557 unloading was performed at the same strain rate of 110–4 s–1. the diagram for loading pattern is shown in fig. 3a. loadelongation data were recorded using data acquisition system for all the tests. from the load-displacement data, the stress vs. strain data was obtained. as an example, fig. 3b shows the stress vs. strain diagram for e911 steel at 873 k for 1.3% strain hold. using the stress vs. strain and strain vs. time data, the stress-relaxation data was acquired by judiciously selecting small time intervals in terms of relaxation stress (r) vs. hold time (t). in fig. 3b, permanent set defines the strain present in the material when it is unloaded to zero stress. figure 1: microstructure of e911 steel in normalised and tempered condition. figure 2: specimen geometry used for stress relaxation tests. figure 3: a) loading waveform for stress relaxation tests and b) stress-strain curve for strain hold of 1.3% at 873 k. j. christopher et alii, frattura ed integrità strutturale, 48 (2019) 554-562; doi: 10.3221/igf-esis.48.53 558 methodology for parametric optimization he physical constants associated with these models have been determined by the minimization of errors between experimental and predicted relaxation stress vs. hold time data for two different strain hold levels of 1.3 and 2.5% at 873 k for e911 steel. in order to obtain the unknown constants such as s and  in model-i, least-square optimisation based on levenberg–marquardt algorithm has been used. tab. 1 shows the optimised constants associated with the model-i for e911at 873 k for the strain holds of 1.3 and 2.5%. an iterative procedure has been invoked to obtain the constants associated with the model-ii. as a first step in the iteration, random initial value of parameters within the bounds has been seeded for numerical integration. the coupled differential equations (i.e. eqns. (3), (8) and (9)) defining the of relaxation stress ( r inc    ), inelastic strain and internal stress with time have been numerically integrated by the fourth-order runge-kutta method. following numerical integration, the least-square error value has been estimated and then the parameter values are adjusted using interior-point algorithm for obtaining low least-square error value [9]. the fitting procedure has been repeated for several iterations to reach the optimised parameters. the optimised constants associated with model-ii for e911at 873 k for the strain holds of 1.3 and 2.5% have been presented in tab. 2. for the numerical integration, the values of constants such as m = 3; b = 0.268 nm;  = 64420 mpa; k = 1.38  1023 j/k; d = 1  1013 s1 and r= 8.314 j mol1 k1 have been considered. the mobile dislocation density values of 1  1013 m2 have been chosen for e911 steel [9]. the activation energy value of 285 kj mol1 has been fixed for e911 steel [11]. for model-ii, the bounds for the physical constants are fixed based on the following consideration. the upper and lower limit values of ro were chosen close to the initial relaxation stress. hence, the bounds are fixed between 275 to 350 mpa. since initial internal stress (io) should be less than the initial relaxation stress, the bounds for io are fixed between 200 to 275 mpa. the value of 'm' is allowed to vary between 0 and 1 based on the literature values [10]. once the three unknown independent parameters (ro, io and m) are optimized, the dependent parameter h has been calculated using 0 0 i m r h    . parameter r0, mpa s, mpa , s1 hold strain levels 1.3 % 311.55 20.0 0.34 2.5 % 327.23 20.8 0.50 table 1: optimised parameters associated with the model-i for e911 steel. parameter r0, mpa i0, mpa m h, mpa 1.3 % 309.55 227.08 0.812 2.15 2.5 % 324.68 238.97 0.809 2.22 table 2: optimised parameters associated with the model-ii for e911 steel. results and discussion he experimental as well as predicted relaxation stress (r)-time (t) data have been shown in fig. 4 as double logarithmic plots for the strain holds of 1.3 and 2.5 % at 873 k. a marginal decrease in relaxation stress with time for the initial hold durations followed by rapid linear decrease in stress values at longer durations has been t t j. christopher et alii, frattura ed integrità strutturale, 48 (2019) 554-562; doi: 10.3221/igf-esis.48.53 559 observed in log-log plot for both the strain holds. it can be seen that the predicted relaxation stress vs. hold time data obtained using model-ii follow the experimental data more closely compared to those derived from the model-i. figure 4: variations in experimental relaxation stress (r) with hold time (t) for a) 1.3% and b) 2.5% strain holds. the predicted r vs. t data using model-i and model-ii have also been superimposed for both strain hold conditions. the variations in the deviation of stress values as r = r,exp  r,pred with time exhibit lower values for model-ii over model-i. this further suggested statistical suitability of the model-ii for describing stress-relaxation behaviour of tempered martensitic 9% cr steels (fig. 5). based on experimental observations in 9% cr steels, it has been shown that the subgrain coarsening accompanied with decrease in dislocation density remains dominant during inelastic deformation under stress-relaxation conditions at elevated temperatures [12,13]. the reported increase in lath width or subgrain size indicated the increase in inter-barrier spacing () for 9% cr steels during stress-relaxation. it is known that inter-barrier spacing () and activation volume (v) is inversely related to internal stress. therefore, the variations in internal stress as well as activation volume with the hold time are expected for 9% cr steels. from the microstructural aspects, it is evident that feltham relation [4] involving constancy in internal stress and activation volume is not applicable for describing the stress-relaxation behaviour of e911 steel. however, model-ii has been able to predict the evolution of internal stress, effective stress and relaxation stress with respect to hold time. this is shown in fig. 6 for the strain hold of 1.3% as an example. based on freidel statistics [14], the internal stress and effective stress can be used to evaluate the inter-barrier spacing and activation volume. the relationships are given as 2 i m b    (10) and   3 1/32( 2 )i e m v b              (11) where 'b' is the burgers vector. fig. 7 depicts the evolution of inter-barrier spacing and activation volume with the hold time. the observed increase in inter-barrier spacing and activation volume confirms that continual substructural coarsening of e911 steel during stress-relaxation. the comments related to the evolution of internal stress (i) and its dependence on relaxation stress (r) following eqn. (9) is noteworthy. in several metals and alloys, based on stress change experiments during steady state creep, it has been observed that the relationship between internal stress and applied stress obeys power law. the exponent values in the range 0.7-1.0 were reported for cd, mg, al-li and al-mg alloys [15-18]. the observed power law exponent m = 0.81 for e911 steel is in agreement with those values observed for different materials [15-18]. based on internal variable approach, it has also been found that the variations in i/a (where a is the applied stress) with a exhibited power law relation as i/a  a0.21 or i = 2.22 a0.79 for p9 steel during secondary creep deformation [8,9]. the equivalence between the results obtained from stress relaxation tests and monotonic creep tests is j. christopher et alii, frattura ed integrità strutturale, 48 (2019) 554-562; doi: 10.3221/igf-esis.48.53 560 reported in literature for 9% cr steels [13,19]. it was demonstrated that the stress exponent values obtained from stressrelaxation data for 9% cr steel compared favourably with monotonic creep tests and falls in dislocation creep regime [19]. since dislocation creep is the main dominating mechanism for 9% cr steels, the power law dependency between variations of internal stress and relaxation stress proposed by argon and takeuchi [10] has been implemented in the present investigation. the reported value of 0.79 for p9 steel is close to the observed exponent value of 0.81 for e911 steel (tab. 2). it indicates that the power law relation between internal stress and applied stress observed for monotonic creep can be successfully implemented for stress-relaxation studies in 9% cr steels. moreover, present investigations clearly suggested that model-ii provides better description of stress-relaxation behaviour of 9% cr steels than feltham model i.e. model-i. figure 5: deviation in predicated relaxation stress with reference to the experimental value i.e. r as a function of hold time. figure 6: variations in relaxation stress (r), internal stress (i) and effective stress (e) with hold time (t) for the strain hold 1.3% for e911 steel at 873 k. figure 7: variations in inter-barrier spacing () and activation volume (v) with hold time (t) for the strain hold 1.3% for e911 steel at 873 k. conclusions omparative evaluation of two physically based models has been performed for the description of stress-relaxation behaviour of e911 steel for the strain holds of 1.3 and 2.5 % at 873 k. as compared to model-i (feltham model), model-ii proposed by christopher and choudhary provides better prediction towards relaxation stress vs. hold c j. christopher et alii, frattura ed integrità strutturale, 48 (2019) 554-562; doi: 10.3221/igf-esis.48.53 561 time data of e911 steel. from the microstructural aspects, it is evident that feltham relation involving constancy in internal stress and activation volume is not applicable for describing the stress-relaxation behaviour of e911 steel. contrary to this, model-ii can capable to capture the evolution of internal and effective stresses, activation volume and inter-barrier spacing with time for e911 steel during deformation under stress-relaxation. the predicted increase in interbarrier spacing and activation volume with hold time confirms that continual substructural coarsening of e911 steel during stress-relaxation. references [1] di gianfrancesco, a., cipolla, l., cirilli, f., cumino, g. and caminada, s. (2005). microstructural stability and creep data assessment of tenaris grades 91 and 911, in proceedings of 1th international conference super-high strength steels, pp. 2-4. [2] manjoine, m. j. and voorhees, h. r. (1982). compilation of stress-relaxation data for engineering alloys, astm. doi: 10.1520/mnl11954d. [3] dotseneo, v.i. (1979). stress relaxation in crystals, phys. status solidi b, 93, pp. 11-43. doi: 10.1002/pssb.2220930102. [4] feltham, p. (1963). stress relaxation in magnesium at low temperatures, phys. status solidi b, 3, pp. 1340-1346. doi: 10.1002/pssb.19630030805. [5] mccarthy, p.r., robertson, d.g., orr, j. and strang, a. (2000). recent development in stress relaxation methodologies within europe, key eng. mater., 171–174, pp. 9-16. doi: 10.4028/www.scientific.net/kem.171-174.9. [6] humphries, s.r., snowden, k.u. and yeung, w. (2010). the effect of repeated loadings on the stress relaxation properties of 2.25cr-1mo steel at 550 ºc and the influence on the feltham ‘a’ and ‘b’ parameters, mater. sci. eng., a, 527, pp. 3240-3244. doi: 10.1016/j.msea.2010.02.011. [7] trojanová, z., máthis, k., lukác, p., németh, g. and chmelík, f. (2011). internal stress and thermally activated dislocation motion in an az63 magnesium alloy, mater. chem. phys., 130, pp. 1146-1150. doi: 10.1016/j.matchemphys.2011.08.045. [8] christopher, j. and choudhary, b. k. (2018). constitutive modelling of stress-relaxation behaviour of tempered martensitic p91 steel using sine hyperbolic rate law, mater. chem. phys., 205, pp. 442-451. doi: 10.1016/j.matchemphys.2017.11.053. [9] christopher, j. and choudhary, b. k. (2016). constitutive description of primary and steady-state creep deformation behaviour of tempered martensitic 9cr–1mo steel, philos. mag. a, 96(21), pp. 2256-2279. doi: 10.1080/14786435.2016.1197435. [10] argon, a.s. and takeuchi, s. (1981). internal stresses in power-law creep, acta metall., 29, pp. 1877-1884. doi: 10.1016/0001-6160(81)90113-9. [11] nakajima, t., spigarelli, s., evangelista, e., & endo, t. (2003). strain enhanced growth of precipitates during creep of t91, mater. trans., 44(9), pp. 1802-1808. doi: 10.2320/matertrans.44.1802. [12] bose, s. c., singh, k., swaminathan, j. and sarma, d. s. (2004). prediction of creep life of x10crmovnbn-91 (p91) steel through short term stress relaxation test methodology, mater. sci. technol., 20(10), pp. 1290-1296. doi: 10.1179/026708304225022304. [13] guguloth, k., swaminathan, j., roy, n. and ghosh, r. n. (2017). uniaxial creep and stress relaxation behavior of modified 9cr-1mo steel, mater. sci. eng., a, 684, pp. 683-696. doi: 10.1016/j.msea.2016.12.090. [14] friedel, j. (1964). dislocations. pergamon press, oxford. [15] northwood, d.o. and smith, i.o. (1984). steady-state creep and strain transients for stress-dip tests in polycrystalline magnesium at 300º c, phys. status solidi a, 85, pp.149-158. doi: 10.1002/pssa.2210850117. [16] northwood, d. o., moerner, l. and smith, i. o. (1985). effect of magnesium content on the stress exponent and effective stress in the steady state creep of al-mg alloys, j. mater. sci., 20(5), pp. 1683-1692. doi: 10.1007/bf00555272. [17] northwood, d.o. and smith, i.o. (1986). stress change tests during the steady .state creep of aluminum alloy 3004 at 300 º c, mater. sci. eng., 79, pp.175-182. doi: 10.1016/0025-5416(86)90402-7 [18] northwood, d.o. and smith, i.o. (1986). internal and effective stresses in the steady-state creep of polycrystalline cadmium at 0.5 tm, phys. status solidi a, 98, pp.163-169. doi: 10.1002/pssa.2210980117. j. christopher et alii, frattura ed integrità strutturale, 48 (2019) 554-562; doi: 10.3221/igf-esis.48.53 562 [19] praveen, c., christopher, j. and choudhary b. k. (2017). critical assessment of short-term stress-relaxation studies for the prediction of creep properties of p91 steel, trans. ind. inst. met., 70 (3), pp. 655-660. doi:10.1007/s12666-017-1090-1. nomenclature t e in 0 r 0 r i 0 total applied strain rate b burgers vector elastic strain rate m taylorsfactor inelastic strain rate s, and t constants involved in model-i t hold time initial relaxation stress relaxation stress initial inte           0 m i rnal stress c effective modulus of sample-machine system m power law exponent characteristic strain rate h power law co-efficient mobile dislocation density shear modulus q activation energy r gas constant internal stress       d debye frequency v activation volume k boltzmann's constant t temperature  << /ascii85encodepages false /allowtransparency false /autopositionepsfiles true /autorotatepages /none /binding /left /calgrayprofile (dot gain 20%) /calrgbprofile (srgb iec61966-2.1) /calcmykprofile (u.s. web coated 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/hrv (za stvaranje adobe pdf dokumenata najpogodnijih za visokokvalitetni ispis prije tiskanja koristite ove postavke. stvoreni pdf dokumenti mogu se otvoriti acrobat i adobe reader 5.0 i kasnijim verzijama.) /hun 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can be opened with acrobat and adobe reader 5.0 and later.) >> /namespace [ (adobe) (common) (1.0) ] /othernamespaces [ << /asreaderspreads false /cropimagestoframes true /errorcontrol /warnandcontinue /flattenerignorespreadoverrides false /includeguidesgrids false /includenonprinting false /includeslug false /namespace [ (adobe) (indesign) (4.0) ] /omitplacedbitmaps false /omitplacedeps false /omitplacedpdf false /simulateoverprint /legacy >> << /addbleedmarks false /addcolorbars false /addcropmarks false /addpageinfo false /addregmarks false /convertcolors /converttocmyk /destinationprofilename () /destinationprofileselector /documentcmyk /downsample16bitimages true /flattenerpreset << /presetselector /mediumresolution >> /formelements false /generatestructure false /includebookmarks false /includehyperlinks false /includeinteractive false /includelayers false /includeprofiles false /multimediahandling /useobjectsettings /namespace [ (adobe) (creativesuite) (2.0) ] /pdfxoutputintentprofileselector /documentcmyk /preserveediting true /untaggedcmykhandling /leaveuntagged /untaggedrgbhandling /usedocumentprofile /usedocumentbleed false >> ] >> setdistillerparams << /hwresolution [2400 2400] /pagesize [612.000 792.000] >> setpagedevice microsoft word numero_46_art_32 j. liu et alii, frattura ed integrità strutturale, 46 (2018) 352-360; doi: 10.3221/igf-esis.46.32 352 experimental study on concrete damage location by computerized tomography technology jinghong liu school of civil engineering, tianjin university, tianjin 300350, china; hebei construction group co., ltd, baoding 071051, china; college of urban and rural construction, agricultural university of hebei, baoding 071001, china liujinghongfree@sina.com (corresponding author) jian xie school of civil engineering, tianjin university, tianjin 300350, china yongjian liu hebei construction group co., ltd, baoding 071051, china panfei shi anyang architectural design & research institute, anyang 455000, china abstract. in order to solve the technical problem of damage localization in the concrete damage process, the computerized tomography (ct) scanning damage localization test was carried out under uniaxial compression. in addition to the three-dimensional meso model, the porosity variation law of concrete pore or cracks at different loading stages are obtained. a damage variable is created based on ct images. the results show that the change of porosity, pore volume and damage variable is consistent with the loading process. the rapid increase of concrete pore volume and damage variable can be the precursor of concrete damage. the whole process of the development and evolution of concrete cracks was observed and analyzed comprehensively by using the three-dimensional reconstruction images. a method for prognosist the evolution and localization of cracks in concrete by comprehensively analyze the ct reconstruction images, rapid increase of concrete pore volume and rapid growth of damage variable is presented. keywords. concrete; three-dimensional meso model; ct test, damage location. citation: liu, j., xie, j., liu, y., shi, p., experimental study on concrete damage location by computerized tomography and acoustic emission technology, frattura ed integrità strutturale, 46 (2018) 352-360 received: 03.08.2018 accepted: 12.09.2018 published: 01.10.2018 copyright: © 2018 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. http://www.gruppofrattura.it/va/46/32.mp4 j. liu et alii, frattura ed integrità strutturale, 46 (2018) 352-360; doi: 10.3221/igf-esis.46.32 353 introduction oncrete is a kind of complex multi-phase composite material, initial defects such as micro cracks and pores generate in concrete structure in the process of pouring for the reason of hydration heat release, shrink, etc. the micro cracks expand to macro-cracks under external load or environmental factors, then lead to the decline of the strength, stiffness and eventually cause stability damage to engineering. the relationship between the macro performance indexes and failure characteristic parameters has been a technical problem in various fields [1]. the current research of concrete is based on the conventional mechanics test method, that is speculate the mechanical character of structural materials through comparative analysis of test data instead of using the change of the internal meso structure directly to explain the damage evolution process under the load [2]. computerized tomography technology (ct technology) can reach dynamic nondestructive observation on the change of internal meso structure in concrete material [3-6], and ct images are visual basic information to establish the meso damage model of concrete [7, 8]. degree of damage in concrete can be judged according to the tests, and this is of great significance to evaluate the concrete performance [9, 10]. the key of the research on concrete meso damage is to identify the existence of meso damage and the expand process of the damage effectively. ct is short as computerized tomography, compared with other methods, ct test has its incomparable advantage on nondestructive detection and real time observation in concrete material under various loading condition. ct images can be obtained by scanning the sections of concrete with industrial ct scanning. both of the meso structure of concrete and its changing process can be analyzed through ct images, then the law of evolution and expansion for damage in concrete failure process is the key to the ct images analysis. therefore, ct test is an effective mean to detect the meso pore structure, crack initiation, propagation and coalescence with no damage. in view of this, quite a lot of research work, from different views with different research methods, was done by scholars at home and abroad. foreign researches started quantitative study on concrete ct detection in 1980s. morgan [11] is the first to use the medical ct to run ct scanning on concrete specimens, and concrete section images for aggregate, mortar, crack was obtained clearly. chotard [12] got pretty effect on the change of the internal structure for cement while hydrating. lawer [13] analyzed failure mode of concrete surface with digital image correlation technique, and the research conclusion could reflect the internal structural change during cracks evolution process, besides, the influence of aggregate shape, crack shape on concrete strength, toughness was discussed based on ct images after concrete cracking. wong [ 14] conducted uniaxial compression ct test to normal and high strength concrete cylinder specimens, then the evolution process of pore under different stress state was studied. meanwhile, a large number of concrete ct tests were carried out in china, and abundant research results were obtained: academician chen houqun using ct real time scanning to observe the meso failure process of concrete under the uniaxial compression, then the whole process ct images of internal meso cracks from initiation, expansion to coalescence was got, finally, quantitative analysis methods based on concrete ct images was established in the cracks area. ding [15] used medical ct machine and special loading equipment to explore morphology change characteristics of micro cracks under the condition of different loading rate by images analyses and the distribution of ct number. wu [16] described the damage property of concrete materials, and the failure process in concrete was revealed in meso view, that are initial crack stress and crack propagation process. liu [17] used ct technique to scan concrete specimens, then reconstructed the images with mimics software, finally the 3d geometric model of concrete specimens can be got. the plastic damage model of concrete 3d numerical specimens was introduced to simulate the uniaxial tension and compression loading process, then the rationality of 3d numerical model was identified. although researchers at homeland and abroad have done much research work based on ct test [18-22], it is rare to see do quantitative analysis on crack initiation and propagation mechanism of concrete by using acoustic emission and ct combined. ct scanning have obvious advantage on real-time and nondestructive detection to internal structural change process, but its disadvantage is for both of the equipment and scanning cost are much higher. the previous real-time monitoring tests are carried out ct scanning after stopping loading when the loading reaches a specific stress stage. the test results may not ideal or the cost may increase if the stresses when scanning are not properly selected. as the unique passive detection technology in nondestructive testing, acoustic emission detection technology can monitor and evaluate the whole concrete structure in real-time, acoustic emission signal can reflect the change situation of the internal structural damage accurately except for its defects that can’t be observed evolution of pore and damage in structures directly. considering their advantages in detection, tests on combination of acoustic emission and ct can be conducted. stop loading when acoustic emission signal prompts there are new cracks generated or the old cracks expanded, then explore the relationship between ct scanning images and acoustic emission by scanning concrete with ct. in this thesis, the meso structure of concrete and its changing process was analyzed with the feature of ct images, then the order of damage evolution in concrete is described by damage variable based on ct images. c j. liu et alii, frattura ed integrità strutturale, 46 (2018) 352-360; doi: 10.3221/igf-esis.46.32 354 ct damage location test in concrete under uniaxial compression he process of cracks propagation was observed with x-ray ct scan detection system in state key laboratory of coal mining, china university of mining and technology (beijing), 3000kn ultra high rigidity servo testing machine under uniaxial compression, the schematic diagram of the test system is shown in fig. 1. figure 1: sketch of experimental system. different amount air entrained agent was added when making concrete blocks, then 4 groups concrete specimens, with initial porosity of 1.1%, 3.3%, 6.7% and 9.2%, were obtained to utilize in this test. the hight and the radium of the concrete cylinder blocks are 190mm, 50mm. the mix proportion of concrete specimens used in the test is shown in tab. 1. the amount of materials in per cube meters concrete cement (kg) water (kg) sand (kg) coarse aggregate (kg) 327 189 755 1133 table 1: mix proportion of concrete specimens in test. displacement control methods was used in the test and its laoding rate was 0.2mm/min. the scanning work was done in the range of upper 100mm, and it is needed add that the scanning interval is 0.2mm. repeat the work like this until test specimens reach the peak strength. continue with the loading after the scanning. the loading curve of the test is shown in fig. 2. the acoustic emission machine was introduced to collect the test data in the whole loading process. figure 2: loading-time curve. as shown in fig. 2, 5 cyclic loading tests were carried out on concrete test specimens, and the loading interval was 30kn in every two adjacent loads, finally the ultimate strength was 134kn. t j. liu et alii, frattura ed integrità strutturale, 46 (2018) 352-360; doi: 10.3221/igf-esis.46.32 355 there are 6 stages of scanning on concrete test specimens, included the initial stage, as shown in tab. 2. ct scan times loading(kn) percent of the peak strength 1st scan 0 0% 2nd scan 30 22.3% 3rd scan 60 44.8% 4th scan 90 67.2% 5th scan 120 89.6% 6th scan 134 100% table 2: the load corresponding to the six scanning time of the concrete specimen. there are 499 ct scanning images in every test specimen, 5 ct scanning images are chosen to conduct the analysis due to the limited space, as shown in fig. 3. figure 3: concrete sections map of ct scan. ct scanning test and acoustic emission test were conducted in 4 groups concrete test specimens under uniaxial compression, then the load-time curve, ct images and acoustic emission parameters were collected during the loading process. the concrete test specimens with initial 9.2% porosity are chosen to analyze in this thesis as the limited space. the ct scanning images of initial state, 30kn, 60kn, 90kn, 120kn, and 134kn when destroyed are listed in fig. 4. figure 4: ct scanning images of concrete in different loading. as shown in fig. 4, there is no obvious cracks during the early loading stages in test specimens with 9.2% initial porosity, and the early loading stages can be considered as a compaction process for the pores for the reason of its relative large porosity. the internal micro cracks connect with micro pore and eventually the main visible cracks generate until the test specimens are destroyed. j. liu et alii, frattura ed integrità strutturale, 46 (2018) 352-360; doi: 10.3221/igf-esis.46.32 356 3d meso scale model of concrete ct image he amira software was used to reconstruct the meso structure in 3d after the ct images were divided [13]. it is needed to say that amira is a 3d visual modeling software system, and two basic components of the system, data and modules with different function, are included. the data are processed with modules by their connection with each other, then the visualization of scientific data can be realized in various application area, such as medical science, materials science, geophysics and engineering etc. the result of the 3d reconstruction shows in fig. 5. figure 5: from left to right: test specimens, aggregate, mortar, spatial distribution of cracks. in fig. 5, the distribution of aggregate in concrete 3d reconstruction model accords with the original ct images, and the volume of each component is almost the same with the mix proportion of concrete. the visualization of cracks realizes with transparent processing, and the spatial shape is relatively clear, finally the cracks structure in concrete materials is shown in a real way. subsequent work like image segmentation and extrusion of cracks can be done with amira software, and the fig. 6 is the characteristic change chart of cracks and pores. figure 6: threshold segmentation map of concrete pore under different scanning stage as shown in fig. 6, there are cracks and pores in concrete surrounded by green area, then the cracks and pores show more clear in ct images through segmentation and extrusion. ct images in the upper of the test specimens from the 20th to 470th ct images were selected to gather statistical information on the volume of pores and the porosity in every 90 ct images, the relation graphs of pore volume, pore ratio with pressure can be seen in fig. 7, fig. 8. t j. liu et alii, frattura ed integrità strutturale, 46 (2018) 352-360; doi: 10.3221/igf-esis.46.32 357 figure 7: pore volume-pressure map. figure 8: pore ratio change with loading. in fig. 7 and fig. 8, the changing law of pore volume, porosity with loading in every ct scanning pieces is almost the same under uniaxial loading. the loading curve decreases slight in the start loading stage but keeps nearly a straight line, as a result that the test specimens is in the elastic stage. in this stage, initial pores are compressed then the volume of the pores and porosity reduce. with the increment of the load, the micro cracks expand gradually, certainly, the volume of the pores enlarge. when the load approaches the peak strength, there are obvious cracks in test specimens from ct images, then the volume of pores and porosity achieve the maximum, thus, the phenomenon that the rapid increment of the volume of pores and porosity indicates the failure of concrete test specimens. figure 9: concrete damage area schematic diagram j. liu et alii, frattura ed integrità strutturale, 46 (2018) 352-360; doi: 10.3221/igf-esis.46.32 358 damage analysis during the concrete loading process he concrete’s effective area is calculated by determining the undamaged area of the center in concrete’s ct image, shown as d2 in fig. 9. the remaining part is considered to be a damaged component and is designated as d1. the definition of damage variable is h = d1/d2. the load damage curves of concrete specimens are shown in fig. 10. figure 10: loading-damage curve of concrete specimen. d1 and d2 are determined by analyzing the crack and damage distribution on the cross sections of concrete’s ct image. a concentric circle is drawn on the cross section of 50 mm. the damage was detected by acoustic emission and verified by ct image. the degree of damage is measured by the density of the damage points. d1 is determined if a damage point in a circle is less than a threshold. if the crack passes through the center of the section, this method is invalid, but this situation is very rare. as shown in fig. 10, the damage points, based on the damage variable of ct images and acoustic emission damage location, in the main cracks area after destruction were compared with the damage points in other area, then the result showed the order of the concrete test specimens. before 30% of the peak load, the damage variable is less than 1 which indicates the damage location is in disorder; when the load reach 80%~100% of the peak load, the damage curve rises steeply, then the cracks appears, finally, the test specimens instability fails. the loading-damage curve reflects the whole process from disorder to order, and it keeps in pace with press-porosity volume cure. though the comprehensive analysis on damage location map with acoustic emission, press-porosity volume cure and the load-time curve, that fact can be get as follows. before 30% of the peak load, the damage points are disordered, and the damage variable in concrete is relatively small, then the volume of the pores in material increase slightly. after the load is steadily increase to 30% of the peak load, the damage points appear in order around the macro failure surface, then the damage variable start to grow, so do the volume of the pores. the change of the pores distribution and the center coordinate are also not obvious, and all of this phenomena indicate that the test specimens are destroying steadily. when the load reaches the peak, the stress of concrete test specimen is almost unchanged, while the damage points around the macro failure surface increase rapidly. the damage variable and the volume of the pores show a marked trend of growth. conclusion (1) the ct reconstruction images, rapid increase of concrete pore volume and rapid growth of damage variable are used comprehensively to prognosist the evolution and localization of cracks in concrete provides a new method for the concrete analyses on the evolution process of cracks and damage location. (2) the damage variable is established based on ct images and ct images’ damage points; then the set of the 3d meso model supplement the traditional stochastic mathematical model in concrete. the 3d model set reflects the relationship between meso structure in concrete and macro characteristics, and this lay foundation to the concrete research on damage mechanism. t j. liu et alii, frattura ed integrità strutturale, 46 (2018) 352-360; doi: 10.3221/igf-esis.46.32 359 (3) the damage variable is less than 1 indicating that the damage is very small randomly distributed before 30% of the peak load. the loading-damage curve increases steadily between 30% and 80% of the peak load, indicating that the damage is orderly changed. when the load reaches 80% of the peak load, the damage variable increases sharply, and the test specimen fails at this stage. the load-damage curve shows the whole failure process consistent with the load-pore volume curve. (4) the rapid increment of the pore volume, porosity and damage variable can be regarded as the destroy of concrete test specimens, therefore, the phenomenon can be a sign of the destroy in concrete. acknowledgements his paper is supported by the key fund project program sponsored by the education department of hebei province (zd2014073). tremendous thanks to several colleagues and graduate students for their support during the various stages of the work summarized here. references [1] dang, f.n., lei, g.y. and ding, w.h. (2015). study on the ct meso-test experiment of static and dynamic failure processes of concrete, journal of hydroelectric engineering, 34(1), pp. 189-196. [2] liu, m.j., zhao, j. and wang, g.w. (2014). microscopic study of damage in carbonated concrete based on computerized tomography, journal of guangxi university: nat sci ed., 39(1), pp. 187-193. [3] liu, j.h., jiang, y.d. and zhao, y.x. (2012). fractal description of coal damage process based on ct image, journal of beijing institute of technology, 32(12), pp. 1219-1222. [4] bossa, n., chaurand, p. and vicente, j. (2015). micro-and nano-x-ray computed-tomography: a step forward in the characterization of the pore network of a leached cement paste, journal of cement and concrete research, 67, pp. 138147. [5] kocur, g.k., saenger, e.h. and vogel, t. (2010). elastic wave propagation in a segmented x -ray computed tomography model of a concrete specimen, construction and building materials, 24(12), 2393 -2400. [6] mao, l.t., sun, q.w. and yuan, z.x. (2016). crack and strain field analysis in the concrete under uniaxial compression based on ct images, journal of building materials, 19(3), pp. 449-4555. [7] tekin, i., birgul, r. and yaman, i.o. (2015). monitoring macro voids in mortars by computerized tomography method, journal of measurement, 63, pp. 299-308. [8] lockner, d. (1993). the role of acoustic emission in the study of rock fracture, int. j. rock mech. min. sci., 30(7), pp. 883-899. [9] lai, y.s., xiong, y. and cheng, l.f. (2015). study of chatacteris of acoustic emission during entire loading tests of concrete and its application, journal of building materials, 18(3), pp.380-386. [10] wang, j.y., dewanckele, j. and cnudde, v. (2014). x-ray computed tomography proof of bacterial-based self-healing in concrete, journal of cement & concrete composites, 53, pp. 289-304. [11] morgan, i.l., ellinger, h. and klinksiek, r. (1980). examination of concrete by computerized tomography, aci journal, 77(1), pp. 23-27. [12] chotard, t.j., boncoeur-martel, m.p. and smith, a. (2003). application of x-ray computed tomography to characterize the early hydration of calcium aluminates cement, cement & concrete composites, 25(1), pp. 145-152. [13] lawer, j.s., keane, d.t. and shah, s.p. (2001). measuring three-dimensional damage in concrete under compression, aci materials journal, 98(6), p. 465-475. [14] wong, r.c.k. and chau, k.t. (2004). estimation of air void and aggregate spatial distributions in concrete under uniaxial compression using computer tomography scanning, cement and concrete research, 35, pp.1566-1576. [15] ding, w.h., chen, h.q. and zhang, j.j. (2006). x ray ct observation on the fracture process under high strain rate, journal of architectural structure, (s2), pp. 758-762. [16] wu, l.q. (2006). the meso scale test research on concrete under uniaxial compression, nan ning: guang xi university. [17] liu, h.k. and li, j. (2014). nonlocal meso damage model in concrete under uniaxial tension, journal of tongji university (natural science edition), (2), pp. 203-209. [18] mao, l.t., lian, x.y. and hao, l.n. (2014). fractal calculation of 3d cracks based on digital volumetric images and its application, journal of china university of mining & technology, 43(6), pp. 1134-1139. t j. liu et alii, frattura ed integrità strutturale, 46 (2018) 352-360; doi: 10.3221/igf-esis.46.32 360 [19] bossa, n., chaurand, p. and vicente, j., (2015). micro-and nano-x-ray computed-tomography: a step forward in the characterization of the pore network of a leached cement paste, journal of cement and concrete research, 67, pp. 138147. [20] liu, j.h., jiang, y.d., zhu, j. and han, w. (2013). fractal characteristics of coal uniaxial compression acoustic emission tests, journal of beijing institute of technology, 33(4), pp. 335-338. [21] wang, w., liu, j.h. and shi, p.f. (2015). the fractal analysis of the rock meso rupture process based on ct technology[j], journal of agricultural university of hebei, 38(3), pp. 124-127. [22] shi, p.f., liu, j.h., yang, y.f. and gao, y. 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can be opened with acrobat and adobe reader 5.0 and later.) >> /namespace [ (adobe) (common) (1.0) ] /othernamespaces [ << /asreaderspreads false /cropimagestoframes true /errorcontrol /warnandcontinue /flattenerignorespreadoverrides false /includeguidesgrids false /includenonprinting false /includeslug false /namespace [ (adobe) (indesign) (4.0) ] /omitplacedbitmaps false /omitplacedeps false /omitplacedpdf false /simulateoverprint /legacy >> << /addbleedmarks false /addcolorbars false /addcropmarks false /addpageinfo false /addregmarks false /convertcolors /converttocmyk /destinationprofilename () /destinationprofileselector /documentcmyk /downsample16bitimages true /flattenerpreset << /presetselector /mediumresolution >> /formelements false /generatestructure false /includebookmarks false /includehyperlinks false /includeinteractive false /includelayers false /includeprofiles false /multimediahandling /useobjectsettings /namespace [ (adobe) (creativesuite) (2.0) ] /pdfxoutputintentprofileselector /documentcmyk /preserveediting true /untaggedcmykhandling /leaveuntagged /untaggedrgbhandling /usedocumentprofile /usedocumentbleed false >> ] >> setdistillerparams << /hwresolution [2400 2400] /pagesize [612.000 792.000] >> setpagedevice microsoft word numero_51_art_29_2541 m. guadagnuolo et alii, frattura ed integrità strutturale, 51 (2020) 398-409; doi: 10.3221/igf-esis.51.29 398 focussed on fracture and damage detection in masonry structures retrofit assessment of masonry buildings through simplified structural analysis mariateresa guadagnuolo, marianna aurilio, giuseppe faella department of architecture and industrial design, università degli studi della campania luigi vanvitelli, s.lorenzo ad septimum abbey, aversa (ce) italy. mariateresa.guadagnuolo@unicampania.it, http://orcid.org/0000-0002-8273-4846 marianna.aurilio@unicampania.it, http://orcid.org/0000-0002-8234-4127 giuseppe.faella@unicampania.it, http://orcid.org/0000-0002-1941-9675 abstract. the current seismic prevention strategy is based on a unitary approach aimed at a risk mitigation, also at territorial level. the italian guidelines for the assessment and mitigation of seismic risk of cultural heritage provides indications for the seismic analysis of protected cultural heritage, with the aim of specifying a path of knowledge, assessing the level of safety and planning possible improvements. the italian building heritage is very vast and heterogeneous and was devastated by earthquakes due to its high vulnerability; therefore, the seismic risk mitigation also requires the availability of simple and handy analysis tools. the aim of this paper is the illustration of an easy, although approximate, procedure for the evaluation of the seismic safety index and the optimization of strengthening interventions. the procedure is applied to buildings located in the province of caserta. the analyses are performed with reference to two types of buildings that are particularly recurrent and representative of the building heritage of this area and placed in areas with different seismic hazard. keywords. seismic risk mitigation; masonry buildings; strengthening optimization; province of caserta. citation: guadagnuolo, m., aurilio, m., faella, g, retrofit assessment of masonry buildings through simplified structural analysis, frattura ed integrità strutturale, 51 (2020) 398-409. received: 15.06.2019 accepted: 01.12.2019 published: 01.01.2020 copyright: © 2020 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. introduction he italian building heritage consists of masonry constructions, a wide part of which is located in historic centres, what deserve particular attention as bearers of inestimable values due to their existence over time, which makes it a rich historical, artistic, and cultural environment. the value of these constructions lies in the inestimable meaning that emerges from them, indissolubly linked to the history and evolution of the italian country [1, 2]. most of these buildings belong to periods when there were no rules to observe in their construction, and many were built using rules different from those used today and without seismic criteria [3]. furthermore, existing buildings are often characterized by problems due to degradation and longevity [4-6]. the desire t http://www.gruppofrattura.it/va/51/2541.mp4 m. guadagnuolo et alii, frattura ed integrità strutturale, 51 (2020) 398-409; doi: 10.3221/igf-esis.51.29 399 to preserve these buildings is linked to the need to transfer the italian heritage, and therefore its history, to posterity. moreover, this issue is as important as extremely complicated, above all due to the presence of an excessive degradation and the low seismic capacity that characterizes these structures [7, 8]. due to the recent code developments and the increasing attention given to the seismic safety of existing structures, especially after the last italian earthquakes, the analysis of existing built heritage and the improvement of its seismic performance have become a fundamental issue [9, 10]. the current seismic prevention strategy is based on a unitary approach that primarily envisages a risk mitigation through the seismic classification of the territory and the retrofitting and strengthening of existing buildings; and any contrast between conservation, interventions, and structural safety must be avoided [11-13]. the italian guidelines for the assessment and mitigation of seismic risk of cultural heritage (directive 2011) [14] provide specific indications for the assessment and reduction of seismic risk of protected cultural heritage. it specifies a path of knowledge, assessment of safety level against seismic loads and planning of possible interventions, conceptually similar to those provided for unprotected buildings, but suitably adapted to the needs and peculiarities of cultural heritage [15]. the italian building heritage is characterized by high complexity and heterogeneity, both from an architectural and structural point of view. a significant number of old stone and masonry buildings do not comply with any provisions of current codes and have low seismic capacity and in general sophisticated analyses are necessary to assess their vulnerability [16, 17]. for all these reasons, is therefore essential to have lean procedures that allow the evaluation of the seismic risk assessment of existing buildings to establish priorities in a long-term prevention policy. in addition, it is important to define a methodology to obtain comparable results to plan future activities of analysis, evaluation and risk management. due to the size and the number of buildings involved, the currently available methodologies for assessing the seismic vulnerability of urban areas usually require the treatment of an enormous volume of data associated with inspection and investigation work. for this reason, the use of simplified procedures is becoming more popular [18]. the vulnerability index method uses the information gathered about the main building parameters (plan, height, structural and nonstructural elements, type and quality of materials), and is one of several general methods for seismic risk analysis. in [19] an easily manageable procedure is presented, adaptable to different buildings, but at the same time able to determine the current state of the structures and their structural deficiencies. the current conditions obviously lead to analyses aimed at improving the seismic performance of as much heritage as possible, avoiding the types of strengthening selected in the past that were not always suitable with respect to both the static condition and characteristics of the buildings and the respect of economic thresholds [20]. in fact, many strengthening adopted in the past have proved ineffective to withstand intense seismic actions [21]. in the present paper, a seismic analysis is performed by applying a simplified method for evaluating the safety index, before and after retrofitting interventions. specifically, an approximate procedure is presented to optimize the type and quantity of the necessary local interventions. the analyses are performed with reference to two types of buildings that are particularly recurrent and representative of the built heritage in the province of caserta and located into areas with different seismic hazard. the aim of the paper is to provide a first step to reduce the seismic risk of the analysed buildings, through very simple analyses of site and existing buildings. cases study he present study analyses two residential buildings, representative of the great majority of the existing buildings in the historic centers of the province of caserta but located into two areas with different characteristics. the choice of these two buildings is representative of the great variation that exists in cities even belonging to the same province. although they are both noble buildings, belonging to two different periods and to two distinct cities is also pointed out in the constructive differences starting from the types of material used and from the development of the construction. these buildings were built in the xv century and in a period between 1800 and the beginnings of 1900. they are mainly simple or massive stones masonry buildings and develop around a court or a central courtyard, generally built for at least two or three stories. the buildings are isolated or enclosed in urban agglomeration, and usually have timber or steel floors and no thrusting roof. “palazzo petrucci-novelli” the building was realized around the xiv century and it is a typical example of the construction typology of the area (fig. 1). it is located in the historic center of carinola (province of caserta), a town that presents a medium-low seismic hazard. t m. guadagnuolo et alii, frattura ed integrità strutturale, 51 (2020) 398-409; doi: 10.3221/igf-esis.51.29 400 the building has a compact shape and an irregular morphology both in plan and in elevation. it is on two levels around a central courtyard, where an external staircase connects the ground floor to the loggia, as shown in fig. 2, fig. 3 and in fig. 4. the masonry consists of simple regular stone blocks; the walls are 60 cm thick. the floors present a large variation: cross vaults, barrel vaults and flat slab are present, while the roof is made by timber trusses. figure 1: external front views. figure 2: ground floor plan. figure 3: elevation. figure 4: sections drawings. “palazzo ducale” the building (fig. 5) is located in the historic center of piedimonte matese, in the province of caserta. it is a prototype of the construction typology of the middle volturno’s area, next to the apennines; therefore, a district with high seismic hazard. the palace, built in the xvi century, consists of a massive stone masonry mixed to fieldstone and brick blocks m. guadagnuolo et alii, frattura ed integrità strutturale, 51 (2020) 398-409; doi: 10.3221/igf-esis.51.29 401 with a thickness of about 80 cm. the building has four levels, arranged around a central courtyard and has a compact shape and an irregular morphology in both in plan and in elevation, as shown in fig. 6, fig. 7 and in fig. 8 figure 5: external front views. figure 6: ground floor plan. figure 7: elevation. figure 8: sections drawings results obtained using the italian guidelines for the assessment and mitigation of seismic risk of cultural heritage he italian national “guidelines for evaluation and mitigation of seismic risk of cultural heritage” [14] identify different simplified mechanical models aimed at evaluating the seismic risk of most common masonry buildings types such as buildings, palaces and other structures with bearing walls and horizontal diaphragms [22], churches t m. guadagnuolo et alii, frattura ed integrità strutturale, 51 (2020) 398-409; doi: 10.3221/igf-esis.51.29 402 and other structures with large halls [23,24], without intermediate diaphragms [25], towers, bell towers, and other tall and slender structures [26].they are strongly linked to the italian building code [27], recently updated with a new version [28], which contains all the parameters necessary to perform a reliable seismic analysis. to evaluate the seismic safety, three different levels of increasing completeness have been identified, of which the lv1 level concerns the assessment of seismic safety index on a territorial scale, also to establish the priority degree of interventions; this method is based on a limited number of geometric and mechanical parameters or visual tests, being linked only to a simplified type of evaluation; as will be better clarified by the following procedure (eqns. 1-9) [14]. same papers compare simplified approaches with more sophisticated procedures [29, 30]; however, retrofitting and strengthening of existing buildings have to be designed through refined non linear analyses [31]. if the seismic safety index estimated using the procedure is greater than the unit, the structure is able to withstand the seismic forces required by the seismic code, on the contrary no. this is useful for highlighting critical situations and establishing a priority for the interventions [27, 28]. the seismic safety index isp is estimated by the ratio between the return period of the seismic action  slvt of the earthquake which gets the building to reach the ultimate limit state and the expected return period of the earthquake on the site , r slvt .  ,  ,  slv sp slv r slv t i t  (1) and ,  ln(1 ) r r slv vr v t p    (2) where: rv is the reference period; vrp is probability of exceedance in the reference period. in the same way, an acceleration safety index isa is computed as the ratio between the peak ground acceleration of the earthquake which gets the building to the limit state of activation slva and the peak ground acceleration of the design earthquake , g slva , related to the site: ,  slv sa g slv a i a  (3) , g slva is the design ground acceleration, corresponding to the assigned return period of the earthquake, related to the subsoil; slva is the ground acceleration leading to the achievement of the structure ultimate limit state (slv), computed as a function of the fundamental period of vibration t1 of the structure [30].  , 1 1 0     e slvslv b c s t a t t t s f     (4)  , 1 1 0  e slv slv c s t t a s f t    1   c dt t t  (5) where the ordinate value of the elastic response spectrum ,  e slvs is: m. guadagnuolo et alii, frattura ed integrità strutturale, 51 (2020) 398-409; doi: 10.3221/igf-esis.51.29 403 , *      slve slv q f s e m    (6) q is the behavior factor, slvf is the lower building shear strength, *e is the mass fraction participant to the first mode of vibration and m is the total seismic mass. the procedure used, in the case in which the mode of collapse is not defined with precision, allows us to assume a triangular modal shape, corresponding to the following values for the mass fraction participant on the first mode and for the coefficient that defines the force at the i-th plane: * 0,750, 75 0, 25   e n   (7) the capacity models assumed for the analyzed structures are subject to shear failure at each level [32, 33]. the shear strength of the building is the lowest among those evaluated in two main direction. , ,                                             yi yi yi yi dixi xi xi xi di slv xi slv yi xi i yi i aa f f              (8)   xia and   yia are shear resistant areas of the i-th floor walls according respectively to x and y direction;    xi and   yi are plan irregularity factors related to the i-th floor;    xi and   yi are coefficients considering, at the i-th floor, the stiffness and strength homogeneity of masonry walls according respectively to x and y direction. the failure mechanisms considered are that expected in masonry walls (fig. 9): collapse of piers due to shear or bending forces, also depending on the strength of the spandrel beams [14, 34]. in masonry piers, the coefficients of failure mechanisms  xi and   yi assume value of 1 in the case of shear failure and 0.8 in the case of eccentric axial force failure; the coefficients related to the spandrel beams resistance xi and yi assume values 1.0 in the case of strong spandrel beams and 0.8 and in the case of weak spandrel beams. figure 9: in-plane failure modes of masonry piers subjected to eccentric axial force: (a) flexural, (b) shear diagonal cracking. the coefficients    xi and   yi are related to the spandrel resistance of the i-th floor masonry walls: their values are 1.0 in case of strong spandrel and 0.8 and in case of weak spandrel, while    di is the design value of the masonry piers shear strength at the i-th floor, defined as: 0 0     1 1.5    i di i       (9) where 0   i is the design shear strength of masonry and 0   i is the average normal stress on walls at the i-th floor. in the preliminary analysis the structure is examined in its actual state before the intervention, identifying the deficiencies and the seismic level at which the limit state of the collapse mechanism activation is achieved. the reference peak ground accelerations are computed using the following seismic parameters: m. guadagnuolo et alii, frattura ed integrità strutturale, 51 (2020) 398-409; doi: 10.3221/igf-esis.51.29 404 latitude longitude vn use class cu site class ag palazzo petrucci novelli 41.188625 13.976842 50 years ii 1 a 0.098 g palazzo ducale 41.365277 14.383055 50 years ii 1 a 0.249 g table 1: values of seismic parameters. “palazzo petrucci novelli” the structure is composed by three different levels; the first one has steel floors and several vaults, the second one has steel and timber floors, while the roof consists of timber structures. the corresponding loads at each level are summarized in the tab. 2. level dead loads: gk live loads: qk masonry weight 1° 12 kn/m2 2 kn/m2 16 kn/m3 2° 6 kn/m2 2 kn/m2 16 kn/m3 3° 1.7 kn/m2 2 kn/m2 16 kn/m3 table 2: values of loads and masonry parameters. the confidence factor fc assumed is equal to 1.35 (corresponding to complete survey of the building geometry but limited knowledge of material mechanical properties). in this case the shear strength is equal to 0.028 mpa while the failure coefficients related to the type of failure expected in masonry piers (cp=𝜉 ) and the resistance of spandrel beams (cs=𝜁 ) are assumed equal to 0.8. according to the procedure provided in [14] for “building structures”, a minimum safety index is (minimum between isp and isa) equal to 0.45 has been computed. therefore, the building is not capable to withstand the design earthquake. “palazzo ducale” the confidence factor fc is equal to 1.35; the shear strength is equal to 0.028 mpa and cp and cs have been also assumed equal to 0.8 in this case. based on the above data, the smaller safety index is equal to is = 0.25, indicating that the structure is unable to withstand the seismic forces provided by the seismic code. level dead loads: gk live loads: qk masonry weight 1°2° 3° 5.4 kn/m2 2 kn/m2 19 kn/m3 4° 0.5 kn/m2 2 kn/m2 19 kn/m3 table 3: values of loads and masonry parameters selection and optimization of interventions he procedure aims at locally strengthening the buildings and increasing their seismic safety index. the choice of retrofit interventions must be based on a motivated strategy aimed at involving only selected building elements to be reinforced to improve structural performance. through the simplified procedure provided by the italian guidelines for the evaluation and mitigation of seismic risk of cultural heritage and following the examples of this paper it is possible to identify the weakest level of a generic building t m. guadagnuolo et alii, frattura ed integrità strutturale, 51 (2020) 398-409; doi: 10.3221/igf-esis.51.29 405 by a few simple steps, to optimize the interventions, focusing them on the story where they need: in fact, starting from the current conditions of the building, it is possible to hypothesize interventions only on some structural elements (piers or spandrel beams) of a generic story. in fact, there are interventions that affect the resistance of single piers and/or spandrels and those that modify their failure mode. this last aspect can be taken into account in the numerical model by increasing the failure coefficient cp or cs relative only to the involved piers or spandrels. then, the structural analysis is performed again to recalculate the safety indices isp and isa. the procedure is then repeated several times until the safety indices reach an acceptable value or until it is possible to increase the strength of the structural elements or change their collapse modes. “palazzo petrucci novelli” in this case, the fig. 10 shows the increment curve of the minimum safety index is of the building, obtained through a combination of gradual increases in the shear strength of masonry piers (shown in the figure through an increase coefficient if), of the failure coefficients of piers and the resistance of spandrel beams (cp, cs) at different floors of the building. it is considered that the if coefficient could not be higher than 1.50 (which corresponds to a maximum increase of 50% in resistance of the masonry piers); the failure coefficients cp and cs cannot, on the other hand, obviously be greater than 1.0. with the aforementioned procedure, it was possible to increase the minimum safety index is from the initial value of 0.45 up to 0.73. the procedure starts from the weak level. in this case the ratio between the shear strength of each level and the shear strength of the entire construction highlights the distribution percentage of this force, immediately identifying the weakest level as shown in fig. 10. the three black points represent the values of the safety index achieved by maximizing the shear strength of piers (if = 1.5) and the failure coefficients (cp = cs = 1), one floor at a time. the gradually increasing curve of the seismic safety index and the points of maximum increase differ from each other in the different design choices. the points of maximum increase correspond to widespread interventions on the entire construction, maximizing the failure coefficients of all piers and spandrel beams (cp, cs) and of piers shear strength (if) in an entire plane. this does not consider that the value of the minimum safety index is could be due to a specific weakness located in the construction rather than to a general stiffness lack. figure 10: safety index curve of “palazzo petrucci novelli”. m. guadagnuolo et alii, frattura ed integrità strutturale, 51 (2020) 398-409; doi: 10.3221/igf-esis.51.29 406 on the contrary it is possible to minimize interventions and consequent costs gradually increasing the shear strength and the specific failure coefficients (where necessary). essentially with a view to achieving the same improvement result but optimizing choices and costs. following the latter approach (hypothesis of targeted and optimized interventions), the maximum increase in the minimum safety index is obtained by increasing the shear strength by 50% at the third and second floors and only 20% on the first floor. the failure coefficients of piers and spandrel beams (assumed equal in both the x and y directions) are increased up to the unity for the third and second floor while they remained unchanged at the first floor. by maximizing all the values of shear strength (if = 1.5) and failure coefficients (cp = cs = 1) at every level of the constructions, the safety index curve rises rapidly to reach the same value of 0.73. in such a case, there would therefore be a waste in terms of costs, uselessly strengthening the first floor too, where instead it is sufficient to increase by only 20% the pier shear strength without changing the failure modes of piers and spandrels. the aforementioned analyses highlight that both design choices allow to improve the seismic capacity of the building, increasing the minimum safety index is from 0.45 to 0.73. however, in the case of optimized interventions, the strengthening would be lower, less expensive and really located on the structural parts affected by structural deficiencies, while in the other case (widespread interventions) there would be unjustifiable and expensive interventions at a global level on the whole building. “palazzo ducale” in this case, as pointed out in fig. 11, the building analysis returns an initial safety index of 0.25, which being lower than 1 shows a significant incapability to cope with a seismic event, a more critical condition than the previously studied case. also, for this second building, a double analysis is carried out based on two different design choices: the first with a gradual increase in resistance and failure coefficients and a second one based on the simultaneous maximization of all increases. figure 11: safety index curve of “palazzo ducale”. m. guadagnuolo et alii, frattura ed integrità strutturale, 51 (2020) 398-409; doi: 10.3221/igf-esis.51.29 407 also, in this case the weakest level is the fourth floor in which there is just the 22% of the shear strength of the entire construction. unlike the previous case, for this type of building, the maximum increase in the safety index (and the related structural improvement) is obtained, for both design approaches, by maximizing both the pier shear strength (if) at all stories in both directions and the failure coefficients of piers and spandrel (cp, cs). this is clearly shown in fig. 11, where the curve representing the gradual increase of the safety index from 0.25 (initial scenario) to 0.52 is obtained by increasing the shear strength by 50% to all levels and assuming a unitary value for all the collapse coefficients cp and cs (assumed equal in both the x and y direction). the black points, representative of widespread interventions on the entire building, confirm that in this case the real improvement of the seismic capacity requires a global strengthening intervention on the entire building structure. this type of simplified method is able to identify the weak level of any structure, succeeding in this way to optimize the interventions and to localize them on the weak parts. the interventions aim to increase the compressive and shear strength. several types of intervention are possible for cultural masonry heritage. there are many strengthening configurations, different in technique and material that achieve the same result and whose geometrical details are difficult to establish in advance. the improvement of the building seismic performances may be achieved using traditional fiber-reinforced composites systems (frp), suitable as structural reinforcing elements. conclusions his paper deals with some issues concerning the vulnerability assessment of masonry buildings and the optimization of the strengthening interventions to be adopted. the case studies are two stone masonry buildings in the area of caserta, southern italy. particular attention is paid to simplified assessment methods that require a less thorough knowledge of the structure, leading to results that can be sufficiently reliable. they are of fast application and are particularly suitable for the analysis of large and complex buildings, especially when they are placed in historic centers. the simplified method illustrated allows an optimization of strengthening and has been applied to two buildings representative of a wide number of residential buildings in caserta: a building in the historic center of carinola, an area with medium-low seismic hazard, representative of regular buildings made of simple stone, and a second building built in the historic center of piedimonte matese, an area of high seismic hazard, highly irregular in its configuration and made with mixed materials of various types. the seismic vulnerability has been assessed using a quantitative method, based on the procedure provided by the italian guidelines for the assessment and mitigation of seismic risk of cultural heritage. for the first examined building ("palazzo petrucci-novelli"), the analyses show an average vulnerability. in this case the seismic capacity of the building can be improved optimizing the strengthening interventions. in this case, in fact, the adopted iterative procedure allows concentrating interventions only on the structural elements characterized by structural deficiencies, avoiding widespread unnecessary interventions throughout the building (that would not lead to a larger increase in the safety index), and which would therefore be economically unjustifiable. the results obtained for the second building ("palazzo ducale") show a high vulnerability. in this case the iterative procedure leads to the same results in terms of increasing the minimum safety index achieved by assuming widespread interventions throughout the building. references [1] de matteis g., brando g., corlito v., criber e., guadagnuolo m. (2019). "seismic vulnerability assessment of churches at regional scale after the 2009 l'aquila earthquake", int. j. masonry research and innovation, 4(1-2), pp.174-196. [2] bergamasco, i., gesualdo, a., iannuzzo, a., monaco, m. (2018). an integrated approach to the conservation of the roofing structures in the pompeian domus, j. cult. herit., 31, pp. 141-151. doi:10.1016/j.culher.2017.12.006. [3] cattari, s., degli abbati, d., ferretti, d., lagormarsino, s., ottonelli, d., rossi, m., et al. (2012). the seismic behaviour of ancient masonry buildings after the earthquake in emilia (italy) on may 20th and 29th, ing sismica., anno xxix(2–3)., pp. 87–111. [4] masi, a., santarsiero, g., ventura, g. (2017). strategie per la riduzione del rischio sismico applicate agli edifici scolastici: un caso studio., anidis 2017 pistoia., pp. 2232 – 2240. t m. guadagnuolo et alii, frattura ed integrità strutturale, 51 (2020) 398-409; doi: 10.3221/igf-esis.51.29 408 [5] costantine, c., spyrakos. (2018). bridging performance based seismic design with restricted interventions on cultural heritage structures. engineering structures., pp. 160:34-43. [6] bosiljkov, v., uranjek, m., zarnìc, r., bokan-bosiljkov, v. (2010). an integrated diagnostic approach for the assessment of historic masonry structures, journal of cultural heritage 11, pp. 239–249. doi: 10.1016/j.culher.2011.11.007. [7] ceroni, f., pecce, m., manfredi, g. (2009). seismic assessment of the bell tower of santa maria del carmine: problems and solutions, journal of earthquake engineering, pp. 14:1, 30-56. doi: 10.1080/13632460902988968. [8] milani, g., shehu, r., valente, m. (2017). seismic assessment of masonry tower by means of nonlinear static procedures, x international conference on strctural dynamics, eurodyn. [9] guadagnuolo, m., faella, g., donadio, a., ferri, l. (2014). integrated evaluation of the church of s. nicola di mira: conservation versus safety. ndt & e international., elsevier., pp. 68, 53-65. [10] giovinazzi, s., lagomarsino, s. (2004). a macroseismic models for the vulnerability assessment of the buildings, 13th world conference on earthquake. 896. [11] zuccaro, g., cacace, f. (2009). modello per la simulazione di scenari sismici per la regione campania., l’ingegneria sismica in italia. bologna, italy. [12] guadagnuolo, m., nuzzo, m., faella, g. (2018). the corpus domini bell tower: conservation and safetys., xiv international conference on bulding pathology and construction repair – cinpar., 11, pp. 444-451. doi: 10.1016/j.prostr.2018.11.057 [13] dolce, m., di pasquale, g., speranza e. (2012). a multipurpose method for seismic vulnerability assessment of urban areas., 15 wcee lisboa 2012. [14] direttiva del presidente del consiglio dei ministri 9 febbraio 2011; riferimento ntc d.m. 14.01.08 valutazione e riduzione del rischio sismico del patrimonio culturale. [15] guadagnuolo, m., aurilio, m., faella, g. (2017). rischio sismico di edifici in muratura: metodi a confronto., anidis 2017 pistoia. pp. 2171 – 2180. [16] monaco, m., bergamasco, i, betti, m. (2018). a no-tension analysis for a brick masonry vault with lunette, journal of mechanics of materials and structures, 13(5), pp. 703-714, doi: 10.2140/jomms.2018.13.703. [17] guadagnuolo m., monaco, m. (2009). out of plane behaviour of unreinforced masonry walls. in: protection of historical buildings, 2, pp. 1177-1180, london, new york: crc press, taylor & francis group. [18] de matteis g., corlito v., criber e., guadagnuolo m., 2016. evaluation of earthquake damage scenario of churches at regional scale_experiences in abruzzi and perspectives in campania, proceedings of thexiv forum internazionale di studi “le vie dei mercanti” – world heritage and degradation smart design, planning and technologies, napoli-capri, italy. [19] cimino, g., ricci, i., gasparini, g., trombetti, t. (2017). seismic vulnerability of building heritage of the university of bologna: methodology and analysis., 16th world conference on earthquake, 16wcee 2017 santiago chile. [20] caterino, n., cosenza e. (2017). evalution of seismic retrofit techniques via a multicriteria approach accounting for italian tax incentives. anidis 2017 pistoia. pp. 2181 – 2190. [21] petrucci, e. (2017). considerazioni sulle procedure attuate dopo il siam del 1997 nella regione marche: nuovi contributi al consolidamento delle opere murarie., anidis 2017 pistoia. pp. 2386 – 2396. [22] guadagnuolo, m., paolillo, a. (2012). territorial seismic safety evaluation and appropriate survey: liberty buildings in naples. proceedings of thex forum internazionale di studi “le vie dei mercanti” – less more architecture, design, landscape, aversa-capri, italy. [23] de matteis g., corlito v., guadagnuolo m. and tafuro a. (2019). seismic vulnerability assessment and retrofitting strategies of italian masonry churches of the alife-caiazzo diocese in caserta, int. j. architectural heritage, doi: 10.1080/15583058.2019.1594450. [24] corlito v., guadagnuolo m., tafuro a., de matteis g., 2017. seismic risk assessment of one nave complex churches. the alife-caiazzo diocese in caserta province, proc. 3rd international conference on protection of historical constructions, lisbon. [25] faella g., guadagnuolo m., 2007. la sicurezza sismica degli opifici mediterranei in muratura, proceedings of thev forum internazionale di studi “le vie dei mercanti” rappresentare il mediterraneo, capri, italy. [26] guadagnuolo m., nuzzo m., faella g., “eismic safety of the “corpus domini” bell tower, proceedings xii forum internazionale di studi “le vie dei mercanti” – best pratice in heritage, conservation, management from the world to pompeii, aversa-capri, italy. [27] mit, 2008. norme tecniche per le costruzioni, d.m. 14/01/2008, official bulletin n. 29, 04.02.2008. m. guadagnuolo et alii, frattura ed integrità strutturale, 51 (2020) 398-409; doi: 10.3221/igf-esis.51.29 409 [28] mit, 2018. norme tecniche per le costruzioni, d.m. 17/01/2018, official bulletin n. 42, 20.02.2018. [29] bartoli, g., betti, m., galano, l., zini, g. (2019). numerical insights on the seismic risk of confined masonry towers. engineering structures, (180) pp. 713 – 727. [30] formisano, a., marzo, a. (2018). simplified and refined methods for seismic vulnerability assessment and retrofitting of an italian cultural heritage masonry building. computers and structures., pp. 13 – 26. [31] ademovi´n., oliveira d.v., lourenço p.b., seismic evaluation and strengthening of an existing masonry building in sarajevo, b&h, buildings 2019, 9, 30; doi:10.3390/buildings9020030. [32] betti, m., galano, l., petracchi, m. and vignoli, a. (2015). diagonal cracking shear strength of unreinforced masonry panels: a correction proposal of the b shape factor, b. earthq. eng., 13(10), pp. 3151-3186. doi: 10.1007/s10518-015-9756-8. [33] betti, m., galano, l., vignoli, a. (2008). seismic response of masonry plane walls: a numerical study on spandrel strength, aip conf. proc., 1020(1), pp. 787-794. doi: 10.1063/1.2963915. [34] monaco, m., calderoni, b., iannuzzo, a., gesualdo, a. 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/hrv (za stvaranje adobe pdf dokumenata najpogodnijih za visokokvalitetni ispis prije tiskanja koristite ove postavke. stvoreni pdf dokumenti mogu se otvoriti acrobat i adobe reader 5.0 i kasnijim verzijama.) /hun 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can be opened with acrobat and adobe reader 5.0 and later.) >> /namespace [ (adobe) (common) (1.0) ] /othernamespaces [ << /asreaderspreads false /cropimagestoframes true /errorcontrol /warnandcontinue /flattenerignorespreadoverrides false /includeguidesgrids false /includenonprinting false /includeslug false /namespace [ (adobe) (indesign) (4.0) ] /omitplacedbitmaps false /omitplacedeps false /omitplacedpdf false /simulateoverprint /legacy >> << /addbleedmarks false /addcolorbars false /addcropmarks false /addpageinfo false /addregmarks false /convertcolors /converttocmyk /destinationprofilename () /destinationprofileselector /documentcmyk /downsample16bitimages true /flattenerpreset << /presetselector /mediumresolution >> /formelements false /generatestructure false /includebookmarks false /includehyperlinks false /includeinteractive false /includelayers false /includeprofiles false /multimediahandling /useobjectsettings /namespace [ (adobe) (creativesuite) (2.0) ] /pdfxoutputintentprofileselector /documentcmyk /preserveediting true /untaggedcmykhandling /leaveuntagged /untaggedrgbhandling /usedocumentprofile /usedocumentbleed false >> ] >> setdistillerparams << /hwresolution [2400 2400] /pagesize [612.000 792.000] >> setpagedevice microsoft word numero_35_art_13 g. dhondt et alii, frattura ed integrità strutturale, 35 (2016) 108-113; doi: 10.3221/igf-esis.35.13 108 focussed on crack paths prediction of three-dimensional crack propagation paths taking high cycle fatigue into account guido dhondt mtu aero engines ag, dachauer str. 665, 80995 munich, germany guido.dhondt@mtu.de abstract. engine components are usually subject to complex loading patterns such as mixed-mode low cycle fatigue loading due to maneuvering. in practice, this lcf loading has to be superimposed by high cyclic fatigue loading caused by vibrations. the changes brought along by hcf are twofold: first, the vibrational cycles which are superposed on the lcf mission increase the maximum loading of the mission and may alter the principal stress planes. secondly, the hcf cycles themselves have to be evaluated on their own, assuring that no crack propagation occurs. indeed, the vibrational frequency is usually so high that propagation leads to immediate failure. in the present paper it is explained how these two effects can be taken care of in a standard lcf crack propagation procedure. the method is illustrated by applying the finite element based crack propagation software cracktracer3d on an engine blade. keywords. crack propagation; mixed-mode; high cycle fatigue; mission; vibrations. introduction rack propagation calculations have become standard in aircraft engine applications. frequently, crack initiation life is not sufficient and has to be augmented by crack propagation life in order to obtain the envisaged component life. this requires crack propagation calculations in the design phase of the engine. however, also later on in the life of the engine fracture mechanics calculations may be necessary to analyze damage observed in-service. by now, threedimensional fully automatic mixed-mode crack propagation calculations are state-of-the-art [1-3]. they generally consist of a pre-processing module which automatically inserts an arbitrary crack into a given mesh, a call to a finite element program to determine the stress field and a post-processing module taking care of the calculation of the stress intensity factors, cycle extraction [4] and the calculation of the new crack front based on a crack propagation law [5-7]. notice that, since the k-factor concept is used, all calculations are linear elastic.in order to take hcf due to vibrations into account all these modules have to be modified. in essence, additional frequency calculations have to be performed for the cracked structure, the results must be scaled based on experimental evidence and the mission containing the mixed-mode k-values at different positions along the crack fronts has to be augmented by the hcf k-values. in addition, the hcf cycles have to be evaluated on their own to check that no propagation occurs. the following sections explain in detail the necessary modifications. finally, an example based on a simplified blade shows a practical application. c g. dhondt et alii, frattura ed integrità strutturale, 35 (2016) 108-113; doi: 10.3221/igf-esis.35.13 109 modifications to the preprocessor and the finite element calculations he preprocessing unit takes the finite element input deck for the uncracked structure, inserts the crack (or cracks) and generates an input deck for the cracked structure. without hcf this input deck usually contains a complete flight mission, i.e. a collection of maybe 100 to 200 loading points along the mission. taking hcf due to vibrations into account requires a careful analysis of the mission. first, the user must identify those loading steps prone to resonances, and for each of these determine due to which eigenmode the resonance arises. indeed, vibrations usually occur selectively at certain engine speeds at which they are triggered. a bending mode may be active at a different engine speed than a torsional mode. this means that the user must be able to specify at the start of the preprocessing step which eigenmode should be superimposed on which loading step in the mission. based on this information, the preprocessing unit will create input decks for frequency calculations consisting of an appropriate static pre-loading step followed by a frequency calculation up to and including the mode of interest. figure 1: lcf-mission. for instance, the mission in fig. 1 contains 9 loading points. suppose that a preliminary analysis has revealed that mode 1, which happens to be a bending mode, is resonant near loading point 2 and mode 4, which happens to be a torsion mode, is resonant near loading point 4. then, the preprocessor has to generate three input decks for the finite element program: a static calculation of the mission (9 loading points), a static step corresponding to loading point 2 followed by a perturbation frequency step for at least the first eigenmode and a static step corresponding to loading point 4 followed by a perturbation frequency step for at least the lowest four eigenmodes. since these calculations can be performed in parallel, this should not significantly increase the overall computation time. notice that these calculations have to be performed for the cracked structure in each iteration of the crack propagation software. modifications to the postprocessor n the postprocessor of cracktracer3d the stress intensity factors are determined by comparing the stress tensor at the integrations points of the collapsed quarter point elements immediately ahead of the crack tip with the asymptotic stress field [1]. a frequency calculation, however, does not yield absolute stress values since it is the solution of a homogeneous set of equations: the results can be freely scaled by a constant. to get absolute values, a scaling has to take place by comparing the engineering strain at a certain location and direction with experimental evidence. this evidence is usually gathered for the uncracked structure, and it is assumed that the experimental reference point is far enough away from the crack location, so that the interaction with the crack is minimal. after scaling the eigenmodes, the mixed-mode stress intensity factors can be determined for the mission and for each of the selected eigenmodes. then, referring to the example in fig. 1, three crack propagation calculations are performed. t i g. dhondt et alii, frattura ed integrità strutturale, 35 (2016) 108-113; doi: 10.3221/igf-esis.35.13 110 figure 2: lcf-mission augmented by hcf-cycles the first one is for the mission augmented by the eigenmodes at the specified locations (fig. 2). this corresponds to a lcf calculation for an extended mission. the usual procedure is followed involving the determination of a dominant loading point to determine the crack propagation direction, the reduction of the mixed-mode k-values to an equivalent k-factor, calculation of the crack propagation of each loading point separately, cycle extraction on the resulting curve and evaluation of the crack propagation of each extracted cycle based on the maximum cycle temperature (for details the reader is referred to [8]). the crack propagation increments from each extracted cycle are summed. including hcf will frequently lead to more crack propagation, since a hcf cycle at a maximum point of a mission will increase the equivalent k-factor. the second and third calculation concerns the eigenmode itself, centered at the appropriate loading point (fig. 3). also here, the usual cycle extraction routines are applied to short missions consisting of the loading point plus the eigenmode and the loading point minus the eigenmodes. since the calculations are linear the k-factors can be summed appropriately. for the pure hcf-evaluation the criterion is that no propagation should occur. indeed, the hcf frequency is usually so high that propagation results in immediate failure. figure 3: hcf cycles. example simple example is presented in the form of an imaginary blade (fig. 4) subject to centrifugal loading. only two loading points are considered, full power and zero loading. an initial quarter circular crack of with radius 0.4 mm is inserted at the location of maximum principal stress about 25 mm above the disk. the orientation of the crack plane was orthogonal to the maximum principal stress, acting in radial direction. at first a calculation consisting of 50 iterations of cracktracer3d was performed without hcf. the mesh in the last calculation is shown in fig. 5. one can clearly see the domain in which the mesh was modified in order to accommodate the crack. at the crack tip a focused a g. dhondt et alii, frattura ed integrità strutturale, 35 (2016) 108-113; doi: 10.3221/igf-esis.35.13 111 20-node reduced integration hexahedral mesh with collapsed quarter point elements was generated, whereas the remaining domain was automatically meshed with quadratic (10-node) tetrahedral elements. figure 4: mesh of the engine blade. figure 5: mesh at the crack tip. in a subsequent calculation the eigenmodes of the blade were determined. the first eigenmode, which is a bending mode (fig. 6) was, taking fictitious experimental data in to account, judged most critical. this mode was appended to the full power loading point. the crack length versus the number of cycles for the original lcf mission and the lcf-mission augmented by the hcf-mode is shown in fig. 7. the superimposed hcf vibration clearly decreased the life of the blade substantially. the shape of the crack, however, did not change. this is illustrated in figs. 8a and 8b. although the crack in fig. 8b is somewhat more rough, the overall shape is the same. this was to be expected since both the centrifugal force and the bending mode lead to a predominantly mode-i loading of the initial crack. this, however, may be different for other missions and vibrational modes. taking the hcf-cycle on its own revealed that no hcf crack propagation takes place, i.e. all equivalent k-values along the crack front in each iteration are below threshold. g. dhondt et alii, frattura ed integrità strutturale, 35 (2016) 108-113; doi: 10.3221/igf-esis.35.13 112 figure 6: first eigenmode (bending mode). figure 7: crack propagation due to lcf and due to combined lcf+hcf. figure 8a: crack propagation due to lcf. figure 8b: crack propagation due to lcf+hcf. conclusions method was presented how to alter a procedure capable of calculating lcf crack propagation in order to take hcf due to superimposed vibrations into account. two aspects were looked into: the augmentation of the lcfmission by interspersed hcf-cycles and the evaluation of hcf cycles alone. the modifications needed in the code are little, provided the program is capable of treating arbitrary mixed-mode loading in three-dimensional structures. it was shown that the augmented lcf-mission usually leads to a decreased life. the hcf evaluation itself is usually reduced to a check whether the threshold value is not exceeded and no hcf-propagation occurs. references [1] dhondt, g., application of the finite element method to mixed-mode cyclic crack propagation calculations in specimens, int. j. fatigue, 58 (2014) 2-11. [2] bremberg, d., dhondt, g., automatic crack-insertion for arbitrary crack growth, eng. frac. mech., 75 (2008) 404416. a g. dhondt et alii, frattura ed integrità strutturale, 35 (2016) 108-113; doi: 10.3221/igf-esis.35.13 113 [3] schöllmann, m., fulland m. richard, h.a., development of a new software for adaptive crack growth simulations in 3d structures, eng. frac. mech., 70 (2003) 249-268. [4] downing, s.d., socie, d.f., int. j. fatigue, (1982), 31-40. [5] dhondt, g, a new three-dimensional fracture criterion, key eng. mater., 251 (2003) 209-214. [6] forman, r.g., kearney v.e., engle r.m., numerical analysis of crack propagation in cyclic-loaded structures, transactions of the asme, j. basic engng., (1967) 459-464. [7] forman, r.g., shivakumar v., cardinal j.w., williams l.c., mckeighan, p.c., fatigue crack growth database for damage tolerance analysis, u.s. department of transportation, federal aviation administration report dot/faa/ar-05/15 (2005). 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/hrv (za stvaranje adobe pdf dokumenata najpogodnijih za visokokvalitetni ispis prije tiskanja koristite ove postavke. stvoreni pdf dokumenti mogu se otvoriti acrobat i adobe reader 5.0 i kasnijim verzijama.) /hun 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can be opened with acrobat and adobe reader 5.0 and later.) >> /namespace [ (adobe) (common) (1.0) ] /othernamespaces [ << /asreaderspreads false /cropimagestoframes true /errorcontrol /warnandcontinue /flattenerignorespreadoverrides false /includeguidesgrids false /includenonprinting false /includeslug false /namespace [ (adobe) (indesign) (4.0) ] /omitplacedbitmaps false /omitplacedeps false /omitplacedpdf false /simulateoverprint /legacy >> << /addbleedmarks false /addcolorbars false /addcropmarks false /addpageinfo false /addregmarks false /convertcolors /converttocmyk /destinationprofilename () /destinationprofileselector /documentcmyk /downsample16bitimages true /flattenerpreset << /presetselector /mediumresolution >> /formelements false /generatestructure false /includebookmarks false /includehyperlinks false /includeinteractive false /includelayers false /includeprofiles false /multimediahandling /useobjectsettings /namespace [ (adobe) (creativesuite) (2.0) ] /pdfxoutputintentprofileselector /documentcmyk /preserveediting true /untaggedcmykhandling /leaveuntagged /untaggedrgbhandling /usedocumentprofile /usedocumentbleed false >> ] >> setdistillerparams << /hwresolution [2400 2400] /pagesize [612.000 792.000] >> setpagedevice microsoft word numero_31_art_10 m. merlin et alii, frattura ed integrità strutturale, 31 (2015) 127-137; doi: 10.3221/igf-esis.31.10 127 on the improved adhesion of niti wires embedded in polyester and vinylester resins mattia merlin, martina scoponi, chiara soffritti, annalisa fortini, raffaella rizzoni, gian luca garagnani department of engineering, university of ferrara, via saragat 1, i-44122 ferrara, italy mattia.merlin@unife.it, martina.scoponi@unife.it, chiara.soffritti@unife.it, annalisa.fortini@unife.it, raffaella.rizzoni@unife.it, gian.luca.garagnani@unife.it abstract. this paper discusses the effect of different surface treatments on shape memory alloy wires embedded in polyester (pe) and vinylester (ve) polymeric matrices. in particular, two types of chemical etching and a chemical bonding with a silane coupling agent have been performed on the surfaces of the wires. pull-out tests have been carried out on samples made from a specifically designed teflon mould. considering the best results of the pull-out tests obtained with pe resin, the debonding induced by strain recovery of 4%, 5% and 6% pre-strained niti wires has been evaluated with the wires being subjected to different surface treatment conditions and then being embedded in the pe matrix. the results prove that the wires functionalised and embedded in the pe resin show the maximum pull-out forces and the highest interfacial adhesion. finally, it has been found that debonding induced by strain recovery is strongly related to the propagation towards the radial direction of sharp cracks at the debonding region. keywords. smart materials; surface treatments; thermosetting resin; adhesion. introduction hape memory alloys (smas) are a class of materials with the unique characteristics of shape memory effect (sme) and superelasticity (se), according to the temperature range and applied load. these properties are due to a crystalline, diffusionless and reversible phase transformation between the phase stable at high temperature (austenite) and the phase stable at low temperature (martensite). the shape memory effect is the ability of the alloy to recover a mechanically induced strain when heated above a critical temperature. for such alloys the knowledge of the four transformation temperatures is fundamental: ms and mf are the initial and final temperatures of the direct martensitic transformation from austenite to martensite on cooling, while as and af are the initial and the final temperatures of the inverse martensitic transformation from martensite to austenite on heating [1]. the specific functional properties of smas have been widely used to realise actuators, sensors, damping systems and devices employed in biomedical applications [2-5]. the ability of these materials to generate large recovery stresses when thermally activated has been recently used for the development of functional structures or composites, in which sma elements are embedded in a polymeric matrix [6-10]. several authors have proposed polymer-composite actuators with sma strips or wires embedded in different polymeric matrices in order to improve mechanical and failure behaviour, fatigue resistance and functionality [11-15]. in particular, thairi et al. [16] and winzek et al. [17] studied the difference s m. merlin et alii, frattura ed integrità strutturale, 31 (2015) 127-137; doi: 10.3221/igf-esis.31.10 128 between the phase transition temperature of the sma and the glass transition temperature of the polymer. barrett [18] developed a low stiffness active composite in which sma filaments are embedded in a silicone matrix to be used for biomedical, surgical and prosthetic applications. according to the specific application, the choice of the suitable matrix and the chemical composition of the shape memory alloy are of great importance. functional composites, also called smart composites, take advantage of the adhesion between the active elements, in the form of sma wires or thin strips, and the matrix. in literature, many works deal with the transformational behaviour of pre-strained niti wires in the martensitic phase (at t<mf) embedded in a polymeric matrix. the mechanical properties of smart composites strongly depend on the efficiency of stress and strain transfer at the interface between the wires and the surrounding matrix. a great number of analytical, numerical and experimental studies of sma fibre reinforced composites have been conducted. james and lagoudas [19] evaluated the thermo-mechanical response of sma hybrid composites subjected to combine thermal and mechanical loads using a finite element method. wang and hu [20] studied the stress transfer for an sma fibre embedded in an elastic matrix by means of pull-out tests. alternative theoretical methods extensively used to analyse the stress transfer in a single fibre reinforced composite are based on the shear-lag model. liu et al. [21] found that the shear stress in the matrix and poisson's ratio significantly influence the stress transfer between the fibre and matrix. hsueh [22] also indicated that the radial stress and poisson's ratio cannot be ignored when investigating stress distribution in composite materials. wang et al. [23, 24] have developed a new theoretical model incorporating brinson's constitutive law of smas for the prediction of internal stress, based on the principle of minimum complementary energy. the authors demonstrated that the new model is more general and reasonable than the classic shear-lag model. the obtained results highlighted a substantial variation in the stress distribution profile for different activation and loading conditions. moreover, the maximum interfacial shear was located near the ends of the composite; the maximum axial stress on the fibre appeared at the midpoint of the fibre embedded length. it is well known that the performance of sma fibres is strongly affected by a weak fibre-matrix interfacial adhesion. in this way, adhesion quality must be improved in order to avoid degradation or premature failure of the actuation response. over the years, laser, excimer laser and laser gas nitriding treatments have been employed [25-30]. the melting process induced by the laser treatments allows for better homogenisation of the morphology and composition of the surface. recent works have highlighted that an improvement in interfacial adhesion can be achieved through mechanical abrasion and chemical passivation, obtained by acid solutions of the surfaces of the sma wires [31, 32]. both these methods increase the superficial roughness of the active elements. the chemical etching produces oxide layers that lead to a reduction in the alloy volume that displays the shape memory effect. moreover, failure could occur at the interface between the oxide layers and the polymeric matrix. interesting treatment methods to improve surface properties of niti alloys are plasma immersion and ion implantation [33, 34]. mechanical polishing followed by a plasma treatment and then the application of a coupling agent followed by a second plasma treatment are able to realise good adhesion between a niti wire and an epoxy matrix [35]. smith et al. [36] proposed functionalising the surface of the niti wires by using silane coupling agents. an improvement of roughly 100% in adhesion was realised as compared to untreated samples or samples functionalised with an unreactive silane coupling agent. several test methods, such as push-out and fragmentation tests have been developed to characterise the wire-matrix interface. however, an important test method widely used to investigate interfacial adhesion quality, interfacial properties and elastic stress transfer between fibres and matrix is the pull-out test [37, 38]. it should be noted that shear stress is related to the position in the embedded length and the debonding starts before the force reaches the maximum value [39]. poon et al. [40] investigated the interfacial bonding behaviour of sma composites using the fracture mechanics theory and considering the conditions of external loading acting on the sma fibre. the sem observations performed by lau et al. [13] showed that failure occurred when the pre-strain in the sma fibre and the actuation temperature are sufficiently high. damage was preferentially localised at the fibre embedded end. the goal of this paper is to investigate the performance of different surface treatments carried out on niti shape memory wires embedded in two polymeric matrices in order to improve interfacial adhesion. in particular, chemical etching by acid solutions and chemical bonding with a silane coupling agent have been evaluated. the matrices have been chosen from thermosetting resins: polyester and vinylester resins. specific pull-out samples have been realised and tested in order to compare the quality of the different surface treatments performed on wires embedded in the polymeric matrices. based on the best results of pull-out tests, the debonding induced by the strain recovery of niti wires has been evaluated with the wires being subjected to different surface treatment conditions and embedded in the polyester resin. the experimental characterisation aims to verify whether the increase in interfacial adhesion due to the modification of the alloy of the surface may be tailored for the design of hybrid composite devices. m. merlin et alii, frattura ed integrità strutturale, 31 (2015) 127-137; doi: 10.3221/igf-esis.31.10 129 materials and methods materials commercially available ti-50.7at% niti alloy wire of 0.5 mm in diameter has been used. several wires of 100 mm in length have been heated at af + 50°c for 20 minutes in a furnace with an uncontrolled atmosphere and then cooled in air, in order to recover the wires initial pre-strain. after heating, the transformation temperatures (ttrs) and the latent heats per unit mass of the alloy have been evaluated by the differential scanning calorimetry (dsc) technique. the dsc sample has been heated and cooled at a constant rate of 10 °c/min in the range of the martensiteaustenite phase changes. the ttrs have been calculated by means of the tangent method (astm f2004) and the main results are collected in tab. 1. mf [°c] ms [°c] as [°c] af [°c] ∆hm [j/g] ∆ha [j/g] 60.00 75.70 93.67 112.00 26.83 26.19 table 1: transformation temperatures and latent heats per unit mass of the niti wire. the wires have been subjected to three different surface treatments, as explained in the following paragraph, and then embedded in the two thermosetting polyester (pe) with a 30%-styrene content and vinylester (ve) commercial resins. the resins need to be cured to complete the polymerisation and to give the suitable mechanical properties. the niti wires must be embedded in the resins before the curing heat treatment. in order to avoid the phase transformation of the niti alloy, a cure temperature lower than the as temperature should be chosen. accordingly, samples in pe and ve resins have been cured at 90 °c for 2 h and the glass transition temperature (tg) of the post-cured resins have been evaluated through dsc measurements. the collected tg values are 127 °c and 114 °c for pe and ve resin, respectively. surface treatments different surface treatments have been performed on the niti wires without removing the external oxide layer. the first one, called a, corresponds to a chemical etching in a 40%hno3 water solution for 30 min, whereas the second treatment, called ab, is a chemical etching in a 5%hno3 + 15%hf water solution for 20 s. finally, the third one, called s, is the immersion in a polydimethylsiloxane coupling agent for 2 h. these three surface treatments have been compared with the wire, called nt, just heated to recover the initial pre-strain and subsequently cleaned in a methanol solution. the different analysed surface conditions are summarised in tab. 2. finally, the morphology of the surface of the wires has been observed and analysed by a zeiss evo ma15 scanning electron microscope (sem) equipped with an energy dispersive spectroscopy (eds) microprobe. surface treatment description nt no surface treatment a chemical etching in a 40%hno3 water solution for 30 min ab chemical etching in a 5%hno3 + 15%hf water solution for 20 s s immersion in a polydimethylsiloxane coupling agent for 2 h table 2: summary of the surface treatments. pull-out tests pull-out tests have been carried out in order to evaluate the interfacial adhesion between the two polymeric matrices and the niti wires in the different surface conditions. the dimensions of the pull-out samples are depicted in fig. 1a; in particular, for each sample the wire has been embedded in a 20 mm high cylindrical specimen with a diameter of 10 mm. a m. merlin et alii, frattura ed integrità strutturale, 31 (2015) 127-137; doi: 10.3221/igf-esis.31.10 130 as can be noted in fig. 1b, a specific cylindrical teflon mould, which consists of three parts, has been designed in order to realise the pull-out samples. a polymeric wax has been applied on the internal walls of the mould to prevent the resin from sticking during polymerisation and to allow the samples to be extracted. the pull-out tests have been carried out by means of an instron 4467 tensile machine with a speed rate of 1 mm/min at room temperature. the gauge length of the wire during the pull-out tests was 70 mm. (a) (b) figure 1: (a) schematic view of the polymeric cylinder with an embedded sma wire; (b) designed teflon mould and pull-out sample. strain recovery tests considering the best results of the pull-out tests obtained with the pe resin, three wires for each surface treatment condition have been pre-strained by the instron 4467 tensile machine at 4%, 5% and 6%, respectively. then the prestrained wires have been embedded in the pe resin by means of the same procedure employed for the pull-out samples. in order to achieve a statistically significant sampling, each polymeric cylinder has been transversely sectioned into discs by means of a micro cutting-off machine. the wheel speed of 3000 rpm has been selected to avoid the degradation of the polymer/wire interfaces and to prevent the wire from overheating up to the as transformation temperature. five specimens of 2 mm in thickness for each surface treatment condition and pre-strained level have been obtained. the samples have been placed into an oven for 10 min at the temperature of 120 °c, which is slightly higher than the af transformation temperature. considering the experimental bias in the determination of ttrs by the tangent method in dsc analyses, this temperature has been chosen in order to achieve the complete reverse martensitic transformation upon heating; moreover, the surface temperature of the samples has been continuously measured by using a k-type thermocouple to avoid reaching the tg of pe resin. during the heating process, the wire tries to recover its initial prestrain so that the pe resin capability of remaining well bonded to the sma wire can be studied. finally, the interfacial adhesion before and after the strain recovery tests has been investigated by means of electron microscopy. results and discussion n general, a typical pull-out curve can be divided into two regions. the first is characterised by a pre-fracture straining of the interface, in which the applied load increases due to the deformation of the free length of the wire. the force increases until the interface fracture occurs, causing the wire inside the composite to slip. in some cases, the debonding generates a sudden drop in force close to zero, while in others the post-fracture region begins. in this second region the force can settle down into a lower fairly constant level or can rapidly oscillate around a mean value due to a stick-slip behaviour until the wire completely pulls out [32]. many theoretical studies [37, 38, 41] showed that the niticomposite interface fails with a typical brittle process and that interfacial bonding can be evaluated following two different criteria. the first is based on the assumption that debonding occurs when the shear stress at the interface exceeds the interfacial shear resistance. the second one suggests that the crack initiates at the point of wire entry due to accumulated strain; then the crack propagates until the complete debonding of the interface, according to brittle fracture propagation theory. i m. merlin et alii, frattura ed integrità strutturale, 31 (2015) 127-137; doi: 10.3221/igf-esis.31.10 131 (a) (b) (c) figure 2: pull-out curves for (a) ve_nt, ve_a and ve_ab samples, (b) pe_nt, pe_a and pe_ab samples, (c) ve_s and pe_s samples. fig. 2 depicts the results obtained from the pull-out tests performed on the samples, in which the niti wires subjected to different surface treatments are embedded in the two pe and ve resins. in particular, fig. 2a shows the curves related to the pull-out samples realised with ve resin and in the surface conditions of the nt, a and ab wires. fig. 2b shows the results of the pull-out tests for the pe resin with embedded wires in the nt, a and ab surface conditions. the pull-out curves of the samples in ve and pe resin with wires functionalised with the silane coupling agent are compared in fig. 2c. in fig. 2 it should be noted that the cutting-off of the pull-out curves corresponding to the sudden drop to the quasi-zero load level is marked with a short vertical solid line. as can be seen, all curves present a small plateau of 0.2-0.3 mm in correspondence to an applied force of ≈15-20 n. this plateau should be compared with the one observed in fig. 3, which reports the engineering stress-strain curve of the same free heated niti wire. therefore, in this initial region of the pull-out test the curve reproduces only the stress-strain behaviour of the free length wire. figure 3: engineering stress-strain curve for the heated niti wire. m. merlin et alii, frattura ed integrità strutturale, 31 (2015) 127-137; doi: 10.3221/igf-esis.31.10 132 in fig. 2a it can be observed that the debonding suddenly occurs after less than 1 mm of displacement with a load value lower than the level necessary to produce the detwinning of the martensitic phase: the pe resin with a no surfacetreatment wire embedded into it also shows the same behaviour (fig. 2b). in contrast, after the small initial plateau in the pe_a and pe_ab samples the load further increases and reaches a level sufficient to induce the martensitic twinning rearrangement of the free length wire. this is in good agreement with the engineering stress-strain curve of the free wire previously heated in order to remove any pre-strain (fig. 3). in the case of the pe_ab sample the load at which the interface failure occurs is greater than the load at which the phase transformation takes place. the pull-out curves for the samples functionalised with the silane coupling agent (fig. 2c) show that the load levels reached by the pe_e and ve_s samples after the martensitic plateau are greater than that reached by the pe_ab sample. moreover, in all the other samples the force drops close to zero after the failure of the interface, while in the ve_s and pe_s samples the force suddenly drops and settles down to a lower value. assuming that at this load level the wire starts to slip inside the composite, the applied load could now be related to the friction acting at the polymer/wire interface. for the pe_s sample this value is close to the peak load value, while for the ve_s sample the actual load level is similar to the detwinning plateau load. by analysing the curves of fig. 2b, but also of fig. 2c, another alternative consideration can be drawn. the rise of the load after the detwinning plateau begins at a level of displacement lower than the onset of the elastic deformation of the detwinned martensite for the free wire (≈ 8%). the increase in load starting at a level of displacement less than 8% could be justified considering that, after the detwinning of the free length of the wire, the detwinning of the embedded length is partially constrained by the polymeric matrix. in the case of the pe_a sample this could be an indication that interface failure occurs before the beginning of the martensitic reorientation of the embedded length of the wire because the adhesion is not strong enough to support the increase of the load. several approaches may be used to explain the peculiar patterns in fig. 2. in agreement with [41, 42], analysis of the loaddisplacement curve enables two different interfacial failure mechanisms to be distinguished. when the interfacial failure occurs without friction acting on the interface, the load-displacement curve increases concave-up prior to the peak load values, corresponding to the interfacial fracture (all cases of fig. 2a and pe_nt plus pe_ab in fig. 2b). moreover, the quasi-zero pffp ("post-fractures friction pull-out") load levels should be a further indication that frictional shear forces do not act on the already debonded wire before the failure of the interface. accordingly, when the frictional shear force acting on the already debonded wire is present, the load increases with a decreasing slope (concave-down) as it approaches the peak load values (pe_ab in fig. 2b and all cases of fig. 2c). however, it should be noted in fig. 2c that in the case of pe_s samples the slope is smaller than the values collected for ve_s specimens and the pffp load levels are close to the peak load value. such behaviour could indicate much more mechanical interactions and not just friction between the niti wire and polymeric matrix. after debonding, particles of wire and/or resin may cause a wedging action that increases the interface friction; thus, the interfacial contact pressure increases which requires additional shrinkage of the wire to pull itself away from the matrix [41]. according to several authors [20, 23, 24] a more adequate approach to the description of the pull-out curves must take into account that several simultaneous processes occur in the specimens in the case of good adhesion (fig. 2c). when large forces are applied to the wire, at least three regions can be considered at the interface: (i) the region where the tensile stress in the wire is small and phase transformation has still not occurred (far from the loaded wire end); (ii) the region in which phase transformation has just taken place (in the middle of the embedded wire length); (iii) the region in which phase transformation is already completed (near the loaded end). it can be noted that, taking into account the interfacial debonding in the pull-out process, the interfacial crack tip (depending on interfacial adhesion and applied load, it can be localised in any of these regions) and the already debonded regions with interfacial friction between the wire and the matrix should also be included. with regards to the shapes of the “tails” in fig. 2c, they can also be due to the fact that the phase transformation region moves along the interface. the difference between the two curves in fig. 2c could result, in turn, from the fact that if the interfacial adhesion for the two specimens is different, then the size and location of the phase transformation regions may also be different. in particular, chang et al. [43] demonstrated that at a relatively high loading rate or in a thermally insulating environment phase transformation involves several nucleation sites and more transformation fronts that will propagate away from one another. the force levels for pulling the functionalised actuators out of the resins can provide useful information about the nature of the adhesion between the niti wires and the ve and pe polymeric matrices. paine et al. [32] demonstrated that good wettability is a fundamental requirement for the chemical cohesion between the polymeric matrix and the surface of the actuator. accordingly, the less viscous pe resin will be easily spread and wet the surface of the wire with a low contact angle. the highest peak load values exhibited by the functionalised wires (fig. 2c) could also be related to the bridging m. merlin et alii, frattura ed integrità strutturale, 31 (2015) 127-137; doi: 10.3221/igf-esis.31.10 133 action caused by the silane coupling agent. the silane is able to covalently attach itself to both a metal oxide surface through a silicon-chlorine or silicon-methoxy bond and the propagating polymer chain. smith et al. [36] proved that the chemical binding to the matrix rather than polymer chain entanglement is the cause of the roughly 100% relative increased adhesion and the higher shear stress strength. another way to enhance interfacial adhesion between the actuator and the resin is by physical adhesion through mechanical interaction. if the surface of the niti wire is made rougher by sandblasting or chemical etching, for example, a polymer of low viscosity can fill the crevices and form mechanical projection that hinders the pull-out of the wire. fig. 4 shows sem micrographs of the surfaces of the wires after the different surface treatment conditions. the sem micrograph for the functionalised wires is not reported since the modification of the surface chemistry does not alter the surface topology of the constituent. based on the peak load levels in fig. 2a and b, the more viscous ve resin suffers in comparison with the pe resin in this aspect of adhesion as well. for rough surfaces (fig. 4b and c) the mechanical interaction with the polymeric matrix is increased as well as the interfacial adhesion and the peak load levels (ve_a, pe_a and much more ve_ab plus pe_ab in fig. 2a and b); in contrast, for smooth surfaces (fig. 4a), if poor mechanical interaction is present the bond strength is completely dependent on the intermolecular attraction based on hydrogen or van der waals bonds, which could be occurred [32]. figure 4: sem micrographs of the surfaces of the wires for the different surface treatment conditions: (a) nt, (b) a and (c) ab samples, respectively. (red arrow indicates the main direction of the wire). for the same four different surface treatment conditions, the sem analysis of the pe/wire interfaces before the strain recovery tests highlighted around a 10 μm-thick native oxide layer interposed between the polymer and metal surfaces (fig. 5). in fig. 5a the native oxide resulting from the oxidation reactions occurring during the heating of the wire is evident. according to rossi et al. [44] the eds analyses performed at the native oxide/metal alloy interface (yellow arrow in fig. 5a) confirmed the titanium depletion in the outer surface of the alloy and the consequent nickel enrichment due to the outward migration of the titanium to form the oxide layer. the increased roughness of the native oxide caused by the chemical etching treatments should be noted in fig. 5b and c. the sem observations are consistent with the demonstrated improvement in both physical adhesion and interfacial adhesion due to the mechanical interaction between the wire and the polymer matrix. it is well known that native oxides usually enhance the interfacial adhesion because of their higher roughness; however, several studies highlighted that they m. merlin et alii, frattura ed integrità strutturale, 31 (2015) 127-137; doi: 10.3221/igf-esis.31.10 134 may also show two drawbacks: reduction of the niti alloy volume that displays shape memory effect and debonding from the matrix when the de-cohesive failure of the oxide occurs [44, 45]. as previously highlighted, the modification of the surface chemistry does not alter the surface topology of the wire. accordingly, the sem micrograph for the wire functionalised with the silane coupling agent is not reported since the appearance of the pe/wire interface is comparable to the pe/wire interface observed for the untreated sample. figure 5: sem micrographs of the pe/wire interfaces before the strain recovery tests: (a) nt, (b) a and (c) ab samples, respectively. (r = resin, no = native oxide and a = alloy). with regard to the interfacial adhesion after the strain recovery tests, the debonding of the wires pre-strained at 5% and 6% are observed for all the polymer/wire interfaces considered. the strain recovery action of the embedded wires produces high interfacial stresses that cause debonding at the end of the bonded region. no evidence of radial cracks in the polymeric matrix is observed. similarly, debonding occurs for the wires pre-strained at 4% whether or not they were chemical treated. at this pre-strain level both untreated and etched in the 40%hno3 water solution, wires do not show the development of radial cracking on the resin surface (fig. 6a). conversely, some cracks appear at the polymer/wire interface in samples with wires etched in the 5%hno3 + 15%hf water solution (fig. 6b). for the functionalised wires, even if the wire is debonded from the matrix, many radial cracks are evident (fig. 6c), meaning it is the highest stress transfer between wire and matrix when compared to the previous surface treatment conditions. several authors [13, 46, 47] have demonstrated that the development of radial shear cracks is related to the residual stresses caused by thermal cycling. moreover, stresses acting at the interface are strongly dependent on the phase transformation that occurs during heating above af and the subsequent cooling down. the thermal mismatch between the embedded sma wire and the surrounding matrix produces high tensile stresses at the end of the bonded region that can lead to the matrix cracking in the radial direction. the higher the pre-strain level, the heavier the stress will be. however, lower magnitude of the increasing stress is reported in the case of an sma wire embedded in carbon or kevlar composites, since these functional structures give negative thermal strain with increasing temperature. finally, it can be demonstrated that the use of pe resin in a smart composite may produce an increase of 60% in the tensile stress at the beginning of the recovery thanks to the increased thermal expansion coefficient of polyester [46]. m. merlin et alii, frattura ed integrità strutturale, 31 (2015) 127-137; doi: 10.3221/igf-esis.31.10 135 figure 6: sem micrographs of the pe/wire interfaces after the strain recovery tests for wires pre-strained at 4%. (a) a and (b) ab samples, respectively; (c) wire functionalised with the silane coupling agent. conclusions ased on the results obtained regarding improved adhesion of niti wires embedded in polyester (pe) and vinylester (ve) resins, the following conclusions can be drawn:  pull-out tests prove the better adhesion between the niti wires and the pe resin. the highest interfacial adhesion is obtained by the functionalisation of the surfaces of the wires with a silane coupling agent.  the physical adhesion between the pe resin and both untreated and chemical etched wires is confirmed. in particular, it is demonstrated by electron microscopy analysis that the adhesion is a result of mechanical interactions due to the increased roughness of the native oxide caused by the chemical etching treatments. conversely, for the functionalised wires chemical adhesion is promoted by the chemical binding of the silane to the resin. cohesion is also enhanced by the good wettability between the polymeric matrix and the surface of the actuator.  the strain recovery tests indicate early debonding of the wires pre-strained at 5% and 6% for all the pe/wire interfaces considered. in the case of wires pre-strained at 4%, radial shear cracks on the resin surface are observed by sem for wires both functionalised and etched in a 5%hno3 + 15%hf water solution. the thermal mismatch between the embedded sma wire and the surrounding matrix produces high tensile stress at the end of the bonded region that can lead to the matrix cracking in the radial direction. references [1] otsuka, k., wayman, c.m., shape memory materials, cambridge university press, cambridge, (1998). [2] lagoudas, d.c., tadjbakhsh, i.g., active flexible rods with embedded sma fibers, smart mater. struct., 1 (1992) 162-167. b m. merlin et alii, frattura ed integrità strutturale, 31 (2015) 127-137; doi: 10.3221/igf-esis.31.10 136 [3] rocher, p., el medawa, l., hornez, j.-c., traisnel, m., breme, j., hildebrand, h.f., biocorrosion and cytocompatibility assessment of niti shape memory alloys, scripta mater., 50 (2004) 255-260. [4] chen, m.f., yang, x.j., liu, y., zhu, s.l., cui, z.d., man, h.c., study on the formation of an apatite layer on niti shape memory alloy using a chemical treatment method, surf. coat. tech., 173 (2003) 229-234. [5] trigwell, s., hayden, r.d., nelson, k.f., selvaduray, g., effects of surface treatment on the surface chemistry of niti alloy for biomedical applications, surf. interface anal., 26 (1998) 483-489. [6] wei, z.g., sandström, r., miyazaki, s., review. shape-memory materials and hybrid composites for smart systems. part i shape-memory materials, j. mater. sci., 33 (1998) 3743-3762. [7] wei, z.g., sandström, r., miyazaki, s., review. shape-memory materials and hybrid composites for smart systems. part ii shape-memory hybrid composites, j. mater. sci., 33 (1998) 3763-3783. [8] hebda, d.a., whitlock, m.e., ditman, j.b., white, s.r., manufacturing of adaptive graphite/epoxy structures with embedded nitinol wires, j. intel. mat. syst. str., 6 (1995) 220-228. [9] tsoi, k.a., stalmans, r., schrooten, j., transformational behaviour of constrained shape memory alloys, acta mater., 50 (2002) 3535-3544. [10] jang, b.k., kishi, t., adhesive strength between tini fibers embedded in cfrp composites, mater. lett., 59 (2005) 1338-1341. [11] kim, c., a smart polymer composite actuator with thin sma strips, int. j. mod. phys. b, 20 (2006) 3733-3738. [12] murasawa, g., tohgo, k., ishii, h., deformation behavior of niti/polymer shape memory alloy composites experimental verifications, j. compos. mater., 38 (2004) 399-416. [13] lau, k.-t., chan, a.w.-l., shi, s.-q., zhou, l.m., debond induced by strain recovery of an embedded niti wire at a niti-epoxy interface: micro-scale observation, mater. des., 23 (2002) 265-270. [14] merlin, m., soffritti, c., fortini, a., study of the heat treatment of niti shape memory alloy strips for the realisation of adaptive deformable structures, metallurgia italiana, 103 (2011) 17-21. [15] rizzoni, r., merlin, m., casari, d., shape recovery behaviour of niti strips in bending: experiments and modelling, cont. mech. therm., 25 (2013) 207-227. [16] tahiri, v.-l., patoor, e., eberhardt, a., an analysis of the thermomechanical behaviour of a shape memory alloy/elastomer composite, j. phys. iv, 115 (2004) 195-203. [17] winzek, b., sterzl, t., rumpf, h., quandt, e., composites of different shape memory alloys and polymers for complex actuator motions, j. phys. iv, 112 (2003) 1163-1168. [18] barrett, r., gross, r.s., super-active shape-memory alloy composites, smart mater. struct., 5 (1996) 255-260. [19] james, g.b., lagoudas, d.c., thermomechanical response of shape memory composites, j. intel. mat. syst. str., 5 (1994) 333-346. [20] wang, x., hu, g., stress transfer for a sma fibre pulled out from an elastic matrix and related bridging effect, compos. part a-appl. sci. manuf., 36 (2005) 1142-1151. [21] liu, p.f., yu, x.z., guo, y.m., tao, w.m., interface debonding criteria in sic fiber-reinforced composites, j. zhejiang univ. (eng. sci.), 40 (2006) 1883-1888. [22] hsueh, c.-h., stress transfer from axially loaded fiber to matrix in a microcomposite, in: proceedings of materials research society symposium, pittsburgh, (1995) 217-227. [23] wang, y., zhou, l., wang, z., huang, h., ye, l., stress distributions in single shape memory alloy fiber composites, mater. design, 32 (2011) 3783-3789. [24] wang, y., zhou, l., wang, z., huang, h., ye, l., analysis of internal stresses induced by strain recovery in a single sma fiber-matrix composite, compos. part b-eng., 42 (2011) 1135-1143. [25] man, h.c., ho, k.l., cui, z.d., laser surface alloying of niti shape memory alloy with mo for hardness improvement and reduction of ni2+ ion release, surf. coat. tech., 200 (2006) 4612-4618. [26] cui, z.d., man, h.c., yang, x.j., the corrosion and nickel release behavior of laser surface-melted niti shape memory alloy in hanks' solution, surf. coat. tech., 192 (2005) 347-353. [27] villermaux, f., tabrizian, m., yahia, l'h., meunier, m., piron, d.l., excimer laser treatment of niti shape memory alloy biomaterials, appl. surf. sci., 109-110 (1997) 62-66. [28] cui, z.d., man, h.c., yang, x.j., characterization of the laser gas nitrided surface of niti shape memory alloy, appl. surf. sci., 208-209 (2003) 388-393. [29] man, h.c., zhao, n.q., phase transformation characteristics of laser gas nitrided niti shape memory alloy, surf. coat. tech., 200 (2006) 5598-5605. [30] man, h.c., zhao, n.q., enhancing the adhesive bonding strength of niti shape memory alloys by laser gas nitriding and selective etching, appl. surf. sci., 253 (2006) 1595-1600. m. merlin et alii, frattura ed integrità strutturale, 31 (2015) 127-137; doi: 10.3221/igf-esis.31.10 137 [31] jonnalagadda, k., kline, g.e., sottos, n.r., local displacements and load transfer in shape memory alloy composites, exp. mech., 37 (1997) 78-86. [32] paine, j.s.n., jones, w.m., rogers, c.a., nitinol actuator to host composite interfacial adhesion in adaptive hybrid composites, in: proceedings of 33rd structures, structural dynamics and materials conference, dallas, (1992) 556565. [33] ju, x., dong, h., plasma surface modification of niti shape memory alloy, surf. coat. tech., 201 (2006) 1542-1547. [34] poon, r.w.y., yeung, k.w.k., liu, x.y., chu, p.k., chung, c.y., lu, w.w., cheung, k.m.c., chan, d., carbon plasma immersion ion implantation of nickel-titanium shape memory alloys, biomaterials, 26 (2005) 2265-2272. [35] neuking, k., abu-zarifa, a., eggeler, g., surface engineering of shape memory alloy/polymer-composites: improvement of the adhesion between polymers and pseudoelastic shape memory alloys, mater. sci. eng. a, 481-482 (2008) 606-611. [36] smith, n.a., antoun, g.g., ellis, a.b., crone, w.c., improved adhesion between nickel-titanium shape memory alloy and a polymer matrix via silane coupling agents, compos. part a-appl. sci. manuf. 35 (2004) 1307-1312. [37] zhou, l.-m., kim, j.-k., mai, y.-w., interfacial debonding and fibre pull-out stresses. part ii a new model based on the fracture mechanics approach, j. mater. sci., 27 (1992) 3155-3166. [38] zhou, l.-m., mai, y.-w., baillie, c., interfacial debonding and fiber pull-out stresses. part v a methodology for evaluation of interfacial properties, j. mater. sci., 29 (1994) 5541-5550. [39] fu, s.-y., yue, c.-y., hu, x., mai, y.w., analyses of the micromechanics of stress transfer in single-and multi-fibre pull-out tests, compos. sci. technol., 60 (2000) 569-579. [40] poon, c.k., zhou, l.m., jin, w., shi, s.q., interfacial debond of sma composites, smart mater. struct., 14 (2004) 2937. [41] paine, j.s.n., rogers, c.a., characterization of interfacial shear strength between sma actuators and host composite material in adaptive composite material systems, in: adaptive structures and material systems asme, ad-35, new york, (1993) 63-70. [42] piggott, m.r., failure processes in the fibre-polymer interphase, compos. sci. technol., 42 (1991) 57-76. [43] chang, b.-c., shaw, j.-a., iadicola, m.a., thermodynamics of shape memory alloy wire: modeling, experiments, and application, continuum mech. thermodyn., 18 (2006) 83–118. [44] rossi, s., deflorian, f., pegoretti, a., d’orazio, d., gialanella, s., chemical and mechanical treatments to improve the surface properties of shape memory niti wires, surf. coat. tech., 202 (2008) 2214-2222. [45] kinloch, a.j., adhesion and adhesives: science and technology, chapman & hall, london, (1987). [46] berman, j.b., white, s.r., theoretical modelling of residual and transformational stresses in sma composites, smart mater. struct., 5 (1996) 731-743. [47] poon, c.-k., lau, k.-t., zhou, l.-m., design of pull-out stresses for prestrained sma wire/polymer hybrid composites, compos. part b-eng., 36 (2005) 25-31. microsoft word numero_30_art_70 a. de iorio et alii, frattura ed integrità strutturale, 30 (2014) 593-601; doi: 10.3221/igf-esis.30.70 593 transverse strength of railway tracks: part 3. multiple scenarios test field antonio de iorio polytechnic school of basic sciences, federico ii university, naples, italy marzio grasso, francesco penta, giovanni pio pucillo, vincenzo rosiello dii department of industrial engineering, federico ii university, naples, italy stefano lisi, stefano rossi, mario testa rfi italian state railways, rome, italy abstract. in the present paper the design and construction choices of a test field for the ballast lateral resistance measurement, in order to produce data useful for the development of a numerical model able to simulate the service critical conditions of a continuous welded rail track, are described. some construction details described herein allow to better understand the methodological approach followed in the design of experiments, the tests management philosophy as well as of the accuracy achieved in their implementation. keywords. ballast resistance; track stability; full scale test; cwr track; railway track; railway scenarios simulation; test field. introduction he analytical and/or numerical determination of the resistance opposed by the ballast to the track displacement due to mechanical and/or thermal loading transmitted or induced by the continuous welded rail (cwr) is a quite complex task. also, it is necessary to have more reliable data of such resistance for the determination of the service critical conditions of railway lines. thus, in order to achieve the aforementioned objectives, the use of full scale experimentation, in line or in laboratory, using track sections is unavoidable. usually, the ballast overall resistance is intended or evaluated as the sum of the three components along the track main directions, both for practical reasons and their easily applicability to any scenario, as well as because sometimes one or more components are used for partial or specific characterizations of the track. in most cases the following constituents are reported in literature: vertical resistance or bearing capacity; longitudinal resistance; lateral displacement resistance. the attention is mainly focused on this latter, due to the role played by the scenarios having the purpose to ensure the stability of the track in making the design choices. it is well known that the track is composed by: rail, rail fastening system, sleeper, ballast bed and substructures. among the above elements, it has been proved that an important safety margin is offered by the ballast lateral resistance [1-3], which is the weakest element of the track, since it is the first to fail under the action of the loads acting on the rails. the lateral resistance is mainly due to the friction between the lower face of the sleeper and the ballast. however, significant t a. de iorio et alii, frattura ed integrità strutturale, 30 (2014) 593-601; doi: 10.3221/igf-esis.30.70 594 contributions are also given by the ballast at the sleeper head and at lateral sleeper surfaces. besides, the magnitude of such resistance depends on several factors, such as: sleeper weight; sleeper width; sleeper length; twin-block sleeper; friction on the lower sleeper surface; increase of ballast grain size; other ballast constituents; increase of lateral shoulder height; ballast shoulder broadening; ballast bed height below the sleeper; ballast height reduction between sleepers; narrower sleeper spacing; rails moment of inertia; track grid torsion-rigidity; track lifting; tamping; dynamic track stabilization; train speeds; increased axle loads; temperature, sleeper anchors and under sleeper pad (usp). therefore, owing to the excessive number of samples to be designed, prepared and tested, the experimental evaluation of the contribution related to each one of these parameters in scenarios which are different among them just for one parameter value becomes practically prohibitive. several institutions have conducted studies regarding the contribution to the resistance provided by the geometric parameters of the track and their evaluation [1, 4-6]. unfortunately, the great part of these studies is incomplete: frequently, the experimental program wasn’t completed [1] or some variables have been estimated rather than measured. also, the tests are rarely repeated; even when they are, the number of repetitions is low and often defined a priori. sometimes, the results are partially withheld (see e.g. [4]). moreover, the data are generally referred to uniform ballast, even if the presence of water pockets [1] or irregularities of any kind alter their behaviour. at the same time, on the basis of these data various models have been developed and numerous software have been implemented to supply with deterministic or probabilistic predictions of the cwr buckling (see e.g. : [2-4, 7-11]). moreover, these data have also been used to establish a buckling probabilistic risk [7, 12-14] by means of risk based approach, which considers, in addition to an event likelihood, the seriousness of its consequences [7]. as a consequence, the models proposed until now are not very robust, if not even negatively affected by the quality of the data used either as input or for their validation. these considerations induced rfi to develop together with the dii a research programme regarding the track stability having as main goal the development of a fe model of the track, which is able to identify the critical service conditions of the continuous welded rail of a pre-defined scenario, on the basis of experimental data to be produced by means of fullscale tests carried out on track sections reproducing a remarkable number of real scenarios [15]. the loading systems and the facilities, which were used during the experimental activities, have been designed and manufactured ad hoc [16] in order to achieve a good reliability of the results. in the present paper, the preliminary activity of the aforementioned programme, developed during the design and construction of a multiple scenarios test field, is described. the multiple scenarios test field is intended as a test campaign on a track composed of predefined scenarios arranged according to a given sequence. this latter has to be compatible with the operative requirements to be used for their construction as well as with the requirements of the test system and the facilities to be used. scenarios definition efore defining the layout of the test field, it was necessary to establish a construction criterion to be used to identify a standard scenario which allows to represent the corresponding real scenario also providing the widest number of useful and reliable data. first of all, it was decided to evaluate the ballast resistance referring to the single sleeper. each test should be repeated at least three or four times under the same conditions, in order to reduce the uncertainty of the result obtained with a test carried out on a single sleeper. moreover, in order to reduce the test duration, it was decided to run all together the three or four equivalent tests, as it is practically done using the discrete cut panel pull test (dcppt). however, the difference with the dcppt is in using a number of independent actuators equal to the number of the sleepers by which the scenario under testing is composed [16]. besides, different scenarios arranged in series, having in common the same short rails were built. this choice was due to economize materials and labour as well as reducing the construction and the operating machines time. to be sure that, during the tests, the displacement of the ballast in the scenario under testing doesn’t alter the compaction of the neighbouring scenario not yet tested, it was decided to insert between two adjacent scenarios one or two “neutral” or “buffer” sleepers, which are not involved in the test. the guidelines useful to define the types of test and their numerousness, needed to evaluate the selected parameters range, have been drawn from the analysis of the data needed to identify the critical service conditions of the track typologies described in the technical specification drawn on purpose by rfi [17] as well as those found in literature the selected parameters are:  type of sleeper;  ballast consolidation; b a. de iorio et alii, frattura ed integrità strutturale, 30 (2014) 593-601; doi: 10.3221/igf-esis.30.70 595  ballast shoulder length;  ballast wall distance from the sleeper head;  ballast shoulder shape;  sleepers anchor type;  cant effect;  ballast height reduction between sleepers for a 2 m section (1 m each side in respect to the track longitudinal axis);  ballast height under sleeper;  applied load;  type of ballast. indeed, the combination of all these parameters would have lead to define an onerous number of scenarios if a minimum of 3÷4 different values were assigned to each parameter. for this reason, it was decided to construct a limited but significant number of scenarios by which it would be possible to develop, on the basis of the collected results, numerical and mathematical models suitable to effectively simulate all the possible scenarios with the parameters values ranging in the respective pre-established variability fields. based on considerations related to either significance or representativeness of given service conditions of the railway network, as well as of scale economy, 28 scenarios, of which the main distinguishing parameters are reported in tab. 1, has been chosen. the first four of them are of immediate interpretation: the compaction, where present, is equivalent to a 80.000 t traffic; the cant is equal to 16 cm; the sleeper anchors are only installed in four scenarios (having 5 sleepers each) either on all the sleepers (each sleeper) or every second sleeper; the load, where present, is equal to 2 t/sleeper. all the scenarios have in common the ballast material and the ballast shoulder dimension. scenario sleeper height under sleeper (cm) ballast wall compaction cant sleeper anchors vertical load 01 rfi 230 30 no no no no no 02 rfi 230 30 no no no no yes 03 rfi 240 30 no no no no yes 04 rfi 240 30 no no no no no 05 rfi 240 30 yes yes no no yes 06 rfi 240 30 yes yes no no no 07 rfi 240 30 no yes no no no 08 rfi 240 30 no yes no no yes 09 rfi 230 30 no yes no no no 10 rfi 230 30 no yes no no yes 11 rfi 230 60 yes yes no no no 12 rfi 230 60 yes yes no no yes 13 rfi 230 60 no yes no no no 14 rfi 230 60 no yes no no yes 15 rfi 240 60 no yes no no no 16 rfi 240 60 no yes no no yes 17 rfi 240 60 no no no no no 18 rfi 240 60 no no no no yes 19 rfi 230 60 no no no no no 20 rfi 230 60 no no no no yes 21 rfi 230 60 no no yes no yes 22 rfi 230 60 no no yes no no 23 rfi 230 60 no yes yes no no 24 rfi 230 60 no yes yes no yes 25 rfi 230 30 no yes no each sleeper yes 26 rfi 230 30 no yes no each sleeper no 27 rfi 230 30 no yes no every two l no 28 rfi 230 30 no yes no every two l yes table 1: combination of parameters characterizing the scenarios chosen for the experiment. a. de iorio et alii, frattura ed integrità strutturale, 30 (2014) 593-601; doi: 10.3221/igf-esis.30.70 596 in the construction of the test field the sequence shown in fig. 1, which has been considered the less expensive among the possible ones, has been used.     transition zone. l=15m transitio n zone. l=15m ul l ul l ul l ul l ul l ul l ul l ul l ul l ul l ul l ul l ul l ul l r f i 2 3 0 r f i 2 3 0 r f i 2 4 0 r f i 2 4 0 r f i 2 4 0 r f i 2 4 0 r f i 2 4 0 r f i 2 3 0 r f i 2 3 0 r f i 2 3 0 r f i 2 3 0 r f i 2 3 0 r f i 2 3 0 r f i 2 3 0 r f i 2 3 0 r f i 2 3 0 r f i 2 3 0 r f i 2 3 0 r f i 2 4 0 r f i 2 4 0 r f i 2 4 0 r f i 2 4 0 r f i 2 4 0 r f i 2 4 0 r f i 2 4 0 r f i 2 3 0 r f i 2 3 0 r f i 2 3 0 r f i 2 3 0 r f i 2 3 0 r f i 2 3 0 r f i 2 3 0 ul: unloaded track panel. l: loaded track panel (2 t/sleeper). 60 cm ballast thickness dts consolidated ballast bed 60 cm ballast should er de-consolidated ballast bed canted track with minimum ballast thikness of 60 cm ballast retaining wall 60 cm apart from the sleeper end transition ramp (l=15m) for canted track 60 cm ballast shouldern . 1 0 b u ff e r s le e p e rs dts consolidated ballast bed ballast retaining wall 60 cm apart from the sleeper end transition ramp. l=15m 60 cm ballast shoulder. sleeper anchors installed on all the sleepers 60 cm ballast shoulder track panel with n. 5 ties 60 cm ballast shoulder 60 cm ballast shoulder. sleeper anchors installed every second sleeper de-consolidated ballast bed dts consolidated ballast bed test field in/out 30 cm ballast thickness test field in/out n . 2 b u ff e r sl e e p e rs n . 2 b u ff e r sl e e p e rs n . 2 b u ff e r sl e e p e rs 60 cm ballast shoulder   figure 1: layout of the test field. test field construction or the construction of the test field , it has been used an area of the campi flegrei railway station (fig. 2) in naples (italy), removing a section of roughly 200 m of two old adjacent tracks and rebuilding a new one having the characteristics defined in the design of the 28 scenarios under testing.     figure 2: top view of the selected site. once the permanent way has been removed for roughly 200 m, it has been carried out an excavation to eliminate the ballast and the old tracks residuals up to a depth compatible with the level of the new track test which has to be roughly 10 cm above the level of the adjacent track to be used to create the fixed point for the test system. the excavation width is such that there is no interference between the new track profile and the excavation shoulders, neither during the construction phase nor in the following experimental activities. the subgrade composed by pozzolana has been levelled by the bulldozed and compacted by the roller, checking continuously the depth of the entire excavation for the total length (fig. 3). for laying the sleepers, longitudinal references along the test field in the area between the two rails of the new track have been used. on the basis of the aforementioned references, the rails have been marked in correspondence of the points where to place the buffer sleepers. once the buffer sleepers were positioned in the said space and in the pre-established order, all the other sleepers have been positioned (fig. 4) according to the layout. once the sleepers were laid and spaced at 60 cm, the two rails have been laid on them, tightening the fastening systems (fig. 5). tightening has been performed by a hydraulic rail coupling shears, applying a torque equal to 240 mn. the sleepers forming the scenarios were equipped with vossloh w 14 fastening system, while, for the intermediate sleepers fs–v–35, the k fastening system have been used. f a. de iorio et alii, frattura ed integrità strutturale, 30 (2014) 593-601; doi: 10.3221/igf-esis.30.70 597 after the sleepers positioning and the fastening system tightening, the ballast has been laid (fig. 6, left) and subsequently settled using the tamping machine, which lifts the track for packing the ballast under the sleepers. also, during the lifting, the driver controls the position of the rails using the “telescope”, assigning the lateral movement to the rails, which is needed in order to ensure the required alignment, by means of a hydraulic system. the final height has been reached by lifting the track step by step.     figure 3: excavation for the construction of the test track on the chosen site.          figure 4: positioning of buffer sleepers (left) and other sleepers according to the layout (right).     figure 5: rails fastened on the sleepers. a. de iorio et alii, frattura ed integrità strutturale, 30 (2014) 593-601; doi: 10.3221/igf-esis.30.70 598       figure 6: deposition of the ballast (left) and removing of the excess (right). during the ballast deposition and the related increasing of the height of the track, the universal ballast distributing and profiling machine with shoulder ploughs has been also used (fig. 6, right) in order to remove the ballast in excess and obtain the desired shoulder shape.     figure 7: construction of scenarios with cant.   the last two scenarios have been constructed with a cant equal to 16 cm in respect to the rail level of all previous scenarios (fig. 7). later sleeper anchors have been installed on the sleepers (fig. 8).       figure 8: shovels installed on the sleepers. at the end of the operations above described, the final settlement and the rails cutting, needed to make independent one from the other the different test scenarios, were carried out. also, the purpose-made planned ballast wall, having dimensions not available off-the-shelf, (fig. 9) were constructed in situ. a. de iorio et alii, frattura ed integrità strutturale, 30 (2014) 593-601; doi: 10.3221/igf-esis.30.70 599 once the elements characterizing the various scenarios have been prepared and before the ballast settlement of the sections for which it has been foreseen, the rails have been cut in correspondence of the end sleepers or the transition sections among groups of consecutive scenarios different in height and/or in ballast compaction. the sectioning was needed in order to reduce the rails free expansion length and to prevent that the temperature variations would alter the desired configuration of the test track. in particular, the cuts have been performed by disk saw and have left a clearance of roughly 1.0 cm (fig. 10).         figure 9: ballast wall constructed in situ.       figure 10: cut performed by disk saw.   these discontinuities don’t limit the movement of the rolling stock on the track, because the underlying sleepers are equipped with k fastening systems, which allow restoring the rail continuity by the u-bolt plates tightening (fig. 10). before rails cutting, needed to create stand-alone scenarios, the edge and the shoulder has been checked and completed as well as the distances among the sleepers have been verified. the cuts have been performed according to the locations specified in fig. 11 and the rails have been subsequently drilled (fig. 12) in correspondence of the loading points of the test system.   a tolerance equal to ± 3 cm has been defined for the distance between the centre-to-centre sleepers in respect to the 60 cm nominal value, whilst for the total length of each scenarios, which are composed of 4 or 5 sleepers, the tolerance value has been chosen equal to ± 4 cm. the dimensions that during the check are found out-of-tolerance have been put into the preset limits modifying the position of the sleepers involved. the characteristics of the materials and components used to build in a single track all the scenarios to be tested are reported in the tab. 2.       figure 11: location of the rails cuts (c: cutting lines). a. de iorio et alii, frattura ed integrità strutturale, 30 (2014) 593-601; doi: 10.3221/igf-esis.30.70 600        figure 12: drilling of the rails.   name type reference standards ballast siliceous rfi dtc inc sp ifs 010 a rail 60e1 en 13674-1 fastening system elastic type en 13481-2, en 131461÷7 concrete sleeper rfi 230 rfi 240 en 13230-2:2002 table 2: track components. at the end of all the operations above described, the test field, constructed on the basis of a parametric approach, has been tested as scheduled. a wide range of homogeneous and reliable results have been produced. these results represent the basis for developing a numerical model useful for the evaluation of the safe service conditions of the continuous welded rail track. conclusions uring a wide research programme focusing on the development of a computational model for the study of the stability of the continuous welded rail track, a preliminary and substantial experimental activity has been carried out on full scale sections of modular scenarios implementing numerous and different track construction and service conditions. this activity has required a preliminary design of the test field as well as suitable test system with related facilities, in order to produce sufficient and reliable data for the implementation of a numerical model. in this paper, for the sake of the length, only the main stages of the design and construction of the test field have been described. moreover, some details have been synthetically discussed in order to provide the reading key of the adopted methodological approach and the accuracy achieved during its implementation. n. 28 scenarios composed of n. 14 different typologies were constructed in a short track of just 180 m, preparing them for the use of a test system designed on purpose [16]. the experimental results reported elsewhere [18] confirm, due to their variety, homogeneity, numerousness and reliability, the validity of the design choices adopted both in defining the test field and in designing the test system. d a. de iorio et alii, frattura ed integrità strutturale, 30 (2014) 593-601; doi: 10.3221/igf-esis.30.70 601 bibliography [1] erri dt202/dt363: improved knowledge of forces in tangential tracks including switches, determination of lateral and longitudinal ballast resistance of a railway track by experimental tests, 2 (1997). [2] kish, a., samavedam, g., wormley, d., new track shift safety limits for high speed rail applications, in: proceedings of world congress on railway research, cologne, germany, (2001). [3] analyses of track shift under high speed vehicle-track interaction, us department of transportation, dot/fra/ord-97/02, dot vntsc-fra-97-3 (1997). [4] esveld, c., improved knowledge of cwr track, delft university of technology, delft, (1997). [5] cepav uno – unieco: relazione tecnica sistema alta velocità linea milano napoli, tratta milano bologna; sovrastruttura ferroviaria, valutazione delle condizioni di stabilità del binario av; rtdv-2008-029-01. [6] sussmann, t., kish, a., investigation on the influence of track maintenance on the lateral resistance of concrete tie track, in: trb annual meeting, (2004). [7] kish, a., samavedam, g., risk analysis based cwr: track buckling safety evaluations, in: proceedings of the international conference on innovations in the design & assessment of railway, (1999). [8] van, m.l., buckling analysis of continuous welded rail track, heron, 41 (1996) 3. [9] esveld, c., a new set of computer models for analyzing cwr, delft university of technology, delft, (1997). [10] esveld, c., a better understanding of continuous welded rail track, rail engineering international edition, 4 (1996). [11] lim, n. y., parametric study on stability of continuous welded rail trackballast resistance and track irregularity, steel structures, 8 (2008) 171-181. [12] sung, w., shih, m., lin, c., go, c. g., the critical loading for lateral buckling of continuous welded rail, journal of zehjiang university science, 6a (8) (2005) 878-885. [13] uic code 720 r, laying and maintenance of cwr track, (2005). [14] kish, a., sussmann, t., trosino, m., effects of maintenance operations on track buckling potential, in: proceedings of international heavy haul association, (2003). [15] de iorio, a., grasso, m., penta, f., pinto, p., pucillo, g. p., rossi, s., testa, m., farneti, g., transverse strength of railway tracks: part 1. planning and experimental setup, frattura ed integrità strutturale, 30 (2014) 478-485; doi: 10.3221/igf-esis.30.58. [16] de iorio, m. grasso, f. penta, g. p. pucillo, v. rosiello, transverse strength of railway tracks: part 2. test system for ballast resistance in line measurement, frattura ed integrità strutturale, 30 (2014) 578-592; doi: 10.3221/igfesis.30.69. [17] technical specification, rfi, rome, (2008). [18] de iorio, a., grasso, m., penta, f., pucillo, g. p., rosiello, v., lisi, s., rossi, s., testa, m., about track resistance evaluation on the running surface: role of the ballast surrounding the sleeper, submitted to proceedings of the institution of mechanical engineers, part f: journal of rail and rapid transit. microsoft word numero_52_art_11_2678 r. hadj boulenouar et alii, frattura ed integrità strutturale, 52 (2020) 128-136; doi: 10.3221/igf-esis.52.11 128 three-dimensional numerical analysis of a joint bonded reinforced with silica nanoparticles (sio2) hadj boulenouar rachid, boutabout benali laboratory of mechanics physics of materials (lmpm), djillali liabes university, department of mechanical engineering, sidi bel abbes, algeria r.hadjboulenouar@gmail.com, bboutabout@yahoo.fr djebbar noureddine laboratory of mechanics physics of materials (lmpm), hassiba benbouali university, department of mechanical engineering, chlef, algeria. djebbarnour@yahoo.fr, https://orcid.org/0000-0002-6496-7996 abstract. nanostructured adhesives may be defined as those materials whose elements imbedded in an epoxy matrix have dimensions in the 1 to 100 nm range. one of the most interesting aspects of ceramic nanoparticles is that their mechanical properties depend strongly upon the particle size and shape. silica nanoparticles (sio2) have different physical and mechanical properties from bulk ceramics. the aim of the present study is to investigate the effect of the nanoparticles rate on the equivalent stress, peeling stress and shear stress as well as the strains developed in the adhesive joint. three-dimensional finite element models of adhesive joint were developed to determine the stress intensity as well as strain with different nanoparticles rate in the epoxy resin. dispersion of nanoparticles with different percent in the epoxy resin allows for reinforcing the adhesive. polymer embedded silica nanoparticles (sio2) proved to be highly effective. keywords. epoxy, finite element method, silica nanoparticles sio2, stress, strain. citation: hadj boulenouar, r., boutabout, b., djebbar, n., three-dimensional numerical analysis of a joint bonded reinforced with silica nanoparticles (sio2), frattura ed integrità strutturale, 52 (2020) 128-136. received: 09.11.2019 accepted: 02.01.2020 published: 01.04.2020 copyright: © 2020 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. introduction here is an increasing interest in polymer/silica nanocomposites for the developments of new materials with improved thermal and mechanical properties [1-3]. polymer nanocomposites are among the most promising materials. the incorporation of a small fraction of nanoparticles into a polymer matrix not only leads to dramatically reinforced mechanical properties [4], but also endows the material with flame-retardant [5, 6], conductivity [7, 8], gas-barrier [9], and optical properties [10, 11], among others. however, these enhanced properties depend strongly on nanoparticle dispersion and the interfacial interactions between the nanoparticles and the polymer matrices [12-15]. polymers are used for high-technology application areas such as coatings, electrical appliances, adhesives, automotive and aerospace industries t https://youtu.be/ke1dutfjuvg r. hadj boulenouar et alii, frattura ed integrità strutturale, 52 (2020) 128-136; doi: 10.3221/igf-esis.52.11 129 [16-18]. the polymeric nanocomposites are usually defined as a combination of a polymer matrix and nanometric particles [19]. the possibilities of improving the mechanical or thermal properties and the development of new materials by nanoparticles have found applications in academia and industry. several experimental and theoretical studies have been carried out on the mechanical properties of microphones and nanocomposites. many papers report improved polymer properties more efficiently using nanoparticles than with microparticles [20]. the epoxy resin is a rigid polymer with good chemical stability, mechanical and electrical properties. it is widely used as a matrix of composite materials reinforced by fillers and as adhesives [21, 22]. when cured, the epoxy is amorphous and highly cross-linked (i.e. thermosetting polymers). this microstructure provides many useful properties for engineering applications, such as a modulus of elasticity, high and failure resistance, low creep, and good performance at high temperatures [23]. however, the structure of the epoxy also leads to very undesirable properties when it is a relatively fragile material, with a low resistance to initiation and growth of the cracks. the thermal loading effect on free vibration characteristics of carbon nanotubes (cnts) with multiple cracks has been studied [24]. the nanoparticles have been widely used in epoxy matrix composites as reinforcements. compared to micro-loaded composites with nanoparticles open up a wide range of potential new applications, due to their improved engineering properties, such as stiffness and hardness, and other beneficial functions such as the barrier against nanoparticles, humidity and flame retardancy [25]. the objective of this work is to analyze by three-dimensional finite element method using the abaqus calculation code, the stress distribution of shear and peeling in the adhesive joint used to assembly two aluminum plates. several parameters have been highlighted such as the stiffness of the nanostructured adhesive and their size, in order to see the effect of the silica nanoparticles' dispersion imbedded in the epoxy resin on the charge transferred in the adhesive layer. geometric model and mechanical properties he adhesively bonded single-lap joint studied in the present work is shown in fig. 1. the two adherends used were aluminum alloy plates (2024-t3) of dimensions 200 mm long, 20 mm wide, 2 mm thickness. the mechanical properties of the adherends were as follows: poisson's ratio ν = 0.33, young's modulus e = 69 gpa. the mechanical properties of the adhesives investigated were: poisson's ratio νad = 0.33, young's modulus e = 3.5 gpa [26]. figure 1: geometrical model. boundary conditions chematic of the entire model (fig. 2), including the fixed connection (zero displacement) at the left end, a distributed load of 40 mpa was applied at the right end of the upper substrate in the x-direction. the joint is oriented along the x, z is the direction of the width and y is the direction normal to the joint plane. figure 2: boundary conditions for the symmetry fe model. t s upper adherend lower adherend 0.2 r. hadj boulenouar et alii, frattura ed integrità strutturale, 52 (2020) 128-136; doi: 10.3221/igf-esis.52.11 130 in the case of fe analysis of adhesively bonded joints the thickness of adhesive layer is much smaller than that of the adherends. the fe mesh must accommodate both the small dimension of the adhesive layer and the larger dimension of the remainder of the whole model. it is essential to model the adhesive layer by a fe mesh which is smaller than the adhesive layer thickness. the result is that the fe mesh must be several orders of magnitude more refined in a very small region than is needed in the rest of the joint. thus the number of degrees of freedom in an adhesively bonded joint is rather high. it is also important that a smooth transition between the adherends and adhesive be provided for later distortion analysis. the original fe mesh is shown in fig. 3. the fe mesh of the joint was created using the abaqus fea pre-processing program. most of the adherends and adhesive were modelled using the 20-node quadratic brick solid elements. figure 3: mesh of the assembly. investigated materials substrates wo substrates are made of a highly ductile 2024-t3 aluminum alloy, which gives the advantage of good solid state plastic deformation shaping properties, with low melting point, about 650 °c. alloy 2024 has better mechanical properties due to higher magnesium content. it has good resistance to toughness and crack propagation. the 2024 is widely used in aircraft construction. adhesives the epoxy resin examined was a standard diglycidyl either of bisphenol a (der331 resin, dow chemical company) with an equivalent molecular weight of 187 g/mol. the nano sio2 particles (3m corporation) with an average particles size of 174nm, 74nm and 23nm were surface modified by a sol-gel process to prevent agglomeration and to maintain a narrow particles size distribution. the nanosilica particles were supplied as pre-mixed concentrates in a dgeba epoxy resin. piperidine (sigma-aldrich) was used as the curing agent. figure 4: synthesis of dgeba. t r. hadj boulenouar et alii, frattura ed integrità strutturale, 52 (2020) 128-136; doi: 10.3221/igf-esis.52.11 131 properties epoxy viscosity (pa.s) at 25c° 12000 13000 density (kg/m3) 1160 temperature distortion (°c) 50 modulus of elasticity e(gpa) 2.4 5 flexural strength (mpa) 60 tensile strength (mpa) 73 maximum elongation (%) 4 table 1: properties of epoxy resin [27]. effect of nanofillers on the epoxy resin he young’s modulus e of the nanocomposite materials were measured using dog-bone shaped tensile specimens [28]. the results are shown in tab. 2 along with the standard deviation (calculated from at least five samples). the presence of the nanosilica particles increases the modulus, e, of the nanocomposite; with the value of e increasing steadily as the weight % of the silica phase is increased [29]. the effect of nanosilica particles content on the young’s modulus is depicted in tab. 2. nanosilica particles sizes (nm) volume (%) e (gpa) unmodified 0 3.50 23 2.5 5 10 15 20 25 30 3.50 3.62 4.24 4.56 4.78 5.22 5.53 74 2.5 5 10 15 20 25 30 3.67 3.80 4.15 4.50 4.76 5.43 5.60 174 2.5 5 10 15 20 25 30 3.50 3.62 4.25 4.60 4.87 5.35 5.78 table 2: values of nanosilica filled dgeba as a function of filler content compared at different sizes of nanosilica particles [30]. t r. hadj boulenouar et alii, frattura ed integrità strutturale, 52 (2020) 128-136; doi: 10.3221/igf-esis.52.11 132 results and discussion n this work, the abaqus calculation code is used to model the simple overlap joint, which is composed of two 2024 aluminum substrates and the epoxy resin loaded with nano-silica particles. using the table, which shows the young’s modulus of the unfilled epoxy resin (ep), and then the same resin loaded with different percentages of the nano-silica particles. effect of the rate of the nanoparticles on the stresses figs. 5, 6 and 7 illustrate respectively the variation of the von mises stress ( σmises), the shear stress (σxy) and the peel stress (σyy) according to the overlap length, without and with nanoparticles and their diameters are equal to 23 nm. the results are obtained numerically by the finite element method for three percentages of nanoparticles (2.5%, 15% and 30%). whatever the rate of the nanoparticles imbedded in the matrix, it is noted that the maximum stresses are located at two free ends of the bonded assembly. however, the minimum stresses are always at the assembly's core. the results obtained show that the curves of the stresses are almost similar because the rate of the nanoparticles is relatively smaller than the volume of the resin, it varies from 2.5% to 30%. it is noted that increasing the rate of the nanoparticles leads to an increase in the maximum stress. it is observed that the value of the maximum stress is proportional to the quantities of nanoparticles imbedded in the adhesive matrix. the addition of inorganic spherical nanoparticles to polymer allows the modification of the polymer physical properties as well as the implementation of new features in the polymer matrix. figure 5: variation of the von mises stress. figure 6: variation of the shear stress. i r. hadj boulenouar et alii, frattura ed integrità strutturale, 52 (2020) 128-136; doi: 10.3221/igf-esis.52.11 133 figure 7: variation of the peel stress. effect of the rate of the nanoparticles on the equivalent stress fig. 8 represents the variation of the maximum value of the equivalent stress as a function of the rate of the nanoparticles for three diameters of nanoparticles. it is noted that whatever the size of the nanoparticles the maximum value of the equivalent stress varies proportionally to the rate of the nanoparticles added in the adhesive, which confirms the results obtained previously. it is also noted that increase the stress is due to an increase of the young's modulus of the adhesive joint. the latter behaves like a brittle material whose young's modulus increases with the rate of the nanoparticles added in the adhesive. it can be seen that whatever the percentage of silica nanoparticles, the difference between the von mises stress, which corresponds to different diameters of the nanoparticles is relatively weak. figure 8: variation of the equivalent stress as a function of the silica nanoparticles diameter. effect of the rate of the nanoparticles on the strains figs. 9, 10 and 11 show the variation of the strain (xx, xy and yy) according to the length of the adhesive joint without and with silica nanoparticles whose diameter is equal to 23 nm. the strain curves have been drawn for three percentages of silica nanoparticles (2.5%, 15% and 30%). it is noted that the maximum strains are located as the ends of the joint. it is noted that the strain depends on the rate of the nanoparticles in the epoxy matrix. the strain curve clearly shows that increasing silica nanoparticles leads to a decrease of the linear and angular strain. indeed, reinforcement of the matrix by ceramic-type nanoparticles makes it possible to transform the resin into a brittle material with a weak strain. r. hadj boulenouar et alii, frattura ed integrità strutturale, 52 (2020) 128-136; doi: 10.3221/igf-esis.52.11 134 figure 9: variation of the strains (xx). figure 10: variation of the strains (xy). figure 11: variation of the strains (yy). r. hadj boulenouar et alii, frattura ed integrità strutturale, 52 (2020) 128-136; doi: 10.3221/igf-esis.52.11 135 effect of the diameter of silica nanoparticles on the strains fig. 12 illustrates the variation of the maximum strain (max) as a function of the rate of the nanoparticles for three diameters (23 nm, 74 nm, 170 nm) of nanoparticles. it is noted that whatever the percentage of silica nanoparticles, the difference between the maximum strains, which correspond to different diameters of silica nanoparticles, is relatively weak. in order, the obtained results show that the maximum strain is almost independent of the nanoparticles diameters. figure 12: variation of the maximum strain as a function of the diameter of silica nanoparticles. conclusion rom the results above, obtained by the three dimensional numerical analysis, one can draw the following conclusions: the mechanical properties of the adhesive reinforced by silica nanoparticles, in particular, its young's modulus depends on the rate of the nanoparticle. increasing the quantities of silica nanoparticles in the matrix leads to increase the von mises stress, shearing and peeling at both ends the recovery length. a significant increase in the rate of the nanoparticles in the adhesive joint leads to a decrease in the maximum strains. decreasing the deformations within the joint, that means that the reinforcement of this resin with different percentages of silica nanoparticles to improve rigidity and its resistance to fracture. whatever, the rate of silica nanoparticles added in the adhesive the maximum strain and stress are almost independent of the nanoparticle size. references [1] knopp, d., tang, d., niessner, r. (2009). review: bioanalytical applications of biomolecule functionalized nanometer-sized doped silica particles, anal. chim. act. 647, pp. 14-30. [2] kohut, a., ranjan, s., voronov, a., peukert, w., tokarev, v., bednarska, o., gevus, o., voronov, s. (2006), design of a new invertible polymer coating on a solid surface and its effect on dispersion colloidal stability, langmuir 22, pp. 6498-6506. [3] zou, h., wu, s., shen, j. (2008). polymer/silica nanocomposites: preparation, characterization, properties, and applications. chem. rev, 108, pp. 3893-957. [4] song, p., cao, z., cai, y., zhao, l., fang, z., fu, s. (2011), fabrication of exfoliated graphene-based polypropylene nanocomposites with enhanced mechanical and thermal properties. polymer, 52, pp. 4001-10. [5] wang, x., kalali, e.n., wan, j., wang, d. (2017). carbon-family materials for flame retardant polymeric materials. prog. polym. sci., 69, pp. 22-46. f r. hadj boulenouar et alii, frattura ed integrità strutturale, 52 (2020) 128-136; doi: 10.3221/igf-esis.52.11 136 [6] wang, d.y., leuteritz, a., wang, y.z., wagenknecht, u., heinrich, g. (2010), preparation and burning behaviors offlame retarding biodegradable poly (lactic acid) nanocomposite based on zinc aluminum layered double hydroxide. polym. degrad. stab, 95, pp. 2474-24. [7] xu, x., chen, j., zhou, j., li, b. (2018), thermal conductivity of polymers and their nanocomposites. adv. mater,30. [8] gao, c., zhang, s.m., wang, f., wen, b., han, c.c., ding, y.f., et al. (2014), graphene networks with low percolation threshold in abs nanocomposites: selective localization and electrical and rheological properties. acs appl. mater. interfaces, 6, pp. 12252-12260 [9] cui, y., kundalwal, s.i., kumar, s. (2016). gas barrier performance of graphene/polymer nanocomposites. carbon, 98, pp. 313-333. [10] pan, z.b., zhai, j.w., shen, b. (2017). multilayer hierarchical interfaces with high energy density in polymer nanocomposites composed of batio3@tio2@al2o3 nanofibers. j. mater. chem. a, 5, pp. 15217-15226. [11] han, c.c., wang, f., gao, c., liu, p., ding, y.f., zhang, s.m., et al. (2015), transparent epoxy-zno/cds nanocomposites with tunable uv and blue light-shielding capabilities. j. mater. chem. c, 3, pp. 5065-5872. [12] kumar, s.k., jouault, n., benicewicz, b., neely, t. (2013). nanocomposites with polymer grafted nanoparticles. macromolecules, 46, pp. 3199-3214. [13] khani, m.m., woo, d., mumpower, e.l., benicewicz, b.c. (2017). poly (alkyl methacrylate)-grafted silica nanoparticles in polyethylene nanocomposites. polymer, 109, pp. 339-348. [14] kumar, s.k., krishnamoorti, r. (2010). nanocomposites: structure, phase behavior, and properties. ann.rev. chem. biomol. eng, 1, pp. 37-58. [15] ahmad, h.m. y., midhat, n. s. and mohd, f. j. (2017), a review: synthetic strategy control of magnetite nanoparticles production. advances in nano research, 6 (1), pp. 1-19. [16] jiang, w., jin, f. and park, s. (2012). thermo-mechanical behaviors of epoxy resins reinforced with nanoparticles al2o3, journal of industrial and engineering chemistry, 18 (2), pp. 594-596. [17] mcgrath, l., parnas, r., king, s., schroeder, j., fischer, d. and lenhart, j. (2008), investigation of the thermal, mechanical, and fracture properties of alumina epoxy composites, polymer, 49 (4), pp. 999-1014. [18] omrani, a. and rostami, a. (2009), understanding the effect of nano-al2o3 addition upon the properties of epoxy based hybrid composites, materials science and engineering: a, 517(1), pp. 185-190. [19] moreira, d.c, sphaier, l.a., reis, j.m.l and nunes, l.c.s. (2011). determination of young’s modulus in polyester al2o3 and epoxy al2o3 nanocomposites using the digital image correlation method. composites part a: applied science and manufacturing, 43, pp. 304-309. [20] vivek, g., joanna, p., ryan, p.s., andrew, j., krzysztof, m., ramanan, k. (2018). structure of block copolymer grafted silica nanoparticles, polymer, pp. 1-38. [21] xuechen, t., hongbin, y., yongbo, g., zeeshan, a. l., changxiao, c., wanli, k. (2018). preparation of a micron-size silica-reinforced polymer microsphere and evaluation of its properties as a plugging agent, colloids and surfaces a, 547, pp. 8–18. [22] constantinescu, d. m., dragos, a. a., catalin, r. p., krzysztof, k., manfred, s. (2017). mechanical properties of epoxy nanocomposites reinforced with functionalized silica-nanoparticles, procedia structural integrity, 5, pp. 647–652 [23] guangshun. w., lichun, m., li, l., lei, c., yudong, h. (2015), preparation of sio2–go hybrid nanoparticles and the thermal properties of methylphenylsilicone resins/sio2-go nanocomposites, thermochimica acta, 613, pp. 77-86. [24] ebrahimi, f. and mahmoodi, f. (2018), vibration analysis of carbon nanotubes with multiple cracks in thermal environment, advances in nano research, 6(1), pp. 57-80. [25] wu, f., zhang, s., chen, z., zhang, b., yang, w., liu, z. (2016), interfacial relaxation mechanisms in polymer nanocomposites through the rheological study on polymer/grafted nanoparticles. polymer, 90, pp. 264-275. [26] madani, k., mokhtari, m., belhouari, m. and hannani, m. (2013). effect of modifying the edges of the adherends and the adhesive on the stress distribution over the width and length of recovery, case of a single lap joint, international journal of mining, metallurgy & mechanical engineering (ijmmme), 1(4). [27] juliana primo basílio, d.s. and joão marciano laredo, d.r. (2014). a thermomechanical and adhesion analysis of epoxy/al2o3 nanocomposites nanomater nanotechnol, pp. 5-18. [28] lim sheau, h. (2010). synthese and micro-mechanical properties of epoxy-alumina nanocomposites, national university of singapore. [29] kinloch, a., mohammed, r., taylor, a., eger, c., sprenger, s., egan, d. (2005). the effect of silica nano particles and rubber particles on the toughness of multiphase thermosetting epoxy polymers, journal of materials science, 40, pp. 5083-5086. [30] dittanet, p. 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can be opened with acrobat and adobe reader 5.0 and later.) >> /namespace [ (adobe) (common) (1.0) ] /othernamespaces [ << /asreaderspreads false /cropimagestoframes true /errorcontrol /warnandcontinue /flattenerignorespreadoverrides false /includeguidesgrids false /includenonprinting false /includeslug false /namespace [ (adobe) (indesign) (4.0) ] /omitplacedbitmaps false /omitplacedeps false /omitplacedpdf false /simulateoverprint /legacy >> << /addbleedmarks false /addcolorbars false /addcropmarks false /addpageinfo false /addregmarks false /convertcolors /converttocmyk /destinationprofilename () /destinationprofileselector /documentcmyk /downsample16bitimages true /flattenerpreset << /presetselector /mediumresolution >> /formelements false /generatestructure false /includebookmarks false /includehyperlinks false /includeinteractive false /includelayers false /includeprofiles false /multimediahandling /useobjectsettings /namespace [ (adobe) (creativesuite) (2.0) ] /pdfxoutputintentprofileselector /documentcmyk /preserveediting true /untaggedcmykhandling /leaveuntagged /untaggedrgbhandling /usedocumentprofile /usedocumentbleed false >> ] >> setdistillerparams << /hwresolution [2400 2400] /pagesize [612.000 792.000] >> setpagedevice microsoft word numero_51_art_11_2602 f. jafari et alii, frattura ed integrità strutturale, 51 (2020) 136-150; doi: 10.3221/igf-esis.51.11 136 reliability-based design of reinforced concrete beams for simultaneous bending, shear, and torsion loadings faezeh jafari malayer university, iran faeze_jafari666@yahoo.com jalal akbari* buali sina university, hamedan, iran j.akbari@basu.ac.ir abstract. the design of structural members is targeted in resisting the loads such that the safety of the structure is preserved regarding different conditions of loadings. the traditional design method in concrete standards is based on the load and resistance factors regardless of the random nature of them. uncertainties in design parameters such as load and resistance have great influences in the safety of the structure and using constant coefficients caused unsafe and uneconomical designs. the present research is focused on a probabilistic design of reinforced concrete beams subjected to simultaneous actions of bending, shear, and torsion. for this purpose, analytical formulas for the limit states have been developed to combine different stresses. monte carlo simulation method is used to estimate the safety indexes for three different t, rectangular and l-shaped cross-sections. then, the load and resistance factors have been calculated in different safety indexes, and the influence of load and resistance factors based-on aci standard has been examined. the proposed method is applicable to all concrete standards. however, here the procedures are based on the aci standard. keywords. reliability-based design; reinforced concrete beam; safety index; load and resistance factors; monte-carlo simulation. citation: jafari, f., akbari, j., reliabilitybased design of reinforced concrete beams for simultaneous bending, shear, and torsion loadings, frattura ed integrità strutturale, 51 (2020) 136-150. received: 29.08.2019 accepted: 07.11.2019 published: 01.01.2020 copyright: © 2020 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. introduction eliability method as a probabilistic design approach that was proposed for the first time by ellingwood in1974, and then many efforts were carried out in order to employ uncertainties and probability of parameters in current design methods [1]. for instance, evan et al [2] calculated the shear force of reinforced concrete beam in aci regulation using new methods of reliability in 2006. the conducted researches in this field indicate this important issue that the various factors are effective in the failure of concrete beams. these factors are the ratio of the span length over effective depth, ratio of longitudinal steel, support conditions, loading conditions, and materials properties. the performance of a concrete beam in the laboratory on the basis of the statistical methods was studied. in 2013, porco et al [3] studied the r http://www.gruppofrattura.it/va/51/2602.mp4 f. jafari et alii, frattura ed integrità strutturale, 51 (2020) 136-150; doi: 10.3221/igf-esis.51.11 137 punching shear using the reliability method in a flat slab. their study was focused on the evaluation of the compressive strength of the flat slab and its effective factors. moreover, in 2014 daniel jensen [4] was carried out research to obtain the reliability index to show the effect of shear forces and reinforcement of concrete bridges. he showed that the use of this method was made the design 10 % to 15 % lighter. in 2014, bakers et al [5] examined the reliability of concrete bridge in which the studied beam was under the effect of the moment and shear forces. there are also numerous researches were conducted by different researchers regarding the concrete safety index, including research by nowak et al [6]. the authors estimated the safety index in their research to investigate the uncertainty parameters in various materials such as high strength concrete, normal concrete, and light concrete by taking into account various concrete structures such as slabs, beams, and columns. in 2013, [7] uva et al proposed a seismic assessment of in-situ concrete on buildings such that concrete resistance can be evaluated by a novel cdd method to considering the effect of random parameters [7]. pérez-rocha (2013) was used the uncertainty method to examine better design and safety of the structures, including beam, column, and wall in mexico regulation. the calibration of design codes was based on the coefficients existing in regulations [8]. later on, in 2014, abejide examined the effects of uncertainties in the safety of section for three flexure, shear and axial compression states in aci 318-11 standard by considering the random nature of the parameters for reinforced concrete[9]. al-ansari et al applied experimental and numerical methods (fem) in order to study the flexural behavior of t and rectangular concrete beams. their experimental study was compared with the fem analysis results for verifying the fem code, which showed that the fem result of rectangular beam is more safer than an experimental result for t-beam[10]. bastidas et al in 2018 studied the combined effects of chloride-induced corrosion, climate change and cyclic loading with a stochastic model.the results of this study show that the climate change lifetime of structure by roughly 1.4 -2.3% [11]. jafari et al studied the safety index of iranian concrete standard for bending, shear and torsion state using monte carlo simulation. in their research, the safety surface for t, l, and rectangular beams obtained and compared with together [12]. akbari and jafari studied the reliability behavior of concrete beam (t, l, and rectangular shape) under bending conditions using monte carlo simulation. the beta indexes, load resistance factors, and strength reduction factors were obtained for different sections[13]. as well, slowik et al applied a probabilistic approach to the reliability analysis of longitudinally reinforced concrete beams [14]. huang et al in 2019 studied the flexural behavior of frp-strengthened reinforced concrete beams using the ultimate limit state method. according to the result of this research, the probability of failure is different for each failure mode and reduction resistance has a significant influence on concrete behavior [15]. comprehensive literature has been published on the reliability-based design of concrete structures. as well, extensive researches were accomplished for safety index calculations; no single study exists, which computes the load and resistance factors that related to the specified safety index. therefore, to our knowledge, detailed studies for calibration of the load and resistance factors were not reported throughout the literature. accordingly, in this investigation, the load and resistance, loading factors for all main loadings are calculated for any desired safety index and any loading ratios. consequently, the methodology of the present paper could be used on the design of the beams under bending, shear, and torsion loadings for a fully probabilistic based approach for all design codes. as a sample, the safety index for aci concrete standard [16] for three limit states of shear, bending and torsion and also for the combination of the above-mentioned limit states are carried out. to achieve this, the safety indexes were obtained by introducing uncertainty factors in beam design equations and applying the monte-carlo simulation method. then, various limit states function such as (shear, torsion, and bending) were assumed and the safety indexes and the load resistance factors which were addressed in the aci standard. method of research n order to calculate the safety index, the limit functions which show the structural effects should be obtained. eqns. 13 are used to calculate bending, shear, and tensional action on the beams.     * * *   ,    1.7 * * * s y r s y s dead load live load c a f m a f d m m m f b d          (1) '    0.16 * * * *   ,   r c w y v s dead load live load d v f b d f a v v v s     (2) i f. jafari et alii, frattura ed integrità strutturale, 51 (2020) 136-150; doi: 10.3221/igf-esis.51.11 138 0    2 * * * ,  y r t s dead load live load f t a a t t t s    (3) in eqns. (1) to (3),   rm ,    rv and  rt are the bending resistance, the shear resistance, and the torsion resistance of the crosssections, respectively. furthermore, the parameters of , , , ,  s y ca f f b d refer to areas of longitudinal steel, the yield strength of steel, 28-day compressive strength of concrete, width and effective depth of the cross-sections, respectively. the nominal values of the steel are calculated according to aci 318m-14.2015 standard[16]. for l and t shaped sections, the proposed equations are obtained [12]. to express the shear and torsion limit state functions, all sections of l, t, and rectangular shapes of concrete beams are considered. the factors considered in the aci standard are: concrete strength reduction factor ( 0.90c  ), dead load increase factor    1.20d  and live load resistance factor( 1.60)l  . in addition, the steel strength reduction factor of steel is   0.90s  . tab. 1 shows the statistical information (mean, covariance and probability density function(pdf)) which are used to obtain the safety indexes. standard deviation mean pdf value of parameters random parameters 0.18-20 19.3 normal 21 cf ( mpa ) 0.12 472.5 normal 420 yf ( mpa ) b/10 h/17 d/15 b h d normal b h d dimension (mm) 0.03-0.05 0.03-0.05 0.03-0.05 s v t a a a normal s v t a a a 2area(mm ) 0.1 0.40-0.25 1.05d l normal gamble d l loading table1: statistical values of the used parameters for design the sections of reinforced concrete [17-20]. limit function and safety index equation eqn. 4 shows the limit state function which is used to the safety design of concrete beams under the simultaneous effects of bending, shear, and torsion.    ;   {{            ,      ,         }}s r s r s rg r s m m v v t t     (4) after employing eqn. (4), in order to predict the safety index ( ) , the values of r (resistance surface) and s (load surface) are calculated for the three mentioned states (bending, shear and torsion) using hasofer-lind equation [17-18]. eqn. 5 shows the value of the safety index [18]. in this study, the safety index is calculated for current limit states functions using monte carlo simulation r s 2 2 r s mean mean   σ σ eta index    (5) safety surface of shear-torsion based on eqn. (4), by limiting the left side of eqn. (6) to a specified value ( ' 2 )  * 3 c c w v f b d        the combination of simultaneous effects of shear and torsion can be achieved for different cross-sections. f. jafari et alii, frattura ed integrità strutturale, 51 (2020) 136-150; doi: 10.3221/igf-esis.51.11 139     ' 2 * * 2 2 * * 3* * 1.7 u wu c c w ww t b dv v f b d b db d           (6) ,  u uv t s the ultimate shear and torsion demand and cv points to the shear strength of concrete. ', ,  w cb d f are the width of the web, the effective depth of the beam, and 28-day compressive strength of concrete, respectively. estimation of the safety surface of aci concrete standard for shear and torsion is as follows: first, the value of shear force, torsion, and bending moment are calculated according to the type of cross-section (l, t and rectangular shaped) using eqn. (1-3). the method of calculation is such that a constant value for the dead load is devoted, and the live load is: live load =dead load*ratio=(1t)/t). for this purpose, t is changed from 0.40 to 1.0 then, the amount of the live load is calculated. the amount of shear load is obtained from the sum of the live load to the dead load and finally, by considering the eqn. (2) the amount of nominal shear steel required is obtained. applying the value of the total moments on the beam (dead load moment+ live load moment) and using eqn. (3), the nominal required torsion steel is obtained. the method of calculating the total moments exerted on the beam is similar to the shear state and is practical by considering the ratio proposed by some researchers [12-13]. the limit state functions considered for solving the problem by taking the special formulas presented in aci standard for shear, torsion and the combination of shear and torsion. eqn. 7 -9 show the torsion shear limit state function. 0 * * r s v w w v v acig b d b d    (7)           2 2 * * 2 * * 2 0 * * 1.7 * * 1.7 r w s w t w w t b d t b d acig b d b d      (8)          & 2 2 * * 2 * * 2 0 * ** * 1.7 * * 1.7 u w s wu s v t w ww w t b d t b dv v acig b d b db d b d        (9) in the above equations, the s index is the load and moment exerted on the cross-section (demand), r is the resistance surface of the cross-section (capacity). in sections 2-3 to 2-5, different levels of standard are presented for various combinations of forces. &  v tacig is limit state function for shear and torsion as well as vacig and tacig is shear and torsion limit sate function, respectively. the safety surface of bending-torsion to investigate the safety surface of the aci standard, the values of torsion and bending steel are calculated using eqns. (1) to (3). after calculating the values of the bending moment and the applied live and dead loads, a limit function as in eqns. (10) and (11) are considered. * * * 0  1.7 * * * s y b s y s c a f acig a f d m f b d          (10)         & 2 2 * * 2 * * 2* *     0 1.7 * * * * 1.7 r w s wr s b t w w t b d t b dm c m c acig i ib d b d        (11) in eqns. 10 and 11, index s refers to the effects of the loads (live + dead), and index r points to the resistance against the exerted loads. &    b taci g is limit state function for bending and torsion as well as bacig and tacig are bending and torsion limit sate functions, respectively. the safety surface of bending-shear the amount of the required steel for three states was calculated in the previous sections. as well, the amount of the forces acting on the cross-section and the strength of the cross-section are obtained for three states of shear, torsion, and bending. in order to consider the combination of the bending and shear state ( & )v bg , eqn. 12 is used. f. jafari et alii, frattura ed integrità strutturale, 51 (2020) 136-150; doi: 10.3221/igf-esis.51.11 140 & * *   0 * * r r s s v b w w v m c v m c acig b d i b d i                 (12) the safety surface of bending-torsion-shear the following limit sate function , &( )v b tacig is considered to obtain the safety surface of the aci standard for three states of shear, bending, and torsion.         , & 2 2 * * 2 * * 2* *     0 * *1.7 * * * * 1.7 r w s wr r s s v b t w ww w t b d t b dm c v m c v acig i b d i b db d b d                        (13) in eqn. 13, three states of shear, bending and torsion effect appear simultaneously and by considering this limit state function, the safety surface is predicted. sections and dimensions in order to calculate the beta index of t, l, and the rectangular cross-section beams, specified geometrical futures are assumed as shown in fig. 1 and tab. 2. the distributed load (25kn/m) is exerted on the beam length. cross-sections of the mentioned beams are selected in such a way that the area of the t-shape section is twice that of l-shape section and the rectangular section area was   *wb d . figure 1: schematic figure of the l, t, and rectangular sections wb (mm) dq (kn/m) f ( mpa )c eb (mm) yf ( mpa ) 450 25 21 850 420 fb (mm) d(mm) l(mm)  * ; 1 /l dm ratio m ratio t t   200 400 2000 0.4-1.0 table 2: the nominal parameters of this study f. jafari et alii, frattura ed integrità strutturale, 51 (2020) 136-150; doi: 10.3221/igf-esis.51.11 141 results he results are presented in two sections. the first part of the results is devoted to the estimation of the safety indexes using the proposed method. the main goal is presenting an approach to the safe design of beams instead of the traditional method. in the second part, the load resistance factors are calculated based on estimated safety indexes. the presented method could be easily applied to other international design codes. namely, the safety indexes are estimated without using specific standards, e.g. aci. on the other hand, the estimation of safety indexes is independent of any regulation. the safety surface of standard for states of torsion-shear the safety index is calculated considering statistical values (mean, covariance and pdf) as given in tabs. 1 and 2 and the limits state functions. the following flowchart shows the calculation of the safety indexes and load factors. figure 2: flowchart of computer code to estimate the beta index and load factors. fig. 3 shows the beta indexes vs t values for different cycle numbers, as seen from the figure the cycle number 15000 for all values of t is good enough for the next calculations. as well, fig. 4 shows the beta index for all types of cross-sections for shear-torsion combination. in this combination, the safety index has higher than the individual actions because of the application of strength reduction and load resistance factors in the design procedure. after the combined mode, the designed beam for shear actions, the sections have the maximum beta value, and finally, the beta in the torsional design of beams has the lowest value, which is similar to the results of previous studies [20,23]. however, the safety indexes range is between 2.65 to 3.35, and according to the suggestions of the previous references, the safety index value is suitable for the safe design. t f. jafari et alii, frattura ed integrità strutturale, 51 (2020) 136-150; doi: 10.3221/igf-esis.51.11 142 figure 3: aci beta index for shear-torsion for different monte carlo cycles figure 4: aci beta index for shear-torsion combination. aci safety surface for bending-torsion in this section, the equations presented in section 2-3 are employed and the aci safety index is calculated for bending and torsion states. fig. 5 shows the beta index for bending and torsion state for three studied cross-sections. the standard surface of aci for torsion is from 2.50 to 3.20 and the standard surface of aci concrete for bending is between 2.50 4.15. the standard surface of aci concrete for bending and torsion is between the values of bending and torsion and it is close to bending state, and the average value is 3.70 for bending-torsion. the maximum value of the safety index for the combination of torsion-bending occurs at t= 0.6. f. jafari et alii, frattura ed integrità strutturale, 51 (2020) 136-150; doi: 10.3221/igf-esis.51.11 143 figure 5: aci beta index for torsion-bending. figure 6: aci beta index for bending-shear. aci safety surface for bending-shear fig. 6 shows the standard safety surface of aci concrete for shear and bending. the aci standard surface for combination states (shear and bending) is close to the shear state. aci safety surface for bending-sheartorsion the combination of shear, bending and torsional states is carried-out using eqn. 13. graph 7 shows the safety index for the three combination states. according to this figure, the aci beta indexes for l, rectangular, and l cross-sections are 4.05, f. jafari et alii, frattura ed integrità strutturale, 51 (2020) 136-150; doi: 10.3221/igf-esis.51.11 144 3.91 and 3.13, respectively. the maximum beta value corresponds to t = 0.5 and afterward, the safety index is decreased due to the decreasing of the live load and the impact of the live load coefficient. the variations of the safety index in the tshaped cross-sections are higher than the other ones, and the maximum safety index is obtained for the slab-shaped sections. figure 7: aci beta index for shear-bending -torsion estimation of the standard safety factors for limit states (shear-torsion-bending) in this section, the values of load resistance and strength reduction factors are estimated, and for them, wide ranges are proposed. then, based on these ranges the safe design of the studied beams is conducted without using constant standard code coefficients. therefore, the presented procedure could be implemented for all standards. however, to show the validation of the proposed method, the estimations are based on the aci code. to obtain the safety index, firstly, a wide range of strength reduction factors were considered and entered into the developed matlab code as an input variable. next, the limit state equations in aci standard were used, and safety indexes were calculated. figs. 8 to 10 show the coefficients obtained from monte carlo simulation and the beta index. the reduction factors have a significant influence on the beta indexes. tab. 3 shows factors for (dead load, live load, and resistance reduction factors) that have been assumed for the calculated beta index. in this research for calculating the beta indexes, eleven groups of factors were used. group factor 1 2 3 4 5 6 7 8 9 10 11 live load resistance factor (𝜸𝑳 1.40 1.42 1.44 1.46 1.48 1.50 1.52 1.54 1.56 1.58 1.60 dead load resistance factor (𝜸𝑫 1.00 1.02 1.04 1.06 1.08 1.10 1.12 1.14 1.16 1.18 1.20 strength reduction factors(∅) 0.70 0.72 0.74 0.76 0.78 0.80 0.82 0.84 0.86 0.88 0.90 table 3: load and resistance factors for calculating the beta indexes. f. jafari et alii, frattura ed integrità strutturale, 51 (2020) 136-150; doi: 10.3221/igf-esis.51.11 145 fig. 8 shows the maximum beta index corresponds to t =0.40 and 0.50. for all values of t and load resistance factors, the safety indexes are between 3.55 to 4.65. as well, the safety index is decreased due to the reduction of the live load effect or increasing of t values. furthermore, the indexes are reduced by increasing the load and resistance factor by a mild slope. as a result, for rectangular type cross-section, the variations of the safety indexes are more dependent on the values of   ,  ,l d c   . figure 8: prediction of load and resistance factors for the rectangular beam in combined state as seen from fig. 9 the maximum beta index corresponds to t =0.40 and 0.50. for all values of t and load resistance factors, the safety indexes are between 3.15 to 4.00, which there are less than indexes for rectangular cross-section. as well, for lshaped beams, the safety indexes are remained constant by variation of the load resistance factors. as a result, for l type cross-sections, the variations of the safety indexes are independent of the values of ,  ,l d c   . f. jafari et alii, frattura ed integrità strutturale, 51 (2020) 136-150; doi: 10.3221/igf-esis.51.11 146 fig. 10 represents the maximum beta index corresponds to t =0.40 and 0.50. for all values of t and load resistance factors, the safety indexes are between 2.65 to 3.70. as well, the safety index is decreased due to the reduction of the live load effect or increasing of t values. furthermore, the indexes are reduced by increasing the load and resistance factors by the mild slope. as a result, similar to rectangular type beams, for t type cross-sections, the variations of the safety indexes are more dependent on the values of   ,  ,l d c   . figs. 8 to 9 clearly show that the safety indexes for t type beams are smallest and l type beams have better performance. generally, the rectangular beams have the highest safety factors. because the torsion on these types of beams has less contribution and the bending moment has a significant effect. figure 9: prediction of load and resistance factors for the l section beam in combined state f. jafari et alii, frattura ed integrità strutturale, 51 (2020) 136-150; doi: 10.3221/igf-esis.51.11 147 figure 10: prediction load and resistance factors for t section beam in combined state discussion he safety surfaces of the aci concrete standard for combined limit sates ( torsion-shear-bending) were studied in this research and the aci standard beta indexes were obtained. in the combined modes, the beta coefficient is greater than 3.0 for the l and rectangular cross-sections, while for the t cross-section, the safety index is less than 3.0 for t>0.5, and according to the suggested references, the safety coefficients should be greater than 2.8 for the bending design of cross-sections and greater than 2 for the design of shear and torsion, which is somewhat the boundary points. figs. 11 and 12 show the maximum and average beta indexes for all limit states for three studied cross-sections. t f. jafari et alii, frattura ed integrità strutturale, 51 (2020) 136-150; doi: 10.3221/igf-esis.51.11 148 figure 11: average aci beta indexes for different cross-sections. figure 12: maximum aci beta indexes for different cross-sections. conclusion ased on the obtained results the following conclusions could be drawn:  in all cross-sections, the obtained beta index for the combination of bending-shear is between shear and bending state such that the beta index is higher than the bending state and lower than the torsion state.  the beta index for a combination of bending-torsion is between torsion and bending state such that the beta index is higher than the bending state and lower than the torsion state. this surface is close to the bending state which means bending equations have a significant effect on the combination surface. b f. jafari et alii, frattura ed integrità strutturale, 51 (2020) 136-150; doi: 10.3221/igf-esis.51.11 149  beta index for a combination of shear-torsion is between torsion and this surface is close to shear state which means shear equations have a significant effect on the combination surface.  for all combination states (shear – torsion and bending –torsion), the beta indexes are greater than 3 which shows the beams are designed safety. according to previous research [20], the values of the beta index should be greater than 2.8 due to the design beam in bending and shear limit state safety.  in combined state(shear bending and torsion), the value of the beta index has the highest value in comparison with other limit states (shear – bending, shear – torsion and bending – torsion ) which shows the aci equations adequately guarantee the safe design. disclosure he authors have no conflict of interest to declare. acknowledgment he second author acknowledges the support from malayer university when he was an assistant professor of civil engineering from september 2008 to june 2019. references [1] ellingwood, b. r.and ang, a. h. (1974). risk-based evaluation of design criteria. journal of the structural division, 100 (proc. paper 10778). [2] bentz, e. c., vecchio, f. j.and collins, m. p. (2006). simplified modified compression field theory for calculating shear strength of reinforced concrete elements. aci materials journal, 103(4), pp.614-621 [3] porco, f., uva, g., sangirardi, m.and casolo, s. (2013). about the reliability of punching verifications in reinforced concrete flat slabs. the open construction and building technology journal, 7(1), pp. 123-133 [4] jensen, d.f. (2014). reliability analysis for shear in lightweight reinforced concrete bridges using shear beam database, m.sc. thesis, utah state university. [5] backes, m. r., fernández ruiz, m.and muttoni, a. (2014). interaction between in-plane shear forces and transverse bending moments in concrete bridge webs. in proc. of the 10th fib international ph.d. symposium in civil engineering, quebec (no. conf, pp. 403-408). [6] nowak, a. s.and szerszen, m. m. (2003). calibration of design code for buildings (aci 318): part 1-statistical models for resistance. aci structural journal, 100(3), pp. 377-382. [7] uva, g., porco, f., fiore, a.and mezzina, m. (2013). proposal of a methodology for assessing the reliability of in situ concrete tests and improving the estimate of the compressive strength. construction and building materials, 38, pp. 7283. [8] pérez-rocha, l. e., fernández, m. a., manjarrez, l. e., maldonado, j. d.and esteva, l (2014). a simplified methodology to obtain reliability indexes for calibration of design code for buildings, 4th international conference on computational methods in structural dynamics and earthquake engineering, kos island, greece. [9] abejide, o. s. (2014). reliability analysis of bending, shear and deflection criteria of reinforced concrete slabs. nigerian journal of technology, 33(3), pp. 394-400. [10] al-ansari, m. s. (2015). reliability and flexural behavior of triangular and t-reinforced concrete beams. international journal of advanced structural engineering (ijase), 7(4), pp. 377-386. [11] bastidas-arteaga, e. (2018). reliability of reinforced concrete structures subjected to corrosion-fatigue and climate change. international journal of concrete structures and materials, 12(1), pp. 10-21. t t f. jafari et alii, frattura ed integrità strutturale, 51 (2020) 136-150; doi: 10.3221/igf-esis.51.11 150 [12] jafar.f, akbari. jand jahanpour, a. (2017). evaluation of safety index and calibration of load and resistance factors for reinforced concrete beams under bending, shear, and torsion demands, journal of structural and constructional engineering, 3(4), pp. 49-64. [13] akbari, j.and jafari, f. (2018). calibration of load and resistance factors for reinforced concrete. civil engineering infrastructures journal, 51(1), pp. 217-227. [14] słowik, m., skrzypczak, i., kotynia, r.and kaszubska, m. (2017). the application of a probabilistic method to the reliability analysis of longitudinally reinforced concrete beams. procedia engineering, 193, pp. 273-280. [15] huang, x., sui, l., xing, f., zhou, y.and wu, y. (2019). reliability assessment for flexural frp-strengthened reinforced concrete beams based on importance sampling. composites part b: engineering, 156, pp. 378-398. [16] aci committee 318. (2015). building code requirements for structural concrete (aci 318m-14): an aci standard: commentary on building code requirements for structural concrete (aci 318m-14). american concrete institute. [17] ellingwood, b., macgregor, j. g., galambos, t. v.and cornell, c. a. (1982). probability-based load criteria: load factors and load combinations. journal of the structural division, 108(5), pp. 978-997. [18] nowak, a. s.and collins, k. r. (2012). reliability of structures. crc press . [19] choi, s. k., grandhi, r.and canfield, r. a. (2006). reliability-based structural design. springer science & business media . [20] mirza, s. a. (1998). monte carlo simulation of dispersions in composite steel-concrete column strength interaction. engineering structures, 20(1-2), pp. 97-104. [21] matlab (2016), the mathworks, inc., natick, release 2016. [22] badarloo, b.and jafari, f. (2019). numerical study on the effect of concrete grade on the cft circular column’s behavior under axial load. civil engineering journal, 5(11), pp. 2359-2376. << /ascii85encodepages false /allowtransparency false /autopositionepsfiles true /autorotatepages /none /binding /left /calgrayprofile (dot gain 20%) /calrgbprofile (srgb iec61966-2.1) /calcmykprofile (u.s. web coated \050swop\051 v2) /srgbprofile (srgb iec61966-2.1) /cannotembedfontpolicy /error /compatibilitylevel 1.4 /compressobjects /tags /compresspages true /convertimagestoindexed true /passthroughjpegimages true /createjobticket false /defaultrenderingintent /default /detectblends true /detectcurves 0.0000 /colorconversionstrategy /cmyk /dothumbnails false /embedallfonts true /embedopentype false /parseiccprofilesincomments true /embedjoboptions true /dscreportinglevel 0 /emitdscwarnings false /endpage -1 /imagememory 1048576 /lockdistillerparams false /maxsubsetpct 100 /optimize true /opm 1 /parsedsccomments true 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/hrv (za stvaranje adobe pdf dokumenata najpogodnijih za visokokvalitetni ispis prije tiskanja koristite ove postavke. stvoreni pdf dokumenti mogu se otvoriti acrobat i adobe reader 5.0 i kasnijim verzijama.) /hun 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/pdfxoutputintentprofileselector /documentcmyk /preserveediting true /untaggedcmykhandling /leaveuntagged /untaggedrgbhandling /usedocumentprofile /usedocumentbleed false >> ] >> setdistillerparams << /hwresolution [2400 2400] /pagesize [612.000 792.000] >> setpagedevice microsoft word 2178 l. marsavina et al., frattura ed integrità strutturale, 47 (2019) 266-276; doi: 10.3221/igf-esis.47.20 266 fracture and structural integrity: ten years of ‘frattura ed integrità strutturale’ mechanical and fracture properties of particleboard liviu marsavina politehnica university of timisoara, department of mechanics and strength of materials, 300 222 timisoara, romania liviu.marsavina@upt.ro ion octavian pop universite de limoges, gc2d, ea 3178, egletons f-19300, france pft bois-construction du limousin, egletons f-19300, france ion-octavian.pop@unilim.fr emanoil linul politehnica university of timisoara, department of mechanics and strength of materials, 300 222 timisoara, romania emanoil.linul@upt.ro, https://orcid.org/0000-0001-9090-8917 abstract. particleboard (pb) are wood-based composites with fine wood fibers bound together by a small amount of polymeric adhesive, widely used in furniture industry and civil engineering. pb plates can be painted, laminated or veneered, and have good dimensional stability and load bearing capacity when properly designed. however, the deformation and fracture of such elements create malfunctions of structures made of mdf. this paper presents experimental results obtained for three point bending (tpb) tests, mode i and mode ii fracture toughness. the bending tests were carried on rectangular specimens, while the fracture toughness tests were performed on single edge notched bend (senb) specimens for mode i, respectively on compact shear (cs) specimens for mode ii loadings. digital image correlation technique allows the determination of the crack relative displacement factor and estimation of the energy release rate. keywords. particleboard; fracture toughness; digital image correlation. citation: marsavina, l., pop, o., linul, e., mechanical and fracture properties of particleboard, frattura ed integrità strutturale, 47 (2019) 266-276. received: 23.08.2018 accepted: 08.10.2018 published: 01.01.2019 copyright: © 2018 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. introduction articleboard (pb) represent a class of wood-based composite with fine wood fibers bound together by a small amount of polymeric adhesive. their main applications are in furniture industry and civil engineering [1]. pb plates can be painted, laminated or veneered, and have good dimensional stability and load bearing capacity when p http://www.gruppofrattura.it/va/47/2178.mp4 l. marsavina et al., frattura ed integrità strutturale, 47 (2019) 266-276; doi: 10.3221/igf-esis.47.20 267 properly designed [2]. however, the deformation and fracture of such elements create malfunctions of structures made of pb. different studies on bending properties of pb were published. in [3] design requirements for pb and medium density fiberboard (mdf) plates under different loading conditions are presented. the performance of pb beams under four point bending are presented in [4]. the effect of different types of coatings on the strength and stiffness of pb are investigated in [5]. kulman et al. [6] studied the effect of density and temperature on modulus of rupture and modulus of elasticity of pb and mdf. the fracture behavior of wood and its composites is reviewed by stanzl-tschegg and navi [7]. however, only a few studies investigates the fracture toughness of pb [8-10]. the same like in the case of mdf, different values of fracture toughness were obtained: matsumoto and nairn [11] 2.57 mpa·m1/2 for density of 609 kg/m3, respectively 3.77 mpa·m1/2 for density of 769 kg/m3 using compact tension (ct) specimens, while for wedge splitting specimens and a density of 710 kg/m3 niemz et al. [12] obtained 1.81 mpa·m1/2. fewer investigations were carried out on mixed mode fracture toughness of pb and mdf, [13]. today, several fracture approaches such as the stress intensity factor (sif) [14-16], the crack relative displacement factor (crdf) [17-20] or the energy release rate [21-24] allow expressing fracture criteria. it should also be noted that usually the damage level could be evaluated from a local approach based on the mechanical fields assigned by the crack tip singularity or by a global approach using the mechanical fields far to the crack tip singularity. starting from this analysis, in the present study, a formalism based on the sif and the crdf was applied to evaluate the fracture process. as will be shown latter the crdf allows definition of the kinematic state around to the crack tip. as defined by dubois et al. [17, 18], pop et al. [19] and jamaaoui et al. [25], the crack opening state represents the relative displacement between two points positioned on the upper and the lower crack flanks. its evaluation can be performed directly from the experimental measurements. associated more often to full fields techniques, the optical methods can be easily applied to observe and to analyze the fracture process. today, several optical techniques and methods are developed in order to measure the different fracture properties. among these methods, we remind here: interferometry, stereo correlation, moiré, photoelasticity, digital image correlation (dic) or marktracking methods [24, 26-32]. nevertheless, their application to analyze the fracture process depends on the observation scale and the environmental boundary conditions (i.e. laboratory or in-situ). concerning the characterization of mechanical and fracture properties of pb the dic and the mark-tracking methods seem to be the better. for this purpose, the crack opening displacement was measured by means the dic. associated with optical full field methods the dic allows measure of the bi-dimensional displacement and strain fields. the interest of this method lies in its possibility to perform the measurements without contact. moreover, the studied zone, sometimes called the zone of interest, can be easily adapted to the analyze scale (i.e. local or global). today several algorithms to perform the dic in order to evaluate the fracture parameters are proposed [29-37]. in the present study, the analysis was performed using correla software’s, developed by pem team of pprim institut of poitiers [38-39]. the present paper presents the original results, obtained for two different densities and thicknesses of pb, for modulus of rupture, modulus of elasticity, the fracture toughness in mode i and predominantly mode ii and the crack relative intensity factors. experimental determination of mechanical and fracture properties materials ests were carried out on medium density pb with thicknesses of 16 and 25 mm. the density was determined on each specimen resulting a mean density of 600 (±12) kg/m3 for the pb with 16 mm thickness, respectively 587 (±15) kg/m3 for the pb with 25 mm thickness. the specimens before testing were conditioned at 22±2°c room temperature and 65±5% relative air humidity. bending tests the tests were performed on a zwick roell z005 electromechanical universal testing machine under displacement control by setting the machine to 10 mm/min. during the test, the force versus deflection was measured by means of linear variable differential transformer (lvdt) position sensor (-/+ 0.01mm) and a load cell of 5 kn (±5%). rectangular specimens, fig. 1, were adopted for the three point bending tests, with dimensions b (height)  b (width)  l (length). for 16 mm thickness the dimensions were b=16 mm, l=250 mm, and the span (distance between supports) s=192 mm respectively for 25 mm thickness b=25 mm, l=250 mm, and s=192 mm. the test program consisted of four test series (two different thicknesses of pb plates of 16 and 25 mm, respectively two orientations 1 and 2) with five tests in each t l. marsavina et al., frattura ed integrità strutturale, 47 (2019) 266-276; doi: 10.3221/igf-esis.47.20 268 series. orientation 1 corresponds to an out-of-plane loading, and orientation 2 corresponds to an in-plane loading direction. typical force displacement curves are shown in fig. 2. it could be observed that for orientation 1, which is the one most used for pb, higher values of loads were obtained comparing with direction 2 and a quasi-brittle behavior figure 1: three point bending specimen figure 2: typical force displacement curves based on the en 310 standard [40], the modulus of rupture (mor) and modulus of elasticity (moe) were determined. the three point bending results are shown in fig. 3. it could be observed that the maximum values of mor and moe were obtained for direction 1 and 16 mm thickness pb: 11.5 mpa, respectively 1782 mpa. the obtained values are in accordance with those from literature for pb, as follow: 11 mpa for mor and 1725 mpa for moe. in fig. 3 boxes marked with 1 and 2 are related to sample orientation according to loading direction. a. modulus of rupture b. modulus of elasticity figure 3: mechanical properties of particleboard mode i fracture toughness tests mode i fracture toughness tests were carried out on single edge notched bend (senb) specimens [41], fig. 4a loaded in three point bending using zwick roell z005, at room temperature, under displacement control with a loading speed of 10 mm/min. the maximum load fmax recorded during the tests was considered to calculate mode i fracture toughness (kic), given by eq. (1): 0 2 4 6 0 100 200 300 400 500 standard trav el in mm f o rc e i n n 11.50 10.63 9.30 9.24 0 2 4 6 8 10 12 14 16_1 25_1 16_2 25_2 m o d u lu s o f ru p tu re [ m p a ] thickness [mm] 1 2 1782.0 1245.6 1406.7 1153.6 0 500 1000 1500 2000 2500 16_1 25_1 16_2 25_2 m o d u lu s o f e la s ti c it y [ m p a ] thickness [mm] 1 2 25_1 25_2 16_2 16_1 l. marsavina et al., frattura ed integrità strutturale, 47 (2019) 266-276; doi: 10.3221/igf-esis.47.20 269  max1/2 /ic f k f a w b w  (1) with w specimen width, b = w/2 specimen thickness and f(a/w) is dimensionless sif for senb specimens, calculated with the following [42]:   2 3/2 1.99 ( / )(1 / ) 2.15 3.93( / ) 2.7( / ) / 6 / (1 2 / )(1 / ) a w a w a w a w f a w a w a w a w         . (2) specimen thickness b [mm] width w [mm] crack length a [mm] maximum load fmax [n] fracture toughness kic [mpa·m1/2] mean fracture toughness kic [mpa·m1/2] i.1 23.8 50.1 24.6 466 0.868 0.841 i.2 23.6 50.1 24.5 465 0.868 i.3 23.6 50.1 24.5 454 0.847 i.4 23.6 50.1 24.5 417 0.778 i.5 23.6 50.1 24.5 452 0.843 i.6 16.3 32 17.8 178 0.784 0.736 i.7 16.1 32 16.8 154 0.618 i.8 16.2 32 18.8 149 0.740 i.9 16.1 32 17.8 153 0.682 i.10 16.1 32 17.5 198 0.855 table 1: mode i fracture toughness results the specimen dimensions, maximum load and mode i fracture toughness are summarized in tab. 1. it could be observed that the maximum value of kic = 0.841 mpa·m1/2 was obtained for the 25 mm pb thickness. on contrary, the mode i fracture toughness for 16 mm thickness was 0.736 mpa·m1/2. mode ii fracture toughness tests compact shear (cs) specimens [43], fig. 4b, were used for mode ii fracture toughness determination. tests were performed on a 100 kn a009 (tc100) universal testing machine, at room temperature and using 10 mm/min displacement control. maximum load was used to estimate the mode i and mode ii stress intensity factors. the sifs solutions could be expressed on the form:  max , ,ic i f k a f a w i i ii h b   (3) with b as the specimen thickness, a as crack length and h as specimen width. a numerical calibration of the specimen was performed earlier by petrova et. al. [44] using finite element analysis in order to determine the non-dimensional sifs fi(a/w), resulting:     4 3 2 4 3 2 / 2.472( / ) 1.784 ( / ) 1.135( / ) 0.213( / ) 0.295 / 6.416( / ) 11.154 ( / ) 8.992( / ) 3.667( / ) 1.01 i ii f a w a w a w a w a w f a w a w a w a w a w           (4) it should be noted that even if the applied load produce shear in front of the crack, a small amount of mode i still exist at the crack tip [44], so the fracture thoughness could be expressed using an effective sif value: l. marsavina et al., frattura ed integrità strutturale, 47 (2019) 266-276; doi: 10.3221/igf-esis.47.20 270 2 2 eff i iik k k  (5) tab. 2 presents the specimen dimensions, maximum load, the mode i, mode ii and effective sifs. a higher value of keff = 0.785 mpa·m1/2 was obtained for the pb with 25 mm thickness comparing with the pb of 16 mm thickness, keff = 0.631 mpa·m1/2. a. single edge notch bend b. compact shear figure 4: test specimens for mode i and mode ii fracture toughness determination. specimen b [mm] w [mm] h [mm] a [mm] fmax [n] ki [mpa·m1/2] kii [mpa·m1/2] keff [mpa·m1/2] mean keff [mpa·m1/2] ii.1 16.4 50.3 76.6 25.0 3110 0.101 0.565 0.574 0.631 ii.2 16.4 50.0 76.0 25.0 3470 0.113 0.630 0.640 ii.3 16.4 51.1 76.0 25.0 3700 0.120 0.672 0.682 ii.4 16.4 49.3 76.3 25.6 3050 0.091 0.532 0.540 ii.5 16.4 50.0 76.0 25.0 3900 0.127 0.708 0.720 ii.6 24 75.0 100 48.5 5911 0.198 0.826 0.850 0.785 ii.7 24 76.0 100 48.5 5189 0.174 0.725 0.746 ii.8 24 76.2 100 49.2 5788 0.194 0.810 0.833 ii.9 24 75.0 100 48.7 5587 0.187 0.781 0.803 ii.10 24 75.4 100 47.7 4814 0.162 0.674 0.693 table 2: mode ii fracture toughness results the obtained results are represented in the fracture envelope plot kii/kic versus ki/kic side by side with the analytical predictions of maximum tensile stress (mts) [45, 46], maximum energy release rate (gmax) [47, 48] and minimum strain energy density (sed) [49, 50]. from fig. 5, it could be observed that the mts and sed criteria fits better with the experimental results. l. marsavina et al., frattura ed integrità strutturale, 47 (2019) 266-276; doi: 10.3221/igf-esis.47.20 271 figure 5: comparison between fracture criteria and experimental results crack relative displacement factor estimation by digital image correlation n the present paper, the fracture process was evaluated trough two parameters, the stress intensity factor and the crack relative displacement factor (crdf), respectively. as shown above, the calculation of sif is most often based on the analytical solutions. the analysis of the analytical equations allowing calculation the sif shows that its estimation depends on sample geometry and the loading amplitude. based on the displacement fields amplitude the crdf can be related with the kinematic state near the crack tip [19, 20, 25]. in this case, the crdf can be calculated from the displacement fields measured by optical metrologies [19, 20, 25]. in the present paper, we propose to use the digital image correlation (dic) in order to measure the displacement fields and to evaluate the crdf. it should be added that the evaluation of crdf allows to separate the mixed mode loading configurations and to identify the part of each mode in the fracture process. principle of digital image correlation as mentioned above, in the present study, the crdf was investigated by means dic. using this optical full field method the evolution of displacement fields was recorded during the fracture test. now concerning the principle of dic, it is important to specify that this technique is based on comparison of two images acquired before and after sample deformation [29-31, 42]. as described in fig. 6, the displacement was calculated in the zone of interest (zoi) meshed by small groups of pixels, called subsets [19, 20, 29-31, 51]. according with the dic hypothesis, the light intensity distribution during the test does not change. by supposing that the displacements may be approximated as homogeneous and bilinear inside the subset, the displacement fields were estimated by searching the subset distortions in terms of translations, rotations and rigid body motions. in fact, the displacement field represents the displacement vectors of the center of gravity of all subsets. concerning the sample preparation, it should be noted that prior to testing, a very thin black and white speckle pattern was sprayed on the specimen surface. then, as had been indicated above the displacement fields are calculated by tracking the deformation of a random grey speckle pattern applied to sample surface. in the present study, the zoi was meshed by using the 3232 pixels² subset sizes. the optical device configuration used in the present study consist of an avt marlin f-201b with a pentax 12.5-75 mm lens and a led light source. the measurement was realized using an aramis a non-contact and material-independent measuring system based on digital image correlation. the image analysis was performed using correla software’s, developed by pem team of pprim institut of poitiers [38-39]. the estimating uncertainty of displacement is about 0.026 pixels. 0.0 0.2 0.4 0.6 0.8 1.0 1.2 0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 k ii /k ic ki/kic mts sed gmax cs 16 cs 25 senb 16 senb 25 i l. marsavina et al., frattura ed integrità strutturale, 47 (2019) 266-276; doi: 10.3221/igf-esis.47.20 272 figure 6: principle of dic evaluation of crack relative displacement factor as detailed in works of [19, 20, 25, 52], the crdf is calculated from the experimental displacement field via an adjustment procedure based on an iterative newton-raphson algorithm (see fig. 7). figure 7: methodology of crdf calculation. this consists in a fitting of analytical solutions of kolossov–muskhelishvili’s series [53, 54] on the displacement fields measured by dic. dubois et al. [16, 17], pop et al. [19] and meite et al. [20] show that by using this approach, an “equivalent” displacement field can be created without experiment noises, the knowledge of the material properties or the nonlinear phenomena presence [17-20]. then, the crdf can be expressed as a function to the weighting coefficients of the analytical solutions of kolossov–muskhelishvili’s series. x1 x2 zoi x1 x2 zoi hsubset v s u b se t dh d v 1 m m*undeformed image deformed image subset x1 x2 subset m (4x4pixels) subset center p ixel x 2 p ix el x 2s u b se t x1 pixel x1 subset sample with black and white speckle pattern zoisubsets optimization                     n / 2 / 2 1 1 2 1 n / 2 / 2 2 1 2 1 u a r f , a r g , u a r l , a r z ,                                    by an adjustment procedureoptimization of displacement field experimental  displacement field equivalent  displacement field experimental boundary conditions  experimental noises adjustment procedure (newton-raphson) identification of the weighting coefficients 1 1 n n 0 0 1 2 1 2 1 2 1 2 0a a a a t t r x x    rigid body motions crack geometry optimized fields  ( ) 11 1k 2 2 a 1         ( ) 122k 2 2 a 1          analytical solutions of kolossov–muskhelishvili’s series crack relative displacement factor l. marsavina et al., frattura ed integrità strutturale, 47 (2019) 266-276; doi: 10.3221/igf-esis.47.20 273 the mean value of crdf calculated for maximum loading given in tabs. 1 and 2, calculated from pop et al. [19] and meite et al. [20] developments are resumed in tabs. 3 and 4. the values of the weighting coefficients associated with opening and shear modes are also summarized in tabs. 3 and 4. the weighting coefficients were estimated according with the methodology illustrated in fig. 7. specimens a11 [m0.5] 10-3 mean crdf mode i (ki) [m0.5] 10-3 a21 [m0.5] 10-3 mean crdf mode i (kii) [m0.5] 10-3 (ki)/(kii) (ki)/(kii) tab. 1 i.1-6 9.8 0.138 0.07 0.001 125 / i.7-14 7.2 0.102 0.05 0.0008 127 / table 3: single edge notch bend test– crack relative displacement factor specimens a11 [m0.5] 10-3 crdf mode i (ki) [m0.5] 10-3 a21 [m0.5] 10-3 crdf mode ii (kii) [m0.5] 10-3 (ki)/(kii) (ki)/(kii) tab. 2 ii.1-5 0.8 0.012 7.5 0.105 0.11 0.18 ii.6-10 2.3 0.032 10 0.142 0.23 0.24 table 4: compact shear test– crack relative displacement factor the data resumed in tabs. 3 and 4 lead us conclude that the opening and shear modes coexist during the test. the crack path observed after the tests indicated that the crack is not rectilinear. this aspect may be connected with the experimental boundary conditions and the pb fiber orientation. it is also interesting to observe that the relationship between the crdf corresponding to mode i and ii, and the relationship to the sif show some similarities. pop et al [19, 20] and meite et al. [25, 52] show also that the energy may be estimated from the crdf and sif values, eq. (6). ( ) ( ) 8 f k k g     (6) where:  ( ) 1 1 8k a k    (7) where 𝐾 is the crack relative displacement factor; 𝐾 is the stress intensity factor and 𝛾 1 𝑜𝑟 2 corresponds to mode 1 and mode 2; 𝐴 , 𝐴 are the weighting coefficients associated with opening and shear modes. tab. 5 resumed the values of the energy release rate calculated from the results obtained in the tab. 1-4. specimens energy release rate mode i [j/m²] energy release rate mode ii [j/m²] i.1-6 15.3 / i.7-14 9.8 / ii.1-5 0.16 8.2 ii.6-10 0.73 13.5 table 5: energy values. l. marsavina et al., frattura ed integrità strutturale, 47 (2019) 266-276; doi: 10.3221/igf-esis.47.20 274 conclusions he paper presents the experimental results for mechanical and fracture properties of particleboard materials. tab. 6 summarizes the obtained results for the two pb thicknesses corresponding to direction 2 of orientation. it could be observed that the pb with thickness of 16 mm has higher mechanical properties (modulus of rupture-mor and modulus of elasticity-moe); while the higher fracture toughness was obtained for pb with 25 mm thickness. thickness mor [mpa] moe [mpa] kic [mpa·m1/2] keff [mpa·m1/2] 16 9.30 1406.7 0.736 0.631 25 9.24 1153.2 0.841 0.785 table 6: a comparison of mechanical and fracture properties for pb using the experimental displacements measured by digital image correlation (dic) the crack relative displacement factor (crdf) was estimated. the evaluation of crdf allowing to evaluate the part of each mode in the fracture process. according to presented approach, all changes in material properties can be directly correlated with the displacement measurement and implicitly with the crdf amplitude. as shown, the calculation of crdf may be performed without knowledge of the material constitutive law. the values of crdf show that even for an opening mode loading, the crack path and experimental boundary conditions induce a mixed mode configuration. even if the value of crdf corresponding to mode ii is small, the results show the presence of the mode ii during the crack propagation in opening mode. as shown in tab. 4, the relationship between the crdf corresponding to mode i and ii of fracture, and the relationship between the stress intensity factor (sif) show some similarities to the shear test. this observation allows consideration of the calculated phase angle. moreover, the fracture energy was evaluated from the crdf and the sif values. it should be noted that this approach allows evaluation of the fracture parameters without the knowledge of the properties of material. classical fracture criteria (maximum tensile stress and minimum strain energy density) provide a good prediction of fracture of particleboard (see fig. 5). acknowledgement art of the experimental work was carried out in the framework of the grant from the romanian national authority for scientific research, cncs – uefiscdi, project code pn-iii-p1-1.1-mcd-2016-0076, contract number 41/8.11.2016, which supports the mobility of dr. pop at the university politehnica timișoara. the authors are grateful to mr. robert moscaliuc for specimen preparation and his contribution to experimental program. references [1] beer, p., sinn, g., gindl, m., stanzl-tschegg, s. (2005). work of fracture and of chips formation during linear cutting of particle-board, journal of materials processing technology 159, pp. 224–228. [2] beer, p., gindl, m., stanzl-tschegg, s. (2008). wedge splitting experiments on three-layered particleboard and consequences for cutting, holz als rohund werkstoff 66, pp. 135-141. [3] ansi a208.1 (1998). particleboard and mdf for shelving, american national standard, composite panel association, gaithersburg, md. [4] johnson, j. a., ifju, g., rogers, h.w. (1976). the performance of composite wood/particleboard beams under two point loading, wood and fiber, 8(2), pp. 85-97. [5] norvydas, v., minelga, d. (2006). strength and stiffness properties of furniture panels covered with different coatings, materials science, 12(4), pp. 328-332. t p l. marsavina et al., frattura ed integrità strutturale, 47 (2019) 266-276; doi: 10.3221/igf-esis.47.20 275 [6] kulman, s., boyko l., antsyferova, a. (2015) bending strength (modulus of rupture) and modulus of elasticity of mdf different density at various temperature, annals of warsaw university of life sciences forestry and wood technology, 91, pp. 101-106. [7] stanzl-tschegg, s.e., navi p. (2009). fracture behaviour of wood and its composites. a review. holzforschung 63, pp. 139–149. [8] ilcewicz, l.b. (1979). on the phenomena of fracture in particleboard, oregon state university. [9] veigel, s., rathke, j., weigl, m., gindl-altmutter, w. (2012). particle board and oriented strand board prepared with nanocellulose-reinforced adhesive, journal of nanomaterials, article id 158503, 1-8. [10] marsavina, l., pop, o., linul, e. (2018). mixed mode fracture toughness of particleboard, proceedia stuctural integrity, 9, pp. 47-54. [11] matsumoto, n., nairn, j.a. (2007). fracture toughness of mdf and other materials with fiber bridging, proc. of 22nd ann. tech. conf. of the amer. soc. of composites, sept. 17-19, seattle, wa, pp. 1-19. [12] niemz, p., diener, m., and pöhler, e. (1997). untersuchungen zur ermittlung der bruchzähigkeit an mdf-platten, holz als rohund werkstoff, 55, pp. 327-330. [13] yoshihara, h. (2010) mode i and mode ii initiation fracture toughness and resistance curve of medium density fiberboard measured by double cantilever beam and three-point bend end-notched flexure tests, engineering fracture mechanics, 77, pp. 2537–2549 [14] sneddon, in., (1946) the distribution of stress in the neighbourhood of a crack in an elastic solid, proc r soc lond, ser a math phys sci 187, 229–260. [15] irwin, gr. (1957) analysis of stresses and strains near the end of a crack traversing a plate, j appl mech, 24, 361–364. [16] erdogan, f. (1962) on the stress distribution in plates with collinear cuts under arbitrary loads, in: proceedings of the fourth us national congress of applied mechanics, 1, 547–574. [17] dubois, f., chazal, c. and petit, c. (2002) viscoelastic crack growth process in wood timbers: an approach by the finite element method for mode i fracture, int j fract, 113, 367–388. [18] dubois, f. and petit, c. (2005) modeling of the crack growth initiation in viscoelastic media by the gθ integral, eng fract mech, 72, 2821–2836. [19] pop. o., meite, m., dubois, f. and absi, j. (2011) identification algorithm for fracture parameters by combining dic and fem approaches, international journal of fracture, 170, 101-114. [20] méité, m., pop, o., dubois f. and absi, j. (2013) characterization of mixed-mode fracture based on a complementary analysis by means of full-field optical and finite element approaches, international journal of fracture, 180, 41-52. [21] cherepanov, g. (1967) crack propagation in continuous media, j appl mech, 31, 476–488. [22] budiansky, e. and rice, j. (1973) conservation laws and energy release rates, j appl mech, 40, 201–203. [23] rice, j. (1968) a path independent integral and the approximate analysis of strain concentration by notched and cracks, j appl mech, 35, 379–386. [24] pop, o., dubois, f. and absi, j. (2013) j-integral evaluation in cracked wood specimen using the mark tracking method, wood science and technology, 47 (2), 257-267. [25] jamaaoui, a., pop, o., dubois, f. and costa, g. (2017) wedge splitting test on douglas genotypes using an integrated mixed-mode approach, theoretical and applied fracture mechanics, 91, 44-51. [26] post, d. (1993) moire interferometry. in: kobayashi as, editor. handbook on experimental mechanics, new york. [27] orteu, jj. (2009) 3-d computer vision in experimental mechanics, optics and lasers in engineering, 47:282–291. [28] wells, a. and post, d. (1958) the dynamic stress distribution surrounding a running crack—a photoelastic analysis, proc soc exp stress anal, 16, 69–92 [29] sutton, m.a., wolters, w.j., peters, w.h., ranson, w.f. and mcneil, s.r. (1983) determination of displacements using an improved digital correlation method, image and vision computating, 1(3), 133-139. [30] sutton, m.a., cheng, m.q., peters, w.h., chao, y.j. and mcneill, s.r. (1986) application of an optimized digital correlation method to planar deformation analysis, image and vision computing, 4(3), 143-151 [31] sutton, m.a., yan, j.h., tiwari, v., schreier, h.w. and orteu, j.j. (2008) the effect of out-of-plane motion on 2d and 3d digital image correlation measurements, optics and lasers in engineering, 46(10), 746-757 . [32] brémand, f., dupré, j. and lagarde, a. (1995) mesure des déformations sans contact par analyse d’images, photomécanique 95 – etude du comportement des matériaux et des structures, ed. eyrolles, 171-177. [33] bretagne, n., valle, v. and dupre, j.c. (2005) development of the marks tracking technique for strain field and volume variation measurements, ndt&e international, 38, 290–298. [34] dupré, j.c., doumalin, p., belrhiti, y., khlifi, i., pop, o. and huger, m. (2018) detection of cracks in refractory materials by an enhanced digital image correlation technique, journal of materials science, 53 (2), 977-993. l. marsavina et al., frattura ed integrità strutturale, 47 (2019) 266-276; doi: 10.3221/igf-esis.47.20 276 [35] belrhiti, y., dupre, j.c., pop, o., germaneau, a., doumalin, p., huger, m and, chotard, t. combination of brazilian test and digital image correlation for mechanical characterization of refractory materials (2017) journal of the european ceramic society, 37 (5), 2285-2293. [36] bourdin, f., stinville, j.c., echlin, m.p., callahan, p.g., lenthe, w.c., torbet, c.j., texier, d., bridier, f., cormier, j., villechaise, p., pollock, t.m. and valle, v. (2018) measurements of plastic localization by heaviside-digital image correlation, acta materialia, 157, 307-325. [37] valle, v., bokam, p., germaneau, a. and hedan, s. (2018) new development of digital volume correlation for the study of fractured materials, experimental mechanics, 1-15. article in press. [38] brémand, f., cottron, m., doumalin, p., dupré, j.c., germaneau, a., valle, v. mesures en mécanique par méthodes optiques, techniques de l’ingénieur, r1850 v2, 1-26. [39] belrhiti, y., gallet-doncieux, a., germaneau, a., doumalin, p., dupre, j.c., alzina, a., michaud, p., pop, i.o., huger, m., chotard, t. (2012) application of optical methods to investigate the non-linear asymmetric behavior of ceramics exhibiting large strain to rupture by four-points bending test, journal of the european ceramic society, 32, 4073-4081. [40] en 310:1993. wood-based panels. determination of modulus of elasticity in bending and of bending strength. [41] linul, e., marsavina, l., sadowski t., kneć, m. (2012) size effect on fracture toughness of rigid polyurethane foams, solid state phenomena, 188, 205-210. [42] marsavina, l. and linul, e., fracture toughness of polyurethane foams. experimental versus micromechanical models, 18th european conference on fracture: fracture of materials and structures from micro to macro scale, ecf 2010; dresden; germany; 30 august 3 september 2010; code 93905 [43] marsavina, l., constantinescu, d.m., linul, e. et al. (2015) shear and mode ii fracture of pur foams, engineering failure analysis, 58, 465-476. [44] petrova, v., marsavina, l., sadowski, t. (2012). revisit of compact mode ii crack specimen. analysis and fracture interpretation, theoretical and applied fracture mechanics, 59(1), pp. 41-48. [45] aliha, m.r.m., linul, e., bahmani, a., marsavina, l. (2018) experimental and theoretical fracture toughness investigation of pur foams under mixed mode i+iii loading, polymer testing, 67, pp. 75-83. [46] erdogan, f., sih, g.c. (1963). on the crack extension in plates under plane loading and transverse shear, journal of basic engineering, 85, pp. 519-525. [47] marsavina, l., constantinescu, d.m., linul, e., stuparu, f.a., apostol, d.a. (2016) experimental and numerical crack paths in pur foams, engineering fracture mechanics, 167, pp. 68-83. [48] hussain, m.a., pu, s.l., underwood j. (1974) strain energy release rate for a crack under combined mode i and mode ii. in: fracture analysis, paris pc, g.r. irwin gr editors, astm stp560, philadelphia, pp. 2-28. [49] sih, g.c. (1974). strain-energy-density factor applied to mixed mode crack problems, international journal of fracture, 10, pp. 305-321. [50] marsavina, l., berto, f., negru, r., serban, d.a., linul, e. (2017) an engineering approach to predict mixed mode fracture of pur foams based on ased and micromechanical modeling, theoretical and applied fracture mechanics, 91, pp. 148-154. [51] hild, f. and roux, s. (2006) measuring stress intensity factors with a camera: integrated digital image correlation (idic), comptes rendus mécanique, 334, 8–12. [52] jamaaoui, a., pop, o., ktari, r., millien, a. and petit, c. (2017) analyzing of wedge splitting test on asphalt pavement using optical measurements, journal of testing and evaluation, 45 (6), 1959-1970 [53] williams, m. (1957) on the stress distribution at the base of a stationary crack, asme journal applied mechanics 24, 109-114. [54] muskhelishvili, in. 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/hrv (za stvaranje adobe pdf dokumenata najpogodnijih za visokokvalitetni ispis prije tiskanja koristite ove postavke. stvoreni pdf dokumenti mogu se otvoriti acrobat i adobe reader 5.0 i kasnijim verzijama.) /hun 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can be opened with acrobat and adobe reader 5.0 and later.) >> /namespace [ (adobe) (common) (1.0) ] /othernamespaces [ << /asreaderspreads false /cropimagestoframes true /errorcontrol /warnandcontinue /flattenerignorespreadoverrides false /includeguidesgrids false /includenonprinting false /includeslug false /namespace [ (adobe) (indesign) (4.0) ] /omitplacedbitmaps false /omitplacedeps false /omitplacedpdf false /simulateoverprint /legacy >> << /addbleedmarks false /addcolorbars false /addcropmarks false /addpageinfo false /addregmarks false /convertcolors /converttocmyk /destinationprofilename () /destinationprofileselector /documentcmyk /downsample16bitimages true /flattenerpreset << /presetselector /mediumresolution >> /formelements false /generatestructure false /includebookmarks false /includehyperlinks false /includeinteractive false /includelayers false /includeprofiles false /multimediahandling /useobjectsettings /namespace [ (adobe) (creativesuite) (2.0) ] /pdfxoutputintentprofileselector /documentcmyk /preserveediting true /untaggedcmykhandling /leaveuntagged /untaggedrgbhandling /usedocumentprofile /usedocumentbleed false >> ] >> setdistillerparams << /hwresolution [2400 2400] /pagesize [612.000 792.000] >> setpagedevice shot peening processes to obtain nanocrystalline surfaces in metal alloys: y. lu et alii, frattura ed integrità strutturale, 53 (2020) 325-336; doi: 10.3221/igf-esis.53.25 325 a new approach of cmt seam welding deformation forecasting based on ga-bpnn yao lu, yanfeng xing*, xuexing li, sha xu school of mechanical and automotive engineering, shanghai university of engineering science, china edison.lu@foxmail.com, smsmsues@163.com, megres.li@foxmail.com, xytongxing376@sina.com abstract. welding deformation affects the quality of the welded parts. in this paper, by introducing improved back propagation neural network (bpnn), a cold metal transfer (cmt) welding deformation prediction model for aluminum-steel hybrid sheets is established. before applying bpnn, important parameters affecting welding deformation were obtained by orthogonal test and gray relational grade theory. the accuracy of welding deformation prediction of bpnn is improved by genetic algorithm. the results show that compared with the prediction method based on traditional theory, the deformation prediction model based on ga-bpnn has higher accuracy. predicted results were applied to the aluminum-steel cmt seam welding in the form of inverse deformation, and the deformation of the welded plate was significantly improved. keywords. cold metal transfer welding; orthogonal test; gray relational grade theory; bp neural network; genetic algorithm. citation: yao, lu., yanfeng, xing., xuexing, li., sha, xu., a new approach of cmt seam welding deformation forecasting based on ga-bpnn, frattura ed integrità strutturale, 53 (2020) 325-336. received: 11.01.2020 accepted: 18.05.2020 published: 01.07.2020 copyright: © 2020 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. introduction luminum alloy has the advantages of light weight, strong corrosion resistance and good durability. therefore, the replacement of the traditional steel structure by the aluminum-steel hybrid structure is an effective means to realize the lightweight of the automobile. aluminum-steel hybrid sheet with traditional joining method has poor mechanical properties, so in recent years, new metal sheet joining technologies such as cold metal transfer welding [1], self-piercing riveting [2], and friction stir welding [3] have received increasing attention and application. cmt technology has the advantages of low heat input and no spatter transition. the basic principle of the cmt process is a short circuit transition. each time the short circuit occurs, the welding wire is mechanically retracted, which assists the droplet to detach at relatively low welding currents, and thus the welding heat input can be significantly reduced. therefore, the cmt process is suitable for the welding of thin gage aluminum alloys with corresponding low distortion and high quality. there is no splash in the welding process, and the weld seam is beautifully formed [4]. due to the large difference in material properties such as linear expansion coefficient and thermal conductivity of aluminum and steel, welding deformation occurs in the aluminum alloy cmt welding process, which affects the a mailto:edison.lu@foxmail.com mailto:smsmsues@163.com mailto:megres.li@foxmail.com https://youtu.be/2l4sjlj15gy y. lu et alii, frattura ed integrità strutturale, 53 (2020) 325-336; doi: 10.3221/igf-esis.53.25 326 manufacturing process of the welded structure. at present, the main methods for researchers to predict welding deformation are three-dimensional thermoelastic finite element method and inherent strain method. deng et al. [5] predicted the residual stress distribution in low alloy steel and stainless steel dissimilar metal round pipe joints based on the thermoelastic model. xia [6] used the three-dimensional thermoelastic finite element method to predict the residual stress and deformation of steel plates with different thicknesses. liang [7] used the three-dimensional thermoelastic finite element method and the inherent strain method to predict the welding deformation of 1mm ultra-thin plate. the threedimensional thermoelastic-plastic finite element method tracks the entire thermal cycle of the welding process, and can obtain the temperature field and stress field of the welded plate at any time during the welding process and the cooling process. however, due to the current computer level limitation, the three-dimensional thermoelastic finite element method cannot be applied to complex practical engineering. the inherent strain method can economically predict large and complex structural deformations with short calculation times, but the precision is low [8]. therefore, it is particularly important to find a method that is highly accurate and can be applied to practical complex engineering problems to predict the deformation of the welded plate. in the actual welding process, the factors affecting the welding deformation are complex and nonlinear [9]. while bpnn has significant advantages in possessing associative inference and adaptive capacity, and particularly it can be applied to processing various kinds of nonlinear problems [10]. bp neural network is a multi-layer feed forward neural network. its essence is to approximate the input-output relationship of complex structures by multiple fittings with simple nonlinear functions [11]. bp neural network has been applied to the prediction of connection technology performance such as pulse mig welding [12], imprint connection [13], resistance spot welding [14], although bpnn has good local optimization ability, it cannot find the optimal solution in the global scope. bpnn is easy to fall into local extreme points, restricting the accuracy of the neural network [15]. genetic algorithm (ga) is an efficient global optimization search algorithm. the search spans the entire solution space and has strong global optimization ability. the combination of ga and bp algorithm can be used to find the best connection right in the global scope, to avoid the network falling into local minimum points, and get the optimal solution [16]. therefore, the combination of ga and bpnn can improve the prediction accuracy of welding deformation of aluminum-steel sheet. moreover，the deformation predicted by the gabpnn method can be controlled by the inverse deformation method. in this paper, cmt welding orthogonal test was carried out on aa6061-t6 aluminum alloy and dp590 steel sheet by cmt welding technology. the gray relational grade theory is used to analyze the influence of cmt welding parameters on the welding deformation of aluminum steel. then, based on bp neural network and ga-bp neural network, the welding deformation is predicted. the predicted results are applied to the welding by the inverse deformation method, which effectively controls the deformation of the welded plate. methodology welding parameter selection method he main parameters of cmt welding include wire feed speed, welding speed, arc correction, aluminum plate thickness, etc. different parameters have different effects on welding deformation. in order to facilitate the research, this paper screens out the main parameters for the large deformation of the welding based on the orthogonal test and grey relational grade theory. the basic idea of the grey relational grade theory is to judge the degree of correlation between the factors according to the degree of similarity between the curves, which can be used to determine the contribution of factors to a certain behavior or indicator by quantitatively analyzing the dynamic development process of the system [17,18]. this method can be used to analyze the extent to which various factors affect the results and can be used for nonlinear data relationships. the reason why this method is used is to screen out the process parameters that have a great influence on cmt welding deformation, thus simplifying the late neural network prediction model. because the welding parameters and the welding deformation amount show a highly nonlinear relationship, the gray correlation analysis theory is used to investigate the influence of cmt welding parameters on the welding deformation. the analysis steps are as follows. let the reference sequence be:  ( ) 1, 2, ,y y k k n= = (1) the comparison sequence is: t y. lu et alii, frattura ed integrità strutturale, 53 (2020) 325-336; doi: 10.3221/igf-esis.53.25 327  ( ) 1, 2, , , 1, 2, ,i ix x k k n i m= = = (2) the four factors selected in this article have different physical meanings, so the data dimensions are different. in order to facilitate the comparison between the factors, the data is first normalized. the normalization formula is as follows: min( ) ( ) , 1, 2, , max( ) min( ) i i x x x k i n x x − = = − (3) calculate the correlation coefficient ( )i k between ( )y k and ( )ix k at time k , which yields: min min ( ) ( ) max max ( ) ( ) ( ) ( ) ( ) max max ( ) ( ) i i i k i k i i i i k y k x k y k x k k y k x k y k x k    − + − = − + − (4) in the formula: k is the time;  is the resolution; the value range is (0,1) [19]; this article takes 0.8; min min ( ) ( )i i k y k x k− and max max ( ) ( )i i k y k x k− are the minimum and maximum differences of the two levels, respectively. since the correlation coefficient is the correlation degree between the comparison sequence and the reference sequence at each time, the value is too scattered to be detrimental to the overall comparison. therefore, the average value of the comparison between the two columns ir is as follows: 1 1 ( ), 1, 2, , n i i k r k k n n  = = = (5) the magnitude of the correlation characterizes the relative influence of the comparison sequence on the reference sequence. establishment of ga-bpnn model the steps of predicting aluminum-steel cmt welding deformation by ga-bpnn are as follows: 1) determine the structure of bpnn. this paper uses a parallel network structure, including the input layer, hidden layer and output layer. the number of input and output layers is determined by test parameters and evaluation indicators. the transfer function used in this paper is: 1 ( ) 1 x f x e − = + (6) this function maps the real field to the [0,1] space smoothly. in addition, the function is monotonically increasing, continuous and derivable, and the derivative form is very simple, which is a suitable function. 2) initialize the weight coefficients connecting the input layer, hidden layer and output layer of the bpnn; 3) code the chromosomes of the weight coefficients and set the ga parameters. in this paper, the individual coding length of the genetic algorithm is 21. the parameters of the genetic algorithm are set as follows: the population size is 10, the number of evolutions is 50, the crossover probability is 0.4, and the mutation probability is 0.2. 4) design the fitness function and calculate the corresponding fitness value of current chromosomes. the fitness function is designed as: 1 ( ) n i i i f abs y o = = − (7) ( n denotes the number of neurons in the output layer, io and iy represent the predicted and actual outputs of the ith neuron, respectively) y. lu et alii, frattura ed integrità strutturale, 53 (2020) 325-336; doi: 10.3221/igf-esis.53.25 328 5) do the selection crossover and mutation to produce the best fitness values; it went on the step 5's process of iterative evolution until getting the near-optimal fitness value or going to the default maximum generation of evolution. the output of this process was the individual with the best fitness, and the individual consists of the weights and threshold, which would be used as the final weights and thresholds of the bpnn. fig. 1 illustrates the solution procedure of the ga optimized bpnn method for deformation forecasting of aluminumsteel cmt welding. data input and normalizationdata input and normalization codecode bpnn training to obtain fitness valuebpnn training to obtain fitness value selectionselection crossovercrossover mulationmulation recalculate the individual fitnessrecalculate the individual fitness termination conditionis satisfied? termination conditionis satisfied? n design the sturcture of the bp neural networkdesign the sturcture of the bp neural network initial weight and thresholdinitial weight and threshold the best weights and thresholdsthe best weights and thresholds simulation resultssimulation results y figure 1: the flow chart of ga optimized bpnn method after the ga-bpnn model is established, it can be used to deal with complex nonlinear problems, which provides a reference for the subsequent prediction of aluminum steel welding deformation. the inverse deformation method the inverse deformation method [20] pre-estimates the direction and size of the structural deformation, and gives the sheet a deformation in the opposite direction during assembly, which is used to offset the deformation caused by the welding, so that the post-weld member maintains the design requirements. after extensive experimental observation, the aluminum-steel sheet cmt welding will undergo warping deformation. the warping deformation shape of the aluminum sheet side is low in the middle and high on both sides. therefore, the same deformation in the opposite direction is applied to the sheet before welding, so that the sheet is restored to a flat shape after welding. in this paper, the estimated size of deformation is given by ga-bpnn. the anti-deformation treatment diagram is shown in fig. 2. y. lu et alii, frattura ed integrità strutturale, 53 (2020) 325-336; doi: 10.3221/igf-esis.53.25 329 figure 2: anti-deformation treatment diagram results and discussion a6061-t6 aluminum alloy and dp590 steel commonly used in the automotive industry are used as test plates. so in this paper, aa6061-t6 aluminum alloy and dp590 steel are used as test plates, and er4043 (alsi5) with a diameter of 1.2mm is used as a filler wire. an aluminum plate having a thickness of 1 mm, 1.2 mm, 1.5 mm, and 2 mm and a steel plate having a thickness of 1.2 mm are cut into a sample having a length × width of 150 mm × 50 mm by a wire cutter. before the test, the aluminum plate is polished with sandpaper to remove the oxide film, and then the surface of the steel plate is cleaned with an acetone solution to remove stains, grease, and the like on the surface. the test adopts the lap joint method, the upper layer is aluminum plate and the lower layer is steel plate., and the lap joint amount is 150 mm × 10 mm. fig. 3 is a schematic view of cmt seam welding of aluminum-steel sheet. figure 3: illustration of seam welding of aa6061-t6/dp590 sheet the welding equipment required for this test includes the tps4000 cmt welder from fronius, welding torch and kuka robot arm. the welding torch and the surface of the welded part are at an angle of 45°, and the aluminum-steel sheet is welded in a single pass. high purity argon was selected as the shielding gas in the test and operated at a flow rate of 15 l/min. during the aluminum-steel cmt seam welding test, the length and width of the aluminum plate and the steel plate were kept unchanged, and 16 groups of tests were carried out according to the five-factor and four-level orthogonal table. the wire feed speed, welding speed, arc correction and aluminum plate thickness were selected as four factors of orthogonal test. the deformation of aluminum-steel sheet was used as the evaluation index of cmt seam welding quality of aluminum-steel. the welding test factor level table is shown in tab. 1. it was observed that the aluminum plate side showed warping deformation at the middle and low sides after welding. select the middle point b of point a and point c on the side of the aluminum plate as the measurement point, and then the welding deformation is the height difference between point b before welding and point b after welding. the measuring point is shown in fig. 3. the coordinates of point b before and after welding is measured by a binocular stereoscopic measuring point device as shown in fig. 4, and the height difference was calculated manually as the amount of welding deformation. welding parameters analysis the orthogonal test results of aluminum-steel cmt welding are shown in tab. 2. in this paper, the deformation of 16 specimens in tab. 2 was taken as the reference sequence. the corresponding horizontal value-wire feed speed, welding speed, arc correction, and aluminum plate thickness were used as comparison sequence. the data were substituted into the above formula to calculate the correlation degree of each cmt welding parameter to the welding deformation a y. lu et alii, frattura ed integrità strutturale, 53 (2020) 325-336; doi: 10.3221/igf-esis.53.25 330 amount. the calculation results are shown in tab. 3. it can be seen from the table that the wire feed speed has the greatest influence on the cmt welding deformation, the welding speed is second, and the arc correction has the least influence. factor level a b c d wire feed speed (m/min) welding speed (mm/s) arc correction (%) aluminum plate thickness (mm) 1 3.6 0.56 -5 1.0 2 3.9 0.62 0 1.2 3 4.2 0.66 5 1.5 4 4.5 0.70 10 2.0 table 1: test level of factor figure 4: binocular stereo vision measurement of mark point device serial number factor result a b c d e δd wire feed speed welding speed arc correction aluminum plate thickness error deformation (mm) 1 1 1 1 1 1 0.52 2 1 2 2 2 2 0.64 3 1 3 3 3 3 0.48 4 1 4 4 4 4 0.50 5 2 1 2 3 4 0.36 6 2 2 1 4 3 0.40 7 2 3 4 1 2 0.46 8 2 4 3 2 1 0.34 9 3 1 3 4 2 0.50 10 3 2 4 3 1 0.76 11 3 3 1 2 4 0.68 12 3 4 2 1 3 0.58 13 4 1 4 2 3 0.42 14 4 2 3 1 4 0.64 15 4 3 2 4 1 0.52 16 4 4 1 3 2 0.38 table 2: orthogonal test results y. lu et alii, frattura ed integrità strutturale, 53 (2020) 325-336; doi: 10.3221/igf-esis.53.25 331 factor wire feed speed welding speed arc correction aluminum plate thickness correlation degree 0.727116 0.723069 0.679584 0.721059 table 3: the correlation degree of each cmt welding parameter to the welding deformation amount prediction of welding deformation based on ga-bpnn from the gray relational analysis, the wire feed speed, welding speed and aluminum plate thickness are three important parameters that affect the welding deformation. therefore, bp neural network is used to study the complex nonlinear relationship between three welding parameters (wire feed speed, welding speed, aluminum plate thickness) and one output parameter (welding deformation) to predict the welding deformation of aluminum-steel sheet. the neural network includes 3 input node, 5 implicit layer node, and 1 output layer node. he prediction model of welding deformation of aluminum-steel sheet based ga-bpnn is shown in fig. 5. figure 5: prediction model of welding deformation based on ga-bpnn in order to obtain the training samples required for the neural network, 120 sets of cmt seam welding tests were performed on the dp590 steel plate and the aa6061-t6 aluminum alloy plate. under the condition that the shielding gas flow rate and the preheating temperature are constant, the welding deformation amount under different heat input is obtained by changing the values of the wire feed speed, the welding speed and the aluminum plate thickness process parameters. the measured deformation point is point b in fig. 3. after establishing the neural network model, based on the 120 sets of data obtained from the experiment, the first 100 groups were selected for training neural network, and the last 20 groups were used for verification. the operation was performed in matlab 2016a. the predicted outputs of bpnn and ga-bpnn are shown in fig. 6 and fig. 7 respectively. fig. 8 is the comparison of bpnn and ga-bpnn error. figure 6: bpnn prediction output as can be seen from the comparison of fig. 6 and fig. 7, the ga-bpnn predicts the amount of welding deformation closer to the actual deformation amount than the bpnn. it can be seen from fig. 8 that both the bpnn and the gabpnn have fluctuations around the zero point and the ga-bpnn has a smaller fluctuation range. the bpnn prediction y. lu et alii, frattura ed integrità strutturale, 53 (2020) 325-336; doi: 10.3221/igf-esis.53.25 332 error range is -0.029mm~0.011mm, the maximum relative error is 0.029mm, and the minimum relative error is 0.003mm. the ga-bpnn prediction error range is -0.016mm~0.004mm, the maximum relative error is 0.016mm, and the minimum relative error is 2.69*10-6mm. figure 7: ga-bpnn predictive output figure 8: comparison of neural network errors the detailed comparison of bpnn and ga-bpnn is given below. fig. 9 shows the training performance of two neural networks. it can be seen from fig. 9 that the training error, validation error and test error of the network are decreasing with time, the generalization error is gradually smaller, the generalization ability is improved, and the test curve and the verification curve are consistent. when the circle position in the figure is reached, the generalization error reaches a minimum. the bpnn converges after 4 epochs, and the ga-bpnn converges after 6 epochs. ga-bpnn has a longer convergence time than bpnn because the evolution process of the population takes a long time, and the larger the initial size range of the population size, the number of iterations, the weight and the threshold, the longer the convergence time. fig. 10 shows the validation results of the trained bpnn. it is noticed from the figure that the gradient index and mutation index of the bpnn is smaller than that of the ga-bpnn. fig. 11 is the regression analysis of the expected output of the network and the actual training results. it can be seen from fig. 11 that the correlation coefficient of bpnn is 0.97074, and the correlation coefficient of ga-bpnn is 0.97843, indicating that ga-bp network has better regression performance and better generalization capabilities. tab. 4 lists the mse (mean squared error), rmse (root mean square error) and mae (mean absolute error) prediction errors. from tab. 4 we can see that the prediction precision of the ga-bpnn is higher than that with bpnn. for the two patterns, the prediction mean absolute error of bpnn is 0.0095. contrast with it, the prediction mean absolute error of ga-bpnn is 0.0054. as a result, we can see that the ga-bpnn algorithm has better performance than bpnn. this comparison indicates that taking the advantage of the ga optimization, the bpnn could be trained well with high generalization ability and hence the forecasting performance is superior to the unoptimized neural networks. xu [21] has studied welding deformation based on the traditional method of elastoplastic deformation. in his study, a three-dimensional finite element model for laser welding of a thin plate was established based on the thermal-elasticplastic fem approach to simulate the temperature field and deformation of the 316l stainless steel in the pulsed laser welding process. a moving volumetric heat source was applied to simulate the laser energy input during the welding process. meanwhile, the welding deformation was measured by a laser displacement sensor. and the computed results were compared with the measured results. y. lu et alii, frattura ed integrità strutturale, 53 (2020) 325-336; doi: 10.3221/igf-esis.53.25 333 fig. 12 shows the welding deformation results measured by xu under simulation and test. it can be seen from fig. 12 that the simulation results have higher accuracy and have good consistency with the test. the mse、rmse and mae of xu’s result are calculated. the results are shown in tab. 4. according to tab. 4, ga-bpnn has higher prediction accuracy. figure 9: comparison of the training performance of two neural networks: (a) bpnn, (b) ga-bpnn. figure 10: the training state of two neural networks: (a) bpnn, (b) ga-bpnn. figure 11. regression of two neural networks: (a) bpnn, (b) ga-bpnn. y. lu et alii, frattura ed integrità strutturale, 53 (2020) 325-336; doi: 10.3221/igf-esis.53.25 334 figure 12: xu’s results of welding deformation under simulation and experiment. mse (mm2) rmse (mm) mae (mm) bpnn 0.00014 0.01205 0.00953 ga-bpnn 0.00005 0.00686 0.00539 xu’s result 0.233172 0.482879 0.174549 table 4: the mse, rmse, mae and mape using bpnn and ga-bpnn prediction method. welding deformation control and verification the welding deformation predicted by bpnn and ga-bpnn was applied to the aluminum-steel sheet by the inverse deformation method to verify the effectiveness of the welding deformation prediction. the aluminum-steel sheets were divided into control experiments, which were no anti-deformation treatment group, bpnn anti-deformation treatment group and ga-bpnn anti-deformation treatment group. in the anti-deformation processing group, the same size deformation was applied to the three points a, b, and c of the steel sheet and the aluminum plate before welding which was opposite to the direction of deformation predicted by the neural network. the results of the deformation control experiment are shown in fig. 13. as can be seen from fig. 13, the post-weld sheet after the reverse deformation treatment is significantly controlled compared to the post-weld sheet without reverse deformation treatment, and the deformation amount of fig. 13(c) is smaller than that of fig. 13(b). (a) post-weld plate without reverse deformation treatment (b) post-weld plate of bpnn reverse deformation treatment (c) post-weld plate for ga-bpnn reverse deformation treatment figure 13: contrast test of deformation treatment y. lu et alii, frattura ed integrità strutturale, 53 (2020) 325-336; doi: 10.3221/igf-esis.53.25 335 tab. 5 shows the results of the deformation amount of the control test. it can be seen from the table that in the case where the welding process parameters are the same, the aluminum-steel sheet without anti-deformation warps obviously, and the deformation amount is 0.67 mm. the post-weld deformation of the sheet with the deformation amount predicted by the bp neural network is reduced, and the post-weld deformation is 0.36 mm, and the post-weld deformation of the sheet with the deformation amount predicted by the ga-bp neural network is 0.11 mm which is much smaller than the sheet with the deformation predicted by the bp neural network. therefore, the ga-bp neural network can effectively predict the cmt welding deformation of the aluminum-steel sheet compared with the bp neural network, and the error is controlled within a reasonable range. wire feed speed (m/min) welding speed (m/min) arc correction (%) aluminum plate thickness (mm) deformation (mm) no anti-deformation 3.9 0.70 0 1.5 0.67 bp inverse deformation processing 3.9 0.70 0 1.5 0.36 ga-bp inverse deformation processing 3.9 0.70 0 1.5 0.11 table 5: test result of welding deformation conclusion n this paper, the welding process parameters affecting the cmt seam welding deformation of aluminum-steel are studied by orthogonal test and gray relational grade theory. the influence degree of cmt welding process parameters on welding deformation is analyzed. then bp neural network and ga-bp neural network were used to predict the welding deformation. the final conclusion is as follows: (1) based on the orthogonal test and the gray relational analysis, the wire feed speed has the greatest influence on the aluminum alloy cmt welding deformation, the welding speed is the second, and the arc correction has the least influence. (2) the bp neural network improved based on genetic algorithm has higher prediction accuracy. the bp neural network prediction error range is -0.029mm~0.011mm, the maximum relative error is 0.029mm, and the minimum relative error is 0.003mm. however, the ga-bp neural network prediction error range is -0.016mm~0.004mm, the maximum relative error is 0.016mm, and the minimum relative error is 2.69*10-6mm. (3) the prediction results of bp neural network and ga-bp neural network are applied to the welding of the sheet in the form of anti-deformation. the results show that the deformation of the welded plate is obviously smaller. moreover, the deformation of the post-weld plate with the anti-deformation amount predicted by ga-bp neural network is smallest, indicating that the ga-bp neural network is more suitable for the prediction of cmt welding deformation of aluminum-steel. in the future, the deformation of aluminum-steel hybrid sheets in more complex assembly forms and under multiple welds will be further studied, and the neural network prediction model proposed in the paper will be used for prediction. references [1] solecka, m., kopia, a., radziszewska, a. and rutkowski, b. (2018). microstructure, microsegregation and nanohardness of cmt clad layers of ni-base alloy on 16mo3 steel, journal of alloys & compounds, 751, pp. 86-95. [2] masters, i., fan, x., roy, r. and williams, d. (2012). modelling distortion induced in an assembly by the self piercing rivet process, proceedings of the institution of mechanical engineers. part b: engineering manufacture, 226(2), pp. 300-312. [3] rai, r., de, a., bhadeshia, h. k. d. h. and debroy, t. (2011). review: friction stir welding tools, science & technology of welding & joining, 16(4), pp. 325-342. [4] lei, h. y., li, y. b. and carlson, b. e. (2017). cold metal transfer spot welding of 1, mm thick aa6061-t6, journal of manufacturing processes, 28, pp. 209-219. i y. lu et alii, frattura ed integrità strutturale, 53 (2020) 325-336; doi: 10.3221/igf-esis.53.25 336 [5] deng, d., kiyoshima, s., ogawa, k., yanagida, n. and saito, k. (2011). predicting welding residual stresses in a dissimilar metal girth welded pipe using 3d finite element model with a simplified heat source, nuclear engineering and design, 241(1), pp. 46-54. [6] xia, j. and jin, h. (2016). numerical study of welding simulation and residual stress on butt welding of dissimilar thickness of austenitic stainless steel, international journal of advanced manufacturing technology, 91(1-4), pp. 1-9. [7] wei, l., liang, z. and xiaolu, s. (2017). prediction of welding deformation of ultra-thin plates by inherent strain method, transactions of the china welding institution, 38 (3), pp. 103-106. [8] jin, z., baohua, c., ye, z. and dong, d. (2010). prediction of welding deformation of aluminum alloy by inherent strain method, welding technology, 39(6), pp. 6-10. [9] liming, l., guoli, l., yujun, l., zan, z., chonghua, z. and peisheng, l. (2002). analysis and prediction of welding deformation of ship high strength steel based on artificial neural network, transactions of the china welding institution, (01), pp. 27-29+33-3. [10] li, z., yan, x., yuan, c., peng, z. and li, l. (2011). virtual prototype and experimental research on gear multi-fault diagnosis using wavelet-autoregressive model and principal component analysis method, mechanical systems and signal processing, 25(7), pp. 2589-2607. [11] baştanlar y. and ozuysal, m. (2012). introduction to machine learning, an introduction to machine learning. springer publishing company, incorporated. [12] chen, b. and feng, j. (2014). modeling of underwater wet welding process based on visual and arc sensor, industrial robot: an international journal, 41(3), pp. 311-317. [13] jiangqi, l., fengchong, l., jiqing, c. and ping, a. y. (2009). mechanical properties prediction of the mechanical clinching joints based on genetic algorithm and bp neural network, chinese journal of mechanical engineering, 22(1), pp. 36-41. [14] liu, j., xu, g., ren, l., qian, z. and ren, l. (2016). defect intelligent identification in resistance spot welding ultrasonic detection based on wavelet packet and neural network, international journal of advanced manufacturing technology, 90(9-12), pp. 1-8. [15] haisheng, l., long, l., li, c., cheng, l. and qiang, c. (2015). the prediction in computer color matching of dentistry based on ga+bp neural network, computational and mathematical methods in medicine, pp. 1-7. [16] qian, l., huan, t., jing, w., qin, z., jie, c. and zhe, q. w. (2018). warfarin maintenance dose prediction for patients undergoing heart valve replacement— a hybrid model with genetic algorithm and back-propagation neural network, scientific reports, 8(1), pp. 9712 [17] niu, h., yu, j. and huang, z. (2017). gray correlation analysis and chebyshev prediction of air gap discharge voltage, international conference on electrical materials & power equipment. ieee. [18] jian, c., jingmin, f. and chenguang, a. (2010). application of grey correlation analysis in chromatograph peak identification of transformer oil, power system technology, 34(7), pp. 206-210. [19] yanbin, l., xinyi，y. and zhijie, w. (2013). risk assessment on photovoltaic power generation project by grey correlation analysis and topsis method, power system technology, 37(6), pp. 1514-1519. [20] xian, s. (2014). the principle and control of the anti-deformation method of weldment in engineering application, modern welding technology, 12, pp. 38-42. [21] hailaing, x., xingye, g., yongping, l., jian, l., hanguang, f., rongshi, x. (2019). welding deformation of ultra-thin 316 stainless steel plate using pulsed laser welding process, optics and laser technology, 119. microsoft word numero_45_art_3 d. peng et alii, frattura ed integrità strutturale, 45 (2018) 33-44; doi: 10.3221/igf-esis.45.03 33 effect of corrosion and fatigue on the remaining life of structures and its implication to additive manufacturing d. peng, r. jones centre of expertise for structural mechanics, department of mechanical and aerospace engineering, monash university, p.o. box 31, monash university, victoria, 3800, australia. f. berto, s.m.j. razavi department of mechanical and industrial engineering, norwegian university of science and technology (ntnu), trondheim 7491, norway abstract. this paper investigates the combined effect of corrosion and fatigue on the growth of cracks that arise from natural corrosion in steel bridges. it is shown that if these two effects need to be simultaneously analyzed. if not, then the resulting life is not conservative. consequently, to enable a better understanding of the remaining life of steel bridges this paper presents a simple methodology for performing this coupled analysis. the implication of this study to additively manufactured ti-6al-4v is also discussed. keywords. steel bridges; corrosion; fatigue crack growth; remaining life. citation: peng., d., jones, r., berto, f., razavi, s.m.j., effect of corrosion and fatigue on the remaining life of structures and its implication to additive manufacturing, frattura ed integrità strutturale, 45 (2018) 3344. received: 02.05.2018 accepted: 25.05.2018 published: 01.07.2018 copyright: © 2018 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. introduction t has long been known that the corrosion of steel bridges can have a marked effect on structural integrity. indeed, the collapse of the i35w bridge in minneapolis, usa led us rep. michael conway (r-tx11) to introduce the bridge life extension act of 2008. transportation for america subsequently conducted an analysis of the us national bridge inventory [1] and reported that one in nine u.s. bridges were rated as being structurally deficient. in this context it should be noted that for steel bridges the primary problems essentially result from either corrosion due to exposure of the steel to atmospheric conditions and/or from small non-detectable initial material discontinuities [2]. as a result, the us national cooperative highway research program, nchrp synthesis study [2] highlighted the need to develop advanced fatigue life calculation procedures that were capable of accounting for non-visible cracks in steel bridges. indeed, the need to be able to account for small sub mm initial defects is reinforced in the us federal highway administration steel bridge design handbook [3] where it was noted that crack growth essentially starts from day one and that the majority of the life of steel i http://www.gruppofrattura.it/va/45/26.mp4 d. peng et alii, frattura ed integrità strutturale, 45 (2018) 33-44; doi: 10.3221/igf-esis.45.03 34 bridges is consumed in growing to a size where a crack can be detected. as explained in [4] this observation coincides with that seen in the growth of cracks in operational aircraft [5, 6]. in this context it is now known that the da/dn versus δk relationship associated with the growth of cracks in bridges steels and in the high strength aerospace steels d6ac and 4340 steel are similar and can be represented by the same nasgro equation [4, 7]. furthermore, it is also known that crack growth in bridge steels repaired with an externally bonded composite patch falls on the same “master curve” as does crack growth in operational aircraft and the growth of cracks in aluminum alloys repaired with an externally bonded composite patch [7]. the need to be able to accurately compute the growth of small sub mm cracks in bridge steels was addressed in [4] which revealed that the crack growth history associated with cracks that arose and grew from natural corrosion in a section of a badly corroded bridge could be predicted as per [8] by using the nasgro equation for bridge steels, viz:                2 10 max 1.5 10 1 thrk kda dn k a (1) and setting the threshold term δkthr to a small value, see [4] for more details. here a is the cyclic fracture toughness, see [4] for more details. turning to the question of corrosion and corrosion-fatigue in steel bridges it should be noted that a detailed discussion of the field of corrosion fatigue in steel is provided in [9]. however, there are only a few available publications on the problems of corroded and fatigue in steel bridges. a probabilistic approach which used a damage stress model to predict fatigue lives was developed in [10]. other methods are focused on the use of s-n curves, which use corrosion rates and cumulative fatigue damage approaches [11, 12], for different atmospheric conditions. a fatigue crack growth evaluation method based on linear elastic fracture mechanics was developed in [13]. no available solutions can be found in the literature for the simultaneous effect of material loss due to corrosion and fatigue crack growth due to operational loads. the prediction of the fatigue life of a corroded bridge steel beam is both difficult and computationally intensive as calculations need to be made at each stage of the life of a beam. this is due to the need to compute the stress intensity factors for each crack configuration; to calculate the amount of crack growth, update the crack geometry, and then recompute the stress intensity factors for this new geometry. this problem was discussed in detail in [8] which presented the fundamental steps needed to compute the crack growth histories associated with naturally occurring cracks in complex geometries subjected to representative operational load spectra. these steps are: a) perform a finite element analysis of the uncracked structure. b) extract the stresses at the fatigue critical locations c) use 3d, or 2d weight functions [14-17], or alternatively trefftz function solutions [18 -20] to compute the k(a, c) solution space. here “a” is the crack depth and “c” is the surface crack length. this generally takes less than 5 minutes on a laptop or a pc. examples of this technique applied to cracking in sideframes, couplers and rail wheels are given in [14, 17] and examples associated with cracking in aerospace materials are given in [8, 21]. d) use the hartman-schijve variant of the nasgro together with the k(a, c) solution space determined above and the associated load spectrum to compute the crack length/depth versus cycles history. however, as explained in [8] when analyzing the more complex problem of the simultaneous occurrence of corrosion and cracks in aging rail bridges the above process needs to be modified to also allow for the reduction in the section thickness as the bridge corrodes. this (unfortunately) means that a range of uncracked models, with different section thicknesses, need to be created and the solution space k(a, c) determined for each. the crack growth analysis then uses the measured (worse case) steady state corrosion rate for the bridge and determines the appropriate k solution from a knowledge of the current crack length and the number of cycles, which are used to determine the amount of material that has been lost, by interpolating between these various solution spaces. to meet this challenge, this paper will discuss the issues associated with fatigue crack growth in a corroded steel beam. as per the approach outlined in steps a) to d) the first step in the analysis is to create a 3d model of the steel bridge beam without corrosion and analyze the region of interest. in this initial model, the crack is not explicitly modelled. steps b) to c) are then used to determine the stress intensity factors (k) for any given crack length. these stress intensity factors are then used in conjunction with equation (1) to compute the crack growth history, i.e. step d). in this analysis, as outlined in [8], for each increment in crack growth the rate of loss of material due to corrosion is simultaneously computed and adjusted crack length, i.e. after allowing for the associated loss of material, is determined as is the new stress state in the new uncracked section thickness. this process is then continued until failure by either fracture or exceeding the ultimate d. peng et alii, frattura ed integrità strutturale, 45 (2018) 33-44; doi: 10.3221/igf-esis.45.03 35 strength of the remaining ligament occurs. the advantage of this approach is that it negates the need to explicitly model cracks, see [8, 14, 17]. a crack of any size can be analyzed using the original (un-cracked) finite element model. as cracks are not modelled explicitly, a coarser mesh can be used to minimize the number of degrees of freedom, thereby reducing the analysis time. solutions for the stress-intensity factors can then be obtained for a variety of cracks using the original finite element analysis quickly and easily. to illustrate how this approach can be used to compute the growth of cracks that arise due to natural corrosion in bridge steels a simplified analysis of v/line bridge 62 in kilmore east, victoria, australia is performed. by comparing the life obtained by i) allowing only for corrosion and ii) by performing a coupled corrosion-fatigue analysis we find that method i) is very un-conservative. we also show that the interaction between fatigue crack growth and the stress increase created by corrosion induced section reduction needs to be considered when assessing the remaining life of an aged steel bridge. having shown how to predict the effect of surface corrosion on the fatigue life of mild steel attention is then focused on the effect of surface roughness on fatigue cracking in additively manufactured t-6al-4v. whilst additive manufacturing (am) offers the potential to economically fabricate customized parts with complex geometries, the mechanical behavior of these materials must be better understood before am can be utilized for critical load bearing applications. this is particularly true for aircraft applications where, as detailed in mil-std 1530, the design and certification approval require analytical tools that are capable of capturing crack growth and the role of testing is to validate or correct the damage tolerance analysis. to this end it is first shown that the growth of small cracks in a 350 mpa mild steel is similar to the growth of fatigue cracks in both conventionally manufactured ti-6al-4v and in in additively manufactured lens (laser engineered net surface) ti-6al-4v. this suggests that the methodology discussed above may also be applicable to study the effect of surface roughness in additively manufactured ti-6al-4v. the aashto corrosion standard efore we can assess the coupled effect of corrosion and fatigue we first need a knowledge of the rate of corrosion. in this paper we will adopt the american association of state highway and transportation officials (aashto) recommended metal loss model [22, 23] which states that the metal loss versus time curve is bi-linear, see fig. 1. however, as can be seen in fig. 1, there is little actual data to support this model and the data shown in fig. 1 is not particularly convincing. this approach to assessing the “steady state” corrosion rate is consistent with the international standard corrosion of metals and alloys corrosivity of atmospheres, iso designation 9224 [24], which specifies guiding values of corrosion rate for metals exposed to the atmosphere consisting of an average corrosion rate during the first 10 years of exposure. a detailed review of the corrosion of bridge steels, the aashto and iso corrosion standards and documented steady state corrosion rates associated with a range of locations and steels is in given in [25]. figure 1: an example of the bi-linear metal loss versus time curve, from [22]. one problem with aging bridges is that if there is any serious corrosion it is likely to have developed over a reasonable number of years. however, to know its significance we need to know how fast the bridge is corroding, i.e. its corrosion rate, at this moment in time. that said you do not have the luxury to locate corrosion sensors or weight loss samples on a b d. peng et alii, frattura ed integrità strutturale, 45 (2018) 33-44; doi: 10.3221/igf-esis.45.03 36 bridge and wait for a further 5 years or so until the sensors/samples themselves reach the steady state corrosion rate that the bridge is seeing. you need answers much sooner. the advantage of the aashto bi-linear approach is that once the bridge is behaving such that the metal loss versus time curve is on the line ab, see fig.1, you know the long-term corrosion rate without having to monitor the bridge for years. for bridges this can be done in the order of four to twelve months using electrical resistance corrosion sensors [2]. a steel electrical resistance corrosion sensor was used to measure the metal loss in bridge 62 at kilmore east which is inland in victoria, australia. fig. 1 substantiates the nchrp and aashto formulation and the advantage gained in real time monitoring of a rail bridge to obtain the long-term corrosion rate. the steady state corrosion rates determined in this test is 0.024 (mm/year). these rates are consistent with those documented in [25]. figure 1: measured thickness loss at east kilmore in victoria. the results of this study support the aashto standard for the loss of metal seen by steel bridges. as such the aashto bi-linear relationship between metal loss and the time in service provides a simple method for estimating the corrosion rates associated with aging structures. operational load spectra s part of the corrosion measurement program mentioned above the strain (load) spectra was also measured. bridge 62 in east kilmore saw passenger trains, including trains pulled by n class locomotives, sprinter carriages, ore trains. armed with this information and details of the number of trains per week, see table 1, the load spectrum associated with the bridge can be determined. train type loco weight wagon weight no of wagons no per week total wt/week n class passenger 118 60 5 14 5852 sprinter 60 2 14 1680 ore train 128 100 20 7 14896 table 1: data on trains using up line over bridge 62. fatigue crack growth with corrosion effect model rmed with a knowledge of the da/dn versus δk behavior of bridge steels, the load spectrum and the steady state corrosion rate we are now in a position to assess the combined effect of corrosion and fatigue on the remaining life of a bridge. a a d. peng et alii, frattura ed integrità strutturale, 45 (2018) 33-44; doi: 10.3221/igf-esis.45.03 37 failure due to material loss (corrosion) the bending couple m applied to the section of interest creates normal stresses in the cross section, while the shear force v creates shearing stresses in that section. corrosion of steel bridge girders will be a maximum where electrolyte can “wick” between the transom and the girder compression flange or where electrolyte is trapped by some other means. in general, the worst case scenario involves a loss of material from the web, top flange and bottom flange. a graphical representation of the corroded i beam is provided in figure 3. using the equation for outer flange fiber stress in beams subject to bending:   /q my i (2) where σ is the stress, m is the applied moment, y the distance from the beam neutral axis to the extreme flange fiber and i is the moment of inertia about the neutral axis, a spread sheet can be raised which tabulates reducing flange thickness due to corrosion and consequential increased girder flange stresses. the limits are the as-new girder measured stress and the material yield stress. let us define the normal and shear stress at point q1 as shown in fig. 3 as σq1 and τq1   1 ( ) /q m y t i (3)   1 ( ) / ( 2 )q h t btv bi (4) with this notation the maximum principle stress at point q1 is:               2 21 1 1 1 1( ) 2 2 q q qq (5) therefore, the maximum stress in the flange is given by      1 1, ( )qmax q (6) if the measured corrosion rate for bridge steel i beam is ξ (mm/year), the maximum stress in i beam σ is function of the corrosion rate ξ. figure 3: graphical representation of the corroded i beam. failure due to the combined action of corrosion and fatigue since, on tension dominated surfaces, the life of the corroded steel bridge is a strong function of both the corrosion rate and the assumed initiating (inherent) crack size this paper addresses the interaction of combined corrosion and crack growth on remaining life. in this analysis the stress intensity factors were computed as outlined in steps b) and c) in section 1. for d. peng et alii, frattura ed integrità strutturale, 45 (2018) 33-44; doi: 10.3221/igf-esis.45.03 38 each iteration, as the section size reduces, the stress intensity factor for a crack in a corroded steel beam ki can be expressed in the form  * * ( )( , ) ( , )i i originalk a c f k a c (7) where, fσ is a “geometry evolution factor” and the stress intensity factor ki(original)(a*, c*) is the value with original geometry (there no materials loss due to corrosion) obtained as per [15, 16]. here (a, c) and (a*, c*) denote the crack depths and surface crack lengths without an allowance for the loss of material due to corrosion and allowing for a reduction in the section thickness due to corrosion respectively. the crack depth ‘a’ is related a*, see figure 4, by the relationship.  *a a t (8) where t is the current time and ξ is the corrosion rate. if we assume that the crack is a semi-elliptical surface crack the relationship for the surface length can be approximated as  * 21 ( / )c c t a (9) if we assume that the rate of corrosion is the same on both the upper and lower surfaces of the beam, then the geometry evolution factor fσ can be approximated as:            * * * * * 2 2 bottom top bottom top y t i f y t i (10) where i and i* are the moment of inertia about the neutral axis with original (no corrosion) and the current corroded section respectively. figure 4: showing a semi-elliptical crack in corroded i beam. having determined the current section thickness and the associated stress intensity factors equation (1), i.e. the da/dn versus δk relationship for bridge steels, is then used to compute the new crack shape. to allow for the simultaneous loss of material due to corrosion both the section thickness and the new crack shape are then modified to account the loss of material due to corrosion. the process is continued until failure either by exceeding the allowable fracture toughness of the material or by exceeding the ultimate strength of the remaining ligament. if the increment in the crack length is less than the loss of material due to corrosion it is assumed that the crack has been “eaten” by the corrosion. in this case the analysis continues using the assumed initial (inherent) crack size input by the user. in this fashion the remaining life of the section can be determined. d. peng et alii, frattura ed integrità strutturale, 45 (2018) 33-44; doi: 10.3221/igf-esis.45.03 39 numerical examples and results analysis n analysis of cracking in bridge 62 with an assumed corrosion rate of 0.024 mm/yr was chosen to illustrate this approach. (this corrosion rate corresponds to the fastest rate measured at the three sites examined in section 2.) in these initial analyses the initiating (inherent) crack was taken from [4], which tested a section from a condemned and badly corroded steel bridge, to be a 0.05 mm deep semi-circular initial crack. the sub-structure of this bridge was subjected to significant moisture and resulting corrosion during the wet seasons. the bridge has two rail tracks, each of which is supported by four girders with 4.87 m length. the dimensions of the girders are given in tab. 2. depth 381mm web thickness 12mm flange width 152mm flange thickness 22mm (average) table 2: dimensions of the bridge 62 girders. the yield stress for this steel was conveyed by v/line staff to be approximately 240 mpa. this implies that retirement resulting from corrosion from an as-new state is approximately 244 years. as mentioned in [28], the deflection requirement of deflection limits of a railway bridge for serviceability limit state under live load plus dynamic load allowance shall be not greater than 1/640 of the span. it is obvious that deflection in this analysis is not a safety issue. the next stage of this study used the finite element model to compute crack growth. for simplicity the loading applied to model was based on the worse case when an ore train (i.e. one g class locomotive and 20 fully loaded wagons) transited the bridge. the g class locomotive has the following specifications: total weight =128 tons, axle loading = 21.3 tons, wheel base = 3810 mm, axle spacing = 1905 mm and leading wheel leading bogie to leading wheel trailing bogie = 12622 mm. due to symmetry considerations only a quarter of the wheel was modelled. the resultant mesh, which was created using the software program femap [29], had 18,146 twenty-one-noded elements and 91,590 nodes (with a total of 274,770 degrees of freedom). the stresses at critical region were in reasonably good agreement with the results obtained from the field strain gauges measurement presented in section 3 and discussed in more detail in [30]. in the coupled “corrosion-fatigue” analysis, if the crack growth in a year is less than 0.024 mm, it was assumed that the crack has been “eaten” by corrosion and its length reset to its initial size of 0.05 mm. in this coupled analysis the section thickness continually reduces with time, i.e. as the loss of metal increases, and the stresses increase accordingly. this coupled analysis yielded a life to failure of approximately 81 years. as such there is a difference of ~18 % in the computed fatigue life between the no corrosion and the coupled “corrosion-fatigue” analyses. figure 5: the resultant computed crack growth histories (ai = ci = 1 mm). 0 2 4 6 8 10 12 14 16 18 20 0 10 20 30 40 50 c ra c k d e p th ( m m ) number of years initial crack size: a = c = 1 mm with corrosion a d. peng et alii, frattura ed integrità strutturale, 45 (2018) 33-44; doi: 10.3221/igf-esis.45.03 40 it is reported in [4] that the initial crack lengths found in the fatigue test on a specimen cut from a badly corroded bridge varied from approximately 0.1 mm to 1 mm [4]. for a 1 mm initial crack the difference between the two analyses is still significant (approximately 11%), see fig. 5. since the life of the bridge is a strong function of the size of the initiating (inherent) defect, the analysis was repeated for a range of initial crack sizes and the resulting lives are shown in fig. 6. this analysis revealed that the percentage difference between the case of no corrosion and the coupled “corrosion-fatigue” analysis reduces as the size of initial (inherent) crack is increased. figure 6: effect of the depth of the crevice on the remaining life of the bridge. implications for additively manufactured structures he work presented above has dealt with cracks that have arisen naturally and subsequently grown from rough, in this instance corroded, surfaces in a 350 mpa mild steel. however, let us now turn our attention to the effect of surface roughness in additively manufactured ti-6al-4v. in this context the review paper [31] noted that whilst additive manufacturing (am) offers the potential to economically fabricate customized parts with complex geometries, the mechanical behavior of these materials must be better understood before am can be utilized for critical load bearing applications. this is particularly true for cracks in aircraft applications where, as detailed in mil-std 1530 [32], the design and certification approval require analytical tools that are capable of capturing crack growth and the role of testing is to validate or correct the damage tolerance analysis. berto et al [33-36], kahlin, ansell and moverare [37, 38], greitemeier et al [39], chan [40] and leuders et al [41] each revealed that the rough surfaces associated with as additively manufactured parts significantly degrade the fatigue performance of am structures. the sentence used in [37] was: “the surface roughness is the single most severe factor for fatigue for additive manufactured materials”. the importance of characterizing the material discontinuities, including surface roughness, associated with am materials is also stressed in [33, 32, 42]. indeed, [42] suggested that, as we have seen in the previous section, the surface roughness of the material can be treated in the same way as short cracks. the present paper therefore suggests that the methodology outlined above has the potential to study the growth of small naturally occurring cracks that arise and grow form rough surfaces in additively manufactured ti-6al-4v. this hypothesis is supported by the fact that the da/dn versus δk curves associated with the growth of small cracks in a 350 mpa mild steel [43] is similar to the growth of fatigue cracks in both conventionally manufactured ti-6al-4v and in in additively manufactured lens (laser engineered net surface) ti-6al-4v. to illustrate this figure 13 presents the da/dn versus δk curves associated with the growth of small cracks in a 350 mpa mild steel [43], which were tested at a range of r ratios, together with: i) the r = 0.1 short crack curve for mill annealed ti-6al-4v [44], ii) the small crack da/dn versus δk curve for the growth of small cracks in additively manufactured lens (laser engineered net surface) ti-6al-4v [45]. 0 1 2 3 4 5 20 30 40 50 60 70 80 90 100 110 d e p th o f t h e i n it ia l f la w ( m m ) remaining life of the bridge (years) remaining bridge life viz. initial flaw size with corrosion no corrosion t d. peng et alii, frattura ed integrità strutturale, 45 (2018) 33-44; doi: 10.3221/igf-esis.45.03 41 iii) the small crack da/dn versus δk curve for the growth of small cracks in the aerospace quality titanium alloys ti-6246 [46] and ti-17 [47]. as can be seen in fig. 7 despite the differences in micro-structures and chemical composition the small crack curves associated with crack growth in the various titaniums, lens ti-6al-4v and the 350 mpa grade mild steel are in good agreement. as a result, it is hypothesized that the methodology outlined above has the potential to study the growth of small naturally occurring cracks that arise and grow form rough surfaces in additively manufactured ti-6al-4v. figure 7: comparison of cracking in a 350 mpa mild steel with cracking in a range of titanium alloys. as an important factor in failure assessments under fatigue and static loading, 3d effect has been studied in numerous researches and 3d effects in the form of stress state have been investigated for wide variety of notch geometries under various in-plane and out of plane loading conditions by considering stress concentration factors and constraint factors throughout the thickness of the specimen [48,49]. as a representative of stress state in cracked and notched components, the variations of the stress concentration factor as a function of the thickness have been studied in some recent researches by berto and co-researchers [50–56]. as an interesting and effective fact, the same concept can be considered for fatigue crack growth assessment in metallic components of steel bridges with presence of natural corrosion in the material. conclusions his paper has presented a methodology that can be used to compute the growth of cracks that arise due to natural corrosion in bridge steels. a simplified analysis of v/line bridge 62 has been used to illustrate the need to perform a coupled corrosion-fatigue analysis. furthermore, comparing the life obtained by allowing only for corrosion and by performing a coupled corrosion-fatigue analysis we find that: a. life allowing for corrosion only = 244 years b. life allowing for the coupled effect of corrosion and fatigue = 81 years therefore, failure as a result of metal loss from only corrosion would appear to be un-conservative. as such the interaction between fatigue crack growth and the stress increase created by corrosion induced section reduction must be considered when assessing the remaining life of steel bridges. we also raise the possibility that the methodology may also be applicable to assessing the effect of surface roughness on additively manufactured parts. 1.0e-10 1.0e-09 1.0e-08 1.0e-07 1.0e-06 1.0e-05 1 10 100 d a /d n ( m /c yc le ) k) (mpa √m) l1 r = 0.14 l2 r = 0.5 l3 r = 0.5 l4 r = -1 l5 r = 0.14 l6 r = 0.5 l7 r = 0.14 l8 r = 0.14 l9 r = 0.5 s11 r = 0.5 s12 r = 0.14 s13 r = 0.5 small crack lens ti6al4v short ti-6al-4v ma ti-17 (all r ratio's) usaf ti-642 r = 0.5 usaf ti-642 r = 0.05 specimens l1-l9, s11-s13 are a 350 mpa mild steel t d. peng et alii, frattura ed integrità strutturale, 45 (2018) 33-44; doi: 10.3221/igf-esis.45.03 42 references [1] the fix we’re in for: the state of our nation’s busiest bridges, transportation for america//october 2011. available on line at: http://t4america.org/docs/bridgereport/bridgereport-metros.pdf. [2] connor, r. j., dexter, r and mahmoud, h. (2005). inspection and management of bridges with fracture-critical details: a synthesis of highway practice, national cooperative highway research program, nchrp synthesis 354, transportation research board, washington, d.c. [3] mertz, d. (2012). steel bridge design handbook: design for fatigue, u.s. department of transportation, federal highway administration, publication no. fhwa-if-12-052 vol. 12. [4] ali, k., peng, d., jones, r., singh, r. r. k., zhao, x. l., mcmillan, a. j. and berto, f. (2017). crack growth in a naturally corroded bridge steel. fatigue & fracture of engineering materials & structures, 40(7), pp. 1117-1127. [5] berens, a. p., hovey, p. w. and skinn, d. a. (1991). risk analysis for aging aircraft fleets volume 1: analysis, wl-tr-913066, flight dynamics directorate, wright laboratory, air force systems command, wright-patterson air force base. [6] barter, s. a., molent, l. and wanhill, r. h. (2012). the lead crack lifing framework. international journal of fatigue, 41, pp. 1-198. [7] ali, k., singh, r. r. k., zhao, x. l., jones, r. and mcmillan, a. j. (2017). composite repairs to bridge steels demystified. journal of composite structures, 169, pp. 180-189. [8] jones, r. (2014). fatigue crack growth and damage tolerance. fatigue and fracture of engineering materials and structures, 37, pp. 463–483. [9] akid, r., richardson, t. ed., (2010). corrosion fatigue. in shreir's corrosion. vol. 2, pp. 928-953. [10] adasooriya, n. d. (2016). fatigue reliability assessment of ageing railway truss bridges: rationality of probabilistic stress-life approach. case studies in structural engineering, 6, pp. 1–10. [11] adasooriya, n. d. and siriwardane, s. c. (2014). remaining fatigue life estimation of corroded bridge members. fatigue and fracture of engineering materials and structures, 37, pp. 603–622. [12] wanninayake, w.t.m.s.m., wasala, w.m.p.r. and bandara, c.s. (2015). life evaluation of critical members of steel bridges located in different atmospheres, proceedings of the 6th international conference on structural engineering and construction management, kondy, sri lonko. [13] zhou, t. q., chan, t. h. t. and hua, y. (2006). fatigue damage analysis on crack growth and fatigue life of welded bridge members with initial crack, key engineering materials, issn: 1662-9795, vols. 324-325, pp 251-254. [14] peng, d., jones, r., constable, t., lingamanaik, s. n. and chen, b. k. (2012). the tool for assessing the damage tolerance of railway wheel under service conditions. theoretical and applied fracture mechanics, 57, 1-13. [15] jones, r., peng, d., pitt, s. and wallbrink, c. (2004). weight functions, ctod, and related solutions for cracks at notches. engineering failure analysis, 11, pp. 79-36. [16] peng, d., wallbrink, c. and jones, r. (2005). stress intensity factor solutions for finite body with quarter-elliptical flaws emanating from a notch. engineering fracture mechanics, 72(9), pp. 1329–1343. [17] peng, d., jones, r. and constable, t. (2013). tools and methods for addressing the durability of rolling stock. engineering failure analysis, 34, pp. 278-289. [18] pitt, s., jones, r. and atluri, s. n. (1999). further studies into interacting 3d cracks. computers and structures, 70, pp 583-597. [19] pitt, s. and jones, r. (1997). multiple-site and widespread fatigue damage in aging aircraft. engineering failure analysis, 4, pp. 237-257. [20] vijayakumar, k. and atluri, s. n. (1981). embedded elliptical crack in an infinite solid, subject to arbitrary crack-face tractions. journal of applied mechanics, transactions asme, 48(1), pp. 88-96. [21] peng, d., jones, r., lo, m., bowler, a., brick, g., janardhana, m. and edwards, d. (2015). crack growth at fastener holes containing intergranular cracking. engineering fracture mechanics, 137, pp. 79-87. [22] fishman, k. l. and withiam, j. l. (2011). lrfd metal loss and service-life strength reduction factors for metalreinforced systems, nchrp 675, transportation research board, washington, dc. [23] aashto, 2009, lrfd bridge design specifications, 4th ed. with interims, american association of state highway and transportation officials, washington, d.c. d. peng et alii, frattura ed integrità strutturale, 45 (2018) 33-44; doi: 10.3221/igf-esis.45.03 43 [24] iso 9224:2012: corrosion of metals and alloys corrosivity of atmospheres guiding values for the corrosivity categories. published in switzerland. [25] albrecht, p. and hall, jr. t. t. (2003). atmospheric corrosion resistance of structural steels. journal of materials in civil engineering, 15, pp. 1-24. [26] wade, s. a., begbie, k. j. and trueman, a. (2007). measuring atmospheric corrosion of industrial infrastructure using electrical resistance corrosion sensors, presented at the corrosion control 007, australasian corrosion association, sydney, paper 118. [27] elston, j., peng, d., baker, j., cairns, k., pitt, s. and thilakarathna, h. (2012). development of inspection and user friendly monitoring program for bms deliverables arisen from facet 5, project title: life cycle management of railway bridges project code: r3.118, crc for rail innovation report. [28] bridge design australian standard, as 5100.2—2004. [29] femap – finite element modelling and post processing, version 11.1.2, structural dynamics research corporation, pennsylvania; 2015. [30] peng, d. and cairns, k. (2012). bridge 62 near kilmore east strain gauge data analysis, rail crc report, monash university. [31] li, p., warner, d. h., fatemi, a. and phan, n. (2016). critical assessment of the fatigue performance of additively manufactured ti-6al-4v and perspective for future research. international journal of fatigue, 85, pp. 130-143. [32] mil-std-1530d, department of defense standard practice: aircraft structural integrity program (asip) (31-aug2016). [33] razavi, s. m. j., ferro, p. and berto, f. (2017). fatigue assessment of ti-6al-4v circular notched specimens produced by selective laser melting. metals. 7(8), pp. 291. [34] razavi, s. m. j., ferro, p., berto, f. and torgersen, j. (in press). fatigue strength of blunt v-notched specimens produced by selective laser melting of ti-6al-4v. theoretical and applied fracture mechanics. (doi: 10.1016/j.tafmec.2017.06.021) [35] branco, r., costa, j. d., berto, f., razavi, s. m. j., martins ferreira, j. a., capela, c., santos, l. and antunes, f. (2018). low-cycle fatigue behaviour of sintered aisi 18ni300 maraging steel produced by selective laser melting. metals, 8(1), pp. 32. [36] razavi, s. m. j., bordonaro, g. g., ferro, p., torgersen, j. and berto, f. (2018). fatigue behavior of porous ti-6al-4v made by laser engineered net shaping. materials, 11(2), pp. 284. [37] kahlin, m., ansell, h. and moverare, j. j. (2017). fatigue behaviour of notched additive manufactured ti6al4v with as-built surfaces. international journal of fatigue, 101, pp. 51-60. [38] kahlin, m., ansell, h. and moverare, j. j. (2017). fatigue behaviour of additive manufactured ti6al4v, with as-built surfaces, exposed to variable amplitude loading. international journal of fatigue, 103, pp. 352-363. [39] greitemeier, d., donne, c. d., syassen, f., eufinger, j. and melz, t. (2016). effect of surface roughness on fatigue performance of additive manufactured ti-6al-4v. materials science and technology, 32(7), pp. 629-634. [40] chan, k. s. (2015). characterization and analysis of surface notches on ti-alloy plates fabricated by additive manufacturing techniques. surface topography: metrology and properties, 3(4). (doi:10.1088/2051672x/3/4/044006) [41] leuders, s., vollmer, m., brenne, f., troster, t. and niendorf, t. (2015). fatigue strength prediction for titanium alloy tial6v4 manufactured by selective laser melting. metallurgical and materials transactions a, 46(9), pp. 38163823. [42] grelik, m. (2017). additive manufacturing in the context of structural integrity. international journal of fatigue, 94, pp. 168-177. [43] jones, r., singh raman, r. k. and mcmillan, a. j. (2018). crack growth: does microstructure play a role?. engineering fracture mechanics, 187, pp. 190-210. [44] wang, k., wang, f., cui, w., hayat, t. and ahmad, b. (2014). prediction of short fatigue crack growth of ti-6al-4v. fatigue & fracture of engineering materials & structures, 37, pp. 1075-1086. [45] sandgren, h. r., zhai, y., lados, d. a., shade, p. a., schuren, j. c., groeber, m. a., kenesei, p. and gavras, a. g. (2016). characterization of fatigue crack growth behavior in lens fabricated ti-6al-4v using high-energy synchrotron x-ray microtomography. additive manufacturing, 12, pp. 132-141. [46] jha, s. k., john, r. and larsen, j. m. (2013). incorporating small fatigue crack growth in probabilistic life prediction: effect of stress ratio in ti-6al-2sn-4zr-6mo. international journal of fatigue, 51, pp. 83-95. [47] cadario, a. and alfredsson, b. (2007). fatigue growth of short cracks in ti-17: experiments and simulations. engineering fracture mechanics, 74, pp. 2293-2310. d. peng et alii, frattura ed integrità strutturale, 45 (2018) 33-44; doi: 10.3221/igf-esis.45.03 44 [48] kotousov, a., lazzarin, p., berto and f., pook, l. (2013). three-dimensional stress states at crack tip induced by shear and anti-plane loading. engineering fracture mechanics, 108, pp. 65–74. [49] kotousov, a., berto, f., lazzarin, p. and pegorin f. (2012). three dimensional finite element mixed fracture mode under anti-plane loading of a crack. theoretical and applied fracture mechanics, 62, pp. 26-33. [50] campagnolo, a., berto, f. and lazzarin, p. (2015). the effects of different boundary conditions on three-dimensional cracked discs under anti-plane loading, european journal of mechanics-a/solids, 50, 76-86. [51] berto, f. and marangon, c. (2013). three‐dimensional effects in finite thickness plates weakened by rounded notches and holes under in‐plane shear. fatigue & fracture of engineering materials & structures, 36(11), pp. 1139-1152. [52] marangon, c., campagnolo, a. and berto, f. (2015). three-dimensional effects at the tip of rounded notches subjected to mode-i loading under cyclic plasticity. the journal of strain analysis for engineering design, 50(5), pp. 299-313. [53] he, z., kotousov, a., berto, f. and branco, r. (2016). a brief review of recent three-dimensional studies of brittle fracture. physical mesomechanics, 19(1), 6-20. [54] berto, f., lazzarin, p., kotousov, a. and pook, l. (2012). induced out-of-plane mode at the tip of blunt lateral notches and holes under in-plane shear loading. fatigue and fracture of engineering materials and structures, 35, pp. 538–55. [55] berto, f., kotousov, a., lazzarin, p. and pook, l. (2013). on scale effect in plates weakened by rounded v-notches and subjected to in-plane shear loading. international journal of fracture, 180, pp. 111–118. [56] pook, l. p., campagnolo, a., berto, f. and lazzarin, p. (2015). coupled fracture mode of a cracked plate under antiplane loading. engineering fracture mechanics, 134, pp. 391–403. << /ascii85encodepages false /allowtransparency false /autopositionepsfiles true /autorotatepages /none /binding /left /calgrayprofile (dot gain 20%) /calrgbprofile (srgb iec61966-2.1) /calcmykprofile (u.s. web coated \050swop\051 v2) /srgbprofile (srgb iec61966-2.1) /cannotembedfontpolicy /error /compatibilitylevel 1.4 /compressobjects /tags /compresspages true /convertimagestoindexed true /passthroughjpegimages true /createjobticket false /defaultrenderingintent /default /detectblends true /detectcurves 0.0000 /colorconversionstrategy /cmyk /dothumbnails false /embedallfonts true /embedopentype false /parseiccprofilesincomments true /embedjoboptions true /dscreportinglevel 0 /emitdscwarnings false /endpage -1 /imagememory 1048576 /lockdistillerparams false /maxsubsetpct 100 /optimize true /opm 1 /parsedsccomments true /parsedsccommentsfordocinfo true 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/hrv (za stvaranje adobe pdf dokumenata najpogodnijih za visokokvalitetni ispis prije tiskanja koristite ove postavke. stvoreni pdf dokumenti mogu se otvoriti acrobat i adobe reader 5.0 i kasnijim verzijama.) /hun 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/pdfxoutputintentprofileselector /documentcmyk /preserveediting true /untaggedcmykhandling /leaveuntagged /untaggedrgbhandling /usedocumentprofile /usedocumentbleed false >> ] >> setdistillerparams << /hwresolution [2400 2400] /pagesize [612.000 792.000] >> setpagedevice microsoft word numero 13 articolo 4 ahanchian mohammad et alii, frattura ed integrità strutturale, 13 (2010) 31-35; doi: 10.3221/igf-esis.13.04 31 investigation of crack propagation in single optical fiber composite with thermal influence by finite element method ahanchian mohammad ph.d. candidate of mechanical engineering, de la salle university arzumanyan hovhannes, verlinski sergey assistant professor of department of mechanics and machine sciences, state engineering university of armenia abstract. two parallel comparative ‘conventional method and computer simulation using ansys software’ for prediction of crack growth and its behavior in optical fiber are studied and presented in this work. corresponding finite element analysis was performed to determine the evolution of stress and strain states. the method is developed and combined with the modified j-integral theory to deal with this problem. the effects of crack length, temperature and mechanical forces are investigated by finite element method in the cracked body. the conditions where the mode i stress intensity factor motivate fracture occurrence is investigated and variations of the different cases are discussed. the most deleterious situation is found to be that wherein the entire model reaches rupture at some stage. the accuracy of the method is investigated through comparison of numerical results with computerized simulation using commercial ansys software. keywords. crack propagation; fracture; temperature loading; stress intensity factor; breaking force. introduction ecently, an increasing attention is attracted by a new development of microstructure optical fibers in telecommunication systems. an optical fiber is a single, hair-fine filament drawn from molten silica glass [1] which is widely used in communication systems. optical fibers are going to be employed as a replacement of metal wires as the transmission medium in high-speed, high-capacity communication systems and are superior to that of conventional copper cable. in this design data is converted into light then transmitted via fiber optic cables with less loss. one of the most important usages of optical fibers is to transfer data sometimes in very long distances [2]. this duty could not be performed with physical failure and if the fiber core transpires fracture the data would not be transmitted properly. since the main failure mode of fracture in optical fiber is mechanical fracture [3] more consideration is needed regarding the strength and associated reliability [4] of optical fibers which are major technical concerns before they can reach the full potential for telecommunication industry. inevitable presence of sub micro cracks, flaws and hollows in the intersection of materials as a result of manufacturing and further processes [5] or on the surface of glass under either tension or bending [6] play a significant role for concentrating stress near the crack tip which decrease the strength of the material. nevertheless, unfortunately, very few investigations have been conducted on their mechanical and fracture behavior of microstructure optical fibers [4]. these studies were conducted without considering temperature impacts. the goal of the current study is to investigate the fracture behavior of microstructure optical fibers containing surface cracks and environmental effects like temperature. therefore, finite r http://www.gruppofrattura.it http://dx.medra.org/10.3221/igf-esis.13.04&auth=true ahanchian mohammad et alii, frattura ed integrità strutturale, 13 (2010) 31-35; doi: 10.3221/igf-esis.13.04 32 element method is coded in mathcad program to inspect fracture behavior and the results are compared with the ansys analysis. the effects of crack configurations, closure stresses and temperature on the failure load have also been investigated. constitutive model of optical fiber he model of optical fiber is a composition of aluminum and silica glass as core which is developed within the framework of small static displacement. the material properties are presented in tab. 1. two isotropic and homogeneous materials, joining to constitute a model of fiber optic in two-dimensional plane stress geometry with an initial circular crack on their meeting line are considered. according to the mentioned significance of optical fiber, ability of fem and since computer modeling is useful to conduct virtual experiments with lower cost [7]; the authors decided to simulate a proper model on this design. material density, kg/m3 modulus of elasticity, mpa modulus of rigidity, mpa poisson's ratio thermal conductivity, w/m.k thermal expansion, 1/c glass 25400 46200 18600 0.245 6.21 8.00e-05 aluminum 26600 71000 26200 0.334 237 2.36e-05 table 1: typical property of materials [8, 9]. the diameter of optical fiber as standard is assumed to be 125 µm having a circular crack in the intersection line of two materials. three different cases considering crack lengths of 3.5, 7 and 10.5 µm are investigated. in the first situation, the crack has the smallest length that is in two dimensional polar coordinate r (radius of crack tip) is equal to the radius of core and θ (angle between crack tip and x direction) had been assumed to be 15 degree. for other cases, radius had been kept constant and θ had been incremented by 15 degree in order to increase crack length. the problem is investigated in linear elastic fracture mechanics (lefm) with plane stress approach. due to symmetry of the problem, a quarter segment of the model is analyzed. boundary conditions are imposed such as horizontal line is constrained in y direction and vertical line is constrained in x direction; both lines are considered as symmetric along their direction. applied forces are imposed in x any y directions with constant values and the breaking forces are calculated for each case. thermal condition is assumed to have constant value in each half of the quarter model, the lower part of quarter model has 50 °c and the upper part has 60 °c in order to have thermal gradient as presented in fig 1. figure 1: applied forces and thermal conditions on the model. t http://www.gruppofrattura.it http://dx.medra.org/10.3221/igf-esis.13.04&auth=true ahanchian mohammad et alii, frattura ed integrità strutturale, 13 (2010) 31-35; doi: 10.3221/igf-esis.13.04 33 conventional fracture analysis o numerically predict crack formation and growth of this model under accidental loading, it is necessary to characterize fracture properties at the microscopic level. to approach this objective a complete code of program using finite element method was written by the authors in mathcad software. the geometrical characteristics, material properties and boundary conditions are attributed to the model. corresponding finite element analysis was performed to determine the evolution of stress and strain states. for more comprehensible results and better facileness for comparison von misses stress had been calculated across the model using eq. (1). (1) according to the theories in fracture mechanics, stress intensity factor was calculated throughout the model and was applied to obtain j-integral. according to energy criterion, the critical energy release rate was determined and the crack extension was predicted and is presented in this paper. the breaking force values which lead the crack to propagate were obtained using trial and error method for each case. the model will start propagation at low stresses and tends to extend at the tip of the crack [10, 11]. if the region be plastic at the tip of the crack, the metal mass around the crack would support the stress and the structure is not endangered [12]. recent work on microstructure silica optical fibers indicated that they failed in a brittle manner and cracks initiated from the fiber surfaces [13]. according to the results, crack will propagate on the brittle area which is glass. the initiation and propagation of crack through brittle materials is at great speeds near the speed of sound [14]. afterwards, thermal conditions were imposed and the complete procedure was done again. based on the results, it is studied that crack will not growth anymore when the model is subjected to breaking force and thermal condition. moreover, the largest crack needs less force to be broken. the contour plots for maximum crack length solved by mathcad are presented in fig 2. fig 2.a shows von misses stress distribution subject to critical loading. based on the data the highest amount of equivalent stress is placed near the crack tip. fig 2.b presents von misses stress distribution subject to critical loading and thermal conditions. it is shown that the maximum amount of equivalent stress is decreased after applying thermal conditions which prevents crack propagation and material failure. the approximation of crack propagation subject to critical loading is illustrated in fig 2.c. (a) (b) (c) figure 2: contour plots for maximum crack length (critical length), solved by mathcad, (a) von misses stress distribution subject to critical loading, (b)von misses stress distribution subject to critical loading and thermal conditions, (c) approximation of crack propagation subject to critical loading. the red region in fig. 2.a shows the highest amount of equivalent stress. it is placed at the crack tip due to the fact that stresses concentrate at the crack tip. in fig. 2.b the reduction of maximum amount of equivalent stress is a result of temperature. the prediction of crack propagation is presented by red region in fig 2.c. it shows that crack will propagate in silica that is a brittle material meaning that it fractures rather than deforming plastically. it responses to increasing mechanical load until a slow-growing microscopic crack exceeds a certain threshold at which point the crack grows rapidly and the material fractures [3]. t )(6)()()( 2 1 222222 zxyzxyxzzyyxeq   http://www.gruppofrattura.it http://dx.medra.org/10.3221/igf-esis.13.04&auth=true ahanchian mohammad et alii, frattura ed integrità strutturale, 13 (2010) 31-35; doi: 10.3221/igf-esis.13.04 34 simulation by ansys onsequently six different cases are discussed and each case is simulated by ansys to justify the accuracy of the written code in mathcad. some results are presented subsequently. the partial zoomed contour plots of ansys analysis of von misses stress distribution for the largest crack size subject to critical loading is presented in fig 3.a. the result after imposing thermal condition to the previous situation is presented in fig 3.b. figure 3: zoomed contour plots for maximum crack length (critical length), simulated by ansys, (a) von misses stress distribution subject to critical loading, (b)von misses stress distribution subject to critical loading and thermal condition. comparing the results of conventional method and ansys simulation n the first situation, the crack has the smallest length that is in two dimensional polar coordinate radius of crack tip is equal to the radius of core and the angle between crack tip and x direction had been assumed to be 15 degree. critical force for this type of crack is -1.95 n; in this case maximum value for equivalent stress is 12.13 mpa, and is placed near the crack tip in aluminum material. by adding thermal condition to applied force, maximum value for equivalent stress would be 12.02 mpa, which is lower than previous case. figure 4: comparison of maximum von misses stress in different cases. c i http://www.gruppofrattura.it http://dx.medra.org/10.3221/igf-esis.13.04&auth=true ahanchian mohammad et alii, frattura ed integrità strutturale, 13 (2010) 31-35; doi: 10.3221/igf-esis.13.04 35 maximum von misses stress and breaking force for different cases are presented in tab. 2. the lowest amount of breaking force occurs in the largest crack size showing that we are near critical crack size. the value of stresses determine by conventional method and ansys simulation are presented and demonstrate that the differences are less than 1% which prove the accuracy of written code. crack length, µm breaking force, n mechanical loading mechanical & thermal loading cm* mpa ansys mpa error cm mpa ansys mpa error 3.5 1.94 12.14 12.22 0.71% 12.02 11.92 0.84% 7 2.28 12.76 12.66 0.85% 12.65 12.56 0.70% 10.5 0.85 10.91 11.01 0.95% 10.81 10.90 0.87% *cm: conventional method table 2: maximum von misses stress distribution and breaking force for different cases. conclusion he computational results presented in this research demonstrate the capabilities of the energy criterion towards modeling fracture in microstructure composites such as optical fiber. critical forces in each case are obtained and it is clear that applying temperature condition would prevent the fracture process and fracture occurs under higher stresses as a result the optical fiber should be protected from low temperatures by adding cladding. it also protects from mechanical loading. moreover, prediction of crack branching and propagation is summarized and compared. the maximum stress magnitudes which instigate the crack are presented and compared. this shows that how big mechanical loading could our design withstand. consequently, there are some parameters that mitigate crack propagation which are higher temperature, lower stresses and smaller grain size. this theory is a result of investigation by conventional method. when the temperature increases, a higher stress is required for a crack to propagate. another point is that large crack size with 45 degree, is critical length and crack propagation occurs under minimum value of mechanical force and shows that production control should be improved properly. references [1] s. b. grassino, what is optical fibers made of?, university of southern mississippi (2003). [2] r. paschota, journal of optik & photonik, 2 (2008). [3] a. d. yablon, “optical fiber fusion splicing” (2005) 181. [4] r. bai, c. yan, 5th australasian congress on applied mechanics, acam 2007. [5] c. yan, r.x. bai, p. k.d.v. yarlagadda, h. yu, 9th global congress on manufacturing and management (gcmm 2008) surfers paradise, australia. [6] c. p. chen, t. h. chang, journal of materials chemistry and physics, issn 0254-0584, 77 (1) (2003) 110. [7] o. c. zienkiewicz, r. l. yaylor, the finite element method, forth ed., mcgraw-hill (1994). [8] f. p. incorpera, d. p. dewitt , introduction to heat transfer, translation of third edition isfahan university,1 (2003). [9] j. e. shigley, c. r. mischke, mechanical engineering design, tehran (2001). [10] d. a. anderson, j. c. tannehill, r. h. pletcher, fracture mechanics, hemisphere, washington, dc (1984). [11] c. atkinson, f. g. leppington, int. j. solids struct., 13 (1977) 1103. [12] http://www.pdhcenter.com/courses/m155/m155.pdf, ‘brittle fracture mechanism’, doe-hdbk-1017/2-93 brittle fracture. [13] c. yan, x. d. wang, l. ye, k. lyytikainen, j. canning, the 18th annual meeting of the ieee, lasers and electrooptics society leos 2005, 529. [14] g. p. cherepanov, mechanics of brittle fracture, mcgraw-hill, new york (1979). t http://www.gruppofrattura.it http://dx.medra.org/10.3221/igf-esis.13.04&auth=true microsoft word numero 25 art 2 g. qian et alii, frattura ed integrità strutturale, 25 (2013) 7-14; doi: 10.3221/igf-esis.25.02 7 special issue: characterization of crack tip stress field crack propagation mechanism and life prediction for very-highcycle fatigue of a structural steel in different environmental medias guian qian, chengen zhou, youshi hong* state key laboratory of nonlinear mechanics, institute of mechanics, chinese academy of sciences, beijing 100190, china *corresponding author. tel: +86 10 82543966, hongys@imech.ac.cn abstract. the influence of environmental medias on crack propagation of a structural steel at high and veryhigh-cycle fatigue (vhcf) regimes is investigated based on the fatigue tests performed in air, water and 3.5% nacl aqueous solution. crack propagation mechanisms due to different crack driving forces are investigated in terms of fracture mechanics. a model is proposed to study the relationship between fatigue life, applied stress and material property in different environmental medias, which reflects the variation of fatigue life with the applied stress, grain size, inclusion size and material yield stress in high cycle and vhcf regimes. the model prediction is in good agreement with experimental observations. keywords. very-high-cycle fatigue; aqueous environment; stress intensity factor; plastic zone. introduction ery-high-cycle fatigue (vhcf) [1-16] of metallic materials is regarded as fatigue failure at stress levels below the conventional fatigue limit and the corresponding fatigue life beyond 107 loading cycles. lots of modern engineering structures and components, such as airplanes, turbines, automobiles and high speed trains are expected to endure the safe performance in the range of 107 1010 load cycles. one typical feature of vhcf for high strength steels is that the s-n curve consists of two parts corresponding to subsurface and surface crack initiations, resulting in a stepwise or duplex shape of the curve [1-16]. generally, the crack initiation in vhcf regime is observed as a fisheye pattern on the fracture surface, which is located at the specimen subsurface region and originated from a nonmetallic inclusion for high strength steels [4-11]. since the pioneering work by naito et al. [17, 18], there have been a variety of studies on the vhcf behavior for different materials [1-16]. among these studies, the crack initiation mechanism in vhcf attracted most of the attention. however, the crack initiation and propagation process of high strength steels in environmental medias in vhcf is still not clear. in addition to experimental investigations, theoretical models for fatigue strength and life prediction in vhcf regime are of significant importance for both scientific and engineering applications. however, models to predict s-n curves in vhcf regime in different environmental medias are lacking due to the complicated crack initiation mechanisms. therefore, in this paper, the process of crack initiation and propagation for a structural steel in environmental medias in vhcf was investigated based on the experiments. the fatigue test was performed in laboratory air, fresh water and 3.5% nacl aqueous solution. the influence of environmental medias on the variation of fatigue strength and cracking process is presented. based on the experimental observations, a model is proposed to study the s-n curves of the material in high cycle and vhcf in different medias. v http://www.gruppofrattura.it http://dx.medra.org/10.3221/igf-esis.25.02&auth=true g. qian et alii, frattura ed integrità strutturale, 25 (2013) 7-14; doi: 10.3221/igf-esis.25.02 8 material and experimental method our-glass shape specimens (fig. 1) of a structural steel 40cr (0.4% c, 1% cr) were tested with a rotary bending machine operating at a frequency of 52.5 hz and the testing environments were of three types, namely laboratory air, fresh water and 3.5% nacl aqueous solution. the average size of original austenite grains is 11.2 m and the average yield stress is 1501 mpa. vickers microhardness indentation on the heat-treated specimen gives the average value of 545 kgf/mm2 with the uniform distribution over the specimen cross section. the ph values of fresh water and 3.5% nacl aqueous solution are 7.70 and 7.47, respectively. based on the fatigue test data and scanning electron microscopy (sem) observations of fracture surfaces, the effect of environment on the fatigue behavior at high cycle and vhcf regimes was examined. figure 1: schematic drawing of hour-glass shape specimen for rotary bending fatigue test (dimensions in mm). s-n curves or specimens tested in laboratory air (triangles in fig. 2), single crack originated from the surface of the specimens with fatigue life or the number of cycles to failure nf less than 107 loading cycles and the corresponding stress levels are above 700 mpa, whereas the crack started from subsurface for the specimens with nf beyond 107 loading cycles and the stress levels are below 700 mpa. for fatigue testing in fresh water, a similar stepwise s-n curve is presented (squares in fig. 2), but the stress corresponds to the transition part of the s-n curve is dramatically decreased. for the fatigue tests in nacl aqueous solution, the s-n curve (circles symbols in fig. 2) displays a continuously descending shape. the fatigue strength is even lower than that tested in water from high cycle to vhcf regime, implying that the effect of nacl aqueous solution on the degradation of fatigue strength for the structural steel is more remarkable than that of water media. 10 5 10 6 10 7 10 8 0 200 400 600 800 1000 m a x im u m s tr e s s  m a x ( m p a ) number of cycles to failure in air in water in 3.5% nacl figure 2: s-n curves for specimens tested at laboratory air, fresh water and 3.5% nacl aqueous solution, hollow symbols: crack origination at surface, solid symbols: crack origination at subsurface, semi-solid symbols: mixed crack origination. h f http://www.gruppofrattura.it http://dx.medra.org/10.3221/igf-esis.25.02&auth=true g. qian et alii, frattura ed integrità strutturale, 25 (2013) 7-14; doi: 10.3221/igf-esis.25.02 9 fractography and fracture mechanics analysis for specimens tested in air or the specimens tested in laboratory air, all the fatigue fracture surfaces of both surface initiation and subsurface initiation modes present the morphology of three regions as shown in fig. 3(a). region a [fig. 3(a), (b)] is the crack initiation and early propagation zone, in which crack propagation velocity is very slow to produce a relatively smooth fracture surface with transgranular cleavage-like morphology and fatigue striations. this region is responsible for a substantially large part of the total fatigue life. as shown in fig. 3 (b), crack initiated at the subsurface of specimen at vhcf regime, forming a fisheye pattern originated from a nonmetallic inclusion with the main chemical compositions examined as al, ca and o. region b is the steady and relatively fast growth zone and fig. 3(c) is a local micrograph of this zone showing quasi-cleavage morphology. region c is the final fracture zone and the fracture surface presents the ordinary morphology of dimple pattern [fig. 3(d)]. figure 3: fracture surface of a specimen tested in laboratory air, at σmax = 610 mpa and nf = 3.27×108, (a) whole fracture surface (c.o.: crack origin), (b) enlargement of region a, (c) enlargement of region b and (d) enlargement of region c. by considering the inner boundary as the crack tip for regions a and b, the stress intensity factor (sif) ki is calculated with the following formula i ak f a  (1) where σa is the applied stress, a is the crack radius and f is the geometry factor. in the calculation, region a is assumed to be elliptical shape and region b is regarded as circular shape. the values of ki almost keep constant at 16 mpam1/2 from f b c a c. o. 1mm (a) (c) 30μm (d) 20μm inclusion fisheye 100μm (b) http://www.gruppofrattura.it http://dx.medra.org/10.3221/igf-esis.25.02&auth=true g. qian et alii, frattura ed integrità strutturale, 25 (2013) 7-14; doi: 10.3221/igf-esis.25.02 10 high cycle to vhcf regime for region a. the values of ki for region b are between 35 and 60 mpam1/2, which correspond to the material fracture toughness kic. ki for region a and b is used to calculate the plastic zone size rp around the crack tip based on the expression 2 p y 1 3 k r           (2) where δk is the amplitude of ki, σy is the yield stress of the material. the calculated plastic zone size for region a is 32.6 μm, which approximately equals to the size of 2-3 grain sizes. in the crack initiation and early propagation stage (region a), grain boundary serves as a microstructural obstacle. in region b, the calculated plastic zone size is 1449 μm. as the increase of the plastic zone, the crack propagation rate increases significantly. in region c, as the decrease of the ligament of the specimen, the specimen displays a plane stress state. thus, the fracture morphology shows a shear fracture with an angle of 45 degree along the tension direction. for the tested specimens, the fracture is plane strain condition in the crack initiation stage and the crack tip has a high constraint effect as a result of the small plastic zone size and high stress triaxiality. with the decrease of ligament in region c, the crack tip has a small constraint which causes large plastic deformation. however, the crack tip constraint effect during the crack propagation needs a further quantification by using a k-t or j-q method. the sif ranges for inclusions and fisheye patterns are calculated by the following formula [2, 6] 0.5 ak area   (3) where area is the square root of the area for inclusions or fisheyes. fig. 4 (a) shows the relationship between δk and nf. δk for inclusions is about 2.83 mpam1/2 irrespective of the fatigue life, which is smaller than the threshold sif range (δkth) of the material. δk for fisheyes is about 10 mpam1/2, which is somewhat higher than δkth of the material. therefore, it is understood that a crack that originates at an inclusion can propagate until it forms a fisheye pattern. according to murakami’s model [2], fatigue strength at 108 cycles, denoted as σw, is predicted by 1 6 1.56( 120) ( area ) w hv    (4) where hv is the vickers hardness of the material. fig. 4 (b) shows the relationship between σmax/σw and number of cycles to failure. the ratio is between 1 and 1.2, indicating that the fatigue strength of the material in the present study is well predicted by the murakami model. 10 6 10 7 10 8 0 4 8 12 16 number of cycles to failure  k ( m p a m 1 /2 ) sif of inclusion sif of fisheye 107 108 109 0.0 0.5 1.0 1.5 number of cycles to failure  m a x / w figure 4: (a) δk for inclusions and fisheyes, (b) relationship between σmax/σw and number of cycles to failure. (a) (b) http://www.gruppofrattura.it http://dx.medra.org/10.3221/igf-esis.25.02&auth=true g. qian et alii, frattura ed integrità strutturale, 25 (2013) 7-14; doi: 10.3221/igf-esis.25.02 11 fractography for specimens tested in environmental medias or the case of fatigue tested in water and 3.5% nacl aqueous solution, the crack origination observed by sem is mainly the surface related initiation. additionally, unlike the single crack origin for specimens tested in air, multiple fatigue crack origins were observed [8], and the fracture surface morphology for fatigue crack steady growth zone is predominantly intergranular, as shown in fig. 5, where the secondary cracks along grain boundaries and cross section of the specimens are observed, which is the phenomenon of grain boundary embrittlement due to the aqueous environmental effect. the presence of widespread secondary cracks is the damage characteristics of the material subjected to aqueous environmental medias. figure 5: (a) cracking surface for the specimen tested in water, at σmax=156 mpa and nf =8 107, (b) secondary cracking (sc) in the cross section of the specimen tested in 3.5% nacl, at σmax=41.3 mpa and nf =9 107. model for s-n curve prediction in different environmental medias t is known that crack initiation related to nonmetallic inclusions (subsurface crack initiation) is attributed to the weak cohesive state between inclusion and matrix. under cyclic loading, a crack may easily form due to the interface debonding and grow into the matrix. in such a case, the subsurface crack initiation cycle ni is [19] i i i 4lw n u   (5) where wi is the surface energy related to subsurface crack initiation and δui is the unit increment of energy for subsurface crack initiation. wi and δui are functions of grain radius l, inclusion radius r (ψ=r/l), stress amplitude δσ and the resistance of dislocation movement k (φ=0.5δσ/k). n is defined to normalize in , such that  22 iawn k l  (6) where  2 1 a      (7) with  being the shear modulus and ν being poisson’s ratio. thus, the normalized ni is denoted as in i i 2 4n n n u     (8) where  u is the dimensionless unit increment of energy for subsurface crack initiation. f i 20 m (a) s c 20 m (b) http://www.gruppofrattura.it http://dx.medra.org/10.3221/igf-esis.25.02&auth=true g. qian et alii, frattura ed integrità strutturale, 25 (2013) 7-14; doi: 10.3221/igf-esis.25.02 12 figure 6: predicted ni of subsurface crack initiation for specimens tested in air, for different loading levels and material properties. the variation of in with φ and ψ are demonstrated in fig. 6 by assuming φ to be 1.1, 1.2, 1.4, 2 and 4, and ψ varying from 0 to 2. it is shown that fatigue life in increases with the decrease of φ, i.e. the decrease of fatigue loading δσ or the increase of the resistance of dislocation movement k. for a given loading state (φ being constant), in generally decreases with the increase of ψ, i.e. the increase of inclusion size r or the decrease of grain size l. the trends are in agreement with the experimental observations. yang et al. [20] observed that the fatigue life increases with the decrease of inclusion size for an alloy steel. it is widely observed that the fatigue life increases with the decrease of the applied loading [1-16]. zhao et al. [10] found that the fatigue life increases with the resistance of the dislocation movement, i.e. the yield stress of material. for fatigue crack initiation at surface, by considering the surface crack factor and half cycling process [7, 19], surface crack initiation cycle ns is   s s 2 4 1.25 2 aw n l k    (9) where ws is surface energy related to surface crack initiation. the normalized surface crack initiation cycle sn is   s s 2 w 4 1.25 1 n n n k    (10) where kw is the ratio of surface energy for crack formation at subsurface to that at surface (wi/ws). note that both in and sn are functions of φ and ψ. in short, eqs. (8) and (10) are used to calculate the fatigue life for crack initiation at surface or at subsurface in different environmental medias. for the case tested in air, kw is taken as 3 in the calculation [8, 21]. for the case tested in 3.5 % nacl solution, kw is taken as 25 times of that in air, i.e. 75, from the relationship of kic in air and the aqueous solution [8, 22]. the fatigue life for surface crack initiation sn and subsurface crack initiation in in air as a function of φ and ψ is compared in fig. 7 (a). it is seen that the subsurface crack initiation life is higher than the surface crack initiation life for a high φ (high loading or low material yield stress). thus, surface crack initiation occurs much easier in this stage. with decreasing φ, the surface crack initiation life is higher than the subsurface crack initiation life at the same φ, which as a consequence leads to the subsurface crack initiation in this stage. at points a, b and c, the subsurface crack initiation life equals to the surface crack initiation. the three points correspond to the transition plateau in an s-n curve from the subsurface to the surface crack initiation. fig. 7 (b) compares the surface crack initiation life with subsurface crack initiation life in 3.5% nacl solution. a similar trend as that in air is found. however, the transition from surface to subsurface crack initiation in 3.5% nacl solution is much lower than that in air. this is in agreement with the experimental observations that in aqueous environmental media, the crack initiation starts from the surface even in vhcf regime. it is also seen from figs. 7 (a) and (b) that when subjected to the same loading, the fatigue life in air is much longer than that in aqueous medias. this explains the characteristics of the s-n curve in fig. 2. http://www.gruppofrattura.it http://dx.medra.org/10.3221/igf-esis.25.02&auth=true g. qian et alii, frattura ed integrità strutturale, 25 (2013) 7-14; doi: 10.3221/igf-esis.25.02 13 figure 7: (a) predicted results of fatigue life for surface and subsurface crack initiation in air, (b) predicted s-n curves for surface and subsurface crack initiation in 3.5% nacl solution. conclusions ased on this study, the following conclusions are drawn: (1) during the crack propagation process for specimens tested in air, fracture surface displays three regions with different crack propagation mechanisms. the formation of different morphologies in these regions is attributed to different crack driving forces and different extents of crack tip constraint ahead of crack tip. (2) the ki value of fisheye crack is close to the corresponding δkth. and there is an early crack steady growth zone named region a with constant ki value between δkth and fracture toughness. (3) the fatigue strength for specimens tested in water and in 3.5% nacl aqueous solution are significantly decreased compared to that tested in air. the fractography characteristics for specimens tested in aqueous solution are multiple crack origination and intergranular mode with widespread secondary cracks in crack steady propagation period. (4) a model is proposed to study the relationship between fatigue life, applied stress and material property in vhcf in different environmental medias. this model predicts that fatigue life decreases with the increase of applied loading and inclusion size, whereas it increases with the increase of material yield stress. in 3.5% nacl solution, the fatigue life decreases significantly and surface crack initiation occurred even in vhcf regime. the model prediction is in good agreement with experimental observations. acknowledgements his work was funded by the national natural science foundation of china (nos. 11172304, 11021262 and 11202210) and the national basic research program of china (2012cb937500). references [1] stanzl, s., tschegg, e., mayer, h. lifetime measurements for random loading in the very high cycle fatigue range, int. j. fatigue, 8 (1986)195-200. [2] murakami, y., yokoyama, n., nagata, j. mechanism of fatigue failure in ultralong life regime, fatigue fract. eng. mater. struct., 25 (2002) 735-746. [3] bathias, c., paris, p., gigacycle fatigue in mechanical practice, marcel dekker, new york, (2005). b t 0.1 1 10 100 0 2 4 6 8 (b) a b  = 0 .5   / k n s and n i in 3.5% nacl  =0.1, ni  =0.4, ni  =0.8, ni surface, ns c 0.1 1 10 100 0 2 4 6 8  =    / k (a) in air  =0.1, ni  =0.4, ni  =0.8, ni surface, ns n s and n i a b c http://www.gruppofrattura.it http://dx.medra.org/10.3221/igf-esis.25.02&auth=true g. qian et alii, frattura ed integrità strutturale, 25 (2013) 7-14; doi: 10.3221/igf-esis.25.02 14 [4] hong, y., zhao, a., qian, g., essential characteristic and influential factors for very-high-cycle fatigue behavior of metallic materials, acta metall. sinica, 45 (2009) 769-780. [5] zhou, c., qian, g., hong, y., fractography and crack initiation of very-high-cycle fatigue for a high carbon low alloy steel, key eng. mater., 324-325 (2006) 1113-1116. [6] qian, g., hong, y., zhou, c., investigation of high cycle and very-high-cycle fatigue behaviors for a structural steel with smooth and notched specimens, eng. failure analysis, 17 (2010) 1517-1525. [7] hong, y., zhao, a., qian, g., zhou, c., fatigue strength and crack initiation mechanism of very-high-cycle fatigue for low alloy steels, metall. mater. trans. a, 43 (2012) 2753-2762. [8] qian, g., zhou, c., hong, y., experimental and theoretical investigation of environmental media on very-high-cycle fatigue behavior for a structural steel, acta mater., 59 (2011) 1321-1327. [9] qian, g., hong, y., effects of environmental media on high cycle and very-high-cycle fatigue behaviors of structural steel 40cr, acta metall. sinica, 45 (2009) 1359-1363. [10] zhao, a., xie, j., sun, c., lei, z., hong, y., effects of strength level and loading frequency on very-high-cycle fatigue behavior for a bearing steel, int. j. fatigue, 38 (2012) 46-56. [11] zhao, a., xie, j., sun, c., lei, z., hong, y., prediction of threshold value for fga formation, mater. sci. eng. a, 528 (2011) 6872-6877. [12] sun, c., xie, j., zhao, a., lei, z., hong, y., a cumulative damage model for fatigue life estimation of high-strength steels in high-cycle and very-high-cycle fatigue regimes, fatigue fract. eng. mater. struct., 35 (2012) 638–647. [13] stepanskiy, l., cumulative model of very high cycle fatigue, fatigue fract. eng. mater. struct., 35 (2012) 513–522. [14] sun, c., lei, z., xie, j., hong, y., effects of inclusion size and stress ratio on fatigue strength for high-strength steels with fish-eye mode failure, int. j. fatigue, 48 (2013)19–27. [15] paolino, d., chiandussi, g., rossetto, m., a unified statistical model for s-n fatigue curves: probabilistic definition, fatigue fract. eng. mater. struct., 36 (2013)187–201. [16] huang, z., wang, q., wagner, d., bathias, c., chaboche, j., a rapid scatter prediction method for very high cycle fatigue, fatigue fract. eng. mater. struct., 2013, doi: 10.1111/ffe.12021. [17] naito, t., ueda, h., kikuchi, m., observation of fatigue fracture surface of carburized steel, japan soc. mater. sci., 32 (1983) 1162-1166. [18] naito, t., ueda, h., kikuchi, m., fatigue behavior of carburized steel with internal oxides and nonmartensitic microstructure near the surface, metall. trans. a, 15a (1984) 1431-1436. [19] tanaka, t., mura, t., a dislocation model for fatigue crack initiation, j. appl. mech. trans. asme, 48 (1981) 97-103. [20] yang, z., li, s., zhang, j., zhang, j., li, g., li, z., hui, w., weng, y., the fatigue behaviors of zero-inclusion and commercial 42crmo steels in the super-long fatigue life regime, acta mater., 52 (2004) 5235-5241. [21] venkataraman, g., chung, y., nakasone, y., mura, t., free energy formulation of fatigue crack initiation along persistent slip bands: calculation of s-n curves and crack depths, acta metall., 38 (1990) 31-40. [22] suresh, s., fatigue of materials, cambridge university press, cambridge, (1998). http://www.gruppofrattura.it http://dx.medra.org/10.3221/igf-esis.25.02&auth=true microsoft word 2229-article text (.docx, max 100 mb)-9975-1-18-20190301 j. f. barbosa et alii, frattura ed integrità strutturale, 48 (2019) 400-410; doi: 10.3221/igf-esis.48.38 400 a comparison between s-n logistic and kohout-věchet formulations applied to the fatigue data of old metallic bridges materials joelton fonseca barbosa federal university of rio grande do norte, natal, brazil & federal rural university of the semi-arid region, mossoró, brazil faculty of engineering, university of porto, porto, portugal joeltonfb@gmail.com, https://orcid.org/0000-0003-3447-8240 josé a.f.o. correia, pedro a. montenegro faculty of engineering, university of porto, porto, portugal jacorreia@inegi.up.pt, jacorreia@fe.up.pt, https://orcid.org/0000-0002-4148-9426 paires@fe.up.pt, http://orcid.org/0000-0001-5699-4428 raimundo carlos silverio freire júnior federal university of rio grande do norte, natal, brazil freirej@ufrnet.br grzegorz lesiuk faculty of mechanical engineering, department of mechanics, material science and engineering, wrocław university of science and technology, smoluchowskiego 25, 50-370 wrocław, poland grzegorz.lesiuk@pwr.edu.pl, https://orcid.org/0000-0003-3553-6107 abílio m.p. de jesus, rui a.b. calçada faculty of engineering, university of porto, porto, portugal ajesus@fe.up.pt, http://orcid.org/0000-0002-1059-715x ruiabc@fe.up.pt, http://orcid.org/0000-0002-2375-7685 abstract. a new formulation of a logistic deterministic s-n curve is applied to fatigue data of metallic materials from ancient portuguese riveted steel bridges. this formulation is based on a modified logistic relation that uses three parameters to fit the low-cycle(lcf), finite-lifeand high-cyclefatigue (hcf) regions. this model is compared to the kohout-věchet fatigue model, which has a refined adjustment from very low-cycle fatigue (vlcf) to very high-cycle fatigue (vhcf). these models are also compared with other models, such as, power law and fatigue-life curve from the astm e739 standard. the modelling performance of the s-n curves was made using the fatigue data considering the stress fatigue damage parameter for the materials citation: barbosa, j., correia, j., montenegro, p., júnior, r., lesiuk, g., jesus, a., calçada, r., a comparison between s-n logistic and kohout-věchet formulations applied to the fatigue data of old metallic bridges materials, frattura ed integrità strutturale, 48 (2019) 400-410. received: 22.10.2018 accepted: 27.12.2018 published: 01.04.2019 http://www.gruppofrattura.it/va/48/2229.mp4 j. f. barbosa et alii, frattura ed integrità strutturale, 48 (2019) 400-410; doi: 10.3221/igf-esis.48.38 401 from the eiffel, luiz i, fão and trezói riveted steel bridges. using a qualitative methodology of graphical adjustment analysis and another quantitative using the mean square error, it was possible to evaluate the performance of the mean s-n curve formulation. the results showed that the formulation of the s-n curve using the logistic equation applied to the metallic materials from the old bridges resulted in a superior performance when compared with others models under consideration, both in the estimation of fatigue behaviour in the low-cycle fatigue (lcf) region and in the lowest mean square error. keywords. fatigue; kohout-věchet model; fatigue-life curve; prediction; logistic formulation. copyright: © 2019 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. introduction he knowledge about the fatigue life expectancy of materials and structural components in engineering design is of great importance for the determination of load bearing during operation. prediction of failure through mathematical and statistical modelling is a complex activity that attempts through an analytical model to consider the effects of cyclic stresses, stress intensity, predominance between traction and compression loading, frequency, number of experimental samples and the effects of manufacturing processes. therefore, fatigue assessment is a difficult and still attractive challenge that remains an open problem in many situations. one way to synthesize the number of factors involved in the fatigue life prediction is to reduce the model to the variables that are able to explain cause/effect, i.e. to fit a fatigue test to a stress level 𝜎 (independent variable) to explain the number of cycles ni (dependent variable) required until failure. this fatigue model is known as s-n curves or wöhler's curves, widely used in standards and standardization manuals such as astm e-739-10 [1], iso 12107:2012 [2], en 1993-1-9 [3], bs5400 [4], aashto [5], for engineering design of material and structural details. these standards are based on the basquin equation [6,7] suggested in 1910, aiming at characterizing the fatigue behaviour in the high(hcf) and low-cycle fatigue (lcf) regions. typically, fatigue data for preliminary design are studied in regions of 103 to 107 cycles. however, depending on the application, there is a need to prioritize estimation in the lcf or hcf regions. for extrapolation of estimates in hcf region, one must observe the adjustment equation and insert more fatigue data for regions of unknown space. for lcf region, the combination between the static strength and low-cycle fatigue data can be used to better fit the model. concepts of engineering design for low-cycle fatigue regimes have been important to the use of advanced materials in different applications in mechanical designs. civil engineering structures, railway and roadway bridges, offshore and ground structures, logistic structures, among others, are designed for the hcf regimes. recently, a series of failures of these structures cannot be explained only with the hcf regime, taking into account the extreme loading conditions to which the structural elements are subject (e.g., earthquakes). recent studies [8,9] suggest the use of s-n or ε-n curves covering both the lcf and hcf regimes. the models used to estimate the s-n and ε-n curves, which have a good adjustment capacity in the low-cycle region, will provide greater reliability in estimating the fatigue damage parameters such as smith-watson-topper, strain, walker-like and energy-based criteria, among others. these approaches will allow the fracture mechanics to be able to predict crack onset by fatigue and residual life, more accurately. in addition, s-n curve with good adjustment in the low-cycle fatigue region allows the generalization of probabilistic fatigue models, and in this way, it is possible to estimate the load limit and reliability of the material or structural component at the beginning of the operation. the use of s-n curves in the fatigue life prediction can be related to fracture mechanics based approaches. additionally, probabilistic approaches can be implemented to handle the uncertainties associated to the materials or models as observed in the research works [10–13] that have been applied and compared with existing fatigue data from the portuguese riveted metallic bridges. with the principle of meeting the most accurate estimates for the low-cycle fatigue regions, ranging from ultimate tensile strength to the high-cycle fatigue region, the kohout-věchet s-n curve is currently being proposed. this model has been increasingly used in fatigue life assessment of existing bridge structures [6,14,15]. another model similar to kohout-věchet relation is the model proposed by mu et al [16], in which a multi-slope model capable of adjusting the s-n curve in the three target regions, low-cycle-, finite-lifeand high-cycle-fatigue, using a logistic function of three parameters is proposed. t j. f. barbosa et alii, frattura ed integrità strutturale, 48 (2019) 400-410; doi: 10.3221/igf-esis.48.38 402 however, the analysis of mu's work was limited to testing the model only for the t300/qy8911 carbon/epoxy composite. knowing that this model has a wide adjustment capacity, in this research it will be applied to represent the fatigue behaviour of metallic materials from the ancient bridges, and in this way verify the performance of the s-n logistic formulation. a comparative study of the performance of the s-n adjustment equations, using models such as kohout-věchet, logistic, astm and generalized power law, will be applied to fatigue data from the old portuguese riveted metallic bridges (eiffel, luiz i, fão and trezói). by means of a graphical adjustment analysis and the mean quadratic error, it will be possible to find the model that best fits with the experimental data. the results will be presented and discussed for a better recommendation on using the model in predicting fatigue of old bridges. methods used in the modelling of the s–n curves power law he generalized power law model is a derivation of the power law model of two terms, commonly used for the interpretation of fatigue data of composite and metallic materials. these models are of direct application and not based on any assumptions, even in limited databases. the estimation of the model parameters is based on the linear regression analysis that can be performed by simple calculations [17]. the generalized power law is given by eqn. 1:  maxlog( ) log c a b n   (1) where 𝜎 is the maximum stress amplitude parameter, n is the number of cycles until the material failure, whereas 𝐴, 𝐵, and 𝐶 are the parameters of the fatigue model derived by linear regression analysis, resulting from the adjustment of the equation to the experimental data. the constant 𝐶 is an adjustment exponent that can smooth the s-n curve in the lowcycle fatigue region. the s-n curve proposed by astm e739 standard1 [1] is widely used by researchers for their reliable and simple modelling process. this model does not recommend an extrapolation outside the experimental data region. the representation of the model can be done by linearized form (log-log) given by eq. 2:    maxlog logn a b   (2) the equations of the power law and astm e739 standard have similar structures for estimating the parameters of the curve in the linearized model (log-log); however, these models have two relevant differences. the first difference presented by astm e739 standard when compared with the power law is to consider fatigue stress as a dependent variable, while the power law considers the fatigue stress an independent variable (the number of cycles to failure, 𝑁 , is assumed as dependent variable). the second difference is the presence of a constant c, included in power law, able to smooth the fit in the lowcycle fatigue region. logistic function the logistic s-n curve model, developed by mu [16], uses a logistic function to describe fatigue life behavior of composite materials, since this function is very similar to the s shape, commonly observed in s-n curves (lin-log). the logistic function is adapted to model the s-n curve and is given by eqn. 3:    log 1 1 n b n c c a ae        (3) where a, b and c are the material constants, obtained by nonlinear least squares, 𝜎 is the normalized stress amplitude n = max/ult and n is the number of cycles until failure. ul is the ultimate tensile strength. kohout-věchet model the full-amplitude s-n curve, based on the stress-damping parameter proposed by kohout and věchet, has been increasingly used in assessing the fatigue life of existing bridge structures [18]. the kohout and věchet s-n curve is a model based on geometric technical adjustment of fatigue behavior, based on stress or other damage linked parameter, that can t j. f. barbosa et alii, frattura ed integrità strutturale, 48 (2019) 400-410; doi: 10.3221/igf-esis.48.38 403 achieve a good fit to the experimental data. the kohout-věchet fatigue model (kv) can estimate the behavior of the material in low-cycle (lcf) and high-cycle (hcf) regions [6], being able to cover the estimate from the ultimate tensile strength to the permanent fatigue limit. this kv model can be expressed by the following eqn. 4:   max b n b c a n c        (4) where a and b are the similar to basquin parameters, b is the number of cycles corresponding to the intersection of the tangent line of the finite life region and the horizontal asymptote of the total tensile strength, and c is the number of cycles corresponding to the intersection of the tangent line of the region of the finite life and the horizontal asymptote of the fatigue limit. the details for obtaining the parameters can be obtained in ref. [6]. normalized stress ranges the normalized stress ranges were suggested by taras and greiner [19] with aims to take into account the mean stress effects. the research work was developed for fatigue experimental results of riveted joints. this approach can be applied for fatigue results from metallic bridge materials to allow the comparison of experimental fatigue data from distinct mean stresses. the normalized stress ranges can be determined by  norm f r      (5) where, ∆σnorm is the normalized stress range, ∆σ is the tested stress range, and f(r) is a normalization function to account for stress ratio effects, defined as a function of the material. for wrought/puddle iron and mild steel manufactured before 1900, f(r) is defined as:     1   1 0 1 0.7 1   0 1 0.75 r f r r r r f r r r                (6) for mild steel after 1900, the normalization function to be used is the following:     1   1 0 1 0.4 1   0 1 0.6 r f r r r r f r r r                (7) however, the proposed normalization functions are only valid for high-cycle fatigue regimes, hence, they are not valid for lowand medium-cycle fatigue regimes. in this sense, fatigue design curves based on goodman [20], soderberg [21] and gerber [22] diagrams become highly important for the fatigue life evaluation of old metallic bridges using local approaches. comparison of the modeling ability of the s–n curve formulations comparison of the modelling performance of the s-n curves was made using the fatigue data of the materials from the ancient portuguese riveted steel bridges (eiffel, luiz i, fão and trezói bridges). the performance of the mean fatigue curves was based on two methodologies of analysis. the first analysis the adjustment of the s-n curve is based on direct graphical observation, where the degree of adjustment in the lcf and hcf regions is empirically assessed. the second analysis, quantitative, estimates the quality of the curve adjustment to the experimental fatigue data by means of the mean square errors (mse). this parameter was calculated for each fatigue model by defining the error as the difference between the logarithms of the experimental and estimated values for the cyclic stresses, based on the following equation: a j. f. barbosa et alii, frattura ed integrità strutturale, 48 (2019) 400-410; doi: 10.3221/igf-esis.48.38 404      2 exp 1 1 log log n est i mse n      (8) where 𝜎 and 𝜎 are the experimental cyclic stress and the estimated cyclic stress levels of the s-n curves, respectively, for all models considered in this research. the stress levels correspond to the same number of cycles, n, of the experimental data. therefore the comparison between fatigue models was evaluated qualitatively and quantitatively. acquisition of each model was examined for its accuracy in modeling, ability to extrapolate and interpolate, number of model parameters, sensitivity to available experimental data, etc. the mse normalized calculation related with the adjustment of the presented s-n models to the experimental fatigue data, can be observed in tab. 1. to facilitate the comparison between the s-n curve models, the results of the mse values presented in tab. 1 are normalized using the following expression norm maxmse mse / mse (9) where msemax is the largest mse (equation 8) between the logistic, kohout-věchet, power law and astm e739 models when compared by the bridge model. material normalized mean squared error (mse) logistic kohout-věchet power law astm n eiffel (r=0)* 0.4946 0.4943 0.5138 1 16 eiffel (r=-1)** 0.6246 0.6741 0.6214 1 27 luiz i (r=-1)** 0.4312 0.6450 0.4343 1 16 fão (r=0)** 0.8618 0.9776 0.8341 1 21 fão (r=-1)** 0.5268 0.4400 0.5705 1 14 trezói (r=-1)** 0.5823 1.0000 0.3960 0.8455 10 all bridges(r=-1)*** 0.6682 0.7312 0.6788 1 66 * fatigue tests under stress-controlled conditions; ** fatigue tests under strain-controlled conditions; *** only bridges r=-1. table 1: normalized calculation of the mean squared error of the derived s-n curves. the obtained s-n curve based on astm e739 standard did not present a satisfactory performance when compared with the other models, such as, logistic formulation, kohout-věchet model and power law. the fatigue model proposed by generalized power law obtained a smaller error in four of the seven fatigue data of the analyzed bridge materials, resulting in a better approximation of the s-n curve to the experimental data set. this method obtained the best estimate considering the mse value computed for the material from the trezoi bridge (see table 1). the logistic model that uses only three parameters in the equation obtained a lower mse value when all the experimental fatigue data are analyzed together, considering only the data of the fatigue tests under strain-controlled conditions at r=-1. in the individual analysis of each bridge material it can be observed that the performance of the model was very similar to that of generalized power law model. for a set of fatigue experimental data with few data, it is possible to observe that some equations can’t obtain such precise estimates. this situation is verified for the material from the trezói bridge at r=-1 (fatigue test under straincontrolled conditions) with a sample of 10 specimens, where the kohout-věchet model obtained a very high mse value when compared to logistic formulation and power law. in general, the s-n curve using the logistic formulation obtained satisfactory performance in terms of mse values for all samples with size lower than 16. in the low-cycle fatigue region (lcf), logistic, khout-věchet and power law curves achieved better adjustments than the astm standard. this can be seen in fig. 1 related with the material from the eiffel bridge at r=0 (fatigue test under stresscontrolled conditions), where these models are able to flatten and smoothen the inflection of the s-n curve in this region. j. f. barbosa et alii, frattura ed integrità strutturale, 48 (2019) 400-410; doi: 10.3221/igf-esis.48.38 405 for the materials from the eiffel (figs. 1 and 2) and luiz i bridges (fig. 3), it is possible to verify the robustness of adjustment of these formulations in the lcf region; in some cases the s-n curve becomes very close to the experimental values. the improvement of the s-n curve in the low cycle region for logistic, power law and kohout-věchet models is justified by the exponent of these equations, responsible for smoothing the rate of degradation in this region and the transition of elasto-plastic behavior. figure 1: comparison of the s-n curves for the fatigue data of the metallic material from the eiffel bridge, r=0 (fatigue tests under stress-controlled conditions). figure 2: comparison of the s-n curves for the fatigue data of the metallic material from the eiffel bridge, r=-1 (fatigue tests under strain-controlled conditions). fig. 2 presents the fatigue data of the material from the eiffel bridge tested at r = -1 (fatigue test under strain-controlled conditions), where it can be seen that the s-n curve based on astm e739 standard does not achieve a good approximation in the low-cycle fatigue region (lcf), even with data availability for the region smaller than 103 cycles. in this region, the logistic and power law curves performed slightly better than the kohout-věchet model. in the high-cycle fatigue region 103 104 105 106 107 108 200 400 600 800 m a x . s tr e s s [ m p a ] n(number of cycles) logistic kohout-vechet power law astm e739 exp. data eiffel r=0 101 102 103 104 105 106 107 108 100 150 200 250 300 350 400 450 m a x . s tr e s s [ m p a ] n(number of cycles) logistic kohout-vechet power law astm e739 exp. data eiffel r=-1 j. f. barbosa et alii, frattura ed integrità strutturale, 48 (2019) 400-410; doi: 10.3221/igf-esis.48.38 406 (hcf) the generalized power law curve presented a very pronounced degradation rate. the kohout-věchet model presented a coherent behaviour in the hcf region and are recommended to better indicate the fatigue limit of the material. regarding the metallic material from luiz bridge tested at r=-1 (fatigue test under strain-controlled conditions), which can be seen in fig. 3, the fatigue curves for the power law and logistic model obtained very similar performance. the differences between them becoming more evident only in number of cycles higher than 106. in the low-cycle fatigue region, for the power law, logistic and kohout-věchet curves a very similar adjustment is observed. a poor performance of the s-n curve obtained from the kohout-vechet model for numbers of cycles to failure between 105 and 106 is verified, improving estimates to values above 106. by analyzing the adjustement of the curve of the astm standard to the experimental data in the lcf region, it is verified an increasing distances between the experimental data and predictions, and consequently increasing the mse value, making this model with the largest mean square error. figure 3: comparison of the s-n curves for the fatigue data of the metallic material from the luiz i bridge, r=-1 (fatigue test under strain-controlled conditions). figure 4: comparison of the s-n curves for the fatigue data of the metallic material from the trezói bridge, r=-1 (fatigue test under strain-controlled conditions). the available fatigue data from the material from the trezoi bridge consists on only 10 experimental points. therefore, the conclusions to be obtained for the lcf and hcf regions are limited. fig. 4 shows a marked difference in the fit of the analyzed s-n curves in the hcf region. the power law formulation obtained the lowest mse (tab. 1) followed by the logistic model. these models achieved a good agreement with the experimental fatigue data above 106 cycles. the astm standard and kohout-věchet methods did not provided good estimates in the hcf region. however, it is not possible to 101 102 103 104 105 106 107 108 100 150 200 250 300 350 400 450 500 m a x . s tr e s s [ m p a ] n(number cycles) logistic kohout-vechet power law astm e739 exp. data luiz r=-1 102 103 104 105 106 100 200 300 400 500 m a x . s tr e s s [ m p a ] n(number of cycles) logistic kohout-vechet power law astm e739 exp. data trezoi r=-1 j. f. barbosa et alii, frattura ed integrità strutturale, 48 (2019) 400-410; doi: 10.3221/igf-esis.48.38 407 assert that the logistic and power law formulations better describe the fatigue life behavior, due to the lack of data mainly in the high-cycle fatigue region. for a more complete analysis of this material, it is necessary to perform further experimental fatigue tests in stress levels between 400 mpa and 300 mpa. regarding the fatigue data from the material of fão bridge, two strain ratios, r, were explored, namely r=0 and r=-1 (fatigue test under strain-controlled conditions). the s-n kohout-věchet formulation and power law resulted in the lowest mse values and very close to each other. the only perceptible difference in a qualitative analysis of the s-n curves at fatigue strain ratio equal to 0, is in the hcf region, where the possible extrapolation to the permanent fatigue limit of the logistic s-n curve would present a more adequate behaviour (fig. 5). figure 5: comparison of the s-n curves for the fatigue data of the metallic material from the fão bridge, r=0 (fatigue test under strain-controlled conditions). figure 6: comparison of the s-n curves for the fatigue data of the metallic material from the fão bridge, r=-1 (fatigue test under strain-controlled conditions). in fig. 6, regarding the fatigue data of the fão bridge at r=-1, the estimation in the lcf region of the power law, logistic and kohout-věchet curves obtained similar and well-adjusted results, while in the hcf region the curve of kohout-věchet obtained better performance and consistent with fatigue limit. based on figs. 5 and 6, it is possible to report that the kohout-věchet curve presents better performance in the hcf region justified by high mse values. one the other hand, the adjustment results based on the astm standard leads to an adjustment not consistent with the experimental results and when compared with the other models. 101 102 103 104 105 106 107 108 100 200 300 400 500 600 m a x . s tr e s s [ m p a ] n(number of cycles) logistic kohout-vechet power law astm e739 exp. data fão r=0 102 103 104 105 106 107 0 100 200 300 400 500 m a x . s tr e s s [ m p a ] n(number of cycles) logistic kohout-vechet power law astm e739 exp. data fão r=-1 j. f. barbosa et alii, frattura ed integrità strutturale, 48 (2019) 400-410; doi: 10.3221/igf-esis.48.38 408 figure 7: comparison of the s-n curves for the fatigue data at r=-1 (strain ratio) of the metallic materials from the all bridges. fig. 7 presents a comparison between the s-n curves generated based on different fatigue formulations, such as astm standard, power law, logistic and kohout-věchet models, for the fatigue data at r=-1 (under strain-controlled conditions) of the metallic materials from the several bridges under consideration in this research. a single s-n curve was estimated for each studied method considering a total of 66 experimental data available. these old metallic materials were extracted from members of the ancient metallic bridges of the 19th century, so this research sought to propose the method that is best suited to these materials. this analysis aims to consolidate what has already been observed in previous cases. the astm standard does not provide a good approximation in the low-cycle region even though experimental data are available in this region. the power law, logistic and kohout-věchet s-n models obtained good adjustments to the low-cycle region when compated with the experimental data, as shown in fig. 7. for the hcf region the logistic, astm and power law methods presented a similar performance, however, only the kohout-věchet model didn’t obtain a good agreement to the fatigue data in the region above 106 cycles. in general the logistic and power law method obtained the best fit according to the mse estimation, however it is not conclusively due to the lack of data in regions above 106 cycles. conclusions he formulations of the s-n curves, using logistic method, kohout-věchet model, power law and astm e739 standard, applied to the metallic materials of old bridges, obtained different performances mainly in the lcf and hcf regions. the astm standard does not perform well in estimating fatigue life in the low-cycle region. all analyzed graphs showed discrepant values of maximum stresses corresponding to the lcf region. even following the recommendations of the astm e739 standard, of not extrapolating analysis beyond the experimental data, it is perceptible the difficulty of the method in approaching the lcf fatigue data. in the low-cycle region, the logistic, kohout-věchet and power law methods presented satisfactory performance when compared with experimental data, however it is not possible to say which one has the best fit. a greater amount of experimental fatigue data would be needed in the lcf region to complete such analysis. in the high-cycle region, there is also a lack of experimental data, but assuming that the extrapolation of this region is expected to follow the permanent fatigue limit, it can be concluded that the kohut-vechet method presented better performance. the s-n curves of this model are distant from experimental fatigue data in regions above 105 cycles. the generalized simple power law model can yield good approximations in the low-cycle region and in some cases in the region above 105 cycles. the s-n logistic curve formulation, which was initially applied only to composite materials, obtained an interesting performance when applied to the metallic materials of old bridges. in terms of mse, this model obtained similar performance to the results of the kohout-věchet model, using only 3 parameters in the equation. both models presented a good agreement with little experimental data. the largest difference between these models is in hcf region. 101 102 103 104 105 106 107 108 0 200 400 600 m a x . s tr e s s [ m p a ] n(number of cycles) logistic kohout-vechet power law astm e739 exp. data all bridges t j. f. barbosa et alii, frattura ed integrità strutturale, 48 (2019) 400-410; doi: 10.3221/igf-esis.48.38 409 the logistic model allowed a better approximation to the experimental data in hcf region and a graphical analysis showed better results for a possible extrapolation of the analysis. the achieved results showed that the s-n curve formulation using the logistic and power law equations obtained a better performance in the lcf and hcf regions and lower mse values when compared to the generalized power law formulations and the astm e739 standard. it was also observed that the logistic, kohout-věchet and power law equations are able to obtain smaller errors for the cases with a reduced number of experimental data. however, in order to generalize which model has a better fit, it is necessary to carry out an exhaustive study with a greater amount of experimental data of fatigue of other metallic materials. acknowledgements his study was financed in part by the coordenação de aperfeiçoamento de pessoal de nível superior brasil (capes) finance code 001. the authors also acknowledge the portuguese science foundation (fct) for the financial support through the postdoctoral grant sfrh/bpd/107825/2015, as well as the funding of fiberbridge fatigue strengthening and assessment of railway metallic bridges using fiber-reinforced polymers (poci-01-0145-feder030103) by feder funds through compete2020 (poci) and by national funds (piddac) through portuguese science foundation (fct). references [1] astm committee and others. (2004). standard practices for statistical analysis of linear or linearized stress-life (sn) and strain-life (ε-n) fatigue data, astm int. west conshohocken, pa, usa. [2] iso, b.s. (2012). 12107: 2003, metallic materials--fatigue testing--statistical planning and analysis of data, int. organ. stand. [3] standard, e. (2003). eurocode 3 : design of steel structures, part 1.9, control, pp. 1–117. [4] bsi (british standards institution). (1980). steel, concrete and composite bridges. 10: code of practice for fatigue, eurocode 3, (1). [5] specifications, a.-l.b.d. (2004). american association of state highway and transportation officials (aashto), washington, dc. [6] kohout, j., vechet, s. (2001). a new function for fatigue curves characterization and its multiple merits, int. j. fatigue, 23(2), pp. 175–83. [7] weibull, w. (1961). fatigue testing and analysis of results: publ. for and on behalf of advisory group for aeronautical research and development, north atlantic treaty organisation, pergamon press. [8] chaminda, s.s., ohga, m., dissanayake, r., taniwaki, k. (2007). different approaches for remaining fatigue life estimation of critical members in railway bridges, steel struct., 7, pp. 263–76. [9] kajolli, r. (2013). a new approach for estimating fatigue life in offshore steel structures. university of stavanger, norway. [10] de jesus, a.m.p., pinto, h., fernández-canteli, a., castillo, e., correia, j.a.f.o. (2010). fatigue assessment of a riveted shear splice based on a probabilistic model, int. j. fatigue, 32(2), pp. 453–62, doi: 10.1016/j.ijfatigue.2009.09.004. [11] jesus, a.m.p. de., silva, a.l.l. da., figueiredo, m. v., correia, j.a.f.o., ribeiro, a.s., fernandes, a.a. (2011). strainlife and crack propagation fatigue data from several portuguese old metallic riveted bridges, eng. fail. anal., 18(1), pp. 148–63, doi: 10.1016/j.engfailanal.2010.08.016. [12] correia, j., apetre, n., arcari, a., de jesus, a., muñiz-calvente, m., calçada, r., berto, f., fernández-canteli, a. (2017). generalized probabilistic model allowing for various fatigue damage variables, int. j. fatigue, 100, pp. 187–194. [13] muniz-calvente, m., de jesus, a.m.., correia, j.a.f.o., fernández-canteli, a. (2017). a methodology for probabilistic prediction of fatigue crack initiation taking into account the scale effect, eng. fract. mech., 185, pp. 101–113, doi: 10.1016/j.engfracmech.2017.04.014. [14] kohout, j., vechet, s. (2008). some estimations of tolerance bands of sn curves, mater. sci., 14(3), pp. 202–205. [15] zapletal, j., věchet, s., kohout, j., obrtlík, k. (2008). fatigue lifetime of adi from ultimate tensile strength to permanent fatigue limit, strength mater., 40(1), pp. 32–35. [16] mu, p.g., wan, x.p., zhao, m.y. (2011). a new s-n curve model of fiber reinforced plastic composite, key eng. mater., 462–463, pp. 484–8, doi: 10.4028/www.scientific.net/kem.462-463.484. t j. f. barbosa et alii, frattura ed integrità strutturale, 48 (2019) 400-410; doi: 10.3221/igf-esis.48.38 410 [17] freire júnior, r.c.s., belísio, a.s. (2014). probabilistic s-n curves using exponential and power laws equations, compos. part b eng., 56, pp. 582–90, doi: 10.1016/j.compositesb.2013.08.036. [18] correia, j.a.f.o., raposo, p., muniz-calvente, m., blasón, s., lesiuk, g., de jesus, a.m.p., moreira, p.m.g.p., calçada, r.a.b., canteli, a.f. (2017). a generalization of the fatigue kohout-věchet model for several fatigue damage parameters, eng. fract. mech., 185, pp. 284–300, doi: 10.1016/j.engfracmech.2017.06.009. [19] taras, a., greine, r. (2010). development and application of a fatigue class catalogue for riveted bridge components, struct. eng. int. j. int. assoc. bridg. struct. eng., doi: 10.2749/101686610791555810. [20] john goodman. (1919). mechanics applied to engineering, longmans, green, and co. [21] soderberg, c.r. (1930). factor of safety and working stress, trans. am. soc. test matls, 52, pp. 146. [22] society of automotive engineers (1997). sae fatigue design handbook: ae-22. << /ascii85encodepages false /allowtransparency false /autopositionepsfiles true /autorotatepages /none /binding /left /calgrayprofile (dot gain 20%) /calrgbprofile (srgb iec61966-2.1) /calcmykprofile (u.s. web coated \050swop\051 v2) /srgbprofile (srgb iec61966-2.1) /cannotembedfontpolicy /error /compatibilitylevel 1.4 /compressobjects /tags /compresspages true /convertimagestoindexed true /passthroughjpegimages true /createjobticket false /defaultrenderingintent /default /detectblends true /detectcurves 0.0000 /colorconversionstrategy /cmyk /dothumbnails false /embedallfonts true /embedopentype false /parseiccprofilesincomments true /embedjoboptions true /dscreportinglevel 0 /emitdscwarnings false /endpage -1 /imagememory 1048576 /lockdistillerparams false /maxsubsetpct 100 /optimize true /opm 1 /parsedsccomments true /parsedsccommentsfordocinfo true /preservecopypage true /preservedicmykvalues true 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can be opened with acrobat and adobe reader 5.0 and later.) >> /namespace [ (adobe) (common) (1.0) ] /othernamespaces [ << /asreaderspreads false /cropimagestoframes true /errorcontrol /warnandcontinue /flattenerignorespreadoverrides false /includeguidesgrids false /includenonprinting false /includeslug false /namespace [ (adobe) (indesign) (4.0) ] /omitplacedbitmaps false /omitplacedeps false /omitplacedpdf false /simulateoverprint /legacy >> << /addbleedmarks false /addcolorbars false /addcropmarks false /addpageinfo false /addregmarks false /convertcolors /converttocmyk /destinationprofilename () /destinationprofileselector /documentcmyk /downsample16bitimages true /flattenerpreset << /presetselector /mediumresolution >> /formelements false /generatestructure false /includebookmarks false /includehyperlinks false /includeinteractive false /includelayers false /includeprofiles false /multimediahandling /useobjectsettings /namespace [ (adobe) (creativesuite) (2.0) ] /pdfxoutputintentprofileselector /documentcmyk /preserveediting true /untaggedcmykhandling /leaveuntagged /untaggedrgbhandling /usedocumentprofile /usedocumentbleed false >> ] >> setdistillerparams << /hwresolution [2400 2400] /pagesize [612.000 792.000] >> setpagedevice microsoft word numero 25 art 13 h. askes et alii, frattura ed integrità strutturale, 25 (2013) 87-93; doi: 10.3221/igf-esis.25.13 87 special issue: characterization of crack tip stress field gradient enriched linear-elastic crack tip stresses to estimate the static strength of cracked engineering ceramics harm askes, luca susmel department of civil and structural engineering, the university of sheffield, sheffield s1 3jd, united kingdom abstract. according to gradient mechanics (gm), stress fields have to be determined by directly incorporating into the stress analysis a length scale which that takes into account the material microstructural features. this peculiar modus operandi results in stress fields in the vicinity of sharp cracks which are no longer singular, even though the assessed material is assumed to obey a linear-elastic constitutive law. given both the geometry of the cracked component being assessed and the value of the material length scale, the magnitude of the corresponding gradient enriched linear-elastic crack tip stress is then finite and it can be calculated by taking full advantage of those computational methods specifically devised to numerically implement gradient elasticity. in the present investigation, it is first shown that gm’s length scale can directly be estimated from the material ultimate tensile strength and the plane strain fracture toughness through the critical distance value calculated according to the theory of critical distances. next, by post-processing a large number of experimental results taken from the literature and generated by testing cracked ceramics, it is shown that gradient enriched linearelastic crack tip stresses can successfully be used to model the transition from the shortto the long-crack regime under mode i static loading. keywords. length scale; gradient elasticity; theory of critical distances; static breakage; ceramics. introduction ertainly linear elastic fracture mechanics (lefm) as formalised by griffith, irwin and others represents a ground-breaking point of no return in the field of fracture and strength of engineering materials, this holding true not only from a scientific, but also from an industrial point of view. what we have achieved in sectors such as, for instance, transportation and energy production would have been impossible without the lefm based design theories. as to the accuracy and reliability of lefm, in 1964 irwin affirms [1]: “… linear elastic fracture mechanics already provides a rather complete set of mathematical tools. additional experimental observations rather than additional methods of analysis are now the primary need for practical applications”. examination of the state of the art suggests that, as far as brittle failures are concerned, the international scientific community has taken the above statement literally: over the last five decades a big effort has been made mainly to experimentally extend the use of the lefm concepts to different materials/loading conditions, rather than to develop new theoretical approaches, lefm being treated as a kind of untouchable “religion”. by challenging irwin’s belief, the present paper aims to show that gradient-enriched linear-elastic crack/notch tip stresses can directly be used to predict the detrimental effect of cracks on the overall static strength of engineering ceramics, the microstructural features of the assessed material being explicitly taken into account through the critical distance calculated according to the theory of critical distances (tcd). this has the potential to represent an important step forward in the way cracked/notched components are designed against static loading. c http://www.gruppofrattura.it http://dx.medra.org/10.3221/igf-esis.25.13&auth=true h. askes et alii, frattura ed integrità strutturale, 25 (2013) 87-93; doi: 10.3221/igf-esis.25.13 88 fundamentals of gradient elasticity ack in 1964, mindlin published the first paper [2] addressing in a systematic way gradient enriched elasticity, where a novel continuum theory containing a number of additional constitutive parameters was proposed. amongst the different attempts made so far to simplify the above approach by reducing the number of material parameters, certainly the model devised by aifantis and co-workers [3-5] deserves to be mentioned explicitly. in more detail, such a model postulates that the enriched stress-strain relationship can be extended with the laplacian of the strain as follows:  2 2c     (1) where  and  are the stresses and strains, respectively, c is a fourth-order tensor containing the elastic moduli, and l is a length scale parameter that represents the underlying microstructure. the most interesting feature of the above formulation of gradient elasticity is that it can efficiently be implemented numerically and then used, according to the procedure summarised below, to address problems of practical interest [6-8]. in particular, initially the following standard equation has to be solved: ku f (2) where k is the conventional linear elastic stiffness matrix, u is the vector containing the nodal displacements, and, finally, f is the vector summarising the externally applied nodal forces. once the displacements are obtained from eq. (2), they can be used to determine the gradient-enriched nodal stresses  from t t 2 tn nn sn s d n b d u                   (3) in the above relation, n is the matrix summarising the shape functions used to interpolate the stresses, b is the matrix containing the derivatives of the displacement shape functions, and, finally, s is the elastic compliance matrix. to conclude, it is worth recalling here that the most important implication of directly incorporating material length scale l into the stress analysis is that, even in the presence of cracks and sharp notches, the resulting stress fields are not singular in spite of the fact that the material being designed is forced to obey a linear-elastic constitutive law [9]. theory of critical distances and static assessment n the presence of cracks subjected to mode i static loading, the tcd postulates that fast fracture takes place when a critical distance based effective stress, eff, exceeds the material inherent strength, 0 [10], i.e.: eff 0   non-propagation of the crack (4) further, as far as the static assessment is concerned, independently from the ductility level of the material being design, the stress analysis can directly be performed by adopting a simple linear-elastic constitutive law [11-13], provided that the material inherent strength 0 is determined consistently [10-13]. the appropriate way of experimentally determining 0 will be reviewed below briefly. the above considerations should make it evident that designing cracked materials against static loading according to the tcd implies performing a bi-parametrical post-processing of the linear-elastic stress fields acting on the material in the vicinity of the crack tips, the critical distance and the inherent material strength being the two adopted design parameters. when specifically dealing with static failures, the tcd’s critical distance is recommended to be determined from: 2 ic 0 k1 l          (5) where kic is the lefm plane strain fracture toughness. the tcd’s effective stress, eff, can then be calculated according to either the point method, the line method, or the area method as follows [1, 14]: b i http://www.gruppofrattura.it http://dx.medra.org/10.3221/igf-esis.25.13&auth=true h. askes et alii, frattura ed integrità strutturale, 25 (2013) 87-93; doi: 10.3221/igf-esis.25.13 89 eff y l 0, r 2          point method (pm) (6)   2 l eff y 0 1 0, r dr 2l     line method (lm) (7)   l2 eff y2 0 0 4 , r drd l          area method (am) (8) the adopted symbols as well as the meaning of the effective stress determined according to definitions (6), (7), and (8) are explained in fig. 1. (a) (b) (c) (d) figure 1: definition of the local systems of coordinates (a) and effective stress, eff, calculated according to the point method (b), line method (c), and area method (d). eq. (4) to (8) clearly show that inherent material strength 0 plays a role of primary importance when the tcd is used to design cracked components against static loading. brittle materials are experimentally seen to have an inherent material strength which is always very close to the material ultimate tensile strength, uts [14-16]. on the contrary, when the fast fracture process zone is characterised by large scale plastic deformations, in general, 0 reaches a value which is somewhat larger than the plain material uts [10, 11, 13]. another important aspect which is worth highlighting here is that 0 adopts a value higher than uts also in those situations in which the breakage of the plain parent material occurs by different mechanisms (such as, for instance, by the propagation of pre-existing microstructural defects) [10]. the considerations reported above clearly suggest that the only way to accurately determine 0 is by testing notched specimens containing stress risers whose presence results in different stress distributions in the vicinity of the tested geometrical features [10-13]. to conclude, when the tcd is used to specifically design cracked engineering ceramics against static loading, the inherent material strength is seen to be equal to the material ultimate tensile strength [15]. this greatly simplifies the problem. according to this remark, in what fallows gm will be used to model the sensitivity of engineering ceramics loaded in mode i to both shortand long-cracks by taking 0 invariably equal to uts. linking the length scales of gm and the tcd y using the area method argument re-interpreted according to non-local mechanics, in two recent investigations [17, 18] we have proven that the length scale parameter, l, employed by gm to perform the stress analysis, eq. (1), can directly be related to critical distance l, eq. (5). since the reasoning resulting in the l vs. l relationship has b http://www.gruppofrattura.it http://dx.medra.org/10.3221/igf-esis.25.13&auth=true h. askes et alii, frattura ed integrità strutturale, 25 (2013) 87-93; doi: 10.3221/igf-esis.25.13 90 already been explained in great detail elsewhere [17, 18], in what follows just its fundamental steps are summarised briefly. in order to coherently link l to l, according to neuber’s structural volume concept [19], the initial hypothesis is formed that the process zone defining the overall strength of the investigated cracked material is circular in bi-dimensional situations and spherical in tri-dimensional bodies, its radius being equal to l [20]. given a generic material point having coordinates (x, y), nonlocal stresses nl at this point can directly be derived from the local stresses  determined at those points having coordinates (x+x,y+y) that are in the vicinity of the point at which the non-local stresses themselves are evaluated, i.e.:  nl 2 2 22 1 ( x, y ) h l x y ( x x, y y ) dy dx l              (9) in the above equation h is the heaviside function where h(s)=1 when s>0 and h(s)=0 otherwise, s being a generic variable. observing that factor l2 is used for normalisation reasons, the local stresses expanded in a taylor series at the material point having coordinates (x, y) take on the following value:  nl 2 2 22 1 h l x y x y dy dx l x y                          (10) by so doing, the stresses and their derivatives are evaluated at point (x, y) and, therefore, they can be taken out of the integral. if the terms in the integral are rewritten according to polar coordinates  and r, where x=r·cos and y=r·sin, the right-hand side of eq. (10) can be elaborated. for instance, the second derivative terms is found to be:   2 l2 2 2 2 2 2 2 2 21 1 1 2 2 82 2 2 2 2 0 0 1 1 h l x y x dy dx r cos r dr d l l x l x x                          (11) according to eq. (11), it easy to observe that all terms with odd powers of x or y cancel. after some straightforward algebra, one obtains: nl 2 21 8 l      (12) finally, by using the explicit-to-implicit transition as formalised by peerlings et al. [20], eq. (12) can be rearranged as follows: nl 2 2 nl1 8 l      (13) eq. (9), which is the starting point of the reasoning summarised above, represents a link between the am [10] and gradient elasticity as formalised by aifantis and co-workers [3-5], so that, if the terms of order l4 and higher are ignored, the the l vs. l relationship can explicitly be written as: 2 21 l 8   l 2 2  (14) gradient enriched tip stresses to estimate static strength of cracked ceramics n order to check the accuracy of gradient enriched tip stresses in estimating the static strength of cracked engineering ceramics under mode i static loading a number of experimental results were selected from the technical literature, the mechanical properties of the investigated materials being summarised in tab 1. such results were generated by testing cracked samples having different geometries which include: controlled surface flaws, surface scratches, large pores, and sharp notches. the selected experimental results are summarised in the normalised kitagawa-takashi diagram plotting the ratio between the nominal gross stress resulting in static breakage, th, and the material ultimate tensile strength, uts, against a normalised equivalent length calculated as f2a/l, where f is the lefm shape factor and a the crack length. the main advantage of the above schematisation is that experimental results generated by testing samples having shape factor different from unity can directly be compared to the case of a central crack in an infinite plate loaded in tension (for which f is invariably equal to 1). i http://www.gruppofrattura.it http://dx.medra.org/10.3221/igf-esis.25.13&auth=true h. askes et alii, frattura ed integrità strutturale, 25 (2013) 87-93; doi: 10.3221/igf-esis.25.13 91 material ref. uts kic l [mpa] [mpa·m1/2] [mm] sic [21] 620 3.7 0.011 si3n4 [21] 650 4.5 0.015 al2o3 [21] 200 3.1 0.076 sialon [21] 920 4.6 0.008 si3n4 [22] 1160 7.8 0.014 al2o3 [22] 290 4.5 0.077 si3n4 [23] 920 5.6 0.012 si3n4 [24] 915 5.0 0.010 si3n4 [25, 26] 880 5.0 0.010 si3n4 [27] 700 5.0 0.016 si3n4 [28] 700 5.0 0.016 si3n4 [29] 510 5.0 0.031 si3n4 [26] 340 5.0 0.069 al2o3 [25] 790 3.5 0.006 al2o3 [25] 610 3.5 0.010 al2o3 [30] 610 3.5 0.010 al2o3 [30] 390 3.5 0.026 al2o3 [31] 390 3.5 0.026 al2o3 [28] 210 3.5 0.088 table 1: mechanical properties of the investigated engineering ceramics. the curve plotted in the chart of fig. 2 summarises the predictions made through the gradient enriched crack tip stresses calculated according to gm, the l vs. l relationship being the one given by eq. (14). such estimates were obtained by solving gm fe models simulating a bi-dimensional rectangular plate with a central through-thickness crack and subjected to tensile loading. the considered gross widths ranged in the interval 0.25mm-64mm. the ratio between the semi-crack length, a, and the gross width was set constant and equal to 0.05. this resulted for the modelled cracked samples in a shape factor, f, invariably equal to unity. finally, the boundary conditions of the gradient-enrichment step were taken as zero neumann conditions throughout. 0.05 0.5 0.01 0.1 1 10 100  th / u t s f2·a/l sic si3n4 al2o3 sialon inherent strength lefm l=2√2 l gm figure 2: accuracy of gradient enriched tip stresses in estimating the transition from the shortto the long-crack regime under mode i static loading, the mechanical properties of the considered engineering ceramics being summarised in tab 1. the chart of fig. 2 clearly suggests that, as far as engineering ceramics are concerned, gradient-enriched crack tip stresses are successful in modelling the transition from the shortto the long-crack regime. in particular, the above diagram makes it evident that gm is capable of matching the inherent material strength in the very short-crack region by correctly modelling, at the same time, the long-crack behaviour as well. http://www.gruppofrattura.it http://dx.medra.org/10.3221/igf-esis.25.13&auth=true h. askes et alii, frattura ed integrità strutturale, 25 (2013) 87-93; doi: 10.3221/igf-esis.25.13 92 conclusions he validation exercise summarised in the present paper strongly supports the idea that gradient-enriched crack tip stresses can successfully be used to perform the static assessment of cracked components. the gm based design methodology proposed and validated in the present paper by post-processing a large number of experimental results generated by testing engineering ceramics has the potential to turn into an important step forward in developing alternative methods to model the detrimental effect of cracks and defects in engineering components and structures. in particular, since, according to gm’s modus operandi, gradient enriched stresses can directly be calculated at any material points (crack tips included), components containing both cracks and defects could directly be designed against static loading by following the same strategy as the one commonly adopted to perform, as suggested by continuum mechanics, the fatigue assessment of un-cracked bodies. references [1] irwin, g.r., structural aspects of brittle fracture, applied materials research, 3 (1964) 65-81. [2] mindlin, r.d., micro-structure in linear elasticity, arch. rat. mech. analysis, 16 (1964) 52–78. [3] aifantis, e.c., on the role of gradients in the localization of deformation and fracture, int. j. engng. sci., 30 (1992) 1279–1299. [4] altan, s.b., aifantis, e.c., on the structure of the mode iii crack-tip in gradient elasticity, scripta metall. mater., 26 (1992) 319–324. [5] ru, c.q., aifantis, e.c., a simple approach to solve boundary-value problems in gradient elasticity, acta mech., 101 (1993) 59–68. [6] askes, h., gutiérrez, m.a., implicit gradient elasticity, int. j. numer. meth. engng., 67 (2006) 400-416. [7] askes, h., morata i., aifantis e.c., finite element analysis with staggered gradient elasticity, comput. struct., 86 (2008) 1266-1279. [8] askes, h., gitman, i.m., non-singular stresses in gradient elasticity at bi-material interface with transverse crack, int. j. fract., 156 (2009) 217-222. [9] askes, h., aifantis, e.c., gradient elasticity in statics and dynamics: an overview of formulations, length scale identification procedures, finite element implementations and new results, int. j. solids struct., 48 (2011) 1962–1990. [10] taylor, d., the theory of critical distances: a new perspective in fracture mechanics, elsevier, oxford, uk (2007). [11] susmel, l., taylor, d., on the use of the theory of critical distances to predict static failures in ductile metallic materials containing different geometrical features, engng. fract. mech., 75 (2008) 4410-4421. [12] susmel, l., taylor, d., the theory of critical distances to estimate the static strength of notched samples of al6082 loaded in combined tension and torsion. part i: material cracking behaviour, engng. fract. mech., 77 (2010) 452–469. [13] susmel l., taylor d., the theory of critical distances to estimate the static strength of notched samples of al6082 loaded in combined tension and torsion. part ii: multiaxial static assessment, engng. fract. mech., 77 (2010) 470– 478. [14] whitney, j.m., nuismer, r.j., stress fracture criteria for laminated composites containing stress concentrations, j. composite mater., 8 (1974) 253-265. [15] taylor, d., predicting the fracture strength of ceramic materials using the theory of critical distances, engng. fract. mech., 71 (2004) 2407-2416. [16] susmel, l., taylor, d., the theory of critical distances to predict static strength of notched brittle components subjected to mixed-mode loading, eng frac mech, 75 3-4 (2008) 534-550. [17] susmel, l., askes, h., material length scales in fracture analysis: from gradient elasticity to the theory of critical distances, computational technology reviews, 6 (2012) 63-80. [18] susmel, l., askes, h., bennett, t., taylor, d., theory of critical distances vs. gradient mechanics in modelling the transition from the shortto long-crack regime at the fatigue limit, fatigue fract. engng. mater. struct., (2013) – in press. [19] neuber, h., theory of notch stresses. springer, berlin, (1958). [20] peerlings, r.h.j., de borst, r., brekelmans, w.a.m., de vree, j.h.v., gradient enhanced damage for quasi-brittle materials, int. j. numer. meth. engng., 39 (1996) 3391–3403. t http://www.gruppofrattura.it http://dx.medra.org/10.3221/igf-esis.25.13&auth=true h. askes et alii, frattura ed integrità strutturale, 25 (2013) 87-93; doi: 10.3221/igf-esis.25.13 93 [21] kimoto, h., usami, s., miyata, h. relationship between strength and flaw size in glass and polycrystalline ceramics. japan soc. mech. engng., 51 (1985) 2482–2488. [22] anw, k., kim, b.a., iwasa, m., ogura, n., process zone size failure criterion and probabilistic fracture assessment curves for ceramics, fatigue fract. engng mater. struct., 15 (2) (1992) 139-149. [23] taniguchi, y., kitazumi, j., yamada, t., bending stress analysis of ceramics based on the statistical theory of stress and fracture location, j. jap. soc. mater. sci., 38 (1988) 777-782. [24] nagase, y., hoshide, t., furuya, h., yamada, t., room and high temperature strengths for ring specimen of sintered silicon nitride, in: 33rd ann. meeting. society of materials science, japan, (1984) 150-152. [25] kirchner, h. p., gruver, r. m., sotter, w. a., characteristics of flaws at fracture origins and fracture stressflaw size relations in various ceramics, mater. sci. eng., 22 (1976) 147-156. [26] bourne, w.c., tressler, r.e., alteration of flaw sizes and kic of si3n4 ceramics by molten salt exposure, in: int. symp. frac. .mech. ceram., plenum, new york 3 (1978) 113-124. [27] kawai, m., abe, h., nakayama, j., the effect of surface roughness on the strength of silicon nitride, in: proc. int. symp. factors densification sinter. oxide nonoxide ceram., tokyo, (1978) 545-556. [28] kimoto, h., usami, s., miyata, h., flaw size dependence in fracture stress of glass and polycrystalline ceramics, japan soc. mech. eng., 841-852 (1984) 34-40. [29] takahashi, i., usami, s., nakakado, k., miyata, h., shida, s., effect of defect size and notch root radius on fracture strength of engineering ceramics, j. ceram. soc. japan, 93 (1985) 186-194. [30] katayama, y., matsuo, y., relationship between strength and defect size in alumina, in: 3rd symp. high temp. mater., ceramic soc. of japan, (1984) 34-38. [31] iseki, t., maruyama, t., hanafusa, k., suzuki, h., effect of surface roughness on the bending strength of graphite and alumina at high temperatures, j. ceram. soc. japan, 86 (1978) 547-552. http://www.gruppofrattura.it http://dx.medra.org/10.3221/igf-esis.25.13&auth=true microsoft word numero_41_art_22.docx j.m. vasco-olmo et alii, frattura ed integrità strutturale, 41 (2017) 157-165; doi: 10.3221/igf-esis.41.22 157 focused on crack tip fields experimental evaluation of ctod in constant amplitude fatigue crack growth from crack tip displacement fields j.m. vasco-olmo, f.a. díaz university of jaén, spain jvasco@ujaen.es fdiaz@ujaen.es f.v. antunes university of coimbra, portugal fernando.ventura@dem.uc.pt m.n. james university of plymouth, uk m.james@plymouth.ac.uk abstract. in the current work an experimental study of the crack tip opening displacement (ctod) is performed to evaluate the ability of this parameter to characterise fatigue crack growth. a methodology is developed to measure and to analyse the ctod from experimental data. the vertical displacements measured by implementing digital image correlation on growing fatigue cracks are used to measure the ctod. fatigue tests at r ratios of 0.1 and 0.6 were conducted on compact-tension specimens manufactured from commercially pure titanium. a sensitivity analysis was performed to explore the effect of the position selected behind the crack tip for the ctod measurement. the analysis of a full loading cycle allowed identifying the elastic and plastic components of the ctod. the plastic ctod was found to be directly related to the plastic deformation at the crack tip. moreover, a linear relationship between da/dn and the plastic ctod for both tests was observed. results show that the ctod can be used as a viable alternative to δk in characterising fatigue crack propagation because the parameter considers fatigue threshold and crack shielding in an intrinsic way. this work is intended to contribute to a better understanding of the different mechanisms driving fatigue crack growth and the address the outstanding controversy associated with plasticity-induced fatigue crack closure. keywords. crack tip opening displacement; fatigue crack growth; plastic deformation; dic. citation: vasco-olmo, j.m., díaz, f.a., antunes, f.v., james, m.n., experimental evaluation of ctod in constant amplitude fatigue crack growth from crack tip displacement fields, frattura ed integrità strutturale, 41 (2017) 157-165. received: 28.02.2017 accepted: 15.04.2017 published: 01.07.2017 copyright: © 2017 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. j.m. vasco-olmo et alii, frattura ed integrità strutturale, 41 (2017) 157-165; doi: 10.3221/igf-esis.41.22 158 introduction atigue crack growth has been traditionally characterised by the paris law [1], that relates the crack growth per cycle, da/dn to the stress intensity factor range, δk. however, there are several controversial issues and unanswered questions in this field. the procedures for analysing constant amplitude fatigue under small-scale yielding conditions are well established, although a number of uncertainties remain. variable amplitude loading, large-scale plasticity, and short cracks introduce additional complications that are not fully understood. in addition, in many materials, it is virtually impossible to characterise the fracture behaviour with lineal elastic fracture mechanics (lefm), and an alternative fracture mechanics model is required. elastic-plastic fracture mechanics (epfm) is applied to materials that exhibit nonlinear behaviour (i.e., plastic deformation). hence in the authors’ view, the linear elastic δk parameter should be replaced by nonlinear crack tip parameter since fatigue crack growth is governed by nonlinear processes at the crack tip. two elastic-plastic parameters have been proposed to be related with crack tip plastic deformation, the crack tip opening displacement (ctod) and the j contour integral. both parameters describe crack tip conditions in elastic-plastic materials, and they can be used as a fracture criterion. ctod is a local parameter, while the j integral is used as a global criterion based on the quasi-strain energy release rate. critical values of ctod or j give nearly size-independent measurements of fracture toughness, even for relatively large amounts of crack tip plasticity. there are limits to the applicability of these parameters but they are much less restrictive than the validity requirements of lefm. in this work, ctod is the parameter used to characterise fatigue crack growth. ctod was first observed by wells [2] when he was attempting to measure kic values in a number of structural steel. wells found that these materials were too tough to be characterised by lefm. while examining fractured test specimens, wells noticed that the crack faces had moved apart prior to fracture; plastic deformation had blunted an initially sharp crack, resulting in a finite displacement at the crack tip. the degree of crack blunting increased in proportion to the toughness of the material. this observation led wells to propose the opening at the crack tip as a measurement of fracture toughness. nowadays, ctod is a classical parameter in elastic-plastic fracture mechanics and it has a high importance for fatigue analysis. crack tip blunting at maximum load and the crack tip re-sharpening at minimum load were used to explain fatigue crack growth [3]. ctod has been experimentally measured using extensometers located remotely to the crack tip. thus, in compact tension (ct) specimens an extensometer with blades is located at the mouth of the specimen notch to measure the opening of the specimen [4]. in the case of middle tension (mt) specimens a pin extensometer is placed at the centre of the specimen by fixing it into two small holes [5]. recently, full field optical techniques have become very popular for the analysis of structural integrity problems. among them digital image correlation (dic) technique can be considered because the displacement fields at the vicinity of the crack tip can be measured with high level of accuracy [6]. thus, in this work dic is implemented to measure the ctod from the relative displacement between both crack flanks. moreover, a finite element analysis has also been employed to measure the ctod numerically. the displacement at the first node behind the crack tip is generally used as an operational ctod [7]. figure 1: (a) dimensions (mm) of the ct specimen tested. (b) experimental set-up used to measure dic data during fatigue testing. in previous work, antunes et al. [8] developed a numerical study to quantify the ctod in a mt specimen for two aluminium alloys in order to analyse the applicability of this parameter to characterise fatigue crack growth. a relationship was found between da/dn and the plastic ctod range for the 6082-t6 aluminium alloy independent of stress ratio, showing that the ctod can be a viable alternative to δk in the analysis of fatigue crack propagation. thus, in the current f (b) (a) j.m. vasco-olmo et alii, frattura ed integrità strutturale, 41 (2017) 157-165; doi: 10.3221/igf-esis.41.22 159 work an experimental study of the ctod is performed by implementing the procedure developed by antunes et al. [8] to evaluate the ability of this parameter to characterise fatigue crack growth. note that the values of δctodp reported in [8] are relatively small, lower than 1 μm, which is certainly a challenge for the experimental determination of plastic ctod since some controversy exists about if dic is able to provide extremely high spatial resolution characterisation of crack tip deformation fields, including crack opening profiles [9]. the vertical displacements measured by dic on growing fatigue cracks are used to measure the ctod as the relative displacement existing between the crack flanks. two fatigue tests at stress ratios of 0.1 and 0.6 were conducted on titanium ct specimens. from the analysis of a full loading cycle, the elastic and plastic ctod could be identified. a linear relationship between da/dn and the plastic ctod was found for both tests, showing therefore that the ctod can be used as a viable alternative in characterising fatigue crack growth. with this work, the authors intend to contribute to a better understanding of the different mechanisms driving fatigue crack propagation and to address the outstanding controversy associated with plasticity-induced fatigue crack closure. experimental work or the experimental analysis of the ctod, two commercially pure titanium ct specimens (fig. 1a) with a thickness of 1 mm were tested at constant amplitude fatigue loading. fatigue tests were conducted at two different stress ratios (0.1 and 0.6) applying 750 n as maximum load level. for the correct implementation of dic, one of the faces of the specimens was prepared by spraying a black speckle over a white background. in addition, the other face of the specimens was polished to assist in tracking the crack tip. fatigue tests were conducted on an electropuls e3000 electromechanical testing machine at a frequency of 10 hz (fig. 1b). a ccd camera fitted with a macro zoom lens to increase the spatial resolution at the region around the crack tip was placed perpendicular to each face of the specimen. during fatigue tests, the loading cycle was periodically paused to allow the acquisition of a sequence of images at uniform increments through a complete loading and unloading cycle. the ccd camera viewing the speckled face of the specimen was set up so that the field of view was 17.3 x 13 mm (resolution of 13.5 μm/pixel) with the crack path located at the centre of the image. illumination of the surface was provided by a fibre optic ring placed around the zoom lens (shown in fig. 1b). experimental methodology n this section, the methodology developed to measure the ctod from experimental data is described. ctod is a parameter that measures the opening at the crack tip. therefore, the vertical displacements obtained from experiments can be used for its measurement. in this work, dic is used to measure the crack tip displacement fields. thus, ctod is explored by analysing the vertical displacements. an example of horizontal and vertical displacement maps measured with dic are shown in fig. 2, corresponding to a crack length of 9.40 mm and a load level of 750 n. figure 2: horizontal (a) and vertical (b) displacement fields measured with dic for a crack length of 9.40 mm at a load level of 750 n. x (pixels) y ( p ix el s) mm 200 400 600 800 1000 1200 100 200 300 400 500 600 700 800 900 -0.05 -0.04 -0.03 -0.02 -0.01 0 0.01 0.02 x (pixels) y ( p ix el s) mm 200 400 600 800 1000 1200 100 200 300 400 500 600 700 800 900 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2 f i (a) (b) j.m. vasco-olmo et alii, frattura ed integrità strutturale, 41 (2017) 157-165; doi: 10.3221/igf-esis.41.22 160 ctod is obtained by measuring the relative displacement between the crack flanks selecting a pair of points behind the crack tip. therefore, a relevant factor is the crack tip location. first, the y-coordinate of the crack tip is determined by plotting perpendicular profiles to the crack direction employing the vertical displacement map since a change in the displacement values is observed when the profiles go through the crack wake. fig. 3a shows as the different plotted profiles around the crack tip intersect in one point which indicates the location of the crack tip in the y-direction. the corresponding displacement value for this point is used to determine the x-coordinate of the crack tip. once the ycoordinate of the crack tip is known, a parallel profile to the crack direction corresponding to the y-coordinate previously obtained is plotted. the x-coordinate of the crack tip is obtained from the point of the profile which presents the same displacement value than that previously known from the y-coordinate. thus, a horizontal profile corresponding to this displacement value is plotted, establishing the x-coordinate as the intersection point between both lines as shown in fig. 3b. according to this procedure, the crack tip was located at the point with coordinates x = 470 pixels and y = 468 pixels (x = 6.49 mm and y = 6.41 mm), being the coordinates origin the upper left corner of the image. figure 3: methodology for locating the crack tip: (a) y-coordinate and (b) x-coordinate. once the location of the crack tip has been established, the experimental ctod is obtained by defining the measurement point behind the crack tip. thus, ctod as a function of load for a complete loading cycle is evaluated by analysing both the loading and unloading branches. in this way, the portion of the cycle at which the crack is closed and open can be (a) (b) j.m. vasco-olmo et alii, frattura ed integrità strutturale, 41 (2017) 157-165; doi: 10.3221/igf-esis.41.22 161 evaluated. in addition, from the analysis of the portion at which the crack is open, the elastic and plastic components of the ctod can be estimated from the slope variation observed in the ctod versus load curves. effect of the position behind the crack tip n this section a sensitivity analysis is performed to explore the effect of the position selected behind the crack tip for measuring the ctod. two parameters are related with the selection of the pairs of points behind the crack tip, the directions along and perpendicular to the crack. as fig. 4 shows, the direction along the crack is referenced as l1, while l2 is used for the perpendicular direction. figure 4: magnification of the region around the crack tip showing a pair or points behind the crack tip employed for the ctod measurement. this analysis is made by measuring the ctod at the maximum load as a function of one of the parameters, maintaining constant the other parameter. in fig. 5a ctod for different l2 distances has been plotted as a function of l1 distance. it can be observed that ctod is higher as the measurement points are moving away the crack tip. this increase in the ctod values along the crack is bigger as the measurement points are located at longer l2 distances. moreover, it is observed that for a same l1 value, ctod is gradually increasing until reaching a stable value from a value of l2 = 136.9 μm (10 pixels). this last observation can be more easily analysable if ctod for different l1 locations along the crack is represented as a function of the perpendicular distance l2 to the crack direction. thus, in fig. 5b is clearly observed as, for a same l1 location, ctod gradually increases until reaching a stable value at the l2 distance indicated above. figure 5: graphs showing the effect of the location of the measurement point. (a) ctod as a function of the distance along the crack direction l1; (b) ctod as a function of the distance at the perpendicular direction l2 to the crack. x (pixels) y ( p ix el s) mm 200 400 600 800 1000 1200 100 200 300 400 500 600 700 800 900 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2 l1l2 l2 l1l2 l2 i (a) (b) j.m. vasco-olmo et alii, frattura ed integrità strutturale, 41 (2017) 157-165; doi: 10.3221/igf-esis.41.22 162 according to this analysis, it can be established that the ctod value depends significantly of the location of the pair or points selected behind the crack tip along the crack direction. however, the effect of the perpendicular distance to the crack direction is not so restrictive since it has been observed that from 10 pixels (136.9 μm) a stable value of ctod is obtained. this established conclusion is validated by plotting the ctod versus load curves along a full loading cycle for different l1 and l2 values. fig. 6a shows different plots of ctod versus load along a full loading cycle for different l1 values using a value of 10 pixels (136.8 μm) for l2. in a similar way, fig. 6b shows different plots of ctod versus load for different l2 values employing a value of 5 pixels (for l1). the ctod values are higher as the distances l1 and l2 increase. in addition, the wide of the loops defined by the elastic portions of the loading and unloading branches increases with l1 and l2, being more clearly observable in the case of a l2 increase (fig. 6b). in addition, in fig. 6b it is observed that the wide of the loops is practically inappreciable for l2 values of 10 and 15 pixels (136.8 and 205.3 μm). figure 6: plots of ctod versus load along a full loading cycle: (a) for different l1 values employing a value of 10 pixels (136.8 μm) for l2 and (b) for different l2 values employing a value for l1 of 5 pixels (68.4 μm). thus, l2 distance used to measure the ctod will be 10 pixels (136.8 μm). however, the selection of the l1 distance is not so clear. all results shown forwards are obtained using a l1 distance of 5 pixels (68.4 μm). experimental results nce the effect of the measurement point location has been studied, ctod along a full loading cycle is measured. fig. 7 shows a typical plot of ctod versus load for the same crack length above analysed (a = 9.40 mm), where the separation existing between every data-point corresponds with a load level of 25 n. from the analysis of the loading and unloading branches, different portions can be identified. crack remains closed between points a and b. this portion presents a slight slope since dic detects very small displacements due to the sensitivity of the technique. in addition, other aspect that must be added is that crack closure is a gradual process at which crack does not change suddenly from fully closed to fully open (as can be observed numerically), and therefore it can be detected experimentally. from point b there is a slope change in the trend followed by the data-points, increasing linearly until reaching point c. from point c there is a change in the linearity until reaching the maximum applied load which is attributed to the plastic deformation. both elastic and plastic components of ctod can be estimated by extrapolating the linear regime to the maximum load. during unloading, there is a linear decrease between points d and e with the same slope than that obtained for the elastic regime in the loading branch. then, again there is a change in the linearity due to reversed plastic deformation, where the crack closes again. the same procedure indicated for the loading branch can be used to estimate the elastic and plastic components of ctod. in fig. 7 it is shown how the range for each component of the ctod is obtained. thus, during loading the elastic and plastic ranges of the ctod obtained were 10.23 μm and 4.71 μm, respectively. on the other hand, during unloading the values for the ranges of the elastic and plastic components were 10.42 μm and 4.52 μm, respectively. the values for the plastic component correspond to a percentage regarding to the total ctod of 31.5 % and 30.3 % for the loading and unloading branches, respectively. o (a) (b) j.m. vasco-olmo et alii, frattura ed integrità strutturale, 41 (2017) 157-165; doi: 10.3221/igf-esis.41.22 163 figure 7: plot of ctod along a full loading cycle indicating its elastic and plastic components at a crack length of 9.40 mm using a l1 value of 5 pixels and a l2 value of 10 pixels. then, the above methodology to obtain the ctod range for the elastic and plastic components is applied along the crack length. fig. 8a shows the elastic and plastic ctod ranges as a function of the crack length. a scatter is observed for the elastic component values, while the values for the plastic component show a gradual increase with the crack length. this last shows that the plastic component of the ctod can be linked to the plastic deformation generated along the crack propagation. it is interesting to note that a very similar trend for the plastic component values has been obtained independent to the stress ratio. it can be due to the fact that the same maximum load value was used to conduct both tests. moreover, in order to remove the scatter obtained for the elastic component, the percentage represented for each component with respect to the total ctod has been plotted in fig. 8b. a realignment is clearly observed for the elastic ctod values, decreasing gradually with the crack length. this is an expected result since it is an opposite behaviour to that shown by the plastic component. figure 8: (a) elastic and plastic ctod ranges as a function of the crack length for both tests. (b) percentage of the elastic and plastic ctod ranges along the crack length for both tests. according to the above results, only the plastic component of the ctod is relevant to characterise fatigue crack growth. fig. 9 shows the da/dn versus δctodp curves obtained for both tests. a different linear relationship has been obtained for each test, being the slope corresponding to the test conducted at low stress ratio higher. this is a logical result since (a) (b) j.m. vasco-olmo et alii, frattura ed integrità strutturale, 41 (2017) 157-165; doi: 10.3221/igf-esis.41.22 164 fatigue crack growth rate in the specimen tested at low r-ratio was bigger. results show that the plastic component of ctod can be directly related to the plastic deformation at the crack tip during crack propagation. therefore, ctod can be used to characterise fatigue crack growth since this parameter considers fatigue threshold and crack shielding in an intrinsic way. figure 9: crack growth per cycle (da/dn) versus plastic ctod range (δctodp) for both tests. in the current work it has been observed that plastic ctod depends on the maximum applied load in the fatigue cycle, independently of the stress ratio. therefore, as future work could be to conduct a test at high stress ratio with the same fatigue loading range than that defined in the test at low r-ratio in order to check if a linear relationship with similar slope is obtained. in this way, an only expression would be achieved that would allow to characterise fatigue crack propagation for the analysed material independent of the stress ratio as it was concluded by antunes et al. [8] in their numerical study. conclusions n experimental evaluation of the ctod has been performed to analyse the ability of this parameter to characterise fatigue crack growth. ctod has been measured from the vertical displacements obtained on growing fatigue cracks by implementing dic, demonstrating that this optical technique is able to provide extremely high spatial resolution characterisation of crack tip fields. two titanium ct specimens were tested at different stress ratios (0.6 and 0.1). from a sensitivity analysis it has been established that the ctod value depends significantly from the location along the crack direction of the pair of points selected behind the crack tip. however, the effect of the perpendicular distance to the crack direction is not so restrictive. elastic and plastic components of the ctod were identified from the analysis of a full loading cycle. the plastic ctod was found to be directly related to the plastic deformation at the crack tip. a different linear relationship between crack growth per cycle and the plastic ctod range was obtained for each test, where a higher slope was obtained for the test at low r-ratio. results show that the ctod can be used as a viable alternative to stress intensity factor range in characterising fatigue crack growth because ctod considers fatigue threshold and crack shielding in an intrinsic way. the authors have intended to contribute to a better understanding of the different mechanisms driving fatigue crack propagation and to address the outstanding controversy associated with plasticity-induced fatigue crack closure. further work must be made to understand the effect of stress ratio when the applied loading cycle is the same. a j.m. vasco-olmo et alii, frattura ed integrità strutturale, 41 (2017) 157-165; doi: 10.3221/igf-esis.41.22 165 acknowledgements his work has been performed thank to the financial support from ‘gobierno de españa’ through the research project ‘proyecto de investigación de excelencia del ministerio de economía y competitividad mat2016-76951c2-1-p’. references [1] paris, p.c., a critical analysis of crack propagation laws, j. basic eng., 85 (1960), 528–534. [2] wells, a.a., unstable crack propagation in metals. cleavage and fast fracture, proceedings of the crack propagation symposium, 1, paper 84, cranfield, uk (1961). [3] laird, c., smith, g.c., crack propagation in high stress fatigue, philos. mag. 8 (1962) 847–857. [4] vasco-olmo, j.m., díaz, f.a., garcía-collado, a., dorado, r., experimental evaluation of crack shielding during fatigue crack growth using digital image correlation, fatigue fract. engng mater. struct., 38 (2013) 223–237. [5] antunes, f.v., branco, r., costa, j.d., rodrigues, d.m., plasticity induced crack closure in middle-tension specimen: numerical versus experimental, fatigue fract. engng mater. struct. 33 (2010) 673–686. [6] chu, t.c., ranson, w.f., sutton, m.a., peters, w.h., applications of digital-image correlation technique to experimental mechanics, exp. mech., 25 (1985) 232–244. [7] de matos, p.f.p., nowell, d., on the accurate assessment of crack opening and closing stresses in plasticity-induced fatigue crack closure problems, eng. fract. mech., 74 (2007) 1579–1601. [8] antunes, f.v., rodrigues, s.m., camas, d., a numerical analysis of ctod in constant amplitude fatigue crack growth, theoretical and applied fracture mechanics, 85 (2016) 45–55. [9] korsunsky, a.m., song, x., belnoue, j., jun, t., hofmann, f., de matos, p.f.p., nowell, d., dini, d., aparicioblanco, o., walsh, m.j., crack tip deformation fields and fatigue crack growth rates in ti-6al-4v, int. j. fatigue, 31 (2009) 1771–1779. t << /ascii85encodepages false /allowtransparency false /autopositionepsfiles true /autorotatepages /none /binding /left /calgrayprofile (dot gain 20%) /calrgbprofile (srgb iec61966-2.1) /calcmykprofile (u.s. web coated \050swop\051 v2) /srgbprofile (srgb iec61966-2.1) /cannotembedfontpolicy /error /compatibilitylevel 1.4 /compressobjects /tags /compresspages true /convertimagestoindexed true /passthroughjpegimages true /createjobticket false /defaultrenderingintent /default /detectblends true /detectcurves 0.0000 /colorconversionstrategy /cmyk /dothumbnails false /embedallfonts true /embedopentype false /parseiccprofilesincomments true /embedjoboptions true /dscreportinglevel 0 /emitdscwarnings false /endpage -1 /imagememory 1048576 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can be opened with acrobat and adobe reader 5.0 and later.) >> /namespace [ (adobe) (common) (1.0) ] /othernamespaces [ << /asreaderspreads false /cropimagestoframes true /errorcontrol /warnandcontinue /flattenerignorespreadoverrides false /includeguidesgrids false /includenonprinting false /includeslug false /namespace [ (adobe) (indesign) (4.0) ] /omitplacedbitmaps false /omitplacedeps false /omitplacedpdf false /simulateoverprint /legacy >> << /addbleedmarks false /addcolorbars false /addcropmarks false /addpageinfo false /addregmarks false /convertcolors /converttocmyk /destinationprofilename () /destinationprofileselector /documentcmyk /downsample16bitimages true /flattenerpreset << /presetselector /mediumresolution >> /formelements false /generatestructure false /includebookmarks false /includehyperlinks false /includeinteractive false /includelayers false /includeprofiles false /multimediahandling /useobjectsettings /namespace [ (adobe) (creativesuite) (2.0) ] /pdfxoutputintentprofileselector /documentcmyk /preserveediting true /untaggedcmykhandling /leaveuntagged /untaggedrgbhandling /usedocumentprofile /usedocumentbleed false >> ] >> setdistillerparams << /hwresolution [2400 2400] /pagesize [612.000 792.000] >> setpagedevice microsoft word numero_51_art_27_2644 a. gesualdo et alii, frattura ed integrità strutturale, 51 (2020) 376-385; doi: 10.3221/igf-esis.51.27 376 focussed on fracture and damage detection in masonry structures minimum energy strategies for the in-plane behaviour of masonry antonio gesualdo*, bruno calderoni university of naples “federico ii”, department of structure for engineering and architecture, napoli, italy via claudio 21, 80125, napoli, italy gesualdo@unina.it, http://orcid.org/0000-0002-7063-8064 calderon@unina.it, https://orcid.org/0000-0001-5596-9829 antonino iannuzzo eth zürich, institute of technology in architecture, zürich, switzerland iannuzzo@arch.ethz.ch, http://orcid.org/0000-0002-6633-149x antonio fortunato university of salerno, department of civil engineering, fisciano (sa), italy a.fortunato@unisa.it, https://orcid.org/0000-0001-9224-2143 michela monaco university of campania “luigi vanvitelli”, department of architecture and industrial design, aversa (ce), italy michela.monaco@unicampania.it, http://orcid.org/0000-0001-7895-7089 abstract. unreinforced masonry is the most diffused construction material in the major part of historical centers in europe. in a building subjected to earthquake forces the contribution of in-plane shear resistance of the masonry walls is a determinant factor for the stability of the whole structure. in particular, the masonry piers are the structural elements subjected to the combination of normal and shear forces. in general, ductile tools to model the in plane behaviour of masonry are always welcome in order to evaluate the capacity of walls subjected to vertical and horizontal actions. in this framework, two no-tension approaches to model the behaviour of masonry walls loaded with in-plane forces, involving a minimum energy procedure, are presented. both the procedures allow the representation of the stress maps in the panel in case of monotonic increase of shear load. the results of the numerical analyses are compared and discussed. keywords. masonry; in-plane loads; minimum potential energy. citation: gesualdo, a., calderoni, b., iannuzzo, a., fortunato, a., monaco, m. minimum energy strategies for the in-plane behaviour of masonry, frattura ed integrità strutturale, 51 (2020) 376-385. received: 28.09.2019 accepted: 25.11.2019 published: 01.01.2020 copyright: © 2020 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. introduction he analysis of masonry structures has been for years a challenging issue to be addressed, especially when seismic actions are involved. masonry buildings are in fact the main part of historical centers in italy and in general all over europe [1]. these buildings are a complex arrangement of masonry walls and different structural elements, t http://www.gruppofrattura.it/va/51/2644.mp4 a. gesualdo et alii, frattura ed integrità strutturale, 51 (2020) 376-385; doi: 10.3221/igf-esis.51.27 377 such as arches and vaults, columns and plane slabs [2]. henceforth existing masonry buildings subjected to seismic loads need a correct modeling of these structural elements and their interaction [3]. in particular, especially in the cases in which the out of plane mechanisms can be considered absent [4], the role of the in plane behavior of masonry elements (piers and spandrels) and their interaction with the horizontal structural elements is a key one [5, 6]. given the importance of the masonry heritage and in view of its rehabilitation, efficient and consistent tools are needed [7], especially constitutive models able to describe the complex patterns of cracks after static and dynamic actions [8, 9, 10]. several constitutive models have been proposed in the last decades to describe the behaviour of masonry, and among them a preminent role can be assigned to the no-tension (nt) model. the first approaches to the unilateral model date back to nineteenth century, [11], although in the indeterminate case of the rectangular table with four legs the problem was for the first time posed in an indirect way by euler at the end of xviii century [12]. the first rational consideration on the constitutive model were developed in the first decades of xix century by signorini [13]. the papers by heyman [14, 15] considered the low tensile stress of masonry negligible, so that a nt material could be taken into account. he introduced the safe theorem of limit analysis for particular masonry structures, according to which an unreinforced masonry vault will stand if a network of compression forces in the section of the structure and in equilibrium with the applied loads can be found. this solution can be considered according the statements of limit analysis a lower-bound solution [16, 17] and was presented for the first time as an application to the case of “voussoir” (or segmental) arch [18], as the author pointed out. since that time, and with limited exceptions [19-21] the nt problem has become an almost exclusively italian question. the first rational assessment was developed since the beginnings of ’80 and mainly thanks to italian contribute, see for example [22, 23]. the classical heyman hypotheses of null tensile strength, infinite compressive strength and no-sliding were since then the basis his theory, together with the static theorem of limit analysis, used mainly for the analysis of arches and vaults [24]. the heyman hypotheses and the limits of their application to masonry structures were successively discussed [25]. this paper presents two nt approaches to model the behaviour of masonry walls subjected to in-plane actions. in both cases a variational strategy is proposed. an extremum problem is in fact solved, in the first case with reference to the complementary energy, in the second one to the potential energy. the first method considers an approximate solution when small strains are involved, with the constitutive hypothesis of unilateral constraints on normal stresses. the solution is a kinematically consistent configuration obtained as a minimum for the complementary energy ce . the numerical problem is solved introducing a curvilinear coordinate system corresponding to the distribution of compression rays [26]. the second approach solves the problem of a 1-d element with variable cross section and symmetric shape defined in the panel domain and corresponding to the compressed area. the solution corresponds to the minimum of total potential energy [27]. the stress maps in case of monotonic increase of shear load is provided [28]. elastic no-tension model general definitions he mechanics of masonry-like –materials, developed by giaquinta and giusti [22] and del piero [23]. fortunato [26] considered the boundary value problem for a masonry-like rectangular panel, traction free on the lateral sides and subjected to zero body forces as well as prescribed rigid body displacements of the top and bottom bases. in particular, the problem is that of a nt body occupying a two dimensional regular region  (fig. 1), with: figure 1: the nt body. t a. gesualdo et alii, frattura ed integrità strutturale, 51 (2020) 376-385; doi: 10.3221/igf-esis.51.27 378 n d  : boundary of the body  and n d   ,n d  : free and constrained boundary of the body  . given the body forces b in  , the tractions p on n and the displacements u on d , the solution of the boundary value problem is the triplet { , }u λ b (displacement, anelastic strain, stress) fulfilling the following relations:  equilibrium and static boundary conditions    , , on ndivt b 0 tn p (1)  kinematic boundary conditions  , on du u (2)  stress-strain law and constitutive restrictions on strain involving fractures     [ ] , tr 0 , det 0t e λ t t (3)  normality law    tr 0 , det 0 , 0λ λ t λ (4) where e is the infinitesimal strain and  is the elastic tensor. the inequalities (3) lead to the following partition of the domain  : 1 2 3 { : tr 0 , det 0} { : tr 0 , det 0} { : tr 0 , det 0}.                x t t x t t x t t (5) the domain 1 is that of biaxial compression and the material has the classical bilateral elastic behaviour. in the domain 2 the material is in uniaxial compression and can show fractures. in this case the compressive lines when b 0 are straight lines. in the 3 domain the material is completely inert and any positive semidefinite fracture field is possible. variational formulation it has been proved [23] the existence of a strain energy density for nt materials, so that a variational formulation of the problem can be derived, i.e. an equilibrium configuration corresponds to a minimum of the total potential energy: 1 ( ) . 2 n p ds       u e e p ue (6) the equilibrium displacement solution may not be unique, due to the presence of the anelastic part. a dual formulation of the problem has been derived by [22], with the stress field 0t as statically admissible solution minimizing the complementary energy functional: 11( ) . 2 d c ds        t t t tn ue (7) defined over the convex set of statically admissible stress fields. a. gesualdo et alii, frattura ed integrità strutturale, 51 (2020) 376-385; doi: 10.3221/igf-esis.51.27 379 analytical formulations of the variational problem 2-d minimum complementary energy approach he analysis considers a nt masonry panel loaded with a constant vertical force and an increasing horizontal one. in the present approach the equilibrium solution is determined by minimizing the complementary energy (7) according the general method reported in [26]. the rectangular domain defined by the panel is traction free on the lateral sides. the body forces are null and the displacements are prescribed at top and bottom bases: the relative displacements of the two bases are defined by the triplet { , }u v . a reference system { , }o x y is defined with origin in the panel centroid, see fig. 2(a). figure 2: masonry panel and displacement vectors (a); angle  with the vector rays (b); vector rays and coordinates system (c) the problem is solved considering an approximate solution over a reduced definition domain, i.e. 2 3  , that is to search the statically admissible stress field 0t in 2 when the free boundary between 2 and 3 is determined. as above remarked, when the body forces are null, the isostatic compressive curves are straight lines, named compression rays. they form an angle  with the y axis and cross the two bases of the panel, since the vertical edges are part of the free boundary. the curvilinear reference system for the compression rays is defined by the coordinate system  1 2{ , }o , see fig. 2(c). within the panel area an uniaxial thrust region is recognized. this compression region is determined by means of the complementary energy minimum. reference is made to a normalized rectangle of unitary base and height /h b h where b and h are respectively the real base and height of the masonry panel as in fig. 2(a). the compression rays are defined by means of the slope function 1( )g  , subjected to the geometrical constraints: 1 1 1 1 1 1 1 2 1 2 ( ) 1 2 1 2 ( ) g h h g h h                 (8) where 1 is the intersection of the slope function with the horizontal axis. the constitutive conditions: t (a) (b) (c) a. gesualdo et alii, frattura ed integrità strutturale, 51 (2020) 376-385; doi: 10.3221/igf-esis.51.27 380 1 1( ) , 0 v g u u u       (9) correspond to the existence of compression rays corresponds to a kinematic constraint on the function 1( )g  . the complementary energy (7) assumes in this case the form (see fortunato, 2010):                1 1 1 2 2 1 2 ( ) 2 1 / 2 (1 ) ln 1 / 2 c u g v g e e d g h g g h (10) where the triplet ( , , )u v represents the given set of relative rigid displacements, 1  and 1 are the geometrical bounds of the compression region and g is the first derivative of 1( )g  with respect to 1 . the minimum of ce is obtained solving the euler equation associated to (10) adopting a multiple shooting technique, in other words looking for the function 1( )g  that minimizes the functional (10) with the constraints (9) and the boundary conditions: 11( ) , ( )g g g g   . (11) the conditions (11) correspond to the upper and lower load conditions. 1-d minimum potential energy approach like in the previous paragraph, body forces are null and the analysis is performed considering a nt masonry panel loaded with a constant vertical force and an increasing horizontal one. as the horizontal load increases, the resultant force r is that corresponding to the triangular distribution with base a in fig. 3(a). the straight line connecting the middle points of the triangular distribution forms and angle 1 with the vertical axis. a partition of the entire rectangular domain due to the constitutive model adopted is recognized, so that the compressive stress area 2 in (5) can be assumed that enclosed in the polygonal domain represented in fig. 3(b), whose geometry is defined by:  2cosminb a ,   2cos max b b where 2 is the angle that the symmetry axis of the domain forms with the vertical one and in general it is distinct from 1 . the problem is skew-symmetric with respect to the vertical axis, and the entire problem can be reduced to onedimensional model, i.e. a masonry strut with variable cross section and symmetric shape. the resulting problem is an euler-bernoulli cantilever beam with variable cross section as in fig. 4(a), loaded by r . the internal forces on the beam are:                1 2 1 2 1 1 2cos( ) , sin( ) , .tan 2 3 2 b a h n r t r m n (12) the variational formulation of the problem in terms of potential energy ( )p ue in (6) is used. the boundary conditions are defined at the beam ends of fig. 4 (b) and in the cross section where there is a stiffness first derivative variation. the problem solution is in this case the triplet 2( , , )b c v v satisfying the displacements boundary conditions and minimizing the ( )p ue expressed by: 1 2 1 2 2 2 2 2 2 1 1 1 1 2 2 2 2 1 1 1 1 2 2 2 2 0 0 0 0 ( ) ( , , ) 1 1 ( ) ( ) ( ) ( ) 2 2 p p b c l l l l cei z dz ei z dz ea z dz ea z dz                               u v v f v e e (13) a. gesualdo et alii, frattura ed integrità strutturale, 51 (2020) 376-385; doi: 10.3221/igf-esis.51.27 381 where the integrals are defined over the two domains in which stiffness is continuous with its first derivative iei , iea , i ,  i are respectively the stiffness and deformation characteristics of the beam and the external force vector is  1 1 1( , , )n t mf . figure 3: (a) masonry panel with in-plane load; (b) shape of the reacting structure. only the bending and the axial strain energies have been taken into account in the relation (13). the problem has been solved taking into account a fifth-order power series expansion for the angle 2 [29]. the minimum condition is given by: 2( , , ) 0b c  v v (14) and the boundary conditions: 1 2 ' ' 1 2 1 1 2 2 ' ' 1 1 2 2 (0) ; (0) 0 (0) ; (0) ( ) ; ( ) ( ) ; ( ) b a b a c b c b v v v v v v v l v v l v v l v l                (15) with ' ( cos )jj a  rotation angle at the cantilever support corresponding to the deformation of the masonry triangle pjk in fig. 3 (a) and considered as rigid, since the real variation of this angle do not determine sensible changes in the resultant stress maps. a. gesualdo et alii, frattura ed integrità strutturale, 51 (2020) 376-385; doi: 10.3221/igf-esis.51.27 382 figure 4: (a) masonry strut within the panel; (b) corresponding cantilever beam. numerical results comparison he numerical tests have been performed considering a masonry wall with dimensions 900×1500×120 mm3, loaded with a constant vertical distributed load of 50 kn and a young modulus of 130 mpa. the shear load t increases till the final value of 27 kn (tab. 1). a b c d e f n [kn] 50 50 50 50 50 50 t [kn] 0 10 15 20 25 27 table 1: valu es of the vertical and horizontal loads on the masonry panel fig. 5 reports the stress maps obtained with the 1-d minimum potential energy approach [28]. the case d) of fig. 5 has been examined with 2-d minimum complementary energy approach. the top and bottom relative displacements , ,u v  have been derived from the absolute displacements obtained in the 1-d model analysis. the 2 region is identified considering that the only compressive stresses run along the compression rays. for the functions 1( )g and  1( )g , as shown in fig. 6 (b), a constant stress distribution along the rays are obtained and the corresponding values for the vertical and horizontal total loads are t=17.8 kn and n=50.1 kn. the approximation of the corresponding values in tab. 1 for the case d is considered sufficient. t a. gesualdo et alii, frattura ed integrità strutturale, 51 (2020) 376-385; doi: 10.3221/igf-esis.51.27 383 figure 5: stress contour plots for 1-d approach [n mm-2]. figure 6: stress map for 2-d approach (a) and representation of the functions 1( )g and  1( )g (b) conclusions he essential elements of two variational approaches for the in plane behaviour of masonry walls, considered as nt structural elements, have been presented in this paper. both the strategies allow the representation of the stress maps in the panel in case biaxial loading. the 1-d approach considers a diagonal strut embedded in the panel, t 1( )g    1( )g (a) (b) a. gesualdo et alii, frattura ed integrità strutturale, 51 (2020) 376-385; doi: 10.3221/igf-esis.51.27 384 whose geometry is imposed by the nt behavior and the solution corresponds to the minimum of total potential energy. the 2-d approach is conversely based on the minimum of the complementary energy, with a definition of the loaded area as a set of compressed rays and the loading actions on the panel are obtained as a solution of the procedure. the agreement between the results of the two procedures is satisfying, both with regard to the reactive area and to the stress intensity. references [1] guadagnuolo, m., faella, g., donadio, a., ferri, l. (2014). integrated evaluation of the church of s. nicola di mira: conservation versus safety. ndt & e international, 68, pp. 53-65. doi: 10.1016/j.ndteint.2014.08.002. [2] bergamasco, i., gesualdo, a., iannuzzo, a., monaco, m. (2018). an integrated approach to the conservation of the roofing structures in the pompeian domus, j. cult. herit., 31, pp. 141-151. doi:10.1016/j.culher.2017.12.006. [3] betti, m., galano, l., petracchi, m. and vignoli, a. (2015). diagonal cracking shear strength of unreinforced masonry panels: a correction proposal of the b shape factor, b. earthq. eng., 13(10), pp. 3151-3186. doi: 10.1007/s10518-015-9756-8 [4] guadagnuolo m., monaco, m. (2009). out of plane behaviour of unreinforced masonry walls. in: protection of historical buildings, 2, pp. 1177-1180, london, new york: crc press, taylor & francis group. [5] betti, m., galano, l., vignoli, a. (2008). seismic response of masonry plane walls: a numerical study on spandrel strength, aip conf. proc., 1020(1), pp. 787-794. doi: 10.1063/1.2963915. [6] calderoni, b., cordasco, e. a., lenza, p., pacella, g. (2011). a simplified theoretical model for the evaluation of structural behaviour of masonry spandrels, int. j. mater. struct. integrity, 5(2-3), pp. 192-214. doi:10.1504/ijmsi.2011.041934 [7] buonocore, g., gesualdo, a., monaco, m., savino, m.t. (2014). improvement of seismic performance of unreinforced masonry buildings using steel frames. civil-comp proceedings, 106. doi:10.4203/ccp.106.117. [8] gatta, c., addessi, d., vestroni, f. (2018). static and dynamic nonlinear response of masonry walls. international journal of solids and structures, 155, pp. 291-303. doi: 10.1016/j.ijsolstr.2018.07.028. [9] iannuzzo, a., angelillo, m., de chiara, e., de guglielmo, f., de serio, f., ribera, f., gesualdo, a. (2018). modelling the cracks produced by settlements in masonry structures. meccanica, 53(7), pp. 1857-1873. doi: 10.1007/s11012-017-0721-2 [10] iannuzzo, a., de luca, a., fortunato, a., gesualdo, a., angelillo, m. (2018b). fractures detection in masonry constructions under horizontal seismic forces. ing. sismica, 35(3), pp. 87-103. doi: 10.1007/s11012-017-0721-2 [11] moseley, h. (1833). on a new principle in statics, called the principle of least pressure, london and edinburgh philosophical magazine and journal of science, 3, 285-288. [12] euler, l. (1774). de pressione ponderis in planum cui incumbit, novi commentarii academiae scientiarum petropolitanae 18, 289-329. [13] signorini, a.(1925). un teorema di esistenza ed unicità nella statica dei materiali poco resistenti a trazione. rend. accad. naz. lincei, 401–406. [14] heyman, j. (1966). the stone skeleton, int. j. solids struct., 2 (2), 265–279, doi:10.1016/0020-7683(66)90018-7. [15] heyman, j. (1966). the stone skeleton. international journal of solids and structures, 2(2), pp. 249-279. doi: 10.1016/0020-7683(66)90018-7 [16] heyman, j. (1977). equilibrium of shell structures, clarendon press, oxford, u.k. [17] heyman, j. (1995). the stone skeleton: structural engineering of masonry architecture, cambridge university press, cambridge, u.k. [18] kooharian, a. (1953). limit analysis of voussoirs and concrete arches, journal of american concrete institute, 49(12), 317-328. [19] zienkiewicz o.c., valliappan, s., king, i.p. (1968). stress analysis of rock as a ‘no tension’ material, géotechnique, 18(1), doi: 10.1680/geot.1968.18.1.56. [20] chen, w.f. (1970). extensibility of concrete and theorems of limit analysis. journal of the engineering mechanics division, 96(3), pp. 341-352. [21] heuzé, f.e., goodman, r.e., bornstein, a. (1971). numerical analyses of deformability tests in jointed rock—“joint perturbation” and “no tension” finite element solutions. rock mechanics, 3(1), pp. 13-24. doi: 10.1007/bf01243549 a. gesualdo et alii, frattura ed integrità strutturale, 51 (2020) 376-385; doi: 10.3221/igf-esis.51.27 385 [22] giaquinta, m., giusti, e. (1985). researches on the equilibrium of masonry structures. arch. ration. mech. anal. 88(4), pp. 359-392, doi: 10.1007/bf00250872 [23] del piero, g. (1989). constitutive equation and compatibility of the external loads for linear elastic masonry-like materials. meccanica 24(3), pp. 150-162. doi:10.1007/bf01559418 [24] monaco, m., bergamasco, i, betti, m. (2018). a no-tension analysis for a brick masonry vault with lunette, journal of mechanics of materials and structures, 13(5), pp. 703-714, doi: 10.2140/jomms.2018.13.703 [25] crisfield, m.a., packham, (1987). a mechanism program for computing the strength of masonry arch bridges, trrl research report, 124. [26] fortunato, a. (2010). elastic solutions for masonry-like panels. journal of elasticity, 98(1), pp. 87-110. doi: 10.1007/s10659-009-9219-z [27] gesualdo, a., calderoni, b., sandoli, a., monaco, m. (2019). minimum energy approach for the in-plane shear resistance of masonry panels. ing. sismica, 36(1), pp. 42-53. [28] monaco, m., calderoni, b., iannuzzo, a., gesualdo, a. (2018). behaviour of in-plane loaded masonry panels, procedia struct. integrity, 11, pp. 388-393. doi: 10.1016/j.prostr.2018.11.050 [29] wolfram s. 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/hrv (za stvaranje adobe pdf dokumenata najpogodnijih za visokokvalitetni ispis prije tiskanja koristite ove postavke. stvoreni pdf dokumenti mogu se otvoriti acrobat i adobe reader 5.0 i kasnijim verzijama.) /hun 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can be opened with acrobat and adobe reader 5.0 and later.) >> /namespace [ (adobe) (common) (1.0) ] /othernamespaces [ << /asreaderspreads false /cropimagestoframes true /errorcontrol /warnandcontinue /flattenerignorespreadoverrides false /includeguidesgrids false /includenonprinting false /includeslug false /namespace [ (adobe) (indesign) (4.0) ] /omitplacedbitmaps false /omitplacedeps false /omitplacedpdf false /simulateoverprint /legacy >> << /addbleedmarks false /addcolorbars false /addcropmarks false /addpageinfo false /addregmarks false /convertcolors /converttocmyk /destinationprofilename () /destinationprofileselector /documentcmyk /downsample16bitimages true /flattenerpreset << /presetselector /mediumresolution >> /formelements false /generatestructure false /includebookmarks false /includehyperlinks false /includeinteractive false /includelayers false /includeprofiles false /multimediahandling /useobjectsettings /namespace [ (adobe) (creativesuite) (2.0) ] /pdfxoutputintentprofileselector /documentcmyk /preserveediting true /untaggedcmykhandling /leaveuntagged /untaggedrgbhandling /usedocumentprofile /usedocumentbleed false >> ] >> setdistillerparams << /hwresolution [2400 2400] /pagesize [612.000 792.000] >> setpagedevice microsoft word numero_59_art_35_3294.docx g. risitano, frattura ed integrità strutturale, 59 (2022) 537-548; doi: 10.3221/igf-esis.59.35 537 fatigue strength evaluation of ppgf35 by energy approach during mechanical tests giacomo risitano, university of messina, italy giacomo.risitano@unime.it, http://orcid.org/0000-0002-0506-8720 abstract. thanks to the progress of research on thermoplastic materials, the properties of composite materials have improved considerably. the aim of this study is the evaluation of fatigue strength of glass-fibrereinforced polypropylene composite (ppgf35) by applying both the risitano thermographic method (rtm) and the new static thermographic method (stm). keywords. glass-fibre-reinforced polypropylene composite; fatigue assessment; risitano thermographic method; static thermographic method. citation: risitano, g., fatigue strength evaluation of ppgf35 by energy approach during mechanical tests, frattura ed integrità strutturale, 59 (2022) 537-548. received: 05.10.2021 accepted: 19.12.2021 published: 01.01.2022 copyright: © 2022 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. introduction hanks to the progress of research on thermoplastic materials, the mechanical and thermal properties of composite materials have improved considerably. the improved performance has made these materials more competitive than traditional thermosetting matrix composites, in particular for the automotive companies where they are used for panels, bearings, gears, etc. in fact, until a few years ago, the use of these composite materials was restricted to automotive applications where mechanical requirements had to be limited. today it is possible to obtain light and low cost components using composites with short fibre reinforced plastics (sfrp). these materials, filled with glass fibres up to 50% by mass, are now used for structural components as reported by several papers: bernasconi et al. [1] worked on fatigue strength of a clutch pedal in short glass fibre reinforced polyamide; casado et al. [2] wrote about the fatigue failure of short glass fibre for railway track; sonsino et al. [3] worked on the fatigue design of highly loaded short glass fibre reinforced polyamide parts in engine compartments; scappatici et al. [4] have optimized the design of horizontal-axis small wind turbines. it must also be considered that the recyclable nature of these materials is clearly an interesting step towards the protection of the natural ecosystem. recently, efforts to reduce the weight of automobiles by the increased use of plastics and their composites, have led to a growing interest of short-fibre-reinforced injection-moulded thermoplastics into fatigue-sensitive applications [5, 6]. one of the most important applications of glass reinforced polypropylene is in automotive body panels made by low cost thermoforming techniques. the design of short fibre reinforced plastic components for structural applications requires an accurate knowledge of the several factors affecting the tensile properties and the fatigue lifetime. the tensile strength and t https://youtu.be/-njqyxwpo54 f. cucinotta et alii, frattura ed integrità strutturale, 59 (2022) 537-548; doi: 10.3221/igf-esis.59.35 538 toughness/impact energy of short fibre reinforced polymer composites would depend on a number of factors such as fibre length, interfacial adhesion and properties of components. indeed, fu sy et al [7] studied the effects of pa66/pp ratio on the mechanical properties of short glass fiber reinforced. the fatigue tests of sfrp materials require even more time consuming than the tests required for metallic materials due to the presence of the viscous behaviour of the matrix which leads to a high accumulation of heat at high test frequencies [3]. in fact, this heat can lead to a change in the mechanical characteristics of the material by altering the test results. ferreira et al. [8] obtained the s-n curves of polypropylene/glass-fibre thermoplastic composites produced from a bidirectional woven cloth mixture of e glass fibres and polypropylene fibres. esmaeillou et al. [9] performed tension-tension fatigue tests on sfrp composites at different applied maximum stress and analysed the specimens at both microscopic and macroscopic scale. the temperature was measured during cyclic loading using an infrared camera and the progressive loss of stiffness was evaluated during the tests. moreover, the effects of the frequency and of the mean stress on the fatigue strength were evaluated. an energy-based approach was proposed by meneghetti and quaresimin [10] to analyse the fatigue strength of plain and notched specimens made of a short fibre-reinforced plastic weakened by rounded notches. toubal et al. [11] used an analytical model based on cumulative damage for predicting the damage evolution in composite materials. fatigue tests of specimens have been monitored with an infrared thermography system. belmonte et al. [12] investigated the influence of short fibre volume fraction presentence in pa66 on the damage mode during an uniaxial fatigue test. wilmes and hornberger [13] discussed different lifetime estimation methods of different pa66gf35 specimens with different shapes and fibre orientation. traditional methods for assessing the fatigue behaviour of materials are time consuming and expensive. for the first time, la rosa and risitano [14] have proposed an innovative method for assessing the fatigue of materials, components and mechanical systems: the risitano thermographic method (rtm). based on the analysis of thermal infrared images, rtm determines the fatigue limit and the wöhler curve of the material with a short test time passing from long months tests to a few days long tests. a review of the scientific results in literature, related to the application of the thermographic techniques to composite materials have been presented by vergani et al. [15]. an innovative method to determinate the fatigue limit during tensile static test has been proposed by clienti et al. [16] for plastic material and by risitano and risitano [17] for metallic material. clienti et al. [16] suggest that during quasi-static tensile tests the area, where first irreversible plasticization occurred, is detectable by the analysis of the t vs curve considering the temperature change of the curve slope. this variation identifies the transition zone between thermoelastic and thermoplastic behaviour, or in other words, the beginning of irreversible micro-plasticization. the authors have suggested that in that transition zone, there is the damage limit of material. this damage limit must be understood as the macroscopic stress value that would cause the material to break if subjected to cyclic loading at any load ratio. then, it is very close to the traditional fatigue limit. this approach, called static thermographic method (stm), correlated the first deviation from linearity of the temperature surface of the material during tensile test to the fatigue limit. this was observed for basalt fibre reinforced composites by colombo et al. [18], high density polyethylene [19] and glass fibre reinforced composites by harizi et al. [20] and crupi et al. [21]. cucinotta et al. [22] monitored the superficial temperature of high strength concrete specimens subjected to compressive loads, observed a deviation from the linear thermoelastic trend. santonocito [23] applied the stm for the first time on pa12 specimens obtained through additive manufacturing. abello et al. [24] applied the “fast” approach to investigate the evolution of thermomechanical variables during cyclic loadings, to perform a comparison between the cyclic dissipated energy given by thermal and mechanical method and, at last, to investigate the relevancy of predicting the fatigue curve from heat build-up measurements for sfrp materials. jegou et al. [25] investigated pa66gf50 specimens predicting the fatigue curve from the temperature measurements, finding a very good correlation to a wöhler curve obtained from classical fatigue measurements. arif & al. [26] studied the fatigue damage behaviour of pa66 gf30 monitoring the evolution of dynamic modulus, strain, temperature to evaluate damage increasing during fatigue loading. kodeeswaran et al. [27] evaluated the fatigue life of the polymer gears at different frequencies observing both thermomechanical and root crack failures. serrano et al. [28] performed three different test cases to fatigue loading; firstly a dissipated energy approach is applied to the samples and then an energetic approach is used to evaluate quickly the fatigue lifetime. the findings are related to the s-n curve and the authors state that dissipated energy field is not giving full access to “life map” of the component, while the dissipated energy approach seems to be dependent on the local structural conditions of the sample. marco et al. [29] used the contribution of thermal measurements to locate and follow the failure crack and to provide a validation case for a numerical model for fatigue testing. katunin et al. [30] studied the self-heating temperature accompanying the fatigue process of polymeric composites and correlated to structural properties. g. risitano, frattura ed integrità strutturale, 59 (2022) 537-548; doi: 10.3221/igf-esis.59.35 539 this paper investigates fatigue behaviour for a glass-fibre-reinforced polypropylene composite (ppgf35). the aim of this study is to apply for the first time both the risitano thermographic method [14] and the static thermographic method [16] for the evaluation of the fatigue strength of the composite material ppgf35. the results obtained were then compared with the results obtained using the traditional procedure. obviously, the analysis took into account that composites have different and more complex fatigue mechanisms than metallic materials. material and methods he material analysed in this study is a glass-fibre-reinforced polypropylene composite (ppgf35). dog bone specimens (fig. 1) were injection moulded (type 1a of the iso 527-2:1993 standard [31]) with processing conditions based on iso 294-1:1996 [32] and iso 1873-2:2007 [33]. the specimens were machined out from injection-moulded plates at orientation angle of 0°. tab. 1 shows the dimensions of the specimen geometry; also in this case the results are processed with a statistical study on 15 specimens and reporting the average and the standard deviation values. a b c d e f r h 30.610.18 30.540.13 169.450.37 9.860.02 19.840.06 3.930.01 25,000.15 83,480.26 table 1: dimensions of the specimen in mm. the tensile tests were carried out using an italsigma’s servo-hydraulic load machine at a crosshead rate equal to 5 mm/min with constant temperature and relative humidity (23 °c and 50% rh). during all tensile tests, the infrared camera flir a40 was used (fig. 2). tab. 2 shows the mechanical properties of the material. in addition, tab. 3 shows the parameters used for the injection moulding of the sample. tensile tests were carried out on 15 specimens; the results were processed with a statistical study and report the average and standard deviation of the tensile strength, the elastic modulus, the failure strain and density. this led to a significant number of data for analyses with good repeatability. tensile strength elastic modulus failure strain density σr [mpa] e [mpa] εf [%] ρ [kg/m3] 1122.3 8915314.8 3.40.16 12163.6 table 2: mechanical properties of ppgf35. feeding temperature mass temperature back pressure holding pressure mould temperature screw speed flow front speed 40 80 °c 230 280 °c low to medium 30 60 mpa 30 50 °c low to medium 100 200 mm/s table 3: injection moulding parameters. in addition, 20 specimens were tested with cyclic loads. the specimens have the same geometry (fig. 1) as the tensile tested specimens and they were made with the same procedure shown in tab. 3. a load ratio r of -0.1 and a test frequency f of 5 hz were used for these cyclic tests. the choice of this test frequency is in order to ensure that the temperatures reached during the cyclic tests do not exceed the glass transition temperature of the polypropylene. indeed, it was verified that higher test frequencies brought the material to too high temperatures thus invalidating the tests. this is a typical situation for composite materials with a plastic matrix; for this reason, fatigue tests are time-consuming for these materials. t f. cucinotta et alii, frattura ed integrità strutturale, 59 (2022) 537-548; doi: 10.3221/igf-esis.59.35 540 figure 1: standard iso 527-2:1993 specimen. test setup he tests were performed at constant temperature and relative humidity (23 °c and 50% rh). as previously mentioned, during all the tests the surface temperature of the specimen was monitored with an ir camera. in order to determine the wöhler curve and the fatigue strength, one series of cycling tests (14 specimens) were traditional fatigue tests:  3 specimens at maximum stress of 72 mpa;  3 specimens at maximum stress of 67 mpa;  3 specimens at maximum stress of 62 mpa;  3 specimens at maximum stress of 57 mpa;  2 specimens at maximum stress of 52 mpa. in order to apply the rtm to determine the fatigue strength, 6 step tests were conducted increasing the maximum stress until failure:  for 3 specimens, four stress steps of 20.000 cycles each were used starting from 52 mpa up to 67 mpa;  for other 3 specimens, eight stress steps of 10.000 cycles each were used starting from 27 mpa up to 67 mpa. it is important to remember that the second type of test was adopted to have more data in order to determine the fatigue strength using the rtm [14]. for this reason, during all cycling tests the infrared camera flir a40 was used (fig. 2). figure 2: experimental setup. t g. risitano, frattura ed integrità strutturale, 59 (2022) 537-548; doi: 10.3221/igf-esis.59.35 541 theoretical approach s repeatedly shown in literature and well explained by clienti et al. [16], during static tests of common engineering materials, the temperature evolution on the specimen surface is characterized by three phases: an initial approximately linear decrease due to the thermoelastic effect (phase 1), then the temperature deviates from linearity until a minimum (phase 2) and a very high further temperature increment until the failure (phase 3). figure 3: typical trend of stress and temperature during a static tensile test. a typical trend of stress and temperature during a static tensile test is shown in fig. 3. for linear isotropic homogeneous material and in adiabatic condition, the variation of temperature during phase i of the static test for uniaxial stress state is:          0 1 0 1 δt= = mt k t c (1) where km is the thermoelastic coefficient. clienti et al. [16] for the first time correlated the damage stress σd, related to the first deviation from linearity of ∆t temperature increment during static test (end of phase i), to the fatigue limit of plastic materials. as reported in [18] “the end of the thermoelastic phase could be related, also for composites, to a stress value σd, which can identify the initiation of a different kind of damage”. this method is recognized as static thermographic method (stm). as repeatedly shown in literature, well explained by la rosa et al. [14] and in subsequent paper of corigliano et al. [34], during hcf tests of common engineering materials, when the specimen is cyclically loaded above its fatigue limit, the temperature evolution on the specimen surface is characterized by three phases: an initial rapid increment (phase i), a plateau region (phase ii), then a very high further temperature increment until the failure (phase iii). the same trend was observed for metals in low cycle fatigue (lcf) by crupi et al. [35], very high cycle fatigue vhcf regimes by crupi et al. [36] and for marine welded joints by corigliano et al. [37]. this method is recognized as “risitano thermographic method” (rtm). handa et al. [38] showed that the temperature evolution during the fatigue tests is different for sfrp composite materials. after an initial linear increment (phase i), there is another linear increment with lower slope (phase ii). the theoretical δtd– n curves, obtained for steel and sfrp composite during constant-amplitude fatigue tests, are shown in fig. 4. as showed in by ricotta et al. [39], different approaches were applied to evaluate the fatigue limit of a cold-drawn aisi 304l stainless steel in push–pull fatigue tests (r = -1), and it was found that the fatigue limits estimated by using all the analyzed approaches were in agreement, allowing a rapid assessment of the fatigue limit similar to that evaluated by carrying out a short staircase procedure at 10 million cycles. in particular, by using the rtm and the thermal response in a static tensile test by static thermographic method stm, a difference of, more or less, 12% and 11% was observed, respectively. a f. cucinotta et alii, frattura ed integrità strutturale, 59 (2022) 537-548; doi: 10.3221/igf-esis.59.35 542 the advantages of the stm are the speed of execution and the ease of the test itself. in particular, an stm test for determining the damage limit takes about 5 minutes. the disadvantages are a lower precision of the fatigue strength value (with values always below and, therefore, in safety) and a not easy applicability on materials with high carbon content. nevertheless, the applicability on plastic and composite materials has repeatedly proved excellent especially considering that the fatigue damage mechanisms are very different for these materials compared to metals. figure 4: typical trend of temperature during a fatigue test. figure 5: applied stress and experimental temperature increment during tensile test. results and discussion uring tensile tests, the temperature of the specimen surface was detected by means of an ir camera. as example given, fig. 5 shows the applied stress and the temperature incrementt during a tensile test. in the initial part of the t–t curve, a linear trend is clearly visible in the curve (phase 1) and its slope corresponds to the thermoelastic coefficient km of eq. (1). then, the temperature deviates from linearity (phase 2) presenting a zero derivative flex. it is possible to draw two linear regression lines, one for phase 1 and the other for phase 2, to determinate the relative equations of the two straight lines. by solving the system of the two equations, it is possible to determine the coordinates of the d g. risitano, frattura ed integrità strutturale, 59 (2022) 537-548; doi: 10.3221/igf-esis.59.35 543 meeting point of the two straight lines and, therefore, the stress value for which there is the transition from phase 1 (thermoelastic phase) to phase 2 (thermoplastic phase). in the specific case, the stress value is 65.2 mpa. obviously, the problem could also be resolved graphically. similar behaviour can also be seen in the other tensile tests and the value of the fatigue strength determinate by stm on 15 specimens is 63.12.1 mpa. fatigue tests at constant amplitude values of the stress range were carried out until failure at a load ratio r= 0.1. tab. 4 shows the results of the first series of cycling test (fatigue test). the temperature of the specimen surface was detected by an ir camera during each fatigue test. fig. 6 plots the typical ∆t vs n curve, during a fatigue test at max= 67 mpa, showing the three phases of temperature evolution as reported by handa et al. [38]: an initial rapid linear increment (phase i), an another linear increment with lower slope (phase ii) and a sudden increase just before the specimen failure (phase iii). test maximum stress [mpa] number of cycles to failure run out 1 72 1.35e+04 no 2 72 2.45e+04 no 3 72 7.34e+03 no 4 67 5.67e+04 no 5 67 8.66e+04 no 6 67 3.52e+04 no 7 62 9.21e+05 no 8 62 6.96e+05 no 9 62 5.10e+05 no 10 57 2.30e+06 no 11 57 7.73e+05 no 12 57 2.48e+06 yes 13 52 2.36e+06 yes 14 52 3.25e+06 yes table 4: summary of the first series of cycling tests (fatigue) on 14 specimens. figure 6: δt vs n curve of test number 5 (cycling test). f. cucinotta et alii, frattura ed integrità strutturale, 59 (2022) 537-548; doi: 10.3221/igf-esis.59.35 544 fig. 7 shows the s-n data obtained applying the traditional procedure, based on fatigue tests carried out at constant amplitude of stress ranges of the first series of cycling test. as can be seen from both tab. 4 and fig. 7, the results presented a typical dispersion for these materials. in addition, 3 tests were runout: 2 at 52 mpa and 1 at 57 mpa. so, if we consider the stress read on the interpolation line of the wohler curve at one million cycles (plausible fatigue life for this material), the fatigue strength is more or less 60 mpa. summarizing the results of the fatigue tests, it can be said with good confidence that the fatigue strength is between 52 mpa (runout test) and 60 mpa (1·106 cycles to failure). figure 7: s-n curve. as mentioned previously, 6 specimens have been tested differently to apply the rtm. in fact, a history of increasing block load has been designed for each specimen. tab. 5 shows the results of the secondo series of cycling test (rtm). fig. 8 shows the fatigue strength predicted by the rtm using the stabilization temperature applied to all the 20 fatigue tests. as recommended by curà et al. [40], two distinct linear regressions have been drawn; the x coordinate of the point in common to the two straight lines is the fatigue strength. as it is easy to see, the number of data is really very large with good repeatability. it is very interesting to note that the fatigue strength is 59.7 mpa. in summary, three different methodologies were applied to determine the fatigue strength of ppgf35:  by traditional procedure – run out (fig. 7), fatigue strength is determined between 52 mpa (3 runout tests) and 60 mpa (1·106 cycles to failure);  by risitano thermographic method (fig. 8), fatigue strength is 59.7 mpa;  by static thermographic method, fatigue strength is 63.12.1 mpa. the values obtained using the different approaches seem to be in good agreement, considering also the dispersion of the value of the fatigue strength of these materials. in fact, it is evident that the results of both the rtm and the stm are within the range determined with the classic method. however, the most important observation concerns the test time. in fact, to perform the 14 cyclic tests at 5 hz, the test days consumed were more than 30. to apply rtm with 6 tests at 5 hz, the test days consumed drop drastically to one and a half. this result confirms the great effectiveness of rtm as an energy method for the determination of fatigue strength compared to traditional methods, totally time consuming. however, the astonishing result is that to perform the 15 tensile tests and obtain a plausible value of the fatigue strength, just over an hour was necessary. g. risitano, frattura ed integrità strutturale, 59 (2022) 537-548; doi: 10.3221/igf-esis.59.35 545 test maximum stress [mpa] number of cycles run out 15 52 2.00e+04 no 57 2.00e+04 62 2.00e+04 67 1.65e+04 16 52 2.00e+04 no 57 2.00e+04 62 2.00e+04 67 5.09e+04 17 52 2.00e+04 no 57 2.00e+04 62 2.00e+04 67 4.28e+04 18 27 1.00e+04 no 32 1.00e+04 37 1.00e+04 42 1.00e+04 47 1.00e+04 52 1.00e+04 57 1.00e+04 62 1.00e+04 67 1.00e+04 19 27 1.00e+04 no 32 1.00e+04 37 1.00e+04 42 1.00e+04 47 1.00e+04 52 1.00e+04 57 1.00e+04 62 1.00e+04 67 1.00e+04 20 27 1.00e+04 no 32 1.00e+04 37 1.00e+04 42 1.00e+04 47 1.00e+04 52 1.00e+04 57 1.00e+04 62 1.00e+04 67 1.00e+04 table 5: summary of the second series of cycling tests (rtm) on 6 specimens. f. cucinotta et alii, frattura ed integrità strutturale, 59 (2022) 537-548; doi: 10.3221/igf-esis.59.35 546 figure 8: fatigue strength predicted by the tm. traditional procedure – run out [mpa] risitano thermographic method [mpa] static thermographic method [mpa] 52-60 59.7 63.12.1 table 6: fatigue strength predicted by traditional procedure and the experimental values by rtm and stm. conclusions his paper investigates fatigue behaviour for a glass-fibre-reinforced polypropylene composite (ppgf35). the aim of this study is to apply for the first time both the risitano thermographic method (rtm) [14] and the static thermographic method (stm) [16] for the fatigue assessment of ppgf35. the predictions of the fatigue strength, obtained by means of stm during tensile test and of rtm during cycling tests, were compared with the value obtained by the traditional procedure. the predicted values are in good agreement with the experimental values of fatigue strength:  by traditional procedure – run out, fatigue strength is determined between 52 mpa and 60 mpa;  by rtm, fatigue strength is 59.7 mpa;  by stm, fatigue strength is 63.12.1 mpa. finally, it is not indifferent to compare the times necessary for the three types of approaches:  traditional procedure, the test days consumed were 31;  rtm, the test days consumed were 1.5;  stm, the test hours consumed were 2. this enormous time saving does not interfere with the accuracy of the results, especially in a field such as fatigue and composite materials where the dispersion of data is very wide. the results gave interesting information for the development of risitano thermographic method and static thermographic method for the fatigue strength assessment of composite material. indeed, results of this kind, like others already obtained [16, 17, 21, 37], suggest that stm is an excellent method for estimating the fatigue resistance of materials by consuming a short test time. in particular, such methodologies can quickly provide information on the fatigue behaviour of components and mechanical systems in operation. methods of this kind would result in a great saving of time and the possibility of having a more detailed design of the mechanical components avoiding approximations on the behaviour of the base material, on the determination of the stresses in exercise, on the real value to be attributed to any notch factors, on the influence of the different technological processes. t g. risitano, frattura ed integrità strutturale, 59 (2022) 537-548; doi: 10.3221/igf-esis.59.35 547 acknowledgements he research reported in this paper was conducted with the financial support of the research project “cerisi” (“research and innovation centre of excellence for structure and infrastructure of large dimensions”), funded by the pon (national operative programme) 2007-2013. references [1] bernasconi, a., davoli, p., armanni, c. (2010). fatigue strength of a clutch pedal made of reprocessed short glass fibre reinforced polyamide. int j fatigue 32, pp. 100–107. doi: 10.1016/j.ijfatigue.2009.02.001. [2] casado, j.a., carrascal, i., polanco, j.a., gutiérrez-solana, f. (2006). fatigue failure of short glass fibre reinforced pa 6.6 structural pieces for railway track fasteners. eng fail anal 13, pp.182–197. doi: 10.1016/j.engfailanal.2005.01.016. [3] sonsino, c.m., moosbrugger, e. (2008). fatigue design of highly loaded short-glass-fibre reinforced polyamide parts in engine compartments. int j fatigue 30, pp. 1279–1288. doi: 10.1016/j.ijfatigue.2007.08.017. [4] scappatici, l., bartolini, n., castellani, f., astolfi, d., garinei, a., pennicchi, m. (2016). optimizing the design of horizontal-axis small wind turbines: from the laboratory to market. j wind eng ind aerodyn 154, pp. 58–68. doi: 10.1016/j.jweia.2016.04.006. [5] karger-kocsis, j., karger-kocsis, j. (2012). structure and fracture mechanics of injection-molded composites. wiley encycl. compos., hoboken, nj, usa: john wiley & sons, inc.; doi: 10.1002/9781118097298.weoc240. [6] mortazavian, s., fatemi, a.(2015). fatigue behavior and modeling of short fiber reinforced polymer composites: a literature review. int j fatigue 70, pp. 297–321. doi:10.1016/j.ijfatigue.2014.10.005. [7] fu, s.y., lauke, b., li, r.k.y., mai, y.w. (2005). effects of pa6,6/pp ratio on the mechanical properties of short glass fiber reinforced and rubber-toughened polyamide 6,6/polypropylene blends. compos part b eng 37, pp. 182–190. doi: 10.1016/j.compositesb.2005.05.018. [8] ferreira, j.a.m., costa, j.d.m., reis, p.n.b. (1999). static and fatigue behaviour of glass-fibre-reinforced polypropylene composites. theor appl fract mech 31, pp. 67–74. doi: 10.1016/s0167-8442(98)00068-8. [9] esmaeillou, b., fitoussi, j., lucas, a., tcharkhtchi, a. (2011). multi-scale experimental analysis of the tension-tension fatigue behavior of a short glass fiber reinforced polyamide composite. procedia eng 10, pp. 2117–2122. doi: 10.1016/j.proeng.2011.04.350. [10] meneghetti, g., quaresimin, m. (2011). fatigue strength assessment of a short fiber composite based on the specific heat dissipation. compos part b eng 42, pp. 217–25. doi: 10.1016/j.compositesb.2010.12.002. [11] toubal, l., karama m, lorrain b. (2006). damage evolution and infrared thermography in woven composite laminates under fatigue loading. int j fatigue 28, pp. 1867–72. doi: 10.1016/j.ijfatigue.2006.01.013. [12] belmonte, e., de monte, m., hoffmann, c.j., quaresimin m. (2017). damage initiation and evolution in short fiber reinforced polyamide under fatigue loading: influence of fiber volume fraction. compos part b eng 113, pp. 331–41. doi: 10.1016/j.compositesb.2017.01.023. [13] wilmes, a., hornberger, k. (2015). influence of fiber orientation and multiaxiality on the fatigue strength of unnotched specimens – lifetime estimation. procedia eng 133, pp. 148–60. doi: 10.1016/j.proeng.2015.12.642. [14] la rosa, g., risitano, a. (200). thermographic methodology for rapid determination of the fatigue limit of materials and mechanical components. int j fatigue 22, pp. 65–73. doi:10. 1016/s0142-1123(99)00088-2. [15] vergani, l., colombo, c., libonati, f. (2014). a review of thermographic techniques for damage investigation in composites. frat ed integrita strutt 8, pp. 1–12. doi: 10.3221/igf-esis.27.01. [16] clienti, c., fargione, g., la rosa, g., risitano, a., risitano, g. (2010). a first approach to the analysis of fatigue parameters by thermal variations in static tests on plastics. eng fract mech 77, pp. 2158–2167. doi: 10.1016/j.engfracmech.2010.04.028. [17] risitano, a., risitano, g. (2013). determining fatigue limits with thermal analysis of static traction tests. fatigue fract eng mater struct 36, pp. 631–639. doi: 10.1111/ffe.12030. [18] colombo, c., vergani, l., burman, m. (2012). static and fatigue characterisation of new basalt fibre reinforced composites. compos struct 2012;94, pp. 1165–1174. doi: 10.1016/j.compstruct.2011.10.007. [19] risitano, g., guglielmino, e., santonocito, d. (2018). evaluation of mechanical properties of polyethylene for pipes by energy approach during tensile and fatigue tests. procedia struct. integr., 13, 1663–1669. doi: 10.1016/j.prostr.2018.12.348. t f. cucinotta et alii, frattura ed integrità strutturale, 59 (2022) 537-548; doi: 10.3221/igf-esis.59.35 548 [20] harizi, w., chaki, s., bourse, g., ourak, m. (2014). mechanical damage assessment of glass fiber-reinforced polymer composites using passive infrared thermography. compos part b eng 59, pp. 74–79. doi: 10.1016/j.compositesb.2013.11.021. [21] crupi, v., guglielmino, e., risitano, g., tavilla, f. (2015). experimental analyses of sfrp material under static and fatigue loading by means of thermographic and dic techniques. compos part b eng 77, pp. 268–277. doi: 10.1016/j.compositesb.2015.03.052. [22] cucinotta, f., d’aveni, a., guglielmino, e., risitano, a., risitano, g., santonocito, d. (2021)thermal emission analysis to predict damage in specimens of high strength concrete. frat ed integrita strutt 15, pp. 258–270. doi: 10.3221/igf-esis.55.19. [23] santonocito, d. (2020). evaluation of fatigue properties of 3d-printed polyamide-12 by means of energy approach during tensile tests. procedia struct integr 25, pp. 355–363. doi: 10.1016/j.prostr.2020.04.040. [24] abello, l.s., marco, y., le saux, v., robert, g., charrier, p. (2013). fast prediction of the fatigue behavior of short fiber reinforced thermoplastics from heat build-up measurements. procedia eng 66, pp. 737–745. doi: 10.1016/j.proeng.2013.12.127. [25] jegou, l., marco, y., le saux, v., calloch, s. (2013). fast prediction of the wöhler curve from heat build-up measurements on short fiber reinforced plastic. int j fatigue 47, pp. 259–267. doi: 10.1016/j.ijfatigue.2012.09.007. [26] arif, m.f., saintier, n., meraghni, f., fitoussi, j., chemisky, y., robert, g. (2014). multiscale fatigue damage characterization in short glass fiber reinforced polyamide-66. compos part b eng 61, pp. 55–65. doi: 10.1016/j.compositesb.2014.01.019. [27] kodeeswaran, m., verma, a., suresh, r., senthilvelan, s. (2017)effects of frequency on hysteretic heating and fatigue life of unreinforced injection molded polyamide 66 spur gears. proc inst mech eng part l j mater des appl 146442071770217. doi: 10.1177/1464420717702176. [28] serrano, l., marco, y., le saux, v., robert, g., charrier, p. (2017). fast prediction of the fatigue behavior of shortfiber-reinforced thermoplastics based on heat build-up measurements: application to heterogeneous cases. contin mech thermodyn, pp. 1–21. doi: 10.1007/s00161-017-0561-2. [29] marco, y., le saux, v., jégou, l., launay, a., serrano, l., raoult, i., (2014). dissipation analysis in sfrp structural samples: thermomechanical analysis and comparison to numerical simulations. int j fatigue 67, pp. 142–150. doi: 10.1016/j.ijfatigue.2014.02.004. [30] katunin, a., wronkowicz, a., bilewicz, m., wachla, d. (2017). criticality of self-heating in degradation processes of polymeric composites subjected to cyclic loading: a multiphysical approach. arch civ mech eng 17, pp. 806–815. doi: 10.1016/j.acme.2017.03.003. [31] iso 527-2:1993. plastics — determination of tensile properties — part 2: test conditions for moulding and extrusion plastics. [32] iso 294-1:1996. plastics — injection moulding of test specimens of thermoplastic materials — part 1: general principles, and moulding of multipurpose and bar test specimens. [33] iso 1873-2:2007. plastics — polypropylene (pp) moulding and extrusion materials — part 2: preparation of test specimens and determination of properties [34] corigliano, p., cucinotta, f., guglielmino, e., risitano, g., santonocito, d. (2020). fatigue assessment of a marine structural steel and comparison with thermographic method and static thermographic method. fatigue fract eng mater struct 43, pp. 734–43. doi: 10.1111/ffe.13158. [35] crupi, v., chiofalo, g., guglielmino, e. (2011). infrared investigations for the analysis of low cycle fatigue processes in carbon steels. proc inst mech eng part c j mech eng sci 225, pp. 833–842. doi: 10.1243/09544062jmes2324. [36] crupi, v., epasto, g., guglielmino, e., risitano, g. (2015). thermographic method for very high cycle fatigue design in transportation engineering. proc inst mech eng part c j mech eng sci ;229, pp. 1260–1270. doi: 10.1177/0954406214562463. [37] corigliano, p., epasto, g., guglielmino, e., risitano, g. (2017). fatigue analysis of marine welded joints by means of dic and ir images during static and fatigue tests. eng fract mech 183, pp. 26–38. doi: 10.1016/j.engfracmech.2017.06.012. [38] handa, k., kato, a., narisawa, i. (1999). fatigue characteristics of a glass-fiber-reinforced polyamide. j appl polym sci 72, pp. 1783–93. doi: 10.1002/(sici)1097-4628(19990624)72:13<1783::aid-app14>3.0.co;2-b. [39] ricotta, m., menegehtti, g., atzori, b., risitano, g. and risitano, a. (2019). comparison of experimental thermal methods for the fatigue limit evaluation of a stainless steel. metals 9(6), pp. 677. doi: 10.3390/met9060677 [40] curà, f., curti, g., sesana, r. (2005). a new iteration method for the thermographic determination of fatigue limit in steels. int j fatigue 27, pp. 453–459. doi: 10.1016/j.ijfatigue.2003.12.009. << /ascii85encodepages false /allowtransparency false /autopositionepsfiles true /autorotatepages /none /binding /left /calgrayprofile (dot gain 20%) /calrgbprofile (srgb iec61966-2.1) /calcmykprofile (u.s. web coated \050swop\051 v2) /srgbprofile (srgb iec61966-2.1) /cannotembedfontpolicy /error /compatibilitylevel 1.4 /compressobjects /tags /compresspages true /convertimagestoindexed true /passthroughjpegimages true /createjobticket false /defaultrenderingintent /default /detectblends true /detectcurves 0.0000 /colorconversionstrategy /cmyk /dothumbnails false /embedallfonts true /embedopentype false /parseiccprofilesincomments true /embedjoboptions true /dscreportinglevel 0 /emitdscwarnings false /endpage -1 /imagememory 1048576 /lockdistillerparams false /maxsubsetpct 100 /optimize true /opm 1 /parsedsccomments true 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/hrv (za stvaranje adobe pdf dokumenata najpogodnijih za visokokvalitetni ispis prije tiskanja koristite ove postavke. stvoreni pdf dokumenti mogu se otvoriti acrobat i adobe reader 5.0 i kasnijim verzijama.) /hun 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can be opened with acrobat and adobe reader 5.0 and later.) >> /namespace [ (adobe) (common) (1.0) ] /othernamespaces [ << /asreaderspreads false /cropimagestoframes true /errorcontrol /warnandcontinue /flattenerignorespreadoverrides false /includeguidesgrids false /includenonprinting false /includeslug false /namespace [ (adobe) (indesign) (4.0) ] /omitplacedbitmaps false /omitplacedeps false /omitplacedpdf false /simulateoverprint /legacy >> << /addbleedmarks false /addcolorbars false /addcropmarks false /addpageinfo false /addregmarks false /convertcolors /converttocmyk /destinationprofilename () /destinationprofileselector /documentcmyk /downsample16bitimages true /flattenerpreset << /presetselector /mediumresolution >> /formelements false /generatestructure false /includebookmarks false /includehyperlinks false /includeinteractive false /includelayers false /includeprofiles false /multimediahandling /useobjectsettings /namespace [ (adobe) (creativesuite) (2.0) ] /pdfxoutputintentprofileselector /documentcmyk /preserveediting true /untaggedcmykhandling /leaveuntagged /untaggedrgbhandling /usedocumentprofile /usedocumentbleed false >> ] >> setdistillerparams << /hwresolution [2400 2400] /pagesize [612.000 792.000] >> setpagedevice microsoft word numero_32_art_2 n. golinelli et alii, frattura ed integrità strutturale, 32 (2015) 13-23; doi: 10.3221/igf-esis.32.02 13 design of a novel magnetorheological damper with internal pressure control nicola golinelli, andrea spaggiari department of sciences and methods for engineering university of modena and reggio emilia, italy nicola.golinelli@unimore.it, andrea.spaggiari@unimore.it abstract. in this work we designed and manufactured a novel magnetorheological (mr) fluid damper with internal pressure control. previous authors’ works showed that the yield stress τb of mr fluids depends both on the magnetic field intensity and on the working pressure. since the increase of the magnetic field intensity is limited by considerations like power consumption and magnetic saturation, an active pressure control leads to a simple and efficient enhancement of the performances of these systems. there are three main design topics covered in this paper about the mr damper design. first, the design of the magnetic circuit; second the design of the hydraulic system and third the development of an innovative pressure control apparatus. the design approach adopted is mainly analytical and provides the equations needed for system design, taking into account the desired force and stroke as well as the maximum external dimensions. keywords. magnetorheological damper; design and manufacturing; squeeze-strengthen effect. introduction owadays, there are several industrial applications in which magnetorheological fluids (mrfs) are used [1-3]. in particular, this paper focuses on the optimal design methodology for magnetorheological dampers (mrds). the purpose of traditional dampers, or so-called shock absorbers, is to dissipate energy. mrds compared to traditional dampers, exploit the change in the rheological behavior of mr fluids in order to achieve variable damping properties. the changing of the properties of mr fluids occurs when a magnetic field is applied. the magnetic field is typically generated by an axial coil, for which connecting leads are usually brought out through the hollow piston rod [4]. the main classification for mrds concerns the methods by which the insertion volume of the rod is accommodated. this is a major design problem because the oil itself is nowhere near compressible enough to accept the internal volume reduction of 10% or more associated with the full stroke insertion. the aim of this work consists in exploiting the effect of pressure on mrfs to generate further controllable damping force, so accommodating the change in volume is very important. clearly, a static pressure can be applied only when nearly incompressible material are used in the system, so no air or gases are allowed in the design. several studies have been carried out in order to comprehend the influence of pressure on the properties of mrfs. in [5], a novel compressible mr fluid has been synthesized with additives that provide compressibility to the fluid. mr fluids are influenced by the presence of internal pressure [6-11]. in combined squeeze-shear mode, with a magnetic field of 300 mt, passing from 0 to 30 bar the yield shear stress to doubles its value. in flow mode instead, with a magnetic field intensity of 800 mt, the yield stress τb increments its value by nearly ten times. there are three basic mrds architectures [4], as is shown in fig. 1: single-tube, double-tube and through-rod. the single-tube architecture (fig. 1a) is based on a single-rod cylinder structure, in which the piston head divides the damper into extension and compression chamber. during piston movement, mr fluid passes through the control valve which is obtained into the piston head. a floating piston separates the mrf from the accumulator filled with compressed n n. golinelli et alii, frattura ed integrità strutturale, 32 (2015) 13-23; doi: 10.3221/igf-esis.32.02 14 gas. the accumulator is used to compensate the volume change due to the piston rod moving inward the cylinder. to eliminate the floating piston, emulsified oil may be used, distributing the expansion and rod-accommodation volume throughout the main oil volume. the gas separates, but quickly re-emulsifies on action. the valves must be rated to allow for the passage of emulsion rather than liquid oil. mineral damper oil has long chain hydrocarbon molecules which do not pack efficiently together. this allows a higher compressibility than a liquid such as water because the long molecular chains can distort. in the double-tube type of telescopic (fig. 1b), a pair of concentric cylinder is used. the external one contains some gas to accommodate the rod displacement volume. the through-rod telescopic (fig. 1c) avoids the displacement volume issue by having a passing-through rod which causes no volume variation. however this has several disadvantages; there are external seals at both ends subject to high pressures that causes additional friction, the protruding free end may be inconvenient or dangerous, and there is still no provision for thermal expansion of the oil. however it is a simple solution which is used for example in some seismic application. even though this architecture has proved impractical for suspension damping, it is sometimes used for damping of the steering. (a) (b) (c) figure 1: telescopic architectures. single-tube (a), double-tube (b) and through-rod (c). materials and methods ince the active control of the pressure is needed, no flexible diaphragms or compressible gases are allowed. this is because flexible parts would absorb the change in pressure. hence, it is necessary an architecture without volume compensation. fig. 2 shows the conceptual scheme of the damper presented in this paper. we used a bottom-rod fixed to the end plug and coupled with the piston head. the bottom-rod has the same diameter of the upper-rod so that there is no volume variation. during piston movement, the bottom-rod is moving inward the chamber obtained into the piston head. the chamber is also directly connected to the canal through the upper-rod in order to bring out the coil’s wire. thereby, overpressure or depression within the chamber will not occur. it is worth noting that two coils were adopted. in this way, the longer axial length of the piston head is exploited to maximize the concatenated magnetic flux. the main dimensions of the damper are shown in tab. 1. cylinder length, (mm) 192 cylinder diameter, (mm) 50 rod diameter, (mm) 20 figure 2: conceptual scheme of the mr damper. table 1: main system dimensions. s n. golinelli et alii, frattura ed integrità strutturale, 32 (2015) 13-23; doi: 10.3221/igf-esis.32.02 15 the design of the mr damper consisted in two main parts: the hydraulic-mechanical design [12, 13] and the magnetic circuit design. the specifications of the damper we developed are listed in tab. 2. maximum force, (n) 2000 maximum cylinder diameter, (mm) 40 maximum working current, (a) 2 maximum pressure, (bar) 40 stroke, (mm) 50 maximum velocity, (mm/s) 100 table 2: damper specifications. in order to keep the manufacturing of the damper as simple as possible, a commercial hydraulic cylinder and the associated cylinder head were chosen [14]. hence, knowing the outer diameter of the cylinder (50 mm) and the wall thickness (5 mm), even the inner diameter of the cylinder was also fixed (40 mm) (fig. 3c, d). the axial length of the hydraulic cylinder is 192 mm. the commercial cylinder head is arranged for a piston rod diameter of 20 mm (fig. 3a) and it has its own system of seals (fig. 3b). the minimum axial length of the piston head was also fixed and had to be at least l = 90 mm. that is because we decided to compensate for the piston volume using the piston head, so it has to host a compensating bottom rod (50 mm), as presented in fig. 2. (a) (b) (c) (d) figure 3: commercial components. cylinder head (a) and sealing system (b). commercial hydraulic cylinder (c) with welded boss. bottom part of the cylinder (d). optimal design of magnetorheological devices requires the knowledge and the characterization of the properties of the materials involved. firstly, the knowledge of the yield shear stress of the fluid as function of the magnetic field is necessary. the yield stress τb hmrf of mrf 140-cg [15] is given by the experimentally-derived equation from [16, 17] and depends on the magnetic field intensity and the particle volume fraction φ:     1.5239 6271700 tanh(6.33 10 )b mrf mrfh c h (1) n. golinelli et alii, frattura ed integrità strutturale, 32 (2015) 13-23; doi: 10.3221/igf-esis.32.02 16 φ is 0.4 and c is a coefficient dependent on the carrier fluid of the mr fluid (c = 1 for hydrocarbons), according to [17] the magnetic b-h relationship of a mr fluid can be defined as [18]:        010.971.133 0 01.91 1    mrfh mrfb e h (2) therefore, a mr fluid’s relative permeability can be defined as:       010.971.133 0 01.91 10.97 mrfhr mrf db e dh (3) where, b is in tesla, hmrf is in a/m, and μ0 = 1.25x10-6 h/m is the permeability of free space. fig. 4 shows the graphs of the b-h relationship of the mrf 140-cg, the values of yield stress τb and the relative magnetic permeability as a function of the magnetic field intensity hmrf. in order to reach the best performances, the material which composes the magnetic circuit should have high magnetic permeability and high magnetic saturation. a material with such properties is the aisi 1010, which is a low-carbon steel (c% < 0.10). this material though, is hardly available because of is being used for niche applications. hence the aisi 430 was used. aisi 430 is a ferritic stainless steel with a high relative magnetic permeability, of about 600. (a) (b) (c) figure 4: mrf 140 cg [15] properties: b-h relationship (a), yield stress τb vs h (b) and relative permeability vs h (c). analytical design of the mr damper fig. 5 shows the forces developed by a magnetorheological damper [19, 20]. considering the parallel-plate bingham model, the forces can be decomposed into three contributions [21]. first, the controllable force fτ, eq. (4), directly correlates with the magnetic field applied through the yield stress τb.    ( )b p a d l a f c sign v h (4) where lp is the axial activation length of the piston head, aa is the annular piston’s area, h is the fluid gap and c is a coefficient that depends on the volumetric flow rate, the viscosity and the yield stress. second, fη, eq. (5), represents the viscous forces and depends on the length of the orifice, the fluid’s viscosity and flow rate.    3 12 aqlaf k wh (5) where q is the flow rate, l is the total axial length of the piston head, w is the mean circumference of the damper’s annular flow path and k is a constant depending on the volumetric flow rate and the velocity. third, ff that stands for the friction forces like those related to the seals system. moreover we should also account for the force derived from the effect of pressure fp. hence, the total force will be obtained by adding up all these contributions:     tot f pf f f f f (6) the dynamic range d, is also a fundamental parameter which provides an estimate of the influence of the control variable on the system behavior. d can be calculated as the controllable forces divided by the uncontrollable forces (eq. 7). n. golinelli et alii, frattura ed integrità strutturale, 32 (2015) 13-23; doi: 10.3221/igf-esis.32.02 17                   fc un f f f ff d f f f (7) figure 5: the total force of mrds can be obtained by summing: friction (dotted blue line), viscous (dashed blue line), magnetic (dashdotted blue line) and pressure (solid red line) driven forces. eq. (4)-(7) were manipulated taking into account the geometrical constraints and the design parameter of the remaining components were determined. in particular, considering that a fluid gap h=1 mm was chosen, the annular area aa is 819.24 mm2 and the viscous forces can be calculated as follow:                       7 3 3 12 122.26 1 100 12 3 10 81954 90 819.24 1 1 191 2 2 81954 122.26 1 d awhv qlaf n q wh (8) in which the velocity vd=100 mm/s and the viscosity η=0.3 pa·s. assuming that the friction forces ff = 250 n and the total force ftot = 2000 n, the required controllable force fτ is:           2000 2000 191 250 1559 ff f f n (9) and the dynamic range turns out to be:                 1559 191 250   4.53   191 250 f f f f f d f f (10) once the controllable force was found, the yield stress of the fluid τb = 20 kpa was set, considering the nominal working current value i = 1 a. the total active pole length is obtainable by manipulating eq.(4):        totp b a f h 1559 1 l 41.32 mm c a 2.30 0.020 819.24 (11) where the coefficient c = 2.30 [12]. the activation areas are four, which implies a single axial length   totp p l l / 4 10 mm. the chosen yield stress implies, by means of the eq. (1)-(2), a magnetic field density bmrf along the active pole of 0.35 t. after that, the piston head (fig. 6a) along with the flange (fig. 6b, c), the rod (fig. 6d) and the bottom-rod (fig. 6e) were manufactured. the piston head and the flange were made of aisi 430. conversely, the rod and the bottom-rod were made of brass because they do not have to influence the magnetic flux during operations. the flange is coupled with the rod by a drilled screw in order to let the coil’s wire passing through it (fig. 6f). n. golinelli et alii, frattura ed integrità strutturale, 32 (2015) 13-23; doi: 10.3221/igf-esis.32.02 18 (a) (b) (c) (d) (e) (f) figure 6: custom components. piston head (a), flange (b, c), rod (d) and bottom-rod with end plug (e). coupling between rod and flange (f). design of the magnetic circuit the aim in the design of a magnetic circuit is to determine the necessary amp-turn (ni) able to develop the required magnetic field and therefore the required damping forces. an optimal design requires to reach the desired magnetic field induction in the fluid gap while minimize the energy lost in steel flux conduit and region of non-working area. the entire circuit should have low reluctance, so soft iron or high permeability steel should be used. for an mr liquid, the permeability may be quite low, as shown in fig. 4c. at high flux density, the iron may saturate, and be a limiting factor, so the cross-section of the iron must be adequate all around the magnetic circuit. the total flux in the circuit is the same at all sections around the circuit, so the critical point of the iron is the part with the lower cross-sectional area. the number of coils may vary to meet system requirements. fig. 7a shows the most common configuration in which the flux lines flow around a single coil. the last two configurations in fig. 7 have multiple coils and similar characteristics, except for the polarity of the magnetic field. in configuration fig. 7b, the magnetic flux lines have all one only direction from the center of the solenoid. in configuration fig. 7c, there is a trade-off between the different coils, which also affects the circuit length. the main advantage of this solution is a decrease of the overall inductance of the circuit that allows, compared to other, less response time of the same device. (a) (b) (c) figure 7: coil configurations. single coil (a), coherent multiple coils (b), incoherent multiple coils (c). the typical design process for a magnetic circuit can be summarized as follow [14]:  determine the magnetic induction bmrf in the mr fluid to give the desired yield stress τb.  determine the magnetic field intensity hmrf by using the b-h relationship of the fluid.  the magnetic induction flux is given by      mrf mrfb a , in which amrf is the effective area of activation of the fluid. since the magnetic induction flux remains constant through all the circuit length, calculate the magnetic induction in the steel bsteel: n. golinelli et alii, frattura ed integrità strutturale, 32 (2015) 13-23; doi: 10.3221/igf-esis.32.02 19     mrf mrfsteel steel steel b a b a a (12)  determine the magnetic field induction bsteel using its b-h relationship.  find the required number of amp-turns (ni) by using kirchhoff’s law of magnetic circuits:     i i mrf steelni h l h h h l (13) where h is the fluid gap and l is the single length of each links which compose the circuit. the required number of coil wire resulted n = 160, considering a working current of 1 a. 304 stainless steel air 304 stainless steel 430 stainless steel air rubber rubber air 20 awg [ i :153] 1020 steel 20 awg [ -i :152] 430 stainless steel density plot: |b|, tesla 1.276e+000 : >1.343e+000 1.142e+000 : 1.209e+000 1.074e+000 : 1.142e+000 9.401e-001 : 1.007e+000 8.730e-001 : 9.401e-001 8.058e-001 : 8.730e-001 7.387e-001 : 8.058e-001 6.715e-001 : 7.387e-001 6.044e-001 : 6.715e-001 5.372e-001 : 6.044e-001 4.701e-001 : 5.372e-001 4.029e-001 : 4.701e-001 3.358e-001 : 4.029e-001 2.686e-001 : 3.358e-001 2.015e-001 : 2.686e-001 1.343e-001 : 2.015e-001 6.715e-002 : 1.343e-001 <0.000e+000 : 6.715e-002 1.209e+000 : >1.276e+000 1.007e+000 : 1.074e+000 (a) (b) (c) (d) figure 8: 2d femm model of the piston head (a), magnetic field values through the magnetic circuit (b). magnification of the central activation area (c) and graph of the magnetic field values b across the activation’s gap along the red line (d). magnetic finite element analysis magnetic finite element analysis was performed after the analytical design of the circuit. this operation is a useful method to compare the calculated values with the simulated ones. furthermore, these simulations allow one to verify that the magnetic saturation will occur in no section of the magnetic circuit. the software femm v4.2 [22] a n. golinelli et alii, frattura ed integrità strutturale, 32 (2015) 13-23; doi: 10.3221/igf-esis.32.02 20 was adopted to perform all the simulations. fig. 8a represents the discretized axially-symmetric model of the magnetic circuit which comprehends part of the piston head, the flange and the cylinder’s wall. the material chosen came from the femm material library. aisi 430 was used for the piston head and the flange. since the material of the hydraulic cylinder is not clearly identified by the producer, a plausible material in terms of magnetic properties was used, which is aisi 1020. for the mr fluids, a new material was set up with the magnetic properties described by eq. (2). fig. 8b shows the path of the magnetic flux and the values of the magnetic field density resulted whit a working current of 1 a. as it can be seen the values of b are lower than 1.5 t that is a critical point after which begins saturation. at the beginning of the design, considering the damping force required and a current of 1 a, a yield stress τb = 20 kpa was needed. that implied a magnetic field of bmrf = 350 mt along the activation area. fig. 8c represents a magnification of the central activation area along with the magnetic flux lines and in fig. 8d the relative values of magnetic field. the simulated values of magnetic field density are slightly lower than those desired. a possible explanation is that the magnetic properties of the aisi 1020 do not match exactly those of the original material, which is fe 510. pressurization system he aim of the pressurization system is the active regulation of the fluid pressure. this task has to be done in a totally controllable manner without the aid of volumetric pumps, which are incompatible with mr fluids because of the too high viscosity. moreover, in hydraulic centralized circuits that use volumetric pumps the pressure regulation is quite expensive in terms of energy required because both the circuit and the control unit have to be constantly working in order to maintain the desired pressure. contrarily, the new system presented does not need a continuous supply of electrical power. the designed pressurization system is schematically shown in fig. 9. (a) (b) figure 9: pressurization system. low pressure configuration (a) and high pressure configuration (b). the system is composed of a stepper motor that converts the motion from rotary to translatory by a screw and nut mechanism. this system controls a slider that insists on the volume of mr fluid. lowering the volume of fluid causes an increase of the internal pressure. such system would be energetically convenient compared with other linear actuators currently present on market, for example coil valves. indeed, due to the friction forces between the threads there is no retrograde motion. hence, the desired static pressure level can be maintained with no power consumption. the mr fluid t n. golinelli et alii, frattura ed integrità strutturale, 32 (2015) 13-23; doi: 10.3221/igf-esis.32.02 21 used is a silicone-based fluid that is quite compressible (bulk modulus β of about 1000 mpa) so a pressure control not excessively abrupt is allowed. considering the low compressibility of the fluid, varying the value of pressure requires slider’s strokes of few millimeters. the stroke of the slider is calculated analytically knowing the bulk modulus β, the total volume of the fluid v and the desired pressure variation. the equations involved are:      p v v (14)      v v p (15)    cu v x a (16) by combining eq. (15)-(16):     cu v x p a (17) in which acu is the area of the slider. stepper motors are the most suitable for this application. by knowing the number of steps and the screw pitch an accurate control of the slider’s stroke ∆x is possible without position sensor. results and discussions ig. 10 shows the section of the 3d model of the damper. to allow the assembly, the piston head is composed of two parts: the main body of the piston head and the flange. the flange connects the piston head to the upper-rod using four screws m4x6. particular attention was paid for the sealing system. a dynamic rod seal was used between the bottom part of the piston head and the bottom rod. moreover, two static seal (o-ring) were adopted between the flange and the inner chamber of the piston head. as it can be seen in fig. 11, the coil wires pass through the drilled screw, the flange and the rod. figure 10: cross-sectional view of the prototype of the damper. figure 11: exploded view. (from the right) piston head, drilled screw, flange, rod and cylinder head. f n. golinelli et alii, frattura ed integrità strutturale, 32 (2015) 13-23; doi: 10.3221/igf-esis.32.02 22 the end-plug and the bottom-rod were glued to the cylinder using an acrylic adhesive (loctite 638). the mr fluid was poured through the welded boss into the cylinder. to eliminate the air into the damper, the system was placed in a vacuum chamber. then, two ball joint ends were screwed to the rod and the end plug (fig. 12). figure 12: final assembled prototype. conclusion his work shows a design method for a magnetorheological damper with pressure control. by means of analytical equations the magnetic circuit and the hydraulic circuit have been designed. the new mr damper has an innovative architecture able to drive the internal pressure level. a bottom-rod has been adopted which has the same diameter of the upper rod. the main consequence is that the internal volume of the damper remains constant during the operation and an accumulator is no more needed. in order to increase the feasibility of the prototype, commercial components were used: a hydraulic cylinder, its cylinder head and two ball joint ends. instead, the piston rod, the piston head and the bottom rod were designed and manufactured. finally, all components were assembled paying particular attention to the concentricity between the cylinder, the piston head and the bottom rod. a conceptual design of pressurization system has also been presented. such system consists of a screw drive mechanism that controls the stroke of a slider. moving the slider leads to control the internal volume of the damper and consequently changes the internal pressure. to our best knowledge the prototype presented is the first of its kind ever realized. several tests will be carried out to test the behavior of this device. the results might bring up new considerations that could lead to an optimization of the properties of the damper and to its commercialization. bibliography [1] kaluvan, s., choi, s.-b., design of current sensor using a magnetorheological fluid in shear mode, smart mater. struct., 23(12) (2014) 127003. [2] alkan, m. s., gurocak, h., gonenc, b., linear magnetorheological brake with serpentine flux path as a high force and low off-state friction actuator for haptics, j. intell. mater. syst. struct., 24(14) (2013) 1699–1713. [3] yadmellat, p., kermani, m. r., adaptive modeling of a magnetorheological clutch, ieee/asme trans. mechatronics, 19(5) (2014) 1716–1723. [4] zhu, x., jing, x., cheng, l., magnetorheological fluid dampers: a review on structure design and analysis, j. intell. mater. syst. struct., 23(8) (2012) 839–873. [5] fuchs, a., rashid, a., liu, y., kavlicoglu, b., sahin, h., gordaninejad, f., compressible magnetorheological fluids, j. appl. polym. sci., 115(6) (2010) 3348–3356. [6] spaggiari, a., dragoni, e., effect of internal pressure on flow properties of magnetorheological fluids, in: asme 2011 conference on smart materials, adaptive structures and intelligent systems, 1 (2011) 7–15. [7] spaggiari, a., dragoni, e., effect of pressure on the physical properties of magnetorheological fluids, fract. struct. integr., 23 (2012) 75–86. [8] spaggiari, a., dragoni, e., combined squeeze-shear properties of magnetorheological fluids: effect of pressure, j. intell. mater. syst. struct., 25(9) (2013) 1041–1053. t n. golinelli et alii, frattura ed integrità strutturale, 32 (2015) 13-23; doi: 10.3221/igf-esis.32.02 23 [9] becnel, a. c., wereley, n. m., demonstration of combined shear and squeeze strengthening modes in a searle-type magnetorheometer, in: development and characterization of multifunctional materials; modeling, simulation and control of adaptive systems; integrated system design and implementation, 1 (2013) v001t03a036. [10] tang, x., zhang, x., tao, r., rong, y., structure-enhanced yield stress of magnetorheological fluids, j. appl. phys., 87(5) (2000) 2634. [11] guo, c., gong, x., xuan, s., qin, l., yan, q., compression behaviors of magnetorheological fluids under nonuniform magnetic field, rheol. acta, 52(2) (2013) 165–176. [12] nguyen, q., choi, s., optimal design methodology of magnetorheological fluid based mechanisms, smart actuation sens. syst., (2012). [13] nguyen, q.-h., choi, s.-b., optimal design of a vehicle magnetorheological damper considering the damping force and dynamic range, smart mater. struct., 18(1) 2009) 015013. [14] gavin, h., hoagg, j., dobossy, m., optimal design of mrf dampers, in: u.s. japan workshop on smart structures for improved seismic performance in urban regions, (2001) 225–236. [15] l. corporation, mrf-140cg magneto-rheological fluid. http://www.lord.com/products-and-solutions/magnetorheological-(mr)/product.xml/1646. (2014) [16] carlson, j. d., magnetorheological fluids, in smart materials, new york, ny, usa: crc press, (2008). [17] lee, j.-h., han, c., ahn, d., lee, j. k., park, s.-h., park, s., design and performance evaluation of a rotary magnetorheological damper for unmanned vehicle suspension systems, scientific world journal., (2013) 894016. [18] wereley, n. m., magnetorheology: advances and applications. royal society of chemistry, (2013). [19] jang, k.-i., min, b.-k., seok, j., a behavior model of a magnetorheological fluid in direct shear mode, j. magn. magn. mater., 323(10) (2011) 1324–1329. [20] yang, g., large-scale magnetorheological fluid damper for vibration mitigation: modeling, testing and control, university of notre dame, (2001). [21] yang, g., spencer, b. f., carlson, j. d., sain, m. k., large-scale mr fluid dampers: modeling and dynamic performance considerations, eng. struct., 24(3) (2002) 309–323. [22] meeker, d., femm 4.2 finite element method magnetics homepage. http://www.femm.info/wiki/homepage, (2015). microsoft word numero_31_art_4 a. abrishambaf et alii, frattura ed integrità strutturale, 31 (2015) 38-53; doi: 10.3221/igf-esis.31.04 38 the influence of fibre orientation on the post-cracking tensile behaviour of steel fibre reinforced self-compacting concrete a. abrishambaf, v.m.c.f. cunha, j.a.o. barros isise, dep. civil eng., school eng., university of minho, campus de azurém 4800-058 guimarães, portugal. vcunha@civil.uminho.pt abstract. adding fibres to concrete provides several advantages, especially in terms of controlling the crack opening width and propagation after the cracking onset. however, distribution and orientation of the fibres toward the active crack plane are significantly important in order to maximize its benefits. therefore, in this study, the effect of the fibre distribution and orientation on the post-cracking tensile behaviour of the steel fibre reinforced self-compacting concrete (sfrscc) specimens is investigated. for this purpose, several cores were extracted from distinct locations of a panel and were subjected to indirect (splitting) and direct tensile tests. the local stress-crack opening relationship (σ-w) was obtained by modelling the splitting tensile test under the finite element framework and by performing an inverse analysis (ia) procedure. afterwards the σ-w law obtained from ia is then compared with the one ascertained directly from the uniaxial tensile tests. finally, the fibre distribution/orientation parameters were determined adopting an image analysis technique. keywords. fibre dispersion and orientation; self-compacting concrete; tensile behaviour; splitting tensile test; inverse analysis. introduction dding fibres to concrete provides several advantages, especially in terms of controlling the crack opening width and propagation, increasing the energy absorption capacity, as well as increasing the post-cracking tensile strength [1, 2]. in composites reinforced with low fibre contents, the contribution of the fibres mainly arises after the crack initiation. crack opening in steel fibre reinforced concrete (sfrc) is restrained by the bond stresses that develop at the fibre / matrix interface during the fibre pull-out. moreover, one of the most important properties of sfrc is its ability to transfer stresses across a cracked section rather uniformly, which depends on the fibre reinforcement effectiveness, i.e. fibre properties (their strength, bond and stiffness), and fibre distribution/orientation towards the active crack plane [3]. in order to optimize the fibre contribution to the post-cracking behaviour, it is important to enhance the distribution and orientation of the fibres at the crack plane. since, fibres are more effective fairly aligned along the principal tensile stresses directions [4, 5]. the dispersion and orientation of fibres in the sfrc bulk hardened-state results from a series of stages, namely [6]: fresh-state properties after mixing; casting conditions into the formwork; flowability properties; and wall-effect introduced by the formwork. among the aforementioned parameters, flowability of steel fibre reinforced self-compacting concrete (sfrscc) is the most important one [7-9]. having in mind that distribution/orientation of the fibres influences significantly the mechanical properties of the sfrscc, it is important to control and consider both parameters, especially in terms of the design applications. a a. abrishambaf et alii, frattura ed integrità strutturale, 31 (2015) 38-53; doi: 10.3221/igf-esis.31.04 39 in this research, the effect of fibre distribution and orientation on the tensile behaviour of a sfrscc panel is investigated. for this purpose, a total number of 46 cores were extracted from various locations of two panels. these cores were subjected to indirect (splitting) and direct (uniaxial) tensile tests. in order to assess the influence of fibre distribution/orientation on the tensile post-cracking parameters, specimens were notched either parallel or perpendicular to the expected concrete flow direction. furthermore, fibre distribution parameters were evaluated through an image analysis procedure. finally, the local stress-crack opening relationship (σ – w) was obtained by modelling the splitting tensile test under the finite element framework and by performing an inverse analysis (ia) procedure. afterwards the σ-w law obtained from ia is then compared with the one ascertained directly from the uniaxial tensile tests. experimental program concrete mixture steel fibre reinforced self-compacting concrete was design with 60 kg/m3 of hooked-end steel fibres (length, lf, of 33 mm; diameter, df, of 0.55 mm; aspect ratio, lf /df , of 60 and a yield stress of 1100 mpa).the mixture constituents are: cement (c), water (w), limestone filler (f), fine sand (fs), coarse sand (cs), coarse aggregate (ca) and superplasticizer (sp). tab. 1 includes the adopted concrete mix composition. in order to evaluate the flowability of the concrete, the slump test was performed according to the efnarc recommendations [10]. the total spread achieved on the slump test was about 670 mm. the young’s modulus and compressive strength were assessed on cylinders with a diameter of 150 mm and height of 300 mm. the average compressive strength (fcm) and the average value of the young’s modulus (ecm) were 47.77 mpa (7.45%) and 34.15 gpa (0.21%), respectively, in which the values in parentheses represent the coefficient of variation. c [kg] w [kg] sp [kg] f [kg] fs [kg] cs [kg] ca [kg] fibre [kg] 413 140 7.83 353 237 710 590 60 table 1: mix composition of steel fibre reinforced self-compacting concrete per m3. 1600 (mm) 1000 (mm) 1600 (mm) 1000 (mm) (a) (b) figure 1: core extracting plan: (a) panel a, (b) panel b. specimens according to barnett et al. [11] casting panels from its centre point can improve the mechanical behaviour, when comparing to other casting methods. thus this method was selected for the production of two panels. the dimensions of the panels were 1600×1000×60 mm3. in order to evaluate the influence of fibre dispersion and orientation on the tensile properties of the sfrscc, twenty three cores were extracted from each panel, and submitted to either indirect (splitting) or direct (uniaxial) tensile tests. the specimens were extracted according to the scheme represented in fig. 1. in this figure the pale dash lines with arrows represent the supposed concrete flow directions. the hatched cores were used in the splitting tensile tests and the remaining was used in the uniaxial tensile tests. for the execution of the splitting tensile tests, two notches were executed on the cores’ opposite sides with the depth of 5 mm. in order to evaluate the influence of crack orientation towards the concrete flow, specimens were notched either parallel or perpendicular toward the expected a a. abrishambaf et alii, frattura ed integrità strutturale, 31 (2015) 38-53; doi: 10.3221/igf-esis.31.04 40 flow direction. by assuming θ as the angle between the notched plane and the direction of the concrete flow, the notch plane was designated parallel for θ = 0° or perpendicular for θ = 90°. since the core scheme was maintained for both panels, for each core location within the panel there were two cores with distinct notch directions, i.e. θ = 0 or 90º. this will enable to evaluate the influence of fibre orientation on the stress-crack width (σ-w) relationship. for instance, θ of a1 specimen is 90° and 0° in panels a and b, respectively (see fig. 1). twenty two cores were sawn to produce prismatic specimens to be used in the uniaxial tensile test with the dimensions of 110×102×60 mm3. following the same notching procedure for the splitting test specimens, the prismatic specimens were notched according to parallel (θ = 0°) and perpendicular (θ = 90°) directions regarding the expected concrete flow. the notch was executed on the four lateral faces of the specimen, at their mid-height, with a thickness of 2 mm and a depth of 5 mm. test setup: splitting tensile test in a first stage, the σ – w relationship was assessed by carrying out splitting tensile tests. the recommendations of astm c-496 standard [12] were followed for this purpose. the tests were executed by closed-loop displacement control. to ensure a proper constant displacement rate, once the crack is initiated, a rather low value of the displacement rate, i.e. 0.001 mm/s, was applied. the crack opening width was averaged from the readouts of five linear variable differential transducers, lvdts, which were mounted on the surface of the specimen, three on the top and two on the bottom surfaces, see fig. 2. 10.0 65.0 65.0 10.0 150.0 37.5 37.5 37.5 37.5 lvdt specimen 60.0 (a) (b) figure 2: geometry of the specimen and setup of the splitting tensile test (dimensions are in mm): (a) specimen front view (top of the panel), (b) specimen lateral view. test setup: uniaxial tensile test the stress – crack opening width (σ – w) relationship was also directly ascertained through uniaxial tensile tests, which were executed according to the rilem tdf-162 [13]. this test was carried under closed-loop displacement control, adopting the following displacement rates during the test: 0.005 mm/min up to a displacement of 0.05 mm, 0.02 mm/min up to a displacement of 0.1 mm, 0.08 mm/min up to a displacement of 0.5 mm, and 0.1 mm/min until the completion of the test. the test was controlled by the averaging signal received from the four lvdts installed on the lateral surface of each prismatic specimen, see fig. 3. 11 0 60 (a) (b) figure 3: uniaxial tensile test setup: (a) specimen front view, (b) specimen lateral view (units in mm) a. abrishambaf et alii, frattura ed integrità strutturale, 31 (2015) 38-53; doi: 10.3221/igf-esis.31.04 41 results and discussion: splitting tensile test fig. 4 depicts both the envelope and average force – crack mouth opening response (f – w) obtained from the splitting tensile tests, when the notch direction was parallel (θ = 0°) and perpendicular (θ = 90°) to the concrete flow direction. during the first phase of the test, the f w relationships were almost linear up to the load at the crack onset, since the lvdts recorded the elastic deformation of the sfrscc specimen. therefore this deformation should have been removed from the f w curves, however since this deformation was marginal it could be neglected. after the crack onset, two distinct behaviours were observed for the θ = 0º and 90° series. regarding the θ = 0º series (fig. 4(a)), the composite exhibited a non-linear hardening behaviour until the peak load was attained, followed by a softening phase. on the other hand, for θ = 90º series it was observed just a softening phase immediately after the crack onset. briefly, these differences between the θ = 0º and 90° series could be ascribed to rather distinct number of fibres intersecting the crack plane at the specimens’ notch, due to a preferential fibre alignment perpendicular to the concrete flow direction. the higher number of fibres at the crack plane of the θ = 0º series specimens will promote a higher stress transfer grade between the crack surfaces and, consequently, higher post-cracking residual forces. the aspects related to the fibre distribution / orientation will be detailed further ahead. 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 0 10 20 30 40 50 60 70 80 envelope average f o rc e ( f ) [k n ] w [mm] 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 0 10 20 30 40 50 60 70 80 envelope average f o rc e ( f ) [k n ] w [mm] (a) (b) figure 4: force – crack opening width relationship, f – w, obtained from splitting tensile test for: (a) θ=0° and (b) θ = 90°. in general, the f – w relationship showed a high scatter. however, in the case of sfrscc the scattering in the results was expected since the mechanical behaviour of this material was significantly dependent on the fibre dispersion/orientation, even for specimens with same geometry and from the same batch. moreover, in this particular case the relatively high scatter could also be enhanced because the specimens were extracted from different locations of the panels, i.e. with distinct distances from the casting point. note that during the casting of the panels, the fibre distribution /orientation was influenced by the viscosity and velocity of the fresh concrete along the flowing process. 0.0 0.5 1.0 1.5 2.0 2.5 3.0 0 10 20 30 40 50 60 70 top average bottom f o rc e [ k n ] w [mm] 0.0 0.5 1.0 1.5 2.0 2.5 3.0 0 10 20 30 40 50 60 70 top average bottom f o rc e [ k n ] w [mm] (a) (b) figure 5: nominal tensile stress – crack opening width relationship, σ– w, obtained from splitting tensile test for the two sides (top and bottom) of the specimens: (a) θ = 0° and (b) θ = 90°. figs 5(a) and 5(b) show three average f – w relationships obtained with the splitting tensile test for specimens from the θ = 0º and 90° series, respectively. the “average” curve was obtained by averaging the readouts of the five lvdts flow direction notch direction flow direction notch direction flow direction notch direction flow direction notch direction a. abrishambaf et alii, frattura ed integrità strutturale, 31 (2015) 38-53; doi: 10.3221/igf-esis.31.04 42 mounted on the specimen, whereas the “top” and “bottom” curves were obtained by averaging only the readouts of the lvdts mounted, respectively, at the upper and lower specimen’s surface. from fig. 5 it was visible that the readouts of the lvdts mounted on the upper surface of specimens showed a relatively higher crack opening width compared to the one recorded by the lvdts at the lower specimen surface. this denotes that the crack opened asymmetrically, which could be ascribed to the variation of effective fibres along the depth of the panel due to segregation. this aspect will be detailed further ahead, when the fibre distribution parameters are endorsed. results and discussion: uniaxial tensile test figs 6(a) and 6(b) illustrate the average and envelope force-crack mouth opening relationship obtained from the uniaxial tensile test for the θ = 0º and 90° series, respectively. the value of the crack opening was determined by averaging the readouts of the four lvdts. for both series (θ = 0° and 90°), the f w curve was almost linear up to the crack initiation. after the crack onset, two distinct behaviours were observed for the θ = 0º and 90° series similarly to what was observed in splitting tensile tests, which could also be ascribed to the distinct number of fibres at the crack plane. 0.0 0.5 1.0 1.5 2.0 2.5 0.0 2.5 5.0 7.5 10.0 12.5 15.0 17.5 20.0 22.5 25.0 envelope average f o rc e [ k n ] w [mm] 0.0 0.5 1.0 1.5 2.0 2.5 0.0 2.5 5.0 7.5 10.0 12.5 15.0 17.5 20.0 22.5 25.0 envelope average f o rc e [ k n ] w [mm] (a) (b) figure 6: force – average crack width relationship, fw, obtained from the uniaxial tensile tests: (a) θ = 0° and (b) θ = 90°. regarding the θ = 0º series, fibres start to be slowly pulled-out being observed a semi-hardening response after the crack onset. afterwards a plateau response was observed until a crack width of about 0.6 mm, and finally it was followed by a smooth reduction in the residual forces. actually, during the uniaxial tensile testing of the θ = 0º specimens, once the peak load was achieved the sound of the fibre rupturing was clearly heard, which caused a rapid reduction in the value of the residual forces. this was also confirmed by inspecting the fracture surface visually after the specimen testing. based on pull-out tests of hooked end fibres [14], fibre rupture may occur between the slip intervals of 0.6-1.0 mm, for the fibre inclination angle with the loading direction of 30°. as it will be discussed further ahead, for this series the most probable fibre orientation angle towards the cracking plane was around about 35º, this value was derived from the orientation probability distribution ascertained from an image analysis procedure. on the other hand, the θ = 90º series, after the crack initiation, shown a sudden force decrease up to a crack width of nearby 0.07 mm followed by a plateau. cunha et al. [5] assessed the micro-mechanical behaviour of hooked end fibres by performing fibre pull-out test. it was verified that after a fibre sliding of nearby 0.1 mm, the fibre reinforcement mechanism was mainly governed by the hook plasticization during the fibre pull-out process. additionally, in some specimens of the θ = 90º series, in particular those located closer to the casting point, shown a pseudo-hardening behaviour as it can be observed by the upper bound of the experimental envelope (fig. 6(b)). afterwards, beyond a crack width of about 0.9 mm, a reduction of the residual force was observed, which corresponded to the fibre rupture. results and discussion: evaluation of fibre distribution parameters in order to assess the distribution and orientation of fibres, an image analysis technique was implemented due to its simplicity and relatively low cost [15, 16]. this technique comprised of four main stages: in the first stage, the fracture surface of the specimen was grinded. then the surface was polished by acetone in order to increase the reflective properties of steel fibres. secondly, by using a high resolution digital photograph camera, a coloured image of the grinded surface was obtained. finally, the achieved image was analysed using imagej [17] software to recognize steel fibres. the analysis procedure of an image was depicted in fig.7. after analysing the results, the following parameters were derived out: flow direction notch direction flow direction notch direction a. abrishambaf et alii, frattura ed integrità strutturale, 31 (2015) 38-53; doi: 10.3221/igf-esis.31.04 43 i) number of fibres per unit area, fn : is the ratio between the total number of fibres counted in the image, ftn , and the total area of the image, a: f f tn n a (1) ii) fibre orientation factor,  : determined as the average orientation towards a certain plane surface by eq. 2: 1 1 . cos f tn if itn      (2) where, ftn is the total number of fibres that can be determined by counting all the visible ellipses and circles at the cross section, θ is the out-plane angle that is defined as the angle between the fibre’s longitudinal axis and a vector orthogonal to the plane. iii) fibre segregation parameter, seg : to calculate the location of the steel fibres gravity centre, an average value of the coordinates in the y axis of entire fibres should be determined in the analysed cross-section. 1 1 . . f tn seg f it y h n     (3) in this equation, y is the coordinate in the y axis of the fibre’s gravity centre, and h is the height (or depth) of the analysed cross-section, iv) number of effective fibres per unit area, feffn : the summation of fibres with deformed hooked in a unit area. since this parameter cannot obtain from the image analysis results, therefore it was executed by visual inspection of the fracture surface. (a) (b) (c) (d) figure 7: image processing steps: (a) converting a colored image to greyscale image (b) adjusting a threshold, (c) defining mask, noise (remove small noises) and watershed (separated fibres that are stuck together) functions, (d) fitting the best ellipse to each fibre. tab. 2 includes the results of the image analysis performed on a plane surface of the uniaxial tensile specimens, see fig. 8. the fibre distribution parameters were assessed on two orthogonal planes for each core location regarding to panel centre point (fig. 1). the θ = 0° series presented a considerably higher average fn and feffn , about 80% and 254%, respectively, when compared to the θ =90° series. the differences between these series corroborate that the fibres were preferentially reoriented due to the concrete flow. this could be clearly noticed if the orientation parameter,  , for each series was a. abrishambaf et alii, frattura ed integrità strutturale, 31 (2015) 38-53; doi: 10.3221/igf-esis.31.04 44 compared (see tab. 2). on the other hand, when the notch plane was parallel to concrete flow direction, a higher orientation factor observed comparing to specimens with θ =90°. therefore, in θ = 0° series, a higher number of the effective fibres in the fracture surface was appeared which increased the concrete fracture parameters. regarding the fibre segregation factor, the obtained average values of seg were insignificantly higher than 0.5 meaning that a slight fibre segregation occurred through the panel’s depth. this could also justify the asymmetric crack opening width observed in the splitting tensile specimens. θ=0° θ=90° specimen distance [cm] f n [fibres/cm2] f eff n [fibres/cm2] ηθ [-] seg [-] f n [fibres/cm2] f eff n [fibres/cm2] ηθ [-] seg [-] b3 20.0 2.071 1.291 0.827 0.580 1.557 0.405 0.688 0.476 a4 23.5 1.889 1.356 0.855 0.518 1.430 0.506 0.737 0.510 c4 32.0 2.036 1.430 0.851 0.555 0.665 0.133 0.630 0.597 d3 32.0 1.913 0.853 0.775 0.491 1.436 0.415 0.666 0.586 b4 40.0 1.956 0.851 0.773 0.530 0.506 0.074 0.561 0.643 a5 46.5 2.220 1.212 0.814 0.479 1.097 0.311 0.672 0.725 a6 69.5 2.304 1.803 0.866 0.557 0.967 0.132 0.604 0.539 c6 77.5 2.142 1.303 0.818 0.600 1.232 0.541 0.756 0.485 d1 77.5 1.921 1.089 0.795 0.532 1.355 0.631 0.760 0.594 average 2.050 1.24 0.820 0.538 1.138 0.35 0.675 0.573 cov (%) 7.16 23.74 4.15 7.33 31.98 57.11 10.20 14.00 table 2: fibre distribution parameters. 102 60 110 figure 8: localization of the plane surface considered in the fibre distribution assessment (units in mm). fig. 9 illustrates the orientation profiles obtained for each average orientation factor in comparison to both the twodimensional (2d) distribution,  = 2/π, [18] and the three-dimensional (3d) isotropic uniform random fibre distribution,  = 0.5, [19]. it was shown that the fibre orientation profile followed a gaussian distribution [20, 21]. the orientation profile for θ= 0°series was represented by a distribution shifted to the left side, while for θ= 90° series the distribution profile tends to the right side. therefore, within the specimens of θ= 0° series, fibres have a tendency to be aligned more perpendicular to the studied plane. the obtained distribution profile for the θ= 0° series was completely distinct from either the 2d or 3d theoretical isotropic uniform random distributions. meanwhile, the distribution obtained for the θ= 90° series was very similar to the 2d theoretical distribution. in conclusion, for sfrscc laminar structures, assuming a 2d or 3d uniform fibre random distribution may be far from the reality, since the influence of fibre orientation due to the concrete flow also needs to be taken in to the account. fig. 10 shows the exponential relationship between the number of fibres, fn , and effective fibres, feffn . a. abrishambaf et alii, frattura ed integrità strutturale, 31 (2015) 38-53; doi: 10.3221/igf-esis.31.04 45 (a) (b) figure 9: predicted orientation profile: (a) θ=0° and (b) θ=90°. 0.00 0.25 0.50 0.75 1.00 1.25 1.50 1.75 2.00 0.25 0.50 0.75 1.00 1.25 1.50 1.75 2.00 2.25 2.50 exponential tendency r-square=0.90 n f [] nfeff [-] figure 10: number of the fibres, fn , versus number of the effective fibres, feffn . numerical simulation he most suited test to derive the mode i fracture parameters is the uniaxial tensile test. however, the latter test involves some difficulties such as: the necessity of specialized and expensive equipment; sophisticated test set-up to avoid detrimental interferences, like load eccentricity, since it decreases the stress at the onset of crack initiation [22]. on the other hand the splitting tensile test could be considered as an alternative option for this purpose, because it is cheaper, less sophisticated testing equipment is needed, and can be executed on both cubes and extracted cores. in this section a methodology to predict the stress – crack width (σ – w) relationship of sfrscc using an inverse analysis, ia, procedure based on the results of the splitting tensile test will be presented and discussed. for this purpose, numerical simulations of the splitting tensile tests were carried out with a nonlinear 3d finite element model. in order to confirm the accuracy of the proposed methodology, the σ – w response obtained through the ia of the splitting test results was compared to the σ – w response obtained from the uniaxial tensile test. modelling and simulation the average experimental force – crack width responses of the splitting tensile tests (fig. 4) were simulated using abaqus® finite element software [23]. eight-node hexahedral shape solid elements with 8-integration points were used. the concrete damage plasticity model was implemented in order to simulate mechanical properties of concrete [24, 25]. because of the symmetry in the specimen geometry, supports and test loading applied in the splitting tensile test, only a quarter of the core was simulated, see fig. 11(a). since the specimen had distinct thicknesses it consists of two main parts namely: notch and un-notch (flush). after meshing each part individually, the assembled mesh is shown in fig. 11(b) with a total number of 5674 elements. similar to the performed in the experimental procedure, in the numerical simulation a prescribed displacement was applied on top of the notch. t a. abrishambaf et alii, frattura ed integrità strutturale, 31 (2015) 38-53; doi: 10.3221/igf-esis.31.04 46 (a) (b) figure 11: three-dimensional view of numerical model [24]: (a) geometry, constraints and prescribed displacement, (b) finite element mesh. concrete constitutive model the concrete damage plasticity, cdp, model was used to simulate the mechanical performance of concrete because it is proficient to model the cracking of concrete in tension and crushing in compression. on the other hand, this model uses the concept of isotropic damage elasticity in combination with isotropic compression and tension plasticity to simulate the inelastic behaviour of concrete under compressive and tensile stresses. the cdp model uses a yield surface that is defined as the loading function proposed by lubliner et al. [26]. the evaluation of the yield surface is controlled by two hardening variables, namely, the plastic strain in tension ( pl t  ) and the plastic strain in compression ( pl c  ). in the case of the effective stress, the yield function is determined as follow:     max max1 3 1 ˆ ˆpl pl c c f q p                (4) where:     0 0 0 0 1 2 1 b c b c         , 0 0.5  (5)        1 1 pl c c pl t t              (6)  3 1 2 1 c c k k     (7) in these equations, p and q are two stress invariants of the effective stress tensor, namely, the hydrostatic stress and the von mises equivalent effective stress, respectively, max ̂ stands for the maximum principal effective stress and is the algebraic maximum eigen value of the effective stress  [27], x represents macauley bracket  1 2 x x  , 0 0b c  is the ratio between the initial biaxial compressive strength and the initial uniaxial compressive strength, ( )pl t t   and ( )pl c c   are the effective tensile and compressive cohesive stresses, respectively. parameter ck is physically assumed as a ratio of the distances between, respectively, the compressive meridian and the tensile meridian with hydrostatic axis in the deviatoric cross section. if this ratio tends to 1, the deviatoric cross section of the failure surface becomes a circle similar to the drucker – prager yielding surface. however, definition of this parameter is only possible if the full triaxial compressive tests are executed on concrete specimens [28]. tab. 3 includes the adopted initial parameters for the cdp model used to simulate the response of the splitting tensile tests. prescribed displacement flush part notch part a. abrishambaf et alii, frattura ed integrità strutturale, 31 (2015) 38-53; doi: 10.3221/igf-esis.31.04 47 dilatation angle [degrees] 40 eccentricity, e [-] 0.1 σbo/σco[-] 1.16 kc [-] 0.667 table 3: the constitutive parameters of cdp model. concrete constitutive model: stress – strain relationship for modeling the sfrscc uniaxial compressive behaviour in cdp model, once the concrete compressive strength ( cu cmf  ) attained, the concrete shifts to the non-linear phase. then, the compressive inelastic strain, in c  , is defined by subtracting the elastic strain component, 0 el c  , from the total strain, c  , in the uniaxial compressive test. 0 in el c c c     (8) 00 el cc e  (9) in the cdp model, from the stress – inelastic strain relationship ( inc c   ) that is provided by the user, the stress versus strain response ( c c  ) can be converted to the stress – plastic strain curve ( pl c c   ) automatically by the software. tab. 4 includes the values of the model parameters used in the numerical simulation of the splitting tensile tests. density, ρ 2.4×106 n/mm3 poisson ratio, υ 0.2 initial young modulus, cme 34.15 n/mm2 compressive strength, cmf 47.77 n/mm2 tensile strength inverse analysis post-cracking parameters inverse analysis table 4: mechanical properties adopted in the numerical simulations. concrete constitutive model: stress – strain relationship for modeling the sfrscc uniaxial tensile behaviour the stress – strain response under uniaxial tension had a linear elastic behaviour until the material tensile strength ( 0t ) was attained. afterward, the tensile response shifted to the post-cracking phase where a non-linear response was assumed. the sfrc post-cracking strain, ck t  , can be determined by subtracting the elastic strain, 0 el t , corresponding to the undamaged part from the total strain, t  : 0 ck t el t t    (10) 0 0 el t t e  (11) from the stress – cracking strain response ( ckt t   ) defined by the user, the stress – strain curve ( t t  ) was converted to a stress – plastic strain relationship ( plt t   ). inverse analysis procedure the σi and wi values that define the tensile stress – crack width law were computed by fitting the numerical load – crack width curve to the correspondent experimental average curve. from the nonlinear finite element analysis, the numerical load – crack width response, fnum – w, was determined, and compared to the experimental one, fexp – w. at last the normalized error, err, was computed as follows: a. abrishambaf et alii, frattura ed integrità strutturale, 31 (2015) 38-53; doi: 10.3221/igf-esis.31.04 48 0 0 u uw w iexp inum iexp i i err f f f      (12) where fiexp and finum were the experimental and the numerical load value at i th crack width value, respectively. the final σ – w relationship was defined by the parameters set that lead to the lowest normalised error between the experimental and numerical compressive force versus crack width curves. numerical results fig. 12 illustrates the numerical response obtained from the inverse analysis of the splitting test results (numsplt), as well as the average and envelope (experimental force – crack width curves, expspltavg and expspltenvelope, respectively. 0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0 0 10 20 30 40 50 60 70 80 exp splt envelope exp splt avg num splt f o rc e [ k n ] w [mm] 0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0 0 10 20 30 40 50 60 70 80 exp splt envelope exp splt avg num splt f o rc e [ k n ] w [mm] (a) (b) figure 12: experimental and numerical force – crack width relationship, f-w, for: (a) θ=0° and (b) θ = 90°. as shown in fig. 12, a good accuracy between the experimental and numerical simulation was achieved, even though a slight difference was observed, but the estimated error (err) was lower than 5%. fig. 13 depicts the σ – w relationship obtained from the inverse analysis that leads to the smallest error. the numerical tensile strengths for the θ = 0° and θ = 90° series were 3.6 and 3.2 mpa, respectively. by comparing the response for both series, similar to the uniaxial tensile test, the post-cracking residual stresses in θ = 0° series were also significantly higher due to the fibre tendency to be reoriented perpendicular to concrete flow direction as previously discussed. therefore, in θ = 0° specimens there are more effective fibres to bridge the crack plane than in θ = 90° series. 0.0 0.5 1.0 1.5 2.0 2.5 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 s tr e s s [ m p a ] w [mm] 0.0 0.5 1.0 1.5 2.0 2.5 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 s tr e s s [ m p a ] w [mm] (a) (b) figure 13: numerical uniaxial stress – crack width relationship, σ – w, obtained from inverse analysis for: (a) θ=0° and (b) θ = 90°. comparison of results figs 14(a) and (b) shows for each series the uniaxial σ – w relationships obtained from the inverse analysis procedure of the splitting tensile test (numsplt), the envelope and average curves from uniaxial tensile test (exputtenvelope, exputtavg.) executed according to the rilem tdf-162 recommendations [13]. moreover, the σ – w response for the splitting test was determined from eq. 13 as recommended by astm c-496 standard (expsplt) [12] and is also represented in fig. 14. a. abrishambaf et alii, frattura ed integrità strutturale, 31 (2015) 38-53; doi: 10.3221/igf-esis.31.04 49 2 splt f ld    (13) where f is the applied line load, d is the diameter of the cylinder (150 mm) and l is the thickness of the net area in the notched plane (50 mm). 0.0 0.5 1.0 1.5 2.0 2.5 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 exp utt envelope num splt exp utt avg exp splt s tr e s s [ m p a ] w [mm] 0.0 0.5 1.0 1.5 2.0 2.5 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 exp utt envelope num splt exp utt avg exp splt s tr e s s [ m p a ] w [mm] (a) (b) figure 14: comparison of the uniaxial stress – crack width relationship, σ – w, for: (a) θ=0° and (b) θ = 90°. the σ – w relationship obtained by the inverse analysis procedure rendered a relatively good approximation of the uniaxial tensile response, principally, for the series θ = 90°. regarding the θ = 0° series, numsplt and expsplt methods showed a very close numerical tensile strength, which were higher than exputt avg. however, as expected, splitting tensile test tends to slightly overestimate the tensile strength compared to the uniaxial tensile test. at the early cracking stages (w < 0.6 mm) numsplt and expsplt methods rendered σ – w responses nearby upper bound limit of the exputt envelope, this overestimation could be correspondent to the effects of the compressive stress along the loading plane. for higher crack opening widths, since in expsplt method, stress was determined from eq. 13 that assumes a linear elastic stress distribution even after cracking of the matrix, this approach was unable to predict post-cracking tensile response with enough accuracy. on the other hand, numsplt started to get closer to the response obtained from the uniaxial tensile test. regarding the θ = 90° series (see fig. 14(b)), the inverse analysis procedure of the splitting tensile tests also overestimated the tensile strength when compared to the tensile strength obtained from the uniaxial tests, although it was within the experimental envelope. based on the exputt results, a sharp stress reduction happened once the crack initiated due to the brittle nature of the matrix and lower number of effective fibres at the fracture plane. the sudden stress decay occurred until the beginning of the hook mobilization, which happened at a crack width of around 0.3 mm. the result of the inverse analysis method reproduced the exputt response with a good accuracy since unlike the θ = 0° series that showed higher residual stresses, the θ = 90° series had lower post-cracking residual stresses, therefore the load bearing capacity of the specimen has decreased and the compressive stresses were not so preponderant in the overall response. correlation between the fracture and fibre distribution parameters ab. 5 shows the fracture parameters obtained experimentally (uniaxial tensile test) and numerically (inverse analysis of splitting test) for the two series (θ = 0° and 90°). in this table, σpeak, σ0.3, σ1 and σ2 represent the stress at peak, 0.3, 1 and 2 mm, respectively; gf1 and gf2 are the dissipated energy up to a 1 and 2 mm crack opening width. it was noticeable that the influence of the notch orientation towards the concrete’s flow on the post-peak behaviour of the material was quite high. the series with a notch inclination of θ = 0º revealed higher residual stresses and hence larger dissipated energy than the specimens with θ = 90º. the observed variation in the post-cracking parameters could be ascribed to a preferential fibre orientation at the crack surface. on the other hand, in the casting process of the panels from the centre, since the wall effects are negligible, the flow velocity is uniform and diffuses outwards radially from the casting point, see fig. 15. therefore, the fibres have a tendency to reorient perpendicular to the concrete flow direction. consequently, in the θ = 0° series because of the high number of effective fibres with favourable orientation, the composite showed a semi-hardening response while in the θ = 90° series, since fibres were rotated due to the concrete flow velocity, the number of the effective fibres was reduced and lower residual forces were achieved. t a. abrishambaf et alii, frattura ed integrità strutturale, 31 (2015) 38-53; doi: 10.3221/igf-esis.31.04 50 series parameter σpeak [mpa] σ0.3 [mpa] σ1 [mpa] σ2 [mpa] gf1 [n/mm] gf2 [n/mm] θ = 0º ( ) numsplt 4.50 4.10 2.60 1.25 3.91 6.35 exputt 3.33 3.24 2.30 1.14 2.94 4.47 θ = 90º ( ) numsplt 3.20 1.06 1.40 0.47 1.26 2.18 exputt 2.72 1.05 1.02 0.56 1.09 1.86 table 5: residual stress and toughness parameters obtained from different analysis. fibre concrete flow direction figure 15: explanation for fibre alignment in flowing concrete of a panel casting from the centre. fig. 16 depicts the relationships between the fibre distribution, feffn , the fibre orientation factor (ηθ) and the post-cracking parameters, as well as their projection for both series obtained from the uniaxial tensile test. since post-cracking parameters were affected by not only the fibre distribution but also the fibre orientation, it is more logical to plot these parameters versus both factors. it was observed, as expected, that the post-cracking parameters, except σpeak, had a tendency to increase with the fibre orientation factor and the number of fibres bridging the fracture surface, being this effect more pronounced in the σ0.3 and σ1. to investigate the influence of each factor ( f effn or ηθ) on the post-cracking parameters, independently, in each figure, the projection of the results in the corresponding plane was executed. in all figures, θ=0° specimens showed higher post-cracking parameters and also lower scattering. as it was proved from the image processing results in the previous section (tab. 2), the covs of feffn and ηθ for the θ=90 ° series were considerably higher than for the θ=0° series. conclusions n this study, the influence of fibre dispersion/orientation on the tensile post-cracking parameters of steel fibre reinforced self-compacting concrete panel was investigated. the σ – w law was determined indirectly from inverse analysis of the splitting tensile test results, as well as directly derived from the uniaxial tensile test. according to the experimental and numerical investigation, the following conclusions could be derived out: 1. the tensile behaviour of the drilled specimens from the panel was influenced by the fibre dispersion and orientation significantly. specimens with notch direction parallel to concrete flow (θ=0°) have significantly higher post-cracking residual stresses than when the notch direction was perpendicular to the flow direction (θ= 90°). 2. roughly, a linear relationship between number of the effective fibres, orientation factor and post-cracking parameters were observed. it was shown that by increasing the number of effective fibres as well as their orientation, fracture parameters tend to raise. this strong dependency could explain that in θ=0° series due to the appearing higher number of effective fibres which were mainly perpendicular to the crack plane, the concrete represented a semihardening behaviour, while in the other series a high stress decay was achieved. 3. in the case of casting panels from the centre, fibres have a tendency to align perpendicular to the radial flow, mainly due to the uniform flow profile velocity that diffuses outwards radially from the centre of the panel. consequently, the total number of the effective fibres was higher in crack planes parallel towards the concrete flow (θ=0°) when compared to the other case of an orthogonal crack plane towards the concrete flow (θ=90°). i a. abrishambaf et alii, frattura ed integrità strutturale, 31 (2015) 38-53; doi: 10.3221/igf-esis.31.04 51 (a) (b) (c) (d) (e) (f) figure 16: relationship between the fibre distribution, the fibre orientation factor and the post-cracking parameters: (a) peak stress, (b), (c) and (d) stress at a 0.3, 1 and 2 mm crack width, respectively; (e) and (f) energy absorption up to 1 and 2 mm crack width, respectively. 4. in this study it was also evidenced that the fibre orientation in a laminar specimen is completely different from the one in a prismatic specimen. in laminar specimens fibres have a tendency to re-orient perpendicular to the concrete flow direction, while in prismatic specimens the fibre’s orientation tends to be parallel to the flow direction, [29, 30]. the determination of the tensile flexural strength of sfrc is usually performed in three-point bending tests on prismatic specimens as recommended by rilem 162-tdf and en-1465 [31, 32], however due to the different fibre orientation profiles in prismatic and planar structural elements, it could lead to an unrealistic tensile behaviour of laminar structural elements like panels, shells or walls. a. abrishambaf et alii, frattura ed integrità strutturale, 31 (2015) 38-53; doi: 10.3221/igf-esis.31.04 52 5. the inverse analysis of the splitting tensile response can estimate with a relatively good accuracy the uniaxial tensile behaviour, in particular, for low fibre contents. in general, in the case of using a relatively high content of fibres, which lead to either a partial or full pseudo-hardening behaviour (as it was the case of the θ=0° series), the proposed methodology could somehow overestimate the σ – w law. in this case it is preferable to use a modified version of the splitting tensile test similar to the one proposed by di prisco et al. [33]. acknowledgements his work is supported by the feder funds through the operational program for competitiveness factors compete and national funds through fct portuguese foundation for science and technology under the project slabsys-hfrc-ptdc/ecm/120394/2010. the authors would like to acknowledge the materials supplied by radmix and maccaferri (fibres), secil (cement), sika and basf (superplasticizers), omya comital (limestone filler), and pegop (fly ash). references [1] aci 544–1r, 2002, state-of-the-art report on fiber reinforced concrete, technical report, american concrete institute, (2002). [2] balaguru, p.n., shah, s.p., fiber reinforced cement composites, mcgraw-hill inc., new york, (1992). [3] vandewalle, l., dupont, d., bending test and interpretation, test and design methods for steel fibre reinforced concrete, background and experiences, rilem publication pro 31, bagneux, (2003) 1-14. [4] banthia, n., trottier, j., concrete reinforced with deformed steel fibres, part i: bond-slip mechanisms, aci materials journal, 91(1994) 435-446. [5] cunha, v.m.c.f., barros,j.a.o., sena-cruz,j.m., pullout behaviour of steel fibres in self compacting concrete, asce journal of materials in civil construction, 22 (2010) 1-9. [6] laranjeira, f., design-oriented constitutive model for steel fiber reinforced concrete, phd thesis, universitat politècnica de catalunya, (2010). [7] ferrara, l., meda, a., relationships between fibre distribution, workability and the mechanical properties of sfrc applied to precast roof elements, materials and structures, 39 (2006) 411-420. [8] pansuk, w., sato, h., sato, y., shionaga, r., tensile behaviours and fibre orientation of uhpc, in proceedings of second international symposium on ultra high performance concrete, kassel, germany (kassel university press), (2008) 161-168. [9] kim, s.w., kang, s.t., park, j.j., ryu, g.s., effect of filling method on fibre orientation and dispersion and mechanical properties of uhpc, proceedings of second international symposium on ultra high performance concrete, kassel, germany (kassel university press), (2008) 185-192. [10] efnarc, the european guidelines for self-compacting concrete, (2005). [11] barnett, s.j., lataste, j.f., parry, t., millard, s.g., soutsos, m.n., assessment of fiber orientation in ultra high performance fibre reinforced concrete and its effects on flexural strength, materials and structures, 43 (2010) 10091023. [12] astm c496, standard test method for splitting tensile strength of cylindrical concrete specimens, annual book of astm standards, american society of testing materials, (2004). [13] rilem tc162-tdf, test and design methods for steel fibre reinforced concrete: uniaxial tension test for steel fibre reinforced concrete, materials and structures, 34 (2001) 3-6. [14] cunha, v.m.c.f., barros, j.a.o., sena-cruz,j.m., an integral approach for modelling the tensile behaviour of steel fibre reinforced self-compacting concrete, cement and concrete research, 41 (2011) 64-76. [15] kang, s.t., kim,j.k., the relation between fibre orientation and tensile behaviour in an ultra high performance fibre reinforced cementitious composites (uhpfrcc), cement and concrete research, 41 (2011) 1001-1014. [16] ferrara, l., ozyurt, n., di prisco, m., high mechanical performance of fiber reinforced cementitious composites the role of casting-flow induced fiber orientation, materials and structures, 44 (2011) 109-128. [17] rasband, w., imagej, national institutes of health, usa, (2008). http://rsb.info.nih.gov/ij/ [18] kamerwararao, c.v.s., effectiveness of random fibres in composites, cement and concrete research, 9 (1979) 685693. t a. abrishambaf et alii, frattura ed integrità strutturale, 31 (2015) 38-53; doi: 10.3221/igf-esis.31.04 53 [19] stroeven, p., hu, j., effectiveness near boundaries of fibre reinforcement in concrete, materials and structures, 39 (2006) 1001-1013. [20] abrishambaf, a., barros, j.a.o., cunha, v.m.c.f., a state of art on the fibre orientation and distribution in steel fibre reinforced concrete, report no. 13-dec/e-16, university of minho, guimaraes, portugal, (2013) 26-31. [21] laranjeira, f., grunewald,s., walraven,j., blom,c., molins,c., aguado, a., characterization of the orientation profile of steel fiber reinforced concrete, materials and structures, 14 (2010) 1093-1111. [22] zhou, f.p., some aspects of tensile fracture behaviour and structural response of cementicious materials, report no. tvbm-1008, division of building materials, lund institute of technology, lund, sweden, (1988). [23] abaqus unified fea software, user manual, dassault systèmes simulia corp., providence, ri, usa, (2009). [24] abaqus unified fea software, analysis user’s manual, volume iv: elements, dassault systèmes simulia corp., providence, ri, usa, (2009). [25] abaqus unified fea software, analysis user’s manual, volume iii: materials, dassault systèmes simulia corp., providence, ri, usa, (2009). [26] lubliner, j., oliver, j., oller, s., onate, e., a plastic-damage model for concrete, international journal of solids structures, 25 (1989) 299-329. [27] jankowiak, t., lodygowski, t., identification of parameters of concrete damage plasticity constitutive model, foundations of civil and environmental engineering, 6 (2005) 53-69. [28] kmiecik, p., kaminski, m., modeling of reinforced concrete structures and composite structures with concrete strength degradation taken into consideration, archives of civil and mechanical engineering, 11 (2011) 623-636. [29] martinie, l., roussel, n., simple tools for fiber orientation in industrial practice, cement and concrete research, 41 (2011) 993-1000. [30] stähli, p., custer, r., on flow properties, fibre distribution, fibre orientation and flexural behaviour of frc, materials and structures, 41 (2008) 189-196. [31] rilem tc162-tdf, test and design methods for steel fibre reinforced concrete: bending test. materials and structures, 33 (2000) 75-81. [32] en 14651, test method for metallic fibered concrete measuring the flexural tensile strength (limit of proportionality (lop), residual), european committee for standardization, brussels, (2005). [33] di prisco, m., ferrara, l., lamperti, m.g.l., double edge wedge splitting (dews): an indirect tension test to identify post-cracking behaviour of fibre reinforced cementitious composites. materials and structures, 46 (2013) 1893-1918. microsoft word numero_34_art_67 c. baron saiz et alii, frattura ed integrità strutturale, 34 (2015) 608-621; doi: 10.3221/igf-esis.34.67 608 thermal stress analysis of different full and ventilated disc brakes c. baron saiz, t. ingrassia, v. nigrelli, v. ricotta università degli studi di palermo, dipartimento di ingegneria chimica, gestionale, informatica, meccanica – 90128 palermo, italy tommaso.ingrassia@unipa.it abstract. during the braking phase, the heat produced by friction between pads and disc cannot be entirely dissipated. consequently, the brake disc, especially if very hard braking occur, can accumulate large amounts of heat in a short time so producing high gradients of temperature on it. under these conditions, functionality and safety of the brake system can be compromised. the object of this study is to investigate, under extreme working conditions, the thermomechanical behaviour of different brake rotors in order to evaluate their efficiency and stability and to identify any compromising weakness on them. in particular, by means of fem thermo-mechanical coupled analyses, one full disc and three ventilated rotors with different shapes have been studied. a very hard (fading) test has been used to evaluate the performances of the discs in terms of temperature distribution, stresses and strains. obtained results demonstrate that the analysed ventilated discs, unlike the full rotor, can be effectively used in very hard working conditions, always ensuring high safety levels. among the studied rotors, the curved-vanes disc was found to be the best solution. keywords. ventilated disc; brake rotor; thermomechanical analysis; fem; fade. introduction uring a braking, most of the kinetic energy of a car is converted into thermal energy due to the dry friction effects and, successively, the generated heat is dissipated in the surrounding environment [1-2]. for this reason, one of the main problem of a braking system is how to handle the thermal energy generated during its action. although the heat dissipation mechanisms could be different (conduction, radiation and convection), the major portion of the generated heat flows out to the air and, consequently, it is dissipated by convection. however, on high-demand repeated braking applications, convection mechanism is unable to dissipate the great amount of incoming heat, so causing overheating of the components and inducing potential failures. previous studies, in fact, showed that thermally induced cyclic stresses strongly affect the crack initiation in the brake discs [3]. nakatsuji et al. [4] studied how cracks, which form around small holes in the flange of one-piece discs, propagate in overloading conditions, whereas gao et al. analyzed the thermal fatigue fracture in brake discs [5-6]. high temperatures during braking, moreover, could cause the brake fade [7], which means losing both efficiency and security during the stopping process. high thermal loads, in fact, can determine considerable distortions of the brake rotor [8], so modifying the system response and increasing the brake judder propensity. for all these reasons, increasing the thermal efficiency and the integrity of the brake components has become an essential objective in the modern automotive engineering field [9]. with this aim, innovative rotors have been designed to improve d c. baron saiz et alii, frattura ed integrità strutturale, 34 (2015) 608-621; doi: 10.3221/igf-esis.34.67 609 the convection mechanism of disc brakes [10-12], so to limit very high temperatures of the system. ventilated disc brakes accomplish this purpose and, due to their braking stability, controllability and ability to provide a wide-range brake torque [10], they have been more and more used. unlike full disks, they are designed with internal vanes that allow to drive greater amount of airflow through the disc. to continuously improve their performances, many new solutions have been proposed over the years by companies that produce disc brakes. in this paper, different geometries of ventilated rotors have been studied to estimate their performances by means of thermo-mechanical coupled analyses. a full disc has been also analysed, in order to quantify the advantages of using air channels in hard braking conditions. the work has been developed as follows: in the first step, a reverse engineering procedure has been setup to create the parametric cad models of the analysed disc brakes. in this phase, moreover, the geometries of the discs have been suitably modified to compare, in the most correct and consistent way, the results. in the second step, using the ansys fem code, brake-fading tests have been simulated through coupled thermal-structural analyses [13,14]. in the last step, the results of all the analysed brake discs have been studied and compared in terms of temperature, strain and stress distributions. working conditions im of this work is to evaluate the effectiveness, in terms of thermomechanical performances, of different internal configurations of ventilated brake rotors. to achieve this purpose, the analysed brake discs have been subjected to very hard conditions using the brembo fading test [15-16]. this test consists of fourteen repeated braking, from an initial velocity, vi, of 160 km/h (44.44 m/s) to stop, with a constant deceleration. between two following braking, there is a recovery time during which the rotor is initially accelerated and, subsequently, maintained at constant velocity vi. fig. 1 shows the acceleration versus time graph during the fading test. figure 1: acceleration versus time in fading test. the recovery time, ∆tr, is established intentionally brief in order to stress the cooling capacity of the brakes. in tab. 1, the most important input data of the fading test are summarized. all the analysed rotors are made of grey cast iron, one of the most common material commercially used for this kind of components. main physical, thermal and mechanical characteristics are presented in tab. 2. to better simulate the real behaviour of the material, the specific heat capacity, the thermal conductivity and the elastic modulus have been considered variable with the temperature, as shown in figs. 2-4. as regards the case studies, three ventilated discs and a full one, all by brembo, have been used. vented rotors differ from each other in vanes shape. in particular, the three ventilated discs have, respectively, straight, curved and pillar-shaped vanes. three-dimensional fully parametric cad models [17] of the discs have been created from 2d technical drawings by brembo [15], following a typical reverse engineering approach [18]. irrelevant details have been removed to simplify the fem models, so reducing the analysis computational time. main sections of the ventilated discs and a frontal view of the full rotor are shown in fig.5. a c. baron saiz et alii, frattura ed integrità strutturale, 34 (2015) 608-621; doi: 10.3221/igf-esis.34.67 610 item value vehicle mass, m (kg) 1445 initial velocity, vi (m/s) 44.444 deceleration, a (m/s2) 5.886 single braking elapsed time, ∆t (s) 7.551 recovery elapsed time, ∆tr (s) 32 tyre rolling circumference, co (m) 1.851 coefficient of adhesion between tyres and road surfaces, fad 0.85 coefficient of friction between pad and disc surfaces, ff 0.43 vehicle inertia coefficient, k 1.1 table 1: fading test input data. property value density, ρ (kg/m3) 7200 thermal expansion coefficient, α (10-5/°c) 967 elastic modulus, e (gpa) 73 40 poisson's ratio, υ 0.27 thermal conductivity, λ (w/m °c) 59.7 – 36.4 specific heat capacity, c (j/kg °c) 469 945 table 2: main properties of the analysed discs material figure 2: specific heat capacity vs temperature. before the numerical analyses, the original geometries of the discs have been suitably modified and scaled in order to compare successively, in the most consistent way, the results obtained for the different rotors. for this purpose, the main dimensions (diameters and thicknesses) and the number of vanes have been standardized for all the configurations. in particular, equal values of the: external and internal diameters of the annular braking surface, hub diameter, front and rear disc thickness, vanes thickness, pad surface, spad, have been imposed. as regard the pad surface, spad, it has been assumed equal to 1/8 of the annular braking surface of the disc (fig.6). c. baron saiz et alii, frattura ed integrità strutturale, 34 (2015) 608-621; doi: 10.3221/igf-esis.34.67 611 figure 3: thermal conductivity vs temperature. figure 4: elastic modulus vs temperature. figure 5: section views of the straight (a), curved (b) and pillar-shaped (c) vanes discs; frontal view of the full disc (d). a) b) d)c) c. baron saiz et alii, frattura ed integrità strutturale, 34 (2015) 608-621; doi: 10.3221/igf-esis.34.67 612 figure 6: main dimensions of the discs the main discs dimensions are summarized in tab. 3. dimension external diameter of braking surface (mm) 295 internal diameter of braking surface (mm) 196 hub diameter (mm) 55 front and rear disc thickness (mm) 10.5 vanes thickness (mm) 12 pad surface, spad (mm2) 5475.8 table 3: common dimensions of the discs. heat flux and braking force inputs o perform the numerical simulations of the brake-fading test, the working conditions of the thermal and structural analyses have been preliminarily defined. in particular, the specific heat flux at the pads/disc interface and the braking forces have been calculated. all calculations have been made considering the input data reported in tab. 1. since the ansys fem code does not allow to setup the disk rotation during a transient thermal analysis, a specific routine has been developed. in particular, the annular braking surface has been subdivided in eight sectors, each one equal to the pad surface (spad). after, for every single wheel turn, the specific heat flux in a braking sector has been calculated and imposed, following an appropriate timing, to suitably simulate the relative rotational motion between pads and disk. heat flux on the basis of the law of conservation of energy, it can be assumed that almost all the kinetic energy of the vehicle during motion is equal to the heat generated after vehicle stops [1,7]. during the braking phase, in fact, due to the friction between pads and disc surfaces, the kinematic energy of a vehicle is transformed into thermal energy. in this study, as t c. baron saiz et alii, frattura ed integrità strutturale, 34 (2015) 608-621; doi: 10.3221/igf-esis.34.67 613 usually happens [10,19], it has been assumed that the thermal conductivity of the pads material is much smaller than the one of the disc. for this reason, it can be hypothesized that the heat generated during the braking is entirely absorbed by the disc. basing on these assumptions, the specific heat fluxes on every sector of the disc braking surface have been calculated as follows. during a braking, the variation of the kinetic energy in a single wheel turn can be calculated as:  2 21 2 f ie m v v    ; where fv and iv are, respectively, the final and the initial velocity during one wheel rotation. since the braking is conducted as uniformly decelerated motion, the variation  2 2f iv v is constant, and can be expressed as:  2 2 2 2f i ov v a d a c        constant; where d represents the distance covered in a wheel turn, equal to the tyre rolling circumference co. consequently, also e has a constant value at every single wheel rotation:  2 21 2 f i oe m v v m a c        constant. neglecting both motion resistance and motor braking, the thermal energy, wheelq , on a single front wheel during a single turn, can be calculated [7,10] as a function of e : 1 2 wheelq f e    constant, where f is the dynamic load distribution coefficient on front wheels [20]. in order to simplify the setup of the boundary conditions, without affecting the results, it has been assumed the heat flux constant over a single wheel rotation and equal to: wheel q q t   ; where t is the wheel turning time. considering that the braking is a uniformly decelerated motion, t increases at every single turn of the wheel and, consequently, q varies accordingly. the routine developed to simulate the relative rotation between pads and disc has required to calculate, from the beginning to the end of the braking, at every wheel turn, the specific heat flux for all the eight sectors in which the braking surface has been subdivided. to do that, knowing q, the specific heat flux in a generic sector of the annular braking surface, equal to spad, has been calculated as: , 1 1 1 8 8 wheel s pad pad pad qq q s t s       . the graph of ,s padq vs time, during a complete braking, for one of the eight sectors is shown in fig. 7. c. baron saiz et alii, frattura ed integrità strutturale, 34 (2015) 608-621; doi: 10.3221/igf-esis.34.67 614 figure 7: specific heat flux (w/mm2) vs time (s) for a sector braking forces braking system works by applying two axial forces that clamp the pads against the disc. in this study, the braking forces have to be enough to arrest the vehicle under the working conditions presented in tab. 1. during a braking, the normal (fn) and tangential (ft) forces on one front wheel can be expressed as [16,20]: 1 2 nf f m g k     , 1 2 t ad adf v f f m g k f        , where: f is the dynamic load distribution coefficient on front wheels, k represents the vehicle inertia coefficient fad is the adherence coefficient between tyre and road. the braking torque applied to one wheel can be calculated as [20,21]: 2 o b t c m f    ; consequently, the braking force padf (normal force on a single pad) is equal to: 1 2 b pad f m f f d    , where: ff is the disc/pad friction coefficient d is moment arm, which value is 125.1 mm. c. baron saiz et alii, frattura ed integrità strutturale, 34 (2015) 608-621; doi: 10.3221/igf-esis.34.67 615 setup of numerical analyses he fading test has been numerically simulated through a thermo-mechanical coupled analysis. during all the 14 braking/recovery steps, the temperature does not have enough time to stabilize in the disc and, for this reason, transient thermal analyses have been performed. after the thermal analyses, a structural simulation has been setup considering both thermal loads and braking forces on the discs. the length of every single braking is 7.55 s, whereas the recovery steps are 32 s length, according to the time between a braking and the next one. during the recovery time simulations, convection is the only applied boundary condition. for all the analysed configurations of the rotors, the convective heat transfer coefficients have been estimated basing on the experiential formulas in literature [16,22], considering an environment (air) temperature equal to 20°. to simulate the cumulative effect of repeated braking, every thermal transient analysis has been linked with the previous and next ones. in this way, the solution of i-th step represents the input data for the following step and so on. the blocks diagram of the implemented procedure is presented in fig. 8. figure 8: blocks diagram of the braking/recovery simulations at the end of the 14th braking, a static structural analysis module has been inserted and linked to the last thermal one. to setup the structural analysis, the temperature distribution over the disc at the end of the last thermal analysis and the braking forces on the pads ( padf ) have been imposed as boundary conditions. moreover, also a cylindrical constraint has been applied on the hub of the disks. all fem models have been meshed with hexahedral elements. the mesh of the straight-vanes disc is shown in fig. 9. figure 9: mesh of the straight-vanes disc. t c. baron saiz et alii, frattura ed integrità strutturale, 34 (2015) 608-621; doi: 10.3221/igf-esis.34.67 616 results thermal results he plots of the maximum temperatures vs time during the fading test are shown in fig. 10. for all the configurations, it can be observed that when braking is taking place, not all the heat generated can be efficiently dissipated and, consequently, disks temperatures remarkably increase. during the recovery stage, instead, since no more heat is introduced in the system, due to the effect of the convective mechanisms, the maximum temperatures tend to decrease. nevertheless, as the recovery time is not long enough to restore initial values, temperatures become higher and higher from the beginning to the end of the test. analysing the temperatures plots, there is no appreciable difference among the analysed vented discs during the first steps of the fading test. going forward in the test, instead, temperatures curves gradually diverge among them (fig. 11). maximum temperature values at the end of the last braking are, respectively, 889 °c for the straight-vanes disc, 841 °c for the curved configuration and 875 °c for the pillar-shaped disc. figure 10: maximum temperature vs time. figure 11: trends of max temperature in the last phases of fading test. concerning the full disc, after completing the sixth braking, the maximum temperature has reached a value slightly above 1100°c, which is over the safety threshold value [23] for this kind of application. for this reason, numerical results of the full disc have not further considered after the sixth arrest. nevertheless, this result is useful to quantify the performances difference between the ventilated disks and the full one, so confirming the use of this last kind of rotor for applications in which moderate braking performances are required. as regards the temperature distribution maps, it can be observed that braking surfaces deal with the highest values. the maximum temperature zones are located on the quarters corresponding to the couple of pads. fig. 12 shows the temperature maps on the external surfaces and the internal vanes of the disks. the maps of temperature distribution on the external surfaces are quite similar among the analysed discs. the efficiency of the vanes in dissipating heat is also appreciable by analysing the temperature distributions on the internal and external surfaces of the discs. in conclusion, with reference to the thermal results, curved vanes represent the best solution because they allow better airflow propagation and, consequently, the maximum temperature reaches a lower value than the straight and the pillar-shaped vanes discs. t c. baron saiz et alii, frattura ed integrità strutturale, 34 (2015) 608-621; doi: 10.3221/igf-esis.34.67 617 figure 12: temperature maps at the 14th braking on straight (left), pillar-shaped (centre) and curved-vanes (right) disc mechanical results maps of von mises stresses at the end of the fading test are shown in fig. 13. the trace due to the pads, because of the braking forces and the thermal gradient, is visible both on the pads-rotor interfaces and on their corresponding vanes (fig. 13-14). c. baron saiz et alii, frattura ed integrità strutturale, 34 (2015) 608-621; doi: 10.3221/igf-esis.34.67 618 figure 13: von mises stress maps at the 14th braking on straight (left), pillar-shaped (centre) and curved-vanes (right) disc. it can be also observed that the effect of pads is restricted to a small area, substantially the same as spad, and it runs out quickly (fig. 13) along the circumference of the braking surface. moreover, high stress values can be found around the hubs, most likely due to the considerable temperature gradients between the outer and inner parts of the rotors and the c. baron saiz et alii, frattura ed integrità strutturale, 34 (2015) 608-621; doi: 10.3221/igf-esis.34.67 619 cylindrical constraints, which limit the thermal expansion. stress distributions over the discs are uniform. curved and pillar-shaped vanes rotors have similar behaviours, both in terms of stress distribution and maximum values reached on them, respectively equal to about 43mpa and 42mpa. figure 14: von mises stress maps on the internal vanes of the straight vanes disc. better results have been obtained with the straight-vanes disc, whose maximum stress value is about 39 mpa, slightly lower than the other two configurations. in an exhaustive study of the performances of brake discs, it is also important to check the structural deformations. in this kind of applications, in fact, thermo-mechanical strains must be under control because excessive values could induce an irregular contact between pads and disc, so compromising the correct functionality of the braking system [8]. in the analysed rotors, strains develop mainly along the radial direction, due to the increase of temperature from the hub to the outer part of the disc. highest deformations have been found at the pads-disc interface. this area is particularly stressed because of the applied braking forces and the thermal flux, which causes locally considerable thermal gradients. fig. 15 represents amplified lateral views of the discs radial deformations; it is possible to perceive how discs start to curve themselves, turning into a cone shape. figure 15: radial deformations on straight (left), pillar-shaped (centre) and curved-vanes (right) disc c. baron saiz et alii, frattura ed integrità strutturale, 34 (2015) 608-621; doi: 10.3221/igf-esis.34.67 620 however, from data in tab. 4, it can be observed that the thermo-mechanical strains reach very low values, so demonstrating a very good behaviour of the analysed discs throughout the brake fading test. disc type min (mm/mm) max (mm/mm) straight -0.00043581 0.0003498 pillar -0.0005097 0.00035072 curved -0.00050126 0.00032796 table 4: minimum and maximum radial strain values. conclusions ehaviour of different types of disc brake rotors has been investigated by means of coupled thermo-mechanical numerical analyses. very hard working conditions have been imposed to the discs in order to evaluate and to compare their performances when subjected to fourteen repeated hard braking. three ventilated discs (respectively with straight, curved and pillar-shaped vanes) and a full one have been studied. this last has shown a poor behaviour, reaching an out-of-use condition after the sixth braking. all the analysed vented rotors, instead, have shown very good performances in terms of heat transfer, so allowing their safe use in extreme braking conditions. by comparing the temperature distribution maps, it can be stated that the best disc is the one with curved vanes, whereas the worst one is the straight-vanes disc. this last one reaches a maximum temperature of about 890 °c, which is appreciably higher than the temperature reached by the curved-vanes disc (840 °c). in terms of stresses, instead, previous results are completely reversed. the best disc, in fact, is the straight vanes one, which reaches a maximum value of von mises stress of about 38 n/mm2, whereas the curved-vanes disc has a maximum value of 43 n/mm2. however, these values are much lower than the material yield strength so, under the imposed working conditions, the discs are not much stressed. also with regard to the deformations, all the analysed discs have shown very good performances, reaching very low value of strains. for these reasons, considering that the maximum stress and strain values over the discs are quite low, the discriminating and most important factor in the choice of the best solution should be related to the thermal results. high values of temperature, in fact, can affect the rotor material properties and, consequently, the right functionality of the whole braking system. then, basing on the obtained results, it could be stated that, among the analysed rotors, the best solution for very hard repeated braking is the curved-vanes disc. the methodology implemented in this work could be effectively used also during the design phase in order to evaluate, in a preliminary stage, the best shape of the brake rotor depending on the planned working conditions. thanks to the developed parametric cad models of the discs, in fact, it is possible interfacing the fem numerical models and an optimization software with the aim to identify the optimal solutions in terms of shape and number of the vanes, rotor thicknesses, etc. references [1] milenković, p. d., jovanović, s. j., janković, a. s., milovanović, m. d., vitošević, n. d., đorđević, m. v., raičević, m. m., the influence of brake pads thermal conductivity on passenger car brake system efficiency, thermal science, 14 (2010) s221-s230 [2] belghazi, h., analytical solution of unsteady heat conduction in a two-layered material in imperfect contact subjected to a moving heat source, ph. d. thesis, university of limoges, limoges, france, (2010). [3] mackin, t. j., noe, s. c., ball, k. j., bedell, b. c., bim-merle, d. p., bingaman, m. c., zimmerman, r. s., thermal cracking in disc brakes, engineering failure analysis, 9(1) (2002) 63-76. [4] nakatsuji, t., okubo, k., fujii, t., sasada, m., noguchi, y., study on crack initiation at small holes of one-piece brake discs (no. 2002-01-0926), sae technical paper (2002). [5] gao, c. h., lin, x. z., transient temperature field analysis of a brake in a non-axisymmetric three-dimensional model, journal of materials processing technology, 129(1) (2002) 513-517. b c. baron saiz et alii, frattura ed integrità strutturale, 34 (2015) 608-621; doi: 10.3221/igf-esis.34.67 621 [6] gao, c. h., huang, j. m., lin, x. z., tang, x. s., stress analysis of thermal fatigue fracture of brake disks based on thermomechanical coupling, journal of tribology, 129.3 (2007) 536-543. [7] talati, f., jalalifar, s., analysis of heat conduction in a disk brake system, heat and mass transfer, 45(8) (2009) 10471059 [8] valvano, t., lee, k., an analytical method to predict thermal distortion of a brake rotor, sae paper 2000-010445, (2000). [9] belhocine, a., bouchetara, m., thermomechanical behavior of dry contacts in disc brake rotor with a grey cast iron composition, thermal science, 17(2) (2013) 599-609. [10] hwang, p., wu, x., investigation of temperature and thermal stress in ventilated disc brake based on 3d thermomechanical coupling model, journal of mechanical science and technology, 24(1) (2010) 81-84. [11] belhocine, a., cho, c. d., nouby, m., yi, y. b., abu bakar, a. r., thermal analysis of both ventilated and full disc brake rotors with frictional heat generation. applied and computational mechanics, 8.1 (2014) 5-24. [12] galindo-lopez, c. h., tirovic, m., understanding and improving the convective cooling of brake discs with radial vanes, journal of automobile engineering, 222(7) (2008) 1211-1229. [13] ingrassia, t., nigrelli v., design optimization and analysis of a new rear underrun protective device for truck, 8th international symposium on tools and methods of competitive engineering, tmce, 2 (2010) 713-725. [14] mineo, c., cerniglia, d., pantano, a., numerical study for a new methodology of flaws detection in train axles, ultrasonics, 54(3), 2014, 841-849. [15] brembo gt, technical information, (2014). [16] gotowicki, p. f., nigrelli, v., mariotti, g. v., aleksendric, d., duboka, c., numerical and experimental analysis of a pegs-wing ventilated disk brake rotor, with pads and cylinders, 10 th eaec conference –5 (2005). [17] ingrassia, t., mancuso, a., nigrelli, v., tumino d., a multi-technique simultaneous approach for the design of a sailing yacht, int. j. interact. design manuf., (2015). doi: 10.1007/s12008-015-0267-2. [18] nalbone, l., adelfio, r., d’arienzo, m., ingrassia, t., nigrelli, v., zabbara, f., paladini, p., campi, f., pellegrini, a., porcellini, g, optimal positioning of the humeral component in the reverse shoulder prosthesis, musculoskeletal surgery, 98 (2) (2014) 135-142. [19] belhocine, a., mostefa b., simulation of fully coupled thermomechanical analysis of automotive brake discs, simulation, 88.8 (2012) 921-935. [20] jazar, r. n., vehicle dynamics: theory and application, springer science & business media, (2013). [21] walker j., the physics of braking systems, stoptech llc, (2005). [22] limpert, r., brake design and safety, second ed., warrendale, society of automotive engineers inc, usa, (1992). [23] adamowicz, a., grzes, p., influence of convective cooling on a disc brake temperature distribution during repetitive braking, applied thermal engineering, 31(14) (2011) 2177-2185. microsoft word numero_37_art_19 m. a. meggiolaro et alii, frattura ed integrità strutturale, 37 (2016) 138-145; doi: 10.3221/igf-esis.37.19 138 focussed on multiaxial fatigue and fracture a multiaxial incremental fatigue damage formulation using nested damage surfaces marco antonio meggiolaro, jaime tupiassú pinho de castro pontifical catholic university of rio de janeiro, puc-rio, r. marquês de são vicente 225, rio de janeiro, 22451-900, brazil meggi@puc-rio.br jtcastro@puc-rio.br hao wu school of aerospace engineering and applied mechanics tongji university, siping road 1239, 200092, shanghai, p.r.china wuhao@tongji.edu.cn abstract. multiaxial fatigue damage calculations under non-proportional variable amplitude loadings still remains a quite challenging task in practical applications, in part because most fatigue models require cycle identification and counting to single out individual load events before quantifying the damage induced by them. moreover, to account for the non-proportionality of the load path of each event, semi-empirical methods are required to calculate path-equivalent ranges, e.g. using a convex enclosure or the moi (moment of inertia) method. in this work, a novel incremental fatigue damage methodology is introduced to continuously account for the accumulation of multiaxial fatigue damage under service loads, without requiring rainflow counters or path-equivalent range estimators. the proposed approach is not based on questionable continuum damage mechanics concepts or on the integration of elastoplastic work. instead, fatigue damage itself is continuously integrated, based on damage parameters adopted by traditional fatigue models well tested in engineering practice. a framework of nested damage surfaces is introduced, allowing the calculation of fatigue damage even for general 6d multiaxial load histories. the proposed approach is validated by non-proportional tensiontorsion experiments on tubular 316l stainless steel specimens. keywords. multiaxial fatigue; variable amplitude loads; non-proportional multiaxial loads; nested fatigue damage surfaces; incremental damage calculation. introduction ost fatigue crack initiation models need to properly identify load events before computing the damage induced by them. hence their fatigue damage calculation routines need to include cycle counting algorithms like the well-known rainflow methodology for uniaxial loads. cycle counting is necessary because traditional fatigue models are discrete in nature, since they only can accumulate damage after a load event (e.g. a half-cycle) is properly identified, detected e.g. from a load reversal or from a hysteresis loop that closes. however, the detection and counting of loading events can be a quite challenging task under multiaxial non-proportional (np) histories. the existing multiaxial rainflow algorithms [1] are not trivial to apply. in fact, they are not even robust, since they can output very different halfm m. a. meggiolaro et alii, frattura ed integrità strutturale, 37 (2016) 138-145; doi: 10.3221/igf-esis.37.19 139 cycles depending on the choice of the initial counting point of a periodic load history [2, 3]. furthermore, multiaxial fatigue damage evaluation requires the semi-empirical calculation of path-equivalent stress or strain ranges from the rainflow-counted paths, increasing even more its computational burden [4]. on the other hand, a completely different fatigue calculation approach assumes damage as a continuous variable, whose increments can be computed as the loading proceeds. most works based on this idea use continuum damage mechanics concepts [5], which need to be supplemented by purely phenomenological damage evolution equations that are difficult to calibrate, to say the least. in fact, despite their academic appeal, such models remain controversial and have not found a wide acceptance in the fatigue design community. other continuous damage approaches are based on an integration of elastoplastic work. however, the accumulated total work required to initiate a microcrack by fatigue certainly is not a material property. moreover, the elastoplastic work still depends on the number of cycles, thus it is impossible to calculate without previous load cycle and/or reversal detection. therefore, even if it could be assumed that fatigue damage can be quantified by this parameter, its calculation routine still would need to include a rainflow or other similar load event counter. alternatively, instead of integrating dubious strain energy or energy-based damage parameters, a more reasonable path is to continuously quantify fatigue damage itself, using some well-proven model that can properly describe multiaxial fatigue damage in the material in question. the so-called incremental fatigue damage (ifd) approach integrates the chosen parameter until reaching 1.0 or any other suitable critical-damage value using traditional accumulation concepts, as originally performed a long time ago for the uniaxial case by wetzel under topper's guidance in 1971 [6], and again by chu in 2000 [7]. it is important to emphasize that in such calculations fatigue damage is continuously computed after each infinitesimal stress or strain increment, so its quantification does not require the prior identification of load cycles. in this work, the ifd approach is revisited and extended to general multiaxial fatigue problems, including no-proportional ones, based on a direct analogy with non-linear incremental plasticity concepts, however calculating damage instead of plastic strains at each load increment. the incremental fatigue damage approach he incremental fatigue damage approach was proposed for uniaxial load histories in wetzel and topper’s rheological model [6, 8]. it makes use of the derivative of the normal stress  with respect to damage d, called here generalized damage modulus d, thus d d dd d dd (1 d ) d        (1) consider, for instance, a uniaxial constant amplitude loading history with stress amplitude a. during a loading half-cycle, the excursion of the stress  from a to a could be integrated according to eq. (1) to find the associated fatigue damage d  1/2n, however without explicitly calculating the fatigue life n. assuming the material is initially virgin, the damage d from the first half-cycle is initially zero in the initial valley when a and thus a)  0, and continuously grows toward d = 1/2n until  reaches the peak a, when a) = 2a. for simplicity, wöhler’s stress-based fatigue damage model is adopted below (but strain-based models will be considered later). a simplified relation between the current stress state  and the continuous damage d from the half-cycle excursion a  a can then be obtained from wöhler’s curve e.g. written in basquin’s notation:   1/bb ba c a c a c( 2 n ) 2 [ ( )] 2 d d ( ) 2                   (2) the generalized damage modulus d during this half-cycle is thus such that   1/ba c a1 d dd d ( ) 2 [ b( )]           (3) from which the fatigue damage d  1/2n can be calculated using the integral t m. a. meggiolaro et alii, frattura ed integrità strutturale, 37 (2016) 138-145; doi: 10.3221/igf-esis.37.19 140       aa aa 1/b 1/b 1/b a a a a c c c 1 1d d b( ) 2 2 2 n                          (4) if this conceptually simple procedure could be generalized to multiaxial np variable amplitude loading (val) histories, integrating damage along a general multiaxial load path, then cycle identification, multiaxial rainflow counting, and stress (or strain) range calculations would not be required to obtain the fatigue damage d. however, this bold statement is easier said than done, since d depends not only on the current stress state ( in this uniaxial case), but also on the previous loading history (the value a from the last reversal), see eq. (3). so, incremental fatigue damage models need to allow d to vary as a function of the stress level and of the existing state of damage [9]. the history dependence of d, often neglected or overly simplified in the few ifd models proposed in the literature, is analogous to the load-order dependence of elastoplastic hysteresis loops. chu [7] outlined the generalization of wetzel’s rheological model to multiaxial loadings, indirectly detecting cycles using two simple rules. however, damage memory is not properly stored in that simple model for general np val histories, where often no hysteresis loop actually closes and thus any virtual loop closure detection makes no sense. the main purpose of this work is to propose the improvements needed to properly extend the interesting ifd idea to general multiaxial loads. multiaxial incremental fatigue damage approach stress-based incremental fatigue damage formulation n this work, instead of using rheological models, a direct analogy between ifd and incremental plasticity is adopted instead to store fatigue damage memory, using internal material variables. in incremental plasticity, a 5d deviatoric stress increment ds  can be used to calculate the associated 5d plastic strain increment plde  from the current generalized plastic modulus p, using a plastic flow rule [10-11]. in particular, it is well known that in the non-linear kinematic (nlk) incremental plasticity formulation, plastic memory is stored by the current arrangement among the hardening surfaces defined by their backstresses i  , from which the surface translation directions iv  are calculated (according to some translation rule) and combined with material coefficients pi to calculate the current plastic modulus p [10-11]. therefore, no plastic straining occurs if the stress increment ds   happens inside the yield surface, whose radius should be equal or smaller than the cyclic yield strength syc. the accumulated plastic strain p is then proportional to the integral of the scalar norm plde  of the deviatoric plastic strain increments. let’s now rephrase the previous paragraph for the desired ifd model, based on the proposed direct analogy between plasticity and fatigue damage. in the ifd model presented here, a 5d deviatoric stress increment ds  can be used to calculate the associated 5d damage increment dd  from the current generalized damage modulus d, using a damage evolution rule. in the ifd formulation, damage memory is stored by the current arrangement among damage surfaces defined by their damage backstresses i  , from which the damage surface translation directions iv  are calculated (according to some translation rule) and combined with material coefficients di to calculate the current damage modulus d. no damage occurs if the deviatoric stress increment ds  happens inside the fatigue limit surface, whose radius should be equal or smaller than the fatigue limit of the material sl. the accumulated damage d is then equal to the integral of the scalar norm dd  of the 5d damage increments. the damage backstress vector   locates the center of the current fatigue limit surface, which can be decomposed as the sum of m damage backstresses  1  ,  2  , …, m  that describe the relative positions between centers of consecutive damage surfaces, as illustrated in fig. 1 for a 2d case. notice in fig. 1 that each damage surface has a constant radius ri, while the radius differences between consecutive surfaces are ri  ri+1  ri. the fatigue limit and failure surfaces are defined, respectively, for i  1 and i  m  1, while the remaining i = 2, 3, …, m are the damage surfaces. the damage backstress lengths are always between i  0  , if consecutive centers coincide, and i ir    , if they are mutually tangent. i m. a. meggiolaro et alii, frattura ed integrità strutturale, 37 (2016) 138-145; doi: 10.3221/igf-esis.37.19 141 1r fatigue limit surface '  1 '  2 '  3 '  s'  2r 3r 4r s1 s2 figure 1: fatigue limit, damage, and failure surfaces in a 2d deviatoric stress space for three moving nested surfaces, showing the damage backstress vector that defines the location of the fatigue limit surface center, and its three components that describe the relative positions between the centers of consecutive surfaces at each load event. the proposed multiaxial ifd model uses a 5d damage vector d   [d1 d2 d3 d4 d5]t that acts as an internal variable that stores the current multiaxial fatigue damage state (to account for the damage memory). the scalars d1 through d5 are signed damage quantities associated with each one of the directions of the 5d deviatoric stress vector s  , defined in [11]. in this way, the total accumulated damage d (which thus works for multiaxial fatigue problems analogously to the accumulated plastic strain p for multiaxial plasticity problems) is obtained from the length of the path described by the 5d damage vector d  , calculated in either continuous or discrete formulations from d dd dd d d        | | | |   (5) if a given stress state s  is on the fatigue limit surface with a normal unit vector n  , and if its infinitesimal increment ds  is in the outward direction, then tds n 0     and a fatigue damage increment is obtained from a damage evolution rule (inspired on the analogous prandtl-reuss flow rule [10-11]): t ms npdd d ds n n f f n               ( 1 ) ( ) ( ) ( , )      (6) m. a. meggiolaro et alii, frattura ed integrità strutturale, 37 (2016) 138-145; doi: 10.3221/igf-esis.37.19 142 where msf ( )  is a scalar mean stress function of the current 6d stress   to account for mean/maximum-stress effects, which can be defined e.g. from goodman’s or gerber’s am relations when applicable; and , npf n ( )    is a np function to account for the additional effects introduced by the non-proportionality of the load path. for materials that fail due to distributed damage in all directions, the mean stress function msf ( )  could be based on the current hydrostatic stress h from   . on the other hand, for materials that fail due to a single dominant crack, like most metallic alloys (whose multiaxial fatigue damage parameters tend to be better described by the critical-plane approach), then msf ( )  could be based on the normal stress  perpendicular to the considered candidate plane. except for the failure surface (which never translates), during this damage process the fatigue limit and all damage surfaces suffer translations , if or , if i i i i i i i id d v dd r d r                     | | 0 | |     (7) where di are coefficients calibrated for each surface, and iv  are the damage surface translation directions adapted e.g. from the general translation rule from [11]. the current generalized damage modulus d is then obtained from the consistency condition, which guarantees that the current stress state is never outside the fatigue limit surface, taken from an analogy to the nlk hardening formulation for plasticity problems  m ti iid d v n        1   (8) allowing the calculation of the evolution of the damage vector d  using eq. (6). the (scalar) accumulated damage d is then obtained from eq. (5). this formulation can deal with any multiaxial stress history, proportional or np, and eliminates the need to count cycles and find equivalent ranges, or even to define them. indeed, for instance, fig. 2 shows continuous ifd damage predictions for a material whose elastic coffin-manson’s parameters are c  772.5mpa and b  0.09, under the uniaxial loading history x = {0  300  300  300}mpa. jiang-sehitoglu’s translation rule was adopted with m  16 surfaces, calibrated between logarithmically spaced damage levels 108 and 0.01. x 10 -5 accumulated stress (mpa) a cc u m u la te d d a m a g e d theoretical (discrete) damage calculated continuous damage x 10 -5 0 200 400 600 800 1000 1200 1400 1600 0 1 2 3 4 5 6 7 -1.5 -1 -0.5 0 0.5 1 1.5 -300 -200 -100 0 100 200 300 signed damage d1 n o rm al s tr es s (m p a ) unloading loading figure 2: hysteresis loops relating applied stress and a signed damage state (left) and resulting accumulated damage (right) for a uniaxial constant amplitude loading history. strain-based incremental fatigue damage formulation all the formulations and the example presented above assumed nominally linear elastic loading histories, whose damage can calculated from sn models such as wöhler-basquin’s and goodman, but this is not a limitation for this methodology. m. a. meggiolaro et alii, frattura ed integrità strutturale, 37 (2016) 138-145; doi: 10.3221/igf-esis.37.19 143 indeed, the proposed ifd approach can be as well extended for elastoplastic loading histories, whose fatigue damage must be quantified by n models. however, instead of using fatigue limit and damage surfaces defined in stress spaces, strain spaces should be used in the continuous damage calculations in such cases. a generalized damage modulus d (instead of d) is thus defined, which for uniaxial loading histories becomes the derivative of the normal strain  with respect to damage d, thus d  d/dd. in the strain-based version of the proposed if approach, a 5d deviatoric strain increment de  , defined in [10], is used to calculate the associated 5d damage increment dd  from the current d, using a suitable damage evolution rule. to do so, damage memory is stored by the current arrangement among damage surfaces defined by their damage backstrains i  , from which the damage surface translation directions iv  are calculated according to some translation rule and combined with material coefficients di to calculate the current d. the accumulated damage d is then equal to the integral of the scalar norm dd  of the damage increments. the same equations from the stress-based version can be used in the strain-based one, as long as the m damage surface backstrains  1  ,  2  , …, m  , radii ri, and radius differences ri  ri+1  ri between consecutive damage surfaces are all defined as strain (instead of stress) quantities. experimental results he proposed ifd formulation is experimentally evaluated using complex 2d tension-torsion stress histories, applied on annealed tubular 316l stainless steel specimens in a multiaxial servo-hydraulic testing machine. the coffin-manson curve for this material is 0 277 0 5822 0 0119 2 n 0 758 2 n     . .. ( ) . ( ) , obtained from uniaxial n tests. the experiments consist of strain-controlled tension-torsion cycles applied to eight tubular specimens, each of them following one of the eight periodic x×xy/3 histories from fig. 3. tab. 1 compares the predicted and observed fatigue lives in number of blocks, where each block consists of a full load period. all predictions were performed using the strainbased version of the proposed incremental plasticity formulation, assuming for simplicity msf 1( )   and , npf n 1 ( )     in eq. (6). cross circle square diamond triangle 1 triangle 2 square/cross square/circle/ diamond figure 3: applied periodic x×xy/3 strain paths on eight tension-torsion tubular specimens, all of them with normal and effective shear amplitudes 0.6%. as shown in tab. 1, albeit the proposed ifd method does not use any cycle detection or counting algorithm, all fatigue lives are predicted with relatively small errors, well within the usual scatter found in all fatigue life measurements. it also automatically applies miner’s rule under val, as it can be seen in the loading path consisting of blocks of consecutive square and cross paths, since the predicted number of blocks 482 is such that 1/482  1/751  1/1314. similarly, the t m. a. meggiolaro et alii, frattura ed integrità strutturale, 37 (2016) 138-145; doi: 10.3221/igf-esis.37.19 144 predicted 327 blocks of consecutive square, circle and diamond paths is such that 1/327  1/751  1/996  1/1436. miner’s rule was also confirmed within the observed experimental results, since e.g. in this latter case it would predict a life of 1/(1/772  1/837  1/976) = 285 blocks, almost the same value as the measured 288 blocks. it is important to note that all the predictions listed in tab. 1 were based only on uniaxial coffin-manson data, without any posterior curve fitting procedure. tension-torsion path: predicted observed error cross 1314 1535 14% diamond 1436 976 47% triangle 1 1135 842 35% triangle 2 1180 840 40% circle 996 837 19% square 751 772 3% square + cross 482 342 41% square + circle + diamond 327 288 14% table 1: predicted and observed lives, in number of blocks, for each applied path. conclusions n this work, a continuous multiaxial incremental fatigue damage formulation that does not needs cycle counting or path-equivalent estimations is proposed, based on a direct analogy with incremental plasticity models. both proposed stress and strain-based approaches can be formulated using traditional stress, strain, or even energy-based sn and n damage models, such as wöhler-basquin, coffin-manson, smith-watson-topper, or fatemi-socie, making it an attractive and practical tool for engineering use. in particular, the proposed ifd models do not require additional fitting parameters, or complex calibration routines, as opposed to equally continuous models that are based on traditional continuum damage mechanics approaches. the results show that the proposed method is able to predict quite well multiaxial fatigue lives under complex tension-torsion histories, even though it does not require any cycle detection, multiaxial rainflow counting, or path-equivalent range computations. references [1] wang, c.h., brown, m.w. life prediction techniques for variable amplitude multiaxial fatigue part 1: theories, j. eng. mater. technology 118 (1996) 367-370. [2] meggiolaro, m.a., castro, j.t.p. an improved multiaxial rainflow algorithm for non-proportional stress or strain histories part i: enclosing surface methods, int. j. fatigue 42 (2012), 217-226. doi:10.1016/j.ijfatigue.2011.10.014. [3] meggiolaro, m.a., castro, j.t.p. an improved multiaxial rainflow algorithm for non-proportional stress or strain histories part ii: the modified wang-brown method, int. j. fatigue 42 (2012) 194-206. doi:10.1016/j.ijfatigue. 2011.10.012. [4] meggiolaro, m.a.; castro, j.t.p.; wu, h. invariant-based and critical-plane rainflow approaches for fatigue life prediction under multiaxial variable amplitude loading, procedia engineering 101 (2015) 69-76. doi: 10.1016/ j.proeng.2015.02.010. [5] kachanov, l.m. introduction to continuum damage mechanics, springer (1986). [6] wetzel, r.m. a method of fatigue damage analysis, ph.d. thesis, u. waterloo, ca, (1971). i m. a. meggiolaro et alii, frattura ed integrità strutturale, 37 (2016) 138-145; doi: 10.3221/igf-esis.37.19 145 [7] chu, c.c. a new incremental fatigue method, in: astm stp 1389 (2000) 67-78. [8] castro, j.t.p., meggiolaro, m.a. fatigue design techniques (in 3 volumes), createspace, scotts valley, ca, usa (2016). [9] kreiser, d., jia, s.x., han, j.j., dhanasekar, m. a nonlinear damage accumulation model for shakedown failure, int. j. fatigue 29 (2007) 1523-1530. doi: 10.1016/j.ijfatigue.2006.10.023. [10] meggiolaro, m.a., castro, j.t.p., wu, h. a general class of non-linear kinematic models to predict mean stress relaxation and multiaxial ratcheting in fatigue problems part i: ilyushin spaces, int. j. fatigue 82 (2016) 158-166. doi: 10.1016/j.ijfatigue.2015.08.030. [11] meggiolaro, m.a., castro, j.t.p., wu, h. a general class of non-linear kinematic models to predict mean stress relaxation and multiaxial ratcheting in fatigue problems part ii: generalized surface translation rule, int. j. fatigue 82 (2016) 167-178. doi: 10.1016/j.ijfatigue.2015.08.0310. << /ascii85encodepages false /allowtransparency false /autopositionepsfiles true /autorotatepages /none /binding /left /calgrayprofile (dot gain 20%) /calrgbprofile (srgb iec61966-2.1) /calcmykprofile (u.s. web coated \050swop\051 v2) /srgbprofile (srgb iec61966-2.1) /cannotembedfontpolicy /error /compatibilitylevel 1.4 /compressobjects /tags /compresspages true /convertimagestoindexed true /passthroughjpegimages true /createjobticket false /defaultrenderingintent /default /detectblends true /detectcurves 0.0000 /colorconversionstrategy /cmyk /dothumbnails false /embedallfonts true /embedopentype false /parseiccprofilesincomments true /embedjoboptions true /dscreportinglevel 0 /emitdscwarnings 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/hrv (za stvaranje adobe pdf dokumenata najpogodnijih za visokokvalitetni ispis prije tiskanja koristite ove postavke. stvoreni pdf dokumenti mogu se otvoriti acrobat i adobe reader 5.0 i kasnijim verzijama.) /hun 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can be opened with acrobat and adobe reader 5.0 and later.) >> /namespace [ (adobe) (common) (1.0) ] /othernamespaces [ << /asreaderspreads false /cropimagestoframes true /errorcontrol /warnandcontinue /flattenerignorespreadoverrides false /includeguidesgrids false /includenonprinting false /includeslug false /namespace [ (adobe) (indesign) (4.0) ] /omitplacedbitmaps false /omitplacedeps false /omitplacedpdf false /simulateoverprint /legacy >> << /addbleedmarks false /addcolorbars false /addcropmarks false /addpageinfo false /addregmarks false /convertcolors /converttocmyk /destinationprofilename () /destinationprofileselector /documentcmyk /downsample16bitimages true /flattenerpreset << /presetselector /mediumresolution >> /formelements false /generatestructure false /includebookmarks false /includehyperlinks false /includeinteractive false /includelayers false /includeprofiles false /multimediahandling /useobjectsettings /namespace [ (adobe) (creativesuite) (2.0) ] /pdfxoutputintentprofileselector /documentcmyk /preserveediting true /untaggedcmykhandling /leaveuntagged /untaggedrgbhandling /usedocumentprofile /usedocumentbleed false >> ] >> setdistillerparams << /hwresolution [2400 2400] /pagesize [612.000 792.000] >> setpagedevice microsoft word numero_51_art_38_2696 m. pepe et alii, frattura ed integrità strutturale, 51 (2020) 504-516; doi: 10.3221/igf-esis.51.38 504 focussed on fracture and damage detection in masonry structures micromodels for the in-plane failure analysis of masonry walls: limit analysis, fem and fem/dem approaches m. pepe, m. pingaro, p. trovalusci sapienza university of rome, italy marco.pepe@uniroma1.it, https://orcid.org/0000-0002-9416-8415 marco.pingaro@uniroma1.it, http://orcid.org/0000-0002-7037-8661 patrizia.trovalusci@uniroma1.com, http://orcid.org/0000-0001-7946-3590 e. reccia university of cagliari, italy emanuele.reccia@unica.it, http://orcid.org/ 0000-0003-0499-4295 l. leonetti university of calabria, italy lorenzo.leonetti@unical.it, http://orcid.org/0000-0001-7182-2149 abstract. in the last decades the modeling of masonry structures has become an argument particularly appealing for many researchers and a large variety of numerical techniques have been formulated with the aim to produce practical applications in civil engineering, with special reference to the preservation and restoration of cultural heritage. nevertheless, the question appears today still far from being resolved in a general way. the characteristics of fragility, heterogeneity and anisotropy of masonry, as well as the extreme variety of the building/construction rules strongly compromise the possibility of a unified description of its mechanical behavior. in this work a comparison of different models and techniques for the assessment of the mechanical behavior of two-dimensional block masonry walls subjected to the static action of in-plane loads is presented. different approaches and numerical models are considered: a limit analysis approach (la), a fem/dem procedure and a non-linear heterogeneous finite element analysis (fe). here a standard limit analysis is adopted via a homemade procedure based on linear mathematical programming, considering friction at interfaces. analyses are performed referring to benchmark examples from literature. keywords. masonry; rigid blocks; limit analysis; distinct element method; finite element method. citation: pepe, m., pingaro, m., trovalusci, p., reccia, e., leonetti, l., micromodels for the in-plane failure analysis of masonry walls: limit analysis, fem and fem/dem approaches, frattura ed integrità strutturale, 51 (2020) 504-516. received: 29.11.2019 accepted: 12.12.2019 published: 01.01.2020 copyright: © 2020 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. http://www.gruppofrattura.it/va/51/2696.mp4 m. pepe et alii, frattura ed integrità strutturale, 51 (2020) 504-516; doi: 10.3221/igf-esis.51.38 505 introduction asonry is a composite (heterogeneous) material obtained by assembling natural or artificial blocks by means of mortar layers or dry joints and it is one of the more common structural materials adopted for centuries for ordinary or monumental constructions. the investigation of its mechanical behavior plays a fundamental role in view of the protection and conservation of architectures of historical and archaeological interest. however, to deal with the structural response of historical masonry structures is a complex task. in the last decades a large variety of numerical models and approaches have been proposed in literature, but no one can be applied in a general manner regardless the constructive typology. the selection of the most appropriate modelling strategy is indeed strictly related with the nature of the object to analyze. depending on the adopted model for analysis it is possible introduce three distinct categories: micro-mechanical, macromechanical models and multiscale models. the choice of a micro-mechanical model involves a distinct representation of masonry constituents (units, mortar and unit/mortar interface) whose properties are obtained from experimental tests on small masonry specimens. a micro-mechanical model is suitable for a very detailed response [1-5], but this approach has a limitation represented by the great computational effort due to the high number of degrees of freedom connected to each unit and joint in case of real masonry structures, characterized by considerable number of units. macro-mechanical models describe masonry as homogeneous continuum, use phenomenological constitutive laws for constituents, including also some inner variables for damage, and friction coefficients. the material parameters are derived by means of experimental tests on small masonry specimens or directly on the single constituents. macro-mechanical models are characterized by high computational efficiency, as they do not provide an accurate description of the internal structure of masonry material [6-8]. multiscale continuum models represent a very promising approach for the analysis of masonry structures since they can accurately retain memory of the mechanical and geometrical properties of the material (micro-structure) together with the capability to contain the computational effort compared to a fully micro-mechanical model [9-12]. these models are often derived by considering only two material scales: a micro-scale where, after deducing the mechanical properties of the components, preferably through experimental tests, a material representative volume element (rve) is defined and a macro-scale continuum model, is obtained by performing a homogenization procedure in most cases based on the solution of notable boundary conditions problems for the rve. among these approaches, both concurrent and semiconcurrent multiscale models have been proposed in the literature for masonry-like materials, the first ones referring to a strong coupling between the microand macro-levels [13-16], the latter ones, often referred to as computational homogenization models, characterized by an only weak (although two-way) coupling between them [17-20]. most of the existing approaches are devoted to the mechanical behavior of periodic (i.e. regular) masonries, for which a suitably defined unit cell plays the role of rve, but there exist also different homogenization techniques for both linear and nonlinear analyses of random microstructures, already applied or directly applicable to irregular masonry structures [21-23]. other multiscale strategies have been proposed that exploit different homogenization techniques based on the so-called cauchy rule, and its, generalizations [24] that allowed the derivation of both classical and generalized continua able to properly represent scale effects, that in masonry materials are prominent [25-29]. in this work the attention is mainly focused on the category of micromodels particularly focusing on limit analysis, which represents a very effective tool to estimate the collapse load and collapse mechanism for one-leaf masonry structures [30-35]. in particular the model here presented considers an associative flow-rule connected to a dilatant behaviour of the joints. this hypothesis has been successfully adopted to study the behaviour of historical masonry structures [36-38] even if it may occur that the flow rule is quasi-associated under shear actions, depending by the level of pre-compression of masonry. it must be pointed out that a limitation of limit analysis (both associated and not associated) concerns ductility that is assumed infinite, and this hypothesis not always fits well the softening behaviour of masonry [39]. a validation of the proposed model is provided, via suitable comparisons with two models that finely describe the microstructure and already adopted to the evaluation of the in-plane failure behavior of masonry panels: (i) a discrete model based on a combined finite/discrete element method (fem/dem) [40, 41], and (ii) a heterogeneous nonlinear finite element model (fem), derived from the works [13, 15, 16]. the three models are used to reproduce the analysis performed in [42] here regarded as a benchmark on several masonry panels with different height-to-width ratio and with or without openings. the comparison of the numerical m m. pepe et alii, frattura ed integrità strutturale, 51 (2020) 504-516; doi: 10.3221/igf-esis.51.38 506 results shows the efficacy of limit analysis for a fast and reliable assessment of the in-plane failure analysis of masonry walls. limit analysis ollowing and reinterpreting the model formulated in [30, 31], masonry is described as a system of n rigid blocks and m joints unable to carry tension and resistant to sliding by friction. the blocks can translate and rotate about the edges of the contact blocks (hinging) as well as slide along the joints. let introduce  1 2 3    t e e ee  the orthonormal basis in the three-dimensional space. we consider the two blocks in fig. 1. loads are applied to the centroid of each rigid block thi : static dead loads are collected in vector  0 01 02 03,   ,   ti i i if f mf , static live loads are collected in vector  1 2 3,   ,   ti i i i l l l lf f mf . for the whole structure it results  0 0if f and  il lf f , with i = 1, …, n  . the vector of the load over the whole system is 0 l f f f  , where live loads are proportional to the dead loads through a non-negative coefficient  called collapse multiplier. let  1 2 3,   ,   ti i i iu u u denote the vector of generalized displacement of the centroid of each thi block. the vector  iu u , with i = 1, …, n  , collect the displacements for the whole structure which correspond in a virtual work sense to loads f . the static variables are the internal forces acting at each thj contact surface between blocks, whose components are the normal force jn , the shear force jt and the moment jm . for each joint they are collected in vector  ,   ,   tj j j jn t mσ . the vector, with j = 1, …, m  , refers to the whole structure. the kinematic variables, or generalized strain, are the relative displacement rates at joints, that is normal displacement j , tangential displacement j and rotation j . for each joint j = 1, …, m  they are collected in the vector  ,   ,   tj j j j  ε . the vector  jε ε refers to the whole structure and corresponds in a virtual work sense to the vector of static variables σ . figure 1: simple two-block structure: dead and live loads, kinematic and static variables masonry is described as a system of rigid blocks directly interacting through contact surfaces unable to carry tension and resistant to sliding by friction. the set of equations for the model are represented by:         t t t t l ε bu b σ f 0 y n σ 0 ε mλ y λ 0 f u 1 (1.1) f m. pepe et alii, frattura ed integrità strutturale, 51 (2020) 504-516; doi: 10.3221/igf-esis.51.38 507 where eqn. (1.1)1 represents the kinematic compatibility for the whole system of interfaces and blocks in which b is the compatibility matrix as in [42], but also in nonlinear static analysis by [43], eqn. (1.1)2 defines the equilibrium for the whole structure, eqn. (1.1)3 describes the generalized yield domain of the system where n is the block-diagonal gradient matrix, eqn. (1.1)4 represents the flow rule which express the vector ε as a linear combination with non-negative coefficients λ, called inelastic multiplier and m is the block-diagonal matrix of the modes of failures. eqn. (1.1)5 is the complementarity condition which defines the plastic behavior of contact surface. moreover, the collapse mechanism must be characterized by a non-negative work of the live loads, defined by eqn. (1.1)6. within the framework of the holonomic perfect plasticity, the same relations govern the problem of a non-standard rigid-plastic discrete materials. resorting this formal analogy, the collapse load for a masonry structure, under the hypothesis of proportional load with the factor 0  , can be determined. after some algebra the authors obtained the following non-linear and non-convex programming problem (nlncp)                  c 1 2 t tt 0 1 0 l 2 1 2 tt 0 1 l tt t 0 l 2 1 2 min   subjected to     0 0 1 0 0                      am m λ a n f f n an σ λ a m f λ f f n an σ (1.2) with the unknowns  , 2σ , λ and the bounds 0λ , where 2σ are the undetermined unknown of the system which represent the statically undetermined term of the generalised contact stress [30] in order to deal with the nlncp, authors [31] developed a specific code, called alma (analisi limite murature attritive), which used a two-step procedure to solve the problem: in the first step a linear programming problem (lp), obtained by replacing friction with dilatancy, is solved; in the second step, the nlncp solution is approached using, as initial guess for the unknowns of the problem, the solution of the first step. however, the problem of limit analysis of structures with frictional interfaces (non-standard la) is numerically very difficult to be solved. the solution could not exist and when it exists it could be a local minimum instead of the global one [44]. on the other hand, due to the presence of non-associative flow rules, the drucker stability postulate no longer holds and the solution in terms of contact actions and collapse load factor loses its uniqueness. moreover, bi-dimensional or three-dimensional real structures, characterized by many degrees of freedom, increase the computational complexity of the problem. from limit analysis theory it is well known that if normality rule holds, i.e. the vector of inelastic strain results normal to the yield surface, the static and kinematic theorems of limit analysis could be formulated in a linear programming context, resulting in two dual problems, which lead to a unique solution. in particular, following the approach of [31], results of this work refer to a linear programming optimization problem related to the kinematic approach of limit analysis, which provides the collapse multiplier and the corresponding mechanism. friction is considered in term of dilatancy. the kinematic problem is defined as (1.3) with the bounds on the unknowns 0λ . to overcome some computational limits of the original code alma, mainly related to the number of blocks and interfaces involved into analysis, a new version of the code, alma 2.0, was implemented using matlab for linear optimization and a python interface for preand post-processing operations. fem/dem analysis he limit analysis model is compared with the models adopted in [40,41], here regarded as a benchmark. in the referred works, two micro-mechanical models have been proposed for the in-plane failure analysis of masonry walls: a discrete element method (dem) and a combined finite/discrete element method (fem/dem). both t        0 1 0 1 2 0 1 min         1 0 tt c tt l subjected to       λ a n f an n λ 0 λ a n f m. pepe et alii, frattura ed integrità strutturale, 51 (2020) 504-516; doi: 10.3221/igf-esis.51.38 508 models considered fall in the field of discrete or distinct element methods, which have been proved to be particularly suitable for the study of masonry structures [45]. dem model is based on the original numerical method formulated by [46], and recently developed by [43]. the model is based on the assumption of rigid block and mortar joints modeled as zero-thickness elastic-plastic interfaces, adopting a mohr-coulomb yield criterion. masonry is seen as a system of rigid blocks, whose interactions are represented by forces and moments depending on their relative displacements and rotations. fem/dem method is a combination of discrete elements, originally formulated by [47], and developed by [48], it consists in a discrete element method in which the individual elements are meshed into finite elements, adopting a triangular discretization of the domain with embedded crack elements that activate whenever the peak strength is reached. the method, initially developed in the field of geo-mechanics, has been adopted to study the behavior of historical masonry [49]. differently from the dem described above, blocks can be assumed to behave as rigid or elastic bodies. mortar joints might be idealized as elastic or elastic–plastic zero-thickness mohr–coulomb interfaces. blocks are modeled by means of finite elements while interfaces are modeled as discrete elements. in this work, discrete models are realized adopting the fem/dem method. heterogeneous fem analysis he second comparison model is a heterogeneous finite element model, by which masonry is described as a system of n deformable blocks and m dry joints in which all the nonlinearities due to unilateral contact together with decohesion and friction phenomena are lumped. in detail, masonry blocks are made by bulk finite elements with linearly elastic and isotropic material properties, whereas dry joints are represented as zero-thickness damage-based cohesive interface elements placed in between, equipped with an intrinsic mixed-mode displacement-based traction-separation law (tsl). the variational formulation for the equilibrium problem at the microscopic scale is rather classic and, thus, not reported here for the sake of brevity. however, with the aim to find more theoretical and computational details, the reader is referred to the works [13,16,17], in which this formulation is embedded within a more general multiscale framework. in this paper the following mixed-mode tsl of the type  =t t  , proposed by [50], is chosen (see fig. 2), incorporating unilateral contact with friction in an approximated manner, exploiting a penalty approach to enforce the highly nonlinear kinematical constraint in the normal direction to the joint surface:         max n n ncn p n n max s n sc s max s s p n n sc 1 f , 0 t k , 0 1 f , 0 t 1 f sign k , 0                            (1.4) where  , tn st tt and  = , t n s  denote the traction and displacement jump vectors, written in the local coordinate system  ,n s attached to the interfaces; nc and sc are the critical values of the normal and tangential displacement jump components, corresponding to the total decohesion in pure mode i and mode ii, respectively; pk is the penalty stiffness constant for contact enforcement;  maxf  is a damage function, defined as follows:     2 max max max max max max 27 1 2 , 1 4 0, 1 t f              (1.5) t m. pepe et alii, frattura ed integrità strutturale, 51 (2020) 504-516; doi: 10.3221/igf-esis.51.38 509 maxt being the normal interfacial strength (assumed equal to the tangential one) and max the maximum valued attained by the effective separation parameter: 2 2 sn n nc sc s n sc , 0 , 0                        (1.6) over the entire deformation history; finally,  is the friction function, defined as: 0.5 0 max 0 max , 1 , 1 s sc               (1.7) 0 being the friction coefficient. it is worth noting that the adopted friction function is different than that appearing in [46], due to the presence of an exponent (in this work set as 0.5, in general less than 1) applied to the dimensionless modeii separation. this novel formulation is able to account for the rapid increase of friction forces between the two sides of masonry joints during its decohesion, coherently with what suggested in [51]. the adopted tsl is versatile, meaning that it can be applied in this form for any masonry type (with dry or mortar joints), characterized by a hybrid cohesive/frictional mechanical behavior. however, for masonries characterized by a dominant frictional behavior, as in the case of dry joints analyzed in this paper, the cohesive part of the tsl (1.4) tends to vanish, so that the adoption of the friction function (1.7) allows friction forces to develop up to their maximum value from the beginning of numerical simulations, i.e. at low separations between adjacent units. figure 2: mixed-mode traction-separation and contact relations in normal (a) and tangential (b) directions on a cohesive interface. numerical results n the following a discussion about comparison of results obtained with limit analysis, fem and fem/dem is presented. the panels analyzed by ferris and tin-loi [42] are chosen as benchmark. authors performed analysis on structures characterized by different size and geometry, providing results in terms of associate and non-associate limit analysis. details of all models are: blocks with full dimension 4x1.75 and half size dimension 2x1.75 and a friction ratio tan 0.65  . fig. 3 shows the geometries considered by the authors. example 1 (33 blocks) and example 2 (55 blocks) are full panels with different ratio length over height, example 3 (46 blocks) is a panel with an opening in the central part, example 4 (55 blocks) is a panel with two horizontal openings, i m. pepe et alii, frattura ed integrità strutturale, 51 (2020) 504-516; doi: 10.3221/igf-esis.51.38 510 example 5 (61 blocks) is a slender panel with two vertical openings and finally example 6 (146 blocks) represents a bigger panel characterized by four openings positioned on two different levels. each block of the structures is subjected to dead load 0f and a live load lf , proportional to the collapse multiplier, acting towards right direction. moreover, in both fem and fem/dem simulations, the elastic constants (i.e. young’s modulus and poisson’s ratio) for masonry units are 20 e gpa and 0.15  . the additional nonlinear parameter for fem simulations, appearing in eqs. (1.4) and (1.5), are: max 00.001 t t , 0t being the average compressive stress associated with the dead load; 0.001 nc sc b   . b being the width of full-size blocks. it is worth noting that these values have been adopted in the subsequent numerical simulations in order to represent the dominant frictional behavior of dry joints, as stated in previous section. finally, the penalty constant is set as 1000 pk e b , i.e. sufficiently high to avoid significant interpenetrations between adjacent units. fig. 4 refers to results obtained for example 1. the mechanism is characterized by a hinging behavior with the rotation of the upper right corner of the panel. limit analysis and fem present also the formation of two ‘stair-stepped’ crack not detected by the fem/dem which on the contrary provide also a sliding of the blocks not observed in the results of the other two techniques. example 1 example 2 example 3 example 4 example 5 example 6 figure 3: geometrical configurations of the panels analyzed by ferris and tin-loi (a) (b) (c) figure 4: collapse mechanism for example 1, horizontal live load: (a) alma 2.0, (𝑏) fem/dem, (𝑐) fem m. pepe et alii, frattura ed integrità strutturale, 51 (2020) 504-516; doi: 10.3221/igf-esis.51.38 511 (a) (b) (c) figure 5: collapse mechanism for example 2, horizontal live load: (a) alma 2.0, (𝑏) fem/dem, (𝑐) fem (a) (b) (c) figure 6: collapse mechanism for example 3, horizontal live load: (a) alma 2.0, (𝑏) fem/dem, (𝑐) fem fig. 5 refers to results obtained for example 2. results are similar to those of the smaller panel previously analyzed, with a hinging behavior which exhibits a rotation of the upper right portion of the panel and three ‘stair-stepped’ cracks of the wall now obtained with all the three models. also, in this case the fem-dem present a sliding of the blocks not observed into result of the other models but, by the adoption of a fictitious cohesion value for head joints, could allow to obtain a mechanism less influenced by sliding. fig. 6 refers to results obtained for example 3, characterized by the presence of an opening. in this case the results obtained with the three models are exactly the same, with a hinging behavior which implies the rotation of half panel around a hinge positioned about at the lower right corner of the panel. all the models compute a principal diagonal crack passing through the opening. some slight differences could be pointed out for the mechanism corresponding to the fem, as for example the position of the hinge which is located at ground level (for limit analysis and fem/dem it is positioned upon the first row of blocks) and the absence of movement of the portion of the panel to the left of the opening (the other two models detect a slight rotation of this macro-block around a hinge positioned exactly at the left lower corner of the window). (a) (b) (c) figure 7: collapse mechanism for example 4, horizontal live load: (a) alma 2.0, (𝑏) fem/dem, (𝑐) fem m. pepe et alii, frattura ed integrità strutturale, 51 (2020) 504-516; doi: 10.3221/igf-esis.51.38 512 (a) (b) (c) figure 8: collapse mechanism for example 5, horizontal live load: (a) alma 2.0, (𝑏) fem/dem, (𝑐) fem (a) (b) (c) figure 9: collapse mechanism for example 6, horizontal live load: (a) alma 2.0, (𝑏) fem/dem, (𝑐) fem fig. 7 refers to results obtained for example 4, characterized by the presence of two openings. results are in this case similar to those obtained for the panel with only one windows. in particular, all the models provide a hinging collapse with rotation around the lower right corner of the wall and the formation of ‘stair-stepped’ cracks. in this case fem/dem provide a hinge positioned at ground level while limit analysis and fem consider the hinge upon the first row of blocks. on the contrary limit analysis and fem/dem reveals also a little rotation of the part of the panel to the left of the first window while fem, as for the previous case, considers this portion of the panel stable. fig. 8 refers to results obtained for the slender panel of example 5. for this case the results of the three different approaches are almost the same, with a hinging collapse due to the formation of several cracks, positioned at correspondence of openings, which divide the panel into several macro-blocks. the more evident difference is noticed for fem/dem which compute the hinge at the lower right corner of the wall at ground level, while for limit analysis and fem it is positioned upon the first row of blocks. fig. 9 refers to results obtained for example 6, characterized by the presence of four openings. the collapse of the panel is due to a hinging behavior with the formation of several diagonal cracks which divide the structure into various macroblocks. about the position of the cracks, the models provide results slightly different, except for those that identify the macro-blocks positioned to the right of the panel. another difference is observed for fem that compute the left part of the panel as stable, while limit analysis and fem/dem reveal in that portion different cracks and rotating macro-blocks. the collapse multiplier 𝛼 obtained with limit analysis, fem/dem and fem has been compared with the results related to the associative (lp) and non-associative (mixed complementarity problem mcp and mathematical program with equilibrium constraints mpec) problems solved by ferris and tin-loi [42]. as expected, results obtained with alma2.0 are very close to the one obtained with the associative case. m. pepe et alii, frattura ed integrità strutturale, 51 (2020) 504-516; doi: 10.3221/igf-esis.51.38 513 referring to results of example 1, fig. 10a, it could be noticed how alma 2.0 as well as fem provide results in good agreement with benchmark ones, with negligible numerical differences. fem/dem instead returns a lower value of the collapse multiplier. (a) (b) (c) (d) (e) (f) figure 10: comparison of the collapse multiplier for: (a) example1, (b) example2, (c) example3, (d) example4, (e) example5, (f) example6, the same is for example 2, fig. 10b, where it could be observed as the limit analysis model reaches the same value of lp problem resulting little higher respect to those of the non-linear problem. fem on the contrary provide a lower value of 𝛼, closer to mcp and mpec problems. also, in this case fem/dem returns a lower value of collapse multiplier. the response of alma 2.0 for example 3, fig. 10c, is always closer to the result of the lp problem but in this case, it is little higher. fem confirms its capacity to get results in good agreement with those of mcp and mpec problems, while fem/dem provides a slightly higher value of collapse multiplier. the difference between models’ responses is more evident referring to figs. 10d, 10e and 10f, where results of examples 4, 5 and 6 confirms, as expected, that the value of collapse multiplier provided by the solution of the linearized problem treated with alma 2.0 is very close to those corresponding to the associative problem. on the other hand, the capacity of fem to get collapse multiplier values closer to the non-linear models becomes clearer as well as the results provided by fem/dem, even if with some negligible numerical difference. m. pepe et alii, frattura ed integrità strutturale, 51 (2020) 504-516; doi: 10.3221/igf-esis.51.38 514 conclusions he present work focuses the attention on the comparison between different modelling techniques. in particular, limit analysis (la), fem/dem and fem strategies have been analyzed and applied to the benchmark masonry panels introduced by ferris and tin-loi [42]. the three models object of this study are able to reproduce correctly the collapse mechanism, taking into account the real texture of masonry walls, describing accurately each block’s geometry and disposition, obtaining useful information about the collapse mechanism and the potential crack patterns that may develop. the comparison of the results obtained by means the different discrete models points out some advantages of using la approaches to model the structural response of masonry panels with respect to the other techniques presented in this work. the la approach requires, indeed, less computational effort with respect to fem/dem and fem techniques, which could present a critical issue especially for structure with a large number of degrees of freedom. moreover, another advantage of the la approach concerns the limited number of mechanical parameters to be introduced as inputs of the numerical model-. indeed, unlike fem/dem and fem, which require more mechanical information, the only parameter needed using la is the friction angle. anyway, by the comparison of results in terms of collapse multiplier, it has been noticed that fem, unlike the other models, is able to get values closer to those related to the non-associative response obtained by ferris and tin-loi [42]. the next step of this research will be focused on the analysis of more complex geometries, including a linearized procedure to take into account pure shear according to coulomb friction as well as crushing of the blocks. the assumption of infinite compressive strength, typical of unreinforced masonry structures, could be removed improving the code with the possibility of a crushing failure of masonry. this aspect is particularly interesting for structures reinforced with metallic ties where a concentration of stress could arise. according to several literature contributes [52] a procedure that iteratively modifies the yield surface, by adding a series of new constraints that consider the limited compressive strength of joints, could be introduced. another further development, that has been recently implemented in the code, is the introduction of contact surfaces with cohesion in the formulation. the study about the influence of settlements on the global structural response is also an ongoing research. acknowledgements his research was supported by italian ministry of university and research: prin 2015, project 2015jw9njt (b86j16002300001); prin 2017 no. 2017hfpkzy (b88d19001130001); sapienza research grants ’progetti medi’ 2017 (b83c17001440005). dr. reccia fully acknowledges the research project funded by p.o.r. sardegna f.s.e. 2014-2020 axis iii education and training, thematic objective: 10, specific objective: 10.5, action of the partnership agreement: 10.5.12, call for funding of research projects – year 2017. lorenzo leonetti gratefully acknowledges financial support from the italian ministry of education, university and research (miur) under the national grant “pon r&i 2014-2020, attraction and international mobility (aim) – azione i.2”, project n° aim1810287, university of calabria”. references [1] lotfi, h., shing, p. s. (1994). interface model applied to fracture of masonry structures, journal of structural engineering-asce, 120(1), pp. 63-80. [2] lourenco, p. b., rots, j. g. (1997). multisurface interface model for analysis of masonry structures, journal of engineering mechanics, 123(7), pp. 660-668. [3] oliveira, d. v., lourenco, p. b. (2004). implementation and validation of a constitutive model for the cyclic behaviour of interface elements, computers and structures, 82(17-19), pp. 1451-1461. [4] alfano, g., sacco, e. (2006). combining interface damage and friction in a cohesive-zone model, international journal for numerical methods in engineering, 68(5), pp. 542-582. t t m. pepe et alii, frattura ed integrità strutturale, 51 (2020) 504-516; doi: 10.3221/igf-esis.51.38 515 [5] serpieri, r., albarella, m., alfano, g., sacco, e. (2017). analysis of failure in quasi-brittle materials by 3d multiplane cohesive zone models combining damage, friction and interlocking, procedia structural integrity, 3, pp. 441-449. [6] del piero, g. (1989). constitutive equation and compatibility of the external loads for linear elastic masonry-like materials, meccanica, 24(3), pp. 150-162. [7] casalegno, c., cecchi, a., reccia, e., russo, s. (2013). heterogeneous and continuous models: comparative analysis of masonry wall subjected to differential settlements, composites: mechanics, computations, applications, 4(3), pp. 187-207. [8] liberatore, d., addessi, d., sangirardi, m. (2017). a nonlinear macroelement formulation for the seismic analysis of masonry buildings, eccomas proceedia id: 5575, conference proceeding id: 17126, pp. 2395-2403. [9] masiani, r., trovalusci, p. (1996). cosserat and cauchy materials as continuum models of brick masonry, meccanica, 31(4), pp. 421-432. [10] trovalusci, p., varano, v., rega, g. (2010). a generalized continuum formulation for composite microcracked materials and wave propagation in a bar, journal of applied mechanics, transactions asme, 77(6), 061002. [11] trovalusci, p. (2014). molecular approaches for multifield continua: origins and current developments., cism international centre for mechanical sciences, courses and lectures, 556, pp. 211-278. [12] macorini, l., izzuddin, b.a. (2013). nonlinear analysis of masonry structures using mesoscale partitioned modelling, advances in engineering software, 60-61, pp. 58-69. [13] leonetti, l., greco, f., trovalusci, p., luciano, r., masiani, r. (2018). a multiscale damage analysis of periodic composites using a couple-stress/cauchy multidomain model: application to masonry structures, composites part b: engineering 141, pp. 50-59. [14] reccia, e., leonetti, l., trovalusci, p., cecchi, a. (2018). a multiscale/multidomain model for the failure analysis of masonry walls: a validation with a combined fem/dem approach, international journal for multiscale computational engineering, 16(4), pp. 325-343. [15] greco, f., leonetti, l., luciano, r., nevone blasi, p. (2016). an adaptive multiscale strategy for the damage analysis of masonry modeled as a composite material, composite structures, 153, pp. 972-988. [16] greco, f., leonetti, l., luciano, r., trovalusci, p. (2017). multiscale failure analysis of periodic masonry structures with traditional and fiber-reinforced mortar joints, composites part b: engineering, 118, pp. 75-95. [17] addessi, d., sacco, e., di re, p. (2018). multi-scale analysis of masonry structures, proceedings of the international masonry society conferences, 0(222279), pp. 307-323. [18] addessi, d., de bellis, m. l., sacco, e. (2016). a micromechanical approach for the cosserat modeling of composites, meccanica, 51(3), pp. 569-592. [19] massart, t.j., peerlings, r.h.j., geers, m.g.d. (2007). an enhanced multi-scale approach for masonry wall computations with localization of damage, international journal for numerical methods in engineering, 69, pp. 10221059. [20] giambanco, g., la malfa ribolla, e., spada a. (2014). ch of masonry materials via meshless meso-modeling, frattura ed integrità strutturale, 29, pp. 150-165. [21] cluni, f., gusella, v. (2004). homogenization of non-periodic masonry structures', international journal of solids and structures, 41, pp. 1911-1923. [22] pingaro, m., reccia, e., trovalusci, p., masiani, r. (2019). fast statistical homogenization procedure (fshp) for particle random composites using virtual element method, computational mechanics, 64(1), pp. 197-210. [23] pingaro, m., reccia, e., trovalusci, p. (2019). homogenization of random porous materials with low-order virtual elements, asce-asme journal of risk and uncertainty in engineering systems, part b: mechanical engineering, 5(3), 030905. [24] capecchi, d., ruta, g., trovalusci, p. (2010). from classical to voigt's molecular models in elasticity, archive for history of exact sciences, 64(5), pp. 525-559. [25] masiani, r., trovalusci, p. (1996). cosserat and cauchy materials as continuum models of brick masonry, meccanica, 31(4), pp. 421-432. [26] trovalusci, p., masiani, r. (2003). non-linear micropolar and classical continua for anisotropic discontinous materials, international journal of solids and structures, 40(5), pp. 1281-1297. [27] pau, a., trovalusci, p. (2012). block masonry as equivalent micropolar continua: the role of relative rotations, acta mechanica, 223(7), pp. 1455-1471. [28] fantuzzi, n., trovalusci, p., dharasura, s. (2019). mechanical behavior of anisotropic composite materials as micropolar continua, frontiers in materials, 6, 59. m. pepe et alii, frattura ed integrità strutturale, 51 (2020) 504-516; doi: 10.3221/igf-esis.51.38 516 [29] leonetti, l., fantuzzi, n., trovalusci, p., tornabene, f. (2019). scale effects in orthotropic composite assemblies as micropolar continua: a comparison between weakand strong-form finite element solutions, materials, 12(5), 758. [30] baggio, c., trovalusci, p., (1998). limit analysis for no-tension and frictional three-dimensional discrete systems, mechanics of structures and machines, 26(3), pp. 287-304. [31] baggio, c., trovalusci, p. (2000). collapse behaviour of three-dimensional brick-block systems using non-linear programming, structural engineering and mechanics, 10(2), pp. 181-195. [32] portioli, f., casapulla, c., gilbert, m., cascini, l. (2014). limit analysis of 3d masonry block structures with nonassociative frictional joints using cone programming, computers & structures, 143, pp. 108-121. [33] baggio, c., trovalusci, p. (2016). 3d limit analysis of roman groin vaults, brick and block masonry: trends, innovations and challenges proceedings of the 16th international brick and block masonry conference, ibmac 2016, pp. 1023-1028. [34] pavlovic, m., reccia, e., cecchi, a. (2016). a procedure to investigate the collapse behavior of masonry domes: some meaningful cases, international journal of architectural heritage, 10(1), pp. 67-83. [35] cascini, l., gagliardo, r., portioli, f. (2018). liablock_3d: a software tool for collapse mechanism analysis of historic masonry structures, international journal of architectural heritage, in press, doi: 10.1080/15583058.2018.1509155. [36] milani, g. (2008). 3d upper bound limit analysis of multi-leaf masonry walls, international journal of mechanical sciences, 50(4), pp. 817-836. [37] milani, g. (2011). simple lower bound limit analysis homogenization model for inand out-of-plane loaded masonry walls, construction & building materials, 25, pp. 4426-4443. [38] milani g., taliercio a. (2016). limit analysis of transversally loaded masonry walls using an innovative macroscopic strength criterion, international journal of solids and structures, 81, pp. 274-293. [39] milani g., tralli a. (2012). a simple meso-macro model based on sqp for the non-linear analysis of masonry double curvature structures, international journal of solids and structures, 49(5), pp. 808-834. [40] baraldi, d., reccia, e., cecchi, a. (2015). dem & fem/dem models for laterally loaded masonry walls, eccomas proceedia id: 3528, conference proceeding id: 715, pp. 2144-2157. [41] baraldi, d., reccia, e., cecchi, a. (2018). in plane loaded masonry walls: dem and fem/dem models. a critical review, meccanica, 53(7), pp. 1613-1628. [42] ferris, m. c., tin-loi, f., (2001) limit analysis of frictional block assemblies as a mathematical program with complementarity constraints, international journal mechanical science, 160(43), pp. 209–224. [43] baraldi, d., cecchi, a. (2016). discrete approaches for the nonlinear analysis of in plane loaded masonry walls: molecular dynamic and static algorithm solutions, european journal of mechanics, a/solids, 57, pp. 165-177. [44] kirsch, u. (2012). structural optimization: fundamentals and applications., springer science & business media, new york. [45] lemos, j. v. (2007). discrete element modeling of masonry structures, international journal of architectural heritage, 1(2), pp. 190-213. [46] cecchi, a., sab, k. (2004). a comparison between a 3d discrete model and two homogenised plate models for periodic elastic brickwork, international journal of solids and structures, 41(9-10), pp. 2259-2276. [47] munjiza, a. (2004). the combined finite-discrete element method, john wiley and sons, chichester. [48] mahabadi, o. k., lisjak, a., munjiza, a., grasselli, g. (2012). y-geo: new combined finite-discrete element numerical code for geomechanical applications, international journal of geomechanics, 12(6), pp. 676-688. [49] reccia, e., cazzani, a., cecchi, a. (2012). fem-dem modeling for out-of-plane loaded masonry panels: a limit analysis approach, open civil engineering journal, 6(spec.iss.1), pp. 231-238. [50] bilbie, g., dascalu, c., chambon, r., caillerie, d. (2008) micro-fracture instabilities in granular solids, acta geotechnica, 3, pp. 25-35. [51] snozzi, l., molinari, j. f. (2013). a cohesive element model for mixed mode loading with frictional contact capability, international journal for numerical methods in engineering, 93(5), pp. 510-526. [52] portioli, f., casapulla, c., cascini, l. 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can be opened with acrobat and adobe reader 5.0 and later.) >> /namespace [ (adobe) (common) (1.0) ] /othernamespaces [ << /asreaderspreads false /cropimagestoframes true /errorcontrol /warnandcontinue /flattenerignorespreadoverrides false /includeguidesgrids false /includenonprinting false /includeslug false /namespace [ (adobe) (indesign) (4.0) ] /omitplacedbitmaps false /omitplacedeps false /omitplacedpdf false /simulateoverprint /legacy >> << /addbleedmarks false /addcolorbars false /addcropmarks false /addpageinfo false /addregmarks false /convertcolors /converttocmyk /destinationprofilename () /destinationprofileselector /documentcmyk /downsample16bitimages true /flattenerpreset << /presetselector /mediumresolution >> /formelements false /generatestructure false /includebookmarks false /includehyperlinks false /includeinteractive false /includelayers false /includeprofiles false /multimediahandling /useobjectsettings /namespace [ (adobe) (creativesuite) (2.0) ] /pdfxoutputintentprofileselector /documentcmyk /preserveediting true /untaggedcmykhandling /leaveuntagged /untaggedrgbhandling /usedocumentprofile /usedocumentbleed false >> ] >> setdistillerparams << /hwresolution [2400 2400] /pagesize [612.000 792.000] >> setpagedevice microsoft word numero 25 art 16 f.a. díaz et alii, frattura ed integrità strutturale, 25 (2013) 109-116; doi: 10.3221/igf-esis.25.16 109 special issue: characterization of crack tip stress field application of thermoelastic stress analysis for the experimental evaluation of the effective stress intensity factor francisco a. díaz universidad de jaén, departamento de ingeniería mecánica y minera, campus las lagunillas, edificio a3, 23071, jaén, spain eann a. patterson university of liverpool, school of engineering, harrison hughes building, the quadrangle, liverpool l69 3gh, uk john r. yates university of manchester, school of mechanical, aerospace and civil engineering, george begg building, manchester, m60 1qd, uk abstract. in recent years, the advent of staring array detectors has made thermoelastic stress analysis (tsa) a technique with considerable potential for fatigue and fracture mechanics applications. the technique is noncontacting and provides full field stress maps from the surface of cyclically loaded components. in addition, the technique appears to have a great potential in the evaluation of the effective stress intensity factor range during fatigue since fracture mechanics parameters are derived directly from the temperature changes in the vicinity of the crack tip rather than from remote data. in the current work tsa is presented as a novel methodology for measuring the effective stress intensity factor from the analysis of thermoelastic images. δk values inferred using tsa have been employed to estimate an equivalent opening/closing load at different r-ratios in a cracked aluminium 2024 ct specimen. results have been compared with those obtained using the strain-offset technique showing a good level of agreement. keywords. thermoelastic stress analysis (tsa); fatigue; effective stress intensity factor. introduction atigue cracks have been one of the main sources of structural failures in machines for two centuries. the application of fracture mechanics to engineering design has led to more efficient use of structures and components, which leads to great economic benefits by avoiding premature retirement of serviceable machines. however, there are still some aspects of fatigue that remain partially understood, such as the crack closure effect. this lack of understanding arises principally from the difficulties associated in quantifying the phenomenon and measuring its effect on the crack driving force [1]. in recent years, advances in infrared thermography together with the development of infrared staring array radiometer detectors have made it possible to apply this technology to fatigue damage assessments. such an example is thermoelastic stress analysis (tsa). this experimental technique makes it possible to infer the in-plane stresses on a solid structure by measuring the small temperature changes induced as a result of a cyclic load. from the fatigue point of view, tsa constitutes a breakthrough over other experimental stress analysis techniques. with tsa the stress intensity factor is directly obtained by computing the cyclic stress field ahead of the crack tip, which makes it possible to evaluate the actual crack driving force for the fatigue advance [2 and 3]. the outcome is that the tsa f http://www.gruppofrattura.it http://dx.medra.org/10.3221/igf-esis.25.16&auth=true f.a. díaz et alii, frattura ed integrità strutturale, 25 (2013) 109-116; doi: 10.3221/igf-esis.25.16 110 method provides a direct measurement of the effective δk that is usually measured indirectly by compliance techniques. this arises from the fact that with tsa the near crack tip stress distribution is obtained from the temperature variations at the specimen surface as a result of the thermoelastic effect, providing a direct assessment of the cyclic strains in the field around the crack tip. hence, the observed crack tip stress pattern is the result of the specimen’s response to the applied loading cycle. to support the idea that tsa can provide accurate information about the real fatigue crack driving force, a set experiments using aluminium 2024 ct specimens have been conducted. as a result, δk results obtained using thermoelastic images have been employed to infer an equivalent value for the opening/closing load for increasing rratios. results have been compared with those obtained using the strain offset technique, showing in all cases a good level of agreement, highlighting the value of tsa for fatigue damage assessment. physical principles of thermoelastic effect he thermoelastic effect was first reported by lord kelvin [4] in 1853. it states that any substance in nature experiences changes in its temperature when its volume is changed due to the application of a force: compressive loads cause an increase in temperature while tensile load produces a decrease in temperature. consequently, if a cyclic load is applied to a component there will be a cyclic change in temperature. under elastic conditions, these temperature variations are normally quite small (tens of mk) and they are normally ignored in the classical theory of elasticity. however, with the use of high precision infrared detectors these temperature changes can be measured. the thermoelastic effect is a reversible conversion between the mechanical and thermal forms of energy, since the temperature variation will reverse when the load is withdrawn. however, this energy conversion is reversible only if the elastic range of the material is not exceeded and there is no significant transport of heat during loading and unloading of the structure. moreover, thermoelastic theory states that under adiabatic and reversible conditions, the temperature variations experienced by the cyclically loaded material are proportional to the sum of principal stresses. the relation between the change in temperature due to the application of a cyclic loading and the stress range of a linear elastic and homogeneous material can be written as:  1 2 p t t c          (1) where  is the coefficient of thermal expansion, t is the absolute temperature of the material,  is the density, cp is the specific heat at constant pressure and 1 and 2 are the principal stresses. to ensure that the experimentally recorded variation is linear, the load cycle must be fast enough to prevent heat transport and thus achieve adiabatic conditions. truly adiabatic conditions may be achieved only if the thermal conductivity of the material is zero or no stress gradients are present in the specimen. however, if the load frequency is high enough the thermal diffusion length is reduced and the presence of non-adiabatic effects is minimized. in modern tsa, an infrared camera based on a staring array of photon detectors is used to measure the temperature changes at the surface of the component as a consequence of an applied cyclic load (figure 1a). the technique measures load-correlated temperature signals in a cyclically loaded body using infrared detectors. thus, the analysis of thermoelastic response has to be done under dynamic conditions at an adequate frequency to ensure adiabatic conditions in order to prevent heat transfer through the test piece. when adiabatic conditions are achieved and maintained during the test, the relation between the induced temperature change and the change in the sum of principal stresses is assumed to be linear, and thus the variation in the sum of principal stresses can be experimentally inferred by processing the thermoelastic signal according to the following equation:      1 2 x y x y e a s 1                  (2) where, e, is the young’s modulus, ν, is the poisson’s ratio, εx and εy, are the strains in two orthogonal directions, s, is the thermoelastic signal and a is a calibration constant. to translate the thermal units into stresses a calibration process needs to be performed [5]. this process consists essentially in defining the stress at a point in the images for a given load on the structure. a common method used for calibration consists of generating an independent measure of stress using strain gauges as illustrated in figure 1.b. t http://www.gruppofrattura.it http://dx.medra.org/10.3221/igf-esis.25.16&auth=true f.a. díaz et alii, frattura ed integrità strutturale, 25 (2013) 109-116; doi: 10.3221/igf-esis.25.16 111 figure 1: a) typical thermoelastic pattern of a fatigue crack. b) schematic illustration of the calibration process. phase shift information at the crack tip region hermoelastic information is normally presented as a vector where the modulus is proportional to the change in temperature experienced by the specimen due to the thermoelastic effect and the phase denotes the angular shift between the thermoelastic and the reference signals (loading signal). thus, the magnitude of the phase is normally constant unless adiabatic conditions are not achieved. however, there are two phenomena that lead to a lack of adiabatic conditions and hence a change in phase: heat generation due to plastic work and the presence of high stress gradients. both are conditions that occur near the crack tip region. in these circumstances heat conduction start taking place blurring the data at those regions, and the direct observation of the crack tip from a thermoelastic image is difficult. for image processing purposes, the reference and the thermoelastic signals are set in-phase. thus, the phase map should be zero in all those points where adiabatic conditions are achieved. however, near the crack tip, plasticity and high stress gradients lead to a loss of adiabatic conditions. this loss of adiabaticity can be easily identified in the phase map (figure 2.a). figure 2: typical phase map for a 6mm fatigue crack. illustration of the phase shift occurring at the crack tip as a result of the loss of adiabatic conditions (dimensions in mm). methodology for calculating the stress intensity factor range from thermoelastic images ifferent approaches have been developed in recent years as general methods for calculating the sif from the analysis of thermoelastic images. some of these approaches act by fitting a mathematical model describing the near crack tip stress field to a set of experimental data points collected at the near crack tip region [2 and 3]. as a result of the mathematical fitting the sif can be inferred. the adopted method for calculating the sif [2] is based on a t d http://www.gruppofrattura.it http://dx.medra.org/10.3221/igf-esis.25.16&auth=true f.a. díaz et alii, frattura ed integrità strutturale, 25 (2013) 109-116; doi: 10.3221/igf-esis.25.16 112 multipoint over-deterministic (mpod) method [6] in conjunction with a description of the near crack tip stress field based on muskhelishvili’s complex potentials [7]. direct observation of the crack tip is often difficult since data very near the crack tip tend to be blurred as a result of plasticity and the presence of high stress gradients. to calculate δk using tsa, it is required to obtain a thermoelastic map of the region near the crack tip. subsequently, a set of data points has to be collected in the region surrounding the crack tip. in this sense care must be taken to avoid collecting data points at those locations affected by near crack tip plasticity. to identify such a region stanley’s methodology has been employed [3]. stanley’s method [8] combines equation 2 with a mathematical expression describing the crack stress sum derived from westergaard’s model [9].     i iix y 1 2 2 k 2 k a s cos sin 2 22 r 2 r                            (3) for the case of pure mode i cracks, stanley observed that a maximum thermoelastic signal, smax, along any line parallel to the crack, occurred at a 60º angle with respect to the crack. taking this into account, equation 3 can be rearranged into a linear equation relating the vertical distance from the crack to any parallel line with the inverse square of the maximum thermoelastic signal along that particular line, 1/s2max. 2 i 2 2 max 3 3 k 1 y 4 a s        (4) if the previous relation for a real thermoelastic image is plotted (figure 3), three different regions can be identified: 1. region a. in this region no linear behaviour is observed since there is a loss of adiabatic conditions due to high stress gradients and crack tip plasticity. 2. region b. in this region a clear linear behaviour is observed. this can be employed to defined the region of validity of the model since the same behaviour as described by equation 6 is observed. 3. region c. in this region there is a deviation from the linear behaviour observed in region b, which indicates inappropriate use of this mathematical model. figure 3: graph of showing the linear relationship between the vertical distance from the crack tip and (smax)-2 employed in the methodology of stanley and chan for the calculation of the stress intensity factor from thermoelastic data. based on previous analyses, the region of validity for the model is identified in (figure 3) as the portion of the graph where a linear relationship is observed (region b). consequently, data is collected from the corresponding region of the thermoelastic image where such a linear relationship in stanley’s plot exists. the collected points are used to fit the stress field equation described by muskhelishvili’s model and to reconstruct the stress field around the crack tip. from the resultant fitting equation the sif can be inferred (figure 4). http://www.gruppofrattura.it http://dx.medra.org/10.3221/igf-esis.25.16&auth=true f.a. díaz et alii, frattura ed integrità strutturale, 25 (2013) 109-116; doi: 10.3221/igf-esis.25.16 113 figure 4: schematic illustration of the methodology for calculating the stress intensity factor from thermoelastic data. experimental set-up o support the idea that tsa can provide accurate information about the real fatigue crack driving force a fatigue test was conducted using aluminium 2024 ct specimens (figure 5.a). the specimen was initially prepared by bonding three strain gauges (tokyo sokki kenkyujo co., ltd., type fpa-2-11, 2 mm, 120  0.5 ) at the different locations. two of the strain gauges were located on the specimen’s surface at 62 mm from the edge of the specimen in line with the notch. one of them was aligned with the notch direction while the other was inclined 45 respect to the notch line (figure 5.b). the third strain gauge was located at the middle part of the back of the specimen (figure 5.b). figure 5: a) illustration the dimension of aluminium ct specimens employed for fatigue tests; b) scheme showing the location and orientation of the strain gauges employed for the calculation of the opening and closing loads from the compliance traces the specimen was initially pre-cracked and a crack was initiated and grown until it was approximately 3 mm from the two surface strain gauges (42 mm crack length). subsequently, increasing load steps were gradually applied with the aim of increasing the r-ratio. for each load step, several load and strain readings were collected over a period of 0.2 s using the three strain gauges. the collected data files were processed and the opening and closing loads estimated using the strain offset technique. at the same time, thermoelastic images corresponding to the crack at the different load steps were captured at the front of the specimen. δk results from tsa were compared to the nominal δk [10] for the r-ratios achieved by the increasing applied load steps.       nom 2 3 4 3/2 p f ( ) a k , wt w 2 f 0.886 4.64 13.32 14.72 5.6 1                     (5) where δp is the load range, a is the crack length and t and w are the specimen thickness and width respectively. t http://www.gruppofrattura.it http://dx.medra.org/10.3221/igf-esis.25.16&auth=true f.a. díaz et alii, frattura ed integrità strutturale, 25 (2013) 109-116; doi: 10.3221/igf-esis.25.16 114 calculation of the opening load from the analysis of the compliance traces he hardware employed consisted of a pc (viglen-pentium 200 mhz intel processor) provided with an enhanced multifunction i/o pci board (national instruments model pci 6052e) connected to a bnc accessory (national instrument model bnc-2090). the system was controlled using lab view software version 6.0 and made it possible to store load and strain data corresponding to a loading-unloading cycle as ascii files. since data were affected by random noise, it was necessary to employ a noise reduction technique. the technique adopted was an incremental polynomial method similar to the recommended astm method for data reduction in fatigue tests [11]. subsequently, for the calculation of the opening/closing loads the strain offset technique was adopted [12]. initially, data was divided into two sets according to the loading and the unloading branches and plotted as load versus strain plots. the unloading branch was first employed to determine the specimen compliance in the absence of closure by fitting a first order polynomial to its upper part. after that, the fitted first order polynomial was employed to perform the strain-offset calculation, which consisted of subtracting the actual strain data (affected by closure) from the fitted equation (not affected by closure). subsequently, the load against strain-offset was plotted to estimate the closing load. the closing load was then calculated as the points where data in the plot last crossed the zero strain offset (figure 6.a). figure 6: illustration showing load vs. strain and load vs. strain-offset plots for a 42 mm crack in an aluminium ct specimen loaded between 0.94 and 0.04 kn (r-ratio 0.04). a) unloading branch. b) loading branch. for the loading branch an identical methodology was followed. however, in this case the strain-offset calculation was performed using the same fitting first order polynomial obtained for the unloading branch. finally, the opening load was calculated following the same criteria as previously adopted for the unloading branch (figure 6.b). results corresponding to the opening and closing loads estimated from data at the different locations (horizontal, 45˚ and back face) are presented in figures 7.b, 7.b and 7.c. figure 7: a) illustration showing the variation of the opening and closing loads with the r-ratio for a 42 mm crack using a horizontal strain gauge, b) a 45˚ strain gauge, c) a back face strain gauge. t a) b) http://www.gruppofrattura.it http://dx.medra.org/10.3221/igf-esis.25.16&auth=true f.a. díaz et alii, frattura ed integrità strutturale, 25 (2013) 109-116; doi: 10.3221/igf-esis.25.16 115 tsa results o proceed to a direct comparison of thermoelastic results with those previously obtained from the analysis of the compliance traces, δk values inferred from tsa (figure 8.a) were also employed to calculate an equivalent opening/closing load according to equation 5. as for the case of compliance-based techniques, the equivalent opening load was plotted for the r-ratios corresponding to every load step and compared to the maximum and minimum applied loads. results are presented in figure 8.b. figure 8: a) plot showing the variation of δk with the r-ratio for a sequence of thermoelastic images corresponding to a 42 mm crack. b) plot illustrating the variation with the r-ratio of the opening load inferred from a sequence of thermoelastic images. discussion he initial aspect investigated was the repeatability of the results based on compliance measurements when using strain gauges bonded at the three locations when applying increasing r-ratio steps. results for the opening/closing were observed in all the cases to give similar results, with slightly smaller values for the case of the 45˚ strain gauge (figures7.a, b and c). in addition, it was also observed that as the r-ratio increased from 0.04 to 0.3, the opening/closing loads remained relatively constant and in all the cases with values higher than the minimum load. this clearly showed the presence of closure at low r-ratios. however, as the r-ratio increased from 0.3 upwards, the opening/closing load was observed to follow the minimum load indicating a considerably reduction in the closure levels. to check the ability of tsa to successfully infer the effective δk, thermoelastic images were captured at the same r-ratio steps simultaneously with compliance experiments. results for δk obtained from the analysis of the thermoelastic images (fig. 8.a) show the same behaviour as observed in the compliance analysis. as the r-ratio increases the δk from tsa tends to approach the nominal δk, showing a reduction in the closure level as the r-ratio increases. moreover, for direct comparison of thermoelastic results with those previously obtained using the strain-offset technique an equivalent opening/closing load was inferred from thermoelastic values of δk using equation 5 (fig. 8.b). results were observed to follow the same tendency as previous results obtained using the strain-offset technique for increasing r-ratio with very similar values to those obtained using the 45˚ strain gauge. this issue clearly support the ability of tsa to measure the effective δk rather that the nominal δk. conclusions sa has been presented as a novel technique to quantify the effective stress intensity factor range during cyclic loading. results from tsa have been compared with those obtained using a standard technique for crack closure measurement namely, the strain-offset technique. compliance results have clearly shown the presence of crack t t t a) b) http://www.gruppofrattura.it http://dx.medra.org/10.3221/igf-esis.25.16&auth=true f.a. díaz et alii, frattura ed integrità strutturale, 25 (2013) 109-116; doi: 10.3221/igf-esis.25.16 116 closure at low r-ratios in the analysed samples. moreover, results inferred from the analysis of thermoelastic images have been observed to be in good agreement with those obtained using the strain offset technique, showing the ability of tsa to successfully quantify the effective δk. references [1] james, m.n., some unresolved issues with fatigue crack closure measurement, mechanisms and interpretation problems, advance in fracture research, proceedings of the ninth international conference on fracture. edited by b.l. karihaloo et al., pergamon press, 5 (1996) 2403-14. [2] díaz, f.a., yates, j.r., patterson, e.a., some improvements in the analysis of fatigue cracks using thermoelasticity, int. j. fatigue, 26, 4 (2004) 365-376. [3] díaz, f.a., patterson, e.a., tomlinson r.a., yates, j.r., measuring stress intensity factors during fatigue crack growth using thermoelasticity, fat. fract. eng. mat. struct., 27 (2004) 571-584. [4] thomson, w. (lord kelvin), on the thermoelastic, thermomagnetic and pyro-electric properties of matters, philosophical magazine, 5 (1878) 4-27. [5] dulieu-smith, s.m., alternative calibration techniques for quantitative thermoelastic stress analysis, strain, 31 (1995) 9-16. [6] sanford, r., dally, j.w., a general method for determining mixed-mode stress intensity factors from isochromatic fringe pattern, engineering fracture mechanics, 11 (1979) 621-633. [7] muskhelishvili, n.i., some basic problems of the mathematical theory of elasticity, third edition, noordhoff ltd., groningen, holland, (1953). [8] stanley, p., chan, w.k., mode ii crack studies using the "spate" technique’, proc. of sem spring conference on experimental mechanics, new orleans, usa, (1986) 916-923. [9] westergaard, h.m., bearing pressures and cracks, j. of applied mechanics, 6 (1939) a49-63. [10] murakami, y., stress intensity factors handbook, pergamon, oxford, (1987). [11] astm, e647-95a, american society of testing and materials, 03.01 (1999). [12] skorupa, m., beretta, s., carboni, m., machniewicz, t., an algorithm for evaluating crack closure from local compliance measurements, fat. fract. eng. mat. struct., 25 (2002) 261-273. http://www.gruppofrattura.it http://dx.medra.org/10.3221/igf-esis.25.16&auth=true microsoft word numero_45_art_1 f. qui et alii, frattura ed integrità strutturale, 45 (2018) 1-13; doi: 10.3221/igf-esis.45.01 1 numerical simulation of dynamic mechanical properties of concrete based on 3d mesoscale model fengyan qin architecture and civil engineering, west anhui university, lu'an 237012, china qinfengyan1207@163.com jingsong cheng, heming wen cas key laboratory for mechanical behavior and design of materials university of science and technology of china, hefei 230026, china hmwen@ustc.edu.cn hongbo liu school of civil engineering and architecture, heilongjiang university, harbin 150080, china hliu@ hlju.edu.cn abstract. this paper attempts to disclose the mechanical properties of concrete under dynamic load. to this end, concrete was considered as a threephase composite of mortar, aggregate and interfacial transition zone (itz) on the mesoscale. in light of the dynamic constitutive relation of concrete, the dynamic response of concrete specimens was numerically simulated on a 3d meso-mechanical model. then, the authors discussed how the loading speed, aggregate volume content, and aggregate particle size affect the dynamic mechanical properties of concrete. the simulation results show that the damage morphology of concrete under dynamic load agrees well with that of theoretical analysis; the peak stress of concrete increased with the loading speed, revealing an obvious strain rate enhancement effect; the peak stress of concrete also increased with aggregate volume content; however, the peak stress of concrete gradually decreased with the increase in aggregate particle size under the constant volume content and grading of aggregate. the research findings shed new light on anti-impact design of concrete structures. keywords. concrete; dynamic mechanical properties; 3d meso-mechanical model; dynamic constitutive relation; numerical simulation; peak stress. citation: qin, f., cheng, j., wen, h., liu, h., numerical simulation analysis of the dynamic mechanical property of concrete based on 3d meso-mechanical model, frattura ed integrità strutturale, 45 (2018) 1-13. received: 15.03.2018 accepted: 02.06.2018 published: 01.07.2018 copyright: © 2018 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. http://www.gruppofrattura.it/va/45/12.mp4 f. qui et alii, frattura ed integrità strutturale, 45 (2018) 1-13; doi: 10.3221/igf-esis.45.01 2 introduction oncrete is one of the most popular materials in structural engineering. it has been extensively applied in buildings, bridges, mines, dams, power plants and transport facilities. in addition to normal static load, all these engineering structures may be subject to such dynamic loads as earthquakes, vehicle vibration, engineering blasting and debris flow. heavy losses of life and property may occur if the concrete of these structures fails or collapses under these loads. considering the high incidence of earthquakes and debris flows in china, it is very meaningful to examine the mechanical properties of concrete under dynamic load. there are obvious differences in macro strength and deformation features of concrete under dynamic load and that under static load. the dynamic load-induced response is a rather complex process, involving the evolution of microdefects in the material, the sensitive effect of material strain rate, and the impact of hydrostatic pressure correlation [1-5]. under dynamic load, the change in concrete deformation and stress is often transmitted in the form of wave, featuring strong instantaneity. it is very difficult to observe the mesoscale destruction or explain the enhancement of mechanical parameters (e.g. concrete strength) through experimental research. by contrast, the deformation, stress change and damage morphology during the impact can be visually presented through numerical simulation, which can provide some guidance on the cost and effect of the experiment. the numerical simulation of dynamic response starts from the microstructure of concrete. in general, a numerical model should be established based on theoretical and experimental results. then, the macro-mechanical properties of the material and the destruction process of concrete can be explored against the microstructure. on the mesoscale, concrete can be regarded as a composite of mortar, aggregate, and the interfacial transition zone (itz). over the years, many micro-mechanical models have been developed, including but not limited to lattice model [6-7], stochastic particle model [8-9], random aggregate model [10-11], and random mechanical property model [12-13]. based on meso-mechanical models, the numerical simulation can partially replace experimental research, provided that the models are rational and concrete parameters are precise enough. nevertheless, the application of numerical simulation has been severely restricted by the lack of experimental data on the mechanical parameters of mortar, aggregate and the itz, and the low computing efficiency of 3d analytical models. much research has been done on the dynamic features of concrete at home and abroad. for example, liu haifeng et al. [1419] investigated the mechanical properties and constitutive models of concrete under dynamic load, and simulated the dynamic features of concrete under the load using the holmquist–johnson–cook (hjc) model. du xiuli et al. [20-21] subdivided the finite-element grids by characteristic unit scale method and projected the grids to the established random aggregate model. in this way, the random multi-scale mechanical model was created and applied to reveal the micro failure mechanism of concrete under dynamic load. ren wenyuan et al. [22] proposed to simulate the constituent materials of concrete in each phase with the micro finite-element model (fem) based on x-ray computed tomography (xct) images. park et al. [23] conducted finite-element simulation of concrete and mortar at high strain rate, and analysed the bearing capacity, energy absorption and microstructure of the two materials under dynamic load. according to the aggregate grading curve of concrete, wang zongmin et al. [24] generated random aggregates by monte carlo method, prepared tensile test specimens with single-edge cracks from the aggregates, and simulated the whole process of the rupture failure of these specimens. considering the random aggregate structure of concrete, ma huaifa et al. [25] put forward a 3d meso-mechanical numerical model that reflects the random aggregate distribution or random mechanical properties of material in each phase. song laizhong et al. [26] ensured the rationality of aggregate distribution through random placement of parameterized aggregates, thereby fulfilling the bulk mass, fully-grade, high-strength requirements of aggregate arrangement simulation. by means of light gas gun, zhang zhu et al. [27] tested the dynamic mechanical properties test of concrete at different loading speeds, and then performed a numerical simulation on ansys autodyn. the simulation results were contrasted with the experimental data to explain the wave propagation during the destruction of the flyer and the target plate. there are only a few reports on how the size, distribution and volume content of aggregate on the dynamic mechanical properties of concrete. taking concrete as two-phase heterogenous composite of aggregate and mortar, liu haifeng et al. [16-19] wrote a random distribution program of 2d spherical aggregate of concrete in ansys parametric design language (apdl), using fuller’s grading curve and walraven plane transformation formula, and employed the program to discuss the effects of aggregate particle size, distribution and volume content on the dynamic mechanical properties of concrete. xu et al. [28] assumed concrete as a three-phase heterogeneous composite of mortar, aggregate and the itz, identified the regularity of aggregate grading and particle size distribution according to fuller’s grading curve, and developed a random distribution program of 3d spherical aggregate of concrete in ansys apdl. since the itz is too thin to simulate, the c f. qui et alii, frattura ed integrità strutturale, 45 (2018) 1-13; doi: 10.3221/igf-esis.45.01 3 aggregate was meshed into grids, the itz was generated by unit reconfiguration, and a 3d micro-mechanical model was created for concrete. the established model enjoys high computing efficiency. in this paper, the dynamic concrete features are simulated at different loading speeds, aggregate volume contents and aggregate particle sizes, using the 3d micro-mechanical model proposed by xu et al., and the influence rule of different factors on the dynamic mechanical properties of concrete are discussed in details. the mortar, aggregate and the itz were built on the material constitutive relation provided by xu and wen [29] and embedded in the business software ansys lsdyna for numerical simulation. establishment of the meso-mechanical model s mentioned above, the ansys ls-dyna dynamic analysis software was adopted to simulate the response of concrete with randomly distributed 3d aggregate under dynamic load. as shown in fig. 1, the test specimens are 100mm, 150mm or 200mm in side length. the upper and lower rigid plates respectively act as an actuator and a support, while the part between them is the concrete sample. the load was imposed onto the upper rigid plate to simulate concrete damage. figure 1: 3d meso-mechanical model. grid size both mortar and aggregate were simulated with the 3d entity unit of the same shape. the grid size was set to 2mm according to the side lengths of the cubic test specimens. compared to mortar, the itz is a weak, porous, nonuniform thin layer wrapped in the outer surface of aggregate particles. the typical thickness of the itz is merely 10~50m, which limits the minimum grid size. to improve the computing efficiency, 3d shell units were introduced to simulate the itz. here, it is assumed that the itz consists of homogeneous materials and its thickness is the average of the maximum and minimum values: 30m. distribution of aggregate particle size considering the effect of aggregate grading on the mechanical behaviour of concrete, fuller’s grading curve was adopted in our model to optimize concrete compactness and strength. the curve can be expressed as [30]:   max n d p d d        (1) where p(d) is the cumulative percentage of aggregates passing a sieve with aperture diameter d; dmax is the maximum size of aggregate particle; n is the shape parameter of the gradation curve and ranges from 0.45 to 0.7. in this paper, n is taken as a common value of 0.5. a f. qui et alii, frattura ed integrità strutturale, 45 (2018) 1-13; doi: 10.3221/igf-esis.45.01 4 if the aggregate particle size distribution obeys fuller’s gradation curve, then the amount of aggregate within the grading segment [ds, ds+1] can be obtained as:           1 agg 1 a all max min , s ss s p d p d v d d v v p d p d      (2) where vagg[ds, ds+1] is the aggregate volume within the grading segment [ds, ds+1], dmin is the minimum size of aggregate particle, va is the volume content of aggregate in concrete; vall is the total volume of concrete. after dividing the grading curve into different segments, it is possible to determine the size and number of aggregate particles by the grading segments containing the largest and smallest particles. for the grading segment [ds, ds+1], the spherical aggregate particles can be generated in the following steps: step 1. calculate the volume of aggregate vagg[ds, ds+1] to be generated in grading segment [ ds, ds+1] according to fuller’s grading curve. step 2. generate a random diameter d within the segment [ds, ds+1] to define the size of aggregate particles. it is assumed that the size d obeys uniform distribution between ds and ds+ 1, that is, d s ≤ d ≤ ds+1. it may also be expressed as d = ds +η (ds+1 − ds ), with η being a random number distributed uniformly between 0 and 1. step 3. calculate the volume of the generated particles and subtract it from the aggregate volume vagg[ds, ds+1]. step 4. repeat steps 2 and 3 until the remaining aggregate to be generated is less than πds3/6. in other words, there is no more room to generate any aggregate particle in the current grading segment. meanwhile, record the random number d ( ds ≤ d ≤ ds+1) in a size array sz(i , s ) = d (i = 1, 2, …, j), and the number of generated aggregate particles in a number array nb(s, 1) = j. next, transfer the volume of the remaining aggregate to the subsequent grading segment. step 5. repeat all the steps above for the next smaller size grading segment until the generation of the last aggregate of the minimum particle size. after obtaining the size and number arrays, select the near-spherical assemblies of elements to represent aggregates by replacing the properties of the mortar with those of the aggregates. once the size and corresponding number arrays have been ob-tained then the assemblies of elements which approximate spheres can be selected to represent aggregates by replacing the proper-ties of the cement mortar with those of the aggregates. generation of random aggregates and the itz in numerical simulations, the concrete specimens are either cylindrical or cubic in shape, depending on the type of concrete materials. here, the randomly generated aggregate particles are confined to cubic specimens. two constraints were imposed to select assemblies of elements as aggregate particles at a free position within each concrete specimen: each assembly of elements must be completely within the boundary of the specimen, and no overlap is allowed with the previously selected assembly. the random aggregates and the itzs were generated in the following procedure. step 1. mesh the mortar of the specimen into regular solid hexahedral grids. the grid size should be determined on the accuracy requirements. step 2. generate random coordinates (x , y , z) in 3d space within the specimen with the centre of the assembly of elements as aggregate. step 3. check the central position against the previous selected size array sz(i , s) to see if both constraints are completely satisfied. if one of the two constraints is violated, do not select the assembly of elements as aggregate. subsequently, repeat the coordinate generation and position check. by this analogy, select the assemblies of elements within nb(s, l) one by one. step 4. after the selection of all assemblies of elements within the grading segment [ds, ds+1], change their material properties from mortar to aggregate. after that, proceed with the selection process in the subsequent grading segment. step 5. repeat the steps above to select the assemblies of elements until all the assemblies of elements as aggregates are successively selected in the specimen and the total volume content of aggregates is satisfied. step 6. for each assembly of elements, select the outer surface nodes as aggregate, and split each node into two along the radial direction. next, generate the itz elements between nodes and the corresponding new nodes. moreover, reconstruct the mortar elements adjacent to aggregate by ert without changing the material properties of these elements. finally, check the quality of new elements and remove those failing the quality test (fig. 2(e)). based on the given distribution of aggregate grading, a 3d meso-mechanical model (fig. 2) was generated for concrete using the program developed by xu et al. [28]. the randomly distributed unit set and near-spherical shape of aggregate completely f. qui et alii, frattura ed integrità strutturale, 45 (2018) 1-13; doi: 10.3221/igf-esis.45.01 5 conform to the design requirements of the program. in addition, the itz was successfully generated through efficient and low-cost computation. (a) concrete specimen. (b) cement mortar. (c) aggregates . (d) interfacial transition zone (itz). (e) partial enlarged sectional view of an aggregate with itz layer. figure 2: schematic diagram of the 3d meso-mechanical model for cubed concrete specimen. f. qui et alii, frattura ed integrità strutturale, 45 (2018) 1-13; doi: 10.3221/igf-esis.45.01 6 contact definition and boundary conditions during numerical calculation, the lower rigid plate was clamped and the speed direction of the upper rigid plate was perpendicular to the concrete specimen. there was no friction between the rigid plate and concrete specimen. to keep the element failure contact effective, the single-face automatic contact *contact_automatic_single_surface was adopted for the simulation. material constitutive model he reliability of numerical simulation hinges on the feasibility of the numerical simulation model and the accuracy of the material constitutive model. as mentioned before, liu haifeng et al. [16-19] simulated the performance of concrete under dynamic load based on the hjc material constitutive model. however, the hjc takes no account of the damage evolution induced by the expansion of concrete volume, and its constitutive relation fails to describe the exact strain rate effect. in this paper, the mortar, aggregate and the itz are all illustrated by the concrete material constitutive model proposed by xu and wen. the model considers the following factors: the tensile and compressive damage effect, pressure correlation, lode corner effect and strain rate effect. since the material properties of the itz have not been fully understood, the material attribute of the itz was assumed to be the same of the mortar, except that its intensity is 60% of the latter. the relevant features of the material constitutive model are introduced as follows. pore state equation the mortar, aggregate and the itz can be considered as porous materials. the pressure-volume strain relationship can be described by the pore state equation (i.e. p~ state equation). the volumetric strain of the fully compacted or solid materials can be expressed as [32]:   0 0 0 1 1 1             (3) where =/0-1 is the volumetric strain;  and 0 are the current density and initial density, respectively; =s/ and 0=s0/0 are the current porosity and initial porosity, respectively; s and s0 are the current density and initial density of the solid material, respectively. when  0, the concrete material belongs to the compressive state. the corresponding state equation can be expressed as:  0 0max 1, min ,1 1 n lock lock crush p p p p                    (4) 2 3 1 2 3p k k k     (5) where k1, k2 and k3 are the bulk modulus of the solid material; pcrush is the pore collapse pressure under the load; plock is the pore densification pressure under the load. when  0, the concrete material belongs to the tensile state. the corresponding state equation can be expressed as: 1p k  (6) intensity model considering the compressive and tensile damage effect of the material, the lode angle effect, and strain rate effect [28-29, 33], the authors established the material constitutive relation to reveal the main mechanical features of concrete and other quasi-brittle materials based on the tripolar constrained face model. the intensity surface of concrete can be expressed according to the stress level on the material [29]: t f. qui et alii, frattura ed integrità strutturale, 45 (2018) 1-13; doi: 10.3221/igf-esis.45.01 7             , , ,' ' ' 3 0 3 + 3 3 / 0 / 3 / / 3 / 3 tt tt cc tt cc cc n cc c c cc c cc p f r e p y f f f p f r e p f f bf p f f f r e p f                       (7) where fcc=f ' c difm_t c and ftt=ftdiftt; f' c and ft are respectively the static compressive strength and static tensile strength; difm_t and dift are respectively the dynamic compressive and tensile enhancement factors resulted from the strain rate effect; c and t are respectively the functions of shear damage and tensile softening of concrete [32-34]; b and n are empirical constants; r(, e) is the lode corner effect [35], with  and e being the ratio between the lode angle and the tensile meridian and the ratio between the lode angle and the compressive meridian, respectively. as shown in fig. 3, the strength surface of concrete can be classified into three segments: the tensile section (p0), the transition section (0pfcc/3) and the compressive section (pfcc/3). figure 3: strength surface of concrete parameters mortar itz aggregate 0(kg/m3) 2100 1800 2600 s0(kg/m3) 2630 2630 2630 pcrush(mpa) 10.7 6.4 23.3 plock(gpa) 3 3 3 n 3 3 3 k1(gpa) 14.2 6.9 17.4 k2(gpa) 30 30 -3.0e3  0.20 0.17 0.30 k3(gpa) 10 10 1.5e5 g(gpa) 10.7 3.2 14.7 f' c (mpa) 32.0 19.2 70.0 ft(mpa) 3.1 2.4 4.5 b 1.54 1.54 1.95 n 0.8 0.8 0.76 table 1: parameter values of the 3d meso-mechanical model. f. qui et alii, frattura ed integrità strutturale, 45 (2018) 1-13; doi: 10.3221/igf-esis.45.01 8 selection of material parameters the model parameters of mortar, aggregate and the itz of this research are listed in tab. 1. specifically, the initial density0 of mortar and aggregate and the uniaxial compressive strength f' c were extracted from ref. [17]. the compaction density s0 was set to 1.01 times of the initial density of aggregate. the uniaxial compressive strength f' c and the elasticity modulus e of the itz were set to 60% of the mortar. the relevant parameter relations are as follows: pcrush=f ' z /3, k1=e/3(1-2v), g=e/2(1+v) and '0.54t cf f . the values of the other parameters were obtained from ref. [28]. numerical simulation and results analysis damage morphology uring the numerical simulation with our model, the aggregate volume content was 40% and the aggregate particle size fell in 5~20mm. the damage morphology of the cubic specimens with the side length of 150mm is presented in fig. 4, where the grey white part is the removed unit. it can be seen that the specimens were basically destroyed along the itz. this phenomenon echoes with the theoretical results. figure 4: damage morphology figure 5: relationship between the peak stress and the loading speed. d f. qui et alii, frattura ed integrità strutturale, 45 (2018) 1-13; doi: 10.3221/igf-esis.45.01 9 effect of loading speed the destruction of cubic concrete specimens (side length: 100mm, 150mm and 200mm; aggregate volume content: 40%; aggregate particle size: 5~10mm and 5~20mm) was simulated at different loading speeds. then, the effect of the loading speed on peak stress of the concrete was analysed by the fem and 3d micro model (fig. 5). as shown in fig. 5, the peak stress gradually increased with the loading speed, whether it was 5m/s, 10m/s or 15m/s. this means the concrete is a sensitive material. under the same condition, the peak stress of the 3d microscopic model is lower than that of the fem, indicating that the former can reflect the inhomogeneity and low strength at the itz of the concrete. there were a large number of microcracks in the concrete. some of them existed before the loading, and some were generated under the load. the original and load-induced microcracked grew steadily in different directions during the simulation. the interaction between the microcracks deflects the propagation direction, making it more time-consuming to achieve full penetration of the specimen. at a low loading speed, the energy generated by the impact was rather small. this leaves enough time for the cracks to propagate and merge. in this case, only a few cracks extended and interacted with each other, resulting in a low stress level and a small peak stress. at a fast loading speed, the impact generated a huge amount of energy, leaving not enough time for stable cracks to propagate and merge. thus, numerous microcracks extended almost simultaneously and interacted with each other. on the macroscale, the material withstood a rather high stress, i.e. the peak stress was on a high level. (a) 100mm100mm100mm specimen (b) 150mm150mm150mm specimen (c) 200mm200mm200mm specimen figure 6: relationship between aggregate volume content and peak stress of concrete. 15 20 25 30 35 40 45 50 55 volume fraction of coarse aggregate(%) 70 75 80 85 5-10mm, v=10m/s 5-15mm, v=10m/s 5-20mm, v=10m/s 5-25mm, v=10m/s 5-40mm, v=10m/s f. qui et alii, frattura ed integrità strutturale, 45 (2018) 1-13; doi: 10.3221/igf-esis.45.01 10 effect of aggregate volume content keeping the loading speed at 10m/s, the destruction of cubic concrete specimens (side length: 100mm, 150mm and 200mm; aggregate particle size 5~10mm, 5~15mm, 5~20mm, 5~25mm and 5~40mm) was simulated at different aggregate volume contents. then, the impact of aggregate volume content on the peak stress of concrete was deliberated in details (fig. 6). it can be seen from fig. 6 that the peak stress increased continuously with the growth in aggregate volume content. this is because the volume of the mortar shrinks with the increase in aggregate volume; since the aggregate is much stronger than the mortar, the aggregate volume content exhibits a positive correlation with the concrete strength. (a) 100mm100mm100mm specimen (b) 150mm150mm150mm specimen (c) 200mm200mm200mm specimen figure 7: relationship between minimum aggregate particle size and peak stress of concrete. effect of minimum aggregate particle size under the constant loading speed (10m/s), aggregate grading and maximum aggregate particle size (25mm), the destruction of cubic concrete specimens (side length: 100mm, 150mm and 200mm; aggregate volume content: 20%, 30%, 40% and 50%) was simulated at different minimum aggregate particle sizes (5mm, 10mm and 15mm). then, the impact of minimum aggregate particle size on the peak stress of concrete was discussed in details (fig. 7). it is clear that the peak stress was on the rise with the growth of aggregate volume content; when the aggregate volume content remained unchanged, the peak stress gradually declined with the increase in minimum aggregate particle size. the maximum value of the peak stress was observed at the aggregate particle size of 5mm. the overall decline of the peak stress under constant aggregate volume content can be explained as follows. first, it is more likely for aggregate particles to have internal defects if they are of a large size. second, the specific surface area is small at a large minimum particle size, meaning 0 5 10 15 20 25 diameter of coarse aggregate(mm) 65 70 75 80 85 20%, v=10m/s 30%, v=10m/s 40%, v=10m/s 50%, v=10m/s f. qui et alii, frattura ed integrità strutturale, 45 (2018) 1-13; doi: 10.3221/igf-esis.45.01 11 that less cement is needed to reach the same aggregate volume content; in this scenario, the binding area between the aggregate and the cement decreases, which weakens the itz and in turn the concrete. effect of maximum aggregate particle size under the constant loading speed (10m/s), aggregate grading and minimum aggregate particle size (5mm), the destruction of cubic concrete specimens (side length: 100mm, 150mm and 200mm; aggregate volume content: 20%, 30%, 40% and 50%) was simulated at different maximum aggregate particle sizes (10mm, 15mm, 20mm, 25mm and 40mm). then, the impact of maximum aggregate particle size on the peak stress of concrete was analysed in details (fig. 8). it can be seen that the peak stress was on the rise with the growth of aggregate volume content; when the aggregate volume content remained unchanged, the peak stress gradually declined with the increase in maximum aggregate particle size. in other words, the peak stress exhibited a gradual declining trend with the growth in the maximum aggregate particle size, when the minimum aggregate particle size remained the same. this trend can be explained as follows. the specific surface area is small at a large maximum particle size, meaning that less cement is needed to reach the same aggregate volume content; in this scenario, a water film can develop easily on the aggregate surface, reducing the strength of the itz and adding to the mechanical nonuniformity of the concrete. due to the porosity induced by the water film, the stress concentrates on the itz, which weakens the itz and in turn the concrete. (a) 100mm100mm100mm specimen (b) 150mm150mm150mm specimen (c) 200mm200mm200mm specimen figure 8: relationship between maximum aggregate particle size and peak stress of concrete p e a k s tr e s s (m p a ) p e a k s tr e s s (m p a ) f. qui et alii, frattura ed integrità strutturale, 45 (2018) 1-13; doi: 10.3221/igf-esis.45.01 12 conclusions he dynamic load-induced response of concrete material is a rather complex process, involving the evolution of microdefects in the material, the sensitive effect of material strain rate, and the impact of hydrostatic pressure correlation and the lode angle. besides, the mechanical performance of concrete relies heavily on the size and distribution of the aggregate. in view of these, this paper attempts to disclose the mechanical properties of concrete under dynamic load. to this end, concrete was considered as a three-phase composite of mortar, aggregate and the itz on the mesoscale. in light of the dynamic constitutive relation of concrete, the dynamic response of concrete specimens was numerically simulated on a 3d meso-mechanical model. then, the authors discussed how the loading speed, aggregate volume content, and aggregate particle size affect the dynamic mechanical properties of concrete. the simulation results show that the damage morphology of concrete under dynamic load agrees well with that of theoretical analysis; the peak stress of concrete increased with the loading speed; the peak stress of concrete also increased with aggregate volume content; however, the peak stress of concrete gradually decreased with the increase in aggregate particle size under the constant volume content and grading of aggregate. the research findings shed new light on anti-impact design of concrete structures. acknowledgments he research of this paper is made possible by the generous support from the national natural science foundation of china (grant no: 51678221); key project of natural science research in anhui universities (grant no: kj2017a405); natural science research project of west anhui university (grant no: wxzr201615; wxzr201626; 2010lw009; kj103762015b12). references [1] bischoff, p.h. and perry, s.h. (1991). compressive behaviour of concrete at high strain rates, materials and structures, 24, pp. 425-450. [2] gary, g. and bailly, p., (1998). behaviour of quasi-brittle material at high strain rate. experiment and modelling, european journal of mechanics-a/solids, 17, pp. 403-420. [3] geng, b.y., ni, w., wu, h., huang, x.y., cui, x.w., shuang, wang, s. and zhang, s.q. (2016). on high-strength lowshrinkage itos-based concrete, international journal of heat and technology, 34, pp. 677-686. [4] brara, a., camborde, f., lepaczko, j.k. and mariotti, c. (2001). experimental and numerical study of concrete at high strain rates in tension, mechanics of materials, 23, pp. 33-45. [5] pedersen, r.r., simone, a. and sluys, l.j. (2013). mesoscopic modeling and simulation of the dynamic tensile behavior of concrete, cement and concrete research, 50, pp.74-87. [6] schlangen, e. and garboczi, e.j. (1997). fracture simulations of concrete using lattice models: computational aspects, engineering fracture mechanics, 57, pp. 319-332. [7] li, g.l. and mier, j.g. (2003). 3d lattice type fracture model for concrete, engineering fracture mechanic, 70, pp. 927941. [8] cundall, p.a., strack, o.d. (1979). a discrete numerical model for granular assemblies, geotechnique, 29, pp. 47-65. [9] bažant, z.p., tabbara, m.r., kazemi, m.t. and pijaudier-cabot, g. (1990). random particle model for fracture of aggregate or fiber composites, journal of engineering mechanics, 116, pp. 1686-1705. [10] liu, g.t. and wang, z.m., (1996). numerieal simulation study of fraeture of concrete materials using random aggrega model, journal of tsinghua university (science and technology), 36, pp. 84-89. [11] wang, z., kwan, a. and chan, h., (1999). mesoscopic study of concrete i: generation of random aggregate structure and finite element mesh, computers & structures, 70, pp. 533-544. [12] zhu, w. and tang, c., (2002). numerical simulation on shear fracture process of concrete using mesoscopic mechanical model, construction and building materials, 16, pp. 453-463. [13] zhu, w., tang, c. and wang, s., (2005). numerical study on the influence of mesomechanical properties on macroscopic fracture of concrete, structural engineering and mechanics, 19, pp. 519-534. t t f. qui et alii, frattura ed integrità strutturale, 45 (2018) 1-13; doi: 10.3221/igf-esis.45.01 13 [14] song, j. and chen, f.y. (2015). calculation model for thermo-mechanical coupling and 3d numerical simulation for concrete tower of cable-stayed bridge, mathematical modelling of engineering problems, 2, pp. 9-12. [15] liu, h.f. and ning, h.f. (2012). constitutive model for concrete subjected to impact loading, journal of southeast university, 28, pp. 79-84. [16] zhang, h.y., (2015). thermodynamic property of concrete and temperature field analysis of the base plate of intake tower during construction period, international journal of heat and technology, 33, pp. 145-154. [17] liu, h.f. and han, l. (2016). numerical simulation of dynamic mechanical behavior of concrete with twodimensional random distribution of coarse aggregate, chinese journal of high pressure physics, 30, pp. 191-199. [18] liu, h.f. and ning, j.g. (2009). a meso-mechanical constitutive model of concrete subjected to impact loading, explosion and shock waves, 29, pp. 2261-267. [19] liu, h.f., wang, y.y. and song, j.x. (2016). numerical simulation of dynamic mechanical behaviors of desert sand concrete, journal of hydraulic engineering, 47, pp. 493-500. [20] du, x.l., tian, r.j., peng, y.j. and tian, y.d. (2009). numerical simulation of concrete dynamic compressive strength under impact loading based on mesomechanics, journal of beijing university of technology, 35, pp. 213-217. [21] du, x.l. and jin, l. (2011). mechanical property reserch on concrete based on random multi-scale mechanical model, engineering mechanics, 28, pp. 151-155. [22] ren, w.y., yang, z.j. and huang, y.j. (2015). meso-scale fracture modelling of concrete based on x-ray computed tomography images, journal of hydraulic engineering, 46, pp. 452-459. [23] park, s.w., xia, q. and zhou, m. (2001). dynamic behavior of concrete at high strain rates and pressures: ii. numerical simulation, international journal of impact engineering, 25, pp. 7887-7910. [24] wang, z.m. and qiu, z.z. (2005). random aggregate structure of mesoscopic concrete and finite element mesh, chinese journal of computational mechanics, 22, pp. 728-732. [25] xu, h. and wen, h.m. (2016). a computational constitutive model for concrete subjected to dynamic loadings ,2016, international journal of impact engineering, 91, pp. 116-125. [26] song, l.z., shen, t. and yu, b. (2013). the approach to establishing a two-dimensional parameterized aggregate model for concrete simulation, engineering mechanics, 30, pp. 5-13. [27] zhang, z.h., zhao, h. and yu, h. (2011). experimental and numerical simulation of concrete dynamic mechanical properties, chinese journal of high pressure physic, 25, pp. 533-538. [28] xu, p.b., xu, h. and wen, h.m. (2016). 3d meso-mechanical modeling of concrete spall tests, international journal of impact engineering, 97, pp. 46-56. [29] xu, h. and wen, h.m. (2016). a computational constitutive model for concrete subjected to dynamic loadings, international journal of impact engineering, 91, pp. 116-125. [30] riggers, p. and moftah, s.o. (2006). mesoscale models for concrete: homogenisation and damage behaviour, finite elements in analysis and design, 42, 623-636. [31] hao, y., hao, h. and zhang, x. (2012). numerical analysis of concrete material properties at high strain rate under direct tension, international journal of impact engineering, 39, pp. 51-62. [32] hartmann, t., pietzsch, a. and gebbeken, n. (2010). a hydrocode material model for concrete, international journal of protective structures, 4, 443-468. [33] xu, h. and wen, h. (2013). semi-empirical equations for the dynamic strength enhancement of concrete-like materials, international journal of impact engineering, 60, pp. 6-81. [34] malvar, l.j., crawford, j.e., wesevich, j.w. and simons, d. (1997). a plasticity concrete material model for dyna3d, international journal of impact engineering, 19, pp. 847-873. [35] william, k. and warnke, e., (1975). constitutive model for the triaxial behavior of concrete, international association for bridge and structural engineering, bergamo, italy. << /ascii85encodepages false /allowtransparency false /autopositionepsfiles true /autorotatepages /none /binding /left /calgrayprofile (dot gain 20%) /calrgbprofile (srgb iec61966-2.1) /calcmykprofile (u.s. web coated \050swop\051 v2) /srgbprofile (srgb iec61966-2.1) /cannotembedfontpolicy /error /compatibilitylevel 1.4 /compressobjects /tags /compresspages true /convertimagestoindexed true /passthroughjpegimages true /createjobticket false /defaultrenderingintent /default /detectblends true /detectcurves 0.0000 /colorconversionstrategy /cmyk /dothumbnails false /embedallfonts true /embedopentype false /parseiccprofilesincomments true /embedjoboptions true /dscreportinglevel 0 /emitdscwarnings false /endpage -1 /imagememory 1048576 /lockdistillerparams false /maxsubsetpct 100 /optimize true /opm 1 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/hrv (za stvaranje adobe pdf dokumenata najpogodnijih za visokokvalitetni ispis prije tiskanja koristite ove postavke. stvoreni pdf dokumenti mogu se otvoriti acrobat i adobe reader 5.0 i kasnijim verzijama.) /hun 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/pdfxoutputintentprofileselector /documentcmyk /preserveediting true /untaggedcmykhandling /leaveuntagged /untaggedrgbhandling /usedocumentprofile /usedocumentbleed false >> ] >> setdistillerparams << /hwresolution [2400 2400] /pagesize [612.000 792.000] >> setpagedevice microsoft word numero_50_art_19_2537 a. salmi et alii, frattura ed integrità strutturale, 50 (2019) 231-241; doi: 10.3221/igf-esis.50.19 231 crack growth study under thermo-mechanical loads: parametric analysis for 2024 t3 aluminum alloy salmi abdallah, elajrami mohamed university of djillali liabès of sidi bel-abbes, algeria salmiabdallah08@gmail.com, https://orcid.org/0000-0001-8352-8801 eladjrami_mohamed@yahoo.fr mohamed el-amine slimani university of science and technology houari boumediene, bab-ezzouar, 16111 algiers, algeria mslimani@usthb.dz, https://orcid.org/0000-0002-8725-4892 abstract. due to their severe operating conditions, many industrial components are subjected to complex combinations of cyclic mechanical stresses and thermal pressures. these combinations are responsible for the initiation and propagation of fatigue cracks in these parts, which can lead to failure. thus, the study of the fatigue strength of these parts in such conditions becomes essential because it allows us to predict the life and safety of components. this study examines the influence of the load ratio and temperature on the propagation rate of long cracks on the outer surface. the propagation of a fatigue crack in abaqus was therefore automatically simulated using an identified paris law of 2024 t3 aluminum alloy. therefore, the study of these components' fatigue resistance in such conditions becomes essential to predict the service life and safety of the components. keywords. 2024 t3 aluminum alloy; crack growth; temperature; finite elements; thermo-mechanical fatigue. citation: salmi, a., elajrami, m., slimani, m. e.a., crack growth study under thermomechanical loads: parametric analysis for 2024 t3 aluminum alloy, frattura ed integrità strutturale, 50 (2019) 231-241. received: 07.06.2019 accepted: 16.08.2019 published: 01.10.2019 copyright: © 2019 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. introduction o determine whether a crack is present in an equipment under thermo-mechanical loads, it is necessary, for obvious safety reasons, to identify accurately its harmfulness degree. when this crack spreads, under thermo-mechanical loads, it is important to quickly assess the evolution of this harmfulness degree and more concretely the residual life of the cracked structure. t http://www.gruppofrattura.it/va/50/2537.mp4 a. salmi et alii, frattura ed integrità strutturale, 50 (2019) 231-241; doi: 10.3221/igf-esis.50.19 232 the resolution of this type of problem, within the framework of fracture mechanics, is carried out classically using the finite element method. but digital simulation of two-dimensional crack growth is challenging to simulate due to mesh-size reasons [1]. the asymptotic behavior of the displacement field in the vicinity of the crack front requires the local use of an extremely refined mesh size. since the remeshing of the complete structure at each stage of the front is prohibitive, one solution is to isolate the discontinuity in a crack block, representing the strict vicinity of the crack, whose mesh size depends on the size of the defect and which can be inserted at any time into the rest of the structure, whose mesh size is fixed once and for all. we can mention, among others. dhondt [2] proposed an alternative solution for local remeshing with a generation of hexahedral elements at the crack passage, within the same framework as the finite element method. more generally, there are so-called "mesh-less" methods, which, in principle, make it possible to get rid of all the difficulties associated with mesh size, but at a higher price. jordan [3] studied the effect of the additional sdb (slide diamond burnishing) parameters on the fatigue behavior of the 2024-t3 al alloy has been studied experimentally. samples of smooth, hourglass-shaped samples were blade-polished using different combinations of additional sdb parameters and then subjected to flexural fatigue tests. residual stresses, introduced by the sdb, were measured by the x-ray diffraction technique. the microstructure close to the surface of the samples polished on a slide was studied. it has been established that the sdb produces two main effects, which depend on additional parameters of the sdb. the essence of the macro-effect is the creation of residual compressive stresses in the superficial and submarine layers. these constraints delay the formation and growth of fatigue macro cracks and thus increase the life of the polished components per blade. monotonic tests were performed from karakaş and szusta [4] to determine the influence of temperature on the mechanical properties of the material. the purpose of the cyclic tests was to acquire the parameters required for the manson-coffin equation in order to plot the stress-fatigue life curves. in addition, the stress-strain behavior of the alloy and the cyclic hardening behavior were evaluated using the ramberg-osgood equation. the results obtained indicate that the fatigue life is reduced when the operating temperature increases. punith gowda [5] reveals the study of the mechanical properties of al2024-tungsten carbide mmcs (metal matrix composites) containing tungsten carbide (wc) particles. the reinforcing particles in al2024 alloy ranged from 0% to 5% by weight. the results of this study revealed that as the tungsten carbide particle content increased, tensile strength, hardness, and young modulus, compressive strength, increased. significantly, accompanied by a reduction in ductility. mohammad zaki [6] reveals the influences of anodizing parameters of al 2024 t3 in tsa (tartaric-sulphuric acid) on the thickness, the weight and corrosion resistance of the anodized layer are studied. the corrosion resistance test was performed by running a salt spray test for 336 hours and anodic polarization measurements using a potentiostat. the results of showed that the most important factor in determining the thickness and weight of the anodized layer is the temperature, followed by the applied voltage, the voltage-temperature interaction, the temperature and the duration of the layer [6]. figure 1: sample (30 mm*10 mm*2.29mm) 10 mm 30 mm plate thickness 2.29 stress crack fixed end a. salmi et alii, frattura ed integrità strutturale, 50 (2019) 231-241; doi: 10.3221/igf-esis.50.19 233 this study presents a tool for simulating the crack growth in thermo-mechanically loaded equipment. this tool is based on the crack block concept and aims to minimize the cost of meshing operations, which are prevalent in this type of application. moreover, this work is based on the creation of a program in python language using the advantages of the abaqus calculation codes, chosen for their respective flexibility in terms of mesh size and geometric modeler, in the absence of a versatile tool. the reminder of the article is organized as follows: section 2 describes the material used to conduct this study. section 3 discusses the results and, finally, section 4 summarizes the results of this work and draws conclusions. to study the characteristics of long-standing cracks, all tests were performed in ambient air with a frequency of 10 hz [7] and under sinusoidal loading of constant amplitude 118 mpa [8], with a load ratio r between 0.1 and 0.7. the purpose of these tests is to characterize the behavior of long cracks in the case of 2024 t3 aluminum alloy plates by determining the propagation threshold and the parisian law coefficients. initial crack size ainit = 5.08mm capable spread to a critical final size a = 7.18 mm. fig. 1 shows the sample (30 mm*10 mm*2.29mm) exposed to an initial temperature of 20°c. this study focuses on the behavior of an external crack, since the rate of crack propagation is more severe [9]. study material 2024-t3 alloy he 2024 alloy is a copper magnesium aluminum alloy with a high copper content of up to 4% by mass. generally, impurities such as iron and silicon are always present in the composition. in addition to the precipitation hardening, fine particles of size ≈ 100 nm formed during heat treatment, alloy 2024 also contains intermetallic particles. these particles are much larger than the hardening precipitates; they are formed during processing and have no effect in the curing process. on the other hand, they have an important role in the phenomena of localized corrosion. baog et al. [10] estimated that the density of intermetallic is in the order of 300,000 particles/cm2. the microstructure of these alloys becomes very complex given the difference in composition and the different forms of this intermetallic, which are of two types: • the particles s (al2cumg): according to bechet et al. [11], the particles s represent 60% of the intermetallic particles present in the alloy 2024-t3. they have a rounded shape, with sizes ranging from 1 to 5 µm [12]. •the particles of al-cu-fe (mn): several authors have worked on the characterization of these particles according to their size and their chemical composition [10, 11, and 13]. al-cu-fe (mn) particles are generally larger than s-phase particles, with sizes ranging from 10 to 25 µm and irregular shapes. tab. 1 summarizes the intermetallic particles of this type present in the 2024-t3 alloy. table 1: synthesis of the different intermetallic compounds of the al-cu-fe (mn) type present in alloy 2024-t3 elastoplastic behaviour tab. 2 presents the standard elastic properties of aluminum 2024 t3 [15]. modulus of elasticity (gpa) poisson coefficient coefficient of thermal expansion (mm/m*k) thermal conductivity (w/m*k) specific heat capacity (j/kg*k) density (g/cm3) 73 0.33 22.8 120 870 2.77 table 2: mechanical properties of 2024-t3 aluminum alloy t composition reference al7cufe2 [10, 13] al12 (fe, mn) 3si [14] al6 (fe, cu, mn) [11, 13, 14] (al, cu) 6mn [11, 13] al6mnfe2 [11] al20 (cu, fe, mn) 5si [10] a. salmi et alii, frattura ed integrità strutturale, 50 (2019) 231-241; doi: 10.3221/igf-esis.50.19 234 tab. 3 provides the 2024t3 aluminum alloy chemical compositions [4]. table 3: chemical composition by mass in percentage. results and discussion aris and erdogan have constructed a quantitative framework of fatigue fracture mechanics, which correlates the fatigue crack growth rate to the range of stress intensity factor as follows [16]: mda c k dn   (1) where c and m are empirical material constants, ∆k = kmax kmin is the stress intensity factor range in fatigue loading, n is number of cycles, and da is crack extension length. the following correlation gives the relation between c and m parameters: log c = a + bm (2) a and b 0  where: a is the ordinate at the origin and b is the slope of the regression line. or c = m a b (3) with a =10 = a p da dn       b =10 = k b p   ( ); ( ) p p da mm k mpa m dn cycle           coordinates of the pivot point [17]. the material constants in paris equation depicted in tab. 4 [18]: plate thickness 2.29 mm plate thickness 6.35 (mm) m = 3.2828 m = 4.224 c = 3.63 e-13 c = 1.51 e-15 table 4: material constants in paris law for aluminum panel. the total number of stress cycles n required for a short crack to propagate from the initial crack length a0 to any crack length a can then be determined as 1 z i i n n    (4) ni stress cycles required for the appearance of the initial crack i = 1; 2; 3; . . . ; z z number of grains transverse by the crack material cu fe si cr mg mn zn ti 2024-t3 4.82 0.18 0.07 0.02 1.67 0.58 0.06 0.15 p a. salmi et alii, frattura ed integrità strutturale, 50 (2019) 231-241; doi: 10.3221/igf-esis.50.19 235 when the crack extends over ten or more grains, the influence of the material structure on the growth of the crack becomes negligible and the theory of mechanics of linear elastic fracture can be applied later [19]. in this simple form, the presence of a growth threshold of fatigue cracks and a limit greater than ∆k (stress intensity factor range) for the fracture are not shown, although, if appropriate, expressions taking into account these limits, as well as the influence of the load ratio of the cycle r = pmin / pmax can be easily found in the literature. load ratio influence ig. 2 shows the curves representing the cracking rate versus the stress intensity factor range for the different load ratios studied. fig. 2 indicates that the propagation rates vary according to the load ratio. the load ratio effect is very important, in fact, the propagation rate at r=0.3 is much higher than at r = 0.1 in the range 19.07 mpa√m<∆k<37.55 mpa√m. for example, for ∆k = 23.55 mpa√m, the propagation rate for r = 0.1 is about 9.89e-5 m/cycle, while it is more than twice as high for r = 0.3 (da/dn =1.11e-4 m/cycle). the same observations can be made if the different load ratios r = 0.3 and r=0.4 are compared. r = 0.4 and r = 0.5 and finally r = 0.5 and r = 0.7. figure 2: load ratio influence on crack propagation the impact of the load ratio r (0.1, 0.3, 0.4, 0.5 and 0.7) was verified. indeed, the load ratio effect has a very significant impact on the crack propagation rate of the 2024 t3 aluminum alloy. to study the influence of the load ratio on the propagation time of a fatigue crack, fig. 3 shows the propagation of a 5 mm crack as a function of the number of cycles for load ratios 0.1, 0.3, 0.4, 0.5 and 0.7 under a maximum stress of 118 mpa. figure 3: propagation time of a 5mm crack for different load ratios. f a. salmi et alii, frattura ed integrità strutturale, 50 (2019) 231-241; doi: 10.3221/igf-esis.50.19 236 the results show that the number of cycles increases with the load ratio, that is the higher the load ratio, the greater the cracking resistance at the same maximum stress. we also note that: the paper presents a computational model for determining the lifetime of crack propagation for 2024 t3 aluminum alloy. the fatigue process is divided into crack initiation (ni) and crack propagation (np) periods, which allows the total lifetime to be determined as n ni np  (5) influence of temperature hese results present a digital calculation of the plate. thermal and mechanical results are exposed respectively. thermal results fig. 4 shows the temperature changes as a function of the x-position in the thickness. figure 4: temperature changes as a function of the x-position in the thickness at different temperatures these results show that the thermal gradient in the thickness continues by conduction and decreases during the inner face of the plate. the temperature field in the plate has been well estimated by our calculations. mechanical results this section presents the results of the calculation with a model in which the mechanical behaviour of each phase is of the elasto-plastic type with linear cinematic hardening. the axial displacement variations follow the thickness are represented by the figs. 5 < a (a=5.08mm); b (a=5.50mm); c (a=6.34mm); d (a=7.18mm)> for differing temperatures at crack widths ranging from 5.08 to 7.18. on the one hand in fig. 5: we note that for each x-position in thickness, when the temperature increases from + 30°c to +60°c, the changes in the very high axial displacement is more apparent for crack widths greater than 7.18 mm. on the other hand, for a x-position in thickness and constant temperature, with an increase in crack width from a=5.08mm to 7.18mm, the changes in axial displacement increase. deformation variations according to thickness are illustrated in fig. 6 < a (a=5.08mm); b (a=5.50mm); c (a=6.34mm); d (a=7.18mm)> to differentiate temperatures at crack widths ranging from 5.08 to 7.18 mm. these results also indicate that: the overall deformations of the plate increase significantly, when the thermal and mechanical aspect are coupled. overall, compared to the thermo-mechanical growth cases presented above, the overall deformations of the plate are less well simulated in this case. t a. salmi et alii, frattura ed integrità strutturale, 50 (2019) 231-241; doi: 10.3221/igf-esis.50.19 237 the equivalent stress variations according to vosmises follow thickness are represented by the figs. 7 < a (a=5.08mm); b (a=5.50mm); c (a=6.34mm); d (a=7.18mm)> to differ from temperatures at crack width between 5.08 and 7.18 mm. 0 2 4 6 8 10 0 1x104 2x104 3x104 4x104 5x104 d is p la c e m e n t (u m ) x-position in the thickness(mm) t=30°c t=40°c t=50°c t=60°c 0 2 4 6 8 10 1x104 2x104 3x104 4x104 5x104 6x104 d is p la c e m e n t (u m ) x-position in the thickness (mm) t=30°c t=40°c t=50°c t=60°c a b 0 2 4 6 8 10 2x104 3x104 4x104 5x104 6x104 7x104 8x104 d is p la c e m e n t (u m ) x-position in the thickness (mm) t=30°c t=40°c t=50°c t=60°c 0 2 4 6 8 10 2x104 3x104 4x104 5x104 6x104 7x104 8x104 9x104 1x105 d is p la c e m e n t (u m ) x-position in the thickness (mm) t=30°c t=40°c t=50°c t=60°c c d figure 5: variations in axial displacement follow from the x-position in the thickness at different temperatures 0 2 4 6 8 10 -200 0 200 400 600 800 1000 1200 1400 1600 1800 2000 d e fo rm a ti o n (u m ) x-position in thickness (mm) t=30°c t=40°c t=50°c t=60°c 0 2 4 6 8 10 -200 0 200 400 600 800 1000 1200 1400 1600 1800 2000 d e fo rm a tio n ( u m ) x-position in thickness (mm) t=30°c t=40°c t=50°c t=60°c a b a. salmi et alii, frattura ed integrità strutturale, 50 (2019) 231-241; doi: 10.3221/igf-esis.50.19 238 0 2 4 6 8 10 0 200 400 600 800 1000 1200 1400 1600 1800 2000 d e fo rm a ti o n ( u m ) x-position in thickness (mm) t=30°c t=40°c t=50°c t=60°c -1 0 1 2 3 4 5 6 7 8 9 10 0 200 400 600 800 1000 1200 1400 1600 1800 2000 2200 2400 d e fo rm a ti o n ( u m ) x-position in thickness (mm) t=30°c t=40°c t=50°c t=60°c c d figure 6: deformation variations determined from the x-position in thickness to various temperatures 0 2 4 6 8 10 -1x107 0 1x107 2x107 3x107 4x107 5x107 6x107 7x107 8x107 9x107 1x108 1x108 st re ss ( p a ) x-position in thickness (mm) t=30°c t=40°c t=50°c t=60°c 0 2 4 6 8 10 -1x107 0 1x107 2x107 3x107 4x107 5x107 6x107 7x107 8x107 9x107 1x108 1x108 st re s s (p a ) x-position in thickness (mm) t=30°c t=40°c t=50°c t=60°c a b 0 2 4 6 8 10 -1x107 0 1x107 2x107 3x107 4x107 5x107 6x107 7x107 8x107 9x107 1x108 1x108 s tr e s s (p a ) x-position in thickness (mm) t=30°c t=40°c t=50°c t=60°c 0 2 4 6 8 10 -1x107 0 1x107 2x107 3x107 4x107 5x107 6x107 7x107 8x107 9x107 1x108 1x108 s tr e s s ( p a ) x-position in thickness (mm) t=30°c t=40°c t=50°c t=60°c c d figure 7: variations in equivalent stress according to vosmises following from x-position in thickness to various temperatures we also note that: a. salmi et alii, frattura ed integrità strutturale, 50 (2019) 231-241; doi: 10.3221/igf-esis.50.19 239 maximal value of the von-mises stress due to the thermo-mechanical effect is located at the level of the crack axis. stress distribution is very different with singularities at the x-position in the thickness. in an aluminum alloy plate, the stresses range from 0 mpa to 100 mpa. the difference is quite significant, around 20 mpa, so we can observe the good thermal and mechanical behavior. decrease in stress on the inside edge. if the temperature increases, the equivalent stress increases at any temperature, which validates the published results. variations in equivalent stress according to vos-mises as a function of axial displacement are represented in figs. 8 < a (a=5.08mm); b (a=5.50mm); c (a=6.34mm); d (a=7.18mm)> at different temperatures for crack width between 5.08 and 7.18. 5,0x103 1,0x104 1,5x104 2,0x104 2,5x104 3,0x104 -1x107 0 1x107 2x107 3x107 4x107 5x107 6x107 7x107 8x107 9x107 1x108 1x108 s tr e s s (p a ) displacement (um) t=30°c t=40°c t=50°c t=60°c 10000 15000 20000 25000 30000 35000 -1x107 0 1x107 2x107 3x107 4x107 5x107 6x107 7x107 8x107 9x107 1x108 1x108 s tr e s s (p a ) displacement (um) t=30°c t=40°c t=50°c t=60°c a b 20000 25000 30000 35000 40000 45000 50000 55000 -1x107 0 1x107 2x107 3x107 4x107 5x107 6x107 7x107 8x107 9x107 1x108 1x108 st re ss ( p a ) displacement (um) t=30°c t=40°c t=50°c t=60°c 4x104 5x104 6x104 7x104 8x104 9x104 -1x107 0 1x107 2x107 3x107 4x107 5x107 6x107 7x107 8x107 9x107 1x108 1x108 st re ss ( p a ) displacement (um) t=30°c t=40°c t=50°c t=60°c c d figure 8: variations in equivalent stress according to von-mises as a function of axial displacement at different temperatures conclusions he obtained results reveal a difference in behaviour at the selected node levels relative to the conditions imposed by the proposed model. thermo-mechanical input was found to show a significant increase in stress relative to the elasticity threshold of this 2024 t3 aluminum alloy, relative to mechanical input. the following conclusions can be made: the proposed model is used to determine the number of ni loading cycles required to initiate fatigue damage through certain loading cycles and the introduction of adequate material fatigue parameters. the method used for numerical t a. salmi et alii, frattura ed integrità strutturale, 50 (2019) 231-241; doi: 10.3221/igf-esis.50.19 240 modelling and the possibility of predicting the initiation of fatigue damage in mechanical elements following a cyclic contact solicitation represent this contribution to the problems examined. the qualitative effect of load ratio is to shift a growth rate curve along a line passing through the inflection points. the observation that this shift is not horizontal forms the basis for stress ratio modeling with the hyperbolic sine when the curve is completed. the use of the appropriate mechanical behavior laws for the different phases of thermo-mechanical growth plays an important role in the mechanical results, in particular on the distribution of residual stresses in the structure. thus, the increase in temperature leads to an increase in the equivalent stresses of von-mises, axial displacements and total deformation of the plates. the thermo-mechanical effect occurring at the conditions of the performed tensile , depends on the temperature and the direction of sampling concerning the plate rolling direction. the effect occurs even at such low temperature as 30°c and is most in-tense in the temperature range 50 60°c. von-mises stresses and overall deformations and plate contact pressures increase significantly when the thermal and mechanical aspect is coupled. the effect of temperature on crack propagation is presented, giving the best lifetime prediction. the damage becomes more pronounced with higher temperature finally, it is important to note that the "strong" coupling between temperature and mechanical variables (stress, strain, strain, and damage) is very important. temperature considerations in plastic or visco-plastic models allow the behaviour of structures to be well represented without complex loads. additional analyses should be conducted to assess the applicability and limitations of the methodology for studying cases in which significant behavior of plastic deformation is involved. acknowledgements he authors are especially grateful for the support provided by the laboratory (lms). department of mechanical engineering, faculty of technology, university djillali liabès of sidi bel-abbes, algeria and research unit in renewable energies in the desert center adrar, algeria. references [1] chapuliot, s. (2000). formulaire de ki pour les tubes avec un défaut de surface semi-elliptique longitudinal ou circonférentiel, interne ou externe, direction des réacteurs nucléaires. rapport de recherche., cea r-5900. [2] dhondt, g. (1998). cutting of a 3d finite element mesh for automatic mode i crack propagation calculations, international journal for numerical methods in engineering., 42, pp. 749-772. doi: 10.1002/(sici)1097-0207. [3] jordan, t.m., angel, p.a., galya, v.d., nikolaj, g., kenan, f.s. and vladimir, p.d. (2018). impact of slide diamond burnishing additional parameters on fatigue behaviour of 2024 -t3 al alloy, fatigue fract eng mater struct., 42, pp. 1– 11. doi:10.1111/ffe.12915. [4] karakaş, ö. and szusta, j. (2016). monotonic and low cycle fatigue behaviour of 2024-t3 aluminum alloy between room temperature and 300 °c for designing vawt components, fatigue fract engng mater struct., 39, pp. 95–109. doi: 10.1111/ffe.12336. [5] gowda, p., prakash, k., shivashankare gowda, j.n., and satish babu, b. (2015). effect of particulate reinforcement on the mechanical properties of al2024-wc mmcs, journal of minerals and materials characterization and engineering, 3, pp. 469-476. doi: 10.4236/jmmce.2015.36049. [6] zaki, m., wahab, m., sutarno and wahyudi, s. (2015). effects of anodizing parameters in tartaric-sulphuric acid on coating thickness and corrosion resistance of al 2024 t3 alloy, journal of minerals and materials characterization and engineering, 3, pp. 154-163. doi: 10.4236/jmmce.2015.33018. [7] manti, r., dwivedi, d.k. and agarwal, a. (2008). pulse tig welding of two al-mg-si alloys, journal of materials engineering and performance, 17, pp. 667–673. doi: 10.1007/s11665-008-9210-z. [8] abdullah, s., beden, s.m. and ariffin, a.k. (2011). fatigue crack growth simulation of aluminum alloy under cyclic sequence effects, in tech pub., 247. doi: 10.5772/14898. [9] guedri, a. (2008). conception et simulation numérique des caractéristiques mécaniques des pipelines, ph.d. thesis, université badji mokhtar. annaba. algeria. t a. salmi et alii, frattura ed integrità strutturale, 50 (2019) 231-241; doi: 10.3221/igf-esis.50.19 241 [10] boag, a., hughes, a.e., wilson, n.c., torpy, a., macrae, c.m., glenn, a.m. and muster, t. (2009). how complex is the microstructure of aa2024-t3, corros. sci., 51(8), pp. 1565–1568. doi: 10.1016/j.corsci.2009.05.001. [11] buchheit, r., grant, r., hlava, p., mckenzie, b. and zender, g. (1997). local dissolution phenomena associated with s phase (al2cumg) particles in aluminum alloy 2024-t3, journal of the electrochemical society, 144(8), pp. 2621–2628. doi: 10.1149/1.1837874. [12] liao, c.m., olive, j., gao, m. and wei, r. (1998). in-situ monitoring of pitting corrosion in aluminum alloy 2024, corrosion., 54(6), pp. 451–458. doi: 10.5006/1.3284873. [13] guillaumin, v. and mankowski, g. (1999). localized corrosion of 2024 t351 aluminum alloy in chloride media, corros. sci., 41(3), pp. 421–438. doi: 10.1016/s0010-938x(98)00116-4. [14] starke jr, e. and staley, j. (1996). application of modern aluminum alloys to aircraft, prog aerosp sci., 32(2-3), pp. 131–172. doi: 10.1016/0376-0421(95)00004-6. [15] hénaff, g. (2005). fatigue des matériaux et des structures, cours ensma, poitiers, france. [16] alihosseini, h., dehghani, k. and faraji, g. (2014). simulation of fatigue life behavior of circular cross-section bar with straight-fronted crack, modeling and numerical simulation of material science., 4, pp. 128-135. doi: 10.4236/mnsms.2014.43014. [17] wang, h. (1997). contribution à l'étude de l'influence des paramètres de chargement sur la modélisation de la propagation de fissure par fatigue sous amplitude de chargement constant, ph.d. thesis, university of science and technology of lille. [18] hosseini-toudeshky, h., mohammadi, b., sadeghi, g. and daghyani, h.r. (2007). numerical and experimental fatigue crack growth analysis in mode-i for repaired aluminum panels using composite material, composites., part a. 38(4), pp. 1141-1148. doi: 10.1016/j.compositesa.2006.06.003. [19] glodez, s. and flasker, j. 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<feff04120438043a043e0440043804410442043e043204430439044204350020044604560020043f043004400430043c043504420440043800200434043b044f0020044104420432043e04400435043d043d044f00200434043e043a0443043c0435043d044204560432002000410064006f006200650020005000440046002c0020044f043a04560020043d04300439043a04400430044904350020043f045604340445043e0434044f0442044c00200434043b044f0020043204380441043e043a043e044f043a04560441043d043e0433043e0020043f0435044004350434043404400443043a043e0432043e0433043e0020043404400443043a0443002e00200020042104420432043e04400435043d045600200434043e043a0443043c0435043d0442043800200050004400460020043c043e0436043d04300020043204560434043a0440043804420438002004430020004100630072006f006200610074002004420430002000410064006f00620065002000520065006100640065007200200035002e0030002004300431043e0020043f04560437043d04560448043e04570020043204350440044104560457002e> /enu (use these settings to create adobe pdf documents best suited for high-quality prepress printing. created pdf documents can be opened with acrobat and adobe reader 5.0 and later.) >> /namespace [ (adobe) (common) (1.0) ] /othernamespaces [ << /asreaderspreads false /cropimagestoframes true /errorcontrol /warnandcontinue /flattenerignorespreadoverrides false /includeguidesgrids false /includenonprinting false /includeslug false /namespace [ (adobe) (indesign) (4.0) ] /omitplacedbitmaps false /omitplacedeps false /omitplacedpdf false /simulateoverprint /legacy >> << /addbleedmarks false /addcolorbars false /addcropmarks false /addpageinfo false /addregmarks false /convertcolors /converttocmyk /destinationprofilename () /destinationprofileselector /documentcmyk /downsample16bitimages true /flattenerpreset << /presetselector /mediumresolution >> /formelements false /generatestructure false /includebookmarks false /includehyperlinks false /includeinteractive false /includelayers false /includeprofiles false /multimediahandling /useobjectsettings /namespace [ (adobe) (creativesuite) (2.0) ] /pdfxoutputintentprofileselector /documentcmyk /preserveediting true /untaggedcmykhandling /leaveuntagged /untaggedrgbhandling /usedocumentprofile /usedocumentbleed false >> ] >> setdistillerparams << /hwresolution [2400 2400] /pagesize [612.000 792.000] >> setpagedevice microsoft word numero_52_art_01_2588 y. xu et alii, frattura ed integrità strutturale, 52 (2020) 1-8; doi: 10.3221/igf-esis.52.01 1 building crack monitoring based on digital image processing yanyan xu, yanxia cai*, dandan li,tierui zhang hengshui university, hengshui, hebei province 053000, china xyy_xu@126.com, yxcyanx@yeah.net, zzaod5@163.com abstract. building crack monitoring is of great value to the judgment of building safety. in this study, the digital image processing technology was studied and applied to the monitoring of building cracks. crack images were collected by ccd camera, and then operations such as graying, correction, denoising and segmentation were carried out to obtain clear crack images. the obtained images were processed morphologically to further improve the quality. finally, the width and length of cracks were calculated. in the case analysis, the results of 15 cracks measured by a microscope were taken as the standards and compared with the calculated results. the results showed that the results calculated in this study and the manual measurement results differed little, and the average errors of the width and length were 0.021 mm and 0.024 mm respectively, which suggested that the method proposed had a high reliability. the findings of this study provide a new idea for the further development of the building crack monitoring field and is conducive to the accurate assessment of building safety. keywords. digital image processing; building crack; monitoring; histogram equalization. citation: xu, y.y., cai, y.x., li, d.d., zhang, t.r., building crack monitoring based on digital image processing, frattura ed integrità strutturale, 52(2020) 1-8. received: 06.08.2019 accepted: 05.12.2019 published: 01.04.2020 copyright: © 2020 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. introduction n the process of concrete production, due to the uneven expansion and contraction, cracks will inevitably occur in the ground. in the process of component transportation and assembly, cracks may also occur due to the influence of external environment. in the process of building use, cracks will gradually occur along with the deformation of materials. building cracks will continue to develop and expand to destroy the integrity of the building structure, resulting in a decline in the mechanical properties of the overall structure; if serious, it may lead to shorter building life and cause safety accidents. cracks in buildings develop slowly, and changes in the width and length can reflect the safety of buildings. therefore, effective monitoring of cracks has important practical values [1]. with the development of technology, digital image processing has shown excellent performance in crack monitoring. riyadi et al. [2] monitored pavement cracks with digital image processing technology, developed detection technology through the gauss pyramid method, classified cracks and non-cracks by linear discrimination, and found that the method had an accuracy of 92.8571% and the processing time of each picture was 1.5 seconds. kim et al. [3] combined unmanned aerial vehicle (uav) technology with digital image processing technology to realize the crack assessment of concrete structures and found that the system could successfully i https://youtu.be/bwlazeacpfw y. xu et alii, frattura ed integrità strutturale, 52 (2020) 1-8; doi: 10.3221/igf-esis.52.01 2 measure cracks with thickness greater than 0.1 mm and the estimated error of the maximum length was 7.3%. hoang et al. [4] studied the detection and classification of cracks in asphalt pavement, processed images with digital image processing technology, classified images by machine learning algorithm, and found that the method was helpful to assist inspectors in assessing pavement conditions. lu et al. [5] studied the cracks of cement matrix composites, designed a double threshold algorithm for image processing, and found through experiments that the proposed method could effectively calculate the crack width. felli et al. [6] studied related cracks of the right foreleg of colleoni equestrian statue and made long-term examination on the crack expansion through pasting fiber bragg grating sensor. in this study, a series of digital image processing methods were designed for building cracks, and the example analysis verified that the proposed method had high monitoring accuracy, which provides some bases for its practical application and is conducive to the effective evaluation of building health and the improvement of safety and reliability of buildings. digital image processing igital images refer to images composed of data points (pixels). taking a 360*500 image as an example, it refers to an image which is composed of 360 rows of pixels and 500 columns of pixels. digital image processing refers to the transformation of image signal to digital signal through computer. digital image processing has many advantages: (1) high accuracy: by processing each pixel in the image, the image can maintain a high accuracy; (2) high processing speed: data-based digital images can perform various operations quickly in the process of processing; (3) easy storage: unlike paper images, digital images are not affected by time and are easy to store; (4) a wide range of applications: no matter what kind of equipment the image is collected, it can be processed by digital image processing; (5) high flexibility: linear and non-linear processing can be realized. in the actual acquisition, the image of building cracks may be affected by illumination, photography, occlusion and so on, which makes the boundary between cracks and background unclear and makes it difficult to accurately extract cracks. clear crack images can be obtained through digital image processing technology to realize the monitoring of cracks. image processing method for building cracks image acquisition n order to obtain high-quality images, the selected image acquisition equipment should have high pixel and resolution. in this study, mv-vdm200sm/sc ccd industrial camera produced by video digital image company (fig. 1) was used. some of its parameters are shown in tab. 1. figure 1: ccd camera. maximum resolution 1600* 1200 pixel size 4.40 μm × 4.40 μm frame rate 12 fps output mode usb2.0 power supply requirements 5v power 2.4w table 1: parameters of ccd camera. d i y. xu et alii, frattura ed integrità strutturale, 52 (2020) 1-8; doi: 10.3221/igf-esis.52.01 3 in the process of acquisition, the lens was located in front of the crack. the stable image was obtained by tripod and level instrument, and a ruler was set around the crack to provide a standard for crack calculation. then the acquired image was input to the computer through usb. image preprocessing under the influence of illumination and noise, the collected images often have some problems, such as low clarity and inconspicuous details, which are not conducive to crack monitoring. therefore, image preprocessing is needed to improve the quality. image graying the image captured by camera is usually color image in rgb format. the amount of calculation involved in the processing is considerable, which can seriously affect the speed of image processing. therefore, it is necessary to gray the rgb image. in this study, graying was achieved by the weighted average method [7]. it is assumed that there is an rgb image  ,f i j . the treatment formula is:        , 0.3 , 0.59 , 0.11 ,f i j r i j g i j b i j   . (1) gray level correction in order to improve the gray resolution of the image, gray correction can be made to the image. in this study, the image was corrected by the histogram equalization method [8]. firstly, the gray histogram  kp r of the image is calculated:   , 0,1, , 225kk n p r k n    , where kr stands for the k -th grayscale, n stands for number of pixels, kn stands for the number of pixels with gray level of k , and  kp r stands for the proportion of kr in the whole image. the cumulative distribution function ks is calculated: 0 k j k j n s n   . (2) ks is taken as a transform function to correct the gray level of the image: 225 0.5kk s g n    , where kg stands for the new grayscale of the corrected image. all the gray levels of the image are corrected according to the above procedures, and then the corrected gray level image is obtained. image denoising the image is denoised by median filter [9], that is, the gray value in window w is ranked. then the median value is used as the gray value of the central point. the calculation formula is:       , , , ,g p q med f p i q j i j w    , (3) where  ,f i j stands for the original gray value in w and  ,g p q stands for the gray value after median filtering denoising. image segmentation cracks and background are separated by image binarization. for the original image  ,f x y , threshold t is set, and the segmented image is:       1 , , 0 , f x y t g x y f x y t     . (4) y. xu et alii, frattura ed integrità strutturale, 52 (2020) 1-8; doi: 10.3221/igf-esis.52.01 4 the method for determining the threshold is as follows. firstly the initial threshold max min 2 t t t   is calculated, where maxt and min t stand for the maximum and minimum gray values in the image respectively. the image gray level is divided into two groups, group 1 with gray level larger than t and group 2 with gray level smaller or equal to t . the average gray values 1 and 2 of the two groups are calculated. suppose 1 2 2 t    . the above procedures repeat until t is stable, and finally the binarization threshold is obtained. crack calculation morphological treatment or the segmented crack image, the morphological algorithm is taken for further improvement, which mainly includes two steps: corrosion and expansion. (1) corrosion:   |a b x b x a   , where a stands for the target image and b stands for the structural element. the noise and burr in the image can be further removed after corrosion. (2) expansion:   |a b x b x x    . after expansion, the image can be restored to the original size. calculation of crack width coordinates are set around the crack to calculate the distance between the two points:    2 2right left right leftw x x y y    , where  represents the pixel scale parameter, which is the actual size represented by the pixel. as cracks are mostly irregular, the coordinates of left pixels are kept unchanged in the calculation, and then the coordinates of right pixels are calculated in turn with the window size of 5×5, and the minimum value is denoted as the crack width. calculation of crack length the length of crack is calculated through the euclidean distance between the starting point of crack  ,s sx y and the ending point  ,e ex y :     2 2 e s e sl x x y y    , where  stands for the pixel proportion parameter. case study crack image acquisition ifteen cracks were collected by ccd camera in building a in hengshui, hebei, china. the data of the length and width of the fifteen cracks were collected using a wysk-40x reading microscope (fig. 2). the specification of the microscope was 50 × 23 × 138 mm. the focus of the microscope was adjustable, and it carried with pure white led light source, had scale, and had 40x magnification. figure 2: the reading microscope. f f y. xu et alii, frattura ed integrità strutturale, 52 (2020) 1-8; doi: 10.3221/igf-esis.52.01 5 image processing the images were processed using the method described in the section of image preprocessing. four of the images were taken as examples, and the original images of the four images are shown in fig. 3. figure 3: original crack images. it was found from fig. 3 that the quality of crack images was poor under the influence of illumination and noise, which was not conducive to crack monitoring. the crack images obtained after the processing of the digital image processing method proposed in this study are shown in fig. 4. figure 4: crack images after processing. it was found from fig. 4 that the crack images obtained were clearer and distinct from the background after processing such as denoising, segmentation and morphological treatment, which was conducive to the subsequent crack calculation. crack calculations the width and length of the extracted crack images were calculated using the method mentioned in the section of crack calculation. the comparison between the calculated results and manual monitoring results is shown in fig. 5 and 6. y. xu et alii, frattura ed integrità strutturale, 52 (2020) 1-8; doi: 10.3221/igf-esis.52.01 6 figure 5: comparison of crack width. figure 6: comparison of crack length. it was found from fig. 5 and 6 that the width and length of cracks calculated by the method were almost the same as the measured values, which showed that the method had a high monitoring accuracy and could replace manual monitoring to achieve effective monitoring of cracks. the errors between the results obtained by the proposed method and those obtained by manual monitoring are shown in tab. 2. number of image width error/mm length error/mm 1 0.01 0.03 2 0.01 0.01 3 0.03 0.02 4 0.01 0.03 5 0.03 0.03 6 0.03 0.04 7 0.01 0.04 8 0.02 0.03 9 0.01 0.01 10 0.03 0.02 11 0.02 0.02 12 0.02 0.02 13 0.03 0.03 14 0.04 0.02 15 0.02 0.01 average error 0.021 0.024 table 2: errors between the results obtained using the method proposed in this study and the manual detection results it was found from tab. 2 that the maximum error of the method was 0.04 mm, the minimum error was 0.01 mm, and the average error was 0.021 mm in the width monitoring; in the length monitoring, the maximum error was 0.04 mm, the minimum error was 0.01 mm, and the average error was 0.024 mm. the errors were so small that could be nearly neglected, which would not affect the evaluation of cracks, suggesting that the method was reliable. all the results showed that the digital image processing method could obtain almost the same results as the manual monitoring, with a good accuracy, and could realize the effective monitoring of building cracks. discussion igital image processing has a good application in many fields [10]. for example, in the field of medicine, it can analyze ultrasound and electrocardiogram images [11] to provide a guidance for doctors’ surgery [12]. in the field of industry, it can realize the analysis and detection of circuits, chips, micro parts, etc [13,14]. in the field of d y. xu et alii, frattura ed integrità strutturale, 52 (2020) 1-8; doi: 10.3221/igf-esis.52.01 7 security, it can identify fingerprints and iris [15]. in the field of art, it can realize the restoration and reconstruction of cultural relic pictures [16]. cracks in buildings are closely related to the overall safety of buildings. monitoring cracks is an important work of building health assessment. traditional manual monitoring methods have many limitations in practical operation, which cannot meet the current needs of building crack monitoring. the emergence of digital image processing technology has brought a new idea for building crack monitoring. this study collected the building crack images by ccd camera, then obtained the clear crack images by a series of pretreatment operations such as graying, denoising and segmentation, and finally realized the monitoring of building cracks by taking the width and length as the criteria. the processing method proposed in this study was found effective in the example analysis. it was found from fig. 4 that the blur, noise and stain in the original images were effectively removed, the image quality was significantly improved, and the cracks were clearly separated from the background, which was conducive to the follow-up operation. then, in the comparison of the results of crack length and width, the data measured by microscope was taken as the result of manual monitoring and compared with those calculated by the method proposed in this study. fig. 5 and 6 show that the results obtained by the two methods were very similar, which was also verified in the calculation of errors. the width error was only 0.021 mm, and the length error was only 0.024 mm. with a high accuracy, the method can realize monitoring of the cracks in buildings. in practice, the method not only has high reliability, but also is convenient, fast and highly usable. however, the manual monitoring method based on microscope is very difficult to achieve in the monitoring of a large number of cracks as it is time-consuming and energy consuming. therefore, the method is more suitable for the monitoring of actual building cracks. in this study, although some achievements have been made in the research of building crack monitoring, there are still many shortcomings, for example, unable to achieve on-line crack monitoring and the identification of complex cracks. in the future work, it is necessary to find more accurate monitoring methods and monitor more characteristics of cracks such as area and depth. conclusion n this study, the monitoring of building cracks was studied, clear crack images were obtained through digital image processing technology, and the length and width of the cracks were calculated and compared with the results obtained by the manual detection. it was found that: (1) the crack image which was processed by digital image processing method was clear and distinguished significantly from the background; (2) the crack results obtained by the method proposed in this study had small errors with the manual detection results, and the average errors of the length and width were 0.024 mm and 0.021 mm respectively; the experimental results verified that the method was reliable in crack monitoring, which is conductive to improving the crack monitoring efficiency and scientifically analyzing crack structure and moreover makes some contributions to the safety monitoring and restoration of buildings. acknowledgement his study is supported by research on the construction of the curriculum system of innovation and entrepreneurship in colleges and universities under the background of "internet +" under grant number jg2018097. references [1] prasanna, p., dana, k. j., gucunski, n., et al. (2016). parvardeh h. automated crack detection on concrete bridges, ieee t. autom. sci. eng., 13(2), pp. 591-599. doi: 10.109/tase.2014.2354314. [2] riyadi, s., sugiarto, a., putra, s. a. and setiawan, 1n. a. (2015). analysis of digital image using pyramidal gaussian method to detect pavement crack, adv. sci. lett., 21(11), pp. 3565-3568. doi: 10.1166/asl.2015.6579. [3] kim, h., lee, j., ahn, e., et al. (2017). concrete crack identification using a uav incorporating hybrid image processing, sensors, 17(9), pp. 2052. doi: 10.3390/s17092052. i t y. xu et alii, frattura ed integrità strutturale, 52 (2020) 1-8; doi: 10.3221/igf-esis.52.01 8 [4] hoang, n. d. and nguyen, q. l. (2018). a novel method for asphalt pavement crack classification based on image processing and machine learning, engineering with computers, accepted, in press (part 1), pp. 1-12. doi: 10.1007/s00366-018-0611-9. [5] lu, c., yu, j. and leung, c. k. y. (2016). an improved image processing method for assessing multiple cracking development in strain hardening cementitious composites (shcc), cement concrete comp., 74, pp. 191-200. doi: 10.1016/j.cemconcomp.2016.10.005. [6] felli, f., brotzu, a., pilone, d. and vendittozzi, c. (2014). use of fbg sensors for monitoring cracks of the equestrian statue of bartolomeo colleoni in venice, frat. integr. strut., 8(30), pp. 48-54. doi: 10.3221/igf-esis.30.07. [7] ren, z. x., bi, j. h., xie, l. and zhang, k. f. (2014). quantitative detection of wood surface defects by image segmentation method, chin. j. liq. cryst. displays, 29(5), pp. 785-792. doi: 10.3788/yjyxs20142905.0785. [8] lai, y. r., tsai, p. c., yao, c. y. and ruan, s. j. (2017). improved local histogram equalization with gradient-based weighting process for edge preservation, multimed. tools appl. 76(1), pp. 1-29. doi: 10.1007/s11042-015-3147-7. [9] aranda, l. a., reviriego, p. and maestro, j. a. (2017). error detection technique for a median filter, ieee t. nucl. sci., pp. 1-1. doi: 10.1109/tns.2017.2666843. [10] prasad, d. s. and reddy, b. s. (2017). digital image processing techniques for estimating power released from the corona discharges, ieee t. dielect. el. in., 24(1), pp. 75-82. doi: 10.1109/tdei.2016.005896 [11] robertson, s., azizpour, h., smith, k. and hartman, j. (2018). digital image analysis in breast pathology-from image processing techniques to artificial intelligence, transl. res. j. lab. clin. med., 194, pp. 19. doi: 10.1016/j.trsl.2017.10.010. [12] scholz, m., konen, w., tombrock, s., et al. (2015). development of an endoscopic navigation system based on digital image processing, comput. aided surg., 3(3), pp. 134-143. doi: 10.1002/(sici)1097-0150(1998)3:33.0.co;2-t [13] zhang, j.j. and meng, x.q. (2015). defect detection of wire rope for oil well based on adaptive angle, frat. integr. strut., 9(34). doi: 10.3221/igf-esis.34.65. [14] boschetto, a., bottini, l., campana, f., consorti, l. and pilone, d. (2013). investigation via morphological analysis of aluminium foams produced by replication casting, frat. integr. strut., 7(26), pp. 01. doi: 10.3221/igf-esis.26.01. [15] ambadiyil, s., prakash, d., sheeja, m. k. and pillai, v. p. m. (2017). secure storage and analysis of fingerprints for criminal investigation using holographic techniques, mater. today proc., 4(2), pp. 4389–4395. doi: 10.1016/j.matpr.2017.04.010. [16] pizurica, a., platisa, l., ruzic, t., et al. 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/hrv (za stvaranje adobe pdf dokumenata najpogodnijih za visokokvalitetni ispis prije tiskanja koristite ove postavke. stvoreni pdf dokumenti mogu se otvoriti acrobat i adobe reader 5.0 i kasnijim verzijama.) /hun 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/pdfxoutputintentprofileselector /documentcmyk /preserveediting true /untaggedcmykhandling /leaveuntagged /untaggedrgbhandling /usedocumentprofile /usedocumentbleed false >> ] >> setdistillerparams << /hwresolution [2400 2400] /pagesize [612.000 792.000] >> setpagedevice microsoft word numero_31_art_11 r. citarella et alii, frattura ed integrità strutturale, 31 (2015) 138-147; doi: 10.3221/igf-esis.31.11 138 fem simulation of a crack propagation in a round bar under combined tension and torsion fatigue loading r.citarella, m.lepore dept. of industrial engineering – university of salerno fisciano (sa), italy. rcitarella@unisa.it a. maligno institute for innovation in sustainable engineering, university of derby, quaker way, de1 3hd derby (uk). a.maligno@derby.ac.uk v. shlyannikov researches center for power engineering problems of russian academy of sciences, lobachevsky street, 2/31, 420111, kazan, russia. shlyannikov@mail.ru abstract. an edge crack propagation in a steel bar of circular cross-section undergoing multiaxial fatigue loads is simulated by finite element method (fem). the variation of crack growth behaviour is studied under axial and combined in phase axial+torsional fatigue loading. results show that the cyclic mode iii loading superimposed on the cyclic mode i leads to a fatigue life reduction. numerical calculations are performed using the fem software zencrack to determine the crack path and fatigue life. the fem numerical predictions have been compared against corresponding experimental and numerical data, available from literature, getting satisfactory consistency. keywords. surface flaw; tension and torsion; crack growth prediction; fem; g-criterion. introduction umerical modelling of three-dimensional (3d) fatigue crack growth under mixed mode conditions represents a crucial factor in fracture mechanics in order to assess the residual life of components. the fatigue growth analysis of surface cracks is one of the most important elements for structural integrity prediction of the circular cylindrical metallic components (bars, wires, bolts, shafts, etc.), in the presence of initial and accumulated in service damages. in most cases, part-through flaws appear on the free surface of the cylinder and defects are approximately considered as semi-elliptical cracks. multi-axial loading conditions including tension/compression, bending and torsion are typical for the circular cylindrical metallic components of engineering structures. the problem of residual fatigue life prediction of such type of structural elements is complex and the closed solution is often not available because surface flaws are three-dimensional in nature. n r. citarella et alii, frattura ed integrità strutturale, 31 (2015) 138-147; doi: 10.3221/igf-esis.31.11 139 in [1], experimental and numerical results of fatigue crack growth for a crack starting from a straight-fronted edge notch in an elastic bar under axial loading with or without superimposed cyclic torsion are given and the influence of different loading conditions on fatigue life of cylindrical specimens is discussed. the relations between crack opening displacement and the crack length measured on the free specimen surface are obtained, and it is shown that the growth of the crack fronts is dependent on the initial notch depth. using the aforementioned relations, the crack front shape and crack growth rate in the depth direction can be predicted. the numerical simulations in [4] are based on the dual boundary element method [2-3] whereas, in this paper, the same calculations are performed based on the finite element method (fem). in the past a comparison between fem and dbem results on this kind of problems was already attempted but considering separately the two loading conditions [4-5]; now the comparison is extended in case of simultaneous application of the torsion and traction fatigue loads. the computational 3d fracture analyses deliver variable mixed mode conditions along the crack front. fracture mechanics simulations by zencrack introduction he numerical studies are based on finite element (fe) analyses using the adaptive remeshing approach. this study employs zencrack [6-8] for automated 3d remeshing and crack propagation calculations along with abaqus [9] as the finite element solver. zencrack is a 3d crack analysis tool able to read in an uncracked finite element model and to produce a cracked finite element model. stress intensity factors are calculated automatically from the results of the cracked finite element analysis. furthermore, crack growth can be undertaken by extending the crack position. an updated finite element model is then created and run to simulate crack growth (fig. 1). user input (fe mesh of uncracked comp.) user input (crack location, size) zencrack (creates mesh of crack comp.) fe code (analysis) zencrack (evaluation of crack growth and update fe mesh) zencrack (next fe analyses)stop no yes user input (fe mesh of uncracked comp.) user input (crack location, size) zencrack (creates mesh of crack comp.) fe code (analysis) zencrack (evaluation of crack growth and update fe mesh) zencrack (next fe analyses)stop no yes figure 1: flow chart for crack growth prediction analysis. crack growth criteria in order to predict linear elastic fracture mechanics (lefm) crack growth using fe method, three basic parameters are required: stress intensity factors (sif), crack propagation direction (cpd) and crack growth material models. there are several approaches to calculating stress intensity factors (sif’s) such as: the crack tip opening displacement (ctod) approach [5], the crack tip stress field approach [10] and the sif extraction method from j-integral [5]. using the crack opening displacement approach the sif values can be obtained as follows:    2 24 1 p p i b b e k u u r             (1a)    2 24 1 p p ii n n e k u u r             (1b)    2 24 1 p p iii n n e k u u r             (1c) t r. citarella et alii, frattura ed integrità strutturale, 31 (2015) 138-147; doi: 10.3221/igf-esis.31.11 140 where  and e are poisson’s ratio and young’s modulus respectively. the displacement up is evaluated at a point p on the crack front sufficiently close to the crack tip. the displacements pbu , p nu , and p tu are projections of up on the coordinate directions of the local crack front coordinate system and  = π and  = -π denote upper and lower crack surfaces respectively. ki, kii and kiii are the mode i, ii and iii sif’s. in the present work the sif’s are extracted from the j-integral using the method illustrated in [11], based on the following equation:    2 2 21 1 2 i ii iiij k k k e g    (2) where 2/ (1 )e e   for plain strain conditions. the quarter-point node technique is used to model the crack-tip singularity. under mixed mode conditions it is necessary to introduce an equivalent stress intensity factor, keq, considering mode i, ii and iii simultaneously. several formulae have been proposed for keq and the most commonly used expression is [12, 13]:  2 2 21eq i ii iiik k k k    (3) in order to determine new crack front positions, the cpd must be computed. although expressions exist to calculate the crack growth angle based upon the stress intensity factors, an alternative method is adopted here based on the maximum energy release rate at a crack front point. the g-criterion states that a crack will grow in the direction of maximum energy release rate. the cpd,  = o, is then determined by: 0 o dg d          ; 2 0 o dg d          the application of a series of virtual crack extensions (fig. 2) ultimately generates a growth angle at the crack front node that, in the general case, may be out-of-plane. (a) (b) figure 2: energy based calculation of gmax (a) and crack grow direction (b). remeshing technique a critical issue that must be addressed in 3d fe fracture mechanics analysis is that of mesh generation. in the simplest of geometric cases where symmetry can be used, it may be possible to utilise standard mesh generation tools to produce a crack of the required size. in the general case, however, the use of standard tools leads to several time consuming problems including: • component geometries are often complex and time consuming to model in their uncracked forms. • defects often occur at geometrically difficult locations e.g. corners, welds, chamfers. • initial cracks of the correct size and shape must be inserted into the component at the correct location. • cracks may develop in a non-planar fashion depending upon the loading. the approach that has been successfully adopted here is the use of ‘crack blocks’ which model the details of the cracked region. crack-blocks are groups of elements arranged in such a way that they contain a section of crack front. fig. 3-4 demonstrate the use of the crack-block methodology in generating a cracked mesh from a user-supplied intact r. citarella et alii, frattura ed integrità strutturale, 31 (2015) 138-147; doi: 10.3221/igf-esis.31.11 141 component. the method works by replacing one or more elements in the uncracked mesh by crack-blocks that contain sections of crack front. two types of crack-blocks are available: a standard crack-blocks. the standard crack-blocks reduce to a single element on their back faces and merge with the rest of the mesh via shared nodal numbers. the crack-blocks are designed to replace elements in the mesh by updating element connectivities and node numbers (fig. 3). the crack-blocks consist of “through” and “quarter circular” crack blocks. b large crack-blocks. the large crack-blocks contain multiple nodes on their back faces and are used with surface-based tying to connect them to the surrounding (dissimilar) mesh. the crack-blocks consist of “through” and “quarter circular” crack blocks. (a) (b) figure 3: standard crack-block mesh (a) and detail of the crack-block (b). (a) (b) (c) figure 4: large crack-block mesh (a), detail of un-meshed large crack-block (b) and meshed crack-block (c). the crack-blocks have a varying number of “rings” of elements around the crack front. the innermost ring contains “collapsed” elements to represent the singularity in the stress and strain field at the crack front. a full control of the nodes along the crack front and the radial nodes closest to the crack front allows to reproduce a singularity best suited to lefm or epfm. although the crack-blocks are referenced as “quarter circular” or “through” crack blocks, the user has control of the initial crack front shape which may be defined by fitting a spline through a series of points for the greatest flexibility in definition. loading (e.g. pressure load) and boundary conditions are updated as the crack blocks are incorporated into a mesh. by processing fracture mechanics parameters from a cracked mesh and adding a crack growth algorithm, it is possible to carry out automatic crack growth prediction. this introduces a number of additional challenges. in order to obtain best results from the mesh within the crack-blocks, their outer boundaries must be manipulated to reduce internal element distortion as much as possible. further, to allow a crack to develop through a model, it must be possible to allow crack-blocks to transfer from one position to another. this requires manipulation of the elements outside the crack r. citarella et alii, frattura ed integrità strutturale, 31 (2015) 138-147; doi: 10.3221/igf-esis.31.11 142 blocks, again to reduce distortion in the mesh. of course there is no single method of crack modelling and remeshing that can be used for all crack geometries. however, the combination of standard and large crack-blocks in conjunction with mesh manipulation algorithms, allows many difficult problems to be handled. test material and specimens he test material is carbon steel r2m. its main mechanical properties including constants of the paris equation (eq. 4) are listed in tab. 1 where e is the young’s modulus, b is the nominal ultimate tensile strength, 0 is the monotonic tensile yield strength, u is the true ultimate tensile strength, n is the strain hardening exponent, c (the numerical value is consistent with a young modulus and remote applied stress expressed in mpa and distances expressed in mm) and m are the paris constants. m da c k dn   (4) e [mpa] b [mpa] 0 [mpa] u [mpa] n c m 209000 810.3 540.8 890 6.134 4.1  10-13 2.818 table 1: mechanical properties of steel r2m. the specimen geometry configuration is shown in fig. 5: the nominal diameter is equal to 10 mm in the test section and the length, including the clamped part, is equal to 100 mm. using linear cutting machine, surface edge cracks were cut with initial flaw depths b0=1.0 mm. figure 5: details of the specimen geometry. the geometric parameters of specimen test section and of growing crack are shown in fig. 6a-b: b is the current crack depth, with the crack front approximated by an elliptical curve with major axis 2c and minor axis 2b. the crack length a is obtained by measuring the distance between the advancing crack break through point and the notch break through point, as shown in fig. 6a. the depth of the initial straight edge notch is denoted by h and the initial notch length by l. the crack opening displacement is measured on the free specimen cylindrical surface, in the central plane of symmetry as shown in fig. 6b. for the simple cyclic axial fatigue tests, the specimens are tested with an applied maximum remote stress equal to 250 mpa and with a stress ratio r=0.1. the combined tension/torsion tests are performed with the same stress ratio, applying synchronous and in-phase tensile and shear stresses whose maximum values are respectively equal to 250 and 100 mpa. two different frequency values (10 and 7 hz) were applied to the specimens in order to highlight the crack front geometry during propagation: during each test, beach marks were produced on each specimen by reducing the applied frequency from 10 to 7 hz, when the surface crack length was approximately equal to a  1mm. the typical beach marks on the post mortem cross section of different specimens are shown in fig. 7a-b. t r. citarella et alii, frattura ed integrità strutturale, 31 (2015) 138-147; doi: 10.3221/igf-esis.31.11 143 a) b) figure 6: edge crack geometric parameters: section view (a) and lateral view (b). a) b) figure 7: photograph of the cross section of specimens (a-pure tension, b-tension+torsion). experimental results he evolution of the crack growth rate of the elliptical-fronted edge cracks during the tests is determined using cod measurement and information from the microscope. in order to study the crack growth in shafts under fatigue tension loading with superimposed cyclic torsion, several specimens are tested with an initial notch depth equal to 1 mm. fig. 8a-b show plots of the break through point advances a and of cod against the number of cycles n under pure tension and combined tension+torsion, respectively: in-phase cyclic torsion loading superimposed on cyclic tension leads to a fatigue life decreasing. a) b) figure 8: fatigue crack growth (a) and cod curves on free surface of specimens (b). t r. citarella et alii, frattura ed integrità strutturale, 31 (2015) 138-147; doi: 10.3221/igf-esis.31.11 144 fig. 9a-b represent the superficial crack growth rate da/dn versus crack length a and versus cod, under pure cyclic tension and combined tension+torsion. it can be seen that there is not a significant reduction of the crack growth rates along the external surface direction when the cyclic mode iii loading is superimposed on the cyclic tension. however, looking at fig. 7b and considering changes in the general durability of the specimens in pure tension and combined loading (fig. 8a-b), significant differences in the crack growth rate in the depth direction b under the above types of loading conditions are expected. a) b) figure 9: crack growth rate as a function of superficial crack length (a) and cod (b). fem model he crack propagation in the cylindrical specimens n.1 and 2 (fig. 10a-b), undergoing combined traction-torsion fatigue loads, is simulated by the fem model shown in fig. 11. such model has a length equal to 60 mm, with one end clamped and the other end constrained along the in plane radial directions and loaded along the axial and tangential directions. the mesh is made with 18960 quadratic elements (brick with 20 nodes “c3d20”): such number of elements is nearly constant during the propagation. the whole propagations take nearly one hour calculus on a powerful pc. the initial crack, as indicated by experimental measurements (beach mark technique) has the following sizes: a=0.855 mm, b=0.852 mm, c=3.705 mm. during the propagation, the average crack advance at each step is equal to 0.2 mm. as previously said, the sif’s along the crack front are calculated by the j-integral approach. the crack growth rate is calculated by the paris formula (eq. 4), whose calibration parameters are shown in tab. 1. the crack path is calculated using the g-criterion. a) b) figure 10: geometry of specimens n. 1 (a) and n. 2 (b). t r. citarella et alii, frattura ed integrità strutturale, 31 (2015) 138-147; doi: 10.3221/igf-esis.31.11 145 figure 11: fem model with highlight of mesh, remote appled tractions and torque. numerical results and discussion n fig. 12 it is possible to see the crack propagation, starting from the initial configuration (step 0) and proceeding through the step 11 up to the final step 21: the crack kinking coming from the superimposed torsion is evident. a qualitative comparison between the numerical and experimental (fig. 7b) crack shape is possible. step 0 step 11 step 21 figure 12: contour plot of von mises stresses (mpa) at different stages of crack propagation, with external and internal views of the growing crack. in fig. 13 it is possible to appreciate the good level of correlation between experimental and numerical (fem and dbem [1]) crack growth rates for both the analyzed specimens. the numerical simulation starts from the first traced crack front, so that there is no comparison available in the initial stage of experimental monitored crack growth. i r. citarella et alii, frattura ed integrità strutturale, 31 (2015) 138-147; doi: 10.3221/igf-esis.31.11 146 in fig. 14 the growth angle from the initial cracked configuration is shown with its variation along the crack front and against the analyzed crack growth criteria: it is possible to see that the all criteria provide similar predictions. at the beginning of crack growth, the growth rate of the crack front midpoint is faster than that at the intersection with the surface (break through points): the reason is that the maximum stress-intensity factor (fig. 15) is attained at the deepest point of the initial crack front. consequently, a straight-fronted notch evolves towards a curved front and the flaw aspect ratio b/c increases. in fig. 16 the crack depth as calculated by dbem [1] and by fem (zencrack) is shown along the crack propagation, proving a satisfactory level of consistency between the aforementioned computational approaches. figure 13: superficial crack length (mm) vs. cycles for the analyzed specimens (considering the outcomes of the dbem code beasy and of the fem code zencrack). figure 14: growth angle, from the four different criteria, as varying along the initial crack front (considering the outcomes of the dbem code beasy and of the fem code zencrack). figure 15: sif’s (mpamm) along the crack front related to the first step (considering the outcomes of the dbem code beasy and of the fem code zencrack). figure 16: crack advance (mm) of crack front center point point vs. number of cycles. conclusions he computed fem crack propagation results are found to be in good qualitative (the crack path) and quantitative (the crack growth rates) agreement with experimental findings and numerical outcomes available from literature. a rather complex 3d crack growth behavior is present in case of superimposed tension and in phase torsion and the fatigue life is decreased if compared to a pure tension fatigue load. this is related to the increase of the mode mixity effect. moreover, it can be emphasized the reduced calculation times of the fem approach, in comparison with the dbem approach shown in [1], the latter providing some advantages in the preprocessing phase (e.g. remeshing during crack propagation). the crack insertion and the whole crack propagation is fully automatic, with repeated remeshing realized at t r. citarella et alii, frattura ed integrità strutturale, 31 (2015) 138-147; doi: 10.3221/igf-esis.31.11 147 each crack step nearly without user intervention. consequently, for the cases analyzed, the functionality of the proposed procedure can be stated. references [1] citarella, r., lepore, m., shlyannikov, v., yarullin, r., fatigue surface crack growth in cylindrical specimen under combined loading, engineering fracture mechanics, 131 (2014) 439-453. [2] calì, c., citarella, r., perrella, m., three-dimensional crack growth: numerical evaluations and experimental tests, european structural integrity society, in: biaxial/multiaxial fatigue and fracture, edited by andrea carpinteri, manuel de freitas and andrea spagnoli, 31 (2003) 3-504. [3] citarella r., perrella m., multiple surface crack propagation: numerical simulations and experimental tests, fatigue and fracture of engineering material and structures, 28 (2005) 135-148. [4] citarella, r., buchholz, f.-g., comparison of crack growth simulation by dbem and fem for sen-specimens undergoing torsion or bending loading, engineering fracture mechanics, 75 (2008) 489–509. [5] citarella, r., cricrì, g., comparison of dbem and fem crack path predictions in a notched shaft under torsion, engineering fracture mechanics, 77 (2010) 1730-1749. [6] zencrack manual, version 7.9. [7] maligno, a.r., rajaratnam, s., leen, s.b., williams, e.j., a three-dimensional (3d) numerical study of fatigue crack growth using remeshing techniques, engineering fracture mechanics, 77 (2010) 94–111. [8] maligno, a.r., citarella, r., silberschmidt, v.v., soutis, c., assessment of structural integrity of subsea wellhead system: analytical and numerical study, fracture and structural integrity (frattura ed integrità strutturale), 31(2015) 97-119. doi: 10.3221/igf-esis.31.08. [9] abaqus user’s and theory manuals, version 6.5, hks inc. (2005). [10] dhondt, g., application of the finite element method to mixed-mode cyclic crack propagation calculations in specimens, international journal of fatigue, 58 (2014) 2–11. [11] shih, c. f., asaro, r. j., elastic-plastic and asymptotic fields of interface cracks, international journal of fracture, 42(2) (1990) 101-116. [12] adrian, pc., aliabadi mh., dual boundary element assessment of three-dimensional fatigue crack growth, engng anal boundary elements, 28 (2004) 1157–73. [13] guagliano, m., vergani, l., a simplified approach to crack growth prediction in a crank shaft, fatigue fract engng mater struct, 17(5) (1994) 1295–306. microsoft word numero_60_art_07_3296.docx a. boukhelkhal et alii, frattura ed integrità strutturale, 60 (2022) 89-101; doi: 10.3221/igf-esis.60.07 89 assessment of fluidity retention, mechanical strength and cost production of blended cement self-compacting concrete using the concept of a performance index boukhelkhal aboubakeur civil engineering research laboratory, university of laghouat, po box 37g, laghouat 03000, algeria. a.boukhelkhal@lagh-univ.dz kenai said geomaterials and civil engineering laboratory, university of blida 1, algeria. sdkenai@yahoo.com abstract. construction industry consumes a large amount of natural resources and energy and produces high amount of co2 emissions and waste materials. for more sustainable construction industry, various waste materials are used as natural aggregates substitution or as cement replacement materials. in this paper, marble powder (mp) is used as a substitution to ordinary portland cement (opc) and its effects on some fresh and hardened properties of self-compacting concrete (scc) are investigated. the tests at the fresh state were slump flow, l-box and sieve segregation. to assess the fluidity retention, slump flow loss was measured after 30, 60 and 90 minutes. at hardened state, two tests were realized: compressive strength and static segregation. the results indicate that adding mp improved the fresh properties but decreased the compressive strength of scc. adding mp allows to maintain the fluidity of scc until 90 minutes. production cost can be reduced by using mp. the performance approach showed that a substitution level of mp of 20% is adequate to produce an eco-efficient scc with high fluidity and acceptable strength. keywords. self-compacting concrete; marble powder; fluidity retention; strength; cost; performance index. citation: boukhelkhal, a., kenai, s., assessment of fluidity retention, mechanical strength and cost production of blended cement self-compacting concrete using the concept of a performance index, frattura ed integrità strutturale, 60 (2022) 89-101. received: 06.10.2021 accepted: 19.01.2022 online first: 27.01.2022 published: 01.04.2022 copyright: © 2022 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. introduction elf-compacting concretes (scc) are very fluid that can flow and fill all the spaces in the formwork under their gravity, without the need for compaction or vibration, and give homogeneous concretes which are resistant to segregation and bleeding. this type of concrete is suitable for the construction of structures that are heavily reinforced or with complicated shapes. scc can only be prepared with superplasticizer, large amounts of ordinary portland cement (opc) and supplementary cementitious materials (scm). building demolition, industrial and agricultural processes generate annually a high quantity of wastes as shown in tab. 1 in which only a low percentage is recycled 1-5]. the utilization of these wastes has become a priority for its economic and ecological benefits. scc is one s https://youtu.be/wrlrkv6p1l4 a. boukhelkhal et alii, frattura ed integrità strutturale, 60 (2022) 89-101; doi: 10.3221/igf-esis.60.07 90 of the most eco-friendly types of special concrete because waste materials have always been used as scm, fine and coarse aggregates 6-14]. according to tennich et al. 15], incorporation of waste from marbles and tiles factories as partial replacement of opc, which are freely and cheaply available in the composition of scc, allows producing environment friendly concretes. the reuse of industrial by-products and wastes as scm for manufacturing eco-cements is a good way to ensure the ecosystem and the biological components of the environment and human health, which contributes to sustainable development 16]. moreover, adding scm such as natural pozzolana and slag to concrete resulted in low hydration heat, higher compressive strength at later ages, lower porosity, improved durability, lower cost and lower environmental impact due to reduced co2 emissions 17-25]. singh et al. 26] reported that using 10% and 15% of marble powder (mp) as partial replacement of cement increased the compressive and split tensile strengths in the range of 15-20%. alyamac et al. 27] successfully prepared an eco-scc by incorporating 60% of mp as partial replacement of cement. ashish 28] showed that the introduction of mp with 15% by partial replacement of sand offered to concrete superior resistance to carbonation. guneyisi et al. 29] have shown that the introduction of mp by partial replacement of opc into self-compacting mortars leads to an increase in the flow time and setting times, while it reduced the compressive strength and the ultrasonic pulse velocity. toubal et al. 30] showed that incorporating mp in cement paste with various replacement rates of 5, 10 and 15% leads to a reduction of the apparent density and compressive strength and an increase of the porosity at age of 3, 7, 28 and 65 days. the authors concluded that acceptable results could be obtained by using 5% of mp. the use of mp in ordinary pastes, mortars and concretes has been widely investigated. however, few studies investigated the effect of mp as partial substitution of opc on the properties of scc especially on fluidity retention and static segregation. this work aims firstly to investigate the effects of mp as a substitute of opc on some properties of scc such as fluidity retention, compressive strength, and production cost. the performance of each scc mixture was also assessed by using a performance index by taking into consideration several performance criteria. this approach allows the selection of a suitable replacement rate that corresponds to the researched scc performance. in this research work, mp was incorporated at substitution levels of 5, 10, 15 and 20%, keeping the other ingredients and proportions constant. scc mixtures were tested at a fresh state to evaluate the filling, passing ability and the risk to segregation. at hardened state, compressive strength and static segregation were evaluated at the ages of 7 and 28 days. a performance approach index was used to find the optimal substitution levels corresponding to the targeted scc performances at fresh and hardened states. waste type quantity (mt) country reference glass 3.45 egypt [1] slag 0.5 algeria [2] marble 0.34 turkey [3] rice husk 120 china, india, indonesia and bangladesh [4] plastic 1.8 australia [5] table 1: statistics for some waste types. experimental procedure materials pc (cemi, 42.5) that complies with the european standard en 197-1 was used in all scc mixtures. the mp is a by-product of marble stone sawing, shaping, and lustration. the chemical composition and physical properties of cement and mp are presented in tab. 2. laser particle distribution analysis was used to determine the particle size distribution of cement and mp (fig. 1). the results indicated that mp is finer than the cement. tab. 2 gives the diameter of particles that correspond to 10%, 50% and 90% of passing. the results showed that more than 50% of mp material has particles less than 6.5 µm, and about 50% of cement particles are smaller than 12.35 µm. fig. 2 shows the results of the scanning electron microscopy (sem) analysis of cement and mp. this test allows to identify the particles shape of the tested material and confirmed the results for particle size distribution presented in fig. 1. the particles of mp are finer and appear to have less angular shape compared to the cement particles. the mineralogical analysis of mp which is presented in fig. 3 indicates that mp is mainly composed of calcite with some traces of quartz and dolomite. o a. boukhelkhal et alii, frattura ed integrità strutturale, 60 (2022) 89-101; doi: 10.3221/igf-esis.60.07 91 chemical composition (%) cement mp sio2 20.14 0.42 cao 63.47 56.01 mgo 2.12 0.12 al2o3 3.71 0.13 fe2o3 4.74 0.06 so3 2.67 0.01 k2o 0.47 0.01 tio2 0.21 0.01 na2o 0.69 0.43 p2o5 0.06 0.03 loss ignition 1.72 42.78 physical properties specific gravity 3.1 2.7 fineness characteristics fineness (m²/kg) 330 360 d10 (µm) 1.19 1.36 d50 (µm) 12.35 6.50 d90 (µm) 40.53 21.09 table 2: chemical composition and physical properties of cement and mp. figure 1: particle size distribution of cement and mp. (a) (b) figure 2: sem analysis of (a) cement and (b) mp. a. boukhelkhal et alii, frattura ed integrità strutturale, 60 (2022) 89-101; doi: 10.3221/igf-esis.60.07 92 figure 3: xrd analysis of mp. a polycarboxylate-based superplasticizer was used as a chemical admixture, it has a density and ph of 1070 kg/m3 and 8, respectively. natural river sand was used as fine aggregate. two classes of coarse aggregate were used. the physical properties of aggregates were meseaured according to european standared en 1097-6 [31] and are given in tab. 3. fig. 4 presented the particle size distribution of aggeregates. properties fine aggregate coarse aggregate 0/5 3/8 8/15 absorption coefficient (%) 0.59 1.56 2.26 density (kg/m3) 2600 2610 2540 water content (%) 0.03 0.17 0.13 table 3: physical properties of aggregates. figure 4: particle size distribution of aggregates. mixture proportions to study the effect of mp on some fresh and hardened properties and production cost of scc, five mixtures were prepared. the control mix included only opc as a binder, whereas in the other mixtures cement was partially substituted with mp at ratios of 5, 10, 15 and 20%. the proportions of all scc mixtures are shown in tab. 4. a. boukhelkhal et alii, frattura ed integrità strutturale, 60 (2022) 89-101; doi: 10.3221/igf-esis.60.07 93 constituents mix id 0mp 5mp 10mp 15mp 20mp cement (kg/m3) 470 448 426 404 382 marble powder (%) 0 5 10 15 20 (kg/m3) 0 22 44 66 88 sand 0/5 (kg/m3) 882.9 coarse aggregate (kg/m3) 8/15 553 3/8 277 water (kg/m3) 188 superplasticizer (kg/m3) 4.23 water/binder 0.4 superplasticizer/binder 0.9 table 4: mix proportions of scc mixtures. testing procedures slump flow, l-box and sieve segregation tests were carried out to characterize the filling and passing ability and the resistance to segregation of fresh scc according to efnarc requirements 32. the fluidity retention was evaluated by measuring slump flow loss after 30, 60 and 90 minutes. this test allows to estimate the practical duration for using each scc mixture, while the trend to segregation can be qualitatively assessed. compressive strength and segregation static tests were carried out according to en 12390-3 and aashto pp58 3334, respectively. prismatic (7×7×28 cm) and cylindrical (16×32 cm) specimens were cast from each scc mixture. after demolding, the specimens were cured in water at controlled conditions (t=20±2oc and hr>=95%). the average compressive strength test results of six prismatic specimens at the age of 7 and 28 days were determined, while three cylindrical specimens were used to visually assess the static segregation. fresh properties mix id acceptance criteria of scc suggested by efnarc [32] min max 0mp 5mp 10mp 15mp 20mp slump flow (cm) 0 min 70.5 71.1 72.7 73 73.5 65 80 30 min 69.3 70 71.1 71.5 72.2 60 min 67 68.5 69 69.4 70.3 90 min 63 66 67 67.3 68.5 t50 flow time (s) 2.53 1.75 1.61 1.52 1.32 2 5 l-box blocking ratio (%) 0.77 0.81 0.82 0.81 0.81 0.8 1 l-box flow time (s) t20 0.76 0.61 0.5 0.47 0.39 t40 1.71 1.53 1.48 1.43 1.38 segregation ratio (%) 5.1 6.3 6.2 11.2 13.5 5 15 t50 : is the time required for the scc slump flow to reach a circle with 50 cm diameter [32]. t20 and t40: are the times required for the scc to reach points 20 cm (t20) and 40 cm (t40) down the horizontal portion of the l-box [32]. table 5: fresh properties of scc mixtures. results and discussion slump flow he results of the fresh properties of scc mixtures are presented in tab. 5. fig. 5 depicted the variation of slump flow and t50 flow time as a function of the amount of mp. the slump flow is a good indicator of the ability of scc to flow under its weight in an unconfined formwork. fig. 4 showed that all the scc mixes had good flowability, with slump flow values ranging from 70 to 74 cm. it can be seen that all the fresh scc mixtures had slump flow diameter generally conforming efnarc (65 to 80 cm) 32. it has been noted an increase in slump flow with increasing mp content, which means that mixtures prepared with mp presented better fluidity and deformability, compared to the reference mixture. this result may be attributed to the shape of the mp particles, which is less angular than that of the cement and hence increasing the flow of scc with mp. on the other hand, the density of mp, which t a. boukhelkhal et alii, frattura ed integrità strutturale, 60 (2022) 89-101; doi: 10.3221/igf-esis.60.07 94 is lower compared to that of cement, increases the volume of paste and reduces the frictions between coarse and fine aggregates 35. furthermore, the substitution of cement by mp decreased the amount of water consumed by hydration reactions, which results in the additional free water that increases deformability. similar findings were stated by uysal and yilmaz 36. however, guneyisi et al. 29 have reported contradictory results, in which they observed a decrease in the fluidity of the scc with the addition of mp. it should be noted that it is possible to reduce the need for superplasticizer and water for scc made with mp to obtain a similar fluidity to control scc, this reduces the production cost, and on the other hand decreases the water/cement ratio which improves the compressive strength and durability. fig. 5 presents also the t50 flow time for scc mixtures. the results indicate that t50 flow time decreases as the amount of mp increases, this means that scc with mp is more fluid and less viscous. it should be noticed that all scc mixtures do not meet the flow time values suggested by efnarc 32, except for reference scc, but the visual control of fresh scc revealed that there was no problem of segregation or bleeding (fig. 6). figure 5: slump flow and t50 flow time of scc mixtures vs mp content. figure 6: scc mixture without segregation or bleeding. fluidity retention the effect of mp on the slump flow loss of scc mixtures over time is plotted in fig. 7. it can be observed that there was a decrease in slump flow diameter with increasing time. the 0mp, 5mp, 10mp, 15mp, and 20mp mixtures have slump flow values of 71, 71, 73, 73 and 74 cm immediately after being mixed, and after 90 minutes these same mixtures experienced slump flow values of 63, 66, 67, 67.3, and 68.5 cm, respectively. it can be seen that the reference scc lost its fluidity after 90 minutes with a slump flow value inferior to 65 cm, while the other mixtures maintained their fluidity even after 90 minutes with slump flow values superior to 65 cm. adding mp improved and maintained the fluidity of scc mixtures, this means that scc can be used for more than 90 minutes after initial mixing or transported for long distances without losing the self-compacting property. these results may be explained by the substitution of cement by mp, which decreased the amount of water evaporated and consumed by hydration reactions, thus offered additional free water in the mixture. 1 2 3 4 5 70 71 72 73 74 75 0mp 5mp 10mp 15mp 20mp t 5 0 f lo w t im e (s ) s lu m p f lo w (c m ) scc mixes slump flow flow time t50 a. boukhelkhal et alii, frattura ed integrità strutturale, 60 (2022) 89-101; doi: 10.3221/igf-esis.60.07 95 figure 7: slump flow loss of scc mixtures vs mp content. blocking ratio the variation of blocking ratio of scc mixtures made with different amounts of mp is presented in fig. 8. efnarc committee suggests that 0.8 and 1 for lower and upper limits of blocking ratio, respectively, are acceptable for designing appropriate scc mixtures. the blocking ratio values ranged between 0.77 and 0.82. the results indicated that mixtures containing mp had a blocking ratio higher than 0.8, whereas the blocking ratio of the reference mixture was less than 0.8. this means that scc mixtures made with mp have great mobility in a confined area. topçu et al. 37 found similar results. figure 8: blocking ratio of l-box of scc mixtures vs mp content. fig. 9 shows the evolution of t20 and t40 flow times in l-box as a percentage of mp. it can be seen from this figure that the replacement of cement by mp reduced the flow times (t20 and t40) due to an increase in the fluidity of these mixtures, this decrease is of the same as the t50 flow time. all t20 and t40 flow time values are within the target range t20 <1.5 s and t40 <3.5 s suggested by jaramillo et al. 38. the flow times t20 and t40 are good indicators of the viscosity, this means that mixtures including mp have lower viscosity compared to the control mixture. alyamac et al. 27 showed that the addition of mp resulted in higher viscosity and consequently the v-funnel time increased. some authors reported that scc made with mp showed an increase in the flow time by increasing mp content 36, 39. dynamic segregation the results of the sieve segregation test are illustrated in fig. 10. this figure shows that increasing the amount of mp increased the segregation ratio, the values obtained are 5.1, 6.3, 6.1, 11.2 and 13.5% for the 0mp, 5mp, 10mp, 15mp, and 20mp scc mixtures, respectively. these values indicate that all the tested mixtures have good resistance to dynamic segregation (5% ≤ is ≤15%) 32. 60 65 70 75 0 20 40 60 80 100 s lu m p f lo w l o ss (c m ) time (min) 0mp 5mp 10mp 15mp 20mp 0,6 0,7 0,8 0,9 1,0 0 5 10 15 20 b lo ck in g r at io ( % ) mp content (%) requested values (65-80 cm) a. boukhelkhal et alii, frattura ed integrità strutturale, 60 (2022) 89-101; doi: 10.3221/igf-esis.60.07 96 figure 9: t20 and t40 flow times in l-box of scc mixtures vs mp content. figure 10: dynamic segregation ratio of fresh scc mixtures vs mp content. the control mixture has developed the highest resistance to segregation. however, using mp reduced the resistance to segregation. the lower segregation ratio for the control mixture is due to its high viscosity. the increase in the segregation ratio of the other mixtures is attributed to their low viscosity. compressive strength fig. 11 shows the compressive strength of scc mixtures at 7 and 28 days. the compressive strength decreased as the amount of mp increased. this may be attributed to the use of mp, which has no pozzolanic property; therefore, it cannot chemically contribute to the development of the strength at later ages. also, the low water retention which characterizes the mp induces a significant amount of water in the mixture which contributes through the dilution effect to decrease of the compressive strength. besides, the reduction of the volume of c3s and c2s that are responsible for the development of strength, as the cement is partially replaced by mp, decreases also the compressive strength. it has been noted that compressive strength values are between 19-28 mpa at 7 days and 26-37 mpa at 28 days. the mix with 5% of mp developed a similar strength to the reference mix at 28 days. furthermore, the control mix had the highest strength at all the curing ages due to the high amount of opc (470 kg/m3). the 20mp mixture with 380 kg/m3 of opc had the same compressive strength as conventional concrete with 350 kg/m3 of opc which is the most used cement dosage in algerian construction sites. these results are close to those reported in the literature 30, 40. however, tennich et al 15 reported contradictory results. the authors found that the presence of waste fillers from marble in the composition of scc, at a dosage of 350 kg/m3 increased the compressive strength by about 6.7% in comparison to ordinary cement vibrated concrete. in recent work, toubal et al. 41 have shown that wet curing of pastes made with mp leads to higher compressive strength compared to air curing. they also reported that increasing wet curing duration helps to improve the compressive strength by reducing the percentage of water evaporated and the porosity. a. boukhelkhal et alii, frattura ed integrità strutturale, 60 (2022) 89-101; doi: 10.3221/igf-esis.60.07 97 figure 11: compressive strength of scc mixtures vs mp content. static segregation fig. 12 illustrates a visual examination of the static segregation of cylindrical specimens. the figure indicated that all mixtures have a regular and homogeneous distribution of coarse particles in all parts and for all levels of mp. no bleeding was noted at the top of the specimens. it can be concluded that all tested mixtures have good resistance to static segregation. (a) 0mp (b) 5mp (c) 10mp (d) 15mp (e) 20mp figure 12: visual control of static segregation in scc mixtures. production cost of scc until now, the use of scc in building constructions is limited due to the high production cost stemming from the use of superplasticizers and large amount of cement. the superplasticisers enable the concrete to obtain the desired fluidity. a. boukhelkhal et alii, frattura ed integrità strutturale, 60 (2022) 89-101; doi: 10.3221/igf-esis.60.07 98 the use of scm reduced the demand of superplasticizer and the quantity of clinker, which allows decreasing the cost of scc and therefore increasing its use. in this context, this study was carried out to examine the effect of mp on the production cost of scc. the production cost of one cubic meter of the various concrete mixes is given in tab. 6. it can be shown that adding mp decreased the production cost of scc. increasing mp content from 5 to 20% reduced the cost of scc by 3 to 13 %, compared to the plain cement mixture. constituents mix. id 0mp 5mp 10mp 15mp 20mp cement ($) 50.25 47.90 45.55 43.20 40.74 marble powder ($) 0 0.22 0.44 0.66 0.89 sand 0/5 ($) 2.21 coarse aggregate ($) 8/1 5 4.93 3/8 2.34 water ($) 0.72 superplasticizer ($) 5.08 global cost ($) / 1 m3 65.54 63.40 61.27 59.14 56.90 production cost gain (%) 0 3.27 6.52 9.77 13.18 prices are considered for algerian market table 6: production cost for 1 m3 of all scc mixtures. the concept of scc performance index the performance of each scc mixture was evaluated by measuring the performance index (pi) 42. this approach is adopted to facilitate the determination of the suitable replacement rate of mp that complies with the researched performance criteria. the required characteristics depend on the concrete application and are generally defined by the consumer. the first step in this approach is to calculate the weight ranking (wi) of all the selected criteria from eqn. (1).              i measured performance for each mixture w best measured performance (1) the mixture with the best test value in a certain criterion scores 1.00, while the remaining mixtures have test values proportional to the best test value (<1.00). in the second step, a numerical index (ri) is calculated. the highest value of (ri) is equal to 5.00. for each mixture, the corresponding numerical index is the product of the previously calculated weight ranking wi and 5.00 as given in eqn. (2).  5  i ir w (2) mix. id fluidity retention compressive strength cost production gain wi ri wi ri wi ri 0mp 0.92 4.60 1.00 5.00 0.00 0.00 5mp 0.96 4.82 0.99 4.94 0.25 1.23 10mp 0.98 4.89 0.93 4.64 0.50 2.48 15mp 0.98 4. 91 0.77 3.87 0.74 3.71 20mp 1.00 5.00 0.70 3.51 1.00 5.00 table 7: performance indices for individual criteria. in this study, three performance principal criteria have been selected: fluidity retention, compressive strength, and cost production. tab. 7 gives the weighted ranks and numerical indices of all scc mixtures. according to the required performance criteria, the related numerical index is multiplied to get a mixture score (sin) as given by eqn. (3). the mixture with the highest score is the most appropriate in terms of the required multiple criteria. a. boukhelkhal et alii, frattura ed integrità strutturale, 60 (2022) 89-101; doi: 10.3221/igf-esis.60.07 99    1 2 .in i i ins r r r (3) tabs. 8 and 9 present the performance indices for multiple criteria and the suitable mp content for different performance criteria. with regards to the fluidity retention and compressive strength requirements (pi-1), using 5% of mp was found to be more suitable. for constructions that require fluidity retention and production cost gain (pi-2) (or compressive strength and production cost gain (pi-3)), a substitution level of 20% is considered the best. if all of the three characteristics (fluidity retention, compressive strength and production cost gain) are required (pi-4), adding 20% of mp is the appropriate substitution level. mix. id multiple performance criterion 0mp 5mp 10mp 15mp 20mp pi-1 22.99 23.79 22.68 19.02 17.56 pi-2 0 5.95 12.11 18.22 25.00 pi-3 0 6.09 11.48 14.36 17.56 pi-4 0 29.36 56.14 70.55 87.81 table 8: performance indices for multiple criteria. performance index required performance criteria mp (%) pi-1 fluidity retention + compressive strength 5-10 pi-2 fluidity retention + production cost gain 20 pi-3 compressive strength + production cost gain 20 pi-4 fluidity retention + compressive strength + production cost gain 20 table 9: appropriate mp content for different performance criteria. conclusions ased on the experimental results and evaluation of scc with mp using the concept of a performance index, the following conclusions can be drawn :  all scc mixtures have satisfactory self-compacting properties at fresh state. the use of mp in scc enhances the filling and passing abilities.  the addition of mp seems to reduce the need for superplasticizer and water to obtain a similar fluidity to the scc control mixture. this not only reduces the production cost, but also the w/c ratio, which allows to enhance the performance of hardened scc.  the time to retain the fluidity of scc can be extended by using mp, this will be very helpful when transporting concrete over long distances.  at a hardened state, the 28-days compressive strength of scc with mp ranged from 26 to 37 mpa. this means that is possible to used mp in scc for construction requiring medium strength. an examination of the risk of static segregation shows that all the mixtures tested are homogeneous and have good resistance to the static segregation.  the use of mp as a partial replacement for cement reduced the production cost and co2 emissions, which means that mp is an interesting material to produce an eco-friendly scc.  the characteristics of scc may be assigned numerical performance index values. these values may constitute a reliable means for concrete producers in finding the rate of cement replacement by other cementitious materials. according to the performance index results, the inclusion of 20% of mp in scc mixtures was beneficial for most of the targeted performance criteria. b a. boukhelkhal et alii, frattura ed integrità strutturale, 60 (2022) 89-101; doi: 10.3221/igf-esis.60.07 100 references [1] bajad, m.n. modhera, c.d and desai, a.k. (2011). effect of glass on strength of concrete subjected to sulphate attack, civ. engin. res. develop., 1(2), pp. 1-13. [2] behim, m. cyr, m and clastres, p. (2011). physical and chemical effects of el hadjar slag used as an additive in cement-based materials, euro. j. envir. civ. engin., 15(10), pp. 1413-1432. doi: 10.1080/19648189.2011.9723352 [3] celik, m.y and sabah, e. (2008). geological and technical characterization of iscehisar (afyon-turkey) marble deposits and the impact of marble waste on environmental pollution, envir. manag., 87, pp. 106-116. doi: 10.1016/j.jenvman.2007.01.004 [4] safiuddin, m. west, j.s and soudki, k.a. (2011). flowing ability of the mortars formulated from self-compacting concretes incorporating rice husk ash, constr. build. mater., 25(2), pp. 973-978. doi: 10.1016/j.conbuildmat.2010.06.084 [5] brulliard, c. cain, r. do, d. dornom, t. evans, k. lim, b. olesson, e and young, s. (2012). the australian recycling sector. report of department of sustainability, environment, water, population and communities. available at: https://www.environment.gov.au/system/files/resources/dc87fd71-6bcb-4135-b91671dd349fc0b8/files/australian-recycling-sector.pdf. [6] laidani, z.e.a. benabed, b. abousnina, r. gueddouda, m.k and kadri, eh. (2020). experimental investigation on effects of calcined bentonite on fresh, strength and durability properties of sustainable self-compacting concrete, constr. build. mater., 230, pp. 1-11. doi: 10.1016/j.conbuildmat.2019.117062 [7] boukhelkhal, a and benabed, b. (2019). fresh and hardened properties of self-compacting repair mortar made with a new reduced carbon blended cement, silic. bas. compos. mater., 71(4), pp. 108-113. doi: 10.14382/epitoanyag-jsbcm.2019.19 [8] santos, s. da silva, pr and de brito, j. (2019). self-compacting concrete with recycled aggregates – a literature review, j. build. eng., 22, pp. 349-371. doi: 10.1016/j.jobe.2019.01.001 [9] boughamsa, o. hebhoube, h. kherref, l. belachia, m. abdelouahed, a and rihia, c. (2020). valorization of marble’s waste as a substitute in sand concrete, adv. concr. constr. 9 (2), pp. 217-225. doi: 10.12989/acc.2020.9.2.217 [10] ouldkhaou, y. benabed, b. abousnina, r and kadri, e.h. (2020). experimental study on the reuse of cathode ray tubes funnel glass as fine aggregate for developing an ecological self-compacting mortar incorporating metakaolin, j. build. engin., 20, pp. 1-11. doi: 10.1016/j.jobe.2019.100951 [11] boukhelkhal, a. azzouz, l. benabed, b and belaïdi, a.s.e. (2017). strength and durability of low-impact environmental self-compacting concrete incorporating waste marble powder, build. mater. struc., 4, pp. 31-41. doi: 10.5281/zenodo.1134146 [12] alipour, p. namnevis, m. tahmouresi, b. mohseni, e and tang, w. (2019). assessment of flowing ability of selfcompacting mortars containing recycled glass powder, adv. concr. constr., 8(1), pp. 65-76. doi: 10.12989/acc.2019.8.1.065 [13] baghabra, al amoudi o.s., shamsad, a. khan, s.m.s and maslehuddin, m. (2019). durability performance of concrete containing saudi natural pozzolans as supplementary cementitious material, adv. concr. constr., 8(2), pp. 119-126. doi: 10.12989/acc.2019.8.2.119 [14] djelloul, o.k. menadi, b. wardeh, g and kenai, s. (2018). performance of self-compacting concrete made with coarse and fine recycled concrete aggregates and ground granulated blast-furnace slag, adv. concr. constr., 6(2), pp. 103-121. doi: 10.12989/acc.2018.6.2.103 103. [15] tennich, m. kallel, a and ben ouezdou, m. (2015). incorporation of fillers from marble and tile wastes in the composition of self-compacting concretes, constr. build. mater., 91, pp. 65-70. doi: 10.1016/j.conbuildmat.2015.04.052 [16] sadek, d.m. el-attar, mm and haitham, a.a. (2016). reusing of marble and granite powders in self-compacting concrete for sustainable development, j. clean. prod., 121, pp. 19-32. doi: 10.1016/j.jclepro.2016.02.044 [17] siddique, r. (2016). compressive strength, water absorption, sorptivity, abrasion resistance and permeability of selfcompacting concrete containing coal bottom ash, constr. build. mater., 47, pp. 1444-1450. doi: 10.1016/j.conbuildmat.2013.06.081 [18] boukhelkhal, a. azzouz, l. kenai, s. kadri, e.h and benabed, b. (2019). combined effects of mineral additions and curing conditions on strength and durability of self-compacting mortars exposed to aggressive solutions in the natural hot-dry climate in north african desert region, constr. build. mater., 197, pp. 307-318. doi: 10.1016/j.conbuildmat.2018.11.233 [19] jalal, m. pouladkhan, a. harandi, o.f and jafarid, d. (2015). comparative study on effects of class f fly ash, nano silica and silica fume on properties of high performance self-compacting concrete, constr. build. mater., 94, pp. 90-104. doi: 10.1016/j.conbuildmat.2015.07.001 a. boukhelkhal et alii, frattura ed integrità strutturale, 60 (2022) 89-101; doi: 10.3221/igf-esis.60.07 101 [20] ardalan, rb. joshaghani, a and hooton, rd. (2017). workability retention and compressive strength of selfcompacting concrete incorporating pumice powder and silica fume, constr. build. mater., 134, pp. 116-122. doi: 10.1016/j.conbuildmat.2016.12.090 [21] boukhelkhal, a. azzouz, l. belaïdi, a.s.e and benabed, b. (2016). effects of marble powder as a partial replacement of cement on some engineering properties of self-compacting concrete, adhes. sci. technol., 30(22), pp. 2405–2419. [22] assi, l. carter, k. deaver, e. anay, r and ziehl, p. (2018). sustainable concrete: building a greener future, j. clean. prod., 198, pp. 1641-1651.doi: 10.1016/j.jclepro.2018.07.123 [23] kim, y. hanif, a. usman, m. munir, mj. kazmi, sms and kim, s. (2017). slag waste incorporation in high early strength concrete as cement replacement: environmental impact and influence on hydration and durability attributes, j. clean. prod., 172, pp. 3056-3065. doi: 10.1016/j.jclepro.2017.11.105 [24] ishak, sa and hashim, h. (2015). low carbon measures for cement plant a review, j. clean. prod., 103, pp. 260274. doi: 10.1016/j.jclepro.2014.11.003 [25] boukhelkhal, d. boukendakdji, o. kenai, s and kadri, e-h. (2018). combined effect of mineral admixture and curing temperature on mechanical behavior and porosity of scc, adv. concr. constr., 6(1), pp. 69-85. doi: 10.12989/acc.2018.6.1.069. [26] singh, m. choudhary, k. srivastava, a. sangwan, ks and bhunia, d. (2017). a study on environmental and economic impacts of using waste marble powder in concrete, j. build. eng., 13, pp. 87-95. doi: 10.1016/j.jobe.2017.07.009 [27] alyamac, ke. ghafari, e and ince, r. (2017). development of eco-efficient self-compacting concrete with waste marble powder using the response surface method, j. clean. prod., 144, pp. 192-202. doi: 10.1016/j.jclepro.2016.12.156 [28] ashish, dk (2019). concrete made with waste marble powder and supplementary cementitious material for sustainable development, j. clean. prod., 211, pp. 716-729. doi: 10.1016/j.jclepro.2018.11.245 [29] guneyisi, e. gesoglu, m and ozbay, e. (2009). effects of marble powder and slag on the properties of selfcompacting mortars, mater. struc., 42, pp. 813-826. doi: doi: 10.1617/s11527-008-9426-2 [30] toubal, ns. mellas, m. sadowski, l and żak, a. (2018). effects of marble powder on the properties of the aircured blended cement paste, j. clean. prod., 183, pp. 858-868. doi: 10.1016/j.jclepro.2018.01.267 [31] european standared en 1097-6 (2013) tests for mechanical and physical properties of aggregates part 6: determination of particle density and water absorption. [32] efnarc(2002).specification and guidelines for selfcompacting concrete. european federation of producers and applicators of specialist products for structures, efnarc, norfolk, uk, pp.32. [33] en 12390-3. (2012). essais pour béton durci partie 3 : résistance à la compression des éprouvettes de béton durci. [34] aashto pp58 (2008). "static segregation of hardened self-consolidating concrete cylinders." american association of state highway and transportation officials, washington, dc. [35] yahia, a. tanimura, m and shimoyama, y. (2005). rheological properties of highly flowable mortar containing limestone filler-effect of powder content and w/c ratio, cem. concr. res., 35(3), pp. 532–539. doi: 10.1016/j.cemconres.2004.05.008 [36] uysal, m. and yilmaz, k. (2011). effect of mineral admixtures on properties of self-compacting concrete, cem. concr. com., 33, pp. 771-6. doi: 10.1016/j.cemconcomp.2011.04.005 [37] topçu, i. bilir, t and uygunoglu, t. (2009). effect of waste marble dust content as filler on properties of selfcompacting concrete, constr. build. mater., 23, pp. 1947-1953. doi: 10.1016/j.conbuildmat.2008.09.007 [38] arbelaez jaramillo, c.a. rigueira victor, j.w. marti vargas, j.r., serna ros, p and pinto barbosa, m. (2003). reduced models test for the characterization of the rheological properties of self-compacting concrete (scc), proceedings of the third international symposium on self-compacting concrete, reykjavik, island, 17-20 august. [39] alyousef, r. benjeddou, o. khadimallah, m.a. mohamed, a.m. soussi, c (2018). study of the effects of marble powder amount on the self-compacting concretes properties by microstructure analysis on cement-marble powder pastes. advan civ eng. doi: 10.1155/2018/6018613. [40] corinaldesi, v. moriconi, g and naik, tr. (2010). characterization of marble powder for its use in mortar and concrete, constr. build. mater., 24, pp. 113-117. doi: 10.1016/j.conbuildmat.2009.08.013 [41] toubal, ns. mellas, m. sadowski, l and żak, a. (2019). the effect of curing conditions on the properties of cement-based composites blended with waste marble dust, mine. met. mater. soc., 71(3), pp. 1002-1015. doi: 10.1007/s11837-018-3254-9. [42] el-dieb, a.s and kanaan, d.m. 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/hrv (za stvaranje adobe pdf dokumenata najpogodnijih za visokokvalitetni ispis prije tiskanja koristite ove postavke. stvoreni pdf dokumenti mogu se otvoriti acrobat i adobe reader 5.0 i kasnijim verzijama.) /hun 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can be opened with acrobat and adobe reader 5.0 and later.) >> /namespace [ (adobe) (common) (1.0) ] /othernamespaces [ << /asreaderspreads false /cropimagestoframes true /errorcontrol /warnandcontinue /flattenerignorespreadoverrides false /includeguidesgrids false /includenonprinting false /includeslug false /namespace [ (adobe) (indesign) (4.0) ] /omitplacedbitmaps false /omitplacedeps false /omitplacedpdf false /simulateoverprint /legacy >> << /addbleedmarks false /addcolorbars false /addcropmarks false /addpageinfo false /addregmarks false /convertcolors /converttocmyk /destinationprofilename () /destinationprofileselector /documentcmyk /downsample16bitimages true /flattenerpreset << /presetselector /mediumresolution >> /formelements false /generatestructure false /includebookmarks false /includehyperlinks false /includeinteractive false /includelayers false /includeprofiles false /multimediahandling /useobjectsettings /namespace [ (adobe) (creativesuite) (2.0) ] /pdfxoutputintentprofileselector /documentcmyk /preserveediting true /untaggedcmykhandling /leaveuntagged /untaggedrgbhandling /usedocumentprofile /usedocumentbleed false >> ] >> setdistillerparams << /hwresolution [2400 2400] /pagesize [612.000 792.000] >> setpagedevice microsoft word numero_35_art_14 v. shlyannikov et alii, frattura ed integrità strutturale, 35 (2016) 114-124; doi: 10.3221/igf-esis.35.14 114 focussed on crack paths surface crack growth subject to bending and biaxial tension-compression v. shlyannikov, a. tumanov, a. zakharov kazan scientific center of russian academy of sciences, russia shlyannikov@mail.ru, tymanoff@rambler.ru, alex.zakharov88@mail.ru a. gerasimenko saint-petersburg university of mines, russia anastasiya.geras@mail.ru abstract. fatigue surface crack growth and the in-plane and out-of-plane constraint effects are studied through experiments and computations for aluminium alloy d16t. subjects for studies are cruciform specimens under different biaxial loading and bending central notched specimens with external semi-elliptical surface crack. both the optical microscope measurements and the crack opening displacement (cod) method are used to monitor and calculate both crack depth and crack length during the tests. the variation of crack growth rate and surface crack paths behaviour is studied under cyclic pure bending and biaxial tension-compression fatigue loading. this work is centered on the relations between crack size on the free surface of specimen considered configurations, cod and aspect ratio under different fatigue loading conditions. for the experimental surface crack paths in tested specimens the t-stress, the local triaxiality parameter h, the out-of-plane tz factor and the governing parameter for the 3d-fields of the stresses and strains at the crack tip in the form of in-integral were calculated as a function of aspect ratio by finite element analysis to characterization of the constraint effects along semi-elliptical crack front. the plastic stress intensity factor approach is applied to the fatigue crack growth on the free surface of the tested bending and cruciform specimens as well as the deepest point of the semi-elliptical surface crack front. as result fatigue surface crack paths or crack front positions as a function of accumulated number of cycle of loading are obtained. keywords. surface crack; biaxial loading; bending; crack growth. introduction n order to provide operation in a safe condition, it is necessary to perform fracture mechanics assessment of a structural component under cyclic loading. the fatigue growth analysis of surface cracks is one of the most important elements for structural integrity prediction of the flat metallic components in the presence of initial and accumulated operation damages. in most cases, part-through flaws appear on the free surface of the structures and defects i v. shlyannikov et alii, frattura ed integrità strutturale, 35 (2016) 114-124; doi: 10.3221/igf-esis.35.14 115 are approximately considered as semi-elliptical cracks. biaxial loading conditions including tension/compression and bending are typical for the metallic components of engineering structures (turbine disk, aeroplane fuselage skin, pressure vessels and so on). the problem of residual fatigue life prediction of such type of structural elements is complex and the closed solution is often not available because surface flaws are three-dimensional in nature. the fatigue failure of structural elements subjected to biaxial stress system maybe develops from surface flaws, and only several analyses have been carried out to determine the stress intensity factors along the front of an edge defects and crack growth rate study on this base [1-4]. an actual surface crack may usually be replaced by an equivalent circular arc or elliptical-arc edge flaw. the elastic stress intensity factors have been published for part-circular, part-elliptical, or straight fronted through-thickness cracks in a cruciform and bending specimens. in this paper, firstly experimental results of fatigue crack growth for a crack starting from a semi-elliptical notch in an cruciform specimens under biaxial loading and bending plate are given. the influence of different loading conditions on fatigue life of cruciform specimens and bending plate is discussed. the relations of crack opening displacement and crack length on the free surface of specimens are obtained and it is shown that the growth of the crack fronts is dependent on the initial notch form. using the aforementioned relations, the crack front shape and crack growth rate in the depth direction can be predicted. the simulations for the crack path assessment are based on the constraint parameters behaviour. the computational 3d fracture analyses deliver a governing parameter of elastic-plastic stress field distributions along the crack front. on this base crack growth interpretation is performed using the traditional elastic and new plastic stress intensity factors [5-7]. different crack growth rate is observed in the direction of the deepest point of the crack front with respect to the free surface of the bending specimen. specimens and material properties he test material is aluminum alloy d16t which main mechanical properties are listed in tab. 1 where e is the young’s modulus, b is the nominal ultimate tensile strength, 0 is the monotonic tensile yield strength, u is the true ultimate tensile strength,  is the elongation,  is the reduction of area, n is the strain hardening exponent and α is the strain hardening coefficient. aluminum alloy 0.2 mpa b mpa  %  % u mpa e gpa n α d16t 439 590 9 9 645 75.922 5.88 1.50 438 598 12 13 686 77.191 5.85 1.58 table 1: main mechanical properties of aluminum alloys. the cruciform specimen (cs) geometry and bending plate (bp) configuration are shown in fig. 1. the thickness of both specimens is equal to 10 mm. using linear cutting machine surface edge cracks were cut with initial flaw depths b0 3.0 mm for both a circular arc and elliptical-arc initial edge notch. the geometric parameters of the specimens and initial notch are shown in fig. 1. in this figure, the crack front approximated by an elliptical curve with major axis 2c and minor axis 2a. the crack length on the free surface of specimen c is obtained by measuring the distance between the advancing crack break through point and the notch break through point. the crack opening displacement is measured on the free specimen flat surface, in the central plane of symmetry as shown in fig. 2. the cs fatigue crack growth tests have been performed with servohydraulic biaxial test equipment at a frequency of 5 hz at a stress ratio r=0.1. the equipment has four independent loading arms with load actuators, which exert up to 50 kn on the both axes. tensile or compressive loads are applied to each pair of arms of the cruciform specimens (fig. 1), developing a biaxial stress field in the working section. the loads are controlled such that the specified forces are produced on opposing arms of the cs according to the given load biaxiality. for pure mode i at crack angle equal  = 90, four biaxial load ratios for cs,  equal to +1.0, +0.5, 0.0 (uniaxial), and -1.0. bending tests were carried out on servohydraulic test system biss-nano with maximal capacity 25 kn at a frequency of 7 hz at a stress ratio r=0.1. the crack length on the specimen lateral surface were monitored using the optical instrumental zoom microscope whereas, to fix the t v. shlyannikov et alii, frattura ed integrità strutturale, 35 (2016) 114-124; doi: 10.3221/igf-esis.35.14 116 crack opening displacement of specimen at the gauge length, a pulley arrangement with an externally axial encoder is introduced (fig. 2). all tests are carried out with sinusoidal loading form with load control. two different stress ratio rf values (0.1 and 0.5) were applied several times to the specimens in order to highlight the crack front geometry during propagation: during each test, beach marks were produced on each specimen by increasing the applied stress ratio from 0.1 to 0.5 at constant value of maximum cyclic nominal stress, when the surface crack length was approximately increased to a  0.1mm. the typical beach marks on the post mortem cross section of different specimens are shown in figs. 2 and 3 for biaxial tension and bending, respectively. from the crack front shape obtained in a) b) c) figure 1: details of the (a) cruciform specimen and (b) plate geometry and (c) initial notches.   figure 2: test equipment for measuring cod and crack path under biaxial loading. a) b)   figure 3: surface crack paths under bending for initial aspect ratio (a) (a/c)0=1.0 and (b) (a/c)0=0.36. v. shlyannikov et alii, frattura ed integrità strutturale, 35 (2016) 114-124; doi: 10.3221/igf-esis.35.14 117 this way, the relations between the relative crack depth a/t and the aspect ratio a/c can be measured using a comparison microscope. in addition, based on periodically measured increments of surface crack length c, the curve of surface crack propagation versus cycle numbers dc/dn can be obtained. afterwards, utilizing the relation of crack depth versus surface crack length, it is possible to obtain the crack growth rates da/dn in the depth direction. another interesting result pointed out in the present study is the aspect ratio increasing under biaxial loading as a function of crack depth a/t (fig.4,a) whereas the aspect ratio decreasing under bending loading (fig.4,b). a) b) figure 4: aspect ratio versus crack depth under (a) different biaxial loading and (b) bending. numerical results rom figs. 2 and 3 can be seen that the length of the arc of semi-elliptical crack front depends on the loading conditions of the cs and bp specimens. moreover, the crack propagation process in cs samples can be divided into two stages. during the first stage a semi-elliptical crack is a part-through-thickness. on the second stage semielliptical crack completely crosses the wall and becomes a through-thickness. to compare the parameter distributions along the semi-elliptical crack front is convenient to introduce the dimensionless coordinates in the following form 2   . in the following representation of numerical results, we will use variable  changing in the range from 0 to 1. constraint parameters characterization of the constraint effects in the present study was performed using the non-singular t-stresses, the local triaxiality parameter h and the tz-factor of the stress-state in a 3d cracked body to illustrate the features of the behavior of surface cracks in the cs and bp specimens. t-stress using the crack flank nodal displacements technique, the t-stress distributions in various specimen geometries were determined from numerical calculations. to this end, the commercial finite element code, ansys [8], was used to calculate the stress distributions ahead of the crack tips. in this part of the fea calculations, the material is assumed to be linear elastic and characterized by e=76.5 gpa and =0.3. tz-factor the tz factor [9] has been recognized to present a measure of the out-of-plane constraint and can be expressed as the ratio of the normal elastic-plastic stress components      zz z xx yy t (1) where zz is the out-of-plane stress, and xx and yy are the in-plane stresses. the variation of this parameter is important to characterize the thickness effect on the crack front stress distribution and the changes of the plastic zone size. f v. shlyannikov et alii, frattura ed integrità strutturale, 35 (2016) 114-124; doi: 10.3221/igf-esis.35.14 118 stress triaxiality as a secondary fracture parameter, a local parameter of the crack-tip constraint was proposed by the authors [10] because the validity of some of the above-mentioned concepts depends on the chosen reference field. this stress triaxiality parameter is described as follows:   3, , 3 2          kk ij ijh r z s s (2) where kk and sij are the hydrostatic and deviatoric stresses, respectively. being a function of both the first invariant of the stress tensor and the second invariant of the stress deviator, the stress triaxiality parameter is a local measure of the inplane and out-of-plane constraint that is independent of any reference field. plastic stress intensity factor here, our primary interests are to obtain an accurate description for the distribution along the crack front of the governing parameter for the elastic-plastic solution in the form of an in-integral and to determine the accuracy that this type of calculation, which will later be used for the general 3d problem, provides for the plastic stress intensity factor (sif). the method developed here for combining the knowledge of the dominant singular solution with the finite element technique to obtain accurate solutions in the neighborhood of a crack tip is also applicable to the treatment of problems involving cracks in finite bodies. the plastic stress intensity factor pk in pure mode i can be expressed directly in terms of the corresponding elastic stress intensity factor using rice’s j-integral. that is             ; 11 2 1 2 0 11 2 0 2 1                       n n n n p i way i k k       wayk 11   (3) where wkk 11  is normalized by a characteristic size of cracked body elastic stress intensity factor and ' e e for plane stress and  2' 1  e e for plane strain. in the above equations,  and n are the hardening parameters, wa is the dimensionless crack length, w is characteristic size of specimen (for our case that is specimen width),  is the nominal stress, and 0 is the yield stress. the numerical constant  ni is obtained from the singularity analysis by means of the conjugation solutions for the far and near fields. in the classical first-term singular hrr-solution [11], the numerical parameter in is a function of only the material strain hardening exponent n. shlyannikov and tumanov [5] reconsidered the hrr-solution for both plane strain and plane stress and supposed that under small-scale yielding, the expression for in depends implicitly on the dimensionless crack length and the specimen configuration. in this section, we extend the analysis to the in-integral behavior in an infinitely sized cracked body [11] to treat the test specimen’s specified geometries. the use of the hutchinson’s theoretical definition for the in-factor directly adopted in the numerical finite element analyses leads to [5]     1 cos sin 1 , , , 1 cos 1                                                            fem fem femn fem fem fem femr e rr r r fem n fem fem fem fem rr r r du dun u u c a n d d i n d w t u u n         (4) in this case, the numerical integral of the crack tip field in changes not only with the strain hardening exponent n but also with the relative crack length c/w and the relative crack depth a/t. more details to determine the in factor for different test specimen configurations are given by refs. [5-7]. v. shlyannikov et alii, frattura ed integrità strutturale, 35 (2016) 114-124; doi: 10.3221/igf-esis.35.14 119 the distributions of the elastic and elastic-plastic constraint parameters along the crack front in the bending specimen under cyclic loading are plotted in figs. 6 and 7. these distributions correspond to the crack front positions at the accumulated number of loading cycles n1=0 (initial front), n2= 28000 (intermediate front), n3= 38000 (intermediate front), n4= 44500 (final failure front). the constraint parameter is plotted against the normalized coordinate  . in this plot  = 0.0 is the crack border (the specimen free surface) while  = 1.0 is the mid-plane of the specimen thickness. it can be observed that all constraint parameters essentially changed along the crack front from the free surface toward the mid-plane. figure 5: constraint parameter distributions for bending plate along crack front (1-initial, 2-3-intermediate, 4-final). figure 6: elastic constraint parameter distributions along crack front under different biaxial loading conditions. the distribution of the elastic-plastic constraint parameters along the crack front in the direction from the free surface toward the mid-plane is plotted in figs. 6 and 7 for the cruciform specimens under different biaxial loading conditions. the constraint parameters are plotted against the normalized angular coordinate  . it can be observed from these figures that all constraint parameters sufficiently changed along the crack front from the free surface toward the mid-plane as a v. shlyannikov et alii, frattura ed integrità strutturale, 35 (2016) 114-124; doi: 10.3221/igf-esis.35.14 120 function of load biaxiality. fig. 6 represents the distributions of the constraint parameters for the biaxial tension and as well as the combined tension-compression loading for the intermediate crack front position (a/c)=0.6. the last part of the numerical calculations of the present study is devoted to the determination of the elastic and plastic stress intensity factors in cruciform and bending samples. in fig.8 shown the distributions of the elastic and plastic sifs for the same tensile loading conditions along the same crack front in the cs configuration. fig. 8 gives a clear illustration of the necessity to take into account the load biaxiality in order to the interpretation of the characteristics of the material resistance to crack propagation. the data shown in fig. 9 the distributions of the elastic and plastic sifs related to the bending plate in more details for several crack front positions. figure 7: plastic constraint parameter distributions along crack front under different biaxial loading conditions. figure 8: elastic (a,b) and plastic (c,d) stress intensity factor behavior for different aspect ratio under biaxial loading. v. shlyannikov et alii, frattura ed integrità strutturale, 35 (2016) 114-124; doi: 10.3221/igf-esis.35.14 121 а) b) figure 9: elastic (a) and (b) plastic stress intensity factor distributions for bending plate along crack front (1-initial, 2-3-intermediate, 4final). experimental results and discussion he evolution of the crack growth rate of the elliptical-fronted edge cracks during the tests is determined using cod and the microscope. in order to study the crack growth under fatigue tension-compression biaxial loading and bending, several flat specimens of aluminum alloy d16 are tested with an initial notch depth equal to 3 mm. fig. 10 shows plot of the break through point advances c and of cod against the number of cycles n under different biaxial loading and bending, respectively. as shown in fig. 10, in-phase cyclic tension-compression leads to different effects on the relationship between crack length on the free surface and crack opening displacement for the cruciform specimens and bending plate for the same main material properties. nevertheless there is a strong correlation between these two parameters that can be very useful for automation of experimental studies of fatigue and fracture under multiaxial stress state. on the base of this experimental data, polynomial functions can be used to express the cod as a function of the superficial crack length. figure 10: relationship between cod and crack length on free surface of cruciform specimens and bending plate. fig. 11a represents the superficial crack growth rate dc/dn versus cod on the cruciform specimens undergoing pure mode i tension and compression loading. it is found that the crack growth rate along the external surface direction as a function of cod fit into a single curve with a small scatter band of the experimental results under different loading conditions when (dc/dn)>10-4 m/cycle and cod>0.4 mm. thus, load biaxiality has a significant influence on the initial stage of surface flaw growth. the bending plate (fig. 11b) has a smaller range of crack growth rates as compared to biaxially loaded cs samples. however, looking at fig. 3 and fig. 4b, significant differences in the crack growth rate in the depth direction a and on the free surface c are expected. t v. shlyannikov et alii, frattura ed integrità strutturale, 35 (2016) 114-124; doi: 10.3221/igf-esis.35.14 122 a) b) figure 11: crack growth rate on free surface of (a) cruciform specimens and (b) bending plate versus cod. а) b) figure 12: crack growth rate as a function of (a) elastic and (b) plastic sifs under bending for different crack front points. fig. 12 shows the typical experimental fatigue fracture diagrams in the coordinates of the crack growth rate versus the values of the stress intensity factors for the plate tested under bending loading. the left picture in fig. 12 depicts the behavior of the da/dn and dc/dn as a function of the elastic sif k1, whereas the right picture in fig. 12 gives us the crack growth rate depending on of the dimensionless plastic stress intensity factor kp. to determine the experimental values of the elastic and plastic sifs for two main points of the crack front, namely, the free surface a and mid-plane section c, was used the distributions represented in fig. 9. looking at fig.12 it should be noted that a significant reduction of the crack growth rates is observed in the direction of the deepest point of the crack front with respect to the crack front intersection with the free surface of the bending specimens in terms of the elastic and plastic sifs. in contrast to the elastic sif k1, the plastic sif kp shows very useful effect of the sensitivity to the plastic properties of the tested materials. it can be seen from fig. 12 that the plastic sif gradually increases by increasing the crack length and crack depth at fixed elastic properties of the aluminum alloy characterized by e=76 gpa and =0.3. the data presented very obvious advantages of using the plastic stress intensity factors to characterize the material's resistance to cyclic crack growth. this conclusion is confirmed by the relative position of crack growth curves in fig.12 for the tested aluminum alloy d16 in the terms of the elastic and plastic sifs. v. shlyannikov et alii, frattura ed integrità strutturale, 35 (2016) 114-124; doi: 10.3221/igf-esis.35.14 123 conclusions atigue crack growth for a semi-elliptical crack with two different initial notch form in cruciform specimens and bending plate of d16 aluminum alloy is studied. experiments and calculations made under biaxial cyclic tensioncompression and bending are described. all the experimental and numerical results are shown: for the same specimen configuration and different the crack front position as a function of cyclic tension-compression and bending loading, the following constraint parameters were analyzed, namely, the non-singular t -stress, zt -factor and the stress triaxiality parameter h in the 3d series of elastic-plastic computations; the governing parameter of the elastic-plastic stress fields in-factor distributions along various crack fronts was also determined from numerical calculations, this governing parameter is used as the foundation of the elastic-plastic stress intensity factor; under cyclic bending, it can be seen that the crack propagation paths differ with diverse initial flaw forms, but under biaxial loading converge to the same configuration when the crack depth ratio is larger than about 0.5; it is found that there is relationship between the crack growth rate on the free surface of specimen and cod for both tested cruciform specimens and bending plate; a significant reduction of the crack growth rates is observed in the direction of the deepest point of the crack front with respect to the crack front intersection with the free surface of the bending plate; the experimental and numerical results of the present study background provide an opportunity to explore the suggestion that crack growth rate may be represented by the plastic stress intensity factor, rather than the magnitude of the elastic sifs alone; it is stated that the elastic-plastic stress intensity factor, which is sensitive to the constraint effects and elastic-plastic material properties, is attractive as the self-dependent unified parameter for characterization of the material fracture resistance properties. acknowledgment he authors gratefully acknowledge the financial support of the russian scientific foundation under the project 1419-01716. references [1] newman, j.c., raju, i.s., an empirical stress-intensity factor equation for the surface crack, eng. fract. mech., 15 (12) (1981) 185-192. [2] carpinteri, a., brighenti, r., part-through cracks in round bars under cyclic combined axial and bending loading, int. j. fatigue, 18 (1) (1996) 33-39. [3] shlyannikov, v.n., tumanov, a.v., an inclined surface crack subject to biaxial loading, int. j. solids struct., 48 (2011) 1778-1790. [4] shlyannikov, v.n., kislova s.yu., tumanov, a.v., inclined semi-elliptical crack for predicting crack growth direction based on apparent stress intensity factors, theoret. appl. fract. mech., 53 (2010) 185-193. [5] shlyannikov, v.n., tumanov, a.v., characterization of crack tip stress fields in test specimens using mode mixity parameters, int. j. fract., 185 (2014) 49-76. [6] shlyannikov, v.n., zakharov, a.p., multiaxial crack growth rate under variable t-stress, eng. fract. mech., 123 (2014) 86–99. [7] shlyannikov, v.n., tumanov, a.v., zakharov, a.p., the mixed mode crack growth rate in cruciform specimens subject to biaxial loading, theoret. appl. fract. mech., 73 (2014) 68-81. [8] ansys mechanical apdl theory reference release 14.5// ansys, inc. southpointe, 275 technology drive, canonburg, pa 2012. [9] guo, w.l., elasto-plastic three dimensional crack border field-i, eng. fract. mech., 46 (1993) 93-104. f t v. shlyannikov et alii, frattura ed integrità strutturale, 35 (2016) 114-124; doi: 10.3221/igf-esis.35.14 124 [10] henry, b.s., luxmoore, a.r., the stress triaxiality constraint and the q-value as ductile fracture parameter, eng. fract. mech., 55 (1997) 375-390. [11] hutchinson, j.w., singular behaviour at the end of a tensile crack in a hardening material, journ. mech. phys. solids, 16 (1968) 13-31. << /ascii85encodepages false /allowtransparency false /autopositionepsfiles true /autorotatepages /none /binding /left /calgrayprofile (dot gain 20%) /calrgbprofile (srgb iec61966-2.1) /calcmykprofile (u.s. web coated \050swop\051 v2) /srgbprofile (srgb iec61966-2.1) /cannotembedfontpolicy /error /compatibilitylevel 1.4 /compressobjects /tags /compresspages true /convertimagestoindexed true /passthroughjpegimages true /createjobticket false /defaultrenderingintent /default /detectblends true /detectcurves 0.0000 /colorconversionstrategy /cmyk /dothumbnails false /embedallfonts true /embedopentype false /parseiccprofilesincomments true /embedjoboptions true /dscreportinglevel 0 /emitdscwarnings false /endpage -1 /imagememory 1048576 /lockdistillerparams false /maxsubsetpct 100 /optimize true /opm 1 /parsedsccomments true /parsedsccommentsfordocinfo 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can be opened with acrobat and adobe reader 5.0 and later.) >> /namespace [ (adobe) (common) (1.0) ] /othernamespaces [ << /asreaderspreads false /cropimagestoframes true /errorcontrol /warnandcontinue /flattenerignorespreadoverrides false /includeguidesgrids false /includenonprinting false /includeslug false /namespace [ (adobe) (indesign) (4.0) ] /omitplacedbitmaps false /omitplacedeps false /omitplacedpdf false /simulateoverprint /legacy >> << /addbleedmarks false /addcolorbars false /addcropmarks false /addpageinfo false /addregmarks false /convertcolors /converttocmyk /destinationprofilename () /destinationprofileselector /documentcmyk /downsample16bitimages true /flattenerpreset << /presetselector /mediumresolution >> /formelements false /generatestructure false /includebookmarks false /includehyperlinks false /includeinteractive false /includelayers false /includeprofiles false /multimediahandling /useobjectsettings /namespace [ (adobe) (creativesuite) (2.0) ] /pdfxoutputintentprofileselector /documentcmyk /preserveediting true /untaggedcmykhandling /leaveuntagged /untaggedrgbhandling /usedocumentprofile /usedocumentbleed false >> ] >> setdistillerparams << /hwresolution [2400 2400] /pagesize [612.000 792.000] >> setpagedevice microsoft word 2195 f. v. antunes et alii, frattura ed integrità strutturale, 48 (2019) 666-675; doi: 10.3221/igf-esis.48.63 666 focused on the “portuguese contributions for structural integrity” fatigue crack growth in notched specimens: a numerical analysis f.v. antunes, r. branco, p. prates, j.d.m. costa university of coimbra, portugal fernando.ventura@dem.uc.pt, http://orcid.org/0000-0002-0336-4729 ricardo.branco@dem.uc.pt, http://orcid.org/0000-0001-2345-6789 pedro.prates@dem.uc.pt, http://orcid.org/0000-0001-2345-6789 jose.domingos@dem.uc.pt abstract. fatigue crack growth (fcg) is linked to irreversible and nonlinear processes happening at the crack tip, which explains different problems observed in the use of da/dn-k curves. the replacement of k by nonlinear crack tip parameters, namely the crack tip opening displacement (ctod) is an interesting alternative. the objective in here is to study the effect of notches on fcg using the plastic ctod range, p. m(t) specimens with lateral notches of different radius (1, 2, 4 and 8 mm were analysed numerically, keeping the total depth constant (8 mm). the increase of crack length increases p and therefore fcg rate. for plane stress state, the formation of the residual plastic wake with crack propagation, produces crack closure which compensates the effect of crack length and there is a stabilization of p. the reduction of notch radius increases p for all crack lengths, particularly for the shortest ones. for plane strain state there is almost no crack closure therefore p is higher than for plane stress state, and the effect of crack length produces a relatively fast increase of p. keywords. fatigue crack growth; notches; plastic ctod; crack closure. citation: antunes, v. v., branco, r., prates, p., costa j.d.m., fatigue crack growth in notched specimens: a numerical analysis, frattura ed integrità strutturale, 48 (2019) 666-675. received: 18.09.2018 accepted: 11.11.2018 published: 01.01.2019 copyright: © 2019 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. introduction he study of fatigue crack propagation is usually based on relations between the crack increment per load cycle, da/dn, and the stress intensity factor range, k. 1. the dn-k relationship is supposed to be invariant relatively to the shape and size of the cracked component. k is a linear elastic parameter, however it controls the small-scale cyclic plastic deformation occurring at the crack tip 2. nevertheless, da/dn-k relations have several limitations, namely: (i) such curves are completely phenomenological, not derived from physics, and the fitting parameters have units with no physical justification; (ii) such curves are only valid in the small-scale yielding range; (iii) and da/dn depends on other parameters, including the stress ratio and the load history. different concepts have been proposed to overcome the limitations identified in the use of dn-k relationships, which are effectively caused by using a linear elastic parameter to quantify the non-linear irreversible processes responsible for t http://www.gruppofrattura.it/va/48/2195.mp4 f. v. antunes et alii, frattura ed integrità strutturale, 48 (2019) 666-675; doi: 10.3221/igf-esis.48.63 667 fatigue crack growth (fcg). crack closure was proposed 3 and has been used as a complementary parameter to explain the effect of plastic deformation on fcg relations. it has been used to explain the effects of stress ratio, overloads, short cracks and specimen thickness. the t-stress is another concept which has been used to explain the effect of specimen geometry 4. the concept of partial crack closure, proposed by donald and paris 5 and kujawski 6, assumes that the contact of crack flanks does not occur immediately behind crack tip and there is, therefore, a contribution of the load range below crack opening to fatigue damage. christopher et al. 7 proposed a new model based on four parameters to describe the stresses around the crack tip: kf (opening mode stress intensity factor), ks (shear stress intensity factor), kr (retardation stress intensity factor) and the t-stress. however, these new concepts only mitigate the problem, without attacking the real source of the problem. in authors’ opinion, the linear elastic k parameter must be replaced by nonlinear crack tip parameters, able to quantify effectively the crack tip plastic deformation which is supposed to control fatigue crack growth rate (fcgr). the effect of physical parameters like thickness, stress state, specimen geometry and/or overloads is naturally accommodated by the non-linear parameters. antunes et al. 8 used non-linear parameters to validate the crack closure concept and to identify the best crack closure parameter. the non-linear parameters identified in the literature review made by antunes et al. 8 were the range of cyclic plastic strain, the size of reversed plastic zone, the total plastic dissipation per cycle and the crack opening displacement. note that these non-linear crack tip parameters, and also the j integral, usually replace k when the lefm is no longer valid. the crack opening displacement (cod) is a classical parameter in elastic-plastic fracture mechanics, still widely used nowadays 9. it has a direct physical meaning and can be measured experimentally. crack tip blunting and re-sharpening has been used to explain fatigue crack propagation under cyclic loading 10. this cyclic blunting and re-sharpening was modeled by different authors in order to predict the fcgr 11. additionally, it was demonstrated that there is a relationship between cod and striation spacing, and between this and the crack propagation rate 12. the experimental measurement of cod has been done using different strategies. in compact-tension (ct) specimens, an extensometer with blades is used to measure the opening of the specimen at the edge. therefore, this parameter is usually called crack mouth opening displacement (cmod). in middle-tension (m(t)) specimens, a pin extensometer is placed at the center of the specimen, fixed in two small holes to avoid sliding. the resulting force versus displacement curves are typically used to calculate the crack closure level. digital image correlation (dic) has been used to define a virtual extensometer, therefore cod can be obtained at different positions relatively to the crack tip. however, analytical or numerical approaches are required to measure the crack tip opening displacement, ctod. in the finite element method (fem) studies the ctod is usually measured at the first node behind crack tip. the use of ctod in the study of fcg in notched samples has not been seen in literature. one of the well-known approaches to deal with the notch effect in fatigue problems was proposed by neuber [13] who stated that the geometric mean value of the stress concentration factor and strain concentration factor is constant and equal to the elastic stress concentration factor. glinka [14 developed an energy-based approach, known as equivalent strain energy density, based on the assumption that the elastic-plastic strain energy density of the material in the yielded zone of the material is equal to the strain energy density assuming an elastic behaviour. other current and important energy-based approaches are, for example, the control-volume technique introduced by lazzarin [15] and the total strain energy density concept formulated by ellyin [16. it should be also mentioned the theory of critical distances which combines a set of alternative approaches which have in common the fact that the effective stresses at the process zone is estimated on the basis of a characteristic material length, also called critical distance [17-19]. however, these methodologies have some limitations. the main objective here is to study numerically the effect of notches on fatigue crack growth rate using the plastic ctod concept recently introduced by antunes et al. [20]. the material studied was the 7050-t6 aluminium alloy, in the form of single-edge notch tension specimens (sent). the radius of the notch was varied, keeping constant the total depth of the notch. an automatic elastic-plastic finite-element procedure was developed and the simulations were computed assuming both plane stress and plane strain conditions. numerical model ig. 1a shows the geometry of the notched samples. four different notches were considered, with radius of 8, 4, 2 and 1 mm, as illustrated by figs. 1c, 1d, 1e and 1f, respectively. the total notch depth was always 8 mm, as indicated. the initial crack length was a0=8.096 mm including the notch, i.e., the initial crack extended 96 m ahead of the notch. the specimens had a thickness of 0.2 mm in order to simulate pure plane stress state. additionally, plane strain state was modeled imposing boundary conditions which avoid out-of-plane plane deformation. only ¼ of the f f. v. antunes et alii, frattura ed integrità strutturale, 48 (2019) 666-675; doi: 10.3221/igf-esis.48.63 668 specimen was modeled considering adequate boundary conditions, as indicated in fig. 1a. a cyclic load was applied remotely from crack tip, as illustrated in fig. 1a, with fmax=400 n; fmin =4 n (r=0.01). the material studied was the 7050-t6 aluminum alloy, which is strengthened mainly by the addition of zn, mg and cu. the t6 heat treatment comprises homogenization and aging, producing hardening by precipitation. the aa7050-t6 has excellent properties, namely good fracture toughness, high strength and stress corrosion resistance, making it ideal for applications in aircraft industry 21, 22. cyclic stress-strain hysteresis loops, obtained in smooth samples, were used to fit the hardening models. the elastic-plastic model adopted assumes that the plastic behavior follows the von mises yield criterion, coupled with voce isotropic hardening law 23: 0 sat 0y( ) y ( y y )[1 exp( c )] p p y      (1) where y0, ysat and cy are material parameters and p is the equivalent plastic strain, and lemaître-chaboche non-linear kinematic hardening law 24: p x satc x       σ x x x  (2) being cx, and xsat material parameters. table 1 shows the identified set of material parameters of voce and lemaîtrechaboche laws. fig. 1 compares experimental results with the analytical model proposed here. several load cycles were applied and the cumulative plastic strain is plotted versus stress. an excellent agreement can be seen, indicating that the analytical model is able to simulate the cyclic plastic deformation. y0 [mpa] ysat [mpa] cy cx xsat [mpa] 420.50 420.50 3.806 228.91 198.35 table 1: material parameters for the 7050-t6 aluminum alloy. figure 1: accuracy of material’s model: experimental results versus analytical model. -800 -600 -400 -200 0 200 400 600 800 0 25 50 75 100 125 st re ss [m p a] equivalent plastic strain [%] aa7050-t6 fit voce law parameters lemaître-chaboche law parameters f. v. antunes et alii, frattura ed integrità strutturale, 48 (2019) 666-675; doi: 10.3221/igf-esis.48.63 669 the finite element mesh illustrated in fig. 2, composed of 3d linear isoparametric elements, has 7175 elements and 7359 nodes. as can be seen in fig. 1b, a refined mesh was defined near the notch, where the elements have 88 m2. the crack was extended at minimum load, after each two load cycles. the total crack propagation was 1598 =1272 m. results distribution of stresses ahead of notch ig. 3 presents the distribution of linear elastic stresses ahead of notch for the different notch radius, rn. these stresses were divided by the remote stress. the stresses are higher for the lower values of rn, as could be expected. for plane stress state there is a turning point at about 1.5 mm, while for the plane strain state this turning point is at about 1 mm. in fact, the comparison of figs. 2a and b indicates that for plane strain state the variation of stresses with distance from the notch is much faster. the stress concentration factors, obtained dividing the local stresses by the remote stress, are presented in table 2. the decrease of stress ratio increases kt, and the plane strain state promotes higher values of kt than the plane stress state. there is an exception for plane stress state, because the notch ratio of 1 mm gave slightly lower kt than rn=2 mm. rn [mm] kt (plane stress) kt (plane strain) 1 3.64 3.99 2 3.70 3.77 3 3.59 3.52 4 3.26 3.05 table 2: stress concentration factors. figure 2: geometry and finite element mesh of the notched samples. (a) loading and boundary conditions. (b) detail of finite element mesh. (c) notch radius of 8 mm. (d) notch radius of 4 mm. (e) notch radius of 2 mm. (f) notch radius of 1 mm. f f. v. antunes et alii, frattura ed integrità strutturale, 48 (2019) 666-675; doi: 10.3221/igf-esis.48.63 670 figure 3: distribution of von mises equivalent stress ahead of the notch (uncracked geometry; elastic behavior). (a) plane stress state. (b) plane strain state. plastic ctod range figs. 4a and 4b present typical results of ctod versus load, measured for crack increments of 40 and 800 m, respectively. the first node behind crack tip is closed at minimum load and only opens when the load reaches point a (fig. 4b), which is the crack opening load. after opening the ctod increases linearly with load, but after point b there is some deviation from linearity which indicates the occurrence of plastic deformation. the maximum ctod occurs at point c, which corresponds to the maximum applied load. after the maximum load there is also a linear variation of ctod with load decrease. with subsequent load decrease, reversed plastic deformation starts and the crack closes again. the plastic deformation increases progressively for loads above point b, up the maximum load. the plastic ctod was obtained subtracting the elastic ctod from the total ctod. the comparison of both figures indicates that the crack increment increases the crack closure level, which is logical because the plastic wake increases. the slope of linear regime increases because the rigidity of the specimen reduces with crack growth. although the increase of crack closure, the crack growth increases the plastic ctod range, which results from the effect of crack length on crack tip stresses. figure 4: crack tip opening displacement (plane stress, rn= 4 mm). (a) a=40 m. (b) a=800 m. 0 0.2 0.4 0.6 0.8 1 0 100 200 300 400 c t o d [ m ] force [n] total ctod plastic ctod a b c 0 0.2 0.4 0.6 0.8 1 1.2 1.4 0 100 200 300 400 c t o d [ m ] force [n] total ctod plastic ctod a b c p 1.0 1.5 2.0 2.5 3.0 3.5 4.0 0.0 0.5 1.0 1.5 2.0 2.5 3.0  vm /  n om xn [mm] rn= 1 mm rn=2 mm rn=4 mm rn=8 mm 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 0 1 2 3  vm /  no m xn [mm] rn=1 mm rn=2 mm rn=4 mm rn=8 mm (b) rn xn (a) f. v. antunes et alii, frattura ed integrità strutturale, 48 (2019) 666-675; doi: 10.3221/igf-esis.48.63 671 fig. 5 presents the variation of plastic ctod range, p, with crack growth for different notch radius. the increase of crack length tends to increase p and therefore fatigue crack growth rate. however, for notch radius of 1 and 2 mm, there is a rapid decrease of p at the beginning of crack growth, followed by a progressive increase. the progressive increase of p with notch radius, rn, is steeper for plane strain state. for plane stress state, a convergence to the same value is evident, as the crack departs from the notch. this asymptote is expected to be the value of p not affected by the notch. for plane strain state, this convergence is not so evident, which seems to indicate that the effect of the notch is more extensive. the decrease of notch radius increases p, due to the increase of stresses. figure 5: variation of plastic ctod range with crack growth. (a) plane stress state. (b) plane strain state. fig. 6 presents the effect of stress state for different notch radius. at the beginning of crack growth plane stress state gives higher values of p. however, rapidly the values for plane strain state raise above those for plane stress state, and become significantly higher. the higher crack growth rate observed for plane strain state explains the curvature of crack fronts in through-cracked specimens. fig. 6 shows the variation of crack closure level, quantified by: f fopen minu 100clos f fmax min     (1) being fmin, fmax and fopen the minimum, maximum and opening loads, respectively. this parameter quantifies the portion of load cycle during which the crack is closed. the plane stress predictions are clearly higher than plane strain results. for plane strain state and notch radius of 1 and 2 mm, there is an initial peak of uclos followed by a progressive stabilization. this peak is linked to an odd deformation produced by the first load cycle. all the curves converge rapidly to about uclos=10%.for plane stress state there is a progressive increase of crack closure with crack length, as the plastic wake is being formed. the decrease of notch radius increases uclos, which has a faster stabilization. the results in fig. 5 are explained by the relatively low level of crack closure observed for plane strain state. the trends of fig. 4 are also explained by crack closure. for plane stress state there is a faster stabilization of p for shorter notch radius because the crack closure level increases more rapidly. the crack closure is responsible for the convergence of all the curves. for plane strain state, the crack closure level is relatively low, therefore the increase of crack length if felt more intensively on p. 0 0.1 0.2 0.3 0.4 0 0.5 1 1.5 2  p [ m ] xn [mm] rn=1 mm rn=2 mm rn=4 mm rn=8 mm 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0 0.5 1 1.5 2  p [ m ] xn [mm] rn=1 mm rn=2 mm rn=4 mm rn=8 mm rn xn (a) (b) f. v. antunes et alii, frattura ed integrità strutturale, 48 (2019) 666-675; doi: 10.3221/igf-esis.48.63 672 figure 6: variation of plastic ctod range with crack growth (a) rn=1 mm. (b) rn=2 mm. (c) rn=4 mm. (d) rn=8 mm. discussion he present study involves two topics of major relevance for fcg, which are notches and short cracks. for short crack, the hypothesis of small-scale yielding may be violated, therefore the use of plastic ctod instead of k is of major importance. the stress concentration associated with the notch reinforces this need. in fact, miller 25 suggested the use of elastic-plastic fracture mechanics to analyse short fatigue crack growth. the increase of crack length produces several effects: the increase of the distance to the notch and consequent reduction of stress concentration. the increase of crack length and, therefore, of crack tip stresses and p. the increase of crack closure as the plastic wake is formed. this is more relevant for plane stress state. it reduces the effective load range and therefore p. the crack closure concept is widely used to explain the short crack behaviour 26,27. 0 0.2 0.4 0.6 0.8 0 0.5 1 1.5 2  p [ m ] xn [mm] plane stress plane strain 0 0.2 0.4 0.6 0.8 0 0.5 1 1.5 2  p [ m ] xn [mm] plane stress plane strain 0 0.2 0.4 0.6 0.8 0 0.5 1 1.5 2  p [ m ] xn [mm] plane stress plane strain 0 0.2 0.4 0.6 0.8 0 0.5 1 1.5 2  p [ m ] xn [mm] plane stress plane strain t (a) (b) (c) (d) f. v. antunes et alii, frattura ed integrità strutturale, 48 (2019) 666-675; doi: 10.3221/igf-esis.48.63 673 the variation of crack length is the cause of the global trend for the increase of p with crack growth. for plane stress state, the increase of crack length is accomplished by an increase of crack closure which stabilizes the values of p. in other words, the effect of crack length is compensated by the increase of crack closure. the decrease of notch radius produces a faster increase of crack closure and therefore a faster stabilization of p. for plane strain state, there is almost no crack closure, therefore p is bigger than for plane stress state. the absence of crack closure produces a faster growth of p with crack propagation, explained by the increase of crack length and by the progressive separation from the notch. ding et al. 28 studied the 1070 steel in the form of round bars and concluded that for positive stress ratios fcg is mainly influence by notch plasticity, while for negative stress ratios crack closure plays a significant role. hammouda et al. 29 attributed the observed short crack growth phenomenon to the combined effect of the notch plasticity and the cracktip plasticity. li 30 suggested that the fatigue crack growth from a notch was dominated by notch plasticity within the notch plasticity zone and the notch plasticity induced crack closure out of the notch plasticity zone. figure 7: variation of crack closure with crack length. conclusions numerical study was developed to study the effect of notches on fatigue crack growth rate. as the crack propagates, there is an increase of p and therefore of fatigue crack growth rate. for plane stress state, the reduction of notch radius increases p for all crack lengths, particularly for the shorter ones. the crack closure level increases with the decrease of notch radius, and this explains the convergence of p for different notch radius as the crack propagates. for plane strain state there is almost no crack closure, therefore the crack length has a greater impact on plastic ctod range. acknowledgements his research is sponsored by feder funds through the program compete (under project t44950814400019113) and by national funds through fct – portuguese foundation for science and technology, under the project ptdc/ems-pro/1356/2014. one of the authors, p.a. prates, was supported by a grant for scientific research also from the portuguese foundation for science and technology (sfrh/bpd/101465/2014). all supports are 0 10 20 30 40 50 0 0.5 1 1.5 2 u cl os [% ] xn [mm] rn=1 mm rn=2 mm rn=4 mm rn=8 mm plane  stress plane  strain a t rn xn f. v. antunes et alii, frattura ed integrità strutturale, 48 (2019) 666-675; doi: 10.3221/igf-esis.48.63 674 gratefully acknowledged. the authors would also like to thank the dd3imp in-house code developer team for providing the code and all the support services. references [1] paris, p.c. and erdogan, j. (1963). critical analysis of crack growth propagation laws, j. basic eng. 85d, pp. 528–534. [2] rice, j.r. 1967). mechanics of crack tip deformation and extension by fatigue, in: fatigue crack propagation. philadelphia: astm stp 415, pp. 256–271. [3] elber, w. (1970). fatigue crack closure under cyclic tension, eng. fract. mech. 2, pp. 37-45. [4] lugo, m. and daniewicz, s.r. (2011). the influence of t-stress on plasticity induced crack closure under plane strain conditions, int. j. fatigue 33, pp.176–185. [5] donald, k. and paris, p.c. (1999). an evaluation of keff estimation procedure on 6061-t6 and 2024-t3 aluminum alloys, int j fatigue 21, pp. s47–57. [6] kujawski, d. (2001) enhanced model of partial crack closure for correlation of r-ratio effects in aluminum alloys, int j fatigue 23, pp. 95–102. [7] christopher, c.j., james, m.n., patterson, e.a. and tee, k.f. (2007). towards a new model of crack tip stress fields, int j fract 148, pp. 361–371. [8] antunes, f.v., sousa, t., branco, r. and correia, l. (2015). effect of crack closure on non-linear crack tip parameters, int. journal of fatigue 71, pp. 53–63. [9] kawabata, t., tagawa, t., sakimoto, t., kayamori, y., ohata, m., yamashita, y., tamura, e., yoshinari, h., aihara, s., minami, f., mimura, h. and hagihara, y. (2016). proposal for a new ctod calculation formula, eng. fract. mech. 159, pp. 16–34. [10] laird, c. and smith, g.c. 1962). crack propagation in high stress fatigue, philos. mag. 8, pp. 847–857. [11] toribio, j. and kharin, v. (2013). simulations of fatigue crack growth by blunting–re-sharpening: plasticity induced crack closure vs. alternative controlling variables, int. j. fatigue 50, pp. 72–82. [12] pelloux, r.m. (1970). crack extension by alternating shear, eng fract. mech. 1, pp. 170-174. [13] neuber, h. (1961). theory of stress concentration for shear strained prismatical bodies with arbitrary non-linear stress-strain law. j appl mech 28, pp. 544–50. [14] molski, k. and glinka, g. (1981). a method of elastic–plastic stress and strain calculation at a notch root. mater sci eng 50, pp. 93–100. [15] lazzarin, p., berto, f., gomez, f.j. and zappalorto, m. (2008). some advantages derived from the use of the strain energy density over a control volume in fatigue strength assessments of welded joints, int. j. fatigue 30, pp. 1345– 1357. [16] ellyin, f. (1997) fatigue damage, crack growth and life prediction, chapman & hall, london. [17] neuber, h. (1958) theory of notch stresses: principles for exact calculation of strength with reference to structural form and material, springer, berlin, germany. [18] peterson, r.e. (1958) notch sensitivity, in: g. sines, j.l. waisman (eds.), metal fatigue, mcgraw hill, new york, pp. 293–306. [19] susmel, l. and taylor, d. (2011). the theory of critical distances to estimate lifetime of notched components subjected to variable amplitude uniaxial fatigue loading, int. j. fatigue 33, pp. 900–911. [20] antunes, f.v., rodrigues, s.m., branco, r. and camas, d. (2016). a numerical analysis of ctod in constant amplitude fatigue crack growth, theoretical and applied fracture mechanics 85, pp. 45–55. [21] williams, j.c. and starke, jr. e.a (2003). progress in structural materials for aerospace systems, acta mater. 51, pp. 5775–5799. [22] wei, l., pan, q., huang, h., feng, l. and wang, y. (2014) influence of grain structure and crystallographic orientation on fatigue crack propagation behavior of 7050 alloy thick plate, int journal of fatigue 66, pp. 55–64. [23] voce, e. (1948). the relationship between stress and strain for homogeneous deformation, j. inst. metals 74, pp. 537–562. [24] chaboche, j.l. (2008). a review of some plasticity and viscoplasticity constitutive theories, international journal of plasticity 24, pp. 1642–1693. [25] miller, k.j. (1982). the short crack problem, fatigue engng. mater. struct. 5, pp. 223–232. [26] tanaka, k., nakai, y. (1983). propagation and non-propagation of short fatigue cracks at a sharp notch, fatigue engng. mater. struct. 6, pp. 315–327. f. v. antunes et alii, frattura ed integrità strutturale, 48 (2019) 666-675; doi: 10.3221/igf-esis.48.63 675 [27] mcclung, r.c. and sehitoglu, h. (1992). closure and growth of fatigue cracks at notches, j. engng. mater. techn. 114, pp. 1–7. [28] ding, f., feng, m. and jiang, y. (2007). modeling of fatigue crack growth from a notch, international journal of plasticity 23, pp. 1167–1188. [29] hammouda, m.m., smith, r.a. and miller, k.j. (1979). elastic–plastic fracture mechanics for initiation and propagation of notch fatigue cracks, fatigue engng. mater. struct. 2, pp. 139–154. [30] li, w. 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can be opened with acrobat and adobe reader 5.0 and later.) >> /namespace [ (adobe) (common) (1.0) ] /othernamespaces [ << /asreaderspreads false /cropimagestoframes true /errorcontrol /warnandcontinue /flattenerignorespreadoverrides false /includeguidesgrids false /includenonprinting false /includeslug false /namespace [ (adobe) (indesign) (4.0) ] /omitplacedbitmaps false /omitplacedeps false /omitplacedpdf false /simulateoverprint /legacy >> << /addbleedmarks false /addcolorbars false /addcropmarks false /addpageinfo false /addregmarks false /convertcolors /converttocmyk /destinationprofilename () /destinationprofileselector /documentcmyk /downsample16bitimages true /flattenerpreset << /presetselector /mediumresolution >> /formelements false /generatestructure false /includebookmarks false /includehyperlinks false /includeinteractive false /includelayers false /includeprofiles false /multimediahandling /useobjectsettings /namespace [ (adobe) (creativesuite) (2.0) ] /pdfxoutputintentprofileselector /documentcmyk /preserveediting true /untaggedcmykhandling /leaveuntagged /untaggedrgbhandling /usedocumentprofile /usedocumentbleed false >> ] >> setdistillerparams << /hwresolution [2400 2400] /pagesize [612.000 792.000] >> setpagedevice microsoft word numero_52_art_23_2761 a.v. tumanov et alii, frattura ed integrità strutturale, 52 (2020) 299-309; doi: 10.3221/igf-esis.52.23 299 crack growth rate prediction based on damage accumulation functions for creep-fatigue interaction a.v. tumanov, v.n. shlyannikov, a.p. zakharov institute of power engineering and advanced technologies, frc kazan scientific center, russian academy of sciences, russia tymanoff@rambler.ru, shlyannikov@mail.ru, alex.zakharov88@mail.ru abstract. the present study is concerned with formulation of a model for the creep–fatigue crack growth rate prediction on the base of fracture damage zone concepts. it is supposed that crack growth rate can be determined by integration of damage accumulation rate equations into the fracture process zone for low-cycle fatigue and creep loading independently. in the case of low-cycle fatigue loading the damage accumulation function proposed by ye and wang was used as well as a classical kachanov-rabotnov power law was employment for the creep damage accumulation characterization. fracture process zone size is calculated on the base of the nonlinear stress intensity factors concept proposed by shlyannikov. the background for the proposed general model of crack growth rate under creep and fatigue interaction is given in order to comparison with the experimental data. experimental study of crack growth rate under creep and fatigue interaction is performed for compact tension specimen made from 20crmov5. crack growth rate carried out at the elevated temperature of 550°c according to astm e2760 standard. the predictions of the crack growth rate were compared with the experimental data for the 20crmov5 steel obtained at an elevated temperature, and the agreement was found to be satisfactory. keywords. creep-fatigue interaction; crack growth rate prediction; nonlinear stress intensity factors. citation: tumanov a.v., shlyannikov v.n., zakharov a.p., crack growth rate prediction based on damage accumulation functions for creep-fatigue interaction, frattura ed integrità strutturale, 52 (2020) 299-309. received: 02.03.2020 accepted: 13.3.2020 published: 01.04.2020 copyright: © 2020 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. introduction tructures in the aviation, space flight, power generation, and petrochemical industries are typically exposed to elevated temperatures. damage accumulation and growth considerations at creep and fatigue owing to changes in the material microstructure, void nucleation, interaction, and growth on the grain boundaries are important in the design and operation of such components in order to ensure structural integrity. it is well known that the creep damage accumulation from the damage caused by cyclic loading is different. at the moment, there are many models in literature allow to take into account the damage accumulation, both during creep and cyclic loading. s https://youtu.be/sueqtvuryuc a.v. tumanov et alii, frattura ed integrità strutturale, 52 (2020) 299-309; doi: 10.3221/igf-esis.52.23 300 the hayhurst model [1] one of the generalized models for the creep damage accumulation. the main disadvantage of this model is necessity to use six parameters as material properties in order to describe the damage accumulation behavior. moreover, the parameters determination methods are mainly indirect. according to this, the rabotnov-kachanov model is used due to the direct method of material constants determination. the lemaitre model [2] is the one of the most frequently used for the fatigue damage accumulation behavior. in similar phenomenological models using the tensor damage parameter leads to considerable difficulties for material constants determination. for the different creep and fatigue laws if the stress state is unchanged the scalar, vector, and tensor damage parameters give almost identical results. in this regard, models with a scalar damage parameter as a simplified alternative can be considered [3-6]. the main problem of the residual life prediction under the creep-fatigue loading conditions is the complex character of their interaction [7-10]. statistical approximations of experimental results by the polynomial functions are most common approach of the creep-fatigue interaction behavior. in present study, continuum damage mechanics is applied to assess the creep-fatigue interaction and the crack growth rate prediction, considering the complete sequence of formulations. fatigue damage accumulation rate he variable critical distance is one of important parameter in modern fracture mechanics, denoted to as the fracture process zone size. a general assumption regarding the distance criterion under elastic–plastic and creep loading conditions is that a crack increment occurs when the fracture resistance parameter (stress, strain, or energy) reaches a critical value at a characteristic distance from the crack tip. in creep–fatigue interaction both the fatigue and the creep crack growth rate can be obtained from damage accumulation rule independently. the crack size is assumed to increase when the local strain energy density at the crack tip reaches the critical value. hence, a material point initially at a characteristic distance, cr , ahead of the crack tip, 0r  , moves to the tip both in time t after an increment in the crack growth for creep and in number of cycles n , in case of fatigue. it is assumed that the crack length increment equal to the fracture process zone size, fa r  , and the crack growth rate, a , becomes [11-12]:   0 fr f f fa r dr   (1) where  fr is the damage accumulation rate. eqn. (1) for creep conditions was proposed initially, however the analogy between the creep time t and the number of cycles n makes possible to use this dependence for low cycle fatigue. usually, the one of the main characteristic in models with a scalar damage parameter is the number of cycles before fracture f n at the stress amplitude a  . in the simplest case of uniaxial tension-compression, the fatigue life can be obtained from: 1 2 ' c a f f n          (2) where ' f  and c are fatigue constants. the damage parameter at constant stress amplitude according to [13] 1 ln 1 ln nf f f f n n n             (3) where 1nf   the critical value of the damage parameter in the penultimate cycle and it is associated with static toughness 0t u by the following relationship: t a.v. tumanov et alii, frattura ed integrità strutturale, 52 (2020) 299-309; doi: 10.3221/igf-esis.52.23 301 1 2 0 1 2n a f teu      (4) where e young's modulus. the fatigue damage accumulation rate can be obtained from the equation (3)   1 ln nff f f f d dn n n n         (5) fatigue crack growth rate or ramberg-osgood hardening law [26] the critical value of a strain energy density cw can be obtained from true stress-strain diagram: 0 pf n y c y w d e e                    (6) where  is the strain hardening coefficient, pn is the strain hardening exponent, y is the yield stress, f ultimate tensile stress. according to the classical hutchinson-rosengren-rice model in the zone where fully plastic singularity is dominated the strain energy density w can be found from following expression [14]: 2 2 1 1 (1 ) 1 p pn np y p e p n w k n e r          (7) where  is poisson's ratio, /r r a crack tip distance, a crack length, e dimensionless equivalent mises stresses which depend only on a polar coordinate  and normalized by   max 1e   . the plastic stress intensity factor pk in small-scale and extensive yielding conditions in eqn.(7) can be expressed directly using rice’s j-integral [15]. that is 1 1 2 pn p p y p j e k i l          (8) where 2 2 2 11 1 2 cos 3 6 1 y np e kk e r n j d e n                      cos sinr ry rr r y rr r u u u u r d d r r                                             (9) in eqns. (8-9), iu are crack tip dimensionless displacement components, l is cracked body characteristic size, in our case is the crack length l a , and pi is the numerical constant of the crack-tip stress–strain field, which should be f a.v. tumanov et alii, frattura ed integrità strutturale, 52 (2020) 299-309; doi: 10.3221/igf-esis.52.23 302 determined for the cracked body with a finite size. in the case of full three-dimensional cracked body, the pi -factor in eqn. (8) changes not only with the strain hardening exponent np but also with the position along the crack front. in eqn. (9), the stress tensor and invariant are both normalized by the yield stress: and ij ij y kk kk y       . more detail in determining the pi factor for different elastic-plastic cracked body configurations are given by refs. [15-18]. in a first approximation the crack growth as a static cracks sequence is considered. thus, the path independent j-integral can be obtained from: 2 2 1 (1 )kj e   (10) substitution eqns. (6) and (8) into (7) give a possibility to obtain the critical distance where the strain energy density reaches a critical value: 2 2 1 1 (1 ) 1 p pn n y f p e c n r k n e w          (11) the fatigue crack growth rate can be calculated by substitution eqns. (5) and (11) into (1) directly, it leads to the following relationship: 2 12 2 2 2 1 12 00 (1 ) 1 1 2 ln( )( ) pf p p nr n n p y e f p f y e p fatigue p t c f f n r kda dr a k dn n eu ew n n n                                  (12) creep damage accumulation n this study the classical kachanov-rabotnov power law is used for the creep damage accumulation description. according to this model, the strain rate during creep is [1-2]: 1 cr e e cr n b             (13) and the creep damage accumulation rate is: 1 m cr e cr cr d d dt             (14) where b and crn are material constants of the norton power law constitutive equation, d and m – are material properties. the damage variable  indicate the measure of creep damage with 0  denoting the undamaged state and 1  the fully damaged state. the creep damage increment cr  at time t can be obtained by integrating the expression (14): .    1 1 3 1 1 m m cr d t c m           . (15) where 3 c is integration constant. this constant can be determined from the initial state. i a.v. tumanov et alii, frattura ed integrità strutturale, 52 (2020) 299-309; doi: 10.3221/igf-esis.52.23 303 1 0 3 0 (1 ) 1 m m e c d t m        (16) based on the fact that the damage parameter is equal to one at failure 1  the fracture time at the known stress level can be calculated directly: 1 ( 1) cr m e t m d   (17) creep crack growth rate or elastic-nonlinear-viscous material behavior, the stress, strain and displacement rate fields can be use in order to account for a creep stress intensity factor crk , which is amplitude of singularity. for extensive creep conditions the relation between the c-integral and creep stress intensity factor is introduced by the authors [19] in the form: 1 * 11 crn cr ref cr c k bi l        (18) 1* cos 1 sin cos crncr e cr r r rr r rr r n c br d n u u u u r d r r                                                            (19) where ref is reference stress, crk is amplitude of singularity in the form of creep stress intensity factor, c* is the cintegral, iu are displacement rate angular functions, ij are stress components. it should be noted that the cri integral values are determined similar to pi and can be determined directly from the finite element analysis by distribution of the displacement rate functions, iu , and dimensionless angular stress functions, ij , [9]. more detail in determining the cri integral for different creeping cracked body geometries are given by refs. [12, 19-22]. for a static crack in the outer region of the small-scale creep zone, the elastic crack-tip field still dominates. in this case, the expression of c-integral has a simple form [5]: 2 2 1 (1 )( ) ( 1)cr cr k c t e n t    (20) the elastic stress intensity factor for a compact tension specimen is [23]: 1 1 f k y b w  (21) where f is applied load, 1y is geometry correction function: 2 3 4 1 3/2 ( 2 / ) (0.886 4.64 / 13.31 14.72 5.6 (1 / ) a w a a a y a w w w wa w                        (22) f a.v. tumanov et alii, frattura ed integrità strutturale, 52 (2020) 299-309; doi: 10.3221/igf-esis.52.23 304 the creep crack growth rate was determined based on the assumption that the crack propagation energy is equivalent to the damage initiation energy in infinite plate. thus, the infinite plate remote stresses were calculated from the following expression: 1 ref k a    (23) substitution eqn.(23) into (17) give a possibility to calculate a reference failure time. a strain energy rate density parameter, w , is employed by the author [20] to obtain the critical distance, crr , in the crack tip vicinity under creep conditions. if fc referred the maximum value of the creep-rupture strength at a specified temperature and creep time, then the creep crack tip critical distance crr r is given by expression: 1 crncrcr e fc k r a             . (24) where e is the dimensionless equivalent von mises stress. substitution of eqns. (14) and (24) into eqn. (1) with take into account that cr crr ar , and integrating leads to the equation for creep crack growth in terms of c*-integral and creep stress intensity factor crk : 1 1 1 0 02 2 0 (1 ) ( 1) ( ) cr m n m mr m fc fcme cr cr creep fc cr cr da dr ad k d m t t dt k k                                           (25) creep-fatigue interaction he general simple superposition lifetime prediction models for creep–fatigue interaction can be differentiated as those that account for the hold-time effects and those that are employed for continuous cyclic scenarios. therefore, we will use a linear summation law for creep-fatigue crack growth rate prediction [22, 24] 1 3600fatigue creep fatigue creep da da da da da dn dn dn dn f dt                           (26) 3600 fatigue creep fatigue creep da da da da da f dt dt dt dn dt                           (27) where da/dt is crack growth rate in mm/hour, da/dn is crack growth rate per cycle (mm/cycle), and f is frequency in hz. it is well known that the creep damage accumulation is different from damage caused by cyclic loading. according to this a fracture process zone will be different for both creep and fatigue cases. material properties he material used in the tests and numerical calculations is 20crmov5 steel, which is used for main power plant components such as steam piping and reheat tubes. all mechanical properties were obtained on smoothed round specimens. uniaxial tension and fatigue tests on the biss nano 25kn servo-hydraulic test system according to astm e8, e466 and e646 standards were performed. creep and damage accumulation law properties were obtained by using uts-1300-1-50-1-a test system. more details about creep damage accumulation law constants determination t t a.v. tumanov et alii, frattura ed integrità strutturale, 52 (2020) 299-309; doi: 10.3221/igf-esis.52.23 305 algorithm can be found in [27]. the main mechanical properties of analyzed material were obtained at the elevated temperature of 5500 c and summarized in tab. 1. property value young’s modulus, e [gpa] 154 poisson's ratio,  0.3 strain hardening coefficient, α 2.06 strain hardening exponent, np 8.22 yield stres, 0 [mpa] 265 ultimate true tensile strength, f [mpa] 577 norton’s constant, b [1/(pa^nhr)] 0.5710-24 norton’s constant, ncr 2.52 damage constant, d [1/(pa^nhr)] 0.5410-24 damage constant, m 2.8 fatigue strength coefficient, ’f [mpa] 750 fatigue coefficient, c -0.087 table 1: the main mechanical properties of 20crmov5 steel. the creep-rupture strength fc at a specified temperature t (kelvin) and creep time t (hours) for 20crmov5 steel approximately can be found from the following equation [25]: ( 156.38 ln( ) 586.36)fc g     (28) 3(ln( ) 2 ln( ) 24.1) 10g t t t     (29) experimental study ne of the main purposes of this present work is to study the influence of the damage accumulation on the creep-fatigue crack growth rate. to this end, subjects for both the experimental studies and numerical analyses are compact tension specimens, which are the most frequently used for characterizing the crack growth rate resistance. in general, the selected dimensions are as recommended by the astm test standard [23]. the length of the specimen working area was chosen 50w  mm and specimen thickness 12.5b  mm. the creep-fatigue tests were carried out on the uts-110mh-5-0u test system with a high-temperature oven and highprecision crack opening displacement extensometer (fig. 1a). the potential drop and unloading compliance methods were used to monitor the crack length during the tests. the waveforms for the loading and unloading portions were trapezoidal, and the loading/unloading times were maintained constant (5 s rise and decay times). a hold time of a predetermined duration, namely 60 s, was superimposed on the trapezoidal waveforms at the maximum load. parts of the 5 s loading and unloading cycles represent low-cycle deformation, while the 60 s dwell under a constant load represents creep (fig. 1b). the tests were conducted at 550c on special high-temperature test equipment with a load ratio r of 0.1 and maximum load value maxp of 11 kn. the specimens were pre-cracked to an initial crack length-to-width ratio /a w of approximately 0.36 to 0.39 under cyclic loading at room temperature. for each tested specimen during the creep–fatigue tests the o a.v. tumanov et alii, frattura ed integrità strutturale, 52 (2020) 299-309; doi: 10.3221/igf-esis.52.23 306 amplitude ratio was changed from 0.1r  to 0.9r  two times for a short time period. this practice helped to determine the intermediate crack front positions during the creep–fatigue loading between the initial (pre-crack) and the final crack fronts (fig.2). a) b) figure 1: tests equipment (a) and the load waveform (b). figure 2: fracture surfaces. after total failure of the specimen, measurements of the crack sizes were taken for four positions of the crack front by means of an optical microscope. for each front, the crack size at five equally spaced points centered on the specimen midthickness line was measured along the crack front. figure 3: finite element method meshes for compact tension specimen. finite element model ull-field finite element analysis is performed using ansys software to study the crack-front stress fields for compact tension specimen. along the thickness direction, an identical planar mesh is repeated from the symmetry plane to the free surface. to catch the drastic change of the stress field near the free surface, the thickness of f a.v. tumanov et alii, frattura ed integrità strutturale, 52 (2020) 299-309; doi: 10.3221/igf-esis.52.23 307 successive finite element layers is exponentially reduced from the mid-plane toward the free surface. the radial sizes of the finite elements are varied according to the geometric progression. according to the symmetrical properties, one quarter of the actual structure was selected to establish the three-dimensional finite element model. the twenty-node quadrilateral brick isoparametric three-dimensional solid elements were used to model for the specimen configuration. typical finite element meshes for the compact tension specimen are illustrated in fig. 3 programming of the numerical calculations includes the analysis for the specified experimental combinations of creep time/number of fatigue cycles and crack length in a compact specimen. three position of the crack front were considered (a/w= 0.38, 0.55 and 0.7). for a/w= 0.55 and 0.7 a curvilinear crack fronts were simulated. results and discussion s result of a finite element simulations a stress-strain fields were obtained for different combinations of crack length and creep time. the governing parameter behavior of crack tip fields i for the compact specimen is plotted in fig. 4 along the crack front towards the thickness direction. a) b) figure 4: i -factor distributions along crack front for plastic (a) and creep (b) state. it should be noted that in real solids, the governing parameter of the crack tip field the i-integral is very sensitive to variations of the material properties, load level and geometry. these distributions of the in-integral are used to calculate the nonlinear stress intensity factors in the compact tension specimen. figure 5: comparison of crack growth rate prediction with experimental results for steel 20crmov5. the main objective of the creep-fatigue tests is to provide substantiation for the theoretical models. fig. 5 illustrates the prediction of the creep-fatigue crack growth rate for the 20cr1mov5 steel plotted against c*-integral for the compact tension specimen. the experimental c*-integral values were obtained from the crack length, determined using the a a.v. tumanov et alii, frattura ed integrità strutturale, 52 (2020) 299-309; doi: 10.3221/igf-esis.52.23 308 technique according to astm e2760 [23]. the experimental data of all tested specimens fall within a relatively narrow scatter band. a good agreement with the theoretical predictions is observed. by the author opinion the shift between prediction and experiment is caused by default value of initial damage w0 for each finite element model. in real specimens the value of initial damage during creep-fatigue depends on load history. for short cracks and small creep times it can be neglected, but influence over time enhanced. the proposed models of the crack growth rate are formulated in terms of nonlinear stress intensity factors. this model can describe the behavior a wide range of the material different properties for creep-fatigue interaction. acknowledges he authors gratefully acknowledge the financial support of the russian science foundation under the project 1879-00279. references [1] rabotnov yn. (1969) creep problems in structure members. north-holland, amsterdam, 822. doi: 10.1002/zamm.19710510726. [2] kachanov lm. (1986) introduction to continuum damage mechanics. martinus-nijhoff, dordrecht, 135 doi: 10.1002/nag.1610110509. [3] brathe l. (1978) estimation of kachanov parameters and extrapolation from isothermal creep rupture data. int j mech sci., 20, pp. 617-624. doi: 10.1016/0020-7403(78)90020-6. [4] hutchinson, j.w. (1983) constitutive behavior and crack tip fields for materials undergoing creep-constrained grain boundary cavitation, acta metall., 31, pp. 1079–1088. doi: 10.1016/0001-6160(83)90204-3. [5] riedel h. (1987) fracture at high temperatures. berlin: springer-verlag, 418. doi: 10.1002/crat.2170230609. [6] bendick w. (1991) analysis of material exhaustion and damage by creep. int j pres ves piping, 47, pp. 57–78. doi: 10.1016/0308-0161(91)90086-h. [7] budden j.p., ainsworth r.a. (1997) the effect of constraint on creep fracture assessments. int. j. fract., 87, pp. 139–149. doi: 10.1016/0029-5493(92)90175-u. [8] wen jf, tu st. (2014) a multiaxial creep-damage model for creep crack growth considering cavity growth and microcrack interaction. eng fract mech, 123, pp. pp. 197–210. doi: 10.1016/j.engfracmech.2014.03.001. [9] katanakha n.a., semenov a.s., getsov l.b. (2015) durability of bends in high-temperature steam lines under der conditions of long-term operation./thermal engineeting, 62(4), pp. 260-270. doi: 10.1134/s0040601515040047. [10] corten h.t. and dolan t.j. (1956) cumulative fatigue damage. in: proceedings of the international conference on fatigue of metals, institute of mechanical engineering, london, pp. 235–246. [11] budden p.j., ainsworth r.a. (1997) the effect of constraint on creep fracture assessments. int. j. fract., 87, pp. 139149. doi: 10.1023/a:1007416926604. [12] shlyannikov v.n., ishtyryakov i.s., tumanov a.v. (2020) characterization of the nonlinear fracture resistance parameters for an aviation gte turbine disc. fatigue fract eng mater struct, pp. 1–17. doi: 10.1111/ffe.13188. [13] ye d.y. and wang z.l. (2001) a new approach to low-cycle fatigue damage based on exhaustion of static toughness and dissipation of cyclic plastic strain energy during fatigue. international journal of fatigue, 23, pp. 679–687. doi: 10.1177/1056789512456030. [14] hutchinson j.w. (1968) plastic stress and strain fields at a crack tip. j. mech. phys. solids. 16, pp. 337-347. doi: 10.1016/0022-5096(68)90021-5 [15] shlyannikov v.n., tumanov a.v. (2014) characterization of crack tip stress fields in test specimens using mode mixity parameters, int. j. fract. 185, pp. 49-76. doi: 10.1007/s10704-013-9898-0 [16] shlyannikov v.n., boychenko n.v., tumanov a.v., fernandez-canteli a. (2014) the elastic and plastic constraint parameters for three-dimensional problems, eng. fract. mech. 127, pp. 83–96. doi: 10.1016/j.engfracmech.2014.05.015 [17] shlyannikov v.n., boychenko n.v., fernandez-canteli a., muniz-calvente m. (2015) elastic and plastic parts of strain energy density in critical distance determination, eng. fract. mech. 147, pp. 100–118. doi: 10.1016/j.engfracmech.2015.08.024. t a.v. tumanov et alii, frattura ed integrità strutturale, 52 (2020) 299-309; doi: 10.3221/igf-esis.52.23 309 [18] shlyannikov v.n., yarullin r.r., zakharov a.p. (2016) structural integrity assessment of turbine disk on a plastic stress intensity factor basis, int. j. fatigue 92, pp. 234–245. doi: 10.1016/j.ijfatigue.2016.07.016. [19] shlyannikov v.n., tumanov, a.v., boychenko, n.v. (2015) a creep stress intensity factor approach to creep-fatigue crack growth, eng. fract. mech. 142, pp. 201–219. doi: 10.1016/j.engfracmech.2015.05.056. [20] shlyannikov v.n. (2017) critical distance for creep crack growth problems, eng. fract. mech. 176, pp. 126–143. doi: 10.1016/j.engfracmech.2017.03.001. [21] shlyannikov, v.n., tumanov, a.v. (2018). creep damage and stress intensity factor assessment for plane multi-axial and three-dimensional problems, int. j. solids struct. 150, pp. 166–183. doi: 10.1016/j.ijsolstr.2018.06.009. [22] shlyannikov v.n. (2019) creep–fatigue crack growth rate prediction based on fracture damage zone models. eng. fract. mech., 214, pp. 449-463. doi: 10.1016/j.engfracmech.2019.04.017. [23] astm e2760-19. (2019) standard test method for creep–fatigue crack growth testing. annual book of astm standards. philadelphia (pa): american society for testing and materials. doi: 10.1520/e2760-19. [24] skelton r.p., gandy d. (2008) creep-fatigue damage accumulation and interaction diagram based on metallographic interpretation of mechanisms. mater. high temp. 25, pp. 27–54. doi: 10.3184/096034007x300494 . [25] guidelines for the heat resistance characteristics and durability of metals determination co 153-34.17.471-2003 ministry of energy of russian federation. moscow (2004). pp. 95 [26] ramberg w., & osgood w. r. (1943). description of stress–strain curves by three parameters. technical note no. 902, national advisory committee for aeronautics, washington dc. [27] tumanov a.v., shlyannikov (2018) v.n. method for creep damage accumulation law constants determination. transactions of academenergo. 4, pp. 115-126. << /ascii85encodepages false /allowtransparency false /autopositionepsfiles true /autorotatepages /none /binding /left /calgrayprofile (dot gain 20%) /calrgbprofile (srgb iec61966-2.1) /calcmykprofile (u.s. web coated \050swop\051 v2) /srgbprofile (srgb iec61966-2.1) /cannotembedfontpolicy /error /compatibilitylevel 1.4 /compressobjects /tags /compresspages true /convertimagestoindexed true /passthroughjpegimages true /createjobticket false /defaultrenderingintent /default /detectblends true /detectcurves 0.0000 /colorconversionstrategy /cmyk /dothumbnails false /embedallfonts true /embedopentype false /parseiccprofilesincomments true /embedjoboptions true /dscreportinglevel 0 /emitdscwarnings false /endpage -1 /imagememory 1048576 /lockdistillerparams false /maxsubsetpct 100 /optimize true /opm 1 /parsedsccomments true 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can be opened with acrobat and adobe reader 5.0 and later.) >> /namespace [ (adobe) (common) (1.0) ] /othernamespaces [ << /asreaderspreads false /cropimagestoframes true /errorcontrol /warnandcontinue /flattenerignorespreadoverrides false /includeguidesgrids false /includenonprinting false /includeslug false /namespace [ (adobe) (indesign) (4.0) ] /omitplacedbitmaps false /omitplacedeps false /omitplacedpdf false /simulateoverprint /legacy >> << /addbleedmarks false /addcolorbars false /addcropmarks false /addpageinfo false /addregmarks false /convertcolors /converttocmyk /destinationprofilename () /destinationprofileselector /documentcmyk /downsample16bitimages true /flattenerpreset << /presetselector /mediumresolution >> /formelements false /generatestructure false /includebookmarks false /includehyperlinks false /includeinteractive false /includelayers false /includeprofiles false /multimediahandling /useobjectsettings /namespace [ (adobe) (creativesuite) (2.0) ] /pdfxoutputintentprofileselector /documentcmyk /preserveediting true /untaggedcmykhandling /leaveuntagged /untaggedrgbhandling /usedocumentprofile /usedocumentbleed false >> ] >> setdistillerparams << /hwresolution [2400 2400] /pagesize [612.000 792.000] >> setpagedevice shot peening processes to obtain nanocrystalline surfaces in metal alloys: a. sarkar et alii, frattura ed integrità strutturale, 50 (2019) 86-97; doi: 10.3221/igf-esis.50.09 86 focused on showcasing structural integrity research in india crack growth based life prediction approach under lcf-hcf interaction a. sarkar, a. nagesha, r. sandhya fatigue studies section, metallurgy and materials group, indira gandhi centre for atomic research, kalpakkam, tamil nadu, india-603102 aritra@igcar.gov.in, https://orcid.org/0000-0002-8438-320x nagesh@igcar.gov.in,https://orcid.org/0000-0002-2025-8100 san@igcar.gov.in m. okazaki department of mechanical engineering, nagaoka university of technology, japan-940-2188 okazaki@mech.nagaokaut.ac.jp, https://orcid.org/0000-0001-7071-0399 abstract. prediction of cyclic life under low cycle fatigue high cycle fatigue (lcf-hcf) interaction is of paramount importance in the context of structural integrity of components in the primary side of fast reactors where such damage under lcf-hcf interaction occurs. the present investigation deals with the crack growth behavior of a type 316ln austenitic stainless steel subjected to simultaneous application of lcf and hcf cycles (blockloading). tests were performed over a wide range of temperatures from ambient to 923 k. experimental results indicate that a critical crack-length (acr) exists, beyond which the lcf-hcf interaction becomes significant. an attempt was made to predict life under block cycling by estimating the acr using fatigue crack threshold (δkth) since the latter is known to be affected significantly by the loading history. a universal equation, based on the concept of an equivalent critical crack length (acr.,eq) which incorporates the damage contribution from dsa and ratcheting under combined lcf-hcf loading, was proposed for life estimation.. keywords. lcf; hcf; lcf-hcf interaction; crack growth; 316ln ss. citation: sarkar, a., nagesha, a., sandhya, r., okazaki, m., crack growth based life prediction approach under lcf-hcf interaction, frattura ed integrità strutturale, 50 (2019) 86-97. received: 26.11.2018 accepted: 24.06.2019 published: 01.10.2019 copyright: © 2019 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. introduction ost of the current investigations pertaining to the fatigue behavior of structural materials are dedicated to either low cycle fatigue (lcf) or high cycle fatigue (hcf) loading even though it is a well known fact that engineering components experience a varying load history (interaction between lcf and hcf) throughout their service life. currently, this is a significant issue in sodium-cooled fast reactors (sfrs) where components of the primary sodium circuit are prone to damage induced by lcf as well as hcf which can lead to a significant reduction in m mailto:aritra@igcar.gov.in https://orcid.org/0000-0002-8438-320x mailto:nagesh@igcar.gov.in https://orcid.org/0000-0002-2025-8100 mailto:san@igcar.gov.in mailto:okazaki@mech.nagaokaut.ac.jp http://www.gruppofrattura.it/va/50/2269.mp4 a. sarkar et alii, frattura ed integrità strutturale, 50 (2019) 86-97; doi: 10.3221/igf-esis.50.09 87 service life of such components [1-2]. prediction of fatigue life under lcf-hcf interaction is thus highly essential to ensure the integrity of the components. in this regard, the well-accepted miner’s linear damage summation rule (ldr) poses serious non-conservatism in terms of huge deviations from linearity due to the large difference in lives between lcf and hcf [3-4]. ldr is further refined by modeling attempts, leading to “damage curve approach” (dca) [5]. however, a major limitation of dca is its semi-empirical nature which does not account for some intrinsic factors like crack length. such disadvantages will become more prominent at extreme conditions such as elevated temperature lcfhcf interactions. this necessitates the development of alternate life-prediction models based on crack propagation with periodic measurement of crack length. in view of this, the block-loading experiments including combinations of both lcf and hcf are specially designed so that crack-growth based life-prediction models can be developed based on the same. experimental methodology ylindrical fatigue specimens with a semi-circular initial surface notch of 100 µm diameter and 50 µm depth (fig. 1) were chosen to study fatigue crack growth behavior under block-loading (as per fig. 2) at 573 k. cumulative fatigue damage in terms of lcf-hcf interaction occurs in sodium-cooled fast reactor (sfrs). a closer simulation of the actual reactor conditions can be realized through a loading pattern involving repeated blocks consisting of lcf as well as hcf cycles. since lcf stress/strain for every start-up and shut-down operation actually results in one cycle and hcf stress/strain are caused by in-service vibrations, the loading pattern in a block shown in fig. 2 consists of one fully reversed lcf cycle followed by a specific number of hcf cycles superimposed on the lcf cycle which introduces mean stress/strain during hcf cycling. short fatigue crack growth rate was reported to increase with increase in notch-tip radius [6]. similar effect was found to follow in case of notch-sensitivity [7]. in the present investigation, the main reason for using a small surface notch was to enable lcf-hcf interaction under block-loading at higher temperatures avoiding extensive intergranularity or tendency towards rupture which is accounted for by creep, ratcheting and their interactions with lcf or hcf. the block-loading experiments are hence redesigned to ensure that specimen fails through initiation and propagation of cracks rather than rupture, so that crack based life-prediction models can be applied to them. the combined cycling experiments on notched specimens were designed in two steps on similar lines as carried out on smooth specimens in earlier investigations [8]. in step-i, the specimens were initially subjected to strain controlled lcf loading up to a specific number of cycles corresponding to stabilization of the cyclic stress response (csr). however, unlike smooth specimen testing, in the present case, the lcf cycling in step-ii was carried out under strain control (t/2lcf: ±0.6%) and not under stress-control to prevent tendencies of rupture through strain accumulation induced by creep and creep assisted ratcheting. hcf cycles of three different bs (1, 10 and 200) with strain amplitude (t/2hcf) of ±0.1% (~ σhcf of 150 mpa, using elastic modulus) were introduced at the maximum lcf strain (fig. 2), once the csr reaches stabilization. bs indicates the ratio of hcf cycles to lcf cycles in a particular block. the notch was considered as the initial crack and propagation of the crack from the notch was studied by taking replicas of the specimen surface after interruption at regular intervals, particularly in the short crack growth domain. in the latter stages of crack growth, travelling microscope was used to measure the crack length. in the present study carried out under strain-controlled mode, significant mean strain will act on the specimen which will lead to plastic ratcheting ahead of the crack tip. this phenomenon was considered for developing the life-prediction model. the model was further refined by carrying out block-loading experiments at higher temperatures, in the range from 573 to 923 k at a high bs of 5000. figure 1: geometry of the specimens used for crack growth experiment c a. sarkar et alii, frattura ed integrità strutturale, 50 (2019) 86-97; doi: 10.3221/igf-esis.50.09 88 figure 2: block loading sequence under strain control used in the crack growth experiments. figure 3: fatigue crack propagation behavior under lcf-hcf interaction with different bs under strain control with t/2lcf: ±0.6% and t/2hcf : ±0.1% (equivalent δσhcf: 150 mpa) t: 573 k results and discussion establishing a critical criterion for occurrence of lcf-hcf interaction ig.3 presents the variation of crack length with the number of loading blocks at 573 k, under a loading sequence given in fig. 2. it is observed that the crack propagation was similar irrespective of the bs till a ‘critical’ crack length (acr) was attained. however, once the crack length extends beyond acr, significant acceleration in the rate of crack growth was noted, depending on the bs. the rate of crack propagation is found to be highest for a higher bs of 200 compared to the lower bs of 10 and 1 (only lcf cycling). this resulted in the shortest fatigue life in the former case (bs: 200) amongst all the three bs used in the present study. it may be noted that bs is an important variable in fig. 3. the concept of “critical crack length” is based on the fact that the crack growth data coincides in a similar manner irrespective of the bs, till a particular crack length is reached, beyond which significant difference in crack growth data is observed with variation in bs. according to miner’s rule, the damage under the hcf cycles in the block is considered as zero when the stress amplitude in hcf is much below the fatigue limit and hence cannot impart any significant damage. in the present case, since the hcf strain amplitude is very low (±0.1%), equivalent σhcf is calculated using elastic modulus at 573 k for nuclear grade 316ln ss (0.07wt.%). at 573 k, e value for nuclear grade 316ln ss (0.07wt.%) was reported as 1.5 gpa [9]. using a strain amplitude of ±0.1%, equivalent σhcf is estimated as 150 mpa which was less than the fatigue limit [1011]. the strain-ratio (r) during the hcf cycling is 0.71. however, the crack is found to propagate even during the hcf cycles, once acris reached, as reflected from the change in crack growth behavior with respect to bs (fig. 3) indicating that miner’s hypothesis may be untrue for the present experimental results. this suggests that even though the hcf stress is far below the fatigue limit, hcf cycling contributes significantly to the crack growth, once the length of the crack (which may be nucleated from the lcf cycle) reaches the critical value of acr. in other words, strong lcf-hcf interaction prevails beyond acr. it may be possible that crack-growth data overlap at low number of cycles (blocks). however, it may be noted that the present tests are carried out at fixed lcf strain amplitude of ±0.6%, varying only the hcf cycles superimposed on it (bs). this suggests that crack growth data should be similar for all the cases unless the hcf cycling imparts considerable influence on the crack growth. hence, the difference incurred in the crack growth data is accounted f a. sarkar et alii, frattura ed integrità strutturale, 50 (2019) 86-97; doi: 10.3221/igf-esis.50.09 89 to the variation in bs only. moreover, in the present case, the similitude in the crack growth data was observed upto 2000 blocks for all the three different bs. it is important to note that 2000 blocks constitute up to almost 30% of life for bs :1 (bs :1 indicates cyclic loading under strain amplitude of ±0.6% without any hcf cycles). on the other hand, 2000 blocks constitute upto almost 60% of life for bs: 200 (bs: 200 indicates cyclic loading under strain amplitude of ±0.6% with 200 hcf cycles per each lcf cycle). clearly, overlapping of crack growth data is possible up to such a large extent of fatigue life. this confirms the previous argument and clearly brings out the importance of bs and the concept of acr in the crack growth behavior under the superimposed loading pattern as used in the present case. once acr is reached, further crack growth is facilitated by lcf as well as the hcf cycling which significantly curtails the fatigue life. this is aptly reflected from the variation in fatigue life presented in fig. 3 with increase in bs. the above point is also corroborated through smooth specimen tests exposed to sequential lcf and hcf cycling where a critical damage marking lcf-hcf interaction was found to occur depending on the degree of lcf pre-exposure and magnitude of lcf strain amplitude employed [12]. this is explained on the basis that at least one stage-ii crack should initiate during the lcf pre-cycling which will grow further during the subsequent hcf phase [13]. the crack-growth experiments depicted in the present study show similar result where the crack will grow at an accelerated rate under the influence of hcf only when acris reached. as observed from fig. 3, bs is an important variable which affects the crack propagation rate. however, the concept of “critical crack length” is based on the fact that the crack growth data coincides in a similar manner irrespective of the bs, till a particular crack length is reached. in other words, the critical crack length acr is not affected by the variation in bs. crack propagation under hcf (minor) cycling is possible only when acris reached, following which a change in crack growth behavior with respect to bs is observed. based on the principle of fracture mechanics, no crack propagation can take place when δk is <δkth [14]. in the present case, crack propagation (stage-ii crack) commences once the critical crack length acr is reached. hence, δkth can be correlated with acr using a mathematical relation between δk and a, as shown in eqn. 1. this expression can be utilized for the estimation of acr. acr＝{δkth/（fδσhcf√π）}2 (1) where f is the boundary correction factor associated with the stress intensity factor and is a function of the shape of the crack. for a semi-circular shaped crack (as in the present case), f is typically considered as 0.64. since acr also marks the onset of lcf-hcf interaction and no such interaction takes place below acr, estimation of acr using the above expression is an important criterion for life-prediction under lcf-hcf interaction. the crack length may not remain fully semi-circular throughout the process of crack growth. however, this may not affect acr since acr is independent of bs and further crack propagation commences only after acr is reached. hence, usage of sif for a semi-circular shaped crack is quite reasonable in the present case. the threshold stress intensity factor, δkth is found to be a strong function of the stress ratio, r [15-16]. δkth shows a gradual decrease with increase in r followed by saturation [14-15]. the value of r was kept at 0.71 in the present blockloading experiments. although δkth is usually computed from stress-controlled experiments, in the present case, σhcf is used for δkth calculation. [17]. the δkth value at r=0.7 on nuclear grade 316ln ss austentitc stainless steel (0.07 wt.%) at ambient temperature was reported by samuel at al. as ~6mpa√m [15]. however, with increase in temperature, there is a further reduction in the δkth value, as reported by okazaki et al [17]. δkth was determined experimentally using a δk decreasing fatigue crack propagation test according to the astm standard [18] at r=0.7. additionally, δkth was estimated using at r=0.7 using the linear variation of δkth with temperature as suggested by shih et al. [19]. using both the methodologies, δkth was determined in the band of 3-4 mpa√m, at 573k with r=0.7. the authors have used these values of δkth for estimation of acr then, acr is approximately estimated using eqn. 1 as follows: acr≒ 220μm (when δkth = 4.0 mpa√m, δσhcf= 25 mpa) acr≒ 140μm (when δkth = 3.0 mpa√m, δσhcf= 25 mpa) these values are displayed in dotted lines in fig. 3. this indicates that the prediction is more reasonable compared to the traditional miner’s rule. hence, in practice, it is essential to ensure that the crack length remains below acr so as to preempt the occurrence of significant lcf-hcf interaction. mechanisms of lcf-hcf interaction crack growth behavior under lcf is characterized by a quick transition from stage-i to stage-ii crack followed by stageii crack growth over the majority of fatigue life. on the other hand, the bulk of the fatigue life is spent in stage-i under a. sarkar et alii, frattura ed integrità strutturale, 50 (2019) 86-97; doi: 10.3221/igf-esis.50.09 90 hcf where the transition from stage-i to stage-ii crack gets much delayed. similar behavior is corroborated through fatigue crack growth experiments conducted on 316l ss by miyahara et al [20] which clearly showed that fatigue crack propagation starts much early at cycle-ratio of 0.1 to 0.2 at high strain amplitudes of ±1.0% or ±0.6% compared to higher cycle ratios of 0.6 to 0.7 for low strain amplitudes of ±0.3% or ±0.2%. this above behavior can be also followed from the relationship between fatigue crack growth and strain amplitude under fm expressed as da/dn=a (δɛin)n a (2) where da/dn=crack propagation rate, δɛin=inelastic strain, a=instantaneous crack length and n & a=material constant. the experiments in the present case are carried out on notched cylindrical specimens under strain control where the crack tip plasticity is quite high. so, the stable crack propagation behavior is governed by a non-linear fracture mechanics parameter δj rather than δk. dowling et al. [21] and el haddad et al. [22] have earlier demonstrated a methodology of using j-integral concept as an elastic–plastic fracture mechanics criterion for predicting crack growth behavior. similar concepts were put forth by starkey et al. [23] and haigh et al [24] where crack growth under high strain conditions was considered. the stress-based crack growth equation which is primarily related to lefm concepts were suitably modified to demonstrate a smooth transition between crack growth rates under high strain conditions involving significant plasticity and that under lefm conditions involving mostly elastic behavior [23]. starkey et al [23] also derived a methodology for computing strain intensity factor using half the elastic plus the plastic strain range eqn. 2 used in the present case can be derived as follows: da/dn = c(δj)m with m=1… (2a) also, δj=δk2/e + f(n)δσδɛina = δk2/e + f(n)b (δɛin)1+na using the cyclic stress-strain relationship of δσ=b(δɛin)n hence [16], δj ≃f(n)b(δɛin)n+1 a …. (2b) where f(n)={3.85(1-n)/√n}+∏n….. (2c) f(n)is computed using a value of ‘n’ as 0.2 which is typical value of cyclic strain hardening exponent in stainless steel [22]. then, equating both 2a and 2b, the expression for eqn. 2 can be derived. it may be noted that this equation does not cover the crack initiation life, ni and remains valid mostly for stage-ii crack propagation. ni is negligibly small enough under lcf (limited to lower cycle-ratios), however, the same is quite significant in the hcf (higher cycle-ratios). hence, ni needs to be accounted for when lcf-hcf interaction is concerned. to utilize this concept under lcf-hcf interaction, crack growth behavior is studied under strain control mode at strain amplitudes ±0.6% (lcf) and ±0.1% (hcf), at 573 k (fig. 4). it is clear from fig. 4 that crack propagation is considerably delayed to higher cycle-ratios in case of hcf as compared to lcf. however, an interruption in the crack growth test under lcf at a given cycle-ratio followed by hcf loading condition will lead to significant lcf-hcf interaction which will change the crack growth behavior (indicated by the arrow in the figure). it is clear from the figure that such sequence (l-h) as indicated by the arrow will significantly curtail the domain of short crack growth under hcf, thereby shortening the crack propagation under hcf. this is the essence of lcf-hcf interaction which leads to drastic fall in remnant hcf lives with prior lcf cycling. development of a unified model for life-estimation under block-loading at different temperatures it is worthwhile to examine whether the method of life-estimation which has been derived from the block-loading experiments conducted at 573 k, can be extended to other temperatures as well, in the range 573-923 k where damage contributions like plastic ratcheting, creep and creep-assisted ratcheting become noticeable. a. sarkar et alii, frattura ed integrità strutturale, 50 (2019) 86-97; doi: 10.3221/igf-esis.50.09 91 figure 4: crack growth behavior at t/2lcf: ±0.6% and t/2hcf : ±0.1% , t: 573 k. predicted value of acr is marked in the figure. the arrow indicates possible lcf-hcf interaction through a sequence of lcf followed by hcf. as indicated earlier, the crack propagation behavior under a given strain amplitude can be expressed through the following mathematical relation: da/dn = a (δɛin)n a (2) where da/dn = crack propagation rate, δɛin= inelastic strain range, a = instantaneous crack length and n & a=material constant. under loading conditions involving extensive creep and ratcheting deformation, the foregoing treatment can be modified by making a minor revision to eqn. (2) as detailed below. significant plastic deformation occurs at higher temperatures like 823 and 923 k leading to accumulation of permanent strain through plastic ratcheting through the mean strain acting on the specimen. this imparts a loss of residual ductility in the material. thus, eqn. (2) can be revised as follows, incorporating the damage contributions from plastic ratcheting (induced through presence of mean strain) by introducing a parameter δc which is the ratcheting strain accumulated per cycle: ( ) nin cda a a dn d   + = (3a) where δc= strain accumulated per cycle through ratcheting, d= material ductility. by integrating eqn. (3a), a ‘ductility normalized equation’ can be naturally derived when δc is zero, as follows: 1 ln( ) ( ) f nin f i a n a a d  = (3b) where af= final crack length and ai = initial crack length. however, for a loading condition where δc>0, the life prediction equation can be derived from eqn. (3a) as: , 1 1 ( ) ( ) ln( ) ln( ) f fn nin in c f in c i i eq i a a n d a a a a       =   + (3c) a. sarkar et alii, frattura ed integrità strutturale, 50 (2019) 86-97; doi: 10.3221/igf-esis.50.09 92 where ai,eq is an equivalent initial crack length incorporating ratcheting as a damage contributor. the crack growth behavior under block loading conditions is presented in fig. 5, which can be clearly explained in the light of eqn. 3(c). for uniform representation at all temperatures, crack length is plotted against block-ratio (ratio of the number of blocks at which the crack length is measured to the total number of blocks to failure, designated as nb/nb). a much higher crack propagation rate at 923 k compared to the lower temperatures as observed in fig. 5 may thus be attributed to a higher accumulation of ratcheting strain per cycle. this is also corroborated from the results of the block-loading tests carried out at 923 k [8, 25] on smooth specimens which showed a significant contribution of creep and ratcheting to the net damage (2.47% strain accumulation per block). however, at 573 k, contribution of creep and ratcheting becomes almost negligible, with a meager 0.001% strain accumulation per block [8, 25] which explains the significant lowering of crack propagation rate at 573 k compared to 923 k, in the present case. this is also reflected from a much higher value of the acr at 573 k compared to 923 k (marked by dotted lines in fig. 5). a similar situation will also occur at 823 k where significant hardening resulting from dynamic strain aging (dsa) will prevent any loss in residual ductility, thus lowering the contribution of ratcheting to net damage, which is corroborated from the test results carried out under block-loading on smooth specimen with a very low strain accumulation of 0.1% per block [8, 25]. it was indicated earlier in [9, 10] that dsa (caused by locking of dislocations by cr atoms at 823 k in type 316ln ss [26]) leads to significant hardening of the matrix during cycling which restricts the local plastic deformation associated with the crack tip, thereby leading to a delay in the crack propagation under hcf. this argument was also supported through a slightly higher value of acr observed at 823 k in the present case, compared to that of 573 k (fig. 5). it is thus clear from the above arguments that the loss of residual ductility due to creep/ratcheting strain accumulation is significantly high at 923 k, resulting in a very high crack growth rate. figure 5: fatigue crack propagation behavior under strain controlled block-loading (ccf) with bs: 5000, t: 573, 823 and 923 k (t/2lcf : ±0.6% and t/2hcf : ±0.1%, equivalent δσhcf: 25 mpa). acr. marked in the figure indicates the onset of significant lcfhcf interaction. nf can be computed from eqn. 3(c) using the values of δc and d for different temperatures once the critical crack length acr is reached. acr can be computed in a similar way as shown in section 3.1. however, acr values will vary with temperature since δkth from which acr is computed (eqn. 1), is a strong function of temperature. in other words, acr is a characteristic of material mechanics which changes with temperature and loading mode of hcf. using eqn. (1), the acr values in the case of t/2hcf : ±0.1% (corresponding δσhcf≃ 150 mpa) were estimated at 140, 147 and 100 μm respectively, at the temperatures of 573, 823 and 923 k. the estimated values are also found to match fairly well with the experimental results (also marked in fig. 4) where the crack growth rate is indeed very low. however, when plastic ratcheting plays a vital role (923 k), the local plastic strain in the vicinity of the crack increases inspite of the crack length being lower than acr. this in turn, will increase the notch sensitivity leading to early failure at 923 k compared to that at 573 k. in such cases, it becomes necessary to impose an additional correction factor to account for the damage contribution from creep/ratcheting. one of the ideas is to introduce the correction in terms of a. sarkar et alii, frattura ed integrità strutturale, 50 (2019) 86-97; doi: 10.3221/igf-esis.50.09 93 the ratio of the reduction of crack length in a case with creep/ratcheting (923 k) to a case with no ratcheting (573 k). to obtain this reduction-ratio, rc, the following method can be used: reduction-ratio (rc) = (af/acr) ratcheting /(af/acr)no ratcheting the value of rc is calculated as rc= 0.71 under the present experimental condition using the acr values as mentioned above. hence, the modified value of acr, designated as acr,eq can be computed at 923 k as follows: acr,eq.= 0.71*acr= 71 μm (923 k) (4) thus, acr,eq. is a common crack size independent of temperature and bswhich takes into account the effect of plastic ratcheting at 923 k. acr,eq.= rc* acr at ambient temperature or 823 k, effect of plastic ratcheting is negligible and rc remains 1, indicating that in such cases, acr,eq.= acr. since acr,eq. marks the onset of crack propagation at 923 k, it must be an important parameter to avoid the occurrence of ratcheting under block-loadings, since ratcheting will not play a dominant role under block-loading when a<acr,eq. hence, at 923 k, the crack should be limited to this value (marked in fig. 6) to avoid the damaging consequences of creep and ratcheting. however, it may be noted that the term acr,eq primarily addresses the effect of plastic ratcheting and not creepinduced ratcheting for which separate equation needs to be used. figure 6: fatigue crack propagation behavior under strain-controlled block-loading (ccf) with bs: 5000, t: 573, 823 and 923 k (t/2lcf : ±0.6% and t/2hcf : ±0.1%, equivalent δσhcf: 25 mpa). acris replaced by acr.,eq at 923 k to account for creep/ratcheting damage (marked in the figure by dotted line) it is clear from the above discussion that eqn. 3 (c) is primarily based on crack propagation under ratcheting in a blockloading condition and hence can be used for predicting the remaining life at 923 k only when acr,eq is reached. similarly, eqn. 3(b) can be used for remaining life spent in crack propagation for other temperatures like 573/823 k where ratcheting is insignificant, only when acr is reached. hence, life-estimation under lcf-hcf loadings follow a two-step procedure (1) estimation of acr or acr,eq using eqn. 1 or eqn. 4 (2) estimation of the life spent in crack propagation using eqn. 3(b) /eqn. 3 (c). hence, the final life-prediction equation is modified as follows: a. sarkar et alii, frattura ed integrità strutturale, 50 (2019) 86-97; doi: 10.3221/igf-esis.50.09 94 1 ( ) ln( ) fn f cr a n d a a   (for no ratcheting) (5) , . 1 ( ) ln( ) fn f cr eq a n d a a   (for ratcheting) (6) thus, eqn. 5 and 6, based on crack propagation may be treated as a universal equation which can be used for lifeprediction under lcf-hcf interaction irrespective of the temperature, using suitable values of acr or acr,eq. it may be noted that changes in crack dynamics due to the accumulation of strain through ratcheting are adequately accounted for, in the above equation. in real-life, crack-sizes can be measured at elevated temperature online using ndt techniques like acoustic emission technique. however, in the present case, critical crack-length (acr) was estimated using fatigue crack threshold, δkth from literature. the procedure for life-estimation for any arbitrary loading sequence consisting of lcf and hcf loads can be expressed through an algorithm (fig. 7) where effect of plastic ratcheting at 923 k or effect of cyclic hardening due to dsa is accounted for incorporating material ductility as an important parameter. life-prediction was carried out based on this algorithm using eqn. 5 and 6, and the tabulated against experimental life in tab. 1. here, the values of ‘a’ and ‘n’ used in the equations are based on previous experiments on 316l ss [20], and the value of ‘d’ is used from the tensile data on 316ln ss [27]. a fairly good estimation was found against experimental life, with ~80% accuracy. it is also clear that usage of correction factor results in a better estimation in a case where ratcheting/creep is strongly prevalent (as in 923 k). the estimation can be further improved by incorporating more data on strain controlled block-loading experiments at different temperatures. figure 7: algorithm depicting the procedure of life-estimation under lcf-hcf interaction for any arbitrary loading sequence in absence of smooth specimen ratcheting data, simulation of ratcheting behavior can be carried out using armstrongfrederick non-linear kinematic hardening model or ohno-wang model [28-29]. however, such models should be refined in the present case incorporating material ductility as an important parameter to account for the effect of cyclic hardening a. sarkar et alii, frattura ed integrità strutturale, 50 (2019) 86-97; doi: 10.3221/igf-esis.50.09 95 or temperature (effect of dsa) for predicting ratcheting strain more accurately, particularly in the dsa temperature regime. although the universal equation based on the concept of fracture mechanics can able to predict life in a much better way compared to the modified dca model, the equation is better suited for fatigue (cycle dependent damage) and hence can also address the issue of plastic ratcheting. it may also be noted that the model is developed based on the assumption that crack nucleates from the surface of the specimen. from a practical point of view, the lcf crack is expected to nucleate on the surface of the inner vessel of the reactor facing the sodium which may be further enhanced by presence of hcf damage/creep or creep-assisted ratcheting damage during the steady state operation. however, initiation of crack from the internal (bulk) cannot be ruled out due to the presence of strong ratcheting and creep damage. in such a case, the present model may not be able to predict life accurately. this envisages the need of refining the present model by using separate constitutive equations based on time dependent creep damage (da/dt) rather than cycle dependent damage. temperature estimated life experimentallife acr accuracy(%) 573 5580 6400 140 82 823 3700 4230 147 85 923 710 287 100 327 71* 83 table1: predicted values of life under lcf-hcf interaction as per the algorithm (*indicates acr value using correction factor for creep/ratcheting). conclusions n attempt was made towards remaining life-estimation under lcf-hcf interaction in block-loading sequence using the concept of a critical crack-length (acr), estimated using fatigue crack threshold, δkth. a unified approach was developed and extended towards remaining life-estimation using acr. the model was also able to address the influence of dsa, creep and ratcheting in prediction of remaining life. references [1] bhoje, s.b. and chellapandi, p. (2000). advanced structural design of high temperature components of fbr, trans. indian inst. metals, 71, pp. 165-173. [2] halford, g.r. (1997). cumulative fatigue damage modeling—crack nucleation and early growth, int. j. fatigue, 19, pp. s253-s260. [3] wong, y.k., hu, x.z. and norton, m.p. (2002). plastically elastically dominant fatigue interaction in 316l stainless steel and 6061-t6 aluminium alloy, fatigue fract. eng. mater. struct., 25, pp. 201-213. [4] wong, y.k., hu, x.z. and norton, m.p. (2002). an alternative definition for two distinct regions of fatigue, proc. struct. integrity and fract. conf., usa [5] manson, s.s. and halford, g.r. (1981). practical implementation of the double linear damage rule and damage curve approach for treating cumulative fatigue damage, int. j. fract., 17, pp. 169-192 [6] suresh, s. (1991) fatigue of materials, cambridge university press, uk [7] dieter, g.e. (1988) mechanical metallurgy, mcgraw-hill book company, uk [8] sarkar, a., okazaki, m., nagesha, a., sandhya, r., parameswaran, p. and laha, k. (2016). mechanisms of failure under low cycle fatigue, high cycle fatigue and creep interactions in combined cycling in a type 316ln stainless steel, mater. sci. eng: a., 683, pp. 24-36 [9] neeharika, v. b., narayana, k. s., krishna v., and. kumar, m. p. (2014) . tensile and creep data of 316ln stainless steel ananlysis, arpn j. eng. appl. sci., 9, pp. 699-705 [10] sarkar, a., nagesha, a., sandhya, r., laha, k. and okazaki, m. (2018). manifestations of dynamic strain aging under low and high cycle fatigue in a type 316ln stainless steel, mater. high temp., 35(6), pp. 523-528 [11] sarkar a, ph.d thesis (2018). low cycle fatigue–high cycle fatigue interaction in type 316ln stainless steel at high temperatures, nagaoka university of technology, nagaoka, japan. a a. sarkar et alii, frattura ed integrità strutturale, 50 (2019) 86-97; doi: 10.3221/igf-esis.50.09 96 [12] sarkar, a., nagesha, a., sandhya, r., parameswaran, p., laha and k., okazaki, m. (2017). investigation of cumulative fatigue damage through sequential low cycle fatigue and high cycle fatigue cycling at high temperature for a type 316ln stainless steel: life-prediction techniques and associated mechanisms, metall. mater. trans a., 48 (3), pp. 953964. [13] sarkar, a., nagesha, a., sandhya, r., parameswaran, p., laha and k., okazaki, m. (2017). investigation of fracture mechanisms and substructural changes under sequential fatigue cycling involving lcf and hcf loads in a type 316ln stainless steel at 923 k. mater. sci. eng: a, 702, pp.360-370 [14] mcdowell, d.l. (1996) basic issues in the mechanics of high cycle metal fatigue, int. j. fract., 80, pp. 103-145. [15] samuel, k.g., sasikala, g. and ray, s.k. (2011). on r ratio dependence of threshold stress intensity factor range for fatigue crack growth in type 316(n) stainless steel weld, mater. sci. tech., 27(1), pp. 371-376. [16] huthman, h., livesy, v.b. and robert, g. (1996) fatigue crack growth threshold and short crack growth in austenitic materials, int. j. press. vess. pip., 65, pp. 231-239. [17] okazaki, m., sawada, t., kasahara n. and kamaya, m. (2011). an investigation on high-cycle thermal fatigue failure based on crack propagation in type 316 stainless steel, structural safety and reliability (jcossar 2011), pp. 127-135. [18] astm standards (2003). e647-00, vol. 03.01, astm international, p. 615. [19] shih, c.f. and hutchinson, j.w. (1976). fully plastic solutions and large scale yielding estimates for plane stress crack problems, trans. asme, j. eng. mater. tech..98, p.289. [20] miyahara, m. and tokimasa, k. (1986). high temperature fatigue properties and life prediction of sus 304 stainless steel under variable straining, trans. soc. mater. science japan, 35, pp. 1030-1036. [21] dowling, n. e., and. begley, j. a. (1976) fatigue crack growth during gross plasticity and the j-integral, in mechanics of crack growth. astm international. [22] el haddad, m. h., smith, k. n and topper., t. h. (1979) fatigue crack propagation of short cracks, journal of engineering materials and technology, 101(1), pp. 42-46. [23] starkey, m.s. and skelton, r.p. (1982). a comparison of the strain intensity and cyclic j approaches to crack growth, fatigue fract. eng. mater. struct., 5(4), pp.329-341. [24] haigh, j.r. and skelton, r.p. (1978) a strain intensity approach to high temperature fatigue crack growth and failure, mater. sci. eng. a 36, pp. 133-137. [25] sarkar, a., nagesha, a., parameswaran, p., sandhya, r., laha, k. and okazaki, m. (2017). evolution of damage under combined low and high cycle fatigue loading in a type 316ln stainless steel at different temperatures, int. j. fatigue, 103, pp. 28-38. [26] mannan, s.l. (1993). role of dynamic strain ageing in low cycle fatigue, bull. mater. sci., 16(6), pp. 561-582. [27] ganesh kumar, j., chowdary, m., ganesan, v., paretkar, r.k., rao, k.b.s., mathew, m.d. (2010). high temperature design curves for high nitrogen grades of 316ln stainless steel, nucl. eng. des., 240, pp. 1363-1370. [28] armstrong, p. j. and frederick, c.o. (1966) report rd/b/n73, central electricity generation board, berkley nuclear laboratories, berkley, uk. [29] ohno, n. and wang, j.d. (1993) kinematic hardening rules with critical state of dynamic recovery: part iformulation and basic features for ratcheting behavior, int. j. plast., 9, pp. 375-390. nomenclature ɛin inelastic strain t/2 lcf strain amplitude σlcf lcf stress amplitude σhcf hcf stress amplitude bs block-size nf number of cycles to failure δkth threshold stress intensity factor δk range of the stress intensity factor δj strain energy release rate a crack length acr critical crack length f boundary correction factor associated with stress intensity factor a. sarkar et alii, frattura ed integrità strutturale, 50 (2019) 86-97; doi: 10.3221/igf-esis.50.09 97 da/dn crack growth rate δc ratchet/creep strain accumulated per cycle d material ductility af final crack length a0 initial crack length ai crack length at ith cycle rc reduction-ratio of crack length ai,eq equivalent crack length acr.,eq equivalent critical crack length a, n material constants in crack growth equation microsoft word numero_60_art_03_3264.docx a. deliou et alii, frattura ed integrità strutturale, 60 (2022) 30-42; doi: 10.3221/igf-esis.60.03 30 mechanical behavior of unidirectional composites according different failure criteria adel deliou university of med seddik benyahia (umsb of jijiel), department of mechanical engineering laboratory of materials and reactive systems lmsr, university djillali, liabes, sidi bel-abbes, algeria. del032003@yahoo.fr,adel.deliou@univ-jijel.dz, deliouadel15@gmail.com benattou bouchouicha laboratory of materials and reactive systems lmsr, university djillali, liabes, sidi bel-abbes, algeria. benattou_b@yahoo.fr abstract. this work is about study of the mechanical behaviour of unidirectional kevlar / epoxy composite laminates according to different failure criteria. varying strength parameters values, makes it possible to compare the ultimate mechanical characteristics obtained by the criteria of tsai-hill, norris, fisher, ashkenazi and tsai-wu. the epoxy matrix of the material in question is reinforced with up to 60 of its volume by aramid fibers. the stack of four layers composing the arbitrarily oriented and alternating [+/-]s materials results in balanced symmetrical laminates. the laminate is subjected to uniaxial tensile membrane forces. estimate of their ultimate strengths and the plotting of the failure envelope constitute the principal axis of this study. using the theory of maximum stress, we can determine the various modes of damage of the composite. the different components of the deformation are presented for different orientations of fibers. keywords. unidirectional kevlar/epoxy composite; failure criterion; membrane stress; deformations; failure envelope. citation: deliou, a., bouchouicha, b., mechanical behavior of unidirectional composites according different failure criteria, frattura ed integrità strutturale, 60 (2022) 3042. received: 07.09.2021 accepted: 07.01.2022 online first: 23.01.2022 published: 01.04.2022 copyright: © 2022 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. introduction omposite materials, in the most common sense of the term, are a set of synthetic materials designed and used mainly for structural applications; the mechanical function is dominant. the mechanical behaviors of the composite, as well as the degradation mechanisms leading to its rupture depend on the nature of the constituents and on the architecture of the fiber preform [1]. c https://youtu.be/c6kcjp7h-5u a. deliou et alii, frattura ed integrità strutturale, 60 (2022) 30-42; doi: 10.3221/igf-esis.60.03 31 the profile is required because it guides the engineer in designing structures with precise properties in relation to the needs. the study of the stability of these structures requires, among other things, knowledge of the limiting behavior of the material. this behavior is expressed by a failure criterion. which expresses the relationships between the components of the tensor of the stresses; indeed, when checked locally, they translate the beginning of the failure. despite the complexity of the failure mechanism for composite materials, in particular due to the heterogeneity and the anisotropy of their structure, some work has attempted to simplify this, by giving a single failure criterion, applicable for any type of stress [2]. the tsai-hill criterion [3-4], initially based on the idea of von-mises for isotropic metallic materials and extended to the case of anisotropic materials, does not take account the difference in behavior, in tension and in compression. the other criterion most commonly used is tsai-wu criterion [5]; it is based on the invariant tensor theory. it appears in quadratic form and it takes into account the interactions between the various components of the stress tensor. the tensor coefficients of the rupture matrix are evaluated by means of tensile, compressive and shear tests, at rupture [67]. the difference between the many criteria, comes mainly from the types of tests and hypotheses used to evaluate these coefficients. for example, certain criteria like those of tsai-hill, fisher, ashkenazi and norris admit the equivalence between the behaviors in tension and in compression, in order to limit even more the number of coefficients. damage to composite materials investigated by the use of failure criteria, is the subject of numerous studies [8-12]. christensen [13] developed a mathematical model to predict the strength and the macromechanical fracture characteristics of unidirectional reinforced composite materials; and thus crack propagation can be optimized by the finite element method. sauder et al. [14] found that this approach is limited, given the restrictive assumptions regarding the composition of the material; however, it allows to obtain reliable results for particular types of composites. reference [15] shows that the number of parameters required for the tsai-wu criterion, can be reduced from seven to five for composite materials that do not rupture at specific hydrostatic or transverse pressure levels. arola [16] presents a finite element model from failure envelopes during drilling tests of the carbon / epoxy composite, representing the values of the tsai-hill failure criterion. then mahdi [17] studied the influence of the mesh on the prediction of cutting forces as a function of the orientation angle of fibers using the same model as arola. m.a. mbacke in his thesis [18], describes the sizing approach for coil reservoirs and multiform reservoirs designed by braiding fibers on the liner side. to assess the mechanical strength of the tanks, several failure criteria, such as tsai-wu, tsai-hill criteria, maximum stresses and strains were used. cazeneuve et al. [19] studied the behavior of carbon/epoxy and kevlar/epoxy tubes. they used their experimental results to modify the tsai criterion and to predict better the failure of these high-performance composites. in the same vein, vicario and rizzo [20] and herring et al. [21] studied the distribution of stresses in boron/epoxy tubes and determined the mechanical characteristics allowing comparison to conventional models. r.m. jones [22] verifies that the tsai-hill criterion used, is in good agreement with the experimental results for unidirectional e-glass / epoxy composites, than that obtained by the maximum stress theory a study known as the "world-wide failure exercise (wwfe)" [23] was conducted with the aim of comparing the different failure models in the case of continuous fiber composite materials. this study is the most complete to date. 18 models were compared using 14 test cases, to assess different types of loads and according to the stacking sequence. among the criteria that give good results in tension, we have those of tsai-hill and tsai-wu. recently, s. li [24] systematically re-examines from a mathematical point of view, the quadratic function of tsai -wu, guided by the principles of analytical geometry in the context of unidirectional composites. the major objective of our work is to contribute to the analysis of the strength studies, by different failure criteria of unidirectional laminate in kevlar/epoxy, according to the stacking sequence under the effect of uniaxial tension. moreover, we must bear in mind that our laminate composite is composed of four balanced and symmetrical layers. prediction of material failure failure criterion is characterized by the knowledge of a scalar function   σ . there is no rupture of the material if prevailing stresses do not exceed the ultimate stress value; that is to say, as long as the following inequality is satisfied:    1 (1) a a. deliou et alii, frattura ed integrità strutturale, 60 (2022) 30-42; doi: 10.3221/igf-esis.60.03 32 when the equality is satisfied, we obtain the failure envelope or the limiting surface [25]. tsai-hill criterion the evaluation of the resistance of the composite material working in tension, is ensured by the rupture criterion of tsai hill. it allows us to predict the ultimate resistance of the least resistant ply, in the case of the plane stress [4-6,25]:                         2 2 2 11 22 12 11 22  .     1 k x y xy s (2) with:     y k x x and y are, respectively, the ultimate tensile strength stresses of the ply [0 °] and [90 °]. s is the ultimate shear stress in the plane (1,2 of the [0°] layer. there is therefore no rupture of the material if the prevailing stresses do not exceed the ultimate constraints. norris criterion norris [25 29] assumes that in the constraint field, the point:     11 22 12 ,   ,   0 x y (3) lies on the fracture surface. so after substitution of (3) in relation (2) we find: k = 1. fisher's criterion fisher's criterion is applied to orthotropic materials and is based on norris analysis. fisher assumes that the point [25,27,28,29,30]: 11 =p,  22 =-p and  12 0 lies on the failure surface. in this case we have:  1 2 k a a (4) with:   1 1 21     1  a e v   2 2 12     1  a e v 1 2,e e : young's modulus in directions 1 and 2. 21v , 21 v : poisson's ratio. ashkenazi criterion this criterion is used for unidirectional composite materials. ashkenazi [25,29,31] assumes that the points:  11   2 t , 22   2 t , 12   2 t (5) lie on the failure surface. t: ultimate tensile strength at 45 ° from the direction of the fibers. it must satisfy the stability condition: a. deliou et alii, frattura ed integrità strutturale, 60 (2022) 30-42; doi: 10.3221/igf-esis.60.03 33        2 2 2 4 1 1 1   x yt s the coefficient k is then:        2 2 1 1   y x k xy x y s t (6) tsai-wu criterion we will retain the tsai-wu criterion       1        ,  1, 6ij i j i if f i j (7) where the constants if and ijf are the components of two tensors, respectively of rank 2 and 4, with the parameters ijf [32,33]:  1 1 1 t c f x x  2 1 1 t c f y y 11 1 t c f x x (8) 22 1 t c f y y  6 66 2 1 0    and      f f s 12 11 22 1     2 f f f xt, xc: ultimate tensile strengths along the longitudinal axis, in tension and compression respectively. yt, yc: ultimate tensile strengths along the transverse axis, respectively in tension and in compression. s: stress at failure in shear, in the plane of the layer. maximum stress criterion this criterion states that the structure withstands the conditions of use if the calculated stresses meet the conditions below.   11cx tx   22cy ty (9)  12 s a. deliou et alii, frattura ed integrità strutturale, 60 (2022) 30-42; doi: 10.3221/igf-esis.60.03 34 if one of the inequalities is no longer true, the limit state is reached; the failure is then attributed to the stress present into this inequality. a failure envelope [34] is a three-dimensional plot of the combinations of the normal and shear stresses that can be applied to an angle laminate just before failure. one may develop failure envelopes for constant shear stress 12 and then use the two normal stresses 11 and  22 as the two axes. then, if the applied stress is within the failure envelope, the laminate is safe; otherwise, it has failed. methods n the case of stresses planes (thin plate), the tensor {σ} as a function of that of the strains for a unidirectional composite layer, is given by the following relation:                              11 11 12 1 22 21 22 2 12 66 12 0 0 0 0 q q q q q (10) figure 1: definition of axis systems for a single stacking order layer. values of the reduced stiffness matrix in membrane [ ijq ]as a function of the elastic constants [35]are as follows:   1 11 12  211 e q v v     12 2 12 21 21   22 12 21       1 v e q q v q v v (11)   2 22 12 211 e q v v 66 12q g 1e : young's modulus in the longitudinal to fiber direction. 2  e : young's modulus in the transverse direction to the fiber. 12  v , 21v : poisson's ratios of the composite material. 12  g : shear modulus of the composite material. i a. deliou et alii, frattura ed integrità strutturale, 60 (2022) 30-42; doi: 10.3221/igf-esis.60.03 35 the indices 1 and 2 refer to the direction longitudinal and perpendicular to the fibers. this constitutive law for a layer of stacking order k in the laminate (fig. 1) ,is not ,in general, that of the structure. when the orientation of the fibers changes, the matrices base change, makes it possible to express the tensor of the stresses in the reference mark of the plate (x, y) according to the transformed reduced stiffness matrix:                               11 11 16 12 22 26 16 26 66 x x y y xy xy q q q q q q q q q (12) in the case of a symmetrical composite plate working only as a membrane, its forces will be expressed in the form [6]:                             0 11 12 16 0 21 22 26 0 61 62 66 xxx y yy xy yx n a a a n a a a n a a a (13)   ija : membrane stiffness matrix. with:     1 1 ( )  n ij k k ij k a h h q (14)  kh , 1  kh : coordinates of the layer k along the z axis. n : total number of layers. according to eqn. (13) the plane strain  0ε is equal to:                              0 1  11 12 16 0 21 22 26 0 61 62 66 xx x yy y xyyx a a a n a a a n a a a n (15) in the case of the balanced symmetrical laminate, working in uni-axial tension we have:             0 0 0 1,1   2,1   3,1   t xx p x t yy p x t xy p x a n a n a n (16) and:         1  p ija a (17) by substituting eqns. (16) in the matrix form (12), and for a layer of order k, we find that: a. deliou et alii, frattura ed integrità strutturale, 60 (2022) 30-42; doi: 10.3221/igf-esis.60.03 36                                          11 12 16 12 22 26 16 26 60 1,1 2,1 3,1 t xx p t t yy p x k t pxy kk q q q a q q q a n aq q q in the (natural) orthotropic plane we have:                11 22 12 t t t k                       1,1 2,1 3,1 p t ij p xk k p k a t q a n a (18) with:   t             2 2 2 2 2 2 2 2 c s sc s c sc sc sc c s (19) where  cosc and  sins we put:                             1 2 12 1,1 2,1 3,1 p pk pk k r a r t q a r a (20) so, formula (18) can be rewritten in the following form:                           11 1 22 2 1212 t t t x k t k k r r n r (21) and by the computation of the tensor of stresses in the orthotropic coordinate system, one can use the energy criteria to predict the limits of membrane forces that the laminate can withstand. these criteria must be applied successively to each ply constituting the laminate, for orientations from 0° to 90° with a step of 1. the membrane force applied to each ply constituting the laminate will be obtained as follows:       2 22 1   32 1 22 2 2 1              t x k n r rr k r r xyx y s (22) the use of the ashkenazi criterion is possible if the breaking stress of the bend oriented at 45° is introduced. to determine the ultimate membrane force either in tension or in compression, we can use the tensor criterion of tsaiwu and find the solution to the following equation:          22 2 2    2 2 211 1 22 2  12 1 2 66 3 1 1 2 2 (       )    ( )    1 0t tx xk kf r f r f r r f r n f r f r n (23) a. deliou et alii, frattura ed integrità strutturale, 60 (2022) 30-42; doi: 10.3221/igf-esis.60.03 37 using the theory of the maximum stress, we determine the various modes of failure by the substitution of the components of the tensor of the stresses in the equation defining the criterion of the maximum stress theory: we have the rupture forces as:    1 t x k x n r    2 t x k y n r (24)    3 t x k s n r therefore, the membrane force applied to each layer,  tx kn , is the minimum of the forces obtained by the last three modes. then, the limit force capable of avoiding the breaking of the least resistant layer, is determined for each failure criterion. results and discussion material used he material examined is a unidirectional composite of kevlar fiber and epoxy resin. it is currently one of the most industrially developed composite families, especially in the production of high-performance parts. its advantages are: low density, high tensile strength, low cost, and high impact resistance. its drawbacks include low compressive properties and degradation in sunlight [34] the elastic constants and the mechanical characteristics obtained experimentally for unidirectional kevlar / epoxy composites (h: the total thickness of the composite plate , vf = 0.6 is the volume fraction of the fiber) are [33]: ( g/m3 ) e1(gpa) e2(gpa) g12(gpa) 21v xt(gpa) yt(gpa) xc(gpa) yc(gpa) s(gpa) t(gpa) h(mm) 1380 80 5.5 2.2 0.34 1.4 0.335 0.03 0.1358 0.049 48.9 8 table 1: properties of kevlar/epoxy. ultimate tensile strengths of laminates figs. 2 and 3 represent the variation of the ultimate tensile force as a function of the orientation of the fibers of the layers composing the laminate [/-]s ranging from 0° to 90°. it is noted that with the orientation of the layers  = 0 °, the ultimate tensile forces obtained by all the criteria are similar and are maximum. in the interval of 0 ° <  <28 °, we notice that there are different spectra of curves which represent the variation of the ultimate tensile force for each criterion. with this interval of angle of orientation, we notice on fig. 3 a very fast reduction of the forces of membrane; and with breaks of the fibers and shears of the matrix, the criteria of rupture considered, do not produce the same ultimate values and become very different as the degree of anisotropy increases. once  reaches the value 28 °, and with the exception of the theory of maximum stress, the curves tend to have the same values. as one moves away from  = 28 ° and approaches 90 °, the membrane forces become more and more equal, monotonous and take more or less the form of a straight line. they then converge parallel to the axis of the abscissa. at this stage, the tensile breaking stresses of the matrix, are responsible. t a. deliou et alii, frattura ed integrità strutturale, 60 (2022) 30-42; doi: 10.3221/igf-esis.60.03 38 moreover, according to fig. 2, the energy failure criteria provide continuous curves, unlike the maximum stress theory (fig. 3) based on three distinct failure equations, where we have a discontinuity. on the other hand, the tensor criterion and the energy criteria have only one equation, therefore only one aspect of the curves. nevertheless, it is the tsai-hill criterion which gives good results comparing to experimental results for unidirectional composites in tension [22, 23, 35, 36, 37]. these three equations (formula 9) represent the three failure modes of the material. it is the outer layers oriented at + that rupture. the first mode is concerned with the orientation angles between 0 ° and 10 °, where we have the tensile breakage of the fibers. when the arrangement of the layer changes to an orientation equal to or less than 38 °. we have a shear failure of the matrix. as we approach the 90 ° angle, the low strength of the epoxy resin, causes it to rupture by tension; and this is the third mode of rupture of the material [35]. figure 2: evolution of the tensile membrane force nx of the laminated composite as a function of the orientation of the fibers obtained by various criteria figure 3: evolution of the membrane force in traction nx and the modes of damage of the laminated composite according to the orientation of the fibers obtained by the maximum stress theory. a. deliou et alii, frattura ed integrità strutturale, 60 (2022) 30-42; doi: 10.3221/igf-esis.60.03 39 strain tensor in figs. 4, we have respectively the tensor of elastic deformations of composite plates [15/-15] s, [45/-45] s, [70/-70]s, [45/0]s and [90/0]s. we see the absence of angular distortion for the balanced laminate [/-] s and [90/0] s. their mechanical behavior is similar to that of isotropic material. on the other hand, the plate [45/0] s presents, in addition to the linear deformations, a significant angular deformation. in addition, we have the absence of bending of the laminates due to the cancellation of the membrane-bending coupling matrix [b]. the shape of the curves of the components of the tensors of the deformations x , y and  xy is linear in form, up to the rupture as a function of the variation of the tensile force. these curves show that the mechanical properties of composites are purely elastic (absence of plastic phase unlike metallic materials) and depend on the orientations of the fibers. for each stacking sequence, we find more of the expansion strain in the (x) direction; contraction in the perpendicular (y) direction more or less important. it can be seen that the layered plate of stacking sequence [45/0]s exhibits an important angular distortion xyγ with elastic linear deformations of expansion in the (x, y) plane. besides, we have a deformation in the (x) direction, that is greater than in (y) axis. these different curves allow us to choose the cross laminate [90/0]s as the best stacking sequence, which must be taken into consideration. (a) (b) (c) (d) (e) figure 4: the components of the strain vector as a function of the tensile forces for the composite plate (a): [15/ -15]s,(b): [45/-45] s (c): [70/-70]s (d): [45/0]s and (e):[90/0]s a. deliou et alii, frattura ed integrità strutturale, 60 (2022) 30-42; doi: 10.3221/igf-esis.60.03 40 curves of boundary surfaces the boundary surface curve (failure envelope) of our composite, allows us to determine the surface where one of the stresses can be applied without breaking the material. in fig. 5, we have the failure envelopes obtained by the tsai-hill criterion in a plane form for shear stresses  12 0 ,   20 gpa  and 48.50 gpa ; they have elliptical shapes as can be seen (interaction between the normal stresses). the transverse stress is obtained as a function of the longitudinal stress and the different values of 12 . the boundary surface curve depends on the orientation of the fibers of the broken layer. it can be noticed that the increase in the shear stress causes the reduction of the surface of the rupture envelope disappears and when it reaches the ultimate shear stress. in addition, and unlike its configuration that obtained by the theory of maximum stress, indicates that the behavior of the material is not asymmetrical. the failure envelope (fig. 6) determined by the theory of maximum stress is characterized by the absence of the interaction between the two stresses 11 and  22 ,which clearly means that it is not a function of the shear stress. the curve consists only of horizontal lines and verticals exhibiting the shape of a rectangle. (a) (b) (c) figure 5: failure envelope by a plane of shears (a): 12τ 0 , (b): 12τ 20 gpa , (c):  12 48.7 gpa obtained with the criterion of tsai-hill. figure 6: failure envelope obtained by the maximum stress theory a. deliou et alii, frattura ed integrità strutturale, 60 (2022) 30-42; doi: 10.3221/igf-esis.60.03 41 conclusion he examined composite material is unidirectional kevlar / epoxy reinforcement. it is composed, in our case, of four layers whose arrangement constitutes symmetrical laminates [/-]s. our study allowed us to observe an elastic phase of the material until rupture, with the absence of the plastic phase. in addition, we noticed the absence of coupling between the tensile membrane force and the angular distortion of the material due to the balanced arrangement of the laminates. the study of the deformations for different stacking sequences made us choose the cross laminate as the best configuration. among variety of failure criteria, we have chosen that of tsai-hill for unidirectional composites, especially when the orientation of the layers is in the vicinity of 0° and smaller than 28°. in addition, results obtained with then different criteria, are similar when moving forward 90°. the maximum stress theory makes it possible to determine three modes of rupture of the outer plies which are resistant. the curves of the envelopes of failure obtained by the criterion of tsai-hill, present elliptical shapes; on the other hand the theory of the maximum stress theory allowed us to obtain rectangles which are independent of the influence of the tangential component of the tensor of the stresses applied to the external layer. references [1] brandt, j. dreschler, k. and arendts, f.j. (1996). mechanical performance of composites based on various threedimensional woven fibre performs. composites science and technology, 56, pp. 381–386. doi: 10.1016/0266-3538(95)00135-2. [2] liu, k.s. and tsai, s.w. (1998). a progressive quadratic failure criterion for a laminate, composites science and technology, 58(7), pp.1023–1032. doi: 10.1016/s0266-3538(96)00141-8. [3] hill, r. (1963). elastic properties of reinforced solids: some theoretical principles. journal of the mechanics and physics of solids, 11, pp.357-372. doi: 10.1016/0022-5096(63)90036-x. [4] azzi, v.d. and tsai s.w. (1965). anisotropic strength of components. experimental mechanics, 5, pp. 286-288. doi: 10.1007/bf02326292 [5] tsai, s. w. and wu, e. m. (1971). a general theory of strength for anisotropic materials. journal of composite materials, 5(1), pp. 58–80. doi:10.1177/002199837100500106. [6] berthelot, j. m. ed. (2012). matériaux composites: comportement mécanique et analyse des structures, paris, lavoisier. [7] renard, j. ed. (2005). elaboration, microstructure et comportement des matériaux composites à matrice polymère. paris: hermes science. [8] puck, a. and schürmann, h. (2002). failure theories of frp laminates by means of physically based phenomenological models. composites sci. technol., 62(12-13), pp. 1633–1662. doi: 10.1016/s0266-3538(01)00208-1. [9] soden, p. (1998). lamina properties, lay-up configurations and loading conditions for a range of fibre-reinforced composite laminates. composites science and technology, 58(7), pp.1011–1022. doi:10.1016/s0266-3538(98)00078-5. [10] hinton, m., kaddour, a. and soden, p. (2002). a comparison of the predictive capabilities of current failure theories for composite laminates, judged against experimental evidence. composites science and technology, 62(12-13), pp.1725–1797. doi:10.1016/s0266-3538(02)00125-2. [11] yeh, h.-l. (2003). quadric surfaces criterion for composite materials. journal of reinforced plastics and composites, 22(6), pp. 517–532. doi:10.1106/073168403023274. [12] irhirane, e. h., echaabi, j., aboussaleh, m., hattabi, m. and trochu, f. (2008). matrix and fibre stiffness degradation of a quasi-isotrope graphite epoxy laminate under flexural bending test. journal of reinforced plastics and composites, 28(2), pp. 201–223. doi:10.1177/0731684407084213. [13] christensen, r. m. (1990). tensor transformations and failure criteria for the analysis of fiber composite materials part ii: necessary and sufficient conditions for laminate failure. journal of composite materials, 24(8), pp. 796– 800. doi:10.1177/002199839002400801. t a. deliou et alii, frattura ed integrità strutturale, 60 (2022) 30-42; doi: 10.3221/igf-esis.60.03 42 [14] sauder, c., lamon, j. and pailler, r. (2002). thermomechanical properties of carbon fibres at high temperatures (up to 2000 °c). composites science and technology, 62(4), pp.504. doi:10.1016/s0266-3538(01)00140-3. [15] deteresa, s. j. and larsen, g. j. (2003). reduction in the number of independent parameters for the tsai—wu tensor polynomial theory of strength for composite materials. journal of composite materials, 37(19), pp.1769– 1785. doi: 10.1177/002199803035183. [16] arola, d. and ramulu, m. (1997). orthogonal cutting of fiber-reinforced composites: a finite element analysis. international journal of mechanical sciences, 39(5), pp.597–613. doi: 10.1016/s0020-7403(96)00061-6. [17] mahdi, m. and zhang, l. (2001). a finite element model for the orthogonal cutting of fiber-reinforced composite materials. journal of materials processing technology, 113(1-3), pp.373–377. doi: 10.1016/s0924-0136(01)00675-6. [18] mbacke, m.a. (2013). characterization and modeling of the mechanical behavior of 3d braided composites: application to the design of ngv tanks, ph.d. dissertation national school of mines of paris. [19] cazeneuve, c., joguet, p., maile, j.-c. and oytana, c.(1992). predicting the mechanical behaviour of kevlar-epoxy and carbon-epoxy filament wound tubes, composites, 23(6), pp. 415-424. [20] rizzo r. r. and vicario, a. a.(1970).a finite element analysis of laminated anisotropic tubes part 1 characterization of the off-axis tensile specimen, journal of composite materials, 4, pp. 344-359. [21] herring, h. w. baucom, r. m. and pride r. a. (1969). mechanical behaviour of boron/epoxy and glass/epoxy filament-wound cylinder under various loads, nasa tn d-5050. [22] jones, r. m. ed.(2018). mechanics of composite materials, boca raton, , taylor & francis. doi: /10.1201/9781498711067 [23] hinton, m.j., soden, p.d. and kaddour, a.s. (2004). failure criteria in fiber-reinforced-polymer composites, elsevier, oxford. elsevier science. pp.30-51. doi: 10.1016/b978-008044475-8/50003-2. [24] li, s., sitnikova, e., liang, y. and kaddour, a-s. (2017). the tsai-wu failure criterion rationalised in the context of ud composites, composites: part a . doi: 10.1016/j.compositesa. 2017.08.007. [25] chevalier, y. (2000). critères de rupture: approche macroscopique, matériaux composites, techniques de l’ingénieur, a 7755, pp.1-16, paris. [26] monnier, c. (1996). influence of the temperature and of the composition of the composite on the damage mechanisms of composite tubes and tanks under different pressure laws, ph.d. dissertation, lille-flandres -artois university of science and technology. [27] somoh, g.b.k. (2013). design and mechanical characterization of composite parts made by hot pressing molding, ph.d. dissertation, paris national school of mines. [28] norris, c. b. (1985). strength of orthotropic materials subjected to combined stresses, report n°1816, us forest product laboratory, in astm stp 853, pp. 381-395. [29] daniel, i.m. (2007). failure of composite materials, strain 43(1), pp.4-12. doi: 10.1111/j.1475-1305.2007.00302.x [30] fischer, l. (1967). optimization of orthotropic laminates. journal of engineering for industry, 89(3), pp. 399-402. doi:10.1115/1.3610064. [31] ashkenazi, e. k. (1965). problems of the anisotropy of strength, polymer mechanics, 1(2), pp.60-70. doi: 10.1007/bf00860686. [32] wang, j. olortegui-yume, j. müller, n. (2010). stress and vibration analysis for woven composite axial impeller. proceedings of asme 2010 power conference power, chicago, illinois, usa. 13-15 july. [33] jaafar, m. (2018). experimental study and numerical simulation of the machining of honeycomb materials. application to milling of nomex® and aluminum structures, ph.d. dissertation, university of lorraine. [34] kaw, autar k. (2006). mechanics of composite materials, boca raton, taylor & francis. doi.10.1201/9781420058291 [35] chevalier, y. (2000). comportements élastique et viscoélastique des composites, techniques de l’ingénieur, a 7750, pp.1-32, paris. [36] aucher, j. (2009). comparative study of the behavior of composites with a thermoplastic or thermosetting matrix, ph.d. dissertation, rouen national institute of applied sciences. [37] michopoulos, j.g.(2008). on the reducibility of failure theories for composite materials, composite structures 86, pp.165–176. doi: 10.1016/j.compstruct.2008.03.008. << /ascii85encodepages false /allowtransparency false /autopositionepsfiles true /autorotatepages /none /binding /left /calgrayprofile (dot gain 20%) /calrgbprofile (srgb iec61966-2.1) /calcmykprofile (u.s. web coated \050swop\051 v2) /srgbprofile (srgb iec61966-2.1) /cannotembedfontpolicy /error /compatibilitylevel 1.4 /compressobjects /tags /compresspages true /convertimagestoindexed true /passthroughjpegimages true /createjobticket false /defaultrenderingintent /default /detectblends true /detectcurves 0.0000 /colorconversionstrategy /cmyk /dothumbnails false /embedallfonts true /embedopentype false /parseiccprofilesincomments true /embedjoboptions true /dscreportinglevel 0 /emitdscwarnings false /endpage -1 /imagememory 1048576 /lockdistillerparams false /maxsubsetpct 100 /optimize true /opm 1 /parsedsccomments 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/pdfxoutputintentprofileselector /documentcmyk /preserveediting true /untaggedcmykhandling /leaveuntagged /untaggedrgbhandling /usedocumentprofile /usedocumentbleed false >> ] >> setdistillerparams << /hwresolution [2400 2400] /pagesize [612.000 792.000] >> setpagedevice microsoft word numero_30_art_27 c. barile et alii, frattura ed integrità strutturale, 30 (2014) 211-219; doi: 10.3221/igf-esis.30.27 211 focussed on: fracture and structural integrity related issues considerations on the choice of experimental parameters in residual stress measurements by hole-drilling and espi c. barile, c. casavola, g. pappalettera, c. pappalettere dipartimento di meccanica, matematica e management, politecnico di bari, viale japigia 182, bari, italy claudia.barile@poliba.it abstract. residual stresses occur in many manufactured structures and components. great number of investigations have been carried out to study this phenomenon. over the years, different techniques have been developed to measure residual stresses; nowadays the combination of hole drilling method (hd) with electronic speckle pattern interferometry (espi) has encountered great interest. the use of a high sensitivity optical technique instead of the strain gage rosette has the advantage to provide full field information without any contact with the sample by consequently reducing the cost and the time required for the measurement. the accuracy of the measurement, however, is influenced by the proper choice of several parameters: geometrical, analysis and experimental. in this paper, in particular, the effects of some of those parameters are investigated: misknowledgment in illumination and detection angles, the influence of the relative angle between the sensitivity vector of the system and the principal stress directions, the extension of the area of analysis and the adopted drilling rotation speed. in conclusion indications are provided to the scope of optimizing the measurement process together with the identification of the major sources of errors that can arise during the measuring and the analysis stages. keywords. residual stress; electronic speckle pattern interferometry (espi); hole drilling method (hd); process parameters; titanium grade 5. introduction he stress field existing in some materials without application of an external source of stress, such as loads or thermal gradients, is known as residual stress. these residual stresses are generated in almost all manufacturing processes such as machining, grinding, forming, rolling, casting, forging, welding, heat treatment, etc. or may occur during the life of structures. the hole drilling method is one of the most widely used techniques for measuring residual stresses [1, 2]. this technique consists in the localized removal of stressed material and in measuring the strain field consequent to the relieved stresses. the hole drilling method using strain gauge rosettes [3, 4] is a consolidated approach for stress determination and it follows the astm test standard [5]. even though strain gauges are usually used to measure these displacements, they have some disadvantages: the specimen surface has to be flat and smooth so that the rosettes can be attached, the surface of the material has to be accurately prepared, the hole has to be drilled exactly in the center of the rosette in order to avoid eccentricity errors, and time and costs associated with installing rosettes are consistent. furthermore the amount of available data is limited: for each measurement, only three discrete readings are available (six in the case of some special rosettes), just sufficient to fully characterize the in-plane residual stresses. t c. barile et alii, frattura ed integrità strutturale, 30 (2014) 211-219; doi: 10.3221/igf-esis.30.27 212 the difficulties connected with the use of strain gauges could be promisingly overcame by using optical techniques [6]. during the past years, in fact, different approaches were explored for implementing hole drilling with optical methods. several techniques can be used to generate fringe patterns, from which the local displacements, in the neighborhood of the hole, can be calculated. the use of moiré interferometry for residual stresses determination was investigated in many situations since mcdonach et al. [7] and martínez et al. [8]. however, bonding a grating can also be time consuming. the feasibility of using holographic interferometry was shown by antonov [9]. hung et al. [10] have used shearography in conjunction with a small ball indentation instead of a hole and also a phase shift shearography [11] was adopted. also the possibility to release residual stresses by using local heat treatment, as in [12], was used by pechersky et al. [13] combined with digital speckle pattern interferometry (dspi). instead zhang [14] has investigated the practicability of the combination between dspi and hole drilling. electronic speckle pattern interferometry (espi) which is an optical method based upon the speckle effect [15] has been increasingly used in the last decades. espi was successfully used to measure displacement field in anisotropic specimen made by selective laser melting [16-18], or orthotropic materials [19] as laminated wood [20] but also in combination with hole drilling method to evaluate the residual stress relieving [21] avoiding rigid-body motions [22]. in this paper the advantages of using espi technique in contrast to the classical method are underlined. moreover all the parameters connected with the adoption of the espi technique that can be considered as a source of errors are analyzed and discussed. in defining the set-up it is necessary to have a good control of all the geometrical parameters involved, such as the angles that define the illumination and detection directions. if their values are not accurately evaluated this introduces an error in the determination of the displacement field which introduces an error in the calculation of the stress field [23]. another factor that must be taken into account is that, in espi, displacement are measured along the sensitivity vector. in this paper the influence of the relative angle between the sensitivity direction and the principal stress is evaluated. another important factor is the choice of the drilling rotation speed. rotation speed, in fact, can affect the heat input to the material during the drilling process modifying the plasticization zone and it can affect the dimension of the drilling chips, introducing problems connected with the choice of the internal radius of analysis area [24, 25]. also the combination of these effects [26, 27] must be taken adequately into account if high accuracy measurements are required. classification of some possible sources of errors in espi-hdm n this section the entire measurement system including espi and hole-drilling equipment will be described as well as the list of potential sources of errors connected with the system, the analysis technique and the hole drilling process. also the magnitude of the potential errors introduced will be estimated. figure 1: experimental set-up for espi+hdm measurements. the espi hole-drilling measurement system used in this work is schematically reported in fig. 1. a beam from a dpss laser source is splitted into two beams and focused into two monomode optical fibers. one beam is collimated and illuminates the sample, while the second beam passes through a phase shifting piezoelectric system and then it goes to the ccd camera where interferes with the light diffused by the optically rough surface of the specimen. i x c. barile et alii, frattura ed integrità strutturale, 30 (2014) 211-219; doi: 10.3221/igf-esis.30.27 213 initial phase and final phase are evaluated by the four-step phase shifting technique, once the initial and the final phase are determined it is possible to calculate the amount of displacement of each point into the analysis area. the holes are drilled by means of a high speed turbine, electronically regulated; it is mounted on a precision travel stage in order to allow accurate positioning of the drilling device. experimental measurements were performed on a titanium grade 5 specimens. geometrical parameters the geometry and mutual position of laser, ccd and specimen should be accurately defined to correctly measure the displacement map. the xyz reference system of the specimen and the x’y’z’ reference system of the ccd camera are considered as shown in fig. 2. to exactly calculate strains from measured displacements, it is necessary to evaluate the pixel size along x and y directions, this means that the angles of ccd camera with respect to the specimen reference system xyz are needed. the α2 angle defines the x axis and the x’ axis; the β2 angle defines the z axis and the z’ axis; the γ2 angle defines the y axis and the y’ axis. figure 2: schematic of the geometrical set-up with the ccd camera and the specimen. moreover, to calculate strains from measured displacements, it is necessary to know the phase changing of the pattern, detected during tests, and the sensitivity of the optical set up that depends on the geometry of the illumination system. due to the cylindrical symmetry of the illumination beam around the propagation direction of the laser, only two angles are necessary in this case to relate the specimen reference system and the illumination reference system. being x’’y’’z’’ the illumination beam reference system, the α1 angle defines the x axis and the x’’ axis, while the β1 angle defines the z axis and the z’’ axis. these geometric angles can be initially measured by a goniometer. the uncertainty in this measurement is estimated to be δ=±2° because of the difficulties to correctly positioning the goniometer inside the measurement system. in order to assess the influence in the geometrical parameters measuring of an error on the results in terms of measured stress, simple experimental tests were run. rectangular cross section titanium specimen was subjected to three point bending load and induced stresses were measured as shown in fig. 3. the profile of the induced stresses was measured. the angle values were α1=42.5°; β1=0°; α2=24°; β2=0°; γ2=0°. then stress profile was recalculated by hypothesizing an error ±2° on each of the considered angles and compared in order to detect the error on stress values δxx. figure 3: top view of the three-point bending load frame. c. barile et alii, frattura ed integrità strutturale, 30 (2014) 211-219; doi: 10.3221/igf-esis.30.27 214 it was found that a ±2° of the in-plane detection angle α2 can introduce the higher error on the measured stress profile with respect to the other angles. fig. 4 shows the effect of an error δα2=±2° while in tab. 1 are reported the numerical results and the effects in terms of percentage error on the calculated stress profile. figure 4: differences in calculated stress in correspondence of an error of δα2=+2° (rumble, blue dots) and δα2=-2° (squared, red dots) with respect to the measured angle depth [mm] σxx [mpa] (α2=24°) σxx [mpa] (α2=22°) σxx [mpa] (α2=26°) δσxx % (δα2=-2°) δσxx % (δα2=+2°) 0.16 -393 -396 -389 0.6 1.2 0.32 -314 -321 -305 2.2 2.9 0.48 -268 -279 -255 3.9 5.0 0.80 -213 -229 -195 7.5 8.4 table 1: calculated stress xx for measured α2 = 24° and percentage errors for δα2=±2°. analysis area definition the size of the analysis area can affect the results in terms of residual stresses (fig. 5). if the radius of the inner circle is too small, error can arise due to the inclusion of some bad pixel in the analysis area due to some chips deposited near the edge of the hole. on the other side, if the outer radius is too large, a region of very small deformations is considered and this can lead to introduce an error especially in the case where low stresses have to be measured in material with high young modulus. in order to evaluate the influence of the analysis area, a bending stress state was induced on the specimen. the stress field was initially measured adopting the values of the inner radius (rint) and the outer radius (rext) commonly used in this kind of experiments. this values are usually defined in terms of ratio with the radius of the drilled hole (rhole), and it is common use to adopt 2 intint hole r r r   . and 4extext hole r r r   .n order to highlight the influence of rint on the obtained stress values, a new calculation was performed by changing the inner radius ratio in the range rint ∈ [2,2.7] and keeping rext unchanged. analogously, the outer radius ratio was changed in the range rext∈ [3,4.36] while keeping rint constant. the upper value 4.36 of the rext range was limited by the image dimensions. tab. 2 reports the stress values for the default radius of rext=4 and the percentage change of stresses using different rext. fig. 6 shows di difference in terms of stress profiles calculated with respect to the reference values rext=4. c. barile et alii, frattura ed integrità strutturale, 30 (2014) 211-219; doi: 10.3221/igf-esis.30.27 215 figure 5: screenshot of the area of analysis included between the outer circle (dashed line) and the inner circle (dotted line). the solid line identifies the drilled hole. depth [mm] σxx [mpa] (rext=4) σxx [mpa] (rext=3) |δσxx %| (δrext=-1) σxx [mpa] (rext=3.5) |δσxx % | (δrext=-0.5) σxx [mpa] (rext=4.36) |δσxx %| (δrext=+0.358) 0.04 148 131 11.5 142 4.0 150 1.3 0.12 126 118 6.3 124 1.6 128 1.6 0.20 103 101 1.9 102 0.9 103 0.0 0.28 103 96 7 99 3.4 107 3.9 0.36 68 72 5.8 70 2.9 68 5.5 table 2: summary of the calculated stress for the default radius of rext=4 and the percentage change of stresses δσxx using different rext. figure 6: plot of the difference in terms of measured stress at different depths. the difference are calculated for three different values of the external radius with respect to the reference value rext=4 it can be observed that increasing the external radius of analysis to the maximum value rext =3.48 mm (rext=4.36), which means an 8.95% of variation with respect to the default value, calculated stress at 0.36 mm depth changes about 5.5 %. analogously, decreasing the external radius of analysis to the value rext=2.4 mm (rext=3), which means a 25% of variation with respect to the default value, the calculated stress at 0.36 mm depth changes about 5.8 %. from fig. 5 it can also infer that the maximum difference (17 mpa) is obtained by using the smallest value of external radius in correspondence of the smallest depth, that is to say at about 11.5 % of variation. this attitude could be connected to the fact that reducing the c. barile et alii, frattura ed integrità strutturale, 30 (2014) 211-219; doi: 10.3221/igf-esis.30.27 216 amount of data for the calculation of residual stress introduce a variation especially in the case when small amount of displacement need to be measured as it happen in the very first step. a further investigation on analysis area was performed by keeping constant the radius ratio of the external circle of analysis rext=4 and by changing the value of rint (fig. 7). tab. 3 summarizes the corresponding numerical stress values with the indication of the percentage variation with respect to the stresses calculated by using the default value rint=2. depth [mm] σxx [mpa] (rint=2) σxx [mpa] (rint=1.25) |δσxx %| (δrint=-0.75) σxx [mpa] (rint=1.5) |δσxx %| (δrint=-0.5) σxx [mpa] (rint=2.5) |δσxx %| (δrint=+0.5) 0.04 148 159 7.4 148 0 146 1.3 0.12 126 121 3.9 122 3.2 135 7.1 0.20 103 85 17.4 94 8.7 115 11.6 0.28 103 104 9.7 107 3.8 99 3.9 0.36 68 56 17.6 62 8.8 73 7.3 table 3: summary of the calculated stress for the default radius of rint=2 and the percentage change of stresses δσxx using different rint. figure 7: plot of the difference in terms of measured stress at different depths. the difference are calculated for three different values of the internal radius with respect to the reference value rint=2 it can be observed that by reducing the internal radius of analysis to the minimum value rint =1 mm (rint=1.25), which means a 37.5% of variation it is possible to observe a variation in the calculated stress up to 17.6 %. analogously, by increasing the internal radius of analysis to the value rint=2 mm (rint=2.5), which means a 25% of variation with respect to the default value, the calculated stress shows a maximum variation of about 11.6 %. from fig. 6 it is possible to infer that, in this case, the entity of the variation doesn’t appear to be in some way connected to the depth. variation stays still quite low if the rint=1.5 ratio is used while the maximum difference (18 mpa) it is obtained by using the smallest value of the internal radius and this could be connected to the fact that by reducing to much the position of the inner circle of analysis, edge effects and bad quality pixel are introduced in the calculation so that an increment of the error can be found. sensitivity vector it needs to be underlined that in the measurement system displayed in fig. 1 the in-plane displacements consequent to the stress relaxation are measured only along the x direction. in this sense the system appears to be different respect to the strain gage rosette where each extensimeter grid measures strain along different directions. the measured amount of displacement depends on the angle between the relieved stress and the sensitivity vector. if one applies a perfect uniaxial load, as tensile or simple bending test, the stress field can be identified by the maximum principal stress σ1 while the minimum principal stress can be put equal to 0. if measurements are executed with σ1 direction overlapped to the sensitivity vector, the relieved strain is proportional to σ1 according to the hooke’s law. on the other hand, if the sample is positioned inside the measurement system so that the σ1 direction is perpendicular to the sensitivity vector, the relieved strain is proportional to ν.σ1 according to the transversal contraction of the material. in view of these observations it appears interesting to understand how the accuracy of the measurement can be affected by the orientation of the principal c. barile et alii, frattura ed integrità strutturale, 30 (2014) 211-219; doi: 10.3221/igf-esis.30.27 217 stresses with respect to the espi sensitivity direction. to this scope a specimen was bent in a four-points frame to obtain an uniaxial stress state with an applied stress σ1=133 mpa and σ2=0 mpa. results can be summarized as it follows:  in all cases the θ angle between the maximum principal stress and the x axis was correctly identified and with a small percentage error. it was found a value of θ=-0.45° for measurement in which the specimen is oriented with the maximum principal stress parallel to the x axis and θ=-0.24° when the specimen is oriented perpendicularly to the x axis;  the measurement of the maximum principal stress is not significantly affected by the orientation of the specimen; the entity of the error is about 10 % and this is a value consistent with errors reported in other studies [28,29];  concerning with the measurement of the minimum principal stress and in particular to its value along the thickness it was found that better results are obtained when the longitudinal axis of the specimen is oriented at 90° with respect to the x direction that is to say when the minimum stress is oriented along the sensitivity direction of the espi system (tab. 4). specimen angle (°) σ2 espi (mpa) σ2 expected(mpa) δ (mpa) 0 13.2 2.3 11.0 90 5.7 2.3 3.4 table 4: results of the measurement of the minimum principal stress, σ2, at 0.4 mm. results seem to be in contrast with the general theory that favors the overlapping of σ1 with the sensitivity vector, but this attitude could be justified considering that the amplitude of load applied in all cases is large enough to be detected at all slopes. the limit condition could be reached decreasing the four-point bending load up to reduce at minimum the number of fringes in correspondence of different angle from the sensitivity vector. drilling speed the effects of the drilling speed have also been analyzed. an electronic controlled drilling machine is used to drill the holes. holes are drilled at three different velocities: 5000 rpm, 35000 rpm, 50000 rpm. the first and the last values represent, respectively, the minimum and the maximum rotation speed attainable by the drilling system. espi was used to detect the displacement map in correspondence of each drilling step. also in this case specimen were loaded in a fourpoint bending frame in order to introduce a well-known stress field. as it can be inferred from fig. 8 the average value of the measured stress state is coherent with the expected theoretical value and almost independent from the drilling speed. however data corresponding to lower speed appear more scattered than data recorded at the maximum speed. in fact the standard deviation for the measurement at 5k rpm is st.dev5k=26.6 mpa that is to say about 20 % of the expected value. this value decreases at 35k rpm being st.dev35k=8.8 mpa that is to say about 6 % of the nominal expected value and it reaches the minimum at 50k rpm where it is st.dev50k=3.9 mpa that is to say less than 3 % of the expected theoretical value. in other words the accuracy and the repeatability of the measurement diminishes by decreasing the rotation speed. this occurrence can be tracked back to the quality of the drilled hole, as reported in fig. 9, left image refers to a hole drilled at 5000 rpm, middle image refers to a hole drilled at 35000 rpm and right image refers to a hole drilled at 50000 rpm. the quality of the hole profile appears to be compromised at lower speed. figure 8: plot of the measured stress at the different rotations speed of the cutter. c. barile et alii, frattura ed integrità strutturale, 30 (2014) 211-219; doi: 10.3221/igf-esis.30.27 218 figure 9: image of the drilled holes obtained at the optical microscope 20x. conclusions ole-drilling method is one of the most adopted and reliable approach for measuring residual stress and it can takes advantages by its application in combination with espi because this can result in cheaper and faster measurements. however getting accurate results with this technique requires a good control over the many factors that can affect the final results. in this paper a review of some major sources of errors were presented and their effects were evaluated for the case of measurements on ti grade 5 sample. a good evaluation of the geometrical parameters it is relevant. in particular, for the adopted configuration, it is important to correctly determine the illumination angle. it was found that an error of ±2° on this parameter can introduce an error of about ±3.5 % on the final calculated stress. also the positioning of the area of analysis is important, in some cases, due to geometrical constraints, this area need to be reduced however it should be taken into account that error of the order of 15 mpa could be introduced if the external radius is reduced too much especially in the very first steps. similar results are obtained if the internal radius of analysis is changed too much with respect to the default value. finally it should be reminded that the final quality of the drilled hole is a key factor in determining a good measurement. this is a goal which is strictly connected with the particular material under study, its machinability and the use of proper drilling material. however, final quality is also related with the proper choice of the drilling rotation speed. this parameter must be optimized as a function of the material under study. in this paper, in particular, effects of drilling rotation speed were studied on ti grade 5. this is an interesting material to be studied in view of its very good strength-to-density ratio, and good corrosion resistance, properties that lead to an increasing demand of this material in aircraft industry [30]. it was found that much better quality is obtained by using higher velocity (50000 rpm), which is suggested therefore for measurements on this specific material. care must be taken, however, to avoid that fine chips resulting from drilling operations, at this speed, stick to the material degrading the quality of the speckle fringe pattern and, as a consequence, the accuracy of the measurement itself. references [1] rendler, n.j., vigness, i., hole-drilling strain-gage method of measuring residual stresses, exp. mech., 6 (1966) 577586. [2] astm e387-92 standard test method for determining residual stresses by the hole-drilling strain gage method. annual book of astm standards, philadelphia: american society for testing and materials, 03.01 (1992) 747–753. [3] schajer, g.s., roy, g., flaman, m.t., lu, j., hole drilling and ring core methods, lu j (ed) handbook of measurement of residual stresses. society for experimental mechanics, bethel, (1996) 5–35. [4] schajer, g.s. advances in hole-drilling residual stress measurements. exp mech., 50 (2009) 159-168. [5] standard test method for determining residual stresses by the hole-drilling strain-gage method standard e837-08. american society for testing and materials, west conshohocken, pa, (2008) [6] furgiuele, f.m., pagnotta, l., poggialini, a., measuring residual stresses by hole drilling and coherent optics techniques: a numerical calibration, j. eng. mater. technol., 113 (1991) 41–50. [7] mcdonach, a., mckelvie, j., mackenzie, p.m., walker, c.a., improved moiré interferometry and applications in fracture mechanics, residual stresses and damage composites, exp. technol., 7 (1983) 20–24. [8] martínez, a., rodríguez-vera, r., rayas, j. a., puga, h. j., fracture detection by grating moiré and in-plane espi techniques, opt. laser. eng., 39 (5-6) (2003) 525–536. h c. barile et alii, frattura ed integrità strutturale, 30 (2014) 211-219; doi: 10.3221/igf-esis.30.27 219 [9] antonov, a.a., inspecting the level of residual stresses in welded joints by laser interferometry, weld. prod., 30 (1983) 29–31. [10] hung, y.y., hovanesian, j.d., fast detection of residual stress in an industrial environment by thermoplastic-based shearography. sem spring conference on experimental mechanics, albuquerque, usa, (1990) 769–775. [11] hung, m. y. y., long, k. w., wang j. q., measurement of residual stress by phase shift shearography, opt. laser. eng., 27(1) (1997) 61–73. [12] barile, c., casavola, c., pappalettera, g., pappalettere, c., feasibility of local stress relaxation by laser annealing and x-ray measurement, strain, 49(5) (2013) 393-398. [13] pechersky m.j., miller r.f., vikram c.s., residual stress measurements with laser speckle correlation interferometry and local heat treating, opt. eng., 34 (1995) 2964–2971. [14] zhang j., two-dimensional in-plane electronic speckle pattern interferometer and its application to residual stress determination, opt. eng., 37 (1998) 2402–2409. [15] cloud, g. l., optical methods of engineering analysis, cambridge university press, new york (1995). [16] barile, c., casavola, c., pappalettera, g., pappalettere, c., mechanical characterization of slm specimens with speckle interferometry and numerical optimization, exp. applied mech., of conference proceedings of the society for experimental mechanics series, springer, newyork, ny,usa, 6 (2011) 837–843. [17] barile, c., casavola, c., pappalettera, g., pappalettere, c., experimental and numerical characterization of sinterized materials with speckle interferometry and optimization methods, proceedings of the 10th youth symposium on experimental solid mechanics (ysesm), chemnitz, germany, (2011) 35–36. [18] barile, c., casavola, c., pappalettera, g., pappalettere, c., mechanical characterization of slm specimens with speckle interferometry and numerical optimization, society for experimental mechanics sem annual conference and exposition on exp. and applied mech., 3 (2010) 2523-2529. [19] baldi, a., full field methods and residual stress analysis in orthotropic material. i linear approach, int. j. solids struct., 44 (25-26) (2007) 8229–8243. [20] barile, c., casavola, c., pappalettera, g., pappalettere, c., hybrid characterization of laminated wood with espi and optimization methods, proceedings of the society for experimental mechanics series conference, 3 (2013) 75–83. [21] sedivý, o., krempaszky, c., holý, s., residual stress measurement by electronic speckle pattern interferometry, 5th australasian congress on applied mechanics, acam 2007, brisbane, australia (2007). [22] schajer, g. s., steinzig, m., full-field calculation of hole drilling residual stresses from electronic speckle pattern interferometry data, exp. mech., 45(6) (2005) 526-532. [23] barile, c., casavola, c., pappalettera, g., pappalettere, c., residual stress measurement by electronic speckle pattern interferometry: a study of the influence of geometrical parameters, structural and integrity in life integritet i vek konstrukcija, 11(3) (2011) 177-182. [24] barile, c., casavola, c., pappalettera, g., pappalettere, c., drilling speed effects on accuracy of hd residual stress measurements, in: conference proceedings of the society for experimental mechanics series, 8 (2014) 119-125. [25] barile, c., casavola, c., pappalettera, g., pappalettere, c., remarks on residual stress measurement by hole-drilling and electronic speckle pattern interferometry, the scientific world journal, (2014). [26] steinzig, m., ponslet, e., residual stress measurement using the hole drilling method and laser speckle interferometry: part iii, exp. techniques, 27(5) (2003) 45–48. [27] barile, c., casavola, c., pappalettera, g., pappalettere, c., analysis of the effects of process parameters in residual stress measurements on titanium plates by hdm/espi, measurement: journal of the international measurement confederation, 48(1) (2014) 220-227. [28] steinzig, m., takahashi, t., residual stress measurement using the hole drilling method and laser speckle interferometry part iv: measurement accuracy, experimental techniques, 27(6) (2003) 59-63. [29] viotti, m.r., albertazzi jr., a.g., kapp, w., experimental comparison between a portable dspi device with diffractive optical element and a hole drilling strain gage combined system, optics and lasers in engineering, 46(11) (2008) 835-841. [30] casavola, c., lamberti, l., pappalettere, c., tattoli, f. a comprehensive numerical stress strain analysis of laser beam butt-welded titanium compared with austenitic steel joints, journal of strain analysis for engineering design, 45(7) (2010) 535-554. microsoft word numero_50_art_11_2543 b. benamar et alii, frattura ed integrità strutturale, 50 (2019) 112-125; doi: 10.3221/igf-esis.50.11 112 using a cohesive zone modeling to predict the compressive and tensile behavior on the failure load of single lap bonded joint benamar badr faculty of technology, university djillali liabes, sidi bel abbes, algeria. a_badroo@yahoo.fr mokhtari mohamed laboratoire rtfm, ecole nationale polytechnique maurice audin, oran, algeria. mokhtarimohamed44@yahoo.fr madani kouider laboratoire lmpm, university djillali liabes, sidi bel abbes, algeria. koumad10@yahoo.fr benzaama habib laboratoire labab, ecole nationale polytechnique maurice audin, oran, algeria. habenza@yahoo.fr abstract. the aim of this work is to analyze the failure behavior of a simple lap joint of type metal / metal consisting of 2024-t3 aluminum plate bonded with an araldite adhesive using the finite element method to predict damage of the metal in tensile and compressive load under the effect of geometric parameters such as the length of the overlap and the geometric shape of the two plates according to the overlap length. the numerical analysis is performed by the abaqus calculation code. the adhesive was modeled by an element of the czm cohesive zone. the adhesive will be submitted in mixed mode given the non-linearity of the two applied load. the calculation of the failure load will be determined according to the different parameters mentioned above. it is well demonstrated that the type of loading and the parameters taken into consideration condition the strength of the structure. the effect of these different parameters on the strength of the adhesive joint is presented as results by failure load curves. keywords. simple lap joint; czm (cohesive zone modeling); vcct (virtual crack closure technique); xfem (extended finite element modeling); tapered plates. citation: benamar, b., mokhtari, m., madani, k., banzaama, h., using a cohesive zone modeling to predict the compressive and tensile behavior on the failure load of single lap bonded joint, frattura ed integrità strutturale, 50 (2019) 112-125. received: 15.06.2019 accepted: 30.07.2019 published: 01.10.2019 copyright: © 2019 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. http://www.gruppofrattura.it/va/50/2543.mp4 b. benamar et alii, frattura ed integrità strutturale, 50 (2019) 112-125; doi: 10.3221/igf-esis.50.11 113 introduction dhesive bonding is frequently used to manufacture complex-shaped structures and in the several fields of engineering; easy manufacturing and possibility to joint different materials [1]. however, the problem of the single lap joints is the concentrated stress at the edges. this concentration is usually due to the misalignment of the two applied forces. many ideas have been proposed to reduce the stresses that occur at the end of the overlap. these ideas can be grouped into two categories: fracture parameter of adhesive and or geometric. groth [2] used the finite element method for predicting breakage in single-cover joints with a spit net. a large number of predictive techniques is available for bonded joints, either analytical or numerical. da silva et al. [3] provide extensive reviews of these methods for analytical methods and x. he [4] for finite element based techniques. analytical methods are easy to use, but they usually consider simplification assumptions [5]. for complex geometries and elaborate material models, a finite element analysis is preferable to obtain the stress distribution. fracture mechanics based methods use the fracture toughness of materials as the leading parameter for fracture assessment [6]. kaye and heller [7] developed an optimal design of free form bonded and double lap joints, with the aim of achieving reduced peel stresses on the bond line region. several parameters determine the quality of a bonded assembly. the strength of the adhesive and the elements to be assembled (brittle or ductile, strong or weak), as well as, the geometry of the joint and the assembled elements. we find the geometric shape of the single lap joint is the most studied in the behavior of assemblies. we find the experimental and numerical comparison work of barbosa et al. [8] who conducted a study on the effect of lap length, in which they concluded that while tronger and more brittle adhesives are recommended for joint geometries. banea et al. [9] also experimentally and numerically studied the strengths of joint adhesion. they concluded that failure is dominated by global adhesive yielding and the geometry influence. luca sorrentino et al. [10] have also studied the single-lap joint where they demonstrated the effect of surface treatments on the strength of assemblies. other works such as costanzo [11] and banea et al. [12], include the thermal effect on the strength of the adhesive joints. the effect of the length and depth of a parallel slot on the stress distribution at the mid-bond line and in the adherend was investigated by yan et al. [13] using the elastic finite element method. in the study of gültekin et al. [14], mechanical properties of different single lap joint configurations with different adherend width values subjected to tensile loading were investigated experimentally and numerically. in the work of pinto et al. [15], the cohesive zone models (czm) are widely used in delaminate on analysis. they not need an pre-existing of crack like (vcct) virtual crack closure technique [16, 17]. many different cohesive element (czm) formulations have been proposed [18, 19]. however, two main difficulties concerning cohesive elements robustness and their application to large-scale structures still exist. firstly, fine meshes are required to appropriate model, which leads to high, and sometimes unaffordable, computational requirements. secondly, recent findings indicate that the mixed-mode crack propagation predicted by cohesive elements might be unreliable because of an improper estimation of the energy dissipated during the fracture process. the current paper addresses this last difficulty. other technique implementation in abaqus® used without meshing again like the extended finite element modeling (xfem) [20]. it has used also by campilho et al. [21] for strength prediction of single and double-lap joints. the objective of this study is to evaluate by numerical simulation the effect of cohesive stiffness, cohesive strength and fracture energy of the adhesive in order to see their effect on the value of the failure load of the assembly type aluminum / aluminum under a compressive and tensile behavior. four overlap lengths and geometrical parameters modification named tapered have been selected, in order to see also their effect on the failure load of the joint. we also put into consideration the effect of the percentile variation of mode i and mode ii on the value of the failure load of the assembly, analyzing the numerical results show that the failure load increases as the adhesive have high strength especially in mode ii. cohesive interfaces and input parameter he separation path using the czm is entirely in the cohesive zone. the model is a linear tensile-separation law as represented in fig. 1, defined by a surface of nodes in a mesh without interaction between the surfaces. this technique of selecting the interface with failure parameters is quite different from those already used before for similar studies. it consists of drawing the complete assembled system in a single geometry, no assembly between the different elements. next, the orphan mesh existing in the abaqus calculation code is chosen and the mesh elements are a t b. benamar et alii, frattura ed integrità strutturale, 50 (2019) 112-125; doi: 10.3221/igf-esis.50.11 114 subsequently selected in the common plane between the plates, introducing the parameters of rupture of the adhesive. during loading, plate separation occurs when the failure conditions are satisfied. the cohesive law initially contains a linear regime up to a stress threshold that initiates a softening as the surfaces move away from each other until a separation translated by a null rigidity [22]. the stiffness parameter inputs (knn, kss and ktt) required by abaqus® are the module of the cohesive (e, g) material divided by its thickness [23]. when knn = young’s modulus / thickness of adhesive layer in normal direction; kss = shear’s modulus / thickness of adhesive layer in tangential direction 1; ktt = shear’s modulus / thickness of adhesive layer in tangential direction 2. a linear constitutive relationship between stresses (σ) and relative displacements (δ) is established (fig. 1). figure 1: the linear softening law for mixed-mode cohesive damage models. the model requires the knowledge of the local strengths (σu,i, i = i, ii, iii) and of the critical strain energy release rates (gic). damage onset is predicted using the following quadratic stress criterion: 2 2 2 1 1 1 if 0 = 0 if 0 i ii iii ui uii uiii                               (1) where σi (i = i, ii) represent the stresses at a given integration point of the interface finite element in each mode. mode i represents the local opening mode and mode ii, iii the shear mode at the interface. crack propagation was simulated by the linear energetic criterion. 1i ii iii ic iic iiic g g g g g g                     (2) the area under the minor triangle of fig.1 represents the energy released in each mode, while the bigger triangle area corresponds to the respective critical fracture energy. when eqn. (2) is satisfied damage propagation occurs and stresses are completely released, with the exception of normal compressive ones [24]. this energy is based on the cohesive damage evolution and it is defined using the benzeggagh–kenane criterion [25], with a linear softening law. fracture energies of gi = 0.3n/mm and gii = 0.6n/mm are used for normal (mode i) and shear (mode ii and mode iii) cohesive failures respectively as used by campilho et al. [26]. the introduced parameters in the calculation code abaqus are: ** materials ** *material, name=cohesive *damage initiation, criterion=quads b. benamar et alii, frattura ed integrità strutturale, 50 (2019) 112-125; doi: 10.3221/igf-esis.50.11 115 40, 24.1, 24.1 *damage evolution, type=energy, mixed mode behavior=power law, power=2.284 0.3, 0.6, 0.6 *damage stabilization 1e-05 *elastic, type=traction 10000. 10000., 10000. analysis he present study consists in a three-dimensional numerical analysis of tensile and compressive loaded (fig. 2) with different overlap length in the first, then with geometrical modification in the second. a non-linear material and geometrical analysis was performed, using plane strain rectangular 8-node and triangular 6-node finite elements. fig. 5 shows a detail of the mesh used at the assembly bond edge. in tensile behavior, the restraining and loading condition consists on clapping of the joint at one edge and applying a vertical restraint and tensile displacement at the opposite edge. the same thing in the compressive behavior but we restraint vertically all length except overlap region the both of the edge in order to favorite the separation, and the tensile replaced by the compressive displace. the choice of our geometric model in three dimensions, in single and double overlap with composite plates is standardized mokhtari [27, 28]. see also the works of benchiha [29] who carried out a study on the influence of defects and the work of bezzerrouki [30], who has carried out several studies in this line of research. the assembled plates are three-dimensional, except for the two-dimensional joint adhesive designed as an interface. the third dimension (the thickness) is geometrically zero; it is introduced in the stiffness properties (knn, kss, ktt). in this study, the joint adhesive was simulated as an interface. this modality allowed us to evaluate the release force under different parameters, such as adhesive, geometry and mechanical behavior. a) b) figure 2: single lap bonded joint geometry. a) tensile behaviour ; b) compressive behaviour. the boundary conditions are not identical for both the tensile and shear behaviors. for the tensile behavior, it is easy to provoke the debonding with a small bending of the plates, so that they align in the same axis of traction where the adhesive is solicited in mixed mode. on the other hand, it is difficult to favor or provoke the detachment in compression behavior. since the completely assembled system is free according to the normal, this results in large deformations in t b. benamar et alii, frattura ed integrità strutturale, 50 (2019) 112-125; doi: 10.3221/igf-esis.50.11 116 flexion and without detachment, hence the introduction of boundary conditions in the near vicinity of the overlap, where the adhesive is solicited purely in shear mode. thickness of the lower and upper adherend tp 2 mm free length of adherend lf 60 mm overlap length w 15 mm applied tensile (compression) displacement u 2 mm table 1: geometrical properties of single lap bonded. figure 3: representation of bonded systems in compression behavior without the conditions add. any interaction was introduced between bonded surfaces. the adhesive was modeled as an interface (zero thickness) with coh3d8 type elements and a number of more than 800 elements depending on the overlap length. debonding was simulated in the finite element model by keeping the same nodes on both adjacent faces of the overlap area. it is necessary to have an appropriate number of mesh elements in the overlapping region on which the damage properties are conditioned. in other words, when the number of nodes increases or decreases, there will be no convergence and subsequently damage (detachment). figure 4: separation presentation of a cohesive interface. the mesh in the assembly of all study structures is constructed by essentially identical elements in their sizes at the overlapping levels, as shown in the present figure. interface finite elements were used to simulate crack onset and growth, as well as to obtain damage in the adhesive layers. aluminum adherends, whose mechanical properties are presented in tab. 2, were used. tab. 3 shows the strength and failure parameters of the adhesive (araldite 420). these parameters are obtained by the experimental tests in mode i and in mode ii realized by campilho [26]. these properties were obtained experimentally in [24]. the dimensions of the geometries are presented in fig. 2. the location of the interface finite elements is shown in figs. 2 and 5. these elements were placed between the parents of aluminum adherends and these adherends were modeled as elastic-plastic solids with an approximate curve to the real (σ-ɛ) curve of aluminum (fig. 6). b. benamar et alii, frattura ed integrità strutturale, 50 (2019) 112-125; doi: 10.3221/igf-esis.50.11 117 figure 5: detail of the mesh and interface element. young’s modulus e 68960 mpa poisson’s ratio ν 0.3 elastic limit stress σe 220 mpa table 2: mechanical properties of the adherend used [1] normal stiffness knn 9.25 x 105 gn/m3 shear stiffness kss = ktt 11.85 x 105 gn/m3 normal strength snn 40 mpa shear strength sss = stt 24.1 mpa mode i fracture energy gi 0.3 n/mm mode ii fracture energy gii = giii 0.6 n/mm table 3: elastic, strength and fracture properties of the adhesive used [26]. figure 6: experimental stress–strain curve of the aluminum 2024t3 [31]. the behavior of the aluminum plates used in this study is elastic-plastic. the properties introduced in the calculation code for the elastic part are mentioned in tab. 2. whereas for the plastic part, they are drawn directly from the curve of fig. 6 [31]. in the assembly, the plates solicit the joint adhesive to complex behaviors at different levels. it is therefore important to take notes and analyze the lamination caused by the axial loads on the assembled system just before detachment. b. benamar et alii, frattura ed integrità strutturale, 50 (2019) 112-125; doi: 10.3221/igf-esis.50.11 118 equivalent stress measurements of von misses were taken to identify the plasticization following the exceeding of the elastic limit. figure 7: behavior of the plates before separation. for the free tensile behavior, plasticization stresses are observed at very low levels which are localized in the bending zones and in order to have the alignment of the plates. but in figs. b) and c) where the plates are not free plasticization stresses are relatively high at different levels, they are located in the plates to the edges of the cover. for the notched plates, which explains their advantages, it is the distribution of the loads on the recovery length which will subsequently make the middle of the adhesive active and have more transfer of constraints. figure 8: behavior of notched plates before debonding. fig. 8 shows the mechanical behavior of notched plates just before debonding. in the case of free or non-free tension, the plastification stresses have very low levels at different concentrations. this is seen in the edges of the lap and at the notch. on the other hand, they reach maximum values at the interface, in the compression behavior, with relatively high levels. cohesive properties effects he edges of an adhesive joint are always tighter than the rest. from these zones, the separation takes place, the geometric parameters of the assembly and that of the adhesive play a determining role in the system resistance; these are the main variables to be evaluated in this study. the objective intended to this section is to cancel the property effect in mode to keep the same rapport (gic / giic, σui /σuii) and to intervener only the effect of values of cohesive properties upon the predicted the failure that occur in assembly with single lap bonded joint configurations, and thus demonstrate the robustness of this type of analysis. the failure loads calculate in this section of analyses show that the compressive and tensile failure of the geometries controlled by the fracture parameters of adhesive. it shows a good agreement between evaluations of parameters; these results were obtained even though the cohesive zone parameters (strength) were estimated, as they were not measured directly. on the force / displacement curve (fig. 9), the triangular shape that presents the energy per unit area of the adhesive's ability to withstand the stress, remains the same. for all cases, if the force increases the displacement decreases and vice t b. benamar et alii, frattura ed integrità strutturale, 50 (2019) 112-125; doi: 10.3221/igf-esis.50.11 119 versa. only that, the conditions (geometry and / or behavior) under which the assembly is subjected influence these values. indeed, the adhesive joint is more solicited than in its ends, the wider the cover widens, the closer the ends are towards the applied loading and subsequently, the assembly will not have enough time to absorb the energy in the form of displacement and deformation. figure 9: effect of stiffness adhesive and adherend on the traction–separation law. cohesive stiffness effect the effect of the cohesive stiffness of the simple lap joint under compressive and tensile stress is analyzed by varying the values of knn and ktt in the definition of cohesive material; knn and ktt have both been modified simultaneously to maintain the ratio between them constant. so as to see the effect of the young's modulus and shear modulus (which are two parameters related to successive cohesive materials; knn and ktt) on the breaking load. in parallel, the breaking energy is kept constant at the base values (gi = 300j/m2, gii = 600j/m2) as well as the cohesion force in the base values (snn = 40mpa, stt = 24.1mpa). the variation in compressive and tensile strength of the sample with cohesive rigidity is shown in fig. 10. the effect of the stiffness of the cohesive zone on tensile and compressive strength is studied. 400 600 800 1000 1200 2,4 2,6 2,8 3,0 3,2 3,4 3,6 3,8 4,0 f a ilu re l o a d ( k n ) cohesive stiffness, k nn (tn/m 3 ) 20 mm 30 mm 25 mm 35 mm 400 600 800 1000 1200 3,0 3,2 3,4 3,6 3,8 4,0 4,2 4,4 4,6 4,8 5,0 f a ilu re lo a d ( k n ) cohesive stiffness, k nn (tn/m 3 ) 20 mm 30 mm 25 mm 35 mm a) b) figure 10: variation of a) tensile failure load and b) compressive failure load as function of cohesive stiffness and overlap length. for the four selected overlapping lengths, it can be seen that as the length increases, the bonding surface increases and therefore the cohesive layer behaves as a linear elastic material with high load resistance, resulting in a considerable increase in the value of the final tensile strength. by increasing the cohesive stiffness, the value of the breaking strength changes slightly. even when the joint is subjected to tension or compression, the value of the failure load changes so that it will be higher in compression. indeed, the cohesive rigid layer does not support large longitudinal displacements and under compressive stress, the joint peels off in mode ii. b. benamar et alii, frattura ed integrità strutturale, 50 (2019) 112-125; doi: 10.3221/igf-esis.50.11 120 fracture energy effect the results of the damage analyses provided for in the adhesive joint are based on the geometric conditions of the bonded system, the properties of the two plates and their dimensions and the damage properties of the adhesive. recent studies have shown that bonded assemblies have significantly different and variable failure energies [32]. therefore, it is appropriate to examine whether variation in this parameter will affect failure mechanisms under tensile and compressive stress. our analysis is based on the variation of the gi and gii fracture energies while ensuring the gi / gii ratio is maintained constant. on the other hand, the different parameters concerning the modeling of the cohesive zone are kept constant and fixed at the reference values indicated in tab. 2. fig. 11 shows the effect of the fracture energy on the maximal fracture load under tensile and compressive solicitation. 100 200 300 400 500 600 700 1 2 3 4 5 6 f a ilu re lo a d ( k n ) fracture energy j i (j/m 2 ) 20 mm 30 mm 25 mm 35 mm 100 200 300 400 500 600 700 3 4 5 f a ilu re l o a d ( k n ) fracture energy j i (j/m 2 ) 20 mm 30 mm 25 mm 35 mm a) b) figure 11: a) compressive and b) tensile failure load as function of the fracture energy and overlap length. it can be seen from fig. 11 that the failure load values are high in the case of compressive stress because the adhesive are more resistant to shear than to tension. for small values of the failure energy of the adhesive, the overlap length has little influence on failure load, the difference in value is more noticeable in the case of compressive stress than in tension. by increasing the breaking energy value, the adhesive will continue to resist efforts to transmit the load to the plates thus giving high strength. compared to other parameters, such as, normal and tangential resistances snn, stt and sss, the separation energies of the adhesive gi, gii and giii play the most important role on the strength of the adhesive and therefore on the value of the breaking force as shown in fig. 11. the failure of this type of assembly is very sensitive to low value failure energy, especially for short overlap lengths. but in contrast to high values of failure energy. however, as the overlap length increases, the value of the failure load increases resulting in high strength of the assembly. it is clearly noted that the values of the breaking force as a function of the length of the overlap under compressive stress are presented with a high level only for tensile stress because the loaded compression joint behaves in pure shear. cohesive zone strength effect the effect of cohesive zone strength of the system under compressive and tensile strength is investigated by varying the values of snn and stt, in the cohesive material definition, that means both snn and stt were varied simultaneously to keep the ratio between them constant. the fracture energy is held constant at the baseline values (gi = 300j/m2, gii = 600j/m2). the variation of compressive strength of the specimen with cohesive strength is shown in fig. 12, for the two solicitations of compressive and tensile. adhesive by its nature can be presented under different behavior; ductile or rigid according to its strength properties. we notice that the value of the failure load increases with the increase in the tensile strength of the adhesive. under tensile stress the value of the failure load reaches a stable value once the value of the tensile strength exceeds 40mpa, whereas in compression, the value of the failure load continues to increase by increasing the value of the tensile strength. on the other hand, by increasing the overlap length, the value of the failure load increases considerably to give a high resistance to the joint. if the adhesive is resistant (snn high) it will support more the applied load, it will have less longitudinal displacement and therefore an increase in the failure load. b. benamar et alii, frattura ed integrità strutturale, 50 (2019) 112-125; doi: 10.3221/igf-esis.50.11 121 it is also shown that all values of the failure load in compressive load are represented with a high level than in tensile load, because, the joint on the compressive load works more in pure shear. it is also shown that all values of the breaking force in compressive stress are represented with a high level than in tensile stress, because the joint on the compressive load works more in pure shear. in the case of tensile loading, the ultimate stress effect disappears once the value snn > 40mpa is exceeded. unlike in the case of compressive stress where the joint strength can be high (fig. 12 b). 10 20 30 40 50 60 70 1,0 1,5 2,0 2,5 3,0 3,5 4,0 f a ilu re l o a d ( k n ) mode i cohesive strength, s nn (mpa) 20 mm 30 mm 25 mm 35 mm 10 20 30 40 50 60 70 1 2 3 4 5 f a ilu re l o a d ( k n ) mode i cohesive strength, s nn (mpa) 20 mm 30 mm 25 mm 35 mm a) b) figure 12: a) compressive and b) tensile failure load as function of the cohesive strength and overlap length. effect of tapered geometry on the failure load in single lap bonded joints, the adhesive works more at the levels of these extremities, however the covering medium remains almost inactive, hence the idea of introducing a so-called tapered geometric modification in order to make it work more easily in all its surface. this part of the study gives the advantage of even the external effect (of the plates) on the resistance of the assembly where the effect of the thickness and length of notch on the results has been evaluated (failure load) for the two behaviors: traction and compression. the percentages by contribution to e = 0.75mm and l = 22.5mm where the length of recovery was fixed at 25mm, as presented in the table and the figure below. the dimensional parameters of the notch are taken at a time and separately to better identify their effects. figure 13: tapered geometry modified of single lap bonded joint. percentile evaluation (℅) -30 -20 -10 0 10 20 30 thickness tapered (mm) 0.5 0.58 0.67 0.75 0.84 0.92 1 length tapered (mm) 10 14.18 18.34 22.5 26.67 30.83 35 table 4: tapered geometry dimensions of adherends used. b. benamar et alii, frattura ed integrità strutturale, 50 (2019) 112-125; doi: 10.3221/igf-esis.50.11 122 in fig. 14, the common effect on the results shows that the presence of the notch in the plates weakened their rigidity and subsequently more elongation in the plates that come from the separation energy is absorbed. the rigidity of the assembled plates is responsible for the detachment force. a) b) figure 14: a) tensile and b) compressive failure load as function of the tapered parameters (overlap length =25mm). sensitivity analyses dditional to the precedent analyses and considering, the two plate geometries at the overlap level, the sensitivity analyses were performed on the cohesive parameters, which play a significant role in the failure process and are not measured by specific experimental tests [33]. a study was conducted. the influence of fracture properties of the adhesive mode i (gic, σui), mode ii (giic, σuii) and overall (gic, σui, giic, σuii) properties on failure load was also analyzed. from -50% to +50% we ranging the values of the initial ones considered in this analysis tab. 3 were considered. fig. 15 presents the failure load under tensile and compressive behavior as function of the cohesive properties. the failure load of the same geometry using the initial properties (f0) normalizes these failure loads. overall, the failure load increases with each group of properties considered in this study. as expected, mode ii properties have a higher effect on the failure load; especially the compressive behavior with the boundary condition is primarily loaded in shear. -50 -25 0 25 50 0,6 0,8 1,0 1,2 %%%% f / f 0 percentile variation g ic , ui g iic , uii g ic , ui ,g iic , uii -50 -25 0 25 50 0,6 0,8 1,0 1,2 1,4 % %% % f / f 0 percentile variation g ic , ui g iic , uii g ic , ui ,g iic , uii a) b) figure 15: a) tensile failure load and b) compressive failure load as function of the cohesive properties (l0 = 25mm). fig. 16 shows that the failure load is conditioned by boundary condition: type of load and the restraining. the results obtained show that the fracture properties of the adhesive have a little influence on the failure load for mode i, while it's a b. benamar et alii, frattura ed integrità strutturale, 50 (2019) 112-125; doi: 10.3221/igf-esis.50.11 123 not the case for the mode ii; the fracture properties present a major influence, it's explained by the fact that shears stresses leading to failure of adhesive. for very low fracture properties, a slight reduction in the joint strength is observed. a) b) figure 16: a) tensile and b) compressive failure load as function of the cohesive properties (overlap length = 25mm). the results for the notched plates show that for all the breaking properties of the adhesive, the higher they are, the higher the peel forces are. the percentage variation of the properties in mode i do not have much effect on the force of separation by contribution to the properties in mode ii, more particularly in compression. this shows that the overlap assembly is stressed much more in shear than in tension, it depends on the geometrical conditions of the loading and fixing joint in which the assembly is subjected. in this case, the compression release forces are not very important compared to the shear behavior as in the case of non-notched plates. conclusion his study has been focused on numerical simulation based on the cohesive zone modeling method of a single lap joint with different situation such as fracture parameter of adhesive, behavior of assembly and geometric adhered, the following conclusions could be deduced from the obtained results:  cohesive zone modeling gives the advantage of numerically predicting the release force by evaluating the parameters of adhesive failure, as well as the geometrical conditions and the behavior in which the assembly is subjected. this method also allows numerically to introduce a damaging interface into a solid without performing an assembly.  the rigidity effect of the interface is negligible except for small values that can destabilize the assembly and give different values of the release force.  failure parameters of the adhesive condition the value of the detachment force of the assembly, the higher the ultimate stress and the breaking energy increase, the more the peel force increases.  the level of the release force depends on the rigidity and geometry of the plates, less deformation and more debonding force.  the level of the debonding force also depends on loading and / or fixation conditions.  the variations of the parameters of adhesive rupture by mode i and / or mode ii, directly affect the level of resistance, hence the influence of the behavior in tension or in compression.  all parameters influencing the debonding force remain limited up to the strength of the adhesive joint. references [1] lee, m.j., cho, t.m., kim, w.s., lee, b.c. and lee, j.j. (2010). determination of cohesive parameters for a mixed– mode cohesive zone model, int. j. adhes. adhes., 30(5), pp. 322-328. doi: 10.1016/j.ijadhadh.2009.10.005. t b. benamar et alii, frattura ed integrità strutturale, 50 (2019) 112-125; doi: 10.3221/igf-esis.50.11 124 [2] groth, h.l. (1988). stress singularities and fracture at interface corners in bonded joints, int. j. adhes. adhes., 8(2), pp. 107-113. doi: 10.1016/0143-7496(88)90031-0. [3] da silva, l.f.m., das neves, p.j.c. and adams, r.d. (2009). analytical models of adhesively bonded joint, part 1: literature survey, int. j. adhes. adhes. 29(3), pp. 319-330. doi: 10.1016/j.ijadhadh.2008.06.005. [4] he x. (2011). a review of finite element analyses of adhesively bonded joints, int. j. adhes. adhes., 31(4), pp. 248-264. doi: 10.1016/j.ijadhadh.2011.01.006. [5] hart smith, l.j. (1973). adhesive bonded single lap joint, nasa cr 112236. [6] chai, h. (1988). shear fracture, int. j. fract., 37(2), pp. 137-159. [7] kaye, r., heller, m. (2002). through-thickness shape optimization of bonded repairs and lap joints, int. j. adhes. adhes., 22 (1), pp. 7-21. doi: 10.1016/s0143-7496(01)00029-x. [8] barbosa, n.g.c., campilho, r.d.s.g., silva, f.j.g. and moreira, r.d.f. (2018). comparison of different adhesivelybonded joint types for mechanical structures, appl. adhes. sci., 6(15). doi: 10.1186/s40563-018-0116-1. [9] banea, m.d., rosioara, m., carbas, r.j.c. and da silva, l.f.m. (2018). multi-material adhesive joints for automotive industry, composites part b: engineering, 151(15), pp. 71-77. doi: 10.1016/j.compositesb.2018.06.009. [10] sorrentino, l., polini, w., bellini, c., and parodo, g. (2018). surface treatment of cfrp: influence on single lap joint performances, int. j. adhes. adhes., 85, pp. 225-233. doi: 10.1016/j.ijadhadh.2018.06.008. [11] bellini, c., parodo, g., sorrentino, l. (2019). effect of operating temperature on aged single lap bonded joints, defence technology. doi: 10.1016/j.dt.2019.05.015. [12] banea, m.d., da silva, l.f.m., carbas, r.j.c. and de barros, s. (2017). debonding on command of multimaterial adhesive joints, journal of adhesion, 93(10), pp. 756-770. doi: 10.1080/00218464.2016.1199963. [13] yana, z.m., youa, m., yib, x.s., zhenga, x.l. and lia, z. (2007). a numerical study of parallel slot in adherend on the stress distribution in adhesively bonded aluminum single lap joint, int. j. adhes. adhes., 27(8), pp. 687-695. doi: 10.1016/j.ijadhadh.2007.02.003. [14] gültekin, k., akpinar, s., özel, a. (2014). the effect of the adherend width on the strength of adhesively bonded single-lap joint: experimental and numerical analysis, composites part b: engineering, 60 pp. 736-745. doi: 10.1016/j.compositesb.2014.01.022. [15] pinto, a.m.g., ribeirob, n.f.q.r., campilho, r.d.s.g. and mendesb, i.r. (2014). effect of adherent recessing on the tensile strength of single lap joints, journal of adhesion, 90(8), pp. 649-666. doi: 10.1080/00218464.2013.766132. [16] krueger, r. (2004). the virtual crack closure technique: history, approach, and applications, appl. mech. rev., 57(2), pp. 109-143. doi: 10.1115/1.1595677. [17] tay, t. (2003). characterization and analysis of delamination fracture in composites: an overview of developments from 1990 to 2001. appl. mech. rev., 56(1), pp. 1-32. doi:10.1115/1.1504848. [18] needleman, a. (1987). a continuum model for void nucleation by inclusion debonding. j. appl. mech., 54(3), pp. 25– 31. doi: 10.1115/1.3173064. [19] jiang, w., hallett, s.r., green, b.g. and wisnom, m.r. (2007). a concise interface constitutive law for analysis of delamination and splitting in composite materials and its application to scaled notched tensile specimens. int. j. numer. methods eng., 69(9), pp. 1982-1995. doi: 10.1002/nme.1842. [20] mohammadi, s. (2008). extended finite element method for fracture analyses of structures, wiley/blackwell. doi: 10.1002/9780470697795.ch7. [21] campilho, r.d.s.g., banea, m.d., pinto, a.m.g., da silva, l.f.m. and de jesus, a.m.p. (2011). strength prediction of single and double lap joint by standard and extended finite element modelling, int. j. adhes. adhes., 31(5), pp. 363372. doi: 10.1016/j.ijadhadh.2010.09.008. [22] turon, a., davila, c.g., camanho, p.p. and costa, j. (2007). an engineering solution for mesh size effects in the simulation of delamination using cohesive zone models. engineering fracture mechanics, 74(10), pp. 1665-1682. doi: 10.1016/j.engfracmech.2006.08.025 [23] abaqus analysis users’ manual. version 6.8. dassault systems, 2008. [24] campilho, r.d.s.g., demoura; m.f.s.f. and domingues, j.j.m.s. (2007). stress and failure analyses of scarf repaired cfrp laminates using a cohesive damage model, j. adhesion sci. technol., 21(9), pp. 855-870. doi: 10.1163/156856107781061477. [25] benzeggagh, m.l., kenane, m. (1996). measurement of mixed-mode delamination fracture toughness of unidirectional glass/epoxy composites with mixed mode bending apparatus. compos sci. technol., 56(4), pp. 439449. doi: 10.1016/0266-3538(96)00005-x. b. benamar et alii, frattura ed integrità strutturale, 50 (2019) 112-125; doi: 10.3221/igf-esis.50.11 125 [26] de moura, m.f.s.f., daniaud, r. and magalhães, a.g. (2006). simulation of mechanical behaviour of composite bonded joints containing strip defects, int. j. adhes. adhes., 26, 464-473. doi:10.1016/j.ijadhadh.2005.06.010. [27] mokhtari, m., madani, k., benzaama, h. and malarino, s. (2017). effects of the composite stacking sequence on the failure load of the single lap bonded joint, journal of theoretical and applied mechanics, 55(4), pp. 1257-1268. doi: 10.15632/jtam-pl.55.4.1257. [28] mokhtari, m., madani, k., belhouari, m., touzain, s., feaugas, x. and ratwani, m. (2013). effects of composite adherend properties on stresses in double lap bonded joints, materials and design, 44, pp. 633-639. doi: 10.1016/j.matdes.2012.08.001. [29] benchiha, a., madani, k. (2015). influence of the presence of defects on the stresses shear distribution in the adhesive layer for the single-lap bonded joint, structural engineering and mechanics, 53(5), 1017-1030. doi: 10.12989/sem.2015.53.5.1017. [30] bezzerrouki, m., madani, k., sahli, a. and mallarino, s. (2019). innovative geometric design improves the resistance of simple metal / metal lap joint, frattura ed integrità strutturale, 13(48), pp. 491-502. doi: 10.3221/igf-esis.48.47. [31] madani, k., touzain, s., feaugas, x., cohendouz, s. and ratwani, m. (2010). experimental and numerical study of repair techniques for panels with geometrical discontinuities, computational materials science, 48(1), pp. 83-93. doi: 10.1016/j.commatsci.2009.12.005. [32] mukherjee, a. (1997). ply drop-off in layered composites-evaluation of design parameters, computational structural mechanics. allied publishers ltd., pp. 473-82. [33] campilho, r.d.s.g., de moura, m.f.s.f. and domingues, j.j.m.s. (2008). using a cohesive damage model to predict the tensile behaviour of cfrp single-strap repairs, international journal of solids and structures, 45(5), pp. 14971512. doi: 10.1016/j.ijsolstr.2007.10.003. << /ascii85encodepages false /allowtransparency false /autopositionepsfiles true /autorotatepages /none /binding /left /calgrayprofile (dot gain 20%) /calrgbprofile (srgb iec61966-2.1) /calcmykprofile (u.s. web coated \050swop\051 v2) /srgbprofile (srgb iec61966-2.1) /cannotembedfontpolicy /error /compatibilitylevel 1.4 /compressobjects /tags /compresspages true /convertimagestoindexed true /passthroughjpegimages true /createjobticket false /defaultrenderingintent /default /detectblends true /detectcurves 0.0000 /colorconversionstrategy /cmyk /dothumbnails false /embedallfonts true /embedopentype false /parseiccprofilesincomments true /embedjoboptions true /dscreportinglevel 0 /emitdscwarnings false /endpage -1 /imagememory 1048576 /lockdistillerparams false /maxsubsetpct 100 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can be opened with acrobat and adobe reader 5.0 and later.) >> /namespace [ (adobe) (common) (1.0) ] /othernamespaces [ << /asreaderspreads false /cropimagestoframes true /errorcontrol /warnandcontinue /flattenerignorespreadoverrides false /includeguidesgrids false /includenonprinting false /includeslug false /namespace [ (adobe) (indesign) (4.0) ] /omitplacedbitmaps false /omitplacedeps false /omitplacedpdf false /simulateoverprint /legacy >> << /addbleedmarks false /addcolorbars false /addcropmarks false /addpageinfo false /addregmarks false /convertcolors /converttocmyk /destinationprofilename () /destinationprofileselector /documentcmyk /downsample16bitimages true /flattenerpreset << /presetselector /mediumresolution >> /formelements false /generatestructure false /includebookmarks false /includehyperlinks false /includeinteractive false /includelayers false /includeprofiles false /multimediahandling /useobjectsettings /namespace [ (adobe) (creativesuite) (2.0) ] /pdfxoutputintentprofileselector /documentcmyk /preserveediting true /untaggedcmykhandling /leaveuntagged /untaggedrgbhandling /usedocumentprofile /usedocumentbleed false >> ] >> setdistillerparams << /hwresolution [2400 2400] /pagesize [612.000 792.000] >> setpagedevice microsoft word 2146 a. chouiter et alii, frattura ed integrità strutturale, 47 (2019) 30-38; doi: 10.3221/igf-esis.47.03 30 prediction of cycle life of expansion bellows for fixed tube sheet heat exchanger a. chouiter, d. benzerga university of sciences and technology of oran, mechanical department, b.p. 1505, 31000 oran, algeria achouiter25@gmail.com, djeb_benz@yahoo.fr a. haddi university of artois, ea 4515, laboratoire de génie civil et géo-environnement, béthune f-62400, france abdelkader.haddi@univ-artois.fr t. tamine university of sciences and technology of oran, mechanical department, b.p. 1505, 31000 oran, algeria ttamine63@yahoo.fr abstract. research on determining the lifetime of an expansion bellows designed to compensate the difference in expansion between the shell and the tubes in a fixed tube sheet heat exchanger has never ceased because of its importance in a heat exchanger. the main function of the expansion bellows is to absorb the difference in expansion between the shell and the tube bundle while resisting the axial thermal deflection and the equivalent internal pressure on the shell side. tema-9 [1] edition attaches great importance to the finite element method in the case of an expansion bellows because of the disadvantages of the old design methods, which lead to overestimation and stress overload in the bellows. the objective of this work is to study the damage in the most stressed zone of the expansion bellows in order to construct a numerical simulation tool of the rupture to determine the lifetime that an expansion bellows can support during the operating conditions of a fixed tube heat exchanger. in a first step, the ansys fem calculation code will allow the determination of the critical zone where the von mises is maximum and where potential cracks can develop. in a second step, a postprocessor based on the concept of continuum damage mechanics and using newton's iterative method will be applied to this critical area for the determination of the bellows critical lifetime. the maximum lifetime will be the value of the number of cycles that corresponds to the critical value of the dc damage (crack initiation). keywords. cycle life; expansion bellow; fixed tube sheet heat exchanger; continuum damage mechanics; damage; finite element. citation: chouiter, a., benzerga, d., haddi, a., tamine. t., prediction of cycle life of expansion bellows for fixed tube sheet heat exchanger, frattura ed integrità strutturale, 47 (2019) 30-38. received: 13.07.2018 accepted: 22.11.2018 published: 01.01.2019 copyright: © 2019 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. http://www.gruppofrattura.it/va/47/2146.mp4 a. chouiter et alii, frattura ed integrità strutturale, 47 (2019) 30-38; doi: 10.3221/igf-esis.47.03 31 introduction he expansion bellows, which permit to compensate the difference in expansion between the tubular bundle and the shell in a fixed tube sheet heat exchanger, is a structural component formed by one or more convolutions. the expansion joint is an integral part of a heat exchanger. it must simultaneously ensure the flexibility due to thermal expansion and withstand the internal pressure in the heat exchanger. in addition, it must be sufficiently flexible longitudinally to accommodate the deviations for which it is designed and must absorb the regular or irregular extension generated by the gradients temperature and pressure. in the literature, we find a wide variety of references related to the calculation of expansion bellows cyclic life. we can cite as an example: lee [2] has used a finite element analysis technique applied to the parameters of the bending and folding process of the metal bellows. becht iv [3] has shown that the fatigue behavior of the bellows can be well predicted by dividing the bellows fatigue data on the basis of geometry parameters. zupei [3] has used approximate calculation methods, which he compared to the results obtained by the finite element method for the u-shaped bellows. broman et al. [5] determined the dynamic characteristics by manipulating the finite element parameters of the bellows beam. kang et al. [6] have studied the process of forming different types of tubular bellows using a single stage hydroforming process. faraji [7, 8] has experimentally and numerically analyzed the optimal parameters for the manufacture of metal expansion bellows. bo-wun huang et al [9], in their work, the dynamic properties of coupled tube-array structures with the axial loads are investigated in heat exchanger. tingxin et al. [10] have experimentally studied the behavior of toroidal bellows compared to u-shaped bellows, they showed that toroidal bellows have a lower stress induced by internal pressure, longer fatigue life, greater ability to resist to instability of internal pressure and are more suited to situations of higher internal pressure. the code asme viii div 1 [11] is widely the most comprehensive code that deal with the design of expansion bellows, their calculations as well as their standards. in this work, we develop a method based on the concept of continuum damage mechanics (cdm), which reaches a stage of maturity allowing modeling any type of degradation. the life of the expansion bellows is obtained by using a post processor based on the of continuum damage mechanics using newton's iterative method which is unconditionally stable and ensures good convergence. in general, the damage is much localized and occupies a small volume, ie a representative volume element rve compared to macroscopic scale of the structure. this is due to the high sensitivity to microscopic damage concentrations. benzerga [12] noted that the damage effect on stress conditions occurs only in a very small area of the material. in other hand, the coupling damage behavior can occur only in rve. it is the principle of the analysis of the local coupling damage-deformation presented by lemaitre and doghri [13]. our approach can be divided into two stages: in a first step, the finite element calculation code (ansys) will allow in elasticity or elasto-plasticity to obtain the critical region of the structure (m*) where the von mises stress is maximal. in a second step, a post processor based on the continuum damage mechanics concept using the newton iterative method was applied at this critical point (m*) for the determination of the critical lifetime of the expansion bellows under service conditions of pressure and thermal expansion. this lifetime is the value corresponding to the critical damage value dc (crack initiation). this method was validated by comparing our numerical results with those of asme code [11]. figure 1: locally coupled analysis of crack initiation. t a. chouiter et alii, frattura ed integrità strutturale, 47 (2019) 30-38; doi: 10.3221/igf-esis.47.03 32 modeling o model the bellows, we used the finite element ansys code. due to symmetry, the design of the joint includes a two-dimensional axisymmetric half u-shape. the dimensions of the structure are the inner radius and the thickness. for meshing the structure, we used 8 nodes quadrilateral axisymmetric elements. these elements have compatible displacement shape, and are well suited for modeling curved boundaries. the meshing in finite element models is the very important step in during analysis because it affects the accuracy and the economy of the solid model. the mesh used in 2d has 10802 elements and 22607 nodes (fig. 2). for the boundary conditions, we respected the symmetry conditions and those of the experiment. consequently, the following boundary conditions are used (fig. 3): (i) the smaller diameter end (right side) is unrestrained axially and restrained in the radial direction, (ii) the large diameter end (left side) is restrained in the axial direction and unrestrained in the radial direction, (iii) the body is subjected to uniform pressure in shell side and displacement in axial direction. figure 2: meshing of the expansion bellows. figure 3: boundary and loading conditions. using ansys finite element software, a subroutine has been developed and implemented in the main code for the determination of the most stressed area (m *) at the curved boundaries (see fig. 2) in which cracks can be developed. the behavior of the critical point (m *) where the equivalent stress σ* is maximal is obtained with the code ansys® and implanted in the post-processor using (lemaitre and doghri, [13]) damage model based on newton iterative method. in continuum damage mechanics, a surface density of microcracks lemaitre and chaboche [14] defines the damage variable: dsd s    (1) t a. chouiter et alii, frattura ed integrità strutturale, 47 (2019) 30-38; doi: 10.3221/igf-esis.47.03 33 critical area critical point (m *) figure 4: macroscopic-microscopic scale. if the damage is isotropic, d is a scalar allowing the introduction of the effective stress notion: 1 d      (2)         * * 1 * 2 2 2 1 3 1 2 3 veq h v eq m sup with r r                       (3) rv is the triaxiality function which depends on the triaxiality coefficient σh /σeq, in most cases this criterion is satisfied in high stress concentration zones with high triaxiality coefficient value σh /σeq. the third step consists in determining the damage evolution by solving the constitutive laws below which will be written in incremental form and will have to be solved by newton's numerical method benallal et al. [14]: 2 0 1 1 1 3 0 2 2 e p ij ij ij e ij kk ij ij d p ij ij eq eq v e d e d p if f f if es d e e e e e p pr p                     (4) numerical procedure he method used for solving the above constitutive equations is integration schemes such as the radial return method m. ortiz and e. p. popov [16]. the method used is a strain driven algorithm: it is assumed in a first step that the stress values and the other variables of the model are known at the initial time (tn) and that the behavior is t a. chouiter et alii, frattura ed integrità strutturale, 47 (2019) 30-38; doi: 10.3221/igf-esis.47.03 34 purely elastic. major headings should be typeset in boldface with the first letter of important words capitalized.  1 2 pntr        (5) where λ and μ are the lamé coefficients and 1 is the identity tensor of order 2. all other "plastic" variables are equal to their values at time (tn). if this "elastic predictor" satisfies the condition of the load function f≤ 0 (see fig. 4), the assumption is then valid, and the calculation procedure for this time increment is completed. in the contrary case f> 0, this elastic state is "corrected" according to the method below to determine the plastic solution: figure 5: plastic flow surface. the constitutive laws (4) are discretized in an incremental form corresponding to the iterative method of newton that has the advantage of being unconditionally stable (lemaitre and doghri, [13]). consequently, the solutions to time (tn+1) must satisfy the following relations: 0 seq f      2     tr p pnσ e1 e e e (6) n p  pe y d p s    where:       1 2 3 d n n eq and n                  (7) substituting ∆ep by its expression in the second equation, the problem is then reduced to two equations where the unknowns are  and p and must satisfy the system: a. chouiter et alii, frattura ed integrità strutturale, 47 (2019) 30-38; doi: 10.3221/igf-esis.47.03 35 f eq s   (8)  1 2 2pnh tre e e n p         (9) this nonlinear system is iteratively solved according to the newton method (benallal et al, [15]) for each iteration (s), we have: : 0 ; : 0 p f h h f h pc c c                (10) where f and h is their partial derivatives taken at time (tn+1) at each iteration (s). the "corrections" c  and cp are defined by:         1 1pn s and ss c p pc          (11) the iteration (s = 0) corresponds to the elastic predictor. when p and  are determined, ep and d are calculated from their discretized forms and the stresses are determined by:  1ij ijd    the method developed above has been implemented in the ansys commercial code and the post-processor. it will use as data, the parameters of the material and the components of the total deformations. as result, it will give, a function of the internal pressure in the fixed tube-plate heat exchanger and the difference of expansion exerted on the bellows, the damage value, the cumulative plastic deformation and the stress components σij at each step, until initiation of macroscopic cracks at the critical zone (von mises maximal stress value). this will permit to determine the number of maximum service cycles that the expansion bellows can withstand as a function of the variations in internal pressure and thermal expansion. validation of the methodology s mentioned earlier in this paper, the objective of the present work is to develop a model that can predict the critical cycle life of expansion bellows for fixed tube sheet heat exchanger. as an example of application, we consider an expansion which material and geometrical properties has been taken from asme sec ii part d [17] (see tab. 1 and fig. 6). figure 6: two-dimensional model of wall expansion bellow. a (12) a. chouiter et alii, frattura ed integrità strutturale, 47 (2019) 30-38; doi: 10.3221/igf-esis.47.03 36 mechanical & thermal properties of material material sa 516 gr. 70 allowable stress 38000 psi mean metal temperature for the shell 129o f mean metal temperature for tube187o f elasticity modulus e 27400000 psi shell stress for case-2 = 1129.5 psi poisson ratio υ 0.3 dimensions of material o.d of outer cylinder=19.6875 inch, i.d of outer cylinder= 19.3125 inch, g=32.125 inch, length of outer cylinder, lo=2 inch, length of inner cylinder, li=13.4962 inch, thickness of bellows, t = 0.375 inch, thickness of shell, ts = 0.4375 inch radius of inner and outer knuckle ra=rb=1.125 inch. table 1: mechanical, thermal properties and dimensions of material. operating conditions he internal pressure of thick wall bellows is acting on shell side shell. the smaller diameter end is unrestrained in axial direction and restrained in radial direction and the large diameter end are restrained in the axial direction and unrestrained in radial direction (see fig. 3 above). the loading in the axial direction is entered as displacement which is calculated as δ = (ss x as) / kfes where ss= shell stress, as=shell cross-sectional area and kfse=spring rate of main shell. in general, δapplied = δ (1/2nfse) where δ=amount of applied displacement and nfse is total number of bellow. the calculated applied displacement from shell stress is given in tab. 2. operating condition shell side pressure (psi) shell stress (psi) applied displacement (δ) inch shell side pr + differential expansion 250 1129.58 0.02043 table 2: operating conditions. the result of life cycles to failure plots obtained from our proposed method and asme viii div 1 are as shown in fig. 7. analysis and interpretation of results rom the results obtained, we can conclude that our results are quite close to the results obtained by asme approach. . we can still optimize our results by decreasing the mesh so that we can get a fine mesh and results much more accurate. we calculated the results for a service condition, considering only the differential expansion and the internal pressure on the shell side, neglecting the tube-side pressure. taking into account the tube-side pressure, our results will be even closer to reality. the results obtained using our model are lower than those of the asme code, which will allow a safer and more secure design, hence the design is safe. t f a. chouiter et alii, frattura ed integrità strutturale, 47 (2019) 30-38; doi: 10.3221/igf-esis.47.03 37 figure 7: cycle life of expansion bellow. conclusions and perspectives n this paper, we presented a new method based upon damage mechanics, which is now in its stage of maturity. our main motivation in this work was to show that this method is a contribution to calculation of expansion bellow failure. in spite of some differences between proposed method results and the asme results, our method has a good performance in predicting the bellow cycle life to failure. we believe that this work opens widely, the way to research and that its logical continuity should be based on the following points:  from a theoretical point of view:  use of a surface of charge taking into account material strain hardeing;  using a damage anisotropic theory.  from the numerical point of view:  use of finite elements more robust. references [1] tema9th. (2007). standard of tubular exchanger manufacturers association. new york .inc. [2] lee, s. (2002). study on the forming parameters of the metal bellows. journal of materials processing technology, pp. 47–53. [3] becht, c. b. (2000). fatigue of bellows, a new design approach. international journal of pressure vessels and piping, pp. 843–850. [4] zupei, s. (1996). approximate calculation of u-shaped bellows. tsinghua science and technology, pp. 305 309. [5] broman, g., jönsson, a and hermann., m. (2000). determining dynamic characteristics of bellows by manipulated beam finite elements of commercial software. international journal of pressure vessels and piping 77, pp. 445–453. [6] kang, h. w., lee, i. h and cho, d.-w. (2006). development of a micro-bellows actuator using microstereolithography technology. microelectronic engineering, pp. 1201–1204. [7] faraji, g., besharati, m. k., mosavi, m and kashanizadeh, h. (2008). experimental and finite element analysis of parameters in manufacturing of metal bellows. the international journal of advanced manufacturing technology, pp. 641–648. [8] faraji, g., mashhadi, m. m and norouzifard, v. (2009). evaluation of effective parameters in metal bellows forming process. journal of materials processing technology, pp. 3431–3437. i a. chouiter et alii, frattura ed integrità strutturale, 47 (2019) 30-38; doi: 10.3221/igf-esis.47.03 38 [9] bo-wun, h., pu-ping, y. and jung-ge, t. (2016). dynamic properties of coupled tube-array structures with the axial loads. latine american journal of solids and structures. [10] tingxin, l., xiaoping, l., tianxiang, l., xigang, h and xinfeng, l.(1995). experimental research of toroid-shaped bellows behavior. international journal of pressure vessels and piping, pp. 141-146. [11] code, a. b. (2010). asme rules for construction of pressure vessels viii division 1. new york: the american society of mechanical engineers. [12] benzerga, d. (2015). burst pressure estimation of corroded pipeline using damage mechanics. multiphysics modelling and simulation, systems design and monitoring 2, pp. 481-488 [13] lemaitre, j., doghri, i. (1994). damage 90: a post processor for crack initiation. computer methods in applied mechanics and engineering, pp. 197-232. [14] lemaitre, j,.chaboche, j.l. (1988). mechanics of solids material, cambridge university press. [15] benallal, a., billardon r. and doghri, i. (1988). an integration algorithm and the corresponding consistent tangent operator for fully coupled elastoplastic and damage equations. international journal for numerical methods in biomedical engineering (e4), pp. 731–740. [16] ortiz, m., popov, e. p.(1985).accuracy and stability of integration algorithms for elastoplastic constitutive relations. international journal for numerical methods in engineering, pp. 1561–1576. [17] code, a. b. 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/hrv (za stvaranje adobe pdf dokumenata najpogodnijih za visokokvalitetni ispis prije tiskanja koristite ove postavke. stvoreni pdf dokumenti mogu se otvoriti acrobat i adobe reader 5.0 i kasnijim verzijama.) /hun 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can be opened with acrobat and adobe reader 5.0 and later.) >> /namespace [ (adobe) (common) (1.0) ] /othernamespaces [ << /asreaderspreads false /cropimagestoframes true /errorcontrol /warnandcontinue /flattenerignorespreadoverrides false /includeguidesgrids false /includenonprinting false /includeslug false /namespace [ (adobe) (indesign) (4.0) ] /omitplacedbitmaps false /omitplacedeps false /omitplacedpdf false /simulateoverprint /legacy >> << /addbleedmarks false /addcolorbars false /addcropmarks false /addpageinfo false /addregmarks false /convertcolors /converttocmyk /destinationprofilename () /destinationprofileselector /documentcmyk /downsample16bitimages true /flattenerpreset << /presetselector /mediumresolution >> /formelements false /generatestructure false /includebookmarks false /includehyperlinks false /includeinteractive false /includelayers false /includeprofiles false /multimediahandling /useobjectsettings /namespace [ (adobe) (creativesuite) (2.0) ] /pdfxoutputintentprofileselector /documentcmyk /preserveediting true /untaggedcmykhandling /leaveuntagged /untaggedrgbhandling /usedocumentprofile /usedocumentbleed false >> ] >> setdistillerparams << /hwresolution [2400 2400] /pagesize [612.000 792.000] >> setpagedevice microsoft word numero_51_art_34_2679 y. dubyk et alii, frattura ed integrità strutturale, 51 (2020) 459-466; doi: 10.3221/igf-esis.51.34 459 stress-strain assessment of plain dents in gas pipelines yaroslav dubyk ipp-centre llc, ukraine dubykir@gmail.com, http://orcid.org/0000-0002-4327-412x iryna seliverstova g. s. pysarenko institute for problem of strength, national academy of sciences of ukraine, ukraine seliverstovairyna24@gmail.com, http://orcid.org/0000-0003-1166-792x abstract. this paper presents the analytical solution of the stress-strain state for a dented pipeline, based on the method of equivalent loads. firstly, a solution for a harmonic imperfection was found, then using fourier series expansion a semi-analytical procedure was proposed to assess a single dent. a comparison between analytical and numerical results for the axial force and pressure load were given. the influence of the dent dimensions, shell radius to thickness ratio and initial loading to stress concentration factor were discussed. keywords. cylindrical shell; plane dent; approximate solution; citation: dubyk y., seliverstova i., stressstrain assessment of plain dents in gas pipelines, frattura ed integrità strutturale, 51 (2020) 459-466. received: 11.11.2019 accepted: 06.12.2019 published: 01.01.2020 copyright: © 2020 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. introduction runk pipelines are one of the most common means used in the transportation of various kinds of energy resources. ensuring trouble-free operation of pipelines is a pledge of both the environmental and energy security of the country through which they pass. the most common cause of accidents on trunk pipelines is the presence of mechanical damage (dents and gauges) and corrosion [1]. therefore, the key point in the study of the technical condition and the extension of the life of trunk pipelines is the determination of their stress state, taking into account these local damages. dents are one of the most common types of defects arising due to external interaction – damage by heavy machinery (excavators, tractors, pipe layers), falling stones on top of a pipeline or resting on supports [2]. local imperfections like dents on pipelines are quite complicated for engineering analysis. to assess this problem, contact mechanics and nonlinearities in both material and geometry have to be considered in all phases of the dent life cycle. recently these problems are addressed using fea only [3, 4]. finite element method is the most largely used method for solving problems of engineering but since it is a numerical study it does not give the total accurate understanding of the problem. to investigate dent problems, it would be best to develop a closed-form analytical model would be the wisest choice to investigate dent problems but it is almost impossible due to the complicated geometry and it doesn't give considerable advantages comparing to fem analysis. instead a semi-analytical numerical procedure is proposed in the current study based on the equivalent load method. t http://www.gruppofrattura.it/va/51/2679.mp4 y. dubyk et alii, frattura ed integrità strutturale, 51 (2020) 459-466; doi: 10.3221/igf-esis.51.34 460 equivalent loads method was proposed by [5], to study the stress behavior of thin–shell structures containing geometric imperfections. the stress behavior of a geometrically imperfect shell under load is equivalent to the sum of two stress fields [6]. the first stress field is produced by the original load acting on the geometrically perfect version of the shell. the second stress field results from applying to the perfect version of the shell a load pattern that results in perturbation stress behavior equivalent to that which would be induced by the geometric imperfection. it should be noted that the equivalent load does not produce the correct dent shape but instead produce a stress field that is similar to that which would have been produced by the dent. equivalent load is given usually in the form [6]: 2x xx x xp n n n        (1) , ,x xn n n   membrane forces, that arise from the action of the initial load on the curved shell; , ,x x     change curves in two main directions and the change curvature in twist. eq. (1) is standard in the solution of non-ideal shell problems and is used by [7], who proposed to improve its accuracy by considering the additional terms for imperfections amplitudes larger than the shell thickness [8]. modern regulatory documents [9] in the damage risk analysis consider only the permissible depth of such defects, neglecting other geometrical parameters and the load level. the main idea of a current study is to develop effective semi-analytical procedure for dent analysis based on equivalent loads method with second order terms to perform the convergency analysis and to investigate the dent shape effect and loading level on the stress concentrator factor. analytical background general equations he theory of the thin-shells is quite well-known and effective for pipelines application. general equation of cylindrical shell equilibrium under external forces:    [ ] l u f (2)    tu v wu is the displacement vector; ,u v and w are the orthogonal components of displacements in the ,x  and radial directions;   2 t x rr h p p p   f is the external loading vector; [ ]l is a matrix differential operator [10]: 1 [ ] [ ] [ ] [ ]d m mod inik h   l l l l (3) differential matrix operator [ ]d m l corresponds to donnel-mushtari shell theory, the simplest one; [ ]mod l modifying operator, for a different shell theory, further we will use flugge shell theory; [ ]ini l differential operator which implies the initial stress influence. these operators are written in explicit form below: 2 2 2 2 2 2 2 2 2 2 4 1 1 2 2 1 1 [ ] 2 2 1 d m s ss s s k s                                                  l (4) t y. dubyk et alii, frattura ed integrità strutturale, 51 (2020) 459-466; doi: 10.3221/igf-esis.51.34 461 2 3 3 2 3 2 2 3 2 2 3 3 3 2 3 2 2 2 1 1 0 2 2 1 1 [ ] 0 3 3 2 2 1 1 3 1 2 2 2 mod s s s s s s s                                                          l (5) 2 2 2 2 2 2 2 2 3 2 2 2 2 2 2 2 2 2 0 1 [ ] 0 2 3 2 2 2 x x ini x x x x x n n n n x ss n n n xs s n n n n n n s x xs                                                                   l (6) the following notations are used: 2 2 2 2 ; ; ; 12 1 h eh k h d h r r         (7) r  shell radius, h  shell thickness, e  young’s modulus,   poisson ratio. the complete explicit solution of eq. (2) can be found only for simplest geometries, and loadings, for a single dent it can’t be obtained, thus a numerical procedure is developed below based on the accurate solution for the harmonic imperfection and fourier series expansion. harmonic imperfection a harmonic imperfection was considered as a base for further solution and the displacements representation can be found using:  cos sinumnu c n x r         ,  sin cosvmnv c n x r         ,  cos coswmnw c n x r         (8) /m r l  , ,n m  wave number in circumferential and axial directions, l  length of the shell, , ,u v wmn mn mnc c c  modes coefficients for corresponded directions. substituting representations (8) in eq. (2), we can get a simple algebraic set of equations:   2 2 2 2 2 2 22 2 2 2 1 1 2 2 2 0 2 2 22 u v w mn mn mnx k n kn n nn c c c k n k knn n n hn h                                   (9)   2 2 2 2 2 22 2 2 3 3 2 1 1 3 2 2 0 2 2 22 u v w mn mn mnx k k n nn n c c c k kn n n h h                                   (10) y. dubyk et alii, frattura ed integrità strutturale, 51 (2020) 459-466; doi: 10.3221/igf-esis.51.34 462 2 2 2 2 2 2 2 2 2 4 2 2 4 2 2 2 2 3 2 2 2 2 2 2 1 2 u v mn mn xw mn xx n nn c k n k kn c k k h h n n n n rl n r m c k k n kn kn k n n h m l                                                     (11) this set of equations can be easily solved using any mathematical software, like maple or mathematica, but its solution is too long to be given here. the solution of a harmonic imperfection is itself useful, as it can be used to approximate the long dent, but the solution for a single dent can be further obtained using fourier series expansion. solution for a single dent dents can have different profiles, which depend on the mechanism of dent formation and working conditions. to work with a specific dent, the profile should be measured directly and afterwards approximated by a fourier expansion but, to test the analytical procedure, the following smooth shape function was used to describe the dent profile: 2 2 0 0 1 1 ( , ) exp exp 2 2 x r x r x                               (12) 0x length of the dent in the axial direction, 0 is the length in circumferential direction,  dent depth. a very common way to deal with single imperfections is to use fourier expansion. thus, to find a solution for a dent, load coefficients (1) for every mode, using double integrals, have to be found: 2 2 2 , 0 2 0 0 00 1 1 1 1 1 exp exp 2 2 l m n x l x x p n dxd l x xx                                                     (13)   2 2 2 , 2 0 0 00 1 1 1 1 1 exp exp cos cos 2 2 l m n xx x l x x p n n x dxd l x x rx                                                           (14)   2 2 2 , 2 0 0 00 1 1 1 1 1 exp exp cos cos 2 2 l m n l x p n n x dxd l x r                                                               (15) these integrals can be computed numerically, so it's possible to deal with any dent form, thus, in contrast to other analytical solutions, the dent form influence can be further investigated. also, it is very useful for analysing the dents found during the inspection. for a complete solution, internal forces and moments with a simple summing for each mode must be found:  2 cos cosu v wx mn mn mn n m h x n c c n c k n r r            (16)  21 cos cosu v wmn mn mn n m h x n c c n c kn k n r r           (17)  2 22 cos cosu v wx mn mn mn n m d x m c c n c n n rr             (18) y. dubyk et alii, frattura ed integrità strutturale, 51 (2020) 459-466; doi: 10.3221/igf-esis.51.34 463  2 22 1 cos coswmn n m d x m c n n rr         (19) stresses were obtained using the following formulas of the shell theory, and were divided into membrane and bending part, which is very common for nuclear, oil and gas industries:   2 6 mx bx x x x n m h h      (20)   2 6 m b n m h h           (21) in the following section, this semi-analytical procedure will be tested in detail, and some properties will be discussed results and discussion o analyze the dent behavior, the stress concentration factor will be introduced, which is the ratio of a local stress caused by the dent to the nominal stress level in a perfect pipe: mx bxforce nom scf      (22) m b pressure nom scf       (23) here nom is a nominal stress level in a shell without a dent. in this study, two main loadings for oil and gas pipelines – internal pressure (p) and axial force (f) were considered: 2 x nom force n f h rh     (24) nom pressure n pr h h    (25) first of all, the convergence criteria will be considered to the analysis, i.e. how many modes should be included in fourier expansion. on fig. 1, the convergence solution can be seen with respect to the number of modes involved (number of terms in fourier expansion) and it is possible to conclude that 50th-60th modes were quite enough for dent assessment. also, for internal pressure loading, it's possible to note that the proposed solution converges faster. on fig. 2 and fig. 3, a comparison with numerical results obtained by the commercial fea ansys can be seen. as an applied load axial force (see fig. 2) and pressure (fig. 3) were used, the nominal stress level was equal to 1 mpa, note that the stress categorization according to eqns. (20) and (21) was used. however, an equivalent load method underestimates the peak stress concentrated value, it predicts quite well the stress profile and from fig. 1b it can be seen that 20-25 modes will be enough for profile prediction. the influence of the nominal stress level was analyzed in fig. 4. it can be seen the continuous reduction of the scf with the increasing of the stress level, this effect is introduced in the model with the initial stress matrix (6), without it horizontal lines would be obtained. the initial stress influence can be explained by the fact that high level forces, especially pressure, tries to ‘fix’ the dent and bring the shell to a perfect condition. in addition, from fig. 4, the effect of non-proportional dent dimensions can be observed and conclude that a dent with a longer dimension perpendicular to a nominal stress is more dangerous. thus, in dent assessment not only dent depth should be considered, but also length and width have to be taken into account. from figs. 2-4, it's possible to conclude that internal pressure leads to bigger stress concentration factors with the same nominal stress level. t y. dubyk et alii, frattura ed integrità strutturale, 51 (2020) 459-466; doi: 10.3221/igf-esis.51.34 464 figure 1: convergence of results with respect to fourier terms of expansion: a stress concentrating factor for pressure and force loading; b – profiles of circumferential bending stress for pressure loading. figure 2: comparison with fem solution for axial force loading: r=400mm, h =10mm, ξ=0.5h, 0r = 0x =60mm, analytical solution; fem solution. figure 3: comparison with fem solution for internal pressure loading; r=400mm, h =10mm, ξ=0.5h, 0r = 0x =60mm, analytical solution; fem solution. y. dubyk et alii, frattura ed integrità strutturale, 51 (2020) 459-466; doi: 10.3221/igf-esis.51.34 465 figure 4: effect of initial stress: a) axial force loading, b) internal pressure loading; r=400mm, h =10mm: 0r = 0x =60mm; 0r =90mm, 0x =60mm; 0r =60mm, 0x =90mm. in fig. 5, the effect of shell radius to thickness ratio was analyzed and again it is possible to see the different behavior for internal pressure and axial force loading. it can be clearly seen from fig. 5 that with increasing r to h ratio a higher scf was obtained and the stress concentration can be up to 40 times. in oil and gas industries typical trunk pipelines have r/h=15…40, so the results will be in the lower part of fig. 5 and with the increasing of the nominal stress level scf factor will decrease (see fig. 4) and this effect will be more significant for flexible shells. nevertheless, if using high strength steels for piping, the thickness can be reduced and must be aware of the increasing in scf for dents in very flexible shells. figure 5: effect of radius to thickness ration: a) axial force loading, b) internal pressure loading; σnom=1mpa, h =10mm: 0r = 0x =60mm; 0r =90mm, 0x =60mm; 0r =60mm, 0x =90mm; conclusions simple engineering approach was developed for analysis of stress-strain state of dented pipelines using equivalent load method. using the harmonic imperfection model, an explicit analytical solution for a single dent was received and for a reliable accurate solution 50 terms in fourie expansion must be used. comparison of analytical stresses a y. dubyk et alii, frattura ed integrità strutturale, 51 (2020) 459-466; doi: 10.3221/igf-esis.51.34 466 with the results of numerical simulation shows the effectiveness of the proposed procedures. however, equivalent load method underestimates the peak stress concentration value, but it predicts quite good the stress profile. the peak stress value can be adjusted by a simple semi-analytical correction. obtained semi-analytical solution allowed to conduct parametric studies for different dent shapes, radius to thickness ratio at different nominal stress level:  for small dents with increasing depth the stresses concentration increases and for small dents, this growth was more significant  the influence of pressure, for unproportional dent was more significant than in case of axial force loading;  concentration due to the pressure load was more significant, and must be taken into account, especially for short dents, since it can exceed the nominal stress level by an excessive value;  increasing in nominal stress level gives a reduction in stress concentration factor, and for pressure loading this decreasing was more significant;  increasing in r to h ratio leads to increasing in stress concentration factor. for pressure and axial force loading this effect is different and should be accounted for very flexible pipelines. the proposed semi-analytical solution is a powerful method for dents assessment, it is especially useful for parametric analysis, and it can be used to understand the factors that influence the pipeline safe operation. references [1] egig. (2015). gas pipeline incidents. 9th report of the european gas pipeline incident data group. available at: https://www.egig.eu/reports/$97/$155. [2] kec, j. and cerny, i. (2017). stress-strain assessment of dents in wall of high pressure gas pipeline, procedia structural integrity, 5, pp. 340–346. doi: 10.1016/j.prostr.2017.07.180. [3] li, c., and dang, c. (2017). plastic damage analysis of oil and gas pipelines with unconstrained and constrained dents. engineering failure analysis, 77, pp. 39–49. doi: 10.1016/j.engfailanal.2017.02.009. [4] ying wu, y., jiewen xiao, j. and peng zhang, p. (2016). the analysis of damage degree of oil and gas pipeline with type ii plain dent, engineering failure analysis, 66, pp. 212–222. doi: 10.1016/j.engfailanal.2016.04.004. [5] calladine, c. r. (1972). structural consequences of small imperfections in elastic thin shells of revolution, international journal of solids and structures, 8(5), pp. 679–697. doi: 10.1016/0020-7683(72)90036-4. [6] rinehart, a. j. and keating, p. b. (2007). stress concentration solution for a 2d dent in an internally pressurized cylinder, journal of engineering mechanics, 133(7), pp. 792–800 doi: 10.1061/(asce)0733-9399(2007)133:7(792). [7] godoy, l. a. (1996). thin-walled structures with structural imperfections, new york, pergamon. doi: 10.1016/b978-0-08-042266-4.x5000-3. [8] godoy, l. a. (1993). on loads equivalent to geometrical imperfections in shells, j. eng. mech, 119(1), pp. 186-190. doi: 10.1061/(asce)0733-9399(1993)119:1(186). [9] api 579-1/asme ffs-1. (2016). fitness-for-service. [10] leissa, a. w. 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/hrv (za stvaranje adobe pdf dokumenata najpogodnijih za visokokvalitetni ispis prije tiskanja koristite ove postavke. stvoreni pdf dokumenti mogu se otvoriti acrobat i adobe reader 5.0 i kasnijim verzijama.) /hun 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can be opened with acrobat and adobe reader 5.0 and later.) >> /namespace [ (adobe) (common) (1.0) ] /othernamespaces [ << /asreaderspreads false /cropimagestoframes true /errorcontrol /warnandcontinue /flattenerignorespreadoverrides false /includeguidesgrids false /includenonprinting false /includeslug false /namespace [ (adobe) (indesign) (4.0) ] /omitplacedbitmaps false /omitplacedeps false /omitplacedpdf false /simulateoverprint /legacy >> << /addbleedmarks false /addcolorbars false /addcropmarks false /addpageinfo false /addregmarks false /convertcolors /converttocmyk /destinationprofilename () /destinationprofileselector /documentcmyk /downsample16bitimages true /flattenerpreset << /presetselector /mediumresolution >> /formelements false /generatestructure false /includebookmarks false /includehyperlinks false /includeinteractive false /includelayers false /includeprofiles false /multimediahandling /useobjectsettings /namespace [ (adobe) (creativesuite) (2.0) ] /pdfxoutputintentprofileselector /documentcmyk /preserveediting true /untaggedcmykhandling /leaveuntagged /untaggedrgbhandling /usedocumentprofile /usedocumentbleed false >> ] >> setdistillerparams << /hwresolution [2400 2400] /pagesize [612.000 792.000] >> setpagedevice microsoft word numero 20 articolo 4 h. jasarevic et alii, frattura ed integrità strutturale, 20 (2012) 32-35; doi: 10.3221/igf-esis.20.04 32 case studies in numerical simulation of crack trajectories in brittle materials h. jasarevic faculty of civil engineering, university of sarajevo, sarajevo (bosnia and herzegovina) haris.jasarevic@gf.unsa.ba s. gagula faculty of engineering and natural sciences, international university of sarajevo, sarajevo (bosnia and herzegovina) sadina@ius.edu.ba abstract. statistical fracture mechanics, formalism of few natural ideas is applied to simulation of crack trajectories in brittle material. the “diffusion approximation” of the crack diffusion model represents crack trajectories as a one-dimensional wiener process with advantage of well-developed mathematical formalism and simplicity of creating computer generated realizations (fractal dimension d = 1.5). however, the most of reported d values are in the range 1.1-1.3. as a result, fractional integration of wiener processes is applied for lowering d and to generate computer simulated trajectories. case studies on numerical simulation of experimentally observed crack trajectories in sandstone (discs tested in indirect tensile strength test) and concrete (compact tension specimens tested in the quasi-static splitting tensile test) are presented here. keywords. statistical fracture mechanics; brittle materials; crack trajectories; fractal dimension; sandstone; concrete. introduction pproach to describe the physics of fracture for cases when failure of single element does not equal to failure of whole body was proposed first by chudnovsky [1]. it evolved afterwards in crack diffusion model [2] and statistical fracture mechanics (sfm) [3, 4], which both describe crack propagation in brittle materials. sfm formalizes following natural ideas [4]: i) crack advance consists of a sequence local fail ures in front of a crack tip, ii) the local failures are random events due to fluctuations of local strength of the material, iii) the crack trajectory is random, i.e. crack can follow any path from a set ω of all admissible crack paths. for each of those paths conditional probability of failure along that path exists. the probability of crack advancing from point a to point b is an average of those conditional probabilities over all admissible crack paths leading from a to b. simulation procedure he “diffusion approximation” of the crack diffusion model (see chudnovsky and gorelik, 1994), represents crack trajectories as a one-dimensional wiener process (brownian motion) w(t). this approach has advantage due to well-developed mathematical formalism and simplicity of creating computer generated realizations with known fractal dimension d = 1.5. however, often it cannot be directly applied to simulate actually observed fracture profiles, a t http://dx.medra.org/10.3221/igf-esis.20.04&auth=true http://www.gruppofrattura.it h. jasarevic et alii, frattura ed integrità strutturale, 20 (2012) 32-35; doi: 10.3221/igf-esis.20.04 33 since the most of reported d values are in the range 1.1-1.3 [5]. as a result, it is necessary to modify w(t) to lower its d. the simulation procedure by applying the operation of fractional integration to realization of w(x) in order to decrease d to desired value is described by kunin and gorelik [5] in detail. the realization w(x) with d = 1.5 is first generated as integral of a white noise e(x) written in discrete form as: ( ) ( ) ( )   i i i w x d e (1) where ei is gaussian random variable with zero mean and unit variance and d is crack diffusion coefficient determined from experimental data. d is statistical parameter reflecting the tendency of crack trajectories to deviate from central axis [5]. once the realization is generated, it is necessary to modify fractal dimension by applying the fractional integration operation to it as follows:      1 0 1 ( ) x w x w x d           (2) where (…) is the gamma-function, and fractal dimension of w(x) is d = 1.5-. a numerical implementation of above described procedure has been coded into the software matlab® for case study simulations presented later in this text. the algorithm requires 3 input parameters, namely d, d and n (number of trajectories to be generated). each realization of w(x) with d = 1.5 incorporating parameter d is generated with 1000 time steps (intervals) and fractional integration operation is performed to create final realization w(x) with d = 1.5-. the process is repeated in do loop till n trajectories are created. due to the above described formalism simplicity and computational performance of modern computers, this whole process is completed in the matter of couple of seconds. however, the major issue is obtaining input parameters (d, d) for simulation from experiments (sufficient number of repeated experimental tests is needed). it should be noted that both parameters are strongly scale dependent. issa at al [6] stated that groups of identically sized concrete specimens prepared with different aggregate sizes have different values of d (one with smaller size aggregate have smaller value of d). in addition, larger sized specimens with identical mix have lower values of d. also, zavarise at al [7] pointed that statistical parameters used in stochastic contact models are scale dependent (being function of profilometer resolution). figure 1: experimentally observed crack trajectories in sandstone discs. figure 2: simulated sandstone crack trajectories with d=1.2 and d=0.01 http://dx.medra.org/10.3221/igf-esis.20.04&auth=true http://www.gruppofrattura.it h. jasarevic et alii, frattura ed integrità strutturale, 20 (2012) 32-35; doi: 10.3221/igf-esis.20.04 34 crack trajectories simulation case studies sandstone he test results on macroscopically identical sandstone discs tested in indirect tensile strength test (astm [8] and isrm [9]) were reported by jasarevic at al [10, 11]. 50.8 mm diameter and 25.4 mm thickness (t/d = 0.5) discs cut from a block of torry buff sandstone are used for the tests. the torry buff material tested is a very fine-grained porous, consolidated sandstone, porosity ~19%, permeability ~3-millidarcy, young’s modulus 10.5 mpa (measured on three 44.5-mm diameter, 92.4-mm length cylinders) and dry unconfined compressive strength ~40 mpa. total of ten discs were tested and observed crack trajectories are shown in fig. 1 (jasarevic, 2009a). results clearly show that crack trajectories are random (i.e. no two coincide) satisfying sfm formalism described before. result of computer simulated crack trajectories for fractal dimension d=1.2 and d=0.01 (see jasarevic [10] for calculation details) is shown in fig. 2 for comparison. concrete the test results for study of size effects in concrete fracture on multiple sizes of macroscopically identical compact tension specimens tested in the quasi-static splitting tensile test (ramp test) were reported by issa at al [6, 12]. the specimens were positioned so that the notch was at the top and the actuator applied the load downward through a wedge at an angle of 8.7. a wedge applied the load on the rollers that passed through rectangular cylinders. the rectangular cylinders had the same dimensions as the rectangular part of the notch. the downward force applied through a wedge was translated into a splitting tensile force through the rollers. the test was conducted in the displacement control mode at a rate of loading of 0.125 mm/min. some of conclusions of this work are that concrete fracture surfaces with the larger aggregate sizes appear to have a higher roughness than those with smaller aggregate sizes. the crack path is less tortuous for geometrically identical specimens with smaller size aggregates. similarly, the crack path deviates from the centerline of the specimen to a less degree for the smaller size aggregates than that for the larger ones. crack trajectories for 6 macroscopically identical specimens with maximum aggregate size of ¾ in. (19mm) are shown in fig. 3. same as for sandstone, experimentally observed crack path appears to be random, i.e., no two macroscopically identical specimens exhibit the same fracture path. result of computer simulated crack trajectories for fractal dimension d=1.1 and d=0.05 (see issa at al [12] and hammad and issa [13] for calculation details) is shown in fig. 4 for comparison. figure 3: experimentally observed crack trajectories in concrete specimens. figure 4: simulated concrete crack trajectories for d=1.1 and d=0.05. conclusion andstone and concrete as brittle materials satisfy the sfm formalism in which no two fracture paths for macroscopically identical specimens coincide. the “diffusion approximation” of the crack diffusion model cannot be applied to crack trajectories experimentally observed in sandstone and concrete, since their fractal dimension is less then 1.5. instead fractional integration of wiener processes together with parameters extracted from experiments was t s http://dx.medra.org/10.3221/igf-esis.20.04&auth=true http://www.gruppofrattura.it h. jasarevic et alii, frattura ed integrità strutturale, 20 (2012) 32-35; doi: 10.3221/igf-esis.20.04 35 used to simulate fracture profiles. computer realizations of crack trajectories for two case studies presented here seem to be in good agreement with experimentally observed ones. procedure for simulation is relatively simple and straightforward once the input parameters (fractal dimension d and diffusion coefficient d) are known. however, sufficient number of repeated experimental tests is needed to extract these parameters. references [1] a. chudnovsky, in: studies on elasticity and plasticity, ed. l. kachanov, leningrad, leningrad university press (1973) 3. [2] a. chudnovsky, b. kunin, j. appl. phys., 62 (1987) 4124. [3] a. chudnovsky, b. kunin, in: microscopic simulation of complex hydrodynamic phenomena, eds. m. mareschal and b.l. holian, plenum press, new york (1992) 345. [4] a. chudnovsky, m. gorelik, in: probabilities and materials, ed. d. breysse,. netherlands, kluwer academic publishers (1994) 321. [5] b. kunin, m. gorelik, j. appl. phys. 70, (1991) 7651. [6] m. a. issa, m. a. issa, h. abdalla, m. s. islam, a. chudnovsky, int. j. of fract., 102 (2000) 25. [7] g. zavarise, m. borri-brunetto, m. paggi, wear, 262 (2007) 42. [8] astm. annual book of standards: standard test method for splitting tensile strength of intact rock core specimens (designation d 4645-87). american society for testing and materials, 4 (1989) 851. [9] isrm, int. j. rock mech. min, sci. & geomech. abstr., 15 (1978) 99. [10] h. jasarevic,. observation, characterization and modeling of fracture initiation phenomena, ph.d thesis, dept. of engineering, univ, ill. at chicago (2009). [11] h. jasarevic, a. chudnovsky, j. w. dudley, g. k. wong, int. j. fract. , 158 (2009) 73. [12] m. a. issa, m. a. issa, h. abdalla, m. s. islam, a.chudnovsky, int. j. of fract., 102 (2000) 1. [13] a. m. hammad, m. a. issa, adv. cem. based mater. 1 (1994) 169. http://dx.medra.org/10.3221/igf-esis.20.04&auth=true http://www.gruppofrattura.it microsoft word numero_58_art_21_3243.docx f.r. andreacola et al., frattura ed integrità strutturale, 58 (2021) 282-295; doi: 10.3221/igf-esis.58.21 282 focussed on steels and composites for engineering structures influence of 3d-printing parameters on the mechanical properties of 17-4ph stainless steel produced through selective laser melting francesca romana andreacola, ilaria capasso, letizia pilotti, giuseppe brando department of engineering and geology, university “g. d'annunzio” of chieti-pescara, viale pindaro, 42, 65127 pescara, italy francesca.andreacola@unich.it ilaria.capasso@unich.it, https://orcid.org/0000-0002-7536-404x letizia.pilotti@unich.it giuseppe.brando@unich.it, https://orcid.org/0000-0003-3169-516x abstract. additive manufacturing (am) is a technological process in which elements are fruitfully built-up adding materials layer by layer. am had a massive development in recent times, thanks to its intrinsic advantages, especially if compared with conventional processes (i.e. subtractive manufacturing methods), in terms of free-form design, high customization of products, a significant reduction in raw materials consumption, low request of postprocessing and heat treatments, use of pure materials and reduced time for final products to be marketed. in order to give an innovative contribution to the knowledge in the field of metal am materials, this paper reports the main outcomes of an experimental campaign focused on the influence of several specific printing parameters on the mechanical features of the 17-4ph stainless steel, which is one of the most used metal for the selective laser melting (slm) technology. the influence of different printing directions and sample inclinations on the material mechanical behavior is assessed, with the aim of considering an innovative use in the field of structural engineering. moreover, the effects due to scanning and recoating times are studied. in addition, the consequences of heat treatment (annealing) on both the residual stresses and the amount of residual austenite are appraised. keywords. selective laser melting (slm); 17-4ph stainless steel; tensile test; 3d-printing parameters; mechanical properties; additive manufacturing. citation: andreacola, f.r., capasso, i., pilotti, l., brando, g., influence of 3dprinting parameters on the mechanical properties of 17-4ph stainless steel produced through selective laser melting, frattura ed integrità strutturale, 58 (2021) 282-295. received: 20.08.2021 accepted: 29.08.2021 published: 01.102.2021 copyright: © 2021 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. introduction dditive manufacturing (am), also known as 3-d printing, is a technology based on the addition of material, superimposed layer by layer, to create pieces or parts of them. this method positively exploits the possibility of direct interfacing with cad (computer aided design), cam (computer aided manufacturing) and cnc (computer numerical control) software [1], for easily obtaining free-form elements. a https://youtu.be/qpebsf8xueg f.r. andreacola et al., frattura ed integrità strutturale, 58 (2021) 282-295; doi: 10.3221/igf-esis.58.21 283 during the last 30 years, am has had a groundbreaking development thanks to its irrefutable advantages, such as its versatility in reproducing whatever geometry, the minimum human interaction requirement, the reduced time of design [2], etc. the development of the current am process passed through different printing technologies proposed in the last decades, which are summarized in fig. 1 [2–6]: in 1980 sls (selective laser sintering) systems were developed; in 1986, hull patented a manufacturing process called sla (stereolithography); in 1988, lom (laminated object manufacturing) systems were developed; in 1989, the first fdm (fused deposition modeling) machine was marketed; in 1995, the first slm (selective laser melting) machines were proposed as an alternative technology to stereolithography; in 1998, arcam ab marketed the first ebm (electron laser melting) based machine. since early 2000, several different 3d printing machines and techniques were developed, and, in the last years, a relevant diffusion of new methodologies, with a significant research effort for using innovative materials, has been recorded worldwide (see tab. 1). figure 1: evolution of the additive manufacturing technology. solid based liquid based powder based fused deposition modeling (fdm) stereolithography (sla) selective laser melting (slm) laminated object manufacturing (lom) multi-jet modeling (mjm) electron beam melting (ebm) digital light processing (dlp) selective laser sintering (sls) multi-jet modeling (mjm) laser metal deposition (lmd) laser engineered net shaping (lens) table 1: classification of am process depending on the state of raw material [3][7]. nowadays, the different types of am (additive manufacturing) processes should be rely on the material used, on the methods adopted for building the layers and on the applications required from the beginning to the end of the process. a cad (computer aided design) representation of the object is the starting point for any am process. the quality of the model directly affects the final result for which an accurate virtual representation phase is essential. however, nowadays, there are several methods for obtaining a cad representation even for non-experts of virtual modeling software. once the cad file is obtained, the following step is to make it readable for the printer. for this purpose, all the machines need to convert the cad model into an stl (standard triangulation language) file, a stereolithography interface format, and then perform the object slicing [3]. among the available am processes, slm has attracted attention more and more in the last recent years, because of its superior flexible manufacturing capability, with fruitful applications in the aerospace, medical, and automotive industries. this am technology uses a high-energy laser beam, by which the piece is built layer-by-layer through the selective melting and consolidation of a metal powder. the layer thicknesses vary in the range of 20 and 100 μm. compared with the traditional casting and forging methods, slm attracted and attracts increasing attention due to its outstanding features, such as the ability to net-shape manufacture without the dies and the high capacity of manufacturing any geometry. the slm process is schematically shown in fig. 2. f.r. andreacola et al., frattura ed integrità strutturale, 58 (2021) 282-295; doi: 10.3221/igf-esis.58.21 284 the laser beam is mounted on the top of the machine and a set of deflection and focus lenses concentrates the beam itself on the material powder bed for the solidification of the layers. once a layer is sintered a building plate goes down and the roller delivers a new layer on the top of the bed. this process continues, layer by layer until the object is complete as designed. further details on the advantages and disadvantages of this technology are shown in tab. 2 [3]. figure 2: schematization of the slm process. in the framing of wider research activity, focused on the implementation of am processes for the manufacturing of special devices for the seismic protection of buildings, this paper presents the first outcomes of an experimental campaign conceived to identify the relation of the mechanical behavior of base material and some of the meaningful printing parameters, i.e. the recoating time, the printing direction and the orientation of the parts on the plate during the production process. advantages disadvantages use of pure materials mainly industrial techniques high density hight processing temperatures no subsequent treatments are required high machinery costs ability to create non-euclidean forms excellent mechanical performance table 2: advantages and disadvantages of slm [8]. the investigated material is the 17-4 precipitation hardening stainless steel. the scope of the testing activity is to detect the optimum printing parameters that will be used for the continuation of the research activity. apart from the tensile tests that will be presented in the paper, also x-ray diffraction analyses will be shown, in order to investigate the effects of residual stresses on metallography and on the microstructural and crystalline composition of the material. the reported analyses have been carried out on coupons either with or without heat treatment, so to emphasize the influence of this process that usually is implemented to reduce the residual stresses developed during the additive manufacturing process and to increase the material ductility. materials and methods manufacturing conditions selective laser melting system (slm 280) from slm solutions gmbh (lubeck, germany) was used for the production of the specimens. the machine has a laser beam (yb-fiber laser) with a power limit of 400 w and offers a 280 x 280 x 320 mm build envelope. the inert atmosphere inside the construction chamber is guaranteed a f.r. andreacola et al., frattura ed integrità strutturale, 58 (2021) 282-295; doi: 10.3221/igf-esis.58.21 285 by the presence of argon gas and the temperature can reach 65 °c. instead, the temperature of the building plate throughout the entire manufacturing process can be increased up to 150 °c. for the experimental tests described in this paper, the following processing parameters were applied:  laser beam diameter: 75 μm  laser beam power: 200 w  laser scanning speed: 800 mm/s  layer thickness: 30 μm  laser scanline spacing: 80 μm  hatch distance: 120 μm  minimum scanning time variable  stripes scanning strategy the selected platform temperature during the printing process was 100 °c while the temperature inside the construction chamber varied between room temperature in the initial phase and 30-35 °c during the additive manufacturing process. when the printing process was completed, the specimens were not subjected to any surface treatment, but only polished after removing the supports. fig. 3 shows a detail of the samples as soon as the additive manufacturing process is complete. a) b) figure 3: specimens after printing process: a) specimen on the building plate with its supports; b) detail of the support structures located at the bottom of the specimen, required for printability in the additive manufacturing process. the studied specimens the material used for this study is 17-4ph stainless steel, also known as 630 steel according to the aisi standard, which is one of the most used steel alloys in additive manufacturing [9–11]. it is a precipitation-hardened stainless steel with high yield strength, good corrosion resistance and high wear resistance [12–15]. an overview of the physical properties of the raw 17-4ph stainless steel powder, provided by slm solutions, is reported in tab. 3, whereas in tab. 4 the nominal mechanical features of the printed metal for two different printing directions are listed [16]. furthermore, tab. 5 shows the chemical composition of the feedstock [16]. property value mass density 7.8 g/cm3 thermal conductivity (at 20° c) 16 w/(m·k) component density > 99.5 % built-up rate (theoretical value) 16.85 cm3/h particle size 10 – 45 μm particle shape spherical table 3: nominal physical properties of 17-4ph powder material. f.r. andreacola et al., frattura ed integrità strutturale, 58 (2021) 282-295; doi: 10.3221/igf-esis.58.21 286 mechanical properties printing direction as-built heat-treated young’s modulus e 0° 90° 171 mpa 154 mpa 154 mpa 182 mpa yield strength σy 0° 90° 517 mpa 506 mpa 1024 mpa 1391 mpa ultimate tensile strength σu 0° 90° 987 mpa 931 mpa 1359 mpa 1308 mpa elongation at break εu 0° 90° 26 % 28 % 16 % 14 % reduction of area δa 0° 90° 56 % 56 % 27 % 26 % table 4: nominal mechanical properties of 17-4ph stainless steel. fe cr ni cu mn si nb + ta c n o p s balance 15.0/17.5 3-5 3-5 1 0.07 0.15/0.45 0.07 0.1 0.04 0.04 0.015 table 5: chemical composition of 17-4ph powder. two groups of specimens, for a total of 30 samples, were manufactured to be subjected to tensile tests, in order to assess how the production process and its parameters affect the mechanical properties [15]. the first group, which was not produced according to a standard, was used as a preliminary investigation to test the printer machine and to evaluate the surface finish of the additive manufactured material and the differences in terms of the final result of samples produced with different orientations and/or inclinations. the dimensions and the geometrical features of these not-standardized samples are shown in fig. 4. figure 4: geometric dimensions of the first group of tensile test specimens. the specimens were printed in three different directions. two directions with the longitudinal axis parallel to the x-y plane (horizontal, 5° and 85° inclined) and one with the longitudinal axis perpendicular to the x-y plane (vertical) were considered. it should be noted, however, that all the samples were printed with an inclination of 5° concerning the considered direction, in order to limit the negative effects of the additive manufacturing process on the angles using this slight inclination to reduce area overhangs. a summary of the first group of samples, with positioning details for all different configurations, is reported in tab. 6, where details about the processing direction, the specimen location on the building plate, the possible application of heat treatment processes (an annealing treatment keeping samples in an oven at a temperature of 650 °c for 2 hours and then cooling until room temperature is reached inside the switched-off oven [12,13,15]) are given. the second group of samples was designed according to the specifications given by astm a370 – “standard test methods and definitions for mechanical testing of steel products” [18]. the dimensions and the geometrical features of the standardized samples are shown in fig. 5. tab. 7 shows the characteristics of the second group of samples. in this case, also the scanning time, namely the time required for the fusion (i.e. the realization of one of the powder layers), was considered as a printing parameter to be f.r. andreacola et al., frattura ed integrità strutturale, 58 (2021) 282-295; doi: 10.3221/igf-esis.58.21 287 controlled: three different scanning speeds, respectively 45, 50 and 65 seconds, were performed on specimens horizontal inclined by 5° [17,19]. moreover, in tab. 7 the applied recoating time, i.e. time that the laser beam takes to return to its initial position once the production of a layer is complete, is specified [17]. specimen id building direction amount of samples heat treatment scanning time recoating time g1_17-4_to5_n(1,2,3) horizontal, 5° inclined 3 no n.a. n.a. g1_17-4_to85_n(1,2,3) horizontal, 85° inclined 3 no n.a. n.a. g1_17-4_tv_n(1,2,3) vertical 3 no n.a. n.a. g1_17-4_to5_ht_n4 horizontal, 5° inclined 1 yes n.a. n.a. g1_17-4_to85_ht_n4 horizontal, 85° inclined 1 yes n.a. n.a. g1_17-4_tv_ht_n4 vertical 1 yes n.a. n.a. * n.a. = not available. table 6: summary of the first group of tensile test specimens characteristics. figure 5: geometric dimensions of the second group of tensile test specimens. specimen id building direction amount of samples heat treatment scanning time recoating time g2_17-4_to5_45_n(1,2,3) horizontal, 5° inclined 3 no 45 8 g2_17-4_to5_50_n(1,2,3) horizontal, 5° inclined 3 no 50 8 g2_17-4_to5_65_n(1,2,3) horizontal, 5° inclined 3 no 65 8 g2_17-4_to5_45_ht_n(4,5,6) horizontal, 5° inclined 3 yes 45 8 g2_17-4_to5_50_ht_n(4,5,6) horizontal, 5° inclined 3 yes 50 8 g2_17-4_to5_65_ht_n(4,5,6) horizontal, 5° inclined 3 yes 65 8 table 7: summary of the second group of tensile test specimens characteristics. all specimens present the typical “dog-bone” shape with a 2.5 mm thick rectangular cross-section. fig. 6 shows some of the samples produced for both groups. f.r. andreacola et al., frattura ed integrità strutturale, 58 (2021) 282-295; doi: 10.3221/igf-esis.58.21 288 a) b) figure 6: some of the produced slm 17-4ph stainless steel specimens: a) first and b) second group of coupons. mechanical characterization tensile tests were performed at room temperature using a galdabini sun60 universal testing machine (see fig. 7) with a maximum load capacity of 600 kn. tests were executed in speed control, setting a speed of 6 mm/min. there is no set applied load limit, so the test ends with the specimen breaking. a summary of the experimental tests setup is provided in tab. 8. moreover, penny & giles linear displacement sensors were employed to measure the deformation of the specimens. these devices, connected to an electronic control unit, are able to monitor stroke lengths ranging of up to 100 mm. figure 7: tensile testing machine detail. evaluation of residual stresses in order to evaluate the residual stresses, x-ray diffraction (xrd) analyses were carried out for both heat-treated and not heat-treated samples. a gnr stressx system was used for this purpose. residual stresses arising during 3d printing are mainly due to the high cooling rate of the layers and could affect the mechanical performance of final products [20,21]. the determination of the residual stresses was performed by x-ray diffraction with a cr kα radiation, within the ψ range from -40° to +40° with a step size of 30-60 s. also, the amount of residual austenite was evaluated by means of xrd analysis through the gnr arexd solution. it is known that its presence, even in small percentages (5%), can cause unexpected deformations that modify the mechanical properties of printed parts [9,12,13]. the percentage amount of austenite was also considered on the virgin powder raw material. the phases of samples were conducted by x-ray diffraction with a point focus molybdenum anode, within the 2θ range from 21.5° to 44.5° with an acquisition time of 180 s. f.r. andreacola et al., frattura ed integrità strutturale, 58 (2021) 282-295; doi: 10.3221/igf-esis.58.21 289 test parameters settings control type speed control load application speed 6 mm/min maximum load 600 kn load limit no preload no gauge length l0 50 mm crosshead speed 300 mm/min unloading speed 3 mm/min end-of-test mode sample failure test temperature room temperature table 8: test machine specifications and test conditions. results and discussion tensile tests results tress-strain curves of the vertically and 5° and 85° horizontally oriented coupons are shown in fig. 9, whereas the stress–strain curves of the samples produced with scanning times (t) of 45 s, 50 s, and 65 s are shown in fig. 10. in both figures, the specimens in either their as-built or heat-treated (ht) conditions have been reported. the values of the yield stress σy, the failure stress σu and the failure strain εu for both sets of samples are summarized in tabs. 9 and 10. both tables contain the average results of the mechanical parameters obtained for each type of specimens and their standard deviation values (sd). fig. 8 displays a detail of the samples during the tests execution. figure 8: detail of tensile test execution: a) specimen before the start of the test; b) specimen at the end of the test. influence of printing direction the yield strength presents average values of 636 mpa, 818 mpa and 616 mpa respectively for specimens manufactured vertically, inclined by 5° and inclined by 85°. s f.r. andreacola et al., frattura ed integrità strutturale, 58 (2021) 282-295; doi: 10.3221/igf-esis.58.21 290 the ultimate tensile strength does not vary significantly with the printing direction. in fact, the obtained mean values are 1282 mpa, 1314 mpa and 1296 mpa respectively for the vertically, horizontally inclined 5° and 85° samples. the failure strain also shows no significant changes in relation to the different printing orientations. the average values recorded were 14.1% for specimens manufactured vertically and horizontally inclined by 5°, and 14.2% for specimens manufactured horizontally inclined by 85°. influence of scanning time the yielding strain displays mean values of 751 mpa, 634 mpa and 593 mpa for samples produced respectively with scanning times of 45 s, 50 s and 65 s. figure 9: engineering stress–strain curves of the first group of slm 17-4ph ss coupons produced. figure 10: engineering stress–strain curves of the second group of slm 17-4ph ss samples produced. f.r. andreacola et al., frattura ed integrità strutturale, 58 (2021) 282-295; doi: 10.3221/igf-esis.58.21 291 specimen id σy mpa sd mpa σu mpa sd mpa εu % sd % g1_17-4_to5 818 ±118 1314 ±8 14.1 ±0.68 g1_17-4_to5_ht_n4 1163 / 1306 / 9.8 / g1_17-4_to85 616 ±131 1296 ±13 14.2 ±0.71 g1_17-4_to85_ht_n4 1024 / 1266 / 10.6 / g1_17-4_tv 636 ±81 1282 ±10 14.1 ±0.78 g1_17-4_tv_ht_n4 1037 / 1268 / 11.8 / note: the average values are calculated among the as-built specimens. table 9: tensile test results for the first group of specimens. specimen id σy mpa sd mpa σu mpa sd mpa εu % sd % g2_17-4_to5_45 751 ±199 1278 ±9 14.2 ±2.24 g2_17-4_to5_45_ht 1116 ±32 1248 ±10 10.9 ±1.51 g2_17-4_to5_50 634 ±58 1264 ±1 15.8 ±0.12 g2_17-4_to5_50_ht 1094 ±32 1268 ±13 10.4 ±0.36 g2_17-4_to5_65 593 ±51 1277 ±14 16.0 ±0.05 g2_17-4_to5_65_ht 1095 ±11 1255 ±11 10.0 ±0.68 note: the average values are calculated both among the as-built and heat-treated specimens. table 10: tensile test results for the second group of specimens. as with the printing direction, the different scanning time does not considerably influence the results obtained in terms of failure stress. in fact, the values achieved for specimens manufactured with scanning times of 45 s, 50 s and 65 s are respectively 1278 mpa, 1264 mpa and 1277 mpa. the same consideration can be made for the failure strain which displays values of 14.2%, 15.8% and 16.0% respectively for the samples produced with scanning rates of 45 s, 50 s and 65 s. effects of heat treatment on mechanical properties the comparison between the as-built and heat-treated specimens showed that the heat treatment changed the stress-strain behavior of the material for all types of samples with different printing features. as far as the yield stress is concerned, it varies with different manufacturing orientations of about +63% for vertically printed specimens, of about +42% for horizontally 5° inclined specimens and of about +66% for horizontally 85° inclined specimens. the annealing treatment induces an increase in yield strength also for samples produced with different scanning times. in particular, this parameter rises of +49%, +73% and +85% for specimens manufactured with scanning rates of 45 s, 50 s and 65 s, respectively. with regard to failure stress, the experimental results do not change significantly due to heat treatment, both for different printing directions and different scanning speeds. in fact, failure stresses decrease of about -1.1% for vertically manufactured specimens, of about -0.6% for specimens horizontally inclined by 5° and of about -2.3% for samples horizontally inclined by 85°. considering the different scanning rates of 45 s, 50 s and 65 s, the ultimate tensile strength changes of about -2%, +0.4% and -2%, respectively. f.r. andreacola et al., frattura ed integrità strutturale, 58 (2021) 282-295; doi: 10.3221/igf-esis.58.21 292 the heat treatment also implies a decrease in failure strain. in fact, a reduction of approximately -16.3%, -30.3% and -25.4% for the vertically, horizontally 5° and 85° inclined specimens, respectively, can be observed. likewise, for specimens processed with scanning times of 45 s, 50 s and 65 s the failure strain varies of about -23.5%, -34.3% and -37.2%. the values of the mechanical parameters obtained after the annealing treatment seem to be in contrast with the trend reported in the literature for steel alloys produced by conventional methods, which are generally more ductile and less resistant after heat treatments, even if beyond certain temperatures, there are no further beneficial effects. however, in addition to the data provided by the manufacturer of the 3d printing machine and the powder materials used (slm solutions) [22], that confirm the obtained results (see tab. 4), there are several scientific findings that support and validate the behavior observed for steel and nickel alloys produced by selective laser melting [16,20,21,23,24]. in particular, precipitation-hardened (17-4ph and 15-5ph stainless steels), martensite-aging steels (e.g. “maraging” 1.2709 steel) and nickel alloys inconel 625 and 718 showed a reduction in ductility and an increase in yield and ultimate strength. in contrast, additive-manufactured aluminum and titanium alloys (alsi10mg aluminum alloy and ti6al4v titanium alloy) exhibit the same behavior as the corresponding metallic materials produced by traditional techniques [19,25–27]. some of the specimens after the tensile test are shown in fig. 11. x-ray diffraction results x-ray diffraction analyses have been conducted on all types of specimens to detect the presence of residual stresses (rs) and the amount of residual austenite (ra). the residual stresses were evaluated both in the parallel (90°) and in the perpendicular (0°) directions with respect to the longitudinal axis of the sample. the values of the standard deviation (sd) for specimens produced at different scanning times were also measured, as three test pieces were analyzed for each rate and only one for those with different printing orientations. the results of the xrd analysis are summarized in tab. 11. a) b) figure 11: location of failure of some tested 17-4ph specimens: a) non-standardized vertically printed group; b) standardized horizontally, 5° inclined printed group, recoating time of 65 s. the different manufacturing strategies led to different values of residual stresses and residual austenite. the value of residual stresses for horizontally 5° inclined specimens, is 212 mpa in the parallel direction and 123 mpa in the orthogonal direction. the specimens horizontally 85° oriented are the only ones with negative residual stress values of -548 mpa in the 0° direction and -568 mpa in the other direction, which correspond to compressive residual stresses. the vertically printed specimens show residual stresses of 190 mpa in the longitudinal direction and 121 mpa in the perpendicular direction. regarding the amount of residual austenite, the values observed are respectively 24.3%, 8.2% and 30.4% for the horizontally 5° inclined, 85° inclined and vertically produced specimens. conversely, the samples produced with different scanning rates do not show significant differences between the values of residual stresses and residual austenite. the results shown are average values, obtained from the three specimens tested for each category. the specimens with a scanning time of 45 s show a residual stress value of 275 mpa in the parallel direction and 116 mpa in the orthogonal direction. the samples with a scanning rate of 50 s exhibit residual stress values of 203 mpa in the 0° direction and 60 mpa in the 90° direction. the specimens produced with a scanning speed of 65 s show residual stresses of 214 mpa in the parallel direction and 44 mpa in the perpendicular one. with regard to the amount of residual austenite, the values recorded were 23.7%, 20.3% and 20.6% for specimens produced at scanning rates of 45 s, 50 s and 65 s respectively. f.r. andreacola et al., frattura ed integrità strutturale, 58 (2021) 282-295; doi: 10.3221/igf-esis.58.21 293 specimen id rs 0° mpa sd mpa rs 90° mpa sd mpa ra % sd % g1_17-4_to5 212 / 123 / 24.3 / g1_17-4_to85 -548 / -568 / 8.2 / g1_17-4_tv 190 / 121 / 30.4 / g1_17-4_to5_ht_n4 31 / 54 / 13.8 / g1_17-4_to85_ht_n4 35 / 25 / 10.7 / g1_17-4_tv_ht_n4 51 / 21 / 10.2 / g2_17-4_to5_45 275 ±19 116 ±14 23.7 ±3.2 g2_17-4_to5_50 203 ±32 60 ±14 20.3 ±1.6 g2_17-4_to5_65 214 ±27 44 ±60 20.6 ±0.7 g2_17-4_to5_45_ht 110 ±10 50 ±6 17.3 ±1.4 g2_17-4_to5_50_ht 111 ±12 44 ±7 11.3 ±1.6 g2_17-4_to5_65_ht 115 ±28 46 ±12 11.4 ±0.3 powdered raw material 35.3 table 11: results obtained from x-ray diffraction analysis, for both batch of specimens. the applied heat treatment causes a homogenization and reduction of the residual stresses, independently from their manufacturing features. for horizontally 5° oriented specimens, the value of residual stresses is 31 mpa in the parallel direction and 54 mpa in the orthogonal direction (-85% and -56% compared to as-built samples). the horizontally 85° oriented specimens exhibit residual stress values of 35 mpa in the 0° direction and 25 mpa in the other direction (-106% and -104% compared to as-built samples). the vertically printed specimens show residual stresses of 51 mpa in the longitudinal direction and 21 mpa in the perpendicular direction (-73% and -83% compared to as-built samples). regarding the amount of residual austenite, the observed values are 13.8%, 10.7% and 10.2% respectively for the horizontally 5°, 85° inclined and vertically produced specimens (-43%, +31% and -67% compared to as-built samples). the specimens with a scanning time of 45 s show a residual stress value of 110 mpa in the parallel direction and 50 mpa in the orthogonal direction (-60% and -57% compared to as-built samples). the samples with a scanning rate of 50 s exhibit residual stress values of 111 mpa in the 0° direction and 44 mpa in the 90° direction (-45% and -26% compared to as-built samples). the specimens produced with a scanning speed of 65 s show residual stresses of 115 mpa in the parallel direction and 46 mpa in the perpendicular one (-46% and +5% compared to as-built samples). the values of residual austenite recorded were respectively 17.3%, 11.3% and 11.4% for specimens produced at scanning rates of 45 s, 50 s and 65 s (-27%, -44% and -44% compared to as-built samples). the results shown in the case of different scanning times are average values, taken from the three specimens tested for each category. conclusions n this paper, the influence of different printing orientations and inclinations, in combination with different scanning times, on the tensile properties of 17-4ph stainless steel specimens, produced via selective laser melting (slm) were investigated. the effects of annealing treatment on the mechanical behavior of slm-produced samples were investigated too. moreover, in order to figure out the impact of the additive manufacturing process on the final products, the residual stresses and the amount of residual austenite were evaluated. based on the experimental tests, the following conclusions can be outlined: i f.r. andreacola et al., frattura ed integrità strutturale, 58 (2021) 282-295; doi: 10.3221/igf-esis.58.21 294  the applied heat treatment increased the tensile strength;  heat treatment reduced the failure strain and thus the ductility;  about the first group of specimens (g1), the highest yield and fracture behavior was provided by the horizontally printed specimen inclined by 5°, both for the as-built and heat-treated samples;  concerning the second group of specimens (g2), the highest yield features are offered by the specimen produced with a recoating time of 45 s, both for heat-treated and as-built specimens. the highest average ultimate tensile strength values were provided by samples with a recoating time of 45 s and 50 s for as-built and annealed specimens respectively;  the highest ductility was obtained for the specimen that was printed horizontally printed with an inclination of 5° (both for as-built and heat-treated specimens) and by samples processed with recoating times of 50 s and 65 s. the heat-treated specimens with the highest mean values of failure strain are those manufactured with a recoating time of 45 s. acknowledgements his research was developed in the framing of the italian research project “3d-damper -processi di ottimizzazione di dampers metallici innovativi stampati in 3d”, in the meaning of the pon action “fabbrica intelligente, agrifood e scienza della vita”, funded by the italian ministry for the economic development. references [1] wang, j.c., dommati, h., hsieh, s.j. (2019). review of additive manufacturing methods for high-performance ceramic materials, int. j. adv. manuf. technol., 103(5–8), pp. 2627–2647, doi: 10.1007/s00170-019-03669-3. [2] coon, c., pretzel, b., lomax, t., strlič, m. (2016). preserving rapid prototypes: a review, herit. sci., 4(1), pp. 1–17, doi: 10.1186/s40494-016-0097-y. [3] abdulhameed, o., al-ahmari, a., ameen, w., mian, s.h. (2019). additive manufacturing: challenges, trends, and applications, adv. mech. eng., 11(2), pp. 1–27, doi: 10.1177/1687814018822880. [4] singh, r., gupta, a., tripathi, o., srivastava, s., singh, b., awasthi, a., rajput, s.k., sonia, p., singhal, p., saxena, k.k. (2019). powder bed fusion process in additive manufacturing: an overview, mater. today proc., 26(may), pp. 3058–3070, doi: 10.1016/j.matpr.2020.02.635. [5] ligon, s.c., liska, r., stampfl, j., gurr, m., mülhaupt, r. (2017). polymers for 3d printing and customized additive manufacturing, chem. rev., 117(15), pp. 10212–10290, doi: 10.1021/acs.chemrev.7b00074. [6] herzog, d., seyda, v., wycisk, e., emmelmann, c. (2016). additive manufacturing of metals, acta mater., 117, pp. 371–392, doi: 10.1016/j.actamat.2016.07.019. [7] karar, g.c., kumar, r., chattopadhyaya, s. (2021). an analysis on the advanced research in additive manufacturing, . [8] gokuldoss, p.k., kolla, s., eckert, j. (2017). additive manufacturing processes: selective laser melting, electron beam melting and binder jetting-selection guidelines, materials (basel)., 10(6), doi: 10.3390/ma10060672. [9] carneiro, l., jalalahmadi, b., ashtekar, a., jiang, y. (2019). cyclic deformation and fatigue behavior of additively manufactured 17–4 ph stainless steel, int. j. fatigue, 123(january), pp. 22–30, doi: 10.1016/j.ijfatigue.2019.02.006. [10] laghi, v., palermo, m., gasparini, g., girelli, v.a., trombetti, t. (2019). experimental results for structural design of wire-and-arc additive manufactured stainless steel members, j. constr. steel res., pp. 105858, doi: 10.1016/j.jcsr.2019.105858. [11] yu, z., zheng, y., chen, j., wu, c., xu, j., lu, h., yu, c. (2020). effect of laser remelting processing on microstructure and mechanical properties of 17-4 ph stainless steel during laser direct metal deposition, j. mater. process. technol., 284, pp. 116738, doi: 10.1016/j.jmatprotec.2020.116738. [12] rafi, h.k., pal, d., patil, n., starr, t.l., stucker, b.e. (2014). microstructure and mechanical behavior of 17-4 precipitation hardenable steel processed by selective laser melting, j. mater. eng. perform., 23(12), pp. 4421–4428, doi: 10.1007/s11665-014-1226-y. [13] facchini, l., vicente, n., lonardelli, i., magalini, e., robotti, p., alberto, m. (2010). metastable austenite in 17-4 precipitation-hardening stainless steel produced by selective laser melting, adv. eng. mater., 12(3), pp. 184–168, doi: 10.1002/adem.200900259. [14] murr, l.e., martinez, e., hernandez, j., collins, s., amato, k.n., gaytan, s.m., shindo, p.w. (2012). microstructures t f.r. andreacola et al., frattura ed integrità strutturale, 58 (2021) 282-295; doi: 10.3221/igf-esis.58.21 295 and properties of 17-4 ph stainless steel fabricated by selective laser melting, j. mater. res. technol., 1(3), pp. 167– 177, doi: 10.1016/s2238-7854(12)70029-7. [15] giganto, s., zapico, p., castro-sastre, m.á., martínez-pellitero, s., leo, p., perulli, p. (2019). influence of the scanning strategy parameters upon the quality of the slm parts, procedia manuf., 41, pp. 698–705, doi: 10.1016/j.promfg.2019.09.060. [16] slm solutions. (n.d.). material data sheet stainless steel 17-4ph/1.4542/a564. [17] larimian, t., kannan, m., grzesiak, d., almangour, b., borkar, t. (2020). effect of energy density and scanning strategy on densification, microstructure and mechanical properties of 316l stainless steel processed via selective laser melting, mater. sci. eng. a, 770(september 2019), pp. 138455, doi: 10.1016/j.msea.2019.138455. [18] astm. (2020). astm a370-20: standard test methods and definitions for mechanical testing of steel products, astm int., , doi: 10.1520/a0370-20. [19] hitzler, l., janousch, c., schanz, j., merkel, m., heine, b., mack, f., hall, w., öchsner, a. (2017). direction and location dependency of selective laser melted alsi10mg specimens, j. mater. process. technol., 243, pp. 48–61, doi: 10.1016/j.jmatprotec.2016.11.029. [20] zhang, h., gu, d., ma, c., guo, m., yang, j., wang, r. (2019). effect of post heat treatment on microstructure and mechanical properties of ni-based composites by selective laser melting, mater. sci. eng. a, 765(march), pp. 138294, doi: 10.1016/j.msea.2019.138294. [21] sarkar, s., kumar, c.s., nath, a.k. (2019). effects of heat treatment and build orientations on the fatigue life of selective laser melted 15-5 ph stainless steel, mater. sci. eng. a, 755(february), pp. 235–245, doi: 10.1016/j.msea.2019.04.003. [22] slm solutions. (n.d.). metal powder optimized for selective laser melting. [23] yadollahi, a., shamsaei, n., thompson, s.m., elwany, a., bian, l. (2017). effects of building orientation and heat treatment on fatigue behavior of selective laser melted 17-4 ph stainless steel, int. j. fatigue, 94, pp. 218–235, doi: 10.1016/j.ijfatigue.2016.03.014. [24] moussaoui, k., rubio, w., mousseigne, m., sultan, t., rezai, f. (2018). materials science & engineering a e ff ects of selective laser melting additive manufacturing parameters of inconel 718 on porosity, microstructure and mechanical properties, mater. sci. eng. a, 735(august), pp. 182–190, doi: 10.1016/j.msea.2018.08.037. [25] mower, t.m., long, m.j. (2016). mechanical behavior of additive manufactured, powder-bed laser-fused materials, mater. sci. eng. a, 651, pp. 198–213, doi: 10.1016/j.msea.2015.10.068. [26] xu, z.w., wang, q., wang, x.s., tan, c.h., guo, m.h., gao, p.b. (2020). high cycle fatigue performance of alsi10mg alloy produced by selective laser melting, mech. mater., 148, doi: 10.1016/j.mechmat.2020.103499. [27] masuo, h., tanaka, y., morokoshi, s., yagura, h., uchida, t. (2018). in fl uence of defects , surface roughness and hip on the fatigue strength of ti6al-4v manufactured by additive manufacturing, int. j. fatigue, 117(april), pp. 163–179, doi: 10.1016/j.ijfatigue.2018.07.020. microsoft word numero_30_art_61 c.j.su et alii, frattura ed integrità strutturale, 30 (2014) 502-514; doi: 10.3221/igf-esis.30.61 502 research on parameters optimization of bilateral ring gear blank-holder in thick-plate fine blanking c.j.su, x.h.dong, s.m.guo, q.l.li, t.t.li college of mechanical and electronic engineering, shandong university of science and technology, qingdao 266590, china suchunjian2008@163.com abstract. to compensate for the poor quality of thick-plate blanking parts in cross-section, this paper suggests using the optimizing bilateral ring gear holder parameters to increase burnish zone and improve cutting precision. with the bilateral gear ring, the hydrostatic pressure of shear deformation zone will increase, plasticity of the material will be lifted to maximum and quality of the cross section will be raised. this paper establishes 8mm aisi-1020 fine blanking model by deform2d, analysis different ring gear parameters and clearance that are influenced the stress-strain and cross section quality to predict forming defects. by using the bilateral gear ring blank holder, the poor quality of thick-plate blanking section is successfully enhanced. therefore, the bilateral gear ring blank holder is vital to improve the quality of blanking parts and provide the reliable theory basis for the practical engineering application. keywords. thick-plate; fine blanking; bilateral gear ring blank holder; cross section quality. introduction ine blanking technology has advantages of high efficiency, low energy-expending and low consumption, so it has been widely used in modern industry in recent years. [1, 2] with the wide application in nearly every field, the research on the process has gradually been a hot topic. t.s.kwak et al. [3] analyzed the influence rules of width and height of euphotic belt by using the element-delete method in the process of fine blanking, and concluded that the euphotic belt increases as the tooth height grows, while reduces as the tooth pitch grows. z.h.chen [4] and ridba hambli [5] found tine blanking can achieve maximum brightness by inhibiting the generation of crack, and the distribution rule of stress and strain is given by a detailed analysis on blanking process. peng qun et al. [6] simulated the fine blanking process by using strength blank-holder technology. the material flowing law and strain and stress distribution have been studied, which provide the theoretical basis for fine blanking technology. under the conditions of negative clearance, w.f.fan et al. [7] simulated the fine blanking process of aisi1045 and aisi-1025 with finite element method using cockcroft and latham criteria. the results showed that the negative clearance blanking could guarantee higher cross section quality than common blanking. at present, fine blanking technology adopting thick plate is imperfect compared with that using the thin plate. therefore, to boost production, here higher-quality thick fine blanking pieces is needed. so it is necessary to carry out more researches. the ring gear gag creates optimal conditions for thick plate fine blanking technology that will not only be applied on diversiform material and different thickness of the plank but also be formed into a work piece with high quality. so it has great pragmatic value thus attracts many scholars to research on blank holder with gear ring. f c.j.su et alii, frattura ed integrità strutturale, 30 (2014) 502-514; doi: 10.3221/igf-esis.30.61 503 sutasn thipprakmas [8] carried the simulation on v-ring blank holder with finite element and researched on the influence rule of material flow and stress distribution of the v-ring blank holder. wen limin et al. [9] established the model of fine blanking on blank holder with unilateral v-ring via the finite element, simulated the circular parts with the thickness of 2.9 mm under different tooth pitches, observed the stress distribution of material during the fine blanking process, and obtained the best relative clearance of blank. lin guozheng et al. [10] analyzed the 7 mm thickness of blank with finite element and found out the best blanking clearance and die entrance. from the above study, it is evident that v-ring can restrain the flow of materials in the shear zone and increases the hydrostatic pressure, and then gets a larger euphotic zone. the blank holder with unilateral v-ring has been widely applied in the plate cutting. however, there may be some problems, such as burr, low shape and dimension precision if the plate is too thick. to solve this problem, this thesis brings forward a new method that is holding the blank with bilateral v-ring. it can not only increase the hydrostatic pressure of shearing deformation zone and allow material give full play to its plasticity, but also enhance the cross section quality of shear plane. the mechanism and theoretical basis of metal plate fine blanking the mechanism of metal plate fine blanking ine blanking is a non-chip machining technology. this is a kind of precision stamping method based on common stamping technology. when used in a stamping forming, it can get more precise size precision, more smooth cutting surface, smaller warping and higher quality stampings of interchangeability than ordinary blanking parts and improve the quality of the products under low cost. fine blanking is a process of plastic shear, in the special three dynamic fine blanking press with special structure, under the action of the plate in the plastic shear. before blanking punch contact sheet, a certain pressure makes the v – ring material pressing on the concave die, thus producing lateral pressure on the inner surface of v-shaped teeth and preventing the material tear and metal horizontal flow in shear. in the punch into the materials at the same time, the backpressure of ejector presses the material and in the pressed state, punch down for blanking operation. the material of shear zone in the three directions compresses the stress state, and then improves the material plasticity. the material will produce plastic separation along the punch and die cutting edge. the theoretical basis of metal plate fine blanking before finite elements analysis, the fine blanking deformation zone should go first. the outside force and stress in fine blanking of the deformation areas of the material are shown in fig. 1. (a) (b) figure 1: force and stress of distribution in fine blanking. in the figure： yf －stamping force for punch act on material, y 1 2 y yf f f  , where y 1f 、 y 2f is stamping force and jacking force, vf －force for the inner edges of v-ring act on the material, n －lateral force, x y,p p －friction force, f c.j.su et alii, frattura ed integrità strutturale, 30 (2014) 502-514; doi: 10.3221/igf-esis.30.61 504 y －the normal stress caused by yf vx vy,  －the normal stress caused by component of vf in the x, y direction n －the normal stress caused by n , z －the normal stress caused by mould to restrict materials,  －shear stress caused by friction force. take a coordinate system for oxyz in deformation zone and its stress tensor is t t t    (1) where t －spherical stress tensor t －stress deviator. x n xy m yx y vy m z m vy y z n vx yx vx n z y vy vx vy n n vx 0 0 0 ( ) 0 = 0 0 0 0 0 0 1 2 ( ) ( ) 0 3 3 1 2 ( ) ( ) 0 3 3 1 2 0 0 ( ) ( ) 3 3 yx t                                                                            (2) m m m 0 0 0 0 0 0 t              (3) m y z vx vy z 1 ( ) 3           (4) the plasticity of material (point o) is affected by the hydrostatic pressure in the department of spherical stress tensor. the spherical stress tensor is the static pressure in deformation zone of fine blanking, and the factors that influence the hydrostatic pressure in deformation zone are known from formula 3, so following ways can increase the hydrostatic pressure and then improve the quality of blanking pieces: 1. magnify v by increasing the kicking force; 2. magnify n through reduce the intensive clearance to some extent; 3. magnify vx vy  by enlarging bhf; 4. pressure angle of blank holder sets for optimum value, as shown in fig. 1(a), vx vy v (cos sin )f f f     (5) take the extreme value: x yd( ) 0 v vf f d   v d(cos sin ) (cos sin )vf f      (6) c.j.su et alii, frattura ed integrità strutturale, 30 (2014) 502-514; doi: 10.3221/igf-esis.30.61 505 bhf is a constant value, vd 0f  therefore: π/4 0sin-cos   the finite element simulation analysis of thick plate fine blanking the model of finite elements analysis efore simulating the process of the fine blanking, the model of v-shaped ring gear blank holder should be built first. li chuanmin(2007) [11] found that because of the symmetrical structure, half of the model is adopted to save the time and ram. aisi-20 steel with 8mm thick is used in the paper and the model is simulated by way of the double-side gear ring blank holder whose results are shown in fig. 2. the simulating parameters are shown in tab. 1. friction coefficient 0.12 unit grid 3000 step 0.002 the pressure/kn 20 bhf/kn 60 figure 2: finite element model. table 1: simulation parameters. process simulation of the double ring gear pressure side from fig. 3 (a) to (e) it can be seen that in the process of double ring gear blank holder blanking, the shear zone of hydrostatic pressure is significantly higher than other parts, and compressive stress is also larger near the punch and die cutting edge. when the punch is down to ½ of the material thickness, the pressure stress of the die cutting edge greatly decreases. when the material is broken, the compressive stress that shear zone materials bears is further reduced and the tensile stress appears in the die cutting edge of shear deformation zone material. the greater the compressive stress of materials deformation zone is, the more conducive it is to give full play to the material plasticity so as to inhibit the crack generation or expansion and guarantee high quality blanking section. consequently when the material is broken, the tensile stress that exists in deformation zone exacerbates the material fracture. to sum up, if we want to obtain high quality punching parts with double ring gear blank holder blanking, we must try to increase the three to the compressive stress of material shear deformation zone. because bilateral gear ring blank holder blanking, gear form, tooth height, pitch, the blank holder force and the blank holder force will have different influences on the hydrostatic pressure, we need to simulate and analyze the process parameters [12]. the impact of ring gear form on thick plate fine blanking using the v-shape, a step shaped and the cone gear form to finite element simulation, the hydrostatic pressure distribution is shown in fig. 4. as can be seen from the graph, the hydrostatic pressure distribution that v ring produced is broad, almost filling the entire fine blanking zone. however, the step shaped and the circular cone gear ring only produce hydrostatic pressure in gear ring near, and the scope is relatively small. although the step shaped and the cone b c.j.su et alii, frattura ed integrità strutturale, 30 (2014) 502-514; doi: 10.3221/igf-esis.30.61 506 gear ring blank holder can also play a pressure side effect, but the effect of hydrostatic pressure is far better than that of the v shaped ring gear. in the fine blanking, the gear ring pressure is only one that is large enough to guarantee the materials hydrostatic pressure required in the shear zone. fig. 5 shows the relationship between the gear form and a hydrostatic pressure distribution. as can be seen from the graph, the hydrostatic pressure generated by v ring is the largest and advantageous to the sheet of plastic. (a) before the blanking began (b) ring gear is pressed into the sheet (c) fine blanking 1/4 (d) fine blanking 1/2 (e) material fracture (f) partial view figure 3: fine blanking process simulation of ring gears with both sides (a) v shape (b) step shaped (c) cone gear form figure 4: the hydrostatic pressure distribution with different gear ring form. c.j.su et alii, frattura ed integrità strutturale, 30 (2014) 502-514; doi: 10.3221/igf-esis.30.61 507 figure 5: the relation of gear ring form and hydrostatic pressure distribution. fig. 6 shows the blanking pieces cross section under different forms of gear ring. it is apparent that different forms of gear ring hedge cutting will produce different effects, and bring about different forming results. in addition, fig. 6 demonstrates that the blanking pieces of v-shaped ring gear have a top quality and the change of euphotic zone length is as high as 50%. the blanking pieces of step shaped have a relatively rough cross section and nearly no euphotic zone. the cross section of blanking pieces with cone gear ring is not ideal, and the cross section of blanking pieces is less than v gear ring form. this is because the hydrostatic pressure that produced by steps form and conical gear ring is not big enough to replace the plastic material in the blanking process. a) v shape b) step shaped c) cone gear form figure 6: the shearing section with different gear ring form. the impact of tooth depth on thick plate fine blanking in the case where other conditions remain unchanged, it takes four different sizes of the tooth depth to simulate the process of fine blanking with bilateral gear ring blank holder. as the v-ring on the die cannot change and is easy to wear, v-ring on the die must be set slightly bigger than on the punch. and simulation parameters of the tooth depth are listed in tab.2. tooth depth(mm) pitch(mm) clearance(mm) upper(under) 0.8(1.2) 3.5 0.05 upper(under) 1.2(1.6) 3.5 0.05 upper(under) 1.6(2.0) 3.5 0.05 upper(under) 2.0(2.4) 3.5 0.05 table 2: simulation parameters of tooth depth. c.j.su et alii, frattura ed integrità strutturale, 30 (2014) 502-514; doi: 10.3221/igf-esis.30.61 508 fig. 7 shows the distribution of hydrostatic pressure which is under the condition of ring gear blank into sheet. hydrostatic pressure is produced when ring gear blank presses in sheet and increases with the growth of press-in and reaches the maximum value when different sizes of the tooth depth are all pressed into the sheet as indicated in fig. 7. thus, the hydrostatic pressure increases with the growth of the tooth depth. the depth of teeth is larger and hydrostatic pressure is greater in the fine blanking area, so that the whole process can make full use of plasticity of sheet and achieve high quality section pieces. figure 7: relation of tooth depth and hydrostatic pressure. fig. 8 indicates the distribution of stress in shear deformation zone when fine blanking process is half finished. along with fine blanking, compressive stress is decreasing in the zone of materials shear deformation and tensile stress is produced near the convex and concave die as it is in fig. 8. tensile stress occurs in the process of punching which leads to the cracks. on the contrary, compressive stress can restrain the generation and extension of cracks and effectively improve the plasticity of materials. a) 0.8mm b) 1.2mm c) 1.6mm d) 2.0mm figure 8: stress distribution of fine blanking 1/2 in deformation zone. the relationship between the maximum contact pressure and punch in plate is shown in fig. 9. before the punching, there is a certain value of hydrostatic pressure in shear zone and it creates a better plastic state for the further deformation of material. fig. 9 signifies that the compressive stresses in shear zone are generally large and they increase obviously with the growth of depth tooth, but less when the upper tooth depth exceeds 1.2mm. the average value of compressive stresses is around 75mpa. fig. 10 shows the effect relation curve of blanking quality by tooth depth. while bright zone increases, fillet belt and fault zone decrease as the tooth depth increases. however there is not a linear relationship between the increasing bright zone and the increasing tooth depth. in the meantime hydrostatic pressure also increases with the increasing of tooth depth, but it will leave deep impressions on the sheet if the tooth depth is too large, thus 1.2 mm is the best value for the tooth depth. c.j.su et alii, frattura ed integrità strutturale, 30 (2014) 502-514; doi: 10.3221/igf-esis.30.61 509 figure 9: the relation of maximum contact pressure and punch in plate. figure 10: the effect of blanking quality by tooth depth. the impact of pitch on thick plate fine blanking the optimum parameter of upper tooth depth is 1.2 mm, and the simulation parameters of tooth pitch are shown in tab.3. pitch(mm) upper tooth depth(mm) clearance(mm) 2.6 1.2 0.05 3.5 1.2 0.05 4.6 1.2 0.05 5.7 1.2 0.05 table 3: simulation parameters of tooth pitch. fig. 11 shows the hydrostatic pressure profiles of the different pitch circle of gear pressure style. we can learn from the numerical results that the position of ring gear also has an effect on the hydrostatic pressure, and the hydrostatic pressure decreases with the increasing of pitch. therefore in the process of stamping sheet, appropriate pitch should be chosen to ensure the sufficient hydrostatic pressure blanking, and to fully improve the plastic sheet to obtain the ideal blanking section. fig. 12 shows that, in different pitches, the materials stress distribution of the punch downward 1/6. before the start of the blanking, the shear zone produced a certain value of hydrostatic pressure, creates a better plastic state for the further deformation of material. in the graph, as the pitch increases and compressive stress area reduces deformation, the shear zone compressive stress becomes larger, but stress is smaller far away from the area of fine blanking parts of the compressive. c.j.su et alii, frattura ed integrità strutturale, 30 (2014) 502-514; doi: 10.3221/igf-esis.30.61 510 figure 11: the hydrostatic pressure with different pitch. a) 2.6 mm b) 3.5 mm c) 4.6 mm d) 5.7 mm figure 12: stress distribution of fine blanking 1/6 in deformation zone. fig. 13 shows the relationship between the maximum compressive stress and the convex molding quantity. it is obvious that the stress of the compressive deformation zone significantly increases along with the increasing pitch. because under the same press, pitch that is too big will produces less hydrostatic pressure. thus the quality of the obtained blanking off surface is relatively poor. if the bhf is increased to obtain a good cutting surface, there will be a corresponding increase in punching die load. through many times of finite element simulations, it can be obtained that smooth surface can reach about 80% when the pitch is equal to 3.5mm, which is considered as the ideal pitch. figure 13: the relationship of maximum equivalent stress and convex of pouch in plate. c.j.su et alii, frattura ed integrità strutturale, 30 (2014) 502-514; doi: 10.3221/igf-esis.30.61 511 as can be seen from fig. 14, with the increase of radius of tooth pitch, changes are relatively stable. the euphotic zone decreases with the bright belt length down by 50%; the fracture zone increases thus the bright band increases. as teeth pitch does not increase linearly, the ring gear is closer to the die cutting edge (i.e. pitch is small), the shear zone will produce higher hydrostatic stress, and metal materials tend more to flow to the shear zone and improve the quality of the cross section. in conclusion, the quality of blanked parts is most ideal when the pitch is 3.5mm. figure 14: the effect of blanking quality by tooth pitch. the impact of blanking clearance on thick plate fine blanking the influence of different blanking clearances on the stress distribution is shown in fig. 15. the equivalent stress concentrating near the shear zone when the clearance value is zero and its values vary from 19mpa to 100mpa. the stress values in the zone near the euphotic belt are basically uniform. when clearances are 0.8%t and 1.6%t, the equivalent stress distribution of the areas spreads and has no big changes. when clearance is 2.4%t, the areas of equivalent stress distribution decrease but still with no big changes. (a) 0 (b) 0.8%t (c) 1.6%t (d) 2.4%t figure 15: equivalent stress of fine blanking 1/4 with different clearance. the effect of blanking quality by blanking clearance is shown in fig. 16. the fault zone length increases as clearance does. the fault zone of cross section achieves the shortest and euphotic zone the longest when the clearance is 0.8%t. so 0.8%t is the best value optimum for blanking clearance. it is consistent with the theoretical value about 0.5%t. the euphotic zone proportion will decrease with the increase of clearance in the process of plate fine blanking. it is because compressive stress is delayed in deformation zone and its crack propagation velocity is less than that caused by tensile stress when the die clearance is too large. c.j.su et alii, frattura ed integrità strutturale, 30 (2014) 502-514; doi: 10.3221/igf-esis.30.61 512 figure 16: the effect of blanking quality by blanking clearance experimental results his experiment in fig. 17 uses fine blanking dies that are of different thickness (6mm, 8mm and 10mm) of steel plate to confirm the feasibility of bilateral ring gear blank holder. parts of this experiment are shown in fig. 18. compared with the simulation, the experiment has consistent results as delivered in fig. 19. the blanking part that blank by bilateral gear ring have a high section quality and the experimental results can satisfy the requirement of practical production. 1-plunger 2-punch seat 3-knockout plate 4-die 5-guide pillar 6-guide sleeve 7-guide sleeve of pinger 8-backing plate 9-press countertop 10-adapter ring, 11-hydraulic piston 12-pressure pad ,13-rubber washer 14-plunger 15-die seat 16-ring gear gag 17-punch 18-plunger 19-bridge plate 20-hydraulic slide 21-pull rod 22-punch fix plate 23-adapter ring 24-hydraulic platform figure 17: structure diagram of fine blanking die. it can be seen that the section quality of final parts is higher, the fault zone is also improved, and fillet and burr get smaller. the quality of the eventual parts is ideal. t c.j.su et alii, frattura ed integrità strutturale, 30 (2014) 502-514; doi: 10.3221/igf-esis.30.61 513 figure 18: sample of blanking parts. figure 19: compare results between simulation and experiment. conclusions n this paper, 8mm aisi 1020 steel on both sides of the ring gear blank holder of the fine blanking mechanism is studied with the commercial finite element software deform. in the fine blanking deformation zone of bilateral gear ring blank mode, analyzed of the material flow law and the state of stress and strain. when to blanking aisi – 1020, simulation the influence law that the different ring gear parameters to hydrostatic pressure and cross section quality of blanking parts and optimized its parameters. in the finite element simulation, when choosing nomalized cockroft & latham fracture criterion predicted cracks and expansion, the conclusion are as follows: 1) adopting fine blanking method that uses bilateral gear ring hold blank can achieve smooth blanking section. at the beginning, three-dimensional compressive stress in shear zone gets the maximum value and then declines gradually throughout the process of fine blanking. 2) hydrostatic pressure increases with the increase of tooth depth. when different sizes of tooth depth are all pressed into the sheet, hydrostatic pressure gets its maximum value. the proportion of bright belt also increases in that process. however, if the tooth depth is too big, it will left a deep imprint on sheet metal and affect the next blanking. for 20 steel material with thickness of 8mm, the blanking pieces will get the top quality when tooth depth is 1.2 mm. 3) the hydrostatic pressure decreases with the increase of pitch. the tooth circle is closer to mold parts (while the pitch is smaller), the shear area can produce higher hydrostatic stress, the metal material tends more to flow to the shear zone, and the proportion of bright band is greater. through the finite element simulation, we can find the best relative pitch: a=3.5mm. 4) the blanking clearance is smaller, the proportion of blanking euphotic zone is higher. when the relative blanking clearance is 0.8%t, the bright band proportion of 20 steel approaches 95%. i c.j.su et alii, frattura ed integrità strutturale, 30 (2014) 502-514; doi: 10.3221/igf-esis.30.61 514 acknowledgements his project is supported by: 1) the national natural science foundation of china (grant no. 51305241). 2) the science and technology project for the universities of shandong province (grant no. 201103095). 3) the innovation fund project for postdoctoral of shandong province in china (grant no. j12la03). 4) taishan scholarship project of shandong province, china (no. tshw20130956). references [1] plastic engineering institute of chinese mechanical engineering society (peicmes). forging press manual: stamping(third edition)[m]. mechanical industry press, (2008). [2] ren lixin., research on computer simulation of thick plate fine blanking and optimization of die edge, qingdao: shandong university of science and technology, (2010). [3] kwak, t.s., kim, y.j., the effect of v-ring indenter on the sheared surface in fine-blanking process of pawl, journal material processing technology, 14 (2003) 656-661. [4] chen, z.h., tang, c.y.,a study of strain localization in the fine-blanking process using the large deformation finite element method, journal of materials processing technology, 86 (1999) 163-167. [5] ridba hambli., finite element simulation of fine blanking process using a pressure-dependent damage model. journal of materials processing technology, 7 (2011) 252-264. [6] qun, p., yanqi, z., numerical simulation of fine blanking, forging technology, 4 (2004) 23-25. [7] fan., w.f., li, j.h., an investigation on the damage of aisi-1045 and aisi-1025 steels in fine-blanking with negative clearance, materials science and engineering a, 499 (2009) 248-251. [8] thipprakmas, s., finite element analysis of v-ring indenter mechanism in fine-blanking process, materials and design, 30 (2011) 526-531. [9] limin, w., shuqin, x., the study of relation between the v-ring position and fine-blanking quality, metal forming equipment & manufacturing technology, 1 (2006) 54-56. [10] guozheng, l., jie, z., ying, t., research of deformation mechanism for thick blank punching based on fem simulation, casting forging welding, 37 (2008) 10-13. [11] chuanmin, l., guiding course of deform5.03 on finite element analysis of metal forming, beijing: mechanical industry press, (2007). [12] zhen, z., xincun, z., an improve ductile fracture criterion for fine blanking process, shanghai jiaotong university, 6 (2008) 702-706. t microsoft word numero_37_art_20 m. margetin et alii, frattura ed integrità strutturale, 37 (2016) 146-152; doi: 10.3221/igf-esis.37.20 146 focussed on multiaxial fatigue and fracture multiaxial fatigue criterion based on parameters from torsion and axial s-n curve m. margetin slovak university of technology, faculty of mechanical engineering, slovakia matus.margetin@stuba.sk r. ďurka vakuumtechnik s.r.o., slovakia durka@vakuumtechnik.sk v. chmelko slovak university of technology, faculty of mechanical engineering, slovakia vladimir.chmelko@stuba.sk abstract. multiaxial high cycle fatigue is a topic that concerns nearly all industrial domains. in recent years, a great deal of recommendations how to address problems with multiaxial fatigue life time estimation have been made and a huge progress in the field has been achieved. until now, however, no universal criterion for multiaxial fatigue has been proposed. addressing this situation, this paper offers a design of a new multiaxial criterion for high cycle fatigue. this criterion is based on critical plane search. damage parameter consists of a combination of normal and shear stresses on a critical plane (which is a plane with maximal shear stress amplitude). material parameters used in proposed criterion are obtained from torsion and axial s-n curves. proposed criterion correctly calculates life time for boundary loading condition (pure torsion and pure axial loading). application of proposed model is demonstrated on biaxial loading and the results are verified with testing program using specimens made from s355 steel. fatigue material parameters for proposed criterion and multiple sets of data for different combination of axial and torsional loading have been obtained during the experiment. keywords. fatigue; multiaxial; s355, criterion, material properties. introduction atigue life time prediction plays an important part in mechanical equipment design, regarding operating safety as well as equipment's reliability and economical design. the ongoing increase of machines' operating parameters and the pursuit of both effective material use and operating reliability make the analysis of fatigue process significant in the area of constructions' mechanical endurance calculation. the critical point of a construction that determines the life time of the whole equipment is often localized on a component that is exposed to a complex loading of external forces. whether it's high-pressure piping systems [1] or f m. margetin et alii, frattura ed integrità strutturale, 37 (2016) 146-152; doi: 10.3221/igf-esis.37.20 147 mobile working machines [2], components of both are subjected to combined loading dependent on external conditions. such a loading causes a stresses in the critical point, and this stress state is nearly always multiaxual. in the process of life time estimation in multiaxial stress state, it is not sufficient to transform this state into uniaxial stress state according to static strength hypotheses, as they especially don't consider the cyclical properties of materials and the different effects of normal and shear stresses on the fatigue life time. therefore, it's necessary to use a mathematical model that is both able to reduce the multiaxial stress state to uniaxial stress state and that respects the mentioned problems at the same time. the methodology of transformation into uniaxial stress state then needs to be able to include also the change in the direction of damage, hence to respect the directional characteristic of the fatigue process. nearly a century passed since first attempts to tackle the problem of multiaxial fatigue have been made, and as for the situation today, there are plenty of criteria that consider component's multiaxial stress state. according to the methodology of assessment of loading process in the critical point, these criteria can be divided into stress-based criteria [3,4,5,6], strain-based criteria [7,8,9] and criteria based on fracture mechanics [10,11,12]. this text presents a new stress-based criterion that transforms the multiaxial stress state of a cyclic loading into an equivalent uniaxial stress. this criterion is based on the critical plane approach. after presentation in the text, the criterion is subsequently verified using proportional tension/compression and torsion loading in an experiment. multiaxial fatigue criterion oday's most used stress-based criteria that transform multiaxial stress state into equivalent stress amplitude in critical plane are in the form the following linear or non-linear combination:     c ea fbσ dτ f n (1) findley [3], mcdiarmid [4] and matake [5] have derived criteria for the calculation of the equivalent amplitude of shear stress as a linear combination of amplitude of shear stress and normal stress in the critical plane in the following form    eq fτ σ kτ f n (2) on the other hand, carpintieri with spagnoli [6] and papuga with ruzicka [13] have derived criteria for the calculation of the equivalent amplitude of normal stress in the critical plane as a non-linear combination in the following form    eq 1 2 fσ k σ k τ f n (3) the difference between the respective criteria is in the definition of the critical plane and in the form of material parameters k that consider the effect of normal and shear stresses. the resultant amplitude of the equivalent stress is then compared with the adequate fatigue life time curve in order to determine the finite fatigue life time or with fatigue limit in order to determine the infinite fatigue life time. the results achieved by presented hypotheses more or less correlate with the experimental results, however, there are some commonly known and well documented problems: parameters weighting the effect of normal and shear stress in hypotheses are independent on the loading level (i.e. number of cycles to failure), which is not true universally [14,15]. material parameters are based on conventional values (yield stress, fatigue limit) that are strongly dependent on the methodology of determination and sometimes their existence itself is questionable (fatigue limit being the example there's no agreement on whether there is an actual amplitude of stress that isn't damaging). neither one of the criteria provides correct results for both boundary loading conditions (pure torsion and pure tension/compression loading). t m. margetin et alii, frattura ed integrità strutturale, 37 (2016) 146-152; doi: 10.3221/igf-esis.37.20 148 based on the previous analysis of the problem, authors have decided to present their own criterion for transformation of multiaxial stress state into equivalent uniaxial stress state. presented criterion results from the following theoretical premises: the criterion is based on the critical plane approach and it assumes that the critical plane is the plane with the maximal shear stress amplitude. the premise that the plane with the maximal shear stress amplitude plays a key role in the process of the crack initiation is well documented in work [16]. the criterion reckons with non-linear combination of shear stress amplitude and normal stress amplitude in the critical plane. 2 2 eq , ,τ kσ τa cr a cr  (4) the criterion doesn't use conventional values of material parameters. parameters that represent cyclical characteristics of the tested material are in the form of baskin equation parameters for pure axial loading eq. 5 and pure torsion loading eq. 6.   b' σa f fσ σ 2n (5)   b' τa f fτ τ 2n (6) the criterion is derived so that it provides correct results for both boundary loading conditions (pure torsion and pure tension/compression loading represented by eqs. 5,6). the parameter weighting normal stress is then in eq. 7 and the resulting form of the criterion is shown in eq. 8.   max 2 b bτ σ2, b f , , f f 2τ 2σ k σ σ 1                    (7)    ma 2 b bτ σ2, b b2 2 ,x max f τ a ff, , f f -1 2τ 2σ τ σ τ τ 2n σ σ r                               (8) experimental assessment o verify the function of the proposed criterion, an experiment was conducted in which experimental specimens were tested at different levels of proportional multiaxial loading. experiment was carried out in the strength and elasticity laboratory of the faculty of mechanical engineering stu, using two experimental stands: inova edyz testing system (tension/compression test) and mts bionix 370.02 axial/torsion testing system (torsion test and tension/torsion test). two sets of experimental specimens were manufactured from steel s355j2+c (chemical composition is in tab. 1 and specimens' geometry in fig. 1.). σy02 [mpa] σu [mpa] a5 [%] 655 680 11.2 c [%] p [%] s [%] mn [%] si [%] cu [%] al [%] mo [%] ni [%] cr [%] 0.16 0.014 0.025 1.31 0.18 0.12 0.018 0.01 0.06 0.07 table 1: mechanical and chemical properties of s355j2+c steel t m. margetin et alii, frattura ed integrità strutturale, 37 (2016) 146-152; doi: 10.3221/igf-esis.37.20 149 figure 1: geometry of the experimental specimens. in the first part of the experiment, baskin equation parameters for pure axial loading and pure torsion loading were acquired. experimental specimens were loaded in the force control mode. failure condition of the experimental specimen was defined by the moment of the so-called “technical initiation of fatigue crack” (0,5–1 mm). the number of cycles prior to the initiation of the fatigue crack was determined on the basis of a continuous measurement of the deformation response to the loading regime of the test specimen σa (or τa) = const.. completion of the test was defined either by the increase of the deformation (or by the angle of the distortion) by 1% in reference to the mean value or by the achievement of the life time of 2.106 cycles. the values of material parameters for the regression line and for the upper and lower prediction intervals of reliability for pure axial loading and pure torsion loading are shown in tab. 2. p=50% p=2.5% p=97.5% τf [mpa] bτ [-] τf [mpa] bτ [-] τf [mpa] bτ [-] r 550 -0.0736 565 -0.0739 536 -0.0732 -0.9876 σf [mpa] bσ [-] σf [mpa] bσ [-] σf [mpa] bσ [-] r 636 -0.0531 655 -0.0531 619 -0.0531 -0.9779 table 2: fatigue properties. to verify the validity of the proposed criterion, the experimental program was carried under multiaxial stress state. the experimental specimen was subjected to a proportional combination of axial and torsion loading using controlled loading force and torque. the test was completed by achieving the same conditions as in the uniaxial loading (see above). conclusions esults of the experiment are tabularly summarized in tab. 4. life time estimated by the help of the presented hypothesis eq. 4 is nf_com and the actual measured life time is nf_exp. for the purposes of comparison, tab. 4 includes also estimated life times with the help of the well known hypotheses based on stresses in critical plane r m. margetin et alii, frattura ed integrità strutturale, 37 (2016) 146-152; doi: 10.3221/igf-esis.37.20 150 presented by findley (nf_find) [3] and mcdiarmid (nf_mcd) [4] eqs 9 and 10. for the calculation of the fatigue life time, material parameters for regression line of fatigue curves were used (tab. 2). material parameters used in eqs 9 and 10 are shown in tabs. 1, 2 and 3.       b* τeq a fin n f fmaxτ τ k σ τ 2n (9)           b'mcd τ eq a n,max f f u k τ τ σ τ 2n 2σ (10) kfin [-] τf* [mpa] kmcd [mpa] 0.131 555 244 table 3: material parameters for eqs 9 and 10 n. τa [mpa] σa [mpa] nf_exp nf_com nf_find nf_mcd 1 159 204 650800 643902 485504 291483 2 180 204 172700 202990 154283 94670 3 167 204 597300 415031 313706 189936 4 209 163 105300 96899 65261 42766 5 183 163 536120 449372 283251 181345 6 196 163 198810 205010 133788 86699 7 209 122 193800 165247 113010 77586 8 201 122 301140 267920 178905 122110 9 193 122 375630 441567 287341 194911 10 185 122 996040 740543 468583 315769 11 209 82 231490 226301 178946 129725 12 201 82 572500 375732 291264 210195 13 193 82 952600 635892 482358 346420 14 185 82 2000000* 1098588 813741 581393 table 4: experimental data. looking at the table, it's evident that estimations using findley's or mcdiarmid's criteria are too conservative for the specimen material and the loading levels we used. at the same time, comparing these two criteria, findley's criterion has smaller deviation from the experimentally acquired data. figure 2 shows comparison of calculated and experimentally acquired life times for the proposed hypothesis. for each specimen, nf_cal are listed in the chart shown in a probabilistic form for the regression line and the lower and the upper prediction reliability intervals of the material parameters (tab. 2). chart shows that the proposed hypothesis correlates well with the experimentally acquired values of the fatigue life time. majority of the experimentally acquired life times are placed within the reliability interval of the estimated life times. experimentally acquired life times of specimens number 3,10,12, 13 and 14 were outside of the reliability interval. for these cases, the criterion provided conservative results. the specimen number 14 was put aside after going through 2 .106 loading cycles. based on the experimental verification of the proposed hypothesis (figure 2) and on its comparison with the well known hypotheses (tab. 4), following can be stated:  the hypothesis correlates well with the experimentally acquired data the majority of measured life times are placed within the prediction interval of the calculated life times.  in case the hypothesis doesn't provide correct results (experimentally acquired life time is outside of the prediction interval of the calculated life time), the results are on the conservative side of the calculation. m. margetin et alii, frattura ed integrità strutturale, 37 (2016) 146-152; doi: 10.3221/igf-esis.37.20 151  in comparison with findley's and mcdiarmid's hypotheses, the life times calculated for the particular experimental program are closer to the measured values. at the same time, both hypotheses provide significantly more conservative results then proposed criterion. figure 2: comparison of experimentally acquired and calculated life times. references [1] garan, m., sulko, m., analysis of the service straining on the beam-axle of lorry, int j a sci tech, 3(7) (2013) 4447. [2] garan, m., monitoring of fatigue damague by sensing the deformation state, phd. thesis, slovak university of technology, slovakia, (2010). [3] findley, w.n., fatigue of metals under combinations of stresses, trans asme, 79 (1957) 1337-1338. [4] mcdiarmid, d.l., a general criterion for high cycle multiaxial fatigue failure, fatigue fract eng m, 14(4) (1991) 429453. doi: 10.1111/j.1460-2695.1991.tb00673.x [5] dang van k., sur la résistance a la fatigue des métaux, phd. thesis, sci techniq l´armement, france, (1973). [6] carpinteri a, spagnoli a., multiaxial high-cycle fatigue criterion for hard metals, int j fatigue, 23(2) (2001) 135-45. doi: 10.1016/s0142-1123(00)00075-x [7] fatemi, a., socie, d.f., a critical plane approach to multiaxial fatigue damage including out-of-phase loading, fatigue fract eng m, 11(3) (1988) 149-166. doi: 10.1111/j.1460-2695.1988.tb01169.x [8] brown, m.w., miller, k.j., a theory for fatigue failure under multiaxial stress-strain conditions, p i mech eng, 187 (1973) 745-756. [9] smith, r.n., watson, p., topper, t.h., a stress-strain parameter for the fatigue of metals, j mater, 5 (1970) 767-778. [10] tanaka, k., fatigue crack propagation from a crack inclined to the cyclic tensile axis, eng fract mech, 6(3) (1974) 493-507. doi: 10.1016/0013-7944(74)90007-1 [11] sih, g.c., barthelemy, b.m., mixed mode fatigue crack growth predictions, eng fract mech, 13(3) (1980) 439-451. doi: 10.1016/0013-7944(80)90076-4 [12] hoshide, t., socie, d.f., crack nucleation and growth modeling in biaxial fatigue, eng fract mech, 29(3) (1988) 287299. doi: 10.1016/0013-7944(88)90018-5 [13] papuga, j., ruzicka, m., two new multiaxial criteria for high cycle fatigue computation, int j fatigue, 30(1) (2008) 5866. doi: 10.1016/j.ijfatigue.2007.02.015 7 11 9 1 2 3 4 5 6 8 10 12 13 14 2,e+04 2,e+05 2,e+06 2,e+04 2,e+05 2,e+06 n f_ ca l nf_exp m. margetin et alii, frattura ed integrità strutturale, 37 (2016) 146-152; doi: 10.3221/igf-esis.37.20 152 [14] karolczuk, a., kluger, l., lagoda, t., a correction in the algorithm of fatigue life calculation based on the critical plane approach, int j fatigue, 83(2) (2016) 174-183. doi: 10.1016/j.ijfatigue.2015.10.011 [15] durka, r., contribution to fatigue life time evaluation of structures under multiaxial loading, phd. thesis, slovak university of technology, slovakia, (2012). [16] polak, j., man, j., vystavel, t., petranec, m., the shape of extrusions and intrusions and initiation of stage i fatigue cracks, mater sci eng a, 517 (2009) 204-211. doi: 10.1016/j.msea.2009.03.070 nomenclature σ, τ normal and shear stress respectively σa, τa, σa,eq normal, shear and equivalent stress respectively σf’, τf’ normal and shear fatigue strength coeficient respectively bσ, bτ normal and shear fatigue strength exponent σn normal stress in computed plane nf cycles to failure σy02 yield strength σu ultimate strength ki material parameters used to weight normal and shear stress respectively r correlation coefficient p probability of occurrence << /ascii85encodepages false /allowtransparency false /autopositionepsfiles true /autorotatepages /none /binding /left /calgrayprofile (dot gain 20%) /calrgbprofile (srgb iec61966-2.1) /calcmykprofile (u.s. web coated \050swop\051 v2) /srgbprofile (srgb iec61966-2.1) /cannotembedfontpolicy /error /compatibilitylevel 1.4 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/hrv (za stvaranje adobe pdf dokumenata najpogodnijih za visokokvalitetni ispis prije tiskanja koristite ove postavke. stvoreni pdf dokumenti mogu se otvoriti acrobat i adobe reader 5.0 i kasnijim verzijama.) /hun 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can be opened with acrobat and adobe reader 5.0 and later.) >> /namespace [ (adobe) (common) (1.0) ] /othernamespaces [ << /asreaderspreads false /cropimagestoframes true /errorcontrol /warnandcontinue /flattenerignorespreadoverrides false /includeguidesgrids false /includenonprinting false /includeslug false /namespace [ (adobe) (indesign) (4.0) ] /omitplacedbitmaps false /omitplacedeps false /omitplacedpdf false /simulateoverprint /legacy >> << /addbleedmarks false /addcolorbars false /addcropmarks false /addpageinfo false /addregmarks false /convertcolors /converttocmyk /destinationprofilename () /destinationprofileselector /documentcmyk /downsample16bitimages true /flattenerpreset << /presetselector /mediumresolution >> /formelements false /generatestructure false /includebookmarks false /includehyperlinks false /includeinteractive false /includelayers false /includeprofiles false /multimediahandling /useobjectsettings /namespace [ (adobe) (creativesuite) (2.0) ] /pdfxoutputintentprofileselector /documentcmyk /preserveediting true /untaggedcmykhandling /leaveuntagged /untaggedrgbhandling /usedocumentprofile /usedocumentbleed false >> ] >> setdistillerparams << /hwresolution [2400 2400] /pagesize [612.000 792.000] >> setpagedevice microsoft word numero 23 articolo 5 r. vertechy et alii, frattura ed integrità strutturale, 23 (2013) 47-56; doi: 10.3221/igf-esis.23.05 47 scilla 2012 the italian research on smart materials and mems compliant actuation based on dielectric elastomers for a force-feedback device: modeling and experimental evaluation r. vertechy, m. bergamasco percro laboratory, scuola superiore sant’anna, pisa, italy r.vertechy@sssup.it, m.bergamasco@sssup.it g. berselli department of engineering “enzo ferrari”university of modena and reggio emilia, modena, italy italygiovanni.berselli@unimore.it v. parenti castelli, g. vassura department of mechanical and aeronautical engineering, university of bologna, bologna, italy vincenzo.parenti@unibo.it, gabriele.vassura@unibo.it abstract. thanks to their large power densities, low costs and shock-insensitivity, dielectric elastomers (de) seem to be a promising technology for the implementation of light and compact force-feedback devices such as, for instance, haptic interfaces. nonetheless, the development of these kinds of de-based systems is not trivial owing to the relevant dissipative phenomena that affect the de when subjected to rapidly changing deformations. in this context, the present paper addresses the development of a force feedback controller for an agonist-antagonist linear actuator composed of a couple of conically-shaped de films and a compliant mechanism behaving as a negative-rate bias spring. the actuator is firstly modeled accounting for the viscohyperelastic nature of the de material. the model is then linearized and employed for the design of a force controller. the controller employs a position sensor, which determines the actuator configuration, and a force sensor, which measures the interaction force that the actuator exchanges with the environment. in addition, an optimum full-state observer is also implemented, which enables both accurate estimation of the time-dependent behavior of the elastomeric material and adequate suppression of the sensor measurement noise. preliminary experimental results are provided to validate the proposed actuator-controller architecture. keywords. dielectric elastomers; agonist-antagonist actuation; force-feedback control; haptic interfaces. introduction ielectric elastomer (de) films are visco-elastic capacitors which experience deviatoric deformations and/or generate forces when subjected to high electric potential (voltage) differences [1,2]. thanks to the large force and power densities, relevant compliance and damping, and low effective inertia and cost, de actuators are a promising technology for the development of affordable mechatronic and robotic systems that have to interact effectively, efficiently and safely with unstructured environments and humans [3]. in particular, as already demonstrated by several proof-of-concept prototypes developed in different research institutes all over the world, de actuators can be profitably used for the realization of practical force feedback devices such as, for instance, haptic interfaces (hi) for immersive virtual reality [4,5]. hi are mechatronic devices capable of modulating the forces exchanged with a human operator in d http://www.gruppofrattura.it http://dx.medra.org/10.3221/igf-esis.23.05&auth=true r. vertechy et alii, frattura ed integrità strutturale, 23 (2013) 47-56; doi: 10.3221/igf-esis.23.05 48 order to provide a global sensations of kinesthetic type or local sensations of tactile type. possible advantages that hi can offer to the society come from the realization of the following systems:  simulation in virtual environments for training people to a specific activity (for instance, medical diagnoses and surgical interventions);  prototyping by computer aided design (cad), where the artist or the designer could use the hi for touching or handling the object or the part they are working on;  teleoperation from a remote position for the execution of delicate tasks in hazardous or hardly accessible environments;  multimodal interaction, by which also disable users (for instance, blinds people) could remotely communicate with personal computers and the net more extensively. nowadays, the availability and diffusion on a large scale of the aforementioned systems is limited as long as existing hi are frequently expensive, difficult to manufacture, assemble and maintain, and characterized by low payload to weight ratio and shock sensitivity. within this scenario, the use of smart materials such as de could pave the way to the realization of non-conventional actuation systems with suitable performances to build better-behaved hi, characterized by large power densities, low costs and shock-insensitivity. nonetheless, these de-based environment-interacting devices require stable, fast and accurate regulation of the exchangeable force. this task can actually become quite challenging owing to the relevant dissipative phenomena that affect the majority of de materials when subjected to rapidly changing deformations. as a first step towards the production of practical de-based force feedback devices and hi, the present paper addresses the development of a force controller for an agonist-antagonist linear actuator (see fig. 1). the actuator quasi-static response is predicted on the basis of a non-linear model previously proposed by the authors [6]. then, the system timedependent behaviour is identified resorting to the well-known quasi-linear viscoelastic (qlv) model [7,8], frequently adopted with the sake of compromising between the simplicity of classical linear theories and the difficulty of nonlinear approaches. the overall actuator model is then linearized and employed for designing a force controller which employs a position sensor, is closed around a custom-made force sensor (measuring the actuator-environment interaction force), and implements a state-feedback control law and a kalman filter [9]. this optimum full-state observer makes it possible to compensate for intrinsic de hysteresis and stress relaxation, and to clean-out the sensor measurement noise that usually degrades controller performance. at last, the force regulation capability of the de actuator-controller system is evaluated in dynamic conditions via a properly predisposed experimental test-bench. description of the actuator prototype he actuator cad model is depicted in fig. 1 and comprises:  a rigid frame made by two coaxial identical rings with internal radii equalling rm=40mm and connected by four rods with lengths equalling 2d = 40mm;  an over-constrained compliant parallel mechanism featuring a rigid circular moving platform with external radius equalling rm = 12mm. the mechanism pseudo-rigid body model [10] is depicted in fig. 2. the platform is connected to one of the rigid frame rings via three symmetrically-located identical legs, each articulated via three revolute elastic joints having parallel axes.  two conically-shaped de films (film #1 and film #2) connecting the two rigid frame rings to the mechanism platform (i.e. the actuator output) in an agonist-antagonist arrangement. as previously described in [6], the over-constrained compliant parallel mechanism behaves as a negative stiffness (bias) spring. in particular, thanks to the employed architecture, the actuator output can only move along the actuator axial direction (i.e. the axis of symmetry of the two rigid frame rings). therefore, each leg of the parallel mechanism behaves as a compliant eccentric slider-crank mechanism (fig. 3) with eccentricity, crank and connecting-rod lengths equal to 32e mm , 34.5cr mm and 21.2rr mm , and elastic joint torsional stiffnesses and undeflected angular positions equal to 1 2 1 /k k mnm rad  , 3 51 /k mnm rad , 0 26c   , 0 0 258c r    and 0 232p   . each de film is a circular membrane of acrylic elastomer (vhb-4905 by 3m) with initial thickness (in its undeformed state) equalling 0 1.5t mm , subjected to an equibiaxial pre-stretch equalling 4p  , and coated with a pair of compliant carbon conductive grease electrodes. prior to their use, these virgin de membranes are subjected to preconditioning loading-unloading cycles (as in [6]), which yields a residual stretch (permanent set, 1.6r  ) whose value has been t http://www.gruppofrattura.it http://dx.medra.org/10.3221/igf-esis.23.05&auth=true r. vertechy et alii, frattura ed integrità strutturale, 23 (2013) 47-56; doi: 10.3221/igf-esis.23.05 49 estimated on sacrificial specimen. a voltage difference 1v ( 2v ) between the electrode pair of the de film #1 (#2) generates a rightward (leftward) force on the actuator output. the bias spring has been designed so that the overall actuator in its off-state mode (i.e. 1 2 0v v  ) possesses a rest (stable) position when the actuator output lies exactly in the middle of the rigid frame rings (i.e. when x d ). also, the actuator maintains a positive stiffness across the desired stroke (see sec. mathematical model of the dielectric elastomer film force). for each actuator output position, reciprocal activation of the agonist-antagonist de films enables feed-forward independent regulation of the actuator interaction force. figure 1: de actuator cad model. figure 2: parallel compliant mechanism. pseudo-rigid model. figure 3: slider-crank schematic. mathematical model of the dielectric elastomer film force et first consider the de film #1. the expression of the overall external force, f(f,1), that must be supplied at o and p (and directed along the line joining these points, fig. 2) to balance the de internal reaction force at a given generic configuration x of the actuator, can be split as: ,1 1 ,1 ,1 1( , , ) ( , ) ( , )f ve emf x x v f x x f x v   (1) where f(ve,1) represents the viscoelastic response of the de film and f(em,1) represents an electrically induced term, having the dimension of a force and usually referred to as maxwell force [11, 12]. as for the electrically induced force, a suitable expression for conically-shaped des has been derived in [6] and it is given by: 2 2 2 ,1 1 1( , ) ( ) /em m mf v x x v r r     (2) l http://www.gruppofrattura.it http://dx.medra.org/10.3221/igf-esis.23.05&auth=true r. vertechy et alii, frattura ed integrità strutturale, 23 (2013) 47-56; doi: 10.3221/igf-esis.23.05 50 where 2 2 20( )m m pr r t     is the de volume, 4.5 8.85 12 /e f m    is the dielectric permittivity of the acrylic film, and 0.6  is a suitable dimensionless correction factor. this expression is based on the assumption that the incompressible de is a right circular conical horn with constant wall thickness in any of its deformed configurations. as for the de viscoelastic response, a possible approach is to consider the force response due to a step change in displacement and to superimpose each contribution of a displacement history, ( )x t , by applying a proper superposition principle. resorting to a one dimensional model, the overall force response is then given by: ,1 0 0 ( ) ( ) ( ) [ ( ) ( )ˆ ˆ] t t ve dx f t t d x t d d              (3) having assumed 0x  for 0t  and a differentiable displacement history. the function ˆ ( , )t x is named relaxation function and specifies the force response to a unit step change in displacement. in the qlv framework [7,8], the relaxation function takes the form: ,1( , ) ( ) ( ) ( ˆ 0) 1           ex t f x g t with g   (4) where f(e,1)(x) is the elastic response, i.e. the force generated by an instantaneous displacement, whereas g(t), called reduced relaxation function, describes the time-dependant behavior of the material. as for the latter term, it is customary to assume a linear combination of exponential functions, the exponents νi identifying the rate of the relaxation phenomena, and the coefficients ci depending on the material: 0 0 ( ) 1           i r r t i i i i g t ce with c       (5) where, in general, 0 0  . finally, the total force at the instant t is the sum of the contributions due to all past changes [13], i.e. ,1 ,1 0 [ ( )] ( ) ( ) ( ) t e ve f x x f t g t d x            (6) ,1 0 ( ) [ ( )] ( ) t eg t k x x d      (7) where ,1 ,1( ) [ ] /e ek x f x x   . by substituting eqs. (4) and (5) in eq. (7), one obtains: ( ),1 ,1 0 10 ( ) ( ) ( )i t r t ve e i i f t k x c ce x d                 (8) in particular, referring to fig. 4, the force response given by the qlv model can be interpreted as that of a nonlinear stiffness connected by a series of r linear kelvin models (i.e. a parallel spring-damper system). figure 4: actuator non-linear lumped parameter model. http://www.gruppofrattura.it http://dx.medra.org/10.3221/igf-esis.23.05&auth=true r. vertechy et alii, frattura ed integrità strutturale, 23 (2013) 47-56; doi: 10.3221/igf-esis.23.05 51 concerning the de quasi-static response, a suitable expression for the elastic force of conically-shaped des has been derived in [6] and it is given by:      3 13 1 2 1 22 2 2 2 1 ,1 1 2 1 2 2 2 1 ( ) [ 3) ] ( )  ie i i m m m m x f x ic r r x r r                           (9) where 2 /p r   and 2 2 1 2 1 / ( )m mx r r    are the longitudinal and latitudinal stretches of the de middle surface, 1 30488c pa , 2 151c pa , 3 8c pa are de constitutive parameters of a yeoh-type hyperelastic strain-energy function [14], and 0.93  is a dimensionless correction factor. concerning the reduced relaxation function, 3r  , 0 0.83c  , 1 0.22c  , 2 1 01c c c   , 1 1 4.30v s  , 12 0.70v s  . at last, the contribution of the compliant frame, ( )sf x can be easily evaluated resorting to the pseudo-rigid-body approximation (figs. 2 and 3). in particular, the following relationships are found from the position analysis of a single slider-crank mechanism:  sin ; ; ( ) ( )      c cp c c r p r r e e asin atan x rcos rcos r x                       (10) from the static analysis of the overall compliant frame having three equal legs, the following equation holds: 1 1 3 32 2 3 ( ) 3 ( )3 ( ) ( ) ( ) ( ) ( ) ψ ψψ           p c s c p c c c c c k cos k cosk cos f r sin r sin x sin e cos               (11) where 1 0ψ c c   , 2 0 0ψ p p c c       , 3 0ψ p p   . concerning the agonistic-antagonistic actuator, denoting  as the actuator output position measured from the off-state rest location along its axial direction x d (hereafter this location is referred to as actuator central position), the overall actuator force will be given by:  ,1 2 1 2 ,1 1 ,2 2, , , ( , , ) ( , , ) ( )f f f sf v v f d v f d v f d               (12) where, with obvious notation, ,2 ,2 ,2f ve emf f f  is the reaction force of the de film #2. in particular, figs. 5 and 6 report the simulated force-position (fp) curves of the prototype actuator for the voltage sets { 1 20, 0v v  } (solid line), { 1 26.7 , 0v kv v  } (circle marks) and { 1 20, 6.7v v kv  } (dot marks), for two sinusoidal trajectories with 10 mm amplitude but different frequencies equalling 1 mhz and 0.5 hz respectively. these plots highlight that, within the considered range of motion, the quasi-static response of the considered de actuator is rather elastic and linear, whereas its dynamic behavior is severely affected by the hysteresis of the acrylic elastomeric material, which worsens the actuator response as the motion speed increases. this time-dependent effect renders actuator control very challenging and, in practice, limits the functioning of this prototype to applications involving movements with limited dynamics (less than 0.5 hz position cycles). for larger movement dynamics, different de materials, such as silicone elastomers, should be employed. figure 5: actuator response (1 mhz position cycle). figure 6: actuator response (0.5 hz position cycle). http://www.gruppofrattura.it http://dx.medra.org/10.3221/igf-esis.23.05&auth=true r. vertechy et alii, frattura ed integrità strutturale, 23 (2013) 47-56; doi: 10.3221/igf-esis.23.05 52 control system his section describes an interaction-force control system for the considered agonist-antagonist de actuator. the controller is based on an optimum observer and on a suitable state-feedback law. in particular, for controller design purposes and owing to simulation results reported in the previous section, the actuator model has been linearized such that the considered prototype can be described via the lumped parameter system depicted in fig. 7, where m (m=105g) is the effective inertia of the actuator output (comprising the sensor mass too), kl (kl = 66.5n/m) is a constant stiffness coefficient capturing the off-state quasi-static linear elastic response of the actuator, fint is the interaction force exchanged with the environment, fdist is a disturbance force accounting for the unmodelled non-linear and time-dependent mechanical response of the system (comprising de film visco-elasticity), and fem,l is the “electric” force generated by the electrical activation of the agonist-antagonist de films. based on eq. (2), for the considered de actuator prototype     2 2 2 1 ,em l l max max v v f k d d v v                      (13) where vmax (vmax = 6.7kv) is the maximum voltage which can be placed between each pair of de actuator electrodes. as a result, the de actuator dynamics can be written as ,int l dist em lf m k f f     (14) figure 7: actuator lumped-parameter model. optimal actuator state estimator controller development requires the complete knowledge of the variables  (along with its time derivative), fint and fdist. the considered actuator is equipped with a position and a force sensor that enable the straight measurement of  and fint; however, no direct information is available for fdist. while this disturbance force could be determined via the visco-elastic model described before, for control purposes we have preferred to estimate it via a kalman filter. specifically, consider the augmented state-space system of the de actuator dynamics  elef   a bcx x uy x w  (15.1) 1 2 0 1 1 1 0 0 0 0 1 0 0 0 0 0 0 1 0, , , ,0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 1 t k m m m m u u                                            a= b= = c=u (15.2) where t dist intf f    x (15.3)  tpos forcew ww (15.4) are respectively the state-space variable and the sensor noise vectors (with wforce and wpos being the effective sensor variances), and u1 and u2 are white noise processes with variances u1 and u2. in the system, fdist and fint have been considered as wiener processes [9], that is as continuous functions which vary slowly with independent increments (namely 1distf u and 2intf u ). then, the estimate t http://www.gruppofrattura.it http://dx.medra.org/10.3221/igf-esis.23.05&auth=true r. vertechy et alii, frattura ed integrità strutturale, 23 (2013) 47-56; doi: 10.3221/igf-esis.23.05 53 ˆ ˆ ˆ ˆˆ t dist intf f     x (16.1) of the state-space variable vector follows as  ,ˆ ˆ ˆem lf   a b l cx x y x (16.2) with l being the steady-state observer gain matrix which can be determined via the procedure described in [9] once the unknown observer parameters u1 and u2 are chosen. actuator controller for a given desired interaction force dintf , the following state-feedback law is chosen for the controller , ˆ ˆ ˆ( ) c d d em l l dist int int intf k f f g f f     (17) with g being the force error gain. then, among all the possible infinite choices granted by eq. (13), the following activation laws have been chosen for the agonist and antagonist de films    1 max , , 2c cem l em l lv v f f k d    (18.1)    2 max , , 2c cem l em l lv v f f k d    (18.2) note that eq. (18) implies reciprocal activation of the agonist-antagonist de films. this is the simplest form of agonistantagonist actuator command. experimental results or validation purposes, a prototype of the agonist-antagonist de actuator depicted in fig. 1 has been embedded and tested in a properly designed test-bench as shown in fig. 8. in the reported set-up, the de actuator output is connected through a custom-made force sensor to a position-controlled linear brushless dc motor equipped with a built-in position sensor. in the experiments, these sensors are used to infer actuator interaction force fint and output position δ respectively. the employed force and position sensors are affected by white noise disturbances wforce and wpos with variances equaling wforce=10e-5 n and wpos=8e-10 m. as for the employed driving electronics, each of the agonist and antagonist de films is activated by an efficient compact and low-cost electronic driver, which is custom-made and based on a two-transistor discontinuous-mode fly-back converter topology. regarding specifications, the two considered drivers are capable of regulating their output voltages (namely v1 and v2) from 0 to vmax (vmax = 6.7kv) with a 12 hz cut-off frequency. a picture of one of the driver prototypes is reported in fig. 9; more details on driver design and performances can be found in [15]. figure 8: actuator test-bench. f http://www.gruppofrattura.it http://dx.medra.org/10.3221/igf-esis.23.05&auth=true r. vertechy et alii, frattura ed integrità strutturale, 23 (2013) 47-56; doi: 10.3221/igf-esis.23.05 54 (a) (b) figure 9: custom made electronic driver prototype. (a) circuit diagram; (b) pcb circuit board prototype. in the experimental tests, the interaction force exchanged between de actuator and dc motor is forced to follow a triangular interaction-force signal dintf , while the dc motor cyclically displaces the de actuator output about its offstate rest position with a sinusoidal trajectory. the gain g of the control law described by eq. (17) is set to 3. with the choice u1=u2=10, the steady-state observer (kalman) matrix to be used in eq. (16) is set to 20363 201 111785 2 3 8.29 0.016 5.6595 316 t e     l= (19) the experimental results for a desired interaction-force varying linearly between 1.5n with frequency equalling 1/6hz and for a sinusoidal output motion varying between 10mm with frequency equalling 0.5hz are reported in fig. 10. figure 10: de actuator force-controller validation. http://www.gruppofrattura.it http://dx.medra.org/10.3221/igf-esis.23.05&auth=true r. vertechy et alii, frattura ed integrità strutturale, 23 (2013) 47-56; doi: 10.3221/igf-esis.23.05 55 imposed output motion and desired interaction force command are shown in the first (upper) plot. measured and estimated interaction force tracking errors are shown in the second plot. the reciprocal de actuator activation voltages computed via eq. (18) are reported in the third plot. real (a-priori measured) and estimated (via eq. (16)) disturbance forces are shown in the fourth plot. in particular, the second plot highlights that, for a large part of the experiment duration, the proposed controller is able to keep the measured interaction-force tracking error within ±0.05n, which is roughly equal to the force sensor measurement noise. problems occur between the time intervals spanning from 4.4s and 5.1s and from 7.5 and 8s which, as the third plot shows, are only due to the saturation of the voltage commands v2 and v1 (respectively) rather than to a fault of the controller. note indeed from fig. 6 that, because of the large hysteresis affecting the employed de films at the imposed motion frequency, the considered agonist-antagonist de actuator cannot generate forces greater than 1n for large part of its backward stroke (forces greater than 1.5n can instead be produced for large part of its forward stroke). conclusions n this paper, a closed-loop interaction-force controller for an agonist-antagonist linear actuator based on conicallyshaped dielectric elastomer films has been proposed and validated. the system represents a first step towards the production of practical de-based force feedback devices and hi. at first, a model accounting for the viscohyperelastic nature of the de films has been presented for actuator electro-mechanical design purposes. the model was then linearized and employed for controller synthesis purposes. the developed controller requires a position sensor and a force sensor, implements a reciprocal activation strategy of the agonist-antagonist dielectric elastomer films, employs a state-feedback control law and features a kalman filter which, beside reducing the measurement noise, enables accurate estimation of the dynamic viscous response of the actuator. experimental results showed that the proposed interactionforce controller possesses good force tracking performance whose accuracy is comparable to that of the employed force sensor. due to the significant hysteretic response of the adopted elastomeric material, the force generating ability of the proposed actuator-controller system demonstrated to be valid only for interaction applications involving movements with small-to-medium dynamics. in case higher speeds of motion are required, different de materials such as silicone elastomers can be used. references [1] r. pelrine, r. kornbluh, j. joseph, sensors actuators a, 64(1) (1998) 77. [2] r. vertechy, g. berselli, v. parenti castelli, g. vassura, journal of intelligent material systems and structures, doi: 10.1177/1045389x09356608, 21(5) (2010) 503. [3] r. vertechy, g. berselli m. bergamasco, v. parenti castelli, in: advances in robot kinematics: motion in man and machine, j. lenarcic and m. stanisic eds., springer, doi: 10.1007/978-90-481-9262-5_14, dordrecht, the netherlands, (2010) 127. [4] f. carpi, g. frediani, d. de rossi, ieee trans. on biomedical engineering, 56(9) (2009) 2327. [5] m. y. ozsecen, m. sivak, c. mavroidis, in: proc. of spie, 7647 (2010) 764737(7). [6] berselli, r. vertechy, g. vassura, v. parenti castelli, ieee transactions on mechatronics, doi: 10.1109/tmech.2010.2090664, 16(1) (2011) 67. [7] y. c. fung, biomechanics: mechanical properties of living tissues, springer-verlag, berlin, (1993). [8] g. berselli, r. vertechy, m. babič, v. parenti castelli, journal of intelligent material systems and structures, doi: 10.1177/1045389x12457251, first published on august 28 (2012). [9] b. friedland, control system design: an introduction to state space methods. dover publications, new york, (2005). [10] l. howell, compliant mechanisms, john wiley and sons, new york, (2001). [11] g. kofod, “the static actuation of dielectric elastomer actuators: how does pre-stretch improve actuation?”. j. phys. d: appl. phys., vol. 41, pp. 215405(11), 2008. [12] j. s. plante, s. dubowsky, smart materials and structures, 16(2) (2007) 227. [13] w. n. findley, j. s. lai, k. onaran, creep and relaxation of nonlinear viscoelastic materials: with an introduction to linear viscoelasticity. dover pubblications, new york, (1989). [14] o. h. yeoh, rubber chemistry and technology, 63 (1990) 792. i http://www.gruppofrattura.it http://dx.medra.org/10.3221/igf-esis.23.05&auth=true r. vertechy et alii, frattura ed integrità strutturale, 23 (2013) 47-56; doi: 10.3221/igf-esis.23.05 56 [15] m. babic, r. vertechy, g. berselli, j. lenarcic, v. parenti castelli, g. vassura, mechatronics, doi: 10.1016/j.mechatronics.2009.11.006, 20(2) (2010) 201. http://www.gruppofrattura.it http://dx.medra.org/10.3221/igf-esis.23.05&auth=true microsoft word numero_46_art_34 i. čamagić et alii, frattura ed integrità strutturale, 46 (2018) 371-382; doi: 10.3221/igf-esis.46.34 371 the impact of the temperature and exploitation time on the tensile properties and plain strain fracture toughness, kic in characteristic areas of welded joint ivica čamagić faculty of technical sciences, kosovska mitrovica, serbia ivica.camagic@pr.ac.rs simon a. sedmak innovation centre of faculty of mechanical engineering, belgrade, serbia simon.sedmak@yahoo.com aleksandar sedmak faculty of mechanical engineering, university of belgrade, serbia asedmak@mas.bg.ac.rs zijah burzić military technical institute, belgrade, serbia zijah.burzic@gmail.com mihajlo aranđelović innovation centre of faculty of mechanical engineering, belgrade, serbia mixaylo23@gmail.com abstract. this paper presents the analysis of the temperature and exploitation time impact on the resistant measure to brittle fracture of welded joint constituents of the new and exploited low-alloyed cr-mo steel a-387 gr. b from the aspect of application of the parameters obtained by tensile testing and parameters obtained by fracture mechanics testing. the exploited parent metal is a part of the reactor mantle which has working for over 40 years and is in the damage repair stage, wherein it is being replaced with a new material. basic characteristics of the material strength, as well as the stress-elongation curves required for stress analysis are obtained by tensile testing. the testing of plane strain fracture toughness is conducted in order to determine the critical stress intensity factor, kic, that is, assessment of behavior of the new and exploited parent metal, welded metal and heat affected zone from the side of the new parent metal and from the side of the exploited parent metal in the citation: čamagić, i, sedmak, s. a., sedmak, a., burzić, z., aranđelović, m., the impact of the temperature and exploitation time on the tensile properties and plain strain fracture toughness, kic in characteristic areas of welded joint , frattura ed integrità strutturale, 46 (2018) 371-382. received: 05.08.2018 accepted: 21.09.2018 published: 01.10.2018 copyright: © 2018 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, http://www.gruppofrattura.it/va/46/34.mp4 i. čamagić et alii, frattura ed integrità strutturale, 46 (2018) 371-382; doi: 10.3221/igf-esis.46.34 372 presence of the crack type error. based on the research results, the analysis of the resistance to brittle fracture was performed in order to compare the obtained values for characteristic areas of welded joint and justify the selection of welding technology. keywords. welded joint; tensile properties; plane strain fracture toughness; critical crack length. and reproduction in any medium, provided the original author and source are credited. introduction long-time exploitation period of a pressure vessel-reactor (over 40 years) has caused certain damages to the reactor mantle. the occurrence of these damages required a thorough inspection of the reactor construction itself, as well as the repair of damaged parts. repairing of the reactor included the replacement of a part of the reactor mantle with newly built-in material. the given pressure vessel was made of low-alloyed cr-mo steel a-387 gr. b in accordance with astm standard with (0.8-1.15)% cr and (0.45-0.6)% mo. for designed working parameters (p = 35 bar and t = 537c) the material is in the area of tendency towards decarbonisation of the surface which is in contact with hydrogen. the surface decarbonisation may reduce the strength of the material. the reactor, based on its construction represents a vertical pressure vessel with a cylindrical mantle. deep lids of the same quality as the reactor mantle are welded to upper and lower side of the mantle. the most important process in motor gasoline production stage takes place in the reactora platforming for altering the structure of hydrocarbon compounds and achieving a higher gasoline octane number. testing of a new and exploited parent metal (pm), the weld metal-wm and heat affected zone (haz), included the determinating of tensile properties and fracture mechanics parameters of the new and exploited pm and welded joint components (wm and haz), at room and working temperature of 540c, [1]. welding technology qualification for sheets made of new and exploited pm was performed in accordance with standard srps en iso 15614-1, [2]. the research performed here was based on the experiences from previous experiments involving the determining of fracture toughness and fatigue crack growth parameters at room and working temperatures, as seen in [3,4]. materials for testing oth exploited (e) and new (n) steel a-387 gr. b with thickness of 102 mm were analyzed. chemical composition and mechanical properties of the exploited and new pm according to the attest documentation are given in tab. 1 and 2, [1]. welding of steel sheets made of exploited and new pm was performed in two stages, according to the requirements given in the welding procedure provided by a welding specialist, and these stages include:  root weld by e procedure, using a coated lincoln s1 19g electrode (aws: e8018-b2), and  filling by arc welding under powder protection (epp), where wire denoted as lincoln lns 150 and powder denoted as lincoln p230 were used as additional materials. chemical composition of the coated electrode lincoln s1 19g, and the wire lincoln lns 150 according to the attest documentation is given in tab. 3, whereas their mechanical properties, also according to the attest documentation, are given in tab. 4, [1]. specimen mark % max. c si mn p s cr mo cu e (exploited) 0.15 0.31 0.56 0.007 0.006 0.89 0.47 0.027 n (new) 0.13 0.23 0.46 0.009 0.006 0.85 0.51 0.035 table 1: chemical composition of exploited and new pm specimens. a b i. čamagić et alii, frattura ed integrità strutturale, 46 (2018) 371-382; doi: 10.3221/igf-esis.46.34 373 specimen mark yield stress, rp0.2, mpa tensile strength, rm, mpa elongation, a, % impact energy, j e 320 450 34.0 155 n 325 495 35.0 165 table 2: mechanical properties of exploited and new pm specimens. additional material % max. c si mn p s cr mo lincoln sl 19g 0.07 0.31 0.62 0.009 0.010 1.17 0.54 lincoln lns 150 0.10 0.14 0.71 0.010 0.010 1.12 0.48 table 3: chemical composition of additional welding materials. additional material yield stress, rp0.2, mpa tensile strength, rm, mpa elongation, a, % impact energy, j at 20c lincoln sl 19g 515 610 20 > 60 lincoln lns 150 495 605 21 > 80 table 4: mechanical properties of filler materials. determination of tensile properties asic characteristics of material strength, as well as the stress-elongation curves required for stress analysis, are obtained by tensile testing. tensile testing of butt welded joint at room temperature, including the shape and dimensions of specimens as well as the procedure itself are defined by srps en 895:2008 standard, [5]. this standard primarily defines transverse tension, i.e. introduction of the load transversely to the welded joint. srps en 895:2008 standard also envisages the determination of the tensile properties of pm and wm at room temperature. determination of tensile properties of pm is defined by srps en 10002-1 standard, [6]. figure 1: tensile test specimens for wm and haz. unlike room temperature testing, the testing procedures at increased temperature of 540c, as well as the specimen geometry are defined by srps en 10002-5 standard, [7]. the specimens used for determining of tensile properties of wm and haz, as well as for working temperature tensile tests are shown in figs. 1 and 2, respectively. b i. čamagić et alii, frattura ed integrità strutturale, 46 (2018) 371-382; doi: 10.3221/igf-esis.46.34 374 testing results of butt welded joint specimens by transverse tension at room temperature of 20c and working temperature of 540c are given in tab. 5, [1]. typical tensile stress-elongation curve for specimen of butt welded joint marked as wj-11, tested at room temperature is shown in fig. 3, left [1], and for specimen marked as wj-2-1, tested at working temperature is shown in fig. 3, right. figure 2: specimens for tensile testing at working temperature. specimen designation testing temperature, c yield stress, rp0.2, mpa tensile strength, rm, mpa elongation1, a, % fracture location wj-1-1 295 451 19.2 expl. pm wj-1-2 20 285 448 20.4 expl. pm wj-1-3 291 454 19.7 expl. pm wj-2-1 217 293 26.3 expl. pm wj-2-2 540 205 285 25.6 expl. pm wj-2-3 211 287 26.9 expl. pm 1 measured at l0 = 100mm, as comparative value (not as a material property). table 5: results of tensile testing of the welded joint. 0 5 10 15 20 25 30 0 100 200 300 400 500 600 wj-1-1 20 o c s tr es s, r , m p a elongation, a, % 0 5 10 15 20 25 30 0 100 200 300 400 500 600 wj-2-1 540 o c s tr es s, r , m p a elongation, a, % figure 3: stress-elongation diagram of a butt welded joint specimen wj-1-1 (left) and specimen wj-2-1 (right). testing results of specimens of the new pm at room temperature of 20c and working temperature 540c are given in tab. 6, [1]. testing of exploited pm was not performed, because during the testing of welded joint specimens all tested specimens fractured in the exploited pm, which provided us with the properties of exploited pm. typical tensile stress-elongation curve for specimen denoted by pm-1-1n, taken from the new pm and tested at room temperature is given in fig. 4, left [1], and for specimen pm-2-1n, also taken from the new pm, but tested at working temperature, is shown in fig. 4, right [1]. i. čamagić et alii, frattura ed integrità strutturale, 46 (2018) 371-382; doi: 10.3221/igf-esis.46.34 375 specimen designation testing temperature. c yield stress. rp0.2. mpa tensile stress. rm. mpa elongation. a. % pm-1-1n 20 342 513 27.5 pm-1-2n 339 505 28.3 pm-1-3n 335 498 28.6 pm-2-1n 540 251 323 29.1 pm-2-2n 242 316 30.8 pm-2-3n 247 320 30.4 table 6: results of tensile testing of new pm specimens. 0 5 10 15 20 25 30 0 100 200 300 400 500 600 pm-1-1n 20 o c s tr es s, r , m p a elongation, a, % 0 5 10 15 20 25 30 0 100 200 300 400 500 600 pm-2-1n 540 o c s tr es s, r , m p a elongation, a, % figure 4: stress-elongation diagram of a new pm specimen pm-1-1n (left) and new specimen pm-2-1n (right). testing results of wm specimens tested at room temperature of 20c and working temperature of 540c are given in tab. 7, [1]. typical tensile stress-elongation curve for wm specimen marked as wm-1-1, tested at room temperature is shown in fig.5, left [1], and for specimen marked as wm-2-1, tested at working temperature is shown in fig. 5, right [1]. specimen designation testing temperature, c yield stress, rp0.2, mpa tensile strength, rm, mpa elongation, a, % wm-1-1 20 518 611 20.9 wm-1-2 510 597 22.7 wm-1-3 514 605 21.3 wm-2-1 540 331 419 26.1 wm-2-2 319 406 27.3 wm-2-3 325 412 27.7 table 7: results of tensile testing of wm specimens. i. čamagić et alii, frattura ed integrità strutturale, 46 (2018) 371-382; doi: 10.3221/igf-esis.46.34 376 0 5 10 15 20 25 30 0 100 200 300 400 500 600 700 800 wm-1-1 20 o c s tr es s, r , m p a elongation, a, % 0 5 10 15 20 25 30 0 100 200 300 400 500 600 700 800 wm-2-1 540 o c s tr es s, r , m p a elongation, a, % figure 5: stress-elongation diagram for wm specimen, wm-1-1 (left) and wm specimen wm-2-1 (right) determination of plane strain fracture toughness, kic he impact of exploitation conditions, i.e. exploitation time and temperature on tendency to brittle fracture of the new and exploited pm, as well as the components of welded joint (wm and haz) was evaluated by determining the plane strain fracture toughness, that is, critical value of stress intensity factor, kic. the testing was performed at room temperature of 20c and working temperature of 540c. for determination of, kic, at room temperature the three point bending specimen (seb) were used, whose geometry is defined by astm e399, [8], and astm e1820 standards, [9]. for determination of kic at working temperature of 540c the modified ct tensile specimens were used, whose geometry is in accordance with bs 7448 part 1, standard, [10]. fracture toughness, kic, is determined indirectly through critical j-integral, jic, using elastic-plastic fracture mechanics (epfm) defined by astm e813, [11], astm e 1737, [12], astm e1820, [9] and bs 7448 part 1 and 2, [10, 13] standards, that is, by monitoring the crack development in the conditions of plasticity. the american society for testing and materials (astm) has established a standard procedure for obtaining the crack growth resistance curves of metallic materials, [12]. the improvement of the standard was carried out within the framework of the european structural integrity society esis, [14]. some of the solutions of this standard are also adopted in this paper and refer to the determination of fitted regression line. standards, [8, 9, 11, 12, 15-17], regularly updates, and it is very important to make sure that the latest versions are applied. the experiments are carried out by the testing method of a single specimen by successive partial unload, i.e. by the single specimen permeability method, as defined by astm e813, standard, 11. based on the obtained data, j-a curve is constructed on which the regression line is constructed according to astm e1152, [16]. from the obtained regression line the critical j-integral, jic, is obtained. knowing the value of critical, jic, integral, the value of critical stress intensity factor or plane strain fracture toughness, kic, can be calculated using the dependence: 21 ic ic j e k     (1) calculated values of critical stress intensity factor, kic, are given in tab. 8 for notched specimens in new pm, and in tab. 9 for notched specimens in exploited pm, tested at room temperature of 20c and working temperature of 540c, [1]. it is important to point out that in calculation of plane strain fracture toughness, kic, one value was used for elastic modulus at room temperature (210gpa) and other value for increased temperatures (approximately 160gpa for 5400c). by applying basic formula of fracture mechanics: ic ck a    (2) t i. čamagić et alii, frattura ed integrità strutturale, 46 (2018) 371-382; doi: 10.3221/igf-esis.46.34 377 and by introducing the values of conventional yield stress, rp0,2 = , [1, 17], the approximate values for critical crack length, ac, can be calculated. specimen mark testing temperature. c critical j-integral. jic, kj/m2 critical stress intensity factor, kic, mpa m1/2 critical crack length, ac, mm pm-1-1n 20 60.1 117.8 38.5 pm-1-2n 63.9 121.4 40.8 pm-1-3n 58.6 116.3 37.5 pm-2-1n 540 43.2 87.2 40.0 pm-2-2n 44.7 88.7 41.4 pm-2-3n 45.3 89.2 41.9 table 8: values of kic notched specimens in new pm. specimen mark testing temperature, c critical j-integral, jic, kj/m2 critical stress intensity factor, kic, mpa m1/2 critical crack length, ac, mm pm-1-1e 20 47.8 105.0 41.7 pm-1-2e 42.1 98.6 36.8 pm-1-3e 40.7 96.9 35.6 pm-2-1e 540 24.5 65.6 30.8 pm-2-2e 22.7 63.2 28.6 pm-2-3e 21.8 61.9 27.4 table 9: values of kic notched specimens in exploited pm. the characteristic diagrams f-, and j-a for specimen taken out from the sample of new pm are given in fig. 6 (left) for specimen marked as pm-1-1n tested at room temperature, and in fig. 7 for specimen marked as pm-2-1n tested at the temperature of 540c, [1]. 0 1 2 3 4 5 6 7 8 0 4 8 12 16 pm-1-1n 20 o c f , k n , mm 0 1 2 3 4 5 6 7 8 0 50 100 150 200 250 pm-1-1n 20 o c j ic = 60,1 kj/m 2 j ic j, k j/ m 2 a, mm figure 6: f-δ (left) and j-δa (right) diagrams of specimen pm-1-1n. i. čamagić et alii, frattura ed integrità strutturale, 46 (2018) 371-382; doi: 10.3221/igf-esis.46.34 378 0 1 2 3 4 5 6 7 8 0 4 8 12 16 pm-2-1n 540 o c f , k n , mm 0 1 2 3 4 5 6 7 8 0 50 100 150 200 250 pm-2-1n 540 o c j ic = 43,2 kj/m 2 j ic j, k j/ m 2 a, mm figure 7: f-δ (left) and j-δa (right) diagrams of specimen pm-2-1n. the influence of testing temperature on the value of critical stress intensity factor, kic, for specimens taken from the new and exploited pm is graphically illustrated in fig. 8 (left), and the impact of the testing temperature on the critical crack length, ac, is graphically illustrated in fig. 8 (right), [1]. 0 100 200 300 400 500 600 0 40 80 120 160 200 parent metal pm new pm exploited pm f ra ct u re t o ug hn es s, k ic , m p a m 1/ 2 testing temperature, o c 0 100 200 300 400 500 600 0 20 40 60 80 100 parent metal pm new pm exploited pm c ri ti ca l cr ac k l en g th , a c , m m testing temperature, o c figure 8: changes in value of kic depending on the testing temperature for the pm (left) and change in value of ac (right) calculated values of critical stress intensity factor, kic, and critical crack length, ac, are given in the tab.10 for notched specimens in wm, tested at room temperature of 20c and working temperature of 540c, [1]. specimen mark testing temperature, c critical j-integral, jic, kj/m2 critical stress intensity factor, kic, mpa m1/2 critical crack length, ac, mm wm-1-1 20 72.8 129.6 20.2 wm-1-2 74.3 130.9 20.7 wm-1-3 71.1 128.1 19.8 wm-2-1 540 50.2 93.9 17.4 wm-2-2 52.6 96.2 18.2 wm-2-3 48.4 92.2 16.8 table 10: values of, kic notched specimens at wm. i. čamagić et alii, frattura ed integrità strutturale, 46 (2018) 371-382; doi: 10.3221/igf-esis.46.34 379 impact of the testing temperature on the value of critical stress intensity factor, kic, for notched specimens in wm is graphically illustrated in fig. 9 (left), and the impact of the testing temperature on the value of the critical crack length, ac, is graphically illustrated in fig. 9, (right) [1]. 0 100 200 300 400 500 600 0 40 80 120 160 200 weld metal wm f ra ct ur e to u gh ne ss , k ic , m p a m 1/ 2 testing temperature, o c 0 100 200 300 400 500 600 0 10 20 30 40 50 weld metal wm c ri ti ca l cr ac k l en g th , a c , m m testing temperature, o c figure 9: changes in value of kic depending on the testing temperature for the wm (left) and change in value of ac (right). calculated values of critical stress intensity factor, kic, and critical crack length, ac, are given in the tab. 11 for notched specimens in haz from the side of the new pm and in tab. 12 for notched specimens in haz from the side of the exploited pm, tested at room temperature of 20c and working temperature of 540c, [1]. specimen mark testing temperature, c critical j-integral, jic, kj/m2 critical stress intensity factor, kic, mpa m1/2 critical crack length, ac, mm haz-1-1n 20 53.6 111.2 34.3 haz-1-2n 51.7 109.2 33.0 haz-1-3n 49.8 107.2 31.8 haz-2-1n 540 33.6 76.9 31.1 haz-2-2n 34.2 77.5 31.6 haz-2-3n 36.1 79.7 33.4 table 11: values of, kic notched specimens at new haz. specimen mark testing temperature, c critical j-integral, jic, kj/m2 critical stress intensity factor, kic, mpa m1/2 critical crack length, ac, mm haz-1-1e 20 42.4 96.3 32.0 haz-1-2e 36.1 91.3 31.5 haz-1-3e 35.6 90.6 31.1 haz-2-1e 540 20.2 59.6 25.4 haz-2-2e 22.5 62.9 28.3 haz-2-3e 21.7 61.8 27.3 table 12: values of, kic notched specimens at exploited haz. i. čamagić et alii, frattura ed integrità strutturale, 46 (2018) 371-382; doi: 10.3221/igf-esis.46.34 380 impact of the testing temperature on the value of critical stress intensity factor, kic, for notched specimens in haz from the side of the new and exploited pm is graphically illustrated in fig. 10 (left), and the impact of the testing temperature on the value of the critical crack length, ac, also for the notched specimens in haz from the side of the new and exploited pm is graphically illustrated in fig. 10, (right) [1]. 0 100 200 300 400 500 600 0 40 80 120 160 200 heat affected zone haz new haz exploited haz f ra ct u re t o u g h n es s, k ic , m p a m 1 /2 testing temperature, o c 0 100 200 300 400 500 600 0 10 20 30 40 50 60 heat affected zone haz new haz exploited haz c ri ti ca l cr ac k l en g th , a c , m m testing temperature, o c figure 10: change in value of kic depending on the testing temperature at haz (left) and change in value of ac (right). discussion esting of the welded joint specimens by introducing the load transversely to welded joint provided necessary data regarding how selected welding technology and exploitation time impact the welded joint strength and welded joint components. the obtained results of testing the welded joint specimens by introducing load transversely to welded joint, tab. 5, indicate that all tested specimens have cracked in exploited pm. this information is of great importance because it indicates the weakening of pm which was in exploitation. the fracture of specimens in pm clearly indicates the character of the welded joint. this is “over-matching”, which means that the strength of the welded metal is higher than the strength of the parent metal, [1, 18]. character of obtained tensile curves at room temperature corresponds to a ductile material with approximate share of homogeneous and non-homogeneous elongation at a ratio of 1/2:1/2. here, homogeneous elongation is considered as elongation up to the maximum force, and non-homogenous elongation is considered as elongation from maximum force to fracture (unstable crack growth, i.e. necking). when testing the welded joint specimens at working temperature, there is a similar tendency of change in the properties of strength as with the testing at room temperature, but the difference occurs at the properties of strain (elongation). namely, here we have the case where the ratio of homogeneous to non-homogeneous elongation is approximately 1/4:3/4, which is rather unfavourable from the aspect of exploitation properties. the reserve of homogenous plasticity of materials is considerably smaller, thus the hazard to pm of the consequences of potentially poor operation of the plant is real. by analysing the results obtained by tensile testing at room temperature of specimens taken from the sample of the new pm, given in tab. 6, it can be concluded that the testing results of the new pm are within the limits of values prescribed by the standard for that material, that is, values provided by a manufacturer in attest documentation. the obtained results of tensile testing of wm specimens given in tab. 7 confirm the properly selected welding technology, i.e. welding parameters. yield stress and tensile strength satisfy values prescribed by the standard, whereas strain properties are much better than those given in the standard for this additional material, [19]. this phenomenon indicates a high-grade selected regime of thermal processing after welding. the behaviour of the haz in the loaded welded joint was conditioned by its small volume portion, as well as by the heterogeneity of the structure and different mechanical properties of certain haz areas. a well-made welded joint, designed according to the principle of higher wm strength, should break in pm, which is exactly what happened in presented tests, [1, 18]. based on the obtained testing results of specimens taken from the new and exploited pm, wm and haz from the side of the new and exploited pm, it can be seen that with the increase of the testing temperature there is a decrease in the value of critical jic, integral, that is, fracture toughness, kic. the value of critical crack length, ac, also decreases. t i. čamagić et alii, frattura ed integrità strutturale, 46 (2018) 371-382; doi: 10.3221/igf-esis.46.34 381 the fracture toughness values, kic, of specimens, taken from the new pm, tab. 8, range from 118mpa m1/2 obtained by testing at 20c and decrease to 88mpa m1/2 at 540c. also, the fracture toughness values, kic, of specimens, taken from the exploited pm, tab. 9, range from 100mpa m1/2 obtained by testing at 20c and decrease to 64mpa m1/2 at 540c. the fracture toughness values, kic, of specimens, taken from wm, tab. 10, range from 130mpa m1/2 obtained by testing at 20c to 94mpa m1/2 obtained by testing at 540c. the fracture toughness values, kic, of specimens, taken from haz from the side of the new pm, tab. 11, range from 109mpa m1/2 obtained by testing at 20c and decrease to 78mpa m1/2 obtained by testing at 540c. the testing of specimens taken from haz from the side of exploited pm, tab. 12, the poorer values of fracture toughness kic are obtained. namely, namely, the value of plane strain fracture toughness, kic, ranges from 93mpa m1/2 obtained by testing at 20c, and decreases to 61mpa m1/2 obtained by testing at 540c, [1]. the obtained values of critical crack length, ac, fig. 10, at new pm are almost unchanged when it comes to room and working temperature. this was to be expected, because for the calculation of critical crack length, ac, the real values of yield stress obtained by tensile testing were used. however, exploitation weakening of pm has led to the fact that value of ac at specimens taken from exploited pm decreases by about 24% and is about 29mm. the obtained values of critical crack length, ac, fig. 12, at wm in relation to the yield stress level are quite low, and range from 20,2mm for the room temperature and decrease to 17,5mm which is the obtained value of ac, at the testing temperature of 540c. however, if values of critical crack length, ac, in relation to yield stress of the new and exploited om are calculated, they are significantly higher and indicate the good resistance to brittle fracture of wm. the obtained values of critical crack length, ac, fig. 14, at haz from the side of the new pm are slightly changed when it comes to room or working temperature. however, exploitation weakening of pm has led to the decrease of the value, ac, at notched specimens in haz from the side of exploited pm and at the testing temperature of 5400c is 27mm, [1]. conclusion ased on the testing results of tensile properties of specimens taken from the welded joint of the new pm and wm at selected temperatures, it can be concluded that a decrease in strength properties, that is, yield stress and tensile strength was obtained with the increase of temperature. likewise, the increase of testing temperature leads to the increase of elongation. the increase of elongation with the temperature increase is explained by the increased overall plasticity of the material at higher temperatures, but also by the significantly unfavorable ratio of homogenous and nonhomogenous elongation. also, the exploitation time significantly impacts the reduction of strength properties and strain properties, which can be related to the microstructures of the exploited and new pm, [1]. based on the obtained testing results of the critical stress intensity factor kic, which was due to inability to satisfy the plane strain conditions determined indirectly through the critical jic integral, we can see that the values of kic also depend on the testing temperature, placement of notches and exploitation time. the heterogeneity of welded joint mechanical properties, i.e. welded joint components significantly impacts the obtained values of plain strain fracture toughness, kic. the weakest resistance to the crack propagation at static action of force, that is, the lowest value, kic, is at notched specimens in haz, and the best resistance to crack propagation is at notched specimens at wm. the character of the curves, exclusively changes depending on the testing temperature, placement of the notches and exploitation time. by analyzing the obtained curves, we see the almost identical character dependence of the individual curves in each group, except that the difference between the specimens is in the values of maximum force, fmax, which is in direct dependence on the fatigue crack length, a, [1]. exploitation time significantly impacted the resistance to crack propagation, which generally should be related to the weakening of mechanical exploitation properties of the used material in relation to the new material. the resistance to crack propagation, at specimens taken from the exploited pm and from haz from the side of exploited pm is for approximately 20% lower than at specimens taken from the sample of the new pm, and haz from the side of the new pm. the obtained testing results of fracture mechanics parameters (kic, jic i ac) indicate two things. first, tendency to brittle fracture in the conditions of static load acting, is the lowest at the notched specimens in wm and pm and is the highest at the notched specimens in haz, i.e. haz in the concrete case has the worst resistance to brittle fracture. second, the obtained testing results of exploited material indicate a significant difference in the results compared to the new material. testing results and their analysis have justified the selected welding technology for the replacement of a part of the reactor mantle. b i. čamagić et alii, frattura ed integrità strutturale, 46 (2018) 371-382; doi: 10.3221/igf-esis.46.34 382 acknowledgement arts of this research were supported by the ministry of sciences and technology of republic of serbia through mathematical institute sanu belgrade grant oi 174001 dynamics of hybrid systems with complex structures. mechanics of materials and faculty of technical sciences university of pristina residing in kosovska mitrovica. references [1] čamagić, i. (2013). investigation of the effects of exploitation conditions on the structural life and integrity assessment of pressure vessels for high temperatures (in serbian), doctoral thesis, faculty of technical sciences, kosovska mitrovica. [2] srps en iso 15614-1:2017, specification and qualification of welding procedures for metallic materials welding procedure test part 1: arc and gas welding of steels and arc welding of nickel and nickel alloys (iso 15614-1:2017, corrected version 2017-10-01), 2017. [3] burzić, m., (2008). analiza parametara prsline toplo–otpornog čelika, integritet i vek konstrukcija, 6(1), pp. 45-56. [4] čamagić, i., sedmak, s., sedmak, a., burzić, z. and todić, a. (2017). impact of temperature and exploitation time on plane strain fracture toughness, kic, in a welded joint, structural integrity and life, 17(3), pp. 239–244. [5] srps en 895:2008, destructive tests on welds in metallic materials transverse tensile test, (2008). [6] srps en 10002-1, metallic materials tensile testing part 1: method of test (at ambient temperature), (1996). [7] srps en 10002-5, metallic materials tensile testing part 5: method of testing at elevated temperature, (1997). [8] astm e399-89, standard test method for plane-strain fracture toughness of metallic materials, annual book of astm standards, 03.01, pp. 522, (1986). [9] astm e 1820-99a, standard test method for measurement of fracture toughness, annual book of astm standards, 03.01, (1999). [10] bs 7448-part 1, fracture mechanics toughness tests-method for determination of kic critical ctod and critical j values of metallic materials, bsi, (1991). [11] astm e813-89, standard test method for jic, a measure of fracture toughness, annual book of astm standards, 03.01, pp. 651, (1993). [12] astm e 1737-96, standard test method for j integral characterization of fracture toughness, annual book of astm standards, 03.01, (1996). [13] bs 7448-part 2, fracture mechanics toughness tests methods for determination of kic, critical ctod and critical j values of welds in metallic materials, bbi, (1997). [14] esis procedure for determining the fracture behavior of materials, european structural integrity society esis p292, (1992). [15] bs 5762-dd 19, standard test method for crack opening displacement, london, (1976). [16] astm e1152-91, standard test method for determining j-r curve, annual book of astm standards, 03.01, pp. 724, (1995). [17] astm e 1290-89, standard test method for crack-tip opening displacement (ctod) fracture toughness measurement, annual book of astm standards, 03.01, (1993). [18] camagic, i., burzic, z., sedmak, a., dascau, h. and milovic, l. (2015). temperature effect on a low-alloyed steel welded joints tensile properties, the 3rd iiw south – east european welding congress, welding & joining technologies for a sustainable development & environment, timisoara, romania, (77-81). [19] burzić, z. (2002). savremene metode provere mehaničko-tehnoloških osobina zavarenih spojeva-deo 2, zavarivanje i zavarene konstrukcije, 47(3), pp. 151-158. p << /ascii85encodepages false /allowtransparency false /autopositionepsfiles true /autorotatepages /none /binding /left /calgrayprofile (dot gain 20%) /calrgbprofile (srgb iec61966-2.1) /calcmykprofile (u.s. web coated \050swop\051 v2) /srgbprofile (srgb iec61966-2.1) /cannotembedfontpolicy /error /compatibilitylevel 1.4 /compressobjects /tags /compresspages true /convertimagestoindexed true /passthroughjpegimages true /createjobticket false /defaultrenderingintent /default /detectblends true /detectcurves 0.0000 /colorconversionstrategy /cmyk /dothumbnails false /embedallfonts true /embedopentype false /parseiccprofilesincomments true /embedjoboptions true /dscreportinglevel 0 /emitdscwarnings false /endpage -1 /imagememory 1048576 /lockdistillerparams false /maxsubsetpct 100 /optimize true /opm 1 /parsedsccomments true 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/hrv (za stvaranje adobe pdf dokumenata najpogodnijih za visokokvalitetni ispis prije tiskanja koristite ove postavke. stvoreni pdf dokumenti mogu se otvoriti acrobat i adobe reader 5.0 i kasnijim verzijama.) /hun 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can be opened with acrobat and adobe reader 5.0 and later.) >> /namespace [ (adobe) (common) (1.0) ] /othernamespaces [ << /asreaderspreads false /cropimagestoframes true /errorcontrol /warnandcontinue /flattenerignorespreadoverrides false /includeguidesgrids false /includenonprinting false /includeslug false /namespace [ (adobe) (indesign) (4.0) ] /omitplacedbitmaps false /omitplacedeps false /omitplacedpdf false /simulateoverprint /legacy >> << /addbleedmarks false /addcolorbars false /addcropmarks false /addpageinfo false /addregmarks false /convertcolors /converttocmyk /destinationprofilename () /destinationprofileselector /documentcmyk /downsample16bitimages true /flattenerpreset << /presetselector /mediumresolution >> /formelements false /generatestructure false /includebookmarks false /includehyperlinks false /includeinteractive false /includelayers false /includeprofiles false /multimediahandling /useobjectsettings /namespace [ (adobe) (creativesuite) (2.0) ] /pdfxoutputintentprofileselector /documentcmyk /preserveediting true /untaggedcmykhandling /leaveuntagged /untaggedrgbhandling /usedocumentprofile /usedocumentbleed false >> ] >> setdistillerparams << /hwresolution [2400 2400] /pagesize [612.000 792.000] >> setpagedevice microsoft word numero_32_art_3 i. telichev, frattura ed integrità strutturale, 32 (2015) 24-34; doi: 10.3221/igf-esis.32.03 24 development of an engineering methodology for non-linear fracture analysis of impact-damaged pressurized spacecraft structures igor telichev university of manitoba, department of mechanical engineering, 75a chancellors circle, e2-327 eitc, winnipeg, manitoba r3t 5v6, canada. igor.telichev@umanitoba.ca abstract. motivated by the dramatic worsening and uncertainty of orbital debris situation, the present paper is focused on the structural integrity of the spacecraft pressurized modules/pressure vessels. the objective is to develop an engineering methodology for non-linear fracture analysis of pressure wall damaged by orbital debris impact. this methodology is viewed as a key element in the survivability-driven spacecraft design procedure providing that under no circumstances will the “unzipping” occur. the analysis employs the method of singular integral equation to study the burst conditions of habitable modules, although smaller vessels containing gases at higher pressures can also be analyzed. keywords. orbital debris; impact damage; pressurized structure; singular integral equation method. introduction he hazard from orbital debris is a growing international concern for the safety of space-based infrastructure. the series of incidents happened in last six years demonstrated that only one or two collisions can drastically change the orbital debris population. with space activity continuously running and expanding, the rate of collisions in space also increases, leading in turn to a new reality for the orbital debris environment where all functioning spacecraft are under higher risk than they were designed for. because of the very high impact velocities and possibility to fail catastrophically when impacted, the pressurized modules and pressure vessels play a crucial role in spacecraft survivability. they are identified as the most critical components on-board spacecraft [1-3]. historically, considerable amounts of resources have been used to developing anti-orbital-debris shielding for such structures to avoid the pressure wall damage. however, the shielding cannot protect the spacecraft from all types of debris. nowadays, the pressurized modules and high pressure tanks of the most heavily shielded spacecrafts are able to withstand the impact of debris up to one centimeter in diameter. the orbital debris between 1 and 10 cm in size which is too small to be tracked but large enough to cause the shielded pressure wall perforation, poses the highest risk for the spacecraft mission. as it was demonstrated experimentally, the case of both shield and pressurized wall perforation presents a potential for the pressure wall failure in an abrupt fashion [1-4]. the answer to the question whether the spacecraft pressurized structure would undergo “unzipping” due to the impact of undetectable debris is crucial for the mission success or failure. essentially, it quantifies the spacecraft survivability. fig. 1 illustrates the survivability-driven design logic where it is assumed that impact of undetectable debris between 1 and 10 cm in size has occurred and the pressure wall is damaged. this design concept requires that when developing spacecraft, all attempts be made to prevent the accidental spacecraft breakups. the mitigation and protection measures are assessed for effectiveness through the fracture analysis (fig. 1, t i. telichev, frattura ed integrità strutturale, 32 (2015) 24-34; doi: 10.3221/igf-esis.32.03 25 module 5). in the event that a pressure wall is predicted to “unzip”, the survivability improvements can be achieved by adding more effective shielding or/and by varying the design parameters of the pressurized module. new protection measures will be evaluated by repeating the steps in the above design procedure until the “no rupture” conditions will be verified. the analysis of interaction of penetrative particles with equipment inside a spacecraft is out of scope of the current paper. figure 1: design procedure of spacecraft with enhanced survivability. orbital debris data (untrackable) pressure wall damage? fracture analysis pressure wall rupture? (“unzipping”) varying the design parameters of pressurized module varying the characteristics of shield spacecraft survived, mission continues yes no spacecraft survived, mission continues yes yes no no pressurized module + shield system actions to enhance the survivability? yes no destruction of critical internal components? 1 2 3 4 5 6 9 7 8 10 13 end of analysis disfunctional trackable spacecraft, mitigation requirement is satisfied 14 11 seal/repair of damaged pressure wall 12 end of analysis 14 i. telichev, frattura ed integrità strutturale, 32 (2015) 24-34; doi: 10.3221/igf-esis.32.03 26 the present paper is focused on the engineering methodology which allows determining the border between the simple perforation and catastrophic fracture of impact-damaged pressurized modules and pressure vessels onboard spacecraft. this methodology is viewed as a key element in the survivability-driven spacecraft design procedure providing that under no circumstances will the “unzipping” occur. addressing this problem will not only improve the survivability of spacecraft itself but also will provide the mitigation effect since each satellite break-up causes not only the loss of space assets but the considerable addition to the orbital debris population. modeling of impact damage xperimental studies have shown that the impact damage has the form of a hole surrounded by a zone of the cracklike defects (fig. 2a, b, c). for the case of both shield and pressure wall perforation the impact damage varies from the petal hole (fig. 2a) to the “cookie-cutter hole” (fig. 2b). the perforation of the unshielded wall is accompanied by a zone of spall cracks adjacent to the impact hole as shown in fig. 2c. for further analysis it suggested to model the cracked area around the penetrated hole by two radial cracks emanating from the rim of the hole perpendicularly to the applied load. the diameter of the model hole is equal to the diameter of the impact hole (dhole), while the length of the fictitious radial cracks is bounded by a damage zone (dcrack). in cylindrical pressurized structure these two radial cracks are set to be normal to the hoop stress, i.e. along the expected fracture path (fig. 2d). figure 2: modeling the impact holes: a) petal hole; b) “cookie-cutter hole”; c) hole with adjacent spall cracks; d) model of impact hole. figure 3: snapshot of the evolution of the stress field after the hole was instantly formed in the loaded plate the penetration process lasts for a matter of microseconds and this process is essentially dynamic. after the appearance of an impact hole in the pre-loaded plate, the field of stress distribution around this hole does not change immediately. this transition process flows as the stress wave travels away from rim of hole. the evolution of the stress field near the hole in the perforated plate were evaluated explicitly using the autodyn® code (fig. 3). the obtained results are consistent e i. telichev, frattura ed integrità strutturale, 32 (2015) 24-34; doi: 10.3221/igf-esis.32.03 27 with the numerical solution of the non-steady-state problem of kirsh [5]. during the transition process the dynamic stress concentration factor k()=() / increases reaching the maximum value of 3.33 and then asymptotically drops to the static value. modeling of fracture solution of singular integral equation he problem of potential fracture and bursting of aerospace pressurized structures was extensively examined by the nasa advanced fracture mechanics group [1-3]. the fracture propagation analysis was conducted analytically using the linear elastic fracture mechanics approach and numerically employing the finite element method and non-linear fracture mechanics technique. comparison to the experimental data showed that the linear elastic fracture mechanics methods are too conservative and non-linear fracture mechanics approach is required for a more realistic treatment of the problem [1]. figure 4: 5-link crack (a, b) and chebyshev’s nodes on the crack face(c, d). we assumed that a single hole with two radial cracks is located in the infinite plate made of an isotropic elastic perfectly plastic material, the zones of plasticity are localized along the crack prolongations and the compressive stresses within the plastic zones pz are equal to the tensile yield limit y (fig. 4a). the problem can be formulated in terms of a singular integral equation (sie) of a form:     ' ,        l g t dt p x x l t x    (1) where t and x are coordinates of the points on the crack contour l , p(x) is a crack surface traction. the unknown function g(t) is expressed using the muskhelishvili's complex variable formulation [6] via the displacement dcontinuity across the crack contour l:        ' v v 2 1 æ ,    d u i u i g i g t t l dt          (2) here u, v are the contour displacement components in x and y directions, respectively,  2 1 e g    is the shear modulus, e is the modulus of elasticity,  is the poisson’s ratio, 3 1 æ      is the elastic parameter for the plane stress and 3 4æ   for the plane strain. t i. telichev, frattura ed integrità strutturale, 32 (2015) 24-34; doi: 10.3221/igf-esis.32.03 28 t singular integral equation technique is a powerful alternative to the finite element method in the non-linear analysis of crack propagation which provides very rapid convergence of the numerical results [7-11]. fig. 5 summarizes the procedure of non-linear fracture analysis which employs the method of singular integral equation and includes the following basic steps: modules 1-2: the analysis starts with specifying the design and material characteristics of the pressure wall and determining the impact hole parameters. module 3: the piecewise traction distribution p(x) is applied to the crack surface as it is shown in fig. 4-b. it divides the contour into 5 portions (links) l0, l1, l2, l3 and l4, where each piece of the traction function is differentiable throughout each individual link. the traction-free link l0 corresponds to the hole, links l1 and l3 are radial cracks and links l2 and l4 represent the plastic zones. the solution of the singular integral eq. (1) must satisfy the condition of single-valuedness of displacements for the crack contour: 0 0 ' ' 0 0 1 ( ) exp( ) ( ) 0 q q ll h q q q q ql l g t dt i g t dt              where h reflects the total number of links within the crack; q is the current number of link; is the angle of link inclination and l is half of the crack link. also, the symmetry of the problem and link angular positions (1=2=0, 3=4=π) were taken into account. module 4: unlike the finite element method the method of singular integral equations is free of mesh generation and only nodes are needed. the chebyshev’s nodes with normalized coordinates  and  changing from -1 to 1are generated on each link of the contour (fig. 4c, d) where      [ ( 2 1) / ( 2 )],   [ / ( 2 )]k mcos k n cos m n , 1,   , k n 1, ( 1)m n  . the open circles indicate the points ξ1,.., ξn on the crack faces where displacements are calculated. the closed circles correspond to the traction nodes η1, .., ηn-1. the normalized coordinates  and  change from -1 to 1. module 5: an efficient approach to account for the jump discontinuities of traction applied to the crack faces was proposed by savruk [7]. following [7] the eq. (1) for the case of 5-link crack is replaced by the system of singular integral equations:                     1 0 0 1 3 1 1 2 4 2 1 0 1 , , ,                       , , } ,     0, 2        0 n n n n n n m m m m m n                                             (3) where m00,..,m02, m10,.., m12, m20,..,m22 are normalized kernels, 0,.., 2 are normalized derivatives of the displacement discontinuity across the crack contour 0()=g0’(l0),..,2()=g2’(l2), and 0,..,2 are normalized tractions 0()=p0(l0),.., 2()=p2(l2). the last equation of the system (3) represents the condition of single-valuedness of displacements for the crack contour. also, the symmetry of the problem and link angular positions are taken into account. module 6: the numerical solution of the system of singular integral eq. (3) is obtained by the method of mechanical quadratures [7]. functions 0(), 1(), 2() are sought in the class of functions unbounded at the ends of intervals 2( ) ( ) / 1n nu     , (n=0, 1, 2) expressing u0(), u1(), u2() in terms of the lagrange interpolation polynomials over the chebyshev nodes:         1 1 1 1 1 2 ,  0, 2 n n n n k r k r k r u u t t n n                     (4) where   [   ( )]rt cos r arccos  is a first kind chebyshev polynomial. boundary conditions  1 1 0u  and  2 1 0u   are applied to complete the system of eq. (3). by applying the gauss-chebyshev quadrature expressions the system of singular integral equations is transformed to the closed system of linear algebraic equations with 3n unknowns where n is number of the chebyshev nodes. module 7: the solution of closed normalized and linearized system of equations is obtained by gauss elimination. i. telichev, frattura ed integrità strutturale, 32 (2015) 24-34; doi: 10.3221/igf-esis.32.03 29 figure 5: steps of the fracture analysis. calculation of length of the plastic zones modules 8-9: once a solution of the linearized system of equations is obtained, the stress intensity factor (sif) at the end of the plastic strip can be evaluated by 2 2 2( ) ( 1)ik l l u   . modules 8-9-10: the stress at the crack tips is considered to be finite. the unknown length of the plastic zones is determined from the condition that the stress intensity factor is equal to zero at the end of the plastic strip:  2  0ik l  . the search is performed by golden section method. calculation of crack tip opening displacement/angle module 11: once a numerical solution of the singular integral equation is obtained, the displacement can be calculated at any point on the crack faces. for the arbitrary point *2 2 2/x x l of the segment l2 we have the following expression:        2 * 2 2 1 ' 2 * * * 2 2 2 2 2 2 2 2 2 2 2 2 22 ( ) (1)  1 l x x u g x g l g t dt l d l g x l g              (5) building the system of singular integral equations chebyshev’s nodes generation applying the method of mechanical quadratures 5 6 solution of normalized and linearized system of equations initial data:  structure  material  damage 2 7 start of analysis 1 applying the boundary conditions 4 3 a end of analysis plastic zone length search calculation of stress intensity factor (sif) yes no sif =0 at the end of plastic zone calculation of ctod/ctoa ctod or ctoa > critical value no crack propagation pressure wall rupture (“unzipping”) 8 9 10 11 12 13 14 15 no yes a i. telichev, frattura ed integrità strutturale, 32 (2015) 24-34; doi: 10.3221/igf-esis.32.03 30 using the expansion of the function u2(ξ) in terms of lagrange interpolation polynomials over the chebyshev’s nodes we obtain the expression for the function * *2 2( )g x :        * 2 1 1 * * * 2 2 2 22 1 1 1 1 ( ) (1) 1 2 1 n n k r k r k rx g x g u t t d n                        (6) after integration   * 2 1 * 221x d arccos x      and     * 2 1 * 22 1   1 r x t d sin r arccos x r         we get         1* * * * *2 2 2 2 2 2 1 1 1 1 ( ) (1)     2   n n k r k k r g x g u arccos x t sin r arccos x n r                    (7) analogously we obtain the expressions for * *0 0( )g x and * * 1 1( )g x at * 0 0 0 0 0/ ,  x x l x l  and * 1 1 1 1 1/ ,    x x l x l  :             1* * * * *0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 ( ) (1) / 2   n n k r k k r g x g g x g l l u arccos x t sin r arccos x n r                          (8)    * * *1 1 1 1 1 1 1 1( ) (1) /g x g g x g l l              1* *1 1 1 1 1 1 1 2   n n k r k k r u arccos x t sin r arccos x n r                  (9) from eq. (2) in the symmetric case we have          '' ' ' 1 æv v v 4 g x x x x g              (10) integrating we obtain the relation: (1 ) ( )v v v( ) 2 4 n n æ g x x c g       , where n is a segment number. the constants of integration cn are determined by displacement at the end of the segment: 2 0c   2 2 1 (1 ) 4 æ g l c g         1 10 1 1 1 2 2 (1 ) (1 ) 4 4 æ g l æ c c g l g l g g            thus the crack opening displacement (cod) for the segment ln is defined as following * * * * (1 ) ( )( ) 2v( ) 2 2 n n n n n n æ l g x cod x x c g     (11) since for the plane stress (1 ) 2 4 æ g e   , the expression for *( )ncod x takes the form                         1 * * * 1 1 4 1 ( ) 2 [ 2   ] ,    0, 1, 2   n n n kn y n n n r k n k ry ul s cod x c arccos x t sin r arccos x n e n s r (12) i. telichev, frattura ed integrità strutturale, 32 (2015) 24-34; doi: 10.3221/igf-esis.32.03 31 the presented technique allows determining the crack opening profile for the entire crack (fig. 6) and calculate the opening displacement (ctod) specifically at the crack tip:  2* 2 2 1 4 ( 1)   n ky ky ul s ctod cod x e n s           (13) fig. 7 illustrates the convergence of the numerical procedure. it allows calculating the crack tip opening angle as well. modules 12-14: the critical crack tip opening displacement is used as a fracture criterion (ctodc). once the value of ctod has been determined and compared with the value of ctodc it is possible to answer the main question if there is a case of simple perforation without crack growth from the impact hole or crack propagation and subsequently catastrophic rupture. we have thus obtained the complete solution of the problem. figure 6: crack profile. figure 7: convergence of ctod calculation. numerical results his section gives the numerical examples which illustrate the application of the method of singular integral equations for the structures with cracks or crack-like damages. the fig. 8 illustrates the evolution of the crack tip opening displacement after an impact hole was suddenly introduced in the loaded plate made of aluminum alloy 2024. once ctod has reached the critical value, the crack starts to propagate. the estimated speed of crack propagation in the metal (vcr) varies in a range of 0.2 c0 to 0.29c0, where c0 is the speed of sound [12-14]. for the calculations it was assumed that vcr  0.27c0. figure 8: evolution of the crack tip opening displacement. t i. telichev, frattura ed integrità strutturale, 32 (2015) 24-34; doi: 10.3221/igf-esis.32.03 32 it is known that the ratio of the radial crack length (lrad.cr.) to the hole diameter (dhole) has a considerable effect on the critical stress. fig. 9 illustrates that the singular integral equations method allows obtaining the accurate result for any specific case of (lrad.cr./dhole)-ratio. the obtained results also illustrate the fact that for lrad.cr./dhole>0.25, the hole with two radial cracks can be considered as a straight crack. figure 9: critical stress for various (lrad.cr./dhole)-ratio in order to verify above method and illustrate its application, numerical calculations were performed and compared with results of impact and tensile tests of the 3-mm thickness specimens fabricated from alloy 2024 with ultimate tensile strength σu =446 mpa, yield strength σy=370 mpa, modulus of elasticity e=70000 mpa, poisson’s ratio ν=0.33 and fracture toughness kc= 53.9 mpa m1/2. the critical ctod was determined assuming the plane stress state and using the relation ctodc=(kc2)/(σye). to account the strain hardening effects the σy was interpreted as an average of the nominal yield stress and ultimate tensile strength. the computational analysis predicted residual strength to within 5% of the experimental data given in [4]. the fig. 10 and 11 illustrate a fair agreement of the obtained computational results with test data [15] where the specimens were perforated by 0.5 ball projectile at ballistic velocities of 206-308 m/s and then subjected to the tensile tests. the specimens with thickness of 4.8 mm and dimension of 460×910 mm were fabricated from 7075-t6 alloy. the following input data were used for the analysis: ultimate tensile strength σu =535 mpa, yield strength σy=468 mpa, modulus of elasticity e=72000 mpa, poisson’s ratio ν=0.33 and fracture toughness kc= 63 mpa m1/2 for transverse grain and kc= 81.6 mpa m1/2 for longitudinal grain. figure 10: computational results vs test data [15] (7075-t6 transverse grain). figure 11: computational results vs test data [15] (7075-t6 longitudinal grain). i. telichev, frattura ed integrità strutturale, 32 (2015) 24-34; doi: 10.3221/igf-esis.32.03 33 the tab. 1 presents a comparison with the computational results obtained by the finite element method [1] to quantify the critical crack length in the cylindrical pressurized module experiencing 68.6 mpa hoop and 34.3 mpa longitudinal stresses respectively. the numerical analysis was performed for 2219-t87 aluminum alloy shell with the following parameters: σu =430 mpa, σy=343 mpa, e=73800 mpa, ν=0.33, wall thickness ts=3.17 mm, toughness at the crack initiation kic= 68 mpa m1/2 and toughness at the maximum load kc max= 92 mpa m1/2 [1]. the comparisons shows that the computational results obtained by the finite element and singular integral equations methods are in a good agreement. the numerical experiments on the reinforced habitable modules of the international space station showed the “unzipping” of the pressure wall is unlikely. method critical crack length, mm crack initiation crack unstable growth elasto-plastic fem [1] <599 1041 present approach 590 1082 deviation,% n/a 3.4 table 1: critical crack length (specimen: 2219-t87, ts=3.17 mm) conclusions he present paper is focused on the engineering methodology which is viewed as a key element in the spacecraft design procedure providing that under no circumstances will the “unzipping” occur. a model of crack propagation in impact-damaged pressurized aerospace structure is presented. the non-linear fracture analysis is performed by the method of singular integral equations. comparisons of the calculated results with the test data and numerical results obtained by finite element method showed good agreement. the suggested sie-based approach is concluded to be effective way of assessing the fracture behavior of the impact damaged aerospace pressurized structures. acknowledgements his work was supported by a discovery grant no. 402115-2012 from the natural sciences and engineering research council of canada. references [1] couque, h. et al. swri-nasa cr 64-00133 (1993). [2] lutz, b.e. & goodwin, c. j.. nasa cr 4720, (1996). [3] elfer, n. c. nasa cr 4706, (1996). [4] telichev, i., unstable crack propagation in spacecraft pressurized structure subjected to orbital debris impact, canadian aeronautics and space journal, 57(1) (2011) 106-111. [5] patsyuk, v. i., rimskii, v. k., instantaneous formation of a round hole in a stretched plate, int. applied mechanics, 27 (1991) 1117-1123. [6] muskhelishvili, n.i., some basic problems of the mathematical theory of elasticity, leyden: noordhoff int. publ. (1975). [7] savruk, m. p., method of singular integral equations in linear and elastoplastic problems of fracture mechanics, mat. sci., 40(3) (2004) 337-351. [8] ladopoulos, e.g., singular integral equations: linear and non-linear theory and its applications in science and engineering, springer verlag gmbh, (2000). [9] chernyakov, y.a., grychanyuk v., tsukrov, v.i., stress–strain relations in elastoplastic solids with dugdale-type t t i. telichev, frattura ed integrità strutturale, 32 (2015) 24-34; doi: 10.3221/igf-esis.32.03 34 cracks, engineering fracture mechanics, 70 (200) 32163–74. [10] chen, y.z., lin, x.y., numerical solution of singular integral equation for multiple curved branch-cracks. structural engineering and mechanics, 34(1) (2010) 85-95. [11] galybin, a.n., dyskin, a.v., random trajectories of crack growth caused by spatial stress fluctuations, international journal of fracture, 128 (2004) 95–103. [12] broek, d., elementary engineering fracture mechanics, noordorf int. publishing, leyden, (1974). [13] ionov, v. n., selivanov, v. v., fracture dynamics of deformed solid body, moscow, mashinostroeniye, (1987). [14] parton, v. z., boriskovsky, v. g., brittle fracture dynamics, moscow, metallurgia, (1988). [15] forman, r. g. et al., vulnerability of aircraft structures exposed to small arms fire projectile impact damage, affdl-tr-67-157, (1967). shot peening processes to obtain nanocrystalline surfaces in metal alloys: a. s. yankin et alii, frattura ed integrità strutturale, 51 (2020) 151-163; doi: 10.3221/igf-esis.51.12 151 influence of static mean stresses on the fatigue behavior of 2024 aluminum alloy under multiaxial loading a.s. yankin, v.e. wildemann, n.s. belonogov, o.a. staroverov center of experimental mechanics, perm national research polytechnic university, perm, russian federation yas.cem@yandex.ru, https://orcid.org/0000-0002-0895-4912 wildemann@pstu.ru, https://orcid.org/0000-0002-6240-4022 cem.belonogov@gmail.com cem_staroverov@mail.ru, https://orcid.org/0000-0001-6095-0962 abstract. axial alternating stress controlled fatigue tests with superimposed static torsional mean stress and shear alternating fatigue tests with superimposed static tensile mean stress are represented. the material used in the current experimental investigation is 2024 aluminum alloy. a decrease in the fatigue life of the material was observed with an increase in the shear and static tensile stresses. marin and modified crossland methods are analyzed by means of the available experimental data. the two modifications of sines method are proposed to take into account the static torsional stress effect (sines+) and different slopes of the s-n curves in tension-compression and torsion tests (sines++). it is shown that sines++ model is the most accurate among others. keywords. multiaxial fatigue; mean stress; multiaxial fatigue criteria; 2024 aluminum alloy. citation: yankin, a.s., wildemann, v.e., belonogov, n.s., staroverov, o.a., influence of static mean stresses on the fatigue behavior of 2024 aluminum alloy under multiaxial loading, frattura ed integrità strutturale, 51 (2020) 151-163. received: 30.09.2019 accepted: 07.11.2019 published: 01.01.2020 copyright: © 2020 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. introduction uring operations the greatest number of critical components of construction elements undertake complex cyclic loadings, thus the estimation of their influence on durability of metal materials is a problem to be solved [1-5]. also, the need in studying fatigue processes under complex stress state brought a number of experimental works in this area, which used specialized equipment and methods of multiaxial loading. here are some major research centers studying the problems of multiaxial fatigue: ensam university in bordeaux, france (t. palin-luc, n. saintier, f. morel) [6, 7], university of opole, poland (t. lagoda) [8], university of sheffield, united kingdom (l. sumsel) [9], university of lisbon, portugal (v. anes, l. reis, m de freitas) [10, 11], s.p. timoshenko institute of mechanics, kiev, ukraine (v.p. golub) [12], ishlinsky institute for problems in mechanics ras, moscow, russia (n.g. burago, a.b. zhuravlev, i.s. nikitin) [13, 14], and others [15]. d http://www.gruppofrattura.it/va/51/2645.mp4 a. s. yankin et alii, frattura ed integrità strutturale, 51 (2020) 151-163; doi: 10.3221/igf-esis.51.12 152 the main loading conditions referred to the literature when studying multiaxial fatigue are biaxial tension of cross-shaped specimens, tension with torsion and bending with torsion of cylindrical specimens. meanwhile attention is paid not only to the proportional cyclic loading but also to more complex modes with phase shifting, different frequencies and other characteristics [16-20]. apart from testing standard hourglass and tubular specimens, one can also test weld joint specimens [21, 22], specimens with grooves [23] and other stress raisers [24]. cyclic effects may be associated with a cycle asymmetry due to static loadings caused, as an example, by gravity force or linear overloading. apart from that, static loads may occur along an axis different from the cyclic ones, which results in bending cyclic loads with constant torsion and so on. gerber [25], goodman [26], morrow [27], smith [28], oding [29], birger [30] and many others [31-35] studied the influence of the asymmetry of the loading cycle on the fatigue behavior of various materials. as a rule, the experimental results are shown in the haigh diagram (the stress amplitude versus the mean stress in the cycle), and different relations for their description are suggested. an increase of the mean stress leads to a decrease of fatigue strength. this effect is quite strong for brittle materials (e.g. cast iron) both in axial and in torsion [34]. however this effect is lower in torsion than in axial for ductile materials such as steels and aluminum alloys [31]. thus, some authors [5, 36, 37] do not suggest taking into account the influence of the mean stress under torsion until the maximum values of shear stress do not exceed yield strength. let us note that under cyclic loadings in the compression area there is an increase in fatigue strength which is more significant for brittle materials and less significant for ductile ones [5, 32]. in general, a similar behavior is demonstrated by the materials under constant static stresses under multiaxial loadings (e.g. an alternating bending with a constant torsion and so on) [5, 36-39]. however, there are much less studies in this area, compared to uniaxial effects, and there is no complex approach to studying this issue. apart from that, works mostly pay attention to fatigue limit under more than 106 cycles, i.e. they consider such loadings that allow a material (conventionally) to endure an unlimited number of loading cycles. but if we design structures with a set (limited) service life in order to save resources, it is important to describe not only the fatigue limit but also s-n curves at different levels of additional static stresses. in the previous work [40] the authors researched the influence of the constant components of multiaxial loading (constant tension and alternating torsion, constant torsion and alternating tension-compression) on the fatigue life of 2024 aluminum alloy. it is shown that the influence of the constant static stresses results in a decrease of the number of cycles to failure. moreover, the realized values of the constant static stresses obviously did not exceed the corresponding values of the conventional yield strength for the alloy. the purpose of this work is to check if it is reasonable to use various criteria for multiaxial fatigue using the experimental data presented in the article [40]. experiments material and specimen he material used in the current experimental investigation is a common aeronautic material, 2024 aluminum alloy. the chemical composition of the alloy consists of cu 4.28, mg 1.48, mn 0.75, fe 0.28, si 0.29, zn 0.12, ni 0.009, ti 0.06, cr 0.017, pb 0.05. mechanical properties for the material are listed in tab. 1. fatigue tests were performed on hourglass specimens. the specimen geometry is shown in fig. 1. the specimens are designed in accordance with recommendations of national standard gost 25.502. stresses used in calculating were in accordance with the minimum cross-section of specimen. property symbol 2024 aluminum alloy unit 0.2% tensile yield strength σy 336 mpa 0.3% torsional yield strength τy 153 mpa ultimate tensile strength σu 450 mpa modulus of elasticity e 75.4 gpa shear modulus g 30.0 gpa table 1: mechanical properties of 2024 aluminum alloy. t a. s. yankin et alii, frattura ed integrità strutturale, 51 (2020) 151-163; doi: 10.3221/igf-esis.51.12 153 loading path σa (mpa) σm (mpa) τa (mpa) τm (mpa) n uniaxial 168.1 0 0 0 476 451 uniaxial 168.1 0 0 0 617 189 tsts1 168.1 0 0 15.3 378 142 tsts1 168.1 0 0 15.3 455 634 tsts1 168.1 0 0 30.6 435 758 tsts1 168.1 0 0 30.6 404 964 tsts1 168.1 0 0 45.9 356 718 tsts1 168.1 0 0 45.9 368 430 tsts1 168.1 0 0 61.2 519 480 tsts1 168.1 0 0 61.2 259 565 tsts1 168.1 0 0 76.5 203 836 tsts1 168.1 0 0 76.5 298 301 tsts1 168.1 0 0 91.8 255 564 tsts1 168.1 0 0 91.8 322 877 tsts1 168.1 0 0 107.1 240 549 tsts1 168.1 0 0 107.1 296 235 tsts1 168.1 0 0 122.4 305 221 tsts1 168.1 0 0 122.4 198 799 uniaxial 205.1 0 0 0 139 913 uniaxial 205.1 0 0 0 149 767 uniaxial 205.1 0 0 0 185 520 uniaxial 205.1 0 0 0 165 011 tsts1 205.1 0 0 18.4 196 496 tsts1 205.1 0 0 18.4 182 057 tsts1 205.1 0 0 36.8 120 610 tsts1 205.1 0 0 36.8 166 584 tsts1 205.1 0 0 55.2 155 908 tsts1 205.1 0 0 55.2 133 260 tsts1 205.1 0 0 73.6 158 711 tsts1 205.1 0 0 73.6 179 106 tsts1 205.1 0 0 92.0 122 202 tsts1 205.1 0 0 92.0 121 562 tsts1 205.1 0 0 110.4 126 479 tsts1 205.1 0 0 110.4 207 306 tsts1 205.1 0 0 128.8 100 577 tsts1 205.1 0 0 128.8 146 293 torsion 0 0 107.1 0 376 148 torsion 0 0 107.1 0 445 992 tsts2 0 16.8 107.1 0 146 622 tsts2 0 16.8 107.1 0 115 265 tsts2 0 33.6 107.1 0 101 503 tsts2 0 33.6 107.1 0 103 000 tsts2 0 67.3 107.1 0 68 057 tsts2 0 67.3 107.1 0 139 743 tsts2 0 100.9 107.1 0 74 294 tsts2 0 100.9 107.1 0 45 391 tsts2 0 134.5 107.1 0 34 385 tsts2 0 134.5 107.1 0 37 224 tsts2 0 201.8 107.1 0 35 651 tsts2 0 201.8 107.1 0 27 162 torsion 0 0 114.8 0 115 648 torsion 0 0 114.8 0 99 285 tsts2 0 16.8 114.8 0 83 350 tsts2 0 16.8 114.8 0 86 779 tsts2 0 33.6 114.8 0 59 443 tsts2 0 33.6 114.8 0 95 959 tsts2 0 67.3 114.8 0 49 145 tsts2 0 67.3 114.8 0 64 942 tsts2 0 100.9 114.8 0 35 866 tsts2 0 100.9 114.8 0 16 966 tsts2 0 201.8 114.8 0 24 661 tsts2 0 201.8 114.8 0 19 823 table 2: summary fatigue tests. a. s. yankin et alii, frattura ed integrità strutturale, 51 (2020) 151-163; doi: 10.3221/igf-esis.51.12 154 figure 1: specimen geometry, all dimensions in millimeters. experimental procedure and results all tests were carried out in the instron electropuls e10000 at room temperature in center of experimental mechanics (russia). the electropuls e10000 linear-torsion is an all-electric test instrument with a dynamic linear load capacity of ±10 kn and dynamic torque capacity of ±100 nm. a summary of the applied loading conditions and experimental fatigue life for each test performed is included in tab. 2. all tests were performed in load-control, using sinusoidal waveforms, and include uniaxial (6 tests), pure torsion (4 tests), tension with static torsional stress (30 tests), and torsion with static tensile stress (22 tests) loading conditions. the range of the torsional mean stress τm was from 0 to 0.84·τy. the normal stress amplitudes σa were 0.5·σy and 0.61·σy. the testing frequency was 50 hz. sin(2 )a m t      =  = (1) the range of the static tensile stress σm was from 0 to 0.6·σy. the shear stress amplitudes τa were 0.7·τy and τa = 0.75·τy. the testing frequency was 3.4 hz. sin(2 )a m t      =  = (2) during the experiments, a decrease in the fatigue life of the material was observed with an increase in the static torsional and tensile stresses. at smaller values of the stress amplitude in the cycle, a decrease in fatigue life with an increase in the static stresses is more evident. correlation of the experimental results with multiaxial fatigue models s has been pointed out before the static torsional stress effect less pronounced than the static tensile stress effect in ductile metals. some researchers [5, 36, 37] propose to neglect this effect as long as the maximum shear stress is within the torsional yield strength (models sines [5], crossland [41] and so on). relevant results of the literature show that the static torsional stress effect is not negligible in ductile metals. the marin method the marin method [42] can be expressed through eqn. (3): 2 2 2 2 1 3 3 1 a m u i i  −        +          (3) ( ) ( ) ( ) ( ) 2 2 2 2 2 21 2 11 22 22 33 11 33 12 23 136 6a a a a a a a a a ai         = − + − + − + + + (4) a a. s. yankin et alii, frattura ed integrità strutturale, 51 (2020) 151-163; doi: 10.3221/igf-esis.51.12 155 ( ) ( ) ( ) ( ) 2 2 2 2 2 21 2 11 22 22 33 11 33 12 23 136 6m m m m m m m m m mi         = − + − + − + + + (5) where σ-1 is the fully reversed axial fatigue limit, σu is the ultimate tensile strength, i2a and i2m are the amplitude and the mean value of the second invariant of the stress deviator tensor. in order to predict the material fracture with an arbitrary number of n cycles, let us replace the fully reversed axial fatigue limit σ-1 in eqn. (3) with the axial s-n curve σa0(n). 2 2 2 2 0 3 3 1 ( ) a m a u i i n         +          (6) let us rearrange eqn. (3) for two types of multiaxial loadings given in the second part. for the first case (see eq (1)), we will write as follows 2 3a ai = , 2m mi = , 2 0 3 ( ) 1 ma a u n        −    (7) for the second one (see eq 2), it will be 2a ai = , 2 3m mi = , 2 0 ( ) 1 3 a m a u n       −    (8) the marin method requires the ultimate tensile strength and the axial s-n curve. the ultimate tensile strength σu of the alloy is equal to 450 mpa. the axial s-n curve was plotted according to the experimental data (σa = 0.5·σy; τm = 0 and σa = 0.61·σy; τm = 0 from tab. 2) and was interpolated through a function σa0(n). ( )'0 ( ) 2a fn n   = (9) ( ) 0'0 ( ) 2a fn n   = (10) where coefficients σf’ = 1478 mpa, τf’ = 370 mpa, and exponents β = -0.156, β0 = -0.051. for different alloys one can observe an increase of fatigue strength in the compression area (at negative static tensile stresses σm) [32]. however, the marin method (see eq 6) does not make it possible to consider this. one can observe the same value of the second invariant i2m (see eq 5) at positive and negative values of static tensile stresses σm. also, the disadvantage of the method is that it predicts the same reduction of fatigue life at constant torsional τm and tensile σm mean stresses (see eq 6). and, as has been mentioned above, for ductile materials an increase of the mean stress in torsion direction leads to a decrease of fatigue strength lower than in axial direction. in order to take into account this effect one can add, for example, the maximum hydrostatic stress (see eq 11) how was made in [31]. the advantage of the model is its relative simplicity and a small number of adjusting experiments (σu; σa0(n)) necessary to determine its parameters. the modified crossland method (crossland+) the crossland method does not take into account the static torsional stress effect. therefore, authors in ref. [31] proposed the modified crossland method: a. s. yankin et alii, frattura ed integrità strutturale, 51 (2020) 151-163; doi: 10.3221/igf-esis.51.12 156 2 2 2 2 max 1 a m h i i a b c        + +          (11) ( )1max 11max 22 max 33 max3h   = + + (12) where σh max is the maximum hydrostatic stress, a, b, c are the model parameters, which were determined as follows: the parameter a was determined by means of the torsional s-n curve τa0(n) 0a m m  = = = , max 0h = , 2 0mi = , 0 ( )a a n = , 2 0 ( )a ai n= (13) 0 ( )aa n= (14) the parameter c was determined by means of the axial s-n curve σa0(n) 0a m m  = = = , 2 0mi = , 0 ( )a a n = , 1 2 03 ( )a ai n= , 1 max 03 ( )h a n = (15) 0 0 ( ) 3 3 ( ) a a n с n a   = − (16) the parameter b was determined by means of the axial s-n curve σaτ(n) with torsional mean stress τm = 126 mpa 0a m = = , 2m mi = , ( )a a n = , 1 2 3 ( )a ai n= , 1 max 3 ( )h a n = (17) 2 2 ( ) ( ) 1 3 3 m a a b n n c a      =     − −        (18) s-n curves τa0(n) and σaτ(n) were plotted according to the experimental data from tab. 2 similarly to curve σa0(n) (see section 3.1, eq (9)). the advantage of this model is that it takes into account the beneficial effect of the mean compressive axial stresses and that the marin method does not predict. also, by using the σh max term in the multiaxial function (11), the mean stress effect in the axial direction is increased compared with the torsion case. it is worth notice that this method is quite complicated, compared to the marin method, and requires a great number of adjusting experiments (at least three s-n curves τa0(n), σa0(n) and σaτ(n)). extension of the sines method extension of the sines method to take into account the static torsional mean stress effect (sines+) he sines method [5] can be expressed through eqn. (19): t a. s. yankin et alii, frattura ed integrità strutturale, 51 (2020) 151-163; doi: 10.3221/igf-esis.51.12 157 2 1 0 0 1 a m i i a b +  (19) 1 11 22 33m m m mi   = + + (20) where i1m is the mean value of the first invariant of the stress tensor, a0 and b0 are the model parameters. in this article the eqn. (19) was modified similarly to the modified crossland method [31] to take into account the static torsional stress effect 2 2 2 2 1 1 1 1 1 a m m i i i a b c        + +          (21) where a1, b1 and с1 are the model parameters, which were determined as follows: the parameter a1 was determined by means of the axial s-n curve σa0(n) 0a m m  = = = , 2 0mi = , 1 0mi = , 0 ( )a a n = , 1 2 03 ( )a ai n= (22) 1 1 03 ( )aa n= (23) the parameter b1 was determined by means of the axial s-n curve σaτ(n) with torsional mean stress τm=126 mpa 2m mi = , 0a m = = , 1 0mi = , ( )a a n = , 1 2 3 ( )a ai n= (24) 1 2 1 ( ) 1 3 m a b n a    =   −    (25) the parameter с1 was determined by means of the torsional s-n curve τaσ(n) with tensile mean stress σm=202 mpa 0a m = = , 1 2 3m m i = , 1m mi = , ( )a a n = , 2 ( )a ai n= (26) 1 22 1 1 ( ) 1 3 m a m c n a b     =    − +        (27) s-n curve τaσ(n) were plotted according to the experimental data from tab. 2 similarly to curve σa0(n) (see section 3.1). this model has all the advantages and disadvantages of the previous modified crossland method. extension of the sines method to take into account different slopes of the s-n curves under tension-compression and torsion (sines++) in some cases, experiments show different slope of the s-n curves in tension-compression σa0(n) and torsion τa0(n) tests. it means that the ratio σa0(ni) / τa0(ni) will not be constant. the modified sines method (sines+) does not take a. s. yankin et alii, frattura ed integrità strutturale, 51 (2020) 151-163; doi: 10.3221/igf-esis.51.12 158 into account this effect because it predicts the constant ratio σa0(ni) / τa0(ni) = √3. therefore, the eqn. (21) was modified as follows: ( ) ( ) 2 2 2 2 2 2 2 1 2 1 1a m m aa i b i c i d i+ + +  (28) 1 11 22 33a a a ai   = + + (29) the parameters of eqn. (28) are written in the numerator. it helps avoiding the division by zero (function jumps) at nk point, when σa0(nk) / τa0(nk) = √3. we think that such a formulation is more convenient for program implementation. the the model parameters a2, b2, с2 and d2 were determined as follows: the parameter a2 was determined by means of the torsional s-n curve τa0(n) 0a m m  = = = , 2 0mi = , 1 0mi = , 1 0ai = , 0 ( )a a n = , 2 0 ( )a ai n= (30) 2 01 ( )aa n= (31) the parameter d2 was determined by means of the axial s-n curve σa0(n) 2 0mi = , 0a m m  = = = , 1 0mi = , 0 ( )a a n = , 1 2 03 ( )a ai n= , 1 0 ( )a ai n= (32) 1 2 03 2 0 1 ( ) ( ) a a a n d n   − = (33) the parameter b2 was determined by means of the axial s-n curve σaτ(n) with torsional mean stress τm = 126 mpa 0a m = = , 2m mi = , 1 0mi = , ( )a a n = , 1 ( )a ai n= , 1 2 3 ( )a ai n= (34) ( ) ( ) 22 1 2 23 2 1 ( ) ( )a a m d n a n b     − − = (35) the parameter с2 was determined by means of the torsional s-n curve τaσ(n) with tensile mean stress σm = 202 mpa 0a m = = , 1 2 3m m i = , 1m mi = , 1 0ai = , ( )a a n = , 2 ( )a ai n= (36) ( ) ( ) 22 1 2 23 2 1 ( )a m m a n b c    − + = (37) thus, the approach presented above has all the advantages of the previous model and allows taking into account the different slopes of the fatigue curves under tension-compression and torsion, however, it requires even more experimental data (four s-n curves τa0(n), τaσ(n), σa0(n) and σaτ(n)). a. s. yankin et alii, frattura ed integrità strutturale, 51 (2020) 151-163; doi: 10.3221/igf-esis.51.12 159 the comparison of the methods given in the article n order to estimate the predictive ability of the models, we assume that the experimental data scatters are approximately the same in logarithmic coordinates with respect to the fatigue life n (that is, the variance of reproducibility are uniform throughout the factor space). in general, it does not contradict the available data. the increase of the fatigue life n leads to the increase of the experimental data scatter, however, in the logarithmic coordinates they remain the same. then one can use the following functional to assess the predictive ability of the models: ( ) 2 2 1 1 ф log n mi i i n n n = =  (38) where n is the experimental fatigue life, nm is the model’s fatigue life, n is the number of the experiments (62 specimens). tab. 3 shows the values of the functionals for different models. adjusting experiments are the experiments necessary to determine models parameters. fig. 2-5 present a comparison of the models with the experimental data. no. model adjusting experiments ф 1 marin the ultimate tensile strength σu; s-n curve σa0(n). 0.135 2 crossland+ s-n curves σa0(n), τa0(n), σaτ(n). 0.135 3 sines+ s-n curves σa0(n), τaσ(n), σaτ(n). 0.056 4 sines++ s-n curves σa0(n), τa0(n), σaτ(n), τaσ(n). 0.025 table 3: the comparison of the models based on ф functional. figure 2: dependences of fatigue life n of 2024 alloy under cyclic tension-compression with the amplitude σа = 0.5·σy versus the torsional mean stresses τm plotted by means of the multiaxial fatigue models (marin, crossland+, sines+, sines++). based on fig. 2-5 one may notice that the modified methods of sines and crossland predict the same result (the curves coincide). an increase of the mean stress in torsion direction virtually does not affect fatigue strength under the amplitude σа = 0.61·σy (fig 3) unlike the amplitude σа = 0.5·σy (fig 2). it is also clear from tab. 3 and fig. 2-5 that model no. 4 (sines++) is the most accurate. finally, one should mention that the number of the experiments carried out with the same loading parameters were not enough to explicitly judge about the model adequacy. it is necessary to increase the amount of the statistical data. i a. s. yankin et alii, frattura ed integrità strutturale, 51 (2020) 151-163; doi: 10.3221/igf-esis.51.12 160 figure 3: dependences of fatigue life n of 2024 alloy under under cyclic tension-compression with the amplitude σа = 0.61·σy versus the torsional mean stresses τm plotted by means of the multiaxial fatigue models (marin, crossland+, sines+, sines++). figure 4: dependences of fatigue life n of 2024 alloy under cyclic torsion with the amplitude τа = 0.7·τy versus the tensile mean stresses σm plotted by means of the multiaxial fatigue models (marin, crossland+, sines+, sines++). figure 5: dependences of fatigue life n of 2024 alloy under cyclic torsion with the amplitude τа = 0.75·τy versus the tensile mean stresses σm plotted by means of the multiaxial fatigue models (marin, crossland+, sines+, sines++). a. s. yankin et alii, frattura ed integrità strutturale, 51 (2020) 151-163; doi: 10.3221/igf-esis.51.12 161 conclusions ased on the analysis of the available experimental data the performed work made it possible to reveal the influence of the constant static stresses on the fatigue life of 2024 aluminum alloy during the tension with torsion experiments of the hourglass specimens. at the same time, the implemented values of the constant static stresses did not exceed the corresponding values of the conventional yield strength of the material in question. some methods of the multiaxial fatigue available in the scientific literature are analyzed; they allow to take into account the patterns of the fatigue behavior noted above. the two modifications of sines multiaxial fatigue model (sines+ and sines++) are proposed. according to the comparison results of marin method and the modified crossland+, sines+ and sines++ methods, the latter (sines++) describes the experimental data in the most accurate way. the obtained results may be used for strength computations with regard to setting the admissible limits of the constant static stresses occurring in constructions that will not reduce durability of products operated under cyclic loading. acknowledgements he work was carried out in perm national research polytechnic university with the financial support of the russian foundation for basic research (grants 19-01-00555 a and 16-01-00239 a). the experimental studies were conducted within the state assignment of the ministry of education and science of the russian federation (9.7529.2017/9.10). nomenclature e modulus of elasticity g shear modulus σy tensile yield strength (0.2%) σm tensile mean stress σa normal stress amplitude σu ultimate tensile strength σ-1 fully reversed axial fatigue limit σa0(n) axial s-n curve (rσ = -1) σaτ(n) axial s-n curve with torsional mean stress (τm = 126 mpa) τy torsional yield strength (0.3%) τm torsional mean stress τa shear stress amplitude τa0(n) torsional s-n curve (rτ = -1) τaσ(n) torsional s-n curve with tensile mean stress (σm = 202 mpa) rσ axial stress ratio, rσ = σmin / σmax rτ shear stress ratio, rτ = τmin / τmax n fatigue life (number of cycles to failure) i2 second invariant of the stress deviator tensor i1 first invariant of the stress tensor σh hydrostatic stress references [1] serensen, s.v. (1985). fatigue of materials and structural elements, kiev, naukova dumka. [2] troshhenko, v.t. and sosnovskij, l.a. (1987). fatigue resistance of metals and alloys, kiev, naukova dumka. [3] terent`ev, v.f. and korableva, s.a. (2015) metal fatigue, moscow, nauka. [4] matvienko, yu.g. (2006). models and criteria for fracture mechanics, moscow, fizmatlit. b t a. s. yankin et alii, frattura ed integrità strutturale, 51 (2020) 151-163; doi: 10.3221/igf-esis.51.12 162 [5] sines, g. (1955). failure of materials under combined repeated stresses with superimposed static stress, washington, national advisory committee for aeronautics (n.a.c.a). [6] hor, a., saintier, n., camille, r., palin-luc t. and morel, f. (2014) statistical assessment of multiaxial hcf criteria at the grain scale, int. j. fatigue, 67, pp. 151-158. doi: 10.1016/j.ijfatigue.2014.01.024. [7] saintier, n., palin-luc, t., benabes, j. and cocheteux, f. (2013) non-local energy based fatigue life calculation method under multiaxial variable amplitude loadings, int. j. fatigue, 54, pp. 68-83. doi: 10.1016/j.ijfatigue.2012.12.013. [8] kluger, k. and lagoda, t. (2014). new energy model for fatigue life determination under multiaxial loading with different mean values, int. j. fatigue, 66, pp. 229-245. doi: 10.1016/j.ijfatigue.2014.04.008. [9] susmel, l. (2014). four stress analysis strategies to use the modified wohler curve method to perform the fatigue assessment of weldments subjected to constant and variable amplitude multiaxial fatigue loading, int. j. fatigue, 67, pp. 38-54. doi: 10.1016/j.ijfatigue.2013.12.001. [10] anes, v., reis, l., li, b., fonte, m. and de freitas, m. (2014). new approach for analysis of complex multiaxial loading paths, int. j. fatigue, 62, pp. 21-33. doi: 10.1016/j.ijfatigue.2013.05.004. [11] reis, l., li, b. and de freitas, m. (2009). crack initiation and growth path under multiaxial fatigue loading in structural steels, int. j. fatigue, 31, pp. 1660-1668. doi: 10.1016/j.ijfatigue.2009.01.013. [12] golub, v.p. (2014). to solving problems of fatigue under biaxial combined loading based on classical fracture criteria, vestnik dvigatelestroeniya, 2, pp.139-146. [13] burago, n.g., zhuravlev, a.b. and nikitin, i.s. (2011). models of multiaxial fatigue fracture and service life estimation of structural elements, mech. of solids, 6, pp. 828-838. doi: 10.3103/s0025654411060033. [14] burago, n.g., zhuravlev, a.b. and nikitin, i.s. (2013). very-high-cycle fatigue facture of titanium compressor disks. pnrpu mech. bull., 1, pp.52-67. [15] shanyavskiy, a.a. (2018). equivalent uniaxial cyclic tensile stress as an energy characteristic of metal fatigue under multiparameter loading. phys. mesomech., 21(6), pp. 483-491. doi: 10.1134/s1029959918060024. [16] anes, v., reis, l. and de freitas, m. (2015). asynchronous multiaxial fatigue damage evaluation. proc. engineering, 101, pp. 421-429. doi: 10.1016/j.proeng.2015.02.051. [17] anes, v., reis, l. and de freitas, m. (2015). multiaxial fatigue damage accumulation under variable amplitude loading conditions. proc. engineering, 101, pp. 117-125. doi: 10.1016/j.proeng.2015.02.016. [18] marciniak, z., rozumek, d. and macha, e. (2008). fatigue lives of 18g2a and 10hnap steels under variable amplitude and random non-proportional bending with torsion loading, int. j. fatigue, 30(5), pp. 800-813. doi: 10.1016/j.ijfatigue.2007.07.001. [19] shamsei, n., gladskyi, m., panasovskyi, k., shukaev, s. and fatemi, a. (2010). multiaxial fatigue of titanium including step loading and load path alteration and sequence effects, int. j. fatigue, 32(11), pp. 1862-1874. doi: 10.1016/j.ijfatigue.2010.05.006. [20] xia, t. and yao, w. (2013). comparative research on the accumulative damage rules under multiaxial block loading spectrum for 2024-t4 aluminum alloy, int. j. fatigue, 48, pp. 257-265. doi: 10.1016/j.ijfatigue.2012.11.004. [21] sonsino, c.m., kueppers, m., eibl, m. and zhang, g. (2006). fatigue strength of laser beam welded thin steel structures under multiaxial loading, int. j. fatigue, 28(5-6), pp. 657-662. doi: 10.1016/j.ijfatigue.2005.09.013. [22] susmel, l. and askes, h. (2012). modified wohler curve method and multiaxial fatigue assessment of thin welded joints, int. j. fatigue, 43, pp. 30-42. doi: 10.1016/j.ijfatigue.2012.01.026. [23] li, j., zhang, z., sun, q. and li, c. (2011). multiaxial fatigue life prediction for various metallic materials based on the critical plane approach, int. j. fatigue, 33(2), pp. 90-101. doi: 10.1016/j.ijfatigue.2010.07.003. [24] gates, n. and fatemi, a. (2014). notched fatigue behavior and stress analysis under multiaxial states of stress, int. j. fatigue, 67, pp. 2-14. doi: 10.1016/j.ijfatigue.2014.01.014. [25] gerber, h. (1874). bestimmung der zulassigen spannungen in eisenkonstructionen. z. bayerischen architeckten ingenieur-vereins, 6, pp. 101-110. [26] goodman, j. (1899). mechanics applied to engineering, london, uk, longmans green. [27] morrow, j. (1968). fatigue properties of metals, section 3.2, in fatigue design handbook, pub. no. ae-4, pa, usa, sae: warrendale. [28] smith, j.o. (1942). the effect of range of stress on the fatigue strength of metals, university of illinois engineering experiment station, bulletin series, 334. [29] oding, i.a. (1935). prochnost' metallov: metallovedenie [metal strength: metallurgy], l., onti nktp. a. s. yankin et alii, frattura ed integrità strutturale, 51 (2020) 151-163; doi: 10.3221/igf-esis.51.12 163 [30] birger, i.a. (1979). raschet na prochnost' detalej mashin: spravochnik [calculation of the strength of machine parts], m., mashinostroenie. [31] pallarés-santasmartas, l., albizuri, j., avilés, a., saintier, n. and merzeau, j. (2018). influence of mean shear stress on the torsional fatigue behaviour of 34crnimo6 steel, int. j. fatigue, 113, pp. 54-68. doi: 10.1016/j.ijfatigue.2018.04.008. [32] pallarés-santasmartas, l.; albizuri, j.; avilés, a. and avilés, r. (2018). mean stress effect on the axial fatigue strength of din 34crnimo6 quenched and tempered steel, metals, 8(213). doi: 10.3390/met8040213. [33] mayer, h., schuller, r., karr, u., irrasch, d., fitzka, m., hahn, m. and bacher-höchst, m. (2015). cyclic torsion very high cycle fatigue of vdsicr spring steel at different load ratios, int. j. fatigue, 8, pp. 322-327. doi: 10.1016/j.ijfatigue.2014.10.007. [34] tovo, r., lazzarin, p., berto, f., cova, m. and maggiolini, e. (2014). experimental investigation of the multiaxial fatigue strength of ductile cast iron, theor. appl. fract. mech., 73, pp. 60-67. doi: 10.1016/j.tafmec.2014.07.003. [35] mayer, h., schuller, r., karr, u., fitzka, m., irrasch, d., hahn, m. and bacher-höchst, m. (2016). mean stress sensitivity and crack initiation mechanisms of spring steel for torsional and axial vhcf loading, int. j. fatigue, 93, pp. 309-317. doi: 10.1016/j.ijfatigue.2016.04.017. [36] bennebach, m. and palin-luc, t. (2015). effect of static and intermittent shear stress on the fatigue strength of notched components under combined rotating bending and torsion, proc. engineering, 133, pp. 107-114. doi: 10.1016/j.proeng.2015.12.635. [37] bennebach, m., palin-luc, t. and messager, a. (2018). effect of mean shear stress on the fatigue strength of notched components under multiaxial stress state. proc. engineering, 213, pp. 25-35. doi: 10.1016/j.proeng.2018.02.004. [38] mocilnik, v., gubeljak, n. and predan, j. (2017). the influence of a static constant normal stress level on the fatigue resistance of high strength spring steeltheor. appl. fract. mech., 91, pp. 139-147. doi: 10.1016/j.tafmec.2017.06.002. [39] papuga, j., halama, r. (2018). mean stress effect in multiaxial fatigue limit criteria. arch. appl. mech., pp. 1-12. doi: 10.1007/s00419-018-1421-7. [40] wildemann, v.e., tretyakov, m.p., staroverov, o.a. and yankin, a.s. (2018). influence of the biaxial loading regimes on fatigue life of 2024 aluminum alloy and 40crmnmo steel, pnrpu mech. bull., 4, pp. 169-177. doi: 10.15593/perm.mech/2018.4.16. [41] crossland, b. (1956). effect of large hydrostatic pressures on the torsional fatigue strength of an alloy steel, proc. int. conf. fatigue of metals, london, pp. 138-149. [42] marin, j. (1956). interpretation of fatigue strengths for combined stresses, pp.184-195. microsoft word numero 25 art 18 j. toribio et alii, frattura ed integrità strutturale, 25 (2013) 124-129; doi: 10.3221/igf-esis.25.18 124 special issue: characterization of crack tip stress field plastic zone evolution near a crack tip and its role in environmentally assisted cracking jesús toribio, viktor kharin university of salamanca, spain abstract. this paper analyzes the effects of crack tip plastic strains and compressive residual stresses, created by fatigue pre-cracking, on environmentally assisted cracking of pearlitic steel subjected to localized anodic dissolution and hydrogen assisted fracture. in both situations, cyclic crack tip plasticity improves the behavior of the steel. in the respective cases, the effects are supposed to be due to accelerated local anodic dissolution of the cyclic plastic zone (producing chemical crack blunting) or to the delay of hydrogen entry into the metal caused by residual compressive stresses, thus increasing the fracture load in aggressive environment. keywords. plastic zone; near-tip stress-strain fields; environmentally assisted cracking. introduction nvironmentally assisted cracking (eac) of metals is usually evaluated by testing of pre-cracked specimens prepared by fatigue (cyclic) loading in laboratory air that produces a redistribution of stresses and strains as a consequence of cyclic plastic deformations. compressive residual stresses generated at fatigue load release, together with plastic strains, affect the stress corrosion behavior of materials [1]. this paper deals with the mechanical effects of pre-loading on the posterior eac in a pearlitic high-strength steel wire used for prestressed concrete structures. the rising load eac experiments are considered in combination with numerical modeling of the elastoplastic stress-strain field near the crack tip subjected to fatigue pre-cracking and subsequent monotonic loading during eac tests. experimental ac experiments were performed with a series of kmax/kic= 0.28, 0.45, 0.60 and 0.80, where kic is the fracture toughness of the material and kmax the maximum stress intensity factor during fatigue precracking. the experiments were rising load tests of pre-cracked specimens in aqueous solution under anodic and cathodic potentials to evaluate the two main mechanisms of eac [2]: localized anodic dissolution (lad) under the anodic regime and hydrogen assisted cracking (hac) under the cathodic regime. the full experimental details are described elsewhere [1]. the tested high-strength steel has the properties given in tab. 1. for the two regimes of environmental cracking (hac and lad), fig. 1 plots the failure load during the eac test (evaluated through the ratio of the failure load in aggressive environment feac to the failure load in air fc) as a function of the severity of the fatigue precracking regime (expressed in dimensionless terms as the maximum stress intensity factor during fatigue precracking kmax divided by the fracture toughness of the material kic). for both lad and hac, heavier pre-cracking is beneficial for the eac resistance of the steel. this may be attributed to the cyclic plastic zones and compressive stresses near the crack tip due to fatigue. the e e http://www.gruppofrattura.it http://dx.medra.org/10.3221/igf-esis.25.18&auth=true j. toribio et alii, frattura ed integrità strutturale, 25 (2013) 124-129; doi: 10.3221/igf-esis.25.18 125 higher the cyclic load level, the stronger the pre-straining/stressing effect which delays environmental damage (metal dissolution in lad or hydrogen entry in hac) and improves material performance in a hostile environment. young modulus e [gpa] tensile yield strength y [mpa] toughness kic [mpam] ramberg-osgood curve = /e+(/p)n (i) p<1.07 (ii) p1.07 pi (mpa) ni pii (mpa) nii 195 725 53 2120 5.8 2160 17 table 1: mechanical properties of the steel. figure 1: failure load during the eac test as a function of the severity of the fatigue precraking regime. fractographic analysis of the samples after hac tests revealed the existence of a particular microscopic fracture mode (fig. 2a) which is a signal of hydrogen assisted microdamage [3] in pearlitic steels as those used in the present work: the so called tearing topography surface (tts) between the fatigue pre-crack and the final cleavage fracture. measured tts depth xtts also depends on the pre-cracking regime, as plotted in fig. 2b. again this may be attributed to the cyclic plastic zones and compressive stresses near the crack tip due to fatigue. (a) (b) figure 2: (a) fractographic appearance of the tearing topography surface (tts), (b) depth of the tts zone in the hac tests (cathodic regime of eac) as a function of the severity of the fatigue precraking regime (kmax/kic). modelling of crack tip mechanics o ascertain the effects of pre-cracking on eac, the evolutions of mechanical variables associated with eac are desired. in previous analyses [4] the rice model [5] was applied. in this paper, a high-resolution numerical modelling of the crack tip stresses and strains during fatigue pre-cracking and rising load eac test was performed t http://www.gruppofrattura.it http://dx.medra.org/10.3221/igf-esis.25.18&auth=true j. toribio et alii, frattura ed integrità strutturale, 25 (2013) 124-129; doi: 10.3221/igf-esis.25.18 126 for an elastoplastic material with von mises yield surface and ramberg-osgood strain-hardening rule. mixed isotropickinematic hardening was used to capture bauschinger-type effects. model parameters corresponded to the steel used in the experiments (tab. 1). finite deformation analysis of a plane strain crack under mode i (opening) load was confined to small scale yielding, so that the stress intensity factor k is the only variable governing the near tip mechanics [6]. the initial crack was modeled as a parallel-sided round-tip slit with initial height b0 = 5 m in agreement with data for fatigue cracks in steels [7]. simulated loading histories consisted of several zero-to-tension cycles with kmax/kic= 0.45, 0.60 and 0.80, followed by rising load representing the eac tests. an updated lagrangian formulation was used in the computations. plastic zones developed fairly self-similar with a scaling factor of (k/y)2, which is natural for the k-dominated crack-tip domain and coincides with the prediction by rice [5]. at loading up to the first load reversal at kmax, the monotonic plastic zone is defined by the equivalent von mises stress eq = y (fig. 1, left) where y is the tensile yield stress. because of strain hardening, after load reversal the y-stress based yield criterion must not indicate further where plastic flow really proceeds. the cyclic plastic zones are defined then by positive equivalent plastic strain rate, eqp > 0 (fig. 1, right). they are approximately the same at cyclic load minima (reversed zones at kmin = 0) and maxima (forward zones at kmax), smaller than the monotonic zone and quite stable with the cycle number. x y z 1 y xz 1 figure 3: monotonic (left) and cyclic (right) plastic zones at k = kmax for kmax/kic = 0.6 (the grid spacing is 50 m). at rising load, plastic flow starts at k = 0.2kmax after elastic reloading and develops identically as the cyclic zone does up to attaining the pre-cracking level of k = kmax, when it bursts and advances as the monotonic plastic zone does. the near tip stress distributions differ substantially from estimation given by rice [5]. they stabilize after few first cycles as soon as a steady state of alternating plastic flow is approached. fig. 4 shows the evolution of the hydrostatic stress in the crack plane beyond the tip,  = (x), where x is the distance to the crack tip in the deformed configuration of a solid, during monotonic loading in the eac test after pre-cracking. this stress component is focused since it is determinant for hac controlled by stress-assisted hydrogen diffusion driven by the gradient  towards maximum stress locations [8, 9]. figure 4: hydrostatic stress distributions beyond the crack tip during monotonic loading at eac test after fatigue pre-cracking at kmax/kic = 0.45 (dashed lines) and 0.80 (solid lines). http://www.gruppofrattura.it http://dx.medra.org/10.3221/igf-esis.25.18&auth=true j. toribio et alii, frattura ed integrità strutturale, 25 (2013) 124-129; doi: 10.3221/igf-esis.25.18 127 discussion o analyze the results of the eac tests on the basis of crack tip mechanics, the critical stress intensity factor for eac to proceed kqeac is evaluated from the experimental failure loads (fig. 1) as kqeac= (feac/fc) kic (air). for lad-controlled fracture, fatigue pre-cracking may cause a strong protective effect characterized by the fracture loads ratio feac/fc (fig. 1). considering mechanical factors of eac, the normal stresses at the crack tip surface (at x = 0) and the crack tip plastic strains may influence lad processes [2]. evolutions of the crack tip mean normal stress (x = 0) during eac after different pre-cracking regimes (fig. 5a) are practically insensitive to the cyclic load level kmax. stresses in the interior at x > 0 must be irrelevant for lad since it is a surface dissolution reaction. therefore, no difference should be expected for lad from the residual stresses produced at different k. toughening effect of the pre-cracking on lad-driven eac may be associated with accelerated dissolution of the cyclic plastic zone due to the inherently higher chemical activity of its damaged crystalline structure [2]. due to cyclic damage accumulation not only ahead of the tip but also aside of the main crack path (fig. 3), lateral strain-enhanced dissolution may allow chemical crack blunting to compete with dissolution-induced crack extension. then, fracture load must increase together with the lad-driven crack blunting. the lad process may be supposed to involve a domain with a cumulative plastic strain above a certain level. this region must be proportional to the zone of accumulated cyclic plastic strain xy, or probably to the active plastic size xapz. fig. 5b displays this correspondence according to the eac tests and numerical data about plastic zones. figure 5: mechanical factors of the crack growth by lad: (a) evolutions of the crack tip hydrostatic stress  during eac test after fatigue pre-cracking at kmax/kic = 0.45 (dashed line) and 0.80 (solid line); (b) sizes of the plastic zones associated with eac tests: the terminal active plastic zone during the lad test (xapz at kqeac) which surpasses the cyclic and the monotonic plastic zones created during fatigue pre-cracking of the specimens, xy (kmax) and xy (kmax) respectively. for hac-controlled fracture, hydrogen transport to prospective rupture sites ahead of the crack tip may be supplied by two different mechanisms [8,9]: (i) sweeping by moving dislocations within the active plastic zone during load rise; (ii) diffusion in metal driven by hydrostatic stress gradient towards the maximum tensile stress locations. with regard to the first, hydrogenation and hydrogen damage area must be about as extensive as the active plastic zone. however, experimental data on the tts width xtts as an indicator of hydrogen damage (fig. 2) do not agree with calculated plasticity extent xapz after different pre-cracking regimes (fig. 6a). although tts overpassing the plastic zone size at lower kmax levels in fig. 6a may be attributed to the subcritical crack growth and plastic (damage) zone displacement next to the crack tip, it cannot be at kmax = 0.8kic when xtts << xapz even for stationary crack. this fact indicates that dislocational transport of hydrogen to rupture sites must not be the responsible for hac in this case. considering stress-assisted diffusion, the near tip distributions of the hydrostatic stress (x) displayed in fig. 4 indicate that, during the rising load eac tests, initially compressive stresses (x) < 0 and accompanying negative gradients d/dx < 0 induced by fatigue pre-cracking delay hydrogen penetration towards rupture sites, and this effect is more pronounced for the heaviest fatigue regimes (i.e., with the highest kmax). this is supported by comparison of the evolutions of the average value of the stress gradient <> over the range 0 < x < x+(kqeac) (fig. 6b) which delays hydrogen transportation into the metal as far as the respective component of the diffusion flux is j proportional to  [8,9]. this scale of averaging x+(kqeac) corresponds to the maximum tensile stress position and possible location of the stresst http://www.gruppofrattura.it http://dx.medra.org/10.3221/igf-esis.25.18&auth=true j. toribio et alii, frattura ed integrità strutturale, 25 (2013) 124-129; doi: 10.3221/igf-esis.25.18 128 controlled microfracture at hydrogen induced failure in experiments. for the precracking regimes compared in fig. 6, this distance is fairly the same x+(kqeac) = 8 m, so that it may be supposed to be a characteristic microstructural scale for hac. therefore, the heaviest fatigue pre-cracking regimes delay the hydrogen accumulation, and thus the progress of hydrogen degradation in the course of a rising load eac test. figure 6: mechanical factors of the crack growth by hac: (a) comparison of the tts extension and the plastic zones associated with hac tests: at lower kmax-levels, the terminal active plastic zone (open square points) at the end of the hac test (xapz at kqeac) surpasses the cyclic and the monotonic plastic zones created during fatigue precracking (triangles), xy(kmax) and xy (kmax) respectively; (b) evolutions of the average value of the hydrostatic stress gradient during hac tests after fatigue pre-cracking at kmax/kic = 0.45 (dashed line) and 0.80 (solid line). conclusions nvironmentally assisted cracking (eac) of high-strength steel is clearly influenced by fatigue pre-cracking, since cyclic loading affects plastic strains and creates compressive residual stresses in the vicinity of the crack tip. cyclic accumulation of plastic strain and compressive residual stresses improve the eac behavior through increase of the failure load in aggressive environment either by: (i) chemical blunting of the crack tip enhanced by accumulated plastic strain in the near-tip area in the case of eac in the anodic regime of localized anodic dissolution (lad) (ii) delay of hydrogen supply to the fracture process zone near the crack tip by stress-assisted diffusion in the case of eac in the cathodic regime of hydrogen assisted cracking (hac). acknowledgements he authors wish to acknowledge the financial support provided by the following spanish institutions: ministry for science and technology (mcyt; grant mat2002-01831), ministry for education and science (mec; grant bia2005-08965), ministry for science and innovation (micinn; grants bia2008-06810, and bia2011-27870) and junta de castilla y león (jcyl; grants sa067a05, sa111a07, and sa039a08). references [1] toribio, j., lancha, a.m., overload retardation effects on stress corrosion behaviour of prestressing steel, constr. building mater., 10 (1996) 501-505. [2] ford, f.p., stress corrosion cracking of iron-base alloys in aqueous environments, in: c.l. briant, s.k. banerji (eds.), treatise on materials science and technology, embrittlement of engineering alloys, academic press, new york, 25 (1983) 235-274. [3] toribio, j., lancha, a.m., elices, m., characteristics of the new tearing topography surface, scripta metall. mater., 25 (1991) 2239-2244. e t http://www.gruppofrattura.it http://dx.medra.org/10.3221/igf-esis.25.18&auth=true j. toribio et alii, frattura ed integrità strutturale, 25 (2013) 124-129; doi: 10.3221/igf-esis.25.18 129 [4] toribio, j., lancha, a.m., effect of cold drawing on susceptibility to hydrogen embrittlement of prestressing steel, mater. struct., 26 (1993) 30-37. [5] rice, j.r., mechanics of crack tip deformation and extension by fatigue, in: fatigue crack propagation, astm stp 41, american society for testing and materials, philadelphia, (1967) 247-309. [6] kanninen, m.f., popelar, c.h., advanced fracture mechanics, oxford university press, new york, (1985). [7] handerhan, k.j., garrison, w.m., jr., a study of crack tip blunting and the influence of blunting behavior on the fracture toughness of ultra high strength steels, acta metall. mater., 40 (1992) 1337-1355. [8] van leeuwen, h.-p., the kinetics of hydrogen embrittlement: a quantitative diffusion model, engng. fract. mech., 6 (1974) 141-161. [9] toribio, j., kharin, v., k-dominance condition in hydrogen assisted cracking: the role of the far field, fatigue fract. engng. mater. struct., 20 (1997) 729-745. http://www.gruppofrattura.it http://dx.medra.org/10.3221/igf-esis.25.18&auth=true microsoft word numero_61_art_32_3573.docx t. g. sreekanth et alii, frattura ed integrità strutturale, 61 (2022) 487-495; doi: 10.3221/igf-esis.61.32 487 natural frequency based delamination estimation in gfrp beams using rsm and ann t. g. sreekanth, m. senthilkumar, s. manikanta reddy department of production engineering, psg college of technology, coimbatore-641004, tamilnadu, india. sreekanthtg007@gmail.com, stg.prod@psgtech.ac.in, https://orcid.org/0000-0003-3848-7419 msk.prod@psgtech.ac.in, https://orcid.org/0000-0002-3720-0941 manikantaslv@gmail.com, https://orcid.org/0000-0003-3643-6052 abstract. the importance of delamination detection can be understood from aircraft components like vertical stabilizer, which is subjected to heavy vibration during the flight movement and it may lead to delamination and finally even flight crash can happen because of that. any solid structure's vibration behaviour discloses specific dynamic characteristics and property parameters of that structure. this research investigates the detection of delamination in composites using a method based on vibration signals. the composite material's flexural stiffness and strength are reduced as a result of delaminations, and vibration properties such as natural frequency responses are altered. in inverse problems involving vibration response, the response signals such as natural frequencies are utilized to find the location and magnitude of delaminations. for different delaminated beams with varying position and size, inverse approaches such as response surface methodology (rsm) and artificial neural network (ann) are utilized to address the inverse problem, which aids in the prediction of delamination size and location. keywords. natural frequency; delaminations; gfrp; ann; rsm. citation: sreekanth, t. g. , senthilkumar, m., reddy, s. m., natural frequency based delamination estimation in gfrp beams using rsm and ann, frattura ed integrità strutturale, 61 (2022) 487-495. received: 30.04.2022 accepted: 16.06.2022 online first: 17.06.2022 published: 01.07.2022 copyright: © 2022 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. introduction omposites are replacing traditional metals in a variety of applications, including aerospace, automotive, and marine structures, due to their high particular strength, corrosion opposition, specific stiffness, and fatigue qualities. laminated fibre reinforced polymers (frps) are one of the most popular composite configurations, and it is relatively easier to tune their properties in different orientations. however, matrix cracking, ply/fibre breaking, delaminations, and other failure modes can occur in such composites in its service period. these failures mostly occur because of static overloading, impact and fatigue loads, design/manufacturing errors, etc. delamination, also known as interlaminar damage, is the separating of the laminate plies and is one of the most serious flaws in composites as it can quickly spread across the entire laminate when subjected to repetitive loads, resulting in c https://youtu.be/bltrdfmywx4 t. g. sreekanth et alii, frattura ed integrità strutturale, 61 (2022) 487-495; doi: 10.3221/igf-esis.61.32 488 costly and devastating failures if not noticed. for example, a vertical stabilizer is a structure composed of composites that is designed to avoid aerodynamic side slip and offer directional steadiness in aircraft and cars. it may be subjected to heavy vibration during the flight movement and it may lead to delamination between different layers and even finally tends to flight crash. in such cases if there is a system developed to predict magnitude of delamination may help us to save human lives and cost. visual inspection, thermography, radiography, ultrasonic testing, and other nondestructive testing (ndt) and structural health monitoring (shm) methods such as acoustic emission technique, vibration-based processes, fibre bragg grating, and others are the delaminations review techniques currently used in practice [1]. most of these approaches involve either transporting the composite structure to the test centre or transporting major testing equipment to the structure site to conduct the test [2]. researchers have recently concentrate their research on creating structural health monitoring (shm) approaches that may detect damages in situ, with vibration-based techniques being one example [3,4]. damages like delaminations diminish the stiffness of composite structures and create local flexibility in the damaged area, changing the dynamic performance of the composite structure. as a result of the change in natural frequencies, mode shapes, frequency response functions, impulsive reaction, and so on, vibration study can be a useful technique for estimating delaminations [5,6]. the existence of damages such as delaminations can be easily recognized by monitoring changes in natural frequencies but determining the location and size of these delaminations is not possible straightforward. but by solving the inverse problem using artificial intelligence tools, location and size of these delaminations can be evaluated [7,8]. methods based on changes in natural frequencies will come under either of the forward problem or the inverse problem. determining the natural frequency changes due to known damage cases is performed during the forward problem and assessment of damage from natural frequencies variation is achieved during the inverse problem [9]. based on this literature review, it was found that relatively little work has been done in the area of composite health monitoring utilising ai techniques. many study works on homogeneous materials can be found internationally, and some researchers are now attempting to use this as a preliminary step for their composite materials research. as a result, it is clear that there is enough room for research into the health monitoring of composites using ai technologies. vibration based monitoring of composites structure health by observing natural frequencies variations of the structures is the research work performed in this work. glass fiber reinforced polymer composite (gfrp) is considered for this study as it is widely used in aircraft and automotive components like stabilizers. vertical stabilizer part will be subjected to heavy vibration during the flight movement and it may lead to delamination in the material. delamination in these like structures may spread quickly throughout the structure when acted upon by fatigue loading which may leads to costly and disastrous failures when not detected priory. the objective of this research is to estimate severity/size and location of these delaminations accurately so that loses due to failures can be avoided. to establish a relationship between input elements and output responses, an inverse technique is used. damage detection based on vibration is an inverse problem for which causes are effectively deduced from effects. damage detection is basically the inverse problem's solution. this problem is separated into two phases for this purpose. following the validation of the experimental results, the initial phase entails training the neural networks, for which a dataset consisting of the first five natural frequencies for various delamination scenarios is constructed using finite element (fe) modeling. in the second step, ann and rsm are used to solve the inverse problem (rsm). experimentation frp beams with and exclusive of delaminations were made to validate the fe model findings. composites investigated in this study are composed of bidirectional woven e-glass fibers. epoxy resin was used as resin because of its high mechanical strength. for curing reasons, a 1:10 ratio of epoxy hardener was applied to the epoxy resin and curing was done in room temperature for a period of 48 hours. the first layer is placed on the plastic sheet, and the mixed resin is carefully applied with a brush over the face of the first layer. the second layer is then piled on top of the first layer, and is pressed with rollers ensuring uniform thickness throughout the area. the procedure is repeated for the remaining layers. the astm d3039 is the standard used to fix the dimensions of the beam as it is the standard used to obtain the mechanical properties of composite. the 16-layer [0/45/90/-45]2s composite beam employed in the experimental and numerical vibration study has a final dimension of 250×25×4 mm. hand layup technique was used for fabrication of plates which were later cut into beams, and delaminations in the beams were created using teflon tapes of 0.09 mm thickness as shown in fig. 1. for experimental validation of numerical results, delaminations were made on beams at four random axial locations and layers with different areas in each location as shown in tab. 1. fig. 2 shows the delamination g t. g. sreekanth et alii, frattura ed integrità strutturale, 61 (2022) 487-495; doi: 10.3221/igf-esis.61.32 489 of specimen 2 alone for better comprehension. width of the delamination was same for all the beams and length of the delaminations is varied to get different sizes of delaminations. figure 1: fabrication of composite figure 2: delamination in specimen 2. specimen delamination size (mm2) layer of delamination position of delamination from the fixed end (‘x’, mm) 1 0 nil nil 2 200 8 60 3 400 11 120 4 500 14 220 table 1: delamination size and location vibration testing setup consists of data acquisition system which converts the analog wave forms into digital values for processing, impact hammer, tri-axial accelerometer with 5 mv/g and labview software installed in the personal computer as shown in fig. 3. finally the series of impact force was given in the beam by using the impact hammer. the software gives the graph of amplitude (y axis) vs frequency (x axis). the objective of the testing’s were to obtain first five natural frequencies for each of the specimen. two beams with the specimen dimensions were made for the experiments and each beam is clamped to act as a cantilever beam. three trials of experiments were performed on both beam cases and the average values of each of the first five natural frequencies were obtained for comparing with numerical results. t. g. sreekanth et alii, frattura ed integrità strutturale, 61 (2022) 487-495; doi: 10.3221/igf-esis.61.32 490 figure 3: experimental setup. finite element analysis nsys software was used to construct a fe model of the 3d cantilever composite beams with and exclusive of damages, as illustrated in fig. 4. there are sixteen layers in the [0/45/90/-45]2s laminate used in this beam type. the material property of the composite beam is determined using the rule of mixture. poisson's ratio (v13, v23 = 0.29, v12 =0.25, young's modulus (e1, e2 = 42.1 gpa, e3= 19 gpa), shear modulus (g13, g23 = 2.4 gpa, g12= 1.6 gpa), and density 1764 kg/m3. the layered solid 185 element was utilized to model the beams. only one element was examined for each layer along the thickness. to establish a balance among computational time and model bound accuracy, a mesh sensitivity analysis was performed to determine the ideal number of elements. it was observed that when the number of elements increases, the accuracy was improved but on the other hand computational time increased largely. modal validation was done by comparing the results from experimental analysis. figure 4: delamination creation in ansys. natural frequencies for each of the specimen cases were obtained using fea. percentage errors of natural frequencies for each of the specimens were calculated. the first five frequencies were compared to the experimental results for undamaged and delaminated composite beam. it was observed that the fe model was able to predict the first five natural frequencies with just an error of less than 8%, showing that fe modeling is sufficient for constructing the dataset rather than the labor-intensive, time-consuming, and pricey experimental method. the main reason for deviations in results may be because of manufacturing difficulties in achieving uniform thickness of layers and errors occurred in noting natural frequencies experimentally. database for training the inverse algorithm database of variations in natural frequencies owing to delaminations is needed for training the inverse algorithm. due to the lack of a well-defined analytical equation for vibration of the delaminated composite beams and the high expense of conducting experiments, the appropriate database is generated using a finite element tool and a a t. g. sreekanth et alii, frattura ed integrità strutturale, 61 (2022) 487-495; doi: 10.3221/igf-esis.61.32 491 validated using experimental data. ansys was used to simulate a big number of composite beams with various sizes and positions of delaminations. the database size required to train ann is important for accurately determining delaminations (location and severity). for this research, 200 delamination scenarios were numerically created by combining delaminations at eight distinct locations along the length, five layer interfaces, and five areas of delaminations. a sample of bending modes 3 and 5 for dataset x=220, layer-3 with delamination size of 250mm2 is shown in fig. 5 (a) and (b) respectively. figure 5 (a): bending mode 3, (b): bending mode 5, for delamination location at x=220, layer-3 with delamination size of 250mm2. the first five natural frequencies were acquired and utilised as input to artificial neural network for each delamination scenario, while delamination size and position were used as output. the ann received a total of 192 input–output datasets for training, with the remainder being utilized for validation. tab. 2 shows an example dataset for a position 30 mm from the fixed end of the beam with various delamination layers and areas, and similar data is generated for the other linear positions also. all these data indicates that the value of natural frequencies changes with location and areas of delaminations. as it is difficult to interpret this relation with human brain, utilizing ai tools is the solution here to relate relation between delaminations and natural frequency. t. g. sreekanth et alii, frattura ed integrità strutturale, 61 (2022) 487-495; doi: 10.3221/igf-esis.61.32 492 delamination location delamination area (mm2) bm1 (hz) bm2 (hz) bm3 (hz) bm4 (hz) bm5 (hz) x axis (mm) layer no. 30 3 250 25.41 159.7 207.91 447.12 874.2 30 3 500 25.32 159.52 207.28 446.9 872.5 30 3 750 25.28 159.87 206.5 444.2 868.64 30 3 1000 25.18 159.25 206.3 441.8 857.65 30 3 1250 25.01 156.8 205.4 435.6 857 30 6 25 25.51 159.65 207.7 445.91 870.85 30 6 50 25.46 158.8 206.97 441.23 857.22 30 6 75 25.41 157.6 206.35 431.29 835.84 30 6 100 25.33 153.9 205.7 417.57 818.26 30 6 125 25.24 149.62 205.3 404.93 807.08 30 8 25 25.548 159.77 207.94 446.4 873.58 30 8 50 25.533 158.9 207.34 442.59 869.54 30 8 75 25.492 156.69 206.8 435.27 866.48 30 8 100 25.427 153.09 206.39 427.88 867.81 30 8 125 25.317 148.32 206.03 422.8 861.22 30 11 25 25.517 159.77 207.94 446.62 873.87 30 11 50 25.484 159.16 207.32 444.01 871.19 30 11 75 25.44 157.69 206.82 438.98 868.76 30 11 100 25.372 155.21 206.36 433.38 866.92 30 11 125 25.286 151.88 206.01 429.08 852.71 30 14 25 25.391 159.73 207.92 447.24 874.35 30 14 50 25.254 159.57 207.28 446.58 872.32 30 14 75 25.132 159.24 206.76 444.96 868.71 30 14 100 25.025 158.66 206.32 441.91 810.61 30 14 125 25.932 157.73 205.97 432.65 852.7 table 2: dataset for delaminations located 30 mm away from the fixed end. inversion using artificial neural network o improve the model and test the hypothesis, inverse methods typically use both the original model of the structure (here, a delaminated beam) and observed data (natural frequencies). the artificial neural network (ann) is a strong interpolator that may be used to map functions and determine a relationship between input parameters and output responses. it's comparable to the brain's biological neural networks. artificial neurons, which receive and process impulses, are the heart of ann. ann was performed using matlab. ann is utilised here to predict the damage characteristics as neural networks are now being employed as universal function approximators for difficult problems. the ann size is critical since smaller networks cannot accurately represent the system, while bigger networks overtrain it. therefore, trial and error method is used to establish the network design. this is accomplished by t t. g. sreekanth et alii, frattura ed integrità strutturale, 61 (2022) 487-495; doi: 10.3221/igf-esis.61.32 493 repeatedly increasing the number of neurons and retraining the neural network. as shown in fig. 6, five input natural frequencies, three outputs (position, interface, and area), and one hidden layer with 13 neurons make up the ann. figure 6: neural network framed for delamination estimation. mean square error (mse) is used as a performance metric for anns, and training is performed employing gradient descent plus momentum and adaptive lr. mlp-based anns are trained using the back propagation neural network (bpnn) methodology. the linear regression analysis of the target (defect dimensions) and anticipated values is shown in fig. 7. for training, validating, testing, and all data, pearson's correlation coefficients (r-values) are 0.97, 0.99, 0.98, and 0.97, respectively. this suggests that the ann-based prediction model is reasonably accurate in predicting the experimental results. figure 7: regression analyses results of data predicted by the ann model inversion using response surface method sm is the development of analytical and statistical approaches utilized in the modeling and analysis of engineering issues in which the output of interest is driven by some input variables and the major purpose is to optimize this output response. rsm is a statistical approach for determining and solving multivariate equations concurrently r t. g. sreekanth et alii, frattura ed integrità strutturale, 61 (2022) 487-495; doi: 10.3221/igf-esis.61.32 494 using quantitative data from appropriate simulations or experiments. the least squares approach makes fitting response surfaces to data in a simpler way. because of their versatility and ease of use, rsm models are commonly used in polynomial approximation systems. the response surface model in the polynomial approximation approach is a polynomial of nth degree whose coefficients are obtained from a linear system of equations. the linear system is solved by minimizing the error between the predicted and actual values using least square minimization. rsm is used here to evaluatet the location and size of the delamination for the given change in frequency. rsm uses surface plots to identify the location and size of the delamination. the response surface plots indicate the variation in the frequency modes with respect to the layer number and the delamination size. for a given change in frequency of a particular mode, rsm is used to anticipate the location and extent of the delamination. rsm was performed using minitab. the location, size, and variation in frequency are all provided. the input factor is the frequency, and the responses are the matching location and size as it is an inverse problem. the rsm plots the location, size, and change in frequencies as a surface plot. the response surface plots indicates the variation in the frequency modes with respect to the layer number and the delamination size it is shown in fig. 8 for x=30mm layer 3. when the test frequency is specified, the data in the surface plot is fitted, and the corresponding range of position and size is displayed. figure 8: response surface plots for modes 3 and 4, for delamination location at x=30mm layer 3 comparison of ann and rsm results he location and size of delamination obtained from rsm is compared with the actual location and size of delamination given in finite element analysis as shown in tab. 3. delamination layer prediction was found to be accurate using both the technique. it is observed that the predicted results obtained from ann are comparatively more accurate than rsm. the rsm, on the other hand, quickly solves the inverse problem and provides an appropriate mathematical equation for forecasting delamination. in comparison to rsm, an ann is a better and more precise modelling method since it better reflects nonlinearities. conclusions his method uses natural frequencies in delamination structures to locate the damaged interface, as well as its size and position. the changes of frequency with various delamination location and size were obtained using experimentation and finite element techniques. the ann and rsm inversion techniques were compared and ann was found to be more accurate, but time consuming technique. the noteworthy delamination estimation results confirm the algorithms' and approach's robustness and accuracy. however, unlike rsm, which gives physical mathematical models that are simple to compute and analyse, one key drawback of ann is the output weights of the network are not easy to infer. the future scopes of this research is using the mode shapes, damping or combination of all these vibration parameters, instead of frequencies alone to detect delamination. t t t. g. sreekanth et alii, frattura ed integrità strutturale, 61 (2022) 487-495; doi: 10.3221/igf-esis.61.32 495 s.no actual [x, a] ann [x, a] rsm [x, a] %error (ann) %error (rsm) 1. (60,500) (59.36, 478.29) (65.93, 552.41) (-1.05, -4.34) (9.88, 10.48) 2. (90,750) (89.16, 717.11) (79.91, 780.32) (-0.92, -4.38) (-11.20, 4.04) 3. (120,750) (122.51, 771.12) (128.96, 767.40) (2.09, 2.81) (7.47, 2.32) 4. (150,1000) (152.23, 1001.31) (156.95, 1009.04) (1.49, 0.13) (4.63, 0.90) 5. (180,1250) (175.73, 1247.62) (184.43, 1254.34) (-2.36, -0.18) (2.46, 0.34) 6. (210,500) (207.52, 501.34) (208.48, 512.85) (-1.17, 0.26) (-0.72, 2.57) 7. (220,750) (210.13, 763.81) (227.37, 762.51) (-4.48, 1.84) (3.35, 1.66) table 3: comparison of actual and predicted delamination parameters using ann and rsm results references [1] senthilkumar, m., sreekanth, t.g. and reddy, s. m. (2020). nondestructive health monitoring techniques for composite materials: a review. polym polym compos 29, pp. 528-540. doi: 10.1177/0967391120921701. [2] tashkinov, m. a. (2017). modelling of fracture processes in laminate composite plates with embedded delaminations. frattura ed integrità strutturale, 39, pp. 248-262. doi: 10.3221/igf-esis.39.23. [3] sreekanth, t.g., senthilkumar, m. and reddy, s.m. (2021). vibration-based delamination evaluation in gfrp composite beams using ann. polym polym compos, 29, pp. 317-324. doi:10.1177/09673911211003399. [4] sreekanth, t.g., senthilkumar, m. and reddy, s.m. (2021). fatigue life evaluation of delaminated gfrp laminates using artificial neural networks. trans indian inst met, 74, pp. 1439–1445. doi:10.1007/s12666-021-02234-5. [5] kindova-petrova, d. (2014). vibration-based methods for detecting a crack in a simply supported beam, j. theor. appl. mech., 44, pp. 69–82. doi: 10.2478/jtam-2014-0023. [6] x.c. arno ult et al. (2016). short review: potential impact of delamination cracks on fracture toughness of structural materials. frattura ed integrità strutturale, 35, pp. 509-522. doi: 10.3221/igf-esis.35.57. [7] imran, m., khan, r., badshah, s. (2019). investigating the effect of delamination size, stacking sequence and boundary conditions on the vibration properties of carbon fibre reinforced polymer composite, mater res, 22, pp. 1-7. doi: 10.1590/1980-5373-mr-2018-0478. [8] bilisik, k., demiryurek, o. (2011). analysis and tensile-tear properties of abraded denim fabrics depending on pattern relations using statistical and artificial neural network models. fibers polym, 12, pp. 422. doi:10.1007/s12221-011-0422-8. [9] montalvao, d., n.m.m. maia. & a.m.r. ribeiro. (2006). a review of vibration-based structural health monitoring with special emphasis on composite materials. shock vibr. dig., 38, pp. 295-324. [10] senthilkumar, m., manikanta reddy, s. & sreekanth, t.g. 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can be opened with acrobat and adobe reader 5.0 and later.) >> /namespace [ (adobe) (common) (1.0) ] /othernamespaces [ << /asreaderspreads false /cropimagestoframes true /errorcontrol /warnandcontinue /flattenerignorespreadoverrides false /includeguidesgrids false /includenonprinting false /includeslug false /namespace [ (adobe) (indesign) (4.0) ] /omitplacedbitmaps false /omitplacedeps false /omitplacedpdf false /simulateoverprint /legacy >> << /addbleedmarks false /addcolorbars false /addcropmarks false /addpageinfo false /addregmarks false /convertcolors /converttocmyk /destinationprofilename () /destinationprofileselector /documentcmyk /downsample16bitimages true /flattenerpreset << /presetselector /mediumresolution >> /formelements false /generatestructure false /includebookmarks false /includehyperlinks false /includeinteractive false /includelayers false /includeprofiles false /multimediahandling /useobjectsettings /namespace [ (adobe) (creativesuite) (2.0) ] /pdfxoutputintentprofileselector /documentcmyk /preserveediting true /untaggedcmykhandling /leaveuntagged /untaggedrgbhandling /usedocumentprofile /usedocumentbleed false >> ] >> setdistillerparams << /hwresolution [2400 2400] /pagesize [612.000 792.000] >> setpagedevice microsoft word numero_50_art_30_2603 g. belokas, frattura ed integrità strutturale, 50 (2019) 354-369; doi: 10.3221/igf-esis.50.30 354 focused on the research activities of the greek society of experimental mechanics of materials probabilistic geotechnical engineering analysis based on first order reliability method georgios belokas university of west attica, greece gbelokas@uniwa.gr, https://orcid.org/0000-0003-2674-7877 abstract. limit equilibrium engineering analysis needs the incorporation of probabilistic approaches for the determination of soil strength statistical measures for deterministic and probabilistic analyses. for the commonly used mohr–coulomb strength model, the uncertainty and the characteristic values of cohesion (c) and angle of shearing resistance (φ) determination is not straightforward. this paper applies the first order reliability method (form) to estimate these values from the direct shear and the typical triaxial tests. the method is verified with test data. furthermore, the form is applied to the planar failure limit equilibrium problem to determine the statistical measures of the safety margin (sm) and safety factor (sf). it is observed that the critical slip surface for the best estimate of the mean (smm, sfm), for a 5% probability of exceedance (smp=5%, sfp=5%) and for the characteristic value (smk, sfk) do not coincide. it is interesting that the maximum probability of having a sm<0 or sf<1 does not correspond to the minimum best estimate of the sm or sf. form can be a very useful tool for complete probabilistic analyses. furthermore, probabilistic approaches applied to soil properties estimation can set a framework for the selection of their characteristic values for deterministic analyses. keywords. soil strength; geotechnical engineering; probabilistic approaches; reliability; characteristic values. citation: belokas, g., probabilistic geotechnical engineering analysis based on first order reliability method, frattura ed integrità strutturale, 50 (2019) 354-369. received: 16.02.2019 accepted: 22.05.2019 published: 01.10.2019 copyright: © 2019 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. introduction he limit equilibrium analysis for the design of geotechnical works requires the application of reliability theory principles for: a) the determination of soil properties in deterministic analyses and b) the uncertainty estimation of the safety margin (sm) or safety factor (sf) in probabilistic analyses. modern codes of practice (e.g. eurocode 7 – ec7) provide the alternative of both types of analysis, which may include one of the following methods: a) monte carlo, b) point estimate, and c) first order reliability. the application of first order reliability method (form) for geotechnical engineering limit states analyses (e.g. [1,2]), a method for the estimation of error propagation, has been commonly t http://www.gruppofrattura.it/va/50/2603.mp4 g. belokas, frattura ed integrità strutturale, 50 (2019) 354-369; doi: 10.3221/igf-esis.50.30 355 applied to the uncertainty estimation of the experimental results of laboratory tests (e.g. gum: 1995, see [3]) and can be applied directly wherever a closed form of analytical solution exists. under the framework of ec7, the reliability analysis (uncertainty calculation) for a limit equilibrium problem can be performed with respect to the safety margin (sm), which is expected to have a value of sm≥0.0 for a certain level of confidence. that requires the knowledge of the uncertainty of the parameters that affect the value of sm. these parameters normally include the value and the uncertainty of the external and internal loads (permanent and mobile) and of the strength constants, as well as the spatial variability and uncertainty of the model (see fig.1 based on kulhawy [4]). one of the most critical components on the overall sm uncertainty is the strength uncertainty both due to spatial variability and model uncertainty. on the other hand, a deterministic analysis requires the best estimate of the loading conditions and the materials properties, which correspond to a specific level of confidence. inherent soil  variability soil in situ or lab  measurement transformation  model estimated soil  property data scatter statistical  uncertainty measurement  error model  uncertainty sampling  disturbance figure 1: factors affecting the property uncertainty (based on kulhawy [4]). therefore, for the mohr – coulomb strength parameters, cohesion (c) and angle of shearing resistance (φ), which are used in limit state analysis, an estimation of their mean value and their corresponding variation (or uncertainty) is required. these measures may be calculated either by direct application of statistical methods (e.g. for the direct shear test) or by an error propagation method (e.g. form for the typical triaxial test). the present work explores on the application of the form for the statistical evaluation of the strength parameters and for the slope stability analytical solution of a wedge failure mechanism. issues with respect to the design and characteristic strength are also discussed, as well as the capability to apply the form into a general limit equilibrium slope stability problem. statistical measures of soil properties deterministic analysis requires the knowledge of the best estimates of its individual components, i.e. loading conditions and material properties, for a specific confidence level. these correspond to the characteristic values of actions (fk) and of soil parameters (xk) defined in ec7 (εν-1997-1). focusing on soil parameters, for any specific parameter, x, that affects the development of the limit state condition, its characteristic value χk is defined as a cautious estimate of the mean value, (i.e. of the best estimate) of the mean, χm (see εν-1997-1). the selection of this characteristic value has to be representative of the volume involved in the considered failure mechanism and it can depend on the type of the failure mechanism (e.g. local vs generalized failure). when the sample size, n, is large enough to apply statistical methods, the characteristic value corresponds to a worse value governing the occurrence of the soil parameter with a calculated probability not greater than 5% (it is 90% confidence interval, see εν-1997-1), which for a single variable model is given by eq.(1).  , ,1 /       k m d x k d x mx x k s x k v v s x (1) where k is the confidence level coefficient for a given probability distribution, sd,x is the sample standard deviation and v the variation coefficient. for a specific sample with unknown standard deviation, the sd,x is the corrected standard deviation, which is related to the corrected – unbiased sample variance (s2) according to eq.(2).    2 22 , 1 1 var( ) 1        n x d x i m i x s s x x n (2) a g. belokas, frattura ed integrità strutturale, 50 (2019) 354-369; doi: 10.3221/igf-esis.50.30 356 the use of the corrected variance (sx2=var(x), eq.(2)) instead the uncorrected sample variance (σx2), implies that there is little confidence that σx2 is a close estimate of the population variance, σ2. had it been σx2σ2, the sample would closely follow a normal distribution, which is not the case in geotechnical engineering investigations as sample size is usually small, despite that population may follow a normal distribution. therefore, the direct use of the statistical methods may not be applicable, because they may lead to non-representative values for the soil mass (see [2]). in order to account for this difficulty on the statistical error, direct values (e.g. [2,5]) or semi-empirical methods (e.g. [5, 6]) have been proposed for the estimation of the variation coefficient v. the v coefficient can also be used to include other types of errors, such as the error uncertainty due to ground spatial variability, the measurement error and the transformation uncertainty of the empirical equations application ([6]). however, a good knowledge of the statistical background can provide a better understanding on the selection of the cautious estimate (see [5,7]), or even to apply bayesian statistical methods (e.g. [2,8]), not only in cases of a small sample but also of complex uncertainties. concerning the characteristic values used in deterministic analysis, due to the different types of uncertainties involved (e.g. inherent soil variability, sampling disturbance, fig.1), engineering judgement is also recommended for their selection (e.g. [9]). such judgement should evaluate the relative importance of the following uncertainties (see also [6]):  sampling quality (sampling type and sample condition).  the extent of the in-situ and laboratory investigation (the number and spatial distribution of samples and in-situ and laboratory tests).  the quality of the laboratory tests (accreditation and uncertainty of the laboratory measurements)  the spatial variability of the parameters and samples distribution with respect to the extent of the considered mechanism of geotechnical soil model. in addition, the following should also be taken into account: a) existing experience and data on similar soil units (including their uncertainty) and b) the failure mechanism with respect to the geotechnical profile (e.g. generalized vs local failure, short term vs long term conditions, small – large strains). for a single variable model (e.g. undrained strength, su) and a small sample size (n) of laboratory data with unknown standard deviation of the population (the usual case for geotechnical engineering) and assuming a normally distributed population, the resulting estimated distribution follows the student t-distribution. the estimated characteristic value (xk), which corresponds to a probability p(xk<μ)=1-p=1-α/2 (i.e. in a certain percentage of the cases the expected value of the true mean, μ, is greater than xk), is then given by eq.(3), in which sex is the sample standard error given by eq.(4). , 1 , 1 ,    k m p n x m p n d xx x t se x t s n (3) ,x d xse s n (4) where tp,n-1 is the n-1 degrees of freedom student distribution confidence parameter for the one-sided 1-p lower confidence limit of the true mean (μ). from eqs.(1,3) we get the coefficient k=tp,n-1/n0.5. schneider [10] proposed the approximate relationship χk=xm–0.5sd,x, which corresponds to p=5% and n=14. as already mentioned, eqs.(3,4) correspond to the single variable model (e.g. strength determined from the unconfined compression test, in which qu=2su, where su undrained shear strength). the mohr – coulomb failure criterion used in limit state analyses, is a two variables linear model that includes two constants (cohesion, c, and angle of shearing resistance, φ) and two variables. the for the cases of: a) the direct shear test is given by eq.(5), in which σn is the imposed normal stress (the nonrandom or independent variable) and τ the measured – observed shear stress (the random or dependent variable) and b) the typical triaxial test is given by eq.(6), in which σ3 is the imposed cell pressure – radial stress (the nonrandom or independent variable) and σ1 the measured – observed vertical stress (the random or dependent variable). τ=c+σntanφ= a+b·σn (5) σ1=2c·cosφ/(1–sinφ)+σ3(1+sinφ)/(1–sinφ)=a+b·σ3 (6) with regards to the experiments, if xi is the imposed value and yi is the corresponding observed value of a sample size n, the linear model is given by eq.(7), where εi is the error and a and b the model constants. eq.(7) gives a best estimate of the mean of y for a given x. the measurement error εi is the deviation of the yi from its best (deterministic) estimate y=a+xib (fig.2). in simple linear regression, the best estimate of the constants may be derived from minimizing the error square sum. yi = a + xib + εi (7) g. belokas, frattura ed integrità strutturale, 50 (2019) 354-369; doi: 10.3221/igf-esis.50.30 357 figure 2: graphical representation of the regression model. assuming that: a) xi is an accurate observation, b) each xi is an independent observation, c) the error εi has a constant variation for each xi and d) the uncertainties of the yi observations are equivalent (otherwise weight coefficients are required), the best mean estimators for the linear regression coefficients are given by eqs.(8,9). observation xi can be a predetermined imposed loading (e.g. the σn in direct shear and the σ3 in the typical triaxial), while observation yi a measured reaction (e.g. the τ in direct shear and the σ1 in the typical triaxial).          ,1 1 1 1 22 ,2 1 1 1 1 , ,1 n n n n i i i i i i d yi i i i m xyn n n d x i i i i i i x x y y x y y x scov x yn b r var x y s x x x x n                               (8) m ma y b x    (9) in eqs.(8,9) (xi, yi) are the data measurements of the two dimensional sample, ,y x are their mean values, sd,x and sd,y are the sample standard deviation of x and y measurements (eqs.(10,11)) and rxy the pearson sample correlation coefficient (given by eq.(12)). the rxy is sensitive only to a linear relationship between two variables (|rxy|≤1, when rxy=1 the correlation is a perfect direct, i.e. increasing). moreover, an unbiased estimate of the variance of y(x) with n-2 degrees of freedom is given by eq.(13). the standard error estimators seb and sea of the b and a regression coefficients are given by εqs.(14,15), respectively. some applications in civil and geotechnical engineering of the two variables linear model have been presented by baecher & christian [1], pohl [8] and kottegoda & rosso [11], as for instance the case of a variation with depth. a classic example is the increasing undrained shear strength with depth. the application of this model in the mohr – coulomb strength failure criterion has some individual characteristics that will be presented later.  2, 1 1 1      n d x i i s x x n             (10)  2, 1 1 1      n d y i i s y y n             (11)    2 22 2                     i i i i xy i i i i n x y x y r n x x n y y         (12)     2 1 , 1 | 2 2        n i i dvar y x s n s n n   , ˆˆi i iy a bx          (13) g. belokas, frattura ed integrità strutturale, 50 (2019) 354-369; doi: 10.3221/igf-esis.50.30 358     2 1 2 2 1 1 var( | ) 1 2            n i i b n n i i i i x y se n x x x x        (14)     2 2 2 1 2 1 1 1 1 1 2                  n in n i a b i i n i i i i x se se x n n n x x        (15) statistical measures for the direct shear test – two variables model he direct shear test gives a direct determination of c and tanφ of the linear mohr – coulomb criterion (eq.(5)), with σn=x and τ=y. for this occasion: a) the best estimates of the mean are cm=am and (tanφ)m=bm given by eqs.(9,8), respectively (with xi=σni and yi=τi being the data measurements) and b) the standards error estimators se(tanφ)=seb and sec=sea are given by εqs.(14,15). concerning the confidence intervals of the linear regression coefficients estimators, the standard method relies on the normality assumption, which is justified if either: a) the errors in the regression are normally distributed (this leads to a t-statistic) or b) the number of observations n is sufficiently large (in this case the estimator is approximately normally distributed). applying a statistical t-test, the linear regression random variables follow a student’s t-distribution with n-2 degrees of freedom (dof), i.e. tc=(cm–c)/sec ~ tn-2, t(tanφ)=[(tanφ)m–tanφ)/se(tanφ) ~ tn-2, where c and tanφ represent the true mean values (or population mean values). the t-test includes the assumptions that the sample is representative of a specific soil unit, the observations are independent, while the variation of x=σn depends only on the uncertainty of the laboratory measurement. the σn variation has a negligible influence on the total uncertainty. ignoring the influence of sampling disturbance and spatial variability, the characteristic values of cohesion, ck, and angle of shearing resistance, (tanφ)k are given by eqs.(16,17) and their standard errors by eqs.(14,15), respectively. the best estimates and their standard errors can be used for probabilistic analyses, by incorporating the standard errors as quantitative measures of the corresponding uncertainties (uc=setanφ=sd,tanφ/n0.5 and utanφ=setanφ=sd,tanφ/n0.5). , 2 k m p n cc c t se (16)     , 2 (tan )tan tan   p nk m t se   (17) eqs.(16,17) may be used to give the characteristic mohr – coulomb failure envelope: τ=ck+σn(tanφ)k. alternatively, an estimate of the characteristic failure envelope (see also [1,11]) can be obtained by incorporating the shear stress estimates for a specific probability (given by eq.(18)). the resulting from eq.(18) failure envelope is non-linear and needs to be approximated by a linear regression to get the characteristic values of the mohr – coulomb failure criterion parameters.         2 2 2 2 1 1 1 1 tan 2                         n n m n n j nm j i i x τ c t n n x x     (18) table 1 shows a fictional example for the application of the abovementioned relationships for a direct shear test. typically, three specimens are obtained from each sample, which sample corresponds to a specific depth and location. applying eqs. (8,9) we obtain the best estimates of strength parameters and their corresponding uncertainties respectively: cm=23.95 kpa, (tanφ)m=0.37950 (i.e. φm=20.8ο) sec=uc=5.3 kpa and setanφ=utanφ=0.01561. applying eqs.(16,17) for a probability p=5% we get the following characteristic values: ck1=14.5 kpa and (tanφ)k1=0.35186 (see fig.3, characteristic 1). applying a linear regression on the characteristic envelope derived from eq.(18) we get the following characteristic values: ck2=16.50 kpa and (tanφ)k2= 0.38500 (see fig.3, characteristic 2), which is less conservative than the characteristic 1. t g. belokas, frattura ed integrità strutturale, 50 (2019) 354-369; doi: 10.3221/igf-esis.50.30 359 sample 1 2 3 4 5 specimen 1.1 1.2 1.3 2.1 2.2 2.3 3.1 3.2 3.3 4.1 4.2 4.3 5.1 5.2 5.1 σn (kpa) 100 300 500 100 300 500 100 300 500 100 300 500 100 300 500 τ (kpa) 56 140 218 56 130 208 69 151 222 48 143 241 76 134 196 table 1: example for direct shear test. 0 50 100 150 200 250 0 50 100 150 200 250 300 350 400 450 500 550 s h e a r  st re ss  τ  ( k p a ) normal stress σn' (kpa) exp data best estimate characteristic 1 characteristic 2 characteristic 3 figure 3: failure envelopes, best estimate and characteristic envelopes. the typical test procedure of applying on the three different specimens of each soil sample the σn = 100, 300 and 500 kpa normal stresses respectively, may raise a question concerning the independence of the observations. an alternative is to consider a single variable model for τ on each one of the three σn values (in our case n=5 samples) and then apply a t-test on the observed τ values, which in our example leads to table 2. applying a linear regression on σn, τp=5% pairs we get the following characteristic values: ck3=14.02 kpa and (tanφ)k3= 0.38056 (characteristic 3). this approach, overcomes the issues concerning the independence of observation and gives similar results to characteristic 1 (fig.3), however, it does not give a standard error of the parameters. for this specific case, the maximum standard error on τ lies close to the previously determined standard error of the cohesion. specimen 1 2 3 σn (kpa) 100 300 500 τm (kpa) 61 139.6 212.8 sd (kpa) 11.27 8.14 10.83 n 5 5 5 se (kpa) 5.0398413 3.641428 4.841487 a/2 0.05 0.05 0.05 tn-1 -2.131847 -2.13185 -2.13185 τp=5%,min 50.255831 131.837 202.4787 table 2: application of t – test on the values of the observed τ for each σn. another approach often used in engineering practice is to apply a t-test on the determined c and tanφ pairs from each sample (again n=5 for the examined case). this approach gives cm=23.95 kpa, (tanφ)m=0.37950 (i.e. same as before), sec=uc=6.6 kpa and setanφ=utanφ=0.02183 (i.e. greater than before). applying eqs.(15,16) for a probability p=5% we get the following cautious estimate of strength parameters: ck4=9.8 kpa and (tanφ)k4=0.33296 (characteristic 4), which are unrealistically conservative, as can been in fig.4, due to the higher uncertainties. g. belokas, frattura ed integrità strutturale, 50 (2019) 354-369; doi: 10.3221/igf-esis.50.30 360 0 50 100 150 200 250 0 50 100 150 200 250 300 350 400 450 500 550 s h e a r  st re ss τ  (k p a ) normal stress σn' (kpa) experimental data best estimate characteristic 1 best estimate (alternative) characteristic 4 (alternative) figure 4: best estimates and corresponding characteristic envelopes comparison. statistical measures for the typical triaxial compression test by form n the typical triaxial compression test the mohr – coulomb failure criterion parameters are determined indirectly. for this test, a constant horizontal radial stress (the cell pressure) σr=σc=σ3 is applied to a cylindrical specimen, while the reaction of the axial stress is measured (δσa, σ1=σ3+δσa). we can consider that the cell pressure is an accurate observation (i.e. the non – random). the mohr – coulomb failure criterion in terms of principal stresses is given by eq.(6), in which the statistical measures of constants a and b can be determined directly from the two variables models, while the best estimates of the mean for c and tanφ constants are calculated indirectly by the transformation of eqs.(19,20), respectively. sinφ=(b–1)/(1+b)  φ=asin[(b–1)/(1+b)] and tanφ=tan{asin[(b–1)/(1+b)}] (19) c=a(1–sinφ)/(2cosφ) (20) a way to calculate the uncertainties of c and tanφ is to apply the form, which method makes use of the second moment statistics (the mean and the standard deviation) of the random variables and assumes a linearized form of their performance function (e.g. z=g(x1,…, xn)) at the mean values of the random variables and independency between all variables. truncating at the linear terms the taylor expansion of the performance function about the mean, it is possible to obtain the first order approximation of the variance (σz2) of the true mean (μz) of z. assuming uncorrelated non – random variables x1, …, xn, the approximation of the variance is given by eq.(21), an equation commonly used to estimate the uncertainties by error propagation for laboratory tests results.   2 2 2 2 , 1 1 var( )                     i n n z i d z x i ii i g g x se se x x (21) the sample variance var(xi)=sxi2=(sd,xi)2 of a xi variable (where xi is tanφ or c) relates to the standard error sexi by eq.(4), while sexi is a quantitative measure of the corresponding uncertainty uxi (i.e. uxi=sexi). the variances stanφ2 and sc2 of the mohr – coulomb constants may be now calculated by applying eq.(21) and considering eqs.(19,20) as the performance functions (i.e. c=g(a, φ) and tanφ=g(b) or φ=g(b)):   2 2      bse se b   ,    2 2 tan tan        bse se b   (22)     22 22              c a c c se se se a       (23) i g. belokas, frattura ed integrità strutturale, 50 (2019) 354-369; doi: 10.3221/igf-esis.50.30 361 where: 2 2 2 2 ( 1) 1 ( 1) / ( 1) )         b bb b ,    3/ 22 2 3 2 ( 1) 1 1 ( a 1 t n )            b b b b (24) 1 – /( ) ( )2     sin cos c a           (25) 21 )2(/( )    c a sin cos              (26) next, the above equations are applied to laboratory results from the herakleion marl (see table 3, data from [12]), with 27 specimens and 9 samples (3 specimens per sample). treating each specimen separately (i.e. sample size n=27), the best estimates of a and b constants of eq.(6) are determined from the linear regression (eqs.( 8,9)), which gives am=229.6 kpa and bm=3.02553. applying these values into eqs.(20,19) we get the best estimates cm=66.0 kpa and (tanφ)m=0.58225. the form (by application of eqs.(23,22,15,14)) gives the corresponding uncertainties sec=uc=15.5 kpa and setanφ=utanφ=0.0347. a tstudent distribution for n-2 dof (eqs.(16,17)) to account for the error propagation leads to the characteristic values ck1= 39.60 kpa and (tanφ)k1=0.52297. the best estimate of the mean failure envelope, as well as the estimated characteristic envelopes are represented in fig.5, in which figure the characteristic 2 and 3 envelopes are explained later in the same section. it is evident from fig.5 that characteristic 1 can be indeed considered as a conservative estimate of the mean failure envelope. sample γς2 (5m) γ1 (2m) γ1 (3.5m) γς13 (17m) γ1 (18m) σ3 (kpa) 117.72 155.98 219.74 62 110 304 95 158 383 110.85 200.12 245.25 104 210 427 σ1 (kpa) 448.32 591.54 736.73 375 606 1488 475 506 1383 593.51 884.86 1044.77 514 785 1339 s (kpa) 283 374 478 219 358 896 285 332 883 352 542 645 309 498 883 t (kpa) 165 218 258 157 248 592 190 174 500 241 342 400 205 288 456 table 3.1: typical triaxial compression data from herakleion marl ([12]). sample γ1 (6m) γς2 (9m) γς13 (24m) γ3 (12.5m) σ3 (kpa) 79 146 265 119.68 258.98 346.29 73.57 141.26 162.85 52 139 222 σ1 (kpa) 365 618 997 640.59 1056.54 1339.07 429.68 587.62 750.47 672 819 1004 s (kpa) 222 382 631 380 658 843 252 364 457 362 479 613 t (kpa) 143 236 366 260 399 496 178 223 294 310 340 391 table 3.2: typical triaxial compression data from herakleion marl ([12]). 0 200 400 600 0 200 400 600 800 1000 1200 1400 1600 σ 3 (k p a ) σ1 (kpa) experimental results best estimate characteristic 1 (form) characteristic 2 (envelope for p>5%) characteristic 2 (linear regression) figure 5: statistical evaluation of the experimental results of table 3. g. belokas, frattura ed integrità strutturale, 50 (2019) 354-369; doi: 10.3221/igf-esis.50.30 362 treating each sample separately we get the mohr – coulomb failure envelope constants of table 4 (sample size n=9), which are represented in fig.6 by the thin coloured lines, in the classic τ – σn mohr – coulomb diagram. again the remaining characteristic envelopes of fig.6 are explained next. alternatively, for the characteristic envelope we can apply a t-student distribution into the y(x) estimate (i.e. the predicted σ1 for given σ3, given by eq.(27)) for a p=5% probability (i.e. tp,n-2=1.70814) and n-2 dof. in fig. 5 the characteristic 2 line shows the σ1, σ3 graph of the characteristic envelope from eq.(27) for a p=5%. this characteristic envelope is non – linear and a linear regression leads to characteristic values ak=190.36 kpa and bk=2.92550 for eq.(5) and then ck2=55.6 kpa and (tanφ)k2=0.56287 for the mohr – coulomb failure criterion (figs.(5,6), characteristic 2). taking into account the results for the direct shear test, it is obvious that eq.(18) or eq.(27) systematically gives a more optimistic characteristic envelope than the one computed based on mean values and uncertainty calculation of c and tanφ. however, this approach does not take into account the error propagation to calculate the uncertainties. sample mean γς2 (5m) γ1 (2m) γ1 (3.5m) γς13 (17m) γ1 (18m) γ1 (6m) γς2 (9m) γς13 (24m) γ3 (12.5m) c (kpa) 64.34 40.99 22.34 21.24 60.41 77.75 29.69 76.83 48.20 201.58 tanφ 0.59415 0.53191 0.83698 0.64201 0.64099 0.4862 0.64606 0.59134 0.63149 0.34038 φ (ο) 30.42 28.01 39.93 32.70 32.66 25.93 32.86 30.60 32.27 18.78 table 4: application of t – test on the values of the observed τ for each σn. figure 6: characteristic and best estimate mohr – coulomb failure envelopes superimposed on the mohr – coulomb failure envelopes of each sample.       2 3 32 1 3 2 2 1 3 3 1 1 1 2                         n m m n j n j i i a b t n n        (27) an alternative for the characteristic envelope is to compute first the characteristic values of a and b constants by applying a t-student distribution (i.e. ak=am-tp,n-2sea and bk=bm-tp,n-2seb) for p=5% and n-2 dof and then apply eqs.(20,19) to compute the mohr – coulomb characteristic constants ck and (tanφ)k. this approach, which does not take into account the error propagation, leads to ak=139.86 kpa and bk=2.58981 constants of eq.(6) (fig.5, characteristic 3) and to ck3=43.4 kpa and (tanφ)k3=0.493949 constants of the mohr – coulomb failure criterion (fig.6, characteristic 3). g. belokas, frattura ed integrità strutturale, 50 (2019) 354-369; doi: 10.3221/igf-esis.50.30 363 finally, as it was applied for the direct shear test, a common approach in engineering practice for the estimation of all statistical measures of c and tanφ is first to derive the mohr – coulomb constants (c, tanφ) for each sample separately (see table 4) and then apply a statistical t-test on each constant independently for n/3-1 dof (where n the complete number of specimens and n/3 the number of specific locations of soil sampling). for the herakleion marl case the n/3-1=8 dof lead to: a) mean values: cm=64.34kpa, (tanφ)m=0.59415, b) standard deviation: sd,c=55.69kpa, sd,tanφ=0.13577, c) standard error: figure 7: characteristic and best estimate mohr – coulomb failure envelopes superimposed on the mohr – coulomb failure envelopes of each sample.   best estimate cm (kpa) (tanφ)m sec (kpa) setan(φ) am, bm from linear regression of all σ1, σ3 data points cm, (tanφ)m from eqs.(20,19) sec and setanφ from form error propagation (this gives characteristic 1) 66.00 0.58225 15.50 0.0347 cm, (tanφ)m from mean values of table 4 sec and setanφ from single variable model (this gives characteristic 4) 64.34 0.59415 18.56 0.0423 table 5: mohr – coulomb failure criterion constants (mean values and uncertainties).   characteristic values ck (kpa) (tanφ)k characteristic 1 (se from form error propagation): ck=cm-tp,n-2sec, tan(φ)k= tan(φ)m-tp,n-2setan(φ) 39.60 0.52297 characteristic 2: ak, bk from linear regression on σ1pred, σ3 data points (σ1pred=am+σ3bm±tn-2seσ1) ck, (tanφ)k from eqs.(20,19) 55.65 0.56288 characteristic 3: ak=am-tp,n-2sea, bk=bm-tp,n-2seb ck, (tanφ)k from eqs.(20,19) 43.43 0.49395 characteristic 4 (se from one variable model, eq.(4), for c and tanφ): cm and tanφ from mean values of table 4 ck=cm-tp,n-2sec, tan(φ)k= tan(φ)m-tp,n-2setan(φ) 29.82 0.50990 table 6: mohr – coulomb failure criterion constants (characteristic values). g. belokas, frattura ed integrità strutturale, 50 (2019) 354-369; doi: 10.3221/igf-esis.50.30 364 sec=18.56kpa, setanφ=0.04526 and d) characteristic values: ck4=29.82kpa, (tanφ)k4=0.5099. the mean value from this alternate approach (characteristic 4, fig.7) is almost the same with the previously calculated. fig.7 compares the character istic value from this approach (characteristic 4) with the characteristic 1 from the form. the alternate approach is very conservative because it gives a higher se than the form. all the above results are summarized into tables 5 for the mean values and the corresponding uncertainties and table 6 for the characteristic values.     application of the form to a simple planar failure problem urther extending the form application to engineering problems calculations, a limit state analysis may be performed in terms of either the safety margin sm=r-e (r is resistance and ε action as defined in ec7) in terms of the safety factor sf=r/e. more specifically, in form applications the sm application is preferable compared to the fs because the actions ε in the denominator of the sf enhances the non-linearity effects in the error propagation. for the safety margin the reliability index is β=smm/sd,sm, where smm is the best estimate of the mean and sd,sm the standard deviation, while by definition it is βsm=1/vsm, where vsm the variation coefficient. since resistances and actions describe different types of random variables, they are expected to be uncorrelated, and their covariance, ρr,d, can be considered zero. moreover, the variation of permanent loads is generally small compared and should not greatly affect the sm or sf value. the form is applied herein to a planar failure problem, which can be adapted to any type of failure surface (e.g. [13]) of limit equilibrium problems (e.g. method of slices). for the planar wedge failure problem considered herein fig.8 shows the geometry. w is the weight of the wedge, h is the height of the slope, β is the angle of the slope to the horizontal, θ is the angle of the plane of failure with respect to horizontal and n and t are the normal and shear reaction forces on the plane of failure. the safety margin is then determined from the equilibrium equations that lead to eq.(28). on the other hand the sf is given by eq.(29).   212= c sin cos tan sin sin sinsm h γh β θ θ φ θ β θ      (28)     = 2c / γ sin cos tan sin sin sin sinsf h β θ θ φ β h β θ θ β          (29) h β θ w wcosθ wsinθ n t α β γ αβ=η/sinθ figure 8: geometry of two dimensional planar failure. applying the form on eq.(28) the standard deviation of the sm is given by eqs 30 to 33, in which uc, utanφ and uγ are the uncertainties of c, tan(φ) and γ respectively. likewise, applying the form on eq.(29) the standard deviation of the sf is given by eqs.(34-37).   2 22 2 2 2 tan tan                      c sm sm sm u sm u u u c    (30) = sin   sm h c θ           (31) f g. belokas, frattura ed integrità strutturale, 50 (2019) 354-369; doi: 10.3221/igf-esis.50.30 365  2 sin1 1= cos tan sin 2 sin         β θsm γh θ θ β           (32)    2 sin1 1 = cos tan sin sin 2 sin         β θsm h θ φ θ γ θ β (33)   2 22 2 2 2 tan tan c sf sf sf u sf u u u c                         (34)   2 1 = sin sin sin sf c h β θ θ β              (35) 1 = tan tan sf                      (36)  2 2 1 = sin sin sin sf c γ γ h β θ θ β        = 2c / γ sin cos tan sin sin sin sinsf h β θ θ φ β h β θ θ β            (37) a slope geometry example of β=60ο and η=25m and the material properties from tables 5 and 6 are considered to exhibit the safety probability calculation. a deterministic calculation of the best estimate of the mean of smm and sfm from eqs.(28,29) respectively is computed first, by the best estimates of the mean of the soil properties (i.e. cm, tan(φ)m and γm). then a normal distribution for sm and sf is applied, in order to estimate their value for a probability not greater than 5% (i.e., eq.(38) with k=1.64485). the uncertainties u(sm) and u(sf) are calculated by eqs.(30,34) applying the best estimates of the mean and the corresponding uncertainties of c, tan(φ) and γ (error propagation considers the standard error of the mean, i.e. u=se). the values of sm and sf for probability p=5% and the corresponding probability p for sm<0 and sf<0, all calculated for the critical plane θcr that gives the minimum smm, are presented in tables 7 and 8. the two sets of statistical measures from table 5 for soil strength properties have been used. ( )  msm sm k u sm ,  ( )msf sf k u sf   (38) cm (kpa) (tanφ)m uc (kpa) utanφ smm= min(smm) (kpa) θcr (o) usm (kpa) smp=5%= smm kusm (kpa) vsm p(sm<0) (%) 66.00 0.58225 15.46 0.03470 1435.08 48 527.49 567.43 2.721 0.33 64.34 0.59415 18.56 0.04526 1396.92 48 631.85 357.62 2.211 1.35 table 7: calculations of sm for p=5% and p for sm<0 based on the minimum best estimate of the smm and the corresponding θcr. cm (kpa) (tanφ)m uc (kpa) utanφ sfm= min(sfm) (kpa) θcr (o) usf (kpa) sfp=5%= sfm kusf (kpa) vsm p(sf<1) (%) 66.00 0.58225 15.46 0.03470 1.639 40 0.241 1.243 6.800 0.40 64.34 0.59415 18.56 0.04526 1.6300 40 0.284 1.163 5.740 1.33 table 8: calculations of sf for p=5% and p for sf<1 based on the minimum best estimate of the sfm and the corresponding θcr. g. belokas, frattura ed integrità strutturale, 50 (2019) 354-369; doi: 10.3221/igf-esis.50.30 366 it is obvious that the minimum values of the estimated means smm=1435.08kpa and sfm=1.639 develop for different critical angle θcr of the plane of failure. however, the corresponding values of smp=5% and sfp=5% (calculated in tables 7 and 8 by applying eq.(38)) are not the minimum ones, nor are psm<0 and psf<1 the maximum ones, as their minimum and maximum values develop for different critical slopes θcr (presented in tables 9 and 10). the differences for the problem examined are of the order of 4% for the sm with respect to the min(smp=5%) value and of the order of 1 to 2% for the sf with respect to the min(sfp=5%). calculations based on min sm for p=5% cm (kpa) (tanφ)m uc (kpa) utanφ min(smp=5%) (kpa) θcr (o) usm (kpa) smm (kpa) vsm psm<0 66.00 0.58225 15.46 0.03470 554.18 46 546.51 1453.11 2.659 0.39 64.34 0.59415 18.56 0.04526 340.75 46 654.42 1417.49 2.165 1.54 table 9.1: calculated minimum sm for p=5% and the corresponding θcr, usm and smm values. calculations based on max p for sm<0 cm (kpa) (tanφ)m uc (kpa) utanφ max(psm<0) (%) θcr (o) usm (kpa) smm (kpa) vsm smp=5% (kpa) 66.00 0.58225 15.46 0.03470 0.40 45 556.72 1475.12 2.650 559.40 64.34 0.59415 18.56 0.04526 1.54 45 667.07 1440.88 2.160 343.64 table 9.2: calculated maximum p for sm<0 and the corresponding θcr, usm and smm values. calculations based on min sf for p=5% cm (kpa) (tanφ)m uc (kpa) utanφ min(sfp=5%) (kpa) θcr (o) usf (kpa) sfm (kpa) vsf psf<0 66.00 0.58225 15.46 0.03470 1.231 42.5 0.260 1.659 6.383 0.56 64.34 0.59415 18.56 0.04526 1.141 43.5 0.317 1.662 5.243 1.83 table 10.1: calculated minimum sf for p=5% and the corresponding θcr, usf and sfm values. calculations based on max p for sf<0 cm (kpa) (tanφ)m uc (kpa) utanφ max(psf<0) (%) θcr (o) usf (kpa) sfm (kpa) vsf sfp=5% (kpa) 66.00 0.58225 15.46 0.03470 0.62 45 0.287 1.718 5.976 1.245 64.34 0.59415 18.56 0.04526 1.90 45 0.338 1.701 5.035 1.145 table 10.2: calculated maximum p for sf<0 and the corresponding θcr, usf and sfm values.. the second set of soil strength parameters lead to more conservative results. the comparison of the results of tables 9.1 and 9.2 with table 7 and of tables 10.1 and 10.2 with table 8 shows that for the probabilistic analyses it is preferable to determine the critical surface that corresponds to the minimum calculated sm or sf for a probability of exceedance 5% (or 90% confidence level, i.e. minsmp=5% or minsfp=5%), instead of calculating the critical surface of the minimum mean value smm or sfm first and then the corresponding smp=5% or sfp=5%. this happens because there is no linear relationship between smm (or sfm) and usm (or usf) for a monotonically increasing or reducing failure plane angle. concerning the influence of the individual uncertainties fig.9 shows their influence on the minimum sm and fig.10 on the probability of having an sm<0. fig.11 shows their influence on the minimum sf and fig.12 on the probability of having an sf<1. it is apparent that for this specific problem, the most influential factor on the probabilistic sm or sf is the uncertainty of cohesion. this is important because cohesion generally has a greater uncertainty from the angle of shearing resistance. the dependence sm and sf with the various uncertainties present the same trends. the above results will now be compared with the results from the deterministic analysis, for which the application of eurocode 7 has been considered and more specifically the design analysis 3 (da-3). da-3 has become the national choice g. belokas, frattura ed integrità strutturale, 50 (2019) 354-369; doi: 10.3221/igf-esis.50.30 367 of many countries for the case of overall stability of natural and cut slopes. according to this, for the drained conditions, the following components are used for deterministic analysis: a) the design strength cd=ck/(γμγm), (tanφ)d=(tanφ)k/(γμγm) with γm=1.0 (irrespectively of the type of analysis) and γμ=1.25, b) the permanent actions gd=γggk, with γg=1.0 and c) the mobile design loads are qd=γqqk, with γq=0 or 1.3 for favourable or unfavourable loads respectively. table 11 shows the results for the deterministic analyses, in which the four characteristic strength values of table 6 have been used, factored by γμ=1.25 for the design strength values. the minimum safety margin (sm) and safety factor (sf)   figure 9: influence of each uncertainty coefficient on the value of sm=smm-kusm.   figure 10: influence of each uncertainty coefficient on the probability of sm<0. figure 11: influence of each uncertainty coefficient on the value of sf=sfm-kusf. g. belokas, frattura ed integrità strutturale, 50 (2019) 354-369; doi: 10.3221/igf-esis.50.30 368 figure 12: influence of each uncertainty coefficient on the probability of sf<1. and their corresponding critical slip surface (θcr) are presented. the material unit weight has been taken γsoil,m=22kn/m3 with uncertainty uγ=2kn/m3. according to the calculations, only characteristic 2 gives acceptable safety margin (sm>0) and safety factor (sf>1.00) and. the critical failure plane determined by sm and sf do not coincide. characteristic values 1 and 4 were derived from the statistical measures used in the above analyses. it is obvious that probabilistic and deterministic analyses can give the opposite result. in our case the deterministic analysis was more conservative, which has to do with the selection of the partial safety factors. i cki (kpa) tanφki cdi (kpa) tanφdi smi θcr,sm,i (o) fsi θcr,fs,i (o) 1 39.60 0.52297 31.38 0.41837 -133.35 41 0.947 42 2 55.65 0.56288 44.52 0.45030 431.74 43 1.174 40.5 3 43.43 0.49395 34.74 0.39516 -86.60 40.5 0.967 41 4 29.82 0.50999 23.86 0.40799 -466.99 40 0.814 43.5 table 11: deterministic stability calculation with design parameters.. conclusions reliability methods can be incorporated for the determination of soil strength statistical measures and for probabilistic limit equilibrium analyses. regarding soil strength, the determination of the uncertainties of the mohr – coulomb failure criterion constants c and tanφ from results of the typical triaxial test can be calculated through an error propagation technique, such as the form, applied to an appropriate performance function. this function relates the measured (σ1) and applied (σ3) quantities to the material constants (c, φ) of the m-c failure criterion by a nonlinear relationship. the form was applied to triaxial data and the results from different approaches for calculating the best estimate of the mean, the uncertainties and the characteristic values of the m-c constants were compared. for the approaches considered, the direct application of the form gave a lower uncertainty, since the consideration of each single specimen as independent increased the sample size. the uncertainties together with the corresponding best estimates were also used to estimate the characteristic failure envelope. regarding the characteristic failure, envelope four different approaches were presented with different results. the form gave the more reliable results. in any case, engineering judgement on the results is necessary. the results were applied to a simple planar failure problem, which allows for a direct comparison of the various statistical measures of the sm and sf, since a single failure surface is considered. it was observed that the maximum probability of having a sm<0 or sf<1 does not correspond to the minimum best estimate of the sm or sf. this is influenced by the non – linear relationship of sm and usm (or sf and usf) function and needs further exploring. the sensitivity analysis showed that the only influential uncertainty was that of cohesion, which generally happens to have the greater variability with regards to other soil constants. a sensitivity analysis is recommended in probabilistic analyses in order to determine the influence of each uncertainty separately. r g. belokas, frattura ed integrità strutturale, 50 (2019) 354-369; doi: 10.3221/igf-esis.50.30 369 the deterministic analyses gave in general more conservative results and only one gave acceptable sm and sf values. these analyses greatly depend on the selection of the partial safety factor selection that determines the characteristic value. the partial factors are indirectly related to an empirical probability of exceedance and the confidence of material properties and method of analysis. on the contrary, all probabilistic analyses gave acceptable sm and sf values, which means that probabilistic analyses could be used for an appropriate selection of partial safety factors. therefore, the application of statistical methods can also set a framework for the selection of the characteristic mechanical properties, for deterministic analyses. references [1] baecher g. and christian j. (2003). reliability and statistics in geotechnical engineering, wiley, p. 618. [2] orr t. and breysse d. (2008). eurocode 7 and reliability-based design. reliability-based design in geotechnical engineering. computations and applications, kok-kwang phoon(edr), taylor & francis, pp. 298–343. [3] iso/iec guide 98-3:2008. uncertainty of measurement – part 3: guide to the expression of uncertainty in measurement (gum: 1995). [4] kulhawy h. (1992). on the evaluation of static soil properties, stability and performance of slopes and embankments – ii, proceedings of a specialty conference, seed r.b. and boulanger r.w. (eds), asce, pp. 95–115. [5] duncan j. m. (2000). factors of safety and reliability in geotechnical engineering, journal of geotechnical and geoenvironmental engineering, 126(4), pp. 307–316. [6] schneider h.r. and fitze p. (2013). characteristic shear strength values for ec7: guidelines based on a statistical framework. proc. 15th european conference on soil mechanics and geotechnical engineering, 4, pp. 318–324. [7] fellin w. (2005). assessment of characteristic shear strength parameters of soil and its implication in geotechnical design, analyzing uncertainty in civil engineering, fellin, w., lessmann, h., oberguggenberger, m., vieider, r. (eds.), springer, pp. 1–15. [8] pohl c. (2011). determination of characteristic soil values by statistical methods. isgsr 2011 vogt, schuppener, straub & bräu (eds), pp. 427–434. [9] frank r., bauduin c., driscoll r., kavvadas m., krebs ovensen n., orr t. and schuppener b. (2004). designers' guide to en 1997-1 eurocode 7: geotechnical design general rules, thomas telford, p. 216. [10] kottegoda n. t. and rosso r. (2008). applied statistics for civil and environmental engineers, 2nd edition, wileyblackwell, p. 736. [11] tsiambaos g. (1988). technicogeological features of the herakleion crete marls. phd, university of patras, p. 358 (in greek). [12] schneider h.r. (1997). definition and determination of characteristic soil properties. proc. 14th international conference on soil mechanics and foundation engineering, 4, pp. 2271–2274. [13] wu t. 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can be opened with acrobat and adobe reader 5.0 and later.) >> /namespace [ (adobe) (common) (1.0) ] /othernamespaces [ << /asreaderspreads false /cropimagestoframes true /errorcontrol /warnandcontinue /flattenerignorespreadoverrides false /includeguidesgrids false /includenonprinting false /includeslug false /namespace [ (adobe) (indesign) (4.0) ] /omitplacedbitmaps false /omitplacedeps false /omitplacedpdf false /simulateoverprint /legacy >> << /addbleedmarks false /addcolorbars false /addcropmarks false /addpageinfo false /addregmarks false /convertcolors /converttocmyk /destinationprofilename () /destinationprofileselector /documentcmyk /downsample16bitimages true /flattenerpreset << /presetselector /mediumresolution >> /formelements false /generatestructure false /includebookmarks false /includehyperlinks false /includeinteractive false /includelayers false /includeprofiles false /multimediahandling /useobjectsettings /namespace [ (adobe) (creativesuite) (2.0) ] /pdfxoutputintentprofileselector /documentcmyk /preserveediting true /untaggedcmykhandling /leaveuntagged /untaggedrgbhandling /usedocumentprofile /usedocumentbleed false >> ] >> setdistillerparams << /hwresolution [2400 2400] /pagesize [612.000 792.000] >> setpagedevice microsoft word numero_52_art_21_2729 j. akbari et alii, frattura ed integrità strutturale, 52 (2020) 269-280; doi: 10.3221/igf-esis.52.21 269 multiple crack detection using wavelet transforms and energy signal techniques jalal akbari* bu-ali sina university, department of civil engineering, hamedan, iran, j.akbari@basu.ac.ir, https://orcid.org/0000-0001-9713-8652 majid ahmadifarid laboratory of earthquake engineering and structural health monitoring of infrastructures (leeshmi), bu-ali sina university, hamedan, iran, mahmadifarid@gmail.com abbas kazemi amiri wind energy and control centre, department of electric & electronic engineering, university of strathclyde, glasgow, uk abbas.kazemi-amiri@strath.ac.uk abstract. wavelet transforms are efficient tools for structural health monitoring (shm) and damage detection. however, these methods are encountered with some limitations in practice. thus, signal energy analysis is used as an alternative technique for damage detection. in this paper, discrete wavelet transforms (dwt) and teager energy operator (teo) is applied to the curvature of the mode shapes of the beams, and the locations of the damages are identified. the results show that in comparison with the discrete wavelet transform, the signal energy operator has better performance. this superiority in detecting the damages, especially near the supports of the beam, is obvious and has enough sensitivities in low damage intensities. additionally, the damage detection in the cases that the response data are noisy is investigated. for this purpose, by adding low-intensity noises to the curvature of the mode shapes, the abilities of the mentioned methods are evaluated. the results indicate that each method is not individually efficient in the detection of damages in noisy conditions, but the combination of them under noisy conditions is more reliable. keywords. multiple crack detection, wavelet transforms, signal energy, mode shape curvature. citation: akbari, j., ahmadifarid, m., kazemi amiri, a., multiple crack detection using wavelet transforms and energy signal techniques, frattura ed integrità strutturale, 52 (2020) 269-280. received: 13.01.2020 accepted: 03.03.2020 published: 01.04.2020 copyright: © 2020 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. https://youtu.be/dfgv79dnbwk j. akbari et alii, frattura ed integrità strutturale, 52 (2020) 269-280; doi: 10.3221/igf-esis.52.21 270 introduction n recent years, structural damage detection is an interesting field for the researchers. from a practical point of view, proposing an effective non-destructive technique is a crucial task to maintain the safety and integrity of the structures. the previous studies [1] have reported that most of the non-destructive techniques could be categorized as local or global damage identification methods. furthermore, with increasing the size and dimensions of the buildings or structural elements, the capabilities of traditional damage detection methods such as ultra-sonic and x-ray tests or schmidt's hammer are not practically possible. because such methods require easy accessibility for testing and knowing the vicinity of the damage, which cannot be guaranteed in most cases in civil or mechanical engineering. as well, the health monitoring of large-scale structures is a time-consuming and costly process. the vibration-based damage identification method as a global technique is developed to overcome these difficulties. the main idea for vibration-based damage identification is that the damage-induced changes in the physical properties such as mass, damping, and stiffness will lead to detectable changes in natural frequencies, modal damping, and mode shapes. therefore, with the appearance of modern computer facilities and digital signal processing techniques, new research on shm has seriously been started. ratcliffe [2] presented a structural health monitoring method that could identify the damage without requiring the modal data of the intact structure. he utilized the curve-fitting technique of mode shape's curvature in one-dimensional beams. in this discipline, weng and deng [3] used the wavelet transforms for the detection of small transverse cracks in static and dynamic loadings for pinned-pinned and clamped-free beams. hou et. al. [4] examined wavelet capabilities for damage detection for a system with the mass and spring as a single degree of freedom model. they claimed that the wavelet has enough capability to identify the time of yielding of spring. chang and chen [5] conducted research on the timoshenko beam based on wavelet distance. the proposed wavelet successfully recognized the damage on beams using the first and second mode shapes. ovanesova and suarez [6] utilized stationary discrete wavelet for detecting damages in beam and frame type structures. loutridis et al. [7] carriedout the research for the detection of a crack in double beams using continuous wavelet transforms. chang and chen [8] studied a cantilever-type beam that the crack was an open crack that has been modeled using torsional spring. in their research, gabor wavelet has been applied to the mode shapes, in order to find the crack location. gökdağ, h., & kopmaz, o [9] conducted the research for identifying crack on beams by a combination of the continuous and discrete wavelet. in their research, the combination of the mode shapes of an intact and damaged beam has been taken into account under the errors of measurement and local damage. ruka [10] studied the effects of higher modes in system identification utilizing discrete wavelet and showed that applying higher modes will result in better performance. zhong and oyadiji [11] considered the modal responses of damaged beams using the finite-element method and experimental data. the results showed that the discrete wavelet when the sampling rate is high could not obviously detect the details of the synthesized signal. in addition, in further research, zhang and oyadji [12] considered the reconstructed mode shapes for damaged beams using a discrete wavelet method. they could identify the damage with a 4% intensity for hinged support beams. algaba et al. [13] defined a new damage index composed of natural frequency and mode shape for damage detection using continuous wavelet. the proposed method could not be able to identify low damages. therefore, solís et.al [14] developed a new damage index for low damages with 5% and 10% intensities. however, both indexes were not able to identify the damages for noisy conditions. khorram et.al [15] implemented continuous wavelet and factorial texting techniques for the detection of multiple damages on beams. cao.m, et.al [16-17] studied the damage detection for noisy data. in their research, the mode shape curvature polluted by noise with a given signal to noise ratio. when the wavelet transforms are not able to identify the damage, a combination of wavelet and teager energy of signal could identify the damages with the intensity of 5 %. akbari and ahmadifarid [18] applied the discrete wavelet transform and energy operator for damage detection of the two-dimensional frames. there are two main reasons for the study on damage detection of simple structures like beams: (1) most of the structures or their major components in civil and mechanical engineering could be simplified as a beam or plate. (2) the problem of identifying specific damage in a beam/plate provides an important benchmark for the effectiveness and accuracy of the identification techniques. therefore, in this paper, the damage identification of beam structures in different support conditions and also various damage scenarios have been carefully investigated. to the knowledge of the authors, multiple cracks usually cause damages with low intensity, which are difficult to be detected. this could be much more difficult when the damage is close to the supports. the authors believe that damage identification in such cases has not received enough attention and comprehensive studies in this regard is required. therefore, this paper focuses on the evaluation of multiple cracks detection near the supports of the beams. i j. akbari et alii, frattura ed integrità strutturale, 52 (2020) 269-280; doi: 10.3221/igf-esis.52.21 271 for this purpose, the mathematical models of two-beam structures with different boundary conditions, including pinedpined and clamped-clamped, were established in matlab [19] by the finite-element modeling, using bernoulli beam elements. two different signal-processing techniques are employed for crack location detection in different damage scenarios by application of mode shape curvature in the absence and presence of noise in the data. signal processing techniques n this paper damage detection of beams with different boundary conditions using discrete wavelet transforms (dwt), teager-energy operator (teo) and the combination of them have been explored. the reason for applying the mentioned methods is due to the capabilities of the methods for damage detection, especially in the presence of noisy conditions. discrete wavelet transforms (dwt) wavelet functions are composed of basis functions that have the capability of synthesizing the signal in time (location) and frequency (scale) domain. in wavelet analysis, the mother wavelet function is defined as eqn. (1)  a,b 1 t-b ψ t = ψ . aa       (1) mother wavelet in addition to time t, is described with a,b parameters in which they are the scaling and transformation parameters, respectively. transformation of continuous wavelet for an arbitrary function, f(t) , is written as eqn.(2)     *1 t - bcwt a,b =   f t .ψ dt  , aa       (2) where j ja=2 , b=2 k . parameters j,k are the indexes of the synthesizing level of an arbitrary signal. by substitution of these parameters in eqn.(2), eqn.(3) could be written as follows.     -j + * -j2 d .wt(j,k)=2 f t .ψ 2 t-k dt     (3) according to eqn.(3), two types of filter is imposed on the signal. the first one is lowpass filter imparted as a scaling function or father wavelet that shows the approximation of a signal, and the second one is a high-pass frequency filter that accounts for the signal components in the higher frequencies (signal details). the coefficients of approximation and details are calculated as eqn.(4)         + j + j ca k = f (t)θ x dx , cd k = f (t)ψ x dx ,       (4) where θ(x) is the scaling function or the father wavelet and ψ(x) is a mother wavelet [20]. the relation between mother and father wavelets could be written as eqn.(5)    mm m d θ x ψ x ( 1) dx   (5) in this paper, for signal processing and damage detection, the daubechies and symlet wavelets [19] with different scaling have been implemented. i j. akbari et alii, frattura ed integrità strutturale, 52 (2020) 269-280; doi: 10.3221/igf-esis.52.21 272 teager -kayser energy operator (teo) the free vibration response of the single degree of freedom (sdf) system with concentrated mass m and stiffness k is written as eqn.(6)  x t =acos(ωt+θ), (6) where, x(t) is the time variable position of the mass, a is the peak amplitude of the vibration, ω refers to the natural frequency of vibration and θ is the phase angle of the free vibration. for the mentioned sdf system, the total energy is computed as eqn.(7) 2 2 2 2 1 1 1 e (t)= kx + mv e= mω a 2 2 2 . (7) this equation indicates that the energy of a system is dependent on the frequency and amplitude of the vibration. for a discrete signal, the free-response could be written as eqn.(8)       n-1 n n+1 x =acos ω(n-1) + φ x =acos ωn+φ x =acos ω(n+1) + φ          (8) where  refers to the natural frequency of the system and  is the phase angle of the vibration. after processing and simplifying the above equation, the following equation could be obtained as eqn.(9)  2 2 2n n-1  n+1a sin ω = x  x x (9) then, teagerkayser operator for a discrete signal nx is defined using  and could be present as eqn.(10) 2 n n n-1  n+1.[x ]= x  x x  (10) problem definition n this paper, the single and multiple damage detection for the beam-type structures with pined-pined and clampedclamped boundary conditions were investigated. for the steel beams as depicted in fig. 1 the geometrical and mechanical specifications are presented at tab.1 figure 1: the schematic figure of the studied beams (a), and the schematic locations of multiple damages (b). i j. akbari et alii, frattura ed integrità strutturale, 52 (2020) 269-280; doi: 10.3221/igf-esis.52.21 273 length (m) b (mm) h(mm) 3ρ (kg/m ) e (gpa) 5.0 100 50 7850 210 table 1: mechanical and geometrical specifications of the studied beams. for finite element modeling, the beam length is evenly divided into 100 elements. thus, the length of each element is 50mm. the modal information of the beams has been extracted from a finite element modeling of each beam. in order to simulate the damaged finite element model, the height of the damaged element is reduced to 0.95h e.g. dh =0.95h for 5% damage. the modal curvature of the beam ( φ ) is calculated using the central finite difference method as eqn.(11). 2 φ(l-δl)-2φ(l)+φ(l+δl) φ = (δl)  (11) where, ,φ are the mode shapes and the curvature of mode shapes, respectively. as well, l refers to the length of the beam. here, for studying of the damage detection in the noisy conditions, the signal to noise ratio (snr) is defined. this ratio is introduced as the ratio of the power of the input signal without any pollution, to the power of the white noise signal. this ratio is a criterion for comparing the desirability of a signal to the noise and is defined as eqn.(12) signal db 10 noise p snr =10log ( ) p (12) where, signal noisep , p are the power of the signal and the power of noise, respectively. the higher values of snr for a signal indicates the lower contamination of the signal. in this paper, snr is set to 75, 65 and 55 db for providing the noisy data. scenario no. support condition no. of damaged elements damage intensity (%) order of mode shape in signal energy order of mode shape in wavelet 1 pined-pined 20,30,80 5,5,5 1 4 2 pined-pined 48,51,54 5,5,5 1 3 3 pined-pined 5,95 5,5 3 1 4 pined-pined 1,99 5,5 6 1 5 pined-pined 20,50,80 10,10,10 1 3 6 pined-pined 20,50,80 5,10,15 1 3 7 clamped-clamped 10,20,90 5,5,5 5 3 8 clamped-clamped 20,23,26 5,5,5 3 3 9 clamped-clamped 30,45,80 5,10,15 3 3 table 2: the proposed scenarios of damage detection on beams without noisy conditions. results without noisy data in this section, damage detection for multipledamage detection for pined-pined and clamped-clamped boundary conditions has been presented. for this purpose, several scenarios with and without noisy conditions have been designated. firstly, the modal data for intact and damaged beams are extracted, and then the discrete wavelet is imposed on the mode shapes using matlab functions [18]. secondly, using eqn.(4) the coefficients of discrete wavelets are obtained, and employing eqn.(10), the energy of the signal is obtained. in tab. 2, the designed scenarios for damage detection without noise on the beams have been presented. j. akbari et alii, frattura ed integrità strutturale, 52 (2020) 269-280; doi: 10.3221/igf-esis.52.21 274 fig. 2 illustrates the damage detection results corresponding to the scenarios no. 1. in figs. a and c the signal energy method has been successfully identified with the damaged elements with clear knobs. this method can identify the multiple damaged elements with a distance of the elements equal to 15cm. however, as can be seen from graphs b and d, the wavelet transform did not succeed in the detection of the damages with a low intensity equal to 5%. figure 2: damage detection using signal energy (a,c) and wavelet (b,d) for scenarios 1,2. according to graphs b,d in fig. 2, in the wavelet method, the disorders (irregularities) in two ends of the support of the beams are observed. therefore this dilemma makes damage detection a difficult task. in order to overcome this problem, the mode shape has been extended from both ends of the beams. for this purpose, from each side of the supports, 50 elements have been artificially added to the finite element model, and the results are depicted in fig. 3. figure 3: damage detection using wavelet for scenario no.3. damages in elements 1 and 100 (a), and damages in elements 5 and 95 (b). j. akbari et alii, frattura ed integrità strutturale, 52 (2020) 269-280; doi: 10.3221/igf-esis.52.21 275 as illustrated in fig. 3, compared to the energy method, wavelet transforms are very sensitive with respect to the starting position of extension and disorders have been appeared in these positions, and this drawback made the damage detection impossible. additionally, the performance of the first mode shape was better in comparison with the use of higher mode shapes. in other words, when the higher mode shapes have been used for finding the locations of damaged elements, negligible knobs or disorders have been seen. therefore, by these small disorders, detections were not possible. as depicted in fig. 4, signal energy could successfully detect the damages near the supports of the pined-pined beams, while the fictitious mode shape extension from the end of the beams is unnecessary. figure 4: damage detection using signal energy for scenario no.3 and no.4. damages in elements 5 and 95 (a), and damages in elements 1 and 99 (b). fig. 5 presents the abilities and sensitivities of the defined methods for different values of the damage intensities. signal energy could detect damage for various intensities of damaged elements with specified knobs in the graph (a). however, in the wavelet method, all of the intensities are the same which is not a good sign for this method. figure 5: damage detection using signal energy for scenario no.5 (a) and scenario no.6. (b). fig. 6 (graphs a,c) shows that the wavelet transforms for clamped-clamped boundary conditions in contrast with pinedpined supports, have better performance even for damaged elements with 5% intensity deficiency. therefore, for such boundary conditions of the beams, the wavelet coefficients are relatively able to detect the local damages. as can be seen from fig. 6-c, when the damaged elements are close to each other, a significant disturbance appears in the vicinity of the damaged elements. in the clamped-clamped beams, when the damages are near the supports, because of the existence of disorders due to the supports, the wavelet coefficients are not able to detect the damages and extension of the mode shapes could not resolve this deficiency (graph a). graphs b, d in fig. 6 reveal that signal energy is successful in detecting damages in clamped-clamped beams. however, it should be noted that mode shapes in this type of beams are not a sinusoidal form, and the energy of mode shapes is not constant but had a curved form. in such a situation, if the damaged j. akbari et alii, frattura ed integrità strutturale, 52 (2020) 269-280; doi: 10.3221/igf-esis.52.21 276 elements are near the supports, the curvature and the value of energy are negligible, and as a result, the detection process is not easy. fig. 7 displays damage identification for a beam with a spread-configuration of damage using the prescribed methods. as can be seen from this figure, the wavelet doesn't show acceptable performance even for this damage configuration. oppositely, signal energy is able to detect the spread of damages very well. figure 6: damage detection: wavelet transform for scenario no. 7 (a), signal energy for scenario no.7 (b), wavelet transform for scenario no. 8 (c) and signal energy for scenario no.8 (d) figure 7: damage detection using wavelet transform for scenario 9 (a), and signal energy for scenario 9 (b) results in noisy conditions when the noise is added to the mode shapes, the damage detection procedure will be influenced by the added noise. for this purpose, using the following function in matlab, the noisy data are produced. j. akbari et alii, frattura ed integrità strutturale, 52 (2020) 269-280; doi: 10.3221/igf-esis.52.21 277 n 0y =awgn(y ,snr ) (13) where 0ny , y are the output signal as a contaminated mode shape and the input signal as a clean mode shape, respectively. in order to simulate the noisy conditions for mode shapes, the scenarios listed in tab. 3 have been taken into account. in all scenarios, the damage intensities are 5%. scenario no. support condition no. of damaged elements snr (%) order of mode shape in wavelet and signal energy 10 pined-pined 10,50 75 1 11 pined-pined 10,50 75 5 12 clamped-clamped 28,72 75 2 13 clamped-clamped 28,72 75 5 14 pined-pined 20,80 65 3 15 clamped-clamped 28,72 65 5 16 clamped-clamped 28,72 55 6 table 3: the scenarios for damage detection in noisy conditions. figure 8: damage detection using signal energy and wavelet transform in scenarios 10 (a) to 13 (d). when the snr=75% is added to the responses, modal curvatures from lower mode shapes are distorted, and both wavelet coefficients and energy signal methods required employing the higher mode shapes, namely higher than the 5th mode. as noted before, the applied wavelet transform does not represent an appropriate performance in the detection of low j. akbari et alii, frattura ed integrità strutturale, 52 (2020) 269-280; doi: 10.3221/igf-esis.52.21 278 intensities in pined-pined beams. it turns out that in the noisy condition ( snr=75%) wavelet transform could not detect damages even using higher modes. however, in clamped-clamped beams, the wavelet transform can detect the damages using 5th mode shape data. fig. 8 presents the damage detection for scenarios 10 to 13 in noisy conditions. in scenario no.10, when the lower mode shape data is used, the detection is impossible, and employing the higher modes is needed. in scenario 11, the 5th mode shape information for damage detection is employed, and detection is clear. in opposite to the signal energy technique, the use of high and low mode shapes in the wavelet transform method doesn’t lead to significant improvement (graphs c, d). when the values of snr are reduced, both wavelet transform and energy signal methods could not detect the damages even after applying of the 5th and 6th order of the mode shapes. in this paper, to solve this problem, a combination of discrete wavelet and signal energy methods has been employed. for detection of damages, firstly, a discrete wavelet is applied on the curvature of the mode shape as a noisy response and then approximate and detail wavelet coefficients have been extracted using eqn.(4). because the signal is noisy, the coefficients are not able to detect the locations of the damaged elements, and the appeared disorders in the damaged elements have been affected by the noise. nevertheless, by applying the signal energy operator in approximate wavelet, damage detection successfully has been obtained. fig. 9, displays the locations of damaged elements in snr=65%. as can be seen from this figure, signal energy and wavelet transform individually are not able to detect the damaged elements. as can be seen from graph d, the combination of the proposed method has enough capability to identify the damages. however, near the supports, undesirable irregularities are clearly observed. figure 9: damage detection for scenario no.14 using: only signal energy operator (a), wavelet coefficient detail (b), wavelet coefficient approximate (c) combination of wavelet and signal energy (d). fig. 10, illustrates the identification of damaged elements for snr=65% and 55%. as seen from this figure, the combination of signal energy and wavelet transforms methods could successfully detect the damaged elements. j. akbari et alii, frattura ed integrità strutturale, 52 (2020) 269-280; doi: 10.3221/igf-esis.52.21 279 figure 10: damage detection using signal energy for scenarios 15 or snr= 65% (a), and for scenario no.16 or snr=55% (b). conclusions his paper utilizes the discrete wavelet transforms and teager energy operator methods for damage detection for noisy and clean data. the results show the superiority of the signal energy in comparison with wavelet coefficients. moreover, the results confirm that each individual method in noisy conditions is not suitable for the detection of damages, but the combination of them has a great performance. based on this investigation for the mentioned wavelet transforms and scenarios, the following conclusions could be drawn. 1the signal energy method is able to detect damage using the 1st and the 2nd mode shapes with a 5% intensity in clampedclamped beams. however, when the cracks are in the vicinity of the supports, the higher mode shape, e.g. the 6th mode shape or higher than it is needed. wavelet transforms in the detection of damages with low intensities have poor performance in pined-pined beams. moreover, for the detection of crack close to the support by means of wavelet transforms, the extension of the mode shape from both sides is required. therefore, this problem makes detection difficult. 2for clamped-clamped beams, signal energy has enough capabilities to detect damage using the first mode shape for low intensities. however, when the detection of damage is required near the supports, the higher mode shape data should be taken into account. wavelet transforms have better performance for clamped-clamped beams, compared to the pined-pined ones. however, when the cracks are near the supports, this method is inefficient. 3the sensitivity of signal energy is higher for all intensities of damages while wavelet transforms are insufficiently sensitive to various intensities. therefore, in practice applying the energy method is recommended. when the value of snr is equal to 75%, the signal energy method with higher mode shapes data can detect even low damages, while lower mode shapes are affected with noise, and detection is impossible. wavelet transforms at noisy conditions could not detect the damages at pined-pined beams. when the values of snr are reduced to 65% or 55%, even the signal energy method could not detect the damaged elements. in these cases, the combination of energy and wavelet is required for proper flaw detection. nonetheless, using the higher mode shapes is strongly recommended. acknowledgment he first author acknowledges the support of malayer university when he was an assistant professor of civil engineering from september 2008 to june 2019. disclosure he authors have no conflict of interest to declare. t t t j. akbari et alii, frattura ed integrità strutturale, 52 (2020) 269-280; doi: 10.3221/igf-esis.52.21 280 references [1] doebling, s. w., farrar, c. r., prime, m. b., and shevitz, d. w. (1996). damage identification and health monitoring of structural and mechanical systems from changes in their vibration characteristics: a literature review (no. la-13070-ms). los alamos national lab., nm (united states). [2] ratcliffe, c. p. (1997). damage detection using a modified laplacian operator on mode shape data. journal of sound and vibration, 204(3), pp. 505-517. [3] wang, q., and deng, x. (1999). damage detection with spatial wavelets. international journal of solids and structures, 36(23), pp. 3443-3468. [4] hou, z., noori, m., and amand, r. s. (2000). wavelet-based approach for structural damage detection. journal of engineering mechanics, 126(7), pp. 677-683. [5] chang, c. c., and chen, l. w. (2003). vibration damage detection of a timoshenko beam by spatial wavelet based approach. applied acoustics, 64(12), pp. 1217-1240. [6] ovanesova, a. v., and suarez, l. e. (2004). applications of wavelet transforms to damage detection in frame structures. engineering structures, 26(1), pp. 39-49. [7] loutridis, s., douka, e., and trochidis, a. (2004). crack identification in double-cracked beams using wavelet analysis. journal of sound and vibration, 277(4-5), pp. 1025-1039. [8] chang, c. c., and chen, l. w. (2005). detection of the location and size of cracks in the multiple cracked beam by spatial wavelet based approach. mechanical systems and signal processing, 19(1), pp. 139-155. [9] gökdağ, h., and kopmaz, o. (2009). a new damage detection approach for beam-type structures based on the combination of continuous and discrete wavelet transforms. journal of sound and vibration, 324(3-5), pp. 1158-1180. [10] rucka, m. (2011). damage detection in beams using wavelet transform on higher vibration modes. journal of theoretical and applied mechanics, 49(2), pp. 399-417. [11] zhong, s., and oyadiji, s. o. (2011). detection of cracks in simply-supported beams by continuous wavelet transform of reconstructed modal data. computers and structures, 89(1-2), pp. 127-148. [12] zhong, s., and oyadiji, s. o. (2011). crack detection in simply supported beams using stationary wavelet transform of modal data. structural control and health monitoring, 18(2), pp. 169-190. [13] algaba, m., solís, m., and galvín, p. (2012). wavelet based mode shape analysis for damage detection. in topics in modal analysis ii, springer, new york, ny., 6, pp. 377-384. [14] solís, m., algaba, m., and galvín, p. (2013). continuous wavelet analysis of mode shapes differences for damage detection. mechanical systems and signal processing, 40(2), pp. 645-666. [15] khorram, a., rezaeian, m., and bakhtiari-nejad, f. (2013). multiple cracks detection in a beam subjected to a moving load using wavelet analysis combined with factorial design. european journal of mechanicsa/solids, 40, pp. 97-113. [16] cao, m., radzieński, m., xu, w., and ostachowicz, w. (2014). identification of multiple damage in beams based on robust curvature mode shapes. mechanical systems and signal processing, 46(2), pp. 468-480. [17] cao, m., xu, w., ostachowicz, w., and su, z. (2014). damage identification for beams in noisy conditions based on teager energy operator-wavelet transform modal curvature. journal of sound and vibration, 333(6), pp. 1543-1553. [18] akbari.j, ahmadifarid.m (2018), damage detection of frames using wavelet transforms and signal energy, 7th national and 3rd international conference on modern materials and structures in civil engineering, buali sina university, hamedan, iran, september 8-9. [19] matlab (2018), the mathworks, inc., natick, release 2018a [20] blatter, c. 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/hrv (za stvaranje adobe pdf dokumenata najpogodnijih za visokokvalitetni ispis prije tiskanja koristite ove postavke. stvoreni pdf dokumenti mogu se otvoriti acrobat i adobe reader 5.0 i kasnijim verzijama.) /hun 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can be opened with acrobat and adobe reader 5.0 and later.) >> /namespace [ (adobe) (common) (1.0) ] /othernamespaces [ << /asreaderspreads false /cropimagestoframes true /errorcontrol /warnandcontinue /flattenerignorespreadoverrides false /includeguidesgrids false /includenonprinting false /includeslug false /namespace [ (adobe) (indesign) (4.0) ] /omitplacedbitmaps false /omitplacedeps false /omitplacedpdf false /simulateoverprint /legacy >> << /addbleedmarks false /addcolorbars false /addcropmarks false /addpageinfo false /addregmarks false /convertcolors /converttocmyk /destinationprofilename () /destinationprofileselector /documentcmyk /downsample16bitimages true /flattenerpreset << /presetselector /mediumresolution >> /formelements false /generatestructure false /includebookmarks false /includehyperlinks false /includeinteractive false /includelayers false /includeprofiles false /multimediahandling /useobjectsettings /namespace [ (adobe) (creativesuite) (2.0) ] /pdfxoutputintentprofileselector /documentcmyk /preserveediting true /untaggedcmykhandling /leaveuntagged /untaggedrgbhandling /usedocumentprofile /usedocumentbleed false >> ] >> setdistillerparams << /hwresolution [2400 2400] /pagesize [612.000 792.000] >> setpagedevice microsoft word numero_35_art_15 a. mehmanparast et alii, frattura ed integrità strutturale, 35 (2016) 125-131; doi: 10.3221/igf-esis.35.15 125 focussed on crack paths welding sequence effects on residual stress distribution in offshore wind monopile structures ali mehmanparast, oyewole adedipe, feargal brennan offshore renewable energy centre, cranfield university a.mehmanparast@cranfield.ac.uk, o.adedipe@cranfield.ac.uk, f.brennan@cranfield.ac.uk amir chahardehi atkins energy amir.chahardehi@atkinsglobal.com abstract. residual stresses are often inevitably introduced into the material during the fabrication processes, such as welding, and are known to have significant effects on the subsequent fatigue crack growth behavior of welded structures. in this paper, the importance of welding sequence on residual stress distribution in engineering components has been reviewed. in addition, the findings available in the literature have been used to provide an accurate interpretation of the fatigue crack growth data on specimens extracted from the welded plates employed in offshore wind monopile structures. the results have been discussed in terms of the role of welding sequence in damage inspection and structural integrity assessment of offshore renewable energy structures. keywords. welding sequence; offshore wind monopole; residual stress; fatigue crack growth. introduction elding is a metal joining process which is widely used in manufacturing of full scale components used in industrial applications. during the welding process inhomogeneous plastic strains, caused by thermal cycles (i.e. localised heating and cooling), are introduced into the material which subsequently lead to formation of residual (locked-in) stresses in the welded components. the extent of residual stresses in weldments can be quantified using different techniques. the non-destructive methods which are commonly employed to measure residual stresses are x-ray diffraction, for thin plates, and neutron diffraction, for relatively thick geometries. it has been shown and discussed in previous studies by other researchers that compressive and tensile residual stresses play an important role in the fatigue crack growth behavior of cracked geometries (e.g. [1, 2]). therefore, an important issue to be investigated and accounted for in the remaining life assessment of engineering components subjected to cyclic loading conditions is the influence of residual stresses on the fatigue crack growth behavior of welded components. in order to assess the structural integrity of offshore renewable energy wind turbine structures, which are subjected to fatigue and corrosion damage during operation, fatigue crack growth (fcg) tests have been recently performed on fracture mechanics compact tension, c(t), specimens made of 355d steel which is the material commonly used in fabrication of offshore wind monopiles. c(t) specimens were extracted from typical monopile weldment sections, example of which is given in fig. 1, with the notch tip located in the middle of the heat affected zone (haz) and tested w a. mehmanparast et alii, frattura ed integrità strutturale, 35 (2016) 125-131; doi: 10.3221/igf-esis.35.15 126 both in air and seawater. the specimen orientation for these tests was chosen in such a way to allow crack growth occurring in through-thickness (i.e. y axis in fig. 1) direction with the load applied along transverse (i.e. x axis in fig. 1) direction. the preliminary results from these tests have shown “bi-linear” da/dn vs. δk fatigue crack growth behavior [3] which is thought to be due to the tensile-compressive residual stress profiles introduced into the material during the welding process [4]. neutron diffraction (nd) measurements are therefore needed to be performed on weldments to provide accurate interpretation of the fatigue crack growth results. large 355d plates with 90 mm thickness, from which c(t) specimens have been extracted, were welded using multi-pass double v-groove butt welding. the plates were preheated at 50-225°c and no post weld heat treatment was conducted. the parent plates were pre-strained through rolling and then welded, with the weld beads parallel to the rolling direction (i.e. along z axis in fig. 1). in this paper the experimental and numerical results available in the open literature have been reviewed to investigate the influence of welding sequence on residual stress fields for different engineering materials. the findings have been discussed in terms of the influence of multi-pass welding sequence on tensile-compressive residual stress fields and considered to investigate the preferred welding sequences for offshore wind turbine monopile structures. x y z figure 1: 90mm 355d steel weldment typical of an offshore wind monopile structure multi-pass welding effects on residual stress fields single v-groove welded plates he experimental and numerical residual stress data available from studies carried out on single v-groove welded plates have been reviewed in this section. experimental neutron strain scanning measurements were performed by james mn et al [5] on rqt701 high strength steel welded plates manufactured using three different types of filler metals; under-matched, matched and over-matched. two heat input values and plate thicknesses were used in multipass weld runs examined in this work (see fig. 2). it has been shown in [5] that the heat input, filler metal yield strength, plate thickness and fusion zone shape influence the position and magnitude of the tensile and compressive residual stress peaks. an example of a welded plate examined in this work is shown fig. 3. also included in this figure are the indicative directions of residual stress components. the neutron diffraction results plotted against “distance from centre of the weld” in [5] have shown that the z-component (i.e. parallel to weld beads) of stress profile is tensile in the weld metal and haz material whereas the x-component (i.e. transverse) and y-component (i.e. through-thickness) of stress profiles have been found to change from tensile to compressive and the measured values to vary as a function of the depth into the plate thickness (a function of y coordinate). the residual strain measurement results plotted against “distance from center of the weld” in [5] show that the x-component (i.e. transverse) of micro-strain profile is strongly tensile in over-matched welded plates, however in those plates welded with under-matched filler metal both tensile and compressive transverse micro-strains have been found to have magnitudes of much lower than the tensile peaks observed in over-matched welded plates. further shown in [5] is that the position of the tensile peak falls upon the region where the maximum weld t a. mehmanparast et alii, frattura ed integrità strutturale, 35 (2016) 125-131; doi: 10.3221/igf-esis.35.15 127 metal volume exists. independent studies on welding residual stress measurements in multi-pass butt-welded austenitic stainless steel thick walled pipes presented in [6] and a36 structural steel thick plates shown in [7] confirm that the welding residual stress is severely sensitive to the yield strength of the weld metal. figure 2: different scenarios of multi-pass weld runs examined in [5]. x y figure 3: an example of a multi-pass welded plate. figure 4: illustration of the plate thickness effects on post-welding residual stress distribution in type 304 stainless steel [8]. a similar study was carried out on aisi type 304 stainless steel in [8] where thin plates during multi-pass manual metal arc welding (mmaw) process were measured using x-ray diffraction. it has been shown in [8] that by increasing the number of passes in single v-groove welded plates, the magnitude of peak tensile stress (at the centre of the weld) gradually reduces and increases on the root side and the top side of the weld pads, respectively. also shown in [8] is that increasing the thickness of the weld pads leads to an increase in the extent of the residual stress distribution region and a reduction in the peak tensile residual stress values (see fig. 4). numerical studies of pass-by-pass residual stress predictions in thick walled plates and thick walled stainless steel pipes can be found in the published literature (e.g. [9, 10]). for instance a finite element study to predict maximum residual stresses in k and v type multi-pass weld joints before and after post weld heat treatment was carried out by cho jr et al [10] in which the predicted results were validated through comparison with hole drilling measurements. it has been shown in [10] that the post weld heat treatment can reduce the maximum residual stress values by around 15%. a. mehmanparast et alii, frattura ed integrità strutturale, 35 (2016) 125-131; doi: 10.3221/igf-esis.35.15 128 double v-groove welded plates a numerical sensitivity analysis was carried out by teng t-l [11] to investigate the influence of welding sequence on residual stress distribution in sae 1020 thick plates. two-dimensional finite element analyses were performed in this work to simulate various combinations of multi-pass butt welding sequence. as seen in fig. 5, simulations were conducted to predict residual stresses induced in double v-groove welded plates for three different cases of welding sequences. in this study the v-grooves at both sides of the welded plates were assumed to be the same size. the predicted residual stresses from this study were plotted against “distance from the weld center” and the results are presented in fig. 6. it can be observed in fig. 6 that the stress trends and peak values are relatively sensitive to the welding sequence and the changes in residual stresses are more pronounced in transverse (along x axis) direction compared to the through thickness (along y axis) direction. the predicted results in this figure show that the highest and the lowest peak tensile residual stresses were found in case (c) and case (a) of welding sequences, respectively. comparing the transverse residual stress trends at the center of the weld region in fig. 6(b) it can be seen that the residual stress value predicted for case (c) is almost double of that of predicted for case (a). comparison of the residual stresses predicted in fig. 6(a) and (b) shows that the through thickness (along y axis) peak tensile residual stresses for all three cases of welding sequences have been found much larger than those of predicted along x direction. finally seen in fig. 6 is that the through thickness (along y axis) residual stress trend shows tensile stresses near the weld bead and compressive stresses away from the weld bead, whereas no compressive residual stress field can be observed in transverse (along x axis) residual stresses. x y z figure 5: different cases of multi-pass butt welding sequence [11]. y t h ro u g h t h ic k n e s s r e s id u a l s tr e s s σ y (p a ) (a) (b) figure 6: predicted residual stress components along (a) y direction (b) x direction , for three cases of welding sequences [11]. a. mehmanparast et alii, frattura ed integrità strutturale, 35 (2016) 125-131; doi: 10.3221/igf-esis.35.15 129 a similar numerical study on the welding sequence effects in multi-pass butt welding of double v-groove stainless steel thick plates has been conducted by ji sd et al [12] in which finite element predications were validated through comparison with experimental data. a schematic illustration of the welding bead numbers and different cases of welding sequences considered by ji sd et al [12] are shown in fig. 7. as seen in fig. 7 the bottom v-groove in this study was considered smaller than the top groove. it has been shown in [12] that the residual stress fields in the weld region are tensile for both through thickness (along y axis) and transverse (along x axis) directions and the peak values were found near the center of the weld region. finite elements simulations were conducted for different cases of the welding sequences shown in fig. 7 and the peak residual stress results are summarized in tab. 1. as seen in tab. 1 the residual stress profiles and peak values were found sensitive to the welding sequence. moreover, the numerical prediction results presented in [12] suggest that lower magnitude of residual stress profiles and peak values may be obtained when two vgrooves are evenly welded with filler metal (see case(e) and case (c) in fig. 7). x y z figure 7: illustration of welding bead numbers and sequences [12]. welding sequence (a) (b) (c) (d) (e) (f) (g) (h) transverse stress σx (mpa) 623 544 405 718 505 511 829 857 through thickness stress σy (mpa) 634 636 507 823 592 607 879 865 table 1: predicted residual stress peak values for different cases of welding sequences [12]. discussion he residual stress measurements and finite element prediction results available in the literature have shown that the welding sequence has significant influence on the residual stress profiles and peak values in multi-pass butt welded plates. the numerical studies performed to predict residual stress profiles in double v-groove butt welded plates suggest that although transverse stresses may be more sensitive to the welding sequence, the through thickness component of residual stresses generally exhibit higher values compared to transverse stresses. this means that if the welded plate is subjected to a loading condition parallel to the through thickness direction, a relatively small percentage increase or decrease in the peak values of through thickness residual stresses, as a result of the change in the welding sequence, may lead to significant changes in crack growth behavior of the material. it has been also noted that the transverse peak stress values shown in fig. 6(b) are much smaller than those of predicted in tab. 1. the lower σx peak t a. mehmanparast et alii, frattura ed integrità strutturale, 35 (2016) 125-131; doi: 10.3221/igf-esis.35.15 130 values in fig. 6(b) compared to tab. 1 might be associated with uneven v-grooves in ref [12], different filler metal properties (e.g. over-matched, under-matched) employed in reference [11] and [12], etc. the peak transverse stresses in thick welded plates used in offshore monopiles (see fig. 1) are expected to be closer to the values predicted in [12] and summarized in tab. 1, though more finite element simulations need to be performed to investigate this further. the residual stress measurement and prediction results for multi-pass welded plates available in the literature suggest that to improve the structural integrity of the offshore wind turbine monopile structures, suitable welding sequences which lead to lower values of damaging (i.e. tensile) residual stresses need to be employed in the fabrication processes. this will provide more robust and cost efficient offshore wind turbine structures. moreover, by measuring the residual stress profiles in welded plates, the time required to inspect damage/cracks initiated in operating structures can be significantly optimized by prioritizing the inspection to be carried out on parts of the structure (e.g. inner surface or outer surface of an offshore monopile) containing tensile residual stresses as opposed to compressive stresses. in other words, in the parts of the offshore monopile welded structures that a tensile residual stress profile exists in a direction parallel to that of the dominant environmental loading axis, frequent inspection will be required since the chance of damage/crack initiation in this region is higher than anywhere else. the fatigue crack growth results from the tests performed on haz c(t) specimens in [3] suggest that the initial part of the fcg behavior with a smaller slope, which can be observed in the bi-linear trend, may be associated with the compressive residual stress effects whereas the latter part of the bi-linear trend, which shows a higher slope, may be related to tensile residual stress profiles remained in the c(t) weld specimens. in order to interpret the fatigue crack growth results performed on specimens extracted from the welded plates employed in offshore monopiles, and also to provide reliable remaining lifetime estimates of the welded structures operating in offshore environments, neutron diffraction residual stress measurements need to be performed on thick welded plates employed in fabrication of offshore monopiles (e.g. fig. 1). these measurements need to be performed along the haz path (through thickness direction) to examine the significance of residual stress effects in the bi-linear fatigue crack growth behavior of c(t) specimens with the crack path located in the haz region. conclusions elding residual stress profiles have been found severely sensitive to the yield strength of the filler metal, heat input, plate thickness, fusion zone shape and welding sequence. numerical studies of multi-pass butt welding in double v-groove thick plates have shown that the highest and the lowest tensile peak stresses are expected to appear when multi-pass welding is performed unevenly and evenly, respectively. the finite element prediction results have shown that the welding sequence influences the residual stress trends and peak values and the changes in residual stresses may be more pronounced in transverse (along x axis) direction compared to the through thickness (along y axis) direction. however, higher values of damaging residual stresses are generally observed in the through thickness residual stress direction. suitable welding sequences which result in lower peak values of tensile residual stresses in thick welded plates need to be employed in manufacturing of offshore wind monopiles. residual stress profiles in offshore structures need to be measured to provide accurate interpretation of the crack growth behavior in offshore welded components. this information also helps to optimize the inspection time required to investigate damage/crack initiation and propagation in offshore wind turbine structures. references [1] jata, k. v., sankaran, k. k., and ruschau, j. j., friction-stir welding effects on microstructure and fatigue of aluminum alloy 7050-t7451, metallurgical and materials transactions a., 31 (2000) 2181-2192. [2] akita, m., nakajima, m., tokaji, k., and shimizu, t., fatigue crack propagation of 444 stainless steel welded joints in air and in 3%nacl aqueous solution, materials & design., 27 (2006) 92-99. [3] adedipe, o., brennan, f., and kolios, a., corrosion fatigue crack growth in offshore wind monopile steel haz material, in: c.g. soares, r.a. shenoi (eds), analysis and design of marine structures v, crc press., (2015) 207-212. [4] jang, c., cho, p.-y., kim, m., oh, s.-j., and yang, j.-s., effects of microstructure and residual stress on fatigue crack growth of stainless steel narrow gap welds, materials & design., 31 (2010) 1862-1870. w a. mehmanparast et alii, frattura ed integrità strutturale, 35 (2016) 125-131; doi: 10.3221/igf-esis.35.15 131 [5] james, m. n., webster, p. j., hughes, d. j., chen, z., ratel, n., ting, s. p., bruno, g., and steuwer, a., correlating weld process conditions, residual strain and stress, microstructure and mechanical properties for high strength steelthe role of neutron diffraction strain scanning, materials science and engineering: a., 427 (2006) 16-26. [6] deng, d., murakawa, h., liang, w., numerical and experimental investigations on welding residual stress in multipass butt-welded austenitic stainless steel pipe, computational materials science., 42 (2008) 234-244. [7] chang, p.-h., and teng, t.-l., numerical and experimental investigations on the residual stresses of the butt-welded joints, computational materials science., 29 (2004) 511-522. [8] murugan, s., rai, s. k., kumar, p. v., jayakumar, t., raj, b., and bose, m. s. c., temperature distribution and residual stresses due to multipass welding in type 304 stainless steel and low carbon steel weld pads, international journal of pressure vessels and piping., 78 (2001) 307-317. [9] liu, c., zhang, j. x., and xue, c. b., numerical investigation on residual stress distribution and evolution during multipass narrow gap welding of thick-walled stainless steel pipes, fusion engineering and design., 86 (2011) 288295. [10] cho, j. r., lee, b. y., moon, y. h., and van tyne, c. j., investigation of residual stress and post weld heat treatment of multi-pass welds by finite element method and experiments, journal of materials processing technology., 155–156 (2004) 1690-1695. [11] teng, t.-l., chang, p.-h., and tseng, w.-c., effect of welding sequences on residual stresses, computers & structures., 81(2003) 273-286. [12] ji, s. d., fang, h. y., liu, x. s., and meng, q. g., influence of a welding sequence on the welding residual stress of a thick plate, modelling and simulation in materials science and engineering., 13 (2005) 553-565. << /ascii85encodepages false /allowtransparency false /autopositionepsfiles true /autorotatepages /none /binding /left /calgrayprofile (dot gain 20%) /calrgbprofile (srgb iec61966-2.1) /calcmykprofile (u.s. web coated \050swop\051 v2) /srgbprofile (srgb iec61966-2.1) /cannotembedfontpolicy /error /compatibilitylevel 1.4 /compressobjects /tags /compresspages true /convertimagestoindexed true /passthroughjpegimages true /createjobticket false /defaultrenderingintent /default /detectblends true /detectcurves 0.0000 /colorconversionstrategy /cmyk /dothumbnails false /embedallfonts true /embedopentype false /parseiccprofilesincomments true /embedjoboptions true /dscreportinglevel 0 /emitdscwarnings false /endpage -1 /imagememory 1048576 /lockdistillerparams false 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/hrv (za stvaranje adobe pdf dokumenata najpogodnijih za visokokvalitetni ispis prije tiskanja koristite ove postavke. stvoreni pdf dokumenti mogu se otvoriti acrobat i adobe reader 5.0 i kasnijim verzijama.) /hun 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can be opened with acrobat and adobe reader 5.0 and later.) >> /namespace [ (adobe) (common) (1.0) ] /othernamespaces [ << /asreaderspreads false /cropimagestoframes true /errorcontrol /warnandcontinue /flattenerignorespreadoverrides false /includeguidesgrids false /includenonprinting false /includeslug false /namespace [ (adobe) (indesign) (4.0) ] /omitplacedbitmaps false /omitplacedeps false /omitplacedpdf false /simulateoverprint /legacy >> << /addbleedmarks false /addcolorbars false /addcropmarks false /addpageinfo false /addregmarks false /convertcolors /converttocmyk /destinationprofilename () /destinationprofileselector /documentcmyk /downsample16bitimages true /flattenerpreset << /presetselector /mediumresolution >> /formelements false /generatestructure false /includebookmarks false /includehyperlinks false /includeinteractive false /includelayers false /includeprofiles false /multimediahandling /useobjectsettings /namespace [ (adobe) (creativesuite) (2.0) ] /pdfxoutputintentprofileselector /documentcmyk /preserveediting true /untaggedcmykhandling /leaveuntagged /untaggedrgbhandling /usedocumentprofile /usedocumentbleed false >> ] >> setdistillerparams << /hwresolution [2400 2400] /pagesize [612.000 792.000] >> setpagedevice microsoft word numero_50_art_23_2552 k. meftah et alii, frattura ed integrità strutturale, 50 (2019) 276-285; doi: 10.3221/igf-esis.50.23 276 a nonlinear elasto-plastic analysis of reissner-mindlin plates by finite element method meftah kamel university of biskra, laboratoire de génie energétique et matériaux, lgem, faculty of sciences and technology, biskra, 07000, algeria k.meftah@univ-biskra.dz, http://orcid.org/0000-0002-5671-602x sedira lakhdar university of biskra, laboratoire de génie mécanique, lgm, faculty of sciences and technology, biskra, 07000, algeria l.sedira@univ-biskra.dz, http://orcid.org/0000-0003-1735-2195 abstract. in this paper, a finite element simulation of nonlinear elastoplastic deformations of reissner-mindlin bending plates is described. the previously proposed four-node q4 element with transverse energy of shearing for thick bending plates is extended to account for isotropic material nonlinearities. an incremental finite element procedure has been used for the elasto-plastic analysis of the thick bending plate. modified newton-raphson method has been used to solve the nonlinear equations. von-mises yield criteria have been applied for yielding of the materials along with the associated flow rule. to verify the present element, simple tests are demonstrated and various elasto-plastic problems in which the development of the plastic zone are solved. keywords. plate element; reissner-mindlin plates; elasto-plasticity; nonlinear analysis. citation: meftah, k., sedira, l., a nonlinear elasto-plastic analysis of reissner-mindlin plates by finite element method, frattura ed integrità strutturale, 50 (2019) 276-285. received: 26.06.2019 accepted: 16.08.2019 published: 01.10.2019 copyright: © 2019 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. introduction n recent years, considerable work has been devoted to the study of nonlinear elasto-plastic responses of reissnermindlin bending plates, since plates are very important parts of engineering structures. the nonlinear elasto-plastic bending plates are analyzed by the finite element methods, the finite difference methods, the discrete element methods and the direct numerical methods. however, the finite element method is a suitable approach and has been successfully used in nonlinear elasto-plastic analysis of plates. for example, a finite element analysis of reissner-mindlin bending plates has been investigated by owen and hinton [1], meftah [2], rezaiee-pajand and sadeghi [3] and kanber and bozkurt [4]. the finite volume formulation is also adopted for the elasto-plastic analysis of reissner-mindlin plates by adapting the layered approach [5] and non-layered model [6]. the elasto-plastic analysis using the element free galerkin i http://www.gruppofrattura.it/va/50/2552.mp4 k. meftah et alii, frattura ed integrità strutturale, 50 (2019) 276-285; doi: 10.3221/igf-esis.50.23 277 method (efgm) was initially applied to fracture problems and subsequently applied to 2d problems and to 3d problems [7, 8]. on the other hand, the incremental cyclic plasticity theory is recently used firstly to determine the actual stress and strain state arising in two-dimensional or axi-symmetric notched components and later is extended by marangon et al. [9] and campagnolo et al. [10] to study the three-dimensional effects at the tip of rounded notches in plates of finite thickness. the first order shear deformation theories (fsdts), which include transverse shear deformation, for bending plates have been initially proposed by reissner [11] and further developed by mindlin [12]. these theories are widely employed in the nonlinear elasto-plastic behavior. in this study, a finite element method for analyzing the elasto-plastic plate bending problems is presented. the previous q4 [13] plate element with transverse energy of shearing is extended to account for nonlinear elasto-plastic. the goal of this work is to present a transverse energy four-node element q4 with only four corner nodes which is significantly superior to the classical four-node element and is not computationally as expensive as a quadratic quadrangle 9-noded hétérosis element. having a finite element method for linear elastic analysis of reissner-mindlin bending plates, we further develop the model to investigate the elasto-plastic behavior and plastic zone of the structures under consideration. a modified newton-raphson method has been used to solve the non-linear equations. von-mises yield criterion has been adopted to deal with yielding of the materials along with the isotropic hardening. a computer program has been developed and a number of plate-bending problems have been solved. as the applications of the present element, the square plates with the various boundary conditions are calculated. the results have been compared with existing benchmark solutions. results obtained with the q4 plate element, with the adopted constitutive laws, are compared with those provided by the quadratic quadrangle 9-noded hétérosis element presented in references [1, 14] with the provision of selective integration and reduced integration. all the computations were carried out in fortran finite element code developed by owen and hinton [1] and hinton and owen [14]. reissner-mindlin plate theory he reissner-mindlin plate theory (also designated first order shear deformation theory, fsdt) is more adequate for the analysis of moderately thick plates. the sign convention for stress resultants, the displacement field and the coordinate system are indicated in fig. 1. general notation is mx, my bending moments, mxy twisting moments, vx, vy transverse shear forces, w deflection in z-direction and x , y rotations of the xzand yz-planes, respectively. figure 1: schematic of the reissner-mindlin plate indicating the sign convention chosen for forces and moments. the displacement field at any point within the element is given by:       , , , x y u z x y v z x y w w x y          (1) the flexural and transverse shear strains in the plate for isotropic homogeneous linear behavior elastic can be written in the concise matrix form as: t k. meftah et alii, frattura ed integrità strutturale, 50 (2019) 276-285; doi: 10.3221/igf-esis.50.23 278    tf x y xy    ;     t s xz yz   (2) the linear relationships between the displacements and strains can be obtained by using the definitions of strains from the theory of elasticity: ; yx x y u v z z x x y y                (3) 2 yx xy xy u v z y x y x                   (4) 2xz xz x w x         ; 2yz yz y w y         (5) assuming normal stress zz to be negligibly small compared to other normal stresses, the stress-strain relationship in the matrix takes the form:  d  (6) where   = { xx yy xy yz zx }t and the matrix  d for isotropic materials is defined:   0 0 f s d d d        (7) with   1 0 . . 0 1s d g k h        ; 3 2 1 0 . 1 0 12(1 ) 1 0 0 2 f e h d                        (8) where h is the thickness of the plate, k is a shear correction coefficient, e is the young's modulus and  is the poisson's ratio. the generalized forces per unit of length of the plate side can be obtained using the stress field; these forces are the bending moments (m) and the shear forces (v):   2 2 h xx yy h xy m z dz                 ;   2 2 h yz xzh v dz            (9) constitutive equation for rate independent elastoplasticity fter initial yielding the material behavior will be partly elastic and partly plastic. during any increment of stress, the changes of strain are assumed to be divisible into elastic and plastic components, so that: a k. meftah et alii, frattura ed integrità strutturale, 50 (2019) 276-285; doi: 10.3221/igf-esis.50.23 279 e pd d d    (10) the elastic-plastic strain increment is given by the incremental form of:   1 fd d d d         (11) where d is a proportional constant called plastic multiplier and f    is the flow vector, which is normal to the adopted yield function, presented in eq. (12), considering that the yield surface only depends on the magnitude of the applied principal stresses and of a hardening parameter h: ( , ) ( , ) ( ) 0yf h f h h     (12) where y is the yield stress and f( ,h) is the yield criterion. in this paper, the elasto-plastic constitutive model based on the von-mises associated yield criterion is adopted for the reissner-mindlin plate theory [15]:     1 2 22 2 2 2 21( ) 6 2 xx yy xx yy xy yz zx yf                       (13) where e is the von-mises effective stress. the elastic-plastic incremental stress strain relationship:  ep e pd d d d      (14) ep e f d d d d            (15) the differential form of eq. (12) is: 0y f df d h h           (16) or ta 0df d ad    (17) in which the flow vector at is define as: ta x y xy yz zx f f f f f f                          (18) eqns. (16) and (17) can be reduced to get the hardening parameter a as: 1 ya d h h      (19) the plastic rate multiplier can be obtained as: k. meftah et alii, frattura ed integrità strutturale, 50 (2019) 276-285; doi: 10.3221/igf-esis.50.23 280 t t a a a d d d a d    (20) by substituting the expression of the plastic multiplier d into eq. (15), the elasto-plastic tangent modulus is derived as: t t a a a a ep d d d d a d    (21) the incremental stress-strain relationship is given as:   0 0 epf ff s s s dd d d dd                     (22) for mindlin plate, yield function f is assumed to be function of f but not of the transverse shear stresses s , the direct stresses associated with flexure only hence sd always remain elastic [1, 16, 17]. finite element formulation he mindlin-reissner theory takes the shear deformation into account by decoupling the rotation of the plate crosssection from the slope of the deformed mid-surface and the displacement field requires c0 continuity only. then the displacement fields (the transverse displacement w and two rotations x, y) are described by the same order of shape functions as follows:   1 0 0 0 0 0 0 i in x i xi i y i yi w n w d n n                              (23) the bending and shear strain-displacement relationships are given as: 1 . n f fi i i b d     ; 1 . n s si i i b d     (24) with 0 0 0 0 0 i i fi i i n x n b y n n y x                       ; 0 0 i i si i i n n x b n n y           (25) the tangential stiffness matrix can be written as follows:      t tt f ep f s s a k b d b b d b da          (26) t k. meftah et alii, frattura ed integrità strutturale, 50 (2019) 276-285; doi: 10.3221/igf-esis.50.23 281 in this study the solution is obtained resorting to the modified newton-raphson method [1]. in this algorithm the modification consists of computing the tangent stiffness matrix only once in the beginning of each load increment than in each iteration. q4 finite element the q4 element shown in fig. 2 is adopted in the present study. this element contains four nodes at the corners and the associated classical interpolation functions given by [13]:   1 1 1 4 i i in     ; i = 1, 2, 3 and 4 (27) with    1 2 3 4, , , 1,1,1, 1       and    1 2 3 4, , , 1, 1,1,1       .   a1 a2 b1  b2 1  2 3 4  1a  2a  1b  2b  figure 2: q4 quadrilateral isoparametric element [13]. for the q4 element the transverse field of distortion  is linearly discretizes in the element of reference by side so that: 1 2 1 2 1 1 2 2 1 1 2 2 a a b b                                     (28) by means of then the relations:    1 , 1 0w d          ;    1 , 1 0w d          ; for 1   and 1   (29) one establishes that:  1 2 1 1 2 1 2 a w w        ;  2 4 3 3 4 1 2 a w w        (30.a)  1 4 1 1 4 1 2 b w w        ;  2 3 2 2 3 1 2 b w w        (30.b) by deferring the two results above in the statement of  , one from of deduced that: k. meftah et alii, frattura ed integrità strutturale, 50 (2019) 276-285; doi: 10.3221/igf-esis.50.23 282 0 0 i i ii i i i i i n n w n n                                                     (31) it is now necessary to express the rotations given here in the element of reference according to rotations in the local coordinate system:   xkk k ykk j                (32) where jk is the inverse jacobian matrix components. numerical examples he resulting mathematical model of the proposed q4 element and the classical associative plasticity model are implemented into a fortran calculation code to account for small strain elasto-plastic problems. a nonlinear elasto-plastic behavior of bending plates under mechanical loading with different boundary conditions and different aspect ratios were studied. both problems involve square plates subjected to a uniformly distributed load of magnitude 1 kn/m². the material is considered as elasto-plastic (where the material is considered elastic perfectly plastic and the von mises model is adopted) with: l = 1.0 ; h = 0.5 and 0.01 ; e = 10.92 gpa;  = 0.3 and yield stress y = 1600 mpa. because of the symmetry, only a quarter of the plate is modeled using 4×4 mesh as shown in fig. 3. x y  l l sym.  sym.  figure 3: square plate, its finite element models. simply supported square plate in the first elasto-plastic example, a simply supported square plate subjected to uniformly distributed load is considered. the results are presented in figs. 4 and 5 and shows the load-deflection curves with respect to the maximum deflection when nondimensional incremental load intensity is 0. ²q l m (m0 fully plastic moment 0 . . ² 4ym l h ). this figure also shows a comparison among the hétérosis finite element solution obtained by owen and hinton [1]. the central displacements, for comparison of plates with different thicknesses (h = 0.01 and 0.5), have been normalized as: 0. . ²w d m l where    3 2. 12(1 )d e h   is the flexural rigidity of the plate. the results obtained from the present 4node element q4 agree well with those obtained from the 9-node hétérosis element reported in reference [1]. from the observation of the figures, it is possible to conclude that the accuracies of the present 4-node new element globally close t k. meftah et alii, frattura ed integrità strutturale, 50 (2019) 276-285; doi: 10.3221/igf-esis.50.23 283 to that of the 9-node hétérosis element. fig. 6 shows the progression of the plastic regions at different levels of loading. from this figure, first yielding is observed at the four corners of the plate and then at the center, and the plastic regions extend along the diagonals. ². . 0 lm dw 0 ². m lq   0 5 10 15 20 25 0 5 10 15 20 25 30 elément hétérosis elément q4gamma hétérosis element q4g element figure 4: load-deflection curves for simply supported square plate (h = 0.01). 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 0 5 10 15 20 25 30 elément hétérosis elément q4gamma ². . 0 lm dw 0 ². m lq hétérosis element q4g element figure 5: load-deflection curves for simply supported square plate (h = 0.5).   0 0 .1 2 5 0 .2 5 0 .3 7 5 0 .5 0 .6 2 5 0 .7 5 0 .8 7 5 1 0 0.125 0.25 0.375 0.5 0.625 0.75 0.875 1 4.60e4+ 4.18e4 to 4.60e4 3.77e4 to 4.18e4 3.35e4 to 3.77e4 2.93e4 to 3.35e4 2.51e4 to 2.93e4 2.09e4 to 2.51e4 1.67e4 to 2.09e4 1.26e4 to 1.67e4 8.37e3 to 1.26e4 4.18e3 to 8.37e3 0.00e0 to 4.18e3 figure 6: progression of yield regions for simply supported square plate (h = 0.01). k. meftah et alii, frattura ed integrità strutturale, 50 (2019) 276-285; doi: 10.3221/igf-esis.50.23 284 clamped square plate a clamped square plate subjected to uniform load is analyzed. fig. 7 shows the load-deflection curve with respect to maximum deflection with (h = 0.01). the present 4-node element q4 results are compared with those of hétérosis finite element reported by owen and hinton [1]. from this figure, it is observed that the results provided by the present fournode q4 element are in a good agreement with those of the converged results of the 9-node hétérosis element given in [1]. the progression of the yield regions at different levels of loading is summarized in fig. 8. in this case, the first yielding of the plate occurs at the middle of the four edges, and the plastic regions extend along these edges until the center of the plate yields. 0 5 10 15 20 25 0 10 20 30 40 50 60 elément hétérosis elément q4gamma ². . 0 lm dw 0 ². m lq hétérosis element q4g element figure 7: load-deflection curves for clamped square plate (h = 0.01).   0 0 .1 2 5 0 .2 5 0 .3 7 5 0 .5 0 .6 2 5 0 .7 5 0 .8 7 5 1 0 0.125 0.25 0.375 0.5 0.625 0.75 0.875 1 1.74e5+ 1.59e5 to 1.74e5 1.43e5 to 1.59e5 1.27e5 to 1.43e5 1.11e5 to 1.27e5 9.52e4 to 1.11e5 7.93e4 to 9.52e4 6.34e4 to 7.93e4 4.76e4 to 6.34e4 3.17e4 to 4.76e4 1.59e4 to 3.17e4 0.00e0 to 1.59e4 figure 8: progression of yield regions for clamped square plate (h = 0.01). conclusions n this work, a finite element method for analyzing the problem of elasto-plastic bending of a square plate is presented. the previously proposed four-node q4 element with transverse energy of shearing for thick bending plates is extended to account for nonlinear elasto-plastic problems. the adopted constitutive model is the classical associative von-mises plasticity model where the modified newton-raphson scheme has been implemented for solving the nonlinear numerical system. to perform numerical tests, various examples within the nonlinear context are used to assess the accuracy against currently existing well-performed elements. the present element shows reliability and i k. meftah et alii, frattura ed integrità strutturale, 50 (2019) 276-285; doi: 10.3221/igf-esis.50.23 285 robustness when compared with some reference elements from the literature. the elasto-plastic results obtained by fournode q4 element for the square bending plates with various boundary conditions can be treated with acceptable accuracy compared with those obtained by 9-node hétérosis element. for the displacement field and for the plastic zone the q4 solutions are very similar to the hétérosis solutions. references [1] owen, d.r.j. and hinton, e. (1980). finite elements in plasticity – theory and practice, pinerdge press limited, swansea, u.k. [2] meftah, k. (2019). analyse non linéaire (élasto-plasticité) des plaques reissner-mindlin, ed. universitaires europeennes, paris, france. [3] rezaiee-pajand, m. and sadeghi, y. (2013). a bending element for isotropic, multilayered and piezoelectric plates, latin american journal of solids and structures, 10(2), pp. 323-348. doi: 10.1590/s1679-78252013000200006. [4] kanber, b. and bozkurt, · o.y. (2006). finite element analysis of elasto-plastic plate bending problems using transition rectangular plate elements, acta mechanica sinica 22, pp. 355–365. doi: 10.1007/s10409-006-0012-y. [5] fallah, n. and parayandeh-shahrestany a. (2014). a novel finite volume based formulation for the elasto-plastic analysis of plates, thin-walled structures, 77, pp. 153-164. doi: 10.1016/j.tws.2013.09.025. [6] fallah, n., parayandeh shahrestany, a. and golkoubi, h. (2017). a finite volume formulation for the elasto-plastic analysis of rectangular mindlin-reissner plates, a non-layered approach, civil engineering infrastructures journal, 50(2), pp. 293 – 310. doi: 10.7508/ceij.2017.02.006. [7] kargarnovin, m.h., toussi, h.e. and fariborz, s.j. (2003). elasto-plastic element-free galerkin method, computational mechanics, 33, pp. 206-14. doi: 10.1007/s00466-003-0521-5. [8] pamin, j., askes, h. and borst, r. (2003). two gradient plasticity theories discretized with the element-free galerkin method, computer methods in applied mechanics and engineering, 192, pp. 2377-403. doi: 10.1007/s00466-003-0521-5. [9] marangon, c., campagnolo, a. and berto, f. (2015). three-dimensional effects at the tip of rounded notches subjected to mode-i loading under cyclic plasticity, j. strain anal. eng. des., 50(5), pp. 299–313. doi: 10.1177/0309324715581964. [10] campagnolo, a., berto, f. and marangon, c. (2016). cyclic plasticity in three-dimensional notched components under in-phase multiaxial loading at r=−1, theor. appl. fract. mech., 81. doi: 10.1016/j.tafmec.2015.10.004. [11] reissner, e. (1945). the effect of transverse shear deformation on the bending of elastic plates. j. appl. mech., 12, pp. 66–77. [12] mindlin, r.d. (1951). influence of rotatory inertia and shear on flexural motion of isotropic, elastic plates, j. appl. mech., 18, pp. 31–38. [13] batoz, j. and dhatt, g. (1992). modelization of structures by finite elements: beams and plates, hermes, paris. [14] hinton, e. and owen, d.r.j. (1984). finite element software for plates and shells, pineridge press limited, swansea, u.k. [15] chen, w.f. and han, d.j. (1988). plasticity for structural engineers, springer-verlag, new york. [16] kanber, b. and bozkurt, o.y. (2006). finite element analysis of elasto-plastic plate bending problems using transition rectangular plate elements, acta mechanica sinica, 22, pp. 355–365. doi: 10.1007/s10409-006-0012-y. [17] belinha, j. and dinis, l. (2006). elasto-plastic analysis of plates by the element free galerkin method, international journal for computer-aided engineering and software, 23, pp. 525-551. doi: 10.1108/02644400610671126. << /ascii85encodepages false /allowtransparency false /autopositionepsfiles true /autorotatepages /none /binding /left /calgrayprofile (dot gain 20%) /calrgbprofile (srgb iec61966-2.1) /calcmykprofile (u.s. web coated \050swop\051 v2) /srgbprofile (srgb iec61966-2.1) /cannotembedfontpolicy /error /compatibilitylevel 1.4 /compressobjects /tags /compresspages true /convertimagestoindexed true /passthroughjpegimages true /createjobticket false /defaultrenderingintent /default /detectblends true /detectcurves 0.0000 /colorconversionstrategy /cmyk /dothumbnails false /embedallfonts true /embedopentype false /parseiccprofilesincomments true /embedjoboptions true /dscreportinglevel 0 /emitdscwarnings false /endpage -1 /imagememory 1048576 /lockdistillerparams false /maxsubsetpct 100 /optimize true 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/hrv (za stvaranje adobe pdf dokumenata najpogodnijih za visokokvalitetni ispis prije tiskanja koristite ove postavke. stvoreni pdf dokumenti mogu se otvoriti acrobat i adobe reader 5.0 i kasnijim verzijama.) /hun 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can be opened with acrobat and adobe reader 5.0 and later.) >> /namespace [ (adobe) (common) (1.0) ] /othernamespaces [ << /asreaderspreads false /cropimagestoframes true /errorcontrol /warnandcontinue /flattenerignorespreadoverrides false /includeguidesgrids false /includenonprinting false /includeslug false /namespace [ (adobe) (indesign) (4.0) ] /omitplacedbitmaps false /omitplacedeps false /omitplacedpdf false /simulateoverprint /legacy >> << /addbleedmarks false /addcolorbars false /addcropmarks false /addpageinfo false /addregmarks false /convertcolors /converttocmyk /destinationprofilename () /destinationprofileselector /documentcmyk /downsample16bitimages true /flattenerpreset << /presetselector /mediumresolution >> /formelements false /generatestructure false /includebookmarks false /includehyperlinks false /includeinteractive false /includelayers false /includeprofiles false /multimediahandling /useobjectsettings /namespace [ (adobe) (creativesuite) (2.0) ] /pdfxoutputintentprofileselector /documentcmyk /preserveediting true /untaggedcmykhandling /leaveuntagged /untaggedrgbhandling /usedocumentprofile /usedocumentbleed false >> ] >> setdistillerparams << /hwresolution [2400 2400] /pagesize [612.000 792.000] >> setpagedevice microsoft word ecf22_206 as d. benasciutti et alii, frattura ed integrità strutturale, 47 (2019) 348-366; doi: 10.3221/igf-esis.47.26 348 the “projection-by-projection” (pbp) criterion for multiaxial random fatigue loadings: guidelines to practical implementation d. benasciutti, d. zanellati, a. cristofori university of ferrara, department of engineering, via saragat 1, 44122, ferrara, italy denis.benasciutti@unife.it, davide.zanellati@unife.it, alessandro.cristofori@unife.it abstract. this work is motivated by the increasing interest towards the application of the “projection-by-projection” (pbp) spectral method in finite element (fe) analysis of components under multiaxial random loadings. to help users and engineers in developing their software routines, this paper presents a set of numerical case studies to be used as a guideline to implement the pbp method. the sequence of analysis steps in the method are first summarized and explained. a first numerical example is then illustrated, in which various types of biaxial random stress are applied to three materials with different tension/torsion fatigue properties. results of each analysis step are displayed explicitly to allow a plain understanding of how the pbp method works. the examples are chosen with the purpose to show the capability of the method to take into account the effect of correlation degree among stress components, and the relationship between material and multiaxial stress in relation to the tension/torsion fatigue properties. a case study is finally discussed, in which the method is applied to a fe structural durability analysis of a simple structure subjected to random excitations. the example describes the flowchart and the program by which to implement the method through ansys apdl software. this final example illustrates how the pbp method is an efficient tool to analyze multiaxial random stresses in complex structures. keywords. multiaxial fatigue; random stress; frequency-domain approach; power spectral density (psd); finite element method. citation: benasciutti, d. zanellati, d., cristofori, a., the “projection-by-projection” (pbp) criterion for multiaxial random fatigue loadings: guidelines to practical implementation, frattura ed integrità strutturale, 47 (2019) 348-366. received: 29.10.2018 accepted: 30.11.2018 published: 01.01.2019 copyright: © 2019 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. introduction t may happen that a new multiaxial fatigue criterion, first published as an article in a scientific journal, gains an increasing interest also in the technical community, among engineers or developers of fatigue-based software. it may also happen, though, that the scientific article (clearly more focused in explaining the theory than providing detailed results or case studies) does not give enough practical information to allow users or engineers to implement correctly the criterion on their i http://www.gruppofrattura.it/va/47/2233.mp4 d. benasciutti et alii, frattura ed integrità strutturale, 47 (2019) 348-366; doi: 10.3221/igf-esis.47.26 349 own. users, in implementing the criterion, may feel not sure to have correctly understood the basic principles of the method and have doubts that their own programs are really free from errors and/or misinterpretations, and that they return a output truly correct. the possibility to have access to detailed results for a number of simple case studies, to be used as a reference, may thus help to solve possible doubts. the “projection-by-projection” (pbp) method is fatigue criterion for multiaxial loadings. it has first been proposed about ten years ago [1,2] as a conventional time-domain criterion, in which stress time-histories are processed directly. it was then reformulated in the frequency-domain to address multiaxial random loadings [3,4]. indeed, like for other multiaxial criteria, a time-domain definition may become computationally time-consuming (and thus impractical), for example when considering medium-to-large finite element models, in which it is required to process long digitalized multiaxial timehistories in hundreds or thousands of nodes [5]. this is perhaps the main limitation (along with others theoretical issues here not mentioned) that motivated the researchers’ effort of reformulating multiaxial criteria (pbp included) from timeto frequency-domain. unlike their time-domain counterparts, frequency-domain multiaxial criteria (also called multiaxial spectral methods) are indeed able to reduce the overall computational time drastically, while keeping high levels of accuracy. in multiaxial spectral methods, the fatigue damage and life are estimated directly from power spectral density (psd) data (i.e. spectra and crossspectra), which characterize a multiaxial random stress in the frequency-domain [5]. this approach proves to be computationally efficient especially if it can exploit results of fe structural dynamic analyses. it has furthermore been demonstrated that the pbp method, unlike other frequency-domain criteria, is sensitive to the local state of stress in a structure as it correctly takes into account the degree of correlation between stress components. at the same time, the method can also account for different material behaviors depending on different types of multiaxial stress [1-4]. this is of great relevance in engineering applications, in which several materials need to be scrutinized and compared for the same component geometry, or it is required to perform a geometric optimization to make the best use of a given material. though the pbp spectral method has been presented in a number of scientific articles published so far [3,4], it is our belief that this work – entirely devoted to its practical application – would be helpful to anyone who wishes to implement the method on his own. after summarizing some theoretical formulas to characterize deviatoric and hydrostatic stress components in frequency-domain, the work discusses all the steps necessary to implement the pbp method. a first numerical case study is considered, in which various biaxial stress states are applied to three different materials. each analysis step is commented on in detail to give an exhaustive description of the procedure. finally, the case of a simple 2d structure subjected to random excitations is considered to show how the pbp method can be easily embedded into a fe durability analysis. frequency-domain description of a multiaxial random stress efore discussing the pbp criterion and the numerical examples, it is useful to summarize the main quantities used in the following (a nomenclature is also given at the end of the article). the next paragraphs will assume that the reader is somehow familiar with the basic concepts and terminology of the frequency-domain approach to random processes. otherwise, a short review is provided in appendix a. equations will be developed for a biaxial stress state; extension to a three-dimensional stress state is straightforward. description of multiaxial stress state in physical space assume that σ(t) represents the time-varying stress tensor in a point of a mechanical component (t is the time variable). if the point is located on the surface, where fatigue cracks usually nucleate, the tensor σ(t) will have three non-redundant stress components σx(t), σy(t), τxy(t) (i.e. biaxial or plane stress), where σ and τ are normal and shear stress, respectively. each stress σx(t), σy(t), τxy(t) is assumed to be a zero-mean and covariant stationary random stress (the term “stationary” means, roughly speaking, that the random stress has statistical properties almost constant over time). the stress components in σ(t) are usually reordered into a stress vector x(t)=(σx(t), σy(t), τxy(t)), also written as x(t)=(x1(t), x2(t), x3(t)). this vector is characterized in the frequency-domain by the two-sided psd matrix:            )()()( )()()( )()()( )( * , * , , * , ,, fsfsfs fsfsfs fsfsfs f xyxyyyxyxx xyyyyyyyxx xyxxyyxxxx s (1) b d. benasciutti et alii, frattura ed integrità strutturale, 47 (2019) 348-366; doi: 10.3221/igf-esis.47.26 350 in which diagonal terms are auto-spectra and out-of-diagonal terms cross-spectra; f is the frequency (hz). matrix s(f) is hermitian (see appendix a). the psd matrix allows the covariance matrix c (symmetric) to be computed:            xyyyxyxy,xx xyyyyyxxyy xyxxyyxxxx ccc ccc ccc , ,, ,, c (2) the i-th diagonal term cii=var(xi(t)) is the variance of stress xi(t), the ij-th out-of-diagonal term is the covariance cij=cov(xi(t), xj(t)) between xi(t) and xj(t). normalizing the covariance cij allows a correlation coefficient to be defined as jjiiijij cccr / . the correlation coefficient represents, for multiaxial random loadings, the statistical equivalent of the phase angle for sinusoidal loadings. it discriminates between two limiting cases: rij=1 for perfectly correlated processes (i.e. proportional stresses), rij=0 for uncorrelated processes (i.e. not-proportional stresses). description of deviatoric and hydrostatic stress the pbp method is an invariant-based multiaxial criterion, so a frequency-domain description of the deviatoric and hydrostatic stresses is needed. the pbp criterion works with the amplitude a2,j of the square root of the second invariant j2 of the deviatoric stress tensor σ'(t), where the decomposition σ(t)=σ'(t)+σh(t)i into deviatoric and hydrostatic tensors is used. the definition )()()(2 tttj ss  relates the second invariant to the stress vector s(t)=(s1(t), s2(t), s3(t)) in the threedimensional deviatoric space. the following transformation rules apply [6]:   3 )()( )( 100 0 2 1 0 0 32 1 3 1 where)()( )()()( )( 2 1 )( 2 1 )( )()(2 32 1 )( 2 3 )( 3 2 1 tt t tt ttts ttts tttts yyxx h xyxy yyyy yyxxxx                                      axas (3) expressions (3) allow both the hydrostatic and deviatoric stress components to be directly computed from the stress vector x(t) in the physical space. when the stress tensor σ(t) changes over time, the tip of vector s(t) describes a curve (loading path ) in the deviatoric space. in a time-domain approach, conventional definitions (e.g. longest chord, minimum circumscribed circle, etc. [6]) are used to identify the amplitude a2,j of the loading path. in a frequency-domain approach, this time-domain procedure is replaced by a spectral characterization of the stress quantities in eq. (3). as a first step, the correlation matrix of s(t) is defined as:       tttt ttette araaxxassr'  )()()()()()(  (4) where r() is the correlation matrix of x(t), with  a time lag (see appendix a). the (symmetric) covariance matrix of s(t) results in the special case =0:              33 2322 131211 'sym '' ''' ')()( c cc ccc tte tt cacassc (5) d. benasciutti et alii, frattura ed integrità strutturale, 47 (2019) 348-366; doi: 10.3221/igf-esis.47.26 351 where c=r() is the covariance matrix of x(t), see eq. (2). similarly to x(t), the psd matrix s'(f) of vector s(t) is the fourier transform of the correlation matrix r'() in eq. (4):           tt)()()(' asaaraarar's  ff t  (6) the previous result yields by the fact that the fourier transform   is a linear operator and a is a matrix of constants. by following the same procedure, it is straightforward to find the psd expression of the hydrostatic stress σh(t):   )(re2)()( 9 1 )( ,h fsfsfsfs yyxxyyxx  (7) its zero-order spectral moment (i.e. area of sh( f )) gives the variance:    yyxxyyxxhh cvvtvarv ,2 9 1 )(   (8) expressions (6)-(7) characterize the deviatoric and hydrostatic stress in the frequency-domain completely. analysis steps of the pbp criterion his section summarizes the main analysis steps to be followed when implementing the pbp criterion (see fig. 1). if the pbp method is applied to the output of a fe analysis, the steps have to be repeated for each nodal result in the model. the input data required by the analysis are:  psd matrix s(f) of the biaxial stress (σx(t), σy(t), τxy(t)), along with the covariance matrix c in eq. (2) calculated from s(f). the stress may refer to a physical point in a structure, or to a node in a fe model (in which case matrix s(f) is output directly by a fe analysis). if s(f) is not known, it may be estimated from measured time-histories;  parameters of tension and torsion s-n curves: strength amplitudes σa, τa at na=2106 cycles and inverse slopes kσ, kτ. the s-n lines may represent design curves at prescribed survival probability (97.7%). figure 1: analysis steps and quantities involved by the pbp spectral method in frequency-domain. step 1 – from stress vector to deviatoric/hydrostatic stress the first step is to characterize the stress vector s(t) by its psd matrix s'(f) in eq. (6), and by its covariance matrix c', see eq. (5) or equivalently compute c' from s'(f). then, characterize the hydrostatic stress σh(t) by its power spectrum sh(f) in eq. (7), and by its variance vh, see eq. (8). input stress psd covariance matrix s(f), c material properties σa, τa (at na cycles) kσ, kτ analysis steps output deviatoric/hydrostatic 1 principal system i‐th damage d1, d2 , d3 reference s‐n line ρref, jaref, kref total damage dtot 3 3 2 4 5 tf=dcr/dtot fatigue life 4 psd (deviatoric) psd (projections) s'(f) s'p(f) c', vh c'p11, c'p22, c'p33 u 2 2 t d. benasciutti et alii, frattura ed integrità strutturale, 47 (2019) 348-366; doi: 10.3221/igf-esis.47.26 352 step 2 – from the original coordinate system to the (rotated) principal coordinate system in general, matrix c' is not diagonal, i.e. some correlation exists between the stress components of s(t). if this happens, it is necessary to compute a new covariance matrix c'p in which all cross-correlations (out-of-diagonal elements) are zero. this outcome yields by solving the following eigenvalue/eigenvector problem for c':             33 22 11 t 00 00 00 ''' p p p pp c' c' c cucuc (9) the eigenvalues are in the main diagonal of c'p, the eigenvectors are the columns of u. in a time-domain perspective, the eigenvalue/eigenvector problem (9) can be viewed as the projection of the loading path  along the axes of a new (rotated) “principal coordinate system”. the new system is located by a rotation angle (whose direction cosines are the eigenvectors in the column of matrix u) from the original system in which s(t) is initially defined. projecting the loading path into the new coordinate system yields 3 new stress components ωp,i(t) (i=1, 2, 3), which are grouped in the vector ω(t)=(ωp,1(t), ωp,2(t), ωp,3(t)). since matrix c'p is diagonal, the stress components in ω(t) are completely uncorrelated, that is cov(ωp,h(t), ωp,k(t))=0 for any h≠k. the diagonal elements in c'p are the variances cpii=var(ωp,i(t)). fig. 2 shows an example for a tension/torsion loading. the non-null deviatoric stress components s1(t), s3(t) give the twodimensional loading path . once projected in the principal system this path gives rise to two stress projections ωp,1(t), ωp,3(t). both vectors s(t) and ω(t) then share the same loading path in the deviatoric space. figure 2: example of random loading path  in the two-dimensional deviatoric space, resulting from a tension/torsion loading. the rotated “principal coordinate system” is located by axes (s1,0, s3,0) and it is used to obtain the stress projections ωp,1(t), ωp,3(t). in a frequency-domain approach, the direct projection  is yet not necessary, as it is replaced by a “rotation” of the psd matrix from the “old” to the “new” coordinate system. indeed, vector ω(t) is characterized in the frequency-domain by the psd matrix s'p(f), which turns out by “projecting” the spectral matrix s'(f) in the new rotated principal system:                     )(00 0)(0 00)( ' '' 33 22 11 p t p fs fs fs fff p p p susus (10) 1000 1500 2000 2500 s3(t) t t s1 (t) s1 s3 load path ψ xx(t) τxy(t) t t d. benasciutti et alii, frattura ed integrità strutturale, 47 (2019) 348-366; doi: 10.3221/igf-esis.47.26 353 matrix s'p(f) is diagonal, by definition, and it collects the auto-spectra s'ii(f) of stress projection ωp,i(t), i=1, 2, 3. thanks to the fact that, in the principal system, the stress projections ωp,i(t) are completely uncorrelated, their fatigue damage can be computed separately. knowing the power spectra s'pii(f), the damage can be estimated through spectral methods for uniaxial loadings (see step 4). to this end, each spectrum needs to be characterized by several parameters (see appendix a): spectral moments (λ0i, λ1i, λ2i, λ4i), bandwidth parameters (α1i, α2i), frequency of up-crossing and peaks (ν0,i, νp,i). step 3 – reference s-n line in the modified wöhler diagram the fatigue damage for each projected stress ωp,i(t) is calculated on a “reference s-n curve” in a modified wöhler diagram (mwd) [7]. this diagram relates the number of cycles to failure, n, to the amplitude of the square root of second invariant of stress deviator, ajj a2, (from now on, this simplified notation will be used to avoid the square root symbol). fig. 3 depicts the relationship between the mwd and the wöhler diagram. the figure shows, on the right, the reference sn line along with the tension and torsion s-n lines in the mwd, and it also clarifies how the tension/torsion lines in mwd have to be sketched from the corresponding lines in the wöhler diagram on the left. from the first and third expression in eq. (3), in the mwd the reference strength amplitudes at na cycles are 3/, aaj   and aaj  , , where σa and τa are the amplitudes for fully-reversed axial and torsion loading, respectively. the inverse slopes for tension and torsion remain unchanged. fig. 3 considers the case in which 3aa   and kτ>kσ. other arrangements of s-n lines are yet possible depending on the combination of fatigue properties characterizing a specific material. the list in tab. 1 shows that materials are indeed characterized by s-n properties over a wide range [8]. material ref. type of loading σa τa kσ kτ σa/τa kσ/kτ aluminium alloy alcumg1 [9] b, t 161 97 7.027 6.868 1.66 0.98 carbon steel c40 (sae1040) [10] a, t 264.2 195.8 17.09 18.2 1.35 1.06 structural steel csn 41 1523 (s355 type) [11] b, t 231.7 144.5 21.21 15.04 1.60 0.71 medium alloy steel 34crmo4 [11] b, t 375 261.1 15.33 11.36 1.44 0.74 low-alloy steel s20c (aisi 1020 type) [9] b, t 227 97.8 6.17 6.06 2.32 0.98 aluminium alloy d-30 [9] b, t 180 120 10.753 9.174 1.5 0.85 structural steel 18g2a (s255 j0) [12] b, t 189.6 141.9 7.9 12.3 1.34 1.56 brass cuzn40pb2 [9] b, t 216 187 5.857 17.172 1.16 2.93 carbon steel c40 (sae1040)* [10] a, t 117.8 152.8 4.62 8.2 0.77 1.77 carbon steel ck 45 (sae1045)* [13], [14] b, t 357 226 7.7 13.4 1.58 1.74 table 1: fatigue parameters for several plain materials or notched specimen). * v-notched (r=0.5 mm) the reference s-n line in the mwd is located by the stress ratio [3,4]:       3 1 ,2 2 3 i iip h,mh ref c v  (11) which is a function of the mean value σh,m and variance vh of the hydrostatic stress σh(t), and of the square root of the sum of variances cp,ii of stress projections ωp,i(t). parameter ρref only depends on the multiaxial stress, not on material. in eq. (11), the numerator approximates the maximum of hydrostatic stress, whereas the denominator estimates the equivalent amplitude of cycles counted in each projection. if all stress components have a zero mean value, it is σh,m=0. in case of constant amplitude multiaxial loading (sinusoidal), the expression (11) returns the definition of ρref given in [1,2] for the time-domain criterion. d. benasciutti et alii, frattura ed integrità strutturale, 47 (2019) 348-366; doi: 10.3221/igf-esis.47.26 354 parameter ρref quantifies the relative contribution of hydrostatic to deviatoric stress components in a multiaxial stress. two limiting cases exist for uniaxial loading: a stress ratio ρref=1 for tension or bending (only normal stress), ρref=0 for torsion (only shear stress). a purely hydrostatic state of stress would have ρref. on either two limiting cases (i.e. ρref =0 or 1), the reference s-n line coincides with the line of the corresponding uniaxial loading (tension or torsion). in any other case in which the loading is multiaxial (i.e. for any other value 0≤ρref≤1), the reference s-n curve would lie between those for tension and torsion, its position being established by ρref. figure 3: relationship between s-n lines in wöhler diagram (left) and modified wöhler diagram (right). the reference s-n line for a general multiaxial stress (ρ=ρref) is also shown. symbol ja stands for a2,j . in a log-log diagram, the reference s-n line is expressed by the equation refcnj  refk a , where cref = na·(ja,ref)kref is a strength constant; ja,ref is the amplitude strength (at na cycles) and kref the inverse slope. they are linearly interpolated as [7]:        kkkk jjjj refref aarefa,a,ref   ,, (12) from the amplitude strengths ja,, ja,τ and inverse slopes kσ, kτ of the tension and torsion s-n curves. step 4 – fatigue damage calculated for each stress projection each stress projection ωp,i(t), obtained in step 2, is a uniaxial random stress. its damage in time unit (damage/s), say d(ωp,i(t)), can be estimated in the frequency-domain by uniaxial spectral methods. no restriction is imposed on which method to use from those available in the literature [15,16], although “wide-band methods” are recommended if the psd of each projection ωp,i(t) is not narrow-band. for example, fairly accurate estimations are given by the “tovo-benasciutti (tb) method” [15,16]:             2 12 i0 1 0 refk ,ref,itb,ip,itb k γcd ref (13) where γ(-) is the gamma function and ηtb,i is a correction factor that accounts for the spectral bandwidth of sp,i(f) and it depends on a proper weighting coefficient bapp (for their expressions, see [15,16]). in the limiting case of narrow-band psd, ηtb,i→1. eqn. (13) has been proved to provide estimations close to those from dirlik’s method, which the reader may be more familiar to [17]:                     i k ii refk ref k ii k ,i ref p,i ipdk drd k kqd c d ref refrefref ,3,2,10, 2 121  (14) parameters d1,i, d2,i, d3,i, qi, ri are best-fitting coefficients; their expressions can easily be found in the literature (see, for example, [15-17]). ja(log) n (log)n (log) σ,τ(log) σa ρ=0 (torsion) ρ=1 (tension) ρ=ρref ja,τ ja, ja,ref τa torsion tension σa/3 kσ kτ kref tension (scaled) kτ kσ d. benasciutti et alii, frattura ed integrità strutturale, 47 (2019) 348-366; doi: 10.3221/igf-esis.47.26 355 step 5 – estimating the total fatigue damage once the fatigue damage d(ωp,i(t)) for every projection has been calculated, the total damage d(ω) caused by stress vector ω(t) (which coincides with the damage of the multiaxial stress x(t)) can be estimated by the following expression:   2 3 1i 2 )( ref ref k k p,idd                    (15) this expression employs a non-linear combination rule to handle damaging events in uncorrelated stress projections. this law is able to account for the phase shift between stress components. its validity versus experimental data has been checked in previous publications [3]. eqn. (15) is very general. its mathematical expression depends on the particular spectral method used for estimating d(ωp,i(t)). if the “tb method” is considered:      refref k k ,itb,i ref reftb k γcd                 3 1i 2 0i0, 1 2 2 1  (16) the dirlik’s method yields, instead, a slightly more complex equation:         2 3 1i 2 ,3,2,1i0, 2 ip, 1 2 121 ref ref refrefrefref k k i k ii refk ref k ii k refdk drd k kqdcd                                      (17) the fatigue life (time to failure) is tf=dcr/d(ω), where dcr is a critical damage value (=1 in palmgren-miner rule). as a final remark, it is worth to observe that the pbp criterion provides damage estimations that are consistent with those for simple uniaxial random loadings (tension or torsion). for a pure axial loading (e.g. σxx(t)≠0 and σyy(t)=τxy(t)=0), the only non-null deviatoric component is c'11=vxx/3, while the variance of hydrostatic stress is vh=vxx/9, which results in ρref=1 and 3/refa, aj  , kref=kσ. the only non-null projection is 3/)()(1 tt xxp,  and the total damage d(ω)=d1(ωp,1(t)) equals the damage that would be obtained by applying eqs. (13) or (14) to the uniaxial random stress σxx(t). for a pure torsion loading (τxy(t)≠0 and σxx(t)=σyy(t)=0), the only non-null projection is ωp,3(t)=τxy(t), while the hydrostatic stress is zero (vh=0) and ρref=0. the reference s-n line thus coincides with the torsion line (ja,ref=τa, kref=kτ), while the total damage d(ω)=d3(ωp,3(t)) matches the damage of the shear stress. practical implementation of pbp criterion: numerical examples test cases with biaxial stress o further clarify the analysis steps sketched in fig. 1, the pbp method is now applied to some simple case studies, in which 4 types of biaxial stress are combined with 3 types of material fatigue properties. the decision to use simple case studies is no coincidence. in fact, it permits a much clearer monitoring of results in each analysis step, which in turn makes the understanding of the pbp method much easier. on the other hand, the case studies here analyzed – though simple – do synthesize combinations of materials and stress states that are actually encountered in mechanical components subjected to multiaxial loadings. the examples, in particular, are also specifically conceived so to better emphasize some peculiarities of the pbp method. each biaxial stress has components σxx(t), σyy(t), τxy(t) that are zero-mean stationary and gaussian, and with a band-limited rectangular psd, see fig. 4. also the use of a rectangular psd, in place of other more realistic (but irregular) spectra, contributes to make results much easier to be understood. the rectangular one-sided psds are centered on frequency fc=30 hz and are characterized by a fixed maximum-to-minimum ratio fmax/fmin=15, which guarantees that psds are wide-band with α1= 0.893, α2= 0.771 (these parameters remain unchanged for the power spectra of deviatoric and hydrostatic stress, t d. benasciutti et alii, frattura ed integrità strutturale, 47 (2019) 348-366; doi: 10.3221/igf-esis.47.26 356 as we as for stress projections). being the frequency range fixed, each psd is fully defined by the height h of each rectangle. through the rectangle area, the height controls the variance vii=hi,i·(fmax–fmin) of auto-psds and the covariance cij=hi,j·(fmax– fmin) of cross-psds (subscript i and j stands for the stress component xx, yy and xy). it is easy to derive the relationship jjiijiji hhrh ,,,,  between the cross-psd height and the correlation coefficient ri,j. the height hi,j is then bounded as jiji hhh  ,0 , see fig. 4. the cross-psd height varies according to the different correlation degrees in the range ri,j=01. figure 4: example of one-sided autoand cross-psd for a tension-torsion loading with non-zero correlation rxx,xy (stress case 3). combining the stress cases (1, 2, 3, 4) in tab. 2 with the materials models (a, b, c) in tab. 3 results in the whole set of load cases (1a, 2a, 3b, …) in tab. 4, which are examined in the numerical examples. the stress cases in tab. 2 are:  case 1: proportional normal stresses σxx(t), σyy(t), i.e. correlation degree equal to one (“in-phase loading”);  case 2: not-proportional normal stresses σxx(t), σyy(t), i.e. correlation degree equal to zero (“out-of-phase loading”);  case 3: tension-torsion loading with proportional stresses σxx(t), τxy(t), i.e. correlation degree equal to one;  case 4: tension-torsion loading with not-proportional stresses σxx(t), τxy(t), i.e. correlation degree equal to zero. all through the examples, the normal stresses have variance vxx=vyy=3 and the shearing stress vxy=1, so that all components of the stress deviator share the same unitary variance. no. of stress case description vxx vyy cxy rxx,yy rxx,xy ryy,xy 1 biaxial tension (correlated) 3 3 0 1 0 0 2 biaxial tension (not correlated) 3 3 0 0 0 0 3 bending-torsion (correlated) 3 0 1 0 1 0 4 bending-torsion (not correlated) 3 0 1 0 0 0 table 2: variance and correlation degree characterizing the biaxial stress states considered in numerical simulations. three hypothetical material models, with different fatigue properties, are investigated:  material a: this material has tension and torsion s-n lines with identical slope (k=kτ) and with amplitude strengths σa and τa=σa/√3, i.e. the torsion line is scaled by 3 . in the mwd, the tension and torsion s-n lines overlap each other, and they also overlap the reference line for any value of ρref. this material model has specifically been conceived for being not sensitive to the type of applied multiaxial stress (i.e. the material is not sensitive to ρref). this situation reflects the hypothesis that the material obeys the von mises equation under fatigue loadings, and it is only sensitive to the deviatoric stress component while not sensitive to hydrostatic stress;  material b: this material model has tension and torsion s-n lines with identical slope (k=kτ), but with fatigue strengths not scaled as in von mises criterion, that is τa≠σa/√3. unlike material a, this material has a fatigue strength that depends on the hydrostatic stress;  material c: this material model has arbitrary tension and torsion s-n lines, i.e. fatigue strengths as per material b, but with different slopes for tension and torsion (k≠kτ). this is the most general situation. like material a, this material is sensitive to the hydrostatic stress, too. in tab. 3, the tension s-n curve is kept fixed, while only the torsion line moves upward from case a to c. f gxx(f) hxx fc f gxy(f) hxy fc f re{gxx,yy(f)} hxx,yy fc xyxxxyxxyyxx hhrh  ,, d. benasciutti et alii, frattura ed integrità strutturale, 47 (2019) 348-366; doi: 10.3221/igf-esis.47.26 357 material type description na a mpa) a (mpa) k k a parallel s-n lines, scaled by 3 2106 100 57.7 3 3 b parallel s-n lines, not scaled by 3 2106 100 70 3 3 c arbitrary s-n lines 2106 100 70 3 5 table 3: fatigue properties of three different material models, considered in numerical simulations. tab. 4 gathers the results of all the load cases examined. in particular, it collects some quantities calculated throughout the analysis: the non-zero elements of covariance matrix c’ in deviatoric space and the variance of hydrostatic stress (step 1), the non-zero elements of covariance matrix c’p in the principal coordinate system (step 2), the parameters of the reference s-n curve in the mwd (step 3), the damage of each stress projection (estimated by narrow-band formula and tb method) (step 4), the total damage estimated by pbp method using the narrow-band formula or tb method (final analysis output). ———————— step 1 ———————— –– step 2 –– ––––– step 3 ––––– ––– step 4 ––– output case no. c'11 c'22 c'33 c'12 c'13 c'23 vh a c'p22 c'p33 ρref ja,ref kref dtb,2 (dnb,2) dtb,3 (dnb,3) dtb (dnb) 1a 0.25 0.75 0 0.433 0 0 1.333 0 1 2.0 57.7 3 0 (0) 2.756 (3.283) 2.756 (3.283) 2a 1.25 0.75 0 -0.433 0 0 0.667 0.50 1.50 1.0 57.7 3 0.974 (1.161) 5.063 (6.032) 7.796 (9.287) 3a 1 0 1 0 1 0 0.333 0 2 0.707b 57.7 3 0 (0) 7.796 (9.287) 7.796 (9.287) 3b 1 0 1 0 1 0 0.333 0 2 0.707b 61.3 3 0 (0) 6.504 (7.748) 6.504 (7.748) 3c 1 0 1 0 1 0 0.333 0 2 0.707b 61.3 3.586c 0 (0) 1.054 (1.308) 1.054 (1.308) 4a 1 0 1 0 0 0 0.333 1 1 0.707b 57.7 3 2.756 (3.283) 2.756 (3.283) 7.796 (9.287) 4b 1 0 1 0 0 0 0.333 1 1 0.707b 61.3 3 2.300 (2.740) 2.300 (2.740) 6.505 (7.749) 4c 1 0 1 0 0 0 0.333 1 1 0.707b 61.3 3.586c 0.304 (0.377) 0.304 (0.377) 1.054 (1.308) table 4: summary of step-by-step results (only non-zero values) of numerical case studies. in step 4 and output, the damage values are multiplied by 1010 (notes: a 1.333=4/3, 0.667=2/3, 0.333=1/3; b 2/1707.0  ; c 25586.3  ). load case 1a and 2a refer to biaxial normal stresses applied to material a; case 1a has “in-phase” stresses (rxx,yy=1), case 2a “out-of-phase” stresses (rxx,yy=0). the comparison of damage values shows that case 2a is more damaging than case 1a. this result is due to the greater contribution of deviatoric stress components in case 2a compared to case 1a (see step 2 in tab. 4), whereas it does not depend on the hydrostatic stress component, which is higher in case 1a. though the hydrostatic stress affects the damage by changing the s-n reference curve via ρref value, material a has specifically been conceived for no reaction to a change in the hydrostatic stress. the comparison case 1a vs. 2a shows that not-proportional stress lead to a greater damage. this effect of stress correlation cannot be generalized, yet. it closely depends on the material type. for example, tab. 4 makes clear that a different material (b or c) would behave differently. for example, case 3b and 4b highlight that damage in material b is not correlated to the proportionality degree. d. benasciutti et alii, frattura ed integrità strutturale, 47 (2019) 348-366; doi: 10.3221/igf-esis.47.26 358 in tab. 4, it is worth noting that cases 2a and 3a yield the same damage value. this outcome may be explained by considering the role of deviatoric and hydrostatic stress components. on one side, either cases have in common (see step 2 in tab. 4) the sum (c'p22+c'p33) of variances of deviatoric stress components in the principal coordinate system (the third projection has c'p11=0). this sum represents a sort of “total variance” of stress projections ωp,2(t), ωp,3(t) and it enters the damage expression (16) in the special case in which the bandwidth parameters ηtb,i , ν0,i take on identical values for all stress projections (a case that actually occurs in all stress states of tab. 2). it is trivial to verify that damage d(ω) is proportional to 2/ 3322 ref)(2 kpp cc  . on the other side, damage (16) is computed on the same s-n curve for both case 2a and 3a, despite they have a different variance vh for the hydrostatic stress and, hence, a different ρref value (see tab. 4). however, as already said, for material a the hydrostatic stress has no effect on damage. cases 3a, 3b and 3c emphasize the effect of different materials under the same tension-torsion loading (stress case 3). it is not surprising that a change of material type determines a change in the estimated damage, too. this result is governed by the reference s-n line, which takes on different positions for each material type, as confirmed by the dissimilar values of parameters ja,ref , kref (see step 3 in tab. 4). for example, the damage increases from material a to c, in relation to the different positions assumed by the reference s-n line. figure 5: effect of hydrostatic stress on fatigue damage for different materials undergoing a tension-torsion loading with cs1+cs3 = 1. the graph in fig. 5 allows the role of material properties to be further pointed out. the figure depicts the trend of the fatigue damage dtb(ω) in the case of a tension-torsion loading, as a function of ρref in the range 01. parameter ρref synthesizes different types of tension-torsion multiaxial loading, bounded by the limiting uniaxial case of pure torsion (ρref=0) to pure tension (ρref=1). the psd of normal and shearing stress are suitably normalized so to keep constant the variance sum cs1+cs3=1, as well as the corresponding sum constc iip  , for stress projections. this makes the damage only a function of the hydrostatic stress via ρref. predictably, the trends in fig. 5 confirm how different materials respond differently to the same multiaxial loading. while materials b and c show a moderate-to-great sensitivity to the type of loading, material a shows no sensitivity at all. in particular, fig. 5 makes crystalline clear that material a is unable to discriminate between different multiaxial states of stress; the estimated damage is constant and always equal to the value for torsion loading. materials like a, however, may be very common in engineering applications. it may characterize those unfortunate situations in which only the tension s-n curve is available from experiments, whereas the torsion s-n curve is only approximated by taking a line parallel and moved downward by 3 (von mises rule). although not recommended, this a-type material represents the only solution feasible for applying the pbp criterion, if no fatigue data for torsion loading are available. it has to be emphasized that such a “von mises approximation” is even hypothesized (implicitly) in some multiaxial criteria (e.g. [18]), which may thus lead to unrealistic estimations (see [4,8]). fe durability analysis an l-shaped structure under random acceleration d. benasciutti et alii, frattura ed integrità strutturale, 47 (2019) 348-366; doi: 10.3221/igf-esis.47.26 359 the purpose of this second example is to illustrate how the pbp method can easily be embedded into a fe durability analysis of a structure undergoing random vibrations. the example considers an l-shaped structure made of steel, whose geometry imitates that one already studied in [18]; some dimensions have been slightly changed [19] to enhance stress concentration effect at the hole and two lateral notches. a finite element model with “shell” elements is used to discretize the structure. a mapped mesh is generated in the notch regions. the average elements size is 3.5 mm; the smallest element dimension of 0.8 mm appears in regions of mesh refinement at notch tip. the model has a total of 1529 elements and 1687 nodes. the structure is clamped at both ends, at which a random acceleration is imposed along the direction normal to the specimen plane. input accelerations have a band-limited (rectangular) one-sided psd, ranging from 1 to 200 hz, with height 25π (m/s2)2·hz-1 (as in [18]). input accelerations applied at the two clamped ends are fully correlated (their cross-psd is different from zero). figure 6: geometry and finite element model of the l-shaped beam. thickness is 0.5 mm. a frequency-domain spectrum analysis is carried out through fe simulations to determine the structure natural frequencies and the stress psd matrix in every fe node. stress spectra are next processed by the pbp method to determine the total fatigue damage caused, in each node, by the local multiaxial state of stress. the whole numerical analysis is performed by software ansys with apdl language, which is also used to implement the pbp method. appendix b provides more details on the numerical algorithm. this analysis strategy, in which all calculations are carried out in ansys software, simplifies the overall data management and thus represents an enhancement of the two-phase procedure followed in [4], in which nodal fe results (psd matrices) were first calculated in ansys, then exported and post-processed in matlab to apply the pbp criterion. the first five natural frequencies returned by modal analysis are: f1=16.1 hz, f2=67.3 hz, f3=82.2 hz, f4=175.7 hz, f5=178.6 hz. in each node the state of stress turns to be biaxial. fig. 7 displays an example of autoand cross-psds in a node close to the round notch. results refer to the “top” layer of shell elements. for fatigue damage estimation, two different types of material (material 1 and 2) were considered for the structure. material 1 (likewise material a in tab. 2) is only sensitive to deviatoric stress components, whereas material 2 (likewise material c in tab. 2) is also sensitive to hydrostatic stress component. the material properties used in simulations are: σa=300 mpa, τa=300/3=173 mpa, k=kτ=8 (material 1); σa=300 mpa, τa=290 mpa, k=8, kτ=5 (material 2). fig. 8 displays the damage maps for either material. the damage is estimated by pbp-tb method in eq. (16) and refers to the “top” layer of shell elements. left figs. (a) show the damage d in linear scale to better highlight the locations of the most damage points; right figs. (b) show the logarithmic values log10(d) to allow the differences in the overall damage distribution to be appreciated best. the comparison of figures makes evident how the damage distribution does change with material type. in particular, the location of the most damaged point in the structure shifts in accordance to the degree by which material is sensitive to the hydrostatic stress value. d. benasciutti et alii, frattura ed integrità strutturale, 47 (2019) 348-366; doi: 10.3221/igf-esis.47.26 360 figure 7: autoand cross-psd (one-sided) in a node close to the round notch. figure 8: comparison of damage maps for material 1 vs. material 2. figs. (b) plots of log10(d) from figs. (a). indeed, in a fe model the stress ratio ρref may vary over a range of values, which depend on the variation of the local multiaxial state of stress among nodes. fig. 9(a) illustrates the distribution of ρref values obtained in numerical simulations. this distribution holds for both materials, being ρref only a function of the local stress, not of material. the figure also marks the values at which the multiaxial stress is close to uniaxial tension or torsion, and the regions a, b, c, d identified in fig. 8(a) (top). the values of ρref then measure if the stress in a point is more tension-like or torsion-like. the capability of the pbp criterion to capture the material sensitivity to the local stress state is well summarized by the graph in fig. 9(b), which plots the values of the damage ratio dmat2/dmat1 vs. ρref for each node of the fe model. if the pbp were not sensitive to the material which the structure is made of, the fe analysis would return the same damage value in every node regardless of the material type, and in turn all the dots in fig. 9(b) would lie on the dashed horizontal line. 0 50 100 150 200 10 -4 10 -2 10 0 10 2 10 4 auto-psds frequency, f [hz] st re ss p s d [ (p a2 )/ h z] g xx g yy g xy 0 50 100 150 200 10 -4 10 -2 10 0 10 2 10 4 cross-psds frequency, f [hz] st re ss p s d [ (p a2 )/ h z] re{g xx,yy } re{g xx,xy } re{g yy,xy } .10e‐15      .82e‐04      .16e‐03      .25e‐03      .33e‐03      .41e‐03      .49e‐03      .57e‐03      .66e‐03      .74e‐03      .82e‐03      .90e‐03      .98e‐03      .11e‐02      .11e‐02      .12e‐02      material 1 material 2 (a) (b) .41e‐16      .18e‐04      .36e‐04      .54e‐04      .72e‐04      .90e‐04      .11e‐03      .13e‐03      .14e‐03      .16e‐03      .18e‐03      .20e‐03      .22e‐03      .23e‐03      .25e‐03      .27e‐03      ‐16.38       ‐15.53       ‐14.68       ‐13.82       ‐12.97       ‐12.11       ‐11.26       ‐10.4        ‐9.55        ‐8.7         ‐7.84        ‐6.99        ‐6.13        ‐5.28        ‐4.42        ‐3.57        ‐15.99      ‐15.12      ‐14.25      ‐13.38      ‐12.51      ‐11.63      ‐10.76      ‐9.89        ‐9.02        ‐8.14        ‐7.27        ‐6.4         ‐5.53        ‐4.65        ‐3.78        ‐2.91        a c b d d. benasciutti et alii, frattura ed integrità strutturale, 47 (2019) 348-366; doi: 10.3221/igf-esis.47.26 361 (a) (b) figure 9: (a) distribution of ρref values in fe nodes; (b) damage ratio dmat2/dmat1 vs. ρref values (each point refers to one nodal result). likewise, the trend in fig. 9(b) remarks how much the fatigue damage (via pbp criterion) is influenced by the hydrostatic stress via ρref values. being dependent on hydrostatic stress, material 2 is characterized by damage values that depend upon ρref more clearly and that differ by up to an order of magnitude from those characterizing material 1. though simple, the numerical example discussed so far shows, in fact, the ability of the pbp method to capture the material sensitivity to the local multiaxial stress in a structure. this result is of great relevance in engineering applications, especially at early design phases, when it is desirable to compare the performance of different materials for the same component or, by contrast, it is required to identify a material whose fatigue properties are the most suitable for a given component subjected to a known vibration input. concluding remarks he writing of this article was primarily motivated by the aim to provide engineers engaged in vibration fatigue with a practical guide to apply the pbp spectral method. after a summary of the main analysis steps of the pbp criterion, the article applied the criterion to some simple numerical case studies, in which three material types are subjected to four different types of biaxial random stress (e.g. tension-tension, tension-torsion, “in-phase” or “out-of-phase”). a simple rectangular psd for the stress is considered to allow a much easier understanding and interpretation of the obtained results. the results of each analysis step were listed in detail to serve as a benchmark for users interested in implementing the pbp method by their own. results are also used to highlight the main features characterizing the pbp criterion. for example, the examples allow the role of material sensitivity to hydrostatic and deviatoric stress to be clearly pointed out. the case studies make apparent the capability of the pbp method to take into account the correlation degree between stress components, as well as the different material behavior as a function of the various states of stress. the article concludes by an example in which the pbp method is applied to the fe-based fatigue analysis of a thin structure submitted to a random acceleration. this example shows the advantage of the pbp method in cae-based design of structural components undergoing multiaxial fatigue loading. it emphasizes, in particular, how the method proves to be an efficient tool in the design of complex structures, e.g. for discriminating among materials with different fatigue properties, or for identifying the material with the most suitable properties. references [1] cristofori, a. (2007). a new perspective in multiaxial fatigue damage estimation. phd thesis, university of ferrara. [2] cristofori, a., susmel, l., tovo, r. (2008). a stress invariant based criterion to estimate fatigue damage under multiaxial loading, int. j. fatigue, 30(9), pp. 1646–1658. doi: 10.1016/j.ijfatigue.2007.11.006 0 0.5 1 1.5 0 50 100 150 200 250 300  ref n o . o f co u n te d n o d e s tensiontorsion a‐b (ρref>1) c‐d (ρref=0.5‐0.9) 0 0.5 1 1.5 10 -2 10 -1 10 0 10 1 10 2  ref d m a t2 /d m a t1 t d. benasciutti et alii, frattura ed integrità strutturale, 47 (2019) 348-366; doi: 10.3221/igf-esis.47.26 362 [3] cristofori, a., benasciutti, d., tovo, r. (2011). a stress invariant based spectral method to estimate fatigue life under multiaxial random loading, int. j. fatigue, 33(7), pp. 887–899. doi: 10.1016/j.ijfatigue.2011.01.013 [4] cristofori, a., benasciutti, d. (2014). “projection-by-projection” approach: a spectral method for multiaxial random fatigue, sae technical paper 2014-01-0924. doi: 10.4271/2014-01-0924 [5] benasciutti, d., sherratt, f., cristofori, a. (2016). recent developments in frequency domain multi-axial fatigue analysis. int. j. fatigue, 91, pp. 397–413. doi: 10.1016/j.ijfatigue.2016.04.012 [6] papadopoulos, i.v., davoli, p., gorla, c., filippini, m., bernasconi, a. (1997). a comparative study of multiaxial highcycle fatigue criteria for metals, int j. fatigue, 19(3), pp. 219–35. doi: 10.1016/s0142-1123(96)00064-3 [7] susmel, l, lazzarin, p. (2002). a bi-parametric wöhler curve for high cycle multiaxial fatigue assessment, fatigue fract. engng. mater. struct., 25, pp. 63–78. doi: 10.1046/j.1460-2695.2002.00462.x [8] benasciutti, d. (2014). some analytical expressions to measure the accuracy of the “equivalent von mises stress” in vibration multiaxial fatigue, j. sound vib., 333(18), pp. 4326–4340. doi: 10.1016/j.jsv.2014.04.047 [9] kurek, m., łagoda, t. (2011). comparison of the fatigue characteristics for some selected structural materials under bending and torsion, mater. sci., 47(3), pp. 334–344. doi: 10.1007/s11003-011-9401-x [10] atzori, b., berto, f., lazzarin, p., quaresimin, m. (2006). multiaxial fatigue behaviour of a severely notched carbon steel, int. j. fatigue, 28, pp. 485–493. doi:10.1016/j.ijfatigue.2005.05.010 [11] papuga, j., růžička, m. (2009). aiming at stress-based critical plane multiaxial method for finite life calculation, in: c.m. sonsino, p.c. mckeighan (eds.), proceedings of the second int. conference on material and component performance under variable amplitude loading, darmstadt, pp. 465–474. [12] niełsony, a. (2010). comparison of some selected multiaxial fatigue failure criteria dedicated for spectral method, j. theor. appl. mech., 48(1), pp. 233–254. [13] simbürger, a. (1975). festigkeitsverhalten zäher werkstoffe bei einer mehrachsigen, phasenverschobenen schwingbeanspruchung mit körperfesten und veränderlichen hauptspannungsrichtungen, lbf frauhofer institute, darmstadt, report no. fb-121 (in german). [14] niełsony, a., sonsino, c.m. (2008). comparison of some selected multiaxial fatigue assessment criteria, lbf fraunhofer institute, darmstadt, report no. fb-234. [15] benasciutti, d., tovo, r. (2005). spectral methods for lifetime prediction under wide-band stationary random processes, int. j. fatigue, 27(8), pp. 867–877. doi: 10.1016/j.ijfatigue.2004.10.007 [16] benasciutti, d., tovo, r. (2006). comparison of spectral methods for fatigue analysis of broad-band gaussian random processes, probab. eng. mech., 21(4), pp. 287–299. doi: 10.1016/j.probengmech.2005.10.003 [17] dirlik, t. (1985). application of computers in fatigue analysis. phd thesis, dept. of engineering, university of warwick, uk. [18] pitoiset, x., preumont, a. (2000). spectral methods for multiaxial random fatigue analysis of metallic structures, int. j. fatigue, 22, pp. 541–550. doi: 10.1016/s0142-1123(00)00038-4 [19] benasciutti d., carlet m., zanellati d. (2018) a bandwidth correction to the allegri-zhang solution for accelerated random vibration testing. matec web of conferences, 165, pp. 07006. doi: 10.1051/matecconf/201816507006 [20] bendat, j.s., piersol, a.g. (2010). random data. analysis and measurements procedures, 4th ed., wiley, usa. [21] lutes, l.d., sarkani, s. (2004). random vibrations: analysis of structural and mechanical systems, elsevier, usa. [22] garbow, b.s. (1974). eispack – a package of matrix eigensystem routines, comput. phys. commun., 7(4), pp. 179– 184. doi: 10.1016/0010-4655(74)90086-1 [23] smith, b.t., boyle, j.m., garbow, b.s., ikebe, y., moler, c.b. (1974). matrix eigensystem routines – eispack guide, 2nd ed., lecture notes in computer science, springer, berlin. doi: 10.1007/3-540-07546-1 [24] martin, r.s., reinsch, c., and wilkinson, j.h. (1968). householder's tridiagonalization of a symmetric matrix, num. math., 11, pp. 181–195. (reprinted in: wilkinson, j.h., reinsch, c. (1971). handbook for automatic computation, vol. ii, linear algebra, contribution ii/2, pp. 212–226, springer). [25] bowdler, h., martin, r.s., reinsch, c., and wilkinson, j.h. (1968). the qr and ql algorithms for symmetric matrices, num. math. 11, pp. 293–306. (reprinted in: wilkinson, j.h., reinsch, c. (1971). handbook for automatic computation, vol. ii, linear algebra, contribution ii/3, pp. 227–240, springer). [26] abramowitz, m., stegun, i.a. (1965). handbook of mathematical functions, with formulas, graphs, and mathematical tables, tenth ed., dover. appendix a – spectral description of uniaxial and multiaxial random stress d. benasciutti et alii, frattura ed integrità strutturale, 47 (2019) 348-366; doi: 10.3221/igf-esis.47.26 363 let x(t) be a zero-mean uniaxial random stress. it is characterized, in time-domain, by the autocorrelation function r()=e[x(t)·x(t+)] ( is a time lag) and, in frequency-domain, by a two-sided power spectral density (psd) function s(f), ∞<f<∞. both functions constitute a fourier transform pair (wiener–khintchine relations) [20]:            fefsrerfs fifi d)()(d)()( 22   (18) in practical applications, where negative frequencies have no direct physical meaning, the two-sided spectrum s(f) is replaced by a one-sided spectrum limited to positive frequencies only, which is defined as g(f)=2s(f), 0<f<∞ and zero elsewhere. it is customary to describe s(f) or g(f) by the set of spectral moments [21]: ...,2,1,0d)(d)( 0        nffgfffsf n n n (19) eqn. (19) shows that the variance of x(t) is the zero-order moment var(x(t))=r(0)=λ0, which corresponds to the area of g(f). if x(t) is gaussian, the frequency of zero up-crossings, ν0, and the frequency of peaks, ν0, are [21]: 2 4 p 0 2 0 ;        (20) spectral moments are also combined into bandwidth parameters, as for example [21]: 40 2 2 20 1 1 ,        (21) where 0≤αm≤1 and α1≥α2. bandwidth parameters summarize the shape of a psd. two limiting cases exist: a narrow-band psd with α1→1, α2→1, a wide-band psd with α1<1, α2<1. the quantities in eq. (19)-(21) enter the analytical expressions used by spectral methods for estimating the fatigue damage. the previous definitions can be generalized to a biaxial stress x(t)=(σx(t), σy(t), τxy(t)). by analogy with eq. (18), x(t) is characterized in time-domain by a correlation matrix r()=e[x(t)·x(t+)] and in frequency-domain by a psd matrix, which are a fourier transform pair:            fefef fifi d)()(d)()( 22   srrs (22) in (22), rii()=e[xi(t)·xi(t+)] (i=1, 2, 3) is the auto-correlation function of xi(t) (i=1, 2, 3) and rij()=e[xi(t)·xj(t+)] (i≠j) is the cross-correlation functions between xi(t) and xj(t). in general rji()≠rij(). the psd matrix takes the form:            )()()( )()()( )()()( )( * , * , , * , ,, fsfsfs fsfsfs fsfsfs f xyxyyyxyxx xyyyyyyyxx xyxxyyxxxx s (23) diagonal elements are auto-psds, out-of-diagonal elements are cross-psds. each auto-psd shh(f) is a non-negative realvalued even function of f. cross-psds are complex-valued functions of f and can be written as )()()( fisfsfs qhk c hkhk  , where i is the imaginary unit. the real part  )(re)( fsfs hkchk  (“co-spectrum”) is a real-valued even function of f, the d. benasciutti et alii, frattura ed integrità strutturale, 47 (2019) 348-366; doi: 10.3221/igf-esis.47.26 364 imaginary part  )(im)( fsfs hkqhk  (“quad-spectrum”) is a real-valued odd function of f. the cross-psd can be positive or negative. matrix s(f) is hermitian because )()( fsfs *hkkh  , where * means complex conjugate. finally, the values of the cross-psd are also bounded by the schwartz's inequality )()()( fsfsfs kkhhhk  , which implies that shk(f) must be zero at any frequency where either shh(f) or skk(f) is zero too, whereas it maximum depends on the values of the auto-psds. also in the multiaxial case, a one-sided psd matrix can be introduced: g(f)=2·s(f) for f>0, zero elsewhere. similarly to eq. (19), a matrix of spectral moments of s(f) is defined as: ...,2,1,0d)(d)( 0        nffffff n n n gsλ (24) diagonal elements λn,hh are the moments of auto-psds, out-of-diagonal elements λn,hk (h≠k) the moments of cross-psds: )(d)(d)(;d)( c,, khffsfffsfffsf hk n hk n hknhh n hhn              (25) eqn. (25) shows that the cross spectral moment λn,hk is only function of the co-spectrum )( fs c hk , as the quad-spectrum )( fsqhk is an odd function of f and it simplifies in the integral computation (25) (this finding has somehow to be expected, since spectral moments are real numbers). eqns. (22) and (24) show that =0 yields the covariance matrix c, which also coincides with the matrix λ0 of zero-order moments. variance and covariance terms are:    )(,)(d)(;)(d)( c,0c,0 txtxcovcffstxvarcffs khhkhkhkhhhhhhh          (27) this final result also confirms how cross-psds (which are complex-values functions) are not involved in the covariance matrix (which is real-valued). appendix b – implementation of pbp method in ansys apdl ig. 10 displays the flowchart of the pbp method, along with the scripts used to implement the method in ansys software. the relationship with the previous approach in matlab is also shown for comparison. in both approaches, the analysis is developed in two separate phases that must be executed in sequence. the first phase is managed in ansys by a main program that generates the finite element model (mesh and boundary conditions) and computes the stress psds in each node (“do/endo” loop) through the procedure of random vibration analysis. throughout this phase, the stress psd for each node is stored into a text file (function “psdcovdata2text.mac”). all text files are gathered in a subfolder for subsequent processing. similarly, also the finite element model is saved into a *.cdb file. the list of nodes and elements need to be exported and stored (function “fenode_elem.mac”) only if the next analysis phase is performed in matlab. the second phase, carried out either in ansys or in matlab, computes the damage in each node according to the pbp method. in ansys, this phase is managed by a main program through a “do/endo” loop, in which the stress psd data for each node are first retrieved from text files (function “text2psdcovdata.mac”) and then used as input for subsequent analysis. also the s-n material properties are specified at the beginning of the analysis. at the end of second phase, results are displayed as a contour plot (damage map), or written into a text file (function “pbpresults2text.mac”). f d. benasciutti et alii, frattura ed integrità strutturale, 47 (2019) 348-366; doi: 10.3221/igf-esis.47.26 365 figure 10: flowchart of the apdl script to implement the pbp in ansys software. the relationship with the previous matlab-based procedure (sketched on the right) is shown. the first phase must be run one time only. once stress psds have been calculated and stored, the second analysis phase is performed to compute the fatigue damage. this phase is repeated as many times as are the combinations of s-n properties that need to be scrutinized. in terms of computation time, the first phase may be slightly longer than the second one (especially with low ram memory). just to provide an order-of-magnitude estimate, for the model in fig. 6, determining the nodal stress psds takes about 4 minutes, while applying the pbp method takes about 3 minutes on a 64-bit workstation (cpu 3.80 ghz, 32 gb ram). compared to the ansys/matlab mixed procedure, the new approach entirely based on ansys has the great advantage to exploit the graphical capabilities of the commercial software in displaying the damage contour maps, especially in 3d complex finite element models. another little advantage, though trivial, is that only one type of software is needed to carry out the whole calculation. on the other hand, the main disadvantage of using ansys as the only computation tool is due to a greater complexity and less flexibility of apdl language in performing the fatigue damage calculations required in the pbp method. although the apdl language – as matlab – can execute a lot of algebraic and trigonometric functions, and it can even manage “do/endo” and “dowhile/endo” loops, it does not have functions to compute the eigenvalues/eigenvalues of a square matrix or the gamma function γ(-) directly. therefore, an apdl macro (called “eigen.mac”) has been written to deal with eigenvalues/eigenvalues computation. this macro took the cue from the software library eispack, written in fortran [22,23]. in particular, the functions involved are: tred2 for tridiagonalization of a symmetric matrix [24], tql2 for the qr eigenvalue algorithm [25]. instead, the gamma function γ(–) was computed by means of stirling’s approximation formula, see for example [26]. to conclude, it is worth emphasizing that the flowchart here described for ansys software is very general and it can easily be adapted to any other finite element code that perhaps the reader knows better. nomenclature a matrix of constants c, c’ covariance matrix of x(t) and s(t) c'p covariance matrix in the principal coordinate system dtb(ωp,i(t)) damage of stress projection ωp,i(t) by tb method d. benasciutti et alii, frattura ed integrità strutturale, 47 (2019) 348-366; doi: 10.3221/igf-esis.47.26 366 d(ω) total damage for stress vector ω(t) e[–] expected value g(f) one-sided psd matrix of x(t) kσ, kτ inverse slope of tension and torsion s-n curve ajj a2, amplitude of the square root of second invariant of stress deviator ja,, ja,τ, k, kτ amplitude strengths and inverse slopes of the tension and torsion s-n curves in mwd ja,ref, kref amplitude strength and inverse slope of the reference s-n curve in mwd na reference number of cycles rij correlation coefficient between xi(t) and xj(t) r() correlation matrix of x(t) r'() correlation matrix of s(t) s(t) deviatoric stress vector sh(f) two-sided psd of hydrostatic stress σh(t) s(f) two-sided psd matrix of x(t) s'(f) two-sided psd matrix of s(t) s'p(f) two-sided psd matrix in the principal coordinate system tf time to failure (seconds) u matrix of eigenvectors (rotation matrix) var(xi(t)) variance of stress xi(t) vh variance of hydrostatic stress σh(t) x(t) stress vector in physical space  time lag ηtb,i bandwidth correction factor for the psd of stress projection ωp,i(t) ρref stress ratio σa, τa strength amplitudes at na cycles σh(t) hydrostatic stress σx(t), σy(t), τxy(t) stress components σ(t) stress tensor σ'(t) deviatoric stress tensor ωp,1(t), ωp,2(t), 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can be opened with acrobat and adobe reader 5.0 and later.) >> /namespace [ (adobe) (common) (1.0) ] /othernamespaces [ << /asreaderspreads false /cropimagestoframes true /errorcontrol /warnandcontinue /flattenerignorespreadoverrides false /includeguidesgrids false /includenonprinting false /includeslug false /namespace [ (adobe) (indesign) (4.0) ] /omitplacedbitmaps false /omitplacedeps false /omitplacedpdf false /simulateoverprint /legacy >> << /addbleedmarks false /addcolorbars false /addcropmarks false /addpageinfo false /addregmarks false /convertcolors /converttocmyk /destinationprofilename () /destinationprofileselector /documentcmyk /downsample16bitimages true /flattenerpreset << /presetselector /mediumresolution >> /formelements false /generatestructure false /includebookmarks false /includehyperlinks false /includeinteractive false /includelayers false /includeprofiles false /multimediahandling /useobjectsettings /namespace [ (adobe) (creativesuite) (2.0) ] /pdfxoutputintentprofileselector /documentcmyk /preserveediting true /untaggedcmykhandling /leaveuntagged /untaggedrgbhandling /usedocumentprofile /usedocumentbleed false >> ] >> setdistillerparams << /hwresolution [2400 2400] /pagesize [612.000 792.000] >> setpagedevice shot peening processes to obtain nanocrystalline surfaces in metal alloys: a. takahashi et alii, frattura ed integrità strutturale, 48 (2018) 473-480; doi: 10.3221/igf-esis.48.45 473 focussed on “crack paths” fatigue crack growth simulation of two non-coplanar embedded cracks using s-version finite element method akiyuki takahashi, ayaka suzuki, masanori kikuchi tokyo university of science, japan takahash@rs.noda.tus.ac.jp, 7516629@ed.tus.ac.jp, kik@rs.noda.tus.ac.jp abstract. in this paper, the fatigue crack growth simulation of two noncoplanar embedded cracks using the s-version finite element method is presented, and the validity and reliability of the alignment rule for two noncoplanar cracks are evaluated. according to the previous numerical and experimental studies on two non-coplanar surface cracks, the simulated fatigue crack growth behavior is categorized into five patterns to discuss the criteria for the application of the alignment rule. the results suggest that the strength of interaction between the non-coplanar embedded cracks is similar to that between non-coplanar surface cracks. finally, the interaction of the cracks is evaluated by the stress intensity factor, and the categorization of the fatigue crack growth behavior is discussed by the stress intensity factor. it can be found that the boundary corresponding to the criteria of the application of the alignment rule can be determined as the ratio of the stress intensity factor is 4%. thus, instead of making a decision of the fatigue crack growth pattern based on the visual inspection, the ratio of the stress intensity factor can be used, and should give more quantitative evaluation of the interaction of two non-coplanar embedded cracks. keywords. non-coplanar embedded cracks; fatigue crack growth; stress intensity factor; alignment rule; s-version finite element method. citation: takahashi, a., suzuki, a., kikuchi, m., fatigue crack growth simulation of two non-coplanar embedded cracks using sversion finite element method, frattura ed integrità strutturale, 48 (2019) 473-480. received: 23.11.2018 accepted: 12.12.2018 published: 01.04.2019 copyright: © 2019 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. introduction atigue crack growth is a classical but critical issue to ensure the structural reliability. up till now, many experimental and numerical studies on the fatigue crack growth of surface cracks have been conducted to model the complex behavior of fatigue crack growth and establish an accurate evaluation method of the residual fatigue life [1-3]. in the fitness-for service (ffs) code for nuclear power plants, flaws detected in structural components are assumed to be simple elliptical cracks and are evaluated using well-established stress intensity factor calculation methods for the simple elliptical cracks [4]. if two non-coplanar cracks appear and are detected in their close vicinity, according to the alignment rule in the ffs code, one of the cracks is projected onto the plane of the other crack. furthermore, if the projected crack touches or overlaps with the other crack, the cracks are combined into a simple elliptical crack. the combination of cracks is controlled f mailto:takahash@rs.noda.tus.ac.jp mailto:7516629@ed.tus.ac.jp http://www.gruppofrattura.it/va/48/2270.mp4 a. takahashi et alii, frattura ed integrità strutturale, 48 (2018) 473-480; doi: 10.3221/igf-esis.48.45 474 by the combination rule in the ffs code. the stress intensity factor calculation methods in the ffs code can then be applicable to the simple elliptical cracks. therefore, the validity and reliability of the alignment and combination rules are of great interest to ensure the appropriate assessment of the structural integrity. in order to evaluate the validity and reliability of the alignment and combination rules, it is necessary to check the fatigue crack growth behavior and the interaction of the non-coplanar cracks. owing to the development of computers and computer simulation techniques, computer simulation is now a powerful approach to complex crack growth problems. kamaya et al. has applied the s-version finite element method (s-fem) to fatigue crack growth simulations, and successfully simulated complex fatigue crack growth behavior [5]. using the s-fem, the cracks are modelled by local meshes. the local meshes are then superimposed onto a global mesh, which models the geometry and boundary conditions of the structure of interest. the global and local meshes can be separately modelled so that the complexity in the mesh generation of cracked structures can be drastically reduced. this remarkable property of sfem in the mesh generation process is a great advantage in the fatigue crack growth simulation, where the finite element meshes must be repeatedly remodeled in accordance with the updated crack shape. in this paper, the fatigue crack growth simulation of two non-coplanar embedded cracks using the s-fem is presented, and the validity and reliability of the alignment rule for two non-coplanar cracks are evaluated. according to the previous numerical and experimental studies on two non-coplanar surface cracks [6], the simulated fatigue crack growth behavior is categorized into five patterns to discuss the criteria for the application of the alignment rule. finally, the interaction of the cracks is evaluated by the stress intensity factor, and the categorization of the fatigue crack growth behavior is discussed in terms of the stress intensity factor. computational method n this study, the fatigue crack growth behavior of two non-coplanar cracks are simulated using the s-fem. in the sfem, as shown in fig. 1, the geometry and boundary conditions of structures are modeled with a global mesh. cracks are modeled with local meshes separately from the global mesh, and can be inserted into the structures by superimposing the local meshes on the global mesh. the displacement functions of the global and local meshes are independently defined. as an example, if the structure has two cracks, the problem is modelled with a global mesh and two local meshes for each crack. the displacement function for the global mesh is defined as ui g (x), and for the local meshes, ui l1 (x) and ui l2 (x). by superimposing the displacement functions, the displacement field of the structure is defined as ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( )1 2 1 2 1 2 ω ω ω ω ω ω ω ω ω g l l ig i g l g i i i i g l g i i i g l l i i i i xu x u x u x x u x u x u x x u x u x u x x   − + −  +  − =  +  −  + +  (1) where, g is the entire volume of the structure, l1 and l2 are for the volumes defined by the local meshes, and i is the volume overlapped with the local meshes. in order to preserve the continuity of the displacement function at the boundaries of local meshes, the displacement at the boundaries of the local meshes are fully constraint. thus, the displacement can be equal to the displacement of global mesh. the displacement equation can then be calculated in accordance with the definition of displacement function given in eqn. (1). the detailed information about the s-fem can be found elsewhere [7]. since the local meshes can be modelled separately from the global mesh, the complex shape of cracks can be easily modelled in the s-fem. thus, due to the remarkable advantage of the s-fem in the modeling of cracks, the fatigue crack growth simulation, where the finite element mesh for cracks must be repeatedly updated, can be performed easily by the s-fem. in our developed fatigue crack growth simulation system, the crack front shape is modelled with a number of segments, and the local meshes are automatically modeled using the segment data. the global mesh is prepared only at the beginning of the simulation, and is used repeatedly for the entire simulation. the energy release rate along the crack tip is calculated by the virtual crack closure method (vccm) [8]. the energy release rate calculated by the vccm is simply converted into the stress intensity factor. then, the stress intensity factor range is calculated with the stress intensity factor and the stress ratio. using the stress intensity factor range, the crack growth amount and direction are then determined by the paris law [9] and i a. takahashi et alii, frattura ed integrità strutturale, 48 (2018) 473-480; doi: 10.3221/igf-esis.48.45 475 the criteria proposed by richard et al. [10]. the positions of crack tip segments are updated in accordance with the calculated crack growth amount and direction. figure 1: a schematics of the s-fem. the geometry and boundary conditions are modeled with global mesh. the cracks are modeled with local meshes separately from the global mesh. the local meshes are superimposed on the global mesh to obtain the displacement solution of the problem. figure 2: finite element mesh for the fatigue crack growth simulation of two non-coplanar embedded cracks. each cracks is modelled with each local mesh separately. the position of the center of two cracks are at 100 mm distance from the surface of the specimen. the horizontal separation and vertical height of the crack tips are denoted by h and s. the maximum tensile stress is 127 mpa, and the stress ratio r is 0.1. the displacement at the bottom surface is fully constraint. fatigue crack growth simulation of two non-coplanar embedded cracks n this paper, we focus on the validity and reliability of the alignment rule in the ffs code, the fatigue crack growth behavior of two non-coplanar embedded cracks are simulated. fig. 2 shows the finite element model of the fatigue crack growth simulation of two non-coplanar embedded cracks. two circular embedded cracks are embedded in a rectangular shape of specimen. the size of the rectangular specimen in x, y and z direction are 750 mm, 250 mm and 200 mm, respectively. the center of two cracks are located at 100 mm distance from the surface of the specimen, and the cracks i a. takahashi et alii, frattura ed integrità strutturale, 48 (2018) 473-480; doi: 10.3221/igf-esis.48.45 476 are aligned parallel to the surface. the rectangular shape of the specimen is modeled with a global mesh. 10-noded tetrahedral elements are used for the global mesh. the numbers of elements and nodes are 115,200 and 171,245, respectively. on the other hand, the two cracks are modeled with two local meshes separately. 20-noded hexahedral elements are used for the local meshes. the initial numbers of elements are nodes are 13,680 and 61,210, respectively. the half-depth and length of crack is denoted by a and c. the initial horizontal and vertical distance of the two cracks are denoted by s and h. in the ffs code, the alignment rule is compiled with the horizontal and vertical distance of two cracks, the horizontal and vertical distance are changed to study how the two cracks grow under cyclic loading. the maximum tensile stress of the cyclic loading is assumed to be 127 mpa, and the stress ratio r is set to 0.1. the tensile stress is applied to the finite element model by giving corresponding traction to the top surface of the specimen. the displacement of the bottom surface is fully constraint. the material is assumed to be a steel, and 1.67×10-12 and 3.23 are used as the coefficient and exponent of the paris law [5]. in the paris law, the units of stress intensity factor range k and crack growth rate da/dn are mpamm0.5 and m/cycle, respectively. (a) fatigue crack growth patterns (b) jsme criterion figure 3: (a) fatigue crack growth patterns of two non-coplanar cracks and (b) the alignment rule given by the japan society for mechanical engineers (jsme). the red bold line in the right figure is determined by the experiments of the fatigue crack growth of surface cracks. finite element mesh for the fatigue crack growth simulation of two non-coplanar embedded cracks. each crack. the alignment rule is defined by the horizontal separation s and the vertical height h. the jsme criterion fully covers the area defined by the bold red line. ando et al. performed experiments of the fatigue crack growth of surface cracks, and categorized the fatigue crack growth behavior into five patterns as shown in fig. 3 [3]. in the pattern a, the crack tips meet each other, and the cracks are naturally combined. in the pattern b, the crack tip direction is within the spacing between the initial crack tips. in the pattern c, the crack tips go to the initial crack. in the pattern d, the crack tips pass the initial cracks. in the pattern e, only one of cracks grows horizontally, and never meet the other crack. ando et al. determined that the alignment rule must be applied if the fatigue crack growth behavior is patterns a, b and c [3]. the border of the application and non-application of the alignment rule shown in fig. 3 with the bold red line is obtained by the experiments of surface cracks; therefore, in order to clarify the applicability of the alignment rule to embedded cracks, the fatigue crack growth behavior of two non-coplanar embedded cracks must be observed, and the crack growth behavior must be categorized into the five patterns. the fatigue crack growth behavior of two non-coplanar embedded cracks is simulated. the crack size is fixed to a=2.5 mm and c=2.5 mm. the initial crack tip distance parameters s and h are changed in a range from 2.5 mm to 25 mm. the fatigue crack growth behaviors obtained by the s-fem simulations for s=10 mm are shown in fig. 4. because the location of the two cracks is non-coplanar, the fatigue crack growth behavior is also non-planar, and the s-fem simulation technique successfully reproduces such a complex fatigue crack growth behavior. the fatigue crack growth behaviors can be categorized into pattern b, c and d as shown in the figure. fig. 5 shows the interaction map of the two non-coplanar embedded cracks obtained by the s-fem simulations. ando et al. discussed about the criteria of the application of the alignment rule based on the experiments of the fatigue crack growth of surface crack. the border of the application a. takahashi et alii, frattura ed integrità strutturale, 48 (2018) 473-480; doi: 10.3221/igf-esis.48.45 477 determined by ando et al. almost coincides with the boundary between the pattern c and d obtained by the s-fem simulations. the results suggest that the strength of interaction between the non-coplanar embedded cracks is similar to that between non-coplanar surface cracks. therefore, the alignment rule given by jsme can still give a conservative evaluation of not only surface cracks and also embedded cracks. (a) h=2.5 mm (b) h=5.0 mm (c) h=7.5 mm figure 4: fatigue crack growth behavior of two non-coplanar embedded cracks. the horizontal separation s of the initial crack tips is 10 mm, and the vertical height h is (a) 2.5 mm, (b) 5.0 mm and (c) 7.5 mm. only crack shape is displayed. the red line shows the crack tip. the top figure is the top view of the crack shape, and the bottom figure is the front view of the crack shape. the crack growth behavior is categorized into (a) pattern b, (b) pattern c, and (c) pattern d, respectively. figure 5: interaction map of two non-coplanar embedded cracks obtained by the s-fem simulations. the marks shows the fatigue crack growth patterns. the borders determined by the jsme and ando et al. are also plotted. a. takahashi et alii, frattura ed integrità strutturale, 48 (2018) 473-480; doi: 10.3221/igf-esis.48.45 478 as shown in fig. 3 and 5, the alignment rule in the ffs code is established with the horizontal and vertical distance of two non-coplanar cracks. however, the unit of the horizontal and vertical distance is defined as mm. therefore, there is a question on the validity of the application of the alignment rule to the other size of cracks. to check if it is valid to apply the same alignment rule to the other size of cracks, fatigue crack growth simulations of two non-coplanar cracks of 2c=10 mm with various horizontal and vertical distances are performed. the results are shown in fig. 6. in the figure, the solid and dotted lines are taken from respectively the jsme ffs code and experimental data obtained by ando et al. [3]. in fig. 5 where the crack size is 2c=5 mm, the numerical results are fully covered by the dotted line taken from the experimental data. however, in fig. 6, the some of the numerical results are over the dotted line. therefore, the categorization of the fatigue crack growth behavior of two non-coplanar cracks has a dependence on the initial crack size. thus, the alignment rule is not applicable to arbitrary size of embedded cracks. to remove the dependence of the categorization on the initial crack size shown in fig. 6, the horizontal and vertical distance of two non-coplanar cracks are normalized by the half of the initial crack size c. the result is shown in fig. 7. as a result of the normalization of the horizontal and vertical distances by the half of the initial crack size, the categorizations of the fatigue crack growth behavior of two non-coplanar cracks with 2c=5 mm and 10 mm become almost identical. thus, the results suggest that the horizontal and vertical distance of two non-coplanar cracks should be normalized by the initial crack size to apply the alignment rule to arbitrary size of cracks. figure 6: interaction map of two non-coplanar embedded cracks obtained by the s-fem simulations. the initial crack size is 2c=10mm. the plot is based on the real length of h and s. the borders determined by the jsme and ando et al. are also plotted. (a) (b) figure 7: interaction map of two non-coplanar embedded cracks obtained by the s-fem simulations. the initial crack sizes are (a) 2c=5mm and (b) 2c=10mm. the plot is based on the length of h and s normalized by the half size of crack c. the borders determined by the jsme and ando et al. are also plotted. a. takahashi et alii, frattura ed integrità strutturale, 48 (2018) 473-480; doi: 10.3221/igf-esis.48.45 479 the categorization of the fatigue crack growth behavior and the discussion on the application of the alignment rule, in this study, is based on the visual inspection. in order to evaluate and discuss the alignment rule, the stress intensity factor of two non-coplanar embedded cracks is examined. as shown in fig. 8, the stress intensity factor of two circular cracks is calculated. in the calculation, the horizontal separation of crack tips is zero. in order to investigate the interaction of the cracks, the stress intensity factor of a single crack with the same shape is also calculated. fig. 8 shows an example of the stress intensity factor distribution along the crack tips. the stress intensity factor near the other crack increases as a result of the interaction. comparing the stress intensity factor of two non-coplanar embedded cracks with that of the single crack, the strength of interaction is represented as the ratio of the maximum stress intensity factor increase to the stress intensity factor of the single crack. fig. 9 shows the interaction map with the ratio. as shown in the figure, the boundary between the pattern b and c can be determined as the ratio of the stress intensity factor is 10%. on the other hand, as for the boundary between the pattern c and d, which is the criteria of the application of the alignment rule, the boundary can be determined as the ratio of the stress intensity factor is 4%. thus, instead of making a decision of the fatigue crack growth pattern based on the visual inspection, the ratio of the stress intensity factor can be used, and should give more quantitative evaluation of the interaction of two non-coplanar embedded cracks. figure 8: stress intensity factor distribution along the crack tip of two non-coplanar embedded cracks. the stress intensity factor increases near the other crack. the position along the crack tip is denoted with the angle theta defined in the figure (left). in order to study the interaction of two embedded cracks, the stress intensity factor of a single embedded crack is also calculated. figure 9: interaction map of two non-coplanar embedded cracks. the value written in the left side of the figure shows the ratio of the maximum stress intensity factor of two non-coplanar embedded cracks to the stress intensity factor of the single crack. the horizontal and vertical axis of the figure is normalized by the initial half-length of the crack. a. takahashi et alii, frattura ed integrità strutturale, 48 (2018) 473-480; doi: 10.3221/igf-esis.48.45 480 conclusions atigue crack growth simulations of two non-coplanar embedded cracks are performed using the s-fem, and the fatigue crack growth behavior is evaluated by the visual inspection and the ratio of stress intensity factor. the sfem has a great advantage in the fatigue crack growth simulation, because the cracks can be modelled as local meshes separately from the global mesh, which is for the geometry and boundary conditions of structures. using the sfem, the fatigue crack growth simulation could be performed automatically. we need to prepare only the global mesh and the crack front information, which is the number of segments along the crack tip. the complex non-planar behavior of two non-coplanar embedded cracks could be simulated with the s-fem. then, the fatigue crack growth behavior was categorized into five patterns to discuss the similarity of the fatigue crack growth behavior of embedded cracks and that of surface cracks. the results suggest that the location and shape of the boundary between the pattern c and d, which corresponds to the criteria for the application of the alignment rule, is very similar to those for the surface cracks. therefore, the existing alignment rule is applicable to the embedded cracks, although the rule is established based on the numerical and experimental results of surface cracks. however, because the horizontal and vertical distance of two cracks are described with a mm unit, the alignment rule gives different results to different initial size of cracks. to remove the dependence of the alignment rule on the initial crack size, the horizontal and vertical distance of two cracks should be normalized by the half size of initial crack. finally, the stress intensity factor of two non-coplanar embedded cracks and single cracks is calculated. then, it could be found that the ratio of the maximum stress intensity factor of two non-coplanar embedded cracks to the stress intensity factor of the single crack can be a parameter to determine the fatigue crack growth pattern and the criteria for the application of the alignment rule. references [1] brighenti r., carpinteri a. (2013). surface cracks in fatigued structural components: a review, fatigue frac. eng. mat. struct., 36, pp. 1209-1222. [2] rozumek d., faszynka s. (2017). fatigue crack growth in 2017a-t4 alloy subjected to proportional bending with torsion, frattura ed integrità strutturale, 42, pp. 23-29 [3] sniezek l, slezak t, grzelak k, hutsaylyuk v. (2016). an experimental investigation of propagation the semi-elliptical surface cracks in an austenitic steel. int. j. pressure vessels and piping, 144, pp. 35–44. [4] codes for nuclear power generation facilities, rules on fitness-for-service for nuclear power plants, jsme, (2016). [5] kamaya, m., miyokawa, m., kikuchi, m. (2010). growth prediction of interacting surface cracks of dissimilar sizes, eng. frac. mech., 77, pp. 3120-3131. [6] ando, k., hirata, t., iida, k. (1983). an evaluation technique for fatigue life of multiple surface cracks: part 2: a problem of multiple parallel surface cracks, j. marine sci. tech., (in japanese), 153, pp. 352-363. [7] fish, j., markolefas, s., guttal, r., nayak, p. (1994). on adaptive multilevel superposition of finite element meshes, appl. numer. math., 14, pp. 135-164. [8] okada, h., higashi, m., kikuchi, m., fukui, y., kumazawa, n. (2005). three dimensional virtual crack closure-integral method (vccm) with skewed and non-symmetric mesh arrangement at the crack front, eng. frac. mech., 72, pp. 17171737. [9] paris, p., erdogan, f. (1963). a critical analysis of crack propagation laws, j. basic eng., trans. american society of mechanical engineers, pp. 528-534 [10] richard, h.a., fulland, m., sander, m. (2005). theoretical crack path prediction, fatigue & frac. eng. mater. sci. 28, pp. 3-12. f microsoft word 2258 j. prawin et alii, frattura ed integrità strutturale, 48 (2019) 513-522; doi: 10.3221/igf-esis.48.49 513 focused on “showcasing structural integrity research in india” damage localization of closing cracks using a signal decomposition technique j. prawin, a. rama mohan rao csir structural engineering research centre, india prawinpsg@gmail.com, http://orcid.org/0000-0002-7579-025x arm2956@yahoo.com, http://orcid.org/0000-0002-6405-3633 abstract. fatigue cracks are a common occurrence in engineering structures subjected to dynamic loading and need to identify at its earliest stage before it leads to catastrophic failure. the presence of fatigue-breathing crack or closing cracks is usually characterised by the presence of sub and superharmonics in the response of the structure subjected to harmonic excitation. it should be mentioned here that the amplitude of nonlinear harmonics are of very less order in magnitude when compared to linear or excitation component. further, these nonlinear components often get buried in noise as both are having matched (low) energy levels. the present work attempts to decompose the acceleration time history response using singular spectrum analysis and propose a strategy to extract the nonlinear components from the residual noisy time history component. a new damage index based on these extracted nonlinear features is also proposed for closing crack localization. the effectiveness of the proposed closing crack localization approach is illustrated using detailed numerical studies and validated with lab level experimentation on the simple beam-like structure. it can be concluded from the investigations that the proposed signal decomposition based damage localization technique can detect and locate more than one crack present in the structure. keywords. pairwise eigenvalues; singular spectrum analysis; closing crack; damage localization; nonlinearity; bilinear. citation: prawin, j., rama mohan rao, a., damage localization of closing cracks using a signal decomposition technique, frattura ed integrità strutturale, 48 (2019) 513-522. received: 15.11.2018 accepted: 22.02.2019 published: 01.04.2019 copyright: © 2019 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. introduction ingular spectrum analysis (ssa) is a popular multivariate analysis technique widely used for signal decomposition and signal approximation. ssa essentially can be described in four steps namely embedding, singular value decomposition (svd), grouping and diagonal averaging. the complete description of the technique can be found in golyandina et al., [1]. ssa is popularly used in several diverse areas like climate change, geophysical phenomena, mineral processing, seismic data processing, and telecommunication applications [1-3]. ssa has been recently applied in the area of structural health s http://www.gruppofrattura.it/va/48/2258.mp4 j. prawin et alii, frattura ed integrità strutturale, 48 (2019) 513-522; doi: 10.3221/igf-esis.48.49 514 monitoring and found to be very effective. a detailed review of earlier works of ssa on structural health monitoring applications can be found in prawin et.al, [4]. in most of the earlier works on ssa in shm applications, the noisy components are neglected during the reconstruction and transformation back to the actual response. oliveria et al., [5] recently reported that the discontinuity related damage sensitive features are found in these ignored residual noise components of the actual response. in view of this, we process further the residual (noisy) components obtained from ssa to reliably check whether any higher order or superharmonic resonances present or buried in the residual signal. further, the proposed ssa based decomposition technique can reliably extract all the higher order harmonic components in contrast to the existing approaches which are based on only first few harmonics and the damage detection can be enhanced with consideration of more number of super harmonics. signal decomposition using singular spectrum analysis he breathing crack is usually assessed by the spectrum of the response of the structure measured at a particular location. the presence of super harmonics (i.e. higher order harmonics) apart from the fundamental excitation harmonic confirms the nonlinear behaviour induced by closing crack when the cracked structure is subjected to harmonic excitation. earlier researchers [6-8] basically employed the ratio of the power spectrum amplitude of the response at second or third order harmonic to the first order/linear/excitation harmonic as damage index for closing crack localization. few other researchers [6-8] have used the spatial curvature of the ratio of the power spectrum of superharmonics to excitation harmonic as damage index due to the fact that the second spatial derivative magnifies the cracks/discontinuity in the response. further, most of the existing techniques consider only one or two higher order harmonic frequencies for closing crack localization and the rich damage sensitive features present in the higher order harmonics have been ignored. the basic reason behind this is that the amplitude of super harmonics (i.e. nonlinear harmonics) are of very less order in magnitude when compared to linear fundamental excitation harmonic. these higher order nonlinear harmonic components also often get buried in noise and difficult to conclude whether it is noise or nonlinear component as both are having matched (low) energy levels. therefore, the extraction of these harmonics under noisy environment and damage detection at its incipient stage is highly challenging. in the proposed closing crack localization technique, the cracked structure i.e. with closing crack is subjected to harmonic excitation with a particular single frequency; therefore the response is also harmonic in nature. as mentioned earlier, the response of the cracked structure, i.e. with closing crack vibrates at the excitation frequency as well as the higher order super harmonics of the excitation frequency. in contrast, the healthy structure (i.e., without breathing crack) vibrates only at excitation frequency due to single tone harmonic excitation. since the response of the structure is harmonic in nature, the decomposition of the time history data of the cracked structure, i.e., structural or structural component with closing/breathing crack at a particular location, by ssa contains only harmonic components (i.e. both linear excitation and nonlinear super harmonic harmonics) and noise. harmonic signals basically exhibit two eigen triples with close singular values [1-5]. therefore, this property helps in easy interpretation and identification of the harmonic signal components during decomposition of the measured response by ssa. the number of pairwise eigenvalues indicates the number of harmonic components present in the response. since the structure is excited by a single tone harmonic load, there exists only one pairwise eigenvalue for the structure without a closing crack. in contrast, there will be more than one pairwise eigenvalues exist for the structure with closing crack due to the presence of super harmonics. these harmonic components (i.e. pairwise singular values) are present in descending order (i.e. decreasing) of their energy corresponding to each frequency due to the property of ssa. the first pairwise eigenvalue will be always the linear excitation harmonic component and it always exhibits dominant energy for both healthy and cracked structure (i.e. structure with breathing crack). this can be easily verified by the fourier power spectrum of the respective harmonic component. the subsequent pairwise singular values (i.e. present with low energy levels) represent the nonlinear superharmonic components. the contribution of higher energy in the case of fundamental excitation harmonic is clearly justified by the fact that the amplitude of fundamental harmonic is of two or three order higher in magnitude when compared to the amplitude of nonlinear superharmonic. in the present work, the linear components can be isolated by the first pairwise singular value. it should be mentioned here even though there is no theoretical evidence, extensive studies carried out on closing crack problems reveal that the energy content of the dominant pairwise eigenvalues corresponding to linear response constitutes 99% of the total energy [4, 7,9]. however, to be on the safer side, we prefer to use the first pairwise singular value for extracting the linear fundamental excitation harmonic component. in order to reliably extract the low energy nonlinear harmonics, we apply ssa again on the residual (noisy) components obtained from ssa after ignoring linear harmonic components. this is in contrast to the earlier works [1-3] where the noisy t j. prawin et alii, frattura ed integrità strutturale, 48 (2019) 513-522; doi: 10.3221/igf-esis.48.49 515 components are usually neglected during the reconstruction of the response. ssa has been performed repeatedly twice on the response in the proposed closing crack localization technique, to isolate the linear components from the actual response in the first instance and to identify the presence or absence of the higher order harmonic resonances from the residual/noisy part of the signal in the second instance. it should be mentioned here that the residual components contain the nonlinear components. the higher order harmonic components, induced by the nonlinear behaviour of the closing crack, are usually buried in the residual component and it is easily detected by the same pairwise eigenvalue concept mentioned earlier in the proposed technique. this clearly demonstrates the ability of the ssa in decomposing the linear, nonlinear harmonic and noise components from the total response. damage diagnostic scheme based on singular spectrum analysis the steps involved in closing crack localization based on the signal decomposition technique are 1. decompose the acceleration time history response obtained at various spatial locations across the structure using ssa. 2. the linear and nonlinear harmonic components are identified through pairwise eigenvalues concept. the first pair indicates the linear component and the rest are nonlinear harmonic components generated by the closing crack. however, these nonlinear harmonics are buried in the noisy components and difficult to extract reliably at this stage 3. reconstruct the residual components (eliminating first eigen pair component) by grouping and diagonal averaging of ssa technique. 4. decompose the residual time history response obtained from step-3 using ssa. the nonlinear components are identified by pairwise eigenvalue concept. 5. the cumulative sum of the peak amplitudes of each of the nonlinear harmonic component is considered as damage index. the damage index is defined as follows 1 nonlinear component) nf peak ,k k di( i ) a (sup erharmonic    (1) where di (i) indicates the damage index of the ith degree of freedom (or sensor node) and nf, peak ,ka represent the number of superharmonic frequencies and the peak fourier power spectrum amplitude of the selected ‘k’th nonlinear harmonic component. the damage index is computed for each sensor location. the sensor node exhibiting the higher magnitude of magnitude index is the true spatial location of the breathing crack numerical investigations simple beam like structures such as simply supported beam and cantilever beam, simulated with closing cracks at varied spatial locations are chosen as numerical examples; to test the ssa based closing crack localization technique. since we have also carried out experimental investigations using the cantilever beam, and the numerical investigations carried out on both the beams are similar in nature, we present only the results of the simply supported beam in this paper to avoid repetition or redundancy. however, the experimental studies on the cantilever beam are presented later in this paper. steel cracked simply supported beam given in fig. 1 is chosen in the present work for numerical investigation. the span of the beam is 0.7m and has an area of 4e-4m2 and moment of inertia as 0.667e-8m4. the natural frequencies of the underlying linear healthy beam are found to be 89.671hz, 354.689hz, 799.16hz, 1419.46hz, 1711.46hz and 2218.17hz. the finite element model of the beam considers standard one-dimensional euler-bernoulli beam elements with two nodes per beam element and each node have three degrees of freedom; longitudinal displacement, translational displacement and bending rotation. heavy side step function, widely preferred by the researchers is used in the present work to model the opening-closing behaviour of the breathing crack. the damaged element stiffness matrix with the bilinear behaviour induced by the rotations ( ,  i j  ) at the nodes of the respective damaged element [6-9] is given by                  1 0 i j i j d i j c i j i j h θ θ , θ θ k k h θ θ k : h θ θ , θ θ (2) a j. prawin et alii, frattura ed integrità strutturale, 48 (2019) 513-522; doi: 10.3221/igf-esis.48.49 516 where h, k, kd, kc indicates the heaviside step function, undamaged, damaged (breathing crack) and cracked (open) stiffness of a particular element connected by nodes ‘i’ and ‘j’. the crack depth is defined in the cracked stiffness matrix kc. the detailed formulations are deliberately omitted here as they are of least consequence. figure 1: simply supported beam with a closing crack. the beam is discretised with 10 elements. the closing crack is simulated near 2/3 span of the simply supported beam from the left end i.e. element no. 7 with the crack depth of about 7% of the total depth. the beam is excited at the centre with an excitation frequency of 90hz. the acceleration time history responses are obtained at nine locations (i.e. finite element model discretised with 10 elements) spatially across the beam with a spacing of 0.07m per element. the obtained acceleration time history spatially across the beam is polluted with 10% standard white gaussian noise (i.e. snr= 30) before postprocessing to test the applicability of the proposed signal decomposition technique in the presence of noise. however, investigations have also been carried out without measurement noise for comparison purposes. 0 90 180 270 360 450 540 630 0.01 0.1 1 10 100 0.01n (w ithout noise) 100 n (w ithout noise) frequency (hz) p s d  a m p li tu d e 0 90 180 270 360 450 540 630 0.01 0.1 1 10 100 100 n (w ithout noise) 100n (w ith 10% noise) frequency (hz) p s d  a m p li tu d e (a) (b) figure 2: fourier power spectrum (a) undamaged and damaged data without noise (b) damaged data with and without noise the acceleration time history responses are obtained from the cracked structure at two different excitation amplitudes of 0.01n and 100n. the spectral density plot of the cracked structure obtained under these two different excitation amplitudes are shown in fig. 2(a). the spectral density plot of the cracked structure using noise-free and noisy measurements under 100n excitation is presented in fig. 2(b). the spectral density plot corresponding to 0.01n, presented in fig. 2(a) shows a single peak at 90 hz. this confirms that the cracked structure behaves linearly under 0.01n excitation as the structure vibrates only at its excitation frequency. the spectral density plot corresponding to 100n excitation with noise-free measurements, in contrast to 0.01n excitation vibrates not only at its excitation frequency i.e. 90hz but also at its super harmonics, 90hz, 180hz, 270hz, 360hz, and so on. this is evident from the peaks at those frequencies in fig. 2 (a). it can be observed from fig. 2(a) that the peak at fundamental excitation harmonic exhibit very high magnitude when compared to the magnitude of the peaks at their respective super harmonics. the presence of additional superharmonics apart from the fundamental excitation harmonic concludes the nonlinear behaviour induced by the closing cracks. it can be observed from fig. 2(b) that the spectral density plot of the cracked structure corresponding to 100n excitation with noisy measurements shows a peak at the excitation frequency and its superharmonics. however, the peak at first superharmonic, i.e. 180hz is only clearly visible, while the higher order superharmonics get buried in the noise as both exhibit similar energy j. prawin et alii, frattura ed integrità strutturale, 48 (2019) 513-522; doi: 10.3221/igf-esis.48.49 517 levels. it should be mentioned here that using the conventional spectral analysis, only one or two superharmonics can be extracted reliably under noisy environment while using the proposed approach (ssa), a large number of superharmonics are extractable. in the present work, for the application of ssa on the time history response, the window length is selected as the time lag corresponding to the first zero crossing between l/4 and l/2, computed based on autocorrelation [4]. more details related to the choice of window length are not discussed here, as it deviates from the scope of the present work. however, details on the choice of the window length can be found in prawin et.al. [4]. 0 500 1000 1500 2000 2500 ‐1.0 ‐0.5 0.0 0.5 1.0 99.5% confidence interval sa m p le  a u to co rr e la ti o n  f u n ct io n lags 1 2 3 4 5 6 ‐10 0 10 20 30 40 50 60 70 e n e rg y  d if fe re n ce eigenvalue pairs w indow length=72 w indow length=390 w indow length=700 w indow length=855 w indow length=1200 (a) (b) figure 3: (a) autocorrelation function (b) window length 1 2 3 4 5 6 7 8 9 10 11 ‐20 0 20 40 60 healthy data without noise (0.01n) damaged data without noise (100n) healthy data with 10% noise (0.01n) damaged data with 10% noise (100n) e n e rg y number of singular values 1 2 3 4 5 6 7 8 9 10 11 ‐20 0 20 40 60 80 100 120 healthy data without noise (0.01n) damaged data without noise (100n) healthy data with 10% noise (0.01n) damaged data with 10% noise (100n) e n e rg y number of singular values (a) (b) figure 4: singular spectrum– (a) actual (b) residual acceleration time history fig. 3 (a) depicts the autocorrelation of the response measured at 0.4m from the left support corresponding to 100n excitation. fig. 3(a) shows the zero crossing of the autocorrelation function of the response at time lags around 72, 232, 387, 545, 698, 851, 1008, 1196, 1315, 1470, and 1625 and so on. fig. 3(b) shows the plot corresponding to the energy difference between eigenpairs with varied window lengths chosen based on the time lags corresponding to zero crossing of the response. the energy difference (of eigenpairs) plot furnished in fig. 3(b) shows zero magnitudes when the length of the window is considered as 1190 (or above). based on this investigation, the above-automated choice of window length is chosen in the present work. once the window length is chosen, the next stage of ssa can be performed on the response to localize the closing crack. the singular spectrum of the noise-free response and response polluted with 10% noise (i.e. node 5) obtained by ssa is given in fig. 4 (a), while the results of the residual response is given in fig. 4 (b). both figs. 4 (a) and 4 (b) furnish the results corresponding to two different excitation amplitudes of 0.01n and 100n. fig. 4(a) concludes that the eigentriples with close singular values exist for the total actual response corresponding to both excitation amplitudes of 0.01n and 1n. while the pairwise component i.e. harmonic signal is absent in fig. 4 (b) for the low amplitude of excitation and present for the high amplitude of excitation even with the noisy measurements. each of the pairwise singular values in the residual signal of 100n excitation corresponds to nonlinear harmonics components i.e. super harmonic components generated due to the j. prawin et alii, frattura ed integrità strutturale, 48 (2019) 513-522; doi: 10.3221/igf-esis.48.49 518 closing crack in the structure. the nonlinear components are isolated using ssa and damage index is then computed for closing crack localization. closing crack localization – two different test cases the simply supported beam is simulated with closing crack at two different spatial locations in order to illustrate the robustness of the proposed technique in localizing the closing crack present anywhere in the structure. the first test case considers the breathing crack located at element no, 4, while the second test case considers the breathing crack at element no.7. both the test cases have the same crack depth equal to 7% of the total depth. the results of the damage index evaluated for these two varied crack locations is shown in fig. 5 using the noise-free and noisy time history response (i.e. actual response polluted with 10% noise before processing) measured at varied locations spatially across the structure. it can be concluded from fig. 5 that the maximum value of the damage index in both the test cases considered is at the damaged element of the beam even with noisy measurements. figure 5: damage index based on ssa – 9 sensors. figure 6: damage index based on ssa – 4 sensors. closing crack localization with limited instrumentation in order to investigate the effectiveness of the proposed closing crack localization approach with limited sensors, we have used the measurements obtained at 4 selective locations (i.e. at nodes 2, 4, 6, 9), identified using the popular effective independence optimal sensor placement technique [10]. the results of the damage index, obtained with limited measurements for the above damage cases of fig. 5 is presented in fig. 6. it can be observed from fig. 6 that the maximum value of the damage index is at node no.4 for the case of damage simulated in element no.4. the maximum value of the damage index for the case of damage simulated in element no. 7 is at node no.6, which is close to the nodes 7-8 (i.e. element no. 7). therefore, with limited instrumentation, the closest possible spatial location of damage can be identified, while with more sensors, the maximum value of damage will be occurring exactly between the two closely spaced nodes corresponding to damaged element (i.e. peak at nodes 7-8 in the case of damage at element no. 7, as evident from fig. 5). this investigation clearly concludes that the proposed algorithm has the ability to localize the closing crack even with limited measurements. comparison with previous work in order to demonstrate the effectiveness of the proposed algorithm in identifying smaller and subtle cracks, the results of the proposed damage index are compared with the previous vibration based breathing crack identification techniques based on only first few super harmonics [6-8]. the various damage indices given in the reported relevant research work in the literature are summarized as follows 1 1 2 2 1 1 1 1 1 2 1 1 2 i=1,2,3,...n; 2 i=2,3,...n-1; x x n i jωj i i ω i i i i i i a ( di ) ; a ( di ) ( di ) ( di ) ( di ) d (( di ) ); d (( di ) ) h          (3) j. prawin et alii, frattura ed integrità strutturale, 48 (2019) 513-522; doi: 10.3221/igf-esis.48.49 519 where the first damage index 1 i( di ) indicates the ratio of the sum of the power spectrum amplitudes of ‘n’ superharmonics to power spectrum amplitude of linear excitation harmonic (i.e fft amplitude (a) at excitation frequency  x ). the second damage index indicates the extension of the first approach to the curvature based index and n represents the total number of degrees of freedom. 1 2 3 4 5 6 7 8 9 10 11 0 2 4 6 8 10 proposed damage index ( without noise) proposed damage index (with 10% noise) di 1 (without noise) di 1 (with 10% noise) di 2 (without noise) di 2 (with 10% noise) d a m a g e  i n d e x sensor nodes 1 2 3 4 5 6 7 8 9 10 11 0 1 2 3 4 5 proposed damage index ( without noise) proposed damage index (with 10% noise) di 1 (without noise) di 1 (with 10% noise) di 2 (without noise) di 2 (with 10% noise) d a m a g e  i n d e x sensor nodes (a) (b) figure 7: various damage indices (a) 20% crack depth (b) 7% crack depth for this investigation on the proposed damage index with previous works, the closing crack is simulated in simply supported beam in element no.4 with crack depth equal to 20% and 7% of overall depth of the beam. the results of the damage index estimated using eqn. (1) and eqn. (3) is furnished in fig. 7 (a) for the beam having crack equal to 20% of total depth. similarly the results of the damage index corresponding to the case of simply supported beam with crack depth equal to 7% of overall depth of the beam is shown in fig. 7 (b). before computing the damage index, the computed acceleration time history responses are polluted with 10% noise. it can be observed from fig. 7 (a) that the peak value of all the damage indices is at the exact location of the breathing crack. however it can be observed from fig. 7 (b), the two damage indices corresponding to the previous approaches fail to detect smaller cracks due to consideration of only a few superharmonics and difficulty in distinguishing noise and true nonlinear harmonic. for example, the damage index 1di shows multiple peaks which creates confusion and difficult to conclude the exact location of the breathing crack. while the damage index 2di shows a peak at the wrong location. therefore, the earlier approaches [6-8] fail to detect subtle cracks; however, the proposed method identifies the minor damages very precisely by reliably extracting all the possible higher order harmonics. experimental validation part from the above numerical investigations, experimental studies have been carried out by considering a cantilever beam with single and multiple breathing cracks (i.e. two test specimens), to test and verify the proposed closing crack localization algorithm. the experimental set up followed in the present work is popularly used by prime et.al. [11] and douka et.al., [12] earlier for validation of their crack diagnosis algorithms. the single crack test beam shown in fig. 8, is constructed by bonding two aluminium alloy beams (i.e. four pieces) together. the faces of the top plates in contact induce breathing behaviour. the instrumentation set up is same for both the specimens and shown in fig. 8. the length of the beam is 1m for both the test specimens. the cross-section dimension of both the specimens is same and found to be 0.0254 x 0.0127m. the ratio of the thickness of the top and bottom plates decides the crack depth. the top and bottom plate thicknesses corresponding to single crack test specimen (case-1) are 1.5875 mm and 11.1125mm respectively. this results in a crack depth of 12.5% of the overall depth of the beam and the crack is simulated at 0.4m (i.e. located between sensor 3 and 4) from the fixed end. similarly, the top and bottom plate thicknesses corresponding to two crack specimen (case-2) are 3.175mm and 9.525mm which results in 25% crack depth of the total depth of the beam. in the case of two crack experimental specimen shown in fig. 9, the first crack at 0.2m is located between sensor 2 and 3 (closer to sensor 2), while the second crack at 0.7m from the fixed end is located between sensor 5 and 6 (closer to sensor 6). the two crack a j. prawin et alii, frattura ed integrità strutturale, 48 (2019) 513-522; doi: 10.3221/igf-esis.48.49 520 experimental specimen, employed in the present work was earlier used by the authors for validating their proposed damage diagnosis algorithm [4]. figure 8: instrumentation set up – single crack crack specimen both the experimental specimens are excited near the centre of the beam with harmonic excitation of 10hz. the acceleration time history responses are measured at the eight spatial locations as indicated in fig. 8. the damage index based on ssa is estimated using eqn. (1) for both the test specimens and the results are furnished in fig. 10. the damage index corresponding to single crack experimental specimen shows a single peak at sensor 4, which coincides with the exact location of the actual crack. it is also evident from fig. 10 that the damage index plot corresponding to two crack experimental specimen shows peaks at the spatial location of sensor 3 and sensor 6 clearly reflect the actual closing crack locations of the considered beam. figure 9: experimental multiple breathing crack specimen [4] 0 1 2 3 4 5 6 7 8 9 0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 two crack specimen (8 sensors) single crack specimen (8 sensors) single crack specimen (4 sensors) two crack specimen (4 sensors) d a m a g e  i n d e x sensor nodes figure 10: damage index – experimental specimen – multiple breathing cracks j. prawin et alii, frattura ed integrità strutturale, 48 (2019) 513-522; doi: 10.3221/igf-esis.48.49 521 in order to test the robustness of the proposed algorithm with limited measurements experimentally, the measurements of both the single and two crack specimens at optimally chosen four sensors i.e., at nodes 1, 3, 5 and 8 are only considered instead of all the 8 sensors. the damage index is computed using the limited sensor information. the corresponding results are also presented in fig. 10. it can be observed from fig. 10 that the damage index exhibit pairwise peaks at nodes 3 and 5 for the single crack specimen where the crack is actually located close to the sensor node 4. it can also be concluded from fig. 10 that in the case of two-crack specimen, only one crack at sensor node 3 (i.e. the crack is actually located between nodes 2 and 3) is detectable, with limited measurements of 4 sensors. this study clearly illustrate that only he possible region of spatial location of closing crack can be identified with limited instrumentation and it is also difficult to localize multiple cracks. from the numerical and experimental investigations, it is clear that the proposed signal decomposition approach based on singular spectrum analysis can identify more than one cracks present anywhere in the structure and of any crack depth with minimum optimal number of sensors. conclusions signal decomposition based technique has been proposed in this paper to identify the smaller and subtle closing cracks present anywhere in the structure. both experimental and numerical investigations have been carried out on simple beam-like structures to test the robustness and effectiveness of the proposed signal decomposition based breathing crack localization technique. the results furnished from the investigations are given below 1. the proposed signal decomposition is capable of isolating linear, nonlinear and noise components effectively. 2. the proposed ssa based damage diagnostic technique is robust enough to locate even more than one crack present in the structure. 3. numerical investigations conclude that the proposed breathing crack localization technique is reference free and can detect minor crack of about 7% crack depth. experimental investigations conclude that the proposed technique can detect crack depth of about 12.5% of overall depth of the beam. 4. the proposed approach can identify the breathing crack even with the acceleration responses being polluted with 10% measurement noise. 5. the proposed closing crack localization technique can also identify smaller cracks due to consideration of more number of super harmonics in contrast to the earlier works which consider only first few super harmonics. acknowledgements he authors thank the technical staff of astar and shml lab of csir-serc for their support during laboratory testing. references [1] golyandina, n., nekrutkin, v. and zhigljavsky, a.a. (2001). analysis of time series structure: ssa and related techniques. chapman and hall/crc. [2] vautard, r., yiou, p. and ghil, m. (1992). singular-spectrum analysis: a toolkit for short, noisy chaotic signals. physica d: nonlinear phenomena, 58(1-4), pp.95-126. [3] loh, c.h., chen, c.h. and hsu, t.y. (2011). application of advanced statistical methods for extracting long-term trends in static monitoring data from an arch dam. structural health monitoring, 10(6), pp.587-601. [4] prawin, j., lakshmi, k. and rao, a.r.m. (2018). a novel singular spectrum analysis–based baseline-free approach for fatigue-breathing crack identification. journal of intelligent material systems and structures, 29(10), pp.2249-2266. [5] de oliveira, m.a., vieira filho, j., lopes jr, v. and inman, d.j. (2017). a new approach for structural damage detection exploring the singular spectrum analysis. journal of intelligent material systems and structures, 28(9), pp.1160-1174. [6] shen, m.h. and chu, y.c. (1992). vibrations of beams with a fatigue crack. computers & structures, 45(1), pp.79-93. a t j. prawin et alii, frattura ed integrità strutturale, 48 (2019) 513-522; doi: 10.3221/igf-esis.48.49 522 [7] giannini, o., casini, p. and vestroni, f. (2013). nonlinear harmonic identification of breathing cracks in beams. computers & structures, 129, pp.166-177. [8] bovsunovsky, a. and surace, c. (2015). non-linearities in the vibrations of elastic structures with a closing crack: a state of the art review. mechanical systems and signal processing, 62, pp.129-148. [9] prawin, j., rao, a.r.m. and lakshmi, k. (2015). nonlinear identification of structures using ambient vibration data. computers & structures, 154, pp.116-134. [10] kammer, d.c. (2005). sensor set expansion for modal vibration testing. mechanical systems and signal processing, 19(4), pp.700-713. [11] prime, m.b. and shevitz, d.w. (1995). linear and nonlinear methods for detecting cracks in beams (no. la-ur-954008; conf-960238-10). los alamos national lab., nm (united states). [12] douka, e. and hadjileontiadis, l.j. 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/hrv (za stvaranje adobe pdf dokumenata najpogodnijih za visokokvalitetni ispis prije tiskanja koristite ove postavke. stvoreni pdf dokumenti mogu se otvoriti acrobat i adobe reader 5.0 i kasnijim verzijama.) /hun 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/pdfxoutputintentprofileselector /documentcmyk /preserveediting true /untaggedcmykhandling /leaveuntagged /untaggedrgbhandling /usedocumentprofile /usedocumentbleed false >> ] >> setdistillerparams << /hwresolution [2400 2400] /pagesize [612.000 792.000] >> setpagedevice microsoft word numero_31_art_5 h.f.s.g. pereira et alii, frattura ed integrità strutturale, 31 (2015) 54-66; doi: 10.3221/igf-esis.31.05 54 numerical simulation of galvanized rebars pullout h.f.s.g. pereira engineering department, school of science and technology, university of trás-os-montes e alto douro, quinta de prados, 5001-801 vila real, portugal. idmec, pólo feup, rua dr. roberto frias, 4200-465 porto, portugal hfpereira@portugalmail.pt v.m.c.f. cunha, j. sena-cruz department of civil engineering, school of engineering, university of minho 4800-058 guimarães, portugal. isise, university of minho 4800-058 guimarães, portugal abstract. the usage of rebars in construction is the most common method for reinforcing plain concrete and thus bridging the tensile stresses along the concrete crack surfaces. usually design codes for modelling the bond behaviour of rebars and concrete suggest a local bond stress – slip relationship that comprises distinct reinforcement mechanisms, such as adhesion, friction and mechanical anchorage. in this work, numerical simulations of pullout tests were performed using the finite element method framework. the interaction between rebar and concrete was modelled using cohesive elements. distinct local bond laws were used and compared with ones proposed by the model code 2010. finally an attempt was made to model the geometry of the rebar ribs in conjunction with a material damaged plasticity model for concrete. keywords. pullout test; local bond; damage; finite element method. introduction he first works associated to the study of the adherence between concrete and steel rebars, probably, were carried out by considère in the end of the xix century [1, 2]. after the latter works, several others were carried out regarding the experimental study of the bond between concrete and rebars, with special incidence in the decades of 70, 80 and 90 of the past century [3 19]. within the two last decades, some numerical works about the bond behaviour between concrete and rebars were carried out, some with special incidence on the behaviour associated to pullout tests, e.g. [20 23], and others related to the bond behaviour in structural elements, e.g. [24]. reinforced concrete can be regarded as a composite material made up of two components (steel and concrete) with rather distinct mechanical and physical properties. in general, due to the external loads applied to a structural concrete element will arise a certain stress field, being the tensile stresses after cracking bridged by the reinforcing rebars due to the bond mechanisms developed at the rebar / matrix interface. “bond stresses” is the designation ascribed to the shear stresses that arise at the rebar / concrete interface. this bond stresses, when efficiently mobilized, enable the two materials to behave as a composite material. in concrete reinforced structures, the bond between the distinct components of the reinforced concrete member has a primordial role on the overall behaviour and if neglected can lead to poor structural t h.f.s.g. pereira et alii, frattura ed integrità strutturale, 31 (2015) 54-66; doi: 10.3221/igf-esis.31.05 55 response. these complex phenomena involved in the bond behaviour have led engineers in the past to rely heavily on empirical formulas for the design of concrete structures, which were derived from numerous experiments, e.g. [7 15]. the properties of the adherence between rebar / matrix depends on several factors, such as friction, mechanical interaction and chemical adhesion [24]. in the past, several experimental investigations have been carried out in order to clarify and understand the behaviour of deformed bars pulled out from a concrete bulk under monotonic as well as cyclic loading conditions. some of these experimental results are well documented in literature, e.g. [7-19, 25]. based exclusively on the experimental results it is difficult to filter out the influences of material and geometrical parameters on the bond behaviour. in order to understand thoroughly the bond behaviour, a reliable numerical model (simulation of the transmission of forces at the interface zone, see fig. 1a) should be employed, thus a three-dimensional finite element, analysis is needed. the numerical modelling of the bond behaviour is principally possible at two different levels: (1) detailed modelling (see fig. 1b) in which the geometry of the bar and the concrete are modelled with three-dimensional elements and (2) phenomenological modelling (see fig. 1c) based on a smeared or discrete formulation of the bar-concrete interface [21]. (a) idealized bond zone. (b) detailed modelling. (c) phenomenological modelling. figure 1: schematic simulation of the idealized bond zone [21]. the phenomenological modelling of bond between rebar / concrete can be discretised by three-dimensional finite elements. the link between the rebar and the concrete can be achieved by a discontinuous approach, where bond is defined by discrete or reduced thickness cohesive elements. within these elements the behaviour is controlled by the local bond stress-slip relationship. this approach is able to realistically predict the pullout behaviour for different geometries and for different boundary conditions only if a realistic constitutive bond relationship is used. however, the model is not able to straightforwardly predict the bond behaviour of a given bar geometry. consequently, the influence of these parameters must be stored in advance in the basic parameters matrix of the bond model. thus, one has the possibility to realistically simulate the behaviour of reinforced concrete structures with relatively low effort in modelling and computing time. by the use of detailed modelling, such as both modelling of the ribs of the reinforcement and the concrete lugs (see fig. 1b) between the ribs of the reinforcement a quite refined finite element mesh has to be generated. this leads again to a high effort in modelling, and also to really long computational time, in particular while carrying out a finite element analysis of complex reinforced concrete structures [21 23]. in the present work a parametric study of the numerical simulations of galvanized rebar pullout tests under the finite element framework is presented and discussed. afterwards, the numerical simulations of galvanized rebar pullout tests are compared with the results obtained by using an analytical model [31], namely, a shear-lag model. the adopted local bondslip laws were similar to the one proposed by the ceb-fip model code 2010 [27]. finally, an attempt is made to model the pullout tests by isolating the distinct bond mechanisms, in particular, the mechanical component of bond due to the rebar’s ribs. therefore, to fulfil this purpose a three-dimensional finite element model considering the geometrical modelling of the rebar ribs was implemented. description of the numerical model geometry he experimental pullout tests were carried out on concrete cubic specimens with a rebar positioned in the middle of the specimen. the rebar’s embedded length was equal to half of the cube edge length, i.e. 100 mm, fig. 2. only one quarter of the experimental specimen was geometrically modelled, because the specimen has double symmetry t h.f.s.g. pereira et alii, frattura ed integrità strutturale, 31 (2015) 54-66; doi: 10.3221/igf-esis.31.05 56 conditions. fig. 3 shows the 3d geometrical model with the representation of the surfaces’ boundary conditions ascribed due to both symmetry conditions and test support conditions. the perpendicular displacements of the finite element nodes at the two symmetry planes were constrained along the yy and zz axis, respectively. moreover, at the specimen’s front plane (where the protruding end of the rebar arises), the displacement of the nodes perpendicular to the plane were also constrained, i.e. in the xx direction. 100mm 100mm 2 0 0 m m 200mm 2 0 0 m m embedded disabled top view front view length bond ø 2 0 .5 m m figure 2: geometry of the specimens used in the pullout test. figure 3: 3d fe mesh and boundary conditions. the pullout specimen was modelled using 3d solid finite elements available from abaqus library [26], namely, c3d8 and c3d6 were used to model the concrete bulk and steel rebar, respectively. additionally, cohesive elements (coh3d8) were considered to model the interface behaviour between the concrete and rebar. (a) (b) figure 4: model with smooth rebar: a) top view, b) front view. (a) (b) figure 5: model with ribbing rebar: a) top view, b) ribbing detail. local bond-slip law the bond properties of a reinforcing rebar can be analytically described by a local bond stress – slip relationship, =(s), in which  is the shear stress acting on the contact surface between rebar and concrete, and s is the corresponding slip, i.e. the relative displacement between steel bar and concrete [31]. once the relation =(s) is known, using equilibrium and compatibility relations, the second order differential equation governing the slip can be defined as: h.f.s.g. pereira et alii, frattura ed integrità strutturale, 31 (2015) 54-66; doi: 10.3221/igf-esis.31.05 57   2 2 0 s s d s d s dx e a    (1) where d is the diameter, as is the cross sectional area, es is the young’s modulus of the reinforcing bars and s(x) is the slip between concrete and the embedded rebar’s length at the abscissa x. using eq. (1), important phenomena can be analysed such as: the anchorage length evaluation, the determination of the tension stiffening effect and crack spacing and opening. these problems can be solved once the boundary conditions of the specific problems are specified and this observation reinforces the importance of a consistent local bond-slip relationship. relatively to the analytical expressions for the bond-slip relationships, several hypotheses have been proposed and used in the past. one simpler alternative is to define the bond stress – slip relationship with linear branches [15]. nevertheless, alternatively, a more robust non-linear relationship between bond stress and slip can be used. the relationship established by eligehausen [15] and afterwards adopted by the model code 2010 [27] is expressed by the following non-linear functions as follows:  max 1 1 ; 0s s ss      (2) max 1 2; s s s    (3)      2 max max 2 3 3 2 ;f s s s s s s s             (4) 3;f s s   (5) fig. 6 depicts the bond stress – slip relationship according to [27]. tab. 1 includes the parameters of the bond-slip relationship proposed by model code 2010 [27] for distinct bond conditions. figure 6: local bond stress-slip law according to [27]. bond conditions max f [-] s1 [mm] s2 [mm] s3 [mm] good 2.5(fcm)0.5 0.4max 0.4 1 3 clear rib spacing of rebar table 1: parameters defining the bond-slip relationship [27]. in the present work two distinct local bond stress – slip laws were used. for the parametric study, the bond stress – slip relationship was modelled using the linear cohesive law provide by abaqus software, as depicted in fig. 7. this constitutive model available in abaqus was originally developed for the delamination of composites, but it can also be used to model cohesion between steel rebar and concrete, assuming that the interaction between concrete and steel rebar can be collapsed to zero-thickness surface. this approach has been already previously adopted by alfano and serpieri [28, h.f.s.g. pereira et alii, frattura ed integrità strutturale, 31 (2015) 54-66; doi: 10.3221/igf-esis.31.05 58 29]. in a second stage, a similar local bond stress – slip law to that proposed by [27] was also used. in order to implement it in the software, it was needed to perform previously a transformation of the bond stress – slip law to a damage – slip relationship. figure 7: linear bond-slip law [26]. with reference to the fig. 7, the first part of the constitutive law is linear elastic up to the maximum bond stress (point a), involving an initial displacement 0n . at this point the interface starts to become damaged. once the maximum bond stress is reached and the crack begins to propagate, the stress starts to reduce up to the maximum displacement 1n (point b). gc is the fracture energy needed to propagate the interfacial crack. concrete and steel constitutive behaviour regarding the mechanical behaviour of the steel rebar, it was assumed an elastic perfectly-plastic behaviour. on the other hand, to model the concrete behaviour two distinct approaches with different levels of complexity were adopted. it was assumed a linear elastic behaviour and nonlinear behaviour by using the concrete damage plasticity (cdp) model comprised in the abaqus software [26]. the cdp model from the abaqus library [26] considers the total strain decomposed into an elastic ( el ) and plastic ( pl ) strain components, el pl    . the stress-strain relation associated with the damage evolution is given by:    01 el pld d     (6) where d is the damage variable (d = 0 no damage, d = 1 fully damaged) and 0 eld is the non-damaged elastic modulus. damage is associated with the typical degradation mechanisms of concrete – cracking in tension and crushing in compression, which involves a decrease of the elastic modulus. damage is governed by the hardening variables pl~ and the effective stress  , pld d    . the hardening variables under compression ( plc~ ) and tension ( plt~ ) are considered independently. figure 8: yield surface of dcp model [26]. h.f.s.g. pereira et alii, frattura ed integrità strutturale, 31 (2015) 54-66; doi: 10.3221/igf-esis.31.05 59 the adopted cdp model used a yield surface that was defined as the loading function proposed by lubliner et al. [30], see fig. 8. the evaluation of the yield surface was controlled by the two hardening variables, namely, the plastic strain in tension ( plt ) and the plastic strain in compression ( pl c ~ ). tab. 2 includes the mechanical properties of concrete and steel used in the numerical simulations. regarding the steel tensile behaviour an elastic – perfectly plastic relationship 1n was considered with a yield stress of 567 mpa. on the other hand, tab. 3 includes the constitutive parameters of the cdp model used to simulate the nonlinear behaviour of concrete when considered. material density, ρ [kg/m3] young modulus, e [gpa] poisson ratio,  [-] steel 7800 200 0.30 concrete 2400 30 0.20 table 2: mechanical properties adopted in the numerical simulations. dilatation angle [º] eccentricity [-] σbo/σco [-] kc [-] 40.0 0.1 1.16 0.667 table 3: the constitutive parameters of cdp model. parametric study his section presents the parametric study that was carried out to calibrate the numerical model for the pullout tests. this study evolves the analysis of the influence of distinct parameters on the numerical responses, such as: the mesh refinement, the cohesive element thickness and the viscosity coefficient. mesh refinement to analyse the influence of the mesh refinement, it was considered in a first stage a linear elastic behaviour for concrete. for the interface behaviour it was used the relationship depicted in fig. 7. for this task, four meshes similar to the one presented in fig. 4 were considered. tab. 4 presents several parameters for mesh characterization, such as number of elements and nodes, and respective computational time for completing the numerical simulation of the pullout test. mesh element quantity nodes quantity computational time 1 2100 2790 48min 21s 2 3100 3945 49min 10s 3 4100 5100 61min 21s table 4: mesh parameters. the parameters to define the behaviour of the cohesive elements layer in terms of nominal stresses are presented in tab. 5. the adopted damage evolution was of the type displacement with linear softening and maximum degradation. moreover, two values for displacement at failure, namely, 5 and 1000 mm were adopted. in the last case, it corresponds practically to assuming no degradation of the bond stresses with the increment of slip. nominal stress normal-only mode [mpa] nominal stress first direction [mpa] nominal stress second direction [mpa] 0 10.26 0 table 5: nominal stress. fig. 9 and 10 depict the results obtained in the numerical simulations considering an elastic behaviour for concrete and the local bond stress – slip relationship defined by fig. 7 for the interface elements behaviour. as it was expectable the t h.f.s.g. pereira et alii, frattura ed integrità strutturale, 31 (2015) 54-66; doi: 10.3221/igf-esis.31.05 60 ultimate slip obtained during pullout was almost 5 mm and 1000 mm, fig. 9 and 10, respectively. in fig. 10 it was opted to depict only the load slip relationship up to a slip of 1 mm, nevertheless the pullout load kept constant practically up to the ultimate displacement (1000 mm). in both simulations, and excluding mesh 1, the maximum pullout load was reached approximately for a slip of 0.2 mm, and the value was of 63.9 and 66.3 kn for the simulations carried out with and without bond stress degradation with slip, i.e. with an ultimate local slip of 5 and 1000 mm, respectively. considering no degradation of the bond, stress increased in nearby 5% de maximum pullout load. figure 9: pullout load slip relationship with a 5 mm displacement at failure. figure 10: pullout load slip relationship with a 1000 mm displacement at failure. after carrying out the simulations considering an elastic behaviour of the concrete surrounding the rebar, it was assessed the influence of the mesh refinement when using the concrete damage plasticity model to model the surrounding concrete behaviour. for this purpose, three meshes were used, in particular, mesh 3 and 4 that were the same used in the simulations when considering an elastic behaviour for concrete, and another mesh with a higher refinement in the rebar zone and a coarser refinement in the concrete farther from the interface zone. regarding the interface cohesive behaviour, the adopted damage evolution also was of the type displacement with linear softening and maximum degradation. the value of displacement at failure was 5 mm. tab. 6 includes the number of nodes and elements, as well as the computational time for completing the simulation of the pullout test. mesh element quantity nodes quantity computational time 3 4100 5100 3h 36min 4 21960 25010 51h 40min 5 20500 24580 29h 46min table 6: mesh parameters. h.f.s.g. pereira et alii, frattura ed integrità strutturale, 31 (2015) 54-66; doi: 10.3221/igf-esis.31.05 61 fig. 11 presents the results obtained for the three meshes when considering the concrete damage plasticity model. as it was expectable the maximum slip was 5 mm. in terms of maximum slip the results are similar to the ones obtained considering an elastic behaviour for concrete. as it is visible in fig. 11 b), it was verified a sharper peak in meshes 3 and 5, which incremented nearby 3% the peak load. based in this analysis it was adopted mesh 4, to carry out the forthcoming analysis. a) b) figure 11: bond stress-slip relationship displacement at failure equal to 5 mm: a) complete curve; b) detail peak curve. cohesive element thickness the interface was simulated with the use of cohesive elements in-between the rebar and surrounding concrete. since these are not pure interface elements, a certain thickness must be ascribed to the element. the cohesive element’s thickness used in the parametric study were 0.1, 0.5 and 1.0 mm, respectively. fig. 12 and 13 show the results for the three thicknesses, adopting an ultimate slip of 5 and 1000 mm, respectively. as foreseeable, with the thickness increase was verified an increase of the maximum pullout load. this occurs because the cohesive elements’ mid surface is farther from the rebar’s surface, consequently, there is an increase of the interface area. therefore for the same bond stress profile it will result in higher shear stresses at the interface and consequently a higher pullout load. figure 12: bond stress-slip relationship displacement at failure equal to 5 mm, with different thickness of cohesive elements. figure 13: bond stress-slip relationship displacement at failure equal to 1000 mm, with different thickness of cohesive elements. viscosity coefficient the viscosity coefficient is a regularization parameter for obtaining convergence in damage models that exhibit a softening response. it allows the analysis to converge after the peak load is attained, but the results can be unrealistic if a proper value is not selected. the influence of the viscosity in the pullout response was carried out. for this purpose three quite distinct values for the viscosity coefficient, namely, 0.001, 0.0001 and 0.00001 were selected. these analyses were carried out for two linear bond stress – slip relationships, adopting an ultimate slip of 5 and 1000 mm, respectively. as it can be observed in fig. 14, for the local bond law defined with an ultimate slip of 5 mm, the viscosity coefficient only does not h.f.s.g. pereira et alii, frattura ed integrità strutturale, 31 (2015) 54-66; doi: 10.3221/igf-esis.31.05 62 have influence if a quite small value is adopted, i.e. equal to 0.00001. for a viscosity value of 0.001 the results were completely incoherent, with the maximum pullout load attaining the value of 200 kn, approximately three times the real value. fig. 15 shows the results adopting a bond stress – slip law with an ultimate slip of 1000 mm. in the latter case, the viscosity coefficient only has influence for the higher viscosity value, i.e. 0.001, causing an increasing in maximum pullout load of approximate 10%. based on these results, it was decided to use the smallest viscosity coefficient in all simulations (0.00001), this option leads to an increase of the computational time cost. figure 14: bond stress-slip relationship displacement at failure equal to 5 mm simulated with different viscosity coefficients. figure 15: bond stress-slip relationship displacement at failure equal to 1000 mm simulated with different viscosity coefficients. numerical modelling of the sena et al. (2009) pullout tests his section presents the numerical results within the finite element framework regarding the simulation of the experimental pullout tests performed by sena-cruz et al. [31]. smooth rebar model the simulations were firstly performed assuming a smooth surface for the steel rebar. the pullout behaviour of three types of rebars, namely, non-alloy, galvanized and galvanized + epoxy rebar were modelled. the obtained numerical results were compared with the experimental results and with the results obtained using the analytical model proposed by sena-cruz et al. [31]. tab. 7 includes the parameters that define the local bond – slip law (fig. 6) used in the numerical simulations. these parameters were obtained by an inverse analysis procedure using an analytical shear-lag model [31]. the inverse analysis procedure consisted in fitting the numerical pullout force – slip relationship with the experimental correspondent one by varying the local bond law parameters. in these simulations the fe mesh depicted in fig. 1 was used. rebar max [-] s1 [mm] error [%] galvanized + epoxy 0.73 (fcm)0.5 0.4 2.00 3.9 galvanized 1.46(fcm)0.5 0.62 1.30 2.5 non-alloy 1.75(fcm)0.5 0.52 1.30 1.8 table 7: parameters of the bond-slip relationship obtained by inverse analysis [31]. fig. 16 depicts both the experimental and numerical results from the finite element analysis, for specimens with non-alloy steel rebars, in terms of pullout force vs. slip. the numerical results were inside of experimental envelope obtained experimentally, however the simulations results by abaqus slightly overestimates the results obtained by the analytical formulation of [31], in terms of stiffness and maximum pullout force. t h.f.s.g. pereira et alii, frattura ed integrità strutturale, 31 (2015) 54-66; doi: 10.3221/igf-esis.31.05 63 numerical results of the specimens with galvanized steel rebars are presented in fig. 17. the numerical results are also inside of experimental envelope, except in initial zone of slip, were the simulations results by abaqus are a little outside of envelope. in terms of stiffness and maximum pullout force, the conclusions are similar to obtained with the non-alloy rebars. the response of abaqus has an initial peak of the pullout force followed by a softening, afterwards it was observed an increase of the pullout force. 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 0 10 20 30 40 50 60 70 80 envelope (non-alloy rebars) numerical model (abaqus) analytical model (sena et al., 2009) p u ll o u t f or ce [ k n ] free end slip [mm] 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 0 10 20 30 40 50 60 70 80 envelope (galvanized) numerical model (abaqus) analytical model (sena et al., 2009) p ul lo ut f or ce [ kn ] free end slip [mm] figure 16: numerical simulation of the experimental pullout curves (non-alloy rebar). figure 17: numerical simulation of the experimental pullout curves (galvanized rebar). numerical results for galvanized + epoxy rebar, presented in fig. 18, are similar to the ones obtained with galvanized rebars. but it is possible to see that experimental results also present an initial peak of pullout force followed by a softening, after the increase of the pullout force. 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 0 10 20 30 40 50 60 70 80 envelope(galvanized + epoxy) numerical model (abaqus) analytical model (sena et al., 2009) p ul lo ut f or ce [ kn ] slip [mm] figure 18: numerical simulation of the experimental pullout curves (galvanized+epoxy rebar). model with the rebar's ribbing in this section the pullout tests [31] were modelled using the geometrical representation of the rebars’ ribbs. note that an approximate geometry was adopted due to the complexity of the real rebar ribs geometry. fig. 4 depicts schematically the adopted mesh, which included 8 ribbs along the embedded length of the steel rebar in the concrete. three different heights of ribbing were considered in the three distinct simulations that were carried out, respectively, 0.20, 0.26 and 0.30 mm. the ribs allowed to simulate the mechanical reinforcement mechanism due to the rib interlock verified between concrete and ribbing in experimental test. moreover, the cohesive elements were used to simulate the effects of steelconcrete chemical adhesion and frictional shear. in these simulations the parameters that defined the behaviour of the cohesive elements layer, in terms of nominal stress, are presented in tab. 8. fig. 19 depicts the pullout force vs. free-end slip relationships for the performed numerical simulations. the results that better agreed with the experimental results were obtained with a ribbing height of 0.26 mm, where the maximum pullout force obtained in the numerical simulation was similar to the experimental. the stiffness of the numerical response was higher than the one of the experimental results. the horizontal plateau of the pullout force vs. slip curve was not possible to reproduce numerically. instead, the softening verified numerically was very pronounced. h.f.s.g. pereira et alii, frattura ed integrità strutturale, 31 (2015) 54-66; doi: 10.3221/igf-esis.31.05 64 the abovementioned differences observed between the numerical results and experimental results could be ascribed to several factors. first of all, note that the geometric representation of the ribs was approximate, since the actual ribs geometry is quite complex and its disposition along the rebar’s surface is non uniform. therefore for modelling accurately the ribs geometry a more complex and full 3d geometrical model should be developed, in which the axisymmetric stress state cannot be considered. as previously stated the numerical responses with the discretization of the ribs were stiffer than the experimental pullout behaviour. to the latter fact may contributed the disposition of the interface elements along the lateral inclined faces of the ribs, which are not submitted to a pure fracture mode ii, since they are also subjected to compressive stresses that will increase the confinement level. this aspect may contributed to an increase of the response stiffness. on the other hand, the steeper softening decay observed in the numerical curves may be related to adopted geometry of the ribs within the numerical model. in the numerical model, the start of the softening stage, after the peak load, coincides with the plastification of the compressive bulk wedges formed in front of the ribs during the pullout procedure, and the increase of the relative displacement between ribs and the surrounding concrete. nominal stress normal-only mode [mpa] nominal stress first direction [mpa] nominal stress second direction [mpa] 0 0.63 0 table 8: nominal stress. figure 19: numerical simulation of the experimental pullout curves (rebars with ribs). conclusions ith the aim of studying the bond behaviour between galvanized rebars and concrete in pullout tests, distinct numerical simulations were carried out using the finite element method framework. a parametric study of the main numerical variables was performed, also to calibrate the model. the numerical simulations of the pullout tests carried out by [31] were compared with both the experimental results and the simulations with an analytical shear-lag model. using the same bond stress – slip relationships the results obtained by the finite element method rendered a higher stiffness and maximum pullout load when compared to ones obtained with the analytical model by [31]. the pullout tests were successfully modelled assuming the steel rebar as smooth, as long a proper local bond stress – slip law is adopted. the numerical simulations including in the geometric model the rebar ribbings, at this stage dis not render so good results and further research should be carried out. the differences observed between the numerical results and experimental results when the ribs were modelled, could be ascribed to the approximate geometric representation of the ribs. therefore for modelling accurately the ribs geometry a more complex and full 3d geometrical model should be developed, in which the axisymmetric stress state cannot be considered. moreover, since some interface elements were not subjected to a pure fracture mode ii, they may also contribute to a stiffening of the initial numerical pullout response. references [1] considère, m., influence des armatures métalliques sur les proprietes des mortiers e bétons, le béton armé, 9 (1899). w h.f.s.g. pereira et alii, frattura ed integrità strutturale, 31 (2015) 54-66; doi: 10.3221/igf-esis.31.05 65 [2] considère, m., influence des armatures métalliques sur les proprietes des mortiers e bétons, le béton armé, 10 (1899). [3] talbot, a. n., tests of concrete i. shear ii. bond, university of illinois bulletin, iv (1906) [4] webb, r., wilsey, g. h., bonding strength of concrete and steel, armour institute of technology, (1908). [5] emin, g. h., laskey, h., tobias, w. r., bond stress of lap reinforced concrete beams, armour institute of technology, (1911). [6] abrams, d. a., test of bond between concrete and steel, university of illinois bulletin, xi (1913). [7] rehm, g., the fundamental law of bond, in: proceeding of the symposium on bond and crack formation in reinforced concrete, stockholm; relim, paris, (1957). [8] rehm, g., the basic principle of bond between steel and concrete, deustcher ausschuss fur stalbeton; wilhelm ernest and sohn, berlin, 138 (1961) [9] goto, y., cracks formed in concrete around tension bars, aci journal, 68(4) (1971) 244-251. [10] tassios, t.p., properties of bond between concrete and steel under load cycles idealizing sismic actions, comité eurointernational du béton, paris, 131 (1979). [11] tepfers, r., cracking of concrete cover along anchored deformed reinforcing bars, magazine of concrete research, 31(106) (1979) 3-11. [12] stanton, j. f., mcniven, h. d., the development of a mathematical model to predict the flexural response of reinforced concrete beams to cyclic loads, eerc report, university of california, berkeley, 79-2 (1979). [13] ciampi, v., eligehausen, r., bertero, v. v., popov, e.p., analytical model for concrete anchorages of reinforcing bars under generalized excitations, earthquake eng. res. center, university of california, berkeley, 82/23 (1982) 121. [14] hawkins, n. m., lin i.j., f.l. jeang, local bond strength of concrete for cyclic reversed loadings, bond in concrete, p. bartos (editor), applied science publishers ltd., london, (1982) 151-161. [15] eligehausen, r., popov, e.p., bertero, v.v., local bond stress-slip relationships of deformed bars under generalized excitation, university of california; national science foundation, ucb/eerc-83/23 (1983). [16] darwin, d., development length criteria for conventional and high relative rib area reinforcing bars, aci structural journal, farmington hills, 93(3) (1992) 709-720. [17] gambarova, p.g., rosati, g.p., bond and splitting in bar pull-out: behavioural laws and concrete cover role, magazine de concrete research, 49(179) (1997) 99-110. [18] sener, s., bazant, z.p., becq-giraudon, e., size effect on failure of bond splices of steel bars in concrete beams, asce – journal of structural engineering, 125(6) (1999) 653-660. [19] kayali, o., yeomans, s. r., bond of ribbed galvanized reinforcing steel in concrete, cement & concrete composites 22 (2000) 459-467. [20] li, c. y., finite element simulations of fiber pullout toughening in fiber reinforced cement based composites, advanced cement based materials, 7 (1998) 123-132. [21] lettow, s., the simulation of bond between concrete and reinforcement in nonlinear three-dimensional finite element analysis, in: 5th international phd symposium in civil engineering, delft, the netherlands, (2004). [22] torres, l., baena, m., turon, a., cahís, x., barris, c., simulation of bond behaviour between fiber reinforced polymer bars and concrete, in: 8th international symposium on fiber reinforced polymer reinforcement for concrete structures, patras, greece, (2007). [23] shafaie, j., hosseini, a., marefat, m. s., 3d finite element modelling of bond-slip between rebar and concrete in pullout test, in: 3rd international conference on concrete & development, iran, (2009). [24] lowes, l.n., finite element modelling of reinforced concrete beam-column bridge connections, ph. d. thesis, civil engineering division, university of california, berkeley, usa, (1999). [25] bond of reinforcement in concrete-state of the art report, fib-bulletin, lausanne, 102000. [26] abaqus version 6.11 user’s manual. ri: hibbitt, karlsson & sorensen inc, (2011). [27] fédération internationale du béton / international federation for structural concrete (fib), “fip model code for concrete structures 2010”, paul beverly, lausanne, switzerland, (2013). [28] alfano, g., marfia, s., sacco, e., a cohesive damage-friction interface model accounting for water pressure on crack propagation, computer methods in applied mechanics and engineering, 196 (2006) 192-209. [29] serperi, r., alfano, g., bond-slip analysis via a thermodynamically consistent interface model combining interlocking, damage and friction, int. j. numer. meth. engng, 85 (2011) 164-186. [30] lubliner, j., oliver, j., oller, s., oñate, e., a plastic-damage model for concrete, j. solid structures, 25 (1989) 299326. h.f.s.g. pereira et alii, frattura ed integrità strutturale, 31 (2015) 54-66; doi: 10.3221/igf-esis.31.05 66 [31] sena-cruz, j., cunha, v.m.c.f., camões, a., barros, j.a.o., cruz, p., modelling of bond between galvanized steel rebars and concrete, in: congresso de métodos numéricos en ingenieria, barcelona, spain, (2009) 20. microsoft word numero_44_art_11 g. testa et alii, frattura ed integrità strutturale, 44 (2018) 140-150; doi: 10.3221/igf-esis.44.11 140 equation chapter 1 section 1 modification of the bonora damage model for shear failure gabriel testa, andrew ruggiero, gianluca iannitti, nicola bonora, domenico gentile university of cassino and southern lazio, cassino, italy gabriel.testa@unicas.it, http://orcid.org/0000-0001-2345-6789 abstract. the bonora damage model was extended to account for shearcontrolled damage. to this purpose, a new definition for the damage dissipation potential in which an explicit dependence on the third invariant of deviatoric stress was proposed. this expression leads to damage rate equation in which two contributions, the first for void nucleation and growth damage process the latter for shear fracture, can be recognized. for the jiii controlled damage contribution, only two additional material parameters are necessary of easy experimental identification the extended model formulation was verified predicting the failure locus for al 2024-t351 alloy. finally, the failure locus for stress state combinations, where the minimum material ductility is expected, was determined. keywords. cdm; ductile damage; failure locus; triaxiality; lode parameter; shear fracture. citation: testa, g., ruggiero, a., iannitti, g., bonora, n., gentile, d., modification of the bonora damage model for shear failure, frattura ed integrità strutturale, 44 (2018) 140-150. received: 11.02.2018 accepted: 18.03.2018 published: 01.04.2018 copyright: © 2018 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. introduction he key role of stress triaxiality on ductile fracture of metals and alloys is well known. rice and tracy [1] and mcclintock [2] were among the firsts to observe that the higher the stress triaxiality the smaller the strain to failure. later, this concept was demonstrated experimentally by a number of experimental studies [3-5]. presently, there are compelling evidences that at low or even negative triaxiality numerous classes of materials and alloys show a reduction of failure strain because of an increased susceptibility to shear fracture. mcclintock [6] reported cases where ductility is terminated by shear localization and shear cracking. johnson and cook [5] reported a fracture strain for 4340 steel obtained from a torsion test ( 0  ) that is well below fracture strains at significantly higher mean stresses obtained under axisymmetric conditions from notched tension specimens. later, bao and wierzbicki [7] showed that experimental data at failure for al2024-t351, for different classes of stress states, falls on two distinct branches of a curve on the stress triaxiality vs ductility plot. more recently, barsoum and faleskog [8] also reported susceptibility to fracture under low triaxiality shearing in both mid-strength and high strength weldox steels under combined tension-torsion loading conditions. these results indicate that stress triaxiality alone is inadequate to describe the effect of multiaxial stress state on material ductility, suggesting that also the third invariant of the stress tensor has an influence. in the last decades, several models have been proposed to account for stress triaxiality effect on material ductility. gurson proposed a model based on the growth of a single isolated spherical void in a ductile matrix. he derived a porosity modified yield criterion in which the softening, due to void growth, is enhanced by stress triaxiality [9]. this model has been used extensively to t g. testa et alii, frattura ed integrità strutturale, 44 (2018) 140-150; doi: 10.3221/igf-esis.44.11 141 predict the occurrence of ductile fracture in samples and components [10] and it still used in number or research studies. in continuum damage mechanics (cdm), the influence of stress triaxiality is obtained from the definition of the damage energy dissipation under a generic multi-axial state of stress. in the framework of cdm, several damage model have been proposed. lemaitre [11] developed the theoretical framework for cdm and proposed a simple linear law for damage evolution with plastic strain. tai and yang [12], modified the original lemaitre model formulation introducing an exponential law for damage evolution. later, bonora [13] proposed an expression for the damage dissipation potential that allows obtaining a general non-linear law of evolution for damage suitable to describe ductile damage in different classes of metals. in the last decades, the bonora damage model (bdm) was validated extensively for different materials and practical engineering cases. iannitti et al. [14, 15] used the bdm to explain while ductile damage cannot occur in taylor impact cylinder test of highly ductile metals (ofhc ad al 1100-o) while, because of the different stress triaxiality state, it does occur in symmetric taylor impact test (rod-on-rod) under equivalent velocity conditions. the bdm was also used to predict ductile tearing initiation and propagation in structural components such as deep water offshore pipeline welds [16-19]. both gurson and cdm based model formulations fail in predicting fracture under shear-controlled fracture condition. in particular, cdm models predict that material ductility has to increase when the stress triaxiality is reduced, with a maximum failure strain for pure torsion (zero stress triaxiality). in shear fracture sensitive materials, this behavior is contradicted by experimental results. for instance, in upsetting tests of al 2024 or ti-6al-4v, fracture under compressive load (and negative stress triaxiality) is observed to occur at low strain, without barreling in the sample. recently, the attempt to extend current damage model formulations to account for the influence of jiii, was pursued mainly for the gurson model. among all, nahshon and hutchinson [20] proposed to add a lode parameter dependent term in the gurson model original formulation without the need to reformulate the model for the stress triaxiality controlled part. for what concerns cdm, only few examples of model formulation modification to incorporate shear effect can be found in the literature. cao et al. [21] modified the lemaitre damage dissipation potential introducing an explicit dependence on the lode parameter. in their approach, stress triaxiality and lode parameter act simultaneously on the damage rate making difficult to exclude a priori mutual influence between material model parameters. in this work, following the considerations that motivated the work of nahshon and hutchinson [20], the bdm was modified formulating a new expression for the damage dissipation potential. the novelty of the proposed extended bdm is that the damage dissipation potential is a positive definite function, which is a mandatory requirement in cdm, and that it allows to separate between stress triaxiality and shear controlled damage contributions which allow preserving all features of the original bdm formulation. the proposed extended bdm (hereafter indicated as xbdm) has been used to reproduce the variability of reported fracture strain for al 2024 alloy over a wide range of tress triaxiality including the combined loading regime. the possibility to identify experimentally the additional material parameters is discussed. damage model development the bonora damage model he bonora damage model (bdm) is derived according to the thermodynamics framework of continuum damage mechanics (cdm) initially introduced by lemaitre [22]. the cdm framework consists of three parts: the first is the definition of the state variables, which establishes the present state of corresponding physical mechanisms; the second is the definition of the state potential, from which one can derive the state laws, and the definition of associated variables; the third is the definition of the potential of dissipation to derive the evolution law of state variables, which are associated with the dissipative mechanisms. for what concerns damage processes, the state variable d is introduced. under the assumption of isotropic damage, d is a scalar defined as the ratio between the damaged and the nominal net resisting area of the material reference volume element (rve),  0 dad a (1) d ranges from 0, for the material in the undamaged state, to crd at rupture when the material load carrying capability is completely lost. under the strain equivalence hypothesis, the following definition for the “effective stress” is obtained, (1 ) ij ij d      (2) t g. testa et alii, frattura ed integrità strutturale, 44 (2018) 140-150; doi: 10.3221/igf-esis.44.11 142 this is the stress that should be applied to an undamaged material to cause the strain occurs in the damaged material under the nominal stress. in cdm, the effective stress replaces the cauchy stress in the set of constitutive equations to account for damage effect on the macroscopic behavior of the material. the use of a state variable requires the introduction of the associated state variable. the variable associated to damage is the damage strain energy density release rate y , which is derived from the state potential [23], (1 ) 2 r y d e   (3) here, e is the young’s modulus and r is the function that accounts for stress triaxiality effects,     22 1 3 1 2 3 r       (4) where  is the poisson’s ratio and  is the stress triaxiality factor defined as the ratio of the means stress m and equivalent von mises stress  , m    (5) the kinetic laws of evolution are obtained from the dissipation potential. because plastic flow can occur without damage and, similarly, damage can occur without noticeable macroscopic plastic flow, it can be assumed that the dissipation potential for plastic deformation and damage are independent, df f f  (6) where f and df are the plastic potential (also the yield function in associative flow) and the damage dissipative potential, respectively. from the generalized normality rule, the damage evolution law is obtained as follow, dfd y      (7) where  is the plastic multiplier equal to the equivalent plastic strain rate scaled by damage effect,  1p d    (8) for the damage dissipation potential, bonora proposed the following expression,     1 2 0 0 1 2 1 ˆ cr d d dsy f s d p                     (9) which is a convex function of the associate variables to ensure fulfillment of the second thermodynamics principle. here, 0 , ,s   are material constants while p̂ is the “active plastic strain” defined as the equivalent plastic strain accumulated under positive triaxiality of the state, 2ˆ 3 p p eq eqp d d dt    (10) g. testa et alii, frattura ed integrità strutturale, 44 (2018) 140-150; doi: 10.3221/igf-esis.44.11 143 is the heaviside function that is equal to 1 when the stress triaxiality is positive and 0 otherwise. under compressive state of stress, damage does not accumulate and its effects are temporarily restored ( 0 0&d d  ). this provides a more consistent unilateral condition for damage accumulation and effects. finally, from eqn. (7) and (9), assuming a power law for the material flow curve, the following expression for the damage rate is obtained,                    1/ 1 ˆ ˆln cr cr f th d p d r d d p (11) in this expression , , ,cr th fd   are the material damage parameters where th is the plastic strain threshold under uniaxial state of stress at which damage process is initiated, f is the failure strain under constant stress triaxiality equal to 1/3, and  is the damage exponent that defines the shape of damage evolution law as a function of the active plastic strain. figure 1: evolution of l,  and t with normalized stress ratio 2 1/  under plane stress condition. figure 2: evolution of l and  with stress triaxiality t, under plane stress assumption (for negative t, 2 30, 0   ). g. testa et alii, frattura ed integrità strutturale, 44 (2018) 140-150; doi: 10.3221/igf-esis.44.11 144 lode-dependent modified bonora damage model for shear-dominated loading although the cdm framework is not derived for a specific micromechanism, however, the underlying micromechanism is the nucleation and growth of voids (nag). in this perspective, the failure locus predicted, by eqn. (27), is consistent with ductile failure occurring by necking of intervoid ligament. the motivation for a modification of the bdm for shear dominated loading stems from the consideration that the volume of microvoids undergoing shear may not increase but void deformation and reorientation contribute to the loss of load carrying capability and constitute an effective increase in damage. under shear-dominated loading, the stress triaxiality is zero or slightly positive and current bdm predicts an increase of damage at the slowest rate which implies the largest ductility that material can exhibit. the lode parameter has been introduced to account for the influence of the third invariant of stress on material ductility, 3 3 27 2 j l    (12) where 3j is third invariant of the deviatoric stress tensor ijs ,      3 1 2 3 1 det 3 ij ij ik jk m m mj s s s s            (13) the following expression for the lode parameter, as a function of the stress ratios 2 1/a   and 3 1/b   can be written, 3/22 2 ( 2 1)( 2 1)( 2)1 2 1 a b a b a b l a ab a b b                (14) for plane stress ( 3 0, 0b   ), it reduces to, 3 2 3/22 1 2 3 3 2 2 1 a a a l a a          (15) the lode parameter is bounded between -1 and 1: l=-1 for uniaxial tension ( 0a b  ), while for equibiaxial plane stress tension ( 1, 0a b  ) l= 1 and for pure shear stress ( 0, 1a b   ), l=0. under plane stress condition, the expression of the lode angle as a function of the stress triaxiality can also be uniquely determined, 227 1 2 3 l t t        (16) nahshon and hutchinson [20] introduced the following parameter, 21 l   (17) the evolution of l and  with the stress ratio a and t, for plane stress condition, is shown in fig. 1 and fig. 2 respectively. in the latter figure, l vs t is plotted over the stress triaxiality range of significance [-1/3, 1/3] under plane stress assumption. in order to extend current bdm model formulation for stress states centered on a pure shear stress plus a hydrostatic contribution, the original expression of the damage dissipation potential is modified, similarly to [20], introducing a dependency on ω and that does not vanish when 0m  as follow,     1 2 0 0 0 0 1 2 1 1ˆ cr k d d ds sy y f a d s d s dp                                  (18) g. testa et alii, frattura ed integrità strutturale, 44 (2018) 140-150; doi: 10.3221/igf-esis.44.11 145 figure 3: damage evolution for different values of the shape factor , (k=1). figure 4: relationship between the critical shear strain f and the torsional fracture strain . this expression satisfies the requirement of being a positive definite function. here, no coupling between t and  dependent terms is assumed. thus, the damage rate can be separated in two contributions: the first for nag governed by stress triaxiality and the latter, for shear controlled fracture, governed by  , dfd d d y           (19) where d is given by eqn. (11). recalling eqn. (7) and eqn. (8), the following expression for d is obtained, kd a d p   (20) the simple power law dependence on the parameter  is justified by barsoum and faleskog [8] findings. these indicate that the presence of voids do not seem to play a major role for predicting ductile failure at low levels of triaxiality while g. testa et alii, frattura ed integrità strutturale, 44 (2018) 140-150; doi: 10.3221/igf-esis.44.11 146 failure seems to be governed by a simple criterion based on a critical measure of plastic shear deformation. consequently, for simplicity purpose, it is assumed that shear deformation induced damage starts to accumulate as soon as plastic deformation start to occur (no threshold). integrating eqn. (20) for  =1, the material constant a can be determined as 0 0 cr fd dd a dp d       (21) from which it follows 1 1 1 f d a        (22) for constant  load paths and 1  , eqn. (20) can be integrated to get 1 1k cr f d d p             (23) where f is the critical strain for pure shear and  is a shape factor. varying  , different shape of d evolution with plastic strain can be obtained, included linear damage law for 0  . in fig. 3, damage evolution for different values of the shape factor  are shown. for   1 an exponential damage law, similarly to rice and tracy void growth law, is obtained   0 exp ln k cr f cr f dd p p d d              (24) in this case, the assumption of an initial damage d0, in association with preexisting voids or nucleating particles, becomes necessary. for constant  (or l) and t deformation process, the damage rate equation can be integrated leading to the following expression, 1 1ln 1 1 ln k th cr f th f p d d r p                                   (25) present model formulation predicts that for torsion (t=0 and =1) there is also a damage contribution due to stress triaxiality for those materials in which the failure strain in torsion is larger than the damage threshold strain th. in these cases, provided the torsional failure strain (from experiment) , the parameter f can be determined for 1  as   (1 ) ln2 1 1 3 ln th f f th                       (26) in fig. 4 the relationship between f and  for al 2024 is shown. it is interesting to note that eqn. (26) states that the relationship between the parameter f and  depends, among all, on the shape of damage exponents  and  suggesting that a possible mutual dependence between these two parameters may exists. g. testa et alii, frattura ed integrità strutturale, 44 (2018) 140-150; doi: 10.3221/igf-esis.44.11 147 fracture locus prediction he concept of fracture, or failure, locus (fl), or limit strain diagram (lsd), was introduced by mackenzie et al. [24]. they analyzed the effect of the stress state on failure strain of several steels (ht80, hy130, marrel, low carbon steel and aluminum alloys) performing traction tests on round notched bar samples. for some materials, also fracture strain in torsion is reported. in their work, stress triaxiality was estimated by means of the bridgman solution derived for a necked bar. as confirmed several years later with the development of finite element technology, this definition of stress triaxiality may differs considerably from the effective stress triaxiality occurring in the sample especially at the failure location. however, they were among the firsts to recognize that the effect of the state of stress on fracture initiation may vary for different classes of alloys. later, the fracture locus was also proposed as possible fracture criterion. to this purpose several phenomenological relationships, between failure strain and stress triaxiality, obtained fitting available experimental data at failure, have been proposed [25, 5]. in cdm, the fracture locus can be derived from the model formulation. in fact, equating eqn. (11) integrated for a generic proportional loading condition and for  equal to 1/3, the material failure strain fp as a function of stress triaxiality can be derived 1 r f f th th p p          (27) for low stress triaxiality ( 3  ), which is that resulting from geometry variations such as notches, the stress triaxiality effect on the damage threshold strain can be neglected ( th thp  ), which lead to 1 r f f th th p           (28) according to this expression, material fracture strain increases with decreasing the stress triaxiality with a maximum for pure shear 0  (torsion). in the present framework, in which stress triaxiality alone is insufficient to describe the effect of the stress state on material fracture strain, eqn. (28) is valid under for =0. similarly, the failure locus for shear controlled fracture can be obtained. in fact, for t=0, equating eqn. (20) integrated for constant  and for =1, we get f f k p    (29) according to this expression, the material failure strain varies hyperbolically with . under plane stress condition ( 3 0  ) the relationship in eqn. (16), between land t, can be substituted in (29) to obtain the failure strain in the shear dominated region of the fracture locus diagram. for uniaxial and equibiaxial tension the failure strain for shear controlled fracture becomes infinite (=0) indicating that shear fracture cannot occurs under these stress states. for pure shear loading (i.e. torsion, =1), the failure strain reaches its minimum. under negative stress triaxiality, with a lower bound at t=-1/3, the solution also predicts that failure under controlled shear can still occur while damage due to void growth cannot develop because of the unilateral condition. model validation: application to al2024-t351 he extended bonora damage model (xbdm) was verified predicting fracture in al2024-t351 alloy under different stress states (different combination of t and ). bao and wierzbicki [7] reported failure strain data measured on different specimen geometries: round notched (rnb) bar samples, cylinders with different diameter over height ratios under uniaxial compression, “butterfly” flat specimen for pure shear and combined loading. although t t g. testa et alii, frattura ed integrità strutturale, 44 (2018) 140-150; doi: 10.3221/igf-esis.44.11 148 these tests cover a wide stress triaxiality range from -1/3 up to 1, the lode parameter, and consequently , is not constant in order to verify the predicting capability of the proposed model formulation, material model parameters for al2024-t351 have been determined based on available experimental data. in particular, the parameters for the stress triaxiality controlled damage contribution dt have been determined by fitting of the experimental data relative to tractions performed on rnb specimens. for these geometries the state of stress state is axisymmetric and =0. thus, th and f can be determined by fitting using the expression for the failure locus given in eqn. (28). similarly, the parameters for the shear controlled damage d have been determined by fitting of the experimental data with t<0, for which the contribution of dt is zero because of the unilateral condition. the damage model parameters for al2024-t351 are summarized in tab. 1. th 0.054 th 0.53 dcr 0.1  0.3  0.35 f 0.23  0.30 table 1: summary of damage model parameters for al 2024-t351. in fig. 5 the comparison of predicted fracture loci for stress triaxiality and shear dominated damage with experimental data is shown. here, it can be noted that the agreement is very good for both regions controlled either by  or by t. the gray shaded area is the region where both  and  contribute to determine the critical condition for fracture. also pure torsion falls in this region, since according to the present model formulation, there is a contribution to damage due to dt for t=0. consequently, as expected, fracture strain predicted by eqn. (29) is larger than that measured in pure torsion test. in the intermediate region, where both t and  play a role, fracture strain can be predicted under the assumption of proportional loading (t=const.) and constant  load path using eqn. (25). at fracture d=dcr and p=pf, thus 1 1ln 1 ln k f th f f th f p r p                        (30) figure 5: comparison of the predicted failure locus with experimental data for al2024-t351. g. testa et alii, frattura ed integrità strutturale, 44 (2018) 140-150; doi: 10.3221/igf-esis.44.11 149 this equation can be solved graphically for given t and  values to obtain pf. in fig. 6, the calculated failure strain for experiments in the combined regions is plotted (square black dots). data points have been determined using eqn. (30) provided the corresponding  that was estimated from finite element simulation. the agreement is very good confirming the capability of the proposed modelling to predict accurately the occurrence of fracture under complex stress states. figure 6: failure locus or al2024-t351: lower bound solution. eqn. (30) can be used to predict the regime of stress triaxiality where the material would exhibit the minimum ductility because of the maximum contribution of shear damage. in fig. 6 the lower-bound ductility line is plotted solving eqn. (30) for =1. it is interesting to note that this solution predicts that the reduction of ductility for stress triaxiality up to 1 approximately. for higher stress triaxiality values, the solution merges on that obtained for stress triaxiality controlled damage. this implies that increasing the stress triaxiality overrules the lode parameter effect. this lower bound line corresponds to in plane shear combined with pressure. under plane strain condition, such stress state can be obtained simply applying a tensile (or a compressive) stress to pure shear deformation. in this view, the plane strain ductility is then the minimum ductility that the material would exhibit for unflawed geometry, consistently with fracture mechanics. conclusions n this work, the bonora damage model was extended to account for shear-controlled fracture. to this purpose, based on the motivations given in [20], the original expression of the damage dissipation potential was modified introducing a dependency on the third invariant of the deviatory stress. this leads to a new definition of the damage rate equation with two terms, the first controlled by stress triaxiality and the latter controlled by  which is related to the lode parameter. the proposed model formulation allows predicting the failure locus for selected state of stress states and to identify the region, in ductility vs stress triaxiality plot, where jiii is expected to have an effect in the reduction of material ductility. model prediction capabilities have been verified predicting fracture strain in al 2024-t351 under different stress states. in particular, it was found that, according to the model solution, shear damage may play a role also for high stress triaxiality range (1>t>1/3). finally fracture is predicted to occur under negative stress triaxiality also below the “cut off” of t=-1/3, provided that a compressive stress is superimposed to a pure shear deformation state. references [1] rice, j. r. and tracey, d. m., (1969). on the ductile enlargement of voids in triaxial stress fields. journal of the mechanics and physics of solids, 17, pp. 201-217. [2] mcclintock, f. a., (1968). a criterion for ductile fracture by the growth of holes. journal of applied mechanics, 35, pp. 363-371. i g. testa et alii, frattura ed integrità strutturale, 44 (2018) 140-150; doi: 10.3221/igf-esis.44.11 150 [3] hancock, j. and mackenzie, a., (1976). on the mechanisms of ductile failure in high-strength steels subjected to multi-axial stress-states. journal of the mechanics and physics of solids, 24, pp. 147-160. [4] le roy, g., embury, j., edwards, g. and ashby, m., (1981). a model of ductile fracture based on the nucleation and growth of voids. acta metallurgica, 29, pp. 1509-1522. [5] johnson, g. r. and cook, w. h., (1985). fracture characteristics of three metals subjected to various strains, strain rates, temperatures and pressures. engineering fracture mechanics, 21, pp. 31-48. [6] mcclintock, f. a. 1971. plasticity aspects of fracture. fracture: an advanced treatise. new york: academic press. [7] bao, y. and wierzbicki, t., (2004). on fracture locus in the equivalent strain and stress triaxiality space. international journal of mechanical sciences, 46, pp. 81-98. [8] barsoum, i. and faleskog, j., (2007). rupture mechanisms in combined tension and shear—experiments. international journal of solids and structures, 44, pp. 1768-1786. [9] gurson, a. l., (1977). continuum theory of ductile rupture by void nucleation and growth: part i—yield criteria and flow rules for porous ductile media. journal of engineering materials and technology, 99, pp. 2-15. [10] needleman, a. and tvergaard, v. an analysis of ductile rupture in notched bars. journal of the mechanics and physics of solids, (1984) 32, pp. 461. [11] lemaitre, j., (1985). a continuous damage mechanics model for ductile fracture. journal of engineering material and technology, 107, pp. 83-89. [12] tai, w. h. and yang, b. x., (1987). a new damage mechanics criterion for ductile fracture. engineering fracture mechanics, 27, pp. 371-378. [13] bonora, n., (1997). a nonlinear cdm model for ductile failure. engineering fracture mechanics, 58, pp. 11-28. [14] iannitti, g., bonora, n., ruggiero, a. and testa, g., (2014). ductile damage in taylor-anvil and rod-on-rod impact experiment. journal of physics: conference series, 500. [15] iannitti, g., bonora, n., bourne, n., ruggiero, a. and testa, (2017). g. damage development in rod-on-rod impact test on 1100 pure aluminum. aip conference proceedings,. [16] carlucci, a., bonora, n., ruggiero, a., iannitti, g. and testa, g. (2014). crack initiation and propagation of clad pipe girth weld flaws. american society of mechanical engineers, pressure vessels and piping division (publication) pvp, [17] testa, g., bonora, n., gentile, d., ruggiero, a., iannitti, g., carlucci, a. and madi, y., (2017). strain capacity assessment of api x65 steel using damage mechanics. frattura ed integrita strutturale, 11, pp. 315-327. [18] bonora, n., gentile, d., ruggiero, a., testa, g., folgarait, p. and calatroni, a. (2013). failure assessment of pipe tee element using continuum damage mechanics. american society of mechanical engineers, pressure vessels and piping division (publication) pvp. [19] ruggiero, a., iannitti, g., testa, g., limido, j., lacome, j. l., olovsson, l., ferraro, m. and bonora, n., (2014). high strain rate fracture behaviour of fused silica. journal of physics: conference series, 500. [20] nahshon, k. and hutchinson, j., (2008). modification of the gurson model for shear failure. european journal of mechanics-a/solids, 27, pp. 1-17. [21] cao, t.-s., gachet, j.-m., montmitonnet, p. and bouchard, p.-o., (2014). a lode-dependent enhanced lemaitre model for ductile fracture prediction at low stress triaxiality. engineering fracture mechanics, 124, pp. 80-96. [22] lemaitre, j., (1990). micro-mechanics of crack initiation. international journal of fracture, 42, pp. 87-99. [23] lemaitre, j. (2012). a course on damage mechanics, springer science and business media. [24] mackenzie, a., hancock, j. and brown, d., (1977). on the influence of state of stress on ductile failure initiation in high strength steels. engineering fracture mechanics, 9, pp. 167-188. [25] manjoine, m., (1982). creep-rupture behavior of weldments. welding j., 61, pp. 50. << /ascii85encodepages false /allowtransparency false /autopositionepsfiles true /autorotatepages /none /binding /left /calgrayprofile (dot gain 20%) /calrgbprofile (srgb iec61966-2.1) /calcmykprofile (u.s. web coated \050swop\051 v2) /srgbprofile (srgb iec61966-2.1) /cannotembedfontpolicy /error /compatibilitylevel 1.4 /compressobjects /tags /compresspages true /convertimagestoindexed true /passthroughjpegimages true /createjobticket false /defaultrenderingintent /default /detectblends true /detectcurves 0.0000 /colorconversionstrategy /cmyk /dothumbnails false /embedallfonts true /embedopentype false /parseiccprofilesincomments true /embedjoboptions true /dscreportinglevel 0 /emitdscwarnings false /endpage -1 /imagememory 1048576 /lockdistillerparams false /maxsubsetpct 100 /optimize true /opm 1 /parsedsccomments true /parsedsccommentsfordocinfo true /preservecopypage true /preservedicmykvalues 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/hrv (za stvaranje adobe pdf dokumenata najpogodnijih za visokokvalitetni ispis prije tiskanja koristite ove postavke. stvoreni pdf dokumenti mogu se otvoriti acrobat i adobe reader 5.0 i kasnijim verzijama.) /hun 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/pdfxoutputintentprofileselector /documentcmyk /preserveediting true /untaggedcmykhandling /leaveuntagged /untaggedrgbhandling /usedocumentprofile /usedocumentbleed false >> ] >> setdistillerparams << /hwresolution [2400 2400] /pagesize [612.000 792.000] >> setpagedevice microsoft word numero_53_art_03_2698 p. r. jaiswal et alii, frattura ed integrità strutturale, 53 (2020) 26-37; doi: 10.3221/igf-esis.53.03 26 focussed on the 1st benelux network meeting and workshop on damage and fracture mechanics unified methodology for characterisation of global fatigue damage evolution in adhesively bonded joints pankaj r. jaiswal, rahul iyer kumar, wim de waele soete laboratory, department of electromechanical, systems and metal engineering (emsme), ghent university, belgium. pankaj.jaiswal@ugent.be, https://orcid.org/0000-0002-9373-4489 rahul.iyerkumar@ugent.be, http://orcid.org/0000-0003-1241-2697 wim.dewaele@ugent.be, http://orcid.org/0000-0002-7196-3328 abstract. this paper reports on the development of a methodology for evaluating the fatigue damage evolution in single and double lap adhesively bonded joints subjected to constant and variable fatigue loading. first, a methodology is developed to monitor the evolution of permanent deformation, stiffness degradation and hysteresis losses of single lap joints subjected to constant amplitude fatigue load. during the test, the global deformation of the adhesive joint is monitored using digital image correlation (dic). a matlab code is developed to analyse and visualize the evolution in stiffness degradation and energy dissipation during the course of a complete fatigue test. hereto ellipses are fitted to the hysteresis loops in the recorded load-deformation data. the slope of the main axis of the ellipse and its enclosed area are extracted to determine stiffness and dissipated energy, respectively. next, the methodology is optimized for implementation during fatigue testing of double lap joints with different bond line thicknesses. the results of the experimental study reveal a distinct relation between stiffness degradation and increase in hysteresis losses with increasing number of fatigue cycles or thus increasing fatigue damage. keywords. single lap adhesive joint; double lap adhesive joint; fatigue test; hysteresis. citation: jaiswal, p. r., kumar, r. i., de waele, w., unified methodology for characterisation of global fatigue damage evolution in adhesively bonded joints, frattura ed integrità strutturale, 53 (2020) 26-37. received: 30.11.2019 accepted: 28.04.2020 published: 01.07.2020 copyright: © 2020 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. introduction dhesives are widely applied for joining dissimilar materials, and adhesive joints are most noticeable for the development of lightweight structures in aviation, ships or trains as it directly affects fuel economy [1]. in fact, it has been reported that 7% enhancement in fuel efficiency could result from a weight reduction of 10% for a vehicle structure [2]. whilst in automotive industry spot-welded joints are widely used to reach this purpose [3], the shipbuilding industry has shown a high interest in adhesive bonding. fiber-reinforced polymers are increasingly being used in the a https://youtu.be/wxnctvlkldo p. r. jaiswal et alii, frattura ed integrità strutturale, 53 (2020) 26-37; doi: 10.3221/igf-esis.53.03 27 superstructure of ships [4, 5], and adhesive bonding is considered to be a robust and reliable joining technology for the connection of primary and secondary ship structures. however, the durability of the adhesive joint is one of the main challenges and currently limits the utilisation of adhesive bonding [6, 7]. therefore, it is necessary to evaluate the fatigue performance of an adhesively bonded joint so as to provide a guarantee of its safety for an extended period of service life. several researchers have performed experimental studies to evaluate the fatigue life of adhesives and adhesive joints.  colombi and fava [8] evaluated the fatigue performance and stiffness degradation of double lap adhesive joints, steel bonded to cfrp with a 1.1 mm thick epoxy adhesive layer, subjected to fatigue tests at stress ratios equal to 0.1 and 0.4 at a frequency of 12 hz. they observed that with an increasing number of fatigue cycles the debonding and hysteretic energy loss increase and the joint stiffness decreases. the effect of stress ratio on fatigue life of the adhesive joint was considered negligible.   likewise, the durability and crack propagation of single lap aluminum-gfrp specimens bonded with 0.1mm twocomponent structural epoxy paste (araldite 2015) were investigated for various load ratios in four-point bending tests by zamani et al. [9]. it was shown that crack initiation life was equal to almost half of the total life for a maximum fatigue load equal to 50% of the static failure load whereas it is negligible for maximum fatigue loads higher than 60% of the static failure load. afendi et al. [10] studied the strength of single-lap hybrid joints (a combination of bolts and 0.2 mm thick adhesive layer) with similar and dissimilar adherends (aluminium alloy aa7075 and glass fibre reinforced epoxy). three different joint configurations were aged for 20 to 120 days at a temperature of 50 degrees under a moist environment and fatigue loaded for 781000 cycles. the dissimilar specimen configuration showed the highest joint strength and the largest failure strain compared to specimens based on similar adherends. similarly, machado et al. [11] studied the performance of single lap joints with similar (cfrpcfrp) and disimilar (cfrpaluminium 5754h22) substrates bonded by a 0.2 mm layer of xnr6852 e-3 epoxy. specimens were fatigue cycled in the following conditions: unaged, aged and dried after hydrothermal ageing. the experimental results allowed to conclude that the fatigue performance of joints can be affected by changes induced by the drying process or losses in the interface strength and that the dissimilar combination of substrates sustains higher number of cycles to failure. ayatollahi et al. [12] and razavi et al.[13] evaluated the fatigue performance of adhesively bonded single lap joints with non-flat sinusoid and zigzag interfaces, respectively. two aluminium (7075-t6) adherends were bonded with a 0.2 mm thick two-component epoxy-based adhesive (uhu plus endfest 300). both types of joints have been subjected to constant amplitude fatigue with a load ratio of 0.1 at a frequency of 7hz. the results demonstrated that the fatigue strength and life of the joints with the non-flat interfaces is significantly higher than for reference joints with a flat interface. kałuża et al. [14] studied the bond behaviour of double lap (steel-to-cfrp) adhesive joints subjected to fatigue loading at a frequency of 5 hz. they determined the most suitable type of methacrylate adhesive based on the test results for seven different methacrylate adhesives. all previously discussed references focus on thin adhesives. to the best of our knowledge, there is no scientific literature on fatigue damage evolution of thick methyl metacrylate adhesive bonds for joining steel and cfrp. the main objective of this work is to develop and evaluate a methodology to quantify the evolution of fatigue damage during constant amplitude tensile fatigue (catf) tests and variable amplitude tensile fatigue (vatf) tests. first, a methodology is developed to monitor the evolution of damage in single lap adhesive joint (slaj) specimens subjected to a catf test. digital image correlation (dic) is used to measure the global elongation of the adhesive joint [15,16]. a matlab routine is developed to post-process the fatigue test data and to quantify and visualize the evolution of global damage in terms of permanent deformation, stiffness degradation and hysteresis losses. second, the methodology has been optimized towards catf and vatf testing of double lap adhesive joint (dlaj) specimens with two different bond line thicknesses. materials and specimens adhesive or the experimental work, a two-component methyl methacrylate (mma) adhesive was used. the selected adhesive exhibits promising properties of high strength and high ductility [14]. the main mechanical properties of the mma adhesive are summarized in tab. 1. substrates and surface treatment conventional s235 carbon steel and high strength shipbuilding steel ah36 (having a minimum specified yield stress of 350mpa) were selected for the substrates of a single-lap adhesive joint and a double lap adhesive joint configuration respectively. carbon fibre reinforced polymer (cfrp) laminates with a minimum tensile strength of 658 mpa were selected as strap material for the dlaj specimens. f p. r. jaiswal et alii, frattura ed integrità strutturale, 53 (2020) 26-37; doi: 10.3221/igf-esis.53.03 28 for manufacturing of the slaj specimens, the substrates were saw-cut from a steel plate to nominal dimensions of 104 x 25 x 6 mm (length x width x thickness). this was followed by sandblasting of the surface (interface between substrate and adhesive) up to a roughness of approximately 2.5 µm, and cleaning with acetone prior to bonding. sandblasting increases the roughness of the surface, which will enhance the adhesive strength of the joint. care was taken as excessive roughness is known to decrease the strength of the joint [17]. property mma tensile strength [mpa] 12 – 15 maximum tensile elongation [%] 40 60 tensile modulus [mpa] 207-276 lap shear strength [mpa] 16-19 service temperature range [°c] -40 to +82 table 1: main mechanical properties of mma [14,18]. (a) (b) (c) figure 1: (a) a three-dimensional representation of the fixture used for the production of slaj specimens, (b) schematic diagram of a single-lap adhesive joint, (c) produced slaj specimen. (all dimensions are in mm) p. r. jaiswal et alii, frattura ed integrità strutturale, 53 (2020) 26-37; doi: 10.3221/igf-esis.53.03 29 production of single and double adhesive lap joint specimens in this work, two different types of adhesively bonded specimens were manufactured. in a first series, a total of eight slaj specimens with 6mm thick steel substrates were produced. the bond line thickness was controlled to 5mm by using the mould presented in fig. 1(a). the curing of the adhesive was done at room temperature for 24 hours according to the supplier guidelines. essential aspects of the joint are the adherend chamfers and adhesive fillets for reducing stress concentrations at the ends of the bonded area. the reduced stress concentrations should improve fatigue strength and extend the lifetime. the geometry and dimensions have been roughly based on standard astm d1002 [19] and are illustrated in fig. 1(b). after manufacturing, the edges of the substrates along the overlap were prepared with the use of a hand grinder, in order to obtain an acceptable surface finish for dic speckling (see further). additionally, alignment tabs were welded to each adherend, to reduce the geometrical eccentricity of the joint while loading. the final appearance of an slaj specimen is shown in fig. 1(c). in a second series, a total of six dlaj specimens with 8mm thick steel (ah36) and 3mm thick composite (cfrp) substrates were produced with two different bond line thicknesses (4mm and 8mm) in the actual working environment of the maritime industry (damen schelde naval shipbuilding, the netherlands). steel substrate surface preparation was performed identically as described for the slaj specimens. the schematic diagram of the dlaj specimen is illustrated in fig. 2. figure 2: schematic diagram of double lap adhesive joint specimen. fatigue testing methodology he fatigue tests on slaj specimens were performed at room temperature on an esh servo-hydraulic machine with a maximum load capacity of 100kn. the fatigue tests on dlaj specimens have been performed on an esh machine with 150kn load capacity. to allow a detailed study of fatigue damage evolution, the load and the global elongation of the adhesive joint need to be recorded throughout the test. for the dlaj specimens, the elongation of the joint can be accurately approximated by the load-line displacement recorded by the machine. the asymmetry and flexibility of the slaj specimens do not allow to use the load-line displacement. therefore digital image correlation (dic) was used to determine the elongation of the joint during fatigue testing. dic is a contactless deformation measurement method, which uses digitally captured images of a surface of the test specimen. a detailed description of the dic technique can be found in [20,21]. it requires a high contrast surface to maintain a good correlation between the captured images during post-processing. hereto a black speckle pattern (randomly distributed paint dots) is applied over the bright white background of the specimen’s surface of interest. the general requirement for the speckled surface is around 50% black and 50% white. a speckle size of 0.042 mm was aimed at, which results in a measurement accuracy of 100 µε [22,23]. a schematic representation of the test setup, including speckled specimen, light sources and cameras is shown in fig. 3(a). on the one hand, dic has been used to evaluate the strains inside the adhesive joint (not reported in this paper). on the other hand, it was used to record the relative vertical displacement between two markers p0 and p1 (see fig. 3(b)), one on each steel adherend, which serves as an accurate approximation of the global elongation of the adhesive joint. the goal of the above is to accurately determine the relation between applied tensile force and the corresponding elongation of the adhesive joint during a single load cycle. due to the viscoelastic behaviour of the adhesive, hysteresis will occur during each load cycle. it means that the load versus elongation curve during loading and unloading follows different trajectories, t p. r. jaiswal et alii, frattura ed integrità strutturale, 53 (2020) 26-37; doi: 10.3221/igf-esis.53.03 30 thus forming a hysteresis ellipse for each fatigue cycle. based on the characteristics of this ellipse, three essential parameters can be determined, as indicated in fig. 4.  the displacement of the centre of the ellipse x0.  the slope of the centre line, quantified by angle ∅, representing the stiffness of the joint.  the enclosed surface area ‘a’ as an indication of the dissipated energy. figure 3: (a) schematic layout of dic set up [15], (b) characterisation of the global deformation of the adhesive joint by tracking the relative vertical displacement of two virtual markers (p0-p1). figure 4: a typical load-elongation hysteresis ellipse recorded during a fatigue test on slaj specimen. a similar approach for the identification of hysteresis loops obtained during fatigue testing of a structural epoxy adhesive has been reported in [24]. a post-processing routine to calculate and plot the evolution in stiffness degradation, hysteretic energy dissipation and permanent elongation during a complete fatigue cycle was developed in matlab code. the displacement of the centre gives an indication of the amount of permanent, viscoplastic deformation that has occurred. the slope of the main axis of the ellipse relates to the stiffness of the joint; a decrease in slope during the test indicates an accumulation of damage [25,26]. an increase in the enclosed area is a measure for the increased dissipation of mechanical energy [27]. in order to avoid the impact of viscous behaviour or excessive heat dissipation on the durability of the adhesive joint, the fatigue tests were performed at frequencies of 2 and 4 hz. marcadon et al. [28] performed fatigue tests on t-joints for marine applications at 0.2, 1 and 5 hz and concluded that the fatigue damage at the lowest frequency was most probably influenced by viscous behaviour. the selected test frequencies also comply with the dnvgl-rp-c301 standard [29], which p. r. jaiswal et alii, frattura ed integrità strutturale, 53 (2020) 26-37; doi: 10.3221/igf-esis.53.03 31 recommends a maximum loading frequency of 4hz. temperature measurements performed with a handheld thermometer (fluke-68) during fatigue testing and focusing on the adhesive proved that no noticeable heat dissipation occurred. this is important since self-heating of the adhesive would affect its mechanical properties and damage evolution. figure 5: data are acquired at discrete time steps during a slow load cycle (0.1hz) following an interval of 99 fast cycles (2hz). the development of the methodology is based on the group of slaj specimens, tested at a frequency of 2hz. in order to ensure manageable dic data file sizes and reducing the post-processing time, data acquisition has been performed at distinct time intervals. after every series of 99 fatigue cycles (at 2hz), a single slow cycle (0.1hz) was included because the rate of image capturing by the dic cameras is limited to 1 picture per second. this allows to determine 10 dic-based elongation measurements during one slow cycle; a similar methodology is reported in [30]. load versus elongation data were collected during the slow cycle in order to construct one hysteresis ellipse; a typical plot with experimental data and the fitted loadelongation loop is shown in fig. 4. it can be observed that the implemented data acquisition and data post-processing allow characterizing a fatigue hysteresis cycle with reasonable accuracy; only a few outliers do not perfectly fit the hysteresis ellipse. the synchronisation of the test rig control system and the dic data acquisition system is illustrated in fig. 5. figure 6: a sinewave for storing data after an interval of 2000 working cycles. p. r. jaiswal et alii, frattura ed integrità strutturale, 53 (2020) 26-37; doi: 10.3221/igf-esis.53.03 32 in order to improve the methodology of global fatigue damage evolution, a fatigue test was performed at a frequency of 4 hz, and dic images were captured at a rate of 3.846hz. a total of 25 images were post-processed to construct one hysteresis ellipse, as shown in fig. 6. the synchronisation of the data acquisition and dic cameras was implemented in such a way that the dic cameras are triggered frequently, at an interval of every 2000 fatigue cycles. the same methodology was also reported in [25,26]. a representative load-displacement output resulting from this methodology is shown in fig. 7. outliers are eliminated and the fitted ellipse fit excellently represents the collection of experimental data points. results and discussion he fatigue results of slaj and dlaj specimens are discussed in the following two subsections. the first subsection discusses the fatigue testing methodology applied to slaj specimens subjected to constant amplitude fatigue loading. the second subsection reports the results of the dlaj specimens subjected to constant and variable amplitude fatigue loading. figure 7: a load-elongation hysteresis ellipse (slaj). sample id range of load amplitude (minmax) kn fatigue life (cycles) frequency (hz) status of a sample at the end of the test load ratio (r=fmin/fmax) sg-05 0.6-6 3119 2 fail 0.1 sg-04 0.5-5 15900 4 fail 0.1 sg-06 0.4-4 100000 2 intact 0.1 sl-06 0.7-7 100000 4 fail 0.1 table 2: overview of fatigue tests performed on slaj specimens. single lap adhesive joint to define a suitable range of fatigue load amplitudes, four slaj specimens have first been subjected to quasi-static tensile tests at a displacement rate of 1mm/min. the maximum failure load observed was 8kn, and all specimens exhibited a relatively high elongation at failure. next, four tensile fatigue tests were conducted on slaj specimens at a load ratio r=0.1 and different maximum load levels (i.e. 87.5%, 75%, 62.5% and 50% of the maximum observed ultimate tensile strength 8kn). the fatigue test details are summarized in tab. 2. specimens sg-05, sg-04 and sl1-06 have been tested up to failure, while the fatigue test on specimen sg-06 was stopped at 105 cycles to constrain the test duration. 1 the abbreviations sg and sl refer to the first and second production batch respectively. production process and geometry are identical for both batches. t p. r. jaiswal et alii, frattura ed integrità strutturale, 53 (2020) 26-37; doi: 10.3221/igf-esis.53.03 33 representative results obtained for specimen sg-04 have been selected to plot hysteresis loops in fig. 8. a general trend of decreasing stiffness and increasing permanent deformation can be clearly observed by the decreasing slope of the ellipses and the shift of the centre point of the ellipse. the onset of failure was accompanied by a more rapid reduction of stiffness and increase in dissipated energy. these observations agree very well with the findings of boyd in his study on the integrity of hybrid steel-to-composite joints for marine applications [30]. figure 8: load-elongation hysteresis loops for slaj specimen sg-04. double lap adhesive joint specimens in total, six dlaj specimens have been tested at room temperature. first, two quasi-static tensile tests were performed on an mts servo-hydraulic machine with 1000 kn load cell capacity at a displacement rate of 0.5 mm/min. the failure loads and corresponding average shear stresses are listed in tab. 3. the tensile test results confirmed that a thin adhesive bond line thickness leads to a higher average shear strength (4.9 mpa) as compared to a thick adhesive joint (2.6 mpa) [31–33]. based on the results of the tensile tests, a maximum fatigue load of 30kn (corresponding to an average shear stress of 1 mpa) was defined; the test frequency was set at 4hz. the catf tests were conducted on specimens dl-02 and dl-07 and stopped prior to failure after 5x106 and 2.7x106 fatigue cycles, respectively, in order to limit the test duration. the ellipses shown in fig. 9 illustrate the load-displacement data of the double lap joint specimen dl-02 until 1x106 cycles. sample id bond line thickness(mm) ultimate load (kn) shear test (mpa) sample after test dl-09 4 147 2.6 fail dl-05 8 78 4.9 fail table 3: overview of tensile tests performed on dlaj specimens. sample id bond line thickness(mm) type of test ultimate/range of load (min – max) kn fatigue life (cycles) frequency (hz) load ratio (r=fmin/fmax) sample after test dl-02 8 caf 3-30 2.7 x 106 4 0.1 intact dl-07 4 caf 3-30 5.0 x 106 4 0.1 intact dl-04 8 vaf stepped loading of 7.5 6.62 x 105 4 0.1 fail dl-10 4 vaf stepped loading of 7.5 8.23 x 105 4 0.1 fail table 4: overview of fatigue tests performed on dlaj specimens. p. r. jaiswal et alii, frattura ed integrità strutturale, 53 (2020) 26-37; doi: 10.3221/igf-esis.53.03 34 the dissipated energy per fatigue cycle remained almost constant throughout the test, indicating that this parameter is probably not very sensitive to slightly increased damage. fig. 10 shows the evolution of the stiffness for dlaj specimen dl-02; the reported values have been normalized by the initial value of stiffness. the graph shows a noticeable decrease of stiffness at the start, followed by steady progress for the first million cycles. this observation indicates that after the initial 50000 cycles, almost no additional damage is introduced in the specimen. figure 9: load-elongation hysteresis loops for dlaj specimen dl-02. figure 10: evolution of damage parameter ∅ for dlaj specimen dl-02. figure 11: evolution of centre of ellipse xo for dlaj specimen dl-02. this corresponds with visual observations during the test. fig. 11 shows the displacement of the centre of the ellipse until 1 million cycles. a significant increase is observed with the increasing number of fatigue cycles. notwithstanding that no further damage could be observed, the viscoplastic deformation of the adhesive joint keeps on slowly increasing. the variable amplitude fatigue tests were performed up to failure for specimens dl-10 and dl-04 with a bond line thickness of respectively 4mm and 8mm. the atmospheric conditions, test frequency and methodology of data acquisition were identical to the constant load fatigue tests. the variable amplitude fatigue tests were force-controlled and characterised by load step changes of 0.25 mpa average shear stress. starting at a load corresponding to 0.25mpa average shear stress, the load was increased every 100 000 cycles. specimens dl-04 and dl-10 reached a maximum of 662 838 and 823 265 cycles, respectively. similar to the observations of the tensile tests, the thick bond line thickness decreases the fatigue strength of the joint compared to a thin adhesive. representative hysteresis ellipses were obtained without any loss of data points, as demonstrated in fig. 12. fig. 13 shows p. r. jaiswal et alii, frattura ed integrità strutturale, 53 (2020) 26-37; doi: 10.3221/igf-esis.53.03 35 the evolution of damage in terms of normalized energy dissipation for dlaj specimen dl-04. the energy dissipation increases throughout the test, with more or less constant values during each block. a continuously decreasing stiffness with the increasing number of cycles was found, in line with the above observations and the observations reported in [24]. fig. 14 shows the displacement of the centre of the ellipse throughout the test. a significant increase is observed at every load block change, and within each load block, the increase in displacement shows a continuous evolution. between 200 000 and 400 000 cycles this increase is slow, from 400 000 cycles on the displacement of the ellipses increases faster and at 600 000 cycles, the displacement is that big that the specimen separated eventually. figure 12: load-elongation hysteresis loops for dlaj specimen dl-04. figure 13: evolution of damage parameter a for dlaj specimen dl-04. figure 14: evolution of change in centre of ellipse xo for dlaj specimen dl-04. conclusion ingle lap adhesive joint specimens and double lap adhesive joint specimens with two different bond line thicknesses were subjected to a series of constant and variable amplitude fatigue tests. due to the viscoelastic nature of the mma adhesive, the load versus elongation curves recorded during fatigue testing show typical hysteretic behaviour. using dic for monitoring these tests proved to be a valuable tool for an accurate elongation measurement of the flexible slaj s p. r. jaiswal et alii, frattura ed integrità strutturale, 53 (2020) 26-37; doi: 10.3221/igf-esis.53.03 36 specimens. to evaluate the fatigue damage, a matlab code was developed that allows to study the evolution of three characteristics of the hysteresis curves; i.e. the canter of the ellipse (representative of permanent viscoplastic deformation), the slope of the ellipse major axis (representative of the stiffness of the joint) and the enclosed area (representative of the dissipated energy per cycle. a general trend of increasing permanent elongation, decreasing slope and increasing enclosed surface area of the hysteresis ellipses was observed. the results from tests on dlaj specimens indicated that a larger adhesive thickness was inferior to a smaller thickness in terms of static and fatigue strength. acknowledgement he authors would like to thanks thomas geldhof, lauren buyck and mika besard for performing the fatigue tests in the framework of their master dissertations. also thanks to damen schelde naval shipbuilding (the netherlands) for manufacturing the double lap joint specimens. funding his research was carried out within the project “qualify–enabling qualification of hybrid joints for lightweight and safe maritime transport”, co-funded by the interreg 2seasmers zeeën programme and the province of east-flanders. references [1] das, s. (2011). life cycle assessment of carbon fiber-reinforced polymer composites, int. j. life cycle assess., 16(3), pp. 268–282. [2] cheah, l. (2010). cars on a diet: the material and energy impacts of passenger vehicle weight reduction in the u.s. doctor of philosophy in engineering thesis, engineering systems division, , pp. 121. [3] farrahi, g.h., kashyzadeh, k.r., minaei, m., sharifpour, a., riazi, s. (2020). analysis of resistance spot welding process parameters effect on the weld quality of three-steel sheets used in automotive industry: experimental and finite element simulation, int. j. eng., 33(1), pp. 148–157, doi: 10.5829/ije.2020.33.01a.17. [4] noury, p., hayman, b., mcgeorge, d., weitzenbock, j. (2002). lightweight construction for advanced shipbuilding– recent development, det nor. verit. norw. [5] jahnke, j., molter, l., mus, r.l. (2019). adhesive free gfrp-steel connection for maritime applications. trends in the analysis and design of marine structures: proceedings of the 7th international conference on marine structures (marstruct 2019, dubrovnik, croatia, 6-8 may 2019), crc press, p. 353. [6] heshmati, m., haghani, r., al-emrani, m. (2015). environmental durability of adhesively bonded frp/steel joints in civil engineering applications: state of the art, compos. part b eng., 81, pp. 259–275, doi: 10.1016/j.compositesb.2015.07.014. [7] heshmati, m., haghani, r., al-emrani, m. (2016). effects of moisture on the long-term performance of adhesively bonded frp/steel joints used in bridges, compos. part b eng., 92, pp. 447–62. [8] colombi, p., fava, g. (2012). fatigue behaviour of tensile steel/cfrp joints, compos. struct., 94(8), pp. 2407–2417, doi: 10.1016/j.compstruct.2012.03.001. [9] zamani, p., jaamialahmadi, a., da silva, l.f.m., farhangdoost, k. (2019). an investigation on fatigue life evaluation and crack initiation of al-gfrp bonded lap joints under four-point bending, compos. struct., pp. 111433. [10] mariam, m., afendi, m., majid, m.s.a., ridzuan, m.j.m., sultan, m.t.h., jawaid, m., gibson, a.g. (2019). hydrothermal ageing effect on the mechanical behaviour and fatigue response of aluminium alloy/glass/epoxy hybrid composite single lap joints, compos. struct., 219, pp. 69–82. [11] machado, j.j.m., marques, e.a.s., barbosa, a.q., da silva, l.f.m. (2019). fatigue performance of single lap joints with cfrp and aluminium substrates prior and after hygrothermal aging, fatigue fract. eng. mater. struct., 42(10), pp. 2325–39, doi: 10.1111/ffe.13067. [12] ayatollahi, m.r., samari, m., razavi, s.m.j., da silva, l.f.m. (2017). fatigue performance of adhesively bonded single lap joints with non-flat sinusoid interfaces, fatigue fract. eng. mater. struct., 40(9), pp. 1355–1363, t t p. r. jaiswal et alii, frattura ed integrità strutturale, 53 (2020) 26-37; doi: 10.3221/igf-esis.53.03 37 doi: 10.1111/ffe.12575. [13] razavi, s.m.j., ayatollahi, m.r., samari, m., da silva, l.f.m. (2019). effect of interface non-flatness on the fatigue behavior of adhesively bonded single lap joints, proc. inst. mech. eng. part l j. mater. des. appl., 233(7), pp. 1277– 1286, doi: 10.1177/1464420717739551. [14] kałuża, m., hulimka, j. (2017). methacrylate adhesives to create cfrp laminate-steel joints–preliminary static and fatigue tests, procedia eng., 172, pp. 489–96. [15] van lancker, b., hertelé, s., de corte, w., dispersyn, j., de waele, w., belis, j. (2016).application of digital image correlation in linear structural adhesive glass-metal connection testing. glasscon global, fca conferences, llc, pp. 305–313. [16] colavito, k., das, m., hahs, d., gorman, j., madenci, e., smeltzer, s. (1816).digital image correlation for adhesive strains in bonded composite lap joints. 49th aiaa/asme/asce/ahs/asc structures, structural dynamics, and materials conference, 16th aiaa/asme/ahs adaptive structures conference, 10th aiaa non-deterministic approaches conference, 9th aiaa gossamer spacecraft forum, 4th aiaa multidisciplinary des, p. 1844. [17] rudawska, a., danczak, i., müller, m., valasek, p. (2016). the effect of sandblasting on surface properties for adhesion, int. j. adhes. adhes., 70, pp. 176–90. [18] hulimka, j., kałuża, m. (2017). preliminary tests of steel-to-steel adhesive joints, procedia eng., 172, pp. 385–392. [19] d-1002-05, a. (2001).standard test method for apparent shear strength of single-lap-joint adhesively bonded metal specimens by tension loading (metal-to-metal). american society for testing materials. [20] dispersyn, j., hertelé, s., de waele, w., belis, j. (2017). assessment of hyperelastic material models for the application of adhesive point-fixings between glass and metal, int. j. adhes. adhes., 77, pp. 102–117. [21] kumar, r.l.v., bhat, m.r., murthy, c.r.l. (2013). experimental analysis of composite single-lap joints using digital image correlation and comparison with theoretical models, j. reinf. plast. compos., 32(23), pp. 1858–1876. [22] (n.d.). resolution and accuracy. available at: https://www.correlatedsolutions.com/support/index.php?/knowledgebase/article/view/8/1/resolution-andaccuracy. [23] rutkiewicz, a., jakobczak, a. (2017). the digital image correlation system accuracy direct testing using strain gauges, proc. 2017 balt. geod. congr. (geomatics), bgc geomatics 2017, pp. 369–373, doi: 10.1109/bgc.geomatics.2017.71. [24] savvilotidou, m., keller, t., vassilopoulos, a.p. (2017). fatigue performance of a cold-curing structural epoxy adhesive subjected to moist environments, int. j. fatigue, 103, pp. 405–414. [25] dattoma, v., giancane, s. (2013). evaluation of energy of fatigue damage into gfrc through digital image correlation and thermography, compos. part b eng., 47, pp. 283–239. [26] giancane, s., panella, f.w., nobile, r., dattoma, v. (2010). fatigue damage evolution of fiber reinforced composites with digital image correlation analysis, procedia eng., 2(1), pp. 1307–15. [27] casas-rodriguez, j.p., ashcroft, i.a., silberschmidt, v. v. (2007). damage evolution in adhesive joints subjected to impact fatigue, j. sound vib., 308(3–5), pp. 467–478. [28] marcadon, v., nadot, y., roy, a., gacougnolle, j.l. (2006). fatigue behaviour of t-joints for marine applications, int. j. adhes. adhes., 26(7), pp. 481–489. [29] veritas, d.n. (2012). design, fabrication, operation and qualification of bonded repair of steel structures, recommended practice, dnv-rp-c301. [30] boyd, s.w., blake, j.i.r., shenoi, r.a., kapadia, a. (2004). integrity of hybrid steel-to-composite joints for marine application, proc. inst. mech. eng. part m j. eng. marit. environ., 218(4), pp. 235–246. [31] kahraman, r., sunar, m., yilbas, b. (2008). influence of adhesive thickness and filler content on the mechanical performance of aluminum single-lap joints bonded with aluminum powder filled epoxy adhesive, j. mater. process. technol., 205(1–3), pp. 183–169. [32] arenas, j.m., narbón, j.j., alía, c. (2010). optimum adhesive thickness in structural adhesives joints using statistical techniques based on weibull distribution, int. j. adhes. adhes., 30(3), pp. 160–165. [33] ojalvo, i.u., eidinoff, h.l. 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can be opened with acrobat and adobe reader 5.0 and later.) >> /namespace [ (adobe) (common) (1.0) ] /othernamespaces [ << /asreaderspreads false /cropimagestoframes true /errorcontrol /warnandcontinue /flattenerignorespreadoverrides false /includeguidesgrids false /includenonprinting false /includeslug false /namespace [ (adobe) (indesign) (4.0) ] /omitplacedbitmaps false /omitplacedeps false /omitplacedpdf false /simulateoverprint /legacy >> << /addbleedmarks false /addcolorbars false /addcropmarks false /addpageinfo false /addregmarks false /convertcolors /converttocmyk /destinationprofilename () /destinationprofileselector /documentcmyk /downsample16bitimages true /flattenerpreset << /presetselector /mediumresolution >> /formelements false /generatestructure false /includebookmarks false /includehyperlinks false /includeinteractive false /includelayers false /includeprofiles false /multimediahandling /useobjectsettings /namespace [ (adobe) (creativesuite) (2.0) ] /pdfxoutputintentprofileselector /documentcmyk /preserveediting true /untaggedcmykhandling /leaveuntagged /untaggedrgbhandling /usedocumentprofile /usedocumentbleed false >> ] >> setdistillerparams << /hwresolution [2400 2400] /pagesize [612.000 792.000] >> setpagedevice microsoft word numero_59_art_17_3269.docx t. cuong-le et alii, frattura ed integrità strutturale, 59 (2022) 232-242; doi: 10.3221/igf-esis.59.17 232 focussed on steels and composites for engineering structures a nonlinear concrete damaged plasticity model for simulation reinforced concrete structures using abaqus thanh cuong-le*, hoang-le minh, thanh sang-to faculty of civil engineering, ho chi minh city open university, ho chi minh city, viet nam cuong.lt@ou.edu.vn, hoang.lm@ou.edu.vn, sang.tt@ou.edu.vn abstract. the reinforced concrete structure is typical and widely used in many fields. the behavior of concrete is nonlinear and complex. especially, when cracks/crushings occurred in softening phase. thus, it is important to find a damaged model of concrete with high reliability in the numerical simulation. the nonlinear behavior of concrete is the most feature used in the simulation. this characteristic is expressed through the parameters defining the yield surface, the flow potential, and the nonlinear relationship of stressstrain in the cases of tension and compression. this paper introduces a damaged concrete model that applies to the simulation of reinforced concrete structures. the reinforced concrete beam and flat slab are selected as examples to evaluate the reliability of the model presented. through the results achieved, the model used in this paper shows high reliability and can be used to simulate more complex reinforced concrete structures. keywords. nonlinear behavior; concrete material; numerical simulation; concrete damaged plasticity. citation: cuong-le, t., le-minh, h., sangto, t., a nonlinear concrete damaged plasticity model for simulation reinforced concrete structures using abaqus, frattura ed integrità strutturale, 59 (2022) 232-242. received: 12.09.2021 accepted: 23.09.2021 published: 01.01.2022 copyright: © 2022 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. introduction ecause of the complicated nonlinear behavior of concrete material. there are many theories about the damaged model in a finite element method (fem) analysis reported in the literature. among the damaged models, the concrete damaged plasticity (cdp) model is considered the most reliable use in simulation. based on this model, by using many other techniques, many damaged models have been proposed. most improved techniques are based on developing a new stress-strain relationship in both compression and tension or proposing a novel function to calculate damaged parameters in compression dc and tension (dt). lubliner et al. [1] was proposed a novel constitutive model lied on plasticity theory for the non-linear analysis of concrete. a new yield criterion was presented which accounts for both elastic and plastic stiffness degradations effects. comparing results between numerical simulation and experimental methods showed that the model responded well to applications. carol et al. [2] was presented as a formulation for tensile damage. one of the important advantages of the model is that closed-form solutions are possible for some loading cases. damaged models which are based on presenting a novel curve of stress-strain in three dimensions stress can find in reports of. ahmed et al. [3]. were proposed a damaged model based on the novel stress accounting for damaged shear. the new stress makes further decompose tensile and compressive parts into pure biaxial shear and pure tensile/compressive biaxial stresses. the theory of lubliner theory [1] was employed to develop a new method to modify b https://youtu.be/2uqyvnhmwha t. cuong-le et alii, frattura ed integrità strutturale, 59 (2022) 232-242; doi: 10.3221/igf-esis.59.17 233 the damaged concrete model by lee et al. [4]. thus, this proposed model was accounted for confinement having a uniform and non-uniform conditions. jason et al. [5] introduced the new function to calculate the damaged elastic-plastic. this model has overcome the limitations of pure elastic-plastic damage in the case un-loading phase. grassl et al. [6] were used the combination of damage mechanics and plasticity flow to investigate the concrete structure under dynamic loading conditions, etc. in this paper, the concrete damaged plasticity model (cdp) in combination with the tensile damage variable (dt) and compressive damage variable (dc) were followed by birtel and mark [7]. this model is employed to simulate the test of a reinforced concrete beam namely c3 in tests of vecchio và shim (2004) [8] and a reinforced concrete slab in test of genikomsou and polak [9] for reliable consideration. a damaged model presented for concrete material parameters for the yield function and plastic flow potential he damaged concrete plasticity model (cdp) is employed in the abaqus manual. this model was improved by lee and fenves [4] . the model cdp based on that definition the yield function of concrete shown in fig. 1 and the parameters of flow potential and yield surface given in tab. 1. where  0 0/b c is the ratio between the strength of biaxial and uniaxial in compression. kc is the ratio between the magnitudes of deviatoric stress in uniaxial tension and compression. figure 1: concrete yield surface dilation angle eccentricity ( )  0 0/b c ck 300~400 0.1 1.16 0.667 table 1: the material parameters in cdp model. compressive and tensile behavior behavior in compression uniaxial loading conditions in compression includes 3 phases shown in fig. 2. the details of phases are described below: t t. cuong-le et alii, frattura ed integrità strutturale, 59 (2022) 232-242; doi: 10.3221/igf-esis.59.17 234 phase 1: in this phase, the relationship of stress-strain is denoted linear given in eqn. (1). at the end of this phase registered   0.4c cmf according to ec2.  1 0c ce (1) phase 2: when the compressive stress is achieved   0.4c cmf , cracks begin to appear accordingly, the relationship of stress-strain of concrete in this phase is nonlinear behavior given in eqn. (2)                     2 12 1 1 1 2 c c ci cm c c cm c c ci cm c e f f e f (2) where cie is the modulus of elasticity of concrete. phase 3: the behavior of concrete in this phase is softening and determined based on the theory which is proposed by kratzig and polling (2004), this model is suitable for numerical analysis because the model depends on the length of mesh elements eql . phase 3 is expressed in eqns. (3-4).                  12 3 1 1 2 2 2 c cm c c c c c c cm c f f (3)                     2 1 2 1 0 ; 2 0.5 (1 b) pl cm c c c in c ch cm cm c eq f b g f f b l e (4) where chg denotes crushing energy,  pl c and  in c are plastic strain and inelastic strain, respectively. figure 2: behavior in compression. behavior in tension the tensile nonlinear behavior of concrete is a curve showing the stress-crack opening relationship proposed by hordijk. the characteristic of this curve is that it does not depend on the element meshing in the fem model. the formulation of this relationship is given in eqn. (5). t. cuong-le et alii, frattura ed integrità strutturale, 59 (2022) 232-242; doi: 10.3221/igf-esis.59.17 235               2 3 3 2 1 1 ( ) 1 (1 )c w c w ct tm c c w w w c e c e f w w (5) where  1 23, 6.93c c and wc is the critical crack opening which can be considered as the fracture crack opening given in eqn. (6).  5.14 fc tm g w f (6) based on the curve of stress-crack opening relationship, it can be obtained a new curve having the feature of stress-strain through eqn. (7). thus, the strain t at tensile strength tm can be evaluated from crack opening. where eql can consider as a length of element (meshed size). after this assumption, the stress-strain curve relationship given in fig. 3.   t tm eq w l (7) figure 3: behavior in tension. compressive damage and tension damaged component compression damage variable (dc) this parameter is used to specify compressive stiffness degradation damage, cd is determined through plastic strain  pl c and a using a constant factor cb with 0 < cb ≤ 1.            1 1 1 1/ 1 c c c pl c c c c e d b e (8) in this paper, assumption  0.7cb to evaluate the parameter cd . fig. 4 illustrates the relationship between compressive damage parameter and inelastic strain with concrete having strength  35cmf calculated in eqn. (8). t. cuong-le et alii, frattura ed integrità strutturale, 59 (2022) 232-242; doi: 10.3221/igf-esis.59.17 236 figure 4: the curve of compressive damage parameter and inelastic strain tension damage variable (dt) similar to the compression damage variable cd , the damaged parameter in tension td depends on  pl t and an experimentally determined parameter  0.1tb . so, unloading is assumed to return almost back to the origin and to leave only a small residual strain.            1 1 1 1/ 1 c c t pl c t t c e d b e (9) figure 5: the curve of compressive damage parameter and crack opening. application for simulation of a reinforce concrete beam beam namely c3 is selected as reported by vecchio và shim (2004) [8]. the geometry and details of beam c3 are shown in fig. 6. the beam has a section; 152mm width and 552mm height. the length of the beam is 6400mm. rebars at the bottom layer arrange (2m30+2m25) and at the top layer is (3m10). experimental geometry and details of c3 beam are shown in fig. 6. the material characteristics of the c3 beam are given in tab. 2. numerical simulation was established using abaqus software. in detail, the beam uses solid element type c3d8r with 1 point of gaussian integration, rebar uses t2d3 element which is only under tension and compression conditions, interaction between rebar and concrete using "embedded" algorithm. this method allows a node or group nodes of rebar to be constrained to the kinetic boundary conditions with the nodes in the concrete elements. in the simulation c3 beam of vecchio and shim (2004) [10], the rebar and the concrete have meshed with the same element size (40mm). the a t. cuong-le et alii, frattura ed integrità strutturale, 59 (2022) 232-242; doi: 10.3221/igf-esis.59.17 237 interaction between the rigid steel plate and the concrete uses the "tie". the progress in the simulation is shown in fig. 7. a comparison of the displacement which is arranged at the middle beam between the simulation and data obtained from the experiment is given in fig. 8. the results in fig. 8 show that the damaged nonlinear model presented satisfies the beam stiffness degradation. simulation result at the complete failure of the beam registered the loading having 266 kn compared with the test loading having 267 kn. figure 6: elevations and cross-sections of c3 beam. concrete       avarage compressive strength fcm 43.5 n/mm2 modulus of elasticity eci 34300 n/mm2 tensile strength ftm 3.13 n/mm2 rebar-m10 diameter  11.3 mm modulus of elasticity e 200000 n/mm2 yield strength fy 315 n/mm2 ultimate tensile strength fu 460 n/mm2 rebarm25 diameter  25.2 mm modulus of elasticity e 200000 n/mm2 yield strength fy 445 n/mm2 ultimate tensile strength fu 680 n/mm2 rebarm30 diameter  29.9 mm modulus of elasticity e 200000 n/mm2 yield strength fy 436 n/mm2 ultimate tensile strength fu 700 n/mm2 rebard4 diameter  3.7 mm modulus of elasticity e 200000 n/mm2 yield strength fy 600 n/mm2 ultimate tensile strength fu 651 n/mm2 table 2: material characteristics of the c3 beam. t. cuong-le et alii, frattura ed integrità strutturale, 59 (2022) 232-242; doi: 10.3221/igf-esis.59.17 238 figure 7: simulation c3 beam using abaqus. figure 8: comparison of the displacement between simulation and experiment. figure 9: cracking pattern in simulation. figure 10: damaged c3 beam in an experiment. figure 11: crushing pattern in simulation. the patterns of cracking and crushing in the simulation are given in fig. 9 and fig. 11. in comparison with the complete failure of the beam in fig. 10. based on the results, we can recognize that the cracking/crushing pattern using simulation is consistent with the experimental results. the damaged model used in this paper can show cracked/crushed elements that having the damaged parameters /t cd d in range value  0, 1 . t. cuong-le et alii, frattura ed integrità strutturale, 59 (2022) 232-242; doi: 10.3221/igf-esis.59.17 239 application for simulation of a reinforce concrete slab his example presents finite element simulations of punching shear in a concrete slab implemented by adetifa and polak [9]. this example is employed to evaluate the reliability of the proposed damaged model for predecting the behavior of a complex structure concrete. the geometry and details of the specimen concrete slab had the dimensions 1800 × 1800 × 120mm. for bending reinforcement, 10m bar were used to embed in the slab. the arrangement of bars in top layer and bottom layer is illustrated in fig. 12. the section a-a is shown in fig. 13 and the material characteristics are given in tab. 3. figure 12: the arrangement of bars: (a) in the top layer, (b) in the bottom layer. figure 13: the section a-a of specimen. concrete avarage compressive strength fcm 44 n/mm2 modulus of elasticity eci 36483 n/mm2 rebar-d10 diameter  10 mm modulus of elasticity e 200000 n/mm2 yield strength fy 455 n/mm2 ultimate tensile strength fu 620 n/mm2 table 3: material characteristics of the concrete slab. t (a) (b) t. cuong-le et alii, frattura ed integrità strutturale, 59 (2022) 232-242; doi: 10.3221/igf-esis.59.17 240 the process of numerical simulation using abaqus is carried out similar to the previous example. this process includes defining geometrical dimensions, defining the nonlinear behavior of steel and concrete materials, establishing the boundary conditions, and setting the loading process until the structure is completely damaged. the geometrical dimensions in the simulation are given in fig. 14. figure 14: simulation reinforce concrete slab using abaqus. the simulation result show that the maximum punching shear force value is 243 kn compared to the of 241 kn obtained from experimental result. the difference between numerical simulation results and experimental results is only 0.82%. the relationship between punching shear force – displacement at the middle of slab using simulation is also very good agreement compared to experimental results as shown in fig. 15. figure 15: comparison of displacement between simulation and experiment. the damaged model of concrete materials using in this paper also allows to predict the crack pattern, which is defined by the elements having plastic deformation, the crack shapes in fig. 16 and in fig. 17 show that the position around the column with 1.5m distance from the edge of the column is the crack appearing with the largest density and width. figure 16: the damaged shape of punching shear in section view. t. cuong-le et alii, frattura ed integrità strutturale, 59 (2022) 232-242; doi: 10.3221/igf-esis.59.17 241 figure 17: comparison the crack pattern on the top of slab between simulation and experiment. conclusion he paper presents a damaged model of concrete in numerical simulation. this model is developed lied on the cdp (available in abaqus) associating with the proposed damaged parameters  0.7cb in compression and  0.1tb tension. this damaged model is employed to simulate the real-test beam namely c3 in vecchio và shim (2004) [8] under static loading and a flat concrete slab in the test of adetifa and polak [9]. the numerical simulation results show that the model satisfies well with the data obtained from testing. the complete failures of the c3 beam the cracking in the top face of slab using numerical simulation illustrated that two damaged parameters responded well to the experiment’s results. the model presenting in this paper can be considered as a reference model with high reliability in simulation structural reinforced concrete. acknowledgements he authors gratefully acknowledge the financial support granted by the scientific research fund of the ministry of education and training (moet), vietnam (no. b2021-mbs-06). reference [1] lubliner, j., oliver, j., oller, s. and onate, e. (1989). a plastic-damage model for concrete. international journal of solids and structures 25, pp. 299-326. [2] carol, i., rizzi, e., willam, k. (2001). on the formulation of anisotropic elastic degradation. ii. generalized pseudorankine model for tensile damage, int. j. solids struct., 38(4), pp. 519–546, doi: 10.1016/s0020-7683(00)00031-7. [3] ahmed, b., voyiadjis, g.z., park, t. (2020). damaged plasticity model for concrete using scalar damage variables with a novel stress decomposition, int. j. solids struct., 191–192, pp. 56–75, doi: 10.1016/j.ijsolstr.2019.11.023. [4] lee, j., fenves, g.l. (1998). plastic-damage model for cyclic loading of concrete structures, j. eng. mech., 124(8), pp. 892–900, doi: 10.1061/(asce)0733-9399(1998)124:8(892). [5] jason, l., huerta, a., pijaudier-cabot, g., ghavamian, s. (2006). an elastic plastic damage formulation for concrete: application to elementary tests and comparison with an isotropic damage model, comput. methods appl. mech. eng., 195(52), pp. 7077–7092, doi: 10.1016/j.cma.2005.04.017. [6] grassl, p., nyström, u., rempling, r., gylltoft, k. (2011). a damage-plasticity model for the dynamic failure of concrete, proc. 8th int. conf. struct. dyn. eurodyn 2011, pp. 3287–3294. [7] birtel, v., mark, p. (2006). parameterised finite element modelling of rc beam shear failure, ababqus user’s conf., , pp. 95–108. [8] vecchio, f.j., shim, w. (2004). experimental and analytical reexamination of classic concrete beam tests, j. struct. t t t. cuong-le et alii, frattura ed integrità strutturale, 59 (2022) 232-242; doi: 10.3221/igf-esis.59.17 242 eng., 130(3), pp. 460–469, doi: 10.1061/(asce)0733-9445(2004)130:3(460). [9] genikomsou, a.s., polak, m.a. (2014). finite element analysis of a reinforced concrete slab-column connection using abaqus, struct. congr. 2014 proc. 2014 struct. congr., , pp. 813–823, doi: 10.1061/9780784413357.072. [10] engineering, s. (2015). compressive behavior of unconfined and confined clay brick masonry compressive behavior of unconfined and confined clay, october, 9445(april 2004), pp. 1562–1569, doi: 10.1061/(asce)0733-9445(2004)130. << /ascii85encodepages false /allowtransparency false /autopositionepsfiles true /autorotatepages /none /binding /left /calgrayprofile (dot gain 20%) /calrgbprofile (srgb iec61966-2.1) /calcmykprofile (u.s. web coated \050swop\051 v2) /srgbprofile (srgb iec61966-2.1) /cannotembedfontpolicy /error /compatibilitylevel 1.4 /compressobjects /tags /compresspages true /convertimagestoindexed true /passthroughjpegimages true /createjobticket false /defaultrenderingintent /default /detectblends true /detectcurves 0.0000 /colorconversionstrategy /cmyk /dothumbnails false /embedallfonts true /embedopentype false /parseiccprofilesincomments true /embedjoboptions true /dscreportinglevel 0 /emitdscwarnings false /endpage -1 /imagememory 1048576 /lockdistillerparams false /maxsubsetpct 100 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/hrv (za stvaranje adobe pdf dokumenata najpogodnijih za visokokvalitetni ispis prije tiskanja koristite ove postavke. stvoreni pdf dokumenti mogu se otvoriti acrobat i adobe reader 5.0 i kasnijim verzijama.) /hun 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can be opened with acrobat and adobe reader 5.0 and later.) >> /namespace [ (adobe) (common) (1.0) ] /othernamespaces [ << /asreaderspreads false /cropimagestoframes true /errorcontrol /warnandcontinue /flattenerignorespreadoverrides false /includeguidesgrids false /includenonprinting false /includeslug false /namespace [ (adobe) (indesign) (4.0) ] /omitplacedbitmaps false /omitplacedeps false /omitplacedpdf false /simulateoverprint /legacy >> << /addbleedmarks false /addcolorbars false /addcropmarks false /addpageinfo false /addregmarks false /convertcolors /converttocmyk /destinationprofilename () /destinationprofileselector /documentcmyk /downsample16bitimages true /flattenerpreset << /presetselector /mediumresolution >> /formelements false /generatestructure false /includebookmarks false /includehyperlinks false /includeinteractive false /includelayers false /includeprofiles false /multimediahandling /useobjectsettings /namespace [ (adobe) (creativesuite) (2.0) ] /pdfxoutputintentprofileselector /documentcmyk /preserveediting true /untaggedcmykhandling /leaveuntagged /untaggedrgbhandling /usedocumentprofile /usedocumentbleed false >> ] >> setdistillerparams << /hwresolution [2400 2400] /pagesize [612.000 792.000] >> setpagedevice microsoft word numero_46_art_16 v. rizov, frattura ed integrità strutturale, 46 (2018) 158-177; doi: 10.3221/igf-esis.46.16 158 developments in the fracture and fatigue assessment of materials and structures analysis of cylindrical delamination cracks in multilayered functionally graded non-linear elastic circular shafts under combined loads victor rizov department of technical mechanics, university of architecture, civil engineering and geodesy, 1 chr. smirnensky blvd., 1046 – sofia, bulgaria v_rizov_fhe@uacg.bg abstract. this paper is focused on delamination fracture analyses of a multilayered functionally graded circular shaft under two loading combinations (centric tension and torsion, and bending and torsion) assuming non-linear elastic mechanical behavior of the material. the loading combinations under consideration generate mixed-mode ii/iii delamination crack loading conditions (the centric tension and bending generate mode ii crack loading, while the torsion is responsible for mode iii crack loading). the shaft is made by concentric longitudinal layers. the number of layers is arbitrary. besides, each layer has individual thickness and material properties. the material in each layer is functionally graded in radial direction. hyperbolic laws are used to describe the continuous variation of material properties in radial direction. a cylindrical delamination crack (the crack front is a circle) is located arbitrary between layers. the delamination fracture is studied in terms of the strain energy release rate by analyzing the energy balance. in order to verify the solution obtained, the strain energy release rate is derived also by differentiating the complementary strain energy with respect to the delamination crack area. parametric investigations of the behavior of the cylindrical delamination crack are carried-out. the present paper is a contribution in the fracture mechanics of multilayered functionally graded non-linear elastic circular shafts under combined loads. keywords. multilayered circular shaft; functionally graded material; cylindrical delamination crack; material non-linearity; combined loads. citation: rizov, v., analysis of cylindrical delamination cracks in multilayered functionally graded non-linear elastic circular shafts under combined loads, frattura ed integrità strutturale, 46 (2018) 158-177. received: 04.05.2018 accepted: 03.06.2018 published: 01.10.2018 copyright: © 2018 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. introduction ne of the main advantages of the functionally graded materials over the traditional structural materials is the material property graded distribution [1 6]. very often, fracture is the critical failure mode for the functionally graded structures to lose their structural capacity [7 10]. therefore, the study of fracture mechanics of o http://www.gruppofrattura.it/va/46/16.mp4 v. rizov, frattura ed integrità strutturale, 46 (2018) 158-177; doi: 10.3221/igf-esis.46.16 159 functionally graded materials plays an important role in the design of various structural members and devices made by these novel un-homogeneous materials. understanding the fracture behavior of functionally graded structures under various loading conditions is vital for the further development of the methods for safety design. the present paper deals with analyses of a cylindrical delamination crack in a multilayered functionally graded non-linear elastic circular shaft under combined loads. it should be mentioned that in one of the previous works of the author, nonlinear analyses of cylindrical delamination cracks in circular shafts have been developed assuming that the shafts are loaded in pure torsion only [10]. however, in reality, the circular shafts usually are under various load combinations which include torsion (this fact is the basic motive for writing the present paper). fracture analysis in terms of the strain energy release rate shaft under centric tension and torsion he multilayered functionally graded circular shaft, shown schematically in fig. 1, is under consideration. the shaft is made of adhesively bonded concentric longitudinal layers. in each layer, the material is functionally graded in radial direction. besides, the functionally graded material exhibits non-linear mechanical behavior. figure 1: multilayered functionally graded circular shaft loaded in centric tension and torsion. the number of layers is arbitrary. also, each layer has individual thickness and material properties. the shaft cross-section is a circle of radius, r . the length of the shaft is 2l . the shaft is loaded in centric tension and torsion, respectively, by longitudinal forces, f , and torsion moments, t , applied at the end sections of the shaft as shown in fig. 1. a circular notch is cut-out in the middle of the shaft in order to generate conditions for delamination fracture. it is assumed that a cylindrical delamination crack of length, 2a , is located symmetrically with respect to the middle of the shaft. the delamination crack represents a cylindrical surface (the crack front is a circle of radius, br ). thus, the internal crack arm is a shaft of length, 2a , and circular cross-section of radius, br . the external crack arm is a shaft of length, 2a , and ringshaped cross-section of internal radius, br , and external radius, r . the delamination crack is located arbitrary between layers. the circular notch divides the external crack arm in two symmetric segments of length, a , each. apparently, the two segments of the external crack arm are free of stresses (fig. 1). due to the symmetry, only half of the shaft, 2l x l  , is analyzed. in the present paper, the delamination fracture is studied in terms of the strain energy release rate. it is obvious that the longitudinal force, f , induces mode ii crack loading conditions. the mode ii component of the strain energy release rate, iig , is determined by analyzing the energy balance. by assuming an increase of the crack length, a , the energy balance is written as f ii c u f u a g l a a        (1) t v. rizov, frattura ed integrità strutturale, 46 (2018) 158-177; doi: 10.3221/igf-esis.46.16 160 where u is the increase of the longitudinal displacement of the end section of the shaft, fu is the strain energy cumulated in half of the shaft as a result of the centric tension by f , cl is the length of the crack front. by substituting of 2c bl r in (1), iig is obtained as 1 2 2 2 f ii b b uf u g r a r a         (2) the expression in brackets in (2) is doubled due to the symmetry (fig. 1). it should be specified that the present delamination fracture analysis is valid for non-linear elastic behavior of the material. the analysis can also be applied for elastic-plastic behavior if the shaft undergoes active deformation, i.e. if the external loading increases only [11, 12]. it should also be mentioned that the present analysis is carried-out assuming validity of the small strains assumption. by using methods of mechanics of materials, one obtains  l hu a l a    (3) where l and h are, respectively, the longitudinal strains in the internal crack arm and the un-cracked shaft portion, 2l a x l   , induced by the longitudinal force, f . figure 2: cross-section of the internal crack arm loaded in centric tension and torsion. the longitudinal strain in the internal crack arm is determined from the following equation for equilibrium of the crosssection of the internal crack arm: 1 1 i i n i i a f da     (4) where 1n is the number of layers in the internal crack arm, i is the distribution of the longitudinal normal stresses in the i-th layer, ia is the area of the cross-section of the same layer. in the present paper, the mechanical behavior of the functionally graded material in the i-th layer is described by the following non-linear stress-strain relation [13]: i i is p      (5) where is and ip are the distributions of the material properties in the same layer,  is the longitudinal strain. v. rizov, frattura ed integrità strutturale, 46 (2018) 158-177; doi: 10.3221/igf-esis.46.16 161 the properties, is and ip , vary continuously in the radial direction of the i-th layer according to the following hyperbolic laws: 1 1 i i b i i d i i s s r r s r r     (6) 1 1 i i b i i d i i p p r r p r r     (7) where ib s , id s , ib p and id p are material properties ( id s and id p control the material gradient of is and ip , respectively), ir and 1ir  are shown in fig. 2. in (6) and (7), the radius, r , varies in the interval  1;i ir r  . it should be mentioned that the distribution of the longitudinal strains is analyzed assuming validity of the hypothesis for plane sections, since the length to diameter of the cross-section ratio of the shaft under consideration is large. thus, l is distributed uniformly in the cross-section of the internal crack arm. hence, by substituting of (5), (6) and (7) in (4), one derives     1 2 2 3 3 1 1 1 2 2 3 i n i i l i i i i i f r r r r                (8) where 1 i i i b l b i i s p       (9) 2 2 2 i i i i i i b d l b d i i i i i b l b i i s s p p s p                  (10) 1i i ir r   (11) 1 i d i i i s r     (12) 1 i d i i i p r     (13) it should be noted that by substituting of 0 id s  and 0 ib p  in (8), one obtains   1 2 2 1 1 1 i i n l i i i b f r r s       (14) v. rizov, frattura ed integrità strutturale, 46 (2018) 158-177; doi: 10.3221/igf-esis.46.16 162 which is exact match of the equation for equilibrium of multilayered circular shaft made by homogeneous linear-elastic layers loaded in centric tension [14]. this fact is an indication for consistency of eqn. (8) since at 0 id s  and 0 ib p  the non-linear stress-strain relation (5) transforms in the hooke’s law assuming that 1/ ib s is the modulus of elasticity in the i-th layer. eqn. (8) should be solved with respect to l by using the matlab computer program. eqn. (8) is applied also to determine h . for this purpose, 1n and l are replaced, respectively, with n and h in (8), (9) and (10). here, n is the number of layers in the un-cracked shaft portion. figure 3: non-linear   diagram. since the external crack arm is free of stresses (fig. 1), the strain energy cumulated in half of the shaft as a result of the centric tension is written as f fl fhu u u  (15) where flu and fhu are the strain energies in the internal crack arm and the un-cracked shaft portion, respectively. the strain energy in the internal crack arm is obtained by addition of strain energies cumulated in the layers 1 0 1 i i i n fl fl i a u a u da     (16) where 0 iflu is the strain energy density in the i-th layer. the strain energy density is equal to the area, opq, enclosed by the stress-strain curve (fig. 3). thus, 0 iflu is written as 0 0 l ifl i u d     (17) by substituting of (5) in (17), one derives 0 1 ln ln i i i i i fl l l i i i i i s s s s u p p p p p                (18) the strain energy cumulated in the un-cracked shaft portion is expressed as v. rizov, frattura ed integrità strutturale, 46 (2018) 158-177; doi: 10.3221/igf-esis.46.16 163   0 1 i i i n fh fh i a u l a u da      (19) where the strain energy density in the i-th layer, 0 ifhu , is obtained by formula (18). for this purpose, l is replaced with h . by substituting of (3), (15), (16) and (19) in (2), one obtains   1 0 0 1 1 1 i i i i i n i n ii l h fl fh i ib b a a f g u da u da r r                       (20) apparently, the torsion moment, t , induces mode iii crack loading conditions (fig. 1). by analyzing the balance of the energy, the mode iii component of the strain energy release rate, iiig , is written as 1 2 2 2 t iii b b ut g r a r a           (21) where  is the angle of twist of the end section of the shaft, tu is the strain energy cumulated in half of the shaft as a result of the torsion. in (21), the expression in the brackets is doubled in view of the symmetry (fig. 1). by applying methods of mechanics of materials, one obtains  qm b a l a r r      (22) where m and q are the shear strains at the periphery of the cross-sections of the internal crack arm and the un-cracked shaft portion, respectively. the shear strain at the periphery of the cross-section of the internal crack arm is determined by using the following equation for equilibrium of the cross-section of the internal crack arm: 1 1 i i n i i a t rda     (23) where i is the distribution of the shear stresses in the i-th layer induced by the torsion. in the present paper, the mechanical behavior of the functionally graded material in torsion is described by the following non-linear stress-strain relation [13]: i i if g      (24) where  is the shear strain, if and ig are the distributions of the material properties in the i-th layer. the continuous variation of if and ig in the radial direction of the i-th layer is described by the following hyperbolic laws: 1 1 i i b i i d i i f f r r f r r     (25) v. rizov, frattura ed integrità strutturale, 46 (2018) 158-177; doi: 10.3221/igf-esis.46.16 164 1 1 i i b i i d i i g g r r g r r     (26) where 1i ir r r   (27) the radiuses, ir and 1ir  , are shown in fig. 2. in (25) and (26), ibf , idf , ibg and idg are material properties ( idf and id f govern the gradient of if and ig , respectively). the distribution of shear strains in radial direction is written as m b r r   (28) by substituting of (24), (25), (26) and (28) in (23), one derives     1 4 4 5 1 1 1 2 1 1 5 4 5 i n m i i i i i i i b t r r r r r                 (29) where 1 i i    (30)  22 21 1 i i i b i b m i d ii i i i b i f g g rr r                (31) id i i f    (32) 1 ib i i i f r     (33) it should be mentioned that at 0 ib g  and 0 id f  eqn. (29) transforms in   1 4 4 1 1 1 2 i i n m i i i b b t r r r f        (34) the fact that (34) is exact match of the equation for equilibrium of a multilayered circular shaft made by linear-elastic homogeneous layers loaded in torsion [14] is an indication for consistency of (34) since at 0 ib g  and 0 id f  the nonlinear stress-strain relation (24) transforms in the hooke’s law assuming that 1/ ib f is the shear modulus in the i-th layer. eqn. (29) should be solved with respect to m by using the matlab computer program. eqn. (29) is used also to determine the shear strain at the periphery of the cross-section of the un-cracked shaft portion. for this purpose, 1n , br and m are replaced, respectively, with n , r and q in (29) and (31). v. rizov, frattura ed integrità strutturale, 46 (2018) 158-177; doi: 10.3221/igf-esis.46.16 165 figure 4: non-linear   diagram. the strain energy cumulated in half of the shaft as a result of the torsion is obtained as t tl thu u u  (35) where tlu and thu are the strain energies in the internal crack arm and the un-cracked shaft portion, respectively. the strain energy in the internal crack arm is written as 1 0 1 i i i n tl tl i a u a u da     (36) where 0 itlu is the strain energy density in the i-th layer as a result of the torsion. in principle, the strain energy density is equal to the area, opq, enclosed by stress-strain curve in fig. 4. thus, formula (18) can be used to obtain 0 itlu . for this purpose, 0 iflu , l , is and ip are replaced, respectively, with 0 itlu ,  , if and ig , where  is expressed by (28). the strain energy cumulated in the un-cracked shaft portion as a result of the torsion is expressed as   0 1 i i i n hl th i a u l a u da      (37) where the strain energy density in the i-th layer, 0 ithu , is obtained by (18). for this purpose, 0 iflu , l , is and ip are replaced, respectively, with 0 ithu , h , if and ig . here, the distribution of the shear strains is written as h q r r   (38) by substituting of (22), (35), (36) and (37) in (21), one obtains 1 0 0 1 1 1 i i i i i n i n qm iii tl th i ib b b a a t g u da u da r r r r                         (39) the total strain energy release rate, g , is written as ii iiig g g  (40) v. rizov, frattura ed integrità strutturale, 46 (2018) 158-177; doi: 10.3221/igf-esis.46.16 166 by substituting of (20) and (39) in (40), one arrives at   1 0 0 1 1 1 i i i i i n i n l h fl fh i ib b a a f g u da u da r r                        1 0 0 1 1 1 i i i i i n i n qm tl th i ib b b a a t u da u da r r r r                         (41) the integration in (41) should be performed by the matlab computer program. in order to verify (41), the strain energy release rate is derived also by differentiating the complementary strain energy with respect to the crack area. the total strain energy release rate is written as [15] *du g da  (42) where *du is the change of the complementary strain energy, da is an elementary increase of the crack area. for the cylindrical delamination crack (fig. 1), da is expressed as 2 bda r da (43) where da is an elementary increase of the crack length. by substituting of (43) in (42), one arrives at * 2 b du g r da  (44) the complementary strain energy cumulated in half of the shaft as a result of the centric tension and torsion is obtained as * * *l hu u u  (45) where *lu and * hu are the complementary strain energies in the internal crack arm and the un-cracked shaft portion, respectively. the complementary strain energy in the internal crack arm is expressed as 1 * * 0 1 i i i n l l i a u a u da     (46) where *0 ilu is the complementary strain energy density in the i-th layer. the complementary strain energy density is equal to the area, oqr, that supplements the area enclosed by the stress-strain curve to a rectangle (fig. 3 and fig. 4). thus, * 0 il u is written as *0 0 0il i l fl i tlu u u       (47) by substituting of (5), (18), (24) and (28) in (47), one obtains v. rizov, frattura ed integrità strutturale, 46 (2018) 158-177; doi: 10.3221/igf-esis.46.16 167 2 * 0 1 ln ln i i i i il l l l i i l i i i i i s s s s u s p p p p p p                     2 1 ln lni i i i i i i i i i i f f f f f g g g g g g                    (48) where  is determined by (28). the complementary strain energy in the un-cracked shaft portion as a result of centric tension and torsion is written as  * *0 1 i i i n h h i a u l a u da      (49) where the complementary strain energy density, *0 ihu , is obtained by (48). for this purpose, * 0 il u , l and  are replaced, respectively, with *0 ihu , h and h , where h is determined by (38). the expression, obtained by substituting of (45), (46) and (49) in (44), is doubled in view of the symmetry (fig. 1). the result is 1 * * 0 0 1 1 1 i i i i n i n l h i ib a a g u da u da r                (50) integration in (50) should be carried-out by the matlab computer program. it should be noted that the strain energy release rate calculated by (50) is exact match of the strain energy release rate determined by (41). this fact verifies the analysis of the cylindrical delamination crack in the multilayered functionally graded circular shaft loaded in centric tension and torsion (fig. 1). shaft under bending and torsion the cylindrical delamination crack is analyzed also when the external loading consists of bending moments, m , and torsion moments, t , applied at the two ends of the multilayered functionally graded circular shaft (fig. 5). figure 5: multilayered functionally graded circular shaft loaded in bending and torsion. obviously, the bending moments induce mode ii crack loading. by considering the balance of the energy, the mode ii component of the strain energy release rate is derived as v. rizov, frattura ed integrità strutturale, 46 (2018) 158-177; doi: 10.3221/igf-esis.46.16 168 1 2 2 2 m mii b b um g r a r a           (51) where  is the angle of rotation of the end section of the shaft due to the bending, mu is the strain energy cumulated in half of the shaft as a result of the bending. it should be noted that the bending induces stresses not only in the un-cracked shaft portion and the internal crack arm, but also in the external crack arm. by using methods of mechanics of materials,  is obtained as  l ha l a     (52) where l and h are the curvatures of the crack arms and the un-cracked shaft portion, respectively. since the bending generates mode ii crack loading conditions, the two crack arms deform with the same curvature. therefore, l is determined in the following way. first, the equation for equilibrium of the cross-section of the internal crack arm is used 1 1 1 i i n d i i a m z da     (53) where dm is the bending moment in the internal crack arm. the distribution of the longitudinal normal stress, i , in the i-th layer, induced by the bending of the shaft, are expressed by (5). the distribution of the longitudinal strains,  , is written as 1l z  (54) by substituting of (5), (6) and (7) in (23), one derives     1 4 4 5 5 1 1 1 1 1 4 5 i n d l i i i l i i i i m r r r r                 (55) where i i i bs    (56) i i d i b i s s    (57) the radiuses, ir and 1ir  , in (55) are shown in fig. 6. it should be noted that at 0 ib p  and 0 id s  eqn. (55) transforms in   1 4 4 1 1 1 4 i i n l d i i i b m r r s      (58) which is exact match of the equation for equilibrium of multilayered circular shaft made of homogeneous linear-elastic layers loaded in bending [14] assuming that 1/ ib s is the modulus of elasticity in the i-th layer. v. rizov, frattura ed integrità strutturale, 46 (2018) 158-177; doi: 10.3221/igf-esis.46.16 169 figure 6: cross-section of the internal crack arm loaded in bending and torsion. figure 7: two three-layered functionally graded circular shafts loaded in centric tension and torsion with cylindrical delamination crack located between (a) layers 2 and 3 and (b) layers 1 and 2. in (55), there are two unknowns, dm and l . one more equation with unknowns dm and l is derived by considering the equilibrium of the cross-section of the external crack arm. obviously, (55) can be used as equation for equilibrium of the cross-section of the external crack arm. for this purpose, 1n has to be replaced with 2n ( 2n is the number of layers in the external crack arm). besides, dm has to be replaced with dm m (this follows from the fact that the sum of the bending moments in the two crack arms is equal to m ). thus, the equation for equilibrium of the cross-section of the external crack arm is written as     2 4 4 5 5 1 1 1 1 1 4 5 i n d l i i i l i i i i m m r r r r                  (59) eqns. (55) and (59) should be solved with respect to l and dm by using the matlab computer program. v. rizov, frattura ed integrità strutturale, 46 (2018) 158-177; doi: 10.3221/igf-esis.46.16 170 eqn. (55) is used also to determine h . for this purpose, dm , 1n and l are replaced, respectively, with m , n and h . the strain energy cumulated in half of the shaft as a result of the bending is obtained as m ml mq mhu u u u   (60) where mlu , mqu and mhu are the strain energies in the internal crack arm, the external crack arm and the uncracked shaft portion, respectively. formula (16) is applied to determine mlu . for this purpose, flu and 0 iflu are replaced with mlu and 0 imlu , respectively. the strain energy density, 0 imlu , in the i-th layer of the internal crack arm as a result of the bending is obtained by formula (18). for this purpose, 0 iflu and l are replaced with 0 imlu and  , respectively (  is expressed by formula (54)). figure 8: two three-layered functionally graded circular shafts loaded in bending and torsion with cylindrical delamination crack located between (a) layers 2 and 3 and (b) layers 1 and 2. formula (16) is used also to determine mqu by replacing of flu , 1n and 0 iflu with mqu , 2n and 0 imqu , respectively. 0 imqu is determined by replacing of l with  . mhu is found by formula (19). for this purpose, fhu and 0 ifhu are replaced with mhu and 0 imhu , respectively. the strain energy density, 0 imhu , in the i-th layer of the un-cracked beam portion as a result of bending is obtained by formula (18). for this purpose, 0 iflu and l are replaced with 0 imhu and b , respectively. the distribution of the longitudinal strains, b , in the cross-section of the un-cracked shaft portion is found by (54). for this purpose,  , l v. rizov, frattura ed integrità strutturale, 46 (2018) 158-177; doi: 10.3221/igf-esis.46.16 171 and 1z are replaced with b , h and 2z , respectively ( 2z is the vertical centroidal axis of the cross-section of the uncracked portion of the shaft). by substituting of (52), mlu , mqu , mhu and (60) in (51), one derives the following expression for the mode ii component of the strain energy release rate as a result of the shaft bending:   1 2 0 0 0 1 1 1 1 i i i i i i i n i n i n mii l h ml mq mh i i ib b a a a m g u da u da u da r r                            (61) the mode iii component of the strain energy release rate induced by the shaft torsion is obtained by formula (39). the total strain energy release rate is found by addition of (39) and (61). the result is   1 2 0 0 0 1 1 1 1 i i i i i i i n i n i n l h ml mq mh i i ib b a a a m g u da u da u da r r                             1 0 0 1 1 1 i i i i i n i n qm tl th i ib b b a a t u da u da r r r r                         (62) integration in (62) should be carried-out by the matlab computer program. figure 9: the strain energy release rate in non-dimensional form plotted against 1d s property (curve 1 – for the shaft configuration shown in fig. 7a, curve 2 – for the shaft configuration shown in fig. 8a, curve 3 – for the shaft configuration shown in fig. 7b, curve 4 – for the shaft configuration shown in fig. 8b). formula (62) is verified by obtaining of g with the help of (44). the complementary strain energy cumulated in half of the shat as a result of bending and torsion is found as * * * *mtl mq mthu u u u   (63) where *mtlu , * mqu and * mthu are the complementary strain energies in the internal crack arm, the external crack arm and the un-cracked shaft portion, respectively. it should be specified that *mqu is due to the bending only, since the external crack arm is not loaded in torsion. v. rizov, frattura ed integrità strutturale, 46 (2018) 158-177; doi: 10.3221/igf-esis.46.16 172 figure 10: the strain energy release rate in non-dimensional form plotted against 1 3 /b bs s ratio: curve 1 – for the shaft configuration shown in fig. 7a (linear-elastic solution), curve 2 – for the shaft configuration shown in fig. 7a (non-linear solution), curve 3 – for the shaft configuration shown in fig. 8a (linear-elastic solution), curve 4 – for the shaft configuration shown in fig. 8a (non-linear solution). formula (46) is applied to determine *mtlu . for this purpose, * lu and * 0 i lu are replaced with * mtlu and * 0 i mtlu , respectively. formula (48) is used to obtain the complementary strain energy density, *0 i mtlu , in the i-th layer of the internal crack arm. for this purpose, *0 i lu and l are replaced, respectively, with * 0 i mtlu and  , where  is expressed by (54). * mqu is obtained by replacing of * lu , 1n and * 0 i lu , respectively, with * mqu , 2n and * 0 i mqu in (46). * 0 i mqu is determined by replacing of *0 i lu and l , respectively, with * 0 i mqu and  in (48) and taking into account the fact that the external crack arm is loaded in bending only. thus, *0 i mqu is written as 2 * 0 1 ln ln i i i i i mq i i i i i i i s s s s u s p p p p p p                    (64) the complementary strain energy cumulated in the un-cracked shaft portion as a result of bending and torsion is calculated by (49). for this purpose, *hu and * 0 i hu are replaced with * mthu and * 0 i mthu , respectively. formula (48) is used to obtain the complementary strain energy density, *0 i mthu . for this purpose, * 0 i lu , l and  are replaced, respectively, with *0 i mthu , b and h , where h is found by (38). finally, *mtlu , * mqu and * mthu are added-up and substituted in (44). the result is 1 2 * * * 0 0 0 1 1 1 1 i i i i i i n i n i n mtl mq mth i i ib a a a g u da u da u da r                     (65) the integration in (65) should be performed by the matlab computer program. it should be noted that the strain energy release rate obtained by (65) is exact match of the strain energy release rate calculated by (62), which is a verification of the v. rizov, frattura ed integrità strutturale, 46 (2018) 158-177; doi: 10.3221/igf-esis.46.16 173 delamination fracture analysis of the multilayered functionally graded non-linear elastic circular shaft loaded in bending and torsion. figure 11: the strain energy release rate in non-dimensional form plotted against 1d p property at three 1 3 /b bp p ratios for the shaft configuration shown in fig. 7a (curve 1 – at 1 3 / 0.5b bp p  , curve 2 – at 1 3/ 1b bp p  and curve 3 – at 1 3/ 1.5b bp p  ). parametric investigations arametric investigations of delamination fracture in the multilayered functionally graded non-linear elastic circular shaft are performed in order to elucidate the effects of material gradients, cylindrical delamination crack location, non-linear mechanical behavior of the material and load combinations. for this purpose, calculations of the strain energy release rate are carried-out by formulae (41) and (62). the results obtained are presented in non-dimension form by using the formula 3 /n bg g s r . two three-layered functionally graded circular shafts loaded in centric tension and torsion are analyzed in order to elucidate the influence of the cylindrical delamination crack location on the fracture behavior (fig. 7). a cylindrical delamination crack is located between layers 2 and 3 in the shaft configuration shown in fig. 7a. a shaft with cylindrical delamination crack located between layers 1 and 2 is also under consideration (fig. 7b). in both shaft configurations, the thickness of the layers is t (fig. 7). it is assumed that 50t  nm, 300f  n and 0.01t  m. in order to elucidate the influence of the load combination on the fracture behavior, two three-layered functionally graded circular shafts loaded in bending and torsion are also analyzed (fig. 8). in the shaft shown in fig. 8a, a cylindrical delamination crack is located between layers 2 and 3. a cylindrical delamination crack is located between layers 1 and 2 in the shaft configuration in fig. 8b. the thickness of each layer is 0.01t  m in both shafts (fig. 8). the loading is 50t  nm and 40m  nm. the strain energy release rate in non-dimensional form is presented as a function of 1d s material property ( 1d s controls the gradient of 1s property in layer 1) in fig. 9 for the four shaft configurations shown in fig. 7 and fig. 8. it is assumed that 2 3 / 0.3d ds s  , 1 3/ 2b bs s  , 2 3/ 1.8b bs s  , 1 3/ 0.3d dp p  , 2 3/ 0.2d dp p  , 3 3/ 0.4d dp s  , 1 3/ 1.7b bp p  , 2 3 / 1.9b bp p  , 3 3/ 0.9b dp p  , 1 3/ 0.4d df f  , 2 3/ 0.3d df f  , 3 3/ 0.5d df s  , 1 3/ 1.7b bf f  , 2 3/ 1.6b bf f  , 3 3 / 1.1b bf s  , 1 3/ 0.2d dg g  , 2 3/ 0.5d dg g  , 3 3/ 0.4d dg s  , 1 3/ 1.5b bg g  , 2 3/ 1.9b bg g  and 3 3/ 0.8b bg s  . curves in fig. 9 indicate that the strain energy release rate decreases with increase of 1d s . this behavior is due to the decrease of the shaft stiffness. it can also be observed in fig. 9 that the strain energy release rate increases when the cylindrical delamination crack position is changed from this shown in fig. 7a and fig. 8a to that shown in fig. 7b and fig. p v. rizov, frattura ed integrità strutturale, 46 (2018) 158-177; doi: 10.3221/igf-esis.46.16 174 8b. this finding is attributed to the increase of the stiffness of the internal crack arm. fig. 9 shows also that the loading combination “bending and torsionˮ generates higher strain energy release rate in comparison with the loading combination “centric tension and torsionˮ for the considered values of f , t and m . figure 12: the strain energy release rate in non-dimensional form plotted against 1d f property at three 1 3 /b bf f ratios for the shaft configuration shown in fig. 7a (curve 1 – at 1 3 / 0.7b bf f  , curve 2 – at 1 3/ 1.2b bf f  and curve 3 – at 1 3/ 1.7b bf f  ). figure 13: the strain energy release rate in non-dimensional form plotted against 1d g property at three 1 3 /b bg g ratios for the shaft configuration shown in fig. 7a (curve 1 – at 1 3 / 0.8b bg g  , curve 2 – at 1 3/ 1.3b bg g  and curve 3 – at 1 3/ 1.8b bg g  ). the strain energy release rate in non-dimensional form is presented as a function of 1 3 /b bs s ratio in fig. 10 for the shaft configurations shown in fig. 7a and fig. 8a. one can observe in fig. 10 that the strain energy release rate increases with increasing of 1 3 /b bs s ratio (this due to the decrease of the shaft stiffness). curves in fig. 10 confirm the finding that when the shat is loaded in bending and torsion the strain energy release is higher in comparison with the case when the v. rizov, frattura ed integrità strutturale, 46 (2018) 158-177; doi: 10.3221/igf-esis.46.16 175 shat is loaded in centric tension and torsion for the considered values of f , t and m . in order to evaluate the effect of the material non-linearity on the delamination fracture, the strain energy release rate obtained assuming linear-elastic behavior of the three-layered functionally graded shafts is plotted in non-dimensional form against 1 3 /b bs s ratio in fig. 10 for comparison with the strain energy release rate generated by the non-linear solution. it should be mentioned that that the linear-elastic solution to the strain energy release rate is derived by substituting of 0 ib p  and 0 ib g  , where 1, 2, 3i  , in formulae (41) and (62). it can be observed in fig. 10 that the material non-linearity leads to increase of the strain energy release rate. the strain energy release rate in non-dimensional form is presented as a function of 1d p material property in fig. 11 at three 1 3 /b bp p ratios for the shaft configuration shown in fig. 7a. the curves in fig. 11 indicate that the strain energy release rate decreases with increase of 1d p . it can be observed also that the strain energy release rate increases with increasing of 1 3 /b bp p ratio (fig. 11). the influence of 1d f material property on the delamination fracture behavior is shown in fig. 12. the shaft configuration in fig. 7a is considered. one can observe that the strain energy release rate decreases with increasing of 1d f (fig. 12). the curves in fig. 12 show that the increase of 1 3 /b bf f ratio leads to increase of the strain energy release rate. figure 14: the /iii iig g ratio plotted against /t f ratio for the shaft configuration shown in fig. 7a. the effect of 1d g material property and 1 3 /b bg g ratio on the delamination fracture is illustrated in fig. 13. the shaft configuration shown in fig. 7a is analyzed. fig. 13 shows that the strain energy release rate decreases when 1d g increases. it can be observed in fig. 13 that the strain energy release rate increases with increasing of 1 3 /b bg g ratio. the influence of the torsion moment to longitudinal force, /t f , ratio on the mode iii component of the strain energy release rate to mode ii component of the strain energy release rate, /iii iig g , ratio is shown in fig. 14. the shaft configuration in fig. 7a is considered. one can observe in fig. 14 that /iii iig g ratio increases with increasing of /t f ratio. v. rizov, frattura ed integrità strutturale, 46 (2018) 158-177; doi: 10.3221/igf-esis.46.16 176 finally, the effect of the bending moment to torsion moment, /m t , ratio on the strain energy release rate is illustrated in fig. 15. the shaft configuration shown in fig. 8a is analyzed. the curve in fig. 15 indicates that the total strain energy release rate increases with increasing of /m t ratio. figure 15: the strain energy release rate in non-dimensional form plotted against /m t ratio for the shaft configuration shown in fig. 8a. conclusions delamination fracture analysis of multilayered functionally graded circular shaft is developed in terms of the strain energy release rate. the shaft is made of an arbitrary number of adhesively bonded concentric longitudinal layers which have different thicknesses and material properties. the material in each layer is functionally graded in radial direction. besides, the material exhibits non-linear mechanical behavior in each layer. the continuous variation of material properties in radial direction is described by hyperbolic laws. a cylindrical delamination crack is located arbitrary between layers (the internal crack arm is a shaft of circular cross-section; the external crack arm is a shaft of ring-shaped cross-section). two load combinations (centric tension and torsion, and bending and torsion) are investigated. these load combinations generate mixed mode ii/iii delamination fracture (the centric tension and bending generate mode ii crack loading conditions, the torsion generates mode iii crack loading conditions). the strain energy release rate is derived by analyzing the balance of the energy. in order to verify the solution obtained, the strain energy release rate is determined also by differentiating the complementary strain energy with respect to the crack area. parametric investigations of the delamination fracture are carried-out in order to evaluate the effects of material gradients, the crack location, the material non-linearity and the load combinations. it is found that the strain energy release rate increases with increasing of 1 3 /b bs s , 1 3/b bp p , 1 3/b bf f and 1 3/b bg g ratios. the increase of 1ds , 1dp , 1df and 1dg leads to decrease of the strain energy release rate. concerning the influence of the delamination crack location on the fracture behavior, it is found that the strain energy release rate decreases when the diameter of the cross-section of the internal crack arm increases. the analysis reveals that the non-linear mechanical behavior of the material leads to increase of the strain energy release rate. the comparison between the strain energy release rates generated by the two loading combinations shows that the strain energy release rate is higher when the shaft is loaded in bending and torsion for the considered values of the longitudinal force, bending and torsion moments. the results obtained in the present paper show that the strain energy release rate in a v. rizov, frattura ed integrità strutturale, 46 (2018) 158-177; doi: 10.3221/igf-esis.46.16 177 multilayered functionally graded circular shafts can be controlled by using appropriate material gradients in radial direction. the present paper is a contribution in delamination fracture mechanics of multilayered functionally graded circular shafts exhibiting non-linear mechanical behavior of the material under combined loads. references [1] hirai, t. and chen, l. (1999). recent and prospective development of functionally graded materials in japan, material science forum, 308-311, pp. 509-514. [2] mortensen, a. and suresh, s. (1995). functionally graded metals and metal-ceramic composites: part 1 processing, international materials review, 40, pp. 239-265. [3] nemat-allal, m.m., ata, m.h., bayoumi, m.r. and khair-eldeen, w. (2011). powder metallurgical fabrication and microstructural investigations of aluminum/steel functionally graded material, materials sciences and applications, 2, pp. 1708-1718. [4] neubrand, a. and rödel, j. (1997). gradient materials: an overview of a novel concept, zeit f met, 88, pp. 358-371. [5] suresh, s. and mortensen, a. (1998). fundamentals of functionally graded materials, iom communications ltd, london. [6] bohidar, s.k., sharma, r. and mishra, p.r. (2014). functionally graded materials: a critical review, international journal of research, 1, pp. 289-301. [7] paulino, g.c. (2002). fracture in functionally graded materials, engineering fracture mechanics, 69, pp. 1519-1530. [8] pan, s.-d., feng, j.-c., zhou, z.-g. and zhi, w.-l. (2009). four parallel non-symmetric mode –iii cracks with different lengths in a functionally graded material plane, strength, fracture and complexity: an international journal, 5, pp. 143-166. [9] tilbrook, m.t., moon, r.j. and hoffman, m. (2005). crack propagation in graded composites, composite science and technology, 65, pp. 201-220. [10] rizov, v.i. (2016). elastic-plastic fracture of functionally graded circular shafts in torsion, advances in materials research, 5, pp. 299-318. [11] lubliner, j. (2006). plasticity theory (revised edition), university of california, berkeley, ca. [12] chakrabarty, j. (2006). theory of plasticity, elsevier butterworth-heinemann, oxford. [13] lukash, p.a. (1998). fundamentals of non-linear structural mechanics, stroizdat. [14] varvak, p.m. (1997). new methods in strength of materials, vishta shkola. [15] rizov, v.i. 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can be opened with acrobat and adobe reader 5.0 and later.) >> /namespace [ (adobe) (common) (1.0) ] /othernamespaces [ << /asreaderspreads false /cropimagestoframes true /errorcontrol /warnandcontinue /flattenerignorespreadoverrides false /includeguidesgrids false /includenonprinting false /includeslug false /namespace [ (adobe) (indesign) (4.0) ] /omitplacedbitmaps false /omitplacedeps false /omitplacedpdf false /simulateoverprint /legacy >> << /addbleedmarks false /addcolorbars false /addcropmarks false /addpageinfo false /addregmarks false /convertcolors /converttocmyk /destinationprofilename () /destinationprofileselector /documentcmyk /downsample16bitimages true /flattenerpreset << /presetselector /mediumresolution >> /formelements false /generatestructure false /includebookmarks false /includehyperlinks false /includeinteractive false /includelayers false /includeprofiles false /multimediahandling /useobjectsettings /namespace [ (adobe) (creativesuite) (2.0) ] /pdfxoutputintentprofileselector /documentcmyk /preserveediting true /untaggedcmykhandling /leaveuntagged /untaggedrgbhandling /usedocumentprofile /usedocumentbleed false >> ] >> setdistillerparams << /hwresolution [2400 2400] /pagesize [612.000 792.000] >> setpagedevice microsoft word numero_51_art_7_2595 p. ferro et al., frattura ed integrità strutturale, 51 (2020) 81-91; doi: 10.3221/igf-esis.51.07 81 alloy substitution in a critical raw materials perspective p. ferro, f. bonollo university of padova, italy paolo.ferro@unipd.it, https://orcid.org/0000-0001-8682-3486 franco.bonollo@unipd.it, https://orcid.org/0000-0002-7196-2886 s.a. cruz eurecat, centre tecnològic de catalunya, unitat de materials metàl·lics i ceràmics, av. universitat autònoma, spain sylvia.cruz@eurecat.org abstract. since many years, the european community has been monitoring some raw materials because of their high importance to the european union economy and their high supply risk. such raw materials, classified as critical, form a strong industrial base, producing a lot of goods and applications used in everyday life and modern technologies. many critical raw materials are used as alloying elements and their high supply risk may constitute a serious problem for the future world economy and technological progress. mitigating actions are therefore needed such as recycling, material efficiency improvements and, when possible, material substitution. in the present work, a systematic approach for alloy substitution and/or optimization in a critical raw materials perspective is developed. the method is illustrated with an example. keywords. raw material; criticality index; materials selection; metals and alloys; alloy substitution. citation: ferro, p., bonollo, f., cruz, s.a., alloy substitution in a critical raw materials perspective, frattura ed integrità strutturale, 51 (2020) 81-91. received: 20.08.2019 accepted: 02.11.2019 published: 01.01.2020 copyright: © 2020 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. introduction aw materials are crucial to world’s economy. they are essential to securing a transition to green energy technologies, to securing growth and sustainable consumption and to securing access to clean and efficient consumer technologies. therefore, monitoring the availability of raw materials is of growing interest within the european union (eu) and across the globe. in this scenario the eu identified a series of raw materials that are critical because they are highly important to the eu economy and, at the same time, they suffer of a high supply risk. for this reason, critical raw materials (crms) are subjected to a regular review and update. the last updated report about crms [1] identified as critical: antimony, beryllium, borates, cobalt, coking coal, fluorspar, gallium, germanium, indium, magnesium, natural graphite, niobium, phosphate rock, silicon metal, tungsten, platinum group metals, light rare r http://www.gruppofrattura.it/va/51/2595.mp4 p. ferro et al., frattura ed integrità strutturale, 51 (2020) 81-91; doi: 10.3221/igf-esis.51.07 82 earths and heavy rare earths, baryte, bismuth, hafnium, helium, natural rubber, phosphorus, scandium, tantalum, and vanadium. the crms list is updated every three years. as it can be observed from the above mentioned ‘black list’, crms are linked to clean technologies. they are irreplaceable in solar panels, wind turbines, electric vehicles, and energy-efficient lighting. unfortunately, the criticality assessment related to raw materials is a very difficult task and there is not a recognized method to reach that goal in literature [2,3]. for example, in a recent paper, hofmann et al. [4] showed that material scientists seem frequently not concerned with the criticality of raw materials so that they suggested to advance the implementation of the concept of materials criticality in materials research and development. an excellent review of the criticality concept, as well as the methodologies used in its assessment, was presented by frenzel et al. [5]. in that work, the authors also discussed a number of risks present in global raw materials markets that are not captured by most criticality assessments and, finally, they proposed measures for the alleviation of such risks. in another recent paper, tkaczyk et al. [6] present a multi-faceted and multi-national review of the essentials for the critical raw materials, co, nb, w, and rare earth elements (rees). such raw materials are relevant for emerging technologies and will thus continue to be of increasing major economic importance. that paper deals with also a ‘sustainability evaluation’ for each element, including essential data about markets, applications and recycling. possibilities for substitution is finally summarized and analyzed. in recent studies, the european commission's joint research centre (jrc) showed that several green technologies could be at risk because of potential supply risks of certain metals [7–9]. in particular, electric vehicles are of particular criticism because their dependence on critical rees used in ndfeb permanent magnets (pm). because of its high energy density, ndfeb is expected to be used also in high-tech applications and energy-related devices such as generators in wind turbines [10]. for these reasons, the global demand for rees is likely to be increasing in the coming years [10-13], despite they are evaluated as ‘critical materials’ [14-19]. among the ‘mitigating strategies’ aimed to face this issue, both recycling and substitution are considered in literature. for instance, substitution was found more feasible in cases where it takes place at the product, component or technology level rather than the element level [20-22]. many works in literature confirm the substitution as a good method to face the increasing challenge of crms supply risk [23-26]. the research framework programs (e.g. fp7 and h2020) provides financial support to relevant projects related to substitution of critical raw materials. gkanas et al. [27] defined four advantages linked to crms substitution: flexibility in materials supply, cost saving, weaken monopoly power of suppliers and environmental benefits. in 2012, the european parliament observed that ‘the majority of substitutes are currently in the research and development stage and market-ready solutions are rarely available’ [28]. therefore, the substitution concept needs to broaden its scope to include, for instance, product design, changes to process, higher material efficiency and product replacement by new technology [29]. in this scenario, pavel et al. studied the possibility to substitute rare earths used both in electric road transport applications [30] and wind turbines [31]. they firstly showed how, despite the benefits of climate change mitigation and from potential fuel savings, several barriers could hinder the widespread adoption of electric vehicles because a potential supply disruption of critical rare earths for magnet-based electric traction motors. they demonstrated how the potential supply risks associated with rare earths for electric road transport applications cannot be easily mitigated as there are no effective substitutes for the rare earths used in permanent magnets. the general feeling is that more effort is needed to develop new solutions and to search for even better alternatives. in another work, rademaker et al. [32] showed that in the brief period waste flows from permanent magnets will remain small relative to the rapidly growing global rare earth elements demand. therefore, during the next decade, recycling is unlikely to substantially contribute to global ree supply security. on the other hand, in the long term, waste flows will increase sharply and will meet a substantial part of the total demand for these metals. future ree recycling efforts should, therefore, focus on the development of recycling technology and infrastructure. perez et al. [33] provides an overview of the present status and outlook on technologies used to recover critical metals from solution, including precipitation, reduction, ion exchange, solvent extraction, electrochemical methods and adsorption onto novel, sustainable materials. they finally suggested key directions to tackle existing challenges in the field of resource recovery and improve the sustainability of future material cycling. despite the different works present in literature aimed to assess the raw materials criticality and suggest mitigating actions such as recycling and substitution, methods aimed to help the designer to play out the necessary ‘mitigating actions’ required to reduce the criticality of industrial products are not yet developed. literature studies are mainly focused on rees substitution with particular reference to specific applications [34] while a systematic methodology for a generic critical material substitution in design is still absent. in the following, an overall indicator for raw material criticality assessment is first proposed. a systematic procedure for alloy substitution in a crms perspective is then developed and illustrated with an example. p. ferro et al., frattura ed integrità strutturale, 51 (2020) 81-91; doi: 10.3221/igf-esis.51.07 83 criticalities assessment n literature, the criticality issues linked to each raw material are quantified by a series of indexes such as the abundance risk, the sourcing and geopolitical risk, the environmental country risk, the supply risk, the economic importance and finally, the end of life recycling input rate in order to use such indicators in design, it would be necessary to aggregate the above-mentioned indexes in an overall general indicator for each critical raw material to reach this goal. one possibility should take the normalized value of each index in order to remove the units and reduce them to a common scale (0-10, for instance). then, they may eventually be weighted to reflect the perceived seriousness of each criticality, and finally, the weighted, normalized measures should be summed or averaged to give the indicator. the abundance risk level (arl) of the crm ‘i’ is associated to the value of the ‘abundance in the earth’s crust (aec) [ppm]’ by the following proposed relation: max 10 10 log i crm i crm aec arl aec             (1) where aeccrmi stays for the amount in the earth’s crust of the crm ‘i’ (measured in ppm) and aeccrmmax is the maximum value found in the crms list. the sourcing and geopolitical risk (sgr) index indicates the supply disruption risk due to political factors, based on the countries in which the element is produced (e.g. in terms of political stability and control of corruption) and the concentration of worldwide production. a higher value means a higher risk. according to eu report of the ad-hoc working group on defining critical raw materials (2010, [35]), the sourcing and geopolitical risk for an element ‘i’ is a modified and scaled herfindahl-hirschmann index, calculated as (eqn. 2):  2wgii ic c c hhi s wgi  (2) where wgic is the world bank's "worldwide governance indicator" for the producing country 'c' and sic is the percentage (%) of worldwide production of the raw material 'i' within country 'c' [35]. the world bank "worldwide governance indicator" measures the political and economic stability of producing countries. in this context it is useful to remember that the herfindahl-hirschmann index (hhi) gives an indication of the level of concentration of production of a raw material within any one country, in terms of its annual worldwide production. in economic terms, it is used to gauge the risk of monopolistic production within the supply chain of the material under consideration. the higher its value, the higher the risk. in this work the sgr index of the crm ‘i’ is normalized and scaled as follows: max 10 wgi i i wgi hh sgr hh   (3) where hhiwgimax is the maximum value reached by the index hhiwgii in the crms list. the environmental country risk (ecr) indicates the risk that worldwide supply of an element may be restricted in future as a result of environmental protection measures taken by any of its producing countries. a higher value means a greater risk that environmental legislation may restrict supply in the future. it is quantified, for an element ‘i’, by the following equation: max 10 epi i i epi hhi ecr hhi   (4) where, i p. ferro et al., frattura ed integrità strutturale, 51 (2020) 81-91; doi: 10.3221/igf-esis.51.07 84  2 10 10 epi c i ic c epi hhi s        (5) and hhiepimax stays for the maximum value reached by the index hhiepii in the crms list. epic is the environmental performance index calculated by yale university, for the producing country 'c' [35]. the environmental performance index (epi) is a method of quantifying and numerically marking the environmental performance of a state's policies [36]. the greater the epic indexes, the lower the risk of supply disruption induced by environmental legislation. the supply risk (sr) indicator quantifies the inadequate supply of a raw material to meet industrial demand. it is calculated by taking into account estimation of how stable the producing countries are (considering the level of concentration of raw material producing countries), the extent to which a raw material ‘i’ may be substituted, and, finally, the extent to which raw material needs are recycled. the formula for the calculation of the sr index for the element ‘i’ is given by equation (6) [5]:  1 wgii i i isr g f hhi  (6) where gi is the raw material substitutability (defined in equation (7)) and fi is the recycling rate that is the ratio of recycling from old scrap to european consumption. the substitutability, g, represents the possibility of substituting the raw material ‘i’ and it is calculated as a weighted average over the end-uses/sectors, as follows [5]: i s s s g a g  (7) where as is the share of material consumption in a given end-use sector (s) and the gs value may be zero if the raw material (rm) is easily and completely substitutable at no additional cost, 0.3 if the rm is substitutable at low cost, 0.7 if the rm is substitutable at high cost (and/or loss of performance) and finally 1.0 if the rm is not substitutable. thus, the higher gi, the lower the substitutability. the supply risk is increased if the producing countries are unstable and provide a high share in the world production, because the substitutability is low (gi is high), and because the recycled rate is low ((1 – fi) is high). in this work, the normalized and scaled sr indicator (nsr) is used: max 10ii sr nsr sr   (8) where srmax stays for the maximum value reached by the index sri in the crms list. the importance for the economy of a raw material is measured by breaking down its main uses and attributing to each of them the value added of the economic sector that has this raw material as input [5]. the economic importance of a raw material ‘i’ (eii), is calculated as the weighted sum of the individual megasectors (expressed as gross value added), divided by the european gross domestic product (gdp) (eqn. 9) [35,37]: 1 i s s si ei a q gdp   (9) in eqn. (9), as is the share of consumption of a rm in a given end-use sector, s, while qs is the economic importance of the sector, s, that requires that raw material and it is measured by its value-added. the values for economic importance of each material were scaled to fit in the range from 0 to 10, with higher scores indicating higher economic importance. in the present work, the normalized and scaled ei indicator (nei) is defined as follows: max 10ii ei nei ei   (10) where eimax stays for the maximum value reached by the indicator eii in the crms list. p. ferro et al., frattura ed integrità strutturale, 51 (2020) 81-91; doi: 10.3221/igf-esis.51.07 85 finally, the end of life recycling input rate (eol-rir) is ‘the input of secondary material to the eu from old scrap to the total input of material (primary and secondary)’. in the ec criticality assessments (ec 2011, 2014), recycling rates and eol-rir (%) refer only to functional recycling. functional recycling is ‘the portion of eol recycling in which the material in a discarded product is separated and sorted to obtain recyclates’. recyclates obtained by functional recycling are used for the same functions and applications as when obtained from primary sources; as opposed to recyclates generated from non-functional recycling which substitute other raw materials, and therefore do not contribute directly to the total supply of the initial raw material. in the present work, in order to assess the overall criticality index for each crm, the eol-rir index is substituted by the recycling drawback index (rdi) defined as follows: max 10 10ii eol rir rdi eol rir      (11) raw materials criticality indicator (cicrm) he criticality indicator for the crm ‘i’ (cicrmi) is obtained by averaging the above-defined, scaled (0-10) and weighted criticalities indexes values (eqn. (12)):   / 6 icrm arl i sgr i ecr i nsr i nei i rdi i ci k arl k sgr k ecr k nsr k nei k rdi      (12) in eqn. (12) k is a non-dimensional coefficient which value is in between 0 and 1, according to the seriousness of the corresponding criticality aspect. when all k values are set equal to 1 in eqn. (12), equal seriousness is perceived for all the criticality aspects. the values of the criticality index in eqn. (12) are calculated by using data taken from the literature [38]. areas of fig. 1 are proportional to the cicrm value while tab. 1 collects the numerical values of each criticality index obtained. it is observed (fig. 1) that the high seriousness of the european union dependence from rare earths is quantified by the highest values of their criticality indicator. figure 1: criticality grade of different crms measured by the rm criticality indicator (k = 1 for all the indexes). t p. ferro et al., frattura ed integrità strutturale, 51 (2020) 81-91; doi: 10.3221/igf-esis.51.07 86 crm arl sgr ecr nsr nei rdi cicrm sb 6.15 6.46 7.68 8.78 5.89 3.64 6.43 ba 2.82 2.59 2.62 3.27 3.97 9.77 4.17 be 5.00 4.49 6.43 4.90 5.34 10.00 6.03 bi 7.52 7.18 8.52 7.76 4.93 9.77 7.61 b 4.45 5.04 5.31 6.12 4.25 10.00 5.86 ce (lrees) 3.63 10.00 9.49 10.00 4.93 9.77 7.97 co 4.05 4.20 3.94 3.27 7.81 10.00 5.55 f 2.68 2.65 5.75 9.77 ga 4.17 6.88 8.19 2.86 4.38 10.00 6.08 ge 5.27 6.97 8.33 3.88 4.79 9.55 6.46 hf 4.97 1.31 2.02 2.65 5.75 9.77 4.41 he 3.27 3.56 9.77 in 6.05 3.57 3.97 4.90 4.25 10.00 5.46 ir 8.45 5.49 6.66 5.71 5.89 6.82 6.50 la 3.86 8.40 10.00 10.00 4.93 9.77 7.83 mg 1.08 7.85 9.33 8.16 9.73 7.95 7.35 natural graphite (carbon) 3.15 6.98 8.33 5.92 3.97 9.32 6.28 nb 4.15 5.48 6.17 6.33 6.58 9.93 6.44 pd 7.27 3.11 3.11 3.47 7.67 7.73 5.39 p 2.43 2.04 6.99 6.14 pt 7.75 3.93 4.71 4.49 6.71 7.50 5.85 pr 4.49 8.40 10.00 10.00 4.93 7.73 7.59 rh 8.45 5.49 6.73 5.10 9.04 4.55 6.56 ru 8.45 5.49 6.73 6.94 4.79 7.50 6.65 sc 4.11 10.00 9.49 10.00 4.93 9.77 8.05 si 0.00 5.37 6.36 2.04 5.21 10.00 4.83 ta 5.15 2.89 3.57 2.04 5.34 9.77 4.79 w 5.35 7.24 8.58 3.67 10.00 0.45 5.88 v 3.37 4.43 5.15 3.27 5.07 0.00 3.55 y (hrees) 3.93 10.00 9.49 10.00 4.93 9.77 8.02 table 1: criticality grade of different crms measured by the rm criticality indicator (k = 1 for all the indexes). alloy substitution in a crms perspective aterial substitution is one of the mitigating actions aimed to reduce the product criticality in a crms perspective. in substituting a material, the designer needs to maintain or increase the component performances while reducing at the same time the criticality issues above described. by taking into account mechanical components, the main designer’s objective is mass reduction, but this is not a limitation of the proposed approach. in the following, the alloy substitution in a pressure vessel new design is considered as an example. when a pressure vessel has to be mobile, its weight becomes important. aircraft bodies, rocket casings and liquid-natural gas containers are examples; they must be light, and at the same time they must be safe, and that means that they must not fail by fast fracture. if it is assumed that the component is, for simplicity, spherical, of specified radius r, and that the wall thickness, t (the free variable), is small compared with r (fig. 2), then the performance equation for the mass m of the pressure vessel is: m p. ferro et al., frattura ed integrità strutturale, 51 (2020) 81-91; doi: 10.3221/igf-esis.51.07 87 24m r t  (13) where  is the alloy density. figure 2: pressure vessel geometry. the tensile stress in the wall of a thin-walled pressure vessel is 2 p r t    (14) where ∆p, the pressure difference across this wall, is fixed by the design. the constraint is that it should not fail by fast fracture; this requires that the wall-stress be less then 1 /ck c , where k1c is the fracture toughness of the material of which the pressure vessel is made, and c is the length of the longest crack that the wall might contain. equating first the tensile stress (eqn. 14) to the yield strength y, then to the fracture strength 1 /ck c and substituting for t in the objective function (eqn. 13) leads to the performance equation (15) and index (m) laid out below. 3 1/2 1 2 ( ) c m p r c k            (15) 1c m k   (16) now, crms may be contained, in different amounts, in the alloy composition. therefore, an alloy criticality index can be defined as follows: 1 % 100 i i n crm a crm i wt ci ci    (17) where n is the number of crms in the alloy chemical composition and wt%crmi is the amount of the crm ‘i’ in the alloy, measured in weight percent. it is observed that the alloy criticality index (cia) represents an overall criticality value per unit of mass of the alloy. in a crms perspective, the objective to be minimized will be the criticality of the designed component (criticality per unit of function). this objective is formulated by multiplying the mass of the component (m) by the alloy criticality index (eqn. 18) [39]: * am m ci (18) r t p. ferro et al., frattura ed integrità strutturale, 51 (2020) 81-91; doi: 10.3221/igf-esis.51.07 88 since cia represents an overall criticality value per unit of mass of the alloy, m* quantifies the criticality of the whole component in a crms perspective. this concept can be easily applied to metallic materials. following the same above described procedure, the new performance equation (19) and index (m*) are: 3 1/2 1 * 2 ( ) a c ci m p r c k            (19) 1 * a c ci m k   (20) m and m* are called material indexes, according to ashby’s definition [40]. pressure vessels are commonly made by low alloy steels, like the uns k32550 (ams 6425). for substitution purpose it is thus more convenient to plot the relative values of the materials indexes as shown in fig. 3, where m0 and m0* are the material indexes value of the uns k32550 steel. figure 3: trade-off plot for the alloy substitution purpose (k coefficient values in eqn. (12) are set equal to 1). each symbol, in fig. 3, represents a different material. those which have the characteristic that no other solution exists with lower values of both the performance metrics are said to be non-dominated solutions; the line on which they lie is called optimal trade-off surface. the point of coordinates (1,1) in fig. 3 is occupied by the steel to be substituted (uns k32550). the two straight lines across that point divide the plot in four quadrants named a, b, c and d. materials lying on the quadrant d are obviously the worst ones since they are heavier and more critical than the reference alloy. materials that are in the quadrant c, are less critical but heavier than the steel to be substitute; on the contrary, alloys belonging to the quadrant b are more critical but less heavy. the solutions stay in the quadrant a, where alloys that allow producing both less heavy and less critical pressure vessels are found. in particular, the best solutions must be sought among the non-dominated solutions of the quadrant a. in the example, if the criticality issues are valued much more seriousness than weight reduction, the solution moves to the titanium grade 1 (en din 3.7025) or the aluminum aa 1080 (strain hardened only). on the other hand, if the criticality issues and weight reduction are valued equally, the nickel-based alloy uns n10004 should be considered as a good substitute in a crms perspective. p. ferro et al., frattura ed integrità strutturale, 51 (2020) 81-91; doi: 10.3221/igf-esis.51.07 89 the analyzed case-study was deliberately simplified in order to demonstrate the potentiality of the method. the obtained solutions must be evaluated by using supporting information and by taking into account other possible constraints defined by the designer such as corrosion resistance, maximum allowed thickness. despite this, the definition of the criticality indicator and the alloy criticality index allow finding an alloy substitute in a systematic approach. finally, it is observed that if only one aspect of the raw materials criticality needs to be reduced (say, the recycling issue, rdi), it will be sufficient to set all the other coefficients k in eqn. (12) equal to 0. conclusions systematic approach, based on the concept of criticality index, was developed to face the problem of alloy substitution in a critical raw materials perspective. the substitution procedure is based on the definition of the criticality indicator for a generic raw material that takes into account different aspects of the raw materials criticality, quantified by indexes proposed by the european union. the aggregation of such indexes was obtained by averaging their normalized and weighted values. by using the criticality indicator, the alloy criticality index was then defined. it allows formulating an objective equation that quantifies the criticality per unit of function of a product. that objective equation is finally used for material substitution using the multi-objective strategy proposed by ashby. acknowledgments his work is part of the results of the european project called ‘design of components in a critical raw materials perspective’ (dermap, project # 17205). authors want to thank eit rawmaterials for the financial support and all the project partners (swerea sweecast ab, mondragon university, agh university, eurecat, enginsoft, fonderie zanardi) for their contribute to the project development. references [1] european commission (2017). communication from the commission to the european parliament, the council, the european economic and social committee and the committee of the regions. brussels, 13/09/2017 com(2017) 490 final. https://ec.europa.eu/transparency/regdoc/rep/1/2017/en/com-2017-490-f1-en-main-part-1.pdf (accessed on 26 june 2019) [2] achzet, b., helbig, c. (2013). how to evaluate raw material supply risks—an overview. resources policy, 38 pp. 435– 447. doi: 10.1016/j.resourpol.2013.06.003 [3] blengini, g.a., nuss, p., dewulf, j., nita, v., peirò, l.t., legaz, b.v., latunussa, c., mancini,l., blagoeva, d., pennington, d., pellegrini, m., maercke, a.v., solar, s., grohol, m., ciupagea, c. (2017). eu methodology for critical raw materials assessment: policy needs and proposed solutions for incremental improvements. resources policy, 53, pp. 12–19. doi: 10.1016/j.resourpol.2017.05.008 [4] hofmann, m., hofmann, h., hagelu ̈ken, c., hool, a. (2018). critical raw materials: a perspective from the materials science community. sustainable materials and technologies, 17, e00074. doi: 10.1016/j.susmat.2018.e00074 [5] frenzel, m., kullik, j., reuter, m.a., gutzmer, j. (2017). raw material ‘criticality’— sense or nonsense? phys. d: appl. phys., 50, 123002. doi: 10.1088/1361-6463/aa5b64 [6] tkaczyk, a.h., bartl, a., amato, a., lapkovskis, v., petranikova, m. (2018). sustainability evaluation of essential critical raw materials: cobalt, niobium, tungsten and rare earth elements. j. phys. d: appl. phys. 2018, 51 203001. doi: 10.1088/1361-6463/aaba99 [7] moss, r.l., tzimas, e., kara, h., willis, p., kooroshy, j. critical metals in strategic energy technologies — assessing rare metals as supply-chain bottlenecks in low-carbon energy technologies, european commission, joint research centre. https://publications.europa.eu/en/publication-detail/-/publication/2239d6b7-cda8-4570-a9f0-13ad60ce3f11 (accessed on 09.07.19). [8] moss, r.l., tzimas, e., kara, h., willis, p., kooroshy, j. (2013). the potential risks from metals bottlenecks to the deployment of strategic energy technologies, energ policy, 55, pp. 556–564. doi: 10.1016/j.enpol.2012.12.053 a t p. ferro et al., frattura ed integrità strutturale, 51 (2020) 81-91; doi: 10.3221/igf-esis.51.07 90 [9] moss, r.l., tzimas, e., willis, p., arendorf, j., espinoza, l.t. critical metals in the path towards the decarbonisation of the eu energy sector — assessing rare metals as supply-chain bottlenecks in low-carbon energy technologies, european commission, joint research centre, https://setis.ec.europa.eu/sites/default/files/reports/jrc-report-critical-metals-energy-sector.pdf (accessed on 09.07.19). [10] stegen, k.s. (2015). heavy rare earths, permanent magnets, and renewable energies: an imminent crisis, energ policy, 79, pp. 1–8. doi: 10.1016/j.enpol.2014.12.015 [11] european rare earths competency network (erecon), strengthening of the european rare earths supply chain — challenges and policy options, http://ec.europa.eu/docsroom/documents/10882/attachments/1/translations/en/renditions/native 2015 (accessed on 09.07.19). [12] alonso, e., sherman, a.m., wallington, t.j., everson, m.p., field, f.r., roth, r., kirchain, r.e. (2012). evaluating rare earth element availability: a case with revolutionary demand from clean technologies, environ. sci. technol., 46, pp. 3406–3414. doi: 10.1021/es203518d [13] nansai, k., nakajima, k., kagawa, s., kondo, y., suh, s., shigetomi, y., oshita, y. (2014). global flow of critical metals necessary for low-carbon technologies: the case of neodymium, cobalt, and platinum, environ. sci. technol., 48, pp. 1391–1400. doi: 10.1021/es4033452 [14] massari, s., ruberti, m. (2013). rare earth elements as critical raw materials: focus on international markets and future strategies, resour. policy, 38, pp. 36–43. doi: 10.1016/j.resourpol.2012.07.001 [15] achzet, b., helbig, c. (2013). how to evaluate raw material supply risk — an overview, resour. policy, 38, pp. 435– 447. doi: 10.1016/j.resourpol.2013.06.003 [16] glo ̈ser, s., espinoza, l.t., gandenberger, c., faulstich, m. (2015). raw material criticality in the context of classical risk assessment, resour. policy, 44, pp. 35–46. doi: 10.1016/j.resourpol.2014.12.003 [17] european commission, report on critical raw materials for the eu, http://ec.europa.eu/docsroom/documents/10010/attachments/1/translations/en/renditions/native 2014 (accessed on 09.07.19) [18] us department of energy, critical materials strategy, http://energy.gov/sites/prod/files/doe_cms2011_final_full.pdf 2011 (accessed on 09.07.19). [19] goe, m., gaustad, g. (2014). identifying critical materials for photovoltaic in the us: a multi-metric approach, appl. energy, 123, pp. 387–396. doi: 10.1016/j.apenergy.2014.01.025 [20] nassar, n.t. (2015). limitations to elemental substitution as exemplified by the platinum-group metals, green chem., 17, pp. 2226–2235. doi: 10.1039/c4gc02197e [21] pavel, c.c., marmier, a., tzimas, e., schleicher, t., schu ̈ler, d., buchert, m., blagoeva, d. (2016). critical raw materials in lighting applications: substitution opportunities and implication on their demand, phys. status solidi a, 216, pp. 2937–2946. doi: 10.1002/pssa.201600594 [22] smith, b.j., eggert, r.g. (2016). multifaceted material substitution: the case of ndfeb magnets, 2010–2015, jom 2016, 7, pp. 1964–1971. doi: 10.1007/s11837-016-1913-2 [23] graedel, t.e. (2002). material substitution: a resource supply perspective, resour. conserv. recycl., 34, pp. 107–115. doi: 10.1016/s0921-3449(01)00097-0 [24] ayres, r.u. (2007). on the practical limits to substitution, ecol. econ., 61, pp. 115–128. doi: 10.1016/j.ecolecon.2006.02.011 [25] nakamura, e., sato, k. (2011). managing the scarcity of chemical elements, nat. mater., 10, pp. 158–161. doi: 10.1038/nmat2969 [26] powell, d. (2011). sparing the rare earths: potential shortages of useful metals inspire scientists to seek alternatives for magnet technologies, sci. news, 180, pp. 18–21. doi: 10.1002/scin.5591800522 [27] gkanas, e.i., bakouros, y.l., and makridis, s. s. (2015). ”substitutionability” of the critical raw materials in energy applications: a short review and perspectives, mater. sci.eng. adv. res., 1(3), pp. 1-9. doi: 10.24218/msear.2015.11 [28] european parliament, substitutionability of critical raw materials (directorate general for internal policies, brussels, 2012). [29] peck, d., kandachar, p. and tempelman, e. (2015). critical materials from a product design perspective. materials & design, 65, pp. 147-159. doi: 10.1016/j.matdes.2014.08.042 p. ferro et al., frattura ed integrità strutturale, 51 (2020) 81-91; doi: 10.3221/igf-esis.51.07 91 [30] pavel, c.c.., thiel, c., degreif, s., blagoeva, d., buchert, m., schu ̈ler, d., tzimas, e. (2017). role of substitution in mitigating the supply pressure of rare earths in electric road transport applications. sustainable materials and technologies, 12, pp. 62–72. doi: 10.1016/j.susmat.2017.01.003 [31] pavel, c.c., arántegui, r.l., marmier, a., schu ̈ler, d., tzimas, e., buchert, m., jenseit, w., blagoeva, d. (2017). substitution strategies for reducing the use of rare earths in wind turbines. resources policy, 52, 349–357. doi: 10.1016/j.resourpol.2017.04.010 [32] rademaker, j.h., kleijn, r., yang, y. (2013). recycling as a strategy against rare earth element criticality: a systemic evaluation of the potential yield of ndfeb magnet recycling, environ. sci. technol., 47, pp. 10129–10136. doi: 10.1021/es305007w [33] perez, j.p.h., folens, k., leus, k., vanhaecke, f., voort, p.v.d., lainga, g.d. (2019). progress in hydrometallurgical technologies to recover critical raw materials and precious metals from low-concentrated streams. resources, conservation and recycling, 142, pp. 177-188. doi: 10.1016/j.resconrec.2018.11.029 [34] pavel, c.c., marmier, a., tzimas, e., schleicher, t., schüler, d., buchert, m. and blagoeva, d. (2016). critical raw materials in lighting applications: substitution opportunities and implication on their demand. phys. status solidi a, 213(11), pp. 2937–2946. doi: 10.1002/pssa.201600594 [35] eu report of the ad-hoc working group on defining critical raw materials, 2010, available on the enterprise and industry directorate general. web site https://ec.europa.eu/growth/tools-databases/eip-rawmaterials/en/community/document/critical-raw-materials-eu-report-ad-hoc-working-group-defining-critical-raw (accessed on 09.07.19) [36] https://epi.envirocenter.yale.edu (accessed 09.07.19) [37] chapman, a., arendorf, j., castella, t., thompson, p and willis, p. study on critical raw materials at eu level, final report. oakdene hollins and fraunhofer isi. https://www.google.com/url?sa=t&rct=j&q=&esrc=s&source=web&cd=1&ved=2ahukewin1zjxpjxhahva4ky khqvyd_0qfjaaegqiahac&url=https%3a%2f%2fec.europa.eu%2fdocsroom%2fdocuments%2f5605%2fa ttachments%2f1%2ftranslations%2fen%2frenditions%2fnative&usg=aovvaw1jupnqztiwkeo38nythhb2 (accessed 09.07.19) [38] study on the review of the list of critical raw materials, critical raw materials factsheets. (2017). isbn 978-92-7972119-9, doi: 10.2873/398823 [39] ferro, p., bonollo, f. (2019). materials selection in a critical raw materials perspective. materials and design, 177, 107848. doi: 10.1016/j.matdes.2019.107848 [40] ashby, m.f. 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can be opened with acrobat and adobe reader 5.0 and later.) >> /namespace [ (adobe) (common) (1.0) ] /othernamespaces [ << /asreaderspreads false /cropimagestoframes true /errorcontrol /warnandcontinue /flattenerignorespreadoverrides false /includeguidesgrids false /includenonprinting false /includeslug false /namespace [ (adobe) (indesign) (4.0) ] /omitplacedbitmaps false /omitplacedeps false /omitplacedpdf false /simulateoverprint /legacy >> << /addbleedmarks false /addcolorbars false /addcropmarks false /addpageinfo false /addregmarks false /convertcolors /converttocmyk /destinationprofilename () /destinationprofileselector /documentcmyk /downsample16bitimages true /flattenerpreset << /presetselector /mediumresolution >> /formelements false /generatestructure false /includebookmarks false /includehyperlinks false /includeinteractive false /includelayers false /includeprofiles false /multimediahandling /useobjectsettings /namespace [ (adobe) (creativesuite) (2.0) ] /pdfxoutputintentprofileselector /documentcmyk /preserveediting true /untaggedcmykhandling /leaveuntagged /untaggedrgbhandling /usedocumentprofile /usedocumentbleed false >> ] >> setdistillerparams << /hwresolution [2400 2400] /pagesize [612.000 792.000] >> setpagedevice shot peening processes to obtain nanocrystalline surfaces in metal alloys: s. bagheri fard et alii, frattura ed integrità strutturale, 7 (2009) 3-16; doi: 10.3221/igf-esis.07.01 3 effects of surfaces nanocrystallization induced by shot peening on material properties : a review sara bagheri fard, mario guagliano dipartimento di meccanica, politecnico di milano, via la masa 1, 20156 milan, italy riassunto. si presenta una breve descrizione del processo di nanocristalizzazione delle superfici per mezzo di deformazioni plastiche severe. in particolare, si concentra l’attenzione sui processi di pallinatura che fino ad oggi si sono dimostrati efficaci per ottenere superfici nano strutturate e se ne descrive lo stato dell’arte. l’influenza del processo utilizzato sul comportamento del materiale in relazione alle differenti proprietà di interesse è, poi, analizzata criticamente. infine, sulla base delle attuali conoscenze si tracciano e sottolineano alcuni possibili sviluppi di ricerca in questo settore. abstract. a brief description of surface nanosrystallization process via severe plastic deformation is presented. to come to the point different shot peening methods which have proved to be able to create nanocrystalline layers are demonstrated clarifying the actual state of the art. then the influence of the process is reviewed on material behavior and a wide range of affected properties are investigated. on this basis some possible addresses for future research in this field are drawn and underlined. keywords. shot peening, nanocrystallization, high energy, surface treatments, severe plastic deformation (spd). introduction n the last few decades, ultrafine-grained materials, especially nanocrystalline (nc) characterized by crystal grains with dimensions up to 100 nm, have attracted considerable scientific interest, since nanostructured materials are expected to possess superior mechanical properties in simple chemical compositions fundamentally different from their conventional coarse-grained polycrystalline counterparts [1-10]. actually, the majority of failures of engineering materials such as fatigue fracture, fretting fatigue, wear and corrosion, etc are very sensitive to the structure and properties of the material surface, and in most cases material failures originate from the surface. accordingly, it is recommended that the entire components made of nc materials may not be necessary in many applications, particularly in components subjected to fatigue and merely optimization of the surface structure and properties may effectively enhance the global behavior and the service lifetime of materials. thus surface nanocrystallization is expected to greatly enhance the surface property without changing the chemical compositions and shape of materials [11]. among various methods proposed to produce ultrafine-grained materials, severe plastic deformation (spd) technique has received the greatest attention due to its simplicity and applicability for all classes of materials. although submicron grained materials can be successfully produced by most spd processes, nc materials are obtained only by nonhomogeneous deformation processes with large strain gradients[12-19]. the basis of the spd method is to increase the free energy of the polycrystals and generate much more defects and interfaces (grain boundaries) in various nonequilibrium processes such as high-pressure torsion [6, 8, 20-23], ball milling [24-35], sliding wear [36, 37], drilling [38-42], shot blasting and annealing [43-46], ultrasonic shot peening [15, 47-52] and air blast shot peening [16, 17, 39, 50, 53-55]. i http://www.gruppofrattura.it http://dx.medra.org/10.3221/igf-esis.07.01&auth=true s. bagheri fard et alii, frattura ed integrità strutturale, 7 (2009) 3-16; doi: 10.3221/igf-esis.07.01 4 among the mentioned techniques, shot peening is a very well known method used to increase the performance of components in different service conditions. fatigue, rolling contact fatigue, fretting and stress corrosion are operative situations where shot peening can strongly improve the performance of mechanical parts and structural elements. the present study focuses on the application of shot peening processes to obtain nc surfaces as this technique is a popular process in industries widely used due to its flexibility, which makes it possible to be used for components of almost any shape. it can be performed on commercial scale to provide nc layers with a high productivity. the paper is written with the aim to describe the actual state of the art and review different properties of nc layered materials in order to describe the effect of nanocrystallization on material behavior. on this basis some possible addresses for future research in this field are drawn and underlined. surface nanocrystallization s stated before, the key point of surface nanocrystallization process of a bulk material is to introduce a large amount of defects and/or interfaces into the surface layer so that its microstructure is transformed into nanosized crystallites while the structure of the coarse-grained matrix remains unchanged without any associated changes in the cross sectional dimensions of the samples [56]. observations of these processes have revealed a rearrangement of dislocations during the process in the way that they move from the grain interiors to the region near the grain boundaries [10]. a schematic illustration of the defect rearrangement is presented in fig. 1. the figure emphasizes that the local density of dislocations at grain boundaries grows, thus increasing their non-equilibrium. typical optical microscopic images of treated surfaces which can describe the initiation of nanocrystals are shown in fig. 2. (a) (b) figure 1: arrangement of grain boundaries in nanostructured layers: (a) the dislocation structure during spd processing (b) the dislocation structure after spd processing leading to formation of non-equilibrium grain boundaries. shot peening hot peening (sp) is a mechanical surface treatment in which small spherical peening media with sufficient hardness are accelerated in peening device of various kinds and impact with the surface of the treated work piece with a quantity of energy able to cause surface plastic deformation. the aim of the process is the creation of compressive residual stresses close to the surface and the work hardening of the same layer of material. these effects are very useful in order to totally prevent or greatly retard the failure of the part [58-62]. there are a lot of papers about the ability of sp to improve the mechanical behavior of materials [62-66]. and most of them affirm that the effect of shot peening is mainly related to the induced residual stresses. miller also hypnotized that shot peening effect could be related to grain distortion and to the increased microstructural barriers. he proposed that due to the multiplication of structural defects and dislocations, a crack would propagate with more difficulty in work-hardened surfaces [67]. recent results show that in some cases surface hardening can be considered as the main cause of modified behavior of shot peened materials [68, 69]. a s http://www.gruppofrattura.it http://dx.medra.org/10.3221/igf-esis.07.01&auth=true s. bagheri fard et alii, frattura ed integrità strutturale, 7 (2009) 3-16; doi: 10.3221/igf-esis.07.01 5 figure 2: typical cross-sectional optical micrographs close to the smat-treated surfaces under different treating conditions (annealed, commercially pure titanium specimens): (a)vibration amplitude50%, treatment time 10s; (b) vibration amplitude50%, treatment time 16s; (c) vibration amplitude100%, treatment time 30s; (d) vibration amplitude100%, treatment time 60s [57]. bearing this fact in mind, it is natural to think to shot peening as a treatment effectual to obtain nanostructured materials. the concept of nanocrystallization by shot peening is that during the process with the hit of high energy particles, many pits and also extruded ridges around the edge of the pit are formed on the surface. when the ridge is hit by another particle, the contact area between sample and the particle can decrease significantly, therefore the strain and strain rate can be increased. additionally, the collision mode also is changed from single direction to multiple directions due to the ridge, which is more favorable to the accumulation of dislocations. with the proceeding of collisions, some areas will approach the critical condition of nanocrystallization after several suitable hits [19]. recent researches have successfully shown that different shot peening processes are able to introduce nanostructured layers with different characteristics, as concern their depth, the dimension of the crystals and microstructural properties. these methods are different both for the needed technological facilities and also for the mechanics of the treatment itself. here is a very brief introduction about each of these processes: shot blasting in this method, in order to obtain nanolayers the specimen’s surface is sandblasted repeatedly by high-speed sand particles and then subsequently annealed [43-46]. in contrast to other sp methods, in shot blasting the size and also the geometry of shots are typically random and accidental and generally speaking shot sizes are smaller in comparison with the shots used in air blast shot peening. the sandblasted surface layer is heavily (plastically) deformed and consequently have highdensity dislocations. after annealing, the initially formed dislocation network or fine “sub-grains” will change to nanosized grains with sharper grain boundaries. it is observed that the mechanical properties of the sandblasted surface are commonly inferior to those of the sandblast-annealed surface [44,45] and it can attributed to the different characteristics of nanograins after annealing. air blast shot peening (absp) absp is a sp process through which the shots are projected by compressed air. the schematic of the equipment is illustrated in fig.3. in air blast shot peening, nc is produced when higher shot speed and larger coverage than http://www.gruppofrattura.it http://dx.medra.org/10.3221/igf-esis.07.01&auth=true s. bagheri fard et alii, frattura ed integrità strutturale, 7 (2009) 3-16; doi: 10.3221/igf-esis.07.01 6 conventional operation is applied [17]. in absp, the shot velocity has a narrow distribution and the impact direction of shot to specimen is almost perpendicular [50]. air pressure, shot size and shot materials are the process parameters that mainly affect the results of the treatment and the characteristic of the nc surface. figure 3: schematic illustration showing the equipment of absp. ultra sonic shot peening in fig. 4 experimental set-up of ussp called at times (smat) is illustrated. in this method shots are resonated by vibration of an ultrasonic transducer and the impact directions of the balls onto the sample surface are rather random. repeated multidirectional impacts at high strain rates onto the sample surface result in severe plastic deformation and grain refinement progressively down to the nanometer regime in the entire sample surface [64-70]. obvious enhancement in the overall properties and performance of the materials is observed after the smat treatment [15, 47, 48, 70-76]. figure 4: sketch of smat surface nanocrystallization and hardening in snh method the specimen is loaded at one end of a cylindrical container. the disc is held in place via mechanical locking. some balls with diameters normally bigger with those used in other peening methods are loaded into the container. the high velocity of the balls is commonly achieved by shaking the container three dimensionally using a spex 8000 mill. such 3d shaking provides kinetic energy to the balls and generates the complex pattern of motion of the balls inside the container [77-80]. this method like previous mentioned ones can provide structural metallic components with several desired features, such as compressive residual stress, work hardened surface layer and also nanocrystalline surface [81-85]. high energy shot peening high-energy shot peening (hesp) is another method reported to be capable of synthesis of nanostructured surface layers. the principle of the hesp treatment is very similar to that of the ussp method, but with lower frequency and bigger shots. similar to previous methods, the entire surface of the sample to be treated is peened by the flying shots with a high energy and the nc layer is achieved using different durations for peening [86]. compressed air shot compressed air shot compressed air shot vibration generator sample vacuum http://www.gruppofrattura.it http://dx.medra.org/10.3221/igf-esis.07.01&auth=true s. bagheri fard et alii, frattura ed integrità strutturale, 7 (2009) 3-16; doi: 10.3221/igf-esis.07.01 7 experimental investigations on nc surfaces obtained by shot peening p processes to obtain nc layers have been successfully used on a variety of materials including pure metals, alloys and intermetallics. majority of these experiments have included characterization of structure and properties of the surface layers by scanning electron microscopy (sem), transmission electron microscopy (tem), microhardness, scratch and so many other tests in order to assess the contribution of the process to improvement of material behavior. here some notable effects of surface nanocrystallization on special properties which have been studied in literature are discussed. fatigue since most fatigue cracks initiate from the surface and propagate to the interior, a component with a nanostructured surface layer and coarse-grained interior is expected to have highly improved fatigue properties because both fatigue-crack initiation and propagation are inhibited by fine grains near the surface and coarse grains in the interior, respectively. moreover, the residual compressive stresses introduced during the severe plastic-deformation process can also effectively stop or retard the initiation and propagation of fatigue cracks [71-74]. there are so many results confirming improvement of fatigue life of different materials using sp nanocrystallization methods [46, 62, 80, 81, 84, 85, 87]. in an experiment conducted by snh process, a c-2000 alloy was treated by five tungsten carbide and cobalt balls with a diameter of 7.9 mm for duration times of 30, 60, 90, and 180 min. load-controlled four-point-bend fatigue tests revealed that the surface nanocrystallization process affected the fatigue behavior of the material in two ways: the nanostructured surface layer, work-hardened region, and residual compressive stresses could enhance the fatigue strength especially in the high-cycle fatigue range (> 106 cycles), while the surface contamination and micro-damages caused by the snh process could somehow deteriorate the fatigue strength. as shown in fig. 5, the 30 min treatment resulted in the best improvement in the fatigue resistance, while prolonged treatments (60, 90, and 180 min) either leaded to no improvements or even decreases in the fatigue resistance. in the shorter cycle fatigue range (<106 cycles), the fatigue lifetimes of all the treated samples except the 30-min treated sample were lower than those of the as-received one. the longer the processing time, the lower the fatigue lifetimes in shorter cycle fatigue range. thus, to fully utilize the snh process to improve the fatigue behavior of the material with a nanostructured surface layer, processing conditions need to be optimized [80]. figure 5: fatigue behavior of snh treated ni-based c-2000 super alloy samples [80]. specimens of the austenitic stainless steel aisi 304 were also shot peened using s170r with coverage of 98% and almen intensities of 0.175, or 0.120 mma, respectively. tension/compression fatigue tests were performed under stress control without mean stresses (r = -1) with a cycling frequency of 5 hz. the investigations revealed that the microstructural changes severely influence the cyclic deformation behavior of the near surface regions as well as of the soft specimen 300,00 350,00 400,00 450,00 500,00 550,00 600,00 650,00 700,00 750,00 100000,00 1000000,00 10000000,00 number of cycles to failure m ax im um s tr es s (m p a) 180 min-snh treated 90 min-snh treated 60 min-snh treated 30 min-snh treated as recieved s http://www.gruppofrattura.it http://dx.medra.org/10.3221/igf-esis.07.01&auth=true s. bagheri fard et alii, frattura ed integrità strutturale, 7 (2009) 3-16; doi: 10.3221/igf-esis.07.01 8 core: plastic strain amplitudes and cyclic creep were drastically decreased by shot peening. furthermore, fatigue crack growth rates are markedly reduced by this mechanical surface treatment. remarkably, as illustrated in fig. 6, the initial residual stress profile and surface strain hardening were not completely eliminated even by applying high cyclic stress amplitudes [62]. figure 6: residual stress depth profiles of shot peened (almen intensity 0.175 mma) aisi 304 before and after cyclic loading with mpaa 320=σ after nf/2 cycles [62]. elastic modulus elastic modulus is another improved characteristic of sp surface crystallized specimens studied by some researchers [44, 88]. in an smat experiment conducted on annealed commercially pure titanium, the results demonstrated that maximum value of the elastic modulus at the top surface showed an increase of about 16% in comparison with the untreated sample. the smat was performed in air at room temperature with stainless steel balls 3 mm in diameter, for 30 min, at a vibration frequency of 20. the results seem to indicate that the increase of modulus from the bulk to the surface follows the grain refinement and as it can be seen in fig. 7 the elasticity modulus decreases as a function of distance from the treated surface [88]. figure 7: reduced modulus versus the distance for the sample surface for a load p=10 mn [88]. in another experiment performed on commercial brass, samples were sand blasted under a blasting pressure of 300 kpa for 10 min to produce nanocrystalline surface layers. the sand flow rate was 5 gs-1. the samples were then annealed at 150, 250, 350, 500 and 600 c, respectively, for 1h and cooled in air to obtain different grain sizes in the sandblasted surface layer. the nanocrystallization resulted in improved elastic behavior. it is said that this happened because the elastic limit or the yield strength was increased when the dislocation motion was retarded by grain boundaries [44]. -600 -500 -400 -300 -200 -100 0 100 0 50 100 150 200 250 300 350 depth (m icrom eter) r es id u al s tr es s (m p a) fatigued initial state 0 20 40 60 80 100 120 140 160 0 100 200 300 400 500 600 700 distance from the surface (m icrom eter) r ed u ce d m o d u lu s (g p a) http://www.gruppofrattura.it http://dx.medra.org/10.3221/igf-esis.07.01&auth=true s. bagheri fard et alii, frattura ed integrità strutturale, 7 (2009) 3-16; doi: 10.3221/igf-esis.07.01 9 chemical reaction kinetics gaseous nitriding is one of the most widely used surface modification techniques to improve the surface hardness, anticorrosion properties and wear resistance of metallic materials by formation of a surface nitrided layer. however nitriding processes are performed at relatively high temperatures (550°c-600°c) for a long duration and may induce serious deterioration of the substrate in many families of materials. it has been experimentally demonstrated that chemical reaction kinetics are greatly enhanced when the grain size is significantly reduced to the nanometer scale. since mechanically induced nanostructures store a large excess energy in the grain boundaries and grain interior in the form of non-equilibrium defects, which constitute an extra driving force for the nitride formation process that may further facilitate their chemical reactivity [89-92]. investigations have reported that surface nanocrystallization of elemental iron samples with a purity of 99.95 wt. % specimens via smat performed in an apparatus in which steel balls (8 mm in diameter) vibrated by a generator with a frequency of 3 khz repeatedly stroke the sample surface, greatly enhances the nitriding kinetics and reduces the activation energy for the diffusion of nitrogen significantly. it has been found that the nitriding temperature of iron processed by smat can be reduced to 300 °c, which is at least 200 °c below the conventional nitriding temperature [93]. in another experiment stainless steel balls (with a mirror like surface and a diameter of 8 mm) struck an iron sample with a purity of 99.95 wt.% at the bottom of a cylinder-shaped vacuum chamber attached to a vibration generator (50 hz) within 60 min, the grains in the surface layer were effectively refined into the nanometer scale. the sample was protected by a high-purity argon atmosphere during the smat to avoid oxidation. the experimental evidence confirmed that the mechanically induced surface nanocrystallization of fe created a considerable amount of stored energy in the surface layer that constituted an effective driving force for the nitriding process at low temperatures [94]. the reduced nitriding temperature is of considerable importance seeing that it may allow for the nitriding of material families (such as alloys and steels) and work-pieces that cannot be treated by conventional nitriding. wear, coefficients of friction and scratch resistance the process of microstructure refinement also has proved to lead to an enhancement of the wear, friction and scratch resistance [44,73,88,93-95]. the coefficients of friction and penetration curves for iron smat treated samples (stainless steel shots with a diameter of 8 and the vibration generator of 50 hz within duration of 60 min) were measured in an experiment. results showed that the coefficient of friction of the treated sample (0.38±0.06) was considerably smaller than that of the original sample (0.52±0.03). the nanoscratch experiments were repeated several times with very consistent results, indicating enhanced wear and friction resistance of the surface layer after smat and nitriding [94]. in another experiment the hardness on top surface nanostructured layer of smat treated pure fe bulk samples, reaches a value as high as about twice that of the coarse-grained matrix. also the wear and friction measurements on a smat lowcarbon steel sheet showed that the wear volume loss is lower than that of the untreated original one. as it is clear in fig. 8, the friction coefficient values at different applied loads for the as-treated sample are evidently smaller (about a half) than those of the original sample [73]. (a) (b) figure 8. variations of the wear volume loss with load (a) and variations of the coefficient of friction with load (b) for the smat and the original low-carbon steel samples [73]. 0 0,05 0,1 0,15 0 2 4 6 8 10 load (n) w ea r v o lu m e l o ss (m m ^3 ) as-treated original 0 0,1 0,2 0,3 0,4 0 2 4 6 8 10 load (n) f ri ct io n c o ef fi ci en t as-treated original http://www.gruppofrattura.it http://dx.medra.org/10.3221/igf-esis.07.01&auth=true s. bagheri fard et alii, frattura ed integrità strutturale, 7 (2009) 3-16; doi: 10.3221/igf-esis.07.01 10 the nanostructured surface layer of pure titanium smat treated in air at room temperature with stainless steel (balls 3 mm in diameter, for 30 min, at a vibration frequency of 20 khz), also revealed a lower friction coefficient, almost 50% smaller than that of the untreated titanium. and approximately 50% higher scratch resistance at the level of the top nanolayer than its value in the bulk. it can be noticed that the variations of the scratch resistance are very similar to that of the hardness [88]. in another experiment, standard nanoscratch tests have been performed using particular nanoindenters on elemental iron plates (with a purity of 99.95 wt. %) which were smat treated: 8 mm diameter steel balls vibrated by a generator with a frequency of 3 khz. repeated nanoscratch experiments indicated that the wear and friction resistance of the surface layer treated by smat were greatly enhanced [93]. micro-scratch tests were also performed to evaluate the wear resistances of sandblast-annealed brass samples. the wear resistance of the brass was considerably improved by nanocrystallization. it was also revealed that with an increase in the annealing temperature; the scratch resistance was lowered significantly. the difference in volume loss reached one order of magnitude larger, when the grain size changed from 20 nm to 80 nm. the increase in the wear resistance by nanocrystallization is consistent with the associated improvement in the mechanical behavior of the material [44]. corrosion there are some results indicating that the corrosion resistance can also be markedly improved by shot peening methods [43, 44, 46,54,55,93]. jiang et al. carried out corrosive immersion tests on sand blasted 35a commercially pure titanium specimens (treated with sio2 particles of 200–300 µm in diameter and compressed air pressure of about 300 psi followed by a recovery treatment below 300 °c, for 30 min with subsequent air cooling).the results indicated that in the surface nano-crystalline layer, the high density of grain boundaries was beneficial to the formation of a thin passive film, which could restrict the movement of metal ions from metal surface to the solution, thus minimizing corrosion and improving polarization behavior of the sandblast-annealed titanium [46]. the effect of air blast shot peening on corrosion resistance in surface nanocrystallization of 1cr18ni9ti stainless steel was also investigated by polarization curves and pit corrosion tests. shot peening was carried out by a flow of stainless steel balls with a diameter of 0.8 mm under 0.5 mpa for 5 min. it was reported that compared with the as-received coarse crystalline counterpart, the passive film on the surface of shot peened sample is easier to form and is more stable. shotpeening-induced surface nanocrystallization can markedly enhance the overall and local corrosion resistance of steel in chlorine–ion-contained solution [55]. fig. 9 shows potentiodynamic polarization curves obtained in 3.5% nacl solution for shot-peened and as received samples. it is demonstrated that shot peening significantly improved the polarization behavior of stainless steel, not only markedly decreasing anodic current density and passivation-maintaining current density, but also having the tendency of shifting cathodic current density to lower value, and slightly lowering the free corrosion potential. additionally, shot peening induced a considerably enlarged passive region of stainless steel and raised the breakdown potential of passive film, and for as-received reference samples, there was no remarkable passive region in polarization curve. figure 9: potentiodynamic polarization curves of shot-peened and as-received samples of 1cr18ni9ti stainless steel obtained in 3.5% nacl solution [55]. http://www.gruppofrattura.it http://dx.medra.org/10.3221/igf-esis.07.01&auth=true s. bagheri fard et alii, frattura ed integrità strutturale, 7 (2009) 3-16; doi: 10.3221/igf-esis.07.01 11 thermal stability in order to investigate thermal stability of nanostructured surface layer, nc layer was fabricated on silicon steel fe-3.29si (and also on an ultra low carbon steel) by means of air blast shot peening with different conditions: (shot size and material: sus304 /0.3 mmfe0.8c /0.8 mmfe1.0c /0.05 mm, air pressure (mpa) and speed (ms-1): 0.4, 50–100, 0.8, 50–100, 0.5, 150–200). after annealing, the nanolayer showed good thermal stability up to 873 k and also a sharp boundary to the underlying work-hardened area which was completely recrystallized. the microstructure of samples with subsequent annealing is shown in fig. 10. it can be seen that the typical recrystallization occurred in the former work hardening region. on the contrary, no obvious change can be detected in nano region by sem. the experience indicates that only slight grain growth may be possible in nanograins. however, the grain coalescence due to grain rotation might be the responsible mechanism to slight grain growth in nanocrystallite [19]. figure 10. microstructure of shot peened fe-3.29si after annealing at 873 k for 3.6 ks: (a) 3,000%, (b) 10,000% [19]. hardness some experiments have been conducted in order to investigate the influence of nc process via sp methods on hardness of different materials [73, 80, 93]. all results indicate that the hardness near the treated surface significantly increases, by the sp process, and that the increase of hardness from the bulk to the surface seems to follow the grain refinement as observed by tem. the variation in hardness with depth agrees well with the structural and compositional analysis results [88, 93]. published results also demonstrate that the hardness increment from the bulk to the surface cannot be explained by the existence of residual stresses but it is certainly due to another mechanism related to the grain size diminution as the increase of dislocation density and deformation bands [73]. technological potential of the snh process has become apparent in preliminary studies where hardness increases dramatically with respect to untreated components. hardness tests were conducted on c-2000 alloy snh treated samples (five tungsten carbide and cobalt (94%wc+ 6%co, in wt%) balls with a diameter of 7.9mm for the duration times of 30, 60, 90, and 180 min). the results showed that compared with the as-received sample, the hardness of the treated sample has been increased substantially [80]. figure 11: hardness profile of the samples [80]. 200 250 300 350 400 450 500 0 100 200 300 400 500 600 700 800 900 1000 1100 distance from the surface (m icrom eter) v ic ke rs 's h ar d n es s (h v) 30 min-snh treated 60 min-snh treated 180 min-snh treated as recieved load: 300gf error: +/10% http://www.gruppofrattura.it http://dx.medra.org/10.3221/igf-esis.07.01&auth=true s. bagheri fard et alii, frattura ed integrità strutturale, 7 (2009) 3-16; doi: 10.3221/igf-esis.07.01 12 fig. 11 exhibits the microhardness distribution along the depth of the samples. compared with the as-received sample, hardness of the treated sample has been increased significantly, but the hardness profile does not change much with the processing time. since work hardening is a consequence of severe plastic-deformation process, it can be seen that after a 30 min treatment, the depth of the deformation-affected zone changes only slightly. in other words, because the intensity of the impact of balls does not change, the plastic-deformation zone remains nearly constant, although it has already been known that the surface nanolayer could continue to extend with the processing time. thermal properties thermal properties of shot peened surface nanocrystallized materials have also been studied in some experiments [96,97]. surface nanocrystallized iron obtained by ultrasonic shot peening with the following process parameters were investigated for thermal properties: material iron with a purity of 99.95 wt. %, vibration frequency of the chamber driven by ultrasonic generator 20 khz and the shot diameter of 3 mm. the samples used in the study were treated in vacuum for 400 s at room temperature [97]. it was found that the thermal conductivity of the nanostructured surface layer decreases clearly compared with that of coarse-grained matrix of the sample. the conducted analysis shows that the decrease of thermal conductivity is mainly due to the decrease of the electron and phonon mean free path and to electron and phonon scattering at the grain boundaries. small grain size with large volume fraction of interfaces within which a large amount of defects as well as high random atomic arrangement may exist, would strongly lead to electron and phonon scattering at grain boundaries. hence, when electrons and phonons pass the interfaces, they are scattered intensely, that inevitably leads to the reduction of thermal conductivity of the microstructure [97]. in fig. 12, it is interesting to observe that, from positions 1 to 2, the average image voltage is almost the same, and from positions 3 to 7, the voltage values increase clearly, then they become approximately stable again. the variations in average image voltage imply that, with the refinement of the microstructure, the thermal conductivity decreases clearly. (a) (b) figure 12: (a) schematic diagram of the scanning positions from the surface layer to the matrix on the cross-sectional surface. (b)variation in average image voltage while scanning from the treated surface layer to the matrix as indicated in (a) [97]. in the treated layers, a large value of residual stress was induced by the ultrasonic shot peening, which leads to an important lattice distortion and a high dislocation density. these residual stresses and dislocations can act as both phonon and electron scatterers and thereby reduce the thermal conductivity of the microstructure [96]. magnetic properties magnetic properties, as an important physical property, have attracted many researchers in ferromagnetic nanocrystalline materials. this phenomenon largely shows dependence on the composition, microstructure, and grain size [98, 99]. magnetic properties were measured for smat fe-30 wt. % ni alloy. the samples were first heated and water quenched in order to obtain uniform grain size. then they were treated at a 50 hz frequency with spherical stainless steel balls of 8 mm in diameter under vacuum at ambient temperature for different durations from 30 to 90 mins. the results indicated that the saturation magnetization (ms) and specially coercivity (hc) of the nanostructured surface layer increase significantly compared to the coarse grains sample prior to smat. experimental and theoretical analysis attributed the increase of ms to the change of lattice structure resulting from strain-induced martensitic transformation. meanwhile, hc was further increased from residual microstress and superfined grains [98]. the enhancement of material’s magnetic properties is significantly favorable for its application in several fields of engineering. treated layer treated layer matrix scanning from the surface of the layer to the matrix 1,02 1,03 1,04 1,05 1,06 1,07 1,08 1,09 1 3 5 7 9 scanning position from the treated surface layer to the m atrix a ve ra g e im ag e vo lt ag e (v ) scanning positions http://www.gruppofrattura.it http://dx.medra.org/10.3221/igf-esis.07.01&auth=true s. bagheri fard et alii, frattura ed integrità strutturale, 7 (2009) 3-16; doi: 10.3221/igf-esis.07.01 13 discussion it is verified experimentally that the nc regions produced by all sp methods have the following characteristics however in different extents: equiaxed grains of around 20nm extremely high hardness separated from adjacent deformed structure regions with sharp boundaries no recrystallization and substantially slow grain growth by annealing dissolution of cementite when it exists surface compressive residual stresses and also work hardening of the surface layer. accordingly it seems that the main properties of the nc structure are independent of the sp techniques used in the experiment [18]. in order to obtain the desired nc region via any of the mentioned sp methods, a proper combination of different parameters attributable to the enhancement of kinetic energy of the shots shall be chosen. it has been reported that the increase in the kinetic energy per one shot such as the increase in the shot velocity and/or the shot size is the most effective parameter to increase the thickness of nc layer. it is also found that there is a certain critical initial hardness of specimens to produce the nc structure by sp: the nc structure forms when the specimen hardness is lower than the shot hardness [18]. another important parameter in the formation of nc layers is the coverage technically defined as: the area fraction of specimen surface deformed by shot bombarding. it is revealed that the nc thickness tends to saturate with coverage irrespective of the shot size. on the other hand, the increasing in the coverage is ineffective to increase the maximum thickness of nc layer, the thickness of nc layer is initially increased with coverage but tends to saturate. it is possible to produce the surface nc layers with several 10 μm thick by sp when the kinetic energy (shot size and/or shot velocity) and the coverage are properly controlled [18]. actually so far apart from assessment of some particular characteristics, no comprehensive comparison between different methods of nc creating sp methods and also no detailed comparison between them and the conventional sp process is available in literature. just some researchers have studied the effect of a number of parameters and have found some results about the contribution of each to the whole process. conclusion and suggestions he formation of nc surface by means of some sp processes is a promising way to improve mechanical properties of metal alloys and in recent years has been the subject of increasing scientific and technological interests. . initial work has been performed to prove the possibility of obtaining nc surfaces by these methods and also to assess the microstructural characteristics of the obtained layers. more recently, researches have been done to evaluate the mechanical properties of nc surfaces obtained by sp processes. the results of sp experiments demonstrate that these methods are so efficient and undemanding to produce nanocrystalline surfaces and have potential application in various fields of industry. the experiments show that a remarkable improvement can be achieved as regards wear, corrosion and hardness. fewer investigations are performed on fatigue but also in this case all the results demonstrate an improved behavior after formation of nc layers. the enhanced material properties of nc materials demonstrate the technological significance of nanomaterials in improving traditional processing techniques even if a clear relation between the modified characteristics and the process parameters is not identified. therefore it seems commendable to perform more comprehensive investigations on sp methods which provide a new approach for selective surface reactions. moreover, it can be concluded that nc layers may not be induced by sp if the impacted energy of small balls is not large enough. therefore, to fully utilize the sp processes to improve the behavior of the material with a nanostructured surface layer there is an optimized processing condition, which shall be investigated in conjunction with microstructural analysis in future. finally sp methods seem to have the potentiality to improve many other material properties not studied in detail up to now such as different surface chemical treatments that are controlled by the diffusion of foreign atoms and many other treatments which may take effect from the grain size. this fact can open new fields of application for shot peening processes, which today are mostly used for enhancing fatigue and fatigue related damage processes. accordingly more investigations shall be planned in future to improve the performance of engineering materials used in industry. t http://www.gruppofrattura.it http://dx.medra.org/10.3221/igf-esis.07.01&auth=true s. bagheri fard et alii, frattura ed integrità strutturale, 7 (2009) 3-16; doi: 10.3221/igf-esis.07.01 14 references [1] r. birringer, h. gleiter, h. klein, p. marquardt, phys lett a, 102 (1984) 365. [2] r.w. cahn, nature, 348 (1990) 389. [3] r. bohn,t. haubopld, r. birringer,h. gleiter, scr. metall. mater., 25 (1991) 811. [4] k. lu, j. wang, w. wei, j appl phys, 69 (1991) 522. [5] c. koch, mater sci forum, 243 (1992) 88. [6] r. valiev, a. korznikov, r. mulyukov, mater sci eng a, 168 (1993) 141. [7] d. morris, ‘mechanical behavior of nanostructured materials’, clausthal, germany: trans. tech. publications ltd. (1998) 70. [8] j. nagahora, k. kita, k. ohtera, mater. sci. forum., 304 (1999) 825. [9] t. kulik, j. non-crystalline solids, 287 (2001) 145. [10] r. valiev, nature materials, (2004) 3. [11] u. erb, a. ei-sherik, g. palumbo, k. aust, nanostruct. mater., 2 (1993) 383. [12] k. lu, j. lu, j. mater sci technol , 15 (1999) 193. [13] l.c. jang, c.c. koeh, scripta metal, 24 (1990) 159. [14] r. valiev, y. ivanisenko, e. rauch, b. baudelet, acta mater., 44 (1996) 4705. [15] n.r. tao, m.l. sui, j. ku, k. lu: nanostructured mater., 11 (1999) 433. [16] m. umemoto, y. todaka, k. tsuchiya, mater. trans., 44 (2003) 1488. [17] m. umemoto ,y. todaka, y. watanabe, j. li, k. tsuchiya, j. of metastable and nanocrystalline materials, 24-25 (2005) 571. [18] y. todaka, m. umemoto, y. watanabe, k. tsuchiya, materials science forum, 503-504 (2006) 669. [19] j.l. liu, m. umemoto, y. todaka, k. tsuchiya, j mater sci, 42 (2007) 7716. [20] a.v.korznikov, i.m.safarov, v.p.pilyugin, r.z.valiev, nanostructured mater., 4 (1994) 156. [21] r.z.valiev, r.k.islamgaliev, i.v.alexandrov, progress in materials science, 45 (2000) 103. [22] g.e. abrosimova, a. s. aronin, s. v. dobatkin, i. i. zverkova, d. v. matveev, o. g. rybchenko, e. v. tatyanin, physics of the solid state, 49-6 (2007) 1034. [23] y.todaka, m.umemoto, j.yin, zh.liu, k.tsuchiya, materials science and engineering a, 462 (2007) 264-268. [24] j.s.c. jang, c.c. koch, scripta metallurgica et materialia, 24 (1990) 1599. [25] h. j. fecht, e. hellstern, z. fu, w.l. johnson: metallurgical and materials transactions a, 21 (1990) 2333. [26] c.h. moelle, h.j. fecht, thermal, nanostructured materials, 6 (1995) 421. [27] j. yin, m. umemoto, z. g. liu, k. tsuchiy, isij int., 41 (2001) 1389. [28] y. todaka, m. umemoto, k. tsuchiya, isij int., 42 (2002) 1429. [29] y. xu, m. umemoto , k. tsuchiya, materials transactions, 43 (2002) 2205. [30] y. xu, z.g. liu, m. umemoto, k. tsuchiya, metallurgical and materials transactions a, 33a (2002) 2195. [31] y. todaka, m. nakamura, s. hattori, k. tsuchiya, m. umemoto, j. japan inst. metals, 66-1 (2002) 34. [32]y. todaka, p.g. mccormick, k. tsuchiya, m. umemoto, materials transactions, 43 (2002) 667. [33] a.l. ortiz, l. shaw, acta materialia, 52 (2004) 2185. [34] l. shaw, h. lou, journal of materials science, 42 (2007) 1415. [35] j.w. tian, k. dai, j.c. villegas, l. shaw, p.k. liaw, d.l. klarstrom, a.l. ortiz: material science and engineering a, in press. [36] p. heilmann, w.a.t. clark, d.a. rigney, acta metall., 31 (1983) 1293. [37] d.a. hughes, d.b. dawson, j.s. korellis, l.i. weingarten, wear, 181-183 (1995) 458. [38] y. todaka, m. umemoto, s. tanaka, k. tsuchiya, materials transactions, 45 (2004) 2209. [39] y. todaka, m. umemoto, j. li, k. tsuchiya, review on advanced materials science, 10 (2005) 409. [40] y. todaka, m. umemoto, j.li, k. tsuchiya, j. of metastable and nanocrystalline materials, 24-25 (2005) 601. [41] m. umemoto, y. todaka, j. li, k. tsuchiya, material science forum, 539-543 (2007) 2787. [42] j.g. li, m. umemoto, y. todaka, k. tsuchiya, journal of alloys and compounds, 434-435 (2007) 290. [43] x.y. wang, d.y. li, electrochim. acta., 47 (2002) 3939. [44] l. wang, d.y. li, surface and coating technology, 167 (2003) 188. [45] l. wang, d.y. li, wear, 255 (2003) 836. [46] x.p. jiang, x.y. wang, j.x. li, d.y. li, c.s. manc, m.j. shepard, t. zhai, material science and engineering a, 429 (2006) 30. [47] g. liu, j. lu, k. lu, materials science and engineering a, 286 (2000) 91. http://www.gruppofrattura.it http://dx.medra.org/10.3221/igf-esis.07.01&auth=true s. bagheri fard et alii, frattura ed integrità strutturale, 7 (2009) 3-16; doi: 10.3221/igf-esis.07.01 15 [48] x. wu, n. tao, y. hong, b. xu, j. lu, k. lu, acta materialia, 50 (2002) 2075. [49] z.g. liu, h.j. fecht, m. umemoto, material science and engineering a, 375-377 (2004) 839. [50] y. todaka, m. umemoto, k. tsuchiya, materials transactions, 45 (2004) 376. [51] f.a. gao, n. trannoy, j. lu, material science and engineering a, 369 (2004) 36. [52] c. wen, z. chen, b. huang, y. rong, metallurgical and materials transactions, 37a (2006) 1413. [53] y. todaka, m. umemoto, y. watanabe, k. tsuchiya, transactions of materials research society of japan, 29 (2004) 3523. [54] k.s. raja, s.a. namjoshi, m. misra, materials letters, 59 (2005) 570. [55] t. wang, j. yu, b. dong, surface & coatings technology, 200 (2006) 4777. [56] y. t. zhu, t. g. langdon, jom, 58 (2004) 63. [57] k.y. zhu, a. vassel, f. brisset, k. lu, j.lu, acta materialia, 52 (2004) 4101. [58] k.j. marsh, ‘shot peening: techniques and applications’ (1993) london, emas. [59] j. o. almen, p.h. black,’residual stresses and fatigue in metals’ (1963) mcgraw-hill publ. company. [60] l. wagner, materials science and engineering a, 263 (1999) 210. [61] a. blarasin, m. guagliano, l.vergani, fatigue fract. engng. mater. struct., 20 (1997) 1171. [62] i. altenberger, b. scholtes, u.martin, h. oettel, materials science and engineering a, 264 (1999) 1. [63] m. guagliano, journal of materials processing technology, 110 (2001) 277. [64] m. guagliano, e.riva, m.giudetti, engineering failure analysis, 9 (2002) 147. [65] c. colombo, m. guagliano, l.vergani, sid, 1 (2005) 253. [66] v. schulze, ‘modern mechanical surface treatment’ (2006) wiley-vch. [67] k.j.miller: the 27th john player lecture (the institution of mechanical engineers) (1991) 205. [68] i.f. pariente, m. guagliano, surface and coating technology, 202 (2008) 3072. [69] k. dai, l. shaw, materials science and engineering a, 463 (2007) 46. [70] n.r. tao, z.b. wang, w.p. tong, m.l. sui, j. lu, k. lu, acta materialia, 50 (2002) 4603. [71] h.w. zhang, z.k. hei, g. liu, j. lu, k. lu, acta materialia, 51 (2003) 1871. [72] k.y. zhu, a. vassel, f. brisset, k. lu, j.lu, acta materialia, 52 (2004) 4101. [73] k. lu, j. lu, materials science and engineering a, 375–377 (2004) 38. [74] z.g. liu, h.j. fecht, m. umemoto, materials science and engineering a, 375–377 (2004) 839. [75] j. ren, a. shan, j. zhang, h. song, j. liu, materials letters, 60 (2006) 2076. [76] y. lin, j. lu, l. wang, t. xua, q. xue, acta materialia, 54 (2006) 5599. [77] k. dai, j. villegas, z. stone, l. shaw, acta materialia, 52 (2004) 5771. [78] k. dai, j. villegas, l. shaw, scripta materialia, 52 (2005) 259. [79] j. villegas, k. dai, l. shaw, p. liaw, materials science and engineering a, 410–411 (2005) 257. [80] j.w. tian, j.c. villegas, w. yuan, d. fielden, l. shaw, p.k. liaw, d.l. klarstrom, materials science and engineering a, 468–470 (2007) 164. [81] y. ochi, k. masaki, t. matsumura, t. sekino, international journal of fatigue, 23 (2001) 441. [82] j. villegas, k. dai, l. shaw, ‘surface roughness evolution in surface nanocrystallization and hardening (snh) process’ t.srivatsan, r.varin, editors. processing and fabrication of advanced materials: xii. materials park, oh: asm international (2003) 358–372. [83] j. villegas, k. dai, l. shaw, p. liaw, ‘experiments and modeling of the surface nanocrystallization and hardening (snh) process’, shaw l, suryanarayana c, mishra r, editors. processing and properties of structural nanomaterials. warrendale, pa: tms (2003) 61–68. [84] t. hanlon, y.n. kwon, s. suresh, scripta mater., 49 (2003) 675. [85] w. yuan, c. stephens,p. liaw, l. shaw, r.a. buchanan, r. mcdaniel, fatigue properties of surface nanocrystalline and hardened titanium, presented at the undergraduate poster competition, university of tennessee; (march 2003). [86] g. liu, s.c. wang, x.f. lou, j. lu, k. lu, scripta mater., 44 (2001) 1791. [87] u. martin, i. altenberger, b. scholtes, k. kremmer, h. oettel, materials science and engineering a, 246 (1998) 69. [88] l. huang, j. lu, m. troyon, nanomechanical, surface & coatings technology, 201 (2006) 208. [89] w.p. tong, n.r. tao, z.b. wang, h.w. zhang, j. lu, k. lu, scripta materialia, 50 (2004) 647. [90] c.c. koch, nanostruct. mater., 2 (1993) 109. [91] h. j. fecht, ‘in nanophase materials: synthesis, properties’, applications, g. c. hadjipanayis, r. w. siegel, eds. (1994) dordrecht, netherlands, kluwer academic. [92] c. suryanarayana, progress in materials science, 46 (2001) 1. [93] w.p. tong, c.z. liu, w. wang, n.r. tao, z.b. wang, l. zuoa, j.c. he, scripta materialia, 57 (2007) 533. http://www.gruppofrattura.it http://dx.medra.org/10.3221/igf-esis.07.01&auth=true s. bagheri fard et alii, frattura ed integrità strutturale, 7 (2009) 3-16; doi: 10.3221/igf-esis.07.01 16 [94] w. p. tong, n. r. tao, z. b. wang, j. lu, k. lu, science, 299 (2003) 686. [95] z.b. wang, n.r. tao, s. li, w. wang, g. liu, j. lu, k. lu, mater. sci. eng. a, 352 (2003) 144. [96] a.l. geiger, d.p.h. hasselman, p. welch, acta mater., 45 (1997) 3911. [97] f.a. guo, n. trannoy, j. lu, materials science and engineering a, 369 (2004) 36. [98] r.c. o’handley, ’modern magnetic materials’, new york, john wiley & sons inc. (2000) 432-466. [99] y. q. wu, t. bitoh, k. hono, a. makino, a. inoue, acta mater., 49 (2001) 4069–4077. http://www.gruppofrattura.it http://dx.medra.org/10.3221/igf-esis.07.01&auth=true microsoft word numero_53_art_15_2764 m. ameri et alii, frattura ed integrità strutturale, 53 (2020) 177-186; doi: 10.3221/igf-esis.53.15 177 evaluating properties of asphalt mixtures containing polymers of styrene butadiene rubber (sbr) and recycled polyethylene terephthalate (rpet) against failures caused by rutting, moisture and fatigue mahmoud ameri, reza mohammadi, milad mousavinezhad, amirhossein ameri, hamid shaker iran university of science and technology, tehran, iran. ameri@iust.ac.ir, r_mohammadi@civileng.iust.ac.ir, miladmosavinezhad1992@gmail.com, amir.ameri7293@yahoo.com, h_shaker@civileng.iust.ac.ir arash fasihpour plan and budget organization, tehran, iran fasihpour@yahoo.com abstract. properties of asphalt mixture play a vital role in structural integrity and performance of flexible pavements structure. in flexible pavements, asphalt concrete surface layer consists of asphalt binder, aggregates and in some cases additives. in this research study styrene butadiene rubber (sbr) and recycled polyethylene terephthalate (rpet) are used to evaluate their individual and also their combinational effects on moisture susceptibly, rutting and low temperature cracking of asphalt concrete mixture. combinations of sbr, rpet and water were vulcanized to form thermoplastic elastomer polymers as bitumen modifier. then conventional bitumen tests including penetration grade, softening point and rotational viscosity (rv) as well as asphalt mixture tests including resilient modulus, dynamic creep, idt fatigue and moisture susceptibility tests were performed on binders and asphalt mixture specimens. the test results indicated that sbr and rpet increase viscosity and softening point and stiffen the binders by reducing their penetration grade. test results of specimens prepared with modified binders showed higher tensile strength and higher rutting resistance than that of control specimen. within the content of this study it is concluded that modification of bitumen with sbr reduces low temperature stiffness of binder and hence reduces failure due to thermal cracking and modification with rpet increases rutting resistance of the mixture at high temperatures. keywords. sbr; rpet; resilient modulus; dynamic creep; moisture susceptibility; fatigue test. citation: ameri, m., mohammadi, r., mousavinezhad, m., ameri, a., shaker, h., fasihpour, a., evaluating properties of asphalt mixtures containing polymers of styrene butadiene rubber (sbr) and recycled polyethylene terephthalate (rpet) against failures caused by rutting, moisture and fatigue, frattura ed integrità strutturale, 53 (2020) 177-186. received: 12.03.2020 accepted: 04.05.2020 published: 01.07.2020 copyright: © 2020 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. https://youtu.be/pplmxiwn6sg m. ameri et alii, frattura ed integrità strutturale, 53 (2020) 177-186; doi: 10.3221/igf-esis.53.15 178 introduction sphalt concrete is commonly used on the surface layer of flexible pavements of the roads and airports. this layer is directly affected by the environment and traffic loads and tolerates the highest level of pressur and stress. thus, researchers have long been trying to improve the quality of the surface layer of flexible pavements by modifying aggregate, bitumen, and their optimum combination usage. it is a well-known fact that the viscoelastic behavior of asphalt concrete mixture results from its bitumen components. therefore, asphalt pavement distresses such as permanent deformation and thermal cracking are related to the quality of asphalt binder utilized in asphalt mixtures [1]. there are various methods for improving the performance of asphalt mixture. use of bitumen modifier is one of the common methods. the thermo-rheological behavior of bitumen causes it to act like a fragile solid at low temperatures, while at high temperatures, it flows and behaves like a newtonian fluid. these characteristics increase the risk of cracking at low temperatures and rutting at high temperatures, and as a result, decrease the service life and increase the maintenance cost of asphalt pavements [2, 3]. one of the most common categories of the bitumen modifiers is polymer materials. among these polymers, elastomers, and thermoplastics, due to their ability to enhance overall viscoelastic properties of bitumen, have a great impact on bitumen characteristics and their resistance to distresses [4]. elastomer polymers are a particular class of polymeric materials characterized by their resilience quality that permits them to stretch in response to stresses and easily return to their original shape when the force or stress is removed. the bitumen modified by elastomer polymer is more elastic and has less temperature sensitivity and a longer fatigue life. also, these polymers decrease bitumen permeability and increase their softening point, resulting in higher resistance to rutting [2]. crumb rubber (cr) and styrene butadiene (sb) are the most commonly used elastomer polymers in the asphalt industry and the combination of these materials, known as styrene butadiene rubber (sbr), is one of the most effective bitumen modifiers [5, 6]. when temperature is raised, thermoplastic polymers gradually become softer until they eventually become liquid-like and when the temperature is dropped, they turn into the solid-state again. furthermore, thermoplastic polymers absorb aromatic oils and light fractions of bitumen, causing a decrease in penetration grade and an increase in bitumen viscosity. also, these polymers increase softening point, leading to better adhesion and improvement of binder performance, particularly in wet conditions [7, 8]. polyethylene (pe), polypropylene (pp), and ethylene vinyl acetate (eva) are three thermoplastic polymers with a high potential to change the properties of binders and asphalt mixtures [9, 10]. research has shown that adding crumb rubber increases bitumen complex modulus (g*) and decreases permanent deformation in asphalt mixtures [11]. sbr is another well-known polymer that is made from styrene, butadiene, and rubber which can positively change the properties of bitumen. more specifically, styrene increases elasticity, and butadiene increases the stiffness of bitumen. also, sbr improves flexibility and elasticity of binders and asphalt mixtures, leading to higher resistance to low-temperature cracking. hence, sbr modified binder is more suitable for areas with cold climate. [12, 13]. despite the positive effects mentioned before, sbr cannot provide all the ideal characteristics of a binder. when the thermoplastic polymers is used in bitumen, the most important goals are to improve functional properties such as permanent deformation at high temperatures without adversely affecting other properties of asphalt mixtures such as fatigue and low temperature cracking. studies have shown that polyethylene (pe) modified binder has a higher complex modulus compared to that of the control sample. when pe is used as a bitumen modifier, the viscosity in high temperatures will increase, leading to greater mixture resistance to vehicle loads, and better performance of asphalt concrete mixture in hot-climate regions [14]. in order to prepare an asphalt binder that can be utilized in both high and low temperatures, researchers have used elastomer and thermoplastic polymers simultaneously together. evaluation of rheological properties showed that bitumen modified with crumb rubber and polyethylene is a less thermally sensitive binder compared to the base bitumen [15]. using recycled crumb rubber and polyethylene as bitumen modifiers increased the rutting resistance of mixtures at high temperatures and reduced thermal cracking at low temperatures [16]. using recycled materials for bitumen modification not only improves the performance of asphalt concrete pavement, but also has many environmental benefits. hence, many recycling additives such as crumb rubber, waste plastics, and recycled glass fiber have been used in the asphalt industry to reduce land consumption and save the natural resources for the next generations [17, 18]. plastic bottles are among the wide variety of man-made scrap materials which are generally produced from polyethylene terephthalate (pet). the recycled version of pet, known as rpet, is a thermoplastic powder-sized polymer that can be used for bitumen modification. researchers have shown that as a bitumen modifier, rpet, can increase the adhesion and viscosity of binder, and at the same time increase the fatigue life of asphalt mixture [19]. in this study, sbr and rpet polymers, categorized as elastomer and thermoplastic polymers, were respectively evaluated to modify properties of the base bitumen and the corresponding asphalt mixtures. a m. ameri et alii, frattura ed integrità strutturale, 53 (2020) 177-186; doi: 10.3221/igf-esis.53.15 179 experimental methods ypically, aggregate forms 90% to 96% of the total weight of the asphalt mixture; hence, the structural, chemical and physical properties of these stone materials have a significant effect on the strength of asphalt mixtures [20, 21]. the crushed limestone aggregates used in this study were obtained from the asbcharan quarry located in the northeastern part of tehran province, rudehen. the gradation and specifications of aggregates are shown in tab. 1. a) grading limit used in the research study sieve number sieve size (mm) weight percentage passing through each 4.0 gpa scale average value 1" 25 3.4" 19 100 100 1.2" 12.5 90-100 95 3.8" 9 #4 4.75 44-74 59 #8 2.36 28-58 43 #16 1.18 #30 0.5 #50 0.3 5-21 13 #100 0.15 #200 0.75 2-10 6 aggregate test aggregate test method bulk specific gravity 2.484 astm c127 absorption course aggregate (%) 2.1 astm 127 absorption fine aggregate (%) 4.3 astm 128 los angeles abrasion loss (%) 23 aashto t96 tow fracture faces (%) 93 astm d5821 b) engineering properties of aggregate source table 1: gradation and specifications of the aggregates asphalt binder is an essential component of asphalt concrete mixture, and it is the binder that holds aggregate together. the quality of the asphalt binder is directly related to the performance of the asphalt mixture [22]. in this experimental investigation, a 60-70-penetration-grade binder obtained from tehran’s pasargad oil company was used. to characterize the properties of the asphalt binder, conventional tests including penetration, softening point and ductility test were carried out. tab. 2 presents the basic properties of the base bitumen. test method criteria result penetration of 25 c ,100gr, (0.1mm) astm d5 60-70 68 softening point (c) astm d36 45-54 48 ductility of 25 (cm) astm d113 100 100 flash point (c) astm d92 250 300 fire point (c) astm d70 230 315 specific gravity at 25 c astm d70 1.05-1.06 1.048 kinematic viscosity 120c (cst) astm d2170 815 kinematic viscosity 135c (cst) astm d2170 425 kinematic viscosity 150c (cst) astm d2170 235 penetration index (pi) 2 𝑃𝐼 2 -1.15 penetration viscosity number (pvn) -0.55 table 2: basic properties of the 60-70 penetration-grade asphalt binder t m. ameri et alii, frattura ed integrità strutturale, 53 (2020) 177-186; doi: 10.3221/igf-esis.53.15 180 the properties of sbr polymer and rpet, which is produced from shredding recycling bottles are presented in tab. 3. property value diffractive index 1.4 density 1.05 viscosity (@100℃) 50 gr/(cm.s) tensile strength (@145℃, 35min, 500mm/min) 20 mpa conductivity 130.3 µs/cm a) sbr properties property value average molecular weight 30,000-80,000 gr.mol-1 density 1.4 gr.cm-3 melting temperature 255-265℃ glass transition temperature 70-115℃ young’s modulus 1700 mpa water absorption (24h) 0.5% b) rpet properties table 3: properties of sbr and rpet polymers in this study sample preparation in order to find the optimum asphalt binder content, the asphalt mixtures were designed and fabricated by using the standard marshal mix design method in accordance with astm d1599. aggregates were heated for 24 h at the temperature of 180℃, then mixed with 140℃ binder with different contents. marshal specimens were fabricated by applying 75 blows on each side of cylindrical samples to simulate heavy-traffic loading [23]. three similar specimens were used for each binder percentage, to increase the precision of optimum binder content determination. the optimum binder content was determined to be 5.6% based on maximum stability, maximum bulk specific gravity and designed limits including 4 percent air voids, percent voids in mineral aggregates and median of other limits for satisfactory asphalt mixture. based on previous research, the optimum mixing content of sbr and rpet are 5% and 10% of the weight content of the base bitumen, respectively [24, 25]. in this research study, both additives were replaced as part of the bitumen with portions of 0%, 25%, 50%, 75%, and 100% of their optimum weight values. the additives were blended with bitumen, using a high shear mixer at 175 ℃ for 30 minutes at speed of 5000 rpm [26]. the different modified binders prepared for this research are presented in tab. 4. sample composition n1 base bitumen n2 base bitumen with 5% sbr n3 base bitumen with 3.75% sbr and 2.5% rpet n4 base bitumen with 2.5% sbr and 5% rpet n5 base bitumen with 1.25% sbr and 7.5% rpet n6 base bitumen with 10% rpet table 4: different modified binder constituents used in this research study result and discussion penetration grade results enetration test is a method to measure hardness and consistency of bituminous materials in accordance with astmd5 [27, 28]. the test is conducted at 25℃ .the results of penetration test of base bitumen (control sample) and modified binders are presented in fig. 1. based on the test results presented in fig. 1, it can be seen that modified binders (at all combination levels of sbr and rpet) are stiffer and have lower penetration indicia than the base bitumen. as can be observed from the test results presented in fig. 1 show that with quantitative increase in the percent weight of sbr and rpet in the additive admixtures the binder penetration value is decreased. p m. ameri et alii, frattura ed integrità strutturale, 53 (2020) 177-186; doi: 10.3221/igf-esis.53.15 181 figure 1: penetration test results of the modified binders and the base bitumen softening point test results the softening point is a temperature at which a substance attains a particular degree of softening. it is a conventional test conducted on bituminous materials to measure their consistency at high temperatures in accordance with astm-d36 test method [29]. the results from softening point test of base bitumen and modified binders are presented in fig. 2. as can be seen modification of the base bitumen with sbr and rpet additive admixtures at all combination levels will increase the softening points of the modified binders. the increase in softening point of the modified binder takes an upward trend when additives (sbr and rpet) quantity is increased in the admixture. it should be pointed out that when binder softening point increases, higher temperature is required to liquify the binder. figure 2: softening point test results of the modified samples and the base bitumen. rotational viscosity test (rv) results viscosity is an important rheological property for measuring the consistency of bitumen. it is defined as the ratio of the applied shear stress to the rate of shear strain [30]. the test is performed in accordance with astm-d44020 [31]. bituminous binder typically exhibit newtonian behavior at high temperatures above 150℃. however, they exhibit non-newtonian behavior as the temperatures decreases, then their viscosity becomes dependent on the shear strain rate. the temperature at which the non-newtonian behavior dominates depends on binder type. nowadays the most practical means to measure the viscosity of bituminous materials is the rotational viscometer device that makes the measurement of viscosity of binders possible at various temperature. fig. 3 shows the trend of viscosity changes of binders as function of type and contents of sbr and rpet modifiers at 135℃. as can be observed from this figure the viscosities of modified binders at all combination levels of sbr and rpet are increased and are within the limits specified by strategic highway research program (shrp) committee. gyratory asphalt concrete sample preparation gyratory samples were prepared in accordance with astm-d6924, with the optimum binder contents obtained from marshall test method. to ensure proper viscosity of modified binders at mixing and compaction temperatures, the aggregates and modified binders were mixed and compacted by super pave gyratory compactor (sgc) at various m. ameri et alii, frattura ed integrità strutturale, 53 (2020) 177-186; doi: 10.3221/igf-esis.53.15 182 temperatures corresponding to viscosities obtained from rv test results. the diameter and highest of cylindrical mold used to compact asphalt mixture samples were 100 mm and 62.5 mm respectively. the air void content for all samples was set to 4% [32]. in this investigation a total of 72 samples were fabricated based on a minimum of three replicate samples per mix, per test type. figure 3: rotational viscosity test results of the modified binders and the base bitumen resilient modulus test results in the first step, the resilient modulus test was conducted on each specimen, considering the fact that the test is a nondestructive. resilient modulus is defined as the ratio of the repeated axial deviator stress to the recoverable axial strain [33]. resilient modulus is one of the main factors in designing asphalt concrete pavements. it shows the asphalt’s potential for possible deformations based on the relation between stress and strain under a specific load [34]. in this research study, the resilient modulus value was determined in accordance with astm-d4123, by using the utm5 device. the 450n load was applied with 0.1 s loading time and 0.4 s rest period, while the temperature was set at 25°c. the resilient modulus is calculated by eq. 1 [35]. rm = p (ν+0.2734) / t. h (1) where rm is the resilient modulus (mpa), p is the repetitious load (n), ν is the poisson ratio (assumed to be 0.35), t is the sample’s thickness (mm), and h is the horizontal reversible deformation (mm). according to fig. 4, the value of the resilient modulus of all specimens prepared with modified binders increased about 100 percent compared to the control sample. to explain this change, it can be noted that asphalt mixes modified with sbr have more elasticity relative to control sample, and the application of rpet in asphalt mixes increase the adhesion between binder and aggregates. the fact that incremental difference between the resilient modulus values of specimens with different additive type and additive contents is not significant, indicates that sbr and rpet have similar influence on permanent deformation potentials of asphalt mixtures. figure 4: the resilient modulus values of the modified and the control mixture m. ameri et alii, frattura ed integrità strutturale, 53 (2020) 177-186; doi: 10.3221/igf-esis.53.15 183 dynamic creep test results in this study flow number (fn) is used to evaluate and compare the rutting resistance of all mixtures. fn is defined as the number of load cycles at which the rate of change of compliance of a mixture is minimum. higher fn value indicates a more stable asphalt mixture with higher resistance to rutting [36, 37]. the fn values calculated from dynamic creep test results of samples per binder type are shown in fig. 5. as can be observed from the results presented in fig. 5 the fn values and hence the rutting resistance of all mixes prepared with admixtures of sbs and rpet binder are higher than that of the control mixture. the highest rutting resistance belongs to the sample prepared with 10 percent rpet. this phenomenon may be attributed to increase in viscosity and adhesive effect of rpet. figure 5: number of cycles to failure (flow number) obtained from dynamic creep test moisture susceptibility test results the moisture susceptibility of asphalt mixtures is assessed by measuring their tensile strength in wet and dry conditions in accordance with aashto-t283 standard [38]. the tensile strength ratio (tsr) is defined as the ratio of the ensile strength of the conditioned (or wet) specimens to that of the dry specimens [39]. the higher the tsr value, the higher the resistance of the mixture to moisture damage [40, 41]. fig. 6 shows the trend of tsr changes as a function of rpet content in the mixtures. as can be observed from this figure the tsr value is increased with increase in rpet content in the mixtures. hence, it may be deduced that modification of bitumen with rpet polymeric materials will enhance resistance of asphalt mixtures against moisture damage. the increase in moisture resistance of the asphalt mixtures prepared with rpet modified binder might be due to conspicuous adhesive effect of rpet modified binder which enhances cohesive bonding between aggregates in the asphalt mixture skeleton. the results also show that the tsr values of all mixture prepared with rpet and sbr modified binders satisfy the minimum requirement of 80% suggested by many asphalt agencies worldwide. a possible explanation for increase in moisture resistance of asphalt mixtures containing sbr may be attributed to the styrene content of the sbr which increases the elasticity of the modified binder leading to higher tensile strength value of the mixture [5]. figure 6: tsr (tensile strength ratio) test results of the modified and the control. m. ameri et alii, frattura ed integrità strutturale, 53 (2020) 177-186; doi: 10.3221/igf-esis.53.15 184 indirect tensile fatigue test results fatigue cracking due to low temperature drop in pavement structures has been a major concern of pavement design engineers, because these types of cracking are generally developed within the pavement structure [42]. to understand the fatigue performance of asphalt mixture prepared with binders at varying combination levels of sbr and rpet modifiers, their behavior were evaluated by repeated load indirect tension test at 0℃ [43] the test results are presented in fig. 7. the results presented in this figure show that fatigue resistance of all mixtures prepared with modified binders is significantly increased and is higher than that of the control mixture. the results also show that, the fatigue parameter of mixture designated as n2 is almost ten times higher than that of the control mixture, indicating that sbr modified binder greatly reduces the low temperature susceptibility of the mixtures and also reduces the chance of thermal cracking. figure 7: idt fatigue test results of the modified and the control mixtures. conclusion ithin the context of this research study it can be concluded that both sbr and rpet polymers improve physical and mechanical properties of the base binder. the results of moisture susceptibility and dynamic creep tests show that by increasing the ratio of rpet ،resistance of the asphalt mixture increases. also, by increasing the ratio of sbr in fatigue test, resistance of mixture increases. considering the results of all the tests conducted in this research study it can be said that the modified asphalt with both polymers compared to the base bitumen has better performance. it can also be mentioned that using rpet and sbr is suitable in road asphalt pavement in regions located in deserts where there is a large difference between the day and night temperature as they decrease the rutting in high temperature and reduce the cracking in low temperature. references [1] yang, h., (2004). pavement analysis and design, 1. [2] nikolaides, a., (2014). highway engineering: pavements, materials and control of quality. crc press. [3] tafti, m. h., aqda, s. a. h., motamedi, h. (2019). the impacts of type and proportion of five different asphalt modifiers on the low-temperature fracture toughness and fracture energy of modified hma, frattura ed integrità strutturale, 47, pp. 169-185. [4] zhu, j., birgisson, b., kringos, n. (2014). polymer modification of bitumen: advances and challenges, european polymer journal, 54, pp.18-38. [5] behnood, a., gharehveran, m. m. (2019). morphology, rheology, and physical properties of polymer-modified asphalt binders, european polymer journal, 112, pp. 766–791. [6] gogoi, r. (2015). performance prediction analyses of styrene-butadiene rubber and crumb rubber materials in asphalt road applications, materials and structures, 49, pp. 3479–3493. [7] senise, s. (2017). thermomechanical and microstructural evaluation of hybrid rubberised bitumen containing a thermoplastic polymer, construction and building materials, 157, pp. 873-884. [8] lu, x. (2001). modification of road bitumens with thermoplastic, polymer testing, 20, pp. 77-86. [9] al-hadidy, a.i. (2018). effect of laboratory aging on moisture susceptibility and resilient modulus of asphalt concrete mixes containing pe and pp polymers, karbala international journal of modern science, 4, pp. 377-381. w m. ameri et alii, frattura ed integrità strutturale, 53 (2020) 177-186; doi: 10.3221/igf-esis.53.15 185 [10] luo, w.-q., chen, j.-c. (2011). preparation and properties of bitumen modified by eva graft copolymer, construction and building materials, 25, pp. 1830-1835. [11] moreno navarro, f. and rubio gamez, m. c., (2012). influence of crumb rubber on the indirect tensile strength and stiffness modulus of hot bituminous mixes, journal of materials in civil engineering, 24, pp. 715-724. [12] mcnally, t. (2011). polymer modified bitumen: properties and characterisation. woodhead publishing, 1th edition. [13] liang, p., liang, m.(2017). improving thermo-rheological behavior and compatibility of sbr modified asphalt by addition of polyphosphoric acid (ppa), construction and building materials, 139, pp. 183-192. [14] murphy, m. (2000). bitumens modified with recycled polymers, materials and structures, 33, pp. 438-444. [15] hussein, a.a., pei feng, c. (2017), effects of high-density polyethylene and crumb rubber powder as modifiers on properties of hot mix asphalt. construction and building materials, 142, pp. 101-108. [16] ge, d., yan, k., you, z. and xu, h., (2016). modification mechanism of asphalt binder with waste tire rubber and recycled polyethylene. construction and building materials, 126, pp. 66-76. [17] karahrodi, m.h., jazani, o.m. (2017). modification of thermal and rheological characteristics of bitumen by waste pet/gtr blends, construction and building materials, 134, pp. 157-166. [18] modarres, a., hamedi, h. (2014). effect of waste plastic bottles on the stiffness and fatigue properties of modified asphalt mixes, materials and design, 61, pp. 8-15. [19] el-naga, i. a., raga, m. (2019). benefits of utilization the recycle polyethylene terephthalate waste, construction and building materials, 219, pp. 81-90. [20] oglesby, c. h. and hicks, r. g. (1982). highway materials, chapters 15, 16 and 17, 4th edition. [21] haghnazar, h. and saneie, m. (2019). impacts of pit distance and location on river sand mining management. modeling earth systems and environment, 5(4), 1463-1472. [22] yoder, e. j. and witczak, m. w. (1975). principles of pavement design, chapter 9, 2nd edition. [23] astm-d1599, (2001). american society for testing and materials for determine the optimal bitumen percentage of asphalt samples. [24] tabatabaei, s. a., kiasat, a., alkouhi, f. k. (2013). the effect of styrene-butadiene-rubber (sbr) polymer modifier on properties of bitumen, international journal of materials and metallurgical engineering, 7(10). [25] ahmad, a. f., razali, a. r. (2017). utilization of polyethylene terephthalate (pet) in bituminous mixture for improved performance of roads, materials science and engineering, 203(1). doi:10.1088/1757-899x/203/1/012005. [26] ameri, m., mohammadi, r. (2017). evaluation the effects of nanoclay on permanent deformation behavior of stone mastic asphalt mixture, construction and building materials, 156, pp.107-113. [27] abson, g. and burton, c. (1964). physical tests and rang of propertics, in a. j. holborg (ed), bituminous materials: asphalt, 1. [28] astm-d5, (2001). american society for testing and materials for determining the penetration grade of bitumen. [29] astm-d36, (2001). american society for testing and materials for determining the softening point of bitumen. [30] chunshui huang, (2018). a new viscoelastic mechanics model for the creep behaviourof fiber reinforced asphalt concrete, frattura ed integrità strutturale, 45, pp. 108-120. [31] astm-d4402, (2001). american society for testing and materials for determining the viscosity of bitumen. [32] astm-d6924, (2001). american society for testing and materials for constructing asphalt samples. [33] yang. h .huang, (2004). pavement analysis and design, chapter 2. [34] ameri, m., nemati, m., shaker, h., jafari, f. (2019). experimental and numerical investigation of the properties of the hot mix asphalt concrete with basalt and glass fiber, frattura ed integrità strutturale, 50, pp. 149-162. [35] astm-d4123, (2001). american society for testing and materials for determining the resilient modulus of asphalt mixture. [36] goh, s.w., you, z., (2009). a simple stepwise method to determine and evaluate the initiation of tertiary flow for asphalt mixtures under dynamic creep test, construction and building materials, pp. 3398–3405. [37] en13697-25a, (2007). european standard test methods for determine the dynamic creep of asphalt mixture. [38] aashto-t283, (2002). american association of state highway and transportation officials methods for determine the moisture sensitivity of asphalt mixture. [39] farazmand, p., hayati, p. (2021). relationship between microscopic analysis and quantitative and qualitative indicators of moisture susceptibility evaluation of warm mix asphalt mixtures containing modifiers, frattura ed integrità strutturale, 51, pp. 215-224. [40] babagoli, r., mohammadi, r. and ameri, m. (2017). the rheological behavior of bitumen and moisture susceptibility modified with sbs and nanoclay, petroleum science and technology, pp. 35 1085-1090. m. ameri et alii, frattura ed integrità strutturale, 53 (2020) 177-186; doi: 10.3221/igf-esis.53.15 186 [41] boyes, a.j. (2011). reducing moisture damage in asphalt mixes using recycled waste additives, master of science thesis, california polytechnic state university. [42] al-khateeb, g. g., ghuzlan, k. a. (2014). the combined effect of loading frequency, temperature, and stress level on the fatigue life of asphalt paving mixtures using the idt test configuration, international journal of fatigue, 59, pp. 254-261. 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can be opened with acrobat and adobe reader 5.0 and later.) >> /namespace [ (adobe) (common) (1.0) ] /othernamespaces [ << /asreaderspreads false /cropimagestoframes true /errorcontrol /warnandcontinue /flattenerignorespreadoverrides false /includeguidesgrids false /includenonprinting false /includeslug false /namespace [ (adobe) (indesign) (4.0) ] /omitplacedbitmaps false /omitplacedeps false /omitplacedpdf false /simulateoverprint /legacy >> << /addbleedmarks false /addcolorbars false /addcropmarks false /addpageinfo false /addregmarks false /convertcolors /converttocmyk /destinationprofilename () /destinationprofileselector /documentcmyk /downsample16bitimages true /flattenerpreset << /presetselector /mediumresolution >> /formelements false /generatestructure false /includebookmarks false /includehyperlinks false /includeinteractive false /includelayers false /includeprofiles false /multimediahandling /useobjectsettings /namespace [ (adobe) (creativesuite) (2.0) ] /pdfxoutputintentprofileselector /documentcmyk /preserveediting true /untaggedcmykhandling /leaveuntagged /untaggedrgbhandling /usedocumentprofile /usedocumentbleed false >> ] >> setdistillerparams << /hwresolution [2400 2400] /pagesize [612.000 792.000] >> setpagedevice microsoft word numero_59_art_05_3298.docx m. madqour et al, frattura ed integrità strutturale, 59 (2022) 62-77; doi: 10.3221/igf-esis.59.05 62 finite element modeling of flexural behavior of reinforced concrete beams externally strengthened with cfrp sheets mahmoud madqour, hilal hassan, khaled fawzy structural department, zagazig university, egypt madqour42@gmail.com https://orcid.org/0000-0002-0994-2884 hilalcivil@yahoo.com https://orcid.org/0000-0001-5486-5497 khaled_lashen1@yahoo.com https://orcid.org/0000-0003-2275-4025 abstract. in this research, the finite element method is used to develop a numerical model to analyse the effect of the external strengthening of reinforced concrete beams by using carbon fiber reinforced polymer (cfrp) sheets. a finite element model has been developed to investigate the behavior of rc beams strengthened with cfrp sheets by testing nineteen externally simple r.c. beams, tested under a four-point load setup until failure. various cfrp systems were used to strengthen the specimens. the numerical results using the (ansys workbench v.19.1) were calibrated and validated with the experimental results. the research results indicate a significant improvement in the structural behavior of the specimens strengthened using cfrp sheet systems. then the validated model investigated the effect of the width of cfrp sheets, no of layers, and cfrp size on the behavior of strengthened r.c. beams. results of this numerical investigation show the effectiveness of increase cfrp width to improve the flexural capacity of r.c. beams. an increase in the flexural capacity up to 100 % compared to the control beam. keywords. strengthening; carbon fiber reinforced polymer; deflection; ansys; ultimate strength. citation. mahmoud madqour, hilal hassan., khalid fawzi., finite element modeling of flexural behavior of reinforced concrete beams externally strengthened with cfrp sheets, frattura ed integrità strutturale, 59 (2022) 62-77. received: 30.08.2021 accepted: 30.09.2021 published: 01.01.2022 copyright: © 2022 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. introduction ver the past decades, (frp) has been commonly used to repair and rehabilitate civil structures, showing signs of aging degradation and distress. (cfrp) is a brittle material that typically fails at a lower load level (i.e., horizontal crack propagation or debonding). as a result, the ultimate capacity of the reinforced concrete structural elements is challenging to achieve., kang et al.,[1]. in the past, various researchers conducted studies on reinforced concrete beams with cfrp retrofitted in flexure, and the failure patterns were observed [2-4]. recent research has focused on the impact of geometric factors such as length and the frp–concrete width ratio. it has been shown that the ultimate stress for debonding increases with bonded length up to a critical bond length. although numerous researchers have presented results demonstrating the influence of frp laminate width on ultimate load, these results are frequently inconsistent [5–7]. the available results in the literature are frequently contradictory. while some o https://youtu.be/fsvmddevrec m. madqour et al, frattura ed integrità strutturale, 59 (2022) 62-77; doi: 10.3221/igf-esis.59.05 63 studies have indicated that average bond strength decreases with frp width [5], others have found that bond strength increases with frp width [8]. travassos et al [9] suggested adding more cfrp composite at the ends of the cfrp plate to prevent premature debonding. two approaches were offered in particular: (i) addition of more layers of rectangular cfrp sheets; and (ii) addition of more layers of cfrp sheets across the main cfrp plate. hasnat et al. [10] studied reinforced concrete beams strengthened by carbon-fiber-reinforced polymer sheets. a cfrp wrap (u-shape) had prevented the premature cover from debonding, increasing the final moment's efficiency. the study on reinforced concrete beams, consisting of a t-section, was carried out by mostafa et al. [11]. lusis et al. [12] investigated the influence of insertion of short fibers on reinforced concrete's mechanical characteristics using a series of experiments and numerical analysis. they had a significant effect on the tensile strength of the structure. abid et al. [13] performed a systematic analysis of previous scientific studies based on the strength and durability of concrete beams externally covered by frp reinforcement. the research study focused on bond behavior, testing techniques, and models used to determine bond performance. bennegadi et al. [14] developed a numerical model for optimization of reinforced concrete beams by external (hfrp) plate, and they found that the ultimate load of the reinforced concrete beam was increased when compared to the reference beam, the geometrical and mechanical properties of the hfrp plate must be optimized. el-ghandour [15] carried out three-point load checks on seven half-scale reinforced concrete beams, strengthened with longitudinal cfrp sheets and u-wraps. kara and ashour [16] developed a numerical system for predicting curvature, deflection, and the moment capacity of reinforced concrete beams strengthened by frp. narmashiri et al. [17] conducted more experimental and numerical research on cfrp-reinforced steel i-beams in terms of failure analysis and structural behavior. they concluded that the geometric and mechanical characteristics control the loadbearing capacity of cfrp plates. kermiche and redjel [18] provided experimental research and an analytical model to simulate the mechanical behavior of concrete and reinforced concrete. osman et al.,[19]. performed experimental studies on seven reinforced concrete beams under four-point loads with specific span-to-depth shear ratios. a comparative analysis of 27 reinforced concrete beams with and without cfrp sheets was also carried out. the findings obtained using ansys have been similar to the experimental outcomes of the studies. considering the previous literature review, it is clear that only few researchers have studied the effect of different cfrp strengthening schemes and locations on bending moment and rc beam failure behaviour. a total of nineteen fe models were developed to study the flexural behavior of rc beams externally bonded with cfrp sheets. ten specimens were used to validate the accuracy of the numerical model by comparing it with experimental results by madqour et al.[20] and nine models were developed to investigate the effect of increasing cfrp sheets size. description of the experimental program he fe model was created to investigate the flexural behavior of rc beams reinforced with cfrp sheets [20] by madqour et al. information on the rc beams is omitted and briefly summarized in the following. geometric features of the beams a total of ten rc beam specimens strengthened with various schemes were tested by madqour et al.[20]. the specimens examined included a control beam (b01) reinforced with two steel bars with a diameter of 10 mm. the tested beam has a rectangular cross-section with a nominal width, depth, length of 150 mm, 200 mm, and 2000 mm and spanned over 1800 mm. the compression reinforcing of the specimens tested consisted of two steel bars of 8 mm diameter fig. 1 also, the 6 mm diameter stirrups spaced at interval 125 mm. table 1 provides the characteristics of the examined beams. the deflection of the beams was measured at mid-span using a displacement transducer (lvdt) placed on the beams fig. 2. t m. madqour et al, frattura ed integrità strutturale, 59 (2022) 62-77; doi: 10.3221/igf-esis.59.05 64 figure. 1. details of the tested beams (in mm) [18]. table 1: description of the examined rc beams. figure. 2. test setup. finite element model development everal computer programs packages have been developed to solve finite element problems. ansys, nastran, adina, ls-dyna, marc, sap, cosmos, abaqus, and nisa are some of the most commonly used packages. the most recent version of ansys 19.1 [21] was selected for use in this research work. it can model non-metal materials and successfully model reinforced concrete as non-homogeneous material with nonlinear response. it also can predict and display the cracking and crushing patterns of the material. ansys 19.0 fe software is used to develop 3d fe specimen models tested by madqour et al. [20]. the geometry, constituent material characteristics, loading, and boundary conditions of the fe models are similar to those of the tested beams previously described in table 1. beams designation [20]. fem designation reinforcement type frp width (mm) b00 s00 control beam without strengthening n/a b02 s01 two layers with lengths 1700, and1400 mm 100 b04 s01s one layer and on both sides with length 1700 mm 100 b05 s01u one layer and 6 (u-shape) 100 s m. madqour et al, frattura ed integrità strutturale, 59 (2022) 62-77; doi: 10.3221/igf-esis.59.05 65 figure 3: fe models elements: (a) solid65 (b) link180 (c) shell181 (d) solid185 layered and solid45 [22-27]. numerical modeling the concrete is modeled by using 8-noded solid65 fig 3(a) element, which has three degrees of freedom at each node and can crack in tension and crushing in compression. fig. 3(a) shows the geometry of the solid65 element. due to the fact that concrete is highly nonlinear in compression, a proper uniaxial stress-strain relationship is used to describe this nonlinearity more precisely, the compressive behavior of concrete is modeled by using the nonlinear stress-strain relation proposed by popovics, [28] and later modified by thorenfeldt et al. [29]. figure (2) shows the curve, which is defined using these equations. the use of thorenfeldt et al., [29]'s stress-strain model for concrete in compression was found to be effective for frp reinforced rc beams by el-tawil et al., [30].               1 ( ) c c o cu nkc o nf n (1)  0.80   17 cfn (2) m. madqour et al, frattura ed integrità strutturale, 59 (2022) 62-77; doi: 10.3221/igf-esis.59.05 66        0.67 1       62 cfk for    1   1 c o (3)  1      k for     1c o (4) figure (4): uniaxial stress-strain curve implemented in the fem for concrete.where,  cu is the maximum compressive strength, εcu is the ultimate strain, and ε0 is the strain at maximum stress. the steel reinforcement modeled with a 3-d spar link 180 element having three degrees of freedom at each node (translation in x, y, z directions), as shown in fig. 3(b). the reinforcement element is assumed to be a bilinear isotropic elastic-perfectly plastic material identical in tension and compression. shell 181 element is used to model the frp sheet. the thickness of a shell element is relatively small compared to other dimensions of the element. this element is a four-node element with six degrees of freedom at each node: x, y, z-direction translations, and x, y, and z-axis rotations fig.2 (c). to exclude the debonding of frp sheets, the effective frp strain should be as recommended by aci 440.2r-08 [31]. therefore, such a recommendation is used to modify the debonding frp strain equation originally proposed by teng et al. [23]. the effective frp strain to consider debonding failure in modified form is given by   0.41      d f f f fc n e t ˋ ≤ 0.9  uf (5) where,  df is the debonding strain of externally bonded frp reinforcement, fc ˋ is specified compressive strength of concrete, (mpa), n is the number of layers, fe is the tensile modulus of elasticity of frp, (mpa), ft is the nominal thickness of one ply of frp reinforcement, (mm), and  uf is the design rupture strain of frp reinforcement. m. madqour et al, frattura ed integrità strutturale, 59 (2022) 62-77; doi: 10.3221/igf-esis.59.05 67 solid 185 element is used to model the loading supports. eight nodes represent this element fig.2(d), each having three degrees of freedom in the nodal directions x, y, and z. plasticity, stress stiffening, creeping, large deflection, and high strain power are all capabilities of the element. the adhesive is modeled using the element solid45 fig. 2(d). it is an eight-node three-dimensional structure with three degrees of freedom at each node, i.e., translations in directions nodal x, y, and z. the element has the capacity for plasticity, creeping, swelling, stress stiffening, large deflection, and significant strain. hawileh et al. [24] used the solid45 element to model adhesive and obtained satisfactory results in the study of rc beams reinforced by frp. this system consists of two nodes, one set of nodes with the concrete element used in this analysis and another with frp elements. the material properties of the concrete, steel reinforcement, cfrp, steel plate, and epoxy used in the developed fe models are summarized in table 2. table 2: material properties concrete, reinforcement steel, cfrp, epoxy, and steel plate. fe model validation he flexural behavior of rc beams externally strengthening with cfrp sheets is studied using a total of nineteen fe models. the accuracy of the numerical model is validated by comparing experimental results with the ten beams reported in table 1, and the remaining models are developed to study the effect of cfrp width and sheet size on the flexural behavior of the beams. fig. 4 shows the developed fe models for a rc beam, externally strengthening with cfrp sheets. the four beams detailed in the previous section are modeled and to evaluate the accuracy of the numerical models. the predicted and obtained experimental data are compared for all beams. for four beams, in fig. 5 are plotted the experimental and predicted results in terms of load versus mid-span deflection. table 3 compares the fe results and experimental measured data in terms of attained load (pu) along with its corresponding mid-span deflection (δu) value. material fe type properties values concrete solid 65 compressive strength (mpa) 32 modulus of elasticity (gpa) 30.6 poisson's ratio(v) 0.25 modulus of elasticity (gpa) 200 open shear transfer 0.50 closed shear coefficient 0.80 uniaxial cracking (ft) 32 uniaxial crushing (fc) 3.4 reinforcement steel link 180 yield strength (mpa) (longitudinal) 525 yield strength (mpa) (stirrups) 400 poisson's ratio(v) 0.20 elastic modulus (mpa) 200 000 cfrp shell 181 modulus of elasticity (gpa) 230 design thickness (mm/ply) 0.129 tensile strength (mpa) 4000 epoxy solid45 modulus of elasticity (gpa) 4.50 tensile strength (mpa) 30 steel plate solid185 elastic modulus (mpa) 200 000 poisson’s ratio 0.3 t m. madqour et al, frattura ed integrità strutturale, 59 (2022) 62-77; doi: 10.3221/igf-esis.59.05 68 figure 5: finite element model of a rc beam: (a) numerical model; (b) modeling of longitudinal reinforcement without stirrups and modeling of longitudinal reinforcement with stirrups. figure 6: comparison between experimental and numerical load-deflection curve for b00, b02, b04, and b05 beams. table 3: comparison between experimental and numerical results for b00, b02, b04, and b05 beams. parametric study n this section, parametric research is carried out by developing and analyzing nine additional fe models to investigate the influence of cfrp laminate size (width) and different schemes of frp laminates on the flexural response and strength of rc beams externally strengthened with sheets as in fig. 7. beam no. ansys (100 mm width) experimental load (kn) deflection (mm) load (kn) deflection (mm) b00 51.39 30 51.20 32.01 b02 72.43 31.76 75.66 31.74 b04 77.67 23.82 75.1 26.13 b05 80.08 24.87 ---- i m. madqour et al, frattura ed integrità strutturale, 59 (2022) 62-77; doi: 10.3221/igf-esis.59.05 69 figure 7: strengthening configurations of specimens to investigate the behavior of the beam when the size (width) of cfrp sheets is changed, nine fe models were developed. one of the beams was modeled as an un-strengthened control, while the other eight were strengthened using cfrp sheets s tr en g th en in g m o d el s one layer s01 (one layer) s01u (one layer + 6u shape) s01s (one layer + on sides) two layers s02 (two layers) s02 u (two-layers + 6u shape) s02 s (two layers + on sides) three layers s03 (three layers) s03u (three-layers + 8u shape) s03 s (three layers + on sides) m. madqour et al, frattura ed integrità strutturale, 59 (2022) 62-77; doi: 10.3221/igf-esis.59.05 70 of varying width of 150 mm. table 3 lists the designations for each studied model. figure 6 shows the predicted load versus mid-span displacement response curves. table 3 further summarizes the predicted ultimate achieved load (pu) and its corresponding mid-span deflection (u). effect of cfrp sheet size for the case one layer as expected, the beams with a width of 150 mm bonded frp sheets obtained a larger load-carrying capacity (flexural strength) than the beams with a width of 100 mm, as shown in fig. 8 and table 4. the load-carrying capacity (pu) of beam s01, which has a 150 mm wide cfrp sheet, is 8% greater than the control specimen. fig.8 further shows that the increase in pu for beams s01u with 150 mm wide cfrp sheets and s01s with 150 mm wide cfrp sheets was 7.98% and 12.95%, respectively. as a result, the increase in the load-carrying capacity of a beam is inversely proportional to the increase in cfrp laminates' size (width). figure 8: numerical load-deflection curve for s01, s01s, and s01u beams. effect of cfrp sheet size for case of two-layers the load versus mid-span deflection curves for the two layers are provided in fig. 9. the load capacity (pu) of beam s02, which has a 150 mm wide cfrp sheet, is 12.8 % greater than that of the control specimen. table 4 further shows that the increase in pu for beams s02u with 150 mm wide cfrp sheets and s02s with 150 mm wide cfrp sheets was 9.58 % and 10.47%, respectively, as a result, the increase in the load capacity of a beam is inversely proportional to the increase in the width of cfrp sheets. m. madqour et al, frattura ed integrità strutturale, 59 (2022) 62-77; doi: 10.3221/igf-esis.59.05 71 figure 9: numerical load-deflection curve for s02, s02s, and s02u beams. effect of cfrp sheet size for in case of three-layers the predicted load versus mid-span deflection curves for the three layers are provided in fig. 10. the ultimate load of beam s03 with a 150 mm wide cfrp sheet is 22.50 % greater than that of the control specimen. table 4 shows that the increase in pu for beams s03u with 150 mm wide cfrp sheets and s03s with 150 mm wide cfrp sheets was 14.10 % and 14.32 %, respectively.   table 4: comparison between analytical and experimental results. beam no. ansys (100 mm width) ansys (150 mm width) experimental load (kn) deflection (mm) load (kn) deflection (mm) load (kn) deflection (mm) cb 51.39 30 51.39 30 51.20 32.01 s01 75.21 23.92 81.78 28.25 69.44 27.72 s01s 72.43 31.76 83.20 34.01 75.66 31.74 s01u 78.43 24.79 85.23 29.85 73.76 32.96 s02 77.67 23.82 89.08 28.14 75.1 26.13 s02s 80.08 24.87 89.45 26.74 ---- s02u 88.03 24.53 97.36 30.96 87.85 36.96 s03 76.39 23.69 98.59 28.50 79.39 23.33 s03s 86.88 26.09 101.41 27.39 ---- s03u 86.43 26.48 100.62 29.93 88.78 30.97 m. madqour et al, frattura ed integrità strutturale, 59 (2022) 62-77; doi: 10.3221/igf-esis.59.05 72 figure 10: numerical load-deflection curve for s03, s03s, and s03u beams. figure 11: strain distribution and force equilibrium conditions for externally strengthened frp beams. theoretical prediction of beam capacities everal research, including wenwei et al. [32] and chellapandian et al. [33], compared the experimental and theoretical flexural and shear capacities of various cfrp strengthening rc beams. s m. madqour et al, frattura ed integrità strutturale, 59 (2022) 62-77; doi: 10.3221/igf-esis.59.05 73 according to aci, the bending moment of externally bonded frp beams is calculated using strain compatibility, internal force equilibrium, and governing modes of failure [31]. the strain distribution and force equilibrium conditions for externally reinforced frp beams are depicted in figure (11). according to gangarao and vijay[34], aci [31], the modes of failure in externally reinforced frp beams are (1) tension-controlled failure with frp rupture (  s  0.005> sy,  frp =  ufrp ); (2) tension-controlled failure without frp rupture (  s  0.005>  sy,   ufrp frp ,  cu = 0.003); (3) tension and compression-controlled failure (  sy  0.005  sy,   ufrp frp ,  cu = 0.003); (4) compression-controlled failure (  s  sy,    frp frpu ); and (5) balanced failure ( s =   u =0.003,  frp frpu ,  s  sy). strain and stress in frp: frp reinforcement is assumed to behave linearly elastic manner until failure. furthermore, the frp stress is proportional to strain. the maximum strain obtained in the frp reinforcement is determined by either the strain level developed in the frp at the point where the concrete crushes, the frp ruptures, or the frp debonds from the substrate. the effective strain level in frp reinforcement at the ultimate can be calculated using the following expression:                                e cu i m u h c f b k f c (6)       dli cr m h kd b i ec (7)                            2 2s s ss f s f s f e e eef ef efh k ec ec ec ec d ec ec (8) the effective stress level in the frp reinforcement can be calculated as follows: fe f ef e f (9) concrete delamination or frp debonding can occur if the substrate cannot sustain the force in frp. to prevent the debonding of frp reinforcement, a limitation should be provided on the strain level developed in the frp reinforcement. the bond dependent coefficient km is given as follows:             1 1 0.90    180, 000 60  360, 000 f f m f f ne t k for ne t fu (10a) or            1 360, 000 1 0.90      180, 000     60  m f f f f k for ne t fu ne t (10b) the flexural strength of beams with frp external reinforcement can be computed using equation (11). the additional strength reduction factor ( f 0.85) is applied to the flexural strength contribution of the frp reinforcement. m. madqour et al, frattura ed integrità strutturale, 59 (2022) 62-77; doi: 10.3221/igf-esis.59.05 74                        2 2 s f f f f a a mn a fy d a e h (11) the theoretical bending moment values are calculated by incorporating the additional strength reduction factor,  f . table 5 shows the final results of the theoretical method. table 5: results of the theoretical method. conclusion he main aim of the research is to investigate the influence of increasing cfrp sheet size and width, the models have been validated by comparing the behaviour and response of nine beam specimens. at all levels of loading until failure, the numerical and experimental data demonstrated a high correlation, and it can conclude that.  the fe models accurately predicted the flexural behaviour of the tested reinforced concrete beam specimens with and without cfrp sheet reinforcement.  increasing the number of layers of frp sheets increases the ultimate strength of rc beams up to 100% compared to the control beam. however, the mid-span deflections are less than those of the control specimen.  by increasing the width of cfrp sheets increases beam load capacity. references [1] kang, t. h. k., howell, j., kim, s. and lee, d. j. (2012). a state-of-the-art review on debonding failures of frp laminates externally adhered to concrete. international journal of concrete structures and materials, 6(2), pp. 123-134. [2] bennati, s., dardano, n. and valvo, p. s. (2012). a mechanical model for frp-strengthened beams in bending. frattura ed integrità strutturale, 6(22), pp. 39-55. [3] cunha, r., oliveira, k., brito, a., vieira, c. and amorim, d. (2021). evaluation of the behaviour of reinforced concrete beams repaired with glass fibre reinforced polymer (gfrp) using a damage variable. frattura ed integrità strutturale, 15(57), pp. 82-92. [4] benaoum, f., khelil, f. and benhamena, a. (2020). numerical analysis of reinforced concrete beams pre cracked reinforced by composite materials. frattura ed integrità strutturale, 14(54), pp. 282-296. [5] ueda, t., sato, y. and asano, y. (1999). experimental study on bond strength of continuous carbon fiber sheet. special publication, 188, pp. 407-416. [6] carloni, c., ali-ahmad, m. and subramaniam, k. (2005, august). scaling effect in frp/concrete interface debonding. in proceedings of the 7th international conference on mesomechanics, pp. 1-4. [7] rilem, t. q. f. s. (2004). quasibrittle fracture scaling and size effect—final report. mater. struct, 37272, pp. 547586. beam no. theoretical load (kn) (100 mm cfrp width) theoretical load (kn) (150 mm cfrp width) cb 47.01 47.01 s01 66.66 72.79 s02 77.85 86.09 s03 86.08 95.58 s01s 79.32 86.52 s02s 85.73 94.43 s03s 90.23 99.82 t m. madqour et al, frattura ed integrità strutturale, 59 (2022) 62-77; doi: 10.3221/igf-esis.59.05 75 [8] kamel, a. s., elwi, a. a. and cheng, r. j. (2004). experimental investigation on frp sheets bonded to concrete. emirates journal for engineering research, 9(2), pp. 71-76. [9] travassos, n. a. c., gomes, a. m. and universidade técnica de lisboa. (2005). caracterização do comportamento da ligação cfrp-betão. [10] hashemi, s. and al-mahaidi, r. (2010). investigation of bond strength and flexural behaviour of frp-strengthened reinforced concrete beams using cement-based adhesives. australian journal of structural engineering, 11(2), pp. 129139. [11] mostafa, a. a. and razaqpur, a. g. (2017). finite element model for predicting post delamination behaviour in frpretrofitted beams in flexure. construction and building materials, 131, pp. 195-204. [12] lusis, v., krasnikovs, a., kononova, o., lapsa, v. a., stonys, r., macanovskis, a. and lukasenoks, a. (2017). effect of short fibers orientation on mechanical properties of composite material–fiber reinforced concrete. journal of civil engineering and management, 23(8), pp. 1091-1099. [13] abid, s. r. and al-lami, k. (2018). critical review of strength and durability of concrete beams externally bonded with frp. cogent engineering, 5(1), 1525015. [14] bennegadi, m. l., sereir, z. and amziane, s. (2013). 3d nonlinear finite element model for the volume optimization of a rc beam externally reinforced with a hfrp plate. construction and building materials, 38, pp. 1152-1160. [15] el-ghandour, a. a. (2011). experimental and analytical investigation of cfrp flexural and shear strengthening efficiencies of rc beams. construction and building materials, 25(3), pp. 1419-1429. [16] kara, i. f. and ashour, a. f. (2012). flexural performance of frp reinforced concrete beams. composite structures, 94(5), pp. 1616-1625. [17] narmashiri, k., sulong, n. r. and jumaat, m. z. (2012). failure analysis and structural behaviour of cfrp strengthened steel i-beams. construction and building materials, 30, pp. 1-9. [18] kermiche, s. and redjel, b. (2012). analyse expérimentale et analytique du comportement en flexion des poutres en béton armé préfissurées renforcées par un matériau composite en toile de fibres de carbone (tfc). synthèse: revue des sciences et de la technologie, 25, pp. 41-58. [19] osman, b. h., wu, e., ji, b. and abdulhameed, s. s. (2018). effect of reinforcement ratios on shear behavior of concrete beams strengthened with cfrp sheets. hbrc journal, 14(1), pp. 29-36. [20] madqour, m. and hassan, h. (2021). experimental and analytical investigations of reinforced concrete beams strengthened by different cfrp sheet schemes. frattura ed integrità strutturale, 15(56), pp. 123-136. [21] ansys. a finite element computer software and user manual for nonlinear structural analysis. canonsburg, pa.: ansys 2007; inc; (2007). [22] aiello, m. a., ascione, l., baratta, a., bastianini, f., battista, u., benedetti, a. and zampa, a. (2014). guide for the design and construction of externally bonded frp systems for strengthening existing structures. [23] teng, j. g., smith, s. t., yao, j. and chen, j. f. (2003). intermediate crack-induced debonding in rc beams and slabs. construction and building materials, 17(6-7), pp. 447-462. [24] hawileh, r. a., naser, m. z. and abdalla, j. a. (2013). finite element simulation of reinforced concrete beams externally strengthened with short-length cfrp plates. composites part b: engineering, 45(1), pp. 1722-1730. [25] version, a. r. (2009). 12.1. 0, a finite element computer software and user manual for nonlinear structural analysis, ansys inc. canonsburg, pa. [26] f. bouziadi, boulekbache, b., haddi, a., djelal, c., hamrat, m. j. c. and b. materials, (2018). numerical analysis of shrinkage of steel fiber reinforced high-strength concrete subjected to thermal loading, construction and building materials, 181, pp. 381-393. [27] bouziadi, f., boulekbache, b., haddi, a., hamrat, m. and djelal, c. (2020). finite element modeling of creep behavior of frp-externally strengthened reinforced concrete beams. engineering structures, 204, 109908. [28] popovics, s. (1970, march). a review of stress-strain relationships for concrete. in journal proceedings, 67(3), pp. 243248). [29] thorenfeldt, e. (1987). mechanical properties of high-strength concrete and applications in design. in symposium proceedings, utilization of high-strength concrete, norway. [30] el-tawil, s., ogunc, c., okeil, a. and shahawy, m. (2001). static and fatigue analyses of rc beams strengthened with cfrp laminates. journal of composites for construction, 5(4), pp. 258-267. m. madqour et al, frattura ed integrità strutturale, 59 (2022) 62-77; doi: 10.3221/igf-esis.59.05 76 [31] aci committee, (2005), building code requirements for structural concrete (aci 318-05) and commentary (aci 318r-05), american concrete institute. [32] wenwei, w. and guo, l. (2006). experimental study and analysis of rc beams strengthened with cfrp laminates under sustaining load. international journal of solids and structures, 43(6), pp. 1372-1387. [33] chellapandian, m., prakash, s. s. and sharma, a. (2019). experimental and finite element studies on the flexural behavior of reinforced concrete elements strengthened with hybrid frp technique. composite structures, 208, pp. 466478. [34] gangarao, h. v. and vijay, p. v. (1998). bending behavior of concrete beams wrapped with carbon fabric. journal of structural engineering, 124(1), pp. 3-10. nomenclature a depth of equivalent rectangular stress block afrp = n tf wf, area of frp external reinforcement as area of non-prestressed steel reinforcement b width of rectangular cross-section c distance from extreme compression fiber to the neutral axis d the effective depth of the beam ec modulus of elasticity of concrete efrp or ef tensile modulus of elasticity of frp es and ec modulus of elasticity of steel and concrete fc the compressive strength of the concrete ffe effective stress in frp; stress level attained at section failure fy yield strength of non-prestressed steel reinforcement cf ˋ compressive strength of concrete h overall depth of the beam icr moment of inertia of cracked section transformed to concrete km bond-reduction coefficient for flexure k the ratio of the depth of the neutral axis to reinforcement depth measured on the same side of the neutral axis mdl bending moment due to dead-load mn nominal bending moment n number of frp layers tf nominal thickness of one ply of frp reinforcement tfrp tensile force in frp ts tensile force in steel β1 the ratio of the depth of equivalent rectangular stress block to the depth of neutral axis εbi strain level in the concrete substrate at the time of frp installation 𝜀𝑐 concrete compressive strain εci initial strain in extreme compression fiber εcl additional strain in extreme compression fiber after strengthening and loading εcu maximum usable compressive strain in concrete ε0 the corresponding compressive strain at the compressive strength εfd debonding strain of externally bonded frp reinforcement, (mm/mm) εfe effective strain level in frp reinforcement; strain level attained at section failure εfrp strain level in frp reinforcement εfrpu strain in frp at the point of incipient rupture εfrpl additional strain in extreme tension fiber after strengthening and loading m. madqour et al, frattura ed integrità strutturale, 59 (2022) 62-77; doi: 10.3221/igf-esis.59.05 77 εfu ultimate rupture strain in frp reinforcement εs strain level in steel reinforcement εsy strain corresponding to the yield strength of steel reinforcement εsi initial strain in steel reinforcement εsl additional strain in steel reinforcement after strengthening and loading  cu the maximum compressive strength  f frp reinforcement ratio s   the ratio of non-prestressed reinforcement  f additional frp strength-reduction factor microsoft word numero_34_art_68 m. scafidi et alii, frattura ed integrità strutturale, 34 (2015) 622-629; doi: 10.3221/igf-esis.34.68 622 2d size, position and shape definition of defects by b-scan image analysis michele scafidi, donatella cerniglia, tommaso ingrassia università degli studi di palermo, dipartimento di ingegneria chimica, gestionale, informatica, meccanica – 90128 palermo, italy tommaso.ingrassia@unipa.it abstract. the non-destructive evaluation of defects by automatic procedures is of great importance for structural components. thanks to the developments of the non-contact ultrasonic techniques, the automation of the inspections is gaining a progressively important role. in this work, an automatic inspection technique for the evaluation of defects by the analysis of b-scan images obtained by a laser ultrasonic system is presented. the data are extracted directly from a b-scan map obtained for a panel with internal defects, and are used to build an image of the cross section of the panel. the proposed automatic procedure allows the definition of size, position and shape of defects in panels of known thickness. keywords. nde; laser ut system; b-scan image analysis; defect size definition; 2d defect shape definition. introduction he laser ultrasonic testing (ut) systems are becoming more common among the non-destructive evaluation (nde) techniques thanks to the possibility to carry out non-contact inspections [1-3]. one of the most important advantage of this technique is related to the use of high frequency ultrasonic waves, that allow the detection of defects with very fine spatial resolution. moreover, laser ut systems can be effectively used for remote inspections with no contact conditions influence and, if proper delivery optics are used to guide the laser beam, they can operate also in hostile environments. since the propagation mechanism of the ultrasonic waves is not influenced by the angle of incidence of the laser beam on the material surface, this kind of system can be used to inspect parts where access is limited. the laser beam, in fact, can be directed to the surface with high angles off axis. the presence of defects, corners and curved surfaces, modifies the waves propagation, causing reflection and mode conversion. the waves resulting from different sources (i.e. reflected or converted waves) can interfere each other, generating very complex patterns. for this reason, the inspection of complex structures by means of laser ut systems can become extremely hard. nevertheless, by knowing the analytical models of the waves propagation in solid structures, the experimental layout can be designed to optimize the results post-processing analysis. with this purpose, laser ut systems can be used to automate the scanning procedure and to make a rapid acquisition of the ultrasonic data by creating b-scan maps in real time [1]. the analysis of the b-scan image allows determining in an automated way the presence of defects in the tested component as well as the characteristics of the defects. a technique of particular importance in the analysis of defects in plates is the time of flight diffraction (tofd) [4-9]. this technique allows to determine the presence of cracks in the material and to determine the position and length of the crack even in t m. scafidi et alii, frattura ed integrità strutturale, 34 (2015) 622-629; doi: 10.3221/igf-esis.34.68 623 components of complex geometry [10-13]. to facilitate the automation of the analysis, tofd b-scan maps with selected wave types can be obtained by optimizing the layout of the laser system. the aim of this work is the automatic definition of size, shape and position of the defects in plates of known thickness. a virtual image of the section of the analyzed component is created by an algorithm that locates the areas with defects. a second algorithm allows determining also the boundary shape of the defect. ultrasonic system and laser layout description he laser system used in this work, shown in fig. 1, consists of: an ir nd:yag pulsed laser for the ultrasonic wave generation; a cw laser interferometer as receiver system for the out-of-plane displacements measurement; a motorized linear micro-slide; a system for data acquisition and processing. figure 1: laser system: (a) ir nd:yag pulsed laser for ultrasonic wave generation; (b) cw laser interferometer receiver; (c) motorized linear micro-slide; (d) sample. in the application here considered, the wave generation and detection are made on the same side of a panel of thickness t at a defined distance d (see fig. 2). the laser source generates longitudinal, shear and surface waves in the ablation regime whose angular dependence is reported in ref. [4]. figure 2: cross-section of a plate with indication of laser source, laser receiver and wave paths. t m. scafidi et alii, frattura ed integrità strutturale, 34 (2015) 622-629; doi: 10.3221/igf-esis.34.68 624 as shown in fig. 2, the surface skimming longitudinal wave, l-wave, travels just below the surface of the plate; the longitudinal back-wall wave, ll-wave, reflected by the opposite plate surface in accordance with the snell’s law, travels with an orientation  that depends on the distance d. being the longitudinal wave velocity vl about twice than the shear and surface wave velocities [14] and considering that the l-wave path (length d) is the shortest between the generation point and the receiver point, the l-wave is the first that reaches the receiver. if the ll-wave travels along a path with length dll=2d, the surface wave, the shear wave and the ll-wave reach the receiver at about the same time. this condition occurs when the triangle of the wave path is equilateral (θ=30°) but, in this case, it is impossible to identify the three different waves apart. choosing a propagation angle θ=45°, instead, the distance between the two lasers is d=2t and the total length of the ll-wave path is dll=2t√2=2.83t1.4d. this choice ensures that the ll-wave can be entirely acquired, cutting off the surface wave and the shear wave from the time window. furthermore, the intensity of the out-of-plane component of the ll-wave for θ=45° is about 70% of the ll-wave intensity. in this way, in line with the purposes of this research, the distance d and the time-window have been then optimized to visualize only the l-wave and the ll-wave. in fig. 3, a signal acquired by the receiver, in a t=5 mm aluminum plate without defect and a source/receiver distance of d=10 mm, is shown. figure 3: typical signal of the longitudinal waves without defect. in fig. 4, the section of the analyzed plate with the laser layout scheme is shown. figure 4: section of the analyzed aluminum plate and laser layout (measures in mm). in the plate two circular holes, d1 and d2, were drilled. their diameters are, respectively, 2.10 mm and 2.09 mm. the distances of the defects centers from the scanning surface (y-depth) are, respectively, y1=1.54 mm and y2=2.45 mm. the distance, l, between the centers of the two defects is 37.26 mm. m. scafidi et alii, frattura ed integrità strutturale, 34 (2015) 622-629; doi: 10.3221/igf-esis.34.68 625 to analyze the plate, a b-scan map has been built by regularly shifting, along a 100 mm straight line, the laser system and storing the signal for each step. fig. 5 shows the b-scan map obtained with the panel of fig. 4. the laser source position defines the abscissa xg of the b-scan map. two perturbations can be noted due to the presence of the defects. figure 5: b-scan map obtained for the plate of fig. 4 with indication of the l-wave negative and ll-wave positive peaks. the b-scan map is shown in false-colours to highlight the peak-to-peak amplitude of the signals. similarly to the case of the waves diffracted by the crack tip [6, 7, 13], the perturbation shows a parabolic-like pattern in the b-scan. in general, the defect affects the shape of the perturbation then, analyzing this last, the defect characteristics can be determined. unfortunately, if the presence of the perturbations on the b-scan map can clearly make in evidence the presence of defects, the definition of their size, position and shape requires a more complex analysis. in the next sections, the proposed procedures for defining the size, the position and the shape of the defects are described. b-scan analysis: size and position definition he ll-wave (red line in fig. 5) is interrupted twice in correspondence of the defect d1. these interruptions are caused by the interposition of the defect along the ll-wave path, as shown in the fig. 6. from the b-scan, it would seem that the defect interrupts also the l-wave. actually, this effect is caused by the superposition of the longitudinal wave, l-wave, and the reflected wave due to the defect, lr-wave. in this case, in fact, due to the little depth (y) of the defect d1, the ll-wave and the lr-wave have similar path lengths. a different case, shown in fig. 7, is represented by the defect d2 that has a greater depth. the ll-wave is interrupted only one time but for a bigger length. for the defect d1, the length of the interruptions depends on the defect size while for the defect d2, the length of the interruption depends also on the depth. as general case, measuring the length of the interruptions of the ll-wave directly on the b-scan map, information about the dimension of the defect can be obtained, while information on its depth can be hardly extracted. for a better definition of the size and position of the defect, the draft of an image of the section, considering the information extracted by the b-scan, is here proposed. this section image consists in drawing, for each scan step, a broken line describing the path of the ll-wave. these path-lines are drawn in a gray colour whose intensity is proportional to the amplitude of the corresponding acquired signal. each pixel of the section image is obtained as intersection of the path-lines of two different steps. the biggest intensity of the (two) intersecting lines is assigned to the pixel. in this way, a bright pixel belongs to one not-interrupted path whereas a dark colored pixel is part of two t m. scafidi et alii, frattura ed integrità strutturale, 34 (2015) 622-629; doi: 10.3221/igf-esis.34.68 626 interrupted paths. therefore, defects cannot be in the bright zones of the section image, while they could be in the dark areas. in fig. 8, the section image built with the data extracted from the b-scan of fig. 5 is shown. figure 6: interruption of the ll-wave due to the defect d1 and corresponding effects on the b-scan map. figure 7: interruption of the ll-wave due to the defect d2 and corresponding effects on the b-scan map. figure 8: section image built from the data of the b-scan of fig. 5. in fig. 8, some “shadow” and unanalyzed zones are highlighted. in these last areas, no signal was acquired because the extreme parts of the plate have not been scanned. the shadow zones, instead, correspond to low-intensity signals. in general, in these areas the presence of defects cannot be excluded observing only the section image built with the described procedure. the shadow zones with no defects could be removed by performing the inspection also from the other side of the panel. for the purposes of this research, the shadow zones and the unanalyzed zones have not been considered. to extract the information about the size and the position of the defect, a binarized section image has been built from the section image of fig. 8 by a threshold procedure. to optimize the results, proper threshold values have been chosen depending on the defect characteristics. in particular, at this stage of the research, they have been defined knowing the value of the defect diameter. the best threshold values are, respectively, 40% and 35 % of the maximum intensity for the defect d1 and d2. the binarized section images are shown in fig. 9. m. scafidi et alii, frattura ed integrità strutturale, 34 (2015) 622-629; doi: 10.3221/igf-esis.34.68 627 figure 9: binarized section images obtained with a threshold value of 40% (a) for d1 and 35% (b) for d2. the analysis of the section images allows to determine the positions of the defects by identifying the center of gravity (cg) of the dark zones. the procedure consists in calculating the coordinates of the cg by the following equations: ig x x n   (1) ig y y n   (2) where xi and yi are the coordinates of the generic dark pixel, while n is the total number of pixels in the dark zones. from the analysis of the section image, the x coordinates of the center of the defects are x1=40.2 mm and x2=77.7 mm, respectively for d1 and d2. consequently, the calculated distance between the two defects is l=37.5 mm. this value is in a very good agreement with the real one, equal to 37.26 mm, and the error is about 0.6%. the y positions (depth) of the center of the defects result y1=1.62 mm for d1 and y2=2.32 mm for d2. the errors on the depth are, respectively, about +5.2% and -5.3%. b-scan analysis: defect shape definition he shape of the defects has been determined by analyzing the b-scan map perturbations due to the defects (fig. 5). because of the regular shape of the drilled holes, the perturbation is not caused by the diffraction [4-9] but is due to the reflection of the longitudinal waves at the smoothed boundary of the hole. as shown in fig. 10, for each scan step, a longitudinal wave (lr-wave), starting from the generation point, hits the defect and is reflected to the receiver point. figure 10: path of a generic lr-wave (left) and corresponding point in the b-scan image (right). at each step, the laser receiver acquires the signal of the lr-wave reflected by the closer point of the defect. in this way, the bottom boundary of the perturbation on the b-scan map is defined. extracting the coordinates xg of the perturbation boundary points from the b-scan, the time of arrival tl(xg) of the lr-waves can be determined (fig. 10). known the wave velocity vl of the longitudinal wave, the length of the path ll(xg) covered by the lr-wave can be determined by the following equation:    l g l l gl x v t x  (3) as seen in fig.10, the path of the lr-wave is composed of two parts: the first one goes from the generation point to the reflection point, the second one from this last point to the receiver. since the initial direction of the lr-wave and the t m. scafidi et alii, frattura ed integrità strutturale, 34 (2015) 622-629; doi: 10.3221/igf-esis.34.68 628 defect shape and position are unknown, the lengths of the two parts of the path cannot be determined separately. under these conditions, all the points for which the sum of the distance from two fixed point (generation and receiver point) is ll(xg) could be reflection points. in particular, all the points on the semi-ellipse with generation and receiver points as foci and with the sum of the distances from them equal to ll(xg) could be reflection points. since the generation and receiver points are on the x-axis (fig. 4), the generic equation of the ellipse having the possible reflection points is:  2 2 2 2 1c x x y a b    (4) where a and b are, respectively, the major and minor semi-axes of the ellipse, whose values, for the analyzed case, are:   2 l gl xa  (5)   2 2 2 2 l gl x db            (6) and xc is the abscissa of the center of the ellipse (central point between the two foci at d distance), that is linked to the generation point by the following relationship: 2 c g d x x  (7) finally, for each scan step, knowing xg and calculating ll(xg), the ellipse passing through the reflecting point of the defect can be drawn. the envelope of all the ellipses determines the shape of the defect. fig. 11 shows, for the defect d1, the envelope of the ellipses superimposed to the circular profile of the drilled hole. a very good agreement is found in the matching of the experimental and real data. figure 11: envelope of the ellipses (blue lines) drawn for the defect d1 and defect contour (black circle). the envelope of the ellipses shown in fig. 8 determines only one half of the defect profile. the other part of the profile can be determined by applying the same algorithm to the experimental data coming from an inspection performed in the opposite side of the panel. conclusions a new procedure of analysis of the b-scan image obtained by laser ut for nde has been presented in this paper. it has been shown that, using an appropriate lay-out optimized to detect the longitudinal wave reflected by the opposite side of the panel, it is possible to define the main characteristics of the defects. in particular, the size, the position and the shape of the defect can be determined. the main dimensions and the position of the defect can be defined analyzing some section images built from the b-scan maps. these section images, if suitably filtered, allow to calculate the coordinates of the defect center. m. scafidi et alii, frattura ed integrità strutturale, 34 (2015) 622-629; doi: 10.3221/igf-esis.34.68 629 the analysis of the perturbation in the b-scan, due to the presence of the defects, allows determining the shape of the defect. the definition of the shape of the defect is achieved by means of the envelope of the ellipses drawn on the image section, by measuring the time of arrival of the wave reflected by the defect from the b-scan. although the research requires a calibration procedure and the automation of some parts of the analysis, the results obtained are in good agreement with the characteristics of the defects created into the aluminum panel used as case study. the next steps of the research are the reduction of the effects of the shadow zones, the improvement and the automation of the procedures to extract position, size and shape of the defects. references [1] cerniglia, d., scafidi, m., pantano, a., rudlin, j., inspection of additive-manufactured layered components, ultrasonics, 62 (2015) 292-298. [2] rudlin, j., cerniglia, d., scafidi, m., inspection of laser powder deposited layers, proceedings of 52nd annual conference of the british institute of non-destructive testing (2013), bindt 2013 – telford (uk), (2013). [3] cerniglia, d., djordjevic, b.b., ultrasonic detection by photo-emf sensor and by wideband air-coupled transducer, research in nondestructive evaluation, 15 (2004) 111-117. [4] scruby, c.b., drain, l., laser ultrasonics: techniques and applications, adam hilger, bristol, (1990). [5] sinclair, a.n., fortin, j., shakibi, b., honarvar, f., jastrzebski, m., moles, m.d.c., enhancement of ultrasonic images for sizing of defects by time-of-flight diffraction, ndt&e international, 43 (2010) 258-264. [6] petcher, p.a., dixon, s., a modified hough transform for removal of direct and reflected surface waves from bscans, ndt&e international, 44 (2011) 139-144. [7] petcher, p.a., dixon, s., parabola detection using matched filtering for ultrasound b-scans, ultrasonics, 52 (2012) 138-144. [8] merazi-meksen, t., boudraa, m., boudraa, b., mathematical morphology for tofd image analysis and automatic crack detection, ultrasonics, 54 (2014) 1642-1648. [9] silk, m. g., the transfer of ultrasonic energy in the diffraction technique for crack sizing. ultrasonics, 17 (1979) 113– 121. [10] nath, s.k., balasubramaniam, k., krishnamurthy, c.v., narayana, b.h., reliability assessment of manual ultrasonic time of flight diffraction (tofd) inspection for complex geometry components, ndt&e international 43 (2010) 152-162. [11] nalbone, l., adelfio, r., d’arienzo, m., ingrassia, t., nigrelli, v., zabbara, f., paladini, p., campi, f., pellegrini, a., porcellini, g., optimal positioning of the humeral component in the reverse shoulder prosthesis, musculoskeletal surgery, 98(2) (2014) 135-142. [12] nath, s. k., effect of variation in signal amplitude and transit time on reliability analysis of ultrasonic time of flight diffraction characterization of vertical and inclined cracks, ultrasonics 54 (2014) 938-952. [13] ferrand, a., darmon, m., chatillon, s., deschamps, m., modeling of ray paths of head waves on irregular interfaces in tofd inspection for nde, ultrasonics 54 (2014) 1851-1860. [14] krautkramer, j., krautkramer, h., ultrasonic testing of materials, springer-verlag berlin heidelberg gmbh, new york, (1977). microsoft word numero_50_art_22_2545 c. c. silva et alii, frattura ed integrità strutturale, 50 (2019) 264-275; doi: 10.3221/igf-esis.50.22 264 focused on structural integrity and safety: experimental and numerical perspectives web rotational stiffness of continuous steel-concrete composite castellated beams carla cristiane silva, rodrigo barreto caldas, ricardo hallal fakury, hermes carvalho, joão victor fragoso dias department of structural engineering, federal university of minas gerais, av. pres. antônio carlos, 6627, pampulha, belo horizonte, minas gerais 31270-901, brazil carlacristianesilva@hotmail.com abstract. continuous composite beams can present a global instability known as lateral distortional buckling (ldb). the design code en 1994-1-1:2004 provides a procedure for the verification of this ultimate limit state, in which the resistant bending moment is calculated considering the behavior of the inverted “u-frame” mechanism. an essential parameter for the determination of this moment is the rotational stiffness of the composite beam, which depends on the web stiffness. the en 1994-1-1:2004 procedure is restricted to composite beams with solid-web steel sections without openings. this paper presents several numerical analyses of the web rotational stiffness of castellated sections such as anglosaxon, litzka and peiner typologies. finally, based on numerical results obtained, three different adjustment coefficients were proposed for the anglo-saxon, litzka and peiner typologies for the calculation of the web rotational stiffness of the castellated profile. the proposed coefficients provided an excellent adjustment between the results obtained numerically and those obtained from the classical formulation of the plate theory, with an average deviation of 2%, indicating low dispersion and homogeneous results. keywords. rotational stiffness; castellated composite beam; lateral distortional buckling; elastic critical moment. citation: silva, c. c., caldas, r. b., fakury, r. h., carvalho, h., dias, j., v., f., web rotational stiffness of continuous steelconcrete composite castellated beams, frattura ed integrità strutturale, 50 (2019) 264-275. received: 16.06.2019 accepted: 16.08.2019 published: 01.10.2019 copyright: © 2019 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. introduction n continuous and semi-continuous composite beams, in the regions of hogging moment, the bottom flange is compressed, which makes it susceptible to buckling in relation to its major axis of inertia (axis located in the plane of flexion), since the buckling in relation to the its minor axis of inertia is restrained by the web. if the web has insufficient stiffness to prevent lateral flexion, the compressed flange shows a lateral displacement, δ, accompanied by a twist, θ, (fig. 1), characterizing an ultimate limit state called lateral distortional buckling (ldb). i http://www.gruppofrattura.it/va/50/2545.mp4 c. c. silva et alii, frattura ed integrità strutturale, 50 (2019) 264-275; doi: 10.3221/igf-esis.50.22 265 figure 1: lateral distortional buckling (oliveira [1]). continuous and semi-continuous composite beams can be used with castellated sections, which are structural elements with multiple hexagonal openings of the same shape, regularly spaced in the web. the main reasons for the use of castellated beams in steel structures are increase of resistant capacity and flexural stiffness around the axis of greater inertia, provided by the increase of the total height of the cross section; elements lighter than a profile without openings of the same height, thus reducing the total weight; larger free spans, reducing the number of columns and foundations, leading to faster and more economical assembly; possibility of passing ducts or pipes through the openings and aesthetic gain, since the openings incorporate to the environment a modern appearance. adding the potential of castellated steel beams for use in composite floors, the effect on material economy is even more promising once the steel-concrete composite beams are a very effective floor system due to the considerable increase in floor stiffness, steel weight reduction and the lower height of the beam-slab section (queiroz et al. [2]). the brazilian standard abnt nbr 8800:2008 [3] provides a procedure for the determination of the lateral distortional buckling-moment resistance capacity of the continuous and semi-continuous steel-concrete composite beams, similar to the en 1994-1-1:2004 [4] european standard. this procedure depends on the determination of the elastic critical moment, calculated considering the behavior of the inverted “u-frame” mechanism. a fundamental parameter for this determination is the rotational stiffness of the composite beam which, in turn, depends on the web stiffness. it should be noted that these code procedures apply only to composite beams without web openings. in the literature there are several studies on lateral distortional buckling (ldb) of continuous composite beams without web openings, among them roik et al. [5], chen [6], dekker et al. [7], hanswille et al. [8], calenzani [9], calenzani [10], chen and wang [11], ye and chen [12], wang [13], guo et al. [14], zhou et al. [15], zhou et al. [16], oliveira [17], amaral [18] dietrich [19], dias [20] and oliveira [1]. the number of researches of castellated composite beams in regions of hogging moments is still limited. salah and gizejowski [21, 22, 23] performed several studies with alveolar beams (cellular and castellated openings) to analyze the influence of beam slenderness (length to height ratio), distortional buckling modes, profile height and steel type. piassi et al. [24] developed an analytical model in order to obtain the expression of the rotational stiffness of composite cellular beams and the results were compared with numerical models developed in the ansys 15.0 [25] program. however, there are no studies on the rotational stiffness of the web castellated profile. therefore, this paper presents a numerical study, validated with results of the literature, with the aim of proposing an equation for the calculation of the bending stiffness of the web of steel-concrete composite beams, which can be used to determine the rotational stiffness of the inverted “u-frame” mechanism and obtain the elastic critical moment of lateral distortional buckling. literature review inverted “u-frame” mechanism he european standard en 1994-1-1:2004 [4] and the brazilian standard abnt nbr 8800: 2008 [3] suggest the use of the inverted “u-frame” mechanism to determine the elastic critical moment of ldb, in which the concrete slab is considered to be over two or more parallel steel beams, as shown in fig. 2. t c. c. silva et alii, frattura ed integrità strutturale, 50 (2019) 264-275; doi: 10.3221/igf-esis.50.22 266 figure 2: inverted “u-frame” mechanism with two beams (oliveira [1]). according to fan [26], the inverted "u-frame" mechanism is more adequate to represent the behavior to ldb compared to the model of a composite beam composed of a single steel profile superimposed on a concrete slab ("t" cross section) because it represents better the lateral displacement and torsional constraints imposed on the steel profile by the concrete slab and the shear connection. the "u-frame" mechanism also has a direct relation with the usual situations, once most constructions use floor systems composed of parallel steel beams equally spaced under the concrete slab. in the literature there are two types of inverted "u" mechanism, the continuous one, which has only rigid internal supports, and the discrete one, which has regularly spaced transversal stiffeners throughout the hogging moment region, which contributes to the restriction of ldb. the en 1994-1-1:2004 [4] and abnt nbr 8800:2008 [3] standards only present formulations considering the continuous "u-frame" mechanism for the verification of composite beams. rotational stiffness a fundamental parameter for the calculation of the elastic critical moment (mcr) is the rotational stiffness of the composite beam, ks, also known as the rotational stiffness of the inverted "u-frame" mechanism. this stiffness, considered simplified by a rotational spring located in the top flange of a steel profile, allows to reproduce the influence of the "u-frame" mechanism at the bending moment resistant to the ldb, considering the bending of the slab, the distortion of the web and the deformation of the shear connection (fig. 3). according to johnson [27], this stiffness is obtained by unit of length, relating the moment at point a, located in the geometric center of the top flange, caused by forces, f, applied to the bottom flanges of the parallel beams of the "u-frame" mechanism, with the corresponding rotation, θ, of these flanges. this rotation is obtained by the ratio between the lateral displacement of the bottom flange (δ) and the distance between the geometric centers of the flanges of the steel profile (ho). the bending moment at point a is the product between force f and distance ho. taking one of the beams, the rotation at point a will be equal to δ/ho, and since the moment in a is given by the product f.ho, the following general expression for the rotational stiffness is obtained: / o s o f h k h  (1) to determine precisely eqn. (1), it is necessary to carry out experimental or numerical analyses. alternatively, the rotational stiffness of the composite beam (ks) can be obtained as a result of the series association of the cracked slab bending stiffness, k1, the steel profile web rotational stiffness, k2, and shear connection bending stiffness, k3, as follows: 1 1 2 3 1 1 1 sk k k k          (2) for the calculation of the slab bending stiffness, k1, the slab is considered as a beam fixed on the profiles. this stiffness is characterized by the bending moments that arise when applying unitary rotations on the fixed ends (fig. 4) and, generally, can be obtained as: c. c. silva et alii, frattura ed integrità strutturale, 50 (2019) 264-275; doi: 10.3221/igf-esis.50.22 267   2 1 ei k a   (3) where a is the distance between the parallel beams of the inverted "u-frame" mechanism, α is a coefficient depending on the position of the beam being considered. if the beam is at the end of the slab, α = 2, and for the internal beam, α = 3 (for internal beams with four or more similar beams, one can adopt α = 4). the term (ei)2 represents the bending stiffness of the homogenized composite section of the slab, disregarding the tensile concrete, per unit length of the beam, taken as the lowest value between the stiffness in the middle of the span and in the internal support. figure 3. rotational stiffness of a composite beam (oliveira [1]). figure 4. cracked slab bending stiffness (calenzani [9]). the steel profile web rotational stiffness is obtained by considering the web as a cantilever plate in the geometric center of the top flange and free in the geometric center of the bottom flange where a force f acts, according to fig. 5. the relation between the force f and the displacement δ2 is given by the expression: 3 2 3 o f d h  (4) c. c. silva et alii, frattura ed integrità strutturale, 50 (2019) 264-275; doi: 10.3221/igf-esis.50.22 268 where d is the plate bending stiffness per unit length. according to eqn. (1) and rearrangement of eqn. (4), we obtain: 2 3 o d k h  (5) figure 5. web rotational stiffness (calenzani [9]). the plate bending stiffness per unit length can be calculated, according to timoshenko and gere [28], as: 3 212(1 ) wetd    (6) where e and ν are, respectively, the young's modulus and the poisson’s ratio of the structural steel and tw is the web thickness of the steel profile. substituting eqn. (6) for eqn. (5), the value of k2 per unit length can be determined by:   3 2 24 1 w o et k h    (7) the web rotational stiffness, k2, determined for the plate without openings, described in eqn. (7), should be adapted in the case of alveolar beams for the consideration of the openings, and being this adaptation the proposal of this article. the shear connection bending stiffness (k3) represents the moment in the geometric center of the top flange when a unitary rotation is imposed for the connection between the steel profile and the reinforced concrete slab (fig. 6). the analytical determination of this stiffness is very difficult. according to johnson and molenstra [29] apud calenzani [9], it tends to have a very high value when the i section has no openings, influencing less than 1% of the rotational stiffness ks for the case of shear connection with two connectors in the cross section and less than 5% for one shear connector. for this reason, the stiffness k3 is usually disregarded in the calculations. in the case of castellated beam, in which the presence of openings reduces the web stiffness, the influence of the shear connection becomes even less relevant. the european standard en 1994-1-1:2004 [4] does not provide an equation for the calculation of the elastic critical moment of ldb, but suggests the use of the inverted "u-frame" mechanism. the elastic critical moment of ldb is obtained, according to brazilian standard abnt nbr 8800:2008 [3], by eqn. (8) (which was also presented in the previous version of the european standard, env 1994-1-1:1992 [29]), initially proposed in the roik et al. [5] studies: 2 2 dist g cr s afy c l m gj k ei l     (8) in which g is the transverse elasticity modulus, e is the young's modulus of the structural steel, j is the st. venant torsion constant of the profile, iafy is the second moment of area of the compressed flange in relation to the y axis (vertical axis), αg c. c. silva et alii, frattura ed integrità strutturale, 50 (2019) 264-275; doi: 10.3221/igf-esis.50.22 269 is a related factor to the cross-section geometry, ks is the rotational stiffness of the composite beam and cdist is a coefficient that depends on the distribution of bending moments in the length l of the analyzed composite beam span. figure 6. shear connection bending stiffness (calenzani [9]). dias [20] proposed a new procedure for the determination of the elastic critical moment of composite beams with web profile without openings subjected to uniform hogging moment according to eq. (10):   2 2, 2 0 g w d b cr k ec m gj n h nl                    (9) where 4 , b w d kl ec   (10) where h0 is the distance between the geometric centres of the steel profile flanges, g the transverse elasticity modulus, e the young's modulus of the structural steel, j the st. venant torsion constant of the steel profile, l the beam length, cw,d the warping constant of the steel profile, n the number of half-waves of the buckling mode, k the spring stiffness in the centre of the upper face of the top flange, ηb is a dimensionless parameter and kg takes into account effects caused by the presence of the slab in the model. the new procedure proposed by dias [20] presented excellent agreement with numerical values, with deviations below 10% in 97.29% of the analyzed models and mean error of 2.33%. results better than the formulations of roik et al. [5] and hanswille et al. [8], which did not lead to satisfactory results, presenting average errors of 12.41% and 16.51%, respectively. these last two works present several simplifications and can lead to results not as precise as those of dias [20]. oliveira [1] extended the equation of dias [20] for composite beams submitted to non-uniform hogging moment. numerical analysis numerical model he formulation of the rotational stiffness discussed in en 1994-1-1:2004 [4] covers only composite beams composed of steel profiles without openings. this stiffness depends substantially on the web rotational stiffness (k2), which can be determined by considering the web as a plate fixed in the geometric center of the top flange and free in the geometric center of the bottom flange (fig. 7). thus, a simplified numerical model of plate was developed to determine the web stiffness of the castellated profiles. the numerical model represents a plate of height (dg), thickness tw and length varying due to the number of openings, in the case of the castellated web (fig. 5). as described previously, by applying a horizontal force f in the geometric center t c. c. silva et alii, frattura ed integrità strutturale, 50 (2019) 264-275; doi: 10.3221/igf-esis.50.22 270 of the bottom flange, the web lateral displacement (δ2) can be determined through eqn. (1) and, from this, the web stiffness, k2, is calculated. three-dimensional models of finite elements were developed in the software ansys 17.0 [25]. shell elements, shell181, were used to represent the steel profile. figure 7. plate model. the young’s modulus of the steel, e, was considered equal to 200000 mpa and the poisson’s ratio, ν, equal to 0.3. in order to simulate the boundary conditions, the displacements and rotations in the three directions were prevented at the top of the web. at the bottom, the nodes displacements were coupled, resulting in a uniform displacement along the lower portion of the web across the model length, condition which normally occurs due to the presence of the bottom flange. the finite element mesh was generated freely by the program, resulting in an unstructured mesh, which does not represent influence due to the great simplicity of the type of analysis. a mesh study was performed, varying the size of the elements from large values to very small values (1.52h0 to 0.003h0, with more than 32 values). the mesh used was 0.152h0 once it presented results with good precision (the variation for smaller meshes is less than 0.1%) and did not present high computational time. validation of numerical model plates with solid-webs were modeled for the validation of the numerical model. the numerical web rotational stiffness without openings (k2,num,sol) was calculated according to eqn. (1), considering the applied force (f) equal to 1 kn and the maximum displacement of the plate (δ2) obtained from the numerical analysis. the analytical web rotational stiffness without openings (k2,an,sol) was calculated according to eqn. (7). the results of the numerical analysis were compared with the analytical results and it was observed that the maximum difference between the two results was less than 0.3% (tab. 1). therefore, it is considered that the numerical model is suitable for simulations of web stiffness. dg (mm) tw (mm) lbeam (m) δ2 (m) k2,num,sol (kn.m/m) k2,an,sol (kn.m/m) k2,num,sol/k2,an,sol 260 6.4 2.85 4.28e-04 55393.01 55398.14 1.000 300 5.0 1.99 1.98e-03 22893.71 22818.77 0.997 600 7.5 4.85 1.93e-03 38543.48 38633.24 0.998 900 10 11.17 1.19e-03 61113.43 61050.06 1.001 1200 15 14.89 6.25e-04 154755.51 154532.97 1.001 table 1: validation of numerical models. c. c. silva et alii, frattura ed integrità strutturale, 50 (2019) 264-275; doi: 10.3221/igf-esis.50.22 271 parametric study he plates evaluated in this study had anglo-saxon, peiner and litzka typologies (tab. 2 shows the geometric ratios for the castellated beam typology patterns and fig. 8 illustrates their parameters) with an expansion ratio equal to 1.5. this value is usual for the alveolar profile, used by several authors in their experimental and numerical works (zaarour and redwood [30]; bezerra [31]; vieira [32]). anglo-saxon litzka peiner p 1.08d 1.7322d 1.5d bw 0.25d 0.5774d 0.5d a0 0.83d 1.155d d b 0.29d bw/2 bw/2 table 2: geometric parameters for the beams. figure 8. definition of geometric parameters for the beams. the parametric study was performed considering four heights, dg, 300, 600, 900 and 1200 mm, covering large and small heights. in relation to the thickness of the castellated web, the web slenderness values (dg/tw) equal to 20, 40, 60 and 80 were analyzed, covering larger and smaller slenderness than usual slenderness values. the profiles were modeled with a number of openings, n, equal to 5, 7, 9, 11, 13, 15, 17, 19 and 21, in order to verify if the increase of the span would influence the stiffness. a total of 432 models were analyzed, with the combinations of properties presented in fig. 9. figure 9. models analyzed in the web rotational stiffness parametric study. dg typology n dg/tw 300 600 900 1200 anglo-saxon litza peiner 20 40 60 80 5 7 9 11 13 15 17 19 21 t c. c. silva et alii, frattura ed integrità strutturale, 50 (2019) 264-275; doi: 10.3221/igf-esis.50.22 272 results and discussion ig. 10 shows the relationship between the results of the numerical analyses of plates with hexagonal openings and the values obtained according to the analytical formulations of web plates without openings (considering the same dimensions) for anglo-saxon, litzka and peiner typologies. the numeric stiffness of the castellated web, k2,num,cast, was calculated according to eqn. (1) and the analytic stiffness of the web without openings, k2,an,sol, calculated by eqn. (7). a linear relationship between the results of k2,num,cast and k2,an,sol is shown for the three typology patterns studied, with the mean of the ratio k2,num,cast/k2,an,sol equal 0.53, 0.54 and 0.55 for the anglo-saxon, litzka and peiner typologies, respectively. figure 10. comparison between the numerical and analytical results of the web stiffness of the anglo-saxon, litzka and peiner typologies. adopting an adjustment coefficient (β), the eqn. (7), used by en 1994-1-1:2004 [4] and abnt nbr 8800:2008 [3], can be adapted for the determination of the rotational stiffness of castellated webs, considering the total height of the castellated beam, dg, instead of the height of web without openings, h0, as below:   3 2 24 1 w g e t k d     (11) in which β is: 0.53 0.54 0.55        anglo-saxon liztka peiner (12) a dispersion analysis of the results was performed as described in the european standard en 1990:2002 [33], and the coefficient of variation for the proposed formulation was equal to 0.22%, indicating low dispersion and homogeneous results. adopting, conservatively, a simplified adjustment coefficient, βsimplified, equal to 0.53 for eqn. (11), can determine only one equation for the stiffness of the castellated beams (anglo-saxon, peiner and litzka typologies), in which the error obtained is less than 4%. it was also observed that the number of openings had no great influence on the rotational stiffness of the castellated web. 0 50 100 150 200 250 0 50 100 150 200 250 k 2 ,n um ,ca st k2,an,sol anglo-saxon peiner litzka f c. c. silva et alii, frattura ed integrità strutturale, 50 (2019) 264-275; doi: 10.3221/igf-esis.50.22 273 conclusion he union between the potential of the continuous composite beams and the castellated steel profiles is promising for material savings. despite this, the construction of these beams runs into deficiency of studies about their behavior. in the case of continuous composite beams, the ultimate limit state of lateral distortional buckling deserves special attention. this ultimate limit state depends fundamentally on the web rotational stiffness. in castellated sections the openings in the web of the composite beams reduce the web rotational stiffness of these profiles when compared to those without openings, which makes these beams more susceptible to this buckling mode. according to the standards en 1994-11:2004 [4] and abnt nbr 8800:2008, in order to obtain the lateral distortional buckling resistant moment, it is necessary to calculate the elastic critical moment which depends on the geometric properties of the steel profile and the rotational stiffness of the composite beam. in this paper, three different adjustment coefficients (β) were proposed for the anglo-saxon, litzka and peiner typologies of castellated beams, 0.53, .054 and 0.55, respectively, for the calculation of the web rotational stiffness of the castellated sections, fundamental variable for obtaining the rotational stiffness of the composite beam and, consequently, the elastic critical moment of lateral distortional buckling. as the web rotational stiffness is reduced, the elastic critical moment will also be smaller and, consequently, the resistant moment. the coefficients were obtained (one for each of the opening patterns) from a parametric numerical study performed in the software ansys 17.0 [25]. the proposed coefficients provided an excellent adjustment between the results obtained numerically and those obtained from the classical formulation of the plate theory. the maximum deviation between the numerical results and the proposed methodology was 2%, considering different adjustment coefficients for each opening pattern. the adjustment coefficient equal to 0.53 (value obtained for the anglo-saxon typology) can be used in the proposed equation for composite beams with three typologies of openings (anglo saxon, liztka and peiner), resulting in a deviation maximum equal to 4% of the numerical results. acknowledgment he authors would like to acknowledge the support provided by the government agencies of brazil: capes, cnpq, fapemig and ifmg. notation a distance between the parallel beams of the inverted "u-frame" mechanism d0 height opening dg web height of the castellated section ho distance between the geometric centers of the flanges of the steel profile k spring stiffness kg coefficient that takes into account effects caused by the presence of the slab in the model ks rotational stiffness of the composite beam k1 cracked slab bending stiffness k2 web rotational stiffness k2,an,sol analytic stiffness of the web without openings k2,num,cast numeric stiffness of the castellated web k2,num,sol numerical web rotational stiffness without openings k3 shear strength stiffness n number of half-waves of the buckling mode cw,d warping constant d plate bending stiffness e young's modulus of the structural steel (ei)2 bending stiffness of the homogenized composite section of the slab f force g transverse elastic modulus of the steel iafy second moment of area of the compressed flange in relation to the y axis j st. venant torsion constant of the profile l beam span mcr elastic critical moment αg related factor to the cross-section geometry β adjustment coefficient βsimplified simplified adjustment coefficient δ lateral displacement δ2 web lateral displacement δ2,ext displacement of the end plate t t c. c. silva et alii, frattura ed integrità strutturale, 50 (2019) 264-275; doi: 10.3221/igf-esis.50.22 274 tw web thickness s distance between openings se distance between the first and last openings cdist coefficient that depends on the distribution of bending moments δ2,cen displacement of the center plate ηb dimensionless parameter ν poisson’s ratio θ twist references [1] oliveira, j.p.s. (2018). nova proposição para verificação do estado-limite de flambagem lateral com distorção de vigas mistas de aço e concreto. ph.d. thesis – departamento de engenharia de estruturas – programa de pósgraduação em engenharia de estruturas, universidade federal de minas gerais, minas gerais. [2] queiroz, g., pimenta, r. j. and mata, l.a.c. (2001). elementos das estruturas mistas de aço-concreto. o lutador, 3ed., belo horizonte, minas gerais, 332p. [3] associação brasileira de normas técnicas. (2008). nbr 8800:2008 projeto de estruturas de aço e de estruturas mistas de aço e concreto de edifícios. rio de janeiro. [4] european committee for standardization. (2004). en 1994-1-1:2004. eurocode 4: design of composite steel and concrete structures. part 1-1: general rules and rules for buildings. brussels. [5] roik, k., hanswille, g. and kina, j. (1990). solution for the lateral torsional buckling problem of composite beams. stahlbau, 59, p.327-332. [6] chen, s. (1992). instability of composite beams in hogging bending. ph.d. thesis, university of warwick, u.k. [7] dekker, n.w., kemp, a.r. and trinchero, p. (1995). factors influencing the strength of continuous composite beams in negative bending. journal of construction steel research, 34, p.161-185. [8] hanswille, g., lindner, j. and munich, d. (1998). lateral torsional buckling of composite beams (em alemão). stahlbau, 67, p.525-535. [9] calenzani, a.f.g. (2008). proposição de procedimento para a determinação da rigidez rotacional de vigas mistas contínuas e semicontínuas com perfis de alma senoidal. ph.d. thesis – centro de pós-graduação em engenharia de estruturas, universidade federal de minas gerais, belo horizonte. [10] calenzani, a.f.g., fakury, r.h., paula, f.a., rodrigues, f.c. and queiroz, g. (2012). rotational stiffness of continuous composite beams with sinusoidal-web profiles for torsional buckling. journal of construction steel research, 79, p.22-33. [11] chen, s. and wang, x. (2012). finite element analysis of distortional lateral buckling of continuous composite beams with transverse web stiffners. advances in structural engineering, 15(9), pp.1067-1616. [12] ye, j.h. and chen, w. (2013). elastic restrained distortional buckling of steel-concrete composite beams based on elastically supported column method. international journal of structural stability and dynamics, 13(1), pp. 1-29. [13] wang, a.j. (2014). numerically integrated analysis and design of continuous composite beams. australian journal of structural engineering, 15(2), pp.203-220. [14] guo, f., zhou, s. and jiang, l. (2015). lateral buckling analysis of the steel-concrete composite beams in negative moment region. advances in materials science and engineering, article id 763634, 8p. [15] zhou, w.b., jiang, l.z., li, s.j. and kong, f. (2015). elastic distortional buckling analysis of i-steel concrete composite beam considering shear deformation. international journal of structural stability and dynamics, 16, pp. 1-22. [16] zhou, w.b., li, s.j. and yan, w.j. (2016). practical formulas towards distortional buckling failure analysis for steel-concrete composite beams. the structural design of tall and special buildings, pp.1-18. [17] oliveira, j.p.s., calenzani, a.f.g., fakury, r.h. and ferreira, w.g. (2016). elastic critical moment of continuous composite beams with a sinusoidal-web profile for lateral-torsional buckling. engineering structures, 113, pp.121132. [18] amaral, t.v., oliveira, j.p.s, calenzani, p.s.o. and fakury, r.h. (2016). momento crítico elástico elástico à flambagem lateral com distorção de vigas mistas de aço e concreto. xxxvii iberian latin american congresso in computational methods in engineering, brasília-df, cilamce 2016. [19] dietrich, m.z. (2017). estudo da rigidez rotacional de vigas mistas de aço e concreto com lajes maciças de concreto armado. dissertação de mestrado – departamento de engenharia civil – programa de pós-graduação em engenharia civil, universidade federal do espírito santo, vitória. c. c. silva et alii, frattura ed integrità strutturale, 50 (2019) 264-275; doi: 10.3221/igf-esis.50.22 275 [20] dias, j.v.f. (2018). determinação do momento crítico elástico à flambagem lateral com distorção de vigas mistas contínuas e semicontínuas. dissertação de mestrado – departamento de engenharia de estruturas – programa de pós-graduação em engenharia de estruturas, universidade federal de minas gerais, belo horizonte. [21] salah, w. and gizejowski, m.a. (2008). numerical modelling of composite castellated beams. international conference on composite construction in steel and concrete, vi, pp. 554 – 565. [22] salah, w. and gizejowski, m.a. (2010). stability and ductility of castellated composite beams subjected to hogging bending. stability and ductility steel structures, rio de janeiro, brazil, pp. 839–846. [23] salah, w. and gizejowski, m.a. (2010). restrained distortional buckling strength of steel-concrete composite beams a review of current practice and new developments, modern building materials, structures and techniques, vilnius, lithuania, pp. 604–612. [24] piassi, a.d., dias, j.v., calenzani, a.f.g. and menandro, f.c.c. (2018). lateral distortional buckling of cellular composite-beams. revista ibracon de estruturas e materiais, 11(2), pp.331-356. [25] ansys, inc. (2016). release 17.0 documentation for ansys. canonsburg. [26] fan, c.k.r. (1990). buckling in continuous composite beams. ph.d. thesis, university of warwick, u.k. [27] johnson, r.p. (2004). composite structures of steel and concrete: beams, slabs, columns and frames for buildings. 3 ed. warwick, u.k.: blackwell, 250p. [28] timoshenko, s.p. and gere, j.m. (1961). theory of elastic stability. 2 ed. nova iorque, mcgraw-hill book co., 541p. [29] european committee for standardization. (1991). env 1994-1-1:1992. eurocode 4: design of composite steel and concrete structures: general rules and rules for buildings. brussels. [30] zaarour, w. and redwood, r. (1996). web buckling in thin-webbed castellated beams; journal of structural engineering, 122(8), paper 11030. [31] bezerra, e.m., fakury, r.h., castro e silva, a.l.r., caldas, r.b. (2010). bending moment resistance for lateral torsional buckling of castellated steel beams, xxxiv jornadas sudamericanas de ingeniería estructural, san juan, argentina. [32] vieira, w.b. (2011). simulação numérica do comportamento estrutural de vigas casteladas de aço com ênfase na flambagem do montante de alma. dissertação (mestrado) universidade federal de viçosa, programa de pósgraduação em engenharia civil. [33] european committee for standardization. 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can be opened with acrobat and adobe reader 5.0 and later.) >> /namespace [ (adobe) (common) (1.0) ] /othernamespaces [ << /asreaderspreads false /cropimagestoframes true /errorcontrol /warnandcontinue /flattenerignorespreadoverrides false /includeguidesgrids false /includenonprinting false /includeslug false /namespace [ (adobe) (indesign) (4.0) ] /omitplacedbitmaps false /omitplacedeps false /omitplacedpdf false /simulateoverprint /legacy >> << /addbleedmarks false /addcolorbars false /addcropmarks false /addpageinfo false /addregmarks false /convertcolors /converttocmyk /destinationprofilename () /destinationprofileselector /documentcmyk /downsample16bitimages true /flattenerpreset << /presetselector /mediumresolution >> /formelements false /generatestructure false /includebookmarks false /includehyperlinks false /includeinteractive false /includelayers false /includeprofiles false /multimediahandling /useobjectsettings /namespace [ (adobe) (creativesuite) (2.0) ] /pdfxoutputintentprofileselector /documentcmyk /preserveediting true /untaggedcmykhandling /leaveuntagged /untaggedrgbhandling /usedocumentprofile /usedocumentbleed false >> ] >> setdistillerparams << /hwresolution [2400 2400] /pagesize [612.000 792.000] >> setpagedevice microsoft word numero_33_art_1 d. nowell et alii, frattura ed integrità strutturale, 33 (2015) 1-7; doi: 10.3221/igf-esis.33.01 1 focussed on characterization of crack tip fields measurement and analysis of fatigue crack deformation on the macroand micro-scale d. nowell, s.j. o’connor, k.i. dragnevski university of oxford, uk david.nowell@eng.ox.ac.uk, samuel.oconnor@eng.ox.ac.uk, kalin.dragnevski@eng.ox.ac.uk abstract. the paper describes an experiment which performs in-situ loading of a small compact tension specimen in a scanning electron microscope. images are collected throughout a number of successive loadincg cycles. these are then analysed using digital image correlation (dic) in order to produce crack flank displacements as a function of load. this data is then compared with a simple elastic approach, and it is concluded that elastic-plastic analysis is required in order to accurately capture the displacements close to the crack tip. a simple approach due to pommier and hamam is therefore employed. this gives a better representation of the data, but predicts a variation of crack tip displacement, , which is difficult to explain from a physical perspective. the need for a more sophisticated analysis of the data is therefore highlighted. keywords. crack tip displacements; digital image correlation; elastic-plastic fracture mechanics. introduction he understanding of fatigue crack propagation is an essential pre-requisite to safe operation of many engineering structures and systems. most damage tolerant life prediction approaches are based on the application of experimental crack propagation data to the real system. for example, the paris law [1] is frequently used to apply experimental da/dn vs delta k data to service loads and to the system geometry. however, most experimental data is obtained for constant amplitude loading whereas engineering systems frequently experience non-uniform loading. the presence of history effects in fatigue crack propagation is well known and this means that life prediction under service loading conditions remains a challenging problem in many cases. a detailed understanding of the crack tip response to a range of load histories is the key to improvements in this area. recent work at oxford has been presented at the forni di sopra [2,3] and malaga [4] ij fatigue/ffems workshops and has concentrated on the use of digital image correlation to measure and analyse the displacements fields around a crack. our work has made use of a long-range optical microscope to examine deformations in a region within 0.5 mm of the crack tip. analysis of these deformations has allowed stress intensity factors to be calculated and crack closure assessed. in the current paper we will seek to extend this approach by reporting measurements taken during in-situ loading of a fatigue crack in a scanning electron microscope. this permits more detailed examination of the displacement field in the neighbourhood of the crack tip. t d. nowell et alii, frattura ed integrità strutturale, 33 (2015) 1-7; doi: 10.3221/igf-esis.33.01 2 macroscopic measurements ur earlier work on the measurement of crack tip displacement fields has employed a long range microscope, focused on an area approximately 600 x 400 m close to the crack tip [2]. a number of images were captured at intervals during the loading cycle, and digital image correlation carried out using a public domain matlab script produced by erbl et al [5]. the data obtained were processed in a number of ways, but a particularly convenient means of presenting the results is to determine the experimental stress intensity factor by comparing the measured crack tip opening displacements with those predicted by an elastic model. the crack flank displacements for an elastic crack are given by 4 2 i i k r u e    (1) where ki is the elastic stress intensity factor, e is young’s modulus, and r is the distance from the crack tip. hence, a plot of ui against r should yield a straight line and the stress intensity factor can be extracted from the gradient. fig. 1(a) shows results from a typical experiment conducted under constant amplitude loading. the dotted line represents the theoretical variation of elastic stress intensity factor with load for the size and type of specimen used (a standard compact tension specimen). it will be seen that the experimental results broadly follow the theoretical ones, and that the slope of the load vs k line is very similar. however the experimental results exhibit an offset, and the experimental k values are lower than predicted. this may be interpreted as being due to plasticity induced crack closure, which causes superposition of an additional negative residual k term (kr). it can be seen from the results that the crack does not open until about 0.5kn of applied load (approximately 25% of the maximum load). figure 1: variation of measured stress intensity factor with load for specimen ctf6 [4] (a) after constant amplitude loading and (b) immediately after an overload. fig. 1(b) shows results from the same specimen immediately after a 50% overload cycle. although the slope of the experimental line remains parallel to the theoretical one, these results exhibit some unusual features. in particular, negative k values are measured, which at first sight appears physically unreasonable. however, if there is a large plastic opening displacement at the crack tip, a crack shape of this form is possible, and closer inspection of the experimental results suggests that this is the measured deformation. the results presented here were obtained by analysing the relative displacement of 5 pairs of points from the recorded images, and the first pair is approximately 100 m from the crack tip. in order to investigate the crack tip deformation in more detail, a novel experiment was therefore proposed, which involved in-situ loading of a small specimen in the scanning electron microscope. o .5 ) .5 ) d. nowell et alii, frattura ed integrità strutturale, 33 (2015) 1-7; doi: 10.3221/igf-esis.33.01 3 microscopic measurements xperiments were conducted in the laboratory for in-situ microscopy and analysis (lima), which is part of the solid mechanics and materials engineering group in the department of engineering science at the university of oxford. the imaging device used was a carl zeiss evo ls15 vp-scanning electron microscope. the chamber of the sem was large enough so that in-situ testing could be performed with a deben testing stage similar to that shown in fig. 2. a 5 kn load cell was attached to the testing stage and an extension rate of 1:25 mm/min was used for this testing. computer software was used to set the drive parameters and to collect live data on the force applied and extension from the testing stage during loading. the specimen design was a modified compact tension specimen and the material used was aluminium alloy with a yield stress of approximately 320 mpa. figure 2: deben in-situ microtest tensile & compression stage with a 2 kn load cell. the specimen was pre cracked before being loaded on the deben stage with the same tensile testing rig used for macroscopic specimen loading. the specimen was loaded at a frequency of 5 hz, signicantly faster than could be achieved with the deben testing stage. 17,000 cycles were applied to the specimen to grow the crack approximately 7mm at the same loads to be used for later testing on the deben stage. once pre cracked and placed on the deben testing stage, the crack was grown slightly further to approximately 7:2mm before in-situ sem images were captured. the maximum applied load was 1:25 kn and the minimum load was 0:125 kn, giving an r ratio of 0.1. a single overload cycle of 1:875 kn was applied as part of the experiment, but only constant amplitude results will be reported here. imaging was carried out using a secondary electron detector at an operating voltage of 15kv and working distance of 9mm and images were captured at a resolution of 3072 x 2304 pixels over an image area of approximately 215 m x 161 m. images were taken every 0:125 kn to give 19 images for a complete cycle between 0:125 kn and 1:25 kn. the images were taken with the crack in approximately the same location within the image. to do this, the load was held at the desired value while the microscope stage and the electron bean were aligned with the crack before the next image was captured. once images were collected, a series of sets of points were selected on either side of the crack and relative displacement was obtained using the dic algorithm [5] for pairs of points within each set. each set of points contained 2000 points (with 200 points in the horizontal x direction and 10 in the y direction), see fig. 4. the procedure adopted therefore produced relative displacement in the y direction at 200 different x direction distances from the crack tip over the series of images. the points were distributed from close to the crack tip up to a distance of approximately 150 m along the crack flanks. displacement data could have been obtained with fewer points, however a large number of points were selected to reduce the chance that badly tracked points may influence the results. due to the high resolution of the images, displacements around the crack were quite large at high loads when measured in pixels. therefore, in order to better track the points, the area surrounding each point that is used for image correlation was increased from a 30 x 30 pixel square used in earlier work up to a 200 x 200 pixel area. in addition to the images taken to analyse displacements around the crack tip, images of the full crack were captured in order to measure crack length for calculation of k. the loading was paused at the highest load of a loading cycle (1:25 kn), magnification reduced and a series of images taken along the full crack. these images were then fitted together using normalised 2-d cross-correlation with the matlab image processing toolbox to give an image of the full crack length to measure from. an example is shown in fig. 5. e d. nowell et alii, frattura ed integrità strutturale, 33 (2015) 1-7; doi: 10.3221/igf-esis.33.01 4 figure 3: dimensions (in mm) of specimens used for in-situ sem testing. specimens were cut from a sheet of aluminium alloy 6082t6. figure 4: typical image collected from the experiment at a load of 1:25 kn. sets of points are selected on either side of the crack to measure displacements. figure 5: series of images aligned to give an image of the full crack length at a load of 1:25 kn d. nowell et alii, frattura ed integrità strutturale, 33 (2015) 1-7; doi: 10.3221/igf-esis.33.01 5 results s shown in eq. (1), if an elastic model is assumed, a plot of log uy vs. log r should be expected to give a straight line with a gradient of 0:5. this can then be used to obtain an experimental measurement of k. fig. 6 shows a typical set of results obtained with a crack length (measured from the notch tip) of approximately 7:2 mm. it will be apparent that the data falls into two distinct sets. points more than about 25m from the crack tip seem to give a good straight line fit, although the slope differs from 0.5 for all but the highest load. points closer to the crack tip give a much shallower slope. it is instructive to compare this distance with the irwin [6] estimate of plastic zone size. 2 1 2 p y k r           (2) where y is the yield stress of the material. this gives a figure of rp  330 m, for the maximum load, although the cyclic plastic zone size will only be about a quarter of this value. hence, whilst an initial elastic analysis sheds some useful light on the problem, an elastic/plastic analysis is likely to be more appropriate at this level of plasticity. in common with our earlier work we will choose to employ a model proposed by pommier and hamam [7]. this partitions the total displacement field into elastic and plastic components. in terms of displacements along the crack flanks, the model leads to 8   2 i y k r u e     (3) i.e., that a constant plastic displacement component  is added to the elastic solution given in eq. (1). in practice, of course the plastic deformation at the tip is unlikely to give rise to a constant deformation along the crack flanks, but close to the tip, eq. (3) is a reasonable approximation. plotting uy against r should give a straight line with a gradient related to k and an intercept of . the data in fig. 6 is re-plotted in this way in fig. 7. figure 6: variation of relative displacement (uy) with distance from the crack tip (r) at five different values of load (p/pmax) during the loading phase of a loading cycle. from fig. 7 it can be seen that the data gives a good straight line fit for r > 5 m0.5, i.e. r > 5 m. the data can be used to plot the loading history in k vs space. pommier and hamam [7] have suggested that the relationship should look like that shown schematically in fig. 8. in particular, they suggest that in cyclic loading, such as the loop indicated by (c) in the figure, there is little change in  in the first part of each cycle. this observation can be used to explain the existence of a threshold k in fatigue. it is postulated that, until the application of a certain level of k, there is very little cyclic plasticity (characterised by ) and the crack does not grow. the experimental data is plotted in fig. 9a, where it can be seen that the experimental loops are similar in general form to those predicted in [7]. however, there is significant variation in  throughout the cycle. in particular,  seems to continue to increase for a while after load reversal at maximum load (and similarly decrease for a while at the minimum load reversal). this feature is difficult to explain physically, and may simply a d. nowell et alii, frattura ed integrità strutturale, 33 (2015) 1-7; doi: 10.3221/igf-esis.33.01 6 be an artefact of the straight line fitting to the uy vs r data. this is illustrated in fig. 10, where it can be seen that fitting a straight line for the data corresponding to p/pmax = 0.5 leads to a negative value for . this may be thought to be physically inadmissible, although it should be remembered that the datum image for the dic is that at minimum load, rather than corresponding to the undeformed material. hence, only variations in  are measured, not the absolute value. figure 7: variations of relative displacement (uy) with distance from the crack tip (r) at eight different values of load (p/pmax) during the loading phase of a single cycle. figure 8: pommier and hamam’s suggested behaviour in k vs  space [7]. cyclic behaviour is indicated by the loop (c). figure 9: variation of k and  for loading cycles. loading phase [black] and unloading [red] are shown for the first cycle. in fig. 9b a second cycle of loading [blue] and unloading [magenta] is included. 0.5 d. nowell et alii, frattura ed integrità strutturale, 33 (2015) 1-7; doi: 10.3221/igf-esis.33.01 7 figure 10: variations of relative displacement (uy) with distance from the crack tip (r) at four different values of load (p/pmax) during the initial loading phase of a single cycle. a line of best fit produced with a least squares method is included for each load in the matching colour. finally, in fig. 9b, data from two consecutive loading cycles are presented. it will be seen that the cycles are very similar, illustrating the reproducibility of the technique. however, a small increase in  can be seen between the first and the second cycle, corresponding to the accumulation of damage at the crack tip and, possibly, crack tip extension. conclusions he paper has presented a technique for in-situ loading of a small compact tension specimen in a scanning electron microscope. it has proved possible to take high quality images of the area close to the crack tip during complete loading cycles. constant amplitude data are reported here, but images from a single overload cycle have also been captured. digital image correlation has been used to analyse the data using both an elastic and an elastic-plastic approach. unsurprisingly, the elastic approach does not model the measured displacements well, particularly close to the crack tip. an elastic-plastic approach provides a better fit, but there are still deficiencies in capturing deformations close to the tip. this may be partly because the existence of the process zone at the tip affects the displacements measured at the grid locations, and these may no longer represent purely crack flank displacement. a more sophisticated elastic-plastic model is almost certainly in order to model the data more accurately, but the experiment had demonstrated the capability to measure displacements close to the crack tip which will be useful in calibrating other models. references [1] paris, p., erdogan, f., a critical analysis of crack propagation laws, jnl basic engineering, 85 (1963) 528-534. [2] nowell, d., kartal, m.e., de matos, p.f.p., measurement and modelling of near-tip displacement fields for fatigue cracks in 6082 t6 aluminium, proc. first i.j. fatigue & ffems joint workshop, forni di sopra, italy, march 7-9, 2011, gruppo italiano frattura, (2011). [3] nowell, d., kartal, m.e., de matos, p.f.p., digital image correlation measurement of near-tip fatigue crack displacement fields: constant amplitude loading and load history effects, fatigue fract. engng mater. struct., 36 (2013) 3-13. [4] nowell, d., kartal, m.e., and de matos, p.f.p., characterisation of crack tip fields under non-uniform fatigue loading, proc. second i.j. fatigue & ffems joint workshop, malaga, spain, april 15-17, 2013, gruppo italiano frattura, (2013). [5] eberl, c. thompson, r., gianola, r., digital image correlation and tracking with matlab, matlab central file exchange (2006) http://www.mathworks.co.uk/matlabcentral/fileexchange/12413-digital-image-correlation-and-tracking. [6] irwin, g.r., plastic zone near a crack and fracture toughness, mechanical and metallurgical behavior, proc. seventh sagamore ordnance materials research conference, iv(1960) 63-78. [7] pommier, s., hamam, r., incremental model for fatigue crack growth based on a displacement partitioning hypothesis of mode i elastic-plastic displacement fields, fatigue fract. engng mater. struct., 30 (2006) 582-598. t 0.5 microsoft word numero_61_art_02_3414.docx e. entezari et alii, frattura ed integrità strutturale, 61 (2022) 20-45; doi: 10.3221/igf-esis.61.02 20 review of current developments on high strength pipeline steels for hic inducing service ehsan entezari, jorge luis gonzález-velázquez, diego rivas lópez, manuel alejandro beltrán zúñiga department of metallurgy and materials, escuela superior de ingeniería química e industrias extractivas, instituto politécnico nacional, mexico ehsan.entezari2014@gmail.com, https://orcid.org/0000-0003-3379-1761 jlgonzalezv@ipn.mx, https://orcid.org/0000-0001-6914-4449 drivasl@ipn.mx, https://orcid.org/ 0000-0003-4591-719x mabz_2205@hotmail.com, https://orcid.org/0000-0003-4201-9896 jerzy a. szpunar department of mechanical engineering, university of saskatchewan, canada jerzy.szpunar@usask.ca, https://orcid.org/0000-0002-1291-8375 abstract. nowadays, an increasing number of oil and gas transmission pipes are constructed with high-strength low alloy steels (hsla; nonetheless, many of these pipelines suffer from different types of hydrogen damage, including hydrogen-induced cracking (hic). many studies are being done to investigate the role of key metallurgical and processing factors to limit the negative effects of hic in hsla steel pipes. the thermomechanical control process (tmcp) is a microstructural control technique that avoids the conventional heat treatment after hot rolling and attempts to obtain the desired mechanical properties during the forming process. recent research has shown that tmcp provides high hic resistance without adding high amounts of alloying elements or applying expensive heat treatments. however, there is an incipient knowledge on predicting hic behavior, both in susceptibility and kinetics, in hsla steel pipe when it is exposed to hydrogen charging service conditions. this paper presents a review of the current developments of hsla and tmcp of pipeline steels, as well as the phenomenological and empirical models proposed to predict the kinetics of hic as a function of key parameters such as heat treatments and microstructures, especially nature and spatial distribution of non-metallic inclusions and the hydrogen permeation rate and the mechanical and fracture mechanics properties. keywords. high strength pipeline steels; hydrogen-induced cracking; thermomechanical controlled process; hic growth rate models. citation: entezari, e., gonzález-velázquez, j.l., rivas lópez, d., beltrán zúñiga, m.a., szpunar, j.a., review of current developments on high strength pipeline steels for hic inducing service, frattura ed integrità strutturale, 61 (2022) 20-45. received: 28.12.2022 accepted: 03.04.2022 online first: 14.04.2022 published: 01.07.2022 copyright: © 2022 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. https://youtu.be/qaqwiuugc6y e. entezari et alii, frattura ed integrità strutturale, 61 (2022) 20-45; doi: 10.3221/igf-esis.61.02 21 introduction he growing demand for high-strength steels with good hic resistance for oil and gas transmission pipelines has led to research on optimizing the composition and thermomechanical processing routes. the alloy design of new generations of pipeline steels is mainly focused on manufacturing micro-alloyed steels. this is because the microstructural features of them allow both improving the mechanical properties and weldability, yet at lower production costs since they eliminate the use of expensive alloying elements and heat treatment [1, 2]. nowadays, thermodynamics models such as mucg83, jmatpro, and thermo-calc will provide the opportunity to design pipeline steels with new chemical compositions [3-5]. salt bath heat treatment (quenching-partitioning process) and thermomechanical control process (tmcp) are two main processing routes for producing pipeline steels [6-8]. zhao and al. [9] suggested that the tmcp provides better microstructural control and shortens processing routes. the balanced combination of finish rolling temperature (frt) and finish cooling temperature (fct) and optimizing the cooling rate during tmcp led to a microstructural refinement that enhances the mechanical properties combination, as shown by jiang and al. [10]. from a metallurgical point of view, pipeline steels with bainitic and martensitic microstructures have been employed in the manufacturing of recent oil and gas pipelines in applications that demand an excellent combination of high strength and toughness with small wall thickness, such as high pressure and long-distance transportation systems [11, 12]. with the increasing acidity of crude oils and natural gas, the hydrocarbon transportation systems are increasingly experiencing hydrogen-induced cracking (hic), stress-oriented hydrogen-induced cracking (sohic), stress corrosion cracking (scc), and sulfide stress cracking (ssc). among these damage mechanisms, hic is considered one of the most important threats to structural integrity, mainly because of its high frequency of occurrence [13]. the standards nace tmo-284, nace tmo-177, and nace tmo-103 were published in the 1980s as laboratory test methods to evaluate the hydrogen cracking resistance of the pipeline steels [14-17]; however, they were basically screening methods for material selection, but do not provide data to predict the hic remaining strength and remaining life of pipeline steels in hydrogen charging environments. arafin and al. [18] and moon and al. [19] showed granular bainite and tempered martensite have excellent resistance against hic cracking. furthermore, it has been demonstrated that non-metallic inclusions (nmi) act as irreversible hydrogen trapping sites where the accumulation of hydrogen atoms at the interface of inclusions and the steel matrix promotes hic [20]. many researchers showed that elements such as manganese (less than 2 wt. %), chromium (less than 0.3 wt. %), molybdenum (less than 0.4 wt. %), phosphorus (less than 0.008 wt. %), and copper (above 0.2 wt.%) along with niobium, vanadium, titanium, and calcium enhance the hic resistance of pipeline steels. it is suggested that these alloying elements may control the phase transformation temperature and the rate of hydrogen diffusion, as well as controlling nmi morphology, providing a path to develop high hic resistance steels for pipeline manufacturing [21-26]. usually, ph and hydrogen partial pressure (ph2s) have been regarded as key environmental factors to determine the severity of hic damage. in general, it has been observed that the reduction of ph and increment of ph2s increase the hydrogen flux, leading to a higher hic susceptibility [27]. also, residual stress caused by inhomogeneous plastic deformation and incorrect welding processes is a well-known factor that increases the severity of hic in sour oil and gas pipelines [27, 28]. ongoing investigations indicate that the kinetics of hic in oil and gas transmission pipes exposed to sour environments can be predicted by phenomenological, empirical, and numerical methods [29, 30]. these findings have encouraged the idea by combining the results of research-oriented to develop high strength steels that are resistant to hic with the phenomenological and analytical methods to predict hic kinetics that can lead to the development of ffs algorithms to assess hic with reasonable accuracy. the present review paper summarizes the processing routes to produce high-strength steel pipes and describes their metallurgical and mechanical characteristics, and also, it reviews the main parameters used in the kinetic modeling of hic such as microstructures, especially nature and spatial distribution of non-metallic inclusions, and the hydrogen permeation rate, and mechanical and fracture mechanics properties. steel processing alloy designing n the modern pipeline industry, the need to reduce costs and time to design and produce improved steels that satisfy requirements of higher strength and defects tolerance has encouraged many researchers to use thermodynamic models such as mucg83, jmatpro, and thermo-calc [3-5]. t i e. entezari et alii, frattura ed integrità strutturale, 61 (2022) 20-45; doi: 10.3221/igf-esis.61.02 22 mucg83 is a thermodynamic model developed by bhadeshia [31] based on thermodynamic and kinetics of solid-state phase transformation in steels. the software uses the chemical composition as an input parameter, and the timetemperature-transformation (ttt) diagrams are the output data of the software. the developments in the design of thermomechanical heat treatment schedules have led to a new multi-platform software known as jmatpro, which generates continuous cooling transformation (cct) diagrams [32]. the advantage of this thermodynamic model is that only a few experimental data are required as input, and since it considers the effect of cooling rate, it can be applied to hot rolling and other processes that involve continuous cooling. another well-known method for optimizing the chemical composition of steels in alloy designing is using thermo-calc tcfe6 database software [33]. many researchers used thermo-calc models to predict microstructural, mechanical properties, and continuous cooling transformations [34-36]. the chemical compositions of high-strength pipeline steels have been continuously modified in the last decades in order to improve strength, toughness, and weldability. usually, the chemical composition of api-5xl steel grades contains < 0.1 wt.% of carbon, < 0.6 wt.% silicon, and up to 20 wt.% manganese, with additions of less <0.6wt.% of each of niobium, titanium, vanadium, and molybdenum [37]. the main role of the alloying elements used for improving the strength is through grain refinement and precipitate dispersion hardening. alloying elements also affect the transformation temperature, which allows microstructural control during hot rolling operations. tab. 1 illustrates the influence of alloying elements on improving the microstructural characteristics and mechanical properties of high strength pipeline steels without compromising weldability, especially [37-39]:  molybdenum (mo), silicon (si), nickel (ni), and nb + v: all contribute to increased steel strength.  ni+ mo: affect microstructure refinement achieved by suppressing austenite recrystallization, as well as steel strengthening through precipitation hardening and hardenability enhancement.  ni+ b: improve hardenability synergistically.  v+mo+nb: affect secondary hardening achieved by producing carbides, nitrides, and carbonitrides.  mo+nb+ti: more effective in improving the strength requirements obtained by finer ferrite grain size and precipitation hardening. the new generations of high-strength pipeline steels are classified into different categories based on microalloying. x70 steel is micro-alloyed with niobium and vanadium with reduced carbon content to enhance the precipitate hardening and grain refinement [40]. x80 steel has further reduced carbon content for weldability improvement [41]. the addition of molybdenum, copper, and nickel enhances the strength and low-temperature toughness of x100 steel. as mentioned before, high-strength pipeline steels, such as grade x100, offer the possibility of constructing high-pressure service (≥ 15 mpa) and high flow rate pipelines that allow reducing the transport and construction costs by 30 % compared with x70 and x80 pipeline steels [40, 42]. recently x120 steel has been introduced for improving the transport efficiency of ultra-high-pressure service. this type of steel is micro-alloyed with nickel, chromium, molybdenum, niobium, titanium, and copper to enhance strength by grain refinement and fine dispersions of hard second phases such as bainite [41]. heat treatment methods salt bath heat treatment is characterized by fast and homogeneous heating, controlled quenching, low surface oxidation, and improved decarburization, which is advantageous compared to traditional oil or water quenching media [43]. tab. 2 shows the types of heat treatment applied in the fabrication of high-strength steels as a function of salt bath chemical composition and temperature [43]. quenchingpartitioningtempering (q-p-t) heat treatment is a combination of heat treatment processes listed in tab. 2. it is used for manufacturing high-strength steel with an excellent combination of strength and toughness. the q-p-t treatment starts with austenitization, followed by quenching in a salt bath at temperatures between martensite-start (ms) and martensite-finish (mf) temperature for a specified time and finally quenching in water. this treatment promotes the diffusion of carbon from the supersaturated martensite to the retained austenite and stable ferrite regions, producing a very fine dispersion of carbides, combined with interstitial solid solution hardening [44, 45]. since salt bath heat treatment processes are time-consuming and are limited by the size of the molten salt bath, a thermomechanical controlled process (tmcp) is another option to produce high-strength pipeline steel [6,7]. thermomechanical controlled processing (tmcp) is a technique for controlling the hot-deformation process in a rolling mill to improve the mechanical properties of steels. by minimizing or even eliminating heat treatment after hot-deformation, such processing saves energy in the steel manufacturing process, increasing productivity for high-grade steels. it usually necessitates a change in alloy design that allows for both a reduction in total alloying additions and improved weldability [39]. further, the preheating temperature, non-recrystallization temperature (tnr), finish cooling temperature (fct), and e. entezari et alii, frattura ed integrità strutturale, 61 (2022) 20-45; doi: 10.3221/igf-esis.61.02 23 finish rolling temperature (frt) are key temperature parameters used in this process [43]. tab. 3 shows the combination of fct, frt, and cooling rate, typically used in tmcp [46-58]. alloying elements strengthening hardenability grain refinement toughness properties suppressing recrystallization controlling phase transformation controlling phase transformation c ● mn ● ● ● ● ni ● ● ● v ● si ● ti ● ● ● mo ● ● ● nb ● ● b ● ● ● ni + mo ● ● ● ni + b ● ● nb + v ● ● v + mo + nb ● ● mo + nb + ti ● ● ● ● table 1: simplified illustration of alloying elements on microstructural and mechanical properties of high-strength pipeline steels. typically, tmcp includes three steps: reheating, rolling, and cooling. strengthening microstructural factors such as grain size, precipitate size and spacing, solid solution, and dislocation hardening can be controlled by key temperature parameters during each step of tmcp [48, 59]. in the last decade, offshore structures have been constructed in colder regions and deeper water, demanding low thickness and high strength pipeline steels with improved toughness, weldability, and excellent hic resistance. this has encouraged steel manufacturers to use processing routes such as tmcp to produce pipeline steels with the desired mechanical and in-service damage resistance properties [46, 60]. the metallurgical characteristics of tmcp steels the new generation of api-5xl steels is classified into four categories based on microstructural control, as indicated in tab. 4 [60-67]. the main strategy to fabricate api 5xl steels is to obtain fine microstructural features by controlling key temperature parameters such as tnr, fct, frt during tmcp, which improves mechanical properties. further, the interaction between chemical composition and controlled cooling rate is more effective in generating a microstructure with fine grain size (low angle boundaries) that inhibits dislocation movement, resulting in an ideal combination of strength and toughness at temperatures as low as -40 °c. as a result, the chemical elements mentioned in tab. 1 can affect the cooling rate and subsequently control the grain size during the tmcp process [39]. accelerated cooling, quenching and tempering, and the online heat treatment process are used for producing pipeline steels with bainite-martensite microstructure. tempering reduces the brittleness of martensite and enhances the toughness of pipeline steels by producing fine dispersions of carbides [44]. the online heat treatment process is applied to produce highstrength low alloy steel plates with thickness up to 40 mm [39]. e. entezari et alii, frattura ed integrità strutturale, 61 (2022) 20-45; doi: 10.3221/igf-esis.61.02 24 table 2: types of heat treatment applied for the manufacturing of high-strength steels with the chemical composition and melting temperature of salt baths. table 3: the overview of a balanced combination of main temperatures parameters in tmcp. heat treatment types heat treatment temperature range (°c) bath components composition (wt.%) melting temperature (°c) operating temperature range (°c) austempering 200-400 kno3 nano2 50-60 40-50 135 160-550 nano3 nano2 50-60 40-50 145 150-500 kno3 nano3 50-60 40-50 225 250-600 martempering above ms kno3 100 337 350-500 nano3 100 370 400-600 kno3 nano2 50-60 40-50 135 160-550 nano3 nano2 50-60 40-50 145 150-500 kno3 nano3 50-60 40-50 225 250-600 hardening 760-1260 nacl kcl bacl2 cacl2 10-15 20-30 40-50 15-20 400 500-800 naco3 kcl 45-55 45-55 450 550-900 bacl2 kcl2 nacl 50 30 20 40 570-900 bacl2 nacl 70-96 4-30 600-800 700-1250 quenching partitioning quenching between ms and mf & partitioning above ms koh naoh 60-75 25-40 130-160 150-350 api5xl steel grades finish rolling temperature (°c) finish cooling temperature (°c) cooling rate (°°c/s) ref x70 750-850 450-600 16-23 [45,46] x80 810-890 500-550 20-40 [47-49] x100 800-830 250-530 30-38 [50-53] x120 800-840 300-450 33-35 [54-56] e. entezari et alii, frattura ed integrità strutturale, 61 (2022) 20-45; doi: 10.3221/igf-esis.61.02 25 api5xl steel grades steel manufacturing process microstructure microstructural features x70 tmcp + qt bainite-martensite multiphase steel: *b+m+f *slender bainitic sheaves along with martensite laths [61]. *smaller prior austenite grain (pag) and fine ferrite grains [62]. *martensite laths [61]. *high volume fraction of filmy austenite [63, 64]. ¤ polygonal and granular ferrite act as the second phase in the bainite matrix [65]. x80 tmcp + acc bainite dual-phase steel: ¤b+f tmcp + acc + hop bainite-martensite multiphase steel: *b+m+a x100 tmcp + acc + hop bainite dual-phase steel: ¤b-f x120 tmcp + acc martensite dual-phase steel: m+f fine ferrite acts as the second phase in the martensite matrix [66]. tempered lath martensite: tlm martensite laths [67]. table 4: classification of the new generation of high-strength pipeline steels based on microstructural control. polygonal and granular ferrite, austenite, martensite laths, slender bainitic sheaves, smaller prior austenite grains, and fine ferrite grains are microstructural features that can be accomplished by controlling temperature parameters during tmcp [60-66]. such microstructural features can be achieved based on the manufacturing process mentioned in tab. 4 and positively influence the mechanical properties of pipeline steels, as shown in fig. 1 and tab. 5 [48, 50, 52, 57, 6269]. microstructure and mechanical properties tab. 6 presents data about the relationship between microstructure and chemical compositions of pipeline steels and their influence on tensile properties [39, 41, 48, 50, 52, 57]. as shown in tab. 6, api x120 steel is micro-alloyed with different chemical elements, and also the amount of carbon content is reduced [41]. figure 1: minimum tensile properties of the new generation pipeline steels. e. entezari et alii, frattura ed integrità strutturale, 61 (2022) 20-45; doi: 10.3221/igf-esis.61.02 26 table 5: the effect of positive microstructural features on microstructuremechanical properties of pipeline steels. api-5xl steel grades microstructure x120 x100 x80 x70 tempered lath martensite (tlm) martensite dual phase steel (m + f) bainite dual phase steel (b + f) bainite martensite multiphase steel (b + m + a) bainite dual phase steel (b + f) bainite martensite multiphase steel (b + m + f) c he m ic al c o m po si ti o n ( w t% ) c 0.075 0.070 0.080 0.080 0.080 0.075 mn 1.10 1.25 1.5 1.5 1.5 1.5 ni 1.25 1 0.6 si 0.5 0.5 0.25 0.25 0.25 0.3 mo 0.5 0.5 0.1 nb 0.07 0.04 0.04 0.04 0.04 0.06 v 0.09 0.06 0.05 ti 0.03 0.03 0.04 yuts (mpa) 980 780 720 550 550 480 uts (mpa) 110 1000 850 680 680 620 el% 15 13 20 25 20 22 table 6: the relationship between microstructures and chemical compositions and effects on tensile properties. microstructural features effects ref fine ferrite grains  decrease in the slip length and slip reversibility.  decrease in the slip deformation around the crack tip during crack propagation.  decrease in dislocation pile-ups or an increase in the barriers of the crack propagation. [65] smaller prior austenite grains polygonal ferrite  as a second phase in the bainite matrix significantly enhances both the yield strength and low-temperature toughness. [68]  the enhancement of the fatigue limit of pipeline steels occurs. [69] martensite laths  the uniform distribution of dislocations and re-arrangement of stress concentration that occurs along the high angle grain boundaries.  blockage of cleavage crack propagation by martensite lath boundaries acting as a barrier. [64] filmy austenite  crack-tip blunting through the transformation retained austenite to the martensite and consumption a large amount of energy at crack tip (trip effect).  decrease in the propagation rate and stress intensity factor of the main crack due to the compressive residual stress formation and propagation of the secondary crack resulting from the trip effect. [69] bainitic sheaves  bainitic microstructures with a smaller width of the bainite laths have a higher stress intensity factor than the threshold value (kth) for crack blunting. [62, 64] e. entezari et alii, frattura ed integrità strutturale, 61 (2022) 20-45; doi: 10.3221/igf-esis.61.02 27 hydrogen induced cracking (hic) hic testing methods hen high-strength pipeline steels are exposed to hydrogen charging environments, such as sour environments, it is necessary to test hic susceptibility. the standard test method nace tmo-284 evaluates the susceptibility to hic by determining three parameters; crack length ratio (clr), crack thickness ratio (ctr), and crack sensitivity ratio (csr). in this testing method, unstressed specimens with dimensions 100 × 20 mm are exposed to synthetic seawater with ph=5 and purging h2s gas or an h2s/co2 mixture at room temperature for 96 hours. fig. 2 illustrates the nace tmo-284 test setup [14]. the acceptance criteria are clr ≤15 %, ctr ≤ 5 %, and csr ≤ 2%, according to the nace mr 0175/ iso 15156 [70]. a higher value of csr indicates a higher susceptibility to hic, whereas a higher value of ctr indicates more stepwise cracking, which makes hic more severe from the mechanical point of view, according to the api 579-1/asme ffs-1 standard. ctr also is related to microstructural banding or nmi content [70]. figure 2: schematic diagram of the nace tmo-284 test. the nace tmo 177 is a testing method aimed to evaluate stress-orientated hydrogen-induced cracking (sohic) resistance in a sour environment [15]. in this testing method, hydraulic loading is applied for a fully machined specimen with dimensions 6.35 mm diameter, 25.4 mm gauge length, and 15-20 mm shoulder radius. loading is controlled by constant load devices to limit load relaxation in the duration of testing. the test is conducted at 30 %, 50 %, and 90 % of the yield strength, as established in the nace tmo103 standard test method. accordingly, specimens that do not crack at 50 % yield have suitable resistance to sohic [15]. additionally, in normal hic, the cracks form groups of individual cracks aligned nearly parallel to the plate wall, but sohic occurs when hic cracks combine with radial oriented cracks and merge to the surface, as shown in fig. 3. tensile or residual stress is required to produce sohic [15]. figure 3: schematic illustration of the morphology of hydrogen-induced cracking (hic) and stress-oriented hydrogen-induced cracking (sohic) in the pipeline. w e. entezari et alii, frattura ed integrità strutturale, 61 (2022) 20-45; doi: 10.3221/igf-esis.61.02 28 an alternative testing method to evaluate the resistance to sohic is four points bent double beam. in this testing method, a steel sample, containing a notch with 2 mm depth and 0.13 mm radius, are bolted back to back across a pair of rollers and thereby placed into 4 points bending and exposed to the hydrogen charging environment for 168 hours, as depicted in fig. 4 [16]. figure 4: full-size double-beam test specimen design. an experimental method to artificially induce hic is cathodic charging, which consists of an electrochemical cell where the test plate is connected as a cathode, and a piece of platinum is known as an anode. by applying a predetermined direct current and voltage, the hydrogen generated by the cathodic reaction is absorbed by the test specimen due to the poisoning effect of the electrolyte, specially formulated for that purpose [17], as shown in fig. 5. since the purpose of this test is to induce and observe the formation and growth of hic cracks, therefore, the concentration and fugacity of hydrogen are not determined. the typical testing conditions of cathodic hydrogen charging are shown in tab. 7 [18]. these conditions are empirical and have been demonstrated to be capable of inducing detectable hic in the matter of several hours, which is very convenient for experimental purposes. during the test, specimens are examined from the unexposed face by straight beam ultrasonics to generate a c-scan map of the hydrogen-induced cracks. this test can be used to determine the hic susceptibility by the nace tm 284 criteria, but its greatest advantage is that it allows experimentally observing the hic kinetics [17]. figure 5: schematic of the cathodic hydrogen charging experimental setup. a) test plate, b) anode (pt), c) electrolyte solution with poison, d) dc power source. e. entezari et alii, frattura ed integrità strutturale, 61 (2022) 20-45; doi: 10.3221/igf-esis.61.02 29 table 7: optimal testing condition of cathodic hydrogen charging. table 8: qualitative effects of steel microstructure on hic resistance and susceptibility. test parameter optimized condition current density test duration electrolyte the total volume of electrolyte argon gas purge testing temperature testing pressure 15-20 ma/cm2 variable h2so4 solution with an addition of 20 mg/l as2o3 750 ml 25 cm3/min ambient ambient microstructure effect on hic ref ferrite-pearlite dual phase f+p  the ferrite-pearlite boundaries. are preferred paths for hydrogen crack propagations.  the intergranular fracture occurs along ferrite-perlite boundaries, and transgranular fracture occurs on slip plane occurs along slip planes. [27]  the cementite lamellae has a lower hydrogen diffusivity than the spheroidal cementite.  high dislocation densities and large grain boundary areas increase hydrogen diffusivity.  acicular ferrite delays hic due to dispersed carbonitride precipitates and high-density of tangled dislocations. [72]  high ferrite grain boundary areas per unit volume provides an efficient diffusion path for hydrogen transport, thus increasing the hydrogen concentration and the probability of hic. [73] martensite dual phase m+f / m+a  martensite-ferrite bands are efficient hydrogen trapping sites. [27]  propagation of hic cracks along lath martensite is more likely because the lath martensite is inherently brittle due to its high dislocation density and high residual stresses.  the diffusion of hydrogen atoms significantly reduces the critical micro-strain for decohesion of ferrite-martensite plates, thus increasing the susceptibility to hic.  hic cracks initiate in martensite islands and propagate into ferrite areas. [74]  phase segregation regions in martensite-austenite microstructure are preferable sites for hic. [75] bainite dual phase gb + af  granular bainite (gb) regions have are more resistance to hic than the ferrite-pearlite regions.  high hic resistance is due to the excellent resistance of ferrite against hic. [76]  bainitic steel with lath morphology has low hic resistance.  the high-volume fraction of bainitic laths leads to faster diffusion of hydrogen atoms, and a higher concentration of sub-surface hydrogen traps, consequently increase in the susceptibility to hic. [76] bainitemartensite multiphase b-m-a / b-m-f  bainite-martensite multiphase steels have better resistance to hic than the martensite dual-phase steels.  bainite-martensite multiphase steel and ferrite-granular bainite perform similarly for hic. [77] tempered martensite  tempered martensite reduces hydrogen damage susceptibility by reducing the dislocations density and stored energy of martensite.  nano-particles in tempered martensite decrease the mobility of hydrogen atoms and hydrogen concentration and thus reducing hic susceptibility. [78]  the quenching and tempering improve hic resistance. [79] e. entezari et alii, frattura ed integrità strutturale, 61 (2022) 20-45; doi: 10.3221/igf-esis.61.02 30 factors of importance for hic control microstructure he metallographic microstructure of the steel differently affects hydrogen diffusion rates and hydrogen atom trapping, thus influencing hic. tab. 8 shows the qualitative influence of microstructural features of api-5xl steels on hic resistance or susceptibility [27, 72-79]. one of the most important microstructural features that affect hic susceptibility is nmi. nmi is considered as the main hydrogen trap site to initiate hic. nmi in pipeline steels typically are aluminum, silicon, magnesium, titanium oxides, and manganese sulfides [20, 27]. there are contradictions about the effect of nmi on hic. liu and al. [80] found that hydrogen cracking does not occur at sio2 precipitates; however, xue and al. [81] observed hic cracks initiate at sio2. xue and al. [81] found that crack initiation did not occur at mns inclusions in an api 5l x80 pipeline steel, even though it has been widely documented that hic cracks initiate at elongated mns inclusions [20, 27, 29]. in general, it is observed that multiple factors play a role in the effect of nmi on hic in pipeline steels, such as morphology and size, the spatial distribution of nmi, elastic properties of the nmi and the matrix, and the crystallographic relationship between nmi and the matrix. in the case of nmi morphology, rahman and al. [82, 83] found that steel plates containing spinal and rectangular nmi are more susceptible to hydrogen cracking than globular nmi, assuming that globular nmi does not create regions with highstress concentrations and they are not sufficiently brittle to initiate cracks. however, the most important factor of nmi that affects hic susceptibility is the inclusion size. the length of hic cracks directly correlates with the length of nmi. large nmi is prone to trap large quantities of hydrogen atoms and thus initiate hydrogen cracking [84]. qin and al. [85] showed that the critical hic cracks nucleation size with mns and tic inclusions is 10 μm and 335 nm, respectively. the spatial distribution of nmi is another critical factor for hic initiation. rahman and al. [82] proposed a mathematical model that indicates that larger inclusion sizes and shorter distances among nmi reduce the plane strain fracture toughness at the interface of nmi, according to eqn. (1).                            -1/2nn n 1+n1+n 1+n 31 2 ic 1 1 2 2 3 3 2a2a 2a k  = b + +   l l l (1) where ∧i, 𝜌i, and ai with i = 1, 2, and 3, represents the probability of cracking initiation at the interface of nmi, the density of nmi, and the average size of the nmi, respectively (i = 1 for spinal, i = 2 for rectangular, and i = 3 for globular shape). l is the inter-distance parameter of two adjacent nmi. l is a crucial component in determining the crack propagation between the two nmi that depends on the density of nmi 𝜌 . generally, an increase in the density of nmi ( 𝜌) decreases inter-distance among nmi (l), increasing the probability of cracking initiation (∧ as a result of reducing fracture toughness (kic . further, b is a material constant, and n is the strain-hardening exponent. based on eqn. (1), it was concluded that the spinal nmi has a much larger contribution to the hydrogen-induced reduction of kic because these nmi are larger and closer to each other than other types of inclusions. thus, spinal nmi reduces fracture resistance by introducing more nuclei for fracture initiation [82]. the distribution of nmi in steel plates is another factor affecting the susceptibility of pipeline steels to hic. domizzi and al. [86] and rahman and al. [82] reported that most nmi with larger size and higher volume fractions are located in the middle thickness of steel pipes. this inhomogeneous distribution of nmi in the pipe suggests that there is a heterogeneity of fracture toughness, so the middle thickness of the pipe has lower fracture toughness and consequently a higher probability of hydrogen cracking than the regions near the surface. this conclusion is corroborated by the observation that most hic cracks are located at the middle thickness of steel pipes. hydrogen trapping at the inclusion-matrix interface is also influenced by the elastic properties of the nmi and steel matrix. peng and al. [20] and qin and al. [85] proposed an elastic-energy-based model obtained from statistical information of nmi and the relation between hydrogen concentration at the inclusion-matrix interface and shear modulus. they concluded that an increase in shear elastic modulus of the matrix promotes hydrogen trapping, reducing the matrix ductility and concentrating elastic stresses around nmi. in such conditions, the hic cracks initiate around nmi and easily propagate in the steel matrix [20, 85]. t e. entezari et alii, frattura ed integrità strutturale, 61 (2022) 20-45; doi: 10.3221/igf-esis.61.02 31 the crystallographic coherency of the inclusion-matrix interface is another factor that has been taken into consideration. in this regard, the lattice parameter of corresponding planes in nmi (ainclusion) and matrix (amatrix) determine the value of the elastic strain (f), as defined by eqn. (2) [85]. inclusion matrix matrix a - a f  =  a (2) when nmi and steel matrix have the same crystallographic structure, crystallographic orientation, and lattice parameter, i.e., a fully coherent inclusion-matrix interface, the elastic strain at the interface has its lowest value [20, 84]. in general, the growth of nmi leads to loss of coherency, so the distribution of dissolved hydrogen atoms around the nmi change. when the length of nmi (l) is larger than the critical length (lc), the hydrogen trapping and crack formation at interfaces depend on the density of misfit dislocations, and when an increase of misfit dislocation density reduces the number of dislocation loops around nmi, the process of plastic deformation is facilitated. furthermore, when l is less than the lc, the coherency is kept at the interface, and the coherency strain facilitates hydrogen trapping and, thus, enhances hic [20, 85]. chemical elements such as manganese, phosphorus, sulfur, nickel, chromium, niobium, vanadium, titanium, copper, calcium, and alloy carbide precipitations have an important role in determining hydrogen diffusion and nmi morphology. the susceptibility to hic reduces with decreasing the content of manganese to less than 2 wt. % [21]. above 2 wt. % manganese, high segregation ratio of manganese to carbon promotes hic through hydrogen enhanced decohesion effect (hede), and hydrogen-enhancedlocalized plasticity (help) [21]. contents of phosphorus higher than 0.008 wt. % reduce carbon activity in the presence of manganese, which enables higher contents of phosphorus migration to grain boundaries and thereby increases susceptibility to hydrogen cracking [21]. additionally, low sulfur content enhances the ratio of longitudinal cracks in pipeline steels, promoting hic [21]. nickel reduces the hydrogen diffusion coefficient in the microstructure of pipeline steels [87, 88]. additions of chromium of 0.3 wt. % delay the eutectoid transformation of austenite and induce microstructural changes in the ferrite-pearlite and ferrite-bainite content, which indicates that by controlling the chromium content, the phase transformation temperature can be controlled to enhance hic resistance. additions of molybdenum of 0.4 wt. % makes hydrogen absorption less likely, improving the hic resistance of pipeline steels [21, 88]. niobium and nanoscale particles of niobium carbide (nbc) and niobium nitride (nbn) disrupt dislocation interactions with hydrogen atoms and hinder crack propagation leading to the transition of intergranular fracture to microvoid coalescence, thus enhancing hic resistance [89]. nanoscale vanadium precipitations reduce hydrogen diffusion into the nmi and delay hydrogen cracking [90]. the effect of titanium addition on hic resistance depends on the size of titanium carbide (tic) and titanium nitride (tin) particles. titanium carbide and titanium nitride ti (c, n) particles less than 0.1 μm diameter enhance hic resistance [87, 88]. contents above 0.2 wt. % of copper improves the resistance of pipeline steels to hic in the environment with a ph value greater than 4.0. this is because a stable copper-containing oxide film can be formed on the surface of the pipeline, reducing the permeation rate of hydrogen. further, nanoscale copperrich precipitates prevent redistribution of hydrogen atoms and improve resistance to hic. copper also affects the shape of ferrite, increasing copper content from 1 to 2 wt. % modifies polygonal ferrite to acicular ferrite that has good hic resistance; nonetheless, this may cause brittleness. interaction between copper and cobalt can also decrease hydrogen uptake and thus reduce hic susceptibility, while copper together with molybdenum has a detrimental effect on hic resistance [21,23, 91]. the addition of calcium controls the shape of sulfide inclusions such as mns and consequently improves hic resistance. the calcium treatment maintaining the ratio of calcium to sulfur above 1.5 is suggested for pipeline steels with sulfur contents higher than 0.001 wt.% [21]. environment environmental factors such as ph and h2s pressure critically affect hydrogen intake in pipeline steel. the decrease of ph and increase of ph2s increase the generation of hydrogen atoms by anodic reaction of iron (eqn. (3)) and the cathodic reaction of the hydrogen ion eqn. (4)) [92].  2+fe  fe +2e (3)  + 22h +2e   2h (atomic hydrogen)  h (4) where hydrogen ions can be generated by dissociation reactions; (eqn. (5)): e. entezari et alii, frattura ed integrità strutturale, 61 (2022) 20-45; doi: 10.3221/igf-esis.61.02 32  + -2h s  h +hs (5) the diffusion of hydrogen atoms into the interstitial lattice sites and inclusion-matrix interface increases hydrogen pressure decreasing the strength of interatomic bonds (cohesive strength) along the grain boundaries and promoting hic by a mechanism known as the hydrogen-enhanced decohesion (hede) [93]. fig. 6 depicts a schematic illustration of hede. to fully understand this result, eqn. (6) shows that the ph and ph2s are the main environmental parameters at ambient temperature affecting hydrogen flux (jperm) and hic resistance [94]. generally, the increase of ph2s and the decrease of ph increase hydrogen permission flux and hydrogen gas pressure into the crack cavity, resulting in the growth of hic crack and then the decrease of hic resistance.    2 0.25 -0.17ph  perm h sj =k d p 10 (6) where the value of k(d) is determined from experimental data of kittel and al. [95] and depends on corrosion layer thickness (d). residual stress steel manufacturing processes such as machining, joining, and rolling have considerable influence on residual stress and strain distribution in steel plates used to manufacture seam pipes for hydrocarbon transport. indeed, heterogeneous residual stress fields and plastic strains caused by inhomogeneous plastic deformation affect hydrogen permeation and hic fracture susceptibility as proposed by kharin and toribio [96]. jack and al. [97] showed that a high level of residual stress, consequently high dislocations density, and the high-volume fraction of high angle grain boundaries led to the hydrogeninduced fracture in x65 pipeline steel. therefore, a precise temperature schedule during tmcp and selection of the proper welding procedure effectively reduces residual stress in pipeline steels [97]. the welding joints of pipeline steels also produce residual stress in the weld metal and the heat-affected zone where hydrogen accumulation and then hydrogen cracking occur. javadi and al. [98] proposed that hydrogen concentration decreased as the distance from the weld metal increased. prediction of hic growth rates phenomenological methods henomenological methods have been applied to predict the hic growth rate in order to develop the ffs assessment criteria for in-service pipelines and to mitigate hydrogen-induced fracture risk [29]. according to the hydrogen pressure mechanism (hpt), the concentration of the atomic hydrogen within trapping sites, such as grain boundaries and internal voids, leads to increased pressure at the cavity, which eventually causes the formation of an embedded crack and thereby initiating hydrogen-induced cracking [99]. another suggested mechanism of hydrogen damage is the hydrogenenhanced decohesion model (hede), which assumes that hic is caused by the diffusion of atomic hydrogen into the interstitial sites, decreasing the strength of interatomic bonds (cohesive strength) along the grain boundaries and resulting in hydrogen cracking, as schematically shown in fig. 6 [100, 101]. figure 6: schematic of hydrogen-enhanced decohesion (hede). a) atomic lattice b) absorbed hydrogen c) hydrogen at particle-matrix interfaces. p e. entezari et alii, frattura ed integrità strutturale, 61 (2022) 20-45; doi: 10.3221/igf-esis.61.02 33 hydrogen-enhanced localized plasticity (help) establishes that hic is caused by hydrogen adsorption into a preexisting crack cavity leading to adsorption-induced dislocation emission (aide), as schematically shown in fig. 7. the accumulation of hydrogen atoms in the crack cavity reduces the plastic zone size around the crack tip, which results in high local triaxial stresses that induce microvoid coalescence and further crack growth [102]. figure 7: effect of hydrogen adsorption on the area of the plastic zone as hydrogen-enhanced localized plasticity (help) mechanism. hede and help mechanisms are primarily related to the final fracture mode, whereas hpt is related to the initiation and stable growth of hic. robertson and al. [103] proposed that the transition from help to hede mechanism occurs in areas with a high concentration of hydrogen. in general, the phenomenological models attempt to correlate hic growth rate with critical strain energy release rate, yield stress, hydrogen-induced fracture toughness, and hydrogen diffusion within the crack opening. the yield stress (σy) and plastic strain (εp) and plain strain fracture toughness (kih) of steels exposed to the atomic hydrogen depend on hydrogen concentration (c) while young's module (e) is little affected, and these effects have to be introduced in the models. generally, the yield stress and fracture toughness of steels exposed to hydrogen charging environments decreases with the increase of hydrogen concentrations into hydrogen trap sites. huang and al. [104] and sofronis and al. [105] proposed a phenomenological model based on the hede mechanism in which the critical energy release rate (gc) is a function of hydrogen concentration, as represented by eqn. (7) and eqn. (8). a high gc value may suppress crack initiation under elastic deformation and promote ductile fracture.  c cg = g   c (7)             c c c 0c c c c c [(ζ-1) ] g               g   c  > ζg cg   c = ζg                            g   c    ζg (8) where c is the total hydrogen concentration, c0 is the initial hydrogen concentration, gc (c) represents the embrittlement function. ζ and ξ are parameters that control the initial and the maximum reduction of the critical energy release rate, with ξgc denoting a lower bound value. the values of ζ and ξ are 0.9-0.8 and 0.5, respectively [104, 105]. furthermore, the crack driving force function ( h ) is presented by eqn. (9) [104, 105]: +e c ψ h=  g la (9) where cg is critical energy release rate, l is a length scale parameter controlling the smoothness of the crack topology, and a and +eψ represent plastic adjustment function and density of stored elastic energy, respectively, as defined by eqn. (10) and eqn. (11) [104, 105]: e. entezari et alii, frattura ed integrità strutturale, 61 (2022) 20-45; doi: 10.3221/igf-esis.61.02 34             p f a a exp (10)   + 2e e e dev   dev+ ψ =k  tr  ε +2μ (ε : ε ) (11) in the above equations, the coefficient α is a material parameter, ε is the equivalent plastic strain, and εf is a critical failure strain. the bracket ⟨x⟩+ is viewed as a function of (x ± |x|) / 2, k denotes the bulk modulus, and μ is the shear modulus. also, tr (ε) expresses the trace of the strain tensor, and εedev is the elastic part of the deviatoric strain tensor expressed as εedev = εe – tr (ε) i/3 with εe and i signifying the elastic strain and second-order identity tensor, respectively [104, 105]. the above phenomenological model incorporated plastic contribution into the crack driving force function, assuming a higher critical energy release rate and consequently lower crack driving force for ductile fracture [104, 105]. this model can predict crack initiation and propagation and brittle-ductile transition in the fracture of pipeline steels. sofronis and al. [105] and liang and al. [106] suggested a help model that describes the hydrogen effect on the local yield stress (σy) as presented by eqn. (12):        1 p y  0 0 ε σ =     1+ ε n h (12) where 0 h is the initial yield stress in the presence of hydrogen, p ε is the plastic strain in uniaxial tension, 0ε is the initial yield strain in the absence of hydrogen and n is the hardening exponent that is assumed unaffected by hydrogen. gerberich and al. [107, 108] proposed a model that calculates hic crack growth in correlation with plane strain fracture toughness (kih) and grain size (d) in the form of the differential equations:   0 eff h ih 1.5 crit 0 2  1+   c d v  kda =  dt 3 d r t (c -c ) (13) the correlation of stable hydrogen crack growth with yield stress (σy) and grain size (d) is:   0 eff h y crit 0 9 c d v  σda =  dt 2 d r t  c -c (14) the unstable hydrogen cracks growth in correlation with plane strain fracture toughness (kih) and grain size (d) is given by:   2 0 eff h ih 2 crit 0 9 c  d v  kda =  dt 2e d r t  c -c (15) where c0 is the initial hydrogen concentration, ccrit is the critical hydrogen concentration, deff is the diffusivity of hydrogen in steel, hv is hydrogen partial molar volume in steel, e is young's module, ϑ is poisson's ratio, and r and t are the universal gas constant, ambient temperature, respectively. these authors [107, 108] proposed a formula (eqn. 16)) to calculate the time required to crack initiation in correlation with yield stress and stress concentration factor (k):                 5 2 4 0.51 1 2 0.5 y c k t =  × × c    1-1 k 2  σ ×e (16) e. entezari et alii, frattura ed integrità strutturale, 61 (2022) 20-45; doi: 10.3221/igf-esis.61.02 35 where c1 is the diffusivity constant, c2 is a constant determined by the correlation between fracture stress and hydrogen embrittlement and   is notch root radius. a phenomenological model proposed by gonzalez and al. [17] assumed that the hic crack growth results from the accumulation of internal hydrogen pressure in a preexisting cavity that increases the stress intensity factor, and when it surpasses the plane strain fracture toughness of steel with dissolved hydrogen in the fracture plane, the crack propagates. they proposed a model that predicts hic crack growth rate based on the fracture mechanics criterion that establishes that the crack will start to grow when the plane strain fracture toughness in the cracking plane (kih) reaches its critical value, eqn. 17. ih h2 a k = 2p π (17) where ph2 is atomic hydrogen pressure and a is the crack length. solving eqn. 18 for the crack length and obtaining the total differential equation, gonzalez and al. [17] reached the following equation for the hic crack growth rate:        h h h 2 ih 3 α r t  e   d v cda = a dt 4 k  b (18) where ∆ch is the hydrogen concentration gradient, deff is the diffusivity of hydrogen in steel, and b is the wall thickness, and r, t, and hv are the universal gas constant, ambient temperature, and hydrogen partial molar volume in steel, respectively. also, the constant α is 11.5 for p= 17500 atm and  2 e e =  1-ν . the hic crack length after exposure time (t) to the hydrogen charging environment is defined by eqn. (19).  0    hta a e (19) where a0 is the initial crack length at time t = 0 and h is:        h  h 2 ih 3 α r t e   d c h= 4 k  b (20) according to this model, the hic crack growth rate will be faster as kih decreases, while a high value of dh and δch will increase the crack growth rate, which is logical since these two parameters indicate the input flux of hydrogen, so the higher input, the higher hic rate. further, gonzalez and al. [17] investigated the mechanism and kinetics of hic by cathodic charging experiments, finding that hic cracks mainly initiate at the interface of elongated mns and steel matrix, and they propagate in a path parallel to the rolling direction along with the interfaces of pearlite and ferrite bands. they also showed that the shape of hic cracks is conditioned by the spatial distribution of hic nuclei, namely non-metallic inclusions, and it is less affected by microstructural anisotropy. however, after some time, the individual cracks begin to interconnect to form large cracked areas with a drastic decrease in the hic growth rate. according to their findings, gonzalez and al. [17] demonstrated that hic occurs in two stages; nucleation and growth of individual cracks, where the maximum hic growth rate is observed, and the second is the interconnection of individual cracks where the kinetics is slowed down to almost zero. however, the phenomenological model presented by gonzalez and al. [17] did not consider the interconnection stage; nonetheless, it showed a good correlation with the observed experimental hic growth rates of individual cracks. fig. 8 shows the comparison of experimental results and the tendency of hic kinetics predicted with gonzalez's model [17], good agreement between experimental and predicted results [109]. diniz and al. [110] suggested a phenomenological model considering the hydrogen transport through interstitial diffusion, as shown in eqn. (21). e. entezari et alii, frattura ed integrità strutturale, 61 (2022) 20-45; doi: 10.3221/igf-esis.61.02 36               t b ct h t d d cdc c c da dt dt (21) where λd denotes the length of the diffusion zone, a represents the crack length, and τd is diffusion time. ct represents hydrogen concentration at the crack tip, and ch indicates the hydrogen concentration for the stationary crack when t>> τd, and cb is the hydrogen concentration for fast crack propagation [110]. figure 8: comparison of experimental and predicted results of hic growth of an api 5l x52 steel plate by cathodic charging and a synthetic sour medium. hydrogen transport through the hydrogen trapping mechanism was modeled by mc-nabb and foster [111] and is represented by eqn. (22).     t l t t θ = kc   1- θ θ t (22) where cl is hydrogen concentration in normal interstitial lattice sites, θt denotes the coverage of trapping sites, k represents the hydrogen capture rate, and  is the hydrogen release rate. it should be noted that the above model describes the threshold hydrogen concentrations at the crack tip. balueva [112] proposed a phenomenological model based on determining the time to grow delamination (t) under hydrogen pressure, given by eqn. 23: 2 βa1 1 a t=2α (a-  βarctan( )) 2 2a + β β (23) where α and β are defined as: c 0 eff πg α=  6rtc d (24) 2 c 0β=8b 2g d   (25) gc is the critical energy release rate specified as: e. entezari et alii, frattura ed integrità strutturale, 61 (2022) 20-45; doi: 10.3221/igf-esis.61.02 37 2 4 h2 c 0 p a g =  128d (26) where ph2 is atomic hydrogen pressure, a is delamination radius and d0 is flexural rigidity defined by eqn. 27:      3 0 2 eh d = 12 1-υ (27) where h is a thin layer of thickness, e is young's modulus, and υ is the poisson ratio. delamination radius (a) under hydrogen pressure overtime is defined by eqn. 28:   1 1a  t =  t+  π β 2α 4 (28) empirical models traidia and al. [94, 113] presented an empirical model considering the effect of temperature on hic growth rate. they found a decrease in temperature at range 0-100 °c for an aggressive environment (ph = 3 and ph2s = 1000 mbar) decreased the mechanical properties of steels, especially the fracture toughness and increased hydrogen pressure in the crack cavity. the combination of these two factors causes hic to develop mainly at low temperatures; however, hydrogen cracking is not observed at a temperature higher than 65 °c [113]. according to these authors [94, 113], the hydrogen cracks growth rate is related to fracture toughness (kih) and ph2, given by the differential equations:   cth2 ih 2 2 h2 cth2 dcda 2a dp πe dk =    +      dt p dt dc dt4 1 p (29) where cct is the hydrogen concentration at the crack tip, while ph2 is defined as: h2  h2 h2 n rt p =  v-n rtb  (30) where nh2 is the total number of hydrogen moles, v is the crack volume determined by integration of the crack opening, t is temperature, and b is given by eqn. 31: 1 2 z b=  + z t (31) where z1 is the first compressibility constant (1.54×10-6 k pa-1), and z2 is the second compressibility constant (4.69×10-8 k pa-1), ph2 is a function of t, and ph2 is a function of kih as follows:         2 cs 2 c t p t = γ p,t  s t (32) crit ih h 2 π k p =  2 πa (33) the hydrogen concentration at the crack surface (ccs) is defined by eqn. 34: e. entezari et alii, frattura ed integrità strutturale, 61 (2022) 20-45; doi: 10.3221/igf-esis.61.02 38   h h cs h2 (γ p,t ) σ  v c =s(t)exp( )  p rt (34) where hydrogen solubility (s) and fugacity factor of gaseous hydrogen (γ (p, t)) are represented by the below equations:  s 0 h s (t)= s  exp ( ) rt (35)   1 2 h2 z γ  p,t =exp[( + z ) p ] t (36) where s0 is the hydrogen solubility pre-exponential factor (0.82 mol/(m3pa–1/2)12), and ∆hs is the enthalpy of solution (28.6 kj mol-1). in more recent work, gonzalez and rivas and al. [114] developed an empirical hic growth rate model based on the bestfit curve of experimental data, which is presented in eqn. (37).   t-μi σ(i)* -ea=a ei (37) where t is the cathodic charging time and also  *a i , σi and μi, which are a function of the applied current density (i)are defined by the below equations:  * 2maxa = a - βii (38) 2-γi iσ = αe (39) 2-ηi iμ =δe (40) parameters α, β, γ,  δ and η are material constants that have to be found experimentally for every specific steel since these are parameters dependent on the microstructure, volume and shape of non-metallic inclusions, strength and chemical composition of the steel [114]. fig. 9 shows a comparison of experimental and simulated results of hic growth of an api 5l x60 steel plate, reported by traidia and al. [94]. they compared the numerical predictions of hic kinetics in two different kih with the experimental data achieved by brouwer and al. [115] and found a good agreement on both the hic initiation and growth of simulated and experimental results, see fig. 9. further considerations to establish hic models the ample evidence available nowadays makes it possible to use the multi-physics models to predict hydrogen cracking behavior in pipeline steels. this evidence indicates that the hoop stress induced by the internal pressure, crystallographic texture, and the tensile mechanical properties, along with the geometry and location of the hic cracks and the pipe thickness, have a little effect on the kinetics of hydrogen cracking in pipeline steels. however, hydrogen permeation rate, the nature and spatial distribution of non-metallic inclusions, in-plane fracture toughness, and the individual crack interconnection events are among the main parameters to establish a comprehensive hic kinetics model. at the service temperatures of most hydrocarbon pipelines, ph and ph2s are the two main operational parameters that control the hic kinetics since they directly affect the hydrogen permeation rates. indeed, the experimental evidence shows that lower ph and higher ph2s decrease the incubation period. the incubation period is the time needed to reach the critical pressure for the hic cracks growth [27, 116]. however, the few available experimental data and in-field evidence indicate that incubation times are a few hours or even less than an hour. therefore, attention has to be placed on the active propagation of already formed hic cracks. e. entezari et alii, frattura ed integrità strutturale, 61 (2022) 20-45; doi: 10.3221/igf-esis.61.02 39 figure 9: comparison of experimental and simulated results of hic growth of an api 5l x60 steel plate. the nature and distribution of nmi control the kinetics of hic cracks of steel pipe by determining the number and separation of initial hic cracks. as observed in this paper, larger inclusions with spinal morphologies that are commonly observed in the middle thickness of steel pipes contribute to low fracture toughness and more numerous initial cracks, which lead to higher kinetics of hic. so, in modeling the kinetic of hic, the role of nmi with respect to spatial distribution and nature should be considered to establish a reliable model. another important consideration is the interconnection of hic cracks which is an inevitable condition after the individual cracks have reached the necessary sizes to interconnect to each other. the experimental observations performed by gonzalez and al. [17] indicate that the more initial hic cracks, the shorter time to begin the interconnection stage, which is only a few days in some cases. furthermore, the model has to incorporate the new hic cracks that continue to appear after several weeks or even months of exposure to hydrogen charging environment, a phenomenon that has been little investigated, i.e., the delayed nucleation of hic cracks. summary and conclusions eat treatments, microstructures, especially nature and spatial distribution of non-metallic inclusions, hydrogen permeation rate, and the mechanical and fracture mechanics properties are the key factors affecting the kinetics of hic. thermomechanical controlled processing (tmcp) is the main processing route for manufacturing the hsla steel pipes with good mechanical properties and high hic resistance. in this regard, controlling various temperature parameters during tmcp, such as preheating temperature, tnr, fct, and frt, leads to microstructural refinement and consequently improves hic resistance. regarding microstructure, pearlitic and martensitic microstructures are susceptible to hic cracking; however, granular bainite and tempered martensite positively influence the hic resistance. another important microstructural factor is also the nature and spatial distribution of non-metallic inclusions. larger inclusions with spinal and rectangular morphologies are the main nuclei for hic, and additionally, contribute to the degradation of fracture toughness and increasing kinetic of hic. furthermore, the growth of non-metallic inclusions increases the density of misfit dislocations, which plays the main role in hydrogen trapping rate and facilitates plastic deformation and, thus, hic growth at the inclusion-matrix interface. further, as another microstructural factor, alloying elements such as manganese (less than 2 wt. %), chromium (less than 0.3 wt. %), molybdenum (less than 0.4 wt. %), phosphorus (less than 0.008 wt. %), copper (above 0.2 wt.%), and calcium, as well as carbide precipitations enriched with niobium, vanadium, and titanium enhance hic resistance in pipeline steels. the ph and ph2s are the environmental factors affecting the hydrogen permission rate. generally, the decrease of ph and increase of ph2s increase hydrogen permission rate through the generation of hydrogen atoms by anodic reaction of iron and the cathodic reaction of the hydrogen ion. the diffusion of hydrogen atoms into the hydrogen trap sites, especially the h e. entezari et alii, frattura ed integrità strutturale, 61 (2022) 20-45; doi: 10.3221/igf-esis.61.02 40 inclusion-matrix interface, increases hydrogen pressure and, thus, hic initiation and growth. moreover, heterogeneous residual stress fields generated by an inappropriate manufacturing process are known as a parameter increasing hydrogen permeation rate and hic fracture susceptibility. the yield stress (σy) and fracture toughness (kih) of steels exposed to the atomic hydrogen depends on hydrogen concentration stored into hydrogen trap sites; the increase of hydrogen concentration, the decrease of yield stress and fracture toughness, and thus, the hic crack growth rate will be faster. acknowledgment he authors e. entesari, j.l. gonzalez and d. rivas are grateful to instituto politécnico nacional (ipn) and conacyt for their financial support. references [1] scherf, s., harksen, s., hojda, r., strötgen, d. (2018).weldability of high toughness x100 seamless pipes with a new low carbon alloying concept for arctic offshore structural applications. the 28th international ocean and polar engineering conference, onepetro. [2] carrasco, j.p., diniz, d.d.s., barbosa, j.m.a., silva, a.a., dos santos, m.a. (2019). numerical simulation of the hydrogen trapping effect on crack propagation in api 5ct p110 steel under cathodic overprotection, int. j. hydrogen energy, 44(5), pp. 3230-3239. [3] da trindade filho, v.b., silva, j.m.s.e., linne, c., boas, a.c.c.v. (2020). high strength micro alloyed steel seamless pipe for sour service and high toughness applications. [4] morales, e. v., bott, i.s., silva, r.a., morales, a.m., de souza, l.f.g. (2016). characterization of carbon-rich phases in a complex microstructure of a commercial x80 pipeline steel, j. mater. eng. perform., 25(7), pp. 2736–2745. [5] stalheim, d.g., muralidharan, g. (2006).the role of continuous cooling transformation diagrams in material design for high strength oil and gas transmission pipeline steels. international pipeline conference, 42630, pp. 231–238. [6] javaheri, v., pohjonen, a., asperheim, j.i., ivanov, d., porter, d. (2019). physically based modeling, characterization and design of an induction hardening process for a new slurry pipeline steel, mater. des., 182, pp. 108047. [7] alaneme, k.k., olanrewaju, s.o., bodunrin, m.o. (2011). development and performance evaluation of a salt bath furnace., int. j. mech. mater. eng., 6(1), pp. 67-74. [8] shikanai, n., mitao, s., endo, s. (2008). recent development in microstructural control technologies through the thermo-mechanical control process (tmcp) with jfe steel's high-performance plates, jfe tech. rep., 11(6), pp. 1-6. [9] zhao, m.-c., yang, k., shan, y. (2002). the effects of thermo-mechanical control process on microstructures and mechanical properties of a commercial pipeline steel, mater. sci. eng. a, 335(1–2), pp. 14-20. [10] jiang, m., chen, l.-n., he, j., chen, g.-y., li, c.-h., lu, x.-g. (2014). effect of controlled rolling/controlled cooling parameters on microstructure and mechanical properties of the novel pipeline steel, adv. manuf., 2(3), pp. 265-274. [11] zikeev, v.n., chevskaya, o.n., mishet'yan, a.r., filippov, v.g., korostelev, a.b. (2021). effect of high strength structural steel structural state on fracture resistance, metallurgist, 65(3), pp. 375-388. [12] koo, j.y., luton, m.j., bangaru, n. v., petkovic, r.a., fairchild, d.p., petersen, c.w., asahi, h., hara, t., terada, y., sugiyama, m. (2003).metallurgical design of ultra-high strength steels for gas pipelines. the thirteenth international offshore and polar engineering conference, onepetro. [13] askari, m., aliofkhazraei, m., afroukhteh, s. (2019). a comprehensive review on internal corrosion and cracking of oil and gas pipelines, j. nat. gas sci. eng., 71, pp. 102971. [14] nace international the corrosion society. (2016). nace standard tm0284: standard test method evaluation of pipeline and pressure vessel steels for resistance to hydrogen-induced cracking. [15] nace international the corrosion society. (2005). ansi/nace tm0177: laboratory testing of metals for resistance to sulfide stress cracking and stress corrosion cracking in h2s environments. [16] nace international the corrosion society. (2003). nace standard tm0103: laboratory test procedures for evaluation of sohic resistance of plate steels used in wet h2s service. [17] gonzalez, j.l., ramirez, r., hallen, j.m., guzman, r.a. (1997). hydrogen-induced crack growth rate in steel plates exposed to sour environments, corrosion, 53(12). t e. entezari et alii, frattura ed integrità strutturale, 61 (2022) 20-45; doi: 10.3221/igf-esis.61.02 41 [18] arafin, m.a., szpunar, j.a. (2011). effect of bainitic microstructure on the susceptibility of pipeline steels to hydrogen induced cracking, mater. sci. eng. a, 528(15), pp. 4927-4940. [19] moon, j., choi, j., han, s.-k., huh, s., kim, s.-j., lee, c.-h., lee, t.-h. (2016). influence of precipitation behavior on mechanical properties and hydrogen induced cracking during tempering of hot-rolled api steel for tubing, mater. sci. eng. a, 652, pp. 120-126. [20] peng, z., liu, j., huang, f., hu, q., cao, c., hou, s. (2020). comparative study of non-metallic inclusions on the critical size for hic initiation and its influence on hydrogen trapping, int. j. hydrogen energy, 45(22), doi: 10.1016/j.ijhydene.2020.02.131. [21] ghosh, g., rostron, p., garg, r., panday, a. (2018). hydrogen induced cracking of pipeline and pressure vessel steels: a review, eng. fract. mech., 199, pp. 609–618. [22] hsu, y.-t., jiang, h.-y., yen, h.-w., lin, h.-c., hong, s. (2020). hydrogen-induced embrittlement of nickelchromium-molybdenum containing hsla steels, j. chinese inst. eng., 43(1), pp. 58-66. [23] shi, x., yan, w., wang, w., shan, y., yang, k. (2016). novel cu-bearing high-strength pipeline steels with excellent resistance to hydrogen-induced cracking, mater. des., 92, pp. 300-305. [24] lin, l., li, b., zhu, g., kang, y., liu, r. (2018). effect of niobium precipitation behavior on microstructure and hydrogen induced cracking of press hardening steel 22mnb5, mater. sci. eng. a, 721, pp. 38-46. [25] gonzález-velázquez, j.l., entezari, e., szpunar, j.a. (2022). on the assessment of non-metallic inclusions by part 13 of api 579-1/asme ffs-1 2016., frat. e integrita strutt., (59). [26] turk, a., san martín, d., rivera-díaz-del-castillo, p.e.j., galindo-nava, e.i. (2018). correlation between vanadium carbide size and hydrogen trapping in ferritic steel, scr. mater., 152, pp. 112-116. [27] mohtadi-bonab, m.a., eskandari, m. (2017). a focus on different factors affecting hydrogen induced cracking in oil and natural gas pipeline steel, eng. fail. anal., 79, doi: 10.1016/j.engfailanal.2017.05.022. [28] li, x., xie, f., wang, d., xu, c., wu, m., sun, d., qi, j. (2018). effect of residual and external stress on corrosion behaviour of x80 pipeline steel in sulphate-reducing bacteria environment, eng. fail. anal., 91, pp. 275-90. [29] traidia, a., chatzidouros, e., jouiad, m. (2018). review of hydrogen-assisted cracking models for application to service lifetime prediction and challenges in the oil and gas industry, corros. rev., 36(4), pp. 323-47. [30] boellinghaus, t., hoffmeister, h. (2000). numerical model for hydrogen-assisted cracking, corrosion, 56(06),. [31] hkdh bhadeshia. hkdh bhadeshia.(n.d.). materials algorithms project. available at: https://www.phase-trans.msm.cam.ac.uk/map/steel/programs/mucg83.html. [32] sente software ltd. sente software ltd.(n.d.). jmatpro®. available at: http://www.jmatpro.com. [33] software development kits. software development kits. (n.d.). thermo-calc software ab. available at: http://www.thermocalc.com/ productsservices/software-development-kits. [34] yamashita, t., okuda, k., obara, t. (1999). application of thermo-calc to the developments of high-performance steels, j. phase equilibria, 20(3), pp. 231-237. [35] lin, l.i., yanlin, h.e., de cooman, b.c., wollants, p., huang, s.g., vleugels, j. (2006). computer-aided designing and manufacturing of advanced steels, rare met., 25(5), pp. 407-411. [36] chen, y., zhou, x., huang, j. (2019). chemical component optimization based on thermodynamic calculation of fe1.93 mn-0.07 ni-1.96 cr-0.35 mo ultra-high strength steel, materials (basel)., 12(1), pp. 65. [37] vervynckt, s. (2010). control of the non-recrystallization temperature in high strength low alloy (hsla) steels. [38] liessem, a., knauf, g., zimmermann, s. (2007).strain based design-what the contribution of a pipe manufacturer can be. the seventeenth international offshore and polar engineering conference, onepetro. [39] rosado, d.b., de waele, w., vanderschueren, d., hertelé, s. (2013). latest developments in mechanical properties and metallurgical features of high strength line pipe steels, int. j. sustain. mech. eng. des., 4(1). [40] liu, c., bhole, s.d. (2013). challenges and developments in pipeline weldability and mechanical properties, sci. technol. weld. join., 18(2), pp. 169-181. [41] yoo, j.-y., ahn, s.-s., seo, d.-h., song, w.-h., kang, k.-b. (2011). new development of high grade x80 to x120 pipeline steels, mater. manuf. process., 26(1), pp. 154-160. [42] yang, x.-l., xu, y.-b., tan, x.-d., wu, d. (2015). relationships among crystallographic texture, fracture behavior and charpy impact toughness in api x100 pipeline steel, mater. sci. eng. a, 641, pp. 96-106. [43] (n.d.). substances and technologies, knowledge source on materials engineering. [44] zhang, k., zhu, m., lan, b., liu, p., li, w., rong, y. (2019). the mechanism of high-strength quenching-partitioningtempering martensitic steel at elevated temperatures, crystals, 9(2), pp. 94. [45] entezari, e., mousalou, h., yazdani, s., gonzález-velázquez, j.l., szpunar, j.a. (2022). the evaluation of quenching temperature effect on microstructural and mechanical properties of advanced high strength low carbon steel after e. entezari et alii, frattura ed integrità strutturale, 61 (2022) 20-45; doi: 10.3221/igf-esis.61.02 42 quenching partitioning treatment, procedia struct. integr., 37, pp. 145-52. [46] zhao, j., jiang, z. (2018). thermomechanical processing of advanced high strength steels, prog. mater. sci., 94, pp. 174242. [47] ohaeri, e., omale, j., tiamiyu, a., rahman, k.m.m., szpunar, j. (2018). influence of thermomechanically controlled processing on microstructure and hydrogen induced cracking susceptibility of api 5l x70 pipeline steel, j. mater. eng. perform., 27(9), pp. 4533-4547. [48] hwang, b., kim, y.m., lee, s., kim, n.j., ahn, s.s. (2005). correlation of microstructure and fracture properties of api x70 pipeline steels, metall. mater. trans. a, 36(3), pp. 725-739. [49] min, z. (2010). microstructure and mechanical properties of x80 pipeline steels in different cooling schedules, acta metall. sin. (english lett., 23(3), pp. 171-175. [50] yu, q.b. (2012).effect of cooling rate on microstructures and mechanical properties of x80 pipeline steel. advanced materials research, vol. 535, trans tech publ, pp. 525–528. [51] zhao, j., hu, w., wang, x., kang, j., cao, y., yuan, g., di, h., misra, r.d.k. (2016). a novel thermo-mechanical controlled processing for large-thickness microalloyed 560 mpa (x80) pipeline strip under ultra-fast cooling, mater. sci. eng. a, 673, pp. 373-377. [52] lan, l., chang, z., kong, x., qiu, c., zhao, d. (2017). phase transformation, microstructure, and mechanical properties of x100 pipeline steels based on tmcp and htp concepts, j. mater. sci., 52(3), pp. 1661-1678. [53] lee, d.h., sohn, s.s., song, h., ro, y., lee, c.s., lee, s., hwang, b. (2018). effects of start and finish cooling temperatures on the yield strength and uniform elongation of strain-based api x100 pipeline steels, metall. mater. trans. a, 49(10), pp. 4536-4543. [54] nafisi, s., arafin, m.a., collins, l., szpunar, j. (2012). texture and mechanical properties of api x100 steel manufactured under various thermomechanical cycles, mater. sci. eng. a, 531, pp. 2-11. [55] zhou, x., zeng, c., yang, h., ma, l., liu, z., wu, d., wang, g. (2016). effect of cooling process on microstructure and mechanical properties of x100 pipeline steel, steel res. int., 87(10), pp. 1366-1375. [56] takeuchi, i., makino, h., okaguchi, s., takahashi, n., yamamoto, a. (2006).crack arrestability of high-pressure gas pipelines by x100 or x120. 23rd world gas conference, amsterdam, citeseer, pp. 1-16. [57] morozov, y.d., simbukhov, i.a., dyakonov, d.l. (2012). study of microstructure and properties of ultrahigh-strength pipe steel of strength category x120 prepared under laboratory conditions, metallurgist, 56(7), pp. 510-518. [58] garcia, c.i., hua, m.j., liang, x., suikannen, p., deardo, a.j. (2012).on the microstructure of plate steels for api-5l x120 applications. materials science forum, vol. 706, trans tech publ, pp. 17-23. [59] garcia, c.i. (2017).high strength low alloyed (hsla) steels. automotive steels, elsevier, pp. 145-167. [60] bannenberg, n., streißelberger, a., schwinn, v. (2007). new steel plates for the oil and gas industry, steel res. int., 78(3), pp. 185-188. [61] contreras, a., lópez, a., gutiérrez, e.j., fernández, b., salinas, a., deaquino, r., bedolla, a., saldaña, r., reyes, i., aguilar, j. (2020). an approach for the design of multiphase advanced high-strength steels based on the behavior of cct diagrams simulated from the intercritical temperature range, mater. sci. eng. a, 772, pp. 138708. [62] lan, h.f., du, l.x., li, q., qiu, c.l., li, j.p., misra, r.d.k. (2017). improvement of strength-toughness combination in austempered low carbon bainitic steel: the key role of refining prior austenite grain size, j. alloys compd., 710, pp. 702-710. [63] entezari, e., avishan, b., mousalou, h., yazdani, s. (2018). effect of electro slag remelting (esr) on the microstructure and mechanical properties of low carbon bainitic steel, kov. mater, 56, pp. 253-263. [64] wu, q., zikry, m.a. (2015). dynamic fracture predictions of microstructural mechanisms and characteristics in martensitic steels, eng. fract. mech., 145, pp. 54-66. [65] kim, s., kwon, j., kim, y., jang, w., lee, s., choi, j. (2013). factors influencing fatigue crack propagation behavior of austenitic steels, met. mater. int., 19(4), pp. 683-690. [66] sami, z., tahar, s., mohamed, h. (2014). microstructure and charpy impact properties of ferrite–martensite dual phase api x70 linepipe steel, mater. sci. eng. a, 598, pp. 338-342. [67] simm, t., sun, l., mcadam, s., hill, p., rawson, m., perkins, k. (2017). the influence of lath, block and prior austenite grain (pag) size on the tensile, creep and fatigue properties of novel maraging steel, materials (basel)., 10(7), pp. 730. [68] ym, k., nj, k. (2002). effect of microstructure on the yield ratio and low temperature toughness of linepipe steels, isij int., 42(12), pp. 1571-1577. [69] qi, x.y., du, l.x., hu, j., misra, r.d.k. (2018). high-cycle fatigue behavior of low-c medium-mn high strength steel with austenite-martensite submicron-sized lath-like structure, mater. sci. eng. a, 718, pp. 477-482. e. entezari et alii, frattura ed integrità strutturale, 61 (2022) 20-45; doi: 10.3221/igf-esis.61.02 43 [70] nace international the corrosion society. (2015). nace mr0175: materials for use in h2s-containing environments in oil and gas production. [71] hwang, y.-i., kim, h.-j., song, s.-j., lim, z.s., yoo, s.-w. (2017). improving the ultrasonic imaging of hydrogeninduced cracking using focused ultrasound, j. mech. sci. technol., 31(8), pp. 3803-3809. [72] findley, k.o., o'brien, m.k., nako, h. (2015). critical assessment 17: mechanisms of hydrogen induced cracking in pipeline steels, mater. sci. technol., 31(14), pp. 1673-1680. [73] dunne, d.p., hejazi, d., saleh, a.a., haq, a.j., calka, a., pereloma, e. v. (2016). investigation of the effect of electrolytic hydrogen charging of x70 steel: i. the effect of microstructure on hydrogen-induced cold cracking and blistering, int. j. hydrogen energy, 41(28), pp. 12411-12423. [74] laureys, a., pinson, m., depover, t., petrov, r., verbeken, k. (2020). ebsd characterization of hydrogen induced blisters and internal cracks in trip-assisted steel, mater. charact., 159, pp. 110029. [75] li, j., gao, x., du, l., liu, z. (2017). relationship between microstructure and hydrogen induced cracking behavior in a low alloy pipeline steel, j. mater. sci. technol., 33(12), pp. 1504-1512. [76] park, j.h., oh, m., kim, s.j. (2017). effect of bainite in microstructure on hydrogen diffusion and trapping behavior of ferritic steel used for sour service application, j. mater. res., 32(7), pp. 1295-1303. [77] shahzad, m., tayyaba, q., manzoor, t., ud-din, r., subhani, t., qureshi, a.h. (2018). the effects of martensite morphology on mechanical properties, corrosion behavior and hydrogen assisted cracking in a516 grade steel, mater. res. express, 5(1), pp. 16516, doi: 10.1088/2053-1591/aaa55f. [78] ohaeri, e., omale, j., rahman, k.m.m., szpunar, j. (2020). effect of post-processing annealing treatments on microstructure development and hydrogen embrittlement in api 5l x70 pipeline steel, mater. charact., 161, pp. 110124, doi: 10.1016/j.matchar.2020.110124. [79] zhu, x., li, w., hsu, t.y., zhou, s., wang, l., jin, x. (2015). improved resistance to hydrogen embrittlement in a highstrength steel by quenching-partitioning–tempering treatment, scr. mater., 97, pp. 21-24, doi: 10.1016/j.scriptamat.2014.10.030. [80] liu, z.y., wang, x.z., du, c.w., li, j.k., li, x.g. (2016). effect of hydrogen-induced plasticity on the stress corrosion cracking of x70 pipeline steel in simulated soil environments, mater. sci. eng. a, 658, pp. 348-354. [81] xue, h.b., cheng, y.f. (2011). characterization of inclusions of x80 pipeline steel and its correlation with hydrogeninduced cracking, corros. sci., 53(4), pp. 1201-1208. [82] rahman, k.m.m., qin, w., szpunar, j.a., kozinski, j., song, m., zhu, n. (2021). new insight into the role of inclusions in hydrogen-induced degradation of fracture toughness: three-dimensional imaging and modeling, philos. mag., 101(8), pp. 976-996. [83] rahman, k.m.m., mohtadi-bonab, m.a., ouellet, r., szpunar, j., zhu, n. (2019). effect of electrochemical hydrogen charging on an api x70 pipeline steel with focus on characterization of inclusions, int. j. press. vessel. pip., 173, pp. 147-155. [84] miyoshi, e., tanaka, t., terasaki, f., ikeda, a. (1976). hydrogen-induced cracking of steels under wet hydrogen sulfide environment. [85] qin, w., szpunar, j.a. (2017). a general model for hydrogen trapping at the inclusion-matrix interface and its relation to crack initiation, philos. mag., 97(34), pp. 3296-3316. [86] domizzi, g., anteri, g., ovejero-garcıa, j. (2001). influence of sulphur content and inclusion distribution on the hydrogen induced blister cracking in pressure vessel and pipeline steels, corros. sci., 43(2), pp. 325-339. [87] beidokhti, b., dolati, a., koukabi, a.h. (2009). effects of alloying elements and microstructure on the susceptibility of the welded hsla steel to hydrogen-induced cracking and sulfide stress cracking, mater. sci. eng. a, 507(1-2), pp. 167173. [88] liou, h.-y., shieh, r.-i., wei, f.-i., wang, s.-c. (1993). roles of microalloying elements in hydrogen induced cracking resistant property of hsla steels, corrosion, 49(05). [89] zhang, s., fan, e., wan, j., liu, j., huang, y., li, x. (2018). effect of nb on the hydrogen-induced cracking of highstrength low-alloy steel, corros. sci., 139, pp. 83-96. [90] li, l., song, b., cai, z., liu, z., cui, x. (2019). effect of vanadium content on hydrogen diffusion behaviors and hydrogen induced ductility loss of x80 pipeline steel, mater. sci. eng. a, 742, pp. 712-721. [91] baba, k., mizuno, d., yasuda, k., nakamichi, h., ishikawa, n. (2016). effect of cu addition in pipeline steels on prevention of hydrogen permeation in mildly sour environments, corrosion, 72(9), pp. 1107-1115. [92] mohtadi-bonab, m.a. (2019). effects of different parameters on initiation and propagation of stress corrosion cracks in pipeline steels: a review, metals (basel)., 9(5), pp. 590. [93] lynch, s.p. (2003). mechanisms of hydrogen assisted cracking-a review, hydrog. eff. mater. behav. corros. deform. e. entezari et alii, frattura ed integrità strutturale, 61 (2022) 20-45; doi: 10.3221/igf-esis.61.02 44 interact., pp. 449-466. [94] traidia, a., alfano, m., lubineau, g., duval, s., sherik, a. (2012). an effective finite element model for the prediction of hydrogen induced cracking in steel pipelines, int. j. hydrogen energy, 37(21), pp. 16214-16230. [95] kittel, j., ropital, f., pellier, j. (2008). effect of membrane thickness on hydrogen permeation in steels during wet hydrogen sulfide exposure, corrosion, 64(10), pp. 788-799. [96] kharin, v., toribio, j. (2005).effect of residual stress profile on hydrogen embrittlement susceptibility of prestressing steel. anales de mecánica de la fractura, vol. 22, citeseer, pp. 464-469. [97] jack, t.a., pourazizi, r., ohaeri, e., szpunar, j., zhang, j., qu, j. (2020). investigation of the hydrogen induced cracking behaviour of api 5l x65 pipeline steel, int. j. hydrogen energy, 45(35), pp. 17671-17684. [98] javadi, y., sweeney, n.e., mohseni, e., macleod, c.n., lines, d., vasilev, m., qiu, z., mineo, c., pierce, s.g., gachagan, a. (2021). investigating the effect of residual stress on hydrogen cracking in multi-pass robotic welding through process compatible non-destructive testing, j. manuf. process., 63, pp. 80-87. [99] zapffe, c.a., sims, c.e. (1941). hydrogen embrittlement, internal stress and defects in steel, trans. aime, 145(1941), pp. 225-271. [100] oriani, r.a. (1972). a mechanistic theory of hydrogen embrittlement of steels, berichte der bunsengesellschaft für phys. chemie, 76(8), pp. 848-857. [101] lynch, s. (2012). hydrogen embrittlement phenomena and mechanisms, corros. rev., 30(3-4), pp. 105-123. [102] beachem, c.d. (1972). a new model for hydrogen-assisted cracking (hydrogen "embrittlement"), metall. mater. trans. b, 3(2), pp. 441-455. [103] robertson, i.m., sofronis, p., nagao, a., martin, m.l., wang, s., gross, d.w., nygren, k.e. (2015). hydrogen embrittlement understood, metall. mater. trans. b, 46(3), pp. 1085-1103. [104] huang, c. (2020). numerical modeling of hydrogen embrittlement. [105] sofronis, p., liang, y., aravas, n. (2001). hydrogen induced shear localization of the plastic flow in metals and alloys, eur. j. mech., 20(6), pp. 857-872. [106] liang, y., sofronis, p., aravas, n. (2003). on the effect of hydrogen on plastic instabilities in metals, acta mater., 51(9), pp. 2717-2730. [107] gerberich, w.w. (1974). effect of hydrogen on high-strength and martensitic steels, hydrog. met., pp. 115-147. [108] gerberich, w.w., chen, s. (1990).environment-induced cracking of metals, fundamental processes: micromechanics. proceedings of the first international conference on environment-induced cracking of metals,(houston, tx: nace, 1989), pp. 167-187. [109] gonzález-velázquez, j.l. (2020). a practical approach to fracture mechanics, elsevier. [110] diniz, d., silva, e., carrasco, j., barbosa, j., silva, a. (2014). effect of reversible hydrogen trapping on crack propagation in the api 5ct p110 steel-a numerical simulation, int. j. multiphys., 8(3), pp. 313-324. [111] mcnabb, a., foster, p.k. (1963). a new analysis of diffusion of hydrogen in iron and ferritic steels, trans. metall. soc. aime, 227(3), pp. 618. [112] balueva, a. (2014). modeling of hydrogen embrittlement cracking in pipelines under high pressures, procedia mater. sci., 3, pp. 1310-1315. [113] traidia, a., el-sherik, a.m., duval, s., lubineau, g., el-yagoubi, j. (2014). model of parameters controlling resistance of pipeline steels to hydrogen-induced cracking, corrosion, 70(1), pp. 87-94. [114] gonzalez jl, rivas d, dorantes h, vazquez p, g.w. (2015).modeling and simulation of cracked area growth rate of hydrogen-induced cracking in pipeline steels. 10th international symposium on advanced science and technology in experimental mechanics-japan. [115] brouwer, r.c., de mul, l.m., van den handel, g. (1995). modelling hydrogen induced crack growth: validation by comparison with experiment, nace international, houston, tx (united states). [116] hara, t., asahi, h., ogawa, h. (2004). conditions of hydrogen-induced corrosion occurrence of x65 grade line pipe steels in sour environments, december 2004, corrosion, 60 (12). nomenclature a austenite acc accelerated cooling aide adsorption-induced dislocation emission e. entezari et alii, frattura ed integrità strutturale, 61 (2022) 20-45; doi: 10.3221/igf-esis.61.02 45 cct continuous cooling transformation f ferrite frt finishing rolling temperature fct finishing cooling temperature gb globular bainite hede hydrogen enhanced decohesion help hydrogen-enhancedlocalized plasticity hic hydrogeninduced plasticity hpt hydrogen pressure mechanism hop heat treatment online process hsla high strength low alloy steel m martensite ms martensite start temperature mf martensite finish temperature nmi nonmetallic inclusions ph2s hydrogen partial pressure ssc stress sulfide corrosion sohic stress-orientated hydrogen-induced cracking tlm tempered lath martensite tmcp thermomechanical control process ttt 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can be opened with acrobat and adobe reader 5.0 and later.) >> /namespace [ (adobe) (common) (1.0) ] /othernamespaces [ << /asreaderspreads false /cropimagestoframes true /errorcontrol /warnandcontinue /flattenerignorespreadoverrides false /includeguidesgrids false /includenonprinting false /includeslug false /namespace [ (adobe) (indesign) (4.0) ] /omitplacedbitmaps false /omitplacedeps false /omitplacedpdf false /simulateoverprint /legacy >> << /addbleedmarks false /addcolorbars false /addcropmarks false /addpageinfo false /addregmarks false /convertcolors /converttocmyk /destinationprofilename () /destinationprofileselector /documentcmyk /downsample16bitimages true /flattenerpreset << /presetselector /mediumresolution >> /formelements false /generatestructure false /includebookmarks false /includehyperlinks false /includeinteractive false /includelayers false /includeprofiles false /multimediahandling /useobjectsettings /namespace [ (adobe) (creativesuite) (2.0) ] /pdfxoutputintentprofileselector /documentcmyk /preserveediting true /untaggedcmykhandling /leaveuntagged /untaggedrgbhandling /usedocumentprofile /usedocumentbleed false >> ] >> setdistillerparams << /hwresolution [2400 2400] /pagesize [612.000 792.000] >> setpagedevice microsoft word numero_46_art_26 l. sorrentino et alii, frattura ed integrità strutturale, 46 (2018) 285-294; doi: 10.3221/igf-esis.46.26 285 performance index of natural stones-gfrp hybrid structures luca sorrentino, costanzo bellini, wilma polini, sandro turchetta university of cassino and southern lazio, department of civil and mechanical engineering, italy luca.sorrentino@unicas.it, http://orcid.org/0000-0002-5278-7357 costanzo.bellini@unicas.it, http://orcid.org/0000-0003-4804-6588 wilma.polini@unicas.it, http://orcid.org/0000-0002-6839-3889 sandro.turchetta@unicas.it, http://orcid.org/0000-0002-8365-8910 abstract. natural stone is a material that presents durableness over time and high aesthetic characteristic, but it is brittle and its tensile strength is significantly lower than compressive one: these peculiarities must be taken into account for material usage; in fact, for applications requiring high flexural and tensile strength, as thin sections or long spans, the particular mechanical behavior of the natural stone constitutes an issue to be overcome. a solution to the above mentioned problem is presented in the present paper: a natural stone tile is reinforced by bonding a sandwich structural laminate made of composite materials. in such manner, a double result is obtained: the mechanical strength increment and the and the tile specific weight decrement. in particular, two different types of sandwich structures, made of glass/epoxy laminates and honeycomb or foam core, were bonded to the lower surfaces of marble and granite tiles; then, 3-point bending tests were carried out on specimens extracted from the produced hybrid tiles. a performance index, considering both strength and weight of tiles, was introduced and the comparison with specimens extracted from traditional unreinforced tiles demonstrated that the considered reinforcement increases the structural characteristics of stone tiles up to an order of magnitude. keywords. natural stones; glass/epoxy sandwich laminate; 3-point bending test; structural behavior improvement. citation: sorrentino, l., bellini, c., polini, w. and turchetta, s., performance index of natural stones-gfrp hybrid structures, frattura ed integrità strutturale, 46 (2018) 285-294. received: 22.06.2018 accepted: 08.08.2018 published: 01.10.2018 copyright: © 2018 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. introduction or a long time, construction and in building furniture use natural stone. only recently, the aesthetic properties of the stone are exploited to decorate the environments. all these applications are limited by the brittle nature and the consequent defects of the stone. in fact, the strength of stone in tension is considerably less than its strength in compression, the compressive strength of a rock exceeds its tensile strength by one to three orders of magnitude typically. this disparity limits the use of stone for long spans or thin sections, where tensile and flexural strength capacity is required. f http://www.gruppofrattura.it/va/46/26.mp4 l. sorrentino et alii, frattura ed integrità strutturale, 46 (2018) 285-294; doi: 10.3221/igf-esis.46.26 286 the durability and the strength of stone are affected by mechanical and chemical weathering processes. the atmosphere, water, dissolved salts, acid rain and temperature fluctuations act as agents of decay, inflicting visible damage to stone as a decay, as demonstrated by winkler [1]. cohen and monteiro [2] showed that limestone and granite are affected by weathering agents and are particularly susceptible to superficial dissolution caused by carbon dioxide (co2), sulfur dioxide (so2) and nitric acid (nox) dissolved in water as acid rain. it is evident that the weathering results in a loss of strength in natural stone. reinforcement provides stone members with flexural strength required for use in long spans, columns and slabs. however, in some cases, reinforced stone may fail to perform to its desired capacity because of faulty design, use of inferior materials, poor construction practices and insufficient maintenance. if such a problem occurs early in a structure's service life, repair and strengthening of the concrete sections may be more favorable than replacement or reconstruction of the failing members. at the beginning of the second half of the last century, the use of external steel reinforcing to strengthen existing concrete bridges and buildings was investigated by researchers in south africa and france. thin steel plates were bonded with epoxy to the tension face of concrete beams to provide additional local stiffness. subsequently, mays [3] applied this technique to reinforce concrete members in europe, the united kingdom, japan, new zeland, south africa and the united states. since steel plates are readily available and relatively inexpensive, repair of structures by externally bonded reinforcement is an attractive alternative to replacement. however, corrosion of the external metal plate remains a problem. a wide variety of civil engineering applications sees the introduction of fibre-reinforced polymers (frps). neale [4] found these materials to be particularly attractive for applications involving the strengthening and rehabilitation of existing structures. composite materials were proposed as a corrosion-resistant alternative to external steel reinforcement of concrete members. iyer et al. [5] used sheets of graphite fibers in an epoxy matrix to strengthen cracked concrete beams in an existing bridge. also, saadatmanesh and ehsani [6] showed that glass fiber composites, well bonded with epoxy to concrete beams, double the ultimate capacity of the beams also employed to increase strength and ductility with encouraging results in terms of mechanical behavior and cost effectiveness. recently it was investigated by sisti et al. [7] and aiello et al. [8] a new type of reinforcement for historic masonry buildings made by recycled old stone or bricks with gfrp grits, that demonstrated to improve the bending capacity of the structure. external composite reinforcement was infrequently applied to natural stone, as demonstrated by kurtis and dharan [9]. to determine the effect of external reinforcement on the load-carrying capacity of two types of stone, 3-point bend tests were performed on marble and travertine marble (actually a limestone) reinforced with hs carbon fibers in an epoxy matrix. the results show how the load capacity of the stone may be increased of about 5-10 times. in a previous work, polini et al. [10] investigated the use of external composite reinforcement on natural stone. it involved the production of a hybrid structure “natural stone/composite” very thin, the use of less expensive composite materials, such as glass fiber, and the comparison between two natural stones that are largely used for decorative application, marble and granite. the results demonstrated that the load capacity of the stone can be increased by a factor of 7 and 6 for granite and marble respectively. in another work, bellini et al. [11] created a new hybrid structure, in which the thin laminate made of composite material was substituted with a sandwich structure. in this work, sandwich structural laminates based on composite materials are used as external reinforcement both to increase the mechanical resistance and to decrease weight of natural stone. high strength glass/epoxy laminates were bonded to the lower surfaces of marble and granite beams, and 3-point bend tests were performed on both reinforced and unreinforced specimens. such reinforcement is useful to increase low initial tensile strength or to restore strength lost by weathering. an increase in strength can result in the use of longer spans and thinner sections, decreasing dead load. therefore, the use of external composite reinforcement of natural stone in application such as exterior cladding, flooring, countertops, and desktops can result in weight saving and possible cost saving. the materials and the methods to produce the specimens are deeply described in the next sections; then, the test to mechanically characterize the stone-composite sandwich specimens are deeply discussed and the obtained results are presented and analyzed. materials and methods n this work, the new hybrid material was constituted by a sandwich structural laminate in composite materials glued to a stone tile. two kinds of sandwiches were considered: the first one was self-produced by gluing two composite skins to a diab divinycell p60 core, the second one was a commercial sandwich of hexcel corporation, that is i l. sorrentino et alii, frattura ed integrità strutturale, 46 (2018) 285-294; doi: 10.3221/igf-esis.46.26 287 called fibrelam® grade 5. the first core material chosen for the core was the diab divinycell p60 panel, that is made of a recyclable closed cell thermoplastic foam. it is addressed to public transport, industrial applications and wind applications, since it offers excellent fst properties (fire and toxicity of fumes), resistance to high temperatures, good thermal insulation and low water absorption. it also offers good mechanical properties, such as excellent resistance to chemical agents and a very low density of 60 kg/m3. this core is compatible with any type of resin, polyester, vinylester, epoxy and it can be used with most prepregs because it resists up to the temperature of 150 °c, so there are no problems for the prepreg oven polymerization. it was used a panel of 8 mm thickness. the composite skins were constituted by glass fiber/epoxy matrix prepreg fabric. the composite fabric consisted of fibers woven at [0/90]; thirteen fabrics were overlapped and cured at a temperature of 125°c for 90 minutes by means of vacuum bagging in autoclave to obtain a board thickness of about 2 mm, so the total thickness of the sandwich structure was 12 mm. composite material density is 1850 kg/m3; moreover, this material has a compressive strength of 650 mpa and a tensile strength of 1750 mpa. the other core material was the fibrelam®, that is made of unidirectional glass fiber skins with a cross pattern of thickness 0.38 mm glued to an aramid alveolar panel to have a total sandwich thickness of about 10 mm. it has excellent resistance to compression (5.5 mpa) and to impact (4.5 nm), that are compatible with stone application. the fibrelam® has a remarkable stiffness, testified by a maximum deformation of 0.8 mm/m, which allows the sandwich structure to be used without any support and a flames extinguish time of 4 seconds after a 60-second exposure; its density is 2.5 kg/m2. perlato royal of coreno and absolute black granite were the natural stones chosen for the tiles. perlato royal of coreno is characterized by a high strength to wear and to impact that together to its resistance to weather agents carried out to be used for buildings. it has a density of 2650 kg/m3; it has a compressive strength of 166 mpa and a tensile strength of 10 mpa. the absolute black granite is very hard and since it is available in small volumes, it has a great commercial value. it has a density of 3030 kg/m3; it has a compressive strength of 295 mpa and a tensile strength of 27 mpa. two adhesives were used to bond the self-produced composite sandwich to stone tiles: the scotch-weldtm ec-2216 b/a gray of 3mtm and the scotch-weldtm af163-2k of 3mtm. the first is an epoxy resin scotch-weldtm ec-2216 b/a gray of 3mtm, whose polymerization time is 7 days at 24°c, 2 hours at 66°c and 30 minutes at 93 °c. it is commonly used for composite material and it is suitable for aerospace applications. the second adhesive is a thermosetting epoxy resin scotch-weldtm af163-2k of 3mtm, which occurs as a veil. it polymerizes in 90 minutes at 107.2 °c. the commercial sandwich hexcel fibrelam® was glued to stone only by means of the resin scotch-weldtm af163-2k of 3mtm, since it allows to reach the best geometrical precision in gluing, so taking full advantage of the high precision of the commercial sandwich. all the samples manufactured are shown in tab. 1, five repetitions were carried out for each parameter combination. after bonding to sandwich panels, each hybrid tile was cut with a diamond saw to produce samples measuring 40 mm x 200 mm for 3-point bending tests. the 3-point bend test was considered for evaluating the structural properties of the obtained samples, according to the uni en 12372 standard for stone products. in detail, the width of the sample should be between 25 mm and 100 mm and it has to be twice the size of the largest grain in the stone. the sample length should be six times its thickness, while the distance between the two pins that sustain the sample should be five times its thickness. factor # levels level value stone type 2 coreno perlato royal, absolute black granite stone thickness [mm] 3 3,4,6 core type 2 diab p60, fibrelam grade 5 adhesive type 2 ec-2216, af163-2k table 1: experimental plan. process to prepare the sample with core diab p60 and ec-2216 adhesive three marble tiles and three granite tiles, whose dimensions were 200 mm x 200 mm x 10 mm, were brushed on the raw side by means of an abrasive paper and, then, they were cleaned by a cloth soaked in ethylic alcohol. the same operations were repeated on the composite laminate of 2.2 mm thickness, once cut through a band-saw at 205 mm x 205 mm. a l. sorrentino et alii, frattura ed integrità strutturale, 46 (2018) 285-294; doi: 10.3221/igf-esis.46.26 288 panel of core diab p60 was cut to obtain six samples of 203 mm x 203 mm, their thickness was reduced from 20 mm to 8 mm by a vertical sawing machine and, then, theirs surfaces were cleaned through a jet of compressed air. now, the adhesive was applied on a raw side of the stone, both sides of the composite laminate and both sides of the core diab p60 in a uniform way (see fig. 1). therefore, the stone was assembled to the composite sandwich and the obtained sample was put into some clamps in order to avoid the development of air bubbles and the leak of adhesive at the interface due to the excessive pressure. the samples were polymerized at room temperature for 120 minutes and at 63° c into an oven for further 120 minutes. process to prepare the sample with core diab p60 and af163-2k adhesive three marble tiles and three granite tiles, whose dimensions were 200 mm x 200 mm x 10 mm, were brushed on the raw side by means of an abrasive paper and, then, they were cleaned by a cloth soaked in ethylic alcohol. the same operations were repeated on the composite laminate of 2.2 mm thickness, once cut through a band-saw at 205 mm x 205 mm. a panel of core diab p60 was cut to obtain six samples of 203 mm x 203 mm, their thickness was reduced from 20 mm to 8 mm by a milling machine and, then, theirs surfaces were cleaned through a jet of compressed air. now, a film of adhesive was taken out the freezer and kept at room temperature for two hours. then, it was cut at the dimensions of the tile and it was applied on the stone surface; then the composite laminate was put on the other side of the adhesive film. another piece of adhesive was applied on the free composite laminate surface and the core diab p60 was put on the other side of the adhesive. a final piece of adhesive was applied to the free core surface and another composite laminate was put on the other side of the adhesive film. the obtained samples were put into a vacuum bag (see fig. 2), previously lined with breather in order to support the vacuum distribution around the samples. the bag was sealed and the air was inhaled up to a pressure of 0.50 bar. now, the bag was put into the oven and the temperature was increased of 4.95 °c per minute for twenty minutes, up to arrive at 135 °c; then, the temperature was kept constant for 1 hour. finally, the oven was turned off and the bag was kept in pressure till the temperature reached 65°c. figure 1: sample with core diab p60 and ec-2216 adhesive. figure 2: process scheme for the manufacturing of sandwich structure with core diab p60 and af163-2k adhesive. l. sorrentino et alii, frattura ed integrità strutturale, 46 (2018) 285-294; doi: 10.3221/igf-esis.46.26 289 process to prepare the sample with fibrelam® and af163-2k adhesive three marble tiles and three granite tiles, whose dimensions were 200 mm x 200 mm x 10 mm, were brushed on the raw side by means of an abrasive paper and, then, they were cleaned by a cloth soaked in ethylic alcohol. the same operations were repeated on the hexcel fibrelam® panels, once cut through a band-saw at 205 mm x 205 mm. now, a film of adhesive was taken out the freezer and kept at room temperature for two hours. then, it was cut at the dimensions of the tile and it was applied on the stone surface; then the fibrelam® panel was put on the other side of the adhesive film (see fig. 3). the obtained samples were put into a vacuum bag (see fig. 4), previously lined with breather in order to support the vacuum distribution around the samples. the bag was sealed and the air was inhaled up to a pressure of 0.50 bar. now, the bag was put into the oven and the temperature was increased of 4.95 °c per minute for twenty minutes, up to arrive at 135 °c; then, the temperature was kept constant for 1 hour. finally, the oven was off and the bag was kept in pressure till the temperature reached 65 °c. figure 3: sample with core hexcel fibrelam® and af163-2k adhesive. figure 4: process scheme for the manufacturing of sandwich structure with core fibrelam® and af163-2k adhesive. results discussion n instron® machine was used to perform 3-point bending test on the specimens manufactured as described above, see fig. 5. the samples were tested in an unconditioned state at room temperature. results from the 3point bending tests are presented in tab. 2. figs. 6-8 show an example of load trend vs displacement in 3-point bend test of samples with a stone tile of 3 mm thickness. three points bending tests results show that the samples with the core diab p60 reached an average maximum load higher than that of samples with the core hexcel fibrelam®. moreover, in figs. 6-8 deflection before failure of the sample with the core hexcel fibrelam® is higher than that of the samples reinforced with the core diab p60, that makes more rigid the sample. if af163-2k adhesive is used instead of ec-2216, the samples reinforced with the core diab p60 show an average maximum load higher of about 0.2-0.5 kn, once fixed the stone type and thickness; this is probably due to, in addition to the best mechanical performances of the adhesive, also and above all to its uniform thickness. a l. sorrentino et alii, frattura ed integrità strutturale, 46 (2018) 285-294; doi: 10.3221/igf-esis.46.26 290 the mechanical performances of the samples increase slightly as the thickness of the stone increases, once fixed the type of stone and adhesive; this is probably due to the fact that stone is as more rigid as greater is its thickness, stiffness that limits the deflection to failure of the samples. among the samples with core diab p60 and adhesive af163-2k that with the highest value of the average maximum load has a marble or granite thickness of 6 mm; it presents a load to bend of about 3.9 kn or 4.8 kn for marble and granite respectively that is 150% or 60% more than the corresponding sample in marble or granite only (see tab. 2). figs. 6-8 show how the deflection before failure of the samples with granite is higher than those with marble, that is due to the greater resistance and homogeneity of the granite compared to the marble. a) b) figure 5: example of 3-point bend test: a) granite with diab® core; b) marble with fibrelam® core. tab. 3 reports the weights, with the same total thickness, of the sandwich structure samples compared to the same ones in marble or granite. as can be seen from the table, the lightest samples have a core of hexcel fibrelam®, since this panel has a weight of 2.5 kg/m2 compared to 9.5 kg/m2 of the sandwich structure constituted by the diab p60 core and the two glass fiber laminates. the lightest sample, that has a marble tile of 3 mm thickness and a hexcel fibrelam® core, has a weight of 11.12 kg/m2 that is about 3 times lower than that of the same sample of marble. the heaviest panel, that has a granite tile of 6 mm thickness and a diab p60 core, weights 28.14 kg/m2 compared to 54.54 kg/m2 of the same sample in granite only. therefore, considering the ratio between flexural load and weight, that is called performance index pi, it can be seen that the sandwich structures have a pi from 2 to 5 times higher than that of the stone sample with the same thickness; in particular, the sandwich structure with hexcel fibrelam® panel and a marble tile of 3 mm thickness has a pi equal to 138.35 n*m2/kg compared to 30.64 n*m2/kg of marble sample with the same thickness. figure 6: trend of load vs displacement in 3-point bending test: stone 3mm+adhesive af163-2k+ core hexcel fibrelam® core. l. sorrentino et alii, frattura ed integrità strutturale, 46 (2018) 285-294; doi: 10.3221/igf-esis.46.26 291 stone type core type adhesive stone thickness [mm] loads [kn] hybrid panel loads [kn] stone difference average value standard deviation average value standard deviation perlato coreno marble diab p60 ec-2216 3 2.071 0.092 1.056 0.004 96.12% af163-2k 3 2.244 0.027 1.056 0.004 112.50% fibrelam af163-2k 3 1.539 0.015 0.915 0.003 68.20% absolute black granite diab p60 ec-2216 3 2.392 0.057 2.029 0.012 17.89% af163-2k 3 2.583 0.028 2.029 0.012 27.30% fibrelam af163-2k 3 1.284 0.043 1.758 0.013 -26.98% perlato coreno marble diab p60 ec-2216 4 2.512 0.026 1.201 0.004 109.16% af163-2k 4 3.011 0.024 1.201 0.004 150.71% fibrelam af163-2k 4 2.110 0.037 1.050 0.005 100.79% absolute black granite diab p60 ec-2216 4 3.029 0.017 2.308 0.013 31.24% af163-2k 4 3.480 0.050 2.308 0.013 50.78% fibrelam af163-2k 4 2.335 0.015 2.019 0.012 15.62% perlato coreno marble diab p60 ec-2216 6 3.275 0.149 1.520 0.005 115.46% af163-2k 6 3.905 0.072 1.520 0.005 156.91% fibrelam af163-2k 6 2.769 0.024 1.351 0.003 104.94% absolute black granite diab p60 ec-2216 6 4.372 0.063 2.921 0.017 49.67% af163-2k 6 4.797 0.169 2.921 0.017 64.22% fibrelam af163-2k 6 2.885 0.032 2.596 0.019 11.11% table 2: results of experimental 3-point bending tests. figure 7: trend of load vs displacement in 3-point bending test: stone 3mm+adhesive ec-2216+ core diab p60. l. sorrentino et alii, frattura ed integrità strutturale, 46 (2018) 285-294; doi: 10.3221/igf-esis.46.26 292 figure 8: trend of load vs displacement in 3-point bending test: stone 3mm+adhesive af163-2k+ core diab p60. stone type core type adhesive stone thickness [mm] weight [kg/m2] pi [n*m2/kg] hybrid panel stone diff. hybrid panel stone diff. perlato coreno marble diab p60 ec-2216 3 18.12 39.75 54.42% 114.29 26.55 330% af163-2k 3 18.28 39.75 54.01% 122.76 26.55 362% fibrelam af163-2k 3 11.12 34.45 67.72% 138.35 30.64 352% absolute black granite diab p60 ec-2216 3 20.00 45.45 56.00% 119.58 44.63 168% af163-2k 3 19.61 45.45 56.85% 131.69 44.63 195% fibrelam af163-2k 3 12.50 39.39 68.27% 102.72 51.50 99% perlato coreno marble diab p60 ec-2216 4 20.50 42.40 51.65% 122.52 28.32 333% af163-2k 4 19.67 42.40 53.61% 153.08 28.32 441% fibrelam af163-2k 4 14.62 37.10 60.59% 144.32 32.37 346% absolute black granite diab p60 ec-2216 4 22.43 48.48 53.73% 135.06 47.61 184% af163-2k 4 22.16 48.48 54.29% 157.06 47.61 230% fibrelam af163-2k 4 15.94 42.42 62.42% 146.47 54.41 169% perlato coreno marble diab p60 ec-2216 6 24.70 47.70 48.22% 132.60 31.86 316% af163-2k 6 25.76 47.70 46.00% 151.57 31.86 376% fibrelam af163-2k 6 18.81 42.40 55.64% 147.22 35.85 311% absolute black granite diab p60 ec-2216 6 28.14 54.54 48.40% 155.36 53.56 190% af163-2k 6 27.90 54.54 48.84% 171.95 53.56 221% fibrelam af163-2k 6 21.94 48.48 54.74% 131.50 60.25 118% table 3: pi comparison between sandwich structure and stone. l. sorrentino et alii, frattura ed integrità strutturale, 46 (2018) 285-294; doi: 10.3221/igf-esis.46.26 293 conclusions n order to increase load-carrying capacity of natural stone, an external sandwich structural laminate in composite material can be efficiently glued to a stone tile. among the samples with core diab p60 and adhesive af163-2k that with the highest value of the average maximum stress has a marble or granite thickness of 6 mm; it presents a load to bend of about 3.9 kn or 4.8 kn for marble and granite respectively that is 150% or 60% more than the corresponding sample in marble or granite only. the lightest sample, that has a marble tile of 3 mm thickness and a hexcel fibrelam® core, has a weight of 11.12 kg/m2 that is about 3 times lower than that of the same sample of marble. the heaviest panel, that has a granite tile of 6 mm thickness and a diab p60 core, weights 28.14 kg/m2 compared to 54.54 kg/m2 of the same sample in granite only. therefore, considering the load/weight ratio, that is called performance index pi, it can be seen that the sandwich structures have a pi from 2 to 5 times higher than that of the stone sample with the same thickness; in particular, the sandwich structure with hexcel fibrelam® panel and a marble tile of 3 mm thickness has a pi equal to 138.35 n*m2/ kg compared to 30.64 n*m2 / kg of marble sample with the same thickness. finally, it is possible to conclude that it is convenient to substitute tiles of natural stone of 20 mm or 30 mm thickness with thin stone tiles reinforced with a sandwich structural laminate in composite material. in this way it is possible to resolve some problems that are typical of stone, such as the difficulty of carriage and of assembly, the impossibility to obtain large tile (i.e. 3000 mm x 1500 mm), the excessive brittleness and so on. moreover, it will be possible to apply the natural stone reinforced with composite sandwich panels to nautical and aerospace field, due to the significant reduction in weight, and, therefore, it will be possible to make precious the rooms of yacht and luxurious airplanes. further testing should be done to determine the optimal number of composite fiber plies required to provide adequate mechanical proprieties. such a determination could result in cost savings and increased ductility of the reinforced stone. in addition, the use of smaller thickness of stone should be investigated. finally, an investigation of the effect of external composite reinforcement of stones that have curved shape should be conducted. acknowledgements he authors are grateful to eng. adriano for his valuable research that has given rice for this work. special thanks to tecnavan interiors s.r.l. (aida project to bring innovation in small and medium firms of frosinone district, italy) for providing materials and in particular to mr m. fiorini and mr s. fini. references [1] winkler, e.m (1994). stone in architecture: properties, durability, new york, springer-verlag inc. [2] cohen, j.m. and monteiro, p.j.m. (1991). durability and integrity of marble cladding: a state-of-the-art review, j. perf constr fac. asce, 5(2), pp. 113-124. doi: 10.1061/(asce)0887-3828(1991)5:2(113). [3] mays, g.c. (1985). structural applications of adhesives in civil engineering, mat. sc. techn., 1, pp. 937-943. doi: 10.1179/mst.1985.1.11.937. [4] neale, k.w. (2000). frps for structural rehabilitation: a survey of recent progress, progress in struc. engin. mat., 2(2), pp. 133-138 doi: 10.1002/1528-2716(200004/06)2:2<133::aid-pse16>3.0.co;2-c. [5] iyer, s., silvaramakrishnan, c and atmaram, s. (1989). testing of reinforced concrete bridges for external reinforcement. in: asce (eds), structural material: proceedings of 7th annual structural congress, new york, usa; pp. 116-122. [6] saadatmanesh, h. and ehsani, m.r. (1989). application of fiber-composites in civil engineering. in: asce (eds), structural material: proceedings of 7th annual structural congress, new york, usa, pp. 526-535. [7] sisti r., corradi m. and borri a. (2016). an experimental study on the influence of composite materials used to reinforce masonry ring beams, con. build. mat., 122, pp. 231-241. doi: 10.1016/j.conbuildmat.2016.06.120. [8] aiello, m., micelli, f. and valente, l. (2007). structural upgrading of masonry columns by using composite reinforcements. j. compos. constr., 11(6), pp. 650-658. doi: 10.1061/(asce)1090-0268(2007)11:6(650). [9] kurtis, k.e. and dharan, c.k.h. (1997). composite fibers for external reinforcement of natural stone, j comp. constr., 1(3), pp. 116-119. doi: 10.1061/(asce)1090-0268(1997)1:3(116) i t l. sorrentino et alii, frattura ed integrità strutturale, 46 (2018) 285-294; doi: 10.3221/igf-esis.46.26 294 [10] polini w., sorrentino l., turchetta s. and fiorini m. (2015). polymeric composite laminate to increase the performance of natural stones, int. j.eng. techn., 7(2), pp. 453-460. [11] bellini, c., polini, w., sorrentino, l., turchetta, s. (2018). mechanical performances increasing of natural stones by gfrp sandwich structures, proc. struct. integr., 9, pp. 179-185. doi: 10.1016/j.prostr.2018.06.028 << /ascii85encodepages false /allowtransparency false /autopositionepsfiles true /autorotatepages /none /binding /left /calgrayprofile (dot gain 20%) /calrgbprofile (srgb iec61966-2.1) /calcmykprofile (u.s. web coated \050swop\051 v2) /srgbprofile (srgb iec61966-2.1) /cannotembedfontpolicy /error /compatibilitylevel 1.4 /compressobjects /tags /compresspages true /convertimagestoindexed true /passthroughjpegimages true /createjobticket false /defaultrenderingintent /default /detectblends true /detectcurves 0.0000 /colorconversionstrategy /cmyk /dothumbnails false /embedallfonts true /embedopentype false /parseiccprofilesincomments true /embedjoboptions true /dscreportinglevel 0 /emitdscwarnings false /endpage -1 /imagememory 1048576 /lockdistillerparams false /maxsubsetpct 100 /optimize true /opm 1 /parsedsccomments true 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can be opened with acrobat and adobe reader 5.0 and later.) >> /namespace [ (adobe) (common) (1.0) ] /othernamespaces [ << /asreaderspreads false /cropimagestoframes true /errorcontrol /warnandcontinue /flattenerignorespreadoverrides false /includeguidesgrids false /includenonprinting false /includeslug false /namespace [ (adobe) (indesign) (4.0) ] /omitplacedbitmaps false /omitplacedeps false /omitplacedpdf false /simulateoverprint /legacy >> << /addbleedmarks false /addcolorbars false /addcropmarks false /addpageinfo false /addregmarks false /convertcolors /converttocmyk /destinationprofilename () /destinationprofileselector /documentcmyk /downsample16bitimages true /flattenerpreset << /presetselector /mediumresolution >> /formelements false /generatestructure false /includebookmarks false /includehyperlinks false /includeinteractive false /includelayers false /includeprofiles false /multimediahandling /useobjectsettings /namespace [ (adobe) (creativesuite) (2.0) ] /pdfxoutputintentprofileselector /documentcmyk /preserveediting true /untaggedcmykhandling /leaveuntagged /untaggedrgbhandling /usedocumentprofile /usedocumentbleed false >> ] >> setdistillerparams << /hwresolution [2400 2400] /pagesize [612.000 792.000] >> setpagedevice microsoft word numero 21 articolo 1.doc c. maletta et alii, frattura ed integrità strutturale, 21 (2012) 5-12; doi: 10.3221/igf-esis.21.01 5 indentation response of a niti shape memory alloy: modeling and experiments c. maletta, f. furgiuele, e. sgambitterra dept. of mechanical engineering, university of calabria, 87036 rende (cs), italy. carmine.maletta@unical.it m. callisti, b. g. mellor, r. j.k. wood engineering sciences, university of southampton, uk. mc3a09@soton.ac.uk abstract. the indentation response of a pseudoelastic nickel-titanium based shape memory alloy (sma) has been analyzed. indentation tests have been carried out at room temperature using a spherical diamond tip and indentation loads in the range 50-500 mn in order to promote a large stress-induced transformation zone in the indentation region and, consequently, to avoid local effects due to microstructural variations. the measured load-displacement data have been analyzed to obtain information on the pseudoelastic response of the alloy. to aid this analysis numerical simulations were performed, by using a commercial finite element (fe) software code and a special constitutive model for smas, so as to understand better the microstructural evolution occurring during the indentation process. finally, the fe model has been used to analyze the effects of temperature on the indentation response of the alloy. this analysis revealed a marked variation of both the maximum and residual penetration depths with increasing test temperature. sommario. nel presente lavoro è stata analizzata la risposta all’indentazione di una lega a memoria di forma (sma – shape memory alloy) a base di nickel e titanio. in particolare, sono state eseguite prove di indentazione mediante l’utilizzo di un indentatore sferico e per livelli di carico compresi tra 50 e 500 mn, al fine di favorire la formazione di zone di trasformazione ampie e, pertanto, evitare effetti locali dovuti a variazioni microstrutturali. le curve carico-spostamento sono state analizzate al fine di ottenere informazioni utili per la comprensione del comportamento pseudoelastico della lega. a tale scopo, sono state condotte analisi numeriche, utilizzando un software commerciale agli elementi finiti, per meglio comprendere i cambiamenti microstrutturali, che avvengono durante il processo di indentazione. infine, il modello numerico è stato utilizzato per analizzare l’effetto della temperatura sulla risposta all’indentazione delle smas. i risultati hanno mostrato una marcata variazione della profondità di penetrazione e della profondità residua al variare della temperatura. keywords. shape memory alloys; indentation tests; finite element simulations. introduction ickel-titanium (niti) based shape memory alloys (smas) have, over recent decades, attracted the interest of the scientific and engineering community due to their unique functional properties, namely the pseudoelastic effect (pe) and the shape memory effect (sme) [1], coupled with their good mechanical properties and biocompatibility. the unique functional response of niti alloys is due to a reversible solid state phase transformation between a parent phase (austenite) and a product phase (martensite), the so called thermoelastic martensitic n http://www.gruppofrattura.it http://dx.medra.org/10.3221/igf-esis.21.01&auth=true c. maletta et alii, frattura ed integrità strutturale, 21 (2012) 5-12; doi: 10.3221/igf-esis.21.01 6 transformation (tmt); the latter is a diffusionless phase transition which can be activated either by temperature (thermally-induced martensitic transformation, tim) or by applied stress (stress-induced martensitic transformation, sim) [1]. as a result of these microstructural changes, niti alloys show high recovery capabilities (up to a maximum deformation of 12%), by either raising the temperature of the material above the characteristic transition temperatures (sme) or by removing the mechanical load (pe). however, despite the increasing interest and the efforts of many researchers to understand these unusual mechanisms, the use of niti alloys is currently limited to high-value applications (e.g. medical devices, mems, etc.), due to high raw material and manufacturing costs, the latter resulting from the need to control precisely the processing parameters since the functional and mechanical properties of niti alloys are significantly affected by the thermo-mechanical loading history experienced during manufacturing. the design of niti based components also needs accurate knowledge of the mechanical and functional response of the material, as well as how this evolves during subsequent thermo-mechanical processes. in addition, as most niti components are characterized by complex shape and small size scale (e.g. endovascular stents, micro-surgery devices, mems etc.) their properties cannot be directly obtained from the bulk raw material. thus the use of non-destructive techniques to analyze the mechanical and functional properties of small volumes of material is essential. among the techniques available, nanoindentation is widely used to measure mechanical properties [2], such as hardness, elastic modulus, scratch resistance, creep, etc., of small volumes of materials with negligible damage to the surface. however, despite the aforementioned advantages, various difficulties arise in analyzing the mechanical properties of smas from the indentation response, due to micro-structural changes, such as phase transition and martensite variant re-orientation. in fact, the latter is expected to play a significant role in the indentation response of smas, as this takes place in the indentation region due to the presence of highly localized stresses. as a consequence, well known contact mechanics theories for conventional metals cannot be directly applied to smas and work has been carried out, in recent years, to understand better the effects of microstructural transitions on the indentation response of both thin films [3-8] and bulk specimens [9-15]. these studies revealed marked effects of material composition, as well as the thermo-mechanical treatments carried out during material processing, on the indentation response of smas. in particular, both the mechanical and thermal recovery mechanisms of nanoindents have been analyzed in order to study the pseudoelastic and shape memory capabilities of the alloys, respectively. furthermore, the effects of the test temperature on the indentation response of a pseudoelastic alloy have been analyzed [11] by numerical simulations. in addition, a method to estimate the phase transformation stresses of a pseudoelastic alloy has been proposed in [13], based on comparing the indentation response of the sma with that of a conventional elastic material. finally, cyclic instrumented indentation was carried out in [14] so as to capture the stress-induced phase transition mechanisms from the experimentally measured load-displacement curves. however, notwithstanding the encouraging results obtained recently, considerable research needs to be carried out to elucidate the relationship between the indentation response of smas and their mechanical and functional properties. in this study a commercial pseudoelastic niti alloy (type s, memory metalle, germany) has been analyzed by indentation tests and finite element analysis. in particular, indents have been made at room temperature using a spherical diamond indenter and indentation loads in the range 50-500 mn, in order to promote a large stress-induced transformation zone in the indentation region and, consequently, to avoid local effects due to microstructural variations. experimentally measured force-displacement curves have been analyzed to obtain information on the pseudoelastic response of the alloy. furthermore, finite element (fe) simulations were developed, by using a special constitutive model for smas implemented in a commercial fe software code, to study the microstructural mechanisms occurring during indentation. the fe models have been used to analyze the stress induced transformation zone in the indentation region and systematic analyses have been carried out to understand better the relationship between the nanoindentation response and the typical thermo-mechanical parameters of smas. finally, the fe model has been used to analyze the effects of temperature and transformation stresses, calculated from the clausius-clapeyron relationship, on the indentation response of the alloy. material and methods material commercial pseudoelastic niti sheet (type s, memory metalle, germany), with a nominal chemical composition of 50.8 at.% ni-49.2 at.% ti and thickness t = 1.5 mm, has been used in this investigation. it was supplied in the flat annealed condition. the raw material was first analyzed by differential scanning calorimetry (dsc) and standard tensile tests in order to determine the main thermo-mechanical parameters of the alloy. fig. 1.a illustrates the a http://www.gruppofrattura.it http://dx.medra.org/10.3221/igf-esis.21.01&auth=true c. maletta et alii, frattura ed integrità strutturale, 21 (2012) 5-12; doi: 10.3221/igf-esis.21.01 7 dsc thermogram of the raw material which was obtained at a heating/cooling rate of 1.6 ks-1 in the temperature range 100°c to 100°c. this analysis revealed the presence of a two-stage phase transformation (b2 r b19’) during cooling, with the presence of r-phase (rhombohedral phase), while a single-stage phase transformation (b2 b19’) was observed during heating, as is usual in ni-rich niti alloys. the figure also gives the values of the transformation temperatures (ms, mf, as, af, rs and rf), which have been estimated by the tangent line method; the alloy shows an austenite finish temperature af = 13,7°c, which indicates a fully austenitic structure at room temperature, i.e. the alloy exhibits a pseudoelastic response. fig. 1.b presents a stress-strain curve of the alloy obtained from an isothermal (t = 298 k) displacement controlled loading-unloading cycle up to a maximum deformation of 6.2% which corresponds to the maximum deformation of the stress-strain transformation plateau. the figure also shows the values of the main mechanical parameters of the alloy, young’s moduli (ea and em), transformation stresses  , , ,s f s fam am ma ma    and transformation strain  l , together with the clausius-clapeyron constants  / , /a ma m amc d dt c d dt   , which have been obtained from isothermal tests carried out at different temperatures. (a) (b) figure 1: thermo-mechanical properties of the alloy investigated: a) dsc thermograph with transformation temperatures and b) loading-unloading isothermal stress-strain cycle (298 k). indentation tests the indentation response of the alloy investigated has been determined by using a nanotest 600 (micro materials ltd, united kingdom) nanoindenter. rectangular shaped samples (20 mm x 10 mm), were cut from the as-received sheet and prepared, prior to indentation tests, by grinding with progressively finer silicon carbide papers (#800-#4000), and polishing with 1 m diamond compound; finally, the specimens were cleaned with acetone and dried in air. after the mechanical polishing procedure the specimens were analyzed by a 3-d optical profilometer (infinite focus, alicona, austria) to ensure that the surface finish was within acceptable limits for micro indentation measurements. indentation tests were carried out at room temperature, using a spherical indenter (r=25 m), as a sharp tip indenter (such as berkovich, vickers, etc.), causes high strain gradients immediately beneath the indenter which promote plastic deformation, which inhibits the subsequent reverse transformation from martensite to the parent phase. in fact, previous research [11] has demonstrated that there is no evidence of superelastic recovery upon unloading when a berkovich indenter is used, while a large recovery is observed when using a spherical tip indenter. preliminary indentation tests were performed to identify optimum test parameters, such as maximum load range, loading/unloading rate and dwell time, in order to reduce measurement errors and avoid creep effects on the p-curve. several indents were made at increasing values of maximum load (50, 150, 300 and 450 mn), with a loading/unloading rate of 2.5 mns-1 and a holding time of 60 seconds at the maximum load; furthermore, a set of 20 indentations were carried out for each value of the maximum load, so as to capture the average response of the material, i.e. to analyze different grains of the polycrystalline structure. http://www.gruppofrattura.it http://dx.medra.org/10.3221/igf-esis.21.01&auth=true c. maletta et alii, frattura ed integrità strutturale, 21 (2012) 5-12; doi: 10.3221/igf-esis.21.01 8 finite element modeling inite element analyses (fea) have been carried out, by using a commercial fe software code and a special sma constitutive model [16, 17] in order to study the microstructural evolution during indentation tests as well as to estimate the evolution of the indentation response of the alloy as a function of the test temperature. in particular, two-dimensional axisymmetric fe analyses were carried out by exploiting the axisymmetry of the indenter, while the sample was assumed to be a cylinder with radius equal to 10 times the diameter of the indenter, in order to avoid boundary effects [18]. the model, illustrated in fig. 2, consists of approximately 50400 2d four-noded quadrilateral elements. the figure also illustrates that a very fine mesh has been used to model the contact region in order to capture the high stress gradient and the complex non-linear effects due to plastic deformation and stress-induced transformation mechanisms, in addition to those due to the contact. this model results from a preliminary convergence study, which was developed by analyzing a standard elastic-plastic material; in particular, systematic comparisons between numerical results and elastic-plastic contact theory have been carried out in order to obtain an optimal balance between accuracy and computational efficiency.     figure 2: axisymmetric fe model used to analyze the indentation process. subsequently, the constitutive model for smas, which is directly implemented in the numerical code, was calibrated using the thermo-mechanical parameters illustrated in the previous section, while linear elastic behavior has been adopted for the diamond indenter (elastic constant: e=1141 gpa, =0.07). the numerical results were compared with the experimentally measured load-displacement curves and, subsequently, the influence of test temperature on the indentation response of the sma has been numerically analyzed, as described in the following section. results and discussions preliminary fe analysis reliminary fe studies have been carried out to investigate the phase transition mechanisms in the indentation region as well as to understand better the main differences with respect to conventional elastic-plastic metals. fig. 3.a illustrates the transformation boundaries in the contact region, for a maximum load of 300 mn, which have been obtained from the fe simulations by comparing the von mises equivalent stress with the characteristic transformation stresses of the sma. starting from the outer region, a fully untransformed austenitic zone is observed (a), i.e. where the von mises stress is below the start transformation stress sam  . the area b represents the transformation zone, i.e. von mises stress between sam and f am and consequently the volume fraction of martensite is between 0 and 1. finally, c and d represent the fully transformed martensitic regions, i.e. where the von mises stress is higher than the transformation stress, fam ; however, in c only elastic deformation of the martensitic structure is observed while in d the local stress exceeds the yield stress of martensite and permanent deformation is observed leading to stabilization of the martensite. this stabilized martensite does not revert to austenite on unloading. it is worth noting that the contours in f p http://www.gruppofrattura.it http://dx.medra.org/10.3221/igf-esis.21.01&auth=true c. maletta et alii, frattura ed integrità strutturale, 21 (2012) 5-12; doi: 10.3221/igf-esis.21.01 9 fig. 3.a represent an average estimate of the different regions near the indenter, i.e. they are obtained from the macroscopic stress field and do not take into account the real microstructure of the alloy. in fact, local stress-induced transformation mechanisms, due to different orientations of the martensite variants, and dislocation movement, could occur around the contact region as a consequence of the stress field. fig. 3.b presents a comparison of the indented profile of a sma and an equivalent elastic-plastic material having the same young’s modulus as the austenite phase and a yield stress equal to the start transformation stress y sam  . in particular, the profiles at the maximum load of 300 mn and upon unloading, normalized with respect to the maximum depth, are compared. the figure clearly illustrates a smaller residual depth in the sma after unloading, i.e. it exhibits higher recovery deformation as a consequence of the reversible stress-induced martensitic transformation in the indentation region. in fact, the recovery mechanisms in smas can be attributed to both elastic and pseudoelastic properties. a) b) figure 3: preliminary fe results: a) stress-induced transformation contours near the contact region; b) comparison of the indentation profile between an elastic-plastic material and a sma. indentation tests fig. 4 shows the load-displacement (p-) curves obtained from indentation tests carried out at increasing values of maximum load: 50 mn (a), 150 mn (b), 300 mn (c) and 450 mn (d). it is worth noting that good repeatability of the p-δ curves was observed, especially at higher values of indentation load; this results from an optimal choice of the test parameters. in fact, the load-displacement curves become smoother and differences between repeat tests decrease with increasing indentation load, due to both a reduction in experimental errors and the greater amount of material undergoing phase transformation. the reversible stress-induced phase transition mechanisms are also demonstrated by the pop-out events [18] which occur in the unloading stage. in addition, as observed from the preliminary fe simulations, the residual depth upon unloading is a useful measure of the functional behavior of the sma in terms of its pseudoelastic recovery capability. fig. 5.a shows the values of the maximum depth (hmax), residual depth (hr) and residual depth ratio (hr/hmax) as a function of the indentation load. the figure illustrates that both the residual depth and the residual depth ratio increase with increasing indentation load, which indicate an overall reduction of the pseudoelastic response of the sma due to an increased volume fraction of dislocations and stabilized martensite (region d in fig. 3.a) immediately beneath the indented surface. similar considerations can be made from an energetic point of view, as illustrated in fig. 5.b. specifically, this figure presents the recovery energy (ee), i.e. the energy associated with the unloading path, the dissipated energy (ed), i.e. the area between loading and unloading curve, the total energy (et= ee+ed), the recovery energy ratio (ee/et) and the dissipated energy ratio (ed/et) as a function of the indentation load. the figure clearly shows an increase of both dissipated and recovery energy with increasing indentation load, which indicate an overall increase of both permanent and recovery deformation, as is also illustrated in fig. 5.a. fig. 5.b shows that the difference between the recovery energy and dissipated energy increases gradually with indentation load above 150 mn. this indicates that, although the residual depth increases with increasing load (fig. 5.a) the recovery energy also increases counteracting the energy dissipated in the formation and movement of dislocations. fig. 5.b also demonstrates almost constant values of the dissipated energy ratio and the a: untransformed austenite b: transformation region c: transformed martensite d: stabilized martensite f am  s f am am    s am  http://www.gruppofrattura.it http://dx.medra.org/10.3221/igf-esis.21.01&auth=true c. maletta et alii, frattura ed integrità strutturale, 21 (2012) 5-12; doi: 10.3221/igf-esis.21.01 10 recovery energy ratio for indentation loads above 150 mn. this suggests that the greater amount of material stressed reversibly at higher indentation loads, and thus the greater recovery energy available, balances the increased amount of dissipated energy involved in the indentation process at higher indentation loads. although plastic deformation beneath the indenter reduces the amount of shape recovery this plastically deformed material decreases the stress gradient in the material surrounding the plastically deformed volume favoring the reverse phase transformation. figure 4: single quasi-static indentation tests for different values of maximum load: (a) 50 mn, (b) 150 mn, (c) 300 mn and (d) 450 mn. a) b) figure 5. recovery and residual capability of the sma after unloading: a) depth recovery and b) energy recovery. http://www.gruppofrattura.it http://dx.medra.org/10.3221/igf-esis.21.01&auth=true c. maletta et alii, frattura ed integrità strutturale, 21 (2012) 5-12; doi: 10.3221/igf-esis.21.01 11 effects of test temperature the effects of test temperature on the indentation response of the sma have been analyzed by fe simulations by using the clausius-clapeyron relationship to calculate the relevant transformation stresses. to that end the fe model was first validated by comparison with experimental measurements carried out at room temperature, as it was not possible to perform indentation tests under temperature-controlled conditions. fig. 6 compares the load-displacement curves obtained from fe simulation and experiment for indentation at room temperature to a maximum load of 300 mn. the figure clearly illustrates good agreement between the numerical results and experiments in terms of both maximum depth and residual depth, as well as in terms of the recovery and dissipated energy. figure 6: comparison of the load-displacement curves obtained from fe simulations and experimentally measured (t=293 k, p=300 mn). fig. 7 shows the load-displacement curves obtained for different test temperatures (t=293 k, t=303 k, t=313 k) for an indentation load of 300 mn. as expected, a marked effect of temperature on the indentation response of the sma is observed, in terms of both maximum depth and residual depth, which is a direct consequence of the changes in transformation stresses of the alloy. the evolution of these parameters as a function of temperature and the direct transformation stress  sam for an indentation load of 300 mn is illustrated in fig. 7.b. a) b) figure 7. effects of test temperature on the indentation response of the sma: a) load-displacement curves of the sma at different temperatures; b) maximum depth and residual depth vs temperature and direct transformation stress. the figure shows a reduction of both maximum depth and residual depth with increasing test temperature; however the residual depth decreases more rapidly, which indicates an overall improvement of the pseudoelastic response of the sma http://www.gruppofrattura.it http://dx.medra.org/10.3221/igf-esis.21.01&auth=true c. maletta et alii, frattura ed integrità strutturale, 21 (2012) 5-12; doi: 10.3221/igf-esis.21.01 12 and an associated reduction in the amount of stabilized martensite present resulting from the increase of transformation stresses with temperature. conclusions he indentation response of a pseudoelastic niti shape memory alloy (sma) has been analyzed in this study, by experimental measurements and numerical simulations. single quasi-static indentation tests have been carried out and load-displacement data have been analyzed to obtain valuable information on the pseudoelastic response of the alloy. in addition, numerical simulations have been carried out to understand better the microstructural evolution occurring during the indentation process, as well as to analyze the effects of test temperature on the indentation response of the sma. the main results of this study are summarized as follows:  stress induced transformation mechanisms occur in the indentation region, as demonstrated by the preliminary fe simulations, which significantly affect the indentation response of smas with respect to conventional elastic plastic materials;  a spherical indenter should be used in order to promote a large stress-induced transformation zone in the indentation region and, consequently, to avoid local effects due to microstructural variations. this allows the overall macroscopic response of the alloy to be measured;  the volume fraction of stabilized martensite immediately beneath the indented surface increases with increasing indentation load in single quasi-static tests, which results in an overall reduction of the shape recovery during unloading;  the functional behavior of niti superelastic alloys is clearly governed by an energy balance between martensite formation and the plastic deformation involved in the indentation process.  systematic finite element (fe) studies revealed a significant effect of the test temperature and the corresponding transformation stress on the indentation response of the alloy in terms of both maximum and residual depth. references [1] k. otsuka, x. ren, progr. mater. sci., 50 (2005) 511. [2] w.c. oliver, g.m. pharr, j. material res., 7 (1992) 1564. [3] g. satoh, a. birnbaum, y.l. yao, in: proc. of int. congress on applications of lasers and electro-optics, temecula ca (2008). [4] p.d. tall, s. ndiaye, a.c. beye, z. zong, w.o. soboyejo, h.j. lee, a.g. ramirez, k. rajan, mater. manuf. processes, 22 (2007) 175. [5] a.k. nanda kumar, c.k. sasidharan nair, m.d. kannan, s. jayakumar, mater. chem. phys., 97 (2006) 308. [6] g.a. shaw, w. c. crone, mater res soc symp proc., 791 (2003) 215. [7] w.c. crone, g.a. shaw, d.s. stone, a.d. johnson, a.b. ellis, in: society for experimental mechanics, sem annual conference proceedings, carlotte, nc (2003). [8] g.a. shaw, d.s. stone, a.d. johnson, a.b. ellis, w.c. crone, appl. phys. lett., 83 (2003) 257. [9] c. liu, y.p. zhao, t. yu, mater. design, 26 (2005) 465. [10] c. liu, y. zhao, q. sun, t. yu, z. cao, j. mater. sci., 40 (2005) 1501. [11] a.j. m. wood, t.w. clyne, acta materialia, 54 (2006) 4607. [12] a.j.m. wood, j.h you, t.w. clyne, proc. spie, 5648(39) (2205) 216. [13] w. yan, q. sun, x.q. feng, l. qina, int. j. solids struct., 44 (2007) 1. [14] m. arciniegas, y. gaillard, j. pena, j.m. manero, f.j. gil, intermetallics, 17 (2009) 784. [15] r. liu, d.y. li, y.s. xie, r. llewellyn, h.m. hawthorne, scripta materialia, 41(7) (1999) 691. [16] m. saeedvafa, a constitutive model for shape memory alloys, internal msc report (2002). [17] m. saeedvafa, r.j asaro, la-ur-95-482, los alamos report, (1995). [18] a.c. fisher-cripps, nanoindentation, second edition, springer (2002). t http://www.gruppofrattura.it http://dx.medra.org/10.3221/igf-esis.21.01&auth=true microsoft word numero_63_art_04_3834.docx t. g. sreekanth et alii, frattura ed integrità strutturale, 63 (2023) 37-45; doi: 10.3221/igf-esis.63.04 37 artificial neural network based delamination prediction in composite plates using vibration signals t. g. sreekanth, m. senthilkumar, s. manikanta reddy department of production engineering, psg college of technology, coimbatore-641004, tamilnadu, india. sreekanthtg007@gmail.com, stg.prod@psgtech.ac.in, https://orcid.org/0000-0003-3848-7419 msk.prod@psgtech.ac.in, https://orcid.org/0000-0002-3720-0941 manikantaslv@gmail.com, https://orcid.org/0000-0003-3643-6052 abstract. dynamic loading on composite components may induce damages such as cracks, delaminations, etc. and development of an early damage detection technique for delamination prediction is one of the most important aspects in ensuring the integrity and safety of such components. the presence of damages such as delaminations on the composites reduces its stiffness and changes the dynamic behaviour of the structures. as the loss in stiffness leads to changes in the natural frequencies, mode shapes, and other aspects of the structure, vibration analysis may be the ideal technique for delamination prediction. in this research work, the supervised feed-forward multilayer back-propagation artificial neural network is used to determine the position and area of delaminations in glass fiber-reinforced polymer (gfrp) plates using changes in natural frequencies as inputs. the natural frequencies were obtained by finite element analysis and results are validated experimentally. the findings show that the suggested technique can satisfactorily estimate the location and extent of delaminations in composite plates. keywords. health monitoring, composite, gfrp, delamination, vibration, natural frequency, artificial neural network. citation: sreekanth, t. g., senthilkumar, m., reddy, s. m., artificial neural network based delamination prediction in composite plates using vibration signals, frattura ed integrità strutturale, 63 (2023) 37-45. received: 05.09.2022 accepted: 15.10.2022 online first: 17.10.2022 published: 01.01.2023 copyright: © 2023 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. introduction omposite materials have been trending in modern engineering designs over the last three decades as a result of their appealing mechanical qualities, stable physical and chemical characteristics, etc. these composites, on the other hand, are prone to failure mechanisms that are unique from those of metallic alloys [1]. there is growing concern about the maintenance of composite components as each non-destructive testing method has technical constraints in terms of size, material composition, and damage/failure modes of fibre reinforced plastics (e.g. weak bond, matrix cracking, delamination and fibre cracking) [2]. glass fiber-reinforced plastics and carbon fiber-reinforced plastics have become popular in present engineering applications and it is expected that this practice will continue in the future also [3]. e-glass laminates have become more common in aviation components such as wings, fuselages, and stabilisers; as stronger, more durable, and tougher resins c https://youtu.be/saxbi03uvj8 t. g. sreekanth et alii, frattura ed integrità strutturale, 63 (2023) 37-45; doi: 10.3221/igf-esis.63.04 38 such as epoxies have evolved [4]. when the plane flies at a higher altitude, the trapped moisture/water expands, causing micro-cracking or delaminations. furthermore, as time passes, aircraft may experience more flight cycles, and this process of freezing and unfreezing will cause micro-cracks to get larger, eventually leading to delaminations. delaminations can be caused by a flaw in the manufacturing, assembly, or in-service stages, or by a combination of these. material/structural discontinuities that cause inter-laminar strains are the most common cause of delaminations [5]. delaminations can also develop at stress-free edges due to mismatches in individual layer properties. it can also happen in areas where there is out-of-plane loading, such as when curved beams bend. delaminations have a substantial impact on the composites' static and dynamic performance [6]. it is also an important type of failure in composites as delamination diminishes the composite's strength. when static loading is applied, there is a risk of local buckling when compression loading is applied. when this local buckling spreads to a relatively big delaminated part, the overall structure may break suddenly. delamination reduces stiffness under dynamic stress, which might result in a larger deflection magnitude for the total structure. foreign object impact is also a common cause of fibre reinforced polymer delaminations [7]. the vibration approach is a global damage detection method in which changes in physical parameters such as mass, damping, and stiffness cause changes in modal variables to be recognised. for damage diagnosis and quantification, the frequency-domain method employs changes in modal properties such as natural frequency, frequency response functions, damping, and mode shapes [8]. there is a requirement for finding natural frequency variations due to delamination generation in the method of delamination diagnosis in composite plates by vibration method, which can be produced using finite element analysis. the composite type utilized for this study was glass fiber-reinforced polymer (gfrp). the inverse problem is used to determine the position and magnitude of delaminations in composite plates using changes in the first five natural frequencies as input. the methodology followed is shown in fig. 1. figure 1: methodology. an analytical model is necessary to solve an inverse problem, which necessitates considerable effort in developing a mathematical framework that is both accurate and reliable. artificial neural network (ann) approaches can be applied to damage assessment techniques to overcome the complexity of framing mathematical frameworks [9, 10]. ann is used to anticipate damage features since neural networks are now being used as universal function approximators for difficult problems. the desire to develop a good data pattern recognition and decision-making system has driven this research. the ann was trained using a learning procedure that depicted the relationship between various inputs (here, the first five natural frequencies) and outputs (location and area of delaminations in plate). fabrication of gfrp plates he fabrication procedure was performed by hand layup. glass fibre, epoxy resin, and hardener are used for the fabrication. there are 16 layers in the composite and the stacking sequence of [0/45/-45/90]2s was considered for the work. the glass fibre is cut from a roll of glass fibre with dimensions 250 mm × 250 mm. in a 10:1 ratio, epoxy resin and hardener are mixed. to shield the working table from resin spillage and easy removal of composite, a layer of polythene is laid over it. over the polythene sheet, the first layer of the bidirectional woven e-glass fibre is laid, and the resin is applied with a brush to the first layer. the second layer is layered on top of the first layer and squeezed with rollers, then resin is softly applied over the second layer, and the process is repeated until the last layer is completed. the fabrication progression is shown in the fig. 2. t t. g. sreekanth et alii, frattura ed integrità strutturale, 63 (2023) 37-45; doi: 10.3221/igf-esis.63.04 39 figure 2: fabrication of composite plates. gfrp specimens without delamination was made initially and the specimens with delamination was fabricated thereafter with a delamination dimensions of 40 mm x 40 mm, 40 mm x 60 mm, and 40 mm x 50 mm, for specimen 2, 3 and 4 respectively. there is no delamination in specimen 1. for the specimen 2, delamination is created at seventh layer (50 mm x 50 mm away from the top right end), for specimen 3, delamination is created at fifth layer (100 mm x 100 mm away from the top right end) and for the specimen 4, delamination is created at ninth layer (150 mm x 150 mm away from the top right end). the delamination is made with teflon tapes. teflon tape was cut to the proportions of the delamination and put in the fibre laminates interface layers. after manufacturing, the gfrp was left to cure. at the carpentry shop, gfrps were cut to 220 mm × 200 mm dimensions using a power tool machine. extra 20 mm is given at one side for clamping purposes. fabricated plate samples are shown in fig. 3. figure 3: fabricated gfrp plates. vibration testing he vibration testing experimental setup is shown in fig. 4. the data acquisition system (daq), impact hammer, triaxial accelerometer, and computer with labview software comprise up the experimental setup. cantilever clamping is used to hold the specimens. the effective dimensions of specimens after clamping are 220 mm × 200 mm. an impact hammer was used to excite the clamping plate, which applied an impulse force to the composite plate. tri-axial accelerometer was used to capture the dynamic behaviour of the excited plate. the accelerometer was fixed in a way that z axis was pointing upwards and it is attached to the surface with petro wax adhesive. the accelerometer was t t. g. sreekanth et alii, frattura ed integrità strutturale, 63 (2023) 37-45; doi: 10.3221/igf-esis.63.04 40 attached to a data acquisition system, which amplified and translated the analogue signals provided by the accelerometer to digital signals. the daq was attached to the pc and labview software was used to interface with it. figure 4: experimental setup of vibration testing. finite element analysis odal analysis is a way for investigating the dynamic features of a structure when it is vibrated. modal analysis can be used to determine a structure's natural frequencies and mode shapes. because modeling composite plates falls under the category of three-dimensional modeling of solid structures, the element type employed to simulate the plates was layered solid 185. the number of elements examined for each layer along the thickness was one, and information about each layer is defined by shell element. first five natural frequencies are considered for this research work. the natural frequencies were compared to the experimental data for undamaged and delaminated composite plates to validate the finite element analysis (fea) results. when the percentage error for each case is determined and compared, plates with and without delaminations have a maximum inaccuracy of 7 %. the differences in results could be due to inaccuracies in specimen production and faults in frequency measurement from vibration tests. figure 5: sample delamination scenario. m t. g. sreekanth et alii, frattura ed integrità strutturale, 63 (2023) 37-45; doi: 10.3221/igf-esis.63.04 41 coordinates (mm) delamination size (mm2) nf 1 (hz) nf 2 (hz) nf 3 (hz) nf 4 (hz) nf 5 (hz) x axis (mm) y axis (mm) z axis (mm) x= 60 y=60 z=0.6 25 258.5 814.45 867.58 1849.3 1894.2 x= 60 y=60 z=0.6 50 254.46 810.39 863.57 1839.9 1889.3 x= 60 y=60 z=0.6 75 250.41 806.37 859.51 1834.7 1884.2 x= 60 y=60 z=0.6 100 246.26 802.28 855.48 1831.2 1879.6 x= 60 y=60 z=0.6 125 241.85 798.13 851.48 18519.6 1874.1 x= 60 y=60 z=1.5 25 256.49 812.42 865.15 1847.1 1892.6 x= 60 y=60 z=1.5 50 254.4 809.6 862.2 1839.2 1879.9 x= 60 y=60 z=1.5 75 250.32 805.26 858.16 1834.2 1874.5 x= 60 y=60 z=1.5 100 245.26 800.84 853.1 1821.6 1870.2 x= 60 y=60 z=1.5 125 240.25 796.25 848.48 1809.4 1859.6 x= 60 y=60 z=2.40 25 256.3 812.24 865.01 1846.5 1892.5 x= 60 y=60 z=2.40 50 253.8 810.21 862.15 1839.8 1878.9 x= 60 y=60 z=2.40 75 249.22 803.84 858.14 1835.2 1873.5 x= 60 y=60 z=2.40 100 245.2 799.4 847.9 1830.8 1868.2 x= 60 y=60 z=2.40 125 240.9 794.54 843.47 1819.7 1860.6 x= 60 y=60 z=3.3 25 256.25 812.22 865.62 1846.2 1892.6 x= 60 y=60 z=3.3 50 254.16 810.26 863.54 1838.5 1890.12 x= 60 y=60 z=3.3 75 249.24 805.46 859.25 1834.4 1885.6 x= 60 y=60 z=3.3 100 245.12 801.03 855.05 1829.4 1881.2 x= 60 y=60 z=3.3 125 241.1 796.95 850.47 1824.6 1877.6 x= 60 y=60 z=4.1 25 256.12 812.2 865.25 1845.5 1892.1 x= 60 y=60 z=4.1 50 253.24 809.46 863.14 1838.4 1889.92 x= 60 y=60 z=4.1 75 249.16 805.03 858.25 1834.4 1885.6 x= 60 y=60 z=4.1 100 245.1 800.95 854.05 1829.31 1881.15 x= 60 y=60 z=4.1 125 241 795.69 849.47 1824.5 1876.6 table 1: dataset for the location x=60 mm y=60 mm. database generation database of shifts in frequencies (due to known delaminations) is required to train the inverse algorithm. with the aid of finite element analysis, the appropriate database is created. a significant number of composite plate samples with various sizes and locations of delaminations were subjected to numerical analysis. the database size required to train ann is important for properly diagnosing delaminations. two hundred and twenty five distinct delamination scenarios were created numerically for this study by combining delaminations at nine different places (combinations of x = 60, 120, 180; and y = 60, 120, 180; where x and y are distance of delaminations location from bottom left end.), five different sizes (25, 50, 75, 100, 125 mm2) and five different layers (layer 2, 5, 8, 11 & 14). fig. 5 shows an example of one of the delaminations scenarios, with delaminations at x=60, y=60 and a delaminations area of 25 mm2 on layer 5. tab. 1 shows the first five natural frequencies of the plate sample with delaminations at x=60, y=60, and z=0.6, for five delamination areas. a similar dataset is created for the remaining eight locations. fig. 6 (a) and (b) illustrate the bending modes for the same sample delaminated plate with delamination size of 25 mm2. a t. g. sreekanth et alii, frattura ed integrità strutturale, 63 (2023) 37-45; doi: 10.3221/igf-esis.63.04 42 figure 6: (a) bending mode 1, (b) bending mode 2. feed-forward back-propagation neural network neural network functions as a processor, storing and retrieving experience based information as and when needed. in terms of accumulating information through the learning process, it functions similarly to the human brain [11]. learning is a process in which the parameters of a neural network, such as synaptic weights and bias levels, are modified in a continuous manner. the difference between a feed forward neural network and a recurrent neural network is that the connections between each unit do not form a loop. furthermore, information only moves in one way, that is, forward, from the input nodes to the output nodes via the hidden nodes. as a result, no loops arise in this network. there are two types of learning processes: supervised learning and unsupervised learning. the system will try to anticipate the results based on known samples dataset in supervised learning approach, which is also the most often used training technique [12]. it will compare its own predictions to known goal values, after which it will learn from the errors encountered throughout each cycle. the data will flow from the input layer to the neurons, which will then transfer the data to the next nodes. weights and connections are given as data passes along, and when the data reaches the successor node, the weights are added and either weakened or intensified. there will be no changes to the weights if the output obtained is equivalent to the expected output [13-15]. however, if the output obtained differs from the real result, the error will propagate backwards through the system, and the weights will be adjusted accordingly. back-propagation refers to the reverse flow of error through the neural network. supervised feed-forward multilayer back-propagation artificial neural network tool in matlab is used for this research based on findings from various literatures [16-17]. neural network training o improve the model and verify the hypothesis, inverse techniques employ both the original model of the structure (here, a delaminated plate) and observed data (here, the first five natural frequencies). the goal here is to see how effective global vibration parameters (natural frequencies) as input to an ann back-propagation algorithm are in locating and predicting the location and magnitude of delaminations. the ann size is critical since smaller networks cannot correctly reflect the system, while bigger networks over-train it. as illustrated in fig. 7, the ann used here has five inputs (frequencies), four outputs (position in x and y directions, layer, and size of delamination), and one hidden layer with 12 neurons. all the parameters are optimized to get the maximum accuracy. the mean square error (mse) is utilised as an ann's performance metric, and the levenberg-marquardt back-propagation technique is employed to train it. as discussed in database generation section, 225 input-output dataset is created and out of which 155 are used for training, 35 each used for testing and validation. fig. 8 depicts the linear regression analysis of the target and anticipated values. the pearson's correlation coefficients (r-values) for training, validating, testing, and total data are 0.908, 0.931, a t t. g. sreekanth et alii, frattura ed integrità strutturale, 63 (2023) 37-45; doi: 10.3221/igf-esis.63.04 43 0.912, and 0.912, respectively. this indicates that the ann-based prediction model is providing a satisfactory match to the data. figure 7: neural network used for delamination prediction. figure 8: regression analyses of data predicted by the ann model. t. g. sreekanth et alii, frattura ed integrità strutturale, 63 (2023) 37-45; doi: 10.3221/igf-esis.63.04 44 results for delamination prediction ive finite element models were created to test the ann approach for determining delamination location and area in composite plates. tab. 2 shows the actual and estimated values of layer, position, and delamination area. in the table, the real values of delaminations are assigned values that are chosen at random. plate number actual predicted percentage error delamination location – x (mm) 1 50 58.2 16.4 2 75 81.25 8.3 3 100 93.6 -6.4 4 125 114 -8.8 5 150 164 9.3 delamination location – y (mm) 1 75 61.3 -18.2 2 100 80.5 -19.5 3 125 109 -12.8 4 150 121.2 -19.2 5 175 163.9 -6.3 delamination location – z (mm) 1 0.9 0.73 -18.9 2 1.2 1.1 -8.3 3 1.8 1.76 -2.2 4 2.1 2.23 6.2 5 3 2.87 -4.3 delamination area (mm2) 1 30 27.6 -8.0 2 60 61.5 2.5 3 90 93.5 3.9 4 110 104.6 -4.9 5 140 121.2 -13.4 table 2: comparison of actual and predicted delamination parameters for composite plates when compared to findings for y direction location, the values for delaminations area, position in x direction, and layer prediction were better for all 5 plate samples. plate 1 seemed to have the highest x axis location prediction error of 16.4 percent, but it was the only example where the x axis location error above 10%. the reason for this error is may be because of the reason that actual location was out of the training dataset. for y direction prediction, it can be understood that all plates except plate 5 have error greater than 10%. layer prediction inaccuracy was within 10% for all plates, except for plate 1. error in delamination area forecast for plate 5 alone crossed 8%. the reason for this case may be that, the actual area was outside the training data considered. the reason for overall error may be because of more complexity in plate delaminations prediction because of more number of inputs (four) to the neural network. it's also worth noting that the inaccuracy was particularly significant when predictions were made outside of the training dataset. this indicates that the findings can be further improved by expanding the training dataset. conclusions ibration-based analysis on composite plates is offered in this study effort to forecast the severity and location of the delamination. after confirming with experiments, numerical models of non-delaminated and delaminated composite plates were built, and the first five natural frequencies for various delamination situations were produced. natural frequencies are degraded by delamination in composite plates, according to research. these findings were utilised to train the neural network, which was then used to create the inverse algorithms. the first five natural frequencies are fed into the ann, which then takes outputs as delamination scenarios. numerical frequency data was used to track the neural network's performance in evaluating delaminations. it was observed that the ann was able to estimate the delaminations in composite plates with reasonably good precision. neural networks have a lot of benefits, such as the need for less statistical training, the capacity to recognise intricate nonlinear correlations among variables, the capacity to recognise all potential interactions among predictor variables, etc. an increased computing overhead, tendency for overfitting, and the empirical nature of model development are drawbacks for neural networks. f v t. g. sreekanth et alii, frattura ed integrità strutturale, 63 (2023) 37-45; doi: 10.3221/igf-esis.63.04 45 references [1] senthilkumar, m., sreekanth, t. g. and reddy, s. m. (2020) nondestructive health monitoring techniques for composite materials: a review. polym polym compos 29, 528-540. doi: 10.1177/0967391120921701 [2] onggar, t., häntzsche, e., hund, r.d. and chokri, c (2019) multilayered glass filament yarn surfaces as sensor yarn for in-situ monitoring of textile-reinforced thermoplastic composites. fibers polym 20, 1945–1957. doi: 10.1007/s12221-019-1237-2 [3] zhou, w., wei, zy., wang, gf., han, kn., liu, r. and ma, lh. (2021) transverse tensile deformation and failure of three-dimensional five-directional braided carbon fiber composites. fibers polym 22, 1099–1110. doi: 10.1007/s12221-021-9199-6 [4] sreekanth, t.g., senthilkumar, m. and reddy, s.m. (2021) vibration-based delamination evaluation in gfrp composite beams using ann. polym polym compos 29, 317-324. doi: 10.1177/09673911211003399 [5] kindova-petrova, d. (2014) vibration-based methods for detecting a crack in a simply supported beam, j. theor. appl. mech. 44, 69–82. doi: 10.2478/jtam-2014-0023 [6] sreekanth, t.g., senthilkumar, m. and reddy, s.m. (2021) fatigue life evaluation of delaminated gfrp laminates using artificial neural networks. trans indian inst met 74, 1439–1445. doi: 10.1007/s12666-021-02234-5 [7] liu, y.j., jiang, z., wen, h.m. (2020) predicting impact induced delamination of frp laminates. int. j. impact eng.. doi: 10.1016/j.ijimpeng.2019.103436 [8] senthilkumar, m., reddy, s. m. and sreekanth, t.g. (2022) dynamic study and detection of edge crack in composite laminates using vibration parameters. trans indian inst met 75, 361–370. doi: 10.1007/s12666-021-02419-y [9] pagani, a., enea, m., carrera, e. (2021) component-wise damage detection by neural networks and refined fes training. j. sound vib. doi: 10.1016/j.jsv.2021.116255 [10] sreekanth, t.g., senthilkumar, m. and reddy, s.m. (2022) natural frequency based delamination estimation in gfrp beams using rsm and ann. frattura ed integrità strutturale 61, 487-495. doi: 10.3221/igf-esis.61.32 [11] bilisik, k., demiryurek, o. (2011) analysis and tensile-tear properties of abraded denim fabrics depending on pattern relations using statistical and artificial neural network models. fibers polym 12, 422. doi: 10.1007/s12221-011-0422-8 [12] ribeiro, j.p., tavares, s.m., parente, m. (2021) stress–strain evaluation of structural parts using artificial neural networks. proc. inst. mech. eng. l p i mech eng l-j mat. doi: 10.1177%2f1464420721992445 [13] aadatmorad, m., talookolaei, r. a.-j., pashaei, m.-h., khatir, s. and wahab, m.a. (2022). pearson correlation and discrete wavelet transform for crack identification in steel beams, mathematics 10, 2689. doi: 10.3390/math10152689 [14] zenzen, r., khatir, s., belaidi, i., le thanh, c., wahab, m. a. (2020) a modified transmissibility indicator and artificial neural network for damage identification and quantification in laminated composite structures, composite structures 248, 112497, doi: 10.1016/j.compstruct.2020.112497. [15] khatir, s., tiachacht, s., le thanh, c., ghandourah, e., mirjalili, s., wahab, m. a. (2021) an improved artificial neural network using arithmetic optimization algorithm for damage assessment in fgm composite plates, composite structures 273, 114287, doi: 10.1016/j.compstruct.2021.114287. [16] al thobiani, f., khatir, s., benaissa, b., ghandourah, e., mirjalili, s. and wahab, m. a. 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can be opened with acrobat and adobe reader 5.0 and later.) >> /namespace [ (adobe) (common) (1.0) ] /othernamespaces [ << /asreaderspreads false /cropimagestoframes true /errorcontrol /warnandcontinue /flattenerignorespreadoverrides false /includeguidesgrids false /includenonprinting false /includeslug false /namespace [ (adobe) (indesign) (4.0) ] /omitplacedbitmaps false /omitplacedeps false /omitplacedpdf false /simulateoverprint /legacy >> << /addbleedmarks false /addcolorbars false /addcropmarks false /addpageinfo false /addregmarks false /convertcolors /converttocmyk /destinationprofilename () /destinationprofileselector /documentcmyk /downsample16bitimages true /flattenerpreset << /presetselector /mediumresolution >> /formelements false /generatestructure false /includebookmarks false /includehyperlinks false /includeinteractive false /includelayers false /includeprofiles false /multimediahandling /useobjectsettings /namespace [ (adobe) (creativesuite) (2.0) ] /pdfxoutputintentprofileselector /documentcmyk /preserveediting true /untaggedcmykhandling /leaveuntagged /untaggedrgbhandling /usedocumentprofile /usedocumentbleed false >> ] >> setdistillerparams << /hwresolution [2400 2400] /pagesize [612.000 792.000] >> setpagedevice microsoft word 2190 t. febra et alii, frattura ed integrità strutturale, 48 (2019) 242-248; doi: 10.3221/igf-esis.48.25 242 focused on the “portuguese contributions for structural integrity” response of fabric insert injection overmolding pp based composites subjected to single and muti-impact t. febra, j.a.m. ferreira, j. d. costa, j. da silva cemmpre, university of coimbra, department of mechanical engineering, portugal tiago_febra@geco-moldes.pt, http://orcid.org/0000-0002-9372-5072 martins.ferreira@dem.uc.pt, http://orcid.org/0000-0002-0295-1841 jose.domingos@dem.uc.pt, http://orcid.org/0000-0002-8274-3734 joel.jesus@uc.pt, http://orcid.org/0000-0002-7133-2331 c. capela instituto politécnico de leiria, estg, department of mechanical engineering, portugal ccapela@ipleiria.pt, http://orcid.org/0000-0003-3334-4945 abstract. this paper presents the results of a current study on the development and impact response of composite plates manufactured by injection overmolding on the two sides of a single reinforcement fibre mat. the injection polymer is a talc-filled polypropylene, nowadays used for structural purposes. three configurations with different insert fibre mats were used: kevlar, biaxial and multiaxial glass fibre mats. the parameters studied were the fibre mat type and the impact energy. for single impact tests, it was concluded that the highest impact energy required to achieve impactor perforation is obtained with kevlar insert, while the highest percentage of energy recovered is achieved with biaxial glass fibre netting. kevlar insert also allows for the maximum impact stiffness. for the multi-impact tests, the recovered energy and the dynamic stiffness show the same tendencies of the single impact tests. on low energy impacts, the effect of the insert fibre and of the previous impact are quite reduced, while for impact energies above 6j, previous impacts reduce significantly the recovered energy and the impact energy for which the perforation was achieved. keywords. composites; impact response; injection overmolding. citation: t. febra, j.a.m. ferreira, j. d. costa, j. da silva, c. capela, response of fabric insert injection overmolding pp based composites subjected to single and mutiimpact, frattura ed integrità strutturale, 48 (2019) 242-248. received: 14.09.2018 accepted: 09.01.2019 published: 01.04.2019 copyright: © 2019 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. introduction his paper is concerned with the manufacture and performance of a single piece final product made from a fibre mat insert with polymer injected overmolding in both sides. polymers and fibre mats have very different mechanical properties but should remain safely bonded throughout their useful life. t http://www.gruppofrattura.it/va/48/2190.mp4 t. febra et alii, frattura ed integrità strutturale, 48 (2019) 242-248; doi: 10.3221/igf-esis.48.25 243 traditional overmolding is a two-stage sequential process in which a previously injected rigid polymer substrate is overmolded with a more flexible thermoplastic material. the final component is a single piece composed by two polymers with very different mechanical properties. the adhesion between the two materials is the key for a successful practice use, by which the component must be safe and the interface remain permanently bonded. nowadays, polypropylene (pp) is a widely used material for structural purposes because of its mechanical properties, reasonable cost, easy processing and recyclability. optimization procedures for overmolding parameters have been developed and published [1-4]. recently, fibre reinforcement mats have been used as the substrate material for some applications where final stiffness can play important role. the overmolding process requires the merging of several characteristics to increase its functionality, including combinations of mechanical strength and touch feeling or grip ability, cushioning against vibration or impact, or esthetical factors like gloss. the rigid substrate provides the basic mechanical properties for structural purposes while the soft polymer cover adds the desired user comfort and product functionalities. the increasing use of overmolding components can be seen in applications such as automotive interiors, medical devices, telephone keypads, toothbrushes, shaving hardware, household appliances and hand tools [5–7]. nowadays, polypropylene (pp) is replacing traditional engineering thermoplastics for structural purposes in automotive applications, due to its mechanical properties, reasonable cost, easy processing and recyclability. a low velocity impact event is one of the most dangerous loads on composite laminates, giving rise to different types of damages, including matrix cracking, fibre fracture, fibre-matrix debonding and delamination between different layers [8]. internal delamination induces premature buckling of the structures with the consequent drop of compressive strength [9, 10] and also in less relevant of the tensile strength [11]. the response of composites subjected to single-impact loading is abundantly reported on scientific literature, also repaired composites [12, 13]. andrew et al. [13] evaluated the residual compression after low-velocity impacts on gfrp composites repaired by kevlar chopped short fibres/epoxy and found higher maximum impact load and lower contact time for repaired specimens relatively to the unrepaired ones. however, scarce information can be found about the performance of composites under repeated impacts. this subject was studied by morais et al [14], concluding that stacking sequences and laminate thickness have a major influence on the composite’s response under repeated impacts. the structural performance under repeated impacts was studied by cholakara et al [15] on kevlar-fibre/epoxy composites, by mouritz et al [16] and by hosur et al [17] on glass reinforced laminates and by wyrick and adams [18] on the carbon/epoxy laminates. the parameters studied were the fibre mat type and the impact energy. the impact response was monitored in terms of the maximum load and displacement, dynamic impact modulus, absorbed and recovered energies and damage area. in addition to the study of the influence of the aforementioned parameters regarding simple impact response, this work also aims to compare the response of the material to simple impact and multi-impact with increasing energies. reference matrix insert mould temp. (ºc) processing temp. (ºc) injection pressure (bar) mgfm talc-filled pp multiaxial glass fiber mesh 22 220 41 bgfn talc-filled pp biaxial glass fiber netting 22 220 41 km talc-filled pp kevlar mat 22 220 41 table 1: formulation and manufacture parameters of the composites. materials and testing he present work studied impact response using square 100x100 mm2 and 3mm nominal thickness specimens. the overmolding matrix was polypropylene (pp) filled by 20% in weight of talk, hostacom trc 352n titan supplied by yonde basel. three configurations with different insert fibre mats were manufactured, as is summarized in table 1. in turn, the glass fibre inserts used were fiberglass multiaxial mesh fabric and biaxial fiberglass reinforcing mesh, supplied by huesker. the third insert was an aramid kevlar 49 mesh, supplied by toray. the injection moulding process was carried out using a sandreto 200 ton machine, using the parameters indicated in table 1. fig. 1 shows the insert fibre mat placed in the mould. t t. febra et alii, frattura ed integrità strutturale, 48 (2019) 242-248; doi: 10.3221/igf-esis.48.25 244 low-velocity impact tests were performed using a drop weight-testing machine instron–ceast 9340. an impactor with a diameter of 10 mm and mass of 3.4 kg was also used. the tests were performed with the impactor stroke at the centre of centrally supporting the 100x100 mm specimens. two types of tests were carried out: single impact tests for different impact energies and multi-impacts tests in which the specimens were subjected to successive impacts with increasing energy. for each condition, two/three specimens were tested at room temperature. figure 1: view of the insert fibre mat placed in mould. results and discussion single impact tests ig. 2a) shows typical energy versus time curves, while fig. 2b) presents the dynamic load against the displacement, both for the three different insert fibre mats samples. all these tests were performed with an impact energy of 6 j. fig. 2a) also shows that maximum energy was achieved quickly in the kevlar mat composite, due to its higher dynamic stiffness, as demonstrated in fig. 3b). for this type of impact energy multiaxial glass fibre mesh has the lower recovered energy, which is quite similar for the other two insert mats. figure 2: influence of the insert material on the impact response for 6 j impact energy: a) energy versus time; b) load versus displacement. fig. 3a) presents the average values of three tests for each condition of the recovered energy versus impact energy, showing that biaxial glass fiber netting insert promotes the highest values of recovered energy, contrary to what happens with multiaxial glass fiber mesh insert which was observed as having a lower perforation energy. fig. 3b) presents the dynamic impact stiffness (calculated as the ratio between the maximum load and the displacement at maximum load) against the displacement, showing a slow decrease for the three insert fibers only for impact energies higher than 10 j. kevlar composites exhibit dynamic stiffness more than 25% higher than both glass fiber composites. f t. febra et alii, frattura ed integrità strutturale, 48 (2019) 242-248; doi: 10.3221/igf-esis.48.25 245 figure 3: influence of impact energy on response parameters: a) recovered energy versus impact energy; b) dynamic modulus versus impact energy. figs. 4a) and 4b) show exemplary photos of the damage zones on a talc filled pp with multiaxial glass fibre mesh insert (mgfm) sample tested for impact energy of 6j in impact side and back side, respectively. as well reported in literature for fiber-reinforced composites [19], higher damage occurred in the backside in which a long failure crack is observed, while in the impact side only a regular plastic deformation caused by impactor occurs. figure 4: exemplary photos of the damage on a mgfm sample tested for impact energy of 6j: a) impact side; b) back side. (a) (b) figure 5: exemplary cscan images of damaged zones for impact energy of 5j: a) bgfn mat; b) km mat. t. febra et alii, frattura ed integrità strutturale, 48 (2019) 242-248; doi: 10.3221/igf-esis.48.25 246 some samples were inspected by c-scan technique, supplied by physical acoustics cooperation, in order to analyze the damaged zone. figure 5 shows the typical and representative images of the bgfn mat and km mat samples, impacted by 5j. it is possible to observe that, in spite of the higher damaged area of the km mat sample, the c-scan image for bgfn mat insert suggests a much more intense damage. these observations are in accordance with the lower dynamic stiffness obtained in fig. 3b) for the bgfn mat inserts. similarly to what happens in sandwich composites, three types of failure can be observed: rupture of the superficial polymer layers, delamination of the interface and in extreme conditions, rupture of the fibers [20]. multi-impact tests the results of the multi-impact tests (in which the same specimen was subjected to successive impacts with impact energy increasing successively 1j for each test) are summarized in figures 6 and 7, in terms of the recovered energy (in percentage of the impact energy) and the dynamic stiffness, respectively. fig. 6 shows the same tendencies of the single impact tests presented in fig. 3a), indicating that biaxial glass fibre netting inserts promote the highest values of recovered energy. however, the multiaxial glass fibre mesh insert shows the lower recovered energy and perforation energy. recovered energy decreases parabolic until failure, according with f. cucinotta et al. [20]. also, as in the single impact tests presented in fig. 3b) kevlar inserts exhibit the highest dynamic stiffness, in contrast to glass fibre inserts (fig. 7). in any case, a significant difference was observed on the dynamic stiffness values for the multi-impacted specimens in comparison with the single impacted tests, decreasing significantly after the peaking for an intermediate impact energy. this fact is caused by the accumulated damage occurred at the intermediate impact energy. figure 6: recovered energy after multi-impact tests. figure 7: dynamic stiffness after multi-impact tests. figure 8: comparison of the recovered energy for multi-impact and single impact tests. t. febra et alii, frattura ed integrità strutturale, 48 (2019) 242-248; doi: 10.3221/igf-esis.48.25 247 fig. 8 compares the results of the recovered energy obtained for the multi-impacts and the single impact tests. the results indicate that for low energy the effect of the insert fibre and of the previous impact is quite reduced. however, for impact energies above 6j, previous impacts significantly reduce the recovered energy and the impact energy for which the perforation was achieved. the bgfn mat insert promotes a slightly improved impact response for both series of tests. conclusions he present work studied the effect of the fiber type on the impact response of insert injection overmolding talc filled pp composites subjected to single impact and the multi-impacts tests, for which successive impacts with increasing energy were applied. the main conclusions that can be drawn were as follows: for single impact tests, the highest impact energy required to achieve impactor perforation is obtained with kevlar insert while the highest percentage of energy recovered is achieved with biaxial glass fiber netting. the maximum impact stiffness was obtained with kevlar insert, with both glass fibre inserts achieving similar results. the maximum post-impact load was also obtained with kevlar insert, while the minimum for the multiaxial glass fibre mesh; for the multi-impact tests, the recovered energy and the dynamic stiffness show the same tendencies of the single impact tests. however, a significant difference was observed on the dynamic stiffness values for the multi-impacted specimens which decrease significantly after the peaking for an intermediate impact energy; the comparison of the recovered energy obtained for the multi-impact and single impact tests show that for low energy the effect of the insert fibre and of the previous impact is quite reduced, while for impact energies above 6j previous impacts reduce significantly the recovered energy and the impact energy for which the perforation was achieved. acknowledgments he authors would like to acknowledge geco-moldes, leiria, portugal, for the supply of the samples and the sponsoring of this research by feder funds through the program compete – programa operacional factores de competitividade – and by national funds through fct – fundação para a ciência e a tecnologia –, under the project uid/ems/00285/2013. references [1] carella, a.r., alonso, c., merino, j.c., pastor, j.m. (2002). sequential injection of thermo-plastic polymers. analysis of processing parameters for optimal bonding conditions, polym eng sci, 42, pp. 2172–2181. [2] schellekens, m., twene, d., vander waals, a. (2011). block copolymers for waterborne coatings—a novel ecofriendly approach for improved coating adhesion to untreated polypropylene based plastics. prog org coat, 72, pp. 138–143. doi: 10.1016/j.porgcoat.2011.03.007 [3] dondero, m., pastor, j.m., carella, j.m., perez, c.j. (2009). adhesion control for injection overmolding of polypropylene with elastomeric ethylene copolymers. polym eng sci, 49, pp. 1 886–1893. [4] nguyen, s., perez, c.j., desimone, m., pastor, j.m., (2013). overmolding of elastomeric propylene copolymers on polypropylene. effects of block and random microstructures. international journal of adhesion & adhesives, 46, pp 44–55. doi: 10.1016/j.ijadhadh.2013.05.016 [5] huang, d.y., chen, r.s. (1999). bonding strength at solid-melt interface for polystyrene in a sequential two-staged injection molding process, polym eng sci, 39, pp. 2159–2171. [6] weng, d., andries, j., morin, p., saunders, k., politis, j. (2000). fundamentals and material development for thermoplastic elastomer(tpe) overmolding. j injection molding technol, 4, pp.22–28. [7] richardson, m.o.w., wisheart, m.j. (1996). review of low-velocity impact properties of composite materials. compos part a-appl s, 27, pp. 1123-1131. doi: 10.1016/1359-835x(96)00074-7. [8] lankford, j. (1997). shear versus dilatational damage mechanisms in the compressive failure of fibre reinforced composites. compos part a-appl s, 28, pp. 215-222. doi: 10.1016/s1359-835x(96)00110-8. [9] lee, s.h., yerramalli, c.s., waas, a.m. (2000). compressive splitting response of glass–fiber reinforced unidirectional composites. compos sci technol, 60, pp. 2957-2966. doi: 10.1016/s0266-3538(00)00159-7. t t t. febra et alii, frattura ed integrità strutturale, 48 (2019) 242-248; doi: 10.3221/igf-esis.48.25 248 [10] reis, p.n.b., ferreira, j.a.m., antunes, f.v., richardson, m.o.w. (2009). effect of interlayer dalamination on mechanical behavior of carbon/epoxy laminates. j compos mater, 43, pp. 2609-2621. doi: 10.1177/0021998309344649. [11] balc, o., çoban, o., bora, m.ö., akagündüz, e., yalçin, e.b. (2017). experimental investigation of single and repeated impacts for repaired honeycomb sandwich structures. mat sci eng a-struct, 682, pp. 23–30. doi: 10.1016/j.msea.2016.11.030. [12] andrew, j.j., arumugam, v., saravanakumar, k., dhakal ,h.n., santuli ,c. (2015). compression after impact strength of repaired gfrp composite laminates under repeated impact loading. compos struct, 133, pp. 911–920. [13] de morais, w.a., monteiro, s.n., d’almeida, j.r.m. (2005). effect of the laminate thickness on the composite strength to repeated low energy impacts. compos struct, 70, pp. 223–228. doi: 10.1016/j.compstruct.2004.08.024. [14] cholakara, m.t., jang, b.z., wang, c.z. (1989). deformation and failure mechanisms in 3d composites. in proc. 34th int. sampe conference, may 8-11, pp. 2153-2160. [15] mouritz, a.p., gallagher, j., goodwin, a.a. (1997). flexural strength and interlaminar shear strength of stitched grp laminates following repeated impacts. compos sci technol, 57, pp. 509-522. doi: 10.1016/s0266-3538(96)00164-9. [16] hosur, m.v., karim, m.r., jeelani, s. (2003). experimental investigations on the response of stitched/unstitched woven s2-glass/sc15 epoxy composites under single and repeated low velocity impact loading. compos struct, 61, pp. 89-102. doi: 10.1016/s0263-8223(03)00032-1. [17] wyrick, d.a., adams, d.f. (1988). damage sustained by a carbon/epoxy composite material subjected to repeated impact. composites, 19, pp. 19-26. doi: 10.1016/0010-4361(88)90540-x. [18] reis, p.n.b., ferreira, j.a.m., zhang, z.y., benameur, t., richardson, m.o.w. (2013). impact response of kevlar composites with nanoclay enhanced epoxy matrix. composites: part b 46, pp. 7–14. doi: 10.1016/j.compositesb.2012.10.028. [19] cucinotta, f., paoli, a., risitano g. and sfravara f.(2018). proceedings of the institution of mechanical engineers part m: journal of engineering for the maritime environment, 232 ( 2), pp. 234-244. doi: 10. 1 177/1475090217720619. nomenclature bgfn biaxial glass fiber netting; gfrp – glass fibre reinforced polymers; km kevlar mat; mgfm multiaxial glass fiber mesh. << /ascii85encodepages false /allowtransparency false /autopositionepsfiles true /autorotatepages /none /binding /left /calgrayprofile (dot gain 20%) /calrgbprofile (srgb iec61966-2.1) /calcmykprofile (u.s. web coated \050swop\051 v2) /srgbprofile (srgb iec61966-2.1) /cannotembedfontpolicy /error /compatibilitylevel 1.4 /compressobjects /tags /compresspages true /convertimagestoindexed true /passthroughjpegimages true /createjobticket false /defaultrenderingintent /default /detectblends true /detectcurves 0.0000 /colorconversionstrategy /cmyk /dothumbnails false /embedallfonts true /embedopentype false 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/hrv (za stvaranje adobe pdf dokumenata najpogodnijih za visokokvalitetni ispis prije tiskanja koristite ove postavke. stvoreni pdf dokumenti mogu se otvoriti acrobat i adobe reader 5.0 i kasnijim verzijama.) /hun 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can be opened with acrobat and adobe reader 5.0 and later.) >> /namespace [ (adobe) (common) (1.0) ] /othernamespaces [ << /asreaderspreads false /cropimagestoframes true /errorcontrol /warnandcontinue /flattenerignorespreadoverrides false /includeguidesgrids false /includenonprinting false /includeslug false /namespace [ (adobe) (indesign) (4.0) ] /omitplacedbitmaps false /omitplacedeps false /omitplacedpdf false /simulateoverprint /legacy >> << /addbleedmarks false /addcolorbars false /addcropmarks false /addpageinfo false /addregmarks false /convertcolors /converttocmyk /destinationprofilename () /destinationprofileselector /documentcmyk /downsample16bitimages true /flattenerpreset << /presetselector /mediumresolution >> /formelements false /generatestructure false /includebookmarks false /includehyperlinks false /includeinteractive false /includelayers false /includeprofiles false /multimediahandling /useobjectsettings /namespace [ (adobe) (creativesuite) (2.0) ] /pdfxoutputintentprofileselector /documentcmyk /preserveediting true /untaggedcmykhandling /leaveuntagged /untaggedrgbhandling /usedocumentprofile /usedocumentbleed false >> ] >> setdistillerparams << /hwresolution [2400 2400] /pagesize [612.000 792.000] >> setpagedevice microsoft word numero_46_art_35 i. shardakov et alii, frattura ed integrità strutturale, 46 (2018) 383-390; doi: 10.3221/igf-esis.46.35 383 investigation of the effect of cracks on the vibration processes in reinforced concrete structures i. shardakov, a. shestakov, r. tsvetkov, i. glot institute of continuous media mechanics, ural branch, russian academy of science, 1, korolev street, perm, russia shardakov@icmm.ru, shap@icmm.ru, flower@icmm.ru, glot@icmm.ru abstract. the validity of the mathematical model describing the propagation of vibrations in the reinforced concrete structures (rc structures) was verified by comparing the experimental and numerical data. the proposed model allowed us to perform numerical experiments aimed at comparing vibrorecords obtained for the structure without defects and the structure with typical fracture caused by crack formation. based on the results of comparison, an informative diagnostic parameter was proposed. this parameter makes it possible to control the nucleation and growth of cracks in a rc structure. keywords. vibration-based diagnostics; rc structure; cracks; full-scale model; experiment; simulation. citation: shardakov i., shestakov, a., tsvetkov, r., glot, i., investigation of the effect of cracks on the vibration processes in rc structures, frattura ed integrità strutturale, 46 (2018) 383-390. received: 12.08.2018 accepted: 22.09.2018 published: 01.10.2018 copyright: © 2018 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. introduction he results of studies of the behavior of complex building structures under critical conditions are important for solving the problems of their safe operation. one of the modern approaches that make it possible to solve problems of safe operation of structures is the use of automated deformation monitoring systems. the most important components of these systems are mathematical models that adequately describe the operation of the structure in subcritical and critical stages of its deformation. the development and verification of such models is possible only when carrying out field experiments. for their implementation, a model structure was designed and assembled. this model reflects the deformation processes in fullscale engineering structure. it is a 4-storey monolithic reinforced concrete building on a scale of 1: 2 (fig.1). its total height is 6m, length is 9m, and width is 6m. automated deformation monitoring systems are based on the non-destructive control methods, in particular, the methods of vibration diagnostics [1, 2, 3, 4], among which one can differentiate between the methods analyzing natural vibrations [5, 6] and those examining the transient vibration processes [7, 8]. the vibration methods have found wide application because of the use of piesoceramic materials, which can operate both as actuators and sensors. they allow fault diagnosis in a broad frequency range and can be installed at the surface of the examined structure [9, 10] or embedded into it [11, 12]. the proposed approach is based on the registration of vibration processes in the structure under the action of impulse loads. it allows us to perform the local analysis of separate fragments of the structure while tracing the evolution of the t http://www.gruppofrattura.it/va/46/35.mp4 i. shardakov et alii, frattura ed integrità strutturale, 46 (2018) 383-390; doi: 10.3221/igf-esis.46.35 384 front of shock waves as they pass through the structure. when the propagating wave front runs across defects, its frequency composition and propagation time change. by comparing the signals from the structure with and without defects, we can detect any faults, their location and size. the effectiveness of the solution of these problems depend on the selection of the place where the elastic wave is initiated, the spectral composition of the impulse and the place of recording the signal passing through the structure. a well-grounded choice of these parameters is possible in the framework of an appropriate mathematical model, which adequately describes the dynamic processes occurring in the structure. figure 1: testing stand with installed model rc structure. in this study, the mathematical model describing the free vibrations of the structure caused by impact loading is verified. in the experiments, elastic waves in different elements of the model structure (columns, slabs) were excited by an impact of a 460g striker. the resulting vibrograms were recorded by accelerometers mounted at different points of the structure. registration of vibration processes in the model structure involved a synchronous recording of data from two accelerometers, one of which was located on the striker, and the other – at a certain point of the structure. the registration of the acceleration at the impact point made it possible to obtain the value of the impact force (as the product of the acceleration by the striker mass) as a function of time. these data were used to determine the force boundary condition at the point of impact necessary for solving the initial-boundary problem of propagation of a shock wave in a structure. this allowed us to compare the vibrograms obtained in the experiment and calculated on the basis of the proposed model. this model was used as a framework for performing a series of numerical experiments, in which vibrograms obtained for the structure with crack formation at typical sites were compared with vibrograms for defect-free structure. based on the results of these solutions we identified an informative diagnostic parameter, which reflects the processes of initiation and growth of cracks in reinforced concrete. this approach makes it possible to create an effective system for vibration control of the process of crack formation in rc structures. conceptual description of the mathematical model he object under study is a monolithic reinforced concrete building (fig. 1), whose columns are mounted on metal supports. the dynamic behavior of the building is described in the framework of the linear theory of viscoelasticity. the concrete is assumed to be viscoelastic and isotropic, and steel reinforcement is modeled within the framework of the linear theory of elasticity. the mathematical model is represented by the following relations. equations of motion: 2 2 div , v t       u x (1) t testing stand model rc structure i. shardakov et alii, frattura ed integrità strutturale, 46 (2018) 383-390; doi: 10.3221/igf-esis.46.35 385 physical relations:    2 e 2 e 1 2 1 2 g i g i                           (2) geometrical relations:   t  u u (3) boundary conditions:      , / ,f t f t mw t s x s    n n 0, /s s   n x (4) initial conditions for t = 0: 0, / 0u du dt  (5) here: c rv v v  is the total volume of the structure, consisting of the volumes vc and vr, occupied by concrete and steel reinforcement; , ,  , е are, the tensors of stresses, strain, strain rates and a unit tensor, respectively;    ,i i  are the first invariants of the strain tensor and of the strain rate tensor; x is radius vector of a point in the cartesian coordinate system; u is the displacement vector; n is the unit vector oriented along the outward normal to the surface s of the structure; s is the surface, to which an external impulse force is applied along its normal; ρ is the material density, f (t) is a scalar that determines the time variation of the force impulse; m is the striker mass, w(t) (scalar) is the striker acceleration in the interval of striker contact with the surface of the structure (this value is recorded experimentally by an accelerometer mounted on the striker); (,  ) denote vector and scalar products;  is the nabla operator; g is the shear modulus,  is the poisson's ratio; β is the parameter characterizing the dissipative properties of concrete. at cx v the values of ρ, g, , β correspond to the physical properties of concrete, and at rx v they correspond to the physical properties of steel reinforcement. figure 2: the finite element model of rc structure: (a) – a fragment of the column; (b) – reinforcement of the joint of the column, slab and cross beams; (c) – assembled structure; (d) – slab fragment; (e) – beam fragment. the numerical implementation of the mathematical model is carried out by the finite element method using ansys software. fig. 2 shows the finite element mesh of the model structure (the number of nodes is 506569). it represents the main components of the structure (columns, crossbars and slabs) and their reinforcement schemes. the characteristic geometric parameters of the model structure and the physical properties of the materials are given below. (a) (b) (c) (d) (e) i. shardakov et alii, frattura ed integrità strutturale, 46 (2018) 383-390; doi: 10.3221/igf-esis.46.35 386  the main geometric characteristics of the model structure: column space is 2 m; height of the floor is 1.5 m; cross section of the column is 200 × 200 mm; cross-section of the cross beam is 200 × 250 mm; thickness of the slab is 150 mm; diameter of the reinforcement of columns and lower chords of cross beams is 12 mm, diameter of the other reinforcement is 8 mm.  physical characteristics of concrete:  0.102 ;  17.2g gpa;   73.46 10 ;  2507 kg/ m3.  physical characteristics of steel:  0.3 ;  76.9g gpa;  0 ;  7800 kg/ m3.  characteristic dimension of the finite element mesh: 0.1 m.  integration time step: 10–5 s. verification of the mathematical model based on experimental results o verify the mathematical model, we performed a series of experiments, in which the dynamic deformation response of the structure to a locally applied external impulse force was analyzed. we used three loading schemes, of which two involved impact loading of the column and the registration of the deformation response to this impact at different points of the columns (fig.3, a, b) and the third (fig. 3, c) provided impact load of the lower edge of the floor slab and the registration of the response at its upper edge. locations of the sensors recording the response of the structure to the externally applied impact loads are indicated by the red dots in the figures. these sensors recorded the vector component of acceleration directed along the normal to the surface, at which the sensors were located. fig. 3 presents the fragments of the general model structure shown in figs. 1 and 2c. these are the fragments in which the deformation response to the impact action was analyzed. the sizes of the selected fragments of the structure were chosen in such a way that at the points of recording the deformation responses there are no waves reflected from the boundaries of the fragment within the time interval under consideration. the external impulse force was generated by a striker with a mass of 460 g. the value of acceleration w (t), resulting from the impact of the striker on the surface of the structure, was recorded by an accelerometer zetlab bc111 fixed to the striker. the range of recorded frequencies of this accelerometer is 0.5-15000 hz. the deformation response of the structure to the impulse force was registered by the zetlab bc110 accelerometers, fixed at various points of the structure (the range of recorded frequencies is 0.5–10000 hz). transformation of the collected sensor data to a digital form was performed synchronously using the adc zet 017-u8 with a frequency of 50 khz. (a) (b) (c) figure 3: schemes of loading and registration of response. as an example, fig. 4 shows the experimentally measured shape of the force impulse and the corresponding fourier image (load diagram is given in fig. 3a). as follows from these data, the impulse duration is 0.28 ms, and the main part of impulse energy is localized in the frequency range of 0-5 khz. it should be noted that the experimentally recorded value of the force impulse was used in the mathematical model (1) (5) to specify the boundary condition (4). then, the results of numerical simulation were compared with experimental data obtained from accelerometers recording the deformation responses to impact. when making a comparison, the calculated and experimental data were subjected to frequency filtering, ensuring the removal of the signal at frequencies above 6 khz. fig. 5 shows a series of vibrograms and the corresponding fourier images for three loading schemes (a, b, c) presented in fig. 3. the experimental data are indicated by blue lines and the simulation data by red lines. a comparison of the results obtained demonstrates good agreement between the model and the experiment in the frequency range from 0 to 6khz. t i. shardakov et alii, frattura ed integrità strutturale, 46 (2018) 383-390; doi: 10.3221/igf-esis.46.35 387 (a) (b) figure 4: impulse load: (a) – force evolution. (b) – fourier transform. scheme vibrogram fourier transform a b c figure 5: vibrograms and corresponding foutier transforms for three loading schemes. analysis of changes in vibrograms caused by crack initiation he proposed model (1)-(5), which passed the verification procedure, was used for numerical analysis of changes in the vibration parameters of the rc structure in the period of nucleation and propagation of cracks. the most probable places for crack formation in the structure are the connections of vertical columns with floor slabs and cross beams. in accordance with fig. 6, we considered a fragment of the structure, for which we simulated the subsequent nucleation of cracks at the crossbar-to-column connections. four crack nucleation stages were identified: the crack t1 appeared at the first stage, and cracks t2, t3 and t4 were successively formed at the next three stages. the numerical experiment consists in solving successively the problems of the dynamic deformation response of the structure to equal, locally applied impulse loads at all stages of crack nucleation. the examined structural fragment, the schemes of loading and registration of deformation response correspond to the scheme shown in fig. 3b. to characterize the external force action, we used the parameters of the force impulse, determined experimentally at the stage of verification of the mathematical model. as before, the implementation of the numerical experiment was based on the finite element method using the ansys software package. to simulate the crack, we excluded from the calculation one layer of finite elements for concrete adjacent to the face of the column, retaining yet the finite elements for the reinforcement to provide simulation of its integrity. as already mentioned, the evolution of crack formation was determined by a sequence of 4 stages: the first stage is associated with the formation of crack t1 followed by successive nucleation of cracks t2, t3, and t4 at the next three t i. shardakov et alii, frattura ed integrità strutturale, 46 (2018) 383-390; doi: 10.3221/igf-esis.46.35 388 stages. the cracks were located in the cross sections of the cross beams. the depth of the crack was 150 mm, the thickness of the undestroyed part of the crossbar was 100 mm. the location of the prospective sensor for recording the dynamic deformation response is indicated by a red dot on the vertical column above the crack formation zone (point s in fig. 6). it is evident that the cracks always locate in the region between the impact point and the sensor. figure 6: location of cracks at the bottom of the column. the results of the numerical simulation in the form of vibrograms and their fourier images for point s are shown by red lines in the graphs in fig. 7. a blue line shown in the same graphs for the sake of comparison corresponds to the experimental data obtained for the defect-free structure (fig. 5, vibrogram b). these results demonstrate that a significant distortion of the vibration patterns and their fourier images occurs at each stage after nucleation of a new crack. stage vibrogram fourier image 1 2 3 4 figure 7: changes in vibrograms at crack formation. the most intense free vibrations of the structure are realized at frequencies around 3400 hz. a comparison of the amplitude value ka of the fourier image at this frequency with the value 0a obtained at the same frequency in the defectfree structure carries important information. the ratio of these values * 0/kk a a can be considered as an informative parameter that responds to the process of crack growth. fig. 7 shows a variation in the criterion *k taken at the i. shardakov et alii, frattura ed integrità strutturale, 46 (2018) 383-390; doi: 10.3221/igf-esis.46.35 389 frequency of 3400 hz (corresponding to the most intense vibrations) with the growth of damage in the structure. the first column corresponds to the defect-free structure, and the other columns – to the structures, in which the number of cracks increases. in this case, the value of the criterion increases markedly. figure 8: criterion * 0/kk a a at different stages of cracking. conclusion n this work, verification of a mathematical model of dynamic processes in a reinforced concrete structure was carried out within the framework of viscoelasticity. a comparison of the experimental and calculated data has demonstrated that this model can be effectively used to describe with sufficient accuracy the propagation of vibration processes initiated by external, locally applied impact loads. a series of numerical experiments performed on the basis of the mathematical model allowed us to investigate changes in the vibration parameters of the rc structure, in which the process of crack formation has started. as a parameter, characterizing the process of crack nucleation, we used the ratio of the amplitude values of the fourier transform in the defect and defect-free structure obtained at the frequency of the most severe vibrations. on the whole, the results of this study served to determine the substance of the desired algorithm for implementing the vibration diagnosis of reinforced concrete structures with the aim to control the process of crack formation. acknowledgments he research was performed at the institute of continuous media mechanics ural branch of russian academy of science with the support of the russian science foundation (project №14-29-00172). references [1] verma, s.k., bhadauria, s.s. and akhtar, s. (2013). review of non destructive testing methods for condition monitoring of concrete structures, j. constr. eng, 834572. doi: 10.1155/2013/834572. [2] fan, w. and qiao, p. (2011). vibration-based damage identification methods: a review and comparative study, structural health monitoring. 10(1), pp. 83-111. doi: 10.1177/1475921710365419. [3] stepinski, t., uhl, t., and staszewski, w. (2013). advanced structural damage detection: from theory to engineering applications., john wiley & sons. doi:10.1002/9781118536148. [4] wang, l. and chan, t.h.t. (2009). review of vibration-based damage detection and condition assessment of bridge structures using structural health monitoring., proc. of the second infrastructure theme postgraduate conference. queensland university of technology. paper id 26738. http://eprints.qut.edu.au/. [5] quaranta, g., carbonu, b. and lacarbonara, w. (2014). damage detection by modal curvatures: numerical issues, j. vibr. contr. 22 (7) pp. 1913-1927. doi: 10.1177/1077546314545528. [6] bykov, a.a., matveenko, v.p., serovaev, g.s., shardakov, i.n. and shestakov, a.p. (2015). mathematical modeling of vibration processes in reinforced concrete structures for setting up crack initiation monitoring, mech. solids, 50 (2), pp. 160-170. doi: 10.3103/s0025654415020053. i t i. shardakov et alii, frattura ed integrità strutturale, 46 (2018) 383-390; doi: 10.3221/igf-esis.46.35 390 [7] raghavan a. and cesnik c.e.s. (2007). review of guided-wave structural health monitoring, shock and vibration digest, 39 (2), pp. 91–114. doi: 10.1177/0583102406075428. [8] liu, x.l., jiang, z.w. and ji, l. (2013). investigation on the design of piezoelectric actuator/sensor for damage detection in beam with lamb waves, exp. mech. 53 (3), pp. 485–492. doi: 10.1007/s11340-012-9646-9. [9] song g., gu h., mo y. l., hsu t. t. c., dhonde h. (2007). concrete structural health monitoring using embedded piezoceramic transducers, smart mater. struct. 16(4), pp. 959–968. doi: 10.1088/0964-1726/16/4/003. [10] bykov, a.a., matveenko, v.p., shardakov, i.n. and shestakov, a.p. (2017). shock wave method for monitoring crack repair processes in reinforced concrete structures, mech. solids 52 (4), pp. 378–383. doi: 10.3103/s0025654417040033. [11] fröjd p. and ulriksen p. (2016). amplitude and phase measurements of continuous diffuse fields for structural health monitoring of concrete structures, ndt&e international, 77, pp. 35–41. doi: 0.1016/j.ndteint.2015.10.003. [12] xu, k., deng, q., cai, l., ho, s. and song, g (2018). damage detection of a concrete column subject to blast loads using embedded piezoceramic transducers, sensors, 18 (5), 1377. doi: 10.3390/s18051377. << /ascii85encodepages false /allowtransparency false /autopositionepsfiles true /autorotatepages /none /binding /left /calgrayprofile (dot gain 20%) /calrgbprofile (srgb iec61966-2.1) /calcmykprofile (u.s. web coated \050swop\051 v2) /srgbprofile (srgb iec61966-2.1) /cannotembedfontpolicy /error /compatibilitylevel 1.4 /compressobjects /tags /compresspages true /convertimagestoindexed true /passthroughjpegimages true /createjobticket false /defaultrenderingintent /default /detectblends true /detectcurves 0.0000 /colorconversionstrategy /cmyk /dothumbnails false /embedallfonts true /embedopentype false /parseiccprofilesincomments true /embedjoboptions true /dscreportinglevel 0 /emitdscwarnings false /endpage -1 /imagememory 1048576 /lockdistillerparams false /maxsubsetpct 100 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can be opened with acrobat and adobe reader 5.0 and later.) >> /namespace [ (adobe) (common) (1.0) ] /othernamespaces [ << /asreaderspreads false /cropimagestoframes true /errorcontrol /warnandcontinue /flattenerignorespreadoverrides false /includeguidesgrids false /includenonprinting false /includeslug false /namespace [ (adobe) (indesign) (4.0) ] /omitplacedbitmaps false /omitplacedeps false /omitplacedpdf false /simulateoverprint /legacy >> << /addbleedmarks false /addcolorbars false /addcropmarks false /addpageinfo false /addregmarks false /convertcolors /converttocmyk /destinationprofilename () /destinationprofileselector /documentcmyk /downsample16bitimages true /flattenerpreset << /presetselector /mediumresolution >> /formelements false /generatestructure false /includebookmarks false /includehyperlinks false /includeinteractive false /includelayers false /includeprofiles false /multimediahandling /useobjectsettings /namespace [ (adobe) (creativesuite) (2.0) ] /pdfxoutputintentprofileselector /documentcmyk /preserveediting true /untaggedcmykhandling /leaveuntagged /untaggedrgbhandling /usedocumentprofile /usedocumentbleed false >> ] >> setdistillerparams << /hwresolution [2400 2400] /pagesize [612.000 792.000] >> setpagedevice microsoft word numero_62_art_24_3672.docx m. tedjini et alii, frattura ed integrità strutturale, 62 (2022) 336-348; doi: 10.3221/igf-esis.62.24 336 on the use of the stepped isostress method in the prediction of creep behavior of polyamide 6  tedjini mohsein, sedira lakhdar, guerira belhi laboratoire de génie mécanique (lgm), university of biskra, algeria mohsein.tedjini@gmail.com l.sedira@univ-biskra.dz, http://orcid.org/0000-0003-1735-2195 b.guerira@univ-biskra.dz kamel meftah laboratoire de génie energétique et matériaux (lgem), university of biskra, algeria university of batna 2, algeria k.meftah@univ-batna2.dz, http://orcid.org/0000-0002-5671-602x abstract. the stepped isostress method (ssm) is an advanced technique which allows the prediction of the long-term behavior and enables the construction of creep master curves of materials with short-term experimental tests. however, the performance of this method is highly dependent on the numerical model and the time spent in data processing. in this paper, the effect of the extrapolation techniques on the creep curves trend is investigated using the ssm data of polyamide test. three extrapolation functions are used to offset the delay of the stress history: polynomial, power and exponential functions. furthermore, a numerical routine is developed during the last step of the ssm, where the shift factors are computed taking into account the rescaling and the dwell times of each level of stresses. the processing of the ssm raw data has revealed that the rescaling parameters are the most determining factors to reach an accurate long-term creep curves. the rescaling process has shown an appropriate time, whether achieved by the exponential or power functions. larger shift factors for exponential functions are assessed and therefore a long period of creep master curve was obtained. keywords. creep; polyamide 6; fitting function; ssm method; master curve. citation: tedjini, m., sedira, l., guerira, b., meftah, k., on the use of the stepped isostress method in the prediction of creep behavior of polyamide 6, frattura ed integrità strutturale, 62 (2022) 336-348. received: 13.07.2022 accepted: 20.08.2022 online first: 01.09.2022 published: 01.10.2022 copyright: © 2022 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. https://youtu.be/w_-8inlvxg8 m. tedjini et alii, frattura ed integrità strutturale, 62 (2022) 336-348; doi: 10.3221/igf-esis.62.24 337 introduction ll mechanical structures are subjected to instantaneous loads which cause either elastic, plastic or combined behaviors. nevertheless, a viscous effect under monotonic loads can be observed under different scenarios, the most common being dependence on the rate of deformation, dependence on temperature, creep and relaxation [1]. although it is generally overlooked for some solid materials, the viscous effects play a major part in defining the mechanical response of polymers. many experiments were conducted with different techniques to predict the mechanical behavior of materials, starting with simple mechanical experiments such as tensile [2], compression [3], finishing by creep and relaxation tests [4]. however, the creep was among the most important natural phenomena which can describe the material behavior overtime just under his weight influence and through that, we can find further mechanical properties. thus, the creep test is conducted on material in order to measure its tendency to deform under constant loading; however, this test requires a very long dwell time [5]. formerly, the heat factor was considered as the main accelerator of the creep behavior with very large scale time. it is assumed that the creep response for one temperature can be achieved by another temperature at delayed time, the time-temperature superposition principle (ttsp) was therefore developed and given serious results [6–8]. however, since the elevated temperature may affect the chemical properties of the tested material, a particular care should be devoted to ttsp when the thermo-sensitive materials are processed. to avoid the negative temperature effect and following an equivalent energy loading, the high stress level is also considered as a creep accelerator factor. therefore, the time stress superposition principle (tssp) was derived from the ttsp and adopted in several researches where improved results are obtained [9,10]. among others, hadid et al. [9] have used this approach to predict the long-term material creep behavior of the injection fiber glass reinforced polyamide, an improved empirical model (power law) is used and an excellent superposition of curves is obtained. based on both temperature and stress effects, a novel approach called time temperature stress superposition concept (ttss) is invented thereafter to reduce abundance of samples and to get more accurate results [11,12]. this last one remains very complex, even though it overcomes the negative heat impact and the samples abundance. dealing with temperature loads as piecewise constant functions is considered afterwards as a revolution in the long term prediction techniques. therefore, the stepped isothermal method (sim) [13] was developed firstly by thornton et al. [14] and successfully used in several subsequent researches. this approach helped to reduce the large number of samples; but it maximizes the heat impact possibility. when dealing with thick specimens, concern regarding the rapid heating and the non-uniform temperature distribution in the specimen needs to be investigated [15]. as logical extension of sim method, the technique of stepped iso-stress method (ssm) is emerged as an enhanced solution to both problems: the multiplicity of samples and the heat effect. recent studies have been performed by giannopoulos et al. [16,17] that have dealt with kevlar material and aramid yarns in terms of mechanical properties, creep, stress and rupture. after that, the effectiveness of this method versus the tssp method, for specimens of polyamide 6 having a large thickness, has been confirmed in co-author's previous work [5]. as a sequel to this work, the authors [15] analyzed the effect of different testing parameters of the ssm on a commercial polyamide 6 creep tests. the obtained master curves based on power law in rescaling process, correlate well with those obtained with the classical tssp. the authors have shown that the variation in the dwell time or the change in the stress increment do not affect the creep of studied material. later, tanks et al. [18] applied two numerical processing in the ssm method in order to investigate the creep behavior of unidirectional carbon lamina used in rehabilitating prestressed concrete structures. both of power-law and prony series methods are used in rescaling procedure for addressing stress history. the power-law was shown to be more conservative by overestimating creep strains, but this is less material efficient for design over the longterm [18]. recently, guedes [19] proposed an analytical method to process the ssm raw data. based on two different viscoelastic models, the method is validated through numerical simulations to assess the creep tests. also, in order to study the effect of multilayered material on the physico-mechanical properties of bamboo-polypropylene composite (bpcs), hsu et al. [20] extended their analysis to time depending behavior using the ssm accelerated creep approach. the results have shown that the ssm creep master curves agree well with the long-term experimental creep. the creep master curves were also not influenced by different stress increments and dwelling time variations. one of the numerical problems encountered with accelerated techniques in construction of the long-term creep curve of plastic materials is uncertainty the fitting method used to address stress or temperature history, which affects the magnitude of the shift factors developed from the data. the uncertainty can be reduced by testing multiple samples but at significant cost. in this context, some convergence problems were raised in our previous works [15], this was due to efficiency of the method used in solving of the optimization problem on one hand, and to the high number of the data a m. tedjini et alii, frattura ed integrità strutturale, 62 (2022) 336-348; doi: 10.3221/igf-esis.62.24 338 points addressed in fitting process, on the other hand. to this end, the extrapolation model was performed using limited number of points from the starting range of the short-term creep, which did not necessarily lead to a perfect model. an approach that help to overcome this problem consists to use an improved solving method, which is enhanced with additional convergence criterion, can fulfill a good convergence with merely random initial conditions. in order to simulate the creep deformations behavior of the adhesive joints through finite element-based numerical analyses, sadigh et al. [21] have used the called levenberg-marquardt algorithm to fit a power-law model at a variety of stress and temperature levels. the goodness of the fitting procedure was checked using the standard error of their estimations. the main goal of the present study is to investigate the effect of the numerical processing data on the construction of the master creep curves of polyamide 6 using the stepped isostress method. three extrapolating functions are tested during the stress history rescaling and an improved method for solving the optimization problems is used. in addition, a numerical routine is developed in order to estimate the shift factors and to perform all the corresponding time shifting operations. this is expected to achieve improved long-term-creep curves. materials and methods preparation of polyamide he material tested in the present work is a polyamide 6, trade mark domamid 6bkbl, with a melting temperature tf =221 °c and density ρ =1.1 g/cm3 (iso 1183). the raw material was mixed using thermo scientific haake polylab qc extruder (screw speed 30 rpm and heated zones about 221 °c as an average temperature). plane sheets of 4 mm thickness were manufactured through a compression molding process: the material was heated to a melt temperature and progressively pressed in a rectangular mold (up to 200 bar). laboratory hydraulic press (schwabenthan polystat 300 s) was used for a total time of 10 minutes (4 minutes for preheating and 6 minutes for compression). cad and a laser process were carried out to design dumbbell-shape specimens. the dimensions of tensile and creep test specimens are chosen as per iso 527-2, type 1b, with thickness h=4 (see fig. 1). the specimens are stored in an atmosphere with 20% of humidity for at least one month. tensile test uniaxial tensile experiments were performed, using moderately thick specimens of pa6. the tests are conducted by instron 5969 testing machine equipped with 5kn cell force. the specimens are loaded at ambient temperature (25 °c) and 30% of humidity. the load was applied by moving the crosshead of the machine at a specific rate of 1 mm/min (according to iso 527-1: plastics-determination of tensile properties). the deformation is measured with an advanced video extensometer (ave). the traction test allows determining the linear mechanical properties of the polyamide, and the stress levels which will be considered for creep tests. ssm method the classical approach (tssp) is generally applied to obtain the creep master curve [15,16,19], using a set of tensile creep tests on at least one specimen per each stress level. to overcome these limitations, the ssm technique is adopted in this work with reduced number of specimens and a valuable gain in time. in this ssm tests, the temperature of 25 °c was set and kept constant throughout a period of the tests. the deformation is measured with a clamp extensometer and the machine is controlled by data acquisition software that allows complex loading sequences to be performed. a starting reference load was initially applied to the specimen (5 mpa), and stair-step loads with five levels are programmed (10, 15, 20, 25, 30 mpa). a dwell time of 2 hours for each load step is considered. the method is generally depending on a set of processes clearly performed in the following sections to reach the final results and to get the adequate master curves. figure 1: dimensions of the test specimens. t m. tedjini et alii, frattura ed integrità strutturale, 62 (2022) 336-348; doi: 10.3221/igf-esis.62.24 339 at the beginning of the experiment, an initial vertical adjustment step is necessary to allow matching of the true starting point for each curve. the change from load to greater level is instantaneous. however, a shift in deformation due to the elastic nature of the material is observed. this step is to erase an element of elasticity and to link the beginning of the current curve with the end of the previous one. in fact, the creep in each step is the accumulation of the creep strain resulting from the applied stress in the current stress level, and also from the creep strain of the previous steps. so, a series of consecutive dependent curves should be separated. however, the creep response of material is considered as a timeinvariant behavior since a time-delay on the applied load directly equates to a time-delay of the output response. this aimed at seeking a rescaling time which physically reflects a loading start point, assuming that the test has been conducted under the same stress but on a previously unstressed specimen. according to the time–temperature superposition principle (ttsp), this preprocessing is essential to fulfill the unified conditions of boltzmann principle. in order to calculate the rescaling factors, an exponential function is proposed to extrapolate the experimental curves of the raw short time creep, eqn.1.         0 1 1 2 2xp expa e t t a t t (1) where t is an independent variable. 0, a1, a2, t1 and t2 are constants. that can be computed by matching with the experiment data through a nonlinear regression for each stress level. two others fitting functions are also analyzed. the third degree polynomial function proposed by achereiner et al. [13], given in eqn.2 and the power law function presented in our previous research [15], eqn.3.        2 30 1 2 3a t a t a t (2)     0 0 n t t (3) where the constants a1, a2, a3, t0 and n are computed as mentioned above. it should be noted that all functions have been fitted considering the full time range in the extrapolation process. further details are discussed in subsequent section. the horizontal shifting is a horizontal displacement of the curves in terms of the logarithmic time. it can be achieved by computing the shifting factor (), which is the ratio between the time for a viscoelastic process to proceed at an arbitrary stress and the time for the same process to proceed at a reference stress [16]. the creep strain is defined as:        , , /r r t t (4) where  is the strain as a function of stress and time, r is the reference stress,  is the elevated stress and ασ is the shift factor. the independent creep curves can be shifted along the logarithmic time axis to obtain the creep master curve at reference stress. the evolution of the shift factor that expresses the creep rate with the stress can be represented by two models, namely the modified model of williams-landel-ferry given in eqn. 5, or the eyring model given in eqn. 6, [15].               1 2 log( ) r r c c (5) where c1 and c2 are material constants.                     * log log 2.30 r r v k t (6) where  and r are the strain rate and a reference strain rate respectively, v* is the activation volume, k is boltzmann’s constant and t is the absolute temperature. eqn. 6 is more suitable for the present case, since the creep temperature is below the glass transition temperature. in addition, polyamide 6 is a semi-crystalline polymer, and it is more appropriate to use the eyring model [15,16,22]. m. tedjini et alii, frattura ed integrità strutturale, 62 (2022) 336-348; doi: 10.3221/igf-esis.62.24 340 however, the strain rate is considered as a control factor in the pa6 response and creep behavior. it can be graphically determined for each stress level from the slope of the secondary creep portion of the strain-time curve of the experiment result, eqn. 7.     t (7) contrary to the method used in previous research, where the strain rate is calculated in a global way and taking into account only two points of the curve, i.e. the total slope of the curve, in this work, an instantaneous strain rate will be considered in computation of the shift factor. for this purpose, the same numerical extrapolation proposed in rescaling process (eqn.1) will be derived and adopted to calculate the strain creep variation, eqn. 8.          1 1 1 2 2 2( ) exp expt a t t t a t t t (8) after that, an average value is then computed over the dwell time for each stress level and substituted in eqn. 6. both the rescaling and the logarithmic shifting can be done graphically but it is better to follow a numerical procedure at each stress step. estimation of shift factor  and t-axis shifted values at each stress level can be obtained following numerical method depicted in fig. 2. figure 2: numerical flowchart of the horizontal shifting. yes nomenclature: ns : number of load steps nps: number of time measurements in each load step (1d table). t : response time (2d table) i : time counter j : load step counter trescaling : rescaling time of each step (1d table).  : shift factor (1d table) start        ns,j=,nps,it(i,j), ns,,j=jt ns,j=nps(j),ns rescale 11 ,1 ,1 , read           2 11111 11    j ,t,npstδt ασ nsj          jt,jt/jδtjα rescaleσ  11  jnpsi           j,tj,jnpstj )+ δt(j-jδt 1 1    1 ii 1 jj write  , t end      j,itjj,it  1i yes no no m. tedjini et alii, frattura ed integrità strutturale, 62 (2022) 336-348; doi: 10.3221/igf-esis.62.24 341 optimization method in this research, the constants parameters of the creep strain function are computed using levenberg-marquardt method. in fitting m(x,t), a function of an independent variable t and a vector of n parameters x, to a set of m data points (ti, i), the summation of the weighted squares of the differences between the experimental data (ti) and the value of the preassumed function m(x,ti) should be minimized [21], (eqn. 9). it consists to find the minimum value of the objective function f, defined as follow:      2 1 1 1 (x) (x) (x) (x) 2 2 m t i i f f f f (9) where fi are the residuals for data points ( , )i it defined as:   i( x ) (x,t )i if m (10) as regards n:f r r , it follows from the first formulation in eqn.9, that       1 (x) (x) (x) x x m t i i ij j ff f (11) thus, its gradient is   t(x) (x) (x)f j f ; (  m nj r is the jacobian of f ) (12) the non linear least squares problem can be solved by general optimization methods. the gauss-newton method is the basic of the very efficient methods, based on a linear approximation to the components of f (a linear model of f ) in the neighbourhood of x : for small h , we can write :    (x h) (h) (x) (x) hf l f j (13) and    1 (x h) (h) (h) (h) 2 tf l l l (14) full expression of l(h) can be obtained by substitution (eqn.13) in (eqn.14). the gradient and the hessian of l are   t t(h) (x) (x) (x) hl j f j ;   t(h) (x) (x)l j j (15) so, at a minimum of the sum of squares f, the gauss–newton step h minimizes l(h) (i.e. l'(h)=0), the unique value can be found by solving    t(x) (x) h (x)j j g ; with (x) (x) (x)g j f (16) a damping parameter  is introduced thereafter by levenberg and marquardt [23]. the step hlm is defined by the following modification to (eqn.16). however, to ensure a good convergence, i.e. steepest descent direction and reduced step length, the method is controlled by additional stopping criteria, (see algorithm 1.) where the damping parameter is adjusted at each iteration [24].    t lmj(x) j(x) i h (x)g (17) m. tedjini et alii, frattura ed integrità strutturale, 62 (2022) 336-348; doi: 10.3221/igf-esis.62.24 342 algorithm 1. levenberg–marquardt method [24] begin : 0k ;  : 2 ;   0:x x : (x) (x)ta j j ; : (x) (x) tg j f    1test: g e ;    : max iia ; (e1 , e2 and τ are chosen by the user) while (not test) and (  maxk k )  : 1k k ; solve    lmha i g if   lm 2 lm 2h he e then test :=true else  new lmx : x h             new lm lm 1 : (x) (x ) h h 2 tf f g if   0 then  newx: x : (x) (x) ta j j ;  t: (x) (x)g j f    1test: g e         3: max 1 3, 1 2 1 ;  : 2 else    : ;   : 2 end results and discussion tensile test he evolution of the stress with respect to the deformation is presented in fig. 3. first the material exhibits a linear relationship depicted as hookean behavior. the slope of the tangent to the stress-strain curve throughout the elastic range is measured (2.9 gpa) and a value of 61 mpa is recorded as a tensile strength at yield elongation (3.40 %). the most important in this curve is the elastic limit 37 mpa to use next as a pilot in the creep experience. ssm test an initial vertical adjustment is performed to the recorded data. all the creep curves are plotted referring to a constant offset (0=0.37 %). however, an increase of strain is observed in each stress jump. in fact, an elastic part which is a real response of the rump function applied in the beginning of each stress is observed between successive stress levels. this elastic strain is measured and eliminated from strain versus time curves of polyamide. since the elastic modulus is affected after a period of creep, the short term creep curves are adjusted vertically according to the reference [16]. this is achieved graphically by matching every end point of the current strain curve with the start point of the next one, fig. 4a. so, a series of purely creep curves for each stress level are illustrated in fig. 4b. however, in order to take into account the stress history and to perform a master curve, a horizontal rescaling of all curves is carried out through the time-axis. the short-term creep results are dependent responses, that reflect a creep behavior under an accumulate stress. these short term curves are extended to the left in order to seeking the rescaling time (tresc). this is depicted by the required time to achieve the onset of strain (0) for the reference stress. for this purpose, the effect of the curve fitting and the extrapolating functions to approximate this time are analyzed using power, third degree polynomial and exponential models. in order to overcome this problem, the already discussed levenberg– marquardt method (algorithm 1) is used in the present work, taking into account the entire database of measurements (n  7200). once the fitting model is aligned to the experimental curve, it is necessary to equalize the expression of the t m. tedjini et alii, frattura ed integrità strutturale, 62 (2022) 336-348; doi: 10.3221/igf-esis.62.24 343 obtained model and the onset strain 0. hence, the requested rescaling time is computed by solving the obtained non linear equation. associated curves are depicted in fig. 4c and show an excellent fitting between the three functions and the experimental results.   figure 3: pa6 tensile curve. the exponential function fits perfectly the experimental data of the short term curve with r2 value of 0.999. (r2= 0.976 and 0.971 for power law and r2=0.997 for third degree polynomial), for 5 and 10 mpa, respectively. however, some differences are noted through the extrapolation domain, moving back to the left where the slopes of the functions give rise to a significant deviation, particularly inherent to polynomial function. the rescaling times deduced by each extrapolating functions are reported in tab. 1. we can see that the results of the power law and exponential function are very close. on the other hand, the polynomial function shows the lowest time, a deviation of up to an hour for high stress levels is occurred. in contrast to some research [18], a greater rescaling time with exponential curve fitting is obtained in the present work. mathematically, this is in good agreement with the effect of the strain rate, once the strain rate increases, the slope of the curve is systematically high, and therefore, the rescaling time is susceptible to take meaningful values. the most advantageous of the present approach that the total dwelling time range is considered in interpolation process. unlike to other researches [5,9,16] where only a limited range of time, before and after the onset of each stress/strain response, is considered. on the other hand, all fitting functions are applied so that theirs curves could mimic those of the first creep experimental curve (5 mpa): the curves obtained by the power and exponential functions are in good agreement with data relating to the zero value (expected zero time at 0). the first raw of tab. 1 shows that the power and exponential functions respectively are close to zero value (-20 s and 5.7 s), in contrast with a higher error (1050 s) assessed by the third polynomial function. in order to complete the process to obtain the shifting factors, equality between the maximum and the lower strain that can be achieve by the reference and the actual stress respectively is considered. the logarithmic shifting can be done graphically but numerical process depicted in the flow chart is adopted, fig. 2. fig. 5a illustrates the computed shifting factors for a set of independent curves obtained by the three extrapolation functions. it can be found that all models give increasing values and the trend of their evolution follows a power function. fig. 5b refers to a bar chart representation for log (), at first sight, an almost linear variation can be noted. the corresponding values of the power and exponential functions are close to each other and exhibit higher values than the polynomial function. it is noteworthy that the deviation observed between the shift factors for different functions is justified by the close dependence on the rescaling time. examining flowchart, fig. 2, an assumed inversely proportional relationship between the shift factor and the rescaled initial time of each level is found. each new shift factor is also inversely related to all previous values of rescaling time. the fact that the exponential function has presented the largest rescaling time values, and therefore the shortest time to achieve the maximum strain of the reference level, thus resulting the largest inverse value that affect the shift factors. the same numerical process is applied to address the shift of the independent creep curves versus t-axis times. the curves for long-term creep prediction in semi-logarithmic and linear time scale are plotted in the figs. 6a and 6b, respectively. the present method has allowed one to achieve smooth master creep curves without gap between the different short creep responses. on the whole, a large deviation between the three curves was shown in figs. 7a and 7b. however, all of them reach the same strain with delayed time: the unified master curve for the polynomial function covers a period of m. tedjini et alii, frattura ed integrità strutturale, 62 (2022) 336-348; doi: 10.3221/igf-esis.62.24 344 14.27 days approximately (t=1.233106 s). however, a significant improvement can be shown by the power function, where t=2.315107 s, (8.92 months) is obtained. in contrast, a long creep time is estimated at about 2.45 years (t=7.624107 s) using the exponential function. figure 4: required handling of the raw data of ssm load (mpa) rescaling time (h) polynomial rescaling time (h) power law rescaling time (h) exponential 5 -0.2917 0.0016 -0.0056 10 1.3750 1.7914 1.8194 15 3.1306 3.6851 3.7889 20 4.8667 5.5500 5.6722 25 6.7222 7.4322 7.6139 30 8.5389 9.2080 9.5083 table 1: rescaling time (trescaling) this large discrepancy between the third-order polynomial, power law and exponential models can be related to the accuracy of the rescaling time assessment in the beginning of each extrapolation functions. an inadequate value has a significant influence on the horizontal rescaling and shifting processes and affects, therefore the final master curve obtained by each model. however, a numerical criterion that could be helpful to judge the quality of the predictions, assumes that the rheological model of the creep behavior should be operative at all stress level. it found that the third order polynomial is less able to imitate this behavior in the reference stress (tab. 1). in contrast, the exponential (prony series approximation) and the power law models that fulfill this assumption, and satisfy the zero time value for zero creep strain, can be considered the better prediction. 0 10000 20000 30000 40000 50000 0,0 0,5 1,0 1,5 2,0 2,5 3,0 3,5 4,0 c re e p  s tr a in  ( % ) time (s)  ssm experimental result 0 10000 20000 30000 40000 50000 0,0 0,2 0,4 0,6 0,8 1,0 1,2 1,4 1,6 polynomial power exponential c re e p s tr a in (% ) time (s) 30 mpa 25 mpa 20 mpa 15 mpa 10 mpa 5 mpa tresc (polynomial) tresc (power) tresc (exponential) 0=0.37 (%) (b) elimination elastic zone and vertical shifting (d) rescaling curves (a)ssm test 0 10000 20000 30000 40000 50000 0,4 0,6 0,8 1,0 1,2 1,4 1,6 c re e p  s tr a in  ( % ) time (s)  5 mpa  10 mpa  15 mpa  20 mpa  25 mpa  30 mpa 0 2000 4000 6000 8000 10000 12000 0,4 0,6 0,8 1,0 1,2 1,4 1,6 30 mpa 25 mpa 20 mpa 15 mpa 10 mpa  polynomial  power  exponential c re e p  s tr a in  ( % ) time (s) 5 mpa (c) extrapolation and rescaling curves m. tedjini et alii, frattura ed integrità strutturale, 62 (2022) 336-348; doi: 10.3221/igf-esis.62.24 345 figure 5: shift factors values vs. accelerating stresses for different extrapolate functions, (a)  and (b) log (). figure 6: final master curves with different extrapolate techniques, (a) logarithmic time scale, (b) linear time scale. m. tedjini et alii, frattura ed integrità strutturale, 62 (2022) 336-348; doi: 10.3221/igf-esis.62.24 346 1e‐02 1e+00 1e+02 1e+04 1e+06 1e+08 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 c re e p  s tr a in  ( % ) log t (s)  exponential  polynomial  power 0.0e+00 2.0e+07 4.0e+07 6.0e+07 8.0e+07 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 c re e p  s tr a in  ( % ) time (s)  exponential  polynomial  power figure 7: effect of extrapolation techniques on the prediction of the long term creep, (a) logarithmic time scale, (b) linear time scale. figure 8: effect of extrapolation functions on the activation volume activation volume the activation volume can be presented as the slope between the log () and the accelerator stress variables, fig. 8. a parabola trends with a coefficient of determination equal to r2=0.999 have been derived from the different fitting functions using experimental data. however, when assessing the quadratic function, the coefficient of the quadratic term is too small compared to the linear term. instead, a very close linear form can be addressed with (r2=0.994). it should be noted that, a parabolic form has been adopted by the co-authors [15], which was shown to be more consistent with the eyring model given in eqn. 6, and agree well with the previous results, further details are given in [17]. therefore, the slightly linear variation in the activation volume of each increased stress creates new configuration of molecular chains. the current chain configuration is a build-up of all the previous creep bearings. the fact that the polymer molecules are continuously pulled during the creep process, the creep behavior of a previously strained material occupies a larger activation volume than an unstrained material [15]. conclusions n the present research, the stepped isostress method is used to predict the long-term creep behavior of moderately thick specimens of polyamide 6. different empirical model were considered to simulate the strong nonlinearity of the viscoelastic behavior of the considered material under a piecewise constant stress. a third degree polynomial, power and exponential fitting functions are developed and examined trough the construction of the master curve. the assessment of the suggested parameters of the fitted models requires an improved numerical solving method to be considered. the use of levenberg-marquardt algorithm allows to overcome the limited use of data points in extrapolation 0 5 10 15 20 25 30 0,0 0,5 1,0 1,5 2,0 2,5 3,0 3,5 4,0 s h ift f a ct o r, lo g (  ) -0 (mpa) polynomial power exponential polynomial fit, r2=0.999 i (a) (b) m. tedjini et alii, frattura ed integrità strutturale, 62 (2022) 336-348; doi: 10.3221/igf-esis.62.24 347 process and leads to excellent convergence and accuracy. the handling and processing of the ssm raw data have been performed automatically, where a computational subroutine is developed. the numerical process reveals that the magnitude of the shift factor is strongly affected by the accuracy of the inverse of the rescaling time on one hand and has a proportional relationship with the dwell time on the other hand. however, a larger shift factors for the exponential as well as for the power functions are obtained and therefore, larger long-term master curves were estimated with a very close agreement. the construction of the master curve confirms the consistence of the eyring equation and the relationship between the shift factor and the creep stress. acknowledgements he authors would like to thank the plastics laboratory staff of biskra cable industry for their help in the preparation of material and specimens. references [1] dan-andrei, ş. (2016).viscoplastic behaviour of polyamides. viscoelastic and viscoplastic materials, intechopen. [2] atidel, g., saintier, n., dhiab, a., dammak, f. (2011). etude du comportement mécanique d’un polyamide 66 chargé de fibres de verre courtes, mec. ind., 12(5), pp. 333–342, doi: 10.1051/meca/2011104. [3] gnip, i.j., kersulis, v.i., vaitkus, s.i., veyelis, s.a. (2005). long-term prediction of creep strain of expanded polystyrene, mech. compos. mater., 41(6), pp. 535–540, doi: 10.1007/s11029-006-0007-6. [4] raghavan, j., meshii, m. (1998). creep of polymer composites, compos. sci. technol., 57(12), pp. 1673–1688, doi: 10.1016/s0266-3538(97)00104-8. [5] hadid, m., guerira, b., bahri, m., zouani, k. (2014). the creep master curve construction for the polyamide 6 by the stepped isostress method, mater. res. innov., 18(sup6), pp. s6-336-s6-339, doi: 10.1179/1432891714z.0000000001022. [6] yang, j.l., zhang, z., schlarb, a.k., friedrich, k. (2006). on the characterization of tensile creep resistance of polyamide 66 nanocomposites. part i. experimental results and general discussions, polymer (guildf)., 47(8), pp. 2791–2801, doi: 10.1016/j.polymer.2006.02.065. [7] dean, d., husband, m., trimmer, m. (1998). time-temperature-dependent behavior of a substituted poly(paraphenylene): tensile, creep, and dynamic mechanical properties in the glassy state, j. polym. sci. part b polym. phys., 36(16), pp. 2971–2979, doi: 10.1002/(sici)1099-0488(19981130)36:16<2971::aid-polb12>3.0.co;2-r. [8] arnold, j.c., venditti, n.p. (2007). prediction of the long-term creep behaviour of hydroxyapatite-filled polyethylmethacrylate bone cements, j. mater. sci. mater. med., 18(9), pp. 1849–1858, doi: 10.1007/s10856-007-3056-z. [9] hadid, m., rechak, s., tati, a. (2004). long-term bending creep behavior prediction of injection molded composite using stress-time correspondence principle, mater. sci. eng. a, 385(1–2), pp. 54–58, doi: 10.1016/j.msea.2004.04.023. [10] luo, w.b., wang, c.h., vu-khanh, t., jazouli, s. (2007). time-stress equivalence: application to nonlinear creep of polypropylene, j. cent. south univ. technol. (english ed., 14(1 suppl.), pp. 310–313, doi: 10.1007/s11771-007-0271-1. [11] luo, w., wang, c., zhao, r. (2007).application of time-temperature-stress superposition principle to nonlinear creep of poly(methyl methacrylate). key engineering materials, 340-341 ii, trans tech publ, pp. 1091–6. [12] larbi, s., berradj, m., djebbar, a., bilek, a. (2011). prediction of creep behaviour of the hybrid composite material using the accelerated characterisation method, adv. mater. res., 324, pp. 356–359, doi: 10.4028/www.scientific.net/amr.324.356. [13] achereiner, f., engelsing, k., bastian, m., heidemeyer, p. (2013). accelerated creep testing of polymers using the stepped isothermal method, polym. test., 32(3), pp. 447–454, doi: 10.1016/j.polymertesting.2013.01.014. [14] thornton, j.s., allen, s.r., thomas, r.w., sandri, d. (1998).the stepped isothermal method for time-temperature superposition and its application to creep data on polyester yarn. proceedings of sixth international conference on geosynthetics, 2, pp. 699–706. t m. tedjini et alii, frattura ed integrità strutturale, 62 (2022) 336-348; doi: 10.3221/igf-esis.62.24 348 [15] hadid, m., guerira, b., bahri, m., zouani, a. (2014). assessment of the stepped isostress method in the prediction of long term creep of thermoplastics, polym. test., 34, pp. 113–119, doi: 10.1016/j.polymertesting.2014.01.003. [16] giannopoulos, i.p., burgoyne, c.j. (2011). prediction of the long-term behaviour of high modulus fibres using the stepped isostress method (ssm), j. mater. sci., 46(24), pp. 7660–7671, doi: 10.1007/s10853-011-5743-x. [17] giannopoulos, i.p., burgoyne, c.j. (2012). accelerated and real-time creep and creep-rupture results for aramid fibers, j. appl. polym. sci., 125(5), pp. 3856–3870, doi: 10.1002/app.36707. [18] tanks, j., rader, k., sharp, s., sakai, t. (2017). accelerated creep and creep-rupture testing of transverse unidirectional carbon/epoxy lamina based on the stepped isostress method, compos. struct., 159, pp. 455–462, doi: 10.1016/j.compstruct.2016.09.096. [19] guedes, r.m. (2018). a systematic methodology for creep master curve construction using the stepped isostress method (ssm): a numerical assessment, mech. time-dependent mater., 22(1), pp. 79–93, doi: 10.1007/s11043-017-9353-0. [20] hsu, c.y., yang, t.c., wu, t.l., hung, k.c., wu, j.h. (2018). effects of a layered structure on the physicomechanical properties and extended creep behavior of bamboo-polypropylene composites (bpcs) determined by the stepped isostress method, holzforschung, 72(7), pp. 589–597, doi: 10.1515/hf-2017-0165. [21] sadigh, m.a.s., paygozar, b., da silva, l.f.m., tahami, f.v. (2019). creep deformation simulation of adhesively bonded joints at different temperature levels using a modified power-law model, polym. test., 79, doi: 10.1016/j.polymertesting.2019.106087. [22] ward, i.m., sweeney, j. (2012). mechanical properties of solid polymers, john wiley & sons. [23] marquardt, d.w. (1963). an algorithm for least-squares estimation of nonlinear parameters, j. soc. ind. appl. math., 11(2), doi: 10.1137/0111030. [24] madsen, k., nielsen, h.b., tingleff, o. 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can be opened with acrobat and adobe reader 5.0 and later.) >> /namespace [ (adobe) (common) (1.0) ] /othernamespaces [ << /asreaderspreads false /cropimagestoframes true /errorcontrol /warnandcontinue /flattenerignorespreadoverrides false /includeguidesgrids false /includenonprinting false /includeslug false /namespace [ (adobe) (indesign) (4.0) ] /omitplacedbitmaps false /omitplacedeps false /omitplacedpdf false /simulateoverprint /legacy >> << /addbleedmarks false /addcolorbars false /addcropmarks false /addpageinfo false /addregmarks false /convertcolors /converttocmyk /destinationprofilename () /destinationprofileselector /documentcmyk /downsample16bitimages true /flattenerpreset << /presetselector /mediumresolution >> /formelements false /generatestructure false /includebookmarks false /includehyperlinks false /includeinteractive false /includelayers false /includeprofiles false /multimediahandling /useobjectsettings /namespace [ (adobe) (creativesuite) (2.0) ] /pdfxoutputintentprofileselector /documentcmyk /preserveediting true /untaggedcmykhandling /leaveuntagged /untaggedrgbhandling /usedocumentprofile /usedocumentbleed false >> ] >> setdistillerparams << /hwresolution [2400 2400] /pagesize [612.000 792.000] >> setpagedevice microsoft word numero_53_art_02_2680 m. c. oliveira et alii, frattura ed integrità strutturale, 53 (2020) 13-25; doi: 10.3221/igf-esis.53.02 13 shear behaviour of reinforced concrete beams under impact loads by the lumped damage framework mateus cardoso oliveira, daniel victor da cunha teles, david leonardo nascimento de figueiredo amorim laboratory of mathematical modelling in civil engineering, post-graduation programme in civil engineering, department of civil engineering, federal university of sergipe, são cristóvão, brazil mateusoliver490@gmail.com, http://orcid.org/0000-0001-6227-8516 danielvcteles@gmail.com, http://orcid.org/0000-0002-9206-6351 david.amorim@ufs.br, http://orcid.org/0000-0002-9233-3114 abstract. impact loadings such as vehicle collisions or falling rocks on a structure could lead it to collapse and, eventually, to fatal victims. among possible alternatives to analyse this issue, lumped damage mechanics is an interesting option due to its formulation and easiness for practical application. therefore, this paper presents a simplified lumped damage model to evaluate reinforced concrete structures under impact loads with shear failure mode. in the proposed approach, the damage variable is considered as an output parameter. such damage variable takes values between zero and one, which quantifies the concrete cracking due to impact loading. the proposed formulation was applied in experiments of reinforced concrete beams under impact loads that presents shear collapse. the obtained results showed good accuracy between the proposed model and the actual structural behaviour. moreover, a possible flowchart for practical applications is also presented. since the model parameters are easily associated to inelastic phenomena, the proposed formulation might become accessible to engineers in practice. keywords. impact load; reinforced concrete beams; shear failure; lumped damage mechanics. citation: oliveira, m.c., teles, d.v.c., amorim, d.l.n.f., shear behaviour of reinforced concrete beams under impact loads by the lumped damage framework, frattura ed integrità strutturale, 53 (2020) 13-25. received: 11.11.2019 accepted: 15.04.2020 published: 01.07.2020 copyright: © 2019 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. introduction ccidents involving impact loads often occur on reinforced concrete structures. some usual accidents are vehicles that collide on structures, explosions, rock-fall, falling of heavy objects or parts of another structure in the construction phase, and impact of ships in docks. in such cases, engineers often need a consistent and immediate result of the structural response. a https://youtu.be/j1ei78unrr4 m. c. oliveira et alii, frattura ed integrità strutturale, 53 (2020) 13-25; doi: 10.3221/igf-esis.53.02 14 during the impact, the structural response can be obtained by fracture mechanics [1] or continuous damage mechanics [2]. however, such theories are applied in a finite element analysis that present an excessive computational cost and depict results that difficult their use for several engineering applications, making their practical application unfeasible in many cases. on the other hand, lumped damage mechanics (ldm) combines and applies fundamental concepts of continuous damage mechanics and fracture mechanics, such as the strain equivalence hypothesis and the griffith criterion, with the concept of plastic hinges. ldm is an interesting alternative for several civil engineering applications. this theory was initially proposed by flórez-lópez [3] to analyse reinforced concrete structures under seismic loads, and the first book about ldm was published in 2015 [4]. ldm has already been used to satisfactorily analyse several structures with actual engineering applications, such as simple and reinforced concrete structures, bridges and masonry arches [5-14]. recently, uchoa et al. [15] proposed a ldm based methodology to estimate the loss of flexural stiffness in simple concrete beams subjected to the four-point bending experimental test. the collapse of reinforced concrete (rc) beams subjected to impact loads can be caused by bending moment [16, 17] or shear force [18-22]. li et al. [23] and pham et al. [24] showed that the contact stiffness has limited effect in impulse and midspan displacement response. previous studies have proposed numerical models to evaluate behaviour response of the rc beams under low impact velocity [25-29]. fan et al. [30] proposed a finite element analysis in order to predict flexural and shear responses of rc beams and columns subjected to low impact velocity. however, due to differences in rc beams behaviour under low and high impact velocities, there are not enough studies in this theme, especially for high velocities. according to zhao et al. [22], shear failure in rc beams has not yet been adequately understood, unlike bending failure. kishi et al. [18] showed that rc beams that under static load fail by bending, may fail by shear when subjected to high impact loads. in order to evaluate the ability of rc beams to resist shear under impact loads, simplified analytical model have been proposed [18-21]. nonlinear analyses using finite elements can also be applied. for instance, zhao et al. [22] used an elastoplastic damage model with three-dimensional finite elements. this type of application results in a high computational cost and complex interpretation of the numerical results. in the light of the foregoing, this paper presents an alternative approach based on ldm that estimates the response of rc beams subjected to shear failure due to impact loads. the proposed formulation is obtained by the thermodynamic of irreversible processes. since the proposed formulation is quite simple, structural safety might be easily analysed with practical engineering criteria. finally, the accuracy of the proposed ldm model is verified by comparing the obtained results with experimental responses [22]. lumped damage mechanics general overview onsider a finite beam element between nodes i and j, as the one depicted in fig. 1a. the deformed shape of the beam element can be described by the flexure rotations i and j at the nodes i and j, respectively. both flexure rotations are set in the matrix of generalised deformations, defined as:    tji φ (1) where the superscript t means ‘transpose of’. in order to take into account the inelastic phenomena, the finite element is now understood as an assemblage of an elasticplastic-damage timoshenko beam with two inelastic hinges at its edges, as shown in fig. 1b. note that the bending inelastic effects are lumped at the hinges and the shear ones are distributed along the beam element. for rc beams, the damage variables di and dj account for the bending concrete cracking, the plastic flexure rotations i p and j p quantify the yielding of the longitudinal reinforcement, the damage variable ds measures the shear concrete cracking and the plastic distortion  p accounts for the yielding of the transversal reinforcement (fig. 1c). the matrix of generalised stresses {m} is defined as a set of bending moments, mi and mj, which are conjugated with generalised deformations i and j (fig. 1c). c m. c. oliveira et alii, frattura ed integrità strutturale, 53 (2020) 13-25; doi: 10.3221/igf-esis.53.02 15    tji mmm (2) figure 1: lumped damage beam: (a) deformed shape, (b) finite element and (c) inelastic variables. according to the deformation equivalence hypothesis [4], the matrix of generalised deformations can be expressed as:            ppdde γφγφφφ  (3) where {e is the matrix of elastic deformations, given by [4]:      mmφ                         lgalga lgalga ei l ei l ei l ei l e 11 11 36 63 (4) being e the young’s modulus, g the shear modulus, i the inertia moment and a the cross section area; {d is the matrix that represents the deformation of the beam due to bending cracking in concrete by means of damage variables (di e dj) in each hinge, given by [4]:        mφ                j j i i d dei ld dei ld 13 0 0 13 (5) {d is the matrix that represents the beam distortion caused by diagonal shear cracks through the damage variable ds, expressed as [4]:            mγ                s s s s s s s s d dlga d dlga d dlga d dlga d 11 11 (6) m. c. oliveira et alii, frattura ed integrità strutturale, 53 (2020) 13-25; doi: 10.3221/igf-esis.53.02 16 {p is the matrix that quantifies the deformation caused by the yielding of the longitudinal reinforcement, i.e.:    tpjpip φ (7) and {p is the matrix that represents the plastic distortion of the beam caused by the yielding of the transversal reinforcement (fig. 1c), given by:    tppp γ (8) hence, the elastic relation is obtained by substituting (4-8) in (3):                        mm mffγφφ                                  ss ss j i ssjif pp dlgadlga dlgadlga dei l ei l ei l dei l d,dd 1 1 1 1 1 1 1 1 136 613 (9) where [ff (di , dj)] and [fs (ds)] are the flexibility matrices due flexural and shear cracking, respectively. thermodynamic approach considering a beam element with a certain level of flexure and shear damage as well as plastic rotations and distortion, the total thermodynamic potential is given by the helmholtz’s free specific energy [34, 35]:      pptpp γφφdεγφφ  2 1  (10) being  the total thermodynamic potential and [e(d)] the stiffness matrix of the damaged element, given by:        1 ssjif d,dd ff]d[ε (11) where (d) = (di , dj , ds) is the set of the damage variables. for a proper definition, the model must be thermodynamically admissible. this condition is achieved through clausiusduhem inequality, which is also called as non-negative dissipation. thus, considering that the process is isothermal, such inequality is expressed as:     0 φm t (12) where the first term is the variation of the internal energy involved in the process and the second one is the variation of the thermodynamic potential. assuming that the total thermodynamic potential can be linearized around the current values of the state variables, then:                ddγγφφφφ  t p t p p t p t                                       (13) therefore, the clausius-duhem inequality is rewritten as: m. c. oliveira et alii, frattura ed integrità strutturale, 53 (2020) 13-25; doi: 10.3221/igf-esis.53.02 17                   0                                           d d γ γ φ φ φ φ m  t p t p p t p t t  (14) eqn. (14) must be obeyed in any thermodynamic process, including one that is fully reversible, where the inelastic effects are null. this can be observed since the derivation of the total thermodynamic potential in relation to the total generalised deformations results in the generalised stress matrix, according to the following expression:        mγφφdε φ          pp (15) the other differential relations of thermodynamic potential in relation to state variables are given by the following expressions:        mγφφdεφ        pp p  (16)        mγφφdεγ        pp p  (17)            y d                                                    s j i s ji j j i i y y y dlga mm dei lm dei lm 2 2 2 2 2 2 12 16 16  (18) it is observed that {m}, –{m}, –{m} and {y} are the thermodynamics variables associated with {}, { p}, { p} and {d}, respectively, being yi and yj the damage driving moments of the hinges i and j, and ys the damage driving moment of the shear cracking along the beam [4]. therefore, by substituting the expressions (15-18) in the inequality (14) and assuming the predominance of shear effects, then:     0 sspt dy γm (19) the inequality (19) must be obeyed throughout the structural analysis. therefore, the positivity of each term must be ensured separately, since both inelastic phenomena (plastic deformations and damage) can occur non-simultaneously (considering any application, not only for rc beams). in the first term of (19) it is noted that the internal stress present in the matrix {m} always have the same signs of the generalised plastic distortion rate, therefore, the positivity of the first term is verified. since the physical and geometric properties of the structural element under analysis, as well as the damage variable, are always positive, then the positivity of the second term is achieved. proposed modelling of impact problems n order to analyse the nonlinear response of simply supported beams under impact loads, fujikake et al. [17] performed experiments in which a known mass body (hammer) is released from four different heights. with these experiments, an analytical model based on the energy balance of a two-degree-of-freedom mass-spring-damping system was i m. c. oliveira et alii, frattura ed integrità strutturale, 53 (2020) 13-25; doi: 10.3221/igf-esis.53.02 18 presented with the purpose of quantify the behaviour of rc beams under impact loads. thus, the energy dissipated (ep) during the impact is given by [17]:       max212 21 21 2 2 22 gwmmv mm mmvm dwwpe p    (20) being m1 and m2 the beam and hammer masses respectively, g the acceleration of gravity, wmax the maximum displacement (mid-span), and v the impact velocity, given by: ghv 2 (21) where h is the drop height. it is worthy noted that the analytical eqn. (20), presented by fujikake et al. [17], has been successfully applied on shear impact problems in the technical literature [18-21]. therewith, by equalling both energy dissipation equations, i.e. (19) and (20), for a simply supported beam as the one depicted in fig. 2 and assuming, for the sake of simplicity, that shear damage and plastic distortion after impact are characterised by their final values (ds and p), then:       ss jp j d dlga m mgwmmv mm mmvm 2 2 max21 2 21 21 2 2 1222      (22) being the bending moment mj calculated with the mean impact force pm (fig. 3):   dt p d p m dttpi t i p 0 (23) where ip is the impulse and td is the impact duration. figure 2: simply supported beam under impact load and its mathematical model in the aftermath. m. c. oliveira et alii, frattura ed integrità strutturale, 53 (2020) 13-25; doi: 10.3221/igf-esis.53.02 19 figure 3: force-time graph for impact loads. results and discussion xperiments performed by zhao et al. [22] and bhatti et al. [37] were used in order to analyse the proposed shear impact model. zhao et al. [22] the beams present 3m span (2l), longitudinal reinforcement composed of four bars with 20mm in the tension side and two bars with 16mm in the compression side, with yield stress of 495.5mpa and ultimate tension of 620.2mpa. the stirrups consisted of 6mm bars spaced by 30cm, with yield stress 344.7mpa and ultimate tension of 550.4mpa [22]. other properties of the beams are presented in tab. 1, as well as some dynamic response values. beam – impact weight (kg) – drop height (m) cross section (cm) compressive strength of concrete (mpa) mean impact force (kn) beam c-1700-4.60 20×50 32.14 205.22 beam c-1300-5.56 30.25 296.88 beam c-868-7.14 26.26 286.71 table 1: properties of the analysed beams. therefore, for each beam, the damage variable (ds) and the plastic distortion are obtained from eqn. (9) and (22). this calculation process was performed to evaluate the applicability of the proposed formulation. the damage and the plastic distortion calculated on each beam is shown in tab. 2. fig. 3 shows a scheme with the crack pattern after impact. the obtained damage values are high, meaning that a severe cracking level in the three beams, which is consistent with the experimentally observed cracking patterns (fig. 4). furthermore, by knowing the value of the plastic distortion ( p), it is possible to determine the plastic displacement of the beam (fig. 2): lw pp  (24) in order to illustrate the proposed approach, the solution of beam c-1700-4.60 [22] is described as follows. firstly, eqn. (9) must be rewritten to agree with the mathematical model of the beam (fig. 2). therewith, it is assumed that the inelastic effects due to bending moment are negligible. then, the constitutive relation for a simply supported beam is given as:      mffγφ ssfp d (25) e m. c. oliveira et alii, frattura ed integrità strutturale, 53 (2020) 13-25; doi: 10.3221/igf-esis.53.02 20 which leads to:   js j p j m dlga m ei l   1 1 3  (26) beam – impact weight (kg) – fall height (m) damage (ds) plastic distortion (p) estimated plastic displacement (cm) experimental plastic displacement (cm) [22] beam c-1700-4.60 0.9681 0.0750729 11.3 not available beam c-1300-5.56 0.9603 0.0402814 6.0 ≅ 5.2 beam c-868-7.14 0.9601 0.0404670 6.1 ≅ 5.0 table 2: damage and plastic distortion results for the analysed beams. figure 4: beam cracking patterns after impact. (source: adapted from zhao et al. [22]). since zhao et al. [22] presented the maximum displacement (wmax) of the beam, eqn. (26) can be rewritten as:   js j p j m dlga m ei l l w   1 1 3 max  (27) note that eqn. (27) is a simple rearrangement of eqn. (9) according to the analysed problem. the young’s modulus can be estimated by any design code regulation. in this paper, the brazilian code [36] was used i.e. m. c. oliveira et alii, frattura ed integrità strutturale, 53 (2020) 13-25; doi: 10.3221/igf-esis.53.02 21 ckfe 5600 (28) being fck the compressive strength of concrete, given in mpa. for beam c-1700-4.60 [22], eqns. (27) and (22) give, respectively, the following relations (units in n and m):  s p d  1 78940000775692.0 850011635391.070786666666.0  (29)  21 969534875.5 9250.15391443033.17227 s sp d d    (30) then, by solving this nonlinear system (29-30) the shear damage (ds) and plastic distortion ( p) are, respectively, 0.9681 and 0.0750729. finally, by using eqn. (24) the plastic displacement (wp) is estimated in 11.3 cm. bhatti et al. [37] the beams presented span of 2.0 m and cross section with 20 cm of basis and 40 cm of height. the concrete compressive strength is 41.2 mpa and its young’s modulus is 25.7 gpa. all beams casted by bhatti et al. [37] present two rebars of 35 mm as longitudinal reinforcement at both sides and two types of transversal reinforcements: 6 mm @ 15.0 cm (type a) and 6 mm @ 7.5 cm (type b). both longitudinal and transversal reinforcements present yield stress and young’s modulus of 373 mpa and 206 gpa, respectively. the impact velocity and the mean impact force on each beam is given in tab. 3. beam – impact velocity (m/s) mean impact force (kn) a-4.6 397.35 a-6.5 463.05 a-8.4 635.66 b-4.6 419.47 b-7.4 509.01 b-9.3 614.62 table 3: properties of the analysed beams. therefore, damage and plastic distortion were obtained by applying the same procedure previously illustrated (tab. 4). fig. 5 shows cracking pattern presented in the beams after impact. beam – impact velocity (m/s) damage (ds) plastic distortion (p) estimated plastic displacement (cm) experimental plastic displacement (cm) [37] a-4.6 0.9446 0.0066656 0.667 ≅ 0.362 a-6.5 0.9505 0.0107417 1.074 ≅ 0.590 a-8.4 0.9516 0.0184035 1.840 ≅ 0.944 b-4.6 0.9327 0.0070843 0.708 ≅ 0.203 b-7.4 0.9469 0.0143020 1.430 ≅ 0.663 b-9.3 0.9579 0.0201287 2.013 ≅ 1.235 table 4: damage and plastic distortion results for the analysed beams. m. c. oliveira et alii, frattura ed integrità strutturale, 53 (2020) 13-25; doi: 10.3221/igf-esis.53.02 22 figure 5: beam cracking patterns after impact. (source: adapted from bhatti et al. [37]). note that the calculated plastic displacements are quite close to the experimental ones. the absolute difference between the estimated and experimental responses varies from 0.305 cm to 0.846 cm, approximately. note that in all cases the estimated response is greater than the experimental one. therefore, the proposed procedure can estimate the actual structural behaviour analytically. since the proposed formulation can be applied to real problems quite easily, a sequence of actions is proposed based on the flowchart shown in fig. 6. thus, during accidents involving impact load on reinforced concrete structures, the field engineer can obtain the necessary parameters for the model damage calculation, which are: data of the structure characteristics, obtained in the design; data of the impact nature that can be measured with an analysis of where the accident occurred and the application of basic concepts of physics. thus, from the level of permanent deformation of the structure, it is possible to calculate the plastic distortion. then the damage (ds) and maximum displacement (wmax) values are calculated based on eqn. (22). finally, as observed in the experiments of zhao et. al. [22], the damage variable indicates how severe the impact load was and, then, could be used to create practical engineering criteria. figure 6: demonstrative flowchart of the structural accident assessment procedure. m. c. oliveira et alii, frattura ed integrità strutturale, 53 (2020) 13-25; doi: 10.3221/igf-esis.53.02 23 conclusions he proposed shear impact model was able to obtain damage, plastic distortion and plastic displacement values for each beam tested by zhao et al. [22] and bhatti et al. [37]. this damage variable is associated with the cracking level of the beam due to the shear effect. analogously, the calculated plastic distortion is associated with the stirrup yielding. note that the damage and plastic displacement values calculated with the proposed formulation are in agreement with the experimental observations of zhao et al. [22]. a possibility for practical applications is represented by a flowchart (fig. 6) that describes the procedure for obtaining the necessary data and then indicates their application in the proposed model, obtaining the damage values and maximum displacement of the structure. by means of the damage value, it is possible to objectively evaluate cracking level of the structural element and then determine its type of rehabilitation. therefore, further experiments are needed to corroborate and validate the accuracy of the proposed formulation. notwithstanding, it is expected that with a larger experimental campaign it will be possible to adjust equations that describe the concrete crack resistance and reinforcement yielding, similar to that performed by teles et. al. [29]. additionally, with more results it is possible to relate damage ranges with repair levels, similar to the ones proposed by flórez-lópez et al. [4] for static loadings. acknowledgements he authors thank the laboratory of mathematical modelling in civil engineering of the post-graduation programme in civil engineering of the federal university of sergipe – lamec/proec/ufs for the physical space during the development of this work. the second author thanks copes/posgrap/ufs for their financial support. references [1] broek, d. (1984). elementary engineering fracture mechanics, dordrecht, martinus nijhoff publishers. [2] lemaitre, j., chaboche, j.l. (1985). mécaniques des matériaux solides, 1. ed., paris, dunod. [3] flórez-lópez, j. (1991). modelos de daño concentrado para la simulación del colapso de pórticos planos, rev. int. metod. numer., 9(2), pp. 123-139. [4] flórez-lópez, j., marante, m.e., picón, r. (2015). fracture and damage mechanics for structural engineering of frames: state-of-the-art industrial applications, hershey, igi global. doi: 10.4018/978-1-4666-6379-4. [5] cipollina, a., lópez-inojosa, a., flórez-lópez, j. (1995). a simplified damage mechanics approach to nonlinear analysis of frames. comput. struct., 54(6), pp. 1113-1126. doi: 10.1016/0045-7949(94)00394-i. [6] liu, y.-b., liu, j.-b. (2004). a damage beam element model for nonlinear analysis of reinforced concrete member, earthq. eng. eng. vib., 24(2), pp. 95-100. [7] araujo, f., proença, s.p.b. (2008). application of a lumped dissipation model to reinforced concrete structures with the consideration of residual strains and cycles of hysteresis, j. mech. mater. struct., 3(5), pp. 1011-1031. doi: 10.2140/jomms.2008.3.1011. [8] faleiro, j., oller, s., barbat, a.h. (2010). plastic-damage analysis of reinforced concrete frames, eng. computation., 27(1), pp. 57-83. doi: 10.1108/02644401011008522. [9] alva, g. m. s., el debs, a. l. h. c. (2010). application of lumped dissipation model in nonlinear analysis of reinforced concrete structures, eng. struct., 132(4), pp. 974-981. doi: 10.1016/j.engstruct.2009.12.024. [10] toi, y., hasegawa, k.h. (2011). element-size independent, elasto-plastic damage analysis of framed structures using the adaptively shifted integration technique, comput. struct., 89(23-24), pp. 2162-2168. doi: 10.1016/j.compstruc.2011.09.002. [11] perdomo, m.e., picón, r., marante, m.e., hild, f., roux, s., flórez-lópez, j. (2013). experimental analysis and mathematical modeling of fracture in rc elements with any aspect ratio, eng. struct., 46, pp. 407–416, doi: 10.1016/j.engstruct.2012.07.005. t t m. c. oliveira et alii, frattura ed integrità strutturale, 53 (2020) 13-25; doi: 10.3221/igf-esis.53.02 24 [12] santoro, m.g., kunnath, s.k. (2013). damage-based rc beam element for nonlinear structural analysis, eng. struct., 49, pp. 733-742. doi: 10.1016/j.engstruct.2012.12.026. [13] amorim, d. l. n. f., proença, s. p. b., flórez-lópez, j. (2013). a model of fracture in reinforced concrete arches based on lumped damage mechanics, int. j. solids struct., 50(24), pp. 4070-4079. doi: 10.1016/j.ijsolstr.2013.08.012. [14] amorim, d. l. n. f., proença, s. p. b., flórez-lópez, j. (2014). simplified modeling of cracking in concrete: application in tunnel linings, eng. struct., 70, pp. 23-35. doi: 10.1016/j.engstruct.2014.03.031. [15] uchoa, b.c.l., amorim, d.l.n.f., assis, w.s. (2018). aplicação da teoria do dano concentrado para estimativa da rigidez à flexão em vigas de concreto simples. proceedings of the 1st iberic conference on theoretical and experimental mechanics and materials / 11th national congress on experimental mechanics, 729-38, porto, portugal. [16] hughes, g., beeby, a.w. (1982). investigation of the effect of impact loading on concrete beams, struct. eng., 60, pp. 45-52. [17] fujikake, k., li, b., soeun, s. (2009). impact response of reinforced concrete beam and its analytical evaluation, j. struct. eng-asce, 135(august 2009), pp. 938–50. doi: 10.1061/(asce)st.1943-541x.0000039. [18] kishi, n., mikami, h., matsuoka, k., ando, t. (2002). impact behavior of shear-failure-type rc beams without shear rebar, int. j. impact eng., 27(9), pp. 955-968. doi: 10.1016/s0734-743x(01)00149-x. [19] saatci, s., vecchio, f. j. (2009). effects of shear mechanisms on impact behavior of reinforced concrete beams, aci struct. j., 106(1), pp. 78–86. doi: 10.14359/56286. [20] cotsovos, d. m. (2010). a simplified approach for assessing the load carrying capacity of reinforced concrete beams under concentrated load applied at high rates, int. j. impact eng., 37(8), pp. 907–917. doi: 10.1016/j.ijimpeng.2010.01.005. [21] yi, w.-j., zhao, d.-b., kunnath, s.k. (2016). simplified approach for assessing shear resistance of reinforced concrete beams under impact loads, aci struct. j., 113(4), pp. 747–756. doi: 10.14359/51688617. [22] zhao, d., yi, w., kunnath, s.k., asce, f. (2017). shear mechanisms in reinforced concrete beams under impact loading, j. sruct. eng., 143(9), pp. 1–13, doi: 10.1061/(asce)st.1943-541x.0001818. [23] li, h., chen, w., & hao, h. (2018). influence of drop weight geometry and interlayer on impact behavior of rc beams, int. j. impact eng., 131, pp. 222-237, doi: 10.1016/j.ijimpeng.2019.04.028. [24] pham, t. m., hao, y., & hao, h. (2018). sensitivity of impact behaviour of rc beams to contact stiffness, int. j. impact eng., 112, pp. 155-164, doi: 10.1016/j.ijimpeng.2017.09.015. [25] wongmatar, p., hansapinyo, c., vimonsatit, v., & chen, w. (2018), recommendations for designing reinforced concrete beams against low velocity impact loads, int. j. struct. stab. dy., 18(09), pp. 1850104-1–1850104-21, doi: 10.1142/s0219455418501043. [26] adhikary, s. d., li, b., & fujikake, k. (2015). low velocity impact response of reinforced concrete beams: experimental and numerical investigation, int. j. prot. struct., 6(1), pp. 81-111, doi: 10.1260/2041-4196.6.1.81. [27] adhikary, s. d., li, b., & fujikake, k. (2016). state-of-the-art review on low-velocity impact response of reinforced concrete beams, mag. concrete res., 68(14), pp. 701-723, doi: 10.1680/jmacr.15.00084. [28] das adhikary, s., & li, b. (2018). simplified analytical models to predict low-velocity impact response of rc beams, pract. period. struct. des. construct., 23(2), pp. 04018002-1– 04018002-10, doi: 10.1061/(asce)sc.1943-5576.0000357. [29] teles, d. v. c., oliveira, m. c., & amorim, d. l. n. f. (2020). a simplified lumped damage model for reinforced concrete beams under impact loads, eng. struct., 205(110070), pp. 1-10, doi: 10.1016/j.engstruct.2019.110070. [30] fan, w., liu, b., huang, x., & sun, y. (2019). efficient modeling of flexural and shear behaviors in reinforced concrete beams and columns subjected to low-velocity impact loading, eng. struct., 195, pp. 22-50, doi: 10.1016/j.engstruct.2019.05.082. [31] saatci, s., vecchio, f. j. (2009). effects of shear mechanisms on impact behavior of reinforced concrete beams, aci struct. j., 106(1), pp. 78–86. doi: 10.14359/56286. [32] cotsovos, d. m. (2010). a simplified approach for assessing the load carrying capacity of reinforced concrete beams under concentrated load applied at high rates, int. j. impact eng., 37(8), pp. 907–917. doi: 10.1016/j.ijimpeng.2010.01.005. [33] yi, w.-j., zhao, d.-b., kunnath, s.k. (2016). simplified approach for assessing shear resistance of reinforced concrete beams under impact loads, aci struct. j., 113(4), doi: 10.14359/51688617. m. c. oliveira et alii, frattura ed integrità strutturale, 53 (2020) 13-25; doi: 10.3221/igf-esis.53.02 25 [34] lemaitre, j., desmorat, r. (2005). engineering damage mechanics, berlin, springer-verlag. [35] ragueneau, f., la borderie, c., mazars, j. (2000). damage model for concrete-like materials coupling cracking and friction, contribution towards structural damping: first uniaxial applications, mech. cohes.-frict. mat., 5(8), pp. 607625. doi: 10.1002/1099-1484(200011)5:8<607::aid-cfm108>3.0.co;2-k. [36] associação brasileira de normas técnicas. nbr 6118: projeto de estruturas de concreto — procedimento. rio de janeiro, pp. 238. 2014. [37] bhatti, a. q., kishi, n., mikami, h., ando, t. 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can be opened with acrobat and adobe reader 5.0 and later.) >> /namespace [ (adobe) (common) (1.0) ] /othernamespaces [ << /asreaderspreads false /cropimagestoframes true /errorcontrol /warnandcontinue /flattenerignorespreadoverrides false /includeguidesgrids false /includenonprinting false /includeslug false /namespace [ (adobe) (indesign) (4.0) ] /omitplacedbitmaps false /omitplacedeps false /omitplacedpdf false /simulateoverprint /legacy >> << /addbleedmarks false /addcolorbars false /addcropmarks false /addpageinfo false /addregmarks false /convertcolors /converttocmyk /destinationprofilename () /destinationprofileselector /documentcmyk /downsample16bitimages true /flattenerpreset << /presetselector /mediumresolution >> /formelements false /generatestructure false /includebookmarks false /includehyperlinks false /includeinteractive false /includelayers false /includeprofiles false /multimediahandling /useobjectsettings /namespace [ (adobe) (creativesuite) (2.0) ] /pdfxoutputintentprofileselector /documentcmyk /preserveediting true /untaggedcmykhandling /leaveuntagged /untaggedrgbhandling /usedocumentprofile /usedocumentbleed false >> ] >> setdistillerparams << /hwresolution [2400 2400] /pagesize [612.000 792.000] >> setpagedevice microsoft word numero 20 articolo 1 r. brighenti et alii, frattura ed integrità strutturale, 20 (2012) 6-16; doi: 10.3221/igf-esis.20.01 6 crack path dependence on inhomogeneities of material microstructure roberto brighenti, andrea carpinteri, andrea spagnoli, daniela scorza department of civil and environmental engineering & architecture, university of parma, viale usberti, 181/a, 43124 parma, italy spagnoli@unipr.it abstract. crack trajectories under different loading conditions and material microstructural features play an important role when the conditions of crack initiation and crack growth under fatigue loading have to be evaluated. unavoidable inhomogeneities in the material microstructure tend to affect the crack propagation pattern, especially in the short crack regime. several crack extension criteria have been proposed in the past decades to describe crack paths under mixed mode loading conditions. in the present paper, both the sih criterion (maximum principal stress criterion) and the r-criterion (minimum extension of the core plastic zone) are adopted in order to predict the crack path at the microscopic scale level by taking into account microstress fluctuations due to material inhomogeneities. even in the simple case of an elastic behaviour under uniaxial remote stress, microstress field is multiaxial and highly non-uniform. it is herein shown a strong dependence of the crack path on the material microstructure in the short crack regime, while the microstructure of the material does not influence the crack trajectory for relatively long cracks. sommario. l’andamento dei percorsi di frattura sotto diverse condizioni di carico e caratteristiche microstrutturali del materiale ha un ruolo importante nella determinazione delle condizioni di nucleazione e propagazione a fatica della fessura. inevitabili disomogeneità nella microstruttura del materiale tendono a influenzare il percorso di propagazione della fessura, particolarmente nel caso di fessure corte. in letteratura sono stati proposti numerosi criteri volti a descrivere i percorsi di frattura in condizioni di modo misto. nel presente lavoro, sia il criterio di sih (della massima tensione principale) che il criterio r (della minima estensione della zona plastica) sono stati adottati per predire i percorsi di frattura alla scala microscopica tenendo conto di fluttuazioni delle microtensioni dovute alle disomogeneità del materiale. anche nel semplice caso di comportamento elastico del materiale in presenza di tensione monoassiale remota, il campo tensionale alla microscala risulta essere multiassiale e non uniforme. viene evidenziata una significativa dipendenza del percorso di frattura nel caso di fessure corte dalla microstruttura del materiale, mentre nel caso di fessure lunghe tale dipendenza risulta trascurabile. keywords. crack path; kinked crack; microstress fluctuation; material microstructure. introduction he evaluation of fatigue crack growth at small scale is still an open problem. as a matter of fact, when the crack size is comparable with a characteristic length of the material (e.g. grain size in metallic materials), mechanical barriers to crack growth are produced by the material microstructure, and the plastic zone size at crack tip t http://dx.medra.org/10.3221/igf-esis.20.01&auth=true http://www.gruppofrattura.it r. brighenti et alii, frattura ed integrità strutturale, 20 (2012) 6-16; doi: 10.3221/igf-esis.20.01 7 happens to be comparable with the crack size, leading to the violation of the small-scale yielding hypothesis. the effects of the material microstructure on the crack growth at small scale [1] can be modelled by taking into account the nonuniform stress field induced by embedded inohomogeneities. even for a uniform remote stress applied to the structural component, an oscillating stress field might develop at the microscale. in the present paper, by using both the solution of a homogeneous elastic infinite plane with a circular elastic inclusion and the superposition principle, the stress field for a regular arrangement of inclusions is determined, and the corresponding mixed mode stress intensity factors (sifs) are computed. crack paths are evaluated by applying both the maximum principal stress criterion (the sih criterion [2, 3]) and the minimum plastic zone extension criterion (the rcriterion [4, 5]). the trajectory described by the crack tip is computed through an incremental method, where the mode i and mode ii sifs of the kinked crack are approximately evaluated as a function of the sifs related to a projected straight crack. finally, some examples related to metallic alloys are examined. it is shown that small-scale fluctuations of the stress field heavily affect the crack path for short cracks while, after reaching a transition point during the crack propagation process, such an influence disappears for sufficiently long cracks. microstress field induced by material inhomogeneities tructural materials always present heterogeneity features due to either the composite nature of the materials (e.g. composite materials characterised by a matrix and a reinforcing phase; concrete-like materials having a cementbased paste with dispersion of aggregates of different sizes) or unavoidable inhomogeneities (e.g. metallic alloys composed by a base material and secondary inclusions), see fig. 1. due to such inhomogeneity characteristics, the stress field in the material at microscopic level might be non-uniform and multiaxial even if a uniaxial uniform remote stress is applied. a local fluctuation of the microstress field can play a crucial role in the crack path assessment for cracks having length comparable with a characteristic material length. (a) (b) figure 1: (a) micrograph of pure iron with ferrite inclusions and crystals having a polygonal shape. (b) typical concrete material with aggregates, cement paste and voids. the modelling rationale here adopted to describe the inhomogeneities contained in the material is based on a periodic distribution of spherical particles embedded in the base material. by considering, for the sake of simplicity, a single inclusion of radius embedded in an infinite plane under remote uniform stress (fig. 2), the elastic stress field can be determined by applying the superposition principle together with the kirsch solution [6]. the resulting stress field, , , x y xy   , is uniform within the inclusion, and can be expressed as a fraction of the remote applied stress 0 y : 0 0, , 0x y xyx y y yk k         (1) on the other hand, the stress field , ,x y xy   under plane stress condition in the region around the inclusion (see point p in fig. 2) can be expressed as follows [6]: s http://dx.medra.org/10.3221/igf-esis.20.01&auth=true http://www.gruppofrattura.it r. brighenti et alii, frattura ed integrità strutturale, 20 (2012) 6-16; doi: 10.3221/igf-esis.20.01 8 2 22 2 2 0 2 2 2 2 2 22 2 2 0 2 2 2 2 2 2 2 2 2 0 4 2 4 (1 ) 3 18 2 3 1 2 (1 ) 3 10 2 1 1 1 2 (1 ) 26 8 12 3 y x x x y y x x y y y x x xy y k k r k rr y y f g r r r r k k r k rr y y f g r r r r k k r xy kr y r y r r r                                                                       2 4 r xy r        (2) where 2 2r x y  . the x-y coordinate system has origin in the inclusion centre (fig. 2). further, the coefficients ,x yk k depend on the elastic constants of the base material ( 1 1,e  ) and of the inclusion ( 2 2,e  ) [6]:     2 2 1 1 2 2 2 2 2 2 2 1 1 1 2 1 2 1 2 2 2 1 2 2 1 2 2 2 2 2 2 1 1 1 2 1 2 1 2 2 (3 1) (1 3 ) (8 2 6 1 ) (1 ) ( 2 2 6 2 ) (3 ) (8 3 ) (8 2 6 1 ) (1 ) ( 2 2 6 2 ) x y c e e e k e c c c e e e c c c e e e c k e c c c e e e c c                                                (3a) with 211c   , and 2 2 2 2 4 4 6 8 (3 2 ) 24 , y r y r y f g r r    (3b) figure 2: circular elastic inclusion in an infinite elastic plane under remote uniform tensile stress 0 y . the elastic stress field in such heterogeneous materials can be computed by exploiting both eqs 1-3 for a single inclusion and the superposition principle, provided that the inclusions are assumed to be non-interacting (as reasonably occurs for widely spaced inclusions). by considering point p belonging to the base material (fig. 3), the resulting stress field is determined approximately by summing up the effects of the inclusions (such as particles 1, 2, 3, 4, etc. in fig. 3), that is: http://dx.medra.org/10.3221/igf-esis.20.01&auth=true http://www.gruppofrattura.it r. brighenti et alii, frattura ed integrità strutturale, 20 (2012) 6-16; doi: 10.3221/igf-esis.20.01 9 figure 3: equally-spaced circular inclusions in an infinite domain arranged in a hexagonal cell pattern having characteristic size d , under remote uniform tensile stress 0 y . ( ) ( ) ( ) 0 ( ) ( ) ( ) 0 ( ) ( ) ( ) ( ) ( , ) ( ) ( , ) ( ) ( , ) x i x i p i p i y y i y i p i p y i xy i xy i p i p i p r p r p r                      (4) where the cartesian stress tensor components ( ) ( ) ( )( , )i x i p i pr  , ( ) ( ) ( ) 0( ( , ) )i y i p i p yr   , ( ) ( ) ( )( , )i xy i p i pr  indicate the stress fluctuations evaluated in p in an elastic infinite plane containing a single inclusion i ( 1, 2, 3, 4, .....i  ), see eq. 2, under the remote stress 0 y . in the above expressions, the summation might be performed by taking into account all the inclusions that are within a significant influence region around the point p under consideration, since the inclusions located at a sufficiently large distance from p produce vanishing fluctuations of the stress components. in fig. 4, sample spatial distributions of the fluctuating stress components along different lines normal to the remote loading axis are shown. 0e+000 4e-004 8e-004 position (m) -0.004 -0.002 0 0.002 0.004 di m en si on le ss s tr es se s,  x/  0y ,  x y/  0y 0.998 0.999 1 1.001 1.002 di m en si on le ss s tr es se s,  y/  0y y / 0y x / 0y xy / 0y (a) 0e+000 4e-004 8e-004 position (m) -0.008 -0.004 0 0.004 0.008 di m en si on le ss s tr es se s,  x/  0y ,  x y/  0y 0.996 1 1.004 di m en si on le ss s tr es se s,  y/  0y y / 0y x / 0y xy / 0y (b) figure 4: stresses along a horizontal straight path (dashed line) located at (a) half distance and (b) one-third distance between two lines of inclusions, in an infinite plane under plane stress remote uniform tension stress 0 y . dots indicate the positions of inclusions in the material. http://dx.medra.org/10.3221/igf-esis.20.01&auth=true http://www.gruppofrattura.it r. brighenti et alii, frattura ed integrità strutturale, 20 (2012) 6-16; doi: 10.3221/igf-esis.20.01 10 approximate sifs for a nominally-mode i kinked crack n the case of an infinite cracked plane under a uniform remote stress 0 y , the sif of a straight crack of semi-length l aligned with the x-axis is ( ) 0i yk l    . assume that such a straight crack is embedded in the stress field (given by eqs 2-4) within the base material. such a stress field can be decomposed in the remote uniform uniaxial tensile stress 0 y and a fluctuating multiaxial stress field ( )xt here assumed to be a one-dimensional function of the x coordinate. furthermore, by observing the courses (reported in fig. 4) of the stress components due to the presence of inclusions, we can suppose that ( )xt is a selfbalanced microstress field characterized by a material length d (related to the inclusion spacing), with two non-zero stress components ( / )y af x d      and ( / )xy af x d      . for the sake of simplicity, we assume    / cos 2f x d x d (this could be regarded as a first order approximation through fourier series of a general periodic function), fig. 5a. under the self-balanced microstresses  and  , the sifs (of the projected crack) are obtained using buckner’s superposition principle:         02 2 2 2 2 20 0 0 02 2 2 2 2 20 0 0 cos 2 2 2 2 2 cos 2 2 2 2 2 l l l i a a a l l l ii a a a f x d x d ll l l k dx dx dx l j dl x l x l x f x d x d ll l l k dx dx dx l j dl x l x l x                                                       (5) where j0 is the zero-order bessel function [7]. (a) (b) figure 5: (a) self-balanced microstress field and periodically kinked crack. (b) kinked crack in an infinite plane. i http://dx.medra.org/10.3221/igf-esis.20.01&auth=true http://www.gruppofrattura.it r. brighenti et alii, frattura ed integrità strutturale, 20 (2012) 6-16; doi: 10.3221/igf-esis.20.01 11 the total sifs of the straight crack with semi-length l are the sums of the two contributions due to remote and microstress fields, that is: ( ) ( ) i i i ii ii ii k k k k k k         (6) in the self-balanced microstress field, we assume that the crack might kink at each material microstructure semi-period, namely at each reversal in the microstress spatial courses. obviously, kinking occurs since the microstress field is multiaxial. because of the symmetry condition related to the y-axis, the crack propagates symmetrically with respect of such an axis. now, considering at first a singly-kinked crack (of projected crack length 2l ), we have that the sifs at the tips of the inclined part of the crack can be expressed through the sifs ik and iik of a straight crack of length equal to the projected length of the kinked crack [8,9], that is:         11 12 21 22 , , , , i i ii ii i ii k a b a k a b a k k a b a k a b a k         (7) where ija are coefficients which depend on the slant angle  (positive counter-clockwise for tip coordinate x > 0) and the length ratio b a between the deflected leading segment and the horizontal trailing (preceding) segment (fig. 5). if a geometry different from that of an infinite plate with a central crack were examined, the sifs defined with respect to the projected crack would change but not the expressions in eq. 7. the coefficients ija for b a   (and, with good approximation, also for 0.3b a  ) are [8]:         3 2 11 1 2 12 1 2 21 1 2 22 cos 2 sin cos sin cos cos 2 cos a a a a                 (8) note that the local sifs in eq. 8 are equal to those of an inclined straight crack of projected semi-length l forming an angle 2  with respect to the loading axis of 0 y [8], fig. 6. figure 6: infinite cracked plane with an inclined crack under remote tensile stress 0 y . then, we assume that, as the crack propagates following the path in fig. 5a, only the latter deflection of the crack path influences the stress field near the crack tips (e.g. along the straight segment 2-3 in fig. 5a, the deflection point 2 has an http://dx.medra.org/10.3221/igf-esis.20.01&auth=true http://www.gruppofrattura.it r. brighenti et alii, frattura ed integrità strutturale, 20 (2012) 6-16; doi: 10.3221/igf-esis.20.01 12 effect, while the deflection point 1 does not have). the local sifs at the crack tip are assumed to be given by eqs 7 and 8 for deflected (mode i+ii) segments (the segments 1-2 and 1 2  in fig. 5b). the approximate calculation (based on the assumption that the near-tip stress field depends on the local crack direction at the crack tip) of the local sifs for the kinked crack is examined for the case of an edge cracked plane under uniform tensile stress, fig. 7a [10]. in particular, a two-equal-segment kinked crack with 1 45   and 2 ranging from 0° to 60° is considered. in fig. 7b, we can observe that the sifs computed by means of a fe model agree quite satisfactory with the analytical values corresponding to an equivalent slant straight crack (see thin line in fig. 7a) having both the direction of the leading segment of the kinked crack and a projected length (normal to the loading axis) equal that of the kinked crack. 1 =  da = a1 fem present study f i f ii 30 45 60 75 90 angle, 2 (degrees) 0.00 0.20 0.40 0.60 0.80 1.00 1.20 1.40 1.60 d im en si on le ss s if s, f i (i i) = k i (i i) /  0 y (  a 2 ) 1 /2 (a) (b) figure 7: (a) edge-cracked plane. (b) sifs obtained from the simplified method (present study, dashed line) and a fe analysis (continuous line) for a two-segment crack. mixed-mode crack propagation criteria he kinked pattern of a crack embedded in the microstress field above described (see sections 2 and 3) can be analysed by adopting a mixed-mode crack propagation criterion. several criteria for both stable and unstable crack propagation have been proposed during the last decades for different materials. according to the mts-criterion (maximum tensile stress) proposed by erdogan and sih [2, 3], the crack grows in the direction perpendicular to the maximum principal stress (  ) direction or, equivalently, parallel to the maximum tangential stress. analytically, the criterion can be stated as follows: 2 2 0, 0            (9) where the polar coordinate  is used to identify the position vector with respect to the crack tip direction. by means of the stress field expressions (2), eq. 9 can be written as follows: 2 1tan tan 0 2 2 2 2       with /i iik k  (10) this classical criterion, used to describe the mixed-mode crack propagation under the local sifs ik and iik , provides a kinking angle  , defined with respect to the general inclined axis of the crack, given by: 2 1 1 2 arctan 8 4 4 i i ii ii k k k k            (11) t http://dx.medra.org/10.3221/igf-esis.20.01&auth=true http://www.gruppofrattura.it r. brighenti et alii, frattura ed integrità strutturale, 20 (2012) 6-16; doi: 10.3221/igf-esis.20.01 13 several others criteria have been proposed, for instance the zero shear stress criterion by maiti et al. [11], the m-criterion proposed by kong et al. [12] based on the maximum value of the stress triaxiality ratio /h eqm   ( h is the hydrostatic stress, whereas eq is an equivalent stress which can be assumed to be equal to the von mises stress), the maximum dilatational strain energy density criterion (t-criterion) proposed by theocaris et al. [13-15]. from experimental tests, it has been observed that the crack propagation direction usually tends to follow the local or global minimum extension of the plastic core region. from a physical point of view, this phenomenon could be explained by considering that the plastic core region is a highly-strained area, and the crack tends to reach the elastic region of the material outside the plastic zone, propagating through the plastic region which develops around the crack tip. therefore, it is reasonable to assume that the crack follows the “easiest” path to reach the elastic region. such a path can be assumed to coincide with the shortest path from the crack tip to the elastic material outside the plastic zone, as is stated by the rcriterion proposed by shafique et al. [4, 5] (fig. 8). the r-criterion can mathematically be written as follows : 2 2 0, 0 p pr r         (12) where pr is the function which defines the radial distance from the crack tip to a generic point of the plastic zone boundary 1 2( , ) 0f i j  , with 1i = first stress tensor invariant and 2j = second deviatoric stress tensor invariant. when the conditions stated in eq. 12 are fulfilled, the direction of minimum radial distance is determined, and the crack propagation direction vector t is assumed to be coincident with such a direction (fig. 8). crack plastic region elastic region t x y  r ( )p  f(i ,j )=01 2 figure 8: graphical representation of the r-criterion. the above criterion can also be justified by considering that the fracture stress f is proportional to the square root of fw , which is the fracture energy per unit surface area. such an energy for a quasi-brittle elastic-plastic material is equal to the summation of the surface energy s and the plastic work p consumed to create a unit surface area, that is, f s pw    . for structural materials, where typically p s  , the fracture stress f appears to be primarily dependent on p only. the shortest distance from the crack tip to the elastic-plastic boundary corresponds to the minimum plastic work which is needed to create a new portion of crack area, that is, such a shortest distance corresponds to the minimum values of fracture energy and fracture stress. applications to short-crack propagation regime he above described model for the assessment of crack propagation at the microscale is herein applied to a carbon steel d6ac whose composition and mechanical parameters are presented in tab. 1, where only the main secondary elements are listed. by performing a weighted average of the physical and mechanical parameters of the secondary constituents, a single equivalent inclusion with the features reported in tab. 2 can be defined. t http://dx.medra.org/10.3221/igf-esis.20.01&auth=true http://www.gruppofrattura.it r. brighenti et alii, frattura ed integrità strutturale, 20 (2012) 6-16; doi: 10.3221/igf-esis.20.01 14 element volume fraction mass density young modulus poisson’s ratio thermal expansion coeff.  [%]  [kg/m3] e [gpa]   [k-1] iron fe ~ 98.00 7870 200 0.29 1.20e-05 molibden mb ~ 1.05 10220 330 0.38 5.35e-06 cromium cr ~ 1.05 7190 248 0.30 6.20e-06 table 1: physical and mechanical parameters of the main elements in a carbon steel d6ac. element volume fraction mass density young modulus poisson’s ratio thermal expansion coeff.  [%]  [kg/m3] e [gpa]   [k-1] base material fe ~ 98.00 7870 200 0.29 1.20e-05 equivalent inclusion -~ 2.10 8705 289 0.34 5.78e-06 table 2: mean physical and mechanical parameters of the base material and the equivalent inclusion in a carbon steel d6ac. now consider an infinite plane under remote uniform tensile stress 0 y , containing an initial straight crack normal to the applied stress. by adopting the equivalent inclusion volume fraction (tab. 2) and considering an average inclusion diameter equal to about 20 m (e.g. see ref. [16]), an inclusion spacing d equal to about 234 m can be computed for a regular hexagonal distribution of inclusions (fig. 3). the static crack extension is determined by applying the above described criteria (the erdogan-sih criterion and the r-criterion) on the crack growth direction. the mixed mode sifs are computed by taking into account only the remote stress 0 y (the local fluctuation of the stress component y is negligible, as is shown in fig. 4) and the micro shear stress fluctuations  . in fig. 9, the crack path predicted for an initially straight crack developing at half distance between two horizontal lines of inclusions (see fig. 4a, with 0/ 0.0026a y   ) is represented. the crack path evaluated by the erdogan-sih criterion is similar to that determined by the r-criterion (fig. 9). nevertheless, it can be observed that the r-criterion produces a slight crack path deviation since the plastic zone shape is influenced in a complex way by the mode i and mode ii sifs which continuously change during the whole process of crack propagation. (a) (b) figure 9: (a) path of an initially straight crack developing at half distance between two lines of inclusions in an infinite plane under remote uniform tensile stress y0 . (b) detail of the crack path at the microscale where the distribution of inclusions is shown. http://dx.medra.org/10.3221/igf-esis.20.01&auth=true http://www.gruppofrattura.it r. brighenti et alii, frattura ed integrità strutturale, 20 (2012) 6-16; doi: 10.3221/igf-esis.20.01 15 fig. 10 shows the crack path determined for an initially straight crack developing at a vertical distance equal to one-third between two horizontal lines of inclusions (see fig. 4b, with 0/ 0.0037a y   ). as in the previous case, the crack path evaluated by the erdogan-sih criterion is rather similar to that determined by the r-criterion. (a) (b) figure 10: (a) path of an initially straight crack developing at one-third distance between two lines of inclusions in an infinite plane under remote uniform tensile stress 0 y . (b) detail of the crack path at the microscale where the distribution of inclusions is shown. by comparing fig. 9 and fig. 10, it can be observed that the kinking angle of the crack tends to increase with increasing the value of the 0/a y  ratio. conclusions n the present paper, a simple analytical model to describe the trajectory of a plane crack propagating within an inhomogeneous material is proposed. with reference to metals, the inhomogeneities are treated by considering a two-phase material with an equivalent mean inclusion characterized by a regular spatial distribution. even under remote uniaxial loading, the equivalent inclusions generate a multiaxial fluctuating stress field which is assumed to be responsible for mixed-mode crack propagation. by adopting different mixed-mode crack growth criteria, the crack path can be connected with the main features of the material microstructure, here accounted in terms of an appropriate microstress field. it is shown that both the maximum principal stress criterion and the r-criterion (based on the minimum extension of the core plastic zone) predict a zig-zag crack pattern, characterised by a length scale related to both the volume fraction of inclusions and their mean size. moreover, it is shown a strong dependence of the crack path on the material microstructure in the short crack regime, while the microstructure of the material does not influence the crack trajectory for relatively long cracks. acknowledgements he authors gratefully acknowledge the research support for this work provided by the italian ministry for university and technological and scientific research (miur). references [1] s. suresh metallurgical trans, 14a (1985) 2375. [2] f. erdogan, g. c. sih, j basic engng, 85 (1963) 519. i t http://dx.medra.org/10.3221/igf-esis.20.01&auth=true http://www.gruppofrattura.it r. brighenti et alii, frattura ed integrità strutturale, 20 (2012) 6-16; doi: 10.3221/igf-esis.20.01 16 [3] g.c. sih, int. j. fract, 10 (1974) 305. [4] m.a.k. shafique, k. k. marwan, engng fract mech, 67 (2000) 397. [5] m.a.k. shafique, k. k. marwan, int. j plasticity, 20 (2004) 55. [6] ye.ye. deryugin, g.v. lasko, s. schmauder, field of stresses in an isotropic plane with circular inclusion uncere tensile stress (http://www.ndt.net/article/cdcm2006/papers/lasko.pdf) [7] a.carpinteri, a. spagnoli, s. vantadori, in: the 13th int. congress on mesomechanics (mesomechanics 2011), 6-8 july 2011, vicenza (italy). [8] h. kitagawa, r. yuuki, t. ohira, engng fract mechs, 7 (1975) 515. [9] yz. chen, theoretical applied fract mech, 31 (1999) 223. [10] a. carpinteri, r. brighenti, s. vantadori, d. viappiani, special issue engng fract mech, 75 (3-4) (2007) 510. [11] s. k.maiti, r. a. smith, int j fract, 23 (1983) 281. [12] x. m. kong, m. schulter, w. dahl, engng fract. mech. , 52 (1995) 379. [13] p. s. theocaris, np. adrianopoulos, engng fract mech, 16 (1982) 425. [14] p. s.theocaris, g. a. kardomateas, np. adrianopoulos, engng fract. mech, 17 (1982) 439. [15] p. s. theocaris, np. adrianopoulos, int. j. fract, 20 (1982) r125. [16] y. murakami, metal fatigue: effects of small defects and nonmetallilc inclusions. elsevier, amsterdam, (2002). http://dx.medra.org/10.3221/igf-esis.20.01&auth=true http://www.gruppofrattura.it microsoft word numero 25 art 7 j. tong et alii, frattura ed integrità strutturale, 25 (2013) 44-49; doi: 10.3221/igf-esis.25.07 44 special issue: characterization of crack tip stress field near tip strain evolution under cyclic loading j. tong, y.-w. lu, b. lin university of portsmouth, uk y. h. tai rolls-royce plc, uk j.r. yates university of manchester, uk abstract. the concept of ratchetting strain as a crack driving force in controlling crack growth has previously been explored at portsmouth using numerical approaches for nickel-based superalloys. in this paper, we report the first experimental observations of the near-tip strain evolution as captured by the digital image correlation (dic) technique on a compact tension specimen of stainless steel 316l. the evolution of the near-tip strains with loading cycles was studied whilst the crack tip was maintained stationary. the strains were monitored over the selected distances from the crack tip for a given number of cycles under an incremental loading regime. the results show that strain ratchetting does occur with load cycling, and is particularly evident close to the crack tip and under higher loads. a finite element model has been developed to simulate the experiments and the simulation results are compared with the dic measurements. keywords. dic; fe; ratchetting; crack tip mechanics; fatigue crack growth. introduction he concept of ratchetting strain as a crack driving force in controlling crack growth has been investigated utilising a variety of constitutive models, including elastic-plastic, visco-plastic and crystal-plastic formulations, for nickelbased superalloys [1-3]. crack tip deformation fields were examined for both stationary and growing cracks at room and 650c using the finite element method. distinctive strain ratchetting behaviour near the crack tip was identified in all cases, leading to progressive accumulation of tensile strains normal to the crack growth plane. it was hypothesised that this tensile strain may be responsible for material separation leading to crack growth. most recently the concept has been applied successfully [4] to fatigue crack growth of a nickel alloy in vacuum at a range of temperatures, where the influence of oxidation is removed. although this latest work appears to be very encouraging, no direct experimental evidence is yet available to support this line of reasoning. in this paper, we present the first series of experimental results on the measurement of the near-tip strains as a function of the number of loading cycles in a compact tension specimen of stainless steel 316l using the dic method. finite element analysis has also been carried out on the specimen and the near-tip strain results from the simulation are compared with those obtained experimentally. t http://www.gruppofrattura.it http://dx.medra.org/10.3221/igf-esis.25.07&auth=true j. tong et alii, frattura ed integrità strutturale, 25 (2013) 44-49; doi: 10.3221/igf-esis.25.07 45 experimental methods he material used for the investigation was stainless steel 316l. a compact tension (ct) specimen was employed with a width of 56 mm, a thickness of 7 mm and a machined notch size of 24 mm. an average grain size of the material along the rolling direction was found to be approximately 28.5 µm. the specimen was pre-cracked first in a servo-hydraulic test machine under cyclic tension, allowing a crack growth of ~2.05 mm to obtain a final crack length of ~26.05 mm. the cyclic testing was then conducted at constant load amplitude with the range of load increased after a given number (20) of cycles, as shown in fig. 1. the evolution of the strain fields near the crack tip was monitored during the cyclic loading using the digital image correlation (dic) technique. the dic system employed is a stereomicroscope system, vic-3d micro™ by correlated solutions [5]. speckle patterns were painted on the specimen surface to facilitate the image analysis, and a resolution of 1224 x 1024 pixels was achieved through the use of the cameras coupled with the microscope. four series of tests were conducted where the near-tip strains were monitored and recorded using the dic method. a loading frequency of 0.1 hz was used for the testing to allow sufficient time to collect the data. the images were captured at a framing rate of 5 per second for each cycle and about 50 images were recorded for each cycle. the field of view of the images was approximately 2.15 x 1.80 mm, giving a pixel size of 1.76 µm. figure 1: the cyclic loading scheme used for the experiment. digital image correlation has been used extensively to determine fracture parameters using the displacement data extracted from digital images [6, 7]. the basic principles of dic are to take a set of sequential images for a deformed object, with the first image taken before deformation serves as a reference and the subsequent images acquired at different deformation stages from the same region correlated with the reference image. the algorithm is based on the mathematical correlation of the intensity changes of the sequentially recorded digital images, and implemented through a procedure of finding the best correlation between the two images. digital images are usually divided into smaller interrogation windows, or sub-sets, a matching process is performed on each of these sub-sets. a full field map of displacements/strains of each subset may be obtained when the correlation process is completed successfully. in the current work, lavision davis 8.1.1 was employed to carry out the image correlation [8]. the size of the subsets was chosen as 28 x 28 pixels with a step size of 3 pixels, sufficient to provide a high spatial resolution and good image correlation quality as well as acceptable computational cost. to study the near-tip strain evolution with load cycles, regions of interest near the crack tip were selected and strain distributions studied. specifically, two points ahead of the crack and on the crack plane, r2 and r4, were monitored, where the distance to the crack tip, r2 = 28.5 µm and r4 = 57 µm, as illustrated in fig. 2. these values were selected to be either the same as the average grain size of the material (r2) or about double the average grain size (r4). the strain data at each location were obtained from an average value of multiple points within a 25 µm x 25 µm square. during the loading cycles, the crack length was also monitored and corrected post testing when micro crack growth was detected, such that the values of r2 and r4 stay the same throughout the tests. micro-crack growth was indeed detected during some of the loading sequences (test series 3-1 to 3-3, omitted in fig. 1). these were excluded in the subsequent ratchetting analyses. 0 1 2 3 4 5 6 60 80 100 120 140 160 l oa d [ k n ] number of cylces test 3-4 test 3-5 test 3-6 test 3-7 t http://www.gruppofrattura.it http://dx.medra.org/10.3221/igf-esis.25.07&auth=true j. tong et alii, frattura ed integrità strutturale, 25 (2013) 44-49; doi: 10.3221/igf-esis.25.07 46 figure 2: the random speckle pattern on the specimen and a typical displacement map extracted from the dic measurement. the locations of r2 and r4 are illustrated with respect to the crack tip. finite element analyses inite element analyses were carried out on the ct specimen using abaqus [9] under plane stress loading conditions to obtain the near-tip strain distribution on the specimen surface, and the results were compared with those measured by the dic. material model the material model by lemaitre and chaboche [10] was adopted where both isotropic and nonlinear kinematic hardening rules were used to describe the monotonic and the cyclic behaviour of ss316l [11, 12]. the equivalent von mises stress is defined as:      3 : 2 dev devf s s       (1) where dev is the deviatoric part of the back stress and s is the deviatoric stress tensor. the size of the yield surface is defined using a simple exponential law:  0 0 1 plbq e      (2) where 0 is the size of the yield surface at zero plastic strain, q and b are isotropic hardening material parameters. the equivalent plastic strain is given by:      2 2 21 2 2 3 3 1 1 1 1 2 pl v                (3) the evolution of the kinematic hardening component is defined as:   0 1 1pl plc c c                (4) where  is the back stress, and are material parameters, and is the rate of change of c with respect to temperature and field variables. a total of five materials parameters are required to run the fe analyses: initial yield stress 0; kinematic hardening parameters c and  and isotropic hardening parameters q∞ and b. the values of these parameters for ss316l were obtained using the experimental data for a strain range 4.0%  [13], and are summarised in tab. 1. f http://www.gruppofrattura.it http://dx.medra.org/10.3221/igf-esis.25.07&auth=true j. tong et alii, frattura ed integrità strutturale, 25 (2013) 44-49; doi: 10.3221/igf-esis.25.07 47 e [gpa] 0 [mpa] kinematic hardening isotropic hardening c [mpa]  q∞ [mpa] b 193 100 60000 280 200 6 table 1: the material parameters for ss316l [13]. the finite element model the compact tension specimen as used in the experiment was modelled using the finite element method (abaqus). due to symmetry of the geometry and the loading, only half of the specimen was meshed with 4-noded quadrilateral plane stress elements, as shown in fig. 3. finer elements were generated around the crack-tip area ( ≈ 1.8 µm) and a rigid line was attached along the symmetry line to prevent the potential penetration of the crack flanks due to crack closure under cyclic loading. a mesh convergence study was carried out, and a mesh size of 3.6 µm was found to be adequate such that the effect of mesh size on the stress-strain responses became negligible. the loading pin (marked in red in fig. 3) was modelled as elastic and no slip was allowed between the loading pin and the specimen [14]. cyclic tensile loading was applied at the centre of the pin according to the loading scheme (fig. 1). a sequential crack tip node-release technique was applied to model the micro-crack growth, where nodes were released incrementally and set to the micro-crack growth length detected, otherwise the crack was assumed stationery. the strain values were calculated at the integration points and the average strain values were obtained for r2 and r4 over a square of 25 µm x 25 µm, similar to those obtained by the dic method. figure 3: the fe mesh for the half-model of a ct-specimen, where a finer mesh ( ≈ 1.8 µm) was used in the crack tip region. results and discussion he strain evolutions with cycles are shown in fig. 4 at r2 and r4 for the four test series (as shown in fig. 1) from both the dic and the fe analyses. it is evident from both analyses that tensile strains increase with the number of cycles in all load cases, although the fe analyses appear to predict higher responses than those from the dic. a closer agreement between the two is achieved at r2, as opposed to r4, indicating that grain size might serve as a suitable candidate as a “critical distance”. micro-crack growths were detected at some of the early test series, such that ratchetting behaviour could not be monitored on these occasions. these may be due to the pre-cracking load history or the notch effect. further work is being carried out on controlled crack growths so that the relation between the ratchetting strain and the micro-crack growth may be explored. t rigid line http://www.gruppofrattura.it http://dx.medra.org/10.3221/igf-esis.25.07&auth=true j. tong et alii, frattura ed integrità strutturale, 25 (2013) 44-49; doi: 10.3221/igf-esis.25.07 48 (a) (b) figure 4: strain responses at (a) r2 and (b) r4 with the number of cycles for the four test series (fig. 1), comparison of the results from the dic and the fe analysis. conclusions e report the first experimental evidence of the near-tip strain evolution as captured by the digital image correlation on a compact tension specimen of stainless steel 316l. the evolution of the near-tip strains with loading cycles was monitored at selected load levels whilst the crack tip remains stationery. the results clearly show that strain ratchetting occurs with cycle, and is particularly evident close to the crack tip and under higher loads. finite element analyses have also been carried out, and the results compare favourably with those measured at a distance about the grain size. references [1] tong, j., zhao, l.g., lin, b., ratchetting strain as a driving force for fatigue crack growth, int. j. fatigue, 46 (2013) 49–57. [2] zhao, l.g., tong, j., a viscoplastic study of crack-tip deformation and crack growth in a nickel-based superalloy at elevated temperature, j. mech. physics solids, 56 (2008) 3363-3378. [3] zhao, l.g., tong, j., byrne, j., the evolution of the crack tip stress-strain fields and plasticity induced crack closure revisited, fatigue fracture engng. mater. struc., 27 (2003) 19-29. [4] tong, j., cornet, c., lin, b., zhao, l.g., unpublished results, (2012). [5] http://www.correlatedsolutions.com/index.php/products/vic-3d-2012/microscopy, (2012) [6] mcneill, s.r., peter, w.h., sutton, m.a., estimation of stress intensity factor by digital image correlation, engineering fracture mechanics, 28(1) (1987) 101–112. [7] durig, b., zhang, f., mcneill, s.r., chao, y.j., peters iii, w.h., a study of mixed mode fracture by photoelasticity and digital image analysis, optics and lasers in engineering, 14(3) (1991) 203–215. [8] lavision gmbh, strainmaster mannual davis 8.1, gottingen, germany, (2012). [9] abaqus 6.8, hibbitt karlsson and sorensen inc, providence, ri, (2009). [10] lemaitre, j., chaboche, j.l., mechanics of solid materials, cambridge university press, (1990). w http://www.gruppofrattura.it http://dx.medra.org/10.3221/igf-esis.25.07&auth=true j. tong et alii, frattura ed integrità strutturale, 25 (2013) 44-49; doi: 10.3221/igf-esis.25.07 49 [11] chaboche, j.l., rousselier, g., on the plastic and viscoplastic constitutive equations–part ii: application of internal variable concepts to the 316 stainless steel, transactions of the asme, journal of pressure vessel technology, 105 (1983) 159–64. [12] chaboche, j.l., constitutive equations for cyclic plasticity and cyclic viscoplasticity, international journal of plasticity, 5 (1989) 247–302. [13] van eeten, p., nilsson, f., constant and variable amplitude cyclic plasticity in 316l stainless steel, journal of testing and evaluation, 34 (2006) 298–311. [14] kuntiyawichai, k., burdekin, f.m., engineering assessment of cracked structures subjected to dynamic loads using fracture mechanics assessment, engineering fracture mechanics, 70 (2003) 1991–2014. http://www.gruppofrattura.it http://dx.medra.org/10.3221/igf-esis.25.07&auth=true microsoft word 2260 a. metehri et alii, frattura ed integrità strutturale, 48 (2018) 152-160; doi: 10.3221/igf-esis.48.18 152 effect of crack position and size of particle on sif in sic particles reinforced al composite aicha metehri, madani kouider, abdelkader lousdad university of sidi bel abbes, faculty of technology, department of mechanical engineering, laboratory of mechanics physical of material (lmpm), 22000, algeria. aicha_vie2009@yahoo.fr, koumad10@yahoo.fr, a lousdad@yahoo.com abstract. in this paper the effect of reinforcement crack position and loading conditions (in mode i) on the stress intensity factors of the al/sicp metal matrix composite was examined using a finite element method. a simple cubic cell model with square reinforcement shapes was developed to investigate its effect on the mechanical properties of the mmc. the finite element technique was used to calculate the stress intensity factors ki and kii for crack in the matrix and in particle. the particle and matrix materials were modelled in linear elastic conditions. the obtained results show the important role on the stress intensity factors played by the relative elastic properties of the particle and matrix. the results also show that the loading conditions and inter-distance between two particles with two interfacial cracks has an important effect on the ki and kii stress intensity factors. keywords. matrix; reinforced; composite; particle; crack; fic. citation: metehri, a., kouider, m., lousdad, a., effect of crack position and size of particle on sif in sic particles reinforced al composite, frattura ed integrità strutturale, 48 (2019) 152-160. received: 16.11.2018 accepted: 28.12.2018 published: 01.04.2019 copyright: © 2019 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. introduction article-reinforced metal–matrix composites (prmmcs) are increasingly attracting the attention of automotive and consumer goods industries. aluminum alloy matrix-reinforced ceramic particles such as sic, al2o3 are such materials normally used in automobile and aviation. it is reported that aluminum reinforced with silicon carbide particles (sicps) exhibited several advantages in structural applications because of unique properties. this included isotropic mechanical properties, high specific stiffness, high specific modulus, thermal stability and strength as well as high wear resistance. thus, these composites have found new applications as structural materials in aerospace and automotive industries zhou (2003) [1]. there are several studies investigating the physical and mechanical properties of metal matrix composites temel varol (2013) [2]. other numerical analyses have been carried out by a number of researchers by considering matrix and reinforcement properties and their respective volume fractions. these analyses approached the problem by considering the unit cell concept of regular array of particles in the matrix. in addition, the shape of the particles was assumed to be either: cylindrical, spherical, rectangular or cubical. p http://www.gruppofrattura.it/va/48/2260.mp4 a. metehri et alii, frattura ed integrità strutturale, 48 (2018) 152-160; doi: 10.3221/igf-esis.48.18 153 liu et al (2007) [3] had found that the numerical results with unity aspect ratio were in good agreement with the published experimental data for the effect of reinforcement morphology on the deformation behavior in al6092/sicp metal matrix composite. a series of finite element models have been constructed. srinivasa et al [4] have shown that the fracture toughness of the composites decreased with an increase in vol% for aln and decreased in al2o3 particle size. all the composites exhibited r-curve behavior which has been attributed to crack bridging by the intact metal ligaments behind the crack tip. the young’s modulus of the composites increased with the vol% of aln whereas the thermal diffusivity and coefficient of thermal expansion followed a reverse trend. the particle size effects on overall deformation behavior of composites come from the particle size effects on deformation and on damage is uniquely determined on the basis of reference length of microstructure such as particle diameter or inter-particle distance. as the fracture strength of brittle materials is higher when the size of sample is smaller, the fracture and debonding of particles in composites is difficult to occur on smaller sized particles this work was the subject of keiichiro (2010) [5]. the results of ramazan and al (2015) [6] showed in analysis of a metal matrix composites reinforced with an in-situ high aspect ratio alb2 flake that 30 vol% of a1b2/al composite show a 193% increase in the compressive strength and a 322% increase in compressive yield strength. results also showed that ductility of composites decreases with adding alb2 reinforcements. bo et al (2015) [7] studied the interaction between a mode i crack and an inclusion in an infinite medium which was examined under consideration of coupled mechanical and thermal loads under plane strain condition. finally, the effects of temperature-dependent elastic properties on the inclusion–crack interaction are estimated. it is also found that the shielding or amplifying effect on the crack growth is dependent on the mismatched expansion coefficient if only the variation of temperature is considered. the results of omyma et al (2014) [8] showed that the densification and thermal conductivity of the composites decreased with increasing the amount of sic and increased with increasing sic particle size. increasing the amount of sic leads to higher hardness and consequently improves the compressive strength of al–sic composite. moreover, as the sic particle size decreases, hardness and compressive strength increase. the use of fine sic particles has a similar effect on both hardness and compressive strength. generally the microscopic failure characteristics of mmcs induced by the coupled loads are in three forms: matrix failure caused by void nucleation and growth; particle breakage and particle/matrix interface de-cohesion. all these authors did not take into account the presence of a non-emergent crack in a particle composite by fem whose different positions were highlighted with respect to the particle, on the other hand, the variation of the particle size following the thickness of the composite material has been taken into account in order to see its effect on the value of the stress intensity factor. the objective of this work is numerically analysis, by fem. the effect of reinforcement crack position, loading conditions (in mode i) and the size of particle on the stress intensity factors of the al/sicp metal matrix composite has been investigated. the first part is to highlight the effect of the crack position (in matrix and in particle) and the size of particle on the stress intensity factors ki and kii. while the second part presents the investigation of the effect of the interaction between two interfacial cracks (spacing particles) on the stress intensity factors ki, kii under mode i. finite element model micromechanical and material model n general, while in fast fracture state, the sic particle size has great influence. this is possibly attributed to the different failure mechanisms of crack growth caused by the actions of sic particle size, shape and distribution [9]. that is why the size of the particle equal to 50µm is selected. in this study the smallest area of the cross-section and special design was selected as the representative area element. it is assumed that the global behavior of the composite is the same as that of the area element. fig. 1 shows the micromechanical model used. a crack of length a starting at x=50µm is assumed to be at the interface between the particle and the matrix. the particle and matrix in the model are bonded perfectly with the exception of the crack faces. frictionless sliding behavior is assumed between the crack faces. a schematic diagram of the randomly arranged particles in the composite material is given in fig. 1a. the complete cell model is also given in fig. 1b. due to symmetry the unit cell model containing only one quarter of particle to reduce the calculation time as well. the length, width and thickness of the particle were 50µm, 50µm and 50µm respectively. i a. metehri et alii, frattura ed integrità strutturale, 48 (2018) 152-160; doi: 10.3221/igf-esis.48.18 154 figure 1: (a) assumed randomly arranged particles in the overall composite material. (b) the symmetric quarter model in 2d. in order to develop a three-dimensional finite element for the analysis of the stress intensity factors mmcs, a special design of al matrix and reinforced particles sic was proposed as shown in fig. 2. the produced mmc was subjected to a mechanical load from 50mpa to the 200mpa. mechanical characteristics of materials are given in the table below [1]: property al sic modulus of elasticity (gpa) 68.3 427 poisson’s ratio 0.33 0.17 table 1: mechanicals properties of materials. figure 2: (a) the schematic of assumed mmc model with crack in particle, (b) finite element mesh of model, (c) spacing particles and interaction of two interfacial cracks, (d) finite element mesh of two cubic particles interaction. a. metehri et alii, frattura ed integrità strutturale, 48 (2018) 152-160; doi: 10.3221/igf-esis.48.18 155 finite element model and bondary condition inite element analyzes are performed using fe code abaqus [10]. fig. 2 shows the configuration of the crack position in the present model. the symmetry conditions were applied in the finite element solutions as shown in fig. 3. hence, it is also assumed that there is no sliding and debonding occurring on the interface of particle– matrix during the loading process. figure 3: boundary conditions for mode i loading for crack in matrix. the distance between the crack in matrix and the interface particle/matrix is c=5µm. the interface crack length is also normalized with 50µm and stress intensity factors are calculated for different y/z ratio of reinforcement is taken as: y/z = 1, y/z= 1.42 and y/z =2.5. we have set "y" because at this dimension the particle will have a resistance according to the width of the composite material with particle and therefore less stress concentration which reduces the value of the stress intensity factor at the head of the crack, on the other hand, according to the dimension "z", the composite material with particle with a weak resistance which pushed us to try to see the variation of dimensioning of the particle following "z" in order to see the consequences on the ability to reduce stress at the crack. the precision of numerical computations is strongly related to the quality of the designed mesh surrounding the crack in matrix, or crack in the particle. thus, a 8-node linear brick (c3d8r) finite element was used for modeling. the elements near the crack are taken as small as possible in order to simulate the stress intensity factors and deformation near the crack more accurately (fib. 2b). the finite element model is shown in fig. 3 with 7200 elements. the stress σ is applied along the x-axis for mode i loading (fig. 3a). as we know the mesh has a presiding role on the determination of the values of the constraints or the factor of stress intensity. these values are related to the type of elements, numbers of elements and the boundary conditions for our work, we had done a study of convergence of the results or we varied the type of elements and the number of elements. the results do not show a difference except that the calculation time is important considering the existing material and it is for this reason that we took just 1/4 of the structure. for our calculations, the choice was made on the finite element type c3d8r for a linear study. the number of element type are shown in the tab. 2 for a 50mpa applied load: c3d8r number of nodes elements number ki 1normal mesh 8729 7200 5.02mpa.mm 1/2 2medium mesh 19286 16848 5.026mpa.mm 1/2 3raffini mesh 38655 34848 5.053mpa.mm 1/2 table 2: number and type of element. f a. metehri et alii, frattura ed integrità strutturale, 48 (2018) 152-160; doi: 10.3221/igf-esis.48.18 156 figure 4: normal mesh figure 5: medium mesh figure 6: raffini mesh results and discussion effect of the crack position on the stress intensity factors or better illustrating the influence of the crack position on the variation of the stress intensity factors in particle/reinforced metal-matrix composites; a crack length a=50µm (the critical state of a crack). in this section it is assumed that the length, width and thickness of particle are 50µm, 50µm, 50µm respectively. the matrix has the following dimensions: the length 180µm, the width 180µm and the thickness is 100µm. we had the choice to vary the length and the width of the crack but for our study, we did not want to highlight several parameters at once, so we took the case where the crack has the same size as the particle. other studies are in progress and which aim to vary the size of the crack and to see the report width of crack, length of the crack on the factor of stress intensity. figure 4: normal and shear stresses distribution at the crack tip for σ = 200mpa in the matrix (mode i): (a) σxx, (b) σyy, (c) σzz, (d) σxy.. f (a) (b) (c) (d) a. metehri et alii, frattura ed integrità strutturale, 48 (2018) 152-160; doi: 10.3221/igf-esis.48.18 157 in the matrix the evaluation of stress intensity factors, ki and kii at the crack tip are determined by using the finite element solutions. the existence of a crack in the matrix at a vicinity of the interface particle/matrix with the distance c=5µm and the length a=50µm was studied as shown in fig. 4 where the normal and shear mechanical stresses distributions at the crack tip are given for σ=200mpa. it is observed that the normal and shear stresses are higher at the crack tip for mode i loading. variations of ki and kii for the crack in the matrix depending on the different ratio of reinforcement and load applied are given in fig. 5. ki values for the crack in matrix in the vicinity of the interface particle/matrix (c=5µm) are higher than kii values. the opening mode ki takes positive values (18 mpa.mm1/2) for all applied loads on the cell that exert to open the crack faces. the cause of this is the higher crack tip nodal displacement due to the load. kii takes a negative value (equal approximately to -1.4 mpa.m m1/2) when the y/z ratio is decrease under mode i loading conditions. it is possible to say that loading condition does not have much effect on kii value for the ratio y/z=2.5. the effect of interaction crack– interface is highlighted when the crack length (a=50µm) tends towards the half of the thickness of the cell (e=100µm) and particularly for that containing the crack [11]. indeed, a tendency of the crack towards the interface leads to a strain field at the crack tip more significant due to the interaction with the interface. the crack position in the matrix leads to the maximum sif values in mode i when the y/z ratio is decrease. these results indicate that deformation fields in the vicinity of the crack tip are dominated by opening mode ki value. figure 5: variation of ki and kii with different ratio of reinforcement and applied load for the crack in the matrix. figure 6: normal and shear stresses distribution for σ = 200mpa in particle (mode i): (a) σxx, (b) σyy, (c) σzz, (d) σxy. (a) (b) (b) (a) (d) (c) a. metehri et alii, frattura ed integrità strutturale, 48 (2018) 152-160; doi: 10.3221/igf-esis.48.18 158 in the particle in this case the presence of a crack (parallel to the interface particle/matrix) in particle is considered and the effect of the different ratio of reinforcement and loading conditions on the energy of crack propagation characterized by the stress intensity factors are taken into account. the crack length is equal to 50µm and the distance between interface and crack in particle is c=5µm. fig. 6 shows the normal and shear stresses distribution at the crack tip given for σ=200mpa. fig. 7 shows the variations of ki and kii stress intensity factors with the different aspect ratio of reinforcement and applied load under mode i loading. it can be seen that for all applied loads, in general, for the crack length (a=50µm), ki and absolute kii values increase. furthermore, one can notice that the opening and the sliding mode of the crack are more intense in the cases of existence of the crack in the particle. it can be also noticed that the existence of a crack in particle facilitates the sliding of the crack. at the same time it facilitates the opening of the crack propagation because the values of ki and kii in particle are higher than the values of ki and kii in matrix which is due to the high elastic modulus of the particle. the increase in ki value is linear depending on the ratio of reinforcement. it is observed that the maximum value of ki or the maximum absolute value of kii are registered at y/z=1 (ki 20 mpa.mm1/2 for a=50m) under mode i loading. the level of this stress intensity factors decreases with the increase in the y/z ratio. figure 7: variation of ki and kii with ratio of reinforcement and applied load for the crack in the particle. inter-distance effect on the sif in this part, we study the inter-distance effect of the two interfacial cracks between two cubic particles on the evolution of the stress intensity factors ki and kii is considered. the distance ‘d’ is the interdistance separating the interfacial cracks tips from the first particle and the second particle as presented in fig. 2c. the displacement of the interfacial cracks of length a=50µm are parallel to the y-axis. the results obtained for the applied loading conditions for σ=150mpa are illustrated in fig. 8. figure 8: mechanical stress distribution at the crack tip cases of interfacial crack–crack interaction (two cubic particles interaction for σ = 150mpa). (a) (b) a. metehri et alii, frattura ed integrità strutturale, 48 (2018) 152-160; doi: 10.3221/igf-esis.48.18 159 fig 9 shows the variations of ki and kii stress intensity factors according to the distance between two interfacial and parallel cracks for two cubic particles and for different applied loads with thickness of particle fixed at 50µm. it is observed that for d=15µm, both ki, absolute values kii are more intense than other inter-distances. ki decreases when‘d’ increases (fig. 9a). as we can see that the variation of the sif ki is inversely proportional to the distance between two interfacial cracks and stabilizes when the two particles either at the end of the model. in fact, an almost 5 time decrease in the inter-particle spacing leads to a significant increase in the ki. the shearing mode kii stress intensity factor (fig. 9b) seems to be independent to inter-distance ‘d’ since these values are very low compared to ki. thus, the opening fracture mode is the preponderant one. the latter shows that this failure criterion is closely linked to the spacing particle. this is mainly due to increased tensile stresses. the risk of failure to the composite material is real when the spacing interfacial cracks are very small. figure 9: variation of ki and kii versus particles spacing (two cubic particles case) and applied load. conclusion n this study a finite element model is developed to calculate the stress intensity factors in mode i and mode ii (ki and kii) under mode i loading condition. from the general results of the investigation the following conclusions can be drawn: for the considered loading conditions (mode i) and for all crack position: ‐ the higher mechanical load occurring at the crack tip and the deformation fields in the vicinity of the crack tip are dominated by the opening mode. ‐ for the position of the crack in the matrix the stress intensity factor ki is high (18 mpa.mm1/2), the stress intensity factor ki decreases if the particle size decreases, by increasing the applied load, the value of the stress intensity factor increase considerably. the difference compared with the other curves (50mpa and 200mpa) is approximately 28% for the ratio y/z =1, and almost 22% for the ration y/z = 2.5 which is almost equal to the 1/4. also, the value of the stress intensity factor kii increases by decreasing the ratio y/z, the increase in the applied load causes an increase in the kii up to a ratio y/z = 1, once this ratio is exceeded, the effect of the applied load disappears. ‐ for the position of the crack in particle the risk of propagation by opening effect is very important since the value of ki is very high ( ki 20 mpa.mm1/2 ). one can conclude that same behavior in this case of the stress intensity factor ki for the position of the crack in the matrix. the difference lies between 23% and 25% for the two ratios (y/z =1 and y/z=2.5). the absolute value of the stress intensity factor kii increase by decreasing of the size of particle. the increase in the applied load causes an increase in the absolute kii value to the ratios y/z =1 and 2.5; with his sign is changed. ‐ the particle spacing can affect the stress intensity factors by influencing the interaction between the particles. the sif increases with a decrease in particle spacing. a 5-time decrease in inter-particle spacing can lead to a 2-time increase in ki stress intensity factor (sif equal to 23mpa.mm1/2 for =200mpa). i (a) (b) a. metehri et alii, frattura ed integrità strutturale, 48 (2018) 152-160; doi: 10.3221/igf-esis.48.18 160 references [1] zhou, y.c, long, s.g., liu, y.w. (2003). thermal failure mechanism and failure threshold of sic particle reinforced metal matrix composites induced by laser beam, mechanics of materials, 35, pp. 1003–1020. doi: 10.1016/s0167-6636(02)00322-8. [2] varol, t., canakci, a. (2013). effect of particle size and ratio of b4c reinforcement on properties and morphology of nanocrystalline al2024-b4c composite powders, powder technology 246, pp. 462 –472. doi: 10.1016/j.powtec.2013.05.048. [3] chan, k.c., tang, c.y. (2007), effect of reinforcement morphology on deformation behavior of particle reinforced metal matrix composites in laser forming, computational materials science, 40, pp. 168–177. doi: 10.1016/j.commatsci.2006.12.007 [4] boddapati, s. r., rodel, j., jayaram, v. (2007). crack growth resistance (r-curve) behavior and thermo-physical properties of al2o3 particle-reinforced aln/al matrix composites, composites: part a 38, pp. 1038–1050. doi: 10.1016/j.compositesa.2006.06.015 [5] tohgo, k., itoh, y., shimamura, y. (2010). a constitutive model of particulate-reinforced composites taking account of particle size effects and damage evolution, composites: part a 41, pp. 313–321. doi: 10.1016/j.compositesa.2009.10.023. [6] ramazan, k, ömer, s. (2015). fabrication and properties of in-situ al/alb2 composite reinforced with high aspect ratio borides, techno press, pp. 777-787. doi: 10.12989/scs.19.3.777. [7] bo, p., miaolin, f., jinquan, f. (2015). study on the crack–inclusion interaction with coupled mechanical and thermal strains, theoretical and applied fracture mechanics, 75, pp. 39-43. doi: 10.1016/j.tafmec.2014.10.006. [8] el-kady, o., fathy, a. (2014). effect of sic particle size on the physical and mechanical properties of extruded al matrix nanocomposites, materials and design, 54, pp. 348–353. doi: 10.1016/j.matdes.2013.08.049 [9] li, w, liang, h., chen, j., zhu, s. q., chen, y. l. (2014). effect of sic particles on fatigue crack growth behavior of sic particulate-reinforced al-si alloy composites produced by spray forming; procedia materials science 3, pp. 1694 – 1699. doi: 10.1016/j.mspro.2014.06.273. [10] abaqus/cae ver 6.9. (2007). user’s manual. hibbitt, karlsson & sorensen, inc. [11] madani, k., belhouari, m., bachir bouiadjra, b., serier, b., benguediab, m. 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can be opened with acrobat and adobe reader 5.0 and later.) >> /namespace [ (adobe) (common) (1.0) ] /othernamespaces [ << /asreaderspreads false /cropimagestoframes true /errorcontrol /warnandcontinue /flattenerignorespreadoverrides false /includeguidesgrids false /includenonprinting false /includeslug false /namespace [ (adobe) (indesign) (4.0) ] /omitplacedbitmaps false /omitplacedeps false /omitplacedpdf false /simulateoverprint /legacy >> << /addbleedmarks false /addcolorbars false /addcropmarks false /addpageinfo false /addregmarks false /convertcolors /converttocmyk /destinationprofilename () /destinationprofileselector /documentcmyk /downsample16bitimages true /flattenerpreset << /presetselector /mediumresolution >> /formelements false /generatestructure false /includebookmarks false /includehyperlinks false /includeinteractive false /includelayers false /includeprofiles false /multimediahandling /useobjectsettings /namespace [ (adobe) (creativesuite) (2.0) ] /pdfxoutputintentprofileselector /documentcmyk /preserveediting true /untaggedcmykhandling /leaveuntagged /untaggedrgbhandling /usedocumentprofile /usedocumentbleed false >> ] >> setdistillerparams << /hwresolution [2400 2400] /pagesize [612.000 792.000] >> setpagedevice microsoft word numero_62_art_42_3578.docx h. samir, frattura ed integrità strutturale, 62 (2022) 613-623; doi: 10.3221/igf-esis.62.42 613 the p-h2 relationship as a function of (hf/hm) in indentation habibi samir laboratory of industrial engineering and sustainable development (lgidd), department of mechanical engineering, ahmed zabana university of relizane, 48000, relizane, algeria habibisamir87@gmail.com abstract.in the present study, a semi-empirical modeling of the mechanical response in pile-up mode is obtained by deriving the load-depth relationship during the indentation loading cycle. the advantage compared to the relations previously used is that this new expression is a function of the predictable criterion of the mode of deformation, (hf/hm), which makes it possible to distinguish the sink-in mode from the pile-up mode. a comparison between the proposed expression and the results of the instrumented indentation tests shows excellent agreement. keywords. indentation test; mechanical response; pile-up; predictable criterion. citation: samir, h., the p-h2 relationship as a function of (hf/hm) in indentation, frattura ed integrità strutturale, 62 (2022) 613-623. received: 05.05.2022 accepted: 05.09.2022 online first: 15.09.2022 published: 01.10.2022 copyright: © 2022 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. introduction he study of the mechanical response by instrumented indentation has aroused the interest of many authors [1-4] although their experimental and numerical approaches are different who demonstrated that the load curve obtained from indentation tests can be described by the following power law: p=kh2 (1) where p is the indentation load applied to the indenter, h the indentation depth and k-factor a material-dependent constant. this relation was obtained experimentally as an alternative to classical approaches to determine the mechanical properties (hainsworth et al., [1]), finite element approach (zeng et rowcliffe, [2]), and dimensional analysis (cheng et cheng, [3]). then, relation (1) was used as a reference for a calibration of the indenter tip radius and load frame compliance (sun et al., [4]). however, hainsworth et al. [1] demonstrated that the value of the k-factor also depends on the geometry of the indenter tip and to the elastoplastic properties. these works [1-6] take as references the model proposed by [1] which is expressed as a function of the instrumented hardness, h, and the reduced modulus, er. this expression of k as a function of reduced modulus of elasticity and instrumented hardness for sink-in mode has been refined by malzbender et al. [5] and for pile-up mode has been refined by habibi et al. [6] is formulated by eqn. (2.a) and (2.b) respectively taking into account the geometry of the indenter and the tip defect as follows: t https://youtu.be/zpmqgivrodw h. samir, frattura ed integrità strutturale, 62 (2022) 613-623; doi: 10.3221/igf-esis.62.42 614                            2 r r r 2 r r r e1 π h e ε       h 4 ec k e1 π h e      h 4 eα. c a b (2) the deformation mode in the vicinity of the indenter depends on the elastoplastic response of the material under indentation. the two corresponding expressions of mechanical responses are different thus necessitating to previously considering one or the other model to determine the mechanical properties. however, to help the users to estimate the deformation mode, a simple criterion based on the ratio between the final depth and the corrected maximum depth reached by the indenter under the maximum load, (hf/hm), can be used [7-9]. the objective of this research is to refine the expression of k as a function of the criterion for identifying the deformation mode relating to the pile-up taking into account the geometry of the indenter and the tip defect. the advantage of the analytical expression proposed is its simplicity and the determination of (hf/hm) beforehand to determine the exact deformation mode of the material and to avoid the substitution by error of the sink-in mode by the pile-up mode or vice versa. the proposed model is then applied to bulk materials presenting pile-up deformation mode, i.e. copper, brass and bronze which have been the subject of previous investigations such as for example [10]. background he methodology developed by oliver and pharr [11] to calculate hardness, h, and young's modulus, e, in nanoindentation is currently applied in the majority of indentation work. on the other hand, this methodology is not justified for materials presenting pile-up as a mode of deformation [12-14]. from where, it is necessary to indicate the methods of calculation of the hardness and the modulus of young in the two modes. oliver and pharr [11] proposed to determine the reduced modulus er, from the contact stiffness (the slope shown in fig. 1.a) as follows:          122 m r c m 1 νs 1 ν e 2 a e e (3) indentation hardness is the ratio of the maximum applied, p, load to its projected contact, ac, area between the indenter and the specimen as following:  c p h a (4) where em and νm are respectively the young's modulus and the poisson's ratio of the indented sample and e and ν are those of the indenter. another relationship has been proposed previously [15] to express hardness as a function of indentation force and stiffness, concerning the two deformation modes by instrumented indentation.                              2 c 2 24.56     7 a 24.56     8      m d m d p h h for sink in a s p h h for pile up b s (5) with the coefficient 24.56 resulting from consideration of the equivalent conical indenter associated with vickers and berkovich indenter tips have a semi-angle at the top of 70.3°. where hm the maximum indentation depth, p the maximum applied load, s is the contact stiffness,  a constant equals to 0.75 for vickers and berkovich indenters (for sink-in mode) and α is a constant equal to 1.2 (for pile-up mode) and hd represents the length of the indenter tip defect. t h. samir, frattura ed integrità strutturale, 62 (2022) 613-623; doi: 10.3221/igf-esis.62.42 615 (a) (b) figure 1: (a) key parameters used in indentation characterization [7], (b) schematic illustration of pile-up and sink-in around a pyramidal indenter [16]. the two semi-empirical relations (2.a) and (2.b) presented by the authors [5] and [6] respectively, are expressed as a function of the ratio of instrumented hardness on the reduced modulus, (h/er). however, this characteristic and specific relationship of the material designated by (h/er) was expressed by the authors [8], according to the predictable criterion relating to the deformation mode (see fig. (1.b)) designated by hf/hm, as follows: h er =        f m h  0.2 1 h (6) note that hf is the residual depth and hm is the maximum depth as shown in fig. (1.a). the calculated value of the hf/hm ratio designates the type of deformation mode under the indenter, namely the sink-in mode or the pile-up mode (see fig. (1.b)). the critical value that separates the sink-in zone from that of the pile-up is estimated at 0.7 [7], 0.875 [8] and 0.83 [9]. for hf/hm lower than the critical value, the sink-in mode is predominant and for hf/hm higher than the critical value, the pile-up mode is predominant [7-9]. that value of 0.875 [8] is not appropriate for this case study because it does not take consider the corrections that have to be applied in order to take into account the bluntness of the indenter, the frame compliance or other factors which affect indentation response. from where, the analytical result when γ=0.875 is used must be compared with data without correction while an analytical results with a γ=0.83 [9] should be compared to data with correction of tip defect and compliance. therefore, the critical value adopted during the present research, to identify the deformation mode by indentation is 0.83 [9]. materials and experimental method n this research, three distinct materials are studied: 99% pure commercial copper, bronze and 63/37 brass, hereafter designated by cu99, sae660 and c27200 respectively. the indentation test is applied to properly prepared specimens to limit surface roughness and the introduction of work hardening resulting from polishing followed by grinding with sic papers of different grain sizes and finishing polishing using a series of diamond pastes up to a grain size of 1 m. the tests are carried out using a csm 2-107 instrumented microindenter (for a vickers diamond indenter, ei=1140 gpa and ʋi=0.07 [17]. the load range available on the indentation device varies from 0.1 to 30 n. the load resolution is given for 100 n and the depth resolution for 0.3 nm. samples reference poisson’s ratio  forces range (n) sae660 0.30 0.2-10 cu99 0.28 0.2-20 c27200 0.36 0.02-10 table 1: materials designation, poisson’s ratio, maximum force range, number of valid tests and tip defect lengths obtained by selfcalibration. i h. samir, frattura ed integrità strutturale, 62 (2022) 613-623; doi: 10.3221/igf-esis.62.42 616 the values of the loading and unloading rates (expressed in mn/min) were set at twice the value of the maximum applied load [18] and a dwell time of 15 s was imposed according to the standard indentation test procedure astm e92 and e384-10e2. before analyzing the characteristic curves by indentation relating to the materials examined, the indentation device is systematically calibrated by identifying the conformity of the frame, cf, by the self-calibration protocol. results and analyses nalysis of the criterion adopted by giannakoupolos et al [8] concerning the relation between the ratio of hardness on the reduced modulus according to the indicator of the deformation mode applied in the present study on copper and its alloys is presented in the following figures: figure 2: the (h/er)-(1-hf/hm) relationship in indentation for c27200, cu99 and sae660. the linear regressions from the graphical representations (see figs. 3 (a,b,c)) show the following slopes: 0.2000, 0.2003 and 0.1999 for the materials c27200, cu99, sae660 respectively. these three slope values are equivalent to the value of the slope equal to 0.2 and which is proposed by giannakopoulos et al. [8]. from where we confirm the value found by these authors [8] to express the relation (6). finally, we substitute the (h/er) ratio by the predictable deformation mode criterion, γ=hf/hm integrated in the relation 0.2*(1-hf/hm). the transformed analytic expressions (2.a) and (2.b) become as follows:                                                  2 rsi2 m d 2 rpu2 m d π. 1 γp 5 e                    0, 83            c. 1 γ 2 5h h π. 1 γp 1 5 1   e             0,83           α c. 1 γ 2 5h h ksi si a kpu si b (7) the expressions (7.a) and (7.b) represent the new analytic expressions of mechanical responses corresponding to sink-in mode and pile-up mode respectively. these relations are expressed as a function of the reduced modulus specific to each deformation mode identified by the prediction mode criterion. we note that γ separates the two zones of sink-in and pileup for a critical value of 0.83 [9]. in the present work we focus on the validation of the expression (7.b) applied to copper and its alloys. tab. 2 below shows that the three characterized materials admit a predominant pile-up deformation mode. a h. samir, frattura ed integrità strutturale, 62 (2022) 613-623; doi: 10.3221/igf-esis.62.42 617 however the expression (7.a) will be used to compare the variations of results of calculation of mechanical responses in the event of substitution of a mode by another by error. samples reference γ erpu(gpa) ersi (gpa) kanal (gpa) kexp (gpa) kanal/erpu(/) sae660 0.96  0.01 128  19 150  22 26.43  0.05 26.30  0.20 0,2065 cu99 0.92  0.01 91  11 105  12 37.00  0.07 36,80 0.80 0,4066 c27200 0.95  0.01 91  8 106  8 23.79  0.05 24.60  0.20 0,2614 table 2: materials designation, reduced moduli ersi (sink-in mode) and erpu (pile-up mode), mechanical responses (kanal, kexp) and corresponding ratio (kanal/erpu) for the tested materials. we calculated er from eqn. (3) as well as eqns. (5.a) and (5.b) relating to sink-in, ersi, and pile-up, erpu, modes respectively. however, the experimental response, kexp, is calculated directly from the experimental data (p/(hm+hd)2) and the analytical response, kanal, is calculated from eqn. (7.b) proposed in this present research. the graphical representations of p-(hm+hd)2 of the three materials are deliberately inverted to show their linear regressions without taking into account the tip defect (hd=0) in continuous lines and taking into consideration the correction imposed by the tip defect equal to 205 nm, 221 nm, 245 nm in discontinuous lines for sae660 (a), cu99 (b) and c27200 (c) respectively (see tab. 1). figure 3: linear regression of mechanical responses p-(hm+hd)2 by indentation of bulk metallic materials. the graphical representation (fig. 4) consists in evaluating the difference between the linear regression taking into account hd (with correction of hm) and the regression without taking into consideration the truncation length, namely neglecting the value of hd (without hm correction) as shown in tab. 3. tab. 3 shows an excellent factorial correlation of the linear regressions with very favourable reproducibility rates which tend towards 100% for the cases with or without the imposed corrections. however, the percentage differences between (hd=0) and (hd=205nm, hd=221nm, hd=245nm) for c27200, cu99 and sae660 register 48.70%, 9% and 4.3% respectively. therefore, the differences are evident according to tab. 3, which tend to affect the precision of the results of the mechanical responses and in particular when it comes to the scales of microindentation and eventually h. samir, frattura ed integrità strutturale, 62 (2022) 613-623; doi: 10.3221/igf-esis.62.42 618 nanoindentation. the magnitudes of the estimated deviations vary from one material to another, for example for c27200 the difference is estimated at 48.7%, considered very substantial and is likely to generate significant characterization errors. for the other two materials, the values of 9% and 4.3% are significantly important in the reliability of the results of the expected mechanical responses. hence the need to integrate the hd in the corrections imposed by the tip defect to take into account the effect of the truncation length in the characterization calculations and in particular in the present work. samples reference regression without correction regression with correction percentage difference [%] sae660 h2 = 20265*p + 3.106 with r2=0.9868 (h+hd)2= 39505*p + 638539 with r2=0,9995 48.7 cu99 h2 = 24845*p – 452152 with r2=0.9995 (h+hd)2= 27288*p – 791652 with r2=0,9996 9.0 c27200 h2 = 41414*p – 2.106 with r2=0.9994 (h+hd)2= 39622*p – 2.106 with r2=0,9997 4.3 table 3: results of linear regressions with and without the introduction of correction imposed by the indenter tip defect. the expressions proposed (eqns. (7.a) and (7.b)) in this work and in particular eqn. (7.b) relating to the pile-up is expressed as a function of the reduced modulus in pile-up mode. figs. 5 show the variation of er (pile-up) as a function of the maximum depth of indentation. figure 4: evolution of reduced modulus in pile-up mode vs. the maximum indentation depth. these figs. 4 clearly show that the er are substantially constant and the effect of the depths is almost insignificant for the three materials studied. hence the confirmation of the intrinsic character of the module examined for copper and its alloys studied. for the three characterized materials, in pile-up mode, we express the relationship between the kexp and the kanal as shown in figs. 5. linear regressions show very favourable factorial correlations with excellent experimental reproducibility rates. this shows that the expression specific to the pile-up mode (7.b) of semi-empirical analytical type is very compatible and coherent with the experimental data. h. samir, frattura ed integrità strutturale, 62 (2022) 613-623; doi: 10.3221/igf-esis.62.42 619 figure 5: correlation between kexp and kanal in the case of pile-up mode. if we reformulate this same relation (7.b) by expressing kanal on er, we obtain a new relation which varies only as a function of γ as is expressed in eqn. 8:                  2 2 m d π. 1 γp 1 5 1       if      γ > 0.83 α c. 1 γ 2 5h h . anal rpu rpu k e e (8) the graphical representations 7 allow the understanding and interpretation of eqn. (8). we have previously found that figs. 5. (a,b,c) of the reduced pile-up moduli of copper and its alloys show a cloud of characteristic points which are substantially constant. when we study the kanal/erpu variation we also find a substantially constant point trend as shown in figs. 6. this implies logically and mathematically (by transitive relation) that the mechanical response kanal is effectively constant. hence the validation of the semi-empirical model proposed in the present investigations. the histograms 8 represents a comparative study between the mechanical responses of the materials examined in pile-up mode, kpu, calculated by eqn. (7.b) and in sink-in mode, ksi, calculated by eqn. (7.a) as well as the (direct) experimental expression assumed to be independent of the deformation modes, namely p/(hm+hd)2 as follows: for the three materials, γ=hf/hm is greater than the critical value of 0.83 [9] which shows the predominance of the pile-up mode. so we try to estimate the ksi, kpu and kexp responses in this interval defined by [7-9] as being the pile-up mode zone. we note that the three calculated responses ksi, kpu and kexp are different and we also notice that kpu is closer to kexp unlike ksi. hence, the computational expression eqn. 7b is more adequate for the pile-up than the inappropriate exploitation of eqn. 7a relating to the sink-in if it is used in the case of a pile-up by error (not justified by the calculation of γ less than 0.83). therefore, the influence of the choice of the deformation mode expressed as a function of γ on the reliability of the results of the mechanical responses. finally we try to evaluate the differences between the different responses ksi, kpu and kexp. h. samir, frattura ed integrità strutturale, 62 (2022) 613-623; doi: 10.3221/igf-esis.62.42 620 figure 6: appreciation of the characteristic point clouds of (kanal/er) according to the maximum indentation load. figure 7: assessment of kexp, kpu and ksi for copper and its alloys according to the deformation mode criterion. h. samir, frattura ed integrità strutturale, 62 (2022) 613-623; doi: 10.3221/igf-esis.62.42 621 figure 8: histogram expressing the averages of the differences in the mechanical responses between the pile-up and the sink-in as a percentage. samples reference (kpu-ksi)/kpu [%] (esi-epu)/esi [%] sae660 16.28 14.67 cu99 15.32 05.71 c27200 15.91 14.15 table 4: estimated mean differences in mechanical responses and reduced moduli between sink-in mode and pile-up mode. the differences in the mechanical responses between the pile-up and sink-in deformation modes of the three materials studied are shown in figs. 9 and are estimated on average at 16% as shown in tab. 4 above. these mechanical responses are functions of the reduced moduli relating to the two deformation modes by indentation from where we note the influence of the reduced moduli differences on the results of the analytical expressions kpu and ksi. the estimated differences of these modules are estimated at 14.67%, 5.71% and 14.15% for sae660, cu99 and c27200 respectively. as other authors have observed [8,19,20] who find an error that can reach 30% if the deformation mode of the projected area is not taken into account in the calculations. so, finally, the mechanical response is a function of the reduced modulus, the deformation prediction criterion expressed by the ratio of (hf/hm), thus reflecting the nature of the material. obviously the chosen indenter geometry also has an influence on the mechanical response knowing that for the vickers indenter the empirical constant integrated in the analytical expression is c=24.56 (see eqns. (7.a) and (7.b)). however, in this work, we cannot estimate the exact influence of the geometry on the mechanical response because we will have to compare other indenters such as the berkovich point and the spherical point. the taking into account of the deformation modes is dominating on the reliability and the precision of the mechanical responses results calculated by the eqns. (2.a) and (2.b) on the one hand. 0 0,05 0,1 0,15 0,2 (k p uk si )/ k p u [% ] hm (nm) (a) c27200 0 0,05 0,1 0,15 0,2 (k p uk si )/ k p u [ % ] hm [nm] (b) cu99 0,13 0,14 0,15 0,16 0,17 0,18 (k p uk si )/ k p u [% ] hm [nm] (c) sae660 h. samir, frattura ed integrità strutturale, 62 (2022) 613-623; doi: 10.3221/igf-esis.62.42 622 conclusion n conclusion, we have derived an analytical expression for the load-depth relationship during loading in an indentation experiment, namely eqn. (7.b). the advantage over similar relationships derived previously is that the proposed equation is expressed as a function of the deformation mode prediction criterion and the reduced modulus which provides computational ease and caution in distinguishing between the sink -in and the pile-up. a comparison between the results achieved by the proposed analytical expression and the experimental expression shows an excellent correlation for the bulk metallic materials studied. the substitution of sink-in mode by pile-up mode and vice versa can generate a significant result error on the mechanical response which is estimated at around 16%. taking into account the correction imposed by the tip defect is necessary because the length of truncation can considerably affect the results of mechanical responses. in perspective, investigations concerning the influence of work hardening on the mechanical response by indentation are provided. acknowledgements his research was supported by the general directorate of scientific research and technological development of algeria (dgrsdt: under the authority of the ministry of higher education and scientific research in charge of scientific research). references [1] hainsworth, s. v., chandler, h. w., page, t. f. (1996). analysis of nanoindentation load-displacement loading curves, j. mater. res., 11, pp. 1987-1995. doi: 10.1557/jmr.1996.0250. [2] zeng, k., rowcliffe, d. (1996). analysis of penetration curves produced by sharp indentations on ceramic materials, philosophical magazine a 74, pp. 1107-1116. doi: 10.1080/01418619608239711. [3] cheng, y.-t., cheng, c.-m. (1998). relationships between hardness, elastic modulus, and the work of indentation, appl. phys. lett., 73, p. 614. doi: 10.1063/1.121873. [4] sun,y., zheng, s., bell, t., smith, j. (1999). indenter tip radius and load frame compliance calibration using nanoindentation loading curves, philosophical magazine letters 79, pp. 649-658. doi: 10.1080/095008399176698. [5] malzbender, j., de with, g., den toonder, j. (2001). the p–h2 relationship in indentation, j. mater. res. 15, pp. 1209 1212. doi: 10.1557/jmr.2000.0171. [6] habibi, s., chicot, d., mejias, a., boutabout, b., zareb, e., semsoum, d.-e., benaissa, s., mezough, a., merzouk h. (2021). the p–h2 relationship on load–displacement curve considering pile-up deformation mode in instrumented indentation, journal of materials research, 36, pp. 3074–3085. doi: 10.1557/s43578-021-00286-3. [7] oliver, w.-c. and pharr, g.-m. (2004). measurement of hardness and elastic modulus by instrumented indentation: advances in understanding and refinements to methodology, journal of materials research , 19(1), pp. 3–20. doi: 10.1557/jmr.2004.19.1.3. [8] giannakopoulos, a.-e., suresh, s. (1999). determination of elastoplastic properties by instrumented sharp indentation. scriptamaterialia, 40,pp. 1191-1198. doi: 10.1016/s1359-6462(99)00011-1. [9] yetnan’jock, m., chicot, d., ndjaka, j.-m., lesage, j., decoopman, x., roudet, f., and mejias, a. (2015). a criterion to identify sinking-in and piling-up in indentation of materials, int. j. mech. sci., 90, pp. 145-150. doi: 10.1016/j.ijmecsci.2014.11.008. [10] chicot, d., puchi-cabrera, e.-s., iost, a., staia, m.-h., decoopman, x., roudet, f., louis, g. (2013). analysis of indentation size effect in copper and its alloys, materials science and technology, 29, pp. 868-876, doi: 10.1179/1743284713y.0000000213. [11] oliver, w.c. and pharr, g.m. (1992). an improved technique for determining hardness and elastic modulus using load and displacement sensing indentation experiments, j. mater. res., 7, pp. 1564-1583. doi: 10.1557/jmr.1992.1564. [12] loubet, j.-l., bauer, m., tonck, a., gauthier manuel, b. (1993). nanoindentation with a surface force apparatus, mechanical properties and deformation behaviour of materials having ultra-fine microstructures, kluwer academic publishers, 233, pp. 429-447. i t h. samir, frattura ed integrità strutturale, 62 (2022) 613-623; doi: 10.3221/igf-esis.62.42 623 [13] guillonneau, g., kermouche, g., bec, s., loubet, j.-l.(2012). determination of mechanical properties by nanoindentation independently of indentation depth measurement. journal of materials research, 27, pp. 2551-2560. doi: 10.1557/jmr.2012.261. [14] bec, s., tonck, a., georges, j-m., georges, e., loubet, j.-l. (1996). improvements in the indentation method with a surface force apparatus, philos. mag., a 74, p. 1061. doi: 10.1080/01418619608239707. [15] semsoum, d.-e., habibi, s., soufiane, b., merzouk, h. (2022). the proposition of analytical expression hm–(√p/s) in microindentation pile-up deformation mode, frattura ed integrità strutturale, 60, pp. 407-415. doi : 10.3221/igf-esis.60.28. [16] fischer-cripps, a.-c. (2006). critical review of analysis and interpretation of nano-indentation test data.surf.coat. technol. 200, pp. 4153–65. doi: 10.1016/j.surfcoat.2005.03.018. [17] field, j.-e., telling, r.-h. (1999). the young modulus and poisson ratio of diamond, research note cambridge, cavendish laboratory. [18] quinn, g.-d., patel, p.-l., loyd, i. (2002). effect of loading rate upon conventional ceramic microindentation hardness, j. res. natl. inst. stand. technol., 107, pp. 299–306. doi: 10.6028/2fjres.107.023. [19] soufiane, b., habibi, s., semsoum, d.-e., merzouk, h., mezough, a., boutabout, b., montagne, a. (2021). exploitation of static and dynamic methods for the analysis of the mechanical nanoproperties of polymethylmetacrylate by indentation, frattura ed integrità strutturale, 56, pp. 46-55. doi: 10.3221/igf-esis.56.03. [20] alcala, j., barone, a.-c., anglada, m. (2000). the influence of plastic hardening on surface deformation modes around vickers and spherical indents, acta materialia, 48, pp. 3451–3464.doi: 10.1016/s1359-6454(00)00370-0. << /ascii85encodepages false /allowtransparency false /autopositionepsfiles true /autorotatepages /none /binding /left /calgrayprofile (dot gain 20%) /calrgbprofile (srgb iec61966-2.1) /calcmykprofile (u.s. web coated \050swop\051 v2) /srgbprofile (srgb iec61966-2.1) /cannotembedfontpolicy /error /compatibilitylevel 1.4 /compressobjects /tags /compresspages true /convertimagestoindexed true /passthroughjpegimages true /createjobticket false /defaultrenderingintent /default /detectblends true /detectcurves 0.0000 /colorconversionstrategy /cmyk /dothumbnails false /embedallfonts true /embedopentype false /parseiccprofilesincomments true /embedjoboptions true /dscreportinglevel 0 /emitdscwarnings false /endpage -1 /imagememory 1048576 /lockdistillerparams false /maxsubsetpct 100 /optimize true /opm 1 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/hrv (za stvaranje adobe pdf dokumenata najpogodnijih za visokokvalitetni ispis prije tiskanja koristite ove postavke. stvoreni pdf dokumenti mogu se otvoriti acrobat i adobe reader 5.0 i kasnijim verzijama.) /hun 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https://orcid.org/0000-0003-4704-1048 abstract. the present paper is devoted to an experimental study on the fracture behaviour of natural stones, commonly used as elements for building cladding, under both monotonic and cyclic loading, with particular emphasis to white carrara marble. the effect of progressive damage produced by inservice thermal fluctuations can be investigated through the application of appropriate cyclic mechanical loads. in the experimental tests conducted, some static mechanical properties of marble are characterized by means of three-point bending tests on edge-cracked prismatic specimens for the determination of young's modulus, tensile strength and fracture energy. moreover, cyclic three-point bending tests are conducted to determine the propagation rate of nominally mode-i fatigue cracks. finally, the fatigue behaviour of the marble is studied through a cohesive crack model, in which the direct tensile strength of the material is determined by a brazilian test, and the behaviour is calibrated by means of a suitable fe model. the effect of crack path on the fracture resistance of marble is discussed. keywords. fatigue crack propagation; marble; quasi-brittle behaviour, thermal cycles. citation: spagnoli, a., cendon franco, d. a., d’angelo, a., experimental investigation on the fracture behaviour of natural stone exposed to monotonic and cyclic loading, frattura ed integrità strutturale, 47 (2019) 394-400. received: 25.10.2018 accepted: 12.11.2018 published: 01.01.2019 copyright: © 2019 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. introduction he carrara marble is a widely used material in the construction field, both in historical and monumental buildings and in recent constructions, for example in the cladding elements of ventilated facades [1]. installed as coating of facades, the marble slabs are exposed to different actions that deteriorate the material, including temperature (daily t http://www.gruppofrattura.it/va/47/2234.mp4 a. spagnoli et alii, frattura ed integrità strutturale, 47 (2019) 394-400; doi: 10.3221/igf-esis.47.29 395 and seasonal excursions, through-thickness gradient), mechanical loads (wind, self-weight), chemical attacks (acid rain) and humidity changes. in particular, temperature may induce stresses due to thermal expansion (restraint effects of the anchorage system, non linear temperature fields and non uniform thermal expansion) and thermal fluctuations tend to cause a progressive damage of the material, sometimes accompanied by a curvature of the surface of the slabs [2]. such bowing phenomenon can progress up to the collapse of the element, with consequences often critical on safety for the users of the buildings where these covering slabs are installed. bowing is generally accompanied by an overall reduction of strength, which increases with increase in degree of bowing, while at the micro structural level of the material bowing is accompanied by a decohesion of calcite grains. the present paper is devoted to an experimental study on the fracture behaviour of natural stones under both monotonic and cyclic loading, with particular emphasis to white carrara marble. the effect of progressive damage produced by thermal fluctuations can be investigated through the application of appropriate cyclic mechanical loads. in the experimental tests conducted, some static mechanical properties of marble are characterized by means of three-point bending tests on edgecracked prismatic specimens for the determination of young's modulus, tensile strength and fracture energy [3]. moreover, cyclic three-point bending tests are conducted to determine the propagation rate of nominally mode-i fatigue cracks [4]. finally, the fatigue behaviour of the marble is studied through a cohesive crack model, in which the direct tensile strength of the material is determined by a brazilian test, and the behaviour is calibrated by means of a suitable fe model [5]. the effect of crack path on the fracture resistance of marble is discussed. in particular, it is shown that different level of meandering in the intergranular cracking of marble is observed and correlated with the so-called xenoblastic or homoblastic texture of calcite grains [4]. experimental testing under monotonic loading preliminary experimental campaign is carried out to quantify the resistance parameters of a carrara marble under monotonic loading. four prismatic specimens were tested under three-point bending. the nominal dimensions of the specimens are as follows: length l=220 mm; span s=180 mm; height w=60 mm; width b=30 mm (fig. 1). one specimen out of the 4 ones is a smooth specimen. notched specimens are characterised by a central edge notch machined by means of a water jet technique. notches with different nominal dimensions are machined, so that the notch depth is between 6.9 mm and 8.1 mm (the notch width is kept equal to 1.5 mm due to some technical constraints). tests were performed by means of an instron testing machine. three lvdt sensors were used to measure the rigid body motionfree mid-span deflection of the beam and a clip-on gauge to measure crack mouth opening displacement (cmod). tests on notched specimens were performed under cmod control with a of less than 10-3 mm/min. digital image correlation technique was adopted to capture full-field two-dimensional displacement maps on specimen surface in the notch vicinity. figure 1: geometrical and testing configuration of notched specimen under three-point bend loading. the rupture load of the smooth specimen is equal to 5.1 kn (corresponding to a nominal bending strength of 12.8 mpa, where the nominal stress  n is equal to 26 / (4 )ps bw ). for the 3 notched specimens, the mean bending stress at failure is equal to 6.7 mpa (corresponding to a mean rupture load of 2.7 kn), with a coefficient of variation equal to 0.13. in fig. 2, the load against mid-span deflection is shown for two notched specimens, along with the corresponding curves of the nominal stress against the crack mouth opening displacement. a a. spagnoli et alii, frattura ed integrità strutturale, 47 (2019) 394-400; doi: 10.3221/igf-esis.47.29 396 from the experimental curves related to notched specimens, fracture toughness of marble is calculated by using two different approaches. the first approach is based on the two-parameter model [6]. note that a modified version of the twoparameter model has recently been proposed in order to take into account the possible crack deflection during the stable crack propagation [7-9]. accordingly, the initial crack length a0 is assumed to grow steadily before the peak load is attained. this nonlinear stable stage terminates when the crack propagates to a critical extent and the sif ki attains a value ksic that differs from the nominal kic (computed on the basis of a0). if the geometric and loading conditions are such that the stress intensity factor is monotonically increasing with the crack length (being the load constant), as occurs in the case of a 3-point bend beam with an edge crack, the critical condition explained before takes place at the peak load. from lefm formulas and from two compliance experimental measurements, the equivalent crack length and the effective toughness ksic are worked out. the second approach is based on the work-of-fracture method in ref. [10] recommended by the rilem technical committee. for 3-point bending tests on edge-notched beams, the method is based on the experimental determination of the work exerted by the applied mid-span force, which corresponds to the area underneath the complete load–displacement curve. such a work is assumed to be fully spent to produce a mode i crack through the mid-span ligament of the beam. 0 0.04 0.08 0.12 0.16 mid-span deflection, [mm] 0 1 2 3 0.5 1.5 2.5 l oa d, p [k n ] (a) figure 2: load vs mid-span deflection curves (a) and nominal stress-cmod curves (b) for notched specimens under three-point bending. in the graph experimental results for two specimens (black thin lines) are reported along with numerical results (red thick lines). the mean value of fracture toughness according to the two-parameter model is equal to 1.90 mpam0.5 (coefficient of variation equal to 0.19). according to the work-of-fracture method, the mean fracture toughness is 1.91 mpam0.5 (coefficient of variation equal to 0.37). for the sake of completeness, a splitting test on four prismatic specimens (nominal dimensions d = 60 mm, l = 30 mm, b = 60 mm) was performed according to astm c496. the resulting indirect tensile strength (  2 / ( )t p dl ) is equal on average to 7.1 mpa (coefficient of variation equal to 0.11). experimental testing under cyclic loading leven three-point bending tests on notched specimens, with the same geometry as that adopted for monotonic loading and with the initial notch length a0 in the range 6.6 to 8.5 mm, under nearly pulsating loading were performed. tests were carried out under load control mode, with blocks of cycles composed by a single square cycle with frequency of 0.1 hz and by 125 sinusoidal cycles with frequency 2.5 hz. square cycles are introduced to take dic photos at maximum load. applied cycles have a loading ratio r = 0.1 and a maximum load expressed as a percentage of the mean failure load pu of three-point bend notched specimens under monotonic loading (pu=2.7 kn). sn-like data are n o m in a l s tr e ss , n [ m p a ] e a. spagnoli et alii, frattura ed integrità strutturale, 47 (2019) 394-400; doi: 10.3221/igf-esis.47.29 397 reported in fig. 3, where the load range level is expressed as the range of the applied sif (calculated for a crack length equal to a0), normalized by the estimated sif threshold  0.5, = 0.74 mpami thk (see the last paragraph of the present section). run-out specimens (see open circle in fig. 3) correspond to unbroken specimens after a number of loading cycles larger than n0 = 100,000. a log-log linear fitting of the experimental points with 0<fn n is attempted (negative inverse slope of 50), bearing in mind that the paucity of experimental data, along with the inherent scatter of the material properties, do not allow us to draw any conclusion on the behavioural trend observed. for illustrative purposes, fig. 4a shows the experimental curve of the cmod at maximum load in the loading cycle against the number of cycles to failure for a notched specimen loaded with a ratio   , = 1.16i i thk k . by means of classical lefm formulas, by knowledge of the applied load and the young modulus of the marble under investigation, the effective crack length can be calculated from the measured cmod. consequently, crack length against number of cycles to failure curves can be obtained (see red curve in fig. 4a). 10 2 10 3 10 4 10 5 10 6 10 7 numer of cycles to failure, nf 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 r e la tiv e s if r a n g e,  k i/ k i,t h figure 3: sn plot of fatigue results on notched specimens (open circles indicate run-out data). the experimental fatigue crack growth results, now expressed in terms of crack length a versus number of loading cycles, are analysed. in particular, the material parameters c and m of the paris law (  / mida dn c k ) are estimated. such a law has been proved to describe well the experimental trend of the fatigue growth of the so-called long cracks for a variety of engineering materials with particular regards to metals. for this purpose, the crack growth rate da/dn versus number of cycles is determined according to astm e647 standard. the experimental da/dn-n data are analyzed by an incremental polynomial method. this method for computing da/dn involves fitting a second-order polynomial (parabola) to sets of (2n+1) successive data points a-n, where n is usually 1, 2, 3, or 4 (n = 4 is assumed here). the rate of crack growth at each central point ai, in the range ai-n– ai+n, is obtained from the derivative of the above parabola. the sif range ki is determined according to classical lefm expression for the current crack length a. as an example, in fig. 4b the da/dn-ki plot is reported for the same specimen of fig. 4a. the mean values based on five experimental tests of the estimated parameters of the paris law are c=0.0002 and m=3.3 expressing da/dn as m/cycle and ki as mpam0.5, although a large scatter in the results is recorded (coefficient of variation of c and m is equal to 0.34 and 0.80, respectively), and a degree of arbitrariness is introduced in the selection of the range of paris law validity for best-fitting of experimental data point. the obtained values are in line with those reported in ref. [4] (c = 0.00029 and m = 3.9). finally, by considering the run-out fatigue tests on notched specimens (considering a conventional number of cycles for the fatigue limit n0 = 100,000), an estimation of a fatigue limit for the marble under investigation is attempted. in particular, a threshold condition in terms of sif range (related to the initial notch length a0) is obtained. the resulting mean value of kth is 0.74 mpam0.5 for loading ratio r = 0.1 (    max, , / (1 )i th i thk k r 0.83 mpam0.5). it is instructive to note that the ratio max, /i th sick k is equal to 0.44, which indicates a behavior slightly in the range of fatigue insensitive materials with flaws according to the seminal work of fleck et al [11]. a. spagnoli et alii, frattura ed integrità strutturale, 47 (2019) 394-400; doi: 10.3221/igf-esis.47.29 398 10 1 10 2 10 3 10 4 numer of loading cycles, n 0 10 20 30 m a xi m um c m o d [ m ] 8 12 16 20 24 28 c ra ck le ng th , a [m m ] cmod a (a) 10-1 100 101 sif range, ki [mpam 0.5] 10-5 10-4 10-3 10-2 c ra ck g ro w th r at e , d a/ dn [m /c yc le ] (b) figure 4: fatigue crack growth data (a) and da/dn-ki plot (b) for a notched specimen with   , = 1.16i i thk k . numerical analysis n order to analyze the results from a meso-mechanics point of view, a numerical simulation based on the cohesive zone model (czm) was conducted. the czm was firstly proposed for the numerical simulation of fracture of quasibrittle materials, such as concrete and rocks by hillerborg and coworkers [12]. the evolution of damage in czm is accounted for by means of the so-called softening curve, which is the mathematical function relating the mode i crack opening displacement, w, with the stress transferred across the crack lips,  (see fig. 5). figure 5: meso-mechanics basis of the cohesive zone model and parameters of the softening curve.  w w =f(w) fdecoh area=gf i a. spagnoli et alii, frattura ed integrità strutturale, 47 (2019) 394-400; doi: 10.3221/igf-esis.47.29 399 the softening curve is defined by three main ingredients: the decohesion strength, fdecoh, which is the value of the softening curve for null crack opening; the area comprised between the curve and the abscissa axis, which represents the specific fracture energy of the material, gf; and the shape of the softening curve, which depends on the way in which the material is damaged as the crack is opened. in the numerical simulations presented in this paper, the czm was implemented in combination with the embedded crack approach. further details about the implementation can be found in [13, 14]. when applying the czm to quasi-brittle materials, the decohesion strength is usually set equal to the tensile strength of the material measured through a splitting tensile test [15], which according to the experimental campaign previously detailed was equal to ft=7.1mpa (young modulus was taken as e = 75 gpa). about the area under the softening curve, it was set equal to the specific fracture energy determined in the three-point-bending tests under static conditions, that is to say, gf = 60 n/m, considering the results of two experimental tests reported in fig. 2. unfortunately, up to date no general procedure has been set to determine the shape of the softening curve for a given material. there are some standard curves, such as the bi-linear curve for plain concrete [16], or the rectangular curve for steels [17] but to the authors' knowledge, no standard has been set in the case of marble. for this reason, a trial-and-error procedure was made by numerical simulation of the three-point-bending tests conducted for the determination of the specific fracture energy, trying different softening curve shapes until achieving a good agreement with the experimental results. to facilitate this trial-and-error process, according to [18], the following family of softening curves was used:    * 1 1 1n nf e e        , where f* is the non-dimensional stress transferred across the crack lips (stress divided by the decohesion strength),  is the non-dimensional crack opening (crack opening divided by the critical crack opening) and n is a material constant. with this family of curves it is possible to modify the shape of the softening curve by playing with the n parameter (n = 0 leads to a linear softening curve). in the case of the marble analyzed in this paper, it was found that a value of n=2 leads to a reasonable agreement between the experimental behaviour and the numerical prediction, as is shown in fig. 2. the numerical simulation of the three-point-bending static tests allowed us to provide a meso-mechanics insight on the results of cyclic loading tests. in quasi-brittle materials, it has been demonstrated that for samples having dimensions of the order of magnitude of the size of the fracture process zone (fpz), the peak load is reached after such an fpz has been largely developed ahead of the notch tip of the specimen. thanks to the czm, it is possible to analyze the initiation and evolution of the fpz, since it is equivalent to the cohesive zone. fig. 6 shows the length of the cohesive zone (fpz) as a function of the nominal stress intensity factor, ki, applied during the simulation of the three-point bending static test. in this plot the ki required to initiate the fpz is marked, which is considerably lower than the ki corresponding to the peak load. in the same plot, the ki corresponding to the fatigue propagation threshold is also highlighted. it can be seen how the latter is mostly inside the region of fpz generation, revealing that a significant level of damage (corresponding to a large fpz) ahead of the notch tip is required for fatigue crack propagation. actually, according to this analysis, those ki ranges below the threshold represented in the figure would not lead to crack propagation in spite of causing appreciable damage (fpz) at the notch tip. it must be reminded that this result is solely based on a numerical simulation, requiring further experimental data to confirm the hypothesis. figure 6: fracture process zone (fpz) size in terms of % of the ligament as a function of the stress intensity ki applied. the figure also shows the ki corresponding to the fatigue crack propagation threshold. 0 5 10 15 20 25 30 35 0 0.2 0.4 0.6 0.8 1 1.2 fpz sizef p z s iz e ( % o f lig a m e n t) k i (mpaꞏm 1/2 ) k i required for fpz initiation k i max in fatigue propagation threshold k i min in fatigue propagation threshold k i corresponding to peak loadk i for fatigue propagation threshold a. spagnoli et alii, frattura ed integrità strutturale, 47 (2019) 394-400; doi: 10.3221/igf-esis.47.29 400 conclusions n experimental campaign on the fracture behavior of carrara marble under monotonic and cyclic loading has been carried out. the results under monotonic loading show a well-known quasi-brittle behavior of the material, which requires for instance a two-parameter approach to correctly estimate fracture toughness. the results under cyclic loading allow us to estimate the material parameters governing the fatigue crack growth. also, such results allow an attempt to estimate a fatigue limit in terms of sif threshold. a comparison of experimental monotonic results with those of a numerical model based on a cohesive crack approach shows a good correlation. finally, the numerical results permit to give an insight on the correlation between fpz and fatigue threshold conditions. further investigation is needed to fully understand the experimental observation under cyclic temperature of the different behavior of marble depending on the microstructural texture of calcite grains (see xenoblastic and homoblastic types of marble) and in turns on the roughness features of intergranular cracking profiles. references [1] ferrero, a.m., migliazza, m., spagnoli, a. theoretical modelling of bowing in cracked marble slabs under cyclic thermal loading (2009) construction and building materials, 23 (6), pp. 2151-2159. [2] spagnoli, a., ferrero, a.m., migliazza, m. a micromechanical model to describe thermal fatigue and bowing of marble (2011) international journal of solids and structures, 48 (18), pp. 2557-2564. [3] spagnoli, a., carpinteri, a., ferretti, d., vantadori, s. an experimental investigation on the quasi-brittle fracture of marble rocks (2016) fatigue and fracture of engineering materials and structures, 39 (8), pp. 956-968. [4] migliazza, m., ferrero, a.m., spagnoli, a. experimental investigation on crack propagation in carrara marble subjected to cyclic loads (2011) international journal of rock mechanics and mining sciences, 48 (6), pp. 1038-1044. [5] cendon, d. a., torabi, a. r., elices, m. fracture assessment of graphite v-notched and u-notched specimens by using the cohesive crack model (2015) fatigue and fracure of engineering materials and structures, 38 (5), pp. 563-573. [6] jenq, y. and shah, s. p. (1985) two parameter fracture model for concrete. j. eng. mech., 111, 1227–1241. [7] carpinteri, a., berto, f., fortese, g., ronchei, c., scorza, d., vantadori, s. (2017), modified two-parameter fracture model for bone. engineering fracture mechanics, 174, 44–53, doi: 10.1016/j.engfracmech.2016.11.002. [8] carpinteri, a., fortese, g., ronchei, c., scorza, d., vantadori, s. (2017), mode i fracture toughness of fibre reinforced concrete, theoretical and applied fracture mechanics, 91, 66-75, doi: 10.1016/j.tafmec.2017.03.015. [9] vantadori, s., carpinteri, a., guo, l.-p., ronchei, c., zanichelli, a. (2018), synergy assessment of hybrid reinforcements in concrete, composites part b: engineering, 147, 197-206, doi: 10.1016/j.compositesb.2018.04.020. [10] bazant, z. p. (1996) analysis of work-of-fracture method for measuring fracture energy of concrete. j. eng. mech. asce, 122, 138–144. [11] fleck, n. a., k. j. kang, and m. f. ashby. (1994). overview no. 112: the cyclic properties of engineering materials. acta metallurgica et materialia 42(2), pp. 365-381. [12] hillerborg, a., modéer, m., and petersson, p. (1976). analysis of crack formation and crack growth in concrete by means of fracture mechanics and finite elements, cement and concrete res. 6. [13] sancho, j.m., planas, j., cendón, d.a., reyes, e., gálvez, j.c. (2007). an embedded crack model for finite element analysis of concrete fracture. eng. fract. mech., 74, pp. 75-86. [14] cendón, d.a., torabi, a.r. and elices, m. (2015). fracture assessment of graphite vand unotched specimens by using the cohesive crack model. fat. and fract. of eng. mats and structures, 38-5, pp. 563-573. [15] bazant, z.p. and planas, j. (1998). fracture and size effect in concrete and other quasibrittle materials. crc press. boca raton, florida. [16] guinea, g.v., planas, j. and elices, m. (1994). a general bilinear fit for the softening curve of concrete. materials and structures 27 (2), pp. 99-105. [17] dugdale, d.s. (1960), yielding of steel sheets containing slits. j. mech. phys. solids, 8, pp. 100. [18] cendón, d.a., jin, n., liu, y., berto, f. and elices, m. 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/pdfxoutputintentprofileselector /documentcmyk /preserveediting true /untaggedcmykhandling /leaveuntagged /untaggedrgbhandling /usedocumentprofile /usedocumentbleed false >> ] >> setdistillerparams << /hwresolution [2400 2400] /pagesize [612.000 792.000] >> setpagedevice microsoft word numero_53_art_08_2740 j. akbari et alii, frattura ed integrità strutturale, 53 (2020) 92-105; doi: 10.3221/igf-esis.53.08 92 focussed on structural integrity and safety: experimental and numerical perspectives numerical investigation of the seismic behavior of unanchored steel tanks with an emphasis on the uplift phenomenon jalal akbari* bu-ali sina university, department of civil engineering, hamedan, iran j.akbari@basu.ac.ir, https://orcid.org/0000-0001-9713-8652 omid salami laboratory of earthquake engineering and structural health monitoring of infrastructures (leeshmi), bu-ali sina university, hamedan, iran omidsalami@gmail.com mohsen isari faculty of civil engineering, university of tabriz, tabriz, iran isari.mohsen@tabrizu.ac.ir abstract. ground steel storage tanks are widely used in different industries. regarding the significance of these structures, ensuring the proper performance of such structures in earthquakes needs evaluating their seismic performance. the present study examines the seismic behavior of an unanchored fluid storage system via abaqus after validation with an experimental model. next, the uplift of the bottom sheet is studied using the accelerogram records of the 1940 el centro and 1994 northridge earthquakes. the overturning moment time history of the fluid storage system and the maximum overturning moments were obtained to identify their behavior. the results indicated that not bracing storage tanks leads to the uplift phenomenon. finally, the maximum axial stress of the storage tank shell was compared with the values recommended in the design codes to control the buckling. keywords. liquid storage tanks; steel cylindrical tanks; unanchored steel tanks; water storage tanks; uplift of steel tanks. citation: akbari, j., salami, o., isari, m., numerical investigation of the seismic behavior of unanchored steel tanks with an emphasis on the uplift phenomenon, frattura ed integrità strutturale, 53 (2020) 92-105. received: 20.01.2020 accepted: 21.03.2020 published: 01.07.2020 copyright: © 2020 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. introduction ylindrical ground fluid storage tanks are widely used in different industries to store water, fuel and chemical materials. the failure of fuel tanks, particularly in oil refineries, can lead to large and uncontrollable fire and impose destructive environmental effects. due to the presence of flammable materials in oil refineries, a small incident can c https://youtu.be/kbs1egqsywi j. akbari et alii, frattura ed integrità strutturale, 53 (2020) 92-105; doi: 10.3221/igf-esis.53.08 93 lead to a large disaster that not only imposes financial and life losses but also imposes irreparable environmental damages whose effects can last for many years. comprehensive studies have been conducted on fluid storage tanks. such studies are classified into three groups of analytical, experimental and numerical. tank studies were mostly conducted in the late 1940s by jacobsen [1] and in the early 1960s by housner [2]. he investigated the dynamic fluid forces on the inner wall of a tank and its surrounding environment. they analytically proposed some graphs to derive the effective mass of the fluid and hydrodynamic forces for different length/diameter ratios of the tank. the effective mass later became an essential factor in obtaining the base shear of tanks. this method was used by engineers to design tanks until 1955. after the 1964 alaska earthquake, an important study was conducted on the failure of tanks, which still is employed by clough [3]. in the late 1970s, analytical studies were conducted on tanks by veletsos, which demonstrated the more realistic behavior of tanks during earthquakes [4-8]. the validity of some of such models is accepted in the engineering society and included in design regulations as design standards. however, some tanks designed based on new regulations are damaged in intensive earthquakes. the weak performance of tanks in earthquakes indicates that the seismic behavior of such tanks is more complicated than that assumed in analytical or even numerical models and regulations. thus, considering the inability of analytical relations and complications, several experimental studies were conducted on the seismic behavior of tanks along with analytical and numerical methods. for example, niwa [9-10], and manos et al. [11] experimentally studied unanchored tanks. they examined scaled models under dynamic and static loads on shaking tables. they employed different conditions in the bottom clamping, support rigidity, the length/radius ratio of the tank and tank top shapes and compared the obtained results. zui et al. [12] investigated the clamping effect of an unanchored cylindrical tank on its seismic behavior. they concluded that the clamping of the tank considerably changed the seismic response. barton et al. [13] derived the seismic responses of fluid storage tanks to horizontal earthquakes via the added mass method chiba [14-15] evaluated the nonlinear vibration of cantilevered cylindrical tanks, including two polyethylene tanks. they found that the nonlinearity of a tank’s behavior is dependent on the heights of the tank and fluid. the general results of experimental studies suggest that the uplift mechanism, which is nonlinear to the excitation frequency, is an important phenomenon in the seismic responses of unanchored tanks. out-of-form wall deformation occurs in both anchored and unanchored seismic-loaded tanks. such deformation and the uplift mechanisms change the stress distribution and lead to compressive stress on the tank wall. such stress is larger in unanchored tanks than in anchored ones. owing to the rapid growth of computers, numerical techniques, particularly the finite element method (fem), have widely been employed to evaluate the behavior of tanks with high accuracy. they employed anchored and unanchored tanks. elzeiny [16] used the eulerian-lagrangian concept for the fluid and structure in their model. they obtained the nonlinear responses of fluid storage tanks by considering the waving of the water surface and the fluid-structure interaction (fsi). their assumptions included unanchored cylindrical metal fluid storage tanks under the strong movement of the ground. malhotra and clough investigated the behavior of steel cylindrical tanks with a simple beam model [17]. as well, malhotra studied the base uplifting phenomenon and simple seismic analysis of liquid-storage tanks [18-20]. souli et al. [21] proposed a procedure known as the arbitrary lagrangian-eulerian (ale) algorithm to solve the fsi problem. the ale algorithm suggests that the grid and material are independent of each other and the grid topology is stable. this allows the fluid surface material to maintain its lagrangian approach without becoming complicated due to large deformation, making it possible to deal with moving boundaries in grids. taniguchi [22] modeled and evaluated the dynamic movement parameters of unanchored cylindrical tanks containing a fluid in a single-direction movement. for fsi problems with large structural deformation and destructive fluid surface wave movements, aquelt et al. [23] proposed a method based on trial and error to model the reaction of the structure with the lagrangian approach and model the reaction of the fluid with the eulerian approach. virella et al. [24] predicted the maximum ground movement that would lead to elastic buckling on top of an anchored tank. in the most important recent experimental study, maekawa et al. [25] analyzed a model with a scale of 1:10 in terms of tank deformation and buckling. they reported that their method was properly consistent with experimental results in analyzing the bucking and behavior of a tank. besides, they found that their method was sufficiently accurate in evaluating the seismic strength of tanks, such as seismic safety. maekawa [2627] studied the seismic behavior of ground steel tanks via numerical modeling and obtained the reduction factor in regulations with higher accuracy. the present study investigates the seismic behavior of unanchored steel tanks via time history analysis with a focus on the uplift mechanism. for this purpose, the relationships between hydrodynamic loads and the bottom sheet uplift and their effects on the structural deformation, structural stress, and fluid movement through the tank were explored. the following assumptions were used for numerical models. the physical properties of the tank material are linear. the fluid is incompressible and non-viscose. j. akbari et alii, frattura ed integrità strutturale, 53 (2020) 92-105; doi: 10.3221/igf-esis.53.08 94 the entire analyses are nonlinear and the time history analyses are an explicit integral. adaptive meshing is used. fsi is incorporated. the interaction between the tank and its bottom support is ignored. the fluid within the tank is generally assumed to be incompressible and non-viscous in the formulation of seismic problems for tanks. as well, the fluid is assumed to be non-rotational. the laplace differential equation is employed based on the velocity potential function to model the ideal fluid movement. the laplace boundary conditions are defined by the dynamic response of the tank structure. these boundary conditions are a combination of ground movement-induced vibration and hydrodynamic load-induced deformation. research methodology validation ue to the complications of the problem, it is required to validate the numerical model before examining the seismic behavior of the tank-fluid model. for this purpose, the study of maykawa [25], which includes a roofless ground tank-fluid tank, was used. the experimental results included the measurement of the pressure, surface wave height, and shell stress in a time of 8 s by an accelerogram. as can be seen, the system (fig. 1) is placed on a rigid rectangular plane. figure 1: the physical model of the experimental tank-fluid system [14] the tank’s height and diameter are both 1.83 m, the tank wall thickness is 2 mm, the tank material is aluminum with an elasticity modulus of 71 gpa, the material density is 2,700 kg/m3, and the yield stress is 100 mpa. the fluid is water with a density of 1,000 kg/m3 in 1.53 m of height. the seismic load is applied by a seismic table with an accelerogram of maximum base acceleration of 0.5 g. fig. 2 demonstrates the acceleration records in the northsouth direction. figure 2: the accelerogram of the experimental model [14] d j. akbari et alii, frattura ed integrità strutturale, 53 (2020) 92-105; doi: 10.3221/igf-esis.53.08 95 modeling was performed with finite-element software. the boundary conditions, loads, and other specifications used in the fem model were the same as those employed in the experimental investigation. double-curved membrane four-node elements with reduced integration and s4r membrane strain formulation (i.e., each element with four nodes and each node with six degrees of freedom) were employed in the tank wall meshing. these elements can properly simulate both local and general buckling. the modeling included the effects of large displacements and nonlinear shapes. welding details were excluded from the model. two separate components appear in water hydrodynamics: the impulsive component and the convective component. here, the surface wave phenomenon plays a key role. hence, specific eight-node elements of eos type known as the c3d8r elements were employed. such elements represent state equations and are used in software to model the states of surface waves. typical fluid-structure interaction (fsi) specifications were used in the fsi problem. the fsi of penalty type with a factor of 0.015 was applied. fig. 3 shows the time history results of pressure (except for the hydrostatic pressure) at two points in the tank with r = 1.83 m, height of z = 0.05 m and 0.45 m from the bottom. figure 3: the time history of pressure at two points between experimental and numerical models as can be seen, the numerical results are in good agreement with the experimental results. the pressure at t= 3s indicates that the pressure response amplitude is affected by the bottom uplift. fig. 4 represents the base shear time history. according to fig. 4, both experimental and fem results follow a similar trend in time. however, the fem results are slightly larger. the equivalent wave height is another essential aspect of tank-fluid systems. here, the time history of the equivalent wave height is derived from numerical values. fig. 5 depicts the equivalent time history responses at two points r=1.72 m and r=-1.72 m. the points were selected on the loading axis. although there are slight deviations from the experimental values in the numerical values, the numerical values are almost consistent with the experimental values in terms of peak times and wave shapes and amplitudes. j. akbari et alii, frattura ed integrità strutturale, 53 (2020) 92-105; doi: 10.3221/igf-esis.53.08 96 figure 4: base shear’s time history between experimental and numerical models. figure 5: a comparison of the surface wave height time histories at points r=1.72 m and r=-1.72 m tab. 1 summarizes the details and parametric features of the tank-fluid system, including the equivalent surface wave height, base shear, overturning moment and axial shell stress. j. akbari et alii, frattura ed integrità strutturale, 53 (2020) 92-105; doi: 10.3221/igf-esis.53.08 97 experiment numerical api (650) euro code (8) nzsee malhotra et al. [19] surface wave height (cm) 8.0 8.9 16 13 14 16 base shear force (kn) 40.7 47.3 37.3 44.3 39.4 45.9 overturning moment (kn.m) 65.1 28.9 21.8 29.0 25.0 30.6 axial shell stress (mpa) 25.8 20.5 n/a n/a 51.8 n/a table 1: a comparison of responses between numerical and experimental methods and regulations codes numerical results ig. 6 illustrates a schematic of the tank and its details. the unanchored roofless tank rests on a rigid bed. tab. 2 provides the specifications of the material. the shell thickness varies at different heights. the fluid is water in the heights of 6, 9, and 12, occupying 50%, 75%, and 100% of the tank capacity, respectively. the young modulus (e), passion’s index (ν), and density (ρ) of 210 gpa, 0.3, and 7800 kg/m3 were applied to the tank material. moreover, the density, bulk modulus, and wave speed of 1000 kg/m3, 2200 mpa, and 1449 m/s were applied to the water, respectively. figure 6: a schematic of the tank and the corresponding fem mesh. six models with different fluid levels were incorporated. tab. 2 provides the models. model fluid height (m) occupied tank capacity (%) record t1 6 50 1940 el centro t2 9 75 1940 el centro t3 12 100 1940 el centro t4 6 50 1994 northridge t5 9 75 1994 northridge t6 12 100 1994 northridge table 2: the models and applied earthquake records for numerical studies f j. akbari et alii, frattura ed integrità strutturale, 53 (2020) 92-105; doi: 10.3221/igf-esis.53.08 98 dynamic time history analyses were performed on the models at three different heights in a time of 12 s with the 1940 el centro and 1994 northridge accelerogram records. fig. 7 represents the specifications of the accelerogram records. the maximum ground accelerations of the el centro and northridge earthquakes occurred to be 0.35 and 0.58 g at 2.1 and 5.4 s, respectively, both in the north-south direction. [28] figure 7: the accelerogram records of a) the el centro (above) , and b) the northridge (below) these analyses were performed to obtain a better insight into the behavior of unanchored fluid storage tanks under seismic loads. figs. 8 and 9 indicate the overturning moment time histories of the tank-fluid system for the northridge and el centro earthquakes, respectively. the first reaction occurred from the beginning for approximately 5 and 4.5 s (figs. 8 and 9, respectively) when the system was subject to the el centro and northridge earthquakes. in this time, the load mostly arose from impulsive modes. figure 8: the overturning moment under the 1940 el centro earthquake. j. akbari et alii, frattura ed integrità strutturale, 53 (2020) 92-105; doi: 10.3221/igf-esis.53.08 99 figure 9: the overturning moment under the 1994 northridge earthquake as can be seen, the second part of the graphs resulted from high-period movements. the fluid pressure loads on the wall were calculated, and their reflection caused the fluid to move within the tank. the observed behavior of lateral loads revealed that the behavior of the fluid was initially induced by impulsive values and then by convective values. tab. 3 provides the numerical results at the maximum load and the corresponding accelerogram record. earthquake tank maximum load units (mn, mn.m) time (s) acceleration (g) 1940 el centro t1 lateral load overturning moment 11.46 28.29 4.51 0.21 1940 el centro t2 lateral load overturning moment 16.62 69.09 9.73 0.04 1940 el centro t3 lateral load overturning moment 74.81 388.40 3.52 0.11 1994 northridge t4 lateral load overturning moment 14.11 36.51 5.44 0.53 1994 northridge t5 lateral load overturning moment 29.28 130.50 5.36 0.47 1994 northridge t6 lateral load overturning moment 54.49 278.10 4.11 0.51 table 3: the obtained results from applied earthquake records. as can be seen, the maximum loads did not occur at the time of the maximum acceleration. a comparison of the earthquake time histories and input accelerogram records with the load time histories reveals three different behaviors in the response time histories: 1. the maximum load occurs when the ground movement is large. for example, t6 overturned at 4.11 s with a ground acceleration of above 0.5g. 2. the maximum load happens when the total of the impulsive and vibrating movements of the fluid is maximum. for example, the maximum load of t2 happened at 9.73 s. 3. the maximum load takes place when the ground movement is medium but the reaction between the fluid movement and tank dynamic response is large. for example, t3 stayed stable at the maximum acceleration but overturned at 3.53 s at a ground acceleration of above 0.11 g. in this respect, higher impulsive modes have a strong effect on the general response of the tank-fluid system. bottom sheet uplift figs. 10 and 11 illustrate the vertical uplift time histories of the bottom sheet under the 1940 el centro and 1994 northridge earthquakes, respectively. for the tank-fluid system with a fluid height of 6 m, the bottom sheet exhibited no uplift when j. akbari et alii, frattura ed integrità strutturale, 53 (2020) 92-105; doi: 10.3221/igf-esis.53.08 100 subjected to the earthquakes. however, at a fluid height of 9 m, the bottom sheet uplifted once under the 1940 el centro earthquake and several times under the 1994 northridge earthquake. at a fluid height of 12 m, the tank overturned under the 1940 el centro and 1994 northridge earthquakes at 3.52 and 4.11 s, respectively. the results show that the tank-fluid system experienced a large uplift when overturning. a comparison of the bottom uplift time histories with the overturning moment time histories suggests that the bottom uplift takes place only when the overturning moment exceeds a specific value. also, a large bottom uplift happens at a large moment. figure 10: the bottom’s uplift time history under the 1940 el centro earthquake. figure 11: the bottom’s uplift time history under the 1994 northridge earthquake. as can be seen, there is a clear trend in the bottom uplift rise versus the overturning moment rise in the results. in general, there is a delay between the maximum overturning moment and the maximum bottom uplift. the magnitude and direction of the overturning moment may undergo significant changes in a short period under seismic loads. the time of the overturning moment-induced bottom uplift is typically small. thus, although the overturning moment is very large, the bottom uplift can remain small. figs. 9 and 10 present the maximum bottom uplift and the uplifted area. as can be seen, the uplifted area can be more than 9% of the tank radius. wozniak et al. [29] provided the ultimate uplift limit. the wave height within the tank. figs. 12 and 13 demonstrate the wave height time histories at the movement axis (θ=0) concerning the hydrodynamic pressure on the fluid free surface under the 1940 el centro and 1994 northridge earthquakes, respectively. as it can be observed from these figures, the maximum equivalent wave heights under the el centro earthquake were obtained to be 2.01 and 2.74 m for t1 and t2, respectively. also, the maximum equivalent wave heights under the northridge earthquake were derived to be 3.11 and 5.03 m for t4 and t5, respectively. specifically, the assumption of ignorable wave heights does not apply to other analytical models under the same conditions. the results suggest that the fluid wave height can be large and strongly damage upper installations during an earthquake. j. akbari et alii, frattura ed integrità strutturale, 53 (2020) 92-105; doi: 10.3221/igf-esis.53.08 101 figure 12: the equivalent wave height time history under the 1940 el centro earthquake. figure 13: the equivalent wave height time history under the 1994 northridge earthquake. the stress and fracture of the tank wall the stress on the tank wall during an earthquake is generally affected by the membrane mechanism. figs. 14-17 illustrate the axial stress time histories near the tank bottom and at the middle level of the tank shell at the movement axis (θ=0). membrane stress is affected by the overturning moment near the bottom. membrane stress variations seem to have the same vibration features as the overturning moment near the tank base. at the middle fluid height level, where the overturning moment effect considerably reduces with an increase in the height, the axial stress is influenced by the wall deformation and has a different vibration pattern from the lower of the tank. as can be seen, the axial stress in the middle of the fluid can be very large. according to figs. 14 and 16, the axial stress at the bottom of the tank with 6 m of fluid height is largely affected by the bottom uplift. the tensile stress compared to the compressive stress reduces from 8 to 12 s in fig. 8 and from 8 to 11 s in fig. 17 for the tank with 9 m of fluid height due to the el centro earthquake. the tensile stress may even become compressive stress because of its reduction, which is dependent on the bottom sheet uplift. it is also observed that the maximum axial stress may not happen at the same time as the maximum turnover moment due to the shell deformation effects. the bending mechanism should also be considered both near the tank bottom, where fixes are applied, and in the locations with the highest deformations. the axial stress near the tank bottom is compressive rather than being tensile due to the bottom uplift-induced compression. the circumferential stress, which is generally tensile stress, arises from the outward fluid pressure and shell deformation. on the contrary, the circumferential stress seems to be compressive since the shell is fixed in the radial direction. j. akbari et alii, frattura ed integrità strutturale, 53 (2020) 92-105; doi: 10.3221/igf-esis.53.08 102 figure 14: the axial stress time history of t1 under the 1940 el centro earthquake. figure 15: the axial stress time history of t2 under the 1940 el centro earthquake. figure 16: the axial stress time history of t4 under the 1994 northridge earthquake. j. akbari et alii, frattura ed integrità strutturale, 53 (2020) 92-105; doi: 10.3221/igf-esis.53.08 103 figure 17: the axial stress time history of t5 under the 1994 northridge earthquake. tank structure failure the most-reported seismic damage is the buckling of the tank wall by high stress in response to seismic loads. tab. 4 provides the highest compressive stress on the tank wall. according to the awwa d100-96 standard [30], the permissible compressive stress is 105 mpa, considering structural stability. according to the analysis results, elephant-foot buckling may happen near the tank base in t2, t3, t5, and t6 due to large compressive stress. also, elephant-foot buckling can occur on the top of t2 due to large compressive circumferential stress. in other cases, buckling may take place due to a combination of axial compression and circumferential stress. based on the time history analysis results, the dynamic behavior of unanchored steel tanks during an earthquake can be summarized as follows: a) the dynamic behavior of unanchored systems is the same as that of anchored systems when the seismic load is not large enough to cause bottom uplift. the major deformations of an unanchored tank in response to seismic loads are bottom sheet uplift and out-of-form circular shell deformation due to the lack of anchoring systems. major tank deformations make the tank-fluid system very flexible. b) the bottom uplift mechanism is very complicated and nonlinear. the bottom sheet uplifts when the overturning moment exceeds the permissible value. although there is an alignment between the bottom uplift rise and the overturning moment rise, the bottom uplift behavior varies in wide overturning moment ranges. c) the lateral loads and the overturning moment may be impulsive or convective, depending on the value and type of the fluid components (i.e., either impulsive or convective). d) the tank’s stress appeared in response to seismic loading is generally influenced by the membrane mechanism. large bending mechanism-induced stress appear in locations with fixtures and large deformation, particularly in the lower part of the tank. e) high axial stress may occur near the tank base, leading to elephant-food buckling and the buckling fracture of the wall. a combination of compressive circumferential stress and tensile stress at a high height of a tank may also lead to elephant-foot buckling. earthquake height (m) axial stress (𝐤pa) height (m) 1940 el centro 6 31.4 0.46 1940 el centro 9 109.6 0.50 1940 el centro 12 662.8 0.00 1994 northridge 6 9.2 0.38 1994 northridge 9 160.0 0.48 1994 northridge 12 377.6 0.48 table 4: the maximum stress in the wall of the tank. j. akbari et alii, frattura ed integrità strutturale, 53 (2020) 92-105; doi: 10.3221/igf-esis.53.08 104 conclusions he numerical model of an unanchored steel ground storage tank demonstrated that the seismic behavior of unanchored tanks in response to seismic loads differs from that of anchored ones due to the nonlinearity of the uplift mechanism. thus, it is necessary to evaluate the effects of the uplift mechanism when designing a seismic load-resistant tank-fluid system. the effects of the uplift mechanism are generally evaluated by simplified equivalent models due to their complications. however, the results are not reliable. the present study investigated the seismic responses of unanchored tanks by time history analyses. the structural deformation due to uplifts, the interaction between the fluid movement and the dynamic structural response, and tank stress were completely discussed. the major conclusions of this study are outlined as follow: 1. bottom uplift occurs only when the fluid-induced overturning moment exceeds the critical value; 2. the uplift mechanism is nonlinear to the overturning moment; 3. the uplift mechanism determines the system’s dynamic response. the wall sheet turns around the bottom point when the bottom sheet uplifts, which causes larger deformation than the vibration-induced deformation. tank-fluid systems become very flexible when uplifting. 4. the bottom uplifting mechanism causes large stress on the tank structure. large compressive stress appears near the bottom and on the top of the shell due to the bottom sheet uplift. acknowledgment he first author acknowledges the all support from malayer university when he was an assistant professor of civil engineering from september 2008 to june 2019. conflict of interests he authors have no conflict of interest to declare. references [1] jacobsen, l.s. (1949). impulsive hydrodynamics of fluid inside a cylindrical tank and of fluid surrounding a cylindrical pier. bull seismol soc amer 39(3), pp. 189204. [2] housner, g.w. (1963). the dynamic behavior of water tanks. bulletin of the seismological society of america, 53 (2), pp. 381-387. [3] clough, d. p. (1977). experimental evaluation of seismic design methods for broad cylindrical tanks. report no. uc/eerc 77-10. earthquake engineering research center, university of california, berkeley, calif. [4] veletsos, a.s. (1974). seismic effects in flexible liquid storage tanks”, proceedings of fifth world conference on earthquake engineering, rome italy, 1, pp. 630-639 [5] veletsos, a. s. and yang, j. y. (1976). dynamics of fixed-based liquid storage tanks. proceedings of 03-japan seminar for earthquake engineering research with emphasis on lifting systems. tokyo, pp. 317-341 [6] veletsos, a. s. and yang, j. y. (1977). earthquake response of liquid storage tanks. advances in civil engineering through engineering mechanics division specialty conference, asce, north carolina, pp. 1-24. [7] veletsos, a.s. (1984). seismic response and design of liquid storage tanks. in: guidelines for the seismic design of oil and gas pipeline systems. asce; pp. 255-370. 443-60. [8] veletsos, a.s., tang, y., and tang, h.t. (1992). dynamic response of flexibly supported liquid-storage tanks, journal of structural engineering, asce, 118 (1), pp. 264-283. t t t j. akbari et alii, frattura ed integrità strutturale, 53 (2020) 92-105; doi: 10.3221/igf-esis.53.08 105 [9] niwa, a. (1978). seismic behavior of tall liquid-storage tanks. report no.78, earthquake engineering research center, university of california at berkeley. [10] niwa, a., clough, r.w. (1982). buckling of cylindrical liquid storage tanks under earthquake loading. earthq eng struct dyn, 10(1), pp. 107_22. [11] manos, g.c., clough, r.w. (1982). further study of the earthquake response of a broad cylindrical liquid storage tank. earthquake engineering research center. report ucb/eerc 82-07. [12] zui, h., osamu, o., tohru, s., and akira, n. (1985). seismic response analysis and dynamic model tests of cylindrical tanks. doboku gakkai ronbunshu 362, pp. 441-450. [13] barton, d. c., and parker j. v. (1987). finite element analysis of the seismic response of anchored and unanchored liquid storage tanks." earthquake engineering & structural dynamics, 15(3), pp. 299-322. [14] chiba, m. (1993). non-linear hydroelastic vibration of a cantilever cylindrical tank—i. experiment (empty case). international journal of non-linear mechanics 28(5), pp. 591-599. [15] chiba, m. (1993). non-linear hydroelastic vibration of a cantilever cylindrical tank—ii. experiment (liquid-filled case). international journal of non-linear mechanics 28(5), pp. 601-612. [16] el-zeiny, a. (1995). nonlinear time-dependent seismic response of unanchored liquid storage tanks. ph.d. dissertation. irvine: department of civil and environmental engineering, university of california. [17] malhotra, p.k., veletsos, a.s. (1994). beam model for the base-uplifting analysis of cylindrical tanks. j struct eng, asce 120(12), pp. 3471-3488. [18] malhotra, p.k. (1995). base uplifting analysis of flexibly supported liquid-storage tanks. earthq eng struct dyn 24(12), pp. 1591-1607. [19] malhotra, p.k. (1997). seismic response of soil-supported unanchored liquid storage tanks. journal of structural engineering, asce, 123 (4), pp. 440-450. [20] malhotra, p.k. (2000). simple procedure for seismic analysis of liquid-storage tanks. structural engineering international, 3, pp. 197-201. [21] souli, m., zolesio j.p. (2001). arbitrary lagrangian_eulerian and free surface methods in fluids mechanics. comput methods appl mech eng 191, pp. 451-466. [22] taniguchi, t. (2004). rocking behavior of unanchored flat-bottom cylindrical shell tanks under the action of horizontal base excitation. eng struct 26, pp. 415-426. [23] aquelet, n., souli, m., olovsson, l. (2006). euler–lagrange coupling with damping effects: application to slamming problems. computer methods in applied mechanics and engineering. 195(1-3), pp. 110-32. [24] virella, j.c., godoy, l.a., suarez, l.e. (2006). dynamic buckling of anchored steel tanks subjected to horizontal earthquake excitation. j constr steel res 62, pp. 521-531. [25] maekawa, a., shimizu, y., suzuki, m. and fujita, k. (2010). vibration test of a 1/10 reduced scale model of cylindrical water storage tank, journal of pressure vessel technology, 132(5), 051801-1-051801-13. [26] maekawa, a. (2012). consideration of a method to estimate seismic response reduction coefficient for liquid storage tanks.,15th wcee, lisboa. [27] maekawa, a. (2013). recent advances in seismic response analysis of cylindrical liquid storage tanks, institute of nuclear safety system, inc. japan, 2(12). [28] pacific earthquake engineering research center, peer strong motion database, (2011) http://peer.berkley.edu.smcat. [29] wozniak, r. s., and warren, w. (1978). basis of seismic design provisions for welded steel oil storage tanks. chicago bridge & iron company. 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can be opened with acrobat and adobe reader 5.0 and later.) >> /namespace [ (adobe) (common) (1.0) ] /othernamespaces [ << /asreaderspreads false /cropimagestoframes true /errorcontrol /warnandcontinue /flattenerignorespreadoverrides false /includeguidesgrids false /includenonprinting false /includeslug false /namespace [ (adobe) (indesign) (4.0) ] /omitplacedbitmaps false /omitplacedeps false /omitplacedpdf false /simulateoverprint /legacy >> << /addbleedmarks false /addcolorbars false /addcropmarks false /addpageinfo false /addregmarks false /convertcolors /converttocmyk /destinationprofilename () /destinationprofileselector /documentcmyk /downsample16bitimages true /flattenerpreset << /presetselector /mediumresolution >> /formelements false /generatestructure false /includebookmarks false /includehyperlinks false /includeinteractive false /includelayers false /includeprofiles false /multimediahandling /useobjectsettings /namespace [ (adobe) (creativesuite) (2.0) ] /pdfxoutputintentprofileselector /documentcmyk /preserveediting true /untaggedcmykhandling /leaveuntagged /untaggedrgbhandling /usedocumentprofile /usedocumentbleed false >> ] >> setdistillerparams << /hwresolution [2400 2400] /pagesize [612.000 792.000] >> setpagedevice microsoft word numero_59_art_15_3246.docx h.a. mobaraki et alii, frattura ed integrità strutturale, 59 (2022) 198-211; doi: 10.3221/igf-esis.59.15 198 focussed on steels and composites for engineering structures forced vibration analysis of laminated composite plates under the action of a moving vehicle h.a. mobaraki, r.-a. jafari-talookolaei babol noshirvani university of technology, shariati ave., 47148-71167 babol, mazandaran, iran hossein.mobaraki1995@gmail.com, https://orcid.org/0000-0002-7713-1215 ra.jafari@nit.ac.ir, http://orcid.org/0000-0003-4357-2597 p.s. valvo university of pisa, largo lucio lazzarino, i-56122 pisa, italy p.valvo@ing.unipi.it, http://orcid.org/0000-0001-6439-1926 r. haghani chalmers university of technology, sven hultins gata 6, se-412 96 gothenburg, sweden reza.haghani@chalmers.se, http://orcid.org/0000-0002-0547-7700 abstract. this paper provides a finite element analysis of laminated composite plates under the action of a moving vehicle. the vehicle is modeled as a rigid body with four suspension systems, each consisting of a springdashpot. overall, the vehicle possesses three degrees of freedom: vertical, rolling, and pitching motions. the equations of motion of the plate are deduced based on first-order shear deformation theory. using the eulerlagrange equations, the system of coupled equations of motion is extracted and solved by using the newmark time discretization scheme. the algorithm is validated through the comparison of both the free and forced vibration results provided by the present model and exact or numerical results reported in the literature. the effects are investigated of several system parameters on the dynamic response. keywords. forced vibration; laminated composites; moving vehicle. citation: mobaraki, h.a., jafari-talookolaei, r.-a., valvo, p.s., haghani dogaheh, r., forced vibration analysis of laminated composite plates under the action of a moving vehicle, frattura ed integrità strutturale, 59 (2022) 198-211. received: 21.08.2021 accepted: 13.10.2021 published: 01.01.2022 copyright: © 2022 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. introduction n recent years, the dynamic analysis of engineering structures, such as bridges, roads, and rails, under the action of moving loads has gained great attention. such structures are often subjected to high stresses and experience severe vibrations. bridges as main substructures can be modeled as plates traversed by three major types of loading: moving loads, moving masses, and moving oscillators. thus, researchers have studied their behavior under the action of these loadings. i https://youtu.be/npted1pabpg h.a. mobaraki et alii, frattura ed integrità strutturale, 59 (2022) 198-211; doi: 10.3221/igf-esis.59.15 199 some researchers have focused their studies on analyzing the effects of moving loads on isotropic beams and plates [1-4], while others have focused on the case of moving masses [5-8]. besides, some works are related to moving oscillators [9-11]. ghafoori et al. [12] provided a semi-analytical method to obtain the dynamic response of a plate subjected to a moving oscillator. also, wu et al. [13] aimed at introducing a technique to replace each 3-dof system consisting of spring-mass by a set of equivalent masses. lin and trethewey [14] investigated the response of elastic beams subjected to an arbitrary springmass damper system and obtained the governing equations of motion based on the finite element method (fem). recently, laminated composites, due to their lightweight and high strength, as well as the material adaptability, have gained in popularity for the construction of civil structures such as bridges. this has brought a new field of interest in studying the response of either laminated composite plates or beams traversed by moving oscillators or loads. malekzadeh et al. [15] studied the dynamic response of cross-ply thick laminated plate under the action of moving load based on three-dimensional elasticity. they applied layerwise theory to discretize the equations of motion. mohebpour et al. [16] investigated the response of laminated composite plate subjected to moving oscillator using the fem based on first-order shear deformation theory (fsdt). in 2004, lee et al. [17] analyzed a multi-span continuous composite plate under multi-moving loads based on third-order shear deformation theory (tsdt). ghafoori and asghari [18] presented an analysis of angle-ply laminated composite plates traversed by moving masses and forces. they applied the fem to obtain equations of motion and solved them by using the newmark method. mohebpour et al. [19] developed an algorithm based on the fem to study the response of laminated composite beams subjected to moving oscillators. they used fsdt to obtain the equations of the beam. kim [20] studied the dynamic stability behavior of damped laminated beams subjected to uniformly distributed forces based on a finite element formulation consistent with vlasov’s beam theory. also, the effect of fiber orientation, boundary conditions, and external and internal damping was studied. it should be mentioned that the dynamic response of an intact plate can be used for damage detection in a defected plate [21-23]. in this paper, the problem of a laminated composite plate subjected to a moving vehicle is investigated. thus, the effects of various parameters, such as vehicle mass, plate damping ratio, etc., are also investigated. the governing equations of the plate are obtained based on fsdt and the vehicle is considered as a rigid body having 3 degrees of freedom: vertical, rolling, and pitching motions. this modelling approach is the major novelty of the present paper. lastly, the newmark time integration procedure is used to find the response of the system in time. mathematical modeling onsider a laminated composite plate under the action of a moving vehicle with constant velocity v along the x-axis as shown in fig. 1. the plate has length a, width b and thickness h with the coordinate frame placed at the midplane. the displacement field based on fsdt is as follows:       0, , , , , , ,xu x y z t u x y t z x y t       0, , , , , , ,yv x y z t v x y t z x y t (1)     0, , , , ,w x y z t w x y t where u , v and w are the displacements of a point of the laminate (x, y, z) in the three coordinate directions. also, 0u , 0v and 0w refer to displacements of a point on the mid-plane (  0z ) and  x ,  y refer to rotations about the xand yaxis, respectively. using eqn.1, the non-zero strain components are derived as follow:       0, 0, ,x x x x x x xu u z zk       0, 0, ,y y y y y y yv v z zk (2)           0, , 0, 0, , ,xy y x y x x y y x xy xyu v u v z z zk c h.a. mobaraki et alii, frattura ed integrità strutturale, 59 (2022) 198-211; doi: 10.3221/igf-esis.59.15 200            0 xz x wu w z x x            0 yz y wv w z y y where x ,  , y and  xy denote the normal and shear strains of an arbitrary point, respectively. furthermore,  0 x ,  0 y , and  0xy are the mid-plane strains, and xk , yk and xyk are the bending curvatures. figure 1: laminated composite plate under the action of a moving vehicle according to the transformed constitutive relations for a 2d orthotropic lamina, the stress-strain relations for the kth lamina can be written as [24]:                                                            11 12 16 44 45 12 22 26 45 55 16 26 66 ,     k kk k kkx x yz yz y y xz xz xy xy q q q q q q q q q q q q q (3) where ijq is the reduced stiffness. the strain energy of the laminated composite plate is:                                      20 0 2 1 ( )      2 h a b k k k k k k k k k k p x x y y xy xy yz yz xz xzhu dz dy dx (4) substituting eqn.3 into eqn.4 and then integrating over the thickness leads to:            2 2 2 2 2 2p 11 0, 22 0, 66 0, 0, 0, 0, 11 , 22 ,0 0 1 u [ 2 2 a b x y y x y x x x y ya u a v a u v u v d d                   2 2 2 266 , , , , 44 0, 0, 16 , 0, 0,2 2 2x y y x x y y x y y y y x x y xd a w w b u v          2 255 0, 0, 12 0, 0, 16 0, 0, 0,2 2 2x x x x x y y x xa w w a u v a u v u             11 , 0, 12 , 0, 16 , , 0, 26 , 0, 0,2 2 2 2x x x y y x x y y x x y y y xb u b u b u b u v (5)            26 0, 0, 0, 12 , 0, 22 , 0, 26 , , 0,2 2 2 2y x y x x y y y y x y y x ya u v v b v b v b v h.a. mobaraki et alii, frattura ed integrità strutturale, 59 (2022) 198-211; doi: 10.3221/igf-esis.59.15 201                66 , , 0, 0, 12 , , 16 , , ,2 2 2x y y x y x y y x x x y y x x xb u v d d             26 , , , 45 0, 0,2 2 ] dy dxx y y x y y x x y yd a w w furthermore, the kinetic energy of the laminated composite plate is:              2 2 2 2 2,t , , , , , , , ,0 0 1 [ ( ) + 2         2 a b p 0 t t 1 t x t t y t 2 x t y tt i u v w i u v i dy dx (6) where  0 1 2,   , i i i are mass moments of inertia, defined as follows:           2 2 0 1 2 2 ,  ,  1,  ,  h h i i i z z z dz (7) as mentioned earlier, a moving vehicle is modeled with 3-dof as shown in fig. 1. the potential energy of the vehicle is:                               2 2 1 1 1 2 3 2 1 2 2 3 2 2 3 1 3 2 3 4 1 4 2 3 1 2 3 4 1 1 2 2 1 1 2 2 4 v v v v v v v v v u k q w b q a q k q w b q a q mg k q w b q a q k q w b q a q w w w w (8) where     0 ,          1, 2, 3, 4i i iw w x y i (9) also, the damped energy of dashpots can be written as:                                         2 2 1 1 1 2 3 2 1 2 2 3 2 2 3 1 3 2 3 4 1 4 2 3 1 1 2 2 1 1 2 2 dv v v v v v v v v w c q w b q a q c q w b q a q c q w b q a q c q w b q a q (10) in the above equations, ik and    1, 2, 3, 4ic i refer to the suspension system stiffness and damping parameters, respectively. moreover, the kinetic energy of the vehicle is:     2 2 21 2 3 1 1 1 2 2 2 v x yt mq i q i q (11) where m is the vehicle total mass and xi and yi are its mass moments of inertia about the xand y-axes respectively. figure 2: rectangular higher-order element h.a. mobaraki et alii, frattura ed integrità strutturale, 59 (2022) 198-211; doi: 10.3221/igf-esis.59.15 202 finite element solution n order to obtain numerical results, we propose a higher-order plate element as shown in fig. 2. the element has 9 nodes and each node has 5 degrees of freedom including the axial displacement 0u , lateral displacements 0 0,  v w , and independent rotations  ,  x y . to obtain the generalized displacement corresponding to each degree of freedom inside an element, the lagrange interpolation is used. this can be stated as:     0 , uu x y n d     0 , vv x y n d     0 , ww x y n d (12)        , xx x y n d        , yy x y n d where  d is the element nodal displacement vector and  un ,  vn ,  wn ,   xn , and   yn are the shape function matrices, defined as:     1 2 90 0 0 0 0 0 0 0 0 0 0 0un n n n     1 2 90 0 0 0 0 0 0 0 0 0 0 0vn n n n     1 2 90 0 0 0 0 0 0 0 0 0 0 0wn n n n (13)       1 2 90 0 0 0 0 0 0 0 0 0 0 0xn n n n       1 2 90 0 0 0 0 0 0 0 0 0 0 0yn n n n where the in functions are            1 1 2 1 1 2 1n           2 4 1 1 2 1n          3 2 1 1 2 1n            4 4 1 2 1 1n         5 16 1 1n (14) i h.a. mobaraki et alii, frattura ed integrità strutturale, 59 (2022) 198-211; doi: 10.3221/igf-esis.59.15 203          6 4 2 1 1n           7 1 2 1 2 1n          8 4 1 2 1n         9   2 1 2 1n here, ζ   e x a . and η e y b are non-dimensional element coordinates and ea and eb are the element length and width, respectively. substituting eqn.12 into eqn.5 and eqn.6 respectively provides:      1 2 t p eu d k d (15)       1  2 t p et d m d (16) where  ek is the element stiffness matrix and  em is the element mass matrix. their expressions are provided in appendix a. after assembling the element matrices and applying the euler-lagrange equations, the coupled governing equations of motion are obtained as follows:                                                                ¨ ¨ 111 ¨ 22 2 33 ¨ 3 δ δδ qqqm c k f qq q qq q (17) where  δ is the plate total displacement vector and  pc is the plate damping matrix, assumed as rayleigh’s proportional damping [25]:       0 1p p pc a m a k (a 18)                      0 1 1/1 1/2 i i i j j j a a (b 18) eqn.17 is discretized by applying the newmark time integration method in which γ 1/ 2 and β 1/ 4 . numerical results n this section, firstly, the free vibration results are compared with those available in the literature. also, a parametric analysis is carried out to study the effects of system dynamic characteristics on the dynamic response of plate. the examples provided are based on the following material properties unless mentioned otherwise: i h.a. mobaraki et alii, frattura ed integrità strutturale, 59 (2022) 198-211; doi: 10.3221/igf-esis.59.15 204    1 2 12 13 240  ,    9.65  ,    0.6 e gpa e gpa g g e     323 2 120.5  ,    0.25,      1389.23  /g e v kg m as a first example, the variation of the non-dimensional natural frequency of a laminated composite plate simply supported along all edges with symmetric cross-ply layup   0 / 90 is considered by changes of /a h . tab. 1 shows the results. refs. /a h 10 20 50 100 kant et al. [26] 15.1048 17.6470 18.6720 18.835 matsunaga ]27] 15.0721 17.6369 18.6702 18.835 reddy [28] 15.1073 17.6457 18.6718 18.835 akavci [29] 15.3684 17.7584 18.6934 18.841 rodriguez et al. [30] 15.1674 17.7471 18.7895 18.956 abedi et al. [31] 15.1056 17.6448 18.6719 18.836 present 15.1425 17.6592 18.6689 18.789 table 1: non-dimensional natural frequency (  2 22ω (ω / h ) ρ/ ea ) of a laminated composite plate simply supported at all edges with symmetric cross-ply layup   0 / 90 . from the above results, it is obvious that an increment in the plate length with respect to its thickness decreases the overall stiffness of the plate. as a consequence, it increases the non-dimensional natural frequency. the next example expresses the effect of plate length to thickness on the first three non-dimensional natural frequencies. the plate has a     0 / 30 / 60 / 0 layup and two alternative boundary conditions: cccc and ssss. (a) (b) figure 3: effect of plate length to thickness on the first three non-dimensional natural frequencies (a) cccc (b) ssss. ( 1 225e e ,  12 13 20.5g g e , 23 20.2g e ) h.a. mobaraki et alii, frattura ed integrità strutturale, 59 (2022) 198-211; doi: 10.3221/igf-esis.59.15 205 in order to obtain non-dimensional forced vibration results, firstly, non-dimensional parameters are discussed as below: (a) velocity parameter α , defined as the ratio of the fundamental period of the plate to the time required for the vehicle passing the span    2 α   p v a (19) where v is the velocity of vehicle. it is supposed that the velocity is constant and the vehicle is moving along the x-axis. (b) mass parameter  , defined as the ratio of vehicle mass to the plate mass     p m m m abh (20) (c) frequency parameter γi , defined as the ratio of the natural frequency of quarter-vehicle to the fundamental frequency of the plate         / 4 γ        1, 2, 3, 4 i i i p p k m i (21) (d) mass moments of inertia ε and χ are defined as below:  2 χ y p i m a (a 22)  2 ε x p i m h (b 22) (e) logarithmic decrement of quarter-vehicle spring-dashpot δi , which is defined as                    δ     1, 2, 3, 4 12 2 4 4 2 / 4 i i i i c c i m kmf m (23) in the following examples, the values of ik and ic for all suspension systems are equal. to validate the forced vibration results, the model of the vehicle is reduced to a moving oscillator as discussed in [16]. fig. 4 shows the comparison of results. it can be seen that the present reduced-order model tracks the reported results with low deviation. therefore, the maximum errors are 2.29% for   1.5 and 2.17% for   2 . the next examples provide a better look at the mid-point deflection of the laminated composite plate. as a first example, the effect of boundary conditions on the dynamic magnification factor (dmf), defined as the ratio of maximum dynamic deflection with respect to maximum static deflection is studied. a laminated plate is considered with   30 / 60 as layup. here, the subscript “as’’ refers to an anti-symmetric stacking sequence. four different boundary conditions are considered: cccc, ssss, cfcf, and sfsf. it should be noted that, for a better comparison among results, the maximum static deflection, in this example and in the further ones, is referred to the condition having lower dmf. it can be concluded that the cccc boundary condition has higher stiffness. thus, it gains lower amounts of dmf, as can be seen from fig. 5. h.a. mobaraki et alii, frattura ed integrità strutturale, 59 (2022) 198-211; doi: 10.3221/igf-esis.59.15 206 figure 4: comparison of present reduced-order model with reference [16] figure 5: influence of various boundary conditions on mid-point dmf (  0.2 , γ 0.1 ,  χ ε 0.1 ,  δ 0.1,    5 %p ). fig. 6 presents the effect of the plate slenderness ratio parameter under cccc boundary condition with   30 / 60 as layup. increasing the length causes dmf to shift towards higher values. this happens because an increase in the length of the plate leads to a decrement in its structural stiffness and an increment in the dynamic deflection. to study the effect of plate damping ratio, consider a plate simply supported along all edges with   30 / 60 as layup. according to fig. 7 increasing damping ratio leads to a reduction in mid-point dynamic deflection which indeed reduces dmf. however, the critical velocity is kept constant. the last example expresses the influence of vehicle mass on the dynamic deflection of the mid-point. the laminated composite plate has     0 / 30 / 60 / 0 layup with cccc boundary condition. fig. 8 shows that, as long as the vehicle h.a. mobaraki et alii, frattura ed integrità strutturale, 59 (2022) 198-211; doi: 10.3221/igf-esis.59.15 207 mass increases, the mid-point dynamic deflection increases during the existence of loading on plate. as a matter of fact, the dmf increases as shown in fig. 9. figure 6: influence of slenderness ratio on mid-point dmf (  0.2 , γ 0.1 ,  χ ε 0.1 ,  δ 0.1,    5 %p ). figure 7: effect of plate damping ratio on mid-point dmf (  0.2 , γ 0.1 ,  χ ε 0.1 , δ 0.1 ). conclusion n this paper, the forced vibrations are investigated of a laminated composite plate under the action of a moving vehicle. several examples are included to study the influence of system dynamic parameters, such as plate damping ratio, vehicle mass, and plate slenderness ratio. the equations of motion of plate are obtained based on first-order shear deformation i h.a. mobaraki et alii, frattura ed integrità strutturale, 59 (2022) 198-211; doi: 10.3221/igf-esis.59.15 208 theory and solved using newmark’s discretization scheme. free and forced vibration results show good agreement with those available in the literature. this modeling algorithm can be extended to a full vehicle model to obtain results that are applicable in practical designs. it is shown that the sfsf boundary condition provides higher values of dmf. besides, decreasing the damping ratio and increasing the slenderness ratio, alongside with the vehicle mass, can have considerable effect on the dmf. figure 8: effect of vehicle mass on mid-point dynamic deflection during the existence of load on plate (  0.2 γ 0.1 ,         0.1, 0.1, 5%, 1)p figure 9: dynamic magnification factor for various vehicle masses (  0.2 , γ 0.1 ,  χ ε 0.1 ,  δ 0.1,    5 %p ) h.a. mobaraki et alii, frattura ed integrità strutturale, 59 (2022) 198-211; doi: 10.3221/igf-esis.59.15 209 appendix a        0 0 0 0 0 0 0 011 , , 22 , , 66 , , , ,0 0[ . . ( . . a b t t t t e u x u x v y v y u y u y v x v xk a n n a n n a n n n n       0 0 0 0, , , , 11 , , 22 , ,. . ) . .x x y y t t t t u y v x v x u y x x y yn n n n d n n d n n           66 , , , , , , , ,( . . . .x x y y x y x y t t t t y y x x y x y xd n n n n n n n n        0 0 0, , 44 , , ,. ) ( . . .y x y y y t t t t x y w y w y w yn n a n n n n n n       0 0 0 0, 55 , , ,. ) ( . . .y x x x t t t t w y w x w x w xn n a n n n n n n     0 0 0 0 0 0 0, 12 , , , , 16 , ,. ) . . ( .xt t t tw x u x v y v y u x u y u xn n a n n n n a n n       0 0 0 0 0 0 0 0, , , , , , 11 , , , ,  . . . ) . .x xt t t t tu x u y v x u x u x v x x u x u x xn n n n n n b n n n n        0 0 0 012 , , , , 16 , , , ,. . ( . .y y x xt t t ty u x u x y y u x u x yb n n n n b n n n n     0 0 0 0 0 0, , , , 26 , , , ,. . ) ( . .y y t t t t x u x u x x u y v y v y u yn n n n a n n n n      0 0 0 0 0 0, , , , 12 , , , ,. . ) . .x xt t t tv x v y v y v x x v y v y xn n n n b n n n n        0 0 0 022 , , , , 26 , , , ,. . ( . .y y x xt t t ty v y v y y y v y v y yb n n n n b n n n n       0 0 0 0, , , , 16 , , , ,. . ) ( . .y y x x t t t t x v y v y x x u y u y xn n n n b n n n n       0 0 0 0, , , , 26 , , , ,. . ) ( . .x x y y t t t t x v x v x x y u y u y yn n n n b n n n n       0 0 0 0, , 66 , , , , , ,. ( . . .y x x x t t t t y v x y u y u y y y v xn n b n n n n n n       0 0 0 0, , , , , , , ,. .   . .x y y y t t t t v x y x u y u y x x v xn n n n n n n n           0 , , 12 , , , , 16 , ,. ) . . ( .y y x x y x xt t t tv x x y x x y y xn n d n n n n d n n           , , , , , , 26 , ,. . . ) ( .x x y x x y x y t t t t x y x x x x y yn n n n n n d n n           , , , , , , 45. . . ) ( .y x y y y y x y t t t t y y x y y xn n n n n n a n n          0 0 0 0, , , ,. . . . .y x x x y y t t t t t w y w y w x w xn n n n n n n n n n   0 0 0 0, , , , . . )]   t tw x w y w y w xn n n n dy dx                                0 10 0[i . . . i ( . .x x a b tt t t t e u u v v w w u um n n n n n n n n n n                                   2 . . )) i . . ] y y x x y y t ttt v vn n n n n n n n dy dx references [1] song, q., shi, j., liu, z., wan, y. (2016). dynamic analysis of rectangular thin plates of arbitrary boundary conditions under moving loads, int. j. mech. sci., 117, pp. 16–29, doi: 10.1016/j.ijmecsci.2016.08.005. [2] frýba, l. (2013). vibration of solids and structures under moving loads, vol. 1. springer science & business media. [3] kim, t., lee, u. (2018). vibration analysis of thin plate structures subjected to a moving force using frequency-domain spectral element method, shock vib., doi: 10.1155/2018/1908508. h.a. mobaraki et alii, frattura ed integrità strutturale, 59 (2022) 198-211; doi: 10.3221/igf-esis.59.15 210 [4] babagi, p.n., navayi neya, b., dehestani, m. (2017). three dimensional solution of thick rectangular simply supported plates under a moving load, meccanica, 52(15), pp. 3675–3692, doi: 10.1007/s11012-017-0653-x. [5] wu, j.j. (2007). vibration analyses of an inclined flat plate subjected to moving loads, j. sound vib., 299(1–2), pp. 373– 387, doi: 10.1016/j.jsv.2006.07.002. [6] mofid, m., shadnam, m. (2000). on the response of beams with internal hinges, under moving mass, adv. eng. softw., 31(5), pp. 323–328, doi: 10.1016/s0965-9978(99)00061-7. [7] esen, i. (2013). a new finite element for transverse vibration of rectangular thin plates under a moving mass, finite elem. anal. des., 66, pp. 26–35, doi: 10.1016/j.finel.2012.11.005. [8] esen, i. (2011). dynamic response of a beam due to an accelerating moving mass using moving finite element approximation, math. comput. appl., 16(1), pp. 171–82, doi: 10.3390/mca16010171. [9] moghaddas, m., sedaghati, r., esmailzadeh, e., khosravi, p. (2009). finite element analysis of a timoshenko beam traversed by a moving vehicle, proc. inst. mech. eng. part k j. multi-body dyn., 223(3), pp. 231–243, doi: 10.1243/14644193jmbd179. [10] ebrahimi, m., gholampour, s., jafarian kafshgarkolaei, h., nikbin, i.m. (2015). dynamic behavior of a multispan continuous beam traversed by a moving oscillator, acta mech., 226(12), pp. 4247–4257, doi: 10.1007/s00707-015-1474-4. [11] pesterev, a.v., yang, b., bergman, l.a., tan, c.a. (2001). response of elastic continuum carrying multiple moving oscillators, j. eng. mech, 127.3, pp. 260-265. [12] ghafoori, e., kargarnovin, m.h., ghahremani, a.r. (2011). dynamic responses of a rectangular plate under motion of an oscillator using a semi-analytical method, jvc/journal vib. control, 17(9), pp. 1310–1324, doi: 10.1177/1077546309358957. [13] wu, j.j. (2006). free vibration characteristics of a rectangular plate carrying multiple three-degree-of-freedom springmass systems using equivalent mass method, int. j. solids struct., 43(3–4), pp. 727–746, doi: 10.1016/j.ijsolstr.2005.03.061. [14] lin, y.h., trethewey, m.w. (1990). finite element analysis of elastic beams subjected to moving dynamic loads. jsv/journal of sound and vib., 136.2, pp. 323-342. [15] malekzadeh, p., fiouz, a.r., razi, h. (2009). three-dimensional dynamic analysis of laminated composite plates subjected to moving load, compos. struct., 90(2), pp. 105–114, doi: 10.1016/j.compstruct.2009.02.008. [16] mohebpour, s.r., malekzadeh, p., ahmadzadeh, a.a. (2011). dynamic analysis of laminated composite plates subjected to a moving oscillator by fem, compos. struct., 93(6), pp. 1574–1583, doi: 10.1016/j.compstruct.2011.01.003. [17] lee, s.y., yhim, s.s. (2004). dynamic analysis of composite plates subjected to multi-moving loads based on a third order theory, int. j. solids struct., 41(16–17), pp. 4457–4472, doi: 10.1016/j.ijsolstr.2004.03.021. [18] ghafoori, e., asghari, m. (2010). dynamic analysis of laminated composite plates traversed by a moving mass based on a first-order theory, compos. struct., 92(8), pp. 1865–1876, doi: 10.1016/j.compstruct.2010.01.011. [19] mohebpour, s.r., fiouz, a.r., ahmadzadeh, a.a. (2011). dynamic investigation of laminated composite beams with shear and rotary inertia effect subjected to the moving oscillators using fem, compos. struct., 93(3), pp. 1118–1126, doi: 10.1016/j.compstruct.2010.09.011. [20] kim, n. il. (2010). dynamic stability behavior of damped laminated beam subjected to uniformly distributed subtangential forces, compos. struct., 92(11), pp. 2768–2780, doi: 10.1016/j.compstruct.2010.04.005. [21] saadatmorad, m., jafari-talookolaei, r.-a., pashaei, m.h., khatir, s. (2021). damage detection on rectangular laminated composite plates using wavelet based convolutional neural network technique, compos. struct., 278, 114656, doi: 10.1016/j.compstruct.2021.114656. [22] khatir, s., tiachacht, s., thanh, c.l., ghandourah, e., mirjalili, s., abdel wahab, m. (2021). an improved artificial neural network using arithmetic optimization algorithm for damage assessment in fgm composite plates. compos. struct., 273, 114287, doi: 10.1016/j.compstruct.2021.114287. [23] zenzen, r., khatir, s., belaidi, i., thanh, c.l., abdel wahab, m. (2021). a modified transmissibility indicator and artificial neural network for damage identification and quantification in laminated composite structures, compos. struct., 248, 112497, doi: 10.1016/j.compstruct.2020.112497. [24] reddy, j.n. (2003). mechanics of laminated composite plates and shells: theory and analysis, crc press [25] chopra, a.k. (2012). dynamics of structures, upper saddle river, nj: pearson education [26] kant, t., swaminathan, k. (2001). analytical solutions for free vibration of laminated composite and sandwich plates based on a higher-order refined theory, compos. struct., 53(1), pp. 73–85, doi: 10.1016/s0263-8223(00)00180-x. [27] matsunaga, h. (2000). vibration and stability of cross-ply laminated composite plates according to a global higher-order plate theory, compos. struct., 48(4), pp. 231–244, doi: 10.1016/s0263-8223(99)00110-5. h.a. mobaraki et alii, frattura ed integrità strutturale, 59 (2022) 198-211; doi: 10.3221/igf-esis.59.15 211 [28] reddy, j.n. (1984). a simple higher-order theory for laminated composite plates, j. appl. mech. trans. asme, 51(4), pp. 745–752, doi: 10.1115/1.3167719. [29] akavci, s.s. (2007). buckling and free vibration analysis of symmetric and antisymmetric laminated composite plates on an elastic foundation, j. reinf. plast. compos., 26(18), pp. 1907–1919, doi: 10.1177/0731684407081766. [30] rodrigues, j.d., natarajan, s., ferreira, a.j.m., carrera, e., cinefra, m., bordas, s.p.a. (2014). analysis of composite plates through cell-based smoothed finite element and 4-noded mixed interpolation of tensorial components techniques, comput. struct., 135, pp. 83–87, doi: 10.1016/j.compstruc.2014.01.011. [31] abedi, m., jafari-talookolaei, r., valvo, p.s. (2016). a new solution method for free vibration analysis of rectangular laminated composite plates with general stacking sequences and edge restraints, comput. struct., 175, pp. 144–156, doi: 10.1016/j.compstruc.2016.07.007. << /ascii85encodepages false /allowtransparency false /autopositionepsfiles true /autorotatepages /none /binding /left /calgrayprofile (dot gain 20%) /calrgbprofile (srgb iec61966-2.1) /calcmykprofile (u.s. web coated \050swop\051 v2) /srgbprofile (srgb iec61966-2.1) /cannotembedfontpolicy /error /compatibilitylevel 1.4 /compressobjects /tags /compresspages true /convertimagestoindexed true /passthroughjpegimages true /createjobticket false /defaultrenderingintent /default /detectblends true /detectcurves 0.0000 /colorconversionstrategy /cmyk /dothumbnails false /embedallfonts true /embedopentype false /parseiccprofilesincomments true /embedjoboptions true /dscreportinglevel 0 /emitdscwarnings false /endpage -1 /imagememory 1048576 /lockdistillerparams false 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/hrv (za stvaranje adobe pdf dokumenata najpogodnijih za visokokvalitetni ispis prije tiskanja koristite ove postavke. stvoreni pdf dokumenti mogu se otvoriti acrobat i adobe reader 5.0 i kasnijim verzijama.) /hun 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can be opened with acrobat and adobe reader 5.0 and later.) >> /namespace [ (adobe) (common) (1.0) ] /othernamespaces [ << /asreaderspreads false /cropimagestoframes true /errorcontrol /warnandcontinue /flattenerignorespreadoverrides false /includeguidesgrids false /includenonprinting false /includeslug false /namespace [ (adobe) (indesign) (4.0) ] /omitplacedbitmaps false /omitplacedeps false /omitplacedpdf false /simulateoverprint /legacy >> << /addbleedmarks false /addcolorbars false /addcropmarks false /addpageinfo false /addregmarks false /convertcolors /converttocmyk /destinationprofilename () /destinationprofileselector /documentcmyk /downsample16bitimages true /flattenerpreset << /presetselector /mediumresolution >> /formelements false /generatestructure false /includebookmarks false /includehyperlinks false /includeinteractive false /includelayers false /includeprofiles false /multimediahandling /useobjectsettings /namespace [ (adobe) (creativesuite) (2.0) ] /pdfxoutputintentprofileselector /documentcmyk /preserveediting true /untaggedcmykhandling /leaveuntagged /untaggedrgbhandling /usedocumentprofile /usedocumentbleed false >> ] >> setdistillerparams << /hwresolution [2400 2400] /pagesize [612.000 792.000] >> setpagedevice microsoft word numero_49_art_47_2275 d. kumar et alii, frattura ed integrità strutturale, 49 (2019) 507-514; doi: 10.3221/igf-esis.49.47 507 focused on showcasing structural integrity research in india optimization of vanadium content for achieving higher wear resistance and hardness in high cr-v white cast irons for ball tube mill liner application dhirendra kumar, g. jayaraman, m. swamy, a. h. v. pavan , antony m. c. harison corporate research & development division, bhel, hyderabad, india, 500093 dkumar@bhel.in, jayaraman@bhel.in, smekala@bhel.in, pavanahv@bhel.in, harisonmc@bhel.in a. n. sudhakar heavy power equipment plant, bhel, ramachandrapuram, hyderabad, india, 502302 ansudhakar@bhel.in abstract. the liner materials in coal fired tube mills are less promising due to lower combination of abrasion wear resistance, hardness and impact toughness properties, thus giving service life of 25,000 to 35,000 hours. in this study, focus was given to develop a high cr-v cast iron of high abrasion wear resistance with higher hardness and impact strength for ball tube mill liner application. the developed liner possesses high abrasive wear resistance and impact resistance simultaneously with expected service life of 40,000 to 50,000 hours. this grade was made using induction melting and sand casting method. the casting was heat treated in two stages to achieve higher abrasion wear resistance and mechanical properties. various tests like chemical analysis, abrasion wear, hardness and impact tests were conducted on the above developed material. abrasion wear test results show a low wear loss value (2.7 to 4.4 mg/min). hardness and impact tests show a high combination of hardness (57 to 64 hrc) and impact strength (44 to 57 j/cm2). prototype tube mill liners were manufactured and tested in a tube mill at 250mw site. results obtained from site testing are also discussed in this study. keywords. high cr cast iron; high cr-v cast iron; abrasion wear; hardness; impact strength. citation: kumar, d., jayaraman, g., swamy, m., pavan, a.h.v., harison, a.m.c., sudhakar, a. n., study of microstructure, abrasion wear and mechanical properties of high cr-v white cast iron for ball tube mill liner application, frattura ed integrità strutturale, 49 (2019) 507-514. received: 24.11.2018 accepted: 21.05.2019 published: 01.07.2019 copyright: © 2019 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. introduction urning coal with higher efficiency has been a great need in coal pulverizing sector wherein coal is burnt like gas. burning coal like gas reduces the co2 emission by reduction of coal consumption. coal is pulverized with the help of liner plates inside the mill. these plates are mostly made of high chromium cast irons (hcrcis) and b http://www.gruppofrattura.it/va/49/2275.mp4 d. kumar et alii, frattura ed integrità strutturale, 49 (2019) 507-514; doi: 10.3221/igf-esis.49.47 508 possess high hardness and wear resistance. hcrcis have m7c3 carbide in their matrices which enables them to have high wear resistance property [1, 2]. these cast irons have continuous distribution of rod-like m7c3 carbide in their respective matrices. the continuous distribution of m7c3 carbide makes their toughness lower. in order to improve their toughness, the morphology of carbides can be modified to chunk-like or even granular [3]. so, with discontinuous distribution of m7c3 carbide, a high chromium cast iron would be quite promising in wearing parts of machines in many industries like coal pulverizes. the demand of higher wear resistant material in coal pulverizing sector has always been encouraging to reduce the dwell time to the great extent. the need ‘to eliminate frequent shutdown of tube mill for replacement of worn out and/or broken liners and loss in terms of power productivity’ have encouraged to develop candidate alloys which provide superior abrasive wear resistance along with adequate toughness [4, 5]. the addition of strong carbide-forming elements, such as vanadium, tungsten, niobium and titanium, improves the mechanical properties of high chromium white irons [6]. vanadium can form vanadium carbide (vc) with vickers hardness of hv2800 which is much harder than that of m7c3 with vickers hardness, hv 1200~1800 in high chromium cast iron [7]. the globular morphology of vc reduces splitting to matrix and enables to get superior toughness. the microstructure of high chromium iron becomes finer with vanadium addition. with good solubility in eutectic m7c3 carbides and austenite, vanadium influences the transformation of austenite in high chromium cast iron. vanadium content favors precipitation of dispersive secondary carbides of vc type in austenite which is favorable for martensitic transformation [8, 9, 10]. with an increase in vanadium content, the impact toughness increases, while hardness decreases and thereby relative wear resistance improves [7]. therefore, influence of vanadium on microstructure, hardness and impact strength and wear properties was studied in this work to develop a high chromium-vanadium cast iron (hcrvci) material for the tube mill liner application. experimental procedure arious grades of hcrci blocks with varying weight percentages of vanadium were cast using induction melting and die casting method. hcrci grade, nfa 32.401 or fb cr26moni with 0.00 wt. % vanadium was considered as base material. the compositions of cast iron grades were analyzed through spark emission spectroscopy (ses) method using spectrax m5 machine. the cast iron blocks were hardened and tempered in two stages. subsequent to this, ultrasonic testing (ut) was carried out on them to detect internal defects, if any. samples were prepared from the casting blocks for microstructure evaluation, phase characterization, hardness, impact value and wear properties evaluation. charpy un-notched impact test samples were prepared with dimensions as, length: 10mm, width: 10mm and height: 55mm. abrasion wear test samples were prepared with dimensions as, length: 25+0.0/-0.2mm, width: 6mm and height: 75mm.the samples for metallographic examination were polished for obtaining extremely good surface finish. the polished samples were etched chemically using villela’s etchant for 40 seconds each. the microstructures were analyzed through optical microscopy method. the etched samples were observed for features pertaining to morphology of grains and precipitates under leica dmi 5000 m inverted metallurgical microscope using the bright field method. the samples were further examined under “zeiss supra® 55 vp make field emission scanning electron microscope (fesem) with compatible energy dispersive x-ray spectroscopy (eds) system to reveal morphologies present in the matrices. hardness test with 10 kg load and 15 seconds dwell time was carried out on the surface of the samples from all cast iron grades using shimadzu-hsv-30 hardness tester. impact test was carried out on charpy un-notched test samples. the machine used for the impact test is iffect technology, inc make dynatup, model 500. the working range of the machine as per the astm-e-23 is 25j to 286.4j. the wear test experiment was carried out as per the astm g 65. abrasion wear test setup and schematic diagram of test apparatus is shown in fig. 1. the samples for wear test were cleaned with methanol and dried. the specimens were weighed to the nearest 0.0001g. each specimen was fixed securely in the holder and erodent (quartz sand; size: 180µm to 250µm) was poured in the hopper. a load of 80n was applied to the specimen against the wheel. the applied force was measured accurately by means of a spring scale which was hooked around the specimen and pulled back to lift the specimen away from the wheel. revolution was set to 200 rpm. the erodent flow rate through the nozzles was approximately 330 g/min. the dwell time between the two tests was considered as 40 minutes. the each test was run for 15 minutes. each time, the specimen was removed and reweighed to the nearest 0.0001 g. using the hcrci grade, fb cr26moni with 0.50 wt. % vanadium, few prototype liners were manufactured and installed in a coal pulverizing tube mill at an identified site along with freshly installed hcrci grade, fb cr26moni liners for their comparative wear study and service life evaluation. v d. kumar et alii, frattura ed integrità strutturale, 49 (2019) 507-514; doi: 10.3221/igf-esis.49.47 509 figure 1: abrasion wear testing setup and schematic diagram of test apparatus result and discussion chemical analysis fter successful casting, the chemical compositions of cast hcrci and hcrvci grades were analyzed and they were found within the range. tab. 1 describes the compositions achieved for the various grades of cast irons. all castings were hardened at 960oc for 10 hours and tempered at 295oc for 7 hours. through ultrasonic testing (ut), all cast iron blocks were confirmed with good homogeneity. grade of cast iron element (wt. %) c si mn ni mo s p cr cu v fe fb cr26moni 2.69 0.99 0.99 0.21 0.29 0.05 0.04 25.09 0.30 nil bal. fb cr26moni +0.25v 2.75 0.95 0.89 0.36 0.21 0.09 0.05 25.20 0.29 0.29 bal. fb cr26moni +0.5v 2.74 0.80 0.99 0.35 0.39 0.05 0.04 24.99 0.39 0.53 bal. fb cr26moni +1.0v 2.68 0.90 0.93 0.19 0.29 0.05 0.05 24.96 0.29 1.01 bal. fb cr26moni +2.0v 2.69 0.72 1.02 0.22 0.30 0.03 0.04 24.99 0.35 2.03 bal. fb cr26moni +3.0v 2.70 0.90 1.00 0.29 0.35 0.05 0.05 24.80 0.20 3.01 bal. fb cr26moni +4.0v 2.58 0.89 1.05 0.22 0.29 0.05 0.05 25.02 0.29 4.02 bal. fb cr26moni +5.0v 2.51 0.91 1.01 0.19 0.21 0.05 0.04 24.99 0.25 5.03 bal. fb cr26moni +6.0v 2.50 0.80 1.10 0.20 0.41 0.05 0.04 25.10 0.19 6.00 bal. fb cr26moni +7.0v 2.69 0.81 0.95 0.22 0.20 0.05 0.05 24.85 0.15 7.02 bal. fb cr26moni +8.0v 2.70 0.80 0.90 0.21 0.29 0.04 0.04 24.90 0.20 8.01 bal. table 1: compositions of the various grades of hcrcis with varying vanadium content microscopic examination the hcrvci grade, fb cr26moni+0.5v has achieved the best combination of hardness and impact strength which are discussed in the later stage. therefore, the microstructures of base material (fb cr26moni) and developed material (fb cr26moni+0.5v) were exclusively examined. microstructure of fb cr26moni material in fig. 2: a) resembles coarse eutectic interdendritic rod-like continuous m7c3 carbides network in the gray tempered martensite matrix. microstructure a d. kumar et alii, frattura ed integrità strutturale, 49 (2019) 507-514; doi: 10.3221/igf-esis.49.47 510 of fb cr26moni+0.5v material in fig. 2: b) shows fine globular mc type carbides and chunk like m7c3 carbides more uniformly distributed in the martensite structure which is reported to contribute better combination of hardness and impact strength. during eutectic solidification of hcrci with vanadium addition, eutectic colonies diameter, ‘de’ is directly proportional to eutectic transition temperature range, ‘∆te’. this can be expressed as eqn. (1) [15]: 𝑑𝑒 ∝ ∆𝑇𝐸   (1) vanadium is found to narrow the eutectic transition temperature range and hence, refines the microstructure. globular and chunk like uniform carbides precipitates distribution in the matrix of martensite is highly favorable for stabilizing the microstructure and imparting a better combination of higher hardness and impact toughness properties. therefore, morphology of fb cr26moni+0.5v cast iron is more suitable for tube mill liner application. figure 2: a) microstructure of hcrci grade, fb cr26moni at 200x magnification and b) microstructure of hcrvci grade, fb cr26moni +0.5v at 200x magnification. field emission scanning electron microscopic analysis after microstructure evaluation, the high chromium cast iron (fb cr26moni) and high chromium-vanadium cast iron (fb cr26moni+0.5v) materials were examined under field emission scanning electron microscope. fesem images and eds spectrums shown in fig. 3: a) confirm the rod-like m7c3 carbide as chromium carbides in the continuous carbide network in the matrix of fb cr26moni material and fig. 3: b) & c) confirm the globular mc type carbide as vanadium carbide and modified chunk like m7c3 type carbide as chromium carbide distribution with vanadium content in the matrix of fb cr26moni+0.5v material. there is more uniform distribution of carbides and the presence of vanadium in the matrix. coarse eutectic interdendritic rod-like continuous m7c3 carbides network in the gray tempered martensite matrix of fb cr26moni material is more prone to easy crack propagation. since, carbides are brittle, their continuous network would provide a preferred path for fast crack growth. tempered martensite matrix holds carbides less firmly which results in splitting of carbides from the surface. more uniform distribution of globular mc type carbides and chunk like m7c3 carbides in the martensite matrix of fb cr26moni+0.5v material is quite favorable for delaying the crack propagation. this type of distribution is studied and found to have a better combination of hardness and impact strength. therefore, morphology of fb cr26moni+0.5v material is highly stable as compared to that of fb cr26moni material. since, eds analysis has shown that mc type carbide is vanadium carbide (vc) and m7c3 carbide is chromium carbide (cr7c3), vc precipitates with 2800hv hardness along with m7c3 precipitates with 1200 ~ 1800hv hardness induce more hardness in the matrix. presence of vanadium in the matrix of cast iron material is reported to gives additional strengthening effect [4] which helps in delaying crack initiation and propagation. hardness behavior hardness was tested on samples from different cast iron blocks. a graph of ‘hardness value’ (hv) with ‘vanadium’ content (wt. %) was plotted and it is shown in fig. 4. hardness test result shows that the hcrci grade, fb cr26moni with vanadium content of 0.5 wt. % has achieved the highest hardness value. vanadium addition, initially, would have led to precipitation of fine vanadium carbides (vc type) which favors martensitic transformation [8, 9, 10]. with vanadium d. kumar et alii, frattura ed integrità strutturale, 49 (2019) 507-514; doi: 10.3221/igf-esis.49.47 511 addition, m7c3 type carbides are reported to restrict continuous needle like carbides precipitation to discontinuous and chunk like carbides. higher hardness and higher affinity to carbon of vc as compared to m7c3 type carbides and the martensitic transformation might have imparted more hardness to the matrix of base material with 0.5 wt. % v content. higher vanadium content is found to stabilize austenite further and thereby reduces hardness value [7]. therefore, fig. 4 shows first increase and then decrease in hardness. figure 3: fesem image and eds spectrum of a) fb cr26moni material precipitate, b) fb cr26moni+0.5v material precipitate and c) fb cr26moni+0.5v material matrix d. kumar et alii, frattura ed integrità strutturale, 49 (2019) 507-514; doi: 10.3221/igf-esis.49.47 512 figure 4: hardness of cast iron grades with varying vanadium content impact strength since, hcrci with 0.50 wt. % vanadium has the highest hardness, impact strength study was made for the hcrci with vanadium content from 0.00 wt. % to 2.00 wt. % v range only. the charpy impact test results (fig. 5) show that the impact strength of the base material improves with increase in the vanadium content. higher impact value with higher hardness is very much favorable for tube mill liner to ensure its higher service life. vanadium forms vc type carbides first at higher temperature and act as heterogeneous nucleation nuclei for chromium carbide precipitation which leads to refinement of carbides and their improved distribution [11, 12, 13, 14]. these morphological changes are observed to improve the impact strength of the cast iron grades. therefore, it is found that the hcrci with 0.5wt% vanadium has the well suited combination of hardness and toughness properties for the parts experiencing impact and wear actions simultaneously. figure 5: impact strength of cast iron grades with varying vanadium content abrasion wear testing the hcrci with 0.5% vanadium content is found to have the highest combination of hardness and impact strength. therefore, an exclusive abrasive wear study of the base material (fb cr26moni) and the developed material (fb cr26moni+0.5v) was made as per the standard astm g 65. the volume loss of materials was calculated as per the eqn. (2). 𝑉𝑜𝑙𝑢𝑚𝑒 𝑙𝑜𝑠𝑠, 𝑚𝑚3 𝑀𝑎𝑠𝑠 𝑙𝑜𝑠𝑠 𝑔 𝐷𝑒𝑛𝑠𝑖𝑡𝑦 𝑔/𝑐𝑚 3 𝑋 1000 (2) d. kumar et alii, frattura ed integrità strutturale, 49 (2019) 507-514; doi: 10.3221/igf-esis.49.47 513 the test results are given in tab. 2. the results show that the hcrci grade, fb cr26moni with 0.5wt% vanadium addition is comparatively a higher wear resistant alloy which is more suitable for wear resistance application. the wear resistance of the developed cast iron grade (fb cr26moni +0.5v) was calculated as the ratio of volume loss of the reference material (fb cr26moni) to the volume loss of that material. the average abrasive wear resistance of fb cr26moni +0.5v material as compared to fb cr26moni material is 2.33. this shows that fb cr26moni +0.5v material has higher wear resistance and it is more suitable for liner applications in coal pulverizers. therefore, the comparative wear study of prototype liners of these materials for 2,667 hours was made by installing them in a coal pulverizing tube mill. the average wear out thickness of the developed liner (fb cr26moni +0.5v) and the normal liner (fb cr26moni) were found to be 0.83mm and 2.08mm, respectively. the above data shows a higher wear life for the cast iron grade, fb cr26moni +0.5v. material: fb cr26moni fb cr26moni +0.5v sample no: a11 a12 a13 a3h1 a3h2 a3h3 test time, min: 45 45 45 45 45 45 initial mass, g: 84.5123 84.7395 84.5744 86.8523 86.8457 81.5244 final mass, g: 84.1666 84.3957 84.1764 86.7301 86.6998 81.3267 mass loss, g: 0.3457 0.3438 0.3980 0.1222 0.1459 0.1977 mass loss, mg/min: 7.7 7.6 8.8 2.7 3.2 4.4 volume loss, mm3: 46.2784 46.0241 53.2798 16.3588 19.5315 26.4659 volume loss per kg of erodent, mm3/kg: 9.3492 9.2978 10.7636 3.3048 3.9457 5.3466 average volume loss per kg of erodent, mm3/kg: 9.8035 4.1991 table 2: abrasive wear test result of the base material and the developed material conclusions etailed study on the abrasion wear, mechanical behavior, microscopic examination and characterization of hcrci and hcrvci grades leads to the following major conclusions: 1. all grades of cast irons were cast using die casting method and chemical compositions were achieved successfully with homogeneous matrix in the respective casting blocks. 2. 0.5 wt. % vanadium addition to the base hcrci grade (fb cr26moni) has refined the microstructure to form globular vc type carbides and chunk like cr7c3 carbides distribution in the martensite matrix. this is quite favorable for improved life of liners in tube mills. 3. hcrvci grade, fb cr26moni+0.5v has higher abrasion wear resistance and higher combination of hardness and impact strength as compared to the reference hcrci grade, fb cr26moni. hence, the hcrci with 0.5 wt. % vanadium addition is more promising with enhanced properties of hardness, impact toughness and higher abrasion wear resistance for tube mill liner application. 4. the study of prototype liners of the developed cast iron shows a higher service life as compared to the existing base material liners. acknowledgement uthors express their gratitude to the managements of bhel, corporate r&d, hyderabad for financially supporting this study. they acknowledge the officials at surface coating department, bhel, corporate r&d, hyderabad for their support in carrying out the wear test of cast iron samples. they acknowledge the concerned d a d. kumar et alii, frattura ed integrità strutturale, 49 (2019) 507-514; doi: 10.3221/igf-esis.49.47 514 officials at quality labs, bhel ramachandrapuram for the chemical analysis and officials at heat treatment shop, bhel, ramchandrapuram for the heat treatment of cast iron blocks. references [1] zhi, x., xing, j., fu, h., gao, y. (2008). effect of titanium on the as-cast microstructure of hypereutectic high chromium cast iron, j. mater. charact. 59, pp. 1221–1226. doi: 10.1016/j.matchar.2007.10.010. [2] filipovic, m., kamberovic, z., korac, m. (2013). microstructure and mechanical properties of fe–cr–c–nb white cast irons, j. mater. des. 47, pp. 41–48. doi: 10.1016/j.matdes.2012.12.034. [3] xinhui, f., lin, h., qingde, z. (1989) a structural study of high chromium cast iron as a grinding ball material, j. met. sci. technol., 5, pp. 401-406. [4] sawamoto, a., ogi, k., matsuda, k. (1986). solidification structures of fe-c-cr-(v-nb-w) alloys, j. afs transactions, 72, pp. 403-416. [5] dodd, j., parks, j. l. (1980). factors affecting the production and performance of thick-section high chromiummolybdenum alloy iron castings, j. metals forum, 3 (1), pp. 3-12. [6] radulovic, m., fiset, m., peev, k., tomovic, m. (1994). the influence of vanadium on fracture toughness and abrasion resistance in high chromium white cast irons, j. journal of materials science, 29, pp. 5085-5094. [7] keming, l., fuming, w, changrong, l., liuyan, s. (2005). influence of vanadium on microstructure and properties of medium-chromium white cast iron, available at: http://vanitec.org/technical-library/paper/influence-ofvanadium-on-microstructure-and-properties-of-medium-chromium-w. [8] yuwei, w., wen s., (1989). the effect of v in high cr cast iron, j. foundry, 5, pp. 9-12. [9] junyi, s., xiangzhong, g., enze, w. (1984). study on high chromium white cast iron containing vanadium with martensite matrix in the as-cast condition, j. journal of xi’an jiaotong university, 18(5), pp. 23-28. [10] yifu, y., tongxiang, f. (1995). spheroidizing of carbides of white cast iron, j. modern cast iron, 3 pp. 28-32. [11] scandian, c., boher, c., de mello, j.d.b., rézaï-aria f., (2009). effect of molybdenum and chromium contents in sliding wear of high-chromium white cast iron: the relationship between microstructure and wear, wear, 267, pp. 401–408. doi: 10.1016/j.wear.2008.12.095 [12] pierson, h.o., (1996). handbook of refractory carbides and nitrides, 1st ed. sandia national laboratories, available at: file:///e:/paper%20published_to%20be%20published/icon2018%20papers/paper%20submission_frattura%20e d%20integrita/references%20hcrvwci/ref%2013.pdf [13] xiang, c., yanxiang, l., (2010). effect of heat treatment on microstructure and mechanical properties of high boron white cast ,iron, j. mater sci eng a, 528, pp. 770–775. doi: 10.1016/j.msea.2007.10.009 [14] xiaohui, z., jiandong, x., yimin, g., (2008). effect of heat treatment on microstructure and mechanical properties of a ti-bearing hypereutectic high chromium white cast iron, mater sci eng a, 487, pp. 171–179. doi: 10.1016/j.msea.2007.10.009 [15] ogi, k., matsubara, y., matsuda, k., (1982). eutectic solidification of high chromium cast iron-mechanism of eutectic growth, afs transactions, 89, pp. 197–204. << /ascii85encodepages false /allowtransparency false /autopositionepsfiles true /autorotatepages /none /binding /left /calgrayprofile (dot gain 20%) /calrgbprofile (srgb iec61966-2.1) /calcmykprofile (u.s. web coated \050swop\051 v2) /srgbprofile (srgb iec61966-2.1) /cannotembedfontpolicy /error /compatibilitylevel 1.4 /compressobjects /tags /compresspages true /convertimagestoindexed true /passthroughjpegimages true /createjobticket false /defaultrenderingintent /default /detectblends true /detectcurves 0.0000 /colorconversionstrategy /cmyk /dothumbnails false /embedallfonts true /embedopentype false /parseiccprofilesincomments true /embedjoboptions true /dscreportinglevel 0 /emitdscwarnings false /endpage -1 /imagememory 1048576 /lockdistillerparams false /maxsubsetpct 100 /optimize true /opm 1 /parsedsccomments true 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can be opened with acrobat and adobe reader 5.0 and later.) >> /namespace [ (adobe) (common) (1.0) ] /othernamespaces [ << /asreaderspreads false /cropimagestoframes true /errorcontrol /warnandcontinue /flattenerignorespreadoverrides false /includeguidesgrids false /includenonprinting false /includeslug false /namespace [ (adobe) (indesign) (4.0) ] /omitplacedbitmaps false /omitplacedeps false /omitplacedpdf false /simulateoverprint /legacy >> << /addbleedmarks false /addcolorbars false /addcropmarks false /addpageinfo false /addregmarks false /convertcolors /converttocmyk /destinationprofilename () /destinationprofileselector /documentcmyk /downsample16bitimages true /flattenerpreset << /presetselector /mediumresolution >> /formelements false /generatestructure false /includebookmarks false /includehyperlinks false /includeinteractive false /includelayers false /includeprofiles false /multimediahandling /useobjectsettings /namespace [ (adobe) (creativesuite) (2.0) ] /pdfxoutputintentprofileselector /documentcmyk /preserveediting true /untaggedcmykhandling /leaveuntagged /untaggedrgbhandling /usedocumentprofile /usedocumentbleed false >> ] >> setdistillerparams << /hwresolution [2400 2400] /pagesize [612.000 792.000] >> setpagedevice microsoft word numero_50_art_32_2607 s. gavela et alii, frattura ed integrità strutturale, 50 (2019) 383-394; doi: 10.3221/igf-esis.50.32 383 focused on the research activities of the greek society of experimental mechanics of materials experimental uncertainty budget for concrete compressive strength test based on a multifactorial analysis stamatia gavela, nikolaos nikoloutsopoulos, george papadakos, dimitra passa, anastasia sotiropoulou school of pedagogical and technological education, department of civil engineering educators matina@gavela.gr, http://orcid.org/0000-0003-0775-2750; nikolasnikoloutso@hotmail.com; gpapadakos@teemail.gr; dimpassa@aspete.gr; sotiropoulou@aspete.gr abstract. the objective of the study is to introduce an experimental uncertainty budget process for concrete compressive strength test, based on a protocol that incorporates effects of multiple factors significant for the measurement result. the proposed procedure is rather useful for laboratories seeking accreditation according to iso/iec 17025, in order to emphasize the contribution of type a uncertainty estimations, rather than relying on type b estimations that are unable to address the correlation between those factors. two independent experiments were performed. experiment i is proposed as a simple, suitably designed, reproducibility trial for laboratories performing en 12390 test method, i.e. when a specified nominal curing age is targeted, following experimental design on multiple uncertainty parameters. a sensitivity analysis was introduced based on a semi-empirical multifactorial regression model (experiment ii) for concrete compressive strength as a function of specimen’s curing age and w/c ratio. the present study is an effort towards an integrated and standardized method for experimental, semi-empirical multifactorial regression estimation of the uncertainty budget for the en 12390 test method, being useful, also, as a baseline for internal quality control programs when adjusted for the specific characteristics of concrete specimens tested by a laboratory. keywords. concrete compressive strength test; multifactorial model; type a uncertainty estimation; sensitivity analysis. citation: gavela, s., nikoloutsopoulos, n., papadakos, g., passa, d., sotiropoulou, a. experimental uncertainty budget for concrete compressive strength test based on a multifactorial analysis, frattura ed integrità strutturale, 50 (2019) 383-394. received: 19.01.2019 accepted: 14.05.2019 published: 01.10.2019 copyright: © 2019 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. introduction etermination of the uncertainty budget in cases of measuring the compressive strength of concrete specimens is critical as it is a quantitative criterion according to which the result of a corresponding test is assessed against the compliance of the specimen with concrete specifications. this is particularly emphasized in the new version of international standard iso/iec 17025:2017, by which it is required that any conformity assessment laboratory output d http://www.gruppofrattura.it/va/50/2607.mp4 s. gavela et alii, frattura ed integrità strutturale, 50 (2019) 383-394; doi: 10.3221/igf-esis.50.32 384 shall be provided according to a predetermined decision rule. most of the attempts to determine the uncertainty budget for a concrete compressive strength test according to european standard en 12390-3 are based mainly on type b estimations, i.e., on external laboratory sources or on reasonable assumptions according to scientific knowledge. type b estimation of uncertainty factors is simple and fast and provides a solution in cases where it is not feasible to perform an experimental (statistical) uncertainty investigation (a type a estimation). this type of assessment leads to a number of disadvantages, such as the inability to assess the degree of positive or negative correlation between the various parameters that contribute to the result of the measurement. in this study, firstly the parameters of uncertainty during an en 12390-3:2009 testing for specimens prepared according to en 12390-1: 2012 are analyzed using an ishikawa (cause and effect) diagram. two experiments were performed for further statistical investigation of the interacting behavior of the most essential parameters presented in the ishikawa diagram. the first experiment is also proposed as a procedure for a laboratory performing the en 12390 test method in order to reveal its type a estimation for the most essential corresponding uncertainty parameters when a specified nominal curing age is targeted. within this framework it is essential to perform a sensitivity analysis on the effect of the specimen’s curing age. to do so, a semi-empirical model, was estimated within the second experiment for the correlation of concrete compressive strength as a function of the parameters of specimen’s curing age and w/c ratio. the proposed procedure is described in a way to be exploitable by any laboratory, especially in the case of seeking accreditation according to iso/iec 17025. the semi-empirical model is expected to be useful, also, for accredited testing laboratories in order to perform their internal quality control program. uncertainty parameters identification and analysis he characteristics of the specimen that is subjected to a compressive strength measurement according to european standard en 12390-3 are subject to a definition detailed in en 12390-1. any deviation from the technical specifications of the specimen, i.e. in terms of its geometrical and other characteristics, also leads to a measurement error. this does not affect directly the numerical quantity resulting from the application of the compressive strength test method if a proper testing apparatus is used. it occurs indirectly, as any measurement result is attributed to a theoretically perfect cube with edges that are all of equal length, e.g. exactly 15cm. this is something that cannot be achieved perfectly, in practice. by testing as many specimens of the same characteristics as possible, is expected to yield measurement results dispersion that is affected by these definitional deviations. such errors contribute to the overall uncertainty of the test result inherently. they are impossible to be eliminated, but it is possible to be minimized [1] by improving the preparation conditions of the specimens (e.g. by improving the manufacturing quality of the moulds being used by the laboratory). the category of factors contributing, due to definitional errors, to the increase of the combined measurement uncertainty include, also, those associated with the definition of the aimed concrete composition for the specimen prepared, and of course, of the concrete used in the corresponding construction. the values for the mix proportions of the concrete constituents, usually expressed in kg/m3, and the particle size of the aggregates used are two of these factors. in particular, however, the ratio of the amount of water to the amount of cement used in the concrete mix has already emerged from the late 19th century as essential for concrete compression strength test results. mathematical models that value this relationship for a given specimen curing age have been early proposed [2,3]. recent work has suggested mathematical models describing the apparent association of the specimen compressive strength with curing age [4-11]. another factor that affects the result of concrete compressive strength for a specimen of a given curing age is the temperature of the environment in which the curing process takes place [5]. it is characteristic that a higher value of this temperature leads to faster curing. at the nominal age (e.g. on 28 days) the specimen may exhibit different value of compressive strength as compared to the case where the same curing procedure would be performed in a lower temperature environment. of course, the combined uncertainty of the result of a test according to en 12390-3 depends on the calibration quality of the uniaxial compression apparatus and the degree of familiarity of its user. an apparatus that has been successfully calibrated according to the requirements of international standard iso 7500-1 may be considered as causing negligible random errors to the test results. however, it should be noted that any systematic errors due to the accuracy of the reference standard (e.g. a force gauge) which is used during the calibration procedure cannot be overlooked. for this reason, the measurement uncertainty for the reference standard should always be incorporated into the uncertainty budget of a test according to en 12390-3. all of the above are summarized in the cause-and-effect diagram (ishikawa diagram, as already been introduced by authors of this paper in a previous study [8]) which has been used according to guidance from eurachem [11], in a way [8,12] that aims at mapping uncertainty factors while simultaneously visualizing synergies between them (fig.1). t s. gavela et alii, frattura ed integrità strutturale, 50 (2019) 383-394; doi: 10.3221/igf-esis.50.32 385 figure 1: cause-and-effect diagram on how uncertainty factors contribute to the final result of a test according to en 12390-3. scope of the experiments scope of experiment i actors like equipment accuracy, testing method selection, e.g. the en 12390-3 method, measurement conditions and equipment handler’s skills should be considered as inherent to the operation characteristics of the laboratory. their reproducibility is a matter under control of the interested laboratory. a simple reproducibility experiment, in which the same equipment is used for all the needed measurements, provides adequately the contribution of all these parameters to the laboratory’s uncertainty estimation, as the specific laboratory will continually use the specific equipment, under the specific measurement conditions, by the same handlers. however, a simple reproducibility experiment cannot incorporate the effect of parameters, that have to do with the specimen’s characteristics (which define the concrete composition under consideration), especially when the specimen is not prepared by the laboratory. such parameters are all those related to the mix composition and to the definitional uncertainty produced by deviations from the definition given for the specimen in en 12390-1, especially its geometrical characteristics. in experiment i of this study, the experimental design incorporated different levels of cement content (cc) and water to cement ratio (w/c), which is adequate in order to produce the majority of the corresponding combinations of mix constituents that the laboratory could encounter when receiving specimens of a specific combination of types of concrete constituents. by fixing the type of the materials for the proposed type a uncertainty estimation makes this protocol materials’ type specific. this is not considered to reduce its effectiveness, especially when a laboratory receives specimens from a specific producer on an ongoing basis. in real circumstances of laboratory operation, small deviations of maximum three days from the nominal curing age of performing the compressive strength test may occur for any reason. a stratification of such deviations was also included in the design of the experiment in order to produce such an uncertainty factor. also, a large number (about 30) of different molds, of three different construction designs, where used randomly for the preparation of the specimens, providing varying geometries, representative to the corresponding variation that a laboratory could encounter when receiving any specimen from any external customer. the aim is to propose a method for determining the uncertainty for an en 12390-3 concrete compressive strength test result, the experimental part being extended, but only in the case where the test method is applied for a specific nominal value of curing age. the method is formulated in such a way that it is reproducible and exploited by any laboratory that applies this test, especially if it seeks accreditation in accordance with iso / iec 17025. this protocol of the proposed method for a type a uncertainty estimation is designed in such a way that it leads to: (a) the optimum economy of used specimens, (b) the aggregation of covariation among all the parameters that vary due to the experimental design, and (c) a (safe-side) maximal estimation of the uncertainty budget, something that is, also, supported by iso in the gum approach. f s. gavela et alii, frattura ed integrità strutturale, 50 (2019) 383-394; doi: 10.3221/igf-esis.50.32 386 scope of experiment ii experiment ii aims at the experimental investigation of the correlation of compressive strength testing results with the parameters of curing age and water to cement ratio at the same time, through sensitivity analysis. a sigmoidal curve was used to fit the experimental results. freiesleben hansen & pedersen [4] and carino [5] firstly proposed a sigmoidal curve for modeling the curing procedure. all of the parameters presented in fig.1 affect the compressive strength testing according to european standard en 12390 series. some essential questions are: to what extent do all these parameters correlate to each other and to the result of the test procedure? are the results of the testing procedure valid if these parameters fail to be accurately determined? for example, should a testing result be put aside if the curing age of the specimen deviates by a few days from the typical nominal 28-days value? the population of parameters affecting the result of a compressive strength test is big so unless performing sensitivity analysis for any subset of these parameters via a specialized experiment it is almost impossible to assess the impact of this subset of parameters. studying the effect of all the above parameters in one single experiment for various levels of those parameters would lead to an enormous specimens’ population. for this reason in the frame of an extended study aiming at the creation of a function that correlates the testing result on the compressive strength of concrete specimens to all the significant of the above parameters, only the experimental investigation of the correlation of compressive strength testing results with the parameters of curing age and water to cement ratio was examined. the integration of various similar experiments of such a protocol by various laboratories and for various parameters of the test procedure could speed the achievement of a standardized semi-empirical model on the relation of concrete compressive strength as a function of a great number of testing parameters and mix materials characteristics [8]. experimental design n the context of this study, tests have been carried out on a number of specimens prepared according to the definition of a 15 cm cementitious concrete test specimen as set out in en 12390-1. for the design of the experiments a combination of characteristics for the composition of the concrete was chosen for the preparation of the specimen. the cement used in the present study was cem ii 32.5. the aggregates used were crushed limestone. determination of particle density and water absorption of fine and coarse aggregates was performed according to en 1097-6. the superplasticizer used was sika viscoflow 700. the concrete compositions of the tested specimens are shown in table 1 as kg of constituent per 1m3 of fresh concrete produced (kg/m3). those compositions were obtained after performing concrete mix design using the densities of raw materials. concrete mix design can lead to errors when raw materials are “fluffy” or lightweight or can absorb big amounts of water [10] because for these materials the error in the determination of its density is bigger but also because of a degree of compaction as the air within the initial amount of this “fluffy” material (before mixing) is displaced by all the other constituents of the mixture (during mixing). in this study, conventional aggregates were used so the errors are expected to be small. deviations in mix proportions have been addressed to the factors contributing to the uncertainty in ishikawa diagram above. if a laboratory reproduces the experiments using concrete mix design (using densities of raw materials) will address the same systematic errors. however, the fresh concrete’s density can be determined according to en 12350-6. knowing the density of fresh concrete, the yield per batch can be determined as the mass of all the ingredients in a batch divided by the density. in this way one can verify if proportions of ingredients that came from concrete mix design (kg/m3) produces indeed 1m3 of fresh concrete. in experiment i, the uncertainty estimation process was performed for the case of applying the 28-day nominal curing age that is set by the corresponding national regulation on structural concrete technical specifications. for each of the experiment i compositions, ten specimens were prepared and tested for compressive strength by pairs, at curing ages equal to 27, 28, 29, 30 and 31 days, respectively. experiment ii was intentionally performed using concrete syntheses different than those used for experiment i. this way, it was possible to assess the extent to which the corresponding multifactorial model can be used for syntheses that lie outside the range of those been used for its estimation. in experiment ii, 13 specimens were prepared for each of the concrete compositions. water to cement ratio values were selected to be separated by equivalent intervals of 0.02. at the same time superplasticizer’s mix proportions were kept the same except from the mixture with the highest water to cement ratio. in this mixture a small decrease of superplasticizer’s mix proportion was needed so the mixture did not become segregated. the cement content expressed in kg/m3 was selected to be kept constant for the entire experiment, and as mentioned before, at a value different than the range used in experiment i. so, inevitably, it was impossible to change the water-to-cement ratio and keep the content of aggregates unchanged as expressed in kg/m3. otherwise the base for the calculation of constituents’ content would not be in all cases equal to 1 m3. i s. gavela et alii, frattura ed integrità strutturale, 50 (2019) 383-394; doi: 10.3221/igf-esis.50.32 387 additionally, ten specimen of composition i-g were prepared, half of which were tested at 7 days of age, while the rest were tested at the age of 14 days. these additional results where needed in order to apply the experiment ii multifactorial model on the results of experiment i tests. composition cement [kg/m3] w/c [-] sand [kg/m3] coarse aggregates 4-16mm [kg/m3] coarse aggregates 16-31.5mm [kg/m3] superplasticizer [kg/m3] slump [mm] experiment i i-a 300 0.45 1021.2 623.1 341.3 4.20 10 i-b 300 0.50 1001.4 610.0 334.7 3.60 200 i-c 300 0.55 980.9 598.5 327.8 3.60 250 i-d 330 0.45 988.4 603.1 330.4 4.62 170 i-e 330 0.50 966.7 589.8 323.1 3.96 240 i-f 330 0.55 944.1 576.1 315.6 3.96 250 i-g 360 0.45 956.7 583.7 319.7 4.32 230 i-h 360 0.50 932.0 568.7 311.5 4.32 250 i-i 360 0.55 908.3 554.2 303.6 3.60 260 i-j 360 0.45 956.7 583.7 319.7 4.32 220 experiment ii ii-a 280 0.46 1112.9 372.0 679.0 6.16 30 ii-b 280 0.48 1104.7 369.2 674.0 6.16 70 ii-c 280 0.50 1090.7 364.5 665.5 6.16 100 ii-d 280 0.52 1088.2 363.7 664.0 6.16 140 ii-e 280 0.54 1081.3 361.4 659.7 5.32 180 table 1: mix compositions. slump test for each composition was performed according to en 12350-2 and slump test results are shown in table 1. curing procedure according to en 12390-2 was followed. after demolding, specimens were immersed in water. the curing temperature was about 20 °c. a number of different metal moulds, labeled with a serial number, were used to prepare the specimens for experiment i. these moulds were used in a randomized manner in order to prepare the specimens for all the various compositions presented in table 1. the use of different moulds has led to an expected and reasonable dispersion of the geometric characteristics of the specimens (e.g. lack of surface flatness and perpendicularity, edge dimensional accuracy). therefore, the following results are expected to be representative of reasonable dispersion of the geometric characteristics of the specimens been tested by a laboratory that uses any of these moulds and the parameter of the specimen’s geometry is expected to have contributed into the results of this study. also, the uniaxial compression apparatus used was successfully calibrated with a subsequent correction of its calibration, according to international standard iso 7500-1. it can be assumed that the calibration of the apparatus contributes to the final combined uncertainty only when the corresponding systematic errors occur. method of analysis xperiment ii results were used into a multifactorial regression analysis procedure leading to a sigmoidal by time equation: 𝐶𝑆 𝑊 𝐶⁄ , 𝑡 𝐶𝑆 ∙ 𝑒 𝑐 𝑐 ∙ 𝑊/𝐶 ∙ 𝑒 (1) e s. gavela et alii, frattura ed integrità strutturale, 50 (2019) 383-394; doi: 10.3221/igf-esis.50.32 388 the left part in the above eq.(1), as described in eq.(2). 𝐶𝑆 𝑐 𝑐 ∙ 𝑊/𝐶 (2) provides the value of compressive strength estimated for a reference curing age. in the case of eq.(1) where the multifactorial model function incorporates the variation of cs(w/c,t) for the entire range of curing age span, csref represents the tested specimens’ compressive strength at infinite curing age, which could be called the final compressive strength csinf. in the case of experiment i, eq.(2) was used for testing specimens at a nominal curing age of about 28 days. the exponential part of eq.(1) provides an estimation of the proportion of the final compressive strength reached at curing age t: 𝑃 𝑡 𝑒 (3) sensitivity analysis and application of the law of propagation of uncertainty is easily performed according to the iso gum procedure when such a multifactorial function is used. specifically, the sensitivity coefficients cw/c and ct can be estimated as the corresponding derivatives of the function in eq.(1). these coefficients provide an assessment for the uncertainty of the result of concrete specimen compressive strength measurement which is attributed to the uncertainty in estimating the values for water-to-cement ratio and curing age, respectively. these two sensitivity coefficients are provided by the following equations: 𝐶 / 𝑐 ∙ 𝑒 𝑐 ∙ 𝑃 𝑡 (4) 𝐶 ∙ ∙ (5) a laboratory performing testing in well-known concrete syntheses could use eq.(1) as a baseline in the frame of quality control. that is, for concrete specimens that are similar in synthesis as those used for establishing eq.(1), the result of any future compressive strength testing should not deviated significantly from the reference value provided by eq.(1). for significantly different syntheses a laboratory should repeat the herein presented experimental procedure in order to fit eq.(1) to the results of the corresponding compressive strength tests. results and discussion ccording to experiment i results, the values c0 = 124 ± 11 mpa and c1 = -150 ± 22 mpa were obtained for the least squares regression line of fig.2a, with a satisfying fitting quality (r2 = 0.68). by interpreting the value obtained for parameter c1, each percentage change in the water to cement ratio (i.e., a change in w/c by 0.01), causes a change for the mean value of the compressive strength of the specimens by approximately 1.5 mpa. at the same time, no statistically significant correlation of cs and cc was detected based on experiment i results (fig.2b). fig.2a depicts the confidence bands of the regression line at the level of 95%. but these limits are not expected to provide a generic conclusion as they correspond only to an experiment based on a similar set of specimens. in contrast, the prediction bands of the regression line can yield the 95% probability limits within which any single iteration of the test is expected to occur. the regression procedure for experiment ii compressive strength tests provided a statistically significant multifactorial function [see fig.3a for the relation of the multifactorial model as a function of w/c and fig.3b for the relation of the model as a function of curing age t] with parameter values: c0 = 143 ± 24 mpa, c1 = -136 ± 38 mpa, τ = 0.45 ± 0.18 days and n = 1.0 ± 0.2, at a confidence level of 95%. the fitting quality is very satisfying (r2 = 0.92). one of the laboratory test results was omitted as an outlier, so 64 results were used in the regression procedure, instead of 65. it should be noted that values for c0, c1 obtained from experiment ii provide a linear function of cs(t) with w/c, which provides an estimation of csinf, i.e. cs(t) for infinite curing age, when values for parameters c0, c1 obtained from experiment i provide a corresponding estimate, strictly dedicated to the nominal value of 28 days for curing age t. if a comparison between these two results is aimed at, then the right part of eq.(1), the p(t), should be taken into account. the correlation of the compressive strength with the curing age parameter was strongly confirmed by the results of experiment ii (fig.3b). for this reason, eq.(1) was applied to the results of experiment i tests, keeping the left part of the equation unchanged and, so limiting the regression process for optimizing the values for the sigmoidal shape parameters a s. gavela et alii, frattura ed integrità strutturale, 50 (2019) 383-394; doi: 10.3221/igf-esis.50.32 389 (a) (b) figure 2: evaluation of the effect of parameters (a) of water to cement ratio, w/c, and (b) cement content, cc, in determining the levels of compressive strength of specimens. (a) (b) figure 3: multifactorial regression model as a function of (a) water-to-cement ratio (w/c) and (b) curing age t. τ = 3.8 ± 0.9 days and n = 0.50 ± 0.08, with a similarly very satisfying fitting quality (r2 = 0.92, fig.4a). it is of great importance that statistically significant parameter values where obtained, although the curing procedure was much slower than the one when experiment ii was performed. however, the correlation of the compressive strength with the curing age parameter, when the figure is narrowed to a curing age range of 27 to 31 days (fig.4b for the results from experiment i), is not significantly apparent. it could be assumed that for such short time deviations, the correlation of compressive strength with curing age is a minor uncertainty factor for ages around the 28-day value. in contrast, as shown in fig.2a, the significance of water to cement ratio, w/c, is confirmed for a range of values varying from 0.45 to 0.55. sensitivity analysis despite the fact that experiment ii regression function corresponds to specific qualitative characteristics of the constituents, the sensitivity analysis of this study is expected to have a more global validity. for example, using eq.(4) on the results of experiment ii, cw/c for curing ages of 7, 28 and 90 days was estimated at -89, -109, -119 mpa per unit of w/c. this means that if we assume a maximum error on w/c of about ±0.02 and a triangular distribution for a type b estimation of w/c standard uncertainty, this would correspond to an effect on the compressive strength of the specimen of 0.7, 0.9 and 1.0 mpa, respectively. the same estimation based on eq.(4) when performed for the results of experiment i provide the values of -65, -94, -111 mpa per unit of w/c respectively, which correspond to standard uncertainties of 0.5, 0.8, and 0.9 mpa for the final result on compressive strength measurement. s. gavela et alii, frattura ed integrità strutturale, 50 (2019) 383-394; doi: 10.3221/igf-esis.50.32 390 (a) (b) figure 4: effect of the specimen curing age on compressive strength test results: (a) for samples with w/c = 0.45 and cc = 360kg/m3 and for ages from 7 to 31 days (the line shows the partial application of eq.(1) as resulted from experiment ii on these results from experiment i), (b) for samples of three different compositions and for curing ages varying from 27 to 31 days. on the other hand, if we assume a maximum error on the curing age t of about ±1 day and a triangular distribution for the corresponding type b estimation of standard uncertainty for variable t, eq.(5) estimates an effect on the compressive strength of the specimen at 0.6, 0.1 and much less than 0.1 mpa when experiment ii results apply. the same estimation based on eq.(4) when performed for the results of experiment i provide the values of 39, 57, 67 mpa per day, respectively, which correspond to standard uncertainties of 0.8, 0.3 and much less than 0.1 mpa for the final result on compressive strength measurement. it is interesting to compare these estimations to the results of experiment i where the expanded uncertainty (k=2) for testing one single specimen according to the en 12390 series procedure was estimated at about 17% for similar concrete syntheses. it is obvious that water to cement ratio and curing age errors cannot build up the major part of the testing procedure uncertainty. major uncertainty parameters should be other like the geometry of the specimen, which is not easily assessed in an experimental way, and the compressive apparatus repeatability. application of eq.(3) on the results of experiment ii provides a value of about 80% of the final compressive strength of each specimen been reached at a curing age of 28 days. when applying eq.(3) on the results of experiment i, this proportion is calculated at 69%. curing procedure was much slower in experiment i, which emphasizes the need to investigate the function of compressive strength by time. it is also evident from fig.2b that the compressive strength still increases significantly after the curing age of 28 days. when testing the specimens only at that curing age, independent for how many are the replicate specimens being used, the figure of p(t) cannot be accomplished. the result will be always assessed on the basis of an assumed proportion of the final compressive strength been reached at 28 days. a laboratory, or a producer, wishing to estimate the final compressive strength of a series of specimens should apply eq.(1). an interesting idea coming from this would be not to test 5 or 6 specimens at exactly 28 days, but testing them in consequent time intervals (e.g. 5, 10, 15, 20, 25 and 30 days) and thus producing the sigmoidal curve of eq.(1). this would even provide directly the result on csinf, with no need for p(t) assumption. such semi-empirical models, especially if completed with all the significant parameters, are expected to be useful, among others, for accredited testing laboratories in order to perform their internal quality control program. specifically, testing results lying outside the prediction bands of eq.(1) should be considered as outliers. finally, one more possibility provided for performing quality control of compressive strength testing is that there is no strict bound for completing the test procedure at the exact nominal 28-days curing age. that means, if a laboratory misses to perform the test at exactly 28 days of curing age, or if a verification testing is to be performed at a significant time interval after the nominal 28-days curing age, it is feasible to reduce the test result by using the eq.(1) to the corresponding value, at curing age equal to the nominal 28-days. prediction intervals when the regression line has been derived from pairs of values [(w/c)i, csi] of i = 1, ... n measurement results, then the prediction interval for the mean estimated cs value out of eq.(1), for a specific value of w/c, is calculated according to eq.(6) [12]. s. gavela et alii, frattura ed integrità strutturale, 50 (2019) 383-394; doi: 10.3221/igf-esis.50.32 391 𝐶𝑆 𝑡 %, ∙ 𝑠𝑒 𝐶𝑆 𝐶𝑆 𝑈 (6) where 𝑠𝑒 𝐶𝑆 𝑠 ∙ 1 / / ∑ / / (7) while 𝑊/𝐶 is the average of all (w/c)i values from all measurements and 𝐶𝑆 is the estimate for cs obtained for the specific (w/c)i value, using equation (1), and s is given in eq.(8): 𝑠 ∑ 𝐶𝑆 𝐶𝑆 (8) based on experiment i, it would appear that the result of a single en 12390-3 testing would lie within ± 17% of the mean value of compressive strength with a 95% probability. this result should be broadly considered inherent for the process, the equipment and the operators that contributed, not taking into account the uncertainty posed by the compressive apparatus calibration procedure. any reduction effort for these uncertainty parameters that are inherent for any laboratory performing the en 12390-3 testing method requires optimization in one of these features of the test method. opportunity for standardizing the procedure in a laboratory which performs compressive strength tests for concrete samples of a particular type of cement and aggregates, maintained at a specific temperature and tested at a certain curing age, a type a estimation of uncertainty for the test result can be made. in order to do that, a simple experiment, as follows, is needed to be designed and implemented: (a) multiple specimens are prepared for compositions that correspond to selected values of the w/c and cc parameters covering the range that the laboratory test method is performed for (e.g. such as the nine compositions presented in table 1 for experiment i). (b) the number of multiple specimens per composition will be derived by obtaining the product of the number of curing age values (when to perform the test) by the preferred number of specimen replicates per composition and curing age. for example, if five curing age values and two specimen replicates per each curing age value are selected, then ten samples per concrete composition are required. curing ages for performing the corresponding compression tests should be selected for reasonable intervals by which the date of the test could deviate from the desired nominal value (i.e. the 28 days in the present study). (c) to prepare the above test specimens, it is desirable to use as many different moulds as possible, for the purposes discussed in the preceding paragraph. (d) by the above combination of samples, the coverage of all uncertainty parameters shown in fig.1 is achieved, except for the possible systematic errors of the uniaxial compression device and the variation/deviation of the cement and aggregate characteristics. (e) a statistical analysis of the test results for the compressive strength of the specimens, can be used to check whether such short deviations in the determination of the curing age and the cement content can influence the result. (f) applying the regression curve from eq.(1) and eqs.(2-4) for all the experimental results yields the uncertainty of the compression strength tests corresponding to the range of concrete compositions as per values selected in step a). (g) according to iso guide for the expression of uncertainty in measurements [13], if the procedure is repeated under the same conditions and the result is obtained as the mean value of n samples, the type a estimated standard uncertainty may be divided by √n. when conducting this uncertainty estimation, the standard uncertainty urs attributed to load cell reference indications (i.e. the load cell used as a reference standard, rs, for the calibration of the test apparatus) shall be added, according to the law for error propagation. in eq.(9), urs is added after been divided by 2, as an example of how the procedure should be applied when urs is referred with a coverage factor k = 2. thus, an expanded uncertainty interval with a coverage factor k = 2 is given in eq.(9): 2 ∙ ∙√ (9) according to eq.(9), a laboratory that has performed an experiment like experiment i proposed in this study, estimating utypea, for testing according to en 12390-3 on a single concrete specimen, at 17%, using a calibration procedure for the test s. gavela et alii, frattura ed integrità strutturale, 50 (2019) 383-394; doi: 10.3221/igf-esis.50.32 392 apparatus that is characterized by a reference standard uncertainty of urs equal to 5%, and also performing the en 123903 testing method for n replicates of the sampled concrete, the corresponding expanded uncertainty is shown in table 2. the above estimations indicate that performing the en 12390-3 method for more than n=3 replicates of the sampled concrete provide a minor optimization on the uncertainty of the results that comes as the mean value of the n test results. n ucs [%] 1 18 3 11 4 10 6 9 10 7 table 2: indicative expanded uncertainty estimations. quality control testing compressive strength as per en 12390-3 method, according to en 12390-1 specimen definition, involves a great number of significant uncertainty parameters. building an experiment that would be able to demonstrate accurately the effect of each parameter to the shape of the “vertical” distribution of the measurement results (e.g. see figs.2,3) would demand so many combinations that would lead to a requirement for hundreds of specimens. lack of homogeneity of specimens is one parameter that could cause strong effects to the shape of measurement results distribution, even when a statistical model is proven to fit them well. for instance, in fig.2b, the greater dispersion in results shown for ccs equal to 300 & 360 kg/m3 could be attributed to an optimized (for such mixes) workability of mixes with cc equal to 330 kg/m3. skewness and kurtosis of the model residuals distribution as compared to the gaussian could be a criterion for assessing whether the experiment results have been totally derailed. exclusion of outlying values should be addressed only in extreme cases as a negative skewness of the measurement results distribution, i.e. there are more extreme cases to the lower values as compared to the mean rather than to the higher values, could be normally explained. the reason for that could be the fact that for a given mix composition, there not a mechanism to produce an extremely high compressive strength performance for a corresponding specimen. on the other hand, lack of homogeneity occurs due to purely random reasons (e.g. a small spot inside the specimen’s matrix where the constituents failed to be mixed properly) leading the specimen to fail during the compressive strength at relatively low compressive load. in any case, a test for outliers could be also performed, i.e., based on the 99% prediction intervals of the cs to w/c linear correlation. this is achieved by substituting the t95%,n-2 statistic in eq.(6) by t99%,n-2. this decision rule was applied at this study leading to the exclusion of three measurement results of experiment i that where lying outside the 99% prediction intervals for the linear correlation presented in fig.2a. outlier analysis should be stricter in the case of the multifactorial model of experiment ii, as this is its essential use. depart from using eq.(1) in order to perform a sensitivity analysis on the effect of c/w and curing age, it could be also used as a baseline for identifying outlying results when compressive strength tests are performed routinely on specimens coming from concrete compositions with the same characteristics as those used to build that baseline. the decision rule for the identification of outliers could be the expanded uncertainty, with a coverage factor equal to 3, for the results provided when eq.(1) is used. conclusions he findings of the present study can be shortly summarized as follows: the mean compressive strength produced as a result of testing according to en 12390-3 can be estimated by a sigmoidal-by-time multifactorial regression function incorporating both the water to cement ratio and curing age parameters. the use of this multifactorial function provides the opportunity to assess whether the compressive strength of the tested synthesis has a significant trend to increase after the nominal curing age of 28-days. the sensitivity coefficient of compressive strength as related to water to cement ratio is a function of curing age, specifically the relation of compressive strength with water to cement ratio is well represented by a line for which the slope t s. gavela et alii, frattura ed integrità strutturale, 50 (2019) 383-394; doi: 10.3221/igf-esis.50.32 393 changes in a sigmoidal relation with curing age. as related to curing age, this coefficient is also changing by time. at a curing age of 28 days it is expected to be non-significant. so, deviations in the order of a few days from the definition of 28 days do not affect significantly the compressive strength test result. the sensitivity on the effect of water to cement ratio and curing age uncertainty is minor as compared to the combined uncertainty of the test result at 28 days. the results of this study are useful for a laboratory seeking accreditation on the method of en 12390 series. if the laboratory decides to follow a type a estimation for the most of the uncertainty parameters, it is only needed to reproduce experiment i as a standardized procedure, using specimens that comply with the characteristics of concrete compositions that this specific laboratory is called to test according to en 12390-3. then this laboratory would gain an estimation of precision under partial reproducibility conditions. reproducing experiment ii would provide the laboratory, an additional opportunity to further evaluate the contribution of w/c and curing age parameters on a sensitivity analysis basis. as the laboratory repeats tests according to en 12390 using the same apparatus, the same operators, for specimens with similar characteristics and for compositions falling within the range covered by the experiment, then the result of this type an uncertainty estimation can be used repeatedly. in the estimation resulting from n such identical samples, the uncertainty parameter due to the systematic errors of the calibration of the test set should always be added. it is estimated that in any of its applications, this method for a type a uncertainty estimating for a test specimen being tested according to en 12390 will yield levels of uncertainty significantly greater than the expected repeatability of the device used, such as, for example, of 17% calculated in this paper. the study could be further extended by proper experiments on a multifactorial sigmoidal curve incorporating also other significant parameters such as the curing temperature, the aggregates characteristics and the type of cement. nomenclature cs(w/c,t) concrete specimen compressive strength as a function of curing age t and w/c [mpa] csref compressive strength reference value for specific curing age t as a function of w/c [mpa] csinf concrete specimen compressive strength at infinite time as a function of w/c [mpa] w/c concrete specimen water-to-cement ratio [-] cc cement content for a specific concrete composition [kg/m3] t curing age of the concrete specimen [days] p(t) proportion of the final value, csinf, at curing age t for a specific w/c value[-] τ regression (shape) parameter of the sigmoidal curve related to curing age [days] n regression (shape) parameter of the sigmoidal curve [-] c0 regression parameter (intercept) related to the estimation of the reference value csref [mpa] c1 regression parameter (slope factor) related to the estimation of the final value csref [mpa] cx sensitivity coefficient of a multifactorial function for the independent variable x [mpa/units of x] references [1] papadakos, g.n., karangelos, d.j., rouni, p.k., petropoulos, n.p., anagnostakis, m.i., hinis, e.p., simopoulos, s.e. (1892). uncertainty in soil radioactivity measurement due to sampling definitional errors, metrologia 2016: 6th national biannual conference in metrology, athens, greece [in greek]. [2] féret, r.. on the compactness of the mortars, annales des ponts et chaussées, 7(4), pp. 5-164. [3] abrams, d.a. (1927). water-cement ratio as a basis of concrete quality, journal of american concrete institute, 23, pp. 452-457. [4] freiesleben hansen, p., pedersen, j. (1985). curing of concrete structures, ceb information bulletin, 166, 42. [5] carino, n.j. and lew, h.s. (1983). temperature effects on strength-maturity relations of mortar, journal of the american concrete institute, proceedings, 80(3), pp. 177-182. [6] yeh, c. (2006). generalization of strength versus water–cementitious ratio relationship to age, cement and concrete research, 36, pp. 1865–1873. doi: 10.1016/j.cemconres.2006.05.013 [7] metwally abd allah, a. (2014). compressive strength prediction of portland cement concrete with age using a new model, hbrc journal, 10(2), pp.145–155. doi: 10.1016/j.hbrcj.2013.09.005 [8] gavela, s., nikoloutsopoulos, n., papadakos, g., passa, d., sotiropoulou, a. (2018). multifactorial experimental analysis of concrete compressive strength as a function of time and water-to-cement ratio, 1st international conference of the greek society of experimental mechanics of materials, structural integrity procedia 10 (2018) 135–140. s. gavela et alii, frattura ed integrità strutturale, 50 (2019) 383-394; doi: 10.3221/igf-esis.50.32 394 [9] gavela, s., papadakos g., kaselouri-rigopoulou v. (2017). a suggestion for standardizing a traceable process for the determination of the mechanical properties of concrete containing thermoplastic polymers as aggregates, in: thermoplastic composites–emerging technology, uses and prospects, materials science and technologies nova publications book, isbn: 978-1-53610-727-2 [10] sotiropoulou, a., gavela, s., nikoloutsopoulos, n., passa, d., papadakos, g. (2017). experimental study of wood shaving addition in mortar and statistical modeling on selected effects, journal of the mechanical behavior of materials, 26, pp. 1-2. doi: 10.1515/jmbm-2017-0013 [11] eurachem/citac guide (qac 2016). guide to quality in analytical chemistry – an aid to accreditation, 3rd edition. [12] gavela, s., papadakos. g., nikoloutsopoulos, n., passa, d., sotiropoulou, a. (2018). determination of type a uncertainty for the concrete compressive strength test, 18th panellenic concrete conference, athens [in greek]. [13] simopoulos, s.e. (2003). technical measurements, handouts for the corresponding lesson ntua school of mechanical engineering, athens. available at: http://nuclear.ntua.gr. 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can be opened with acrobat and adobe reader 5.0 and later.) >> /namespace [ (adobe) (common) (1.0) ] /othernamespaces [ << /asreaderspreads false /cropimagestoframes true /errorcontrol /warnandcontinue /flattenerignorespreadoverrides false /includeguidesgrids false /includenonprinting false /includeslug false /namespace [ (adobe) (indesign) (4.0) ] /omitplacedbitmaps false /omitplacedeps false /omitplacedpdf false /simulateoverprint /legacy >> << /addbleedmarks false /addcolorbars false /addcropmarks false /addpageinfo false /addregmarks false /convertcolors /converttocmyk /destinationprofilename () /destinationprofileselector /documentcmyk /downsample16bitimages true /flattenerpreset << /presetselector /mediumresolution >> /formelements false /generatestructure false /includebookmarks false /includehyperlinks false /includeinteractive false /includelayers false /includeprofiles false /multimediahandling /useobjectsettings /namespace [ (adobe) (creativesuite) (2.0) ] /pdfxoutputintentprofileselector /documentcmyk /preserveediting true /untaggedcmykhandling /leaveuntagged /untaggedrgbhandling /usedocumentprofile /usedocumentbleed false >> ] >> setdistillerparams << /hwresolution [2400 2400] /pagesize [612.000 792.000] >> setpagedevice microsoft word numero_51_art_19_2651 a. a. lakhdari et alii, frattura ed integrità strutturale, 51 (2020) 236-253; doi: 10.3221/igf-esis.51.19 236 finite element modeling of the behavior of a hollow cylinder in a hydrogen-containing environment a. a. lakhdari université des sciences et de la technologie d'oran mohamed boudiaf, algeria amina.lakhdari@univ-usto.dz, https://orcid.org/0000-0003-0627-0194 s.a. bubnov ryazan state radio engineering university, russia serbubnov@inbox.ru, https://orcid.org/0000-0002-0274-8341 a. seddak université des sciences et de la technologie d'oran mohamed boudiaf, algeria sed_dz@yahoo.fr, https://orcid.org/0000-0003-4539-8350 i. i. ovchinnikov, i. g. ovchinnikov saratov state technical university gagarin y.a., russia bridgeart@mail.ru, http://orcid.org/0000-0001-8370-297x bridgesar@mail.ru, https://ordic.org/0000-0003-0617-3132 abstract. the two main research orientations on the problem of hydrogen embrittlement are examined: the study of fundamental principles and the disclosure of micromechanisms and the relation between hydrogen embrittlement and metal aging; the development of models and methods for predicting the kinetics of change in stress-strain state and for evaluating the longevity of structures subjected to hydrogen embrittlement. the state of the problem of hydrogen embrittlement of metals in the first direction is briefly analyzed. more attention is paid to the importance of predicting the behavior of charged metal structures under the influence of hydrogen embrittlement. we then examine the use of finite element modeling using the ansys software to compute the calculation analysis of a hollow cylinder subjected to internal and external pressures and hydrogen embrittlement. the cylinder material is nonlinear elastic and its properties depend on the hydrogen concentration at each point of the cylinder. consideration is given to the influence of the rigidity of the stress state and the hydrogen concentration on the diffusion kinetics of hydrogen in the cylinder body. the problem is solved in time steps. the distributions of the hydrogen concentration and the stresses for a quarter of the volume of the cylinder are given, as well as the citation: a. a. lakhdari, s.a. bubnov, a. seddak, i. i. ovchinnikov, i. g. ovchinnikov, finite element modeling of the behavior of a hollow cylinder in a hydrogen-containing environment, frattura ed integrità strutturale, 51 (2020) 236-253. received: 06.10.2019 accepted: 26.11.2019 published: 01.01.2020 copyright: © 2020 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. http://www.gruppofrattura.it/va/51/2651.mp4 a. a. lakhdari et alii, frattura ed integrità strutturale, 51 (2020) 236-253; doi: 10.3221/igf-esis.51.19 237 graphs of these values according to the thickness of the wall of the cylinder at different times. it is shown that the ansys software package adapted to the resolution of such problems can model the behavior of different structures in a hydrogencontaining environment, taking into account the effects caused by both the influence of hydrogen on mechanical properties of the material and by the stress state of the structures, as well as by the influence of the stress state on the interaction kinetics of hydrogen with the structures. keywords. hydrogen embrittlement; hollow cylinder; physical nonlinearity; hydrogen effect; finite element modeling. introduction he influence of hydrogen on the mechanical properties of structural material is a topical problem, because in recent times hydrogen is widely used in various industrial fields. hydrogen has a destructive effect on materials and structures at elevated temperatures and pressures, as well as at normal temperatures known as conventionally low temperatures [1-6]. at the present time, the term "embrittlement by hydrogen" is understood to include all the detrimental influence of hydrogen on the properties of materials. hydrogen embrittlement (he) is a direct consequence of a critical local hydrogen concentration in a metallic material. there are two main mechanisms of hydrogen-assisted rupture [7-9]: hede (hydrogen-enhanced decohesion); help (hydrogen-enhanced localised plasticity). the hypothesis of the hede mechanism is based on the favoring of the formation of microcracks following the reduction of the cohesion of the metal network, that is to say on the weakening of the inter-atomic bonds, following a high concentration of hydrogen in crack tip. in contrast, the help mechanism is based on the ductile nature of hydrogen assisted rupture. the help mechanism involves hydrogen-plasticity interactions of an elastic nature. the help model represents variations in crack tip plasticity and the hede model explains the speed of propagation of microcracks. there is also another adsorption induced dislocation emission (aide) model, which suggests, as with the hede mechanism, that hydrogen embrittlement is due to the weakening of inter-atomic bonds. as is known, hydrogen interacts differently with metals, depending on the temperature and pressure exerted on the structure. the introduction of hydrogen into metals and alloys can take place by one of two qualitatively different mechanisms [10]: 1.as a result of low temperature electrochemical processes with the participation of hydrogen ions, which are reduced and absorbed by steel. at low temperatures (i.e. ordinary temperatures), hydrogenation of the metal occurs, resulting in embrittlement by hydrogen and modification of the mechanical properties of the metal. this process is often called low temperature hydrogen embrittlement. 2. from a hydrogenated gaseous medium, at temperatures (above 200°c) and high pressures, as a result of thermal dissociation of hydrogen molecules, forming atomic hydrogen absorbed by steel, which interacts with carbides. high temperature hydrogen corrosion occurs which destroys the material of the structural elements. many studies have been devoted to the problem of high temperature hydrogen corrosion of metal structures [7-10]. this process is called high temperature hydrogen corrosion. according to the work [11], there are two main lines of research on low-temperature hydrogen embrittlement: a) study of the fundamentals of hydrogen embrittlement processes ; b) development of deformation models and estimation of the longevity of structural elements interacting with hydrogen. the first axis has been studied and analyzed in sufficient detail in many studies and it has been found that the processes of hydrogen embrittlement and degradation of the mechanical properties of pipeline materials were not sufficiently studied [12-16]. t a. a. lakhdari et alii, frattura ed integrità strutturale, 51 (2020) 236-253; doi: 10.3221/igf-esis.51.19 238 the development of deformation models and the evaluation of the longevity of structural elements subjected to hydrogen embrittlement have been the subject of several studies [11], and in this work the finite difference method was generally used to calculate the structures. in the work [17], the process of hydrogenation and deformation of a hollow cylinder was studied, taking into account the effect of the stress state on the hydrogen saturation kinetics of the structure. in this work, we examine finite element modeling of the behavior of a long hollow cylinder under hydrogenation conditions, taking into account the effect and concentration of hydrogen as well as the rigidity of the flow diagram state of stress on the kinetics of penetration of hydrogen into the cylinder. low temperature hydrogen embrittlement t is observed at temperatures below 200°c (-20 to 200°c), and in this case, the source of hydrogen is either hydrogen itself, or hydrogen is a by-product in some technological processes, so hydrogen enters the metal simply under pressure. the effect of hydrogen at low temperature is distinguished by the penetration of hydrogen by diffusion in the elements of metal structures under constraints or not. in addition, the hydrogen penetrates intensively in the zones under traction, and much less in the zones under compression. thus, it accumulates and after reaching a certain concentration, it causes a change in the mechanical properties of the material of the structure, depending on its concentration. for a low concentration of hydrogen, there is practically no change in the mechanical properties. but by reaching a critical concentration level, the hydrogen causes an intense degradation of the properties, and for a maximum concentration (saturation limit), the change of the mechanical properties is slowed down, although the hydrogen saturation of the material continues [17, 18]. in the structures under stress and subjected to a hydrogenation at low temperature, there is a more intense variation of the mechanical properties of the material in the zones under traction than in the other zones under compression. the non-uniform variation of the mechanical properties causes a redistribution of the stress field, which in turn influences the distribution of the hydrogen concentration. the redistribution of the stresses and the hydrogen field in the mass of the structural element will remain unstable as long as the state of the structure is not stabilized. during the low temperature hydrogenation, a physico-chemical interaction of the steel with the hydrogen takes place, leading to an irreversible change of the mechanical properties. this is mainly due to the destruction of the carbide component. this physico-chemical phenomenon is called hydrogen corrosion of steel. hydrogen corrosion develops in carbon steels after long operation at high temperature and pressure in an environment containing hydrogen. at the base of the mechanism of hydrogen corrosion is the interaction of hydrogen with carbon with the formation of methane. this reaction begins with the decarburization of the surface and the formation of microcracks, which progressively propagate in the metal, reducing its strength and plasticity. hydrogen embrittlement of metal structures is closely related to their microstructure, and in particular to the processes of segregation and diffusion occurring at interfaces and defects. formulation of the problem he behavioral model of a long hollow cylinder under low temperature hydrogen embrittlement conditions is examined, in which hydrogen, without chemical interaction with the metal, penetrates into the volume of the structural element and accumulates there. it is accepted that the penetration of hydrogen takes place by the diffusion mechanism. in this case, as the experimental data show, the hydrogen does not penetrate equally in the different zones of the structural element in the zones where the compressive stresses predominate, the hydrogen penetrates more slowly, in the zones where tensile stresses are predominant, hydrogen penetrates faster. thus, we have a medium whose diffusion characteristics depend on the state of stress [17, 18]. also according to experimental data, the diffusion characteristics of the cylinder material depend on the hydrogen concentration. therefore, it is further assumed that the diffusion coefficient of hydrogen in structure d (c, s) depends on the rigidity of the state of stress s and the hydrogen concentration c:    0  , 1d c s d c s     (1) i t a. a. lakhdari et alii, frattura ed integrità strutturale, 51 (2020) 236-253; doi: 10.3221/igf-esis.51.19 239 where: d diffusion coefficient, without taking into account the effect of hydrogen in not charged structure;   and   coefficients to be determined based on experimental data; c hydrogen concentration; s parameter, characterizing the rigidity of the state of stress schema, with: s = σо / σi (2) where: σо mean stress; σi intensity of the constraints. according to formula (1), with increasing hydrogen concentration, the diffusion coefficient also increases. the s parameter takes negative values, if the compression components predominate in the constraint state schema. in this case, the diffusion coefficient decreases. on the other hand, with a predominance of traction components, the parameter s takes positive values, which leads to an increase in the diffusion coefficient. we consider that the structural element consists of a nonlinear elastic material whose deformation diagram is approximated by the function: m i i i  a b      (3) where: a, b and m known coefficients; εi intensity of deformations. to take into account the influence of hydrogen on the deformation diagram, by analogy with [16, 17], we use an influence function θ (c, s):  m-1mi i i  ,a b c s        (4) where:      0 0 0 1       ,      ba then s s c s exp k c s s then s s           in these formulas: 0  s a threshold value of parameter s, to which hydrogen does not affect the material deformation diagram; k, a, b known coefficients. the modeling work involves analyzing the redistribution of stresses in the volume of a structural element as a result of low-temperature hydrogen corrosion, as well as identifying the most dangerous modes of operation. implementation of the model in the ansys finite element software package. o solve this problem, we chose the ansys software implementing the finite element method (fem) [19-22 ]. the idea of the approach is that in ansys, each finite element (ef) can define its own properties. for example, when solving a structural problem, each finite element can be assigned an individual elasticity modulus, a transverse strain coefficient or points of the strain diagram. with the adpl language, built into ansys, we have written a number of macros, which solved this problem. all model parameters are conventionally divided into groups: the geometrical parameters of the hollow cylinder (inner and outer radii, length); the loading parameters of the structural element (internal and external pressures, hydrogen concentrations on the internal and external surfaces, number of time steps); t a. a. lakhdari et alii, frattura ed integrità strutturale, 51 (2020) 236-253; doi: 10.3221/igf-esis.51.19 240 the parameters of the initial mechanical properties of the material (modulus of elasticity, transverse deformation coefficient, diffusion coefficient, density, stress diagram, etc.); the parameters of the finite element model which determine the quality of the mesh; the massive parameters, containing the mechanical properties of the material that vary in time and space. there are also massive-parameters for storing the results of calculations. in tab. 1, the names and dimensions of the massifs used are presented. name of the massif content dimension psy_func values of the function ψ(εi, c, s) for each fe at each time step _n el amount nu_func values of the function ν(εi, c, s) for each fe at each time step _n el amount teta_func values of the function θ(c, s) for each fe at each time step _n el amount strain_stress values of deformations and corresponding stresses under the influence of hydrogen _n el amount s_factor parameter values, characterizing the rigidity of the constraint state diagram for each ef at each time step _n el amount d_factor diffusion coefficient values for each fe at each time step _n el amount strain_int deformation intensity values for each fe at each time step _n el amount stress_int constraint intensity values for each fe at each time step _point el amount n  stress_avg values of the average stress for each fe at each time step _n el amount concentr hydrogen concentration values for each fe at each time step _n el amount table 1: names and dimensions used in mass calculations in tab. 1: n number of time steps needed to solve the problem; _el amount total number of finite elements of the model; point number of points by which the deformation diagram is constructed. the massive strain_stress is three-dimensional. it is therefore possible to save a deformation diagram for each fe at each time step. the solution of the problem is conveniently divided into several stages: step 1: construction of the geometric model of the structural element. at this stage, the construction of a geometric model of a fragment of the long hollow cylinder. the construction of the geometric model was carried out according to the bottom-up principle, that is to say, first, the key points are defined, and then the lines passing through these points are drawn. according to the lines, was built the axial section of the cylinder. then, by rotating the section around the oz axis, at a 90 degree angle, is built a volume cylinder fragment (in order to save the memory of the computer). the section could be rotated 360 degrees, to obtain the entire cylinder. for the construction of the geometric model, the cylindrical coordinate system was chosen. step 2: construction of the finite element model as is known, the use of an ordered mesh makes it possible to obtain more precise solutions, with respect to a disordered mesh. to build an ordered mesh, you have to prepare a model. for this, each line forming part of the volume must be a. a. lakhdari et alii, frattura ed integrità strutturale, 51 (2020) 236-253; doi: 10.3221/igf-esis.51.19 241 divided into a determined number of segments. for the axial, radial and angular directions, the number of segments is given as parameters n_axis, n_tang and n_thickness. by modifying the values of these parameters, it is possible to easily enlarge or refine the mesh of finite elements in the whole of the structural element. when applying the mesh of finite elements, it is important to have on several thicknesses of the wall of the cylinder (not less than 10), because as a result of the influence of the hydrogenated medium will have changes in the mechanical properties, including the thickness of the cylinder. in this case, follow the form ef. elements that are too thin and elongated may give a greater error. in case of gross violation of the geometry of the finite element, ansys will issue a warning. that is why, by increasing the number of elements according to the thickness, it is desirable to increase it and according to other directions. to solve the problem, it took three types of finite element from the ansys library. for the diffusion problem, was chosen element solid239, for the structural problem solid95, and for the mesh of finite elements mesh200. all element types have a modification of 20 nodes (hexahedra), so changing the element type to solve the corresponding problem does not add any difficulties all the nodes of the finite element model remain in place. the finite element solid95 was chosen because it supports the material, for which a deformation diagram can be given. at present, this type of element is considered obsolete, but it is suitable for the resolution of some problems. the number of points on the deformation diagram must not exceed 100. step 3: load application and problem resolution at this point, the initial conditions and limits are defined and the problem is solved. to construct the initial deformation diagram (before the effect of hydrogen, θ (c, s) =1), we need the values of stress strain intensities, which will calculate the stress intensities according to the equation (4). this is why, first of all, the problem of blade is solved for a hollow cylinder in linearly elastic material for the pressures (external and internal), which we will use later in calculations under the action of hydrogen. the initial strain diagram is shown in fig. 1. figure 1: initial diagram of material deformation the solution of the problem occurs according to the following algorithm: 1. define the boundary conditions and determine the initial stress-strain state of the structural element. determine the value of the s parameter for each finite element. 2. define the boundary conditions for the diffusion equation and determine the initial value of the hydrogen c concentration for each finite element. 3. perform a new calculation: the diffusion coefficient d for each finite element according to relation (1); points of the deformation diagram for each finite element according to relation (4). 4. definite the boundary conditions corresponding to a given time step for the diffusion equation and its resolution with new values of the diffusion coefficient for each finite element. 5. define the boundary conditions corresponding to a given time step and determine the new stress-strain state and the new values of the s parameter for each finite element. a. a. lakhdari et alii, frattura ed integrità strutturale, 51 (2020) 236-253; doi: 10.3221/igf-esis.51.19 242 6. incremental time step. 7. repeat steps 3-6 until the destruction of the structural element. fig. 2 shows the deformation diagram, constructed taking into account the effects of low temperature hydrogen. step 4: results analysis. figure 2: initial deformation diagram (col2) and modified by the influence of hydrogen (col1). calculation and analysis of the results alculations were made for a hollow cylinder with the parameters: inner radius of 0.3 m; outer radius of 0.5 m; cylinder length of 3.5 m. the characteristics of the material: modulus of elasticity e=3.0e10; transverse deformation coefficient nu=0.2; thermal conductivity coefficient alpha=1.4e-5 ; density of the material dens=7659 ; coefficients of the function of approximation of the deformation diagram: a0=3.0e10, b0=2.0e11. the modulus of elasticity, the parameters of the strain diagram and all the constraints on the figures are measured in pa (pascal), the time is measured in hours. tab. 2 shows the different loading cases of the hollow cylinder. № loading in , mpаp out , мpаp 3 in ,1/ mc 3 out ,1/ mc 1. 0 20 3.2e-4 3.2e-4 2. 0 20 7.2e-4 1.5e-4 3. 0 30 7.2e-4 1.5e-4 4. 20 11 0.5 4 0.00005e t   3.2e-4 table 2: loading cases and effects of hydrogen loading №1. the hollow cylinder is under external pressure pout; the concentration field of the hydrogen is homogeneous. the concentration field has the form shown in fig. 3, and it does not change over time. the intensity of the constraints is shown in fig. 4. the radial, tangential and axial stresses at time t=10 are shown in figs 5, 6, 7. fig. 8 shows the stress intensity curves sint, axial stresses sz, radial and tangential sx and sy according to the thickness of the wall of the cylinder. c a. a. lakhdari et alii, frattura ed integrità strutturale, 51 (2020) 236-253; doi: 10.3221/igf-esis.51.19 243 figure 3: concentration field of hydrogen. figure 4: intensity of constraints at the moment   10.t  figure 5: radial constraints at the moment   10t  . a. a. lakhdari et alii, frattura ed integrità strutturale, 51 (2020) 236-253; doi: 10.3221/igf-esis.51.19 244 figure 6: tangential constraints at the moment   10. t  figure 7: axial constraints at the moment   10t  . figure 8: stress curves according to the thickness at the moment   10.t  a. a. lakhdari et alii, frattura ed integrità strutturale, 51 (2020) 236-253; doi: 10.3221/igf-esis.51.19 245 calculations show that there is no redistribution of stresses because the hydrogen concentration does not change in both time and volume of the structural element. as a result, hydrogen has virtually no effect on the stress state of the structural element. loading №2. the hollow cylinder is under external pressure outp 20 мpа , the internal pressure is equal to 0. the hydrogen concentration on the inner and outer surfaces is kept constant, but with different values. the concentration field of hydrogen is shown in fig. 9. the intensity of the stresses is shown in fig. 10. the radial, tangential and axial stresses at time t = 10 are shown in figs 11, 12.13. figure 9: concentration field of hydrogen. figure 10: intensity of constraints at the moment   10.t  in fig. 14, the stress intensity curves sint, the axial stresses sz, radial and tangential stresses sx and sy are presented according to the thickness of the wall of the cylinder at time t =10. note that the deformation pattern does not change over time; however, it is individual for each finite element due to the fact that the concentration field is not uniformly distributed in the volume of the structural element. the graphs show a change in the character of the stress curves. the redistribution of the tangential stresses and, consequently, of the stress intensities is particularly remarkable. loading №3. the loading is similar to the load №2, only the external pressure is outp 30  mpa. the concentration field is stationary and is shown in fig. 15. the intensity of the stresses is shown in fig. 16. the radial, tangential and axial stresses at time t =18 are presented in figs. 17, 18, 19. in fig. 20, the stress intensity curves sint, the axial stresses sz, radial and tangential stresses sx and sy are presented according to the thickness of the wall of the cylinder at time t =18. a. a. lakhdari et alii, frattura ed integrità strutturale, 51 (2020) 236-253; doi: 10.3221/igf-esis.51.19 246 figure 11: radial constraints at the moment 10. t  figure 12: tangential constraints at the moment   10t  .   figure 13: axial constraints at the moment   10t  .   a. a. lakhdari et alii, frattura ed integrità strutturale, 51 (2020) 236-253; doi: 10.3221/igf-esis.51.19 247 figure 14: stress curves according to the thickness at the moment   10.t  figure 15: concentration field of hydrogen. figure 16: intensity of constraints at the moment   18t  . a. a. lakhdari et alii, frattura ed integrità strutturale, 51 (2020) 236-253; doi: 10.3221/igf-esis.51.19 248 figure 17: radial constraints at the moment 18t  . figure 18: tangential constraints at the moment 18t  . figure 19: axial constraints at the moment   18t  . a. a. lakhdari et alii, frattura ed integrità strutturale, 51 (2020) 236-253; doi: 10.3221/igf-esis.51.19 249 in this case, the redistribution of the constraints is also observed. loading №4. the hollow cylinder is subjected to the internal and external pressures inp and outp respectively, and in out p p , the concentration of hydrogen on the outer surface is constant, and on the inside it increases linearly with each time step from a certain initial value. as a result, we obtain a time-varying concentration field (figs. 21 and 22). the intensity of the stresses is shown in fig. 23. the radial, tangential and axial stresses at time t = 11 are presented in figs. 24, 25, and 26. there is also a redistribution of the constraints, and more intense than in the cases of loading previously envisaged. in fig. 27, the stress intensity curves sint, the axial stresses sz, radial and tangential stresses sx and sy are presented according to the thickness of the wall of the cylinder at time t =11. figure 20: stress curves according to the thickness at the moment   18t  . figure 21: concentration field of hydrogen at the moment   5t  . a. a. lakhdari et alii, frattura ed integrità strutturale, 51 (2020) 236-253; doi: 10.3221/igf-esis.51.19 250 figure 22: concentration field of hydrogen at the moment   11t  . figure 23: intensity of constraints at the moment 11t  . figure 24: radial constraints at the moment 11t  . a. a. lakhdari et alii, frattura ed integrità strutturale, 51 (2020) 236-253; doi: 10.3221/igf-esis.51.19 251 figure 25: tangential constraints at the moment 11t  . figure 26: axial constraints at the moment   11t  . figure 27: stress curves according to the thickness at the moment   11t  . a. a. lakhdari et alii, frattura ed integrità strutturale, 51 (2020) 236-253; doi: 10.3221/igf-esis.51.19 252 conclusions 1. the study showed that the use of the finite element software ansys allows numerical simulations of the changes in the hydrogen concentration field and the stress-strain state of a hollow cylinder, not only the action of hydrogen at high pressure and temperature, as has been as done in the work [16], but also when hollow cylinder interacts with hydrogen at low temperature. 2. adapted to the resolution of such problems, the ansys software package is used to model the behavior of different structures in a hydrogen-containing environment, taking into account the effects caused by both the influence of hydrogen on the mechanical properties of hydrogen material and stress state of structures, and considering the influence of state of stress on the kinetics of the interaction of hydrogen with structures. 3. the elaborate model of material behavior of structural elements in a hydrogenated medium takes into account the selective effect of low temperature hydrogen on the mechanical properties of materials. the selectivity is expressed as a function of the anisotropy induced by the hydrogen concentration and the rigidity of the stress state scheme. 4. the proposed model takes into account the influence of the type and the level of the stress state of the material on the kinetics of hydrogen penetration into the material by the dependence of the diffusion coefficient and the absorption limit of the material. hydrogen. 5.it should be noted that the established relationships fairly adequately describe the behavior of the tube under the combined action of charge and hydrogenation, while taking into account the destructive action of hydrogen. 6. the numerical simulation shows that the most dangerous case is the case of the simultaneous action of the charge and the hydrogen on the inner surface of the wall of the tube, because in this case the combination of the action of the stresses of traction and hydrogen leads to an intensive degradation of the tube material. 7.it should be noted that, contrary to the case of hydrogen at high pressure and temperature, the penetration of hydrogen occurs through the mechanism of activated diffusion and that the kinetics of hydrogen penetration depends on the rigidity of the scheme of the state of constraint. since the state of stress changes with time under the influence of hydrogen entering the structure, the kinetics of hydrogen penetration into the structural element also changes over time. 8. hydrogen embrittlement of metal structures is closely related to their microstructure, and in particular to the processes of segregation and diffusion occurring at interfaces and defects. references [1] lynch, s. (2019). discussion of some recent literature on hydrogen-embrittlement mechanisms: addressing common misunderstandings, corrosion reviews; 37(5), pp. 377-395. doi: 10.1515/corrrev-2019-0017. [2] djukic, m.b., bakic, g.m., sijacki zeravcic, v., sedmak, a., rajicic, b. (2016). hydrogen embrittlement of industrial components: prediction, prevention, and models, corrosion; 72 (7), pp. 943-961. doi: 10.5006/1958. [3] bueno, a., moreira, e., gomes, j. (2014). evaluation of stress corrosion cracking and hydrogen embrittlement in an api grade steel, engineering failure analysis; 36, pp. 423–431. doi: 10.1016/j.engfailanal.2013.11.012. [4] serebrinsky, s., carter, e.a., ortiza, m. (2004). a quantum mechanically informed continuum model of hydrogen embrittlement, j. of the mechanics and physics of solids; 52 (10), pp. 2403 – 2430. doi: 10.1016/j.jmps.2004.02.010. [5] kolachev, b.a. (1999). hydrogen in metals and alloys, metal science and heat treatment; 41(3), pp. 93-100. doi: 10.1007/bf02467692. [6] woodtli, j., kieselbach, r. (2000). damage due to hydrogen embrittlement and stress corrosion cracking, eng. failure analysis; 7, pp. 427450. doi: 10.1016/s1350-6307(99)00033-3. [7] lynch, s. (2012). hydrogen embrittlement phenomena and mechanisms, corrosion reviews; 30(3-4), pp. 105–123. doi: 10.1515/corrrev-2012-0502. [8] may, l.m., dadfarnia, m., nagao, a., wang, s., sofronis, p. (2019). enumeration of the hydrogen-enhanced localized plasticity mechanism for hydrogen embrittlement in structural materials, acta materialia; 165, pp. 734-750. doi: doi.org/10.1016/j.actamat.2018.12.014. [9] djukic, m.b., bakic, g.m., zeravcic, v. s., sedmak, a., rajicic, b. (2019). the synergistic action and interplay of hydrogen embrittlement mechanisms in steels and iron: localized plasticity and decohesion, eng. fracture mechanics; 216, pp. 106-528. doi: 10.1016/j.engfracmech.2019.106528. a. a. lakhdari et alii, frattura ed integrità strutturale, 51 (2020) 236-253; doi: 10.3221/igf-esis.51.19 253 [10] djukic, m.b., sijacki zeravcic, v., bakic, g.m., sedmak, a., rajicic, b. (2015). hydrogen damage of steels: a case study and hydrogen embrittlement model, eng. failure analysis; 58 (2), pp. 485-498. doi: 10.1016/j.engfailanal.2015.05.017. [11] ovchinnikov, i.g. and khvalko, t.a. (2003). serviceability of structures under high-temperature hydrogen corrosion, ed. sarat. gos. tekhn. un-t. saratov, russia. [12] balueva, a. (2014). modeling of hydrogen embrittlement cracking in pipe-lines under high pressures, procedia materials science.; 3, pp. 1310-1315. doi: doi.org/10.1016/j.mspro.2014.06.212. [13] hardie, d., charles, e.a., lopez, a.h. (2006). hydrogen embrittlement of high strength pipeline steels; corrosion science. ; 48 (12), pp. 4378–4385. doi: 10.1016/j.corsci.2006.02.011. [14] novak, p., yuan, r., somerday, b.p., sofronis, p., ritchie, r.o. (2010). a statistical, physical-based, micro-mechanical model of hydrogen-induced intergranular fracture in steel, j. of mechanics and physics of solids; 58 (2), pp. 206– 226. doi: 10.1016/j.jmps.2009.10.005. [15] kim, n.h., oh, c.s., kim, y.j., yoon, ke, b., ma, y.w. (2012). hydrogen-assisted stress corrosion cracking simulation using the stress-modified fracture strain model, j. of mechanical science and technology; 26 (8), pp. 2631-2638. doi 10.1007/s12206-012-0642-x. [16] bubnov, a.a., bubnov, s.a. and ovchinnikov, i. i. (2011). modelling of stress state and fracture of thick-walled piping in hydrogen corrosion and heterogeneous thermal field, ed. goryachaya liniya –telekom. moscow, russia. [17] ovchinnikov, i.i. (2013). models of deformation and delayed destruction of materials in a hydrogen-containing environment, vestnik sstu; 2 (70), pp. 178-183. (russian) [18] ovchinnikov, i.i. (2013). modeling the behavior of a long hollow cylinder in a hydrogen-containing environment, the diffusion characteristics of which depend on the stressed state, vestnik sstu; 2 (70), pp. 183-191. (russian) [19] ansys element reference. ansys release 18.0. documentation inc., 2017. [20] ansys theory reference. ansys release 18.0. documentation inc., 2017. [21] ansys parametric design language guide. ansys release 18.0. documentation inc., 2017. 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can be opened with acrobat and adobe reader 5.0 and later.) >> /namespace [ (adobe) (common) (1.0) ] /othernamespaces [ << /asreaderspreads false /cropimagestoframes true /errorcontrol /warnandcontinue /flattenerignorespreadoverrides false /includeguidesgrids false /includenonprinting false /includeslug false /namespace [ (adobe) (indesign) (4.0) ] /omitplacedbitmaps false /omitplacedeps false /omitplacedpdf false /simulateoverprint /legacy >> << /addbleedmarks false /addcolorbars false /addcropmarks false /addpageinfo false /addregmarks false /convertcolors /converttocmyk /destinationprofilename () /destinationprofileselector /documentcmyk /downsample16bitimages true /flattenerpreset << /presetselector /mediumresolution >> /formelements false /generatestructure false /includebookmarks false /includehyperlinks false /includeinteractive false /includelayers false /includeprofiles false /multimediahandling /useobjectsettings /namespace [ (adobe) (creativesuite) (2.0) ] /pdfxoutputintentprofileselector /documentcmyk /preserveediting true /untaggedcmykhandling /leaveuntagged /untaggedrgbhandling /usedocumentprofile /usedocumentbleed false >> ] >> setdistillerparams << /hwresolution [2400 2400] /pagesize [612.000 792.000] >> setpagedevice microsoft word numero_31_art_6 j. lopes et alii, frattura ed integrità strutturale, 31 (2015) 67-79; doi: 10.3221/igf-esis.31.06 67 inter-laminar shear stress in hybrid cfrp/austenitic steel j. lopes, m. freitas icems and departamento de engenharia mecânica. instituto superior técnico. universidade de lisboa. av. rovisco pais 1049-001 lisboa. portugal joao.ribeiro.lopes@ist.utl.pt d. stefaniak dlr, institute of composite structures and adaptive systems, ottenbecker damm 12, 21684 stade, germany p.p. camanho idmec. pólo feup. rua dr. roberto frias. 4200-465 porto. portugal abstract. bolted joints are the most common solution for joining composite components in aerospace structures. critical structures such as wing to fuselage joints, or flight control surface fittings use bolted joining techniques. recent research concluded that higher bearing strengths in composite bolted joints can be achieved by a cfrp/ titanium hybrid lay-up in the vicinity of the bolted joint. the high costs of titanium motivate a similar research with the more cost competitive austenitic steel. an experimental program was performed in order to compare the apparent inter-laminar shear stress (ilss) of a cfrp reference beam with the ilss of hybrid cfrp/steel beams utilizing different surface treatments in the metallic ply. the apparent ilss was determined by short beam test, a three-point bending test. finite element models using cohesive elements in the cfrp/steel interface were built to simulate the short beam test in the reference beam and in the highest interlaminar shear stress hybrid beam. the main parameters for a fem simulation of inter laminar shear are the cohesive elements damage model and appropriate value for the critical energy release rate. the results show that hybrid cfrp/steel have a maximum ilss very similar to the ilss of the reference beam. hybrid cfrp/steel is a competitive solution when compared with the reference beam ilss. fem models were able to predict the maximum ilss in each type of beam. keywords. fracture; fatigue; durability; case studies; experimental techniques; numerical techniques. introduction omposite materials have been used in aerospace applications in the past four decades. their use has grown in the share of weight of aircrafts (from the very specific use in nose cones and radomes of the airbus a300 to the full barrel composite fuselage of the boeing 787) and also in complexity. the development of composite manufacturing has enabled the shift from rather simple shells and sandwich structures to full composite assemblies like elevators, horizontal and vertical tail planes, and the already mentioned full barrel composite fuselage. this shift from modular architecture to integral architecture [1] has had many advantages: it has reduced the number of components of an assembly and therefore the number of fasteners. it has simplified the manufacturing process by reducing the number c j. lopes et alii, frattura ed integrità strutturale, 31 (2015) 67-79; doi: 10.3221/igf-esis.31.06 68 of parts to manufacture and to assemble. a composite component, however complex, still needs to be assembled to other components. bolted joints are the most common joining technique between composite components. bolted joints offer the advantage of being capable of carrying large loads, are simple to install and to inspect. this type of joint is more challenging in composite structures than in metallic structures due to their low bearing strength, high notch sensitivity, brittle and anisotropic nature, and high dependence on composite configuration. the typical solution to joint composite parts is to do a thickness build-up in the vicinity of the bolted area. this solution leads to an increase in weight, therefore cost, and additional stresses caused by eccentricities. the research work of the german aerospace centre with other partners has demonstrated that a significant improvement in bearing load can be achieved by replacing some cfrp plies by metallic plies in the vicinity of the bolted area. fink and kolesnikov [2] demonstrated the suitability of hybrid cfrp/metal composites in experimental tests using cfrp and ti6al4v alloy. the inter-laminar shear stress was measured using the short beam test method in several conditions of temperature and humidity. bearing ultimate strength tests were also performed with different ratios of ti alloy contents. it was concluded that hybrid cfrp/ti has a high bearing strength, high shear strength, and high compression strength. also, the hybrid specimens have a low sensitivity to temperature and humidity. kolesnikov and fink [3] performed impact tests, bearing tests and dynamic tests in cfrp/ti6al-4v. the research concluded that compressive strength of hybrid material is higher than monolithic cfrp; the bearing tests using a three row bolted joint showed that cfrp/ti has a joint efficiency over 65% in the case of a 0º-on axis loading, and a satisfactory fatigue behaviour. camanho et al. [4] investigated the experimental and numerical response of bolted joints using a hybrid cfrp and ti– 15v–3cr–3sn–3al alloy with several percentages of ti content. the experimental results showed that the bearing strength increases with the increase of ti content, a hybrid joint with 50% titanium has a higher specific stiffness than the reference monolithic cfrp; the critical region in a hybrid joint is the bolt-bearing region and not the transition zone from hybrid to cfrp; the numerical models yielded good results in predicting the bearing strength of hybrid and monolithic composites. fink et al. [5] investigated the mechanical response and the manufacturability of hybrid cfrp/ti alloy in a spacecraft payload adaptor. using cfrp and ti–15v–3cr–3sn–3al the research concluded that the cfrp/metal hybridization had, among others, the advantages of high bearing, shear and pull-out strength, high specific bearing strength, and considerable weight savings. fink and camanho [6] performed inter-laminar shear stress by the use of the short beam method and experimental and numerical response of the bearing strength of a hybrid cfrp/ti alloy. this research concluded that hybrid bearing strength increase to a factor of 2.5 when compared with typical cfrp laminates. also it concluded for the feasibility and mechanical effectiveness of hybrid joints. all the previous works were done using titanium alloys as reinforcement material. however the use of steel was already considered as a potential alternative to titanium [5, 6]. titanium has the advantage of high specific strength, galvanic compatibility, and lower coefficient of thermal expansion (cte) than corrosion resisting steel. corrosion resisting steel has the advantage of higher stiffness, higher ultimate strength, excellent fatigue properties and much lower cost when compared with ti alloys. it has the disadvantage of having a higher cte producing a significant residual thermal stress. although these stresses are not addressed in the present work, stefaniak et. al could show that due to mechanical interaction, residual stresses in multi-layered fmls are lower than often assumed when only thermo-mechanical behavior is considered [7]. additionally, by modifications in the curing process, the “smart curing” [8], residual stresses can be lowered significantly. in this research the objective is to measure the inter-laminar shear stress in a hybrid cfrp/steel composite. this research comprises an experimental test program and a numerical simulation in a finite element commercial package. the test program is exposed in detail as well as the numerical simulations. the results of both the experiments and the simulations are presented and compared. experimental testing n experimental program on apparent inter-laminar shear stress (ilss) was determined by short beam three-point bending tests with two main objectives: i) to identify the most suitable surface treatment method for the metal foil in this particular fibre metal laminate; ii) to determine the required cohesive element parameters to simulate delamination failure. a j. lopes et alii, frattura ed integrità strutturale, 31 (2015) 67-79; doi: 10.3221/igf-esis.31.06 69 stainless steel 1.4310 (x10crni18-8) [9] is used due to the need of a high yield point of the metallic component and the galvanic corrosion compatibility between carbon and steel. the selected cfrp is 8552/as4 ud prepreg from hexcel with 134 g/m2, a widely used cfrp in the aerospace industry. the basic properties of these materials are given in tab. 1. material tensile stiffness e1 (gpa) tensile stiffness e2 (gpa) density ρ (g/cm3) steel 1.4310 [10] 178 178 7.9 cfrp 8552/as4 [11] 141 10 1.58 table 1: material properties. in order to assess the adhesion between the metal and cfrp two different lay-ups are used. the reference pure cfrp specimens consist of 16 layers ud [016] whereas for the hybrid specimens the steel layer is positioned as the centre layer [08/st/08]. to increase comparability, the steel foil is chosen to 0.05 mm, as thin as possible during treatment. these layups result in a laminate thickness of 1.98 mm for the reference beam and 2.03 mm for the hybrid beam. two plates per treatment method are manufactured and specimens are then cut by diamond sawing. cure temperature is 180ºc as per prepreg manufacturer’s recommendations. adhesion performance is evaluated by determination of the apparent inter-laminar shear strength by the short-beam method en iso 14130 [12] a three-point bending test. specimen length is 20±0.1 mm and width is 10±0.1 mm. fig. 1 shows the dimensions of the hybrid specimen in which the difference to the reference beam specimen is that the steel layer is absent in the reference beam. figure 1: dimensions of the short beam specimen. the testing length, the distance between supports, is 9.9±0.1 mm with a radius of 2 mm. the radius of the loading member is 5mm. a testing machine zwick 1476 with a maximum capacity of 100 kn was used. the displacement was measured with and lvdt placed in the movable part of the machine with a range of 49.5mm and accuracy below <0.1μm. fig. 2 shows a schematic representation of the short beam fixture. figure 2: schematic representation of the short beam fixture. j. lopes et alii, frattura ed integrità strutturale, 31 (2015) 67-79; doi: 10.3221/igf-esis.31.06 70 a standard surface treatment for stainless steel before adhesive joining is the ‘boeing sol-gel process’. following this process, the material is degreased and then deoxidized by using a wet or dry grit-blasting method. finally, an aqueous solgel system [13], a dilute solution of a stabilized alkoxy zirconium organometallic salt and an organosilane coupling agent, is applied. an adhesive coating is then applied to the treated surface to generate a durable bond [14]. this treatment is conducted in this work and regarded as a reference. the surface treatment process can be subdivided into surface preand post-treatment. the pre-treatments are further differentiated into mechanical, physical, chemical and electrochemical treatments. the aim of the surface post-treatment process is to increase adhesion with the help of a coupling agent and to conserve the surface activity achieved by the pretreatment. a surface treatment process always consists of a particular pre-treatment in combination with a particular posttreatment. as shown in fig. 3, the sol-gel system is used in each approach, but an additional epoxy primer is applied only on the reference ‘boeing sol-gel’-specimens. figure 3: schematic representation of the surface treatment process then different categories of pre-treatments for the steel foils are investigated. at first, grit-blasting is regarded and parameters as time, pressure, grit material and grit size are varied. after degreasing, the aqueous sol-gel is applied. as second category, vacuum blasting is examined, varying grit material as well as grit size. finally, sol-gel is applied. as pickling is the most prevalent chemical pre-treatment for stainless steel [15], different pickling processes were examined to replace mechanical treatment of the thin steel foils. specimens for the evaluation of the adhesion performance were fabricated using nitric-hydrofluoric and nitric-phosphoric-hydrofluoric acid as well as a nitrate-free solution consisting of hydrofluoric acid and hydrogen peroxide as oxidizing agent [16, 17]. acid concentrations and pickling durations were varied and the pre-treated metal foils were rinsed with deionized water before drying in an oven. after drying, the foils were also post-treated with the aqueous sol-gel system. foils are laminated with prepreg within one hour after treatment to prevent environmental influences. however, as the manufacturing process may be constricted by this limitation, for one vacuum blasting configuration the foils were stored one day at room temperature with 50% relative humidity after treatment before positioning in the lay-up. 600 specimens were tested in total, whereas is was ensured by a second manufacturing and testing loop that 10 valid test results are existent for the most promising surface treatment configurations of each category, vacuum blasting, grit blasting, pickling and boeing sol-gel process. specimens manufactured utilizing these configurations and pure cfrp specimens were then additionally tested at different conditions. dry specimens were tested at -55°c as well as 120°c and moisture saturated specimens were tested at room temperature. cure temperature is 180°c, therefore, comparing the hybrid specimens with pure cfrp-ud reference specimens it has to be considered that the curing shear stresses act on the same plane as the inter-laminar shear stresses. as curing temperature is above testing temperature, the differing coefficients of thermal expansion inevitably lead to residual stress in the laminate which can cause deformations. these inter-ply stresses may significantly lower the mechanical properties of the hybrid laminate, especially the residual inter-laminar shear strength. different investigations have been performed to reduce residual stresses in pure composite as well as in fibre metal laminates, utilizing modified curing processes, an additional clamping tool to reduce thermal mismatch or post-stretching to reduce residual stress level of an already cured laminate [7]. however, these approaches are regarded in research only and the measurement of the residual stress level is j. lopes et alii, frattura ed integrità strutturale, 31 (2015) 67-79; doi: 10.3221/igf-esis.31.06 71 still unsatisfactory. essentially, it has to be considered in the following investigations that these residual stresses increase with lower testing temperatures as the difference between manufacturing and testing temperature increases. numerical models numerical techniques in fracture modelling here are two main techniques used to model fracture onset and fracture propagation: vcct and czm also known as cohesive elements, or in some literature as interface elements. the vcct technique is based on the principle that when a crack extends for a small amount the energy released in the crack propagation is equal to the work necessary to close the crack. this concept was first introduced by rybicki and kanninen [18] and developed further by krueger [19]. in this technique the values of gi, gii, and giii are computed from the nodal forces and displacements obtained from the solution of the finite element model. vcct enables the calculation of these parameters in a single simulation. it does require however complex meshing techniques and an initial delamination. therefore vcct can predict crack propagation but not crack initiation. mendes [20, 21] examined the failure criteria for mixed mode delamination in glass/epoxy and cfrp/epoxy specimens. the purpose of an extensive program of tests was to determine the inter-laminar energy release rate of mode i, mode ii, mixed-mode i+ii, and mode iii. the tests were dcb, enf, mmb, and ect. mendes calculated the energy release rate analytically, through the beam theory, and numerically through the vcct technique. by comparing the experimental results with numerical simulations using vcct mendes concluded that the power law [22] criteria showed reasonable results in modes i+ii, b-k [23] criteria had better results when mode iii was present. b-k extended to mode iii as proposed by reader [24] seems more convincing. cohesive elements are a more recent technique than vcct. the concept of the cohesive elements is actual finite elements that are intended to model the resin layer between ply interfaces. cohesive elements are able to predict the onset and propagation of delamination without requiring pre-cracks. however, cohesive elements must be placed along all possible interfaces where delamination may occur. in the proposed method [25, 26] a softening law for mixed-mode delamination can be applied to any interaction criterion. the constitutive equation of the cohesive elements uses a single variable, the maximum relative displacement, to track the damage at the interface under general loading conditions. the material properties required to define the element constitutive equation are: i) the inter-laminar fracture toughness; ii) the penalty stiffness, iii) and the strengths. the b–k interaction law requires additionally a material parameter  that is determined from standard delamination tests [25]. these elements have zero thickness and typically are rectangular elements with two nodes at each vertex as shown in fig. 4. figure 4: zero thickness cohesive element. figure retrieved from [25]. ankersen and davies [27] discuss some advantages and limitations of the cohesive elements by comparing two different constitutive laws of the cohesive elements: the bi-linear law and the exponential law. according to this research both constitutive laws are identical in delamination prediction. exponential constitutive law is more appropriate to use with dynamic implicit solvers whereas the bi-linear constitutive law is more suited with explicit solvers. mesh size is also a critical parameter in the cohesive elements technique due to the high stress gradients ahead of the cohesive zone. however for a sufficiently refined mesh the results are mesh independent. the main characteristics of the two techniques are summarized in the tab. 2. in this research the numerical modelling is based on previous researches where cohesive elements were proposed and developed [25, 26, 28]. this is the main reason why the cohesive elements were used. t j. lopes et alii, frattura ed integrità strutturale, 31 (2015) 67-79; doi: 10.3221/igf-esis.31.06 72 vcct cohesive elements  requires nodal variables and topological information ahead and behind the crack front  requires remeshing for crack propagation  requires initial delamination  predicts propagation of existing delamination  does not need an onset delamination  predicts delamination initiation and propagation  requires a refined mesh  requires complex input parameters  computationally expensive table 2: summary of main features of vcct and cohesive elements techniques finite element model abaqus finite element code was used in all the numerical analysis in this work. two models were built. the reference beam with monolithic cfrp, and the hybrid beam with cfrp and the steel layer. the main feature of these models is the use of zero thickness cohesive elements. the geometrical model took advantage of the symmetries in the three-point bending test. only one half of the beam’s length was modelled applying a proper boundary condition in the mid span. the model has a unit width with appropriate symmetry boundary conditions on both faces parallel to the lengthwise direction of the beam (x-direction). the negligible poisson effect in the y-direction allows this simplification. fig. 5 shows the actual beam of 20mm x 10mm (represented in transparency) and the finite element geometric model 5mm x 1mm. figure 5: short beam (in translucent grey) and geometrical model of the beam (in solid grey) for finite element simulation. the reference beam was modelled with one layer of zero thickness cohesive elements in the neutral fibre and the hybrid beam was modelled with zero thickness cohesive elements in the interface between the cfrp and the steel. the models have 8 elements per thickness in the cfrp and 40 elements across length with a bias ratio of 4, i.e. 40th element in mid-span is 4 times smaller than the 1st element in the extreme of the beam. the largest element has 0.460mm in length and the smaller element has 0.115 mm in length. the fem model of the reference beam has:  640 cubic 8 node c3d8r elements with reduced integration: 320 elements for each half thickness.  40 coh3d8 zero thickness cohesive elements in the neutral fibre.  1478 nodes.  5400 dof’s. the fem model of the hybrid beam has:  680 cubic 8 node c3d8r elements with reduced integration: 320 elements for each half thickness plus 40 elements in the steel layer.  80 coh3d8 zero thickness cohesive elements: 40 elements on each cfrp/steel interface  1640 nodes.  5892 dof’s. fig. 6 shows the fem model of the hybrid beam in abaqus: j. lopes et alii, frattura ed integrità strutturale, 31 (2015) 67-79; doi: 10.3221/igf-esis.31.06 73 figure 6: model of the unit width hybrid beam loading member and support modelled as rigid bodies. the cohesive elements use the quadratic nominal stress criterion (quads) shown in eq. 1. 2 2 2 0 0 0 1n s t n s s t t t t t t                    (1) the variables nt , st , tt are the normal stress and the shear tensions on both directions respectively of the cohesive models. the variables 0nt , 0 st , 0 tt are the damage threshold values of the cohesive elements. the macaulay operator in the normal stress nt is used to ensure that the damage does not occur when 0nt  . the damage evolution of the cohesive elements uses the mixed mode criterion proposed by benzeggagh and kenane, the b-k criterion [23]. this criterion accounts for the variation of fracture toughness as function of the mode ratio. in order to match the experimental result with the numerical simulation several values of giic were tested as the dominant failure mode in this test is mode ii (tab. 3). in order to replicate the actual test, the numerical model has to include the contact interaction between the beam and the loading member and the beam and the support. a penalty formulation was established for the contact properties and interaction definition was set to surface to surface interaction. simulations with contact formulation are prone to severe discontinuous nonlinearities. therefore the entire displacement was divided by 10 equal steps of 0.1mm to reduce severe discontinuities in the solver. the accumulated effect of cohesive elements with damage model and damage evolution, and the contact formulation causes a very intense computational effort. some initial settings of the steps module, namely the tolerances of the line search control parameters and the time incrementation parameters had to be increased from their initial settings in order to enable the solver to reach a solution. results and analysis experimental results he apparent inter-laminar shear strength for the reference beam (monolithic cfrp) was calculated based on the load measured by the testing machine using eq. (2) [12]: 3 4 f b h     (2) where: f is the load in (n), b and h are the width and thickness of the specimens respectively (mm),  is the apparent inter-laminar shear strength (mpa). t j. lopes et alii, frattura ed integrità strutturale, 31 (2015) 67-79; doi: 10.3221/igf-esis.31.06 74 for hybrid beams however a modified version of eq. (2) is used to account for the different stiffness of the constituents in the laminate [3]:       2 2 23 3 3 4 3 4 metal cfrp f s t eb s t s t s t t e              (3) where: s and t are the specimen thickness and metal layer thickness in millimetres respectively metale and cfrpe are the elastic modulus of the metal and cfrp respectively in gpa. eq. (1) and (2) were used for every individual width and thickness of the specimens as they differ slightly from nominal dimensions due to manufacturing tolerances. tab. 3 presents the experimental results with the average maximum ilss for all types of beams and a comparison between the reference beam and the hybrid beams. the average maximum ilss is in the range of [125 mpa – 130 mpa] which corresponds to a maximum load of [3.4kn – 3.5 kn] types of beams ilss (mpa)  std ilss (mpa) hybrid referenceilss ilss (mpa) hybrid reference ilss ilss reference beam 130.03 1.40 vacuum blasting (one day storage) 129.87 3.76 -0.16 0.999 vacuum blasting 128.20 2.36 -1.83 0.986 grit blasting 126.11 5.00 -3.92 0.970 pickling 125.63 2.15 -4.4 0.966 table 3: ilss experimental results – comparison between reference beam and the hybrid beams with different surface treatments. fig. 7 shows the typical behaviour of reference and hybrid specimens: an almost linear elastic displacement, followed by a gradual yielding of the resin rich neutral fibre (in the case of the reference beam) or cfrp/metal interface (in the case of the hybrid beam), until the beam reaches its maximum load. failure occurs shortly after. the crack propagates in one of two ways: by a sudden and continuous propagation or by several steps due the heterogeneity of the resin. figure 7: plot of typical examples of reference beam and hybrid beam with vacuum blasting. j. lopes et alii, frattura ed integrità strutturale, 31 (2015) 67-79; doi: 10.3221/igf-esis.31.06 75 numerical results from the finite element model the displacement and the reaction force of the loading member were extracted. from these two data sets the apparent inter-laminar shear stress was calculated using eq. (2) and (3) for the reference beam and the hybrid beam respectively. tab. 4 presents the numerical results and compares them with the experimental results. in the upper part of the table is the average experimental ilss and the numerical ilss for several values of giic of the reference beam. similarly in the lower part of the table is the average ilss and the numerical ilss for several values of giic of the vacuum blasting tests. reference beam ilss (mpa) difference experimental 130.03 numerical giic =1.1 n.mm-1 132.90 2.2% giic =1.0 n. mm-1 123.70 4.9% giic =0.8 n. mm-1 110.10 15.3% giic =0.9 n. mm-1 101.40 22.0% hybrid beam ilss (mpa) difference experimental 128.20 numerical giic =1.0 n.mm-1 123.68 3.5% giic =1.1 n.mm-1 132.94 3.7% giic =0.9 n.mm-1 113.49 11.5% giic =0.8 n.mm-1 110.14 14.1% table 4: comparison between experimental average results and numerical results figure 8: reference beam. comparison between numerical and experimental results (specimen #4). figure 9: hybrid beam. comparison between numerical and experimental results (specimen #2). j. lopes et alii, frattura ed integrità strutturale, 31 (2015) 67-79; doi: 10.3221/igf-esis.31.06 76 fig. 8 and fig. 9 show the plots of several numerical simulations for several values of giic for the reference beam and the hybrid beam respectively. fig. 8 shows an initial linear trend followed by a slight decrease in slope. this decrease is the beginning of the yielding of the cohesive elements. the load increases at an apparently linear rate until it reaches its peak. after the peak there is a sudden drop in the apparent shear stress load indicating the unstable crack propagation. after the shear stress increases again. this increase is the result of the reaction of two half beams fully delaminated one above the other and it is no longer meaningful. in the case of the reference beam the solver is able to converge to a solution in every step. in the case of the hybrid beam after the peak shear stress the abaqus solver is unable to converge to a solution of its current step. this is due to the fact that in the case of an unstable crack propagation the kinetic energy associated with it is relevant and it’s not considered in an abaqus implicit analysis. however the maximum load is correctly calculated by the solver. one common feature of either the reference or hybrid beams is that the stiffness of the numerical simulation is higher than the stiffness of the experimental results. this discrepancy is analysed in the next section. discussion he numerical models predict a maximum ilss shear strength close to the experimental maximum ilss provided that the proper giic is set. the results predicted by the numerical models have a higher stiffness than the stiffness of the experimental tests. there are several factors that contribute for this discrepancy: i. in the experimental tests the displacement is measured by an lvdt above the specimen in the movable part of the testing machine while in the numerical simulation the displacement is measured directly in the loading member. the effect of the compliance of the testing machine is therefore expected; ii. there is an unavoidable initial slack in the experimental test that does not occur in the numerical simulation; iii. the testing machine has some elasticity that, however small, cannot be ignored. the first factor is considered as the most relevant. in these tests the measured displacement until failure is extremely low (≈ 0.45mm). it is possible that the lvdt may be unable to measure accurately the displacement in such a small range. there is also a small contribution of the initial slack of the testing fixtures. it is observed some irregular data in the beginning of the experimental tests plots. the third factor is the less significant. the maximum measured loads [3.4 kn – 3.5 kn] are far lower than the maximum capacity of the testing machine (100 kn). these accumulated factors, although in different weights, are responsible for the discrepancy in slope between the numerical and experimental curves. the experimental results show that the maximum ilss of the hybrid beams is very close to the ilss of the reference beam. vacuum blasting surface treatment is clearly the best in terms of hybrid ilss performance. the one day storage between surface treatment and composite manufacturing does not affect ilss performance. the remainder surface treatments are clearly less competitive. the numerical results show that with a proper adjustment of the critical energy release rate giic it is possible to predict accurately the maximum load (therefore the ilss) of both the reference and hybrid beams. the standard deviation of the ilss of the hybrid beams is considerably higher that the reference beam. it is also noted that the standard deviation of the treatment with one day storage is higher than the same treatment with no storage. however, it is unlikely that it will have an impact in actual aircraft design due to the conservative factor of safety of composite aircraft structures. the short beam test method was chosen due to the previous experiences in assessing ilss in hybrid composites [2],[6]. the small size of the specimens does not affect a purely experimental research where different specimens are compared and any eventual effect of the compliance of the testing machine has an identical impact in all results. however, it poses a greater difficulty when trying to replicate the test in a fem simulation because the eventual effect of the compliance of the testing machine is increased with specimens that have such a small displacement. it is suggested therefore that in a future research of inter-laminar shear stress by three-point bending the size of the specimens should be bigger than the size prescribed by en14130 in order to reduce the effect of the factors that induce uncertainty in this test. t j. lopes et alii, frattura ed integrità strutturale, 31 (2015) 67-79; doi: 10.3221/igf-esis.31.06 77 conclusions and future work ybrid cfrp/steel composites have a maximum ilss very close to the ilss of a reference beam. hybrid cfrp/steel composites are a competitive and cost effective alternative to cfrp/ti alloy. it has a similar maximum ilss while the cost of the austenitic steel is significantly lower than the cost of ti alloys. vacuum blasting is the surface treatment that withstands higher ilss from all the tested surface treatments. it is also simpler than pickling or grit blasting. the vacuum blasting treatment with one day storage has a maximum apparent ilss close to the reference beam (less 0.16 mpa). this shows that the one day storage between treatment and lay-up does not affect the shear stress capability. this is a very important advantage in terms of manufacturing process. the fem model is able to predict the maximum ilss of the hybrid cfrp/steel beam which is the main engineering parameter. the discrepancy between the measured displacement and the numerical displacement is not fully understood. although the available data suggests that it is due to the compliance of the testing machine, only a dedicated test program to determine the eventual compliance using dic technology [29] would definitely demonstrate the effect of the compliance the size of the specimens prescribed by en14130 is very small. this small size enhances the effect of the compliance of the testing machines. it is suggested therefore that in a future research of inter-laminar shear stress by three-point bending the size of the specimens should be bigger than the size prescribed by en14130 in order to reduce the effect of the factors that induce uncertainty in this test. the short beam tests have some shortcomings, particularly when comparing with numerical simulations. it involves contact formulation and the shear stress is an induced stress caused by transverse shear of the loading member. these disadvantages leads to a next step of the study of shear stress of hybrid cfrp/steel composites that is the single lap shear tests (sls). acknowledgements he first author’s research is supported by the research grant bd/51597/2010 provided by the portuguese foundation for science and technology. the support of the institute of composite structures and adaptive systems of the german aerospace centre in the manufacturing and testing of the specimens is acknowledged. acronyms and definitions cfrp – carbon fibre reinforced polymer cte – coefficient of thermal expansion czm – cohesive zone method dcb – double cantilever beam dic – digital image correlation ect – edge crack torsion enf – end notch flexure fem – finite element method ilss – inter-laminar shear stress lvdt – linear variable differential transformer mmb – mixed mode bending quads – quadratic nominal stress criterion sls – single lap shear vcct – virtual crack closure technique references [1] esd symposium committe, esd terms and definitions (version 12), massachussets institute of technology engineering systems division, (2001). h t j. lopes et alii, frattura ed integrità strutturale, 31 (2015) 67-79; doi: 10.3221/igf-esis.31.06 78 [2] fink, a., kolesnikov, b., hybrid titanium composite material improving composite structure coupling, in: spacecraft structures, materials and mechanical testing 2005, 581 (2005) 135. [3] kolesnikov, b., herbeck, l., fink, a., cfrp/titanium hybrid material for improving composite bolted joints, compos. struct., 83(4) (2008) 368–380. [4] camanho, p.p., fink, a., obst, a., pimenta, s.,hybrid titanium–cfrp laminates for high-performance bolted joints, compos. part appl. sci. manuf., 40(12) (2009) 1826–1837. [5] fink, a., camanho, p. p., andrés, j. m., pfeiffer, e., obst, a., hybrid cfrp/titanium bolted joints: performance assessment and application to a spacecraft payload adaptor, compos. sci. technol., 70(2) (2010) 305–317. [6] fink, a., camanho, p., reinforcement of composite bolted joints by means of local metal hybridization,composite joints and connections, pedro camanho and liyong tong, eds. woodhead publ., (2011). [7] stefaniak, d., kappel, e., kolotylo, m., huhne, c., experimental identification of sources and mechanisms inducing residual stresses in multi layered fiber-metal laminates, in: euro-hybrid 2014, pfh – private university of applied sciences, stade, germany, (2014). [8] kim, h. s., park, s. w., hwang, h. y., lee, d. g., effect of the smart cure cycle on the performance of the co-cured aluminum/composite hybrid shaft, in: thirteen. int. conf. compos. struct. iccs13, 75(1–4) (2006) 276–288. [9] lamineries matthey sa. stahl 1.4310. [10] de freitas, m., reis, l., li, b., comparative study on biaxial low-cycle fatigue behaviour of three structural steels, fatigue fract. eng. mater. struct., 29(12) (2006) 992–999. [11] marlett, k., hexcel 8552 im7 unidirectional prepreg 190 gsm & 35%rc qualification material property data report, faa, faa special project number sp4614wi-q, (2011). [12] en 14130 fibre-reinforced plastic composites determination of apparent interlaminar shear strength by short-beam method, (1998). [13] mazza, j.j., sol-gel technology for low-voc, nonchromated adhesive bonding applications serdp; project pp1113, task 1. storming media, (2004). [14] rider, a., williams, i., shum, e., mirabella, l., environmental durability trial of bonded composite repairs to metallic aircraft structure, dtic document, (2005). [15] covino, b. s., scalera, j. v., fabis, p. m., u. s. b. of mines, pickling of stainless steels–a review. united states dept. of the interior, bureau of mines, (1984). [16] stefaniak, d., kappel, e., kolesnikov, b., hühne, c., improving the mechanical performance of unidirectional cfrp by metal-hybridization, in: eccm15 15th european conference on composite materials, venice, italy, (2012). [17] narváez, l., cano, e., bastidas, j. m., effect of ferric ions in aisi 316l stainless steel pickling using an environmentally-friendly h2so4-hf-h2o2 mixture, mater. corros., 54(2) (2003) 84–87. [18] rybicki, e. f., kanninen, m. f., a finite element calculation of stress intensity factors by a modified crack closure integral, eng. fract. mech., 9(4) (1977) 931–938. [19] krueger, r., the virtual crack closure technique: history, approach and applications, nasa, nasa/cr-2002211628 icase report no. 2002-10, (2002). [20] marat-mendes, r., critérios de delaminação em materiais compósitos sob solicitações multiaxiais, phd thesis in mechanical engineering, universidade técnica de lisboa instituto superior técnico, lisboa, (2009). [21] marat-mendes, r. m., freitas, m. m., failure criteria for mixed mode delamination in glass fibre epoxy composites, compos. struct., 92(9) (2010) 2292–2298. [22] whitcomb, j. d., analysis of instability-related growth of a through-width delamination, national aeronautics and space administration, langley research center, technical report nasa-tm-86301, nas 1.15:86301, (1984). [23] benzeggagh, m. l., kenane, m., measurement of mixed-mode delamination fracture toughness of unidirectional glass/epoxy composites with mixed-mode bending apparatus, compos. sci. technol., 56(4) (1996) 439–449. [24] reeder, j. r., 3d mixed-mode delamination fracture criteria–an experimentalist’s perspective, in: american society for composites 21st annual technical conference, dearborn, mi; united states, (2006). [25] camanho, p. p., dávila, c. g., mixed-mode decohesion finite elements for the simulation of delamination in composite materials, nasa-tech. pap., 211737(1) (2002) 33. [26] camanho, p. p., davila, c. g., de moura, m. f., numerical simulation of mixed-mode progressive delamination in composite materials, j. compos. mater., 37(16) (2003) 1415–1438. [27] ankersen, j., davies, g. a. o., interface elements-advantages and limitations in cfrp delamination modelling, in: 17th international conference on composite materials, edinburgh, uk, (2009). [28] turon, a., davila, c. g., camanho, p. p., costa, j., an engineering solution for solving mesh size effects in the simulation of delamination with cohesive zone models, (2007). j. lopes et alii, frattura ed integrità strutturale, 31 (2015) 67-79; doi: 10.3221/igf-esis.31.06 79 [29] pan, b., qian, k., xie, h., asundi, a., two-dimensional digital image correlation for in-plane displacement and strain measurement: a review, meas. sci. technol., 20(6) (2009) 062001. microsoft word numero_51_art_32_2700 c. bellini et alii, frattura ed integrità strutturale, 51 (2020) 442-448; doi: 10.3221/igf-esis.51.32 442 interlaminar shear strength study on cfrp/al hybrid laminates with different properties costanzo bellini, vittorio di cocco, luca sorrentino department of civil and mechanical engineering, university of cassino and southern lazio, 03043 cassino, italy costanzo.bellini@unicas.it, http://orcid.org/0000-0003-4804-6588 vittorio.dicocco@unicas.it, http://orcid.org/0000-0002-1668-3729 luca.sorrentino@unicas.it, http://orcid.org/0000-0002-5278-7357 abstract. fml (fibre metal laminate) is a hybrid material that presents outstanding structural properties, such as resistance to cyclic and dynamic loads, together with low specific weight. this material consists of metal sheets alternating to composite material layers. in the present work, the ilss (interlaminar shear strength) was evaluated for different types of carbon fibre/aluminium fml, produced varying the layer thickness and the bonding solution of layers. in fact, fmls consisting of one or two metal sheets (a parameter strictly connected to the layer thickness, as the metal/composite volume fraction was kept at constant value) and bonded with structural adhesive or prepreg resin were considered for this study. the ilss was determined according to the three-point bending method with short beam specimens. the experimental tests evidenced an effect of the adhesion methodology on the ilss value, while the layer thickness did not influence the interlaminar strength. the mechanical behaviour after the maximum load point was investigated too, evaluating the trend of the shear stress as a function of the loading nose displacement. keywords. carall; short beam flexural test; bonding strength. citation: bellini, c., di cocco, v., sorrentino, l., interlaminar shear strength variation of cfrp/al hybrid laminates with different properties, frattura ed integrità strutturale, 51 (2020) 442-448. received: 17.10.2018 accepted: 03.12.2019 published: 01.01.2020 copyright: © 2020 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. introduction ml is a particular hybrid material constituted by metal sheets alternated to composite material laminates. the mechanical properties of this material are very interesting, since it combines the high strength/weight ratio of composite materials with the ductility of metals [1]. one of the most widespread fml is the glare (glass laminate aluminium reinforced epoxy), that consists in aeronautical grade aluminium sheets joined with glass fibre laminates. however, this kind of fml does not possess high stiffness, so in the past other types of fml have been investigated [2,3]. in particular, carbon fibre composites were considered for this application, giving rise to caralls (carbon fibre reinforced aluminium laminates), that have higher stiffness, but they also are troubled with galvanic f http://www.gruppofrattura.it/va/51/2700.mp4 c. bellini et alii, frattura ed integrità strutturale, 51 (2020) 442-448; doi: 10.3221/igf-esis.51.32 443 corrosion [4]. indeed, the composite material nature strongly determines the structural characteristics of the whole hybrid laminate; in fact, a higher impact toughness is given by the aramid fibres, while carbon fibres are not suitable for this purpose; furthermore, the latter is more appropriate for high-cycle fatigue applications, while the former for low-cycle fatigue ones [5]. in the present work, the influence of both the metal/composite bonding and the layer thickness on the ilss value of different hybrid laminates was investigated. this kind of mechanical test was chosen because it highlights the characteristics of the interface between the constituents of the fml. in a composite material, the ilss is a property that depends on the matrix, since it relies on the adhesion between matrix and fibres. in an fml, the adhesion between metal sheets and composite material layer holds the same role; in fact, the rupture generally happens at the interface between these materials. the surface preparation is a factor that must be evaluated when designing fmls and composites in general for critical applications [6]. the ilss of a laminate is an important parameter since the separation of the layers, that is the delamination, makes the bending stiffness drop and, consequently, the bending deformation grow. it is important to emphasize that the attention was paid not only to the maximum reached loads but also to the whole force-displacement curves, in order to evaluate the behaviour prior to and after the main damage occurrence. other significant singularities of the present work consist in the reinforcement architecture and the stacking sequence: other researchers considered unidirectional reinforcements and metal sheet as external layers, while this work deals with woven fabric and the external layers are made of composite material. in the literature there are some other works dealing with the ilss of fmls, but, to our best knowledge, the analysis of the effect of both the layer thickness and the metal/composite interface on the ilss and the loading curves has never been investigated. several works aimed at improving the bonding between metal and composite material. three different solutions for carall were compared by ning et al.: the enhancement of the composite-metal interface due to the addition of nanoparticles and the chemical etching or mechanical patterning on the surface of the metal sheet. the influence of the surface treatment of the sheet for the production of glare was investigated by mamalis et al. [7] and park et al. [8]. the advisability of a glass layer at the metal/composite interface of a carall was evaluated by jakubczak et al. [9]. the influence of the fibre treatment on the mechanical characteristics was compared for a composite laminate and a fml by lawcock et al. [10,11]. the effects of adhesive thickness between metal and composite on the structural characteristics of glare was investigated by li et al. [12]; instead, the influence of loading conditions on the shear strength and the damage mechanism were studied by liu et al. [13]. the influence of the hygrothermal ageing on the ilss of carall was investigated by botelho et al. [14] and by pan et al. [15], while that of testing temperature on the ilss of glare was studied by hinz et al. [16]. an in-depth study on the flexural behaviour of different types of carall, characterized by different layer thickness and composite/metal bonding, was carried out by bellini et al. [17–20]. materials and methods s mentioned in the introduction paragraph, in this work the shear strength of cfrp/al hybrid laminates was examined. in particular, the aim consisted in assessing the influence of the layer thickness and the interface bonding on the ilss of this type of material. an experimental plan was conceived, that considered two levels for each explored factor; therefore, a total of three different laminates were produced. as concerns the layer thickness, a type of laminate presented three cfrp layers and two aluminium sheets, while the other was constituted by two aluminium sheets and a cfrp layer. it must be remembered that all the laminates presented the composite material as external layers, while the metal was inside. moreover, the thickness of the various layers was chosen in order to obtain a constant composite material/metal ratio and a total laminate thickness equal to 5 mm. consequently, the metal sheet thickness was 0.3 mm or 0.6 mm (for the fml with two sheets or a single sheet, respectively) and the number of prepreg plies was 12, that were grouped in threes or fours to produce both types of fml. as regards the other parameter, that is the bonding solution between aluminium and cfrp, a kind of laminates was produced inserting a layer of structural adhesive, the af 162 2k, at the interface, while in the other one any adhesive was absent, hence the adhesion relied on the prepreg resin only. all the fml analysed in this work were manufactured considering the prepreg hand layup process, also known as vacuum bag process, a manufacturing technique common in the aeronautical industry. several steps were necessary to make the laminates. the process started with the mould preparation: a release agent was spread on the surface of a steel plate, that had a thickness of 10 mm, in order to allow part removal at the end of the curing process. after, the prepreg plies and the metal sheets were cut in the suitable dimensions and stacked on the mould, paying attention to respect the established stacking sequence. then, the vacuum bag was prepared using all the necessary ancillary materials, as the release film and the breather fabric, and the laminates were sealed under the vacuum bag. once the sealing operation was concluded, the mould a c. bellini et alii, frattura ed integrità strutturale, 51 (2020) 442-448; doi: 10.3221/igf-esis.51.32 444 with the prepreg was inserted in the autoclave for curing. six specimens were extracted from each laminate by diamond disk saw cutting, then they were tested according to astm d 2344. in fig. 1 a type of specimen, that one with one metal sheet, is visible. this test method calculated the ilss of laminate through the three-point bending of a short beam, that is a bending test with a span-to-thickness ratio of four. considering that the laminate thickness was 5 mm, the span was set to 20 mm, so the length of the specimens was decided to be 25 mm, while the width was 10 mm. the astm standard prescribed also a fixed load speed of 1 mm/min. figure 1: short beam specimens with a single aluminium sheet. figure 2: a specimen during the three-point bending test. results he results of the experimental tests carried out on short beam specimens are presented in this section. both the maximum ilss and the trend of the shear strength were reported and discussed. in particular, a statistical analysis was carried out on the values found for the ilss in order to establish if the layers thickness and the metal/composite interface affected this structural parameter. considering a specimen width b and a specimen thickness h, the ilss due to the load p can be determined through the following relation, as stated in the astm d 2344 standard: 3  4    p ilss b h  (1) the ilss values obtained from the three-point bending tests carried out on all the specimens produced in this activity are presented in fig. 3. it can be noted that the highest shear strength was equal to 49.03 mpa and it was reached by the laminate characterised by a single metal sheet and metal/composite bonding assured by structural adhesive, while the lowest value was equal to 39.08 mpa and was obtained by the other laminate with a singular metal sheet, that one without structural adhesive. considering the average value, this finding was confirmed, in fact the highest strength belonged to the laminate with a single metal sheet bonded with adhesive and the lowest strength to the one bonded with the prepreg resin, while the strength of the remaining laminate reached a value between the former two. moreover, the experimental values are quite accurate since the cov (coefficient of variation) of the results is low, in fact it ranged between 3.6% and 3.7% for all the t c. bellini et alii, frattura ed integrità strutturale, 51 (2020) 442-448; doi: 10.3221/igf-esis.51.32 445 tests. the presence of the adhesive improved the ilss of the material, but it must be remembered that it was detrimental for the flexural strength of the laminate, as found in previous works [17,20]. figure 3: results relevant to the three-point bending tests carried out on the produced fml. the consistency of the data obtained from the experimental tests was assessed by statistical analysis; in particular, an anova (analysis of variance) was carried out, and the results are reported in tab. 1. this statistical tool asserted that the contribution factor of the layer thickness was quite low, less than 5%, while the contribution of the interface solution was high, more than 75%. the interaction contribution was calculated too, but the result was negligible and so it is not present in tab. 1. in order to confirm these findings, the anova was completed with the estimation of the p-value, another statistical parameter: the studied factor is not influencing the results if its p-value is higher than 5%, that is the value commonly used as limit. as visible in the table, the adhesion factor had a p-value equal to 0%, so it was influencing, while the number of sheets had a value of almost 13%, so it was unaffecting. therefore, it can be concluded that among the studied factor, the only one that conditioned the ilss value was the presence of the structural adhesive at the interface between metal and composite material. source contribution p-value number of sheets 4.85% 12.9% presence of adhesive 75.84% 0.0% experimental error 19.31% total 100% table 1: ilss value measured for all the tested specimen. the factor influence on the short beam strength was investigated also through the main effects plot, another statistical instrument, and the results of this analysis are presented in fig. 4. as it can be seen from the chart in the figure, the ilss increased with the adhesive presence, while it decreased with the increment of the number of sheets, even if this decrement was lower compared to the variation induced by the former factor, as stated also by the anova. the trend of the shear strength as a function of the loading nose displacement is presented in fig. 5. for each kind of laminate, a single curve is reported, that is representative of the relevant group because the data scatter was narrow. the shear stress trend was found comparable for all the specimen type; in fact, at first a shear stress increment was found, then, after the attainment of maximum load, each curve showed a fluctuating trend, due to the presence of various failures. the first part of the curve, till the maximum load, showed a linear trend for the laminate without the adhesive, while the other two types presented a slight knee before attaining the maximum value. this behaviour was probably caused by the plasticization of the adhesive layer, that in the former kind of laminate was not present. the slope of the first part of the c. bellini et alii, frattura ed integrità strutturale, 51 (2020) 442-448; doi: 10.3221/igf-esis.51.32 446 curves, that is faintly connected to the stiffness of the laminate, was steeper for the laminate without the adhesive. this finding is due to the lower stiffness of the adhesive, that conditioned the behaviour of the whole laminate, and it confirmed what found in a previous work [20]. the laminates with a single aluminium sheet presented a steep stress decrease after the maximum value, that was equal to 36% for the fml bonded with the prepreg resin and 22% for the laminate bonded with the structural adhesive, while for the laminate with two metal sheet the shear decrease was more gradual. the laminate without the adhesive presented also a load recovery, while this load increment was negligible for the other laminates; in fact, the shear stress level after the first drop increased till a value equal to 82% of the maximum load. finally, it must be noted that all the laminates presented a residual load capacity; in particular, the laminate with two metal sheets presented the highest value, that was equal to 64% of the maximum load, while it was 46% for the laminate with a single sheet bonded with prepreg resin and 41% for that one bonded with adhesive. in conclusion, it can be stated that the best choice was the laminate with two aluminium sheets bonded with the adhesive, since it presented a maximum ilss slightly lower than the highest one, that was relevant to the other laminate bonded with adhesive, the highest residual load capacity and after the attainment of the maximum ilss the shear stress trend did not show a drop. figure 4: main effect plot relevant to experimental tests. figure 5: shear stress as a function of displacement for the tested specimens. 21 46 45 44 43 42 41 40 39 38 37 presentabsent n sheets s h o rt b ea m s tr en g th adhesive c. bellini et alii, frattura ed integrità strutturale, 51 (2020) 442-448; doi: 10.3221/igf-esis.51.32 447 conclusions lms are hybrid laminates, constituted by metal sheets and composite material layers interposed, that present high structural properties. however, the reliability of the interface between metal and composite is very important; for this reason, the influence of the metal/composite interface and the stacking sequence on the ilss (interlaminar shear strength) was investigated in the present work. in particular, for the first factor the bonding agent consisted in a structural adhesive or the resin of the prepreg itself, while, for the second factor, the number of metal sheets was varied: a single sheet or two ones were considered, maintaining at a constant value the volume ratio between carbon fibre and aluminium, in order to obtain different layer thickness. the ilss was chosen as parameter to be studied since it relied on the interface effectiveness, and it was determined through the three-point bending test on short beam. three types of specimens were produced and tested: the first one with a single metal sheet bonded with adhesive, the second one with a single metal sheet bonded with prepreg resin and the third one with two aluminium sheets bonded with adhesive. the experimental tests found that the laminate showing the highest ilss was the first one, while the second one presented the lowest value. moreover, a statistical analysis was performed on the experimental results for stating the influence level of the different factors, and it was discovered that the layer thickness had a low effect on the shear strength, while the interface typology was the most influencing factor. the work was completed with the analysis of the shear stress trend as a function of the loading nose displacement. all the specimens showed a linear (or almost linear) shear stress increase till a maximum value, followed by a sharp drop, except for the laminate with two aluminium sheets that presented a smoother load decrease. the same laminate was characterized also by the highest residual load at the end of the experimental test. references [1] fu, y., zhong, j., chen, y. (2014). thermal postbuckling analysis of fiber-metal laminated plates including interfacial damage, compos. part b eng., 56, pp. 358–364, doi: 10.1016/j.compositesb.2013.08.033. [2] lee, b.e., park, e.t., kim, j., kang, b.s., song, w.j. (2014). analytical evaluation on uniaxial tensile deformation behavior of fiber metal laminate based on srpp and its experimental confirmation, compos. part b eng., 67, pp. 154– 159, doi: 10.1016/j.compositesb.2014.06.031. [3] li, h., hu, y., xu, y., zheng, x., liu, h., tao, j. (2015). reinforcement effects of aluminumelithium alloy on the mechanical properties of novel fiber metal laminate, compos. part b eng., 82, pp. 72–77, doi: 10.1016/j.compositesb.2015.08.013. [4] hamill, l., hofmann, d.c., nutt, s. (2018). galvanic corrosion and mechanical behavior of fiber metal laminates of metallic glass and carbon fiber composites, adv. eng. mater., 20(2), pp. 1–8, doi: 10.1002/adem.201700711. [5] botelho, e.c., silva, r.a., pardini, l.c., rezende, m.c. (2004). evaluation of adhesion of continuous fiber-epoxy composite/aluminum laminates, j. adhes. sci. technol., 18(15–16), pp. 1799–1813, doi: 10.1163/1568561042708377. [6] sorrentino, l., polini, w., bellini, c., parodo, g. (2018). surface treatment of cfrp: influence on single lap joint performances, int. j. adhes. adhes., 85, pp. 225–233, doi: 10.1016/j.ijadhadh.2018.06.008. [7] mamalis, d., obande, w., koutsos, v., blackford, j.r., ó brádaigh, c.m., ray, d. (2019). novel thermoplastic fibremetal laminates manufactured by vacuum resin infusion: the effect of surface treatments on interfacial bonding, mater. des., 162, pp. 331–344, doi: 10.1016/j.matdes.2018.11.048. [8] park, s.y., choi, w.j., choi, h.s., kwon, h. (2010). effects of surface pre-treatment and void content on glare laminate process characteristics, j. mater. process. technol., 210(8), pp. 1008–1016, doi: 10.1016/j.jmatprotec.2010.01.017. [9] jakubczak, p., bienias, j., surowska, b. (2018). interlaminar shear strength of fibre metal laminates after thermal cycles, compos. struct., 206, pp. 876–887, doi: 10.1016/j.compstruct.2018.09.001. [10] ye, l., afaghi-khatibi, a., lawcock, g., mai, y.w. (1998). effect of fibre/matrix adhesion on residual strength of notched composite laminates, compos. part a appl. sci. manuf., 29(12), pp. 1525–1533, doi: 10.1016/s1359-835x(98)00071-2. [11] lawcock, g., ye, l. (1998). effects of fibre / matrix adhesion on carbon-fibrereinforced metal laminates i. residual strength, compos. sci. technol., 3538(97), pp. 1609–1619. [12] li, h., hu, y., fu, x., zheng, x., liu, h., tao, j. (2016). effect of adhesive quantity on failure behavior and mechanical properties of fiber metal laminates based on the aluminum-lithium alloy, compos. struct., 152, pp. 687–692, doi: 10.1016/j.compstruct.2016.05.098. f c. bellini et alii, frattura ed integrità strutturale, 51 (2020) 442-448; doi: 10.3221/igf-esis.51.32 448 [13] liu, c., du, d., li, h., hu, y., xu, y., tian, j., tao, g., tao, j. (2016). interlaminar failure behavior of glare laminates under short-beam three-point-bending load, compos. part b eng., 97, pp. 361–367, [14] doi: 10.1016/j.compositesb.2016.05.003. [15] botelho, e.c., pardini, l.c., rezende, m.c. (2007). evaluation of hygrothermal effects on the shear properties of carall composites, mater. sci. eng. a, 452–453, pp. 292–301, doi: 10.1016/j.msea.2006.10.127. [16] pan, l., ali, a., wang, y., zheng, z., lv, y. (2017). characterization of effects of heat treated anodized film on the properties of hygrothermally aged aa5083-based fiber-metal laminates, compos. struct., 167, pp. 112–122, doi: 10.1016/j.compstruct.2017.01.066. [17] hinz, s., heidemann, j., schulte, k. (2005). damage evaluation of glare 4b under interlaminar shear loading at different temperature conditions, adv. compos. lett., 14(2), pp. 47–55. [18] bellini, c., di cocco, v., iacoviello, f., sorrentino, l. (2019). performance evaluation of cfrp/al fibre metal laminates with different structural characteristics, compos. struct., 225, pp. 111117, doi: 10.1016/j.compstruct.2019.111117. [19] bellini, c., di cocco, v., iacoviello, f., sorrentino, l. (2019). flexural strength of aluminium carbon/epoxy fibre metal laminates, mater. des. process. commun., 1, pp. e40, doi: 10.1002/mdp2.40. [20] bellini, c., cocco, v. di., iacoviello, f., sorrentino, l. (2019). influence of structural characteristics on the interlaminar shear strength of cfrp/al fibre metal laminates, procedia struct. integr., 18, pp. 373–378, doi: 10.1016/j.prostr.2019.08.177. [21] bellini, c., di cocco, v., iacoviello, f., sorrentino, l. 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/hrv (za stvaranje adobe pdf dokumenata najpogodnijih za visokokvalitetni ispis prije tiskanja koristite ove postavke. stvoreni pdf dokumenti mogu se otvoriti acrobat i adobe reader 5.0 i kasnijim verzijama.) /hun 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can be opened with acrobat and adobe reader 5.0 and later.) >> /namespace [ (adobe) (common) (1.0) ] /othernamespaces [ << /asreaderspreads false /cropimagestoframes true /errorcontrol /warnandcontinue /flattenerignorespreadoverrides false /includeguidesgrids false /includenonprinting false /includeslug false /namespace [ (adobe) (indesign) (4.0) ] /omitplacedbitmaps false /omitplacedeps false /omitplacedpdf false /simulateoverprint /legacy >> << /addbleedmarks false /addcolorbars false /addcropmarks false /addpageinfo false /addregmarks false /convertcolors /converttocmyk /destinationprofilename () /destinationprofileselector /documentcmyk /downsample16bitimages true /flattenerpreset << /presetselector /mediumresolution >> /formelements false /generatestructure false /includebookmarks false /includehyperlinks false /includeinteractive false /includelayers false /includeprofiles false /multimediahandling /useobjectsettings /namespace [ (adobe) (creativesuite) (2.0) ] /pdfxoutputintentprofileselector /documentcmyk /preserveediting true /untaggedcmykhandling /leaveuntagged /untaggedrgbhandling /usedocumentprofile /usedocumentbleed false >> ] >> setdistillerparams << /hwresolution [2400 2400] /pagesize [612.000 792.000] >> setpagedevice microsoft word numero_36_art_6 j. kováčik et alii, frattura ed integrità strutturale, 36 (2016) 55-62; doi: 10.3221/igf-esis.36.06 55 focused on fracture mechanics in central and east europe scaling of compression strength in disordered solids: metallic foams j. kováčik slovak academy of science ummsjk@savba.sk j. jerz, n. mináriková slovak academy of science ummsjerz@savba.sk, ummsnmin@savba.sk l. marsavina, e. linul university politehnica timisoara liviu.marsavina@upt.ro, emanoil.linul@upt.ro abstract. the scaling of compression strength with porosity for aluminium foams was investigated. the al 99.96, almg1si0.6 and alsi11mg0.6 foams of various porosity, sample size with and without surface skin were tested in compression. it was observed that the compression strength of aluminium foams scales near the percolation threshold with tf ≈ 1.9 2.0 almost independently on the matrix alloy, sample size and presence of surface skin. the difference of the obtained values of tf to the theoretical estimate of tf = 2.64 ± 0.3 by arbabi and sahimi and to ashby estimate of 1.5 was explained using an analogy with the daoud and coniglio approach to the scaling of the free energy of sol-gel transition. it leads to the finding that, there are two different universality classes for the critical exponent tf: when the stretching forces dominate tf = f = 2.1, respectively when bending forces prevail tf = .d = 2.64 seems to be valid. another possibility is the validity of relation tf ≤ f which varies only according to the universality class of modulus of elasticity in foam. keywords. metallic foams; aluminium foams; compression; compression strength; percolation. introduction he compression strength is a key property, which determines the industrial applications of the disordered solids, such as natural rocks, porous ceramics or metallic foams [1-8]. the traditional approaches to the failure phenomena of solid materials are mostly valid for the solids that are macroscopically homogeneous. moreover, they deal with the problem without considering the effect of the microscopic disorder. in disordered materials, the presence of pores of various sizes, shapes and orientations makes the problem more complex. the initiation and growth t j. kováčik et alii, frattura ed integrità strutturale, 36 (2016) 55-62; doi: 10.3221/igf-esis.36.06 56 of the cracks, which leads to the macroscopic failure in the disordered system is in general a non-equilibrium and nonlinear phenomenon. the scaling model [9] considers that the compression strength of the disordered material is a function of the compression strength of solid material and the degree of disorder (porosity or volume fraction of solid material). benguigui, ron and bergman [10] in 2d and sieradzki and li [11] in 3d found experimentally that the compression strength cs of disordered solids scales according to the power law:   ftccs pp  (1) where p is the degree of disorder, pc is a percolation threshold, i.e., the value of disorder below which the compression strength vanishes, and tf is a critical exponent for the compression strength. in 3d sieradzki and li [11] obtained tf = 1.7 ± 0.1 for the system composed of a 2 mm thick aluminium plate with holes punched at positions corresponding to the triangular networks. on the other hand, bergman [12] proposed the theoretical bounds for tf, which in 3d give 2.58 < tf (d=3) < 2.76. using computer simulation, sahimi and arbabi [13] found tf ~ 2.64 ± 0.3 in 3d, which agrees with the bounds proposed by bergman. they assumed that the lower value of tf = 1.7 ± 0.1 by sieradzki and li [11] was due to the fact that the measurements were done far from pc and also due to the significant size effect. recently, author [14] used the scaling model for the study of the tensile strength of copper and nickel foams. the obtained results for tf agree reasonably with the sahimi and arbabi estimated value tf ~ 2.64. unfortunately, the data are far from the percolation threshold and the obtained values can be over or under estimated. the scope of this work is to study the scaling of the compression strength of the aluminium foams prepared by powder metallurgical route [15]. the metallic foams are the disordered solids consisting of a metal matrix filled with gas pores. the metallic foams around 0.1 and less volume fraction of metal can be prepared thus enabling to study the scaling of the compression strength near the percolation threshold. experimental investigations o investigate the scaling of the compression strength, the metallic foams of various densities were prepared by powder metallurgical route [15]. the samples were made from aluminium alloy powders al 99.96, almg1si0.6 and alsi11mg0.6, which were mixed together with a foaming agent (0.4 wt.% of titanium hydride), cip-ed and then continuously hot extruded at 450 °c into a foamable precursor. the precursor was expanded into the porous cellular solid by hydrogen, which is released from the foaming agent, during the heating of the precursor above the melting temperature of the metal matrix. then the rapid cooling process takes place to freeze the obtained cellular structure. the samples of various geometry were prepared: cylinders with the diameter of 20 mm and the length of 10, 20, 25, 30 and 40 mm without surface skin, with the diameter of 28 mm and the length of 32 mm with surface skin and finally with the diameter of 40 mm and the length of 51 mm with surface skin. the prepared foam samples were usually from the range of 0.07 0.45 volume fraction of metal (see tab. 1). the metallic surface skin always covers the foam prepared by the powder metallurgical route. the surface skin was removed via the electric discharge machining thus excluding the possible effect of the skin on the compression strength scaling. it enabled also to evaluate the effect of the surface skin using a couple of samples with the skin. the compression test was carried on instron testing machine with constant ram speed of 10 mm/min. from the load-deflection curve, the stress-strain curve was obtained and the compression strength of the foam sample was determined (see fig.1). results and discussions to model the compression strength of aluminium foams, the following assumption was made: because the foams with 0.1 and less volume fraction of metal can be successfully prepared, the percolation threshold was set to zero and eq. (1) was rewritten in the following way: ft 0 0cscs           (2) t j. kováčik et alii, frattura ed integrità strutturale, 36 (2016) 55-62; doi: 10.3221/igf-esis.36.06 57 where cs0 is the compression strength of the solid material without porosity; is the density of foam; 0 is the density of solid material; /0 is the volume fraction of metal. the fitting of the experimental results to eq. (2) showed that the scaling exponent tf is in the range of 1.89 – 2 depending on alloy composition, sample size and surface skin presence (see tab. 1 and figs. 2 and 3). the results indicate that it is a universal critical exponent: it is independent on the compression mechanisms of the cell-walls and is almost the same for both brittle compression of casting aluminium alloy alsi11mg0.6 (see fig. 1.a) and plastic deformation of wrought aluminium alloys al 99.96 and almg1si0.6 (see fig. 1.b). the lowest values of tf were obtained for the samples with surface skin, because the skin oriented parallel to the applied load increases the sample strength at constant volume fraction of metal. it must be further noted, that the data for the compression strength of metallic foams showed statistical fluctuations due to various pore sizes, shapes and orientations at constant porosity (see fig. 4). figure 1: typical stress-strain curves for, the definition of the compression strength of and the macroscopic structural changes at compression strength for: (a) brittle alsi11mg0.6 foam, 0.18 volume fraction of metal, (b) ductile al 99.96 foam, 0.31 volume fraction of metal. matrix alloy geometry [mm] range of volum fraction cs0 [mpa] tf [ ] 2 [ ] n [ ]  20 x 25 0.09 0.44 69.8±2.6 1.96±0.11 6.67 16 al 99.96  28 x 32 (skin) 0.18 0.41 69.9±0.8 1.94±0.04 0.65 8  40 x 51 (skin) 0.17 0.32 70.0±0.8 1.89±0.04 0.68 12 almg1si0.6  20 x (10-40) 0.07 0.40 114.9±1.5 1.97±0.03 2.20 65 alsi11mg0.6  20 x (10-40) 0.10 0.89 305.0±4.1 2.00±0.04 40.0 77 table 1: composition, sample geometry and observed scaling exponents for investigated metal foams determined via eq. (2). 2 is the error of the fitting. n is the number of measured foam samples used for fitting. j. kováčik et alii, frattura ed integrità strutturale, 36 (2016) 55-62; doi: 10.3221/igf-esis.36.06 58 0.01 0.1 1 0.1 1 10 100 1000  c s [ m p a ] volume fraction of metal [-] 0.01 0.1 1 0.01 0.1 1 10 100 1000  c s m p a ] volume fraction of metal [-] figure 2: scaling of the compression strength for alsi11mg0.6 foam without surface skin  20 x {10, 20, 30, 40} mm2. figure 3: scaling of the compression strength for almg1si0.6 foam without surface skin  20 x {10, 20, 30, 40} mm2. the observed values are also in contradiction with the prediction of the compression yield stress dependence on volume fraction of metal for closed cell foams according to ashby et al. [2]:                      0 1 2/3 0 10 ys cs 'ccc '       . (3) basically this equation is in general a combination of cell face stretching and cell edge bending. it is evident that the obtained dependence is almost the straight line in log-log space. for that reason, let us assume that the cell edge bending part can be neglected. therefore the cell face stretching will prevail and the results ought to scale with the exponent of 3/2, but it is significantly lower value as was experimentally observed. why obtained values of tf are low in comparison with the theoretical value 2.64 ± 0.3 and higher than 1.5 derived by ashby et al. [2]? one significant solution can be the fact, that with the increasing porosity, the pore size in metallic foams becomes comparable with sample geometry and the size effect takes place. nevertheless, after enlarging the volume of samples by 30% no increase of tf was observed (see al 99.96 foams in tab. 1 and fig. 5). it is evident, that the question why the compression strength of metallic foams scales near the percolation threshold with tf of 1.89 – 2 cannot be simply explained by the sample size and the distance from the percolation threshold. it is necessary to look for another explanation. a possible solution can be found in the experimental work of daoud and coniglio [17]. they proposed that the free energy f of sol-gel transition scales as: fd .b.af   , c c p pp   (4) where a, b are numerical constants, p is the volume fraction of sol, pc is the percolation threshold,  is the critical exponent for the correlation length, d is dimension of the problem and f is the critical exponent for the modulus of elasticity. the critical exponent f possesses two different universality classes in 3d [16]: f = 2.1 for central-force model when stretching forces dominate, and f = 3.76 for bond-bending model when bending forces dominate. the first term in eq. (4) represents the contribution of the finite gel clusters below and above the percolation threshold. the second term to the free energy is the contribution of an infinite gel cluster. in 3d  = 0.88 [9] thus giving .d = 2.64, which coincide with the theoretical prediction for tf = 2.64 ± 0.3 by sahimi and arbabi and also with bergman’s bounds on tf. j. kováčik et alii, frattura ed integrità strutturale, 36 (2016) 55-62; doi: 10.3221/igf-esis.36.06 59 figure 4: effect of the pore size and orientation on the compression strength of alsi11mg0.6 foam with surface skin  40 x 51 mm2 at 0.19 volume fraction of metal: vertically oriented pores with apparent diameter of (a) 2.25 mm, (b) 3.03 mm, (c) 5.94 mm and (d) randomly oriented pores with apparent diameter of 4.52 mm. 0.01 0.1 1 0.1 1 10 100  28 x 32 mm  40 x 51 mm  c s [ m p a ] volume fraction of metal [-] figure 5: effect of the sample size on the scaling of compression strength for al 99.96 foam with surface skin. this fact can support the following analogy: the energy necessary for the compression failure of the metallic foam is an area under the stress-strain curve and its value depends on the compression strength and foam structure. therefore, one can suppose, that eq. (4) can be used to describe the compression energy and also to model the scaling of the j. kováčik et alii, frattura ed integrità strutturale, 36 (2016) 55-62; doi: 10.3221/igf-esis.36.06 60 compression strength of the metallic foams. using this analogy, the first term can be identified with the interaction of the existing macrocracks inside the cell-walls of the foam which are not involved in foam fracture. the macrocracks (see fig. 6) are created during the cooling process due to the hydrogen pressure within the pores and due to subsequent nonuniform cell-wall contraction during cooling. the second term can be connected with the interaction of some amount of the existing macrocracks and also microcracks initiation and growth thus leading to the breakage/plastic failure of foam sample weakest region and therefore to macroscopic failure of the sample (see fig. 1 – start of the densification of weakest region of foam by crack propagation/plastic bending depending on alloy composition [18]). a) b) figure 6: macro cracks inside the cell walls in (a) alsi11mg0.6 foam and (b) almg1si0.6 foam as a result of foaming process (0.2 volume fraction of metal). in eq.(4),  is in the range of [0, 1], thus implying that the term with lower exponent represents the dominant part of the compression energy. therefore, when the stretching forces dominate, the leading term is the second one with f = 2.1. in this case, the foam fails mostly via interaction and growth of some macrocracks and after sufficient concentration of microcracks is generated in foam cell walls by stretching (compression/tension). on the contrary, when microcracks are created by bending forces with f = 3.76, material fails by the growth and interaction of the existing macrocracks and the first term ought to prevail with .d = 2.64. the critical exponent f = 1.66 ± 0.07 has been experimentally found for the modulus of elasticity of identical aluminium foams [15]. the obtained value belongs to the universality class of the central-force model 2.1. the lower value of f was found due to the significant size effect and the anisotropy of the samples. it implies that the metallic bonds inside the cell walls of the aluminium foams fail predominantly by the stretching forces and confirms tf ≈ 1.9 2.0. one can conclude that, the theory seems to be correct. however, it is necessary to check the proposed ideas. the validity can be simply proved using the metallic foams or other disordered solids that belongs to the bond-bending universality class in 3d with f = 3.76. in this case, the compression strength of such material ought to scale with tf approximately 2.64. summarising, the critical exponent of the compression strength seems to possess two different universality classes in 3d: tf ≤ f = 2.1 (5) when central-forces dominate (stretching forces). when bond-bending forces dominate, the compression strength depends on the correlation length of macrocracks, and tf = .d = 2.64 (6) this scaling relation coincides with the limits proposed by bergman and is in agreement with the theoretical prediction by sahimi and arbabi [13]. latest research in the field of ti–6al–4v foams [19] produced by additive manufacturing gives f = 2.96 and tf = 2.81 (yield point). also in the field of replicated microcellular materials, one finds f = 2.6–3, and the value of f tends to increase as percolation threshold decreases [20, 21]. therefore it can be expected that these materials fails in compression via bending mechanism and therefore their scaling exponents possess higher values as powder metallurgical metallic foams. another possibility is following: eq. (5) is usually found experimentally in the form of: tf ≤ f (7) j. kováčik et alii, frattura ed integrità strutturale, 36 (2016) 55-62; doi: 10.3221/igf-esis.36.06 61 where f varies according to the stretching/bending forces acting in the foam microstructure and therefore exponent for compression strength depends on the corresponding universality class for modulus of elasticity. as a final remark it can be mentioned that the compression strength of the solid material determined using eq. (2) (see tab. 1) more or less coincide with tensile strength of corresponding aluminium alloys prepared by pm route. conclusions ummarising, the compression strength of aluminium foams scales near the percolation threshold with tf ≈ 1.9 2.0 almost independently on the matrix alloy, sample size and presence of surface skin. the obtained values of tf are the same for the brittle and ductile aluminium alloys thus proving that the scaling exponent tf is a universal critical exponent. however, tf ≈ 1.9 2.0 is in contradiction with the theoretical estimate of tf = 2.64 ± 0.3 by arbabi and sahimi, and also significantly higher than ashby estimate of 1.5. this problem was solved, using an analogy with the daoud and coniglio approach to the scaling of the free energy of sol-gel transition. it leads to the finding that, there are either two different universality classes for the critical exponent tf: when the compression of the cell-walls is caused by stretching forces tf = f = 2.1. when bending forces prevail, the scaling relation tf = .d = 2.64 seems to be valid. another possibility is the validity of relation tf ≤ f which varies only according to the universality class of modulus of elasticity in foam. acknowledgements his work was supported by the grant of the romanian national authority for scientific research, cncsuefiscdi, project pn-ii-id-pce-2011-3-0456, contract number 172/2011, slovak research and development agency under contract apvv-0692-12, bilateral agreement between upt and sas, contract no. sk-ro-0014-12 and 653/2013. references [1] gibson, l.j., ashby, m.f., cellular solids, structure and properties, second ed., cambridge university press, (1997). [2] ashby, m.f., evans, a.g., fleck, n.a., gibson, l.j., hutchinson, j.w., metal foams: a design guide, butterworth heinemann, boston, (2000). [3] onck, p.r., van merkerk, r., raaijmakers, a., de hosson, j.th.m., fracture of openand closed-cell metal foams, j. mater. sci., 40 (2005) 5821–5828. [4] motz, c., pippan, r., deformation behavior of closed-cell aluminium foams in tension, acta mater., 49 (2001) 2463– 2470. [5] olurin, o.b., fleck, n.a., ashby, m.f., deformation and fracture of aluminium foams, mat. sci. eng., a291 (2000) 136–146. [6] koza, e., leonowicz, m., wojciechowski s., simančík, f., compressive strength of aluminium foams, mater. lett., 58 (2003) 132– 135. [7] kováčik, j., simančík, f., comparison of zinc and aluminium foam behaviour kovove materialy-metallic materials, 42 (2) (2004) 79-90. [8] voiconi, t., linul, e., marsavina, l., kováčik, j., kneć, m., experimental determination of mechanical properties of aluminium foams using digital image correlation, key eng. mat., 601 (2014) 254-257. [9] stauffer, d. and aharony, a., introduction to percolation theory, 2nd edition, taylor & francis, london, (1992). [10] benguigui, l., ron p., bergman, d.j., strain and stress at the fracture of percolative media, j. phys., 48 (1987) 1547. [11] sieradzki k., li, r., fracture behavior of a solid with random porosity, phys. rev. lett., 56 (1986) 2509-2512. [12] bergman, d.j., fragmentation, form and flow in fractured media, ann. israel phys. soc., 8 (1986) 266-272. [13] sahimi m., arbabi, s., mechanics of disordered solids. iii. fracture properties, phys. rev. b, 47 (1993) 713-722. [14] kováčik, j., the tensile behaviour of porous metals made by gasar process, acta mater., 46(15) (1998) 5413 – 5422. [15] kováčik, j., simančík, f., aluminium foam modulus of elasticity and electrical conductivity according to percolation theory, scripta mater. 39 (1998) 239-248. s t j. kováčik et alii, frattura ed integrità strutturale, 36 (2016) 55-62; doi: 10.3221/igf-esis.36.06 62 [16] sahimi, m., applications of percolation theory, taylor & francis, london, (1994). [17] daoud, m., coniglio, a., singular behaviour of the free energy in the sol-gel transition, j. phys. a, 14 (1981) l301l306. [18] marsavina, l., kováčik, j., linul, e., experimental validation of micromechanical models for brittle aluminium alloy foam, theor. appl. fract. mec., (2016, in press). doi: 10.1016/j.tafmec.2015.12.020 [19] hernández-nava, e., smith, c.j., derguti, f., tammas-williams, s., léonard, f., withers, p.j., todd, i., goodall, r., the effect of density and feature size on mechanical properties of isostructural metallic foams produced by additive manufacturing, acta mater., 85 (2015) 387-395. [20] despois, j.f., mueller, r., mortensen, a., uniaxial deformation of microcellular metals, acta mater, 54 (2006) 41294142. 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can be opened with acrobat and adobe reader 5.0 and later.) >> /namespace [ (adobe) (common) (1.0) ] /othernamespaces [ << /asreaderspreads false /cropimagestoframes true /errorcontrol /warnandcontinue /flattenerignorespreadoverrides false /includeguidesgrids false /includenonprinting false /includeslug false /namespace [ (adobe) (indesign) (4.0) ] /omitplacedbitmaps false /omitplacedeps false /omitplacedpdf false /simulateoverprint /legacy >> << /addbleedmarks false /addcolorbars false /addcropmarks false /addpageinfo false /addregmarks false /convertcolors /converttocmyk /destinationprofilename () /destinationprofileselector /documentcmyk /downsample16bitimages true /flattenerpreset << /presetselector /mediumresolution >> /formelements false /generatestructure false /includebookmarks false /includehyperlinks false /includeinteractive false /includelayers false /includeprofiles false /multimediahandling /useobjectsettings /namespace [ (adobe) (creativesuite) (2.0) ] /pdfxoutputintentprofileselector /documentcmyk /preserveediting true /untaggedcmykhandling /leaveuntagged /untaggedrgbhandling /usedocumentprofile /usedocumentbleed false >> ] >> setdistillerparams << /hwresolution [2400 2400] /pagesize [612.000 792.000] >> setpagedevice microsoft word numero_35_art_20 g. meneghetti et alii, frattura ed integrità strutturale, 35 (2016) 172-181; doi: 10.3221/igf-esis.35.20 172 focussed on crack paths experimental estimation of the heat energy dissipated in a volume surrounding the tip of a fatigue crack g. meneghetti (http://orcid.org/0000-0002-3517-9464) m. ricotta (http://orcid.org/0000-0002-4212-2618) university of padova, department of industrial engineering, italy giovanni.meneghetti@unipd.it, mauro.ricotta@unipd.it abstract. fatigue crack initiation and propagation involve plastic strains that require some work to be done on the material. most of this irreversible energy is dissipated as heat and consequently the material temperature increases. the heat being an indicator of the intense plastic strains occurring at the tip of a propagating fatigue crack, when combined with the neuber’s structural volume concept, it might be used as an experimentally measurable parameter to assess the fatigue damage accumulation rate of cracked components. on the basis of a theoretical model published previously, in this work the heat energy dissipated in a volume surrounding the crack tip is estimated experimentally on the basis of the radial temperature profiles measured by means of an infrared camera. the definition of the structural volume in a fatigue sense is beyond the scope of the present paper. the experimental crack propagation tests were carried out on hot-rolled, 6-mm-thick aisi 304l stainless steel specimens subject to completely reversed axial fatigue loading. keywords. crack tip; crack propagation; heat energy; aisi 304l; averaging approaches. introduction umerical or experimental evaluation of plastic dissipation at the tip of fatigue cracks have attracted the attention of several researchers, who investigated, just as few examples, crack propagation assessment criteria [1,2], the thermal effects on stress intensity factors [3,4], the plastic zone size and energy dissipation [5-7]. in the field of the experimental approaches, the development of infrared cameras having increased performances (for example in terms of thermal sensitivity, spatial resolution and frame rate) has given impulse to temperature-related fatigue studies. in a previous paper, dealing with fatigue assessment of notches, the heat energy dissipated in a unit volume of material per cycle, q, has been assumed as a fatigue damage index and a proper experimental procedure has been put forward to estimate the q parameter at any point of a specimen or a component undergoing fatigue loadings [8]. such experimental technique is based on temperature measurements performed by means of an infrared camera or a thermocouple glued at the point of a component where the fatigue assessment is to be performed and it has the advantage that thermal boundary conditions do not need to be controlled during experimental tests. the q parameter has been applied to correlate fatigue test results obtained on smooth and bluntly notched specimens made of an aisi 304l stainless steel subjected either to constant amplitude [9,10] and two load level [11] fatigue tests. being a point-related quantity, q can hardly correlate fatigue test results generated from severely notched specimens, because the well known notch support effect makes questionable the use of peak quantities (stress-, strainor energy-based) evaluated at the notch tip in order to assess fatigue life. in particular, the use of peak quantities evaluated at the apex of stress concentrators fails by a large amount in the case n g. meneghetti et alii, frattura ed integrità strutturale, 35 (2016) 172-181; doi: 10.3221/igf-esis.35.20 173 of fatigue cracks. to account for the notch support effect, peterson postulated that the controlling factor is the stress at the distance of the structural size ahead the notch tip [12]; on the other hand, neuber introduced the structural volume concept, inside which stresses are to be averaged [13]. in view of the extension of the heat energy-based approach to severely notched specimens, a theoretical frame and an experimental procedure have been established in the present paper, by considering a specimen containing a propagating fatigue crack. in particular, the specific heat loss q has been averaged over a volume v surrounding the tip of the propagating crack, leading to the definition of the averaged energy parameter q*. the volume v, even though on the order of the size of the structural volume for construction steels, has been chosen arbitrarily, since the focus of the present paper is the thermal problem and not yet the validation of a fatigue assessment method. q* has been estimated starting from the temperature field measured close to the fatigue crack tip. experimental temperature distributions have been compared with an analytical solution available in the literature. theoretical background n order to derive the energy per cycle dissipated in a volume v surrounding a crack tip, a previous theoretical model [8] has been adopted. let us consider a material undergoing a fatigue test and consider a control volume v surrounding the crack tip, as shown in fig. 1. the external surface s of the control volume v can be divided into three parts, namely scv, scd and sir through which the heat q is transferred to the surroundings by convection, conduction and radiation, respectively. the first law of thermodynamics states: ( ) v v w dv q u dv      (1) where w is the input mechanical energy and u the variation of the internal energy. all quantities are referred to a unit volume of material per cycle. eq. (1) can be written in terms of mean power exchanged over one loading cycle as:   mij ij l p v v v t d f dv h dv c e dv t                     (2) where fl is the frequency of the applied mechanical load, h=hcd+hcv+hir is the thermal power dissipated by conduction, convention and radiation, respectively,  the material density, c the specific heat and pe the rate of accumulation of damaging energy in a unit volume of material. let us consider a plane problem and assume that the temperature of a material undergoing a constant amplitude, sinusoidal fatigue loading is given by:  ( , ; ) ( , ) 2 ( , ; )a l mt r t t r sen f t t r t       (3) where ta is the amplitude of temperature oscillations due to the thermoelastic effect and tm is the mean temperature evolution. ta and tm depend on the position (r,) considered in the component. it is worth noting that the thermoelastic effect consists of a reversible exchange between mechanical and thermal energy, that does not produce a net energy dissipation or absorption over one loading cycle [14-17]. since eq. (2) considers the rate of energy contributions averaged over one cycle, then only the mean temperature evolution tm(t) appears on the right hand side of eq. (2). the specific net heat generation hgen is given by:  gen ij ij l ph d f e      (4) therefore eq. (2) can be written in order to put into evidence only the thermal problem: m gen v v v t h dv h dv c dv t             (5) i g. meneghetti et alii, frattura ed integrità strutturale, 35 (2016) 172-181; doi: 10.3221/igf-esis.35.20 174 typically, the mean temperature tm increases at the beginning of a fatigue tests and, after some time, it stabilises as soon as thermal equilibrium is reached with the surroundings. at thermal stabilisation, tm is constant with time, therefore the last term on the right hand side of eq. (5) disappears. as it will be demonstrated later on, hcd can be supposed much greater than hcv and hir, therefore it can be assumed h hcd. the thermal power extracted from volume v of fig. 1 by conduction can be calculated starting from the thermal flux through its boundary: ( , ) cd m m cd v s r r t r h dv gradt n ds z r d r                            (6) where gradtm is the gradient of the temperature field t(r,),  is the material thermal conductivity, z is the specimen’s constant thickness, dscd=z·ds (see fig. 1) and r the radius of the circular volume shown in fig. 1. in eq. (6), mh gradt n      is the specific thermal flux evaluated at the point (r,) of the boundary of v.  sr v r scd scv sir h w q u figure 1: energy balance for a volume of material v surrounding a crack tip subject to fatigue loadings. after having calculated the thermal power dissipated by conduction by means of eq. (6), it is possible to estimate the energy per cycle averaged in the volume v: * 1 l v q h dv f v    (7a) making use of eq. (6), it is obtained: * ( , )1 m l r r t r q z r d f v r                  (7b) in previous papers, the specific heat loss q=h/fl was used as a fatigue damage indicator to perform fatigue assessments [8-11]. being a point-related quantity, its use was limited to the analysis of the fatigue strength of bluntly notched specimens. following neuber’s structural volume concept [13], in the present paper the energy term q is averaged over a control volume v according to eq. (7), in view of the application of the energy-based approach to severely notched or cracked components. however, it should be noted that the aim of the present paper is to formulate the fatigue related thermal problem and validate an approach able to estimate experimentally q*. therefore, the control volume surrounding the crack tip of fig. 1 was fixed arbitrarily and has not a precise relation to the fatigue properties of the material. as it will be shown later on, in order to apply eq. (7b) the surface material temperature was monitored by means of an infrared camera operating at a sample frequency facq. in order to estimate tm(r,) at a given time ts during the fatigue test, a trigger signal was given to the infrared camera at t=ts and a number of infrared images nmax were acquired with a sampling rate facq. by recalling eq. (3), the mean temperature field was estimated as pixel-by-pixel average value: g. meneghetti et alii, frattura ed integrità strutturale, 35 (2016) 172-181; doi: 10.3221/igf-esis.35.20 175    max 1 , max 2 ( 1) / n a l s acq m n m estimate t sen f t n f t t n           (8a)   max 1 max , max max 2 ( 1) / n a l s acq n m m estimate t sen f t n f t n t n n           (8b) where ts is the time when the temperature acquisition starts. a error index can be defined between the estimated (tm,estimate) and the actual (tm) mean temperature field: ,m estimate m a t t t    (9) by using eq. (8b) into eq. (9), the error index results:   max 1 max 2 ( 1) / n l s acq n sen f t n f n         (10) eq. (10) says that for typical testing conditions adopted in the present work, i.e. fl=37hz, facq=200hz, nmax=1000, the relative error  in the estimation of the mean temperature is lower than 0.1%. material, specimens’ geometry and test procedure ingle edge v-notched specimens were machined from a 6-mm-thick hot rolled aisi 304l stainless steel plate (elastic modulus e=194700 mpa, engineering proof stress rp0.2=327 mpa, engineering tensile strength rm=690 mpa [9]), according to the geometry shown in fig. 2. constant amplitude, push-pull stress-controlled fatigue tests were carried out by using a servo-hydraulic schenck hydropuls psa 100 machine equipped with a 100 kn load cell and a trio sistemi rt3 digital controller. load test frequencies between 30 and 37 hz were adopted. crack propagation was monitored by using a travelling optical stereo-macroscope operating with a magnification of 40x. the material surface temperature was monitored by means of a flir sc7600 infrared camera, having a 1.5-5.1 m spectral response range, 50 mm focal lens, a noise equivalent temperature difference (netd) < 25 mk, an overall accuracy of 0.05°c, operating at a frame rate, facq, equal to 200 hz and equipped with an analog input interface, that was used to sample synchronously the force signal coming from the load cell. the infrared camera and the travelling microscope monitored the opposite surfaces of the specimens, respectively. to increase the infrared camera spatial resolution, a 30 mm extender ring was adopted, which allowed a spatial resolution ranging from 20 to 23 m/pixel, depending on the distance between the specimen’s surface and the focal lens. due to the extender ring, the field of view (fov) was reduced to 320x256 pixels, which corresponds to a minimum of 6.4 mm x 5.1 mm and a maximum of 7.4 mm x 5.9 mm. the specimens’ surface were polished by using progressively finer emery papers, namely starting from grade 100 up to grade 1000, and after that the surface was polished with a diamond abrasive powder. finally, a black paint was applied to the specimens’ surface to increase the emissivity. the acquired temperature maps were processed first by using the flir motionbyinterpolation tool to correct the relative motion between the fixed camera lens and the moving specimen subject to cyclic loads, whose displacements ranged from 6 to 14 pixels, depending on the crack length. the infrared images were analysed by means of the dedicated altair 5.90.002 software, in order to calculate the mean temperature distribution tm(r,) at a given time t=ts during the fatigue s g. meneghetti et alii, frattura ed integrità strutturale, 35 (2016) 172-181; doi: 10.3221/igf-esis.35.20 176 test according to eq. (8a). by using eq. (10), being typically fl=37 hz, nmax=1000, facq=200hz and 0< ts < 0.5/fl, it is obtained 10-3; such a reduced error was considered acceptable from an engineering point of view. after having determined the distribution of the mean temperature tm(r,), the heat power dissipated by conduction was calculated by solving eq. (6) numerically on the basis of a finite number of radial temperature profiles: in particular, 7 radial paths were considered emanating from the crack tip at different  angles (see fig. 1), namely 0°, 45°, 90°, 135°, -45°,-90° and-135°. in the present paper, the radius r of the volume surrounding the crack tip was assumed equal to 3·10-4 m. even though such a radius may be on the order of the neuber’s structural volume size of a construction steel, it has been assumed as a pure reference example in the present paper, in order to demonstrate the applicability of the proposed approach. 150 8 90 90° machine grip machine grip 46 figure 2: specimens’ geometry (thickness 6 mm). fatigue test results and temperature profiles close to the crack tip hree specimens were tested and the relevant crack growth data are shown in fig. 3. linear elastic, twodimensional, plane stress finite element analyses were performed to evaluate the mode i stress intensity factor range, k=kmax-kmin, for different crack lengths. to account for the machine grip effect, displacements were applied in the numerical model to the lines shown in fig. 2. the paris curve relating the crack growth rate to k was evaluated and plotted in fig. 3b. 0 5 10 15 20 25 30 35 40 45 0 50000 100000 150000 n, number of cycles a [m m ] v_3 v_4 v_5 1.e-08 1.e-07 1.e-06 1.e-05 10 100 k [mpa m0.5] d a/ d n [ m /c y cl e] v_3 v_4 v_5 14.211 k1037.9 dn da   figure 3: tension-compression a) crack propagation curves and b) paris curve of aisi 304 l stainless steel specimens. the crack length and the temperature field at different k values were measured at several times t=ts, regularly distributed during each fatigue test. as stated above, 1000 infrared images were acquired at each time ts and then processed according to eq. (8a). some typical radial temperature profiles evaluated at =0° are shown in fig. 4a and 4b, in the case of k=26 mpa·m0.5 (i.e. kmax=13 mpa·m0.5) and k=60 mpa·m0.5 (i.e. kmax=30 mpa·m0.5), respectively. in the former case a temperature drop equal to about 0.8 k within a distance of 2.5 mm from the crack tip can be observed; conversely, in the latter case, the temperature decreases much more, being the drop about 3 k. therefore, the signal-to-noise ratio is t g. meneghetti et alii, frattura ed integrità strutturale, 35 (2016) 172-181; doi: 10.3221/igf-esis.35.20 177 significantly higher in fig. 4b than in fig. 4a. to evaluate the first derivative at r=r (eq. (6)), the temperature-distance data along the seven considered paths were fitted using a proper polynomial function, shown with a continuous line in fig. 4. (a) 293 293.2 293.4 293.6 293.8 294 294.2 294.4 r [m] t m [ k ] =0° r=3·10-4 m fl=37 hz k=26 mpa·m0.5rrr t   0 5.0·10-4 1·10-3 1.5·10-3 2.0·10-3 2.5·10-3 r=r (b) 315 316 317 318 319 320 321 322 0 r [m] t m [ k ] 5.0·10-4 1·10-3 1.5·10-3 2.0·10-3 2.5·10-3 =0° r=3·10-4 m fl=35 hz k=60 mpa·m0.5 rrr t   r=r figure 4: typical radial temperature profiles measured during the tension-compression fatigue tests in the case of (a) k=26 mpa·m0.5 and (b) k =60 mpa·m0.5. energy per cycle averaged in a volume at the crack tip ig. 5a, 5b and 5c show the specific thermal flux h at the different points along the boundary of v (fig. 1) for specimen v_3, v_4 and v_5, respectively, using =16 w/(m·k) [8]. finally, fig. 5d shows, as an example, the specific energy flux per cycle q, obtained simply dividing h by the load test frequency. in the authors’ opinion, for the material and the experimental conditions analysed in the present paper, a reasonably accurate evaluation of the heat power can be achieved by considering k values higher than 25 mpa·m0.5 (kmax>12.5 mpa·m0.5). having in hand the specific thermal flux h evaluated at different angles  of the boundary of v, numerical integration was performed according to eq. (6). to evaluate the errors due to the discretisation, eq. (6) was solved by dividing the 360° angle starting from a minimum of 4 intervals (=90°) to a maximum of 24 (=15°). a 0.51% variation on results was found by using 8 as compared to 24 intervals. therefore, 8 intervals (=45°) were adopted in numerical calculations. finally, the energy per cycle averaged in the volume v, q*, was evaluated by means of eq. (7b). results are listed in tab. 1 and it can be seen that q* increases as k increases. it should be noted that k are elastically calculated, independently on plastic zone size evaluations. v_3 specimen k [mpa·m0.5] q* [mj/m3 cycle] 26.3 0.813 26.8 0.504 28.4 0.655 31.2 0.727 35.6 0.829 45.2 1.02 49.6 1.32 55.3 1.33 64.1 3.28 v_4 specimen k [mpa·m0.5] q* [mj/m3 cycle] 31.5 1.21 36.7 1.47 42.0 1.55 78.7 4.64 98.0 5.19 v_5 specimen k [mpa·m0.5] q* [mj/m3 cycle] 28.5 0.581 30.3 1.80 32.9 1.91 36.9 2.18 40.6 1.93 45.7 2.60 53.2 2.99 60.1 4.00 66.9 5.96 table 1: q* values calculated for different specimens at different k values. f g. meneghetti et alii, frattura ed integrità strutturale, 35 (2016) 172-181; doi: 10.3221/igf-esis.35.20 178 (a) 0° -45° -90° -135° 180° 135° 90° 45° k=26.3 mpa·m0.5 k=28.4 mpa·m0.5 k=35.6 mpa·m0.5 k=49.6 mpa·m0.5 k=64.1 mpa·m0.5 v_3 specimen 102 103 104 4·104 h [w/m2] crack (b) -45° -90° -135° 180° 135° 90° 45° 102 103 104 5·104 h [w/m2] k=31.5 mpa·m0.5 k=36.7 mpa·m0.5 k=78.7 mpa·m0.5 k=98.0 mpa·m0.5 v_4 specimen 0° crack (c) k=30.3 mpa·m0.5 k=36.9 mpa·m0.5 k=45.7 mpa·m0.5 k=53.2 mpa·m0.5 k=66.9 mpa·m0.5 v_5 specimen 103 104 6·104 0° h [w/m2] -45° -90° 180° crack -135° 135° 90° 45° (d) 102 103 2·103 q [j/(m2·cycle)] k=30.3 mpa·m0.5 k=36.9 mpa·m0.5 k=45.7 mpa·m0.5 k=53.2 mpa·m0.5 k=66.9 mpa·m0.5 v_5 specimen 0° -45° -135° 135° 90° 45° -90° crack 180° 10 figure 5: distribution of the thermal flux h along the boundary of the control volume for different  angles for (a) v_3, (b) v_4 (c) v_5 specimen and (d) and corresponding energy flux per cycle q of v_5 specimen. comparison between experimental and theoretical temperatures close to the crack tip n analytical solution is available in order to evaluate the time-dependent temperature field in the case of a homogeneous and isotropic infinite plate with a time-independent heat generation hl distributed along a line in the thickness direction [18]. at the time t=0 when the heat generation starts, the temperature is supposed homogeneous and equal to t0. between time t=0 and t, the temperature variation t(r,t)=t(r,t)-t0 can be expressed by eq. (11) [18]: 2 ( , ) 4 4 lh rt r t ei t c                (11) where ei is the integral exponential function given by u x ei e u du    and x= 2 4r tc         . since the major source of heat power is the cyclic plastic zone, the linear heat generation hl was applied in its centre, according to [3]. fig. 6a shows the cyclic plastic zone idealised as a circle having radius rp. according to irwin [20], the cyclic plastic zone radius in the plane stress condition is equal to: 2 ' ,02 1 2 2 p p k r          (12) a g. meneghetti et alii, frattura ed integrità strutturale, 35 (2016) 172-181; doi: 10.3221/igf-esis.35.20 179 where ' ,02p is the material cyclic proof stress. for the aisi 304l steel material analysed in this paper, =7940 kg/m3, c=507 j/(kg·k) [19], ' ,02p =290 mpa [9]. with the aim to compare experimental results with the analytical solution eq. (11), a dedicated fatigue tests was performed. a specimen containing a crack as long as half the width (i.e. the ligament length was about 23 mm according to fig. 2) was installed in the fatigue machine to allow for thermal equilibrium with the surroundings so that the homogeneous temperature t0 could be measured. then the fatigue test was started with fl=37 hz and the load was adjusted to apply a linear elastic stress intensity factor range equal to k=36.9 mpa·m0.5; therefore rp is equal to 6.44·10-4 m according to eq. (12). the temperature field as well as the signal coming from the load cell were registered synchronously by the infrared camera using a sampling rate facq=200 hz. to disregard the thermoelastic temperature oscillations superimposed to the mean temperature evolution tm, which are not taken into account in eq. (11), an infrared image captured at a time t=t* was considered, when the applied force was close to zero. (a) vp  s r rp  2rp (b) 0 5·10-4 1.0·10-3 1.5·10-3 2.0·10-3 2.5·10-3 293.5 294 294.5 295 295.5 r [m] 296 t m (r ) [° k ]  k=36.9 mpa·m0.5 rp=6.44·10-4 m fl=37 hz t=1.835 s hl=63.4 w/m t0=293.25° k eq. 11 experimental data rp figure 6: a) cyclic plastic zone vp and (b) comparison between experimental and theoretical radial temperature profile. fig. 7 shows the evolution of the temperature averaged inside the plastic zone vp, t*(t), defined as: 1 ( ) 1 * ( ) ( ) pixel p n i i p p pixelv t t t t t t dv v n       (13) where npixel is the number of pixel inside the cyclic plastic zone size vp. fig. 7b shows the enlarged view of the “detail a” of fig. 7a, where the thermoelastic effect superimposed to the mean temperature evolution t*m can be appreciated. considering the radial temperature profiles that have been measured at t*=1.835 s (the applied force was approximately zero at this time), the total heat generated inside the cyclic plastic zone vp was calculated according to eqs (5) and (6). to evaluate the last contribution on the right hand side of eq. (5) (the internal energy contribution), a linear fit of t* in a time window equal to 1s (fig. 7b) was done and the slope of t*m(t) was considered. after that, the constant heat generation per unit thickness hl to input in eq. (11) was calculated as: 1 p l gen p v h h dv z    (14) and resulted equal to 63.0+0.4=63.4 w/m, where the first contribution is the conduction and the second is the internal energy term. fig. 6b shows a comparison between the temperature field evaluated according to eq. (11) and the experimental data for =0°. according to [2], it can be seen that outside the cyclic plastic zone the measured temperature field is in good agreement with that evaluated under the hypothesis of linear heat generation, which eq. (11) is based on. g. meneghetti et alii, frattura ed integrità strutturale, 35 (2016) 172-181; doi: 10.3221/igf-esis.35.20 180 inside the cyclic plastic zone differences are more pronounced because heat generation is actually distributed inside vp, while in eq. (11) it has been lumped to the centre of the cyclic plastic zone. (a) 19 19.5 20 20.5 21 21.5 22 22.5 23 23.5 24 0 2.5 5 7.5 10 12.5 15 time [s] t * [° c ] t*=1.835 s a k=36.9 mpa·m0.5 fl=37 hz (b) t*m(t) = 0.337·t + 20.1 20 20.5 21 21.5 22 22.5 1.5 1.75 2 2.25 2.5 time [s] t * [° c ] t=t* detail a figure 7: a) temperature evolution during a fatigue test and b) enlarged view of detail a discussion s stated above, eq (6) was derived under the assumption that the energy dissipated by convection and radiation is negligible, i.e. h hcd. the specific thermal flux power extracted by natural convection hcv and that dissipated by radiation hir are given by   ( , ; ) , ;cvh r t t r t t      (15a)   4 4( , ; ) , ;ir nh r t t r t t        (15b) where  is the heat transfer coefficient by convection,  is the surface emissivity, n the stephan–boltzmann constant and t the room temperature. by considering, as an example, the experimental conditions of v_5 specimen and k=40.6 mpa·m0.5, the mean temperature averaged inside v, t*m, was equal to 28.1°c, t =19°c, =0.92 [8] and fl=35 hz. by assuming a reasonable heat transfer coefficient under the hypothesis of natural convection on the order of 10 w/(m2 k) and considering that scv=sir=2·r2, q*cv and q*ir can be calculated by means of eqs 15 and 7a: * cv cv cv l h s q f v    (16) the result is q*cv=867 j/(m3·cycle) and q*ir=472 j/(m3·cycle), respectively, that are four order of magnitude lower than the relevant q* values reported in tab. 1, that take into account only the conduction term. conclusions theoretical framework has been defined to estimate the specific heat energy per cycle averaged in a defined volume surrounding the tip of a propagating crack, q*. a two-dimensional thermal and structural problem has been considered. experimental tests were executed on aisi 304l stainless steel cracked specimens subjected to push-pull fatigue loads and the q* parameter has been determined starting from temperature measurements performed in the vicinity of the crack tip by means of an infrared camera. with reference to the material and experimental equipment available in the present paper, a reasonably accurate estimation of q* was possible only for kmax>13 mpa·m0.5. the experimental temperatures close to the crack tip were compared successfully with an analytical solution available in the literature. a a g. meneghetti et alii, frattura ed integrità strutturale, 35 (2016) 172-181; doi: 10.3221/igf-esis.35.20 181 acknowledgements his work was carried out as a part of the project code cpda145872 of the university of padova. the authors would like to express their gratitude for financial support. references [1] klingbeil, n.w., a total dissipated energy theory of fatigue crack growth in ductile solids. int j fatigue, 25 (2003) 117128. [2] ondracek, j., materna, a., fem evaluation of the dissipated energy in front of a crack tip under 2d mixed mode loading condition. procedia materials science, 3 (2014) 673-678. doi: 10.1016/j.mspro.2014.06.111. [3] ranc, n., palin-luc, t., paris, p.c., thermal effect of plastic dissipation at the crack tip on the stress intensity factor under cyclic loading. eng fract mech, 78 (2011) 961-972. doi: 10.1016/j.engfracmech.2010.11.010. [4] ranc, n., palin-luc, t., paris, p.c., saintier, n., about the effect of plastic dissipation in heat at the crack tip on the stress intensity factor under cyclic loading, int j fatigue, 58 (2014) 56-65. doi: 10.1016/j.ijfatigue.2013.04.012. [5] bär, j., seifert, s., investigation of energy dissipation and plastic zone size during fatigue crack propagation in a highalloyed steel, procedia materials science, 3 (2014) 408-413. doi: 10.1016/j.mspro.2014.06.068. [6] plekhov, o., fedorova, a., kostina, a., panteleev, i., theoretical and experimental study of strain localization and energy dissipation at fatigue crack tip, procedia materials science, 3 (2014) 1020-1025. doi: 10.1016/j.mspro.2014.06.166. [7] fedorova, a.yu., bannikov, m.v., plekhov o.a., infrared thermography study of the fatigue crack propagation, fracture and structural integrity, 21 (2012) 46-53. doi: 10.3221/igf-esis.21.06. [8] meneghetti, g., analysis of the fatigue strength of a stainless steel based on the energy dissipation, int j fatigue, 29 (2007) 81–94, doi:10.1016/j.ijfatigue.2006.02.043. [9] meneghetti, g., ricotta, m., the use of the specific heat loss to analyse the lowand high-cycle fatigue behaviour of plain and notched specimens made of a stainless steel, eng. fract. mech. 81 (2012) 2–17. doi: 10.1016/j.engfracmech.2011.06.010 [10] meneghetti, g., ricotta, m., atzori, b., a synthesis of the push-pull fatigue behaviour of plain and notched stainless steel specimens by using the specific heat loss, fatigue fract. engng. mater. struct., 36 (2013) 1306-1322. doi: 10.1111/ffe.12071. [11] meneghetti, g., ricotta, m., atzori, b., experimental evaluation of fatigue damage in two-stage loading tests based on the energy dissipation, proc imeche part c: j mechanical engineering science, 229 (2015) 1280-1291. doi: 10.1177/0954406214559112. [12] peterson, r. e., notch sensitivity, in: g. sines and j. l. waisman (eds.) metal fatigue, macgraw-hill, new york, (1959) 293-306. [13] neuber, h., über die berücksichtigung der spannungskonzentration bei festigkeitsberechnungen. konstruction, 20 (1968) 245-251. [14] ellyin, f., fatigue damage, crack growth and life prediction, chapman & hall, london, (1997). [15] pandey, k.n., chand, s., deformation based temperature rise: a review, int j pres ves pip, 80 (2003) 673-687. [16] charkaluk, e., constantinescu, a., dissipation and fatigue damage. proceedings of the fifth international conference on low cycle fatigue lcf 5, berlin, germany, (2003). [17] plekhov, o.a., panteleev, i.a., naimark, o.b., energy accumulation and dissipation in metals as a result of structuralscaling transitions in a mesodefect ensemble, physical mesomechanics, 10 (2007) 294-301. [18] carslaw, hs., jaeger, jc, conduction of heat in solids, clarendon press, oxford, (1947). [19] atzori, b., meneghetti, g., ricotta, m. analysis of the fatigue strength under two load levels of a stainless steel based on energy dissipation, in: bremand f, editor. proceedings of the 14th international conference on experimental mechanics icem 14, the european physical journal epj web of conferences, 6 (2010). 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/hrv (za stvaranje adobe pdf dokumenata najpogodnijih za visokokvalitetni ispis prije tiskanja koristite ove postavke. stvoreni pdf dokumenti mogu se otvoriti acrobat i adobe reader 5.0 i kasnijim verzijama.) /hun 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/pdfxoutputintentprofileselector /documentcmyk /preserveediting true /untaggedcmykhandling /leaveuntagged /untaggedrgbhandling /usedocumentprofile /usedocumentbleed false >> ] >> setdistillerparams << /hwresolution [2400 2400] /pagesize [612.000 792.000] >> setpagedevice microsoft word numero 21 articolo 3.doc a. de iorio et alii, frattura ed integrità strutturale, 21 (2012) 21-29; doi: 10.3221/igf-esis.21.03 21 a three-parameter model for fatigue crack growth data analysis a. de iorio, m. grasso, f. penta, g.p. pucillo università di napoli federico ii, dipartimento di meccanica ed energetica,via claudio 21 – 80125 napoli antdeior@unina.it abstract. a three-parameters model for the interpolation of fatigue crack propagation data is proposed. it has been validated by a literature data set obtained by testing 180 m(t) specimens under three different loading levels. in details, it is highlighted that the results of the analysis carried out by means of the proposed model are more smooth and clear than those obtainable using other methods or models. also, the parameters of the model have been computed and some peculiarities have been picked out. keywords. fatigue crack growth; data analysis; non-linear regression. introduction he assessment of the fatigue damage by means of phenomenological models notoriously is closely linked to the analysis of experimental results obtained from standard specimens of a given material tested with suitably chosen loading programs. however, it is well known that crack growth data have stochastic nature, as the phenomenon which generates them, due to, essentially, the random evolution of the local combinations, at each point of the crack front, of the induced stress state and material properties. for this reason, in order to identify a deterministic law describing the phenomenon, that is able to represent the common data trend independently of the global scatter or the position of the single data point, data have to be elaborated by means of a best-fit method after having selected an analytical model. since the availability of a reliable crack propagation model has a tremendous impact on the fatigue design practice, for over half a century this problem has been faced by many researchers [1]. for the same reason, the attention of the researchers has been focused also on the accuracy by which the experimental data are produced and analysed, with the aim of defining a standard procedure for material testing and related results analysis (astm) and to formulate interpretative models of the experimental data. the most used methods for crack growth testing and data analysis are those suggested by astm standard [2], which, concerning the data analysis, proposes two different approaches: the secant method and the incremental polynomial method. since both methods are based on local interpolation of experimental data, irregularities and/or anomalies in the data distribution, for the first method, and the number of data points chosen for the best-fit parabola, for the second one, affect significantly the results. on the other hand, the foremost polynomial or exponential analytical formulas found in literature [3-6] do not seem to have solved completely the problem. hence our interest in facing this problem, in order to contribute, if possible, to improve on the quality of raw crack propagation data analysis by formulating an interpretative model for the whole lives field of the acquired data. formulation of the model mong the various analysis methods developed till now, besides those proposed by the astm standards, we mention for their popularity: mukherjee method [3], which is based on the linear interpolation of the finite differences computed between t a http://www.gruppofrattura.it http://dx.medra.org/10.3221/igf-esis.21.03&auth=true a. de iorio et alii, frattura ed integrità strutturale, 21 (2012) 21-29; doi: 10.3221/igf-esis.21.03 22 two consecutive points, in order to estimate the rate of growth at the central point; polynomial expressions of smith [4], davies and feddersen [5], that interpolate locally or globally the experimental data; polak and knesl method [6], which uses splines to fit and reduce the scatter in the data. most of the methods until now proposed are local interpolations of experimental points, as already stated in the introduction, and are strongly affected by the real distribution of the analysed data, being unable to filter both the irregularities and anomalies that are always present in the sample. therefore, most analytical models derived in such a way are very often closely linked to the particular experimental practice adopted to produce the data and, above all, do not fit all data with the needed and controlled accuracy in the whole cycles number range of each test. in a previous paper [7], some of the authors already discussed the possibility to use splines of an arbitrary order to globally interpolate the raw data and reduce the scatter of the crack growth material constants when gapped or noisily data are used. in order to formulate a new model able to (at least) partially fill the aforementioned lacks, the results of 180 crack growth tests carried out by ghonem and dore [8] have been analysed. to find the curve that better interpolates all the examined data, different analytical formulations have been tested. by means of successive refinements, the following three parameters model has been defined:   0 β f a γ a α n 1 n         where: a0 = initial crack length; nf = number of cycles to failure;  , β, γ = model parameters identified by a non-linear least squares method; n = number of cycles corresponding to a given crack length. the crack growth rate can be directly evaluated in the range [n0-nf] by means of the previous expression without amplify the irregularities and/or anomalies of the raw data and without losing information in the initial and final part of the aforementioned range, as it occurs with other procedures as those suggested by astm standards. verification of the model he data of the 180 tests of ghonem and dore, which are fully described in term of both specimens and testing conditions in the paper [8], are summarized in fig. 1-3. each figure reports the results of a series of 60 tests carried out under the same loading conditions. once the model has been defined, the goodness-of-fit has been evaluated computing the residuals and the values attained by the coefficient of determination r2 , which is reported in the graphs of fig. 4-6, for each data set. for a quick (non-objective) evaluation of the goodness of the interpolation, the results of some tests together with the related best-fitting curves obtained by the proposed model are also reported in fig. 7. figure 1: fatigue crack growth curves set i (r = 0.6). figure 2: fatigue crack growth curves set ii (r = 0.5). t http://www.gruppofrattura.it http://dx.medra.org/10.3221/igf-esis.21.03&auth=true a. de iorio et alii, frattura ed integrità strutturale, 21 (2012) 21-29; doi: 10.3221/igf-esis.21.03 23 figure 3: fatigue crack growth curves set iii (r = 0.4). figure 4: coefficient of determination, mean and standard deviation for set i. figure 5: coefficient of determination, mean and standard deviation for set ii. figure 6: coefficient of determination, mean and standard deviation for set iii. http://www.gruppofrattura.it http://dx.medra.org/10.3221/igf-esis.21.03&auth=true a. de iorio et alii, frattura ed integrità strutturale, 21 (2012) 21-29; doi: 10.3221/igf-esis.21.03 24 figure 7: crack growth data with best-fit curves. moreover, normality tests of the residuals have been carried out using the χ2 test and the frequency distributions of the residuals computed for each specimen tested have been also diagrammed to verify that the mean was close to zero and the standard deviation was very small, in other words that the conditions to guarantee a small error in the estimation of the crack lengths by means of the model were satisfied [9]. in fig. 8, as an example, three of the aforementioned distributions are reported, one for each set. figure 8: pdf of residuals of three selected best-fit, one for each set. from the examination of the normality test results, it has been noted that the majority of them verify the expected conditions (see. tab. 1), whereas the others do not pass the test due to some large anomalies present in the frequency distribution diagrams. however, if the graphs of the raw data are observed in details in the fields corresponding to each anomaly, it can be seen that the data points move away from the trend of all other points in either an irregular or anomalous manner. numbers of best-fit with normal distribution of residuals numbers of best-fit with non normal distribution of residuals set _ i 47 13 set _ ii 32 28 set _ iii 31 29 table 1: results of normality tests. the outliers in the graphs of the mean and standard deviation are not only due to the random scatter in the raw data, but also to the fact that in some experimental curves there are data points sequences that do not follow the trend of the whole test. this anomaly affects the response of the optimization algorithm used in the non-linear least square method. the best-fitting model parameters obtained for these latter experimental curves define a solution with a residual distribution http://www.gruppofrattura.it http://dx.medra.org/10.3221/igf-esis.21.03&auth=true a. de iorio et alii, frattura ed integrità strutturale, 21 (2012) 21-29; doi: 10.3221/igf-esis.21.03 25 distorted in mean and asymmetric. to highlight what said, three curves with irregular points and a curve with anomalous data, in which the residuals distribution exhibits an unbalanced mean and a marked asymmetry due to the solely effect of the irregular data in the anomalous part (spotlighted), are reported in fig. 9-11 and fig. 12, respectively. figure 9: crack length vs. number of cycles (left) and corresponding residuals (right). figure 10: crack length vs. number of cycles (left) and corresponding residuals (right). figure 11: crack length vs. number of cycles (left) and corresponding residuals (right). http://www.gruppofrattura.it http://dx.medra.org/10.3221/igf-esis.21.03&auth=true a. de iorio et alii, frattura ed integrità strutturale, 21 (2012) 21-29; doi: 10.3221/igf-esis.21.03 26 figure 12: crack length vs. number of cycles (left) and corresponding residuals (right). in any case, the best-fitting with the proposed method appears visually acceptable and the coefficient of determination r2 is very close to one. it follows that if the normality test of the residuals distribution does not verify the optimum conditions for the approximation of the experimental data with the proposed model, it is due to the defectiveness of some experimental points or of short parts of some experimental curves. this result, apparently negative, can even be profitably used to filter the experimental data, that is eliminate all data that move away in an excessive or anomalous manner from the unique natural trend of all the other data points, as unique must be the physical law that characterizes the crack propagation phenomenon in each material that is free of geometrical singularities and structural inhomogeneities. this way to see the experimental data allows minimizing and improving the information derivable from testing and, in this particular case, to improve the evaluation of the model parameters α, β, γ using all available data. identification and variability of the parameters α, β, γ he interpolation of the experimental data of each test, through the proposed model and best-fitting technique, allows identifying the parameters α, β, γ of the model. the numerical values of these parameters are represented in three distinct groups of three diagrams, each group being relative to a data set obtained under the same loading condition (fig. 13-15). the parameters values assigned to each data set are the statistical averages of the values obtained for each experimental curve of the set. they are given in tab. 2, where the standard deviations of the three samples of parameter estimates are also reported. β α γ set _ i µ 1.37 0.47 -0.062 σ 0.35 0.078 0.073 set _ ii µ 1.55 0.43 -0.105 σ 0.42 0.069 0.15 set _ iii µ 1.62 0.43 -0.15 σ 0.53 0.01 0.176 table 2: model parameters values. t http://www.gruppofrattura.it http://dx.medra.org/10.3221/igf-esis.21.03&auth=true a. de iorio et alii, frattura ed integrità strutturale, 21 (2012) 21-29; doi: 10.3221/igf-esis.21.03 27 figure 13: α, β, γ parameters with corresponding mean value for set i. figure 14: α, β, γ parameters with corresponding mean value for set ii. figure 15: α, β, γ parameters with corresponding mean value for set iii. from the achieved results it can be seen that the parameter α has a small deviation around the mean value in respect to that of β and γ. also, the two parameters β and α, plotted one as function of another (see fig. 16), are related with the following law: log(1 ) c     in fig. 16, for each data set, the values of the constant c together with the fitting curves are reported; in order to show the goodness of fit, also the values of the coefficient of determination r2 are reported in the same figure. moreover, since the constant c remain almost unchanged for the three data sets, it could be considered as a material constant, appearing independent from the loading conditions that differentiate the three testing groups. figure 16: correlation between α and β values for each set. http://www.gruppofrattura.it http://dx.medra.org/10.3221/igf-esis.21.03&auth=true a. de iorio et alii, frattura ed integrità strutturale, 21 (2012) 21-29; doi: 10.3221/igf-esis.21.03 28 further relations seem to be detectable between the loading ratio r and the parameters β and γ, on the one end, and between the parameter γ and the constant c, on the other end, as it can be seen in fig. 17 and 18. figure 17: correlation between β, γ values with the loading ratio. figure 18: correlation between β, γ values with the constant c. obviously, about these latter relations, further experimental investigations on other materials and with a greater number of loading conditions are needed. conclusions n analytical model to interpolate the experimental crack growth curves (actual crack length as function of the number of cycles), that is alternative to the methods proposed by the astm 647-95a standard, has been derived analysing the data of 180 fatigue crack propagation tests carried out by ghonem and dore. by a cross-check performed by means of the normality test of the residuals and the coefficient of determination r2, it has been highlighted that it is possible to identify those data groups, if present, which move in an anomalous and non influential manner away from the trend of the other data points, so as to be able to take in count of them in the analysis of the results. furthermore, the model parameters have been evaluated and some interesting correlations have been found between them, which, after further validation by means of an extended experimentation, could be useful to build up a new phenomenological model, that is robust and well-rounded at the same time, to compute the fatigue crack growth rates. a http://www.gruppofrattura.it http://dx.medra.org/10.3221/igf-esis.21.03&auth=true a. de iorio et alii, frattura ed integrità strutturale, 21 (2012) 21-29; doi: 10.3221/igf-esis.21.03 29 references [1] a.k. head, phil .mag., 44(7) (1953) 925. [2] astm e 647, standard test method for measurement of fatigue crack growth rates, astm (1995), philadelphia, pa, usa. [3] b. mukherjee, int. j. of fracture, 8(4) (1972) 449. [4] r. a. smith, int. j. of fracture, 9(3) (1973) 352. [5] k.b. davies, c.e. feddersen, int. j. of fracture, 9 (1973)116. [6] j. polak, z. knesl, int. j. of fracture, 11 (1975) 693. [7] a. de iorio, d. ianniello, f. penta, e. santoro, in: 8th eccm, naples, (1998). [8] h. ghonem, s. dore, engineering fracture mechanics, 27(1) (1987) 1. [9] s. c. chapra, r. p. canale, numerical methods for engineers with pc applications, mcgraw-hill, (1985). http://www.gruppofrattura.it http://dx.medra.org/10.3221/igf-esis.21.03&auth=true microsoft word numero_51_art_1_2597 a. vedernikova et alii, frattura ed integrità strutturale, 21 (2020) 1-8; doi: 10.3221/igf-esis.51.01 1 focussed on igf25 – fracture and structural integrity international conference 2019 three approaches to evaluate the heat dissipated during fatigue crack propagation experiments a. vedernikova, a. iziumova, a. vshivkov, o. plekhov institute of continuous media mechanics ub ras, 614013 perm, russia terekhina.a@icmm.ru, https://orcid.org/0000-0003-1069-7887 fedorova@icmm.ru, https://orcid.org/0000-0002-1769-9175 vshivkov.a@icmm.ru, https://orcid.org/0000-0002-7667-455x poa@icmm.ru, https://orcid.org/0000-0002-0378-8249 abstract. this work is devoted to the comparative analysis of three techniques for measurement of energy dissipation in metals under fatigue crack propagation: use of original contact heat flux sensor, post-processing of infrared thermography data and lock-in thermography. contact heat flux sensors allow real-time recording of heat source values. non-contact temperature measurements by infrared thermography techniques make it possible to calculate the heat source field on the specimen surface by solving a heat conductivity equation. lock-in thermography is a well-established technique for measuring energy dissipation under cyclic loading conditions based on the analysis of the second harmonic amplitude of the thermal signal. this paper describes the results of the experiments with v-notched flat specimens made of stainless steel aisi 304 which were subjected to cyclic loading. it was shown that the values of energy dissipation estimated by different techniques are in good qualitative agreement. contact and noncontact measurements can be used for investigation of energy dissipation either separately or in combination. based on the measurements, the power dependence of fatigue crack growth rate on dissipated heat near the crack tip can be obtained. keywords. ir-thermography; lock-in thermography; heat flux sensor; dissipated energy; fatigue crack propagation. citation: vedernikova, a., iziumova, a., vshivkov, a., plekhov, o., three approaches to evaluate the heat dissipated during fatigue crack propagation experiments, frattura ed integrità strutturale, 51 (2020) 1-8. received: 27.08.2019 accepted: 08.10.2019 published: 01.01.2020 copyright: © 2020 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. introduction ne of the key problems of fracture mechanics and strength analysis is to predict the fatigue life of cracked parts of engineering constructions subjected to cyclic loading. the fatigue crack growth well correlates with energy dissipation at the crack tip [1-25]. different experimental approaches focused on the experimental study of the dissipated energy are described in the literature. o http://www.gruppofrattura.it/va/51/2597.mp4 a. vedernikova et alii, frattura ed integrità strutturale, 21 (2020) 1-8; doi: 10.3221/igf-esis.51.01 2 one of the techniques is based on the application of original seebeck effect-based contact heat flux sensor, which ensures the quantitative integral heat flow values in some area near the crack tip. such methodology was originally used for studying energy dissipation in liquid flows [3] and the failure of metals [2, 4]. the second method for heat flux estimation involves analysis of temperature distribution measurements obtained for the specimen surface by means of infrared (ir) thermography. plastic strain-induced heat sources were calculated by solving the volume-averaged heat conduction equation. the main difficulties associated with application of the second technique can be attributed to the necessity to differentiate strongly oscillating signals and to determine the parameters responsible for the interaction between the specimen and the external environment. nevertheless, ir thermography data are widely used to gain deeper insight in the process of plastic deformation and fracture of metallic materials [5-10]. it was shown in [11, 12] that the results of contact (heat flux sensor) and non-contact (ir thermography) measurements of energy dissipation during irreversible deformation agree well. the third, lock-in thermography, method provides space-resolved measurements, extracts thermoelastic information directly from the thermal signal [13] and investigates energy dissipation using the double frequency method proposed by sakagami [14]. lock-in thermography is employed to detect crack initiation and propagation in structural materials using thermographic mapping [15-25]. in this study, we have shown that the energy dissipation values measured by the thermography techniques are in good qualitative agreement with the results obtained by the method in which contact heat flux sensors are used. this provides evidence that contact and non-contact measurements can be used either separately (fast assessment of the material state at different loading stages) or in combination (verification of the heat source value and estimation of its distribution over the material surface). experimental series of tests were performed on v-notched flat specimens made of stainless steel aisi 304 and subjected to cyclic loading at a frequency of 10 hz (constant stress amplitude 12 kn and stress ratio r = 0). fig. 1 shows the geometry of the specimens and the experimental setup scheme. the chemical composition of the material examined is given in tab. 1. c cr fe mn ni p s si 0.08 18-20 66.34-74 2 8-10.5 0.045 0.03 1 table 1: chemical composition (wt. %) of stainless steel aisi 304. (a) (b) (c) figure 1: (a) specimen geometry; (b) schematic of the measuring equipment: 1 – test specimen, 2 – grips of the testing machine, 3 – contact heat flux sensor, 4 –potential drop measuring setup to monitor the crack length, 5 – infrared camera; (c) photo of the specimen and the measuring equipment. a a. vedernikova et alii, frattura ed integrità strutturale, 21 (2020) 1-8; doi: 10.3221/igf-esis.51.01 3 specimens were cyclic loaded in a servohydraulic testing machine instron 8802. the potential drop technique was used to measure and characterize the crack propagation process [26]. crack sizes in a steel specimen were predicted by applying a constant direct current or an alternating current to the specimen and by measuring an increase in electrical resistance due to the crack propogation. to analyze the energy dissipation at the crack tip during mechanical tests, we have used the seebeck effect-based heat flux sensor. in order to improve the heat flow, a heat-conductive paste was applied to the specimen surface beneath the sensor. the evolution of the temperature field was recorded with an infrared camera flir sc 5000. the features of the ir camera are as follows: the spectral range of 3-5 μm, the maximum frame size is 320×256 pixels, the spatial resolution is 10-4 meters, and the temperature sensitivity is in the range from 25 mk to 300 k. the camera was calibrated based on the standard calibration table. the application of the lirsc5000 mw g1 f/3.0 close-up lens (with distortion less than 0.5%) made it possible to investigate the plastic zone in detail. the specimen surface intended for infrared shooting was polished in several stages and coated by a thin layer of amorphous carbon to improve the surface emissivity. specimens were tested and monitored by means of the infrared camera in order to acquire thermographic sequences during tests at regular intervals (1000 cycles each). direct heat flux measurement technique he heat flux measurement technique relies on the use of seebeck effect-based contact heat flux sensor [2]. the heat dissipated by specimens is directly proportional to the current intensity and the time it takes for the current to pass through the specimens:   abp i (1) where p is the heat flux power (w), i is the direct current (a), and  ab is the peltier coefficient (v), which is related with a coefficient of thermal electromotive force. structurally, the sensor comprises two peltier elements ("measuring" and "cooling"), thermocouples, and a radiator. to measure the heat flow through the "measuring" peltier element during the experiment, the temperature on its free surface is kept constant. the cooling peltier element caulked with a radiator was connected with the "measuring" peltier element. this cooling system has feedback and is controlled based on two temperature sensors located between "measuring" and cooling peltier elements and far from the studied specimen in the zone with constant temperature. the heat flux emitted from the specimen surface passes through the heat flux sensor. the sensor was fixed on the specimens by applying thermal paste and then pressed against the spring to provide the necessary thermal contact. the negligibility of heat dissipation which was caused by sensor – specimen friction was experimentally proved [2]. the signal from the flux sensor was measured by the amplifier and registered in the adc of the microcontroller. then the data were transmitted to personal computer for further processing. the sensors were calibrated using a device with a controlled heat flux. indirect heat flux measurement technique estimation of the heat sources field based on the heat conductivity equation o calculate the heat source field induced by plastic deformation, we use heat conduction eqn. (2) for processing the obtained infrared thermography data:                 2 2 2 2 2 2 ( ) ( ) ( ) ( ) ( ) t x, y,z, t t x, y,z, t t x, y,z, t t x, y,z, t c q x, y,z, t k t x y z (2) where ( )t x, y,z, t is the temperature field,  is the material density (kg/m3), c is the heat capacity ( j/(kg·k)), k is the heat conductivity (w/(m·k)), ( )q x, y,z,t is the heat source field, x, y,z are the coordinates, and t is the time. the ir camera allows one to register the temperature distribution only over the specimen surface that is the reason why eq. 2 has to be averaged over the z-coordinate (thickness). t t a. vedernikova et alii, frattura ed integrità strutturale, 21 (2020) 1-8; doi: 10.3221/igf-esis.51.01 4 difference  '( )x, y,t between the averaged specimen temperature ( )t x, y,z,t and the initial specimen temperature in the thermal balance with the environment 0t is defined as:        /2 0 0 /2 1 '( ) ( ( ) ) ( ) h h x, y, t t x, y,z, t t dz x, y, t t h (3) where h is the specimen thickness. the following boundary conditions are considered:                  2 2 /2 0 /2 2 ( , , , ) ( , , , ) ( , , , ) ( ( , , , ) ) h hz z h h z h t x y z t t x y z t x z t x y z t k t x y z t t dz z h (4) where  is the heat exchange coefficient in perpendicular direction to the specimen surface. one boundary condition describes the symmetry of the heat source, whereas the second boundary condition is responsible for the heat exchange of the specimen with the environment. therefore, integrating eq. (2), considering expressions (3) and boundary conditions (4), we obtain relation (5) to estimate the heat source field caused by irreversible deformation:              0 int ( , , ) ( , , ) ( , , ) ( , , ) x y t t q x y t c x y t k x y t (5) where  is the time constant, which is related to the heat losses [27, 28]. the parameter  was measured before each test by the additional experimental procedure of specimen cooling after pulse point heating. the identification process consisted in estimating the time derivative and the laplacian of the temperature function if there was no internal and external heat source on the specimen during its cooling. for steel aisi 304, the value of parameter  amounted to 10 sec. the numerical finite-difference scheme of eqn. (5) applied to the ir thermography data allows one to investigate the heat source evolution on the specimen surface. to calculate the heat sources from the noisy temperature fields, the procedure of the movement compensation and filtering of infrared data was performed. these algorithms are described in detail in [9]. estimation of the dissipated energy based on the lock-in thermography energy dissipation can be estimated by applying the lock-in thermography technique. lock-in thermography is based on a correlation in frequency, amplitude and phase of the detected signal with a reference signal coming from the loading system. temperature variations on the specimen surface are monitored with the ir camera during mechanical tests. the evaluation of the dissipated energy is based on post-processing of the recorded thermal data using the discrete fourier transformation (eq. 6) and performed for each pixel of the recorded frames.        sin 2 sin 2 2m e l e d l dt t t t f t t f t t               (6) where mt is the mean temperature, lf is the mechanical loading frequency, e and d are the phase shifts, et is the thermo-elastic amplitude (e-mode), dt is the plasticity effect amplitude (d-mode), and  t is the noise of the temperature signal. it was shown that in case of plastic deformation the second mode coupled with the double loading frequency (d-mode) correlated with the dissipative energy [14]. eq. (6) is integrated in the algorithm of altair li software. for each analysed sequence of ir frames, the evaluation provides an amplitude and a phase image for different modes. a. vedernikova et alii, frattura ed integrità strutturale, 21 (2020) 1-8; doi: 10.3221/igf-esis.51.01 5 results and discussion n order to compare the heat flux sensor results and the results of thermography measurements, we have studied the temperature evolution in a small rectangular area which covered all temperature fluctuations near the crack tip. the size of the area coincides with heat flux sensor dimensions. a comparison of the results obtained by contact sensor and the infrared thermography data (heat conduction eqn. (5)) during crack propagation tests is illustrated in fig. 2. the heat flux sensor allows measurement of the integral heat flux only. the infrared thermography technique was used to obtain the image of temperature distribution and the field of heat source distribution in the crack tip region. to compare the ir results with the data of the contact sensor, we integrated the heat source field over the space equal to the size of contact sensor. fig. 2a presents the characteristic curve describing the heat flux variation during the fatigue tests: solid line heat flux measured by the contact heat flux sensor, squares heat flux measured by the infrared thermography technique. three zones were identified on the heat flux curve during the crack propagation experiment. the short initial increasing zone corresponds to the crack initiation stage. the second zone with a constant heat flux corresponds to the steady state crack growth stage. the last zone is characterized by a sharp increase in heat dissipation and is ended with specimen failure. it can be seen that the power heat source detected by the contact sensor and determined on the basis of ir thermography data (eqn. (5)) are in good quantitative agreement throughout the test. figs. 2b,c present the relation between the heat flux power  q and crack growth rate  da dn for the stainless steel aisi 304 specimen. the power law relation for predicting the fatigue crack growth is determined as follows:  int . bda aqdn (6) (a) (b) (c) figure 2: (a) ir-thermography data and heat flux sensor measurements; (b) heat flux power during crack propagation experiments; (c) relation between heat flux power and crack growth rate for the stainless steel aisi 304 specimen. the obtained results led us to conclude that the techniques applied to estimate heat dissipation on the basis of contact and non-contact measurements can be used in engineering practice for fatigue crack growth predictions.let us now consider the possibility of using lock-in thermography to predict fatigue crack growth. with the altair li software it is possible to calculate the resulting amplitude of temperature variations (amplitude image) and the distribution of phase shifts between the thermographic signal and the mechanical loading (phase image) for the e-mode and d-mode, respectively (eq. 6). as shown by bremond [13], the d-mode provides information about the dissipated energy. the values of the amplitude related to the double loading frequency were determined. fig. 3a shows the results of the normalized lock-in thermographic and the heat flux sensor measurements of the crack propagation experiment with a constant force exerted on the stainless steel aisi 304 specimen. for normalization of lock-in thermography data, a scaling factor was used. we assume a linear relationship between each point of thermography data and the results of the contact heat flux sensor. the scaling factor is computed for one point as the ratio of the power of heat source obtained by contact sensor to the value of d-amplitude. then the values of d-amplitude at other time moments are multiplied by a scaling factor. for steel aisi 304, the value of scaling factor amounts to 0.32. it can be seen that the dissipated energy measured by lock-in i a. vedernikova et alii, frattura ed integrità strutturale, 21 (2020) 1-8; doi: 10.3221/igf-esis.51.01 6 thermography and the heat flux sensor are in good qualitative agreement over the high heat dissipation period. the averaged d-amplitude values are rising with loading cycles what caused by processes in front of the crack tip. the d-amplitude behaviour and, in particular, its increase are similar to that of the crack growth rate. therefore, the value of the d-mode amplitude can be used to describe crack propagation. figs.3b,c present the relation between d-mode variation and crack growth rate for the stainless steel aisi 304 specimen. the power law relation is determined as follows:  bdda asdn (7) where ds is the maximum amplitude of the thermal signal that changes at the double of loading frequency. (a) (b) (c) figure 3: (a) lock-in thermography data and heat flux sensor measurements; (b) heat flux during crack propagation experiments; (c) relation between second order temperature variation and crack growth rate for the stainless steel aisi 304 specimen. analysis of the results has revealed that lock-in thermography can be used for evaluating the crack growth rate. it is interesting that the fatigue crack growth can be described by the d-amplitude signal in very similar to the paris law. conclusion r-thermography data, lock-in thermography data and heat flux sensor measurements were used to investigate energy dissipation under fatigue crack propagation in stainless steel aisi 304. comparison of the obtained results demonstrates that they are in good qualitative agreement. at the scaling factor of 0.32 the heat flux sensor results coincide quantitatively with the lock-in thermography data. the thermographic and heat flux sensor measurements showed an increase in the energy dissipated ahead of the crack tip with increasing crack growth rate. the measured energy dissipation values can be used to determine a linear correlation between these two parameters. acknowledgments his work was supported by the russian foundation for basic research (grant №18-31-00293) and the presidium of the russian academy of sciences (program no. 16 “development of physicochemical mechanics of surface phenomena as the fundamental basis for the development of modern structures and technologies). references [1] iziumova, a., plekhov, o. (2014). calculation of the energy j-integral in plastic zone ahead of a crack tip by infrared scanning, fatigue fract. eng. mater. struct., 37, pp. 1330-1337. doi: 10.1111/ffe.12202. i t a. vedernikova et alii, frattura ed integrità strutturale, 21 (2020) 1-8; doi: 10.3221/igf-esis.51.01 7 [2] vshivkov, a., iziumova, a., plekhov, o., bär, j. (2016). experimental study of heat dissipation at the crack tip during fatigue crack propagation, frat. ed integrita strutt., 35, pp. 131-137. doi: 10.3221/igf-esis.35.07. [3] pradere, c., joanicot, m., batsale, j.-c., toutain, j., gourdon, c. (2007). processing of temperature field in chemical microreactors with infrared thermography, quant. infrared thermogr. j., 3, pp. 117-135. doi: 10.3166/qirt.3.117-135. [4] wang, c., blanche, a., wagner, d., chrysochoos, a., bathias, c. (2014). dissipative and microstructural effects associated with fatigue crack initiation on an armco iron, int. j. fatigue, 58, pp. 152-157. doi: 10.1016/j.ijfatigue.2013.02.009. [5] izyumova, a.y., plekhov, o.a., vshivkov, a.n., prokhorov, a.a., uvarov, s. v. (2014). studying the rate of heat dissipation at the vertex of a fatigue crack, tech. phys. lett., 40, pp. 810-812. doi: 10.1134/s1063785014090211. [6] iino, y. (1979). fatigue crack propagation work coefficient-a material constant giving degree of resistance to fatigue crack growth, eng. fract. mech., 12, pp. 279-299. doi: 10.1016/0013-7944(79)90120-6. [7] chow, c.l., lu, t.j. (1991). cyclic j-integral in relation to fatigue crack initiation and propagation, eng. fract. mech., 39, pp. 1-20. doi: 10.1016/0013-7944(91)90018-v. [8] dowling, n., begley, j. (1976).fatigue crack growth during gross plasticity and the j-integral. mechanics of crack growth, astm stp, 590, pp. 80-103. [9] fedorova, a.y., bannikov, m. v., terekhina, a.i., plekhov, o.a. (2014). heat dissipation energy under fatigue based on infrared data processing, quant. infrared thermogr. j., 11(1), pp. 2-9. doi: 10.1080/17686733.2013.852416. [10] plekhov, o.a., saintier, n., palin-luc, t., uvarov, s. v., naimark, o.b. (2007). theoretical analysis, infrared and structural investigations of energy dissipation in metals under cyclic loading, mater. sci. eng. a, 462(1-2), pp. 367-369. doi: 10.1016/j.msea.2006.02.462. [11] iziumova, a., vshivkov, a., prokhorov, a., plekhov, o., venkatraman, b. (2016). study of heat source evolution during elastic-plastic deformation of titanium alloy ti-0.8al-0.8mn based on contact and non-contact measurements, pnrpu mech. bull., 1, pp. 68-81. doi: 10.15593/perm.mech/2016.1.05. [12] plekhov, o., vshivkov, a., iziumova, a., zakharov, a., shlyannikov, v. (2019). the experimental study of energy dissipation during fatigue crack propagation under biaxial loading, frat. ed integrita strutt., 48, pp. 50-57. doi: 10.3221/igf-esis.48.07. [13] brémond, p. (2007). new developments in thermo elastic stress analysis by infrared thermography. iv panamerican conference for non destructive testing, buenos aires, argentina, 22-26 october. [14] sakagami, t., kubo, s., tamura, e., nishimura, t. (2005). identification of plastic-zone based on double frequency lock-in thermographic temperature measurement. international conference of fracture icf 11, turin, italy, 20-25 march. [15] bär, j. (2016). determination of dissipated energy in fatigue crack propagation experiments with lock-in thermography and heat flow measurements, procedia struct. integr., 2, pp. 2105-2112. doi: 10.1016/j.prostr.2016.06.264. [16] de finis, r., palumbo, d., ancona, f., galietti, u. (2017). fatigue behaviour of stainless steels: a multi-parametric approach. conference proceedings of the society for experimental mechanics series, 9, pp. 1-8. [17] de finis, r., palumbo, d., galietti, u. (2018). energetic approach to study the plastic behaviour in ct specimens. 14th quantitative infrared thermography conference, berlin, germany, 25-29 june. doi: 10.21611/qirt.2018.133. [18] bär, j., seifert, s. (2014). investigation of energy dissipation and plastic zone size during fatigue crack propagation in a high-alloyed steel, procedia mater. sci., 3, pp. 408-413. doi: 10.1016/j.mspro.2014.06.068. [19] bär, j., seifert, s. (2014). thermographic investigation of fatigue crack propagation in a high-alloyed steel, adv. mater. res., 891-892, pp. 936-941. doi: 10.4028/www.scientific.net/amr.891-892.936. [20] bär, j. (2016). determination of dissipated energy in fatigue crack propagation experiments with lock-in thermography and heat flow measurements, procedia struct. integr., 2, pp. 2105-2112. doi: 10.1016/j.prostr.2016.06.264. [21] bär, j., urbanek, r. (2019). determination of dissipated energy in fatigue crack propagation experiments with lock-in thermography, frat. ed integrita strutt., 48, pp. 563-570. doi: 10.3221/igf-esis.48.54. [22] palumbo, d., de finis, r., galietti, u. (2019). evaluation of the heat dissipated around the crack tip of aisi 422 and cf3m steels by means of thermography, procedia struct. integr., 18, pp. 875-885. doi: 10.1016/j.prostr.2019.08.238. [23] rigon, d., ricotta, m., meneghetti, g. (2019). analysis of dissipated energy and temperature fields at severe notches of aisi 304l stainless steel specimens, frat. ed integrita strutt., 47, pp. 334-347. doi: 10.3221/igf-esis.47.25. [24] plekhov, o., vshivkov, a., iziumova, a., venkatraman, b. (2019). a model of energy dissipation at fatigue crack tip in metals, frat. ed integrita strutt., 48, pp. 451-458. doi: 10.3221/igf-esis.48.43. a. vedernikova et alii, frattura ed integrità strutturale, 21 (2020) 1-8; doi: 10.3221/igf-esis.51.01 8 [25] plekhov, o., vshivkov, a., iziumova, a., zakharov, a., shlyannikov, v. (2019). the experimental study of energy dissipation during fatigue crack propagation under biaxial loading, frat. ed integrita strutt., 48, pp. 50-57. doi: 10.3221/igf-esis.48.07. [26] nayeb-hashemi, h., swet, d., vaziri, a. (2004). new electrical potential method for measuring crack growth in nonconductive materials, meas. j. int. meas. confed., 36(2), pp. 21-129. doi: 10.1016/j.measurement.2004.05.002. [27] boulanger, t., chrysochoos, a., mabru, c., galtier, a. (2004). calorimetric analysis of dissipative and thermoelastic effects associated with the fatigue behavior of steels, int. j. fatigue, 26, pp. 221-229. doi: 10.1016/s0142-1123(03)00171-3. [28] chrysochoos, a., louche, h. 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/hrv (za stvaranje adobe pdf dokumenata najpogodnijih za visokokvalitetni ispis prije tiskanja koristite ove postavke. stvoreni pdf dokumenti mogu se otvoriti acrobat i adobe reader 5.0 i kasnijim verzijama.) /hun 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dottora 4/5 invited l mi. erale come fin con titolo da d ell’associazio ione più effic 4 (2010); notiz abruzzi 24, co cosmi, giuse eretta, franc mel. i riferim gf. ndo il sito es ca susmel ermare, refer tional journa beretta e k.h. schwa ato. lecturers o 2 nanziamento definire, refer ne, in partico cace; ziario 97 on il eppe esca menti sis e ente al of albe, h di per renti olare fra 98 pun no il p con la con ris (te pun vie nor ea con ig pun pro pre co il p dop all’ il tele all’a il p me del pun ne pun il p per l’a il n ve il n attura ed integrità è necessario nella diffico newsletter l’eventuale prossimo c nto 6 all’o.d.g on ci sono var presidente sci nsiglio di presid riunione ha i n il seguente o comunicazi attività igf ecf 20 sito e rivista varie ed eve sultano prese esoriere), stef nto 1 all’o.d.g ene letta la re rmativa non as comporta n conseguent gf, considerat nto 2 all’o.d.g summe osegue l’orga esso le associ onvegno. giornat presidente rip po lunga ed appoggio org assemb 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ravvedim tive detassazi menti obbliga i vedono part 2010. l cdp sono i rganizzate du i offerte per opportuno lim ativo ad altre organizzare l nche di quelli munque defini uovo evento a ditrici interna upportato in q didare l’italia. associazione ri del consigli in ottobre, c al 9th ysesm bile di soci; nno 2010 dat are un confro enersi appena ede di metallu esidente), fra i cui non è s mento in sana ione delle quo atori previsti ticolari proble invitati a con ue cene sociali l’organizzazi mitare il co associazioni/ l’annuale ass i assenti) ad o ita entro la fin a forni di so azionali. il pr questo da sus . vengono pr italiana di m io di presiden on un lavoro m. to il fitto cale onto aperto e a prima di que urgia dell’uni ancesca cosm stato possibil atoria. l'omes ote associativ per le societ emi. ntribuire alla i, una in occa ione della gio ntributo dell /enti. semblea dei organizzare u ne di maggio opra nel 2011 residente si f smel. il consi roposte divers metallurgia ed nza igf. introduttivo ndario di imp e democratico ella ordinaria iversità di ro mi (segretario le adempiere. ssa presentazi ve e dei contri à commercia pubblicizzazi asione della s ornata su ust l’igf al sol soci. dopo una giornata 2010. . tale evento fa carico di d iglio approva se sedi. icf e l’imp di james. pegni, si ritien o; a in occasione oma la sapie o), angelo fi . al moment ione del mod ibuti istituzio ali. nel caso ione degli ev scuola, una p tica. il consig lo patrocinio o aver verifi igf da assoc o consisterà in definire i det a all’unanimità pegno necess ne la e del enza, nelli to la dello nali, dell’ venti per il glio, o ed cato ciare n un ttagli à. sario pun no il p con la seg 1) c 2) c 3) f 4) c 5) e 6) m 7) g 8) v ri (te ap ale pun a nor par com co sot ma il p isi del pun l'a ore di pun sus pre lim l'in (pe atti luc pun il p di l mo sar avr pun a p per icf on mo nto 5 all’o.d.g on vi sono va presidente sci nsiglio di presid riunione ha i guente ordine comunicazio convocazion 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fonicamente e della partec iù a ripetersi. qualità di dir o necessarie a incaricherà de i soci ta a bologna i semblea si sv oltà di ingegn zione del joi la struttura ilità di discus videoregistra viste pubblich lità di tenere u terrà a cassin emblea strao no le session d il prof. w. n i lavori prose no novità. informa il co alla digitalizza oltre, l’igf ha a del presiden 2010 presso acoviello (pre stefano beret risultato evi el 7 luglio. c via mail all’ el 7 luglio co la procedura cipazione ai rettore della r alcune modifi ell’attivazione in data 29 ott volgerà presso neria). int meeting d del meeting ssione. la sca azioni dell’eve heranno uno un meeting b no dal 13 al 1 rdinaria dei s ni avranno ini nicodemi del eguiranno mer onsiglio che azione dell’int a offerto all’i nte, come per fr l'edificio h3 esidente), fra tta, giuseppe idente l’impo considerata l ’intero cons ome istruttor a straordinar consigli di p rivista igf, h iche organizz e delle proced tobre 2010 all o l’università di int. journa sarà quella d adenza per l'a ento e la pub special issue ilaterale italia 15 giugno. la soci convocat izio con due l politecnico rcoledì 15 giu è in corso un tero patrimon cf la propria raltro già not rattura ed integri dell'universi ancesca cosm e ferro, dom ossibilità di ra la necessità d siglio di dero ria ai fini di ria all’unanim presidenza, a ha attivato la p zative, fra cui dure. le ore 11.00 i à di bologna, al of fatigue di un worksh adesione è il 7 bblicazione d e con una pag a/irlanda nel a prima sessio ta con un sol memorie inv di milano. l ugno, per con na stretta col nio culturale a collaborazio to al consigli ità strutturale, 1 ità degli studi mi (segretario menico genti aggiungere il di deliberare ogare in via una approva mità. il presid auspicando v procedura pe una differen n prima conv , al terzo pian e e fatigue an hop ad inviti 7/11 e per l'in degli atti su s gina di apertu mese di gen one avrà inizio lo punto all’o vitate. il relat l’assemblea o 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resources sh vourable, pub her productio is income fr o in order to to be done w dresden in a der an arrang uctures” ndrea carpin he 3rd interna h september, rea carpinteri agnoli (parma mechanics”, v (cp 2009)”, h fr n prima conv o l’università di ingegneria) magna della delich (ge), p re are regular d january 2010 elsevier sup 5000 euro f hould be sear blishing hous on of special i rom elsevier enable a sup without a clea august 2010. gement of a t nteri (parma) ational confer 2009. i (parma), pr a): guest edit vol.77, 2010, held in vicen rattura ed integri vocazione, ed di bologna, ). a facoltà di prof. j. janov r meetings an 0) devoted to port for esis for each speci rched for. ne e should be f issues or stp r for two spe pport for you ar backgroun dr. fedelich tc2 workshop , professor rence on “cr rofessor paolo tors of a spec with papers s nza, italy, 23rd ità strutturale, 1 d alle ore 11 al terzo pian ingegneria d vec (svk), d nd workshops o tc2 were p s will be subs ial issue publ evertheless, th found. p´s will be sus ecial issues. t ung scientists nd and an app h promised to p in oxford, u paolo lazza rack paths (cp o lazzarin (p cial issue on “ selected from d to 25th sep 4 (2010); notiz 1.15 in secon no della sede dell’università dr. v. kozhu s each year. t ublished. stantially redu lished in sele he esis/else spended until this amount to participat propriate supp o organize a t uk, in 2012. arin (padua) p 2009)”, hel padua), profe “crack paths m those presen ptember, 2009 ziario 101 nda del à di usko two uced cted evier l the was te at port tc2 and ld in essor s” of nted 9. fra 102 (c) (d) (e) (f) am or es com es adh for co (les tec con th in en live act th aim sho (b.b attura ed integrità 2 professor (darmstad in parma, i professor (darmstad fatigue”, v fatigue and professor guest edi mechanics fatigue and professor e approach t the main o 1. develop strain en 2. develop frequen 3. improv subjecte mong the mos 1. karolcz techno 2. rozum univers rganization of 1. the 6th (poland 2. the xv (poland sis tc4 "poly mmittee meeting is tc4 cont hesives and to rward meetin 22nd-24th se 18th-20th m 11th-15th se 15th-16th se ommittee me sdiablerets@e chnical comm nferences he 5th esis t les diablere ngineering fra e in july 2010 ctive work areas he following a m that these w ould either co blackman@im à strutturale, 14 andrea carp t): chairmen italy, 7th to 9 andrea carp t): guest ed vol.33, 2011, d fracture (ic andrea carp itors of a sp ”, vol.78, 20 d fracture (ic ewald macha to multiaxial f objectives of pment of new nergy density pment of a s ncy domain. vement of pr ed to multiax st important r zuk a., nonology, opole 2 ek d., mixed sity of techn f two internat h internationa d). v internationa d). lymers and p gs tinues to me o organise an ng dates for th ept 2010 (tc may 2011 (tc4 ept 2011 (6th i ept 2011 (tc eetings are eurotel-victor mittee secretary tc4 internatio ets, switzerla acture mecha 0. see www.tc s are active wor will become fu ontact the w mperial.ac.uk) 4 (2010); notizi pinteri (parm of the 9th in 9th june, 2010 pinteri (parm ditors of a s , with papers cmff9), to b pinteri (parm pecial issue 011, with pap cmff9), to b a (chairman o fatigue using the project ar w procedures y parameter at spectral meth rocedures of ial service loa results, public -local method 2009, 152 pag d mode fatig ology, opole tional confer al conferenc al colloquium polymer compo et twice a ye international he committee c4 committee 4 committee international 4 committee open to a ria.ch) to ma ry, bamber bl onal confere and. selecte anics, 76 (18) c4pca.elsevier rk areas, in w ull iso stand work area co) for further d iario ma), professo nternational c 0. ma), professo special issue s selected fro be held in par ma), professor on “multiax ers selected f be held in par of the esis t the critical pl re: s for accurate t the strength hod for fatigu f fatigue dam ading by calcu cation of hab ds in fatigue ges. gue cracks o e 2009, 152 pa rences: ce on mecha m on mechan osites" ear to develo l confernece e, all to be hel e meeting) e meeting) l esis tc4 co e meeting) all. please ake room bo lackman (b.bl nce on the f ed papers fro december 2 r.com which the tech dands in due c ordinator (se details. or les p. p conference on or les p. p on “multiax om those pre rma, italy, 7th r les p. poo xial fracture” from those p rma, italy, 7th tc 3.1 sub-c lane. stage 4” e determinatio h test stand. ue life assess mage map de ulations with ilitation disse e calculation, f constructio ages. atronic system nical fatigue o op fracture m every three ye ld in les diab onference) contact th ookings. an lackman@im fracture of po om this con 009. the ‘ca hnical comm course. anyo ee below) or pook (londo n multiaxial f pook (londo xial fatigue m esented at th h to 9th june, ok (london) ” of the inte presented at th h to 9th june, committee “m ”. on of fatigue ment of mat etermination fem or bem ertations: studies and onal material ms and mate of metals (xv mechanics tes ears. berets, switze he eurotel n agenda for perial.ac.uk). olymers, com ference have all for papers’ mittee are deve one wishing t the committ n) and prof fatigue and f n) and prof models” of t he internation , 2010. and profess ernational jo he internatio , 2010. multiaxial fati characteristic terials under for machine m and spectra monographs s, studies and erials (msm v-icmfm), 1 st methods fo erland are: victoria in r the meeting mposites and a e been publi ’ for the 6th i eloping esis to get involve tee technical fessor cetin fracture (icm fessor cetin the “internat nal conferen or andrea s ournal “engin onal conferen igue”): projec cs of material multiaxial ran e component al methods. s z. 241, opo d monograph 2010), 5-8 j 13-15 septem or polymers, les diabl g can be ob adhesives to ished as a sp international s tc4 test pr ed in these ex secretary, ba morris son mff9), to be h morris son tional journa nce on multia pagnoli (parm neering frac nce on multia ct “energy-ba ls with contro ndom loadin ts and struct ole universit hs z. 241, op uly 2010, op mber 2010, op composites erets via em btained from ook place in 2 pecial edition conference w rotocols with xciting work a amber blackm sino held sino al of axial ma): cture axial ased olled ng in tures ty of pole pole pole and mail the 2008 n of went h the areas man 1. p fol in loa pro 2. c fol 135 cur polymers: llowing the su short fibre c ading (iso 17 otocols in the 1.1 work are the commit criteria for k multi-specim adhesives an measure the modified tes 1.2 work are the commit published in composites, insufficiently poor reprodu 1.3 work are the commit cutting techn specimen via by measuring been comple 1.4 work leonardo.cas the commit various hosti and will perm round-robin composites: llowing the su 586-2) and fo rrently develo 2.1 work andrea.pavan the commit rate (iso 1 committe fo include the i and fibre ori 2.2 work andreas.brun the commit engineering fabrics and completed. 2.3 work i.horsfall@cr the commit rates (iso measuremen uccessful dev omposites (i 7281) and un e following ar ea: jc testing; ttee aims to d kc and gc. men techniqu nd composit crack growt t and analysis ea: essential ttee aims to n 2001 (esis , elsevier 20 y reproducibl ucibility in th ea: determina ttee aims to d nique. a test a orthogonal g forces in tw eted and a sec k area: stellani@polim ttee aims to d ile environme mit different testing is due uccessful dev or delaminati oping test pro area: short n@polimi.it) ttee aims to e 3586-2) to fa or determining dentification ientation effec area: dela nner@empa.c ttee aims to laminates wh through-thic area: dela ranfield.ac.uk ttee aims to e 15024) to hi nt of accurate velopment of so 13586-2) nder tension-t reas: co-ordinator develop a tes a protocol w ue (esis pub tes, elsevier th in the test. s schemes un work of fract develop a p publication 2 01) but in th le to warrant he results via r ation of gc v evelop an alte protocol has cutting at a c wo directions, cond is now u environmen merieuropa.co develop a test ents. the act test environm e to commen velopment of ion resistance otocols in the t fibre com extend the te aster rates (ci g kc and gc and teatmen cts. amination o ch) extend the te here other fib ckness (3d) amination o k) extend the tes igher rates ( e and reliable standards for and of the tension fatigu r: francesco b st protocol to was develope blication 28, 2001). the . developme der considera ture; co-ordi plane stress f 28, chapter 2 he view of t t standardisati round-robin s via cutting; c ernative techn s been develo constant spee , in the directi undeway with nal stress om) t protocol to tivity started ments to be nce. standards fo e of unidirec following are mposites at echniques dev irca 1m/s). c in bulk poly t of ‘pop-in’ of ud and echniques de bre orientatio reinforceme of ud lam st developed (circa 1m/s). test data and r slow rate k develoment o ue loading (is baldi (email: o characterise ed by the com chapter 2, major limitin ent of the tes ation. inator: marta fracture test 2, fracture m the committe tion within is studies and ad co-ordinator: nique for the oped in which ed (eng frac ion of cutting hin the comm cracking; o determine th in 2010. the studied. an r slow rate k ctional lamina eas: high laodi veloped to de such develop ymers at highe failure, the m d cross-ply eveloped to d ons are typic ents. round minates at for the deter the challe d the treatme fr kc and gc det of a test stan so 15850), t baldi@ing.un e toughness i mmittee mem fracture m ng factor has t method is rink (email: for polymeri mechanics tes ee, the result so. the com dditional exp gordon will determinatio h a tool is used ct mech 76, (1 g and transve mittee. co-ordina he sensitivity test adopted initial esis t kc and gc det ates in mode ing rates; c etermine kc pment will bu er rates (iso mitigation of d laminates; determine gi ally used. t d-robins on high rates rmination of enges include ent of kinetic rattura ed integri termination in ndard for the the committe nibs.it) in polymers w mbers hale an mechanics tes s proved to b still underwa marta.rink@p ic films. a ting methods s produced b mmittee is in erimental and liams (email: on of gc in to d to remove a 18) p.2711-27 erse to this dir ator: leon of different d will follow a tc4 protoco termination in e i (iso 150 co-ordinator and gc of sh uild upon th 17281). tech dynamic effec co-ordinato ic via delami these can inc various diffe , co-ordina delamination e the mitigat c energy efect ità strutturale, 1 n polymers (i ese properties ee is currently which fail th nd ramsteine sting method be the difficu ay within the polimi.it) version of t s for polymer by this meth nvestigating th d theoretical c g.williams@i ough, ductile a thin layer o 730, 2009). g rection. one nardo cas polymes to s a fracture mec ol has been d n short fibre 024: 2000), t r: andrea hort fibre co e tecniques d hnical issues cts and specim or: andy b ination in ud clude cross-pl erent compo ator: ian h n resistance a tion of dyna ts. a protoco 4 (2010); notiz so 13586-1) s at high rate y developing he lefm vali er, based upo ds for polym ulty to accura committee, w the protocol rs adhesives hod are curre he origins of contributions imperial.ac.uk polymers usi f polymer fro gc is determi e round-robin stellani (em stress crackin chanics appro development, composites ( the committe pavan (em mposites at s developed by being addre men manufac brunner (em d composite ly layups, wo osites have b horsfall (em at quasi-static amic effects, ol was drafted ziario 103 and es of test idity on a mers ately with was and ently f the s. k) ng a om a ined n has mail: ng in oach and (iso ee is mail: slow y the ssed cture mail: es to oven been mail: test the d by fra 104 3. a es a s pas sho du ma es 20 fol gro the ma tec cra ka sin wit ass in elab thr lead no sui com and attura ed integrità 4 bamber blac round robin 2.4 work are the commi delamination applied crac completed, a adhesives: 3.1 work are the commit structural ad mode i fract standard in developmen ratio mixedconditions. 3.2 work are the commit a flexible lay made of ‘ho difficult it is packaging la structural ad arm. an es polymers ad prepared for sis tc8 “ n special issue st year tc8 d ould be discu uring ecf in aterial modelli sis tc10 “ e years esis t llowing a kic oup was form e areas of fra aterials. the chniques and acking). in 19 arpenko physi nce then, tc th contributio sessment; dam the past, the boration of f rough the gra d to the intro ow, tc 10 ta ted. knowle mplex technic d working pa à strutturale, 14 ckman and a is planned in ea: delaminat ttee aims to n fatigue. th ck opening d and a second ea: fracture o ttee aims to d dhesive joints ture is now c 2009 (iso 2 t of a mode i mode (frmm ea: peel testin ttee aims to d yer by peeling w well a sub to peel the aminates and dhesives. the sis test pro dhesives and r submission t numerical meth about the fis did not achie ssed in the ne n dresden pr ing. environmenta tc10 on env ck-off works mally establish acture mecha work has alw their applica 995, a sub-com ico-mechanic 10 and its sub ons typically a mage mechani work of tc fracture contr ant of two res oduction of a akes up new dge managem cal problems arties (comm 4 (2010); notizi a round-robin n the near futu tion fatigue in o develop a he quasi-stati displacement. round robin of structural a develop linear under modes complete follo 25217: 2009). ii test using m) test. the ng of flexible develop test p g. the centra strate is bond substrate.’ in more recen e major challe otocol is avail d composites to iso. hods" t meeting of eved much p ext meeting. rof. yuan ha ally assisted c vironmentally shop at gks hed as esis t anics as a m ways been st ation to prob mmittee on “ cal institute o b-committee addressing m isms and thei c 10 was focu rol guidelines search projec new iso stan eac related ment in the are new cha munities of pr iario n using a ud ure. n ud laminat test protoco ic test protoc . a first ro is now under adhesive joint r elastic fractu s i, ii and mi owing the pu the curren the calibrated re is a future laminates; co protocols to d al goal has be ded’ as oppo nitial round r nt activity has enge here is t lable esis pu s, elsevier 20 the re-launch rogress in ro as organized cracking” and y-assisted cra ss in 1990 rel tc 10 in 1991 method of fa trongly relate lems of eac “hydrogen d of the nationa have jointly materials prope ir prevention; used on the d s for controll cts which invo ndard on acce d tasks for w area of env allenges, and ractice) and th d carbon fib tes; co-ordin ol to measur col (iso 150 ound robin u rway. ts; co-ordiona ure mechanics ixed i/ii load ublication of nt round robi d end-loaded e goal to exten o-ordinator: n determine the een to develo sed to the m robins focuss s been direct to accurately ublication 28 001, and a m hed tc8 has ound-robin on a meeting fo d subcommittee acking ated to the to 1. the main o ilure assessm ed to the de c, with main degradation” al academy o organised a n erties under e ; corrosion m development ling eac. th olved more th elerated eac which the ope vironmental d the participat he formation bre peek co ator: gerald p e the fatigue 24) has been using a carb ator: bamber s (lefm) tes ding regimes. a british stan in activities in split (c-els nd the lefm neal murphy e adhesive fra op geometry i much more co sed on the m ted towards account for t 8, chapter 3, more fully dev just been pub n cohesive m or tc8 as we e on "hydroge opic of "envi objective of t ment, and of evelopment o emphasis on was founded of sciences of number of suc environmenta management. of innovative he work was han 30 europ c testing. en and versat degradation o tion in existin n of new netw omposite has pinter (email: e resistance n modified fo on fibre rein r blackman (b st standards f the develop ndard in 2001 n the commi s) test and in m tests to hig (email: neal.m acture toughn independent ommonly mea measurement o the peeling o the energy di fracture me veloped versi blished onto model. a maj ell as a work en degradation ironmentally tc10 was to environmen of fracture m n monotonic d following an f ukraine. ccessful techn al degradation e methods fo supported b pean laborato tile structure of metallic m ng networks works will pla been compl : pinter@unil of composit or fatigue loa nforced com b.blackman@ for the determ pment of the 1 (bs 7991:2 ittee are direc mixed-mode gh rates and t murphy@ucd ness, ga, for t tests where a asured peel st of adhesion b of metallic la issipated plast echanics test ion of this is eng. fract. m or problem i kshop for mi n" assisted crac merge resear ntal degradati mechanics tes loading (i.e., n initiative of nical meeting n; inspection or testing of by the europ ories and rese of the group materials and such as techn ay an importa leted. a sec leoben.ac.at) tes to failure ading at cons mposite has b @imperial.ac.u mination of g test protocol 001) and an cted towards e using the fix to fatigue load d.ie) the debondin a measuremen trength, i.e. ‘h between layer ayers bonded tically in the ting methods s currently b mechanics. in is funding wh icroand ma cking", eac, rch experienc ion/corrosion t and evalua stress corro f members of gs and worksh and control; eac and on ean commis earch groups p appears ide the solution nical associati ant role in fut cond e by stant been uk) gc in l for iso the xedding ng of nt is how rs in d by peel s for eing n the hich acro, the ce in n of ation sion f the hops risk n the sion and eally n of ions ture. on scie ind ap we tc org for en sym es at ch vic tre sec in lin (ep pet uk (in uk th of t 1. i th act fur 2. g 2.1 th wh the 2.2 du co th by sta to t ne example is entists and e dustry needs i part from this re the 4th internati ukraine, in c 11th polish-u 12th quadren conference c10 was also ganized in the r the forthco nhanced effe mposium. sis tc11 " h the agm he hairman ce chairman easurer cretary addition the ncoln,uk), m pri, usa), m tten, nl), dr k), mr p. m nstron, hi k), mr mike s he following a tc11 activiti introduction he committee tivity continue rther informa general activit 1 european stru he high temp hilst retaining e activities of 2 conferences an uring 2009-10 ommittee effo he first of the phil jones an ff from serco their hard wo s the “medite engineers with in the mediter s, tc10 conti ional confere combination w ukrainian-ge nnial internat "wear pro o strongly inv e frame of na oming 18th e ects" compris high tempera eld at serco dr hellmu (bam, ge mr larry c dr peter b (doosan b mr malcol (npl, ted following we mr colin austi mr carl barr r stuart hold mccarthy (co igh wycomb spindler (brit are extracts fr ies during 200 e has continu es and plans d ation about th ties ructural integrity perature mech its status as the htmtc nd seminars 0 no formal co ort during 200 se will be a m nd mike lyn o assurance, ork. erranean net h expertise in rranean coun inued to supp ence "fractu with the rman summe tional confer ocesses 20 volved in th ato “scienc european co sing a total ature mechanic o, risley, uk uth klingelhö ermany) candler (exo barnard babcock, tipt lm s loveday ddington, uk ere elected to tin (serco a rett (ukas, dsworth (emp onsultant, cr be, uk), prof tish energy, g rom the outgo 09: ued to be ac developed fo he htmtc m ty society hanical testin a uk charity c have been p onferences or 09-10 has focu meeting on h ch, to be hel have put sign twork on co n corrosion, ntries. port and co-s ure mechanic er school on rence on frac 009", 19-20 n he workshop ce for peace” onference on of six sessio ical testing" on tuesday 2 öffer va, uk) ton, uk) y k) o the main co assurance, ri feltham, uk pa, zurich, s rawley, uk), f. kamran ni gloucester, u oing chairma tive througho r future activ may be found ng committe y and a com ublished in th r seminars we ussed upon e high tempera d on 20th an nificant effor orrosion and environment sponsor eac cs of materia fracture mec cture, icf12, j november 200 p "integrity o in biskra, alg fracture tc ons, and wil 20th april 20 ommittee : m isley, uk), pr k), mr. s. co switzerland), , dr p. mor ikbin (imperi uk). an’s report, p out the past vities / meetin d on the webee (htmtc) mpany limited he esis new ere held. events for the ature mechan nd 21st april rt into its org fr integrity” in tally assisted c related con als and struc chanics, 23 2 july 12-17, 20 09 in szczecin of pipelines geria, april 2 c10 has orga ll hold a tec 010 the follow miss kate ab rof. martin ba ollins (inco mr phil jone rris (corus rial college, l prepared by m year. two ngs of the com site at www.h operates as t d by guarant wsletter. e next two yea nical testing i 2010. the s ganisation and rattura ed integri nitiated by tc cracking and ferences and ctural integrit 27 june 2009 009, in ottaw n-świnoujście transporting 6-29 2010. anised a symp chnical meeti wing officers bott (siemen ache (univ. s o, hereford, u es (alstom po s, rotherham london, uk) mr paul mcc meetings hav mmittee. htmtc.com technical com tee. contact ars. in controlled steering group d the success ità strutturale, 1 c10 and aime d material sci workshops. ty", 23 -27 j , in lviv, ukr wa, canada. e, poland. g hydrocarb posium on " ing in conju were elected ns industrial t swansea, uk) uk), dr. p ower turbom, uk), mr ) mr owen o carthy, which ve been held mmittee 11 (t with esis ha d environmen p, plus organ of this work 4 (2010); notiz ed at connec ience to supp the most re june 2009, l raine. ons" which "environmen nction with : turbomachin ), prof. b. do hähner (ie-j -systems, ru i. mcenteg o’grady (ex gives a summ d, working gr tc11) of e as continued nts, co-ordin nisational supp kshop will be ziario 105 cting port cent lviv, was ntally this nery, ogan jrc ugby, ggart ova, mary roup esis, and ated port due fra 106 th me ber a t in me me 2.3 pub the 2.4 du a th t s t n th 2.5 2.5 th em min 3. c th res as our of dev attura ed integrità 6 he second ev echanical fati rlin,germany third event, ad n addition to eetings outsid echanical testi 3 publications blications by e htmtc um 4 working gro uring the year although the he past year, the subject h tand). the temperat novel tempera hermal fixed p the miniatu appropriate the crack work in this a) the colla ‘code of b) vamas held in co c) the eu p 5 related activi members o committees testing (dr standards (d involved bo proceeding the germa mirrored th committee i fatigue stan voting right regime but projects in t 5 main commit he main comm mpa, dubend nutes and anc conclusion he committee ulting in the in 2008/9, th r remit to ma practice issu velopments in à strutturale, 14 vent, co-ordin igue, to be he y,see www.tm ddressing qu the above, i de the htmt ing. the commit mbrella have p oups r the following testing of w its code of has also been ture measurem ature measure points. work ure testing g e, will expand initiation gr s area within a aboration in v practice for c twa31 –w onjunction wi project ‘cre ities of the comm during the y r. klingelhöf dr. klingelh oth mr. lov (mr mccarth an standard c he iso tc16 intends to be dard commit ts on the iso according to the fatigue reg ttee meetings mittee met tw dorf, switzerl cillary papers e continues to development he latter item aintain testing ued by the c n technology 4 (2010); notizi nated by dr. eld on 12th an mf-workshop. uality assuran individual me tc umbrella, ttee during th progressed to g working g weldments w practice on n taken up b ment workin ement techni k on developin group is main its activities. roup, under t astm, vam vamas tw creep/fatigu weldments is ith welds 200 eete’ has bee mittee have c year. work h ffer, dr häh öffer, mr lo veday and m hy, mr loved ommittee on 64 sc5 comm e active in al ttee activated o scale. it can european re gime. but we wice during 2 land; the seco from these m o operate as t of new testin m has involved g methods for committee h and operatio iario . hellmuth k nd 13th may .bam.de nce issues for embers have and have be he year have o the publicati group activity working grou testing of w by internatio ng group, und iques, such a ng a code of ntaining a wat the chairman mas and the e wa25compo ue testing of c s continuing t 09, in florida en completed contributed t has now com hner & mr l oveday & dr mr. mccarthy ay, mr mcen n “fatigue test mittee which ll working gr d austria to b n be summari egulations fiv are confiden 2009/10. th ond was at d meetings have an effective ng technique d significant r the high tem ave been ke onal practice. klingelhöffer 2011, at bam r high tempe continued t een heavily in been limited ion stage. y has taken pla up, under the weldments is onal institute der the chair as an in-situ c practice cont tching brief o ship of prof european pro onent testing cracked com to discuss cra a in june 2009 d and the resu to a number me to fruition loveday) and peter morri ; and revisio nteggart). ting” has bee h contains 14 roups of iso be active in th ized that fou ve countries a nt that a fifth he first meet doosan babco e been circula thematic ne s, or contribu effort from m mperature test ept under rev our aim for r, is the 2n m federal in erature testin to participate nvolved in th during 2009 ace: chairmansh s making prog e of welding rmanship of m calibration m tinues. on developme kamran nik oject crete g – has produ mponents’. ack initiation 9. ults are incorp r of national n on the prep d the revisio s). iso 204 on of the is en re-establis 4 working gr o tc164 sc5 he fatigue sta r european c are needed th european co ting was the ock, tipton, ated to all mem etwork. in-d uting to the p members of t ting field at a view and wil the future, as nd internation nstitute for m ng, is planned in several v he developme 9/10; no activ hip of prof. b gress towards g (iiw) selec mr malcolm l method exploi ents in this fi kbin (imperia e: uced a final v in welds and porated in to l, european paration of a n of the iso 4 – creep te so extensom hed after 15 roups with re 5. furthermo andard regim countries are hat europe is ountry will be agm held o uk on tues mbers. depth technic preparation of the committe “state of the ll, when nec s a committee nal worksho materials resea d for later in 2 very successfu ent of new is vities being u b. dogan, ha s becoming a ct committe loveday, con iting phase ch ield and, whe al college), h version of the d haz. a sm the iso/tta and interna new iso st o & eciss sting – is no meter verifica years inactiv elated fatigue re a member me, too. now active in the s able to star found. on friday 24 sday, 27th oc cal networkin f european & ee over the pa e art” level. in cessary, be re e, continues to op on ther arch and test 2011. ul testing rel so standards undertaken un as not met du an iso stand e standards ntinues to exp hanges to de en the situatio has progressed e iso/tta* mall meeting a 5. ational stand tandard on t tensile tes ow published ation standar vity and has b e standards. r of the germ austria has e fatigue stand rt standardiza 4th april 200 ctober 2009. ng has continu & iso standa ast year, fulfil n addition, co evised to ref o be focussed rmoting, lated s on nder uring dard. (sc plore efine on is d its 5 was ards tmf sting has rd is been the man also dard ation 09 at the ued, ards. lling odes flect d on the act th wh can for dr eic e-m mr tel e-m es pro mo sub 201 sol in he foll h d r f p t it i be th the (w har th est exp e generation o tivity during th he agm was hich was atte ncellations du r further info r hellmuth. k chen 87,1220 mail: hellmuth r m. s. loved l.+44 (0) 193 mail: malcolm sis tc24 "in of beretta and ost of the con bmit the revis 10). this spe lutions by gk autumn 2009 e will host in lowing aspect high cycle and damage releva relationship b fatigue strengt propagation o the impact of is intended to limited to ab he date is not e opportunity wolaxim an rmonized. here is also a ablished afte plosion of a ta of other such he year focus followed by a ended by ov ue to volcanic ormation abou klingelhöffer 5 berlin, ger h.klingelhoef day, htmtc 2 561576 m.loveday@n ntegrity of rai d zerbst have ntributions at sed version) h ecial issue wi kss, polimi a 9 prof. zerbs n autum a m ts are envisag d ultra-high cy ant loading am between differ th and initial f short cracks f corrosion o provide amp out 50 person yet fixed. pos y for a presen nd eureka a plan to inv er the viareg ank wagon. h codes of pr ssed on plann a two day wo ver 50 peopl c ash from ice ut the htmt , htmtc c rmany. phone ffer@bam.de c secretary, npl.co.uk ilway structure e organized a t the worksho has taken a lo ill also conta and iwm that st moved to t meeting of a f ged: ycle fatigue o mplitudes in h rent design ph defects (nons in axles ple time for d ns. ssible dates ar ntation of the a). tc24 plan volve in tc2 ggio accident ractice, benef ning major w orkshop on ‘h le despite a eland. furthe tc – tc11 pl chairman, ba e +4930 8104 national phy res” a special issue op held in m ong time for ain a coopera t had been pr the federal in forum for di of railway axle high cycle fat hilosophies (s -metallic inclu discussion. to re september e uk project ns to be the p 24 meetings t, where a b fiting both th workshops/ se high temper considerable r details may lease contact: am, federal i 4 1521. fax + ysical labora about about milan on octo the preparati ative paper ( resented indep nstitute for m iscussion of es tigue safe life vs. da usions, corro o enhance dis r 27-28, octo rssb-t728 place where th also the er broken axle c fr he european a eminars to be rature mecha e number of be found on institute for +4930 8104 15 atory, queens t “damage t ober 2008. th on but it is n (a real result pendently by materials resea methods for amage toleran sion pits etc.) cussion and i ober 11-12 an and of the n he results of ra (europea caused the tr rattura ed integri and global te e held in 2010 anical testing f people una the htmtc materials re 527 s road, tedd tolerance of r he special iss now at the arr of the tc2 the three bod arch and tes r structural in nce) ) informal exch d october 25 ew eu proje the different an railway a rain derailme ità strutturale, 1 esting commu 0 & 2011. g in controlle able to atten c website: ww esearch & te dington, midd railway axles sue (three pa rival line (it w 24 activity) in dies. ting (bam, b ntegrity of ra hange of idea 5-26. this me ects that will s projects cou agency) com ent with the 4 (2010); notiz unities. the m d environme nd due to fl ww.htmtc.com esting, unter dx., tw11 0l s” which cont apers have jus will appear wi ncorporating berlin, germa ailway axles. s, attendance eeting will also start in fall 2 uld be shared mmittee that e disastrous f ziario 107 main ents’ light m den lw, tains st to ithin sif any). the will o be 2010 and was final fra 108 es tw or 1) 2) 3) attura ed integrità 8 sis procedu wo kinds of do esis p4-92d p means "p d following d prior to t p1-92 esis recom responsible b p2-92 esis proce responsible b p3-03d draft uni responsible bo p4-92d esis recom responsible bo p5-00/vama procedur responsible bo p6-98 esis proce using not responsible bo p7-00 esis proce responsible bo p8-99d esis draft responsible bo p9-02d guidance (under pre p10-02 a code of responsible bo p11-02 technical inclusion responsible bo d1-92 fracture responsible b d2-99 fracture the esis tc6 this activity. th responsible bo à strutturale, 14 ures and do ocuments are d, where: procedure", an g the year (eg the year (eg: d mmendation body: tc1 subcom edure for de body: tc1 subcom ified proced ody: tc1 subcom mmendation ody: tc10 comm as re for deter ody: tc6 commit edure to me tched tensil ody: tc8 commit edure for dy ody: tc5 subcom t code of pra ody: tc11 comm on local ap eparation no practice fo ody: tc11 high t l recomman ns ody: tc20 comm control gu body: tc10 comm toughness 6 and vamas tw he final form of th ody: tc6 commit 4 (2010); notizi ocuments ( e produced by nd 2 and 4 are : 92d) means d1-92) means ns for deter mmittee on fractur etermining mmittee on fractur dure for det mmittee on fractur ns for stress mittee on environm rmining the ttee on ceramics. asure and ca le specimen ttee on numerical ynamic tens mmittee on dynam actice for t mittee on high tem pproach of r ot available) or conductin temperature mech ndations for mittee on inclusion uidelines fo mittee on environm of ceramics wa3 developed a t he test method has ttee on ceramics. iario (www.esisw y esis techn e the current s "draft", ie: n s "document rmining the re mechanics test the fractur re mechanics test termining t re mechanics testi s corrosion mental-assisted cr e fracture to alculate ma s. l methods. sile tests mic testing at inter the determi mperature mechan rupture of m ). ng notched hanical testing co r the extrem ns. r stress cor mental assisted c s using the s test method and co s appeared as p5-0 web.org) nical commit numbers, wh not yet approv t" other than e fracture re ting standards. re behaviou ting standards. the fracture ing standards (un testing usin racking. oughness of aterial para rmediate strain rat nation and nical testing. metallic mat d bar creep r ommittee. me value an rrosion crac racking. evnb metho onducted a round 00. tees with the hile 92 is the y ved, while test methods esistance of ur of materi e behaviour nder prepara ng pre-crack f ceramics u ameters for tes. interpreta terials. rupture test nalysis of dat cking of hig od; round ro robin for its valid following de year of issue. s. f ductile ma ials. r of materia ation not ava ked specime using the sev the local a ation of cycl ts and inter ta on large gh strength obin, test pr dation. d2-99 pres esignatory syst aterials. al. ailable). ns. vnb method approach to lic stress-st rpreting th nonmetall h alloys. rogramme. sents a detailed do tem: esis p2 d . o fracture train data. e data. lic cumentation of 2-92 << /ascii85encodepages false /allowtransparency false /autopositionepsfiles true /autorotatepages /none /binding /left /calgrayprofile (dot gain 20%) /calrgbprofile (srgb iec61966-2.1) /calcmykprofile (u.s. web coated \050swop\051 v2) /srgbprofile (srgb iec61966-2.1) 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can be opened with acrobat and adobe reader 5.0 and later.) >> /namespace [ (adobe) (common) (1.0) ] /othernamespaces [ << /asreaderspreads false /cropimagestoframes true /errorcontrol /warnandcontinue /flattenerignorespreadoverrides false /includeguidesgrids false /includenonprinting false /includeslug false /namespace [ (adobe) (indesign) (4.0) ] /omitplacedbitmaps false /omitplacedeps false /omitplacedpdf false /simulateoverprint /legacy >> << /addbleedmarks false /addcolorbars false /addcropmarks false /addpageinfo false /addregmarks false /convertcolors /converttocmyk /destinationprofilename () /destinationprofileselector /documentcmyk /downsample16bitimages true /flattenerpreset << /presetselector /mediumresolution >> /formelements false /generatestructure false /includebookmarks false /includehyperlinks false /includeinteractive false /includelayers false /includeprofiles false /multimediahandling /useobjectsettings /namespace [ (adobe) (creativesuite) (2.0) ] /pdfxoutputintentprofileselector /documentcmyk /preserveediting true /untaggedcmykhandling /leaveuntagged /untaggedrgbhandling /usedocumentprofile /usedocumentbleed false >> ] >> setdistillerparams << /hwresolution [2400 2400] /pagesize [612.000 792.000] >> setpagedevice microsoft word numero_59_art_26_3301.docx h. nykyforchyn et alii, frattura ed integrità strutturale, 59 (2022) 396-404; doi: 10.3221/igf-esis.59.26 396 focussed on fracture and structural integrity methodology of hydrogen embrittlement study of long-term operated natural gas distribution pipeline steels caused by hydrogen transport hryhoriy nykyforchyn, olha zvirko, myroslava hredil, halyna krechkovska, oleksandr tsyrulnyk, oleksandra student karpenko physico-mechanical institute of the national academy of sciences of ukraine, lviv, ukraine hnykyforchyn@gmail.com, http://orcid.org/ 0000-0003-1012-2901 olha.zvirko@gmail.com, https://orcid.org/0000-0002-6973-6804 mysya.lviv@gmail.com, https://orcid.org/0000-0001-5070-8259 krechkovskahalyna@gmail.com, https://orcid.org/0000-0001-7392-7753 otsyrulnyk@gmail.com, https://orcid.org/0000-0001-9038-966x oleksandrastudent1@gmail.com, https://orcid.org/0000-0002-5638-2744 leonid unigovskyi naftogazbudinformatyka ltd., kyiv, ukraine unileonid2@gmail.com abstract. a methodology of experimental research on hydrogen embrittlement of pipe carbon steels due to the transportation of hydrogen or its mixture with natural gas by a long-term operated gas distribution network is presented. the importance of comparative assessments of the steel in the as-received and operated states basing on the properties that characterize plasticity, resistance to brittle fracture and hydrogen assisted cracking is accentuated. two main methodological peculiarities are pointed out, (i) testing specimens should be cut out in the transverse direction relative to the pipe axis; (ii) strength and plasticity characteristics should be determined using flat tensile specimens with the smallest possible thickness of the working part. the determination of hydrogen concentration in metal, metallographic and fractographic analyses have been supplemented the study. the effectiveness of the proposed methodology has been illustrated by the example of the steel research after its 52-year operation. keywords. exiting natural gas distribution network; pipeline steel; hydrogen transportation; hydrogen embrittlement; dissipated microdamaging. citation: nykyforchyn, h., zvirko, o., hredil, m., krechkovska, h., tsyrulnyk, o., student, o., unigovskyi, l., methodology of hydrogen embrittlement study of long-term operated natural gas distribution pipeline steels caused by hydrogen transport, frattura ed integrità strutturale, 59 (2022) 396-404. received: 13.10.2021 accepted: 17.11.2021 published: 01.01.2022 copyright: © 2022 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. https://youtu.be/tn0n4tjwopk h. nykyforchyn et alii, frattura ed integrità strutturale, 59 (2022) 396-404; doi: 10.3221/igf-esis.59.26 397 introduction nvironmental challenges are a global problem, and attention to these has become especially acute in recent years. one of the ways to minimize environmental challenges is considered to be a radical modernization of energy policy, in particular, by decarbonizing energy sources. this implies the use of hydrogen as an environmentfriendly fuel; therefore, the problem has been arising to transport hydrogen from potential places of its production to consumption places. to solve this task, the possibility of using the existing gas pipeline networks (both transmission and distribution) is considered [1–6]. at the first stages, a mixture of natural gas with a certain percentage of hydrogen is expected to transport. in different eu countries the maximum blend level of hydrogen in natural gas infrastructure is currently in the range 0–12% [4]. hydrogen transportation by gas pipelines is a complex problem, in which a particularly important aspect is the possible integrity violation of the pipes due to the well-known detrimental effect of hydrogen on the mechanical properties of steels. investigations of influence of natural gas/hydrogen mixtures on mechanical properties of pipeline steels demonstrate their susceptibility to hydrogen-induced embrittlement, which increases with the hydrogen partial pressure increasing [3]. added hydrogen significantly influences on deterioration of mechanical properties of notched specimens [3, 5]. it should be noted that hydrogen embrittlement in pipes is considered mainly due to a possible hydrogenating effect of the soil environment in the case of insulation cover damages [7–11], whereas less attention is paid to corrosion processes on the pipe inner surface, however, these could also serve as factors of pipe integrity violation [12–15]. the main issue is possible hydrogenation of the pipe wall from its inner surface because of humidity of the transported gas which causes electrochemical processes leading to hydrogen evolution [16, 17]. hydrogen transportation by pipelines is assumed to intensify the metal hydrogenation for two reasons: (i) due to hydrogen dissociative adsorption [18] and (ii) an increase in the amount of electrochemically formed hydrogen [19] absorbed by the pipe wall. on the other hand, gas pipeline networks usually have been operating for a long time, which leads to the essential deterioration of initial (as-received) physico-mechanical properties of steels, mostly affecting their brittle fracture resistance [20–26]. in the case of hydrogen transportation, a decrease in the resistance to hydrogen embrittlement is especially important since it can cause hardly predictable pipeline failures [19, 20, 27]. developing the study [6], this work presents a set of experimental techniques adapted to assessing the technical state of long-term operated steels of distribution gas pipelines for hydrogen transport in a mixture with natural gas. a carbon pipeline steel after 52-year operation was investigated using the proposed methodology. materials and methods he object of research is carbon steel (ukrainian code is vst3ps) of distribution gas pipelines with an outer diameter of 159 mm and a pipe wall thickness of 4.5 mm made of rolled steel. the steel in the as-received state (spare pipes) and after 52 years of operation has been tested. the chemical composition of the steel in both states is presented in table 1. note a relatively low si content in the operated steel that can affect its quality. elements (wt.%) c si mn cr ni cu p s as-received steel 0.12 0.006 0.36 0.04 0.01 0.01 0.036 0.034 after operation 0.11 0.001 0.45 0.03 0.02 0.02 0.047 0.055 table 1: chemical composition of the carbon steel in the as-received state and after operation. metallography using sem evo-40xvp revealed ferrite-pearlite microstructure of the tested steel (fig. 1). cementite precipitation at the ferrite grain boundaries and an essential amount of traces from non-metallic inclusions (max. 2 m in size) was noted in the as-received steel, and in the case of the operated steel – some cracking at the boundaries of small ferrite grains. standard mechanical properties of strength (σuts, σy) and plasticity (elongation, reduction in area (ra) were determined by tensile testing ( = 3×10-4 s-1) using flat specimens, and impact toughness kcv by charpy testing. besides these tests, the effect of preliminary hydrogenation on steel’s strength and plasticity was evaluated. e t h. nykyforchyn et alii, frattura ed integrità strutturale, 59 (2022) 396-404; doi: 10.3221/igf-esis.59.26 398 figure 1: microstructure of the carbon steel in the as-received (a) and operated (b) states. two main methodical peculiarities should be distinguished in the preparation of the specimens; (i) all specimens are cut transversally to the rolling direction/pipe axis, (ii) working part thickness for the flat specimens is 2 mm. the former one concerns with an essentially higher sensitivity of steel characteristics to operational degradation and hydrogen embrittlement determined on transversal specimens [23, 24]. this choice is explained by the fact that operational damaging of rolled steel pipes mainly consists of microdelaminations along components of the ferrite-pearlite structure and nonmetallic inclusions elongated in the rolling direction [23, 26, 28] leading to such orientation of defects. the orientation of these defects coincides with the fracture plane of transversal specimens (in contrast to longitudinal ones) facilitating the fracture processes, thus, transversal specimens are preferable for testing. this regularity is inherent not only for pipeline steels but also for metal structures of port cranes [29] and pipes of thermal power plants [30]. the latter methodical peculiarity i.e. the use of specimens with a small thickness is reasonable taking into account that steel hydrogenation in both laboratory and field (during hydrogen transportation) conditions starts from its surface. fig. 2 illustrates the shape of flat tensile specimens cut from a pipe in the transversal direction after having applied the manufacture procedure summarized in fig. 3. their thickness and width of the working part are 1.2 mm and 4.0 mm respectively. non-working parts of the specimens are slightly thickened (1.7 mm) to prevent plastic deformation during loading. figure 2: a set of flat tensile specimens. the manufacture of transverse specimens for mechanical tests from thin-walled pipes became possible due to the implementation of a number of engineering solutions. special attention was paid to tensile specimens: a workpiece in the form of a segment of the required size (fig. 3a) was cut out from the pipe section with subsequent straightening of its (a) (b) h. nykyforchyn et alii, frattura ed integrità strutturale, 59 (2022) 396-404; doi: 10.3221/igf-esis.59.26 399 sides (fig. 3b), avoiding deformation of the central part, which fell on the working part of the specimen (fig. 3c). thanks to this procedure, a length of the straightened workpiece made it possible to manufacture the specimen of the required thickness, and the working part of such specimen did not undergo changes. figure 3: fabrication steps for a flat tensile specimen. transversal impact specimens are segment-shaped with the pipe’s radius. to ensure their fixedness during the testing, special tabs were used in which the ends of the specimens were fixed. (fig. 4). this design made it possible to determine the impact strength of steels on specimens with a standard height of 10 mm and a thickness equal to the pipe wall thickness, in this case, 4.5 mm, with a notch depth of 2 mm. figure 4: specimen with tabs for the impact testing. susceptibility of the steel to hydrogen embrittlement was estimated by assessing the changes in characteristics σuts, σy, elongation and ra caused by specimen hydrogenation prior the tensile testing. the results are presented by the parameter λ as the ratio of the corresponding characteristics determined for the steel in the as-received and operated states:    100%h p p p , (1) where strength and plasticity characteristics of steels are given for hydrogenated (ph) and non-hydrogenated (p) specimens. preliminary hydrogenation was done electrochemically in the h2so4 water solution (рн 3.5) under a cathodic current density of 1 mа/сm2 during 100 h. this electrolyte ensures, from the one hand, relatively low corrosion and, from the other hand, the absence of the shielding effect of surface films, which is inherent for solutions with рн ≥ 4. prolonged hydrogenation provides the uniform distribution of hydrogen in the bulk of the specimens. after the completion of the hydrogen charging, the specimens were removed from the cell, dried, and loaded by tension in the air until fracture at the same deformation rate as the non-hydrogenated specimens. the time between the processes of hydrogenation and fracture of specimens did not exceed 10 min, thus, the desorption of hydrogen from the metal is considered insignificant. h. nykyforchyn et alii, frattura ed integrità strutturale, 59 (2022) 396-404; doi: 10.3221/igf-esis.59.26 400 the content of the residual hydrogen in steels was determined using hydrogen analyser eltra h-500 at temperature 950 ºс. rectangular specimens 19.0×4.7×4.1 mm were polished, degreased with acetone, and then washed with ether. residual ether was removed with a rapid stream of hot air. assessment of steel sensitivity to hydrogen embrittlement in the as-received and operated states he results of tensile tests averaged from three specimens is presented in table 2. note a lower (by 12-15%) strength of the operated steel comparing to the as-received one. plasticity is relatively low as for a given steel grade, however, it was determined using transversal (t) specimens for which plasticity characteristics are expectedly lower than for longitudinal (l) ones. in particular, as derived from [30], the ratio rat/ral≈0.95 for a lowalloyed heat-resistant steel in the as-received state and can drop to ≈0.85 for the operated one due to the intensification of the steel anisotropy with operation time. for pipeline steels with clearly detectable defects oriented in the longitudinal direction, this ratio is expected to be higher. in addition, specimens of a small thickness (1.2 mm) were tested, which could also affect the results [31]. steel state specimen no. y [mpa] average y [mpa] uts [mpa] average uts [mpa] elongation [%] average elongation [%] rat [%] average ra [%] as-received steel 1 330 344 487 468 18 17 58 59 2 356 456 14 58 3 345 460 16 60 after operation 4 303 302 407 404 15 16 54 54 5 308 404 16 56 6 296 402 17 51 table 2: standard mechanical properties of steels in the as-received and operated states. plasticity is only slightly decreased due to operation; however, this is accompanied by strength loss, which corresponds to the main regularities of the operational degradation [19, 25, 26] – a simultaneous decrease of both strength and plasticity indicates the development of operational microdamages in the material. impact testing results averaged three specimens are (98±4) j/сm2 and (9±4) j/сm2 respectively for the as-received and operated steel. these data indicate not only an order of magnitude difference between kcv values of steel in the asreceived and operated states, but also an extremely low level of brittle fracture resistance for the operated steel. figure 5: fracture surfaces of impact specimens (notch on the left) of the carbon steel in the as-received steel (а) and after operation (b). t (a) (b) h. nykyforchyn et alii, frattura ed integrità strutturale, 59 (2022) 396-404; doi: 10.3221/igf-esis.59.26 401 microfractographic analysis (fig. 5) confirmed fundamental differences in brittle fracture resistance of steels in different states. steel in the as-received state is characterized by more high-energy fracture type with clear signs of fracture surface texture due to delaminations along the rolling direction. thin nonmetallic inclusions (identified as manganese sulphides by morphological features) were found, as a rule, at the bottom of delaminations oriented along the texture. their decohesion from the matrix led to the occurrence of such delaminations. as a rule, chains of these inclusions are located in ferrite grain layers crossing their boundaries; therefore, smooth delamination surfaces were associated with fracture within the ferrite. ridges formed as a result of the stretching of the bridges between the delaminations, with small dimples on their surface, were considered a sign of ductile fracture by micro-void coalescence within pearlite grains. fractographic features associated with the steel texture were not observed only in the areas of brittle fracture, which correspond to the zone of spontaneous fracture in as-received steel specimens. the main fractographic peculiarity of the operated steel is in the dominance of the cleavage fracture (fig. 5b) that can explain its extremely low resistance to brittle fracture. such fracture surface formation did not imply only transgranular fracture. in particular, intergranular facets were observed in some places, as well as significant secondary cracking along the grain boundaries. it should be emphasized that intergranular fracture on the fracture surfaces in the as-received steel was not detected at all. it was assumed that steel hydrogenation during long-term operation could contribute to the development of operational microdamages in the form of intergranular cracking. it is known, after all, that hydrogen promotes fracture along both the grain boundaries and interphase ones [27]. thus, such intergranular damage was clearly visualized against the background of a predominantly transgranular relief in the zone of spontaneous fracture in the operated steel during impact testing. note that the extremely low impact toughness for the operated steel concerns the metal with yield strength approx. 300 mpa, whereas such kcv (kcu) value of ~ 1 j/cm2 is typical for hardened steels with martensitic structure (σy > 1500 mpa). this phenomenon can be explained only by taking into account the regularities of the operational degradation of structural steels with the intensive development of dissipated damage in the bulk of the pipe wall. similar results on low brittle fracture resistance (kcv ≤ 20 j/cm2) were reported for pipeline steels and structural steels of portal cranes [19, 29]. the results of hydrogen concentration measurements in the tested steels are presented in table 3. specimen no. steel state hydrogen concentration сн (ppm) average сн value (ppm) 1 as-received 0.134 0.111 2 0.109 3 0.090 4 after operation 0.818 0.459 5 0.482 6 0.317 8 0.149 9 0.656 10 0.331 table 3: hydrogen concentration in steels of different states a significant data scattering on the hydrogen content in specimens from the operated steel is obviously due to its intense operational damage, which has an uneven character. the residual hydrogen content in the operated metal is more than 4 times higher than that of steel in the initial state. evidently, it is the operational hydrogenation of the pipe wall that led to such an intensive operational decrease in the resistance to brittle fracture of the steel. figure 6 illustrates the results obtained by tensile testing of hydrogenated and non-hydrogenated specimens made of the carbon steel in different states. the mechanical properties of hydrogenated specimens were compared with the corresponding characteristics obtained for non-hydrogenated ones depending on the steel state. it can be stated that preliminary hydrogenation insignificantly affected steel strength in both as-received and operated states whereas the influence on plasticity is more noticeable. for the plasticity characteristics, the coefficient λ was calculated as the indicator of the hydrogen effect on steel, namely, of its susceptibility to hydrogen assisted cracking (table 4). the obtained results indicated no effect of preliminary hydrogenation of the steel on its plasticity in the as-received state, however, the operated metal revealed high sensitivity to hydrogen action. reduction in area is a more sensitive parameter for the assessment of hydrogen embrittlement of operated metal than elongation, which is consistent with general regularities [19, 25, 26]. however, at assessment of asreceived steels to hydrogen embrittlement, a high sensitivity of failure elongation was reported in [4]. h. nykyforchyn et alii, frattura ed integrità strutturale, 59 (2022) 396-404; doi: 10.3221/igf-esis.59.26 402 (a) (b) figure 6: strength (a) and plasticity (b) of the carbon steel under tensile testing of non-hydrogenated (white bars) and hydrogenated (black bars) specimens. steel state λ (%) elongation ra as-received 0 2 after operation 26 35 table 4: assessment of metal susceptibility to hydrogen embrittlement based on plasticity characteristics. conclusions he methodology of hydrogen embrittlement evaluation of structural steels has been adapted to the problem of a possible integrity violation of long-term operated gas pipelines in the case of transporting hydrogen or its mixture with natural gas. it implies comparative assessing the state of the as-received and operated steels based on tensile testing with the evaluation of strength and plasticity, determination of the resistance to brittle fracture (impact toughness) and hydrogen assisted cracking (tensile testing of preliminary hydrogenated specimens). the main peculiarities of the proposed methodology are: (i) the use of the specimens cut out transversally relative to the rolling direction (pipe axis), and (ii) the minimization of the plain tensile specimen thickness (in the presented case, to 1.2 mm) to assess the resistance of the steel to hydrogen assisted cracking. the former peculiarity is explained by a higher sensitivity of transversal specimens to operational degradation of rolled steels as compared to longitudinal ones. another peculiarity is due to the need to redistribute the hydrogen formed on the surface into the entire cross-section of the specimens. some engineering solutions have been proposed to ensure these conditions for the specimens cut out from gas distribution pipelines with a small diameter and wall thickness. the applicability of the proposed methodology for hydrogen embrittlement testing has been demonstrated by the example of the carbon steel (0.11-0.12 mass. % of c) of gas distribution pipelines in the as-received and 52-year operated states. the residual hydrogen content in the operated steel was 4 times higher than in the unoperated steel. operational degradation of the steel was revealed by a significant decrease in impact toughness and brittle fracture resistance. deterioration of mechanical properties of the operated steel accompanied by high concentration of residual hydrogen was explained by intensive development of dissipated damages in the bulk of the pipe steel, which could be facilitated by the steel hydrogenation during its operation. microfractographic studies were consistent with the results of mechanical testing on brittle fracture resistance: for the steel in the initial state, a combination of ductile fracture with delaminations in the rolling direction dominated, whereas, in the operated steel, a combination of cleavage with some elements of brittle intergranular fracture and secondary microcracking prevailed. since intergranular cracking was not observed at all on the fracture surface of the as-received steel, it was assumed that intergranular fracture elements were the manifestation of operational damage, the appearance of which was accelerated by steel hydrogenation, and cleavage was a sign of embrittlement of the operated metal. transgranular cleavage of the fracture surface at the stage of spontaneous t h. nykyforchyn et alii, frattura ed integrità strutturale, 59 (2022) 396-404; doi: 10.3221/igf-esis.59.26 403 fracture made it possible to visualize operational damage in the metal in the form of intergranular fragments visible against the background of the flat relief of the transgranular cleavage. references [1] haeseldonckx, d., and d’haeseleer, w. (2007). the use of the natural-gas pipeline infrastructure for hydrogen transport in a changing market structure, int. j. hydrog. energy, 32(10–11), pp. 1381-1386. doi: 10.1016/j.ijhydene.2006.10.018. [2] vries, h., mokhov, a.v., and levinsky, h.b. (2017). the impact of natural gas/hydrogen mixtures on the performance of end-use equipment: interchangeability analysis for domestic appliances, appl. energy, 208, pp. 1007– 1019. doi: 10.1016/j.apenergy.2017.09.049. [3] meng, b., gu, c., zhang, l., zhou, c., li, x., zhao, y., zheng, j., chen, x., han, y. (2017). hydrogen effects on x80 pipeline steel in high-pressure natural gas/hydrogen mixtures, int. j. hydrog. energy, 42(11), pp. 7404-7412. doi: 10.1016/j.ijhydene.2016.05.145. [4] pluvinage, g., toth, l., and capelle, j. (2021). effects of hydrogen addition on design, maintenance and surveillance of gas networks, processes, 9(7), 1219. doi: 10.3390/pr9071219. [5] zhou, d., li, t., huang, d., wu, y., huang, z., xiao, w., wang, q., wang, x. (2021). the experiment study to assess the impact of hydrogen blended natural gas on the tensile properties and damage mechanism of x80 pipeline steel. int. j. hydrog. energy, 46(10), pp. 7402-7414. doi: 10.1016/j.ijhydene.2020.11.267. [6] nykyforchyn, h., unigovskyi, l., zvirko, o., tsyrulnyk, o., and krechkovska, h. (2021). pipeline durability and integrity issues at hydrogen transport via natural gas distribution network, procedia struct. integr., 33, pp. 646-651. doi: 10.1016/j.prostr.2021.10.071. [7] kim, c., kim, w., and kho, y. (2002). the effects of hydrogen embrittlement by cathodic protection on the ctod of buried natural gas pipeline, met. mater. int., 8, pp. 197–202. doi: 10.1007/bf03027018. [8] shipilov, s. a., and may, i. l. (2006). structural integrity of aging buried pipelines having cathodic protection, eng. fail. anal., 13, pp. 1159–1176. doi: 10.1016/j.engfailanal.2005.07.008. [9] bueno, a.h.s., castro, b.b., and ponciano, j.a.c. (2008). assessment of stress corrosion cracking and hydrogen embrittlement susceptibility of buried pipeline steels, environment-induced cracking of materials, 2, pp. 313-322. doi: 10.1016/b978-008044635-6.50068-6. [10] cabrini, m., lorenzi, s., marcassoli, p., and pastore, t. (2011). hydrogen embrittlement behavior of hsla line pipe steel under cathodic protection. corros. reviews, 29(5-6) pp. 261-274. doi: 10.1515/corrrev.2011.009. [11] voloshyn, v. а., zvirko, о. і., sydor, p. ya. (2015). influence of the compositions of neutral soil media on the corrosion cracking of pipe steel, mater. sci., 50(5), pp. 671–675. doi: 10.1007/bf03027018. [12] .askaria, m., aliofkhazraeia, m., and afroukhteh, s. (2019). a comprehensive review on internal corrosion and cracking of oil and gas pipelines, j. nat. gas sci. eng., 71, 102971. doi: 10.1016/j.jngse.2019.102971. [13] hredil, m., and tsyrulnyk, o. (2010). inner corrosion as a factor of in-bulk steel degradation of transit gas pipelines. proc. of the 18th european conference on fracture (ecf-18), dresden, germany, 30.08 – 03.09. no.483. [14] zhao, w., zhang, t., wang, y., qiao, j., and wang, z. (2018). corrosion failure mechanism of associated gas transmission pipeline. materials 11, 1935. doi: 10.3390/ma11101935. [15] zvirko, o.i., mytsyk, a.b., tsyrulnyk, o.t., gabetta, g., nykyforchyn h.m. (2017). corrosion degradation of steel of an elbow of gas pipeline with large-scale delamination after long-term operation, mater. sci., 52(6), pp. 861–865. doi: 10.1007/s11003-017-0032-8. [16] tsyrul’nyk, o. t., slobodyan, z. v., zvirko, o. i., hredil, m. i., nykyforchyn, h. m., and gabetta, d. (2008). influence of operation of kh52 steel on corrosion processes in a model solution of gas condensate, mater. sci., 44(5), pp. 619–629. doi: 10.1007/s11003-009-9138-y. [17] capelle, j., dmytrakh, i., azari, z., pluvinage, g. (2013). evaluation of electrochemical hydrogen absorption in welded pipe with steel api x52. int. j. hydrog. energy, 38(33), pp. 14356–14363. doi: 10.1016/j.ijhydene.2013.08.118. [18] sun, y., cheng, y. f. (2021). thermodynamics of spontaneous dissociation and dissociative adsorption of hydrogen molecules and hydrogen atom adsorption and absorption on steel under pipelining conditions, int. j. hydrog. energy, 46(69), pp. 34469-34486. doi: 10.1016/j.ijhydene.2021.07.217. [19] nykyforchyn, h., zvirko, o., dzioba, i., krechkovska, h., hredil, m., tsyrulnyk, o., student, o., lipiec, s., pala, r. (2021) assessment of operational degradation of pipeline steels, materials, 14(12), 3247. doi: 10.3390/ma14123247. h. nykyforchyn et alii, frattura ed integrità strutturale, 59 (2022) 396-404; doi: 10.3221/igf-esis.59.26 404 [20] nechaev, yu.s. (2008). metallic materials for the hydrogen energy industry and main gas pipelines: complex physical problems of aging, embrittlement, and failure, uspekhi fizicheskikh nauk, 51(7), pp. 681–697. doi: 10.1070/pu2008v051n07abeh006570. [21] filippov, g.a., livanova, o.v., chevskaya, o.n., shabalov, i.p., 2013. pipe steel degradation during operation and brittle failure resistance, metallurgist, 57, pp. 612–622. doi: 10.1007/s11015-013-9778-x. [22] maruschak, p., panin, s., danyliuk, i., poberezhnyi, l., pyrig, t., bishchak, r., and vlasov i. (2015). structural and mechanical defects of materials of offshore and onshore main gas pipelines after long-term operation, open engineering 5(1), pp. 365-372. doi: 10.1515/eng-2015-0045. [23] zvirko, o.i., kret, n.v., tsyrulnyk, o.t., and vengrynyuk, t.p. (2018). influence of textures of pipeline steels after operation on their brittle fracture resistance, mater. sci., 54(3), pp. 400–405. doi: 10.1007/s11003-018-0198-8. [24] marushchak, p. о., kret, n. v., bishchak, r. т., and kurnat, і. м. (2019). influence of texture and hydrogenation on the mechanical properties and character of fracture of pipe steel, mater. sci., 55(3), pp. 381–385. doi: 10.1007/s11003-019-00313-z. [25] degradation assessment and failure prevention of pipeline systems. lecture notes in civil engineering; bolzon, g., gabetta, g., nykyforchyn, h., (2021) springer: cham, switzerland, 102, 252 p. doi: 10.1007/978-3-030-58073-5. [26] zvirko, о.і., кryzhanivskyi, e.і., nykyforchyn, h.м., krechkovska, h.v. (2021). methods for the evaluation of corrosion-hydrogen degradation of steels of oil-and-gas pipelines, mater. sci., 56(5), pp. 585-592. doi: 10.1007/s11003-021-00468-8. [27] mcmahon jr., c.j. (2001). hydrogen-induced intergranular fracture of steels, eng. fract. mech., 68(6), pp. 773–788. doi: 10.1016/s0013-7944(00)00124-7. [28] venegas v., caleyo f., baudin t., espina-hernández, j.h., and hallen, j.m. (2011). on the role of crystallographic texture in mitigating hydrogen-induced cracking in pipeline steels, corros. sci., 53, pp. 4204–4212. doi: 10.1016/j.corsci.2011.08.031. [29] nemchuk, o.o., and nesterov o.a. (2020). in-service brittle fracture resistance degradation of steel in a ship-toshore portal crane, strength of mater., 52(2), pp. 275–280. doi: 10.1007/s11223-020-00175-w. [30] student, o.z., and krechkovs’ka, h.v. (2012). anisotropy of the mechanical properties of degraded 15kh1m1f steel after its operation in steam pipelines of thermal power plants, mater. sci., 47(5), pp. 590–597. doi: 10.1007/s11003-012-9432-y. [31] gussev, m. n., busby, j. t., field, k. g., sokolov, m. a., and gray, s. e. 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can be opened with acrobat and adobe reader 5.0 and later.) >> /namespace [ (adobe) (common) (1.0) ] /othernamespaces [ << /asreaderspreads false /cropimagestoframes true /errorcontrol /warnandcontinue /flattenerignorespreadoverrides false /includeguidesgrids false /includenonprinting false /includeslug false /namespace [ (adobe) (indesign) (4.0) ] /omitplacedbitmaps false /omitplacedeps false /omitplacedpdf false /simulateoverprint /legacy >> << /addbleedmarks false /addcolorbars false /addcropmarks false /addpageinfo false /addregmarks false /convertcolors /converttocmyk /destinationprofilename () /destinationprofileselector /documentcmyk /downsample16bitimages true /flattenerpreset << /presetselector /mediumresolution >> /formelements false /generatestructure false /includebookmarks false /includehyperlinks false /includeinteractive false /includelayers false /includeprofiles false /multimediahandling /useobjectsettings /namespace [ (adobe) (creativesuite) (2.0) ] /pdfxoutputintentprofileselector /documentcmyk /preserveediting true /untaggedcmykhandling /leaveuntagged /untaggedrgbhandling /usedocumentprofile /usedocumentbleed false >> ] >> setdistillerparams << /hwresolution [2400 2400] /pagesize [612.000 792.000] >> setpagedevice microsoft word numero_60_art_08_3278.docx t. messas et alii, frattura ed integrità strutturale, 60 (2022) 102-113; doi: 10.3221/igf-esis.60.08 102 experimental investigation on the mechanical behavior of concrete reinforced with alfa fibers tidjani messas materials, geomaterials and environment laboratory, badji mokhtar university, abbèss laghrour university, algeria. messas_tidjani@univ-khenchela.dz, https:// orcid.org / 0000-0002-0399-3541 djamel achoura materials, geomaterials and environment laboratory, badji mokhtar university, algeria. achoudj@yahoo.fr, https://orcid.org/0000-0003-1692-3523 abdelaziz boutrid mineral processing and environmental laboratory, badji mokhtar university, abbèss laghrour university, algeria. abdelaziz.boutrid@univ-khenchela.dz, https://orcid.org/ 0000-0002-1041-3904 belgacem mamen abbèss laghrour university, algeria. belgacem.mamen@univ-khenchela.dz, https://orcid.org/ 0000-0003-2342-9363 abstract.currently, the reinforcement of ordinary concrete with synthetic fibers poses ecological problems because the manufacturing process of these products is very polluting. plant fiber composites are a new challenge for environmental protection. the present article aims to investigate the mechanical behavior of concrete reinforced with natural fibers, called alfa fibers. compression and three-point bending tests have been performed on cubic and prismatic samples, respectively. different fiber lengths (2.5, 5, and 8 cm) and content (0.6, 1.2, and 1.8 % by volume) of alfa fibers have been used to examine their influence on the mechanical behavior of the fiberreinforced concrete. the obtained results show that for a volume content of 1.2 % of plant fibers of 5 cm length, the tensile strength of the reinforced concrete increases up to 54.41 % compared to the ordinary concrete (bt). however, for a content of 1.8 % of fibers with 8 cm length, both the compressive and tensile strength of the reinforced concrete decrease slightly. at this level, an excess of both fiber content and their length produces the formation of voids within concrete. moreover, such an excess made the hydration reaction slower. it is worth noticing that the orientation of fibers also plays a significant role in the nucleation and propagation of microcracks. the fibers arranged both horizontally and obliquely are more resistant to microcracking than those oriented in the loading direction. keywords. fiber-reinforced concrete; alfa fiber; fiber length; volume citation: messas, t., achoura, d., boutrid, a., mamen, b., experimental investigation on the mechanical behavior of concrete reinforced with alfa fibers, frattura ed integrità strutturale, 60 (2022) 102-113. received: 25.09.2021 accepted: 17.01.2022 online first: 17.01.2022 published: 01.04.2022 copyright: © 2022 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. https://youtu.be/dx1sjlygddc t. messas et alii, frattura ed integrità strutturale, 60 (2022) 102-113; doi: 10.3221/igf-esis.60.08 103 fraction; mechanical behavior; microcracks. introduction oday, concrete is the main building material used in civil, industrial constructions and bridges due to its features, such as versatility and durability in many environments. nevertheless, it has a certain brittleness, low tensile strength, and low ductility. therefore, faster collapse is observed after the first signs of fracture or other pathologies [1]. these disadvantages have restricted its use. consequently, the need to develop fiber-reinforced concrete offers the possibility to overcome such a drawback. the inclusion of fibers in concrete used in civil constructions reduces its conventional brittleness by providing better tensile strength [2-4]. fibers are discontinuous elements of variable nature, uniformly distributed in the matrix according to a random or forced orientation. the addition of fibers to concrete allows to absorb and dissipate energy and reduce the propagation of cracks. they also improve the post-cracking behavior of concrete. several types of fibers can be used, such as steel [5-7], polypropylene [8-11]. the fiber should be chosen according to the needs of the work required. over the past decade, bio-fibers have replaced synthetic fibers to produce environmentally friendly concrete because several types of these fibers are available and abundant in some parts of the world. various studies on the influence of natural fibers on the strength, properties, and structural behavior of concrete proof that the inclusion of natural fibers improves the mechanical properties of concretes and gives a better resistance to crack propagation. in recent years, many natural fibers have been used to reinforce the ordinary concrete: find wood fibers [1213], date palm fibers [14-16], bamboo [17-19], coconut [20-22], and alfa [23-25]. the natural fiber examined here is the alfa (stippa tenacissima), a bushy plant that belongs to the poaceae family with upright stems 60 to 150 or even 200 cm long. the sheath of the leaves presents auricles from 10 to 12 mm of height. this species is native to the arid regions of the western mediterranean basin, and mainly used in both the paper and rope industries. this plant does not need additional water to grow, nor the use of pesticides or amendment. the effect of alfa reinforcement on the mechanical properties of concrete has not been widely studied to date [23-25]. they reported that 1 % of alfa fibers is the most suitable intake for concrete reinforcement. more specifically, our results reveal that a fiber content of 1.2 % (by volume) with a length of 5 cm can be considered as the optimal parameters for alfa fiber-reinforced concrete. these results show the key role of alfa fibers: they delay cracking and reduce concrete bursting better than polypropylene. additionally, the alfa fibers offer economic and environmental benefits to society. this work aims to investigate the effect of alfa fibers on the mechanical behavior of the reinforced concrete. compressive and three-point bending tests are performed with different fiber contents (0.6, 1.2, and 1.8 % by volume). for each of the above content, three different fiber lengths (2.5, 5, and 8 cm) are examined. materials he mixture of fiber-reinforced concrete examined is prepared according to the standard nf p 18-101 [26]. cement the cement used is a cem ii/a-42 portland-composite cement, produced by hadjar soud cement company-skikda (algeria). it consists mainly of clinker ≥ 74 wt %, gypsum (4–6 wt %), limestone (16–18 wt %), and slag ≤ 20 wt %. the physical characteristics and chemical composition are summarized in tabs. 1 and 2, respectively. apparent density (g/cm³) absolute density (g/cm³) normal consistency (%) fineness (retained on 0.065 mm sieve) (%) initial setting time (h/min) 1.057 3.00 27 3.1 2/34 table 1: physical properties of cem ii/a-42 portland-composite cement. t t t. messas et alii, frattura ed integrità strutturale, 60 (2022) 102-113; doi: 10.3221/igf-esis.60.08 104 elements cao al2o3 sio2 fe2o3 mgo nao2 k2o cl¯ so3 wt % 62.80 5.68 22.25 3.52 0.74 0.27 0.47 0.004 1.94 table 2: chemical composition of cem ii/a-42 portland-composite cement. aggregates the aggregates, according to the nf p 15-433 [27], consist of crushed limestone sand (0/4 mm) and siliceous sand dune (0-1, 25 mm). two gravels crushed limestone ((4/8) and (8/16) mm) coming from the same quarry are employed in the mixture as the crushed sand. the physical characteristics of the aggregates are presented in tabs. 3 and 4. physical characteristics crushed limestone sand sand dune apparent density (t/m³) 1.561 1.2 absolute density (t/m³) 2.5 2.3 sand equivalent (%) 64.06 85 water absorption (%) 2.3 2.45 fineness modulus 3.76 1.6 cleanliness 0.75 0.9 table 3: physical characteristics of crushed and dune sand. physical characteristics gravel (4/8) gravel (8/16) apparent density (t/m³) 1.431 1.428 absolute density (t/m³) 2.56 2.56 flattening coefficient (%) 11.25 9.43 water absorption (%) 1.1 0.9 micro deval in presence of water (%) 13.74 13.74 los angles coefficient (%) 29.63 29.63 table 4: physical characteristics of gravels crushed limestone. alfa fibers alfa plant presents numerous morpho-physiological adaptations that allow it to withstand extreme environments, particularly the complex mediterranean ecosystem. as shown in fig. 1a, the alfa leaf is a circular, smooth, shiny, and solid ribbon. its diameter decreases gradually from the bottom to the top [25]. to determine the fracture stress of alfa fiber, a uniaxial test is carried out by using the zwick roell apparatus shown in fig. 1b. the load-displacement curve is shown in fig. 1c. the chemical composition, physical and mechanical properties are reported in tabs. 5-7, respectively. (a) (b) (c) figure 1: a) alfa fibers, b) zwick roell apparatus and c) load-displacement curve. 0 20 40 60 80 100 120 140 160 0 0.5 1 1.5 2 2.5 displacement (mm) l o ad ( n ) t. messas et alii, frattura ed integrità strutturale, 60 (2022) 102-113; doi: 10.3221/igf-esis.60.08 105 cellulose hemicelluloses lignin ash wax 45 % 24 % 24 % 2 % 5 % table 5: chemical composition of alfa fibers [28]. microfibril angle (°) diameter (mm) length (mm) 31 1 2 10 1000 table 6: physical properties of alfa fibers. young's modulus (gpa) elongation (mm) tensile stress (mpa) density breaking stress (mpa) 14.48 2.27 200.56 0.89 645.82 table 7: mechanical tensile properties of alfa fibers. experimental procedure he specimens are prepared according to the standard nf en 12390-2 [29]. the mixing is carried out by employing a concrete mixer of capacity 50 l. for the ordinary concrete, the mixing time is taken to be about five minutes, whereas and for the fiber-reinforced concrete is more than six minutes. the alfa fibers are added into the tank during the mixing phase with a specific content. then, the compaction procedure is performed on a vibrating table for a one minute. finally, the samples are removed from the molds after 24 hours and stored in a saturated humid medium at a temperature of 20±2°c (see fig. 2a). tab. 8 reports the specimen’s designation, together with the corresponding fiber length and content by volume. designation bt bfv1 bfv2 bfv3 bfv4 bfv5 bfv6 bfv7 bfv8 bfv9 fiber length (cm) 5 2.5 5 2.5 5 2.5 8 8 8 content (%) 1.2 1.2 0.6 0.6 1.8 1.8 1.8 1.2 0.6 table 8: specimen designation, length and content of alfa fibers. to evaluate the compressive strength of the above samples, compression tests are carried out on cubic specimens of dimension (10 x 10 x 10) cm at the age of 28 days, according to the standard nf en 12390-3 [30], by using a testing machine "utest" of 2000 kn capacity (see fig. 2b). for the tensile strength evaluation, three-point bending tests are performed on notched prismatic specimens (10 x 10 x 40) cm according to the nf en 12390-5 [31] standard by using a "strassentest" testing machine with a maximum capacity of 100 kn (see fig. 2c). (a) (b) (c) figure 2: experimental procedure: (a) fiber reinforced-concrete samples; (b) uniaxial compression testing and (c) three-point bending testing. t t. messas et alii, frattura ed integrità strutturale, 60 (2022) 102-113; doi: 10.3221/igf-esis.60.08 106 results and discussion effect of alfa fiber content and length on compressive strength n fig. 3 is plotted the influence of fiber content on the compressive strength, for different values of fiber length. the results obtained show that all the curves related to fiber lengths of (2.5 and 5 cm) are characterized by a similar trend. the highest value of the compressive strength is that of ordinary concrete (bt), equal to 57.7 mpa. however, the lowest value is obtained for bf v9 specimen with 32.19 mpa, for a fiber content of 1.8 % and a fiber length of 8 cm. a decreasing in the compressive strength is observed for a fiber content greater than 1.2 %. at a content of 1.8 %, the drop in compressive strength ranges about 26.42 % for fibers of 5 cm in length, 31.19 % for fibers of 2.5 cm, and 44.21 % for ones of 8 cm in length. here, the drop in strength is calculated compared to the initial compression strength of ordinary concrete. this decrease is essentially due to the nature of the fibers (vegetable fiber) containing mainly cellulose, thus causing a slowing down of the hydration process. the morphology of the fibers (smooth fiber) decreases the adherence matrix-fiber and consequently decreases the resistance to the compression. the influence of fiber length on the compressive strength is presented in fig. 4 for different values of fiber content. based on the results obtained, the compressive strength decreases by increasing fiber length. the maximum recorded drop in compressive strength is around 25.51 mpa. this decreasing is due to the disruption of the matrix's crystal lattice arrangement due to the inclusion of longer fibers and the formation of urchin balls during the concrete casting (see fig. 4). figure 3: effect of fiber content on the compressive strength of concrete. figure 4: effect of fiber length on the compressive strength of concrete. effect of alfa fiber content and length on tensile strength according to fig. 5, an enhancement in tensile strength is observed only when the concretes reinforced with fibers having a length of 2.5 and 5 cm. furthermore, no improvement is obtained for a content of 1.8 %; this is due to a possible disorder in the distribution of fibers in the concrete volume. regarding the influence of fiber length on tensile strength, it remains relatively constant compared to that of the ordinary concrete (bt) that is 6.12 mpa (see fig. 6). the strength is around 6.12 mpa for reinforced concrete with fibers length of 8 cm and a content of 0.6 and 1.2 %. however, for fiber-reinforced concrete using fibers length of 8 cm and content of 1.8 %, the strength is estimated at around 6.30 mpa. according to the ordinary concrete tensile strength (bt, see fig. 6), the maximum improvement of the tensile strength of reinforced concrete is obtained with fibers of 5 cm in length and contents of 0,6 % and 1.2 %. the obtained resistances are respectively 9,45, and 9,15 mpa for the specimens bf v2 and bf v5, with gains in the percentage of resistances respectively of the order 54,41 % and 49,51 %. here, the gain in strength is calculated compared to the tensile strength of ordinary concrete. with the same content and fiber of 2.5 cm in length, the strengths are respectively of the order of 8.55 mpa for the specimen bf v1 and 8.10 mpa for that bf v4. their percentage increase strength is 39.70 and 32.35 %, respectively. as previously mentioned, percentage increase strength is calculated compared to the tensile strength of ordinary concrete. 0 10 20 30 40 50 60 0 0.3 0.6 0.9 1.2 1.5 1.8 fiber content by volume (%) c o m p re s s iv e s tr e n g th ( m p a ) bt l=2.5 cm l=5.0 cm l=8.0 cm 0 10 20 30 40 50 60 0 1 2 3 4 5 6 7 8 9 10 fiber length (cm) c o m p re s s iv e s tr e n g th ( m p a ) bt 0.60% 1.20% 1.80% i t. messas et alii, frattura ed integrità strutturale, 60 (2022) 102-113; doi: 10.3221/igf-esis.60.08 107 figure 5: influence of fiber content on the tension strength. figure 6: effect of fiber length on the tension strength of concrete. failure compressive failure igs. 7a and 7b show the compressive failure modes of ordinary concrete and fiber-reinforced concrete, respectively. the ordinary concrete specimen breaks abruptly and collapses during the compression test. in contrast, the sample with fiber-reinforced concrete nucleates cracks that propagate progressively up to the material fails. the addition of alfa fibers take up the stresses caused by the deformations and thus slows down the nucleation of cracks. crack propagation in compression-loaded fiber reinforced concrete specimens is strongly influenced by the orientation of the fibers [25]. on the one hand, fibers aligned perpendicular to the cracking plane oppose the nucleation of cracks. on the other hand, fibers aligned parallel to the cracking plane have little influence on the propagation of microcracks. based on the microstructure analysis of the present investigation, the majority of the fibers are arranged perpendicular and oblique to the cracking plane. (a) (b) figure 7: compressive failure of a specimen made of: (a) ordinary concrete and (b) fiber-reinforced concrete. tensile failure during the tensile test (fig. 8), the fiber-reinforced concrete specimens, contrary to ordinary concrete, show microcracks during the elastic step. at a given load value, the microcracks become visual, and then progressively propagate and increase in width, leading to a decrease in the residual strength of the fiber-reinforced concrete because of the loss of adhesion between the fibers and the cementitious matrix. 0 2 4 6 8 10 0 0.6 1.2 1.8 fiber content by volume (%) t e n s io n s tr e n g th ( m p a ) bt l=2.5 cm l=5.0 cm l=8.0 cm 0 2 4 6 8 10 0 1 2 3 4 5 6 7 8 9 10 fibre length (cm) t e n s io n s tr e n g th ( m p a ) bt 0.60% 1.20% 1.80% f t. messas et alii, frattura ed integrità strutturale, 60 (2022) 102-113; doi: 10.3221/igf-esis.60.08 108 figure 8: tensile fracture of alfa fiber concrete specimen. sem micrographs of alfa-reinforced concrete and ordinary concrete are respectively shown in figs. 9a-c and d-f. these sem micrographs demonstrate two zones with different aspects. the texture of the first zone, adjacent to the alfa fibers, appears to be uncracked (see figs. 9b-c). this suggests a better adhesion between the concrete and the alfa fibers. this better adhesion contributes to the limitation of cracking and the formation of hydrated phases in the cementitious matrix. however, the second zone within the ordinary concrete shows multi-identified cracks producing a localized damage zone (see figs. 9e-f). figure 9: sem micrographs: (a-c) alfa-reinforced concrete and (d-f) ordinary concrete. in fig. 10a the load-deflection curves obtained under three-point bending test for the specimens bt, bfv7, bfv8, and bfv9 are reported, whereas in fig. 10b those related to bt, bfv3, bfv6 and bfv9 specimens are shown. the curves plotted show that for ordinary concrete, in the first elastic stage, the load varies in a quasi-linear manner up to a given t. messas et alii, frattura ed integrità strutturale, 60 (2022) 102-113; doi: 10.3221/igf-esis.60.08 109 load. at this point, the resistance drops abruptly. for fiber reinforced concretes, three stages are observed: a linear trend characterized the first stage, whereas in the descending branch (second stage); the fibers limit the cracks and their opening by sewing. finally, in the third stage, the load tends to be constant and is vanished only after a large deformation. this decreasing is due to the presence of fibers at the level of the crack. the failure then occurs either by tearing or by fiber breakage. (a) (b) figure 10: load-deflection curve: (a) for a fiber content of 1.8 % and (b) for a fiber length of 8 cm. (a) (b) (c) figure 11: maximum deflection versus fiber length for fiber content: (a) 0.60 %, (b) 1.20 %, and (c) 1.80 % by volume. figs. 11a-c show the improvement of the ductility of concrete. for the length of alfa fibers more than 5 cm, the deflection is negatively affected by the presence of fibers. the mechanical behavior in tensile bending of the different types of concrete is better by using short fibers 2.5 cm in length. by considering the fibers content, a content of 1.20 % leads to good results in terms of deflection. fiber content  1,8 % 0 2 4 6 8 10 12 14 16 18 20 22 0 0.5 1 1.5 2 2.5 3 deflection (mm) l o ad ( k n ) bt bfv7 (l=2.5 cm) bfv8 (l=5 cm) bfv9 (l=8 cm) fiber length 8 cm 0 2 4 6 8 10 12 14 16 18 20 22 0 0.5 1 1.5 2 2.5 3 deflection (mm) l o a d ( k n ) bt bfv3 (0,6%) bfv6 (1,2%) bfv9 (1,8%) 0 2 4 6 8 10 0 1 2 3 4 5 6 7 8 9 10 fiber length (cm) m a x im u m d e fl e c ti o n ( m m ) 0 2 4 6 8 10 12 14 l o a d ( k n ) maximum deflection (mm) load (kn) 0.60 % 0 2 4 6 8 10 0 1 2 3 4 5 6 7 8 9 10 fiber length (cm) m a x im u m d e fl e c ti o n ( m m ) 0 2 4 6 8 10 12 14 l o a d ( k n ) maximum deflection (mm) load (kn) 1.20 % 0 2 4 6 8 10 0 1 2 3 4 5 6 7 8 9 10 fiber length (cm) m a x im u m d e fl e c ti o n ( m m ) 0 2 4 6 8 10 12 14 l o a d ( k n ) maximum deflection (mm) load (kn) 1.80 % t. messas et alii, frattura ed integrità strutturale, 60 (2022) 102-113; doi: 10.3221/igf-esis.60.08 110 in fig. 12 the load-crack width curves obtained under three-point bending test for the specimens bfv7, bfv8, and bfv9 are reported, whereas in fig. 12b those related to bfv3, bfv6 and bfv9 specimens are shown. the loadcrack opening curves in fig. 12 show a linear elastic trend up to a given load value corresponding to the nucleation of the first crack. the maximum load varies according to the fiber length and content. then the trend is characterized by a load deceasing and an increasing in the crack opening. finally, the curves become flattered (horizontal) and then vanishonly after a large crack, confirming that the specimens have reached their total failure (see fig. 12a and fig. 12b). (a) (b) figure 12: load-crack width curve: (a) for a fiber content of 1.8% and (b) for a fiber length of 8 cm. (a) (b) (c) figure 13: maximum crack opening versus fiber length for fiber content: (a) 0.60 %, (b) 1.20 %, and (c) 1.80 % by volume. it can be observed that the fiber length is an important factor that greatly affects the mechanical behavior and cracking of the concrete for the different contents examined. thus, the crack opening of the specimen reinforced with alfa fibers of 8 fiber content 1,8 % 0 2 4 6 8 10 12 14 16 18 20 22 0 1 2 3 4 5 crack width (mm) l o a d ( k n ) bfv7 (l=2.5 cm) bfv8 (l=5 cm) bfv9 (l=8 cm) fiber length 8 cm  0 2 4 6 8 10 12 14 16 18 20 22 0 1 2 3 4 5 crack width (mm) l o a d ( k n ) bfv3 (0,6%) bfv6 (1,2%) bfv9 (1,8%) 0 5 10 15 20 0 1 2 3 4 5 6 7 8 9 10 fiber length (cm) m a x im u m c ra c k o p e n in g (m m ) 0 1 2 3 l o a d ( k n ) maximum crack opening (mm) load (kn) 0.60 % 0 5 10 15 20 0 1 2 3 4 5 6 7 8 9 10 fiber length (cm) m a x im u m c ra c k o p e n in g (m m ) 0 1 2 3 l o a d ( k n ) maximum crack opening (mm) load (kn) 1.20 % 0 5 10 15 20 0 1 2 3 4 5 6 7 8 9 10 fiber length (cm) m a x im u m c ra c k o p e n in g (m m ) 0 1 2 3 l o a d ( k n ) maximum crack opening (mm) load (kn) 1.80 % t. messas et alii, frattura ed integrità strutturale, 60 (2022) 102-113; doi: 10.3221/igf-esis.60.08 111 cm length can reach 13 mm without breaking for a content of 1,8 %, whereas the reinforced one with fibers of 5 cm length can reach 18 mm. the length of the fibers and their contents become essential parameters characterizing the opening of cracks. indeed, the load required to pull out the fibers is a function of the adherent length of the fiber, see fig. 14. figure 14: resistance of alfa fibers to crack propagation. conclusion he objective of the present study is to evaluate the performance and mechanical behavior of alfa fiber reinforced concrete by varying two parameters, that is the fiber content and length. the main conclusions drawn from this research study are:  the addition of alfa fibers in the concrete does not increase the compressive strength. on the contrary, a slight decreasing has been found for fiber content 0.6 and 1.2 % by volume. on the other hand, this fall is remarkable, with a content of 1.8 %. in particular, for the case with a length of 8 cm, one can explain it by slowing down the phenomenon of hydration because of the presence of the cellulose and the discontinuity of the crystalline network of the cement matrix with the formation of balls (excess of fibers).  the higher compressive strength of fiber-reinforced concrete is obtained for a content 1.2 % of fibers with a length of 5 cm (bfv 5), whose compressive strength is close to that of the ordinary concrete (57.7 mpa).  the addition of alfa fibers in concrete allowed the increase of the tensile strength compared to that of the ordinary concrete (bt), particularly for fiber contents of 0.6 and 1.2 % and lengths of 2.5 and 5 cm. the gains of tensile strength going up to the value of 54,41 %.  on the other hand, a fiber content of 1.8 % and a length of 8 cm did not give satisfaction or significant improvements in tensile strength. for this point, the gain in strength has been calculated compared to the tensile strength of ordinary concrete.  overall, the addition of alfa fibers has a favorable effect on the crack nucleation and post-cracking behavior.  the failure mode of the tested specimens shows that the inclusion of alfa fibers improves the ductility of the concrete. this ductility varies according to the content and the length of alfa fibers. acknowledgments he work presented in this paper has been supported by badji mokhtar university (annaba, algeria), and abbès laghrour university (khenchela, algeria). their support is gratefully acknowledged. t t t. messas et alii, frattura ed integrità strutturale, 60 (2022) 102-113; doi: 10.3221/igf-esis.60.08 112 references [1] herscovici, h.l., roehl, d., sánchez filho, e. de s. (2019). experimental studies of short concrete reinforced steel fiber beams under bending. revista ibracon de estruturas e materiais, 12(2), pp. 288–307. doi: 10.1590/s1983-41952019000200005. [2] jiang, c., fan, k., wu, f., chen, d. (2014). experimental study on the mechanical properties and microstructure of chopped basalt fibre reinforced concrete. materials & design, 58, pp. 187–193. doi: 10.1016/j.matdes.2014.01.056 [3] yao, w., li, j., wu, k. (2003). mechanical properties of hybrid fiber-reinforced concrete at low fiber volume fraction. cement and concrete research, 33(1), pp. 27–30. doi: 10.1016/s0008-8846(02)00913-4. [4] hefni, y., zaher, y. a.e.w., mona a. (2018). influence of activation of fly ash on the mechanical properties of concrete. construction and building materials, 172, pp. 728–734. doi: 10.1016/j.conbuildmat.2018.04.021. [5] kaïkea, a., achoura, d., duplan, f., rizzuti, l. (2014). effect of mineral admixtures and steel fiber volume contents on the behavior of high performance fiber reinforced concrete. materials & design, 63, pp. 493–499. doi: 10.1016/j.matdes.2014.06.066. [6] vantadori, s., carpinteri, a., guo, l-p., ronchei, zanichelli, a. (2018). synergy assessment of hybrid reinforcements in concrete. composites part b: engineering, s1359836818305262. doi: 10.1016/j.compositesb.2018.04.020 [7] zarei, a., rooholamini, h., ozbakkaloglu, t. (2021). evaluating the properties of concrete pavements containing crumb rubber and recycled steel fibers using response surface methodology. int. j. pavement res. technol. doi: 10.1007/s42947-021-00049-7. [8] melais, s., melais, f.z., achoura, d. (2015), influence of fiber type and volume contents on the physical and mechanical behaviour of sandcrete with blast furnace slag fillers rev. sci. technol., synthèse, 30, pp. 91-102. [9] lura, p., terrasi, g.p. (2014). reduction of fire spalling in high-performance concrete by means of superabsorbent polymers and polypropylene fibers. cement and concrete composites, 49, pp. 36–42. doi: 10.1016/j.cemconcomp.2014.02.001. [10] chai, l-j., guo, l-p., chen, b., wang, m., carpinteri, a., scorza, d., vantadori, s. (2020). fracture mechanics-based mixture optimization of ecological high-ductility cementitious composites modified with recycled asphalt concrete. construction and building materials, 264(1-10), 120686. doi: 10.1016/j.conbuildmat.2020.120686. [11] chai, l., guo, l., chen, b., cao, y. (2020). effects of curing age on compressive and tensile stress-strain behaviors of ecological high ductility cementitious composites. journal of southeast university (english edition), 36 (1), pp. 73-80. doi: 10.3969/j.issn.1003-7985.2020.01.010. [12] coutts r.s.p. (2005). a review of australian research into natural fibre cement composites. cement and concrete composites, 27(5), pp. 518–526. doi: 10.1016/j.cemconcomp.2004.09.003. [13] tonoli, g.h.d., savastano jr, h., fuente, e., negro, c., blanco, a., rocco lahr, f.a. (2010). eucalyptus pulp fibres as alternative reinforcement to engineered cement-based composites. industrial crops and products, 31(2), pp. 225– 232. doi: 10.1016/j.indcrop.2009.10.009. [14] kriker, a., debicki, g., bali, a., khenfer, m.m., chabannet, m. (2005). mechanical properties of date palm fibres and concrete reinforced with date palm fibres in hot-dry climate. cement and concrete composites, 27(5), pp. 554–564. doi: 10.1016/j.cemconcomp.2004.09.015. [15] benaimeche, o., carpinteri, a., mellas, m., ronchei, c. scorza, d., vantadori, s. (2018). the influence of date palm mesh fibre reinforcement on flexural and fracture behaviour of a cement-based mortar. composites part b: engineering, 152, 292–299. doi: 10.1016/j.compositesb.2018.07.017. [16] benaimeche, o., łukasz, s., mellas, m. (2019). the utilization of vegetable fibers in cementitious materials. reference module in materials science and materials engineering, pp. 1-14. doi: 10.1016/b978-0-12-803581-8.11596-6 [17] sudin, r., swamy, n. (2006). bamboo and wood fibre cement composites for sustainable infrastructure regeneration. j mater sci 41, pp. 6917–6924. doi: 10.1007/s10853-006-0224-3. [18] li, y., mai, y-w, ye, l. (2000). sisal fibre and its composites: a review of recent developments. composites science and technology, 6 60(11), pp. 2037–2055. doi: 10.1016/s0266-3538(00)00101-9. [19] tolêdo filho, r.d, ghavami, k., england gl., scrivener, k. (2003). development of vegetable fibre–mortar composites of improved durability. cement and concrete composites, 25(2), pp. 185–196. doi: 10.1016/s0958-9465(02)00018-5. [20] ali, m. (2014). seismic performance of coconut-fibre-reinforced-concrete columns with different reinforcement configurations of coconut-fibre ropes. construction and building materials, 70, pp. 226–230. doi: 10.1016/j.conbuildmat.2014.07.086. t. messas et alii, frattura ed integrità strutturale, 60 (2022) 102-113; doi: 10.3221/igf-esis.60.08 113 [21] rahim, m., douzane, o., tran le, a.d., promis, g., laidoudi, b., crigny, a., dupre, b., langlet, t. (2015). characterization of flax lime and hemp lime concretes: hygric properties and moisture buffer capacity. energy and buildings, 88, pp. 91–99. doi: 10.1016/j.enbuild.2014.11.043 [22] sellami, a., merzoud, m. amziane, s. (2013). improvement of mechanical properties of green concrete by treatment of the vegetals fibers. construction and building materials, 47, pp. 1117–1124. doi: 10.1016/j.conbuildmat.2013.05.073 [23] khelifa, m.r., leklou, n., bellal, t., hebert, r.l., ledesert, b.a. (2016). is alfa a vegetal fiber suitable for making green reinforced structure concrete?. european journal of environmental and civil engineering, pp. 1–21. doi: 10.1080/19648189.2016.1217792 [24] elhamdouni, y., khabbazi, a., benayad, c., dadi, a., ahmid, o.i. (2015). effect of fiber alfa on thermophysical characteristics of a material based on clay. energy procedia, 74, pp. 718–727. doi : 10.1016/j.egypro.2015.07.807 [25] ben brahim, s., ben cheikh, r. (2007). influence of fibre orientation and volume fraction on the tensile properties of unidirectional alfa-polyester composite. composites science and technology, 67(1), pp. 140–147. doi: 10.1016/j.compscitech.2005.10.006 [26] nf p 18-101: aggregates terminology definitions – classification, afnor, (1990). [27] nf p 15-433: methods of testing cement. determination of shrinkage and swelling, classification, afnor, 1994. [28] el-abbassi, f.z, assarar, m., ayad, r., bourmaud, a., baley, c. (2020). a review on alfa fibre (stipatenacissima l.): from the plant architecture to the reinforcement of polymer composites. composites part a: applied science and manufacturing, 128, 105677. doi: 10.1016/j.compositesa.2019.105677 [29] nf en 12390-2: testing hardened concrete — part 2: making and curing specimens for strength, afnor, p 18455, 2001. [30] nf en 12390-3 testing hardened concrete part 3: compressive strength of test specimens. afnor, june 2019 [31] nf en 12390-5 testing hardened concrete part 5: flexural strength of test specimens. afnor, april 2012 << /ascii85encodepages false /allowtransparency false /autopositionepsfiles true /autorotatepages /none /binding /left /calgrayprofile (dot gain 20%) /calrgbprofile (srgb iec61966-2.1) /calcmykprofile (u.s. web coated \050swop\051 v2) /srgbprofile (srgb iec61966-2.1) /cannotembedfontpolicy /error /compatibilitylevel 1.4 /compressobjects /tags /compresspages true /convertimagestoindexed true /passthroughjpegimages true /createjobticket false /defaultrenderingintent /default /detectblends true /detectcurves 0.0000 /colorconversionstrategy /cmyk /dothumbnails false /embedallfonts true /embedopentype false /parseiccprofilesincomments true /embedjoboptions true /dscreportinglevel 0 /emitdscwarnings false /endpage -1 /imagememory 1048576 /lockdistillerparams false /maxsubsetpct 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/hrv (za stvaranje adobe pdf dokumenata najpogodnijih za visokokvalitetni ispis prije tiskanja koristite ove postavke. stvoreni pdf dokumenti mogu se otvoriti acrobat i adobe reader 5.0 i kasnijim verzijama.) /hun 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can be opened with acrobat and adobe reader 5.0 and later.) >> /namespace [ (adobe) (common) (1.0) ] /othernamespaces [ << /asreaderspreads false /cropimagestoframes true /errorcontrol /warnandcontinue /flattenerignorespreadoverrides false /includeguidesgrids false /includenonprinting false /includeslug false /namespace [ (adobe) (indesign) (4.0) ] /omitplacedbitmaps false /omitplacedeps false /omitplacedpdf false /simulateoverprint /legacy >> << /addbleedmarks false /addcolorbars false /addcropmarks false /addpageinfo false /addregmarks false /convertcolors /converttocmyk /destinationprofilename () /destinationprofileselector /documentcmyk /downsample16bitimages true /flattenerpreset << /presetselector /mediumresolution >> /formelements false /generatestructure false /includebookmarks false /includehyperlinks false /includeinteractive false /includelayers false /includeprofiles false /multimediahandling /useobjectsettings /namespace [ (adobe) (creativesuite) (2.0) ] /pdfxoutputintentprofileselector /documentcmyk /preserveediting true /untaggedcmykhandling /leaveuntagged /untaggedrgbhandling /usedocumentprofile /usedocumentbleed false >> ] >> setdistillerparams << /hwresolution [2400 2400] /pagesize [612.000 792.000] >> setpagedevice microsoft word numero_37_art_1 a. eberlein et alii, frattura ed integrità strutturale, 37 (2016) 1-7; doi: 10.3221/igf-esis.37.01 1 focussed on multiaxial fatigue and fracture crack front segmentation under combined mode iand mode iiiloading a. eberlein university of paderborn, institute of applied mechanics, pohlweg 47-49, 33098 paderborn, germany eberlein@fam.upb.de, http://mb.uni-paderborn.de/fam/ h. a. richard university of paderborn, institute of applied mechanics, pohlweg 47-49, 33098 paderborn, germany richard@fam.upb.de, http://mb.uni-paderborn.de/fam/ abstract. this article approaches the topic of crack initiation and crack growth behaviour under combined mode iand mode iii-loading conditions. such loading combinations especially lead to a crack, which unscrew out of its initial orientation and segments into many single cracks respectively facets. this characteristic depicts the crucial difference to a crack growth under pure mode i-loading, pure in-plane shearing (mode ii) as well as 2d-mixed-mode-loadings. since this stepped fractured surfaces thus far are proved little and therefore their characterisation remains to be done, a facets quantification using some characteristic dimensions will be performed within this article. after the description of experiments for facet creation the facet’s quantification using the crack profile near the initial position each facet will be analysed concerning characteristic dimensions. finally the findings will be illustrated and discussed in this contribution. keywords. 3d-mixed-mode; facets; fatigue; fracture; ctsr-specimen. introduction by today unsolved and long existing research matter in fracture mechanics is the characterisation of crack initiation and growth behaviour under combined mode iand mode iii-loading. this loading combination specially leads the initial crack to twist out of its previous direction and separate at once into multiple daughter cracks, afterwards called facets. building on the researches and findings from sommer [1], knauss [2] as well as pons and karma [3] within this article a quantification of facets will be presented and discussed. the purpose is to get new insights and facts about facets creation and initiation. experiments for facet creation reating facets experiments under mixed-mode i + iii-loading were performed using the ctsr-specimen and corresponding loading device [4, 5]. a detailed explanation of the experimental procedure and ctsr-specimen’s geometry follows below. a c a. eberlein et alii, frattura ed integrità strutturale, 37 (2016) 1-7; doi: 10.3221/igf-esis.37.01 2 ctsr (compact tension shear rotation) -specimen referring to the afm-specimen a new specimen, so-called ctsr-specimen (fig. 1) has been developed [4]. relevant specimen’s dimensions are listed in the chart on the right hand side of fig. 1. hereby the specimen thickness t is a compromise between a thick specimen with a high torsional stiffness and high testing load levels. the appropriate loading device is shown in fig. 2. in combination with the new specimen this loading device enables any combination of mixedmode-loading including pure mode i-, pure mode iiand pure mode iii-loading. a detailed explanation and illustration of adjusting the mixed-mode-loading can be found in [4, 5, 6]. specimen length l 103 mm specimen width w 55 mm initial crack length a0 27.5 mm specimen thickness t 15.5 mm figure 1: ctsr-specimen with characteristic dimensions. experimental procedure under combined mode i-mode iii-loading for the creation of facets crack growth experiments with changing loading directions were performed. after a crack growth of a crack length a = 3.5 mm under mode i-loading condition with a constant cyclic comparative stress intensity factor δkv the loading direction by turning the loading device and rotating the specimen was changed into mixedmode i + iii-loading with δki ≠ 0 and δkiii ≠ 0 (fig. 2). figure 2: mixed-mode i + iii-loading by shifting the loading device. then the tests started again under constant cyclic load range δf set so, that the cyclic comparative stress intensity factor δkv before and after the loading direction was identically. crack length-cycle curves and fractured surfaces typical a-n-curves resulting from such experiments with changing loading directions are shown in fig. 3. the mixedmode i + iii-loading was adjusted by varying both loading angles α and β. a crack length a of 3.5 mm under mode iloading, due to that high cyclic stress intensity factor δkv = δki, is reached after ca. n = 70,000 cycles. afterwards changing the loading direction the crack growth delays. significant crack growth retardations were noticed by stress intensity factor ratios 1 < kiii/ki < ∞. a. eberlein et alii, frattura ed integrità strutturale, 37 (2016) 1-7; doi: 10.3221/igf-esis.37.01 3 figure 3: crack growth retardation after changing the loading direction from mode i to mixed-mode i + iii. on the one hand the retardation effects are caused by the new crack growth direction due to mode iii-loading part. hereby the crack twists at an angle ψ0 out of its previous orientation. additionally the crack separates in many facets, which influence the crack growth rate too. characteristic fractured surfaces with facet formation after changing the loading direction from mode i-loading to mixed-mode i + iii-loading are pictured in fig. 4. this row on fractured surfaces shows the facet formation depending on mode iii-part on the total stress intensity factor kiii/(ki + kiii). the figures indicate that facet formation begins at a specific mode iii-part on the total stress intensity factor of kiii/(ki + kiii) = 0.37. within this experimental research no facets were observed below that ratio. the first fractured surface on the left hand side of fig. 4, captured by mode iii-part on the total stress intensity factor of kiii/(ki + kiii) = 0.26, shows that the crack continuously and smoothly without any facet initiation changes its direction. furthermore, the crack front is still coherent. with increasing mode iii-part on the mixed-mode i + iii-loading the facets’ shape changes clearly. figure 4: facet formation with increasing mode iii-part. a. eberlein et alii, frattura ed integrità strutturale, 37 (2016) 1-7; doi: 10.3221/igf-esis.37.01 4 to get a better knowledge of such facet formation under mixed-mode i + iii-loading for its consideration in existing hypotheses for crack growth prediction under 3d-mixed-mode-loadings a facet quantification was performed, which is presented and discussed in the next section. characterization of crack front segmentation he first step to understand the crack growth behaviour under mode i-mode iii-loading conditions is to quantify the crack front segmentation respectively the facet formation. therefor some characteristic dimensions and angles were defined. definition of characteristic dimensions first of all, the geometry of each facet will be simplified to a circular shape. then due to the non-planar shear stress τz facets initiate twisted under a facet angle ψf as fig. 5 a) shows. reflecting the work of lin et al. [7] this facet quantification distinguishes between two facet types – ascending facets fas indicated in fig. 5 b) by red lines – and falling facets ffa indicated in fig. 5 b) by dashed lines, which finally connects the ascending facets fas. ascending facets fas initiate induced by a local opening mode-loading [8] whereas falling facets ffa form in a bridging region b making a connection to each fas facet. figure 5: definition of characteristic dimensions for facet quantification: a) schematic facet formation at the crack front due to τz; b) facet’s geometry and characteristic dimensions in the y-z-plane the ffa facets are unfavourable oriented to a local opening mode-loading. consequently, another local mechanisms, like local friction or plasticity [7], are probably responsible for their formation. so higher energies respectively loads for the creation of ffa facets are required. as a conclusion such facet formation proceeds at a later crack growth stage as the initiation of fas facets [3, 7]. other characteristic dimensions for facet quantification are the projected facet length d, the facet distance c and the width e of the bridging region b (see fig. 5 b)). approach for quantification of facet’s geometry for facet quantification the fractured surfaces were analysed microscopically. hereby the crack’s profile was measured close to the initial notch that is after a short crack extension δa. fig. 6 illustrates a typical crack’s profile of a mode iii fractured surface. the measurement plane of crack’s profile, indicated by the arrow, lies in a distance of about δa ≈ 285 µm from the wire eroded notch. in the front view (indicated by the red arrow) the crack’s profile looks as in fig. 6 b) shown. thereby the fas facets, which were considered for the quantification, are marked in the graph. furthermore, it is visible that in the middle of the specimen the biggest facets creates. the analysis of all fas facets reveals an average projected facet length of d = 1.23 mm and an average distance of c = 1.63 mm. the biggest facet angles ψf exhibit the fas facets fas,3, fas,4 and fas,5 (see fig. 6 b)). the angles ψf lie within an expected range between 42.3° and 49.3°. starting from the middle of the specimen to the specimen borders a decreasing facet angle was noted. the reason for this is the decreasing shear stress τz and an increasing mode ii-part by moving from the middle of the specimen to the border. due to no pure mode iii-loading condition facets near the specimen border initiate under smaller twist angles. the measurement of the bridging regions b exposed an average width e of 342 µm. such a systematic analysis approach for facet quantification was performed for all fractured surfaces within this experimental research. in the next section the results of facet quantification are shown and discussed. t a. eberlein et alii, frattura ed integrità strutturale, 37 (2016) 1-7; doi: 10.3221/igf-esis.37.01 5 figure 6: analysis of facet formation: a) fractured surface under pure mode iii-loading; b) crack’s profile: measurement of each formed facet. results of facet’s quantification the results of facet’s quantification are illustrated in fig. 7. due to the fact that within this experimental research no facets below kiii/(ki + kiii) of 0.37 initiated, the number of facets in fig. 7 a) for lower kiii/(ki + kiii)-ratios is zero. when facets create their quantity decreases with increasing mode iii-part to an average number of five facets at pure mode iiiloading. moreover, an increasing projected facet length d and facet distance c can be detected by means of fractured surfaces (shown in fig. 7 b)). at pure mode iii-loading an average projected facet length d of 2.5 mm and an average facet distance c of 3.4 mm result. since the shear stress τz declines by moving along the specimen thickness from the middle of the specimen to the border, the conditions for pure mode iii-loading are mostly given only in a limited range around the centre plane [9]. therefore, for the measurement of the facet angles ψf only three facets around the centre plane of the specimen thickness are considered. fig. 7 c) displays the results of the measured facet angles. in contrast to the hypothesis by richard for the crack twisting angle ψ0 the measured facet angles partially are ca. 10° smaller as the hypothesis predicts. however, the measured facet angle ψf for pure mode iii-loading coincides very well with the hypothesis by richard. the determination of the facet angles respectively the crack twisting angles is principally very difficult. the measured deviations can be formed e. g. by local plastic deformations of the facets while final rupture. in addition a strong correlation between the projected facet length d, the facet distance c and the bridging width e (see fig. 7 d)) of the bridging regions b (see fig. 7 e)) with the measured facet angles ψf exist. such a correlation between this characteristic dimensions lin et al. found too [7]. this correlation they explain on the basis of energy’s balance consideration. the result of the bridging regions analyses is pictured in fig. 7 d). here the characteristic width e increases with rising mode iii-part. the magnitude of the bridging width e is in comparison with the projected facet length d and the facet distance c significantly smaller and is in a direct contact with both values. at pure mode iii-loading the bridging width e is almost 1 mm. further the fractured surfaces with higher mode iii-loading parts in the bridging regions b exhibit no fatigue characteristics. instead the fractured surfaces show a classical strength failure due to cleavage fracture as well as shear fracture. based on this experimental knowledge of facet’s creation and crack front segmentation under combined mode imode iii-loading the next step will be an establishing of a criterion for crack growth initiation under mixed-mode i + iiiloadings. in this field today only a few approaches subsist, which are subjected to many assumptions and restrictions [7, 10, 11, 12, 13]. a. eberlein et alii, frattura ed integrità strutturale, 37 (2016) 1-7; doi: 10.3221/igf-esis.37.01 6 figure 7: overview of facets quantification’s results (averages): a) number of facets depending on mode iii-part; b) projected facet length d and facet distance c depending on mode iii-part; c) facet angle ψf depending on mode iii-part in contrast to the crack twisting angle ψ0 by richard [6]; d) bridging width e of regions b depending on mode iii-part; e) bridging regions b of a pure mode iii fractured surface references [1] sommer, e., formation of fracture ‘lances’ in glass, engng. frac. mech., 1 (1969) 539–546. [2] knauss, w.g., an observation of crack propagation in anti-plane shear, int. j. frac., 6 (1970) 183-187. [3] pons, a.j., karma, a., helical crack-front instability in mixed-mode fracture, nature, 464 (2010) 85-89. [4] schirmeisen, n.-h., risswachstum unter 3d-mixed-mode-beanspruchung, vdi-verlag, düsseldorf, (2012). [5] eberlein, a., einfluss von mixed-mode-beanspruchung auf das ermüdungsrisswachstum in bauteilen und strukturen. vdi-verlag, düsseldorf, (2016). [6] richard, h.a., schramm, b., schirmeisen, n.-h., cracks on mixed-mode loading – theories, experiments, simulations, int. j. fat., 62 (2014) 93-103. a. eberlein et alii, frattura ed integrità strutturale, 37 (2016) 1-7; doi: 10.3221/igf-esis.37.01 7 [7] lin, b., mear, m.e., ravi-chandar, k., criterion for initiation of cracks under mixed-mode i + iii loading, int. j. frac., 165 (2010) 175-188. [8] pollard, d.d., segall, p.e., delaney, p.t., formation and interpretation of dilatant echelon cracks, geol. soc. am. bull., 93 (1982) 1291-1303. [9] kullmer, g., richard, h.a., wang, c., eberlein, a., numerische untersuchungen zur ermittlung der rissablenkungs und rissverdrehungswinkel bei allgemeiner mixed-mode-belastung, dvm-bericht 245, bruchmechanische werkstoffund bauteilbewertung: beanspruchungsanalyse, prüfmethoden und anwendungen, deutscher verband für materialforschung und –prüfung e.v. berlin (2013) 59-68. [10] cambonie, t., lazarus, v., quantification of the crack fragmentation resulting from mode i + iii loading, proc. mater. science 3 (2014) 1816-1821. [11] pham, k.h., ravi-chandar, k., further examination of the criterion for crack initiation under mixed-mode i + iii loading, int. j. frac. 189 (2014) 121-138. [12] leblond, j.-b., lazarus, v., karma, a., multiscale cohesive zone model for propagation of segmented crack fronts in mode i + iii fracture, int. j. frac. 191 (2015) 167-189. [13] ronsin, o., caroli, c., baumberger, t., crack front echelon instability in mixed mode fracture of a strong nonlinear elastic solid, europhys. lett. 105 (2014) 34001. << /ascii85encodepages false /allowtransparency false /autopositionepsfiles true /autorotatepages /none /binding /left /calgrayprofile (dot gain 20%) /calrgbprofile (srgb iec61966-2.1) /calcmykprofile (u.s. web coated \050swop\051 v2) /srgbprofile (srgb iec61966-2.1) /cannotembedfontpolicy /error /compatibilitylevel 1.4 /compressobjects /tags /compresspages true /convertimagestoindexed true /passthroughjpegimages true /createjobticket false /defaultrenderingintent /default /detectblends true /detectcurves 0.0000 /colorconversionstrategy /cmyk /dothumbnails false /embedallfonts true /embedopentype false /parseiccprofilesincomments true /embedjoboptions true /dscreportinglevel 0 /emitdscwarnings false /endpage -1 /imagememory 1048576 /lockdistillerparams false /maxsubsetpct 100 /optimize true /opm 1 /parsedsccomments 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can be opened with acrobat and adobe reader 5.0 and later.) >> /namespace [ (adobe) (common) (1.0) ] /othernamespaces [ << /asreaderspreads false /cropimagestoframes true /errorcontrol /warnandcontinue /flattenerignorespreadoverrides false /includeguidesgrids false /includenonprinting false /includeslug false /namespace [ (adobe) (indesign) (4.0) ] /omitplacedbitmaps false /omitplacedeps false /omitplacedpdf false /simulateoverprint /legacy >> << /addbleedmarks false /addcolorbars false /addcropmarks false /addpageinfo false /addregmarks false /convertcolors /converttocmyk /destinationprofilename () /destinationprofileselector /documentcmyk /downsample16bitimages true /flattenerpreset << /presetselector /mediumresolution >> /formelements false /generatestructure false /includebookmarks false /includehyperlinks false /includeinteractive false /includelayers false /includeprofiles false /multimediahandling /useobjectsettings /namespace [ (adobe) (creativesuite) (2.0) ] /pdfxoutputintentprofileselector /documentcmyk /preserveediting true /untaggedcmykhandling /leaveuntagged /untaggedrgbhandling /usedocumentprofile /usedocumentbleed false >> ] >> setdistillerparams << /hwresolution [2400 2400] /pagesize [612.000 792.000] >> setpagedevice microsoft word numero_35_art_42 g. kullmer et alii, frattura ed integrità strutturale, 35 (2016) 368-378; doi: 10.3221/igf-esis.35.42 368 focussed on crack paths fatigue crack paths under the influence of changes in stiffness g. kullmer, b. schramm, h. a. richard paderborn university, germany kullmer@fam.upb.de abstract. an important topic of the collaborative research centre trr 30 of the deutsche forschungsgemeinschaft (dfg) is the crack growth behaviour in graded materials. in addition, the growth of cracks in the neighbourhood of regions and through regions with different material properties belongs under this topic. due to the different material properties, regions with differing stiffness compared to the base material may arise. regions with differing stiffness also arise from ribs, grooves or boreholes. since secure findings on the propagation behaviour of fatigue cracks are essential for the evaluation of the safety of components and structures, the growth of cracks near changes in stiffness has to be considered, too. depending on the way a crack penetrates the zone of influence of such a change in stiffness and depending on whether this region is more compliant or stiffer than the surrounding area the crack may grow towards or away from this region. both cases result in curved crack paths that cannot be explained only by the global loading situation. to evaluate the influence of regions with differing stiffness on the path of fatigue cracks the paths and the stress intensity factors of cracks growing near and through regions with differing stiffness are numerically determined with the program system adapcrack3d. therefore, arrangements of changes in stiffness modelled as material inclusions with stiffness properties different from the base material or modelled as ribs and grooves are systematically varied to develop basic conclusions about the crack growth behaviour near and through changes in stiffness. keywords. curved crack path; crack growth simulation; material inclusion; change in stiffness; finite elements. introduction n important topic of the collaborative research centre trr 30 of the deutsche forschungsgemeinschaft (dfg) is the crack propagation behaviour in graded materials. in addition, the growth of cracks in the neighbourhood of material boundaries belongs under this topic. in particular, accidentally embedded extraneous material causes material boundaries. in many cases, material inclusions represent regions with stiffness properties different from the base material and the boundaries of these regions represent local changes in stiffness. furthermore, ribs, grooves or boreholes cause similar changes in stiffness. depending on the way a crack penetrates the zone of influence of a region with different stiffness and depending on whether this region is more compliant or stiffer than the surrounding area the crack may grow towards or may tend to grow away from the change in stiffness. if the crack crosses the change in stiffness, the crack growth behaviour reverses. if the region with different stiffness is locally bordered, the crack may grow around this region. all mentioned cases result in curved crack paths. curved crack paths result from mixed mode loading at the crack tip. thereby in general the basic crack opening modes co-occur, see fig. 1. mode i describes normal loading leading to a a g. kullmer et alii, frattura ed integrità strutturale, 35 (2016) 368-378; doi: 10.3221/igf-esis.35.42 369 symmetrical opening of the crack surfaces. mode ii is valid for shear loading causing in-plane sliding of the crack surfaces. mode iii represents shear loading generating anti-plane sliding of the crack surfaces. f f f f f f mode i mode ii mode iii x y z x y z x y z figure 1: basic crack opening modes, richard and sander [1]. since the present study only deals with plane problems, mode iii is irrelevant. whereas a crack propagates self-similar under mode i-loading it deflects under mode ii-loading about the angle φ0 ≈ 70° as represented in fig. 2. under plane mixed-mode-loading with continuously changing ratios of mode i and mode ii curved cracks form in the x-y-plane according to fig. 1. figure 2: crack propagation under different crack opening modes, richard and sander [1] simulation model for the investigation of the fatigue crack growth in the neighbourhood of changes in stiffness imulation models based on the ct-specimen, see fig. 3, are used to investigate the basic influence of line-shaped regions with differing stiffness and different orientation on the path of fatigue cracks. the default thickness of the specimen is 5mm and the default value of young´s modulus is 210.000mpa. the material behaviour is idealised as linear elastic, isotropic and homogeneous. poisson´s ratio is zeroed to avoid stresses in thickness direction of the specimen and thickness influences and therefore to ensure a state of plane stress in spite of using a three-dimensional model. a three-dimensional model is required for the present investigation since the crack growth is simulated with the program system adapcrack3d developed by the institute of applied mechanics of the university of paderborn (fulland [2]). as shown in fig. 3 a rectangular partition inserted into the cad-model of the ct-specimen represents the line-shaped region with differing stiffness. the simulation models differ since young´s modulus, the thickness, the distance to the starter notch and the orientation of the line-shaped change in stiffness vary. to evaluate the influence of the stiffness mismatch, on the one hand, with default thickness young´s modulus of the line-shaped region is varied and on the other hand, with standard young´s modulus the thickness of the line-shaped region is modified. to analyse the influence of the orientation of the change in stiffness in relation to the nominal global mode i-loading of the initial crack, the orientation of the change in stiffness is varied by stepwise rotation of the line-shaped region about the centre a. thus, for a fixed distance d = 9.7mm the orientation angle α varies between 90° and 30°. to investigate the influence of the distance d between the starter notch and the change in stiffness with default thickness and constant orientation angle α = 45° the distance d varies in steps of 2.5mm from 9.7mm to 19.7mm. for this investigation, young´s modulus of the line-shaped region is once double and once half the value of default young´s modulus. s g. kullmer et alii, frattura ed integrità strutturale, 35 (2016) 368-378; doi: 10.3221/igf-esis.35.42 370 17 3 32,4 18 3 9 ,6 90 8 6 ,4 9 0° 32,4 2 4 0 5 d a  14,4 line-shaped region with differing stiffness figure 3: geometry of the ct-specimen and positioning of the line-shaped region with differing stiffness. the ct-specimen is partitioned according to fig. 4. inside the partitions p1 and p2, the default properties of young´s modulus and the thickness of the specimen are valid. whereas inside partition p3, that represents the region with differing stiffness, depending on the type of examination either young´s modulus or the thickness varies. the partition p2 guarantees a comparable fine mesh in the neighbourhood of the partition p3 and identical boundary conditions independent from the orientation angle α and the distance d of the change in stiffness. therefore, the border of partition p2 is sufficiently distant from the partition p3 for all investigated orientations and positions of the change in stiffness. furthermore, fig. 4 shows the boundary conditions. all simulation models are supported at the positions a, b and c. the bearing is statically determined and symmetrical. the specimen is loaded with distributed line loads of 2500n/mm at the upper and lower inner side of the bore. with a specimen thickness of 5mm the resulting load is 12.5kn. the boundary conditions are chosen in a way that the bearing reactions vanish and a symmetrical deformation of the specimen occurs if all partitions of the specimen have the same young´s modulus and the same thickness. in this case, a pure mode i-loading is present at the crack tip and the crack should grow straight ahead. figure 4: partitioning of the ct-specimen and definition of the boundary conditions. fig. 5 shows a typical global mesh exemplary for the ct-specimen with a change in stiffness with an orientation angle α = 45°. the mesh consists of 10-noded quadratic tetrahedral elements. inside the partitions p2 and p3 where the crack most likely will propagate the edge length of the elements is chosen 1mm whereas in partition p1 an edge length of 2.5mm is sufficient. g. kullmer et alii, frattura ed integrità strutturale, 35 (2016) 368-378; doi: 10.3221/igf-esis.35.42 371 figure 5: exemplary mesh for the ct-specimen with a change in stiffness, orientation angle of the change in stiffness α = 45°. for the crack growth simulation with adapcrack3d the global mesh is unstitched along the crack path with the aid of a crack model. the crack model is a surface mesh that contains only the surface of the crack. at first, the crack model is built up of the mesh of the initial crack as shown in fig. 6. therefore, linear triangle elements with an edge length of 0.5mm are used. the initial crack has a lateral length of 2mm as defined in fig. 3. for a growing crack, the crack model is incrementally extended with additional crack surfaces in the direction depending on the estimated mixed mode ratio. since, as already mentioned, the present investigation in principle represents a plane problem, poisson´s ratio is zeroed to ensure a state of plane stress and the stress intensity factor kiii is neglected to avoid a twisting of the crack surface. furthermore, adapcrack3d is modified in a way that with every simulation step a uniform crack increment over the specimen thickness with a fixed lateral length is achieved. additionally it is meaningful to use the mapped mesh-method to mesh the initial crack as shown in fig. 6 to achieve constant crack deflection angles, because adapcrack3d uses local coordinate systems based on the mesh of the previous crack surface to calculate the coordinates of the new crack front nodes. x y z model of the initial crack mesh of the initial crack figure 6: positioning of the crack model inside the ct-specimen, orientation angle of the change in stiffness α = 45°. for the calculation of the stress intensity factors ki und kii adapcrack3d uses the modified virtual crack closure integral (mvcci) after rybicki and kanninen [3] applied to a comoving submodel composed of a regular linear g. kullmer et alii, frattura ed integrità strutturale, 35 (2016) 368-378; doi: 10.3221/igf-esis.35.42 372 hexahedral mesh containing the crack front. thereby for every node at the crack front, first the energy release rates gi and gii for the respective crack opening modes are calculated. to evaluate the stress intensity factors ki and kii the mean values of the energy release rates gi and gii over the thickness of the specimen and the equations valid for the state of plane stress egk ii  (1) egk iiii  (2) are used. since plane mixed mode loading is existent, the crack deflection angles are calculated with the maximum tangential stress criterion after erdogan and sih [4]. verification of the crack growth simulations efore the execution of the actual numerical simulations of ct-specimens with different changes in stiffness, the simulation model and the modified version of adapcrack3d are verified. therefore, simulations with the intended different values of young´s modulus, the different thicknesses and a constant orientation angle α = 90° are conducted. due to symmetry mode ii should be zero and the crack should grow straight through the changes in stiffness independent of young´s modulus or the thickness of the change in stiffness. the numerically determined resulting crack paths for all cases are almost straight with slight deviations from zero in y-direction. the extent of the deviations is for the ct-specimen with a homogeneous partition p3 with default young´s modulus and default thickness as big as for the ct-specimens with different changes in stiffness. already numerical inaccuracies due to an asymmetric fe-mesh, typical for using the free mesh option, cause slight deviations from a straight crack path. the maximum deviation from the straight line is in all cases for a simulated additional crack length of more than 20mm less than 0.2mm. thus, the simulation model and the modified version of adapcrack3d are suitable for the intended investigation. moreover, crack growth simulations with the ct-specimen with a change in stiffness with young´s modulus double the default young´s modulus and an orientation angle α = 45° are executed with crack growth increments of 0.2mm, 0.5mm und 1mm. because the resulting crack paths are almost the same, the fixed default crack increment of 0.5mm for the further simulations is chosen, since this uniform crack increment has turned out to be a reasonable compromise between effort and accuracy. crack paths for different orientations of an inclusion he simulated crack paths for different orientations angles of a change in stiffness modelled as an inclusion and the alignment of the inclusion for the extreme orientation angles α = 30° as well as α = 90° are presented in fig. 7. for the stiff inclusion, young´s modulus is double the default young´s modulus and for the compliant inclusion, young´s modulus is half the default young´s modulus. figure 7: simulated crack paths with variable orientation of the inclusion, a) stiff inclusion, b) compliant inclusion. b t b) a) g. kullmer et alii, frattura ed integrità strutturale, 35 (2016) 368-378; doi: 10.3221/igf-esis.35.42 373 for α = 90° the crack propagates independently of the inclusion stiffness straight through the inclusion. with increasing inclination angle of the inclusion, the deflection of the crack rises. if the crack penetrates the region influenced by the stiffness mismatch of an inclined inclusion the crack tends to grow around the boundary to the stiff material and to grow towards the boundary to the compliant material. this can be clearly seen with the simulation results for the inclusion with orientation angle α = 30°. in this case, the crack hardly enters the stiff inclusion. furthermore, the crack grows along the boundary of the compliant inclusion and leaves the inclusion at the farthest corner. in both cases the orientation angle α = 30° seems to be a lower limit so that the crack properly traverses the inclusion. if the crack traverses the inclusion the crack growth behaviour reverses approaching the second material boundary. when the crack leaves the region influenced by the stiffness mismatch the crack approaches tangentially a parallel to the extension line of the initial crack. the offset of the parallel to the extension line increases with the inclination of the inclusion. where the crack crosses a material boundary, the crack path has an inflexion point and the curvature of the crack path changes. this means that the stress intensity factor kii is zero at the material boundary and the crack locally grows straight under mode i conditions. the maximal magnitude of kii corresponds with the maximal curvature of the crack path and the maximal stiffness asymmetry around the crack tip due to the inclusion. anyway, kii is small compared to ki leading to slightly curved crack paths. crack paths for stiff changes in stiffness ig. 7 shows crack paths through changes in stiffness due to doubling or halving young´s modulus in partition p3. these results are already discussed in [5, 6]. fig. 8 presents the comparison between crack paths due to changes in stiffness with double young´s modulus or double thickness for the orientation angles α = 45° and α = 60°. figure 8: crack paths for different orientation angles of stiffenings the comparison of crack paths in fig. 8 shows that in the neighbourhood of different kinds of stiffenings the principle characteristics of the crack paths are similar. if the crack enters the region of influence of a stiffening, the crack grows away from the stiffening. with increasing inclination of the stiffening, the deflection of the crack rises with the tendency that the crack tangentially passes by this region, see fig. 7. if the extent of the stiffening is too big or the inclination of the stiffening is moderate, the crack penetrates the stiffening under a certain angle as defined in fig. 11. furthermore, the curvature of the crack paths changes at this point. inside of the stiffening, the cracks extend steadily curved. on the backside of the stiffening, they grow towards the boundary of the stiffening. again, the curvature of the crack paths changes where the cracks leave the stiffening. with increasing distance behind the stiffening, the crack paths approach tangentially a parallel to the extension of the initial crack. the offset of this parallel increases with rising inclination of the stiffening. the results show that the influence of the stiffening on the deflection of the crack path depends on the orientation of the stiffening and on the stiffness mismatch of the stiffening as also shown in fig. 15. obviously, the effective stiffness mismatch due to a local stiffening through doubling young´s modulus with constant thickness is greater than due to a local stiffening through doubling the thickness with constant young´s modulus. here it becomes noticeable, that a three dimensional fe-model is used for the crack growth simulation. thus, particularly inside of the thickening, the stresses are not constant over the whole thickness of the specimen but the outer edges of the thickening are stress-free regions. these stress free regions do not participate in the stiffness mismatch. therefore, obviously the effect on the crack path of a thickening with double thickness is weaker than the effect of a stiff inclusion with double young´s modulus. f g. kullmer et alii, frattura ed integrità strutturale, 35 (2016) 368-378; doi: 10.3221/igf-esis.35.42 374 1.0921.0741.0851.0791.1471.1461.2491.256 1.268 1.206 1.242 809 854 888 906 938 1.033 ‐1,5 ‐1 ‐0,5 0 0,5 0 1 2 3 4 5 6 7 8 y ‐a x is  i n  m m x‐axis in mm region outside the thickening region inside the thickening 1.082 1.1111.134 1.2421.2401.328 1.418 1.515 2.354 2.300 2.508 2.400 2.2152.224 2.194 2.147 ‐1,5 ‐1 ‐0,5 0 0,5 8 9 10 11 12 13 14 15 16 y ‐a x is  i n  m m x‐axis in mm region outside the thickening region inside the thickening figure 9: ki-values along the crack path through a thickening with orientation angle α = 45°. fig. 9 exemplarily shows the distribution of the stress intensity factor ki on the path through the thickening with the orientation angle α = 45° using a bubble diagram whereupon the diameter of the bubbles represents the local value of ki. when the crack approaches the stiffening, ki drops although the crack grows, by the reason that the stiffening causes a stress shield at the crack tip. ki reduces about the factor 2 when the crack enters the thickening. inside the thickening, ki increases. when the crack exits the thickening ki rises about the factor 2 . if in contrast an inclusion with double young´s modulus causes the stiffening then ki rises about the factor 2 when the cracks enters the inclusion and ki reduces about the factor 2 when crack exits the inclusion [5, 6]. since the relations for the stress intensity factor egk ii  and for the energy release rate dadugi  , which is the energy release –du over the increment of the crack surface da, are valid and since with every section crossing the thickness or young´s modulus rise or reduce by the factor 2, obviously, the energy release is continuous when the crack crosses the boundaries of the stiffening. the evaluation of the stress intensity factor kii yields that the values of kii are overall small compared to the values of ki. the greatest values of kii occur, where the stiffening causes the greatest local stiffness asymmetry. at the boundaries of the stiffening, the course of kii shows a zero crossing and the sign of kii changes, so that at these points, the crack path has inflexion points and locally mode i-loading exists. crack paths for compliant changes in stiffness ig. 10 illustrates the comparison between crack paths due to changes in stiffness with halving young´s modulus or halving the thickness in partition p3 for the orientation angles α = 45° and α = 60°. firstly, the cracks grow towards the change in stiffness. with increasing inclination of the change in stiffness, the deflection of the cracks rises, whereby the entrance angle according to fig. 11 increases. at the transition point into the compliant region, the curvature of the crack paths changes. inside of the compliant region, the crack extends steadily curved. on the backside of the compliant region, the crack paths deflect more with increasing inclination of the change in stiffness and tend to run tangential to the region boundary. if the compliant region is big enough, the crack leaves this region on the backside, whereat the curvature of the crack path changes again. with greater distance behind the compliant region, the crack paths approach tangentially a parallel to the extension of the initial crack. the offset of this parallel to the initial crack increases with rising inclination of the change in stiffness. in contrast to the crack paths due to a stiffening through doubling young´s modulus or doubling the thickness as shown in fig. 8 the crack paths due to a compliant region through halving young´s modulus or halving the thickness are rather similar. obviously, this may be reasoned by the fact that inside a cut-out in contrast to a thickening no stress-free regions occur, so that the effective stiffness mismatches due to both methods to generate a compliant change in stiffness are similar. the characteristics of the courses of the stress intensity factors ki and kii for the compliant regions are corresponded to the characteristics of the courses of the stress intensity factors ki and kii for the stiffening. f g. kullmer et alii, frattura ed integrità strutturale, 35 (2016) 368-378; doi: 10.3221/igf-esis.35.42 375 figure 10: crack paths for different orientation angles of compliant changes in stiffness comparison of crack paths for stiff and compliant changes in stiffness ig. 11 illustrates the definition of the transition angles of the crack paths at region transitions. initial crack stiffstiff compliant initial crack β γ γ stiffcompliant compliant figure 11: definition of the entrance angle β and the exit angle γ of the crack path at region transitions. the comparison of the transition angles in fig. 12 and the crack paths through stiff and compliant changes in stiffness in the figs. 7, 8 and 10 show that in both cases at the transition from a compliant to a stiff region the crack grows away from the region boundary. therefore, the transition angle from compliant to stiff according to the definition of the transition angles in fig. 11 becomes smaller than the orientation angle of the change in stiffness. at the transition from a stiff to a compliant region, the crack grows towards the region boundary and the transition angle becomes greater than the orientation angle of the change in stiffness. furthermore, fig. 12 indicates that the transition angles are equal at transitions with the same stiffness mismatch independent of what causes the change in stiffness. figure 12: comparison of the entrance and the exit angles depending on the type of the change in stiffness f g. kullmer et alii, frattura ed integrità strutturale, 35 (2016) 368-378; doi: 10.3221/igf-esis.35.42 376 crack paths depending on the distance of the change in stiffness from the starter notch he crack paths for a stiff inclusion and a compliant inclusion with constant orientation angle α = 45° and varying distance to the starter notch are represented in fig. 13. the distance varies in steps of 2.5mm from 9.7mm to 19.7mm. figure 13: crack paths for stiff inclusions (top image) and compliant inclusions (lower image) with constant orientation angle α = 45° and varying distance from the starter notch as shown in fig. 13 the characteristics of the particular crack paths for the stiff inclusions and the compliant inclusions are equal. in the region of influence of the inclusion, the crack deflects and the deviation of the crack path from the initial crack increases with the distance from the starter notch. behind the inclusion, the crack grows parallel to the initial crack with a certain offset. the parallel offset behind the stiff inclusion is the bigger the greater the distance of the inclusion from the starter notch. whereas, the parallel offset behind the compliant inclusion is the smaller the greater the distance of the inclusion from the starter notch. superposing the crack paths, so that the entry points and the exit points coincide, shows that the crack paths through the inclusions and the transition angles according to fig. 11 are independent of the distance of the inclusion from the initial crack but dependent on the stiffness mismatch. this is represented exemplarily in fig. 14 for crack paths through the compliant inclusions. the dependence of the transition angles on the stiffness mismatch represents fig. 15. here the transition angles for an inclusion with constant distance d = 14.7mm from the starter notch and constant orientation angle α = 45° and varying young´s modulus are plotted over the stiffness mismatch. the stiffness mismatch ē is defined as follows: di di ee ee e    (3) whereat ei is young´s modulus of the inclusion and ed is the default young´s modulus. if ei and ed are equal the stiffness mismatch is zero. therefore, the crack does not deflect and the transition angles are equal to the orientation angle. if ei is less than ed the stiffness mismatch ē is negative but at least -1. if ei is greater than ed the stiffness mismatch ē is positive but not more than +1. the course of the entrance angle and the course of the exit angle over ē show a counter similar behaviour. if ē is less than a critical negative value, the entrance angle reaches a constant value and t g. kullmer et alii, frattura ed integrità strutturale, 35 (2016) 368-378; doi: 10.3221/igf-esis.35.42 377 the exit angle is zero. this means that a crack enters a sufficiently compliant inclusion but does not leave it. if ē is greater than a critical positive value, the exit angle reaches a constant value and the entrance angle is zero. this means that a crack does not enter a sufficiently stiff inclusion. obviously, both critical values of ē have the same absolute value and only if ē is within this range, the crack is able to cross the inclusion. figure 14: comparison of the crack paths through the compliant inclusions with constant orientation angle α = 45° and varying distance from the initial crack. figure 15: transition angles of cracks through inclusions with varying stiffness mismatch (α = 45°, d = 14.7mm) conclusions he results of the presented investigations on the influence of changes in stiffness on the paths of fatigue cracks show, that changes in stiffness cause curved crack paths when they generate an asymmetric stiffness distribution in the neighbourhood of the crack. the deflection of the crack paths and therefore the transition angles at changes in stiffness depend on the stiffness mismatch and the orientation angle between the initial crack and the change in stiffness but they are independent on the distance between the initial crack and the change in stiffness. only if the magnitude of the stiffness mismatch is less than a critical value the crack is able to cross the change in stiffness. where the crack crosses the boundary of a change in stiffness the energy release is continuous and the crack path has an inflexion point. references [1] richard, h. a., sander, m., ermüdungsrisse, vieweg+teubner verlag, wiesbaden, (2009). [2] fulland m., risssimulationen in dreidimensionalen strukturen mit automatischer adaptiver finite-elementenetzgenerierung, fortschritt-bericht vdi, reihe 18: mechanik/bruchmechanik nr. 280, vdi-verlag, düsseldorf, (2003). t g. kullmer et alii, frattura ed integrità strutturale, 35 (2016) 368-378; doi: 10.3221/igf-esis.35.42 378 [3] rybicki, e. f., kanninen, m. f., a finite element calculation of stress intensity factors by a modified crack closure integral, engineering fracture mechanics, 9 (1977) 931-938. [4] erdogan, f., sih, g.c., on the crack extension in plates under plane loading and transverse shear, journal of basic engineering, 85 (1963) 519-525. [5] kullmer, g., schramm, b., richard, h.a., einfluss linienförmiger fremdeinschlüsse mit variabler orientierung und unterschiedlichen elastizitätsmodulen auf den verlauf von ermüdungsrissen. in: dvm-bericht 246, bruchmechanische werkstoffund bauteilbewertung: beanspruchungsanalyse, prüfmethoden und anwendungen, deutscher verband für materialforschung und -prüfung e.v., berlin, (2014) 73-82. [6] kullmer, g., schramm, b., richard, h.a., about the influence of line-shaped inclusions on the path of fatigue cracks, procedia materials science, 3 (2014) 110-115. << /ascii85encodepages false /allowtransparency false /autopositionepsfiles true /autorotatepages /none /binding /left /calgrayprofile (dot gain 20%) /calrgbprofile (srgb iec61966-2.1) /calcmykprofile (u.s. web coated \050swop\051 v2) /srgbprofile (srgb iec61966-2.1) /cannotembedfontpolicy /error /compatibilitylevel 1.4 /compressobjects /tags /compresspages true /convertimagestoindexed true /passthroughjpegimages true /createjobticket false /defaultrenderingintent /default /detectblends true /detectcurves 0.0000 /colorconversionstrategy /cmyk /dothumbnails false /embedallfonts true /embedopentype false /parseiccprofilesincomments true /embedjoboptions true /dscreportinglevel 0 /emitdscwarnings false /endpage -1 /imagememory 1048576 /lockdistillerparams false /maxsubsetpct 100 /optimize true /opm 1 /parsedsccomments true 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can be opened with acrobat and adobe reader 5.0 and later.) >> /namespace [ (adobe) (common) (1.0) ] /othernamespaces [ << /asreaderspreads false /cropimagestoframes true /errorcontrol /warnandcontinue /flattenerignorespreadoverrides false /includeguidesgrids false /includenonprinting false /includeslug false /namespace [ (adobe) (indesign) (4.0) ] /omitplacedbitmaps false /omitplacedeps false /omitplacedpdf false /simulateoverprint /legacy >> << /addbleedmarks false /addcolorbars false /addcropmarks false /addpageinfo false /addregmarks false /convertcolors /converttocmyk /destinationprofilename () /destinationprofileselector /documentcmyk /downsample16bitimages true /flattenerpreset << /presetselector /mediumresolution >> /formelements false /generatestructure false /includebookmarks false /includehyperlinks false /includeinteractive false /includelayers false /includeprofiles false /multimediahandling /useobjectsettings /namespace [ (adobe) (creativesuite) (2.0) ] /pdfxoutputintentprofileselector /documentcmyk /preserveediting true /untaggedcmykhandling /leaveuntagged /untaggedrgbhandling /usedocumentprofile /usedocumentbleed false >> ] >> setdistillerparams << /hwresolution [2400 2400] /pagesize [612.000 792.000] >> setpagedevice microsoft word numero 1 art 3.doc v. tvergaard, frattura ed integrità strutturale, 1 (2007) 25-28 25 1 introduction many procedures for the analysis of crack propagation are based on using critical values of parameters characterising the crack-tip stress and strain fields, such as the stress intensity factor, the j-integral, the crack-tip opening displacement, or the crack-tip opening angle. alternatively, the prediction of crack growth may be directly based on the fracture mechanism operating on the microscale, either by incorporating the failure mechanism in the constitutive equations for the material, or by representing the failure mechanism through a cohesive zone model of the fracture process zone. the present paper will give a survey of a number of investigations where the prediction of crack growth has been based on models of the actual fracture mechanism. one of the most well known material models that accounts for the micromechanics of damage is the modified gurson model [1,2], which models the evolution of ductile fracture by the nucleation and growth of voids to coalescence. some of the analyses using this model to predict ductile crack growth will be discussed. also for creep failure in metals at high temperatures material models [3] have incorporated the micromechanisms of diffusive cavity growth in grain boundaries, leading to open micro-cracks at grain boundary facets at a rate strongly affected by grain boundary sliding. results on creep crack growth based on this failure model will be mentioned. the term continuum damage mechanics is used for constitutive relations, which are able to represent the effect of damage evolution on the macro level, by developing appropriate expressions in which free material parameters can be fitted to experiments, as in the case of low cycle fatigue [4]. as an example, predictions of micro-crack formation in a metal matrix composite, based on this material model, will be presented here. cohesive zone models have been used in recent years in a number of analyses of crack growth resistance in elasticplastic solids [5]. some of the predictions obtained in these studies will be briefly mentioned here. 2 material models with damage evolution when the failure mechanism is incorporated in in the constitutive relations, the crack growth follows directly from the predicted loss of stress carrying capacity in one or more integration points in an element. then it is natural to kill the failed elements, by using the element vanish technique [6]. this procedure has been used for the predictions of crack growth to be discussed in the following three subsections. crack growth by ductile failure much interest has been devoted to the development of elastic-plastic or viscoplastic constitutive equations that account for the effect of ductile damage development. the most well known model is that suggested by gurson [1], which makes use of an approximate yield condition ( , , ) 0ij fmσ σφ = for a material containing a volume fraction f of voids, where ijσ is the average macroscopic cauchy stress tensor and mσ is an equivalent tensile flow stress representing the actual microscopic stress-state in the matrix material. with some modifications to improve predictions of plastic flow localization numerical modelling in non linear fracture mechanics ( da esis newsletter 2005) viggo tvergaard dept. of mechanical engineering, solid mechanics, technical university of denmark, nils koppels allé, building 404, dk-2800 kgs. lyngby, denmark abstract: some numerical studies of crack propagation are based on using constitutive models that account for damage evolution in the material. when a critical damage value has been reached in a material point, it is natural to assume that this point has no more carrying capacity, as is done numerically in the element vanish technique. in the present review this procedure is illustrated for micromechanically based material models, such as a ductile failure model that accounts for the nucleation and growth of voids to coalescence, and a model for intergranular creep failure with diffusive growth of grain boundary cavities leading to micro-crack formation. the procedure is also illustrated for low cycle fatigue, based on continuum damage mechanics. in addition, the possibility of crack growth predictions for elastic-plastic solids using cohesive zone models to represent the fracture process is discussed. keywords: damage evolution, crack growth, coesive zone v. tvergaard., frattura ed integrità strutturale, 1 (2007) 25-28 26 ( ) ( ) ( ) ( ) i local 1 ˆˆ ˆyi i i i v f y f w y y dv w y = −∫& & [7] and of final failure by void coalescence [8] this yield condition is of the form ( ) 2 2* *2 1 12 2 cosh 1 02 k e k m m q q f q f σ σ σ σ ⎛ ⎞ ⎡ ⎤φ = + − + =⎜ ⎟ ⎢ ⎥⎣ ⎦⎝ ⎠ (1) where ( )½3 / 2ije ijs sσ = is the macroscopic effective mises stress, and / 3ij ij ij kks gσ σ= − is the stress deviator. this material model accounts for the growth of the void volume fraction f due to plastic flow of the material around voids and due to the nucleation of new voids, and final failure is directly predicted when f reaches the critical value, at which the yield surface has shrunk to a point. this material model has been applied in a number of numerical studies of crack growth, including some studies where two populations of void nucleating particles are modelled; large weak particles that nucleate voids at relatively small strains and small strong particles that nucleate voids at much larger strains. for an edge cracked specimen under dynamic loading [9] results of a plane strain analysis are shown in fig. 1, where contours of constant void volume fraction define the predicted crack growth path in a case of a random distribution of the larger inclusions ahead of the initial crack-tip. also a full three dimensional analysis has been used to analyse this type of specimen [10]. here the computer requirements were much larger, but the advantage is that more realistic spherical shapes of the larger inclusions can be accounted for, and that 3d modes of growth are accounted for, such as tunnelling and shear lip formation. continuations of the 3d fracture study have been carried out recently in analyses that do not directly focus on crack growth, e.g. the failure of a metal matrix composite [11] or of a charpy v-notch specimen cut through a weld [12]. some attempts to include a damage dependent material length scale in this constitutive model have been carried out by leblond et al. [13] and tvergaard and needleman [14], using an integral condition on the rate of increase of the void volume fraction. the expressions used in [14] are (2) (3) where 0l > is the material characteristic length, i j ijz g y y= , and 8p = , 2q = . the usual local formulation corresponds to the limit 0l → , and it has been shown, as for other non-local continuum models, that the mesh dependence of numerical solutions in a softening regime are removed by taking 0l > . this nonlocal damage model has been applied by needleman and tvergaard [15] to predict ductile crack growth in the edge cracked specimen under dynamic loading also analysed in [9,10]. figure 1: crack growth indicated by contours of constant void volume fraction, f , for random distribution of larger particles. (a) 1.5 ,t sμ= 0.09 mmaδ = ; (b) 1.6 ,t sμ= 0.27 mmaδ = . (from [9]). creep crack growth high temperature failure leading to crack growth has been modelled in terms of continuum damage mechanics (hayhurst et al. [16]), where damage parameters are fitted to material behaviour on the macro level. the micromechanisms of creep failure in polycrystalline metals involve the nucleation and growth of small voids to coalescence; but here diffusion plays an important role, and the cavities occur primarily on grain boundary facets perpendicular to the maximum principal tensile stress (e.g. ashby and dyson [17]), where a creep constraint on the rate of cavitation is often a dominant mechanism. cavity coalescence on a grain boundary facet leads to a microcrack, and final intergranular failure occurs as such micro-cracks link up. grain boundary sliding is an important mechanism that further complicates the analysis of creep failure. a micromechanically based constitutive model for creep failure in a polycrystalline metal has been proposed (tvergaard [3,18]), in which the macroscopic creep strain rate is given by the expression ( ) ( )0 0 3 1 * 2 n nijc c e ij e e s c f σ η ε ε σ σ ⎛ ⎞ ⎡ = + +⎜ ⎟ ⎢ ⎝ ⎠ ⎣ && 2* * * *3 1 2 2 1 1 ij n n ij e e e s s sn m n n σ σ ρ σ σ σ ⎤⎧ ⎫⎛ ⎞− −−⎪ ⎪⎥+⎨ ⎬⎜ ⎟ + + ⎥⎝ ⎠⎪ ⎪⎩ ⎭⎦ (4) here, n is the creep power, 0c > represents substructure induced acceleration of creep, and expressions for other parameters are determined by axisymmetric cell ( ) ( ) ( ) ( )1 ˆˆ, 1 / q i i i i p v w y w y w y y dv z l ⎡ ⎤ = = −⎢ ⎥ +⎢ ⎥⎣ ⎦ ∫ v. tvergaard., frattura ed integrità strutturale, 1 (2007) 25-28 27 model studies for a grain with a cavitating facet and sliding boundaries [3]. if there is no sliding, *f is unity, *ρ is the density of cavitating facets *ijm is a direction tensor for cavitating facets, and * ns σ− is the difference between the maximum principal stress and the normal stress on a cavitating facet. the material model has been used to predict crack growth [18], by applying the element vanish technique when cavity coalescence was predicted on a grain boundary. for a double edge cracked panel under tension fig. 2 shows the predicted damage near the crack-tip at two stages of time, where the damage parameter a/b is the cavity radius divided by the cavity half spacing on a facet, and vanished triangular elements are painted black. figure 2: distributions of creep damage ahead of a crack-tip. continuous cavity nucleation, no grain boundary sliding, and 40c = . (a) 0/ 0.064ft t = . (b) 0/ 0.686ft t = . (from [18]). plane strain multi-grain cell models for a polycrystalline aggregate have been used by van der giessen and tvergaard [19] to study the final creep fracture process, as microcracks formed at grain boundary facets link up. such analyses are however limited by the unrealistic grain geometry and the reduced constraint on sliding. but a great advantage is that large grain arrays can be analysed if a crude mesh is used within each grain, and this allows for direct modelling of intergranular crack growth in a plane strain multi-grain aggregate (onck and van der giessen [20]). fatigue cracking among the many applications of continuum damage mechanics [4], studies of failure by low cycle fatigue are an important example, where a material model directly based on the micro mechanics of failure has not been developed. as the development of fatigue fracture depends strongly on the plastic strain range in each cycle, an accurate cyclic plasticity model is needed (e.g. ohno and wang [21]), with damage mechanics incorporated. the scalar damage parameter d is taken to be zero initially, but when the accumulated plastic strain p reaches a threshold value dp , it is assumed that damage starts to develop according to the evolution law 1 , if ( ) , 0 , if d d p py d p p p ps α α ≥⎧ = = ⎨ <⎩ & & (5) here, s is a material parameter describing the energy strength of damage, the strain energy release rate is given by ( )( )22 / 2 1e vy r e dσ= − , and the expression for vr depends on the mean stress / 3 ,kkσ so that fatigue develops more rapidly under tensile stresses. when the damage parameter reaches a critical value cd , this is taken to represent such a high density of microcracks that coalescence into a macrocrack occurs. in a finite element analysis this failure event is represented in terms of the element vanish technique, such that the model can be used to predict the growth of a macroscopic crack. this type of numerical study has been carried out in [22] for a metal matrix composite, where the fatigue crack growth occurs in the metal matrix around short brittle fibres. 3 modelling by coesive zone as an alternative to the continuum models discussed above, a number of crack growth analyses describe the fracture process separately in terms of a traction separation law for the crack surface, while the inelastic deformations around the crack are accounted for by standard plasticity without damage. this gives an attractive possibility for separating effects of fracture process parameters from effects of the material parameters determining inelastic deformations, e.g. in relation to determining crack growth resistance curves. thus, analyses of this type determine directly the ratio between the remote fracture toughness and the local fracture toughness determined by the assumed cohesive model. in [5] a rather general case of crack growth along the interface between an elastic-plastic solid and a rigid solid was studied. here, a cohesive zone model was needed that accounts for both normal and tangential separation, or mixtures of these, not only in order to study effects of remote mixed mode loading, but also because of the oscillating elastic singularity resulting from the elastic mismatch across the interface, which gives varying mixtures of normal stress and shear stress along the interface. this work has been continued in a number of different studies of interface debonding, for different types of material systems. thus, in [23] resistance curves have been determined numerically for crack growth along an interface joining two elastic-plastic solids, or an elastic-plastic solid to an elastic substrate. the steady-state value ss k of the remote fracture toughness is found when the resistance curves reach their maximum, which depends on the local mode mixity 0ψ near the crack-tip. as an example fig. 3 shows such steady-state values for a case with an elastic substrate, where the elastic modulus 2e in the substrate is twice that in the elastic-plastic solid. the angular measure 0ψ is near o0 for mode i loading and would be near o90 or o90− for mode ii loading. the steady-state toughnesses are normalised by the value 0k corresponding to a purely elastic solid, for the separation v. tvergaard., frattura ed integrità strutturale, 1 (2007) 25-28 28 energy assumed in the traction separation law. the different curves correspond to different values of the peak stress σ̂ for the traction separation law, normalised by the initial yield stress. the curves show two typical features of such results, that the fracture toughness level is very sensitive to small increases of the peak stress, and that the curves have minima for near mode i conditions at the crack-tip. figure 3: steady-state interface toughness as a function of the local mixity measure 0ψ , for 1 1/ 0.003y eσ = and 2yσ ∞ , considering different values of 1/ ,yσ σ 2 1/ 2e e = . (from [23]). 4 references [1] a.l. gurson, engng. mater. technol., 99 (1977) 2. [2] v. tvergaard, advances in applied mechanics, academic press, inc., 27 (1990) 83. [3] v. tvergaard, acta metallurgica, 32 (1984) 1977. [4] j. lemaitre, a course on damage mechanics. springer-verlag, (1992). [5] v. tvergaard, j.w. hutchinson, j. mech. phys. solids, 41 (1993) 1119. [6] v. tvergaard, j. mech. phys. solids, 30 (1982) 399. [7] v. tvergaard, int. j. fracture, 17 (1981) 389. [8] v.tvergaard, a.needleman, acta metall., 32 (1984) 157. [9] v. tvergaard, a. needleman, j. mech. phys. solids, 40 (1992) 447. [10] k.k. mathur, a. needleman, v. tvergaard, j. mech. phys. solids, 44 (1996) 439. [11] v. tvergaard, modelling simul. mater. sci. eng., 9 (2001) 143. [12] v. tvergaard, a.needleman, 3d charpy specimen analyses for welds, to appear in proc. charpy centenery conf. (2001). [13] j.b. leblond, g. perrin, j. devaux, j. appl. mech. 61 (1994) 236. [14] v. tvergaard, a. needleman, int. j. solids structures 32 (1995) 1063. [15] a. needleman, v.tvergaard, eur. j. mech., a/solids, 17 (1998) 421. [16] d.r. hayhurst, p.r.brown, c.j. morrison, philosophical transactions, royal society london a311 (1984) 131. [17] m.f. ashby, b.f. dyson, national physical laboratory, report dma(a), (1984) 77. [18] v. tvergaard, int. j. fracture, 42 (1990) 145. [19] e. van der giessen, v. tvergaard, acta metall. mater., 42 (1994) 959. [20] p.r. onck, e. van der giessen, mech. mater, 26 (1997) 109. [21] n. ohno, j.-d. wang, int. j. of plasticity, 9 (1993) 375. [22] v. tvergaard, t.ø. pedersen, arch. mech., 52 (2000) 799. [23] v. tvergaard, j. mech. phys. solids, 49 (2001) 2689. microsoft word numero_37_art_29 m. kurek et alii, frattura ed integrità strutturale, 37 (2016) 221-227; doi: 10.3221/igf-esis.37.29 221 focussed on multiaxial fatigue and fracture estimation of fatigue strength under multiaxial cyclic loading by varying the critical plane orientation marta kurek, tadeusz łagoda department of mechanics and machine design, opole university of technology opole, poland andrea carpinteri, sabrina vantadori department of civil-environmental engineering and architecture, university of parma parma, italy abstract. the main purpose of this paper is to examine the influence of the critical plane orientation on the estimated fatigue strength of metals under multiaxial loading. the algorithm employed to evaluate fatigue strength implements the criterion of maximum normal and shear stress on a suitable damage plane (critical plane). the angle  defining the critical plane orientation is measured with respect to the direction that maximises the applied normal stress. eleven (11) structural materials under combined bending and torsion cyclic loading are examined. for each analysed material, the value of  angle is selected so that the value of the scatter, defined by a root-mean-square value, is minimum. on the basis of such a calculation, an empirical expression for  is proposed, that takes into account the values of bending and torsion fatigue strengths at a reference number of loading cycles. according to such an expression,  is constant for a given material. keywords. critical plane; fatigue strength; multiaxial loading. introduction tructural components of machines and devices are subjected to service loads which often include multiaxial load conditions. the complex nature of the fatigue processes has produced several fatigue criteria which, implemented in algorithms, constitute a basic tool for estimating fatigue strength/life. these criteria generally reduce the spatial stress state to an equivalent uniaxial one. among all multiaxial fatigue criteria, it is possible to distinguish a group based on the critical plane concept, which assumes that material fatigue failure is caused by stresses (strains) related to the critical plane. in 1935, stanfield suggested the use of the critical plane to describe multiaxial fatigue [1]. currently, such a concept gains an increasing interest. the paper presents both a model for estimating fatigue life and the analysis of the influence of the critical plane orientation on such an estimation. particular attention is paid to the proposal of a new function to determine the critical plane orientation, based on both the analysis of scatters and the ratio between the fatigue strength for bending and that for torsion, at the given number of loading cycles. the calculation employs the criterion of maximum normal and shear stresses acting on the critical plane [2]. s m. kurek et alii, frattura ed integrità strutturale, 37 (2016) 221-227; doi: 10.3221/igf-esis.37.29 222 fatigue strength evaluation enerally, the estimation of fatigue strength consists of several stages. the first step includes measurement, generation or calculation of the stress tensor components according to the following equations, in the case of biaxial fatigue (for example, cyclic bending and torsion): )(sin)( tt axx   (1) )(sin)(   tt axy (2) where )(txx refers to stress induced by bending, and )(txy refers to torsion-induced stress. further: a amplitude of normal stress induced by bending; a amplitude of shear stress induced by torsion;  pulsation;  phase shift; t time. then, the following step involves the computation of the critical plane orientation, which can be performed by using one of three established methods: weight functions, damage accumulation, variance. one damage accumulation method to determine the critical plane is that proposed by carpinteri et al. [3], according to which the normal to the critical plane is defined by the angle  :                 45 1 1 2 3 2 2b  (3) measured with respect to the direction of the maximum normal stress, and being: af af b   2 (4) where af and af are the fatigue limits for fully-reversed bending and torsion, respectively. as far as the multiaxial fatigue criteria based on the critical plane concept are concerned, macha [2] formulated the criterion of maximum normal and shear stress in fracture plane for random loading, which can be generalised for different loading conditions. the general form can be written as follows: )()()( tktbt seq    (5) where kb , are constants used for a specific criterion form [4], )(t is the normal stress and )(ts is the shear stress, both acting on the critical plane:  2sin)(cos)()( 2 ttt xyxx  (6)  2cos)(2sin)( 2 1 )( ttt xyxxs  (7) where g m. kurek et alii, frattura ed integrità strutturale, 37 (2016) 221-227; doi: 10.3221/igf-esis.37.29 223    (8) being  the angle defined by the direction of the maximum normal stress if the above damage accumulation method [3] is applied. an alternative method is that to determine the direction for which the normal stress variance reaches its maximum [5,6]:    dtt t t  0 0 2 0 1   (9) where 0t is the observation time interval. the criterion proposed by macha (see eq. (5)) is here employed on the critical plane, where the determination of the critical plane orientation is performed according to the above damage accumulation method. the weighted factors b and k can be determined by equating eq.(1) to af and eq.(2) to af : )290cos( cos2 )290sin(2sin cos )290sin( 2 22           b b (10)   2cos2 2sin2 b k   (11) by substituting eq. (10) in eq. (11), we get: af af k    2 (12) according to eq. (12), we can notice that the parameter k is a constant depending on the material fatigue properties. the final step is the calculation of the fatigue strength. for constant amplitude cyclic loading, the fatigue strength is evaluated by using basquin’s fatigue characteristics ( a and m ) in compliance with the relevant astm standard [7]. the formula for strength calculation under cyclic loading is expressed as follows: aeq ma ncal ,lg10   (13) where aeq , is the amplitude of the equivalent stress related to the critical plane (eq.(5)). materials examined atigue test results related to 11 selected construction materials are analysed. according to the astm recommendations [7], such results are also used to calculate the regression equation for fully-reversed bending (or uniaxial push-pull): af man  loglog  (14) and for fully-reversed torsion: f m. kurek et alii, frattura ed integrità strutturale, 37 (2016) 221-227; doi: 10.3221/igf-esis.37.29 224 af man  loglog  (15) being  mama , , , the coefficients of the regression equations for bending and torsion, respectively. the values of coefficients of the above regression equations for each analysed material are listed in tab. 1. eq. (3) proposed by carpinteri et al. involves only fatigue limits, and can be applied for 2b ranging from 1 to 3 . by analysing the values of coefficients m and m listed in tab. 1, all materials can be noted to be characterized by values of m different from those of m , which means that such materials have non-parallel mutual fatigue characteristics. therefore, a dependence of  angle on the ratio between bending strength and torsion strength in correspondence to a given number of loading cycles, fin , is proposed in next section. material bending torsion )(tmin fin )( )( 2 fia fia n n b    number of tests a m a m [°] [cycles] d30 [8] 30.50 10.75 25.40 9.20 8 2000000 1.496 6 ggg40 [9] 32.39 10.95 35.48 12.41 1 1000000 1.110 15 10hnap [10] 30.88* 9.50* 25.28 8.20 45 2000000 1.874 108 pa4 (6082) [11] 23.80 8.00 21.40 7.70 45 2000000 1.680 45 30crnimo8 [12] 27.54 8.05 69.56 24.62 0 100000 1.500 9 cuzn40pb2 [13] 19.99 5.86 45.30 17.17 16 1000000 0.920 55 gts45 [9] 53.00 19.40 35.50 12.80 20 250000 1.265 11 cast iron ic2 [8] 23.7 8.80 44.00 19.50 0 1000000 1.155 4 hard steel 982fa [8] 36.60 12.10 49.50 18.60 14 1000000 1.550 11 sm45c [14] 31.10 10.30 49.40 18.60 0 100000 1.402 5 sus304 [15] 19.8* 7.04* 22.5 8.7 5 2500 1.379 18 *push-pull table 1: coefficients of regression eqs. (14) and (15) and fatigue properties of the examined materials. the number of tests is also reported. fatigue strength scatter calculation n order to analyse how the fatigue life is influenced by the value of  angle, simulation studies are carried out by assuming  ranging between 0° and 45°, with an increment equal to 1 °. for each of the 46 angle values, the parameter b is computed according to eq. (10), whereas the parameter k is a constant according to eq. (11) and depends only on the fatigue material properties. fig. 1 shows the value of the parameter b against the  angle (fig. 1(a)) and that of the parameter k (fig. 1(b)) for 10hnap steel [10]. in order to perform a suitable analysis of the fatigue strength scatter, the logarithmic dependence of the ratio between the experimental and calculated fatigue strength should be examined. a new method to determine such a scatter has been proposed by walat et al. [16], who have defined the root mean square error: n n n e n i cal   1 exp2log (16) i m. kurek et alii, frattura ed integrità strutturale, 37 (2016) 221-227; doi: 10.3221/igf-esis.37.29 225 therefore, the scatter can be determined as follows: et 10 (17) fig. 2 shows the relationship between the scatter value t and the angle  , for two selected materials. 0 5 10 15 20 25 30 35 40 45 -60 -50 -40 -30 -20 -10 0 , 0 b 0 5 10 15 20 25 30 35 40 45 , o 0.1261k figure 1: dependence of the parameter b on (a) the angle  and (b) k value for 10hnap steel. 0 5 10 15 20 25 30 35 40 45 0 5 10 15 20 25 x: 45 y: 2.128  0 t 0 5 10 15 20 25 30 35 40 45 2 3 4 5 6 7 8 9 10  0 t figure 2: relationship between the scatter t and the angle  for: (a) 10 hnap steel [10]; (b) pa4 aluminum alloy [11]. scatters are computed only for experimental tests under combined bending and torsion. the angle  corresponding to the minimum scatter value is registered for each examined material and listed in table 1. the present authors propose a new expression for  : 4 )( )( 2 31 5.22arcctg                           fia fia n n    (18) where  is a function of the fatigue strength ratio 2b : )( )( 2 fia fia n n b    (19) (a) (b) (a) (b) m. kurek et alii, frattura ed integrità strutturale, 37 (2016) 221-227; doi: 10.3221/igf-esis.37.29 226 fin is the number of loading cycles computed from eq. (18) by inserting the value of  that minimises the scatter t . fin is considered as a material constant, and such a value is listed in table 1 for each analysed material. in fig. 3, the angle  corresponding to the minimum scatter value is plotted against 2b for each examined material. eq. (18) is also plotted in fig. 3 (see the dashed curve). note that such a relationship can be applied to a range of 2b larger than  3 ;1 . 0 5 10 15 20 25 30 35 40 45 0.5 1 1.5 2 β ° σa(nfi) / τa(nfi) cuzn40pb2 gts45 sus304 d30 hard steel pa4 10hnap 30crnimo8sm45c ggg40 cast iron figure 3:  against ' 2 b by employing eq. (18). the value of  in correspondence of the minimum value of the scatter is also plotted. conclusions he following conclusions can be drawn: 1. in the present paper, the influence of the critical plane orientation on the fatigue strength estimation is analysed. 2. an empirical expression of the angle  used to define the critical plane orientation is proposed, the idea starting from the observation of experimental fatigue test results under combined cyclic bending and torsion. 3. such an expression is a function of the ratio 2b between bending and torsion fatigue strengths at a reference number of loading cycles, and is a constant for a given material. 4. the dependence of  on the above strength ratio 2b (instead of the fatigue limit ratio) is here proposed for those materials characterised by m different from m . 5. this expression of  can be used for a 2b range larger than  3 ;1 . references [1] stanfield, g., discussion of the strength of metals under combined alternating stresses, in: h.gough, h.pollard (eds.), proc. inst. of mechanical engineers., 131 (1935) 93. t m. kurek et alii, frattura ed integrità strutturale, 37 (2016) 221-227; doi: 10.3221/igf-esis.37.29 227 [2] macha, e., generalization of fatigue fracture criteria for multiaxial sinusoidal loadings in the range of random loading, in: m. brown, k.j. miller (eds.), biaxial and multiaxial fatigue, mechanical engineering publications, london, (1989) 425–436. [3] carpinteri, a., spagnoli, a., vantadori, s., multiaxial assessment using a simplified critical plane-based criterion, int. j. fatigue, 33 (2011) 969-976. doi:10.1016/j.ijfatigue.2011.01.004 [4] łagoda, t., ogonowski, p., criteria of multiaxial random fatigue based on stress, strain and energy parameters of damage in the critical plane, mat.-wiss. u. werkstofftech, 36 (2005) 429-437. doi: 10.1002/mawe.200500898 [5] kluger, k., łagoda, t., fatigue life of metallic material estimated according to selected models and load conditions, j. theoret. appl. mech., 51 (2013) 581-592. [6] walat, k., kurek, m., ogonowski, p., łagoda, t., the multiaxial random fatigue criteria based on strain and energy damage parameters on the critical plane for low-cycle range, int. j. fatigue, 37 (2012) 100-111. doi: 10.1016/j.ijfatigue.2011.09.013 [7] astm e 739–91, standard practice for statistical analysis of linearized stress–life (s–n) and strain life fatigue data, in: annual book of astm standards, vol. 03.01, philadelphia (1999) 614–628. [8] nishihara, t., kawamoto, m., the strength of metals under combined alternating bending and twisting, memoirs of the college of engineering, kyoto imperial university, japan, (1941). [9] muller, a., zum festigkeitsverhalten von mehrachsig stochastisch beanspruchten gußeisen mit kugelgraphit und tempergu, fraunhofer – institut fur betriebsfestigkeit, darmstadt, (1994). [10] pawliczek, r., badanie wpływu parametrów obciążenia i geometrii karbu na trwałość przy zmiennym zginaniu i skręcaniu, rozprawa doktorska, politechnika opolska, opole (in polish) (2001). [11] niesłony, a., łagoda, t., walat, k., kurek, m., multiaxial fatigue behaviour of aa6068 and aa2017a aluminium alloys under in-phase bending with torsion loading condition, mat.-wiss. u. werkstofftech., 45 (2014) 947-952. [12] sanetra, c., untersuchungen zum fetigkeitsvwrhalten bei mehrachsiger randombeanspruchung unter biegung und torsion, dissertation, technische universitat clausthal, (1991). [13] kohut, m., łagoda, t., badania zmęczeniowe mosiądzu mo58 w warunkach proporcjonalnego cyklicznego zginania ze skręcaniem, in: seweryn, a. (ed.), iii sympozjum mechaniki zniszczenia materiałów i konstrukcji, dział wydawnictw i poligrafii politechniki białostockiej, poland (2004). [14] lee, s.b., a criterion for fully reversed out of phase torsion and bending, in: miller, k.j, brown, m.w. (eds), multiaxial fatigue, astm stp 853, philadelphia, usa, (1985) 553-568. [15] sakane, m., ohnami, m., sawada, m., fracture modes and low cycle biaxial fatigue life at elevated temperature, j. of engineering and technology 109 (1987) 236-243. doi:10.1115/1.3225970 [16] walat, k., łagoda, t., lifetime of semi ductile materials through the critical plane approach, int. j. fatigue, 67 (2014) 73-77. << /ascii85encodepages false /allowtransparency false /autopositionepsfiles true /autorotatepages /none /binding /left /calgrayprofile (dot gain 20%) /calrgbprofile (srgb iec61966-2.1) /calcmykprofile (u.s. web coated \050swop\051 v2) /srgbprofile (srgb iec61966-2.1) /cannotembedfontpolicy /error /compatibilitylevel 1.4 /compressobjects /tags /compresspages true /convertimagestoindexed true /passthroughjpegimages true /createjobticket false /defaultrenderingintent /default /detectblends true /detectcurves 0.0000 /colorconversionstrategy /cmyk /dothumbnails false /embedallfonts true /embedopentype false /parseiccprofilesincomments true /embedjoboptions true 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can be opened with acrobat and adobe reader 5.0 and later.) >> /namespace [ (adobe) (common) (1.0) ] /othernamespaces [ << /asreaderspreads false /cropimagestoframes true /errorcontrol /warnandcontinue /flattenerignorespreadoverrides false /includeguidesgrids false /includenonprinting false /includeslug false /namespace [ (adobe) (indesign) (4.0) ] /omitplacedbitmaps false /omitplacedeps false /omitplacedpdf false /simulateoverprint /legacy >> << /addbleedmarks false /addcolorbars false /addcropmarks false /addpageinfo false /addregmarks false /convertcolors /converttocmyk /destinationprofilename () /destinationprofileselector /documentcmyk /downsample16bitimages true /flattenerpreset << /presetselector /mediumresolution >> /formelements false /generatestructure false /includebookmarks false /includehyperlinks false /includeinteractive false /includelayers false /includeprofiles false /multimediahandling /useobjectsettings /namespace [ (adobe) (creativesuite) (2.0) ] /pdfxoutputintentprofileselector /documentcmyk /preserveediting true /untaggedcmykhandling /leaveuntagged /untaggedrgbhandling /usedocumentprofile /usedocumentbleed false >> ] >> setdistillerparams << /hwresolution [2400 2400] /pagesize [612.000 792.000] >> setpagedevice microsoft word numero_35_art_56 l. chunjiang et alii, frattura ed integrità strutturale, 35 (2016) 500-508; doi: 10.3221/igf-esis.35.56 500 influence of different sizes of concrete and roller compacted concrete on double-k fracture parameters liu chunjiang school of civil engineering, chang’an university, shanxi, xi’an, 710061, china liuchunjiang23@sina.com zhang huabo shandong rong cheng construction group co., ltd., shandong, rongcheng, 264300, china lv ninghua rongcheng jiu zhou project management ltd., shandong, rongcheng, 264300, china abstract. affected by physical properties of various components, characteristics and stress states of junction surface and other multiple factors, concrete, as a kind of multi-phase composite material, has complicated failure mechanism, thus making its fracture mechanism research difficult. but concrete has been widely used in engineering construction, so research on concrete fracture theory is of important realistic significance and construction value. this study discusses influence rule of specimen size and crack-depth ratio (α0/h) on doublek fracture parameters (initial fracture toughness iniick and unstable fracture toughness un ick ) and its size effects by using fracture test. different sizes of concretes and roller compacted concrete (rcc) specimens are adopted to explore influence of specimen size on concrete double-k fracture parameters. results reveal that initial fracture toughness iniick and unstable fracture toughness un ick increase as specimen size enlarges, showing a size effect; besides, subcritical crack extends with the increase of specimen size. with regard to specimens with different crack-depth ratios, its unstable fracture toughness unick is unrelated to initial crack-depth ratio when crack-depth ratio is more than or equal to 0.4, while initial fracture toughness iniick is correlated with initial crack-depth ratio, which indicate that double-k fracture parameters can be considered as material constants describing concrete initial fracture, stable expansion and whole process of stability failure. keywords. concrete; fracture; double-k fracture parameters; crack-depth ratio. introduction o date, fracture mechanics is applied in concrete structure from three aspects [1]: first is research on fracture mechanism of concrete; second is decision of endanger degree of some serious cracks in concrete structure, for example, stability analysis of crack in pier, upstream face crack in massive-head dam and pressure vessel crack of prestressed concrete (pc) in atomic power station; third is improvement of design method of concrete structure, for t chunjiang et alii, frattura ed integrità strutturale, 35 (2016) 500-508; doi: 10.3221/igf-esis.35.56 501 instance, decision of stability of various thorough cracks in concrete pouring blocks and calculation of cracking load of reinforced concrete (rc) in diagonal direction, etc. people are expected to improve design methods of gravity dam and arch dam using fracture mechanics [2]. two-parameter model considers actual crack in combination with micro-crack zone as an effective crack, then obtains results using theory of linear elastic fracture mechanics and combines it with numerical computation method. its essence lies in using valid crack tip opening displacement (ctod) to reach critical valid ctod, i.e., fracture criterion. xu shilang [3], a scholar from china, put forward a simple and applicable fracture criterion in 1999, namely, double-k fracture criterion. this criterion, belonging to the first type, not only corrects linear elastic fracture mechanics model based on a complete theory, but also decides its fracture parameters with the help of simple test methods, which is expected to be popularized and applied in practical engineering. two fracture parameters are introduced into this criterion, initial fracture toughness iniick and unstable fracture toughness un ick . test indicates that those two parameters without size effect under a certain size, as fracture parameters, can be well applied in the analysis of concrete structure crack extension, and have drawn much attention [4-7]. a relevant trial [8] reveals that maximum seam strain is 10 times of average value of ordinary bending ultimate strain, which is exactly a ratio of theoretical strength and breaking stress of a point of concrete material. this thesis aims to explore characteristics of double-k fracture parameters (initial fracture toughness iniick and unstable fracture toughness unick ) of concrete using data obtained from test. design of concrete fracture stiffness test with wedge splitting method material selection and mix proportion aterials include tap water for life, 32.5 ordinary portland cement, fly ash (level ii), natural medium sand with particle size of over 5mm, macadam with maximum particle size of 20 mm (level i), high efficiency slushing agent suitable for mass concrete, and mix proportion is shown in tab. 1. wedge splitting specimen [14, 15] is adopted in this test (fig. 1) and tab. 2 displays specimen parameters. all specimens are divided into two categories containing 12 kinds of working conditions, the quantity of specimen in each working condition is presented in tab. 2 and testing devices are in fig. 2. materials tap water cement fly ash sand stones additives rcc kg/m3 130 134 90 805 1280 0.75% common concrete kg/m3 203.7 407 0 535 1245 0 table 1: mix proportion of roller compacted concrete (rcc) and common concrete. rcc prefabricated crack construction structural adhesives marble figure 1: shape and size of specimen. m l. chunjiang et alii, frattura ed integrità strutturale, 35 (2016) 500-508; doi: 10.3221/igf-esis.35.56 502 categories serial number quantity size of specimen (1×h×t/mm) crackdepth ratio depth of cracks [mm] thickness of cracks [mm] rcc rcc1504 12 150×150×150 0.4 60 3 rcc1504 6 150×150×150 0.5 75 3 rcc1504 6 150×150×150 0.6 90 3 rcc1504 6 300×300×150 0.4 120 3 rcc1504 6 400×400×150 0.4 160 3 rcc1504 6 500×500×150 0.4 200 3 common concrete pc1504 9 150×150×150 0.4 60 3 pc1504 6 150×150×150 0.5 75 3 pc1504 6 150×150×150 0.6 90 3 pc1504 9 300×300×150 0.4 120 3 pc1504 9 400×400×150 0.4 160 3 pc1504 9 500×500×150 0.4 200 3 table 2: working conditions of specimen. testing devices testing devices are shown in fig. 2. clip-on extensometer wedge holder load sensor top board signal amplifier data acquisit ion system computer figure 2: acquisition of test data with wedge splitting method test results specimen over 150×150×150 mm3 is calculated with following formula, and specimen (150×l50×l50 mm3) uses regular computing method [9-11]. unilateral opening specimen is affected by axial tension, and stress intensity factor (sif) can be calculated with formula below:  1 /lk af a d  (1) where,  /hp d t   and           2 3 4 / 1.122 0.231 / 10.55 / 21.71 / 30.382 /f a d a d a d a d a d     chunjiang et alii, frattura ed integrità strutturale, 35 (2016) 500-508; doi: 10.3221/igf-esis.35.56 503 unilateral opening specimen is affected by bending moments only, and sif is:  2 2 6 /l m k a g a d td  (2) where, 1/ 2 1/ 2h vm p d p e  and           2 3 4 / 1.122 1.4 / 7.33 / 13.08 / 14 /g a d a d a d a d a d     overlapping formula (1) and (2), sif expression of crack tip in any load time with wedge splitting geometry is obtained: 1 2i l lk k k  (3) as some problems may exist in part of specimen making and maintenance, here, the quantity of several effective specimens with good surface, basically complete trial curve, small deviation and calculative in double-k fracture parameter is listed in tab. 3. arithmetic mean value of initial fracture of 4~6 specimens from each group is taken as trial results. when the difference between single value and average value is over 15% of the average value, this value is excluded, and mean value of the rest of values is considered as trial result. trial result is:   1 n ic icj j k k mpa m    (4) categories size [mm] p [kn] cmod [mm] e [gpa] ac [mm] ca [mm] k1 k2 ki pc 300 4.91 141.1 19.45 166.4 46.5 0.432 0.872 1.304 pc 300 5.08 170.3 16.04 165.4 45.3 0.438 0.881 1.319 pc 300 4.61 130.4 18.02 160.5 40.4 0.381 0.771 1.152 pc 300 5.03 133.3 15.77 161.4 41.3 0.416 0.840 1.256 pc 300 4.52 118.0 21.36 165.5 45.3 0.399 0.804 1.203 pc 300 5.03 138.3 17.58 158.4 38.5 0.400 0.810 1.210 pc 400 5.55 183.9 16.53 234.4 74.5 0.466 0.913 1.379 pc 400 5.76 222.1 15.45 240.3 80.2 0.509 0.991 1.500 pc 400 6.60 245.5 16.02 241.6 81.6 0.582 1.131 1.713 pc 400 6.49 252.4 16.89 240.7 80.8 0.569 1.104 1.673 pc 400 6.44 266.9 15.32 245.2 85.3 0.592 1.145 1.737 pc 500 8.16 180.2 16.33 275.4 75.5 0.510 0.997 1.507 pc 500 8.31 210.2 15.78 298.5 98.4 0.615 1.183 1.798 pc 500 7.68 252.4 15.58 300.4 100.7 0.534 1.124 1.658 pc 500 8.26 208.6 20.00 300.1 100.4 0.621 1.193 1.814 rcc 300 4.53 155.0 15.51 174.0 54.2 0.444 0.887 1.331 rcc 300 5.37 226.3 14.91 176.2 56.0 0.525 0.903 1.428 rcc 400 5.58 221.1 16.19 245.0 85.3 0.521 1.010 1.531 rcc 400 5.76 216.3 14.38 248.1 88.1 0.554 1.070 1.624 rcc 400 4.78 200.7 15.33 243.0 83.0 0.457 0.890 1.347 rcc 500 8.30 239.8 15.02 314.2 114.2 0.705 1.039 1.744 rcc 500 6.92 246.4 15.00 309.8 109.9 0.604 1.154 1.758 rcc 500 6.37 257.5 15.09 311.9 112.0 0.546 1.043 1.589 table 3: trial results of various working conditions. l. chunjiang et alii, frattura ed integrità strutturale, 35 (2016) 500-508; doi: 10.3221/igf-esis.35.56 504 influence of crack-depth ratio on concrete fracture stiffness edge splitting specimens (crack-depth ratio: 0.3:0.4:0.5:0. 6 and size: 150 mm × 150 mm × 150 mm) are selected for studying influence of a/h on double-k fracture parameter and crack mouth opening displacement (cmodc) and influence rule of crack-depth ratio in concrete fracture process and fracture strength. test design tap water, 32.5 ordinary portland cement, fly ash (level ii), natural medium sand with particle size of over 5mm, macadam with maximum particle size of 20 mm (level i) and high efficiency slushing agent suitable for mass concrete are used in the test and their mix proportions are shown in tab. 4. material tap water cement fly ash sand stones additives rcc [kg/m3] 130 134 90 805 1280 0.75% ordinary concrete [kg/m3] 203.5 407.5 0 535 1245 0 table 4: mix proportions of rcc and ordinary concrete. wedge splitting specimen is applied in the trial, containing two categories (12 kinds of working conditions), and quantity of specimen in each working condition is shown in tab. 5. categories serial number quantity size 1×h×t [mm3] crack-depth ratio depth of cracks [mm] thickness of cracks [mm] rcc rcc1504 6 150×150×150 0.4 60 3 rcc1505 4 150×150×150 0.5 75 3 rcc1506 4 150×150×150 0.6 90 3 ordinary concrete pc1504 6 150×150×150 0.4 60 3 pc1505 2 150×150×150 0.5 75 3 pc1506 3 150×150×150 0.6 90 3 table 5: working conditions of specimen. phenomenological analysis of wedge splitting test this test is carried out on a 200kn compression-testing machine and adopts formula to calculate valid crack growth quantity. from cracks in damaged trial (figs. 3, 4), effective subcritical growth quantity can be obviously found in figures, and direction of crack growth is not smooth, which is mainly caused by reasons of concrete itself, as well as various construction aggregates. cracks will bypass and keep on growing when encountering construction aggregates with large particle size. figure 3: damaged cracks of rcc specimen. figure 4: damaged cracks of concrete specimen (type 150). w chunjiang et alii, frattura ed integrità strutturale, 35 (2016) 500-508; doi: 10.3221/igf-esis.35.56 505 analysis of calculation results p-mod curve character parameters of wedge splitting specimen are figured out based on test results (tab. 6). serial number of specimen size (mm) crack-depth ratio pmax [kn] cmodc [mm] rcc-1 150 0.4 5.29 110 rcc-2 150 0.4 5.08 115 rcc-3 150 0.4 6.13 89 rcc-4 150 0.4 4.52 109 rcc-5 150 0.4 4.70 109 rcc-6 150 0.4 5.13 102 rcc-7 150 0.5 4.62 163 rcc-8 150 0.5 4.69 139 rcc-9 150 0.5 4.65 152 rcc-10 150 0.5 4.23 155 rcc-11 150 0.6 3.03 215 rcc-12 150 0.6 3.61 186 rcc-13 150 0.6 3.97 189 rcc-14 150 0.6 4.02 229 c-1 150 0.4 7.76 101 c-2 150 0.4 6.70 92 c-3 150 0.4 7.71 98 c-4 150 0.4 5.44 101 c-5 150 0.4 5.53 96 c-6 150 0.4 5.75 93 c-7 150 0.5 6.19 102 c-8 150 0.5 6.20 103 c-9 150 0.6 6.52 101 c-10 150 0.6 6.31 100 c-11 150 0.6 5.98 113 table 6: basic test results. l. chunjiang et alii, frattura ed integrità strutturale, 35 (2016) 500-508; doi: 10.3221/igf-esis.35.56 506 tab. 7 makes a list of unstable fracture toughness calculated by initial crack-depth ratio and maximum load pmax, serial number of specimen valid crack growth quantity [cm] unstable fracture toughness [mpam] initial fracture toughness [mpam] rcc-1 8.1 0.944 0.415 rcc-2 8.6 1.039 0.316 rcc-3 8.3 1.016 0.420 rcc-4 7.8 0.968 0.351 rcc-5 8.7 0.957 0.344 rcc-6 7.8 0.996 0.486 rcc-7 9.9 0.775 0.385 rcc-8 9.4 0.784 0.360 rcc-9 9.6 0.811 0.407 rcc-10 9.5 0.797 0.359 rcc-11 11.6 0.815 0.361 rcc-12 11.4 0.900 0.307 rcc-13 10.9 0.852 0.305 rcc-14 11.6 0.948 0.269 c-1 8.3 1.01 0.481 c-2 7.7 1.06 0.582 c-3 6.8 1.09 0.555 c-4 8.0 1.05 0.648 c-5 7.9 1.11 0.621 c-6 7.8 1.19 0.648 c-7 8.7 1.18 0.517 c-8 7.6 1.15 0.529 c-9 8.0 1.23 0.514 c-10 9.6 1.21 0.518 c-11 8.6 1.20 0.543 table 7 unstable fracture toughness under different working conditions it can be seen from above table that sick value gets smaller as initial crack-depth ratio increases, so s ick based on initial crack-depth ratio not only has size effect, but also changes with the changes of initial crack-depth ratio. that indicates that subcritical growth quantity of wedge splitting specimen changes with size, related to initial crack-depth ratio as well, which is different from three-point bending beam. thus, it is obvious that small specimen has to take stable growth of crack into consideration. flexibility coefficient applied in calculating valid subcritical crack growth length ( ca ) with double-k fracture criterion is diverse, thereby leading to different ca . after obtaining ca , fracture toughness s ick and cmodc can be figured out, so valid subcritical crack growth length ( ca ) is believed to be an important parameter [12-13]. in two-parameter model, chunjiang et alii, frattura ed integrità strutturale, 35 (2016) 500-508; doi: 10.3221/igf-esis.35.56 507 because unloading point in test is hard to be controlled in a specified point, valid subcritical crack growth length ( ca ) obtained by computer is biased compared with theoretical value. however, double-k fracture criterion is with no need for unloading process and controlling unloading point in test, simply works out valid subcritical crack growth length ( ca ) with pmax and its corresponding cmodc, and the test results are relatively close to theoretical value. ordinary concrete has the same change rule of unstable fracture toughness with rcc. crack-depth ratio has an effect on the fracture toughness of ordinary concrete and rcc, but there are also differences. the fracture toughness of ordinary concrete decreases as crack-depth ratio increases, and this principle is basically suitable for crr. discussion t is summarized from analysis of fracture test results of rcc and ordinary concrete wedge-splitting specimens that double-k fracture criterion may have some differences although it is simple, practical and without human distractions. concrete fracture toughness has size effect, that is to say, concrete fracture toughness increases as size of specimen increases; besides, crack-depth ratio affects concrete fracture toughness to some extent, but the influences are not all consistent. change rules of unstable fracture toughness of ordinary concrete and rcc are basically the same, and crack-depth ratio plays a role in fracture toughness of ordinary concrete and rcc, but not identical. the rule to ordinary concrete is that concrete fracture toughness is reduced with the increase of crack-depth ratio, and the rule to rcc partially conforms to ordinary concrete rule. in addition, crack-depth ratio of specimen also has a great influence on fracture toughness, and varies non-uniformly; when 0 / 0.4a h  , s ick increases as 0 /a h rises; it decreases as 0 /a h rises when 0 / 0.4a h  , and reaches maximum when 0 / 0.4a h  , i.e., unstable value. references [1] mingyong, c., the application of fractal theory in rock material damage, j. sci., 36 (2007) 64. [2] zuyi, c., lihong, c., discussions on the wedge stability analysis method specified in the gravity dam design code, j. journal of hydroelectric engineering, 2 (2002) 101-108. doi:10.3969/j.issn.1003-1243.2002.02.014. [3] zhimin, w., shilang, x., jinlai, w., double-k fracture parameters based on the fictitious crack model, in: the 1st international joint symposium between chuangnam national university and dalian university of technology, korea, 111 (1998) 29-34. doi:10.3321/j.issn:1000-8608.2000.03.027. [4] zhimin, w., shilang, x., xijing, l., influence of initial crack-depth ratio of specimen on silicon double-k fracture parameters, j. journal of hydraulic engineering, 4 (2000) 35-39. doi:10.3321/j.issn:0559-9350.2000.04.007. [5] zhimin, w., shilang, x., jinlai, w., research on concrete double-k fracture parameters and its size effect with threepoint bending beam, j. journal of hydroelectric engineering, 4 (2000) 16-23. doi:10.3969/j.issn.1003-1243.2000.04.002. [6] zhimin, w., shilang, x., shenggen, d., xijing, l., yining, d., jiayi, l., the double-k fracture parameter of concrete for non-standard three-point bending beam specimens, j. engineering science, 3 (2001) 76-81. [7] shaowei, h., zhengxiang, m., experimental study on double-k fracture characteristics of standard reinforced concrete three-point beam, j. journal of building structures, 34(3) (2013) 152-157. [8] shilang, x., hougui, z., hongbo, g., shouyang, z., an experimental study on double-k fracture parameters of concrete for dam construction with various grading aggregates, j. china civil engineering journal, 39(11) (2006) 5062. [9] xiufang, z., shilang, x., hongbo, g., superposition calculation of double-k fracture parameters of concrete using wedge splitting geometry and boundary effect, j. journal of dalian university of technology, 46(6) (2006) 867-874. [10] weilian, q., lijun, l., ming, l., calculation of the maximum stress intensity factor of 3-d fatigue crack in engineering structures, j. earthquake engineering and engineering vibration, 27(6) (2007) 58-63. [11] dongfeng, l., guoqiang, l., research on relationship between stress intensity factor and strain energy releasing rate of type ii crack, j. journal of water resources architectural engineering, 11(1) (2013) 184-186. [12] xiangqian, f., shaowei, h., jun, l., experimental research on double-k fracture toughness of non-standard threepoint bending concrete beam, j. journal of building structures, 33(10) (2012) 152-157. [13] shilang, x., jianmin, w., crack propagation in a concrete dam under water pressure and determination of the doublek fracture parameters, j. china civil engineering journal, 2 (2009) 119-125. i l. chunjiang et alii, frattura ed integrità strutturale, 35 (2016) 500-508; doi: 10.3221/igf-esis.35.56 508 [14] xiufang, z., shilang, x., hongbo, g., superposition calculation of double-k fracture parameters of concrete using wedge splitting geometry and boundary effect, j. journal of dalian university of technology, 46(6) (2006) 868-874. [15] aoshuang, t., xuezhi, w., effect of incision shapes of prefabricated crack on fracture energy of concrete wedge splitting specimens, j. concrete, 8 (2011) 67-69. doi:10.3969/j.issn.1002-3550.2011.08.022 << /ascii85encodepages false /allowtransparency false /autopositionepsfiles true /autorotatepages /none /binding /left /calgrayprofile (dot gain 20%) /calrgbprofile (srgb iec61966-2.1) /calcmykprofile (u.s. web coated \050swop\051 v2) /srgbprofile (srgb iec61966-2.1) /cannotembedfontpolicy /error /compatibilitylevel 1.4 /compressobjects /tags /compresspages true /convertimagestoindexed true /passthroughjpegimages true /createjobticket false /defaultrenderingintent /default /detectblends true /detectcurves 0.0000 /colorconversionstrategy /cmyk /dothumbnails false /embedallfonts true /embedopentype false /parseiccprofilesincomments true /embedjoboptions true /dscreportinglevel 0 /emitdscwarnings false /endpage -1 /imagememory 1048576 /lockdistillerparams false /maxsubsetpct 100 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/pdfxoutputintentprofileselector /documentcmyk /preserveediting true /untaggedcmykhandling /leaveuntagged /untaggedrgbhandling /usedocumentprofile /usedocumentbleed false >> ] >> setdistillerparams << /hwresolution [2400 2400] /pagesize [612.000 792.000] >> setpagedevice microsoft word numero_63_art_09_3836.docx o.a. staroverov et alii, frattura ed integrità strutturale, 63 (2023) 91-99; doi: 10.3221/igf-esis.63.09 91 description of fatigue sensitivity curves and transition to critical states of polymer composites by cumulative distribution functions o.a. staroverov, a.i. mugatarov, a.s. yankin, v.e. wildemann center of experimental mechanics, perm national research polytechnic university, russia cem_staroverov@mail.ru, https://orcid.org/0000-0001-6095-0962 cem_mugatarov@mail.ru, https://orcid.org/0000-0002-2229-8181 yas.cem@yandex.ru, https://orcid.org/0000-0002-0895-4912 wildemann@pstu.ru, https://orcid.org/0000-0002-6240-4022 abstract. in this paper, a novel model is presented to describe the composite mechanical properties degradation during cyclic loading. the model is based on cumulative distribution functions using. weibull probability distribution law and beta distribution are considered. the dependences of the fatigue sensitivity coefficient on the preliminary cyclic exposure are derived. the damage value function derivative using is proposed to define damage accumulation stages boundaries. model parameters are obtained using experimental data. determination coefficients are calculated. a high descriptive capability is noted. rationality and expediency of using cumulative distribution functions as the approximation of experimental data on mechanical characteristics reduction after preliminary cyclic exposure is concluded. keywords. composite, damage accumulation, mechanical properties degradation, cumulative distribution functions. citation: staroverov, o.a., mugatarov, a.i., yankin, a.s., wildemann, v.e., description of fatigue sensitivity curves and transition to critical states of polymer composites by cumulative distribution functions, frattura ed integrità strutturale, 63 (2023) 91-99. received: 06.09.2022 accepted: 15.10.2022 online first: 31.10.2022 published: 01.01.2023 copyright: © 2023 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. introduction redicting the remaining life of composite materials used in structures that can operate under cyclic loading represents a relevant scientific mission of deformable solid mechanics. a number of papers dedicates to experimental studies of mechanical characteristics of various classes of composites exposed to cyclic effects [1-5]. staging of damage accumulation processes is noted in many of them [6-9]. the initial stage, also called the initiation stage, suggests fast damage accumulation. multiple fatigue damages related to matrix cracking, damage to phase interfaces, and rupture of some fibers were found in [10-13]. the second stage, also called the stabilization stage, suggests slow damage accumulation. some authors suggest that it involves matrix cracking processes. the stabilization stage is followed by intensified accumulation of damages and transition to the third stage, or the final breakdown stage, which implies fiber destruction and macro-failure of the specimen. damage accumulation in the composites frequently leads to mechanical properties (young’s modulus, ultimate strength, etc.) reduction [14-18]. p https://youtu.be/4wwgmu2fmti o.a. staroverov et alii, frattura ed integrità strutturale, 63 (2023) 91-99; doi: 10.3221/igf-esis.63.09 92 a number of models which enable damage value calculations under fatigue loading exist. the most famous of them are the palmgren–miner model (linear summing of damages) [19-22] and the marco-starkie model (non-linear summing) [23-27]. however, neither of these models takes into account the aforementioned three stages, so formally they are not suitable to describe damage accumulation processes in composites. an approach where the damage parameter is related to the varying mechanical characteristic takes place in [5, 9, 28-29]. moreover, some papers [8, 30-32] model the degradation of composite mechanical characteristics by setting random values of strength and deformation parameters of the reinforcing component and matrix. the modeling results are good, but their disadvantage is the high number of required constants. this paper proposes a new model to describe the degradation of composite mechanical characteristics after preliminary cyclic loading. the model is based on experimental data approximation by probability distribution functions. material and methods wenty-six fiber-glass laminate specimens with the reinforcement pattern of [0/90]8 were used in the experimental studies. the test method is based on the existing standards of quasi-static and fatigue tension of polymer composite materials. nominal values of ultimate strength σu and elasticity modulus e were taken from quasi-static uniaxial tension tests (astm d3039). the maximum number of cycles to failure nmax was found for uniaxial cyclic tension at the maximum stress value σmax = 0.5·σu, the asymmetry coefficient r = 0.1, and the frequency ν = 20 hz (astm d3479). three specimens were tested for quasi-static and cyclic tension. the other 20 specimens were exposed to preliminary cyclic loading and then statically tested. preliminary cyclic exposure was implemented within 0.1 to 0.8 nominal fatigue life nmax. the test method is schematically shown in fig. 1. figure 1: the order of experimental tests procedure: 1 – quasi-static tension tests; 2 – fatigue tests; 3 – preliminary cyclic loading; 4 – quasi-static tension after preliminary cyclic loading. for each specimen, the fatigue sensitivity coefficients are found using the formula     0 0 ; ue b u e k k e (1) where e is young’s modulus; e0 is the mean young’s modulus for a non-damaged material; σu is the ultimate strength of the material; σu0 is the ultimate strength of a non-damaged material. the fatigue sensitivity coefficient takes values from 0 (completely failed material) to 1 (non-damaged material). fatigue sensitivity coefficients correspond to the following damages values   1 ; 1 -e e b bk k (2) the preliminary cyclic exposure is found using the formula  0 n n n (3) t o.a. staroverov et alii, frattura ed integrità strutturale, 63 (2023) 91-99; doi: 10.3221/igf-esis.63.09 93 where n is the number of preloading cycles; n0 is the fatigue life for this loading cycle. the test data set represents the dependency of the fatigue sensitivity coefficient kb (ke) on the preliminary cyclic exposure n. the results are processed using the model below. model description ypical points of the fatigue sensitivity curve in the coordinates of preliminary cyclic exposure vs. fatigue sensitivity coefficient (n – kb) are shown in fig. 2a. the following conversion can be made: the same points are built in the coordinates of damage value vs. preliminary cyclic exposure (ωb – n) as shown in fig. 2b. some features of this dependency can be noted. first, it is limited by zero and one. second, if the “healing” of the material is absent, this dependency is monotone-increasing. third, the characteristic segment of slow damage accumulation in the diagram middle can be noted. these features also have some probability distribution integral functions. in the case of non-damaged material before preliminary cyclic exposure, the n(ωb) function passes through the coordinate system center. therefore, consideration of the two-parameter weibull law of probability distribution [33] and beta distribution is convenient. as an example, the integral curve of the weibull distribution law is given in fig. 2c. a b c figure 2: residual properties dependence on preliminary cyclic exposure in the coordinates of “kb–n” (a) and “n–ωb” (b); the integral curve of the two-parameter weibull distribution law (c) two-parameter weibull distribution the dependency of the preliminary cyclic exposure on the damage can be described by the following equation:           1 b bn e (4) where λ>0 is the scale parameter; κ>0 is the form parameter. both these values are material properties characterizing its ability to keep strength and rigidity after some operating time. in a general case, these parameters can depend on the temperature, exposure amplitude, frequency, etc. the dependency of the residual strength coefficient on the preliminary cyclic exposure can be described as:      1 1 ln 1 -bk n n (5) the parameters λ and κ can be defined both numerically and using the method of least squares from the equation of a straight line approximating data in logarithmic coordinates (these approaches give close but slightly different results):         1 ln 1 ln ln ln 1 -bk n (6) 0 1 0 1 k b n 0 1 0 1 n ωb 0 1 0 1 f (x ) x t o.a. staroverov et alii, frattura ed integrità strutturale, 63 (2023) 91-99; doi: 10.3221/igf-esis.63.09 94 an example of this dependence is shown in fig. 3. figure 3: model parameters receiving example to divide the fatigue sensitivity curve into damage accumulation stages, the derivative of the damage value function can be considered:      1 -1 1 ' ln 1 1 b n n (7) the graph of this function is given in fig. 4a. the physical sense of this function is the damage accumulation rate. for a low number of cyclic exposures, the intensity of damage accumulation is high (stage i), this stage is followed by an area of slow damage accumulation (stage ii); when the number of cyclic exposures approaches the limit, the damage accumulation rate rapidly grows (stage iii). earlier, the authors in [9] proposed a definition of boundaries for these stages using the points ns1 and ns2, where ωb'=0.3. such division is conditional and may vary depending on the material (and its class). the values of ns1 and ns2 are defined by solving the transcendent eqn. (7). an example of a kb(n) curve with the highlighted stages is given in fig. 4b. the values of the fatigue sensitivity coefficient in exposures ns1 and ns2 are designated as kbs1 and kbs2, respectively. the characteristic of the material defining the average rate of fatigue sensitivity coefficient reduction in the area of slow damage accumulation ψ can be introduced as:   1 2 2 1 . bs bs s s k k n n (8) a b figure 4: damage accumulation rate curve (a) and fatigue sensitivity coefficient vs. preliminary cyclic exposure graph (b) with highlighted stages -2 -2,5 ln (1 -k b ) ln(-ln(1-n)) 0 0 0 1 ω b ' n i ii iii 0.3 ns1 ns2 0 1 0 1 k b n i ii iii ns1 ns2 kbs1 kbs2 o.a. staroverov et alii, frattura ed integrità strutturale, 63 (2023) 91-99; doi: 10.3221/igf-esis.63.09 95 the model has some disadvantages. first, when n→1, kb becomes less than 0. however, this will take place only for the number of cycles close to the limit, so this specific feature can be neglected. second, taking the logarithm is not suitable to describe data where the values of kb and n exceed 1. this problem can be solved by a numerical search of the parameters from eqn. (5), where taking the logarithm is not required. beta distribution the dependency of kb(n) can be described as follows                             1-1 -1-1 -1 0 0 , 1 ; , 1 ; , 1 , nn b n b k n b t t dt b t t dt b (9) where bn(α,β) is an incomplete beta-function; b(α,β) is a beta-function. the parameters α and β must exceed zero and are numerically searched. a derivative of the damage function:            -1-1 1 ' , b n n n b (10) in comparison with the previous one, this function has some advantages. first, for n=1, the value kb=1. second, all experimental points can be used to find the parameters α and β without the logarithm taking. no n, cycles n e, gpa ke σu, mpa kb 1 0 2.19 369 2 0 2.32 392 3 0 2.36 382 4 25000 0.1171 2.11 0.9214 351 0.9213 5 25000 0.1171 2.10 0.9170 332 0.8714 6 25000 0.1171 2.00 0.8734 343 0.9003 7 25000 0.1171 2.08 0.9083 327 0.8583 8 25000 0.1171 1.96 0.8559 327 0.8583 9 75000 0.3514 2.03 0.8865 287 0.7533 10 75000 0.3514 2.00 0.8734 317 0.8320 11 75000 0.3514 1.96 0.8559 307 0.8058 12 75000 0.3514 1.94 0.8472 318 0.8346 13 75000 0.3514 2.02 0.8821 310 0.8136 14 125000 0.5856 1.81 0.7904 296 0.7769 15 125000 0.5856 1.84 0.8035 300 0.7874 16 125000 0.5856 1.95 0.8515 310 0.8136 17 125000 0.5856 1.94 0.8472 306 0.8031 18 125000 0.5856 1.97 0.8603 299 0.7848 19 175000 0.8199 1.87 0.8166 274 0.7192 20 175000 0.8199 1.81 0.7904 269 0.7060 21 175000 0.8199 1.80 0.7860 264 0.6929 22 175000 0.8199 1.72 0.7511 269 0.7060 23 175000 0.8199 1.86 0.8122 250 0.6562 24 182321 0.00 0 25 228810 0.00 0 26 229212 0.00 0 table 1: experimental data. o.a. staroverov et alii, frattura ed integrità strutturale, 63 (2023) 91-99; doi: 10.3221/igf-esis.63.09 96 results and discussion he experimental data are given in tab. 1. the average young’s modulus of a non-damaged material e0=2.29 gpa, the average ultimate strength of a non-damaged material σu=381 mpa, and the average durability for this amplitude n0=213448 cycles. approximation function parameters were found for the following cases: weibull distribution, using data approximation in logarithmic coordinates (wl); weibull distribution, the numerical search of parameters (wn); beta distribution, the numerical search of parameters (bn). for all cases, the determination coefficient was found. tab. 2 and 3 contain the model parameters found for the full data set. because r2>0.7 for all cases, the model has a high descriptive capability. close determination coefficient values for all the cases can be noted. fig. 5 represents curves of fatigue sensitivity coefficient and damage accumulation rate for young’s modulus (a, c) and ultimate strength (b, d) decrease. the similarity of these curves can be noted. rationality and expediency of using probability distribution functions as the approximation of experimental data on mechanical characteristics reduction after preliminary cyclic exposure is concluded. a significant advantage of this approach is the small amount of required experimental data for parameter definition (4 tests required) and simplicity in modeling. method wl wn bn parameter 1 κ=3.67383 κ=3.54769 α=0.23774 parameter 2 λ=0.17364 λ=0.17651 β=0.04566 ns1 0.0854 0.0891 0.0756 ns2 0.9196 0.9125 0.8685 ns2-ns1 0.8343 0.8234 0.7929 ks1 0.9101 0.9096 0.9102 ks2 0.7767 0.7731 0.7797 ψ 0.1599 0.1657 0.1646 r2 0.7164 0.7196 0.7265 table 2: calculated model parameters (young’s modulus reduction) method wl wn bn parameter 1 κ=2.86946 κ=2.81928 α=0.31281 parameter 2 λ=0.23938 λ=0.24205 β=0.08719 ns1 0.1704 0.1767 0.1516 ns2 0.7933 0.7818 0.7439 ns2-ns1 0.6229 0.6051 0.5923 ks1 0.8666 0.8646 0.8704 ks2 0.7195 0.7190 0.7307 ψ 0.2362 0.2405 0.2359 r2 0.8456 0.8469 0.8536 table 3: calculated model parameters (ultimate strength reduction) t o.a. staroverov et alii, frattura ed integrità strutturale, 63 (2023) 91-99; doi: 10.3221/igf-esis.63.09 97 a b c d figure 5: fatigue sensitivity coeffitient curves for young’s modulus (a) and utimate strength (b) reduction with corresponding curves of damage accumulation rate (c, d) and highlighted stages conclusions  an ability to describe experimental data on deformation and strength properties reduction of composites after preliminary cyclic exposure using probability distribution functions is considered.  two probability distributions are considered: two-parameter weibull law and beta distribution. for the weibull distribution, a method to find parameters by approximation of experimental data in logarithmic coordinates is described.  using of damage value function derivative is proposed to find damage accumulation stages boundaries.  experimental data are processed for reduced mechanical characteristics of structural fiber-glass laminate. model parameters are obtained. fatigue sensitivity coefficient and damage accumulation rate curves are built. boundaries of damage accumulation stages are defined. determination coefficients are calculated. because r2 exceeds 0.7, the high descriptive capability of the model can be noted.  all parameter calculation methods showed close results. beta distribution usage is more perspective due to the function having a value from 0 to 1. each model requires only 4 experiment tests to define parameters (1 static test, 1 fatigue test, and 2 intermediate points on the curve). these models can be used in the modeling of the deformation and failure processes of various composite structures.  the future planned research will contain this method's usage for the description of other experimental data and loading conditions. moreover, experimental study of the fast reduction of properties stages seems expedient for the purpose of more competent description. 0.0 0.2 0.4 0.6 0.8 1.0 0.0 0.2 0.4 0.6 0.8 1.0 k e n data wl wn bn 0.0 0.2 0.4 0.6 0.8 1.0 0.0 0.2 0.4 0.6 0.8 1.0 k b n data wl wn bn 0.0 0.3 0.6 0.9 0.0 0.2 0.4 0.6 0.8 1.0 ω e ' n wl wn bn 0.0 0.3 0.6 0.9 0.0 0.2 0.4 0.6 0.8 1.0 ω b ' n wl wn bn o.a. staroverov et alii, frattura ed integrità strutturale, 63 (2023) 91-99; doi: 10.3221/igf-esis.63.09 98 acknowledgements he work was carried out in perm national research polytechnic university with financial support of grant of president of russian federation for government support of young russian scientists (no mk-1545.2022.4) and within the state assignment of the ministry of science and higher education of the russian federation (no. fsnm-2020-0027). references [1] almeida, r.s.m., besser, b., tushtev, k., li, y. and rezwan, k. (2022). fatigue behavior and damage analysis of pip c/sic composite, journal of the european ceramic society, 42(13), pp. 5391–5398. doi: 10.1016/j.jeurceramsoc.2022.06.053. [2] mortazavian, s. and fatemi, a. (2015). fatigue behavior and modeling of short fiber reinforced polymer composites: a literature review, int. j. fatigue, 70, pp. 297–321. doi: 10.1016/j.ijfatigue.2014.10.005 [3] vassilopoulos, a.p. ed., (2010). fatigue life prediction of composites and composite structures, woodhead publishing. [4] degrieck, j. and van paepegem, w. (2001). fatigue damage modeling of fibre-reinforced composite materials: review, appl. mech. rev., 54(4), pp. 279–300. doi: 10.1115/1.1381395. [5] philippidis, t.p. and passipoularidis, v.a. (2007). residual strength after fatigue in composites: theory vs. experiment, int. j. fatigue, 29(12), pp. 2104–2116. doi: 10.1016/j.ijfatigue.2007.01.019. [6] de vasconcellos, d.s., touchard. f. and laurence, c.-a. (2014). tension–tension fatigue behaviour of woven hemp fibre reinforced epoxy composite: a multi-instrumented damage analysis, int. j. fatigue, 59, pp. 159–169. doi: 10.1016/j.ijfatigue.2013.08.029. [7] van paepegem w. and degrieck j. (2002). a new coupled approach of residual stiffness and strength for fatigue of fibre-reinforced composites, int. j. fatigue, 24(7), pp. 747–762. doi: 10.1016/s0142-1123(01)00194-3 [8] schaff, j.r. and davidson, b.d. (1997). life prediction methodology for composite structures. part i constant amplitude and two-stress level fatigue, journal of composite materials, 31(2), pp. 128–157. doi: 10.1177/002199839703100202. [9] wil'deman, v.e., staroverov, o.a. and lobanov, d.s. (2018). diagram and parameters of fatigue sensitivity for evaluating the residual strength of layered gfrp composites after preliminary cyclic loadings, mechanics of composite materials, 54(3), pp. 313–320. doi: 10.1007/s11029-018-9741-9. [10] zhao, x., wang, x., wu, z. and zhu, z. (2016). fatigue behavior and failure mechanism of basalt frp composites under long-term cyclic loads, int. j. fatigue, 88, pp. 58–67. doi: 10.1016/j.ijfatigue.2016.03.004. [11] liang, s., gning, p.-b. and guillaumat, l. (2014). properties evolution of flax/epoxy composites under fatigue loading, int. j. fatigue, 63, pp. 36–45. doi: 10.1016/j.ijfatigue.2014.01.003. [12] brod, m., just, g., dean, a., jansen, e., koch, i., rolfes, r. and gude, m. (2019). numerical modelling and simulation of fatigue damage in carbon fibre reinforced plastics at different stress ratios, thin-walled structures, 139, pp. 219–231 doi: 10.1016/j.tws.2019.03.005. [13] brighenti, r., carpinteri, a. and scorza, d. (2015). effect of fibre arrangement on the multiaxial fatigue of fibrous composites: a micromechanical computational model, frattura ed integrità strutturale, 9(34), pp. 59–68. doi: 10.3221/igf-esis.34.05. [14] strizhius, v. (2016). fatigue failure criterion of laminated composites under a complex stress-strain state, mechanics of composite materials, 52(3), pp. 369-378. doi: 10.1007/s11029-016-9589-9. [15] shokrieh, m.m. and lessard, l.b. (2000). progressive fatigue damage modeling of composite materials, part ii: material characterization and model verification, journal of composite materials, 34(13), pp. 1081–1116. doi: 10.1177/002199830003401302. [16] epaarachchi, j.a. and clausen, p.d. (2003). an empirical model for fatigue behavior prediction of glass fibre-reinforced plastic composites for various stress ratios and test frequencies, composites part a: applied science and manufacturing, 34(4), pp. 313–326. doi: 10.1016/s1359-835x(03)00052-6. [17] post, n.l., case, s.w. and lesko, j.j. (2008). modeling the variable amplitude fatigue of composite materials: a review and evaluation of the state of the art for spectrum loading, int. j. fatigue, 30(12), pp. 2064–2086. doi: 10.1016/j.ijfatigue.2008.07.002. t o.a. staroverov et alii, frattura ed integrità strutturale, 63 (2023) 91-99; doi: 10.3221/igf-esis.63.09 99 [18] carrella-payan, d., magneville, b., hack, m., lequesne, c., naito, t., urushiyama, y., yamazaki, w., yokozeki, t. and van paepegem, w. (2016). implementation of fatigue model for unidirectional laminate based on finite element analysis: theory and practice, frattura ed integrità strutturale, 38, pp. 184-190. doi: 10.3221/igf-esis.38.25. [19] miner, m.a. (1945). cumulative damage in fatigue, j. appl. mech., 12, pp. 159–164. [20] fatemi, a. and yang, l. (1998). cumulative fatigue damage and life prediction theories: a survey of the state of the art for homogeneous materials, int. j. fatigue, 20(1), pp. 9-34. doi: 10.1016/s0142-1123(97)00081-9. [21] liu, y. and mahadevan, s. (2007). stochastic fatigue damage modeling under variable amplitude loading, int. j. fatigue, 29(6), pp. 1149–1161. doi: 10.1016/j.ijfatigue.2006.09.009. [22] santecchia, e., hamouda, a.m.s., musharavati, f., zalnezhad, e., cabibbo, m., el mehtedi, m. and spigarelli, s. (2016). a review on fatigue life prediction methods for metals, advances in materials science and engineering, 2016, no 9573524. doi: 10.1155/2016/9573524. [23] marco, s.m. and starkey, w.l. (1954). a concept of fatigue damage, trans. asme, 76(4), pp. 627–640. doi: 10.1115/1.4014922. [24] okutan, b. (2002). the effects of geometric parameters on the failure strength for pin-loaded multi-directional fiberglass reinforced epoxy laminate, composites part b: engineering, 33(8), pp. 567–578. doi: 10.1016/s1359-8368(02)00054-9. [25] aeran, a., siriwardane, s.c., mikkelsen, o. and langen, i. (2017). a new nonlinear fatigue damage model based only on s-n curve parameters. int. j. fatigue, 103, pp. 327–341. doi: 10.1016/j.ijfatigue.2017.06.017. [26] nouri, h., meraghni, f. and lory, p. (2009). fatigue damage model for injection-molded short glass fibre reinforced thermoplastics, int. j. fatigue, 31(5), pp. 934–942. doi: 10.1016/j.ijfatigue.2008.10.002. [27] zuo, f.-j., huang, h.-z., zhu, s.-p., lv, z. and gao, h. (2015). fatigue life prediction under variable amplitude loading using a non-linear damage accumulation model, international journal of damage mechanics, 24(5), pp. 767–784. doi: 10.1177/1056789514553042. [28] van paepegem, w., degrieck, j. and de baets, p. (2001). finite element approach for modelling fatigue damage in fibrereinforced composite materials, composites part b: engineering, 32(7), pp. 575–588. doi: 10.1016/s1359-8368(01)00038-5. [29] carraro, p.a and quaresimin, m. (2018). fatigue damage and stiffness evolution in composite laminates: a damagebased framework, procedia engineering, 213, pp. 17–24. doi: 10.1016/j.proeng.2018.02.003. [30] hwang, w. and han, k.s. (1986). cumulative damage models and multi-stress fatigue life prediction, journal of composite materials, 20(2), pp. 125–153. doi: 10.1177/002199838602000202. [31] kawai, m. and ishizuka, y. (2018). fatigue life of woven fabric carbon/epoxy laminates under alternating r-ratio loading along non-proportional path in the σm-σa plane, int. j. fatigue, 112, pp. 36–51. doi: 10.1016/j.ijfatigue.2018.02.036. [32] subramanian, s., reifsnider, k.l. and stinchcomb, w.w. (1995). a cumulative damage model to predict the fatigue life of composite laminates including the effect of a fibre-matrix interphase, int. j. fatigue, 17(5), pp. 343–351. doi: 10.1016/0142-1123(95)99735-s. [33] weibull, w. 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can be opened with acrobat and adobe reader 5.0 and later.) >> /namespace [ (adobe) (common) (1.0) ] /othernamespaces [ << /asreaderspreads false /cropimagestoframes true /errorcontrol /warnandcontinue /flattenerignorespreadoverrides false /includeguidesgrids false /includenonprinting false /includeslug false /namespace [ (adobe) (indesign) (4.0) ] /omitplacedbitmaps false /omitplacedeps false /omitplacedpdf false /simulateoverprint /legacy >> << /addbleedmarks false /addcolorbars false /addcropmarks false /addpageinfo false /addregmarks false /convertcolors /converttocmyk /destinationprofilename () /destinationprofileselector /documentcmyk /downsample16bitimages true /flattenerpreset << /presetselector /mediumresolution >> /formelements false /generatestructure false /includebookmarks false /includehyperlinks false /includeinteractive false /includelayers false /includeprofiles false /multimediahandling /useobjectsettings /namespace [ (adobe) (creativesuite) (2.0) ] /pdfxoutputintentprofileselector /documentcmyk /preserveediting true /untaggedcmykhandling /leaveuntagged /untaggedrgbhandling /usedocumentprofile /usedocumentbleed false >> ] >> setdistillerparams << /hwresolution [2400 2400] /pagesize [612.000 792.000] >> setpagedevice microsoft word numero_30_art_62 l. zhang et alii, frattura ed integrità strutturale, 30 (2014) 515-525; doi: 10.3221/igf-esis.30.62 515 energy dissipation mechanism and damage model of marble failure under two stress paths liming zhang college of science, qingdao technological university, qingdao, shandong 266033, china; dryad_274@163.com co-operative innovation center of engineering construction and safety in shandong peninsula blue economic zone, qingdao technological university ; qingdao, shandong 266033, china; dryad_274@163.com mingyuan ren, shaoqiong ma, zaiquan wang college of science, qingdao technological university, qingdao, shandong 266033, china; email: myfly90@163.com, msq_qq@163.com, zqw4521@163.com abstract. marble conventional triaxial loading and unloading failure testing research is carried out to analyze the elastic strain energy and dissipated strain energy evolutionary characteristics of the marble deformation process. the study results show that the change rates of dissipated strain energy are essentially the same in compaction and elastic stages, while the change rate of dissipated strain energy in the plastic segment shows a linear increase, so that the maximum sharp point of the change rate of dissipated strain energy is the failure point. the change rate of dissipated strain energy will increase during unloading confining pressure, and a small sharp point of change rate of dissipated strain energy also appears at the unloading point. the damage variable is defined to analyze the change law of failure variable over strain. in the loading test, the damage variable growth rate is first rapid then slow as a gradual process, while in the unloading test, a sudden increase appears in the damage variable before reaching the rock peak strength. according to the deterioration law of damage and the impact of confining pressure on the elastic modulus, a rock damage constitutive model is established, which has a better fitting effect on the data in the loading and unloading failure processes. keywords. marble; energy evolution; damage variable; constitutive equation. introduction ock mass, which is a typical non-homogeneous material, shows initial damage during formation and long geological processes. in the rock loading process, internal damage continues to accumulate, micro-cracks are expanded and aggregated, and these ultimately connect to cause rock failure. damage characterizes the rock r l. zhang et alii, frattura ed integrità strutturale, 30 (2014) 515-525; doi: 10.3221/igf-esis.30.62 516 1 3 o a b c failure process from the microscopic perspective. cao et al. [1] considered that rocks with partial damage may also withstand the loads, and the rock damage statistical model was established accordingly. qin et al. [2] build a damage constitutive equation based on the rock uniaxial-compression. ha et al. [3] studied rock failure mechanism under unloading stress path. huang et al. [4, 5] believed that rock unloading damage had obvious tension-shear failure characteristics. wu and zhang [6] regarded failure parameter as one of the parameters of rock mechanic characteristics. shi et al. [7] believed that the rock deformation curve was consistent with weibull distribution, and hoek-brown’s guideline was used to establish the rock damage model. zhang et al. [8] proposed the concept of basic damage, and provided the damage equation under the condition of rock uniaxial compression. xu and wei [9] used the proportion of damaged micro-unit volume accounting for the total as the damage variable to establish a rock failure statistical model. in recent years, the energy perspective has become a new perspective for rock failure research. chen et al. [10] conducted rock failure experiments before and after the peak strength. they proposed a new index of rock energy discrimination. xu et al. [11] studied the energy consumption characteristics of sandstone under loading and unloading stress paths. they draw that the various energy indicators are elevated with the larger confining pressure. jin et al. [12] analyzed the change law of dissipated energy in the uniaxial cyclic loading and unloading processes, and used the energy method to determine the rock damage thresholds in different loading paths. based on the relationship between damage and energy dissipation, du [13] defined the failure variable and established the damage mechanics model for structured soils. hua and you [14] observed that without external force, the elastic energy accumulated in the rock loading process may release itself to cause failure. the rock three-point bending tests conducted by zhou et al. [15] showed that the strain energy density would show a nonlinear increase with the increase of loading rate. gaziev [16] believed that the fracture energy caused by the failure of rock in brittle materials was closely related to stress state. xie et al. [17] believed that the essence of rock failure is the damage caused by energy dissipation. liu et al. [18] draw a conclusion that most of external work was converted into rock elastic strain energy before yielding. however, the dissipation strain energy increased rapidly after yielding. zhang et al. [19] believed that the rate of dissipated strain energy change went up with the unloading rate increase. the above studies analyze rock failure from the perspective of damage, but there is currently a lack of combining energy dissipation mechanism to study the characteristics of rock failure, and research regarding the rock failure constitutive model under triaxial loading and unloading paths is scarce. in this study, by analyzing energy accumulation, dissipation and release characteristics throughout the entire process of marble deformation under loading and unloading stress paths, the damage variable is defined from the perspective of energy dissipation, and a rock failure mechanics model is established. test stress paths he test is completed on mts rock testing machine. marble rock blocks are processed with a diameter of 50 mm and height of 100 mm. the rock sample precision meets the requirements of the rock mechanic test. in order to ensure the uniformity of the rock sample, the screen is conducted in two steps: first the significantly-jointed rock samples are removed, then a rock sample with the wave velocity of 4000-4400 m/s is selected. figure 1: stress paths of marble loading and unloading test. there are two stress paths in the test, i.e. the conventional triaxial loading and unloading (fig. 1). oac is the conventional triaxial test path, and oab is the test path with confining pressure unloading, of which the respective unloading rates of confining pressure are 0.2, 0.4 and 0.8 mpa/s. t l. zhang et alii, frattura ed integrità strutturale, 30 (2014) 515-525; doi: 10.3221/igf-esis.30.62 517 energy dissipation characteristics of marble failure process calculation method of energy ccording to the energy principle, the acting of external forces on the test system is as shown below: d eu u u  (1) where u is the total work done by external force on the rock specimens, du is the dissipated strain energy, eu is the elastic strain energy. the calculation relationship is shown in fig. 2, [17]. figure 2: the numerical relationship between the dissipated strain energy and the elastic strain energy [17]. analysis of energy dissipation characteristics fig. 3 shows the relation between the marble axial stress, strain energy and axial strain at different stress paths. the energy curve has the following characteristics: (1) compaction stage: the dissipated strain energy is very small, while elastic strain energy grows slowly. (2) elastic stage: external force continues to work, elastic strain energy is developed approximately parallel to total strain energy, while the dissipated strain energy increases slowly. it is believed that the elastic stage is the stage of energy accumulation, when most of the energy absorbed by the rock speciments can be stored as elastic strain energy. (3) pre-peak plastic stage: total strain energy continues to increase. the propagation of internal cracks must dissipate a large amount of external force work, so that the energy is absorbed and begins converting into surface energy for crack propagation, and the growth rate of the dissipated strain energy is increased significantly, while that of the elastic strain energy is slowed. (4) post-peak stage: from the peak point to stress drop point, a large number of micro-cracks are propagated and accumulated until the emergence of macroscopic rupture occurs, and this must overcome the work of the frictional force, resulting in a substantial increase in dissipated strain energy. when the stress drops sharply, the internally accumulated elastic strain energy is released rapidly, causing rock failure. (a) (b) figure 3: energy change curves under two stress paths (confining pressure: 10 mpa): (a) the conventional triaxial loading test (b) the conventional triaxial unloading test (i axial stress, ii absorbed total strain energy, iii elastic strain energy, iv dissipated strain energy) a l. zhang et alii, frattura ed integrità strutturale, 30 (2014) 515-525; doi: 10.3221/igf-esis.30.62 518 unlike conventional triaxial loading, it is clear that brittle failure occurs in the rock samples with unloading failure. as the confining pressure decreases, stress drop occurs rapidly after the peak strength, and internal stored energy is released quickly. elastic stain energy and dissipated stain energy are no longer gradual processes, but rather sharp increase processes. elastic strain energy is significantly reduced, while dissipated stain energy is instantly and sharply increased to the total strain energy value. determination of marble failure position n both the conventional triaxial loading test and unloading test, the failure points occur posterior to the peak strength. how to determine the failure point is a matter which requires in-depth discussion. as viewed from the energy conversion relationship in the rock failure process, the energy dissipation process is associated with the entire process of rock deformation, thus resulting in rock failure. the change rate of dissipated energy is used to determine the position of the failure point. the slipping point regression analysis method is used [20], and the first-order derivative of dissipated energy against strain is taken to express the change rate of dissipated energy du : /d ddu d u  (2) where ddu is the dissipated energy increment, d is the strain increment corresponding to ddu and du is the change rate of dissipated energy. the slipping point regression method is used to take a calculated interval for linear regression at each dissipated energy-strain point, so as to obtain the slope of the interval represented by the point, and then the curves of the relationship between slope and strain at each point are prepared (fig. 4). figure 4: slipping point regression method [13]. the relation between the change rate of dissipated strain energy and strain at different stress paths is shown in fig. 5. for the loading test, dissipated strain energy is increased slowly in the compaction and elastic stages, and the change rate of the dissipated strain energy is very small. in the plastic deformation stage, the change rate of the dissipated strain energy is increased, gradually approaching the linear growth law. after the peak to the stress drop stage, the change rate of dissipated energy shows a non-linear growth, then sharply increases to the extreme point at the drop point, leading to rock macroscopic failure plane connected, i.e. the failure point. similar to the loading test, the change rate of dissipated strain energy in the unloading test is maintained at a constant level before unloading. the change rate of dissipated strain energy at the unloading position is slightly jumping. due to changes of stress path, the rock stress state is changed, leading to change in the allocation of absorbed total strain energy, which corresponds to the growth rates of elastic strain energy and dissipated strain energy. the change rate of dissipated strain energy is slowly increased between the unloading point and peak point, then it suddenly increases at the stress drop point. this sudden increase in the change rate of dissipated strain energy indicates a sudden release of stored elastic strain energy, thus leading to rock failure. as viewed from the stress-strain relationship, the sudden change point corresponds to the stress drop point, i.e. the failure point. it should be noted that for the rock samples with the unloading rate of confining pressure equal to 0.8 mpa/s, a second stress drop exists, and the change rate of dissipated strain energy also shows a small sudden jump at the initial drop point, indicating that partial failure occurs to the rock mass at the stress position, and this sudden jump value is significantly smaller than that at the final failure. i st ra in e ne rg y regression point axial strain l. zhang et alii, frattura ed integrità strutturale, 30 (2014) 515-525; doi: 10.3221/igf-esis.30.62 519 0 20 40 60 80 100 120 0 0.005 0.01 0.015 -100 100 300 500 700 900 0 20 40 60 80 100 120 0 0.002 0.004 0.006 0.008 -400 0 400 800 1200 1600 (a) (b) 0 20 40 60 80 100 0.000 0.003 0.006 0.009 -200 0 200 400 600 800 1000 0 10 20 30 40 50 60 70 80 0.000 0.002 0.004 0.006 0.008 -500 0 500 1000 1500 2000 (c) (d) figure 5: change rate of dissipated energy of different stress paths: (a) the conventional triaxial loading test; (b) unloading rate of confining pressure 0.2 mpa/s; (c) unloading rate of confining pressure 0.4 mpa/s; (d) unloading rate of confining pressure 0.8 mpa/s ( i axial stress, change rate of dissipated strain energy). the change rate of dissipated strain energy can be used not only to distinguish the various stages of the marble deformation process, but also to determine the position of the failure point, which is a new method that may be used to determine the failure point. the position of the first sudden jump point in the change rate of energy is the unloading point, and the greatest sudden jump point represents the overall failure of the rocks. the stage with a constant change rate of dissipated strain energy is the elastic stage, while that with a growth trend is the plastic stage. definition of failure variable nergy dissipation is achieved through internal crack propagation and failure surface friction, and this process is directly related to rock failure [17]. therefore, the extent of rock damage is characterized from the perspective of dissipated energy, so as to define the damage variable d as follows: d /d u u (3) the change law of damage variable over axial strain under different confining pressures is shown in fig. 6. for the loading test, the change in dissipated strain energy is very small in the elastic stage, and the damage variable is basically unchanged. in the plastic deformation stage, the damage variable is increased as the strain grows, and the curve slope gradually increases, which is a gradual process. after the peak strength point, the slope becomes smaller. between the peak strength point and failure point, the damage variable curve is concave. after rock failure, the damage variable remains constant in the residual deformation stage. unlike the damage variable of the loading test, the change of the damage variable is very small in the initial stages after unloading. the damage variable is only rapidly increased when approaching the peak strength point, which is a sudden e ⅱ a xi al s tr es s[ m p a] c ha n ge r at e o f di ss ip at ed en er gy [m j/ m 3 ] a b c d o ⅰ ⅱ ⅰ ⅰ ⅱ ⅱ axial strain axial strain axial strain axial strain a xi al s tr es s [m p a] a xi al s tr es s[ m p a] c h an ge r at e of d is si p at ed en er gy [ m j/ m 3 ] c h an ge r at e o f di ss ip at ed en er gy [m j/ m 3 ] unloading point a xi al s tr es s [ m p a] c h an ge r at e of d is si p at ed en er gy [ m j/ m 3] unloading point unloading point ⅰ l. zhang et alii, frattura ed integrità strutturale, 30 (2014) 515-525; doi: 10.3221/igf-esis.30.62 520 increase process. posterior to the peak strength point of the rock sample in the unloading test, it soon reaches the failure point. after the peak strength point in the loading test, the failure of the rock sample only occurs after the generation of large deformation. it will be a long period of time from the peak strength point to the failure point, and unloading failure is characterized by more sudden occurrence than loading failure. 0.0 0.2 0.4 0.6 0.8 1.0 0.000 0.005 0.010 0.015 0.0 0.2 0.4 0.6 0.8 1.0 0.000 0.002 0.004 0.006 0.008 0.010 (a) (b) 0.0 0.2 0.4 0.6 0.8 1.0 0.000 0.002 0.004 0.006 0.008 0.010 0.0 0.2 0.4 0.6 0.8 1.0 0.000 0.002 0.004 0.006 0.008 (c) (d) figure 6: change of damage variable at different stress paths: (a) the conventional triaxial test; (b) unloading rate of confining pressure 0.2 mpa/s; (c) unloading rate of confining pressure 0.4 mpa / s; (d) unloading rate of confining pressure 0.8 mpa/s. the deformation control mode is used in the test, and the strain is a constant in the unit of time, i.e.: /d dt c  (4) and dd dd d dt d dt    (5) eq. (4) is then substituted into eq. (5), as follows: dd dd c dt d  (6) eq. (6) shows that the damage variable is proportional to the time evolution rate and it is similar to the strain evolution rate. it is indicated that for the deformation control mode with a constant strain rate, the evolutionary law of the damage variable over time may be speculated according to its evolutionary law over strain, which is of reference value to the study of rock creep failure. peak point failure point d am ag e va ri ab le unloading point axial strain axial strain axial strain axial strain d am ag e va ri ab le d am ag e va ri ab le d am ag e va ri ab le failure point failure point peak point peak point unloading point failure point peak point unloading point l. zhang et alii, frattura ed integrità strutturale, 30 (2014) 515-525; doi: 10.3221/igf-esis.30.62 521 failure constitutive equation change law of elastic modulus over confining pressure ock mass is a type of non-continuous and non-homogeneous material, the interior of which contains both large and small cracks. in the rock compression process, the increase of confining pressure may improve the crack closure rate, as well as the rock compressive strength and the elastic modulus. under high confining pressure, the occurrence of slipping requires a large external force, so that the rock strength is higher and the elastic modulus is greater. considering the impact of confining pressure on the elastic modulus, it is found, by fitting the experimental data, that the elastic modulus is closely related to the confining pressure, and the change law is shown as below: 31 1 1 exp 1r a e e c e                 (7) where re is the elastic modulus after confining pressure correction, 1e is the elastic modulus under uniaxial compression, and 1re e in the uniaxial loading test. in addition, a is the correction coefficient of the curve peak, and c is a parameter used to characterize the change rate of the confining pressure. c is equal to 1 in the conventional triaxial test, while c is changed over the confining pressure in the unloading test. establishment of constitutive equation the rock itself is shown to contain certain initial damage. according to eq. (7), rock damage will be increased with higher dissipated strain energy in the compression process. assuming that the rock stress has a power function relationship with the damage variable, the elastic modulus after the confining pressure correction is used to establish the damage constitutive equation:  1 be d   (8) eq. (7) is then substituted into eq. (8), so to obtain:  31 1 1 exp 1 1 ba e c d e                     (9) where b is the correction coefficient of curve shape. taking the conventional triaxial loading test data as an example (confining pressure: 10 mpa), the impact of the eq. (9) parameters on the stress-strain curve distribution characteristics is analyzed. fig. 7 shows the stress-strain curve by assuming b equal to 0.5 and different values for parameter a . as the value of a increases, steeper pre-peak curve, higher peak strength and smaller residual strength can be observed, thus indicating that a is correlated with the compressive strength. under the same stress, the greater the a value is, the smaller the pre-peak deformation will be, so the a value also reflects the rock deformation characteristics. figure 7: stress-strain curves of different parameter a (b=0.5). figure 8: stress-strain curves of different parameter b (a=500). r l. zhang et alii, frattura ed integrità strutturale, 30 (2014) 515-525; doi: 10.3221/igf-esis.30.62 522 fig. 8 shows the stress-strain curve obtained by assuming a equal to 500 and by varying b value. the b value has little effect on the pre-peak stage, and the various curves are basically overlapped. a smaller b value determines a slightly higher peak strength. on the contrary, it has a greater impact on post-peak softening and on the residual strength of the rock. the greater the b value is, the more significant the post-peak strain softening phenomenon of the rock sample will be, and the smaller the residual strength will be. b has a great impact on the curve shape between the peak strength and the stress drop point. rock has a plastic flow tendency with the reduction of b while it shows a significant brittle stress drop with the increase of b. stress path confining pressure [mpa] unloading rate [mpa/s] a b c r2 (%) the conventional triaxial test 10 427 0.36 1 98 20 442 0.38 97 30 468 0.41 95 40 500 0.45 94 unloading test 10 0.2 1.2052 0.5022 320.36 98 0.4 1.2164 0.5059 338.32 97 0.8 1.2850 0.4938 332.19 97 20 0.2 1.1320 0.5385 310.12 99 0.4 1.2540 0.5382 324.50 99 0.8 1.0350 0.7922 342.50 90 30 0.2 0.9735 0.7860 345.80 99 0.4 0.9509 0.7120 333.64 98 0.8 0.8321 0.7226 373.89 98 40 0.2 0.8635 0.6894 342.5 98 0.4 0.8456 0.7011 368.32 97 0.8 0.8247 0.7376 328.47 98 table 1: parameter value setting based on the test data, the parameters, i.e. a , b and c , are adjusted to simulate the constitutive equation, and the matlab nonlinear fitting tool is used to perform test data regression. tab. 1 lists the parameters, i.e. a , b and c , under different stress paths. figs. 9 and 10 show the fitting curves of the constitutive equation on the conventional triaxial loading and unloading tests, respectively. the stress-strain curve simulated by this constitutive equation is highly consistent with the experimental curve, with a correlation coefficient greater than 94%. the internal cracks caused by rock compression are closed, so that an initial compression stage will likely exist in the stress-strain curve. the initial stage of the stress-strain curve simulated by this constitutive equation can reflect the concave shape of the curve in the compaction stage. under static loading conditions, the rocks are loaded from the initial state to the failure process, i.e. internal crack compaction, fissure propagation, aggregation and connection, which is a continuous process, so that the entire process of stress-strain equation becomes unified. in this study, a unified equation is used to simulate the deformation process, so as to avoid the shortcomings of staged fitting. this constitutive equation considering the confining pressure impact contains only three parameters. through adjusting these three parameters, the rock deformation processes under various stress paths may be simulated, thus this model is highly adaptable. l. zhang et alii, frattura ed integrità strutturale, 30 (2014) 515-525; doi: 10.3221/igf-esis.30.62 523 0 20 40 60 80 100 120 140 0.000 0.002 0.004 0.006 0.008 0.010 0 20 40 60 80 100 120 140 160 0.000 0.003 0.006 0.009 0.012 (a) (b) 0 30 60 90 120 150 180 0.000 0.003 0.006 0.009 0.012 0 40 80 120 160 200 0.000 0.005 0.010 0.015 (c) (d) figure 9: stress-strain curves of conventional triaxial tests: (a) confining pressure 10 mpa; (b) confining pressure 20 mpa; (c) confining pressure 30 mpa; (d) confining pressure 40 mpa. (a) (b) (c) figure 10: stress-strain curves of different unloading rates: (a) unloading rate of confining pressure 0.2 mpa/s; (b) unloading rate of confining pressure 0.4 mpa/s; (c) unloading rate of confining pressure 0.8 mpa/s.     1 [ m p a]  1 [m p a]  1 [ m p a]  1 [m p a]    1 [m p a]    1 [ m p a]  1[ m p a] l. zhang et alii, frattura ed integrità strutturale, 30 (2014) 515-525; doi: 10.3221/igf-esis.30.62 524 conclusions he energy dissipation process is associated with the entire process of rock deformation, thus resulting in rock failure. the compaction and elastic stages mainly form the accumulation process of elastic strain energy. after the peak strength, dissipated strain energy is increased significantly. in the unloading test, the elastic strain energy is released at the stress drop point, while the dissipated strain energy increases sharply. the change rates of dissipated strain energy can be used not only to distinguish the various stages of deformation process, but also to determine the position of the failure point. the stage with a constant change rate of energy is the elastic stage, while that with a growth trend is the plastic stage. the ratio between dissipated strain energy and total stain energy is defined as the damage variable. the change of damage variable is a gradual process for the conventional triaxial loading test, while it is a sudden increase process for the unloading test. the damage mechanics model in the marble deformation process is established from the perspective of energy dissipation, which may reflect the impacts of confining pressure changes on the marble strength. acknowledgement he study is supported by the national natural science foundation of china (41472270, 41372298), shandong province higher educational science and technology program (j10le01) and qingdao science and technology program (12-1-4-4-(10)-jch). references [1] cao, w., g., zhang, s., zhao, m., h., study on statistical damage constitutive model of rock based on new definition of damage, rock and soil mechanics, 27(1)(2006) 41-46. [2] qin, y., p., zhang, j., f., wang, l., preliminary discussion on theoretical model of rock damage mechanics, chinese journal of rock mechanics and engineering, 22(4) (2003) 646-650. [3] ha, q., l., rock slope engineering and unloading nonlinear rock mass mechanics, chinese journal of rock mechanics and engineering, 16(4)(1997)386-391. [4] huang, r., q., huang, d., experimental research on mechanical properties of granites under unloading condition, chinese journal of rock mechanics and engineering, 27(11) (2008) 2205-2213. [5] huang, d., huang, r., q., zhang, y., x., experimental investigations on static loading rate effects on mechanical properties and energy mechanism of coarse crystal grain marble under uniaxial compression, chinese journal of rock mechanics and engineering, 31(2) (2012) 245–255. [6] wu, z., zhang, c., j., unidirectional loading and mechanical damage model of rock properties, chinese journal of rock mechanics and engineering, 15(1) (1996) 55–61. [7] shi, c., jiang, x., x., zhu, z., d., et al., study of rock damage age constitutive model and discussion of its parameters based on hoek-brown, chinese journal of rock mechanics and engineering, 30(1) (2011) 2647-2652. [8] zhang, q., s., yang, g., s., ren, j., x., new study of damage variable and constitutive equation of rock, chinese journal of rock mechanics and engineering, 22(1) (2013) 30-34. [9] xu, w., y., wei, l., d., study on statistical damage constitutive model of rock, chinese journal of rock mechanics and engineering, 21(6) (2002) 787–791. [10] chen, w., z., lu, s., p., guo, x., h., et al., research on unloading confining pressure tests and rock burst criterion based on energy theory, chinese journal of rock mechanics and engineering, 28(8) (2009) 1530-1540. [11] xu, g., a., niu, s., j., jing, h., w., et al., experimental study of energy features of sandstone under loading and unloading, rock and soil mechanics, 32(12) (2011)3611-3617. [12] jin, f., n., jiang, m., r., gao, x., l., defining damage variable based on energy dissipation, chinese journal of rock mechanics and engineering, 23(12) (2004) 1976-1980. [13] du, w., the isotropic damage constitutive model based on the principle of energy dissipation, journal of sichuan building, 30(2) (2010) 183-185. [14] hua, a., z., you, m., q., rock failure due to energy release during unloading and application to underground rock burst control, tunnelling and underground space technology, 16(3) (2001) 241-246. t t l. zhang et alii, frattura ed integrità strutturale, 30 (2014) 515-525; doi: 10.3221/igf-esis.30.62 525 [15] zhou, x., p., yang, h., q., zhang, y., x., rate dependent critical strain energy density factor of huanglong limestone, theoretical and applied fracture mechanics, 51(1) (2009) 57-61. [16] gaziev, e., rupture energy evaluation for brittle materials, international journal of solids and structures, 38(42-43) (2001) 7681-7690. [17] xie, h., p., ju, y., li, l., y., criteria for strength and structural failure of rocks based on energy dissipation and energy release principles, chinese journal of rock mechanics and engineering, 24(17) (2005) 3003-3010. [18] liu, x.,m., xiong, l., liu, j.,h., et al, slacking mechanism of red sandstone based on energy dissipation principle, journal of central south universty (science and technology), 42(10) (2011) 3143-3149 [19] zhang, x., y., cheng, j., kang, y., h., et al, analysis on damage and energy during rock deformation under cyclic loading and unloading conditions, nonferrous metals, 63(5) (2011) 41-45. [20] eberhardt, e., stead ,d., stimpson, b., et al, identifying crack initiation and propagation thresholds in brittle rock, canada geotechnical journal, 35 (1998) 222-233. microsoft word numero_33_art_52 c. gao et alii, frattura ed integrità strutturale, 33 (2015) 471-484; doi: 10.3221/igf-esis.33.52 471 a new micromechanical model of cnt-metal nanocomposites with random clustered distribution of cnts chongyang gao, yu lu school of mechanical engineering, zhejiang university, hangzhou 310027, china corresponding author: gcysci@163.com y.t. zhu 2school of materials science and engineering, nanjing university of science and technology, nanjing 210094, china abstract. uniform dispersion of carbon nanotubes (cnts) is a key issue for utilization of their reinforcement potential in cnt-reinforced metal matrix nanocomposites (mmncs). it was reported that cnt clusters often exist in mmncs prepared by various techniques, which reduces the load transfer efficiency between the matrix and reinforcement. in this paper, a new micromechanical constitutive model of cnt-reinforced mmncs is developed, which takes into account of the influences of cnt clusters and misorientations. the strength values of a cnt/al nanocomposite predicted by the new model are compared first with experimental data for validation. then, the developed model is applied to predict the size effect, temperature effect and strain rate effect of the nanocomposite in its overall elastoplastic response. keywords. micromechanical modelling; metal matrix nanocomposites; carbon nanotubes; cluster effect; misorientation angle. introduction n recent years, it has been reported that incorporating carbon nanotubes (cnts) into polymers [1-3], ceramics and metals [4-7] can dramatically improve their mechanical properties. this is due to the high strength; high young’s modulus and super thermal conductivity of cnts. metal matrix nanocomposites (mmncs) reinforced with cnts have enhanced yield strength and a low thermal expansion coefficient, which render them substantial potential in some weight sensitive applications such as aerospace structures [8]. yang et al. [9] demonstrated that the yield strength of a 1.5 wt. % cnt/al nanocomposite produced by an improved chemical vapor deposition (cvd) is 2.2 times that of the pure aluminum, while the result obtained in compression tests [10] is not so high due to different preparation technique of the sample. kim et al. [11] showed that the measured tensile strength of cnt/cu nanocomposite with 10 vol. % cnts is 281mpa, which is approximately 1.6 times higher than that of unreinforced pure copper. li et al. [12] made cntnanocrystalline cu nanoacomposite using ball-milling and high-pressure torsion consolidation, which has very high yield strength of 1100 mpa at 1 wt% cnt addition. thus, cnts can be an ideal reinforcement for material design to improve mechanical properties of composites. the high aspect ratio of length to diameter of curved cnts makes them prone to entangle with each other resulting in clustering in matrix, and consequently difficult to be uniformly dispersed in matrix. to solve this problem, various preparation techniques have been employed to achieve a more uniform distribution of cnts in mmncs so as to realize i c. gao et alii, frattura ed integrità strutturale, 33 (2015) 471-484; doi: 10.3221/igf-esis.33.52 472 their full strengthening potential. however, agglomeration and imperfect interfacial load transfer of cnts still often exist in these composites. to facilitate the applications of cnt-reinforced metal matrix nanocomposites, it is essential to develop a reliable micromechanical constitutive model that can be used to describe and predict their mechanical properties. some modeling efforts have been made to describe the mechanical properties of the cnt-reinforced nanocomposites. courtney [13] established a classic model for short-fiber-reinforced plastic-matrix composites by introducing the effect of the aspect ratio into the basic role-of-mixture model, which can be applicable to cnt-reinforced nanocomposites. based on the generalized shear-lag model [14] for metal matrix composites with reinforcement in cylindrical forms, kim et al. [11] proposed a strength model to describe a two-stage yielding process in the experimental stress–strain curves of the cnt/cu nanocomposites, and also observed elongated cnt clusters in the microstructure of the composite. barai and weng [15] developed a two-scale micromechanical model to make a pioneering analysis of the effect of cnt agglomeration and interface condition on the strength of cnt-reinforced mmncs. obviously, it is inevitable that a lot of cnt agglomerations in metallic matrix materials will appear because of easy entanglement of cnts, especially for those with the high aspect ratio, as observed in [16-18]. although there are also some other models proposed for cnt-reinforced polymers matrix nanocomposites [1, 3, 19, 20], a model with consideration of clustering phenomenon is still lacking. to describe the flow stress and estimate the plastic strength of cnt-reinforced metal matrix composites, a new micromechanical constitutive model, with consideration of the effect of cnt clusters and the influence of cnt misorientation angle, will be proposed in this paper. in the "modelling of cnt-reinforced mmncs" section, the cluster effect is introduced into the new model by using the statistically average equivalent length and diameter of cnts, and the misorientation angle effect is reflected by a definition of an effective load transfer coefficient. in the next section, the model parameters are determined for the cnt/al nanocomposite by a nonlinear multi-variable global optimization method, i.e., generic algorithm. in the "results and discussion" section, the new model is experimentally validated, and some important predictions of the model are given and discussed. modelling of cnt-reinforced mmncs acroscopically, the cnt reinforced metal matrix nanocomposite is deformed homogeneously, in which the metal matrix is plastic and the cnt fiber is elastic. the mmncs derive their plasticity from the good plastic behavior of the metallic matrix materials. the flow stress of cnt-reinforced mmncs during the elastoplastic deformation process can be generally expressed below with the classical rule of mixtures as widely used for two-phase composites [20]:  1c f f f m       (1) where c the flow stress of nanocomposites is, f is the stress of cnts at composite failure, m is the flow stress of the pure matrix material. fv denotes the volume fraction of cnts. for mmncs reinforced with discontinuous cnts, the applied load transfers from the matrix to cnts along the cnt– matrix interface by the way of shear stress, and interfacial bonding significantly affects the strength of the composite. in order to load high-strength fibers to their maximum strength, the metallic matrix will flow plastically in response to the high shear stress developed. plastic deformation of a matrix implies that the shear stress at the interface will never go above the matrix shear yield strength. in such a case, the following equation can be derived on a perfect bonding interface based on the equilibrium of forces [13]: 2 4 2 fm i y d l d    (2) where i y is the shear yield strength of the interface and fm is the maximum stress in cnts, l and d are the average length and diameter of primary cnts, respectively. it can be seen that the maximum stress in cnts varies with the length of cnts. if a carbon nanotube is sufficiently long, it should be possible to load the cnt to its breaking stress, fm fb  , by means of load transfer through the metallic matrix flowing plastically around it. that is to say, there exists a critical m c. gao et alii, frattura ed integrità strutturale, 33 (2015) 471-484; doi: 10.3221/igf-esis.33.52 473 length of cnts, crl , which is the minimum length necessary to reach fracture for a given cnt diameter. based on eq. (2), the critical length of cnts can be deduced as: 2 cr fb i y d l    (3) if crl l , the matrix will flow plastically around cnts and load a cnt to a stress in its central position given by 2( / )f myl d  . for crl l , the average stress in a cnt can be written as:   0 cr cr cr 1 1 [ ( )] [1 (1 )] l f f f f f x dx l l l l l l l               (4) where  can be regarded as a load transfer function and f represents the average stress of cnts over a portion crl . the value of  will be precisely 1/2 for an ideally plastic matrix with no strain hardening, i.e., the increase in stress in a cnt over the portion was assumed as being linear. now, by amending the cnt stress in eq. (1) with the average stress in eq. (4), a basic model of cnt-reinforced mmncs can be obtained as:  11 1 4 f b c f f f m i y d l                  (5) thermo-viscoplastic constitutive model of fcc metal matrix materials for cnt reinforced mmncs, the reported matrices are mostly the lightweight metal materials such as aluminum, copper, magnesium and their alloys. although the carbon nanotubes are dispersed in the matrices to enhance their mechanical properties, the matrix materials play the most significant role in the plastic deformation behavior of the cnt reinforced composites. to reasonably describe the plastic deformation behaviors of the composite, a reliable plastic constitutive model should be established for the metallic matrix material. the plastic deformation of metals can be explained as the process of dislocation motion and accumulation under the ratecontrolled and thermally-activated mechanism. in the thermal activation analysis, dislocation motion is resisted by both short-range and long-range barriers. the short-range barriers may be overcome by thermal activation, while the longrange barriers are essentially not related with temperature (i. e. it is athermal). hence, the flow stress of the metal materials, which is essentially defined by the material resistance to dislocation motion, can be decomposed into two parts: m ath th    (6) where m is the flow stress of the matrix material; ath is the athermal component of the flow stress reflecting the longrange barriers, while th is the thermal component of the flow stress reflecting the short-range barriers which depends on the thermal activation. by using the mechanical threshold stress (mts, denoted as ̂ ) as a reference stress that characterizes the constant structure of a material, the thermal stress can be expressed as:   ˆ,th thf t    (7) where ˆth is the thermal component of mts according to ˆ ˆ ˆath th    ,  ,f t is the thermal activation function (<1.0) representing the coupling effects of strain rate (  ) hardening and temperature ( t ) softening. based on the wellknown relation of dislocation speed and thermal activation energy (or called free energy) proposed by johnston and c. gao et alii, frattura ed integrità strutturale, 33 (2015) 471-484; doi: 10.3221/igf-esis.33.52 474 giman [21] and the expression of free energy given by kocks and ashby [22], the thermal activation function can be expressed as:   11 2 0 , 1 ln pq f t t                          (8) on the other hand, with consideration of the effect of grain size in the flow stress by using the hall-petch relationship, the athermal stress can be written as: ath = 1 2 g kd   (9) where g is the stress due to initial defect, d is the grain size and k is a microstructural stress modulus. the athermal stress can be treated as a constant as a whole because the grain size can be measured for a particular matrix. for a face-centered cubic (fcc) matrix (e.g., pure aluminum and its alloys), the thermal component of mts has been deduced in [23]. finally, the constitutive model of fcc metal matrix materials was determined as: 11 1 2 0 0 ˆ exp ln 1 ln pq n m ath s y t t                                              (10) where ŷ is the reference thresholds of the thermal stress; n is strain hardening exponent;  31 0ˆ s mk g g b  and  32 0ˆ mk g g b  (here k̂ is the boltzmann constant, 0g and 0sg are the normalized and saturated free energies, mg is the shear modulus of the matrix material, b is the burgers vector representing the excursion induced by dislocation); 0 and 0s are the reference and saturated strain rates; q and p are a pair of parameters representing the shape of crystal potential barrier. compared with the conventional modelling of matrix materials which just adopt the yield strength of the matrix [10, 18], the new model of matrix materials is a physics-based thermo-viscoplastic constitutive relation that can describe the plastic flow stress of cnt reinforced mmncs during plastic deformation with consideration of strain rate hardening and temperature softening effects. consideration of the misorientation angel of cnts because cnts are randomly distributed in matrix and are highly curved when dispersed in matrix, the misorientation angle,  , between the loading direction and the nanotube length direction for a cnt always varies along its length. to reflect the influence of misorientation angle of cnts in the constitutive model, it was assumed that the curved cnts can be regarded as a chain of multiple straight segments, as shown in figure 1. figure 1: cutting of the curved cnts as a chain of short straight ones (case 1single curved cnts; case 2straight clustered cnts; case 3curved clustered cnts). c. gao et alii, frattura ed integrità strutturale, 33 (2015) 471-484; doi: 10.3221/igf-esis.33.52 475 for cnt-reinforced mmncs fabricated by hot extrusion, an exponential function was proposed as the probability density function of the distribution of misorientation angle [14]: ( ) exp( )f b k   (11) where b is a constant, and k is a constant dependent on the alignment of cnts. now, if the effective strengthening stress of cnts can be expressed as f (where  is an effective load transfer coefficient defined with the misorientation distribution function), the basic model of cnt-reinforced mmncs in eq. (5) may be improved as one with consideration of the influence of misorientation angle. however, the definition of the load transfer coefficient is always assumed in an empirical approach and lacks physical basis of constitutive modelling. in addition, the average length of the cnts dispersed in mmncs is generally less than the critical length, which is estimated as several dozens of micrometers. so the model in eq. (5) may be not suitable for further modelling of the misorientation angle effect. therefore, a physically-based model of short fibre-reinforced composites [24] was introduced below, so as to calculate the direct strengthening of cnts for cnt-reinforced mmncs with a known distribution of misorientation angle and under the assumption that perfect bonding exists between fibers and the matrix. for simplicity, an isotropic poisson’s ratio,  , was assumed for the composite. since cnts with smaller inclination angles from the loading direction bear larger stresses and break first during tensile loading, we assumed that 0 is a critical inclination angle within which every cnt has been broken, i.e., cnts with the inclination angle 0 bear a stress equal to their ultimate strength and are just about to break. then, the stress in a cnt can be derived as [24] 0 2 2 02 2 0 0 2 2 2 2 0 0 0 0 cos sin ( ) cos sin (cos sin ) cos sin 2 f f f f                                           (12) where f is known as 2sin 1/ (1 )f   . to obtain the total load, ( )p  at a specimen cross-section, a , perpendicular to the loading direction, the orientationdensity distribution of cnts intercepted by the cross-section, ( )cn  , is also needed and deduced as 1 ( ) 11 ( )cos f c f f mf ea d n f a l g                  (13) where 2 / 4fa d , fe is young’s modulus of cnts, mg is the shear modulus of the matrix. ( )f  is the misorientation distribution of three-dimensional randomly-oriented cnts. the exponential function proposed in eq. (11) was adopted here for the distribution, as distinct from the previously used ones. the total load is a function of 0 and can be calculated as 0 /2 0( ) ( ) ( ) cosc fp n a d          (14) its maximum value at 0 0  can be considered as the load that cnts can carry at composite failure. thus, by substituting eqs. (12) and (13) into eq. (14), the strengthening stress (  ) contributed directly by cnts can be finally integrated as c. gao et alii, frattura ed integrità strutturale, 33 (2015) 471-484; doi: 10.3221/igf-esis.33.52 476 0 max ( ) 1 ( ) 11 f f f f mf ep d r a l g                     (15) where ( ) [ (0) ( / 2) 2 ( )]f fr b w w w     (16) and  2 2 2 2 3 1 ( ) cos(4 ) sin(4 ) 1 8 8( 16) 2( 16) 1 cos( 2 ) sin( 2 ) 2( 4 ) 4 k k w k k k k e k k                             (17) model modification with consideration of cnt cluster effect as seen in figure 2, cnts always agglomerate in the metallic matrix and form a lot of clusters [16], though various techniques were used to make the dispersion of reinforcement as uniform as possible. this is why the strength of the nanocomposite measured in tests is actually far lower than the prediction of theoretical models. figure 2 clusters of carbon nanotubes after dry mixing of cnts and al powders [16] (with kind permission from springer science and business media). as summarized in the introduction, most models of cnt reinforced mmncs were established with the assumption that the cnts are uniformly distributed in the matrix as shown in figure 3(a). however, there exists serious cluster phenomenon of cnts in general as shown in fig. 3(b). therefore, a modified constitutive model of cnts reinforced mmncs with consideration of the cluster effect was specially proposed as follows. it was proved by the experimental observation by luo et al. [25] that the free-path spacing of cnts follows a logarithmic normal distribution. and tyson et al. [26] pointed out that the particle size of clustered cnts also follows the lognormal distribution, and proved in their experiments that the lognormal distribution has the same mean value and standard deviation as the associated normal distribution. in our modelling, a cnt cluster, which is resulted from a group of intertwined cnts, was regarded as an equivalent large reinforced particle, the shape of which can be approximately described by an equivalent length ( cl ) and an equivalent diameter ( cd ) as shown in figure 3(b). so, the two sizes should follow the lognormal distribution, respectively. their probability density functions of the lognormal distribution can be written as follows: c. gao et alii, frattura ed integrità strutturale, 33 (2015) 471-484; doi: 10.3221/igf-esis.33.52 477 2 1 1 ln ( ) exp , 0 ( , ) 22 c c x m f x x x l d nnx             (18) and 2 2 2 2 2 2 ln , ( , ) ln i i i i c c i i i i m i l d n              (19) where l and d represent the mean values of the associated normal distribution of the equivalent length and diameter, respectively; l and d represent the standard deviations of the associated normal distribution of the equivalent length and diameter, respectively. (a) (b) figure 3: comparison of random distributions of cnts (a) uniform pattern; (b) with clusters according to the lognormal distribution of the equivalent length and diameter of cnts in eq. (18), the average values of the equivalent length ( cl ) and diameter ( cd ) of cnts can be statistically calculated as:   2 , max , min 2 l c c l c c n l m c c c cl l l f l dl e     (20) 2 , max , min 2= ( ) dc c dc c n d m c c c cd d d f d dd e    (21) where ,maxcl and ,maxcd are the maximum values of the equivalent length and diameter of the cnt clusters; ,mincl and ,mincd are the minimum values of them. the upper and lower boundaries of the equivalent length and diameter following the lognormal distribution were illustrated in figure 4. obviously, there exist minimum and maximum boundary values for the equivalent length and diameter in reality. the minimum values can be regarded as several times of the average original length and diameter of cnts (about 15 times as presented in [16]), and the maximum values can be evaluated by c. gao et alii, frattura ed integrità strutturale, 33 (2015) 471-484; doi: 10.3221/igf-esis.33.52 478 experimental observations like figure 2. in addition, the standard deviations of the associated normal distribution of the equivalent length and diameter will be eliminated in their average values of lognormal distribution under the presupposed condition in eq. (19) for the lognormal distribution. p ro b a b ili ty d e n si ty f u n ct io n p ( x ) radom variable x (l c or d c ) (nm) x min x max logorithmic normal distribution figure 4: illustration of the actual upper and lower boundaries of the equivalent length and diameter of cnt clusters with the lognormal distribution. since the equivalent length and diameter of cnts are closely related with the volume fraction of cnts, l and d was assumed to change with the volume fraction. the depending relationship of them on the volume fraction are still unknown, however, they can be evaluated by using the polynomial function interpolation method to numerically fit the real nonlinear curves. based on the experimental stress-strain curves at four different volume fractions [9], the cubic spline function was used to match these data points, then l can be expressed as: 3 21 1 1( ) ( )l f f f fh v l a v b v c v l     (22) since the change of d with volume fraction ( 0 1f  ) is faster than l and the change of d is also faster than l , then d and d can be expressed by a quadric polynomial interpolation function:    4 3 22 2 2d f f f fg d a b c d        (23) finally, by substituting eqs. (20-23) into eq. (15) and then into eq. (1) together with eq. (10), we can get the modified micromechanical model of cnt reinforced metal matrix composites to describe their thermo-viscoplastic flow behaviors: 1/2 2 2 2 2 2 1 1 1 11 1 2 0 0 ( ) 1 = ( ) 11 ( ) ˆ(1 ) exp ln 1 ln f f f c f f f f f f mf pq n f ath s a v b v c ed r v l a v b v c g y t t                                                                              (24) c. gao et alii, frattura ed integrità strutturale, 33 (2015) 471-484; doi: 10.3221/igf-esis.33.52 479 determination of model parameters luminum and its alloys are widely used in aerospace and automotive industries because of their good mechanical properties [27]. cnts can be an ideal reinforcement to design aluminum matrix nanocomposites (cnt/al) to improve their wear and creep properties. so a typical cnt-reinforced mmnc (cnt/al) is chosen as the example in this paper. determination of model parameters for pure aluminum matrix as the matrix model is relatively independent to the strengthening component in the composite model, the material parameters in the matrix model in eq. (10) can be determined firstly. for the pure aluminum matrix, the two reference strain rates 0s and 0 can be evaluated in advance. the two parameters lie in logarithmic functions and produce a smaller influence than 1 and 2 together with them. so their evaluation errors can be offset by fitting of 1 and 2 . the value of 0 is evaluated as 7 11 10 s  , and the value of 0s can be estimated as 9 11 10 s  which is generally two orders greater than 0 . the remaining seven parameters, ath , ŷ , n , 1 , 2 , p , q , can be determined by a global multi-variables nonlinear optimization method, i.e. generic algorithm (ga) as used in [23], based on a group of experimental stress-strain curves of pure aluminum [9, 28] at different strain rates and temperature. a matlab program has been developed to realize the optimization calculations. the optimized results of the matrix model parameters were listed in table 1. model parameters theoretically allowed ranges optimized results units ath [0, 20] 12.0 mpa ŷ [100, 1000] 456 mpa n [0, 1] 0.293 / 1 [ 6 59 10 , 9 10   ] 51.11 10 1/k 2 [ 6 59 10 , 9 10   ] -51.04 10 1/k p (0, 1] 0.939 / q [1, 2] 1.712 / table 1: optimized results of the material parameters of the al matrix model determination of model parameters for cnt/al composite for the cnt/al composite in [9], the average original length and diameter of cnts can be known as 0 1l m and 0 25d nm . the cnt strength parameters in the composite model of eq. (24) can be first ascertained as 30f gpa  and 100fb gpa  [29]. the shear yield strength of perfect bonding interface should be equal to that of the matrix, 45i y mpa  . the parameters in the distribution function of misorientation angle were evaluated as 0.874b  and 6.47k  . the cnt weight fractions were transformed into volume fractions by using the measured density, and the congruent relationship of weight fractions and volume fractions for cnt/al was listed in table 2. weight fractions wt ( % ) 0 0.5 1.5 2.0 measured density  ( 3g cm ) 2.636 2.642 2.638 2.625 volume fractions fv ( % ) 0 0.68 1.88 3.12 table 2: the congruent relationship of volume fractions and weight fractions for cnt/al a c. gao et alii, frattura ed integrità strutturale, 33 (2015) 471-484; doi: 10.3221/igf-esis.33.52 480 the remaining seven parameters，( 1a , 1b , 1c , 2a , 2b , 2c , f ), were determined based on the experimental stress-strain curves of cnt/al composite [9] at different volume fractions, by using the same optimization method as mentioned above. the physically available ranges of these parameters were ascertained by the cubic spline interpolation curve matching. the optimized constitutive parameters of the cnt/al composite were finally shown in table 3. model parameters 1a 1b 1c 2a 2b 2c f varying ranges [2.5e5, 2.5e6] [-4.5e4, -5e3] [100, 900] [1.5e7, 3.5e7] [-7e5, -3e5] [6e3, 1.4e4] ( 55 , 90  ) optimized results 52.96 10 41.35 10  873 73.1 10 55.6 10  6030 62.6 table 3: final optimized constitutive parameters of cnt/al nanocomposite. results and discussion n this section, the new model established and determined for the cnt/al nanocomposite will be compared with experimental data for validation, and then some of important predictions of the new model will be presented. validation of the new model as shown in figure 5, the true stress-strain curves calculated from the proposed new model were compared with the experimental data obtained in compression tests [9] for cnt/al composite of 0.68 %, 1.88 % and 3.12 % cnt volume concentrations. the curve of 0 % cnt composite namely corresponds to the pure aluminum matrix material. obviously, the strength of the cnt/al composite is effectively enhanced by the addition of cnts at volume fractions of 0.68% and 1.88%. however, the strength of the composite drops at a higher volume concentration of 3.12 %, which should be caused by the presence of too many cnt clusters. it was indicated that the new model can well describe the true stressstrain relation of the composite at different volume fraction, especially at large strain because that the new matrix model has the ability of reflecting the plasticity of composites during large deformation. 0.00 0.02 0.04 0.06 0.08 0.10 0.12 0 50 100 150 200 250 t ru e s tr e s s (m p a ) true strain volume fraction exp.dat our model v f =0% v f =0.68% v f =1.88% v f =3.12% figure 5: comparison of the model description and experimental data [9] of the true stress-stain curves for cnt/al composite at different volume fractions (under quasi-static loading and at room temperature). the dependence of the flow stress of cnt/al composite on the volume fraction at different strains was shown in figure 6 so as to validate the new model based on experimental data [9]. it is obvious that there exists an extreme point in the strength of the composite with the variation of volume fraction. for the sample of cnt/al composite, its strength gets the maximum value at about 2.0 vol.% in experiments, and the model prediction of the maximum strength appears at 2.5 vol.%, showing a certain error with the experimental result but well describing the varying trend of the experimental data i c. gao et alii, frattura ed integrità strutturale, 33 (2015) 471-484; doi: 10.3221/igf-esis.33.52 481 within the whole range of volume fraction. obviously, the strength of the composite increases with the increasing volume fraction at relatively lower volume fractions, and then begins to drop when the volume fraction exceeds a critical point. the reason for this noticeable phenomenon should be resulted from the cluster effect of cnts which varies with volume fraction. the number of cnt clusters dramatically goes up at higher volume fraction for a large amount of cnts tend to entangle in the matrix, which is definitely detrimental to the mechanical properties of the composites. 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 50 100 150 200 250 300    t ru e s tr e ss ( m p a ) volume fraction v f (%) model prediction experimental data =0.10 =0.06 =0.03 figure 6: model validation by the experimental data [9] of the dependence of the flow stress of cnt/al composite on the volume fraction at different strains (under quasi-static loading and at room temperature). the predictions of the basic model [13] which does not consider the cluster effect as well as misorientation angle were presented in figure 7 at the volume fractions of 0.68 %, 1.88 % and 3.12 %, so as to demonstrate the correctness of the new model modified. it can be seen that the predicting curves monotonously increase with the increasing volume fraction of cnts, and that the predictive values at 3.12 vol.% are much higher than those of the experimental results in [9]. this is mainly caused by the ignorance of the cluster effect and imperfect interface influence in the basic model. the interfacial bonding between pure aluminum and cnts will be weaken due to the agglomeration of cnts, as a consequence, the effective load transfer between the al matrix and cnts will be seriously obstructed on the imperfect interface. thus, compared with the traditional model, it is obvious that the new model with consideration of the cluster effect can give satisfactory predictions. 0.00 0.04 0.08 0.12 40 80 120 160 200 240 280 f lo w s tr e ss ( m p a ) true strain predictions of the model in [13] v f =2.5% v f =1.5% v f =0.5% figure 7: the predictions of the basic model [13] without consideration of the cluster effect and misorientations at different volume fractions under quasi-static loading and at room temperature. model predictions and discussion the dependence of the model prediction of direct strengthening of cnt/al composite on the average aspect ratio of the primary length to diameter of cnts ( /l d ) was given in figure 8 at a strain of 0.04. it can be seen in the figure that the c. gao et alii, frattura ed integrità strutturale, 33 (2015) 471-484; doi: 10.3221/igf-esis.33.52 482 strengthening stress nonlinearly goes up with the increasing aspect ratio. the significant increase in strengthening with increasing length is obvious when the aspect ratio is less than 50 (or cnt length is less than 1 m at a given cnt diameter of 20 nm). however, the curve tends to an asymptote when the cnt length is greater than 1 m . in other words, beyond a critical length, the strengthening effect reaches a saturated value, which is consistent with the fact that the clustering of cnts rapidly increases with increasing aspect ratio. in addition, the strengthening increases with the decreasing cnt diameter at a given cnt length, as found in [15] with perfect bonding interface. 10 100 1000 0 20 40 60 80 100 aspect ratio of primary length to diameter of cnts (log (l /d )) model predictions cnt v f =2.0% cnt v f =1.5% cnt v f =1.0% s tr e n g th e n in g s tr e ss   ( m p a ) figure 8: the dependence of the strengthening stress of cnt/al composite on the average aspect ratio of primary length to diameter of cnts under different volume fractions at a strain of 0.04. the new model's predictions of the dependence of flow stress of the cnt/al composite on temperature at different volume fractions were presented under quasi-static and dynamic loading and at a strain of 0.04 in figure 9. a wide temperature range from low temperature (50k) to high temperature (1000k) was provided for the wide application conditions of mmncs. when the volume fraction of cnts is equal to 1.88 %, the flow stress under quasi-static loading descends about 75 mpa from room temperature to high temperature. and the flow stress of the cnt/al composite under high-strain-rate loading is about 80 mpa higher than that at quasi-static loading. 0 200 400 600 800 1000 0 50 100 150 200 250 300 350 -1=1000s   1=0.001s  f lo w s tr e s s (m p a ) temperature t(k) 0.68 vol.% cnt 1.88 vol.% cnt figure 9: dependence of the flow stress of cnt/al composite on temperature at different volume fractions under quasistatic and dynamic loading. the strain rate sensitivities of the flow stress of the cnt/al composite at different volume fractions were predicted under room and high temperature and at a strain of 0.04 in figure 10. it was indicated that the ascending trend of the flow stress with increasing logarithmic strain rate is basically linear at room temperature and somewhat nonlinear at high c. gao et alii, frattura ed integrità strutturale, 33 (2015) 471-484; doi: 10.3221/igf-esis.33.52 483 temperature. the flow stress of cnt/al composite will increase about 50-60 mpa from 3 110 s  to 3 110 s  , with a similar growth ratio to pure aluminum. thus, the strain rate effect of cnt-reinforced mmncs during plastic deformation should mainly be reflected in the metal matrix materials. -3 -2 -1 0 1 2 3 4 80 120 160 200 240 280 strain rate (log s -1 ) f lo w s tr e ss  m m n c ( m p a ) 0.68% cnt 1.88% cnt t=673k t=293k figure 10: strain rate sensitivities of the flow stress of cnt/al composite at different volume fractions under room and high temperature. conclusions n this paper, we have developed a new micromechanical constitutive model to capture the overall elasto-plastic response of carbon nanotube reinforced metal matrix nanocomposites. the significant influences of cnt clusters and misorientations on the mechanical properties of the nanocomposites were considered in the proposed model. the cluster effect was introduced into the new model by using the statistically-averaged equivalent length and diameter of cnt clusters with a logarithmic normal distribution, and the misorientation angle was considered by using an improved physically-based strength model of short fibre-reinforced composites. for the cnt/al nanocomposite, the new model was validated by experimental results first, and was also compared with the traditional model without considering the cluster effect. it was demonstrated that the new model is reasonable and reliable. the predictions of the new model of the cnt/al nanocomposite indicated that the strengthening stress nonlinearly goes up with the increasing aspect ratio of the length to diameter of cnts and eventually tends to a saturated value. in addition, the flow stress of the composite descends with increasing temperature under quasi-static and dynamic loading, while ascends with the increasing logarithmic strain rate basically linearly at room temperature and somewhat nonlinearly at high temperature. acknowledgements his research work was supported by the national natural science foundation of china (no. 11272286), the zhejiang provincial natural science foundation of china for distinguished young scholars (lr13e050001) and the open foundation of state key lab of explosion science and technology of china (no. kfjj14-9m). references [1] jarali, c.s., patil, s.f., pilli, s.c., lu, y.c., modeling the effective elastic properties of nanocomposites with circular straight cnt fibers reinforced in the epoxy matrix, j mater sci., 48 (2013) 3160-3172. [2] wang, x., yong, z.z., li, q.w., bradford, p.d., liu, w., tucker, d.s., cai, w., wang, h., yuan, f.g., zhu, y.t., ultrastrong, stiff and multifunctional carbon nanotube composites, mater res lett., 1 (2013) 19-25. i t c. gao et alii, frattura ed integrità strutturale, 33 (2015) 471-484; doi: 10.3221/igf-esis.33.52 484 [3] dastgerdia, j.n., marquis, g., salimi, m., micromechanical modeling of nanocomposites considering debonding and waviness of reinforcements, compos struct., 110 (2014) 1-6. [4] sridhar, i., narayanan, k.r., processing and characterization of mwcnt reinforced aluminum matrix composites, j mater sci., 44 (2009) 1750-1756. [5] habibi, m.k., paramsothy, m., hamouda, a.m.s., gupta, m., enhanced compressive response of hybrid mg–cnt nano-composites, j mater sci., 46 (2011) 4588-4597. [6] salimi, s., izadi, h., gerlich, a.p., fabrication of an aluminum–carbon nanotube metal matrix composite by accumulative roll-bonding, j mater sci., 46 (2011) 409-415. [7] joo, s.h., yoon, s.c., lee, c.s., nam, d.h., hong, s.h., kim, h.s., microstructure and tensile behavior of al and almatrix carbon nanotube composites processed by high pressure torsion of the powders, j mater sci., 45 (2010) 46524658. [8] rawal, s., metal-matrix composites for space applications, jom., 53 (2001) 14-17. [9] yang, x.d., shi, c.s., he, c.n., liu, e.z., li, j.j., zhao, n.q., synthesis of uniformly dispersed carbon nanotube reinforcement in al powder for preparing reinforced al composites, compos: part a., 42 (2011) 1833-1839. [10] liao, j.z., tan, m.j., sridhar, i., spark plasma sintered multi-wall carbon nanotube reinforced aluminum matrix composites, mater & design., 31 (2010) 96-100. [11] kim, k.t., cha, s., hong, s.h., hong, s.h., microstructures and tensile behavior of carbon nanotubes reinforced cu matrix nanocomposites, mater sci and eng a., 430 (2006) 27-33. [12] li, h., misra, a., horita, z., strong and ductile nanostructured cu-carbon nanotube composite, appl phys lett., 95 (2009) 071907. [13] courtney, t.h., mechanical behavior of materials, mcgraw-hill book co., singapore. (2000). [14] ryu, h.j., cha, s.i., hong, s.h.j., generalized shear-lag model for load transfer in sic/al metal-matrix composites, mater res., 18 (2003) 2851-2858. [15] barai, p., weng, g.j., a theory of plasticity for carbon nanotube reinforced composites, int j plasticity, 27 (2011) 539559. [16] morsi, k., esawi, a., effect of mechanical alloying time and carbon nanotubes (cnt) content on the evolution of aluminum (al)–cnt composite powders, j mater sci., 42 (2007) 4954-4959. [17] kwon, h.s., park, d.h., silvain, j.f., kawasaki, a., investigation of carbon nanotube reinforced aluminum matrix composite materials, compos sci technol., 70 (2010) 546-550. [18] esawi, a.m.k., borady, m.a.e., carbon nanotube-reinforced aluminum strips, compos sci technol., 68 (2008) 486492. [19] coleman, j.n., cadek, m., blake, r., nicolosi, v., ryan, k.p., belton, c., fonseca, a., nagy, j.b., gunko, y.k., blau, w.j., high-performance nanotube-reinforced plastics: understanding the mechanism of strength increase, adv funct mater., 14(8) (2004) 791-798. [20] villoria, r.g., miravete, a., mechanical model to evaluate the effect of the dispersion in nanocomposites, acta mater., 55 (2007) 3025-3031. [21] johnson, w.g., gilman, j.j., dislocation velocities, dislocation densities, and plastic flow in lithium fluoride crystals, j appl phys., 30 (1959) 129-144. [22] kocks, u.f., argon, a.s., ashby, m.f., thermodynamics and kinetics of slip, prog mate sci, 19 (1975) 1-281. [23] gao cy, zhang lc. a constitutive model for dynamic plasticity of fcc metals, mater sci eng a., 527 (2010) 31383143. [24] zhu, y.t., blumenthal, w.r., lowe, t.c., the tensile strength of short fibre-reinforced composites, j mater. sci., 32 (1997) 2037-2043. [25] luo, z.p., koo, j.h., quantifying the dispersion of mixture microstructures, j microscopy, 225 (2007) 118-125. [26] tyson, b.m., al-rub, r.k.a., yazdanbakhsh, a., grasley, z., a quantitative method for analyzing the dispersion and agglomeration of nano-particles in composite materials, compos: part b, 42 (2011) 1395-1403. [27] surappa, m.k., aluminium matrix composites: challenges and opportunities, sadhana, 28 (2003) 319-334. [28] kima, w.j., lee, s.h., high-temperature deformation behavior of carbon nanotubes (cnt)-reinforced aluminum composites and prediction of their high-temperature strength, compos: part a., 67 (2014) 308-315. [29] cha, s.i., kim, k.t., arshad, s.n., mo, c.b., hong, s.h., extraordinary strengthening effect of carbon nanotubes in metal matrix nanocomposites processed by molecular level mixing, adv mater, 17 (2005) 1377-1381. microsoft word 2261 p.h. nayak et alii, frattura ed integrità strutturale, 48 (2019) 370-376; doi: 10.3221/igf-esis.48.35 370 characterization and tensile fractography of nano zro2 reinforced copper-zinc alloy composites prasad h. nayak vtu rrc, belgaum, dept. of mechanical engineering, oxford college of engineering, bangalore, karnataka, india prasadnayak990@gmail.com h. k. srinivas dept. of mechanical engineering, sjbit, bangalore, karnataka, india madeva nagaral aircraft research and design centre, hindustan aeronautics limited, bangalore, karnataka, india madev.nagaral@gmail.com, http://orcid.org/0000-0002-8248-7603 v. auradi dept. of mechanical engineering, sit, tumkur, karnataka, india vsauradi@gmail.com abstract. nano particulates fortified metal lattice composites are finding extensive variety of utilizations in car and sports hardware fabricating businesses. in the present investigation, an endeavor has been made to create copper-zinc-nano zro2 particulates strengthened composites by utilizing fluid liquefy technique. 4, 8 and 12 wt. % of nano zro2 particulates were added to the cu-zn base grid. microstructural studies were finished by utilizing sem and eds examination. mechanical behavior of cu-zn-4, 8, 12 wt. % of nano zro2 composites were assessed according to astm benchmarks. checking electron micrographs uncovered the uniform dispersion of nano zro2 particulates in the copper zinc composite network. eds examination affirmed the nearness of zr and o components in nano zro2 strengthened composites. further, it was noticed that hardness, uts, yield quality of cuzn composite expanded with the expansion of 4, 8 and 12 wt. % of nano zro2 particulates. ductility of nano composites was decreased by adding zirconium oxide particulates. fractography of tensile specimens were carried out by using sem micrographs to understand the failure mechanisms. keywords. cu-zn alloy; nano zro2 particulates; liquid melt method; mechanical behavior; fractography. citation: prasad, h., n., srinivas, h, k., nagaral, m., auradi, v., characterization and tensile fractography of nano zro2 reinforced copper zinc alloy composites, frattura ed integritàstrutturale, 48 (2019) 370-376. received: 17.11.2018 accepted: 21.01.2019 published: 01.04.2019 copyright: © 2019 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. http://www.gruppofrattura.it/va/48/2261.mp4 p.h. nayak et alii, frattura ed integrità strutturale, 48 (2019) 370-376; doi: 10.3221/igf-esis.48.35 371 introduction he common name being composition material or simply a composite is combination of two or many materials with non-identical physical and chemical behaviors, when intermixed produces entirely different product with distinct characteristic when compared with the individual material characteristic. the blending of the material is usually done at a macroscopic level. these materials are intermixed in such a ratio that its certain properties get enhanced. the ratios of two materials are optimized based on their applications. these composites are used not only for their improvised mechanical properties, but also for thermal, electrical and environmental applications [1, 2]. these materials are generally preferred for different applications like concretes, reinforced plastics such as fiber reinforced polymers, metal composites, ceramic composites. ceramic matrix composites & metal matrix composites are generally used for bridges and structure such as boat house, panels of swimming pools, bodies of sports cars, bath tubs, and storage tanks & also advanced materials in spacecrafts & aircrafts building which are in high demand [3, 4]. the composites usually consist of fiber or particulate phase which is stronger & stiffer when compared with the matrix phase. the fiber or particulates commonly known as reinforcement phase have good mechanical, thermal & electrical properties when compared to the matrix phase [5]. nano metal matrix composites are gradually getting to be distinctly appealing materials for cutting edge aviation applications and yet their properties can be custom-made by the proper chose of reinforcement. among three different composites, particulate strengthened mmcs as of late discovered unique intrigue on account of their quality and firmness at a normal room and raised temperatures. it is important to note that the properties of the nano metal matrix are unequivocally affected by secondary parameters of the reinforcement, for example, shape, size, introduction, circulation and volume [6]. among any of other commonly used metals, copper is one characterized by the best thermal conductivity and resistance to corrosion which explains why it is commonly chosen in the first instance for metal material. on the other hand, having very low mechanical properties, it must be strengthened by ceramic particles, for example, which is one of the most reliable methods of reinforcement. copper based metal lattice composites (cmcs) have discovered more prominent applications in the field of car, air ships and machine apparatus enterprises attributable to their low thickness and associative high wear opposition, quality, consumption obstruction, firmness and warm conductivity. copper and its combination are to a great extent utilized as a material for heading [7, 8]. since copper-based materials have a relativity high temperature and low wear obstruction, the copper network has been effectively fortified with nano zirconium oxide and graphite particles, proceeds or irregular strands, called metal matrix composite (mmcs). there is a globally developing attention in assembling clay particulate fortified metal grid materials which forms joined properties of its fortifications and display enhanced physical and tribo-mechanical properties. in the present investigation, copper-10%zn amalgam-based composites were manufactured by stir process. nano zro2 particulates were utilized as the support. the 4, 8 and 12 wt. level of earthenware production fortifications were taken to create the copper-zro2 composites. the composites were tried for mechanical properties like hardness, extreme rigidity, yield quality and rate stretching according to astm guidelines. elements content wt. % cu 89.20 zn 9.90 others 0.90 table1: the chemical composition of cu-zn alloy experimental details he copper-zn-nano zro2 composites created in this investigation contains 4, 8 and 12 wt. % of artistic nano zro2 particulates. the density of copper-zinc compound is 8.737 g/cm3 and that of zro2 is 5.68 g/cm3. the density of composites diminishes with expansion of nano zro2 particulates. the concoction creation of copperzinc combination is appeared in the tab. 1. the fabrication of copper-zinc-zro2 composites was carried out by liquid metallurgy route via stir casting technique. the preparation of copper-zinc-nano zro2 composites was accomplished by two-stage stir casting technique. pre-calculated t t p.h. nayak et alii, frattura ed integrità strutturale, 48 (2019) 370-376; doi: 10.3221/igf-esis.48.35 372 quantity of cu-zn alloy ingots were charged into the heating furnace to liquefy. though the cu-zn alloy melts at 1080˚c, the melting furnace was superheated to a temperature of 1150˚c. thermocouples were used to measure temperature. the melt metal in crucible was then degassed to remove unwanted byproducts using a chemical called hexa-chloro-ethane (c2cl6) upto 3 mins. a steel impeller used was coated with a ceramic material known as zirconium which is used to agitate by rotating the molten metal such that the vortex is created. the process of stirring was carried out at a speed of 300 rpm & the impeller was immersed for about 60% height of molten metal from the top surface of melt within the crucible. simultaneously during the process of stirring the pre-calculated amount of reinforcement was added into the vortex in two-stages, to ensure good wet-ability stirring was continued for upto 5 mins. the reinforcing materials zro2 was preheated upto 500˚c in oven to remove moisture content before adding it into molten metal vortex. now, cu-zn alloy along with 4 wt. % zro2 particulates were poured into solid cast iron mould to get a composite after solidification. similarly, cu-zn-8 and 12 wt. % of zro2 composites were fabricated for the further studies. the microstructural analysis completed by utilizing sem instrument. tests around 5 mm thickness across taken from the casting samples and were cleaned appropriately. a reagent named keller's was utilized to etch the examples. hardness of as cast copper-zinc-zro2 amalgam composites were coordinated to know the influence of nano scale zro2 particles in the system material astm e 10 standard [11]. the cleaned precedents were striven for their hardness, using brinell hardness testing machine, which is having a ball indenter and applying a load of 250 kg and tolerate time of 30 seconds, three courses of action of readings were noted at better places of the sample and an average of all the value was used for figuring. the tensile properties of the prepared samples are established as per the astm e8 method upon tension test piece of gauge-diameter 9mm with gauge-length of 45mm. metal & its alloys are to be designed to provide material properties tailored to applications. universal testing machine (utm) is used to conduct tensile test to find out the effect of nano zro2 particulates on tensile behavior of cu-zn alloy composites. results and discussion microstructural analysis ig. 1(a) shows microstructure of as cast copper-10% zinc alloy, fig. 1b represents cu-zn-12 wt.% of nano zro2 composites. the sem micrographs reveal almost uniform distribution of zro2 particulates throughout the matrix as observed in the fig. 1b. uniformly distributed particulates increase the overall strength and other properties reducing the porosity of the mmc. fig. 2 is the eds spectrum of copper-zinc and 12 wt.% of nano zro2 reinforced composites. eds spectrum revealed the presence of nano zro2 particles in the copper-zinc alloy matrix in the form of zr and o elements along with cu and zn matrix elements. (a) (b) figure 1: sem micrographs of (a) as cast copper-zinc alloy (b) copper-12 wt. % zro2 composite f p.h. nayak et alii, frattura ed integrità strutturale, 48 (2019) 370-376; doi: 10.3221/igf-esis.48.35 373 figure 2: eds spectrum of copper-zinc-12 wt. % zro2 composite hardness measurements ardness is a property of a material that demonstrates the capacity of the material to oppose nearby plastic disfigurement. fig. 3 demonstrates the impact of the nano zro2 molecule substance on the hardness of the copper-zinc compound. the hardness esteems are decidedly related with the weight level of nano particles, since particles fortified the lattice. moreover, the outcomes demonstrate that nano particles fortified mmcs harder than copperzinc composite because of hall-petch and orowan fortifying components and in addition the great interface between the fortification and framework. copper-zinc and 12 wt. % nano zro2 composites demonstrate more hardness; the expansion in hardness of these composites can be ascribed to the scattering fortifying impact [13]. by including 12 wt. % nano zro2 particulates into the copper combination, the hardness of copper amalgam expanded to 85.4 bhn from 126.7 bhn. figure 3: showing the hardness of as cast copper-zinc alloy and nano zro2 composites tensile behavior ig. 4 and 5 demonstrating the tensile properties of copper-zinc combination and copper-zinc-4, 8 and 12 wt. % nano zro2 composite. fig. 4 demonstrating the ultimate strength (uts) of copper-10% zinc compound and zro2 composites. fig. 4 it is apparent that uts of copper-zinc-zro2 composite is much more than the base lattice h f p.h. nayak et alii, frattura ed integrità strutturale, 48 (2019) 370-376; doi: 10.3221/igf-esis.48.35 374 combination. by including 3, 8 and 12 wt. % of nano zro2 nano particulates to the base amalgam uts has expanded from 329.7 mpa to 435 mpa. from the fig. 4 it was discovered that yield quality of the copper-zinc base compound is 275.6 mpa and in copper-zinc-12 wt. % nano zro2 composite is 356.2 mpa. it demonstrated a change of 29 % in yield quality. the expansion in uts and ys is essentially because of solid holding between fortification particles and copper-zinc grid, plays an imperative role on the load exchanging from network to support. this is a result of grain refinement and molecule fortifying [14, 15]. the upgrades of quality are influenced by the higher load bearing and confound fortifying caused by nano zro2 particles. in contrast with the base copper, the immense improvement in the quality saw in the composites is because of the nearness of the particles as obstructions that confine the movement of separations caught by zro2 particulates. this will prompt increment the strength of the nano composites during tests. fig. 5 demonstrates the elongation of as cast copper-zinc amalgam and its composites. the rate prolongation was lessened in copper-zinc-zro2 composite when contrasted with the base combination. it very well may be seen from the diagram that the flexibility of the composites diminishes fundamentally with the 4, 8 and 12 wt. % nano zro2 fortified composites. this diminishing in rate prolongation in correlation with the base combinations is a most regularly happening burden in particulate fortified metal lattice composites. the lessened flexibility in copper-zinc-4, 8 and 12 wt. % composites can be ascribed to the nearness of zro2 particulates which may get broke and have sharp corners that make the composites inclined to confined break commencement and engendering. the embrittlement impact that happens because of the nearness of the hard-artistic particles causing expanded neighborhood stretch focus destinations may likewise be the reason [16]. figure 4: showing the ultimate tensile and yield strength of as cast copper alloy and copper-zinc-4, 8 and 12 wt. % nano zro2 composite. figure 5: showing the percentage elongation of as cast copper alloy and copper-zinc-4, 8 and 12 wt. % nano zro2 composite. fractography he study of fractured surface of alloys & its composites becomes necessary to find the cause of failure of the fabricated materials. there are two important things to be remembered during analysis of fractography, a ductile material when fails there is a formation of small dimple like structure in the broken areas whereas in case of brittle fractures there is transgranular (fracture through grains) or inter-granular (fracture through grain boundaries) failures which can be observed in sem images taken from a failed material. the fractured surfaces of copper-zinc along with 12 wt. % of nano zro2 composite resulted from tension tests, are shown in fig. 6 (a-b). fig. 6a represents the ductility fracture in copper-zinc alloy. sem analysis of the fractured surfaces shows the dimpled fracture surface for the reinforced & unreinforced material. t p.h. nayak et alii, frattura ed integrità strutturale, 48 (2019) 370-376; doi: 10.3221/igf-esis.48.35 375 (a) (b) figure 6: sem tensile fractured surfaces of (a) copper-zinc alloy (b) copper-zinc-12 wt.% of nano zro2 composites conclusions n this research, by using stir casting fabrication technique the nano zro2/copper-zinc nano composites have been fabricated by considering 4, 8 and 12 wt. % of reinforcement. the micro-structural analysis, major mechanical behaviors like hardness, ultimate and yield strength, percentage elongation, and fractography behavior of prepared samples are studied as per astm standards. the matrix is almost free from pores in as cast alloy and uniformly distributed of nano particles in the prepared composite, which is evident from sem microphotographs. the eds analysis confirms the presence of nano zro2 particles in the cu-zn alloy matrix. compared to unreinforced material the mechanical properties of cu-zn-4, 8 and 12 wt. % nano zro2 composite are superior and enhanced. due to strain localization, the fracture surface of the composite material consists of small voids. references [1] baradeshwaran, a., elaya perumal, a. (2014). study on mechanical and wear properties of al7075-al2o3-graphite hybrid composites, composites part:b, 56 , pp. 464-471. [2] mohsen, (2011). on the role of processing parameters in producing cu/sic metal matrix composites via friction stir processing: investigating microstructure, microhardness, wear andtensile behavior, materials characterization, 62, pp. 108-117. [3] suhas, j, quadros, d., vaishak, n. l., (2016). evaluation and characterization of tensile properties of short coated carbon fiber reinforced aluminium 7075 alloy metal matrix composites via liquid stir casting method, material science research india, 13(2), pp. 66-73. [4] naher, s., brabazon, d., looney, l. (2003). simulation of the stir casting process, journal of materials processing technology, 143-144(9), pp. 567-571. [5] zare, h., zahedi, m., toroghinejad, m. r., meratian, m., knezevic, m. (2016), compressive, shear, and fracture behavior of cnt reinforced al matrix composites manufactured by severe plastic deformation, materials and design, 106 , pp. 112-119. [6] bagheri et al., (2016). the effect of reinforcement percentages on properties of copper matrix composites reinforced with tic particles, journal of alloys and compounds, 676 , pp. 120-125. [7] doddamani, s., kallemulla, m. (2017). fracture toughness investigations of al6061-graphite particulate composite using compact specimens, frattura ed integrità strutturale, 41 , pp. 484-490. i p.h. nayak et alii, frattura ed integrità strutturale, 48 (2019) 370-376; doi: 10.3221/igf-esis.48.35 376 [8] nagaral, m., hiremath, v., auradi, v., kori, s, a., (2018). influence of two stage stir casting process on mechanical characetization of aa2014-zro2 nano composites, transactions of the indian institute of metals, 71(11), pp. 2845-2850. [9] nagaral, m., kalgudi, s., auradi, v., kori, s. (2018). mechanical characterization of ceramic nano b4c-al2618 alloy composites synthesized by semi solid processing, transactions of the indian ceramic society, 77(3), pp. 1-4. [10] manjunatha, t. h.., basavaraj, y., nagaral, m., venkataramana, v., (2018). investigations on mechanical behavior of al7075nano b4c composites, iop conf. series: materials scinece and engineering, 376, 012091. [11] pujar, v., srinivas, h, k., nagaral, m. (2018). processing and mechanical characterization of nano b4c particulates reinforced al2218 alloy composites, international journal of advanced mechanical engineering, 8(1), pp. 117-126. [12] nagaral, m., pavan, r., shilpa, p, s., auradi, v. (2017). tensile behavior of b4c particulate reinforced al2024 alloy metal matrix composites, fme transactions, 45(1), pp. 93-96. [13] unlu, s. (2009). investigation of tribological and mechanical properties of metal bearings, bulletin of materials science, pp. 451-457. [14] fazil, n., venkataramana, v., nagaral, m., auradi, v. (2018). synthesis and mechanical characterization of micro b4c particulates reinforced aa2124 alloy composites, international journal of engineering and technology uae, 7, pp. 225-229. [15] nagaraj, n., mahendra, k, v., nagaral, m. (2018). microstructure and evaluation of mechanical properties of al-7si flyash composites, materials toady proceedings, 5(1), pp. 3109-3116. [16] jadhav, p., sridhar, b, r., nagaral, m. (2018). a comparative study on microstructure and mechanical properties of a356-b4c and a356-graphite composites, international journal of mechanical and production engineering and development, 8(2), pp. 273-282. << /ascii85encodepages false /allowtransparency false /autopositionepsfiles true /autorotatepages /none /binding /left /calgrayprofile (dot gain 20%) /calrgbprofile (srgb iec61966-2.1) /calcmykprofile (u.s. web coated \050swop\051 v2) /srgbprofile (srgb iec61966-2.1) /cannotembedfontpolicy /error /compatibilitylevel 1.4 /compressobjects /tags /compresspages true /convertimagestoindexed true /passthroughjpegimages true /createjobticket false /defaultrenderingintent /default /detectblends true /detectcurves 0.0000 /colorconversionstrategy /cmyk /dothumbnails false /embedallfonts true /embedopentype false /parseiccprofilesincomments true /embedjoboptions true /dscreportinglevel 0 /emitdscwarnings false /endpage -1 /imagememory 1048576 /lockdistillerparams false /maxsubsetpct 100 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can be opened with acrobat and adobe reader 5.0 and later.) >> /namespace [ (adobe) (common) (1.0) ] /othernamespaces [ << /asreaderspreads false /cropimagestoframes true /errorcontrol /warnandcontinue /flattenerignorespreadoverrides false /includeguidesgrids false /includenonprinting false /includeslug false /namespace [ (adobe) (indesign) (4.0) ] /omitplacedbitmaps false /omitplacedeps false /omitplacedpdf false /simulateoverprint /legacy >> << /addbleedmarks false /addcolorbars false /addcropmarks false /addpageinfo false /addregmarks false /convertcolors /converttocmyk /destinationprofilename () /destinationprofileselector /documentcmyk /downsample16bitimages true /flattenerpreset << /presetselector /mediumresolution >> /formelements false /generatestructure false /includebookmarks false /includehyperlinks false /includeinteractive false /includelayers false /includeprofiles false /multimediahandling /useobjectsettings /namespace [ (adobe) (creativesuite) (2.0) ] /pdfxoutputintentprofileselector /documentcmyk /preserveediting true /untaggedcmykhandling /leaveuntagged /untaggedrgbhandling /usedocumentprofile /usedocumentbleed false >> ] >> setdistillerparams << /hwresolution [2400 2400] /pagesize [612.000 792.000] >> setpagedevice microsoft word numero_37_art_14 k. yanase et alii, frattura ed integrità strutturale, 37 (2016) 101-107; doi: 10.3221/igf-esis.37.14 101 focussed on multiaxial fatigue and fracture high cycle torsional fatigue properties of 17-4ph stainless steel k. yanase fukuoka university kyanase@fukuoka-u.ac.jp, http://www.fukuoka-u.ac.jp/english/ b.m. shönbauer university of natural resources and life sciences (boku) bernd.schoenbauer@boku.ac.at, https://www.boku.ac.at/en/ m. endo fukuoka university endo@fukuoka-u.ac.jp, http://www.fukuoka-u.ac.jp/english/ abstract. sensitivity to small defects under torsional fatigue loading condition is examined in the high cycle fatigue regime. fatigue crack initiation and small crack growth behaviors were observed during fatigue testing and fractographic investigations were performed. the results are compared to the data obtained in the uniaxial fatigue tests, which allows the effect of biaxial stresses on the surface of material to be discussed. finally, an approach for predicting the fatigue limit of 17-4ph stainless steel under torsional and tension-compression fatigue loadings is presented. keywords. 17-4ph; small defect; torsion; biaxial fatigue; fatigue limit. introduction recipitation-hardened chromium-nickel-copper stainless steel 17-4ph possesses high strength, toughness and good corrosion resistance. therefore, it is widely used in applications where good corrosion resistance as well as high strength are required, e.g., in the aerospace, chemical, food processing, paper and power industry. in the last few decades, a number of investigations on the uniaxial fatigue properties of 17-4ph have been performed; however, no results of torsional fatigue tests are presently available. in practice, there are several applications for the material in which components (e.g., bearing outer rings, propeller shafts and pressure safety valve springs) are exposed to torsional fatigue loading and where a high number of load cycles is accumulated within service life. given the substantial knowledge on uniaxial fatigue, it is of practical merit to propose a predictive method that can connect the fatigue strength under multiaxial loading with that under uniaxial loading. in our previous studies [1,2], a series of tension-compression fatigue tests were carried out to elucidate the uniaxial fatigue properties of 17-4ph stainless steel in the high and very high cycle fatigue regimes. it was found that the material exhibits interesting properties that are different from those noted for conventional steels. for example, the defect tolerance under cyclic loading is highly dependent on the notch root radius, which makes the prediction of the fatigue strength in the presence of small flaws challenging. p k. yanase et alii, frattura ed integrità strutturale, 37 (2016) 101-107; doi: 10.3221/igf-esis.37.14 102 as an extension of our previous work [1,2], further fatigue tests under torsional loading at r = ˗1 were conducted and the results yielded are reported in this paper. in particular, material sensitivity to small defects under torsional fatigue loading condition is examined in the high cycle fatigue regime. furthermore, fatigue crack initiation and small crack growth behavior were observed during fatigue testing and fractographic investigations were performed. the results are compared to the data obtained in the tension-compression fatigue tests and the effects of biaxial stresses on the surface of material are discussed. finally, the experimental data are evaluated to examine the predictive approach (cf. [3-7]) for the fatigue strength of 17-4ph stainless steel under torsional and tension-compression fatigue loadings. material and experiment he testing material used in the present investigation was a chromium-nickel-copper stainless steel 17-4ph precipitation hardened at 913 °c and age hardened at 621 °c for 4 h (condition h1150). the material properties at room temperature are summarized in tab. 1, and the average grain size is 11 m (independent of orientation). for more details, we refer to schönbauer et al. [1]. the surface of a round-bar specimen was ground and electropolished to remove the residual stress. artificial defects (onehole, two-hole, and three-hole, respectively) were introduced in the gage length of the specimen (length = 10 mm, fig. 1). the major axes of two-hole and three-hole defects were intentionally set to be perpendicular to the direction of the major principal stress. to remove any residual stresses that were possibly generated during drilling, the specimens were stressrelief annealed in a vacuum at 600°c for one hour. fatigue tests were performed by using a servohydraulic testing machine at stress ratio r = ˗1. tensile strength (mpa) yield strength (mpa) elongation (%) reduction of area (%) vickers hardness (kgf/mm2) 1030 983 21 61 352 table 1: mechanical properties of the 17-4ph at room temperature. figure 1: specimen shape and geometry for the torsional fatigue test. results and discussion n this section, the obtained experimental data are examined by considering the effects of the principal stresses on the surface of specimen and area [8]. here, area is defined as the square root of the projection area perpendicular to the major principal stress direction. furthermore, the characteristic properties of 17-4ph stainless steel are discussed. fatigue crack growth behavior concerning the one-hole defect (diameter = 100 µm, depth = 63 µm, area = 70 µm), all specimens failed from smooth part rather than originating from the hole. accordingly, this defect had no influence on the fatigue limit. however, small mixed mode cracks (mode iii and i) were observed at the bottom and at the edge of the hole, respectively, as shown in fig. 2. examination of the specimens with the two-hole defect (diameter = 2100 µm, depth = 131 µm, area = 161 µm) and the three-hole defect (diameter = 3100 µm, depth = 280 µm, area = 274 µm) showed that failure originated from t i k. yanase et alii, frattura ed integrità strutturale, 37 (2016) 101-107; doi: 10.3221/igf-esis.37.14 103 holes associated with mode i fatigue crack growth in the principal stress direction (i.e., 45 degrees from the specimen axis), as shown in fig. 3. figure 2: one-hole defect (a) before and (b) after fatigue testing at shear stress amplitude, a = 320 mpa and number of cycles, n = 2.8107 cycles. figure 3: mode i fatigue crack growth from a two-hole defect under torsional loading at shear stress amplitude, a = 290 mpa. 10 0 10 1 10 2 10 ‐13 10 ‐12 10 ‐11 10 ‐10 10 ‐9 10 ‐8 10 ‐7 stress intensity factor range k i  (mpam) c ra ck  g ro w th  r a te  d a /d n  ( m /c y cl e ) * for torsional loading, the crack is assumed as a semicircular crack fitting curve torsion tension‐compression figure 4: fcgr curves for mode i crack under torsional loading and tension-compression loading [9]. specimen axis specimen axis k. yanase et alii, frattura ed integrità strutturale, 37 (2016) 101-107; doi: 10.3221/igf-esis.37.14 104 in fig. 4, the fatigue crack growth rate (fcgr) under torsional loading is compared to that under tension-compression loading [9]. it is noted that, for torsional loading, the stress intensity factor range is calculated by assuming a semi-circular crack. as shown, fcgr can be uniquely characterized irrespective of the difference of loading condition. however, the crack shape is not necessarily semi-circular, as was noted for a medium carbon steel (jis s35c) (fig. 5, [10]). accordingly, a further study is necessary to inspect the evolution of crack shape and its effect on the torsional fatigue behavior of 174ph. figure 5: crack profile propagating from an artificial defect in a medium carbon steel (jis s35c) under torsional loading (r = ˗1) [10]. fatigue limit by considering the major principal stress 1 and the minor principal stress 2 on the surface of material, the fatigue limit can be expressed as [3]:       1 2 w 1/6 1.43( 120) ( ) k hv area (1) where hv signifies the vickers hardness. under torsional loading, the principal stresses are rendered as  1 and   2 (fig. 6). therefore, eq. (1) can be rewritten to yield:            w w1/6 1/6 1.43( 120) 1.43( 120)1 (1 ) 1( ) ( ) hv hv k karea area (2)    two‐hole defect applied torque applied torque figure 6: stress transformation on the specimen surface (cf. fig. 3). k. yanase et alii, frattura ed integrità strutturale, 37 (2016) 101-107; doi: 10.3221/igf-esis.37.14 105 according to the previously reported results [3-7],  0.18k holds for carbon steels, cr-mo steel, ductile cast irons, and high tension brass. if the effect of biaxial stress is negligible (i.e.,  0k ), the torsional fatigue limit is solely determined by the major principal stress as follows (cf. fig. 6):     w w1/6 1.43( 120) ( ) hv area (3) on the other hand, schönbauer et al. proposed that the fatigue limit in the presence of a large defect or a long crack can be estimated by the following equation [2]:      th,lc w 2 0.65 k area (4) where the threshold stress intensity factor range of th,lcδk =6.7 mpa m for the investigated 17-4ph steel at r = ˗1 was determined by schönbauer et al. [9]. fig. 7 shows the relationship between the shear stress amplitude a and area . when a specimen endured the number of cycles n = 1.2107, it was regarded as a run-out specimen. as shown, the prediction for fatigue limit with k = 0 (fig. 7(b)) renders higher correlation to the experimental data than using k = ˗0.18 (fig. 7(a)). further, for the torsional loading, fatigue limit can be reasonably estimated by the two prediction lines:   0.6 (1.6 )a hv and the threshold for long crack (cf. eq. (4)). 10 1 10 2 10 3 100 150 200 250 300 350 400 area (m) s h e a r  st re ss  a m p li tu d e ,   a  ( m p a ) "1‐hole defect" "2‐hole defect" "3‐hole defect"  a  = 0.6(1.6hv) threshold for long crack area parameter model  with "k = ‐0.18" failure run‐out prediction for fatigue limit (a) prediction with k = ˗ 0.18 (b) prediction with k = 0 figure 7: relationship between shear stress amplitudea and area . in fig. 8, fatigue limit for torsional loading and tension-compression loading is compared [2]. it is noted that, in the tension-compression data, various types of defects are considered (e.g., drilled hole, circumferential notch, corrosion pit). as shown, the respective fatigue limit can be reasonably estimated by considering the major principal stress (i.e., k = 0) and area . the torsional fatigue limit becomes insensitive to the defect when  100μmarea , which is in strong contrast 10 1 10 2 10 3 100 150 200 250 300 350 400 area (m) s h e a r  st re ss  a m p li tu d e ,  a  ( m p a ) "1‐hole defect" "2‐hole defect" "3‐hole defect"  a  = 0.6(1.6hv) threshold for long crack area parameter model with "k = 0"              failure run‐out prediction for fatigue limit k. yanase et alii, frattura ed integrità strutturale, 37 (2016) 101-107; doi: 10.3221/igf-esis.37.14 106 to that for tension-compression loading. concerning the tension-compression loading, the area parameter model (cf. eq. (3)) can be used for 17-4ph when  100μmarea , which is much less than area < 1000 µm for the conventional carbon steels. fig. 8 clearly shows that the aforementioned one-hole defect ( area = 70 µm) has negligible influence on fatigue limit under torsional loading. finally, as some experimental data significantly deviate from the prediction line, a further study is necessary to elucidate the reasons behind these discrepancies. 10 1 10 2 10 3 0 100 200 300 400 500 600 area (m) s tr e ss  a m p li tu d e  ( m p a )  a  = 1.6hv  a  = 0.6(1.6hv) threshold for long crack area parameter model with k = 0                torsion tension‐compression failure run‐out prediction for fatigue limit failure run‐out prediction for fatigue limit figure 8: relationship between stress amplitude and area . conclusions n this study, the torsional fatigue behavior of precipitation-hardened chromium-nickel-copper stainless steel 17-4ph was investigated in the presence of small defects. it was shown that the dimensions of defects can be evaluated by the square root of the projection area perpendicular to the major principal stress direction, area . the results pertaining to the fatigue crack growth behavior and fatigue limit demonstrate that the effect of biaxial stress on the surface of specimen is negligible and the major principal stress governs the fatigue behavior under torsional loading. references [1] schönbauer, b.m., yanase, k. and endo, m., vhcf properties and fatigue limit prediction of precipitation hardened 17-4ph stainless steel, int. j. fatigue, 88 (2016) 205-216. doi: 10.1016/j.ijfatigue.2016.03.034. [2] schönbauer, b.m., yanase, k. and endo, m., to be submitted to int. j. fatigue. [3] endo, m. and ishimoto, i., the fatigue strength of steels containing small holes under out-of-phase combined loading, int. j. fatigue, 28 (2006) 592-597. doi: 10.1016/j.ijfatigue.2005.05.013. [4] endo, m. and ishimoto, i., j. solid mech. mater. engng. (jsme), 1 (2007), 343-354, doi: 10.1299/jmmp.1.343. [5] yanase, k., a study on the multiaxial fatigue failure criterion with small defects, astm mater. perform. charact., 2 (2013) 1-9. doi: 10.1520/mpc20130013. [6] yanase k., endo m., multiaxial high cycle fatigue threshold with small defects and cracks, engng. fract. mech., 123 (2014) 182-196. doi: 10.1016/j.engfracmech.2014.03.017. i k. yanase et alii, frattura ed integrità strutturale, 37 (2016) 101-107; doi: 10.3221/igf-esis.37.14 107 [7] endo, m., yanase, k., effects of small defects, matrix structures and loading conditions on the fatigue strength of ductile cast irons, theor. appl. fract. mech., 69 (2014) 34-43. doi: 10.1016/j.tafmec.2013.12.005. [8] murakami, y., metal fatigue: effects of small defects and nonmetallic inclusions, elsevier, oxford (2002), chapter 4 – effects of size and geometry of small defects on the fatigue limit. doi: 10.1016/b978-008044064-4/50004-9. [9] schönbauer, b.m., stanzl-tschegg, s.e., perlega, a., salzman r.n., rieger, n.f., turnbull, a., zhou, s., lukaszewicz, m., gandy, d., the influence of corrosion pits on the fatigue life of 17-4ph steam turbine blade steel, engng. fract. mech., 147 (2015) 158-175. doi: 10.1016/j.engfracmech.2015.08.011. [10] ikeda, s. the effects of biaxial stress and stress gradient on fatigue crack growth behavior, master thesis (2008), fukuoka university. << /ascii85encodepages false /allowtransparency false /autopositionepsfiles true /autorotatepages /none /binding /left /calgrayprofile (dot gain 20%) /calrgbprofile (srgb iec61966-2.1) /calcmykprofile (u.s. web coated \050swop\051 v2) /srgbprofile (srgb iec61966-2.1) /cannotembedfontpolicy /error /compatibilitylevel 1.4 /compressobjects /tags /compresspages true /convertimagestoindexed true /passthroughjpegimages true /createjobticket false /defaultrenderingintent /default /detectblends true /detectcurves 0.0000 /colorconversionstrategy /cmyk /dothumbnails false /embedallfonts true /embedopentype false /parseiccprofilesincomments true /embedjoboptions true /dscreportinglevel 0 /emitdscwarnings false /endpage -1 /imagememory 1048576 /lockdistillerparams false /maxsubsetpct 100 /optimize true /opm 1 /parsedsccomments true /parsedsccommentsfordocinfo 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can be opened with acrobat and adobe reader 5.0 and later.) >> /namespace [ (adobe) (common) (1.0) ] /othernamespaces [ << /asreaderspreads false /cropimagestoframes true /errorcontrol /warnandcontinue /flattenerignorespreadoverrides false /includeguidesgrids false /includenonprinting false /includeslug false /namespace [ (adobe) (indesign) (4.0) ] /omitplacedbitmaps false /omitplacedeps false /omitplacedpdf false /simulateoverprint /legacy >> << /addbleedmarks false /addcolorbars false /addcropmarks false /addpageinfo false /addregmarks false /convertcolors /converttocmyk /destinationprofilename () /destinationprofileselector /documentcmyk /downsample16bitimages true /flattenerpreset << /presetselector /mediumresolution >> /formelements false /generatestructure false /includebookmarks false /includehyperlinks false /includeinteractive false /includelayers false /includeprofiles false /multimediahandling /useobjectsettings /namespace [ (adobe) (creativesuite) (2.0) ] /pdfxoutputintentprofileselector /documentcmyk /preserveediting true /untaggedcmykhandling /leaveuntagged /untaggedrgbhandling /usedocumentprofile /usedocumentbleed false >> ] >> setdistillerparams << /hwresolution [2400 2400] /pagesize [612.000 792.000] >> setpagedevice microsoft word numero_61_art_20_3443.doc r. elsadany et alii, frattura ed integrità strutturale, 61 (2022) 294-307; doi: 10.3221/igf-esis.61.20                                                        294 x effect of gfrp and steel reinforcement bars on the flexural behavior of rc beams containing recycled aggregate rasha a. el-sadany egyptian atomic energy authority, national center for radiation research and technology, egypt rasha_sadani@yahoo.com, http://orcid.org/0000-0002-1506-5232 sherif h. al-tersawy higher technological institute 10th of ramadan city, egypt al_tersawy@hotmail.com, http://orcid.org/0000-0001-5880-5088 hossam el-din m. sallam faculty of engineering, zagazig university, egypt hem_sallam@yahoo.com, http://orcid.org/0000-0001-9217-9957 abstract. concrete containing wastes from the demolition of old deteriorated buildings are produced enormously. concrete is a brittle matrix that is usually reinforced by ductile reinforcement such as steel bars. however, due to the susceptibility of steel to corrosion, fiber-reinforced polymers (frp) bars are used as an alternative reinforcement. the main drawback of frp bars is their brittleness. these two types of reinforcements, i.e., steel and glass frp (gfrp) bars, have been used in the present work. the flexural behavior of twelve rc beams reinforced with different ratios of gfrp or steel areas containing recycled aggregate has been experimentally studied and compared with beams without recycled aggregate. the present results show that beams reinforced with gfrp and containing recycled aggregate exhibit a lower loadcarrying capacity, lower the first crack, and the highest deflection. all gfrp rc beams exhibited brittle failure, i.e., concrete crushing in the compression zone, except one beam, with 2�16 bars and concrete without recycled aggregate, which ruptured gfrp bars. however, ductile failure modes are observed for all beams reinforced with steel bars, i.e., yielding in steel bars followed by concrete failure. the novelty and advantage of the present results are that the large deflection of gfrp rc beams represents enough warning before failure, as found in ductile rc beams. keywords. recycled aggregates; gfrp bars; steel bars; rc beam. citation: elsadany, r.a., tersawy, s.h., sallam, h.e.m, effect of gfrp and steel reinforcement bars on the flexural behavior of rc beams containing recycled aggregate frattura ed integrità strutturale, 61 (2022) 294-307. received: 30.01.2022 accepted: 01.06.2022 online first: 05.06.2022 published: 01.07.2022 copyright: © 2022 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. https://youtu.be/c_bm5s-gx1k r. elsadany et alii, frattura ed integrità strutturale, 61 (2022) 294-307; doi: 10.3221/igf-esis.61.20  295 introduction ao et al. [1] stated that most of the total solid waste produced in the world is construction and demolition waste. recycling such solid waste is considered an environmental challenge [2-3]. recycled aggregate is a sustainable solution for the environmental depletion of the construction sector [4]. therefore, using this recycled solid waste to partially replace aggregates in concrete manufacturing has attracted considerable attention from many researchers [5-7]. the workability of the recycled concrete is reduced due to an increase in coarse aggregate porosity, and additional water may be required to get the same slump [8]. the microstructure of the interfacial transition zone (itz) depends mainly on the w/c ratio of the new paste; moreover, the itz of the concrete made with recycled aggregate is influenced by the pre-saturation water, which can be released into the new paste, disrupting its microstructure [9]. when the recycled aggregate replacement level is increased by weight, the compressive strength decreases for normal, medium, or highstrength concrete [10]. also, the concrete made with 10% recycled aggregate is weaker than concrete made with natural aggregate at the same water to cement ratio. this may be due to the influences of crushing types on recycled aggregates characteristics. the method of preparing recycled aggregate for mixing concrete influences the concrete workability when using different percentages of coarse recycled aggregate content (0%, 50%, and 100%). when using recycled aggregate that is water-saturated and a surface dry, similar workability is achieved. besides, the same workability can be achieved after a prescribed time when using dried recycled aggregate and adding additional water during the concrete mix. the time taken to achieve the same workability is called the additional water time. the amount of recycled aggregate affects the amount of water absorption of concrete. this means that the increase of the recycled aggregate amount will proportionally increase the amounts of water absorption. otherwise, increasing the recycled aggregate to 100% leads to an increase in the compressive strength up to 25% and increases the deflection to 4% [11]. this discrepancy may appear because the recycled aggregate was made by crushing waste concrete of laboratory test cubes and precast concrete columns. the corrosion problem is initiated in hot countries such as the middle east due to hot weather and high level of humidity [12]. frp reinforcement emerged as a practical solution because of its non-corrosive properties, high strength-to-weight ratio, and good fatigue resistance [13]. due to this brittle nature of frp, it was recommended to direct the flexure members to fail in compression rather than fail in tension [14, 15]. in such brittle characteristics, this type of failure is less catastrophic and more progressive. to determine the deflection of frp reinforced beams, most code guidelines adopted a simple elastic method, branson’s equation [16], and an effective moment of inertia equation to describe the reduced stiffness of cracked sections. the effective moment of inertia originally modified by aci 316 [16] was adopted by aci 440.1r-06 [17]. most experimental results of gfrp reinforced beams in the literature [18-20] showed higher ultimate moment capacities than those predicted by most code guidelines. when using high-strength concrete in gfrp reinforced beams, a brittle behavior, sudden failure, and fewer width cracks were observed compared to beams made of normal concrete [21]. in ref. [22], it was shown that cfrp-reinforced concrete beams' performance and behavior are comparable to the conventional steel-reinforced concrete beams. a new proposed tension stiffening model for concrete members reinforced with gfrp predicted significantly better experimental results than the existing models [23]. considering the shear performance of steel-reinforced concrete beams cast with recycled aggregate [24], an equation for estimating the shear was proposed. it showed satisfactory results when verified against the experimental results. a study of the effect of recycled aggregate on the behavior of structural beams in flexure, shear, and bond showed a minimum difference in the peak load and load-deflection behavior attributed to the percentage replacement of natural concrete aggregate with recycled concrete aggregate [25]. it is worth noting that hamad et al. [25] carried out a bond splitting (bond beams) test to measure the bond strength. research significance ptimal use of recycling construction and demolition waste in the concrete industry is one of the most important environmental challenges. this research work attempts to understand the behavior of reinforced concrete (rc) containing recycled coarse aggregate (rca) from demolition waste either with ductile or brittle reinforcement. the characteristics of gfrp made by a manual method are tested. the characteristics of concrete made with the rca from demolition were also studied and compared to the characteristics of new concrete, i.e., concrete with the natural r o r. elsadany et alii, frattura ed integrità strutturale, 61 (2022) 294-307; doi: 10.3221/igf-esis.61.20                                                        296 coarse aggregate (nca). finally, a comparative study was made between the behavior of beams reinforced with steel reinforcements new concrete and beams reinforced with the manually made gfrp bars and the recycled aggregate. experimental program he experimental program was divided into three stages. the first stage was the fabrication and testing of gfrp bars. a manual method was used in the fabrication of gfrp bars. samples of the fabricated bars are tested in tensile and bond strength to get the gfrp mechanical characteristics. in the second stage, a comprehensive experimental test was carried out to measure the properties of both new concrete and concrete containing rca. the flexural characteristics of the gfrp and steel-reinforced beams made with 11 recycled and new concrete were studied in the last stage. four main aspects were studied, load-carrying capacity, deflection, load at first crack, and failure mode. the materials used in this research were natural sand, natural crushed stone (dolomite) for new concrete, dolomite-based crushed concrete as the source of recycled aggregate, ordinary portland cement, steel bars, and gfrp bars. fabrication of gfrp bars gfrp bars were fabricated in the experimental program using a hand lay-up technique [26]. this was done by stretching the thread of glass fiber between two hooks. the homopolymer polypropylene series resin used was fabricated in vetrotex company, usa. it consists of two main components, polyesters and hardeners. the physical and mechanical properties of the used glass fiber and resin are listed in table 1. the relation between the number of rolls and the final diameter of the bars was deduced, as listed in table 2. materials specific gravity tensile elongation % tensile strength (mpa) flexural strength (mpa) tensile modulus (gpa) flexural modulus (gpa) glass fiber 2.54 4.5% 3250 -69 - resin --140 210 -7.5 table 1: the physical and mechanical properties of the glass fiber and resin as reported by the manufacturer. no. of rolls* bar diameter 35 10 mm 45 12 mm 65 16 mm table 2: relation between the number of rolls and diameter of gfrp bars (*the weight of one batch of rolls equal 20 kg). for every 1 m of gfrp bars, the resin polyester was pushed with a 150 gm force using the movable hook. to press out the excessive quantity of the used resin, the movable arm will rotate and pull out the fibers to make it twisted fiber after being saturated with resin. when the clear distance between the two hooks reaches the required length, the process may be stopped [26], as shown in fig.1. after sufficient curing of the gfrp bars, samples of bars were taken to examine their tensile and bond characteristics. samples from gfrp bars having a length of 1.2 meters each were tested in tension to get tensile strength and young's modulus to use these characteristics in the design equations of beams [27]. using a standard procedure of pullout test according to astm d7913 [28], the bond strength specimens’ tests were made to all gfrp bars diameters; 10, 12, 16 mm. three samples representing each nominal diameter (10, 12, 16 mm) were tested to get the bond strength of the gfrp bars. during the fabrication of bars, no coating material was glued to the surface of bars to increase t r. elsadany et alii, frattura ed integrità strutturale, 61 (2022) 294-307; doi: 10.3221/igf-esis.61.20  297 the bond strength between gfrp bars and the surrounding concrete. the bonding response was dependent completely on the normal surface of bars as resulted from initial fabrication. a) the device for fabricating gfrp bars b) continuous fibers are tensioned between 2 hooks. c) saturating the fibers with the resin. d) pulling out and twisting the fibers to squeeze out the excessive amount of the resin. figure 1: fabrication processes of gfrp bars. properties of concrete with and without rca in this stage, a natural crushed stone (dolomite) was used as a coarse aggregate, which is common and available in egypt. dolomite had a specific weight of 2.61, a bulk density of 1.65 t/m3, water absorption, and 2.05%. fine aggregate (sand) had a specific weight of 2.36 and bulk density of 1.7 t/m3. recycled coarse aggregate had a specific weight of 2.41, bulk density of 1.74 t/m3, and water absorption of 5.51%. the cement used was cemi42.5n. for both recycled and new concretes, the compressive strength in 7 days and 28 days and indirect tensile strength in 28 days was determined. the tests were made according to astm c469-96 [29] and astm c469-94 [30], respectively. the mix design of new and recycled concrete was summarized in table 3. type of concrete cement (kg) natural coarse agg. (kg) recycled coarse agg. (kg) fine agg (kg) w/c new concrete 416.7 992 0 724.5 0.48 recycled concrete 416.7 496 496 724.5 0.48 table 3: mix design of new and recycled concrete. preparation of beams in this stage, gfrp rc beams and s te el r c be ams w ith and w it hout rca we re pr e pa red. a three-point bend test was adopted to determine the first crack, deflection, load carrying capacity, and failure mode of rc beams as a function of reinforcement type (gfrp and steel rods) and matrix type (concrete with and without rca). the twelve beams were categorized into three series; each series was composed of four beams with identical reinforcement areas but different types of reinforcement (gfrp and steel rods) and different types of concrete (with and without rca). in the first series, r. elsadany et alii, frattura ed integrità strutturale, 61 (2022) 294-307; doi: 10.3221/igf-esis.61.20                                                        298 tensile reinforcement was 2ф16 mm, while top reinforcement was 2ф10 mm. in the second series, tensile reinforcement was 4ф16 mm, while top reinforcement was 2ф12 mm. in the third series, tensile reinforcement was 6ф16 mm, while top reinforcement was 3ф12 mm. all beams had 2200 mm long provided with f8 mm steel stirrups at 167 mm center to center (6ф8/m), 2000 mm span, 240 mm depth, and 150 mm width. the experimental setup, instrumentation, and details of the test beams are shown in fig. 2. details of reinforcements of all beams are listed in table 4. (a) the test set up and instrumentation of beams (b) (c) details of beams figure 2: the test setup, instrumentation, and details of beams table 4: details of reinforced concrete beams (*identification codes: b: beam; n: new concrete; r: recycled concrete; g: gfrp bars; s: steel bars; 1, 2, and 3: series number). beams* bottom (tensile) reinforcement top (compression) reinforcement bng1 2 gfrp rods 16 2 gfrp rods  10 brg1 bns1 2 steel rods 16 2 steel rods  10 brs1 bng2 4 gfrp rods  16 2 gfrp rods  12 brg2 bns2 4 steel rods  16 2 steel rods  12 brs2 bng3 6 gfrp rods  16 3 gfrp rods  12 brg3 bns3 6 steel rods 16 3 steel rods  12 brs3 4 beams-series1 4 beams-series2 4 beams-series3 2 4 0 m m 150 mm 2 4 0 m m 150 mm 2 4 0 m m 150 mm 25 mm 2200 mm 2 4 0 2000 mm 100100 dial gauge p r. elsadany et alii, frattura ed integrità strutturale, 61 (2022) 294-307; doi: 10.3221/igf-esis.61.20  299 mechanical properties of reinforcements and concretes three samples from each nominal diameter (10, 12, and 16 mm) were tested to get its tensile characteristics. the mechanical properties of steel bars are summarized in table 5. the results of tensile and bond strength of gfrp bars are presented in table 6. as expected, the gfrp bars had a typical linear behavior up to failure, i.e., exhibited brittle failure, as shown in fig. 3. for all nominal diameters, the ultimate tensile strength (uts) of gfrp bars is higher than those corresponding in steel bars, as shown in tables 5 and 6. steel bars nominal diam. (mm) 10 12 16 yield stress (mpa) 360 430 510 uts (mpa) 415 520 600 table 5: tensile properties of steel bars. 0 100 200 300 400 500 600 700 0.000 0.005 0.010 0.015 0.020 0.025 0.030 s tr e s s ( m p a ) strain (mm/mm) sam ple (1) sam ple (2) sam ple (3) gfrp 12 mm figure 3: stress-strain curve of 2 gfrp. nominal/actual ave. diam. (mm) average tensile strength (mpa)/ (coefficient of variation (%) average bond strength (mpa)/ (coefficient of variation (%) 10/10.23 435.6 / (5.1%) 7.0 / (4.3%) 12/12.32 597.3 / (7.2%) 5.0 / (9.2%) 16/16.5 620.4 / (7.6%) 3.1 / (8.0%) table 6: tensile and bond strength of gfrp bars. fig. 4 shows new and recycled concrete's compressive and tensile strengths at 7 and 28 days. it is shown that the compressive strength of concrete with rca was less than those of concrete without rca by 28.8 % and 13.3 % for 7 and 28 days, respectively. furthermore, it was found that the 28 days tensile strength of concrete with rca was less than that of concrete without rca by 30 %. this reduction may be attributed to the presence of the cement paste or a certain amount of mortar surrounding the particles of rca. the percentage of water absorption of concrete with rca was 60% higher than that of concrete without rca. this may be due to the attached mortar around the rca particles. these observations are in agreement with the results obtained in the literature [31]. structural behavior of rc beams the experimental results of all tested beams (first crack, deflection, load-carrying capacity, and mode of failure) are r. elsadany et alii, frattura ed integrità strutturale, 61 (2022) 294-307; doi: 10.3221/igf-esis.61.20                                                        300 summarized in table 7. in general, the first crack load and ultimate load of all rc beams containing rca are lower than those of corresponding rc beams without rca. the opposite trend was observed for maximum deflection. 242.7 173.7 401.7 348.2 74.33 52 0 50 100 150 200 250 300 350 400 450 normal c.agg. recycled c.agg. s tr en g th ( n /m m 2 ) comp. st rengt h (7 days) comp. st rengt h (28 days) tensile st rengt h (28 days) figure 4: compressive and tensile strength of concrete with and without rca. beam first crack load (kn) ultimate load, pult, (kn) maximum deflection (mm) pult-rca/pult-nca for beams failed due to concrete crushing failure mode bng1 15 57 27 rupture in frp brg1 12 54 35 n/a concrete crushing bns1 18.5 70 22 yielding in steel followed by concrete crushing brs1 15 63 25 0.90 yielding in steel followed by concrete crushing bng2 21 70 25 concrete crushing brg2 17 62 32 0.89 concrete crushing bns2 28 79 18 yielding in steel followed by concrete crushing brs2 24 78 22 0.99 yielding in steel followed by concrete crushing bng3 31 79 23 concrete crushing brg3 25 72 31 0.91 concrete crushing bns3 39 89 17 yielding in steel followed by concrete crushing brs3 28 85 19 0.96 yielding in steel followed by concrete crushing table 7: flexural test results of all rc beams in the beginning, a comparison between the measured values of ultimate loads of gfrp rc beams and those predicted by the aci 440.1r-06 provision [17] was made. the approach of the aci code was based on the forces equilibrium, strain compatibility of sections and considers the equivalent stress block. the equations of moment capacity depend on whether the reinforcement ratio is lesser or higher than the balanced ratio: r. elsadany et alii, frattura ed integrità strutturale, 61 (2022) 294-307; doi: 10.3221/igf-esis.61.20  301  ff a bd (1) ' 10.85      f cuc fb fu f cu fu ef f e f (2) when  f fb 10.8 2        b n f fu c m a f d (3)           cu b cu fu c d (4) when 1.4 f fb  2 ' 10.85 0.5 4                   f cu c f f cu f cu fu f e f f e e f (5) 2       n f f a m a f d (6) '0.85  f f c a f a f b (7) also nm can be calculated from 2 ' 1 0.59          f fn f f c f m f bd f (8) theoretical and experimental ultimate loads are compared in table 8. there is a good agreement between them. crack pattern and mode of failure crack pattern and mode of failure of steel rc beams are typical of under-reinforced rc beam behavior, as shown in fig. 5. a and b. the first crack loads ranged from 15 to 39 kn based on the tensile reinforcement ratio and concrete type, see table 7. in general, steel rc beams with rca had lower first crack loads than steel rc beams without rca, as listed in table 7. flexural cracks propagate upwards as loading progress but remain very narrow throughout the loading history. with increasing load, flexural-shear cracks initiated propagated towards the point of load. with a further increase in the applied load, crushing of concrete at the top compression side around the point of load application occurred at the ultimate load after yielding steel reinforcement. on the other hand, all gfrp rc beams failed due to concrete crushing in the compression zone, i.e., brittle failure, except beam bng1, which failed due to the rupture of tensile gfrp bars, i.e., catastrophic failure, fig. 5. c-e. r. elsadany et alii, frattura ed integrità strutturale, 61 (2022) 294-307; doi: 10.3221/igf-esis.61.20                                                        302 beam code pu aci 440 (kn) pu exp. (kn) pu exp. /pu aci 440 bng1 56 57 1.02 bng 2 66 70 1.06 bng 3 77 79 1.03 brg 1 56 54 0.96 brg 2 61 62 1.02 brg 3 70 72 1.03 table 8: ultimate theoretical and experimental loads. figure 5: crack pattern and mode of failure of rc beams. in the case of gfrp rc beams, the failure mode of beams may be predicted by computing the gfrp reinforcement ratio and comparing it to the balanced gfrp reinforcement ratio from equations (1) and (2). the ratio of the balanced frp reinforcement was a ratio when the crushing in the concrete happened at the same time as the rupture in frp when the ratio of frp reinforcement is less than the balanced ratio, (ρf < ρfb ), the failure mode is expected to be a rupture in frp. (a) (b) (c) (e) (d) r. elsadany et alii, frattura ed integrità strutturale, 61 (2022) 294-307; doi: 10.3221/igf-esis.61.20  303 oppositely, when the balance ratio of the frp reinforcement is less than the ratio of the frp reinforcement (ρfb < ρf), the mode of failure is expected to be crushing of concrete at the top middle part of the beam. it may be noted that the balanced ratio for frp reinforcement ρfb is lower than the balanced ratio for steel reinforcement ρb [32-34]. beam bng1 (2 #16) had a gfrp reinforced ratio of ρf = 0.0112, which is less than the balanced ratio (ρfb) =0.0116. the first crack at the tension face of the beam appeared at 12 kn. when increasing the load, another crack in the tension face appeared. after that, the shear cracks almost 45 degrees. at a load of 57 kn, the beam failed due to gfrp rupture, see fig. 5.c. beams bng2 and bng3 were made of new concrete and had a reinforced ratio of frp bars ρf = 0.0223 and 0.033, respectively. both ratios were bigger than the balanced ratio, and the first cracks appeared at mid-span at the loads 17 kn and 25 kn. at loads 70 kn and 79 kn, the beams failed in the compressive region due to crushing in the middle of the beam. the mode of failure of beams bng3 was illustrated in fig. 5.d. the ρf of beams with rca, brg1, brg2, and brg3; were similar to beams bng1, bng2, and bng3, but the ρfb ratio was lower due to using of a lower strength concrete. the balanced ratio ρfb = 0.001. the first crack of brg1, brg2, and brg3 appeared at 15, 21, and 27 kn. the beams failed in the compression zone at loads of 54, 62, and 72 kn, respectively, as shown in fig. 5. it is worth noting that failures in bns3 and bng3 are quite similar, and it complies with what was stated in the literature, i.e., steel and gfrp have a similar effect on the flexural behavior of the beams. however, rc beams with rca, i.e., lower concrete's compressive strength, showed a significant difference in the crack patterns, see fig. 5.b. (brs3) and fig. 5.e. (brg3). where brg3 showed diffuse cracks near the supports may be due to the lower concrete's strength and lower modulus of elasticity of the reinforcements (gfrp bars). it is clear from table 7 that the ratios of ultimate load of rc beams with rca to that of rc beams with nca (pult-rca/pult-nca) are lower in the case of gfrp rc beams than steel rc beams. therefore, the ultimate loads of gfrp rc beams are more affected by the compressive strength of concrete than steel rc beams due to the lower modulus of elasticity of gfrp. this is a limitation on the use of either gfrp bars or rca. 0 10 20 30 40 50 60 70 80 90 100 0 5 10 15 20 25 30 35 40 lo a d   ( k n )  deflection (mm) brg1 brg2 brg3 bng1 bng2 bng3 analytical bng1 analytical brg3 figure 6: load-central deflection curves of gfrp rc beams. flexural behavior of rc beams the experimental results of load-central deflection for gfrp rc beams and steel rc beams are shown in figs. 6 and 7, respectively. relative linear elastic behavior was observed in all beams until reaching the cracking limit of the beam at the tension face. it can be seen that the deflections of gfrp rc beams with rca are higher than those of gfrp rc beams without rca by about 1.3 to 1.55 times, see fig. 6 and table 7. the same trend was observed in the case of steel rc beams, see fig. 7. the deflection increase is attributed to the recycled concrete's modulus of elasticity and strength r. elsadany et alii, frattura ed integrità strutturale, 61 (2022) 294-307; doi: 10.3221/igf-esis.61.20                                                        304 reduction. this means the material is easier to be deformed and cracked. a greater deflection was obtained at a lower 1oad in beams made of recycled aggregate than beams made with new concrete [8]. furthermore, the deflection of rc beams reinforced with gfrp was higher than that of corresponding beams reinforced with steel by about 1.7 times. this may be due to the lower gfrp bar’s modulus of elasticity than that of the steel. these observations agree with the results found in the literature; it was found that beams reinforced with gfrp had a higher deflection by about 2.5 to 3.0 times than that of the beam reinforced with steel [33]. 0 10 20 30 40 50 60 70 80 90 100 0 5 10 15 20 25 30 35 40 lo a d  ( k n ) deflection (mm) brs1 brs2 brs3 bns1 bns2 bns3 analytical bns1 analytical brs3 figure 7. load-central deflection curves of steel rc beams. the present experimental results have been compared with the analytical model proposed previously by sallam and colleagues [35-36], see figs 6 and 7. assumptions and details of the analytical model can be found in refs. [35-36]. in both cases (steel and gfrp rc beams), the final failure of the beams is due to concrete crushing in the compression zone, while in steel rc beams, the tensile reinforcement reached its yield stress before concrete crushing. however, in gfrp rc beams, concrete crushing occurred before the tensile reinforcement reached its ultimate tensile strain. in the case of steel rc beams, bns1 and brs3 (fig. 7), there is good agreement between the analytical data and the experimental results, and this may be due to the occurrence of steel yielding before concrete crushing. however, there is a fair agreement between the analytical data and the experimental results of bgn1 and bgr3 (fig. 6). it may be because concrete crushing occurred after the first crack in the tensile zone without any events between them. therefore, the analytical model cannot describe the nonlinearity of the p-d curve of gfrp rc beams. fig. 8 shows the effect of the presence of rca and reinforcement type and area on the maximum deflection. by comparing the reduction in maximum deflection due to the increase of reinforcement area in different cases, it can be stated that the increase of steel area is more pronounced than that of gfrp in decreasing the maximum deflection in the case of concrete without rca. in the case of lower strength concrete (concrete with rca), the increase of reinforcement area for both types of reinforcement has the same effect. the effect of rca in concrete is more pronounced in the case of gfrp rc beams. fig. 9 shows the effect of the presence of rca and reinforcement type and area on the ultimate load of rc beams. it can be seen that the ultimate loads of gfrp rc beams with/without rca were slightly lower than those of steel rc beams. this may be attributed to the steel interlocking effect, which improves the bond between steel bars and concrete, increasing load-carrying capacity. when the reinforcement bars cannot transfer the bond force, cracks parallel to the rebar are developed [34]. furthermore, it can be observed that the rc beams made of recycled aggregate and reinforced with either gfrp or steel reinforcement had a load-carrying capacity lower than that beams made of natural coarse aggregate by about 5%, 11 %, and 9% for beams brg1, brg2, and brg3, respectively, and about 10%, 1.3%, and 4% for beams r. elsadany et alii, frattura ed integrità strutturale, 61 (2022) 294-307; doi: 10.3221/igf-esis.61.20  305 brs1, brs2, and brs3, respectively. this reduction is attributed to the lower compressive strength of concrete made with recycled aggregate than concrete made with natural aggregate. 27 25 23 35 32 31 22 18 17 25 22 19 0 10 20 30 40 50 beam 1 beam 2 beam 3 bng brg bns brs d e fl e ct io n , m m figure 8: maximum deflection for all rc beams. 57 70 79 54 62 7270 79 89 63 78 85 0 20 40 60 80 100 beam 1 beam 2 beam 3 bng brg bns brs u lt im a te lo a d  ( k n ) figure 9: ultimate loads values for beams. conclusion ased on this study, the following conclusions can be drawn:  the characteristics of concrete made with rca showed an acceptable lower compressive strength value than concrete without rca (≈ 13% reduction) and a higher absorption ratio (≈ 60 % higher than natural aggregate concrete).  the gfrp rc beams with rca had sufficient load-carrying capacities compared to those beams without rca (≈ reduction of 5%, 11%, and 9 % for reinforcement ratios 0.011, 0.022, and 0.033, respectively).  the steel rc beams with rca had a good load carrying capacity compared to those without rca (≈ reduction of 10%, 1.3%, and 4 % for reinforcement ratios 0.011, 0.022, and 0.033, respectively).  ll gfrp rc beams had lower ultimate loads than those of corresponding steel rc beams. these reductions are b r. elsadany et alii, frattura ed integrità strutturale, 61 (2022) 294-307; doi: 10.3221/igf-esis.61.20                                                        306 about 19%, 11%, and 11% for beams without rca and 14%, 21%, and 15% for beams with rca, considering reinforcements ratios (0.011, 0.022, and 0.033), respectively.  the use of rca increases the deflection of rc beams compared to rc beams without rca due to the lower modulus of elasticity of gfrp.  the ultimate loads of gfrp rc beams are more affected by the compressive strength of concrete than steel rc beams due to the lower modulus of elasticity of gfrp. this is a limitation on the use of either gfrp bars or rca.  based on the strength, durability, and sustainability points of view, the economic benefit is considered another limitation of using either gfrp or rca. therefore, additional research should be conducted to cover the durability and sustainability of such materials. references [1] rao, a., jha, k. n., and misra, s. (2007). use of aggregates from recycled construction and demolition waste in concrete. resources, conservation and recycling, 50(1), pp. 71-81. doi: 10.1016/j.resconrec.2006.05.010. [2] sormunen, p., and kärki, t. (2019). recycled construction and demolition waste as a possible source of materials for composite manufacturing. journal of building engineering, 24, 100742. doi: 10.1016/j.jobe.2019.100742. [3] da rosa azambuja, r., de castro, v. g., trianoski, r., and iwakiri, s. (2018). utilization of construction and demolition waste for particleboard production. journal of building engineering, 20, pp. 488-492. doi: 10.1016/j.jobe.2018.07.019. [4] salgado, f.d-a., and silva, f.d-a. (2022). recycled aggregates from construction and demolition waste towards an application on structural concrete: a review. journal of building engineering, in press, 104452. doi: 10.1016/j.jobe.2022.104452 [5] de brito, j., ferreira, j., pacheco, j., soares, d., and guerreiro, m. (2016). structural, material, mechanical and durability properties and behavior of recycled aggregates concrete. journal of building engineering, 6, pp. 1-16. doi: 10.1016/j.jobe.2016.02.003. [6] leite, m. b., and santana, v. m. (2019). evaluation of an experimental mix proportion study and production of concrete using fine recycled aggregate. journal of building engineering, 21, pp. 243-253. doi: 10.1016/j.jobe.2018.10.016. [7] sainz-aja, j., carrascal, i., polanco, j. a., and thomas, c. (2020). fatigue failure micromechanisms in recycled aggregate mortar by μct analysis. journal of building engineering, 28, 101027. doi: 10.1016/j.jobe.2019.101027 [8] mcneil, k., and kang, t. h. k. (2013). recycled concrete aggregates: a review. international journal of concrete structures and materials, 7(1), pp. 61-69. [9] djerbi, a. (2018). effect of recycled coarse aggregate on the new interfacial transition zone concrete. construction and building materials, 190, pp. 1023-1033. doi: 10.1016/j.conbuildmat.2018.09.180. [10] prince, m. j. r., and singh, b. (2015). bond behaviour of normal‐and high‐strength recycled aggregate concrete. structural concrete, 16(1), pp. 56-70. doi: 10.1002/suco.201300101. [11] malešev, m., radonjanin, v., and marinković, s. (2010). recycled concrete as aggregate for structural concrete production. sustainability, 2(5), pp. 1204-1225. doi: 10.3390/su2051204. [12] makhlouf, h. m., ahmadi, b. h., and al jabal, j. (1991). preventing concrete deterioration in the arabian gulf. concrete international, 13(5), pp. 65-67. [13] federation international du beton, fib, task group 9.3, frp reinforcement in rc structures, lausanne, switzerland, (2007). [14] pilakoutas, k., neocleous, k., and guadagnini, m. (2002). design philosophy issues of fiber reinforced polymer reinforced concrete structures. journal of composites for construction, 6(3), pp. 154-161. [15] mufti, a. a., and isis canada. (2001). reinforcing concrete structures with fibre reinforced polymers [computer file]. isis canada. [16] aci committee. (2008). building code requirements for structural concrete (aci 318-08) and commentary. american concrete institute. [17] aci committee. (2006). guide for the design and construction of concrete reinforced with frp bars (aci r. elsadany et alii, frattura ed integrità strutturale, 61 (2022) 294-307; doi: 10.3221/igf-esis.61.20  307 440.1r-06), american concrete institute. [18] al-sunna, r., pilakoutas, k., hajirasouliha, i., and guadagnini, m. (2012). deflection behaviour of frp reinforced concrete beams and slabs: an experimental investigation. composites part b: engineering, 43(5), pp. 2125-2134. doi: 10.1016/j.compositesb.2012.03.007. [19] theriault, m., and benmokrane, b. (1998). effects of frp reinforcement ratio and concrete strength on flexural behavior of concrete beams. journal of composites for construction, 2(1), pp. 7-16. [20] tavares, d. h., giongo, j. s., and paultre, p. (2008). behavior of reinforced concrete beams reinforced with gfrp bars. revista ibracon de estruturas e materiais, 1(3), pp. 285-295. doi: 10.1590/s1983-41952008000300004. [21] goldston, m. w., remennikov, a., and sheikh, m. n. (2017). flexural behaviour of gfrp reinforced high strength and ultra high strength concrete beams. construction and building materials, 131, pp. 606-617. doi: 10.1016/j.conbuildmat.2016.11.094. [22] nor, n. m., boestamam, m. h. a., and yusof, m. a. (2013). carbon fiber reinforced polymer (cfrp) as reinforcement for concrete beam. international journal of emerging technology and advanced engineering, 3(2), pp. 6-10. [23] sheikh, s. a., and kharal, z. (2018). replacement of steel with gfrp for sustainable reinforced concrete. construction and building materials, 160, pp. 767-774. doi: 10.1016/j.conbuildmat.2017.12.141 [24] etman, e. e., afefy, h. m., baraghith, a. t., and khedr, s. a. (2018). improving the shear performance of reinforced concrete beams made of recycled coarse aggregate. construction and building materials, 185, pp. 310-324. doi: 10.1016/j.conbuildmat.2018.07.065. [25] hamad, b. s., dawi, a. h., daou, a., and chehab, g. r. (2018). studies of the effect of recycled aggregates on flexural, shear, and bond splitting beam structural behavior. case studies in construction materials, 9, e00186. doi: 10.1016/j.cscm.2018.e00186. [26] reda, r. m., sharaky, i. a., ghanem, m., seleem, m. h., and sallam, h. e. m. (2016). flexural behavior of rc beams strengthened by nsm gfrp bars having different end conditions. composite structures, 147, pp. 131-142. doi: 10.1016/j.compstruct.2016.03.018. [27] aci committee (2012). guide for test methods for fiber reinforced polymers (frp) for reinforcing and strengthening concrete structures (aci 440.3r-12), aci committee 440, american concrete institute. [28] astm d7913/d7913m-14(2020), standard test method for bond strength of fiber-reinforced polymer matrix composite bars to concrete by pullout testing, astm international, west conshohocken, pa, usa. [29] astm c496–96 (1996), standard test method for splitting tensile strength of cylindrical concrete specimens, astm committee (philadelphia). [30] astm, c469–94, (1994) standard test method for static modulus of elasticity and poisson's ratio of concrete in compression, philadelphia ,astm committee . [31] sivakumar, n., muthukumar, s., sivakumar, v., gowtham, d., and muthuraj, v. (2014). experimental studies on high strength concrete by using recycled coarse aggregate. international journal of engineering and science, 4(1), pp. 2736. [32] american concrete institute. committee 440. (2003). guide for the design and construction of concrete reinforced with frp bars: aci 440.1 r-03. american concrete institute. [33] san, a. r.m and swany, r. n (2005). flexural behavior of concrete beams reinforced with glass fiber reinforced polymer bars. malaysian journal of civil engineering, 17, pp. 49-57. [34] rafi, m. m., nadjai, a., and ali, f. (2007). experimental testing of concrete beams reinforced with carbon frp bars. journal of composite material, 41(22), pp. 2657-2673. doi: 10.1177/0021998307078727. [35] sallam, h.e.m., saba, a.m., shaheen, h.h. and abdel-raouf, h. (2004). prevention of peeling failure in plated beams, j adv concr technology, jci, 2(3), pp. 419-429. [36] sharaky, i.a., torres, l. and sallam, h.e.m. (2015). experimental and analytical investigation into the flexural performance of rc beams with partially and fully bonded nsm frp bars/strips, composite structure, 122, pp. 113126. << /ascii85encodepages false /allowtransparency false /autopositionepsfiles true /autorotatepages /none /binding /left /calgrayprofile (dot gain 20%) /calrgbprofile (srgb iec61966-2.1) /calcmykprofile (u.s. web coated \050swop\051 v2) /srgbprofile (srgb iec61966-2.1) /cannotembedfontpolicy /error /compatibilitylevel 1.4 /compressobjects /tags /compresspages true /convertimagestoindexed true /passthroughjpegimages true /createjobticket false /defaultrenderingintent /default /detectblends true /detectcurves 0.0000 /colorconversionstrategy /cmyk /dothumbnails false /embedallfonts true /embedopentype false /parseiccprofilesincomments true /embedjoboptions true /dscreportinglevel 0 /emitdscwarnings false /endpage -1 /imagememory 1048576 /lockdistillerparams false /maxsubsetpct 100 /optimize true /opm 1 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can be opened with acrobat and adobe reader 5.0 and later.) >> /namespace [ (adobe) (common) (1.0) ] /othernamespaces [ << /asreaderspreads false /cropimagestoframes true /errorcontrol /warnandcontinue /flattenerignorespreadoverrides false /includeguidesgrids false /includenonprinting false /includeslug false /namespace [ (adobe) (indesign) (4.0) ] /omitplacedbitmaps false /omitplacedeps false /omitplacedpdf false /simulateoverprint /legacy >> << /addbleedmarks false /addcolorbars false /addcropmarks false /addpageinfo false /addregmarks false /convertcolors /converttocmyk /destinationprofilename () /destinationprofileselector /documentcmyk /downsample16bitimages true /flattenerpreset << /presetselector /mediumresolution >> /formelements false /generatestructure false /includebookmarks false /includehyperlinks false /includeinteractive false /includelayers false /includeprofiles false /multimediahandling /useobjectsettings /namespace [ (adobe) (creativesuite) (2.0) ] /pdfxoutputintentprofileselector /documentcmyk /preserveediting true /untaggedcmykhandling /leaveuntagged /untaggedrgbhandling /usedocumentprofile /usedocumentbleed false >> ] >> setdistillerparams << /hwresolution [2400 2400] /pagesize [612.000 792.000] >> setpagedevice microsoft word numero_62_art_01_3673.docx v. shlyannikov et alii, frattura ed integrità strutturale, 62 (2022) 1-13; doi: 10.3221/igf-esis.62.01 1 elastic and nonlinear crack tip solutions comparison with respect to failure probability valery shlyannikov, andrey tumanov, natalia boychenko frc kazan scientific center of russian academy of sciences, russia shlyannikov@mail.ru, http://orcid.org/0000-0003-2468-9300 tumanoff@rambler.ru, http://orcid.org/0000-0002-2345-6790 tasha1203@mail.ru abstract. this study represents a methodology to assess the probability of failure based on three the driving force formulations defined by the corresponding brittle and ductile fracture criteria for compact and bending specimens made of 34xh3ma and s55c steels. the elastic stress intensity factor (sif) and two types of the non-linear plastic sifs were considered as the driving force or generalized parameter (gp) to determine the probability of failure assuming a three-parameter weibull distribution. the elastic sif were experimentally obtained for studied materials and specimen geometries whereas the plastic sifs were numerically calculated for the same material properties, specimen configurations and loading conditions according to classical j2 and strain gradient plasticity theories. different specimen types with varying relative crack lengths and thicknesses were investigated. proposed the normalized generalized parameter accounting for brittle or ductile fracture can be used as a suitable failure variable that is confirmed by comparison of the obtained failure cumulative distribution functions based on the three studied gps. keywords. failure probability; weibull distributions; nonlinear stress intensity factors; generalized parameters. citation: shlyannikov, v., tumanov, a., boychenko, n., elastic and nonlinear crack tip solutions comparison with respect to failure probability, frattura ed integrità strutturale, 61 (2022) 1-13. received: 10.07.2022 accepted: 19.07.2022 online first: 20.07.2022 published: 01.10.2022 copyright: © 2022 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. introduction he main objective of experimental studies in fracture mechanics is to determine the critical value of a parameter characterizing the failure of a material. in most cases, the results of experimental studies must be evaluated statistically owing to the scatter of the critical fracture resistance parameter. if the fracture parameter is chosen correctly and the measuring instruments provide the required accuracy, the dispersion density corresponds to the normal gaussian–laplace distribution [1]. to evaluate the fracture resistance parameters and probability of failure, it is convenient t https://youtu.be/swjqge6ot4i v. shlyannikov et alii, frattura ed integrità strutturale, 62 (2022) 1-13; doi: 10.3221/igf-esis.62.01 2 to use the weibull distribution function [2]. the analysis of the weibull parameters suggests that the studied characteristic is applicable as a fracture criterion. the generalized probabilistic local approach (gpla), developed by muniz-calvente et al. [3–7], allows the primary failure cumulative distribution function (pfcdf) owning to a certain failure type to be determined for a given material from experimental data and used subsequently for probabilistic design. such approach introduce a realistic safety boundary provided that the failure criterion represented by an adequate generalized parameter (gp) and the corresponding failure criterion is properly recognized as a reference variable to be considered in the failure assessment. the authors [3] supposed that the three-parameter weibull distribution could be extended to any type of failure using the driving force (xc) defined by the corresponding fracture criterion. this methodology is feasible to apply for any kind of failure provided the experimental results for this specific failure are available and the corresponding reference driving force controlling such a failure is recognized. the reference driving force is characterized by the different weibull distribution obtained, which influences the resulting predictions for brittle and ductile type of failure. the authors [3] draw attention to the need to apply the statistical technique denoted confounded data [8,9]. this approach allows the cumulative distribution functions (cdf) for any of the flaw populations to be separately achieved without neglecting the mutual statistical interference between several distributions. in the present study, an extension of such a probabilistic failure approach is presented allowing the consideration of different constitutive equation of the material behavior, as well as the influence of scale effects, when specimens of different size are tested. the results are compared for states when the most suitable failure generalized parameter to determine the probability of failure is identified among three alternatives, namely, elastic solution, classical j2 theory of plasticity and strain gradient plasticity theory. probabilistic model he model for a probability–statistical assessment used in this study is based on a generalized local model, described in [3–7]. this generalized probabilistic local approach (gpla) allows a direct relationship to be found between the critical reference variable, as defined by the fracture criterion, and the failure probability. the relationship, known as primary failure cumulative distribution function (pfcdf) can be expressed by means of a three parameter weibull cumulative distribution function (cdf) [10]. accordingly, the failure probability pfail of an element subjected to a certain critical factor xc uniformly distributed on the element can be represented as follows 1 expfail gp p                (1) where λ, β and δ are, respectively, the location parameter, the shape parameter and the scale parameter associated with the selected reference area. generalized parameter gp in eq.1 is determined in terms of the driving force for accepted either brittle or ductile failure criterion. the following is the iterative procedure applied to achieve fitting of the optimal primary distribution function from an experimental data set exhibiting three different failure types. it implies estimation of the nine weibull parameters, three for any of the failure mechanisms. fig. 1 shows a flaw chart that describes the iterative procedure applied consisting in the following steps:  in an experimental program, failure tests are carried out and the corresponding results for the critical parameter determined.  the loading process up to failure for any test is simulated by means of a finite element code. in this way, the type and value of the driving force at failure for any element are known.  the failure results are ranked in increasing order according to the value of the driving force reached by any specimen at failure. subsequently, using bernard’s expression [11]: , 0.3 0.4 fail i i p n    (2) the accumulated failure probability is provided for any population individually referred to the specific specimen size and failure type obtained. in eq.2 i = 1, ..., n, and n is the number of cases studied. t v. shlyannikov et alii, frattura ed integrità strutturale, 62 (2022) 1-13; doi: 10.3221/igf-esis.62.01 3  the weibull parameter are estimated by applying eq.1 to the generalized parameter and the failure probability as obtained for any test. once fitting is accomplished, the value of the nine weibull parameters are estimated for the iteration being.  with the aim of assessing the convergence of the procedure, the parameter values obtained at any iteration are compared with those found in the preceding iteration until the summation of the variations in the values of each of them is less than a prescribed threshold value ε: 1 1 1i i i i i i              (3) when this occurs, the parameter values obtained in the last iteration are considered to be the final solution. figure 1: flow-chart representing the iterative procedure applied for data fitting. as can be observed, the procedure proposed is implemented by merely mentioning without specifying the “failure criterion” bound to the driving force being considered. this allows the approach to be applicable to any specific failure problem handled irrespective of its complexity provided the weakest link principle is applicable referred to either brittle or ductile failure. generalized parameters n this section we will consider both elastic and nonlinear formulations for the generalized parameter which characterizes the fractures of the tested specimens according to brittle and ductile failure criteria. three gps were analyzed in this study, related to the following fracture parameters: elastic stress intensity factor (sif) k1 (gpk1), plastic stress intensity factor kp (gpkp) based on the classical j2 hutchinson-rice-rosengren (hrr) solution, and plastic sif ksgp (gpksgp) backgrounded on strain gradient plasticity theory. i v. shlyannikov et alii, frattura ed integrità strutturale, 62 (2022) 1-13; doi: 10.3221/igf-esis.62.01 4 elastic generalized parameter gpk1 he values of the elastic sif k1 were obtained in accordance with standard astm e399 [12] by the following equations. for the compact tension c(t) configuration: 1 1 qp a k y wb w           2 3 4 1 1.5 2 0.886 4.64 13.31 14.72 5.6 1 / a wa a a a a y w w w w wa w                                      (4) and for the single-edge-notched bend (senb) configuration: 1 1 13 2 qp l a k y wbw       2 3 4 1 1.93 3.07 14.53 25.11 25.8 a a a a a y w w w w w                                  (5) where a is the crack length, b is the specimen thickness, w is the specimen width, l1 is the span of the bending specimen, and y1 is the geometry-dependent sif correction factor. the values of the pq loads were obtained using the typical load versus load-line crack opening displacement curves for the c(t) and senb configurations. hrr-plastic generalized parameter gpkp he classical hrr singular solution [13,14] for an infinite size cracked body of a strain-hardening material was completed by shlyannikov and tumanov as numerical method [15] for plastic stress intensity factor determination applied to mixed mode plane strain/plane stress problems and general three-dimensional (3d) structural element configurations. according to this method, the plastic sif kp can be expressed directly in terms of the corresponding elastic sif k1:    1 1 2 2 1 0 n yn p n k a k i w                    (6) where α and n are the strain hardening parameters, yn is the nominal stress, 0 is the yield stress, and in is the governing parameter of the elastic–plastic stress–strain fields in the form of dimensionless factor:     , , ( , ,fem femni n a w n a w d                1, , cos sin 1 1 cos 1 fem fem femfem n fem fem fem femr e rr r r fem fem fem fem rr r r du dun n a w u u n d d u u n                                                    (7) t t v. shlyannikov et alii, frattura ed integrità strutturale, 62 (2022) 1-13; doi: 10.3221/igf-esis.62.01 5 in this case, the numerical integral of the crack-tip field in changes not only with the strain-hardening exponent n, but also with the relative crack length a/w and specimen configuration. numerical results regarding the behavior of the in-integral in the most common experimental configurations for test specimens in fracture mechanics can be found in refs. [16–18]. sgp-plastic generalized parameter gpksgp he third generalized parameter is presented in the form of a plastic stress intensity factor based on the strain gradient plasticity (sgp) theory. in this case the aim of the conventional mechanism-based strain gradient plasticity theory [19-21] is to capture the role of geometrically necessary dislocation (gnd) density in the mechanics of crack initiation and growth. the advantage of sgp plasticity theory, which grounded on the taylor’s dislocation model [22], is sensitivity to the intrinsic material plastic length parameter ℓ. according to sgp theory, the tensile flow stress is related to a reference stress σref, the equivalent plastic strain εp and the effective plastic strain gradient ηp:  2 p pflow ref f l     (8) where  2218 refl b   (9) here, ā is an empirical coefficient that is assumed to be equal to 0.5, μ is the shear modulus and b is the burgers vector length. the first-order version of the conventional mechanism-based strain gradient (cmsg) plasticity model is implemented in the computation of the material jacobian and, consequently, of the rate of the stress tensor: 3 2 2 m e ij kk ij ij ij e flow k                           (10) where ij is the deviatoric strain rate tensor. as with other continuum strain gradient plasticity models, the cmsg theory is intended to model a collective behaviour of dislocations and is therefore not applicable at scales smaller than the dislocation spacing. taking into account the singular nature of the stress distribution at the crack tip for the cmsg plasticity theory of plasticity eqs.8-10, shlyannikov et al. [23-25] introduced a new plastic stress intensity factor in the following form:    ˆ, ,fem fem feme sgp er k r r     (11)      ˆ, , ,fem fem femp ij ija r r r     (12) fem fem sgp pk a r  (13) where r r l is the normalized distance to the crack tip, and  is the power of the stress singularity. in eq.11, the angular distributions of the dimensionless stress component  ˆ ,femij r  are normalized, such that   1 2 ,max max ˆ 3 2 1fem fem feme ij ijs s   and fem femij ij y   . in the further presentation of numerical and experimental results, we will use the following notation for plastic sif femsgp sgpk k . in this study, tested compact and bending specimens made of 34xh3ma and s55c steels are considered as a subject for application of the conventional elasticity, the classical j2 and cmsg plasticity theories. the implementation of a mechanismt v. shlyannikov et alii, frattura ed integrità strutturale, 62 (2022) 1-13; doi: 10.3221/igf-esis.62.01 6 based sgp theory in ansys [26] using a user material subroutine usermat has been described in more detail by the authors [23-25]. material properties and numerical data he algorithm described in section 2 was used for the probabilistic assessment based on the experimental data. several experiments and corresponding numerical calculations were performed on ct and senb specimen configurations produced from steels 34xh3ma and js55c. the fracture toughness tests were performed in accordance with astm e399 [12]. the experimental data for the fracture toughness characteristics of the senb specimens of js55c steel were obtained from meshii et al. [27]. the main mechanical properties of the analyzed materials are listed in tab. 1, where е is the young’s modulus, σ0 is the yield stress, σf is the tensile strength, σu is the true ultimate tensile stress, α is the strain hardening coefficient, and n is the strain hardening exponent. steel e, gpa σ0, mpa σf, mpa σu, mpa a n 34xh3ma 216.2 714.4 1040 1260 0.529 7.89 js55c 212.4 393 703 1274 1.265 5.45 table 1: main mechanical properties of the steels. a) b) figure 2: senb (a) and c(t) (b) specimen configuration. the loading configuration and specimen geometry are shown in fig. 2. the relative crack length a/w and relative thickness b/w were varied for each specimen configuration. the relative crack length a/w was varied in the range of 0.245–0.645. three types of c(t) specimens with b/w ratios of 0.125, 0.25, and 0.5 and four types of senb specimens with b/w ratios of 0.25, 0.5, 1.0, and 1.5 were used. the specimen sizes and crack lengths are listed in tab. 2. a full-field 3d finite-element analysis was performed using the experimental set of pq loads for each tested specimen to determine the elastic–plastic stress fields along the through-thickness crack front in the senb and c(t) specimens subjected to bending and tension loadings. in all numerical calculations for a strain-hardening material with a pure power-law behavior, the ramberg–osgood constitutive relationship with n, a, and 0 constants, listed in tab. 1, was used. the numerical calculations for the conventional mechanism-based strain gradient plasticity model according to the constitutive eqs.8-10 were performed for the value of the intrinsic material plastic length parameter ℓ = 5 μm. to accurately characterize the strain gradient effect, a high-density fe mesh was formed near the crack tip and along crack front in senb and c(t) specimens. the fe-mesh sensitivity parametric study shown that a quadrilateral brick element size less than 0.15 μm provided mesh-independent results. for the elastic-plastic analysis of both specimen fe models, the initial crack tip was assigned a radius of curvature ρ = 0.87 μm. a typical fe mesh for the c(t) specimen configuration has 9,625,812 nodes, while for the senb specimen has 17,903,812 nodes. the ansys [26] finite-element code was applied to obtain the distribution of stresses along the crack front for the tested specimen, which were used to determine both the elastic and nonlinear stress intensity factors. the obtained gps in the form of elastic and plastic sifs for all specimen configurations are listed in tab. 2. t v. shlyannikov et alii, frattura ed integrità strutturale, 62 (2022) 1-13; doi: 10.3221/igf-esis.62.01 7 results and discussion n this work, the method of confounded data is employed to the consideration of the cumulative distribution functions (cdf) for three flaw populations, characterized by corresponding the generalized parameters, namely, elastic k1 and two types of plastic kp and ksgp stress intensity factors. the first of them represent brittle material behavior, while the second and third parameters are related to ductile fracture. the maximum elastic or plastic stress intensity factor is considered to be the critical parameter (gp) under static failure conditions. recall that, the method of confounded data allows the cumulative distribution functions for any of the flaw populations to be separately achieved. material specimen type w, mm b, mm b/w a/w a, mm k1 kp ksgp 34xh3ma c(t) 40 20 0.5 0.350 14.0 66.012 0.6965 1.301 0.350 14.0 63.343 0.6864 1.308 0.625 25.0 62.72 0.6860 1.302 0.645 25.8 68.152 0.6965 1.342 10 0.25 0.380 15.2 77.563 0.7209 1.401 0.425 17.0 78.99 0.7245 1.441 0.475 19.0 77.551 0.7188 1.490 0.487 19.5 76.35 0.7140 1.399 5 0.125 0.380 15.2 71.4 0.7071 1.332 0.358 15.4 60.67 0.682 1.269 0.4625 18.5 70.17 0.7021 1.330 0.475 19.0 69.44 0.6995 1.326 34xh3ma senb 20 10 0.5 0.245 4.9 68.12 0.7945 1.288 0.250 5.0 57.24 0.7629 1.272 0.445 8.9 64.35 0.7659 1.289 0.445 8.9 57.5 0.7576 1.310 0.610 12.2 55.25 0.745 1.285 0.615 12.3 57.53 0.7525 1.238 20 1 0.605 12.1 52.146 0.7289 1.232 0.620 12.4 55.964 0.7328 1.258 s55c senb 25 6.25 0.25 0.507 12.67 58.112 0.709 1.985 0.501 12.53 67.492 0.75 2.442 0.499 12.47 58.12 0.7 1.872 0.503 12.58 65.81 0.732 2.232 0.500 12.51 67.79 0.744 2.323 12.5 0.5 0.500 12.49 55.214 0.699 1.891 0.504 12.61 63.259 0.733 2.329 0.5008 12.52 56.896 0.71 1.983 0.5028 12.57 61.94 0.725 2.120 0.5016 12.54 61.359 0.722 2.104 25.0 1.0 0.497 12.43 59.295 0.722 1.943 0.498 12.45 59.24 0.715 1.935 0.502 12.54 62.902 0.741 2.149 0.497 12.43 62.17 0.735 2.064 37.5 1.5 0.494 12.35 60.122 0.723 1.897 0.502 12.56 62.74 0.733 2.031 0.499 12.48 64.635 0.749 2.132 0.501 12.53 61.516 0.73 2.039 table 2: generalized parameters for tested specimens. i v. shlyannikov et alii, frattura ed integrità strutturale, 62 (2022) 1-13; doi: 10.3221/igf-esis.62.01 8 primary failure cumulative distribution function n order to illustrate the methodology applied for checking the suitability of the failure criterion, as represented by an adequate generalized parameter (gp), taking into account the critical parameter distribution and the size of the specimen tested the following examples are exposed. three experimental programs consisting of senb and c(t) specimen tests with different sizes (tab. 2) are simulated. for each of the considered generalized parameter, we distinguish three separate populations: senb specimen from js55c steel, senb specimen from 34xh3ma steel and c(t) specimen from 34xh3ma steel. thus, we will consider the behavior of two different materials that are implemented on test samples of two configurations. k1 kp ksgp js55c senb 34xh3m senb 34xh3m c(t) js55c senb 34xh3m senb 34xh3m c(t) js55c senb 34xh3m senb 34xh3m c(t) λ 55.697 51.103 57.030 0.643 0.707 0.668 1.835 1.220 1.256 δ 7.782 8.395 15.019 0.089 0.054 0.039 0.277 0.060 0.109 β 1.456 1.359 1.986 6.079 2.459 2.477 1.481 1.595 1.479 table 3: the resulting three-parameter weibull distribution characteristics for tested steels. test data are simulated assuming that n=18 senb specimens from js55c, n=8 senb specimens from 34xh3ma and n=12 c(t) specimens from 34xh3ma are loaded up to failure, which may caused by three different initiating failure mechanisms related to elasticity, classical and strain gradient plasticity. in this experimental program, the values of the failure load for each test is registered from which the corresponding driving force (in this case, stress intensity factors) distribution at failure is determined using a finite element code. thereafter, the fem results are used for estimating the three sets of weibull parameters corresponding to any failure type following the steps as indicated above. making use of the data numerically simulated, nine cdfs are fitted separately. the weibull parameters being found in this procedure are listed in tab. 3, from which the adequacy of the fitting performed is apparent, provided a sufficient number of experimental data results are at disposal. a) b) c) figure 3: probabilities of failure for (a) elastic, (b) plastic kp and (c) ksgp sifs for senb js55c steel specimens. figs. 3-5 represent the experimental failure cumulative distribution function (efcdf) for each test type and their fitting by eq.1. as shown in figs. 3-5, the pfcdf leads to a satisfactory adjustment of the experimental results for each experimental programs have been implemented on senb and c(t) test samples produced from js55c and 34xh3ma steels, which would not be possible if the failure criterion were unsuitable. however, as can be observed, the primary failure cumulative distribution function, based on the nonlinear generalized parameters (plastic sifs kp and ksgp), give more uniform behavior with respect to the gp related with elastic sif k1. the use of the material property pfcdf (figs. 3-5) in combination with the weibull parameters (tab. 3) generated for each experiment permits us to conclude that the division into three external (k1, kp and ksgp) and three internal (senb-js55c, senb-34xh3ma and c(t)-34xh3ma) populations was justified. i v. shlyannikov et alii, frattura ed integrità strutturale, 62 (2022) 1-13; doi: 10.3221/igf-esis.62.01 9 a) b) c) figure 4: probabilities of failure for (a) elastic, (b) plastic kp and (c) ksgp sifs for senb 34xh3ma steel specimens. a) b) c) figure 5: probabilities of failure for (a) elastic, (b) plastic kp and (c) ksgp sifs for c(t) 34xh3ma steel specimens. figs. 3-5 show probability diagrams as a function of the elastic sif k1, plastic sifs kp and ksgp for js55c and 34xh3ma steels with different ranges of values and scales, which make it not convenient to compare the pfcdf in specimens with different thicknesses and configurations. using only the information as presented so far is impossible to determine if a test specimen subjected to bending or tension loading, characterized by elastic generalized parameter, has higher or lower probability of failure than the same sample interpreted in terms of plastic gps. in addition, it is not clear whether there are differences in the assessments of the failure probability from the point of view of the classical and modern gradient theories of plasticity. dimensionless generalized parameters o overcome these problems, the authors proposed for representing the results the following normalized coordinates for each of the generalized parameters: min max min i n gp gp gp gp gp    (14) where gpmin and gpmax are the minimum and maximum values of the gp for each failure probability diagram, respectively; gpi denotes the current value of the generalized parameter; n = k1, kp, ksgp. in the following analysis of the experimental results, we use the pfcdf and the dimensionless variables gpn which change in the range from 0 to 1. the dimensionless t v. shlyannikov et alii, frattura ed integrità strutturale, 62 (2022) 1-13; doi: 10.3221/igf-esis.62.01 10 gpn enables the arrangement of the generalized parameters depending on the probability of failure and identification of the gp having the largest probability of failure at a given material and the specimen configuration. fig. 6 summarizes the failure probability pfail versus the dimensionless gpn in terms of elastic k1 and plastic kp, ksgp sifs for js55c (fig. 6a) and 34xh3ma (figs. 6b, c) steels based on eq.14. as can be seen, the primary failure cumulative distribution function, related to the elastic and nonlinear generalized parameters do not match each other for the three internal populations (senb-js55c, senb-34xh3ma and c(t)-34xh3ma). this conclusion once again confirms the possibility of applying the statistical technique known as confounded data to the analysis of elastic-plastic problems of fracture mechanics. since the reference driving force is different (elastic k1 and plastic kp and ksgp sifs), the type of failure is characterized by the different weibull distribution obtained, which influences the resulting predictions for either brittle or ductile type of fracture. a) b) c) figure 6: probabilities of failure versus normalized gp for (a) and (b) senb and (c) c(t) specimens in terms of elastic and plastic sifs. in fig. 6a, for senb sample made of js55c steel, the elastic solution (gpk1) and the theory of gradient plasticity (gpksgp) predict approximately the same probability of failure, while the classical theory of plasticity (gpkp) gives significantly underestimated results. in senb specimen made of 34xh3ma steel, the elastic solution shows the highest probability of failure (fig. 6b), and the nonlinear solutions are close to each other. in a compact c(t) sample of that material, the highest probability of failure corresponds to strain gradient plasticity theory (fig. 6c). summarizing the presented results, we can say that the observed differences in the probability of failure are due to the use of various constitutive equations of material behavior in the range from elasticity to gradient plasticity. the failure cumulative distribution functions pfail and normalized gps may be interpreted as material characteristics enabling the prediction of the failures of structure elements depending on the formulation of the constitutive equation of the material behavior. the failure distribution functions of the senb and compact c(t) specimens of 34xh3ma steel were compared in figs. 7a, b to analyze the influences of the sample configuration with the elastic and plastic approaches of fracture mechanics point of view. as observed in these figures, the probabilities of failure based on the elastic solution (fig. 7a, gpk1) and plastic solution (fig. 7b, gpkp and gpksgp) for the two test specimen geometries do not coincide with each other. differences in the distributions of the failure probability increase in the transition from elastic to plastic analysis. moreover, a higher failure probability is predicted by the gradient theory of plasticity when applied to a compact sample. for the same geometry of the bending sample, figs.7c, d represent the results of assessing the influence of the elastic-plastic properties of the steels under consideration. recall that js55c and 34xh3ma steels (tab. 1) have approximately the same elastic properties (e and poisson’s ratio ν), but differ significantly in plastic (σ0, α, n) and fracture resistance (σf, σu) characteristics. the failure probability distribution functions of the same senb specimen configuration for elastic solution in terms of gpk1 are shown in fig. 7c for the considered materials. as expected for the elastic conditions, the distribution curves are considerably close to each other with a slight difference at high values of the failure probability. fig. 7d shows a comparison of results for senb specimen of js55c and 34xh3ma steels for two plasticity theories based on the classical approach (gpkp) and plastic strain gradient effects (gpksgp). as can be seen, significant differences in these nonlinear solutions take place in the more ductile steel js55c. in this case, a high fracture probability corresponds to the generalized parameter for gradient plasticity. obviously, this is due to the fact that in the gradient plasticity theory, in comparison with the classical j2 theory, an additional parameter in the form of the intrinsic material plastic length scale ℓ is added to the set of traditional material properties (e, ν, σ0, α, n). v. shlyannikov et alii, frattura ed integrità strutturale, 62 (2022) 1-13; doi: 10.3221/igf-esis.62.01 11 a) b) c) d) figure 7: comparison of failure probability versus normalized gp for elastic and nonlinear solutions, (a) and (b) 34xh3ma steel, (c) and (d) js55c and 34xh3ma steels. conclusions he principal conclusions of the present study are:  the application of the confounded data concept allows the primary failure cumulative distribution functions to be obtained for elastic and ductile fracture types that may appear in an experimental test campaign.  the comparison of the results obtained from the experimental programs carried out on senb and c(t) specimens of different sizes from js55c and 34xh3ma steels is possible using the weibull parameters estimated from the elastic and plastic generalized parameter behaviors.  the applicability and suitability proposed of the normalized generalized parameters are confirmed by means of an example using simulated data corresponding to elastic and nonlinear fracture mechanics approaches.  it is assumed that the use of nonlinear generalized parameters in comparison with elastic ones is justified due to the fact that in some cases the gradient theory of plasticity predicts the highest probability of failure. acknowledgements he authors gratefully acknowledge the financial support of the russian science foundation under the project 2019-00158. t t v. shlyannikov et alii, frattura ed integrità strutturale, 62 (2022) 1-13; doi: 10.3221/igf-esis.62.01 12 references [1] wentzel, e.s. (1969). probability theory, science, moscow. [2] weibull, w. (1951). a statistical distribution function of wide applicability, j. appl. mech., 18(3), pp. 293-297. [3] muñiz‐calvente, m., fernández canteli, a., shlyannikov, v., castill, e. (2015). probabilistic weibull methodology for fracture prediction of brittle and ductile materials, appl. mech. mater., 784, pp. 443-451. doi: 10.4028/www.scientific.net/amm.784.443. [4] muñiz‐calvente, m., fernández‐canteli, a. (2016). joint evaluation of fracture and fatigue results from distinct specimen size and geometry, proced. struct. integr., 1, pp. 142-149. doi: 10.1016/j.prostr.2016.02.020. [5] muñiz‐calvente, m., shlyannikov, v., meshii, t., giner, e., fernández‐canteli, a. (2016). joint evaluation of fracture results from distinct test conditions, implying loading, specimen size and geometry, proced. struct. integr., 2, pp. 720727. doi: 10.1016/j.prostr.2016.06.093. [6] muñiz‐calvente, m., ramos, a., pelayo, f., lamela, m., fernández‐canteli, a. (2016). statistical joint evaluation of fracture results from distinct experimental programs: an application to annealed glass, theoret. appl. fract. mech., 85 (part a), pp. 149-157. doi: 10.1016/j.tafmec.2016.08.009. [7] vantadori, s., muñiz‐calvente, m., scorza, d., fernández‐canteli, a., álvarez vázquez, a., carpinteri, a. (2018). the generalised local model applied to fibreglass, compos. struct., 202, pp. 1353-1360. doi: 10.1016/j.compstruct.2018.06.073. [8] castillo, e., fernández‐canteli, a., garcía-prieto, m.a., lamela, m.j. (2004). strength characterization of glass by means of the statistical theory of confounded data, key eng. mater., 264-268, pp. 1923-1926. doi: 10.4028/www.scientific.net/kem.264-268.1923. [9] przybilla, c., fernández-canteli, a., castillo, e. (2013). maximum likelihood estimation for the three-parameter weibull cdf of strength in presence of concurrent flaw populations, j. eur. ceram. soc., 33, pp. 1721-1727. [10] muñiz‐calvente, m., ramos, a., shlyannikov, v., lamela, m., fernández‐canteli, a. (2016). hazard maps and global probability as a way to transfer standard fracture results to reliable design of real components, eng. fail. anal., 69, pp. 135-146. doi: 10.1016/j.engfailanal.2016.02.004. [11] bernard, a., bos-levenbach, e. (1955). the plotting of observations on probability-paper, stichting mathematisch centrum. statistische afdeling. [12] astm e399-90 (1997). standard test method for plane-strain fracture toughness of metallic materials. annual book of astm standards. philadelphia (pa): american society for testing and materials. doi: 10.1520/e0399-90r97. [13] hutchinson, j.w. (1968). singular behaviour at the end of a tensile crack in a hardening material, j. mech. phys. solids, 16 (1), pp. 13-31. doi: 10.1016/0022-5096(68)90014-8. [14] rice, j.r., rosengren, g.f. (1968). plane strain deformation near a crack tip in a power-law hardening material, j. mech. phys. solids, 16 (1), pp. 1-12. doi: 10.1016/0022-5096(68)90013-6. [15] shlyannikov, v., tumanov, a. (2014). characterization of crack tip stress fields in test specimens using mode mixity parameters, int. j. fract., 185, pp. 49-76. doi: 10.1007/s10704-013-9898-0. [16] shlyannikov, v.n., boychenko, n.v., tumanov, a.v., fernández‐canteli, a. (2014). the elastic and plastic constraint parameters for three-dimensional problems, eng. fract. mech., 127, pp. 83-96. doi: 10.1016/j.engfracmech.2014.05.015. [17] shlyannikov, v.n. (2013). t-stress for crack paths in test specimens subject to mixed mode loading, eng. fract. mech., 108, pp. 3-18. doi: 10.1016/j.engfracmech.2013.03.011. [18] shlyannikov, v.n., zakharov, a.p. (2014). multiaxial crack growth rate under variable t-stress, eng. fract. mech., 123, pp. 86-99. doi: 10.1016/j.engfracmech.2014.02.013. [19] gao, h., huang, y., nix, w.d., hutchinson, j.w. (1999). mechanism-based strain gradient plasticity—i. theory, j. mech. phys. solids, 47 (6), pp. 1239-1263. doi: 10.1016/s0022-5096(98)00103-3. [20] qiu, x., huang, y., wei, y., gao, h., hwang, k.c. (2003). the flow theory of mechanism-based strain gradient plasticity, mech. mater., 35 (3-6), pp. 245-258. doi: 10.1016/s0167-6636(02)00274-0. [21] huang, y., qu, s., hwang, k.c., li, m., gao, h. (2004). a conventional theory of mechanism-based strain gradient plasticity, int. j. plast., 20 (4-5), pp. 753–782. doi: 10.1016/j.ijplas.2003.08.002. [22] taylor, g.i. (1938). plastic strain in metals, j. inst. metals, 62, pp. 307–324. [23] shlyannikov, v., martínez-pañeda, e., tumanov, a., tartygasheva, a. (2021). crack tip fields and fracture resistance parameters based on strain gradient plasticity, int. j. solids struct., 208-209, pp. 63-82. doi: 10.1016/j.ijsolstr.2020.10.015. v. shlyannikov et alii, frattura ed integrità strutturale, 62 (2022) 1-13; doi: 10.3221/igf-esis.62.01 13 [24] shlyannikov, v., martínez-pañeda, e., tumanov, a., khamidullin, r. (2021). mode i and mode ii stress intensity factors and dislocation density behaviour in strain gradient plasticity, theoret. appl. fract. mech., 116, 103128. doi: 10.1016/j.tafmec.2021.103128. [25] fedotova, d., khamidullin, r., shlyannikov, v. (2022). inversion of dislocation densities under mixed mode fracture, eng. fail. anal., 138, 106311. doi: 10.1016/j.engfailanal.2022.106311. [26] ansys mechanical apdl theory reference release 21.r1. (2021). ansys, inc. southpointe, 275 technology drive, canonburg, pa. [27] meshii, t., lu, k., takamura, r. (2013). a failure criterion to explain the test specimen thickness effect on fracture toughness in the transition temperature region, eng. fract. mech., 104, pp. 184-197. doi: 10.1016/j.engfracmech.2013.03.025. << /ascii85encodepages false /allowtransparency false /autopositionepsfiles true /autorotatepages /none /binding /left /calgrayprofile (dot gain 20%) /calrgbprofile (srgb iec61966-2.1) /calcmykprofile (u.s. web coated \050swop\051 v2) /srgbprofile (srgb iec61966-2.1) /cannotembedfontpolicy /error /compatibilitylevel 1.4 /compressobjects /tags /compresspages true /convertimagestoindexed true /passthroughjpegimages true /createjobticket false /defaultrenderingintent /default /detectblends true /detectcurves 0.0000 /colorconversionstrategy /cmyk /dothumbnails false /embedallfonts true /embedopentype false /parseiccprofilesincomments true /embedjoboptions true /dscreportinglevel 0 /emitdscwarnings false /endpage -1 /imagememory 1048576 /lockdistillerparams false /maxsubsetpct 100 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/hrv (za stvaranje adobe pdf dokumenata najpogodnijih za visokokvalitetni ispis prije tiskanja koristite ove postavke. stvoreni pdf dokumenti mogu se otvoriti acrobat i adobe reader 5.0 i kasnijim verzijama.) /hun 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can be opened with acrobat and adobe reader 5.0 and later.) >> /namespace [ (adobe) (common) (1.0) ] /othernamespaces [ << /asreaderspreads false /cropimagestoframes true /errorcontrol /warnandcontinue /flattenerignorespreadoverrides false /includeguidesgrids false /includenonprinting false /includeslug false /namespace [ (adobe) (indesign) (4.0) ] /omitplacedbitmaps false /omitplacedeps false /omitplacedpdf false /simulateoverprint /legacy >> << /addbleedmarks false /addcolorbars false /addcropmarks false /addpageinfo false /addregmarks false /convertcolors /converttocmyk /destinationprofilename () /destinationprofileselector /documentcmyk /downsample16bitimages true /flattenerpreset << /presetselector /mediumresolution >> /formelements false /generatestructure false /includebookmarks false /includehyperlinks false /includeinteractive false /includelayers false /includeprofiles false /multimediahandling /useobjectsettings /namespace [ (adobe) (creativesuite) (2.0) ] /pdfxoutputintentprofileselector /documentcmyk /preserveediting true /untaggedcmykhandling /leaveuntagged /untaggedrgbhandling /usedocumentprofile /usedocumentbleed false >> ] >> setdistillerparams << /hwresolution [2400 2400] /pagesize [612.000 792.000] >> setpagedevice microsoft word numero_36_art_7 a. sedmak et alii, frattura ed integrità strutturale, 36 (2016) 63-68; doi: 10.3221/igf-esis.36.07 63 focused on fracture mechanics in central and east europe integrity and life estimation of turbine runner cover in a hydro power plant a. sedmak, s. bosnjak faculty of mechanical engineering, the university of belgrade, kraljice marije 16, belgrade, serbia. asedmak@mas.bg.ac.rs m. arsic institute for materials testing, bulevar vojvode mišića 43, belgrade, serbia. miodrag.arsic@institutims.rs s.a. sedmak innovation centre of faculty of mechanical engineering, the university of belgrade, kraljice marije 16, belgrade, serbia. z. savic institute for materials testing, bulevar vojvode mišića 43, belgrade, serbia. abstract. this paper presents integrity and life estimation of turbine runner cover in a vertical pipe turbines, kaplan 200 mw nominal output power, produced in russia, and built in six hydro-generation units of hydroelectric power plant „đerdap 1” in serbia. fatigue and corrosion-fatigue interaction have been taken into account using experimentally obtained material properties, as well as analytical and numerical calculations of stress state, to estimate appropriate safety factors. fatigue crack growth rate, da/dn, was also calculated, indicated that internal defects of circular or elliptical shape, found out by ultrasonic testing, do not affect reliable operation of runner cover. keywords. hydro power plant; runner cover; fatigue; corrosion. introduction esigning, construction and running hydro power plants is a complex task. due to limited possibilities of periodic inspections, hydro turbines and their components are designed for at least 40 years of operation. therefore, extensive researches and testing of hydro power plant equipment have been carried out all over the world. turbine and hydromechanical equipment testing has been introduced recently in serbia as well. special attention has been given to the problem of reduced material plasticity, as explained below. along with experimental tests carried out on the cover, made of cast steel 20gsl (gost), tests were performed in order to determine mechanical properties and fracture mechanics parameters. test results indicated large dispersion of material plasticity, i.e. elongation (a5) and contraction (z), [1,2]. namely two specimens met the demands of the standard (a5 = d a. sedmak et alii, frattura ed integrità strutturale, 36 (2016) 63-68; doi: 10.3221/igf-esis.36.07 64 23% and 27%), while two other had significantly lower values of elongation (a5 = 8% and 9%). obtained values of fracture mechanics parameters (critical stress intensity factor kic, critical fatigue crack length ac, fatigue threshold δkth, coefficient in paris equation c, exponent in paris equation mp, fatigue crack growth rate da/dn) are presented in tab. 1, as shown also in [1,2]. specimen kic [mpam] ac [mm] ∆kth [mpam] c mp da/dn [m/cycle] with reduced plasticity 46.3 9.3 7.4 5.7·10-11 3.15 6.36·10-08 with adequate plasticity 50.4 8.7 3.0 3.0·10-11 3.02 5.11·10-08 minimum allowed value of kic for 20gsl at temperature below 0°c is kic = 41 44 mpa·m1/2 table 1: fracture mechanics parameters at 23°c, for the stress intensity factor range δk = 10 mpam. stress state urbine runner cover at the hydro power plant ''djerdap 1'' is presented in fig. 1. loading is defined for normal operation conditions, comprising combined action of pressure, axial force and torsion moment, as explained in [1]. finite element mesh for axisymmertic model is shown in fig. 2. the results, indicating max. stress 81.1 mpa, is shown in fig. 3. a) q2 q q1 q q q2 q q1 b) figure 1: vertical kaplan turbine, with nominal output power of 200 mw. figure 2: finite element mesh for axisymmetric model. t a. sedmak et alii, frattura ed integrità strutturale, 36 (2016) 63-68; doi: 10.3221/igf-esis.36.07 65 figure 3: equivalent stresses for combined loading (pressure, axial force, torsion). fatigue and fatigue-corrosion estimation atigue and fatigue-corrosion interaction are the most important aspects of turbine cover life and integrity estimation. here, this combined effect of fatigue and corrosion is estimated by using the equation for safety factor, [3]:            1 a ( )m моn where σ-1 is the fatigue strength, obtained by standard testing, in conditions simulating the real, i.e. in water, ψσ coefficient of loading asymmetry, equal to ratio of maximum fatigue strength to the maximum static strength (470 mpa in this case); σm mean cycling stress; σмо residual stress – in this case σmо = 60 мpа, [1]; σа amplitude of cycling stress. fatigue strength depends on number of cycles and can be evaluated by using logarithm curve, obtained from weller’s curve:    1lg lga b n in the case of new material: f a. sedmak et alii, frattura ed integrità strutturale, 36 (2016) 63-68; doi: 10.3221/igf-esis.36.07 66 lg (-1) = 2.787 – 0.155  lg (n). taking into account 1,000 cycles per year (shut down start up) and 40 years of designed life, one should use 40103 as relevant number for fatigue strength estimation for material with adequate plasticity: lg σ-1 = 2.787-0.155·lg n = 2.787 0.155·lg(40·103) = 2.073, σ-1 = 118.5 мра; for the turbine under consideration the maximum stress at shut down and start up is max = 81.1 мpа, thus the amplitude stress a=40.55 mpa. coefficient of sensitivity to cycle asymmetry is         1 118.5 0.25 470 a whereas the corrosion-fatigue safety coefficient is:                 1 118.5 0.25 (40.55 60) 2.30 40.55 m mo a n taking into account 5% of the amplitude as the usual value for corrosion fatigue, one gets:       81.1 0.025 81.1 2.03 m a mpа mpa for the number of cycles one can get: n = nн·60·7000·40 = 71.43·60·7000·40 = 1.2·109 cycles, where nн – number of rotation/min, (nн = 71.43 min-1); 60 – minutes in an hour; 7000 – number of operating hours per year; 40 – designed life (years). now, one can get: lg σ-1 = 2.787 0.155·lg n = 2.787 0.155·lg(1.2·109) = 1.379, σ-1 = 23.9 мра; having in mind coefficient of sensitivity to cycle asymmetry:         1 23.9 0.05 470 a safety coefficient for corrosion-fatigue strength is then:                   1 23.9 0.05 (81.1 60) 8.34 2.02 m i i a n influence of internal defects on fatigue of cast steel 20gsl is an important issue and should be carefully evaluated. toward this aim the mechanisms of microcrack initiation and conditions of propagation of microcracks to macrocracks have been established, [2,3]. based on test results establishment of the following empirical relation has been established: a. sedmak et alii, frattura ed integrità strutturale, 36 (2016) 63-68; doi: 10.3221/igf-esis.36.07 67           * 1 1 1/2 max1 d where: σ-1 lower limit of fatigue strength dispersion; β – material coefficient, dmax maximum size of the defect in cast material. for the cast steels with defects (material with reduced plasticity), the following equation for fatigue strength holds: lg -1 = 2.69 – 0.155· lg n based on this equation, one can conclude that defect sizes up 0.5 mm do not influence fatigue strength, whereas the maximum acceptable defect size (d = 1.5 mm) reduces fatigue strength σ-1 from 118.5 mpa to 91.15 mpa. anyhow, the corrosion-fatigue safety factor is still satisfactory, sσ = 1.63. estimation of service life of the runner cover through the use of fracture mechanics stimation of runner cover service life through the use of fracture mechanics has been carried out according to methodology presented in paper [3]. in the area of stable crack growth, paris' equation describes the behaviour of the material with sufficient accuracy:     pm da c k dn where ∆k is the stress intensity factor range, defined by ∆k=m∆σ√a, m=1.21πq, defect shape parameter. in the case of an internal defect, measuring 6 mm in diameter, detected by ultrasonic inspection, q=1.65, [4]. if the critical crack length is calculated for σmax=81.1+60=141.1 mpa,              2 2 max 1 1 46.3 45.2 2.38 141.1 ic cr k a mm m number of cycles until reaching the critical size of the internal defect within the turbine runner cover, made of cast steel 20gsl with reduced plasticity (mp=3.15, cp=5.7∙10-11), can be calculated by the integration of paris’ equation:                       10 2 2 2 2 2 0 2 1 1 2.35 10 2 m m mp p p m p p p cr n m c m a a for ∆σ=4.055 mpa, a0=6 mm, acr= 45.2 mm. taking into account number of load cycles per year period (nu = nh·60·7000 = 71,43·60·7000 = 3·107 cycles), one can estimate service life of the turbine runner cover with reduced plasticity as n/nu=783 years. conclusions esults of fatigue strength tests carried out on large specimens, as well as obtained values of fracture mechanics parameters, enabled the estimation of service life of turbine runner cover with reduced plasticity. defects up to 0.5 mm have no influence on fatigue strength, whereas defects with acceptable value (1.5 mm) reduce fatigue strength from 118.5 to 91.15 mpa, still enabling reliable operation of the cove. e r a. sedmak et alii, frattura ed integrità strutturale, 36 (2016) 63-68; doi: 10.3221/igf-esis.36.07 68 finally, internal defect with size of 6 mm, as recorded by ndt, does not jeopardize integrity of turbine cover, since predicted fatigue life is more than 783 years. acknowledgement he authors acknowledge the support from the serbian ministry of education and science for projects tr 35002, tr 35040 and tr 35006. references [1] arsić, m., vistać, b., analysis of operational capability and a possibility of operational safety of the turbine cover in a life cycle at least 30 years long, institute for materials testing, belgrade, (2005). [2] arsić, m, bošnjak, s., odanović, z., grabulov, v., vistać, b., influence of plasticity reduction on strength and fracture of turbine runner cover in hydro power plant đerdap 1, in: the first international conference on damage mechanics, icdm 1, belgrade, (2012) 57-60. [3] arsić, m, karić r., sedmak a., burzić m., methodological approach to integrity assessment and servica life of rotating equipment at hydropower plant – turbine shaft, structural integrity and life, 13(2) (2013) 117124. [4] hertzberg, r., deformation and fracture mechanics of engineering materials, new york, john wiley & sons, inc, (1995). t << /ascii85encodepages false /allowtransparency false /autopositionepsfiles true /autorotatepages /none /binding /left /calgrayprofile (dot gain 20%) /calrgbprofile (srgb iec61966-2.1) /calcmykprofile (u.s. web coated \050swop\051 v2) /srgbprofile (srgb iec61966-2.1) /cannotembedfontpolicy /error /compatibilitylevel 1.4 /compressobjects /tags /compresspages true /convertimagestoindexed true /passthroughjpegimages true /createjobticket false /defaultrenderingintent /default /detectblends true /detectcurves 0.0000 /colorconversionstrategy /cmyk /dothumbnails false /embedallfonts true /embedopentype false /parseiccprofilesincomments true /embedjoboptions true /dscreportinglevel 0 /emitdscwarnings false /endpage -1 /imagememory 1048576 /lockdistillerparams false /maxsubsetpct 100 /optimize true /opm 1 /parsedsccomments true /parsedsccommentsfordocinfo true 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/hrv (za stvaranje adobe pdf dokumenata najpogodnijih za visokokvalitetni ispis prije tiskanja koristite ove postavke. stvoreni pdf dokumenti mogu se otvoriti acrobat i adobe reader 5.0 i kasnijim verzijama.) /hun 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can be opened with acrobat and adobe reader 5.0 and later.) >> /namespace [ (adobe) (common) (1.0) ] /othernamespaces [ << /asreaderspreads false /cropimagestoframes true /errorcontrol /warnandcontinue /flattenerignorespreadoverrides false /includeguidesgrids false /includenonprinting false /includeslug false /namespace [ (adobe) (indesign) (4.0) ] /omitplacedbitmaps false /omitplacedeps false /omitplacedpdf false /simulateoverprint /legacy >> << /addbleedmarks false /addcolorbars false /addcropmarks false /addpageinfo false /addregmarks false /convertcolors /converttocmyk /destinationprofilename () /destinationprofileselector /documentcmyk /downsample16bitimages true /flattenerpreset << /presetselector /mediumresolution >> /formelements false /generatestructure false /includebookmarks false /includehyperlinks false /includeinteractive false /includelayers false /includeprofiles false /multimediahandling /useobjectsettings /namespace [ (adobe) (creativesuite) (2.0) ] /pdfxoutputintentprofileselector /documentcmyk /preserveediting true /untaggedcmykhandling /leaveuntagged /untaggedrgbhandling /usedocumentprofile /usedocumentbleed false >> ] >> setdistillerparams << /hwresolution [2400 2400] /pagesize [612.000 792.000] >> setpagedevice microsoft word numero_53_art_09_2769 r. m. reda et al., frattura ed integrità strutturale, 53 (2020) 106-123; doi: 10.3221/igf-esis.53.09 106 focussed on structural integrity and safety: experimental and numerical perspectives effect of different parameters controlling the flexural behavior of rc beams strengthened with nsm using nonlinear finite element analysis ramy reda higher technological institute, egypt ramy_mostafa12000@yahoo.com, http://orcid.org/0000-0002-3298-7925 zeinab omar, hossam sallam, seleem s. e. ahmad zagazig university, egypt zomar73@yahoo.com, http://orcid.org/0000-0002-5531-9014 hem_sallam@yahoo.com, http://orcid.org/0000-0001-9217-9957 seleemahmad62@yahoo.com, http://orcid.org/0000-0001-9894-0209 abstract. near surface mounted technique become the most attractive technique for strengthening rc structures. a lot of research had been conducted to study experimentally the flexural behavior of rc members strengthened with nsm technique unlike the numerical research. a numerical investigation utilizes the non-linear finite element (fe) modeling using ansys was performed. the developed fe model considers the behavior of the epoxy-concrete interface using cohesive zone model (czm) which is capable of predicting the failure mode of the strengthened beams. the parametric study include the effect of different parameters such as nsm bar number, nsm bar length, end inclination angle and end inclination leg length on the flexural behavior of strengthened beams. the results showed that, the developed fe model able to predict the expected modes of failure in nsm technique, the nsm bar length was effective till 0.5 of beam span, beams strengthened with end inclined angle 45º nsm bar gives the highest improvement in load carrying capacity, this improvement was very close in case of using end inclined angle of 60º and 90º. keywords. finite element modeling; near surface mounted; debonding; end anchorage; inclination angle; flexural strengthening. citation: reda, r.m., zeinab, o., sallam, h.e.m, seleem s. e. ahmad, effect of different parameters controlling the flexural behavior of rc beams strengthened with nsm using nonlinear finite element analysis, frattura ed integrità strutturale, 53 (2020) 106-123 received: 21.03.2020 accepted: 12.04.2020 published: 01.07.2020 copyright: © 2020 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. introduction einforced concrete constructions are widely used over the world, after a while use it will deteriorates, demolition or rebuild will lead to bleeding the time and cost. in the last decade several techniques were conducted by many researchers to repair and strengthen the rc structures such as near surface mounted (nsm) and externally bonded r https://youtu.be/vkotlhiotts r. m. reda et al., frattura ed integrità strutturale, 53 (2020) 106-123; doi: 10.3221/igf-esis.53.09 107 (eb) [1-7]. nsm is more effective than eb due to increasing the flexural strength for rc structures over eb by increasing bond capacity due to larger bonded surface area, furthermore it needs less installation time and makes protection against external damage by embedding the frp bars in the concrete cover [8-10]. in nsm technique grooves are cut in the concrete cover and half of the groove filled with the adhesive, frp bars inserted into the groove, the remaining half of the adhesive filled in the groove and leveled [7]. nsm technique has a better bond performance compared to eb, the two interfaces of nsm (concrete-adhesive, adhesive-frp) are affected by frp properties, frp bar length, bar diameter, frp bar surface treatment, groove geometry, groove size and concrete properties [11, 12]. several investigations were performed to study the flexural behavior of rc beams strengthened with nsm frp reinforcement. hassan et al. [13] studied the effect of cfrp bar length, groove width and the strength of concrete on the flexural behavior of concrete structures, the results suggested that the nsm cfrp bars length should not be less than 80 times the diameter of the used bars and the resistance of concrete split failure increased by the increasing of the groove width and/or using high strength concrete. al-mahmoud et al. [14] studied the effect of using two different diameter of cfrp bars; 6 and 12mm, type of concrete conventional or high-strength concrete and two types of filling materials (resin and mortar) on the flexural behavior. the results concluded that using cfrp bars with 12mm diameter increase the carrying load capacity by 83.6% compared with beams strengthened with 6mm bar diameter, on the other hand the concrete strength doesn’t effect on the load carrying capacity if the failure of the strengthened beams are due to nsm system failure, also the failure mode can be changed by the type of adhesive used. finite element analysis either by ansys or abaqus software showed that it is a good solution in different structures problems [15-17]. hawileh [18] developed 3d nonlinear fe ansys model to predict the load carrying capacity of rc beams strengthened with nsm frp bars and validate this model by comparing the predicted results with the experimental results obtained by al-mahmoud et al. [14]. then study the effect of using different types of frp bars materials such as cfrp, afrp and gfrp and cfrp bar diameter. the results showed very good agreement between the ansys model and the experimental results, all types of frp bars enhance the flexural strength especially cfrp which increase the strength by 18.5% and 43.8% compared to afrp and gfrp bars, respectively. furthermore the increasing of the frp diameter has a significantly effect on load carrying capacity of the strengthened rc beams [18]. reda et al. [8] studied the effect of gfrp bar length on the flexural strength of rc beams, the beam strengthened with gfrp bar length 1000, 1200, 1400 and 1800mm, and also studied different epoxy length effect and end anchorage using gfrp bars with bent end inclined by 45º and 90º and others straight on the flexural strength of rc beams. the author concluded that the beam strengthened with gfrp bars of length 1400mm gives the higher load carrying capacity, the results showed that either the beams strengthened with bent end gfrp bars inclined by 45º showed superior flexural behavior over the beams strengthened with bent end gfrp bars inclined by 90º or straight bars. on the other hand a little effect of partial bonded in the constant moment region on the flexural behavior of strengthened beam. el-emam et al. [19] studied experimentally and numerically the effect of nsm gfrp bars length, area of main steel reinforcement and the thickness of the concrete cover on the flexural response of strengthened rc beams, the author used different gfrp bars length; 550, 1150 and 1800mm, also used 30mm and 50mm concrete cover. the results showed that increasing of gfrp bar length increase the flexural strength, the same observation when increasing the main steel reinforcement ratio from 2-ø10mm to 2-ø16mm the ultimate load will be increased, the opposite observation when increasing the concrete cover thickness the flexural capacity will be decreased, the numerical results showed a good agreement with the experimental results [19]. sharaky et al. [20] studied the effect of nsm strengthening location, nsm strengthening pattern, nsm frp strips number and of the groove depth on the flexural behavior strengthened rc beams. two different location of nsm strengthening, near the bottom surface of the beams and beneath the stirrups, the results showed that a significantly enhancement on the ultimate load of the strengthened beams in case of installing the nsm strengthening beneath the stirrups compared with installing the nsm strengthening near the bottom surface of the beam, furthermore using two nsm frp strips installed in one slot beneath the stirrups increase the load carrying capacity by 187% if compared with control beam. also the groove depth gives a noticeable effect. although a lot of research had been carried out to study the flexural behavior of rc members strengthened with nsm technique experimentally, further numerical researches are still required to understand the effect of several parameters on the flexural behavior of rc members. in this paper the effect of many parameters such as nsm bar number, nsm bar length, end inclination angle and end inclination leg length on the flexural behavior of strengthened beams with nsm technique were studied numerically using non-linear finite element fe modeling. the numerical fe model was compared with experimental results conducted from another research [8]. r. m. reda et al., frattura ed integrità strutturale, 53 (2020) 106-123; doi: 10.3221/igf-esis.53.09 108 finite element fe model on-linear finite element fe using (ansys -version 19.0) was performed to study the flexural behavior of rc beams strengthened with nsm technique [21]. first the present model was verified by comparing the model with the experimental results conducted by reda et al. [8]. after validation, a parametric study was conducted. elements description ansys element library includes several elements which can be used to simulate the different types of materials [21]. in this research (solid65) was used to simulate concrete and epoxy adhesive, (solid65) has eight nodes with three degrees of freedom at each node – translations in the nodal x, y, and z directions. solid65 has the ability to crack in tension and crush in compression. the willam and warnke criterion was used to define the failure of concrete [15, 22], it is the available model in ansys material library to model concrete [15]. a (link180) element was used to model the steel reinforcement and nsm frp bars. two nodes are required for this element. each node has three degrees of freedom, – translations in the nodal x, y, and z directions. the element is also capable of plastic deformation. an eight-node solid element (solid45) was used for the steel plates (loading or supports) in the models. the element is defined with eight nodes having three degrees of freedom at each node-translations in the nodal x, y, and z directions [21]. (a) concrete in compression (b) concrete in tension [22] (c) steel (d) gfrp figure 1: the stress strain curves used in model; concrete, steel and gfrp. materials modeling concrete, steel and gfrp stress strain curves used in model are shown in (fig.1). (fig. 1-a) defined the concrete as a material with a nonlinear behavior with a compressive strength, tensile strength, elastic modulus and poisson’s ratio of 30 mpa and 2.9 mpa, 20 gpa and 0.2 respectively, open and closed crack shear coefficients were taken as 0.4 and 0.8 respectively, (ε0 is the strain at the ultimate compressive strength = 2fc’/ec and; ec is the concrete elastic modulus [23]). (fig. 1-d) shows the concrete behavior in tension simulated by smeared crack approach. smeared crack approach has been adopted to define the concrete behavior in tension. the smeared crack approach was discussed previously by the authors [24]. the steel reinforcement was assumed to have an elastic-perfectly plastic response, (fig. 1-c) shows the elastic-strain hardening behavior for the reinforcing steel bars with yield stress, elastic modulus and poisson’s ratio of 420 mpa, 200 gpa and 0.3 respectively. the nsm gfrp bars were considered to be linear elastic up to failure, (fig. 1-d), with tensile strength, elastic 0 5 10 15 20 25 30 35 0 0.0005 0.001 0.0015 0.002 0.0025 0.003 0.0035 0.004 s tr e ss  [ m p a ] strain [mm mm^‐1] n r. m. reda et al., frattura ed integrità strutturale, 53 (2020) 106-123; doi: 10.3221/igf-esis.53.09 109 modulus and poisson’s ratio of 820 mpa, 44.8 gpa and 0.26 respectively. the material used to model concrete was also used to define the adhesive behavior with tensile strength, elastic modulus and poisson’s ratio of 24.8 mpa, 4.48 gpa and 0.37 respectively. while the steel plates (loading or supports) were modeled as rigid elastic material having a modulus of elasticity and poisson’s ratio of 200 gpa and 0.3 respectively. concrete-epoxy interface the epoxy-concrete interface was defined by two element types (conta174 and targe170) which can be used for pairbased contact, element type targe170 was used to model the target surface (concrete), while the element type (conta173) was used to model the contact surface (epoxy). conta174 is applicable to 3-d structural and coupled-field contact analyses, the element is used to represent contact and sliding between 3-d target surfaces and a deformable surface defined by this element. on the other hand targe170 is capable to represent various 3d target surfaces for the associated contact elements [21, 25 and 26]. mixed-mode debonding based on normal tension stress-gap and shear stress-slip was assigned to the contact surface by developing the czm in ansys menu [25, 26]. the maximum normal contact stress (eqn. (1) [26]) and the contact gap at the completion of debonding (eqn. (2) [26]) used to the tension stress-gap model were 3.28 mpa and 0.045 mm respectively. σmax   0.6 'fc (mpa) (1) ucn = gfo   '   0.2 10    24.3 c f mm         (2) where is the σmax is the maximum normal contact stress, fc′ the concrete compressive strength, ucn is the contact gap at the completion of debonding and gfo is the base value of fracture energy which depends on the maximum aggregate size and equal 0.03475 n/mm as reported in ceb-fip model code [27]. for the shear stress-slip model, the maximum equivalent tangent contact stress and tangential slip at the completion of debonding were 6.74 mpa and 1.086 mm respectively, as calculated using eqs. (3)-(5) [26]. τmax = (0.802 + 0.078 φ) fc′0.6 (mpa) (3) uct =   0.5260.976     0.802 0.078  mm   (4) φ = groove depth 1 mm groove width 2 mm   (mm/mm) (5) where τmax is the maximum shear contact stress, φ the aspect ratio of the interface failure plane, fc′ the concrete compressive strength, and uct the contact slip at the completion of debonding [26]. model geometry the same geometry, dimensions, material properties and boundary conditions for all simulated beams. concrete beam, boundary conditions and meshing of the fe model for cb, beam 2g-0.8/s and beam 2g-0.5-60/100 as an example were shown in (fig. 2). furthermore two rigid steel supports and loading plates were also modeled to transfer the applied loads and reduce the stress concentration if the loads are applied directly to the concrete elements. sensitivity analysis was performed by studying the effect of element size 15, 20, 25 and 30 mm on the results of the numerical model for cb compared to the experimental results [8] as shown in (fig. 3), from the comparisons the mesh element size 20 mm was more suitable to use to model all beams, and was used for all elements; concrete, steel, nsm bars, adhesive (epoxy) and steel plates (loading and supports). r. m. reda et al., frattura ed integrità strutturale, 53 (2020) 106-123; doi: 10.3221/igf-esis.53.09 110 (a) (b) (c) figure 2: the simulated beams: (a) cb beam, (b) generated mesh for 2g-0.8/s beam and its cross section, (c) generated mesh for 2g0.5-60/100 beam. figure 3: the effect of element size on the sensitivity of the cb model: (a) load deflection curve, (b) maximum deflection. 0 20 40 60 80 0 10 20 30 40 50 l oa d , ( k n ) deflection, (mm) cb -expremental [8] element size= 15 mm element size= 20 mm element size= 25 mm element size= 30 mm 0 0.2 0.4 0.6 0.8 1 1.2 0 10 20 30 40 u lt . d ef le ct io n r a ti o , n u m /e x p element size, (mm) loading plate support beam steel reinforcement frp bars (a) (b) r. m. reda et al., frattura ed integrità strutturale, 53 (2020) 106-123; doi: 10.3221/igf-esis.53.09 111 parametric study the non-linear finite element models were extended to investigate the effect of various parameters on the flexural behavior of nsm frp strengthened beams such as; nsm bar numbers, nsm bar length, end anchorage inclination angle and end anchorage inclination length. all beams had a total length of 2200mm and a rectangular cross-section having a width of 150mm and depth of 350mm. the beams reinforcement consisted of two 12mm diameter bars for bottom reinforcement and two 10mm diameter bars for top reinforcement. as well as 8mm diameter steel stirrups were placed at a distance of 200mm. the beam details; full dimensions, reinforcement arrangements, the loading configuration and the groove locations of the modified beams were shown in (fig. 4). the modified beams consists of one un-strengthened beam (control beam cb), and 63 strengthened beams. all beams were tested under two point loading flexural tests. the fe models were conducted to investigate the effect of various parameters on the flexural behavior of the nsm strengthened beams. full details of the parametric study of the models are listed in (fig. 5), tab. 1 and explained below. figure 4: beam details and grooves locations. figure 5: full details of the parametric study of the models. 20 300 30 350 150 110 8 @ 175mm 2 bars 12mm 2 bars 10mm stirrups 8mm 350 600 2200 1900 1600 groove 20 x 20 150 30 6565 150 30 36 38 36 groove 20 x 20 r. m. reda et al., frattura ed integrità strutturale, 53 (2020) 106-123; doi: 10.3221/igf-esis.53.09 112 the strengthened beams were divided into four groups according to end anchorage inclination angle; s (straight without inclined leg), 45º, 60º and 90º. the first group contains six beams, the first beam was strengthened with one straight nsm bar of length 1600mm, the second beam was strengthened with one straight nsm bar of length 1000mm and the third beam was strengthened with one straight nsm bar of length 500mm. the remaining three beams are similar to the above beams but with two straight nsm bars. the three remaining groups having inclined leg, each group divided to subgroups according to the inclined leg length (50, 100 and 150mm). second group consisted of eighteen beam divided into three subgroups as mention. first subgroup contain six beams, the first beam was strengthened with one nsm bar of length 1600mm with end inclined angle 45º and end inclined leg 50mm in length, the second beam was strengthened with one nsm bar of length 1000mm with end inclined angle 45º and end inclined leg 50mm in length, the third beam was strengthened with one nsm bar of length 500mm with end inclined angle 45º and end inclined leg 50mm in length, the remaining three beams with the same details but with two nsm bars. second subgroup contain six beams with the same configuration of the first subgroup but with end anchorage inclination leg length of 100mm. third subgroup contain six beams with the same configuration with end anchorage inclination leg length of 150mm. the third and fourth groups with end anchorage inclination angle of 60º and 90º respectively. tab. 1 summarizes the configuration of the modified beams. the identifications are as follows: ng-l-i/y where n is refers to no of nsm bars, g = gfrp nsm bars, l = length of nsm gfrp bar (0.8 =1600 mm, 0.5 =1000 mm and 0.25 =500 mm), i is the inclination angle of the end anchorage (s = no leg, 45º, 60º and 90º) and y is refers to end anchorage inclination length; 50, 100 and 150mm. validation of the fe models comparison between the modified model and experimental results; load deflection curve and mode of failure produced by reda et al. [8] for the control beam (cb) and (f2-180/90) beam are shown in (fig. 6). the comparison showed a good agreement between the developed models and experimental results at all stages of loading and in mode of failure. figure 6: comparison between experimental results presented in [8] and fe model: (a) load–deflection curve for cb, (b) load– deflection curve of beam f2-180/90 and (c) failure mode of beam 2f-180/90 and the predicted from fe. a r. m. reda et al., frattura ed integrità strutturale, 53 (2020) 106-123; doi: 10.3221/igf-esis.53.09 113 test variables end anchorage length (mm) end anchorage inclination angle nsm bar length (mm) nb (-) beam id reference beam -cb nsm strengthening straight 1600 1 1g-0.8-s nsm strengthening and nsm bar length10001g-0.5-s nsm strengthening and nsm bar length500 1g-0.25-s nsm strengthening and nsm bar number straight 1600 2 2g-0.8-s nsm strengthening, nsm bar length and bars no;10002g-0.5-s nsm strengthening, nsm bar length and bars no;500 2g-0.25-s end anchorage 50 45 1600 1 1g-0.8-45/50 end anchorage and bar length 10001g-0.5-45/50 end anchorage and bar length 500 1g-0.25-45/50 end anchorage and leg length 100 16001g-0.8-45/100 end anchorage, bar length and leg length10001g-0.5-45/100 end anchorage, bar length and leg length500 1g-0.25-45/100 end anchorage and leg length 150 16001g-0.8-45/150 end anchorage, bar length and leg length10001g-0.5-45/150 end anchorage, bar length and leg length500 1g-0.25-45/150 end anchorage and bars no; 50 45 1600 2 2g-0.8-45/50 end anchorage, bars no; and bar length10002g-0.5-45/50 end anchorage, bars no; and bar length500 2g-0.25-45/50 end anchorage, bars no; and leg length 100 16002g-0.8-45/100 end anchorage, bars no;, bar length and leg length10002g-0.5-45/100 end anchorage, bars no;, bar length and leg length500 2g-0.25-45/100 end anchorage, bars no; and leg length 150 16002g-0.8-45/150 end anchorage, bars no;, bar length and leg length10002g-0.5-45/150 end anchorage, bars no;, bar length and leg length500 2g-0.25-45/150 leg inclination angle 50 60 1600 1 1g-0.8-60/50 inclination angle and bar length 10001g-0.5-60/50 inclination angle and bar length 500 1g-0.25-60/50 inclination angle and leg length 100 16001g-0.8-60/100 inclination angle, bar length and leg length10001g-0.5-60/100 inclination angle, bar length and leg length500 1g-0.25-60/100 inclination angle and leg length 150 16001g-0.8-60/150 inclination angle, bar length and leg length10001g-0.5-60/150 inclination angle, bar length and leg length500 1g-0.25-60/150 inclination angle and bars no; 50 60 1600 2 2g-0.8-60/50 inclination angle, bars no; and bar length10002g-0.5-60/50 inclination angle, bars no; and bar length500 2g-0.25-60/50 inclination angle, bars no; and leg length 100 16002g-0.8-60/100 inclination angle, bars no;, bar length and leg length1000 2g-0.5-60/100 inclination angle, bars no;, bar length and leg length500 2g-0.25-60/100 inclination angle, bars no; and leg length 150 16002g-0.8-60/150 inclination angle, bars no;, bar length and leg length10002g-0.5-60/150 inclination angle, bars no;, bar length and leg length500 2g-0.25-60/150 leg inclination angle 50 90 1600 1 1g-0.8-90/50 inclination angle and bar length 10001g-0.5-90/50 inclination angle and bar length 500 1g-0.25-90/50 inclination angle and leg length 100 16001g-0.8-90/100 inclination angle, bar length and leg length10001g-0.5-90/100 inclination angle, bar length and leg length500 1g-0.25-90/100 inclination angle and leg length 150 16001g-0.8-90/150 inclination angle, bar length and leg length10001g-0.5-90/150 inclination angle, bar length and leg length500 1g-0.25-90/150 inclination angle and bars no; 50 90 1600 2 2g-0.8-90/50 inclination angle, bars no; and bar length10002g-0.5-90/50 inclination angle, bars no; and bar length500 2g-0.25-90/50 inclination angle, bars no; and leg length 100 16002g-0.8-90/100 inclination angle, bars no;, bar length and leg length10002g-0.5-90/100 inclination angle, bars no;, bar length and leg length500 2g-0.25-90/100 inclination angle, bars no; and leg length 150 16002g-0.8-90/150 inclination angle, bars no;, bar length and leg length10002g-0.5-90/150 inclination angle, bars no;, bar length and leg length500 2g-0.25-90/150 table 1: details of the parametric study of the models. r. m. reda et al., frattura ed integrità strutturale, 53 (2020) 106-123; doi: 10.3221/igf-esis.53.09 114 results and discussion he key points of the load–deflection curves obtained from the fe analysis; such as cracking load pcr, yield load py, yield deflection δy ultimate load pu and maximum deflection δu, percentage of increase in maximum load carrying capacity for strengthened beams with respect to cb pu%, in addition to ductility index μ (the ratio of the ultimate deflection to the deflection at yielding), stiffness e, energy absorption ω (the area under load–deflection curve) and also failure mode of the strengthened beams were presented in tab. 2. the control beam failed due to concrete crushing after yielding of the steel reinforcement, while beams 1g-0.25/s, 2g-0.5-45/150, 2g-0.5-60/100 and 2g-0.25-90/150 for example failed due to epoxy debonding as shown in (fig. 7) which mean that the developed fe model is capable of predicting the epoxy-concrete interface debonding failure. beam id pcr (kn) py (kn) δy (mm) pu (kn) δu (mm) pu % μ e (kn/mm) ω (kn.mm) failure mode cb 27.5 85 4.3 90.55 21 4.9 65.8 1706 cc 1g-0.8-s 33 94 4.2 122.9 14.7 35.7 3.5 65.9 1403.1 ccs 1g-0.5-s 32 92 4.2 119.7 11 32.2 2.6 65.9 953 ccs 1g-0.25-s 28 91 4.5 94.7 30 4.6 6.7 66.0 2636.4 eed-ccs 2g-0.8-s 32 106 4.5 154.1 13.6 70.2 3.0 66.1 1492.4 ec 2g-0.5-s 33 105 4.6 129.9 10.1 43.5 2.2 66.2 941.9 eed 2g-0.25-s 35.5 90 4.2 96.4 19.4 6.5 4.6 66.2 1664 ccs 1g-0.8-45/50 31 93 3.6 153.6 23.15 69.6 6.4 70.8 2796.8 cc 1g-0.5-45/50 29 102 4.3 143.14 16.189 58.1 3.8 69.0 1797.7 ccs 1g-0.25-45/50 29 103 4.6 128.58 17.17 42.0 3.7 68.9 1790.5 eed 1g-0.8-45/100 29 98 0.4 145.6 18.8 60.8 47.0 68.9 2158.1 ccs 1g-0.5-45/100 29 105 4.65 147.7 28.2 63.1 6.1 68.9 3517.2 cc 1g-0.25-45/100 29 101 4.4 130.3 17.7 43.9 4.0 68.8 1864.4 ccs-ec 1g-0.8-45/150 29 99 4.1 150.5 20.9 66.2 5.1 68.9 2474.2 ec 1g-0.5-45/150 29 99 4.1 150.8 28.5 66.5 7.0 68.7 3606.5 cc 1g-0.25-45/150 29 103 4.6 139.1 24.01 53.6 5.2 68.9 2724.2 eed 2g-0.8-45/50 33 104 4 180.8 24.11 99.7 6.0 70.3 3440.1 ccs 2g-0.5-45/50 31 104 4.1 172.15 18.37 90.1 4.5 70.1 2393.9 ccs 2g-0.25-45/50 36 103 4.2 152 29.3 67.9 7.0 70.1 3664.9 ec 2g-0.8-45/100 31 117 4.9 178.28 24.8 96.9 5.1 70.1 3563.1 cc 2g-0.5-45/100 31 101 3.7 162.5 12.5 79.5 3.4 70.1 1428.7 ccs 2g-0.25-45/100 31 103 4.3 141.1 19.7 55.8 4.6 71.5 2241.2 cc 2g-0.8-45/150 34 101 4 176.2 27.2 94.6 6.8 68.8 3801.5 cc 2g-0.5-45/150 31 105 4.1 166.9 14 84.3 3.4 70.1 1688.9 eed 2g-0.25-45/150 31 100 3.9 146.9 18.3 62.2 4.7 70.0 2105.2 ec 1g-0.8-60/50 31 101 4.4 150.9 23.2 66.6 5.3 70.1 2817.6 cc 1g-0.5-60/50 30 104 4.6 150.6 23.4 66.3 5.1 70.0 2837 ccs 1g-0.25-60/50 37 103 4.8 139.5 33.2 54.1 6.9 70.4 3966.5 eed 1g-0.8-60/100 29 107 4.8 159.8 33.4 76.5 7.0 70.2 4403.5 ied 1g-0.5-60/100 29 104 4.7 160.6 33.46 77.4 7.1 69.9 4382.5 cc 1g-0.25-60/100 36 95 4 135 19.88 49.1 5.0 69.9 2152.1 ccs 1g-0.8-60/150 30 105 4.6 154.6 28.6 70.7 6.2 70.2 3661 cc 1g-0.5-60/150 30 101 4.2 146.2 20.9 61.5 5.0 70.0 2481.9 ccs 1g-0.25-60/150 33 96 4.1 136.6 22.2 50.9 5.4 70.1 2478.7 eed t r. m. reda et al., frattura ed integrità strutturale, 53 (2020) 106-123; doi: 10.3221/igf-esis.53.09 115 2g-0.8-60/50 32 108 4 175.5 23.7 93.8 5.9 71.0 3375.9 ccs 2g-0.5-60/50 33 96 3.4 169.5 15.8 87.2 4.6 71.2 1975.7 eed 2g-0.25-60/50 31 103.8 4.4 148.1 30.6 63.6 7.0 71.1 3776.9 eed 2g-0.8-60/100 30 97 3.8 167.4 12.6 84.9 3.3 69.7 1460.4 ccs 2g-0.5-60/100 31 107 4.1 164.7 15.3 81.9 3.7 71.3 1881.1 eed 2g-0.25-60/100 31 101 3.9 142.3 19.7 57.2 5.1 70.2 2287.1 sf 2g-0.8-60/150 37 104 4.2 167.9 19.5 85.4 4.6 71.0 2593.5 ccs 2g-0.5-60/150 31 106 4 167.5 15.4 85.0 3.9 71.5 1933.9 ccs 2g-0.25-60/150 31 107 4.5 143.9 24.7 58.9 5.5 70.8 2933.4 ccs 1g-0.8-90/50 29 96 3.8 153.1 29 69.1 7.6 70.0 3646.9 cc 1g-0.5-90/50 30 100 4.4 148.6 25.2 64.1 5.7 69.9 3057.1 cc 1g-0.25-90/50 30 93 3.8 131.6 21.7 45.3 5.7 69.9 2345.8 eed 1g-0.8-90/100 29 103 4.4 152.6 35.14 68.5 8.0 69.9 4528.8 cc 1g-0.5-90/100 31 95 3.8 140.2 22.1 54.8 5.8 69.7 2576.6 eed 1g-0.25-90/100 29.5 95 4 135.2 22.1 49.3 5.5 69.7 2442.8 cc 1g-0.8-90/150 31 96 3.9 153.1 25.15 69.1 6.4 70.5 3123.8 cc 1g-0.5-90/150 30 103 4.5 145.1 20.4 60.2 4.5 69.8 2370.7 eed 1g-0.25-90/150 34 99 4.5 137.6 33.7 52.0 7.5 69.9 3970.7 eed 2g-0.8-90/50 30 106 4.2 169.8 13.3 87.5 3.2 70.2 1533.6 cc 2g-0.5-90/50 31 100.1 3.8 168.6 15.75 86.2 4.1 70.3 1932.2 ccs 2g-0.25-90/50 30 104 4.6 145.4 34 60.6 7.4 70.0 4131.2 ccs 2g-0.8-90/100 34 103 4.2 165.6 13.5 82.9 3.2 68.8 1559.9 cc 2g-0.5-90/100 33 105 4.45 156.24 14.3 72.5 3.2 68.7 1631.5 ccs 2g-0.25-90/100 35 105 4.4 141.4 31 56.2 7.0 69.6 3734 ccs 2g-0.8-90/150 33 99 3.6 168.3 16.5 85.9 4.6 70.0 2077.2 ied 2g-0.5-90/150 29 95 3.7 165 17.3 82.2 4.7 70.0 2142.8 ccs 2g-0.25-90/150 31 101 4.2 144.6 16.9 59.7 4.0 69.1 1774.8 eed pcr = load at cracking, py and δy = load and deflection at yielding, pu and δu = load and deflection at ultimate, pu% is the percentage increase in the load carrying capacity, μ = ductility index, e= stiffness, ω = energy absorption (area under p-δ curve). cc concrete crushing, ccs concrete cover separation, eed end epoxy debonding, ec epoxy crushing, ied intermediate epoxy debonding and sf shear failure. table 2: fe analysis from ansys results and failure modes of the beams. effect of nsm bar length the effect of the nsm bar length on the flexural behavior of strengthened beams was investigated in this section. (fig. 9) shows load deflection curves, mid-span steel strain and mid span frp bars strain for different beams, the bars length were 0.8, 0.5 and 0.25 of the beam span; 1600, 1000, and 500 mm. it is clear from (fig. 9-a) that increasing of the nsm bar length played a significant effect in increasing the ultimate load carrying capacity, similar result was reported in [8, 19 and 25]. the load carrying capacity for beams 2g-0.8-150/90, 2g0.5-150/90 and 2g-0.25-150/90 were 168.3, 165 and 130.9kn with increasing of 85.9, 82.2 and 44.6% respectively if compared with cb. a small noticeable enhancement in load carrying capacity between beams strengthened with nsm bar length 0.8l and 0.5l which was 2%, this may be due to the covering of the constant moment region with the bar length of 0.5l unlike the beam strengthened with frp bar of length 0.8l which extended outside the constant moment region which lead to a little effect in increasing the load carrying capacity over beam strengthened with 0.5l bar length. the same observation in the nsm frp load strain curve see (fig. 9-c). r. m. reda et al., frattura ed integrità strutturale, 53 (2020) 106-123; doi: 10.3221/igf-esis.53.09 116 (a) (b) (c) (d) figure 7: failure modes of the beams: (a) 1g-0.25/s, (b) 2g-0.5-45/150, (c) 2g-0.5-60/100 and (d) 2g-0.25-90/150. (fig. 8) shows the predicted crack patterns from the fe analysis at failure for cb and strengthened beams; 2g-0.5-s, 2g0.25-s and 1g-0.25-s. (fig. 10) shows the effect of nsm bar length for the strengthened beams on load carrying capacity with respect to load carrying capacity of the corresponding beam but without end anchorage pu/pu, θ=0, noticeable enhancement (and close together) in all beams strengthened with one nsm frp bar when use nsm bar length of 0.5l and 0.8l if compared with the same beam but without end anchorage see (fig 10-a), greater improvement in load carrying capacity when use one nsm bar of length 0.25l with respect to the same beam without end anchorage, the big improvement reflect the great effect of the end anchorage in small nsm bars length. beam strengthened with two nsm bars shown in (fig 10-b), the figure confirm that the efficiency of the end anchorage increase with the decrease of the nsm bar length from length 0.8l to length 0.25l, there are noticeable enhancement in load carrying capacity when use nsm bar length of 0.5l if compared with 0.8l. the load carrying capacity of beams strengthened with same nsm bar length gives close results even though they had different parameters such as end inclination angle and end inclination leg length, this mean that the bar length is the main factor controlling the increasing of load carrying capacity of strengthened beams. r. m. reda et al., frattura ed integrità strutturale, 53 (2020) 106-123; doi: 10.3221/igf-esis.53.09 117 (a) (b) (c) (d) figure 8: predicted crack patterns of the beams at failure: (a) cb, (b) 2g-0.5-s, (c) 2g-0.25-s and (d) 1g-0.25-s. figure 9: effect of nsm bar length: (a) load-deflection curve, (b) steel strain and (c) frp strain. 0 20 40 60 80 100 120 140 160 180 200 0 5 10 15 lo a d ,  (k n ) strain, (microstrain x 103) 2g‐0.8‐90/150 2g‐0.5‐90/150 2g‐0.25‐90/150 0 20 40 60 80 100 120 140 160 180 200 0 5 10 15 lo a d ,  (k n ) strain, (microstrain x 103) cb 2g‐0.8‐90/150 2g‐0.5‐90/150 2g‐0.25‐90/1500 20 40 60 80 100 120 140 160 180 200 0 5 10 15 20 25 30 35 lo a d ,  (k n ) deflection, (mm) cb 2g‐0.8‐90/150 2g‐0.5‐90/150 2g‐0.25‐90/150 (c)(b)(a) r. m. reda et al., frattura ed integrità strutturale, 53 (2020) 106-123; doi: 10.3221/igf-esis.53.09 118 figure 10: the effect of nsm bar length on pu/pu, θ=0 for: (a) beams strengthened with one nsm bar and (b) beams strengthened with two nsm bars. figure 11: the effect of nsm bar length on δu/δu, θ=0 for: (a) beams strengthened with one nsm bar and (b) beams strengthened with two nsm bars. figure 12: the effect of nsm bar length on e/eθ=0 for: (a) beams strengthened with one nsm bar and (b) beams strengthened with two nsm bars. the effect of nsm bar length for the strengthened beams on maximum deflection with respect to maximum deflection of the corresponding beam but without end anchorage δu/δu, θ=0 were shown in (fig. 11), the highest increasing in maximum deflection were for beam strengthened with one nsm bar of length 0.5l see (fig. 11-a). the same observation in beams strengthened with two nsm bars with end inclination angle 60º and 90º see (fig. 11-b). (fig. 12) shows the effect of nsm bar length on the beams stiffness compared to the stiffness of the corresponding beams but without end anchorage e/eθ=0, there are no noticeable changes in the stiffness of beams strengthened with one nsm bar when use different nsm bar length 0.8l, 0.5l and 0.25l see fig (12-a). 1.00 1.01 1.02 1.03 1.04 1.05 1.06 1.07 1.08 1.09 1.10 0 50 100 150 e /e θ = 0 nsm bar length (mm) two nsm bars 45    50 45    100 45    150 60    50 60    100 60    150 90    50 90    100 90    150 0.8l                        0.5l                      0.25l leg        leg           angle   length       1.00 1.01 1.02 1.03 1.04 1.05 1.06 1.07 1.08 1.09 1.10 0 50 100 150 e /e   θ = 0 nsm bar length (mm) one nsm bar 45    50 45    100 45    150 60    50 60    100 60    150 90    50 90    100 90    150 0.8l                        0.5l                      0.25l leg        leg           angle   length       0.00 0.50 1.00 1.50 2.00 2.50 3.00 0 50 100 150 δ u /δ u ,θ = 0 nsm bar length (mm) two nsm bars 45    50 45    100 45    150 60    50 60    100 60    150 90    50 90    100 90    150 0.8l                        0.5l                      0.25l leg        leg           angle   length       0.00 0.50 1.00 1.50 2.00 2.50 3.00 0 50 100 150 δ u /δ u ,θ = 0 nsm bar length (mm) one nsm bar 45    50 45    100 45    150 60    50 60    100 60    150 90    50 90    100 90    150 0.8l                        0.5l                      0.25l leg        leg           angle   length       1.00 1.10 1.20 1.30 1.40 1.50 1.60 0 50 100 150 p u /p u ,θ = 0 nsm bar length (mm) two nsm bars 45    50 45    100 45    150 60    50 60    100 60    150 90    50 90    100 90    150 leg        leg           angle   length      0.8l                        0.5l                      0.25l 1.00 1.10 1.20 1.30 1.40 1.50 1.60 0 50 100 150 p u /p u ,θ = 0 nsm bar length (mm) one nsm bar 45    50 45    100 45    150 60    50 60    100 60    150 90    50 90    100 90    150 leg        leg           angle   length       0.8l                        0.5l                      0.25l (a) (b) (b) (a) (a) (b) r. m. reda et al., frattura ed integrità strutturale, 53 (2020) 106-123; doi: 10.3221/igf-esis.53.09 119 effect of nsm bar number the effect of the nsm frp bar number was shown in (fig. 13), the figure clarify that the increasing of bar number in the strengthened beams from one bar to two bars increase the load carrying capacity of the strengthened beams, the load carrying capacity for beams 2g-0.5-50/90 and 1g-0.5-50/90 were 168.6 and 148.6kn with increasing of 86.2 and 64.1% respectively if compared with cb, using two bars instead of one bar increase the load carrying capacity by 13.5%, this result agree with this reported in [11], (fig13-c) shows the same observation for the effect of nsm bar length on the strain of nsm frp bars. figure 13: effect of nsm bar number: (a) load-deflection curve, (b) steel strain and (c) frp strain. figure 14: the effect of nsm bar number on pu/pu, θ=0 for: (a) beams strengthened with bar length 0.8l, (b) beams strengthened with bar length 0.5l and (c) beams strengthened with bar length 0.25l. figure 15: the effect of nsm bar number on δu/δu, θ=0 for: (a) beams strengthened with bar length 0.8l, (b) beams strengthened with bar length 0.5l and (c) beams strengthened with bar length 0.25l. figure 16: the effect of nsm bar number on e/e θ=0 for: (a) beams strengthened with bar length 0.8l, (b) beams strengthened with bar length 0.5l and (c) beams strengthened with bar length 0.25l. 1 1.01 1.02 1.03 1.04 1.05 1.06 1.07 1.08 1.09 1.1 0 50 100 150 e /e   θ = 0 leg inclination length (mm) bar length 0.8l 45    1 bar 45    2 bars 60    1 bar 60    2 bars 90    1 bar 90    2 bars leg        bar        angle     no;       1 1.01 1.02 1.03 1.04 1.05 1.06 1.07 1.08 1.09 1.1 0 50 100 150 e /e θ = 0 leg inclination length (mm) bar length 0.5l 45    1 bar 45    2 bars 60    1 bar 60    2 bars 90    1 bar 90    2 bars leg        bar        angle     no;       1 1.01 1.02 1.03 1.04 1.05 1.06 1.07 1.08 1.09 1.1 0 50 100 150 e /e θ = 0 leg inclination length (mm) bar length 0.25l 45    1 bar 45    2 bars 60    1 bar 60    2 bars 90    1 bar 90    2 bars leg        bar        angle     no;       0.50 0.70 0.90 1.10 1.30 1.50 1.70 1.90 2.10 2.30 2.50 2.70 2.90 3.10 0 50 100 150 δ u /δ u ,θ = 0 leg inclination length (mm) bar length 0.25l 45    1 bar 45    2 bars 60    1 bar 60    2 bars 90    1 bar 90    2 bars leg        bar       angle     no;      0.50 0.70 0.90 1.10 1.30 1.50 1.70 1.90 2.10 2.30 2.50 2.70 2.90 3.10 0 50 100 150 δ u /δ u ,θ = 0 leg inclination length (mm) bar length 0.5l 45    1 bar 45    2 bars 60    1 bar 60    2 bars 90    1 bar 90    2 bars leg        bar       angle     no;      0.80 1.00 1.20 1.40 1.60 1.80 2.00 2.20 2.40 2.60 2.80 3.00 3.20 0 50 100 150 δ u /δ u ,θ = 0 leg inclination length (mm) bar length 0.8l 45    1 bar 45    2 bars 60    1 bar 60    2 bars 90    1 bar 90    2 bars leg        bar            angle     no;        1.00 1.10 1.20 1.30 1.40 1.50 1.60 0 50 100 150 p u /p u ,θ = 0 leg inclination length (mm) bar length 0.8l 45    1 bar 45    2 bars 60    1 bar 60    2 bars 90    1 bar 90    2 bars leg        bar     angle     no;     1.00 1.10 1.20 1.30 1.40 1.50 1.60 0 50 100 150 p u /p u ,θ = 0 leg inclination length (mm) bar length 0.5l 45    1 bar 45    2 bars 60    1 bar 60    2 bars 90    1 bar 90    2 bars leg        bar        angle     no;       1.00 1.10 1.20 1.30 1.40 1.50 1.60 0 50 100 150 p u /p u ,θ = 0 leg inclination length (mm) bar length 0.25l 45    1 bar 45    2 bars 60    1 bar 60    2 bars 90    1 bar 90    2 bars leg        bar     angle     no;     0 20 40 60 80 100 120 140 160 180 200 0 5 10 15 lo a d ,  (k n ) strain, (microstrain x 103) 1g‐0.5‐90/50 2g‐0.5‐90/50 0 20 40 60 80 100 120 140 160 180 200 0 5 10 15 lo a d , ( kn ) strain, (microstrain x 103) cb 1g‐0.5‐90/50 2g‐0.5‐90/50 0 20 40 60 80 100 120 140 160 180 200 0 5 10 15 20 25 30 35 lo a d ,  (k n ) deflection, (mm) cb 1g‐0.5‐90/50 2g‐0.5‐90/50 (a) (b) (c) (a) (b) (c) (c) (b) (a) (a) (b) (c) r. m. reda et al., frattura ed integrità strutturale, 53 (2020) 106-123; doi: 10.3221/igf-esis.53.09 120 the effect of the nsm frp bar number for the strengthened beams on load carrying capacity with respect to load carrying capacity the corresponding beam but without end anchorage pu/pu, θ=0 were shown in (fig. 14), the beams strengthened with one nsm frp bar gives higher enhancement compared to the beams strengthened with two nsm frp bars in case of strengthening with nsm bar length of 0.8l, this may be because of the large confinement of the nsm bar compared to two bars show (fig. 14-a). unlike beams strengthened with two bars of length 0.5l and 0.25l gives more enhancement over beams strengthened with one nsm bar as shown in (fig. 14-b and c), this may be due to the occurrence of the full length of the nsm bars in the maximum moment region which made it more effective, and the increasing of the bars number leads to increasing the load carrying capacity. the stiffness of the strengthened beams give the same trend of load carrying capacity see (fig. 16). effect of end anchorage inclination angle in this section the effect of end anchorage inclination angle on the flexural response for cb, 2g-0.5/s, 2g-0.5-45/50, 2g0.5-60/50 and 2g-0.5-90/50 beams are shown in (fig. 17). in general beams strengthened with nsm frp having end anchorage inclined by 45º gives higher load carrying capacity compared to those beams strengthened with nsm frp having end anchorage inclined by 60º, 90º and others with straight bars that may be due to enhancement of the shear capacity of the strengthened beams, the same result was reported in [8, 24], beams strengthened with end inclination angle of 60º gives load carrying capacity close to beams strengthened with end inclination angle of 90º, as shown in (fig. 17-a); beam 2g-0.545/50 with inclination angle of 45º gives the highest load carrying capacity 172.15kn which increased by 90.1% if compared with cb. the next 2g-0.5-60/50 beam with inclination angle of 60º gives 169.5kn with increase of 87.2% if compared with cb, beam 2g-0.5-90/50 with inclination angle of 90º gives 168.6kn with increase of 86.2% if compared with cb. the lower increase in load carrying capacity was in beam 2g-0.5/s with straight end which gives 129.9kn with 43.5% enhancement when compared with cb. figure 17: the effect of end anchorage inclination angle: (a) load-deflection curve, (b) steel strain and (c) frp strain. the effect of end anchorage inclination angle on maximum load carrying capacity pu, maximum deflection δu and stiffness e for the strengthened beams with respect to corresponding beam without end anchorage were shown in (figs. 18, 19 and 20). from (fig. 18) it is very clear that the beam strengthened with end anchorage inclination angle of 45º gives highest enhancement in load carrying capacity if compared with beam strengthened with end anchorage inclination angle of 60º and 90º in cases of using two nsm bars see (fig. 18-b) and lowest enhancement in beam stiffness in beam strengthened with one nsm bar. while the large enhancement in beam stiffness in beams strengthened with two nsm bars and end anchorage inclination angle of 60º as shown in (fig. 20-b). beams strengthened with end anchorage inclination angle of 90º gives the lowest load carrying capacity if compared with beams strengthened with end anchorage inclination angle of 45º and 60º as shown in (fig.18). effect of end anchorage leg length the effect of the nsm frp end anchorage leg length on the flexural behavior of beams was shown in (figs. 18 to 21), the figures presents a comparison between different beams with the same nsm frp bar numbers, bar length and end anchorage inclination angle, the difference was in end anchorage length 50, 100 and 150mm. as shown in the (fig. 21) beams strengthened with end anchorage length of 50 and 150mm gives nearly the same load carrying capacity and highest than beams strengthened with end anchorage length of 100mm. 0 20 40 60 80 100 120 140 160 180 200 0 5 10 15 lo a d ,  (k n ) strain, (microstrain x 103) 2g‐0.5/s 2g‐0.5‐45/50 2g‐0.5‐60/50 2g‐0.5‐90/500 20 40 60 80 100 120 140 160 180 200 0 5 10 15 lo a d ,  (k n ) strain, (microstrain x 103) cb 2g‐0.5/s 2g‐0.5‐45/50 2g‐0.5‐60/50 2g‐0.5‐90/500 20 40 60 80 100 120 140 160 180 200 0 5 10 15 20 25 30 35 lo a d ,  (k n ) deflection, (mm) cb 2g‐0.5/s 2g‐0.5‐45/50 2g‐0.5‐60/50 2g‐0.5‐90/50 (a) (b) (c) r. m. reda et al., frattura ed integrità strutturale, 53 (2020) 106-123; doi: 10.3221/igf-esis.53.09 121 figure 18: the effect of end anchorage inclination angle and length on pu/pu, θ=0 for: (a) beams strengthened with one nsm bar and (b) beams strengthened with two nsm bars. figure 19: the effect of end anchorage inclination angle and length on δu/δu, θ=0 for: (a) beams strengthened with one nsm bar and (b) beams strengthened with two nsm bars. figure 20: the effect of end anchorage inclination angle and length on e/e θ=0 for: (a) beams strengthened with one nsm bar and (b) beams strengthened with two nsm bars. figure 21: the effect of end anchorage length: (a) load-deflection curve, (b) steel strain and (c) frp strain. 0 20 40 60 80 100 120 140 160 180 200 0 5 10 15 lo a d ,  (k n ) strain, (microstrain x 103) 2g‐0.5‐90/50 2g‐0.5‐90/100 2g‐0.5‐90/150 0 20 40 60 80 100 120 140 160 180 200 0 5 10 15 lo a d ,  (k n ) strain, (microstrain x 103) cb 2g‐0.5‐90/50 2g‐0.5‐90/100 2g‐0.5‐90/150 0 20 40 60 80 100 120 140 160 180 200 0 5 10 15 20 25 30 35 lo a d ,  (k n ) deflection, (mm) cb 2g‐0.5‐90/50 2g‐0.5‐90/100 2g‐0.5‐90/150 1.00 1.01 1.02 1.03 1.04 1.05 1.06 1.07 1.08 1.09 1.10 0 50 100 150 e /e θ = 0 leg inclination length (mm) two nsm bars 45        0.8l 45        0.5l 45        0.25l 60        0.8l 60        0.5l 60        0.25l 90        0.8l 90        0.5l 90        0.25l leg             bar angle     length      1.00 1.01 1.02 1.03 1.04 1.05 1.06 1.07 1.08 1.09 1.10 0 50 100 150 e /e θ = 0 leg inclination length (mm) one nsm bar 45        0.8l 45        0.5l 45        0.25l 60        0.8l 60        0.5l 60        0.25l 90        0.8l 90        0.5l 90        0.25l leg             bar angle     length      0.00 0.50 1.00 1.50 2.00 2.50 3.00 0 50 100 150 δ u /δ u ,θ = 0 leg inclination length (mm) one nsm bar 45        0.8l 45        0.5l 45        0.25l 60        0.8l 60        0.5l 60        0.25l 90        0.8l 90        0.5l 90        0.25l leg             bar angle     length      0.00 0.50 1.00 1.50 2.00 2.50 3.00 0 50 100 150 δ u /δ u ,θ = 0 leg inclination length (mm) two nsm bars 45        0.8l 45        0.5l 45        0.25l 60        0.8l 60        0.5l 60        0.25l 90        0.8l 90        0.5l 90        0.25l leg             bar angle     length      1.00 1.10 1.20 1.30 1.40 1.50 1.60 0 50 100 150 p u /p u ,θ = 0 leg inclination length (mm) two nsm bars 45        0.8l 45        0.5l 45        0.25l 60        0.8l 60        0.5l 60        0.25l 90        0.8l 90        0.5l 90        0.25l leg             bar             angle     length          1.00 1.10 1.20 1.30 1.40 1.50 1.60 0 50 100 150 p u /p u ,θ = 0 leg inclination length (mm) one nsm bar 45        0.8l 45        0.5l 45        0.25l 60        0.8l 60        0.5l 60        0.25l 90        0.8l 90        0.5l 90        0.25l leg             bar angle     length      (a) (b) (a) (b) (b)(a) (a) (b) (c) r. m. reda et al., frattura ed integrità strutturale, 53 (2020) 106-123; doi: 10.3221/igf-esis.53.09 122 beam strengthened with end inclination leg of length 0.25l gives the highest enhancement in term of load carrying capacity if compared to same beam without leg in beams strengthened with both one and two nsm frp bars as shown in (fig. 18a, b). conclusions ased on the results presented in this paper conducted from the developed fe model, the following conclusions can be drawn: the developed fe model is suitable for modeling and analyzing rc beams strengthened using nsm technique in flexure, and capable of predicting the different expected modes of failure. increasing the nsm bar length up to 0.5l has a considerable effect on the load-carrying capacity of the strengthened rc beams, while a little effect if the length increased to 0.8l if compared with beams strengthened with nsm bar length 0.5l. in case of strengthening with nsm bar length of 0.8l, the efficiency of inclined leg is more pronounced in one bar than that in two bars i.e. (pu for beams strengthened by nsm with leg/pu for beams strengthened by nsm without leg) in case of one bar ranged from 1.18 to 1.30 and in case of two bars ranged from 1.07 to 1.17. a different conclusion in case of using two nsm bars with length of 0.5l and 0.25l which gives the higher enhancement, this may be due to the occurrence of the nsm bars in the maximum moment region which made it more effective, and the increasing of the bars number leads to increasing the load carrying capacity. the strengthened beam with end anchorage inclined angle of 45º showed superior flexural behavior in term of load carrying capacity over strengthened beam with end anchorage inclined angle of 60º, 90º and other straight. references [1] wu, z., wang, x. and iwashita, k. (2007). state-of-the-art of advanced frp applications in civil infrastructure in japan, composites & polycon, american composites manufacturers association, tampa, fl usa, pp. 1-13. [2] lorenzis, l.d. and teng, j.g. (2007). near-surface mounted frp reinforcement: an emerging technique for strengthening structures, composites part b, 38, pp.119-143. [3] laraba, a., merdas, a. and chikh, n. (2014). structural performance of rc beams strengthened with nsm-cfrp, proceedings of the world congress on engineering, ii, pp. 958-966. [4] bilotta, a., ceroni, f., nigro, e. and pecce, m. (2015). efficiency of gfrp nsm strips and ebr plates for flexural strengthening of rc beams and loading pattern influence, composites structures, 124, pp. 163-175. [5] american concrete institute aci 440. (2017). guide for the design and construction of externally bonded frp systems for strengthening concrete structures. mi, usa: farmington hills; (aci 440.2r-17). [6] zhang, s.s., yu, t. and chen, g.m. (2017). reinforced concrete beams strengthened in flexure with near-surface mounted (nsm) cfrp strips: current status and research needs, composites part b, 131, pp. 30-42. [7] zhang, s.s. (2018). bond strength model for near-surface mounted (nsm) frp bonded joints: effect of concrete edge distance, composite structures, 201, pp. 664-675. [8] reda, r.m., sharaky, i.a., ghanem, m., seleem, m.h. and sallam, h.e.m. (2016). flexural behavior of rc beams strengthened by nsm gfrp bars having different end conditions, composite structures, 147, pp. 131-142. [9] sharaky, i.a., torres, l. and sallam, h.e.m. (2015). experimental and analytical investigation into the flexural performance of rc beams with partially and fully bonded nsm frp bars/strips, composite structure, 122, pp. 113126. [10] sallam, h.e.m., saba, a.m., shaheen, h.h. and abdel-raouf, h. (2004). prevention of peeling failure in plated beams, j adv concr technolo, jci, 2(3), pp. 419-429. [11] sharaky, i.a., torres, l., comas, j. and barris, c. (2014). flexural response of reinforced concrete (rc) beams strengthened with near surface mounted (nsm) fibre reinforced polymer (frp) bars, composite structures, 109, pp. 8-22. [12] parretti, r. and nanni, a. (2004). strengthening of rc members using near-surface mounted frp composites: design overview, advances in structural engineering, 7(6), pp. 469-483. [13] hassan, t. and rizkalla, s. (2004). bond mechanism of near surface mounted fibre reinforced polymer bars for flexural strengthening of concrete structures, aci structure journal, 101(6), pp. 830-839. b r. m. reda et al., frattura ed integrità strutturale, 53 (2020) 106-123; doi: 10.3221/igf-esis.53.09 123 [14] al mahmoud, f., castel, a., françois, r. and tourneur, c. (2009). strengthening of rc members with near-surface mounted cfrp rods, composite structure, 91(2), pp. 138-147. [15] pereira, s. s. r., carvalho, h., dias, j. v. f., verga m, v. r. and montenegro, p. a. (2019). behaviour of precast reinforced concrete columns subjected to monotonic short-term loading. frattura ed integrita strutturale, 13(50), 242250. doi: 10.3221/igf-esis.50.20. [16] dias, j. v. f., oliveira, j. p. s., calenzani, a. f. g. and fakury, r. h. (2019). elastic critical moment of lateral-distortional buckling of steel-concrete composite beams under uniform hogging moment. international journal of structural stability and dynamics, 19(7). doi: 10.1142/s021945541950079. [17] santos, l. r. d., cardoso, h. d. s., caldas, r. b. and grilo, l. f. (2020). finite element model for bolted shear connectors in concrete-filled steel tubular columns. engineering structures, 203. doi:10.1016/j.engstruct.2019.109863. [18] hawileh, r.a. (2012). nonlinear finite element modeling of rc beams strengthened with nsm frp rods, construction and building materials, 27, pp. 461-471. [19] el-emam, h., el-sisi, a., reda, r.m., seleem, m.h. and bneni, m. (2020). effect of concrete cover thickness and main reinforcement ratio on flexural behavior of rc beams strengthened by nsm-gfrp bars, frattura ed integrità strutturale, 52, pp.197–210. doi: 10.3221/igf-esis.52.16. [20] sharaky, i.a., selmy, s.a.i., el-attar and m.m., sallam, h.e.m. (2020). the influence of interaction between nsm and internal reinforcements on the structural behavior of upgrading rc beams, composite structures, 234-111751. [21] ansys, inc. (2018). release 19.0 documentation for ansys. [22] hawileh, r.a., rahman, a. and tabatabai, h. (2010). nonlinear finite element analysis and modeling of a precast hybrid beam–column connection subjected to cyclic loads, applied mathematical modelling, 34, pp. 2562-2583. [23] yan, f. and lin, z. (2016). bond behavior of gfrp bar-concrete interface: damage evolution assessment and fe simulation implementations, composite structures, 155, pp. 63-76. [24] sharaky, i.a., reda, r.m., ghanem, m., seleem, m.h. and sallam, h.e.m. (2017). experimental and numerical study of rc beams strengthened with bottom and side nsm gfrp bars having different end conditions, construction and building materials, 149, pp. 882-903. [25] shabana, i.s., sharaky, i.a., khalil, a., hadad, h.s. and arafa, e.m. (2018). flexural response analysis of passive and active near surfacemounted joints: experimental and finite element analysis, materials and structures, 51(107), pp. 115. [26] omran, h.y. and el-hacha, r. (2012). nonlinear 3d finite element modeling of rc beams strengthened with prestressed nsm-cfrp strips, construction and building materials, 31, pp. 74-85. 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/hrv (za stvaranje adobe pdf dokumenata najpogodnijih za visokokvalitetni ispis prije tiskanja koristite ove postavke. stvoreni pdf dokumenti mogu se otvoriti acrobat i adobe reader 5.0 i kasnijim verzijama.) /hun 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can be opened with acrobat and adobe reader 5.0 and later.) >> /namespace [ (adobe) (common) (1.0) ] /othernamespaces [ << /asreaderspreads false /cropimagestoframes true /errorcontrol /warnandcontinue /flattenerignorespreadoverrides false /includeguidesgrids false /includenonprinting false /includeslug false /namespace [ (adobe) (indesign) (4.0) ] /omitplacedbitmaps false /omitplacedeps false /omitplacedpdf false /simulateoverprint /legacy >> << /addbleedmarks false /addcolorbars false /addcropmarks false /addpageinfo false /addregmarks false /convertcolors /converttocmyk /destinationprofilename () /destinationprofileselector /documentcmyk /downsample16bitimages true /flattenerpreset << /presetselector /mediumresolution >> /formelements false /generatestructure false /includebookmarks false /includehyperlinks false /includeinteractive false /includelayers false /includeprofiles false /multimediahandling /useobjectsettings /namespace [ (adobe) (creativesuite) (2.0) ] /pdfxoutputintentprofileselector /documentcmyk /preserveediting true /untaggedcmykhandling /leaveuntagged /untaggedrgbhandling /usedocumentprofile /usedocumentbleed false >> ] >> setdistillerparams << /hwresolution [2400 2400] /pagesize [612.000 792.000] >> setpagedevice microsoft word numero_35_art_34 y. besel et alii, frattura ed integrità strutturale, 35 (2016) 295-305; doi: 10.3221/igf-esis.35.34 295 focussed on crack paths influence of joint line remnant on crack paths under static and fatigue loadings in friction stir welded al-mg-sc alloy y. besel, m. besel, u. alfaro mercado institute of materials research, german aerospace center (dlr), linder hoehe, 51147 cologne, germany yasuko.besel@dlr.de, michael.besel@dlr.de, ulises.alfaro@dlr.de t. kakiuchi, y. uematsu department of mechanical engineering, faculty of engineering, gifu university, 1-1 yanagido, gifu 501-1193, japan kakiuchi@gifu-u.ac.jp, yuematsu@gifu-u.ac.jp abstract. the influence of the joint line remnant (jlr) on tensile and fatigue fracture behaviour has been investigated in a friction stir welded al-mg-sc alloy. jlr is one of the microstructural features formed in friction stir welds depending on welding conditions and alloy systems. it is attributed to initial oxide layer on butting surfaces to be welded. in this study, two different tool travel speeds were used. jlr was formed in both welds but its spatial distribution was different depending on the tool travel speeds. under the tensile test, the weld with the higher heat input fractured partially along jlr, since strong microstructural inhomogeneity existed in the vicinity of jlr in this weld and jlr had weak bonding. resultantly, the mechanical properties of this weld were deteriorated compared with the other weld. fatigue crack initiation was not affected by the existence of jlr in all welds. but the crack propagated preferentially along jlr in the weld of the higher heat input, when it initiated on the retreating side. consequently, such crack propagation behaviour along jlr could bring about shorter fatigue lives in larger components in which crack growth phase is dominant. keywords. friction stir weld (fsw); joint line remnant (jlr); lazy s; zigzag line; aluminium alloy; fatigue. introduction onventionally, riveting has been used to join high strength aluminium plates for fuselage structures. for increasing demand towards improvement of energy consumption of an aircraft, weight reduction of a fuselage is one of the most effective solutions. as some material overlap is necessary for rivet joining, it is feasible to achieve weight reduction by replacing those rivet joints by welded butt joints. however, some aviation aluminum alloys such as precipitation hardening 2xxx and 7xxx series have poor weldability in case of fusion welding. friction stir welding (fsw) is solid state welding invented by twi [1]. in the fsw processes, a non-consumable rotating tool consisting of cylindrical shoulder and pin is inserted into and moved along the butt joint line of two sheets. frictional heating generated during this process causes softening of the material and local plastic deformation occurs. the plasticized material is stirred together by the rotation process resulting in a solid state join. since the joining process by fsw basically c y. besel et alii, frattura ed integrità strutturale, 35 (2016) 295-305; doi: 10.3221/igf-esis.35.34 296 takes place well below the melting point of the joined materials, it can even be used to join such non-fusion-weldable aluminium alloys mentioned above. characteristics of the weld depend strongly on welding parameters such as tool rotating speed and tool travel speed. high strength joints without defects such as voids or lack of penetration (lop) can be produced when using appropriate welding parameters [2, 3]. however, other types of weld imperfections or weld flaws can arise even under the optimized welding conditions, that may or may not compromise the integrity of the welded join. especially at low heat input, a faint zigzag line is sometimes formed in the stir zone [4, 5]. sato et al. revealed by tem observation that this zigzag line comprised a high density of amorphous al2o3 particles and suggested that they originated from the initial butt surfaces and its native oxide layer [6]. so, the zigzag line is also called “joint line remnant (jlr)” or “lazy s”. in the following, the term of jlr is used for this zigzag line microstructural feature in the weld. the intensity, spatial distribution and location of jlr depend mainly on the aluminium alloy system, welding parameters (esp. welding speed) and tool configuration. “root flaw” (sometimes “kissing bond”) is a weld defect with partially unwelded or only weakly bonded butt surfaces on the root side of the weld due to insufficient plunging of the tool, poor joint to tool alignment or inappropriate welding parameters [2, 7, 8, 9]. jlr can be formed accompanying root flaws depending on the welding conditions. these insufficient bonds at the bottom part of the jlr (i.e. root flaws) are not always detectable by non-destructive inspection but generally they open at root bend tests, while the jlr with sufficient root bonding does not deteriorate either root bending properties [4, 8] or tensile properties under as-welded conditions [10, 11]. fatigue properties of the fs welds with jlr formation have been investigated for various al alloys, e.g. 5083 and 6082 [8], 2024 and 5083 [12], 2024-t4 [13], 2198-t8 [14], and 1050-o [15]. some researchers reported that kissing bonds or weak bonds on the root side caused fatigue crack initiation resulting in lower fatigue strengths [8, 12, 13]. in [14] and [15] it has been observed that fatigue fracture can take place independently from the existence of the jlr and cause hardly influence on fatigue strengths. uematsu et al. investigated the fatigue initiation site in 1050-o with jlr and showed that localized plastic deformation at the boundary between tmaz and haz at the advancing side of the fsw line caused fatigue crack initiation [15]. they also investigated fatigue behavior in fswed samples of both heat-treatable and non-heat treatable alloys and concluded that fatigue fracture location was dependent on alloys due to their different microstructures and hardness distributions. while fsw is a promising candidate as future joining technology, al-mg-sc alloys are promising candidates as next baseline material for metallic fuselage structures. they have lower density and better corrosion resistance than conventional fuselage material, e.g. 2024, and they basically show good weldability [16]. the characteristic al3sc dispersoids in al-sc alloys show high thermal stability and act as recrystallization inhibitor [17]. due to these thermally stable precipitations in al-mg-sc alloys, they are expected not to have pronounced degradation of mechanical properties by fsw processing, which are generally found in heat-treatable 2xxx alloys without post-welding heat treatment. it has been demonstrated that the formation of joint line remnant and the mechanical integrity of the fsw joint are controlled by the welding parameters [4]. consequently, in this study, the friction stir welding technique was applied to an al-mg-sc alloy at two different tool travel speeds. formation of the joint line remnant was examined, tensile and fatigue tests were performed and the influence of the jlr on the fracture behavior under tensile as well as fatigue loadings of the fswed al-mg-sc alloy was investigated. experimental procedures he material used in this study was al-mg-sc alloy 5024 –h116 plate with a nominal thickness of 3.3 mm. its nominal chemical composition is listed in tab. 1. the fsw tool consisted of a conical threaded pin (diameter 4.5 mm) and a cylindrical shoulder (diameter 12.5 mm). two plates were butted and position-controlled friction stir welded at constant tool rotation speed of 1200 rpm. the surface of the plates to be welded was ground directly before the fsw process to remove the native oxide layer, and thus, minimize the influence of initial surface conditions on the joint quality. however, as a common matter of fact, an amorphous aluminum oxide film layer can be rapidly formed in laboratory air [18]. the tool travel speed was controlled at two levels: 480 and 720 mm/min (hereafter welds produced with these parameters are referred to as weld-480 and weld-720, respectively). temperature during welding was monitored with a thermocouple plunged at 7 mm away from the joint line in the retreating side plate at a depth of 1 mm from the top surface. the root bending tests revealed no cracking, i.e. no root flaws were produced with those welding parameter sets. structural features of the welds including the jlr were examined with a light microscope on the polished cross sections etched with 5 wt% naoh aqueous solution. hardness profiles on the mid-section in the welds were measured by means of a micro-vickers hardness tester under a load of 9.8 n. t y. besel et alii, frattura ed integrità strutturale, 35 (2016) 295-305; doi: 10.3221/igf-esis.35.34 297 for tensile tests, specimens with a parallel section length of 70 mm, a gauge length of 30 mm, width of 12 mm and nominal thickness of 3.3 mm were prepared (fig.1). the weld center line passed through the center of the gauge length. the tensile tests were carried out at room temperature with the specimens as welded without removing any surface features of the weld such as weld flashes. the geometry of the fatigue specimens is shown in fig. 2. the weld center line lies perpendicularly to the loading direction in the center of the specimen. tool marks and flashes formed by fsw on the surface were removed to eliminate their geometrical influence (e.g. notch effect) on crack initiation behavior. prior to the fatigue tests, the specimen surfaces were mechanically polished with emery papers and finished with buff-polishing using 1µm-diamond suspension. the fatigue tests were carried out under cyclic loading conditions with a stress ratio of r = -1 at a frequency of 10 hz. si fe cu zn mg mn ti sc al 0.25 0.4 0.2 0.2 3.9 0.25 0.2 0.4 bal. table 1: nominal chemical composition of al-mg-sc alloy in wt%. figure 1: tensile test specimen. figure 2: fatigue test specimen. results and discussion weld structures ig. 3 shows optical micrographs of the cross sections of weld-480 and weld-720. in order to verify formation of jlr in those welds, stir-in-plate friction stir welding (one plate welding) was performed in al-mg-sc plate with the tool travel speed of 600 mm/min. the macroscopic structure of the stir-in-plate weld is shown in fig. 3(c). dashed lines in the figures indicate the pin width. all welds had a stir zone (sz) in the center surrounded by a thermomechanically affected zone (tmaz). fine recrystallized and equiaxed grains were formed in sz around the weld center in all welds. based on ebsd-measurements the average grain sizes in sz of weld-480 and 720 were determined as 1.12 µm and 1.63 µm, respectively. obviously, no zigzag line was observed in the stir-in-plate weld, see fig. 3(c). on the contrary, zigzag lines were observed in the butt weld for all weld conditions, as seen in figs. 3(a) and (b), where the zigzag lines were highlighted with freehand lines for aid of visualization. although the native oxide layer had been removed before the welding process, it seems that a new thin oxide film grew rapidly on the butting surfaces in laboratory air condition. this new oxide film was so thick that incomplete breakups remained resulting in formation of the zigzag line i.e. joint line remnant (jlr) in the welds. the degree of breakup of the oxide layer can sometimes be estimated based on the heat input during fsw [4, 5]. generally, the heat input in fsw is considered to correlate with tool rotational speed and tool travel speed, where higher heat input is caused by higher tool rotational speed or lower tool travel speed, respectively [3, 19]. consequently, in this study, the f y. besel et alii, frattura ed integrità strutturale, 35 (2016) 295-305; doi: 10.3221/igf-esis.35.34 298 higher heat input is expected for weld-480 than weld-720. indeed, the maximum temperatures measured at 7 mm away from the joint line were 377 and 339 °c for weld-480 and weld-720, respectively. the distribution of the jlr of weld-480 was wider on both advancing side (as) and retreating side (rs) than that of weld720. as marked with the rectangle i in fig. 3(a), the jlr was extended towards the edge of sz on the retreating side. in weld-720 (lower heat input), the jlr distributed more around the weld center in sz (fig. 3(b)). this spatial distribution of jlr serves as an indicator for the degree of material flow and mixing during the fsw process. seidel and reynolds visualized the material flow in the weld using marker insert technique and observed increased mixing in the weld with a decreasing weld pitch which is defined as the tool advance per rotation [20]. they suggested that the higher heat input might result in the softening of a greater amount of material, and consequently more material flow in the weld zone. in our study, comparing the distribution of the jlr in each weld, it can be said that greatest material flow was brought about in weld-480, i.e. higher heat input. this finding is consistent with the results of seidel and reynolds. (a) weld 480 (b) weld 720 (c) stir-in plate weld figure 3: macroscopic weld structure. hardness and tensile test results vickers hardness profiles of the different welds are shown in fig. 4. in all weld conditions, softening occurred in sz and hardness was mostly recovered in the neighboring tmaz. the hardness in sz of weld-720 was higher than that of the other two welds and the lowest hardness was observed in weld-480. this order reflects inversely the order of the heat input: i.e. higher heat input brought about greater softening in sz. tensile test results are summarized in tab. 2. fracture occurred in sz in all welds. tensile strength and yield stress of weld-480 are lower than those of weld-720. in particular, the degradation in elongation of weld-480 is significant: the reduction is more than 30% compared to weld-720, although sz (i.e. the fracture site) in weld-480 was softer than weld720. weld id e-modulus [mpa] 0.2% yield stress 0.2 [mpa] tensile strength ts [mpa] elongation max [%] weld-480 70793 218 311 4.61 weld-720 72182 237 329 6.77 table 2: tensile test results. y. besel et alii, frattura ed integrità strutturale, 35 (2016) 295-305; doi: 10.3221/igf-esis.35.34 299 figure 4: hardness profiles along midsection of weld. in order to identify fracture location of each weld, cross sections of the fractured samples were metallographically prepared, i.e. polished followed by etching. as clearly seen in fig. 5, fracture behavior in weld-480 seems different from that in weld-720. while in weld-720 fracture occurred nearly through the center of the weld, weld-480 was fractured on the retreating side. fig. 6 shows the intersection of jlr and the fracture plane of weld-480 in more detail; the area corresponds to the dashed rectangle in fig. 5(a). the fracture path in the lower part was smooth and steadily curved while the fracture face in the upper part was jagged but macroscopically nearly straight, see also upper part of fracture face in fig. 5(a). the lower smooth fracture path presumably originated from jlr; as pointed by an arrow in fig. 6 fracture face and jlr meet tangentially. furthermore, taking into account the jlr spatial distribution in the weld seam (see fig. 3(a)), it can be finally concluded that the fracture in the lower part took place along jlr. scanning electron microscope (sem) fractography was performed on the fracture surfaces in the upper and lower areas, as shown in fig. 7(a) and (b), respectively. the sem fractographs revealed different fracture behavior in both areas: comparably large dimples were observed in the upper area, while very finely shallow dimples covered the fracture surface in the lower area. the shallow dimples indicate low ductility or weak bonding. since jlr was formed at the location of originally abutting free surfaces, it can be considered that the shallow dimples in the lower area were attributed to weak or incomplete bonding at jlr. because more than about 30 % of the fracture path proceeded along jlr (lower part a-a’ in fig. 5(a)), weld-480 exhibited significantly lower elongation and strengths than the other welds showing jlr independent fracture paths. heat input in fsw is described to be proportional to tool rotational speed and inversely proportional to tool travel speed [3, 19]. it has been reported that high zigzag line pattern (herein jlr) is not formed in the high heat input welds, since degree of stirring increases with heat input and results in sufficient break-up of the initial oxide layer [4]. in this study, friction stir welding was performed at two different tool travel speed, i.e. two different heat input levels. jlr was formed in all welds, but the distribution of jlr in each weld was different. in the weld with the highest heat input (weld-480), the specimen was fractured partially along jlr which resulted in lower elongation than the other welds with lower heat input. since the high heat input in weld-480 facilitated the material transport, the spatial distribution of jlr became wider. in the area where the fracture occurred, jlr located around the boundary of sz and tmaz, see fig. 8, which corresponds to area i marked with square in fig. 3(a). since the direct stirring of the material, fine-recrystallized, equiaxed grains were formed in sz. meanwhile, the material in tmaz experienced strong shear deformation that resulted in a unique wavy structure as seen on the right-hand side in fig. 8. additionally, jlr at the fracture site lay almost normal to the loading direction and seemed to have comparably weak bonding properties. furthermore, local inhomogeneity and mismatch of microstructure may induce local strain concentration under mechanical loading. as a consequence, it can be concluded that the fracture factually occurred along jlr in this area in weld-480 although higher heat input was applied than weld720 not showing this kind of fracture along jlr. y. besel et alii, frattura ed integrità strutturale, 35 (2016) 295-305; doi: 10.3221/igf-esis.35.34 300 (a) weld 480 (b) weld 720 figure 5: cross sections of tensile fractured welds. figure 6: magnified view of intersection of jlr and fracture surface (see dashed rectangle in fig. 5) figure 7: sem fractographs of tensile fracture surface of weld-480: (a) upper part of weld, (b) lower part of weld along jlr. y. besel et alii, frattura ed integrità strutturale, 35 (2016) 295-305; doi: 10.3221/igf-esis.35.34 301 figure 8: micrograph of weld-480 in area i of fig. 3(a) around tensile fracture site. fatigue fracture behavior s-n data of the fsw joints are drawn together with that of the base material in fig. 9. since the welds showed softening in all conditions, their fatigue lives were lower than the base material. open marks indicate that fatigue crack initiation took place at weld defects. more details of the fatigue behavior of the fswed al-mg-sc alloy have been discussed somewhere else [21]. in this study, the focus is limited to the influence of jlr on the fatigue behavior. in weld-720, jlr didn’t play any roles in either initiation or propagation behavior: i.e. fatigue cracks in those welds were initiated independently from the jlr distribution and their growth was not affected by jlr. in weld-480, fatigue crack initiation sites scattered around the weld both on the advancing side (as) and retreating side (rs), as marked in fig. 10. when a crack initiated on as (at stress amplitudes a = 240 mpa and 200 mpa), its propagation was also within as and no influence of jlr was observed. similarly, in the case of the crack initiation on rs (at stress amplitudes a = 220 mpa and 180 mpa), the crack propagation was also in rs. fig. 11 shows sem image of the fracture surface of the sample tested at a = 220 mpa. the crack origin was located on the bottom surface as indicated with an arrow, and the crack grew from this origin radially towards the opposite top surface. macroscopic crack growth directions according to the striation patterns on the fracture surface are indicated with several white arrows. even after the crack reached the opposite surface of the specimen, the crack front trace was not parallel to the through-thickness direction as it is typically observed for through-thickness cracks in homogeneous material under tensile cyclic loading. figure 9: fatigue data of friction stir welds and base material (r=-1). y. besel et alii, frattura ed integrità strutturale, 35 (2016) 295-305; doi: 10.3221/igf-esis.35.34 302 figure 10: fatigue crack initiation sites of weld-480. irregular fracture morphology was observed in the lower and left-hand part of the specimen. in order to investigate the fatigue crack growth behavior on this irregular fracture, a cross section at b-b’ was examined, as shown in fig. 12. macroscopically large flexure was observed on this cross section (fig. 12(a)). the profile c-c’ corresponds to the irregular fracture site (see fig. 11). jlr was well pronounced in this cross section, and the crack encountered jlr. as seen in the enlarged image (fig. 12(b)) of the rectangle in fig. 12(a), it can be observed that the crack propagation partially occurred along jlr. this area was nearly consistent with the fracture site along jlr in the tensile test as mentioned in the previous section (see fig. 8). thus, also fatigue crack propagation partially along jlr resulted in macroscopic flexure of the crack path. sem fractography was performed for more detailed observation in the areas marked by the rectangles ii in fig. 11. fig.s 13(a) shows area ii where the irregular fracture began to appear. the lower part of the image displays the irregular fracture surface, i.e. jlr-fracture site, see arrow (1). in the upper part fine striations were observed with intervals of a few micrometers. major crack propagation direction in this area was upwards according to the orientation and the development of intervals of the striations, see arrow (2), and it indicates that the crack propagated from the jlr-fracture. fig. 13(b) shows higher magnification image of area iii marked in fig. 13(a). no striation was observed in the jlrfracture part (lower part of fig. 13(b)). instead, very fine asperity was formed. since the asperity of jlr fracture in the lower part of fig. 13(b) was equivalent to the average grain size of weld-480 (1.67 µm), it is considered that the crack propagated intergranularly at jlr. figure 11: fatigue fracture surface of weld-480 tested at a = 220 mpa. figure 12: cross section at b-b’ in fig. 11: (a) macrograph, (b) magnified view of the area defined by the rectangle in (a). y. besel et alii, frattura ed integrità strutturale, 35 (2016) 295-305; doi: 10.3221/igf-esis.35.34 303 figure 13: sem observation of fatigue fracture surface of weld-480: (a) magnified view of area ii in fig. 11, (b) magnified view of area iii. based on the evidence of the crack growth direction in the surrounding matrix as seen in fig. 13(b), it can be concluded that when the crack approached there the fatigue crack propagated preferentially at jlr because of its weak bonding, and grew further from the jlr-fracture site into the matrix. as a result, the macroscopic crack growth direction in this area became not totally perpendicular to the through-thickness direction as seen in fig. 11. the fine dimples in area vii of jlr-fracture surface in the residual fracture regime resembled the monotonic tensile fracture as seen in fig. 7(b). taking into account the elevated net stress in this section due to the already long through-thickness crack, it can be concluded that the weakly bonded jlr was ruptured quasi-statically. thus, when the fatigue crack approached jlr, it propagated firstly at jlr and then into the matrix. the fracture area at jlr was about 10% of the total fracture surface. the locally weak bonding clearly accelerated local crack growth rate around jlr. however, significant decrease in fatigue life of the two specimens where jlr-fracture occurred on rs was not observed as seen in fig. 9. it is generally known that most part of fatigue lives of a metallic component is spent on initiation and early propagation phases. the fracture at jlr occurred in the phase of comparably fast striation growth as seen in fig. 13. therefore, the crack propagation at jlr could shorten the fatigue life to some extent but its contribution to the total life was insignificant in the laboratory size specimens used in this study. in contrast, when the component is large, i.e. crack propagation phase may occupy a significant amount of fatigue life, the crack growth along jlr could lead to significantly shorter life time of such components. summary and conclusions nfluence of joint line remnant (jlr) in friction stir welded (fswed) al-mg-sc alloy on tensile and fatigue fracture behavior was investigated. butt welding was performed under two different heat input conditions by changing tool travel speeds. fatigue tests were conducted with polished specimens, i.e. without welding flash and root flaws. although the native oxide layer was removed before fs welding, a new oxide layer was immediately formed under lab air condition. this newly generated oxide layer was thick enough to form pronounced jlr in the welds. the distribution of jlr in the welds clearly were differed by the heat input levels: in the lower heat input weld, jlr distributed mainly around the weld center. higher heat input facilitated the material flow during the welding process, and consistently jlr in the weld with the high heat input was more widely distributed and reached the boundary of stir zone (sz) and thermomechanically affected zone (tmaz) on retreating side (rs) of the weld, where microstructural mismatch exists. when jlr located within sz, tensile fracture occurred independently of the existence of jlr. however, because of the local microstructural mismatch between sz and tmaz existing at jlr in addition to weak bonding of jlr, tensile fracture occurred partially along jlr in the higher heat input weld. as a result, this weld showed lower yield and tensile strengths and less ductility than the other weld. fatigue crack initiation was not influenced by jlr in all welds. but in the higher heat input weld, when a crack initiated on rs and approached jlr, the fatigue fracture occurred preferentially along jlr. due to the weak bonding, the fatigue crack propagated intergranularly at jlr. contribution of this preferential fatigue crack growth at jlr towards the total fatigue life was insignificant because it happened in the striation growth stage in a comparably small specimen. in the case that the fatigue crack growth phase contributes significantly to fatigue lives, i.e. in large components under moderate i y. besel et alii, frattura ed integrità strutturale, 35 (2016) 295-305; doi: 10.3221/igf-esis.35.34 304 fatigue loading, the effect of jlr on crack growth rates as well as the applicability of linear elastic fracture mechanics and e.g. its k-concept should be investigated. acknowledgement he authors would like to express their sincere gratitude to the japanese society for the promotion of science for funding most of this work under the “jsps postdoctoral fellowship (short-term) for north american and european researchers” (fy 2012). further thanks to the colleagues from the institute for materials research of the german aerospace center in cologne, namely mr. sauer for providing the fsw joints and mr. fuchs for mechanical testing. references [1] thomas, w. m., nicholas, e. d., needham, j. c., murch, m. g., temple-smith, p., dawes, c. j, improvements relating to friction welding. european patent specification ep 0 615 480 b1, (1992). [2] leonard, a.j., lockyer s.a., flaws in friction stir welds, proc. of 4th int. symposium on friction stir welding, park city, utah, usa, (2003). [3] kim, y.g., fujii, h., tsumura, t., komazaki, t., nakata, k., three defect types in friction stir welding of aluminum die casting alloy, mat. sci. eng. a, a415 (2006) 250–254. [4] sato, y.s., takauchi, h., park, s.h.c., kokawa, h., characteristics of the kissing-bond in friction stir welded al alloy 1050, mater. sci. eng. a, a405 (2005) 333–338. [5] peel, m., steuwer, a., preuss, m., withers, p.j., microstructure, mechanical properties and residual stresses as a function of welding speed in aluminium aa5083, acta mater., 51 (2003) 4791–4801. [6] sato, y.s., yamashita, f., sugiura, y., park, s.h.c., kokawa, h., fib-assisted tem study of an oxide array in the root of a friction stir welded aluminium alloy, scripta mater., 50 (2004) 365–369. [7] oosterkamp, a., oosterkamp, l.d., nordeide, a., ‘kissing bond‘ phenomena in solid-state welds of aluminum alloys, welding journal, 83, (2004) 225–231. [8] dickerson, t.l., przydatek, j., fatigue of friction stir welds in aluminium alloys that contain root flaws, int. j. of fatigue, 25 (2003) 1399–1409. [9] vugrin, t., schmuecker, m., staniek, g., root flaws of friction stir welds – an electron microscopy study, in k.v. jata et al. (ed.): friction stir welding and processing iii, the minerals, metals and materials society, 2005, pp. 277284. [10] liu, h.j., chen, y.c., feng, j.c., effect of zigzag line on the mechanical properties of friction stir welded joints of an al-cu alloy, scripta mater., 55 (2006) 231–234. [11] ren, s.r., ma, z.y., chen, l.q., effect of initial butt surface on tensile properties and fracture behavior of friction stir welded al-zn-mg-cu alloy, mater. sci. eng. a, a479 (2008) 293–299. [12] zhou, c., yang, x., luan, g., effect of oxide array on the fatigue property of friction stir welds, scripta mater., 54 (2006) 1515–1520. [13] di, s., yang, x., luan, g., jian, b., comparative study on fatigue properties between aa2024-t4 friction stir welds and base materials, mater. sci. eng. a, a435–436 (2006) 389-395. [14] jolu, t.l., morgeneyer, t.f., gourgues-lorenzon, a.f., effect of joint line remnant on fatigue lifetime of friction stir welded al-cu-li alloy, science and technology of welding and joining, 15 (2010) 694–698. [15] uematsu, y., tokaji, k., shibata, h., tozaki, y., ohmune, t., fatigue behavior of friction stir welds without neither welding flash nor flaw in several aluminium alloys, int. j. of fatigue, 31 (2009) 1443–1453. [16] filatov, y.a., yelagin, v.i., zakharov, v.v., new al-mg-sc alloys, mater. sci. eng. a, a280 (2000) 97–101. [17] riddle, y.w., sanders, t.h., a study of coarsening, recrystallization, and morphology of microstructure in al-sc-(zr)(mg) alloys, metall. mater. trans. a, 35a (2004) 341–350. [18] michel, s.a., oxidation and fatigue crack growth in aluminium alloys, proc. of 3rd int. conf. microscopy of oxidation, cambridge uk, (1996). [19] frigaard, o., grong, o., mildling, o.t., a process model for friction stir welding of age hardening aluminum alloys, metall. mater. trans a, 32a (2001) 1189–1200. t y. besel et alii, frattura ed integrità strutturale, 35 (2016) 295-305; doi: 10.3221/igf-esis.35.34 305 [20] seidel, t.u., reynolds, a.p., visualization of the material flow in aa2195 friction-stir welds using a marker insert technique, metal. mater. trans. a, 32a (2001) 2879–2884. [21] besel, m., besel, y., alfaro mercado, u., kakiuchi, t., uematsu, y., fatigue behavior of friction stir welded al-mg-sc alloy, int. j. fatigue, 77 (2015) 1-11. doi: 10.1016/j.ijfatigue.2015.02.013. << /ascii85encodepages false /allowtransparency false /autopositionepsfiles true /autorotatepages /none /binding /left /calgrayprofile (dot gain 20%) /calrgbprofile (srgb iec61966-2.1) /calcmykprofile (u.s. web coated \050swop\051 v2) /srgbprofile (srgb iec61966-2.1) /cannotembedfontpolicy /error /compatibilitylevel 1.4 /compressobjects /tags /compresspages true /convertimagestoindexed true /passthroughjpegimages true /createjobticket false /defaultrenderingintent /default /detectblends true /detectcurves 0.0000 /colorconversionstrategy /cmyk /dothumbnails false /embedallfonts true /embedopentype false /parseiccprofilesincomments true /embedjoboptions true /dscreportinglevel 0 /emitdscwarnings false /endpage -1 /imagememory 1048576 /lockdistillerparams false /maxsubsetpct 100 /optimize 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/hrv (za stvaranje adobe pdf dokumenata najpogodnijih za visokokvalitetni ispis prije tiskanja koristite ove postavke. stvoreni pdf dokumenti mogu se otvoriti acrobat i adobe reader 5.0 i kasnijim verzijama.) /hun 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/pdfxoutputintentprofileselector /documentcmyk /preserveediting true /untaggedcmykhandling /leaveuntagged /untaggedrgbhandling /usedocumentprofile /usedocumentbleed false >> ] >> setdistillerparams << /hwresolution [2400 2400] /pagesize [612.000 792.000] >> setpagedevice microsoft word numero_58_art_28_3248.docx r. capozucca et alii, frattura ed integrità strutturale, 58 (2021) 386-401; doi: 10.3221/igf-esis.58.28 386 focussed on steels and composites for engineering structures rc beams damaged by cracking and strengthened with nsm cfrp/gfrp rods r. capozucca, e. magagnini, m.v. vecchietti struct.section dicea, università politecnica delle marche, ancona, italy r.capozucca@staff.univpm.it, e.magagnini@staff.univpm.it, m.v.vecchietti@pm.univpm.it s. khatir soete laboratory, faculty of engineering and architecture, ghent university, belgium samir.khatir@ugent.be abstract. the near surface mounted (nsm) method of inserting fiber reinforced polymer (frp) elements (rods or lamina) into notches has been shown to be a good way for restoring reinforced concrete (rc) elements. the knowledge about the use of glass-frp rod following the nsm to reinforce rc beams is limited. this paper deals with the analysis of static and dynamic behaviour of rc beams with and without strengthening. the response of rc beams was assessed at different concrete’s damage level by non-destructive vibration tests. first, a couple of beams have been analysed: one rc beam subjected to bending and under vibration tests; another one beam, damaged by bending and strengthened with nsm carbon-frp rods tested again under vibration. further, one rc beam damage was analysed under bending and vibration tests without strengthening; successively, the beam model with nsm gfrp rod has been tested following the same loading path. below experimental results are shown and commented; in particular, changes in frequency values are related to the evolution of damage level affected rc beams with nsm cfrp and gfrp rods. keywords. nsm, cfrp/gfrp, damage, bending and vibration tests, frequency. citation: capozucca, r., khatir, s., magagnini, e., vecchietti, m.v., rc beams damaged by cracking and strengthened with nsm cfrp/gfrp rods, frattura ed integrità strutturale, 58 (2021) 386-401.. received: 26.08.2021 accepted: 02.09.2021 published: 01.10.2021 copyright: © 2021 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. introduction he near surface mounted (nsm) technique for the strengthening of reinforced concrete (rc) elements foresees grooves along the concrete cover where the fibre reinforced polymer (frp) rods are glued with the use of mortar or epoxy resin. t https://youtu.be/injd0o7k8ym r. capozucca et alii, frattura ed integrità strutturale, 58 (2021) 386-401; doi: 10.3221/igf-esis.58.28 387 the advantages of using nsm frp rods as strengthening compared to external bounded (eb) frp strips are several: greater simplicity of installation; more remarkable ability to prevent loss of bond; and above all, minor susceptibility to damage deriving from collision, high temperature and fire [1-3]. although the nsm technique appears capable of solving several aspects related to the strengthening with composite materials, the current knowledge on nsm strengthening is more limited than eb method. the effectiveness of nsm frp rods for strengthening is contingent on preserving the rod-to-concrete bond [4-7]. in fact, bond behaviour has an influence on the ultimate capacity of reinforced elements as well as on serviceability aspects such as crack width and spacing [8-12]. experimental results of pull-out tests [12-13] show that the filler used to fill the grooves and its properties greatly influences the bond behaviour. the response of the nsm frp bars in terms of load carrying capacity increases if a filler able to give a better redistribution of the bond stresses along the anchor length is adopted. the most common filler used for the nsm technique is a bi-component epoxy resin [4,5-14]. experimental data show that the tensile strength values of the epoxy resin can vary between 13.8 and 42.6mpa, while those of cement mortar between 6.3 and 9 mpa. moreover, some geometrical parameters could affect the adherence and, therefore, the structural behaviour, such as dimensions of the rod section; thickness and height for rectangular section bars; width and depth of the groove; distance between two adjacent grooves; distance between the groove and the edge of the beam [14,15]. numerical modelling by finite element (fe) has proved that the tensile stresses in concrete decrease as the width of the groove increases [14]. some experimental investigations [15-17] have dealt with assessing the bond behaviour in the case of non-circular frps. for rectangular frp lamina, it is suggested that the minimum width of a groove should not be less than three times the thickness of the rectangular bar and the minimum depth should not be less than 1.5 times the height of the bar itself [18]. few experimental researches deal with investigating the behaviour of rc beams strengthened with nsm frp elements made by different composite materials [19-22] and the assessment of strengthened rc beams with nsm frp rods with non-destructive free vibration tests [23,24]. this paper deals with the investigation by static and dynamic tests on rc beams strengthened both with cfrp and gfrp rods. a couple of beams with one rc beam subjected to bending and under vibration tests at different damage degrees is analyzed, while a second beam, damaged by bending and strengthened with nsm carbon-frp rods, has been tested. another rc beam damaged by bending strengthened by nsm gfrp rod has been experimentally studied. the response of rc beams has been assessed through non-destructive vibration monitoring at different level of damage due to concrete cracking or decrease of bond of frp rods. static and vibration results are shown and discussed below. static and dynamic tests of rc beams with nsm cfrp rods wo rc beams, labelled and b0 and b1, having a rectangular section of 150x220 mm and a length of 1700 mm were subjected to static bending tests. both beam samples were reinforced with 2+2∅10 mm longitudinal steel bar and shear resistant reinforcement consisting of ∅6/60 mm stirrups. the reinforcement’s entity has been defined to give a scaled behavior with respect to a real beam with greater dimensions; moreover, the stirrup’s disposition has been designed to guarantee the failure of the specimens by bending and not by shear. two notches with dimensions of 20x20 mm were realized at the beam’s intrados; the grooves were made for both specimens, but the two ∅8 mm cfrp reinforcing bars were inserted only in specimen b1 (fig. 1) [4]. the beam b0, on the other hand, was tested in the condition without strengthening. preliminary tests were carried out on concrete, steel and cfrp elements. preliminary tests showed that the concrete used has a characteristic cylindrical strength equal to fc,av.~ 53.34 n/mm2 and young’s modulus ~36·103 n/mm2. monotonic tensile tests were carried out under displacement control on three samples of steel bars, leading to determine an average yielding stress equal to fy,av.~509 n/mm2 and young’s modulus about ~2.1·105 n/mm2. the cfrp rods used have a nominal diameter of ø8mm and are superficially treated to have better adherence. cfrp rods were tested in tension following the suggestion of [25] and the results are shown in tab. 1. the average young’s modulus was evaluated equal to ef,av ~ 1.42·105n/mm2. a bi-component epoxy resin was adopted to glue the cfrp rods to the concrete. the behaviour of rc beams with and without frp nsm strengthening was assessed through four points bending tests, where the two supports and the two loading points were placed, respectively, at 1500 mm and 300 mm form the centerline. the static tests were carried out, on all the specimens, by means of loading and unloading cycles and, successively, to increased bending load until failure (tab. 2). t r. capozucca et alii, frattura ed integrità strutturale, 58 (2021) 386-401; doi: 10.3221/igf-esis.58.28 388 b0 b1 figure 1: rc beam section with and without cfrp rods. specimen nominal diameter ø [mm2] real diameter ø [mm2] section area a [mm2] failure load fm [n] tensile strength ft [n/mm2] average tensile strength ft,av. [n/mm2] 1 8 9.1 65.04 144270 2218.21 2153.27 2 8 9.1 65.04 135870 2089.06 3 8 9.1 65.04 134490 2067.84 4 8 9.1 65.04 137200 2109.51 5 8 9.1 65.04 148400 2281.71 table 1: results of uniaxial tensile test on cfrp rods. with the aim to obtain information about the strain’s evolution in the steel bars and in the cfrp rod, three electronical strain gauges were adopted; specifically, two of them were applied on the steel longitudinal reinforcement, both positioned at the centerline, one on the beam’s extrados and the other one on the intrados; the last one was positioned in the middle of the beam on one of the two cfrp rods. two horizontal lvdt’s recorded the concrete’s deformations in the compressed zone. an inductive lvdt with a full scale of 100 mm and a sensitivity of 0.01 mm was used to evaluate the beam’s deflection at the centerline. another displacement transducer was also positioned at 100 mm from the support. a hydraulic jack with a maximum capacity of 500 kn together with a load distribution’s system was utilized for the application of the two forces symmetrically applied in the center line at a wheelbase of 300 mm. for each step of cyclic loading a corresponding damage level, identified as di with i=1,…,7, was defined. from laboratory static tests, on specimens b0 (without strengthening) and b1 (strengthened with cfrp rods), the experimental results shown in tab. 3 and tab. 4 were obtained. the comparison between the envelopes of experimental diagrams moment, m, vs curvature, χ, for beams b0 and b1 is given in fig. 2. r. capozucca et alii, frattura ed integrità strutturale, 58 (2021) 386-401; doi: 10.3221/igf-esis.58.28 389 damage degree beam b0 beam b1 with nsm cfrp rod moment [knm] load [kn] moment [knm] load [kn] d1 2.16 7.21 2.13 7.10 d2 4.28 14.32 4.29 14.29 d3 9.46 31.50 9.48 31.61 d4 11.61 38.73 11.63 38.77 d5 14.30 47.80 26.39 87.97 d6 31.48 104.92 d7 34.62 115.39 table 2: experimental step of loading. deflection δ [mm] concrete strain εc,sup steel strain extradoss εs1 steel strain intradoss εs2 curvature χ [1/mm·10-6] d1 0.56 -0.000203 -0.000136 0.000660 5.31 d2 1.79 -0.000494 -0.000181 0.001092 8.48 d3 5.07 -0.001011 -0.000362 0.002399 18.41 d4 8.62 -0.001796 -0.000154 0.004676 32.2 d5 28.02 table 3: experimental data obtained by static tests for beam b0. deflection δ [mm] concrete strain εc,sup steel strain extradoss εs1 steel strain intradoss εs2 cfrp strain εcfrp curvature χ [1/mm10-6] d1 0.25 -0.000070 -0.000096 0.000034 0.000093 1.02 d2 0.67 -0.000171 -0.000186 0.000238 0.000329 2.78 d3 2.17 -0.000421 -0.000422 0.000925 0.001373 9.70 d4 2.88 -0.000530 -0.000510 0.001231 0.001767 12.31 d5 7.17 -0.001208 -0.001039 0.002873 0.004151 28.05 d6 10.66 -0.001690 -0.001290 0.002764 0.005748 38.04 d7 15.25 -0.001997 -0.001459 0.002836 0.008690 54.86 table 4: experimental data obtained by static tests for beam b1. r. capozucca et alii, frattura ed integrità strutturale, 58 (2021) 386-401; doi: 10.3221/igf-esis.58.28 390 the experimental modal testing was performed adopting the so call “mobile accelerometer” technique where an accelerometer, positioned at several points during tests, measures the beam’s acceleration after the excitation by an impact hammer positioned at a fixed point. the fixed point of specimen’s excitation by impact was established as the one placed at 4.5 cm from one end (point ch1 in fig. 3). the response of the structure is obtained as an average of 10 impacts for each accelerometer position, for a total of 14 accelerometer positions. the accelerometer used for the dynamic experimentation is model 4508 piezoelectric ccld accelerometer, 100mv/g, 1 slot, top connector, by brüel & kjær; it is a piezoelectric transducer. this accelerometer model has a very low weight (4.8 g) and covers a frequency range from 0.3 hz to 8000 hz with a sensitivity of 10 mv/g. one of the aims of the dynamic experimental program is to obtain a comparison between the experimental and theoretical characterization of the beam models, to check the reliability of the experimental results. we then proceeded to the theoretical determination of the first four natural frequencies for the specimens with and without cfrp nsm reinforcement according to the euler-bernoulli continuous beam model. figure 2: experimental diagrams bending moment, m, curvature, χ, beams b0 and b1. figure 3: instrumentations for vibration tests. 0 5 10 15 20 25 30 35 0 0.00001 0.00002 0.00003 0.00004 0.00005 0.00006 m [knm] χ [1/mm] b0 b1 r. capozucca et alii, frattura ed integrità strutturale, 58 (2021) 386-401; doi: 10.3221/igf-esis.58.28 391 for beam b0, tab. 5 contains the natural frequencies obtained for each position of the accelerometer at different level of damage. fig. 4 shows the variations of the experimental frequencies with reference to the damage-free state (d0) for cracking due to the increase in bending; the variation of the experimental frequencies with respect to d0, for all damage levels, for the first four vibration modes, is expressed as:    0 0 0 100r d di d d f f f f f (1) where dif is the frequency obtained for the damage condition di and 0df is the frequency obtained in the undamaged condition d0. for beam b1, tab. 6 summarized the natural frequencies obtained for each position of the accelerometer at different level of damage. the variations of the experimental frequencies with reference to the damage-free state (d0) for cracking due to the increase in bending are shown in fig. 5. figure 4: variation percent of frequencies for beam b0 at different damage degree. figure 5: variation percent of frequencies values for beam b1 at different damage degree. 0 3 5 8 10 13 15 18 20 23 25 28 30 33 35 1 2 3 4 δ f/ f d 0 [% ] mode d0-d1 d0-d2 d0-d3 d0-d4 0 2 4 6 8 10 12 14 16 18 20 22 24 26 1 2 3 4 δ f/ f d 0 [% ] mode d0-d1 d0-d2 d0-d3 d0-d4 d0-d5 d0-d6 r. capozucca et alii, frattura ed integrità strutturale, 58 (2021) 386-401; doi: 10.3221/igf-esis.58.28 392 mode 1 mode 2 frequency [hz] frequency [hz] theor. d0 d1 d2 d3 d4 theor. d0 d1 d2 d3 d4 m1 308 275 252 228 215 180 848 706 686 635 579 519 m2 308 275 251 227 215 180 848 706 686 635 580 521 m3 308 276 251 226 215 180 848 706 685 635 579 521 m4 308 275 250 228 215 180 848 706 685 635 579 520 m5 308 275 250 228 216 180 848 706 685 635 580 521 m6 308 275 250 227 216 180 848 706 684 634 580 520 m7 308 275 249 228 216 180 848 706 684 635 580 521 m8 308 275 250 228 216 180 848 m9 308 275 249 228 216 180 848 706 684 636 581 520 m10 308 275 249 227 216 180 848 706 684 635 581 520 m11 308 275 249 226 216 180 848 706 684 635 581 520 m12 308 275 250 226 216 180 848 706 684 635 581 521 m13 308 275 249 228 216 180 848 706 684 635 581 522 m14 308 275 250 228 217 180 848 706 684 635 582 520 average 308 275 250 227 216 180 848 706 685 635 580 520 mode 3 mode 4 frequency [hz] frequency [hz] theor. d0 d1 d2 d3 d4 theor. d0 d1 d2 d3 d4 m1 1663 1274 1238 1192 1076 999 2749 1875 1823 1753 1657 m2 1663 1237 1149 1079 999 2749 1824 1753 1658 m3 1663 1237 1193 1077 1000 2749 1822 1752 1659 m4 1663 1274 1235 1193 1075 999 2749 1822 1751 1658 m5 1663 1274 1235 1194 1076 999 2749 1823 1754 1662 m6 1663 1233 1079 1000 2749 1881 1822 1751 1662 m7 1663 1274 1233 1195 1077 1000 2749 1824 1755 1662 m8 1663 1274 1233 1195 1077 1000 2749 m9 1663 1274 1233 1195 1079 999 2749 1878 1821 1755 1663 m10 1663 1274 2749 1879 1823 1753 1664 m11 1663 1275 1233 1193 1080 1000 2749 nc 1824 1753 nc m12 1663 1275 1232 1193 1080 1001 2749 1878 1820 1753 1665 m13 1663 1274 1232 1196 1079 1001 2749 1877 1816 1753 1664 m14 1663 1275 1231 1196 1084 2749 nc 1820 1755 average 1663 1274 1234 1190 1078 1000 2749 1878 1822 1753 1661 table 5: average experimental frequency values recorded for all mark points mi with i=1,…,14 at different damage degree on beam b0. r. capozucca et alii, frattura ed integrità strutturale, 58 (2021) 386-401; doi: 10.3221/igf-esis.58.28 393 mode 1 mode 2 frequency [hz] frequency [hz] theor. d0 d1 d2 d3 d4 theor. d0 d1 d2 d3 d4 m1 311 284 281 272 254 248 857 723 719 710 674 659 m2 311 284 281 272 254 249 857 723 719 710 674 659 m3 311 284 281 272 255 249 857 723 719 710 674 660 m4 311 284 281 272 255 249 857 723 719 710 676 660 m5 311 284 280 272 256 249 857 722 719 710 676 660 m6 311 284 280 272 256 249 857 722 719 710 676 660 m7 311 284 280 272 256 249 857 723 719 711 677 660 m8 311 284 280 272 256 249 857 m9 311 284 280 272 256 249 857 722 719 711 676 660 m10 311 284 280 272 256 250 857 722 719 711 677 661 m11 311 284 280 272 256 250 857 722 719 711 677 661 m12 311 284 280 272 256 250 857 723 719 711 677 661 m13 311 284 280 272 257 250 857 723 719 711 677 662 m14 311 284 280 272 256 250 857 722 719 710 677 662 average 311 284 280 272 256 249 857 723 719 710 676 660 mode 3 mode 4 frequency [hz] frequency [hz] theor. d0 d1 d2 d3 d4 theor. d0 d1 d2 d3 d4 m1 1680 1298 1294 1281 1216 1195 2777 1923 1915 1893 1833 1809 m2 1680 1237 1221 1216 1195 2777 1923 1914 1895 1835 1812 m3 1680 1298 1293 1280 1216 1196 2777 1923 1913 1894 1835 1812 m4 1680 1298 1293 1281 1218 1197 2777 1922 1913 1893 1835 1816 m5 1680 1299 1293 1281 1218 1197 2777 1924 1914 1896 1837 1811 m6 1680 1245 1232 1220 1196 2777 1923 1914 1894 1838 1811 m7 1680 1299 1293 1281 1219 1197 2777 1924 1913 1896 1839 1811 m8 1680 1299 1293 1282 1219 1197 2777 m9 1680 1298 1293 1281 1219 1197 2777 1922 1913 1895 1839 1812 m10 1680 1300 1292 1282 1219 1197 2777 1922 1914 1893 1839 1813 m11 1680 1301 1293 1281 1219 1198 2777 1923 1913 1894 1840 1813 m12 1680 1298 1293 1282 1219 1198 2777 1922 1914 1896 1839 1814 m13 1680 1299 1292 1281 1219 1198 2777 1922 1913 1894 1839 1814 m14 1680 1301 1292 1283 1219 1199 2777 1924 1914 1894 1840 1814 average 1663 1274 1234 1190 1078 1000 2749 1878 1822 1753 1661 table 6: average experimental frequency values recorded for all mark points mi with i=1,…,14 at different damage degree on beam b1. r. capozucca et alii, frattura ed integrità strutturale, 58 (2021) 386-401; doi: 10.3221/igf-esis.58.28 394 moment [knm] curvature χ [1/mm·10-6] mode 1 mode 2 mode 3 δf = fd0-fdi δf/fd0 [%] δf = fd0-fdi δf/fd0 [%] δf = fd0-fdi δf/fd0 [%] d0 0 0 d0-d0 d0-d0 d0-d0 d1 1.803 0.0858 d0-d1 9.14 d0-d1 3.04 d0-d1 3.16 d2 4.287 0.848 d0-d2 17.35 d0-d2 10.06 d0-d2 6.59 d3 9.463 1.84 d0-d3 21.55 d0-d3 17.80 d0-d3 15.38 d4 11.461 2.22 d0-d4 34.56 d0-d4 26.28 d0-d4 21.54 d5 11.606 3.22 table 7: exp. values by static test and frequency variations δf/fd0 for each damage di – b0. moment [knm] curvature χ [1/mm·10-6] mode 1 mode 2 mode 3 δf = fd0-fdi δf/fd0 [%] δf = fd0-fdi δf/fd0 [%] δf = fd0-fdi δf/fd0 [%] d0 0 0 d0-d0 d0-d0 d0-d0 d1 2.1309 0.102 d0-d1 1.31 d0-d1 0.49 d0-d1 1.04 d2 4.287 0.278 d0-d2 4.23 d0-d2 1.67 d0-d2 1.96 d3 9.482 0.970 d0-d3 9.98 d0-d3 6.44 d0-d3 6.21 d4 11.631 1.231 d0-d4 12.22 d0-d4 8.60 d0-d4 7.86 d5 26.39 2.805 d0-d5 13.93 d0-d5 11.75 d0-d5 12.05 d6 31.477 3.804 d0-d6 25.68 d0-d6 20.56 d0-d6 20.86 d7 34.617 5.486 table 8: exp. values by static test and frequency variations δf/fd0 for each damage di – b1. tab. 7 and tab. 8 summarize the experimental values of frequency variations δf/fd0 evaluated for beams b0 and b1 in relation to the curvatures, χ, obtained by static tests at different damage degree di. in fig. 6 the frequency variations in percent for equivalent steps of damage di in relation to the undamaged state d0 for the first four vibration modes r=1,…4 are compared considering both beam models. figure 6: frequency value variations for equivalent steps of damage di in relation to the undamaged state d0 for the first four modes r=1,…4 – beams b0 and b1 0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 1 2 3 4 δ f/ f d 0 [% ] mode b1[d0-d1] b1[d0-d2] b1[d0-d3] b1[d0-d4] b0[d0-d1] b0[d0-d2] b0[d0-d3] b0[d0-d4] r. capozucca et alii, frattura ed integrità strutturale, 58 (2021) 386-401; doi: 10.3221/igf-esis.58.28 395 static and dynamic tests of rc beams with nsm gfrp rods n this section, the experimental behaviour of one rc beam, identified as b2, with and without nsm gfrp rod strengthening, is assessed by free vibration consider the undamaged condition and the damaged condition obtained by concrete cracking due to bending. the rc beam was initially subjected to static tests without strengthening; once obtained a relevant crack patter, the nsm gfrp rod strengthening was applied, and the rc beam was once again subjected to loading. figure 7: geometric section of rc beam b2 with steel reinforcement. concrete steel gfrp rod epoxy resin cylindrical compressive strength [n/mm2] young’s modulus [n/mm2] density [ns2/mm4] yielding strength [n/mm2] young's modulus [n/mm2] tensile strength [n/mm2] young's modulus [n/mm2] young's modulus [n/mm2] poisson’s coefficient 44 35.0·103 2.4·10-9 500 34.50 1040 34·103 1.6·103 0.20 table 9: results of preliminary tests on materials. figure 8: configuration of modal testing: impact hammer and accelerometer. i r. capozucca et alii, frattura ed integrità strutturale, 58 (2021) 386-401; doi: 10.3221/igf-esis.58.28 396 in this phase, the static and dynamic investigations were carried out on a rc beam model characterized by a rectangular section of 120x160 mm and a length of 2200 mm, as shown in fig. 7. the sample is reinforced with upper and lower longitudinal reinforcement of 2ø10 and shear resistant reinforcement of ø6 stirrups. also in this case, a 2x2 cm intradosal groove has been prepared to allow the accommodation of the ø9-gfrp rod following the nsm technique, after the first phase of testing (fig. 7). tab. 9 contains a summary of the mechanical characteristics of each material, as concrete, steel, gfrp rod and epoxy resin, experimentally got by preliminary tests. the mechanical features of the gfrp rod were obtained by laboratory tests on two samples carried out following the astm-d 3039 standard [25]. as already introduced, the experimental characterization of beam b2 involves static and dynamic tests. the hinge ends configuration was adopted for the investigation to reach the condition of simply supported beam. in fig. 8, it can be observed the apparatus adopted for reproduced the hinge constraint at the ends of beam. this condition was maintained for both static bending and vibration tests. for reproduce the hinge constraints, customized metal devices were realized; 3 mm metal disk and a 3 mm thick neoprene lamina were used to solve contact problems at the extremities. first of all, the undamaged condition of beam b2 without strengthening was tested by vibration. the beam was excited by applying an impulse with a hammer as impact device. the impact was applied in a point maintained fixed during tests (fig. 8). a response transducer, that is a piezoelectric accelerometer, was adopted for sensing force and motion of the beam. it was placed in 9 different positions and an average of 10 impacts was considered for each location. a fast fourier transformation (fft) two-channel analyser and pulse software allowed the data acquisition. the geometrical and mechanical parameters given above were considered for the evaluation of theoretical frequencies adopting the euler-bernoulli beam model. fig. 9 gives a comparison between the frequency values obtained theoretically and experimentally from free vibration tests on the beam with different constraint conditions at the ends and always in an undamaged condition d0. this comparison allowed us to check the quality of the experimental apparatus, in such a way as to have a control over the reliability of the experimental measurements. after the first dynamical characterization, rc beam b2 was subjected to a series of load step p by bending. for each phase of loading, different damage conditions di with i=1,…,3 due to concrete cracking were identified. three different cycles of loading were identified: p1=4.0kn, p2=8.0kn, p3=18.0kn (fig. 10). the bending tests involve the use of vertical hydraulic jack together with a load cell, as system to transfer and measure the applied load; strain gauges, as electronic devices to measure the strain on the steel reinforcement; two lvdts, as mechanical devises to record deflection at the centerline and near the support. (a) (b) figure 9: theoretical and experimental frequencies for undamaged rc beam b2: (a) free-free ends and (b) hinge-hinge ends. for each each level of damage by bending (fig. 10), the rc beam b2, in the un-strengthened condition, was subjected to vibration monitoring. the average frequencies obtained by dynamic tests, for each state of damage di with i =1,…,3, are summarized in fig. 11. after the first phase of concrete’s cracking, the damaged rc beam b2 were tested with the presence of a nsm gfrp rod filled into the notch. in this case four damage level were identified: p1 = 4kn – damage degree d1; p2 =8 kn – d2; p3 =16kn – d3; p4=28kn d4. in fig. 12, the crack pattern obtained at the fourth level of damage d4 is shown. also in this case, after each cycle of loading, modal testing was carried out. fig. 13 contains the average frequency values measured for strengthened beam b2, considering the first four vibration modes. r. capozucca et alii, frattura ed integrità strutturale, 58 (2021) 386-401; doi: 10.3221/igf-esis.58.28 397 figure 10: load-deflection diagrams for the first three damage level on un-strengthened rc beam b2. figure 11: average frequency values obtained for b2 without strengthening. figure 12: crack pattern at damage level d4 for beam b2 with nsm gfrp rod. figure 13: average frequency values obtained for b2 with nsm gfrp rod strengthening. for each damage levels, modal testing gives the frequency response functions (frfs). in fig. 14, it can be seen the overlap of all frfs obtain for each state of damage. 0 2 4 6 8 10 12 14 16 18 20 0 2 4 6 8 10 12 load p [kn] deflection [mm] d1 d2 d3 r. capozucca et alii, frattura ed integrità strutturale, 58 (2021) 386-401; doi: 10.3221/igf-esis.58.28 398 figure 14: frfs obtained at each level of damage di i=1,…,4 for beam b2 strengthened with nsm gfrp rod strengthening. discussion of experimental results he results provided by the experimentation allow us to define some useful aspects for the strengthening technique of rc beams according to the nsm method with cfrp and gfrp rods. the influence of the rc beam’s nonlinear behavior due to concrete cracking under loading on the beams is reflected in the different vibration modes considered. it can be summarized thus: the variation percent of the frequency values as compared to the integral, nondamaged state, d0, is always increasing from the elastic-linear uncracked phase to the elastic-linear cracked phase, till the inelastic and plastic phase. the natural frequency values tend to describe the beam’s global response relative to loss of bending stiffness, and they are less sensitive to local stiffness variations. another result that needs to be underlined is the excellent behaviour of the nsm strengthening both with cfrp and gfrp rods in terms of maintaining adherence without exhibiting loss of adherence or damage, with increased resistance capacity of the c-gfrp rod strengthened beams. fig. 6 shows for beams b0 and b1, with and without cfrp nsm rods, the comparison between the frequency variations in relation to the average experimental values obtained on undamaged beams, that is on the initial condition for the loading program. it can be noted that the decrease of frequency is more accentuated for beam b0 without strengthening compared to beam b1 damaged and then strengthened with cfrp rods. this result is also highlighted in the case of beam b2 damaged and then reinforced with nsm gfrp rod. for the beam without strengthening, the increasing of damage corresponds to the reduction of frequencies, confirmed by variations equal to 10%÷20% for mode r=1 (fig. 15). the reduction of frequency values at the increment of damage state is less significant for the strengthened beam with nsm gfrp rod (fig. 16). in this case, the maximum of the frequency variations is equal to about 4%. the presence of the nsm strengthening with c-gfrp acts by reducing the width of the cracks even for high loads and this is experimentally recorded by the vibrational response of the strengthened beam. t r. capozucca et alii, frattura ed integrità strutturale, 58 (2021) 386-401; doi: 10.3221/igf-esis.58.28 399 figure 15: frequency value variations in percent for the first four modes (beam b2 without strengthening). figure 16: frequency value variations in percent for the first four modes (beam b2 with nsm gfrp rod). conclusion his paper describes an investigation on rc beams strengthened with nsm cfrp and gfrp rods. the investigation foresaw both static and free vibration tests. the main results of the experimental campaign are as follows:  excellent behavior of the strengthened beams both with nsm cfrp and nsm gfrp rods in terms of maintaining adherence without exhibiting loss of bond or damage before the collapse of compressive concrete;  the presence of the nsm strengthening both with nsm cfrp and nsm gfrp rods acts by reducing the width of the cracks even for high entity of load;  the analysis of experimental frequencies is an adequate ndm to monitor rc beams with reinforcement or with strengthening by frp rods. t r. capozucca et alii, frattura ed integrità strutturale, 58 (2021) 386-401; doi: 10.3221/igf-esis.58.28 400 acknowledgement he polytechnic university of marche supplied research funds to enable this experimental study. the authors would like to thank all the technicians and students who assisted in the development of this research work. references [1] de lorenzis, l., teng, j.g. (2007). near-surface mounted frp reinforcement: an emerging technique for strengthening structures, composites part b: engineering, 38(2), pp. 119–143. [2] capozucca, r. (2009). static and dynamic response of damaged rc beams strengthened with nsm cfrp rods, composite structures 91(3), 237–248. [3] el-hacha, r., rizkalla, s. (2004). near-surface mounted fibre reinforced polymer reinforcements for flexural strengthening of concrete structures. aci structural journal, 101(5), pp. 717-726. [4] capozucca, r. (2013). analysis of bond-slip effects in rc beams strengthened with nsm cfrp rods. composite structures, 102, pp. 110-123. [5] capozucca, r. (2011) bond-slip effects in rc beams strengthened with near surface mounted cfrp rods, in: proceedings fib symposium, prague 2, pp. 779–782. [6] cosenza, e., manfredi, g., realfonzo, r. (1997). behavior and modeling of bond of frp rebars to concrete, asce journal of composites for construction, 1(2), pp. 40–51. [7] de lorenzis, l., nanni, a. (2002). bond between near surface mounted fiber reinforced polymer rods and concrete in structural strengthening. aci structural journal, 99(2), pp. 123–133. [8] hassan, t.k., rizkalla, s. (2004). bond mechanism of nsm frp for flexural strengthening of concrete structures, aci structural journal, 101(6), pp. 830–839. [9] lees, j.m. (2009). sensitivity of nsm reinforcement forces to bond-slip effects, in: 4th international conference on advanced composites in construction (acic 09), pp. 227–238, edinburgh. [10] perera, k., ibell, t., darby, a., denton, s. (2009). bond mechanisms of various shapes of nsm cfrp bars. in: 4th international conference on advanced composites in construction, (acic 09), pp. 250–257, edinburgh. [11] lu, x.z., teng, j.g., ye, l.p., jiang, j.j. (2005). bond–slip models for frp sheets/plates bonded to concrete, engineering structures, 27(6), pp. 920–937. [12] sharaky, i.a., torres, l., baena, m., miàs, c. (2013). an experimental study of different factors affecting the bond of nsm frp bars in concrete. composite structures, 99, pp. 350–365. [13] de lorenzis, l., nanni, a. (2001). shear strengthening of reinforced concrete beams with nsm fibre-reinforced polymer rods. aci struct. j., 98(1), pp. 60–68. [14] hassan, t., rizkalla, s. (2003). investigation of bond in concrete structures strengthened with near-surface mounted carbon fibre reinforced polymer strips. j. of comp. for constr., 7(3). [15] sena cruz, j.m., barros, j.a.o., gettu, r., azevedo, a.f.m. (2006). bond behavior of near-surface mounted cfrp laminate strips under monotonic and cyclic loading. asce, journal of composites for construction, 10, pp. 295-303. [16] capozucca, r., bossoletti, s., montecchiani, s. (2015). assessment of rc beams with nsm cfrp rectangular rods damaged by notches. composite structures, 128, pp. 322-341. [17] blaschko m. (2003). bond behaviour of cfrp strips glued into slits. in: proceedings frprcs-6. singapore: world scientific, pp: 205–214. [18] nanni, a., di ludovico, m., parretti, r. (2004). shear strengthening of a pc bridge girder with nsm cfrp rectangular bars. advances in structural engineering, 7(4), pp. 297-309. [19] issa, m.s., metwally, i.m., elzeiny, s.m. (2011). influence of fibres on flexural behavior and ductility of concrete beams reinforced with gfrp rebars. eng. structures, 33, pp.1754-1763. [20] capozucca, r. (2014). on the strengthening of rc beams with near surface mounted gfrp rods. composite structures, 117c, pp: 143-155. [21] ding, y., ning, x., zhang, y., pacheco-torgal, f., aguiar, j.b. (2014). fibres for enhancing of the bond capacity between gfrp rebar and concrete. construction and building materials, 51, pp: 303-312. [22] masmoudi, a., ouezdou, m., ben, bouaziz j. (2012). new parameter design of gfrp rc beams. construction and building materials, 29, pp. 627-632. t r. capozucca et alii, frattura ed integrità strutturale, 58 (2021) 386-401; doi: 10.3221/igf-esis.58.28 401 [23] capozucca, r. (2018). vibration analysis of damaged rc beams strengthened with gfrp. composite structures, 200, pp. 624-634. [24] capozucca, r., bossoletti, s. (2014). static and free vibration analysis of rc beams with nsm cfrp rectangular rods. composites part b: engineering, 67, pp. 95-110. [25] astm d 3039/d 3039 m 08. standard test method for tensile properties of polymer matrix composite materials. american standard of testing and materials, (2008). microsoft word numero_61_art_25_3527.docx k. belkaid et alii, frattura ed integrità strutturale, 61(2022) 372-393; doi: 10.3221/igf-esis.61.25 372 a simple and efficient eight node finite element for multilayer sandwich composite plates bending behavior analysis khmissi belkaid, nadir boutasseta, hamza aouaichia, djamel eddine gaagaia, badreddine boubir research center in industrial technologies crti p.o.box 64, cheraga, algeria khmissi.belkaid85@gmail.com, n.boutasseta@crti.dz, h.aouaichia@crti.dz, d.gaagaia@crti.dz, b.boubir@crti.dz adel deliou university of med seddik benyahia (umsb of jijiel), department of mechanical engineering laboratory of materials and reactive systems lmsr, university djillali, liabes, sidi bel-abbes, algeria. del032003@yahoo.fr, adel.deliou@univ-jijel.dz, deliouadel15@gmail.com abstract. in this paper, a c0 simple and efficient isoparametric eight-node element displacement-model based on higher order shear deformation theory is proposed for the bending behavior study of multilayer composites sandwich plates. difficult c1-continuity requirement is overcome efficiently by choosing seven degrees of freedom for each element node: two displacements for inplane behavior and five bending unknowns namely: a transverse displacement, two rotations and two shear angles, which results in the approximation formulation having only first order derivative requirement. the governing equations of the element (constitutive, virtual work and equilibrium equations) are implemented for the prediction of approximate solutions of deflections and stresses of sandwich plates linear elastic problems. the formulation element is able to present a cubic in-plane displacement along both core and faces sandwich cross-sectional, as well as, the shear stresses are found to vary as quadratic field without requiring shear correction factors and independent from any transverse shear locking problems when the plate is thin. the accuracy and validity of the proposed formulation is verified through the numerical evaluation of displacements and stresses and their comparison with the available analytical 3d elasticity solutions and other published finite element results. keywords. third order shear deformation theory; sandwich composite plates; finite element; bending behavior. citation: belkaid, k., boutasseta, n., aouaichia, h., gaagaia, d. e., boubir, b., deliou, a., a simple and efficient eight node finite element for multilayer sandwich composite plates bending behavior analysis, frattura ed integrità strutturale, 61 (2022) 372-393. received: 27.03.2022 accepted: 01.06.2022 online first: 10.06.2022 published: 01.07.2022 copyright: © 2022 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. https://youtu.be/222xnmsjfzm k. belkaid et alii, frattura ed integrità strutturale, 61(2022) 372-393; doi: 10.3221/igf-esis.61.25 373 introduction andwich composite plates are being increasingly used in many fields of modern technology due to their high strength, weight ratio and low maintenance cost. a good understanding of their behavior in terms of deformations and stresses distribution through the structures provide an effective vision for their applications. generally, sandwich composite structures are made-up of a very rigid isotropic or orthotropic face sheets and relatively soft thick core material. in mechanical analysis of the bending sandwich plate, displacement fields vary in a zigzag manner through the thickness, thus making the displacements very discontinuous at the layer interfaces due to the large variation in stress between layers. hence, the development of a suitable computational theory is required for accurately predicting the responses of these laminated sandwich structures. in this context, a number of shear deformation theories have been developed in order to accurately model multilayer plate. in the literature, the simplest equivalent single layer esl laminate approach is the classical laminated plate theory (clpt) kirchhoff assumptions [1]. their finite element model spatial approximations [2] contain c0-requirement for the in-plan displacements using lagrange interpolation function, and transverse displacement c1-requirement using hermite interpolation functions over the element. however, these elements models are characterized by a complex mathematical formulation due to the c1-requirement, and the theory is only appropriate for thin laminate plate analysis due to neglecting the effects of transverse shear deformation. the simplest theory which takes into account the transverse shear deformation is the first order shear deformation theory [fsdt] [3, 4]. their finite element models [5] are characterized by a simple formulation with c0-requirement for all degrees of freedom using lagrange interpolation function. however, the theory requires shear correction factors and the transverse shear stresses show at least a quadratic distribution through the plate thickness according to pagano three-dimensional elasticity theory [6]. various analytical higher order theories (hsdt) have been proposed for the multilayer composite structures analysis, taking into account shear deformation effects without shear correction. their kinematics assumption is expanded up to higher powers of the thickness coordinate and quadratic transverse shear [7-10]. barut et al. [11] analyzed a thick sandwich plate by third and second order theories in which the in-plane and the transverse displacements show cubic and quadratic variations respectively through the thickness of the plate. other analytical and experimental works can be found for the sandwich plate and shell analysis: noor et al. [12], kant et swaminathan [13], mantari et al. [14], grover et al.[15], kanematsu et al. [16], torabizadeh and fereidoon, [17], m. michele et al. [18], deliou adel [19]. however, analytical methods are only suitable for specific simple boundary conditions and geometries. in this case, several (2d) finite element models based on higher order shear deformation theory (hsdt) have been developed [20] for the static analysis of multilayer composite sandwich plates. b. pandya , t. kant [21] have presented a simple isoparametric finite element formulation based on a higher-order displacement model for flexure analysis of multilayer symmetric sandwich plates. b.s. manjunatha, t. kant [22] have evaluated the transverse stresses between layers of laminated composite and sandwich laminates using c0 nine and sixteen finite element formulation based on higher order theory. however, the models resort to use selective numerical integration scheme in order to overcome the shear locking problem. t. kant and j. kommineni, [23] presented a simple c0 quadrilateral lagrange finite element formulation with nine-nodes and nine degrees of freedom per node based on refined higher-order shear deformation theory for the linear and geometrically non-linear analysis of fiber reinforced composite and sandwich plates. however, the selective integration scheme based on gauss quadrature rules is introduced in order to overpass the shear locking problem. c.-p. wu and c.-c. lin [24] have presented the stress and displacement analysis of the thick sandwich plates using an interlaminar stress mixed nine-node finite element based on high order deformation theory. however, the formulation element possesses eleven nodal field variables in each node. r.p. khandelwal et al. [25] have developed an efficient c0 continuous nine-node finite element model with eleven nodal field variables for each node based on combined theories refined higher order shear deformation theory (rhsdt) and least square error (lse) method for the static analysis of soft core sandwich plates, the model satisfied the continuity of transverse shear stress condition between layer interfaces and zero transverse shear stress at the top and bottom of the sandwich plate. m.k. pandit et al. [26] proposed a computationally efficient c0 nine-node finite element based on improved higher order zigzag theory for the static analysis of laminated sandwich plate with soft compressible core. however, the element has elven nodal field variables for each node adopting a reduced integration technique for the evaluation of stiffness matrix. t.m. tu , t.h. quoc [27] have developed a nine-nodded rectangular element with nine degrees of freedom at each node for the bending and vibration analysis of laminated and sandwich composite plates. the theory accounts for parabolic distribution of the transverse shear strains through the thickness of the plate and rotary inertia effects. a. nayak et al. [28] analyzed the bending behavior of isotropic, laminated composite and sandwich plates using two c0 quadrilateral finite element formulations based on highers k. belkaid et alii, frattura ed integrità strutturale, 61(2022) 372-393; doi: 10.3221/igf-esis.61.25 374 order theory where the element possess seven nodal field variables in each node. however, the formulations introduced assumed strain interpolations for the transverse shear strain in order to overcome the shear locking problem. chalak et al. [29] presented an improved c0 2d nine-node finite element with eleven field variables per node. the model is based on higher order zigzag plate theory and has been applied to the analysis of laminated composites and sandwich plates. r. sahoo and b. singh [30] suggested an efficient c0 eight nodded isoparametric element with seven degrees of freedom per node based on a new inverse trigonometric zigzag theory for the static analysis of laminated and sandwich plates. however, the selective integration scheme is used in order to solve the locking shear problem. according to this literature survey, hsdt finite element models impose inconvenients such as: large number of nodal field variables, often encounter a locking problem when the plate is thin and resort to impose stiffness penalty in the formulation to remedy this problem. on the other hand, single layer reddy’s theory is one of the higher-order theories used most often for analyzing multilayer plates, being able to evaluate stresses and transverse shear strains with a small variables number, not depending on the number of layers [9]. however, reddy’s theory encounter formulation complications when the finite element requires c1 second-order derivatives. the same problem also arises in the classical theory of thin plates [31]. therefore, many finiteelement models (2d) based on reddy’s third order theory have been proposed in the literature [20] for the bending behavior analysis of isotropic and multilayer composite plates. furthermore, reddy finite elements usually use conforming and nonconforming formulation where the c1 transverse displacement and its derivatives are interpolated by a modified bicubic hermite functions, while the in-plane displacement and shear rotations are interpolated c0 lagrange functions (jn reddy [32], phan and reddy [33], averill and reddy [34], j. ren, . hinton [35], ine-wei liu [36]) the objective of this work is to propose an efficient plate bending elements based on reddy’s shear deformation theory, which has a simple formulation that overcome the difficult c1 requirement with small nodal field variables and that does not need to impose any stiffness penalty in the formulation and is also able to predict accurately the response of multilayer plates. based on the recently proposed displacement-model [37], a serendipity isoparametric eight nodes finite element is formulated for the study of multilayer sandwich plate bending behavior. in the formulation of the element, seven nodal field variables are chosen in an efficient manner so that there is no need to impose any stiffness penalty and present simple mathematical formulation. in this work, the present sandwich plate element is used to solve many multilayer sandwich plates problems for various parameters such as, different loadings, geometry, boundary conditions, and materials. kinematics he displacement field of the plate according to reddy’s third order shear deformation theory (tsdt) [9] can be expressed as follows: 3 1 4 3         x x z w u u z h x 3 2 4 3           y y z w u v z h y (1) 3 u w where: u1, u2, u3 are the displacements field in the x, y and z directions respectively. u, v displacement of a point  ,x y on the mid-plane of the plate.  x ,  y are rotations about the axes y and x respectively, and h is the thickness of the plate. the strain associated with displacement field (1) are given as follows:  0 0 2 211 1 1 1       u z z x  0 0 2 222 2 2 2       u z z y t k. belkaid et alii, frattura ed integrità strutturale, 61(2022) 372-393; doi: 10.3221/igf-esis.61.25 375 3 3 0      u z (2) 0 2 23 3 32 4 4 4                   u u uu z z y y z 0 2 23 3 31 5 5 5                   u u uu z z x x z  0 0 2 23 31 26 6 6 6                     u uu u z z y x x y where: 2 0 0 2 1 1 1 2 2 4 ;   ;     3                    x x u w x x xh x 2 0 0 2 2 2 2 2 2 4 ;   ;   3                    y y u w y y yh y 0 2 4 4 2 4 ;                  y y w w y yh 0 2 5 5 2 4 ;                x x w w x xh 0 0 6 6;   ;                   yx u v w w y x x y y x 2 2 6 2 4 2 3                yx w y x x yh constitutive equations he laminate is usually made of several orthotropic layers (fig 1). each layer must be transformed into the laminate coordinate system (x, y, z) [2]. the stress–strain relationship is given as: 11 12 16 12 22 26 16 26 66                                 xx xx yy yy xy xykk c c c c c c c c c ; 44 45 45 55                    xz xz yz yzkk c c c c (3) where  ijc are the transformed material constants: t k. belkaid et alii, frattura ed integrità strutturale, 61(2022) 372-393; doi: 10.3221/igf-esis.61.25 376   4 2 2 4 11 11 12 66 222 2   c c c c c c s c s   2 2 4 412 11 22 66 124 ( )    c c c c c s c c s    2 2 2 216 11 12 66 222    c c c c c s c c s cs  4 2 2 422 11 12 66 222 2   c c s c c c s c c   4 2 2 426 11 12 66 222 ( )    c c s c c c s c c cs   2 2 2 266 11 22 12 664 ( )    c c c c c s c c s 2 2 44 44 55 c c c c s  45 55 44 c c c cs 2 2 55 55 44 c c c c s where cos ,   sin  c s and  is angle between global axis and local axis for each laminate layer. 1 12 2 2 11 12 22 12 21 12 21 12 21 ;   ;   ;   1 1 1              e e e c c c 66 12 55 13 44 23;   ;    c g c g c g figure 1: geometry and coordinate system of the sandwich plate the differential equilibrium equations for transverse stress analysis are given as follows [2]: 11              k k kkn h xyxx xz h k dz x y 11                k k k kn h xy yy yz h k dz x y (4) k. belkaid et alii, frattura ed integrità strutturale, 61(2022) 372-393; doi: 10.3221/igf-esis.61.25 377 virtual work principle he static equations of the theory can be derived from the virtual work principle [9] by expressing the strain energy variation as follows:   0                xx xx yy yy xy xy xz xz yz yz v v dv q wdv (5) according to the substitution of equations (2) in the static equation (5) we obtain: 2 2 2 2 2 2 4 4 3 3                                                   y yx x xx xx xx yy yy yy a u w v w n m p n m p x x x y y yh x h y 2 2 4 2 3                                                   y yx xxy xy xy xx x u v w w n m p q y x y x y x x y xh (6) 2 2 4 4 0                                         xx x yy y yy y w w w r q r q w da x y yh h where the resultants forces are defined as follows:   1 3 1 1, ,                         k k xx xx xx xxn h yy yy yy yyh k xy xy xy xy n m p n m p z z dz n m p ;   1 2 1 1,                 k k n hxx xx xz h yy yy yzk q r z dz q r (7) therefore, from the eq (7) and eq (3), we obtain the generalized relations resultants forces as follows [9]:       0 0 2                                                 ij ij ij ij ij ij a b en m sym d f p sym sym h                                     ss s ij ij s s ij a dq r sym f (8) where: 0 0 0 0 0 0 2 2 2 0 0 2 1 2 6 1 2 6 1 2 6                   t t 0 0 2 2 4 5 4 5             t ts s     1 2 3 4 6 , 1 , , , , 1, , , , ,      k k hn ij ij ij ij ij ij ij k h a b d e f h c z z z z z dz , , 1, 2, 6i j     1 2 4 1 , , 1, , ,   , 4, 5      k k hn s s s ij ij ij ij k h a d f c z z dz i j t k. belkaid et alii, frattura ed integrità strutturale, 61(2022) 372-393; doi: 10.3221/igf-esis.61.25 378 substituting the resultant forces (8) in equation (6), the static equation becomes                   0 t 0 0 t 0 0 t 2 0 t 0 0 t 0 0 t 2 a 2 t 0 2 t 0 2 t 2 st s s st s s st s s st s s ( a b e b d f e f h a d d f q w )da 0                                                      (9) finite element formulation n this work, a c0 isoparametric serendipity eight-node element (fig.2) is employed for the bending analysis of sandwich plates based on reddy’s third order shear deformation. in the present formulation element the complexities associated with c1 continuous plate are overcome with efficient manner by choosing seven nodal degrees of freedom (dof) [37, 38] as follows: two displacements    ,  u v for the membrane behavior and five displacements ( ,   ,   , , )   x y x yw for describing the bending behavior, where ,                 x x y y w w x y are shear angles. figure 2: eight-node isoparametric finite element the generalized field variable and element geometry of the model at any point may be expressed in terms of nodal approximation as follows:         8 8 1 1 , , ;   , ,              i i i i i i x n x y n y                         8 8 8 8 1 1 1 1 8 8 1 1 , , ;   , ,  ; , , ;   , ,  ; , , ;   , ,                                                   i i i i x i xi y i yi i i i i x i xi y i yi i i u n u v n v n n n n where corner nodes are defined as follows:    i i i i i 1 n , 1 (1 )( 1), i 1, 2, 3, 4 4             and mid side nodes as: i k. belkaid et alii, frattura ed integrità strutturale, 61(2022) 372-393; doi: 10.3221/igf-esis.61.25 379    2i i 1 n , 1 (1 ), i 5, 7 2           2i i 1 n , 1 (1 ), i 6, 8 2        , in are the bi-nonlinear interpolation functions of lagrange type corresponding to node i=1-8 [39]. the strain displacements vectors can be formed as derivative elementary nodal matrix [b] multiplied by the proposed nodal field variable   as follows:          0 0 0 0 2 2;   ,   ,   ,                                      s s s sb b b b b (10) i ,x 0 i , y i , y i ,x n 0 0 0 0 0 0 b 0 n 0 0 0 0 0 n n 0 0 0 0 0                 ; i ,x 0 i , yk i , y i ,x 0 0 n 0 0 0 0 b 0 0 0 n 0 0 0 0 0 n n 0 0 0                i ,x 2 i , y1 i , y i ,x 0 0 0 0 0 n 0 b c 0 0 0 0 0 0 n 0 0 0 0 0 n n                 ; i , y is i ,x i 0 0 n 0 n 0 0 b 0 0 n n 0 0 0             is 2 i 0 0 0 0 0 0 n b c 0 0 0 0 0 n 0                , , , , , , , 1 8      t i i i xi yi xi yiu v w i with: c1=-4/3h2, c2=-4/h2 according to the substitution of strain matrix (10) in the static equation (9), the elementary stiffness matrix    ek is deduced according the static system      ek f [37] as follows:   1 1 0 0 0 0 0 2 0 0 0 0 0 2 1 1 2 0 2 0 2 2 ([ ] [ ][ ] [ ] [ ][ ] [ ] [ ][ ] [ ] [ ][ ] [ ] [ ][ ] [ ] [ ][ ] [ ] [ ][ ] [ ] [ ][ ] [ ] [ ][ ] [ ] [ ][ ] [ ] [ ][ ] [ ] [ ][ ] [ ]                                           t t t t t t e t t t s t s s s t s s s t s s s k b a b b b b b e b b b b b d b b f b b e b b f b b h b b a b b d b b d b b  [ ][ ])det  t s sf b j d d (11) where    , f are elementary nodal vectors of forces and degrees of freedom, respectively. the analytical integration can be converted to gauss’s numerical integration [40]. full integration scheme quadrature rules, namely (3×3) is employed in the energy expression for the evaluation of the element stiffness property. k. belkaid et alii, frattura ed integrità strutturale, 61(2022) 372-393; doi: 10.3221/igf-esis.61.25 380 numerical examples and comparison studies n this section, several sandwich plates examples are solved to verify the effectiveness of the proposed formulation in the prediction of displacements and stresses results including different parameters such as, thickness ratios, materials, loading distribution, laminated face sheet, boundary conditions. the results of proposed model are compared with the three-dimensional elasticity solutions and other element models available in the literature. bending of a simply supported sandwich square plate subject to a doubly sinusoidal transverse load for this example, the proposed element convergence and ability of the bending behavior is studied by considering a simply supported (f/c/f) symmetrical square sandwich plate subject to a doubly sinusoidal transverse load   0, sin sin  yx q x y q a b for different thickness ratios a/h = 4,10,50,100. the properties of the core and those of the sheets are shown in (table 1). it is noted that normalized central deflection displacement results converge for different uniform mesh sizes toward pagano 3d-elasticity solution [6] (table 2). the increasing meshes indicate the accuracy and convergence rate of central transverse displacements results with a fast decrease of relative errors for both thin and moderately thick sandwich plates with no shear locking in the thin plates (a/h=50, 100). the simply supported boundary conditions used for the bending example are as follows: / 2 0      y yx a v w ; / 2  y b 0     x xu w the normalized deflection, stresses and in-plan are defined by: 3 2 2 22 4 2 2 0 0 0 , , 0 10 ,   , , , , , , 2 2 2 2 2 2 2 2                                      xx xx yy yy h ea b a b h h a b h h w w q a q a q a 2 2 0 00   0, 0, ,   0, , 0 ,   , 0, 0 2 2 2                                       xy xy xz xz yz yz h h b h a h q a q aq a 3 3 2 2 4 4 0 0 100 100 ,                h e h e u u v v q a q a proprieties e1 e2 g12 g13 g23 v12 thickness sandwich plate core 275.8 mpa 275.8 mpa 110.32 mpa 413.68 mpa 413.68 mpa 0.25 0.8h sheet 172369.9 mpa 6894.76 mpa 3447.38 mpa 1378.95 mpa 3447.38 mpa 0.25 0.1h table 1: mechanical proprieties of a sandwich plate. reference theory , , 0 2 2       a b w a/h=4(err%) a/h=10(err %) a/h=50(err %) a/h=100(err %) present (2×2) 6.5668 (13.55) 1.8739 (14.83) 0.60962 (34.78) 0.3439 (61.43) present (4×4) 7.1009 (6.52) 2.07035 (5.91) 0.91441 (2.181) 0.8604 (3.5) present (6×6) hsdt(q8) 7.1377 (6.03) 2.081172 (5.41) 0.92644 (0.89) 0.8845 (0.796) present (8×8) 7.1461 (5.927) 2.08326 (5.32) 0.92844 (0.68) 0.8888 (0.323) present (10×10) 7.1492 (5.88) 2.08396 (5.29) 0.92901 (0.61) 0.89005 (0.185) present (12×12) 7.1508 (5.86) 2.08426 (5.27) 0.92923 (0.59) 0.89053 (0.131) pagano[6] elasticity solution 7.5962 2.2004 0.9348 0.8917 table 2: normalized center deflection convergence of a simply supported square sandwich plate subject to a doubly sinusoidal transverse load. i k. belkaid et alii, frattura ed integrità strutturale, 61(2022) 372-393; doi: 10.3221/igf-esis.61.25 381 in fig 3 the central normalized w deflection is plotted for different a/h ratios. in fig 4, the in-plane displacements u1(a/2,0,0) and u2(0,b/2,0) are described through the plate thickness as a cubic variation. it can be seen that the obtained bending responses by the present formulation are in excellent agreement with the elasticity solution of pagano [6]and with those obtained by t. kant and k. swaminathan analytical solution [13]. figure 3: evolution of normalized central transverse deflection w with aspect ratio a/h of a simply supported sandwich plate  0 / / 0 c subject to a doubly sinusoidal transverse load. figure 4: evolution of normalized in-plane displacements 1 2,u u as function of the thickness of a simply supported  0 / / 0 c sandwich plate subject to a doubly sinusoidal transverse load a/h=4. in table 3, the bending sandwich plate  0 / / 0   c is studied for different aspect ratios a/h in order to present the normalized transverse deflection and maximum stresses using the constitutive equation. furthermore, the transverse shear stresses are evaluated using the equilibrium equations. a close agreement has been found between the obtained results by the proposed element and those obtained using pagano elasticity-3d solution [6], as well as with those obtained by finite element models based on different theories. furthermore, it’s noting that in thin sandwich plate cases (a/h=50,100), the results of the proposed model do not have locking shear problems with additional better accuracy in comparison with other model elements that have used stiffness penalty with a high number of nodal variables than the proposed model (e.g. b. pandya , t. kant [21], t. kant and j. kommineni, [23], m.k. pandit et al. [26], chalak et al. [29], r. sahoo and b. singh [30]). 0 20 40 60 80 100 0 5 10 15 20 25 n o n d im en si o n al t ra n sv er se d is p la ce m en t w a/h present (12×12) pagano -2,0 -1,5 -1,0 -0,5 0,0 0,5 1,0 1,5 2,0 -0,6 -0,4 -0,2 0,0 0,2 0,4 0,6 t h ic k n es s co o rd ia n te ( z/ h ) nondimensional displacements u present u1 analytic hsdt u1 present u2 analytic hsdt u2 k. belkaid et alii, frattura ed integrità strutturale, 61(2022) 372-393; doi: 10.3221/igf-esis.61.25 382 a/h reference theory w  xx  yy  xz  yz xy 2 present (12×12) hsdt(q8) 21.356 2.770 0.386 0.2174* 0.1535* 0.2288 0.1880+ 0.1317+ pagano [6] elasticity solution 21.653 2.6530 0.3920 0.1850 0.1400 0.2340 ramtekkar et al. [41] mfem-3dlw 2.6840 0.3960 0.1860 0.1420 0.2360 kant et kommineni [23] fem-q9tsdt 21.3707 2.7985 0.2371 4 present (12×12) hsdt(q8) 7.1508 1.4929 0.2375 0.279* 0.1154* 0.1377 0. 2418+ 0.0997+ pagano [6] elasticity solution 7.5962 1.5160 0.2595 0.2390 0.1072 0.1440 ramtekkar et al. [41] mfem-3dlw -1.5700 0.2600 0.2400 0.108 0.149 wu et lin [24] mfem-3dlw -1.5480 0.2413 0.2497 0.1339 pandya et kant [21] fem-q9hsdt 0.6947 1.247 0.2338 0.2382 0.1132 0.1343 manjunatha et kant [22] fem-q9hsdt 7.1596 0.2750 0.1137 kant et kommineni [23] fem-q9tsdt 7.1502 1.4989 --0.1428 kant et swaminathan [13] hsdt 7.0551 1.5137 0.2648 --0.1379 iga [42] tsdt 7.0872 1.4244 0.2361 0.2708 0.1169 0.1383 iga [42] hsdt 7.0686 1.4791 0.2391 0.3074 0.1274 0.1406 5 present (12×12) hsdt(q8) 5.1389 1.334 0.1955 0.299* 0.0986* 0.1149 0.2592+ 0. 0851+ pagano [6] elasticity solution 5.4746 1.3704 0.2094 0.2569 0.0918 - khandelwal et al. [25] fem-q9hzzt 5.4464 1.3617 0.2216 0.2530 0.1025 - 10 present (12×12) hsdt(q8) 2.08426 1.1419 0.1035 0.3454* 0.05797* 0.0672 0.2986+ 0.0493+ pagano [6] elasticity solution 2.2004 1.1531 0.1104 0.3000 0.0530 0.0707 pandit et al.[26] fem-q9hzzt 2.2002 1.1483 0.1086 0.3158 0.0570 0.0709 tu et al.[27] fem-q9tsdt 2.2027 1.1466 0.1105 0.3181 0.0532 0.0715 khandelwal et al. [25] fem-q9hzzt 2.1786 1.1539 0.1184 0.3185 0.0598 chalak et al.[26] fem-q9hzzt 2.1775 1.1528 0.1143 0.3058 0.0575 0.0705 ramtekkar et al. [41] mfem-3dlw 1.1590 0.1110 0.3030 0.0550 0.0720 wu et lin [24] mfem-3dlw 1.2100 0.1115 0.3177 0.0713 pandya et kant [21] fem-q9hsdt 2.023 1.110 0.1017 0.2841 0.05593 0.0666 kant et kommineni[23] fem-q9tsdt 2.0864 1.1657 -0.0692 k. belkaid et alii, frattura ed integrità strutturale, 61(2022) 372-393; doi: 10.3221/igf-esis.61.25 383 kant et swaminathan[13] hsdt-anal 2.0798 1.1523 0.1100 0.3465 0.0538 0.0685 nayak et al. [28] fem-q4hsdt 1.1410 0.1034 0.3506 0.0534 0.0685 nayak et al. [28] fem-q9hsdt 1.1510 0.1043 0.2815 0.0532 0.0689 iga [42] tsdt 2.0629 1.1299 0.1028 0.3302 0.0578 0.0679 iga [42] hsdt 2.0515 1.1424 0.1031 0.3781 0.0628 0.0682 20 present (12×12) hsdt(q8) 1.1937 1.1019 0.0678 0.3648* 0.04227* 0.0493 0.31374+ 0.03401+ pagano [6] elasticity solution 1.2264 1.1100 0.0700 0.3174 0.0361 0.0511 pandit et al. [26] fem-q9hzzt 1.2254 1.1055 0.0694 0.3342 0.0392 0.0509 khandelwal et al. [25] fem-q9hzzt 1.2128 1.1113 0.0769 0.3374 0.0415 chalak et al.[29] fem-q9hzzt 1.2121 1.1103 0.0742 0.3272 0.0399 0.0508 ramtekkar et al. [41] mfem-3dlw 1.1150 0.0700 0.3170 0.0360 0.0510 wu et lin [24] mfem-3dlw -1.1730 0.0724 0.3530 0.0525 kant et kommineni [23] fem-q9hsdt 1.1947 1.1246 -0.0506 kant et swaminathan [13] hsdt 1.1933 1.1110 0.0705 --0.0504 iga [42] tsdt 1.1876 1.1027 0.0678 0.3467 0.0408 0.0501 iga [42] hsdt 1.1850 1.1061 0.0678 0.3974 0.0443 0.0502 50 present (12×12) hsdt(q8) 0.92923 1.0918 0.0563 0.3799* 0.4283* 0.0435 0.3147+ 0.02646+ pagano [6] elasticity solution 0.9348 1.0990 0.0569 0.3230 0.0306 0.0446 pandit et al. [26] fem-q9hzzt 0.9341 1.0948 0.0566 0.3403 0.0333 0.0445 chalak et al. [29] fem-q9hzzt 0.9248 1.0997 0.0611 0.3300 0.0321 0.0443 iga [42] tsdt 0.9284 1.0965 0.0565 0.3520 0.0352 0.0444 iga [42] hsdt 0.9280 1.0971 0.0565 0.4036 0.0383 0.0445 kant et kommineni [23] fem-q9hsdt 0.9299 1.1118 0.0448 100 present (12×12) hsdt(q8) 0.8905 1.0904 0.0546 0.4118* 0.05132* 0.0427 0.30167+ 0.02157+ pagano [6] elasticity solution 0.8917 1.098 0.0550 0.324 0.0297 0.0433 rosalin sahoo, b.n. singh [30] itzzt-q8 0.8919 1.1088 0.0555 0.3433 0.0276 0.044 chalak et al.[29] hozt-q9 0.8814 1.0982 0.0592 0.3426 0.0332 0.0433 pandit et al. [26] hozt-q9 0.8917 1.1093 0.0547 0.3412 0.0324 0.0434 iga [42] tsdt 0.8908 1.0957 0.0548 0.3528 0.0344 0.0436 k. belkaid et alii, frattura ed integrità strutturale, 61(2022) 372-393; doi: 10.3221/igf-esis.61.25 384 iga [42] hsdt 0.8907 1.0958 0.0548 0.4046 0.0374 0.0436 pandya et kant [21] fem-q9hsdt 0.891 1.108 0.0554 0.3001 0.03362 0.044 kant et kommineni [23] fem-q9hsdt 0.8915 1.1058 0.044 *constitutive +equilibre table 3: normalized transverse displacement, plane stresses, transverse shear stresses of a simply supported sandwich plate  0 / / 0 c under doubly sinusoidal loading. through figs (5, 6, 7, 8, 9, 10,11), the normal , ,  xx yy xy and transverse shear , xz yz stresses states are described through thickness of the sandwich plate in bending behavior for aspect ratios a/h=10,4 according to the constitutive and equilibrium equations. the obtained results stresses are in close agreement with those obtained by pagano elasticity solution [13] and by tsdt numerical solution [42]. figure 5: normal stress distribution  xx through the thickness of a simply supported sandwich plate  0 / / 0 c subject to a sinusoidal load (a/h =10, 4). figure 6: normal stress distribution  yy through the thickness of a simply supported sandwich plate  0 / / 0 c subject to a sinusoidal load (a/h =10, 4). -1,5 -1,0 -0,5 0,0 0,5 1,0 1,5 -0,6 -0,4 -0,2 0,0 0,2 0,4 0,6 normalized t h ic k n es s co o rd in at e (z /h )  xx (a/2,b/2,z) reddy iga a/h=10 present a/h=10 reddy iga a/h=4 present a/h=4 -0,15 -0,10 -0,05 0,00 0,05 0,10 0,15 -0,6 -0,4 -0,2 0,0 0,2 0,4 0,6 normalized t h ic k n es s co o rd in at e (z /h )  xy (0,0,z) reddy iga a/h=10 present a/h=10 present a/h=4 reddy iga a/h=4 k. belkaid et alii, frattura ed integrità strutturale, 61(2022) 372-393; doi: 10.3221/igf-esis.61.25 385 figure 7: normal stress distribution xy through the thickness of a simply supported sandwich plate  0 / / 0 c subject to a sinusoidal load (a/h =10, 4). figure 8: transverse shear stress distribution  yz through the thickness of a simply supported sandwich plate  0 / / 0 c subject to a sinusoidal load (a/h =10, 4) (constitutive equations). figure 9: transverse shear stress distribution  xz through the thickness of a simply supported sandwich plate  0 / / 0 c subject to a sinusoidal load (a/h =10, 4)(constitutive equations). -0,3 -0,2 -0,1 0,0 0,1 0,2 0,3 -0,6 -0,4 -0,2 0,0 0,2 0,4 0,6 normalized t h ic k n es s co o rd in at e (z /h )  yy (a/2,b/2,z) reddy iga a/h=10 present a/h=10 reddy iga a/h=4 present a/h=4 -0,02 0,00 0,02 0,04 0,06 0,08 0,10 0,12 0,14 0,16 -0,6 -0,4 -0,2 0,0 0,2 0,4 0,6 normalized t h ic k n es s co o rd in at e (z /h )  yz (0,b/2,z) reddy iga a/h=10 present a/h=10 reddy iga a/h=4 present a/h=4 -0,2 0,0 0,2 0,4 0,6 0,8 1,0 -0,6 -0,4 -0,2 0,0 0,2 0,4 0,6 normalized t h ic k n es s co o rd in at e (z /h )  xz (a/2,0,z) reddy iga a/h=10 present a/h=10 reddy iga a/h=4 present a/h=4 k. belkaid et alii, frattura ed integrità strutturale, 61(2022) 372-393; doi: 10.3221/igf-esis.61.25 386 figure 10: transverse shear stress distribution  yz through the thickness of a simply supported sandwich plate  0 / / 0 c subject to a sinusoidal load (a/h =10, 4) (equilibrium equations). figure 11: transverse shear stress distribution  xz through the thickness of a simply supported sandwich plate  0 / / 0 c subject to a sinusoidal load (a/h =10, 4)(equilibrium equations). three-layer sandwich square plate subject to a uniform load in this example, the effect of the scale factor r  face corec rc variation on deflection and stresses state of a simply supported sandwich square plate  0 / / 0 c is studied under a uniform transverse load with aspect ratio a/h =10 and face and core layers thickness hc/hf = 8. this sandwich example has been suggested by srinivas [43]. the material properties of core layer are defined as: 0.999781 0.231192 0 0 0 0.231192 0.524886 0 0 0 0 0 0.262931 0 0 0 0 0 0.26681 0 0 0 0 0 0.159914                corec the normalized deflection and stresses are defined by:             1 1 1 2 0 0 0 1 12 3 1 2 0 0 0 2 3 0.999781 / 2, / 2, 0 / 2, / 2, / 2 / 2, / 2, 2 / 5 ,   , , / 2, / 2, / 2 / 2, / 2, 2 / 5/ 2, / 2, 2 / 5 ,   , , / 2, / 2                                                         x x xx xx y yx xx yy yy y yy w a b a b h a b h w q h q q a b h a b ha b h q q q a b  0 , 2 / 5       h q table 4 shows the deflection and normal stresses solution by the proposed model for different factor scales r = 5, 10, 15 compared with those obtained using the exact solution reported by srinivas [43], hsdt finite element by pandya and kant [21], hsdt meshfree solution by ferreira et al. [44], trsdt trigonometric shear deformation theory solution by mantari 0,00 0,02 0,04 0,06 0,08 0,10 0,12 -0,6 -0,4 -0,2 0,0 0,2 0,4 0,6 normalized t h ic k n es s co o rd ia n te ( z/ h ) present a/h=10 pagano a/h=10 present a/h=4 pagano a/h=4  yz (0,b/2,z) -0,05 0,00 0,05 0,10 0,15 0,20 0,25 0,30 0,35 -0,6 -0,4 -0,2 0,0 0,2 0,4 0,6  xz (a/2,0,z)normalized t h ic k n es s co o rd ia n te ( z/ h ) pagano a/h=10 present a/h=10 pagano a/h=4 present a/h=4 k. belkaid et alii, frattura ed integrità strutturale, 61(2022) 372-393; doi: 10.3221/igf-esis.61.25 387 et al. [14] and ihsdt inverse hyperbolic shear deformation theory by grover et al.[15]. it is noted that the obtained results are in very good correlation with all scale factor r cases when compared with the exact solution. r theory w 1 xx 2 xx 3 xx 1 yy 2 yy 3 yy 5 present hsdt(q8) (12×12) 257.4323 60.1869 46.6913 9.3382 38.3327 30.07465 6.0149 exact [43] 258.97 60.353 46.623 9.34 38.491 30.097 6.161 fem-hsdt [21] 256.13 62.380 46.910 9.382 38.930 30.330 6.065 mrbf-hsdt [44] 257.110 60.366 47.003 9.401 38.456 30.242 6.048 cfs-ihsdt [15] 255.644 60.675 47.055 9.411 38.522 30.206 6.041 cfs-trsdt [14] 256.706 60.525 47.061 9.412 38.452 30.177 6.035 10 present hsdt(q8) (12×12) 155.9531 65.3098 49.3654 4.936 43.2633 33.42849 3.3428 exact [43] 159.38 65.332 48.857 4.903 43.566 33.413 3.5 fem-hsdt [21] 152.33 64.650 51.310 5.131 42.830 33.970 3.397 mrbf-hsdt [44] 154.658 65.381 49.973 4.997 43.240 33.637 3.364 cfs-ihsdt [15] 154.550 65.741 49.798 4.979 43.4 33.556 3.356 cfs-trsdt [14] 155.498 65.542 49.708 4.971 43.385 33.591 3.359 15 present hsdt(q8) (12×12) 116.9587 66.9283 49.3353 3.289 45.8775 34.9577 2.3305 exact [43] 121.72 66.787 48.299 3.238 46.424 34.955 2.494 fem-hsdt [21] 110.430 66.620 51.970 3.465 44.920 35.410 2.361 mrbf-hsdt [44] 114.644 66.919 50.323 3.355 45.623 35.167 2.345 cfs-ihsdt [15] 115.820 67.272 49.813 3.321 45.967 35.088 2.339 cfs-trsdt [14] 115.919 67.185 49.769 3.318 45.910 35.081 2.339 table 4: the normalized deflection and stresses of square sandwich plates under uniform load. an additional analysis is considered for the effect of different scale factors r = 5, 10, 15 on the evolution of in-plane displacements    1 2/ 2, / 2, ,   / 2, / 2,u a b z u a b z , normal stresses    / 2, / 2, ,   / 2, / 2, xx yya b z a b z and transverse shear stresses    0, / 2, ,   / 2, 0, xz yzb z a z with respect to the sandwich plate thickness. in fig 12, it is noted for the bending behavior that the in-plane displacements are reduced along the thickness when the scale factor r is increased. in addition, in figs 13, 14 it can be seen that the normal and transverse shear stresses have also reduced only through the core of plate, whereas they have increased through the faces. k. belkaid et alii, frattura ed integrità strutturale, 61(2022) 372-393; doi: 10.3221/igf-esis.61.25 388 (a) (b) figure 13: effect of scale factor r variation on the distribution of normal stresses ,   xx yy through the thickness of a simply supported  0 / / 0   c sandwich plate subject to a uniform transverse load. (a) (b) figure 14: effect of scale factor r variation on the distribution of transverse shear stresses ,   xz yz through the thickness of a simply supported  0 / / 0   c sandwich plate subject to a uniform transverse load. sandwich plates with laminated face sheets in this example, the proposed element is evaluated for different laminated face sheets of rectangular sandwich plates. kanematsu et al. [16] carried out experimental solution of clamped rectangular sandwich plates (450×300 mm) with four types laminated composite orientation faces sp1, sp2, sp3 and sp4 (fig. 15). the faces of the sandwiches are symmetrical laminated composite made of carbon/epoxy (carbon fiber–reinforced plastic-cfrp) e1=105 gpa, e2=8.74 gpa, g12= g13= g23=4.56 gpa, v=0.327, while the core is an aluminum honeycomb material (aluminum honeycomb core) e1=68.6 mpa, e2=68.6 mpa, g12=26.4 mpa, g13=103 mpa, g23=62.1 mpa, v=0.3. the thickness of each layer is 0.125mm, while the core thickness is 10mm for the sp1 and sp2 types, and 7mm core thickness for the sp3 and sp4 types. the plate is subject to a uniform distributed load of intensity q=1.01 kpa. in addition, the authors provided analytical solutions based on the rayleigh-ritz method for the same plate problem, using two types boundary conditions, simply supported (ssss) and clamped (cccc). the obtained results of the transverse displacement using the proposed element are given in table 5, compared with those obtained using analytical solutions and from experimental work given by -0,0015 -0,0010 -0,0005 0,0000 0,0005 0,0010 0,0015 -0,6 -0,4 -0,2 0,0 0,2 0,4 0,6 t h ic k n es s co o rd in at e (z /h ) nondimensional displacement u 1 r=5 r=10 r=15 -4 -2 0 2 4 -0,6 -0,4 -0,2 0,0 0,2 0,4 0,6 t h ic k n es s co o rd in at e (z /h ) nondimensional displacement u 2 r=5 r=10 r=15 0,0 0,1 0,2 0,3 0,4 -0,6 -0,4 -0,2 0,0 0,2 0,4 0,6 normalized t h ic k n es s co o rd in at e (z /h )  xz r=5 r=10 r=15 -0,05 0,00 0,05 0,10 0,15 0,20 0,25 0,30 0,35 -0,6 -0,4 -0,2 0,0 0,2 0,4 0,6 normalized t h ic k n es s co o rd in at e (z /h )  yz r=5 r=10 r=15 k. belkaid et alii, frattura ed integrità strutturale, 61(2022) 372-393; doi: 10.3221/igf-esis.61.25 389 kanematsu et al. [16]. the results have also been compared with those obtained by finite element models of lee and fan [45] and nayak et al. [28], m. o. belarbi et al. [46]. the comparison results show the reliability and practicality of the proposed element for the studies of laminated faces sandwich structures. figure 15: different types of laminated faces sandwich structures [46] references theory central deflection (mm) sp1 sp2 sp3 sp4 clamped (cccc) present (12×12) fem-q8-tsdt 0.04891 0.056578 0.074968 0.05469 kanematsu et al. [16] analytical solution 0.05040 0.05400 0.07720 0.06130 kanematsu et al. [16] experimental solution 0.06900 0.08500 0.09400 0.09000 lee et fan [45] fem-q9-lw 0.05190 0.05524 0.07834 0.06216 nayak et al. [28] fem-q9-hsdt 0.05248 0.05797 m. o. belarbi et al. [46] fem-q4-rsft52 0.04906 0.05647 0.07506 0.05525 simply supported (ssss) present (12×12) fem-q8-tsdt 0.12124 0.17823 0.17213 0.2067 kanematsu et al. [16] analytical solution 0.1173 0.1829 0.1794 0.2206 lee et fan [45] fem-q9-lw 0.1213 0.1774 0.1729 0.2138 nayak et al. [28] fem-q9-hsdt 0.1754 0.2111 m. o. belarbi et al. [46] fem-q4-rsft52 0.1160 0.1733 0.1695 0.2010 table 5: deflection laminated faces sandwiches plates under uniformly transverse load. k. belkaid et alii, frattura ed integrità strutturale, 61(2022) 372-393; doi: 10.3221/igf-esis.61.25 390 conclusion n this paper, an improved c0 two-dimensional plate finite element (fe) model has been developed for the static analysis of laminated thin and thick sandwich plates. the reddy’s third order shear deformation theory (tsdt) is employed by adopting single layer approach when the warping cross-sectional of in-plane displacements is considered to be cubic for both the face sheets and the core of sandwich. the problem of c1 continuity requirement of the second order derivatives of transverse displacements is circumvented by selecting the degrees of freedom nodal field in an efficient manner. for the present analysis, an eight-node c0 finite element is successfully implemented having seven degrees of freedom for each element node: two displacements    ,  u v for in-plane behavior and five bending unknowns: a transverse displacement, two rotations and two shear angles ( ,   ,   , , )   x y x yw . whereas element stiffness matrices, which have first order derivative requirement, are solved through a computationally (3×3) gauss integration scheme. in the proposed formulation, there is no stiffness penalty requirement such as: shear correction factors, and numerical techniques to overcome transverse shear locking phenomenon that as used in previous element models. in order to demonstrate the effectiveness and validity of the proposed formulation, many sandwich plates numerical examples are solved and displacements as well as stresses are calculated for different problems and which give results better than other existing 2d finite element models. the results obtained by using the present fe model are successfully compared with those of analytical and numerical solutions available in the literature. the numerical results show that the performance of the present finite element model is excellent in predicting the bending response of thin and thick laminated composites sandwich structures as the error percentage with respect to the 3d elasticity solution is considerably low. the present fe model may, therefore, be recommended for use as accurate tool in other behavior analysis of laminated sandwich plates. statements and declarations competing interests and funding he authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper. there is no funding to declare. nomenclature 1 2 3, ,u u u displacement field in the x, y and z directions respectively , ,u v w displacement of a point on the mid-plane , x y rotations of normal to the mid-plane about the y and x axes respectively , x y shear angles to the mid-plane about the y and x axes respectively  i strain , ,a b h dimensions of the plate along the x, y and z directions respectively  ij stress tensor   ijc constitutive matrix at the lamina level ie young modulus 12 13 23,   , g g g shears modulus 12 21,   poisson’s ratios  n ,    m ,    p , q ,    r resultants forces ,, , , ,ij ij ij ij ij ija b d e f h extensional, coupling and flexural stiffnesses , ,s s sij ij ija d f transverse shear stiffnesses i t k. belkaid et alii, frattura ed integrità strutturale, 61(2022) 372-393; doi: 10.3221/igf-esis.61.25 391 in interpolation functions 0 0 2, ,   , ,                         s sb b b b b strain displacement matrices   element nodal field variables  f element load vector  ek element stiffness matrix , c fh h core and face thicknesses of sandwich, respectively references [1] kirchhoff, g. (1850). über das gleichgewicht und die bewegung einer elastischen scheibe, journal für die reine und angewandte mathematik (crelles journal), 1850 (40), pp. 51-88. doi: 10.1515/crll.1850.40.51 [2] reddy, j.n. (2004). mechanics of laminated composite plates and shells: theory and analysis, crc press. [3] reissner, e. (1945). the effect of transverse shear deformations on the bending of elastic plates, journal of applied mechanics, 12 pp. a69-a77. doi: https://doi.org/10.1115/1.4009435 [4] whitney, j.m. (1969). the effect of transverse shear deformation on the bending of laminated plates, journal of composite materials, 3 (3), pp. 534-547. doi: 10.1177/002199836900300316 [5] carrera, e. (2002). theories and finite elements for multilayered, anisotropic, composite plates and shells, archives of computational methods in engineering, 9 (2), pp. 87-140. doi: 10.1007/bf02736649 [6] pagano, n. (1970). exact solutions for rectangular bidirectional composites and sandwich plates, journal of composite materials, 4 (1), pp. 20-34. doi: 10.1177/002199837000400102 [7] reddy, j. , robbins, d. (1994). theories and computational models for composite laminates, applied mechanics reviews, 47 (6), pp. 147-169. doi: 10.1115/1.3111076 [8] ghugal, y. , shimpi, r. (2002). a review of refined shear deformation theories of isotropic and anisotropic laminated plates, journal of reinforced plastics and composites, 21 (9), pp. 775-813. doi: 10.1177/073168402128988481 [9] reddy, j.n. (1984). a simple higher-order theory for laminated composite plates, journal of applied mechanics, 51 (4), pp. 745-752. doi: 10.1115/1.3167719 [10] reddy, j.n. (1984(c)). a refined nonlinear theory of plates with transverse shear deformation, international journal of solids and structures, 20 (9), pp. 881-896. doi: 10.1016/0020-7683(84)90056-8 [11] barut, a., madenci, e., heinrich, j., tessler, a. (2001). analysis of thick sandwich construction by a {3,2}-order theory, international journal of solids and structures, 38 (34), pp. 6063-6077. doi: 10.1016/s0020-7683(00)00367-x [12] noor, a.k., burton, w.s., bert, c.w. (1996). computational models for sandwich panels and shells, applied mechanics reviews, 49 (3), pp. 155-199. doi: 10.1115/1.3101923 [13] kant, t. , swaminathan, k. (2002). analytical solutions for the static analysis of laminated composite and sandwich plates based on a higher order refined theory, composite structures, 56 (4), pp. 329-344. doi: 10.1016/s0263-8223(02)00017-x [14] mantari, j., oktem, a., soares, c.g. (2012). a new trigonometric shear deformation theory for isotropic, laminated composite and sandwich plates, international journal of solids and structures, 49 (1), pp. 43-53. doi: 10.1016/j.ijsolstr.2011.09.008 [15] grover, n., maiti, d., singh, b. (2013). a new inverse hyperbolic shear deformation theory for static and buckling analysis of laminated composite and sandwich plates, composite structures, 95 pp. 667-675. doi: 10.1016/j.compstruct.2012.08.012 [16] kanematsu, h.h., hirano, y., iyama, h. (1988). bending and vibration of cfrp-faced rectangular sandwich plates, composite structures, 10 (2), pp. 145-163. doi: 10.1016/0263-8223(88)90044-x [17] torabizadeh, m.a., fereidoon, a. (2021). applying taguchi approach to design optimized effective parameters of aluminum foam sandwich panels under low-velocity impact, iranian journal of science and technology, transactions of mechanical engineering, pp. doi: 10.1007/s40997-021-00441-5 [18] marino, m., nerilli, f., vairo, g. (2014). a finite-element approach for the analysis of pin-bearing failure of composite laminates, frattura ed integrita strutturale, 8 (29), pp. 241-250. doi: 10.3221/igf-esis.29.21 [19] deliou, a., bouchouicha, b. (2018). fatigue crack propagation in welded joints x70, frattura ed integrità strutturale, 12 (46), pp. 306-318. doi: 10.3221/igf-esis.46.28 k. belkaid et alii, frattura ed integrità strutturale, 61(2022) 372-393; doi: 10.3221/igf-esis.61.25 392 [20] zhang, y., yang, c. (2009). recent developments in finite element analysis for laminated composite plates, composite structures, 88 (1), pp. 147-157. doi: 10.1016/j.compstruct.2008.02.014 [21] pandya, b. , kant, t. (1988). higher-order shear deformable theories for flexure of sandwich plates-finite element evaluations, international journal of solids and structures, 24 (12), pp. 1267-1286. doi: 10.1016/0020-7683(88)90090-x [22] manjunatha, b.s. , kant, t. (1993). on evaluation of transverse stresses in layered symmetric composite and sandwich laminates under flexure, engineering computations, 10 (6), pp. 499-518. doi: 10.1108/eb023922 [23] kant, t. , kommineni, j. (1992). c 0 finite element geometrically non-linear analysis of fibre reinforced composite and sandwich laminates based on a higher-order theory, computers & structures, 45 (3), pp. 511-520. doi: https://doi.org/10.1016/0045-7949(92)90436-4 [24] wu, c.-p., lin, c.-c. (1993). analysis of sandwich plates using a mixed finite element, composite structures, 25 (1), pp. 397-405. doi: 10.1016/0263-8223(93)90187-u [25] khandelwal, r.p., chakrabarti, a., bhargava, p. (2013). an efficient fe model based on combined theory for the analysis of soft core sandwich plate, computational mechanics, 51 (5), pp. 673-697. doi: 10.1007/s00466-012-0745-3 [26] pandit, m.k., sheikh, a.h., singh, b.n. (2008). an improved higher order zigzag theory for the static analysis of laminated sandwich plate with soft core, finite elements in analysis and design, 44 (9-10), pp. 602-610. doi: 10.1016/j.finel.2008.02.001 [27] tu, t.m., quoc, t.h. (2010). finite element modeling for bending and vibration analysis of laminated and sandwich composite plates based on higher-order theory, computational materials science, 49 (4), pp. s390-s394. doi: 10.1016/j.commatsci.2010.03.045 [28] nayak, a., moy, s.j., shenoi, r. (2003). quadrilateral finite elements for multilayer sandwich plates, the journal of strain analysis for engineering design, 38 (5), pp. 377-392. doi: 10.1243%2f03093240360713441 [29] chalak, h.d., chakrabarti, a., iqbal, m.a., hamid sheikh, a. (2012). an improved c0 fe model for the analysis of laminated sandwich plate with soft core, finite elements in analysis and design, 56 pp. 20-31. doi: 10.1016/j.finel.2012.02.005 [30] sahoo, r., singh, b. (2013). a new shear deformation theory for the static analysis of laminated composite and sandwich plates, international journal of mechanical sciences, 75 pp. 324-336. doi: 10.1016/j.ijmecsci.2013.08.002 [31] batoz, j.l., tahar, m.b. (1982). evaluation of a new quadrilateral thin plate bending element, international journal for numerical methods in engineering, 18 (11), pp. 1655-1677. doi: 10.1002/nme.1620181106 [32] reddy, j.n. (1989). on refined computational models of composite laminates, international journal for numerical methods in engineering, 27 (2), pp. 361-382. doi: 10.1002/nme.1620270210 [33] phan, n. , reddy, j. (1985). analysis of laminated composite plates using a higher‐order shear deformation theory, international journal for numerical methods in engineering, 21 (12), pp. 2201-2219. doi: 10.1002/nme.1620211207 [34] averill, r. , reddy, j. (1992). an assessment of four‐noded plate finite elements based on a generalized third‐order theory, international journal for numerical methods in engineering, 33 (8), pp. 1553-1572. doi: 10.1002/nme.1620330802 [35] ren, j. , hinton, e. (1986). the finite element analysis of homogeneous and laminated composite plates using a simple higher order theory, communications in applied numerical methods, 2 (2), pp. 217-228. doi: 10.1002/cnm.1630020214 [36] liu, i.-w. (1996). an element for static, vibration and buckling analysis of thick laminated plates, computers & structures, 59 (6), pp. 1051-1058. doi: 10.1016/0045-7949(95)00350-9 [37] belkaid, k. (2019). development of a 2d isoparametric finite-element model based on reddy’s third-order theory for the bending behavior analysis of composite laminated plates, mechanics of composite materials, 55 (2), pp. 241-258. doi: 10.1007/s11029-019-09807-y [38] belkaid, k. (2019). buckling analysis of isotropic and composite laminated plates: new finite element formulation. in computational methods and experimental testing in mechanical engineering of conference. springer. doi: 10.1007/978-3-030-11827-3_8 [39] zienkiewicz, o.c., cheung, y.k. (1964). the finite element method for analysis of elastic isotropic and orthotropic slabs. in ice proceedings of conference. thomas telford. [40] hughes, t.j., cohen, m., haroun, m. (1978). reduced and selective integration techniques in the finite element analysis of plates, nuclear engineering and design, 46 (1), pp. 203-222. doi: 10.1016/0029-5493(78)90184-x [41] ramtekkar, g., desai, y., shah, a. (2003). application of a three-dimensional mixed finite element model to the flexure of sandwich plate, computers & structures, 81 (22-23), pp. 2183-2198. doi: 10.1016/s0045-7949(03)00289-x k. belkaid et alii, frattura ed integrità strutturale, 61(2022) 372-393; doi: 10.3221/igf-esis.61.25 393 [42] nguyen-xuan, h., thai, c.h., nguyen-thoi, t. (2013). isogeometric finite element analysis of composite sandwich plates using a higher order shear deformation theory, composites part b: engineering, 55 pp. 558-574. doi: 10.1016/j.compositesb.2013.06.044 [43] srinivas, s. (1973). a refined analysis of composite laminates, journal of sound and vibration, 30 (4), pp. 495-507. doi: 10.1016/s0022-460x(73)80170-1 [44] ferreira, a.j.m., roque, c.m.c., martins, p.a.l.s. (2003). analysis of composite plates using higher-order shear deformation theory and a finite point formulation based on the multiquadric radial basis function method, composites part b: engineering, 34 (7), pp. 627-636. doi: 10.1016/s1359-8368(03)00083-0 [45] lee, l.j., fan, y.j. (1996). bending and vibration analysis of composite sandwich plates, computers & structures, 60 (1), pp. 103-112. doi: 10.1016/0045-7949(95)00357-6 [46] belarbi, m., tati, a. 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can be opened with acrobat and adobe reader 5.0 and later.) >> /namespace [ (adobe) (common) (1.0) ] /othernamespaces [ << /asreaderspreads false /cropimagestoframes true /errorcontrol /warnandcontinue /flattenerignorespreadoverrides false /includeguidesgrids false /includenonprinting false /includeslug false /namespace [ (adobe) (indesign) (4.0) ] /omitplacedbitmaps false /omitplacedeps false /omitplacedpdf false /simulateoverprint /legacy >> << /addbleedmarks false /addcolorbars false /addcropmarks false /addpageinfo false /addregmarks false /convertcolors /converttocmyk /destinationprofilename () /destinationprofileselector /documentcmyk /downsample16bitimages true /flattenerpreset << /presetselector /mediumresolution >> /formelements false /generatestructure false /includebookmarks false /includehyperlinks false /includeinteractive false /includelayers false /includeprofiles false /multimediahandling /useobjectsettings /namespace [ (adobe) (creativesuite) (2.0) ] /pdfxoutputintentprofileselector /documentcmyk /preserveediting true /untaggedcmykhandling /leaveuntagged /untaggedrgbhandling /usedocumentprofile /usedocumentbleed false >> ] >> setdistillerparams << /hwresolution [2400 2400] /pagesize [612.000 792.000] >> setpagedevice shot peening processes to obtain nanocrystalline surfaces in metal alloys: g. cocchetti et alii, frattura ed integrità strutturale, 51 (2020) 356-375; doi: 10.3221/igf-esis.51.26 356 focussed on fracture and damage detection in masonry structures analytical and numerical analysis on the collapse modes of leastthickness circular masonry arches at decreasing friction giuseppe cocchetti politecnico di milano, dipartimento di ingegneria civile e ambientale, piazza l. da vinci 32, i-20133 milano, italy giuseppe.cocchetti@polimi.it, http://orcid.org/0000-0002-9695-2967 egidio rizzi* università degli studi di bergamo, dipartimento di ingegneria e scienze applicate, viale g. marconi 5, i-24044 dalmine (bg), italy egidio.rizzi@unibg.it, http://orcid.org/0000-0002-6734-1382 abstract. departing from pioneering heyman modern rational investigations on the purely-rotational collapse mode of least-thickness circular masonry arches, the hypothesis that joint friction shall be high enough to prevent inter-block sliding is here released. the influence of a reducing coulomb friction coefficient on the collapse modes of the arch is explicitly inspected, both analytically and numerically, by tracing the appearance of purely-rotational, mixed sliding-rotational and purely-sliding modes. a classical doubly built-in, symmetric, complete semi-circular arch, with radial joints, under self-weight is specifically considered, for a main illustration. the characteristic values of the friction coefficient limiting the ranges associated to each collapse mode are first analytically derived and then numerically identified, by an independent self-implementation, with consistent outcomes. explicit analytical representations are provided to estimate the geometric parameters defining the limit equilibrium states of the arch, specifically the minimum thickness to radius ratio, at reducing friction. these formulas, starting from the analysis of classical heymanian instance of purely-rotational collapse, make new explicit reference to the mixed slidingrotational collapse mode, arising within a narrow range of limited friction coefficients (or friction angles). the obtained results are consistently compared to existing numerical ones from the competent literature.1 keywords. circular masonry arches; couplet-heyman problem; reducing friction; purely-rotational mode; mixed sliding-rotational mode; purely-sliding mode. citation: cocchetti, g., rizzi, e., analytical and numerical analysis on the collapse modes of least-thickness circular masonry arches at decreasing friction, frattura ed integrità strutturale, 51 (2020) 356-375. received: 30.06.2019 accepted: 05.11.2019 published: 01.01.2020 copyright: © 2020 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. 1 an earlier version of the present work with preliminary developments was presented at the sahc12 conference in wroclaw, poland, october 15-17, 2012 [7]. http://orcid.org/0000-0002-9695-2967 http://orcid.org/0000-0002-6734-1382 http://www.gruppofrattura.it/va/51/2554.mp4 g. cocchetti et alii, frattura ed integrità strutturale, 51 (2020) 356-375; doi: 10.3221/igf-esis.51.26 357 introduction irst rational studies on the statics of masonry arches were blooming in 1700, with the development of so-called pre-elastic theories. in recent times, they have culminated, in the second half of 1900, in the modern reinterpretation and application of limit analysis to masonry constructions, according to the fundamental pioneering work by jacques heyman [1-4]. specifically, heyman stated three classical behavioural assumptions for masonry structures (1 no tensile strength; 2 infinite compressive strength; 3 no sliding failure), and investigated the five-hinge purely-rotational collapse mode of continuous symmetric circular masonry arches under self-weight (taken as uniformly-distributed along the geometrical centreline of the arch, with self-weight per unit length w =  t d ), by providing analytical representations for the determination of the characteristic parameters of the masonry arch in the critical, least-thickness condition, such as (figs. 1a,b): • angular position  of the rupture (radial) joint with inner intrados hinge at the haunches; • critical thickness to radius ratio  = t/r ; • non-dimensional horizontal thrust h = h/(w r ) acting in such a limit state of minimum thickness still available to sustain the arch (couplet-heyman problem). this classical least-thickness problem in the statics of masonry arches has been revisited by the present authors within a wide research project that has been considering different characteristic aspects, by employing both self-consistent analytical and numerical techniques [5-10]. arches of a general half-angle of embrace 0 <  <  (including for undercomplete and over-complete, horseshoe circular masonry arches) have been systematically analysed in analytical terms. different solutions have been explicitly derived, and numerically explored, which appeared fully consistent with updated outcomes from a re-discussion by heyman [4], and prior developments by ochsendorf [11-12], as well as with classical earlier work by milankovitch [13] (see foce [14]), and several most recent attempts that meanwhile have appeared [15-24]. an earlier account on these developments was provided in sahc10 conference paper [5]; later, a comprehensive analytical treatment with unprecedented closed-form explicit representations was provided in [6], while in [8], consistent comparisons were developed by a discrete element method implementation, in the form of a discontinuous deformation analysis (dda) tool. then, first new developments on the role of friction have been preliminarily investigated in such a research mainstream, as initially reported in sahc12 conference work [7], prodromal to the present one, by releasing heyman hypothesis 3 of no sliding failure, and accounting for both mixed sliding-rotational and purely-sliding collapse modes (figs. 1c,d). here, within that context, a new, complete, analytical treatment is developed, starting from the developed analytical solutions that had earlier been derived for purely-rotational collapse [6,8], with additional comprehensive numerical verification. very recently, separate innovative numerical implementations as an optimisation problem to be solved by non-linear mathematical programming are being developed [9,10], with results that turn out truly consistent with the ones here derived and presented. specifically, the limit values of coulomb friction coefficient  = tan (and friction angle  ), at the theoretical (radial) joints of a continuous arch, marking the transitions between the three collapse modes depicted in figs. 1b-d are here explicitly derived, together with the determination of the analytical dependence of the mixed-mode collapse characteristics (fig. 1c), as a function of friction coefficient , namely m( ), m( ), hm( ). it is newly shown that, at decreasing friction coefficient  at the (radial) joints of the arch, horizontal thrust hm( ) under mixed mode becomes fixed (decreasing), by finite (reducing) friction. this induces, as a consequence, non-linear increasing dependencies of ( ) and ( ). in other words, at a decreasing friction coefficient at the joints of the arch, an increase in the critical value of least thickness is required to warrant the equilibrium of the self-standing masonry arch. here, a main reference is made to complete semi-circular arches with a 2 =  opening (fig. 1a), for a comprehensive illustration and discussion. for such a reference case, the friction range in which mixed-mode collapse is shown to appear turns out quite narrow, in practical terms, i.e. with friction angles  between around 22° and 17° ( = tan between around 0.4 and 0.3). despite, that the value of these findings shall appear to be more of a theoretical type (complete behaviour of a codified mechanical system), than of a practical nature (usually friction coefficients in masonry constructions shall safely be above that; arches are normally built with much higher margins in terms of thickness to radius ratios, with respect to the critical least-thickness condition; and so on), conditions that may be associated to a reducing friction, such as loosening joints, insertion of external materials among the blocks, non-firm or spreading supports, etc., may come up into the picture, leading to considerable interest in anyway reaching a full understanding on arch “stability” (say, equilibrium) at reducing f g. cocchetti et alii, frattura ed integrità strutturale, 51 (2020) 356-375; doi: 10.3221/igf-esis.51.26 358 friction, as in the present setting. moreover, the critical value of friction coefficient up to induce possible sliding may increase with the opening angle of the arch (specifically for over-complete horseshoe arches, see later discussion in section 2.3), thus possibly approaching the ranges of friction coefficients that may be encountered in practice and maybe leading to the potential appearance of sliding within the failure mode. figure 1: sketches of a symmetric semi-circular masonry arch under self-weight: (a) characteristic parameters, primarily: half-angle of embrace , inner rupture joint angular position , thickness to radius ratio , non-dimensional horizontal thrust h; (b) purely-rotational collapse mode; (c) mixed sliding-rotational collapse mode; (d) purely-sliding collapse mode. the present analytical and numerical results appear to be consistent to ones numerically developed in the existing literature, specifically concerning the effects of friction in masonry arches. for instance, gilbert et al. [25] have numerically investigated the role of friction, by estimating for a semi-circular arch a minimum thickness to radius ratio  = 0.1068, in the presence of a purely-rotational collapse mode, when  is greater than 0.396 (friction angle larger than  = 21.60°). this marks, at decreasing friction, the transition from the purely-rotational mode to the mixed slidingrotational mode. furthermore, a value of  = 0.31 ( = 17.22°) was found, which then located the shift from the mixed sliding-rotational mode to the purely-sliding mode. in gilbert et al. [25] a characteristic, sort of l-shaped diagram depicts the critical value of thickness to radius ratio  as a function of friction coefficient , with a double kink at these two critical values of , a constant value of  for  > 0.396 and rapidly-growing values of  right on  = 0.31. these outcomes appear in good agreement with numerically developed earlier results by sinopoli et al. [26-28], which individuated the above-mentioned kinks respectively at  = 0.395 ( = 21.55°) and  = 0.309 ( = 17.17°). here, the following “exact” analytical results for the complete semi-circular arch are going to be consistently derived: rm = 0.395832 (rm = 21.5952°), for the transition from purely-rotational to mixed sliding-rotational modes; ms = 0.309215 (ms = 17.1824°), for the transition between mixed and purely-sliding modes. (a) (b) (c) (d) g. cocchetti et alii, frattura ed integrità strutturale, 51 (2020) 356-375; doi: 10.3221/igf-esis.51.26 359 in the present paper, two sorts of analyses on the role of reducing friction in circular masonry arches are carried-out, as respectively presented in sections 2 and 3, with mutually consistent results, as eventually outlined in resuming section 4: • first, a complete analytical approach in the wake of previous original analytical solutions for purely-rotational collapse [6,8] is developed, towards the characterisation of the mixed sliding-rotational collapse mode and of the relevant friction bounds. this analytical analysis starts from the presumed purely-rotational collapse mode due to heyman [1-4] and, by decreasing friction, derives, through a static approach, the modes that subsequently arise, with explicit “exact” solutions. • second, a comprehensive, original self-implemented numerical approach is developed, which sets an optimisation analysis in the sense of the lower-bound (static) theorem of limit analysis, within a classical commercial spreadsheet wherein an optimisation function is made available. there, the constitutive behaviour of the circular masonry arch is stated and equilibrium conditions are varied towards the determination of the critical least-thickness condition and of the attached collapse mode. thus, the collapse mode, whether purely-rotational, mixed sliding-rotational or purely-sliding, is not there a priori hypothesised, while correctly numerically recovered, through an optimisation process, with outcomes that turn out fully coherent with those “exact” ones from the previous analytical analysis, and also to the above-quoted findings from the preceding literature [25-28]. analytical approach tarting from the classical analysis of purely-rotational collapse of circular masonry arches in the so-called couplet-heyman problem [1-4], the determination of collapse characteristics , , h for a symmetric circular arch of general half-angle of embrace  (figs. 1a,b) may be stated by the solution of the following system of three characteristic equations, in terms of unknown non-dimensional horizontal thrust variable h [5,6,8]: 2 2 2 ( 2 ) sin 2(1 cos )(1 / 12) 2 ( 2 )cos 2 (1 / 12), cot 2 2 ( 2 ) (sin cos ) 2sin (1 / 12) cot (1 / 6) ( 2 )sin 2 m m m e ccr m h h h h h a a h h h                                 − − − + = = + − −  = = − + = +  − + − +  = = = − + − −  1 2 (1) eqns. (1)a and (1)b represent two equilibrium relations, respectively the rotational equilibrium of any upper portion ab of the half-arch (symmetry conditions apply) with respect to inner intrados hinge at haunch b, and of whole half-arch ac with respect to extrados hinge at shoulder c (fig. 1b); the latter introduces the dependence on opening angle , through variable a =  cot(/2). importantly, eqn. (1)c truly corresponds to the correct tangency condition of the line of thrust (locus of pressure points) at haunch intrados b and may be derived from the following stationary condition: num[ ]( ) ( ) 0 den[ ] hdh h h h d h     = =  = =  11 1 e 1 (2) where symbol ( )′ denotes a differentiation with respect to  [6] and advantage has been taken from the quotient rule of differentiation. notice that the correct statement of this tangency condition actually sets a main difference to classical heyman solution, which stated the tangency condition on the thrust force itself (h = hh in eqn. (1)c), and may be considered as leading to a sort of approximation of the true solution, at least until when  keeps small. moreover, in eqns. (1) ccr and m are two control flags allowing to shift from classical heyman solution (ccr = 0, m = 0), to the correct solution of heyman problem (ccr = 1, m = 0), and to milankovitch solution considering the true s g. cocchetti et alii, frattura ed integrità strutturale, 51 (2020) 356-375; doi: 10.3221/igf-esis.51.26 360 self-weight distribution along the arch (ccr = 1, m = 1), respectively leading to a “linear”, a “quadratic” and a “cubic problem” in the algebraic solution for unknown triplet a( ), ( ), h( ). this is originally and extensively derived, described and discussed in [6]. all what will be considered in the following will stick to classical hypothesis m = 0, i.e. by assuming a self-weight distribution along the geometrical centreline of the arch, in classical heyman sense, though with correct evaluation ccr = 1 of the tangency condition in eqn. (1)c. an extensive discussion on the differences between the three arising solutions has been reported in [6], including about the spreading discrepancies appearing for over-complete (horseshoe) circular masonry arches. known heyman “linear” solution may finally be obtained from eqns. (1), for ccr = 0, m = 0, and can be classically represented as: ( ) ( ) ( ) 2 2 2 cos sin cos sin cot cot 2 2 cos sin cos sin cos sin 1 cos 2 1 cos cot h h a h h                         + + = = + −  − − = = +  = =   (3) going to properly correct ccr solution (ccr = 1, m = 0), for the complete semi-circular arch, i.e.  = a = /2, system (1) renders the following characteristic ccr solution triplet for the purely-rotational collapse mode to be recorded: 0.951141 54.4963 , 0.107426, 0.621772 ( / 2)r r rrad h   = =  = = = (4) more generally, at variable half-opening angle  of the circular masonry arch (thus at variable a =  cot (/2)), the solution of system (1) for ccr = 1, m = 0 can be analytically represented in closed-form as follows [6]: 2 2 2 2 2 2 2 ( 2 ) 2 2 2 2 f f gs s a g s g s g s f gs s f g f s f gs s h s    − +  = −  − − + = +  −  − + =   with 2 ( ) ( sin )' ( ) ( ) sin ( ) cos f f s c g g s cf sc s s c c            = = = + = = + = + = = = = (5) indeed, triplet a( ), ( ), h( ) becomes a double-valued function of inner hinge position , coming from the solution of the following “quadratic problem” [6]: 2 2 2 2 ( 2 ) 2 0 ( ) 4( ) 4( ) 0 2 2( ) 0 s g s a fg a g f g g s g f s h f s h g f    − − + =  + − − + − =  − − + − = (6) the above three quadratic equations in a, , h can be obtained from system (1) by eliminating in turn couples (, h ), (a, h) and (a, ). notice that solutions (5)b and (5)c for  and h can be obtained from a 2×2 subsystem formed by eqns. (1)a and (1)c, namely those independent on a( ) in source system (1). functions a( ), ( ), h( ) become single-valued at  = s = 1.12909 rad = 64.6918°, namely at the value of  setting to zero the term under square roots g. cocchetti et alii, frattura ed integrità strutturale, 51 (2020) 356-375; doi: 10.3221/igf-esis.51.26 361  [rad] a =  c o t(  /2 ) heyman ccr  2 −  2/3  [rad]  heyman ccr  4/12  [rad] h heyman ccr 1 −  2/3 in eqns. (5): f 2 – 2gs + s 2 = 0. this corresponds to a stationary (maximum) point of the curves ( ) or (a ) at variable arch opening [6,8]. the characteristic solution for  = a = /2 keeps in the pre-peak branch (a+, –, h+) of solution (5). solutions (5)a, (5)b and (5)c can be analytically plotted as a function of hinge position , as depicted in fig. 2, with comparison between correct ccr solution [6] and classical (say “approximated”) heyman solution. similar representations occur as well for milankovitch solution accounting for the true self-weight distribution along the circular arch, though leading to the following more involved “cubic problem”: ( ) ( ) ( ) ( ) ( ) ( ) ( )( ) ( ) 2 3 2 2 3 3 2 2 3 2 2 3 2 3 3 2 0 3 12 12 0 6 3 3 2 3 2 2 0 s g s a g f g s a f g a g s f g g s g f s h s f g s h g f f s h g f     =     − + − − + + + − − + − = − − − − + − =  − − (7) with rather similar results and minor differences, to those recovered for the above “quadratic problem” [6]. thus, the value of milankovitch solution is not further inspected here, since focus is now going to be made on the effect of reducing friction, on correct ccr solution, vs. “approximated” heyman one, in the kept hypothesis of self-weight distribution along geometrical centreline of the circular arch. moreover, ccr solutions (5)b and (5)c can be analytically plotted by parametric plots (( ), h( )) and (, h( )), for 0 ≤  ≤ s, showing (with important implications in the present forthcoming analysis on the role of reducing friction) non-linear dependencies of (h ) and (h ) at variable non-dimensional horizontal thrust h (figs. 3a,b), in the critical condition of purely-rotational collapse (fig. 1b). figure 2: analytical parametric plot of solution triplet a( ), ( ), h( ) as a function of inner hinge angular position  for ccr and heyman solutions, with common trends for small  (a =  cot(/2), : half-angle of embrace; : thickness to radius ratio; h: nondimensional horizontal thrust; refer to fig. 1). g. cocchetti et alii, frattura ed integrità strutturale, 51 (2020) 356-375; doi: 10.3221/igf-esis.51.26 362 this remarkably shows that (h ) becomes a non-linear increasing function at decreasing h and that (h ), in the pre-peak branch, is also a non-linear increasing function at lowering h. thus, if h is set by external conditions (e.g., here, through friction reduction), in the least-thickness limit equilibrium state,  and  vary accordingly to the trends represented in figs. 3a,b (non-linearly and with opposite concavities). these considerations display a crucial implication in the forthcoming investigation analysis at reducing friction. (a) (b) figure 3: analytical parametric plot as a function of non-dimensional horizontal thrust h( ): (a) least thickness to radius ratio ( ); (b) inner hinge angular position . reducing friction the whole above solution holds true in heyman sense for high values (infinite, in the limit) of friction coefficient  = tan, apt to prevent sliding failure within the arch. by imaging now to decrease friction coefficient  (not present in system (1)) from infinity or from such high values, one seeks when, and where in the arch, a first sliding joint may arise, for a critical value of  = rm marking the transition between purely-rotational and mixed sliding-rotational modes. this should occur when limit sliding activation condition t/n =   is reached for the first time, where t( ) and n( ) are the shear (clock-wise positive) and normal (compression positive) components of the internal thrust force at each theoretical (radial) joint of the continuous arch. from the translational equilibrium of any upper portion ab of the half-arch of general half-opening , one gets, in non-dimensional terms: ( ) ( ) sin cos ( ) ( ) cos sin t t h w r n n h w r            = = −     = = +  (8) it may be noticed that non-dimensional internal force components t( ) and n( ) are just functions of geometrical angular position variable , at a given value of horizontal thrust h (which is constant along the arch). specifically, thickness to radius ratio parameter  does not intervene in eqns. (8). at the shoulders of the arch ( = ), internal action component ratio t/n becomes: sin cos ( ) cos sin t h n h         − = = + (9) for the complete semi-circular arch, at the half-arch extremes (namely crown a and shoulder c) one has, respectively:  = 0, t = 0, n = h, thus t/n = 0;  =  = /2, t = h sin –  cos = h, n = h cos +  sin = /2, thus t/n = 2h/. g. cocchetti et alii, frattura ed integrità strutturale, 51 (2020) 356-375; doi: 10.3221/igf-esis.51.26 363 plots in fig. 4a represent the variation of local slope t/n of the internal thrust (to the local joint normal) at variable half-opening  of upper portion ab, for fixed values of h ranging from 0.1 to 1, together with the maps of stationary points appearing in the t/n curves at variable h. (a) (b) figure 4: local slope t/n of non-dimensional shear/normal internal force components at variable  for the complete semi-circular arch ( = /2): (a) curves for different values of non-dimensional horizontal thrust h, with stationary maps; (b) limit situations of collapse mode transition with sliding activation at  = rm and  = ms. two main facts clearly appear from the inspection of fig. 4a: absolute maxima of thrust slope are always attained at the shoulder ( =  = /2); relative minima (maxima on negative side) occur at stationary points at intermediate locations 0 ≤  ≤ 0.5, at variable thrust 0 ≤ h ≤ 1. this shows, on one hand, that the first sliding joint, at decreasing , should appear at the shoulder when t/n = +, leading to: cos sin sin cos h h         + = = − (10) g. cocchetti et alii, frattura ed integrità strutturale, 51 (2020) 356-375; doi: 10.3221/igf-esis.51.26 364 which provides transition mark  = rm at h = hrm = hr and then fixes the horizontal thrust within the arch, h = hm( ), under mixed sliding-rotational mode, as linearly decreasing with friction coefficient : 2 0.395832 ( 21.5952 ), 0.621772 ; ( ) ( ) / 2 2 r rm r rm rm r m h h h h h h         = = = =  = = = = (11) notice that generally h( ) is a non-linear function of , at variable . for the complete semi-circular arch ( = /2; cos = 0, sin = 1), it just becomes a linear function of , namely h = /2 . on the other hand, in analytically seeking the stationary points marked in fig. 4a, one then searches for the additional joint where further sliding may occur. thereby, the corresponding stationary condition leads to: 2 (1 )cos sin1 0 (1 ) sin cos hd t t t n tn t t t t n d n n n n n n hn            − − +−       = = = − =  = =       − +      (12) thus, since such sliding joint is activated when, there, t/n = –, while h = h, one has to solve the following system of three governing equations (independently from thickness parameter  ): 2 2 0 (sin cos ) (cos sin ) 0 cos sin (sin cos ) (cos sin ) 0 sin cos t t h h n n t h n h h h                         =  − + =    = −  + − − =   + = =  − − + = − (13) remark that eqn. (13)a states the map of stationary points of t/n as  2 = h – h2 = h(1–h) or  2 + (h – 1/2)2 = (1/2)2 (see the circle insert in fig. 4a). this is also obtained either by eliminating couple (,  ) from system (13), or variable  from eqns. (13)a and (13)b. instead, by eliminating couple (, h ) from system (13), and couple (, h ) from system (13) or variable h from eqns. (13)a and (13)b, one also gets, respectively: 2 2 2 [ 2 sin 2( )] [1 4 cos 2( )] [ 2 sin 2( )] 0           + + − − − + + − + = (14) 2 ( 2 sin 2 ) 2 cos 2 2 sin 2 0      + − + − = (15) the latter equation leading to following symbolic solution  = ±( ): 2 cos 2 1 4 ( ) 2 sin 2         − = + (16) where higher root + holds true for  ≥ cos1/(1+sin1) = 0.293408, with  ≤ 1/2. thus, from eqn. (14), with  = /2, one may numerically solve for position  = s of the new sliding joint. then, in cascade, at that value of  = s, eqn. (15), or eqn. (16), leads to transition friction coefficient ms (higher root); finally, eqn. (13)a gives, at  = s, thrust hms (lower root, corresponding to hms = hms). in doing so, or either by directly numerically solving system (13), one gets: 0.499796 28.6362 , 0.309215 ( 17.1824 ), 0.485714s ms ms msrad h  = =  = =  = (17) g. cocchetti et alii, frattura ed integrità strutturale, 51 (2020) 356-375; doi: 10.3221/igf-esis.51.26 365 notice that, once friction mark ms is known, thus hms = /2 ms, stationary condition (13)a, i.e.  2 = h(1–h), gives the following explicit expression of the angular position of the inner sliding joint for the purely-sliding collapse mode: (1 ) 1 2 2 s ms ms ms msh h        = − = −    (18) since hms is near 0.5, s is also near 0.5 (see circle insert in fig. 4a). mixed sliding-rotational mode at this stage, the friction boundaries for the appearance of the mixed sliding-rotational collapse mode have been located. notice that: • at  = rm, any 2-dof linear combination of 1-dof modes in figs. 1b and 1c is possible; • at  = ms, any 2-dof linear combination of 1-dof modes in figs. 1c and 1d is feasible; • in range ms <  < rm, the mixed-mode mode in fig. 1c is found, with variable position m( ) of inner hinge b, thickness to radius ratio m( ) and horizontal thrust hm( ), at variable friction coefficient . this last occurrence is ruled by a new system of governing equations, in place of those in system (1), in which second equilibrium eqn. (1)b is replaced by sliding equation h = h = /2 , namely: 1( , ) ( , ) ( , )e h h h h h h         =  =  = (19) the solution of this system actually brings back to the previous analysis for the purely-rotational mode. indeed, equations h = h1 and h = he are still the same, with same solutions (5)b and (5)c for ( ) and h( ), as previously explained. by setting h = h = /2  in the expression of h( ) in eqn. (5)c and solving for ( ) = h( ) 2/, or by eliminating h = /2  in two eqns. (19)a and (19)c, this leads to trends m( ) and m( ). these can be analytically plotted, by parametric plots at variable rm ≤  ≤ ms (figs. 7-8, section 4), where ms can be found from ( ), eqn. (5)b, at  = ms. similarly, ms is found as (ms), at hms = /2 ms, so that: 1.05616 60.5134 , 0.200637, 0.485714ms ms msrad h = =  = = (20) since this leads to an increase of ( ) at decreasing , constant trace  = r of the purely-rotational mode is abandoned, since ( ) is higher and thus provides a new least thickness condition (fig. 7). accordingly, the hinge at the shoulder, co-present with the sliding joint there at  = rm, closes down. the inner haunch hinge b keeps instead on, and moves further down at decreasing . basically, the trends of ( ) and ( ) are read in figs. 7 and 8a, as they were in figs. 3a and 3b at decreasing h. indeed, h is limited by friction to h = /2 , with the linear decreasing trend at lowering  represented in fig. 8b. such a trend is linear for the exposed case of  = /2. tab. 1 reports analytically-evaluated (“exact”) mixed-mode collapse characteristics , , h at variable friction coefficient . at new transition  = ms, trends m( ), m( ), hm( ) stop. limit equilibrium states associated to modes in fig. 1d do not depend on thickness parameter , thus they would require any value of  > ms in the least thickness condition. thus, the inner hinge at the haunch also closes down and from the two modes in figs. 1c and 1d, co-present at  = ms, only the purely-sliding mode in fig. 1d survives for  > ms. however, all these states at  = ms are right-away limit equilibrium states, thus equilibrium is no-longer possible in practice, at any value  > ms. notice also that, at  = ms, inner hinge and sliding joints are differently located, respectively at  = ms = 1.05616 rad = 60.5134° (hinge joint) and  = s = 0.499796 rad = 28.6362° (sliding joint), thus interestingly at nearly 60° and 30°. the present analytical outcomes are going to be further commented in section 4, with comparison as well to independent, matching, numerical results by a self-made spreadsheet implementation, as derived in the next section. g. cocchetti et alii, frattura ed integrità strutturale, 51 (2020) 356-375; doi: 10.3221/igf-esis.51.26 366   h  [rad] [deg]   h  [rad] [deg] 0.7 0.107426 0.621772 0.951141 54.4963 0.35 0.152920 0.549779 1.01227 57.9986 0.3959 0.107426 0.621772 0.951141 54.4963 0.34 0.163977 0.534071 1.02392 58.6661 0.395832 0.107426 0.621772 0.951141 54.4963 0.33 0.175448 0.518363 1.03499 59.3003 0.3958 0.107455 0.621721 0.951188 54.4991 0.32 0.187338 0.502655 1.04548 59.9016 0.39 0.112750 0.612611 0.959654 54.9841 0.31 0.199653 0.486947 1.05540 60.4702 0.38 0.122192 0.596903 0.973737 55.7910 0.3093 0.200531 0.485847 1.05608 60.5088 0.37 0.132031 0.581195 0.987190 56.5618 0.309215 0.200637 0.485714 1.05616 60.5134 0.36 0.142273 0.565487 1.00003 57.2974 0.3092 no equilibrium solution table 1: “exact” critical solution values of triplet , h,  obtained for the complete semi-circular arch by the analytical analysis at variable friction coefficient . sliding joints appear at  = /2 rad = 90° for 0.309215 = ms ≤  ≤ rm = 0.395832 and at  = s = 0.499796 rad = 28.6362° for  = ms = 0.309215. comment on present mixed mode at variable opening angle of the arch the previous relations, generally set for any half-angle of embrace , and illustrated in detail for the considered reference case of the complete semi-circular arch ( = /2), could be used to further explore the output of the discovered mixed mode, at reducing friction, for arches with variable opening angles. it can be shown that the analytical solution for the representation of the mixed mode here derived holds true for a range of opening angles up to the following limit one (0 <  ≤ lm). indeed, if one seeks the condition leading to the common satisfaction of systems of three eqns. (1) and three eqns. (13), namely those that mark the rotational mode and the sliding mode, one achieves the following numerical solution of the six equations in six unknowns lm (limit opening angle for present mixed sliding-rotational mode), lm (friction coefficient), lm (thickness to radius ratio), hlm (non-dimensional horizontal thrust),  rlm, (angular position of inner rotational joint),  slm (angular position of inner sliding joint): ( )/22.48716 142.504 ( cot 0.844185), 1.41527 ( atan =0.955669 54.7558 ), 0.679605, 0.0978058, 1.03749 59.4435, 0.297052 = 17.0198° lmlm lm lm lm lm lm lm lm r s lm lm rad a rad h rad rad         = =  = = = = =  = = = = = (21) thus, the documented solution of mixed mode is achieved until for an angle of embrace of about lm = 142.5°, anyway requiring considerable friction (and thickness) for the arch to withstand under self-weight, in the limit condition of least thickness. at that value of  (marking a rather open, thick, horseshoe arch), the two solutions for rotational collapse and sliding collapse, together with that for mixed mode collapse, unify all together and are co-present at the same time for the values of the characteristic coefficients reported in eqn. (21). further numerical results and representations of the collapse characteristics of the circular masonry arch at variable angle of embrace, implicitly described by the present analytical treatment, and fully consistent with such analytical solutions, are additionally presented in [9,10], by a separate numerical treatment, based on a comprehensive non-linear mathematical programming formulation and implementation. a simpler, straightforward numerical strategy is instead proposed next, for independent and complete validation of the achieved analytical results. g. cocchetti et alii, frattura ed integrità strutturale, 51 (2020) 356-375; doi: 10.3221/igf-esis.51.26 367 numerical approach n immediate, self-implemented numerical algorithm for the individuation of the collapse modes of symmetric circular masonry arches has been further created within commercial spreadsheet software excel, to independently inspect and validate the previous analytical outcomes on the arch’s collapse characteristics, as revealed at reducing friction. it makes use of an optimisation function named “solver”, which allows for the selection of a grg (generalised reduced gradient) engine, towards the solution of smooth non-linear optimisation problems. similar, independent numerical tools of thrust-line or limit analysis, which may as well involve the use of spreadsheets and formulations of mathematical programming have been proposed [29-35]. an approach that shall be quite similar to the present one has been earlier developed by de rosa and galizia [34], for the analysis of pointed masonry arches. discrete element method tools (see e.g. [8], and references therein quoted) may as well be employed toward the stated validation purpose, though the correct and precise evaluation of the threshold values of friction coefficients, and relevant arch thicknesses and collapse characteristics, with respect to the analytically determined benchmark values above, may constitute a rather delicate quest. the feeling, confirmed by first trials by an available dda program already adopted in [8], within the present research endeavours, is that such numerical tools may not turn out as refined enough, to become capable to feel the subtle differences in the effects of variable friction, especially in correctly getting the transition values of friction coefficient, as exactly derived by the earlier analytical derivation. likely, general trends may be qualitatively reproduced, in the best option, but it may be hard to recover true quantitative matchings with the analytical results. thus, a separate and dedicated numerical tool was eventually conceived and implemented, as delivered in the present section, to provide a final confirmation of the analytical results, with truly matching outcomes, on a real quantitative basis, as then resumed in the subsequent section. input for the present spreadsheet numerical implementation within excel is constituted by two kinds of data: • geometrical: arch width d, mean radius r (both nominally fixed to 1 m); • material: limit tension stress t (set to zero, according to heyman hypothesis 1), limit compression stress c (set to 1000 kn/m2, i.e. a high value apt to comply with heyman hypothesis 2), variably-fixed friction coefficient , weight per unit volume  (set to 25 kn/m3). based on these input data, the trends of internal actions n( ), t( ), m( ) along the arch are recovered by equilibrium and confronted to the limit values that define section resistance, specifically in terms of shear force t and moment m. then, an iterative procedure is put in place at variable thickness t, which constitutes the cell variable within the optimisation process, to evaluate the limit condition of least thickness. characteristics  (angular position of rupture joints), , h in the limit condition are then obtained, together with the variation of internal actions n( ), t( ), m( ) along the arch, and associated thrust-line eccentricity e( ) = m/n from geometrical centreline. thus, the numerical analysis is carried out by a static approach and the collapse mode is found out by the analysis in the limit thickness condition, as the output of the optimisation (thickness minimisation) process. like that, notice that the collapse mode is not a priori imposed but truly obtained out of the numerical process. the analysis is here carried out on a complete semi-circular masonry arch (angle of embrace 2 =  ). due to symmetry, only one half of the arch is considered, with “hyperstatic” actions (moment x = ma and horizontal thrust y = h) acting at geometrical centreline at crown section a. statically-admissible configurations are those warranting equilibrium of any upper portion of the arch of angular opening . they are described in non-dimensional terms by expressions (8), which determine shear t( ) = t( ) w r and normal n( ) = n( ) w r actions in each theoretical section of the arch, and by the following expression of moment m( ) = m( ) w r2. consistently with relations (8), in non-dimensional terms: ( ) 2 ( ) (1 cos ) sin (1 cos ) x m h w r     = + − − − − (22) cross section resistance may be set as follows. given that 0 = t t d ≤ n( ) ≤ c t d should always be satisfied within the arch, focus is made on moment and shear resistances. since eccentricity e( ) = m( )/n( ), with n( ) > 0 for h > 0 (compression), should not exceed  t/2 (no tensile strength) and assuming that shear is limited by a coulomb friction law with friction coefficient , one states the following two resistance inequalities to hold: ( ) ( ) ; ( ) ( ) 2 t m n t n      (23) a g. cocchetti et alii, frattura ed integrità strutturale, 51 (2020) 356-375; doi: 10.3221/igf-esis.51.26 368 within the optimisation process, toward the determination of least-thickness condition t = tmin still making the whole self-standing equilibrium possible, cell constraints are then represented by resistance conditions (23) and by the enforcement that, at crown section a, y = h > 0 and |x| = |ma| ≤ y t/2. equilibrium values of n( ), t( ), m( ) from eqns. (8) and (22) are then determined at discretised angular positions, with angle-step  = 0.001 rad. the optimum search of tmin is iteratively performed, by varying the initial values of x = ma, y = h and t, in order to satisfy all given constraints (with tolerances in the order of 10-6). rotational and sliding joints are respectively detected, and their angular position  recorded, when limit conditions (23)a and (23)b, with numerical equalities, are reached (fig. 5). a high value of friction coefficient is first set, namely  = 0.7 (  35°), which should allow for predicting a purely-rotational collapse mode, due to heyman hypothesis 3 (see analytical results in tab. 1). the analysis is then repeated at lowering values of friction coefficient , which has been reduced by steps up to  = 0.0001, until the numerical algorithm becomes no-longer able to find equilibrium solutions. transition conditions at  = rm and  = ms have been numerically found, by looking at activated hinge and/or sliding joints (figs. 5 and 6). results have been recorded in terms of characteristic arch parameters , , h at variable . salient numerical outcomes are reported in tab. 2 below (to be consistently compared with analytical results in earlier tab. 1). it may be noted from tab. 2 that for  = 0.3959 ( = 21.5986°) the algorithm numerically detects the simultaneous presence of a rotational and a sliding joint at  =  = 90°. this provides a consistent numerical estimate of “exact” friction coefficient rm = 0.395832 (rm = 21.5952°), as earlier analytically derived. further, the lack of equilibrium solutions for  < 0.3093 ( < 17.1868°) provides a consistent numerical approximation of “exact” bound ms = 0.309215 (ms = 17.1824°). these numerical results are also consistent with earlier independent numerical outcomes in [25-28], as mentioned in the introduction. also, the approximate numerical values of characteristic parameters , , h fit quite well with the “exact” predictions from the analytical approach (tab. 1), as analysed, represented and resumed next.   h hinge joints  [deg] sliding joints  [deg]   h hinge joints  [deg] sliding joints  [deg] 0.7 0.107426 0.621772 0-54.4883-90 0.35 0.152920 0.549779 0-58.0120 90 0.396 0.107426 0.621772 0-54.4883-90 0.34 0.163977 0.534071 0-58.5563 90 0.3959 0.107663 0.621878 0-54.4883-90 90 0.33 0.175448 0.518363 0-59.3011 90 0.3958 0.107456 0.621721 0-54.4883 90 0.32 0.187338 0.502655 0-59.9027 90 0.39 0.112750 0.612611 0-54.9753 90 0.31 0.199653 0.486947 0-60.5043 90 0.38 0.122191 0.596903 0-55.7774 90 0.3094 0.200406 0.486004 0-60.5043 90 0.37 0.132031 0.581195 0-56.6082 90 0.3093 0.200531 0.485847 0-60.5043 28.6479-90 0.36 0.142273 0.565487 0-57.2958 90 0.3092 no equilibrium solution table 2: approximate critical solution values of triplet , h,  obtained for the complete semi-circular arch by the numerical analysis at variable friction coefficient . summary of analytical and numerical outcomes igs. 7-8 below all together resume the present analytical and numerical results, by showing classical collapse characteristics of the masonry arch , , h at variable (reducing) friction coefficient . numerical data out of the analysis in section 3 are over-scored with cross markings on continuous analytical trends (parametric plots) out of the “exact” analysis in section 2, with very good matching among them. specifically, fig. 7 first reports a main outcome of the derivation, as the limit curve in the (,  ) plane, in the sort of typical representation pointed out by gilbert et al. [25] and sinopoli et al. [26-28], and recently by aita et al. [23], there generalised to masonry arches of various typologies and shapes. f g. cocchetti et alii, frattura ed integrità strutturale, 51 (2020) 356-375; doi: 10.3221/igf-esis.51.26 369 figure 5: numerical optimisation results for the trends of shear t( ) and moment m( ) at friction coefficient  = 0.3959. figure 6: numerical optimisation results for the trends of shear t( ) and moment m( ) at friction coefficient  = 0.3093. moreover, fig. 8 accordingly as well shows the non-linear trend of inner angular position  variation at reducing friction  in the mixed collapse mode and the associated (linear) decreasing trend of non-dimensional horizontal thrust h, as limited by reducing friction  at the sliding joint forming at the springing of the arch at  =  = /2. this constitutes a key feature for the appearance and interpretation of the arising mixed mode, as revealed by the present analytical and numerical investigation on the role of reducing friction. on the hierarchy of the collapse modes at variable (decreasing) friction coefficient , it may be resumed that for  >rm the collapse mode in the least-thickness condition is purely-rotational (fig. 1b). collapse characteristics , , h remain unvaried at changing : since purely-rotational collapse is uniquely determined by arch geometry, they are not dependent on the values of friction coefficient if greater than rm. at transition  = rm = 0.395832 (rm = 21.5952°), a first sliding joint appears at the shoulder of the arch ( =  = /2), for a non-dimensional horizontal thrust h = hr matching h = h( ) = /2 . this marks the transition from purely-rotational to mixed sliding-rotational collapse modes. the simultaneous presence of a hinge and a sliding joint at the shoulders is detected in both analytical and numerical analyses. the 2-dof collapse mode in such a transition state could be represented by any linear combination of 1-dof modes in figs. 1b and 1c. when friction coefficient  is then further decreased from rm, non-dimensional horizontal thrust h keeps fixed by friction as h = h( ). the least thickness required for equilibrium is forced to increase. indeed, since a lower friction coefficient is related to a lower resistance to sliding, a larger section (thickness) is needed to prevent collapse. also, the purely-rotational collapse mode cannot be further triggered, since a thickness larger than value r required by purely-rotational collapse (independent on  ) is needed to avoid sliding. hence, the collapse mode that appears first, when thickness is decreased from a super-critical value to the critical one, is the mixed sliding-rotational mode in fig. 1c. at the same time, the inner g. cocchetti et alii, frattura ed integrità strutturale, 51 (2020) 356-375; doi: 10.3221/igf-esis.51.26 370 hinge at the haunches moves further down, at decreasing , from the location at purely-rotational collapse. this is due to the non-linear increasing trends of  and  at lowering h (fixed here by friction) in the purely-rotational solution (fig. 3). figure 7: least thickness to radius ratio  at variable friction coefficient , obtained by the analytical and numerical analyses. the mixed sliding-rotational mode range, ms <  < rm, is limited by ms = 0.309215 (ms = 17.1824°) and rm = 0.395832 (rm = 21.5952°). the shaded region represents the possible arch equilibrium states of couples (,  ). reducing friction  sets a required increase of least thickness to radius ratio . at  = ms = 0.309215 (ms = 17.1824°) an additional sliding joint opens up at ms = 0.499796 rad = 28.6362°, when  = ms = 0.200637, with h = hms = 0.485714. at  = ms, this sliding joint coexists with a hinge at the haunches at m(ms) = 1.05616 rad = 60.5134°, and the corresponding 2-dof mixed collapse mode would be any linear combination of 1-dof collapse modes in figs. 1c and 1d. any larger value of  > ms would instead represent limit equilibrium conditions at  = ms for which purely-sliding collapse would develop (fig. 1d). in practice, at  = ms any value of  > ms would correspond to limit states associated to purely-sliding modes in fig. 1d and the arch would no longer be able to withstand under self-weight. nothing should be said, by the present static approach, for values of  < ms, since then equilibrium is no-longer possible at any value of . thus, it may be concluded that the shaded region in fig. 7 represents the equilibrium states of couples (,  ) allowing for arch equilibrium under self-weight. the inferior boundary of this domain is set by constant line  = r at  ≥ rm, then by curve  = m( ) at ms ≤  ≤ rm, finally by vertical line  ≥ ms at  = ms (fig. 7). tab. 3 below further resumes all the main solution characteristics obtained by the analytical results, for the various traced collapse modes of the complete semi-circular arch (2 =  ), at reducing friction, according to the above detailed discussion and the corresponding illustration of the collapse modes. notice that the collapse mechanisms were already drawn, on scale, in figs. 1b,c,d, as indeed corresponding to the main cases on the 1st, 3rd and 5th rows of tab. 3, now reported. remark that these constitute the three basic collapse cases that are revealed by the study. the other two intermediate rows in the table represent transition cases, among couples of them, where any possible combination of the two underlying mechanisms meeting at such a transition instance becomes possible. conclusions he role that friction coefficient  at the theoretical (radial) joints of a continuous circular masonry arch plays in the definition of geometrical collapse of continuous arches has been fully investigated, with specific reference illustration to the classical case of the complete semi-circular arch (half-angle of embrace  = /2 = 90°). the analytical treatment presented in [5,6,8] for purely-rotational collapse has been complemented and extended, by releasing heyman hypothesis 3 of no sliding failure and looking at the induced changes of the collapse mode through the role of a reducing friction, leading to sliding onset. t g. cocchetti et alii, frattura ed integrità strutturale, 51 (2020) 356-375; doi: 10.3221/igf-esis.51.26 371 (a) (b) figure 8: trends of characteristic parameters , h at variable friction coefficient , obtained by the analytical and numerical analyses: (a) inner hinge angular position ; (b) non-dimensional horizontal thrust h. reducing friction  sets a non-linear increase of angular position  of the inner hinge and a linear (for 2 =  ) decrease of non-dimensional horizontal thrust h. then, at decreasing friction coefficient , different masonry arch collapse modes have been located as follows (figs. 1b-d, tab. 3): • for  > rm classical purely-rotational collapse (fig. 1b), with five hinges in the symmetric configuration of the whole arch (one at the crown, two at the haunches and two at the shoulders); • for ms <  < rm mixed sliding-rotational collapse (fig. 1c), with three hinges in the whole arch, one at the crown and two at the haunches, and with two sliding joints at the shoulders; • for  = ms and  > ms purely-sliding collapse (fig. 1d), with four sliding joints in the whole arch, symmetrically placed at the shoulders and at the haunches (at an angle s ≃ 30° differing from that m(ms) ≃ 60° locating the last inner hinge position in the previous collapse mode at  = ms). at two transition instances  = rm and  = ms, 2-dof modes obtained as any linear combinations of the two adjacent 1-dof modes above become possible. the reducing friction range in which the newly (analytically) discovered mixed sliding-rotational mode occurs is quite narrow, with friction angles between near 22° and 17°. this result obviously holds true for the ideal case of perfectly holding shoulders (i.e. no abutment settlements). as a crucial feature, at decreasing friction coefficient , horizontal g. cocchetti et alii, frattura ed integrità strutturale, 51 (2020) 356-375; doi: 10.3221/igf-esis.51.26 372 thrust h decreases with it, as set by friction, linearly for 2 = , by ranging from hr to about 0.78 hr. at the same time,  non-linearly increases from r to about 1.87 r (then, critical thickness almost doubles) and  also increases from near r ≃ 54.5° to about 1.11r ≃ 60.5°. an inner sliding joint finally appears at  = ms at a different s location near 30° from the crown. table 3: summary of analytical collapse characteristics at variable friction coefficient  for the complete semi-circular arch with 2 =  (refer also to fig. 1). this analytical and numerical investigation has enquired the role of friction in the framework of classical heyman masonry arch analysis. focus has been explicitly made on the case of a complete semi-circular arch (2 =  ), to report detailed results and understand crucial features, specifically for the present mixed sliding-rotational mode. the analysis could be further generalised to cases of general half-opening angles , as implicitly analytically here defined and independently numerically outlined in [9,10] by an innovative non-linear mathematical programming procedure, accounting for both static and kinematic admissibilities, all together. this considers a general formulation apt to address possible issues of non-normality in the prediction of the limit analysis formulation and potential instances of non-uniqueness in the determination of the limit thickness condition. indeed, these aspects have been previously discussed in the literature [36-39], particularly in the context of accounting for friction effects in masonry constructions [40-45]. specifically, gilbert et al. [25] have mentioned that "casapulla and lauro (2000) have identified a special class of non-associative friction problems for which provably unique solutions exist. the class comprises arches with symmetrical loading and geometry.", as handled in the present case. these outcomes have also been confirmed by the recent analysis by aita et al. [23]. despite, further, general analytical and numerical formulations shall investigate the subject, in inspecting if friction reduction effect may induce a resulting non-uniqueness in the prediction of the least-thickness condition, as instead still recorded in the present setting devoted to the analysis of symmetric masonry arches under self-weight, for more unspecific configurations and loading conditions. collapse mode friction coefficient  collapse characteristics , , h ( =  / 2) purely rotational (r)  > rm 1 2 0, / 2 90 ( , ) 0.951141 54.4963 ( , ( )) ( , ) 0.107426 0.621772 r r r r r r e r r rad h h rad h h a h h h             = = =   = = =  + =   = =   = rotational/ mixed shift (rm)  = rm = 0.395832 (rm = 21.5952°) 0 0.951141 54.4963 , / 2 90 r rm r rm r s rm rm rad rad      = = =  = = =  0.107426,rm = 0.621772rmh = mixed slidingrotational (m) ms <  < rm 1 0, / 2 90 ( , ) ( ) ( , ) ( , ) ( ) ( ) / 2 r s m m r m e m m rad h h h h h h h h                     = = =   = = + =   = =   = = mixed/ sliding shift (ms)  = ms = 0.309215 (ms = 17.1824°) 0, / 2 90 1.05616 60.5134 , 0.499796 28.6362 r s ms ms r ms s ms rad rad rad      = = =  = =  = =  0.200637,ms = 0.485714msh = purely sliding (s)  = ms 0.499796 28.6362 / 2 90 s s s s rad rad    = =  = =  , 0.200637,s ms  = 0.485714s msh h= = –  < ms no equilibrium solution g. cocchetti et alii, frattura ed integrità strutturale, 51 (2020) 356-375; doi: 10.3221/igf-esis.51.26 373 further remarks on the present study, its implications, practical value and perspectives may be outlined as follows: • issue of dilatancy at the blocks’ interfaces. matter of dilatancy may be pertinent, like as due to interlocking arising among masonry joints, for the mutual surfaces of the chunks being not perfectly planar, with a relative roughness that shall locally be present there. then, a little relative normal displacement among the joints may accompany a tangential relative displacement, when sliding is activated, the resulting friction angle being the arctangent of the relevant normal to sliding displacement ratio. this shall indeed introduce a further characteristic parameter of the joint, within the analysis, beyond the already considered main one, namely the friction coefficient. this further effect may likely be secondary in the analysis, explicitly focusing on the role of friction, in the considered context of masonry arches; a main novelty, in analytical terms. possibly, the dilatancy effect may induce some variations in the threshold friction coefficient values that are derived within the present paper, for the potential sliding onset and the transitions among the various possible collapse modes, and for the recorded collapse characteristics. moreover, it looks hard to state, a priori, if such a dilatancy effect may lay on the safe or the unsafe approximation side, for the critical arch behaviour. as a conjecture, the dilatancy process may lead to further resources of the arch to withstand under self-weight, if confinement within the arch shall hold true (like with firm supports). in that sense, the present analysis neglecting dilatancy may turn out to lay on the conservative side, meaning that the predicted least-thickness condition may anyway be safe (even a lower arch thickness may suffice for arch equilibrium, due to dilatancy). certainly, dilatancy shall anyhow lead to another, different source of non-normality, and possible related effects. thus, the perspective handling of the issue of dilatancy may certainly be appropriate, for a complete understanding of arch collapse but shall require a dedicated and comprehensive treatment, and may then constitute the subject of future research work. • issue of real friction values, in practical contexts, as pertinent to a reducing friction, apt to prevent/induce sliding. the present investigation is mainly and firstly endowed of a theoretical value. the results look useful in terms of the overall behaviour of the considered mechanical system; a full recognition of all its possible features. however, there may be reasons that may induce or be associated to a reducing friction effect among the blocks, as possibly connected to external conditions, like loosening of the joints, fading or spreading supports, percolation of rain, humidity, rubbish and mud within the joints, loosening of the mortar, if present, in cemented joints, and possible damage within that, existing interfaces between different composing materials (concrete, soil, earth, stone, masonry, etc.) among the arch’s blocks, bearing interface on underlying pier, wall or ground with underfilled loosened material, like earth, natural sediments, etc. these effects may lead the friction coefficient values to reduce and possibly approach the critical ranges where sliding may be triggered, so that a verification about that shall anyway be attempted. moreover, arches of different opening angles or of varied morphological shapes, symmetric or unsymmetric, do display a variation of the critical friction coefficient value possibly leading to the onset of sliding. indeed, the discussion in section 2.3, still concerning symmetric arches but with variable opening angles, already shows that the transition value of friction apt to prevent any sliding within the arch raises up to a value of friction coefficient around 1.4 (friction angle about 55°), for the limit case where the range of mixed mode vanishes (limit horseshoe arch). for this case, and other overcomplete arch cases, the critical value of friction leading to possible sliding onset may be nearing the range for practical applications, where, with the further possible intervention of some of the above effects, may really come to induce arch collapse with sliding. thus, the issue of quantifying the amount of friction that shall be necessary to avoid sliding seems anyway much important, also in practical terms, for investigating the whole equilibrium ranges of the arch. • arch discretisation. the analysis actually refers to that of a continuous arch, i.e. in strict heyman sense, where rupture joint may appear at critical locations, precisely where they shall be. this leads to the definition of the true least-thickness critical condition that nature by the gravitational field will find to let the arch to first collapse once thickness is gradually reduced. if fracture joints shall instead occur only at pre-defined locations, due to specific block arrangements, this should lead to lower critical thicknesses, for the arch to withstand. this aspect was widely discussed in previous works [6,8], in the context of infinite friction, and shall apply as well in the present, finite friction one. thus, specific block patterns, within the arch, may lead to some variations, of the general characteristics of a continuous arch, though the latter truly mark the real underlying least-thickness condition, at variable friction. acknowledgements his work has been carried-out at the university of bergamo, school of engineering (dalmine). the financial support by ministerial (miur) funding “fondi di ricerca d’ateneo ex 60%” at the university of bergamo is gratefully acknowledged. t g. cocchetti et alii, frattura ed integrità strutturale, 51 (2020) 356-375; doi: 10.3221/igf-esis.51.26 374 references [1] heyman, j. (1969). the safety of masonry arches, international journal of mechanical sciences, 11(4), pp. 363−385, doi: 10.1016/0020-7403(69)90070-8. [2] heyman, j. (1977). equilibrium of shell structures, clarendon press, oxford. [3] heyman, j. (1982). the masonry arch, ellis horwood ltd., chichester. [4] heyman, j. (2009). la coupe des pierres, in: proceedings of the 3rd international congress on construction history, brandenburg university of technology, cottbus, germany, 20–24 may 2009, 2, pp. 807–812. [5] rizzi, e., cocchetti, g., colasante, g., rusconi, f. (2010). analytical and numerical analysis on the collapse mode of circular masonry arches, in: proceedings of 7th international conference on structural analysis of historical constructions (sahc-2010), eds. xianglin gu and xiaobin song, shanghai, china, october 6-8, 2010, trans tech publications, switzerland, periodical of advanced materials research 133-134, pp. 467–472, doi: 10.4028/www.scientific.net/amr.133-134.467. [6] cocchetti, g., colasante, g., rizzi, e. (2011). on the analysis of minimum thickness in circular masonry arches. part i: state of the art and heyman's solution. part ii: present ccr solution. part iii: milankovitch-type solution, applied mechanics reviews, asme, september 01, 2011, 64(5), paper 050802 (oct. 01, 2012), pp. 1–27. doi: 10.1115/1.4007417. [7] rizzi, e., colasante, g., frigerio, a., cocchetti, g. (2012). on the mixed collapse mechanism of semi-circular masonry arches, in: proceedings of 8th international conference on structural analysis of historical constructions (sahc-2012), wroclaw, poland, october 15–17, 2012, ed. jerzy jasienko, dwe, vol. 1, pp. 541–549. [8] rizzi, e., rusconi, f., cocchetti, g. (2014). analytical and numerical dda analysis on the collapse mode of circular masonry arches, engineering structures, 60(february 2014), pp. 241–257, doi: 10.1016/j.engstruct.2013.12.023. [9] cocchetti, g., rizzi, e. (2018). limit analysis of circular masonry arches at reducing friction, in: proceedings of the 10th international masonry conference (10th imc), politecnico di milano, july 9–11, 2018, eds. gabriele milani, alberto taliercio and stephen garrity, the international masonry society (ims), pp. 486–503. [10] cocchetti, g., rizzi, e. (2019). non-linear programming numerical formulation to acquire limit self-standing conditions of circular masonry arches accounting for limited friction, international journal of masonry research and innovation, accepted 29 october 2019, in press (corrected proofs). [11] ochsendorf, j. (2002). collapse of masonry structures, doctoral dissertation, university of cambridge, uk. [12] ochsendorf, j. (2006). the masonry arch on spreading supports, the structural engineer, 84(2), pp. 29–36. [13] milankovitch, m. (1907). theorie der druckkurven, zeitschrift für mathematik und physik, 55, pp. 1–27. [14] foce, f. (2007). milankovitch’s theorie der druckkurven: good mechanics for masonry architecture, nexus network journal, 9(2), pp. 185−210. [15] alexakis, h., makris, n. (2013). minimum thickness of elliptical masonry arches, acta mechanica, 224(12), pp. 2977−2991. [16] makris, n., alexakis, h. (2013). the effect of stereotomy on the shape of the thrust-line and the minimum thickness of semicircular masonry arches, archive of applied mechanics, 83(10), pp. 1511−1533. [17] alexakis, h., makris, n. (2015). limit equilibrium analysis of masonry arches, archive of applied mechanics, 85(9−10), pp. 1363−1381. [18] bagi, k. (2014). when heyman’s safe theorem of rigid block systems fails: non−heymanian collapse modes of masonry structures, international journal of solids and structures, 51(14), pp. 2696−2705. [19] lengyel, g. (2018). minimum thickness of the gothic arch, archive of applied mechanics, 88(5), pp. 769–788. doi: 10.1007/s00419-018-1341-6. [20] cavalagli, n., gusella, v., severini, l. (2016). lateral loads carrying capacity and minimum thickness of circular and pointed masonry arches, international journal of mechanical sciences, 115−116(september 2016), pp. 645−656. [21] nikolić, d. (2017). thrust line analysis and the minimum thickness of pointed masonry arches, acta mechanica, 228(6), pp. 2219−2236. doi: 10.1007/s00707-017-1823-6. [22] gáspár, o., sipos, a.a., sajtos, i. (2018). effect of stereotomy on the lower bound value of minimum thickness of semi−circular masonry arches, international journal of architectural heritage, 12(6), pp. 899–921. doi: 10.1080/15583058.2017.1422572. [23] aita, d., barsotti, r., bennati, s. (2019). looking at the collapse modes of circular and pointed masonry arches through the lens of durand−claye’s stability area method, archive of applied mechanics, pp. 1−18. doi: 10.1007/s00419-019-01526-z. g. cocchetti et alii, frattura ed integrità strutturale, 51 (2020) 356-375; doi: 10.3221/igf-esis.51.26 375 [24] angelillo, m. (2019). the model of heyman and the statical and kinematical problems for masonry structures, international journal of masonry research and innovation, 4(1−2), pp. 14−31. doi: 10.1504/ijmri.2019.096820. [25] gilbert, m., casapulla, c., ahmed, h.m. (2006). limit analysis of masonry block structures with non-associative frictional joints using linear programming, computers and structures, 84(13-14): pp. 873–887. [26] sinopoli, a., corradi, m., foce, f. (1997). modern formulation for preelastic theories on masonry arches, journal of engineering mechanics, asce, 123(3): pp. 204–213. [27] foce, f., aita, d. (2003). the masonry arch between «limit» and «elastic» analysis. a critical re-examination of durand-claye’s method, in: proc. of the 1st int. congress on construction history, madrid, 20-24 january 2003, s. huerta (ed.), madrid: instituto juan de herrera, i, pp. 895–908. [28] sinopoli, a., aita, d., foce, f. (2007). further remarks on the collapse mode of masonry arches with coulomb friction, in: proc. of 5th int. conference on arch bridges (arch’07), funchal, madeira, portugal, pp. 649–657. [29] baggio, c., trovalusci, p. (2000). collapse behaviour of three-dimensional brick-block systems using non-linear programming, structural engineering and mechanics, 10(2), pp. 181-195. [30] ponterosso, p., fishwick, r.j., fox, d.st.j., liu, x.l., begg, d.w. (2000). masonry arch collapse loads and mechanisms by heuristically seeded genetic algorithm, computer methods in applied mechanics and engineering, 190(8-10), pp. 1233–1243. [31] harvey, b., maunder, e. (2001). thrust line analysis of complex masonry structures using spreadsheets, in: “historical constructions 2001 – possibilities of numerical and experimental techniques”, proc. of the 3rd int. seminar, edited by lourenço p.b. and roca p., guimarães, portugal, pp. 521–528. [32] vermeltfoort, a.t. (2001). analysis and experiments of masonry arches, in: “historical constructions 2001 – possibilities of numerical and experimental techniques”, proc. of the 3rd int. seminar, pp. 489–498. [33] hughes, t.g., hee, s.c., soms, e. (2002). mechanism analysis of single span masonry arch bridges using a spreadsheet, in: proceedings of the institution of civil engineers−structures and buildings, 152(4), pp. 341–350. [34] de rosa, e., galizia, f. (2003). evaluation of safety of pointed masonry arches through the static theorem of limit analysis, in: proc. of 5th int. conference on arch bridges, arch’07, pp. 659–668. [35] portioli, f., casapulla, c., gilbert, m., cascini, l. (2014). limit analysis of 3d masonry block structures with non−associative frictional joints using cone programming, computers and structures, 143, pp. 108−121. [36] casapulla, c., lauro, f. (2000). a simple computation tool for the limit-state analysis of masonry arches, in: proc. of 5th int. congress on restoration of architectural heritage, pp. 2056-2064. [37] casapulla, c., d’ayala, d. (2001). lower bound approach to the limit analysis of 3d vaulted block masonry structures, in: proc. of the 5th int. symposium on computer methods in structural masonry, strumas v, pp. 28– 36. [38] d’ayala, d., casapulla, c. (2001). limit state analysis of hemisferical domes with finite friction, in: “historical constructions 2001 – possibilities of numerical and experimental techniques”, proc. of the 3rd int. seminar, pp. 617–626. [39] d’ayala, d., tomasoni, e. (2011). three-dimensional analysis of masonry vaults using limit state analysis with finite friction, int. j. of architectural heritage, 5(2), pp. 140–171. [40] boothby, t.e., brown, c.b. (1992). stability of masonry piers and arches, j. of engineering mechanics, asce, 118(2), pp. 367–383. [41] boothby, t.e. (1994). stability of masonry piers and arches including sliding, j. of engineering mechanics, asce, 120(2), pp. 304–319. [42] boothby, t.e. (1995). collapse modes of masonry arch bridges, masonry international, 9(2), pp. 62–69. [43] smars, p. (2000). etudes sur la stabilité des arcs et voûtes: confrontation des méthodes de l’analyse limite aux voûtes gothique en brabant, doctoral thesis, katholieke universiteit leuven, belgium, p. 229. [44] smars, p. (2008). influence of friction and tensile resistance on the stability of masonry arches, in: proc. of the 6th int. conference on structural analysis of historic construction, pp. 1199–1206. [45] audenaert, a., peremans, h., reniers, g. (2007). an analytical model to determine the ultimate load on masonry arch bridges, j. of engineering mathematics, 59(3), pp. 323–336. microsoft word numero_51_art_9_2656 a. chikh, frattura ed integrità strutturale, 51 (2020) 115-126; doi: 10.3221/igf-esis.51.09 115 investigations in static response and free vibration of a functionally graded beam resting on elastic foundations abdelbaki chikh department of civil engineering, faculty of applied sciences, ibn khaldoun university, tiaret, algeria cheikhabdelbakki@yahoo.fr abstract. in this article, an analytical study was done to predict the behavior of the beam vis-à-vis bending, buckling, and dynamic responses of isotropic homogeneous beams based on an elastic foundation. the material properties of the fg-beams vary across the thickness using the power law. in this work, the sinusoidal shear deformation beams theory is used to investigate the static and dynamic behavior of fg beams. the present theory fulfills the condition of nullity of edge stresses and does not require the use of a shear correction factor. hamilton's principle is used to deduce equations of motion, and analytical solutions for simply supported beams were obtained using the navier resolution method. nondimensional displacements, eigenfrequencies and critical-buckling loads of isotropic homogeneous beams were obtained for various values of the foundation parameters. the numerical results obtained by the present technique have been compared with the results of literature and are in excellent agreement with them. it can be concluded that the current hsdbt is simple and accurate in solving the bending, eigenfrequency and critical-buckling load problems for fgm beams. keywords. undetermined integral terms; free vibration; isotropichomogeneous beams; navier’s solution; elasticity. citation: a. chikh, investigations in static response and free vibration of a functionally graded beam resting on elastic foundations, frattura ed integrità strutturale, 51 (2020) 115-126. received: 08.10.2019 accepted: 04.11.2019 published: 01.01.2020 copyright: © 2020 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. introduction he functionally graded materials (fgm) may be defined as materials having a progressive variation of material properties. this material is produced by mixing two or more materials in a certain percentage of volume (ceramic and metal). the mixing ratio of the constituents varies regularly and the material properties change without any interruption throughout the thickness. there are a large number of works have been done on the dynamics, flexion and buckling behavior of fgm structures. the conventional composite structures suffer from a discontinuity in the properties of materials at the interface of layers and constituents. therefore, constraint fields in intersection areas create interface problems and thermal stress concentrations in high-temperature environments. many authors have studied the dynamic behavior of fgm beams, mostly, t http://www.gruppofrattura.it/va/51/2656.mp4 a. chikh, frattura ed integrità strutturale, 51 (2020) 115-126; doi: 10.3221/igf-esis.51.09 116 by means of both the classical beam theory (cbt), fsdbt and hsdbt wang et al. [1] given a solution to solve the free vibration, buckling and bending problems of the timoshenko and euler-bernoulli beams based on different models of elastic foundations. there are many areas of application for composite materials (chikh et al. [2]; akbaş et al. [3]; chikh et al. [4]; fahsi et al. [5]) same the aircraft and aerospace industry. omidi et al [6] studied the dynamic stability of simple supported fg beams reposing on a linear elastic foundation; with piezoelectric-layers under a periodic axial compression load. zhong et al. [7] provided an analytical solution for console beams subjected to various types of mechanical loads. thai et al. [8] studied the free vibration and bending of fg beams by the use of different higher-order beams theories. zhu, h. [9] established threedimensional finite element model using finite element software to simulate and compare the stress performance of the strengthening beams with different numbers of cfrp plates. bouchikhi, a. s et al. [10] investigated the 2d simulation used to calculate the j-integral of the main crack behavior emanating from a semicircular notch and double semicircular notch and its interaction with another crack which may occur in various positions in (tib/ti) fgm plate under mode i. yassine khalfi et al. [11] developed a refined and simple shear deformation theory for mechanical buckling of composite plate resting on two-parameter pasternak’s foundations. meftah kamel [12] presented a finite element method for analyzing the elasto-plastic plate bending problems. saidi hayat [13] presented a new shear deformation theory for free vibration analysis of simply supported rectangular functionally graded plate embedded in an elastic medium. in this paper, a higher-order shear deformation beams theory for bending; buckling and free vibration of fg beams are developed. the present theory differs from other higher-order theories because, in present theory the displacement field which includes undetermined integral terms, which is not considered by the other researchers. the results of the present model are compared with the known data in the literature. variational formulation and cinematics onsider an fg beam with length l, width b, and thickness h made of al/al2o3 as represents in fig. 1. the lower part of the fg-beam was totally ceramic and the upper surface was completely made of metal. the beam 0 x l; b / 2 y b / 2; h / 2 z h / 2        in the cartesian coordinate systems. assumed to be positive in the proposed direction, and the beam is deformed in the x-z plane solely. the x-axis coinciding with the beam inert axis. the beam is supported by winkler–pasternak foundations. figure 1: fgm beam supported by winkler–pasternak type elastic foundation. kinematics and constitutive equations n the fundamental of the assumptions expressed in the previous section, the displacement field of present theory can be obtained by:  00 1 0 ( , , ) ( , , , ) ( , , ) ( ) , , ( , , , ) ( , , ) w x y t u x y z t u x y t z k f z x y t dx x w x y z t w x y t         (1) where: ( ) ( ) sin , ( ) z f zh f z g z h z         c o a. chikh, frattura ed integrità strutturale, 51 (2020) 115-126; doi: 10.3221/igf-esis.51.09 117 the deformations related to the displacement-field in eq. (1) contains only three unknowns  0 0, ,u w  . the linear strains corresponding with the displacement field in eq. (1) are: 0 1 2 0( ) , ( )x x x x xz xzz f z g z         where        0 00 1 2 01 1 , , ² , , , , ' , , , , , ² x x x xz u x y t w x y t k a x y t k x y t dx x x                 (2) the integral appearing in the above expressions shall be resolved by a navier type solution and can be represented as: 'dx a x      (3) where the coefficient '" "a is depending on the type of solution chosen, in this case via navier. therefore, '" "a and 1k is expressed as follows: ' 2 12 1 ,a k      (4) according to the polynomial material law, the effective young’s modulus e(z)   ( ) 0.5 pm c me z e e e z h    (5) the constitutive relations of an fg plate can be written as: 11 55 0 0 x x xz xz c c                    (6) where ijc are, the three-dimensional elastic constants given by:    11 552 ( ) ( ) , 2 11 e z e z c c     (7) the equilibrium equations can be obtained using the hamilton principle, in the present case yields:   2 1 0 t t u v k dt     (8)   /2 /2 /2 0 /2 , ( ) , ( ) h x x xz xz h e l h h u d d z v q f w d k z u u w w dzdydx                                   (9) a. chikh, frattura ed integrità strutturale, 51 (2020) 115-126; doi: 10.3221/igf-esis.51.09 118 where  is the top surface, and ef is the density of reaction force of foundation. for the pasternak foundation model: 2 2 ( , ) ( , )e w p w x y f k w x y k x     (10) the equilibrium equations can be acquired using the hamilton principle. 2 3 3 '20 0 0 1 2 3 12 2 2 2 2 2 3 4 4 0 0 0 0 0 0 1 2 4 52 2 2 2 2 2 2 2 2 2 4 ' ' 2 '2 '0 1 1 3 1 5 12 2 2 : 0 : ( , ) 0 : x b x e s xzx n u w u i i i k a x t t x t x m w w u w w q x t n f i i i i x x t t x t x t x qm u k a k a i k a i k a xx t x t                                                       4 2 '4 6 12 2 2 0i k a x t x       (11) where  xn denote the resulting force in-plane,    ,b sx xm m denote the total moment resultants and  xzq are transverse shear stress resultants and they are defined as /2 /2 /2 /2 /2 /2 /2 /2 , , ( ) , ( ) h h b x x x x h h h h s x x xz xz h h n dz m zdz m f z dz q g z dz                 (12) following the navier solution process, we assume the following solution form for  0 0, ,u w  and that check the boundary conditions, 0 0 1 cos( ) sin( ) e sin( ) i t m u u x w w x x                              (13) where , ,u w and  are arbitrary parameters to be determined,  is the natural frequency, and m l    . the transverse load ( )q x is also expanded in fourier series as:   1 ( ) sinm m q x q x     (14) where 0 2 ( )sin( ) l mq q x x dx l   (15) in the case where a sinusoidally distributed load, we have 1 01 ,m q q  (16) in the case where uniform distributed the load, we have a. chikh, frattura ed integrità strutturale, 51 (2020) 115-126; doi: 10.3221/igf-esis.51.09 119  0 4 1 , , 1, 3, 5...m q m q m m    (17) in the case where static problems, we have the following equation:     k f  (18) where    , , tu w   and  k is the symmetric matrix given by   11 12 13 12 22 23 13 23 33 s s s k s s s s s s          (19) in the case of free vibration problem problems, the analytical solutions can be obtained by:      2 0k m   (20) where  m is the symmetric matrix given by   11 12 13 12 22 23 13 23 33 m m m m m m m m m m          (21) for buckling problems, can be expressed as     0k n   (22) in which: 2 3 11 11 12 11 13 1 11 4 2 2 22 11 1 0 2 2 3 2 2 2 23 1 11 33 1 55 1 11 11 1 12 2 13 1 3 22 1 4 2 2 4 2 23 5 33 1 6 , , ' , ' , ' ' , , , ' , , ' , p w s s a s b s k a d s e k k n k s k a f s k a a k a g m i m i m k a i m i i m i m k a i                                    (23) where     2 2 2 11 11 11 11 11 11 11 2 2 2 55 55 2 , , , , , 1, , ( ), , ( ), ( ) , ( ) h h h s h a b d e f g c z f z z zf z f z dz a c g z dz       (24)     2 2 2 1 2 3 4 5 6 2 , , , , , ( ) 1, , ( ), , ( ), ( ) h h i i i i i i z z f z z zf z f z dz    (25) a. chikh, frattura ed integrità strutturale, 51 (2020) 115-126; doi: 10.3221/igf-esis.51.09 120 results and discussion n this study, bending; buckling and free vibration investigation on ss fg beam by the present theory is suggested for investigation. the fg beams are made of aluminum (al; em = 70 gpa, ρm = 2702 kg/m3, νm = 0.3) and alumina (al2o3; ec = 380 gpa, ρc = 3960 kg/m3, νc = 0.3) and their properties vary in the direction of the thickness of the beam according to power-law. the lower part of the fg-beam is rich in aluminum, while the upper part of the fg-beam is alumina rich. for convenience, the following dimensionless parameters are used: 24 2 4 2 04 4 ( / 2)100 , ( / 2) , , , pc c w w p k la l w l e i k l n l w l k k n ei ei ei eiql         (26) the buckling answer of an fg beam under axial force  0n has been studied. a dimensionless; critical-buckling load is shown in tab. 2. the critical-buckling load was obtained for various values regarding the foundation parameters wk and pk . the results were contrasted with those delivered by rao et al. [16]. tab. 2 reveals that this study's results agreed with those available in the literature. tab. 3 present the comparisons of the dimensionless natural frequency obtained by the present beam theory with other beams theories results of chen et al. [14] and ying et al. [15] for three divers values of the thickness-to-length ratio, and for divers values of foundation parameters wk and pk . as can be seen, the new results are in excellent concordat with previous ones. foundation parameters l/h = 120 l/h = 15 l/h = 5 wk pk chen et al. [14] ying et al. [15] present chen et al. [14] ying et al. [15] present chen et al. [14] ying et al. [15] present 0 0 1.30229 1.30229 1.30416 1.31528 1.31527 1.30416 1.42026 1.42024 1.30416 10 0.64483 0.64483 0.64527 0.64835 0.64830 0.64527 0.67820 0.67451 0.64527 25 0.36611 0.36611 0.36624 0.36742 0.36735 0.36624 0.38170 0.37667 0.36624 10 0 1.18057 1.18057 1.18210 1.19140 1.19134 1.18210 1.28260 1.27731 1.18210 10 0.61333 0.61333 0.61372 0.61656 0.61649 0.61372 0.64639 0.64025 0.61372 25 0.35567 0.35567 0.35579 0.35692 0.35684 0.35579 0.37206 0.36568 0.35579 102 0 0.64007 0.64007 0.64051 0.64377 0.64343 0.64051 0.69610 0.66848 0.64051 10 0.42558 0.42558 0.42576 0.42741 0.42716 0.42576 0.45927 0.43881 0.42576 25 0.28285 0.28285 0.28291 0.28380 0.28360 0.28291 0.30516 0.28944 0.28291 table 1 comparisons of the mid-span deflection 4 ( / 2)100 ( / 2) c w l e i w l ql  of an isotropic-homogeneous beam on elastic foundations due to a uniform pressure. i a. chikh, frattura ed integrità strutturale, 51 (2020) 115-126; doi: 10.3221/igf-esis.51.09 121 wk theories 2 pk  0 0.5 1 2 0 rao et al. [16] 9.8696 14.8040 19.7390 34.5440 present 9.8538 14.7886 19.7234 29.5930 1 rao et al. [16] 9.9709 14.9070 19.8410 34.6450 present 9.9551 14.8899 19.8247 29.6943 102 rao et al. [16] 20.0020 24.9370 29.8710 44.6760 present 19.9859 24.9207 29.8555 39.7251 104 rao et al. [16] 1023.1000 1028.0000 1032.9000 1047.7000 present 1023.0656 1028.0004 1032.9352 1042.8048 table 2 comparisons of buckling load parameter n of an isotropic-homogeneous beam on elastic foundations l/h = 20 foundation parameters l/h = 120 l/h = 15 l/h = 5 wk 2 pk  chen et al. [14] ying et al. [15] present chen et al. [14] ying et al. [15] present chen et al. [14] ying et al. [15] present 0 0 3.14143 3.14145 3.14028 3.13025 3.13227 3.13730 3.04799 3.06373 3.11161 1 3.73588 3.73587 3.73520 3.72657 3.72775 3.73165 3.65802 3.66645 3.70107 2.5 4.29687 4.29689 4.29646 4.28809 4.28886 4.29237 4.21834 4.22319 4.25717 102 0 3.74823 3.74823 3.74757 3.73895 3.74012 3.74400 3.67050 3.67882 3.71333 1 4.14356 4.14357 4.14309 4.13472 4.13558 4.13915 4.06636 4.07200 4.10521 2.5 4.58227 4.58227 4.58192 4.57347 4.57410 4.57757 4.49914 4.50278 4.53999 104 0 10.02403 10.02403 10.02407 9.99582 9.99583 10.01451 7.34081 7.34081 7.84931 1 10.04813 10.04812 10.04816 10.01970 10.01971 10.03857 7.34095 7.34095 7.84931 2.5 10.08394 10.08393 10.08398 10.05519 10.05520 10.07435 7.34116 7.34116 7.84931 table 3. comparisons of the fundamental frequency parameter 4 2 4 c al ei     of an isotropic-homogeneous beam on to elastic foundations using diverse beam theories a. chikh, frattura ed integrità strutturale, 51 (2020) 115-126; doi: 10.3221/igf-esis.51.09 122 0,0 0,5 1,0 1,5 2,0 2,5 3,0 0,2 0,3 0,4 0,5 0,6 0,7 0,8 0,9 1,0 1,1 1,2 1,3 1,4 w kp/ 2 kw=0 kw=10 kw=20 kw=50 kw=100 figure 2: variation of the non-dimensional transverse displacement 4 ( / 2)100 ( / 2) c w l e i w l ql  of an isotropic-homogeneous beam with pasternak parameter pk and winkler parameter wk . 0,0 0,5 1,0 1,5 2,0 2,5 3,0 5 10 15 20 25 30 35 40 45 50 n kp/ 2 kw=0 kw=10 kw=20 kw=50 kw=100 figure 3: variation of the non-dimensional buckling load parameter n of an isotropic-homogeneous beam with pasternak parameter pk and winkler parameter wk . a. chikh, frattura ed integrità strutturale, 51 (2020) 115-126; doi: 10.3221/igf-esis.51.09 123 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.00 3.25 3.50 3.75 4.00 4.25 4.50 4.75  kp/ 2 kw=0 kw=10 kw=20 kw=50 kw=100 figure 4: variation of the nondimensional fundamental frequency 4 2 4 c al ei     of isotropic homogeneous beam with pasternak parameter pk and winkler parameter wk . 0,0 0,5 1,0 0 6 12 18 x/l mode (m=1) kw=0 kw=10 2 kw=10 3 figure 5: mode shape of w at the base surface of the beam with various aspect ratios for the first mode frequency  21 , / 20 , / 2.5pm l h k    a. chikh, frattura ed integrità strutturale, 51 (2020) 115-126; doi: 10.3221/igf-esis.51.09 124 0,0 0,5 1,0 -2 0 2 x/l mode (m=2) kw=0 kw=10 2 kw=10 3 figure 6: mode shape of w at the base surface of the beam with various aspect ratios for the second mode frequency  22 , / 20 , / 2.5pm l h k    0,0 0,5 1,0 -0,5 0,0 0,5 x/l mode (m=3) kw=0 kw=10 2 kw=10 3 figure 7: mode shape of w at the base surface of the beam with various aspect ratios for the third mode frequency  23 , / 20 , / 2.5  pm l h k . a. chikh, frattura ed integrità strutturale, 51 (2020) 115-126; doi: 10.3221/igf-esis.51.09 125 figure 8: effect of shear deformation, pasternak parameter pk , and winkler parameter wk on the deflection of isotropic homogeneous beams under uniform load. in fig. 2, the non-dimensional transverse displacement is plotted against the pasternak parameter and several values of the winkler parameter. it can be drawn from this curve that the higher the pasternak’s foundation parameter, the lower the transverse displacement and the same thing for the winkler parameter. fig. 3 presents the variation of the dimensionless critical-buckling load as a function of the pasternak parameter and for various values of the winkler parameter. it can be drawn from this curve that the dimensionless critical-buckling load increases linearly with the pasternak parameter. fig. 4 presents the variation of the non-dimensional fundamental frequency in function of the pasternak parameter and for various values of the winkler parameter. it can be drawn from this curve that the higher the pasternak’s foundation parameter is, the higher the vibration frequency. figs. 5, 6 and 7 are respectively the first, second and third-order of mode shapes of the displacement w at the lower surface of the isotropic homogeneous beam on an elastic foundation. the impact of shear deformation on the deflection of fg beams is shown in fig. 8 for various values of pasternak parameter and tow values of winker parameter  20 , 10w wk k  . conclusion n this paper; an efficient theory is presented for bending; free vibration and analysis of the dimensionless critical buckling load for functionally graded simply-supported beams reposed on two elastic parameters. this theory incorporates both shear deformation. the governing equations and the boundary conditions are calculated using hamilton’s principle. the closed-form solutions are obtained by using navier solution. numerical comparisons are made to illustrate the mastery of the current theory. the present theory satisfies the stress-free boundary conditions on the conditions on the upper and lower surfaces of the beam, and do not need a shear correction factor. i a. chikh, frattura ed integrità strutturale, 51 (2020) 115-126; doi: 10.3221/igf-esis.51.09 126 detailed mathematical formulations are given and numerical results are established, while the emphasis is set on examining the effect of the several parameters. the results of the actual theory are almost identical to each other and conform well with the existing solutions. references [1] wang, c. m., lam, k. y., and he, x. q. (1998). exact solutions for timoshenko beams on elastic foundations using green’s functions∗. mechanics of structures and machines, 26(1), 101–113. doi: 10.1080/08905459808945422. [2] chikh, a., bakora, a., heireche, h., houari, m. s. a., tounsi, a., and bedia, e. a. a. (2016). thermo-mechanical postbuckling of symmetric s-fgm plates resting on pasternak elastic foundations using hyperbolic shear deformation theory. structural engineering and mechanics, 57(4), 617–639. doi:10.12989/sem.2016.57.4.617. [3] akbaş, ş. d. (2015). free vibration and bending of functionally graded beams resting on elastic foundation. research on engineering structures and materials, 1(1), 25–37. doi:10.17515/resm2015.03st0107 . [4] chikh, a., tounsi, a., hebali, h., and mahmoud, s. r. (2017). thermal buckling analysis of cross-ply laminated plates using a simplified hsdt. smart structures and systems, 19(3), 289–297. doi: 10.12989/sss.2017.19.3.289. [5] fahsi, a., tounsi, a., hebali, h., chikh, a., bedia, e. a. a., and mahmoud, s. r. (2017). a four variable refined nthorder shear deformation theory for mechanical and thermal buckling analysis of functionally graded plates. geomechanics and engineering, 13(3), 385–410. doi: 10.12989/gae.2017.13.3.385. [6] omidi, n., khorramabadi, m. k., and niknejad, a. (2009). dynamic stability of functionally graded beams with piezoelectric layers located on a continuous elastic foundation. journal of solid mechanics, 1(2), 130–136. http://jsm.iau-arak.ac.ir/article_514296.html. [7] zhong, z., and yu, t. (2007). analytical solution of a cantilever functionally graded beam. composites science and technology, 67(3–4), 481–488. doi: 10.1016/j.compscitech.2006.08.023. [8] thai, h.-t., and vo, t. p. (2012). bending and free vibration of functionally graded beams using various higher-order shear deformation beam theories. international journal of mechanical sciences, 62(1), 57–66. doi: 10.1016/j.ijmecsci.2012.05.014. [9] hua zhu. (2018). stress performance of embedded carbon fiber reinforced plastics plate consolidated reinforced concrete structure. frattura ed integrità strutturale, 12(46), 361-370. doi: 10.3221/igf-esis.46.33. [10] bouchikhi, a. s., lousdad, a., yassine, k., bouida, n. e., gouasmi, s., and megueni, a. (2019). finite element analysis of interactions between two cracks in fgm notched plate under mechanical loading. frattura ed integrità strutturale, 13(48), 174-192. doi: 10.3221/igf-esis.48.20. [11] khalfi, y., bouchikhi, a. s., and bellebna, y. (2019). mechanical stability investigation of advanced composite plates resting on elastic foundations using a new four-unknown refined theory. frattura e integrita strutturale, (48), 208-221. doi: 10.3221/igf-esis.48.22. [12] meftah, k., and sedira, l. (2019). a nonlinear elasto-plastic analysis of reissner-mindlin plates by finite element method. frattura ed integrità strutturale, 13(50), 276-285. doi: 10.3221/igf-esis.50.23. [13] saidi, h., and sahla, m. (2019). vibration analysis of functionally graded plates with porosity composed of a mixture of aluminum (al) and alumina (al2o3) embedded in an elastic medium. frattura ed integrità strutturale, 13(50), 286-299. doi: 10.3221/igf-esis.50.24. [14] chen, w. q., lü, c. f., and bian, z. g. (2004). a mixed method for bending and free vibration of beams resting on a pasternak elastic foundation. applied mathematical modelling, 28(10), 877–890. doi: 10.1016/j.apm.2004.04.001. [15] ying, j., lü, c. f., and chen, w. q. (2008). two-dimensional elasticity solutions for functionally graded beams resting on elastic foundations. composite structures, 84(3), 209–219. doi: 10.1016/j.compstruct.2007.07.004 [16] rao, g. v., and raju, k. k. (2002). elegant and accurate closed form solutions to predict vibration and buckling behaviour of slender beams on pasternak foundation. indian journal of engineering & materials sciences, 9, 98–102. http://nopr.niscair.res.in/handle/123456789/19729. << /ascii85encodepages false /allowtransparency false /autopositionepsfiles true /autorotatepages /none /binding /left /calgrayprofile (dot gain 20%) /calrgbprofile (srgb iec61966-2.1) /calcmykprofile (u.s. web coated \050swop\051 v2) /srgbprofile (srgb iec61966-2.1) /cannotembedfontpolicy /error /compatibilitylevel 1.4 /compressobjects /tags /compresspages true /convertimagestoindexed true /passthroughjpegimages true /createjobticket false /defaultrenderingintent /default /detectblends true /detectcurves 0.0000 /colorconversionstrategy /cmyk /dothumbnails false /embedallfonts true /embedopentype false /parseiccprofilesincomments true /embedjoboptions true /dscreportinglevel 0 /emitdscwarnings false /endpage -1 /imagememory 1048576 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/hrv (za stvaranje adobe pdf dokumenata najpogodnijih za visokokvalitetni ispis prije tiskanja koristite ove postavke. stvoreni pdf dokumenti mogu se otvoriti acrobat i adobe reader 5.0 i kasnijim verzijama.) /hun 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can be opened with acrobat and adobe reader 5.0 and later.) >> /namespace [ (adobe) (common) (1.0) ] /othernamespaces [ << /asreaderspreads false /cropimagestoframes true /errorcontrol /warnandcontinue /flattenerignorespreadoverrides false /includeguidesgrids false /includenonprinting false /includeslug false /namespace [ (adobe) (indesign) (4.0) ] /omitplacedbitmaps false /omitplacedeps false /omitplacedpdf false /simulateoverprint /legacy >> << /addbleedmarks false /addcolorbars false /addcropmarks false /addpageinfo false /addregmarks false /convertcolors /converttocmyk /destinationprofilename () /destinationprofileselector /documentcmyk /downsample16bitimages true /flattenerpreset << /presetselector /mediumresolution >> /formelements false /generatestructure false /includebookmarks false /includehyperlinks false /includeinteractive false /includelayers false /includeprofiles false /multimediahandling /useobjectsettings /namespace [ (adobe) (creativesuite) (2.0) ] /pdfxoutputintentprofileselector /documentcmyk /preserveediting true /untaggedcmykhandling /leaveuntagged /untaggedrgbhandling /usedocumentprofile /usedocumentbleed false >> ] >> setdistillerparams << /hwresolution [2400 2400] /pagesize [612.000 792.000] >> setpagedevice microsoft word numero_35_art_7 a. vshivkov et alii, frattura ed integrità strutturale, 35 (2016) 57-63; doi: 10.3221/igf-esis.35.07 57 focussed on crack paths experimental study of heat dissipation at the crack tip during fatigue crack propagation a. vshivkov, a. iziumova, o. plekhov institute of continuous media mechanics ub ras, 614014 perm, russia vshivkov.a@icmm.ru j. bär university of the federal armed forces, institute for materials science, 85577 neubiberg, germany abstract. this work is devoted to the development of an experimental method for studying the energy balance during cyclic deformation and fracture. the studies were conducted on 304 stainless steel aise and titanium alloy ot4-0 samples. the investigation of the fatigue crack propagation was carried out on flat samples with different geometries and types of stress concentrators. the heat flux sensor was developed based on the seebeck effect. this sensor was used for measuring the heat dissipation power in the examined samples during the fatigue tests. the measurements showed that the rate of fatigue crack growth depends on the heat flux at the crack tip. keywords. heat flow; fatigue crack; dissipated energy. introduction oday, the investigation of material durability is the research trend of vital importance. different types of structures have bottleneck areas, whose destruction can lead to irreversible consequences. material durability is the problem of current concern due to universal use of structures and mechanisms, whose resources are not endless. the issue of timely replacement of these devices is a compromise between the prevention of catastrophic consequences and economic efficiency. any real engineering construction contains stress concentrators, welded joints and other potential sources of defects. the analysis of the kinetics of damage accumulation, the process of crack nucleation and kinetics of the crack development allows specialists to predict the time of structure failure and to perform in proper time a partial replacement or repair of deteriorated units of complex structures. moreover, the repair or replacement of the worn-out parts on a timely basis is more effective than their complete replacement after mechanical damage. it is therefore very important to know the time during which the defects in the ill-behaved areas are reaching critical values. theoretical and experimental study of the processes accompanying the evolution of the material structure during its deformation and fracture is an actual problem of modern experimental mechanics. its solution enables researchers to gain deeper insight into the nature of the fracture processes and to develop new, high-performance techniques for assessing t a. vshivkov et alii, frattura ed integrità strutturale, 35 (2016) 57-63; doi: 10.3221/igf-esis.35.07 58 the service life of both traditional and advanced structural materials. one of the most effective approaches to the development of fracture criterion is the energy approach. the energy balance can be calculated based on the analysis of evolution of the temperature field (for instance, measured by infrared thermography) on the sample surface, at least for flat samples. this calculation is usually associated with the need to differentiate strongly oscillating signals and to determine the parameters responsible for the interaction of the sample with environment. one of the options for improving the reliability and accuracy of the results is the development of an independent method for measuring the power of heat sources. such an idea was originally used for studying the energy dissipation under liquid flow [1] as well as the failure of metals [2]. in our work, this problem was solved by using a contact heat flux sensor, which was developed based on the seebeck effect. the results of analysis of the energy balance in the fracture zone obtained with the new heat flux sensor during the propagation of fatigue cracks in stainless steel aise 304 and titanium alloy ot4-0 lend support to the validity of the proposed method. in this study, the thermodynamic characteristics of the process of fatigue crack propagation, such as the dissipation rate and the rate of energy accumulation at the crack tip was investigated also the possibility of predicting the rate of fatigue crack propagation and the time of fatigue crack transition from the stationary to nonstationary regime were considered. the contact heat flux sensor o analyze the energy balance at the crack tip a contact heat flux sensor was designed and constructed. the proposed sensor is based on the seebeck effect, which is the reverse of the peltier effect [3]. the peltier effect is a thermoelectric phenomenon, in which the passage of electric current through conducting medium leads to the generation or absorption of heat at the point of contact (junction) of two dissimilar conductors. the quantity of heat and its sign depend on the type of materials in contact, the direction and the strength of the electric current: abq п i t   (1) where q is the quantity of dissipated or absorbed heat; i is the electric current; t is the time of current flow; пab is the peltier coefficient, which is related with a coefficient of thermal electromotive force. the effect was discovered by j. peltier in 1834 [3]. this effect is more pronounced in semiconductors, which explains their usage in the peltier elements. a peltier element consists of one or more pairs of small semiconductor parallelepipeds – each pair comprises one n-type and one p-type semiconductor (bismuth telluride, bi2te3, and silicon germanide), which are connected pairwise by means of metal straps. the seebeck effect [3] lies in the fact that thermoelectromotive force occurs in a closed circuit consisting of dissimilar conductors provided that the contact zones are kept at different temperatures. a circuit including only two different conductors is called a thermocouple. the quantity of heat absorbed or dissipated by the element is directly proportional to the current intensity and the time of its passage. fig. 1 presents a schematic diagram of the heat flux sensor. the following notation is used in fig. 1: sample (1), the heat flux sensor (2). a thermal contact between the sample and the sensor is provided due to the introduction of the thermal paste. structurally, the sensor comprises two peltier elements ("measuring" (2) and "cooling" (3)), thermocouples (5), (6) and the radiator (4). the measuring peltier element is connected to a low-resistance resistor of 1.2 � (7). to measure the heat flow through the "measuring" peltier element during the experiment the temperature on its free surface keeps constant. the cooling peltier element caulked with a radiator was connected with the "measuring" peltier element. this cooling system has feedback and is controlled based on two temperature sensors located between "measuring" and cooling peltier elements and far from the studied sample in the zone with constant temperature. the signal from the sensor (voltage at the resistor (7)) is measured by the amplifier and registered in the adc of the microcontroller. the data are transmitted from the microcontroller to the personal computer for further processing. the "cooling" peltier element is controlled via pulse width modulation. these sensors were calibrated using a device with a controlled heat flux. the calibration scheme is shown in fig. 2. a wire resistor with the known resistance is glued on a plastic plate with a size equal to that of test samples. the heat isolating system provides the heat flux from the resistance to the sensor only. the heat flow was calculated using the values of the resistor voltage and the electric current across the resistor. t a. vshivkov et alii, frattura ed integrità strutturale, 35 (2016) 57-63; doi: 10.3221/igf-esis.35.07 59 figure 1: schematic of the device.1 – testing sample; 2 – “measuring” peltier element; 3 – “cooling” peltier element; 4 – radiator; 5, 6 – thermocouple; 7 – resistor. figure 2: sensor calibration scheme (1 – back side of testing machine, 2 – spring, 3 – sensor, 4 resistor 5 plastic sample 6 dc power supply source). the sensor is calibrated directly in the testing machine, in conditions closely approximating the experimental conditions. a calibration curve for each sensor was obtained based on the experimental data (fig. 3). the sensor signal is correlated to the heat flux dissipated by the resistor. the graphs presented in fig. 3 show a linear dependence that agrees well with the theoretical prediction. figure 3: calibration graph of heat flow sensors. a. vshivkov et alii, frattura ed integrità strutturale, 35 (2016) 57-63; doi: 10.3221/igf-esis.35.07 60 experimental setup series of samples made from stainless steel aise 304 and titanium alloy ot4-0 were tested in the developed device. the tests were carried out for samples of different sizes and with different types of stress concentrators. the geometry of the samples is shown in fig. 4. during tests the samples were subjected to cyclic loading of 10 hz with a constant amplitude and stress ratio r = -0.1. the crack length in the course of the experiment was measured by the potential drop method [4]. a) b) c) figure 4: geometry of samples: a, b – steel, c – titanium. contact heat flux sensors were made for each type of the sample. the sizes of sensor are shown in fig. 5. a) b) c) figure 5: sizes of sensors: a) – peltier element 10x10 mm., b) – peltier element 50x50 mm., c) – peltier element 30x30 mm. (1 – plastic, 2 – copper plate, 3 – termocouple, 4 – peltier elements). a a. vshivkov et alii, frattura ed integrità strutturale, 35 (2016) 57-63; doi: 10.3221/igf-esis.35.07 61 the study of the thermoelastic effect he sensitivity of the sensors was illustrated by the study of thermoelastic effects in metals under investigation. the amplitude of applied stress did not exceed 40% of the limit of proportionality, which provided the absence of sample heating caused by plastic deformation. in the goal of the experiments was the investigation of the accuracy of the proposed method and the influence of the conditions of heat exchange with the environment. the experimental data was compared with the analytical solution of the kelvin equation. additionally, the influence of the conditions of contact between the sensor and the sample on the measured parameters was checked. the amplitude of the stress was 5 kn, the frequency of 1 hz, the stress ratio r = -1. the experimental results for various conditions of sensor contact with the sample are shown in fig. 6. figure 6: power of heat flux during the thermoelastic test (1 – the analytical solution of the kelvin equation; 2 – the experimental data from the sensor pressed by the spring to the sample; 3 – the experimental data from the sensor corrected by the consideration of whole free surface of the sample; 4 – the experimental data from the sensor located with a gap of 0.5 mm. from the sample; 5 – the experimental data from the sensor located with a gap of 0.1 mm. from the sample.) fig. 6 shows three variants of mounting the sensor to the sample: a tripod with a gap of 0.5 mm (4) and 0.1 (5), and the pressing of sensor to the sample by the spring (3). analysis of the results presented in fig. 6, allows us to conclude that there is no influence of friction on the measured heat flow. the measured value with a tripod is substantially less than the theoretically calculated (graphs (4) and (5) in fig. 6). in this case, it is assumed that the sensor does not change the conditions of heat exchange of the sample and the environment (heat dissipation is the same in all directions). to correct the heat measured data from the pressed sensor (2) we assumed that the sensor with cooling system does not change the heat transfer conditions and multiply the data by a factor taking into account the whole free surface of the sample. taking these hypothesis into account we can obtain a complete coincidence of measured and theoretical values (graphs (1) and (3) in fig. 6). the study of fatigue crack propagation he developed sensor was used to study the heat dissipation caused by growth of fatigue cracks. typical result of measurements of the heat flux during the experiment is presented in fig. 7. the plots can be divided into three parts. short initial increasing part corresponds to starting of crack propagation (part 1). the second part with constant heat flux corresponds to the regime of short crack propagation (part 2). the last part of the plot (part 3) is characterized by sharp increasing of heat dissipation. during this part we observe the long crack propagation process. the last part is finished by specimen failure. fig. 8 presents the experimental data to illustrate general regularities in the dynamics of fatigue crack growth. the tests presented in the figure were carried out on the samples made from steel. the geometry of the samples is presented in fig. 4a. the stress amplitude was constant during the test. the unfilled point corresponds to the results of the heat measurement with the developed sensors. there are three different stress amplitudes in fig. 8 with corresponds to following applied forces: 13 kn (unfilled squares), 15 kn (unfilled circles) and 17 kn (unfilled diamonds). the filled marks t t a. vshivkov et alii, frattura ed integrità strutturale, 35 (2016) 57-63; doi: 10.3221/igf-esis.35.07 62 corresponds the heat flux calculated by treatment of surface temperature evolution measured by independent way. based on the data presented in fig. 8 we can conclude that there is a linear relation between crack rate and product of crack length and heat power from the crack tip. this conclusion was confirmed by the results obtained with the other sample geometries presented in fig. 4. all tests were carried out with constant stress amplitude. figure 7: the characteristic dependence of the power of heat flux from the crack tip. figure 8: the relation between fatigue crack rate and the fatigue crack length multiplied by the power of heat flow. conclusion he paper describes the structure and performance of the heat flux sensor which was designed based on the seebeck effect. this sensor can be used to analyze the energy balance of the material during the deformation process either in combination with the method of infrared thermography (for its verification), or independently. in the case of its independent usage the loss of information about the spatial distribution of the heat is compensated by the possibility of long-term measurements. with this technique a comprehensive investigation into the processes of energy dissipation during the propagation of fatigue cracks in metal alloys was done. the analysis of the results allowed putting forward the hypothesis for a linear relationship between the rate of fatigue crack propagation and the product of the rate of energy dissipation by the length of the crack. the developed method can be used to calculate the value of the dissipated energy at any moment of the material lifetime. one of possible promising continuation of the work is a combination of this result with the calculation of applied energy. it could give us an opportunity to estimate a stored energy (cold work) of deformation. the stored energy is widely used to formulate a criterion of material failure [5, 6]. thus, the proposed method can be applied to assess the state of the material. acknowledgments his work was supported by the perm regional government № с-26/619 and grants rfbr (№ 14-01-96005, 1401-00122). references [1] pradere, c., joanicot, m., batsale, j.-c., toutain, j., gourdon, c., processing of temperature field in chemical microreactors with infrared thermography, qirt journal, 3 (2006) 117-135. [2] izyumova, a. yu., plekhov, o. a., vshivkov, a. n., prokhorov, a. a., uvarov, s. v., studying the rate of heat dissipation at the vertex of a fatigue crack, technical physics letters, 40(9) (2014) 810-812. [3] kyhling, h., spravochnik po fizike [guide to physics], moscow, (1982). t t a. vshivkov et alii, frattura ed integrità strutturale, 35 (2016) 57-63; doi: 10.3221/igf-esis.35.07 63 [4] bowler, n., theory of four point direct current potential drop measurements on a metal plate, research in nondestructive evaluation, 17 (2006) 29-48. [5] fedorov, v.v., thermodynamic aspects of strength and fracture of solids, fan, tashkent, (1979). 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<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> /enu (use these settings to create adobe pdf documents best suited for high-quality prepress printing. created pdf documents can be opened with acrobat and adobe reader 5.0 and later.) >> /namespace [ (adobe) (common) (1.0) ] /othernamespaces [ << /asreaderspreads false /cropimagestoframes true /errorcontrol /warnandcontinue /flattenerignorespreadoverrides false /includeguidesgrids false /includenonprinting false /includeslug false /namespace [ (adobe) (indesign) (4.0) ] /omitplacedbitmaps false /omitplacedeps false /omitplacedpdf false /simulateoverprint /legacy >> << /addbleedmarks false /addcolorbars false /addcropmarks false /addpageinfo false /addregmarks false /convertcolors /converttocmyk /destinationprofilename () /destinationprofileselector /documentcmyk /downsample16bitimages true /flattenerpreset << /presetselector /mediumresolution >> /formelements false /generatestructure false /includebookmarks false /includehyperlinks false /includeinteractive false /includelayers false /includeprofiles false /multimediahandling /useobjectsettings /namespace [ (adobe) (creativesuite) (2.0) ] /pdfxoutputintentprofileselector /documentcmyk /preserveediting true /untaggedcmykhandling /leaveuntagged /untaggedrgbhandling /usedocumentprofile /usedocumentbleed false >> ] >> setdistillerparams << /hwresolution [2400 2400] /pagesize [612.000 792.000] >> setpagedevice microsoft word numero 2 art 2 finale.doc al. carpinteri et al., frattura ed integrità strutturale, 2 (2007) 10-16; doi: 10.3221/igf-esis.02.02 10 1 introduction fatigue crack growth data for ductile materials are usually presented in terms of the crack growth rate, da/dn, and the stress-intensity factor range, ( )max mink k kδ = − . at present, it is a common practice to describe the process of fatigue crack growth by a logarithmic d / da n vs. kδ diagram (see e.g. fig. 1). three regions are generally recognized on this diagram for a wide collection of experimental results [1]. the first region corresponds to stress-intensity factor ranges near a lower threshold value, thkδ , below which no crack propagation takes place. this region of the diagram is usually referred to as region i, or the near-threshold region [2]. the second linear portion of the diagram defines a power-law relationship between the crack growth rate and the stress-intensity factor range and is usually referred to as region ii [3]. finally, when maxk tends to the critical stress-intensity factor, ick , rapid crack propagation takes place and crack growth instability occurs (region iii) [4]. in region ii the paris’ equation [5,6] provides a good approximation to the majority of experimental data: d ( ) d ma c k n = δ (1) where c and m are empirical constants usually referred to as paris’ law parameters. from the early 60’s, research studies have been focused on the nature of the paris’ law parameters, demonstrating that c and m cannot be considered as material constants. in fact, they depend on the testing conditions, such as the loading ratio min max min max/ /r k kσ σ= = [7], on the geometry and size of the specimen [8, 9] and, as pointed out very recently, on the initial crack length [10]. however, an important question regarding the paris’ law parameters still remains to be answered: are c and m independent of each other or is it possible to find a correlation between them based on theoretical considerations? concerning this point, it is important to take note of the controversy in the literature about the existence of a correlation between c and m. for instance, cortie [11] stated that the correlation is formal with a little physical relevance, and the high coefficient of correlation between c and m is due to the logarithmic data representation. similar arguments were proposed in [12], where a correlation-free representation was presented. on the other hand, a very consistent empirical relationship between the paris’ law parameters was found by several authors [13, 14] and supported by experimental results [3, 13, 15–18]. in this paper, the correlation existing between the paris’ law parameters is derived on the basis of theoretical arguments. to this aim, both self-similarity concepts [9] and the condition that the paris’ law instability corresponds to the griffith-irwin instability at the onset of rapid crack growth are profitably used. comparing the functional expressions derived according to these two inare the paris’ law parameters dependent on each other? alberto carpinteri, marco paggi politecnico di torino, dipartimento di ingegneria strutturale e geotecnica, corso duca degli abruzzi 24, 10129 torino, italy riassunto. nel presente articolo si riesamina la questione relativa all’esistenza di una correlazione tra i parametri c ed m della legge di paris. in base all’analisi dimensionale ed ai concetti di autosomiglianza incompleta applicati alla fase lineare della propagazione della frattura per fatica, si propone una rappresentazione asintotica che mette in relazione il parametro c ad m ed alle altre variabili che governano il fenomeno in oggetto. gli esponenti della correlazione vengono poi determinati in base alla condizione che l’instabilità alla griffith-irwin debba coincidere con l’instabilità alla paris nel punto di transizione tra la propagazione sub-critica e quella critica. si riscontra infine un ottimo accordo tra la correlazione proposta e l’evidenza sperimentale relativamente alle leghe di alluminio, titanio ed acciaio. abstract. the question about the existence of a correlation between the parameters c and m of the paris’ law is re-examined in this paper. according to dimensional analysis and incomplete self-similarity concepts applied to the linear range of fatigue crack growth, a power-law asymptotic representation relating the parameter c to m and to the governing variables of the fatigue phenomenon is derived. then, from the observation that the griffith-irwin instability must coincide with the paris’ instability at the onset of rapid crack growth, the exponents entering this correlation are determined. a fair good agreement is found between the proposed correlation and the experimental data concerning aluminium, titanium and steel alloys. keywords. fatigue crack growth, paris’ law parameters, correlation, dimensional analysis, griffithirwin instability. http://www.gruppofrattura.it http://www.gruppofrattura.it http://dx.medra.org/10.3221/igf-esis.02.02&auth=true al. carpinteri et al., frattura ed integrità strutturale, 2 (2007) 10-16 11 dependent approaches, a relation between the paris’ law parameters c and m is proposed. as a result, it is shown that only one macroscopic parameter is needed for the characterization of damage during fatigue crack growth. 2 correlation derived according to self-similarity concepts according to dimensional analysis, the physical phenomenon under observation can be regarded as a black box connecting the external variables (called input or governing parameters) with the mechanical response (output parameters). in case of fatigue crack growth in region ii, we assume that the mechanical response of the system is fully represented by the crack growth rate, 0 =d / dq a n , which is the parameter to be determined. this output parameter is a function of a number of variables: ( )0 1 2 1 2 1 2, , , ; , , , ; , , , ,n m kq f q q q s s s r r r= k k k (2) where iq are quantities with independent physical dimensions, i.e. none of these quantities has a dimension that can be represented in terms of a product of powers of the dimensions of the remaining quantities. parameters is are such that their dimensions can be expressed as products of powers of the dimensions of the parameters iq . finally, parameters ir are nondimensional quantities. as regards the phenomenon of fatigue crack growth, it is possible to consider the following functional dependence: (3) where the governing variables are summarized in tab. 1, along with their physical dimensions expressed in the length-force-time class (lft). from this list it is possible to distinguish between three main categories of parameters. the first category regards the material parameters, such as the yield stress, yσ , and the fracture toughness, ick . the second category comprises the variables governing the testing conditions, such as the stressintensity factor range, kδ , the loading ratio, r , and the frequency of the loading cycle, ω . concerning environmental conditions and chemical phenomena, they are not considered as primary variables in this formulation and variable definition symbol dimensions 1q tensile yield stress of the material σy fl –2 2q material fracture toughness kic fl –3/2 3q frequency of the loading cycle ω t –1 1s stress-intensity range δk = kmax kmin fl –3/2 2s characteristic structural size d l 3s characteristic internal length h l 4s initial crack length a0 l 1r loading ratio – ( )ic 0 d , , ; , , , ;1 , d y a f k k d h a r n σ ϖ= δ − figure 1. scheme of the typical fatigue crack propagation curve max min k k r = table 1. main variables governing the fatigue crack growth phenomenon. al. carpinteri et al., frattura ed integrità strutturale, 2 (2007) 10-16 12 their influence on fatigue crack growth can be taken into account as a degradation of the material properties. finally, the last category includes geometric parameters related to the material microstructure, such as the internal characteristic length, h, and to the tested geometry, such as the characteristic structural size, d , and the initial crack length, a0. considering a state with no explicit time dependence, it is possible to apply the buckingham’s π theorem [19] to reduce by n the number of parameters involved in the problem (see e.g. [8, 20–26] for some relevant applications of this method in solid mechanics). as a result, we have: (4) at this point, we want to see if the number of the quantities involved in the relationship (4) can be reduced further from five. considering the nondimensional parameter ic/k kδ , it has to be noticed that this is usually small in the region ii of fatigue crack growth. however, since it is well-known that the fatigue crack growth phenomenon is strongly dependent on this variable (see e.g. the paris’ law in eq. (1)), a complete self-similarity in this parameter cannot be accepted. hence, assuming an incomplete self-similarity in 1π , we have: (5) where the exponent β1 and, consequently, the nondimensional parameter 1φ , cannot be determined from considerations of dimensional analysis alone. moreover, the exponent β1 may depend on the nondimensional parameters iπ . it has to be noticed that 2π takes into account the effect of the specimen size and it corresponds to the square of the nondimensional number z defined in [8], and to the inverse of the square of the brittleness number s introduced in [20, 21, 27]. moreover, the parameter 4π is responsible for the dependence of the fatigue phenomenon on the initial crack length, as recently pointed out in [10]. repeating this reasoning for the parameter (1 )r− , which is a small number comprised between zero and unity, a complete self-similarity in 5π would imply that fatigue crack growth is independent of the loading ratio. however, this behavior is in contrast with some experimental results indicating an increase in the response d / da n when increasing the parameter r [28]. therefore, assuming again an incomplete self-similarity in 5π , we have: (6) comparing eq. (6) with the expression of the paris’ law, we find that our proposed formulation encompasses eq. (1) as a limit case when: (7) as a consequence, from eq. (7) it is possible to notice that the parameter c is dependent on two material parameters, such as the fracture toughness, ick , and the yield stress, yσ , as well as on the loading ratio, r, and on the nondimensional parameters 2π , 3π , and 4π . moreover, eq. (7) demonstrates, from the theoretical standpoint, the existence of a relationship between the parameters c and m. 3 correlation derived according to the crack growth instability condition in this section we derive a correlation between the paris’ law parameters similar to that in eq. (7) on the basis of the condition of crack growth instability. in fact, as firstly pointed out by forman et al. [4], the crack propagation rate, d / da n , is not only a function of the stress-intensity factor range, kδ , but also on the condition of instability of the crack growth when the maximum stress-intensity factor approaches its critical value for the material. focusing our attention on this dependence, forman et al. [4] observed that the crack propagation rate must tend to infinity when max ick k→ , i.e. (8) this rapid increase in the crack propagation rate is then responsible for the fast deviation from the linear part of the region ii in the fatigue plot (see e.g. fig. 1). considering the transition point labeled cr in fig. 1 between region ii and region iii, the following relationship between the crack growth rate and the stress-intensity factor range can be derived according to the paris’ law: (9) ( ) 2 ic y 2 2 2 02 2 2 ic ic ic ic 1 2 3 4 5 d d , , , ;1 , , , , . y y y ka n k d h a r k k k k σ σ σ σ ⎛ ⎞ =⎜ ⎟⎜ ⎟ ⎝ ⎠ ⎛ ⎞δ = φ − =⎜ ⎟⎜ ⎟ ⎝ ⎠ = φ π π π π π ( ) 1 2 ic 1 2 3 4 5 y ic d , , , , d ka k n k β σ ⎛ ⎞ ⎛ ⎞δ = φ π π π π⎜ ⎟ ⎜ ⎟⎜ ⎟ ⎝ ⎠⎝ ⎠ ( ) ( ) ( ) 1 2 1 2 1 2 ic 2 2 3 4 y ic 2 2 ic y 2 2 3 4 d d (1 ) , , (1 ) , , . a n k k r k k r k β β β β β σ σ− − = ⎛ ⎞ ⎛ ⎞δ = − φ π π π =⎜ ⎟ ⎜ ⎟⎜ ⎟ ⎝ ⎠⎝ ⎠ = − δ φ π π π ( ) ( )2 1 2 2 ic y 2 2 3 4 , (1 ) , , .m m c k r β β σ− − = = − φ π π π max ic d lim dk k a n→ = ∞ ( )cr cr cr d d ma v c k n ⎛ ⎞ = = δ⎜ ⎟ ⎝ ⎠ al. carpinteri et al., frattura ed integrità strutturale, 2 (2007) 10-16 13 where crkδ denotes the value of the stress-intensity factor range at the point cr. due to the fact that a rapid variation in the crack propagation rate takes place when the onset of crack instability is reached, it is a reasonable assumption to consider crmax ick k≅ . as a consequence, it is possible to correlate the value of crkδ with the material fracture toughness: (10) hence, introducing eq. (10) into eq. (9), an approximate relationship between the paris’ constants is derived according to the condition that the onset of the paris’ instability corresponds to the griffith-irwin instability: (11) moreover, as regards the parameters crv and ick entering eq. (11), it has to be remarked that they are almost constant for each class of material. the dependence on the loading ratio is also put into evidence in eq. (11). a closer comparison between eq. (11) and eq. (7) permits to clarify the role played by crv . in fact, eq. (11) corresponds to the correlation derived according to selfsimilarity concepts when: (12) confirming the experimental observation reported in [3] that crv should depend on the material properties, on the geometry of the tested specimen, and on the material microstructure. therefore, considering the same testing conditions, this conventional crack growth rate is almost constant for each class of material and eq. (11) establishes a one-to-one correspondence between the c and m values. 4 experimental assessment of the proposed correlation: aluminium, titanium and steel alloys parameters c and m entering the paris’ law are usually impossible to be estimated according to theoretical considerations and fatigue tests have to be performed. however, many authors [3, 13, 29] experimentally observed a very stable relationship between the parameters c and m, which is usually represented by the following empirical formula: (13) usually written in a logarithmic form: (14) taking the logarithm of both sides of the theoretically based relationship between c and m in eq. (11), we obtain (15) which corresponds to eq. (14) if (16) in order to check the validity of the proposed correlation derived according to the instability condition of the crack growth, an experimental assessment is performed by comparing the experimentally determined values of b with those theoretically predicted according to eq. (16). concerning steels and aluminium alloys, radhakrishnan [13] collected a number of data from various sources and proposed the following least square fit relationships ( kδ being in mpa√m and da/dn in m/cycle): (17) in order to compare the prediction of our proposed correlation with the experimentally determined values of b, parameters m and kic have to be known in advance. however, only in a few studies both the values of the fatigue parameters and of the fracture toughness are experimentally determined and reported. therefore, to avoid experimental tests, the values of the material fracture toughness are taken from selected handbooks. concerning steels, we assume a = crv = 7.6x10 -7 m/cycle, as experimentally determined by radhakrishnan, 0r = , and we try to estimate the parameter b on the basis of the values of the fracture toughness proposed in the asm handbook [30]. this book provides a collection of values in a diagram kic vs. both the prior austenite grain size, and the temperature test. over a large range of temperatures (t from –269°c to 27°c) and grain sizes (d from 1 μm to 16 μm), ick varies from 20 mpa√m to 100 mpa√m with an average value of ic 60k = mpa√m. the comparison can also be extended to aluminium alloys. according to the same procedure discussed above, the estimated average value of the critical stress-intensity factor from handbooks [30–33] is equal to ic 35k = mpa√m with minimum and maximum values equal to 15 mpa√m and 49 mpa√m, respectively. using the average values we find: (18) cr ic(1 )k r kδ = − cr ic 1 (1 ) m c v r k ⎡ ⎤ ≅ ⎢ ⎥−⎣ ⎦ ( ) 1 2 2 ic cr 2 2 3 4 y , , , , m k v β β σ = = − ⎛ ⎞ = φ π π π⎜ ⎟⎜ ⎟ ⎝ ⎠ mc ab= log log logc a m b= + cr ic 1 log log log (1 ) c v m r k ⎡ ⎤ = + ⎢ ⎥−⎣ ⎦ cr ic , 1 . (1 ) a v b r k = = − 7 2 6 2 log log(7.6 10 ) log(1.81 10 ) for steels, log log(2.5 10 ) log(4.26 10 ) for al alloys. c m c m − − − − = × + × = × + × 7 2 6 2 log log(7.6 10 ) log(1.67 10 ) for steels, log log(2.5 10 ) log(2.86 10 ) for al alloys. c m c m − − − − ≅ × + × ≅ × + × al. carpinteri et al., frattura ed integrità strutturale, 2 (2007) 10-16 14 in both cases, a good agreement between the proposed estimation based on an average value of the critical stress-intensity factor and the experimental relationships in eq. (17) is achieved. another source of experimental data is [34], and is based on the nasgro program [35], which is one of the most comprehensive database of fatigue crack growth curves for aerospace alloys. these experimental data concern the material fracture toughness, the paris’ law parameters, as well as the crack growth rate corresponding to kmax ≅ kic for fatigue tests characterized by 0r = (see tab. 2). as previously outlined, the fracture toughness data and the values of νcr are almost constant for each class of materials. this property is very well evidenced by the 2219-t62, 2219-t87, 6061-t62 and 7075-t73 aluminium alloys. the application of eq. (9) permits to predict the value of the paris’ law parameter c as a function of m and to compare it with the experimental one reported in the fifth column of tab. 2. the agreement between the experimental data and the predictions made according to our correlation is noticeably good, as also evidenced by the relative percentage error reported in the last column of tab. 2. 5 conclusions to shed light on the controversy about the existence of a correlation between the paris’ constants, both selfsimilarity concepts and the condition that the paris’ law instability corresponds to the griffith-irwin instability at the onset of rapid crack growth have been profitably used. comparing the functional expressions derived from these two independent approaches, an approximate relationship between c and m has been proposed. according to this theory, the parameter c is also dependent on the fracture toughness of the material, on the crack growth rate at the onset of crack instability, and on the loading ratio. the main consequence of this correlation is that only one macroscopic parameter is needed for the characterization of damage during fatigue crack growth. a good agreement between the theoretical predictions obtained using this correlations and experimental data has been achieved. from the engineering standpoint, it has to be emphasized that our proposed correlation constitutes a useful tool for design purposes. in fact, in case of a lack of experimental fatigue data for a new material to characterize, one could, as a first approximation, determine the parameter c as a function of the exponent m according to eq. (11). then, a parametric analysis by varying the exponent m in its usual range of variation can be performed and numerical simulations of fatigue crack growth can be put forward. parameters crv and ick entering the correlation can be either known in advance, or estimated from materials with similar composition, thermal treatment and mechanical properties (see also [36–38]). 6 acknowledgements support of the european union to the leonardo da vinci project “innovative learning and training on fracture (iltof)” is gratefully acknowledged. 7 references [1] r.o. ritchie, “influence of microstructure on nearthreshold fatigue-crack propagation in ultra-high strength steel”, metal science, 11 (1977) 368–381. material experimental data present correlation m c c relative error (%) alum-2219-t62 (l-t) 28.2 3.5 x 10–6 2.87 2.40 x 10–10 2.41 x 10–10 0 alum-2219-t87 (l-t) 27.3 3.5 x 10–6 3.30 6.27 x 10–11 6.38 x 10–11 2 alum-6061-t62 (l-t) 25.0 3.5 x 10–6 3.20 1.63 x 10–10 1.18 x 10–10 –28 alum-7075-t73, forged (l-t) 27.3 3.5 x 10–6 2.98 1.80 x 10–10 1.84 x 10–10 2 pure titanium (fty = 380 mpa) 46.0 1.0 x 10–5 3.41 1.95 x 10–11 2.14 x 10–11 10 ti–6al–4v-rt (mill annealed) 15.5 2.0 x 10–7 3.11 3.80 x 10–11 3.97 x 10–11 4 ph13-8mo-h1000 (steel alloy) 100.0 3.0 x10–5 3.40 5.00 x 10–12 4.75 x 10–12 –5 table 2. experimental assessment of the proposed correlation for aluminium, titanium and steel alloys according to the nasgro database [35]. )( mmpa k ic ( ) vcr m/cycle al. carpinteri et al., frattura ed integrità strutturale, 2 (2007) 10-16 15 [2] d. taylor, “fatigue thresholds”, butterworths, london (1981). [3] h. kitagawa, “introduction to fracture mechanics of fatigue”, in an. carpinteri, editor, handbook of fatigue crack propagation in metallic structures, vol. i, 47–105, elsevier science b.v. (1994). [4] r.g. forman, v.e. kearney and r.m. engle, “numerical analysis of crack propagation in cyclic-loaded structures”, asme journal of basic engineering, 89 (1967) 459–464. [5] p.c. paris, m.p. gomez and w.p. anderson, “a rational analytic theory of fatigue”, the trend in engineering 13 (1961) 9–14. [6] p.c. paris and f. erdogan, “a critical analysis of crack propagation laws”, asme journal of basic engineering, 85d (1963) 528–534. [7] v.m. radhakrishnan, “parameter representation of fatigue crack growth”, engineering fracture mechanics, 11 (1979) 359–372. [8] g.i. barenblatt and l.r. botvina, “incomplete selfsimilarity of fatigue in the linear range of fatigue crack growth” fatigue and fracture of engineering materials and structures, 3 (1980) 193–202. [9] g.i. barenblatt, “scaling, self-similarity and intermediate asymptotics”, cambridge university press, cambridge (1996). [10] a. spagnoli, “self-similarity and fractals in the paris range of fatigue crack growth”, mechanics of materials, 37 (2005) 519–529. [11] m.b. cortie, “the irrepressible relationship between the paris law parameters”, engineering fracture mechanics, 30 (1988) 49–58. [12] f. bergner and g. zouhar, “a new approach to the correlation between the coefficient and the exponent in the power law equation of fatigue crack growth”, international journal of fatigue, 22 (2000) 229–239. [13] v.m. radhakrishnan, “quantifying the parameters in fatigue crack propagation”, engineering fracture mechanics, 13 (1980) 129–141. [14] l. tóth and a. krasowsky, “fracture as the result of self-organised damage process”, journal of materials processing technology, 53 (1995) 441–451. [15] j.b. lee and d.n. lee, “correlation of two constants in the paris equation for fatigue crack propagation rate in region ii”, in proceedings of the 6th international conference on fracture icf6, new delhi, india, 1727–1733. pergamon press (1984). [16] m. cavallini and f. iacoviello, “fatigue models for al alloys”, international journal of fatigue, 13 (1991) 442–446. [17] m. cavallini and f. iacoviello, “a statistical analysis of fatigue crack growth in a 2091 al-cu-li alloy”, international journal of fatigue, 17 (1995) 135–139. [18] f. iacoviello. d. iacoviello and m. cavallini, “analysis of stress ratio effects on fatigue propagation in a sintered duplex steel by experimentation and artificial neural network approaches”, international journal of fatigue, 26 (2004) 819–828. [19] e. buckingham, “model experiments and the form of empirical equations”, asme transactions, 37 (1915) 263–296. [20] a. carpinteri, “notch sensitivity in fracture testing of aggregative materials”, engineering fracture mechanics, 16 (1982) 467–481. [21] a. carpinteri, “plastic flow collapse vs. separation collapse in elastic-plastic strain-hardening structures”, rilem materials & structures, 16 (1983) 85–96. [22] a. carpinteri, “size effects on strength, toughness and ductility”, journal of engineering mechanics, 115 (1989) 1375–1392. [23] a. carpinteri, “cusp catastrophe interpretation of fracture instability”, journal of the mechanics of physics of solids, 37 (1989) 567–582. [24] a. carpinteri, “scaling laws and renormalization groups for strength and toughness of disordered materials”, international journal of solids and structures, 31 (1994) 291–302. [25] a. carpinteri, “strength and toughness in disordered materials: complete and incomplete similarity”, in sizescale effects in the failure mechanisms of materials and structures, proceedings of the international union of theoretical and applied mechanics (iutam), turin, italy, 3–26, london: e & fn spon, (1994). [26] r.o. ritchie, “incomplete self-similarity and fatigue-crack growth”, international journal of fracture, 132 (2005) 197–203. [27] a. carpinteri, “static and energetic fracture parameters for rocks and concretes”, rilem materials & structures, 14 (1981) 151–162. [28] i. milne, r.o. ritchie and b.l. karihaloo, eds. “comprehensive structural integrity: fracture of materials from nano to macro”, vol. 4: cyclic loading and fatigue, elsevier, amsterdam (2003). [29] e.h. niccolls, “a correlation for fatigue crack growth rate”, scripta metallurgica, 10 (1976) 295–298. [30] materials park: asm international. asm handbook, (1985-1988). fatigue and fracture. [31] materials park: asm international. metals handbook, (1985). [32] materials park: asm international 10th ed. metals handbook, (1990). properties and selection: nonferrous alloys and special-purpose materials. [33] cindas/purdue university, west lafayette, in. structural alloys handbook, (1996). [34] b. farahmand, “analytical method of generating da/dn curves for aerospace alloys”, in: gdoutos ee, editor. fracture of nano and engineering materials and structures (proceedings of the 16th european conference of fracture, alexandroupolis, greece, 2006), paper no. 140 on cd–rom. springer, dordrecht (2006). [35] r.g. forman, v. shivakumar and j.c. newman, “fatigue crack growth computer program nasa/flagro”, technical report jsc-22267a, nasa, january 1993. [36] a. carpinteri and m. paggi, “self-similarity and crack growth instability in the correlation between the al. carpinteri et al., frattura ed integrità strutturale, 2 (2007) 10-16 16 paris’ constants”, engineering fracture mechanics, 74 (2007) 1041–1053. [37] n. pugno, m. ciavarella, p. cornetti and a. carpinteri, “a generalized paris’ law for fatigue crack growth”, journal of the mechanics and physics of solids, 54 (2006) 1333–49. [38] n. pugno, p. cornetti and a. carpinteri, “new unified laws in fatigue: from the wöhler to the paris’ regime”, engineering fracture mechanics, 74 (2007) 595– 601. microsoft word numero_41_art_29.docx h. šimonová et alii, frattura ed integrità strutturale, 41 (2017) 211-219; doi: 10.3221/igf-esis.41.29 211 focused on crack tip fields modelling of interfacial transition zone effect on resistance to crack propagation in fine-grained cement-based composites h. šimonová, m. vyhlídal, b. kucharczyková, p. bayer, z. keršner brno university of technology, faculty of civil engineering, veveří 331/95, 602 00 brno, czech republic simonova.h@vutbr.cz, http://orcid.org/0000-0003-1537-6388 michal.vyhlidal@vutbr.cz barbara. kucarczykova@vutbr.cz, http://orcid.org/0000-0002-7123-5099 bayer.p@fce.vutbr.cz kersner.z@fce.vutbr.cz, http://orcid.org/0000-0003-4724-6166 l. malíková, j. klusák institute of physics of materials, academy of sciences of the czech republic, v. v. i., žižkova 22, 602 00 brno, czech republic malikova.l@fce.vutbr.cz, http://orcid.org/0000-0001-5868-5717 klusak@ipm.cz abstract. in this paper, the attention is paid to investigation of the importance of the interfacial transition zone (itz) in selected fine-grained cement-based composites for the global fracture behaviour. this is a region of cement paste around the aggregate particles which specific features could have significant impact on the final behaviour of cement composites with a crack tip nearby this interface under applied tension. the aim of this work is to show the basic interface microstructure by scanning electron microscopy (sem) done by mira3 tescan and to analyse the behaviour of such composite by numerical modelling. numerical studies assume two different itz thicknesses taken from sem analysis. a simplified cracked geometry (consisting of three phases – matrix, itz, and aggregate) is modelled by means of the finite element method with a crack terminating at the matrix–itz interface. itz’s modulus of elasticity is taken from generalized self-consistent scheme. a few conclusions are discussed based on comparison of the average values of the opening stress ahead of the crack tip with their critical values. the analyses dealing with the effect of itz’s properties on the stress distribution should contribute to better description of toughening mechanisms in silicate-based composites. keywords. fine-grained concrete; interfacial transition zone; scanning electron microscopy; three-point bending fracture test; effective fracture toughness. citation: šimonová, h., vyhlídal, m., kucharczyková, b., bayer, p., keršner, z., malíková, l., klusák, j., modelling of interfacial transition zone effect on resistance to crack propagation in fine-grained cementbased composites, frattura ed integrità strutturale, 41 (2017) 211-219. received: 28.02.2017 accepted: 15.04.2017 published: 01.07.2017 copyright: © 2017 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. h. šimonová et alii, frattura ed integrità strutturale, 41 (2017) 211-219; doi: 10.3221/igf-esis.41.29 212 introduction ement-based composites belong to traditional and broadly used building materials [1]. despite their long-term using, the investigation of damage of elements made of such materials under static loading is still developing. concrete, as representative of such composites, shows nonlinear, more precisely, quasi-brittle behaviour – the ability to carry load continues even after the deviation from the linear branch of load–displacement diagram until the peak point and then the decrease of loading force follows until the failure, so called tensile softening. on the other hand, the individual components of primarily considered two-stage composite, cement paste and aggregate, show very often brittle elastic behaviour. this difference in cement-based composites behaviour is caused by development of multiple microcracking predominantly in the so called interfacial transition zone (itz) [2] and others toughening mechanisms. the aim of this paper is quantification of basic mechanical fracture parameters of selected fine-grained cement-based composites – static modulus of elasticity, fracture toughness and fracture energy and investigation of effect of itz between cement matrix (mtx) and aggregate (agg) on stress distribution in cement based composite with crack terminating at the itz–mtx interface. interfacial transition zone (itz) he existence of interfacial transition zone (originally „aureole de transition“) between aggregate and cement paste was introduced in the fifties of last century by farrran [3]. properties of itz and its impact on behaviour of cement-based composites have been studied numerically and experimentally from many points of view since that. number of publications concerned with mechanical properties of individual components of cement-based composites are connected with homogenization techniques, such as e. g. mori-tanaka scheme [4] or generalized self-consistent scheme [5] used in this paper to estimation of itz’s elasticity modulus. although investigation of concrete fracture is connected with the recognition that for description of its structural behaviour are necessary other independent material parameters, such as fracture toughness [6, 7] and not only compressive/tensile strength, only a few publications about itz are concerned with this fact, e.g. [8, 9]. fracture mechanics based on analytical-numerical approaches, mainly connected with finite element method (fem), is widely used to simulate structural response of materials with internal defects (microcracks, voids, pores) which lead to initiation, propagation of cracks and consequent fracture. the problem with crack–interface interaction of two elastic materials is long-term investigated by team gradually created by prof. knésl from institute of physics of materials of the academy of sciences of the czech republic, v. v. i. [10, 11]. experimental part materials and specimens wo fine-grained cement-based composites mixtures with various water to cement (w/c) ratios and amount of plasticizer have been prepared for purpose of this study. mixtures have been prepared on the basis of the standard čsn en 1961 [12]. portland cement type 42.5 r as a binder and quartz sand with the maximum nominal grain size of 2 mm standardize according to čsn en 196-1 [12] for the fine aggregate were used. the w/c ratio was different for both mixtures. the second mixture’s w/c ratio was reduced by addition of super-plasticizer svc 4035 in amount of 1 % by cement mass. mixtures were prepared by a mixing device with controllable mixing speed. the basic information about the composition and properties of the fresh composites are given in tab. 1. the properties of the fresh composites were determined in accordance with čsn en 1015-3 [13] and čsn en 1015-6 [14]. the three specimens of 1000 mm in length and with 60 × 100 mm in cross-section were made from each mixture and primarily used for recording the length changes. after the stabilization of shrinkage values, approximately after 90 days, the beam specimens with nominal dimensions 40 × 40 × 160 mm were cut from these specimens and subsequently used for three-point bending fracture tests. this procedure was chosen primarily because of exclusion of specimen boundary effect. the specimens for microscopy measurements were prepared from former mentioned specimens. c t t h. šimonová et alii, frattura ed integrità strutturale, 41 (2017) 211-219; doi: 10.3221/igf-esis.41.29 213 composite id components and properties units 04042016 09052016 quartz sand [kg] 45.9 45.9 cement i 42.5 r [kg] 15.3 15.3 super-plasticizer svc 4035 % by cement mass ‒ 1.0 water to cement ratio [‒] 0.5 0.35 workability [mm] 140 135 bulk density [kg/m3] 2200 2280 table 1: composition and properties of fresh composites. fracture tests the fracture tests in three-point bending were carried out using a heckert fp 10/1 testing machine with measuring range of 0−2000 n. the beam specimens were provided by initial central edge notch with approximately depth 1/3 of specimen depth situated in the middle of span length; span length was 120 mm. the displacement increment loading was performed, which allowed to record load versus displacement diagrams (l–δ diagrams) during the tests. the l–δ diagrams were used for the determination of elasticity modulus from the first (almost linear) part of the diagram, and for the calculation of effective fracture toughness using the effective crack extension method [15] and specific fracture energy using work-of-fracture method [16]. because of stability loss during loading, it was not possible to reconstruct the descending part of l–δ diagrams. therefore, the work of fracture wf* value is determined as area under l–δ diagrams before stability loss occurred. for details about determination above mentioned mechanical fracture parameters see [17]. the results of performed fracture tests evaluation are introduced in tab. 2 in form mean values and standard deviations ordinarily from six specimens. the monitored mechanical fracture parameters were following: modulus of elasticity e, effective fracture toughness kice and specific fracture energy gf* (determined using mentioned work of fracture wf* value). composite id parameter units 04042016 09052016 modulus of elasticity e [gpa] 32.1±1.6 34.2±2.6 fracture toughness kice [mpa·m1/2] 0.759±0.054 1.093±0.067 fracture energy gf* [j·m–2] 10.76±1.78 24.37±2.89 table 2: selected fracture tests results of 04042016 and 09052016 composites. microstructure of tested specimen’s material microscopy measurements for quantitative description of microstructure of itz were carried out using scanning electron microscopy (sem) mira3 tescan. the projection of specimen’s surface was performed using secondary electrons (se) or backscattered electrons (bse). the selected micrographs caused by detection of se with accelerating voltage of electrons 20 kv are introduced bellow. microstructure of fracture surfaces at the aggregate–cement paste interface for both tested specimens are introduced in fig. 1. sem image of fracture surface of the specimen with greater w/c ratio (on the left) shows less compact microstructure in compare with the other one. it is possible to identify the elemental minerals forming interface, namely ettringite, portlandit and c-s-h gel. on the contrary, there wasn't found any ettringite on the right sem image. it can be caused by random selection of fracture surface part. the other advantage of sem is a possibility of length measurements. it has to be mentioned that measurements are made on a two dimensional sections through a three dimensional microstructure. nevertheless, the distances, used here for the primary information about size and shape of the itz, are uncorrected distances measured on 2d sections. h. šimonová et alii, frattura ed integrità strutturale, 41 (2017) 211-219; doi: 10.3221/igf-esis.41.29 214 the measured values of distances between individual grains of aggregate are shown in fig. 2. these distances, even though they don’t correspond to the idealized concept of a thickness and shape of the itz, come from real measurements. these measurements prove that the formation of the discrete zone (itz) with constant thickness around grain of aggregate is practically impossible. therefore, the distances between these individual grains and the larger one, or more precisely their mean values, are considered as the thicknesses of the itz in following study [2, 18]. figure 1: microstructure of fracture surface at aggregate–cement paste interface by detection of se with magnification 5000×, specimens 04042016 (left) and 09052016. figure 2: distances between grains of aggregate measured using sem with detection of se, specimens 04042016 (left, magnification 70×) and 09052016 (magnification 60×). h. šimonová et alii, frattura ed integrità strutturale, 41 (2017) 211-219; doi: 10.3221/igf-esis.41.29 215 numerical model simplified model of the cracked specimen was created in ansys software to determine clearly the impact of the itz. note that the configuration assumed is based on the three-point bending fracture test of a beam with central edge notch, see fig. 3 (left). in the process of model creating the effects of the vertical position of inclusion, size of the aggregate and its circular shape were ignored. the crack was modelled by introduction of appropriate boundary conditions with its tip at the interface between mtx and itz, see the scheme in fig. 3. materials were modelled as linear, elastic and isotropic, which are represented by their elastic constants, i.e. poisson's ratio  and young's modulus e. thickness of itz for both composites was considered as the mean value of distance of individual grains of aggregate obtained from sem micrographs, see fig. 2. modulus of elasticity value of cement paste (emtx) was taken from above mentioned results of fracture tests (see tab. 2) and was statistically processed – the value of 5 % quantile (emtx, 0.05), mean value (emtx, mean) and 95 % quantile (emtx, 0.95) were taken into consideration. this simplification was chosen because of absence of nanoindentation tests and because of the same ratio of components (aggregate:cement) in both composites. the last information means that the elasticity modulus value of emtx is approximately k-multiple of elasticity modulus of the composite mentioned in tab. 2. the elasticity modulus values of itz (eitz) were considered as 50 % values of emtx according to the procedure called generalized self-consistent scheme [5]. the elasticity modulus value of aggregate (quartz sand) was taken from [19] as the mean value. the complex overview is introduced in tab. 3. figure 3: scheme of the three-point bending fracture tests with central edge notch in the middle of span length (left), scheme of simplified 2d model of the cracked specimen created in software ansys. composite id parameter units 04042016 09052016 thickness of itz [μm] 55 40 emtx [gpa] 32.1±1.6 34.2±2.6 mtx [‒] 0.21[20] 0.21 [20] eitz [gpa] 0.5emtx [5] 0.5emtx [5] itz [‒] 0.21 [20] 0.21 [20] eagg [gpa] 73±1.6 [19] 73±1.6 [19] agg [‒] 0.20 [20] 0.20 [20] table 3: overview of the elastic constants used in the numerical model. results or quantitative description of the influence of itz on the stress state in the crack tip vicinity the opening stress   yy is observed and evaluated. the mean stress  yy and the stress range  yy are calculated: a f h. šimonová et alii, frattura ed integrità strutturale, 41 (2017) 211-219; doi: 10.3221/igf-esis.41.29 216     0 1 , 0 d d yy yy x y x d , (1)     agg itz,max ,minyy yy yy , (2) where d is a size of region, where the stress is averaged. for each configuration critical applied stress is evaluated by means of critical value of mean opening stress  cyy [21]:      icc 2 itz 2 yy k d (3) then the critical applied stress is:      c appl ,c appl  yy yy (4) and it determines the magnitude of applied stress under which the crack will propagate through itz. in the following calculations it was taken kic = 0.5 mpa·m1/2. this value is estimated as equal to usual fracture toughness of matrix of the composite. composites 04042016 and 09052016 as it was mentioned above the thickness of itz was taken from sem measurement and in the composite 04042016 it was 55 μm, while in the composite 09052016 it was 40 μm. figure 4: distribution of the opening stress  yy in itz and agg; itz thickness 55 μm and 40 μm. in fig. 4, the opening stresses   yy (for both composites) are shown in dependence on the distance from the crack tip x, where the value x = 0 μm refers to the crack tip. the step changes of the stresses   yy are apparent at the interface between itz and agg. here the average values  yy are evaluated over the whole itz thicknesses. the average values  yy and the stress ranges  yy for the composite 04042016 (d = 55 μm) are stated in tab. 4 while for the composite 09052016 (d = 40 μm) they can be found in tab. 5. 0 2 4 6 8 10 0 100 200 300 400 o pe n in g st re ss [ m p a] x [μm] 04042016 09052016 agg (d =55 μm) (d =40 μm) itz h. šimonová et alii, frattura ed integrità strutturale, 41 (2017) 211-219; doi: 10.3221/igf-esis.41.29 217 emtx [gpa] eitz [gpa] eagg [gpa]  yy [mpa]  yy [mpa]  c  yy [mpa] appl ,c [mpa] emtx, 0.05 29.50 14.75 73.00 [19] 5.49 5.42 53.79 9.80 emtx,mean 32.10 16.05 73.00 [19] 5.90 4.92 53.79 9.12 emtx, 0.95 34.70 17.35 73.00 [19] 6.04 4.83 53.79 8.91 table 4: the mean stress yy , its critical value yyc , stress range yy and critical applied stress appl,c for various emtx and eitz values considering the itz thickness 55 μm. emtx [gpa] eitz [gpa] eagg [gpa]  yy [mpa]  yy [mpa]  c  yy [mpa] appl ,c [mpa] emtx, 0.05 29.90 14.95 73.00 [19] 5.09 5.91 63.08 12.39 emtx,mean 34.20 17.10 73.00 [19] 5.54 5.43 63.08 11.39 emtx, 0.95 38.50 19.25 73.00 [19] 5.97 4.97 63.08 10.57 table 5: the mean stress   yy , its critical value  yyc , stress range  yy and critical applied stress appl ,c for various emtx and eitz values considering the itz thickness 40 μm. comparison of results and their discussion in the following, the main results obtained for both composites with different itz thickness values and elasticity moduli of mtx and itz are compared and discussed. the graphical expression of the dependences can be seen in fig. 5 where the values of critical applied stress appl ,c are plotted in dependence on the elasticity modulus of itz. figure 5: the values of the critical applied stress appl ,c in dependence on the elasticity modulus of itz. the critical applied stress appl ,c corresponds to the level of the applied stress under which further crack propagation through itz is expected. the values of appl ,c are gained from the average values of the opening stress and their critical values. they depend on the distance d where the average stress is evaluated. we suppose that further crack propagation will occur by the crack increment through whole itz, we take d equal to the itz thickness and we can see that the results depend just on this. the plots in fig. 5 clearly show that composites with thicker itz exhibit lower critical applied stress. thus they violate easier than the composites with thinner itz. similarly, it can be observed (from the tabs. 4 and 5 and from the fig. 5) that the stiffer itz leads (for particular itz thickness) to lower values of appl ,c . these pilot results can lead to more reliable description of toughening mechanisms of composites of this kind. further it can be used for design of more resistant silicate-based composites. 8 9 10 11 12 13 14 14 16 18 20 c ri ti ca l a p p lie d st re ss [m p a] eitz [gpa] 4042016 9052016 (d =55 μm) (d =40 μm) h. šimonová et alii, frattura ed integrità strutturale, 41 (2017) 211-219; doi: 10.3221/igf-esis.41.29 218 conclusions he authors focused their attention on the evaluation of the influence of the interfacial transition zone on the stress distribution in the cracked specimen. the crack tip was located at the interface between mtx and itz. as the average stress is used for stability criterion suggestion in cases of general singular stress concentrators [21], it can be used for quantification of the severity of the crack with its tip at a bi-material interface. therefore, the opening stress   yy was observed and the average stress  yy ahead of the crack tip calculated. not only the influence of the various itz thicknesses but also of various elastic moduli of itz on the near-crack-tip stress field was studied and discussed. critical applied stress was evaluated based on knowledge of critical opening stress. knowledge of the effect of the itz on the stress distribution will contribute to better understanding of the toughening mechanisms of the itz and aggregate in silicate-based composites. acknowledgement his outcome has been achieved with the financial support of the czech science foundation under project no. 1618702s “amiri – aggregate-matrix-interface related issues in silicate-based composites”. references [1] nevile, a.m., properties of concrete, pearson education limited, harlow, (2011). [2] scrivener, k.l., crumbie, a.k., laugesen, p. the interfacial transition zone (itz) between cement paste and aggregate in concrete, interface science, 12 (2004) 411–421. issn 1573-2746. doi: 10.1023/b:ints.0000042339.92990.4c [3] farran, j., contribution mineralogique a l'etude de l'adherence entre les constituants hydrates des ciments et les materiaux enrobes, revue des matiriaux de construction, 491 (1956) 155–157, 492 (1956) 191–209. [4] mori, t., tanaka, k., average stress in matrix and average elastic energy of materials with misfitting inclusions, acta metallurgic, 21 (1973) 571–574. doi: 10.1016/0001-6160(73)90064-3. [5] hashin, z., monteiro, p.j.m., an inverse method to determine the elastic properties of the interphase between the aggregate and the cement paste, cement and concrete research, 32 (2002) 1291–1300. doi: 10.1016/s0008-8846(02)00792-5 [6] li, c.v., maalej, m., toughening in cement based composites. part i: cement, mortar and concrete, cem concr comp. 18 (1996) 223–237. doi: 10.1016/0958-9465(95)00028-3 [7] shah, s.p., fracture toughness of high strength concrete, aci mater j, 87 (1990) 260–265. [8] wriggers, p., moftah, s.o., mesoscale models for concrete: homogenisation and damage behaviour, finite elements in analysis and design , 42 (2006) 623–636. doi: 10.1016/j.finel.2005.11.008 [9] vervuurt, a., van mier, j.g.m., fracture of the bond between aggregate and matrix: an experimental and numerical study, in: a. katz, a. bentur, m. alexander, g. arligue, (eds.) rilem second international conference on the interfacial transition zone in cementitious composites, e & fn spon, new york, (1998) 51–58. [10] klusák, j., profant, t., knésl, z., kotoul, m., the influence of discontinuity and orthotropy of fracture toughness on conditions of fracture initiation in singular stress concentrators, eng fract mech. 110 (2013) 438–447. doi: 10.1016/j.engfracmech.2013.05.002 [11] knésl, z., klusák, j., náhlík, l., crack initiation criteria for singular stress concentrations, part i.–iv, eng mech, 14 (2007) 399–408, 409–422, 15 (2008) 99–114, 263–270. [12] čsn en 196-1:2005, methods of testing cement – part 1: determination of strength, prague: čni, 2005, (the czech version of the european standard en 196-1:2005). [13] čsn en 1015-3:2000, methods of test for mortar for masonry – part 3: determination of consistence of fresh mortar (by flow table), prague: čni, 2000, (the czech version of the european standard en 1015-3:2000). [14] čsn en 1015-6:1999, methods of test for mortar for masonry – part 6: determination of bulk density of fresh mortar, prague: čni, 1999, (the czech version of the european standard en 1015-6:1999). t t h. šimonová et alii, frattura ed integrità strutturale, 41 (2017) 211-219; doi: 10.3221/igf-esis.41.29 219 [15] karihaloo, b.l., fracture mechanics and structural concrete, wiley, new york, (1995). [16] rilem tc-50 fcm recommendation, determination of the fracture energy of mortar and concrete by means of three-point bend tests on notched beams, materials and structures, 18 (1985) 287–290. doi: 10.1007/bf02498757. [17] rovnaník, p., šimonová, h., topolář, l., bayer, p., schmid, p., keršner, z., carbon nanotube reinforced alkaliactivated slag mortars, construction and building materials, 199 (2016) 223–229. doi: 10.1016/j.conbuildmat.2016.05.051 [18] diamond, s., huang, j., interfacial transition zone: reality or myth? in: a. katz, a. bentur, m. alexander, g. arligue, (eds.) rilem second international conference on the interfacial transition zone in cementitious composites, e & fn spon, new york, (1998) 3–39. [19] acker, p., micromechanical analysis of creep and shrinkage mechanisms. in: f.j. ulm, z.p. bažant, f., wittman, (eds.) creep, shrinkage and durability mechanics of concrete and other quasi-brittle materials, elsevier, oxford, uk, (2001) 15–25. [20] sorelli, l., constantinides, g., ulm, f.j., toutlemonde, f., the nano-mechanical signature of ultra high performance concrete by statistical nanoindentation techniques, cement and concrete research, 38 (2008) 1447– 1456. doi: 10.1016/j.cemconres.2008.09.002 [21] knésl, z., a criterion of v-notch stability, int j fracture, 48 (1991) r79–r83. << /ascii85encodepages false /allowtransparency false /autopositionepsfiles true /autorotatepages /none /binding /left /calgrayprofile (dot gain 20%) /calrgbprofile (srgb iec61966-2.1) /calcmykprofile (u.s. web coated \050swop\051 v2) /srgbprofile (srgb iec61966-2.1) /cannotembedfontpolicy /error /compatibilitylevel 1.4 /compressobjects /tags /compresspages true /convertimagestoindexed true /passthroughjpegimages true /createjobticket false /defaultrenderingintent /default /detectblends true /detectcurves 0.0000 /colorconversionstrategy /cmyk /dothumbnails false /embedallfonts true /embedopentype false /parseiccprofilesincomments true 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can be opened with acrobat and adobe reader 5.0 and later.) >> /namespace [ (adobe) (common) (1.0) ] /othernamespaces [ << /asreaderspreads false /cropimagestoframes true /errorcontrol /warnandcontinue /flattenerignorespreadoverrides false /includeguidesgrids false /includenonprinting false /includeslug false /namespace [ (adobe) (indesign) (4.0) ] /omitplacedbitmaps false /omitplacedeps false /omitplacedpdf false /simulateoverprint /legacy >> << /addbleedmarks false /addcolorbars false /addcropmarks false /addpageinfo false /addregmarks false /convertcolors /converttocmyk /destinationprofilename () /destinationprofileselector /documentcmyk /downsample16bitimages true /flattenerpreset << /presetselector /mediumresolution >> /formelements false /generatestructure false /includebookmarks false /includehyperlinks false /includeinteractive false /includelayers false /includeprofiles false /multimediahandling /useobjectsettings /namespace [ (adobe) (creativesuite) (2.0) ] /pdfxoutputintentprofileselector /documentcmyk /preserveediting true /untaggedcmykhandling /leaveuntagged /untaggedrgbhandling /usedocumentprofile /usedocumentbleed false >> ] >> setdistillerparams << /hwresolution [2400 2400] /pagesize [612.000 792.000] >> setpagedevice microsoft word numero_51_art_37_2551 c. anselmi et alii, frattura ed integrità strutturale, 51 (2020) 486-503; doi: 10.3221/igf-esis.51.37 486 focussed on fracture and damage detection in masonry structures 3d limit analysis of masonry pavilion domes on octagonal drum subjected to vertical loads c. anselmi, f. galizia university of naples “federico ii”, department of structures for engineering and architecture, italy anselmi@unina.it, fgalizia@unina.it e. saetta sapienza university of rome, department of structural and geotechnical engineering, italy e.saetta@virgilio.it abstract. within the framework of limit design applied to masonry structures, this paper aims at analyzing the different behavior of a pavilion dome according to the adopted construction and reinforcement technologies. by using the static theorem applied to the dome discretized in rigid macroblocks of variable shape aligned along parallels and meridians, a mathematical model has been constructed in order to search for the load collapse multiplier, and thus to evaluate the degree of structural safety. then, the associated failure mechanism is represented at the instant in which the collapse is reached. the program implementing the model is sufficiently versatile and, in addition to the mechanical characteristics, allows to define the intrados profile, the thickness variability, as well as to insert any window opening in the drum, the lantern at the top and the hoops at each level. the results shown here are concerned with some numerical applications carried out on a theoretical dome, as well as with a preliminary analysis of the dome of santa maria del fiore in florence by brunelleschi. keywords. masonry; dome on octagonal drum; limit analysis; no-tension material; yield surface. citation: anselmi, c., galizia, f., saetta, e., 3d limit analysis of masonry pavilion domes on octagonal drum subjected to vertical loads, frattura ed integrità strutturale, 51 (2020) 486-503. received: 26.06.2019 accepted: 12.12.2019 published: 01.01.2020 copyright: © 2020 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. introduction ithin the framework of limit design applied to masonry structures, this paper aims at analyzing the different behavior of a pavilion dome according to the adopted construction and reinforcement technologies; for example, if in correspondence of the ribs the bricks of the contiguous sails are well interlocked (as in the santa w http://www.gruppofrattura.it/va/51/2551.mp4 c. anselmi et alii, frattura ed integrità strutturale, 51 (2020) 486-503; doi: 10.3221/igf-esis.51.37 487 maria del fiore dome) the dome shows a much greater load-bearing capacity compared to the case of interlocking between the bricks completely missing (santa maria dell’umiltà dome in pistoia). in several previous works [1, 2, 3, 4] the authors had already dealt with rotation domes subject to vertical and horizontal loads; by using the static theorem of the limit analysis applied to the dome discretized in rigid macro-blocks of variable shape aligned along the parallels and the meridians, several optimization models have been implemented in order to search for the load collapse multiplier, thus to evaluate the degree of structural safety. it should be noted that many different modelling approaches in the literature were used to investigate the behaviour of masonry constructions, and particularly of domes. among those, it is worth mentioning the works by o’dwyers on the funicular analysis of masonry vaults [5], and those using analytical and finite element models [6, 7, 8, 10, 11, 12]. rigid block models based on limit analysis and contact dynamics were also adopted [9, 13]. in the previously papers, as in this, the yield domain conditions for the quadrilateral interfaces between the macro-blocks are expressed in terms of stress resultants, in observance of the following mechanical assumptions: inability to carry tension, unlimited or limited compressive strength (in the second case the domain is suitably linearized), frictional sliding with dilatancy. this last hypothesis, even if not realistic, has been assumed because in some cases the influence of failure for sliding is negligible in the kinematic mechanism of the domes; that allows us to base the formulation on simple optimization problems rather than more involved nonlinear analyses, with considerable reduction of computational costs. the yield domain conditions for the quadrilateral interfaces between the macro-blocks are expressed in terms of stress resultants, in observance of the following mechanical assumptions: inability to carry tension, unlimited or limited compressive strength (in the second case the domain is suitably linearized), frictional sliding with dilatancy. this last hypothesis, even if not realistic, has been assumed because in some cases the influence of sliding failure is negligible in the kinematic mechanism of the domes; that allows us to base the formulation on simple optimization problems rather than more involved nonlinear analyses, with considerable reduction of computational costs. it should be pointed out that the sliding failure was taken into account assuming a friction coefficient fc = 0.75. this value is perhaps excessive when compared with those taken by other authors in the most recent literature [14, 15, 16, 17] where, for different materials, coefficients varying from 0.63 to 0.69 are used. however, even when a value included into that range is taken into account, the results static and kinematic are almost identical to those which are here presented (at least for the tested cases 7 and 11 of tab. 1). furthermore, analyzing the response even in the case of a further reduction in the friction coefficient, it was found that the result remains unchanged up to the value fc = 0.2 0.22 for which the value of the collapse multiplier decreases and the kinematic mechanism shows an evident failure for sliding. finally, for fc = 0.18 0.20 there is a further reduction of the multiplier, but the collapse mechanism is qualitatively equivalent. compared to previous tackled problems, in this work there are two new aspects: a different type of dome, because it is set on octagonal and not circular drum, and the role played by the interlocking between the bricks in correspondence of the ribs on the bearing capacity of the dome. as we consider vertical loads, we studied a dome segment corresponding to one sixteenth between two contiguous meridian symmetry planes (fig. 1). in this context, we have developed a program through excel and its solver to solve the static optimization problem that provides the collapse multiplier. once the collapse multiplier has been defined, again using excel, the corresponding kinematic problem is implemented to represent the failure mechanism at the instant in which the collapse is reached. in order to simulate the lack of interlocking between the bricks at the ribs or its presence, an advantageous aspect in the present modeling is that the yield conditions on the related interfaces of the macro-blocks can be either introduced (the failure is possible) or not (the failure is not possible). although for the considered application cases has always been used a discretization in only eight macro-elements (six for the dome and two for the drum), the program implemented in excel appears sufficiently versatile and, in addition to the mechanical characteristics, allows to define the intrados profile, the thickness variability, as well as to insert any window opening in the drum, the lantern at the top and the hoops at each level. some results of application cases are shown and, finally, a first approach was made to the analysis of the santa maria del fiore dome in florence, built by brunelleschi. of course, models with reduced block dimensions could be implemented to take into account failure mechanisms which were not considered in the present work. however, it should be noted that the configuration of the macro-blocks taken into consideration aimed at reproducing the main features of the crack patterns which are frequently observed on masonry domes, such as those investigated in this manuscript. as the authors pointed out in the manuscript, such crack patterns usually involve the ribs and the webs along radial and meridian interfaces which correspond to the ones considered in the model that was presented. however, it is clear that further analysis could be carried out to investigate the effect of interlocking and block size on the obtained failure mechanism. c. anselmi et alii, frattura ed integrità strutturale, 51 (2020) 486-503; doi: 10.3221/igf-esis.51.37 488 preliminary and geometric features ince only vertical loads are considered, a dome segment has been studied corresponding to a sixteenth between two contiguous meridian planes of symmetry, one passing through the center line of a sail, the other for a rib (fig.1a). in the horizontal section of the dome, the angle between the two symmetry planes is π/8, and the segment can be studied at least in this first approach as fixed at the drum base and subject to dead loads due to their own weight and live loads corresponding to increasing overloads, as well as to the actions on the interfaces belonging to the symmetry planes, which are the redundant unknowns of the static problem. with regard to a dome segment of amplitude = /8 (fig. 1b), a discretization in rigid blocks is made, each one bounded by two consecutive cross-sections i and i+1 defined by the angles θi and θi+1 respectively with the dome’s z-axis (fig. 1c). symmetry plane of a sail symmetry plane passing for a rib x y π/8 (a) x z y (b) (c) φ=π/8 φ=π/8 o x z θi θi+1 (c) figure 1: the dome segment. (a) the two contiguous meridian symmetry planes; (b) 3d view; (c) section in the x-z plane. the generic block like this defined have six faces: two of them named radial lying on the aforesaid radial cross-sections i and i+1, two other named meridian lying on meridian symmetry planes, and finally two other again lying on the extrados and intrados surfaces of dome respectively (fig. 2). j ce i+1 1 2 3 7 8 6 4 5 le i+1 meridian face j (1-2-4-3) meridian face j+1 (5-6-8-7) radial face i (1-2-6-5) radial face i+1 (3-4-8-7) extrados face (1-5-7-3) intrados face (2-6-8-4) figure 2: the generic block have been used two reference: the fixed one (o, x, y, z), to define the vertices coordinates of generic block (fig.1), and a local one (gf , n, r, t) placed in gf centroid of each contact interface with a contiguous block (fig.3a), to define the stress resultants interacting through this generic interface, as shown below. s c. anselmi et alii, frattura ed integrità strutturale, 51 (2020) 486-503; doi: 10.3221/igf-esis.51.37 489   (a) (b) x y z o rj nj ri gj gi gj+1 gi+1 ri+1 nj+1 ni+1 nitj rj+1 ti+1 ti tj+1 nj nnj mrj gj gi g p tj ni ti mtj nni mni mritri tti mti ri rj x y z o figure 3: (a) fixed and local references; (b) own weight p acting in the g centroid of block and stress resultants applied on the i radial face and on j meridian face. forces acting on the single block ith reference to fig. 3b, the generic block is subjected to the own weight p applied on its center of gravity g, and to the stress resultants applied on the centroid of each contact interface with a contiguous block, referred to the local reference n, r and t. the resultants on the radial interfaces are six, named normal force nn (or simply n), shear forces tt and tr, twist moment mn, bending moments mt and mr, respectively applied on the interfaces i and i+1. whereas, on the meridian interfaces j and j+1, lying on symmetry planes, the resultants are only three: the normal force nn and the two bending moments mt and mr . with reference to i and j interfaces, all these forces can be expressed in matrix form by the si and sj vector respectively:                                  i i i i i i x i x i x i r t n r t n )13( )13( )16( m m m t t n m r s                           j j j )x( j )x( j )x( j r t n 12 11 13 m m n m r s besides, must be consider the overload acting on the dome named ol understood as a covering load applied in the centroid of extrados face (see fig. 2), that in the present formulation increases through a collapse multiplier α(fig. 4a). if a lantern is present at the top of dome, also a force pl corresponding to one sixteenth of the lantern own weight will act on the block top (fig. 4b), together with the oll overload related to the small dome of the lantern (also increasing through the α multiplier). (a) (b) x y z o ge ∙ol pl oll figure 4: (a) the overload acting on the dome, increasing through an α multiplier(b) the force on the block on top corresponding to one sixteenth of the lantern own weight, together with the overload (which also increases through αacting to the small dome of the lantern. w c. anselmi et alii, frattura ed integrità strutturale, 51 (2020) 486-503; doi: 10.3221/igf-esis.51.37 490 finally, if hoops are inserted, the possible action of them is represented by a fh force applied on extrados face, lying in a plane parallel to the dome springing and oriented towards the inside. having fixed a suitable nh pretension effort, the resultant force fh = nh· tan(/8) is positioned at half the height with respect to the height of the generic parallel ring with hoop (point c in fig. 5). x y z o c fh nh nh fh fh π/8 π/8 fh fh π/8 π/8 nh nh z b a c x fh d ht za zb zc=(za+zb)/2 (a) (b) (c) figure 5: force depending by the hoop. (a) the resultant force fh; (b) nh pretension effort and fh resultant force; (c) level of c application point of fh force. equilibrium conditions for the single block he equilibrium conditions for the generic block, in the global reference frame x, y and z are so formulated: 0fffsdscybxa  eeeeeeeeeee 1h010  (1) where ea and eb are (6x3) matrices of the coefficients of the redundant unknowns ex and ey on the meridian interfaces j and j+1 respectively, listed in (3x1) vectors, while ec and ed are (6x6) matrices of the unknowns e0s and e 1s on the radial interfaces i and i+1 respectively, listed in (6x1) vectors; e0f is the (6x1) vector of the dead loads, e hf is the (6x1) vector of the possible action of the hoop, and e1f the (6x1) vector of the live load increasing through the α collapse multiplier it is necessary to specify that, in the problem under examination, only the unknowns 1s remain on the radial faces, because the 0s ones are zero on the face of the block at the top and, as regards to every other block, they coincide with the unknowns 1s of the i+1 face of the previous block. yield domains for the generic interface ith reference to a generic quadrilateral interface (fig.6), the six stress resultants on generic radial interface i+1 have to respect the yield conditions related to rocking and sliding domains; whereas, on generic interfaces j and j+1 lying on meridian symmetry planes, the stress resultants only are three (the normal force and the two bending moments) and just have to respect the conditions related to rocking domain. in the following, linearized yield domains circumscribing the actual nonlinear ones are shown. t w c. anselmi et alii, frattura ed integrità strutturale, 51 (2020) 486-503; doi: 10.3221/igf-esis.51.37 491 t gr figure 6: generic quadrilateral interface and local reference linear rocking yield domains for the case of unlimited compression strength, a linear yield domain was proposed in [3, 4] with reference to the quadrilateral section of fig. 7; within a coherent kinematic mechanism, the rotation axis has to coincide with one of the four section sides, so we imposed four limit conditions: 0mnd  iii (2) with di (fig.7a) distance between the g centroid and the generic side i (i=1, 2, 3, 4), and ii km m , being ttrr mm kkm  the cartesian expression of the bending moment m (fig.7b). k3 d4          d3 d1 k2 k4 k1 g d2 (a) mr di k i m t gr mi mt (b) figure 7: the quadrilateral interface. (a) geometric aspect; (b) mechanical aspect. these conditions define four planes passing through the origin o of the 3d-reference (mt, mr, n), that form the pyramid of fig. 8, having cross section homothetic to the quadrilateral interface (coincident with the linear domain proposed in [18] starting by a different formulation). mr o′ mt o mr mt n (a) mr o mt (b) figure 8: yield domain. (a) the four planes through the origin o; (b) cross section. as the present paper only consider vertical loads, here we have assumed a limited compression strength of the masonry; in order to include a limit to the compressive stress into domain of fig. 8, we have added four planes parallel to n-axis of the 3d-reference (mt, mr, n), and four other planes forming an opposite pyramid passing through the q point at abscissa n=n0, being n0 the limit normal force applied in the g centroid which leads the entire section to the collapse. this linear yield domain results circumscribed to the approximate nonlinear one proposed in [18], where an additional quadratic term c. anselmi et alii, frattura ed integrità strutturale, 51 (2020) 486-503; doi: 10.3221/igf-esis.51.37 492 on n was enclosed to take into account the limited compression strength. we note that the cross section of the two domains coincide at abscissa n=n0/2 (fig. 9, referred to the (m1, m2, n) 3d space, being m1 and m2 the components of m in the section principal reference). the twelve planes are summarized by the following equations: 0)k(km)k(kmnd ttrr  iiii (3) 04nd)k(km)k(km 0ttrr  /iii (4) 0nd)k(km)k(kmn-d 0ttrr  iiiii (5) being i the generic side (i=1, 2, 3, 4).   domain in [4] domain proposed [3] m2 m1 in [4]  (a) (a) m1 m2 no q (b) domain proposed domain in [5]domain in [18] figure 9: yield domain for rocking in the 3d space (m1, m2, n). (a) cross section at n=n0/2.; (b) 3d view (axonometric projection) of linearized yield domain proposed and the approximate non linear one proposed in [18]. if in the eqns. (3)-(5) the sign (=) is replace with (≤), the conditions for n, mr and mt that define the linearized yield domain are obtained. linear sliding yield domains as mentioned above, the twelve conditions (3)-(5) related to rocking domain are necessary for all the interfaces, while further conditions related to sliding domain (fig.10) must be added about radial interfaces.   tgφ tgφ φ φ o tt (or tr, or mn) n figure 10: yield domain for sliding. in particular, the yield domain normal force n – shear force t is defined by a cone (fig.11a), with axis coinciding with the naxis has been opportunely replaced, in this first approach, by a pyramid circumscribed to the cone having four faces. therefore we impose four conditions making reference to the cartesian components tt and tr of t shear force: c. anselmi et alii, frattura ed integrità strutturale, 51 (2020) 486-503; doi: 10.3221/igf-esis.51.37 493 0tntan t0  (6) 0tntan r0  (7) thus, in fig. 10,  coincide with the angle of friction 0. g d3 r d4 d1 d2 k3 k2 k4 k1(a) (b) φ0 n tr tt φ0 figure 11: yield domain for sliding. (a) yield domain normal force n shear force t; (b) yield domain normal force n twisting moment mn, "equivalent" circular section. instead, for the yield domain normal force n twisting moment mn reference was made to an "equivalent" circular section having radius r equal to the mean of the distances of g by the sides of quadrilateral section (fig.11b): )ddd(d 4321  41 r (8) therefore two conditions are imposed: 0mnrtan n03 2  (9) being, in the yield domain by sliding of fig. 10, tanφ = ⅔ r tanφ0. in matrix form, the conditions on the generic meridian interface and on radial one can be expressed respectively by: 0tnxdy  mfmfmfx mf (10) 0tnsdy  rfrf1 rf s rf (10′) where mfy is a (12x1) vector, mfxd is a (12x3) matrix of the coefficients of the redundant unknowns mfx (that is )f( jx or 1)f( jy on the meridian faces j and j+1 respectively), listed in (3x1) vector, while mftn is a (12x1) vector of known terms. moreover rfy is a (18x1) vector, rfsd is a (18x6) matrix of the only rf 1s unknowns on the radial faces i+1, listed in a (6x1) vector, while rftn is a (18x1) vector of known terms. governing equations of whole structure and assessment of the collapse multiplier  amed m the number of balance equations for whole structure and n the number of the unknowns on the interfaces, in matrix form we have: 0ffax  1α (11) where a is a (mxn) matrix of the coefficients of the unknowns x on the interfaces, listed in the (nx1) vector, while f is the (mx1) vector of the dead loads and of the possible actions of the hoops, and 1f the (mx1) vector of the live load increasing by the unknown collapse multiplier α n c. anselmi et alii, frattura ed integrità strutturale, 51 (2020) 486-503; doi: 10.3221/igf-esis.51.37 494 moreover, named d the number of the yield domain conditions, in matrix form we have: 0tnxdy  (12) where y is a (dx1) vector, d is a (dxn) matrix and finally tn is a (dx1) vector of known terms. now the static theorem of limit analysis can be applied to evaluate the collapse multiplier αby implementing the following problem of mathematical optimization: maximize α subject to: (13) 0ffax  1α (balance equations) 0tnxdy  (yield domain conditions) 0α (not negativity of α) being x and α the unknowns of the problem. reconstruction of the collapse mechanism nce the unknowns α and x have been defined through the static theorem of the limit analysis (paragraph 5), is possible pursue the kinematic problem to identify the corresponding collapse mechanism. the unknowns of problem are: (mx1) vector u which collects the degrees of freedom, six for every block of the discretized structure; (nx1) vector δ which collects the possible displacements between the interfaces (six for every radial interface and three for every meridian one); (dx1) vector λ which collects the generalized strain rates associated to the yield conditions y (eq.12). these unknowns are bounded by kinematic conditions: δua t (14) and by the flow rule λdδ t (15) from which, by eliminating δ, we obtain the compatibility conditions: 0λdua  tt (16) being ta and td the transposed matrices of a and d respectively (defined in paragraph 5). if we denote with δxufuf tt1 t v αl  the virtual work done by the forces through the associated displacements and by the stress resultants through the mutual displacements between the interfaces, the problem of mathematical optimization is set in the following way: it is imposed 0l v  subject to: (17) 0λdua  tt (compatibility conditions) 0λ  (not negativity of λ) once solved the problem (17), the kinematic mechanism is represented at the instant in which the collapse is reached through suitable matrices of directional cosines. o c. anselmi et alii, frattura ed integrità strutturale, 51 (2020) 486-503; doi: 10.3221/igf-esis.51.37 495 results he above described discrete model has been implemented by using excel and its solver. although for the considered application cases has always been used a discretization in only eight macro-elements (six for the dome and two for the drum), the implemented program appears sufficiently versatile and, in addition to the mechanical characteristics, allows to define the intrados profile, the thickness variability, as well as to insert any window opening in the drum, the lantern at the top and the hoops at each level. once the collapse loads multiplier has been found, through the introduction of appropriate matrices of directional cosines and taking advantage of the symmetry, the program provide the collapse mechanism of a quarter of a dome, represented through axonometric and zenithal views, and a section. in order to test the validity of the procedure, was considered a single dome with the same geometric and mechanical characteristics, and was analyzed the effect on the load-bearing capacity of the following features: (a) lack/presence of interlocking between the bricks at the ribs; (b) hoops in the case of possible failure at the ribs; (c) absence/presence of window openings in the drum; (d) drum width. the dome examined have the following geometric and mechanical characteristics: the internal angular profile sa is a sixth of an acute fifth horizontal internal semi diameter his = 11.5 m thickness on top s0 = 1.5 m thickness at base plane of dome si = 1.5 m thickness of drum st = 1.5 ÷ 2.5 m drum height ht= 8 m height window opening hf= 6 m half-width window opening lf= 2 m lantern radius rl = 2 m lantern weight on a segment of dome pl= 100 kn limit compressive strength σ0 = -4000 kn/m2 friction coefficient fc= 0.75 masonry density γm= 18 kn/m3 density of covering material (as overload) γc= 10 kn/m3 pre-tension force of a single hoop nh = 200 kn the numeric results (multiplier α) are summarized in the tab. 1 and compared in tab. 2. case failure at ribs lf (m) nh (kn) st (m) α 1 no 0 0 1,5 24.129 2 no 2 0 1,5 14.224 3 no 0 0 2,5 32.374 4 no 2 0 2,5 29.112 5 yes 0 0 1,5 7.567 6 yes 0 400 1,5 10.211 7 yes 2 0 1,5 3.168 8 yes 2 400 1,5 7.624 9 yes 0 0 2,5 17.621 10 yes 0 400 2,5 18.857 11 yes 2 0 2,5 13.046 12 yes 2 400 2,5 14.342 table 1: examined cases. t c. anselmi et alii, frattura ed integrità strutturale, 51 (2020) 486-503; doi: 10.3221/igf-esis.51.37 496 features compared cases increase % decrease % (a) 1-5 68.637 (a) 2-7 77.73 (a) 3-9 45.570 (a) 4-11 55.188 (b) 5-6 34.940 (b) 7-8 140.693 (b) 9-10 7.012 (b) 11-12 9.936 (c) 1-2 41.049 (c) 3-4 10.074 (c) 5-7 58.141 (c) 9-11 25.964 (d) 1-3 34.171 (d) 2-4 104.672 (d) 5-9 132.853 (d) 7-11 311.843 table 2: compared cases.   no fa ilure a t ribs 0 2 4 6 8 10 12 14 16 0 200 400 600 800 1000 1200 1400 al ph a nh diagram alpha vs nh (lf=2m) fa ilure a t ribs a lpha vs nh   0 5 10 15 20 25 30 0 0,5 1 1,5 2 2,5 a lp h a lf diagram alpha vs lf (st=1,5m) fa ilure a t ribs no fa ilure a t ribs 0 5 10 15 20 25 30 35 1,5 2 2,5 3 3,5 a lp h a st diagram alpha vs st (lf=2m) fa ilure a t ribs no fa ilure a t ribs figure 12: variability of αmultiplier as a function of nh, lf and st. fig. 12 shows the variability of α multiplier as a function of nh, lf and st parameters. furthermore, some compared cases of tab. 2 are shown in the following subparagraph 7.1 together with the relative collapse mechanisms. finally, in subparagraph 7.2, some results obtained by examining the most famous pavilion dome in the world, that of s. maria del fiore by brunelleschi in florence, are illustrated. some compared cases with relative collapse mechanisms we refer to compared cases shown in bold in tab. 2. only for practical display reasons the comparisons relating to the four features listed above with (a), (b), (c) and (d) will be illustrated below in order (c), (a), (b) and (d). as previously mentioned, figs. 13-17 show the collapse mechanism of a quarter of a dome, represented through axonometric and zenithal views, and a section. c. anselmi et alii, frattura ed integrità strutturale, 51 (2020) 486-503; doi: 10.3221/igf-esis.51.37 497 feature (c): absence/presence of window openings in the drum with reference to the cases 1 and 2 shown in bold in tab. 1, for the dome analyzed without failure at ribs and without windows (case 1 shown in fig.13) the multiplier α is equal to about 24, while with a window the value decreases to about 14 (case 2 shown in fig.14). figure 13: collapse mechanism for case 1 (no failure at ribs / lf=0 / nh=0 / st=1.5 / multiplier α=24.129) figure 14: collapse mechanism for case 2 (no failure at ribs / lf=2 / nh=0 / st=1.5 / multiplier α=14.224) feature (a): lack/presence of interlocking between the bricks at the ribs; for the same dome with window (case 2 shown in fig.14) in case of possible failure at ribs the multiplier value decreases from 14 to about 3 (case 7 shown in fig.15). c. anselmi et alii, frattura ed integrità strutturale, 51 (2020) 486-503; doi: 10.3221/igf-esis.51.37 498    figure 15: collapse mechanism for case 7 (failure at ribs / lf=2 / nh=0 / st=1.5 / multiplier α=3.168) feature (b): hoops in the case of possible failure at the ribs; for the same case 7 shown in fig.15 with possible failure at ribs, if you introduce 2 hoops the α value increases to about seven and half (case 8 shown in fig.16).   figure 16: collapse mechanism for case 8 (failure at ribs / lf=2 / nh=400 / st=1.5 / multiplier α=7.624) feature (d): drum width. finally, if instead of introducing the hoops (fig.16), the thickness of the drum is increased from 1.5 to 2.5 meters, the α value increases from about 3 (case 7 shown in fig.15) to about 13 (case 11 shown in fig.17). c. anselmi et alii, frattura ed integrità strutturale, 51 (2020) 486-503; doi: 10.3221/igf-esis.51.37 499   figure 17: collapse mechanism for case 11 (failure at ribs / lf=2 / nh=0 / st=2.5 / multiplier α=13.046) the case of s. maria del fiore to validate the optimization program developed in excel, also on a actual dome, a first approach was made to the analysis of the most famous dome on octagonal drum: the one built by brunelleschi for the cathedral of florence between 1420 and 1436, of which numerous researchers have dealt [19-22]. obviously as has already been done by other authors who have carried out various types of analysis it is assumed that the drum is a regular octagon, and with it also the dome; this allows us to study only one sixteenth of the dome, as for the theoretical one examined above. actually, compared to the theoretical model assumed, the octagonal dome shows some irregularities concerning geometry and static behavior: the sides have different lengths each-other, the drum rests alternately on four solid walls (inclined at 45° with respect to the axis of the nave) and on four ogival arches (two parallel to the axis of the nave and two to that of the transept), with a consequent different crack pattern, also determined from the different structural elements that surround it. moreover, the architectural reliefs carried out over the centuries present notable differences between them. to overcome the uncertainties related to the dimensions of some elements that characterize the structure, we have taken the dimensions assumed by m. como [19] using some rounding done by g. conti [20]. in the excel program, which for the dome (excluding the drum) provided a discretization in six elements, an further block was introduced on top, at the base of the lantern, in analogy to what was done by como [19], while the other 30 voussoirs of its discretization have been incorporated by us, in groups of 5, into our 6 blocks. however, despite using the average value of the unit weight of the brick masonry assumed by him, we have taken into account the different unit weight of the portions of masonry made of sandstone present both in the part at the base of the dome and in the ring on top, named serraglio. anyway, the weight of the dome (including the lantern) estimated by us is 29,272 t, quite close to the value reported by other scholars. the hypothesis that, despite the octagonal form, brunelleschi have built a rotational dome (and therefore without the use of a supporting framework), remained secret for 500 years, but in recent times shared by all the most recent scholars of masonry structures, starting by di pasquale [21], supports the conviction that in correspondence of the ribs there is a continuity of masonry texture, with good interlocking between the bricks. this has allowed us to introduce the assumption that in the (j+1) faces (see fig.2) of the blocks of the analyzed segment belonging to the meridian plane passing through the rib there is no failure. furthermore, having the purpose of making a comparison with the pressure curve shown by como [19], that starting from the top of the dome involves the whole upper part of the drum, 13 meters high, we had to make a second modeling. in fact, the limitation imposed by the program implemented in excel just two blocks to discretize the drum led us to c. anselmi et alii, frattura ed integrità strutturale, 51 (2020) 486-503; doi: 10.3221/igf-esis.51.37 500 adopt a different modeling of the oculus (circular hole). however, as for the first modeling, the same horizontal maximum width of 5.8 meters assumed in [19] as average diameter was utilized: modeling 1 (later called mod1). the oculus has been modeled with a hexagonal shape, but the drum is not considered in all its height, because the basic section of our calculation model was placed in the horizontal plane that cuts in half the aforementioned oculus. to this plan belong the faces (i+1) (fig.2), i.e. those that have the smallest area and are therefore more prone to crushing failures. modeling 2 (later called mod2). to be able to consider the whole upper part of the drum, the oculus has been modeled with a lozenge shape having vertical axis equal to the height of the drum (13 m), and the horizontal one equal to 5.8 m. the mechanical and geometrical characteristics assumed for the dome are listed below in tabs. 3 and 4. mechanical data values and units of measure friction coefficient fc 0.75 masonry density γm 18.5 kn/m3 sandstone density γs 25 kn/m3 density of covering material (as overload) γc 10 kn/m3 limit compressive strength σ0 -4000 kn/m2 lantern weight on a segment of dome pl 469 kn table 3: mechanical data of s. maria del fiore dome. geometric data in the plane passing from ribs dimensions (m) in the plane that cuts the sails dimensions (m) heights and other dimensions (m) outer diameter 54 49.88 internal diameter 45 41.57 radius of arch pointed-fifth 36 dome thickness at the base 4.5 4.15 outside diameter of the lantern base 7 6.47 drum thickness 5 4.6 dome height 35.75 drum height for mod1 7.5 height of the drum upper block for mod1 4.6 height of the drum lower block for mod1 2.9 drum height for mod2 13 height of the drum upper block for mod2 7.5 height of the drum lower block for mod2 5.5 average diameter of the oculus 5.8 table 4: geometric data of s. maria del fiore dome. with the program implemented in excel, for mod1 and mod2, three different analyses were performed: (1) the classical one already applied to the theoretical dome (see previous sub-paragraph 7.1); (2) a similar analysis but applied to the dome in the current state, taking into account the cracks already present; (3) a comparison between the pressure curve obtained from m.como and shown in [19] and those obtained with mod2. more precisely, as regards points (1) and (2), the value of the collapse load multiplier obtained is the same, so this value can provide an indication, even if approximate, about the safety of the actual dome subject to vertical loads. on the other hand, the almost coincident values obtained with mod2 are justified by the fact that, as for the mod1, the failure occurs by crushing at the lower area section, corresponding to interface between the two blocks of the drum, belonging to the plane c. anselmi et alii, frattura ed integrità strutturale, 51 (2020) 486-503; doi: 10.3221/igf-esis.51.37 501 that cuts the oculus in half. mod2 involves a slight increase in the volume of the oculus with a consequent slight decrease in the weight of the drum blocks, and this leads to the negligible growth of the α multiplier value. finally, with regard to point (3), for a slice of dome equal to 1/8 of the entire dome, corresponding to a single sail of the dome subjected to its own weight and to that of the lantern on top, in [19] is shown the construction of the pressure curve that, starting from the upper end of the section of the voussoir at the crown, is tangent to the intrados of the dome near the haunches, and intercepts the center of the section at the drum base (fig.20a). instead, still using the program implemented in excel, which analyzes a segment equal to 1/16 of the dome, two similar pressure curves were obtained using two different objectives in the optimization problem: for the first, it was imposed that the multiplier has value zero, in compliance with the condition that the curve intercepts the center of the section at the base of the drum (fig.20b); for the second, it was imposed that the horizontal thrust transferred from the dome to the drum assumes the value of 2000 kn, in accordance with that of 400 t estimated by como [19] (fig.20c). the results of the analyses referred to in points (1) and (2) are summarized in tab. 5 (in it the ratios wc1/wa1 and wc2/wa2 provide indicative coefficients on collapse safety), while the most significant collapse mechanisms are shown in figs. 18 and 19. instead, for the comparison referred to in point (3), the pressure curve in [19] and those obtained in this paper pursuing two different objectives are shown in fig. 20. dome slice analysis mod1  multiplier actual weight wa1(kn) weight at collapse wc1 (kn) ratio wc1/wa1 mod2  multiplier actual weight wa2(kn) weight at collapse wc2 (kn) ratio wc2/wa2 without and with cracks 30.096 23,900 122,621 5.131 30.226 27,272 126,419 4.635 table 5: comparison between the values obtained with mod1 and mod2 figure 18: collapse mechanism of s. maria del fiore dome (mod1) figure 19: collapse mechanism of s. maria del fiore dome (mod2) c. anselmi et alii, frattura ed integrità strutturale, 51 (2020) 486-503; doi: 10.3221/igf-esis.51.37 502   (a) (b) (c) figure 20: comparison between our pressure curves and that of como [19]. (a) curve in [19]. (b) curve obtained by imposing that it intercepts the center of the section at the drum base. (c) curve obtained by imposing the thrust assumes the value referred in [19]. obviously, the simplicity of the proposed model, sufficient to successfully compare the answers obtained with those expected based on the experience, does not allow a comparison to be made between the solution obtained for brunelleschi's dome and that provided by the model illustrated in [13]. the latter, having a more dense discretization, allows the insertion of the vertical elements of the herringbone and to obtain crises due to sliding, even if with very low values of the friction coefficient. conclusions ithin the framework of limit analysis applied to masonry structures, this paper has aimed at analyzing the different behavior of a pavilion dome according to the adopted construction and reinforcement technologies. by using the static theorem applied to the dome discretized in rigid macro-blocks of variable shape aligned along parallels and meridians, a mathematical model has been constructed in order to search for the load collapse multiplier, so to evaluate the degree of structural safety. then, the associated failure mechanism is represented at the instant in which the collapse is reached. the excel program that implement the modeling is sufficiently versatile and, in addition to the mechanical characteristics, allows to define the intrados profile, the thickness variability, as well as to insert any window opening in the drum, the lantern weight on top and hoops at each level. the so far carried out applications, in the case of possible failure at the ribs, have shown the effectiveness of the hoops, that increases as the pre-tensioning stress increases or, alternatively, according to hoops number placed; however, for an reasonable overall force of pre-tensioning, the value of the multiplier obtained is anyway inferior to that computed in the case of a good interlocking between the bricks at the ribs. for the dome discretization into six blocks, the introduction of the hoops also seems to produce better effects if it’s concentrated at the fifth ring starting from the top, rather than if distributed over several rings, for the same overall pre-tensioning force. the applications have also confirmed the effect of window openings in the drum: the value of the collapse multiplier decreases as the openings width increases. as further developments, in addition to using the present excel program to investigate other aspects, such as the problem of the double-shell domes and the search for the minimum thickness of the pavilion domes, the authors are implementing a matlab program, also eventually reducing the macroblocks size in order to refine the solutions already obtained and to study also the pavilion domes under horizontal loads. obviously, the aim is to extending these new analyses also to the dome of santa maria del fiore in florence and compare to this dome the one of santa maria dell'umiltà in pistoia, apparently similar, in which, instead, cracks at the ribs appeared already during its construction. the comparison between the two different construction methods of the two domes (with and without interlocking between the bricks at ribs), could provide confirmation that, when it is assumed that there are no cracks at ribs, it follows that the two half-segments w c. anselmi et alii, frattura ed integrità strutturale, 51 (2020) 486-503; doi: 10.3221/igf-esis.51.37 503 in contact along a rib constitute a single block. a similar assumption has been considered also by foraboschi [22] to analyse the behaviour of the brunelleschi dome. references [1] anselmi, c., de rosa, e. and fino, l. (2004). limit analysis of masonry structures, proceedings of the 4th international seminar on structural analysis of historical constructions (edited by: c. modena, p. b. lourenço, p. roca), padova, italy 1, pp .545–550. [2] anselmi, c., de rosa, e., galizia, f. and maniello, d. (2006). evaluation of the safety coefficient of axi-symmetric masonry domes with drum and lantern having variable profile and carrying their own weight, proceedings of the seventh international masonry conference, london, gb 5, pp. 1–6. [3] anselmi, c., de rosa e. and galizia, f. (2009). evaluation of horizontal collapse for a rigid dome supported by radial masonry columns subjected to own weight. in: w.w. el-dakhakhni, r.g. drysdale. proceedings of the eleventh canadian masonry symposium, toronto, ontario, canada, may 31–june 3, pp. 543-550. [4] anselmi, c., de rosa, e., galizia, f. and maniello, d. (2009). limit analysis of masonry domes subjected to horizontal loads, protection of historical buildings prohitec 09 (edited by f.m. mazzolani), rome, italy 2, pp. 10971101. [5] o’dwyer, d. (1999). funicular analysis of masonry vaults, comput. struct., 73(1-5), pp. 187-197. [6] pavlovic, m., reccia, e. and cecchi, a. (2016). a procedure to investigate the collapse behavior of masonry domes: so-me meaningful cases, int. j. archit. herit., 10(1), pp. 67-83. [7] baggio, c., and trovalusci, p. (2016). 3d limit analysis of roman groin vaults, proc. 16th international brick and block masonry conference (ibmac 2016) padova (italy), pp. 1023-1028. [8] li, t. and atamturktur, s. (2013). fidelity and robustness of detailed micromodeling, simplified micromodeling, and macromodeling techniques for a masonry dome, journal of performance of constructed facilities, 28(3), 480-490. [9] casapulla, c., mousavian, e. and zarghani, m. (2019). a digital tool to design structurally feasible semi-circular mason-ry arches composed of interlocking blocks, comput. struct., 221, pp. 111-126. [10] velilla, c., alcayde, a., san-antonio-gómez, c., montoya, f.g., zavala, i. and manzano-agugliaro, f. (2019). rampant arch and its optimum geometrical generation, symmetry, 11(5), art. no. 627. [11] olmati, p., gkoumas, k. and bontempi, f. (2019). simplified fem modelling for the collapse assessment of a masonry vault, frattura ed integrita strutturale, 13(47), pp. 141-149. [12] simon, j. and bagi, k. (2016). discrete element analysis of the minimum thickness of oval masonry domes, int. j. archit. herit., 10(4), pp. 457-475. [13] beatini, v., royer-carfagni, g. e tasora, a. (2019). a non-smooth-contact-dynamics analysis of brunelleschi’s cupola: an octagonal vault or a circular dome? meccanica, 54 (3), pp. 525-547. [14] lourenço, p.b. e ramos, l.f. (2004). characterization of cyclic behavior of dry masonry joints, journal of structural engineering, 130(5), pp. 779-786. [15] casapulla, c. and portioli, f. (2016). experimental tests on the limit states of dry-jointed tuff blocks, materials and structures, 49(3), pp. 751-767. [16] vasconcelos, g. and lourenço, p.b. (2009). experimental characterization of stone masonry in shear and compression, construction and building materials, 23(11), pp. 3337-3345. [17] lee, h.s., park, y.j., cho, t.f. and you, k.h. (2001). influence of asperity degradation on the mechanical behaviour of rough rock joints under cyclic shear loading, international journal of rock mechanics and mining sciences, 38(7), pp. 967-980. [18] orduña, a. and lourenço, p. (2005). three-dimensional limit analysis of rigid blocks assemblages. part i: torsion failure on frictional interfaces and limit analysis formulation, international journal of solids and structures, 42 (18-19), pp. 5140-5160. [19] como, m. (2017). statics of historic masonry constructions, third edition, springer, 4.11, pp. 242-271. [20] conti, g. (2014). la matematica nella cupola di santa maria del fiore a firenze, in ithaca: viaggio nella scienza, n. 4, anno 2014 arte e scienza, pp. 5-11. [21] di pasquale, s. (2002). brunelleschi. la costruzione della cupola di santa maria del fiore. marsilio, venice. [22] foraboschi, p. 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/hrv (za stvaranje adobe pdf dokumenata najpogodnijih za visokokvalitetni ispis prije tiskanja koristite ove postavke. stvoreni pdf dokumenti mogu se otvoriti acrobat i adobe reader 5.0 i kasnijim verzijama.) /hun 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/pdfxoutputintentprofileselector /documentcmyk /preserveediting true /untaggedcmykhandling /leaveuntagged /untaggedrgbhandling /usedocumentprofile /usedocumentbleed false >> ] >> setdistillerparams << /hwresolution [2400 2400] /pagesize [612.000 792.000] >> setpagedevice microsoft word numero_62_art_02_3579.docx b. kebaili et alii, frattura ed integrità strutturale, 62 (2022) 14-25; doi: 10.3221/igf-esis.62.02 14 effect of parent concrete strength on recycled concrete performance bachir kebaili civil engineering laboratory (lgc), badji mokhtarannaba university, p. o. box 12, 23000 annaba, algeria ba_kebaili@hotmail.com, https://orcid.org/0000-0001-7017-4071 mohammed benzerara civil engineering laboratory (lgc), badji mokhtarannaba university, p. o. box 12, 23000 annaba, algeria materials, geomaterials and environment laboratory (lmge), department of civil engineering, badji mokhtarannaba university, p. o. box 12, 23000 annaba, algeria mohammed.benzerara@univ-annaba.dz, mohammed.benzerara@yahoo.com souad menadi, nadia kouider, redjem belouettar civil engineering laboratory (lgc), badji mokhtarannaba university, p. o. box 12, 23000 annaba, algeria smenadi2000@yahoo.fr, kouider.nadia23@gmail.com, r.belouettar@yahoo.fr abstract. reusing concrete wastes as a secondary aggregate might be an efficient solution for long-term environmental protection and sustainable development. however, the different properties of waste concrete, particularly compressive strengths might have a negative impact on recycled concrete. the main purpose of this experimental investigation is to evaluate the influence of parent concrete quality on recycled concrete performance. three categories of compressive strength (10 to 15 mpa), (20 to 25) mpa, and (30 to 40 mpa) are used to complete this assignment. as a random parameter, an unknown compressive strength was also incorporated. the experimental mix contains 40% secondary aggregates (both coarse and fine) and 60% natural aggregates. to achieve the necessary workability, the significant water absorption properties of recycled concrete aggregate necessitate water content adjustment. as a result, the compressive strength of recycled concrete decreases by 14 to 23.7 percent when compared to conventional concrete. to compensate for this loss, a quantity of cement content deemed to be absorbed by porous attached mortar equal to 4% of the weight of the recycled aggregate was added. the results show that the strength qualities of the original concrete have only a little impact on the compressive strength of the recycled concrete. when crushed, low compressive strength parent concrete produces a considerable volume of fine aggregate and a high proportion of clean recycled coarse aggregates with less attached mortar and has the same compressive strength as excellent parent concrete. in comparison, cement content adjustment does not enhance flexural strength; this appears to be due to a weak interface zone between the aggregate and the old adhering mortar. citation: kebaili, b., benzerara, m., menadi, s., kouider, n., belouettar, r., effect of parent concrete strength on recycled concrete performance, frattura ed integrità strutturale, 62 (2022) 14-25. received: 06.05.2022 accepted: 15.07.2022 online first: 24.07.2022 published: 01.10.2022 copyright: © 2022 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. https://youtu.be/tqzh7pmoize b. kebaili et alii, frattura ed integrità strutturale, 62 (2022) 14-25; doi: 10.3221/igf-esis.62.02 15 keywords. recycled concrete; waste recovery; environment; aggregates; mechanical behavior. introduction lgeria is now undergoing a massive development program that includes nearly one million new homes, basic infrastructure, and a 1200 km east-west motorway [1,2]. this task necessitates the use of massive volumes of raw materials in concrete, road construction, and engineering fill, which harms the natural environment [3,4]. concrete debris, which is generated by the demolition of old buildings and seismic disasters, has somehow been overlooked as a source of aggregate [5]. this waste is disposed as trash. fig. 1 shows an uncontrolled landfill rubble discharge that affects the natural landscape. figure 1: uncontrolled concrete waste dumping (annaba, algeria). reusing concrete waste as substitute aggregates would be a feasible solution to the aforementioned challenges, as well as a strategy to protect the environment by allowing for far more effective use of natural resources. construction waste consumption in algeria is 5%, with the remaining disposed of, providing a management and environmental policy issue [6]. the primary aim of this study is to show the potential benefits of employing concrete waste in the production of concrete. recycled concrete aggregate (rca) exhibited a wide variety of properties when compared to natural aggregate (na). the percentage of rca employed in concrete manufacturing varies from 25% to 100%; this range of replacement has been used to generate excellent recycled concrete. the substitution of natural aggregates by recycled aggregates in the production of fresh concrete provides a new aggregate supply while also allowing for the conservation of natural resources [6,7]. when 100 percent rca was employed, the loss was determined by [8] to be decreased by roughly 20–25 percent when compared to normal concrete. other research [7] observed a similar trend for strength to decline by roughly 8% when strength exceeds 60mpa. according to [9] the rca has a high level of water absorption due to the porosity induced by the attached mortar, absorbing up to 8%. as a result, the rca need more water to be as usable as na. when crushed, rca from low strength concrete has less attached mortar than rca from high strength concrete as seen by [10]. when compared to na, the increase in water content associated to rca's porosity is thought to be responsible for the loss of compressive strength [11]. the water absorption coefficient may differ from the free water absorption calculated in the laboratory, and the pores of recycled aggregate are most likely filled with cement paste during mixing. this might result in an excess of water in the mixture [12]. even when the fraction of coarse rca replacement approaches 80 percent, structural concrete may be produced [10]. some efficient and easy approaches, such as adjusting the water-cement ratio, aggregate water content, mixing technique, and additive [13], can enhance the concrete within a given range. furthermore, increasing the cement content in recycled aggregate concrete (rac) by around 6.2 percent without affecting the w/c ratio results in compressive strength and consistency comparable to that of ordinary concrete [14]. they also observed that compressive strength loss was just approximately 2.5 percent and 0.4 percent lower. according to [15], when rac is mixed, a thin layer of cement slurry is generated on the surface, which penetrates through the porous attached mortar and fills cracks and voids. in the flexure strength it was found that the crack originated not just at the interfaces of the recycled aggregates and the mortar, but also at the rca themselves [16]. some studies revealed that the compressive strength of rac decreased with a b. kebaili et alii, frattura ed integrità strutturale, 62 (2022) 14-25; doi: 10.3221/igf-esis.62.02 16 the degree of aggregate replacement [17]. as a substitute, the rca raises the water absorption coefficient [18]. it has also been examined to utilize recycled fine aggregate (rfa) instead of natural sand. according to published research, the high porosity of rfa may influence the rac's long-term durability. for a 100 percent replacement, the compressive strength drops by up to 30% [19]. replacement levels ranging from 30% to 60% rfa showed minimal effect on rac characteristics [20]. the increased porosity of the rca can be mitigated by maintaining a consistent water-cement ratio (w/c) and adding a plasticizing admixture [21]. the rca, according to the findings, had the same properties as the na. few studies have explored the influence of recycled aggregate ra derived from parent concrete (pc). the results for 28-day nominal cube crushing strengths of 20 mpa, 40 mpa, and 60 mpa indicated that the grade of initial concrete had no effect on mechanical features, despite all of them reporting lesser strength than the concrete created just with na [22]. few researchers investigated rac made from various pc strengths and discovered that the reduction in compressive strength of concrete achieved by adding rca derived from a low concrete was greater than the drop observed for rac derived from an excellent concrete. the flexural strength of concrete 25 and 50 percent replacement of natural fine aggregate by rfa was similar after 28 and 56 days, but at 75 and 100 percent replacement, the flexural strength was lower than conventional concrete [23]. the 28-day flexural strength of rac produced by substituting 50% and 100% of coarse na with rca revealed a 7.5– 13.8 percent drop for 100% [20]. when rca is employed, compressive and flexural strength drop, however the reduction is less pronounced in low strength concrete than in stronger concrete [12]. using rca composed of concrete with strength of 50 mpa resulted in concrete compressive and tensile strengths equivalent to natural coarse aggregate [24]. a good amount of concrete waste may be recycled; however it is worth considering whether it is essential to classify concrete waste based on compressive strength before usage. this will result in a difficult, if not impossible, procedure. the primary goal of this experimental investigation is to establish if a concrete mixture design integrating recycled concrete aggregates derived from varying strength parent concrete as a replacement for raw aggregates may achieve appropriate performance for structural purposes. experimental program he recycled aggregates were obtained from laboratory grade concrete that had not yet been utilised. the specimen was kept in an open room for preservation. the rca was produced by testing until demolishing various concrete test specimens 16x32 cm² of unknown age, but over than six months, (fig. 2). the compressive strength was measured as the failure of cylindrical concrete specimens in the compression-testing machine, and sorted according to their compressive strength. the pc crushed as described before, exhibited a wide range of compressive strength with lower and higher limits ranging from 10 to 40 mpa. three pc strength classes arrangement were considered, (10 to 15) mpa, (20 to 25) mpa and (30 to 40) mpa. three pc grades were established: (pc15), (pc25), and (pc40), which are described as low, up to 15mpa, normal, up to 25 mpa, and excellent concrete, up to 40 mpa, as is typical for concrete in algeria. as an arbitrary rca, an unknown pc strength was also put into the investigation. figure 2: test specimen crushed as concrete waste. t b. kebaili et alii, frattura ed integrità strutturale, 62 (2022) 14-25; doi: 10.3221/igf-esis.62.02 17 crushing of concrete as indicated in fig. 3, the damaged concrete was crushed to sizes smaller than 25 mm using a small jaw crusher. the aggregates were separated by size via mechanical sieving, providing the 03 rca proportions, fine (0/5) mm and coarse (5/10), (10/20) mm. the resulting rca were heterogeneous, consisting of natural coarse aggregate with attached mortar as seen in fig. 4. . figure 3: jaw crusher apparatus and the machine in operation. figure 4: produced recycled concrete aggregates fine and coarse. figure 5: fine crushed mass of parent concretes. mass of fine recycled aggregates when pc is crushed, each class generates a different amount of rfa. the quantity of rfa in pc15 is more than in pc25 and pc40. because the bond between mortar and aggregate is weaker in low pc crush, most of weak attached mortar was separated from the aggregate, which is hardly removed by mechanical sieving. 21,5% 17,6% 15,5% 0% 5% 10% 15% 20% 25% pc15 pc25 pc40 f in e  c ru sh e d  m a ss  ( % )  parent concrete  b. kebaili et alii, frattura ed integrità strutturale, 62 (2022) 14-25; doi: 10.3221/igf-esis.62.02 18 because of the strong link between aggregate and attached mortar, the quantity of attached mortar grows as pc strength increases. as a result, the mass of fine particle formed in the form of rfa is substantially higher for aggregates produced from low pc than for aggregates produced from normal and excellent pc fig. 5. after sieving, the rca from pc15 are slightly cleaner and contain less attached mortar. apparent density the main distinction between na and rca is the attached mortar. it has a porous structure and a low bulk density. the rca made from high-quality concrete had the most attached mortar. as pc strength grows, so does bulk density (fig. 6). except in the case of low pc, the rca has less attached mortar and an apparent density that is fairly equivalent to rca derived from excellent parent concrete. this property influences other characteristics such as specific density, porosity, and strength. figure 6: apparent density of recycled aggregates. water absorption coefficient the capacity of rca and na to absorb water distinguishes them (nf en 1097-6) [25]. in reality, it is related to the quantity of attached mortar, and it must be analysed in order to compare the diverse rca obtained from different pc. the absorption capacity is another key property that determines the characteristics of both fresh and hardened concrete. the proportion of water absorption increases when the strength of the pc from which the recycled aggregate is produced increases, due to a large amount of attached mortar in rca obtained from higher strength pc, as shown in fig. 7. this attached mortar is more porous, which increases rca's water absorption capacity. because of that, water content must be adjusted to get the necessary workability. in contrast, as the amount of attached mortar decreases, so does the water absorption, which is most likely for low pc. the grading curve incorporating 40% rca and 60% na, including rfa, was obtained for each pc category. the study team assumed that 40% was a suitable quantity to maximize usage without impacting other concrete qualities. the grading size analysis enabled the concrete mix to be evaluated using the bolomey dosages method [13], with a desired slump range from 50 to 70 ±10 mm as a plastic concrete. the mix design was developed for the second phase of concrete testing; rca and na, taking into account varied water/cement ratios. the compressive strength objective was 20 mpa, as specified by the algerian seismic standard [26]. concrete mix the cement-water ratio was adjusted to generate a plastic concrete slump in the mix. four rac categories were investigated: rac15, rac25, and rac40, which were derived from pc15, pc25, and pc40, respectively, and rac for unknown recycled aggregates. tab. 1 displays the mix proportions obtained using the bolomey dosage method. the cement content amount of cem.ii 42.5 was 350 kg/m3. 1 1,05 1,1 1,15 1,2 1,25 1,3 1,35 1,4 na (5/10) na (10/20) rca15 (5/10) rca15 (10/20) rca25 (5/10) rca25 (10/20) rca40 (5/10) rca40 (10/20) a p p a re n t  d e n si ty  ( g /c m 3 ) recycled aggregates b. kebaili et alii, frattura ed integrità strutturale, 62 (2022) 14-25; doi: 10.3221/igf-esis.62.02 19 figure 7: water absorption capacity. figure 8: grading size analysis. categories fa na (5-10) na (10-20) rfa rac (5-10) rac (10-20) cement w/c kg rac15 418 172 482 279 114 321 350 0.65 rac25 0.7 rac40 0.65 rac 0.7 nc 697 286 803 0.5 table 1: amount of aggregate, cement and water. 0% 1% 2% 3% 4% 5% 6% 7% 8% 0 5 10 15 20 25 30 35 w a te r  a b so rp ti o n  c a p a ci ty  ( % ) time (min) na5/10 na10/20 rca15 5/10 rca15 10/20 rca25 5/10 rca25 10/20 rca40 5/10 rca40 10/20 0% 10% 20% 30% 40% 50% 60% 70% 80% 90% 100% 0,01 0,1 1 10 c u m u la ti v e  u n d e rs iz e d   p a rt ic le s  si ze  m a ss  ( % ) particles size (mm) fra ra10 ra20 fna na20 na10 b. kebaili et alii, frattura ed integrità strutturale, 62 (2022) 14-25; doi: 10.3221/igf-esis.62.02 20 the trial mix concrete was required to comply with the nf p 480-1 standard [27], and the consistency was assessed using the nf en 12350 standard slump test [28]. the slump test results for all recycled aggregate concrete, rac15, rac25, rac40, rac and nc, varied between 50 and 70 mm, confirming the assumption of plastic concrete. for the same workability, the w/c ratio was higher for the rac than for conventional concrete; this was mostly attributed to the porosity of recycled aggregate and the nature of attached mortars with their larger absorption coefficient. in this manner, 12 specimens were cast in 10x10x10 cm3 and 10x10x40 cm3 for compression and flexural testing for each type of mix. the specimens were made on a shaking table in accordance with the nf p18-422 standard [29]. a comparison is done with a na for a minimum compressive strength objective of 20 mpa, which is typical for construction applications. mechanical behaviour under the nf p18-405 [30], tests on the four categories of rac and nc were conducted at 28 days, with the specimens conserved and covered by a plastic tray to avoid moisture loss. the compression test was carried out on a calibrated 500 kn hydraulic press at a constant speed in accordance with the standard nf en 12390-3 [31]. three-point bending tests were performed on 10x10x40 cm3 specimens to assess the flexural strength characteristics using a hydraulic press with a capacity of 150 kn in accordance with the standard nf en 12390-5 [32]. results and discussion compressive strength hen recycled coarse aggregates are employed, the strength of rac15, rac25, and rac40 decreases; the drop in compressive strength was 23% for pc25 and 15% for pc15 and pc40. this finding is analogous to that of etxeberria m et al [8]. this loss is due to water absorption; the rac requires more water than the nc to attain the same workability. when tested, tabsh sami w et al [11] observed that the porosity of attached mortar affects the compressive strength. also, the bond between the coarse aggregate and the old attached mortar, which was impacted by the crushing machine when it was made, appears to be accountable for that loss. the reduction in rac compressive strength was less severe when the pc was low. the strength decrease was around 16.0 percent, which is the same as excellent pc. contrary to expectations, the compressive strength of rac is not related to the grade of pc [21]. when the pc has a lower strength, the rac has the same characteristics as when the pc is excellent. this can be explained by the old mortar-aggregate bond; with pc40, the bond was stronger than with pc25. whereas the rac strength obtained from pc15 dropped at the same rate as the compressive strength produced from pc40. the loss in rac resulting from unknown pc strength was 10.34 percent, as shown in fig. 9. figure 9: compressive strength of recycled and normal concrete before the mix correction. 10 12 14 16 18 20 22 24 nc rcpc15 rcpc25 rcpc40 rc c o m p re ss iv e  s tr e n g th  ( m p a ) concretes w b. kebaili et alii, frattura ed integrità strutturale, 62 (2022) 14-25; doi: 10.3221/igf-esis.62.02 21 further analysis was required to clarify this experimental distinction of the assertion that more pc has lower compressive strength; hence, the impact on the rac strength will be negative. the coarse aggregates formed while crushing pc15 are more like natural aggregates since the bond between the mortar and aggregates is weak. the interface was significantly cleaner, with less adhered mortar, as noticed by [5], which increased the bond in the new mix. as a consequence, the compressive strength of the rac significantly increased. according to the comparative study of the findings obtained from different rca, the percentage reductions in compressive strength for the rac15; rac40 were roughly 16 percent, but this depletion was 23.7 percent for the rac25. in contrast to prior research [16], which linked rac strength to parent concrete strength, this claim was seen for rac generated from strong pc, despite the fact that the results were obtained without using a low concrete as low as 15 mpa. it is observed that for unknown pc, the compressive strength drops by less than 13.9 percent. as a result, the impact of the rca's origins may be less substantial than originally thought. the necessity of sorting concrete waste according to compressive strength, which may make reuse of concrete waste practically more difficult, is unnecessary. statistical analysis of concrete test results is important for understanding the concrete failure stress; the strength characteristic may be reliable by using the standard deviator to assess the dispersion of this data to evaluate the strength characteristic and to compare different concrete tab. 2. table 2: strength characteristics for different rac. rac's strength properties were slightly different. the amount and quality of attached mortar determine the strength of rac. the standard deviator, which demonstrates the disparity of compressive strength is greater for rac than nc, might be a source of confusion due to the heterogeneous and variable quality of the recycled aggregates. the standard deviation was minimal in all concretes. when compared to the target concrete, the findings obtained for recycled concrete demonstrate that the pc strength characteristic has a minimal influence on the compressive strength of the rac. thus, it may be argued that rca can be reused without regard for their origin and without sorting. it may also be claimed that unknown pc has the same compressive strength, which confirms the previous conclusion. concrete mix correction the study was done to describe a way to improve the compression strength of rac as a regular concrete, which would most likely be employed as structural concrete. because of the attached mortar, the rca has a higher superficial porosity, which affects the rac compressive strength. when the concrete is mixed, a certain quantity of cement powder is supposed to be absorbed by these pores [14], requiring the addition of extra water to maintain the same workability. we may suppose that pores contribute to a drop in cement content as well; as a result, compressive strength diminishes proportionate to the rate of replacement. after 10 minutes, the differential porosity between the na and rca was determined to approximate the cement powder ratio roughly absorbed by the clear porosity of the rca. this may be the time it takes to mix the concrete fig. 8. this trend can be used as a basis for cement content adjustment. given that the rca porosity was determined to be 5.90%, meanwhile the na porosity was 1.90%. the apparent porosity of the rca is defined as the difference between the two porosities. this permitted for the consideration that the difference between the absorption coefficients of the rca and the na is the loss of cement content, which filled the attached mortar pore at the start of the mix. the addition of cement content, roughly 4 percent of the weight of the rca, is probably acceptable to improve the compressive strength of the rac. using the same proportions and adding 4% of the weight of the rca introduced in the mix, a new recycled aggregate concrete corrected (racc) mix was created. tab. 3 displays the modified mix proportions. when the cement amount is adjusted to increase the strength of the concrete, the cement water ratio for the racc drops, and the slump test on the revised mix showed a slump between 70 and 90 mm. this new mix performed was tested under the same conditions as the previous recycled concrete. the results demonstrate that the extra cement content enhanced compressive strength, as seen in fig. 10. n° 1 2 3 4 5 6 7 8 9 10 average deviator fc mpa loss % nc 23.76 23.88 23.88 23.88 24.24 24.96 25.20 25.44 25.68 25.80 24.67 3.35 23.32 0.00 rac15 21.20 20.16 20.64 20.88 21.00 21.12 21.36 21.48 22.32 24.48 21.46 5.59 19.50 16.40 rac25 18.36 18.60 18.60 18.60 18.96 18.96 18.96 19.20 19.56 21.12 19.09 4.15 17.79 23.70 rac40 22.30 20.40 20.40 20.40 20.52 21.72 21.84 21.84 21.96 23.64 21.50 4.98 19.75 15.30 rac 20.16 20.88 21.00 21.60 21.60 21.96 22.98 22.92 23.04 23.88 21.95 5.17 20.09 13.90 b. kebaili et alii, frattura ed integrità strutturale, 62 (2022) 14-25; doi: 10.3221/igf-esis.62.02 22 table 3: amount of aggregate, cement corrected and water. figure 10: compressive strength for normal and recycled corrected concrete after the mix correction. figure 11: flexural strength for normal and recycled concrete before and after mix correction. this method might be used to adjust the rac mix prepared with a different recycled aggregate by using simply the absorption coefficient of each component. as can be seen, the racc standard deviator was more than the na. the racc has a higher average strength than na, although the standard deviator reveals that racc is still more various. flexural strength 10 12 14 16 18 20 22 24 26 28 nc rccpc15 rccpc25 rccpc40 rcc c o m p re ss iv e  s tr e n g th  ( m p a ) concretes 4,10 3,85 3,18 3,65 3,39 4,71 4,19 3,21 3,71 3,51 0 1 2 3 4 5 nc pc15 pc25 pc40 up f le x u ra l  st re n g th  ( m p a ) concretes normal corrected categories fa na (5-10) na (10-20) rfa rac (5-10) rac (10-20) cement w/c kg racc15 418 172 482 279 114 321 350+4%.rac 0.6 racc25 0.65 racc40 0.6 racc 367 0.65 nc 697 286 803 0.5 b. kebaili et alii, frattura ed integrità strutturale, 62 (2022) 14-25; doi: 10.3221/igf-esis.62.02 23 the results reveal that flexural strength increases for nc and racc15 but is very moderately influenced for racc25, racc40, and unknown parent concrete corrected racc. when an amount of cement content is supplied, the changes in flexural strengths indicated in fig.11 enhance the bond between the aggregate for nc and pc15 due to the characteristic stated above, racc15, are cleaner with less attached mortar. the cracked surface in the other cases revealed that the majority of failures in parent concrete occurred near the interface between the old attached mortar and the aggregate. the weaker interface zones in racc impact failure, as observed in pc25 and pc40, where adding cement content has little effect. conclusions he results show that the strength qualities of the parent concrete have only a little influence on the compressive strength of the recycled concrete. furthermore, when crushed, low compressive strength parent concrete produces a significant volume of fine aggregate and a high proportion of recycled coarse aggregates with less attached mortar and the same compressive strength as excellent parent concrete. from a methodological point of view, the analyses of the obtained outcomes of the experimental test program have revealed five main issues.  low compressive strength concrete, when crushed, generates more amounts of fine recycled aggregates and gives recycled coarse aggregates more clean with less attached mortar than normal and excellent parent concrete.  for the same workability, the w/c ratio in rac is more essential than na, but less critical than rac25 for rac15 and rac40. this has an effect on the compactness of concrete, resulting in a lower rac25 compressive strength..  for a given target mean strength, the obtained strength increases with pc quality, as well as with low compressive strength; due to less attached mortar.  the percentage loss in compressive strength due to 40% recycled aggregate replacement is between 15 and 25%, however the offset in strength can be reduced by correcting the cement content by about 4% of the weight of recycled concrete aggregate replacement.  flexural strength is unaffected by cement content adjustment, which appears to be related to interface weakness between aggregate and attached mortar. nomenclature fna : fine natural aggregate. na : natural aggregate. nc : natural concrete. na20 : natural aggregate up to 20 mm. na10 : natural aggregate up to 10 mm. na (5/10) : natural aggregate fractions 5 to 10 mm. na (10/20) : natural aggregate fractions 10 to 20 mm. pc : parent concrete. pc15 : parent concrete 15 mpa. pc25 : parent concrete 25 mpa. pc40 : parent concrete 40 mpa. rfa : recycled fine aggregate. rca : recycled concrete aggregate. rca15 (5/10) : recycled concrete aggregate from pc15 fractions 5 to 10 mm. rca15 (10/20) : recycled concrete aggregate from pc15 fractions 10 to 20 mm. rca25 (5/10) : recycled concrete aggregate from pc25 fractions 5 to 10 mm. rca25 (10/20) : recycled concrete aggregate from pc25 fractions 10 to 20 mm. rca40 (5/10) : recycled concrete aggregate from pc40 fractions 5 to 10 mm. rca40 (10/20) : recycled concrete aggregate from pc40 fractions 10 to 20 mm. rac : recycled aggregate concrete. rac15 : recycled aggregate concrete from pc15. rac25 : recycled aggregate concrete from pc25. t b. kebaili et alii, frattura ed integrità strutturale, 62 (2022) 14-25; doi: 10.3221/igf-esis.62.02 24 rac40 : recycled aggregate concrete from pc40. racc : recycled concrete corrected. racc15 : recycled concrete corrected from pc15. racc25 : recycled concrete corrected from pc25. racc40 : recycled concrete corrected from pc40. w/c : water-cement ratio. acknowledgments he authors would like to thank lgc-civil engineering laboratory, badji mokhtar annaba university (annaba, algeria) who provided facilities for conducting the various tests in the laboratory. references [1] benzerara, m., guihéneuf, s., belouettar, r., perrot, a. (2021). combined and synergic effect of algerian natural fibres and biopolymers on the reinforcement of extruded raw earth, constr. build. mater., 289, pp. 123211. [2] rahim, o., achoura, d., benzerara, m., bascoulès-perlot, c. (2022). experimental contribution to the study of the physic-mechanical behavior and durability of high-performance concretes based on ternary binder (cement, silica fume and granulated blast furnace slag)., frat. e integrita strutt., 16(59), pp. 344–358. [3] melais, s., bouali, m.f., melaikia, a., amirat, a. (2021). effects of coarse sand dosage on the physic-mechanical behavior of sand concrete, 56, pp. 151–159, doi: 10.3221/igf-esis.56.12. [4] djedid, t., mani, m., ouakouak, a., guettala, a. (2022). effect of varying silica-limestone sand fines on the physicalmechanical performance of concrete, frat. ed integrità strutt., 59(16), pp. 580–591, doi: 10.3221/igf-esis.59.38. [5] pani, l., francesconi, l., rombi, j., stochino, f., mistretta, f. (2020).the role of parent concrete in recycled aggregate concrete. international conference on computational science and its applications, pp. 368–378. [6] boudina, t., benamara, d., zaitri, r. (2021). optimization of high-performance-concrete properties containing fine recycled aggregates using mixture design modeling, frat. ed integrità strutt., 15(57), pp. 50–62, doi: 10.3221/igfesis.57.05. [7] agarwal, a., bhusnur, s., priya, t.s. (2020). experimental investigation on recycled aggregate with laboratory concrete waste and nano-silica, mater. today proc., 22, pp. 1433–1442. [8] etxeberria, m., vázquez, e., mari, a., barra, m. (2007). influence of amount of recycled coarse aggregates and production process on properties of recycled aggregate concrete, cem. concr. res., 37(5), pp. 735–742. [9] de juan, m.s., gutiérrez, p.a. (2009). study on the influence of attached mortar content on the properties of recycled concrete aggregate, constr. build. mater., 23(2), pp. 872–877. [10] etxeberria, m., mari, a.r., vázquez, e. (2007). recycled aggregate concrete as structural material, mater. struct., 40(5), pp. 529–541. [11] tabsh, s.w., abdelfatah, a.s. (2009). influence of recycled concrete aggregates on strength properties of concrete, constr. build. mater., 23(2), pp. 1163–1167. [12] de oliveira, m.b., vazquez, e. (1996). the influence of retained moisture in aggregates from recycling on the properties of new hardened concrete, waste manag., 16(1–3), pp. 113–117. [13] tam, v.w.y., tam, c.m., wang, y. (2007). optimization on proportion for recycled aggregate in concrete using twostage mixing approach, constr. build. mater., 21(10), pp. 1928–1239. [14] domingo, a., lázaro, c., gayarre, f.l., serrano, m.a., lópez-colina, c. (2010). long term deformations by creep and shrinkage in recycled aggregate concrete, mater. struct., 43(8), pp. 1147–1160. [15] rao, a., jha, k.n., misra, s. (2007). use of aggregates from recycled construction and demolition waste in concrete, resour. conserv. recycl., 50(1), pp. 71–81. [16] ghafoori, e., motavalli, m., zhao, x.-l., nussbaumer, a., fontana, m. (2015). fatigue design criteria for strengthening metallic beams with bonded cfrp plates, eng. struct., 101, pp. 542–557, doi: 10.1016/j.engstruct.2015.07.048. [17] xiao, j., li, j., zhang, c. (2005). mechanical properties of recycled aggregate concrete under uniaxial loading, cem. concr. res., 35(6), pp. 1187–1194. [18] khatib, j.m. (2005). properties of concrete incorporating fine recycled aggregate, cem. concr. res., 35(4), pp. 763–9. t b. kebaili et alii, frattura ed integrità strutturale, 62 (2022) 14-25; doi: 10.3221/igf-esis.62.02 25 [19] talamona, d., hai tan, k. (2012). properties of recycled aggregate concrete for sustainable urban built environment, j. sustain. cem. mater., 1(4), pp. 202–210. [20] matias, d., de brito, j., rosa, a., pedro, d. (2013). mechanical properties of concrete produced with recycled coarse aggregates--influence of the use of superplasticizers, constr. build. mater., 44, pp. 101–109. [21] bhat, j.a. (2021). effect of strength of parent concrete on the mechanical properties of recycled aggregate concrete, mater. today proc., 42, pp. 1462–1469. [22] eguchi, k., teranishi, k., nakagome, a., kishimoto, h., shinozaki, k., narikawa, m. (2007). application of recycled coarse aggregate by mixture to concrete construction, constr. build. mater., 21(7), pp. 1542–1551. [23] ahmed, s.f.u. (2014). properties of concrete containing recycled fine aggregate and fly ash, j. solid waste technol. manag., 40(1), pp. 70–78. [24] moghadam, a.s., omidinasab, f., abdalikia, m. (2021). the effect of initial strength of concrete wastes on the fresh and hardened properties of recycled concrete reinforced with recycled steel fibers, constr. build. mater., 300, pp. 124284. [25] nf en 1097-6. (2014). essais pour déterminer les caractéristiques mécaniques et physiques des granulats partie 6 : détermination de la masse volumique réelle et du coefficient d’absorption d’eau, eur. stand. afnor. [26] national earthquake engineering center cgs. (2003). algerian seismic design regulation rpa99/version 2003, d.t.r.-b.c-2.48. [27] nf en 480-1. (2014). adjuvants pour béton, mortier et coulis méthodes d’essais partie 1: béton et mortier de référence pour essais., eur. stand. afnor. [28] nf en 12350-2. (1999). essai pour béton frais. partie 2: essai d’affaissement, eur. stand. afnor. [29] nf p 18-422. (1981). bétons mise en place par aiguille vibrante, eur. stand. afnor. [30] nf p 18-405. (1981). confection et conservation des éprouvettes, eur. stand. afnor. [31] nf en 12390-3. (2000). essai pour béton durci partie 3: résistance à la compression des éprouvettes, eur. stand. afnor. [32] nf en 12390-5. 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can be opened with acrobat and adobe reader 5.0 and later.) >> /namespace [ (adobe) (common) (1.0) ] /othernamespaces [ << /asreaderspreads false /cropimagestoframes true /errorcontrol /warnandcontinue /flattenerignorespreadoverrides false /includeguidesgrids false /includenonprinting false /includeslug false /namespace [ (adobe) (indesign) (4.0) ] /omitplacedbitmaps false /omitplacedeps false /omitplacedpdf false /simulateoverprint /legacy >> << /addbleedmarks false /addcolorbars false /addcropmarks false /addpageinfo false /addregmarks false /convertcolors /converttocmyk /destinationprofilename () /destinationprofileselector /documentcmyk /downsample16bitimages true /flattenerpreset << /presetselector /mediumresolution >> /formelements false /generatestructure false /includebookmarks false /includehyperlinks false /includeinteractive false /includelayers false /includeprofiles false /multimediahandling /useobjectsettings /namespace [ (adobe) (creativesuite) (2.0) ] /pdfxoutputintentprofileselector /documentcmyk /preserveediting true /untaggedcmykhandling /leaveuntagged /untaggedrgbhandling /usedocumentprofile /usedocumentbleed false >> ] >> setdistillerparams << /hwresolution [2400 2400] /pagesize [612.000 792.000] >> setpagedevice microsoft word numero_37_art_2 c. madrigal et alii, frattura ed integrità strutturale, 37 (2016) 8-14 doi: 10.3221/igf-esis.37.02 8 focussed on multiaxial fatigue and fracture plastic flow equations for the local strain approach in the multiaxial case c. madrigal, a. navarro, c. vallellano dpto. ing. mecánica y fabricación, escuela técnica superior de ingeniería avda. camino de los descubrimientos, s/n. 41092, seville university of seville navarro@us.es abstract. this paper presents a system of plastic flow equations which uses and generalizes to the multiaxial case a number of concepts commonly employed in the so-called local strain approach to low cycle fatigue. everything is built upon the idea of distance between stress points. it is believed that this will ease the generalization to the multiaxial case of the intuitive methods used in low cycle fatigue calculations, based on hysteresis loops, ramberg‐osgood equations, neuber or esed rule, etc. it is proposed that the stress space is endowed with a quadratic metric whose structure is embedded in the yield criterion. considerations of initial isotropy of the material and of the null influence of the hydrostatic stress upon yielding leads to the realization of the simplest metric, which is associated with the von mises yield criterion. the use of the strain‐hardening hypothesis leads in natural way to a normal flow rule and this establishes a linear relationship between the plastic strain increment and the stress increment. keywords. low cycle fatigue; plastic flow rule; kinematic hardening; non-proportional loading; multiaxial fatigue introduction e are trying to develop a theory of cyclic plasticity which allows fatigue designers to make calculations for multiaxial loads in a way as similar as possible to which they do when using the well-known local strain methodology for uniaxial low cycle fatigue problems. we would like to define concepts that translate to multiaxial loadings in a simple manner the tools of that trade, namely, the use of the cyclic stress-strain curve and hysteresis loops, the invocation of the memory rule when hysteresis loops are “closed”, the extension of the neuber or esed rules to multiaxial loading, etc. we have found it useful to base our theory in the idea of distance between stress points and to calculate these distances by using the expression for the yield criterion [1-6]. the local strain method constitutes nowadays a standard tool for fatigue life predictions in many industries. it has been incorporated in commercial software [7, 8] and it is very well described in textbooks [9, 10]. the extension of the local strain method to the multiaxial case requires at least three main steps. the first one is the development of plastic flow rules which reproduce the way we operate with hysteresis loops, cyclic curves, memory effect and so on in the simple uniaxial case. the second step would be the development of multiaxial neuber-type rules for dealing with inelastic strains at notches. this relies heavily on the use of a theory of plasticity and hence on the previous step. there are already a w c. madrigal et alii, frattura ed integrità strutturale, 37 (2016) 8-14 doi: 10.3221/igf-esis.37.02 9 number of proposals in this respect [11, 12]. the third step is probably the most difficult and it is the area where more work has been invested so far: the multiaxial cycle counting and fatigue life criteria. there are too many of them to single any one out. a comparison of several criteria is provided in [13]. they need the stresses and strains as inputs and therefore they also depend on the two previous steps. we are concerned here with the first step. our theory does not make use of yield or loading surfaces that move about in stress space, a common ingredient of existing cyclic plasticity theories. it uses the concept of distance in a stress space endowed with a certain metric measurable from the yield criterion. the full mathematical details of the method have been given elsewhere [1-6] and we would just like here to provide a first insight of this idea of distance in the stress space and show some comparison with experimental results. to keep the discussion at the simplest possible level we will restrict the treatment given here to the case of combined tension and torsion loading. plastic strains calculations he local strain method revolves around a simplified description of the stress-strain behaviour. a very characteristic feature of the calculations of plastic strains in low cycle fatigue problems is the clear distinction between loading and unloading. in the uniaxial case, one speaks of loading when the stress goes up in the cycle of applied stress and of unloading when it goes down. during the first quarter of the very first cycle, we “move” along the cyclic curve (dashed line in fig. 1) until unloading starts, marking the first point of load reversal (point a). we then “depart” from the cyclic curve and switch to the hysteresis loop. after a while moving along the descending branch of the hysteresis loop another point of load reversal (point b) will be reached and we will leave the current branch of the loop being traversed and start a new branch going up, and so on. one of the key elements in the simulation of the   behaviour at a notch for variable amplitude loading is the correct application of the memory effect (see [9, chapters 12-14] and [10, chapter 5]), both for closing hysteresis loops and for switching the axes where neuber’s hyperbolas are drawn for each load excursion. this is shown to occur in fig. 1 as one moves, for example, from point d to point e. after reaching point e the strain is then decreased to point f, following the path determined by the hysteresis loop shape. upon re-loading, after reaching point ee', the material continues to point a along the hysteresis path starting from point d, proceeding just as if the small loop e-f-e had never occurred. the same thing happens in the loop b-c-b. as we will point out later on, this memory rule is a simplified representation of the so-called kinematic hardening. figure 1: uniaxial memory effect. t c. madrigal et alii, frattura ed integrità strutturale, 37 (2016) 8-14 doi: 10.3221/igf-esis.37.02 10 as can be seen, the application of the memory effect depends on a precise control of the distance or separation, in terms of stress, between the successive points of load reversal. thus, for example, when the stress is descending from c, the memory effect is invoked at b' when the distance between the current stress point and c becomes equal to the distance previously established between b and c. distances between stress peaks and valleys are kept in a stack for comparison and this kind of comparison (at the applied stress level) are really the basis of the cycle counting methods, such as the well-known rainflow algorithm. it is not at all clear how we can perform these checks in a multiaxial situation, where some of the components of stress may be increasing while others are decreasing. the question then is how we reckon distances in the multiaxial case and how we apply the memory effect. we have proposed a way to answer these questions by looking at the yield criterion in a particular way. the development of the theory is still ongoing and the reader interested in the rigorous derivation is directed to [1-6]. to put it in a nutshell, we believe the yield criterion defines the metric of the stress space and we show how to obtain all the equations of plasticity from this idea. the metric is the mathematical device that allows one to calculate distances and angles in a vector space, in the stress space in our case. how does it work? first, we treat the stress and strain tensors as vectors, just listing all the components in succession. let’s illustrate the procedure with a relatively simple example. consider a tension-torsion experiment: a thin-walled cylindrical specimen is subjected to combined tension and torsion under strain controlled conditions. there are only two components of the stress vector σ different from zero in this case, the longitudinal stress  and the shear stress  . let’s assume the material follows the von mises yield criterion. the mises yield locus is a circle of radius 2k or 2 3 y in the deviatoric plane, where k and y denote the yield stresses in pure shear and uniaxial tension (or compression) respectively (see [14, p. 62]). then, we define the magnitude of the stress vector in the following way, which allows us to say simply that yielding begins when the length or magnitude of the stress vector attains the critical radius   2 2 2 2 2 3 σ (1) we notice that we are not using the usual euclidean norm in eq. (1), for the coefficients of this quadratic form, which is what it is called the metric1 of the space, are not equal to unity. mathematically, this signals that our space is not euclidean, which means, loosely speaking, that the basis vectors are not orthogonal. they form an oblique basis. we calculate angles between vectors by means of the familiar dot product, but we have to realize that with the metric chosen the rule is a little different from the usual one. thus for two stress vectors   1 1 1,σ and   2 2 2,σ ,      1 2 1 2 1 2 2 2 3 σ σ (2) and the angle  between the two vector follows from    1 2 1 2 cos σ σ σ σ (3) what about the plastic strain vector? do we use the same rule as in the stress case? not really, because plastic strain components are slightly different. look at the dot product in eq. (2). can we apply this to calculate the plastic work? the result would be:        2 2 3 pσ dε p ppdw d d (4) this is obviously not correct. the plastic work is simply 1 eq. 1 is really an integrated form of the metric since the metric is in fact defined in terms of differentials c. madrigal et alii, frattura ed integrità strutturale, 37 (2016) 8-14 doi: 10.3221/igf-esis.37.02 11     p ppdw d d (5) how come? remember the oblique basis business? when we have an oblique basis, we also have a reciprocal basis. the plastic strain components have to do with this reciprocal basis. in more precise mathematical terms, stresses and plastic strains behave as dual vector spaces. if we have a vector expressed in the original basis and another vector expressed in the reciprocal basis, since the vectors of both bases are, so to speak, orthogonal, then it turns out that their dot product has exactly the form given in eq. (5). thus everything is all right. so, finally, how do we calculate the magnitude of plastic strain vectors? one of the nice surprises of the mises’ metric in eq. (1) is that the rule for calculating the norm of the plastic strain vector turns out to be the usual euclidean formula:                           2 2 2 2 2 23( ) ( ) ( ) ( ) 2 2 2 ε p p p p p p p (6) please note that in the tension-torsion experiment, while there are only two components of the stress tensor different from zero ( and  ), there are more than two components of plastic strain that must be taken into account, for the hoop and the radial strains are not zero on account of the fact that plastic deformation preserves volume. so if  p is the axial plastic strain, the hoop and radial plastic strains both equal     2 p . this comes out nicely from the general equations given in [2-6]. the usual strain hardening hypothesis, which assumes that the radius of the mises circle (the so-called equivalent stress) is a function only of the generalized or equivalent plastic strain increment (see [14, p. 68]) now takes the form   σ ε ph d (7) where the integral is taken along the strain path starting at some initial state.   h is a function characteristic of the metal concerned that must be determined experimentally. it is usually a steadily increasing function, for most metals harden when deformed plastically. under this condition, the function   h has an inverse,  1   h whose derivative  φ   relates the length of plastic strain vector to the increment of the magnitude of the stress vector   φε σ σpd d (8) we call this new function,  φ σ the hardening modulus. it can be derived empirically from conventional uniaxial cyclic tests. this rule (8) implies that plastic deformation only occurs when there is a positive increment in the magnitude σ of the stress vector σ . that is, hardening only depends on the increment of the distance. this fact naturally leads to the normality flow rule. then, the strain increment vector is given by     φε ε n σ σ np pd d d (9) where n is the normal unit vector to the yielding surface, i.e., the iso-distance surface in our view, at the stress point. the normal vector is thus given by the gradient of the magnitude σ of the stress vector,      1 2 3 σ σ n (10) c. madrigal et alii, frattura ed integrità strutturale, 37 (2016) 8-14 doi: 10.3221/igf-esis.37.02 12    2 2 τ σ σ n (11) and it is easy to see that substituting back in (9) we obtain precisely the prandtl-reuss equations. now, situations where load reversals occur are obviously more complicated. we have found that the definition of distance, or rather separation, between stress points after load reversals, from the point of view of plasticity, must involve the angle formed by the lines joining the current stress point and the point of load reversal and this with the origin. however, given the introductory nature of this presentation, this will not be discussed here further. the reader is kindly directed to our last publication [6] to see how this leads to an alternative representation of kinematic hardening and how a multiaxial memory rule can be defined in a rather intuitive way. the flow equations derived can be seen to involve explicitly the points of reversal in each loading segment and there is no need to use yield surfaces moving around in stress space. everything is controlled by distance. application to experimental results his section discusses the application of the proposed model to experimental results reported by lamba and sidebottom [15] on a tubular specimen of oxygen-free high-conductivity (ofhc) copper subjected to combined tension and torsion. the specimen was used for investigating the subsequent strain hardening behaviour after shear strain cycling through the strain control program shown in fig. 2. the cyclic path sequence was 0-1-0-1-0-2-0-2-etc. all paths started at the crossing point, in the left top corner of the figure. prior to this strain history the specimen had been cycled under shear strain control until it cyclically stabilized and then along a 90° out-of-phase path until it restabilized. a comparison made between uniaxial and out-of-phase hardening cycling showed that the cyclic hardening produced by out-of-phase cycling was appreciable greater. figure 2: imposed strain history for the subsequent strain hardening experiment. (the cyclic path sequence was 0-1-0-1-0-2-0-2-etc). this experiment was employed by lamba and sidebottom [15] to show the erasure of memory effect observed if the material had been stabilized by 90° out-of-phase strain cycling. according to the authors, as long as the subsequent strain paths remain in the region enclosed by the out-of-phase cycling, one “big” strain cycle with the same or slightly lesser maximum strain as that imposed for the out-of-phase cycling always brings the material to one particular plastic state. the importance of this observation is that the entire strain hardening behaviour can be studied with just one specimen as long as it is subjected to one “big” cycle between each pair of strain paths. t c. madrigal et alii, frattura ed integrità strutturale, 37 (2016) 8-14 doi: 10.3221/igf-esis.37.02 13 the stress-strain response to the path in fig. 2 appears in fig. 3, along with the predicted results. in the calculations reported here only the path sequence in fig. 2 has been considered. the out-of-phase hardening has been taken into account by obtaining the model parameters, namely the metric constants and the hardening modulus function from the stress response and from the stable effective cyclic stress-strain curve derived in a 90° out-of-phase experiment, respectively. figure 3: stress response to strain path in fig. 2. the model predictions quantitatively agree with the experimental results. the strain and stresses at the end of each path are shown in tab. 1, along with the model predictions. the model’s average error is around 7,5 %, which is much lower than similar studies reported in the literature [16, 17]. strain path experimental results model predictions point ε (%) γ (%) σ (mpa) τ (mpa) σ (mpa) error (mpa) error (%) τ (mpa) error (mpa) error (%) 0 0.0 -1.1 0.0 -94.5 0.0 0.0 -98.8 4.3 -4.6 1 0.4 -0.8 80.9 -86.7 77.9 3.0 3.7 -90.5 3.8 -4.4 2 0.5 -0.4 99.7 -80.5 108.5 -8.8 -8.9 -81.9 1.4 -1.7 3 0.6 0.2 142.4 -64.2 152.2 -9.8 -6.9 -60.3 -4.0 6.2 4 0.4 0.9 198.6 -8.8 178.2 20.4 10.3 -7.1 -1.6 18.6 5 0.2 1.1 162.9 44.3 170.7 -7.8 -4.8 49.9 -5.6 -12.6 table 1: comparison of experimental results and model predictions. acknowledgements he authors would like to thank the spanish ministry of education for its financial support through grant dpi2014-56904-p. t c. madrigal et alii, frattura ed integrità strutturale, 37 (2016) 8-14 doi: 10.3221/igf-esis.37.02 14 references [1] navarro, a, brown, m.w., miller, k.j. j., a multiaxial stress-strain analysis for proportional cyclic loading, strain anal. eng., 28 (1993) 125-133. [2] navarro, a., brown m.w., a constitutive model for elasto-plastic deformation under cyclic multiaxial straining, fatigue fract. eng. mater. struct., 20 (1997) 747-758. [3] navarro, a., plastic flow and memory rules for the local strain method in the multiaxial case, in: susmel l., tovo r., (eds)., progettazione a fatica in presenza di multiassialità tensionali, proceedings of the igf workshop, ferrara, (2005) [4] http://www.gruppofrattura.it/ocs/index.php/gigf/gigf2005/schedconf/presentations. [5] navarro, a., giráldez, j.m., vallellano, c., a constitutive model for elastoplastic deformation under variable amplitude multiaxial cycling loading, int. j. fatigue 27 (2005) 838-846. [6] madrigal, c., navarro, a., chaves, v., numerical implementation of a multiaxial cyclic plasticity model for the local strain method in low cycle fatigue, theor. appl. fract. mech., 80 (2015) 111-119. [7] madrigal, c., navarro, a., chaves, v., biaxial cyclic plasticity experiments and application of a constitutive model for cyclically stable material behaviour, int. j. fatigue, 83 (2016) 240-252. [8] msc.fatigue, msc software corporation. [9] fe-fatigue, ncode international. [10] dowling, n.e., mechanical behaviour of materials. engineering methods for deformation, fracture and fatigue, prentice hall, inc., englewood cliffs, nj, (1993). [11] bannantine, j.a., comer, j.j., handrock, j.l., fundamentals of metal fatigue analysis, prentice hall, inc., englewood cliffs, nj, (1990). [12] hoffman, m., seeger, t.a., a generalized method for estimating multiaxial elastic-plastic notch stresses and strains, part 1: theory, j. eng. mater.-t. asme, 107 (1985) 250-254. [13] glinka, g., buczyński, a., ruggeri, a., elastic-plastic stress-strain analysis of notches under non-proportional loadings paths, arch. mech., 52 (2000) 589-607. [14] socie, d.f., marquis, g.b., multiaxial fatigue, society of automotive engineers, inc., warrendale, pa, (2000). [15] chakrabarty, j., theory of plasticity, 3rd ed., elsevier butterworth-heinemann, oxford, (2006). [16] lamba, h.s., sidebottom, o.m., cyclic plasticity for nonproportional paths: part 1 – cyclic hardening, erasure of memory, and subsequent strain hardening experiments, j. eng. mater. technol., 100 (1978) 96-103. [17] mcdowell, d.l., socie, d.f., lamba, h.s., multiaxial nonproportional cyclic deformation, astm stp, 770 (1982) 500-518. [18] lamba, h.s., sidebottom, o.m., cyclic plasticity for nonproportional paths: part 2 – comparison with predictions of three incremental plasticity models, j. eng. mater. technol., 100 (1978) 104-111. << /ascii85encodepages false /allowtransparency false /autopositionepsfiles true /autorotatepages /none /binding /left /calgrayprofile (dot gain 20%) /calrgbprofile (srgb iec61966-2.1) /calcmykprofile (u.s. web coated \050swop\051 v2) /srgbprofile (srgb iec61966-2.1) /cannotembedfontpolicy /error /compatibilitylevel 1.4 /compressobjects /tags /compresspages true /convertimagestoindexed true /passthroughjpegimages true /createjobticket false /defaultrenderingintent /default /detectblends true /detectcurves 0.0000 /colorconversionstrategy /cmyk /dothumbnails false /embedallfonts true /embedopentype false /parseiccprofilesincomments true /embedjoboptions true /dscreportinglevel 0 /emitdscwarnings false /endpage -1 /imagememory 1048576 /lockdistillerparams false /maxsubsetpct 100 /optimize 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/hrv (za stvaranje adobe pdf dokumenata najpogodnijih za visokokvalitetni ispis prije tiskanja koristite ove postavke. stvoreni pdf dokumenti mogu se otvoriti acrobat i adobe reader 5.0 i kasnijim verzijama.) /hun 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can be opened with acrobat and adobe reader 5.0 and later.) >> /namespace [ (adobe) (common) (1.0) ] /othernamespaces [ << /asreaderspreads false /cropimagestoframes true /errorcontrol /warnandcontinue /flattenerignorespreadoverrides false /includeguidesgrids false /includenonprinting false /includeslug false /namespace [ (adobe) (indesign) (4.0) ] /omitplacedbitmaps false /omitplacedeps false /omitplacedpdf false /simulateoverprint /legacy >> << /addbleedmarks false /addcolorbars false /addcropmarks false /addpageinfo false /addregmarks false /convertcolors /converttocmyk /destinationprofilename () /destinationprofileselector /documentcmyk /downsample16bitimages true /flattenerpreset << /presetselector /mediumresolution >> /formelements false /generatestructure false /includebookmarks false /includehyperlinks false /includeinteractive false /includelayers false /includeprofiles false /multimediahandling /useobjectsettings /namespace [ (adobe) (creativesuite) (2.0) ] /pdfxoutputintentprofileselector /documentcmyk /preserveediting true /untaggedcmykhandling /leaveuntagged /untaggedrgbhandling /usedocumentprofile /usedocumentbleed false >> ] >> setdistillerparams << /hwresolution [2400 2400] /pagesize [612.000 792.000] >> setpagedevice microsoft word numero_52_art_07_2686 m.f. bouali et alii, frattura ed integrità strutturale, 52 (2020) 82-97; doi: 10.3221/igf-esis.52.07 82 alternative estimation of effective young’s modulus for lightweight aggregate concrete lwac meriem fakhreddine bouali department of civil engineering, faculty of sciences & technology, university of mohamad cherif messaadia, souk ahras, 41000, algeria m.bouali@univ-soukahras.dz b.meriemfakhreddine@gmail.com, http://orcid.org/0000-0002-6986-980x abdelkader hima department of electrical engineering, faculty of technology, university of el-oued, 39000, algeria abdelkader-hima@univ-eloued.dz, http://orcid.org/0000-0002-5533-3991 abstract. the prediction of effective mechanical properties of composite materials using analytical models is of significant practical interest in situations in which tests are impossible, difficult, or costly. many experimental and numerical works are attempting to predict the elastic properties of lightweight aggregate concrete (lwac). in order to choose the optimized prediction composite model, the purpose of this paper is to appraise the effective young’s modulus of lwac using two-phase composite models. to this effect, results of previous experimental research have used as a platform, upon which, 07 two-phase composite models were applied. the outcomes of this comparative analysis show that not all two-phase analytical models can be directly used for predicting young’s modulus of lwac. the maxwell, counto1 and hashin-hansen models are in close concordance with the experimental young’s modulus of all lwac used for comparison in this study (119 values). they were found more appropriate for reasonable prediction of elasticity modules of the lwac. keywords. analytic model; concrete; young’s modulus; lightweight aggregate; two-phase. citation: bouali, m. f., hima, a. alternative estimation of effective young’s modulus for lightweight aggregate concrete lwac, frattura ed integrità strutturale, 52 (2020) 8297. received: 15.11.2019 accepted: 08.01.2020 published: 01.04.2020 copyright: © 2020 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. introduction ecently, special attention has been paid to the development of lightweight aggregate concrete (lwac) 1, 2, 3 which offers many advantages as a building material, including low weight, easier construction and better resistance compared with ordinary concrete. lightweight aggregate concrete (lwac) primarily improves the thermal and sound insulation properties of buildings next to its basic applications 4. the lightweight concrete are created by substituting the natural aggregates with the lightweight aggregates (lwa), which are classified into two fundamental r https://youtu.be/y01qadxmwdw m.f. bouali et alii, frattura ed integrità strutturale, 52 (2020) 82-97; doi: 10.3221/igf-esis.52.07 83 categories: natural (like pumice, diatomite, volcanic ash, etc.) and manufactured (such as perlite, extended schist, clay, slate, sintered powdered fuel ash (pfa), etc.) 3, 5. beside its technical and financial interests, lwac can be integrated into the demarche of sustainable improvement by utilizing in specific artificial aggregates which are lighter than natural aggregates 6. the young’s modulus (elastic modulus) is a very important material property which is measured directly on concrete. engineers need to know the value of this parameter to conduct any computer simulation of structure. various experimental works have concerned the study of behavior of lwac 1, 7, 8, 9, 10, 11, 12. however from an experimental point of view, this is not always easy. therefore when the tests are impossible, difficult, costly, or timeconsuming, the research about prediction models for the elastic modulus using properly validated composite models is of great practical interest. the aim of the composites materials approach is to develop a model that will enable expression of average properties of the mixtures through properties and volume fractions of its constituents 11. diverse explicit models of the literature are utilized. their application to the prediction of lwac behaviors shows a wide dissimilarity between the different approaches particularly when the volume fraction of reinforcement is more than 40% and when the contrast between the phases grows 9. for this purpose and to distinguish the most appropriate two-phase composite model for predicting lwac's effective modulus of elasticity, the estimation of the young’s modulus of lwac using two-phase composite models was applied. furthermore, an efficient and accurate model is useful to reduce the cost and duration of the experimental mix design studies. in this present work, a large bibliography data for different lwac tested experimentally and published in the literature are used: de larrard 7, yang and huang 8, and ke y et al. 9. for lwac test results investigated in this study, the volume fraction vg of the lightweight aggregate varies from 0% (the matrix) to 47.8% and the contrast of the characteristics of the phases eg/em (young’s modulus of lightweight aggregate and matrix) varies between 0.20% and 95% except for four types of concretes for which this ratio exceeds 1 because of a very low value of em (eg  em) 7. in order to determine the models likely to yield the lowest number of errors; the results of effective young’s modulus of lwac obtained by using 07 two-phase composite models were compared with the experimental results obtained by de larrard 7, yang and huang 8 and ke y et al. 9 (119 values) and discussed. therefore, prediction possibilities using composite material models in determination of modulus of elasticity were sought and some suggestions were made accordingly to a statistical study. prediction of elastic modulus for lwac two-phase composite models ore attention has been paid to lightweight aggregate concrete. the weakest component of lwac is not the cement matrix or the interfacial transition zone (itz) but the aggregates. therefore, the research about prediction model for lwac’s young modulus is valuable for the concrete application 6. lo and cui 13 illustrate that the ‘’wall effect’’ does not exist on the surface of expanded clay aggregates in lightweight concrete by sem and bsei imaging, resulting in a better bond and much more slender interfacial zone than the ordinary concrete 14. so, materials which are produced can be considered a two-phase composite material. the purpose of the composites materials approach is to develop a model that will enable expression of average properties of the mixtures through properties and volume fractions of its constituents 1, 11. we look for the models to estimate the young modulus for lightweight aggregate concrete (lwac) in terms of the properties and volume fractions of its constituents. these include the mortar matrix and the lightweight aggregate as reinforcing material. before analyzing lightweight aggregate concrete as a composite material, some assumptions must be considered. first, the heterogeneous composite material (lwac) is considered to be comprised of only two linear-elastic phases (the mortar and the lightweight aggregate). second, the unit cell is assumed sufficiently large to account for the heterogeneity of the system, and the deferring geometry of the phases. however, it is extremely small so that the composite is described homogeneous on a macro scale 10, 15, 16. fig. 1 presents the models for an idealized unit cell of a two-phase composite material 10, 11, 17. the lwac comprises a dispersed phase of lightweight aggregate with a young’s modulus eg and volume fraction vg and a continuous phase of the mortar matrix, with a young’s modulus em and volume fraction vm. m m.f. bouali et alii, frattura ed integrità strutturale, 52 (2020) 82-97; doi: 10.3221/igf-esis.52.07 84 as explained by gilormini and brechert 18, the choice of a model is governed by several parameters including the geometry of the heterogonous medium, the mechanical contrast between the phases (eg/em) and the volume fraction of reinforcement (vg). therefore, the equivalent homogenous behavior of lwac depends of the characteristics of the mortar (matrix, phase m) and lightweight aggregate (dispersed phase, phase g). figure 1: composite models: (a) voigt model, (b) reuss model, (c) popovics model, (d) hirsch-dougill model, (e) hashin-hansen model, (f) maxwell model, (g) counto1 model, (h) counto2 model. voigt model 10, 19: c _ voigt m m g ge e v e v  . (1) reuss model 10, 19:   m g c _ reuss g g m g e e   e e v e e    (2) popovics model 10, 20:  voigt reussc _ popovics c c1e e e 2   . (3) hirsch-dougill model 10, 15, 21: c _ hirsch c _ voigt c _ reuss 1 1 e 2 1 1 e e         (4) hashin-hansen model 10, 11, 22:         m g g m g c _ hashin m m g g m g e e e e v e e e e e e v            . (5) maxwell model (dispersed phase) 10, 15:         g c _ maxwell m g g m 1 2v α 1 / α 2 e e 1 v α 1 / α 2 e e                   . (6) counto1 mod 17, 23:   g c _ counto1 m m g g g m v e e 1 e v v e e                . (7) counto2 model 17:   g c _ counto2 m g g g m v e e 1 e v e e              . (8) bache and nepper-christensen model 15, 24: gm vv c _ bache m ge e e  (9) m.f. bouali et alii, frattura ed integrità strutturale, 52 (2020) 82-97; doi: 10.3221/igf-esis.52.07 85 the models of voigt (eq. and reuss (eq.2) provide the upper and lower bound of effective properties, respectively. it has been indicated 11, 19 that the upper bound relation of the parallel phase ‘voigt model’ might be applied as a first approximation to lwac when g me e . however, the relation of the series phase ‘reuss model’ validates the results of normal weight concrete with g me e 11, 19. the biphasic models of popovics (eq. 3) and hirsch-dougill (eq. 4) originally designed for composites with particles (like concrete) [25], propose elastic modulus of the composite by combining the voigt and reuss models. hirsh 21 derived an equation to express the elastic modulus of concrete in terms of empirical constant, and also provided some experimental results for the elastic modulus of concrete with different aggregates. the model composite spheres was introduced by hashin 25. this model consists of a gradation of size of spherical particles embedded in a continuous matrix 26. hansen 19 evolved mathematical models to predict the elastic modulus of composite materials based on the individual elastic modulus and volume portion of the components. from the concentric model, hashin-hansen model (eq. 5) supposes that the poisson ratios of all phases and the composite are equal (c=m=0.2) 10, 19. the dispersed phase model ‘’maxwell model’’, eq. (6), describes concrete as a dispersed phase composite material 10, 11. as a concentric model 10, zhou et al. 17 indicate that a more realistic counto1 model (eq.7) can be considered (fig. 1g). another version of counto’s model (eq.8) 17 is presented in fig. 1h. the strength-based bache and nepperchristensen model (eq. 9), gives a geometric average of component properties in relation to their volume fractions vm and vg. this is a mathematical model with no physical meaning 17. experimental data from published literature in this section, the bibliography data for different lightweight aggregate concrete (lwac) tested experimentally by de larrard 7, yang and huang 8 and ke y et al. 9 are compiled in tabs. 1, 2 and 3, respectively. the mechanical properties em, eg are the young’s modulus of the matrix (mortar: phase m) and lightweight aggregate (dispersed phase, phase g), respectively. the young’s modulus of the composite obtained experimentally by de larrard 7, yang and huang 8 and ke y et al. 9 are _  exp de larrarde , _exp yange and _eexp ke respectively. for lwac test results by de larrard 7 compiled in tab. 1, it can be seen that the volume fraction vg (the volume fraction of the lightweight aggregate) varies from 25.5% to 47.8% and that the contrast of the characteristics of the phases eg/em varies between 27.74% and 95% except for four types of concretes for which this ratio exceeds 1 because of a very low value of em (eg  em). in their experimental program yang and huang 8 have tested three types of artificial coarse aggregates with young's modulus of 6.01, 7.97 and 10.48gpa made of cement and fly ash with various combinations through a cold-pelletizing process. each type of aggregate was mixed with four types of mortar matrices with a young's modulus of 29.330, 28.130, 26.440 and 24.870gpa. this corresponds to a contrast ratio eg/em between the two phases ranging from 20.49% to 42.14%. by supposing a poisson’s ratio of 0.2, the strength of coarse aggregate was computed from the elastic moduli of the components and the strength of concrete. the rate of lightweight aggregate volume fraction vg was between 18% and 36%, the diameter of the gold aggregates assumed as spherical for all concretes tested had a d/d ratio in the order of (5/10) mm (tab. 2). in their study, concrete was considered as a composite material in which coarse aggregate were embedded in a matrix of hardened mortar. in the experimental study of ke y et al. 9, five lwas are used: three expanded clay aggregates (a) of quasi-spherical shape (0/4 650a, 4/10 550a, 4/10 430 a) and two aggregates of expanded shale (s) of irregular shape (4/10 520s, 4/8 750 s). the three used matrices (called m8, m9 and m10) are made of portland cement mortar cem i 52.5 and normal sand 0/2 mm. normal, high performance (hp) and very high performance (vhp) mortar matrices, were utilized for the realization of the concrete specimens tested by ke y et al. 9. in their work, the volume fraction of aggregate was 0% (mortar), 12.5%, 25%, 37.5% and 45% with a contrast of the properties varying from 12.26% to 69.61%. the young’s modulus of the three mortar matrices were experimentally determined as 28.6, 33.2 and 35.4 gpa for m8, m9 and m10, respectively, as seen in tab. 3 9. they correspond to a normal, hp and vhp matrix, respectively 9. mechanical properties of the lightweight aggregate are shown in tab. 4 9. the elastic modulus of lwac is estimated by utilizing some composite material models _c anale like popovics, hirschdougill, hashin-hansen, maxwell, counto1, counto2, and bache and nepper-christensen (eqs.(2)-(9)). m.f. bouali et alii, frattura ed integrità strutturale, 52 (2020) 82-97; doi: 10.3221/igf-esis.52.07 86 this study try to figure out that these composite material models, mentioned above, got reliable prediction abilities for the modulus of elasticity of lwac. the modulus of elasticity values were predicted utilizing the composite models and then, the predicted results were compared to the experimental results of de larrard 7, yang and huang 8 and ke y et al. 9 respectively. ref. grav. d/d (mm) vg eg (gpa) em (gpa) eexp_de larrard (gpa) 8 argi 16 8 isol s 8 leca 7j. 8 leca 28j. 8 surex 675 8 galex 7j. 8 galex 28j. 9 schiste 15j. 9 schiste 28j. 9 leca 1j. 9 leca 2j. 9 leca 7j. 9 leca 28j. 9 leca 90j. 9 surex 1j. 9 surex 2j. 9 surex 7j. 9 surex 28j. 9 surex 90j. 3 lwc1 crush 3 lwc1 crush 3 lwc1 pellet 3 lwc1 pellet 3 hslwc pel. 3 hslwc pel. 1 liapor 2 liapor 16 javron 16 g/s -0.2 16 g/s +0.2 16 eau + 16 eau – 4-12 3.15-8 4-10 4-10 6.3-10 3-8 3-8 4-10 4-10 4-10 4-10 4-10 6.3-10 6.3-10 6.3-10 6.3-10 6.3-10 10-20 10-20 5-20 5-20 5-20 5-20 0-16 4-16 4-10 4-10 4-10 4-10 4-10 0.414 0.414 0.414 0.414 0.414 0.425 0.425 0.391 0.391 0.414 0.414 0.414 0.414 0.414 0.414 0.414 0.414 0.414 0.414 0.403 0.403 0.414 0.414 0.255 0.255 0.473 0.432 0.463 0.443 0.478 0.473 0.453 8 13.1 7.6 7.6 16.2 33 33 21 21 8.6 8.6 8.6 8.6 8.6 19 19 19 19 19 13.6 13.6 14 14 14 14 21.5 21.5 16 16 16 16 16 25.2 25.2 23.5 25.2 25.2 20.6 21.9 24.9 25.6 11 15 20 25.2 31 11 15 20 25.2 31 33.2 33.2 32.8 32.8 38.5 38.5 29.7 27.9 23.8 24.6 23.1 26.6 21.1 15.6 19.2 14.1 15.7 21 25.5 25.8 23.9 23.4 10 12 13.9 16 17.8 14.6 17.1 20.6 22.3 22.6 23 24.3 22.7 24.3 27.6 28.3 25.5 24.8 19.7 19.9 19.7 20.9 18.1 table 1: characteristics of lwac tested by de larrard 7. ref. grav. d/d (mm) vg eg (gpa) em (gpa) eexp_yang (gpa) a3 a4 a5 a6 5-10 0.18 0.24 0.30 0.36 6.01 6.01 6.01 6.01 29.33 28.13 26.44 24.87 23.020 20.600 18.210 15.800 b3 b4 b5 b6 0.18 0.24 0.30 0.36 7.97 7.97 7.97 7.97 29.33 28.13 26.44 24.87 23.790 21.530 19.010 17.220 c3 c4 c5 c6 0.18 0.24 0.30 0.36 10.48 10.48 10.48 10.48 29.33 28.13 26.44 24.87 24.660 22.580 20.320 18.650 table 2: characteristics of lwac tested by chung-chia yang and ran huang 8. m.f. bouali et alii, frattura ed integrità strutturale, 52 (2020) 82-97; doi: 10.3221/igf-esis.52.07 87 eexp_ke e0ke e0.125ke e0.250ke e0.375ke e0.450ke m8 0/4 650a 4/10 550a 4/10 430a 4/10 520s 4/8 750s 28.588 23.539 26.157 24.900 25.135 27.367 20.665 21.680 21.391 22.471 26.262 16.743 17.900 17.293 19.428 25.281 15.669 16.606 15.699 18.286 24.324 m9 0/4 650a 4/10 550a 4/10 430a 4/10 520s 4/8 750s 33.183 29.396 29.159 27.568 29.480 31.931 23.712 24.934 23.778 26.521 30.987 19.871 21.358 20.818 22.188 30.146 17.175 19.696 18.935 20.184 29.311 m10 0/4 650a 4/10 550a 4/10 430a 4/10 520s 4/8 750s 35.397 31.147 32.089 30.220 32.783 34.213 26.753 27.991 26.033 27.998 33.845 22.427 23.684 22.296 24.340 32.945 20.346 21.724 20.082 22.024 33.002 table 3: characteristics of lwac tested by ke y et al. 9 (gpa). lwa 0/4 650a 4/10 550a 4/10 430a 4/10 520s 4/8 750s eg 6.870 6.790 4.340 6.490 19.900 table 4: mechanical properties of lightweight aggregate tested by ke y et al. 9 (gpa). results and discussions comparative analysis omparison between the estimative results of effective elastic modulus of lwac obtained as a result of calculations of the eqns. (2-9) and those of experimental data have been presented in tabs. 5, 6 and 7 respectively. a confrontation of lwac young’s modulus between experimental results in 7, 8, 9 and the predictions of 07 composite models material models are shown in fig. 2, fig. 3 and fig. 4 respectively. the differences between the various predictive composite models and the experimental results in 7, 8, 9 have been computed according to the proportion of reinforcement vg in lwac. when the volume fraction of aggregates vg grows, the errors between the predictions and the experimental results increase for all composite material models. since the weakest component of lwac is not the cement matrix but the lightweight aggregates, the effect of volume fraction of lightweight aggregate on young’s modulus of lwac is very clear. the increase in the volume fraction of lightweight aggregates vg substantially reduces the young’s modulus of the lwac. to compare the experimental and predicted young’s modulus of lwac, the error percentage e . is determined using the following expression:   c _ anal exp exp e e e  % 100 e          (10)  e abs e   , absolute value of e  it appears for first time that all models are generally suitable for predicting the modulus of elasticity of the lwac. tabs. 8-9-10 give the error percentages of the composite material models and experimental results in 7, 8, 9 respectively. in order to choose the models which have good performances, the error percentages below 10% are chosen as desired range and the model’s error percentages below this value are indicated in bold. therefore, the models which verified this condition have been underlined. c m.f. bouali et alii, frattura ed integrità strutturale, 52 (2020) 82-97; doi: 10.3221/igf-esis.52.07 88 ref. grav. eexp_de larrard ec_popovics ec_hirsch ec_hashin ec_maxwell ec_counto1 ec_counto2 ec_bache 8 argi 16 8 isol s 8 leca 7j. 8 leca 28j. 8 surex 675 8 galex 7j. 8 galex 28j. 9 schiste 15j. 9 schiste 28j. 9 leca 1j. 9 leca 2j. 9 leca 7j. 9 leca 28j. 9 leca 90j. 9 surex 1j. 9 surex 2j. 9 surex 7j. 9 surex 28j. 9 surex 90j. 3 lwc1 crush 3 lwc1 crush 3 lwc1 pellet 3 lwc1 pellet 3 hslwc pel. 3 hslwc pel. 1 liapor 2 liapor 16 javron 16 g/s -0.2 16 g/s +0.2 16 eau + 16 eau – 15.6 19.2 14.1 15.7 21 25.5 25.8 23.9 23.4 10 12 13.9 16 17.8 14.6 17.1 20.6 22.3 22.6 23 24.3 22.7 24.3 27.6 28.3 25.5 24.8 19.7 19.9 19.7 20.9 18.1 15.71 19.21 14.76 15.39 20.98 25.19 26.09 23.29 23.69 9.93 11.91 14.10 16.17 18.32 13.82 16.54 19.58 22.42 25.30 23.15 23.15 23.05 23.05 29.44 29.44 25.49 24.93 19.80 20.33 19.38 20.92 18.61 15.35 19.16 14.44 14.98 20.97 25.17 26.07 23.29 23.69 9.93 11.89 14.00 15.88 17.69 13.80 16.54 19.58 22.41 25.28 22.95 22.95 22.88 22.88 29.17 29.17 25.49 24.93 19.80 20.32 19.38 20.90 18.61 16.30 19.37 15.29 16.04 21.04 25.09 26.02 23.30 23.70 9.94 11.97 14.33 16.68 19.24 13.73 16.54 19.58 22.43 25.40 23.61 23.61 23.45 23.45 30.31 30.31 25.52 24.94 19.84 20.38 19.41 21.00 18.63 16.98 19.67 15.91 16.76 21.19 25.32 26.20 23.33 23.73 9.96 12.11 14.69 17.31 20.20 13.90 16.57 19.58 22.50 25.63 24.25 24.25 24.04 24.04 31.08 31.08 25.62 25.01 19.96 20.53 19.51 21.21 18.68 16.76 19.57 15.71 16.52 21.14 25.24 26.13 23.32 23.72 9.95 12.06 14.57 17.10 19.88 13.84 16.56 19.58 22.48 25.55 24.05 24.05 23.84 23.84 31.07 31.07 25.58 24.98 19.91 20.47 19.47 21.12 18.66 15.79 19.16 14.82 15.50 20.93 24.96 25.91 23.28 23.67 9.92 11.87 14.08 16.22 18.51 13.63 16.51 19.58 22.39 25.24 23.13 23.13 23.02 23.02 29.38 29.38 25.46 24.90 19.77 20.29 19.35 20.87 18.59 15.67 19.22 14.73 15.34 20.99 25.17 26.07 23.30 23.69 9.93 11.91 14.10 16.15 18.23 13.79 16.54 19.58 22.42 25.31 23.17 23.17 23.06 23.06 29.75 29.75 25.49 24.93 19.80 20.33 19.38 20.92 18.61 table 5: modulus of elasticity of lwac predicted by various composite models compared with the experimental results of de larrard 7(gpa). ref. grav. eexp_yang ec_popovics ec_hirsch ec_hashin ec_maxwell ec_counto1 ec_counto2 ec_bache a3 a4 a5 a6 23.020 20.600 18.210 15.800 21.201 18.879 16.701 14.879 20.471 18.055 15.920 14.190 23.102 20.559 18.039 15.905 23.967 21.501 18.963 16.770 24.121 21.523 18.860 16.570 21.589 19.265 17.018 15.124 22.049 19.422 16.953 14.915 b3 b4 b5 b6 23.790 21.530 19.010 17.220 22.635 20.398 18.248 16.445 22.276 19.987 17.863 16.112 23.848 21.481 19.106 17.095 24.530 22.218 19.820 17.754 24.653 22.236 19.739 17.600 22.709 20.504 18.340 16.515 23.198 20.784 18.451 16.510 c3 c4 c5 c6 24.660 22.580 20.320 18.650 24.047 21.963 19.900 18.166 23.898 21.794 19.746 18.039 24.723 22.568 20.369 18.512 25.214 23.093 20.867 18.960 25.305 23.106 20.810 18.854 23.944 21.900 19.854 18.130 24.370 22.195 20.030 18.221 table 6: modulus of elasticity of lwac predicted by various composite models compared with the experimental results of yang and huang 8(gpa). m.f. bouali et alii, frattura ed integrità strutturale, 52 (2020) 82-97; doi: 10.3221/igf-esis.52.07 89 ref. grav. eexp_ke ec_popovics ec_hirsch ec_hashin ec_maxwell ec_counto1 ec_counto2 ec_bache m8 0/4 650 a 28.588 23.539 20.665 16.743 15.669 28.588 23.182 19.563 16.762 15.308 28.588 22.870 18.903 15.954 14.504 28.588 24.522 20.996 17.908 16.234 28.588 25.101 21.886 18.912 17.233 28.588 25.303 21.886 18.652 16.845 28.588 23.253 19.833 17.044 15.556 28.588 23.921 20.016 16.748 15.050 m8 4/10 550 a 28.588 26.157 21.680 17.900 16.606 28.588 23.132 19.499 16.693 15.237 28.588 22.810 18.820 15.863 14.413 28.588 24.499 20.956 17.857 16.176 28.588 25.084 21.855 18.870 17.185 28.588 25.288 21.855 18.607 16.793 28.588 23.215 19.781 16.984 15.492 28.588 23.886 19.957 16.675 14.971 m8 4/10 430 a 28.588 24.900 21.391 17.293 15.699 28.588 21.195 17.227 14.366 12.906 28.588 20.297 15.597 12.534 11.142 28.588 23.769 19.699 16.216 14.357 28.588 24.561 20.895 17.543 15.667 28.588 24.828 20.895 17.203 15.162 28.588 21.878 18.062 15.041 13.450 28.588 22.586 17.845 14.099 12.240 m8 4/10 520 s 28.588 25.135 22.471 19.428 18.286 28.588 22.939 19.253 16.429 14.967 28.588 22.576 18.499 15.516 14.063 28.588 24.414 20.808 17.662 15.959 28.588 25.022 21.740 18.711 17.002 28.588 25.233 21.740 18.439 16.597 28.588 23.067 19.583 16.756 15.250 28.588 23.752 19.733 16.395 14.669 m8 4/10 750 s 28.588 27.367 26.262 25.281 24.324 28.588 27.305 26.095 24.948 24.286 28.588 27.304 26.091 24.942 24.280 28.588 27.335 26.137 24.988 24.322 28.588 27.396 26.237 25.110 24.448 28.588 27.421 26.237 25.077 24.397 28.588 27.236 26.027 24.895 24.244 28.588 27.322 26.113 24.957 24.288 m9 0/4 650 a 33.183 29.396 23.712 19.871 17.175 33.183 26.167 21.778 18.468 16.763 33.183 25.636 20.708 17.195 15.512 33.183 28.147 23.821 20.065 18.040 33.183 28.904 24.978 21.363 19.328 33.183 29.166 24.978 21.028 18.829 33.183 26.435 22.283 18.937 17.160 33.183 27.253 22.383 18.384 16.336 m9 4/10 550 a 33.183 29.159 24.934 21.358 19.696 33.183 26.108 21.707 18.394 16.688 33.183 25.562 20.611 17.093 15.410 33.183 28.123 23.780 20.012 17.981 33.183 28.887 24.947 21.320 19.279 33.183 29.151 24.947 20.982 18.776 33.183 26.392 22.228 18.874 17.094 33.183 27.214 22.318 18.303 16.250 m9 4/10 430 a 33.183 27.568 23.778 20.818 18.935 33.183 23.852 19.220 15.934 14.259 33.183 22.477 16.848 13.338 11.782 33.183 27.365 22.485 18.333 16.127 33.183 28.353 23.970 19.975 17.743 33.183 28.684 23.970 19.555 17.121 33.183 24.953 20.430 16.871 15.001 33.183 25.733 19.955 15.475 13.285 m9 4/10 520 s 33.183 29.480 26.521 22.188 20.184 33.183 25.881 21.435 18.113 16.405 33.183 25.274 20.234 16.699 15.021 33.183 28.034 23.627 19.812 17.759 33.183 28.824 24.830 21.158 19.093 33.183 29.095 24.830 20.811 18.577 33.183 26.232 22.020 18.638 16.845 33.183 27.060 22.067 17.996 15.923 m9 4/10 750 s 33.183 31.931 30.987 30.146 29.311 33.183 31.075 29.150 27.371 26.362 33.183 31.069 29.133 27.346 26.335 33.183 31.170 29.276 27.490 26.466 33.183 31.303 29.493 27.749 26.732 33.183 31.355 29.493 27.679 26.626 33.183 30.943 29.031 27.287 26.298 33.183 31.128 29.201 27.393 26.363 m10 0/4 650 a 35.397 31.147 26.753 22.427 20.346 35.397 27.567 22.816 19.271 17.450 35.397 26.907 21.515 17.742 15.953 35.397 29.889 25.176 21.098 18.905 35.397 30.735 26.466 22.541 20.334 35.397 31.026 26.466 22.169 19.781 35.397 27.953 23.452 19.839 17.925 35.397 28.838 23.494 19.141 16.926 m10 4/10 550 a 35.397 32.089 35.397 27.504 35.397 26.826 35.397 29.865 35.397 30.718 35.397 31.011 35.397 27.909 35.397 28.796 m.f. bouali et alii, frattura ed integrità strutturale, 52 (2020) 82-97; doi: 10.3221/igf-esis.52.07 90 27.991 23.684 21.724 22.742 19.195 17.373 21.411 17.633 15.847 25.135 21.045 18.845 26.434 22.497 20.285 26.434 22.123 19.727 23.396 19.776 17.858 23.426 19.057 16.837 m10 4/10 430 a 35.397 30.220 26.033 22.296 20.082 35.397 25.099 20.162 16.680 14.904 35.397 23.460 17.394 13.683 12.055 35.397 29.096 23.825 19.351 16.977 35.397 30.180 25.451 21.146 18.742 35.397 30.541 25.451 20.687 18.063 35.397 26.427 21.564 17.748 15.746 35.397 27.229 20.946 16.112 13.766 m10 4/10 520 s 35.397 32.783 27.998 24.340 22.024 35.397 27.261 22.459 18.906 17.085 35.397 26.510 21.007 17.218 15.439 35.397 29.775 24.980 20.843 18.621 35.397 30.654 26.316 22.334 20.098 35.397 30.954 26.316 21.950 19.527 35.397 27.743 23.183 19.536 17.606 35.397 28.634 23.163 18.737 16.498 m10 4/10 750 s 35.397 34.123 33.845 32.945 33.002 35.397 32.858 30.576 28.491 27.317 35.397 32.847 30.546 28.449 27.273 35.397 33.001 30.762 28.665 27.469 35.397 33.176 31.047 29.002 27.815 35.397 33.244 31.047 28.912 27.677 35.397 32.695 30.437 28.398 27.249 35.397 32.938 30.651 28.522 27.316 table 7: modulus of elasticity of lwac predicted by various composite models compared with the experimental results of ke y et al. 9(gpa). figure 2: confrontation of lwac young’s modulus between experimental results in 7 and the predictions of 07 composite material models. figure 3: confrontation of lwac young’s modulus between experimental results in 8 and the predictions of 07 composite material models. 5 10 15 20 25 30 35 5 10 15 20 25 30 e c_ a n a l (g p a ) eexp_de larrard (gpa) ec_hashin ec_popovics ec_hirsch ec_bache ec_counto2 ec_maxwell ec_counto1 5 10 15 20 25 30 5 10 15 20 25 30 e c_ a n a l (g p a ) eexp_yang (gpa) ec_hashin ec_popovics ec_hirsch ec_bache ec_counto2 ec_maxwell ec_counto1 m.f. bouali et alii, frattura ed integrità strutturale, 52 (2020) 82-97; doi: 10.3221/igf-esis.52.07 91 figure 4: confrontation of lwac young’s modulus between experimental results in 9 and the predictions of 07 composite material models. ref. grav. popovics hirschdougill hashinhansen maxwell counto1 counto2 bache and nepperchristensen 8 argi 16 8 isol s 8 leca 7j. 8 leca 28j. 8 surex 675 8 galex 7j. galex 28j. 9 schiste 15j. 9 schiste 28j. 9 leca 1j. 9 leca 2j. 9 leca 7j. 9 leca 28j. 9 leca 90j. 9 surex 1j. 9 surex 2j. 9 surex 7j. 9 surex 28j. 9 surex 90j. lwc1 crush 3 lwc1 crush 3 lwc1 pellet 3 lwc1 pellet 3 hslwc pel. 3 hslwc pel. 1 liapor 2 liapor 16 javron 16 g/s -0.2 16 g/s +0.2 16 eau + 16 eau – 0.68 0.05 4.65 -1.98 -0.09 -1.21 1.11 -2.53 1.24 -0.66 -0.76 1.42 1.05 2.93 -5.36 -3.25 -4.95 0.52 11.96 0.66 -4.73 1.54 -5.15 6.65 4.02 -0.03 0.52 0.52 2.16 -1.61 0.09 2.84 -1.62 -0.21 2.40 -4.61 -0.15 -1.28 1.06 -2.53 1.24 -0.67 -0.90 0.70 -0.76 -0.63 -5.48 -3.26 -4.95 0.52 11.87 -0.21 -5.55 0.80 -5.84 5.68 3.06 -0.05 0.51 0.48 2.11 -1.64 -0.01 2.83 4.48 0.89 8.44 2.16 0.18 -1.60 0.84 -2.52 1.27 -0.61 -0.23 3.12 4.27 8.07 -5.96 -3.30 -4.95 0.60 12.37 2.66 -2.83 3.29 -3.51 9.82 7.11 0.07 0.57 0.71 2.41 -1.47 0.47 2.91 8.87 2.46 12.87 6.77 0.93 -0.69 1.55 -2.41 1.42 -0.38 0.91 5.68 8.20 13.50 -4.79 -3.08 -4.94 0.91 13.39 5.43 -0.21 5.88 -1.09 12.61 9.82 0.49 0.85 1.34 3.14 -0.94 1.48 3.22 7.42 1.93 11.40 5.24 0.67 -1.03 1.28 -2.44 1.38 -0.46 0.52 4.82 6.90 11.71 -5.22 -3.15 -4.95 0.81 13.04 4.56 -1.03 5.01 -1.90 12.57 9.79 0.30 0.74 1.07 2.86 -1.18 1.04 3.09 1.21 -0.23 5.14 -1.29 -0.33 -2.13 0.43 -2.59 1.16 -0.77 -1.04 1.27 1.36 3.98 -6.64 -3.44 -4.96 0.39 11.67 0.57 -4.81 1.40 -5.28 6.45 3.81 -0.17 0.40 0.34 1.94 -1.77 -0.13 2.72 0.46 0.11 4.44 -2.28 -0.06 -1.30 1.04 -2.53 1.25 -0.66 -0.71 1.45 0.92 2.42 -5.53 -3.26 -4.95 0.54 12.00 0.74 -4.65 1.57 -5.12 7.78 5.11 -0.04 0.52 0.52 2.17 -1.62 0.07 2.84 table 8: error percentages of composite models and experimental results in 7 (%). 10 15 20 25 30 35 40 10 15 20 25 30 35 40 e c_ a n a l (g p a ) eexp_ke (gpa) ec_hashin ec_popovics ec_hirsch ec_bache ec_counto2 ec_maxwell ec_counto1 m.f. bouali et alii, frattura ed integrità strutturale, 52 (2020) 82-97; doi: 10.3221/igf-esis.52.07 92 it can be observed from tab. 8 that: for the hirsch-dougill, popovics, bache and nepper-christensen, counto2 and hashin-hansen models, 31/32 cases lead to e smaller than 10%. all these models give a maximum e for a contrast equal to eg/em= 61.29% with a volume fraction of the aggregates vg = 41.4% (aggregate: 9 surex 90j.). for the popovics and bache and nepper-christensen models, 28/32 cases give e smaller than 5% and 3/32 cases give e smaller than 10%. e ranges from –5.53% to 12.00%. for the hirsch-dougill and counto2 models, 27/32 cases give e smaller than 5% and 4/32 cases give e smaller than 10%. e ranges from –5.84% to 11.87%. for the hashin-hansen model, 31/32 cases lead to e smaller than 10%. hence, for 26/32 cases it is smaller than 5%. e ranges from –5.96% to 12.37%. for the counto1 and maxwell models, 28/32 cases lead to e smaller than 10%, e ranges from –4.94% to 13.50%. it is clear from these results that the selected models are able to effectively estimate the young’s modulus of lwac tested by de larrard [7] with a max difference e equal to 13.50% (obtained by the maxwell model) using 32 measurements. ref. grav. popovics hirschdougill hashinhansen maxwell counto1 counto2 bache and nepperchristensen a3 a4 a5 a6 -7.90 -8.36 -8.29 -5.83 -11.07 -12.35 -12.57 -10.19 0.36 -0.20 -0.94 0.66 4.11 4.37 4.13 6.14 4.78 4.48 3.57 4.87 -6.22 -6.48 -6.54 -4.28 -4.22 -5.72 -6.90 -5.60 b3 b4 b5 b6 -4.85 -5.26 -4.01 -4.50 -6.36 -7.17 -6.04 -6.44 0.25 -0.23 0.50 -0.72 3.11 3.20 4.26 3.10 3.63 3.28 3.84 2.21 -4.54 -4.77 -3.53 -4.09 -2.49 -3.47 -2.94 -4.12 c3 c4 c5 c6 -2.49 -2.73 -2.07 -2.59 -3.09 -3.48 -2.82 -3.28 0.26 -0.05 0.24 -0.74 2.25 2.27 2.69 1.66 2.62 2.33 2.41 1.09 -2.90 -3.01 -2.29 -2.79 -1.17 -1.70 -1.42 -2.30 table 9: error percentages of composite models and experimental results in 8 (%). compared with the experimental data of yang and huang 8 (tab. 6, tab. 9), bache and nepper-christensen, counto2, popovics, hirsch-dougill, underestimate the measured young’s modulus. on the other hand, the maxwell and counto1 models overestimate the young’s modulus measured by yang and huang [8]. as seen in tab. 9, for the hashin-hansen and counto1 models, 12/12 cases give e smaller than 5%. e ranges from 0.94% to 4.87%. the maxwell gives 12/12 cases smaller than 10% and 11/12 smaller than 5%. e ranges from 1.66% to 6.14%. in all composite models, the error percentages differ between 0.05% and 12.57%. it can be seen that the most accurate models are those of hashin-hansen, counto1 and maxwell which give less errors percentages. the predictions of the lwac young’s modulus using the 07 composite material models are compared with experimental data of ke y et al. [9] (tab. 7 and tab.10) in fig. 4. all selected composite models appear applicable to predict the young’s modulus of lwac tested by ke y et al [9]. for the maxwell model, 50/75 cases give e smaller than 5% and 22/75 cases smaller than 10%. this means that 72/75 cases have e smaller than 10%. this model converges on the experimental values measured by ke y et al. [9] with an absolute maximum difference e of 15.72%. for the counto1 model, 47/75 cases lead to e smaller than 5% and 23/75 smaller than 10%, which gives 70/75 cases with e smaller than 10%, with a maximum difference of 16.14%. for the hashin-hansen model, 59/75 cases give e smaller than 10% of which 38/75 cases smaller than 5%. e ranges from 0% to 16.77%. for the counto2 model, 36/75 cases have e smaller than 10%, of which 27 cases have e smaller than 5%, with the maximum difference of 21.59%. for the popovics model, 34/75 cases give e smaller than 10% with 25/75 cases smaller than 5%. the maximum e is 25.78%. m.f. bouali et alii, frattura ed integrità strutturale, 52 (2020) 82-97; doi: 10.3221/igf-esis.52.07 93 ref. grav. popovics hirschdougill hashinhansen maxwell counto1 counto2 bache and nepperchristensen m8 0/4 650 a 0.00 4.18 1.60 6.96 3.61 0.00 -2.84 -8.53 -4.71 -7.43 0.00 1.52 5.33 0.12 2.31 0.00 6.63 5.91 12.96 9.98 0.00 7.49 5.91 11.40 7.50 0.00 1.21 4.03 1.80 0.72 0.00 1.62 -3.14 0.03 -3.95 m8 4/10 550 a 0.00 6.34 3.34 0.24 2.59 0.00 -12.80 -13.19 -11.38 -13.21 0.00 11.56 10.06 6.74 8.25 0.00 4.10 0.81 5.42 3.49 0.00 3.32 0.81 3.95 1.13 0.00 11.25 8.76 5.12 6.71 0.00 -8.68 -7.95 -6.84 -9.85 m8 4/10 430 a 0.00 4.54 7.91 6.23 8.55 0.00 -18.49 -27.09 -27.52 -29.03 0.00 14.88 19.47 16.93 17.79 0.00 1.36 2.32 1.45 0.20 0.00 0.29 2.32 0.52 3.42 0.00 12.14 15.56 13.02 14.33 0.00 -9.29 -16.58 -18.47 -22.04 m8 4/10 520 s 0.00 2.87 7.40 9.09 12.72 0.00 -10.18 -17.68 -20.14 -23.09 0.00 8.74 14.32 15.44 18.15 0.00 0.45 3.25 3.69 7.02 0.00 0.39 3.25 5.09 9.24 0.00 8.23 12.85 13.75 16.60 0.00 -5.50 -12.18 -15.61 -19.78 m8 4/10 750 s 0.00 0.12 0.48 1.16 0.01 0.00 -0.23 -0.65 -1.34 -0.18 0.00 0.23 0.63 1.32 0.16 0.00 0.11 0.09 0.68 0.51 0.00 0.20 0.09 0.81 0.30 0.00 0.48 0.90 1.53 0.33 0.00 -0.16 -0.57 -1.28 -0.15 m9 0/4 650 a 0.00 4.25 0.46 0.98 5.04 0.00 -12.79 -12.67 -13.46 -9.68 0.00 10.99 8.16 7.06 2.40 0.00 1.67 5.34 7.51 12.54 0.00 0.78 5.34 5.82 9.63 0.00 10.07 6.03 4.70 0.09 0.00 -7.29 -5.60 -7.49 -4.89 m9 4/10 550 a 0.00 3.55 4.63 6.30 8.71 0.00 -12.34 -17.34 -19.97 -21.76 0.00 10.46 12.94 13.88 15.27 0.00 0.93 0.05 0.18 2.12 0.00 0.03 0.05 1.76 4.67 0.00 9.49 10.85 11.63 13.21 0.00 -6.67 -10.49 -14.30 -17.50 m9 4/10 430 a 0.00 0.74 5.44 11.94 14.83 0.00 -18.47 -29.14 -35.93 -37.78 0.00 13.48 19.17 23.46 24.69 0.00 2.85 0.81 4.05 6.29 0.00 4.05 0.81 6.07 9.58 0.00 9.48 14.08 18.96 20.77 0.00 -6.66 -16.08 -25.67 -29.84 m9 4/10 520 s 0.00 4.90 10.91 10.71 11.97 0.00 -14.27 -23.71 -24.74 -25.54 0.00 12.21 19.18 18.37 18.68 0.00 2.23 6.38 4.64 5.36 0.00 1.31 6.38 6.21 7.92 0.00 11.02 16.97 16.00 16.50 0.00 -8.21 -16.79 -18.90 -21.07 m9 4/10 750 s 0.00 2.38 5.52 8.81 9.71 0.00 -2.70 -5.98 -9.29 -10.15 0.00 2.68 5.93 9.21 10.06 0.00 1.97 4.82 7.95 8.80 0.00 1.80 4.82 8.18 9.16 0.00 3.09 6.31 9.48 10.28 0.00 -2.51 -5.76 -9.13 -10.06 m10 0/4 650 a 0.00 4.04 5.89 5.92 7.08 0.00 -13.61 -19.58 -20.89 -21.59 0.00 11.50 14.71 14.07 14.24 0.00 1.32 1.07 0.51 0.06 0.00 0.39 1.07 1.15 2.78 0.00 10.26 12.34 11.54 11.90 0.00 -7.41 -12.18 14.65 -16.81 m.f. bouali et alii, frattura ed integrità strutturale, 52 (2020) 82-97; doi: 10.3221/igf-esis.52.07 94 m10 4/10 550 a 0.00 6.93 10.20 11.14 13.25 0.00 -16.40 -23.51 -25.55 -27.05 0.00 14.29 18.75 18.95 20.03 0.00 4.27 5.56 5.01 6.63 0.00 3.36 5.56 6.59 9.19 0.00 13.03 16.42 16.50 17.80 0.00 -10.26 -16.31 -19.54 -22.49 m10 4/10 430 a 0.00 3.72 8.48 13.21 15.46 0.00 -22.37 -33.18 -38.63 -39.97 0.00 16.94 22.55 25.19 25.78 0.00 0.13 2.24 5.16 6.67 0.00 1.06 2.24 7.22 10.05 0.00 12.55 17.16 20.40 21.59 0.00 -9.90 -19.54 -27.73 -31.45 m10 4/10 520 s 0.00 9.18 10.78 14.37 15.45 0.00 -19.13 -24.97 -29.26 -29.90 0.00 16.85 19.78 22.32 22.42 0.00 6.49 6.01 8.24 8.74 0.00 5.58 6.01 9.82 11.34 0.00 15.37 17.20 19.74 20.06 0.00 -12.66 -17.27 -23.02 -25.09 m10 4/10 750 s 0.00 3.29 9.11 12.99 16.77 0.00 -3.74 -9.75 -13.65 -17.36 0.00 3.71 9.66 13.52 17.22 0.00 2.77 8.27 11.97 15.72 0.00 2.57 8.27 12.24 16.14 0.00 4.18 10.07 13.80 17.43 0.00 -3.47 -9.44 -13.43 -17.23 table 10: error percentages of composite models and experimental results in 9 (%). the bache and nepper-christensen and hirsch-dougill models underestimate the young’s modulus of lwac measured in [3]. bache and nepper-christensen model, 43/75 cases give e smaller than 10% and e ranges from 31.45% to 1.62%. for the hirsch-dougill model, 29/75 cases give e smaller than 10% with 23 cases smaller than 5%. it can be seen by examining fig. 4 that the most accurate models are those of maxwell, counto1 and hashin-hansen which give less errors percentages (fig. 4 and tab. 10). statistical analysis in order to confirm what has been announced previously and distinguish the most suitable model for predicting the effective elasticity modulus of the lwac, a global statistical study was carried out on all the experimental values of the three researchers (119 measures). to this effect, the mean values and standard deviation for all composite models used in this study and experimental data are calculated as seen in tab. 10. popovics hirschdougill hashinhansen maxwell counto1 counto2 bache and nepperchristensen mean values standard deviation -6.90 8.24 -9.66 11.14 -2.72 5.72 0.29 5.27 -0.23 5.32 -5.94 7.12 -6.42 8.46 table 10: mean values and standard deviation of composite models and all experimental data in 7, 8, 9. fig. 5 shows the normal distribution approximation of error percentage for all 07 composite analytical models. every estimator has a pick on the mean value and a standard deviation presented by a tight or wide curve. as expected, the maxwell, counto1 and hashin-hansen composite models provide a good prediction of experimental young’s modulus of all lwac tested by de larrard 7, yang and huang 8 and ke y et al. 9 (119 values) with a maximum volume fraction of aggregates vg equal to 49.37%. it is clear from curves of fig. 5 that the best curves that fit experimental data are respectively maxwell, counto1 and hashin-hansen models because the mean values are closest to zero than others. it is also important to notice that the standard deviation of both models (maxwell 5.27, counto1 5.32 and hashin-hansen 5.72) are tight which indicates that there is a high concentration of estimated values around of zero. m.f. bouali et alii, frattura ed integrità strutturale, 52 (2020) 82-97; doi: 10.3221/igf-esis.52.07 95 figure 5: error percentage distribution approximation to normal statistic low of each composite material model. conclusion he modulus of elasticity is a very important mechanical parameter, its determination sometimes involves impossible, difficult or costly tests, the alternative use of the biphasic laws in these cases appears very interesting but the choice of a model and not another remains a question which requires a precise examination and strongly depends on the type of materials chosen. in order to choose the optimized prediction composite model for lightweight aggregate concrete, the purpose of this paper was to appraise the effective young’s modulus of lwac using two-phase composite models. from the obtained numerical predictions, as confronted to existing experimental data and analytical results, the main findings are summarized below: when the young’s modulus of lightweight aggregates eg is much less than the young’s modulus of the mortar matrix in the lightweight aggregate concrete em, hirsch-dougill models remain distant from experimental results and cannot be applied to predict the modulus of elasticity of lwac. using popovics, counto2 and bache-nepper christensen composite models may not always produce accurate results. for 119 experimental values of young’s modulus for lwac, the maxwell, counto1 and hashin-hansen seem the most reasonable for this purpose. the maxwell model takes into account in the calculation of the effective elastic modulus of the contrast between the two phases (the mortar matrix and the light aggregates) represented by the coefficient  (eg/em) which made it possible to simulate the materials well and offered consequently more precise results if compared with other models. thus, the precision of this prediction model demonstrates its effectiveness and potential application as a model for lightweight aggregate concrete. the maxwell model remains close from the experimental values with a man value error equal to 0.29 and a standard deviation equal to 5.27. in addition the counto1 and hashin-hansen models provide a good prediction of t m.f. bouali et alii, frattura ed integrità strutturale, 52 (2020) 82-97; doi: 10.3221/igf-esis.52.07 96 experimental young’s modulus of all lwac tested by de larrard 7, yang and huang 8 and ke y et al. 9 (119 values) with a maximum volume fraction of aggregates vg equal to 49.37%. in conclusion, it can be suggested that additional studies about investigation for predicting modulus of elasticity of lwac, may contribute to confirm the reliability and the accuracy of maxwell, counto1 and hashin-hansen models. nomenclature e : young’s modulus ge : young’s modulus of lightweight aggregate (dispersed phase) me : young’s modulus of matrix (mortar) gv : volume fraction of aggregate (dispersed phase) mv : volume fraction of matrix (mortar) ce : young’s modulus of composite c _ voigte : young’s modulus of composite using voigt model (upper bound) c _ reusse : young’s modulus of composite using reuss model (lower bound) c _ hashine : young’s modulus of composite using hashin-hansen model c _ hirsche : young’s modulus of composite using hirsch-dougill model c _ popovicse : young’s modulus of composite using popovics model c _ maxwelle : young’s modulus of composite using maxwell model : empirical factor c _ counto1e : young’s modulus of composite using counto1 model c _ counto 2e : young’s modulus composite using counto2 model c _ bachee : young’s modus of composite using bache and nepper-christensen model deexp larrard e : young’s modulus of lwac tested by de larrard and le roy (1995) exp _ yange : young’s modulus of lwac tested by yang and huang (1998) exp _ kee : young’s modulus of lwac tested by ke y et al (2010) c : poisson’s ratio of composite m : poisson’s ratio of matrix (mortar) g : poisson’s ratio of aggregate (dispersed phase) d: smallest diameter of aggregates in concrete d: largest diameter of aggregates in concrete c _ anale : young’s modulus predicted from analytic model e : error percentage e : absolute value of error percentage references [1] muhammad riaz, a. and bing, c. (2019). experimental research on the performance of lightweight concrete containing foam and expanded clay aggregate, composites part b: engineering, 171, pp. 46-60. doi: 10.1016/j.compositesb.2019.04.25 m.f. bouali et alii, frattura ed integrità strutturale, 52 (2020) 82-97; doi: 10.3221/igf-esis.52.07 97 [2] rashad, a. m. (2018). lightweight expanded clay aggregate as a building material – an overview. construction and building materials, 170, pp. 757–775. doi: 10.1016/j.conbuildmat.2018.03.009. [3] colangelo, f. and ilenia, f. (2019). lightweight concrete with polyolefins as aggregates. use of recycled plastics in eco-efficient concrete, pp. 167-187, elsevier. doi: 10.1016/b978-0-08-102676-2.00008-6. [4] muhammad riaz, a., bing, c. and farasat ali shah, s. (2019). investigate the influence of expanded clay aggregate and silica fume on the properties of lightweight concrete, construction and building materials, 220, pp. 253-266. doi: 10.1016/j.conbuildmat.2019.05.171 [5] chandra, s., berntsson, l. (2002). lightweight aggregate concrete. elsevier. [6] ke, y., beaucour, a. l., ortola, s., dumontet, h., cabrillac, r. (2009). influence of volume fraction and characteristics of lightweight aggregates on the mechanical properties of concrete, constr. build. mater. 23(8), pp. 2821–2828. doi: 10.1016/j.conbuildmat.2009.02.038 [7] de larrard, f. (1995). une approche de la formulation des bétons légers de structure, bulletin de liaison des laboratoires des ponts et chaussées lcpc, 195, pp. 39–47 (in french). [8] yang, c. c., huang, r. (1998). approximation strength of lightweight aggregate using micromechanics method, adv. cem. based mater, 7(3–4), pp. 113–138. doi: 10.1016/s1065-7355(98)00002-9. [9] ke, y., ortola, s., beaucour, a.l., dumontet, h. (2010). identification of microstructural characteristics in lightweight aggregate concretes by micromechanical modelling including the interfacial transition zone (itz). cem. conc. res., 40(11), pp. 1590–1600. doi: 10.1016/j.cemconres.2010.07.001. [10] kurugöl, s., tanaçan, l., ersoy, h.s. (2008). young’s modulus of fiber-reinforced and polymer-modified lightweight concrete composites, constr. build. mater, 22(6), pp. 1019–1028. doi: 10.1016/j.conbuildmat.2007.03.017. [11] tanaçan, l. ersoy, h.y. (2000). mechanical properties of fired clay-perlite as composite material, j. mater. civil eng. asce, 12(1), pp. 55–59. doi: 10.1061/(asce)0899-1561(2000)12:1(55). [12] cui, hz. (2011). study of prediction model for compressive strength of lightweight aggregate concrete. adv mater res, pp. 1204–1209. doi: 10.4028/www.scientific.net/amr.335-336.1204 [13] lo, t.y., cui, h.z. (2004). effect of porous lightweight aggregate on strength of concrete, mater. lett. 58, pp. 916919. doi: 10.1016/j.matlet.2003.07.036. [14] ardakani, a., yazdani, m. (2014). the relation between particle density and static-elastic moduli of lightweight expanded clay aggregates, appl. clay sci. 93–94, pp. 28–34. doi: 10.1016/j.clay.2014.02.017. [15] ohama, y. (1987). principle of latex modification and some typical properties of latex-modified mortar and concrete, aci mater. j., 84(6), pp. 511–518. [16] kocataskin, f., özturan, t., ersoy, h.y. (1988). a composite materials approach for the prediction of concrete properties, bull. techn. univer. istanbul, 41(2), pp. 333–347. [17] zhou, f.p., lydon, f.d., barr, b.i.g. (1995). effect of coarse aggregate on elastic modulus and compressive strength of high performance concrete, cem. conc. res., 25(1), pp. 177–186. doi: 10.1016/0008-8846(94)00125-i. [18] gilormini, p., bréchet, y. (1999). syntheses: mechanical properties of heterogeneous media: which material for which model? which model for which material?, mod. simul. mater. sci. eng., 7(5), pp. 805–816. doi: 10.1088/0965-0393/7/5/312. [19] hansen, t.c. (1960). strength elasticity and creep as related to the internal structure of concrete. in: chemistry of cement, proceedings of fourth international symposium, monograph, 2, pp. 709–723, washington. [20] popovics, s., erdey, m. (1970). estimation of the modulus of elasticity of concrete-like composite materials, m.r.a. mater. struct., 3(4), pp. 253–260. doi: 10.1007/bf02474013. [21] hirsch, t.j. (1962). modulus of elasticity of concrete affected by elastic moduli of cement paste matrix and aggregate, aci j., 59(3), pp. 427–452. [22] hansen, t.c. (1965). influence of aggregate and voids on modulus of elasticity of concrete, cement mortar, and cement paste, aci j., 62(2), pp. 193–216. [23] counto, u.j. (1964). the effect of the elastic modulus of the aggregate on the elastic modulus, creep and creep recovery of concrete, mag. conc. res., 16(48), pp.129–138. doi: 10.1680/macr.1964.16.48.129 [24] bache, h.h., nepper-christansen, p. (1965). observations on strength and fracture in lightweight and ordinary concrete-the structure of concrete and its behavior under load, proceedings of international conference, cement and concrete association, pp. 93–108, london. [25] nielsen, l.e., chen, p.e. (1968). young’s modulus of composites filled with randomly oriented short fibers, j. mat., 3(2), pp. 352–358. [26] hashin, z. (1962). the elastic moduli of heterogeneous materials. j. appl. mech, 29(143). << /ascii85encodepages false /allowtransparency false /autopositionepsfiles true /autorotatepages /none /binding /left /calgrayprofile (dot gain 20%) /calrgbprofile (srgb iec61966-2.1) /calcmykprofile (u.s. web coated \050swop\051 v2) /srgbprofile (srgb iec61966-2.1) /cannotembedfontpolicy /error /compatibilitylevel 1.4 /compressobjects /tags /compresspages true /convertimagestoindexed true /passthroughjpegimages true /createjobticket false /defaultrenderingintent /default /detectblends true /detectcurves 0.0000 /colorconversionstrategy /cmyk /dothumbnails false /embedallfonts true /embedopentype false /parseiccprofilesincomments true /embedjoboptions true /dscreportinglevel 0 /emitdscwarnings false /endpage -1 /imagememory 1048576 /lockdistillerparams false /maxsubsetpct 100 /optimize true /opm 1 /parsedsccomments true /parsedsccommentsfordocinfo true /preservecopypage true /preservedicmykvalues true 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/hrv (za stvaranje adobe pdf dokumenata najpogodnijih za visokokvalitetni ispis prije tiskanja koristite ove postavke. stvoreni pdf dokumenti mogu se otvoriti acrobat i adobe reader 5.0 i kasnijim verzijama.) /hun 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can be opened with acrobat and adobe reader 5.0 and later.) >> /namespace [ (adobe) (common) (1.0) ] /othernamespaces [ << /asreaderspreads false /cropimagestoframes true /errorcontrol /warnandcontinue /flattenerignorespreadoverrides false /includeguidesgrids false /includenonprinting false /includeslug false /namespace [ (adobe) (indesign) (4.0) ] /omitplacedbitmaps false /omitplacedeps false /omitplacedpdf false /simulateoverprint /legacy >> << /addbleedmarks false /addcolorbars false /addcropmarks false /addpageinfo false /addregmarks false /convertcolors /converttocmyk /destinationprofilename () /destinationprofileselector /documentcmyk /downsample16bitimages true /flattenerpreset << /presetselector /mediumresolution >> /formelements false /generatestructure false /includebookmarks false /includehyperlinks false /includeinteractive false /includelayers false /includeprofiles false /multimediahandling /useobjectsettings /namespace [ (adobe) (creativesuite) (2.0) ] /pdfxoutputintentprofileselector /documentcmyk /preserveediting true /untaggedcmykhandling /leaveuntagged /untaggedrgbhandling /usedocumentprofile /usedocumentbleed false >> ] >> setdistillerparams << /hwresolution [2400 2400] /pagesize [612.000 792.000] >> setpagedevice microsoft word numero_37_art_30 g. beretta et alii, frattura ed integrità strutturale, 37 (2016) 228-233; doi: 10.3221/igf-esis.37.30 228 focussed on multiaxial fatigue and fracture biaxial fatigue tests of notched specimens for aisi 304l stainless steel g. beretta, v. chaves, a. navarro university of sevilla. departamento de ingeniería mecánica y fabricación. escuela técnica superior de ingeniería. universidad de sevilla. avda. camino de los descubrimientos, s/n. 41092, sevilla. spain. guido.bere@gmail.com, chavesrv@us.es, navarro@us.es abstract. high cycle fatigue tests were conducted for stainless steel aisi 304l. the geometry was a thin walled tube with a passing through hole. the tests were axial, torsional and in-phase axial-torsional, all of them under load control with r = −1. the s-n curves were constructed following the astm e739 standard and the fatigues limits were calculated following the method of maximum likelihood proposed by bettinelli. the crack direction along the surface was analysed, with especial attention to the crack initiation zones. the notch fatigue limits for different hole diameters were compared with the predictions done with a microstructural fracture mechanics model. keywords. fatigue limit; biaxial tests; notch; crack direction. introduction tress concentrations are the cause of fatigue failure in many industrial components. during the last few decades a great effort has been done by many researchers to understand the notch behaviour, either testing materials with notched geometries and/or proposing models to make predictions. just focusing in the high cycle fatigue regime and the fatigue limit, many experimental works can be found in the literature: gough tested v-notches in cylindrical specimens under combined stresses [1], frost did tests on double v-notch flat plates made of mild steel [2], el haddad et al. [3] and duquesnay et al. [4] did push-pull tests in plates with circular holes, lukás et al. did push-pull tests of cylindrical specimens with circumferential semi-circular notches in 2.25cr-1mo steel and copper [5], tanaka and akinawa tested plates with elliptical notches [6], meneghetti et al. tested double u-notch plates [7]. susmel and taylor conducted experiments using vshaped notches loaded in tension at various angles of inclination [8] and endo tested cylindrical specimens with a small surface hole, under axial, torsional and combined axial-torsional loading [9]. many methods have been proposed to predict the fatigue limit of notches under multiaxial fatigue loading, as the square root of the defect area method proposed by murakami and endo to deal with defect-containing components [10], the point method of taylor using the susmel-lazzarin critical plane criterion [8], the damage model extended to stress gradients proposed by brighenti and carpinteri [11], or the extension of the short crack growth model of navarro and de los rios [12] to specimens containing holes under in-phase biaxial loading [13]. however, despite all this work, it is a fact that the mechanisms of fatigue crack growth at notches are still not fully understood. in particular, it still remains unclear the direction of the crack during the initial growth of the crack, known as s g. beretta et alii, frattura ed integrità strutturale, 37 (2016) 228-233; doi: 10.3221/igf-esis.37.30 229 stage i. according to the critical plane approaches, the stage i occurs on the maximum shear stress plane. susmel and taylor [8] conducted experiments using v-notches at various angles of inclination to reproduce a multiaxial loading condition, and observed that the stage i crack growth occurred on the plane of maximum shear stress. endo [9], conducted tests on cylindrical specimens with a small surface hole, under axial, torsional and combined axial-torsional loading and observed that the crack grew approximately normal to the first principal stress from the start, regardless of the applied stress. so, these two experimental studies show a disagreement in the stage i direction. the knowledge of this direction is crucial, as most of the methods for predicting the fatigue limits are based on a stress gradient along a certain line, which is supposed to be representative of the stage i crack path. this paper reports on an experimental study conducted with stainless steel aisi 304l under proportional biaxial loading, from pure tension to pure torsion, in the high-cycle-fatigue regime. the geometry was a thin walled tube with a passing through hole. the direction of the crack on the specimen surface was examined. finally, theoretical predictions were compared with the experimental results. material data and tests he material was commercial aisi 304l stainless steel. its chemical composition (in wt.%) was as follows: 0.021 c, 0.029 p, 0.024 s, 0.34 si, 1.485 mn, 18.227 cr, 8.148 ni, 0.215 mo, 0.0005 ti, 0.08 n and 0.39 cu. the microstructure was formed by equiaxed austenite grains with some delta ferrite bands and the average austenite grain size was 80 µm. the specimens were machined from 22-mm-diameter round bars. no heat treatment was applied after the machining. the monotonic mechanical properties, as determined from 5 tensile tests, were as follows: tensile strength, σuts = 654 mpa; yield strength, σys (0.2%) = 467 mpa; and elongation, a = 56%. fatigue tests were performed either in a servo-hydraulic axial–torsion load frame, at a frequency of 6-8 hz, or in a resonance testing machine, at 80-100 hz, in both cases under fully-reversed loading (r =-1). each test was completed when the crack grew to be several millimetres long or after 3.5 × 106 cycles (run-outs). the fatigue limit in tension–compression (r = -1), as determined for cylindrical specimens and expressed in terms of stress amplitude, was σfl = 316 mpa, and the torsional fatigue limit τfl = 288 mpa (for further details, please see [14]). the fatigue limits were calculated using the method proposed by bettinelli [15], an alternative to classical choices such as the staircase method. the probability of being a run-out is expressed by a binomial distribution, and the value of the fatigue limit is estimated using the maximum likelihood method. figure 1: geometry of the notched specimen with the passing through hole. t g. beretta et alii, frattura ed integrità strutturale, 37 (2016) 228-233; doi: 10.3221/igf-esis.37.30 230 the geometry of the notched specimen was a thin walled tube with a passing through hole (see fig. 1). the diameters d of the holes were 1, 2 and 3 mm. the external surface of the gauge section was carefully polished to remove machining marks until reaching an average roughness (ra) of 0.1 µm. the passing hole and the internal surface of the tube were machined with great care. unfortunately, it was not possible to polish these two surfaces. fatigue limit predictions with the microstructural model avarro and de los rios [12] developed a model for short fatigue cracks growing in un-notched bodies. the authors assumed that plastic displacement ahead of the crack take place in rectilinear slip bands cutting across the grains of the material. this model was recently applied to a circular notch under proportional biaxial loading [13]. the problem is sketched in fig. 2. for simplicity, the remote applied stresses σy∞, τ∞ defining the biaxial load are considered to range between 0 and 1. the crack and the barrier, which represents the grain boundary, are modeled with dislocations. to keep the symmetry in the problem two opposing cracks are considered. the crack is modeled as a straight line and its initiation point and its direction can be whatever, defined by the angles θ and θ1. the solution of the equilibrium equations for the two distributions of dislocations (one with burger’s vector perpendicular to the crack and the other parallel to the crack) under the remote applied stresses, provides the stresses at the barrier, σ3i and τ3i, for successive crack lengths (a=id/2), which are expressed in terms of half grains d (i=1,3,5,...). these barrier stresses depend linearly on the applied stresses, as it was shown in a previous publication [16]. then, the value of the load required to overcome the i-th barrier, λ(θ, θ1, i) is just the value that multiplied by the stresses at the barrier lead to the fulfilment of the biaxial activation criterion, which has the following expression:                1 3 3 * * 1 , , i i i c i c i m m (1) figure 2: sketch of the microstructural model applied to an infinite plate with a circular hole subjected to proportional biaxial loading. in the previous expression,   * i cm and   * i cm are the activation constants, which depends on the material and can be calculated from the plain fatigue limits in tension and torsion and the kitagawa diagram. the maximum value of λ for all these crack lengths a=id/2 (i=1, 3, 5, ...) will provided the minimum load λ(θ, θ1), required to overcome all the barriers along the direction defined by the angles θ and θ1. as an estimation this maximum value is generally reached for a crack n g. beretta et alii, frattura ed integrità strutturale, 37 (2016) 228-233; doi: 10.3221/igf-esis.37.30 231 length that oscillates between 1 and 10 grain diameters, depending on the material, the stress gradient ahead of the notch, etc. this procedure must be repeated for all the directions given by θ and θ1 and the minimum value of all the obtained λ(θ, θ1), will be the predicted notched fatigue limit, λ0n:      0 1min ,n (2) the values of θ, θ1 for λ0n will provide the predicted crack initiation point at the notch and the predicted crack direction along the first grains (stage i). for a full explanation of the microstructural model applied to a circular notch under proportional biaxial loading, please see the reference [13]. experimental results and predictions he experimental fatigue limits for the aisi 304l stainless steel and the predictions with the microstructural model are shown in fig. 3. there are results for three hole diameters, d=1 mm, d=2 mm and d=3 mm. besides, the experimental data for smooth specimens, already published [14], and its theoretical curve (ellipse quadrant) is plot. it is seen that the predictions for d=2 mm agree quite well with the experimental data, while for d=1 mm and d=3 mm the agreement is not so good. more experimental data is required to get a reliable evaluation of the model. figure 3: comparison of experimental and predicted fatigue limits for the aisi 304l stainless steel. crack initiation point and crack direction during the stage i figs. 4, 5 and 6 show examples of cracks emanating from the hole for tension-compression, pure torsion and in-phase biaxial loading (σy∞= τ∞), respectively, for applied stresses close to the fatigue limit. the crack initiation point was, in the majority of the tests, located close to the point of maximum principal stress, which according to fig. 2, means a value of θ=0º for the axial tests, θ=45º for the torsion tests and θ=31.7º for the biaxial tests (σy∞= τ∞). the crack direction along the first 400 µm (5 average grains long), considered as the stage i of the crack growth, was also studied. the experimental directions were close to the maximum principal stress direction, which means values of θ1=0º for axial tests, θ1=45º for torsional tests and θ1=31.7º for biaxial tests (σy∞= τ∞). with respect to the model, an approximately similar minimum value of λ is obtained for several combinations of θ, θ1. it means that the predicted notched fatigue limit, λ0n, is associated with several initiation points and crack directions. certainly, this is not fully correct, as the experimental values of θ, θ1 are quite precise and with low scatter. further work needs to be done in the model in order to discriminate directions and correctly predict the crack initiation point and the stage i crack direction. t g. beretta et alii, frattura ed integrità strutturale, 37 (2016) 228-233; doi: 10.3221/igf-esis.37.30 232 figure 4: tension-compression. cracks emanating from the hole at an applied stress close to the fatigue limit. d = 1 mm, σy∞ = 200 mpa, n = 308 700 cycles. figure 5: cracks emanating from the hole at an applied stress close to the fatigue limit. d = 1 mm, τ∞ = 146 mpa, n = 1 454 269 cycles. figure 6: cracks emanating from the hole at an applied stress close to the fatigue limit. d = 1 mm, σy∞ = τ∞ = 140 mpa, n = 206 765 cycles. conclusions n experimental program has been conducted for tubes with a passing through hole of aisi 304l stainless steel under in-phase biaxial loading. biaxial fatigue curves were constructed using the experimental fatigue limits. the predictions of the fatigue limits obtained with a microstructural model reasonably agreed with the experimental a g. beretta et alii, frattura ed integrità strutturale, 37 (2016) 228-233; doi: 10.3221/igf-esis.37.30 233 values. the crack initiation point was close to the point of maximum stress, that is, 0º for axial tests and 45º for torsional tests. the crack direction along the stage i was close to the maximum principal stress direction. acknowledgements he authors would like to thank the spanish ministry of education for its financial support through grant dpi2014-56904-p. references [1] gough, h.j, pollard, h.v., clenshaw, w.j., ministry of supply, aeronautical research council reports and memoranda. london: his majesty’s stationary office (1951). [2] frost, n.e., proc instn mech eng, 173 (1959) 811-827. [3] el haddad, m.h., topper, t.h., smith, k.n., prediction of non-propagating cracks eng fract mech, 11 (1979) 573584. [4] duquesnay, d.l., yu, m.t., topper, t.h., in: the behaviour of short fatigue cracks, miller, k.j, de los rios, e.r. (ed), elsevier, (1986) 323-335. [5] lukás, p., kunz, l., weiss, b., stickler, r., fatigue fract engng mater struct, 9 (1986) 195-204. [6] tanaka, k., akinawa, y., in: fatigue’87. ritchie, r.o., starke jr., e.a. (ed), engineering materials advisory services, (1987) 739-748. [7] meneghetti, g., susmel, l., tovo, r., high-cycle fatigue crack paths in specimens having different stress concentration features, eng failure anal, 14 (2007) 656-672. [8] susmel, l., taylor, d., wo methods for predicting the multiaxial fatigue limits of sharp notches, fatigue fract engng mater struct, 26 (2003) 821-833. [9] endo, m. (2003), in: biaxial/multiaxial fatigue and fracture, esis publication 31, carpinteri, a., de freitas, m. and spagnoli, a. (ed), elsevier, (2003) 243-364. [10] murakami, y., endo, m., effects of defects, inclusions and inhomogeneities on fatigue strength, int j fatigue, 16 (1994) 163-82. [11] brighenti, r, carpinteri, a., a notch multiaxial-fatigue approach based on damage mechanics, fatigue fract engng mater struct, 39 (2012) 122-133. [12] navarro, a., de los rios, e.r., philos mag a, 57 (1988) 12-36. [13] chaves, v., navarro, a., beretta, g., madrigal, c., microstructural model for predicting high cycle fatigue strength in the presence of holes under proportional biaxial loading, theor appl fract mech, 73 (2014) 27-38. [14] chaves, v., navarro, a., madrigal, c., stage i crack directions under in-phase axial–torsion fatigue loading for aisi 304l stainless steel, int j fatigue, 80 (2015) 10-21. [15] bettinelli, s., tesi di laurea, universita degli studi di padova. supervisor: prof. r. tovo, (2006). [16] chaves, v., navarro, a., fatigue limits for notches of arbitrary profile, int j fatigue, 48 (2013) 68-79. t << /ascii85encodepages false /allowtransparency false /autopositionepsfiles true /autorotatepages /none /binding /left /calgrayprofile (dot gain 20%) /calrgbprofile (srgb iec61966-2.1) /calcmykprofile (u.s. web coated \050swop\051 v2) /srgbprofile (srgb iec61966-2.1) /cannotembedfontpolicy /error /compatibilitylevel 1.4 /compressobjects /tags /compresspages true /convertimagestoindexed true /passthroughjpegimages true /createjobticket false /defaultrenderingintent /default /detectblends true /detectcurves 0.0000 /colorconversionstrategy /cmyk /dothumbnails false /embedallfonts true /embedopentype false /parseiccprofilesincomments true /embedjoboptions true /dscreportinglevel 0 /emitdscwarnings false /endpage -1 /imagememory 1048576 /lockdistillerparams false /maxsubsetpct 100 /optimize true /opm 1 /parsedsccomments true /parsedsccommentsfordocinfo true /preservecopypage true 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can be opened with acrobat and adobe reader 5.0 and later.) >> /namespace [ (adobe) (common) (1.0) ] /othernamespaces [ << /asreaderspreads false /cropimagestoframes true /errorcontrol /warnandcontinue /flattenerignorespreadoverrides false /includeguidesgrids false /includenonprinting false /includeslug false /namespace [ (adobe) (indesign) (4.0) ] /omitplacedbitmaps false /omitplacedeps false /omitplacedpdf false /simulateoverprint /legacy >> << /addbleedmarks false /addcolorbars false /addcropmarks false /addpageinfo false /addregmarks false /convertcolors /converttocmyk /destinationprofilename () /destinationprofileselector /documentcmyk /downsample16bitimages true /flattenerpreset << /presetselector /mediumresolution >> /formelements false /generatestructure false /includebookmarks false /includehyperlinks false /includeinteractive false /includelayers false /includeprofiles false /multimediahandling /useobjectsettings /namespace [ (adobe) (creativesuite) (2.0) ] /pdfxoutputintentprofileselector /documentcmyk /preserveediting true /untaggedcmykhandling /leaveuntagged /untaggedrgbhandling /usedocumentprofile /usedocumentbleed false >> ] >> setdistillerparams << /hwresolution [2400 2400] /pagesize [612.000 792.000] >> setpagedevice microsoft word numero_53_art_04_2704 v. rizov et alii, frattura ed integrità strutturale, 53 (2020) 38-50; doi: 10.3221/igf-esis.53.04 38 longitudinal fracture analysis of inhomogeneous beams with continuously varying sizes of the cross-section along the beam length victor rizov department of technical mechanics, university of architecture, civil engineering and geodesy, 1 chr. smirnensky blvd., 1046 – sofia, bulgaria, e-mail: v_rizov_fhe@uacg.bg holm altenbach lehrstuhl für technische mechanik und geschäftsführender leiter institut für mechanik g10/58, fakultät für maschinenbau, otto-von-guericke-universität magdeburg, universitätsplatz 2, 39106 magdeburg, deutschland, holm.altenbach@ovgu.de abstract. analyses of longitudinal fracture behavior of inhomogeneous beams which have continuously varying sizes of the cross-section along the beam length are carried-out. beams of a rectangular cross-section are studied. it is assumed that beams exhibit continuous (smooth) material inhomogeneity along the width and height of the cross-section. a longitudinal crack located arbitrary along the beam height is analyzed. first, a cantilever beam with linearly varying width and height along the beam length is considered. the material of the beam has non-linear elastic mechanical behavior. the external loading consists of one bending moment applied at the free end of the lower crack arm. the fracture behavior is analyzed in terms of the strain energy release rate assuming that the modulus of elasticity is distributed continuously in the beam cross-section. the balance of the energy is considered in order to derive the strain energy release rate. a solution to the strain energy release rate is obtained also by considering the complementary strain energy for verification. the longitudinal fracture behavior of the inhomogeneous nonlinear elastic cantilever beam configuration is studied also for the cases when the variation of the width and height of the cross-section is described by sine and power laws. keywords. beam of varying cross-section; longitudinal fracture; material non-linearity; inhomogeneous material citation: v. rizov, h. altenbach, longitudinal fracture analysis of inhomogeneous beams with continuously varying sizes of the cross-section along the beam length, frattura ed integrità strutturale, 53 (2020) 38-50. received: 09.12.2019 accepted: 20.04.2020 published: 01.07.2020 copyright: © 2019 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. introduction ne of the efficient ways to improve the stability and to increase the strength and load bearing capacity of the structures, and at the same time to reduce their weight is to use beams of continuously varying sizes of the cross-section along the beam length. structural members and components with variable cross-section in the o https://youtu.be/wsetdvfgdss v. rizov et alii, frattura ed integrità strutturale, 53 (2020) 38-50; doi: 10.3221/igf-esis.53.04 39 length direction are commonly used in various engineering applications in aeronautics, robotics, power stations, shipbuilding and car industry where the weight saving is of basic importance. beam structures with varying cross-section can be sophisticated further by using inhomogeneous materials. in contrast to the conventional homogeneous materials, such as metals, the material properties of inhomogeneous materials vary smoothly along one or more directions in the solid. thus, the properties of inhomogeneous materials are continuous functions of spatial coordinates. the interest to the inhomogeneous materials is due mainly to the fact that certain kinds of inhomogeneous materials, such as functionally graded materials, have been widely used in aeronautical and mechanical engineering in the last thirty years [1 12]. the mechanical characteristics and microstructure of functionally graded materials can be tailored technologically during the manufacturing process in order to optimize the performance of the structural members and components to the external loadings and influences. the fracture behavior of inhomogeneous (functionally graded) structures and materials is of tremendous importance for practical engineering [13 15]. various studies of the fracture behavior of functionally graded composite materials have been reviewed in [13]. cracks oriented both parallel and perpendicular to the gradient direction have been analyzed by using methods of linear-elastic fracture mechanics. fracture behavior under fatigue crack loading conditions has also been investigated. rectilinear as well as curved cracks have been considered [13]. an approach for studying of delamination fracture behavior of a beam structure under creep loading conditions has been developed in [14]. the analysis has been carried-out assuming validity of the principles of linear-elastic fracture mechanics. an elevated temperature has been used to accelerate the delamination fracture at constant external loads. a double cantilever beam configuration has been examined. it has been found that the service lifetime can be successfully predicted by using a form of paris law. various techniques for analyzing of functionally graded layers and sandwich beam constructions have been presented and discussed in [15]. analyses of different beam configurations under static or dynamic loading conditions have been carriedout by using methods of linear-elastic fracture mechanics. works on buckling behavior of sandwich constructions have also been reviewed. static analyses of functionally graded beam structures resting on pasternak elastic foundation have been reviewed too. investigations of viscoelastic bending behavior of sandwich structures have been presented. it should be noted that all of the above mentioned publications have been focused on fracture in beam configurations with constant cross-section along the beam length. besides, linear-elastic behavior of the material has been assumed. therefore, the aim of the present paper is to analyze the longitudinal fracture behavior of inhomogeneous beam configurations with constantly varying sizes (width and height) of the cross-section along the beam length. the analysis is carried-out assuming non-linear elastic mechanical behavior of the material. one of the motives for the present paper is the fact that certain kinds of inhomogeneous materials, such as functionally graded materials, can be built-up layer by layer [11, 12] which is a premise for appearance of longitudinal cracks between layers. it should be mentioned that the previous works of the author are concerned with longitudinal fracture analyses of inhomogeneous (functionally graded) beam configurations with constant sizes of the cross-section along the beam height [16 – 19]. the beam under consideration in the present paper exhibits smooth material inhomogeneity in both width and height directions. the longitudinal fracture is analyzed in terms of the total strain energy release rate by applying the theory for bending of prismatic beams since this theory can be used also for beams with varying cross-section along the beam length provided that the variation is not abrupt and the angle of inclination of the beam edge is small [20]. theoretical model n inhomogeneous non-linear elastic cantilever beam configuration with linearly varying cross-section along the beam length is shown in fig. 1. the length of the beam is l . the beam is clamped in section d . the crosssection of the beam is a rectangle of width, b , and height, h . the variations of b and h along the beam length are given by the following linear laws: 3 t n n b b b b x l    , (1) 3 t n n h h h h x l    , (2) a v. rizov et alii, frattura ed integrità strutturale, 53 (2020) 38-50; doi: 10.3221/igf-esis.53.04 40 where 30 x l  . (3) in (1) and (2), nb and nh are the width and height in the free end of the beam, the width and height in the clamping are denoted by tb and th , 3x is the longitudinal centroidal axis of the beam (fig. 1). figure 1: geometry and loading of inhomogeneous cantilever beam with linearly varying sizes of the cross-section in the length direction. the beam under consideration exhibits continuous (smooth) material inhomogeneity in both height and width directions of the cross-section. thus, the distribution of the modulus of elasticity, e , in the beam cross-section is described by the following power law:     3 3 12 2 g f t l s l l b y z e e e e e e b h                   , (4) where 3 2 2 b b y   , (5) 3 2 2 h h z   . (6) v. rizov et alii, frattura ed integrità strutturale, 53 (2020) 38-50; doi: 10.3221/igf-esis.53.04 41 in (4), le , te and se are, respectively, the values of the modulus of elasticity along the edges, 1 2l l , 1 2t t and 1 2s s of the beam (fig. 1), f and g are material properties that control the material inhomogeneity in the height and width directions, respectively. figure 2: cross-section of the lower crack arm. a longitudinal crack of length, a , is located arbitrary along the beam height (fig. 1). it should be noted that the present paper is motivated also by the fact that certain kinds of inhomogeneous materials, such as functionally graded materials, can be built-up layer by layer which is a premise for appearance of longitudinal crack between layers [8]. the thicknesses of the lower and upper crack arms in the free end of the beam are denoted by 1nh and 2nh , respectively. the variations of the thicknesses of the lower and upper crack arms, 1h and 2h , along the crack length are written as 1 1 3 2 t n n h h h h x l    , (7) 2 2 3 2 t n n h h h h x l    , (8) where 30 x a  . (9) the external loading of the beam consists of one bending moment, m , applied at the free end of the lower crack arm (fig. 1). thus, the upper crack arm is free of stresses. the longitudinal fracture behavior of the beam shown in fig. 1 is studied in terms of the total strain energy release rate, g . for this purpose, the balance of the energy is analyzed. by assuming a small increase, a , of the delamination crack length, the balance of the energy is expressed as u m a gb a a        , (10) where  the increase of the angle of rotation of the free end of lower crack arm, u is the strain energy cumulated in the beam. from (10), the strain energy release rate is derived as 1m u g b a b a       . (11) the angle of rotation of the free end of lower crack arm is obtained by applying the castigliano’s theorem for structures exhibiting material non-linearity v. rizov et alii, frattura ed integrità strutturale, 53 (2020) 38-50; doi: 10.3221/igf-esis.53.04 42 *u m     , (12) where *u is the complementary strain energy in the beam. since the upper crack arm is free of stresses, the complementary strain energy is written as * * *1 2u u u  , (13) where *1u and * 2u are, respectively, the complementary strain energies cumulated in the lower crack arm and in the uncracked beam portion, 3a x l  . the complementary strain energy in the lower crack arm is expressed as 1 1 2 2 * * 1 01 3 1 1 0 2 2 hb a b h u u dx dy dz      , (14) where *01u is the strain energy density, 1y and 1z are the centroidal axes of the cross-section of the lower crack arm (fig. 2). the strain energy density is written as [16] *01 01u u  , (15) where  is the normal stress,  is the strain, 01u is the strain energy density in the lower crack arm. the mechanical behavior of the material is treated by the following stress-strain relation [21]: me h    , (16) where h and m are material properties which describe the material non-linearity. the strain energy density is obtained by integrating of (16) 2 1 01 2 1 me h u m       . (17) by substituting of (16) and (17) in (15), one drives 2 1 * 01 2 1 me mh u m       . (18) by using (4), the distribution of the modulus of elasticity in the lower crack arm is written as     1 1 12 1 2 g f t l s l l b y z h e e e e e e b h h                    , (19) where 1 2 2 b b y   , (20) v. rizov et alii, frattura ed integrità strutturale, 53 (2020) 38-50; doi: 10.3221/igf-esis.53.04 43 1 11 2 2 h h z   . (21) since beams of high length to height ratio are under consideration in the present paper, the distribution of the strains in the cross-section of the lower crack arm is treated in accordance with the bernoulli’s hypothesis for the plane sections. thus,  is expressed as 1 1 11 1c y z y z      , (22) where 1c  is the strain in the centre of the lower crack arm cross-section, 1y  and 1z  are the curvatures of lower crack arm in the 1 1x y and 1 1x z planes, respectively. the curvatures of the lower crack arm and the strain in the centre of the cross-section are found from the equations for equilibrium of the elementary forces in the cross-section of the lower crack arm 1 1 2 2 1 1 1 22 h b h b n dy dz     , (23) 1 1 1 2 2 1 1 1 22 h b y h b m z dy dz     , (24) 1 1 1 2 2 1 1 1 22 h b z h b m y dy dz     , (25) where 1n is the axial force, 1ym and 1zm are the bending moments with respect to the centroidal axes, 1y and 1z ,  is the normal stress, b and 1h are the width and height of the cross-section (fig. 2). it is obvious that (fig. 1) 1 0n  , (26) 1y m m , (27) 1 0zm  . (28) after substituting of (16) in (23), (24) and (25) the equations for equilibrium are solved with respect to 1c  , 1y  and 1z  by using the matlab computer program. then *01u is found by substituting of (19) and (22) in (18). the complementary strain energy in the un-cracked beam portion is written as 2 2 * * 2 02 3 2 2 2 2 hb l b ha u u dx dy dz      , (29) where *02u is the strain energy density, 2y and 2z are the centroidal axes. formula (18) is used to obtain * 02u . for this purpose,  is replaced with d where d is the distribution of the strains in the un-cracked beam portion. the v. rizov et alii, frattura ed integrità strutturale, 53 (2020) 38-50; doi: 10.3221/igf-esis.53.04 44 distribution of d is found by replacing of 1c , 1y and 1z with 2c , 2y and 2z in (22) where 2c is the strain in the centre, 2y  and 2z  are the curvatures of the un-cracked beam portion. the strain in the centre and the curvatures are obtained by using the equations of equilibrium (23), (24) and (25). for this purpose, 1h ,  , 1y and 1z are replaced with h , d , 2y and 2z , respectively. the stresses, d , is found by replacing of  with d in formula (16). the strain energy cumulated in the beam is obtained as 1 2u u u  , (30) where the strain energies in the lower crack arm and in the un-cracked beam portion are denoted by 1u and 2u , respectively. formulae (14) and (29) are used to determine 1u and 2u . for this purpose, * 01u and * 02u are replaced with 01u and 02u , respectively. the strain energy density in the un-cracked beam portion, 02u , is found by replacing of  with d in formula (17). finally, by substituting of  and u in (11), one obtains the following expression for the strain energy release rate: 1 1 2 2 2 2 * * 01 1 1 02 2 2 2 2 22 hb b h b h b h m g u dy dz u dy dz b m                1 1 2 2 2 2 01 1 1 02 2 2 2 2 22 hb b h b h b h u dy dz u dy dz              (31) the integration in (31) is carried-out by using the matlab computer program. matlab is used also to determine the derivative,  ... m   , in (31). it should be noted that b , h , 1h , 01u , 02u , * 01u and * 02u in (31) are obtained by (1), (2), (7), (17) and (18) at 3x a . the strain energy release rate is derived also by differentiating the complementary strain energy in the beam with respect to the crack are *du g da  , (32) where da is an elementary increase of the crack area. since da bda , (33) expression (32) takes the form *du g bda  , (34) where da is an elementary increase of the crack length. by substituting of *u in (34), one obtains the following expression for the strain energy release rate: 1 1 2 2 2 2 * * 01 1 1 02 2 2 2 2 22 1 hb b h b h b h g u dy dz u dy dz b               , (35) where b , h , 1h , * 01u and * 02u are found by (1), (2), (7), and (18) at 3x a . the integration in (35) is performed by using the matlab computer program. the fact that the strain energy release rate obtained by (35) is exact match of that v. rizov et alii, frattura ed integrità strutturale, 53 (2020) 38-50; doi: 10.3221/igf-esis.53.04 45 found by (31) is an indication for correctness of the longitudinal fracture analysis of the inhomogeneous cantilever beam with linearly varying cross-section along the beam length carried-out in the present paper. case studies his section of the paper reports results which illustrate the influence of the varying cross-section of the beam in the length direction on the longitudinal fracture behavior. for this purpose, calculations of the strain energy release rate are performed by applying (31). the results obtained are presented in non-dimensional form by using the formula  /n lg g e b . the influence of the material inhomogeneity in the height and width directions, crack length, material non-linearity and the crack location along the beam height on the longitudinal fracture behavior are also analyzed. it is assumed that 0.008nb  m, 0.006nh  m, 0.130l  m, and 2m  nm. the variation of the height of the cross-section along the beam length is characterized by /t nh h ratio. figure 3: the strain energy release rate in non-dimensional form plotted against /t nh h ratio (curve 1 at / 0.5t le e  , curve 2 – at / 1.0t le e  and curve 3 – at / 1.5t le e  ). figure 4: the strain energy release rate in non-dimensional form plotted against /t nb b ratio (curve 1 at / 0.25a l  , curve 2 – at / 0.50a l  and curve 3 – at / 0.75a l  ). the influence of the variation of the height on the longitudinal fracture is illustrated in fig. 3 where the strain energy release rate in non-dimensional form is plotted against /t nh h ratio at three /t le e ratios (it should be mentioned that /t le e ratio characterizes the material inhomogeneity along the width of the cantilever beam configuration). it is evident form fig. 3 that the strain energy release rate decreases with increasing of /t nh h ratio. the curves in fig. 3 indicate also that increase of /t le e ratio leads also to decrease of the strain energy release rate. the effect of the variation of the beam width in the length direction on the longitudinal fracture behavior is investigated too. the variation of the width is characterized by /t nb b ratio. in order to evaluate the influence of the crack length on the longitudinal fracture, /a l ratio is introduced. one can get an idea of the influence the crack length in fig. 4 where the strain energy release rate in non-dimensional form is plotted against /t nb b ratio at three /a l ratios. it can be observed in fig. 4 that the strain energy release rate decreases with increasing of /t nb b ratio. the strain energy release rate decreases also with increasing of /a l ratio since the height and width of the beam cross-section increase towards the clamping. the influence of the material inhomogeneity along the beam height on the longitudinal fracture behavior is analyzed. for this purpose, /s le e ratio is introduced. calculations of the strain energy release rate are performed at various /s le e ratios. the results obtained are presented in fig. 5 where the strain energy release rate in non-dimensional is plotted against /s le e ratio at three 1 /n nh h ratios. it can be observed in fig. 5 that the strain energy release rate decreases with t v. rizov et alii, frattura ed integrità strutturale, 53 (2020) 38-50; doi: 10.3221/igf-esis.53.04 46 increasing of /s le e ratio. the crack location along the beam height is characterized by 1 /n nh h ratio. one can observe in fig. 5 that the increase of 1 /n nh h ratio leads to decrease of the strain energy release rate. figure 5: the strain energy release rate in non-dimensional form plotted against /s le e ratio (curve 1 – at 1 / 0.3n nh h  , curve 2 – at 1 / 0.5n nh h  and curve 3 – at 1 / 0.7n nh h  ). figure 6: the strain energy release rate in non-dimensional form plotted against m (curve 1 – at non-linear elastic behavior of the material and curve 2 – at linear-elastic behavior). figure 7: the strain energy release rate in non-dimensional form plotted against f (curve 1 – at / 0.5s te e  , curve 2 – at / 1.0s te e  and curve 3 – at / 2.0s te e  ). the effect of the magnitude of the external loading of the beam on the longitudinal fracture behavior is studied also. for this purpose, calculations of the strain energy release rate are carried-out at various values of m . the calculated strain energy release rate in non-dimensional form is presented as a function of m in fig. 6. the curves in fig. 6 show that the strain energy release rate quickly increases with increasing of m . the influence of the non-linear mechanical behavior of the material on the longitudinal fracture is investigated too. for this purpose, the strain energy release rate obtained assuming linear-elastic mechanical behavior of the inhomogeneous material is presented as a function of m in fig. 6. it should be noted that the linear-elastic solution to the strain energy release rate is derived by substituting of 0h  in formula (31) which follows from the fact that at 0h  the non-linear stress-strain relation (16) transforms into the hooke’s law where the modulus of elasticity of the inhomogeneous material is expressed by (4). it is evident from fig. 6 that the non-linear mechanical behavior of the material causes increase of the strain energy release rate. the influence of the material property f on the longitudinal fracture behavior of the inhomogeneous non-linear elastic cantilever beam with linearly varying cross-section in the length direction is evaluated. the strain energy release rate in v. rizov et alii, frattura ed integrità strutturale, 53 (2020) 38-50; doi: 10.3221/igf-esis.53.04 47 non-dimensional form is presented as a function of f in fig. 7 at three /s te e ratios. the curves in fig. 7 indicate that the strain energy release rate decreases with increasing of f . one can observe also in fig. 7 that the increase of /s te e ratio leads to decrease of the strain energy release rate. it is interesting to investigate the effect of the law for variation of the sizes of rectangular cross-section along the beam length on the longitudinal fracture behavior. in order to elucidate this effect, a further two laws (sine and power) for continuous variation of the beam cross-section are considered. the variations of the width and height of the beam according to the sine law are written as   3sin 2 n t n x b b b b l         , (36)   3sin 2 n t n x h h h h l         , (37) where 30 x l  . (38) formulae (36) and (37) indicate that the width and height vary smoothly from nb and nh at the free end of the beam to tb and th at the clamped end of the beam. the variations of thicknesses of the lower and upper crack arms when the sine law is used are expressed as 31 1 sin 2 2 t n n h h x h h l         , (39) 32 2 sin 2 2 t n n h h x h h l         , (40) where 30 x a  . (41) when the power law is used, the variations of the width and height of the beam cross-section are written as   3 2 3 n t n x b b b b l          , (42)   3 2 3 n t n x h h h h l          (43) where 30 x l  . (44) correspondingly, the variations of the thicknesses of the two crack arms are obtained as 3 3 2 1 1 2 t n n xh h h h l         , (45) v. rizov et alii, frattura ed integrità strutturale, 53 (2020) 38-50; doi: 10.3221/igf-esis.53.04 48 3 3 2 2 2 2 t n n xh h h h l         , (46) where 30 x a  . (47) it is obvious from formulae (45) and (46) that the width and height vary smoothly from nb and nh at the free end of the beam to tb and th at the clamped end of the beam. the effect of the law for continuous variation of the beam cross-section on the longitudinal fracture behavior of the inhomogeneous non-linear elastic beam is illustrated in fig. 8 where the strain energy release rate in non-dimensional form is presented as a function of the material property, g , for the three laws (linear, sine and power). it is evident from fig. 8 that when the sine law is used the strain energy release rate is lower in comparison to that obtained at the linear law for variation of the width and height of the beam cross-section (this finding is explained by the fact that when the sine law is used the height and width of the beam cross-section are higher compared with the height and width according to the linear law). figure 8: the strain energy release rate in non-dimensional form plotted against g at three different laws for variation of the beam cross-section in the length direction (curve 1 – at power law, curve 2 – at linear law and curve 3 – at sine law). the use of power law leads to obtaining of higher strain energy release rate compared to that calculated at linear law (this behavior is attributed to the lower sizes of the beam cross-section when the power law is used for describing the variation of the height and width along the beam length). it should be noted that when the sine and power laws are applied for describing the variation of the beam cross-section in the length direction, the strain energy release rate is obtained by (31). for this purpose, the sizes of the cross-section, b , h and 1h , which are involved in (31) are calculated, respectively, by formulae by (36), (37) and (39) or by (42), (43) and (45). concerning the effect of g , the curves in fig. 8 show that the strain energy release rate decreases with increasing of g . conclusions he main novelty of the present paper is that in contrast to previous papers [16 19] which deal with longitudinal fracture analysis of inhomogeneous beams with constant cross-section, the inhomogeneous beam considered here has continuously varying height and width in the length direction. the fracture is studied in terms of the total strain energy release rate assuming non-linear elastic mechanical behavior of the material. a solution to the strain energy release rate is derived by considering the balance of the energy. the strain energy release rate is obtained also by t v. rizov et alii, frattura ed integrità strutturale, 53 (2020) 38-50; doi: 10.3221/igf-esis.53.04 49 differentiating of the complementary strain energy in the beam with respect to the crack area for verification. the longitudinal fracture behavior is analyzed assuming continuous (smooth) material inhomogeneity in both height and width directions of the beam cross-section (the distribution of the modulus of elasticity in the cross-section is described by applying a power law). special attention is paid to the influence of the continuously varying sizes of the beam crosssection on the longitudinal fracture behavior. it is found that the strain energy release rate decreases with increasing of /t nh h and /t nb b ratios (these ratios characterize the variation of the cross-section along the beam length). concerning the effects of the crack length and the crack location along the beam height on the longitudinal fracture, the analysis reveals that the strain energy release rate decreases with increasing of /a l and 1 /n nh h ratios. the decrease of the strain energy release rate with increasing of /a l ratio is due to the fact that the sizes of the cross-section increase towards the clamped end of the beam. the longitudinal fracture behavior is studied also when the continuous variation of the height and width of the cross-section along the beam length is described by using sine and power laws. the investigation shows that when the sine law is used the strain energy release rate is lower in comparison to that derived when the sizes of the cross-section vary linearly along the beam length. when variation of the sizes is described by the power law the strain energy release rate is higher compared to that obtained by using linear law for describing the variation of beam crosssection. the research performed shows that the longitudinal fracture behavior of inhomogeneous beam structures can be controlled by using appropriate laws for continuous variation of the sizes of the beam cross-section in the length direction. the results obtained in the present paper could be useful in preliminary structural design of inhomogeneous beams with continuously varying cross-section in the cases when their longitudinal fracture behaviour is also required to be addressed. acknowledgments izov is grateful for the financial support from the german academic exchange service (daad) for his research stay in department of technical mechanics, institute of mechanics, otto-von-guericke-university, magdeburg, germany. references [1] mortensen, a., suresh, s., functionally graded metals and metal-ceramic composites: part 1 processing, international materials review, 40 (1995) 239-265. [2] gasik, m.m., functionally graded materials: bulk processing techniques, international journal of materials and product technology, 39 (1995) 20-29. [3] neubrand, a., rödel, j., gradient materials: an overview of a novel concept, zeit f met, 88 (1997) 358-371. [4] suresh, s., mortensen, a., fundamentals of functionally graded materials, iom communications ltd, london (1998). [5] hirai, t., chen, l., recent and prospective development of functionally graded materials in japan, material science forum, 308-311 (1999) 509-514. [6] butcher, r.j., rousseau, c.e., tippur, h.v., a functionally graded particulate composite: measurements and failure analysis, acta matererialia, 47 (1999) 259-268. [7] nemat-allal, m.m., ata, m.h., bayoumi, m.r., khair-eldeen, w., powder metallurgical fabrication and microstructural investigations of aluminum/steel functionally graded material, materials sciences and applications, 2 (2011) 1708-1718. [8] saidi, h., sahla, m., vibration analysis of functionally graded plates with porosity composed of a mixture of aluminum (al) and alumina (al2o3) embedded in an elastic medium, frattura ed integrità strutturale, 13 (2019) 286299. [9] chikh, a., investigations in static response and free vibration of a functionally graded beam resting on elastic foundations, frattura ed integrità strutturale, 14 (2019)115-126. [10] nagaral, m., nayak, p. h., srinivas, h. k., auradi, v., characterization and tensile fractography of nano zro2 reinforced copper-zinc alloy composites, frattura ed integrità strutturale, 13 (2019) 370-376. [11] marae djouda, j., gallittelli , d., zouaoui, m., makke, a., gardan , j., recho, n., crépin, j., local scale fracture characterization of an advanced structured material manufactured by fused deposition modeling in 3d printing, frattura ed integrità strutturale, 14 (2019) 534-540. r v. rizov et alii, frattura ed integrità strutturale, 53 (2020) 38-50; doi: 10.3221/igf-esis.53.04 50 [12] bohidar, s.k., sharma, r., mishra, p.r., functionally graded materials: a critical review, international journal of research, 1 (2014) 289-301. [13] tilbrook, m.t., moon, r.j., hoffman, m., crack propagation in graded composites, composite science and technology, 65 (2005) 201-220. [14] al-khanbashi, a., hamdy, a.e., fracture mechanics approach to predict delamination lifetime in mode ii under constant loads, journal of adhesion science and technology, 18 (2004) 227-242. [15] sayyad, a.s., ghugal, y.m., modeling and analysis of functionally graded sandwich beams: a review, mechanics of advanced materials and structures, 1 (2018) 1-20. [16] rizov, v.i., non-linear elastic delamination of multilayered functionally graded beam, multidiscipline modeling in materials and structures, 13 (2017) 434-447. [17] rizov, v.i., delamination analysis of a layered elastic-plastic beam, international journal of structural integrity, 4 (2017) 516-529. [18] rizov, v.i., analysis of cylindrical delamination cracks in multilayered functionally graded non-linear elastic circular shafts under combined loads, frattura ed integrità strutturale, 46 (2018) 158-177. [19] rizov, v.i., influence of material inhomogeneity and non-linear mechanical behavior of the material on delamination in multilayered beams, frattura ed integrità strutturale, (2019) 468-481. [20] timoshenko, s., strength of materials. part ii. advanced theory and problems, science (1965). [21] lukash, p.a., fundamentals of non-linear structural mechanics, m. 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/hrv (za stvaranje adobe pdf dokumenata najpogodnijih za visokokvalitetni ispis prije tiskanja koristite ove postavke. stvoreni pdf dokumenti mogu se otvoriti acrobat i adobe reader 5.0 i kasnijim verzijama.) /hun 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can be opened with acrobat and adobe reader 5.0 and later.) >> /namespace [ (adobe) (common) (1.0) ] /othernamespaces [ << /asreaderspreads false /cropimagestoframes true /errorcontrol /warnandcontinue /flattenerignorespreadoverrides false /includeguidesgrids false /includenonprinting false /includeslug false /namespace [ (adobe) (indesign) (4.0) ] /omitplacedbitmaps false /omitplacedeps false /omitplacedpdf false /simulateoverprint /legacy >> << /addbleedmarks false /addcolorbars false /addcropmarks false /addpageinfo false /addregmarks false /convertcolors /converttocmyk /destinationprofilename () /destinationprofileselector /documentcmyk /downsample16bitimages true /flattenerpreset << /presetselector /mediumresolution >> /formelements false /generatestructure false /includebookmarks false /includehyperlinks false /includeinteractive false /includelayers false /includeprofiles false /multimediahandling /useobjectsettings /namespace [ (adobe) (creativesuite) (2.0) ] /pdfxoutputintentprofileselector /documentcmyk /preserveediting true /untaggedcmykhandling /leaveuntagged /untaggedrgbhandling /usedocumentprofile /usedocumentbleed false >> ] >> setdistillerparams << /hwresolution [2400 2400] /pagesize [612.000 792.000] >> setpagedevice microsoft word numero 14 articolo 2 in a br fed bra lob ab as 33 we par and kw ac cor rel rel str ke in pro con stru cra phe con pro the esti ma bas th cor t nfluence astm a raitner lob deral universi asília, brazil, batoae@gmail. bstract. t stm a743 c specimens ere tested un rameters tha d its scatter wofie’s relati ccording to t rrectly the r ation are co ation makes ength. eywords. f ntroductio he ast compon develop ogressive and nditions. thi ucture, on the ack growth an enomenon is nditions of t ocedures to e e use of these imate the effe achine elemen sic relations of he fatigue life rrelated with t e of mea 743 ca6 bato da silv ity of brasília, 70940-910. com.br, jorge@ the objective ca6nm allo were experi nder stress at describe th bands. in th ions were te the obtained reduction ef onsistent an s it possible fatigue; goo on tm a743 ca nents be desig ment and th d located pro is failure pro e presence of nd it can cul s common in these compo estimate the e e methodolog ects of mean nts subject to f load characte is described the alternat b. lo an stres 6nm al va, jorge l mechanical e @unb.br, felip e of this wo oy steel. it is imentally ev ratio 0, 1/3 he fatigue be he assessmen ested in orde d results it w ffect fatigue nd the walk to evaluate odman; gerb a6nm alloy gned for infin e propagation ocess of struc ocess depend f residual stre lminate in fra n axes’ flaw nents indent endurance lim gies demands stress in the complex load erization by the wöh ting stress, s obato da silva et ss on the lloy stee luiz de alm engineering d peo2@gmail.co ork is to ev s used in sev valuated und 3 and 2/3. ehavior of th nt of the me er to evaluat was possible life and pre ker’s relation in a consiste ber; walker; steel is used nite fatigue lif n of those cr ctural degrad s strongly on esses, on the g acture of the s, blades and tified that re mit of structu s a solid char fatigue streng ds, for the us hler curve or sa. this met alii, frattura ed e fatigu el meida ferr department, ca om, alex07@ valuate the e veral hydrog der axial load based on t he evaluated ean stress eff te the validi to verify th esented high n presented ent way the kwofie; as d in several fe, fatigue cra racks are asso dation that h n the stress geometric de e structural co d rotors. sta sidual stresse ural compone racterization gth and to ide ed material. s-n curve, s thod is a rel d integrità struttu ue streng reira, felipe ampus univer unb.br effects of m genator turbi ds with stres the obtained d material, ob fects of fatig ity of the us hat goodman h scatter. th d smaller sca effect of th stm a743 c hydrogenato acks usually ar ociated to th appens in a levels that a tails and on t omponent af arting from t es are fundam ents are much of the mater entify the mo stress-life, wh lation that c urale, 14 (2010) gth of e oliveira, rsitário darcy mean stress o ine compon ss ratio of d results it btain its s-n gue life, goo se of such ru n and gerb he prediction atter than k he presence o ca6nm. r turbine co re found at th e fatigue pro material und ctivate in the the material. t fter a certain the producti mental facto h known and rial. in that w del to be cap here the num can be well ) 17-26; doi: 10 , josé alex ribeiro, on the fatig ents. in ord 1 and mor was possibl n curves, its odman, gerb ules for the er’s relation ns of walke kwofie’s rel of mean stre mponents. i he root of tur ocess. fatigue der stress and e most loade these condit number of on, assembly rs to cause d relatively re way, the prese able to predic mber of cycles used to adju .3221/igf-esis. xander araú gue behavior der to achiev e 60 specim le to determ endurance li ber, walker tested mate ns do not mo er and kwof lation. walk esses on fati n spite of th rbine blades. e is a perman d strain dyna ed points of tions can deve cycle loads. t y and operat the fatigue. eliable. howe ent work aim ct the strengt s to failure, n ust appropria 14.02 17 újo r of ve it, mens mine imit and erial. odel fie’s ker’s igue hese the nent, amic f the elop this tion, the ever, ms to th of n, is ately http://dx.medra.org/10.3221/igf-esis.14.02&auth=true http://www.gruppofrattura.it mailto: lobatoae@gmail.com.br mailto: jorge@unb.br mailto: felipeo2@gmail.com mailto: alex07@unb.br b. l 18 exp cyc som cha min of an by th the exp me ini com pro go fati pro the in hig end sim dat wid mo stre sy. ex lobato da silva perimental da cles. this rela a as  me practical a aracterize the nimum value the range stre ms s  mssm  mssa  nd to describe eq. 5. the re ma m s s r  1 1 as    he standard co e eq. 1 can be perimental res ar s  ean stress effect tially, empiri mpensate the oposed a par oodman intro igue data in oposed as imp e fatigue stren order to ove gh mean stre durance limit milar to swt, ta, eq. 14. a despread mat odel consists i ess, sm, on th according to a s  xpressed in fo a s  et alii, frattura ata in the sen ation can be e bn applications a e constant am , eq. 2. the ess is called am max mins 2 minmax s 2 minmax s e the mean str elation betwe ax in . m r s r   ondition to de e express in t sults. ' b f n  t predition mo ic models w e effect of m rabolic repres oduced a theo the graphic provement of ngth coefficie ercome the fa esses, smith, for the load , however usi according to thematical rel in the substit e limit of fati o this model, m rts ar s e         orm of power m rts ar s e           ed integrità stru nse to correla expressed as in and also fatig mplitude load mean stress, mplitude stre ress, a factor en sa, sm e r etermine the the form of e odels ere proposed mean stress in sentation of oretical line t sa versus sm. f the previou nt and that th ailure predicti watson and ratio, r = -1 ing a factor  empiric con lations to des tution of the b igue strength the stress-life r series, the e 0 1 ! n i i s           utturale, 14 (201 ate the alterna n eq. 1, wher gue tests in m ds. the stres sm, is the ave ess, sa, eq. 4. used to char is expressed parameters o eq. 7. it is call d by gerber n the high cyc the wöhler’s to represent since 1960, s models. fat he compressio ion’s problem d topper s 1, sar, is expre  that makes nsiderations, scribe the effe basquin’s equ for the rever e relation can eq. 8 can be e i m rt s     10) 17-26; doi: ate stress and re a and b ar materials invol ss range, s erage between these are ba racterize the d in the eq. 6. of wöhler cur led basquin’s r (1874), go cle fatigue st s limit fatigu the evaluated some mode tigue tests ind on normal m m under load swt [3] prop essed in the e possible an a berkovits an fect of mean s uation’s const rse load condi be presented expressed by e 10.3221/igf-esi d the numbe e the constan lve maximum s , is the diff n maximum v asic relations t degree of sym rve is to assum s equation. w oodman (189 trength, accor ue data on th d fatigue data els to determ dicate that the ean stress sho conditions w posed a mod eq. 13. on th adjustment o nd fang [5] stress on the tant, eq. 7, fo ition, srt, and d by eq. 8. eq. 9: is.14.02 r of cycles to nt and the cur m and minimu ference betwe value and mi that character mmetry of the me alternating where ’f e b a 9), haigh (1 rding to lee he graphic sm a, eq. 11. ha mine the effec e tensile norm ould increase with relatively del in which his same year f the curve in and more r fatigue beha or a function on the ultim o failure betw rve exponent, um constant l een the maxi inimum value rize one load e load, load ra g load, null m are material co 1917) e sode [1] and dow max/su versus s aigh was the ct of mean s mal mean stre it [1]. y low amplitu the equivale , walker [4] p n relation to ecently kwo avior of endu that will dep ate strength, ween 103 and , respectively. (1) level stresses imum value e, eq. 3. the cycle. (2) (3) (4) atio, r, is defi (5) (6) mean stress. t onstants base (7) erberg (1930) wling [2]. ge smin/su , eq. first to plot stress have b ess should red ude and relati ent stress to presented crit the experime ofie [6] propo urance limit. s end on the m or yield stren (8) (9) d 106 . that and half fined thus, ed in ) to rber 12. t the been duce ively the teria ental osed such mean ngth, http://dx.medra.org/10.3221/igf-esis.14.02&auth=true http://www.gruppofrattura.it ad of sta des ma ma yiel spe th 466 for t dmitting that superior orde a a s  arting from th scribe some m aterial an aterial he mate martens strength ld strength, sy ecimen design he specimens 6-96 [8]. the r samples a a t the argument er converge q 1 m ar rt s        his last expres models presen  ,f r   ,f r  nd method erial used in t sitic. this typ h and that res sy) of the sam of the samp ese standards nd b, fig. 1 a b. lo t of the expo quickly to zero    ssion, one can nted in the ta hypothes 1  m rt f s          , 2 rt m s    , rt m s     table 1 ds the developm pe of steel is sist to the cor ple a and sam table le a were de specify the m and only spec sam a b obato da silva et onential funct o. in this spec n verify with e ab. 1. ses m rt s      1 2 2 rt m s ln        1 2 rt m s r ln         1: particular sol ment of this r used in the rrosion. the mple b are sh e 2: mechanic esigned accor main dimensi cimen 2 for sa figure 1: spe mple e ( a 1 b 1 alii, frattura ed tion tend to z cific conditio easiness that resulti a ar s  a ar s   r    a s  r    a s  lutions of wide research was production o mechanical p howed in tab cal properties rding to ast ions. in this w ample b, fig cimen 1 for sa (gpa) srt 198 8 198 9 d integrità struttu zero,  m s  n, the eq. 9 a depending on ing equation 1m rt s    2 1m y s         1 21 2 ar r s         1 2 ar r s          espread kwofi the astm a of structural c properties (yo b. 2. of sample a tm e 606-04 work three d 2. tab. 3 sho ample a and b (mpa) sy ( 890 6 918 6 urale, 14 (2010)  0 rt s  , the c assumes the f n the value of model goodman gerber swt walker ie model. a743 ca6nm components oung modulu and b. [7] and samp different spec ows the respec . (mpa) 637 665 ) 17-26; doi: 10 consequence following form f α, the wides equation (11) (12) (13) (14) m alloy steel that request us, e, tensile ple b starting imens were u ctively data. .3221/igf-esis. is that the te m: (10) spread model l, a stainless i high mechan strength, srt, g from astm used: specime 14.02 19 erms l will inox nical and m e en 1 http://dx.medra.org/10.3221/igf-esis.14.02&auth=true http://www.gruppofrattura.it b. l 20 fa th 90 the cur obs th stre stre str th me cha equ app end and alte lobato da silva tigue tests he fatigue test [9] and astm e critical value rve, 2 specim served the tes he s-n curves ess levels. th ess, s-n curv rategy for evalu he strategy us ean stress, sm aracterize the uation when plication of t durance limit, d sar basquin sh ernating stres et alii, frattura s under axial m 739-91 [10 es of design i mens were tes sts were repro s were obtaine he stress relat ves were desig uation of mean ed to evaluat m, alternating e mean and sm = 0, the e he value of r , called sar basq hould be iden s, sar model. fatigu experime data specimen / 1 / a 1 / b 2 / b ed integrità stru loads were p 0] , the minim is 12 specime sted for each oduced, guara ed considerin ted to the in gned for the f n stress models te models’ ad stress, sa, an alternating s equivalent fa resulting life, quin then, if th ntical statistic figure 3: st ue ental a  ,a m   n / sample a a 15 b 15 b 15 utturale, 14 (201 figure 2: s tab erformed in t mum number ens with repr h one of the anteeing at le ng the total cr finite life is d following rati s’ adherence dherence con nd the resulti stress in one atigue strength n, in the ba he prediction cally. tab. 4 trategy for eval extrapol    ars   ar   ars   a (mm) b (mm 51.42 63.7 51.13 61.5 52.40 58.8 10) 17-26; doi: specimen 2 for ble 3: specimen the mts 810, of necessary roduction of 5 chosen str ast 58% of re rack growth u defined as lim o loads, r, -1 nsists in the u ing life, n. a mean stress h according asquin’s equa model was ad shows a resu luation of mea late data n sm   ,a m  m) c (mm) 71 24.00 57 28.00 87 34.66 10.3221/igf-esi r sample b. n data , universal tes specimens to 50 to 75%. t ress levels. in eproduction. under dynami mit of fatigue 1, 0, 1/3 and 2 use of three p according to s model allow to specific m ation allows t dherent to th ume of the e an stress model cycle numbe ms  experimental d d (mm) e 10.00 12.00 12.50 is.14.02 sting machine o obtain a cur then, for a pr n the three le ic loads, repe e. in order to 2/3. parameters th fig. 3, the a ws to evalua model, called to estimate a e experiment equations use ls’ adherence er s     ata e (mm) f (m 6.00 48. 7.00 28. 7.00 56. e. according rve s-n in or reliminary an evels where la ating the pro o evaluate th hat characteri application o ate, through sar model. in a new value fo tal results, the ed to estimat statistical analysis modelar s basquinar s mm) g(mm) 00 50.00 00 50.00 00 to astm e 4 rder to determ nalysis of the arger scatter cess for diffe e effect of m ize a fatigue f the data wh extrapolation a similar way, or the equiva e values of sar te the equiva 468mine s-n was erent mean test: hich n of , the alent r model alent http://dx.medra.org/10.3221/igf-esis.14.02&auth=true http://www.gruppofrattura.it to res th obt re tes f estimate the pectively. 1 ' ra f s    2 1 a r         he estimate of tained results esults and sts with ratio l or the ra 7 show t f e exponents o   m rtse n          1 1 ' r f s n         f parameters s. p d discussio loading, -1 atio loading e the statistic b sa ( sa / m dev cv mod goodm gerb walk kwo b. lo table 4: equ of the kwofi  1rb  1r b   and  was parameter e   table 5: par ns equal -1, 11 sp ehavior of th (mpa) 4 srt (%) 4 mean 9.63 viation 5.46 v (%) 5 table 6: s del equat man ber ker ofie obato da silva et uations used to fie and walke s accomplish expected estimate sta 0.407 1.453 rameters that c pecimens wer he estimated f 417 4 46.9 4 3 e+05 3.51 6 e+05 5.73 56.7 1 statistic behavi tion to estima s s ar s alii, frattura ed o estimate the e er’s models,  ed using the d value andard error 0.019 0.084 characterize kw re used of sam fatigue lives fo 440 4 49.4 52 e+05 1.99 3 e+04 4.92 6.3 0 ior of fatigue li ate the equiva 1 a ar m rt s s        1 a ar m rt s s        2 1 r a r       s ar a s e        d integrità struttu equivalent alter  and  , resp levenberg-m confiden estimate 0.346 1.187 wofie and wal mple a and 2 or such stress 463 5 2.1 57 e+05 8.03 e+02 2.63 0.2 32 ives (r = -1) alent alternatin m t    2    1 r     m rt s     urale, 14 (2010) rnating stress. pectively, the marquardt m nce intervals standard erro 0.468 1.720 ker’s models. 22 specimens s level. 09 56 7.2 63 e+04 9.38 e+04 * 2.7 * sample a. ng stress eq ) 17-26; doi: 10 e eqns. 21 an ethod [11]. t or of sample b 66 3.3 e+03 * * quation (17) (18) (19) (20) .3221/igf-esis. nd 22 were u (21) (22) tab. 5 shows b. the tab. 6 14.02 21 used, the and http://dx.medra.org/10.3221/igf-esis.14.02&auth=true http://www.gruppofrattura.it b. l 22 tes for stat tes for the tes for fati lobato da silva sts with ratio l r the ratio loa tistic behavio sts with ratio l r the ratio loa e statistic beh sa (m sa / s me devia cv sts with ratio l r the ratio lo igue lives esti et alii, frattura sa ( sa / m dev cv loading, 0 ading, r = 0, or of fatigue li sa (mp sa / srt mea deviat cv (% sa (mp sa / srt mea deviat cv (% loading, 1/3 ading, r = 1/ avior of the f mpa) 19 srt (%) 29. ean 4.9 e+ ation 1.1 e+ (%) 22. ta loading, 2/3 oading, r = 2 imated for su sa (mp sa / su médi desv cv (% ed integrità stru (mpa) 3 srt (%) 3 mean 1.73 viation 5.49 v (%) 3 table 7: s 13 specimen ives estimated pa) 260 (%) 29.2 an 6.2 e+ tion 5.5 e+ %) 88.9 table 8: st pa) 260 (%) 29.2 an 7.9 e+ tion 3.5 e+ %) 44.7 table 9: st /3, 7 specime fatigue lives e 7 200 .2 29.8 +05 3.5 e+ +05 * .7 * able 10: statisti 2/3, 19 spec ch stress leve pa) 133 (%) 14.7 ia 8.7 e+0 vio 3.7 e+0 %) 42.3 table 11: sta utturale, 14 (201 353 3 38.4 3 3 e+06 1.13 9 e+05 8.82 31.6 7 statistic behavi ns were used d for such str 265 2 29.8 05 5.3 e+05 05 * * tatistic behavio 265 2 29.8 05 1.7 e+05 05 * * tatistic behavio ens were used estimated for 211 33.7 05 4.0 e+05 1.4 e+05 35.7 ic behavior of cimens of the el. 135 14.8 05 7.8 e+05 05 4.1 e+05 52.2 atistic behavior 10) 17-26; doi: 364 4 39.6 43 3 e+06 4.53 2 e+05 8.32 78.1 1 ior of fatigue li of sample a ress level. 300 33.7 5 1.8 e+05 4.4 e+04 24.6 or of the fatigue 300 33.7 5 2.0 e+05 1.5 e+03 0.8 or of the fatigue d of the samp such stress le 216 37.3 5 2.7 e+05 5 * * the fatigue live e sample b w 140 15.5 5 4.4 e+05 5 1.5 e+05 33.8 r of the fatigue 10.3221/igf-esi 400 4 3.6 47 e+05 2.61 e+02 1.09 8.4 0 ives (r = -1) and 14 specim 332 37.3 9.3 e+04 4.1 e+04 43.7 e lives (r = 0) 332 37.3 8.8 e+04 3.8 e+04 42.7 e lives (r = 0) ple a and 7 s evel. 223 38.9 1.5 e+04 * * es (r = 1/3) were used. ta 141 15.6 3.7 e+05 4.0 e+04 10.6 e lives (r = 2/3 is.14.02 40 50 7.9 55 e+05 5.75 e+03 9.74 0.4 16 sample b. mens of samp 347 38.9 7.0 e+04 1 1.0 e+04 2 14.3 sample a. 347 38.9 9.7 e+04 2 3.8 e+04 3 38.8 sample b. specimens of 228 44.0 1.3 e+04 7 * * samples a and ab. 11 shows 143 15.8 2.0 e+03 6 * * 3) sample b. 09 5.5 e+04 e+03 6.9 ple b. tabs. 8 391 44.0 1,9 e+04 2.4 e+03 12.4 391 44.0 2.7 e+04 3.2 e+03 11.7 f the sample b 235 26.0 7.1 e+04 3.4 * * d b s the statistic 148 16.4 6.2 e+01 * * 8 and 9 show b. tab. 10 sh 270 29.0 4 e+04 * * behavior of w the hows f the http://dx.medra.org/10.3221/igf-esis.14.02&auth=true http://www.gruppofrattura.it bas eff th cha the end mo fig adh arri lev sed on the ob ffect of the mea he experiment aracterize the e parallel proj durance limit odels’s adheren g. 5 shows th herence. the ives to 300 m vels around 34 f 1e 2 3 4 5 6 7 8 9 100 1000 s ar ( m p a) btained result an stress tal data and i e fatigue stren ection metho considering a r m -1 14 0 99 1/3 72 2/3 15 nce to experime he fatigue ex trend line a mpa. in addi 4% upper tha figure 5: good e+2 1e+3 1e numb r = -1 r = 0 r = 1/3 r = 2/3 trend lin confiden trend lin confiden b. lo ts it is possibl its respective ngth are summ od [12]. basic an extrapolati figu basquin’s co (a) [mp mean stand 406.9 1 96.8 1 29.8 9 52.3 table ental results: xperimental d adjusts to bas tion, for ratio an real failure dman’s predicti 1e+4 100 1000 s a (m p a) e+4 1e+5 1e+ ber of cycle (n) ne goodman eq. nce interval goodman ne basquin eq. nce interval basquin obato da silva et le to verify a s trend lines, marized in th cally, this met ion of the fat ure 4: s-n curv onstant pa] ard error m 02.9 -0 46.8 -0 91.2 -0 7.4 -0 e 12: paramete goodman’s m data and the squin’s curve o loading of condition. ion. 1e +6 1e+7 n eq. eq. alii, frattura ed significant dis for such ratio he tab. 12. t thod consists tigue curve fo ves about the ef basquin’s ex (b) mean stan 0.0941 0 0.0962 0 0.0987 0 0.0077 0 ers that charact model predictions e but reveal b 2/3, the mo e+5 n (number of c d integrità struttu spersion of fa o loading, are the enduranc in achieving or life identifi ffect of mean s xponent dard error m 0.0059 0.0125 2 0.0101 0.0039 terize the s-n based on g big scatter, a del predicts t figure 1e+6 cycle) experim 100 2 3 4 5 6 7 8 9 100 1000 s ar g o o d m an ( m p a) urale, 14 (2010) atigue life for e shown in f ce limit, s`f, c s-n curve fo ed as infinite stress. enduranc (s`f) [m mean stand 383.2 2 263.9 186.7 136.9 curves goodman’s m as shown in f the possibilit e 6: goodman 1e+7 mental data r = -1 r = 0 r = 1/3 r = 2/3 trend line sar bas r = -1 r = 0 r = 1/3 r = 2 ) 17-26; doi: 10 all stress rati fig. 4 and the an be easily o or the steel an fatigue life. ce limit mpa] dard error 28. 0 28.0 23.3 6.7 model. the re fig. 6. the c ty to apply, o n’s scatter diagr squin (mpa) 0 2/3 trend .3221/igf-esis. os tested. e parameters obtained thro nd estimating esults reveal confidence lim on average, st ram. 1000 d line 14.02 23 that ough g the low mits tress http://dx.medra.org/10.3221/igf-esis.14.02&auth=true http://www.gruppofrattura.it b. l 24 mo fig res out lev mo th obt we ord mo th res exp are adh lobato da silva odels’s adheren gs. 7 and 8 sh ults, it is veri t of the conf vels around 72 odels’s adheren he fatigue exp tained results re adjusted v der of size, ap odels’s adheren he figs. 11 an ults presente pressively hig e around 100 herent. 1e 2 3 4 5 6 7 8 9 100 1000 s ar ( m p a) 1e 2 3 4 5 6 7 8 9 100 1000 s ar ( m p a) et alii, frattura nce to experime how the fatig ified a relative fidence limits 2% lower than figure 7: ger nce to experime perimental da s indicate that very well to b pproximately figure 9: wa nce to experime nd 12 show d it is verifie gh. the obtai mpa, twice e+2 1e+3 1e num trend li confiden trend li confiden e+2 1e+3 1e num r = -1 r = 0 r = 1/3 r = 2/3 trend li confiden trend li confiden ed integrità stru ental results: g gue experimen ely high scatte s of the basq n real failure rber’s predictio ental results: w ata and the p t this model h asquin’s curv 50 mpa. alker’s predictio ental results: k the fatigue e d that in a w ned results w larger than t e+4 1e+5 1 mber of cycle (n) r = -1 r = 0 ine gerber eq. nce interval gerber ine basquin eq. nce interval basqui e+4 1e+5 1 mber of cycle (n) ine walker eq. nce interval walker ine basquin eq. nce interval basqui utturale, 14 (201 gerber’s model ntal data and er, approxima quin’s equatio conditions an on. walker’s mode predictions b has a level of ve. in addition on kwofie’s model experimental way similar to were adjusted the value pre e+6 1e+7 r = 1/3 r = 2/3 r eq. in eq. e+6 1e+7 r eq. in eq. 10) 17-26; doi: l d the predictio ately 300 mp on. this mod nd it is extrem del based on wa adherence sig n, the confide l data and the walker’s mo well by the esented by w 10.3221/igf-esi ons based on pa. the trend del predicts t mely conserva figu alker’s model gnificantly hig ence intervals figu e predictions odel, kwofie’s basquin’s tre walker’s mode 100 2 3 4 5 6 7 8 9 100 1000 s ar g er b er ( m p a) 100 2 3 4 5 6 7 8 9 100 1000 s ar w al k er ( m p a) is.14.02 n gerber’s m line of the pr the possibility ative. ure 8: gerber’s l are showed gh to the exp s associated t ure 10: walker’ based on k s model also end line. how el. in other w sar ba r = -1 r = r = 1/3 r = sar ba r = -1 r = r = 1/3 r = model. based o redict results y to apply, o s scatter diagra d in the figs erimental res to both mode ’s scatter diagr kwofie’s mod presents a le wever, its con words, kwofi squin (mpa) 0 2/3 tre squin (mpa) 0 2/3 tre on the presen for this mod on average, st am. . 9 and 10. ults because t els have the s am el. based on evel of adhere nfidence inter ie’s model is 1000 end line 1000 end line nted del is tress the they ame the ence rvals less http://dx.medra.org/10.3221/igf-esis.14.02&auth=true http://www.gruppofrattura.it co bet we lim sup des goo to d ac re [1] [2] [3] [4] [5] [6] [7] [8] t t onclusion he aim o alloy ste results w tween basqui re used to pr mit for this all perior reducti scribe the me od prediction describe the e cknowledg his proje are grate eferences y-l. lee, j butterworth n. e. dowl k. n. smith k. walker, testing and a. berkovit s. kwofie, i astm / e 6 astm / e 4 1.0e+3 2 3 4 5 6 7 8 9 100 1000 s ar [ m p a] t t figure 11: kw ns of this resear eel. in that se were used to in’s alternatin edict the mea loy steel is 38 tion around 5 ean stress effe n for the pres effect of the m gements ect was suppo efully acknow s j. pan, r. h h-heinemann ling, mechani h, p. watson, effect of e d materials, w ts, d. fang, in int. j. fatigue 606-04 stand 466-96 stand 3 1.0e+4 num r = -1 r = 0 r = 1/3 r = 2/3 trend line kw basquin eq. bas confidence inte b. lo wofie’s predicti ch was to eva nse, s-n curv o determine t ng stress and an stress effec 83 mpa; b) th 50% in the e fect on the fa ence of mean mean stress o orted by cen wledged. we a hathaway, m n, usa (2005) ical behaviou , t. h. toppe environment west conshoh nt. j. fatigue, e, 23 (2001) 8 dard practice fo dard practice fo 1.0e+5 1.0 mber of cycle (n) wofie eq. sed on experimental da rval limits basquin eq confidence interval limits obato da silva et ion. aluate the eff ves were exp the enduranc predictions o cts. by means he fatigue lif endurance lim atigue strength n stress but p on the fatigue trais elétricas are thankful t m. e. barkey ). ur of material er, journal of and comple hocken, pa, ( , 15 (1993) 17 829. for strain con for conducting 0e+6 1.0e+7 ta . kwofie eq. alii, frattura ed fect of mean erimentally d ce limit of th of such mode s of the obtai fe is strongly mit; c) good h, turning its presents relativ e strength of a s do norte do o god for th y, fatigue t s, 2nd edition, f materials, as ex load hist (1970) 1. 73. ntrolled fatigu g constant am d integrità struttu figu stress of the determined fo he material a el. the good ined results it influenced b dman and g s use non-rec vely high scat astm a743 o brasil s. a. he blessing of testing and a , prentice-ha stm, 5(4) (19 tory on fatig ue testing, (20 mplitude axial 0 1 0 100 200 300 400 500 600 700 800 900 1000 s a r [m p a ] k w o fi e urale, 14 (2010) ure 12: kwofie’ fatigue behav or loading rati and to evalua dman, gerber t is possible t by the presen erber’s mode ommended; d tter; e) walke ca6nm allo eletronorte to live, to pro analysis (th all, englewood 970) 99.767. gue life, ast 004). l fatigue tests 100 200 300 400 sar [mp r = -1 r = 0 r = 1/3 r = 2/3 trend line ) 17-26; doi: 10 ’s scatter diagra vior of astm ios of -1, 0, 1 ate the comp r, walker and o infer: a) the ce of mean s el were show d) kwofie’s m er’s model wa oy steel. e and finatec oduce and to heory and pr d cliffs, nj, ( tm stp 462 s of metallic m 500 600 700 80 pa] eq (2.2.1) .3221/igf-esis. am. m a743 ca6 1/3 and 2/3. parative diagr d kowfie’s mo e fatigue stren stresses, havin wn inadequate model presen as the best mo c. these supp develop scie ractice), else (1998). 2, am. soc. materials, (200 00 900 1000 14.02 25 nm the rams odel ngth ng a e to nts a odel ports ence. evier for 02). http://dx.medra.org/10.3221/igf-esis.14.02&auth=true http://www.gruppofrattura.it b. l 26 [9] [10 [11 [12 re t lobato da silva astm / e (1990). 0] astm / e (-n), (1991 1] p. r. gill, w press, (1981 2] s-k. lin, y esponsibili he autho t et alii, frattura e 468-90 sta 739-91 stan 1). w.murray, m 1) 136. y-l. lee, m-w ity notice ors are the on ed integrità stru andard practi ndard practic m. h.wright, t w.lu, int. j. o e nly responsibl utturale, 14 (201 ice for presen ce for statistic the levenbe of fatigue, 23 le for the prin 10) 17-26; doi: ntation of co cal analysis o erg-marquard (2001) 75. nted material 10.3221/igf-esi onstant amp of linear or l dt method in included in th is.14.02 plitude fatigu linearized str practical oti his paper. ue test for m ress-life (s-n imization, lo metallic mater n) and strainondon: acade rials, -life emic http://dx.medra.org/10.3221/igf-esis.14.02&auth=true http://www.gruppofrattura.it << /ascii85encodepages false /allowtransparency false /autopositionepsfiles true /autorotatepages /none /binding /left /calgrayprofile (dot gain 20%) /calrgbprofile (srgb iec61966-2.1) /calcmykprofile (u.s. web coated \050swop\051 v2) /srgbprofile (srgb iec61966-2.1) /cannotembedfontpolicy /error /compatibilitylevel 1.4 /compressobjects /tags /compresspages true /convertimagestoindexed true /passthroughjpegimages true /createjobticket false /defaultrenderingintent /default /detectblends true /detectcurves 0.0000 /colorconversionstrategy /cmyk /dothumbnails false /embedallfonts true /embedopentype false /parseiccprofilesincomments true /embedjoboptions true /dscreportinglevel 0 /emitdscwarnings false /endpage -1 /imagememory 1048576 /lockdistillerparams false /maxsubsetpct 100 /optimize true 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/hrv (za stvaranje adobe pdf dokumenata najpogodnijih za visokokvalitetni ispis prije tiskanja koristite ove postavke. stvoreni pdf dokumenti mogu se otvoriti acrobat i adobe reader 5.0 i kasnijim verzijama.) /hun 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can be opened with acrobat and adobe reader 5.0 and later.) >> /namespace [ (adobe) (common) (1.0) ] /othernamespaces [ << /asreaderspreads false /cropimagestoframes true /errorcontrol /warnandcontinue /flattenerignorespreadoverrides false /includeguidesgrids false /includenonprinting false /includeslug false /namespace [ (adobe) (indesign) (4.0) ] /omitplacedbitmaps false /omitplacedeps false /omitplacedpdf false /simulateoverprint /legacy >> << /addbleedmarks false /addcolorbars false /addcropmarks false /addpageinfo false /addregmarks false /convertcolors /converttocmyk /destinationprofilename () /destinationprofileselector /documentcmyk /downsample16bitimages true /flattenerpreset << /presetselector /mediumresolution >> /formelements false /generatestructure false /includebookmarks false /includehyperlinks false /includeinteractive false /includelayers false /includeprofiles false /multimediahandling /useobjectsettings /namespace [ (adobe) (creativesuite) (2.0) ] /pdfxoutputintentprofileselector /documentcmyk /preserveediting true /untaggedcmykhandling /leaveuntagged /untaggedrgbhandling /usedocumentprofile /usedocumentbleed false >> ] >> setdistillerparams << /hwresolution [2400 2400] /pagesize [612.000 792.000] >> setpagedevice shot peening processes to obtain nanocrystalline surfaces in metal alloys: y. yang et alii, frattura ed integrità strutturale, 41 (2017) 339-349; doi: 10.3221/igf-esis.41.45 339 research on differences and correlation between tensile, compression and flexural moduli of cement stabilized macadam yi yang school of traffic and transportation, changsha university of science & technology, hunan 410004, china; modern investment co., ltd., hunan 410004, china 114949297@qq.com jianlong zheng school of traffic and transportation, changsha university of science & technology, hunan 410004, china zjl@csust.edu.cn songtao lv school of traffic and transportation, changsha university of science & technology, hunan 410004, china lstcs@126.com abstract. in order to reveal the differences and conversion relations between the tensile, compressive and flexural moduli of cement stabilized macadam, in this paper, we develop a new test method for measuring three moduli simultaneously. by using the materials testing system, we test three moduli of the cement stabilized macadam under different loading rates, propose a flexural modulus calculation formula which considers the shearing effect, reveal the change rules of the tensile, compression and flexural moduli with the loading rate and establish the conversion relationships between the three moduli. the results indicate that: three moduli become larger with the increase of the loading rate, showing a power function pattern; with the shear effect considered, the flexural modulus is increased by 47% approximately over that in the current test method; the tensile and compression moduli of cement stabilized macadam are significantly different. therefore, if only the compression modulus is used as the structural design parameter of asphalt pavement, there will be a great deviation in the analysis of the load response. in order to achieve scientific design and calculation, the appropriate design parameters should be chosen based on the actual stress state at each point inside the pavement structure. keywords. road engineering; cement stabilized macadam; laboratory test; tensile-compression-flexural modulus; loading rate. citation: yang, y., zheng, j., lv, s., research on differences and correlation between tensile, compression and flexural moduli of cement stabilized macadam, frattura ed integrità strutturale, 41 (2017) 339-349. received: 14.03.2017 accepted: 23.04.2017 published: 01.07.2017 copyright: © 2017 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. y. yang et alii, frattura ed integrità strutturale, 41 (2017) 339-349; doi: 10.3221/igf-esis.41.45 340 introduction ue to high intensity and rigidity and good resistance, the cement stabilized semi-rigid base can adapt to heavy traffic and complex climate environment, making it become one of the major types of base course for highgrade highway asphalt pavement in china [1]. restricted by economic and technological conditions, for a long period of time, semi-rigid base will still be widely applied as a major base course of pavement. therefore, we should further understand its characteristics and improve and utilize them so as to give full play to the advantages of this semirigid base material [2]. the asphalt pavement design code currently in use in china is simple, in which unconfined compressive resilient modulus is used as the parameters in the structural design of asphalt mixture and semi-rigid base material [3,4], and the pavement material is similar to most of the engineering materials, showing different characteristics under different tensile and compression moduli. when the difference between the tensile and compression moduli of the material is large, it is inappropriate to use a single modulus to calculate and analyze the mechanical response [5]. reference [6,7] studied the constitutive relations of materials with different tensile and compressive elastic moduli and the fracture mechanical responses thereof. reference [8-11] discussed and analyzed the application of the elastic theory of different moduli like tensile and compression moduli in the theories of beam, shell and plate, established elasticity solutions to beams, shells and plates with different tensile and compression moduli under different loads, and proposed a static equilibrium equation and calculation methods for stress and displacement under external force. for the pavement material, in 1992, changsha university of science & technology (formerly changsha communications college) proposed a calculation method when differences between tensile and compression moduli are considered for the rigid pavement [12], then analyzed the drawbacks of flexible pavement design using tensile and compression moduli as the moduli of the structural layer and deduced the basic formula and test method of the double modulus theory [13]. the semi-rigid base is formed through stratified compaction, with significant differences in its tensile and compressive moduli. under the action of traffic load, the neutral surface of the semi-rigid base course is not at the geometric center of the structural layer; instead, it shifts towards the compressive zone. the existing asphalt pavement design method does not consider the actual stress distribution of the semi-rigid base, and performs the structural load response analysis according to the compressive elastic modulus, which will lead to the unbalance between the working state of the structural design parameter and the actual stress state, and further resulting in large deviation in calculation and analysis results. in order to achieve scientific calculation and analysis, the corresponding design parameters should be determined according to the stress state of the points inside the pavement structure. therefore, it is necessary to set up the mechanical response analysis method for asphalt pavement structure using the double modulus theory with different tensile and compressive moduli, especially the method to obtain the corresponding material parameters. in this paper, by using the mts (material test system), we propose a new test method for measuring tensile, compression and flexural moduli simultaneously. we test three moduli of the cement stabilized macadam under different loading rates, propose a flexural modulus calculation formula which considers the shearing effect and reveal the change rules of the tensile, compression and flexural moduli with the loading rate and the differences and correlations between the three moduli so as to provide theoretical basis for the selection and optimization of material parameters in the asphalt pavement structure design. specimen molding and test preparation specimen molding he cement used as the raw material of cement stabilized macadam is xing’an hailuo ordinary portland cement pc32.5 and its information are shown as tab.1. the aggregate is the limestone aggregate manufactured by yangjiaqiao crushing plant and its information are shown as tab.2. the test results show that the technical indexes of these raw materials meet the requirements as specified in the code. in the basis of practical engineering, the gradation of csm aggregate was designed to realize framework-dense structure according to the testing methods of material stabilized with inorganic binders for highway engineering [14].the mineral aggregate gradation adopted is shown in tab. 3: according to the mineral aggregate gradation listed in tab. 3, we carry out the heavy compaction test on cement stabilized macadam. first, we determine the optimum water content and maximum dry density at different cement dosages, and then determine the dosage of cement that meets the requirements by performing the unconfined compressive strength d t y. yang et alii, frattura ed integrità strutturale, 41 (2017) 339-349; doi: 10.3221/igf-esis.41.45 341 test at each dose. the final test results are: the dosage of cement added into the cement stabilized macadam is 4.5%, the maximum dry density is 2.35g/cm3 and the optimum water content is 4.5%. test results specification fineness (sieve size 80μm) 1.8 ≤10% initial setting time (min) 302 ≥180 final setting time (min) 364 ≥360 stability (mm) 3 ≤5 3 day flexural strength of cement mortar (mpa) 4.7 ≥2.5 3 day compressive strength of cement mortar (mpa) 19.9 ≥10 table 1: the characterization of xing’an hailuo ordinary portland cement pc32.5. test coarse aggregate specification content of needle and plate particle 11.7% ≤20% crushing value 19.8% ≤30% liquid limit& plasticity index of particles less than 0.6mm liquid limit≤28% 26.5% plasticity index≤9 6.2 table 2: the characterization of the limestone aggregate. mesh size (mm) pass rate (%) 26.5 100 19 92.5 16 85.5 13.2 77.0 9.5 62.7 4.75 34.4 2.36 21.2 1.18 17.0 0.6 11.5 0.3 8.2 0.15 5.1 0.075 3.6 table 3: synthetic aggregate gradation of cement stabilized macadam. based on the above data, according to the requirements in the test regulations [14], we make specimens for flexural strength and flexural modulus, whose size is 100mm×100mm×400mm. we use the static molding method in the specimen molding. after that, specimens are put in a standard preservation room (temperature: 20°c±2°c; humidity≥ 95%) for 90 days of preservation. description of the tensile, compression and flexural test method we use mts (material test system) for modulus testing. the test principle is shown in fig. 1, 2 and 3. the mid-span deflection is measured using a micrometer placed on the upper surface of the specimen, which is used to calculate the flexural modulus of the specimen; the compressive strain of the mid-span upper surface and the tensile strain of the lower surface are measured by the strain gauges attached to the surface, respectively, which are used to calculate the compression modulus and tensile modulus of the specimen. y. yang et alii, frattura ed integrità strutturale, 41 (2017) 339-349; doi: 10.3221/igf-esis.41.45 342 in order to eliminate the friction between the load head, the support and the specimen, we use a cylindrical load head and a cylindrical support and apply butter to the load head and the support before the test. the loading rate includes 0.1mm/min, 0.4mm/min, 0.7mm/min, 1mm/min four grades. figure 1: testing principle for tensile, compression and flexural moduli (1-beam specimen; 2-cylindrical support; 3-micrometer; 4strain gage). the strain gages are foil resistance strain gages, with a grid length of 80mm and a resistance of 120ω. due to the rough beam surface of the cement stabilized macadam specimen, it is necessary to put cement paste on the upper and lower surfaces to fill the gaps in areas where strain gages will be put on one week before the test. while attaching 4 strain gages on the upper and lower surfaces respectively, i.e. 8 strain gages in total, we measure the compressive and tensile strains of the test beam (as shown in fig. 1 and fig. 2). at the same time, considering the edge effect of strain, the center of the most marginal strain gage should be 20mm away from the edge of the beam. the strain gage pasting method and test device are shown in fig. 2 and fig. 3. the center of the most marginal strain gage is 20mm away from the edge of the beam. the way the strain gage is pasted and the test device are shown in fig. 2 and fig. 3. figure 2: schematic of strain gauges pasted figure 3: installation drawing of modulus test derivation of the tensile, compression and flexural moduli calculation formulas traditional flexural modulus calculation formula hen the length of the bar l is much greater than the cross-sectional height h, i.e. l>5h, the analytical formula for pure bending can be used. the current test procedure calculates the flexural modulus without considering the shear effect [14]. the calculation and derivation process is as follows: p/2 p/2p/2 p/2 p (a) p/2 (b) p/2 l/2-x l/2 x l/6 l/3l/3l/3 figure 4: force analysis diagram of specimen w y. yang et alii, frattura ed integrità strutturale, 41 (2017) 339-349; doi: 10.3221/igf-esis.41.45 343 fig. 4(a) shows the simplified force diagram of the specimen. (b) shows the equivalent force diagram for the right part of the specimen. the approximate differential line of deflection equation for the beam can be expressed by section as follows: when 0≤x≤l/6: ω ='' 6f pl e i (1) when l/6≤x≤l/2: ω = −'' 4 2f pl px e i (2) where, ef is the traditional flexural modulus; i is the inertia moment; w is the mid-span deflection; p is the load applied; l is the specimen span. by integrating formula (1) and (2) twice respectively, based on the boundary conditions and continuity conditions, we will know that when l/6≤x≤l/2, ω = − − + 2 3 2 3 8 12 144 2592f plx px pl x pl e i (3) when x=l/2, by substituting the inertia moment i=bh3/12 into formla (3), we obtain the flexural modulus calculation formula: ω = 3 3 23 108 f pl e bh (4) where, h is the mid-span sectional height; b is the cross section width of the specimen; other symbols are the same meanings as above. flexural modulus calculation correction formula considering the shear effect when the span height of the beam is greater than 5, the positive stress formula for pure bending can be applied to the positive stress calculation for transverse bending. however, for a deep beam with a span height of less than 5, if we use the pure bending theory and assumptions for slender beam in material mechanics, the error will increase rapidly with the decreasing depth-span ratio [15]. in the current inorganic binder test regulation for flexural modulus, the span height ratio l/h used is 3, but it did not consider the shear effect on the beam deflection, so the result is inconsistent with the actual situation [14]. therefore, this paper deduces the flexural modulus calculation correction formula considering the shear effect. (the flexural modulus mentioned later is the result considering the shear effect). ¦ ¤¦ ø γ τ p/2 p/2 τ p/2 p/2p/2 p/2 figure 5: force analysis diagram of specimen considering the shear effect as shown in fig. 5, let the additional deflection caused by the shear effect be ω∆ . then: ω γ∆ = ⋅ 3 l (5) y. yang et alii, frattura ed integrità strutturale, 41 (2017) 339-349; doi: 10.3221/igf-esis.41.45 344 where, τ γ = g is the shear strain; is the shear stress; τ = t a is the shear force; = 2 p t is the sectional area; µ = +2(1 ) feg is the shear modulus; μ is poisson’s ratio. we substitute this into formula (5) and obtain µ ω + ∆ = 2(1 ) 3 f pl e bh . the deflection ω ' under the mutual action of moment and shear can be expressed as: ω ω ω= + ∆' . by substituting the above equations, we obtain: µ ω + = + 3 3 2(1 )23 ' 3108 ff plpl e bhe bh (6) then the flexural modulus 'fe considering the shear effect can be expressed as: µ ωω + = + 3 3 2(1 )23 ' 3 '108 ' f plpl e bhbh (7) if we compare the flexural modulus formula (7) considering the shear effect and formula (4) without considering the shear effect, the change ratio of the two is: µ− + = 2 2 ' 216(1 ) 69 f f f e e h e l . as the required span height ratio l/h of the cement stabilized macadam beam specimen is 3, we know that with the shear effect taken into account, the flexural modulus is increased by about 47% (poisson’s ratio μ is 0.25). derivation of tensile modulus calculation formula based on flexural test the tensile and compressive stress distribution of the mid-span section is shown in fig. 6(b). x y x dx h1 h h2 h1 h2 ¦ òp ¦ òt (a) (b) ep et b figure 6: stress distribution of specimen mid-span section let the micro-area unit parallel to the neutral axis (as shown in fig. 6(a)) =da bdx . for the mid-span section, the bending moment m caused by the internal force can be expressed as follows: σ σ − = +∫ ∫ 01 2 2 0 21 2 h p t h m bx dx bx dx h h (8) where, m is the bending moment; σ p is the compressive stress of the upper surface; σt is the tensile stress of the lower surface; h1 is the vertical distance between the upper surface of the specimen and the neutral axis moved up; h2 is the vertical distance between the lower surface of the specimen and the neutral axis; other symbols have the same meanings as above. by integrating this formula, we obtain: σ σ= +2 21 2/ 3 / 3p tm bh bh (9) y. yang et alii, frattura ed integrità strutturale, 41 (2017) 339-349; doi: 10.3221/igf-esis.41.45 345 that is: ε ε= +2 21 2/ 3 / 3p p t tm e bh e bh (10) the plane hypothesis: ε ε=2 1/ /t ph h (11) where, ε p is the compressive strain of the upper surface; εt is the tensile strain of the lower surface; other symbols have the same meanings as above. equilibrium condition: σ σ σ σ − = ⇒ =∫ ∫ 01 1 20 21 2 h p t p th bxdx bxdx h h h h (12) as the tensile modulus σ ε= /t t te and the compression modulus σ ε= /p p pe , by combining formula (10), (11) and (12), we obtain: ε ε ε= + 2 23 ( ) /t p t te m b h (13) ε ε ε= + 2 23 ( ) /p p t pe m b h (14) where, et is the tensile modulus; ep is the compression modulus. therefore, the tensile compression modulus ratio is: ε ε = = 2 2 1 2 2 2 pt p t e h e h (15) the mid-span bending moment of the specimen: = / 6m pl (16) by substituting eq. (16) into formula (13) and formula (14), we obtain the tensile and compression modulus calculation formulas as follows: ε ε ε + = t p 2 2 t ( ) 2 t pl e bh (17) ε ε ε + = t p 2 2 p ( ) 2 p pl e bh (18) analysis on tensile, compression and flexural moduli test results analysis on the change rules of the three moduli with the loading rate ccording to the deduced tensile, compressive and flexural modulus calculation formulas, we use the triple mean variance to eliminate the abnormal test results and calculate the test mean value of 9 groups of specimens. the test results of the three moduli under different loading rates are shown in tab. 2. a y. yang et alii, frattura ed integrità strutturale, 41 (2017) 339-349; doi: 10.3221/igf-esis.41.45 346 loading rate ν /(mm/min) flexural modulus ef’/mpa tensile modulus et/mpa compression modulus ep/mpa 0.1 2341.94 9304.05 15949.03 0.4 2515.55 9492.45 16872.67 0.7 2617.37 9565.97 17355.81 1 2660.74 9645.57 17401.38 table 2: tensile, compression and flexural modulus test results under different loading rates. according to the change rules of the three moduli with the loading rate, we use a power function (19) to fit the data: = ⋅ be a v (19) the fitting results are shown in tab. 3 and fig. 7. fitting parameters correlation coefficient r2 a b flexural modulus 2661.22 0.056 0.996 tensile modulus 9631.25 0.015 0.993 compression modulus 17493.15 0.039 0.985 table 3: summary of three modulus fitting results under different loading rates. 0.0 0.2 0.4 0.6 0.8 1.0 2300 2350 2400 2450 2500 2550 2600 2650 2700 fl ex ur al m od ul us e f / / m p a loading ratesv/(mm/min) 0.0 0.2 0.4 0.6 0.8 1.0 9300 9350 9400 9450 9500 9550 9600 9650 loading ratesv/(mm/min) te ns ile m m od ul us e t / m p a (a) flexural modulus (b) tensile modulus 0.0 0.2 0.4 0.6 0.8 1.0 15800 16000 16200 16400 16600 16800 17000 17200 17400 17600 loading ratesv/(mm/min) c om pr es si ve m od ul us e p / m p a (c) compression modulus figure 7: change rules of the three moduli with the loading rates. y. yang et alii, frattura ed integrità strutturale, 41 (2017) 339-349; doi: 10.3221/igf-esis.41.45 347 from the above fitting results, it can be seen that the tensile modulus, compression modulus and flexural modulus increase with the increase of the loading rate, showing a good power function relationship. it has been proved in the existing research that when the loading rate increases, the stress state inside the specimen is not exactly one-dimensional stress state, but rather a mechanical response characteristic towards the one-dimensional strain state. in particular, in the middle part of the specimen, under a higher loading rate, due to the inertia of the material, the lateral strain of the specimen is restricted, and the higher the strain rate is, the more obvious the restriction will be, showing an obvious strain ratio effect, which causes the material modulus and strength to increase with the growth of loading rate [16]. the modulus and strength of asphalt mixture has a similar change pattern [17-20]. in the same way, in this paper, the change rule that the modulus of the cement stabilized macadam material changes with the loading rate also proves this conclusion. comparison and analysis of the three moduli according to the test results in tab. 2, we get to know: (1) under different loading rates, the ratio between the compression and tensile moduli is 1.71, 1.78, 1.81 and 1.80, with an average value of 1.78. the cement stabilized macadam material shows significant differences between the tensile and compression moduli, and the compression modulus is greater than the tensile modulus, it proved the differences between the tensile and compressive modulus of cement stabilized macadam material. (2) the tensile modulus is respectively about 3.97, 3.77, 3.65 and 3.63 times the flexural modulus, with a mean value of 3.76; the compression modulus is about 6.81, 6.71, 6.63 and 6.54 times the flexural modulus, respectively, with a mean of 6.68. in other words, the tensile and compression moduli are much greater than the flexural modulus. it can be seen that, regardless of the stress state inside the cement stabilized macadam semi-rigid base structure, it is obviously inappropriate to simply use the unconfined compressive resilient modulus to calculate the structural load response. as the compressive resilient modulus is the largest among the three moduli, the structural deformation response calculated based on this modulus will be the smallest. as a result, the asphalt pavement structure, which takes the surface deflection as the indicator, will be thin and unsafe, and the road pavement is likely to be damaged at an early stage. (3) under different loading rates, the ratios between each two of the tensile, compressive and flexural moduli, are stable, showing that even the loading rate has direct impact on the moduli of cement stabilized macadam material, but it does not affect the ratio relationship between the three moduli[19]. this provides basis and convenience for the conversion between the three moduli. conversion relations between the three moduli with the loading rate as the intermediate variable, according to formula (19) and the fitting results in tab. 3, we can establish the conversion relations between the three moduli. (1) conversion relation between the tensile modulus and the flexural modulus: ′= 0.271164.79t fe e (20) (2) conversion relation between the compression modulus and the flexural modulus: ′= 0.772.04p fe e (21) (3) conversion relation between the tensile modulus and the compression modulus: = 0.39224.81t pe e (22) according to the conversion relations between the three moduli in formula (20), (21) and (22), as long as we can get one modulus value, we can easily calculate the other two modulus, which facilitates the selection of modulus design parameters based on the stress state inside the pavement structure. conclusions (1) when the shear effect is considered, the flexural modulus of the beam specimen of cement stabilized macadam will be greatly increased. therefore, when measuring the modulus of the indoor middle beam made of semi-rigid material, we should consider the shear effect. y. yang et alii, frattura ed integrità strutturale, 41 (2017) 339-349; doi: 10.3221/igf-esis.41.45 348 (2) the tensile, compression and flexural moduli of the cement stabilized macadam increase with the increase of the loading rate, showing a power function growth pattern. (3) the tensile and compression moduli of cement stabilized macadam are significantly different. if only the compression modulus is used as the structural design parameter of asphalt pavement, there will be unbalance between the working state of the structural design parameter and the actual stress state, and further resulting in large deviation in load response analysis and affecting the safety of the design results. in order to improve the accuracy of the design calculation, we should select the corresponding design parameters according to the stress state of the points inside the pavement structure. (4) this paper reveals the differences between the tensile, compression and flexural moduli of cement stabilized macadam and their conversion relations, but it does not consider the impacts of different mineral aggregate gradations, which, however, are rather significant on the moduli of cement stabilized macadam. in order to improve the resistance of the semi-rigid base material against load damages, the gradation optimization will be one of the focuses in our future research. references [1] sha, q.l., the design and construction of long life semi-rigid pavement for heavy traffic with heavy wheelload, beijing: china communications press, (2011). [2] sha, a.m., material characteristics of semi-rigid base, china journal of highway & transport, 1 (2008) 21. [3] yao, z.k., asphalt pavement structure design, beijing: china communications press, (2011). [4] jtg d50-2006, specifications for design of highway asphalt pavement [s]. [5] wu, x., zhao, h.j., huang, z.g., yang, l.j., thermal bending and buckling calculations bimodulous plate, journal of chang’ an university (natural science edition), 34(6) (2014) 117-124. [6] patel, b.p., khan, k., nath, y.a., new constitutive model for bimodular laminated structures: application to free vibrations of conical/cylindrical panels, composite structures, 110(1) (2014) 183-191. [7] luo, z.y., xia, j.z., gong, x.n., unified solution for expansion of cylindrical cavity in strain-softening materials with different elastic moduli in tension and compression, engineering mechanics, 25(9) (2008) 79-92. [8] he, x.t., chen, s.l., elasticity solution of simple beams with different modulus under uniformly distributed load, engineering mechanics, 24(10) (2007) 51-56. [9] kong, j., yuan j.y., pan, x.m., elasto-plastic analysis of thick spheric shell with different elastic moduli for tensile and compressive deformations, mechanics in engineering, 32 (1) (2010) 41-45. [10] wu, x.., yang, l.l., huang c., sun. j., large deflection bending calculation and analysis of bimodulous rectangular plate, engineering mechanics, 27(1) (2010) 17-22. [11] he, x.t., chen, s.l., sun, j.y., applying the equivalent section method to solve beam subjected lateral force and bending-compression column with different moduli, international journal of mechanical sciences, 49 (2007) 919924. [12] zhang, q.s., zheng, j.l., the double moduli calculation method of rigid pavements, journal of changsha communications institute, 8(3) (1992) 40-47. [13] liu, j.l., ying, r.h., the application research of double modulus theory in flexible pavement design, hunan communication science and technology, 1(27) (2001) 16-23. [14] jtg e51-2009, test methods of materials stabilized with inorganic binders for highway engineering [s]. [15] wang, z.z., zhu j.z., chen, l., guo, j.l., tan, d.y., mi, w.j., the stress calculation method for deep beams with the shear-bending coupling distortion under concentrated load, engineering mechanics, 25(4) (2008) 115-119. [16] wang, d.r., hu s.s., influence of aggregate on the compression properties of concrete under impact, journal of experimental mechanics, 17(1) (2002) 23-27. [17] zheng, j.l., new structure design of durable asphalt pavement based on life increment, china journal of highway and transport, 27(1) (2014) 1-7. [18] zheng, j.l., lv s.t., nonlinear fatigue damage model for asphalt mixtures, china journal of highway and transport, 22(5) (2009) 21-28. [19] lv s.t., fatigue equation of asphalt mixture considering the influence of loading rate, engineering mechanics, 29(8) (2012) 276-281. [20] mannan, u.a., islam, m.r., tarefder, r.a., effects of recycled asphalt pavements on the fatigue life of asphalt under different strain levels and loading frequencies, international journal of fatigue, 78 (2015) 72–80. y. yang et alii, frattura ed integrità strutturale, 41 (2017) 339-349; doi: 10.3221/igf-esis.41.45 349 nomenclature l test beam span p test load applied ω mid-span deflection of the specimen under pure bending h mid-span sectional height of the specimen b mid-span sectional width of the specimen e resilient modulus of the specimen i mid-span sectional inertia moment of the specimen ef flexural modulus without the shear effect taken into account ω∆ change in the mid-span deflection of the specimen caused by the shear effect γ shear strain τ shear stress t shear force a mid-span sectional area of the specimen g shear modulus µ poisson’s ratio ω ' mid-span deflection of the specimen under the mutual action of moment and shear ef’ flexural modulus with the shear effect considered 1h vertical distance from the upper surface of the specimen to the neutral axis 2h vertical distance from the lower surface of the specimen to the neutral axis σ p compressive stress of the upper surface of the specimen σt tensile stress of the lower surface of the specimen ε p compressive strain of the upper surface of the specimen εt tensile strain of the lower surface of the specimen ep compression modulus et tensile modulus m mid-span bending moment of the specimen ν loading rate r2 correlation coefficient microsoft word numero_31_art_7 j.a.f.o. correia et alii, frattura ed integrità strutturale, 31 (2015) 80-96; doi: 10.3221/igf-esis.31.07 80 modelling probabilistic fatigue crack propagation rates for a mild structural steel j.a.f.o. correia, a.m.p. de jesus university of trás-os-montes e alto douro, vila real, portugal ucve-idmec-laeta, porto, portugal jcorreia@utad.pt, ajesus@utad.pt a. fernández-canteli university of oviedo afc@uniovi.es r.a.b. calçada faculty of engineering, university of porto, porto, portugal ruiabc@fe.up.pt abstract. a class of fatigue crack growth models based on elastic–plastic stress–strain histories at the crack tip region and local strain-life damage models have been proposed in literature. the fatigue crack growth is regarded as a process of continuous crack initializations over successive elementary material blocks, which may be governed by smooth strain-life damage data. some approaches account for the residual stresses developing at the crack tip in the actual crack driving force assessment, allowing mean stresses and loading sequential effects to be modelled. an extension of the fatigue crack propagation model originally proposed by noroozi et al. (2005) to derive probabilistic fatigue crack propagation data is proposed, in particular concerning the derivation of probabilistic da/dn-δk-r fields. the elastic-plastic stresses at the vicinity of the crack tip, computed using simplified formulae, are compared with the stresses computed using an elasticplastic finite element analyses for specimens considered in the experimental program proposed to derive the fatigue crack propagation data. using probabilistic strain-life data available for the s355 structural mild steel, probabilistic crack propagation fields are generated, for several stress ratios, and compared with experimental fatigue crack propagation data. a satisfactory agreement between the predicted probabilistic fields and experimental data is observed. keywords. fatigue, crack propagation, fracture mechanics, local approach, probabilistic approach, finite element modelling. introduction atigue of materials and structures has been investigated for more than 150 years [2]. although it still attracts a lot of attention of engineers and scientists. concerning the investigation of the fatigue crack propagation, significant developments were carried out since the original paris et al. [3] milestone contribution. paris et al. [3] was pioneer suggesting the stress intensity factor range as a crack driving force parameter. the so-called paris’s law stated this relation f j.a.f.o. correia et alii, frattura ed integrità strutturale, 31 (2015) 80-96; doi: 10.3221/igf-esis.31.07 81 in a very simple form: the power function. it has been rather documented in the literature the paris’s law limitations [4]: i) it only models stable fatigue crack propagation behaviour (propagation regime ii) and ii) does not account for stress ratio effects. many alternative fatigue crack propagation relations have been proposed to overcome the limitations of the paris’s law and also to deal with variable amplitude loading. nevertheless, the paris’s law still has been intensively used to model fatigue crack growth under constant amplitude loading due to its attractive simplicity. the number of parameters involved in the more comprehensive fatigue crack propagation models may increase significantly which makes their evaluation a costly task and very often discouraging engineers of their application. fatigue crack growth testing is costly and alternative less expensive approaches to derive fatigue crack growth data are consequently welcome. local strain-based approaches [5-8] were originally proposed to model fatigue crack initiation on notched components [9]. a link between the local strain-based approaches to fatigue and the fracture mechanics based fatigue crack propagation models has been proposed by some authors [1, 10-14]. glinka [13] was one of the first researchers to use the local strain approaches to model fatigue crack propagation. the original idea of glinka was later followed and developed by his collaborators, such as noroozi et al. [1, 10-11], using crack tip residual stress concepts to explain stress ratio effects as well as loading interaction effects on fatigue crack growth rates. peeker and niemi [12], based on the original idea of glinka, made also independent contributions, using crack closure concepts to explain stress r-ratio and load interaction effects. in general, elastoplastic stress analysis at the crack tip vicinity has been performed using analytical approaches, however numerical approaches based on finite element analysis were followed by hurley and evans [14]. the underlying concept behind the proposed local approaches for fatigue crack propagation modelling consists of assuming fatigue crack propagation as a process of continuous failure of consecutive representative material elements (continuous re-initializations). such a kind of approaches has been demonstrated to correlate fatigue crack propagation data from several sources, including the stress ratio effects [1, 10-14]. the crack tip stress-strain fields are computed using elastoplastic analysis, which are applied together a fatigue damage law to predict the failure of the representative material elements. the simplified method of neuber [15] or moftakhar et al. [16] may be used to compute the elastoplastic stress field at the crack tip vicinity using the elastic stress distribution given by the fracture mechanics [1, 16-17]. this paper proposes an assessment and extension of the model proposed by noroozi et al. [1, 10-11] to predict the fatigue crack propagation rates, based on local strain approach to fatigue. this model has been denoted as unigrow model and classified as a residual stress based crack propagation model [18]. the model is applied in this paper to derive probabilistic fatigue crack propagation da/dn-δk fields for the s355 structural mild steel, for distinct stress r-ratios (p-da/dn-δk-r). results are compared with available experimental fatigue crack propagation data from testing of compact tension specimens [19]. a central parameter in the unigrow model is the material representative element size, ρ*, which is tuned in this research by means of a trial and error procedure. the elastoplastic stresses at the vicinity of the crack tip are computed using both simplified formulae and elastoplastic finite element analyses for comparison purposes. the deterministic strain-life damage relation adopted in the original unigrow model is replaced by a probabilistic counterpart. the probabilistic model as proposed by castillo and fernández-canteli [20] for the strain-life field, based on weibull distribution, was generalized in order to incorporate a damage parameter definition able to account for mean stress effects. in particular, the smith-watson-topper damage parameter was selected resulting the p-swt-n which was applied to derive the probabilistic crack propagation fields. theoretical background n this section, an overview of the unigrow model that has been proposed to predict the fatigue crack growth by means of a local approach to fatigue, is presented. also, a recently proposed probabilistic strain-life model is introduced. an extension/generalization of the probabilistic strain-life approach, to account for mean stress effects, is proposed which will be applied latter, in this chapter, in conjunction with the unigrow model to predict probabilistic fatigue crack propagation data. overview of the deterministic unigrow model the unigrow model as proposed by noroozi et al. [1] is supported on the following assumptions: the material is composed of elementary particles of a finite dimension ρ* also called material representative elements, below which material cannot be regarded as a continuum, fig. 1.a); the fatigue crack tip is considered equivalent to a notch with a radius equal to ρ*, fig. 1.b). i j.a.f.o. correia et alii, frattura ed integrità strutturale, 31 (2015) 80-96; doi: 10.3221/igf-esis.31.07 82 the fatigue crack growth results from a process of successive crack increments due to crack re-initializations over the distance ρ*. thus, the fatigue crack growth rate can be established according the following relation: fn ρ dn da *  (1) where nf is the number of cycles required to fail the material representative element, which can be computed using a fatigue damage relation such as the so-called strain-life relations. (a) (b) figure 1: crack configuration according to the unigrow model: a) crack and the discrete elementary material blocks; b) crack geometry at the tensile maximum and compressive minimum loads [1]. noroozi et al. [1] suggested the use of a strain-life relation based on smith, watson and topper fatigue damage parameter [8]:       cbfffbff nεσenσswtεσ  2''2'2δ 22max (2) alternatively, peeker and niemi [12] in a similar approach for the fatigue crack propagation suggested the use of the morrow’s equation [7] to compute the failure of the material representative element:     ' 2 ' 2 2 b cf m f f fn n e         (3) the morrow’s equation was derived from the coffin-manson relation [6, 7] of the material, and allows mean stress effects to be accounted for:    cffbff nεn e σε 2'2 ' 2 δ  (4) swt-life equation, eq. (2), was originally derived by the multiplication of the coffin-manson eq. (4) by the basquin relation [21] available for a stress r-ratio equal to −1:  bff nσσσ 2' 2 δ max  (5) in the previous two equations, fσ ' and b represents, respectively, the fatigue strength coefficient and exponent; fε' and c represents, respectively, the fatigue ductility coefficient and exponent and e is the young modulus. the maximum stress, σmax, mean stress, σm, and the strain range, ε have to be evaluated as the average values at the elementary material block size, ρ*, taking into account an elastoplastic analysis. to compute the elastoplastic stresses and strains at the elementary material blocks ahead of the crack tip, noroozi et al. [1,10] proposed the following analytical procedure: the elastic stresses are computed ahead of the crack tip, using the creager-paris solution [22] for a crack with a tip radius ρ*, using the applied stress intensity factors. j.a.f.o. correia et alii, frattura ed integrità strutturale, 31 (2015) 80-96; doi: 10.3221/igf-esis.31.07 83 the actual elastoplastic stresses and strains, ahead of the crack tip, are computed using the neuber [15] or glinka’s approaches [23]. multiaxial approaches may be adopted using the procedures presented by moftakhar et al. [16] and reinhard et al. [17]. the residual stress distribution ahead of the crack tip is computed using the actual elastoplastic stresses computed at the end of the first load reversal and subsequent cyclic elastoplastic stress range, along the y direction: σσσr δmax  (6) the residual stress distribution computed ahead of the crack tip is assumed to be applied on crack faces, behind the crack tip, in a symmetric way with respect to the crack tip. the compressive stress distribution, acting on crack faces, is equivalent to a residual stress intensity factor which is used to correct the applied stress intensity factor range leading to a total (effective) stress intensity factor range, which excludes the effects of the compressive stresses. the residual stress intensity factor, kr, is computed using the weight function method [24]:     a rr dxaxmxσk 0 , (7) where  a,xm is the weight function [24] and  xr is the residual stress field computed from the elastoplastic stress analysis (see eq. (6)). the applied stress intensity factors (maximum and range values) are then corrected using the residual stress intensity factor, resulting the total kmax,tot and ktot values [1,10]. for positive stress r-ratios, which is the range covered by the experimental data used in this research, kmax,tot and ktot may be computed as follows: rappliedtot rappliedtot kkk kkk   δδ max,max, (8) where kr assumes a negative value corresponding to the compressive stress field. for high stress r-ratios, the compressive stresses ahead of the crack tip may be neglected and the applied stress intensity factor range is assumed fully effective; for low stress r-ratios the compressive stresses increases and the effectiveness of the applied stress intensity factor range decreases accordingly. using the total values of the stress intensity factors, the first and second steps before are repeated to determine the corrected values for the maximum actual stress and actual strain range at the material representative elements. then, eq. (2) is applied together with eq. (1) to compute the fatigue crack growth rates. the described methodology does not lead to close-form (explicit) solutions for the fatigue crack propagation rates. nevertheless, adopting some simplified assumptions about the elastoplastic conditions, such as predominantly elastic behaviour of the material at the crack tip or predominantly plastic behaviour of the material at the crack tip, it is possible to derive those close-form solutions for the stress-strain histories at the crack tip and for the number of cycles to failure of the material representative element. in these cases, the fatigue crack propagation rates may be expressed in the following two-parameters crack driving relation [1, 10]:     γqtotptot kkc dn da δmax, (9) where c, p, q and γ are constants to be correlated with the cyclic constants of the material in a form depending on the elastoplastic conditions at the crack tip. this two-parameters (kmax and k) fatigue crack propagation relation allows the simulation of mean stress effects on fatigue crack propagation rates. the crack propagation models based on a two parameters crack driving force has been recently followed by several authors [25, 26]. probabilistic ε–n and swt–n fields the fatigue crack propagation modelling based on local approaches requires a fatigue damage relation to compute the number of cycles to fail the elementary material blocks. in this paper, probabilistic fatigue damage models are proposed rather than the deterministic swt–n, coffin-manson or morrow models often used in the literature. the probabilistic εa– n model proposed by castillo and fernández-canteli [20] is used. however, and since this probabilistic εa–n model does not account for mean stress effects, an alternative probabilistic swt–n field is also proposed, as an extension of the p–εa– n field suggested by castillo and fernández-canteli [20], to account for mean stress effects. j.a.f.o. correia et alii, frattura ed integrità strutturale, 31 (2015) 80-96; doi: 10.3221/igf-esis.31.07 84 castillo and fernández-canteli [20] proposed a probabilistic model to describe the strain-life field of the material (p-εa-n field), based on weibull distribution. the model assumes that the fatigue life, nf, and the total strain amplitude, εa, are random variables. based on several physical and statistical considerations, such as the weakest link principle, stability, limit behaviour, range of the variables and compatibility, castillo and fernández-canteli [20] derived a strain-life model, which shows exactly the same formulation as proposed the authors for the stress-life field. the interested readers can see the detailed assumptions in castillo et al. [27, 28], where the stress version of the model has been studied and successfully applied to different cases of lifetime problems. this leads to the weibull strain-life model [28]:         0 0* * 0 0 log log ( ; ) 1 exp log log f a a f a f a a n n p f n n n                         (10) where p is the probability of failure, n0 and εa0 are normalizing values, and λ, δ and β are the non-dimensional weibull model parameters. their physical meanings (see fig. 2) are: n0: threshold value of lifetime; εa0: endurance limit of εa; λ: parameter defining the position of the corresponding zero-percentile curve; δ: scale parameter; β: shape parameter. note that the strain-life model (eq. (10)) has a dimensionless form and reveals that the probability of failure p depends only on the product ** af εn , where  0* log nnn ff  and  0* log aaa εεε  , that is: * * * * * ~ ( , , ) ~ , ,f a f a a n w n w                 (11) i.e., ** af εn has a weibull distribution. this model provides a complete analytical description of the statistical properties of the physical problem being dealt with, including the quantile curves without the need of separating the total strain in its elastic and plastic components but dealing with the total strains directly [20]. with respect to the conventional coffin-manson approach, the strain-life probabilistic model show some advantages: it arises from sound statistical and physical assumptions and not from an empirical arbitrary assumption; it provides a probabilistic definition of the whole strain-life field; it does not need to consider separately the elastic and the plastic strains; the run-outs can also be used in the analysis, and facilitates damage analysis. log nf  c=log εa0 lo g  ε a b = lo g  n 0    p=0  p=0.05  p=0.5  p=0.95 figure 2: percentile curves representing the relationship between dimensionless lifetime, nf*, and the strain amplitude, εa*: p-εa-n field. the swt (=σmax.εa) parameter was proposed by smith et al. [8] in order to account for mean stress effects on fatigue life prediction. any combination of maximum stress and strain amplitude that leads to the same swt parameter should lead j.a.f.o. correia et alii, frattura ed integrità strutturale, 31 (2015) 80-96; doi: 10.3221/igf-esis.31.07 85 to the same fatigue life. the swt-n and εa -n fields exhibit similar characteristics. therefore the p-ε-n field proposed by castillo and fernández-canteli [20] may be extended to represent the p-swt-n field as:         0 0* * 0 0 log log ( ; ) 1 exp log log f f f n n swt swt p f n swt n n swt swt                    (12) where p is the probability of failure, n0 and swt0 are normalizing values, and λ, δ and β are the non-dimensional weibull model parameters. similarly to the p-ε-n field, the physical meaning of the parameters from eq. (12) (see fig. 3) are: n0: threshold value of lifetime; swt0: fatigue limit of swt; λ, δ and β: weibull distribution parameters. eq. (12) has also a dimensionless form and reveals that the probability of failure p depends only on the ** swtn f product, where  0* log nnn ff  and  0* log swtswtswt  that is: * * * * * ~ ( , , ) ~ , ,f fn swt w n w swt swt              (13) i.e., ** swtn f follows a weibull distribution. the parameters log n0 and log εa0 of the p-εa-n model, log n0 and log swt0 of the p-swt-n model can be estimated by least square method. the weibull parameters can be estimated using the maximum likelihood method [27, 28]. log nf* swt0 n0  p=0 p=0.05 p=0.5 p=0.95l o g  s w t *    figure 3: percentile curves representing the relationship between dimensionless lifetime, nf*, and the swt* damage parameter: pswt-nf field. procedure to generate probabilistic fatigue crack propagation fields he procedure proposed to derive probabilistic fatigue crack propagation fields may be summarized into the following steps: 1) estimation of the weibull parameters for the p-swt-n or p-εa-n fields, using experimental εa-n or swt-n data from smooth specimens; 2) application of the unigrow model together with the probabilistic fatigue damage models; 3) computation of the p-da/dn-k-r fields. the unigrow model was implemented in a worksheet, supported on vba programming, specifically developed for compact tension (ct) specimens. the input data are the material properties, loads, dimensions of the ct specimen, including the initial and final crack size to be simulated. additionally, the elementary material block size, ρ*, is required. this parameter may be evaluated by a trial and error procedure in order the numerical results fit satisfactorily the t j.a.f.o. correia et alii, frattura ed integrità strutturale, 31 (2015) 80-96; doi: 10.3221/igf-esis.31.07 86 experimental data. fig. 4 gives a general overview of the procedure. the probabilistic fatigue crack propagation fields were evaluated using, alternatively, the probabilistic ε-n and swt-n fields. the residual stress fields ahead of the crack tip were evaluated in this paper using an elastoplastic finite element model of the ct specimens. end yes elastic stress analysis creager‐paris solution elastoplastic stresses analysis neuber or glinka approach elastoplastic stress  analysis  fem σr= σmax ‐ σ    kr (weight function method)    kmax,tot and ktot    σmax and ε/2  p‐ε‐n weibull field p‐swt‐n weibull field  ε‐n exp. data da/dn=ρ*/nf  p‐da/dn‐k‐r field  iterate ρ*  (p‐da/dn‐k‐r)predicted vs. (da/dn‐k‐r)exp.    satisfactory? no first estimate of ρ* figure 4: procedure to generate probabilistic fatigue crack propagation fields. experimental fatigue data of the s355 mild steel he fatigue behaviour of the s355 mid steel was evaluated by de jesus et al. [19], based on experimental results from fatigue tests of smooth specimens and fatigue crack propagation tests. the fatigue tests of smooth specimens were carried out according to the astme606 standard [29], under strain-controlled conditions. tab. 1 and 2 summarize the elastic (e: young modulus) and monotonic strength properties (fy: yield strength; fu: tensile strength) as well as the cyclic elastoplastic constants (k’: cyclic strain hardening coefficient; n’: cyclic strain hardening exponent) and the strain-life constants (refer to eq. (3)–(5)). the crack propagation tests were performed using compact tension (ct) specimens, according to the procedures of the astm e647 standard [30], under load-controlled conditions. fig. 5 t j.a.f.o. correia et alii, frattura ed integrità strutturale, 31 (2015) 80-96; doi: 10.3221/igf-esis.31.07 87 presents the experimental fatigue crack propagation rates obtained for the s355 steel, where stress ratio effects on fatigue crack propagation rates are shown. an increase in fatigue crack propagation rates is clear, when the stress ratio changes from 0 to any positive stress ratios considered in the experimental program. also, it is clear that all the positive stress ratios resulted in similar crack propagation rates. this behaviour is consistent with a crack closure effect that occurs between rσ=0.0 and rσ=0.25. for rσ=0.0 there is some crack closure, the applied stress intensity factor range being not fully effective. for rσ=0.25 and higher, there is no crack closure, the applied stress intensity factor range being fully effective. details about the properties evaluation for the s355 steel can be found in reference [19]. e [gpa] fu [mpa] fy [mpa] k’ [mpa] n’ 211.60 744.80 422.00 595.85 0.0757 table 1: monotonic and cyclic elastoplastic properties of the s355 mid steel. ’f [mpa] b ’f c 952.20 -0.0890 0.7371 -06640 table 2: morrow constants of the s355 mid steel.  k  [n.mm‐1.5] d a /d n  [ m m /c yc le ] p‐00‐01 (r=0.0) p‐00‐03 (r=0.0) p‐25‐01 (r=0.25) p‐25‐02 (r=0.25) p‐05‐01 (r=0.5) p‐05‐02 (r=0.5) 1.0e‐6 1.0e‐4 400 500 1500 1.0e‐5 1.0e‐3 1000 1.0e‐2 figure 5: experimental fatigue crack propagation data of the s355 steel for distinct stress ratios: experimental results. 1.0e‐04 1.0e‐03 1.0e‐02 1.0e‐01 1.0e+01 1.0e+02 1.0e+03 1.0e+04 1.0e+05 1.0e+06 1.0e+0 cycles to failure, n f  / 2  [ ‐] p=1% p=5% p=50% p=95% p=99% experimental data postulated data b = ‐3.2593 c = ‐9.1053 β = 4.6952 λ = 36.6676  = 5.8941 0.1 1 10 100 1.0e+01 1.0e+02 1.0e+03 1.0e+04 1.0e+05 1.0e+06 1.0e+0 cycles to failure, n f s w t  [ m p a ] p=1% p=5%  p=50% p=95% p=99% experimental data postulated data b = ‐4.1079 c = ‐4.4317 β = 3.6226 λ = 53.8423  = 7.2698 figure 6: p-ε-n field for the s355 steel. figure 7: p-swt-n field for the s355 steel. the p-ε-n and p-swt-n fields of the s355 steel are presented in figs. 6 and 7, respectively. the constants of the weibull fields are also referred in the figures. the extrapolations using the weibull field should be avoided for highand low-cycle fatigue lives. since the number of cycles to fail the representative volume element, in the crack propagation regime, may j.a.f.o. correia et alii, frattura ed integrità strutturale, 31 (2015) 80-96; doi: 10.3221/igf-esis.31.07 88 be low, it was decided to postulate some fatigue data at the lowto very low-cycle fatigue domain, using the morrow equation of the material, for that purpose. the morrow equation is more reliable to perform extrapolations for very low number of cycles than the weibull field since the weibull field shows an abnormal asymptotic behaviour for very lowcycle fatigue. probabilistic fatigue crack propagation rates predictions he probabilistic fatigue crack propagation rates predictions were based on the application of the unigrow model to the ct specimens. the elementary material block size, ρ*, is required. a trial and error procedure was adopted in order to result a good agreement between the numerical and experimental da/dn vs. k data, for the materials under consideration (see fig. 4). the probabilistic fatigue crack propagation fields were evaluated using both the probabilistic εa-n and swt-n fields, for comparison purposes. the procedure to generate the probabilistic fatigue crack propagation fields was aforementioned and illustrated in the fig. 5. finite element analysis of the ct geometry in order to assess the accuracy of the simplified elastoplastic analysis proposed in the unigrow model for the residual stress estimation, a bi-dimensional parametric finite element model of the ct specimen was built and used in an elastoplastic finite analysis, using ansys® 12.0 commercial code [31]. fig. 8 illustrates the typical finite element mesh of the ct geometry with the respective boundary conditions. figure 8: typical finite element mesh of the ct specimen, using 6-noded quadratic triangular plane stress elements. only ½ of the geometry is modelled, taking into account the existing plane of symmetry. plane stress conditions were assumed since the thickness of specimens are relatively reduced (b=8mm). plane stress quadratic 6-noded triangular elements were used in the analysis (solid183), with 3 integration points. in order to simulate the pin loading, rigid-toflexible contact was used with a friction coefficient, µ=0.3. the pin was modelled as a rigid circle controlled by a pilot node, using targe169 elements. the surface of the holes was modelled as a flexible surface using conta172 elements. the augmented lagrange contact algorithm was used. the associative von mises (j2) yield theory with multilinear kinematic hardening was used to model the plastic behaviour. fig. 9 shows the superposition of the rambergosgood relation [32] with the response of a finite element model reproducing a uniaxial stress state (single cubic element t j.a.f.o. correia et alii, frattura ed integrità strutturale, 31 (2015) 80-96; doi: 10.3221/igf-esis.31.07 89 model). besides the symmetry boundary conditions, the pilot node controlling the pin displacement was restricted along the loading direction. finally, the load was applied directly to the pilot node. it is interesting to note that the crack was modelled with a tip radius of ρ*, according the assumptions of fig. 1b. the mesh size at crack tip was calibrated using a convergence study taking into account the elastic stresses along the crack plane (σx: crack plane direction; σy: crack plane normal direction). fig. 10 illustrates the crack tip meshes considered in this convergence study and mesh 2 was the one adopted for the numerical simulations. tab. 3 presents the maximum elastic stresses (σx and σy) ahead of the crack tip, resulting from distinct mesh densities, for the s355 steel. the results are compared between the adopted reference mesh 2 and the other tested meshes. mesh 2 gives a good compromise between computational cost and stability of the solution. 0 100 200 300 400 500 600 700 0.00e+00 1.00e‐02 2.00e‐02 3.00e‐02 4.00e‐02 5.00e‐02 strain [‐] s tr e ss  [ m p a ] ramberg‐osgood fem ‐ multilinear figure 9: cyclic curve of the s355 steel. mesh 5 mesh 4 mesh 1 mesh 2 mesh 3 figure 10: finite element meshes used in the convergence study for the s355 steel (ρ*=55µm). j.a.f.o. correia et alii, frattura ed integrità strutturale, 31 (2015) 80-96; doi: 10.3221/igf-esis.31.07 90 maximum stress mesh 5 mesh 4 mesh 1 mesh 2 mesh 3 y [mpa] 1637.00 1772.00 1797.00 1926.90 1928.80 dev. [%] -15.04 -9.04 -6.71 0.10 x [mpa] 419.70 423.83 416.67 417.89 417.78 dev. [%] 2.83 1.42 -0.29 -0.03 table 3: maximum elastic stresses for distinct finite element mesh densities for the s355 steel (fmax=5443.5n, a=10mm, ρ*=55µm). the finite element model was used to simulate a loading and unloading sequence. the residual stresses are computed from the stress field at the end of the unloading load step. alternatively, the simplified analytical solution based on multiaxial neuber’s approach [15] was implemented for comparison purposes. in this case, the residual stresses resulted from the subtraction of the cyclic elastoplastic stress range to the maximum elastoplastic stress, both computed in an independent way. the finite element model was initially applied to perform elastic and elastoplastic stress analyses in order to allow the comparison of the elastic and elastoplastic stress distributions, respectively with the creager-paris solution [22] and multiaxial neuber’s approach [15]. according to the unigrow model, the compressive residual stresses computed ahead the crack tip are assumed to be applied symmetrically, in the crack faces. using the weight function method [24], the residual stress intensity factor, kr, was computed for the stress r-ratios considered in the experimental program. the elastic stress distributions from the numerical and analytical solutions for the ct specimens made of the s355 steel are compared in fig. 11. fig. 12 compares the elastoplastic stress distributions. the results were computed for a crack tip radius, ρ*=5.5×10-5m, which was found to be the best value for the s355 steel, that gives the best predictions for the crack growth rates, based on swt fatigue damage probabilistic field. 0.0e+00 8.0e+08 1.6e+09 2.4e+09 3.2e+09 4.0e+09 0.0e+00 2.0e‐04 4.0e‐04 6.0e‐04 8.0e‐04 1.0e‐03 distance from the crack tip [m] e la st ic  s tr e ss ,   y  [p a ] fem (a=10mm) creager‐paris (a=10mm) fem (a=15mm) creager‐paris (a=15mm) fem (a=20mm) creager‐paris (a=20mm) r=0.0 0.0e+00 2.0e+08 4.0e+08 6.0e+08 8.0e+08 0.0e+00 2.0e‐04 4.0e‐04 6.0e‐04 8.0e‐04 1.0e‐03 distance from the crack tip [m] e la st ic  s tr e ss ,   x  [p a ] fem (a=10mm) creager‐paris (a=10mm) fem (a=15mm) creager‐paris (a=15mm) fem (a=20mm) creager‐paris (a=20mm) r=0.0 a) σy stress distribution (fmax=5443.5n, ρ*=55µm). b) σx stress distribution (fmax=5443.5n, ρ*=55µm). figure 11: elastic stress distribution ahead of the crack tip and along the crack plane line (y=0) for ct specimens made of the s355 steel: comparison between analytical and numerical results. distinct crack sizes considered. 0.0e+00 2.0e+08 4.0e+08 6.0e+08 8.0e+08 0.0e+00 1.0e‐03 2.0e‐03 3.0e‐03 4.0e‐03 5.0e‐03 6.0e‐03 distance from the crack tip [m] e la st o p la st ic  s tr e ss ,   y  [p a ] fem (a=10mm) neuber (a=10mm) fem (a=15mm) neuber (a=15mm) fem (a=20mm) neuber (a=20mm) r=0.0 0.0e+00 1.0e+08 2.0e+08 3.0e+08 4.0e+08 5.0e+08 0.0e+00 1.0e‐03 2.0e‐03 3.0e‐03 4.0e‐03 5.0e‐03 6.0e‐03 distance from the crack tip [m] e la st o p la st ic  s tr e ss ,   x  [p a ] fem (a=10mm) neuber (a=10mm) fem (a=15mm) neuber (a=15mm) fem (a=20mm) neuber (a=20mm) r=0.0 a) σy stress distribution (fmax=5443.5n, ρ*=55µm). b) σx stress distribution (fmax=5443.5n, ρ*=55µm). figure 12: elastoplastic stress distribution ahead of the crack tip along the crack plane line (y=0) for ct specimens made of s355 steel: comparison between analytical and numerical results. distinct crack sizes considered. j.a.f.o. correia et alii, frattura ed integrità strutturale, 31 (2015) 80-96; doi: 10.3221/igf-esis.31.07 91 the residual stress distributions are illustrated in fig. 13, for distinct crack sizes and stress r-ratios, for the ct specimens made of s355 steel and assuming ρ*=5.5×10-5m. these residual stresses were computed using both analytical and numerical solutions. ‐5.0e+08 ‐4.0e+08 ‐3.0e+08 ‐2.0e+08 ‐1.0e+08 0.0e+00 1.0e+08 2.0e+08 0.0e+00 5.0e‐04 1.0e‐03 1.5e‐03 2.0e‐03 2.5e‐03 3.0e‐03 distance from the crack tip [m]  re si d u al  [ p a ] fem (a=10mm) neuber (a=10mm) fem (a=15mm) neuber (a=15mm) fem (a=20mm) neuber (a=20mm) r=0.0 ‐5.0e+08 ‐4.0e+08 ‐3.0e+08 ‐2.0e+08 ‐1.0e+08 0.0e+00 1.0e+08 2.0e+08 0.0e+00 5.0e‐04 1.0e‐03 1.5e‐03 2.0e‐03 2.5e‐03 3.0e‐03 distance from the crack tip [m]  re si d u al  [ p a ] fem (a=10mm) neuber (a=10mm) fem (a=15mm) neuber (a=15mm) fem (a=20mm) neuber (a=20mm) r=0.25 a) rσ=0.0 (fmax=5443.5n, ρ*=55µm). b) rσ=0.25 (fmax=7185.5n, ρ*=55µm). ‐5.0e+08 ‐4.0e+08 ‐3.0e+08 ‐2.0e+08 ‐1.0e+08 0.0e+00 1.0e+08 2.0e+08 3.0e+08 0.0e+00 1.0e‐03 2.0e‐03 3.0e‐03 4.0e‐03 5.0e‐03 6.0e‐03 distance from the crack tip [m]  re si d u al  [ p a ] fem (a=10mm) neuber (a=10mm) fem (a=15mm) neuber (a=15mm) fem (a=20mm) neuber (a=20mm) r=0.5 c) rσ=0.5 (fmax=10778.2n, ρ*=55µm). figure 13: residual stress distribution ahead of the crack tip along the crack plane line (y=0) for ct specimens made of s355 steel: comparison between analytical and numerical results. distinct stress ratios and crack sizes considered. a) stress field, in mpa, at the end of the 1st loading reversal. b) stress field, in mpa, at the end of the 1st unloading reversal. c) strain field at the end of the 1st loading reversal. d) strain field at the end of the 1st unloading reversal. figure 14: stress and strain fields, along the load direction, obtained for the ct specimens made of s355 steel, resulting from elastoplastic finite element analysis (ρ*=55µm, a=15mm, rσ=0.0, fmax=5443.5n). j.a.f.o. correia et alii, frattura ed integrità strutturale, 31 (2015) 80-96; doi: 10.3221/igf-esis.31.07 92 the stress and strain fields along the y (load) direction assuming a material representative element of ρ*=55µm, a crack size a=15mm, a maximum load fmax=5443.5n, and a stress r-ratio, rσ=0.0, obtained for the ct specimens using the elastoplastic finite element analysis, are illustrated in fig. 14. it is clear the compressive stress field at the crack tip vicinity and at some extension of the crack wake. the stress and strain fields are shown at the end of the first loading reversal and at the end of the unloading reversal. fig. 15 presents the residual stress intensity factor as a function of the applied stress intensity factor range obtained for the ct specimens made of s355 steel, using the numerical analysis. kresidual = ‐0.3935kapplied + 94.978 r 2  = 0.9987 kresidual = ‐0.3264kapplied + 83.854 r 2  = 0.9994 kresidual = ‐0.2212kapplied + 49.136 r 2  = 0.9999 ‐500 ‐400 ‐300 ‐200 ‐100 0 0 200 400 600 800 1000 1200 1400 kapplied [n.mm ‐1.5 ] k re si d u al  [ n .m m ‐1 .5 ] r=0.0 r=0.25 r=0.5 figure 15: residual stress intensity factor as a function of the applied stress intensity factor range obtained for the s355 steel (ρ*=5.5×10-5m). the elastic stress distributions presented a satisfactory agreement between the analytical and numerical results, for several crack sizes (measured from loading line), within a small distance from the crack tip. for higher distances, slight deviations are found for σy stresses. for σx stresses, the maximum deviation is found in the maximum absolute value. for small and high distances from the crack tip, the deviations on σx stresses are minimal. additional simulations with further mesh refinements did not produce noticeable changes in the elastic stress distributions, demonstrating a good mesh refinement. besides the numerical solution for the elastoplastic analysis, results from the multiaxial neuber’s analysis are also considered. despite the same global trends are observed for the σy and σx stress distributions, deviations in maximum absolute values are verified in the elastoplastic stresses. in general, the analytical solutions lead to maximum absolute stresses higher than the elastoplastic fe analysis. σx stresses are more stepped than the corresponding numerical stresses near the crack tip. also, the analytical solution shows some instability near the crack tip. the analysis of the σy stress distribution shows an inflection point which is related to the size of the plastic zone. the analytical solution does not show this behaviour, which is a clear limitation of the analytical approach. the compressive residual stresses decrease progressively with increasing stress ratio, making the applied stress intensity range more effective. the extension of the compressive residual stresses increases with the crack size. the numerical model always predicts a compressive stress region which is lower than that predicted using the analytical model. the comparison between the numerical and analytical results highlighted some inconsistencies in the analytical results. the analytical procedure produces reliable results at the crack notch root, but the residual stress distribution along the crack front path (away from the crack notch root) seems to be inconsistent, which is in part justified by the incapacity of the analytical model to handle the stress redistribution due to yielding. therefore, the numerical solution, for the residual stresses, was adopted in the crack propagation prediction, based on the unigrow model. a linear correlation between the residual stress intensity factor and the applied stress range is verified, for each stress rratio. this linear relation agrees with the proposition by noroozi et al. [10]. p-da/dn-k-r results and discussion the unigrow model was applied to compute the fatigue crack propagation for the same experimental conditions used to derive the aforementioned fatigue crack propagation data. the residual stress intensity factor was computed based on compressive residual stress distribution from the finite element analysis, and using the weight function method [24], as proposed in the unigrow model. the strain range and maximum stress required by the probabilistic strain-life or swt-life j.a.f.o. correia et alii, frattura ed integrità strutturale, 31 (2015) 80-96; doi: 10.3221/igf-esis.31.07 93 models were assessed using the analytical approach, applied to the first elementary material block, keeping the original structure of the unigrow model. average strain and stress values, along the first elementary material block, were used instead of peak values. the analytical solution produces reliable results at the crack tip notch root as verified in previous section. the original structure of the unigrow model has some advantages: i) a direct correspondence with fracture mechanics based analyses, which facilitates the physical understanding of the process; ii) allows close form solutions for fatigue crack propagation laws in the same format of existing fracture mechanics approaches; iii) requires inexpensive computations. the elastoplastic finite element analysis was used for the derivation of the residual stresses which were afterwards used for the computation of the residual stress intensity factor, using the weight function method. the p-swt-n or the p-εa-n fields were used to derive the probabilistic fatigue crack propagation fields (p-da/dn-k-r fields). for each case, an independent identification of the elementary material block size, ρ*, was performed. fig. 16 shows the probabilistic fatigue crack propagation fields that were obtained, for the s355 steel, using the p-εa-n field. fig. 17 illustrates the probabilistic fatigue crack propagation fields predicted for the s355 steel, resulting from the p-swt-n field. an elementary material block size of 5.5×10-5m was found suitable for both p-swt-n and p-εa-n damage fields. concerning the p-da/dn-k-r fields predicted for the s355 steel, the field that resulted from the p-swt-n damage model produced the best results. this observation is justified by the fact that the s355 steel shows a markedly stress ratio influence on fatigue crack propagation rates, requiring a fatigue damage model that is able to account for the mean stress effects.  k  [n.mm‐3/2] d a /d n  [ m m /c yc le ] experimental data: r=0.0 p=0.01 p=0.05 p=0.50 p=0.95 p=0.99 1.0e‐6 1.0e‐3 1.0e‐2 200 1500500 1.0e‐4 1.0e‐5 1000  k  [n.mm‐3/2] d a /d n  [ m m /c y cl e ] experimental data: r=0.25 p=0.01 p=0.05 p=0.50 p=0.95 p=0.99 1.0e‐6 1.0e‐3 1.0e‐2 200 1500500 1.0e‐4 1.0e‐5 1000 a) b)  k  [n.mm‐3/2] d a /d n  [ m m /c y cl e ] experimental data: r=0.5 p=0.01 p=0.05 p=0.50 p=0.95 p=0.99 1.0e‐6 1.0e‐3 1.0e‐2 200 1500500 1.0e‐4 1.0e‐5 1000 c) figure 16: probabilistic prediction of the fatigue crack propagation based the p-ε-n field, for the s355 steel: a) rσ=0; b) rσ=0.25; c) rσ=0.5. j.a.f.o. correia et alii, frattura ed integrità strutturale, 31 (2015) 80-96; doi: 10.3221/igf-esis.31.07 94  k  [n.mm‐3/2] d a /d n  [ m m /c yc le ] experimental data: r=0.0 p=0.01 p=0.05 p=0.50 p=0.95 p=0.99 1.0e‐6 1.0e‐3 1.0e‐2 200 1500500 1.0e‐4 1.0e‐5 1000  k  [n.mm‐3/2] d a /d n  [ m m /c y cl e ] experimental data: r=0.25 p=0.01 p=0.05 p=0.50 p=0.95 p=0.99 1.0e‐6 1.0e‐3 1.0e‐2 200 1500500 1.0e‐4 1.0e‐5 1000 a) b)  k  [n.mm‐3/2] d a /d n  [ m m /c y cl e ] experimental data: r=0.5 p=0.01 p=0.05 p=0.50 p=0.95 p=0.99 1.0e‐6 1.0e‐3 1.0e‐2 200 1500500 1.0e‐4 1.0e‐5 1000 c) figure 17: probabilistic prediction of the fatigue crack propagation based the p-swt-n field, for the s355 steel: a) rσ=0; b) rσ=0.25; c) rσ=0.5. conclusions n assessment of the unigrow model was presented in this paper, based on available experimental data for the s355 mild steel. the unigrow model was also extended to predict probabilistic fatigue crack propagation fields, replacing the deterministic swt-n relation proposed in the unigrow model by p-swt-n or p-εa-n fields. the pswt-n field was firstly proposed in the present paper, as a generalization of the p-εa-n field, in order to take into account the mean stress effects. elastoplastic finite element analysis was used to compute the residual stress field which is a more accurate than using the analytical elastoplastic formulae that does not account for stress redistribution due to yielding. the predicted p-da/dn-k-r field for the s355 steel, based on the material p-swt-n field, showed a satisfactory agreement with the available experimental data. the proposed p-da/dn-k-r fields were able to model conveniently the stress rratio effects on crack propagation rates as well as to represent the scatter on these fatigue crack propagation rates. the elementary material block size found for the material is within the same order of magnitude for this parameter found by noroozi et al. [10]. acknowledgements he authors acknowledge the portuguese science foundation (fct) for the financial support through the doctoral grant sfrh/bd/66497/2009. a t j.a.f.o. correia et alii, frattura ed integrità strutturale, 31 (2015) 80-96; doi: 10.3221/igf-esis.31.07 95 references [1] noroozi, a.h., glinka, g., lambert, s., a two parameter driving force for fatigue crack growth analysis, international journal of fatigue, 27 (2005)1277-1296. [2] schütz, w., a history of fatigue, engineering fracture mechanics, 54 (1996) 263-300. [3] paris, p.c., gomez, m., anderson, w.e., a rational analytic theory of fatigue, trend engineering, 13 (1961) 9-14. [4] beden, s.m., abdullah, s., ariffin, a.k., review of fatigue crack propagation models for metallic components, european journal of scientific research, 28 (2009) 364-397. [5] coffin, l.f., a study of the effects of the cyclic thermal stresses on a ductile metal, translations of the asme, 76 (1954) 931-950. [6] manson, s.s., behaviour of materials under conditions of thermal stress, naca tn-2933, national advisory committee for aeronautics, (1954). [7] morrow, j.d., cyclic plastic strain energy and fatigue of metals, int. friction, damping and cyclic plasticity, astm stp 378, (1965) 45-87. [8] smith, k.n., watson, p., topper, t.h., a stress-strain function for the fatigue of metals, journal of materials, 5(4) (1970) 767-778. [9] shang, d.-g., wang, d.-k., li, m., yao, w.-x., local stress–strain field intensity approach to fatigue life prediction under random cyclic loading, international journal of fatigue, 23 (2001) 903–910. [10] noroozi, a.h., glinka, g., lambert, s., a study of the stress ratio effects on fatigue crack growth using the unified two-parameter fatigue crack growth driving force, international journal of fatigue, 29 (2007) 1616-1633. [11] noroozi, a.h., glinka, g., lambert, s., prediction of fatigue crack growth under constant amplitude loading and a single overload based on elasto-plastic crack tip stresses and strains, engineering fracture mechanics, 75 (2008) 188206. [12] peeker, e., niemi, e., fatigue crack propagation model based on a local strain approach, journal of constructional steel research, 49 (1999) 139–155. [13] glinka, g., a notch stress-strain analysis approach to fatigue crack growth, engineering fracture mechanics, 21 (1985) 245-261. [14] hurley, p.j., evans, w.j., a methodology for predicting fatigue crack propagation rates in titanium based on damage accumulation, scripta materialia, 56 (2007) 681–684. [15] neuber, h., theory of stress concentration for shear-strained prismatic bodies with arbitrary nonlinear stress–strain law, trans. asme journal of applied mechanics, 28 (1961) 544–551. [16] moftakhar, a., buczynski, a., glinka, g., calculation of elasto-plastic strains and stresses in notches under multiaxial loading, international journal of fracture, 70 (1995) 357-373. [17] reinhard, w., moftakhar, a., glinka, g., an efficient method for calculating multiaxial elasto-plastic notch tip strains and stresses under proportional loading, fatigue and fracture mechanics, astm stp 1296, r.s. piascik, j.c. newman, n.e. dowling, eds., american society for testing and materials, 27 (1997) 613-629. [18] mikheevskiy, s., glinka, g., elastic–plastic fatigue crack growth analysis under variable amplitude loading spectra,” international journal of fatigue, 31 (2009) 1828–1836. [19] de jesus, a.m.p., matos, r., fontoura, b.f.c., rebelo, c., simões da silva, l., veljkovic, m., a comparison of the fatigue behavior between s355 and s690 steel grades, journal of constructional steel research, 79 (2012) 140–150. [20] castillo, e., fernández-canteli, a., a unified statistical methodology for modeling fatigue damage, springer, (2009). [21] basquin, o.h., the exponential law of endurance tests, in: proc. annual meeting, american society for testing materials, 10 (1910) 625-630. [22] creager, m., paris, p.c., elastic field equations for blunt cracks with reference to stress corrosion cracking, international journal of fracture mechanics, 3 (1967) 247–252. [23] molski, k., glinka, g., a method of elastic-plastic stress and strain calculation at a notch root, materials science and engineering, 50 (1981) 93-100. [24] glinka, g., development of weight functions and computer integration procedures for calculating stress intensity factors around cracks subjected to complex stress fields, progress report no.1: stress and fatigue-fracture design, petersburg ontario, canada, (1996). [25] sadananda, k., vasudevan, a.k., kang, i.w., effect of superimposed monotonic fracture modes on the δk and kmax parameters of fatigue crack propagation, acta materialia, 51(22) (2003) 3399-3414. j.a.f.o. correia et alii, frattura ed integrità strutturale, 31 (2015) 80-96; doi: 10.3221/igf-esis.31.07 96 [26] kajawski, d., a new (δk+kmax)0.5 driving force parameter for crack growth in aluminum alloys, international journal of fatigue, 23(8) (2001) 733-740. [27] castillo, e., galambos, j., lifetime regression models based on a functional equation of physical nature”, journal of applied probability, 24 (1987) 160-169. [28] castillo, e., fernández-canteli, a., hadi, a.s., lópez-anelle, m., a fatigue model with local sensitivity analysis, fatigue and fracture of engineering material and structure, 30 (2006) 149–168. [29] astm e606: standard practice for strain-controlled fatigue testing, annual book of astm standards, astm, west conshohocken, pa, usa, 03.01 (1998) [30] astm e647: standard test method for measurement of fatigue crack growth rates, annual book of astm standards, astm, west conshohocken, pa, usa, 03.01 (2000). [31] sas, ansys, swanson analysis systems, inc., houston, version 12.0, (2011). [32] ramberg, w., osgood, w.r., description of the stress-strain curves by the three parameters, naca tn-902, national advisory committee for aeronautics, (1943). microsoft word numero_33_art_51 j. fan et alii, frattura ed integrità strutturale, 33 (2015) 463-470; doi: 10.3221/igf-esis.33.51 463 weight function method for computations of crack face displacements and stress intensity factors of center cracks junling fan, dengke dong, li chen, xianmin chen avic aircraft strength research institute, xi’an 710065, china fanjunling@mail.dlut.edu.cn xinglin guo state key laboratory of structural analysis for industrial equipment, dalian university of technology, dalian 116024, china abstract. the weight function method provides a powerful and reliable tool for the determination of the stress intensity factor around the crack tip in a linearly elastic cracked solid subjected to arbitrary loading conditions. however, it is difficult to exactly compute the crack face displacement whose partial derivative is responsible for the weight function calculation. in the present paper, only one reference stress intensity factor is used for the purpose of establishing a general expression of the crack face displacement. then, the generalized and simple expression is applied to calculate the weight function and the stress intensity factor of the center crack configuration. the calculation of the weight function is reduced to the simple integration of the correction function and of the partial derivative of the crack face displacement. it is shown that the present expressions for the computations of the crack face displacement and its partial derivative are in good agreement with their exact solutions. keywords. weight function; crack face displacement; stress intensity factor; center crack configuration. introduction s is known, the stress intensity factors (sifs) dominate the singular stress states around the crack tip. thus, the calculation of the sifs is of quite importance for assessing the load capacity, fatigue crack growth rate and fracture failure control of a cracked component. although the sifs are possibly available in some of the sif handbooks [1], the documented solutions are sometimes inapplicable in practical problems due to complicated non-linear stress fields. the weight function method provides a reliable method to calculate the sif around a crack tip in a 2d linearly elastic body subjected to any arbitrarily chosen load systems [2]. wu and carlsson [3] presented the generalized weight function method based on the physical judgment on the shape of the opened crack, and subsequently derived the sifs for center cracks in finite width plates with mixed boundary conditions. shen and glinka [4] used two linearly independent reference stress intensity factors together with the characteristic properties of the weight function to determine the three unknown parameters in the universal weight function. overall, the weight function method makes it possible to determine exact and reliable stress intensity factors which are useful for the evaluation of fatigue crack growth and residual strength of aircraft structures in service. a j. fan et alii, frattura ed integrità strutturale, 33 (2015) 463-470; doi: 10.3221/igf-esis.33.51 464 nevertheless, the weight function is strongly dependent on the solution of the crack face displacement whose functional dependence on the crack is undetermined. therefore, it is necessary to make appropriate assumption on the opened crack shape. the present paper is aimed at developing an approximate and simple expression of the crack face displacement for collinear cracks and center crack subjected to mode i loading conditions. weight function method he weight function method has been widely applied to determine the sifs of cracked structures since it is able to take complex loading conditions into consideration. it has been shown that, if the sif k(a)(1) and the crack face displacement u(1)(x, a) of any linearly elastic cracked solid are known as functions of the crack length a for a symmetrical load system (1), then for the same cracked solid subjected to any other symmetrical load system (2), the sif k(a)(2) can be obtained by the simple integration of the weight function h(x, a) and the stress function σ(2)(x): ( 2 ) ( 2 ) 0 ( ) ( ) ( , ) a k a x h x a dx  (1) where the weight function, independent of σ(2)(x), is defined as: ( 1) ( 1) ( , ) ( , ) ( ) u x ah h x a k a a    (2) in eq. (1) and (2), a is the half or full crack length for edge cracks and center cracks, respectively; h is a material constant, h=e for plane stress condition and h=e/(1-v2) for plane strain condition with e the young’s modulus and v the poisson’s ratio; k(a)(1) and u(1)(x, a) are, respectively, the known reference stress intensity factor and the crack face displacement in mode i loading conditions for the known load system (1); and σ(2)(x) is the stress distribution function across the plane of the crack in the crack free solid subjected to the load system (2). from eq. (1), it is known that if the weight function is set to be a known function for a particular crack geometry, the sif for any stress distribution is able to be calculated by integrating eq. (1). therefore, the main problem is to exactly determine the weight function h(x,a) and the corresponding partial derivative (1) ( , ) /u x a a  of the crack face displacement. for a reference sif k(a)(1), it is possibly available in the sif handbooks for a wide range of crack configurations and loading conditions. however, there are often no detailed databases about the crack face displacement u(1)(x, a), and it is difficult to rigorously calculate u(1)(x, a) since the functional dependence of u(1)(x, a) on both x and a is undetermined. thus, approximate u(1)(x, a)-solutions across the crack line of a cracked solid are of primary importance for determining the weight function h(x, a) and stress intensity factor k(a)(2) [5]. crack opening displacements across the center crack n eq. (1) and (2), if k(a)(1)=k(a)(2)=k(a), and σ(1)(x)= σ(2)(x)= σ(x). then, substituting (2) into (1), it leads to: 2 0 ( , ) ( ) ( ) a u x a k a h x dx a      (3) so, the crack face displacement u(x, a) in eqn. (3) is the only unknown function dependent on the crack line x and half of the crack length a. as is well known that u(x=a, a)=0 for any crack tip. as a result, eq. (3) becomes: 2 0 ( ) ( ) ( , ) a k a h x u x a dx a       (4) integrating eq. (4) over the half crack length a, we have: 2 0 0 ( ) ( ) ( , ) a a k a da h x u x a dx   (5) t i j. fan et alii, frattura ed integrità strutturale, 33 (2015) 463-470; doi: 10.3221/igf-esis.33.51 465 based on the previous works [3], the crack face displacement u(x, a) is assumed to be dependent on x and a:   * *0 0 1 1, ( ) ( ) x x u x a u a u u a u a a             (6) where u0(a) and u1(a) are the unknown functions relative to the half crack length a;  *0 /u x a describes the deformation of the center crack;  *1 /u x a is assumed to be the higher order of   * 0 /u x a . to approximately determine the crack face displacements u(x, a) across the whole crack line of a central through crack, u(x, a) should also follow the given criterions below [3, 5]: (i) exhibiting proper limiting behavior near the crack tip; (ii) deforming as a shape of the ellipse when the cracked solid is subjected to a remotely uniform stress field; (iii) demonstrating the consistent behavior for the small crack; (iv)   0 , | 0x u x a a     . if an infinite solid with a central through crack of the length 2a is subjected to a remotely uniform tensile stress filed σ0, the crack face displacements and the sif are, respectively, presented as:      0 0 2 , 2 and yu x a a k a a h         (7) where ξ=0 is the coordinate with its origin at one of the crack tips, and ξ=2a is the other crack tip. based on eqn. (7), if a finite solid, with a center crack of the length 2a, is also undergoing a remotely uniform tensile stress σ0, the crack face displacements and the sif are able to be written as:           0 0 2 , and y f a u x a a x a x k a f a a h        (8) where x is the coordinate with its origin at the crack center; x=±a are set to be the two crack tips of the crack; 2b is the width of the elastic cracked solid; f(a) is defined as the correction function which is dependent on the crack geometry and the size of the cracked solid. in the criterion (ii), it is assumed that the crack face displacement of the center crack deforms as a shape of the ellipse when the cracked body is subjected to a uniformly distributed stress field perpendicular to the crack line. so, the shape of the opened crack can be expressed as an elliptic function:   2 * 0 1 x xu aa        (9) as a consequence, from eq. (8) and (9) the first term in the right hand side of eq. (6) is determined as: 2 * 0 0 0 2 ( ) ( ) ( ) 1 f a ax x u a u a h a        (10) here, the first term u(x, a) satisfies the criterions (i) and (ii). so, the second term u(x, a) should make the full expression of u(x, a) satisfy all the four criterions. upon that, *1 x u a       is taken as a higher order of *0 x u a       :   3/22* 1 1 x u x a a          (11) j. fan et alii, frattura ed integrità strutturale, 33 (2015) 463-470; doi: 10.3221/igf-esis.33.51 466 to make u(x, a) demonstrate the consistent behaviour for the small crack, u1(a) should have the characteristic properties: u1(a)=0(1/a) if the half crack length a tends to be zero. based on the above criterions, an approximate and simple expression of the crack face displacement is derived as:           3/22 2 * * 0 0 0 1 1 2 , 1 1 f a a g ax x x x u x a u a u u a u a a h a a a                                  (12) where g(a) is the only unknown function of the half crack length a. substituting eqn. (12) into (5), and assuming the stress function σ(x) is equal to a constant value σ0, it leads to: 3/22 22 2 2 0 0 0 0 0 0 2 ( ) ( ) ( ) 1 1 a a af a a g ax x f a ada h dx dx h a a a                             (13) and solving eq. (13), the unknown function g(a) is determined as:  2 20 00( ) 16 ( ) 8 ( ) 3 a g a f a ada f a a h   (14) finally, substituting eqn. (14) into (12), the fully expression of the crack face displacements is derived as:   3/22 22 2 0 00 0 16 ( ) 8 ( )2 ( ) , 1 1 3 a f a ada f a af a a x x u x a h a ha a                       (15) results and discussions calculations of u(x,a) and  , /u x a a  for collinear cracks o check the accuracy of the expression for u(x, a) of the central through crack, an array of collinear cracks in an infinite plate, subjected to a uniformly tensile stress field σ0, is taken into account. so, the correction function f(a) is: 2 ( ) tan 2 b a f a a b         (16) where 2a is the full crack length; and 2b is set as the distance between the two adjacent crack center lines. substituting eqn. (16) into (15) and simplifying the expression, the dimensionless displacement is determined as:       2 0 3/22 0 , 2 2 tan 1 2 32 8 2 tan tan 1 3 2 3 2 a hu x a a a x ab b b a a a xda aa b b b                                    (17a) also, a generalized formula for the crack face displacements has been given by wu and carlsson [3]:   2 2 0 , 4 2 ln cos 1 2 hu x a b a x b a b a                             (18a) t j. fan et alii, frattura ed integrità strutturale, 33 (2015) 463-470; doi: 10.3221/igf-esis.33.51 467 for the same situation, the exact u(x, a)-solution was presented as [3]:   2 2 0 , 4 ln cos cos cos ln cos 2 2 2 2 hu x a x x a a b b b b b                                          (19a) fig.1(a) presents the variations of the dimensionless crack face displacements hu(x, a)/(σ0b) for collinear cracks in an infinite plate, respectively, determined by eq. (17a), (18a) and (19a). it is clearly shown that if the values of a/b≤0.5, values of hu(x, a)/(σ0b) calculated through eq. (17a) and (18a) are in good agreement with the exact u(x, a)-solutions given by eqn. (19a). for this situation, the maximum difference between the results by eq. (18a) and (19a) is about 0.359% occurred at a/b=0.5 and x/a=0.95; but the maximum difference between eq. (17a) and (19a) is only 0.0071% when a/b=0.5 and x/a=0. once the values of a/b≥0.7, the differences between the crack face displacements by eq. (18a) and (19a) increase sharply from 1.9% (a/b=0.7 and x/a=0.95) to 17.06% (a/b=0.95 and x/a=0.95). but, the differences between eq. (17a) and (19a) are still in the small range of 0.092% to 5.1%. therefore, it is concluded that the present expression of the crack face displacement for collinear cracks can give much better u(x, a)-solutions than that calculated by eqn. (18a) since the higher order term √[1-(x/a)2] is taken into account. fig.1(b) gives the relationship between hu(x, a)/(σ0b) and a/b-values for collinear cracks according to eqn.(17a). it is then seen that the crack face displacements increase with the increasing values of a/b. figure1: comparisons of the dimensionless crack face displacements for collinear cracks (a) hu(x, a)/(σ0b) versus x/a; (b) hu(x, a)/(σ0b) versus a/b. according to eq. (17a), (18a) and (19a), the dimensionless partial derivatives of u(x, a) for an array of collinear cracks are, respectively, derived as (17b), (18b) and (19b) below: 2 2 2 2 22 0 2 2 2 2 2 tan ( , ) 8 22 2 1 ln tan 1 2 1 8 tan 1 1 tan 2 2 2 1 1 tan 2 2 b a h u x a x x bx aa b a a a a a bx a a a x a b b a bx x a aa a b b                                                                                       3/22 2 3/2 22 2 32 tan 3 2 tan 1 tan 4 2 2 2 2 1 ln tan 1 23 3 tan 4 2 2 b a a b a a a x b a b b b a ba a a b b                                                                                (17b) j. fan et alii, frattura ed integrità strutturale, 33 (2015) 463-470; doi: 10.3221/igf-esis.33.51 468       2 2 2 2 0 1 2( , ) 4 8 ln cos tan 1 2 2 1 x h u x a b a b aa x aa a b a bx a                                    (18b) 0 2 2 2 2 sin ( , ) 2 tan 2 cos cos cos cos cos 2 2 2 2 2 a h u x a a b a b x x a x a b b b b b                                                        (19b) fig.2 shows the variations of the dimensionless partial derivatives  , /u x a a  which is used for calculating the weight function h(x, a). through fig.2 (a), it is clearly found that for the values of a/b≤0.5, the dimensionless derivatives, separately, obtained by eq. (17b) and (18b) agree quite well with those from the exact u(x, a)-solutions presented in eq. (19b). for 0.7≤a/b≤0.9, the predicted values of  , /u x a a  by eq. (17b) can give lower errors than eq. (18b) due to the consideration of the higher order of  21 x a . from fig.2 (b), it is obviously observed that once the values of a/b>0.9, great differences are presented between the partial derivatives determined by eq. (17b) and (18b) to (19b). figure 2: dimensionless partial derivatives of collinear cracks (a) 0≤a/b≤0.8; (b) 0.95≥a/b≥0.9. calculations of weight functions and stress intensity factors to calculate the weight function through eq. (2), the only unknown information is k(a)(1). to make the problem easier, it is better to choose the uniformly distributed stress field as the reference load system (1) since the basic assumption relevant to the crack shape is most suited for this type of loading condition. therefore, the formula for computing the weight function of a finite width plate is in the form given below: 0 ( , ) ( , ) ( ) u x ah h x a af a a     (20) for a finite width plate with a central through crack, the correction function, dependent on the crack length 2a and the width of the finite plate 2b, is given as [1]: 2 3( ) 1 0.128 0.288 1.525f a p p p    (21) where p=a/b is defined as the ratio between the crack length 2a to the width of the plate 2b. substituting (21) into (15), the partial derivative u(x, a) for the center crack is solved as the function of a and x: j. fan et alii, frattura ed integrità strutturale, 33 (2015) 463-470; doi: 10.3221/igf-esis.33.51 469 2 2 2 '0 3/22 2' 0 2 0 2( , ) ( ) ( ) 1 ( ) 1 16 3 ( ) ( ) ( ) 1 1 3 8 3 3 u x a x x x f a f a a f a a aa h a g a g a g ax x h a a a a a h                                                                   3/22 2 2 '( ) 1 ( ) ( ) 1 x x x f a f a a f a a a a                                       (22) where f ′(a), g(a) and g′(a) are, respectively, determined as:       ' 2 2 6 2 3 4 5 6 ' 6 2 3 4 5 6 2 3 1 ( ) 0.128 0.576 4.575 ( ) 0.5 0.0853 0.1399 0.5953 0.0789 0.1255 0.2907 ( ) 2 0.5 0.0853 0.1399 0.5953 0.0789 0.1255 0.2907 + 0.0853 0.2798 1.7858 0 f a p p b g a a b p p p p p p g a a b p p p p p p a p p p                     4 5 6.3156 0.6274 1.7442p p p           (23) subsequently, substituting (22) into (20), the weight function h(x, a) for the center crack in a finite plate by the present method is obtained and written as: 2 2 2' 0 3/22 2' 2 ( , ) ( ) ( , ) 2 1 1 1 ( ) ( ) 3 ( ) ( ) ( )16 1 1 3 ( ) ( ) ( ) u x a f a ah x x x h x a a a af a a f a a g a g a g ax x f a a a f a a f a a a                                                                   3/22 2 2' ( )8 3 1 1 1 3 ( ) f a ax x x a a f a a                                          (24) the weight function for a central through crack in an infinitely wide plate has been derived by paris and sih [4]:  , a x a xh x a a a x a x        (25) from eq. (25), if x/a-value tends to be zero, the dimensionless weight function h(x, a)√(πa) tends to be a constant value of 2. this is the limiting condition for collinear cracks in an infinite plate and for center cracks in a finite plate. based on eq. (17b), (24) and (25), fig.3(a) shows the variations of the weight function h(x, a)√(πa) for collinear cracks in an infinite plate and for center cracks in a finite plate at the center of the crack x/a=0. according to eq. (1), (24) and (25), the sifs for center cracks in mode i conditions are computed and presented in fig.3(b). it is obviously found that the eq. (25) used for crack problems will result in significant error for the calculations of weight functions and sifs in finite plates since the correction function has not been considered. conclusions general approach has been presented to calculate the crack face displacement of collinear cracks in an infinite plate and of center cracks in a finite plate. the approximate and simple expression is able to be determined based on only one reference stress intensity factor and some criterions around the crack tip. the crack face a j. fan et alii, frattura ed integrità strutturale, 33 (2015) 463-470; doi: 10.3221/igf-esis.33.51 470 displacement and its partial derivative, respectively, computed by the present expression and the exact solution are confirmed to be in good agreement if the values of a/b≤0.8. the calculation of the weight function for center cracks in mode i loading conditions is reduced to the simple quadrature of the correction function and of the partial derivative of the crack face displacement. it is concluded that the limiting value of the stress intensity factor in an infinite plate might introduce significant error into the weight function and stress intensity factor evaluation. figure 3: comparisons of collinear cracks and center crack (a) weight function variation; (b) sif variation. references [1] tada, h., paris, p., irwin, g., the analysis of cracks handbook, asme press, new york, (2000). [2] rice, j., some remarks on elastic crack-tip stress fields, int j solids struct., 8 (1972) 751-758. [3] wu, x., carlsson, j., the generalised weight function method for crack problems with mixed boundary conditions, j mech physics solids., 31(1983) 485-497. [4] shen, g., glinka, g., determination of weight functions from reference stress intensity factors, theo appl fract mech. 15(1991) 237-245. [5] he, z., kotousov, a., branco, r., a simplified method for the evaluation of fatigue crack front shape under mode i loading, int j fract., 188 (2014) 203-211. microsoft word numero_37_art_15 les p. pook et alii, frattura ed integrità strutturale, 37 (2016) 108-113; doi: 10.3221/igf-esis.37.15 108 focussed on multiaxial fatigue and fracture coupled fracture modes under anti-plane loading les p. pook 21 woodside road, sevenoaks tn13 3hf (uk) les.pook@tesco.net f. berto department of management and engineering, university of padova, stradella s. nicola 3, 36100, vicenza (italy) berto@gest.unipd.it a. campagnolo department of industrial engineering, university of padova, via venezia 1, 35131, padova (italy) alberto.campagnolo@unipd.it abstract. the linear elastic analysis of homogeneous, isotropic cracked bodies is a twentieth century development. it was recognised that the crack tip stress field is a singularity, but it was not until the introduction of the essentially two dimensional stress intensity factor concept in 1957 that widespread application to practical engineering problems became possible. the existence of three dimensional corner point effects in the vicinity of a corner point where a crack front intersects a free surface was investigated in the late 1970s: it was found that modes ii and iii cannot exist in isolation. the existence of one of these modes always induces the other. an approximate solution for corner point singularities by bažant and estenssoro explained some features of corner point effects but there were various paradoxes and inconsistencies. in an attempt to explain these a study was carried out on the coupled in-plane fracture mode induced by a nominal anti-plane (mode iii) loading applied to plates and discs weakened by a straight crack. the results derived from a large bulk of finite element models showed clearly that bažant and estenssoro’s analysis is incomplete. some of the results of the study are summarised, together with some recent results for a disc under in-plane shear loading. on the basis of these results, and a mathematical argument, the results suggest that the stress field in the vicinity of a corner point is the sum of two singularities: one due to stress intensity factors and the other due to an as yet undetermined corner point singularity. keywords. finite elements; mixed modes; coupled modes; stress intensity factors; corner point singularities. introduction he linear elastic analysis of homogeneous, isotropic cracked bodies is a twentieth century development [1, 2], with the first papers appearing in 1907, but it was not until the introduction of the stress intensity factor concept in 1957 [3] that widespread application of linear elastic fracture mechanics (lefm) to practical engineering t les p. pook et alii, frattura ed integrità strutturale, 37 (2016) 108-113; doi: 10.3221/igf-esis.37.15 109 problems became possible. a stress intensity factor is the leading term of a series expansion of a crack tip stress field. the first application of finite elements to the calculation of stress intensity factors for two dimensional cases was in 1969 [4]. finite element analysis had a significant influence on the development of lefm. corner point singularities were investigated in the late 1970s [5]. it was soon found that the existence of corner point effects made interpretation of calculated stress intensity factors calculated using finite element analysis difficult, and their validity questionable. one of the main interests dealing with fracture mechanics is to quantify the crack tip surface displacement [6]. by superimposing the displacements due to the three modes of loading (mode i, mode ii, mode iii), shown in fig. 1, it is possible to fully describe the crack tip surface displacements. if a crack surface is considered as consisting of points then the three modes of crack surface displacement provide an adequate description of the movements of crack surfaces when a load is applied. assuming a poisson’s ratio, v, greater than zero, and also assuming that the crack front is perpendicular to a surface of a body, as is done in this paper, then it is possible to prove that modes ii and iii at the crack tip cannot exist in isolation [7, 8]. mode ii causes mode iiic and mode iii generates mode iic. these induced modes are properly named coupled modes. the superscript c is usually employed for their representation. there are no coupled modes when v is zero, and the magnitude of coupled modes increases with v [9]. it is not clear what happens when v is less than zero. figure 1: notation for modes of crack tip surface displacement. figure 2: notation for crack tip stress field. a series expansion is able to represent the stress field in the neighbourhood of the crack tip [3, 10]. the leading order term of this series is the stress intensity factor, k. subscripts i, ii, ii are used to denote mode. in agreement with the well known fracture mechanics framework, the stress components are proportional to kr where r is the distance from the σ z τ rz τ θz τ θr σ θ r θ x crack tip y z 2α = 0 les p. pook et alii, frattura ed integrità strutturale, 37 (2016) 108-113; doi: 10.3221/igf-esis.37.15 110 crack tip (fig. 2). displacements are instead proportional to kr. the leading order term tied to the stress intensity factor provides an accurate description of the stress field in a k–dominated region characterized by a radius r  a/10 where a is crack length, [6]. the concept of a corner point singularity was introduced by bažant and estenssoro first and later by pook [5, 11]. some pioneering results were given also by benthem [21]. an approximate solution showed that the of intensity of the stress field near the point of corner singularity can be done by defining a stress intensity measure called k. however, explicit expressions for k, and the stress and displacement fields associated to it are not available. the only statement based on the initial assumption used is that stresses are proportional to k/r and displacements to kr1 – . the distance r is in this particular case the distance of a generic point from the corner point and  is a function of poisson’s ratio. application of bažant and estenssoro’s analysis was successful in explaining some aspects of behaviour in the vicinity of a corner point, but various paradoxes and inconsistencies appeared [1]. in an attempt to resolve these an extensive finite element research programme has been carried out [13-15]. the purpose of the present paper is to present some of the results obtained, and also to present a possible approach to resolution of paradoxes and inconsistencies. the research programme wo models were considered. firstly, discs of finite thickness under anti-plane (remote nominal mode iii) loading [13]. the radius of the disc, r, is equal to 50 mm. a through the thickness crack with its tip at the centre of the disc has been considered, with a length, a, equal to 50 mm. different ratios have been considered between the disc thickness t and the crack length a. in particular the following ratios have been modelled: t/a = 0.25, 0.5, 0.75, 1, 1.25, 1.5, 1.75, 2, 2.25, 2.5, 2.75 and 3. finite element models have been analysed by means of ansys 11. stress intensity factors were evaluated from the stress components in the neighbourhood of the crack tip using standard equations [6,10]. the material has been considered linear elastic and the poisson’s ratio has been set equal to 0.3 while the young’s modulus, e, has been set equal to 200 gpa. the load has been applied in terms of displacement on the nodes corresponding to the cylindrical surfaces. the applied displacements correspond to a nominal mode iii stress intensity factor kiii = 1 mpam0.5 (31.62 n·mm0.5). recently, results have been obtained for in-plane shear loading of a disc, t/a = 1. in plane displacements were applied on the cylindrical surface, corresponding to a nominal mode ii stress intensity factor kii = 1 mpam0.5 (31.62 n·mm0.5). figure 3: stresses τyz and τxy on crack surface at s = 0 mm from disc and plate surfaces, t/a =1. t les p. pook et alii, frattura ed integrità strutturale, 37 (2016) 108-113; doi: 10.3221/igf-esis.37.15 111 secondly, plates of finite thickness under anti-plane (remote nominal mode iii) [14]. a square plate with a constant width equal of 100 mm has been considered. the thickness of the plate t has been varied in the models keeping constant the crack length (a = 50mm). the following ratios between t and a have been considered: 0.25, 0.5, 0.75, 1, 1.25, 1.5, 1.75, 2, 2.25, 2.5, 2.75 and 3. as for the case of the discs the material has been considered obeying a linear elastic law with v = 0.3 and e = 200 gpa. in this case the load has been applied by means of a constant displacement equal to 10-3 mm applied on the external edge of the plate. displacements uz were applied to the side containing the crack mouth. t/a s = 0 mm s = 0.25 mm s = 1 mm disc plate disc plate disc plate 0.25 0.505 0.538 0.497 0.498 0.497 (0.508) 0.497 (0.507) 0.50 0.520 0.527 0.497 0.498 0.497 (0.506) 0.497 (0.506) 0.75 0.530 0.523 0.497 0.498 0.497 (0.507) 0.497 (0.506) 1.00 0.538 0.520 0.497 0.498 0.497 (0.507) 0.497 (0.506) 1.25 0.544 0.517 0.497 0.498 0.497 (0.506) 0.497 (0.506) 1.50 0.549 0.515 0.497 0.498 0.497 (0.506) 0.497 (0.506) 1.75 0.553 0.513 0.497 0.498 0.497 (0.506) 0.497 (0.506) 2.00 0.556 0.512 0.497 0.498 0.497 (0.506) 0.497 (0.506) 2.25 0.559 0.510 0.497 0.498 0.497 (0.507) 0.497 (0.506) 2.50 0.542 0.510 0.497 0.498 0.497 (0.506) 0.497 (0.505) 2.75 0.545 0.509 0.497 0.498 0.497 (0.506) 0.497 (0.506) 3.00 0.547 0.508 0.497 0.498 0.497 (0.507) 0.497 (0.506) table 1: values of λ for τxy, s is the distance from the surface in the z direction. values in brackets are for τyz. stress components , τyz and τxy were obtained from finite element models at different distances, s, from the free surfaces of the plate or disc. in particular, distances of 0 mm, 0.25 mm, 1 mm and 2 mm have been considered. typical results are shown fig. 3, plotted on logarithmic scales. results from discs and plates are very similar. values of λ obtained are listed in tab. 1 comparing the results from discs and plates. for s = 0 and 0.25 mm τyz does not behave as a straight line. for values of s ranging between 0.25 to 2 mm the slope characterizing τxy is constant and almost equal to the theoretical value of 0.5. hence, mode ii stress intensity factor kii can be correctly defined and calculated for these values of s. dealing with cracked plates at s = 0 the slope λ reaches its maximum at t/a = 0.25 remaining in all the cases considered significantly lower than the value of 0.598 usually assumed for the case of a corner point singularity. these latest results are different from those obtained in the case of discs where the slope λ increases for increasing values of t/a. both for plates and discs the mode iii stress intensity factor kiii can be well defined at s = 1 mm and 2 mm because the slope is close to that theoretically expected (0.5). for in plane shear loading stresses τyz and τxy on the crack surface at s = 0 mm are similar to the stress distributions for nominal mode iii loading. the value of λ, calculated from τxy, is 0.541, is virtually the same as for nominal mode iii loading. the finite element results obtained at the coordinate s = 0 (fig. 4) show that the stress component τyz is very far from the linear theoretical trend corresponding to a straight line on log log coordinates. this is true both for discs and plates, and the corresponding stress intensity factors are shown in fig. 12: the apparent value of the mode iii stress intensity factor kiii is strongly dependent on the coordinate x. for s=0 realistic values of kiii cannot be calculated. values of λ, calculated from τxy and τyz, are 0.499 and 0.506, in excellent agreement with the nominal mode iii results. similarly, stresses τyz and τxy on the crack surface at s = 2 mm from the disc are similar to the stress distributions for nominal mode iii loading. values of λ are in excellent agreement. distributions of kii and kiii at s = 0 mm from the disc surface are similar to those for nominal mode iii loading, shown in fig. 4. however, through the thickness distribution of kii and kiii, differ from those for nominal mode iii loading. this difference is because the use of nominal mode ii loading has eliminated disc les p. pook et alii, frattura ed integrità strutturale, 37 (2016) 108-113; doi: 10.3221/igf-esis.37.15 112 bending. the results show that the change of loading mode from nominal mode iii to nominal mode ii has had no effect on the distributions of τyz and τxy on and near the crack surface, but has significantly changed the through thickness distributions of kii, kiii. discussion and conclusions s previously pointed out [13-15] the results in tab. 1 show that bažant and estenssoro’s solution is incomplete. there is no clear pattern to values of λ shown in the table, and attempts to find a three dimensional stress function for the stresses in the vicinity of a corner point have so far been unsuccessful. figure 4: kii and kiii at s = 0 mm from disc and plate surfaces, t/a =1. a corner point stress function could be expected to reduce to a westergaard stress function as a special case, but the following argument suggests that this is impossible. the westergaard method of stress analysis [10] makes use of complex variables in which it is assumed that i2 = -1. complex numbers can be represented by a point on a plane. a three dimension equivalent to a westergaard stress function would have to be based on a hypercomplex number system. hamilton’s quaternions are a hypercomplex number system [16] that is sometimes used in elasticity [17]. in a quaternion it is assumed that i2 = j2 = k2 = -1. a quaternion can be represented by a point in 4 dimensional space. quaternions can be represented as pairs of complex numbers, but do not include complex numbers as a special case. a three dimensional equivalent of the westergaard method would have to be based on quaternions. this suggests that a corner point stress function could not include westergaard stress function as a special case. this implies that stresses in the vicinity of a corner point are sums of stresses due to two different singularities of different orders: stress intensity factors and corner point singularities. the latter being asymptotic to zero as distance from the corner point increases. in other words bažant and estenssoro’s analysis is incomplete. it is therefore not surprising that values of λ derived from finite element analysis are inconsistent. to make progress the next step is to use the finite element results to separate the two singularities numerically and see whether this gives clues to the form of corner point singularities. a les p. pook et alii, frattura ed integrità strutturale, 37 (2016) 108-113; doi: 10.3221/igf-esis.37.15 113 references [1] pook, l.p., a 50-year retrospective review of three-dimensional effects at cracks and sharp notches. fatigue fract. engng. mater. struct., 36 (2013) 699-723. [2] pook, l.p., the linear elastic analysis of cracked bodies and crack paths. theoretical and applied fracture mechanics, 79 (2015) 34-50. [3] williams, m.l., on the stress distribution at the base of a stationary crack. j. appl. mech.., 24 (1957) 109-114. [4] dixon, j.r., pook, l.p., stress intensity factors calculated generally by the finite element technique. nature, 224 (1969). 166-167. [5] bažant, z.p., estenssoro, l.f., surface singularity and crack propagation. int. j. solids struct., 15 (1979) 405-426. [6] pook, l.p., linear elastic fracture mechanics for engineers. theory and applications. wit press, southampton (2000) [7] kotousov, a., lazzarin, p., berto, f., pook, l.p. three-dimensional stress states at crack tip induced by shear and anti-plane loading. eng. fract. mech., 108 (2013) 65-74. [8] lazzarin, p, zappalorto, m., a three‐dimensional stress field solution for pointed and sharply radiused v‐notches in plates of finite thickness. fatigue fract. eng. mater. struct., 35 (2012) 1105–1119. [9] kotousov, a., berto, f., lazzarin, p., pegorin, f., three dimensional finite element mixed fracture mode under antiplane loading of a crack. theoretical appl. fract. mech., 62 (2012) 26-33. [10] paris, p.c., sih, g.c., stress analysis of cracks. in fracture toughness testing and its applications. astm stp 381. american society for testing and materials, philadelphia, (1965) 30-81. [11] pook, l.p., some implications of corner point singularities. eng. fract. mech., 48 (1994) 367-378. [12] benthem, j.p., the quarter-infinite crack in a half-space; alternative and additional solutions. int. j. solids struct., 16 (1980) 119-130. [13] pook, l.p., berto, f., campagnolo, a., lazzarin, p., coupled fracture mode of a cracked disc under anti-plane loading. eng. fract. mech., 128 (2014) 22-36. [14] pook, l.p., campagnolo, a., berto, f., lazzarin, p., coupled fracture mode of a cracked plate under anti-plane loading. eng. fract. mech., 134 (2015) 391-403. [15] pook, l.p., campagnolo, a., berto, f., coupled fracture modes of discs and plates under anti‐plane loading and a disc under in‐plane shear loading. fatigue fract. eng. mater. struct., (2016) doi: 10.1111/ffe.12389 [16] pulver, s., quaternions: the hypercomplex number system. mathematical gazette, 92 (2008) 431-436. [17] weisz-patrault, d., bock, s., gülebeck, k., three-dimensional elasticity based on quaternion-valued potentials. int. j. solids struct., 51 (2014) 3422-3430. << /ascii85encodepages false /allowtransparency false /autopositionepsfiles true /autorotatepages /none /binding /left /calgrayprofile (dot gain 20%) /calrgbprofile (srgb iec61966-2.1) /calcmykprofile (u.s. web coated \050swop\051 v2) /srgbprofile (srgb iec61966-2.1) /cannotembedfontpolicy /error /compatibilitylevel 1.4 /compressobjects /tags /compresspages true /convertimagestoindexed true /passthroughjpegimages true /createjobticket false /defaultrenderingintent /default /detectblends true /detectcurves 0.0000 /colorconversionstrategy /cmyk /dothumbnails false /embedallfonts true /embedopentype false /parseiccprofilesincomments true /embedjoboptions true /dscreportinglevel 0 /emitdscwarnings false /endpage -1 /imagememory 1048576 /lockdistillerparams false /maxsubsetpct 100 /optimize true /opm 1 /parsedsccomments true 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can be opened with acrobat and adobe reader 5.0 and later.) >> /namespace [ (adobe) (common) (1.0) ] /othernamespaces [ << /asreaderspreads false /cropimagestoframes true /errorcontrol /warnandcontinue /flattenerignorespreadoverrides false /includeguidesgrids false /includenonprinting false /includeslug false /namespace [ (adobe) (indesign) (4.0) ] /omitplacedbitmaps false /omitplacedeps false /omitplacedpdf false /simulateoverprint /legacy >> << /addbleedmarks false /addcolorbars false /addcropmarks false /addpageinfo false /addregmarks false /convertcolors /converttocmyk /destinationprofilename () /destinationprofileselector /documentcmyk /downsample16bitimages true /flattenerpreset << /presetselector /mediumresolution >> /formelements false /generatestructure false /includebookmarks false /includehyperlinks false /includeinteractive false /includelayers false /includeprofiles false /multimediahandling /useobjectsettings /namespace [ (adobe) (creativesuite) (2.0) ] /pdfxoutputintentprofileselector /documentcmyk /preserveediting true /untaggedcmykhandling /leaveuntagged /untaggedrgbhandling /usedocumentprofile /usedocumentbleed false >> ] >> setdistillerparams << /hwresolution [2400 2400] /pagesize [612.000 792.000] >> setpagedevice microsoft word numero_30_art_63 l. bing et alii, frattura ed integrità strutturale, 30 (2014) 526-536; doi: 10.3221/igf-esis.30.63 526 time-history simulation of civil architecture earthquake disaster reliefbased on the three-dimensional dynamic finite element method liu bing college of mechanical and electronic engineering, china university of petroleum, qingdao 266580, china college of mechanical and electronic engineering, shandong university of science and technology, qingdao 266510, china. liubing5195@163.com qi yaoguang, du jiyun college of mechanical and electronic engineering, china university of petroleum, qingdao 266580, china abstract. earthquake action is the main external factor which influences long-term safe operation of civil construction, especially of the high-rise building. applying time-history method to simulate earthquake response process of civil construction foundation surrounding rock is an effective method for the anti-knock study of civil buildings. therefore, this paper develops a civil building earthquake disaster three-dimensional dynamic finite element numerical simulation system. the system adopts the explicit central difference method. strengthening characteristics of materials under high strain rate and damage characteristics of surrounding rock under the action of cyclic loading are considered. then, dynamic constitutive model of rock mass suitable for civil building aseismic analysis is put forward. at the same time, through the earthquake disaster of time-history simulation of shenzhen children’s palace, reliability and practicability of system program is verified in the analysis of practical engineering problems. keywords. earthquake disaster; three-dimensional dynamic finite element method (fem); civil architecture; time-history analysis method. introduction nderground structure seismic research involves many subjects such as seismology, dynamics, rock mechanics, the theory of spray anchor bracmg and so on and it has always been a hot research topic at home and abroad. this paper from the viewpoint of engineering application, focuses on civil building earthquake disaster dynamic process simulation and system application development, carried on the comprehensive study of the civil construction dynamic time-history seismic analysis method and developed the three-dimensional dynamic finite element numerical simulation system of civil building earthquake disaster process. the explicit central difference method is adopted to realize the incremental solution to basic differential equation of kinematics. strengthening characteristics of materials under high strain rate and damage characteristics of surrounding rock under the action of cyclic loading are considered and dynamic constitutive model of rock mass suitable for civil building aseismic analysis is put forward. finally, a three-dimensional dynamic simulation of the earthquake disaster process was carried out of shenzhen children’s palace. the results show that calculation speed can satisfy the requirement of engineering analysis program. the law is correct and calculation result is reasonable. therefore, it can be applied to earthquake disaster process simulation in actual underground engineering. u l. bing et alii, frattura ed integrità strutturale, 30 (2014) 526-536; doi: 10.3221/igf-esis.30.63 527 the explicit finite element solution of the seismic wave field henzhen children’s palace, which is under design is located at the foot of lotus hill. its seismic response is mainly affected by the seismic wave propagation, which is a question of near field wave. solution of seismic wave field in the area of engineering is the key to the earthquake disaster process simulation of the children’s palace. for threedimensional simulation for complex engineering, finite element method is generally used to realize the integral solution of wave equation. the solution ways of finite elements can be divided into two kinds of implicit and explicit. the explicit central difference method based on system kinematics basic theorem, wave equation can be expressed as differential equation of motion of incremental lagrange format [11] as follows:   int ext dampma f f f (1) in the equation, a is the acceleration of mesh nodes; int , extf f are internal forces and external forces of mesh nodes respectively; dampf is the damping force; m is the mass matrix. the lumped mass matrix form is adopted in the program and is defined as follows:       t m ρ dv (2) in the equation,   is the matrix ofi , i selects 1 within the area of i and 0 outside the area. in the program, for hexahedral 8 node unit, the volume of node region of i is 1 8 of its neighboring units. for ease of matrix inversion, local damping force is adopted, defined dampf as follows:   int damp extf α f f signa (3) in the equation, signa is sign of grid node's speed and direction.  is the local damping coefficient,   d . d is the critical damping ratio. for geotechnical materials, the scope of d is generally 2%~5%. for the explicit solution of eq. (1) there are many methods. and central difference method with second order accuracy is adopted in this paper, as shown in fig. 1: 0t 1nt 2/1nt nt nt 2/1nt 1nt 2/1 nt2/1 nt figure 1: timeline of central difference method assume that displacement, velocity and acceleration of 1 20,  nt , t , ,t are known, then, displacement, velocity and acceleration of 1nt can be calculated by central difference approximation, as follows: s l. bing et alii, frattura ed integrità strutturale, 30 (2014) 526-536; doi: 10.3221/igf-esis.30.63 528     1 1 intn ext dampa m f f f (4)   1 2 1 2  n / n/ na a δta (5)     1 2 1 21 n nn na a δt a (6)           1 2 1 2 1 2 12n / n/ n / n nt t t / , t t t (7) in the equation, 1n na , a are respectively displacement of 1n nt ,t ;  1 2 1  n n / na , a , a are respectively velocity of  1 2 1n n / nt ,t ,t ; na , 1na is respectively accelerated speed of 1n nt , t . the explicit central difference method calculation process can be described as follows: (1) according to the initial condition 0a , 0a , we can calculate that    0 1 0 1 2 0,  damp n/a m f f a a . (2) for each time step: 1 2n /a is calculated by eq. (5); displacement 1na of 1nt is calculated by eq. (6); accelerated speed 1na is calculated by eq. (4). finite element explicit calculation is a conditional stability algorithm which is often constrained by the solution stability and calculation time consuming. this is because to ensure the stability of calculation, we generally need to select the smaller calculation time step t to increase system cycle count and extend the calculation time. therefore, on the premise of ensuring stability calculation, we need to choose the larger t . considering the physical meaning of the wave finite element, t can be regarded as the minimum duration in a computational time step, that wave propagation distance is not more than any one unit size. it can be calculated as follows:     min 0 80 0 98e e e l t α . α . c (8) in the equation, ec is the unit wave velocity; el is the ratio of the largest area between element volume and unit 6 surface. the system time step of eq. (8) only considers the seismic wave transmission stability in calculation model rather than artificial boundary conditions and computational stability requirements of supporting measures such as anchor bars to the system time step. therefore, in the practical engineering calculation, according to different situations, we need to make adjustments of t . node internal force solution in the explicit solution of type (1), the key is the solution to node internal force fint. in incremental variational type calculation, we first calculate unit stress increment and update the unit stress. then the updated nodes stress is integral to the unit nodes to obtain internal forces. deformation description in the delta lagrange explicit calculation, deformation is described by strain rate ije :                       1 1 2 2 i i j i j ij ij ij j j i i i v v v v v e ω d x x x x x (9) in the equation, ijω is the spin rate tensor; ijd is the deformation rate tensor; iv is the velocity component; jx is the weight coordinates, ,i j =1, 2, 3. l. bing et alii, frattura ed integrità strutturale, 30 (2014) 526-536; doi: 10.3221/igf-esis.30.63 529 stress update the numerical algorithm of integral rate constitutive equation is called as stress update algorithm. stress  ijσ t dt of t dt can be obtained by ij as follows:        ij ij ijσ t dt σ t dt (10a) the cauchy stress rate can be expressed as:  ij      ij ik jk jk ikω ω (10b) in the equation,  ij is the jaumann rate,  ij  ijkl klc d , ijklc is the elastic constitutive tensor. stress integral  ijσ t dt obtained through eq. (10a) is performed to the unit nodes, and then node’s internal force vector intf is obtained. the dynamic elastoplastic damage constitutive of the surrounding rock the dynamic elastoplastic damage constitutive model of civil construction foundation surrounding rock he dynamic elastoplastic damage constitutive model of civil construction foundation surrounding rock is the basis of simulation of the children’s palace earthquake disaster process. on the basis of theoretical study, we need to combine with a large number of indoor and outdoor tests, and establish a scientific and practical dynamic damage constitutive model of rock. civil construction foundation surrounding rock shows the dynamic strengthening characteristics and fatigue damage properties of the surrounding rock. the research results [5] showed that: under dynamic loading, the surrounding rock strain rate increases. and elastic modulus of surrounding rock materials and damage resistance are improved. while under cyclic loading conditions, there appears fatigue damage of surrounding rock and elastic modulus of surrounding rock materials and destruction resistant properties are reduced. the two factors are in opposition to each other and coexist at the same time. it should be considered in the constitutive model as follows: (1) the study on rock dynamic strengthening characteristics is mainly divided into high strain rate    2 110 s and middle strain rate      4 1 1 110 10s s study. among which, high strain rate is mainly to solve the problem of shock blasting. because the loading ways are simple, there are relatively more tests. while children’s palace earthquake effect strain rate is generally at the range of     6 1 1 110 10s s , belonging to medium strain rate and there are less tests. from the existing research results [5, 14 ~ 17] we can get the following conclusions:  rock dynamic strength and modulus of elasticity increase with the increase of strain rate.  rock dynamic strength increases with strain rate. this is because that cohesion increases with strain rate while internal friction angle is not affected by strain rate.  the dynamic characteristics of medium strain rate of the rock are affected by the way of loading, loading rate, rock type and test equipment. all kinds of test results are with large discreteness, so consistent rules are difficult to conclude based on experiments. (2) there are many rock damage constitutive researches. damage description is usually with tensor description form of first, second and fourth order. in view of the aeoplotropism of seismic wave propagation, this paper adopts second order damage tensor to describe the damage of surrounding rock in the earthquake. considering the above two kinds of characteristics of surrounding rock in the earthquake, the dynamic elastic modulus of surrounding rock of dynamic constitutive model can by expressed as:  0 e p e (11) in the equation, e is the static elastic modulus of surrounding rock; t l. bing et alii, frattura ed integrità strutturale, 30 (2014) 526-536; doi: 10.3221/igf-esis.30.63 530  p is the strain rate function greater than 1. the mohr-coulomb yield criterion is adopted and assumes that the compressive stress is negative and tensile stress is positive. line ab is the shear yield criterion  0sf , line bc is the tensile yield criterion  0tf , that is:               * * 1 3 * 3 2 ( )s t t f n tq c n f (12a) among which, n       1 sin 1 sin (12b) in the equation, ,c are respectively cohesion and internal friction angle; * 1 σ , * 3 σ are respectively first and third effective principal stress;  t is ultimate tensile strength,  max / tan t c ; t is the damage effect coefficient. under the second order tensor form,    2 2 21 2 31t d d d , 1 2 3, ,d d d are damage coefficient of principal stress direction, solved by the damage evolution equation. within every calculation step,  , t q is constant. according to the non-correlation of surrounding rock, corresponding potential function to yield criterion is as follows:       * $ 1 3 * 3 s ψ t g σ σ n g σ (13a) among which,       1 sin 1 sin n (13b) in the equation,  is the surrounding rock dilatancy angle. in the calculation, element stress applies the effective force form considering damage:                   1 1 2 2 3 3 1 0 0 0 1 0 0 0 1 * σ d h σ σ d h σ d h (14) under the tension cases, assume  1.0h ; in press conditions,  0.2h . the damage process of surrounding rock is along with the micro fissure development and micro porosity increase and decrease of strength of materials. in the larger sense, damage of surrounding rock is caused by tension. according to some practical observation results, most of the surrounding rock tensile damage is caused by the actual strain exceeding the limit tensile strain of surrounding rock. for the three-dimensional situation, it can be considered that element stress enters plasticity and first principal tensile strain exceeds ultimate tensile strain. then damage will occur, that is:                     1 1 0 0 0 s s ij or f d h and f (15) in the equation,   ijh is the three-dimensional damage evolution equation, l. bing et alii, frattura ed integrità strutturale, 30 (2014) 526-536; doi: 10.3221/igf-esis.30.63 531 1 is the first principal tensile strain of the surrounding rock,   is the ultimate tensile strain of the surrounding rock. for the situation of the ultimate tensile strain of untested surrounding rock in practical engineering, we adopt specific value of rock tensile strength sr and elasticity modulus e , that is:      sr ke (16) in the equation, k is the safety coefficient. in the damaged area, surrounding rock stress and physical parameters decrease with the increase of slant plastic strain. the greater the cumulative plastic deformation is, the higher the damage degree of surrounding rock will be. in the adjacent area in front of the ultimate strength of surrounding rock material, micro crack damage increase is very rapid. this kind of change rate of damage can usually be described by exponential function. therefore, three-dimensional damage evolution equation can be expressed as follows:        1 exp 1, 2, 3p pi i id r i (17) in the equation,  pi is the slant plastic strain in the principal strain direction, r is damage constant of the material. for the purposes of showing the state of surrounding rock damage in the post-processing, second order damage tensor is converted to a first-order damage scalar when output the results file, expressed as   2 2 21 2 3d d d d . stress correction and damage calculation unit stress calculation is the core of the explicit finite element method. in the elastic and plastic damage calculation of the tn+1 moment, the gauss point elastic stress is calculated using unit material initial parameters and whether unit is in a state of damage is judged (when    0d tn , unit damage coefficient of the moment is calculated). if the unit is in a state of damage, each gaussian point stress is revised as the effective stress. on this basis, considering damage effect on yield surface and carry out yield judgment. in case of yield, plastic stress correction is required. also, we need to judge whether principal tensile strain exceeds the ultimate tensile strain. if there is exceeding, it's considered unit damage and damage coefficient is calculated. this stress correction method is applicable to the situation that yield function  nf is the linear function. based on the principle that plastic stress should flow on the yield surface, it is required that plastic stress of tn + 1 moment as follows:     0n nf σ σ (18) for the linear function, eq. (18) can be converted to:       0n n*f σ f σ (19a)          0n*f f f (19b) in the equation, * (·)f is calculated by yield function minuses to the constant term  0nf . based on this transformation, linear yield function plastic stress correction formula was deduced by service manual [20] as follows:             n i i i i n g s (20) in the equation,  is the plastic flow factor; is is the elastic constitutive; l. bing et alii, frattura ed integrità strutturale, 30 (2014) 526-536; doi: 10.3221/igf-esis.30.63 532  ii ,  n i are respectively elastic assumed stress and the revised plastic stress. within each computing time step t, in the constitutive model,  q is the constant and yield function is the linear function. eq. (20) can be applied to carry out plastic correction of unit effective stress considering the damage. for the plastic shear failure, there is:                     * 1 1 1 2 * 2 2 * 3 3 2 1 2 1 n i n i n i s ψ s ψ s ψ σ σ λ α α n σ σ λ α n σ σ λ α n α (21a)                * * 1 3 1 2 1 2 ,s i i s ψ f σ σ λ n n n (21b) among which,     1 2 4 2 , 3 3 k g k g (21c) in the equation, k , g are respectively bulk modulus and shear modulus;  *in is the equivalent elastic assumed stress after damage correction. for the ultimate tensile damage, there is:                  * * 1 1 3 * * 2 2 3 3 2 1 2 1 nt i i nt i i nt t t t α σ σ σ σ α α σ σ σ σ α σ σ (22) in the damage calculation, damage coefficient id should be calculated according to the damage evolution equation. computation formula is as follows:                      ( 1) ( ) * 2 ( 1) ( 1) 01 exp ( ) p p s i tn i tn i i p p i tn i tn f d r (23) among which,          0 1 ( 1) 2( 1) 3( 1) 3p p p ptn tn tn (24) engineering projects establishment of the model he children’s palace subject has a maximum altitude of 37.25 m and a maximum span of 24 m. its foundation is in the dolomite limestone of lower cambrian system. the rock is of hard property and fissure is of medium development. there are mainly iii category and partial iv category of surrounding rock. physical and mechanical parameters are shown in tab. 1. this example temporarily is regardless of the anchor rod, anchor rope, lining and other supporting measures. since this project did not carry out live stress test, initial geostatic stress field calculation in this paper considers self-weight stress field affected by river valley and excavation slope. and local damping is adopted and set as 0.157 1. this project did not carry out the test of rock mass deformation modulus and cohesion-strain rate test. considering engineering safety, the p, q value is set as 1. t l. bing et alii, frattura ed integrità strutturale, 30 (2014) 526-536; doi: 10.3221/igf-esis.30.63 533    3/ g cm e gpa  c mpa         t mpa 2.7 4.0 0.3 0.8 45 43 0.3 table 1: the children's palace foundation rock physics parameters considering that the children’s palace is close to the earth surface, seismic wave field inversion model in the engineering area and the children’s palace cavity analysis model can use the same model. finite element model is established including administrative building, draft tube gate chamber, the tailrace tunnel, bus tunnel and diversion tunnel. and it is a total of 272 304 hexahedron eight nodes unit containing 301112 nodes. the axis of the main building is the y direction x axis and y axis are perpendicular to the downstream, z-axis coincides with geodetic coordinates. the calculation scope along three direction x, y, z axis are respectively 176.0, 108.0, 141.0 m. the children’s palace finite element calculation model is shown in fig. 2. to reflect the three dimensional input features, seismic wave in this paper applied three-dimensional earthquake acceleration time history recorded by wolong tv station in wenchuan earthquake and make an interception of 20 s for calculation. this project filter frequency range is 0.1~10.0 hz. corresponding maximum grid feature sizes is not greater than 7.0 m. after filtering, baseline correction were carried out on original recorded seismic waves, measured acceleration time history curve is as shown in fig. 2. seismic wave incident reference point is the origin of coordinates, as shown in fig. 2 (a), incident direction vector is (1, -1, 1). note: look for a new perspective of (a) and change (b) into an architectural renderings of the children’s palace (shown in fig. 3), keeping the draft tube gate chamber, bus tunnel, diversion tunnel, tailrace tunnel. and make administration main workshop into the hall. (a) (b) figure 2: the finite element calculating model for the children's palace: (a) fem model; (b) excavation model cavity earthquake disaster simulation on the basis of rock damage and stress disturbance around children’s palace foundation, datum plane wave and power attenuation coefficient β would be of inversion. the process of earthquake disaster in children's palace group will be calculated and simulated. there are about 27 myriad of hexahedral eight nodes units in this model�dynamic calculation lasts about 25 s (there is seismic wave input in former 20 s). flac3d general numerical analysis software is adopted about 10.8h, then fig. 4 is obtained. the analysis of calculation results is as following: 1) as can be seen from the fig. 4, the displacement time history law is basically in line with inversion input seismic waves. because of the airport surface effect, peak ground displacement of each monitoring point has experienced a sharp increase compared with input seismic waves. among which, the main building roof arch monitoring point a increased by 80%, l. bing et alii, frattura ed integrità strutturale, 30 (2014) 526-536; doi: 10.3221/igf-esis.30.63 534 upstream wall monitoring point b increased by 55%, downstream sidewall monitoring point d increased by 45%, slope monitoring point f increased by 58%. the amplification effect of free face is unfavorable for surface surrounding rock stability. when the 25s of calculation is finished, along with layman of seismic wave and damping dissipation, kinetic energy of the whole of model system is basically to 0 and reaches a steady state. figure 3: 3d model for the children's palace. 0.20 0.00 0.04 0.08 0.12 0.16 0 5 10 15 20 25 t/s crown of measuring point a upstream sidewall point b downstream sidewall point d the slope point f figure 4: displacement time history curve of dynamic calculation process monitoring. under the impact of wave time difference, space contour, plastic damage and damping dissipation, displacement time history curve of the monitoring point shows difference in quantity and there appears the relative motion. this is also an important reason for instability of the children's palace under the action of earthquake. from fig. 4, we can see that largest relative displacement between main workshop upstream sidewall and downstream sidewall is 6 cm; which is 50% of input waveform amplitude load value. considering install the backfill of concrete to the factory units can slow down the situation to a certain extent. 2) as can be seen from the fig. 5, under the action of seismic wave load, third principal stress of surrounding rock is in the cycle of severe shock. this kind of cyclic loading results in a sharp increase in damage of surrounding rock and can cause fatigue failure of surrounding rock. the three curves show that after the calculation unit stress state and the initial stress state are quite similar. it suggests that after the earthquake surrounding rock stress state did not produce large disturbance. due to unit stress state in the earthquake changing with time, stress state cannot reflect the stability of surrounding rock objectively. the author thinks that damage degree and stress state should be adopted together to describe degradation degree and the stability of surrounding rock in the earthquake. to sum up, in the earthquake disaster of shenzhen children’s palace, cave surrounding rock produced large absolute and relative displacement (upstream and downstream sidewall 6cm). in the process of seismic wave propagation, surrounding rock stress disturbance is strong. some areas were in the alternative changing of elastic and plastic stress state and caused fatigue damage of surrounding rock. with the development of time, cumulative plastic strain increases, which causes irreversible damage to the surrounding rock material and reduce of the bearing capacity of surrounding rock and surrounding rock stability is influenced. at the 13″ moment, part of rock whole interval was filled with plastic damage area. after the calculation of 25″ moment, cave surrounding rock plastic damage zone was widened and damage degree of surrounding rock was significantly improved. under earthquake loading effect, children’s palace foundation rock mass may lose stability in the earthquake. l. bing et alii, frattura ed integrità strutturale, 30 (2014) 526-536; doi: 10.3221/igf-esis.30.63 535 figure 5: time-history curves of 3rd principal stress at typical area of surrounding rock. figure 6: time-history curves of 3rd plastic damage elements of global model. we could see from fig. 6 that, with the spread of seismic wave, part of the surrounding rock has been in the alternate change state between elastic stress and plastic stress for a long time. at the moment of 13 s, the number of whole model’s plasticity damage has reached peak, there are 56 545 units as a whole. the biggest moment of plastic damage zone is consistent with seismic displacement peak time. at the time of 13 s, most of the sidewall rocks in children’s palace have entered the plastic damage area (see fig. 6). the depth of local cracking area is as high as 7m, plastic damage zone depth is as much as 20m, children’s palace has the possibility of instability. conclusion his paper is to expound the finite element simulation theory of earthquake disaster in children’s palace and develop three-dimensional dynamic finite element numerical simulation system in the earthquake disaster process of children’s palace through starting from engineering analysis. the dynamic constitutive model of rock mass adaptive to seismic analysis of children’s palace is put forward through adopting central difference method and considering the enhancement of material parameter, as well as fatigue damage of material under circulating load effect. the earthquake disaster simulation is performed on children’s palace in shenzhen through applying software. it has t l. bing et alii, frattura ed integrità strutturale, 30 (2014) 526-536; doi: 10.3221/igf-esis.30.63 536 indicated that computation speed of procedure in this paper could satisfy the requirement of engineering analysis, and this procedure has performed relatively real and reasonable simulation on earthquake disaster of children’s palace. due to that article’s length is limited, there inevitably exists vulnerable spot of initial defects and structure on other perspective. the architecture is regarded as continuum medium field through applying damage mechanics. the material containing various microfracture and microdefect is indistinctly deemed as continuous medium with damage field. the occurring and development of damage is considered as the evolution process of damage. the appropriate damage variable is introduced to describe physical and mechanical properties of this continuum. heterogeneity and mesoscopic structure characteristics are grasped. the corresponding numerical model and theoretical analysis is constructed at micro and macro level respectively. analysis about the initiation extension of building micro cracks, formation of macroscopic fracture, adhesive failure, damage fracture criterion as well as the influence of mesoscopic composition on macro elastic modulus and so on is performed. the failure mechanism of structure is further demonstrated, and it has certain promotive role in perfecting material and structural design. acknowledgements he issue of national sci-tech support plan -‘the application demonstration of industrializing oil equipment's research and development platform’, no (2012bah26f04). references [1] liu, j. b., du, y. x., wang, z. y., 3d viscous-spring artificial boundary in time domain, earthquake engineering and engineering vibration, 5(1) (2006) 93–102. [2] du, x. l., zhao, m., wang, j. t., artificial stress boundary condition of the near field wave simulation, acta mechanica sinica, 38(1) (2006) 49–56. [3] li, x. j, lu, t., explicit finite element analysis of earthquake response for underground caverns of hydropower stations, journal of hydroelectric engineering, 28(5) (2009) 41–46. [4] zhang, x. z., xie, l. l., problems in numerical solution of complex open system by using explicit finite element method, earthquake engineering and engineering vibration, 25(2) (2005) 10–15. [5] qian, q. h., qi, c. z., dynamic strength and dynamic fracture criteria of rock and rock mass, journal of tongji university (natural science), 36(12) (2008) 1599–1605. [6] qi, c. z., qian, q. h., physical mechanism of dependence of material strength on strain rate for rock-like material, chinese journal of rock mechanics and engineering, 22(2) (2003) 177–181. [7] zhao, j., li, h. b., estimating the dynamic strength of brittle rock using mohr-coulomb and hoek-brown criteria, journal of rock mechanics and engineering, 22(2) (2003) 171–176. [8] li, h. b., zhu, l., lu, t., dynamic response analysis of large underground excavations in jointed rock, chinese journal of rock mechanics and engineering, 27(9) (2008) 1757–1766. [9] chen, j. y., hu, z. q., lin, g., 3d seismic response study on large scale underground group caverns, chinese journal of geotechnical engineering, (2001). t microsoft word numero_35_art_43 š. major et alii, frattura ed integrità strutturale, 35 (2016) 379-388; doi: 10.3221/igf-esis.35.43 379 focussed on crack paths fatigue life prediction of pedicle screw for spinal surgery š. major the institute of theoretical and applied mechanics, academy of science, prosecká 809/76, 19000 praha 9, czech republic major@itam.cas.cz v. kocour the institute of theoretical and applied mechanics, academy of science, prosecká 809/76, 19000 praha 9, czech republic kocour@itam.cas.cz p.cyrus department of technical education, faculty of education, university hradec králové, rokitanského 62,500 03 hradec králové, czech republic cyrus@uhk.cz abstract. this paper is dedicated to fatigue estimation of implants for spinal surgery. this article deals especially with special case of hollow pedicle screw. implant systems utilizing specially designed spinal instrumentation are often used in these surgical procedures. the most common surgical procedure is spinal fusion, also known as spondylodesis, is a surgical technique used to join two or more vertebra. implants are subjected to many loading cycles during their life, especially in the case of other degenerative changes in the skeleton, there are often changes in loading conditions, which often cannot be accurately determined. these changes often lead to further bending load in the thread. hollow screws studied in this work show higher fatigue resistance than other types of implants. keywords. pedicle-screw; titan alloy; fatigue life; finite element analysis. introduction edicle screws are used for treating several types of spinal injuries. together with rods and plates, they are used to form intrapedicular fixation or transpedicle screw devices [1-4] for spinal fusion. fusing of the spine is used to eliminate the pain caused by abnormal motion of the vertebrae by immobilizing the faulty vertebrae or to treat most spinal deformities, such as scoliosis. basicaly, this method involves the insertion however, screw breakage and loosening have been reported, which may create post-surgery problems [2]. currently various types of pedicle screw are used: cylindrical and conical, hollow and solid. in this work are considered solid and hollow cylindrical screws. hollow screws are used for filling the wound with cement. since the bone during drilling fulfills blood and other impurities, which could be the cause internal inflammation. filling takes place through of a hollow screw. for filing are used various cements. in this work was used polymethyl methacrylate bone cement with multi-waled carbon nanotubes [5]. the prediction of fatigue failure is important forprevention of serious medical complications. for the fatigue life p š. major et alii, frattura ed integrità strutturale, 35 (2016) 379-388; doi: 10.3221/igf-esis.35.43 380 prediction of pedicle-screws was used the method proposed by navarro [6, 7, 8] and comparison with other methods used in multiaxial fatigue [9]. in the work, fatigue resistance of hollow pedicle-screw and solid pedicle-screws were compared. materials characterization crews used in this study were made of commercially titanium alloy 6al4v eli also known as grade 23. it is an α-β phase titanium alloy made of 6% al and 4% v in weight with a reduced content of interstitial elements such as oxygen and carbon (extra low intersticials) and also iron. chemical composition of material is shown in tab. 1. this table compared the maximum value of the chemical elements specified by the manufacturer and the values measured by x-ray spectrometers. c[%] n[%] o[%] h[%] v[%] al[%] fe[%] manufacturer 0.08 0.03 0.013 0.0125 3.5-4.5 5.5-6.5 0.25 measurement 0.073 0.025 0.012 0.0113 4.12 6.015 0.17 table 1: chemical composition of titanium alloy grade 23. in the first row are the maximal values of the elements specified by the manufacturer. in the second row line element values are obtained by measuring. figure 1: crack growth rate of grade 23 titanium alloy. the crack growth properties were measured on standard test method for measurement of fatigue crack growth rates introduced by astme 647. mechanical properties of material are: the young modulus of this material is e = 104.5 gpa. test were performed to determine the ultimate tensile strength, σu = 860 mpa and yield stress σy = 820 mpa. further mechanical properties are elongation at break a = 14%, reduction area si = 25% and vickers hardness 350 hv. the crack growth properties were measured on standard test method for measurement of fatigue crack growth rates introduced by astme 647 [9]. this test method covers the determination of fatigue crack growth rates from nearthreshold to kmax controlled instability. results are expressed in terms of the crack-tip stress-intensity factor range (δk), defined by the theory of linear elasticity. the experimental measurement was performed on specimen with diameter ds = 4 mm. the measured properties, obtained constants are c = 5.1 10-12 and n = 4.2 for the crack growth in m/cycle, stress intesity factor k in mpa.m0.5. the mechanical properties and biocompability of implant can be improved by surface s š. major et alii, frattura ed integrità strutturale, 35 (2016) 379-388; doi: 10.3221/igf-esis.35.43 381 treatment. in this work, specimens with two types of surface treatment and implants without surface treatment were used. the first surface treatment was based on deposition tio2. the second deposition was based on tin surface. the both screws with surface treatment have a higher surface roughness than a screw without surface treatment. roughness of a screw without treatment is ra = 0.1 μm while roughnesses of the nitrided and tio2 covered screws are ra = 2.7 μm and ra = 3.1 μm. the rougher surface improves the reception of the material by bones. fig. 1 show experimental determination of paris law for titanium alloy grade 23. paris law can be written for this material as: 12 4.25.1 10 da k dn   (1) also fatigue test were carried out, results of these experiments are shown in fig. 2. this figure shows fatigue curve (stress to number of cycle) σ-n. fatigue test were carried out by room temperature on cylindrical specimen with diameter 4 mm. loading frequency of fatigue experiment was 50 hz and the loading was full reserve r = −1. in fig. 2 is clearly visible reduction of fatigue limit for both types of surface treatments. figure 2: fatigue curves in grade 23 titanium alloy with surface layer tio2 and tin and without surface treatment. figure 3: specimen used in fatigue tests. š. major et alii, frattura ed integrità strutturale, 35 (2016) 379-388; doi: 10.3221/igf-esis.35.43 382 implant testing or experiments wee used two types of pedicle-screw, the solid cylindrical and hollow screw. both types have the same dimensions and geometry of thread. the implants were clamped in an artifical vertebra during test, so that the device simulates the bone-metal contact. the implants were subjected to bending loading. the pedicle-screw is loaded by a pair of forces perpendicular to the screw axis, the two forces are perpendicular to each other. both forces are offset from the axis so that also create torque. the second bending force reaches its maximum when the first force reaches its second maximum, i. e. the period of the second load is doubled, i. e. t2 = 2t1. the experiments were carried to the final rapture of specimen. final rapture is defiden as the complete fracture of the pedicle-screw. fracture appeared the point where the screw enters into the bone, i. e. at the point highest stresses. since the bone consists of two basic parts, it is necessary to construct an artificial pedicle so that this fact was simulated. surface of bone is composed from hard “compact bone” and cover layer of periosteum. the interior of the bone consists of a more flexible and softer tissue so-called “spongy bone”. artificial pedicle consists of two layers, a hard layer on the surface of 4 mm thick and the rest of the softer. the hollow bolt is fixed tightly by the entire length of the thread, whereas the vicinity of the thread is filled with cement everywhere. schematic representation of the sample with loading forces is pictured in fig. 3. during experiments the samples were loaded by this forces l1 = 200, 300, 400, 500 n and l2 = 50 n. the experiments were performed the room temperature and loading frequency was f1 = 24 hz respectively f2 = 12 hz. numerical model d-model of implant was prepared in solidworks software and exported in ansys software. the model was meshed and solwed in ansys, see fig.4. the aim of this model was determination of stress and strains in the pedicle-screw. another finite element model was prepared for calculation of stress-intensity factor along the crackpath. figure 4: meshed finite element model of pedicle screw. first model of pedicle-screw is composed of 556.024 tetrahedral elements (type of element solid187) for solid, and 442.052 for hollow screw. in the case of solid screw, as model of the contacts between thread and bone for first 4 mm from point of entry into the bone was used null displacement, for the rest of the contact is allowed to move in a plane perpendicular to the axis of the screw (0.5 mm allowable displacement). depth of hard part of bone corresponds to almost one loop of the thread. in the case of hollow screw. conditions of null displacement were applied to all degrees of freedom (due the cement presence) of the nodes along the entire length of the thread in the bone. for second model, model of the crack initiation area, is used refinement of net and the size of the elements is 5 μm, see fig. 5. the important fact is, that in the region of crack initiation is elastoplastic deformation, while rest of volume is under elastic deformation. plasticity of material was simulated kinematic hardening. figure 5: meshed finite element model of crack. figure 6: von misses stress in the thread. f 3 š. major et alii, frattura ed integrità strutturale, 35 (2016) 379-388; doi: 10.3221/igf-esis.35.43 383 distribution of the von mises stress obtained for elastic deformation of thread area of screw is shown in fig.6. in this figure is clearly visible local maximum of stress concentration at the bottom of thread (lower diameter of thread). the crack initiates in this region. the evolution of normal stress along the crack path is displayed in fig. 7, for four different loads. for analysis of crack propagation phase is necessarily calculate the stress intensity factor at the bottom of thread, respectively at the forehead of crack. for this calculation second finite element model was prepared. for this model semieliptical crack is assumed. it is assumed, that the crack initiates on te lower diameter of thread and subsequently grows along the bottom of the thread (crack grows along the helix, with inclination 14.5°, which corresponds to the thread pitch) and propagates into core of the screw, see fig. 8. the crack is characterized by two axes a and b, these two axis define the ellipse. the major axis is tangential to the thread and the secondary axis is perpendicular to the axis of the helix, respectively to the axis of screw. figure 7: the evolution of normal stress along the crack path, for four different loads (200 n, 300 n, 400 n, 500 n). when the diameter of crack is smaller then 50 μm, it is assumed that the crack flat. this assumption cannot be used for crack diameter greater then 50 μm. for greater crack is necessarily use submodelling, becose the number of elements is too large. the calculation of stress-intensity factor at the front of crack was based on j-integral method. for calculation was assumed that the material can be characterized by linear elastic deformation. stress-intensity factor is a function of crack length a. this relations is can be determined by repeated simulations. the lenght of crack at the start of simulation was 5 μm. this length is much smaller than the initial crack length for the propagation phase. with paris' law, a relationship n s s d d k a a k          (2) can be obtained where δas and δad are increments of crack on surface and deepest poit of crack. the δks and δkd are appropriate increments of stress-intensity factors and n is exponent in paris law. with new increment of δas, crack length at the surface changed and a new finite element model can be solved and the stress-intensity factor calculated. this process is repeated by software until the final length of crack is reached. the shape changes in the process of crack growth can be described by the ratio a/b, where a and b are values corresponding to the lengths axis of the ellipse. relations between ratio a/b and the length of crack is shown in fig. 9. a sharp decline in the ratio a/b (see fig. 9) indicates that the crack propagates faster along the helix (around the circumference of the screw cylinder) then into body of material. the following figure shows realitions between crack intensity factor (at the bottom of the thread) and crack length. gradient of stress-intensity factor is is much greater at the š. major et alii, frattura ed integrità strutturale, 35 (2016) 379-388; doi: 10.3221/igf-esis.35.43 384 beginning of process, see fig. 10. the stress intensity factor grows much faster at the surface of screw. therefore, it is necessary to implement a plurality of simulations for the initial phase of the process. figure 8: crack in the thread, growing plane. figure 9: relations between ratio a/b and the length of crack. figure 10: relations between gradient of stress-intensity factor and the length of crack. theoretical model or theoretical analysis of fatigue process was used new method proposed by navarro [7, 8] and multiaxial fatigue criteria modified for notched specimens were tested [9]. model proposed by navarro combined initiation and propagation phase, without the need to define boundary length of crack, to differentiate between the two phases of crack growth. it is necessary, to calculate the number of cycles needed to reach the length a (curve a-ni, is necessary to know fatigue curve σ-n. the fatigue curve σ-n is in fig. 1. this curve can be expressed by parameters obtained from f š. major et alii, frattura ed integrità strutturale, 35 (2016) 379-388; doi: 10.3221/igf-esis.35.43 385 some multiaxial fatigue criteria, becose the pedicle screw is under multiaxial loading. if fatemi-socie criteria is used, socalled “initiation curves” can obtained [6, 7, 8], see fig. 11. in the fig. 11 initiations curves for length of crack a1 and a2 are displayed. these curves shows the number of cycles required to achieve a crack length a1, respectively a2 , if fatemi-socie parameters fs are known. the damage parameter is given by the equation: max max1 2 y fs k            (3) in this equation, δγmax is the shear strain increment in the plane where it has maximum value, k is a constant that is obtained from the fatigue tests, σmax is the normal stress perpendicular to the plane where is the maximum shear strain, and σy is the yield strength. the number of cycle can be calculated by equation    , fa i total n a da n fs a n fs c k    (4) figure 11. initiations curves for length of crack a1 and a2 figure 12. application of the prediction model in the test with f = 400 n (nitrided pedicle screw). š. major et alii, frattura ed integrità strutturale, 35 (2016) 379-388; doi: 10.3221/igf-esis.35.43 386 in propagation stage, the number of cycles needed to propagate a crack to final failure, is calculated using fracture mechanics. this phase is described by the curve a-np. this curve is obtained by integration of growth law for any crack length to failure. the growth law can be expressed as 1 2 , 0 0 n ff n th long f f f da a c k k dn a a l                     (5) where δkth,long is the growth threshold for long cracks, f is a parameter (for this case f = 2.5), a0 is the el haddad parameter [11, 12] and l0 is the average distance to the first microstructural barrier. el haddad parameter is defined as 2 , 0 1 th long fl k a          (6) where δσfl is the fatigue limit of the material. the growth of threshold for long cracks in eq. 5 was multiplicated by factor which was derived from the theoretical approximation of the kitagawa–takahashi diagram [13,14]. the stress intensity factor is can be calculated as     22 1 2 0 2 1 1i s s k a m m s ds a as              (7) where σ is the stress normal to the growth plane of the crack and s is a coordinate running through the crack from the tip of crack to the surface. s and a parameters depend on the dimensions of the cross section of the specimen and crack length. when two curves (number of cycles to length and number of cycles to rupture, a-ni and a-np) are known, they can be merged, so that the entire fatigue life can be described. this curve for total life of screw is shown in fig. 12. from this picture is clearly visible, that the initiation life is much smaller than propagation life. figure 13: fatigue tests in implants and theoretical prediction.of hollow and solid pedicle screws. symbols: specimen without treatement – circle, nitride surface – square, oxide surface triangle. results ollow screws show higher fatigue resistance at the same load than full screws. this could be explained with more suitable distribution of stress along thread. results of experimental load of pedicle-screw are shown at fig. 13. fig. 13 shows that the crack initiation phase is about 10 % of fatigue life of implant. h š. major et alii, frattura ed integrità strutturale, 35 (2016) 379-388; doi: 10.3221/igf-esis.35.43 387 this figure shows also curves of theoretical lifespan obtained with help of a model based on navarro method. other methods of lifespan forecast have been tested for a comparison with our new method. in article [9], there are described various multiaxial criteria, adapted for lifespan forecast of notched samples, which corresponds to the case of the screw. a criterion proposed by goncalves gives the best forecast of all criteria described in [9]. goncalves criterion has been modified with help of ag and bg parameters for sample analysis. 5 2 1. max 1 1 g gam i g gam i a a d b b f        (8) and       max min / 2i i id s t s t  , (9) where parameters di can be determined from minimum and maximum values of the transformed deviatoric stress tensor. the material variables are set from fatigue limits as:   1 2 1 1 3 ga     , (10) 3 3 1 gb    . (11) if we perform a comparison of theoretical lifespan forecast of the screw based on navarro method [6, 7, 8], and older methods [9] (goncalves method is best of them), it can be said that navarro method gives 50 % better result than goncalves method. navarro method respects conditions of fixation of the screw in the bone better than older methods. the most important advantage of navarro method is a possibility of including an influence of filling cement. conclusions ollow screws with the performance show higher fatigue resistance with the same load, which can be explained by stronger deposition over the entire length of the screw. results of fatigue test were compared with theoretical predictions and theoretical model predicts that initiation phase is about 10% of fatigue life of implant. references [1] chen, c.s., chen, w.j., cheng, c.k., jao, s.h., chuech, s.c., wang, s.c., failure analysis of broken pedicle screws on spinal instrumentation, medical engineering & physics, 27 (2005) 487–496. doi:10.1016/j.medengphy.2004.12.007. [2] griza, s., de andrade, c.e.c., batista, w.w, tentardini, e.k., strohaecker, t.r., case study of ti6al4v pedicle screw failures due to geometricand microstructural aspects, engineering failure analysis, 25 (2012) 133–143. doi:10.1016/j.engfailanal.2012.05.009. [3] amaritsakul, y., ching-kong , ch., jinn, j., biomechanical evaluation of bending strength of spinal pedicle screws, including cylindrical, conical, dual core and double dual core designs using numerical simulations and mechanical tests, medical engineering & physics, 36 (2014) 1218–1223. doi: 10.1016/j.medengphy.2014.06.014. [4] krag, m. h., biomechanics of thoracolumbar spinal fixation: a review, spine, 16 (1991) 84–99. [5] ormsby, r. mcnally, t., oharre, p., burke, g., mitchell, g., fatigue and biocompability of properties of poly(methyl methacrylate) bone cement with multi-waled carbon nanotubes, acta biamaterialia 8 (2012) 1201–1212. doi: 10.1016/j.actbio.2011.10.010. [6] ayllón, j.m, navarro, c., vázquez, j., domínguez, j., fatigue life estimation in dental implants, engineering fracture mechanics, 123 (2014) 34–43. doi:10.1016/j.engfracmech.2014.03.011. h š. major et alii, frattura ed integrità strutturale, 35 (2016) 379-388; doi: 10.3221/igf-esis.35.43 388 [7] navarro, c., muńoz, s., domínguez, j., on the use of multiaxial fatigue criteria for fretting fatigue life assessment, int j fatigue, (2008) 32–44. doi:10.1016/j.ijfatigue.2007.02.018. [8] navarro, c., vázquez, j., domínguez, j., a general model to estimate life in notches and fretting fatigue. engineering fracture mechanics, (2011) 1590–601. doi:10.1016/j.engfracmech.2011.01.011. [9] major, s, hubálovský, s., kocour, v., valach, j., effectiveness of the modified fatigue criteria for biaxial loading of notched specimen in high-cycle region, applied mechanics and materials, 732 (2015) 63-70. doi: 10.4028/www.scientific.net/amm.732.63. [10] astm e647. standard test method for measurement of fatigue crack growth rates. west conshohocken, pa, united states, http://www.astm.org/standards/e647.htm. [11] lazzarin, p., tovo, r., meneghetti, g,. fatigue crack initiation and propagation phases near notches in metals with low notch sensitivity. int j fatigue, 19 (1997) 647–65. doi:10.1016/s0142-1123(97)00091-1. [12] el haddad, m.h., topper, t.h., smith, k.n., prediction of non-propagating cracks, engineering fracture mechanics, 11 (1979) 573–584. doi: 10.1016/0013-7944(79)90081-x. [13] kitagawa, h., takahashi, s., applicability of fracture mechanics to very small cracks or the cracks in the early stage, in: proceedings of the second international conference on mechanical behavior of materials. metals park, oh: asm; (1976) 627–31. [14] peters, j.o., boyce, b.l., chen, x., mcnaney, j.m., hutchinson, j.w., ritchie, r.o., on the application of the kitagawa–takahashi diagram to foreign-object damage and high-cycle fatigue, engineering fracture mechanics. 69 (2002) 1425–1446. doi:10.1016/s0013-7944(01)00152-7. << /ascii85encodepages false /allowtransparency false /autopositionepsfiles true /autorotatepages /none /binding /left /calgrayprofile (dot gain 20%) /calrgbprofile (srgb iec61966-2.1) /calcmykprofile (u.s. web coated \050swop\051 v2) /srgbprofile (srgb iec61966-2.1) /cannotembedfontpolicy /error /compatibilitylevel 1.4 /compressobjects /tags /compresspages true /convertimagestoindexed true /passthroughjpegimages true /createjobticket false /defaultrenderingintent /default /detectblends true /detectcurves 0.0000 /colorconversionstrategy /cmyk /dothumbnails false /embedallfonts true /embedopentype false /parseiccprofilesincomments true /embedjoboptions true /dscreportinglevel 0 /emitdscwarnings false /endpage -1 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/hrv (za stvaranje adobe pdf dokumenata najpogodnijih za visokokvalitetni ispis prije tiskanja koristite ove postavke. stvoreni pdf dokumenti mogu se otvoriti acrobat i adobe reader 5.0 i kasnijim verzijama.) /hun 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/pdfxoutputintentprofileselector /documentcmyk /preserveediting true /untaggedcmykhandling /leaveuntagged /untaggedrgbhandling /usedocumentprofile /usedocumentbleed false >> ] >> setdistillerparams << /hwresolution [2400 2400] /pagesize [612.000 792.000] >> setpagedevice microsoft word numero_50_art_33_2608 k. kaklis et alii, frattura ed integrità strutturale, 50 (2019) 395-406; doi: 10.3221/igf-esis.50.33 395 focused on the research activities of the greek society of experimental mechanics of materials a simplified damage evolution relationship and deformation characteristics of a pozzolanic lime mortar when subjected to unloading-reloading cycles in the pre-peak region kostas kaklis school of mineral resources engineering, technical university of crete, chania 73100, greece kaklis@mred.tuc.gr, https://orcid.org/0000-0003-2722-5915 zach agioutantis department of mining engineering, university of kentucky, lexington, kentucky 40506, usa zach.agioutantis@uky.edu, https://orcid.org/0000-0002-9799-4114 stelios mavrigiannakis school of mineral resources engineering, technical university of crete, chania 73100, greece smaurig@mred.tuc.gr, https://orcid.org/0000-0002-6409-6043 pagona maravelaki-kalaitzaki school of architectural engineering, technical university of crete, chania 73100, greece nmaravel@elci.tuc.gr, https://orcid.org/0000-0002-8776-6695 abstract. two series of uniaxial and triaxial compression tests including unloading-reloading cycles were performed under different confining pressures, in order to study the stress-strain and the deformation behavior of a pozzolanic lime mortar subjected to cyclic loading. each test included a cyclic loading sequence using five loops in the pre-peak region. the experimental results showed that the specimens exhibit a strain-softening behavior for uniaxial and low pressure triaxial tests and a strain-hardening behavior for higher triaxial compression tests. the mortar specimens subjected to triaxial compressive cyclic loading at higher confining pressures failed along a single or conjugate shear planes accompanied by considerable lateral expansion. the marked young’s modulus degradation behavior in the prepeak region is related to damage that occurs in each specimen. keywords. pozzolanic lime mortar; cyclic loading; plastic strain; young’s modulus degradation; damage evolution. citation: kaklis k., agioutantis z., mavrigiannakis s., maravelaki-kalaitzaki p., a simplified damage evolution relationship and deformation characteristics of a pozzolanic lime mortar when subjected to unloading-reloading cycles in the pre-peak region, frattura ed integrità strutturale, 50 (2019) 395-406. received: 22.01.2019 accepted: 25.05.2019 published: 01.10.2019 copyright: © 2019 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. introduction he authors have previously investigated and published the mechanical properties of a pozzolanic lime mortar, which consists of carbonate sand, hydrated lime and metakaolin (ml) [1]. pozzolanic mortars have multiple appli-t http://www.gruppofrattura.it/va/50/2608.mp4 k. kaklis et alii, frattura ed integrità strutturale, 50 (2019) 395-406; doi: 10.3221/igf-esis.50.33 396 cations in the restoration of ancient monuments or historic structures. this particular mortar is often used as a filler or joint material in restoration projects [2, 3], subjected to shear stresses that may develop along the mortar-stone interface. stone blocks in ancient monuments were typically joined together using metallic connectors in order to provide structural integrity in case of dynamic loading. more specifically, the structural elements of the monuments on the acropolis of athens were initially joined together using “i”-shaped metallic connectors placed in appropriate grooves which were filled with molten lead [4]. the restoration process of the parthenon in athens, greece involved the replacement of a number of marble epistyles [5] where titanium connectors were placed in carved grooves which were then filled with a cement based mortar. titanium prohibits the use of lead as the “titanium-lead” bimetallic contact forms a strong galvanic element [4]. pozzolanic mortars can also be used as filler material when seating metallic connectors in grooves carved into the original or restored stone fragments. apart from this explicit use as filling material, pozzolanic mortars used as rubble, joint, finishing and capping mortars can provide particular durability to the masonry with respect to both external loading and weathering. the longevity of some ancient structures, such as the pantheon, the colosseum, hagia sofia, etc., can also be attributed to the use of pozzolanic mortars as the main joint material. therefore, pozzolanic mortars and especially the lime-metakaolin system studied in this research, are very important in the conservation field and particularly when repair mortars are intended to be integrated in ancient structures. this work aims to provide evidence that pozzolanic lime mortars can replace cement-based mortars in historic structure restoration projects, thus mitigating potential problems arising from salt-induced decay and material incompatibility in physico-chemical and mechanical terms, which are typically attributed to the cementitious component of cementbased mortars. although mortars are typically characterized by their elastic properties and material strength values, it is very important to also include their inelastic or plastic characteristics as the latter are often responsible for their successful longterm performance. deformations and resulting damage of materials such as concrete and mortars typically follow the elastic-plastic damage model. the elastic-damage and elastic-plastic models differ in that the elastic-plastic models can simultaneously take into account the accumulation effect of plastic strains and elastic modulus degradation [6]. in order to investigate the deformation characteristics and damage evolution with respect to rocks and concrete, it is necessary to perform a series of experiments. many uniaxial and triaxial experiments under a loading-unloading-reloading regime (cyclic loading) have been conducted and are reported in the international literature (e.g., test on rocks [7, 8] and concrete [9, 10]). the authors have also performed such tests on mortars [1, 11] and have shown that such specimens predominantly exhibit a plastic behavior. some of these experiments [11] were focused on examining the stress-strain behavior and deformation characteristics of a pozzolanic lime mortar in the pre-peak region of the stress-strain curve. the term “cyclic loading” refers to the loading-unloading-reloading procedure which was utilized to gain a better understanding of the elasto-plastic properties of the material. details on this test are given by gatelier et al. [7]. this investigation further analyzes the results from two series of uniaxial and triaxial compression tests under cyclic loading, which were recently completed by the authors [11]. future work will aim at experimentally investigating the post-peak region behavior of the material in order to suggest a complete damage evolution law. material and methods composition of the pozzolanic mortar he properties and constitution of the pozzolanic mortar used in the experiments previously conducted by the authors are described in detail in [11]. in summary, a mix design of sand, lime and metakaolin (at 50, 30 and 20% w/w, respectively) was developed utilizing a water to binder ratio of 0.92. mixing took place at ambient conditions. the specific weight ratio of hydrated lime and metakaolin of 1.5 used, ensured that a fully developed pozzolanic reaction of the metakaolin with hydrated lime could occur. eventually, any unreacted proportion of the hydrated lime is considered to contribute to the plasticity of the final mortar after its carbonation [12]. through this process the mortar is assumed to acquire a pore size distribution similar or compatible to porous stone, thus facilitating the homogeneous distribution of water and more importantly allowing the water vapor to escape through the composite system [2, 3]. additionally, in an effort to improve the performance characteristics of the mortar, the sand used in the mix consisted of equal proportions of carbonate sand passing through the 125 and 63 μm sieves. preparation of specimens for mechanical experiments the preparation of specimens has been described in detail in [11]. previous research by the authors [1] indicated that it is better to develop cylindrical mortar specimens by coring mortar blocks compared to direct casting into cylinders. mortar specimens were cast in prismatic molds constructed out of wooden particle boards. the mold was removed two days after casting and the mortar was allowed to cure in a curing chamber at a relative humidity (rh) of 90-95% t k. kaklis et alii, frattura ed integrità strutturale, 50 (2019) 395-406; doi: 10.3221/igf-esis.50.33 397 and a temperature (t) of 20 °c with respect to the en 196–1 standard. specimens were allowed to cure for 26 days in the curing chamber and followed by two days in ambient conditions prior to testing as outlined in the methodology described by gameiro et al. [13]. cored cylinders were then cut and ground to provide smooth loading surfaces for both the uniaxial and triaxial tests following the recommendations for rock mechanics tests [14, 15]. the diameter of the mortar cylinders was 50 mm (±2 mm) and their height was 100 mm (±3 mm) thus ensuring a height to diameter ratio (h/d) approximately equal to 2. experimental setup series of uniaxial and triaxial compression tests were performed on mortar specimens using a stiff 1600 kn mts hydraulic testing frame (model 815) which could apply the axial load either through load-control or displacement-control. the tests were used to obtain the stress-strain behavior and the deformation characteristics of the pozzolanic lime mortar specimens under cyclic (loading-unloading and reloading) conditions. as mentioned in previous studies [1, 11], this particular pozzolanic mortar has been considered as an isotropic material due to the finegrained materials that it contains as well as the mixing and casting procedures used. although all of the specimens were considered equivalent, irrespectively of how they were oriented during preparation and testing, in the present study specimens were extracted parallel to the casting direction in order to avoid any variations in the calculated mechanical parameters of the mortar, due to the consolidation direction in the casting block. tests were typically conducted using load control at a constant load rate during the initial loading stages and displacement (stroke) control during the final loading stage. the final loading stage starts from the bottom of the unloading curve of the last loop. thus, apart from the pre-peak stress-strain curve and the peak stress value, the post-peak stress-strain curve was also recorded. an external 500 kn load cell by maywood was inserted between the loading platen and the specimen in the uniaxial tests. triaxial tests were conducted using a wykeham farrance triaxial chamber (fig.1a) with a maximum lateral pressure capacity of 14 mpa. the triaxial cell was mounted on the testing frame and axial load was directly applied to the loading piston without an external load cell. figure 1: (left) the triaxial chamber mounted inside the mts 815 frame; (right) the external lvdt experimental setup for measuring the axial deformation values during the triaxial compression cyclic tests. the triaxial compression tests were carried out under confining pressures of 1.15, 2.09, 3.96, and 6.06 mpa. a cyclic loading sequence with five loops was used in both the uniaxial and the triaxial compression tests. the five unloadingreloading loops were performed in the pre-peak region and the axial load was applied under load control with a rate of 200 n/s. the load increment from one loop to the next ranged from 2.5 to 3.5 kn. in the final loading step the axial load was applied under displacement control with a rate of 0.01 mm/s in order to obtain the complete stress-strain curve in the post-peak region. axial strain was measured during the uniaxial and triaxial compression tests using the displacement sensor of the loading frame as well as an external lvdt sensor, in order to get more accurate and comparable strain measurements from these tests (fig.1b). as the most representative and reliable strain measurements are realized using electrical strain gages, uniaxial tests were instrumented with strain gages as well. however, strain gages were not utilized in triaxial compression tests, as the triaxial chamber did not allow for that. in cyclic loading, when a specimen is compressed up to a deviator stress level, then unloaded to zero deviator stress and then reloaded, the unloading and reloading branches are in most cases different from the initial loading curve (fig. 2), as well from each other, forming a narrow loop that can be approximated by a straight line. the young’s modulus of the material can be derived from the slope of this line [8, 16]. in cyclic loading the strain is partly elastic and partly plastic. the elastic strain 𝜀 is defined as the recovered deformation by unloading to zero deviator stress, while the plastic strain 𝜀 is defined as the accumulated residual axial strain a k. kaklis et alii, frattura ed integrità strutturale, 50 (2019) 395-406; doi: 10.3221/igf-esis.50.33 398 of the material after being unloaded to zero stress (fig.2) [16, 17]. this plastic strain includes various types of unrecoverable deformation due to dislocation, viscous-flow and micro-fracturing [18]. in this study the young’s modulus was calculated as shown in fig.2. this method is only based on elastic strain when compared to methods proposed by other investigators [19, 20, 21] who utilize additional deformation parameters for the calculation of young’s modulus. figure 2: typical stress-strain curve under cyclic loading. experimental results and discussion unloading – reloading (cyclic) stress – strain relation ig.3a presents typical deviator stress-strain curves with five loading-unloading cycles under uniaxial compressive and conventional triaxial compressive loading for confining pressures of 1.15 mpa, 2.09 mpa and 6.06 mpa. the stress-strain responses indicated that the mortar becomes ductile even under low confining pressure. the initial part of deformation before yielding, the so-called elastic part, is significantly curved and includes appreciable permanent deformation. in addition, two different types of deformation are illustrated in fig.3a: (a) specimens under uniaxial compression and triaxial compression at low confining pressure (1.15 mpa) exhibited a strain-softening behavior with an easily identifiable peak stress, and (b) specimens under triaxial compression at higher confining pressures (2.09 mpa and 6.06 mpa) exhibited a strain-hardening behavior. at higher confining pressures, peak stress which corresponds to failure is not easily recognized due to the large strain on a strain-hardening curve [22]. (a) (b) figure 3: (a) the complete deviator stress-strain curve for pozzolanic lime mortar specimens tested in uniaxial and triaxial cyclic loading under confining pressures of 1.15 mpa, 2.09 mpa and 3.96 mpa; (b) the mean young’s modulus for each loop of the triaxial cyclic loading under confining pressures of 2.09 mpa and 3.96 mpa. the young’s modulus values were calculated at each cycle as discussed previously [8, 16] and are presented in fig.3b for each of the four last loops in the case of triaxial compression tests under confining pressures of 2.09 mpa and 6.06 mpa. in both cases of cyclic triaxial compressive loading, it is obvious that the young’s modulus decreases with increasing strain. 0 2 4 6 8 10 12 14 0.00 0.01 0.02 0.03 0.04 0.05 d ev ia to r st re ss , σ 1 σ 3 (m p a) axial strain uniaxial 1.15 mpa 2.09 mpa 6.06 mpa 5th 4th 5 th4 th3rd 2nd 0 2 4 6 8 10 12 14 0.001 0.003 0.005 0.007 0.009 0.011 0.013 d ev ia to r st re ss , σ 1 σ 3 (m p a ) axial strain 2.09 mpa 6.06 mpa f k. kaklis et alii, frattura ed integrità strutturale, 50 (2019) 395-406; doi: 10.3221/igf-esis.50.33 399 deformation characteristics one uniaxial compression test and four triaxial compression tests under cyclic loading conditions were performed in order to examine the deformation characteristics of the pozzolanic lime mortar. by processing the experimental data the plastic strain, the total strain as well as the young’s modulus of the material were determined and presented in table 1, for each one of the five loops. note that in the loops performed at relatively low stress levels of the triaxial cyclic compression test with lateral pressures of 2.09 mpa and 3.96 mpa, the calculated values of the young’s modulus did not range within the acceptable limits for this material and were excluded from table 1. in addition, these values are not taken into account in the subsequent calculations and they do not appear in the respective diagrams. loops uniaxial triaxial confining pressure of 1.15 mpa deviator stress (mpa) plastic strain, εpl (x10-3) total strain, ε (x10-3) young’s modulus, ε(mpa) deviator stress (mpa) plastic strain, εpl (x10-3) total strain, ε (x10-3) young’s modulus, ε(mpa) 1st 1.85 0.447 0.672 7720 3.50 0.203 0.466 14105 2nd 2.98 0.552 0.967 6720 4.64 0.332 0.702 12328 3rd 4.67 0.845 1.591 6228 6.40 0.512 1.181 9426 4th 5.78 1.319 2.314 5972 8.13 1.150 2.113 8374 5th 7.04 2.244 3.525 5537 loops triaxial confining pressure of 2.09 mpa triaxial confining pressure of 3.96 mpa deviator stress (mpa) plastic strain, εpl (x10-3) total strain, ε (x10-3) young’s modulus, ε (mpa) deviator stress (mpa) plastic strain, εpl (x10-3) total strain, ε (x10-3) young’s modulus, ε (mpa) 1st 3.09 0.912 0.946 2.26 1.041 1.041 2nd 4.14 1.257 1.545 3.12 1.313 1.380 3rd 5.35 1.960 2.549 9256 4.71 1.931 2.315 12343 4th 6.36 3.164 3.957 8391 6.20 3.463 4.073 10091 5th 7.87 6.594 7.665 7705 7.78 6.881 7.707 9531 loops triaxial confining pressure of 6.06 mpa deviator stress (mpa) plastic strain, εpl (x10-3) total strain, ε (x10-3) young’s modulus, ε(mpa) 1st 3.36 1.466 1.466 2nd 5.19 1.929 2.216 18170 3rd 6.25 3.349 3.810 13663 4th 7.31 5.924 6.560 11601 5th 8.94 10.458 11.247 11.358 table 1: results of uniaxial and triaxial compressive tests under cyclic loading. fig.4a and fig.4b show the relationship between the plastic strain and the elastic strain, respectively, as a function of the total strain of the mortar specimens subjected to both uniaxial and triaxial compressive cyclic loading for each of the five unloading-reloading loops. these diagrams show clearly the different behavior of the mortar specimens tested in uniaxial and triaxial cyclic loading. from a regression analysis, linear relationships between the plastic strain and total strain, as well as the elastic strain and total strain are derived, with a correlation coefficient higher than 0.95, both in uniaxial (1) and triaxial (2) compressive cyclic loading scenarios. it should be noted that the fitting of results for the triaxial cyclic compression tests took into account the data points from all three different confining pressures. k. kaklis et alii, frattura ed integrità strutturale, 50 (2019) 395-406; doi: 10.3221/igf-esis.50.33 400 (a) (b) (c) figure 4: (a) plastic strain vs. total strain; (b) elastic strain vs. total strain; (c) εpl/ε and εεl/ε ratios vs deviator stress. for uniaxial compression cyclic test: 𝜀 0.61 ∙ 𝜀, 𝜀 0.39 ∙ 𝜀 (1) for triaxial compression cyclic test: 𝜀 0.89 ∙ 𝜀, 𝜀 0.11 ∙ 𝜀 (2) the variation of the εpl/ε and εel/ε ratios with the deviator stress is presented in fig.4c for the last loops of the same experimental tests; the red lines correspond to the εpl/ε ratio, while the blue lines correspond to the εel/ε atio. as expected, each pair of points corresponding to the same loop of the same test, satisfy eq.(3). 1 (3) fig.5a presents the relationship between the plastic strain and the deviator stress for the uniaxial and the triaxial cyclic compression test under confining pressures of 2.09 mpa, 3.96 mpa and 6.06 mpa. this diagram confirms the different behavior of the mortar specimens tested in uniaxial and triaxial cyclic loading. using regression analysis, exponential (a) (b) figure 5: (a) plastic strain vs. deviator stress; (b) εpl/ε vs. confining pressure. εpl = 0.89 ε r2 = 0.99 εpl = 0.61 ε r² = 0.98 0 2 4 6 8 10 12 0 2 4 6 8 10 12 14 p la st ic a x ia l st ra in , ε p l (x 1 0 -3 ) total axialstrain, ε (x10-3) uniaxial 2.09 mpa 3.96 mpa 6.06 mpa εel = 0.11 ε r² = 0.95 εel = 0.39 ε r² = 0.95 0 1 2 3 4 5 0 2 4 6 8 10 12 14 e la st ic a x ia l st ra in , ε e l (x 1 0 -3 ) total axial strain, ε (x10-3) uniaxial 2.09 mpa 3.96 mpa 6.06 mpa 0.0 0.2 0.4 0.6 0.8 1.0 1.2 0.0 0.2 0.4 0.6 0.8 1.0 1.2 0 2 4 6 8 10 e la st ic s tr a in , ε e l / t o ta l st ra in ,ε p la st ic s tr a in , ε p l / t o ta l st ra in ,ε deviator stress, σ1 σ3 (mpa) uniaxial 2.09 mpa 3.96 mpa 6.06 mpa uniaxial 2.09 mpa 3.96 mpa 6.06 mpa εpl = 0.34e 0.37(σ1-σ3) r2 = 0.96 εpl = 0.23e 0.31(σ1-σ3) r² = 0.98 0 2 4 6 8 10 12 0 2 4 6 8 10 p la st ic a x ia l st ra in , ε p l (x 1 03 ) deviator stress, σ1 σ3 (mpa) uniaxial 2.09 mpa 3.96 mpa 6.06 mpa εpl/ε = 0.78 σ3 0.07 r2 = 0.89 0.0 0.2 0.4 0.6 0.8 1.0 1.2 0 1 2 3 4 5 6 7 8 p la st ic s tr a in , ε p l / t ot al s tr ai n , ε confining pressure, σ3 (mpa) 2nd loop 3rd loop 4th loop 5th loop k. kaklis et alii, frattura ed integrità strutturale, 50 (2019) 395-406; doi: 10.3221/igf-esis.50.33 401 relationships between the plastic strain and deviator stress are derived, with a correlation coefficient higher than 0.96, for uniaxial compression (4) and triaxial compression (5) cyclic tests. the exponential relationships in fig.5a are not applicable near the zero deviator stress values, since there are no plastic strains at this loading condition. for uniaxial compression cyclic test: 𝜀 0.23 ∙ 𝑒 . (4) for triaxial compression cyclic test: 𝜀 0.34 ∙ 𝑒 . (5) the effect of the confining pressure σ3 of the triaxial compression cyclic tests on the εpl/ε ratio is presented in fig. 5b. the fitting results for the triaxial cyclic compression tests were derived by including all of the data points from the four last loops. using regression analysis, a power relationship between the εpl/ε ratio and the confining pressure is derived with a correlation coefficient equal to 0.89, as expressed by eq.(6). 0.78 ∙ 𝜎 . (6) young’s modulus degradation the degradation of young’s modulus is a crucial parameter that reflects the damage of the pozzolanic lime mortar under compressive loads. in the present study, the slope of the line replacing the loop which is formed by the unloading and reloading curve is defined as the elastic modulus 𝐸 (fig.2). the young’s modulus of every cycle, determined from the cyclic uniaxial and triaxial compressive tests is listed in table 1. in order to avoid possible errors caused by low stress levels, the young’s modulus values of the first cycles in some of the triaxial compression tests are ignored. the variation of the calculated young’s modulus with the confining pressure for each loop is presented in fig.6a. the increasing trend of the elastic modulus as a function of the confining pressure is evident. fig.6b shows the young’s modulus variation with the total strain for all of the mortar specimens tested in both uniaxial and triaxial compression tests under different confining pressures. the results indicate that the young’s modulus decreases with increasing total strain, which may be due to the propagation of initial defects, which were amplified upon increased load and successive loading cycles. this degradation behavior is related to weak patterns of damage, such as microvoids and microcracks, which are not able to modify and influence the elastic modulus of the specimen. (a) (b) figure 6: the variation of young’s modulus with (a) the confining pressure and (b) the total strain for mortar specimens tested in uniaxial and triaxial cyclic loading under different confining pressures. failure mode as previously discussed, the failure mode of the pozzolanic lime mortar specimens subjected to uniaxial and triaxial cyclic compressive loading is directly related to the type of stress-strain behavior (i.e., strain-softening vs. strain-hardening) as well as to the stress level of the confining pressure in triaxial compression tests. in the case of uniaxial compression cyclic tests and triaxial compression cyclic test at low confining pressure (1.15 mpa) (fig.3a), the mortar exhibits a strain-softening behavior. two different failure modes were observed during the uniaxial compressive loading of mortar. some specimens failed along a single shear plane (fig.7a) and others failed in axial splitting (fig.7b). the specimen subjected to triaxial compression cyclic test with confining pressure of 1.15 mpa failed along a single shear plane (fig.7c). as previously stated, the mortar specimens subjected to triaxial compressive cyclic loading at higher (2.09 – 6.06 mpa) confining pressures exhibited a strain-hardening behavior (fig.3a). in this case, the failure mode is characterized by large axial strain up to the maximum compressive stress and large lateral expansion of the cylindrical specimen. a con0 4000 8000 12000 16000 20000 0 1 2 3 4 5 6 7 y o u n g 's m o d u lu s, e ( m p a ) confining pressure, σ3 (mpa) 2nd loop 3rd loop 4th loop 5th loop 0 4000 8000 12000 16000 20000 0 2 4 6 8 10 12 14 y o u n g 's m o d u lu s, e ( m p a ) total axial strain, ε (x10-3) uniaxial 1.15 mpa 2.09 mpa 3.96 mpa 6.06 mpa k. kaklis et alii, frattura ed integrità strutturale, 50 (2019) 395-406; doi: 10.3221/igf-esis.50.33 402 jugate shear plane failure with lateral expansion is presented in fig.8a for the case of triaxial compression test with confining pressure of 2.09 mpa. in the case of the 3.96 mpa confining pressure, conjugate shear planes are observed (fig.8b), combined with a remarkable lateral expansion and some trace of lüders lines [23]. (a) (b) (c) figure 7: typical crack patterns in pozzolanic lime mortar cylindrical specimens. (a) shear plane failure in uniaxial compression test; (b) axial splitting failure in uniaxial compression test; (c) single shear plane failure in triaxial compression test with confining pressure of 1.15 mpa. (a) (b) figure 8: typical crack patterns in pozzolanic lime mortar cylindrical specimens under triaxial loading. (a) failure on conjugate shear planes for a confining pressure of 2.09 mpa; (b) failure on conjugate shear planes for a confining pressure of 3.96 mpa. simplified damage evolution relationship for cyclic tests under triaxial compression the pozzolanic lime mortar uniaxial and triaxial compression cyclic tests exhibit young’s modulus degradation caused by progressive damage accumulation. as mentioned before, fig.6b confirms this degradation process and can be utilized to characterize the damage evolution relationship. the damage part can be implemented by a damage index, d, which is equal to zero in the absence of damage and equal to one in the case of complete damage. under uniaxial and triaxial loading conditions, the calculated “damaged” elastic modulus, ed is related to the initial “undamaged” elastic modulus eo, according to the following equation: 𝐸 1 𝑑 ∙ 𝐸 (7) the values of damaged young’s modulus 𝐸 were calculated graphically from each loop of the triaxial compressive cyclic loading (table 1). ιt is important to note that in this study as initial undamaged elastic modulus eo was assumed to be the modulus that was calculated using the second or third loop for each confining pressure of the triaxial compression tests. the corresponding values of the damage index were calculated by rearranging relationship (7): 𝑑 1 (8) fig.9a illustrates the calculated values for the damage index using eq.(8), for the triaxial compression cyclic tests with confining pressures of 2.09 mpa, 3.96 mpa, and 6.06 mpa. note, that the values obtained for the series of triaxial tests k. kaklis et alii, frattura ed integrità strutturale, 50 (2019) 395-406; doi: 10.3221/igf-esis.50.33 403 with a lateral pressure of 1.15 mpa were not used in fig.9a and in the subsequent derivation of the damage index relationship because of two reasons: (a) these tests exhibited a strain-softening behavior, while specimens under higher triaxial compression pressures exhibited a strain-hardening behavior and (b) the behavior of the specimen tested under a lateral pressure of 1.15 mpa exhibited a failure mode (fig.7c) similar to that of uniaxial test (fig.7a) and dissimilar to that of high pressure triaxial tests (fig.8). (a) (b) figure 9: (a) fitting results of damage index d for triaxial compression cyclic tests with confining pressures of 2.09 mpa, 3.96 mpa and 6.06 mpa. (b) fitting results for coefficients 𝑎, 𝑏 and 𝑐. in this work, a similar model with those proposed for concrete [24, 25, 26, 27, 28, 29] was adopted in order to predict the damage evolution relationship for the pozzolanic lime mortar, which is described in eq.(9): 𝑑 𝑎 𝑏 ∙ 𝜀 (9) where a, b are coefficients of the damage evolution relationship; c is an optimum order related to the speed of damage propagation, which controls the curvature of the damage evolution curve. the fitting curves on the calculated damage index for each confining pressure are plotted in fig.9a, while the fitting results for coefficients a, b and c are listed in table 2. σ3 a b c 2.09 0.31 0.73 0.83 3.96 0.29 0.62 1.10 6.06 0.42 0.91 1.32 table 2: fitting results for coefficients a, b and c. as illustrated in fig.9b, the coefficients a, b and c are functions of the confining pressure. from a regression analysis, these coefficients are determined in eqs.(10-12). the corresponding fitting lines and least square correlation coefficients are shown in fig.9b. 𝑎 0.0284 ∙ 𝜎 0.2253 (10) 𝑏 0.0498 ∙ 𝜎 0.5557 (11) 𝑐 0.123 ∙ 𝜎 0.5866 (12) the evolution of d as a function of the confining pressure (eq.(13)) is calculated by substituting eqs.(10-12) in eq.(9): 𝑑 0.0284 ∙ 𝜎 0.2253 0.0498 ∙ 𝜎 0.5557 ∙ 𝜀 . ∙ . (13) the verification of this damage model expressed in eq.(13) is shown in fig.10, where the predicted elastic moduli ed for each loop of the triaxial compression cyclic tests with confining pressure of 2.09 mpa (fig.10a) and 6.06 mpa (fig. 10b) are compared with the corresponding experimental values. the values of the predicted elastic moduli are in good agreement with the elastic moduli that were determined experimentally. the different behavior between uniaxial and triaxial compression tests with respect to plastic strain versus total strain and plastic strain versus deviator stress can be d = 0.42 0.91 ε-1.32 d = 0.29 0.62 ε-1.10 d = 0.31 0.73 ε-0.83 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0 2 4 6 8 10 12 14 d a m a g e in d ex , d total axial strain, ε (x10-3) 2.09 mpa 3.96 mpa 6.06 mpa α = 0.0284 σ3 + 0.2253 r2=0.65 b = 0.0498 σ3 + 0.5557 r2=0.42 c = 0.123 σ3 + 0.5866 r2=0.99 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 0 1 2 3 4 5 6 7 8 c o ef fi ci en ts a ,b ,c confining pressure, σ3 (mpa) a b c k. kaklis et alii, frattura ed integrità strutturale, 50 (2019) 395-406; doi: 10.3221/igf-esis.50.33 404 attributed to the completely different stress fields that are developed in each test, as a result of the application of lateral pressure in the triaxial compression tests. note that the proposed damage evolution equation applies only to the prepeak region. as presented experimentally [16, 17], the degradation of the elastic modulus becomes more pronounced in the post-peak region and to the specific mortar design. therefore, additional experimental work should be carried out in the future in order to investigate whether the young’s modulus degradation process can be utilized to lead to a complete damage evolution law. (a) (b) figure 10: comparison of experimental results and the proposed model for damage evolution on triaxial compression cyclic tests with (a) 2.09 mpa and (b) 6.06 mpa confining pressure. conclusions n the present study, uniaxial and triaxial compression tests under unloading-reloading (cyclic loading) conditions were conducted to elucidate the stress-strain and the material deformation behavior, as well as to derive a damage evolution relationship in the pre-peak region of a pozzolanic lime mortar. linear equations can be used to describe the relationship between the plastic strain and total strain, while exponential equations can be utilized to correlate the plastic strain and deviator stress in the case of both uniaxial and triaxial compression cyclic tests. the ratio εpl/ε is very high (0.89) for the triaxial compression tests, while it becomes lower (0.61) for uniaxial compression. in addition, a power relationship was derived between the εpl/ε and the confining pressure σ3. a strain-softening behavior can be used to describe the uniaxial test and the triaxial compression test at low confining pressure (1.15 mpa). triaxial compression tests at higher confining pressures can be described by a strain-hardening behavior. these different types of deformations are also reflected in the macroscopic failure mode of the pozzolanic lime mortar specimens subjected to uniaxial and triaxial cyclic compressive loading. the macroscopic crack pattern of mortar specimens under uniaxial compression are mainly shear failure and, in some cases, split failure, while the specimen subjected to triaxial compression cyclic test with relatively low confining pressure (1.15 mpa) failed along a single shear plane. under triaxial compression tests with higher confining pressures, failure occurs along a single shear plane or conjugate shear planes combined with lateral expansion. given that the young’s modulus is related to stress, strain and the susceptibility to crack initiation, propagation and coalescence, the quantification of changes in the elastic modulus can be used to describe the effects of cyclic loading on material deformation. the observed decrease of young’s modulus with increasing strain is attributed to the propagation of initial defects and microfractures in these mortar specimens. increasing the confining pressure in triaxial compression tests affects the degradation of the elastic modulus which can be expressed using a damage index. a mathematical expression is proposed which can calculate the damage index as a function of the confining stress for the case of pozzolanic lime mortars under triaxial compressive cyclic loading. this expression was derived based on a specific pozzolanic mortar design but can be easily expanded to similar mortar designs. the predicted elastic moduli for different unloading-reloading loops are in good agreement with the experimental values. as the damage evolution relationship quantifies changes in the elastic modulus of the material as a function of the confining stress, a full characterization of the pre-peak behavior of the material under different loading scenarios can be obtained. this information can be fully exploited when modeling the behavior of these mortars for a specific application. acknowledgements this research was co-financed by the european union (european social fund-esf) and greek national funds through the operational program “education and lifelong learning” of the national strategic reference framework 0 2 4 6 8 10 12 14 0.001 0.003 0.005 0.007 0.009 d ev ia to r st re ss , σ 1 σ 3 (m p a) axial strain 2.09 mpa 0 2 4 6 8 10 12 14 0.001 0.003 0.005 0.007 0.009 0.011 0.013 d ev ia to r st re ss , σ 1 σ 3 (m p a ) axial strain 6.06 mpa i k. kaklis et alii, frattura ed integrità strutturale, 50 (2019) 395-406; doi: 10.3221/igf-esis.50.33 405 (nsrf) research funding program: thales: reinforcement of the interdisciplinary and/or inter-institutional research and innovation. references [1] kaklis, k.n., mavrigiannakis, s.p., agioutantis, z.g. and maravelaki-kalaitzaki, p. (2018). characterization of pozzolanic lime mortars used as filling material in shaped grooves for restoring member connections in ancient monuments, international journal of architectural heritage, 12(1), pp. 75-90. doi: 10.1080/15583058.2017. 1377313. [2] veiga, r.m., velosa, a. and magalhaes, a. (2009). experimental applications of mortars with pozzolanic additions: characterization and performance evaluation, construction and building materials, 23, pp. 318-327. doi: 10. 1016/j.conbuildmat.2007.12.003. [3] aggelakopoulou, e., bakolas, a. and moropoulou, a. (2011). properties of lime–metakaolin mortars for the restoration of historic masonries, applied clay science, 53(1), pp. 15-19. doi: 10.1016/j.clay.2011.04.005. [4] kourkoulis, s.k., pasiou, e.d., triantis, d., stavrakas and i., hloupis, g. (2015). innovative experimental techniques in the service of restoration of stone monuments part i: the experimental set up, procedia engineering, 109, pp. 268-275. doi: 10.1016/j.proeng.2015.06.232. [5] kourkoulis, s.k. and pasiou, e.d. (2015). interconnected epistyles of marble monuments under axial loads, international journal of architectural heritage, 9(3), pp. 177-194. doi: 10.1080/15583058.2012.756079. [6] benin, a.v., semenov, a.s., semenov, s.g., beliaev, m.o. and modestov, v.s. (2017). methods of identification of concrete elastic-plastic-damage models, magazine of civil engineering, 8, pp. 279–297. doi: 10.18720/mce. 76.24. [7] gatelier, n., pellet, f., loret, b. (2002). mechanical damage of an anisotropic porous rock in cyclic triaxial tests, international journal of rock mechanics and mining sciences, 39(3), pp. 335-354. doi: 10.1016/s1365-1609 (02)00029-1. [8] jia, c., xu, w., wang, r., wang, w., zhang, j. and yu, j. (2018). characterization of the deformation behavior of fine-grained sandstone by triaxial cyclic loading, construction and building materials, 162, pp. 113-123. doi: 10. 1016/j.conbuildmat.2017.12.001. [9] neuenschwander, m., knobloch, m. and fontana, m. (2016). suitability of the damage-plasticity modelling concept for concrete at elevated temperatures: experimental validation with uniaxial cyclic compression tests, cement and concrete research, 79, pp. 57-75. doi: 10.1016/j.cemconres.2015.07.013 [10] li, b., xu, l., chi, y., huang, b. and li, c. (2017). experimental investigation on the stress-strain behavior of steel fiber reinforced concrete subjected to uniaxial cyclic compression, construction and building materials, 140, pp. 109-118. doi: 10.1016/j.conbuildmat.2017.02.094. [11] kaklis, k., agioutantis, z., mavrigiannakis, s. and maravelaki-kalaitzaki, p. (2018). on the experimental investigation of pozzolanic lime mortar stress-strain behavior and deformation characteristics when subjected to unloading-reloading cycles, procedia structural integrity, 10, pp. 129-134. doi: 10.1016/j.prostr.2018.09.019. [12] costigan, a. and pavia, s. (2010). influence of mechanical properties of lime mortar on the strength of masonry, 2nd conference on historic mortars hmc 2010 and rilem tc 203-rhm final workshop, editor(s): j. valek, c. groot and j.j. hughes, e-isbn: 978-2-35158-112-4, publisher: rilem publications sarl, pp. 457-466. [13] gameiro, a., santos silva, a., faria, p., grilo, j., branco, t., veiga, r. and velosa, a. (2014). physical and chemical assessment of lime–metakaolin mortars: influence of binder: aggregate ratio, cement and concrete composites, 45, pp. 264-271. doi: 10.1016/j.cemconcomp.2013.06.010. [14] bieniawski, z.t. and bernede, m.j. (1979). suggested methods for determining the uniaxial compressive strength and deformability of rock materials, international journal of rock mechanics and mining sciences & geomechanics abstracts, 16(5), pp. 135-140. doi: 10.1016/0148-9062(79)90262-6. [15] vogler, u.w. and kovari, κ. (1978). suggested methods for determining the strength of rock materials in triaxial compression, international journal of rock mechanics and mining sciences & geomechanics abstracts, 15(2), pp. 47-51. doi: 10.1016/0148-9062(78)91677-7. [16] mogi, k. (2007). experimental rock mechanics, geomechanics research series 3, balkema proceedings and monographs in engineering, water and earth sciences, the netherlands, taylor & francis/balkema. [17] bahn, b.y. and hsu, c.t.t. (1998). stress-strain behavior of concrete under cyclic loading, aci materials journal, 95(2), pp. 178-193. [18] chen, w.f. and han, d.j. (1988). plasticity for structural engineers, new york, springer-verlag. [19] li, b., xu, l., chi, y., huang, b. and li, c. (2017). experimental investigation on the stress-strain behavior of steel fiber reinforced concrete subjected to uniaxial cyclic compression, construction and building materials, 140, pp. 109-118. doi: 10.1016/j.conbuildmat.2017.02.094. k. kaklis et alii, frattura ed integrità strutturale, 50 (2019) 395-406; doi: 10.3221/igf-esis.50.33 406 [20] sima, j.f., roca, p. and molins, c. (2008). cyclic constitutive model for concrete, engineering structures, 30(3), pp. 695-706. doi: 10.1016/j.engstruct.2007.05.005. [21] lam, l. and teng, j.g. (2009). stress–strain model for frp-confined concrete under cyclic axial compression, engineering structures, 31(2), pp. 308-321. doi: 10.1016/j.engstruct.2008.08.014. [22] farmer, i. (1982). engineering behaviour of rocks. second edition, new york, chapman and hall. [23] olsson w.a. (2000). origin of lüders' bands in deformed rock, journal of geophysical research atmospheres, 105(b3), pp. 5931-5938. doi: 10.1029/1999jb900428. [24] osorio, e., bairán, j.m. and marí, a.r. (2013). lateral behavior of concrete under uniaxial compressive cyclic loading, materials and structures, 46(5), pp. 709–724. doi: 10.1617/s11527-012-9928-9. [25] sinaie, s., heidarpour, a., zhao, x.l. and sanjayan, j.g. (2015). effect of size on the response of cylindrical concrete samples under cyclic loading, construction and building materials, 84, pp. 399-408. doi: 10.1016/ j.conbuildmat. 2015.03.076. [26] breccolotti, m., bonfigli, m.f., d’alessandro, a. and materazzi, a.l. (2015). constitutive modeling of plain concrete subjected to cyclic uniaxial compressive loading, construction and building materials, 94, pp. 172-180. doi: 10.1016/j.conbuildmat.2015.06.067. [27] he, w., wu, y.f. and liew, k.m. (2008). a fracture energy based constitutive model for the analysis of reinforced concrete structures under cyclic loading, computer methods in applied mechanics and engineering, 197(51-52), pp. 4745-4762. doi: 10.1016/j.cma.2008.06.017. [28] yu, t., zhang, b. and teng, j.g. (2015). unified cyclic stress–strain model for normal and high strength concrete confined with frp, engineering structures, 102, pp. 189-201. doi: 10.1016/j.engstruct.2015.08.014. [29] hafezolghorani, m., hejazi, f., vaghei, r., jaafar, m.s.b. and karimzade k. 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/hrv (za stvaranje adobe pdf dokumenata najpogodnijih za visokokvalitetni ispis prije tiskanja koristite ove postavke. stvoreni pdf dokumenti mogu se otvoriti acrobat i adobe reader 5.0 i kasnijim verzijama.) /hun 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/pdfxoutputintentprofileselector /documentcmyk /preserveediting true /untaggedcmykhandling /leaveuntagged /untaggedrgbhandling /usedocumentprofile /usedocumentbleed false >> ] >> setdistillerparams << /hwresolution [2400 2400] /pagesize [612.000 792.000] >> setpagedevice microsoft word numero_59_art_37_3282.docx t. djedid et alii, frattura ed integrità strutturale, 59 (2022) 566-579; doi: 10.3221/igf-esis.59.37 566 analysis of workability, mechanical strength and durability by the ft-ir method of concrete based on silica-limestone sand preserved in aggressive environments tarek djedid laboratory of exploitation and valorisation of saharan energy resources " levres " department of hydraulic and civil engineering, faculty of technology, university of el-oued, 39000, algeria tarek-djedid@univ-eloued.dz mohammed mani department of hydraulic and civil engineering, faculty of technology, university of el-oued, 39000, algeria m.mani39@gmail.com abdelhamid guettala research laboratory in civil engineering « lrgc » university mohamed khider biskra, bp 145 rp, 07000 biskra, algeria guettalas@yahoo.fr abdelkader hima* department of electrical engineering, faculty of technology, university of el-oued, 39000, algeria abdelkader-hima@univ-eloued.dz, http://orcid.org/0000-0002-5533-3991 abstract. the interest of using combined sand of equal percentage of silica and limestone becomes evident in the formulation of compacted concrete in several previous works around the world due to the formidable percentage of fines that improves the compactness and increases various mechanical resistances, which produces a more durable construction against different probable aggressions. this paper examines the effect of using this type of sand on workability, compressive strength, flexural strength, and splitting tensile strength. a durability test was consulted using infrared spectroscopy to assess diverse types of hydration products formed. the obtained results show clearly the advantages of using sand with silica and limestone grains (50/50)% in ordinary concrete infected by aggressive water. there is also an improvement in compactness, different mechanical resistances, and a reduction in the formation of harmful hydration products. citation: djedid, t., mani, m., guettala, a., hima, a., analysis of workability, mechanical strength and durability by the ft-ir method of concrete based on silica-limestone sand preserved in aggressive environments, frattura ed integrità strutturale, 59 (2022) 566-579. received: 28.09.2021 accepted: 19.12.2021 published: 01.01.2022 copyright: © 2022 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. https://youtu.be/j6gurlx4gm0 t. djedid et alii, frattura ed integrità strutturale, 59 (2022) 566-579; doi: 10.3221/igf-esis.59.37 567 keywords. silica-limestone sand; concrete; workability; mechanical strength; infrared spectroscopy. introduction and is the second most used material in the world after water. fifteen billion tons of sand are extracted every year, mainly for construction (roads and concrete manufacturing). it takes 200 tons of sand to build a single house and 30.000 tons of sand for one kilometer of road [1]. in order to meet the growing needs, industrials are exploiting huge quarries, dredging rivers and seabed with sometimes disastrous ecological consequences. the increasing extraction of natural sand in riverbeds is causing many problems, losing water, deepening river courses and provoking bank slides, loss of vegetation on river banks, etc. [2, 3]. one of the adopted methods to reduce the environmental impact of the construction industry is the use of alternative raw materials [3-5] by partially or totally replacing the constituents of concrete in order to reduce the total cost of construction. aggregate properties affect the durability and performance of concrete, so fine aggregate is an essential component of concrete and cement mortar. the most commonly used fine aggregate is natural river sand. fine and coarse aggregate account for about 75% of the total volume of concrete [6]. it is therefore important to obtain an abundant alternative aggregate of good quality on site as the aggregate forms the main matrix of the concrete or mortar. one of the problems encountered in achieving adequate workability in concrete and mortar mixtures based on crushed limestone sand is the increased water demand. this adverse effect is mainly due to the presence of a high percentage of fines, the shape and texture of the crushed sand. this increase in water demand can be reduced by using super plasticizers [7-9]. cement and concrete of australia (ccaa) [10] indicates that the shape and texture of aggregate particles have a significant influence on the workability of freshly mixed concrete, as they affect the water demand and the water-cement ratio. t. shanmugapriya and r. n. uma [11] reported that the optimum percentage of replacement of natural sand with crushed limestone sand is 50%. the results also revealed that increasing the percentage of partial replacement of cement with silica fume increased the compressive and flexural strength of high performance concrete. puneeth, g. t. and mamatha, a [12] reported that the optimum percentage of manufactured sand and microsilica were 50% and 15% respectively. the concrete with this percentage of micro silica and manufactured sand has higher compressive, tensile and flexural strength than conventional concrete. nisnevich et al [13] showed that lightweight concrete containing thermal power plant rejects and quarry sand had a strength multiplied by 2 or more when the crushed sand was close to 50%. prakash, rao, and giridhar, kumar [14] deduced that concrete cubes containing crusher sand developed about 17% higher compressive strength, more than 7% higher tensile strength, and 20% higher flexural strength than concrete cubes and prisms with river sand as fine aggregate. vasumathi [15] examined the strength of concrete by partially replacing cement with fly ash and natural sand with quarry sand. it is concluded that there is a gain in strength at young age, but the strength does not increase at least after 28 days and workability decreases. there are other researchers who reported that the semi-substitution of river sand by crushed limestone sand participates in the reduction of the porosity of concrete and contributes to the improvement of its strength and durability. the southeastern region of algeria suffers from the penury of the river sands and the rising of groundwater phenomenon. in addition, waters in this region are loaded with chlorides (cl-) and sulphates (so4-2) and strongly affected the stability and durability of constructions. therefore, this work investigates the effects of the semi-substitution of river sand by crushed limestone sand (at the same w/c ratio and plasticity range) on several properties of fresh and hardened concrete. the performance and durability of the concrete formulation were evaluated through the measure of various parameters i.e. slump, density of fresh concrete, compressive strength, flexural strength, tensile strength, and infrared spectroscopy. materials cement he used cement in this experiment is of type cemi42.5n-lh/sr5 (sulfate resistant cement). it comes from the cement factory of ain el kebira, setif (algeria), whose physico-chemical and mineralogical characteristics are indicated in tab. 1. s t t. djedid et alii, frattura ed integrità strutturale, 59 (2022) 566-579; doi: 10.3221/igf-esis.59.37 568 aggregates two types of sand were used during this work; the first is a river sand (rs) that comes from the sand pit of asila sandpit (el meghaier, algeria), and the second is a crushed sand (cs) that is brought from the quarry refusals of ben brahim (hassi messoud, algeria). rs has a continuous particle size distribution ranging from 0.08 to 5 mm with a fraction of grains smaller than 0.08 mm is about 1%.however, the particle size of cs is altered between 0.08 and 3 mm with a proportion of grains smaller than 0.08 mm being about 17% (fig. 1). two types of gravels are used g1 (3/8) and g2 (8/16) of the same mineralogical source as cs. the main physicalmechanical and chemical characteristics of the used aggregates are presented in tab. 2. the mineralogical analysis by xrd shows us the siliceous nature of rs, and the essentially calcareous nature of cs (fig. 2). adjuvant the used admixture in this formulation is a brown super plasticizer with a high water reducer which makes it possible to obtain very high quality concretes and mortars. it is supplied by the company granitex and marketed under the name: medaplast sp 40, with a density of 1.20 ± 0.01, a ph of 8.2, and a chloride content ˂ 1g/l, in accordance with the standards nf en 934-2 and na 774. the authorized percentage by the manufacturer is 0.6 2.5% by weight of cement depending on the performance required. technical requirements of formulation the cement dosage is 400kg/m3 and the same strength class of concrete c 30/37 mpa has been chosen for all the studied formulations. the used method in the preparation of concrete is the graphical method of dreux gorisse [16]. two compositions of concrete were made in this context; the first is based on 50% substitution of river sand by crushed limestone sand [9] named c1, and the other is a control concrete c0 of 0% limestone sand to access the comparison. in order to choose a suitable percentage of w/c and super plasticizer, three w/c ratios were tested (0.4, 0.42, 0.43) and for each ratio, two percentages of super plasticizer were used (2 and 2.5% as upper limits allowed by the manufacturer). for the follow-up of this investigation, five time periods were proposed (28, 60, 90, 180, 360 days) in order to guarantee the effect of this formulation stored in a moderately aggressive environment (based on an equal percentage of fine siliceous and calcareous grains) on the different mechanical strengths and the results given by infrared spectroscopy. chemical composition (% wt) cao al2o3 sio2 fe2o3 na2o so3 k2o clir loss on ignition free cao 63.69 4.55 20.9 5.03 0.18 2.08 0.33 0.001 0.75 0.7 0.75 mineralogical composition (%) c3s c2s c3a c4af 67.35 9.42 3.33 16.2 physical and mechanical properties specific gravity (g/cm3) 3.22 blaine specific surface area (cm2/g) 3025 initial set (min) 185 final set (min) 285 consistency of cement paste (%) 25.09 strength class (mpa) 42.5 table 1: characteristics and composition of the used of cement. t. djedid et alii, frattura ed integrità strutturale, 59 (2022) 566-579; doi: 10.3221/igf-esis.59.37 569 type sand gravel rs cs cg 3/8 8/16 apparent volumetric mass (g/cm3) 1.65 1.44 1.43 1.40 absolute volumetric mass (g/m3) 2.55 2.55 2.72 2.45 fineness modulus 2.29 2.62 compactness (%) 62 56 52 57 porosity (%) 38 44 48 43 void ratio (%) 61 78 92 75 visual sand equivalent (%) 71.37 80.87 piston sand equivalent (%) 72.65 82.60 aggregate cleanness (%) 98.84 99.95 water absorption after 24 h (%) 2.13 4.1 2.38 3 flatness coefficient (%) 17 14 los angeles testing (%) 24 25 water content (%) 1.73 0.6 0.45 0.45 methylene blue test 1.5 0.8 table 2: physical, mechanical and chemical properties of aggregates. figure 1: size analysis of the studied aggregates. experimental procedures wo tests were carried out in the fresh state, the first is the abrams cone slump test according to the specification of en 12350-2 [17]. the other is the density determination test according to the recommendations of en 123506 [18]. the aim was to optimize the water and super plasticizer dosage to reduce the overall pore volume [19]. three types of moulds were used, 100×100×100 mm cubes for compressive strength, 70×70×280 mm prisms for flexural strength, and 110×220 mm cylinders for tensile strength (brazilian test). the execution of these mechanical strengths is performed according to the european standards, i.e. en 12390-3, en 12390-5 and en 12390-6 respectively [20-22]. t t. djedid et alii, frattura ed integrità strutturale, 59 (2022) 566-579; doi: 10.3221/igf-esis.59.37 570 (a) (b) figure 2: xrd analysis of investigated sands: (a) rs, (b) cs. ft-ir spectroscopy is a technique that is based on the interaction between ir radiation and a sample which can be solid, liquid or gas. it measures the frequencies at which the sample absorbs the radiation as well as the intensity of these absorptions. the frequencies are useful for identifying the chemical composition of the sample because the chemical functional groups are responsible for absorbing radiation at different frequencies. the concentration of a component can be determined from the absorption intensity. this test is performed at the laboratory of chemical research of the university of el oued at the age of 360 days. ft-ir spectra were recorded using a shimadzu iraffinity-1 spectrophotometer. the spectra of the concrete samples were recorded by grinding the samples into powder, mixing the powder with a small amount of kbr (potassium bromide) powder (0.198g kbr powder + 0.002g concrete) and compacting the mixture into a disk. specifically, the mid-infrared frequency range (4000 to 400 cm-1) with a resolution of 8 cm-1. thirty scans were recorded each time. environmental conditions to accelerate the degradation process, the concrete specimens are exposed to three chemically aggressive environments of water rising in three locations (named a, b, c) of el oued region (algeria) during one year. it should be noted that wetting-drying cycles are opted for after the first twenty-eight days of continuous immersion in drinking water, which represents a total of 22 wetting-drying cycles of up to 360 days. the concentrations of the chemical elements through these environments are represented in tab. 3. it is also worth mentioning that these environments can be considered as moderately aggressive environments xa2 [23]. the specimens are naturally dried in the open air, which was more relevant for the service conditions. a wet-dry cycle lasted 15 days. first, the specimens were continuously immersed in each environment for 7 days, and then were put in the open air to dry naturally for another 8 days [24,25]. designation of specimens and aggressive environments c0a, c0b, and c0c: ordinary concrete specimens based on river sand (siliceous) in each environment a, b and c subjected to wetting-drying cycles. c1a ,c1b, and c1c: ordinary concrete specimens based on 50% quarry sand (limestone) and 50% silica sand in each environment a, b and c subjected to wet-dry cycles. c1a ic, c1b ic, and c1c ic: ordinary concrete specimen based on 50% quarry sand (limestone) and 50% silica sand in each environment a, b, and c subjected to continuous immersion. environment a: rising waters from the chott area. environment b: rising waters from the sidi mastour area. environment c: rising waters from the sahane 1 area. t. djedid et alii, frattura ed integrità strutturale, 59 (2022) 566-579; doi: 10.3221/igf-esis.59.37 571 ph t sal ca+2 mg+2 nh4+ clrs hco3no3no2so4-2 °c ‰ mg/l env a 7.71 10-22 4.1 761.5 140.9 0.53 5739.8 4400 185.44 7.05 0.47 2610.81 env b 7.35 10-22 7.7 689.3 165.2 0.6 2290.2 10400 488 3.79 0.04 1119 env c 7.44 10-22 9.6 521.0 680.5 0.23 4956.3 7200 229.36 2.59 0.04 2120 table 3: physico-chemical characteristics of rising waters. results and analysis effect of substitution on workability rom the results of fig. 3, it is noticed that the slump rate increases with increasing water and super plasticizer dosages for both types of concrete. comparing the results of c0 and c1, it is undoubtedly stipulated that the shape of the grains and the nature of the texture are the most responsible for the workability of the concrete [26]. fig. 4 shows the high densification of c1 with w/c equals to 0.42 and the percentage of super plasticizer in relation to the weight of cement of 2.5%. on the other hand, the concretes c0 with w/c equal to 0.42 and sp percentages equal to 2%, 2.5% are almost comparable. this situation states that the ratio of w/c is 0.42 and the percentage of super plasticizer of 2.5% becomes the most suitable for this formulation. the workability of concrete is made with 50% substitution of river silica sand by crushed limestone sand which is much more influenced by the amount of water and super plasticizer they introduce due to the high specific surface area of the limestone fines. however, in order to keep a good densification and an excellent quality of the plastic concrete in accordance with the position of a more compact and durable concrete, it was necessary to choose the right volume of water and to increase the quantity of admixture until a workable mixture was obtained. figure 3: slump rate of c0 and c1 as a function of w / c and percentage of sp. figure 4: density of c0 and c1 as a function of e/c and percentage of sp. an excellent correlation equation (fig. 5) between the slump values and the specific weights is obtained in the fresh state of all the formulations tested with different w/c and super plasticizer dosage has the value y= 0.18x34.93x2 + 42.56x + 2304.6, and the correlation coefficient r2 = 0.95, where y represents the specific density values and x represents the slump values. this predictive equation has been adapted in the case of ordinary concrete based on alluvial sand or silicalimestone sand (50/50) % where w/c is between 0.4 0.43 and sp content is between 2 % and 2.5 %. f t. djedid et alii, frattura ed integrità strutturale, 59 (2022) 566-579; doi: 10.3221/igf-esis.59.37 572 figure 5: relationship between the slump values and the specific weights obtained in the fresh state. effect of substitution on mechanical strength: compressive strength compressive strength is an important characteristic of concrete and one of the main parameters of this research. the compressive strength has been measured at different times. it represents the average of the strengths of a series of three cubic specimens subjected to crushing. compressive strengths were monitored on 10x10x10 cm specimens subjected to alternating cycles of wetting-drying and continuous immersion in groundwater until the day of testing. fig. 6 shows the compressive strength values at different measurement times: 28, 60, 90, 180, and 360 days. figure 6: evolution of compressive strengths of different concretes in environment a, band c. the results show that the compressive strengths of c0, c1 and c1 ic concrete in all environments often increase with age and do not show any decrease except for a slight reduction of the compressive strength of c1 ic in environment a at the age of 360 days by 0.45% compared to that at the age of 180 days. when comparing the strength values at 360 days, c1 concretes have better compressive strengths than c0 (control) concretes in all environments. in fact, c1 concretes with a 50% limestone sand base and whatever the storage condition (c1 ic contained immersion, c1 wetting -drying) present a superiority in the development of mechanical compressive performance compared to the c0 control (wetting -drying) of the order of 1.40%, 0.73% in environment a , 4.84%, 3.74% in environment b and 18.82%, 13.89% in environment c respectively. the increase in compressive strength of c0a between 28 and 360 days (fig. 6) is due to the crystallization of new products in the voids of the interfacial transition zone by slow chemical reactions between the cement paste constituents and the aggregate, formation of calcium silicate hydrates in the case of siliceous aggregates. these interactions then contribute to the development of the strength over time [19]. t. djedid et alii, frattura ed integrità strutturale, 59 (2022) 566-579; doi: 10.3221/igf-esis.59.37 573 furthermore, the mechanical behavior of c1 concrete is constantly immersed in the aggressive waters of environments a, b and c and it is therefore better than the same concrete kept alternately. these results are in agreement with those found by the united states bureau of reclamation which states that the rate of degradation of an alternately immersed specimen for one year is equivalent to that degraded under continuous immersion for eight years [27-29]. in this case and up to the age of one year, the existence of 50% of limestone sand in the cement matrix is infected by aggressive species resulting from the phenomenon of rising water considerably, improves the compressive strength. this is due to the appropriate percentage of fines which promote capillary pore sealing and thus gradually increase the compressive strength. this was confirmed by priyanka [30] who proved that the substitution of 50% of natural sand by artificial limestone sand in the mortar mix, presents an excellent compressive strength especially with a w/c ratio equal to 0.5. another assertion was provided by adams [31] who said that the substitution of natural sand by 50% of crushed limestone sand in high performance concrete presents a better compressive strength of concrete. effect of substitution on mechanical strength: flexural strength fig. 7 shows the flexural strength values at the different ages mentioned above. the results indicate that most of the flexural strength values of the different types of concrete in all environments peak at the age of 180 days and then were decreased at the last maturity at 360 days with the exception of c0a and c1a ic of environment a, which peaked at the age of 60 days and c1c ic of environment c that shows its highest value at 90 days. these values can provide an overall indication of the intensity of aggressiveness of each environment. thus it can be said that environment a and c and especially a are more severe than environment b, as also shown in tab. 3. generally the values of the mechanical strength to compression and bending are more optimized in environment b, then in c respectively, while environment a is characterized by lower values than the other two mentioned above. in our investigation, we observed optimum values of flexural strength of c1 type concrete in all environments at the age of 180 days, of the order of 11, 10.38 and 7.98 mpa respectively in a,b, and c. these figures no longer persist and will be reduced by 38.36%, 23.12%, and 1.12% successively at age 360 days. this scenario explains that the hydration products, especially c-s-h and ch evolved gradually, until that time, the harmful hydration products like monosulfoaluminate will be enlarged and occupy space at the interfacial transition zone between aggregate and paste [32-34] which finally decreases the flexural strength. it has been observed that the increase in 180 day flexural strength of c1b, c1c, may be due to the additional and continuous formation of caco3 during wetting-drying periods. for this reason, some researchers found that the reaction between the amount of caco3 and the minerals in the cement, in particular c3a, c4af, produces a solid compound (c3a.caco3.11h2o) [6, 19]. at the age of 360 days, c1 concrete is better than c0 in all environments, the results clearly show that the flexural strengths of different types are almost comparable in environment a. while in b, c1 and c1 ic concretes show an increase in flexural strength of 12.55 % and 4.83% compared to c0. similarly, c1c and c1c ic showed an increase of 15.51% and 10.98% compared to c0. figure 7: evolution of flexural strengths of different concretes in the environment a, b and c. t. djedid et alii, frattura ed integrità strutturale, 59 (2022) 566-579; doi: 10.3221/igf-esis.59.37 574 effect of substitution on mechanical strength: tensile strength fig. 8 describes the evolution of the splitting tensile strength over time. the results show that the concrete c1 reached a peak at the age of 28 days in all the environments, then the resistances of the same type of concrete were decreased over time and they were recovered again at the last deadline. however, the c0 concrete marked its high value in a at the same time as c1. on the other hand, in the b and c environment, it showed an improved resistance at 90 days. this study allows us to compare the different splitting tensile strength by an obtained splitting at the beginning and at the end of the deadlines. it was found that the concrete c1 has evolved 8.95%, 40.62% and 9.38% at 28 days as well as 8.44%, 15.59% and 1.80% at 360 days in a, b, and c respectively compared to the control concrete. fig. 8 shows us in another way that the c1 specimens kept in environment b present results superior to the order of 4.95 mpa and 4.3 mpa at 28 and 360 days in succession compared to the other specimens in the other environments. the results of the previous paragraph confirm once again that environment b favors the good hydration of cement compared to a and c. this situation is in agreement with those given in tab. 3. figure 8: evolution of tensile strengths of different concretes in the environment a,b and c. effect of substitution on durability by ft-ir spectroscopy he ft-ir spectra (fig. 9, 10, 11) of all 360-day-old samples are almost similar. the main absorption bands in all samples in various environments are presented as the following: the ir spectra of these 360-day old samples implanted in environment a are shown in fig. 9. first, signals are due to ettringite, s-o at 1118 cm-1 of sample c0a, c1a and c1a ic and at 420 cm-1 for c0a, as well as o-h at 3410 cm-1 for all samples can be seen [35-37]. there were also o-h bands from sample c0a,c1a ic at 1029 cm-1 due to aluminate hydration products, c3ah6 [38] and an o-h absorption band at 428,459 cm-1 due to alo6 at c1a and c0a respectively [36]. the infrared spectra of the composition of the study concretes (fig. 9), indicate that the bands associated with different forms of gypsum were evident. thus, the present spectra, in addition to the main band s-o of ettringite at 1118 cm-1, another absorption of s-o at 601, 671 cm-1 for c1a and c1a ic and 601, 667 cm-1 from c0a explains the existence of gypsum. another signal of the latter mineral of s-o band located at 1620 cm-1 between the two mixtures and regardless of the environment indicates bassanite (2caso4.h2o) [35].the results also show another s-o band at 1103 cm-1 of hemihydrates at c1a [39]. an o-h band of aluminate hydration products, c3ah6 is found at 1029 cm-1 within sample c0a and c1a ic. in addition the 459 cm-1 band due to alo6 observed within sample c0a[36]. the absorption bands are observed for calcium carbonate phases are due to co3-2 ion were numerous which are presented at 713, 875,1377, 1423,1797 and 2511 cm-1of the c0a mixture and 709, 798, 875, 1392, 1435, 1465, 1477, 1797, 2511, 470, and 497 cm-1 of the c1a compound, finally the signals of c1a under continuous immersion (ci) are: 709, 798, 875, 1419,1797, and 2511 cm-1 [36]. t. djedid et alii, frattura ed integrità strutturale, 59 (2022) 566-579; doi: 10.3221/igf-esis.59.37 575 figure 9: infrared spectroscopies of c0a, c1a and c1a ic concrete at 360 days of age. concerning the environment b (fig. 10), the ft-ir spectroscopy does not present any significant difference, the signals which are due to ettringite s-o are always met at 1118 cm-1 in all the samples, and at 2191 cm-1[40] of band o-h in c0b. one notices in this stage that the environment b is less infected by ettringite and gypsum. indeed, the specters of gypsum in the various samples are located at the s-o bands: 601, 671 cm-1 as well as another at 1620 cm-1 representing the bassanite. the o-h bands of aluminate hydration products, c3ah6 are found at: 1029, 1026 and 3525 cm-1 of c0b, c1b ic and all samples respectively. another additional o-h band is found at 3406 cm-1 indicates the existence of bayerite al(oh)₃ in all samples, in addition to the 459 cm-1 band that is due to alo6 [36]. finally, the caco3 spectra are distributed at bands 713, 779, 875, 1427, 1797 and 2515 cm-1 for the c0b mixture and 713, 779, 798, 875, 1419, 1797, and 2515 cm-1from c1b and c1b ic. from the environment c (fig. 11), it is confirmed once again that the spectral behavior of the tested samples is much more similar than those of environments a and b. initially, it can be said that the signals of the obtained ettringite are grouped in the following bands: a band s-o at 1118 cm-1 represented in all the tested samples. others are noticed within the o-h bands at 2198, 2191, 3417, and 3410 cm-1, the first and the last band show the fines of the c0c and c1c ic concrete as well as the two intermediary ones, illustrate the c1 concrete. the s-o gypsum bands are localized as it has been seen before at the following regions: 601, 671, and 1620 cm-1 in the different samples. the compound c3ah6 is observed within the o-h bands: 1029, 3525, and 3545 cm-1, the first one indicates c0c concrete, c1c ic and the last two show c0c concrete. bayerite al(oh)₃ is found at the o-h band at 3406, 3545cm-1 regions of the c0c sample. the alo6 band is restricted to 459, 416 cm-1 within the c0c and c1c samples. t. djedid et alii, frattura ed integrità strutturale, 59 (2022) 566-579; doi: 10.3221/igf-esis.59.37 576 figure 10: infrared spectroscopies of c0b, c1b and c1b ic concrete at 360 days of age. the caco3 spectra are equally distributed at the co3-2 bands: 713, 779, 875, 1427, 1797, 1863, and 2511 cm-1 for the c0c mixture. in addition peaks found at the regions: 713, 775, 875, 1006, 1033, 1427, 1797, and 2515 cm-1 characterizes the c1c concrete and finally the c1c ic mixture also shows that the peaks are localized at the following locations: 713, 779, 875, 1396, 1446, 1469, 1797, and 2511 cm-1. generally and in all environments, it was noticed that more intense peaks (signals) of ettringite and gypsum in the c0 samples. the calcite are in great quantity resulting from the conversion of ca(oh)2 to caco3. this finding certainly indicates the advantage of using concrete that it based on an equal percentage of limestone sand and silica sand than ordinary concrete that are based on silica sand in a chemically aggressive environment. conclusion he use of half of the sand in a concrete formulation as sand from limestone crushing gives favorable results compared to conventional concrete. after this study, the following remarks can be drawn:  the concrete based on 50% river sand and 50% crushed limestone sand gains the best specific weight according to a well chosen plasticity range. t t. djedid et alii, frattura ed integrità strutturale, 59 (2022) 566-579; doi: 10.3221/igf-esis.59.37 577 figure 11: infrared spectroscopies of c0c, c1c and c1c ic concrete at 360 days of age.  a statistical correlation was obtained when measuring the workability and the corresponding specific weight with coefficient r2 = 0.95. this polynomial form approach can give a preliminary indication of the compactness during the measurement of the workability.  in the rising water table and in any studied environment in this investigation, the underground structures that are built with silica-limestone sand show higher mechanical strength compared to those built with natural river sand.  the followed policy for the degradation of the samples is based on the use of alternative cycles of wetting-drying is very interesting and proves that the continuous immersion favors a good chemical hydration of c-s-h and ch and generates good mechanical strengths of all the elaborated samples.  intense harmful hydration products were created from the conventional concrete compared to the studied concrete such as ettringite and gypsum.  increased number of ettringite and gypsum peaks and other aluminate products in control samples compared to silica-limestone sand concrete (50/50) %.  the positive effect of limestone in sand based concrete of equal percentage of silica and limestone was certainly noticed by the formation of a whitish layer on the outer surface of the specimens, which also creates a barrier against the infiltration of aggressive agents inside the concrete.  the limestone grains are cheaper and available compared to the silica ones, which are in strong daily decline. this solution helps to decrease the overall cost of the works and preserve the environment. t. djedid et alii, frattura ed integrità strutturale, 59 (2022) 566-579; doi: 10.3221/igf-esis.59.37 578 nomenclature rs river sand cs crushed sand xrd x-ray diffraction c 30/37 compressive strength class 30/37 w/c water/cement ratio cg crushed gravel g1 gravel (3/8) g2 gravel (8/16) ft-ir fourier-transform infrared spectroscopy xa2 moderate aggressive environment sp superplasticizer references [1] alger, e.n.g.(1999). document: sable la nouvelle donne, algérie, pp. 01-05. [2] ahmad, s. and mahmood, s. (2008). effects of crushed and natural sand on the properties of fresh andhardened concrete. in: 33rd conference on our world in concrete and structures, singapore, 100033006. [3] elavenil, s., vijaya, b. and hariharan, k. (2005). manufactured sand, a solution and an alternative to river sand and in concrete manufacturing. j eng comput appl sci (jec&as), 2(2), pp. 20–24. [4] mounir, l. and idrees, z. (2019). effect of total substitution of crushed limestone sand on concrete durability, european journal of environmental and civil engineering. doi: 10.1080/19648189.2019.1649199. [5] ahmed ahmed, e. and ahemed kourd, a. e. (1989). properties of concrete incorporating natural and crushed stone very fine sand, aci material journal, 86(4), pp. 417-424. [6] neville, a. m. (1995). properties of concrete. fourth edition, england, longman, pp.844. [7] chi, c., wu, y. and riefler, c. (2004). the use of crushed dust production of self consolidating concrete (scc), recycling concrete and other materials for sustainable development.aci symposium, 219, pp. 115-130. [8] kenai, s., benna, y. and menadi, b. (1999). the effect of fines in crushed calcareous sand on properties of mortar and concrete. proceedings of the international conference on infrastructure regeneration and rehabilitation, sheffield, pp. 253-261. [9] djedid, t., guettala, a. and mani, m. (2019). study of the workability and mechanical strength of concrete in the face of upwelling (case of the el oued region of algeria. j fundam appl sci. 11(1), pp. 368-384. doi: 10.4314/jfas.v11i1.24. issn 1112-9867. [10] ccaa, t 60. (2008). guide to the specification and use of manufactured sand in concrete, australia, cement concrete aggregate, pp. 1-15. [11] shanmugapriya, t. and uma, r. n. (2012). optimization of partial replacement of m-s and by natural sand in high performance concrete with silica fume. int j eng sci emerg technol, 2(2), pp.73-80. [12] puneeth, g. t., mamatha, a. (2016).an experimental investigation on the strength of concrete by partial replacement of cement with micro silica and naturel sand with manufactured sand. international journal of civil and structural engineering research, 3 (2), pp. 52-57. [13] nisnevich, m., sirotin, g. and eshel, y.(2003). light weight concrete containing thermal power station and stone quarry waste, magazine of concrete research, 55, no. 4, pp. 313-320. doi:10.1680/macr.2003.55.4.313. [14] prakash, rao. d. s. and kumar, v. g. (2004). investigations on concrete with stone crusher dust as fine aggregate. indian concrete journal, 78(7), pp. 45-50. [15] vasumathi, a.m. (2003). a study on the strength of the concrete by partial replacement of cement with fly ash and sand with quarry dust, proceedings of national seminar on futuristics in concrete and construction engineering, s.r.m engineering college, chennai, pp. 8-14. [16] dreux, g. and jean, festa. (1998). nouveau guide du béton et de ses constituants. paris, eyrolles. p. 416. [17] en 12350-2. (1999). essais pour béton frais partie 2: essais d'affaissement. institut de normalisation, serbie. [18] en 12350-6. (1999). essai pour beâton frais partie 6: masse volumique. institut de normalisation, serbie. [19] neville, a. and brooks, j.j. (2010). concrete technology.second edition. isbn.978-0-273-73219 8(pbk). t. djedid et alii, frattura ed integrità strutturale, 59 (2022) 566-579; doi: 10.3221/igf-esis.59.37 579 [20] nf en 12390-3. (2003). essai pour béton durci – partie 3: résistance à la compression des éprouvettes, france, afnor. [21] nf en 12390-5. (2001). essai pour béton durci – partie 5: résistance à la flexion sur éprouvettes, france, afnor. [22] nf en 12390-6. (2000). essai pour béton durci partie 6: résistance en traction par fendage d'éprouvettes, france, afnor. [23] nf en 206-1. (2004). béton partie 1: spécification, performances, production et conformité, france, afnor. [24] lei, jiang, a. and ditao, n. b. (2016). study of deterioration of concrete exposed to different types of sulfate solutions under drying-wetting cycles. construction and building materials, 117, pp. 88 – 98, doi: 10.1016/j.conbuildmat.2016.04.094 0950-0618/_ 2016 elsevier ltd. [25] ahmed, m. d., abd elmoaty, m., and ayman, a. aly.(2016). long term study of mechanical properties, durability and environmental impact of limestone cement concrete. alexandria eng. j.55 (2), pp. 1465-1482, doi: 10.1016/j.aej.2016.01.031. [26] swapnil, s. f. (2014). concrete with smart material (manufactured crushed sand)a review. international conference on advances in engineering & technology. journal of mechanical and civil engineering, 6(11), pp. 2729. [27] kamali, s., gerard, b., and moranville, m. (2003). modelling the leaching kinetics of cement based materials-influence of materials and environment. cem concr compos; 25, pp. 451–458. doi: 10.1016%2fs0958-9465(02)00085-9. [28] agostini, f., lafhaj, z., skoczylas, f. and loodsveldt, h. (2007). experimental study of accelerated leaching on hollow cylinders of mortar. cem. concr. res., 37, pp. 71–78. doi: 10.1016/j.cemconres.2006.09.018. [29] bederina, m., makhloufi, z., bounoua, a., bouziani, t., queneudec, m. (2013). effect of partial and total replacement of siliceous river sand with limestone crushed sand on the durability of mortars exposed to chemical solutions, construction and building materials, 47, pp.146–158. doi: 10.1016/j.conbuildmat.2013.05.037. [30] priyanka, a.j. and dilip, k. k. (2013). effect of replacement of natural sand by manufactured sand on the properties of cement mortar. international journal of civil and structural engineering, 3, pp. 621-628. doi: 10.6088/ijcser.2 201203013057. [31] adams, j.m., rajesh, a.m., brightson, p. and anand, m.p. (2013). experimental investigation on the effect of msand in high performance concrete, american journal of engineering research (ajer); v 02, pp. 46-51. [32] kumar mehta, p. and monteiro, p. j. m. (2006). concrete microstructure, properties, and materials, third edition, new york, mcgraw-hill. doi: 10.1036/0071462899. [33] tokyay, m. (2016). cement and concrete mineral admixtures, middle east technical university, ankara, turkey, crc press. taylor & francis group, p.325. [34] mani, m., bouali, m. f., kriker, a. and hima, a.(2021).experimental characterization of a new sustainable sand concrete in an aggressive environment,frattura ed integrità strutturale, 55 (1), pp.50-64, doi: 10.3221/igf esis.55.04. [35] fernandez-carrasco, l., torrens-martin, d., morales, l.m. and martinezramirez, s. (2012). infrared spectroscopy in the analysis of building and construction materials. in: infrared spectroscopy—materials science, engineering and technology. london, intech open edition, pp. 369–382. [36] trezza, m.a. and lavat, a. (2001). analysis of the system 3cao.al2o3-caso4.2h2o-caco3-h2o by ft-ir spectroscopy. cement and concrete research 31, pp. 869-872, doi: 10.1016/s0008-8846(01)00502-6. [37] djedid, t. (2020). effet de la substitution du sable de rivière par du sable de carrière sur la durabilité des bétons à base de différents ciments algériens dans des environnements chimiques. thèse de doctorat en génie civil. univ biskra. 213p. [38] fernandez-carrasco, l. and vazquez, t. (1996). aplicacion de la espectroscopia infrarroja al estudio del cemento aluminoso. mater. constr., 46, pp. 53–65. doi: 10.3989/mc.1996.v46.i241.540. [39] mandal, p. k. and mandal, t. k. (2002). anion water in gypsum (caso4-2h2o) and hemihydrate (caso4-1/2h2o). cem. concr. res.,3 2, pp.313–316. [40] ramachandran, v. s. and beaudoin, j. 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/hrv (za stvaranje adobe pdf dokumenata najpogodnijih za visokokvalitetni ispis prije tiskanja koristite ove postavke. stvoreni pdf dokumenti mogu se otvoriti acrobat i adobe reader 5.0 i kasnijim verzijama.) /hun 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can be opened with acrobat and adobe reader 5.0 and later.) >> /namespace [ (adobe) (common) (1.0) ] /othernamespaces [ << /asreaderspreads false /cropimagestoframes true /errorcontrol /warnandcontinue /flattenerignorespreadoverrides false /includeguidesgrids false /includenonprinting false /includeslug false /namespace [ (adobe) (indesign) (4.0) ] /omitplacedbitmaps false /omitplacedeps false /omitplacedpdf false /simulateoverprint /legacy >> << /addbleedmarks false /addcolorbars false /addcropmarks false /addpageinfo false /addregmarks false /convertcolors /converttocmyk /destinationprofilename () /destinationprofileselector /documentcmyk /downsample16bitimages true /flattenerpreset << /presetselector /mediumresolution >> /formelements false /generatestructure false /includebookmarks false /includehyperlinks false /includeinteractive false /includelayers false /includeprofiles false /multimediahandling /useobjectsettings /namespace [ (adobe) (creativesuite) (2.0) ] /pdfxoutputintentprofileselector /documentcmyk /preserveediting true /untaggedcmykhandling /leaveuntagged /untaggedrgbhandling /usedocumentprofile /usedocumentbleed false >> ] >> setdistillerparams << /hwresolution [2400 2400] /pagesize [612.000 792.000] >> setpagedevice microsoft word numero_63_art_23_3679.docx v. loginov et alii, frattura ed integrità strutturale, 63 (2023) 301-308; doi: 10.3221/igf-esis.63.23 301 metallurgical hydrogen as an indicator and cause of damage of rolled steel victor p. loginov, vladimir a. polyanskiy, yuriy a. yakovlev institute for problems in mechanical engineering of the russian academy of sciences, russia lvp@ipme.ru vapol@mail.ru; http://orcid.org/0000-0002-1199-1028 yura.yakovlev@gmail.com; http://orcid.org/0000-0002-5041-0441 anatoly m. polyanskiy rdc electron and beam technologies, russia ampol@electronbeamtech.com; http://orcid.org/0000-0002-6470-9583 vecheclav m. olekov, grigory n. rostovykh research institute of bridges and defectoscopy, russia olekov48@mail.ru, g@rostovykh.com abstract. fatigue tests and measurements of the volumetric distribution of metallurgical hydrogen in specimens cut from rolled i-beam 60sh3 made of steel 10khsnd were carried out. fatigue tests show a 20% reduction in fatigue limits compared to similar sheet material. on the fractures of the samples, there are flock-like defects in the areas of interface of the flanges of the i-beam or in the so-called zones of difficult deformation. the concentration of metallurgical hydrogen is unevenly distributed and varies from 0.17 ppm to 1.8 ppm. large concentrations of hydrogen are observed in the zones of difficult deformation, which indicates the hydrogen nature of the metal defects observed at the fracture. the result of mechanical tests and hydrogen diagnostics is a manufacturing defect of rolled products that cannot be corrected. hydrogen diagnostics using metallurgical hydrogen (without hydrogen charging samples) requires essentially less time than mechanical tests and yields the adequate result. keywords. i-beam, fatigue, hydrogen diagnostics, metallurgical hydrogen. citation: loginov, v. p., polyanskiy, v. a., yakovlev, y. a., polyanskiy, a. m., olekov, v. m., rostovykh, g. n., metallurgical hydrogen as an indicator and cause of damage of rolled steel, frattura ed integrità strutturale, 63 (2023) 301-308. received: 15.07.2022 accepted: 03.10.2022 online first: 16.12.2022 published: 01.01.2022 copyright: © 2023 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. introduction he strong influence of hydrogen on the mechanical properties of structural metals has been studied for about 150 years. as a rule, all studies of this effect on metals include preliminary saturation or "charging" of samples with hydrogen in a hydrogen-containing environment. such saturation is standardized [1-3]. tests for hydrogen t https://youtu.be/58ibni_cafc v. loginov et alii, frattura ed integrità strutturale, 63 (2023) 301-308; doi: 10.3221/igf-esis.63.23 302 induced cracking or resistance to hydrogen cracking are also standard [4]. the study of the effect of natural, so-called "metallurgical" hydrogen, has long passed into the field of industrial testing [6] and is currently being studied only in the weld metal [7, 8]. in other cases, for each type of alloy there are maximum allowable concentrations of hydrogen which are controlled, most often, directly in the molten metal at the production stage. we do not have information about modern scientific research on "metallurgical" hydrogen and its effect on the mechanical properties of metals. as a rule, the hydrogen concentration changes significantly at various processing stages: crystallization of ingots, rolling, forging. this is the general practice of a single control for each type of products. for example, during the production of steel products it is controlled only in the melt, during the production of aluminum it is controlled only in the ingot. it is also difficult to find studies on the effect of hydrogen on the deformation and destruction of structural metals in a conventional "non-aggressive" environment. at the same time, over the years that have passed since the discovery of the hydrogen problem, the influence of hydrogen dissolved in metals on its mechanical properties has greatly increased. modern structural alloys begin to “feel” this effect starting from hydrogen concentrations of 0.1 ppm [9]. it is generally accepted that hydrogen is located inside the metal in traps of various nature [10]. in this case, each type of trap corresponds to a certain binding energy of hydrogen [11]. the most popular procedure for measuring the degree of occupancy of traps with hydrogen and their binding energies is based on the method of thermal desorption spectra (tds) [12], which is lengthy and is almost never applied to “metallurgical hydrogen”, since it is too small to measure the spectrum [13]. these difficulties lead to the fact that all hydrogen accumulated in the metal is usually divided into two classes: diffusible hydrogen and bound hydrogen. together they form the total hydrogen concentration. there is no single approach in the methods of dividing hydrogen into diffusible and bound ones. the standard [5] defines diffusible hydrogen with the help of the method of its extraction. “the primary method for the measurement of diffusible hydrogen in ferritic arc weld metal is based upon collection and measurement, over mercury, of the hydrogen evolved from a standard-sized weld sample. the evolution takes place at room temperature and consequently the collection time is typically about 14 d.” in other sources, it is considered to be hydrogen with a binding energy or diffusion activation energy of less than 0.3 0.4 ev cf.[14]. it is postulated in [15] that the diffusible h content is determined by hot extraction at 300oc. in our work [16], we showed that using the model of multichannel diffusion of hydrogen in a solid it is possible to determine the distribution of its concentration over binding energy levels based on the results of standard measurements by the hot vacuum extraction method. the av-1 industrial mass-spectrometric analyzer of hydrogen makes it possible to obtain the dependence of hydrogen flows from metal samples on time. this relationship is referred to as the extraction curve. the volume of hydrogen is proportional to the integral of the flow (of the extraction curve). we have shown that the uniform distribution of hydrogen inside the sample is associated with a certain energy level of the hydrogen bond in each peak., see [16]. thus, metallurgical hydrogen has several diagnostic features at once: total concentration, population of various energy levels or distribution of concentration by binding energy levels, the form of the distribution of the total, diffusible and bound hydrogen concentration inside the metal. the relationship of these features with the mechanical state of structures will allow the development and practical application of hydrogen diagnostics of structural metals. materials and experimental equipment echanical fatigue tests and studies of the distribution of hydrogen in the material of the rolled i-beam no. 60sh3 from steel 10khsnd were carried out. the chemical composition of steel is given in tab. 1. c si mn ni s p cr n cu as fe 0.12 0.8-1.1 0.5-0.8 0.5-0.8 < 0.04 < 0.035 0.6-0.9 < 0.008 0.4-0.6 < 0.04 96 table 1: chemical composition (in%) of steel 10khsnd. for mechanical testing, 12 standard corset samples were cut from the lower and upper flanges of the i-beam with the length, width and thickness of the working part 420x75x40 mm3. the main dimensions of the samples are shown in fig.1. m v. loginov et alii, frattura ed integrità strutturale, 63 (2023) 301-308; doi: 10.3221/igf-esis.63.23 303 the thickness of the lower and upper flanges of the beam is 24 mm; therefore, a part of the vertical flange about 15 mm high was preserved on the samples. figure 1: corset test sample cut from the i-beam flange. fatigue tests were carried out on a cdm-200 pu pulsator press (see fig. 2.) at a frequency of 324 cycles per minute based on 2 million load cycles. the cycle characteristic for all the samples is as follows 0.1 min max      here min , max are the minimal and maximal tension stresses. the stresses in the samples during the tests were determined by the tensometric sensors and the test load. figure 2: tests of a corset specimen cut from the i-beam flange for comparison, the similar corset samples were made and tested from rolled sheet steel 10khsnd with a thickness of 30 mm. to measure the distribution of hydrogen concentration in the metal of the i-beam, an industrial mass-spectrometric hydrogen analyzer av-1 was used. it is designed to measure the hydrogen concentration in metals and alloys in the factory laboratory during the final control of castings from various alloys [16-18]. for measurements, prismatic samples were cut out with dimensions of 6x6x25 mm3 or 6x6x40 mm3 (depending on the thickness of the metal). the cutting of samples for measuring the distribution of hydrogen concentration was carried out with a hand saw so that their temperature did not rise higher than 50 – 60oc. one set of samples was cut from the corset sample (i-beam) which collapsed during testing at the clamping point (the fracture line is shown schematically in fig. 1). the scheme of sample cutting is shown in fig. 3. samples in which the hydrogen measurements were carried out are marked on the diagram with the symbol “x”. v. loginov et alii, frattura ed integrità strutturale, 63 (2023) 301-308; doi: 10.3221/igf-esis.63.23 304 figure 3: scheme of cutting samples for the analysis of hydrogen content. we also studied the distribution of hydrogen concentrations over the cross section of the i-beam "as is" without preloading. the scheme of sampling (cutting samples) is shown in fig. 4. figure 4: scheme of sampling (cutting samples) from the i-beam experimental results he dependences of the maximum applied mechanical stress on the number of the test cycles for specimens cut from the i-beam and specimens cut from a sheet are shown in fig. 5. an analysis of the fracture surfaces of samples made from 60sh3 beams indicates the presence of defects in all tested samples (see fig. 6.). no defect was observed in the samples cut from a 30 mm sheet. fig. 7 shows the distribution of hydrogen concentrations over the area of the sample destroyed at the clamping point (the sampling scheme is shown in fig. 3). points 1 and 11 correspond to the left and right borders of the sample, respectively. the distribution of hydrogen over the cross section of the i-beam was measured according to the cutting scheme. (see fig. 4.). the map of the positions of samples with color-coded hydrogen concentrations is shown in fig. 8. t v. loginov et alii, frattura ed integrità strutturale, 63 (2023) 301-308; doi: 10.3221/igf-esis.63.23 305 figure 5: test results of specimens cut from i-beam 60sh3 flanges and from 30 mm rolled sheet. figure 6: photograph of fracture of a sample cut from the i-beam. figure 7: distribution of total hydrogen concentrations ch in a sample cut from the i-beam after its break, see fig.3 for the sample’s code. v. loginov et alii, frattura ed integrità strutturale, 63 (2023) 301-308; doi: 10.3221/igf-esis.63.23 306 figure 8: distribution map of the total hydrogen concentration ch over the cross section of the i-beam. discussion of results ll defects on the fractures of the samples are concentrated in the so-called zone of difficult deformation, where the metal is deformed with the lower compression forces. the causes of these defects may include: poor calibration of rolls of section rolling mills, insufficient heating of the metal before hot rolling, cooldown of the metal during rolling on the last passes in the finishing stands, violation of the regime of hot plastic deformation by rolling, high concentrations of hydrogen in the metal unevenly distributed in the slab. this manufacturing defect is final and cannot be eliminated by any heat treatment, without plastic deformation. the distribution of hydrogen both over the cross section of the i-beam and over the area of the flange is extremely uneven. it significantly exceeds the average level in zones of complex strain (see fig. 7.8). we can unambiguously say that the cause of defects at the sample fracture is the hydrogen porosity. in the most technical requirements and specifications for structural steels, the concentration of hydrogen in rolled products is not standardized; the hydrogen control is carried out on a sample of about 15 g cut from the molten metal. such an approach, as this study shows, does not fully characterize the quality of the rolled products because of the multiple difference in the measured values of hydrogen concentration in the cold products. the uneven distribution of hydrogen concentrations in the cold metal can be associated with the distribution of non-metallic particles that could not be removed from the molten metal due to their adhesion to small hydrogen bubbles. this phenomenon is especially important in the case of extensive metal recycling and requires additional research. due to the standard requirements the maximum permissible concentration of hydrogen in steels is normalized at the level of 2-4 ppm. but it is necessary to consider the specifics of sampling during the standard industrial testing. very rarely, the measurements of hydrogen concentration are carried out in solid cold rolled products. the data of numerous studies [8,19-22] show that the hydrogen concentration 0.5 1.5 ppm in the cold metals is critical for the strength of modern structural steels, [8,20]. mechanical testing is very time consuming. for example, in this study each of the 12 samples was tested from 12 to 96 hours depending on the number of load cycles. due to the large scatter of fatigue test results, at least four samples are needed to obtain the average results. hydrogen diagnostics is much faster and cheaper, the time for measuring the hydrogen concentration in one sample is about an hour, and the same statistical reliability is reached ten times faster. in this study, we used the total hydrogen concentration as the single indicator. the distribution over binding energies can provide additional information, [17]. for example, diffusive hydrogen in steels is much more dangerous for the mechanical characteristics of the metal than the bound hydrogen, and its concentrations in the zone of localization of structural defects can be tens times higher than the average values. conclusions a v. loginov et alii, frattura ed integrità strutturale, 63 (2023) 301-308; doi: 10.3221/igf-esis.63.23 307 comprehensive study of a rolled steel i-beam was carried out consisting of the fatigue tests and the hydrogen diagnostics. the distribution of hydrogen concentrations over the volume of the i-beam is measured. the dependences of the cyclic maximum mechanical stresses on the number of load cycles to the destruction of corset specimens cut from the i-beam were obtained. we observe a good correlation between zones of the high hydrogen concentration and the places of sample fracture. high hydrogen concentrations explain both the defect nature and decrease in the fatigue limits of the metal in 60sh3 beam compared to the sheet. technical testing using the hydrogen diagnostics is faster and cheaper than the traditional mechanical testing. this indicates the advantages of hydrogen diagnostics. the data obtained from studies of industrial rolled products indicate the insufficiency of monitoring the concentration of hydrogen in samples from the molten metal. references [1] iso11114-4:2017, (2017). test methods for selecting metallic materials resistant to hydrogen embrittlement. international organization for standardization. https:// www.iso.org/standard/64587.html. [2] iso16573:2015, (2015). steel measurement method for the evaluation of hydrogen embrittlement resistance of high strength steels. international organization for standardization. https://www.iso.org/standard/57128.html. [3] tm0284-2106-sg, (2016). evaluation of pipeline and pressure vessel steels for resistance to hydrogen-induced cracking. ansi/nace standard, nace international, houston, tx. https://store.nace.org/ansi-nace-tm0284-2016. [4] iso 3690^2018, (2018)/ welding and allied processes determination of hydrogen content in arc weld metal. international organization for standardization url: https://www.iso.org/standard/72150.html. [5] hassel, a., merzlikin, s., mingers, a., georges, c., flock, j., bergers, k., tomandl, a., muhr, a. and zwettler, f., (2013). methodology of hydrogen measurements in coated steels, luxembourg, publications office of the eu. doi: 10.2777/10253. [6] klett, j., mattos, i. b., maier, h. j., e silva, r. h. and hassel, t. (2021). control of the diffusible hydrogen content in different steel phases through the targeted use of different welding consumables in underwater wet welding. mater. corros., 72(3), pp. 504-516. doi : 10.1002/maco.202011963. [7] brätz, o., klett, j., wolf, t., henkel, k. m., maier, h. j. and hassel, t. (2022). induction heating in underwater wet welding—thermal input, microstructure and diffusible hydrogen content. materials, 15(4), 1417. doi: 10.3390/ma15041417 [8] wang, m., akiyama, e. and tsuzaki, k. (2007). effect of hydrogen on the fracture behavior of high strength steel during slow strain rate test. corrosion science, 49(11), pp. 4081-4097. doi: 10.1016/j.corsci.2007.03.038. [9] oriani, r. a. (1970). the diffusion and trapping of hydrogen in steel. acta metallurgica, 18(1), pp. 147-157. doi : 10.1016/0001-6160(70)90078-7. [10] hirth, j.p. (1980).effects of hydrogen on the properties of iron and steel. metall. mater. trans. a 11, pp. 861–890. doi: 10.1007/bf02654700. [11] kissinger, h. e. (1957). reaction kinetics in differential thermal analysis. analytical chemistry, 29(11), pp. 1702-1706. doi: 10.1021/ac60131a045. [12] tapia-bastidas, c. v., atrens, a. and gray, e. m. (2018). thermal desorption spectrometer for measuring ppm concentrations of trapped hydrogen. int. j. hydrog. energy, 43(15), pp. 7600-7617. doi: 10.1016/j.ijhydene.2018.02.161. [13] park, i. j., jeong, k. h., jung, j. g., lee, c. s. and lee, y. k. (2012). the mechanism of enhanced resistance to the hydrogen delayed fracture in al-added fe–18mn–0.6c twinning-induced plasticity steels. int. j. hydrog. energy, 37(12), pp. 9925-9932. doi: 10.1016/j.ijhydene.2012.03.100. [14] depover, t. and verbeken, k. (2018). the detrimental effect of hydrogen at dislocations on the hydrogen embrittlement susceptibility of fe-cx alloys: an experimental proof of the help mechanism. int. j. hydrog. energy, 43(5), pp. 3050-3061. doi: 10.1016/j.ijhydene.2017.12.109. [15] polyanskiy, a. m., polyanskiy, v. a. and yakovlev, y. a. (2014). experimental determination of parameters of multichannel hydrogen diffusion in solid probe. int. j. hydrog. energy, 39(30), pp. 17381-17390. doi: 10.1016/j.ijhydene.2014.07.080 a v. loginov et alii, frattura ed integrità strutturale, 63 (2023) 301-308; doi: 10.3221/igf-esis.63.23 308 [16] belyaev, a. k., polyanskiy, a. m., polyanskiy, v. a., sommitsch, c. and yakovlev, y. a. (2016). multichannel diffusion vs tds model on example of energy spectra of bound hydrogen in 34crnimo6 steel after a typical heat treatment. int. j. hydrog. energy, 41(20), pp. 8627-8634. doi:10.1016/j.ijhydene.2016.03.198 [17] andronov, d. y., arseniev, d. g., polyanskiy, a. m., polyanskiy, v. a. and yakovlev, y. a. (2017). application of multichannel diffusion model to analysis of hydrogen measurements in solid. int. j. hydrog. energy, 42(1), pp. 699710. doi: 10.1016/j.ijhydene.2016.10.126 [18] wang, m., akiyama, e. and tsuzaki k., (2005) effect of hydrogen and stress concentration on the notch tensile strength of aisi 4135 steel. mater. sci. eng. a, 398(1), pp. 37–46. doi: 10.1016/j.msea.2005.03.008. [19] venezuela, j., hill, t., zhou, q., li, h., shi, zh., dong, f., knibbe, r., zhang, m., dargusch, m.s. and atrens, a., (2021). hydrogen-induced fast fracture in notched 1500 and 1700 mpa class automotive martensitic advanced highstrength steel. corrosion science, 188, 109550, doi: 10.1016/j.corsci.2021.109550. [20] liu, q. and atrens, a. , (2013). a critical review of the influence of hydrogen on the mechanical properties of medium strength steels, corros. rev. 31, pp. 85–104. doi: 10.1515/corrrev-2013-0023. [21] ramamurthy, s., lau, w. m. l. and atrens, a. 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can be opened with acrobat and adobe reader 5.0 and later.) >> /namespace [ (adobe) (common) (1.0) ] /othernamespaces [ << /asreaderspreads false /cropimagestoframes true /errorcontrol /warnandcontinue /flattenerignorespreadoverrides false /includeguidesgrids false /includenonprinting false /includeslug false /namespace [ (adobe) (indesign) (4.0) ] /omitplacedbitmaps false /omitplacedeps false /omitplacedpdf false /simulateoverprint /legacy >> << /addbleedmarks false /addcolorbars false /addcropmarks false /addpageinfo false /addregmarks false /convertcolors /converttocmyk /destinationprofilename () /destinationprofileselector /documentcmyk /downsample16bitimages true /flattenerpreset << /presetselector /mediumresolution >> /formelements false /generatestructure false /includebookmarks false /includehyperlinks false /includeinteractive false /includelayers false /includeprofiles false /multimediahandling /useobjectsettings /namespace [ (adobe) (creativesuite) (2.0) ] /pdfxoutputintentprofileselector /documentcmyk /preserveediting true /untaggedcmykhandling /leaveuntagged /untaggedrgbhandling /usedocumentprofile /usedocumentbleed false >> ] >> setdistillerparams << /hwresolution [2400 2400] /pagesize [612.000 792.000] >> setpagedevice microsoft word numero_62_art_41_3855.docx r. andreotti et alii, frattura ed integrità strutturale, 62 (2022) 602-612; doi: 10.3221/igf-esis.62.41 602 a simplified formula to estimate the load history due to ballistic impacts with bullet splash. development and validation for finite element simulation of 9x21mm full metal jacket bullets riccardo andreotti callens® area3, via merini 37 21100 varese, italy dipartimento di meccanica, politecnico di milano, via la masa 1, 20156 milano, italy riccardo.andreotti@callens.it andrea casaroli dipartimento di meccanica, politecnico di milano, via la masa 1, 20156 milano, italy andrea.casaroli@polimi.it mauro quercia callens® area3, via merini 37 21100 varese, italy mauro.quercia@area3.it marco v. boniardi dipartimento di meccanica, politecnico di milano, via la masa 1, 20156 milano, italy marco.boniardi@polimi.it abstract. an original simplified formula is proposed to estimate the load history caused by ballistic impacts characterized by the so-called bullet splash phenomenon, consisting in the complete bullet fragmentation with no penetration of the target. the formula is based on the progressive momentum variation of the mass of the bullet impacting on a planar plate normal to the impact direction. the method aims at creating a simplified approach to assess the response of structures by means of explicit finite element simulations without the need of modelling the interaction between impactor and target. the results demonstrate that the proposed method can be used to estimate the forces generated by bullet-splash phenomena of 9x21mm full metal jacket bullets and effectively applied to finite element simulations allowing significant reductions in computational cost. keywords. ballistic impact; load history; bullet splash; stainless steel plate; finite element simulation (fem); explicit solver. citation: andreotti r., casaroli a., quercia m., boniardi m.v., a simplified formula to estimate the load history due to ballistic impacts with bullet splash. development and validation for finite element simulation of 9x21mm full metal jacket bullets, 62 (2022) 602-612. received: 12.08.2022 accepted: 14.09.2022 online first: 15.09.2022 published: 01.10.2022 copyright: © 2022 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. https://youtu.be/1laacexm1gm r. andreotti et alii, frattura ed integrità strutturale, 62 (2022) 602-612; doi: 10.3221/igf-esis.62.41 603 introduction n today’s aerospace and defense industry, the optimization of protective capabilities of a structural system is mainly done by means of finite element explicit simulations, with a similar approach to what is done for passive safety requirements like bird strike [1]. this paper aims at proposing and discussing the effectiveness of an easy-to-use formula to estimate the evolution in time of the impactor-target interaction forces due to bullet splash [2], which represent a typical load case of a properly working protective structure able to locally withstand the interaction with the impactor, therefore generating high intensity reaction forces that propagate to the surrounding structures threatening their general integrity. the estimation of the load history allows analysts to conduct finite element simulations of bullet splash phenomena to predict the response of protective structural systems with the significant advantage of avoiding the cost of modelling and simulating the interaction phenomena between impactor and target. a similar approach was followed by the u.s. army ballistic research laboratory of aberdeen, maryland with the development of the epic-2 code [3], but the code is not available. the available literature mostly proposes simulation techniques for ballistic impacts focusing on the effects of rigid projectiles on deformable targets, to predict the ballistic limit velocity and the failure modes of the target. in 2021 goda et al. [4] analyzed the damage and stress field of a modern ceramic/composite protection impacted and penetrated by rigid projectiles. in 2022 the same author focused on the effects of the shape and angle of impact on the energy absorption of woven-fabric protections again impacted and penetrated by rigid projectiles [5]. yunfei et al. [6] (2014) verified both numerically and experimentally the effects of impactors of different strengths and deformability on penetrating metallic plates. rajput & iqbal (2017) [7] instead showed the effects of the nose shapes of rigid projectiles impacting on aluminum plates at different velocity. regarding the effects of the fragmentation of the bullet, bresciani et al. [8] in 2016 published a study about the use of adaptive remeshing and smooth particle hydrodynamics (sph) methods to investigate the interactions between impactor and target when they both encounter fragmentation. in this context, andreotti et al. (2021) [9] proposed a simplified finite element approach to simulate the interaction between bullet fragments and target during bullet splash phenomena. the model then proposed was based on an arbitrary lagrangianeulerian (ale) formulation to simulate the interaction between fragments and target as a fluid structure interaction (fsi), therefore avoiding the mechanical characterization of the deviatoric components of the constitutive law assigned to the bullet’s material. the approach was experimentally validated for 4 mm thick plates made with aisi 304 steel hit by 9x21mm full metal jacket bullets both in terms of back plate residual displacements and in terms of plastic strain field in the impact area. the work here presented was conceived to take advantage of that experience and propose an even more efficient way to face the problem of assessing protective structural systems against bullet splash phenomena once the focus of the simulations to be carried out is to investigate the response of the structures in the surroundings of the impact point without the need of a detailed reproduction of the local strain field due to the direct pressure of the fragments hitting the epicenter of the impact. this paper presents a formula to estimate the resultant load history due to bullet splash interactions, based only on the geometry of the bullet, its mass distribution, and its initial impact velocity. the formula is aimed to be useful to define load curves to be applied to simplified finite element models to conduct explicit dynamics analyses on any simulation platform featured with an explicit structural solver. the approach has been validated by comparing the results of the detailed fluid-structure interaction already experimentally validated by andreotti et al [9] with the results of a simplified simulation in which the load history is estimated by means of an analytical-numerical approach based on the proposed theoretical formula. the comparisons between the history of global reaction forces and the stress waves being transferred through the plates during the simulations show a clear consistency of the method. moreover, the comparison between the fsi and non-fsi calculation times shows a clear advantage in terms of computational cost. section 2 of the article illustrates the development of the load history formula and its practical application to the 9x21 fmj bullet considered by andreotti et al. [9]. section 3 explains how the finite element simulations were conducted. in section 4 the results are discussed comparing them with the ones obtained by means of the fsi model. section 5 summarizes the results and conclusions introducing possible further developments to the research. estimation of the load history ccording to andreotti et al. [9], bullet splash phenomena are mainly governed by the inertial, geometrical and compressibility properties of the impactor, while the deviatoric part of the constitutive law of the bullet’s materials can be considered neglectable. the simplification effectively introduced to treat bullet splash as a fluid structure i a r. andreotti et alii, frattura ed integrità strutturale, 62 (2022) 602-612; doi: 10.3221/igf-esis.62.41 604 interaction, where the fluid represents the mass of the bullet’s debris flowing against the target’s surface, suggests therefore a further simplification, valid for splashing bullets hitting planar surfaces at 90° incidence angle, which is the worst impact angle a ballistic protection can face. this simplification consists in estimating the load generated by the interaction between bullet’s debris and target as the resultant force needed to progressively deviate the trajectory of the flux of bullet’s material, considering the displacements of the target as neglectable. this allows to decouple the fluid-structure interaction and treat the problem as a transient phenomenon during which the structure is loaded by an already known load history, therefore avoiding the computational cost due to modelling the fsi. the resultant force f(t) to be applied in the impact direction x is estimated as the time derivative of the momentum of the bullet fragments under the hypothesis that the only effect of the impact on bullet’s material is a 90-degree deflection of its trajectory, gradually happening during the relative movement of the bullet with respect to the target, considered rigid and fixed (fig. 1). to calculate the load history, let’s consider a generic time t after the first contact between impactor and target and consider the elementary variation of the momentum dq, happening from time t to time t+dt, that would be  ( )x xi xfdq dm v v (1) where dm is the mass of debris deflected from time t to t+dt while vxi and vxf are the x components of the velocity of the debris before and after the deflection. as a result of the 90-degree deflection hypothesis vxf can be considered null, and considering only 90-degree impacts vxi is equal to the initial impactor velocity v, therefore eqn. (1) becomes: dq dmv (2) in the hypothesis that the bullet is homogeneous, and no perturbations occur to the bullet’s particles until they ideally intersect the target’s surface, the elementary mass dm can be expressed as:  ( )dm a t vdt (3) where a(t) represents the area of intersection between the bullet’s undeformed volume and the plane lying on the impact surface of the target at time t, ρ is the density of the associated material and vdt represents the elementary displacement ds describing the kinematics of the unperturbed part of the bullet from time t do t+dt: ds vdt (4) we can now substitute eqn. (3) into eqn. (2) and divide both terms for dt, obtaining the estimation of the impact force f at time t, as a function of initial velocity, inertia, and geometry of the impactor:   2 ( ) ( ) ( ) dq t f t a t v dt (5) by integrating in time eqn. (5) we obtain the definition of the initial momentum q of the impactor:         ( ) ( ) ( )q f t dt v a t vdt v a s ds v v vm (6) where v is the volume of the homogeneous impactor and m is its total mass. however, most bullets are not homogeneous, so the hypothesis of homogeneity must be overcome to apply the formula to real world problems. we can easily generalize the formula to consider heterogeneous bullet’s sections by introducing the resultant impact force as the sum of m contributions:    1 ( ) ( ) m i i f t f t (7) r. andreotti et alii, frattura ed integrità strutturale, 62 (2022) 602-612; doi: 10.3221/igf-esis.62.41 605 where m is the number of different materials composing the impactor and fi(t) is the force contribution due to the i-material at time t. therefore, the load history due to the bullet splash of an impactor whose generic section is composed by m different materials can be expressed as:    2 1 ( ) ( ) m i i i f t v a t (8) where 𝜌 is the density of the i-material, and ai(t) is the area of the i-material ideally intersecting the surface of the target at time t. figure 1: schematic simplification of the 90-degree bullet splash. the deflection of the debris is a continuous process during which the portion of the bullet ideally intersecting the target’s surface is perfectly deflected in radial direction and no perturbation occurs to the portion of the bullet not yet having intersected the surface of the target. figure 2: graphic representation of the bullet’s section composed by the brass jacket (orange) and the lead filler (gray). application of the method to estimate the load history due to 9x21mm fmj bullet splash at 322m/s a concrete application of the proposed method consists in analyzing the section of the bullet (fig. 2 and fig. 3) to identify the material distribution along its cross section to build the ai(t) functions (fig. 4), and then applying eqn. (8) to calculate r. andreotti et alii, frattura ed integrità strutturale, 62 (2022) 602-612; doi: 10.3221/igf-esis.62.41 606 the resultant load history (fig. 5). considering ρ = 10750 kg/m3 as the density of the lead-based alloy filler and ρ = 8730 kg/m3 as the density of the brass jacket, the process leads to the calculation of the load history, giving as a result a force history that grows from null to 68430 n in around 0.03s and keeps that intensity until t=0.0466s when the estimated interaction phenomenon ends. as a control, the integration in time of the estimated total load history f(t) (fig. 5) gives a total variation of the bullet’s momentum equal to 2.576 kgm/s, which correctly corresponds to the product of the impact velocity (322 m/s) multiplied by the nominal mass of the 9x21mm fmj bullet (8 g). figure 3: measured radius values (ordinate axis in mm) of the boundary surfaces of the materials all along the axial coordinate of the bullet (abscissa in mm). figure 4: values of the intersectional areas ai [mm2] (ordinate) as functions of interaction time t [s] (abscissa) and their sum. figure 5: values of the estimated impact forces fi [n] (ordinate) as functions of interaction time t [s] (abscissa). the total value of the impact force is represented in blue, the component due to the lead filler is represented in red, the component due to the brass jacket is represented in gray. r. andreotti et alii, frattura ed integrità strutturale, 62 (2022) 602-612; doi: 10.3221/igf-esis.62.41 607 finite element simulations o validate the load history approach we simulated the same impact analyzed by andreotti et al. [9] to validate the fsi method. the simulated impact is therefore a 9x21mm full metal jacket (fmj) bullet hitting a 250x250mm 4 mm thick aisi 304l plate at 322 m/s with an impact angle of 90degree. geometrical discretization of the plate to allow proper comparison between fsi approach and load history approach, a first round of simulations was performed with the same structural finite element model used by andreotti et al. [9], with a squared 60x60 mm area of the plate around the impact point discretized in 8-nodes solid elements with 0.2 mm size. the remaining part of the plate was instead simplified with 2.5mm shell fully integrated 4-nodes elements connected to the solids. a double symmetry plane boundary condition is associated with the model. the displacements of the external boundary nodes of the shell plate are constrained in the impact direction (fig. 6). figure 6: geometrical discretization of the plate: shell elements (blue), solid elements (green). mechanical characterization of the plate to allow proper comparisons, the static and dynamic constitutive model of the aisi 304l associated with the plate was taken from andreotti et al. [9]. comparative simulations four simulations have been conducted. the first simulation (a) is a repetition of the fsi simulation based on the arbitrarylagrangian-eulerian method (ale) adopted by andreotti et al. [9]. the second simulation (b) is the application of the estimated load history as a distributed load acting on the epicenter as a uniform pressure applied on a circular area equal to the nominal cross section of the bullet, i.e. with 4.5mm radius. the third simulation (c) is again the application of the estimated load history as a uniform distributed load acting on a circular area, this time with a radius increased by 50% to take into account the real interaction area as experimentally analyzed by andreotti et al. [9]. at last, some fourth and fifth simulations (d and e) were conducted on a full-shell plate model loaded with the estimated load history again distributed on a circular area with respectively 4.5mm and 6.75mm radiuses. tab. 1 summarizes all the features of the conducted simulations. all the numerical simulations were conducted by means of the explicit solver lsdyna [10]. simulation loading method pressure distribution fe model of the plate a fsi [9] variable pressure field (ale) [9] solid (0.2mm) – shell (2.5mm) b estimated load history uniform circular (4.5mm radius) solid (0.2mm) – shell (2.5mm) c estimated load history uniform circular (6.75mm radius) solid (0.2mm) – shell (2.5mm) d estimated load history uniform circular (4.5mm radius) shell (2.5mm) e estimated load history uniform circular (6.75mm radius) shell (2.5mm) table 1: summary of the simulations conducted. t r. andreotti et alii, frattura ed integrità strutturale, 62 (2022) 602-612; doi: 10.3221/igf-esis.62.41 608 results and validation o evaluate how well the proposed load history method could effectively substitute the fsi approach for the purpose of assessing the response of a structural system impacted by ballistic impacts with bullet splash, in the following we compare the results of the simulations in terms of resultant forces at the constraints, local stress waves transmitted from the epicenter to the periphery of the plate and normalized computational cost of each simulation. having the fsi approach been experimentally validated by andreotti et al. [9], the results of simulation a will be treated as a benchmark for the proposed alternative method. further considerations will be carried out by comparing the predicted back-plate residual deformations of the plate with the experimental data. total reaction forces the comparison between the histories of the total reaction force needed to contrast the impact along the boundary of the plate shows very good adhesion of the results, with the peaks corresponding to the first back-and-forth bounces being very similar both in amplitude and phase. no significant spread is visible between benchmark simulation a and test simulations b and c, with less than 10% difference in peaks amplitude, showing substantial equivalence between the fsi method and the proposed estimated-load-history method in terms of global reaction forces. full-shell simulations d and e show slightly shorter oscillation periods in the bounces happening at the end of the simulation time; the difference in phase is evident after 0.3ms and is due to the slightly higher stiffness resulting from the reduction in degrees of freedom due to the adoption of a looser shell mesh. moreover, the comparison between b and c as well as between d and e shows the invariance of the global forces with respect to the arbitrarily chosen pressure distribution areas. figure 7: comparison between the total reaction forces in the impact direction, showing good adhesion of the results. stress waves propagation the propagating stress waves generated by the simulated impacts are very similar. as displayed in fig. 11, the amplitude of the stress waves propagating from the epicenter at the end of the interaction time is very similar across all the simulations. to compare in more detail those results, we chose two points at half-way radial distance from epicenter to the constrained perimetry of the plate (fig. 8). point 1 stays on the diagonal of the plate (maximum radial distance from epicenter to the constrained nodes). point 2 stays on the cross section of the plate where the radial distance from the loaded point to the fixed nodes at the boundary is minimum. in general, the comparison between the histories of maximum principal stress shows good adhesion of the stress waves. at point 1 (fig. 9) simulations b and c underestimate the peak stress by around 20% with respect to a. full-shell simulations d and e also slightly underestimate the peak stress of about 8%. at point 2 (fig. 10) simulations b and c underestimate the peak stress of around 5%; simulations d and e, instead, overestimate the peak stress of about 10%. no significant differences are visible between simulations b and c, and no significant differences are visible between simulations d and e, again confirming that the arbitrary extension of the loaded area and the local intensity of the pressure field is non relevant within the tested range. t r. andreotti et alii, frattura ed integrità strutturale, 62 (2022) 602-612; doi: 10.3221/igf-esis.62.41 609 as already observed on the reaction forces, full shell simulations d and e show slightly shorter oscillation periods in the bounces happening at the end of the simulation time. the difference in phase and amplitude is evident after 0.3ms and is due to the slightly higher stiffness due to the less degrees of freedom characterizing the looser shell mesh adopted. figure 8: points of comparison between the stress waves. figure 9: comparison between the stress waves in terms of maximum principal stress at point 1. figure 10: comparison between the stress waves in terms of maximum principal stress at point 2. r. andreotti et alii, frattura ed integrità strutturale, 62 (2022) 602-612; doi: 10.3221/igf-esis.62.41 610 figure 11: comparison between the stress waves in terms of maximum principal stress at 0.05ms (right after the end of the interaction time). on first row simulation a, on second row simulations b and c (left to right), on third row simulations d and e (left to right). the stress scale is in mpa. residual displacements compared to the experimental data and the a simulation (fig. 12) the residual displacements predicted by the simulations b, c, d and e are overestimated between +56% (simulation b) and +15% (simulation e). it is evident, however, how the radius of the chosen circular area on which the uniform pressure was arbitrarily applied has a very significant impact on residual displacements, with simulations c and d (6.75mm radius) giving much better predictions than b and d (4.5mm radius). even though local effects are out of the scope of this study, this observation suggests the possibility to even identify an equivalent radius that could better predict the residual back plate deformation. r. andreotti et alii, frattura ed integrità strutturale, 62 (2022) 602-612; doi: 10.3221/igf-esis.62.41 611 figure 12: comparison between residual displacements as measured experimentally (from left: the minimum, maximum and average values) and simulations results. calculation times compared to simulation a, the elimination of the fsi allowed simulations b and c to finish in around 45% the amount of calculation time. furthermore, the substitution of shell elements in place of the detailed 3d solid mesh from, needed at the epicenter to conduct detailed investigation using fsi, allowed simulations d and e to run enormously faster, in less than 0.2% of the time needed by simulation a (fig. 13). the comparison was obviously conducted at equal conditions. figure 13: comparison between the calculation times needed to obtained the above results. the histogram represents the percentage ratios between the calculation’s times needed by the simulations divided by the calculation time needed by our benchmark simulation a. simulations b, c and d, e are represented in the same column because their calculation times are equal due to the same structural model used (see tab. 1). 0 1 2 3 4 5 6 7 8 r e si d u a l  d e fo rm a ti o n  [ m m ] 1 0 0 ,0 % 4 5 ,2 % 0 ,2 % s im ulation   a si mulat io ns   b   and  c sim ulations   d  a nd   e c o m p a r e d  c a lc u la t io n  t im e s  [ % ]  r. andreotti et alii, frattura ed integrità strutturale, 62 (2022) 602-612; doi: 10.3221/igf-esis.62.41 612 conclusions he aim of this study was to identify and validate a more efficient way to assess the global response of a structural system to ballistic impacts with bullet splash. the method proposed is based on the ideal continuous fragmentation of the bullet. the impact forces are calculated as the time derivative of the momentum of the flux of fragments. the proposed formula was applied to estimate the load history due to the impact of a 9x21 fmj bullet at 322 m/s. the load history was applied to impact simulations with progressively simplified finite element models. the results demonstrated good adhesion to the results obtained on the same case by means of the already validated fsi method developed by andreotti et al. [9]. the method allowed to reproduce the dynamic stress condition of the plates both in terms of local stress waves as well as in terms of history of resultant reaction forces. these results demonstrated to be independent from the radius of loaded area in the range of 4.5mm to 6.75mm. moreover, the efficiency of the method has demonstrated to be significantly high, with calculation times reduced to less than 0.2% of the time needed by the locally detailed fsi-based method used as a benchmark. the study therefore demonstrates the method as useful for industrial applications and suggests further investigations of its applicability on different ammunitions and targets. references [1] heimbs, s. (2011). computational methods for bird strike simulations: a review, comput. struct., 89(23–24), pp. 2093– 112, doi: 10.1016/j.compstruc.2011.08.007. [2] parker, s.p. parker, s.p.(2003). bullet splash. available at: https://encyclopedia2.thefreedictionary.com/bullet+splash. [accessed may 29, 2021]. [3] quigley, e.f. (1989). epic-2 calculated impact loading hlstory for finite element analysis of ballistic shock, aberdeen, maryland. [4] goda, i., girardot, j. (2021). numerical modeling and analysis of the ballistic impact response of ceramic/composite targets and the influence of cohesive material parameters, int. j. damage mech., 30(7), pp. 1079–1122, doi: 10.1177/1056789521992107. [5] goda, i. (2022). ballistic resistance and energy dissipation of woven-fabric composite targets: insights on the effects of projectile shape and obliquity angle, def. technol., doi: 10.1016/j.dt.2022.06.008. [6] yunfei, d., wei, z., guanghui, q., gang, w., yonggang, y., peng, h. (2014). the ballistic performance of metal plates subjected to impact by blunt-nosed projectiles of different strength, mater. des., 54, pp. 1056–1067, doi: 10.1016/j.matdes.2013.09.023. [7] iqbal, m.a., diwakar, a., rajput, a., gupta, n.k. (2012). influence of projectile shape and incidence angle on the ballistic limit and failure mechanism of thick steel plates, theor. appl. fract. mech., 62(1), pp. 40–53, doi: 10.1016/j.tafmec.2013.01.005. [8] bresciani, l.m., manes, a., romano, t.a., iavarone, p., giglio, m. (2016). numerical modelling to reproduce fragmentation of a tungsten heavy alloy projectile impacting a ceramic tile: adaptive solid mesh to the sph technique and the cohesive law, int. j. impact eng., 87, pp. 3–13, doi: 10.1016/j.ijimpeng.2015.10.003. [9] andreotti, r., abate, s., casaroli, a., quercia, m., fossati, r., boniardi, m. v. (2021). a simplified ale model for finite element simulation of ballistic impacts with bullet splash – development and experimental validation, frat. ed integrita strutt., 15(57), pp. 223–245, doi: 10.3221/igf-esis.57.17. [10] lstc. 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can be opened with acrobat and adobe reader 5.0 and later.) >> /namespace [ (adobe) (common) (1.0) ] /othernamespaces [ << /asreaderspreads false /cropimagestoframes true /errorcontrol /warnandcontinue /flattenerignorespreadoverrides false /includeguidesgrids false /includenonprinting false /includeslug false /namespace [ (adobe) (indesign) (4.0) ] /omitplacedbitmaps false /omitplacedeps false /omitplacedpdf false /simulateoverprint /legacy >> << /addbleedmarks false /addcolorbars false /addcropmarks false /addpageinfo false /addregmarks false /convertcolors /converttocmyk /destinationprofilename () /destinationprofileselector /documentcmyk /downsample16bitimages true /flattenerpreset << /presetselector /mediumresolution >> /formelements false /generatestructure false /includebookmarks false /includehyperlinks false /includeinteractive false /includelayers false /includeprofiles false /multimediahandling /useobjectsettings /namespace [ (adobe) (creativesuite) (2.0) ] /pdfxoutputintentprofileselector /documentcmyk /preserveediting true /untaggedcmykhandling /leaveuntagged /untaggedrgbhandling /usedocumentprofile /usedocumentbleed false >> ] >> setdistillerparams << /hwresolution [2400 2400] /pagesize [612.000 792.000] >> setpagedevice microsoft word numero_59_art_24_3316 c. mallor et alii, frattura ed integrità strutturale, 59 (2022) 359-373; doi: 10.3221/igf-esis.59.24 359 focussed on fracture and structural integrity a probabilistic fatigue crack growth life approach to the definition of inspection intervals for railway axles c. mallor*, s. calvo, j.l. núñez, r. rodríguez-barrachina area of research and development, instituto tecnológico de aragón, maría de luna, 8-50018 zaragoza, spain cmallor@itaiinova.es, https://orcid.org/0000-0001-8047-4211 a. landaberea caf s.a., j.m. iturrioz, 26, beasain, gipuzkoa, spain abstract. different options that rely on fracture mechanics are currently used in engineering during the design and assessment of components. one of the most important aspects is the time taken for a crack to extend to its critical size. if this time is known and it is sufficiently large, a design concept based on inspection intervals can be applied in a viable way, as is it the case of a railway axle component. to define inspection intervals that ensure the continuous and safe operation of a damage-tolerant railway axle, a reliable estimation of its fatigue crack growth life is required. due to the uncertainties involved in the fatigue process, inspections must be devised not only considering the uncertainties in the performance of the inspection technique, but also based on a probabilistic lifespan prediction. from this premise, this paper presents a procedure for determination of inspection intervals that uses a conservative fatigue crack growth life estimation based on the lifespan probability distribution. a practical example to illustrate the reliability-based inspection planning methodology in a railway axle under random bending loading is given. the inspection intervals are further assessed in terms of overall probability of detecting cracks in successive inspections and in terms of probability of failure, considering the probability of detection curve of the non-destructive testing technique. the procedure developed provides recommendation for the definition of inspection intervals and associated inspection techniques. keywords. probabilistic fatigue crack growth; damage tolerance; inspection intervals; probability of detection; nasgro. citation: mallor, c., calvo, s., núñez, j..l., rodríguez-barrachina, r., landaberea, a., a probabilistic fatigue crack growth life approach to the definition of inspection intervals for railway axles, frattura ed integrità strutturale, 59 (2022) 359-373. received: 25.10.2021 accepted: 22.10.2021 published: 01.01.2022 copyright: © 2020 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. https://youtu.be/0dubv-ac1t8 c. mallor et alii, frattura ed integrità strutturale, 59 (2022) 359-373; doi: 10.3221/igf-esis.59.24 360 introduction urrently, the design and operation of a railway axle is based on a two-stage safety concept comprising “safe life” and “damage tolerance analysis (dta)” approaches [1,2]. the primary level of safety, safe life, consists in designing the axles for fatigue strength in accordance with en 13103 standard [3] applicable for both non-powered and powered axles. the secondary level of safety, damage tolerance, relies on periodic non-destructive inspections (ndi) for crack detection, which in current practice are defined on the basis of service experience or, more recently and under development, based on fracture mechanics. the latter mainly relies on the lifespan prediction governed by the fatigue crack growth (fcg) process which is affected by many uncertainties. for instance, the experimental variability of material properties among test replications [4,5], the scattering of non-uniform loading patterns during the component operation [6,7], and the uncertainties inherent to geometrical parameters [8]. these uncertainties cause variability in the lifespan prediction and, therefore, several works propose the use of probabilistic approaches [9–13] as an alternative to deterministic ones. over recent years, the definition of inspection intervals in railway axles based on fracture mechanics is an active topic of research [1,14–21]. in these investigations, despite the different considerations of, initial and final crack sizes, they all use the fatigue crack growth lifespan for the subsequent inspection planning. a reliable fatigue crack growth life estimation is therefore key aspect [22]. it would thus be of interest to improve the procedures for fatigue crack growth lifespan estimation considering its stochastic nature in order to better define inspection periodicities. to obtain a probabilistic fatigue crack growth life estimation, one such interesting strategy is to construct the probability distribution of the axle lifespan as a result of the randomness of the input sources, using the pearson distribution family based on prescribed statistical moments. this moments can be estimated by applying the full second order approach (fsoa) to the well-known fatigue crack growth nasgro model [23] as thoroughly described in [24–26]. the levels of safety assessment for railway axles are illustrated in fig. 1. it also includes an additional stage ``in-service damage indication systems'' with further options that offer potential for establishing a third stage safety concept. for completeness, the fig. 1 also indicates the maturity of the technologies in the three stages, by using a three-level scale as follows: (*) state-of-the-art; (**) present and future development; and (***) original contribution within this research article. the figure is adapted from an extended review on safe life and damage tolerance aspects of railway axles in [1] therefore the reader is referred to this paper for full details. it is important to note that the developments in this paper aim at enriching the secondary safety level dta, by improving the periodic inspections definition currently based on operating experience or based on a limited use of deterministic approaches using a more comprehensive probabilistic approach that provides a higher level of safety assurance. in consequence, they constitute an extension of the nowadays and under development practices by proposing the use of probabilistic fracture mechanics together with non-destructive testing methods. figure 1: components of a safety assessment system for railway axles. c c. mallor et alii, frattura ed integrità strutturale, 59 (2022) 359-373; doi: 10.3221/igf-esis.59.24 361 the purpose of this paper is to provide a new methodology for determination of inspection intervals in railway axles that relies on a conservative fatigue crack growth life estimation based on the lifespan probability distribution. the procedure developed extends the current state-of-the-art in damage tolerance in railway axles considering the fatigue crack growth from a probabilistic point of view. the proposed reliability-based inspection planning method is discussed through a numerical example of fatigue crack growth in a railway axle, providing recommendations for the calculation of practical inspection intervals and the associated cumulative probability of detection (cpod) and probability of failure (pf) depending on the probability of detection (pod) curve of the non-destructive testing (ndt) technique. probabilistic fatigue crack growth methodology in the damage tolerance assessment of railway axles he essence of damage tolerance in railway axles is to detect cracks before they become critical, providing certain level of safety for the axles in a fleet of trains by performing periodical inspections in-service. thus, damage tolerance analyses are based on fracture mechanics to simulate crack propagation. within the frame of the damage tolerance concept, the possibility of using probabilistic fatigue lifespan estimation is developed here. for that purpose, this section gives an overview of the steps of the damage tolerance of railway axles. then, the propagation of uncertainty in fatigue crack growth using the fsoa and the probability distribution fit using the pearson distribution family are outlined. finally, the two previous elements are combined providing a reliability-based inspection interval definition. steps of the damage tolerance analysis the steps of a damage tolerance analysis of a railway axle comprise [27–29]: step 1. establishment of the initial crack location, orientation, shape, and size, step 2. simulation of sub-critical crack extension, i.e., the fcg process, step 3. determination of critical crack size for component failure, step 4. determination of residual lifetime of the component, and step 5. establishment of inspection intervals and computation of the overall probability of crack detection. the aim of the damage tolerance analysis in this paper is to determine inspection intervals with an associated cpod, what is also function of the performance of the ndt method. the different steps of the analysis are explained in detail for a particular example dealing with the fatigue crack growth in a railway axle. probabilistic fatigue crack growth life starting from the assumption of an initial crack-like defect (step 1), the crack growth simulation (step 2) considers: (i) the component geometry and dimensions; (ii) the loading conditions including the bending moment (cyclic), the load spectra (in-service load sequences) and the press-fit (static); (iii) the material properties, primary the da/dn–δk curve and (iv) the considered crack growth equation, commonly the nasgro model. the nasgro equation is shown in eqn. (1).                   δ 1 1 δ δ 1 1 p th n q max c k fda k c k dn r k k (1) where da/dn is the crack propagation rate, n is the number of applied cycles, a is the crack depth, r is the stress ratio, k is the stress intensity factor (sif) range and f is the crack opening function, kth is the threshold stress intensity factor range, kc is the critical stress intensity factor, and c, n, p, and q are material empirically derived constants. it is important to note that the crack geometry is described by two parameters that represent the two axes of a semiellipse. therefore, the crack growth rate that also depends on the boundary conditions, is calculated at two different points, the deepest point, and the crack surface point. for a more detailed description of the previous considerations please refer to [23,24]. after that, different definitions of the critical crack size (step 3) are in use. for instance, the break through the wall of the surface crack is adopted in [29], final cracks of 60 mm and 30 mm are used in different analyses in [30], and a crack depth of 20 mm is taken as the failure criterion in [31]. however, since the growth rate of long cracks is usually so high due to its exponential nature, the failure is imminent whatever the relatively large critical crack depth. in other words, as the critical t c. mallor et alii, frattura ed integrità strutturale, 59 (2022) 359-373; doi: 10.3221/igf-esis.59.24 362 crack size is selected in the unstable region, characterized by rapid, accelerating over time, unstable crack, where kmax asymptotically approaches kc, the fracture is imminent, and therefore, the number of cycles calculated slightly varies when different criteria for the critical crack size are adopted. next, the residual lifetime is calculated (step 4), that is, the number of loading cycles or the distance in kilometres, which the assumed initial crack, (step 1), would need to grow up to the final crack size, (step 3). among all the different aspects which affect the residual lifetime (step 4), it strongly depends on the fcg process (step 2), and, as it is stochastic in nature, the residual lifetime also depends on the uncertainties inherent to the factors listed in (i) to (iv). addressing the fcg problem from a probabilistic point of view is, therefore, a crucial point for the final (step 5), establishing inspection intervals with a probability of crack detection associated. in order to obtain a probabilistic fatigue crack growth life estimation, this work applies a procedure that uses the first four moments of the fatigue crack growth life predicted by the fsoa to fit the parameters of a probability distribution based on the pearson distribution family. the fsoa for the moments of functions of random variables presented in [24] enables the prediction of the expected value and the variance of the fatigue lifespan of interest. further extensions developed in [25] enable the prediction of the skewness and the kurtosis of the probabilistic fatigue crack growth life. the first-order second-moment (fosm) method is the theoretical foundation of the fsoa, and, the most general equations for the expected value and covariance matrix in matrix form are presented in [26]. on this basis, the complete mathematical derivation of the fsoa for the first to fourth moments of functions of random variables using summation notation is presented in [24,25]. they present the expressions involving tensors of different orders in a simple and comprehensible way. notice that, the first to fourth moments are related, by definition, to the expected value (first raw moment), the variance (second central moment), the skewness and the kurtosis (third and fourth central standardized moments, respectively) of the random output variable. for a detailed description, the manner in which the fsoa is applied to the fatigue crack growth nasgro model for propagating the first to fourth moments of the fatigue life n is illustrated in [24–26] through the use of the probabilistic nasgro equations (pr. eqn.). finally, the expected value of n, its variance, the skewness, and the kurtosis are calculated based on the first to fourth predicted moments. at this point, the problem of fitting a probability distribution from prescribed moments arises. commonly, the normal distribution is assumed when there is not much information available about the underlying probability distribution, notwithstanding that this assumption might not reflect the reality in some scenarios. among the different distributions that can be considered, the pearson distribution family is used in the methodology presented in [25,26] as it is a versatile family that covers a broad range of distribution shapes. additionally, it enables the expression of the parameters of the distribution as a function of the first four moments of the distribution without a priori hypotheses. depending on these quantities, different common probability distributions arise, for instance, the beta, symmetrical beta, gamma, cauchy, inverse-gamma distribution, beta prime, student's t and the normal distribution. the formulas to calculate the parameters for each type of pearson distribution as a function of the expected value, variance, skewness and kurtosis, are enclosed in [32]. summarizing, once the fsoa method and the pearson family fit are applied, there is available a probabilistic description of the fatigue crack growth life, that provides relevant information about the statistical distribution of the output random variable fatigue life. figure 2: probabilistic fatigue life. reliability-based inspection interval definition the damage tolerance methodology overviewed in steps of the damage tolerance analysis is commonly based on the deterministic calculation of the fatigue crack growth (step 2), but as mentioned, given the uncertainties inherent to geometric c. mallor et alii, frattura ed integrità strutturale, 59 (2022) 359-373; doi: 10.3221/igf-esis.59.24 363 parameters, the variability of loads and the scatter of the material properties, the calculation of an axle lifespan should not be done with a simple deterministic calculation, and instead, a probabilistic approach is preferred. as shown in fig. 2, the random nature of the fatigue crack growth in the railway axle needs a probabilistic description taking into account of the variabilities given by the geometric accuracy, the material properties and the actual in-service loads. with such an uncertainty, applying the probabilistic approach outlined in probabilistic fatigue crack growth life, the probability distribution of the fatigue crack growth life is available. that is, the distribution of the fatigue life predictions with allowance for these sources of uncertainty is obtained, thus leading to an enhanced and more robust control over the safety required by these critical components. the probability distribution can be described in various forms, such as by the survival function (sf), by the cumulative distribution function (cdf) or by the probability density function (pdf). in the context of probabilistic fatigue crack growth life in railway axles, the sf is the function that gives the probability that an axle will survive beyond any specified time, number of cycles or kilometers travelled. frequently, in engineering, the survival function is also known as the reliability function. alternatively, the reliability function can also be evaluated for a given reliability percent obtaining the corresponding number of kilometers travelled. in other words, in this way it provides the minimum mileage travelled for a given surviving proportion of axles. another name for the survival function is the complementary of the cumulative distribution function (ccdf). moreover, as it is well known, the cdf and the pdf are closely related. given these basic premises, the working approach selects a reliability level in such a way that a conservative lifespan balancing safety and economic issues is achieved. notice that, the input uncertainties and scatter are implicitly in the output probability distribution provided by the pr. eqn. and represented by its survival, cumulative distribution, and probability density functions of fatigue life. the stated procedure is illustrated in fig. 3. as a result of the procedure, a conservative estimation of the lifespan is obtained, taking advantage of the knowledge available at the lower tail of the distribution of lives. finally, instead of the deterministic lifespan calculation, the conservative lifespan estimation is considered as the fcg process (step 2) outcome, which is the basis for the subsequent steps oriented to the interval inspection definition. figure 3: conservative reliability-based life estimation from probabilistic fatigue life, illustrated by the survival function (sf), cumulative distribution function (cdf) and probability density function (pdf) of fatigue life. c. mallor et alii, frattura ed integrità strutturale, 59 (2022) 359-373; doi: 10.3221/igf-esis.59.24 364 the idea for determining the periodicity of the non-destructive inspections (ndi) is depicted simply in fig. 4. first, based on the conservative lifespan estimation, the residual lifetime (step 4) is delimited. this portion of lifetime is denoted as ndef in fig. 4 in reference to the lifetime for the definition of inspection intervals. keeping in mind the considerations on the two-dimensional shape of the crack, and on its evolution due to fatigue loads, the ndef covers the propagation from amin to amax (steps 1 and 3), being the minimum and the maximum crack sizes considered for the lower and the higher lifetime bounds, respectively, and it is calculated through the eq (2).     def max minn n a n a (2) the usual assumption made is that amin corresponds to crack size apod% that has certain probability of being detected by ndt, for instance the crack size a95% which has a pod = 95%. finally, the inspection interval tins is determined by dividing ndef by a number of times ntimes that takes account of the number of times that the crack can be detected before a failure could occur. this simple procedure is formulated in eq (3).  defins times n t n (3) for example, the usual assumption considering ntimes equal to 2 or 3 [14], allows the crack to be observed at least twice or three times before it leads to catastrophic failure. this assumption is based on the fact that a crack could be missed at an inspection. it is, however, evident that even two or more inspections cannot ensure the crack detection. figure 4: calculation of the periodicity of ndt inspections, i.e., inspection intervals of maintenance. in particular, as it is not known exactly when crack growth is triggered by an accidental event, the component will always be subjected to inspection every tins km, and depending on the inspection method used, the cumulative probability of detecting (cpod) a crack in the axle or its complementary cumulative probability of failure (cpof) or simply referred to as probability of failure (pf ) can be computed as described in [22]. summarizing, the cpod of a crack growing according to an a-n curve, can be calculated based on the given number of inspections #i and the pod-a curve of the ndt method used. the easiest way to calculate the cpod is to convert the pod of the individual inspections, #1, #2, #3, …, designated with the sub-index #i, to probability of non-detection (pond) by the relationship pond(a#i) = 1 − pod(a#i) where a #i is the corresponding crack depth at the #i inspection. these ponds, when multiplied give a cumulative probability of nondetection in successive inspections (cpond). notice, that the individual pond decreases with increasing crack length. finally, the cpond is converted back to its complementary cpod. in short, the cumulative probability of detection cpod of a crack can be evaluated as in eq (4).             # # # #cpo 1 cpon 1 1 1i i i ii id d pond a pod a (4) c. mallor et alii, frattura ed integrità strutturale, 59 (2022) 359-373; doi: 10.3221/igf-esis.59.24 365 the probability of failure pf, also denoted as cpof, given that all the inspections failed to detect an actual crack, can be considered as the cpond as expressed in eq (5).         # # # #1 1f i i i iip cpof cpod cpond pod a (5) it is important to recall the hypothesis made here, that is, the presence of a crack (step 1) and so the probability of failure equals the probability of not detecting the crack in due time throughout the axle lifetime. this must be distinguished from the probability of failure of an arbitrary axle in a fleet of trains since an existing defect an its nucleation to a crack of that size is very unlikely. to calculate the real probability of failure, the pf obtained in the damage tolerance analysis should be multiplied by the probability of having a defect on the axle and by the probability that a crack will nucleate from that defect and further grow during the service life. therefore, the real probability of failure of an axle is, by orders of magnitude, smaller than the one obtained in a damage tolerance analysis. the calculation of the real probability of failure is beyond the scope of this work. note that, in this context, damage tolerance does not mean that a crack detected during an inspection is considered acceptable even when its size is far from being critical. in some other applications, this is a possible option, but it should be handled with care especially for safety relevant applications, as it is the case of a railway axle. in consequence, preventive maintenance is a prevailing principle in the railway industry. in summary, the approach presented here extends the current damage tolerance principles in railway axles by means of improving the crack growth simulation (step 2), replacing the deterministic crack growth estimation by a probabilistic one. the damage tolerance assessment benefits from a better knowledge of the distribution of fatigue lifespan. as a result, it would give a more conservative recommendation for the definition of inspection intervals as it is based on a probabilistic fatigue propagation instead of on a deterministic one. the specific in-service inspection procedures shall be improved continuously in order to benefit of the continuous advance in the state-of-the-art technology. results and discussion his example shows the use of probabilistic fatigue life estimation in defining inspection intervals for railway axles within the frame of a damage tolerance concept. first, it uses the fsoa to obtain the expected value, variance, skewness, and kurtosis of the fatigue lifetime based on nasgro model. secondly, it presents the probability distribution of a particular pearson distribution type adjusted using these first four prescribed moments. thirdly, a conservative estimation of the lifespan is obtained based on the lifespan probability distribution. finally, instead of the deterministic lifespan calculation, the conservative lifespan estimation is used as basis for the interval inspection definition and the subsequent cpod calculation associated with the selected ndt technique. the methodology was applied to the example in [26]. the numerical example investigates the fatigue crack growth in the railway axle shown in fig. 5 under random bending moment. the axle was 173 mm in diameter and it was made of ea1n steel defined in the en 13261 standard [33]. a semicircular initial crack aini of 2 mm was postulated at the t-transition, as indicated in the cross-section of the fig. 5. the crack grows keeping a semielliptical shape up to a final crack depth afin of 50 mm following the direction of the radial coordinate x in fig. 5. the fatigue crack growth material parameters for the nasgro model were those collected in [24]. note that, the pod of a crack depends not only on the ndt technique but also on the actual crack size, as illustrated in fig. 6 where the pod versus crack size curve for various ndt methods is shown. it is worth mentioning that ultrasonic techniques have notable different pod curves, as shown in fig. 6, depending on the near-end or far-end application conditions pictured in fig. 5. on the other side, magnetic particle inspections provide very good results and, also, deal with comparatively short crack depths. based on the pod curves, the cpod of cracks and defects in railway axles or its complementary pf, can be computed by using the backward detection scheme described in [22]. the loads considered were the bending moment loading in the railway axle due to the vehicle weight and cargo and the press-fit loading produced by the wheel mounting with interference. the bending moment was assumed as a random input variable normally distributed with a standard deviation equal to the 1.5% of the mean value. the parameters of the bending moment distribution were: mean value = 70.32 [mn mm] and variance = 1.11 [mn mm]2. the bending moment level selected m corresponded to the highest load amplitude in the spectrum of a 22.5 tonnes per axle railway, plus additional forces, generated when the train goes through curved track, over crossovers, switches, rail joints, braking efforts, etc. this assumption implied a worst case scenario since such stress level corresponded to the maximum one for axle bodies according to the en 13103 standard [3]. moreover, the present example considered the load spectrum acting on a railway axle over its service. the load spectrum was derived from the one available in the uic b 169/rp 36 report [34]. the resulting service t c. mallor et alii, frattura ed integrità strutturale, 59 (2022) 359-373; doi: 10.3221/igf-esis.59.24 366 loading spectrum is shown in fig. 7. in addition, the wheel was press-fitted with 0.286 mm interference in diameter. as a result of the spectrum combined with the randomness of the load, different number of blocks are eventually damaging, i.e., contribute to the crack growth. the reference bending stress amplitude for the mean value of bending moment and the interference stress normal to the crack surface needed for the stress intensity factor kmax and kmin evaluation were calculated via the finite element method (fem) in [24]. figure 5: general view of a railway axle with a postulated crack in the t-transition inspected using near-end scan and far-end scan. figure 6: probability of crack detection (pod) as a function of crack size for several non-destructive testing (ndt) methods [28]. figure 7: stress spectrum (mileage 15 000 km) considered in the probabilistic analysis. c. mallor et alii, frattura ed integrità strutturale, 59 (2022) 359-373; doi: 10.3221/igf-esis.59.24 367 the fsoa was applied to calculate the first moment, the second central moment, the third central moment and the fourth central moment of dni at every crack depth, with the two input random variables kimax and kimin. then, the expected value, the variance, the skewness  and the kurtosis  of the fatigue life n were obtained from the ith moments, providing a continuous result along the crack depth a. the results provided by the proposed methodology were compared with the results of 10 000 monte carlo (mc) simulations. to check the accuracy of the method in terms expected value, standard deviation, skewness  and kurtosis, the values of these moments of n for a crack depth equal to 50 mm provided by the monte carlo (mc) and by the probabilistic nasgro equations (pr. eqn.) using the fsoa method are gathered in tab. 1. units mc pr. eqn. pr. eqn.-mc error [%] a [mm] 50 50 – n [km] 4 514 673 4 287 909 -5.02% n [km] 1 402 147 1 325 913 -5.44%  [–] 1.13 1.10 -2.65%  [–] 5.13 5.38 4.87% table 1: expected value, standard deviation, skewness and kurtosis of n provided by monte carlo (mc) and by the probabilistic nasgro equations (pr. eqn.). the results demonstrated that:  the expected value, the standard deviation or variance, the skewness and the kurtosis provided by the mc and by the probabilistic nasgro equations are very similar, therefore, the fsoa is reasonably accurate.  the key advantage of the fsoa method is the lower computational time, which is close to the computation time of a deterministic calculation.  due to the accuracy and the computational efficiency, the fsoa outperforms the conventional mc method. at this point, the probability distribution was fitted based on the prescribed moments of the lifespan provided by the fsoa. three scenarios were considered: (i) the lifespan was assumed to be normally distributed; (ii) the lifespan was assumed to be log-normally distributed; (iii) the pearson distribution family was used to model the lifespan, thus avoiding the need of assuming a distribution in advance. notice that in case (iii), the pearson distribution type was automatically determined based on the skewness and kurtosis, leading in this example to the pearson type vi that corresponds to the beta prime distribution. the probability density functions of the three aforementioned distributions, and the mc histogram of the fatigue life n for a crack depth equal to 50 mm are compared in fig. 8. figure 8: histogram of fatigue life n provided by the monte carlo (mc) and probability density function (pdf) of the normal, the log-normal and the beta prime distributions constructed from moments provided by the probabilistic nasgro equations (pr. eqn.) for 50 mm crack depth. c. mallor et alii, frattura ed integrità strutturale, 59 (2022) 359-373; doi: 10.3221/igf-esis.59.24 368 the following outcomes are achieved:  the expected value, the variance, the skewness, and kurtosis provided by the pr. eqn. enable the construction of pdfs with more than two parameters as it is the case of the versatile pearson distribution family.  the automatic selection of the pearson distribution type that is based on the moments of the underlying distribution is a more general procedure than the selection of an arbitrary probability distribution to fit.  the method of moments makes calculating the parameters of the pearson distribution type quite simple and fast.  the similarity between the pearson type vi, i.e., the beta prime distribution, and the mc histogram confirms that the pearson family accurately captures and provides a good description of the underlying lifespan distribution.  the beta prime distribution agrees well with the mc histogram for all the lifespan range, including the tails and the peak. the superiority of the beta prime distribution over the normal and the lognormal distributions to represent the mc results is clear, especially when describing the lower tail of the distribution of lives, which is of great importance in reliability and in damage tolerance assessment. as mentioned above, the beta prime distribution of the fatigue life n fitted using the fsoa, can be represented by the sf, by the cdf and by the pdf as shown in fig. 9 for a crack depth equal to 50 mm. the normal and the log-normal distributions are also plotted for comparative purposes. figure 9: survival function (sf), cumulative distribution function (cdf) and probability density function (pdf), of the normal, the log-normal and the beta prime distributions constructed from moments provided by the probabilistic nasgro equations (pr. eqn.) for 50 mm crack depth. c. mallor et alii, frattura ed integrità strutturale, 59 (2022) 359-373; doi: 10.3221/igf-esis.59.24 369 the reliability-based inspection interval definition described in reliability-based inspection interval definition, which is applied below, takes advantage of the probabilistic information contained in the fig. 9. in order to apply the reliability-based inspection interval definition, it is necessary to briefly review the principles and requirements for the safety, serviceability and durability of structures concerning the probability of failure and reliability. the en 1990:2002 [35] standard describes the basis for the design and verification of structures and gives guidelines for related aspects of structural reliability. it provides recommendation for the probability of failure, pf, for structural design. it should be emphasized that these values are only notional, and therefore, do not necessarily represent the actual failure rates but, they can be used as operational values and for comparison of reliability levels of structures. as for the failure probability of a railway axle, the standard defines for a construction during the entire life, a probability of failure pf, en 1990 = 7 × 10-5. taking this guidance, in the present case study, the probability of failure was chosen to be 7 × 10-5 since the railway axles are non-redundant primary components whose failure consequences are extremely severe. accordingly, the complementary reliability level is 99.993%. the sf, cdf and pdf of the lifespan probability distribution determined, consider the input variabilities involved in the fatigue problem. the sf of the beta prime distribution fitted based on the fsoa moments, was evaluated for a 99.993% reliability percent, following the procedure described in reliability-based inspection interval definition. the conservative estimation of the fatigue life based on the pearson probability distribution for 99.993% reliability is shown in fig. 10. figure 10: estimation of a conservative number of kilometres for 99.993% reliability. the selected proportion of axles surviving led to a minimum mileage travelled of 1.4 × 106 km, that is, according to the probabilistic fatigue crack growth simulation, 99.993% of axles survive beyond that conservative mileage. the calculations in fig. 10 are conservative when compared to the deterministic estimation since there is the additional prescription of a reliability percent during the sf evaluation. it is worth noting that, apart from a reliability percent, the shape of the distribution significantly influences the conservative life estimate. therefore, the ability of the method in describing the lower tail of the lifespan is a key aspect. note further that because of the conservatism introduced in the adoption of a 99.993% reliability percent, the fatigue crack growth lifetime obtained from a probabilistic basis was shorter than the one obtained by simply using the deterministic calculation. this is somehow comparable to the use of a safety factor but, rather than being arbitrarily chosen, this procedure uses the available knowledge of the lifespan response as a result of the randomness of the input sources and, therefore, its application has a probabilistic foundation. in this example, the conservative lifespan calculated in this manner is obtained according to the randomness of the input loads/stresses. finally, the conservative lifespan estimation in fig. 10 was considered as basis for the interval inspection definition and the for the subsequent evaluation of the cpod and pf associated with the selected ndt technique. the assumptions adopted to calculate the lifetime ndef (step 4) from amin to amax and the number of times that the crack can be detected before a failure could occur, considered for the inspection interval definition (step 5), are given in tab. 2. amin amax ntimes [mm] [mm] [–] 2 50 3 table 2: assumptions on the inspection period definition. c. mallor et alii, frattura ed integrità strutturale, 59 (2022) 359-373; doi: 10.3221/igf-esis.59.24 370 the suggested inspection interval (step 5) according to the idea depicted in fig. 4 led to approximately 462 000 km. that is, the axle will always be subjected to periodic inspection every tins = 462 000 km. then, given the length of the inspection interval suggested, the history values of cpod in successive inspections considering the backward detection scheme and the ultrasonic near-end scan ndt method are calculated according to eq (4) and shown in fig. 11. figure 11: cumulative probability of detection (cpodi) considering the backward detection scheme and the near-end scan technique. nine inspections were possible for the span of this particular case. it can be observed an increase in instantaneous cpod value due to the repetition inspections. note that, the individual pod increases with increasing crack length, fig. 6, and thus the cpod in successive inspections becomes also higher. the results of the overall cpod using eq (4), and the results of pf using eq (5), for the backward detection scheme and the ultrasonic near-end scan technique, are enclosed in tab. 3. tins no. of ins. near-end scan and backward detection scheme [km] [-] cpod pf = 1 cpod 462 000 9 0.999 984 429 4 1.56 × 10-5 table 3: cpod and pf probabilities in the case of ultrasonic near-end scan technique and backwards detection scheme. it is necessary to emphasize that the maintenance plan of railway axles for freight wagons prescribes additional off-service inspection during main wheelset overhauling, typically every ≈ 1 × 106 km for freight trains application. in these circumstances the inspection of axles is performed by using mpi. performing such an inspection is not considered in the previous calculations, what would further increase the cpod values and, accordingly, it would decrease the pf values. the goal is to have a tins associated with a permissible level for probability of failure. a crucial question is what permissible probability of failure is justifiable in engineering practice. for safety critical components, as it is the case of a railway axle, a probability of failure during the entire lifetime in the order the pf, considered in en 1990:2002 [35] standard, pf, en 1990 = 7 × 10-5, seems reasonable. the objective in the design of the maintenance inspection plan is to achieve a pf, lower than the previous specific threshold. it can be observed that the pf for an inspection interval of 462 000 km is compliant with the acceptable probability of failure selected as the threshold. it is demonstrated that the selected inspection intervals were adequate to ensure a high cpod using the ultrasonic near-end scan, prior to the potential failure. the observations of this results lead to the following general outcomes:  the stochastic approach provides viable means for evaluating the effect of random parameters upon the definition of interval inspections within the damage tolerance concept.  a probabilistic lifespan prediction can be integrated in the design and inspection planning of railway axles.  the methodology devised can handle conservative fatigue crack growth estimations that are related to the input variabilities involved in the fatigue crack growth phenomenon. c. mallor et alii, frattura ed integrità strutturale, 59 (2022) 359-373; doi: 10.3221/igf-esis.59.24 371  according to the assumptions of: (i) pf ≤ 7 × 10-5; (ii) backward detection scheme; and (iii) ultrasonic near-end scan, from the results analysed, it is recommended to perform ndt using the ultrasonic near-end application condition every approximately 462 000 km.  the procedure establishes a reliability-based inspection planning and thus, enables the optimization of maintenance expenses selecting an appropriate inspection periodicity. conclusions his paper presents a simple procedure devised for the determination of inspection intervals within the damage tolerance analysis of railway axles, that is based on a probabilistic description of fatigue lifespan, and it is applicable for both non-powered and powered axles. it considers the input uncertainties through a conservative fatigue crack growth life estimation based on the lifespan probability distribution, benefiting from the knowledge available at the lower tail of the distribution of lives. the most important advantage of this approach is that it is based on a more conservative probabilistic rather than deterministic fatigue crack growth lifespan calculation. the benefit consists in a simple relationship between the adopted reliability in the probabilistic lifespan and the conservative prediction of the residual fatigue lifetime for practical use. moreover, this methodology allows to focus on establishing an optimum inspection interval combining probabilistic approaches into the damage tolerance assessment phase. however, it must also balance a variety of sensitive issues of safety, economic, and vehicle availability. the probability distribution fitted from the first four prescribed moments is helpful to describe the fatigue crack growth process under stochastic conditions such as under a random bending moment loading and loading spectrum. the present approach offers potential application in practice, and it could have a remarkable effect onto the definition of inspection intervals. in the future work, the application of methodology presented will be extended, considering more parameters as random variables such as the material properties. further investigations regarding limit state functions and conditional probability events involving fatigue failure, crack detection and reliability updating by actual observations are required. continued efforts are needed to make reliability-based procedures and probabilistic analyses more integrated in the maintenance planning of damage-tolerant railway axles. acknowledgements he authors acknowledge the spanish ministry of economy, industry and competitive through the national programme for research aimed at the challenges of society that financially supported the project rtc-2016-4813-4. references [1] zerbst, u., beretta, s., köhler, g., lawton, a., vormwald, m., beier, h.th., klinger, c., černý, i., rudlin, j., heckel, t., klingbeil, d. (2013). safe life and damage tolerance aspects of railway axles – a review, eng. fract. mech., 98, pp. 214–271. doi: 10.1016/j.engfracmech.2012.09.029. [2] zerbst, u., klinger, c., klingbeil, d. (2013). structural assessment of railway axles – a critical review, eng. fail. anal., 35, pp. 54–65. doi: 10.1016/j.engfailanal.2012.11.007. [3] en 13103-1:2017. railway applications. wheelsets and bogies. part 1: design method for axles with external journals, european committee for standardization. [4] cervello, s. (2016). fatigue properties of railway axles: new results of full-scale specimens from euraxles project, int. j. fatigue, 86(supplement c), pp. 2–12. doi: 10.1016/j.ijfatigue.2015.11.028. [5] beretta, s., carboni, m. (2011). variable amplitude fatigue crack growth in a mild steel for railway axles: experiments and predictive models, eng. fract. mech., 78(5), pp. 848–862. doi: 10.1016/j.engfracmech.2010.11.019. [6] pokorný, p., náhlík, l., hutař, p. (2014). comparison of different load spectra on residual fatigue lifetime of railway axle, procedia eng., 74, pp. 313–316. doi: 10.1016/j.proeng.2014.06.269. [7] pokorný, p., hutař, p., náhlík, l. (2016). residual fatigue lifetime estimation of railway axles for various loading spectra, theor. appl. fract. mech., 82, pp. 25–32. doi: 10.1016/j.tafmec.2015.06.007. [8] traupe, m., landaberea, a. (2017). euraxles a global approach for design, production and maintenance of railway axles: wp2 development of numerical models for the analysis of railway axles, mater. werkst., 48, pp. 687–698. t t c. mallor et alii, frattura ed integrità strutturale, 59 (2022) 359-373; doi: 10.3221/igf-esis.59.24 372 doi: 10.1002/mawe.201600570. [9] bea, j.a. (1997). simulación del crecimiento de grietas por fatiga aleatoria mediante elementos probabilistas. phd thesis, universidad de zaragoza. [10] bea, j.a., doblaré, m., gracia, l. (1999). evaluation of the probability distribution of crack propagation life in metal fatigue by means of probabilistic finite element method and b-models, eng. fract. mech., 63(6), pp. 675–711. doi: 10.1016/s0013-7944(99)00053-3. [11] núñez, j.l. (2003). análisis del fenómeno de la fatiga en metales en etapa de nucleación mediante la utilización de modelos estadísticos de daño acumulado y elementos finitos probabilistas. phd thesis, universidad de zaragoza. [12] calvo, s. (2008). determinación de la probabilidad de fallo en componentes métalicos sometidos a estados multiaxiales de tensión mediante la utilización de elementos finitos probabilistas y modelos estadísticos de daño acumulado. phd thesis, universidad de zaragoza. [13] calvo, s., canales, m., gómez, c., valdés, j.r., núñez, j.l. (2011). probabilistic formulation of the multiaxial fatigue damage of liu, int. j. fatigue, 33(3), pp. 460–465. doi: 10.1016/j.ijfatigue.2010.10.003. [14] broek, d. (1989). the practical use of fracture mechanics, dordrecht, the netherlands, kluwer academic publishers. [15] beretta, s., carboni, m., cantini, s., ghidini, a. (2004). application of fatigue crack growth algorithms to railway axles and comparison of two steel grades, proc. inst. mech. eng. part f j. rail rapid transit, 218(4), pp. 317–326. doi: 10.1243/0954409043125888. [16] beretta, s., carboni, m. (2006). experiments and stochastic model for propagation lifetime of railway axles, eng. fract. mech., 73(17), pp. 2627–2641. doi: 10.1016/j.engfracmech.2006.04.024. [17] cocheteux, f., pouillart, t. (2009). design, manufacture and maintenance of wheelset at sncf, int. j. railw., 2(1), pp. 8–17. [18] zerbst, u., schödel, m., beier, h.th. (2011). parameters affecting the damage tolerance behaviour of railway axles, eng. fract. mech., 78(5), pp. 793–809. doi: 10.1016/j.engfracmech.2010.03.013. [19] luke, m., varfolomeev, i., lütkepohl, k., esderts, a. (2011). fatigue crack growth in railway axles: assessment concept and validation tests, eng. fract. mech., 78(5), pp. 714–730. doi: 10.1016/j.engfracmech.2010.11.024. [20] mädler, k., geburtig, t., ullrich, d. (2016). an experimental approach to determining the residual lifetimes of wheelset axles on a full-scale wheel-rail roller test rig, int. j. fatigue, 86, pp. 58–63. doi: 10.1016/j.ijfatigue.2015.06.016. [21] náhlík, l., pokorný, p., ševčík, m., fajkoš, r., matušek, p., hutař, p. (2017). fatigue lifetime estimation of railway axles, eng. fail. anal., 73, pp. 139–157. doi: 10.1016/j.engfailanal.2016.12.014. [22] carboni, m., beretta, s. (2007). effect of probability of detection upon the definition of inspection intervals for railway axles, proc. inst. mech. eng. part f j. rail rapid transit, 221(3), pp. 409–417. doi: 10.1243/09544097jrrt132. [23] forman, r.g., mettu, s.r. (1990). behavior of surface and corner cracks subjected to tensile and bending loads in ti6al-4v alloy, astm stp 1131 am. soc. test. mater. phila. pa, pp. 519–46. [24] mallor, c., calvo, s., núñez, j.l., rodríguez-barrachina, r., landaberea, a. (2020). full second-order approach for expected value and variance prediction of probabilistic fatigue crack growth life, int. j. fatigue, 133, pp. 105454. doi: 10.1016/j.ijfatigue.2019.105454. [25] mallor, c., calvo, s., núñez, j.l., rodríguez-barrachina, r., landaberea, a. (2020). uncertainty propagation using the full second-order approach for probabilistic fatigue crack growth life, int. j. numer. methods calc. des. eng. rimni, 36(3), pp. 37. doi: 10.23967/j.rimni.2020.07.004. [26] mallor c., calvo s., núñez j.l., rodríguez-barrachina r., landaberea a. (2020). propagation of uncertainty in fatigue crack growth for probabilistic life estimation, procedia struct. integr., 28, pp. 619–626. doi: 10.1016/j.prostr.2020.10.072. [27] zerbst, u., schwalbe, k.-h., ainsworth, r.a. (2003). 7.01 an overview of failure assessment methods in codes and standards. in: milne, i., ritchie, r.o., karihaloo, b., (eds.), comprehensive structural integrity, oxford, pergamon, pp. 1–48. [28] zerbst, u., mädler, k., hintze, h. (2005). fracture mechanics in railway applications – an overview, eng. fract. mech., 72(2), pp. 163–194. doi: 10.1016/j.engfracmech.2003.11.010. [29] zerbst, u., vormwald, m., andersch, c., mädler, k., pfuff, m. (2005). the development of a damage tolerance concept for railway components and its demonstration for a railway axle, eng. fract. mech., 72(2), pp. 209–239. doi: 10.1016/j.engfracmech.2003.11.011. [30] carboni, m., cantini, s. (2016). advanced ultrasonic “probability of detection” curves for designing in-service inspection intervals, int. j. fatigue, 86, pp. 77–87. doi: 10.1016/j.ijfatigue.2015.07.018. [31] benyon, j., watson, a. (2001). the use of monte-carlo analysis to increase axle inspection interval. proceedings of the 13th international wheelset congress, rome, italy, pp. 17–21. c. mallor et alii, frattura ed integrità strutturale, 59 (2022) 359-373; doi: 10.3221/igf-esis.59.24 373 [32] johnson, n.l., kotz, s., balakrishnan, n. (1994). continuous univariate distributions, vol. 1–2, wiley-interscience. [33] en 13261:2009+a1:2010: railway applications – wheelsets and bogies – axles – product requirements, european committee for standardization. [34] uic b 169 rp 36:2013-12 defect tolerance concept (dtc) permitted defects and surface properties for axles under maintenance., uic standard. 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/hrv (za stvaranje adobe pdf dokumenata najpogodnijih za visokokvalitetni ispis prije tiskanja koristite ove postavke. stvoreni pdf dokumenti mogu se otvoriti acrobat i adobe reader 5.0 i kasnijim verzijama.) /hun 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can be opened with acrobat and adobe reader 5.0 and later.) >> /namespace [ (adobe) (common) (1.0) ] /othernamespaces [ << /asreaderspreads false /cropimagestoframes true /errorcontrol /warnandcontinue /flattenerignorespreadoverrides false /includeguidesgrids false /includenonprinting false /includeslug false /namespace [ (adobe) (indesign) (4.0) ] /omitplacedbitmaps false /omitplacedeps false /omitplacedpdf false /simulateoverprint /legacy >> << /addbleedmarks false /addcolorbars false /addcropmarks false /addpageinfo false /addregmarks false /convertcolors /converttocmyk /destinationprofilename () /destinationprofileselector /documentcmyk /downsample16bitimages true /flattenerpreset << /presetselector /mediumresolution >> /formelements false /generatestructure false /includebookmarks false /includehyperlinks false /includeinteractive false /includelayers false /includeprofiles false /multimediahandling /useobjectsettings /namespace [ (adobe) (creativesuite) (2.0) ] /pdfxoutputintentprofileselector /documentcmyk /preserveediting true /untaggedcmykhandling /leaveuntagged /untaggedrgbhandling /usedocumentprofile /usedocumentbleed false >> ] >> setdistillerparams << /hwresolution [2400 2400] /pagesize [612.000 792.000] >> setpagedevice microsoft word numero_35_art_57 x.c. arnoult et alii, frattura ed integrità strutturale, 35 (2016) 509-522; doi: 10.3221/igf-esis.35.57 509 short review: potential impact of delamination cracks on fracture toughness of structural materials x.c. arnoult, m. růžičková, k. kunzová centrum výzkumu řež s. r. o., husinec-řež, czech republic xavier.arnoult@cvrez.cz a. materna czech technical university in prague, faculty of nuclear sciences and physical engineering prague, czech republic abstract. the current energy policy envisages extended lifetime for the current nuclear power plants (gen ii npp). this policy imposes a large research effort to understand the ageing of power plant components. in this goal, it is necessary to improve knowledge about safety, reliability and components’ integrity for more than forty years of operation. in central and eastern europe, the majority of npps are vver types, where some of the components are produced from austenitic steel 08ch18n10t. irradiated 08ch18n10t may exhibit brittle behavior, namely delamination cracks are found in some cases on the fracture surface of irradiated 08ch18n10t with elongated δ-ferrite. delamination cracks have also been observed on the fracture surface of high-strength steels or aluminum-lithium alloys. this article presents a state-of-the art review to provide a detailed analysis of the influence of delamination cracks on the toughness of metal alloys. in general, the delamination cracks are present in metal alloys having a high texture and microstructure anisotropy. three types of delamination cracks have been observed and are classified as crack arrester delamination, crack divider delamination and crack splitting delamination. the microscopy characterization, 3d fracture theories and computational studies explaining possible causes and effects of delamination cracks on the mechanical properties of metal alloys are presented. keywords. delamination cracks; fracture mechanics; steels; ferrite. introduction elamination cracks, i.e. secondary cracks parallel to the rolling plane, have been observed on high strength steels [1-10], aluminum-lithium alloys [11-15], ti-stabilized stainless steels [16, 17] and ultrafine-grained steels [18]. different types of delamination cracks in combination with different orientations of the specimen direction had been identified [13, 19]. the delamination cracks have been classified (a) as crack divider, (b) crack arrester and (c) crack splitting as shown on the figure 1. in the last 4 decades, some researcher noticed the existence of delamination cracks and tried to understand the origins, mechanisms and consequences on the fracture toughness, impact toughness and tensile properties. some delamination cracks are shown on the fracture surfaces of irradiated 08ch18n10t with elongated δ-ferrite [16, 17], the 304 l and the 316 l after exposure in pwr [20] environments and degraded by hydrogen embrittlement [21]. d x.c. arnoult et alii, frattura ed integrità strutturale, 35 (2016) 509-522; doi: 10.3221/igf-esis.35.57 510 as the current energy policy envisages an extended lifetime for the current generation ii nuclear power plants, large research effort must be devoted to understanding the ageing of power plant components, where delamination cracking is one of the possible ageing mechanisms. in this short review, the mechanism of delamination cracking is presented and open questions are identified in determining if the delamination cracks have negative or positive impact on the material toughness, which applies especially to the crack divider orientation. (a) l-t and t-l orientation: crack divider. (b) t-s and l-s orientation: crack arrester. (c) s-l and s-t orientation: crack splitting. figure 1: terminology used to describe the various orientation of delamination cracks [13, 19]. influence of heat treatment, test temperature and irradiation tensile fracture surface ramfitt and marder [22] tested a very low-carbon steel (vlc steel) under tensile loading at room temperature to understand the influence of the finishing temperature of heat treatment (960°c 150°c) on the fracture surface of this steel. after fracture, delamination cracks were observed in all transverse specimens from plates where the finishing temperatures were at 480°c and below. in the case of longitudinal specimens, delamination cracks occurred on specimens made from plates having a finishing temperature at 370°c and below. thus finishing temperatures at least 260°c below the a1 temperature (i.e. the eutectoid temperature above which austenitic phase is formed) promoted the development of delamination cracks in the fracture process of the vlc steel. it was also observed that the number of delamination cracks increased with decreasing finishing temperature of heat treatment and delamination cracks were always orientated parallel to the rolling plane. baldi et buzzichelli [23] investigated the influence of finishing temperature (cf. table 1) and microstructure on seven different high-strength-low-alloy-steels (hsla steels). they studied the tensile behavior of these steels as a function of finishing temperature and specimen orientation (0° and 90° relative to the rolling direction). the authors observed that on all studied hsla steels, the fracture surface displayed longitudinal delamination cracks in both directions. code heat temperature, °c rolling schedule finishing temperature, °c final thickness, mm cooling mc1 1150/2h 80% r.a. at < 750°c 700 12 air mc2 1150/2h 80% r.a. at < 750°c 700 12 air mc3 1150/2h 80% r.a. at < 800°c 750 12 air mc4 1150/2h 80% r.a. at < 750°c 700 12 oil quench f2a 1150/2h 80% r.a. at < 750°c 700 12 air c1b 1150/2h 80% r.a. at < 750°c 700 12 air m1 1150/2h 66% r.a. at < 900°c 750 12 air table 1: rolling and heat-treatment schedule [23]. similarly, yan et al [6] investigated the influence of tempering temperature on a hsla steel. the 200°c, 400°c and 700°c tempered specimens exhibited a typical cup-and-cone tensile fracture (cf. figure 2). there were no delamination cracks on the fracture surface. however, large and deep delamination cracks were observed on the fracture surfaces of tensile specimens tempered in the range between 500°c and 650°c (cf. figure 9). the latter specimens did not have a typical cup-and-cone fracture shape, which indicates a low or very low ductility, and the fracture surfaces were divided in two b x.c. arnoult et alii, frattura ed integrità strutturale, 35 (2016) 509-522; doi: 10.3221/igf-esis.35.57 511 parts by the center. guo 2002 [1] observed a similar phenomenon on ct specimens fabricated from api x70 steel. as guo et al, yan et al observed small delamination cracks close and parallel to the main delamination cracks. figure 2: sem picture of a fracture observed on a 200°c-tempered tensile specimen [6]. figure 3: sem picture of fracture of 600°c tempered tensile specimen [6]. tankoua et al [10] studied the influence of test temperature on the fracture surface of arcelor pipeline steel. specimen orientations were 0° and 90° according to the rolling direction. for both orientations, the authors observed three fracture modes in competition on notch tensile specimen. at 20°c, 100°c and -196°c the ductile fracture, ductile fracture with central delamination cracks and cleavage fracture were observed, respectively. this indicates a ductile-brittle-transitiontemperature in the fracture behavior of this steel. in the case of -196°c, the cleavage fracture mode was accompanied by a small number of micro delamination cracks. baldi and buzzichelli [23] found central delamination cracks on a welldeveloped ductile fracture surface. in the last decade, irradiated 08ch18n10t specimens (chemically equivalent to a321) originating from the reactor vessel of the decommissioned vver-440-type 230 nuclear power plant located in greifswald in northern germany was evaluated by hojna et al. [16, 17]. the authors observe a complex fracture surface after a tensile test at room temperature: ductile fracture zone and many different types of secondary cracks, among which delamination cracks were present [17]. x.c. arnoult et alii, frattura ed integrità strutturale, 35 (2016) 509-522; doi: 10.3221/igf-esis.35.57 512 charpy impact toughness properties the charpy impact test may be used to evaluate the fracture energy at different temperatures, to characterize qualitatively the fracture mode (ductile or brittle facture) and to estimate the ductile-brittle-transition temperature (dbtt). this test is interesting to understand in which fracture mode the delamination cracks are displayed. all studies, cited in this section, used specimens with a v shape notch. bramfitt and marder [22] obtained four different charpy curves at different heat treatment finishing temperature before being cooled down and the range of test temperature was from 24°c to -150°c. as heat treatment finishing temperature decreases, the upper shelf energy decreases from 160 j to 50 j and the dbtt was shifted to lower temperature and disappeared for specimen having a finishing temperature at 316°c. charpy specimens manufactured from the plate finished at 960°c and tested at 24°c showed a fully ductile fracture surface. the same material tested at -18°c and -73°c showed a completely developed cleavage fracture. for the charpy specimens manufactured form the plate finished at 707°c that were tested at 24°c and -18°c, the fracture surface showed delamination cracks which were parallel to the rolling plane. at -18°c the number of delamination cracks was higher than at room temperature. when specimens were tested at -73°c, the fracture appearance was fully cleavage. the same phenomenon was observed for specimens manufactured from the plate finished at 538°c. however, the number of delamination cracks at equivalent test temperature was observed higher compared with the previous plate. for the specimens made from the plate having finishing temperature at 316°c, delamination occurred at all three temperatures, and the delamination has still occurred at -129°c where only 5% of the area was a cleavage fracture. this study shows the influence of heat treatment and test temperature on the number of delamination cracks developed and their length present on the fracture plane, however, these qualitative results did not provide a clue on the role that the delamination cracks play in the fracture behavior of metal alloys. baldi 1978 [23] and song et al [18] observed a similar evolution of the number and length of delamination cracks related to the decrease of test temperature. figure 4: effect of banding concentration on dbtt and upper shelf energy [24]. shanmugan and pathak [24] demonstrated the influence of the number of delamination cracks present on the fracture surface and how the charpy toughness properties are influenced by these special cracks. they used a micro-alloyed steel and subjected it to a suitable heat treatment in order to implement a variation of ferrite bands in terms of density per mm. figure 4 shows the effect of ferritic banding density present inside the microstructure on the charpy toughness properties. during the charpy test, the delamination crack density on the fracture surface corresponded approximately with the density of ferrite bands per mm. for temperatures higher than 10°c, a high number of ferrite bands led to a decrease of upper shelf energy and a shift of the dbtt to lower temperatures has been observed, as compared to the case of no ferrite bands present in the specimen. contrarily, a low density of ferrite bands led to a higher upper shelf energy than in the case without ferrite bands. similarly to bramfitt and marder [22], shanmugan and pathak [24] observed that delamination cracks seem to disappear with decreasing test temperature. according to them, this is due to the fact that at very low temperature, not enough time is given for delamination cracking process to take place. in this study, it was x.c. arnoult et alii, frattura ed integrità strutturale, 35 (2016) 509-522; doi: 10.3221/igf-esis.35.57 513 shown that delamination cracks may have positive effect on the impact toughness properties if their number is relatively low. fracture surface of specimens from plate of hsla steels which underwent a tempering step [6] and were tested at room temperature did not display any delamination cracks, unlike those tested at -30°c (cf. table 2 and figure 5). tempering temperature, °c cvn impact energy, j delamination cracks as-rolled 56 no 200 60 no 300 50 no 400 51 small and local 500 47 large and global 550 45 large and global 575 49 large and global 600 50 large and global 625 53 large and global 650 49 large and global 700 55 small and local table 2: charpy impact toughness of tempered specimens and tested at -30°c [6]. figure 5: sem picture of fracture surface of charpy specimens tempered at 200°c a), 400°c b), 500°c c), 600°c d) and tested at 30°c. x.c. arnoult et alii, frattura ed integrità strutturale, 35 (2016) 509-522; doi: 10.3221/igf-esis.35.57 514 it was observed that at higher tempering temperatures delamination cracks increase both in number and in length, then decrease both in number and in length when the tempering temperature reaches 700°c. yang et al [2] observed for api x70 pipeline steel a temperature dependence on the appearance of the fracture surface. at -60°c, specimen 10 mm thick and in t-l orientation showed a ductile fracture whereas at -20°c, authors observed some delamination cracks on the fracture surface. joo et al [9] showed also an orientation dependence on the charpy impact toughness. this could probably be explained by the development of delamination cracks during the fracture process. the api x80 [9] t-l and l-t oriented specimen had a ductile failure between 25°c and -60°c, with the presence of delamination cracks on fracture surface for temperatures from -20°c to -60°c, and cleavage failure mode without delamination cracks at -80°c and 100°c. figure 6: charpy specimens’ orientation [9]. figure 7: charpy impact test as function of temperature a), as function of orientation b), fracture surface of l-t orientation of charpy specimens broken at room temperature c), -60°c d), and -100°c e) [9] x.c. arnoult et alii, frattura ed integrità strutturale, 35 (2016) 509-522; doi: 10.3221/igf-esis.35.57 515 for d-d orientation (cf. figure 6), api x80 steel developed some delamination cracks only at -20°c and the impact energy was comparable for the other two orientations at the same temperature. for the other test temperatures (from 60°c to -100°c), cleavage fracture was the main failure mode for d-d specimen orientation (cf. figure 7). for the authors, good resistance to impact of specimens with t-l and l-t orientation at ductile-brittle transition region is due to the capacity of delamination to take place during the failure process. their assumption is reinforced by the fact that the impact energy dropped sharply below -60°c for the t-l and l-t oriented specimens and the only time when the d-d orientated specimens showed a similar magnitude of impact energy as t-l and l-t oriented specimens was when some delamination cracks were present during the failure process. relationship between metallography and delamination cracks s described in the two previous sections, heat treatment and specimen orientation have a strong effect on the occurrence of delamination cracking as one of the fracture modes. it seems obvious that microstructure and texture of the studied steels is an important factor in this process. different steels with various microstructure and texture were investigated. steels code microstructure hsla steel [23] mc1, f2a acicular ferrite mc2 acicular ferrite mc3 acicular ferrite mc4 polygonal ferrite, acicular ferrite c1b polygonal ferrite, acicular ferrite, thin filament of cementite along grain boundaries m1 polygonal ferrite d=7µm, d=6µm, acicular ferrite pearlite hsla steel [24] banding of ferrite banding of pearlite c-mn steel [18] ferrite pearlite average grain size = 6.8 µm ultrafine grained cmn steel [18] ferrite with globular cementite particle in the grain cementite located at ferrite grain boundaries average grain size = 1.3 µm x100 steel [8] a ferrite, bainitic-martensitic dual phase, ferrite fraction: 20% b ferrite and bainitic-martensitic dual phase, ferrite fraction: 70% c ferrite and bainitic-martensitic dual phase, ferrite fraction: 75% d deformed ferrite, bainitic-martensitic dual phase, ferrite fraction: 20% hsls [6, 7] ferrite lower bainite carbides and nitrides api x80 [9] coarse allotriomorphics ferrite, pearlite, ma constituent, bainite micro-alloyed low carbon steel [10] ferrite, bainite 08ch18n10t [25] austenite delta-ferrite table 3: different steels and their microstructure investigated for the understanding of delamination cracks. a x.c. arnoult et alii, frattura ed integrità strutturale, 35 (2016) 509-522; doi: 10.3221/igf-esis.35.57 516 as seen in table 3, there are various kinds of steels where the delamination cracks could be one of the fracture modes. all these steels have a common characteristic, which is the presence of ferrite in the microstructure. different authors performed metallography analyses to understand the origins and the mechanisms of the delamination cracking process. typically, it has been concluded that the region between delamination cracks was similar to a ductile tensile failure (cf. figure 8a) or cup-and-cone shape [1, 18, 19, 22]. figure 8: sem image of charpy specimen tested at -170°c a), orientation map of grains around the delamination cracks b), and orientation map of grains at the top of subunits c) [18]. furthermore, dimples were often present in the vicinity of the delamination cracks [1, 22].the necking-like shape of the region between delamination cracks indicates a relatively high degree of ductility even at low and very low test temperatures [1, 18, 22]. moreover, the arrows in figure 8a show chains of large voids in the specimen under the fracture surface parallel to the delamination cracks. however baldi and buzzichelli [23] note that delamination cracks have a propensity to propagate in brittle manner, and usually the delamination cracks were displayed on brittle fracture surface [8-10, 17, 18, 20, 23]. that is a paradox of delamination cracks. when the failure mode is ductile, majority of investigators claim that the delamination cracks are not developed, but around a transition region, where the shear failure mode and the brittle failure mode are in competition, the delamination cracks have chances to be promoted. as seen above, the delamination cracks are consequences of a very ductile behavior it was observed that delamination crack initiation and growth was located along weak interfaces [2], some delamination cracks follow along the path of the grain boundaries of highly elongated grains [22], or occurred between coarse ferrite grains and a region richer in martensite, bainite or pearlite phases, i.e. between softer and harder phase [9]. figure 8b [18] shows grain orientation around delamination cracks; two colors dominate, indicating that the texture is highly anisotropic inside this ultrafine-grained steel. the red is for the family crystal orientation {100} and the blue for the family crystal orientation {111}. it can be seen that delamination cracks opened the interface of elongated clusters of grains with different crystal orientation components, demonstrating that the delamination cracks spread along the boundaries of grains having high-angle grain boundary misorientation. hara et al [3, 8] made a relationship between the microstructure, texture and ctoa (crack tip opening angle) results. table 4 shows the results of ctoa related to the phases present inside different steels and the texture. according to the authors, for the steel a, there were no delamination cracks on the fracture surface. for the steels b and c, few small delamination cracks were shown on the fracture surface, however, for the steel d, large delamination cracks were present on the fracture surface, and it is for the steel d that the ctoa was the lowest. in this case, delamination cracks can have a negative impact on mechanical properties. the steel d is the one having the highest intensity of crystal plane family {100}. the comparison between the microstructure of steel b (or c) compared with that of steel d clearly shows that deformed ferrite increases sharply the intensity of crystal plane family {100}, and the differences in the x.c. arnoult et alii, frattura ed integrità strutturale, 35 (2016) 509-522; doi: 10.3221/igf-esis.35.57 517 microstructure between steel a, b and c did not influence the ctoa properties but only the fracture surface. in this case, the factor promoting the delamination cracks is microstructure composed of hard and soft phases and a high intensity of plane {100}. steels microstructure {100} intensity parallel to rd ctoa a bainite 1.5 12 to 18° b and c ferrite and bainitemartensitic 1.6 to 1.7 11 to 18° d deformed ferrite bainite-martensite more than 2.5 <10° table 4: relationship between ctoa, the intensity of the {100} texture parallel to the rolling direction and the microstructure [8]. to understand the role of elongated grains, yan et al [6,7] used the as-rolled steel and subjected it to the triple-oil-quench heat treatment, thus the elongated grain microstructure changed to equiaxed grain microstructure. charpy test conducted at -30°c indicated that the samples with equiaxed grains exhibited no delamination cracks on the fracture surface. this result signifies that the presence of elongated grains in the microstructure are a necessary but not sufficient condition. for the authors, the presence of precipitates is assumed to be one of the causes of the delamination cracks. the precipitates have been formed by tempering the hsla steel at temperatures in the range between 500 to 650°c. then the elongated grains and aligned precipitates seem together responsible for the delamination cracking process in this steel. for steels having microstructural bands [9], bands could be an important cause of delamination occurrence. figure 9 shows a significant difference in the crystallography of areas designated x and y located on opposite sides of the delamination crack. crystal face orientation is (101) for the area x and (111) for the area y and a clear difference is apparent in the grain orientation spread map. the different orientations may create a weakness between the bands and allow the development of a delamination crack. figure 9: delamination crack in a l-t orientation charpy sample broken at -40°c: top: sem picture, bottom: orientation maps and grain orientation spread maps with the key in degrees [9]. x.c. arnoult et alii, frattura ed integrità strutturale, 35 (2016) 509-522; doi: 10.3221/igf-esis.35.57 518 in case of crack divider, formation of delamination crack is mainly driven by stress component zz . in front of the crack in a finite thickness plate (for example a ct-specimen), zz reaches its maximum in the middle of the thickness. to evaluate the intensity of zz over the thickness of specimen, the out-of-plane constraint factor zt , for a mode i through thickness crack, has been given by [26]       0.58 1 / 2.3 1 1/2 3/2 2 0.94 / 1 1 1 1 1.218 0.395 0.361 2 2 1 n n z p r b r r r r t r b b b z b                                                (1) for 0zt  where b  thickness, n  strain hardening exponent, pr  average size of plastic zone through the thickness of the plate [26]. as was observed in [1-3, 10, 27], a large delamination crack occurs at the middle of specimen. as a result of equation (1), its size increases with increasing thickness of the specimen [1]. newly created free surface causes local drop in zt (cf. figure 10) and condition for the formation of smaller delamination cracks at the quarter of the thickness. figure 10: the out-of-plane constraint factor t_z in front of a mode i crack, solid line with delamination crack, dashed line without delamination crack [1]. a number of authors [1, 8-10, 18, 19, 22, 28] noticed an enhancement of the fracture toughness properties ( ck , cj ), significantly higher lower-shelf energy and shifting at lower temperature of the dbtt during charpy impact tests. the same authors observed the development of multi-delamination cracks that were found on the fracture surface of charpy and ct-specimens as well as a single central delamination crack on tensile notch or smooth specimens [6, 10]. when fracture toughness tests are performed using ct-specimens, the parameters ck and cj are thickness dependent [29]. due to the stress distribution at the crack tip, ck and cj increase when the ct-specimen with decreasing thickness. thin specimens are in plane-stress condition whereas thick specimens are in plane-strain condition. the same dependence was also shown for the charpy impact test [2]. then as shown on figure 10, there is a triaxial stress relaxation, (because zz is reduced to zero), and transformation of the global plane-strain fracture into a serie of local plane-stress failure x.c. arnoult et alii, frattura ed integrità strutturale, 35 (2016) 509-522; doi: 10.3221/igf-esis.35.57 519 caused by delamination cracks. thus the multi-delamination cracks acts as a sum of plane-stress subunits (cf. figure 11). [1, 2, 19, 28] and the fracture toughness and impact toughness could increase. figure 11: effective thickness b1, nominal thickness b [1]. yan et al [6] provided an interesting explanation about the development of delamination taking into account the plastic zone near the crack tip. in the case of charpy impact test, the specimen bends and a plastic zone is generated at the notch and the contraction in the thickness direction is constrained. in this way, a triaxial stress state is created. when the crack grows, the location of this plastic zone will move from the zone close to the notch to extend across the thickness. the magnitude of stresses in this plastic zone is significantly higher than the yield stress that the delamination cracks generated. both the low strain-hardening capacity for tempered steel and the elongated grains in the triaxial tensile stress zone facilitate the generation of delamination cracks along the weak paths and lead to distinct delamination cracks. rao et al [13] noticed similar behavior in aluminum-lithium alloys, having small strain hardening and elongated grains, when they performed fracture toughness tests with ct-specimens. no large delamination cracks or only minor local delaminations were observed in steels having medium capacity for elongation and necking. during a charpy impact test, delamination cracks may appear if the stresses in the thickness direction are high enough to delaminate the anisotropic microstructure along its weak paths. perhaps, it is one of the reasons why the delamination cracks are more likely generated at the temperature transition where the fracture mode is mixed for non-active material, and around 11 dpa for irradiated austenitic steel with delta-ferrite content [16, 17]. guo et al [1] defined a criterion to estimate when the delamination crack will occur in the case of fracture toughness test. it is assumed that the in-plane strength of the material is c , and the strength in the thickness direction is zc and zc c  . when  yy c cr  , macrocrack will occur, when  zz c zcr  delamination cracks will occur and the delamination cracks will appear before macrocrack will propagate if zc c  . kalyanam et al [15] show the influence of the stress distribution of a central delamination crack in ct-specimen. near the tip of the macrocrack, the delamination crack produced a small region of traction free surfaces on the center plane, where the delamination crack is located, which then led to a sharp gradient in stress fields similar to those observed at the outside surface. it can be noticed that the stress component zz is equal to zero at the delamination crack location, thus locally, the material is in plane-stress condition. at the head of delamination crack, the stress component yy is about 1.4 ys in the absence of delamination cracks and increases to about 2.1 ys in the presence of delamination cracks. for the stress component xx , the presence of delamination cracks represents a difference in the order of 0.5 ys near the center plane. thus at the head of the macrocrack near the delamination crack, there is plane-stress condition whereas at the head of the delamination crack far from the macrocrack, the triaxial state of stress prevails. to estimate simply the “subunit toughness” in assuming that the steel behaves as a laminate, the following equation could be used [32] x.c. arnoult et alii, frattura ed integrità strutturale, 35 (2016) 509-522; doi: 10.3221/igf-esis.35.57 520 1/2 l c a pmf w k bw       (2) where  m is the number of ligaments, p the load on each ligament, w and b are full specimen width and thickness, and a f w       the function of the crack length-to-width ratio. when the subunit toughness is estimated, the global fracture toughness can be computed using the following equation [33]: 01 24 l c ic f ys k k e b b           (3) where ys is the yield strength,  e the elastic modulus, f the true fracture strain for plain stress condition, b the full thickness of specimen, and 0b the maximum thickness in which the plane-stress fracture can fully develop. rao et al [13] used these two equations to estimate the fracture toughness of aluminum-lithium alloys and the agreement between the experimental results and estimation was excellent according to them. conclusion s seen above, numerical simulation by finite-element-analysis [15] may be used to provide the stress distribution close to the back and the head of delamination crack. nevertheless, this type of simulation accounts only for one delamination crack and therefore, cannot provide information on the impact of multi-delamination cracks on ck and cj . furthermore, no explanation can be provided about the influence of delamination cracks on the crack growth rate of the macrocrack. neither is it clear if the delamination cracks appear before or during the propagation of the macrocrack. thus to clarify these two questions it is necessary to develop a simulation methodology that could foresee if there are some reciprocal influences between the macrocrack and the delamination cracks. the use of multi-scale modeling to estimate the stress and strain distribution inside grains and at grain boundaries could help to progress in this field and define a delamination cracks criterion.  heat treatment, test temperature, thickness of specimen and stress distribution significantly influence the number, width and length of delamination cracks.  for charpy impact test, the upper shelf energy decreases, the dbtt shifts to lower temperatures and the lower shelf energy increases in the presence of delamination cracks.  large number of delamination cracks yields to inferior toughness.  the presence of ferrite together with a harder phase combined with high intensity of {100} orientation plane favors the occurrence of delamination cracks.  the delamination cracks occur in brittle manner at weak interfaces.  the delamination cracks change the stress distribution from plane-strain to plane-stress condition. the presented work was financially supported by the susen project cz.1.05/2.1.00/03.0108 realized in the framework of the european regional development fund (erdf). reference [1] guo,w., dong, h., lu, m., zhao, x., the coupled effects of thickness and delamination on cracking resistance of x70 pipeline steel, int. j. pressure vessels pip., 79 (2002) 403-412. [2] yang, z., huo, c.y., guo, w., the charpy notch impact test of x70 pipeline steel with delamination cracks. key eng. mater., 297-300 (2005) 2391-2396. a x.c. arnoult et alii, frattura ed integrità strutturale, 35 (2016) 509-522; doi: 10.3221/igf-esis.35.57 521 [3] hara, t., shinohara, y., asahi, h., terada, y., effects of microstructure and texture on dwtt properties for high strength line pipe steels, in: asme. proceeding of the international pipeline conference, calgary, alberta, canada, (2006) 245-250. [4] yang, z., guo, w.l., huo, c.y., wang, y., fracture appearance evaluation of high performance pipeline steel dwtt specimen with delamination cracks, key eng. mater., 324-325 (2006) 59-62. [5] hara, t., shinohara, y., terada, y., asahi, h., dwtt properties for high strength line pipe steels. proceeding of the 18th international offshore and polar engineering conference, vancouver, canada, (2008) 189-193. [6] yan, w., sha, l., zhu, w., wang, y., shan, y., yang., k., delamination fracture related to tempering in a highstrength low-alloy steel. metall, mater. trans. a., 41 (2009) 159-171. [7] yan, w., sha, l., zhu, w., wang, y., shan, y., yang.,k., change of tensile behavior of a high-strength low-alloy steel with tempering temperature, mater. sci. eng. a., 517 (2009) 369-374. [8] hara, t., t. fujishiro, effect of separation on ductile crack propagation behavior during drop weight tear test. proceeding of the 18h international offshore and polar engineering conference, vancouver, canada, (2008) 321-327. [9] joo, m.s., suh, d.w., bae, j.h., bhadeshia, h.k.d.h., role of delamination and crystallography on anisotropy of charpy toughness in api-x80 steel, mater. sci. eng. a., 546 (2012) 314-322. [10] tankoua, f., crepin, j., thibaux, p., arafin, m., cooreman, s., gourgues, a.f., delamination of pipeline steels: determination of an anisotropic cleavage criterion, mech. ind., 15 (2014) 45-50. [11] rao, k.t.v., ritchie, r.o., fracture-toughness behavior of 2090-t83 aluminum lithium alloy sheet at ambient and cryogenic temperatures, scr. mater., 23 (1989) 1129-1134. [12] rao, k.t.v., ritchie, r.o., mechanical properties of al–li alloys part 1 fracture toughness and microstructure, mater. sci. technol., 5 (1989) 882-895. [13] rao, k.t.v., yu, w., ritchie, r.o., cryogenic toughness of commercial aluminum-lithium alloys: role of delamination toughening, metall. mater. trans. a., 20 (1989) 485-497. [14] rao, k.t.v., ritchie, r.o., mechanisms influencing the cryogenic fracture-toughness behavior of aluminum-lithium alloys, acta. metall. mater., 38 (1990) 2309-2326. [15] kalyanam, s., beaudoin, a.j., dodds, r.h., barlat, f., delamination cracking in advanced aluminum–lithium alloys – experimental and computational studies, eng. fract. mech., 76 (2009) 2174-2191. [16] hojná, a., falcnik, m., hietanen, o., hulinová, l., korhonen, r., oszvald, f., behaviour of 08ch18n10t steel after 15 years of operation as core shroud of wwer 440 plant, proceeding of the 11th international conference material issues in design, manufacturing and operation of nuclear power plants equipement, st-perterburgs, federation of russia, (2010). [17] hojná, a., ernestová, m., hietanen, o., hulinová, l., korhonen, r., oszvald, f., irradiation assisted stress corrosion cracking of austenititc stainless steel wwer reactor core internals. proceeding of the 15th international conference on environmental degradation of materials in nuclear power systems-water reactors, cheyenne montain resort, colorado springs, colorado, usa, (2011). [18] song, r., ponge, d., raabe, d., mechanical properties of an ultrafine grained c–mn steel processed by warm deformation and annealing, acta mater., 53 (2005) 4881-4892. [19] embury, j.d., petch, n. j., wraith, a. e., wright, e. s., fracture of mild steel laminates, trans. metall. soc. aime, 239 (1967) 114-118. [20] vaillant, f., tribouilloy-buissé, l., couvant., t., stress corrosion cracking propagation of colf-worked austenitic strainless steels in pwr environment. proceeding of the 14th int. conf. on environmental degradation of materials in nuclear power systems, virginia beach, va, usa, (2009). [21] michler, t., naumann, j., hydrogen environment embrittlement of austenitic stainless steels at low temperatures, int. j. hydrog. energy., 33 (2008) 2111-2122. [22] bramfitt, b.l., a.r. marder, study of delamination behavior of a very low-carbon steel, metall. mater. trans. a., 8 (1977) 1263-1273. [23] baldi, g., buzzichelli, g., critical stress for delamination fracture in hsla steels, metal science, 12 (1978) 459-472. [24] shanmugam, p. and s.d. pathak, some studies on the impact behavior of banded microalloyed steel, eng. fract. mech., 53 (1996) 991-1005. [25] srba, o., michalicka, j., keilova, e., kocik, j., tem study of radiation induced defects in baffle-former-barrel assembly from decommissioned npp greifswald, ieee trans nucl sci, pp 99 (2014) 1-6. [26] wanlin, g., elasto-plastic three-dimensional crack border field—iii. fracture parameters, eng. fract. mech., 51 (1995) 51-71. x.c. arnoult et alii, frattura ed integrità strutturale, 35 (2016) 509-522; doi: 10.3221/igf-esis.35.57 522 [27] shin, s.y., hong, s. bae, j., kim, h.k., s. lee, separation phenomenon occurring during the charpy impact test of api x80 pipeline steels. metall. mater. trans. a., 40 (2010) 2333-2349. [28] rao, k.t.v., yu, w., ritchie, r.o., cryogenic toughness of commercial aluminum-lithium alloys – role of delamination toughness. metall trans a., 20 (1989) 485-497. [29] anderson, t.l., fracture mechanics: fundamentals and applications, third edition in crc press (eds.) linear elastic fracture mechanics, taylor & francis, (1994) 29-116. [30] bridgman, p.w., studies in large plastic flow and fracture with special emphasis on the effects of hydrostatic pressure, harvard university press, ma, (1964) [31] yan, w., shan,y.y., yang, k., influence of tin inclusions on the cleavage fracture behavior of low-carbon microalloyed steels, metall trans a., 38 (2007) 1211-1222. [32] bluhm, j.j., a model for the effect of thinckness on fracture toughness, astm proc., 61 (1961) 1324-31. 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/hrv (za stvaranje adobe pdf dokumenata najpogodnijih za visokokvalitetni ispis prije tiskanja koristite ove postavke. stvoreni pdf dokumenti mogu se otvoriti acrobat i adobe reader 5.0 i kasnijim verzijama.) /hun 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can be opened with acrobat and adobe reader 5.0 and later.) >> /namespace [ (adobe) (common) (1.0) ] /othernamespaces [ << /asreaderspreads false /cropimagestoframes true /errorcontrol /warnandcontinue /flattenerignorespreadoverrides false /includeguidesgrids false /includenonprinting false /includeslug false /namespace [ (adobe) (indesign) (4.0) ] /omitplacedbitmaps false /omitplacedeps false /omitplacedpdf false /simulateoverprint /legacy >> << /addbleedmarks false /addcolorbars false /addcropmarks false /addpageinfo false /addregmarks false /convertcolors /converttocmyk /destinationprofilename () /destinationprofileselector /documentcmyk /downsample16bitimages true /flattenerpreset << /presetselector /mediumresolution >> /formelements false /generatestructure false /includebookmarks false /includehyperlinks false /includeinteractive false /includelayers false /includeprofiles false /multimediahandling /useobjectsettings /namespace [ (adobe) (creativesuite) (2.0) ] /pdfxoutputintentprofileselector /documentcmyk /preserveediting true /untaggedcmykhandling /leaveuntagged /untaggedrgbhandling /usedocumentprofile /usedocumentbleed false >> ] >> setdistillerparams << /hwresolution [2400 2400] /pagesize [612.000 792.000] >> setpagedevice microsoft word numero_36_art_8 f.a. stuparu et alii, frattura ed integrità strutturale, 36 (2016) 69-77; doi: 10.3221/igf-esis.36.08 69 focused on fracture mechanics in central and east europe failure analysis of dissimilar single-lap joints f.a. stuparu, d.a. apostol, d.m. constantinescu, m. sandu, s. sorohan university politehnica of bucharest, romania stuparu.florin@gmail.com, apostolda@yahoo.com, dan.constantinescu@upb.ro, marin.sandu@upb.ro, stefan.sorohan@upb.ro abstract. single-lap joints made of aluminium and carbon fibre adherends of different thickness are tested to understand better the behaviour of such dissimilar joints. the overlap length and the thickness of the adhesive are kept constant. local deformation fields are monitored by using the digital image correlation method. peeling and shearing strains are investigated, emphasizing that peeling is important in the region where failure is initiated, towards an extremity of the overlap region. the use of only carbon fibre adherends is not recommended for a smaller thickness as an additional interface failure is produced and compromises the integrity of the lap joint. however, a dissimilar joint (aluminium-carbon) with smaller thickness adherends succeeds to maintain the stiffness of the assembly, but its strength is diminished. the obtained results are suggesting that a complete monitoring of the failure processes in the overlap region can be fully understood only if local deformation measurements are possible. keywords. sigle-lap joints; dissimilar adherends; digital image correlation; peeling and shearing. introduction eronautical, automotive or naval structural integrity is of great importance and any presence of imperfections can reduce significantly the load bearing capacity. without a better understanding of progressive failure, the fracture criteria and predictive capabilities will be limited. in many cases adhesive joints have to be used and single-lap joints are of particular interest. several parameters have a significant influence as: the thickness of the adherends, the overlap length, and the adhesive thickness. on the other hand, the use of dissimilar materials in such joints represent new challenges and the complete understanding of the local phenomena deserve further investigations. in many engineering applications the gluing of metallic and composite materials starts to be a necessity. it is known that the thickness of the adhesive influences the strength of the assembly but its effect is not completely understood. experimental results have shown that the strength of the joint decreases with the increase of the adhesive thickness. gleich et al. [1] showed that the interface stresses grow proportionally with the thickness, and grant et al. [2] pointed out through experimental testing that the strength decreases due to the increase of the bending moment. the increase of the thickness leads to the increase of the arm of the force and therefore of the bending moment. it looks like the optimum strength of an epoxy adhesive is to be obtained when its thickness is between 0.1 and 0.5 mm. however, as pointed by banea and da silva [3], the results may vary due to the type of loading, the ductile or fragile behaviour of the adhesive and the rigidity of the adherends. opposite to what was expected, they showed that for a fragile adhesive a better performance of the lap-joint was obtained for the thicker adhesive. an explanation of the peculiar behaviour relied on the different thermal inertia of the thicknesses which resulted after the thermal cycle. the contradiction between the classical a f.a. stuparu et alii, frattura ed integrità strutturale, 36 (2016) 69-77; doi: 10.3221/igf-esis.36.08 70 elastic analysis and the experimental results generated further studies of da silva et al. [4]. the adherends were made from steel as to diminish the level of deformations. their conclusion suggests that the stresses at the interface adherendadhesive are responsible for the strength decrease when the thickness of the adhesive increases. a different approach is proposed by matihas and lemaire [5] which emphasize that in engineering applications the thickness of the adhesive is seldom constant and a probabilistic analysis is needed to study the reliability of such adhesive joints. they used aluminium and carbon fibre adherends of constant thickness and using volkensen's model calculated a coefficient of safety for which the probability of failure should be below 0.01%. their results pointed out that a thicker adhesive will help in reaching the reliability goal, that is contrary to the experimental findings obtained in [1, 2, 4]. the increase of the adherend thickness diminished the peeling effect at the extremities of the adhesive length and led to the increase of the shearing strength of an epoxy adhesive [6], and the increase of the adhesive overlap length increased the failure force of the assembly [7], but in fact the strength of the adhesive layer diminishes. in [8] different adhesives were used for single-lap joints of carbon fibre adherends with an overlap between 10 and 80 mm. for a ductile adhesive the failure force increases with the increase of the overlap, but for a fragile adhesive the force increases only up to 30 mm overlap and afterwards decreases due to the interlaminar failure of the adherends. in [9], when increasing the thickness of the steel adherends from 1 to 5 mm the maximum force and failure strength increases as already established in other studies. a complex analysis was performed by da silva et. al [10] which analysis the influence of several parameters (stiffness of adherend, thickness of adherend, thickness of adhesive, overlap length) on the strength of the single-lap joint by using the taguchi method. starting from an initial configuration the influence of each parameter is quantified as giving a maximum percentage increase of the strength of the assembly. the increase of the values of the analyzed parameters is beneficial to obtain strength increase with specified values, with one exception, the thickness of the adhesive, by which increase the strength of the single-lap is diminished. it was also noticed that the different procedures used to prepare the surfaces to be glued haven't influenced the obtained results. the digital image correlation (dic) method has inspired several researchers to analyze the strength of lap-joints. moreira and nunes [11] investigated the behaviour of a flexible adhesive and the critical shearing deformations which decrease towards the ends of the overlap, suggesting that the peeling strains are responsible for the initiation of the failure. they pointed out that it is essential to consider the peeling effects for the correct interpretation of the strength of the joint. moutrille et al. [12], nunes and moreira [13], and silva and nunes [14] used also dic for studying several geometrical configurations and successfully analyzed the influence of the aforementioned different parameters on the shearing strength of the joints. in this article the type and the thickness of the adhesive as well as the overlap length are kept constant. the single-lap joints are configured by using aluminium and carbon fibre adherends of 3 mm and 5 mm thickness combined differently. dic is used to monitor the local failure in the adhesive and give insides on the particular phenomena. peeling (opening or mode i) and shearing (mode ii) deformations are analyzed in detail and some conclusions concerning the particularities of using dissimilar adherends are drawn. it is emphasized that only local measurements, in the overlap region, can provide correct information about the deformation and failure of the adhesive. tested configurations and materials he single-lap joints used in the investigations have the dimensions presented in fig. 1. the thickness of the adhesive is kept constant to 0.5 mm and the overlap length is 20 mm. the thickness t of the adherends was changed from one configuration to another. the adherends were made from aluminium or carbon fibre. at the ends of the overlap a 5 mm gap is kept on each side of the overlap as used to control the thickness of the adhesive layer with a wax layer of 0.5 mm. the adhesive used in the experiments is araldite 2015 with the elastic constants established with dic on bulk specimens as: longitudinal modulus of elasticity e = 1790 mpa and poisson's ratio  = 0.32. this adhesive has a ductile behaviour. the adherends were made from aluminium 6060 t6 and unidirectional carbon fibre of 250 g/m2 with epoxy resin matrix. the considered thicknesses of the adherends for both materials were either 3 mm or 5 mm, having all of them a width of 30 mm. the adherends were further denoted as aluminium and carbon having the thickness indicated afterwards. the elastic constants of these adherends were established through traction tests on bulk iso standardized specimens, as indicated in tab.1. tests were done on a zwick z010 (10 kn) machine. speed of testing was of 1 mm/min. the increase of stiffness of the 3 mm carbon adherend can be explained due to the higher volume fraction of carbon fibres which resulted for this thickness. t f.a. stuparu et alii, frattura ed integrità strutturale, 36 (2016) 69-77; doi: 10.3221/igf-esis.36.08 71 the single-lap joint prepared for dic measurements is shown in fig. 2. on the left side it is better noticed the uneven surface due to the wax of constant 0.5 mm thickness which filled the overlap for 5 mm on each side as to control the adhesive thickness. figure 1: dimensions of the single-lap joints. aluminium carbon 3 mm carbon 5 mm modulus of elasticity [mpa] 70000 76000 64000 poisson's ratio 0.33 0.35 0.37 table 1: elastic constants of adherends. figure 2: surface of a single-lap joint prepared for dic measurements. overall, six different geometrical configurations were used for testing, as mentioned in tab.2. for each configuration five lap joints were tested. if the failure was not cohesive the test was disregarded. adherend 1 adherend 2 material thickness material thickness configuration 1 aluminium 3 mm aluminium 3 mm configuration 2 carbon 3 mm carbon 3 mm configuration 3 aluminium 3 mm carbon 3 mm configuration 4 aluminium 5 mm aluminium 5 mm configuration 5 carbon 5 mm carbon 5 mm configuration 6 aluminium 5 mm carbon 5 mm table 2: configurations used for testing with aluminium and carbon adherends of different thickness. f.a. stuparu et alii, frattura ed integrità strutturale, 36 (2016) 69-77; doi: 10.3221/igf-esis.36.08 72 the relative displacements between the adherends were monitored in the overlap region and both peeling and shearing deformations were measured by using dic. for each configuration out of the five performed tests only the representative one was chosen for further comparisons. plots of the shearing stress as a function of the displacement between the grips as indicated by the testing machine were also represented. experimental evaluation of local deformations he lateral surface of the single-lap joint was analyzed by using dic. the aramis 2m system was used to measure the deformations of the adhesive. for all tests a calibre of 35 x 28 mm was considered. one frame per second was acquired. in order to obtain a map of the deformations along the overlap length three virtual gauges were chosen on each side of the overlap as seen in fig. 3. configuration 4 is presented in the figure, both adherends being aluminium of 5 mm thickness. top and bottom gauges are positioned on the edges of the adhesive layer. the relative displacements of the adherends are measured along the x axis as to investigate the peeling deformation and the corresponding strain, and along the y axis to monitor the shearing displacement of the adherends and the shearing strain. local peeling strains are shown with their values in fig. 3. a maximum strain of about 9 % was obtained at the lower extremity of the adhesive shortly before the failure of the joint. as getting towards the middle region of the overlap compression is produced in the adhesive, thus indicating the bending of the adherends. figure 3: peeling relative strains in the adhesive. figure 4: shearing strain in the adhesive along the overlap. t f.a. stuparu et alii, frattura ed integrità strutturale, 36 (2016) 69-77; doi: 10.3221/igf-esis.36.08 73 shearing is produced along the whole overlap length and values of the shearing strain can be depicted in fig. 4. the same frame as in fig. 3 is presented. shearing is mainly constant in the adhesive with a maximum value, again, towards the lower extremity of the overlap. an initial crack started from there and propagated. this is due to the possible slightly unsymmetrical geometric arrangement of the single-lap joint. behaviour of lap joints made of dissimilar adherends s different adherends were used for understanding the behaviour of similar and dissimilar single-lap joints, we initially tested aluminium adherends of 3 mm, respectively 5 mm thickness (configurations 1 and 4). shearing stress is represented as a function of the displacement of the grips measured by the testing machine. the shearing stress is an average value and is calculated as the ration between the force and the surface of the adhesive overlap. the measured displacement includes the deformations of the adhesive, of the adherends, and a possible slippage of the adherend in the mechanical grips, although this was not evident by analyzing the specimen after failure. this is why this value is greater than the one measured by using dic. from fig. 5 it is to be noticed that the stiffness of the joint is increased for the thicker aluminium adherend. as stiffness decreases (3 mm) the peeling effect is greater and the joint fails at a smaller force. 0.0 2.0 4.0 6.0 8.0 10.0 12.0 14.0 16.0 18.0 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 s h ea ri n g s tr es s [ m p a] displacement [mm] aluminium 3 mm aluminium 5 mm figure 5: influence of the aluminium adherend thickness. in fig. 6, for carbon adherends, it is to be noticed that for a thickness of 3 mm the stiffness is lower than for a thickness of 5 mm (which is not surprising). however, the failure force is much smaller and the shearing stress decrease to about 11 mpa. failure is produced suddenly, without a decrease of the maximum force as happens for the 5 mm thickness. 0.0 2.0 4.0 6.0 8.0 10.0 12.0 14.0 16.0 18.0 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 s h ea ri n g s tr es s [m p a] displacement [mm] carbon 3 mm carbon 5 mm figure 6: influence of the carbon adherend thickness. a f.a. stuparu et alii, frattura ed integrità strutturale, 36 (2016) 69-77; doi: 10.3221/igf-esis.36.08 74 for carbon adherends a delamination between the layers of the adherend appears especially for the 3 mm thickness adherends (configuration 2). the strength of the joint is in fact dictated by the interface strength of the carbon laminas and not given by the cohesive strength of the adhesive. if the interface strength is assumed to be constant regardless the thickness of the carbon adherends it results that a lower stiffness will lead to a higher peeling force as the thickness of the adherend is decreased. one can notice in fig. 7 the pull-out of the carbon fibres due to the interlaminar failure of the adherend. figure 7: interlaminar failure of the 3 mm carbon adherend. it is also recommended to avoid any mechanical machining or scratching on the surface of the carbon adherend as to increase its roughness prior to the application of the adhesive. this may also contribute to the unexpected interlaminar failure. for adherends of 5 mm thickness the shearing failure stress is about 16 mpa regardless the joint configuration (fig. 8). a slightly larger displacement until failure is obtained for the aluminium-aluminium lap joint (configuration 4). however, the aluminium-carbon lap joint is stiffer but fails sooner. 0.0 2.0 4.0 6.0 8.0 10.0 12.0 14.0 16.0 18.0 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 s h ea ri n g s tr es s [ m p a] displacement [mm] aluminium carbon aluminium carbon figure 8: influence of material combinations for 5 mm adherend thickness. for 3 mm adherends, as to be seen in fig. 9, the best results were clearly obtained for aluminium adherends, that is maximum shearing stress and maximum displacement at failure. if one of the adherends was carbon, interlaminar failure resulted eventually. lower stiffness is undesirable as it increases the bending of the adherend and the peeling stresses in the adhesive. the global values of the displacements of the single-lap joint measured through the displacement of the grips of the testing machine is at failure about 3 mm for the 5 mm adherends, and about the same value or less for the 3 mm adherends (not less than 2.5 mm). this globally measured displacement is significantly larger than the local relative displacements of the adherends measured on x and y directions (figs. 3 and 4 for aluminium adherends) with dic. only the local relative displacements are reflecting the correct behaviour of the adhesive. f.a. stuparu et alii, frattura ed integrità strutturale, 36 (2016) 69-77; doi: 10.3221/igf-esis.36.08 75 0.0 2.0 4.0 6.0 8.0 10.0 12.0 14.0 16.0 0 0.5 1 1.5 2 2.5 3 3.5 s h ea ri n g s tr es s [ m p a] displacement [mm] aluminum carbon aluminium carbon figure 9: influence of material combinations for 5 mm adherend thickness. local deformations of single-lap joints hortly before the failure of the single-lap with 5 mm aluminium adherends the relative peeling displacement between the adherends is about 0.07 mm (fig. 3 or fig. 4) along the x axis at the lower extremity of the overlap as measured by the first virtual gauge, then becomes 0.04 mm in the next virtual gauge, and 0.02 mm in the third virtual gauge; so the peeling displacement decreases rapidly. failure initiated from this region. in the other side of the overlap the relative displacements are smaller. the shearing displacement along the y axis is 0.58 mm; this value remains mainly constant along the overlap length at this stage of loading. a comparison of the results obtained for relative shearing displacements is given in fig. 10 for 5 mm adherends (configurations 4, 5, and 6). the three adherends combinations behave quite similarly (see also fig. 8) but the local relative displacements are much smaller. the carbon-carbon joint behaves very well for this thickness; on the contrary the aluminium-carbon joint fails sooner, although it is stiffer. probably some delaminations in the carbon adherend were produced for this particular test. maximum relative shearing displacements are about 0.5-0.7 mm, much smaller than the ones obtained in following the indications of the testing machine. 0 2 4 6 8 10 12 14 16 18 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 s h ea ri n g s tr es s [ m p a] displacement [mm] aluminium carbon aluminium carbon figure 10: relative shearing displacements for adherends of 5 mm. the 3 mm adherends give a satisfactory behaviour, as before, only for the aluminium adherends (configuration 1). smaller thickness and stiffness carbon adherends imply higher bending moments and delamination of the carbon layers. failure is produced sooner for configurations 2 and 3, at less than 0.2 mm relative shearing displacement (fig. 11). as commented before, local relative displacements are much smaller less than 0.3 mm, that is 10 times smaller than the global displacements (see fig. 9). s f.a. stuparu et alii, frattura ed integrità strutturale, 36 (2016) 69-77; doi: 10.3221/igf-esis.36.08 76 if we analyze the peeling and shearing displacements for the aluminium and carbon adherends of 3 mm (fig. 12) where failure will initiate it is evident that the peeling deformations are much smaller. for the carbon adherends these deformations indicate an initial negative displacement, which has the significance of the reduction of the initial gauge length due to the local bending effects which are more pronounced for this thickness. at higher forces the peeling is evident (at about 10 mpa shearing stress) and the lap joint fails soon afterwards. as mentioned before, additional delaminations between the carbon fibre laminas are accelerating the failure event. for both adherends the peeling deformations cannot be neglected and influence the moment of failure although they are of small values. 0 2 4 6 8 10 12 14 16 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 s h ea ri n g s tr es s [ m p a] displacement [mm] aluminium carbon aluminium carbon figure 11: relative shearing displacements for adherends of 3 mm. 0 2 4 6 8 10 12 14 16 ‐0.1 0.0 0.1 0.2 0.3 0.4 0.5 s h ea ri n g s tr es s [ m p a] displacement [mm] x aluminium 3 mm y aluminium 3 mm x carbon 3 mm y carbon 3 mm figure 12: variation of local relative displacements for aluminium and carbon 3 mm adherends. conclusions he use of dissimilar single-lap joints is of great importance and this is why it is investigated in this article. by keeping constant the overlap length and the thickness of the adhesive we analyze the influence of the thickness and material (aluminium or carbon fibre) of the adherends. digital image correlation measurements done in the immediate vicinity of the adhesive layer can provide correct information about the shearing and peeling deformations. it was shown that failure initiates where peeling is significant. for carbon fibre adherents, especially for the lower thickness of 3 mm, additional interlaminar damage compromises the integrity of the joint and leads to premature failure of the assembly. dissimilar joints (aluminium-carbon) with smaller t f.a. stuparu et alii, frattura ed integrità strutturale, 36 (2016) 69-77; doi: 10.3221/igf-esis.36.08 77 thickness adherends succeed to maintain the stiffness of the assembly as compared to the aluminium joints, but their strength is diminished by the pull-out and delamination of carbon fibres. it is of great importance to rely on local deformation measurements and not on the global ones as indicated by the testing machine, which include also the deformation of the adherends. only by using such an approach a proper understanding of adhesive failure is possible. acknowledgements his work was supported by a grant of the romanian national authority for scientific research, cndi– uefiscdi, project number pn-ii-pt-pcca-2011-3.2-0068, contract nr. 206/2012. references [1] gleich, d.m., van tooren, m.j.l., beukers, a., analysis and evaluation of bondline thickness effects on failure load in adhesively bonded structures, j. adhes. sci. technol., 15 (2001) 1091–1101. doi:10.1163/156856101317035503. [2] grant, l.d.r., adams, r.d., da silva, l.f.m., experimental and numerical analysis of single-lap joints for the automotive industry, int. j. adhes. adhes., 29 (2009) 405–413. doi:10.1016/j.ijadhadh.2008.09.001. [3] banea, m.d., da silva, l.f.m., mechanical characterization of flexible adhesives, j. adhesion, 84 (2009), 261–285. doi:10.1080/00218460902881808. [4] da silva, l.f.m., rodrigues, t.n.s.s., figueiredo, m.a.v., de moura, m.f.s.f., chousal, j.a.g., effect of adhesive type and thickness on the lap shear strength, j. adhesion, 82 (2006) 1091–1115. doi:10.1080/00218460600948511. [5] mathias, j.d., lemaire, m., reliability analysis of bonded joints with variations in adhesive thickness, j. adhes. sci. technol., 27 (2013) 1069–1079. doi:10.1080/01694243.2012.727176. [6] pereira, a.m., ferreira, j.m., antunes, f.v., bártolo, p.j., analysis of manufacturing parameters on the shear strength of aluminium adhesive single-lap joints, j. mater. process. tech., 210 (2010) 610–617. doi:10.1016/j.jmatprotec.2009. 11.006. [7] park, j.h., choi, j.h., kweon, j.h., evaluating the strengths of thick aluminum-to-aluminum joints with different adhesive lengths and thicknesses, compos. struct., 92 (2010) 2226–2235. doi:10.1016/j.compstruct.2009.08.037. [8] neto, j.a.b.p., campilho, r.d.s.g., da silva, l.f.m., parametric study of adhesive joints with composites, int. j. adhes. adhes., 37 (2012) 96–101. doi:10.1016/j.ijadhadh.2012.01.019. [9] de morais, a.b., pereira, a.b., teixeira, j.p., cavaleiro, n.c., strength of epoxy adhesive-bonded stainless-steel joints, int. j. adhes. adhes., 27 (2007) 679–686. doi:10.1016/j.ijadhadh.2007.02.002. [10] da silva, l.f.m., critchlow, g.w. figueiredo, m.a.v., parametric study of adhesively bonded single lap joints by the taguchi method, j. adhes. sci. technol., 22 (2008) 1477–1494. doi:10.1163/156856108x309585. [11] moreira, d.c., nunes l.c.s., experimental analysis of bonded single lap joint with flexible adhesive, appl. adhesion sci., 2 (2014). doi:10.1186/2196-4351-21. [12] moutrille, m.p., derrien, k., baptiste, d., balandraud, x., grédiac, m., through-thickness strain field measurement in a composite/aluminium adhesive joint, compos. part a-appl. s., 40 (2009) 985–996. doi:10.1016/j.compositesa. 2008.04.018. [13] nunes, l.c.s., moreira, d.c., simple shear under large deformation: experimental and theoretical analyses, eur. j. mech. a-solid., 42 (2013) 315–322. doi:10.1016/j.euromechsol.2013.07.002. 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can be opened with acrobat and adobe reader 5.0 and later.) >> /namespace [ (adobe) (common) (1.0) ] /othernamespaces [ << /asreaderspreads false /cropimagestoframes true /errorcontrol /warnandcontinue /flattenerignorespreadoverrides false /includeguidesgrids false /includenonprinting false /includeslug false /namespace [ (adobe) (indesign) (4.0) ] /omitplacedbitmaps false /omitplacedeps false /omitplacedpdf false /simulateoverprint /legacy >> << /addbleedmarks false /addcolorbars false /addcropmarks false /addpageinfo false /addregmarks false /convertcolors /converttocmyk /destinationprofilename () /destinationprofileselector /documentcmyk /downsample16bitimages true /flattenerpreset << /presetselector /mediumresolution >> /formelements false /generatestructure false /includebookmarks false /includehyperlinks false /includeinteractive false /includelayers false /includeprofiles false /multimediahandling /useobjectsettings /namespace [ (adobe) (creativesuite) (2.0) ] /pdfxoutputintentprofileselector /documentcmyk /preserveediting true /untaggedcmykhandling /leaveuntagged /untaggedrgbhandling /usedocumentprofile /usedocumentbleed false >> ] >> setdistillerparams << /hwresolution [2400 2400] /pagesize [612.000 792.000] >> setpagedevice microsoft word numero_50_art_29_2600 n. alexopoulos et alii, frattura ed integrità strutturale, 50 (2019) 342-353; doi: 10.3221/igf-esis.50.29 342 focused on the research activities of the greek society of experimental mechanics of materials simulation of the corrosion-induced damage on aluminum alloy 2024 specimens with equivalent surface notches nikolaos d. alexopoulos, nikoleta siskou, christina-margarita charalampidou university of the aegean, school of engineering, department of financial and management engineering, 41 kountouriotι str, 82132, chios, greece nalexop@aegean.gr, http://orcid.org/0000-0001-7851-1845 stavros k. kourkoulis national technical university of athens, department of mechanics, laboratory for testing and materials, theocaris building, 5 heroes of polytechnion avenue, 157 73, athens, greece abstract. the effect of corrosion environment aggressiveness on the tensile mechanical properties degradation of aa2024-t3 was investigated. tensile specimens were pre-corroded for various exposure times to different corrosive solutions, i.e., exfoliation corrosion (exco) and 3.5 wt. % nacl. then they were tested mechanically. in non-corroded specimens, surface notches of various depths were machined to simulate the degradation of the tensile mechanical properties due to the presence of artificial surface defects. a mechanical model was developed to correlate the corrosion-induced tensile ductility degradation due to pitting and possible hydrogen embrittlement with the equivalent artificially induced surface notches. the cases studied for this physical correlation were: a) exco exposure with artificial notches, b) exco with 3.5 wt.% nacl exposure and c) 3.5 wt.% nacl exposure with artificial notches. higher correlation was noticed for short exposure times for all cases where the dominant degradation mechanism is slight pitting formation. it was found that 1 h exco exposure is equivalent to 92 h exposure to nacl solution regarding the tensile ductility degradation while 24 h exco exposure has the same effect on ductility decrease with a 240 μm surface notch or 4000 h exposure to nacl solution. keywords. corrosion; notches; mechanical properties; aluminum alloy. citation: alexopoulos, n.d., siskou, n., charalampidou, c.m., kourkoulis, s.k., simulation of the corrosion-induced damage on aluminum alloy 2024 specimens with equivalent surface notches, frattura ed integrità strutturale, 50 (2019) 342-353. received: 25.01.2019 accepted: 27.05.2019 published: 01.10.2019 copyright: © 2019 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. introduction uring the last decades attention has been paid by the aviation industries to the reduction of aircrafts maintenance costs. damage tolerance evaluation for the skin and the fuselage of the aircraft is of major importance for the decrease of the inspection intervals and therefore of the respective maintenance costs. among the greatest d http://www.gruppofrattura.it/va/50/2600.mp4 n. alexopoulos et alii, frattura ed integrità strutturale, 50 (2019) 342-353; doi: 10.3221/igf-esis.50.29 343 problems in maintenance and repair of aircraft structures is corrosion. the possibility that corrosion will interact with other forms of damage, e.g. fatigue cracks, impact etc. can result in significant loss of the structural integrity and may lead to fatal consequences, e.g. the aloha airlines accident. the synergetic interaction of corrosion and fatigue has a deteriorating effect on the mechanical performance of aeronautical aluminum alloys, mainly because of accelerated crack propagation [1]. the major damage mechanism on the corroded surface affecting the integrity of aircraft structures is the formation of pitting, e.g. [2-4]. corrosion-induced pits initiate on the surface due to chemical or physical heterogeneities such as intermetallic particles, dislocations or mechanical damage and flaws, e.g. [5,6]. wrought aluminum alloys used in aircraft applications, contain numerous intermetallic particles increasing substantially the mechanical properties (yield stress, fatigue crack growth etc.), nevertheless they play a pivotal role in the nucleation of pitting, e.g. [7,8]. aluminum alloy 2024, is highly used in the aircraft industry due to its improved mechanical properties and high damage tolerance capability, nevertheless it shows high susceptibility to corrosion attack due to its microstructure [9-11]. corrosion involves several electrochemical mechanisms; in acidified solutions, the basic anodic reaction is the metal dissolution while the cathodic reactions are oxygen and hydrogen reduction resulting from aluminum ion hydrolysis [2]. dealloying of stype (al2cumg) particles, that are the most common intermetallic phases in 2xxx aluminum alloys, leads to cu-rich remnants within the clusters [12] that switch the anode reaction to the alloy matrix adjacent to the particle and eventually to the grain boundaries; thus, it assists the formation of sub-surface micro-cracks [13-15]. cracking formation generally starts at local defects such as microstructural features inside the material, surface features such as notches or in-service damage process such as corrosion (e.g. pitting) that act as stress concentrators [16,17]. accumulated corrosion damage can be noticed on aging aircrafts due to corrosion-induced embrittlement mechanisms. hydrogen embrittlement phenomenon along with corrosion of aluminum alloys can lead to the rapid failure of the materials. hydrogen is usually produced by surface corrosion reactions and afterwards diffuses into the material and is trapped at preferential sites [18] as shown in [19,20]. it can be adsorbed at crack tips or notches or diffuse ahead of cracks [21] that embrittles the material below the crack tip. to face the corrosion-induced structural degradation issue, available data usually refer to accelerated laboratory tests. many researchers focused on the development of damage functions to account for the corrosion assessment on the mechanical properties, e.g. [21-23]. the most common accelerated corrosion test used for the aluminum alloys of the 2xxx and 7xxx alloy series is the exfoliation corrosion (exco) test according to astm g34. it has been reported that 24 h exposure of the aluminum alloy 2024-t4 to the exco solution corresponds to nearly 6 years of natural exposure of the same structural element regarding its surface exfoliation [24]. various mechanical tests had been carried out on aa2024-t3 to assess the effect of the corrosion damage on the material’s structural integrity. tensile and fatigue mechanical tests had been carried out in pre-corroded material, resulting to the mechanical properties degradation [25,26]. corrosion of aa2024 was found to result in a moderate decrease of the strength properties (yield stress and ultimate tensile strength) with a significant reduction of tensile ductility [27,28]. according to alexopoulos and papanikos [29] the cross-sectional area of aa2024 specimens which was supposed to be unaffected by micro-cracks (referred as ‘effective thickness’), decreases exponentially with increasing exposure time to exco solution due to the crack propagation mechanism that leads to higher corrosion penetration into the material. corrosion exposure was found to have a negative effect on yield stress mainly due to the cross-sectional decrease at higher exposure times as well as on tensile ductility decrease due to the combination of hydrogen embrittlement in the low exposure times and decrease of the cross-section for the higher exposure times [30]. the reduction of the load carrying cross section of the specimens as well as the notch effects caused by pitting formation and exfoliated areas are sufficient to explain the moderate reduction of tensile strength properties. the corrosion problem includes several degradation mechanisms and the damage could be described and analyzed as the sum of several parameters downgrading the mechanical properties. in order to better interpret the corrosion-induced damage, various mechanisms involved in the corrosion process should be taken into consideration; they may depend on material, temper, corrosive environment and exposure time. the aggressiveness of the corrosive environment is a significant parameter influencing corrosion damage evolution as well as the underlying corrosion mechanism. recent investigations [31] indicate that in-service obtained corrosion damage correlates well to the one caused by a 3.5 wt. % nacl solution, with pitting density, depth and shape evolving with exposure time. vasco et al. [32] performed correlations between corrosion damage from accelerated corrosion tests of varying aggressiveness by accounting for both, the metallographic features of corrosion damage and the mechanical properties of the corroded material. correlations regarding geometrical metallographic features were found under dominance of pitting corrosion and up to 8 hours in exco solution; higher variations after the occurrence of pit coalescence and transition to dominance of exfoliation corrosion were presented. the aim of the present work is to simulate the real corrosion-induced degradation of the mechanical properties due to corrosion surface pits and possible hydrogen embrittlement and to correlate it with the equivalent degradation by the artificially induced surface notches. moreover, a comparison between the effects of the aggressiveness of the corrosion environment on the mechanical behavior of aa2024 specimens subjected to exco and 3.5 wt.% nacl solution will be investigated. n. alexopoulos et alii, frattura ed integrità strutturale, 50 (2019) 342-353; doi: 10.3221/igf-esis.50.29 344 experimental procedure he material used was a wrought aluminum alloy 2024-t3 which was received in sheet form of 3.2 mm nominal thickness. the weight percentage chemical composition of the alloy is 4.35 % cu, 1.50 % mg, 0.64 % mn, 0.50 % si, 0.50 % fe, 0.25 % zn, 0.10 % cr, 0.15 % ti and al rem. tensile specimens were machined from the material sheet according to astm e8 specification with 12.5 mm x 50 mm being the reduced cross section of the specimen. all the specimens were cut parallel to the longitudinal (l) rolling direction of the material. reference specimens were tensile tested according to astm e8 specification, while two series of tensile specimens were exposed for various times to different laboratory corrosion environment, namely exfoliation corrosion (hereafter called exco solution) and 3.5 wt. % sodium chloride (hereafter called nacl solution) according to the specifications astm g34 and g44, respectively. the exco solution consisted of the following chemicals diluted in 1 l distilled water; sodium chloride (4.0 m nacl), potassium nitrate (0.5 m kno3) and nitric acid (0.1 m hno3). the results of the exco solution exposure have been performed and reported in a previous article of the authors [33]. the concentration of the nacl solution consisted of 3.5 g nacl for each 96.5 ml of water. the solution volume was calculated per exposure area of the specimens and it was constant for all specimens. in both experimental procedures, the specimens were cleaned with alcohol prior to corrosion exposure according to specification astm g1. additionally, the specimens were masked with appropriate insulating pvc tape in order to be exposed only at the reduced surface area of approximate 55 mm in length. the experimental procedure was carried out in laboratory environmental conditions and at room temperature. according to the literature [26], corrosion damage and hydrogen embrittlement is evident on the large surfaces of the tensile specimen’s gauge length and not so intense on the side surfaces. machining of the artificial notches was decided to be performed on the large surfaces of the tensile specimen, namely vertical to the loading axis. a drawing of the specimen with manufactured two surface notches can be seen in fig.1. the two artificial notches facing one the other (on the same vertical level) can be well seen in the figure as well as the maximum depth of 0.5 mm per notch. this notch depth per surface was the maximum depth of attack of corrosion products (pits and cracks) generated after approximating 72 h exposure time in exfoliation corrosion solution. in different specimens, notches with smaller depths were manufactured (ranging from 0.1 till 0.5 mm) to incrementally simulate the corrosion surface damage on aa2024-t3 as well as the specimen’s residual tensile strength and tensile ductility after the corrosion exposure. tensile tests were carried out in a servo-hydraulic instron 8801 100 kn testing machine according to astm e8m specification, with a constant deformation rate of 3.3 x 10-4 sec. an instron extensometer 50 mm ± 10 mm maximum travel was attached to the specimen’s gauge length before the tensile test. a data logger was used during all tensile tests to store the values of load, displacement and axial strain in a computer. to get representative average values of the tensile properties, at least three tensile tests have been carried out per each test series. evaluated properties were the conventional yield stress rp0.2% (0.2 % proof stress), ultimate tensile strength rm and elongation at fracture af. figure 1: sketch of the tensile specimen with machined two (upper and lower) surface notches on the large surfaces. results and discussion surface characterization of pre-corroded specimens he exposure of aa2024 specimens to the corrosive environment (exco or 3.5 wt. % nacl solution in the present study) results in the deterioration of the surface of the specimens due to the nucleation of corrosioninduced surface pits, as can be seen in fig.2. the depicted corroded area has dimensions of 12.5 mm x 55 mm being t t n. alexopoulos et alii, frattura ed integrità strutturale, 50 (2019) 342-353; doi: 10.3221/igf-esis.50.29 345 (a) (b) (c) (d) (e) (f) figure 2: typical photographs of aa2024-t3 pre-corroded tensile specimens exposed to the exco solution for (a)-(c) 2 h, 4 h and 24 h of exco solution and (d) – (f) 6 h, 168 h and 720 h of 3.5 wt. % nacl solution, respectively. the width and the length of the exposed area of the specimens, respectively. for short exposure times to exfoliation corrosion solution and up to 2 h, pitting formation on the corroded surfaces remains rather limited. with increasing exposure time to exco solution, an increase in the pitting density is evident. corrosion damage initiates in the form of surface corrosion pits and evolves to the formation of micro-cracks and exfoliation areas due to the presence of intergranular corrosion. regarding the corrosion environment of 3.5 wt. % nacl solution, it is evident that for the short exposure times the surface deterioration remains limited since pits were not identified after 6 h of exposure. however, the pitting density and size tend to increase with increasing exposure time; corrosion damage in the form of pits was observed after 168 h of exposure while more pits of higher diameter as well as pit coalescence are evident after 720 h exposure. typical tensile curves of pre-corroded specimens typical nominal tensile stress-strain curves for the investigated exposure times of aa2024-t3 to exco and 3.5 wt. % nacl solutions can be seen in figs.3(a,b), respectively. the nominal stress calculation was based on the nominal cross-section of the tensile specimens, namely width x thickness = 12.5 mm x 3.2 mm. it can be noticed that for the short corrosion exposure times to exco solution and up to 2 h, the values of axial nominal stress are not essentially influenced by the corrosion exposure while for higher exposure times, e.g. after 4 h, a significant stress drop was noticed [33]. this stress drop was attributed to the decrease of the specimen’s cross-section – due to the corrosion-induced micro-cracks formation that withstand the applied mechanical loading, so called as “effective thickness” [29]. on the contrary, an essential decrease of tensile ductility is evident even for the very short exposure times, e.g. 0.5 h that can be attributed to the hydrogen embrittlement phenomenon. for even higher exposure times, both the axial nominal stress and axial nominal strain are essentially decreased. regarding corrosion exposure to 3.5 wt. % nacl solution, no essential stress decrease was noticed even for the highest exposure time, e.g. 4200 h. however, elongation at fracture exhibited a significant degradation even for the very short exposure times such as 6 h. it is worth mentioning that higher ductility degradation was observed at the time range between 6 and 168 h, where pitting incubation takes place, as well as in the time range of 720 and 2184 h, probably because of the change in the degradation mechanism, e.g. pit growth and coalescence. typical nominal tensile curves for the specimens of aa2024-t3 with machined surface notches can be seen in fig.3c; the surface notch depth is a varying parameter. in the same figure, a reference tensile curve without any notches (black circles) was added for comparison. as can be seen, the surface notches act as stress concentrators and tend to decrease the tensile mechanical properties of the alloy and especially elongation at fracture that decreases in higher rates than the yield stress. an essential decrease of the axial nominal strain was noticed even for the low-depth notches; nevertheless, this was not the case for the strength properties that seem to be almost unaffected even for the notch depth of 0.30 mm. for instance, the tensile curves of 0.10 and 0.15 mm notch depths showed quite the same behavior with the reference one with the exception of the significant loss in ductility. by increasing the notch depth, up to 0.50 mm in this work, a continuous elongation at fracture decrease was noticed (magenta circles) exhibiting extremely low tensile elongation at fracture values. characterization of the fracture mechanism stereoscopical examination on the fractured, pre-corroded specimens of aa2024-t3 (fig.4) revealed that the pitting corrosion mechanism is extremely limited for the very short corrosion exposure times, i.e., up to 2 h to exco solution. it is evident that with increasing exposure time to exco solution, the pitting density tends to increase. a ductile fracture mechanism is evident from the 45˚ slope of the fracture surface as can be seen in figs.4(a,b). for the higher exposure times, e.g. 24 h in fig.4c, it seems that the fracture paths follow a non-linear pattern and definitely from pit to pit. for the specimens exposed to 3.5 wt. % nacl solution, pitting was not as evident as observed in the respective exco specimens. pitting density for relatively short exposure times of 6 h (fig.4d) and 168 h (fig.4e) was extremely small, while the pits substantially increased for higher exposure times, e.g. 720 h (fig.4f). however, the 45˚ slope of the fracture surface remains even after 720 h of exposure revealing a ductile fracture mechanism. n. alexopoulos et alii, frattura ed integrità strutturale, 50 (2019) 342-353; doi: 10.3221/igf-esis.50.29 346 (a) (b) (c) figure 3: typical tensile nominal stress strain curves of aa2024-t3 after corrosion exposure for different exposure times to (a) exco solution, (b) 3.5 wt. % nacl solution and (c) varying depth of artificial surface notches. (a) (b) (c) (d) (e) (f) figure 4: typical photographs of aa2024-t3 pre-corroded tensile specimens exposed to the exco solution (a)-(c) for 2 h, 4 h and 24 h, respectively and 3.5 wt. % nacl solution (d)-(f) for 6 h, 168 h and 720 h, respectively. 0.00 0.05 0.10 0.15 0.20 0 100 200 300 400 500 nominal axial strain ε [-] aluminum alloy 2024-τ3 t = 3.2 mm, l direction exposure at exco solution n o m in a l a xi a l st re ss σ [ m p a ] reference 0.5 hours 1 hour 2 hours 4 hours 12 hours 8 hours 24 hours stress drop 0.00 0.05 0.10 0.15 0.20 0 100 200 300 400 500 2184 hours aluminum alloy 2024t3 t= 3.20 mm, l direction exposure at 3.5 % nacl solution n o m in a l a xi a l st re ss σ [ m p a ] nominal axial strain ε [-] reference 6 hours168 hours 720 hours 4200 hours 0.00 0.05 0.10 0.15 0.20 0 100 200 300 400 500 0.50 mm 0.30 mm 0.15 mm n o m in a l a x ia l s tr e s s σ [ m p a ] nominal axial strain ε [-] aa2024-t3 l, t = 3,2 mm with artificial surace-notches reference0.10 mm n. alexopoulos et alii, frattura ed integrità strutturale, 50 (2019) 342-353; doi: 10.3221/igf-esis.50.29 347 effect on the conventional yield stress the experimental results of the conventional yield stress rp0.2% (nominal values) for the (a) exposure times to exco solution, (b) exposure times to 3.5 wt. % nacl solution and (c) notch depths are presented in fig.5. the results are presented in decreasing normalized values (y-axis) from the initial value of the conventional yield stress for comparison purposes. the black circles and dotted line represent the experimental results and fitting line of exposure to exco solution in both figures, the orange triangles and line corresponds to the fitting results of exposure to 3.5 wt. % nacl solution and the blue squares and dashed line to the respective results of notch depth. regarding the comparison of conventional yield stress decrease between the two investigated corrosive environments, it is evident that the more aggressive solution (exco) leads to higher decrease of conventional yield stress up to 12 h of exposure. for the very short exposure times, the stress decrease seems to be almost the same for both investigated solutions; however specimens exposed to the mild corrosion solution (3.5 wt. % nacl) needed more hours for the same degradation percentage, e.g. approximately 99 % normalized decrease of rp0.2% can be noticed after 168 h of exposure to nacl solution as well as after 1 h of exposure to exco solution (fig.5a). it is worth to mention that the 3.5 wt. % nacl solution does not reveal any exfoliation of the corrosion attacked material surfaces which could represent a more pronounced notch effect reducing the specimens’ cross-sectional area. however, the decrease of conventional yield stress, remains limited for all the investigated corrosion exposure times of both investigated environments and does not exceed 40 % at maximum and for the investigated exposure times. the highest normalized decrease of rp0.2% was approximately 68 % for the specimens exposed to 3.5 wt. % nacl solution and 79 % for the specimens exposed to exco solution. the comparison of the conventional yield stress decrease between the exposure to exfoliation corrosion solution and machined notch depths, is performed in fig.5b. the specimens exposed to exfoliation corrosion exhibited higher conventional yield stress rp0.2% degradation than the specimens with the machined artificial surface notches up to 12 h of corrosion exposure as well as 0.3 mm notch depth. corrosion exposure decreases the conventional yield stress with higher rates even from the short exposure times, e.g. 2 h where the pitting formation is limited, probably because of the hydrogen embrittlement phenomenon. no essential decrease of rp0.2% was noticed even after the notch depth of 0.30 mm, e.g. a 97 % normalized decrease on rp0.2% was observed. for the short exposure times and low notch depth values, the contribution of exco and notch depth to the normalized property decrease is almost the same, e.g. the 0.1 and 0.15 mm notch depths resulted approximately in the same decrease as for the 0.5 and 1 h of exposure to exco solution; however, after 2 h corrosion exposure a higher decrease rate is noticed because of the synergetic effect of pitting corrosion and hydrogen embrittlement. nevertheless, the machined notch depth of 0.50 mm yielded the same normalized conventional yield stress decrease as for the highest exposure time to exco, with the normalized decrease, reaching almost 80 %. the decrease in the conventional yield stress with increasing notch depth is well accepted since high notch depth values tend to increase the plasticity induced in front of the notch tip; plastic region increases with increasing stress level and general yielding at the reduced cross-section occurs for lower applied force level, thus resulting in lower nominal stress level. (a) (b) figure 5: normalized decrease of conventional yield stress rp0.2% values for the various exposure times of aa2024-t3 to the exco solution compared with (a) 3.5 wt. % nacl solution and (b) notch depths. 0 4 8 12 16 20 24 0,0 70 80 90 100 aluminum alloy 2024-τ3 t = 3.2 mm, direction l n o rm a liz e d d e cr e a se o f co n ve n ti o n a l yi e ld s tr e ss r p 0 .2 % [% ] exposure time to exco solution [hours] exco solution 0 700 1400 2100 2800 3500 4200 exposure time to nacl solution [hours] 3.5 wt. % nacl solution 0 4 8 12 16 20 24 0,0 70 80 90 100 exposure time to exco solution [hours] n o rm a liz e d d e cr e a se o f co n ve n ti o n a l yi e ld s tr e ss r p 0 .2 % [% ] exco solution 0,0 0,1 0,2 0,3 0,4 0,5 aluminum alloy 2024-τ3 t = 3.2 mm, direction l notch depth [mm] artificial notches n. alexopoulos et alii, frattura ed integrità strutturale, 50 (2019) 342-353; doi: 10.3221/igf-esis.50.29 348 effect on tensile ductility the results of the residual elongation at fracture af values can be seen in fig.6 for the three investigated cases, namely the exco exposure, the nacl exposure as well as the artificial notches. the results are presented in the form of normalized decrease from the initial value of af with double x-axis for comparison reasons. corrosion exposure has a deleterious effect on tensile ductility (elongation at fracture in the present case) even from the short exposure times to both investigated corrosive solutions. the normalized decrease of elongation at fracture af is almost the same for both solutions at short exposure times where the pitting formation remains limited; approximately 75 % remaining percentage of the initial mechanical property was observed after only 1 h of exposure to exco solution while the same decrease was noticed for the case of exposure to 3.5 wt. % nacl solution after 48 h (fig.6a). the same was observed for 2 h at exco and 168 h at 3.5 wt. % nacl with a normalized decrease value of 68 %. nevertheless, higher exposure times are needed for the 3.5 wt. % nacl solution in order to result in the same degradation percentage with the respective specimens exposed to exco solution. it should also be taken into consideration that the hydrogen embrittlement phenomenon takes place in this case, especially at the short exposure times in exco solution. the respective results for the comparison between corrosion exposure to exco solution and artificial surface notches are presented in fig.6b. it is evident that the normalized af decrease is not linear proportional to the notch depth nor to the exposure time increase in the reduced cross-section. an essential af decrease was observed even for the low-depth notches, e.g. approximately 70 % normalized decrease for 0.10 mm, as well as for the short exposure times such as 75 % normalized decrease after 1 h of exposure. after 12 h of exposure to exfoliation corrosion solution, the af decrease seems to reach a plateau value and further corrosion exposure did not decrease the tensile ductility considerably while for the increasing notch depth it decreases continuously to extremely low values such as 6 % for the 0.50 mm notch depth; this is evidence of maximum depth of attack of the surface corrosion-induced cracks [30]. it is well accepted that the ductility decrease from the short corrosion exposure times can be attributed to the hydrogen embrittlement phenomenon. (a) (b) figure 6: normalized decrease of elongation at fracture af values for the various exposure times to the exco solution of aa2024-t3 compared with (a) 3.5 wt. % nacl solution and (b) notch depth. correlation of corrosion exposure times to notches regarding ductility degradation as shown in the previous two sections, the increase of the surface notch depth decreases the tensile elongation at fracture (ductility) of aa2024-t3 and to a lesser extent the conventional yield stress. from the experimental tensile test results of pre-corroded 2024-t3 specimens, an essential decrease in tensile ductility was noticed even for the short corrosion exposure times, for both investigated corrosive solutions as well as for small artificial notch depth values. hence, it is obvious that the empirical correlation between the problem of corrosion-induced degradation and the equivalent problem with artificial surface notches should be assessed through the residual tensile ductility property. the experimental results of the residual elongation at fracture af of the pre-corroded in exco solution tensile specimens of aa2024-t3 can be seen in fig.7. in the same figure, the exponential decrease curve fitting was plotted as well. for the 0 4 8 12 16 20 24 0 20 40 60 80 100 aluminum alloy 2024-τ3 t = 3.2 mm, direction l exposure time to nacl solution [hours] n o rm a liz e d d e cr e a se o f e lo n g a ti o n a t fr a ct u re a f [ % ] exposure time to exco solution [hours] exco solution 0 700 1400 2100 2800 3500 4200 3.5 wt. % nacl solution 0 4 8 12 16 20 24 0 20 40 60 80 100 n o rm a liz e d d e cr e a se o f e lo n g a ti o n a t fr a ct u re a f [ % ] exposure time to exco solution [hours] exco solution 0,0 0,1 0,2 0,3 0,4 0,5 aluminum alloy 2024-τ3 t = 3.2 mm, direction l notch depth [mm] artificial notches n. alexopoulos et alii, frattura ed integrità strutturale, 50 (2019) 342-353; doi: 10.3221/igf-esis.50.29 349 conversion of the total depth of the surface notches in equivalent exposure time to corrosion solution, an empirical coefficient was devised. the value of this coefficient was selected such as to ‘tailor’ the equivalent ductility decrease curve of the surface notches in order to take approximate values with the experimental ductility decrease curve of the pre-corroded specimens. the empirical correlation factor m in [h/mm] was calculated based on the following equation to correlate the available elongation at fracture test results as: equivalent notch depth (mm) = . (1) fig.7 shows the correlation of the elongation at fracture decrease induced by the exposure to exco solution as well as by the presence of the surface notches. the best calculation results were found by using the value m = 20 for the empirical coefficient and the simulation of the ductility decrease curve of the investigated aa2024-t3 specimens for the short exposure times, where the synergy of pitting formation and hydrogen embrittlement is the dominant degradation mechanism. by using this coefficient value, it is obvious that the results of the artificial notch depths are very close to the experimental values for the short corrosion exposure times and up to 2 h. it seems that the total notch depth of 0.10 mm corresponds to 2 h of exfoliation corrosion regarding the elongation at fracture decrease. on the other hand, the empirical coefficient that better simulates the tensile ductility decrease for the long exposure times, where the exfoliation of the corroded surfaces along with hydrogen embrittlement are the responsible mechanisms for the elongation at fracture decrease, was found to be approximate m = 100. for instance, a total depth of 150 μm surface notch results in the same af decrease as for 15 h of exposure to exfoliation corrosion solution. summarizing the available test results, the factor m takes values as: mexco to notch= 20, 0 𝑡 4 h, 100, 16 𝑡 48 h, . (2) figure 7: correlation of the elongation at fracture af decrease due to exposure to the exco solution as well as to the presence of the artificial surface notches. fig.8 shows the correlation of elongation at fracture decrease resulting from the exposure to 3.5 wt. % nacl solution, along with the respective results from the artificial surface notches. it can be noticed that the residual elongation at fracture of the two different cases is well correlated for the short exposure times by using a coefficient value m = 500. this means that 50 h of exposure to 3.5 wt. % nacl solution results in the same elongation at fracture decrease as for 0.1 mm surface notch depth. the pitting corrosion mechanism is responsible for the ductility decrease for the short exposure times. however, a different value of this coefficient should be used, m = 15000, in order to obtain good correlation for the long exposure times and high notch depths, wherein the effect of micro-cracks formation due to pit growth and coalescence is responsible for the af degradation. hence, the following equation can be drawn by the findings of the results of the experimental protocols: mnacl to notch = 500, 0 𝑡 400 ℎ, 15.000, 2000 𝑡 8000 ℎ . (3) 0 10 20 30 40 50 60 70 0 2 4 6 8 10 12 14 16 18 m = 20 exposure time to exco solution [hours] e lo g a ti o n a t fr a ct u re a f [% ] aluminium alloy 2024-t3, t = 3.2 mm exposure to exco solution experimental results of exposure to exco solution results of the empirical correlation total depth of the notches with exposure time to exco solution m = 100 n. alexopoulos et alii, frattura ed integrità strutturale, 50 (2019) 342-353; doi: 10.3221/igf-esis.50.29 350 figure 8: correlation of the elongation at fracture af decrease due to exposure to the 3.5 wt. % nacl solution as well as to the presence of the artificial surface notches. fig.9 shows the correlation results of the effect of the two corrosive environments, i.e. exco and 3.5 wt. % nacl solutions, with regard to the same corrosion-induced tensile ductility decrease. to this end, for the conversion of exposure times to exco solution to the respective times of exposure to nacl solution, the n coefficient in [-] is formulated as: nexco to nacl = . (4) the best calculation results were found by using the value n = 92 for the empirical coefficient and for the simulation of the tensile ductility decrease curve of the investigated specimens for short exposure times regime. the same rate decrease is evident between the two different corrosive solutions at the short exposure times where slight pitting formation is the dominant degradation mechanism. by using this coefficient value, it is obvious that the results of the exfoliation corrosion are very close to the experimental values of exposure to 3.5 wt. % nacl up to 1 h of exposure and 14 % elongation at fracture. thus, it can be concluded that 1 h of exposure to exco solution is equivalent to 92 h of exposure to 3.5 wt. % nacl solution regarding the af degradation. for higher exposure times, there is no correlation between the corrosive environments regarding the ductility decrease since the corrosion-induced degradation mechanism is different. by exploiting this empirical tool, the design engineer could estimate the equivalent surface notches problem (fictitious notch) with the true problem of corrosion exposure of aa2024-t3. this might be a very useful tool as through experimental data or through finite element calculations, the design engineer could estimate the residual mechanical properties of the sheet alloy for maintenance and repair actions. it is obvious that the proposed empirical correlation for 2024-t3 gives reliable results for short exposure duration in exfoliation corrosion solution. in short corrosion exposure times, the degradation mechanism of ductility has been correlated in the open literature with the hydrogen embrittlement. to this end, the above-mentioned empirical correlation is suggested to be exploited for exposure times higher than 2 h, where the first surface pits and sub-sequent micro-cracks are beginning to be formed in the investigated cross-section of the aa2024-t3. conclusions ummarizing the findings of the present experimental study, it could be concluded that surface pitting corrosion remains limited for the short exposure times to both corrosive environments, e.g. up to 2 h in exco and 168 h in nacl solution; a substantial increase in pitting density and size was observed with increasing exposure times for both investigated solutions. moreover, all investigated tensile mechanical properties of aa2024-t3 are exponentially decreasing with increasing exposure time to corrosive solutions as well as surface notch depth; tensile ductility decreases with higher 0 1000 2000 3000 4000 5000 6000 7000 8000 0 2 4 6 8 10 12 14 16 18 20 e lo n g a ti o n a t fr a ct u re a f [ % ] exposure time to nacl times solution [hours] aluminium alloy 2024-t3, t = 3.2 mm exposure to 3.5 % nacl solution experimental results of exposure to 3.5 % nacl solution results of the empirical correlation total depth of the notches with exposure time to 3.5 % nacl solution m = 15000 m = 500 s n. alexopoulos et alii, frattura ed integrità strutturale, 50 (2019) 342-353; doi: 10.3221/igf-esis.50.29 351 figure 9: correlation of the elongation at fracture af decrease due to exposure to the exco solution as well as to 3.5 wt. % nacl solution. rates than conventional yield stress for both, exco and 3.5 wt. % nacl solutions as well as for artificial surface notches. in addition, it was shown that a ductile fracture mechanism is evident from the 45˚ slope of the fracture surface for up to 4 h for the specimens exposed to exco solution and even after 720 h for the specimens exposed to nacl solution; however, for higher exposure times to exco solution, the fracture path seems to follow the surface pits. another interesting finding of the study is that the more aggressive environment (exco) results in higher decrease of the conventional yield stress, especially for the short exposure times. higher exposure times to 3.5 wt. % nacl solution are needed for the same degradation of rp0.2% as for the exco solution, e.g. approximately 99 % normalized rp0.2% decrease was noticed after 1 h of exposure to exco solution while the same decrease is evident after 168 h of exposure to nacl solution. the specimens exposed to exfoliation corrosion exhibited higher conventional yield stress rp0.2% degradation than the specimens with the machined artificial surface notches, especially for the short exposure times and low depth of notches. however, the highest notch depth of 0.50 mm resulted in the same normalized decrease, approximately 80 %, as for the highest exposure time. an empirical coefficient was introduced for the correlation between the corrosion-induced tensile ductility degradation with the equivalent artificially induced surface notches. three cases were investigated: (a) exco exposure with artificial notches, (b) exco exposure with 3.5 wt. % nacl exposure and (c) 3.5 wt. % nacl exposure with artificial notches. higher correlation regarding the ductility decrease was noticed for the short exposure times, where the slight pitting formation as well as hydrogen embrittlement for the case of exco solution are the dominant degradation mechanisms, and low-depth notches for all investigated cases. the best correlation between exposure to exco solution and artificial surface notches was found by using m = 20 for the short exposure times where the main degradation mechanisms are the pitting formation along with hydrogen embrittlement; thus, a total notch depth of 0.10 mm corresponds to 2 h of exfoliation corrosion with regard to the same tensile ductility degradation. for the case of correlation between 3.5 wt. % nacl solution and artificial notches, the coefficient value that better simulates the corrosion-induced ductility decrease was found to be m = 500 for exposure times less than 400 h, where the incubation of pits is the dominant degradation mechanism; hence, 100 μm surface notch depth results in the same elongation at fracture decrease as for 50 h of exposure to 3.5 wt. % nacl solution. for the case of correlation between exposure to exco and 3.5 wt. % nacl solutions, it is proposed that 1 h exco exposure is equivalent to 92 h exposure to nacl solution regarding tensile elongation at fracture decrease. references [1] menan, f., henaff, g. (2009). influence of frequency and exposure to a saline solution on the corrosion fatigue crack growth behavior of the aluminum alloy 2024, int. j. fatigue, 31, pp. 1684-1695. doi: 10.1016/j.ijfatigue.2009. 02.033 0 500 1000 1500 2000 2500 3000 3500 4000 4500 0 2 4 6 8 10 12 14 16 18 exposure time to nacl solution [hours] e lo n g a tio n a t fr a ct u re a f [ % ] aluminium alloy 2024-t3, t = 3.2 mm experimental results of exposure to nacl solution results of the empirical correlation exposure to nacl exco solution n = 92 n. alexopoulos et alii, frattura ed integrità strutturale, 50 (2019) 342-353; doi: 10.3221/igf-esis.50.29 352 [2] davis, j.r. (1999). corrosion of aluminum and aluminum alloys, asm international materials park, united states. [3] chen, g.s., gao, m., wie, r.p. (1996). microconstituent-induced pitting corrosion in aluminum alloy 2024-t3. corrosion, 52, pp. 8-15. doi: 10.5006/1.3292099. [4] szklarska–smialowska, z. (1999). pitting corrosion of aluminum. corros. sci., 41, pp. 1743-1767. doi: 10.1016/ s0010-938x (99)00012.-8. [5] shreir, l.l., jarman, r.a., burstein, c.t. (1994). corrosion: metal/environmental reactions, oxford: butterworth & heinemann ltd. doi: 10.1016/c2013-0-04015-7. [6] strehblow, h.h. (1995). mechanisms of pitting corrosion, in: corrosion mechanisms in theory and practice, new york, marcel dekker inc.; pp. 201-238. [7] birbilis, n., cavanaugh, m.k., buchheit, r.g. (2006). electrochemical behavior and localized corrosion associated with al7cu2fe particles in aluminum alloy 7075-t651. corros. sci., 48, pp. 4202-4215. doi: 10.1016/j.corsci.2006. 02.007. [8] boag, a., taylor, r.j., muster, t.h., goodman, n., mcculloch, d., ryan, c., rout, b., jamieson, d., hughes, a.e. (2010). stable pit formation on aa2024-t3 in a nacl environment. corros. sci., 52, pp. 90-103. doi: 10.1016/ j.corsci.2009.08.043. [9] boag, a., hughes, a.e., glenn, a.m., muster, t.h., mcculloch, d. (2011). corrosion of aa2024-t3 part i: localised corrosion of isolated im particles. corros. sci., 53, pp.17-26. doi: 10.1016/j.corsci.2010.09.009. [10] blanc, c., lavelle, b., mankowski, g. (1997). the role of precipitates enriched with copper on the susceptibility to pitting corrosion of the 2024 aluminum alloy. corros. sci., 39, pp. 495-510. doi: 10.1016/s0010-938x (97) 86099-4. [11] derose, j.a., suter, j., bałkowiec, t., michalski, a., kurzydlowski, k.j., schmutz, p. (2012). localised corrosion initiation and microstructural characterization of an al2024 alloy with a higher cu to mg ratio. corros. sci., 55, pp. 313-325. doi: 10.1016/j.corsci.2011.10.035. [12] shi, h., tian, z., hu, t. liu, f. han, e.h., taryba, m. lamaka, s.v. (2014). simulating corrosion of al2cumg phase by measuring ionic currents, chloride concentration and ph. corros. sci., 88, pp. 178-186. doi: 10.1016/j.corsci. 2014.07.021. [13] hughes, a.e., boag, a., glenn, a.m., mcculloch, d., muster, t.h., ryan, c., luo, c., zhou, x., thompson, g.e. (2011). corrosion of aa2024-t3 part ii: co-operative corrosion. corros. sci., 53, pp. 27-39. doi: 10.1016/ j.corsci.2010.09.030. [14] buchheit, r.g., grant, r.p., hlava, p.f., mckenzie, b., zender, g.l. (1997). local dissolution phenomena associated with s phase (al2cumg) particles in aluminum alloy2024-t3, j. electrochem. soc., 144, pp. 2621-2628. .doi: 10.1149 /1.1837874. [15] hashimoto, t., zhang, x., zhou, x., skeldon, p., haigh, s.j., thompson, g.e. (2016). investigation of dealloying of s phase (al2cumg) in aa 2024-t3 aluminium alloy using high resolution 2d and 3d electron imaging. corros. sci., 103, pp. 157-164. doi: 10.1016/j.corsci.2015.11.013. [16] lyon, k.n., marrow, t.j., lyon, s.b. (2015). influence of milling on the development of stress corrosion cracks in austenitic stainless steel. j. mater. process. technol., 218, pp. 32-37. doi: 10.1016/j.jmatprotec.2014.11.038. [17] ishihara, s., saka, s., nan, z.y., goshima, t., sunada, s. (2005). prediction of corrosion fatigue lives of aluminium alloy on the basis of corrosion pit growth law. fatigue fract. eng. mater. struct., 29, pp. 472-480. doi: 10.1111/ j.1460-2695.2006.01018.x. [18] azofeifa, d.e., clark, n., amador, a., saenz, a. (1997). determination of hydrogen absorption in pd coated al thin films. thin solid films, 300, pp. 295-298. doi: 10.1016/s0040-6090(96)09493-x. [19] kamoutsi, h. (2004), “corrosion-induced hydrogen embrittlement in high-strength aluminum alloys”, phd thesis, department of mechanical and industrial engineering, university of thessaly, volos. [20] kamoutsi, h., haidemenopoulos, g., bontozoglou, v., pantelakis, s.g. (2006). corrosion-induced hydrogen embrittlement in aluminum alloy 2024, corros. sci., 48, pp. 1209-1224. doi: 10.1016/j.corsci.2005.05.015 [21] lynch, s.p. (2013). mechanisms and kinetics of environmentally assisted cracking: current status, issues, and suggestions for further work, metall. mater. trans. a, 44, pp. 1209-1229. doi: 10.1007/s11661-012-1359-2. [22] liao, m., bellinger, n.c., komorowski, j.p. (2003). modeling the effects of prior exfoliation corrosion on fatigue life of aircraft wing skins. int. j. fatigue, 25, pp. 1059-1067. doi: 10.1016/j.ijfatigue.2003.08.005. [23] chen, g.s., wan, k.c., gao, m., wei, r.p., flournoy, t.h. (1996). transition from pitting to fatigue crack growthmodeling of corrosion fatigue crack nucleation in a 2024-t3 aluminum alloy. mater sci. eng. a, 219, pp. 126-132. doi: 10.1016/s0921-5093(96)10414-7. [24] sprowls, d.o., walsh, j.d., shumaker, m.b. (1972). simplified exfoliation testing of aluminum alloys, astm stp 516. doi: 10.1520/stp35415s. n. alexopoulos et alii, frattura ed integrità strutturale, 50 (2019) 342-353; doi: 10.3221/igf-esis.50.29 353 [25] jones, k., hoeppner, d.w. (2006). prior corrosion and fatigue of 2024-t3 aluminum alloy. corros. sci., 48, pp. 3109 3122. doi: 10.1016/j.corsci.2005.11.008. [26] kermanidis, a.t., petroyiannis, p.v., pantelakis, s.g. (2005). fatigue and damage tolerance behaviour of corroded 2024 t351 aircraft aluminum alloy. theor. appl. fract. mech., 43, pp. 121-132. doi: 10.1016/j.tafmec.2004.12.008. [27] pantelakis, s.g., daglaras, p.g., apostolopoulos, c.a., (2000). tensile and energy density properties of 2024, 6013, 8090 and 2091 aircraft aluminum alloy after corrosion exposure. theor. appl. fract. mech., 33, pp. 117-134. doi: 10.1016/s0167-8442 (00)00007-0. [28] petroyiannis, p.v., kermanidis, a.t., kamoutsi, h., pantelakis, s.g., bontozoglou, v., haidemenopoulos, g.n. (2005). evidence on the corrosion induced hydrogen embrittlement of the 2024 aluminum alloy. fatigue fract. eng. mater. struct., 28, p.p. 565-574. doi: 10.1111/j.1460-2695.2005.00900.x. [29] alexopoulos, n.d., papanikos, p. (2008). experimental and theoretical studies of corrosion-induced mechanical properties degradation of aircraft 2024 aluminum alloy. mater. sci. eng. a, 498, pp. 248-257. doi: 10.1016/j.msea. 2008.08.024. [30] alexopoulos, n.d., dalakouras, c.j., skarvelis, p., kourkoulis, s.k. (2012). accelerated corrosion exposure in ultrathin sheets of 2024 aircraft aluminium alloy for glare applications. corros. sci., 55, pp. 289-300. doi: 10. 1016/j.corsci.2011.10.032. [31] gurin, m., andrieu, e., odemer, g., alexis, j., blanc, c. (2014). effect of varying conditions of exposure to an aggressive medium on the corrosion behavior of the 2050 alculi alloy. corros sci., 85, pp. 455-470. doi: 10.1016 /j.corsci.2014.04.042. [32] vasco, m.c., chamos, a.n., pantelakis, s.g. (2017). effect of environment's aggressiveness on the corrosion damage evolution and mechanical behavior of aa 2024-t3. fatigue fract. eng. mater. struct., 40, pp 1551-1561. doi: 10.1111/ffe.12651. [33] alexopoulos, n.d., velonaki, z., stergiou, c.i., kourkoulis, s.k. 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can be opened with acrobat and adobe reader 5.0 and later.) >> /namespace [ (adobe) (common) (1.0) ] /othernamespaces [ << /asreaderspreads false /cropimagestoframes true /errorcontrol /warnandcontinue /flattenerignorespreadoverrides false /includeguidesgrids false /includenonprinting false /includeslug false /namespace [ (adobe) (indesign) (4.0) ] /omitplacedbitmaps false /omitplacedeps false /omitplacedpdf false /simulateoverprint /legacy >> << /addbleedmarks false /addcolorbars false /addcropmarks false /addpageinfo false /addregmarks false /convertcolors /converttocmyk /destinationprofilename () /destinationprofileselector /documentcmyk /downsample16bitimages true /flattenerpreset << /presetselector /mediumresolution >> /formelements false /generatestructure false /includebookmarks false /includehyperlinks false /includeinteractive false /includelayers false /includeprofiles false /multimediahandling /useobjectsettings /namespace [ (adobe) (creativesuite) (2.0) ] /pdfxoutputintentprofileselector /documentcmyk /preserveediting true /untaggedcmykhandling /leaveuntagged /untaggedrgbhandling /usedocumentprofile /usedocumentbleed false >> ] >> setdistillerparams << /hwresolution [2400 2400] /pagesize [612.000 792.000] >> setpagedevice microsoft word numero_43_art_8 m. davydova et alii, frattura ed integrità strutturale, 43 (2018) 106-112; doi: 10.3221/igf-esis.43.08 106 the effect of porosity on fragmentation statistics of dynamically loaded zro2 ceramics marina davydova, sergei uvarov, oleg naimark institute of continuous media mechanics ural branch russian academy of sciences, 1, ac. korolev str., perm 614013, russia. 1957davydova@gmail.com, http://lab13.icmm.ru/index.php/en/ pia@icmm.ru, http://lab13.icmm.ru/index.php/en/ naimark@icmm.ru, http://lab13.icmm.ru/index.php/en/ abstract. the effect of load intensity and porous material structure on the fragmentation statistics of zro2(mgo)-based ceramics is studied. cylindrical samples were fragmented under dynamic compression. experimental data processing showed that the shape of stress-strain curves, the fragment size distribution and distribution of time intervals between the fractoluminiscense impulses depend on the sample porosity and load intensity. the x-ray computed tomography (ct) study of porous material structures allowed us to link the fragmentation statistics with pronounced porosity clustering (about 97% of the total pore volume) formed due to sintering. keywords. fragmentation; ceramic; crack cluster. citation: davydova, m., uvarov, s., naimark, o., the effect of sample porosity on statistical regularities of dynamical fragmentation of ceramic zro2, frattura ed integrità strutturale, 43 (2018) 106-112. received: 17.10.2017 accepted: 28.10.2017 published: 01.01.2018 copyright: © 2018 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. introduction ynthesis of ceramic materials with projected properties implies studying the relationship between physical and mechanical characteristics and porosity of the material. on the one hand, the role of porosity as the main structural factor is associated with the absence of the effective mechanism of structural relaxation due to a dislocation motion, and, on the other hand, with the long–range interactions in the ensemble of pores growing during the deformation. these features determine the pore clustering, damage-failure kinetics and mechanical properties in a wide range of load intensity [1]. study of the effect of porosity revealed the influence of the porous cluster morphology on the deformation properties of ceramics zro2(y2o3) [1,2]. this is associated with a change in pore distributions related to the transition from the isolated pore structure to the structure with pore clustering. in this paper, the effect of pore cluster morphology of the ceramic material subject to dynamic loading and fragmentation was studied based on the analysis of 2d and 3d structure images obtained by x-ray computed tomography (ct). samples and experimental technique he samples used in the experiment were fabricated at the institute of strength physics and material sciences (sb ras, tomsk) from the ceramics of zro2-mgo system (8.6 % mol mgo) by the plasmochemical method [4]. the manufacture of ceramic samples was carried out by powder metallurgy technique, which consisted in powder s t m. davydova et alii, frattura ed integrità strutturale, 43 (2018) 106-112; doi: 10.3221/igf-esis.43.08 107 compacting within the steel molds with a hydraulic punch under compacting pressure of 70 mpa. the obtained compacts were sintered in air at 1550°с and then subjected to isothermal exposure within an hour. the samples had the shape of cylinders of diameter from 8.5 to 13 mm, length from 6.8 to 12.2 mm and weight from 2.2 to 6.3g. porosity of the initial powder before compacting varied from 10% to 60%. figure 1: a) the scheme of experimental set-up (1-sample, 2-input bar, 3-output bar, 4-photomultiplier tube (pmt), 5teflon ring, 6 impedance matched wc insert, 7plastic cylinder); b) stress-strain curve for ceramic samples with porosity of 10%, 20%, 45%, 60%. dynamic tests were carried out using a split hopkinson pressure bar, (fig.1(a)), which consists of the input (3 m in length and 25 mm in diameter) and output (1 m in length and 25 mm in diameter) bars to provide single-pulse loading conditions. the bars were made of high-strength steel ( ~ 1900b gpa ). a sample was sandwiched between the bars and separated from them by the impedance–matched tungsten carbide (wc) inserts, which prevented samples from being indented into the bars, the hardness of which was less than the hardness of the examined ceramics. the position of the bars was carefully adjusted before each loading to ensure a uniform distribution of the force applied to the end faces of the samples. in order to eliminate the effect of dispersion in the bars and to provide the dynamic stress equilibrium conditions (the equality of forces applied to the specimen ends) during tests, we used a brass pulse shaper, which was a 7x7 mm plate of thickness 1.4 mm. by varying the striker velocity, we managed to increase the deformation rate from 400 to 3000 s-1. the study of fragmentation statistics (fragment size distribution and distribution of time intervals between the fractoluminiscence impulses) required modification of the traditional scheme of the split hopkinson bar. the samples and the ends of the bars adjacent to the samples were placed into plastic cylinders, which allowed the fragments of ceramics to remain confined within the cylinder and provided dimming necessary for registration of the fractoluminiscence impulses. the formation of fracture surfaces during sample fragmentation initiated light emission, which was recorded by the two a) b) m. davydova et alii, frattura ed integrità strutturale, 43 (2018) 106-112; doi: 10.3221/igf-esis.43.08 108 photomultiplier tubes (pmt) with the rise time of 0.8 ns, which were located at the opposite lateral surfaces of the sample. to improve reliability of experiments, two pmt were used. from the pmt signal was transmitted to the tektronix digital oscilloscope dp07254 with a band width of 3.5 ghz and sampling rate less than 10 ghz. thus, the modified setup had the advantage of getting both the deformation curves and the statistic characteristics of the fragmentation process, based on the data on the two types of distribution: size distribution of the spatial parameter (fragment size) and size distribution of the temporal parameter (the interval between fractoluminiscence impulses). figure 2: sample with porosity of 30%: a) ct image of the sample cross section; b) fragment size distribution function for 5 specimens; c) typical time interval distribution function. dynamic fragmentation results ig. 1(b) shows typical stress-strain curves for ceramic samples with different porosity before sintering. it should be noted that for the samples with porosity less than 45%, the stress-strain  ( ) curves have one stress maximum, whereas for the samples with porosity of 45% and 60% the  ( ) curves show two maxima. the experimental data were used to construct the cumulative fragment size distribution, i.e., the relationships between the number of fragments, n , the size (mass) of which is larger than a prescribed value, and the size, r (mass m ), of the fragment. the fragment mass was measured by weighing fragments on the electronic balance hr-202i. fig. 2(b) and fig. 3(b) present the log-log plots of the cumulative fragment size distribution for the samples, in which the initial porosity of the powder component was 20%, (fig. 2(b)), and 60%, (fig. 3(b)). the above distributions are well described (r2>0.96) by the power law function: f a) b) m. davydova et alii, frattura ed integrità strutturale, 43 (2018) 106-112; doi: 10.3221/igf-esis.43.08 109  dsn cr (1) figure 3: sample with porosity 2 %: a) ct image of the sample cross section; b) fragment size distribution function for 3 samples; c) typical time interval distribution function. the value of the power law exponent sd depends on the material porosity and load intensity. the time intervals between the fractoluminiscence impulses was about 2÷103 ns in the active fracture stage, while in the final stage it increased up to 106 ns. the change in porosity from 10% to 60% led to a growth of the impulse number by a factor of 18. fig. 2(c) and fig. 3(c) present the log-log-plots of the time interval distribution function, which depicts the dependence of the number of intervals, tn , with the size larger than or equal to t . the distribution function for the samples with porosity of 10÷45% is well described (r2>97%) by two power laws (two straight lines), (fig. 3(c)). whereas for the samples with porosity of 60% it is described by power law (one straight line), (fig. 2(c)):  1 dt tn c t (2) the value of power law exponent td in the relation (2) is affected by the porosity and load value. the ceramic material under study has a cellular structure, which is formed by hollow powder particles (particle porosity) separated by interparticle pores [3,4]. therefore, it was suggested in [5] that the difference in the time interval distribution functions, (fig. 2(c) and fig. 3(c)), for samples of different porosity and a weak sensitivity of the power law exponent to load intensity for low porosity samples, (fig. 3(b)), should be explained by the competition between two pore systems. the a) b) m. davydova et alii, frattura ed integrità strutturale, 43 (2018) 106-112; doi: 10.3221/igf-esis.43.08 110 study of porous structure of the non-deformed samples using x-ray computed tomography (ct) indicates that the key role in fracture and fragmentation process for studying ceramic is belong to the interparticle pores system. x-ray computed tomography (ct) study he investigation of porous structure (inter-particle porosity) of ceramic samples with initial powder porosity of 20% and 60% was done using x-ray computed tomography (nikon metrology xt h 225+180 lc, perm state university). the ct data obtained for the sample with initial porosity of 60% (diameter is 13 mm and height is 12 mm) were represented by a stack of 1039 cross-section images of the sample, (fig.2(a)), and for the sample with initial porosity of 20% (diameter is 8 mm and height is 7 mm) – by a stack of 1350 images, (fig.3(a)). dark areas in fig.2(a) and fig.3(a) correspond to pores. processing of the ct data was done using the imagej (ij1.46r) open source software, which allowed us to calculate the number and volume of the pores, porosity, area and perimeter of the pores in all slices and to perform 3d visualization. the results of stack processing showed that the real porosity of the sample produced from the powder with initial porosity of about 60% was 30% and the real porosity of the sample with initial powder porosity of about 30% was 2%. the cumulative pore size distribution function for the pore size greater than a prescribed value is presented in fig.4. in the calculation we used the stack of 1350 slices in the case of 2% porosity sample and the stack of 900 slices in the case of 30% porosity sample. gray dots indicate the pore size distribution for the low porosity (2%) sample. the pore size distribution for the sample with porosity of 30% is described by a curve consisting of orange dots and separately located big red dot. the construction of 3d images, (fig.5 and fig.6), of the sample pore structure allowed us to establish that volume of 374 mm3 (red dot) is the pore cluster, and the orange curve describes the size distribution of pores that stand alone (outside the cluster). moreover, cluster covers 98% of porosity and this is the main reason of its considerable influence on the fracture process. note that it will be impossible to obtain the above cluster if we try to construct 3d image of the pore ensemble using a small number of slices, (10 or 20, fig.6(a)): the formation of 3d cluster is feasible only with a sufficiently large number of slices, (more than 100, fig. 6(b)). figure 4: cumulative pore size distribution functions for samples with porosity 2 % and 30% conclusion he experiments on dynamical fragmentation of zro2 ceramics showed, that the initial porosity of the samples has effect on the shape of the stress-strain curves, (fig. 1(b)), the scatter of the power law exponent of the fragment size distribution, (fig. 2(b) and fig.3(b)), and the type of the time interval distribution function, (fig. 2(c), fig. 3(c)). t t m. davydova et alii, frattura ed integrità strutturale, 43 (2018) 106-112; doi: 10.3221/igf-esis.43.08 111 figure 5: 3d image of the pore system for 2% porosity sample (100 slices). figure 6: 3d image of the pore cluster for 30% porosity sample: a) 10 slices; b) 100 slices. a) b) m. davydova et alii, frattura ed integrità strutturale, 43 (2018) 106-112; doi: 10.3221/igf-esis.43.08 112 processing of ct images of non-deformed samples using the imagej code allowed us to conclude, that mentioned features of ceramics fragmentation with different porosity should be associated with a large cluster, which is formed in the process of preparation of ceramic samples with porosity of 30% (from the initial powder compact with 60% porosity) and combines up to 98% of all sample pores. initial fracture stage, which involves multiple initiation and growth of porous defects plays the key role in fragmentation of sample with low porosity 2% (initial 20%). but for the samples with 30% porosity (initial 60%), this stage is practically absent due to the presence of pore cluster, and the failure is caused by the loss of stability of the partitions between the pores. this hypothesis is confirmed by the following facts:  stress-strain curves for high porosity samples have two maxima, the first of which corresponds to the pore collapse and the second to the deformation of compacted material;  in the initial stage of fracture, the intervals between the fractoluminescence impulses for the sample with 2% porosity are two or three times longer than for the sample with 30% porosity. the increase in porosity from 2% to 30% leads to an 18-fold growth of the number of fractoluminescence impulses, which corresponds to the scale-invariant power law distribution of time intervals (straight line in fig. 2(c)). the scatter of power law exponent (fig. 2(b)) for the sample with 30% porosity is also due to the formation of a cluster, which provides a wide range of possible fracture variants. the scale invariant law associated with the increase of porosity is also the fundamental subject of research, because it characterizes the material ability to demonstrate the criticality of damage-failure transition due to the involvement of total spectra of the space-time scales into the mechanisms of the defect-induced structural relaxation. the established characteristic features of fragmentation may be crucial for studying the absorption mechanisms [6,7], which can exhibit scaling (structural wave fronts [8]) in a wide range of load intensity. references [1] buyakova, s.p., maslovskii, v.l., nikitin, d.s., kulkov, s.n., mechanical instability of a porous material, technical physics letters, 27(12) (2001) 981-983. doi: 10.1134/1.1432322 [2] kulkov, s.n., maslovskii, v.l., buyakova, s.p., nikitin, d.s., the non-hooke’s behavior of porous zirconia subjected to high-rate compressive deformation, technical physics. the russian journal of applied physics., 47(3) (2002) 320324. doi: https://doi.org/10.1134/1.1463121 [3] buyakova, s. p., kulkov, s. n., effect of mechanical processing of ultrafine zro2 + 3 wt % mgo powder on the microstructure of ceramics produced from it, inorganic materials, 46 (2010) 1155–1158. doi:10.1134/s0020168510100249 [4] kalatur, e.s., kozlova, a.v., buyakova, s.p., kulkov, s.n., deformation behavior of zirconia-based porous ceramics, iop conf. series: materials science and engineering, 47 (2013) p.012004. doi: 10.1088/1757-899x/47/1/012004. [5] davydova, m.m., uvarov, s.v., naimark, o.b., space-time scale invariance under dynamic fragmentation of quasibrittle materials, phys. mesomechanics, 19(1) (2016) 86-92. doi: 10.1134/s1029959916010094. [6] naimark, o.b., some regularities of scaling in plasticity, fracture, and turbulence, phys. mesomechanics, 19(3) (2016) 307-318. doi: 10.1134/s1029959916030097. [7] naimark, o.b., defect induced transitions as mechanisms of plasticity and failure in multifield continua in: g. capriz, p. m. mariano (eds.), advances in multifield theories of continua with substructure, birkhäuser, boston, (2004) 75114. doi: https://doi.org/10.1007/978-0-8176-8158-6. [8] grady, d., structured shock waves and the fourth-power law, j. of applied physics, 107 (2010) 013506. doi: http://dx.doi.org/10.1063/1.3269720. << /ascii85encodepages false /allowtransparency false /autopositionepsfiles true /autorotatepages /none /binding /left /calgrayprofile (dot gain 20%) /calrgbprofile (srgb iec61966-2.1) /calcmykprofile (u.s. web coated \050swop\051 v2) /srgbprofile (srgb iec61966-2.1) /cannotembedfontpolicy /error /compatibilitylevel 1.4 /compressobjects /tags /compresspages true /convertimagestoindexed true /passthroughjpegimages true /createjobticket false /defaultrenderingintent /default /detectblends true /detectcurves 0.0000 /colorconversionstrategy /cmyk /dothumbnails false /embedallfonts true /embedopentype false /parseiccprofilesincomments true /embedjoboptions true /dscreportinglevel 0 /emitdscwarnings false /endpage -1 /imagememory 1048576 /lockdistillerparams false /maxsubsetpct 100 /optimize true /opm 1 /parsedsccomments true 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can be opened with acrobat and adobe reader 5.0 and later.) >> /namespace [ (adobe) (common) (1.0) ] /othernamespaces [ << /asreaderspreads false /cropimagestoframes true /errorcontrol /warnandcontinue /flattenerignorespreadoverrides false /includeguidesgrids false /includenonprinting false /includeslug false /namespace [ (adobe) (indesign) (4.0) ] /omitplacedbitmaps false /omitplacedeps false /omitplacedpdf false /simulateoverprint /legacy >> << /addbleedmarks false /addcolorbars false /addcropmarks false /addpageinfo false /addregmarks false /convertcolors /converttocmyk /destinationprofilename () /destinationprofileselector /documentcmyk /downsample16bitimages true /flattenerpreset << /presetselector /mediumresolution >> /formelements false /generatestructure false /includebookmarks false /includehyperlinks false /includeinteractive false /includelayers false /includeprofiles false /multimediahandling /useobjectsettings /namespace [ (adobe) (creativesuite) (2.0) ] /pdfxoutputintentprofileselector /documentcmyk /preserveediting true /untaggedcmykhandling /leaveuntagged /untaggedrgbhandling /usedocumentprofile /usedocumentbleed false >> ] >> setdistillerparams << /hwresolution [2400 2400] /pagesize [612.000 792.000] >> setpagedevice microsoft word numero_58_art_29_3252.docx r. capozucca et alii, frattura ed integrità strutturale, 58 (2021) 402-415; doi: 10.3221/igf-esis.58.29 402 focussed on steels and composites for engineering structures analysis of static response of rc beams with nsm cfrp/gfrp rods r. capozucca, e. magagnini, m.v. vecchietti struct.section dicea, università politecnica delle marche, ancona, italy r.capozucca@staff.univpm.it, e.magagnini@staff.univpm.it, m.v.vecchietti@pm.univpm.it abstract. in this paper experimental results of investigation on reinforced concrete (rc) beams strengthened with the near surface method (nsm) are analyzed considering the response under bending tests on two beams. one of the rc beams was damaged by bending until the yield of reinforcement and successively strengthened with carbon fiber polymer (cfrp) rod, while the second beam was strengthened with glass-frp rod. both the beams have been subjected to bending tests until failure. experimental diagrams and discussion on static response are presented in the paper. it also places a particular emphasis on the non-linear response of rc sections strengthened with cfrp and gfrp rods under bending moment beyond the first elastic behavior. keywords. rc beams; nsm; cfrp-gfrp rod; static test. citation: r. capozucca, e. magagnini, m.v. vecchietti, analysis of static response of rc beams with nsm cfrp/gfrp rods, frattura ed integrità strutturale, 58 (2021) 402-415. received: 26.08.2021 accepted: 03.09.2021 published: 01.10.2021 copyright: © 2021 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. introduction he damage of reinforced concrete (rc) structures both for civil building and bridges is an important duty of structural engineering. rehabilitation of structures requests innovative techniques with new material [1-4]. in the last decades the use of fiber reinforced polymers (frps) has been growing and, in general, two methods of strengthening have been adopted. first it was the frp strips or laminates glued to surface of rc beams [2,3]; this technique may be indicated as external bonded (eb) strengthening. it appears an available method to strengthen rc beams, but it may be loss validity for impact or due to fire because the frp strips or laminate are non-sufficiently protected. a second technique is the near surface mounted (nsm) that foresees to insert frp rods in grooves on the concrete cover [4-10]. this technique appears available in many experimental studies thought the bond between concrete and frp rods is a yet open problem to analyze [10-13]. in fact, the maintaining of bond is the most important condition that must be monitored in the beams strengthened with nsm frp rods [14-18]. experimental works have been developed by researchers to analyze the static [14,15] and vibration responses of strengthened rc beams in real scale or in small scale [19-22]. other aspects that may influence the response under loading are: shape of frp rods, circular or rectangular; distance between rods and surface of grooves; roughness of frp rods’ surface; tensile strength of frp rods [23-25]. in literature, investigations on the behavior of rc beams strengthened with cfrp and gfrp rod are present [26-30] also considering new methods [30]; further codes of practice [31] have been developed and they may be utilized by engineers. unfortunately, many aspects of nsm technique t https://youtu.be/d5fo9xktxka r. capozucca et alii, frattura ed integrità strutturale, 58 (2021) 402-415; doi: 10.3221/igf-esis.58.29 403 must be develop more and other experiments are necessary to define modelling and responses both in service and ultimate conditions. this paper deals with the investigation by static tests on rc beams strengthened both with cfrp and gfrp rods. a couple of beams in real scale with one rc beam subjected to bending tests at different damage degree is analyzed: one beam, damaged by bending and strengthened with nsm carbon-frp rod, has been tested; another one rc beam strengthened by nsm gfrp rod, has been experimentally studied. static results are shown and discussed below considering the nonlinear behavior of rc beams under loading. experimental bending tests set-up and strengthening material xperimental tests were carried out on two rc beams, b1 and b2, with a cross-section of 120·160 mm and length of 2200 mm, the steel reinforcement consisted of four longitudinal steel bars of 10 mm diameter and stirrups of 6 mm diameter. a groove of 20·20 mm was created at the bottom of each beam to locate an nsm reinforcement bar. after static tests, beam b1 was strengthened with a cfrp rod measuring 9.7 mm in diameter and 2000 mm in length, while beam b2 was strengthened with a gfrp rod of 9.5 mm diameter and 2000 mm length. fig. 1 depicts geometric configuration of the specimens. the two beams tested in laboratory were characterized by concrete with a tested average cylinder compressive strength equal to fc=44.31 mpa and young’s modulus ec=34492 mpa; steel bars with a yielding stress equal to fy=450 mpa and young’s modulus es=210 000 mpa. figure 1: beam model with steel reinforcing and nsm frp rod: geometrical features. specimens diameter, d [mm] section area, acfrp [mm2] tensile strength, f [mpa] young’s modulus, e [mpa] cfrp rod 9.7 73.90 2000 155 000 gfrp rod 9.53 71.26 760 40 800 table 1: results of tensile tests on frp rods. (a) (b) figure 2: (a) specimens of cfrp and gfrp rods for tensile tests; (b) failure of specimens after tensile tests. e r. capozucca et alii, frattura ed integrità strutturale, 58 (2021) 402-415; doi: 10.3221/igf-esis.58.29 404 company mapei produced the cfrp and gfrp rods used in this research. tensile tests on three specimens for each type of fiber were used to determine the mechanical and geometrical properties of the c-gfrp rods (fig. 2a); all the samples’ failures were in the xgm category – explosive, gage, middle – as defined by astm d-3039 [32] (fig. 2b). main results obtained by tensile tests are summarized in tab. 1. a two-component epoxy structural adhesive (eres=5130 mpa) was adopted for the bonding of the frp rod to the concrete surfaces into the notch. static response of beams damaged and strengthened the first phase of static bending tests involves experimentation on the un-strengthened rc beam b1. the apparatus was design to reproduce a simply supported condition with hinge restraints at the extremities, as presented in fig. 3. figure 3: experimental apparatus for static bending tests. the external load was applied in two points placed at a distance of 300mm through vertical jacks; the compressed concrete’s and the tensile steel’s strains were monitored using electronic strain gauges positioned at the centreline (fig. 4). the beam’s deflection was recorded by a linear inductive displacement trasducer (lvdt) applied at the midspan section. the beam without strengthening was subjected to static tests using an increasing bending loading path. three cycles of loading were adopted. for each cycle of loading pi, a damage level di with i=1,2,3 was identified, as shown in tab. 2. results of static bending tests, in terms of deflection, concrete and steel strain and curvature, are summarized in tab. 2. the experimental diagrams displayed in fig. 5 were developed by measurements taken in terms of deflection and strains at the midspan of rc beam b1. therefore, it is possible to characterize the static behavior of beam b1 before the application of nsm cfrp strengthening, based on these data. after reaching a consistent state of concrete’s cracking, a cfrp circular rod was positioned in the notched and then it was filled by adhesive epoxy resin. the strengthened beam b1 was subjected once again to cyclic bending loading. the first three damage levels were the same as for the previous unreinforced case. two additional cycles of loading, d4 and d5, were adopted, for a total of five degrees of damage. damage steps load, p [kn] deflection at midspan, δ [mm] strain at compressive concrete, εc (‰) strain at steel reinforcement (at intrados), εs (‰) curvature at midspan section, χ (10-5) d1 4.00 1.65 0.21 0.85 0.81 d2 8.00 4.67 0.50 1.64 1.64 d3 16.00 11.38 0.94 3.10 3.11 table 2: experimental results obtained for un-strengthened beam b1. r. capozucca et alii, frattura ed integrità strutturale, 58 (2021) 402-415; doi: 10.3221/igf-esis.58.29 405 after the fifth damage level, the strengthened beam b1 was subjected to increasing load until the collapse. the maximum load reached during test, that lead to the specimen’s failure, was equal to pu= 49.06 kn. as previously described, the recording of the strains achieved during the test, has been entrusted to one strain gauges placed on the cfrp rod, as shown in fig. 5. tab. 3 contains a summary of the main data acquired from the instrumentation used for each loading step and the curvature at the midspan section evaluated for the strengthened beam b1. figure 5: instruments for strain and displacement monitoring at the midspan. damage steps load, p [kn] deflection at midspan, δ [mm] strain at compressive concrete, εc (‰) strain at steel reinforcement (at intrados), εs (‰) strain at cfrp rod, εcfrp (‰) curvature at midspan section*, χ (10-5) d1 4.00 0.96 0.09 0.24 0.14 0.03 d2 8.02 0.80 0.24 0.52 0.55 0.21 d3 18.01 3.29 0.59 1.42 1.50 0.61 d4 24.01 7.36 0.83 2.10 2.06 0.82 d5 30.01 9.45 1.05 2.73 1.12 table 3: main results obtained by static bending tests for beam b1 with nsm cfrp. * curvature evaluated from deformation on compressive edge and cfrp bar. (a) 0 5 10 15 20 0 2 4 6 8 10 12 lo a d p [k n ] δ [mm] d1 d2 d3 r. capozucca et alii, frattura ed integrità strutturale, 58 (2021) 402-415; doi: 10.3221/igf-esis.58.29 406 (b) (c) figure 5: diagrams (a) load, p, vs deflection, δ; (b) load, p, vs strain, ɛc, at the edge of compressive concrete and (c) load, p, vs strain of tensile steel, ɛs – rc beam b1 without strengthening. (a) 0 5 10 15 20 0 200 400 600 800 1 000 lo a d p [k n ] εc (· 10-6) d1 d2 d3 0 5 10 15 20 0 500 1 000 1 500 2 000 2 500 3 000 3 500 lo a d p [ kn ] εs (· 10-6) d1 d2 d3 0 5 10 15 20 25 30 35 40 45 0 5 10 15 20 lo a d p [ kn ] δ [mm] d1 d2 d3 d4 d5 failure conditio n r. capozucca et alii, frattura ed integrità strutturale, 58 (2021) 402-415; doi: 10.3221/igf-esis.58.29 407 (b) figure 6: diagrams (a) load, p, vs deflection, δ, and (b) load, p, vs strain of cfrp rod, ɛcfrp, rc beam b1 with nsm cfrp rod. in fig. 7 the diagrams of moment, m, versus curvature, χ, refer to the cross-sectional area, obtained by static bending tests are illustrated: the first one is referred to un-strengthened specimen b1, where χ is calculated from values recorded on compressive concrete edge and on steel bar; the second one is referred to strengthened beam b1, where χ is obtained from strain values measured on compressive concrete edge and on cfrp rod. results of static bending tests obtained for beam with nsm cfrp strengthening are shown in fig. 6 in term of load deflection (p δ) and load – strain of tensile cfrp rod (p εcfrp) diagrams evaluated at midspan section of beam. during the tests, the propagation of cracks was also visually observed: after the first load cycle, with p1 = 4 kn, the cracks on the un-strengthened specimen, was almost absent; when the load was increased, the crack pattern followed the trend of a typical rc beam, with vertical cracks in midspan and oblique cracks nearby the supports, as shown in fig. 8. in the nsm cfrp strengthened beam, the crack pattern developed following the fractures occurred during the previous test on the un-strengthened specimen; only for the last two loading cycles the cracks increased in depth and width (fig. 9). if we analyze the collapse mode of beam b1 strengthened with nsm cfrp, it can be seen that the specimen reached failure for the crushing of compressed concrete and the debonding of the cfrp rod that began at the maximum moment region region and propagated to an extremity of beam. in particular, the debonding between adhesive and the surrounding concrete was recorded at midspan; moving away from the midspan section, also part of concrete cover was interested (fig. 10). (a) 0 5 10 15 20 25 30 0 500 1 000 1 500 2 000 2 500 3 000 lo a d p [k n ] εcfrp (· 10-6) d1 d2 d3 d4 d5 0 1 2 3 4 5 6 7 8 0 1 2 3 m o m e n t m [ kn m ] curvature χ [1/mm · 10-5] d1 d2 d3 r. capozucca et alii, frattura ed integrità strutturale, 58 (2021) 402-415; doi: 10.3221/igf-esis.58.29 408 (b) figure 7: diagrams moment, m, vs curvature, χ, evaluated at the midspan section for(a) un-strengthened and (b) nsm cfrp strengthened rc beam b1. figure 8: visualization of cracks by bending loading at damage level d3 for rc beam b1 without strengthening. figure 9: visualization of cracks by bending loading at damage level d5 for rc beam b1 strengthened with nsm cfrp rod. 0 2 4 6 8 10 12 14 0 1 m o m e n t m [ kn m ] curvature χ [1/mm · 10-5] d1 d2 d3 d4 d5 r. capozucca et alii, frattura ed integrità strutturale, 58 (2021) 402-415; doi: 10.3221/igf-esis.58.29 409 figure 10: collapse of beam b1 strengthened with nsm cfrp rod. following the same strategy, rc beam b2, strengthened with nsm gfrp rod was tested statically, adopting the same setup and the same instrumentation. static bending tests were carried out on the beam applying four cycles of bending loading and then increasing the load until the collapse of the sample. in this case as well, the steps of loading were related to the degree of damage di with i=1,2,3,4. tab. 4 presents the main level of loading adopted durin tests together with the main data achieved from experimentation. fig. 11 presents the trace of the deflection, δ, recorded at the centerline of beam in relation to the increasing of bending load, p; in addition, the development of strain on tensile gfrp rod, εgfrp, is traced. the evolution of the curvature, χ, relative to the cross-sectional area and computed from data measured on compressive concrete and gfrp rod, in relation to the increasing of moment, m, is depicted in fig. 12. damage steps load, p [kn] deflection at midspan, δ [mm] strain at compressive concrete, εc (‰) strain at steel reinforcement (at intrados), εs (‰) strain at gfrp rod, εgfrp (‰) curvature at midspan section*, χ (10-5) d1 4.00 1.87 0.14 0.39 0.34 0.13 d2 8.06 3.69 0.30 0.79 0.72 0.28 d3 16.02 7.55 0.66 1.69 1.80 0.76 d4 24.02 12.10 0.99 2.61 3.01 1.35 table 4: main results obtained for strengthened beam b2 by static bending tests. * curvature evaluated from deformation on compressive edge and gfrp bar. in terms of fracture’s propagation, a condition like the previous one occurs during the test, as shown in fig. 13. after attaining a load value of pu= 38.40kn, the specimen b2 collapses, resulting in the crushing of compressed concrete and total debonding of the nsm gfrp rod. the strengthening’s debonding interested the portion of beam from the midspan section to the end section, leading the detachment of the concrete cover. interfacial debonding cover separation r. capozucca et alii, frattura ed integrità strutturale, 58 (2021) 402-415; doi: 10.3221/igf-esis.58.29 410 (a) (b) figure 11: diagrams (a) load, p, vs deflection, δ, and (b) load, p, vs strain of gfrp rod, ɛgfrp – rc beam b2 strengthened with nsm gfrp rod figure 12: diagram moment, m, vs curvature, χ, at the midspan section rc beam b2 strengthened with nsm gfrp rod. 0 5 10 15 20 25 30 35 40 0 5 10 15 20 25 30 35 40 lo a d p [ kn ] δ [mm] d1 d2 d3 d4 failure conditio n 0 5 10 15 20 25 0 500 1 000 1 500 2 000 2 500 3 000 3 500 lo a d p [ k n ] εgfrp (· 10-6) d1 d2 d3 d4 0 2 4 6 8 10 12 0 1 m o m e n t m [ k n m ] curvature χ [1/mm · 10-5] d1 d2 d3 d4 r. capozucca et alii, frattura ed integrità strutturale, 58 (2021) 402-415; doi: 10.3221/igf-esis.58.29 411 figure 13: visualization of cracks by bending loading at damage level d4 for rc beam b2 strengthened with nsm gfrp rod. discussions of experimental results his experimental research performed on rc beams strengthened with nsm cfrp and gfrp rod permits the highlighting of numerous aspects that could be helpful in the civil applications for the structural repair of damaged elements. the effectiveness of the near surface mounted approach is the first outcome that should be highlighted. this technique allows for beams to be strengthened until their collapse under bending, preserving the frp rods' connection without any separation. the strengthened elements reached failure for the attaining of the ultimate strain of compressive concrete. an improvement in the rigidity capacity of rc beams with nsm cfrp and gfrp during bending tests was verified. if we examine the load versus deflection experimental diagrams for the models with strengthening, it can be seen how ductility and ample deflections typify the response of strengthened elements until failure condition. in fig. 14 the behavior of two beams under bending loading cycles until failure are compared. we can see that the strengthening of beams with frp rod is adequate for both beams. stiffnesses of beams b2 is lower than that of beam b1 and this is a direct result of the mechanical properties of the strengthening bar of cfrp respect to gfrp rod being the young’s modulus of gfrp is much lower than that of the cfrp while the area of section is almost equal between cfrp and gfrp rods. this result is also reflected on the ultimate capacity in terms of load pu which is minor of 30% for the beam strengthened with gfrp rod. figure 14: diagrams load, p, vs deflection, δ for strengthened beams b1 and b2 until failure. moreover, another important aspect emerging from experimental campaign, is the impossibility to apply the bernoulli's hypothesis in the study of rc sections of beams strengthened with nsm frp rod; this is due to the presence, under bending, of a frp stress-strain lag that which makes it impossible to consider the section as plane. the entity of strain collected at the midspan section at damage degree di has been diagrammed and depicted, respectively, for the un-strengthened beam b1, t r. capozucca et alii, frattura ed integrità strutturale, 58 (2021) 402-415; doi: 10.3221/igf-esis.58.29 412 in fig. 15, for the nsm cfrp strengthened beam b1, in fig. 16 and for the nsm gfrp strengthened beam b2, in fig. 17. the measurement of strains obtained for the edge of compressive concrete and at the level of steel bars underlines the maintaining of plane section in the case of un-strengthened rc beam b1 (fig. 15). in fig. 16 the point of compressive edge of concrete, tensile steel and tensile cfrp rod is considered for beam b1 strengthened with cfrp rod. in this case, it is noted the non-linear distribution of strains through the full depth of the beam; in particular, the strains on the cfrp rod aren’t linearly congruent with the strains of steel and of the compressed concrete fiber and are affected by a stress-strain lag. it means that the hypothesis of preserving the planarity of the bending section isn’t satisfied. also, in the case of beam b2 the non-planarity of section appears at midspan since the first load cycle d1=4kn, as fig. 17 shows. figure 15: distribution of strain at mid length cross section at di, with i=1,2,3 un-strengthened beam b1. figure 16: distribution of strain at mid length cross section at di, with i=1,2,3 beam b1 with nsm cfrp rod. 0 20 40 60 80 100 120 140 160 -1.0 -0.5 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 h [m m ] ε ‰ d1 = 4kn d2 = 8 kn d3 = 16 k n edge of compressive concrete level of tensile steel 0 20 40 60 80 100 120 140 160 -1.0 -0.5 0.0 0.5 1.0 1.5 2.0 2.5 h [m m ] ε ‰ d1 = 4kn d2 = 8 kn d3 = 18 k n d4 = 24kn edge of compressive concrete level of tensile steel level of tensile cfrp r. capozucca et alii, frattura ed integrità strutturale, 58 (2021) 402-415; doi: 10.3221/igf-esis.58.29 413 figure 17: distribution of strain at mid length cross section at di, with i=1,2,3 beam b2 with nsm gfrp rod. the entity of stress-strain lag can be estimate considering the ratios (1) and (2) (tab. 5), where εfrp is the strain that cfrp and gfrp rod should exhibits if the bernoulli's plane section hypothesizes is verified. the calculus of k1 and k2 coefficients was made both for the strengthened rc beams b1 and b2, considering the levels of damage d1 to d4 thus until values of steel strain greater than yield strain of steel. it can be observed that the average values k1,av ≅ 0.93  0.99 and k2,av≅ 0.24  0.18 (respectively for b1 and b2), are quite different and lead to results more or less conservative. nevertheless, in the study of the behaviour of rc section with the presence of nsm frp rods, it can be a good strategy the adoption of one of the coefficient k1,av (or k2,av) to prevent overestimation of the beam’s strength.  frp1 s ε k   ε (1)   frp frp2 frp ε* ε k   ε* (2) rc beams damage steps load, p [kn] k1 = εfrp/εs k2 = ε*frp-εfrp /ε*frp b1 d1 4.00 0.60 0.51 d2 8.00 1.06 0.13 d3 18.00 1.06 0.13 d4 24.00 0.98 0.19 b2 d1 4.00 0.87 0.28 d2 8.00 0.91 0.25 d3 16.00 1.07 0.12 d4 24.00 1.15 0.05 table 5: lag coefficients k. 0 20 40 60 80 100 120 140 160 -1.0 -0.5 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 h [m m ] ε ‰ d1 = 4kn d2 = 8 kn d3 = 16 k n d4 = 24kn edge of compressive concrete level of tensile steel level of tensile gfrp r. capozucca et alii, frattura ed integrità strutturale, 58 (2021) 402-415; doi: 10.3221/igf-esis.58.29 414 conclusions he following are the main outcomes derived from this experimental study on the behaviour of rc beams strengthened with cfrp and gfrp rods using the near-surface method: 1. the nsm approach proves to be adequate, both for cfrp and gfrp rods, with no loss of the concrete cover’s bond up to collaps under bending. 2. the ultimate phase of rc beams strengthened was characterized by loss of strength of compressive concrete without detachment of cover. 3. the adoption of frp rod seems to be suitable; the performance of a rc beam with frp strengthening is highly reliant on the properties of the frp itself. 4. the bernoulli’s hypothesis of planarity of sections is not valid for sections with frp rods and the calculus of sections must follow a non-linear development until ultimate state. acknowledgement he polytechnic university of marche supplied research funds to enable this experimental study. the authors would like to thank all the technicians and students who assisted in the development of this research work. references [1] de lorenzis l., nanni a., la tegola a. flexural and shear strengthening of reinforced concrete structures with near surface mounted frp rods. proc. third int. conf. advanced composite materials in bridges and structures, ottawa (canada); 2000. pp.521-528. [2] teng jg, chen jf, smith st, lam l. frp-strengthened rc structures. west sussex: wiley; 2002. [3] lu, x.z., teng, j.g., ye, l.p., jiang, j.j.: bond–slip models for frp sheets/plates bonded to concrete, engineering structures, 27(6), pp. 920–937 (2005). [4] kotynia r. analysis of the flexural response of nsm frp-strengthened concrete beams. proc. of the eight int. conf.on fibre-reinforced plastics for reinforced concrete structures, patrasso (grecia); 2007 [5] bilotta a, ceroni f, nigro e, pecce m. efficiency of cfrp nsm strips and ebr plates for flexural strengthening of rc beams and loading pattern influence. compos struct 2015; 124:163e75. [6] de lorenzis, l., teng, j.g.: near-surface mounted frp reinforcement: an emerging technique for strengthening structures, composites part b: engineering, 38(2), pp. 119–143 (2007). [7] de lorenzis, l., nanni, a.: bond between near surface mounted fiber reinforced polymer rods and concrete in structural strengthening. aci structural journal, 99(2), pp. 123–133 (2002). [8] de lorenzis, l., nanni, a.: shear strengthening of reinforced concrete beams with nsm fibre-reinforced polymer rods. aci struct. j., 98(1), pp. 60–8 (2001). [9] el-hacha, r., rizkalla, s.: near-surface mounted fibre reinforced polymer reinforcements for flexural strengthening of concrete structures. aci structural journal, 101(5), pp. 717-726 (2004). [10] capozucca, r.: on the strengthening of rc beams with near surface mounted gfrp rods. composite structures, 117c, pp: 143-155 (2014). [11] cosenza, e., manfredi, g., realfonzo, r.: behavior and modeling of bond of frp rebars to concrete, asce journal of composites for construction, 1(2), pp. 40–51 (1997). [12] hassan, t.k., rizkalla, s.: bond mechanism of nsm frp for flexural strengthening of concrete structures, aci structural journal, 101(6), pp. 830–839, (2004). [13] hassan, t., rizkalla, s.: investigation of bond in concrete structures strengthened with near-surface mounted carbon fibre reinforced polymer strips. j. of comp. for constr., 7(3) (2003) [14] sena cruz, j.m., barros, j.a.o., gettu, r., azevedo, a.f.m.: bond behavior of near-surface mounted cfrp laminate strips under monotonic and cyclic loading. asce, journal of composites for construction, 10, pp. 295-303 (2006). [15] coelho mrf, sena-cruz jm, neves lac. a review on the bond behavior of frp nsm systems in concrete. constr build mater 2015; 93:1157e69. t t r. capozucca et alii, frattura ed integrità strutturale, 58 (2021) 402-415; doi: 10.3221/igf-esis.58.29 415 [16] blaschko m. bond behaviour of cfrp strips glued into slits. in: proceedings frprcs-6. singapore: world scientific, pp: 205–14 (2003). [17] capozucca, r.: analysis of bond-slip effects in rc beams strengthened with nsm cfrp rods. composite structures, 102, pp. 110-123 (2013). [18] ceroni f, pecce m, bilotta a, nigro e. bond behavior of frp nsm systems in concrete elements. compos part bengineering 2012;43(2):99e109. [19] capozucca, r.: static and dynamic response of damaged rc beams strengthened with nsm cfrp rods, composite structures 91(3), 237–248 (2009). [20] capozucca, r., bossoletti, s., montecchiani, s. assessment of rc beams with nsm cfrp rectangular rods damaged by notches. composite structures, 128, pp. 322-341 (2015). [21] capozucca, r.,vibration analysis of damaged rc beams strengthened with gfrp. composite structures, 200, pp. 624634 (2018) [22] capozucca, r., bossoletti, s., static and free vibration analysis of rc beams with nsm cfrp rectangular rods. composites part b: engineering, 67, pp. 95-110 (2014) [23] perera, k., ibell, t., darby, a., denton, s.: bond mechanisms of various shapes of nsm cfrp bars. in: 4th international conference on advanced composites in construction, (acic 09), pp. 250–257, edinburgh (2009). [24] yost jr, gross sp, dinehart dw, mildenberg jj. flexural behavior of concrete beams strengthened with near-surface mounted cfrp strips. aci struct j 2007;104(4):430e7. [25] sharaky, i.a., torres, l., baena, m., miàs, c.: an experimental study of different factors affecting the bond of nsm frp bars in concrete. composite structures, 99, pp. 350–365 (2013). [26] teng jg, zhang ss, chen jf. strength model for end cover separation failure in rc beams strengthened with nearsurface mounted (nsm) frp strips. eng struct 2016; 110:222e32. [27] nanni, a., di ludovico, m., parretti, r. shear strengthening of a pc bridge girder with nsm cfrp rectangular bars. advances in structural engineering, 7(4), pp. 297-309 (2004) [28] ding, y., ning, x., zhang, y., pacheco-torgal, f., aguiar, j.b.: fibres for enhancing of the bond capacity between gfrp rebar and concrete. construction and building materials, 51, pp: 303-312 (2014). [29] masmoudi, a., ouezdou, m., ben, bouaziz j.: new parameter design of gfrp rc beams. construction and building materials, 29, pp. 627-632 (2012) [30] c. sabau, c. popescu, g. sas, j.w. schmidt, t. blanksvärd, b. täljsten, strengthening of rc beams using bottom and side nsm reinforcement, compos. b eng. 149 (2018) 82–91 [31] aci 440 1r-15. guide for the design and construction of structural concrete reinforced with frp bars. farmington hills, mi: american concrete institute (aci); 2007. [32] astm d 3039/d 3039 m 08. standard test method for tensile properties of polymer matrix composite materials. american standard of testing and materials, 2008. microsoft word numero 23 articolo 8 a. spaggiari et alii, frattura ed integrità strutturale, 23 (2013) 75-86; doi: 10.3221/igf-esis.23.08 75 scilla 2012 the italian research on smart materials and mems effect of pressure on the physical properties of magnetorheological fluids a. spaggiari, e. dragoni dept. of engineering sciences and methods, university of modena and reggio emilia, italy andrea.spaggiari@unimore.it abstract. to date, several applications of magnetorheological (mr) fluids are present in the industrial world, nonetheless system requirements often needs better material properties. in technical literature a previous work shows that mr fluids exhibit a pressure dependency called squeeze strengthen effect. since a lot of mr fluid based devices are rotary devices, this paper investigates the behaviour of mr fluids under pressure when a rotation is applied to shear the fluid. the system is designed in order to apply both the magnetic field and the pressure and follows a design of experiment approach. the experimental apparatus comprises a cylinder in which a piston is used both to apply the pressure and to shear the fluid. the magnetic circuit is designed to provide a nearly constant induction field in the mr fluid. the experimental apparatus measures the torque as a function of the variables considered and the yield shear stress is computed. the analysis of the results shows that there is a positive interaction between magnetic field and pressure, which enhances the mr fluid performances more than twice. keywords. magnetorheological fluids; shear mode; pressure; design of experiment. introduction agnetorheological (mr) fluids are smart materials that are increasingly used in many applications, such as controllable clutches and dampers [1]. an external magnetic induction field reversibly changes the apparent viscosity of mr fluids. mr fluids are capable to switch from a free-flow liquid at no induction, to a quasi solid state when a strong magnetization is present. the quickness of change (5-10 milliseconds) when a magnetic field is applied, makes this material interesting for adaptive damping and dissipative applications. mr fluids can be used to build silent, fast and tunable mechanical devices, which are enhanced by the ease of integration with the electronic control unit. the mr effect is obtained by a 30-40% in volume of ferromagnetic particles dispersed in the carrier fluid (silicon or hydrocarbon oil). when a magnetic field is applied to mr fluids, the particles are subjected to a dipole magnetic moment and align with the flux lines. consequently there is a formation of linear chains of particles (at a micro-scale) which means that, at the macro-scale, the mr fluid becomes a solid-like material. one of the most important design parameter of mr fluids is the yield shear stress (τy), which is the maximum stress the fluid can withstand before shear occurs. this value is fundamental in the design of any mr fluid devices, because the higher is the stress the higher is the dissipated power of the system. since many mrf devices are dissipative (e.g. dampers) the higher the power the better the performance. the yield shear stress, τy is controlled by the magnetic field, as shown in the technical datasheet supplied by the producer (lord corporation [2]) for the commercial mr fluid 140-cg. there is a magnetic saturation of the magnetic particles in mr fluids at high magnetic flux levels [2] which causes a typical sigmoid shape of the b-h curve of the material as reported in the producers datasheets. this saturation leads to a limitation of τy, and unfortunately the dissipated power reaches a maximum no matter how high the magnetic field is. it is possible to increase the value of τy by changing the m http://www.gruppofrattura.it http://dx.medra.org/10.3221/igf-esis.23.08&auth=true a. spaggiari et alii, frattura ed integrità strutturale, 23 (2013) 75-86; doi: 10.3221/igf-esis.23.08 76 volume fraction of the particle in suspension, but also in this case there is a physical limit, otherwise the viscosity of mr fluid would increase too much. a finite element analysis was performed by ginder et al. [3] to study the effect of magnetic nonlinearity and saturation of magnetic particles. they found a limit for the volume fraction at 50% in volume, which gives a maximum of τy = 210 kpa. in any case for industrial applications, a value of 50% volume fraction is too high, and the normal volume fraction ranges from 20% to 40%, which corresponds to a typical iron particle content in weight of 75% 85%) as reported in lord corp. datasheets [4-5]. mr fluids in squeeze mode (with the magnetic field acting in the same direction of the movement) provide higher forces compared to shear and flow mode. the main drawback is that squeeze mode enables only very short strokes to be performed and this prevents mr fluid application in many industrial contexts. a mr fluid compressed along the direction of the magnetic field, according to tang et al [6], shows an increment of τy of nearly ten times. the explanation is the formation of thicker and thus stronger columns of particles that are able to sustain the load. zhang et al. [7] designed an apparatus to evaluate the effect of a mechanical compression on mr fluids in linear shear mode. the apparatus they used, described in [7], which was quite complex and bulky, consisted of a non magnetic container for the mr fluid compressed through a big bolt, and a metal sheet was pulled off from the container to assess the shear strength under several pressure levels. their experimental campaign revealed that a very high compression could enhance τy by more than 20 times for a given magnetic field, thus showing a so called squeeze strengthen effect. they also correlated this behaviour not only with the magnetic force of the dipoles formed by the ferromagnetic particles, but also with the friction between the particles. a hybrid tribological-magnetic model provided a good explanation of the very high yield stress data retrieved in the experiments. the authors previous work on the squeeze strengthen effect in flow mode [17] highlights the beneficial effect of the pressure on the mr yield stress. the aim of this paper is to estimate the squeeze strengthen effect of an mr fluid under a shear stress, obtained by a relative rotation of the parts. the majority of the mr fluid based device working in shear mode are rotary devices like brakes and clutches and their performances would improve by exploiting the squeeze strengthen effect. hence, a rotary experimental test is needed to gather experimental data on the influence of magnetic field and pressure, possibly using and architecture close to the common industrial application. moreover this architecture gives a useful insight on important industrial aspects, like chemical compatibility of the sealing and geometrical tolerances needed to hold the mr fluid under pressure. the behaviour of lord 140-cg [2] commercial fluid was investigated under several magnetic field and pressure values using an ad-hoc apparatus. a design of experiment technique [8] was applied to the experimental tests in order to verify statistically the influence of the variables and to provide an empirical relationship to link the pressure, the applied field, and the yield shear stress. a surface response was obtained on the basis of the experimental points and a design equation which correlates yield stress, pressure and induction field was provided. the experimental results cover magnetic induction up to 300 mt and pressure levels up to 30 bar. the internal pressure influences the yield stress and there is a positive interaction between the magnetic field and the pressure. this study confirms that the findings of [7] are also valid under a rotational shear stress and thus there is the chance to increase mr fluid based clutches and brakes by simply changing the working pressure of the fluid. method experimental set-up his section outlines the design of the experimental apparatus and describes the architecture of the system implemented to test the mr fluids. the cross-section of the magneto-hydraulic system used in the experiments is depicted in fig. 1. the system consists of a lower frame (7), which is welded to the bottom flange (8) used to couple with the load cell of the testing machine. another flange (6) is welded to the frame and is used to support the external tube (3), which is made in ferromagnetic material and is used to close the path of the magnetic flux (see electromagnetic system section), as well as the upper flange (2). the mr fluid vessel (10), which is supported by the lower frame, has three main functions. first it contains the mr fluid, second it is used to enforce the coupling with the pressure transducer (9) and third it allows the correct alignment with the central piston (1). the pressure sensor (9) is a kellerdruck 25y piezoresistive flush transducer [11], which exhibits a particular architecture compatible with mr fluids. thanks to its stainless steel flat membrane, used as a sensitive element, the sensor is not affected by the presence of the microparticles and moreover its g½ threaded connection ensures the correct sealing of the fluid. the upper sealing system (5) is made by a polypac ring (fig. 1 in black) [10], which is a commercial system for sealing liquids under pressure. t http://www.gruppofrattura.it http://dx.medra.org/10.3221/igf-esis.23.08&auth=true a. spaggiari et alii, frattura ed integrità strutturale, 23 (2013) 75-86; doi: 10.3221/igf-esis.23.08 77 the polypac ring consists of an external o-ring and an internal ptfe ring reinforced with glass fibres. the o-ring is energized by the fluid and hence its compression inside the groove pushes the ptfe ring on the piston (1). the ring material provides both the sealing and low friction. this system allows the central piston to be moved up and down to generate the desired pressure and to rotate in order to shear the mr fluid. the torque measure will be affected by the different friction due to the pressure sensitive sealings (due to different pressure levels) and proper techniques will be used to extrapolate the correct yield shear stress. figure 1: cross-section of the hydraulic system. the central piston (1), shown in fig. 1 (not cross-hatched), has a deep central hole which is used to focus the magnetic field only into an annular area in conjunction with the washer (11) bonded to bottom of the vessel (10). parts (1) and (11) are made in low carbon steel, with high magnetic permeability, while the vessel (10) is made in brass, amagnetic, likewise the central plug (4) made in ptfe, represented in light grey in fig. 1. the ptfe is useful to prevent accidental torque transmission between the central part of the piston where the magnetic field is low and no torque should be present. the mr-fluid 140-cg by lord corporation [2] is entrapped between (10), (9), (5) and is shown in dark grey in fig. 1. the magnetic field is applied with the coil (12) which consists of 1932 turns made in awg22 wire, wounded around a plastic housing (in black). further details about the magnetic properties of the system, the flux path, and the applied currents are provided in the electromagnetic system section. the small chamfer of the central piston (1) is necessary to prevent damage of the ptfe ring during the insertion of the piston through the polypac (5) seal [10]. the system is designed to have a mr fluid chamber with height of 1mm at the maximum pressure. the mr fluid used [2] is based on silicon oil which is more compressible compared to other hydrocarbon oils. this peculiarity makes the system easier to control because the pressure is changed by moving the central piston, and the little compliance given by the fluid prevents dangerous overloading. the wires coming out from the coil exit from the central part of the system through holes in element (2), not visible in the cross section in fig. 1, in order to be connected to a dc power source. the experimental apparatus provides a rotational shear mode test of mr fluids under several levels of internal pressure. the design of the system is completely different zhang’s [7], and is much more compact and easy to manufacture. the electro-magnetic coil is displaced around the central ferromagnetic piston and is used to vary the magnetic excitation in the fluid (see section shear stress in the mr fluid). the system was placed under a universal biaxial machine, mts bionix http://www.gruppofrattura.it http://dx.medra.org/10.3221/igf-esis.23.08&auth=true a. spaggiari et alii, frattura ed integrità strutturale, 23 (2013) 75-86; doi: 10.3221/igf-esis.23.08 78 858, which is able to compress the fluid applying the desired pressure and to shear the fluid through a rotation at the same time. the tensile machine is controlled both in compression, to hold the same pressure during the test and in angle, meanwhile the torque is measured. from the recorded data, the yield stress values were calculated with analytical formulas and the effect of the pressure was estimated. the tests were performed at low rotational speed to limit viscous effects and to focus exclusively on the yield shear stress. in magnetorheological applications (e.g. dampers) the magnetorheological effect is from ten to hundrends times higher than viscous one. therefore for the purpouse of this quasi static analysis the viscous effect are neglected. the shear rate, the pressure values applied and the magnetic field values are described in the subsequent sections. the experimental test equipments are displayed in fig. 2. fig. 2a shows the complete system mounted on the mts bionix 858, with the tti dc current supply on the left and the red display to monitor the pressure inside the mr fluid chamber in the centre. the mr fluid is placed inside the brass vessel and then, using the upper grip of the tensile machine the central piston is applied to seal the circuit (see fig. 2b). the fluid volume is constant, the thickness is slightly changed to achieve the desired pressure level, but this small change do not affect the magnetorheological behaviour of the system. (a) (b) figure 2: mr fluid insertion (a) central ferromagnetic piston fit (b) and full system mounted on the tensile machine. shear stress in the mr fluid mr fluids, especially for quasi-static applications, can be conveniently modeled as bingham fluids [9]. the typical behaviour of such a fluid is described by the solid line in fig. 3 in terms of shear stress versus shear rate. the fluid exhibits a yield stress τy at no shear rate, and only when this value is reached the mr fluid starts to flow like a classic newtonian fluid. the considered model involves two parameters: τy and the fluid viscosity η. the bingham model shows the basic function of the mr fluid, but does not take into account shear thinning or thickening whereas other more complex model like the herschel-bulkley one does [12]. the τy value is a function of the applied magnetic field, b. since the geometry of the chamber containing the mr fluid is quite simple the shear stress calculation can be done through analytical considerations.  y b     (1) the angular rotation is applied with a very low speed, 5°/min, with a corresponding shear rate under 1 s-1, so the procedure can be considered quasi static. this makes the pure viscous effects negligible. the mr fluid is active only where the magnetic field is on and the particles are aligned with the flux lines. the magnetic system is designed to focus the field only in an annular area with internal radius rint = 10mm and external radius rext = 20mm. the yield shear stress is considered constant because the magnetic field is constant, as shown in the magnetic electromagnetic simulation section, and acts on the annular area, fa which is:  2 2intf exta r r   (2) http://www.gruppofrattura.it http://dx.medra.org/10.3221/igf-esis.23.08&auth=true a. spaggiari et alii, frattura ed integrità strutturale, 23 (2013) 75-86; doi: 10.3221/igf-esis.23.08 79 figure 3: bingham model, suitable for mr fluids and the classical viscous newton model. the static torsional moment due to the yield shear stress acting on the frontal annular area is: int 2 3 3 2 int 0 2 3 extr ext y y r r r t r drd         (3) the chamfer present in the central rod creates another active lateral cylindrical surface on which the yield stress τy is acting. the axial length of the chamfer is l = 2mm and the cylindrical lateral area, al is thus: 2l exta r l (4) according to the magneto-static analyses shown in the subsequent section the magnetic field in the frontal area is similar to the one in the lateral area. hence the shear stress can be computed considering the effect of the applied torque, t , over the two above calculated surfaces: 3 3 int2 3 y ext l ext t r r a r       (5) the pressure is regulated using the central piston until the desired value is reached. after that the system control keeps the piston still in the axial direction and the pressure is maintained constant. then the central piston rotates and the fluid is sheared. the measured torque is caused both by the yield stress of the fluid according to eq. (5) but also by the friction of the sealing system, which is pressure dependent. the friction due to sealing is quite difficult to consider analytically and consequently it will be handled by considering a particular experimental procedure useful to eliminate any effect not related to the magnetic field and the internal pressure. the experimental procedure is organized in five steps: 1. the current is turned on at the beginning of the test to create the magnetic field. 2. the machine applies a prescribed rotation up tp to 2.5°3.5° and records the total (gross) torque. 3. the current is suddenly turned off, so the torque values drops down because the mr effect has vanished. 4. the torque due to pure friction is measured. 5. the net torque is computed by subtraction of the two values of torque measured in step 2 and 4. this procedure allows the pure mr fluid shear stress to be calculated disregarding all the frictional effects since the only difference between the first and the second part of the test is due to the current and thus to the mr effect. electromagnetic system applying a magnetic field correctly is a key point in exploiting the potential of any kind of mr fluid. the main problem in magnetic circuit design is to avoid flux losses due to flux dispersion in non ferromagnetic material (e.g. air). since the application is quasi static there are no other losses due to eddy currents the first problem in dealing with mr fluids is that the fluid itself has low magnetic properties. the relative magnetic permeability can be retrieved by the producer technical specification [2]. according to electromagnetism fundamentals, the induction field b is a function of the magnetic field h and the magnetic permeability, as shown in eq. (6) http://www.gruppofrattura.it http://dx.medra.org/10.3221/igf-esis.23.08&auth=true a. spaggiari et alii, frattura ed integrità strutturale, 23 (2013) 75-86; doi: 10.3221/igf-esis.23.08 80 0 rb h    (6) hence, by approximating the b-h curve linearly (assumption valid when h<200 ka/m) the value of the relative magnetic permeability is: 7 0 4 10 r b b h h          (7) as can be seen in the producers datasheets [4] when h = 125000a/m, b = 0.8t the relative permeability is µr = 5.09. the comparison between the linear approximation and the non-linear curve is not reported for the sake of brevity, however a linear approximation with µr = 5 is in good agreement (r2 = 0.978) with the manufacturer’s curves [2] in the hypothesis that h<200 ka/m. the value of µr = 5 is considered in the analysis, which is also in accordance with the literature [12][13]. the magnetic system was designed using finite element magnetic software, femm 4.0 [14], which is useful for two dimensional magnetostatic problems. since the software is 2d only, the analyses were run in axisymmetric mode, in order to consider the complete geometry. the material choice is crucial in designing magnetic circuits. the main parts (1-2-3-67-8) were realized in low carbon steel, because of its high magnetic permeability. the only non magnetic part in addition to the copper coil is the brass vessel (10). the first femm analyses, not reported for the sake of brevity, showed that using a ferromagnetic vessel would have deviated the magnetic flux from the mr fluid. thus the use of amagnetic materials in the system design was needed to force the flux to go inside the mr fluid. the brass was chosen because it is a good tradeoff between mechanical strength, cost and amagnetic properties. in order to complete the magnetic analyses only the coil properties are needed. since the copper wires were awg 22 (wire diameter of 0.64 mm) there current density was limited only by thermal considerations, not critical for this particular applications. design of experiment applying a statistical method can be convenient in dealing with experimental problems involving multiple variables. the design of experiment procedure, a well-founded statistical method based on the analysis of variance (anova) [15], can be applied to such scientific problems as shown in [16]. in this experiment the variables involved are the applied magnetic induction field (b) and the internal pressure of the mr fluid (p). literature results showed an interaction between the two variables both in linear shear mode [7] and in flow mode [17]. the experiments were designed to verify the same interaction under a rotational loading, which is the typical configuration of brakes and clutches. the most frequent application of the design of experiment is the two-level factorial experiment, which is used mainly for exploratory experiments in order to obtain quick qualitative insights on the process. in this work, on the other hand, we adopted the "general factorial" approach, which allows to consider multiple levels per variables. in this case four levels are considered for both pressure and magnetic field, and it is possible to capture eventual non linearity of the variables. the method is focused only on two variables which influence the behaviour of the system, it is able to identify the interaction between these variables more precisely, and is able to provide a more reliable model to describe how the system behaves. the magnetic induction ranges from 0 to 300 mt, while the internal pressure spans the 0-30 bar range. the complete experimental plan is reported in tab. 1. the experimental tests consider explicitly only non zero value of magnetic induction field, mainly because of the particular differential procedure adopted to calculate the net torque as described in the previous section. the zero level is intrinsically obtained in each test when the current is turned off according to the above described procedure. the experiments at zero current give only information on the pure frictional forces since the viscous effect is negligible due to quasi static rotation of the central piston (1). electromagnetic simulation results the simulation of the magnetic system using femm 4.0 at a current of 2.3 a is reported in fig. 4a. the flux lines passes through the mr fluid as requested and the magnetic field, thanks to the presence of the ptfe central plug (4) assumes an annular shape as desired. the system provides a magnetic induction field in the mr fluid up to 300 mt with a supply current of 2.3 a. the distribution of the magnetic induction field inside the mr fluid is provided in fig. 4b, confirming the nearly constant value in the annular region and a lower value in the central part of the system. the electromagnetic simulation, like the one showed in fig. 4a, were carried out for the four values of magnetic induction field considered. http://www.gruppofrattura.it http://dx.medra.org/10.3221/igf-esis.23.08&auth=true a. spaggiari et alii, frattura ed integrità strutturale, 23 (2013) 75-86; doi: 10.3221/igf-esis.23.08 81 levels i ii iii iv induction field, b, (mt) 50 100 200 300 internal pressure, p (bar) 0 10 20 30 replicates 3 for each combination experimental points 16 grand total 48 table 1: experimental plan. (b) (a) figure 4: flux density inside the hydro-magnetic system for a current of 2.31 amp (a), scale 0-1.5t, and flux distribution along the radius of the mr fluid chamber (b). the direct measurement of the magnetic field inside the mr fluid is not possible for two reasons. there is no way to access the mr fluid chamber when the system is completely assembled because it is perfectly sealed. even if it was possible the hall effect probe of the gaussmeter hirst gm05 would not have been compatible with mr fluid, since the micronsized particles are almost impossible to be cleaned and the subsequent magnetic measure would have been affected by their presence. in order to verify the femm predictions of fig. 4 two indirect experimental measurements were done on the system. the first measures were done without the fluid, removing the pressure transducer (9) an accessing the chamber from the bottom threaded hole with the flexible hall effect probe of the gaussmeter. the second measures were performed on the complete system putting the thin gaussmeter probe in the gap between part (1) and (2) and comparing the femm values with the experimental ones. current (a) first point, inside ⑩, no mrf second point, in the gap between ① and ② exp. femm difference exp. femm difference 0.385 24.7 26.275 6.38% 54.84 57.375 4.62% 0.77 52.5 52.55 0.10% 105.2 114.75 9.08% 1.54 105.1 107.98 2.74% 212.57 229.5 7.96% 2.31 210.2 217.74 3.59% 426.5 459 7.62% table 2: experimental and femm values of the induction magnetic field (mt). http://www.gruppofrattura.it http://dx.medra.org/10.3221/igf-esis.23.08&auth=true a. spaggiari et alii, frattura ed integrità strutturale, 23 (2013) 75-86; doi: 10.3221/igf-esis.23.08 82 the collected and the simulated values are reported in tab. 2. the femm model is able to provide a good prediction of the magnetic field both in the first access point and in the second. the numerical prediction is always larger than the experimental values, probably due to an overestimate of the magnetic permeability of the steel used to manufacture the experimental test fixture. results and discussion experimental results n order to explain the post processing of the raw experimental data a typical torque-angle raw curve is reported in fig. 5. as highlighted in the red circle the torque suddenly drops down in the middle of the test. this is because the current is turned off in order to obtain two field levels from the same test. the net torque is obtained upon subtraction of the average torque level in the second part of the diagram from the first one. the net torque is significantly lower than the absolute torque, this behaviour is mainly due to sealing chosen in the experimental system. since it was much important to prevent the leakage of the fluid with several pressure values, rather than having low frictional forces, the seal provided an extraforce which could be subtracted a posteriori. figure 5: typical raw experimental torque-angle curve. the red circle highlights the moment of the current turn off. the procedure is applied for all the 48 experimental test curves obtained from the design plan and the results in terms of net torque are reported in fig. 6. fig. 6a shows the curves obtained at ambient pressure, fig. 6b-c-d shows the curves at 10-20-30 bar respectively. this procedure allows retrieving only the difference in torque levels, while the difference of in the turning off angle (reported along the x-axis), visible in fig. 6 is not an issue. the complete set of experimental torque values are reported in tab. 3, as well as the average net torque value and the average shear stress valued obtained from application of eq. (5). the experimental results shows some high dispersion of the data, but, on the whole the standard deviation is around 12% of scatter. two possible explanation are envisioned. first some stick slip effect on the sealing could have occurred despite the teflon ring used to ensure the seal, second a residual magnetization of the particles could have influenced some outlier experimental points (e.g. p = 10 bar, b = 100 mt, r1). this dispersion seems acceptable since the experimental intrinsic scatter do not change the general trend of the system under magnetic field and pressure. the main difference between the net torque curves of fig. 6 and the raw data of fig. 5 is that the there is an important offset which is disregarded in the shear stress measure. the post processing procedure is justified by the fact that τy do not depend on the frictional forces, but particular attention must be paid to the fact that the higher the pressure, the higher the forces due to sealing. i http://www.gruppofrattura.it http://dx.medra.org/10.3221/igf-esis.23.08&auth=true a. spaggiari et alii, frattura ed integrità strutturale, 23 (2013) 75-86; doi: 10.3221/igf-esis.23.08 83 net torque (nmm) τy (kpa) p (bar) b (mt) r1 r2 r3 average std. dev. average std. dev. 0 50 172.08 213.56 146.21 177.28 33.97516 9.25 19.16% 0 100 514.47 543.45 507.13 521.68 19.20442 27.22 3.68% 0 200 1204.06 998.46 1168.5 1123.67 109.8859 58.64 9.78% 0 300 1156.95 1020.73 1393.3 1190.33 188.5142 62.12 15.84% 10 50 255.78 225.71 248.84 243.44 15.74466 12.70 6.47% 10 100 915.54 482.43 445.15 614.38 261.4832 32.06 42.56% 10 200 1658.38 1704.4 2001.82 1788.20 186.4258 93.31 10.43% 10 300 2374.80 2683.51 2688.13 2582.15 179.5823 134.75 6.95% 20 50 198.97 229.18 157.53 195.23 35.97138 10.19 18.43% 20 100 605.44 665.52 573.83 614.93 46.57584 32.09 7.57% 20 200 1901.04 2037.91 2084.71 2007.89 95.44484 104.78 4.75% 20 300 2824.34 2523.62 2949.16 2765.70 218.7452 144.32 7.91% 30 50 237.58 249.54 291.72 259.61 28.44097 13.55 10.96% 30 100 931.46 753.29 739.61 808.12 107.0344 42.17 13.24% 30 200 2347.10 1808.65 2181.02 2112.25 275.7325 110.22 13.05% 30 300 2992.63 3084.06 2802.75 2959.81 143.4975 154.45 4.85% table 3: experimental net torque and yield shear stresses τy retrieved using eq. (4). both from the experimental curves in fig. 6 and the experimental data in tab. 3 it is possible to qualitatively sense that the pressure does have an important effect on the shear stress and it is a positive effect. since a design of experiment procedure was applied the data are analyzed applying an analysis of variance: this statistical method is able to quantify variable influence and variable interaction on the process under scrutiny. analysis of variance on the yield stress an analysis of the variance was applied using design expert 8.0 software [18]. anova calculates the variance of a response by considering a specific variable and the global variance in the responses. among the possible approaches to graphically represent the results, one of the most popular is the normal plot, which is used to estimate whether a certain set of data follows a gaussian distribution or not. if the data approximates a straight line, the phenomenon is statistically "normal" i.e. follows a stochastic law and can be attributed to background noise. the variables or the interactions affecting the system’s behaviour will then fall outside the normal distribution line, thus their effect cannot be ascribed to a stochastic process. the greater the deviation of the point from the normal line, the larger the confidence interval (i.e. the probability that the variables are significant). the half normal plot used in this paper is interpreted in the same way as the normal plot, but allows absolute values of the effects to be considered. since the half normal line starts at the origin, this produces a more sensitive scale to detect significant outcomes [15], which are immediately detected at a glance. the half normal plot of the experimental values of yield shear stress is shown in fig. 7. the straight line is built thanks to replicates (triangles) and provides an estimation of the normal distribution of the experimental error, which by definition has a stochastic distribution. the triangles are an expression of the sum of errors [15], which is calculated by design expert software [18]. since both points representing the two variables (pressure and magnetic field) are far from the error line, anova demonstrates that these variables influence the process. the interaction between the variables is also important, which means that the increase in shear yield stress due to the combined action of pressure and magnetic field is greater than the sum of the two effects taken separately. the experimental test points have a little dispersion, as demonstrated in fig. 8, provided by the design expert software, where the i-beams bars represent the standard deviation. http://www.gruppofrattura.it http://dx.medra.org/10.3221/igf-esis.23.08&auth=true a. spaggiari et alii, frattura ed integrità strutturale, 23 (2013) 75-86; doi: 10.3221/igf-esis.23.08 84 (a) (b) (c) (d) figure 6: experimental torque-angle curves for 50mt (grey solid lines), 100mt (dotted lines), 200mt (dashed line) and 300mt (solid black line). pressures of 0,10,20 and 30 bars, reported in (a), (b), (c) and (d), respectively. figure 7: half normal plot of the yield shear stress: effect of the magnetic field (black square), pressure (white square) and their interaction (hollow black square). http://www.gruppofrattura.it http://dx.medra.org/10.3221/igf-esis.23.08&auth=true a. spaggiari et alii, frattura ed integrità strutturale, 23 (2013) 75-86; doi: 10.3221/igf-esis.23.08 85 it is interesting to compare the response surface with the producer experimental curves [2] in order to assess the performances of the mr fluid. the value at no pressure and 50mt are in good agreement with the producer yield stress, while as the pressure goes up to 30 bar the yield shear stress has an increment ranging from a 40% at low magnetic fields up to 200% for the highest values of magnetic fields. the experimental tests on the whole confirm the findings of [6], [7] and [17] and provide useful information to exploit mr fluids at the maximum of their capabilities. exploiting the squeeze strengthening effect could be quite useful and simple in devices like the by-pass damper or the single rod damper, where a pneumatic accumulator is already present in the system. in this case the accumulator pressure could be controlled to enhance mr device performances. in other systems, like the clutches, the applications seems less useful mainly for sealing issues, but still applicable if better performances are needed with tight dimensional constraints. figure 8: error bars and experimental yield shear stress for the considered pressure (along the x-axis) and magnetic field levels, 50mt (dashed line), 100 mt (dotted line), 200 mt (dot-dashed line) and 300 mt (solid line). conclusion he paper explored the behaviour of magnetorheological fluids in shear mode under the combined action of a magnetic field and internal pressure. the experimental apparatus was designed and developed to characterize the mr fluids under the rotary action typical of mr brakes and clutches. the experimental tests showed the influence on the shear yield stress both of the magnetic field and of the applied pressure. in addition analysis of variance revealed a positive interaction between the two factors considered in the experimental plan. the shear stress values under pressure were found to be more than two times the values reached with no pressure. the experimental test procedure ensure to eliminates the influence of the sealing and to focus only on the mr effect augmented by the pressure. this mr fluid peculiarity can be exploited to modify existent mr based devices with little changes in system architecture, like in the systems with pneumatic accumulator, but strong improvement in terms of performances. references [1] m. r. jolly, j.w. bender, j. d. carlson, in: spie 5th int. symposium on smart structures and materials, san diego, ca (1998). [2] lord corporation, cary, nc http://www.lordfulfillment.com/upload/ds7012.pdf. [3] j. m. ginder, l. c. davis, appl. phys. lett., 65 (1994) 3410. [4] lord corporation, cary, nc , http://edge.rit.edu/content/p07307/public/lord%20mr%20fluid. [5] lord corporation, cary, nc ftp://ftp.elet.polimi.it/users/luigi.piroddi/mrd/lord/mrf132ld.pdf. [6] x. tang, x. zhang, r. tao, y. rong, j. appl. phys., 87 (2000) 2634. [7] x. zhang, x. l. gong, p. q.zhang, j. appl. phys., 96 (2004) 2359. [8] d. c. montgomery, design and analysis of experiments, wiley, new york (1997). t http://www.gruppofrattura.it http://dx.medra.org/10.3221/igf-esis.23.08&auth=true a. spaggiari et alii, frattura ed integrità strutturale, 23 (2013) 75-86; doi: 10.3221/igf-esis.23.08 86 [9] e. c. bingham, fluidity and plasticity, mcgraw-hill, new york (1922). [10] polypac ring t.e.f. e/gr http://tinyurl.com/68hy5nu. [11] keller-druck, http://tinyurl.com/3u7p6or. [12] m. zubieta, s. eceolaza, m. j. elejabarrieta, m. m. bou-ali, smart mater. struct., 18 (2009) 095019. [13] p. forte, m. paternò, e. rustighi, int. j. rotating mach, 10(3) (2004) 175. [14] femm 4.0 finite element method magnetics http://www.femm.info/wiki/homepage. [15] m. j. anderson, p. j. whitcomb, doe simplified: practical tools for effective experimentation, productivity press (2007) . [16] r. f. ierardi, a. bombard, journal of physics: conference series,149 (2009) 012037. [17] a. spaggiari, e. dragoni, j. fluids engineering, 134 (2012) 0091103-1. [18] stat-ease, design-expert 8 http://tinyurl.com/yers2w6. [19] matlab 7.10, mathwoks, http://tinyurl.com/jof3k http://www.gruppofrattura.it http://dx.medra.org/10.3221/igf-esis.23.08&auth=true microsoft word numero_53_art_17_2780 s. m. damadi et alii, frattura ed integrità strutturale, 53 (2020) 202-209; doi: 10.3221/igf-esis.53.17 202 fatigue analysis of bitumen modified with composite of nano-sio2 and styrene butadiene styrene polymer seyed mohsen damadi payame noor university, iran mohsendamadi@hotmail.com, ali edrisi, mansour fakhri kn toosi university of technology, iran edrisi@kntu.ac.ir, http://orcid.org/ 0000-0001-9231-8371 fakhri@kntu.ac.ir, http://orcid.org/ 0000-0002-9980-7853 sajad rezaei, mohammad worya khordehbinan pooyesh institute of higher education, iran rezaei@pooyesh.ac.ir, http://orcid.org/ 0000-0001-7394-8001 mkhordebinan@ut.ac.ir, http://orcid.org/ 0000-0003-0975-7256 abstract. since fatigue cracking is caused in the middle-temperature conditions due to the stresses from heavy traffic and as the bitumen plays a very important role in controlling this failure, therefore, in recent years, the production of the modified bitumen that can give a good performance in the middle temperatures has always attracted the interest of researchers. one of these bitumen modifiers is the styrene butadiene styrene (sbs) polymer. due to the phase separation of bitumen and polymer, aging and oxidation, this polymer may not exhibit expected field performance at middle temperatures. therefore, in this research, it is attempted to analyze the middle-temperature performance using the combination of nano-sio2 and sbs polymer in the bitumen modification. in this paper, the addition of sbs and nano-sio2 to the base bitumen resulted in the reduction of the complex modulus, phase angle, storage modulus and loss modulus at middle temperatures, thereby improving the potential of fatigue failure resistance. in general, considering the requirement for the rotational viscosity value up to 3 pa.s at 135 °c and also, regarding the economic issues in choosing a lower percentage, the combination of 4.5% sbs + 3% nano-sio2 is selected as the optimal composite. keywords. bitumen; functional analysis; middle temperature; nano-sio2; sbs. citation: damadi, s. m., edrisi, a., fakhri, m., rezaei s., khordehbinan, m. w., fatigue analysis of bitumen modified with composite of nano-sio2 and styrene butadiene styrene polymer, frattura ed integrità strutturale, 53 (2020) 202-209. received: 05.04.2020 accepted: 06.05.2020 published: 01.07.2020 copyright: © 2020 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. https://youtu.be/yha_jj5p4ei s. m. damadi et alii, frattura ed integrità strutturale, 53 (2020) 202-209; doi: 10.3221/igf-esis.53.17 203 introduction itumen is usually the byproduct in the crude oil production process, which, therefore, may not have all the specifications required for the production of asphalt mixtures [1]. asphalt mixtures are subjected to the temperature changes and stresses caused by the passing heavy vehicles, which increase the growth of rutting, fatigue and lowtemperature cracking failures. the bitumen plays an important role in the occurrence of these failures. therefore, in order to achieve the pavements of longer service life, the modification of bitumen is inevitable [2]. every year, different modifiers are used to improve bitumen properties and behavior. among these modifiers, in recent decades, the polymers and nanomaterials are increasingly used to improve the rheological behavior of bitumen [3-8]. the modification of bitumen with styrene butadiene styrene (sbs) polymer improves the resistance to rutting, fatigue cracking, and low-temperature cracking [9,10], but involves the phase separation and is degraded under the ultraviolet light, as well as oxygen [11,12]. research results show that modifying the polymer bitumen with nano-materials improves the highand low-temperature performance, aging, oxidation and phase separation [13,14,3,4,5]. there are some limited studies on the effect of polymer nano-composites; hence, this paper analyzes the middle-temperature performance of the sbs additive and the combined sbs and nano-sio2 additive in 10, 15, 20, and 25 oc to the bitumen pg 64-16 as the most common bitumen in iran. for this purpose, the bitumen performance, dual composite of bitumen and sbs, and triad composite of bitumen, sbs and nano-sio2 were evaluated based on the softening point, needle penetration, ductility, rotational viscosity, rtfo mass loss, and dynamic shear rheometer (dsr) tests. method materials itumen pg 64-16 was prepared from pasargad oil company of tehran, sbs polymer (lg 501) was prepared from lg company, south korea, and nano-sio2 was prepared from degussa company, germany. the chemical composition of the base bitumen and the physical and chemical characteristics of sbs and nano-sio2 are given in tab. (1), tab. (2), and, tab. (3). composition wt.% saturates 8.1 naphthene-aromatics 48.9 polar-aromatics 30.8 asphaltenes 12.2 table 1: chemical composition of base bitumen. physical and chemical properties content molecular structure linear styrene/butadiene ratio 31/69 density (g/cm3) 0.94 oil content (phr) none melting index (g 10 minutes 200 °c / 5 kg) < 1 volatile rate (%) 0.5 hardness (shore a) 79 toluene solution viscosity 13.4 table 2: physical and chemical properties of sbs. b b s. m. damadi et alii, frattura ed integrità strutturale, 53 (2020) 202-209; doi: 10.3221/igf-esis.53.17 204 physical and chemical properties content sio2 >99% ti <120ppm ca <70ppm na <50ppm fe <20ppm aps 11-13 nm ssa 180-600 m2/gr bulk density <0.10 g/cm3 true density 2.4 g/cm3 table 3: physical and chemical properties of nano-sio2 preparation of samples to prepare the combined bitumen, sbs and nano-sio2 samples, the high shear mixer was used at 175 °c and 4000 rpm for two hours. on this basis and in order to perform all the tests, 1 kg from each of the samples was prepared including the base bitumen, compound of bitumen and sbs polymer as 2.5, 3, 3.5, 4, 4.5, 5, 5.5 and, 6 wt% of the bitumen and the threefold compound of bitumen, sbs polymer with constant 4.5 wt% of bitumen and nano-sio2 with 1, 2, 3, 4 and, 5 wt% of bitumen, which resulted in preparation of 1 samples of base bitumen, 8 samples of polymeric bitumen and 5 samples of nano polymeric bitumen. physical properties tests the conventional physical tests including the softening point (astm d36), needle penetration at 25 °c (astm d5), ductility at 25 °c (astm d113), rotational viscosity (astm d4402) at 120, 135, 150, and 165 °c, and rolling thin-film oven (rtfo) mass loss (astm d2872) tests were performed on the base bitumen and all modified bitumen samples. moreover, the needle penetration index was calculated according to equation (1) [12].     25 25 1952 500 log 20 50 log 120 pen sp pi pen sp         (1) where the pen25 is the needle penetration at 25 °c (0.1 mm) and sp is the temperature of the softening point of bitumen samples (°c). dynamic shear rheometer test dynamic shear rheometer (dsr) test (astm d7175) was conducted using the controlled stress method at constant frequency (10 rad/s) and 10, 15, 20, and 25 °c for different sbs, nano-sio2 composites with base bitumen on which the short-term aging process was carried out on an rtfo machine (astm d2872). the complex modulus (g*), phase angle (δ), storage modulus (g'=g*×cosδ) and loss modulus (g"=g*×sinδ) were determined for bitumen samples. in order to improve the resistance potential to fatigue, the energy loss should be reduced as much as possible. the energy loss in each loading cycle is directly proportional to g*×sinδ parameter. for the bitumen to be acceptable in the fatigue test at a given temperature, the value of g*×sinδ should be less than or equal to 5000 kpa for the aged bitumen with rtfo [15]. this means that it is desirable to reduce the values of g* and δ. results physical properties he results of softening point, needle penetration, pi, ductility, rotational viscosity and rtfo mass loss for various composites of sbs and sbs/nano-sio2 with base bitumen are given in tab. (4). these tests were selected for the purpose of fatigue analysis of the bitumen modified by sbs polymer and nano-sio2 among the tests of physical properties of the bitumen. as for investigating the performance at the intermediate temperatures i.e. at temperatures t s. m. damadi et alii, frattura ed integrità strutturale, 53 (2020) 202-209; doi: 10.3221/igf-esis.53.17 205 between 10 and 25 celsius degrees, where failure of the asphalt mixture occurs due to the fatigue, analysis of these tests is appropriate for this purpose. according to tab. (4), the addition of sbs and sbs/nano-sio2 to bitumen generally increases the softening point, pi, and rotational viscosity and decreases the needle penetration. reducing the needle penetration, increasing the softening point, pi and viscosity will reduce the bitumen's sensitivity to temperature changes and improve its performance at middle temperatures. considering the effect of sbs polymer, it could be due to the creation of 3d networks in the bituminous environment after creation of long and dispersed chains of sbs polymer. so that the polystyrene and polybutadiene chains would increase the strength and flexibility of the modified bitumen, respectively, which result in reduced fluidity and increased elasticity. concerning the nano-sio2 effect, it is due to the interaction between nano-sio2 material, bitumen and sbs polymer. so that nano-sio2 by adsorption, establishes intense adhesion with the bitumen and polymer which leads to increased hardness and concentration of bituminous mortar. this in turn reduces the bitumen needle penetration and increases the softening point, pi and rv values. reduced the needle penetration and increased softening point, pi and rv lead to reduced sensitivity of the bitumen to variation in temperature which is good for it. in the sbs with higher than 4.5 wt%, the reducing trend of the needle penetration and increasing trend of softening point and pi is mitigated which is due to the dominating polymer phase. also this process is seen in threefold compound consisting of bitumen, sbs polymer and nano-sio2, where for nano-sio2 with higher than 4 wt% , the reducing trend of penetration degree and increasing trend of softening point and pi are mitigated which could be due to saturation of the bituminous mortar by nano particles. so that the balanced phase network of bitumen and sbs polymer is disturbed when using too much nano-sio2. compounds properties softening point (oc) penetration at 25oc (dmm) ductility at 25oc (cm) pi rtfo (mass loss%) rv (pa.s) 120 oc 135 oc 150 oc 165 oc base bitumen 50.3 65 >100 0.13 0.67 0.32 0.16 0.10 sbs (wt% of bitumen) 2.5% 57.5 54 >100 0.17 0.23 0.86 0.47 0.26 0.15 3% 59.5 54 >100 0.26 0.23 1.11 0.62 0.33 0.19 3.5% 67 49 >100 0.49 0.24 1.40 0.72 0.39 0.22 4% 79.5 48 >100 0.79 0.23 1.76 0.88 0.47 0.27 4.5% 84.5 45 >100 0.86 0.22 1.93 0.97 0.52 0.32 5% 85 43 95 0.85 0.27 2.14 1.08 0.57 0.33 5.5% 86.5 42 99 0.87 0.25 2.47 1.25 0.64 0.37 6% 84.5 42 94.8 0.84 0.26 2.71 1.37 0.76 0.41 sbs/nano-sio2 (wt% of bitumen) 4.5% sbs+1%nanosio2 85 35 >100 0.78 0.21 2.18 1.60 0.65 0.35 4.5% sbs+2%nanosio2 85.5 36 >100 0.80 0.21 3.39 1.72 0.87 0.52 4.5% sbs+3%nanosio2 86 37 >100 0.82 0.20 4.49 2.96 1.13 0.53 4.5% sbs+4%nanosio2 86.5 34 >100 0.80 0.21 4.86 3.63 1.62 0.74 4.5% sbs+5%nanosio2 85 38 >100 0.81 0.21 5.42 3.87 1.88 0.95 table 4: physical properties of base bitumen, bitumen/sbs, and bitumen/sbs/nano-sio2. the maximum levels of sbs that can provide the ductility greater than 100 [15] are the composites with the sbs level of 4.5% by weight of bitumen. the appropriate bitumen temperature for mixing and compaction is the temperature equivalent to rv values of 0.17±0.2 and 0.28±0.3, respectively, and the maximum temperature for heating of the bitumen is equal to 176°c [15]. according to tab. (4), adding sbs polymer to the base bitumen from 2.5 to 6 wt% of bitumen causes continuous increase of rv, but it does not exceed 3 pa.s at 135°c temperature. in these compounds the maximum rv value at 135°c is equal to 1.37 for a compound of base bitumen and sbs polymer with 6 wt% of the bitumen. also, addition of nano-sio2 s. m. damadi et alii, frattura ed integrità strutturale, 53 (2020) 202-209; doi: 10.3221/igf-esis.53.17 206 to the bitumen containing sbs polymer with 4.5 wt% of the bitumen, causes increase in the rv value. this value exceeds the limit of 3 pa.s for the compounds of 4.5%sbs+4%nano-sio2 and 4.5% sbs+5% nano-sio2. therefore, on this basis the maximum value of nano-sio2 is equal to 3 wt% of the bitumen in the compound of bitumen modified by sbs polymer with 4.5 wt% of the bitumen. by increase in the temperature, the rv values is reduced. for the compound of bitumen and 4.5% sbs and the threefold compound of bitumen, sbs polymer and nano-sio2, the mixing and compaction temperatures are both greater than 165 °c which are too close to 176°c and create problems in terms of applicability. thus, to resolve this problem it is recommended to use admixtures that reduce viscosity such as fischer-tropsch wax. as seen in tab. (4), adding sbs polymer to bitumen and also adding nano-sio2 to polymeric bitumen containing sbs polymer with 4.5 wt% of the bitumen, the weight loss is nearly constant and its value in all the compounds is less than 1 wt%. complex modulus, phase angle, and storage modulus the results of complex modulus, phase angle and storage modulus for various composites of sbs, nano-sio2 with base bitumen are presented in figs. (1–3), respectively. according to the figures, adding sbs and nano-sio2 to the base bitumen continuously decreases the complex modulus, phase angle and storage modulus at 10 to 25 °c with the constant frequency of 10 rad/s, indicating the improvement in fatigue resistance potential and middle-temperature performance. concerning the results of complex modulus at intermediate temperatures (temperatures between 10 and 25 celsius degrees), as the base bitumen, modified bitumen with 4 wt% of sbs polymer and different threefold combinations of bitumen, nano-sio2 and 4.5 wt% of sbs polymer, had passed the short term and long term processes of aging prior to the dynamic shear rheometer test, and the aging process of rtfo+pav could result in further hardness of the bitumen by change in the molecular structure of the bitumen, therefore, the higher the share of bitumen, the higher would be the complex modulus. thus, adding sbs polymer and also adding nano-sio2 to the polymeric bitumen with 4.5 wt% sbs polymer at intermediate temperatures could reduce the complex modulus. as the reduction in complex modulus at the intermediate temperatures, leads to increase of resistance to fatigue failure, therefore the performance of modified bitumen at intermediate temperatures is improved. as seen in fig. (2), it is observed that adding sbs polymer and nano-sio2 to the sbs polymeric bitumen at temperatures between 10 and 25 celsius degrees and at constant frequency of 10 radians per second, the phase angle is continuously reduced. this could be due to interaction between nano-sio2, bitumen and sbs polymer, so that nano-sio2 particles by adsorption develop enhanced adhesion with the bitumen and polymer compounds which has resulted in reduced phase angle. as stated before, reduction in δ value reduces loss in viscosity and therefore improves the performance at intermediate temperatures of modified bitumen samples. figure 1: the complex modulus results from dsr test for base bitumen, bitumen/sbs, and bitumen/nano-sio2/sbs in 10, 15, 20, and 25 oc. s. m. damadi et alii, frattura ed integrità strutturale, 53 (2020) 202-209; doi: 10.3221/igf-esis.53.17 207 figure 2: the phase angle results from dsr test for base bitumen, bitumen/sbs, and bitumen/nano-sio2/sbs in 10, 15, 20, and 25 oc. figure 3: the storage modulus (g’) results from dsr test for base bitumen, bitumen/sbs, and bitumen/nano-sio2/sbs in 10, 15, 20, and 25 oc. loss modulus (fatigue resistance) the values of the loss modulus (g"=g*×sinδ) for various composites of sbs, nano-sio2 with rtfo-aged base bitumen are shown in fig. (4). as seen in the figure, by adding sbs and nano-sio2 to the base bitumen, the loss modulus is reduced at 10 to 25 °c with the constant frequency of 10 rad/s, which results in improved fatigue resistance potential and middletemperature performance of the modified bitumen samples. all different composites of sbs, nano-sio2 with the base bitumen at temperatures 10 to 25 °c and constant frequency of 10 rad/s have the g*×sinδ values less than 5000 kpa, among which two composites of 4.5% sbs + 3 % nano-sio2 and 4.5% sbs + 4% nano-sio2 have the minimum values. as seen in fig. (4), continuous addition of sbs polymer and nano-sio2 to the sbs polymer modified bitumen, causes reduction in the parameter values of g*×sinδ, at temperatures of 10-25 celsius degrees and with constant frequency of 10 radians per seconds, and consequently resistance against fatigue and performance at intermediate temperatures of the modified bituminous samples are both improved. this could be due to the reduced complex modulus and phase angle by addition of nano-sio2 to the 4.5 wt% sbs polymer modified bitumen at intermediate temperatures which was explained. s. m. damadi et alii, frattura ed integrità strutturale, 53 (2020) 202-209; doi: 10.3221/igf-esis.53.17 208 figure 4: the loss modulus (g”) results from dsr test for base bitumen, bitumen/sbs, and bitumen/nano-sio2/sbs in 10, 15, 20, and 25 oc. conclusion y adding nano-sio2 and sbs to the base bitumen, the needle penetration is decreased and the softening point, pi, and rotational viscosity are increased. these results decrease the sensitivity of various composites to temperature changes, reduce the fatigue cracking and improve the performance at the middle temperatures. in all of the various composites of sbs and nano-sio2 with base bitumen, the ductility at 25 °c was found to be more than 100 cm, indicating the good performance at middle temperatures. the maximum rotational viscosity of bitumen samples at 135 °c is considered equal to 3 pa.s. all bitumen samples, except for 4.5% sbs + 4% nano-sio2 satisfied this requirement. all composites were controlling the maximum mass loss in the rtfo test, which is 1%, indicating the resistance to oxidation and short-term aging. by adding nano-silica to the sbs polymer bitumen, the complex modulus, phase angle, storage modulus, and loss modulus at 10 to 25 °c and constant frequency of 10 rad/s were constantly reduced, resulting in the improved fatigue resistance and middle-temperature performance in the bitumen samples. in general, according to the requirement of rotational viscosity up to 3 pa.s at 135 °c and also, regarding the economic issues in selecting a lower percentage, the combination of 4.5% sbs + 3% nano-sio2 is selected as the optimal composite. references [1] kim, y. r. (2008). modeling of asphalt concrete. newyork, ny:mcgraw-hill construction. [2] reddy, k. s., umakanthan, s.and krishnan, j. m. (2012). constant strain rate experiments and constitutive modeling for a class of bitumen. mechanics of time-dependent materials, 16(3), pp. 251-274. doi: 10.1007/s11043-011-9155-8. [3] rezaei, s., ziari, h.and nowbakht, s. (2016a). low temperature functional analysis of bitumen modified with composite of nano-sio2 and styrene butadiene styrene polymer. petroleum science and technology, 34(5), pp. 415-421. doi: 10.1080/10916466.2016.1143841. [4] rezaei, s., ziari, h.and nowbakht, s. (2016b). high-temperature functional analysis of bitumen modified with composite of nano-sio2 and styrene butadiene styrene polymer. petroleum science and technology, 34(13), pp. 11951203. doi: 10.1080/10916466.2016.1188112. b s. m. damadi et alii, frattura ed integrità strutturale, 53 (2020) 202-209; doi: 10.3221/igf-esis.53.17 209 [5] rezaei, s., khordehbinan, m., fakhrefatemi, s. m. r., ghanbari, s.and ghanbari, m. (2017). the effect of nano-sio2 and the styrene butadiene styrene polymer on the high-temperature performance of hot mix asphalt. petroleum science and technology, 35(6), pp. 553-560. doi: 10.1080/10916466.2016.1270301. [6] farazmand, p., hayati, p., shaker, h.and rezaei, s. (2020). relationship between microscopic analysis and quantitative and qualitative indicators of moisture susceptibility evaluation of warm-mix asphalt mixtures containing modifiers. frattura ed integrità strutturale, 14(51), pp. 215-224. doi: 10.3221/igf-esis.51.17. [7] saltan, m., terzi, s.and karahancer, s. (2018). performance analysis of nano modified bitumen and hot mix asphalt. construction and building materials, 173, pp. 228-237. doi: 10.1016/j.conbuildmat.2018.04.014. [8] shi, x., cai, l., xu, w., fan, j.and wang, x. (2018). effects of nano-silica and rock asphalt on rheological properties of modified bitumen. construction and building materials, 161, pp. 705-714. doi: 10.1016/j.conbuildmat.2017.11.162. [9] liang, m., liang, p., fan, w., qian, c., xin, x., shi, j.and nan, g. (2015). thermo-rheological behavior and compatibility of modified asphalt with various styrene–butadiene structures in sbs copolymers. materials & design, 88, pp. 177-185. doi: 10.1016/j.matdes.2015.09.002. [10] karakas, a. s., kuloglu, n., kok, b. v.and yilmaz, m. (2015). the evaluation of the field performance of the neat and sbs modified hot mixture asphalt. construction and building materials, 98, pp. 678-684. doi: 10.1016/j.conbuildmat.2015.08.140. [11] cortizo, m. s., larsen, d. o., bianchetto, h.and alessandrini, j. l. (2004). effect of the thermal degradation of sbs copolymers during the ageing of modified asphalts. polymer degradation and stability, 86(2), pp. 275-282. doi: 10.1016/j.polymdegradstab.2004.05.006. [12] galooyak, s. s., dabir, b., nazarbeygi, a. e.and moeini, a. (2010). rheological properties and storage stability of bitumen/sbs/montmorillonite composites. construction and building materials, 24(3), pp. 300-307. doi: 10.1016/j.conbuildmat.2009.08.032. [13] eslami, i., khordehbinan, m., rezaei, s.and eslami, z. (2019). a model of dsr performance to evaluate the rutting parameter of bitumen at high temperatures. journal of biochemical technology, special issue (2), pp. 174-179. [14] ziari, h., farahani, h., goli, a.and sadeghpour galooyak, s. (2014). the investigation of the impact of carbon nano tube on bitumen and hma performance. petroleum science and technology, 32(17), pp. 2102-2108. doi: 10.1080/10916466.2013.763827. 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can be opened with acrobat and adobe reader 5.0 and later.) >> /namespace [ (adobe) (common) (1.0) ] /othernamespaces [ << /asreaderspreads false /cropimagestoframes true /errorcontrol /warnandcontinue /flattenerignorespreadoverrides false /includeguidesgrids false /includenonprinting false /includeslug false /namespace [ (adobe) (indesign) (4.0) ] /omitplacedbitmaps false /omitplacedeps false /omitplacedpdf false /simulateoverprint /legacy >> << /addbleedmarks false /addcolorbars false /addcropmarks false /addpageinfo false /addregmarks false /convertcolors /converttocmyk /destinationprofilename () /destinationprofileselector /documentcmyk /downsample16bitimages true /flattenerpreset << /presetselector /mediumresolution >> /formelements false /generatestructure false /includebookmarks false /includehyperlinks false /includeinteractive false /includelayers false /includeprofiles false /multimediahandling /useobjectsettings /namespace [ (adobe) (creativesuite) (2.0) ] /pdfxoutputintentprofileselector /documentcmyk /preserveediting true /untaggedcmykhandling /leaveuntagged /untaggedrgbhandling /usedocumentprofile /usedocumentbleed false >> ] >> setdistillerparams << /hwresolution [2400 2400] /pagesize [612.000 792.000] >> setpagedevice microsoft word numero_60_art_19_3448.docx r. gerosa et alii, frattura ed integrità strutturale, 60 (2022) 273-282; doi: 10.3221/igf-esis60.19 273 on the peak strength of 7050 aluminum alloy: mechanical and corrosion resistance riccardo gerosa, barbara rivolta, marco boniardi, andrea casaroli politecnico di milano, italy riccardo.gerosa@polimi.it , https://orcid.org/0000-0003-0810-0279 barbara.rivolta@polimi.it, https://orcid.org/0000-0002-8949-0549 marco.boniardi@polimi.it, https://orcid.org/0000-0002-2438-7890 andrea.casaroli@polimi.it, https://orcid.org/0000-0001-5207-5547 abstract. this work consists of an experimental study on the ageing response and resulting properties of aa7050 plate material. new heat treatments are investigated for achieving a peak-aged temper, as a t6 temper may be said to be, that achieves yield and tensile strengths superior to those of the documented t7 treatments. for this alloy, the standard establishes t7x tempers which were developed to obtain a very good compromise between mechanical strength and corrosion resistance. nevertheless, for all those applications in which the environment is not considered critical for corrosion behaviour, the peak strength condition could be beneficial. in this experimental work, the authors use standard hardness testing to investigate mechanical response as a function of ageing time at several ageing temperatures, all applied immediately after solution. upon identifying specific times and temperatures of interest, specimens aged under the selected treatments were subjected to tensile testing and intergranular corrosion testing. the results show that a single-step ageing heat treatment is able to produce a significantly high both yield and ultimate tensile strength. moreover, the corrosion test data indicates that this new heat treatment produces corrosion resistance similar to that of the t76 heat treatment. keywords. aluminum alloys; aa7050; heat treatment; mechanical strength; corrosion. citation: gerosa, r., barbara, r., boniardi, m., casaroli a., , n., on the peak strength of 7050 aluminum alloy: mechanical and corrosion resistance, frattura ed integrità strutturale, 60 (2022) 273-282. received: 02.02.2022 accepted: 07.02.2022 online first: 08.02.2022 published: 01.04.2022 copyright: © 2022 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. introduction he 7xxx series aluminum alloys are heat treatable alloys based on the al−zn−mg (−cu) system and they are widely used in high performance structural aerospace and transportation applications. together with the chemical composition and the fabrication process, their properties are significantly influenced by the heat treatments: t https://youtu.be/n2kdlfdj2-i r. gerosa et alii, frattura ed integrità strutturale, 60 (2022) 273-282; doi: 10.3221/igf-esis60.19 274 precipitation hardening provides one of the most widely used mechanisms for the strengthening of light alloys. this process involves three basic steps: solution treatment, quenching and ageing, where the peak hardening condition is achieved thanks to phases nucleating at precise treatment times and temperatures. depending on the chemical composition, the precipitation sequence can be very complicated and can involve many stable and/or metastable compounds. for the 7xxx alloys, the possible existing phases depend on the mg/zn ratio and include guinier-preston zones (gp zones), metastable precipitates t and , stable precipitate  (mg(al,cu,zn)2) and t ((al,zn)49mg32). it is well known that when the mg/zn ratio is between 0.15 and 0.4,  and  precipitates appear, whereas for mg/zn ratios between 0.5 and 6, t phase appears [1, 2, 3]. in 7xxx alloys containing copper,  (al2cu) and s (al2cumg) phases can also be present [4, 5]. in recent years, several studies were proposed to increase both the strength and corrosion resistance of 7xxx alloys, such as retrogression and reageing (rra) [6, 7], step-quench and ageing treatment [8] and some other thermomechanical treatments [9]. for increasing the corrosion resistance while keeping the strength levels similar to t6 temper, park et al. [10] proposed the rra and a new two-step ageing process was introduced by wang et al. [11] to achieve higher stress corrosion cracking resistance and strength. peng et al. [12] proposed that the dual-rra could further improve stress corrosion cracking (scc) resistance with retention strength comparable to rra temper. several studies were also published investigating the effect of ecap (equal channel angular pressing) in grain refinement and its combination with age hardening in achieving superior strength [13, 14, 15]. for achieving excellent mechanical properties and satisfactory corrosion resistance of 7050 alloy, non-isothermal ageing was proposed by d. jiang et al. [16], the effect of the size and distribution of precipitates on stress corrosion cracking of 7050 alloy was clarified in [17] and the effect of homogenization on corrosion resistance of extruded bars was intensively studied in [18]. the relationships between microstructure, i.e. the nature, density and size of precipitates, and corrosion properties was also deeply investigated in [19]. nevertheless, it is well known [1, 2, 3] that 7xxx aluminum alloys are more susceptible to intergranular corrosion (igc) in the one step t6 temper than in the two step t7 temper and in [20], the role of the grain boundary precipitates was extensively clarified. for most engineering applications, a good compromise between mechanical properties and corrosion resistance is usually required. in this sense the content of astm b918/b918m standard [1] will be considered that, for the 7050 aluminum alloy, suggests only the overaged two-step ageing t7x tempers, thereby assuring good corrosion performance but an outof-peak strength condition. nevertheless, in the applications in which corrosion behaviour does not have a primary role, for example in the space industry (for satellites and space vehicles), in the fabrication of plastic moulds and generally in all those situations in which the components are painted or coated, the maximization of the alloy’s strength can be an important achievement. the aim of this work is to study the peak strength condition for a single-step t6 heat treatment. in this experimental work, the authors use standard hardness testing to investigate mechanical response as a function of ageing time at several ageing temperatures, all applied immediately after solution. upon identifying specific times and temperatures of interest, specimens aged under the selected treatments were subjected to tensile and corrosion testing. experimental procedure n this work a 7050 t7451 aluminum alloy plate 100 mm thick was investigated after solution treatment followed by different ageing conditions. the nominal chemical composition is reported in tab. 1. % zn % mg % cu % zr % al 6.21 2.10 2.19 0.10 bal. table 1: nominal chemical composition of the alloy investigated. from the plate, samples for the hardness, tensile and corrosion tests were machined. a solution treatment was performed on each specimen at 477°c for 60 minutes according to the astm b918/b918m standard [1] and ageing treatments at different temperatures were carried out (tab. 2). both the solution and the ageing treatments were performed in a laboratory furnace. in the astm b918/b918m standard, the initial condition before ageing is ‘w51’, i.e. stress-relieved by cold stretching to a permanent set of 1.5 to 3 % in the solution heat-treated condition. since it is not possible to reach this condition in the laboratory tests, after the standard ageing treatment the samples were designated as t76 rather than t7651. i r. gerosa et alii, frattura ed integrità strutturale, 60 (2022) 273-282; doi: 10.3221/igf-esis60.19 275 id details t76 (w) + 121°c x 4.5h + 166°c x 13.5h 121 (w) + 121°c x 0.5h-96h 140 (w) + 140°c x 0.5h-162h 166 (w) + 166°c x 0.5h-48h table 2: scheme of the different heat treatment conditions. the ageing response was studied using hardness tests (hbw 2.5/62.5 according to the bs en iso 6506-1 standard [21]) at different ageing times. then, tensile tests were performed on specimens aged at times and temperatures selected on the basis of the hardness curves. these specimens were machined in the long transverse (lt) direction of the original plate. the tensile tests were carried out according to the astm b557m-15 standard [22] on circular cross section specimens ( 9mm) using an instron 4507 tensile testing machine. finally, intergranular corrosion tests were performed on 20 x 20 x 10 mm3 samples treated with the same parameters used for the tensile specimens. according to the astm g110-92 standard [23], the testing solution consists of 57 g of sodium chloride and 10 ml of hydrogen peroxide diluted to 1 litre with reagent water. in order to quantify and compare the corroded specimens, an analysis was carried out according to the method already described in [24]. in technical literature several methods are available for evaluating the intergranular corrosion behaviour, such as in [25]. the authors followed the astm g110-92 standard [23], which is the reference standard used for engineering applications. as described in [24], referring to fig. 1, each pit can be characterized by its roundness, depth and width according to eqn. (1). figure 1: image analysis of a corrosion pit. * i i i i h r r l  (1) where ri=pi2/4πsi, ri* is called the modified roundness and ri, pi and si are the roundness, the perimeter and the area of the i-th defect respectively. when ri*increases, the local notch effect increases. in order to evaluate the overall effect of multiple corrosion pits, the corroded surface cs was defined as the ratio between the total length of the defects and the total length of the original profile. 100 ii s tot l c l    (2) where li is the length of the i-th corrosion pit and ltot is the observed total length of the original profile (with no corrosion pits). finally, a parameter describing the overall surface condition is reported in eqn. (3): *c sr r c  (3) r. gerosa et alii, frattura ed integrità strutturale, 60 (2022) 273-282; doi: 10.3221/igf-esis60.19 276 where r* is the average of the modified roundness values ri*. twenty images per condition were examined. the orientation of the specimens in respect to the rolling direction was selected carefully. since it is known [2] that the st direction is the one with the weakest corrosion resistance, the 10 mm thick specimens were aligned with such rolling direction. the largest surface, 20 x 20 mm2, laid in the l-lt plane, was the reference surface during the exposure in the testing solution. the specimens were immersed in the corrosive solution for 24 hours and at the end of the test, they were cut along the l-st plane in order to observe the corrosion pits developed in the st direction. a scheme of the described procedure is reported in fig. 2. (a) (b) (c) figure 2: procedure for the analysis of the corroded profiles. (a) sample to be immersed in the testing solution; (b) cut along the lt-st plane; (c) corroded profile observed. results and discussion ageing response ne important aim of this work is to determine the ageing condition able to give peak strength conditions. for this reason, three ageing temperatures, i.e. 121°c, 140°c and 166°c, were selected in order to cover the whole temperature range reported in astm b918/b918m. as described in tab. 2, hardness tests were performed varying the ageing time in order to study the precipitation response. the results obtained are reported in fig. 3. figure 3: hardness curves at different ageing temperatures, varying the soaking time. as expected [2], the precipitation rate increases as the ageing temperature increases. the heat treatments performed at 121°c and 166°c showed a continuous hardness increase until the peak condition, then over-ageing occurred and the corresponding hardness decreased. the ageing tests at 140°c showed a different behaviour, because, after the first hardness peak, a second peak was observed for longer soaking times. in tab. 3, the ageing times at peak hardness are summarized. o r. gerosa et alii, frattura ed integrità strutturale, 60 (2022) 273-282; doi: 10.3221/igf-esis60.19 277 ageing temperature ageing time at peak hardness peak hardness 121°c 24h 186 hbw 140°c 12h (1st peak) 81h (2nd peak) 187 hbw (1st peak) 189 hbw (2nd peak) 166°c 3h 188 hbw table 3: peak hardness and peak hardness times for the ageing temperatures investigated. it is well known from the technical literature [2, 3, 6, 26, 27, 28] that in the al – zn – mg (-cu) system, in the temperature range of 120°c – 130°c, there is a response to hardening due to the precipitation of gp zones and  phase. at higher temperatures, 160°c – 170°c,  and  phases precipitate [26, 27, 28]. these phases can also contain increasing contents of copper if its amount is higher than 1% in the alloy [19]. it is well known [20] that  and  phases improve corrosion resistance, especially stress corrosion cracking and this result is further enhanced by the presence of copper in the previous compounds. by observing the ttt curve for 7xxx alloys published in the technical literature [26, 27, 28], the first peak observed during the tests at 140°c is associated with the precipitation of gp zones and  and the second peak is associated with the nucleation of  phase. as described in the technical literature [2, 3, 26], the  precipitates are plate-shaped particles, whereas  precipitates can assume a plate, rod or lath shape. sha et al. [26] reported that the chemical composition of precipitates can involve different amounts of zn, cu and mg, i.e. the zn/mg ratio for such phases increases as the ageing time increases starting from a zn/mg ratio  1 for gp zones up to a zn/mg ratio equal to about 1.2-1.3 for  precipitates and higher values for  precipitates. after the standard metallographic preparation, the specimens were etched using keller reagent and the phases observed were investigated using a scanning electron microscope (sem) and edxs (energy dispersion x-ray system). fig. 4 shows an example of the precipitates observed and their relative edxs analysis. the zn/mg ratios show values compatible with those found in technical literature for  and  precipitates, as reported in [26]. the presence of copper, on the other hand, can be related to the gp zones that anticipate the formation of  and  precipitates. some authors, in fact, found copper percentages up to 12 at% [26]. a) b) figure 4: zn-cu-mg rich precipitates observed after different ageing times. r. gerosa et alii, frattura ed integrità strutturale, 60 (2022) 273-282; doi: 10.3221/igf-esis60.19 278 tensile tests n order to determine the mechanical strength of the alloy at the peak hardness conditions described in tab. 3, new specimens were machined from the as delivered plate in the lt direction. after the solution treatment and ageing, tensile tests were carried out. besides the specimens aged in the non-standard conditions described in tab. 3, it was decided to prepare some samples in the t76 temper as well, according to the time-temperature cycle described in the astm b918/b918m standard. the comparison between the results obtained is shown in figs. 5 and 6. figure 5: comparison between the yield and uts values obtained. from the mechanical strength point of view, all the non-standard treatments resulted in higher yield and uts values compared to the t76 temper. among the non-standard conditions, the best performance was obtained by the specimens treated at 140°c for 81 hours: as shown in fig. 5, the uts value was comparable with the others, but the yield stress was remarkably higher. in terms of the percentage elongation and the reduction of area, no appreciable differences were detected among the ageing conditions tested. figure 6: comparison between the percentage elongations (a%) and the reductions of area (z%). i a  r. gerosa et alii, frattura ed integrità strutturale, 60 (2022) 273-282; doi: 10.3221/igf-esis60.19 279 intergranular corrosion tests n order to complete the alloy characterization in the ageing conditions investigated, intergranular corrosion tests were performed according to the astm g110-92 standard. in fig. 7, some of the corrosion pits observed are shown. applying the procedure described previously, the corrosion damages were quantified and compared with the t76 treatment. in fig. 8, the modified roundness (r*) was plotted against pit area values for different ageing parameters and compared with t76 temper. the results show that only the samples treated at 140°c-81h has a behaviour similar to that of t76. a) b) c) d) e) figure 7: results of intergranular corrosion tests in samples with different ageing parameters – a) 121°c, 24h; b) 140°c, 12h; c)140°c, 81h; d) 166°c, 3h; e) t76. in tab. 4 all the corrosion parameters associated with the investigated specimens were summarized. the results confirm that the one step ageing at 140°c, 81h has similar corrosion behaviour to the two step ageing t76 temper. park et al. [10] published tem studies on retrogression and reageing (rra) of aa7075, a closely related material. this work suggests conversion of η' precipitates to η, particularly at grain boundaries, which may be responsible for the improved corrosion resistance imparted by the rra heat treatments to aa7075. this is also confirmed in [29]. i r. gerosa et alii, frattura ed integrità strutturale, 60 (2022) 273-282; doi: 10.3221/igf-esis60.19 280 the presence of the more stable η precipitates after one step ageing at 140°c, 81h, confirmed by the ttt curve, is in agreement with the good corrosion resistance of the new heat treatment. a) b) c) d) figure 8: modified roundness vs pit area for different ageing parameters compared with t76 temper. 121°c – 24h 140°c – 12h 140°c – 81h 166°c – 3h t76 r* 13.8 13.8 1.3 10.0 1.1 cs 44.0 26.6 2.1 9.4 3.4 rc 609.4 371.7 2.8 95.3 3.2 table 4: comparison of the corrosion resistance for the ageing conditions investigated. the mechanical and the corrosion characterization of the alloy described in the previous paragraphs represents a clear overview of the alloy performances varying the heat treatment conditions. such information is useful for the designer to suggest the best solution for a specific application. the aging parameters resulted in the best mechanical and corrosion properties are 140°c for 81h. nevertheless, other aging conditions were considered and characterized from mechanical and corrosion points of view. they represent possible choices for the designer on the base of a cost/benefit analysis. from metallurgical point of view, the high mechanical strength, particularly the yield stress, obtained after long soaking at 140°c is related to the precipitate resistance to the dislocation motion. it is well known that the highest pinning effect is obtained with specific particle size: small precipitates are too week, whereas coarse precipitates are less effective because of the larger spacing among them. the particle size and distribution are function of the temperature and of the aging time [2, 3]. the results of the tensile tests suggest that at 140°c the precipitation condition is not enough effective when the soaking time is equal to 12h, but when the treatment time increases, the slight coarsening of the existing precipitates, , and the nucleation of the  phase create a very efficient obstacle to dislocation movement. the precipitate type, size and distribution influence the corrosion resistance as well. as reported in the previous paragraphs, coarser  precipitates are associated to a higher corrosion resistance. this is confirmed by the corrosion tests on the specimens aged at 166°c. at 140°c, the formation of such phase, together with the precipitate coarsening occurring after long soakings, explain the good corrosion resistance observed after 81h. the technical literature [30, 31, 32] states that the precipitate coarsening increases the particles inter-spacing, reducing the anodic tunnel effect at grain boundary and the electrochemical potential difference among the r. gerosa et alii, frattura ed integrità strutturale, 60 (2022) 273-282; doi: 10.3221/igf-esis60.19 281 matrix and the grain boundary. summarizing, the temperature of 140°c proved sufficiently high to activate both the precipitate types and to obtain an increase of the inter-spacing, but not too high to result in an excessive particle coarsening with consequent decrease of the mechanical resistance. further investigation of aging temperatures close to 140°c is hence justified by the possibility to reduce the soaking time necessary to get maximum mechanical and corrosion resistance. concluding remarks his experimental work aimed to find the peak strengthening condition for aa7050 by developing out-of-standard ageing times and temperatures.  the analysis of the obtained results revealed a very good behaviour of all the non-standard ageing conditions, especially the specimens aged at 140°c, 81 hours. if compared with the standard t76 temper, the ageing at 121°c 24h, 140°c 12h, 140°c 81h and 166°c 3h showed a yield stress increase of about 2%, 6%, 11% and 8% respectively.  the intergranular corrosion tests performed on samples treated at the peak strength condition were analysed using a suitable procedure able to quantify the observed defects. among the non-standard treatments, only the one at 140°c, 81h showed a very good behaviour, comparable to that for the standard t76 temper.  considering the overall performance of the materials tested, ageing at 140°c for 81 hours showed the best combination of mechanical strength and corrosion resistance. this is consistent with the technical literature which suggests the presence of  precipitates. future development of this experimental work will be a deeper study of the ageing temperature of 140°c, with other mechanical (fatigue and toughness) and stress corrosion cracking tests. furthermore, ageing temperatures close to the 140°c will be investigated by means of dilatometric and calorimetric techniques. the raw/processed data required to reproduce these findings cannot be shared at this time due to technical or time limitations. the authors certify that they have no affiliations with or involvement in any organization or entity with any financial interest (such as honoraria; educational grants; participation in speakers’ bureaus; membership, employment, consultancies, stock ownership, or other equity interest; and expert testimony or patentlicensing arrangements), or nonfinancial interest (such as personal or professional relationships, af filiations, knowledge or beliefs) in the subject matter or materials discussed in this manuscript references [1] astm 918/b918m−09, standard practice for heat treatment of wrought aluminum alloys, astm international, 2009. [2] totten, g.e. and mackenzie, d.s. (2003). handbook of aluminum, 7, physical metallurgy and processes, marcel dekker, inc, isbn: 0-8247-0494-0. [3] aluminum science and technology, asm handbook (2018), vol. 2a, asm international, isbn: 978-1-62708-158-0. [4] chinella j.f., z. guo (2011). computational thermodynamics characterization of 7075, 7039, and 7020 aluminum alloys using jmatpro, u.s. army research laboratory. [5] li, j., li, f., ma, x., li, j., liang, s. (2018). effect of grain boundary characteristic on intergranular corrosion and mechanical properties of severely sheared al-zn-mg-cu alloy, mater. sci. eng. a, 732, pp. 53-62. doi: 10.1016/j.msea.2018.06.097 [6] wang, y.l., pan, q.l., wei, l.l., li, b., wang, y. (2014). effect of retrogression and reaging treatment on the microstructure and fatigue crack growth behavior of 7050 aluminum alloy thick plate, mater. des. 55, pp. 857–863. doi: 10.1016/j.matdes.2013.09.063. [7] abúndez, a., pereyra, i., campillo, b., serna, s., alcudia, e., molina, a., blanco, a., mayén, j. (2016). improvement of ultimate tensile strength by artificial ageing and retrogression treatment of aluminum alloy 6061, mater. sci. eng. a 668, pp. 201–207, doi: 10.1016/j.msea.2016.05.062. [8] binlung, o.u., yang, j., yang, c. (2000) effects of step-quench and aging on mechanical properties and resistance to stress corrosion cracking of 7050 aluminum alloy, mater. trans., 41, pp. 783–789. [9] zuo, j., hou, l., shi, j., cui, h., zhuang, l., zhang, j., (2017). enhanced plasticity and corrosion resistance of high strength al-zn-mg-cu alloy processed by an improved thermomechanical processing, j. alloy. compd., 716, pp. 220– 230, doi: 10.1016/j.jallcom.2017.05.047. t r. gerosa et alii, frattura ed integrità strutturale, 60 (2022) 273-282; doi: 10.3221/igf-esis60.19 282 [10] park, j.k., ardell, a.j. (1984). effect of retrogression and reaging treatments on the microstructure of al-7075-t651, metall. mater. trans. a, 15, pp. 1531–1543. [11] wang, d., ni, d.r., ma, z.y. (2008). effect of pre-strain and two-step aging on microstructure and stress corrosion cracking of 7050 alloy, mater. sci. eng. a, 494, pp. 360–366, doi: 10.1016/j.msea.2008.04.023. [12] peng, g.s., chen, k.h., chen, s.y., fang, h.c. (2013). influence of dual rra temper on the exfoliation corrosion and electrochemical behavior of al-zn-mg-cu alloy, mater. corros., 64, pp. 284–289, doi: 10.1002/maco.201106234. [13] vaseghi, m., taheri, a.k., sun, i.h., kim, h.s. (2010). dynamic ageing and the mechanical response of al-mg-si alloy through equal channel angular pressing, mater. des., 31(9), pp 4076–4082. doi: 10.1016/j.matdes.2010.04.056. [14] shaeri m.h., salehi m.t., seyyedein s.h., abutalebi m.r., park j.k. (2014). microstructure and mechanical properties of al-7075 alloy processed by equal channel angular pressing combined with aging treatment, mater. des., 57(5), pp. 250–257. doi: 10.1016/j.matdes.2014.01.008. [15] zheng, l.j., li, h.x., hashmi, m.f., chen, c.q., zhang, y., zeng, m.g. (2006). c, evolution of microstructure and strengthening of 7050 al alloy by ecap combined with heat-treatment, j. mater. process. technol., 171(1), pp. 100– 107. doi: 10.1016/j.jmatprotec.2005.06.049. [16] jiang, d., liu, y., liang, s., xie, w. (2016). the effects of non-isothermal aging on the strength and corrosion behavior of al-zn-mg-cu alloy, journal of alloys and compounds, 681, pp. 57-65, doi: 10.1016/j.jallcom.2016.04.208. [17] chen, j., zhang, x., zou, l., yu, y. q. li, (2016). effect of precipitate state on the stress corrosion behavior of 7050 aluminum alloy, materials characterization, 114, pp. 1-8, doi: 10.1016/j.matchar.2016.01.022. [18] hou, w., ji, w., zhang, z., xie, j., cheng, x. (2014). the effect of homogenization temperature on the corrosion resistance of extruded 7050 al-alloy bars, journal of materials processing technology, 214(3), pp. 635-640. doi: 10.1016/j.jmatprotec.2013.11.009. [19] [19] gupta, r. k., deschamps, a., cavanaugh, m. k., lynch, s. p., birbilis, n. (2012). relating the early evolution of microstructure with the electrochemical response and mechanical performance of a cu-rich and cu-lean 7xxx aluminum alloy, journal of the electrochemical society, 159, pp. 492-502. [20] ramgopal, t., gouma p. i., frankel, g. s. (2002). role of grain-boundary precipitates and solute-depleted zone on the intergranular corrosion of aluminum alloy 7150, corrosion, 58(8), pp 687-697. [21] bs en iso 6506-1:2014, metallic materials — brinell hardness test, part 1: test method, 2014. [22] astm b557m-15, standard test methods for tension testing wrought and cast aluminumand magnesium-alloy products (metric), 2015. [23] astm g110 − 92 (reapproved 2015), standard practice for evaluating intergranular corrosion resistance of heat treatable aluminum alloys by immersion in sodium chloride + hydrogen peroxide solution, 2015. [24] gerosa, r., rivolta, b., derudi, u. (2010). influence of ageing on tensile and stress corrosion cracking behaviour of 7075 aluminum alloy plates, int. j. microstructure and materials properties, 5(1), doi: 10.1504/ijmmp.2010.032498. [25] sekhar, a. p., das, d. (2019). corrosion behavior of under-, peak-, and over-aged 6063 alloy: a comparative study, materials and corrosion, 70, pp. 2052-2063, doi: 10.1002/maco.201910961 [26] sha, g., cerezo, a. (2000). early-stage precipitation in al–zn–mg–cu alloy (7050), acta materialia. 52, pp. 4503–4516. doi: 10.1016/j.actamat.2004.06.025 [27] archambault, p., godard, d. (2000). high temperature precipitation kinetics and ttt curve of a 7xxx alloy by in-situ electrical resistivity measurements and differential calorimetry. scripta materialia, 42, pp. 675-680, doi: 10.1016/s1359-6462(99)00419-4 [28] ber, l.b. (2000). accelerated artificial ageing regimes of commercial aluminum alloys. ii: al–cu, al–zn–mg–(cu), al– mg–si–(cu) alloys, materials science and engineering a, 280, pp. 91–96, doi: 10.1016/s0921-5093(99)00661-9. [29] polmear, i. j. (2006). light alloys, elsevier, isbn: 9780080496108. [30] [30] li, b., pan, q., chen, c., yin, z. (2016). effect of aging time on precipitation behavior, mechanical and corrosion properties of a novel al−zn−mg−sc−zr alloy, trans. nonferrous met. soc. china, 26, pp. 2263−2275, doi: 10.1016/s1003-6326(16)64347-9 [31] mavropoulos, a., skolianos, s. (2018). effect of heat treatment on the corrosion behaviour of high strength aluminum alloy, international journal of advanced engineering and management research, 3(1). [32] umamaheshwer rao, a.c., vasu, v., govindaraju, m., sai srinadh, k. v. (2016). stress corrosion cracking behaviour of 7xxx aluminum alloys: a literature review, trans. nonferrous met. soc. china, 26, pp. 1447−1471, doi: 10.1016/s1003-6326(16)64220-6. << /ascii85encodepages false /allowtransparency false /autopositionepsfiles true /autorotatepages /none /binding /left /calgrayprofile (dot gain 20%) /calrgbprofile (srgb iec61966-2.1) /calcmykprofile (u.s. web coated \050swop\051 v2) /srgbprofile (srgb iec61966-2.1) /cannotembedfontpolicy /error /compatibilitylevel 1.4 /compressobjects /tags /compresspages true /convertimagestoindexed true /passthroughjpegimages true /createjobticket false /defaultrenderingintent /default /detectblends true /detectcurves 0.0000 /colorconversionstrategy /cmyk /dothumbnails false /embedallfonts true /embedopentype false /parseiccprofilesincomments true /embedjoboptions true /dscreportinglevel 0 /emitdscwarnings false /endpage -1 /imagememory 1048576 /lockdistillerparams false /maxsubsetpct 100 /optimize true /opm 1 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/hrv (za stvaranje adobe pdf dokumenata najpogodnijih za visokokvalitetni ispis prije tiskanja koristite ove postavke. stvoreni pdf dokumenti mogu se otvoriti acrobat i adobe reader 5.0 i kasnijim verzijama.) /hun 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can be opened with acrobat and adobe reader 5.0 and later.) >> /namespace [ (adobe) (common) (1.0) ] /othernamespaces [ << /asreaderspreads false /cropimagestoframes true /errorcontrol /warnandcontinue /flattenerignorespreadoverrides false /includeguidesgrids false /includenonprinting false /includeslug false /namespace [ (adobe) (indesign) (4.0) ] /omitplacedbitmaps false /omitplacedeps false /omitplacedpdf false /simulateoverprint /legacy >> << /addbleedmarks false /addcolorbars false /addcropmarks false /addpageinfo false /addregmarks false /convertcolors /converttocmyk /destinationprofilename () /destinationprofileselector /documentcmyk /downsample16bitimages true /flattenerpreset << /presetselector /mediumresolution >> /formelements false /generatestructure false /includebookmarks false /includehyperlinks false /includeinteractive false /includelayers false /includeprofiles false /multimediahandling /useobjectsettings /namespace [ (adobe) (creativesuite) (2.0) ] /pdfxoutputintentprofileselector /documentcmyk /preserveediting true /untaggedcmykhandling /leaveuntagged /untaggedrgbhandling /usedocumentprofile /usedocumentbleed false >> ] >> setdistillerparams << /hwresolution [2400 2400] /pagesize [612.000 792.000] >> setpagedevice microsoft word numero 21 articolo 5.doc d. benasciutti et alii, frattura ed integrità strutturale, 21 (2012) 37-45; doi: 10.3221/igf-esis.21.05 37 a numerical approach for the analysis of deformable journal bearings d. benasciutti, m. gallina, m. gh. munteanu dip. di ingegneria elettrica gestionale meccanica (diegm), università di udine, via delle scienze 208, 33100, udine f. flumian centro ricerche danieli (crd), danieli officine meccaniche s.p.a., via g.b. beltrame 30, 33042, buttrio (ud) abstract. this paper presents a numerical approach for the analysis of hydrodynamic radial journal bearings. the effect of shaft and housing elastic deformation on pressure distribution within oil film is investigated. an iterative algorithm that couples reynolds equation with a plane finite elements structural model is solved. temperature and pressure effects on viscosity are also included with the vogel-barus model. the deformed lubrication gap and the overall stress state were calculated. numerical results are presented with reference to a typical journal bearing configuration at two different inlet oil temperatures. obtained results show the great influence of elastic deformation of bearing components on oil pressure distribution, compared with results for ideally rigid components obtained by raimondi and boyd solution. keywords. journal bearing; finite elements; deformation; lubrication. introduction ournal bearings are machine elements in which the applied force is entirely supported by an oil film pressure. they are used in many different engineering applications, for example as supports of rotating shafts. they are considered superior to roll bearings because of their higher load-bearing capacity, higher operating angular speed, lower cost and easier manufacturing. furthermore, a proper design can assure very large service lives. the fluid-dynamic motion of oil film within the lubrication gap is described by the well-known reynolds equation [1]. explicit analytical solutions for the pressure distribution can be obtained only for asymptotic configurations (e.g. infinitely short and long journal bearings) [1, 2], while for other journal bearing configurations numerical solution of reynolds equation is required. the early studies on journal bearing performance under different operating conditions, based on the numerical solution of reynolds equation, date back to the fundamental work of raimondi and boyd (r&b) [3, 4]. they summarized their results in useful dimensionless charts ready for design, which are nowadays accepted also in code standards [5]. raimondi and boyd analysis is based on some simplified assumptions: constant viscosity of oil film, independency of viscosity on pressure and finally the postulation of perfectly rigid components (shaft and support). such assumptions, however, can be somewhat oversimplified, considering for example that the deformation of journal bearing components under the imposed oil film pressure is expected to produce a change in the real lubrication gap and thus a modification in the resultant pressure distribution. moreover, also the assumption of constant viscosity and its independence on pressure should be critically reviewed, as it is experimentally known that viscosity varies, other than with temperature, also with pressure, as summarized by many constitutive models [6]. it would be then of interest to investigate in a more detail the correlation existing between all the above-mentioned aspects and journal bearing performance and design. j http://ww.gruppofrattura.it http://dx.medra.org/10.3221/igf-esis.21.05&auth=true d. benasciutti et alii, frattura ed integrità strutturale, 21 (2012) 37-45; doi: 10.3221/igf-esis.21.05 38 in light of the above considerations, the present paper aims to present a general numerical approach to study the behavior of hydrodynamic radial journal bearings, by including in the analysis the effect of the aforementioned aspects. attention will focus on the computation of pressure distribution as a function of both temperature variation within lubrication gap and on viscosity-to-pressure sensitivity (according to the vogel-barus constitutive model [6]), as well as on components elastic flexibility. an iterative algorithm using a finite difference scheme will be developed to solve the reynolds equation, based on the deformed lubrication gap calculated by a structural finite elements (fe) model coupled with the hydrodynamic equation. the numerical approach will be able to compute the pressure distribution and the local stress field by including shaft and support elastic deformation. results will clearly emphasize the strong influence of component flexibility on journal bearing performance, with a significant reduction of the oil pressure distribution peak caused by components deformation, compared to the case of perfectly rigid elements. journal bearing: basic concepts typical configuration of a radial journal bearing under a vertical load (see fig. 1) consists of a shaft rotating inside a fixed support (choke), where it is usually fitted a bush. the nominal radial clearance between shaft (diameter d=2r) and choke (diameter d=2r) is c=r-r. the steady-state response of a journal bearing is governed by the fundamental equation of lubrication theory (reynolds equation) [1]:  d d61 33 2 h r u z ph z ph r                     (1) where h(θ )=c−e·cos(θ) is the oil film thickness as a function of angular coordinate θ, symbol e is the eccentricity, u=ωr is the tangential velocity of shaft, ω is its angular velocity, p(θ) is the resultant oil pressure distribution over angle β (attitude angle), μ is the oil dynamic viscosity. the numerical solution of reynolds equation gives the pressure distribution p(θ) within the lubrication gap together with other system operating parameters (eccentricity, minimum lubrication gap, force resultant components, etc.), as summarized for example in r&b diagrams [3, 4]. figure 1: sketch of a hydrodynamic journal bearing and parameters used in numerical simulations a http://ww.gruppofrattura.it http://dx.medra.org/10.3221/igf-esis.21.05&auth=true d. benasciutti et alii, frattura ed integrità strutturale, 21 (2012) 37-45; doi: 10.3221/igf-esis.21.05 39 during service, due to the relative velocity between shaft and support, the oil generates a pressure p(θ) over the attitude angle β, where pmax is the peak pressure that occurs at angle θpmax. the system moves in a new equilibrium configuration, where the eccentricity e characterizes the position of shaft axis with respect to the axis of fixed support, along the direction defined by the angle θh0 (which also specify the direction of minimum oil thickness h0). several design charts are available in literature [3, 4], which provide journal bearing operation parameters as a function of sommerfeld number s=(r/c)2(μn/pm), defined in terms of shaft radius r and rotational speed n, while pm=f/(ld) is the average (specific) pressure defined as the ratio of the applied radial force f and the nominal projected area (l is the length of journal bearing). such diagrams were determined by r&b through numerical solution of reynolds equation under the hypothesis of constant temperature (and thus viscosity) of lubrication film and also under the assumption of perfectly rigid components (shaft and support). an improvement of the analysis can be obtained by including in the reynolds equation a more sophisticated constitutive model for viscosity. as it is well known, viscosity of lubricating oils is very sensitive to the operating temperature, showing a quite rapid decrease with increasing temperature. in literature several viscosity-temperature equations are available (for example, the most commonly used are those by reynolds, slotte, walther, vogel, see [6]). while the most widely used viscosity-temperature chart is astm chart based on walther’s equation, the most accurate model is that of vogel, which can be written as μ=a·exp(b/(t-c)), where a, b, c are oil characteristic parameters. the lubricant viscosity also depends on pressure, especially for high pressures as in heavily loaded concentrated contacts (elastohydrodynamic lubrication). a number of attempts have been made to propose explicit formulae to synthesize lubricant pressure sensitivity. the best known equation for moderate pressures is the barus equation μ=μ0·exp(αp), in which μ0 is the viscosity at ambient atmospheric pressure and α [mpa-1] is a pressure-viscosity coefficient related to oil film pressure (typical values are α=0.01÷0.02 mpa-1). in accordance to this constitutive model, an increase in dynamic viscosity occurs for high pressures, with a solid-like behavior for very high pressures. this effect, well-known in elastohydrodynamic studies (e.g. lubricated contacts), has not been investigated in the field of journal bearings. the simultaneous coupled effect of temperature and pressure can then be evaluated by combining two of the above mentioned relationships. for example, a very simple model is the vogel-barus equation μ=μ0·exp(αp), where now the pressure-independent viscosity term μ0 is only function of temperature according to the vogel equation: μ0=a·exp(b/(t-c)). a further improvement in journal bearing study can be obtained by including in the numerical solution of reynolds equation the deformed geometry of lubrication gap, caused by elastic deformation of shaft and support under the imposed oil pressure p(θ). this would allow a more realistic estimate of the overall stress distribution on journal bearing components (shaft and housing), compared to other approaches (see for example [7]) that are based on approximate analytical (asymptotic) solutions of reynolds equation. shaft diameter d [mm] 500 support diameter d [mm] 500.5 bearing length l [mm] 300 load f [kn] 3600 angular velocity n [rpm] 65 mean pressure pm [mpa] 24 table 1: parameters used in numerical simulations this paper will develop a general numerical approach to solve reynolds equation and to compute the resultant oil pressure distribution by including both temperature and pressure effects on viscosity, as well as the effect of components elastic flexibility. a typical journal bearing configuration (see tab. 1), operating at two different inlet oil temperatures (tin=40 and 70 °c), will be investigated. a viscosity-temperature curve typical of oil iso vg 680 will be used [6]. numerical simulations n numerical simulations a plane model for the journal bearing is adopted. in the first part of this paper the hypotheses used are perfectly rigid components and viscosity function of both temperature and pressure according to the vogel-barus equation. in the second part of the paper, the pressure effect will be neglected, while shaft and i http://ww.gruppofrattura.it http://dx.medra.org/10.3221/igf-esis.21.05&auth=true d. benasciutti et alii, frattura ed integrità strutturale, 21 (2012) 37-45; doi: 10.3221/igf-esis.21.05 40 support elastic deformation will be included into the analysis. temperature and pressure effect (with rigid components) the reynolds eq. (1) is solved by using the finite difference method based on a central difference scheme. the numerical algorithm is sketched in fig. 2. the input data are: journal bearing geometry, applied force f, bearing rotational speed n, inlet oil temperature tin and pressure-viscosity coefficient α, other than the vogel-barus model μ(t, p). the unknown function in eq. (1) is the pressure p(θ) that, upon integration, must equal the resultant applied load f. however, the problem at hand is actually non-linear for several reasons. although the pressure p(θ) is the unknown function, eq. (1) does not explicitly depends on the input load f (that is, the pressure resultant), but on the eccentricity e through the lubrication gap h(θ)=c−e·cos(θ). therefore, at the beginning of the analysis a guess value of eccentricity e0 (not of the force f) must first be imposed to obtain a tentative lubrication gap and the resultant first-attempt pressure distribution. the newton-raphson rule is then applied to compute (based on the resultant of pressure fi) an eccentricity increment, δei, that is next used to update the eccentricity value for next iteration, ei+1=ei+δei, and to compute an updated lubrication gap geometry hi+1(θ) for solving again eq. (1). at each iteration, the numerically calculated pressure distribution p(θ) must also be checked for negative values, which have no physical meaning and are set to zero. this adjustment inevitably modifies the overall pressure resultant that balances the applied force, giving rise to another source of nonlinearity in problem solution. several iterations are required to converge at the correct eccentricity value (a tolerance is checked for both eccentricity and force), which gives the correct pressure distribution p(θ) that solves eq. (1) and also balances (as a resultant of pressure) the applied input force f. start hi(θ)=c-ei·cos(θ) pi(θ) with p(θ)>0 θ   dcos)(ii pf no yes output p(θ), e, h(θ) end fluid-dynamic analysis (reynolds eq.) (newton-raphson) c=r-r ei=e0 fi e1ii     ff eei=i+1 input f, μ(t,p), n, tin, r, r, α  i1i i1i i i ee ff ff e        start hi(θ)=c-ei·cos(θ) pi(θ) with p(θ)>0 θ   dcos)(ii pf no yes output p(θ), e, h(θ) end fluid-dynamic analysis (reynolds eq.) (newton-raphson) c=r-r ei=e0 fi e1ii     ff eei=i+1 input f, μ(t,p), n, tin, r, r, α  i1i i1i i i ee ff ff e        figure 2: sketch of the numerical algorithm for fluid-dynamic analysis of journal bearing (rigid components) to evaluate the effect of temperature on viscosity (and then on pressure), the journal bearing in tab. 1 was studied at two operating conditions (jb1, jb2) characterized by two different inlet temperatures (tin=40, 70 °c). two hypotheses were then adopted to compute the pressure-independent viscosity term μ0 as a function of oil temperature: in the first, using an average constant temperature tm resulting by a thermal balance inside the oil film (as in r&b approach) [1], in the second using, as a first approximation, a linear variation from inlet tin to outlet temperature tout (that has been calculated by previous thermal balance); note that in both cases the same average oil film temperature tm is obtained. http://ww.gruppofrattura.it http://dx.medra.org/10.3221/igf-esis.21.05&auth=true d. benasciutti et alii, frattura ed integrità strutturale, 21 (2012) 37-45; doi: 10.3221/igf-esis.21.05 41 configuration tin [°c] tm [°c] tout [°c] μ [pa·s] s [] e [mm] pmax [mpa] pmax [deg] h0 [mm] h0 [deg] jb1 r&b (l/d~) ↑ 40 ↓ ↑ 60 ↓ ↑ 80 ↓ ↑ 0.1678 ↓ ↑ 0.00786 ↓ 0.2352 87.30 15.50 0.0148 tm const. =0 0.2335 82.26 15.62 0.0165 26.29 tm const. =0.01 0.2286 83.74 15.03 0.0214 27.03 tin-tout lin. =0 not defined not defined 0.2392 83.17 22.82 0.0108 32.15 tin-tout lin. =0.01 0.2350 80.18 22.43 0.0150 33.76 jb2 r&b (l/d~) ↑ 70 ↓ ↑ 80 ↓ ↑ 90 ↓ ↑ 0.0655 ↓ ↑ 0.00298 ↓ 0.2447 205.50 6.60 0.0053 tm const. =0 0.2440 136.92 10.27 0.0060 16.27 tm const. =0.01 0.2412 149.54 9.34 0.0088 16.67 tin-tout lin. =0 not defined not defined 0.2453 151.08 10.85 0.0047 16.18 tin-tout lin. =0.01 0.2431 173.29 9.80 0.0069 16.47 table 2: overall comparison of results for numerical simulations with rigid components. for both temperature distributions within lubrication gap (constant tm, linear tin-tout), the vogel-barus equation has been implemented with two different pressure factors (α=0 and α=0.01). tab. 2 shows an overall comparison of obtained results, while fig. 3 compares the pressure distribution for different pressure sensitivity values for viscosity (assuming a linear temperature variation within oil film). the effect of temperature variation of oil film is now commented first. referring to jb1 configuration in tab. 2, a negligible difference is observed between the case of constant and linearly varying temperature, for both α=0 and α=0.01 values. instead, larger differences (with a 10-12% increase of pmax value) are observed for jb2 configuration, considering both α=0 and α=0.01 values. this emphasizes how the variation of oil film temperature could have some effect on pressure distribution, at least for high temperature values. considering the viscosity-temperature strong correlation, this seems to confirm that pressure distribution is more sensitive to a change of small (rather than high) viscosity values within lubrication gap. in any case, the constant temperature assumption used in r&b calculations seems too simplified. numerical solutions for constant tm and α=0 were also compared with results given by r&b charts, showing a good agreement only for jb1 configuration, while some difference characterizes jb2 configuration. the observed discrepancy can be attributed to the very low sommerfeld number (s=0.00298) characterizing jb2 configuration, which makes difficult using r&b design charts and thus can be source of interpolation errors. (a) jb1 (=0) (b) jb1 (=0.01) (c) jb2 (=0) (d) jb2 (=0.01) figure 3: effect of viscosity-to-pressure sensitivity on oil pressure distribution, calculated at two different linear temperature ranges: (a)-(b) tin=40 °c – tout=80 °c; (c)-(d) tin=70 °c – tout=90 °c http://ww.gruppofrattura.it http://dx.medra.org/10.3221/igf-esis.21.05&auth=true d. benasciutti et alii, frattura ed integrità strutturale, 21 (2012) 37-45; doi: 10.3221/igf-esis.21.05 42 in general, a non-zero viscosity-to-pressure sensitivity (α=0.01) determines a variation in the overall pressure distribution (change of attitude angle β) and in its maximum value pmax, depending on the general pressure levels attained. limiting the attention to the case with tin-tout linear temperature variation, for peak pressures pmax<100 mpa (case jb1), the pressure effect is actually negligible, as shown in fig. 3(a)-(b), with only a small decrease of the maximum pressure of about 3.5%. for larger pressure levels (case jb2), an increment of pmax of about 12% is observed, see fig. 3(c)-(d). the minimum oil thickness increment (h0=c-e) produced by the pressure effect is relevant in both cases, with a variation respectively of 28% and 32%. the obtained results can be summarized by saying that, if the influence of pressure on viscosity is taken into consideration, when α increases the peak pressure pmax increases, while the eccentricity e decreases. however, the pressureto-viscosity effect is smaller compared to temperature influence, at least for the maximum pressure peaks encountered in the examples studied. accordingly, pressure dependence will be intentionally neglected in the rest of this paper. effect of component elastic deformation (with α=0, t linear) in the second part of this work, the pressure distribution will be calculated by considering the real geometry of lubrication gap resulting from component elastic deformation. the pressure values calculated by solving the reynolds equation (1) are applied as input mechanical loads in a fe model to compute the real meatus after deformation, which is next used to solve again equation (1) with an iterative analysis scheme. a fluid-dynamic and structural coupled approach is developed in matlab environment; the flow chart in fig. 2 has been integrated with a structural fe analysis toolbox, see fig. 4. for the structural analysis, the plane fe model and the global stiffness matrices for shaft and support, [kshaft] and [ksupp], are first calculated once at the beginning of the analysis. yes output p(θ), e, h(θ) end hi'(θ)=c-ei·cos(θ)+gi(θ) fe model (mesh) [kshaft], [ksupp] start fluid-dynamic analysis (reynolds eq.) ei, pi(θ) with pi(θ)>0 θ fe structural analysis ushaft-usupp= gi(θ)    i max 1)(i max (i) max p pp h0(θ)=c-e0·cos(θ) ei=e0 pmax,i=0 no i=i+1 input f, μ(t,p), n, tin, r, r, α yes output p(θ), e, h(θ) end hi'(θ)=c-ei·cos(θ)+gi(θ) fe model (mesh) [kshaft], [ksupp] start fluid-dynamic analysis (reynolds eq.) ei, pi(θ) with pi(θ)>0 θ fe structural analysis ushaft-usupp= gi(θ)    i max 1)(i max (i) max p pp h0(θ)=c-e0·cos(θ) ei=e0 pmax,i=0 no i=i+1 input f, μ(t,p), n, tin, r, r, α figure 4: sketch of the numerical algorithm for fluid-dynamic and structural numerical analysis of journal bearing. at first iteration, a guess value of eccentricity e0 is entered into reynolds equation (1) to compute the pressure distribution p(θ) and the eccentricity e for the case of not deformable components (with the algorithm of fig. 2). the calculated pressure distribution is next applied as a boundary load in fe model, to calculate components elastic deformations; the relative difference of radial displacements between shaft and support is used to define a nominal gap as g(θ)=ushaft-usupp. a new oil film geometry h'(θ)=c-e·cos(θ)+g(θ) that incorporates mechanical deformation (thus it differs from the case of perfectly rigid components) can thus be calculated. at second iteration step, this updated gap geometry h'(θ) is entered again in eq. (1) to get a new pressure distribution p'(θ). this iterative procedure is repeated until convergence is achieved with respect to an imposed threshold tolerance on the maximum pressure, calculated at each iteration. http://ww.gruppofrattura.it http://dx.medra.org/10.3221/igf-esis.21.05&auth=true d. benasciutti et alii, frattura ed integrità strutturale, 21 (2012) 37-45; doi: 10.3221/igf-esis.21.05 43 the plane fe models of both shaft and housing used in the analysis are shown in fig. 5. the shaft is modeled by a mapped mesh with 4-nodes isoparametric linear elements, while the housing is free meshed using 3-nodes cst triangular elements. shaft and support are loaded by the same oil pressure distribution p(θ) applied on the outer and inner surfaces, respectively. the analysis assumes small displacements and a plane strain condition. material has linear elastic behavior, with properties typical of a structural steel. (a) (b) figure 5: finite element model of (a) shaft and (b) housing it is worth noting that the use of a plane fe model for the structural analysis of a journal bearing requires a special attention in modeling mechanical constraints. in fact, in a real journal bearing the applied load f and the resulting pressure distribution are actually applied along different longitudinal locations along the shaft axis. instead, in the plane fe model here adopted the external load f that balances the oil pressure is replaced by an appropriate constrain on shaft geometry. for this purpose, the shaft has been modeled with a central hole and all nodes on the inner circumference have imposed zero radial displacements; the support, instead, has all the external edges constrained. this modeling strategy, however, affects the shaft structural stiffness: a large inner radius determines an anomalous increment of shaft stiffness, while a very small inner hole gives rise to very large deformations and abnormally high reaction forces at constrained nodes. a proper sensitivity analysis has been preliminary carried out, in order to find the optimal radius of inner hole. (a) (b) figure 6: (a) pressure distribution for jb1 configuration (α=0, tin=40°c – tout=80 °c) with deformable components; (b) lubrication meatus for rigid and deformable components. as an example, the coupled fluid-structural numerical approach that includes journal bearing elastic deformation was applied for the analysis of jb1 configuration for the case of α=0 and linear temperature variation in the range tin=40°c−tout=80°c. fig. 6(a) shows the calculated pressure distribution, which has to be compared to that of perfectly rigid components shown in fig. 3(a). the comparison emphasizes that elastic deformation contributes to a reduction of about 48% (from 83 mpa to 43 mpa) of the maximum peak pressure and, accordingly, an increase in the attitude angle β (since the resultant of pressure distribution is always the same applied force f). the pressure profile, more uniform http://ww.gruppofrattura.it http://dx.medra.org/10.3221/igf-esis.21.05&auth=true d. benasciutti et alii, frattura ed integrità strutturale, 21 (2012) 37-45; doi: 10.3221/igf-esis.21.05 44 compared to the result for rigid components (r&b solution), seems to support the idea of using the average specific pressure pm as a structural design parameter, as suggested in some design codes [5]. the elastic deformation also induces an increase in eccentricity, from e=0.2392 mm (rigid components) to e=0.2953 (elastic components). fig. 6(b) compares the geometry of lubrication meatus for the case of deformable and rigid components (angles are referred to the position of minimum oil gap θh0). in particular, it is observed that for deformable components the meatus is not symmetric and that eccentricity can assume values greater than the nominal clearance c, as the elastic deformation can increase the gap between shaft and support. -200 -100 0 100 200-50 -40 -30 -20 -10 0 10 20 30 angle [deg] s tr es s [m p a] radial hoop axial von mises (a) (b) (c) figure 7: (a) radial and (b) von mises stresses in the support (mpa units); (c) stress components on inner surface of support. for what concerns the calculated mechanical stresses, fig. 7(a)-(b) show the overall distribution of radial and von mises stresses within the housing, while fig. 7(c) plots the values of stress components (radial σr, hoop σθ, axial σz) and von mises stress on the hole surface of the housing, as a function of angle θ (the vertical symmetry axis is at angle θ=0). all stress values are compressive and show a similar trend with θ. the maximum absolute radial stress is 43 mpa, exactly equal to the maximum oil pressure (pmax=43 mpa) applied on the inner hole. hoop and axial stress components have approximately similar values, with the axial stress under plane strain condition calculated as σz=ν(σθ+σr), where ν is the poisson ratio. since the stress distribution of fig. 7(c) is partly hydrostatic, the maximum von mises stress (σvm=21 mpa) is shown to be significantly lower than the maximum absolute radial stress σr=43 mpa. in particular, the elastic deformation of journal bearing elements gives a maximum von mises stress on the hole surface that is smaller than the maximum oil pressure pmax and that is comparable with the static strength of materials usually employed (for instance, white metal generally used as internal coating has a yield stress of about 50 mpa [8]). instead, in the region underneath the hole surface the overall stress state becomes “less hydrostatic” and a larger von mises stress (σvm=35 mpa) then develops. conclusions n this paper, a numerical procedure for the static analysis of hydrodynamic radial journal bearings has been developed. influence of temperature and pressure on viscosity and thus on resultant pressure distribution were studied. a mechanical plane finite element model, coupled with solution of reynolds equation, was also developed to study journal bearing structural behavior and its influence on pressure distribution. the main findings of the work can be summarized as follows:  a temperature increase was shown to give a decrease of attitude angle β and an increase in pressure peak;  an increase of viscosity-to-pressure sensitivity (α value) gives a general increase of peak pressure, especially for pressure peaks greater than about 100 mpa;  the temperature effect was shown to be generally larger than pressure effect on pressure distribution;  the elastic deformation of journal bearing elements gives a more uniform pressure distribution, with a reduced maximum pressure peak compared to the case of perfectly rigid components. in addition, the overall stress state on the surface hole in the support is partly hydrostatic, so that the maximum von mises stress is lower than the maximum radial stress modulus (i.e. the maximum peak pressure). i http://ww.gruppofrattura.it http://dx.medra.org/10.3221/igf-esis.21.05&auth=true d. benasciutti et alii, frattura ed integrità strutturale, 21 (2012) 37-45; doi: 10.3221/igf-esis.21.05 45 references [1] a.z. szeri, fluid film lubrication (2nd ed.), cambridge university press), 2011. [2] g. genta, vibration of structures and machines (3rd ed.), springer, new york, 1998. [3] j. boyd, a. a. raimondi, j. appl. mech., trans. asme, 73 (1951) 298 (part i), 310(part ii). [4] a. a. raimondi, j. boyd, trans. asle, 1(1) (1958) 159 (part i), 175 (part ii), 194 (part iii). [5] din 31652 (part 1-3), hydrodynamic plain journal bearings designed for operation under steady-state conditions, (1983). [6] g. w. stachowiak, a. w. batchelor, engineering tribology (3rd ed.), elsevier butterworth-heinemann, burlington, (2005). [7] m. ciavarella, p. decuzzi, g. demelio, g. monno, d.a. hills, j. strain anal. eng. des., 34(3) (1999) 165. [8] asm handbook, properties and selection: nonferrous alloys and special-purpose materials. asm international, 2 (1990). http://ww.gruppofrattura.it http://dx.medra.org/10.3221/igf-esis.21.05&auth=true microsoft word numero_62_art_04_3530.docx m. saltan et alii, frattura ed integrità strutturale, 62 (2022) 54-63; doi: 10.3221/igf-esis.62.04 54 investigation of the effect of yarn waste fibers and cocamide diethanolamide chemical on the strength of hot mix asphalt mehmet saltan, gizem kaçaroğlu*, öznur karadağ suleyman demirel university, turkey mehmetsaltan@sdu.edu.tr, gizemkacaroglu07@gmail.com, oznurkaradag92@gmail.com abstract. in this study, conventional bitumen tests were performed on bituminous binder modified with cocamide diethanolamide chemical at different ratios. according to results of tests, the most suitable additive ratio has been determined as 5%. however, it was concluded that indirect tensile strength and resistance to moisture of samples prepared with bituminous binder modified with 5% cocamide diethanolamide has been adversely affected. it was desired to investigate that whether these properties could be strengthened by yarn waste fibers. firstly, the effect of 0.1%, 0.2% and 0.3% yarn waste fibers on samples prepared with reference bituminous binder was investigated. obtained results showed that both indirect tensile strength and resistance to moisture of samples containing 0.1% yarn waste fiber increased. therefore, 0.1%, 0.2% and 0.3% yarn waste fibers were added to the aggregate mixture and mixing of them with bituminous binder modified with 5% cocamide diethanolamide was provided. according to obtained results, different ratios of yarn waste fibers added to aggregate mixture did not have a positive effect on moisture sensitivity. tensile strength ratio values of samples containing bituminous binder modified with 5% cocamide diethanolamide and yarn waste fibers added to the aggregate mixture did not provide specification limit. keywords. cocamide diethanolamide; yarn waste fiber; superpave; moisture sensitivity. citation: saltan, m., kaçaroğlu, g., karadağ, ö, investigation of the effect of yarn waste fibers and cocamide diethanolamide chemical on the strength of hot mix asphalt, frattura ed integrità strutturale, 62 (2022) 54-63. received: 29.03.2022 accepted: 11.07.2022 online first: 25.07.2022 published: 01.10.2022 copyright: © 2022 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. introduction lthough bituminous hot mixtures contain a relatively small amount of bituminous binder, this material plays an important role achieving the expected performance from pavements. bituminous binder has a significant effect on deformation and fatigue resistance of the pavement besides load distribution ability. loading conditions and temperature are two important parameters in terms of the deformation resistance and stiffness of bituminous binder, a material which have viscoelastic and thermoplastic properties. bituminous binder exhibits variable behaviors depending on climate and environmental conditions because of its thermoplastic structure. for instance, this material is hard and brittle in cold weather but soft and fluid in hot weather [1]. these properties which belong to bitumen, also are transferred to hot a https://youtu.be/-wtu444avau m. saltan et alii, frattura ed integrità strutturale, 62 (2022) 54-63; doi: 10.3221/igf-esis.62.04 55 mix asphalt when bituminous binder mixed with aggregates. variable behaviors of bituminous binder cause decrease in the performance of pavement. these decreases in the performance are caused by deformations in the pavement. in order to prevent deformations by improving pavement performance, bituminous binder has been modified with various additives and many studies which aim to improve bituminous binder properties have been carried out [2-7]. not only the properties of bituminous binders, but also the moisture which the mixture is exposed to can cause deformations, too. for example, loss of strength and permanent deformation in the pavement are problems which caused by moisture [8]. there are also studies in the literature which have investigated the effects of different materials on the moisture sensitivity of hot mix asphalt [9-13]. it is considered that surfactant additives are suitable for use in modification of bituminous binders as they can also meet the mentioned expectations while protecting the mechanical properties of the mixture. due to the properties of the existing surfactants and their possible effects on the rheological properties of the bituminous binders, the usage of surfactants to modify the bituminous binder can significantly change the binder performance. therefore, interest in researches which are conducted on the usage of surfactants with the aim of modify the bitumen is quite a lot [14-18]. in addition, various fibers have been used for many years on the purpose of strengthen the pavement. it is known that the fibers increase the stability, resistance to fatigue and rutting and provide benefits in preventing the formation of cracks [19]. there are studies in which fibers of different properties and forms are used in hot mix asphalt [20-23]. in one of the studies in the literature, by emphasizing to the fact that the use of waste fibers which emerge from the textile industry abundantly will contribute to the improvement of the pavement, waste polyester fibers have been used [24]. in another study, the effects of various fibers used in mixtures on the mechanical properties of the hot mix asphalt have been examined [25]. besides all these, it is known that the addition of fibers increases the fracture toughness of asphalt concrete [26]. fracture toughness is a measure of the resistance to propagation of cracks observed in materials [27]. limited availability of studies reported on the fracture properties of fiber-reinforced asphalt mixtures show that addition of fibers can positively affect the toughness resistance of asphalt mixtures depending on the type and usage rates of fibers [28-36]. in this study, cocamide diethanolamide (cdea) was added to bituminous binder at the ratios of 1%, 3% and 5%. with the help of a temperature – controlled high shear mixer, cdea and bituminous binder were homogeneously mixed for 1 hour at 2000 rpm and 165 ℃. conventional bitumen tests were carried out to determine the consistency of modified bituminous binders. according to the obtained results, the most suitable cocamide diethanolamide ratio was determined as 5%. samples suitable for asphalt surface course were prepared by superpave volumetric mix design method. indirect tensile strength test was performed on the prepared samples. the resistance to moisture of the samples was determined according to aashto t 283 standard. indirect tensile strength and the resistance to moisture of samples prepared with bituminous binder modified with 5% cdea were negatively affected. to this respect, it was desired to investigate that whether these properties could be strengthened by yarn waste fibers. primarily, the indirect tensile strength and the resistance to moisture of the samples containing 0.1%, 0.2% and 0.3% yarn waste fibers with reference bituminous binder were investigated. according to the obtained results, a positive effect was observed on the indirect tensile strength and the resistance to moisture of the samples containing 0.1% yarn waste fiber. then, 0.1%, 0.2% and 0.3% yarn waste fibers were added to the aggregate mixture and mixing of them with bituminous binder modified with 5% cdea were provided. however, the fibers added to the aggregate mixture did not have a positive effect on the indirect tensile strength and moisture sensitivity. materials and bitumen modification aggregates he limestone aggregates have been used in the study. specific bulk gravity [ts en 1097-6], water absorption, los angeles abrasion test [astm c 131-03] and micro – deval abrasion test [ts en 1097-1] were performed on limestone aggregates used in experimental studies. the results of tests applied on coarse aggregates, fine aggregates and filler are shown in tab. 1. bituminous binder bituminous binder which has a penetration class of 50/70 has been used in the study. penetration [ts en 1426], softening point [ts en 1427], ductility [ts en 13589] and specific gravity [ts en 15326+a1] tests were performed on the bituminous binder used in the study. obtained results are given in tab. 2. t m. saltan et alii, frattura ed integrità strutturale, 62 (2022) 54-63; doi: 10.3221/igf-esis.62.04 56 properties coarse aggregates fine aggregates filler specific gravity (g/cm3) 2.701 2.606 2.501 resistance (los angeles wear loss) (%) 18.48 resistance (micro-deval wear loss) (%) 9.95 table 1: physical properties of coarse aggregates, fine aggregates and filler. test 50/70 bituminous binder standard penetration (25˚c) 50 ts en 1426 softening point 49.8 ts en 1427 ductility (5cm/min) >100 ts en 13589 specific gravity (g/cm3) 1.021 ts en 15326+a1 table 2: properties of bituminous binder. yarn waste fibers there are a wide variety of fibers that are used to create yarns and they come from a variety of sources. yarns are comprised of a group of fibers twisted together to form a continuous strand. the fibers used to create these yarns include animal fibers and plant fibers which are named as natural fibers, besides synthetic fibers. all materials in the form of clippings, pieces, fibers are described as textile waste. textile wastes can be collected under three main groups. the first is wastes from artificial yarn factories, the second is textile manufacturing waste, and the third is textile waste of consumers [37]. it has been known that, a lot of textile waste comes out of the factories, houses, workshops. disposal of these wastes into the environment causes both environmental pollution and the recyclable wastes to disappear. in the study, the effect of using of yarn waste fibers which comprise the majority of textile wastes on the strength of the pavement was evaluated. the yarn waste fibers were added to the aggregate mixture at the ratios of 0.1%, 0.2% and 0.3%, after they were cut in 2.5 cm size (fig. 1). figure 1: yarn waste fibers which cut to the size of 2.5 cm. cocamide diethanolamide cocamide diethanolamide (cdea) material was used in the modification of bituminous binder. cdea is known as a surfactant material and has the chemical formula in the way that ch3(ch2)nc(=o)n(ch2ch2oh)2. cdea is a water – soluble derivative of a mixture of fatty acids obtained from coconut oils. it is a non – ionic material that increases viscosity and provides foam stabilization in anionic based systems such as soaps, shampoos, cosmetics. cdea decreases the viscosity by thinning the bituminous binder because it is a smaller molecule material compared to bitumen which has a long – chain and high flow resistance. the properties of cdea chemical are shown in tab. 3. m. saltan et alii, frattura ed integrità strutturale, 62 (2022) 54-63; doi: 10.3221/igf-esis.62.04 57 properties 50/70 bituminous binder boiling point 169-275˚c melting point 23-35 ˚c specific gravity (g/cm3) 0.976-0.99 ph 9 (1% solution) table 3: properties of cdea chemical. bitumen modification cocamide diethanolamide was added to bituminous binder at the ratios of 1%, 3% and 5%. different parameters have been tried to modify the chemical material with bituminous binder. conventional bitumen tests were carried out on modified bituminous binders and the most suitable parameter was selected. with the help of a temperature – controlled high shear mixer, cdea and bituminous binder were homogeneously mixed for 1 hour at 2000 rpm and 165 ℃. methods ethods used in this study can be grouped as follows; aggregate tests, conventional bitumen tests and evaluation of moisture sensitivity of samples prepared by using superpave volumetric mix design method. conventional bitumen tests penetration, softening point, ductility and specific gravity tests were performed on bituminous binders modified with cdea. evaluation of moisture sensitivity of bituminous hot mixtures superpave volumetric mix design method consists of four steps: material selection, aggregate gradation, optimum bituminous binder content and moisture sensitivity. during all these steps, the temperatures and traffic volume of isparta province where asphalt surface course will serve have been taken into consideration. it is estimated that the number of 20 years of traffic in isparta province where asphalt surface course will serve is more than 30*106 esals. within the scope of study, optimum bituminous binder content has been determined using volumetric mix design. ndesign has been selected as 125 gyros in accordance with the 20 – year traffic load. while the optimum bituminous binder content is calculated, vma (min 14%), vfa (65 – 75%) limit values and 4% air void criteria have been taken into consideration. the final step of the superpave volumetric mix design method is to determine the moisture sensitivity of the prepared mixtures. in order to determine the moisture sensitivity, indirect tensile strength (its) test is performed on the prepared mixtures in accordance with aashto t-243 standard. according to the determined optimum bituminous binder content, the prepared mixtures are compacted with superpave gyratory compactor. two sets which have three samples are prepared and while one of them is conditioned, other set is unconditioned. the indirect tensile strength (its) values of the samples are determined. for all samples, unconditioned (itsdry), conditioned (itswet) values are recorded and the tensile strength ratio (tsr) values are calculated. the limit of tsr values is 80% [38]. results and discussion results of conventional bitumen tests o determine the basic properties of samples, softening point, penetration ductility and specific gravity tests have been applied on all modified samples. test results are given in tab. 4. as can be seen from the table, the penetration values have increased according to the reference binder as the cdea ratio increases for each sample. also, the softening point temperatures have decreased according to the reference binder as the cdea ratio increases. the reference bituminous binder and all modified samples have indicated elongation without breakage by exceeding the specification limit value of 100 cm at 25 °c. m t m. saltan et alii, frattura ed integrità strutturale, 62 (2022) 54-63; doi: 10.3221/igf-esis.62.04 58 sample penetration (25˚c) softening point (˚c) ductility (5cm/min) specific gravity (g/cm3) reference 50 49.8 >100 1.021 1% cdea 53 47.8 >100 1.028 3% cdea 66 45.5 >100 1.015 5% cdea 71 44.5 >100 1.022 table 4: results of conventional bitumen tests. figure 2: graphs of reference bituminous binder. figure 3: graphs of reference bituminous binder modified with 5% cdea. m. saltan et alii, frattura ed integrità strutturale, 62 (2022) 54-63; doi: 10.3221/igf-esis.62.04 59 evaluation of moisture sensitivity according to the results of conventional bitumen tests, optimum additive ratio was determined as 5%. in order to provide the 4% air void criteria of the mixtures prepared by using superpave volumetric mix design method, bituminous binders at the rates of 4.5%, 5%, 5.5% and 6% were added to the aggregates and they were mixed until completely coated with bituminous binder. then the mixture was compacted with gyratory compactor. firstly, the amount of bituminous binder corresponding to 4% air void was determined from the air void graph. it was checked whether the determined amount of bituminous binder has a minimum value of 14% on the vma graph and 65 – 75% on the vfa graph. after all these steps were carried out, the optimum bitumen content for reference bituminous binder and bituminous binder modified with 5% cdea were determined as 5.20% and 5.25%, respectively. graphs of obtained results are given in fig. 2 – 3. the final step of the superpave volumetric mix design method is to determine the moisture sensitivity of the prepared mixtures. in order to determine the moisture sensitivity, indirect tensile strength (its) test was performed on the prepared mixtures according to aashto t-283 standard. unconditioned and conditioned tensile strengths and tsr values were found for samples. tsr value of the samples prepared with reference bituminous binder is above the specification limit, 80%. the obtained results are given in tab. 5. name of sample itsdry(kpa) itswet(kpa) tsr (%) reference sample 798 725 91 modified sample with 5% 464 table 5: indirect tensile strength of samples. itswet strength of samples prepared by using bituminous binder modified with 5% cdea could not be tested. in the conditioning stage, after the samples were placed in a water bath which have 60 ℃ temperature, separation of the aggregates from the bituminous binder was observed (fig. 4). when the bituminous binder modified with cdea which is a chemical material was exposed to a water bath which have 60 ℃ temperature, it has been observed that the adhesion between bituminous binder and aggregates has decreased. according to the obtained results, it was concluded that the strength of samples prepared with bituminous binder modified with 5% cdea has been adversely affected. figure 4: sample prepared by using bituminous binder modified with 5% cdea, after conditioning. after this step, the indirect tensile strength and the resistance to moisture of the samples prepared by using the reference bituminous binder and 0.1%, 0.2% and 0.3% yarn waste fibers were investigated. according to the obtained results, as 0.1% yarn waste fiber added to the aggregate mixture prepared with the reference bituminous binder increased the interlocking, the indirect tensile strength of mixtures increased (fig. 5). the graph in fig. 5 shows that the indirect tensile strength of the samples prepared with 0.3% yarn waste fiber added to the aggregate mixture with the reference bituminous binder decreased compared to the reference samples. it was observed that the resistance to moisture of the samples prepared with 0.1% yarn waste fibers added to the aggregate mixture and reference bituminous binder increased (fig. 6). according to this, yarn waste fibers which were added to the aggregate mixtures and reference bituminous binder have a positive effect on the indirect tensile strength and moisture sensitivity of the mixtures. so, it has been thought that it can also have a positive effect on the aggregate mixtures containing bituminous binder modified with 5% cdea. as seen in fig. 4, samples prepared with bituminous binders modified with 5% cdea did not provide strength in conditioned conditions. to improve this situation, 0.1%, 0.2% and 0.3% yarn waste fibers in 2.5 cm size were added to the m. saltan et alii, frattura ed integrità strutturale, 62 (2022) 54-63; doi: 10.3221/igf-esis.62.04 60 aggregate mixture and samples were prepared with this mixture and bituminous binder modified with 5% cdea. samples containing bituminous binder modified with 5% cdea and 0.1% yarn waste fibers were broken after conditioning (fig. 7). 0.1% yarn waste fibers which were added to the aggregate mixture did not have a positive effect on the indirect tensile strength and moisture sensitivity. figure 5: indirect tensile strength values of samples prepared with yarn waste fibers added to mixtures prepared with reference bituminous binder. figure 6: tensile strength ratios of samples prepared with yarn waste fibers added to mixtures prepared with reference bituminous binder. figure 7: samples prepared by using bituminous binder modified with 5% cdea and 0.1% yarn waste fibers, after conditioning. m. saltan et alii, frattura ed integrità strutturale, 62 (2022) 54-63; doi: 10.3221/igf-esis.62.04 61 samples prepared with bituminous binder modified with 5% cdea and 0.2%, 0.3% yarn waste fibers gave wet strength after conditioning. however, these samples did not meet the tsr specification limit (tab. 6). according to the obtained results, the indirect tensile strength and moisture sensitivity of the samples prepared with bituminous binder modified with 5% cdea could not be increased by using different ratios of yarn waste fibers. since samples containing bituminous binder modified with 5% cdea and 0.1%, 0.2% and 0.3% yarn waste fibers do not meet the specification limits, they are not suitable for use in pavement. name of sample itsdry (kpa) itswet (kpa) tsr (%) reference sample 798 725 91 sample modified with 5% cdea 464 sample modified with 5% cdea+0.1% yarn waste fibers 339 34 sample modified with 5% cdea+0.2% yarn waste fibers 376 41 sample modified with 5% cdea+0.3% yarn waste fibers 356 49 table 6: indirect tensile strength and tsr values of samples. conclusions he obtained results after the tests were interpreted as follows: according to the consistency tests, when compared to the reference binder, bituminous binders modified with cdea chemical at the ratios of 1%, 3% and 5% are more fluid and softer. the results of softening point and penetration tests are consistent with each other. it is known that, bituminous binders which have low softening point and high penetration values can be used for pavement construction in cold regions. so, it can be said that, bituminous binders modified with cdea are suitable for cold climatic regions. the strength of samples prepared with bituminous binder modified with 5% cdea could not be calculated. asphalt mixtures prepared with bituminous binder modified with 5% cocamide diethanolamide decreased resistance to moisture sensitivity. it is concluded that the samples prepared with bituminous binder modified with 5% cdea are not suitable for use in the asphalt surface course solitary. in order to reduce the negative effect on the indirect tensile strength and moisture sensitivity of the samples prepared by using bituminous binder modified with 5% cdea, it was considered to add yarn waste fibers to the aggregate mixtures. therefore, in order to examine the effect of yarn waste fiber added to the aggregate mixture, 0.1%, 0.2% and 0.3% yarn waste fibers were added to the aggregate mixtures and samples were prepared by using the reference bituminous binder. according to the obtained results, the indirect tensile strength and the resistance to moisture of the samples prepared by using 0.1% yarn waste fiber added to the aggregate mixture and the reference bituminous binder increased. therefore, 0.1%, 0.2% and 0.3% yarn waste fibers were added to increase the indirect tensile strength and to decrease the resistance to moisture of the samples prepared with bituminous binder modified with 5% cdea. although the strength values of the samples prepared with 0.1%, 0.2% and 0.3% yarn waste fibers added to aggregate mixture and the bituminous binder modified with 5% cdea were measured after conditioning, the tsr values did not meet the specification limit. according to obtained results, even if usage of different ratios of yarn waste fibers alone are suitable for hot mix asphalt, it has been seen that the usage of different ratios of yarn waste fibers together with bituminous binder modified with 5% cocamide diethanolamide does not provide an additional benefit. based on the observed positive effects of the usage of different fibers on the fracture toughness of asphalt concrete, it is considered to investigate the effect of yarn waste fiber on toughness resistance of asphalt mixtures in future studies. fracture toughness can be improved by using different ratios of yarn waste fibers in hot mix asphalt. however, it is considered that cdea additive will have no positive effect on fracture toughness of material, since the usage of it does not have a positive effect on strength of asphalt mixtures. references [1] arslan, d., gürü, m. and çubuk, m. (2012). improvement of bitumen and bituminous mixtures performance properties with organic based zincphosphate compound, j. fac. eng. archit. gazi. univ., 27, pp. 459-466. [2] gama, d. a., junior, j. m. r., de melo, t. j. a. and rodrigues, j. k. g. (2016). rheological studies of asphalt modified with elastomeric polymer, constr. build. mater., 106, pp. 290-295. doi: 10.1016/j.conbuildmat.2015.12.142. t m. saltan et alii, frattura ed integrità strutturale, 62 (2022) 54-63; doi: 10.3221/igf-esis.62.04 62 [3] lin, y., hu, c., adhikari, s., wu, c. and yu, m. (2019). evaluation of waste express bag as a novel bitumen modifier, appl. sci., 9, p. 1242. doi: 10.3390/app9061242. [4] eskandarsefat, s., hofko, b., rossi, c. o. and sangiorgi, c. (2019). fundamental properties of bitumen binders containing novel cellulose-based poly-functional fibres, compos. part b, 163, pp. 339-350. doi: 10.1016/j.compositesb.2018.11.031. [5] cuadri, a. a., navarro, f. j. and partal, p. (2020). synergistic ethylcellulose/polyhosphoric acid modification of bitumen for paving applications, mater. struct., 53 (6). doi: 10.1617/s11527-019-1437-7. [6] azahar, w. n. a. w., jaya, r. p., hainin, m. r., bujang, m. and ngadi, n. (2016). chemical modification of waste cooking oil to improve the physical and rheological properties of asphalt binder, constr. build. mater., 126, pp. 218226. doi: 10.1016/j.conbuildmat.2016.09.032. [7] rossi, c. o., caputo, p., loise, v., miriello, d., teltayev, b. and angelico, r. (2017). role of a food grade additive in the high temperature performance of modified bitumens, colloids surf. a physicochem. eng. asp., 532, pp. 618-624. doi: 10.1016/j.colsurfa.2017.01.025. [8] hamzah, m. o., kakar, m. r. and hainin, m. r. (2015). an overview of moisture damage in asphalt mixtures, j. technol., 73 (4). doi: 10.11113/jt.v73.4305. [9] hamedi, g. h. (2018). effects pf polymeric coating the aggregate surface on reducing moisture sensitivity of asphalt mixtures, int. j. civ. eng., 16 (9), pp. 1097-1107. doi: 10.1007/s40999-017-0263-y. [10] hamedi, g. h., nejad, f. m. and oveisi, k. (2016). estimating the moisture damage of asphalt mixture modified with nano zinc oxide, mater. struct., pp. 1-10. doi: 10.1617/s11527-015-0566. [11] nasrekani, a. a., nakhaei, m., naderi, k., fini, e. and aflaki, s. (2017). improving moisture sensitivity of asphalt concrete using natural bitumen (gilsonite), in: transportation research board 96th annual meeting, transportation research board: washington, dc., p.16. [12] kanitpong, k., charoentham, n. and likitlersuang, s. (2012). investigation on the effects of gradation and aggregate type to moisture damage of warm mix asphalt modified with sasobit, int. j. pavement eng., 13 (5), pp. 451-458. doi: 10.1080/10298436.2011.565058. [13] hamedi, g. h. and tahami, s. a. (2018). the effect of using anti-stripping additives on moisture damage of hot mix asphalt, int. j. adhes. adhes., 81, pp. 90-97. doi: 10.1016/j.ijadhadh.2017.03.016. [14] chomicz-kowalska, a., mrugala, j. and maciejewski, k. (2017). evaluation of foaming performance of bitumen modified with the addition of surface active agent, iop conf. ser. mater. sci. eng., 245 (3). doi: 10.1088/1757-1899x/245/3/032086. [15] mazurek, g. and nowakowski, k. (2015). the evaluation of sma mixture properties with the surface-active agent in vma technology, proc. eng. matbud, 108, pp. 22-29. doi: 10.1016/j.proeng.2015.06.115. [16] kakar, m. r., hamzah, m. o., akhtar, m. n. and woodward, d. (2016). surface free energy and moisture susceptibility evaluation of asphalt binders modified with surfactant-based chemical additive, j. clean. prod., 112, pp. 2342-2353. doi: 10.1016/j.jclepro.2015.10.101. [17] perez-martinez, m., moreno-navarro, f., martin-marin, j., rios-losada, c. and rubio-gamez, m. c. (2014). analysis of cleaner technologies based on waxes and surfactant additives in road construction, j. clean. prod., 65, pp. 374-379. doi: 10.1016/j.jclepro.2013.09.012. [18] iwanski, m., cholewinska, m. and mazurek, g. (2017). impact of the ageing on viscoelastic properties of bitumen with the liquid surface active agent at operating temperatures, iop conference series-materials science and engineering, 245 (3). [19] mcdaniel, r.s. (2015). fiber additives in asphalt mixtures, nchrp synthesis of highway practice, 475, pp. 1-67. [20] abiola, o. s., kupolati, w. k., sadiku, e. r. and ndambuki, j. m. (2014). utilisation of natural fibre as modifier in bituminous mixes: a review, constr. build. mater., 54, pp. 305-312. doi: 10.1016/j.conbuildmat.2013.12.037. [21] serin, s., morova, n., saltan, m. and terzi, s. (2012). investigation of usability of steel fibers in asphalt concrete mixture, constr. build. mater., 36, pp. 238-244. doi: 10.1016/j.conbuildmat.2012.04.113. [22] klinsky, l. m. g., kaloush, k. e., faria, v.c. and bardini, v. s. s. (2018). performance characteristic of fiber modified hot mix asphalt, constr. build. mater., 176, pp. 747-752. doi: 10.1016/j.conbuildmat.2018.04.221. [23] bdour, a. n., khalayleh, y. and al-omari, a. a. (2015). assessing mechanical properties of hot mix asphalt with wire wool fibers, adv. civ. eng. doi: 10.1155/2015/795903. [24] anurag, k., xiao, f. and amirkhanian, s. n. (2009). laboratory investigation of indirect tensile strength using roofing polyester waste fibers in hot mix asphalt, constr. build. mater., 23 (5), pp. 2035-2040. doi: 10.1016/j.conbuildmat.2008.08.018. m. saltan et alii, frattura ed integrità strutturale, 62 (2022) 54-63; doi: 10.3221/igf-esis.62.04 63 [25] slebi-acevedo, c. j., lastra-gonzales, p., pascual-munoz, p. and castro-fresno, d. (2019). mechanical performance of fibers in hot mix asphalt: a review, constr. build. mater., 200, pp. 756-769. doi: 10.1016/j.conbuildmat.2018.12.171. [26] cao, p., tang, c., liu, z., shi, f., wang, z., wang, x. and zhou, c. (2022). study on fracture behaviour of basalt fibre reinforced asphalt concrete with plastic coupled cohesive model and enhanced virtual crack closure technique model, int. j. pavement eng., pp. 1-21. doi: 10.1080/10298436.2022.2080830. [27] landes, j. (2012). fracture toughness testing methods, characterization of materials, e.n. kaufmann (ed.), john wiley&sons, inc, new jersey, u.s. doi: 10.1002/0471266965.com024.pub2. [28] hajiloo, h. r., karimi, h. r., aliha, m. r. m., zanjirani farahani, h., salehi, s. m., hajiloo, m. and jafari haghighatpour, p. (2022). crack resistance of fiber‐reinforced asphalt mixtures: effect of test specimen and test condition, ffems, 45 (3), pp. 921-937. doi: 10.1111/ffe.13647. [29] pirmohammad, s., amani, b. and shokorlou, y. m. (2020). the effect of basalt fibres on fracture toughness of asphalt mixture, ffems, 43 (7), 1446-1460. doi: 10.1111/ffe.13207. [30] pirmohammad, s., shokorlou, y. m. and amani, b. (2020). laboratory investigations on fracture toughness of asphalt concretes reinforced with carbon and kenaf fibers, eng. fract. mech., 226, 106875. doi: 10.1016/j.engfracmech.2020.106875. [31] pirmohammad, s., shokorlou, y. m. and amani, b. (2020). influence of natural fibers (kenaf and goat wool) on mixed mode i/ii fracture strength of asphalt mixtures, constr. build. mater., 239, 117850. doi: 10.1016/j.conbuildmat.2019.117850. [32] pirmohammad, s. and mengharpey, m. h. (2020). influence of natural fibers on fracture strength of wma (warm mix asphalt) concretes using a new fracture test specimen, constr. build. mater., 251, 118927. doi: 10.1016/j.conbuildmat.2020.118927. [33] mohammed, m., parry, t., thom, n. and grenfell, j. (2020). microstructure and mechanical properties of fibre reinforced asphalt mixtures, constr. build. mater., 240, 117932. doi: 10.1016/j.conbuildmat.2019.117932 [34] motamedi, h., fazaeli, h., aliha, m. r. m. and amiri, h. r. (2020). evaluation of temperature and loading rate effect on fracture toughness of fiber reinforced asphalt mixture using edge notched disc bend (endb) specimen, constr. build. mater., 234, 117365. doi: 10.1016/j.conbuildmat.2019.117365 [35] aliha, m. r. m., razmi, a. and mansourian, a. (2017). the influence of natural and synthetic fibers on low temperature mixed mode i+ ii fracture behavior of warm mix asphalt (wma) materials, eng. fract. mech., 182, pp. 322-336. doi: 10.1016/j.engfracmech.2017.06.003 [36] mansourian, a., razmi, a. and razavi, m. (2016). evaluation of fracture resistance of warm mix asphalt containing jute fibers, constr. build. mater., 117, pp. 37-46. doi: 10.1016/j.conbuildmat.2016.04.128 [37] kozak, m. (2010). investigation of the usage of textile waste as construction materials, electronic journal of construction technologies, 6 (1), pp. 62-70. [38] federal highway administration, 2000. superpave fundamentals: reference manual, fhwa, nhi course # 131053, washington, dc. << /ascii85encodepages false /allowtransparency false /autopositionepsfiles true /autorotatepages /none /binding /left /calgrayprofile (dot gain 20%) /calrgbprofile (srgb iec61966-2.1) /calcmykprofile (u.s. web coated \050swop\051 v2) /srgbprofile (srgb iec61966-2.1) /cannotembedfontpolicy /error /compatibilitylevel 1.4 /compressobjects /tags /compresspages true /convertimagestoindexed true /passthroughjpegimages true /createjobticket false /defaultrenderingintent /default /detectblends true /detectcurves 0.0000 /colorconversionstrategy /cmyk /dothumbnails false /embedallfonts true /embedopentype false /parseiccprofilesincomments true /embedjoboptions true /dscreportinglevel 0 /emitdscwarnings false /endpage -1 /imagememory 1048576 /lockdistillerparams false /maxsubsetpct 100 /optimize true /opm 1 /parsedsccomments true /parsedsccommentsfordocinfo true 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/hrv (za stvaranje adobe pdf dokumenata najpogodnijih za visokokvalitetni ispis prije tiskanja koristite ove postavke. stvoreni pdf dokumenti mogu se otvoriti acrobat i adobe reader 5.0 i kasnijim verzijama.) /hun 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/pdfxoutputintentprofileselector /documentcmyk /preserveediting true /untaggedcmykhandling /leaveuntagged /untaggedrgbhandling /usedocumentprofile /usedocumentbleed false >> ] >> setdistillerparams << /hwresolution [2400 2400] /pagesize [612.000 792.000] >> setpagedevice microsoft word numero_37_art_31 y. hos et alii, frattura ed integrità strutturale, 37 (2016) 234-240; doi: 10.3221/igf-esis.37.31 234 focussed on multiaxial fatigue and fracture growth of long fatigue cracks under non-proportional loadings – experiment and simulation y. hos, m. vormwald technische universität darmstadt, materials mechanics group, franziska-braun-straße 3 64287 darmstadt/germany hos@wm.tu-darmstadt.de, vormwald@wm.tu-darmstadt.de abstract. an experimental campaign was carried out on thin-walled tubes under tension and torsion. the results from experiments are measured and compared. it is observed that cracks follow a shear-dominated growth pattern with increasing crack length, instead of a tension-dominated one. the experiments are performed with high amplitudes applied to the specimens, resulting in large cyclic plastic deformations and crack growth rates up to 10-3 mm/cycle. stress intensity factors were calculated for the proportional loading case. keywords. multiaxial fatigue; non-proportional loadings; crack growth; fracture mechanics; experimental mechanics; numerical simulation introduction atigue crack growth under non-proportional mixed-mode loading depends on many factors. a recently issued review [1] identified seven such factors. the first one, mode-mixity, is arguably the most obvious one. the maximum tangential stress criterion has been supported by several experimental results [2-4], whereas roberts and kibler [5] have discovered cases where maximum shear stress criterion is more suitable. natural mode i cracks were produced firstly, and then loaded with mode ii loading, without observing a change in the direction of the crack. only the maximum shear stress criterion can model this behavior. it could be concluded that increasing mode-mixity leads to a tendency for a shear-dominated crack growth. secondly, the material itself is a dominant factor. for example, qian and fatemi [2] conclude that “mode ii crack growth occurs more often in aluminum alloys than in steels”. thirdly, the magnitude of cyclic plastic deformation is an influencing factor, as increasing cyclic plastic deformation creates a tendency towards shear-dominated crack growth. results published by tanaka [6], brown and miller [7], otsuka and tohgo [8], socie [9] and doquet and bertlino [10] support this argument. the fourth factor to be specified is the crack closure, which is directly dependent on the cyclic plastic deformation. roughness along the crack front leads sometimes to the interlocking of the crack fronts, and interlocking results in a shielding of the crack tip from mode ii (especially in low stress intensity factor ranges). moreover, the mean stress effect (the fifth factor) is very relevant to the crack closure and therefore needs to be taken into account. in addition, the geometry of a structure is obviously a very important factor in every type of crack growth phenomenon. finally, the mode-mixity changes along the crack front in three-dimensional cases. with so many plastic effects playing a role in crack growth under non-proportional loading, a crack tip parameter, which takes plasticity into account, has to be used in further research. several studies [11-15] have shown that j is a very f y. hos et alii, frattura ed integrità strutturale, 37 (2016) 234-240; doi: 10.3221/igf-esis.37.31 235 successful parameter to model fatigue crack growth under proportional and non-proportional loadings, therefore an opportunity might arise to extend this solution to long cracks. the j-integral should be interpreted according to the definitions of dowling and begley [16], wüthrich [17] and hertel et al. [18]. however, short cracks usually grow in a single plane without significant kinks or curvature, so the modeling could be simplified to an iterative search of this plane. more about the plastic simulations can be found in [19, 20]. a research project was launched on the abovementioned basis, seeking further knowledge on the mechanisms. this paper covers the achievements of this project. the investigation embarked on high amplitude loading, accompanied by large cyclic plastic deformation, high crack growth rates and short fatigue lives, and the cracks being all naturally produced. description of the problem onstant amplitude fatigue tests have been performed on thin-walled tubes which were put under either uniaxial tension-compression load, or torsional load, or a combination of both (proportional and non-proportional). the specimen geometry is depicted in fig. 1. longitudinally welded tubes were sawed and the starter notch was machined onto the specimen. the centers of holes at the ends of the starter notch are 10 mm apart from each other (length of an arc at the outer surface). the notch was positioned opposite to the weld. figure 1: specimen geometry inducing cyclic plastic deformation was a primary goal in the experiments. for this purpose, the tubes were ordered to be manufactured from the low strength constructional steel s235. the experimental results are shown in fig. 2. the blue points in fig. 2 correspond to strain-controlled tests and they show the upper end of the hysteresis at each strain level, measured at half-life each. a more detailed discussion of material properties could be found in previous works of the authors. [19, 20, 25, 26]. figure 2: cyclic stress-strain curves of the used material. c y. hos et alii, frattura ed integrità strutturale, 37 (2016) 234-240; doi: 10.3221/igf-esis.37.31 236 e in mpa rp0.2 in mpa k’ in mpa n’ 210000 378 680 0.11 table 1: mechanical properties of s235 two different types of crack growth experiments were performed. in the first series of experiments, photos of the specimen were taken during experiment at predefined intervals. (length of the interval is dependent on the nature of the experiment) three cameras were installed in front of the starter notch, one facing the notch directly, the second with a 45° angle to the right and the third with a 45° angle to the left. after a certain number of cycles, the experiment was stopped, and a load corresponding to 90% of the maximum cyclic load was applied. during the short hold time, the photos of the specimen surface were taken. the specimen was unloaded again and the cyclic loading continued. the pictures were evaluated after the experiment, with the help of the laser-engraved dot pattern on the surface. five different loading sequences were used in the experiments: pure tension-compression loading, pure torsion loading, proportional loading resulting from the superposition of these two and out-of-phase loading with phase angles of 45° and 90°. the experiments were conducted under load/moment control, using a servo-hydraulic, four-pillar tension-torsion machine, with frequencies ranging between 0.25 hz and 2 hz. a temperature of 21°c and a relative air humidity of 50% were kept constant. the cracks were assumed to be through-wall cracks with a straight crack front. the crack length is defined as the arc length, where the crack starts at the crack initiation location in each test. the scheme of the presentation of the results in references [20] and [22] were taken as a guide, with crack 1 being left and crack 3 being right. in the second series of experiments, the tests were interrupted in the fashion that was described above, only this time, the whole cycles were recorded and analyzed applying the digital image correlation (dic) technique. more details about dic can be found in references [19] and [20]. later, the results of this analysis are utilized while dealing with crack closure in the simulations. experimental results uniaxial tension-compression loading he specimen r-002 was tested uniaxially with a cyclic tension-compression force (fmax = 35 kn and rf = -1). two symmetric cracks grew in the centre cross-section, check fig.3. the crack growth curve was indicated in fig. 4. figure 3: cracks in the specimen r-002, pure tension-compression with fmax = 35 kn and rf = -1, steel s235. figure 4: crack growth curve of specimen r-002, pure tension-compression with fmax = 35 kn and rf = -1, steel s235. t y. hos et alii, frattura ed integrità strutturale, 37 (2016) 234-240; doi: 10.3221/igf-esis.37.31 237 multiaxial loading three types of multiaxial loading were conducted: proportional loading, 90° out-of-phase loading and 45° out-of-phase loading, namely the specimens r-004, r-005 and r-006 respectively. the amplitudes of the loadings are fmax = 33 kn, mmax = 382 nm and rf = rm = -1. the nominal stresses in the gross section corresponding to these loads are σn,max = 101.5 mpa and τn,max = 62.6 mpa. again two cracks were initiated at the notch. the different crack paths can be seen in figs. 5-7 with a summary in fig. 8. the crack growth directions in fig. 5 are inclined 17° and 18° to the cross-section plane, respectively for crack 1 and 3. some cyclic mode ii loading is expected to have contributed to the fatigue crack growth. this argument was discussed with more detail in the forthcoming chapters about simulation. figure 5: cracks in specimen r-004, proportional loading with fmax = 33 kn, mmax = 382 nm and rf = rm = -1, steel s235. after putting a 90° phase shift between the two loadings, the cracks stopped growing symmetrically, as shown in fig. 6. crack 1 grew straight, with an angle of 45° approximately to the specimen axis, and after a crack length of 17 mm, the crack changes direction to a direction perpendicular to the specimen axis, and soon after that the specimen fails. figure 6: cracks in specimen r-005, 90° out-of-phase non-proportional loading with fmax = 33 kn, mmax = 382 nm and rf = rm = -1, steel s235. last but not least, the specimen, which was loaded with 45° out-of-phase loading, was shown in fig. 7. crack 1 had a kink quite early, but crack 3 continued linearly, and after some time, it made a kink too. crack 1 continued in a zigzag pattern after the kinking, which leads to an argument that the crack cannot decide between two options and switches back and forth continuously. fig. 8 shows a comparison of these three cracks and this zigzag pattern is more obviously visible. figure 7: cracks in specimen r-006, 45° out-of-phase non-proportional loading with fmax = 33 kn, mmax = 382 nm, rf = rm = -1, steel s235. y. hos et alii, frattura ed integrità strutturale, 37 (2016) 234-240; doi: 10.3221/igf-esis.37.31 238 figure 8: crack growth curves of specimens r-004, r-005 and r-006 with fmax = 33 kn, mmax = 382 nm and rf = rm = -1 the crack growth simulation multiaxial loading proportional loading nder the light of the data taken from the real experiments, linear elastic simulations have been done on abaqus for the experiment r-004. the data concerning the position of the crack tip was already available. as previously been postulated, a significant portion of shear mode (about %20 of the opening mode) was observed among both cracks. fig. 9 and 10 9 depict the growth of the stress intensity factors with the crack length. figure 9: stress intensity factors in specimen r-004, crack 1 proportional loading with fmax = 33 kn, mmax = 382 nm, rf = rm = -1, steel s235. figure 10: stress intensity factors in specimen r-004, crack 2 proportional loading with fmax = 33 kn, mmax = 382 nm, rf = rm = -1, steel s235. u y. hos et alii, frattura ed integrità strutturale, 37 (2016) 234-240; doi: 10.3221/igf-esis.37.31 239 conclusion atigue crack growth under non-proportional loading cases lead to crack paths, which are not understood fully. a collection of results was presented in this paper. a number of conclusions can be derived from these results: the assumption of planar symmetrical crack growth in axial specimens is quite plausible, in spite of bending effects. in [20], another similar experiment with a larger load was discussed and simulated. a change in crack path because of the bending load, which increases with increasing crack length, was not observed. the crack that was loaded proportionally undergoes a non-negligible shear mode (about %20), as the crack growth pattern with zigzags suggest. a final conclusion, why the crack sees this as a second option is though not clear. a general tendency for cracks under non-proportional loadings is difficult to derive from the morphology. however, dic [19] and fe-simulations (ongoing) can lead to some important conclusions. such simulations can be compared with the dic results in [19] and a clearer answer for this alternating crack growth pattern might be found. acknowledgements he german research foundation (deutsche forschungsgemeinschaft) is greatly acknowledged by the authors for financial support under grant vo729/13-1. references [1] zerres, p., vormwald, m., review of fatigue crack growth under non-proportional mixed-mode loading, int. j. fatigue, 58 (2014) 75-83. [2] qian, j., fatemi, a., mixed mode fatigue crack growth: a literature survey, eng. fract. mech., 55(6) (1996) 969-990 [3] highsmith, j., phd thesis, georgia institute of technology, usa, (2009). [4] richard, h.a., fulland, m., sander, m., theoretical crack path prediction, fatigue fract. eng. mater. struc., 28 (2005) 3-12 [5] roberts, r., kibler, j., mode ii fatigue crack propagation, j. basic eng., 93d (1971) 671-680 [6] tanaka, k., fatigue crack propagation from a crack inclined to the cyclic tensile axis, eng. fract. mech., 6 (1974) 493-507 [7] brown, m.w., miller, k.j., initiation and growth of cracks in biaxial fatigue, fatigue fract. eng. mater. struc., 1 (1979) 231246. [8] otsuka, a., tohgo, k., fatigue crack initiation and growth under mixed mode loading in aluminum alloys 2017-t3 and 7075-t6, eng. fract. mech., 28 (1987) 721-732. [9] socie, d.f., in: fatigue 87, proc. 3rd int. conf. fatigue and fatigue thresholds, 2 (1987) 599-616,. [10] doquet, v., bertlino, g., local approach to fatigue cracks bifurcation, int. j. fatigue, 30 (2008) 942-950 [11] hoshide, t., socie, d.f., mechanics of mixed mode small fatigue crack growth, eng. fract. struc., 26 (1987) 841-850. [12] savaidis, g., seeger, t., consideration of multiaxiality in fatigue life prediction using the closure concept, fatigue fract. eng. mater. struc., 20 (1997) 985-1004. [13] döring, r., hoffmeyer, j., seeger, t., vormwald, m., short fatigue crack growth under nonproportional multiaxial. elasticplastic strains, int. j. fatigue, 28 (2006) 972-982. [14] hertel, o., vormwald, m., short-crack-growth-based fatigue assessment of notched components under multiaxial variable amplitude loading, eng. fract. mech. 78 (2011) 1614-1627. [15] hertel, o., vormwald, m., multiaxial fatigue assessment based on a short crack growth concept, theor. appl. fract. mech., 73 (2014) 17-26. [16] dowling, n.e., begley, j.a., fatigue crack growth during gross plasticity and the j-integral, astm stp 590 (1976) 82-103. [17] wüthrich c., the extension of the j-integral concept to fatigue cracks, int. j. fract., 20 (1982) r35-7. [18] hertel, o., döring, r., vormwald, m., cyclic j-integral under nonproportional loading, proc. 7th int. conf. biaxial/multiaxial fatigue fract. (2004) 513-518. [19] hos, y., freire, j.l.f., vormwald, m., measurements of strain fields around crack tips under proportional and nonproportional mixed-mode fatigue loading, int. j. fatigue (2016) (in press). f t y. hos et alii, frattura ed integrità strutturale, 37 (2016) 234-240; doi: 10.3221/igf-esis.37.31 240 [20] hos y, vormwald m., experimental study of crack growth under non-proportional loading along with first modeling attempts, int j fatigue (2016) (in press). [21] zerres, p., brüning, j., vormwald, m., risswachstumsverhalten der aluminiumlegierung almg4.5mn unter proportionaler und nichtproportionaler schwingbelastung, mater. test., 53 (2011) 109-117. [22] zerres, p., brüning, j., vormwald, m., fatigue crack growth behavior of fine-grained steel s460n under proportional and non-proportional loading, eng. fract. mech., 77 (2011) 1822-1834. [23] hos, y., vormwald, m., freire, j.l.f., using digital image correlation to determine mixed mode stress intensity factors in fatigue cracks, proceedings of coteq 2015, conference on technology of equipment, organized by abendi, brazilian society for ndt and inspection, june, 2015. [24] vormwald, m., fatigue crack propagation under large cyclic plastic strain conditions, procedia mater. sc. 3 (2014) 301306 [25] vormwald, m., hos, y., freire, j.l.f., measurement and simulation of strain fields around crack tips under mixed-mode fatigue loading, frattura ed integrita strutturale, 33 (2015) 42-55. [26] hos, y., vormwald, m., measurement and simulation of crack growth rate and direction under non-proportional loadings, frattura ed integrita strutturale, 34 (2015) 133-141. << /ascii85encodepages false /allowtransparency false /autopositionepsfiles true /autorotatepages /none /binding /left /calgrayprofile (dot gain 20%) /calrgbprofile (srgb iec61966-2.1) /calcmykprofile (u.s. web coated \050swop\051 v2) /srgbprofile (srgb iec61966-2.1) /cannotembedfontpolicy /error /compatibilitylevel 1.4 /compressobjects /tags /compresspages true /convertimagestoindexed true /passthroughjpegimages true /createjobticket false /defaultrenderingintent /default /detectblends true /detectcurves 0.0000 /colorconversionstrategy /cmyk /dothumbnails false /embedallfonts true /embedopentype false /parseiccprofilesincomments true /embedjoboptions true /dscreportinglevel 0 /emitdscwarnings false /endpage -1 /imagememory 1048576 /lockdistillerparams false /maxsubsetpct 100 /optimize true /opm 1 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/hrv (za stvaranje adobe pdf dokumenata najpogodnijih za visokokvalitetni ispis prije tiskanja koristite ove postavke. stvoreni pdf dokumenti mogu se otvoriti acrobat i adobe reader 5.0 i kasnijim verzijama.) /hun 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can be opened with acrobat and adobe reader 5.0 and later.) >> /namespace [ (adobe) (common) (1.0) ] /othernamespaces [ << /asreaderspreads false /cropimagestoframes true /errorcontrol /warnandcontinue /flattenerignorespreadoverrides false /includeguidesgrids false /includenonprinting false /includeslug false /namespace [ (adobe) (indesign) (4.0) ] /omitplacedbitmaps false /omitplacedeps false /omitplacedpdf false /simulateoverprint /legacy >> << /addbleedmarks false /addcolorbars false /addcropmarks false /addpageinfo false /addregmarks false /convertcolors /converttocmyk /destinationprofilename () /destinationprofileselector /documentcmyk /downsample16bitimages true /flattenerpreset << /presetselector /mediumresolution >> /formelements false /generatestructure false /includebookmarks false /includehyperlinks false /includeinteractive false /includelayers false /includeprofiles false /multimediahandling /useobjectsettings /namespace [ (adobe) (creativesuite) (2.0) ] /pdfxoutputintentprofileselector /documentcmyk /preserveediting true /untaggedcmykhandling /leaveuntagged /untaggedrgbhandling /usedocumentprofile /usedocumentbleed false >> ] >> setdistillerparams << /hwresolution [2400 2400] /pagesize [612.000 792.000] >> setpagedevice http://www.gruppofrattura.it http://www.gruppofrattura.it http://dx.medra.org/10.3221/igf-esis.04.01&auth=true microsoft word numero_41_art_46.docx r. m. de salvo, frattura ed integrità strutturale, 41 (2017) 350-355; doi: 10.3221/igf-esis.41.46 350 an original method of direct calculation for the identification of the last hinge and the definition of the deformative state at collapse roberto maria de salvo retired professor at architecture faculty of mediterranean university of reggio calabria, italy robertomariadesalvo@libero.it abstract. the subject matter of these notes refers to the ultimate strength design of 2-d steel framed structures and in particular to the analysis of the deformation state at collapse. the idea is based on the consideration that, if the structure at its collapse condition is subjected to an articulated movement, similar and concordant to the crisis motion, this will not change the stress state of the system. this motion is known once a single parameter is fixed, namely the displacement of a point or the rotation of a beam. when the collapse mechanism of the structure is already determined through any instrument of the limit analysis, a subsequent (k+1) plastic hinge can be arbitrarily fixed and assumed as the last developed one. it is therefore possible to solve the modified scheme through the rotation method and make a comparison in the verses between the known plastic moments and the rotations at the corresponding hinges. if the comparison is successful, in the sense that the checked verses are concordant, the selected hinge is actually the one formed as the last. on the contrary, the rotations resulting from an imprinted motion in the verse of collapse movement are algebraically added. if, for each hinge, the product between the plastic moment and the correspondent algebraic sum is made, this product has to be surely positive, due to the verses concordance. this can be translated in k+1 inequalities, with each one furnishing a lower limit for the parameter from which the articulated motion depends. among these, the highest value is that one which makes all the inequalities to be simultaneously verified. the substitution of this value into the expressions for rotations permits to arrive to the simultaneous identifying of the last hinge and of the complete picture of deformations. keywords. final hinge; plastic hinge; plastic moments; collapse. citation: de salvo, r., an original method of direct calculation for the identification of the last hinge and the definition of the deformative state at collapse, frattura ed integrità strutturale, 41 (2017) 350-355. received: 05.04.2017 accepted: 06.05.2017 published: 01.07.2017 copyright: © 2017 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. r. m. de salvo, frattura ed integrità strutturale, 41 (2017) 350-355; doi: 10.3221/igf-esis.41.46 351 introduction t is made reference to the previously wrote monograph titled “un procedimento originale per l’individuazione della cerniera ultima e per la determinazione della deformazione completa allo stato di collasso”, published in the journal laborest n.11 [1]. the topic is taken up in relation to the fact that, thanks to the introduction of a fundamental concept, it has been possible to arrive to the solution of the same problem through direct calculation and therefore not through an iterative procedure. concise contents of the above-mentioned monograph he main aspects that led to the solution of the problem can be subdivided in the following points: a. demonstration that it is necessary to individualize the last plastic hinge with the aim to know the deformation state at collapse; b. formulation, by means suitable analyses, of the last hinge theorem, that can be stated as follows: given a framed structure, k-times hyper-static, whose collapse mechanism is known, if one of the k+1 plastic hinges is chosen as the last one, therefore the concordance of verses between plastic moments and rotations at all the k plastic hinges is necessary and sufficient condition to assert that this configuration is the real one; c. choice of any of the k+1 plastic hinges and assumption that it is the last one to be formed, and solution of the structure through the rotation method. knowing the deformed state of the system, this method allows to proceed to the comparison of verses of plastic moments and rotations of the correspondent hinges. if, according to what already said, the comparison between verses concordance returns a positive result, then the selected hinge is the last one to be formed. on the contrary, the evaluation must be repeated considering a different hinge as the last one. the procedure will end once the above concordance will be satisfied for all the k residual plastic hinges. in this case, the last plastic hinge will be known as well as the complete deformation of the system (rotations at all the plastic hinges and displacements). the procedure illustrated above inevitably needs, for each iteration, the compilation and solution of a system of equations with the aim to obtain the deformative state of the structure in relation to the position of the plastic hinge assumed as the last one to be formed. the new procedure n this work an innovative criterion is presented. it moves from the consideration that, if the structure at its collapse condition is subjected to an articulated movement, similar and concordant to the crisis motion, this will not change the stress state of the system because at this stage all the bending moments already reached their pick values. the imposed articulated movement produces the kinematical effect to modify the deformative state of the system, determining the passage from one configuration to another one. this motion is known once a single parameter is fixed, namely the displacement of a point or the rotation of a beam. it can be therefore inferred that a bijective correspondence exists between this parameter and the resulting deformed configuration: the one is known once the other is fixed and vice-versa. on the basis of what above said and under the hypothesis that the kinematics at collapse is known by applying any suitable procedure (in particular the first or second theorem of the limit analysis [2, 3]), one of the k+1 plastic hinges can be arbitrarily fixed and, under the hypothesis that this is the last one to be formed, the obtained scheme can be studied through the rotation method [4]. the comparison, in verses, between the plastic moments (known) and rotations of the correspondent hinges (obtained by applying the above method) can be now carried out. it is useful to denote the set of these deformations as “configuration 1”. if the comparison returns a positive result in terms of verses concordance, then the selected hinge is that one really formed as the last one and the search for it ends here. but the most interesting case (and that is clearly the most frequent) is when the comparison reveals at least one discordance. in the second case, an articulated movement in the sense of the collapse motion is imposed through the choice of a unique parameter, so that a deformed configuration is obtained where each plastic hinge has a rotation whose value is dependent by this parameter. it is useful to denote the set of these deformations as “configuration 2”. i t i r. m. de salvo, frattura ed integrità strutturale, 41 (2017) 350-355; doi: 10.3221/igf-esis.41.46 352 the rotations of the two above-mentioned configurations are now algebraically summed up. these are obviously functions of the parameter that originated the configuration 2. by making, for each plastic hinge, the product between the bending moment and the correspondent rotation (which is the sum of configurations 1 and 2), the result, for the verses concordance, must be necessarily negative. this leads to k+1 inequalities, with each one furnishing a lower limit for the parameter  from which the configuration 2 depends. clearly, the highest value between these limits is that one which simultaneously verifies all the inequalities. the substitution of this value in the expressions for rotations, permits to come to the simultaneous identification of the plastic hinge and of the complete picture of deformations. convention on signs s it is known, using the displacement method for applications to 2-d framed structures, the rotations at the extremes of a beam are assumed positive if clockwise. the sign convention, according to the fracture calculus, is different. there is therefore the problem to adequate one convention to the other one. to this end, if the beam is arranged in a horizontal way and with the stretched fibers pointed downwards (fig. 1), the rotation at the right extreme of the beam is transferred to the plastic hinge with the same sign, the rotation to the left extreme of the beam is instead transferred with the opposite sign. figure 1: sign convention. the rotation of the plastic hinge will result, in value and sign, equal to the algebraic sum of the two rotations. as a consequence, if the angle formed by the two beams adjacent to the plastic hinge increases, the rotation of the plastic hinge will be positive; negative on the contrary (fig. 1). figure 2: collapse scheme. numerical application ith the aim to make the above theory more accessible, it is considered worthwhile to solve in detail the case of the frame reported in fig. 2. a w r. m. de salvo, frattura ed integrità strutturale, 41 (2017) 350-355; doi: 10.3221/igf-esis.41.46 353 figure 3: hypothesis of plastic hinge at node c. the plastic moments of the elements are assumed equal to 2mp for beams and mp for pillars. the stiffness of the beams is fixed twice that of pillars. the stretched fibers of the elements are the internal ones except for the central pillar whose stretched fibers are indicated by a small rectangle. in figure the plastic hinges are localized together with the bending moment distribution at collapse. the multiplier at collapse is equal to p =5.50mp/pl. these results have been obtained making use of the fundamental theorems of the limit analysis. it is worth to note that, being the structure six times hyperstatic, at collapse the number of plastic hinges is seven. hypothesis is made that the last formed plastic hinge is that at node c (fig. 3). in the same figure the rotations at plastic hinges are reported. these were calculated through the solution of the system of equations obtained by applying the displacement method and taking into account the convention on signs at section 4. the horizontal displacement at node d (assumed positive if rightward) and the vertical displacement at section e (assumed positive if downward) are also reported, both clearly deducted by solution of the above-mentioned system. for rotations, the factor mpl/ei is omitted, for displacements the factor mpl/ei. for a greater clarity, the diagram of moments has been superimposed. the analysis of these results shows that the choice of the last plastic hinge at node c is false. it is in fact sufficient to observe that the rotation at node e is negative while the plastic moment at the same section has a positive sign. on the basis of the criterion showed in section 3, an articulated movement similar and concordant to the collapse motion has to be built. it is defined by a clockwise rotation  of the pillar ad (expressed for less than the factor mpl/ei). this rotation, accordingly with the convention on signs in section 4, gives to each plastic hinge a rotation well defined in value and sign, as indicated in fig. 4. under the hypothesis that the last plastic hinge finds at node c (fig. 3), the rotations of plastic hinges are now summed to the rotations obtained through the impressed articulated motion (fig. 4). figure 4: scheme with an imprinted articulated motion. in this way, the following sums are obtained: r. m. de salvo, frattura ed integrità strutturale, 41 (2017) 350-355; doi: 10.3221/igf-esis.41.46 354 for the concordance on verses, each one of these sums must have a verse concordant to the corresponding plastic moment and this implies that, for each plastic hinge, their product must be always not negative. this condition implies that the following inequalities must be satisfied: each one of these conditions furnishes a lower limit for the parameter . by selecting, among these, the greatest value, that is =0.0938*mpl/ei, all the inequalities associated to the seven plastic hinges characterizing the collapse kinematics are simultaneously satisfied. therefore, by substitution into the expressions of the above sums of rotations, the complete picture of all rotations is obtained. these are depicted in fig. 5 together with the diagram of bending moments at collapse. remind is made that rotations are expressed less than the factor mpl/ei. the analysis of the result, as obvious, highlights everywhere the concordance in verses between plastic moments and rotations at correspondent hinges. it is also to be noted that, in the case under study, the last hinges are two, namely at the middle section e of the left beam and at the head section 3 of the central pillar. for a better understanding these have been individualized through a white circle. the procedure ends here, once the two plastic hinges have been found together with the rotations of other hinges and displacements, at an instant just before the collapse. regarding, it has been considered appropriate to perform some checks. in particular, the structure has been separately solved by applying the rotation method under three hypotheses: last hinge at section e, last hinge at the head section 3 of the central pillar; last hinges simultaneously at the two positions. in all the three cases the result coincided with that one above reported. figure 5: collapse kinematic mechanism. r. m. de salvo, frattura ed integrità strutturale, 41 (2017) 350-355; doi: 10.3221/igf-esis.41.46 355 the frame has been further studied employing a step-by-step procedure: the same result was obtained together with the confirmation of the simultaneous appearance of the two plastic hinges in sections e and 3. also, even the horizontal displacement at d node and vertical displacement at e node coincide with those found using this last procedure. final remarks part its different theoretical structure, the procedure above developed, theoretically first and by means of an application on a double portal then, shows how much advantageous this new structure is from an operative point of view. according to the criteria developed in the previous monograph, in the procedure to localize the last hinge the number of systems to build and solve may result high (one for each hypothesis on the plastic hinge chosen as the last). in this new procedure, instead, it is sufficient to formulate a single hypothesis and to build only one system of equations whose solution permits to arrive to the desired result through a direct calculus. it is important to note that the hypothesis on the hinge chosen as the last one is not just an attempt (and therefore to be eventually repeated), but it is the first step of an algorithm that leads to the direct solution of the problem. references [1] de salvo, r.m., un procedimento originale per l’individuazione della cerniera ultima e per la determinazione della deformazione completa alla stato di collasso, laborest, 11 (2015) 85. [2] massonnet, c., save, m., calcolo a rottura delle strutture, bologna (1967) 49. [3] corradi dell’acqua, l., meccanica delle strutture la valutazione della capacità portante, the mcgraw-hill companies, 3 (2003) 38. [4] de salvo, r.m., lezioni di scienza delle costruzioni. il metodo delle deformazioni nelle strutture piane, editor laruffa (1993). a << /ascii85encodepages false /allowtransparency false /autopositionepsfiles true /autorotatepages /none /binding /left /calgrayprofile (dot gain 20%) /calrgbprofile (srgb iec61966-2.1) /calcmykprofile (u.s. web coated \050swop\051 v2) /srgbprofile (srgb iec61966-2.1) /cannotembedfontpolicy /error /compatibilitylevel 1.4 /compressobjects /tags /compresspages true /convertimagestoindexed true /passthroughjpegimages true /createjobticket false /defaultrenderingintent /default /detectblends true /detectcurves 0.0000 /colorconversionstrategy /cmyk /dothumbnails false /embedallfonts true /embedopentype false /parseiccprofilesincomments true /embedjoboptions true /dscreportinglevel 0 /emitdscwarnings false /endpage -1 /imagememory 1048576 /lockdistillerparams false /maxsubsetpct 100 /optimize true /opm 1 /parsedsccomments true /parsedsccommentsfordocinfo true 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/hrv (za stvaranje adobe pdf dokumenata najpogodnijih za visokokvalitetni ispis prije tiskanja koristite ove postavke. stvoreni pdf dokumenti mogu se otvoriti acrobat i adobe reader 5.0 i kasnijim verzijama.) /hun 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can be opened with acrobat and adobe reader 5.0 and later.) >> /namespace [ (adobe) (common) (1.0) ] /othernamespaces [ << /asreaderspreads false /cropimagestoframes true /errorcontrol /warnandcontinue /flattenerignorespreadoverrides false /includeguidesgrids false /includenonprinting false /includeslug false /namespace [ (adobe) (indesign) (4.0) ] /omitplacedbitmaps false /omitplacedeps false /omitplacedpdf false /simulateoverprint /legacy >> << /addbleedmarks false /addcolorbars false /addcropmarks false /addpageinfo false /addregmarks false /convertcolors /converttocmyk /destinationprofilename () /destinationprofileselector /documentcmyk /downsample16bitimages true /flattenerpreset << /presetselector /mediumresolution >> /formelements false /generatestructure false /includebookmarks false /includehyperlinks false /includeinteractive false /includelayers false /includeprofiles false /multimediahandling /useobjectsettings /namespace [ (adobe) (creativesuite) (2.0) ] /pdfxoutputintentprofileselector /documentcmyk /preserveediting true /untaggedcmykhandling /leaveuntagged /untaggedrgbhandling /usedocumentprofile /usedocumentbleed false >> ] >> setdistillerparams << /hwresolution [2400 2400] /pagesize [612.000 792.000] >> setpagedevice microsoft word numero_33_art_49 f. castro et alii, frattura ed integrità strutturale, 33 (2015) 444-450; doi: 10.3221/igf-esis.33.49 444 focussed on multiaxial fatigue estimation of fretting fatigue life using a multiaxial stress-based critical distance methodology f. c. castro, j. a. araújo, m. s. t. pires department of engineering mechanics, university of brasilia fabiocastro@unb.br l. susmel department of civil and structural engineering, the university of sheffield l.susmel@sheffield.ac.uk abstract. this work presents a methodology for life estimation of mechanical couplings subjected to fretting fatigue. in this approach, a stress-based multiaxial fatigue parameter is evaluated at a critical distance below the contact surface. the fatigue parameter is based on an improved formulation of the modified wöhler curve method, in which the shear stress amplitude is measured via the maximum rectangular hull method. to apply the theory of critical distances in the medium-cycle fatigue regime, the critical distance is assumed to depend on the number of cycles to failure. available fretting fatigue data, conducted on a cylinder-plane contact configuration made of al alloy 4% cu, were used to assess the methodology. most of the life estimates were within an error band given by a factor of 2. keywords. fretting fatigue; multiaxial fatigue; life estimation; theory of critical distances. introduction retting fatigue refers to the conjoint action of a small oscillatory motion between contacting bodies and a cyclic remote loading. the oscillatory motion often leads to surface damage phenomena that may speed up the formation of micro-cracks. due to the remote loading, these cracks may propagate until catastrophic failure occurs. many engineering assemblies are prone to fretting fatigue problems as, for instance, the blade/disk interfaces of gas turbine engines, wires of overhead conductors and riveted joints. fretting fatigue usually displays high stress gradients that affect observed lives [1, 2]. among the different formulations that account for the stress gradient in fretting, non-local approaches have received considerable attention in the literature [3]. the appeal of such approaches derives from their relative simplicity and from satisfactory correlations with experimental data [2, 4-7]. the theory of critical distances (tcd) [8-10] has been one of the most used non-local approaches in the last ten years. in this approach, the size of the fatigue process zone is related to fatigue thresholds of cracked or sharply notched specimens. the success of the tcd in correlating fatigue thresholds of notched members has been widely reported in the literature (see [9, 10] and references therein). due to the similarities between notch and fretting fatigue, an attempt to estimate fretting fatigue thresholds using the tcd has been carried out by araújo et al. [6]. in that paper, the modified f f. castro et alii, frattura ed integrità strutturale, 33 (2015) 444-450; doi: 10.3221/igf-esis.33.49 445 wöhler curve method (mwcm) [11] was applied at a point located at a critical distance below the trailing edge of the contact. estimates of fretting fatigue thresholds fell within an error interval of ±20% when compared to experimental data. the methodology proposed by araújo et al. [6] is only applicable to design situations involving threshold conditions. in this paper, an extension of this approach to the medium-cycle fatigue regime is presented. a first attempt to assess the new methodology is carried out based on available fretting fatigue tests [1]. multiaxial fatigue life estimation he mwcm [10-12] is a multiaxial stress-based critical plane approach where the driving parameters for crack nucleation are the maximum shear stress amplitude, a, and the maximum normal stress acting on the maximum shear stress plane, n,max. once the values of a and n,max have been evaluated, the stress ratio  is defined as n,max a     (1) it is noteworthy that  is sensitive not only to mean stresses, but also to the degree of multiaxiality and nonproportionality of the stress path [10]. also, it is worth recalling that for an unnotched specimen under fully reversed uniaxial loading the  ratio is equal to unity, whereas under fully reversed torsional loading  equals zero [10]. the mwcm is based on a modified wöhler diagram where a is plotted against the number of cycles to failure, nf (fig. 1). this diagram is made of different fatigue curves, each one corresponding to a certain value of  ratio and being unambiguously described by its negative inverse slope  and by a reference shear stress amplitude, a,ref, corresponding to an appropriate number of cycles to failure, na. to obtain the diagram, one should properly define the  vs.  and a,ref vs.  relationships, and correctly calibrate them by running appropriate experiments. the following linear relationships have been found by lazzarin and susmel [12] to correlate a wide range of experimental data: ( ) ba    (2) a,ref ( ) c d    (3) where a, b, c and d are material constants. when these constants are obtained from fully-reversed uniaxial and torsional tests on plain specimens, eqs. (2) and (3) are stated as figure 1: modified wöhler diagram. ( ) [ ( ) (1 0)] ( )0             (4) 0 a,ref 0 0( ) 2            (5) where (=1) and 0 are, respectively, the inverse slope of the modified wöhler curve and the fatigue limit under uniaxial loading condition, whereas (=0) and 0 are the corresponding quantities for torsional loading. it is noteworthy that, for t f. castro et alii, frattura ed integrità strutturale, 33 (2015) 444-450; doi: 10.3221/igf-esis.33.49 446 materials that do not exhibit a fatigue limit, 0 and 0 must be defined as endurance limits corresponding to an appropriate number of cycles to failure. after a proper calibration of eqs. (2) and (3), any curve of the modified wöhler diagram can be obtained. hence, the number of cycles to failure can be estimated as a,ref ( ) f,e a a ( ) n n            (6) usually, the value of a in the mwcm is determined via the minimum circumscribed circle (mcc) method [13]. here, the maximum rectangular hull (mrh) approach is adopted, since fatigue estimates based on the mwcm are improved when a is measured by the mrh rather than by the mcc [14]. the mrh method is schematically represented in fig. 2. the halves of the sides of the rectangular hull with orientation  are calculated as 1 max , m( ) ( in , , 1( 2 2 ) ) ,i i i tt t ia t           (7) where i(,t) (i=1,2) are the components of the shear stress vector (t) with respect to the -oriented frame. the amplitude of each -oriented rectangular hull can be evaluated as 2 2 a 1 2( ) )) (( a a    (8) the shear stress amplitude is then defined as the maximum value of eq. (8) among all  -oriented rectangular hulls: 2 2 a mrh 1 2 90 º0 max ( ) ( )a a        (9) figure 2: amplitudes of the -oriented rectangular hull bounding the shear stress path. critical distance approach he stress gradient effect is a crucial aspect in the design of stress raisers such as notches and mechanical contacts. among the formulations that account for this effect, the tcd [8-10] has been recognized as one of the most attractive due to its simplicity and good results for a number of notch configurations. the central idea of the tcd is the definition of an effective stress, eff, based on an averaging procedure over a volume surrounding the stress raiser. fatigue failure is expected to occur if eff exceeds a reference material strength, ref. simplified methods can also be formulated by considering averages over an area or a line (area and line methods, respectively) or the effective stress of the point located at a critical distance, l, from the stress raiser (point method). in this paper attention is focused on the point method, as schematically illustrated in fig. 3. taylor [8] has developed fitting procedures to determine the critical distance, which are based on the fatigue thresholds of cracked or sharply notches specimens. in particular, the critical distance for the point method has been found to be expressed as 2 th 0 1 2 l k          (10) t f. castro et alii, frattura ed integrità strutturale, 33 (2015) 444-450; doi: 10.3221/igf-esis.33.49 447 where kth is the threshold stress intensity factor range and 0 is the uniaxial plain fatigue limit range. further work [10, 15] has investigated the extension of the tcd to stress raisers under multiaxial loadings, concluding that the combination of the mwcm with the point method requires the same critical distance given by eq. (10). figure 3: schematic representation of the point method. an extension of the tcd to estimate fatigue life of stress raisers has been developed in refs. [16, 17]. to explain the formulation, it should be recalled that the appropriate critical distance to estimate static failure of notched members is given as [9, 18]: i 2 s c r 1 2 k l          (11) where kic is the plane strain material fracture toughness and r is a reference material constant which can be equal or larger than the ultimate tensile strength, uts [9]. as the values of the critical distances at the threshold and static conditions are usually different, it can be assumed that the critical distance at the medium-cycle fatigue regime, lm, depends on the number of cycles to failure, nf. in particular, a power law relationship between lm and nf has been proposed by susmel and taylor as follows: m f f( ) bl n an (12) where a and b are material constants. two fitting procedures have been developed to obtain these constants: one based on critical distances determined at threshold and static conditions (eqs. (10) and (11), respectively), and another based on fatigue curves of plain and sharply notched specimens. although the latter procedure has proved to provide more accurate notch life estimates when compared to experimental data, the former is simpler to work with as the material constants required to determine a and b are usually available or can be extracted from empirical correlations. application to fretting fatigue everal attempts to address the fretting fatigue problem using notch methodologies have been investigated in the literature [2-7] due to the similarities between notch and fretting fatigue. indeed, the stress fields in both problems are characterized by stress gradients and multiaxial stresses. in the fretting fatigue problem, however, there is also a wear process due to the relative motion between the contacting surfaces. in this setting, notch methodologies could be applied to fretting fatigue if the surface damage could be regarded as negligible. this approximation is considered in this paper, at least for the partial slip case where the amount of wear debris is usually small [19]. the use of the methodology for a typical fretting fatigue problem is shown in fig. 4. the contact configuration involves a normal force p, a cyclic tangential loading q(t), and a cyclic remote stress (t). as a first step, the crack initiation point must be determined. this task can be accomplished, for instance, by searching the point where a given fatigue parameter achieves its maximum value. normally, the crack initiation point occurs at the trailing edge of the contact, as illustrated in fig. 4a. subsequent analysis is carried out on the straight line that emanates from the crack initiation point and is perpendicular to the contact surface. in order to obtain the number of cycles to failure, the critical distance corresponding to a trial number of cycles to failure, n, is determined as follows: m ( ) bl n an (13) s f. castro et alii, frattura ed integrità strutturale, 33 (2015) 444-450; doi: 10.3221/igf-esis.33.49 448 the stress quantities a, n,max, and  are then evaluated at this critical distance, and the number of cycles to failure, nf,e, is calculated using eq. (6). if the calculated nf,e is different from the trial value n, a new iteration is started considering n = nf,e. this process is repeated until convergence between the trial and calculated fatigue lives has been attained. figure 4: procedure to estimate fretting fatigue life: (a) location of the critical distance and (b) flowchart of the iterative procedure for life estimation. comparison with experimental data vailable fretting fatigue data [1] were used to assess the methodology. such tests were carried out with a pair of cylindrical pads pressed against a flat dog-done specimen, both made of an al alloy 4% cu. in each series of tests, the tests were run (each one with a different pad radius) at constant values of peak contact pressure, tangential force and remote stress. hence, the magnitude of the stress field of each test was the same, but different stress gradients were induced by the contact. constants for the methodology are given in tab. 1. the constants a and b in the lm versus nf relationship, eq. (12), were determined using l values calculated at the threshold and static conditions, eqs. (10) and (11), respectively. the values of  and a,ref were extracted from fully reversed uniaxial and torsional fatigue curves. these curves were estimated by fitting fatigue data for 103 cycles and 107 cycles, using empirical relationships [20] to obtain the fatigue strengths at 103 cycles from the ultimate tensile strength. uts 0 kic kth (=0) a,ref (=0) (=1) a,ref (=1) (mpa) (mpa) (mpam0.5) (mpam0.5) (mpa) (mpa) 500 124 34 4.4 12.8 161 12.8 115 table 1: constants for the methodology for al alloy 4% cu. due to the geometry of the experimental setup and the applied loadings, analytical techniques [21] were employed to solve the elastic contact problem. the surface tractions are characterized by a hertzian contact pressure distribution, and by shear tractions that are similar to the mindlin-cattaneo one except that the stick zone is not symmetrical with respect to the center of the contact zone but shifted due to the presence of an alternating remote stress. once the surface tractions have been determined, subsurface stresses can be obtained by using a muskhelishvili potential. the time varying elastic stress field in any material point in the specimen can be finally calculated by superposing the effects of contact pressure, shear traction and remote stress. a f. castro et alii, frattura ed integrità strutturale, 33 (2015) 444-450; doi: 10.3221/igf-esis.33.49 449 estimated and observed number of cycles to failure is shown in fig. 5. the solid diagonal line corresponds to a perfect correlation between estimated and observed fatigue lives, and the two dashed lines define the factor of 2 bandwidth. as can be clearly seen in this figure, most of the life estimates fall within a error band given by a factor of 2. considering the well known scatter that characterizes the fatigue phenomena this can be considered a very good correlation. figure 5: observed and estimated fatigue lives for fretting fatigue tests conducted by nowell [1]. conclusions n engineering methodology for fatigue life estimation of mechanical couplings subjected to fretting fatigue was presented in this paper. constants for the methodology are relatively simple to determine, as only experimental data from conventional fatigue tests on plain and sharply notched (or cracked) specimens are required. it can also be easily incorporated in a finite element method based software for fast assessment of fretting fatigue life in more realistic type of mechanical couplings. fatigue life estimates correlated well with the experimental results [1], falling in most cases within a factor of two bandwidth. although some of the required material constants were obtained either from literature or from empirical relations, the methodology was still capable of producing satisfactory life estimates. however, further assessment considering different contact configurations and other materials is still required to corroborate the proposed life methodology. acknowledgments he supports provided by cnpq (contracts 310845/2013-0 and 309748/2013-5) and by finatec are gratefully acknowledged. references [1] nowell, d., an analysis of fretting fatigue. ph.d. thesis, oxford university, (1988). [2] amargier, r., fouvry, s., chambon, l., schwob, c., poupon, c., stress gradient effect on crack initiation in fretting using a multiaxial fatigue framework, int j fatigue, 32 (2010) 1904–1912. [3] nowell, d., dini, d., hills, d.a., recent developments in the understanding of fretting fatigue, eng fract mech, 73 (2006) 207–222. a t f. castro et alii, frattura ed integrità strutturale, 33 (2015) 444-450; doi: 10.3221/igf-esis.33.49 450 [4] araújo, j.a., nowell, d., the effect of rapidly varying contact stress fields on fretting fatigue, int j fatigue, 24 (2002) 763–776. [5] araújo, j.a., castro, f.c., a comparative analysis between multiaxial stress and δk-based short crack arrest models in fretting fatigue engineering fracture mechanics, 93 (2012) 34–47. [6] araújo, j.a., susmel, l., taylor, d., ferro j.c.t., mamiya, e.n., on the use of the theory of critical distances and the modified wöhler curve method to estimate fretting fatigue strength of cylindrical contacts, int j fatigue, 29 (2007) 95–107. [7] navarro, c., muñoz, s., domínguez, j., on the use of multiaxial fatigue criteria for fretting fatigue life assessment, int j fatigue, 30 (2008) 32–44. [8] taylor, d., geometrical effects in fatigue: a unifying theoretical model. int j fatigue, 21 (1999) 413–20. [9] taylor, d., the theory of critical distances: a new perspective in fracture mechanics. elsevier bv, (2007). [10] susmel, l., multiaxial notch fatigue: from nominal to local stress-strain quantities. woodhead & crc, cambridge, uk, (2009). [11] susmel, l., lazzarin, p., a bi-parametric wöhler curve for high cycle multiaxial fatigue assessment, fatigue fract eng mater struct, 25 (2002) 63–78. [12] lazzarin, p., susmel, l., a stress-based method to predict lifetime under multiaxial fatigue loading, fatigue fract eng mater struct, 26 (2003) 1171–1187. [13] castro, f.c., araújo, j.a., zouain, n. on the application of multiaxial high-cycle fatigue criteria using the theory of critical distances. engng fract mech. 2009; 76:512–24. [14] araújo, j.a., dantas a.p., castro f.c., mamiya e.n., ferreira j.l.a., on the characterization of the critical plane with a simple and fast alternative measure of the shear stress amplitude in multiaxial fatigue, int j fatigue, 33 (2011) 1092– 1100. [15] susmel, l., taylor, d., two methods for predicting the multiaxial fatigue limits of sharp notches, fatigue fract engng mater struct, 26 (2003) 821–833. [16] susmel, l., taylor, d., a novel formulation of the theory of critical distances to estimate lifetime of notched components in the medium-cycle fatigue regime, fatigue fract engng mater struct, 30 (2007) 567–581. [17] susmel, l., taylor, d., the modified wöhler curve method applied along with the theory of critical distances to estimate finite life of notched components subjected to complex multiaxial loading paths, fatigue fract engng mater struct, 31 (2008) 1047–1064. [18] susmel l, taylor d., on the use of the theory of critical distances to predict static failures in ductile metallic materials containing different geometrical features, eng fract mech, 75 (2008) 4410–4421. [19] vingsbo, o., söderberg, s., on fretting maps, wear, 126 (1988) 131-147. [20] susmel, l., fatigue design: summary, class notes, (2012). [21] hills, d.a., nowell, d., mechanics of fretting fatigue. dordrecht: kluwer academic publishers, (1994). microsoft word numero_37_art_3 p. bernardi et alii, frattura ed integrità strutturale, 37 (2016) 15-21; doi: 10.3221/igf-esis.37.03 15 focussed on multiaxial fatigue and fracture numerical simulation of early-age shrinkage effects on rc member deflections and cracking development p. bernardi, r. cerioni, e. michelini, a. sirico dept. of civil, environmental, land management engineering and architecture, university of parma (italy) patrizia.bernardi@unipr.it, roberto.cerioni@unipr.it, elena.michelini@unipr.it, alice.sirico@studenti.unipr.it abstract. shrinkage effects on short-term behavior of reinforced concrete elements are often neglected both in design code provisions and in numerical simulations. however, it is known that their influence on serviceability performance can be significant, especially in case of lightly-reinforced beams. as a matter of fact, the restraint provided by the reinforcement on concrete determines a reduction of the cracking load of the structural element, as well as an increase of its deflection. this paper deals with the modeling of early-age shrinkage effects in the field of smeared crack approaches. to this aim, an existing non-linear constitutive relation for cracked reinforced concrete elements is extended herein to include early-age concrete shrinkage. careful verifications of the model are carried out by comparing numerical results with significant experimental data reported in technical literature, providing a good agreement both in terms of global and local behavior. keywords. reinforced concrete; shrinkage; cracking; short-term loading; non-linear analysis; fem. introduction n the design of reinforced concrete (rc) members, creep and shrinkage effects are usually taken into account for the evaluation of long-term deflections and pre-stress losses. it is indeed well known that these phenomena have a significant influence on the behavior of rc elements under sustained loads, by increasing their deformations and crack width over time. on the contrary, their effects on short-term response are often disregarded [1, 2]. several theoretical and experimental works (among others, e.g. [3, 4]) have however pointed out that the restraining of concrete shrinkage (usually due to the presence of embedded reinforcement) significantly affects the cracking resistance of structural elements, as well as their deformations even under short-term loading. as a consequence, a proper numerical modelling should consider this effect, so as to avoid inaccurate predictions of structural performances at serviceability conditions. to this aim, concrete shrinkage can be explicitly considered by treating it as a prescribed deformation or as a fictitious force in the analyses [5-9]. in this work, an existing smeared-crack model for rc elements subjected to in-plane stresses, named 2d-parc [10-12], is extended so as to correctly take into account early-age shrinkage effects. in more detail, concrete shrinkage is rigorously modelled by inserting it explicitly into 2d-parc general algorithm as a prescribed deformation. the effectiveness of the proposed procedure is verified herein through the modelling of two experimental programs [13, 14] on rc shrunk beams with low reinforcement ratio tested to short-term bending. these elements are highly sensitive to shrinkage effects, especially in presence of a non-symmetric arrangement of steel reinforcement in the element cross-section. the restraint i p. bernardi et alii, frattura ed integrità strutturale, 37 (2016) 15-21; doi: 10.3221/igf-esis.37.03 16 provided by embedded bars produces indeed a not uniform distribution of induced tensile stresses in concrete, with a consequent initial warping of the member. comparisons between numerical and experimental results prove that the proposed approach is able to correctly catch the effects of concrete shrinkage strains on member deflection, as well as on cracking strength and development. numerical model n this work, the original formulation of 2d-parc constitutive relation is properly revised so as to include concrete shrinkage effects in short-term analyses. as already mentioned, this model, which is based on a smeared-fixed crack approach, was developed for a concrete membrane element containing n reinforcing layers with different orientations, subjected to plane stress conditions. the main features of 2d-parc, as well as its governing equations can be found in [10-12], to which reference is made. in the following sections the attention will be only focused on the main changes made to the original structure of the model in order to include concrete shrinkage. uncracked stage in the uncracked stage, perfect bond is assumed between steel bars and the surrounding concrete, so the total strain vector {ε} is coincident with the strain in concrete {εc} and steel {εs}:      sc   , (1) the total stress vector {σ} can be then simply evaluated as the sum of the stresses acting in concrete, {σc}, and in steel reinforcement, {σs}. to take into account shrinkage effects, concrete stresses {σc} are here computed as a function of concrete net strains ({εc} {εsh}), being {εsh} the free shrinkage strain vector. according to 2d-parc conventions, free shrinkage strains are assumed as negative, since they cause concrete shortening. the terms of vector {εsh} can be either set equal to the shrinkage strain values measured during experimental tests, if available, or properly calculated according to classical formulations obtained from technical literature (e.g. [15-17]). in any case, the component of {εsh} associated to shear strains is usually assumed equal to zero. the equilibrium equation for the uncracked rc element can be then written as:                 ssshccsc dd   , (2) where [dc] and [ds] respectively represent concrete and steel stiffness matrix, whose construction has been discussed elsewhere ([10] and [12], in a more recently revised form). cracked stage crack formation takes place when the current state of stress violates the concrete failure envelope in the cracking region (see [12]). in presence of shrinkage, the transition from uncracked to cracked stage occurs in correspondence of a lower load level, since the restraint provided by the embedded reinforcement causes the appearance of tensile stresses in concrete even before the application of any external load. crack pattern is hypothesized to develop with a constant spacing am1 and a strain decomposition procedure is adopted, so leading to the following compatibility condition:      1crc   , (3) where the total strain vector {ε} is obtained as the sum of the strains {εc} in rc between two adjacent cracks (still intact, even if damaged), and those in the fracture zone, {εcr1}, related to all the kinematics that develop after crack formation. as known, crack opening and sliding activate indeed several resistant mechanisms, such as aggregate bridging and interlock, tension stiffening and dowel action, which provide strength and stiffness. according to the procedure described in [10], the two strain vectors, {εc} and {εcr1}, are obtained by inverting the equilibrium conditions in the uncracked rc between cracks and at crack location, respectively. moreover, the stresses in rc between adjacent cracks, {σc}, and those in the crack, {σcr1}, are assumed to be coincident with each other and consequently to the total stress vector {σ}. in more detail, the equilibrium condition in rc between cracks is formally identical to eq. 2, even if concrete and steel stiffness matrices, [dc] and [ds], are slightly modified with respect to the uncracked stage, so as to consider the degradation i p. bernardi et alii, frattura ed integrità strutturale, 37 (2016) 15-21; doi: 10.3221/igf-esis.37.03 17 that occurs after cracking, as explained in [10, 12]. moreover, since in the cracked stage the hypothesis of perfect bond is no longer valid (and consequently the two strain vectors {εc} and {εs} cannot be set equal to each other), the steel strain {εs} is assumed coincident with the total average strain {ε}, with a negligible approximation in excess. by inverting the equilibrium condition in rc between cracks, concrete strains {εc} can be then expressed as:             shs1cc dd    . (4) the strain vector { εcr1} can be in turn determined by inverting the equilibrium equation at crack location:       11cr1cr d  , (5) being [dcr1] the crack stiffness matrix, whose expression – which is not modified in presence of shrinkage – can be still found in [10]. by substituting eqs 4 and 5 into the compatibility eq. 3, the total stress {σ} vector in case of shrinkage can be then expressed as follows:                   shs1c111cr1c ddidd    , (6) being [i] the identity matrix. model validation he effectiveness of the above described procedure, as well as of its correct implementation into a commercial finite element (fe) code (abaqus), are verified herein through comparisons with detailed test data on shrunk rc beams subjected to short-term bending. the first considered experimental program (carried out by gribniak, [13]) mainly focuses on the effects of concrete shrinkage on beam deflection and first cracking moment in case of different amounts of top reinforcement, while the second one (by sato et al. [14]) compares the flexural behavior of rc beams subjected or not to shrinkage prior to loading. numerical vs. experimental results for rc beams with different amounts of top reinforcement [13] four rc beams tested by gribniak [13] – respectively named s1, s1r, s2, s2r – and subjected to four-point bending are first analyzed. the considered specimens were characterized by the same geometry, with a rectangular cross-section (300 mm deep and 280 mm wide) and a total length equal to 3280 mm, with a net span of 3000 mm. series 1 and 2 were obtained from different concrete batches, showing slightly different compressive strengths fc, as reported in tab. 1. sample steel concrete as,bottom [mm2] as,top [mm2] es [gpa] fsy [mpa] fc [mpa] εsh (10-6) φc s1 309.0 56.6 212 566 47.3 -194.6 1.6 s1r 309.0 749 212 566 47.3 -188.2 1.6 s2 309.0 56.6 212 566 48.7 -152.6 1.4 s2r 309.0 749 212 566 48.2 -155.7 1.4 table 1: material properties of rc beams tested by gribniak [13]. all the specimens contained the same amount of lower tensile reinforcement (denoted as as,bottom in tab. 1, corresponding to 4ϕ10 mm bars), as well as of transverse reinforcement (ϕ6 mm / 100 mm spaced). the two specimens with designation “r” had an higher amount of top reinforcement (as,top, tab. 1), constituted by 3ϕ18 mm bars, instead of 2ϕ6 mm bars. the main mechanical properties of steel reinforcement are summarized in tab. 1 for reading convenience, together with t p. bernardi et alii, frattura ed integrità strutturale, 37 (2016) 15-21; doi: 10.3221/igf-esis.37.03 18 concrete compressive strength fc, shrinkage strains εsh and creep coefficient φc measured at the test date (see [13] for details). the experimental value of εsh is used herein to compose the shrinkage strain vector that must be defined in the numerical model, as described in the previous section. since shrinkage-induced stresses develop gradually with time, the relief caused by creep should be included in numerical simulations, as suggested by many authors in the literature (e.g., [1, 8]). the creep coefficient φc reported in tab. 1 is therefore adopted in the initial step of the analyses to correct the stresses in concrete, by applying the effective modulus method [1]. all tests were carried out under loading control. on the contrary, numerical analyses are performed under displacement control, in order to achieve a better numerical convergence. taking advantage of the symmetry of the problem, only one half of each beam is simulated, by adopting a fe mesh constituted by quadratic, isoparametric 8-node membrane elements with reduced integration (4 gauss integration points). 0 20 40 60 80 100 0 3 6 9 12 15 s1 experimental [13] numerical p [kn] δ [mm] p [kn] δ [mm] (a) mcr,exp [knm] 16.8 mcr,num [knm] 14.9 δi,num [mm] 0.13 0 20 40 60 80 100 0 3 6 9 12 15 s1r experimental [13] numerical p [kn] δ [mm] (b) mcr,exp [knm] 19.8 mcr,num [knm] 17.5 δi,num [mm] -0.16 0 20 40 60 80 100 0 3 6 9 12 15 s2 experimental [13] numerical p [kn] δ [mm] (c) mcr,exp [knm] 15.9 mcr,num [knm] 15.4 δi,num [mm] 0.09 0 20 40 60 80 100 0 3 6 9 12 15 s2r experimental [13] numerical p [kn] δ [mm] (d) mcr,exp [knm] 17.9 mcr,num [knm] 17.6 δi,num [mm] -0.13 figure 1: comparison between numerical and experimental [13] results in terms of total applied load p vs. midspan deflection δ for beams: (a) s1; (b) s1r; (c) s2; (d) s2r. a first comparison between numerical and experimental results is provided in fig. 1, in terms of total applied load p vs. midspan deflection δ. since the initial deflection due to shrinkage was not experimentally measured, numerical analyses are shifted to the origin along the horizontal axis, so as to match experimental results. the values of initial shrinkage deflection δi, as obtained from numerical analyses before the application of external loading, is however reported in each graph of fig. 1. a good agreement is found for all the considered specimens. beams with a larger amount of top reinforcement (designation “r”, fig. 1b,d) are characterized by an initial negative deflection δi due to shrinkage. moreover, they show an higher cracking resistance with respect to their twin specimens (fig. 1a,c). this can be attributable to the increment of moment of inertia due to the presence of a heavier top reinforcement, but mainly to the difference of tensile stresses caused by shrinkage in the extreme bottom fiber of the cross-section. to better clarify this last aspect, the numerical variation within the depth of the section of the total strain ε, as well as of the stresses in concrete σc and in steel σs just before loading are reported in fig. 2 for the twin beams s1 and s1r. the presence of a not symmetric reinforcement in the beam cross-section determines a not uniform restraint to free shrinkage, which in turn causes the element curvature p. bernardi et alii, frattura ed integrità strutturale, 37 (2016) 15-21; doi: 10.3221/igf-esis.37.03 19 and the appearance of a stress gradient. heavy compressive reinforcement (s1r specimen) provides a larger restraint to the top of the beam, so leading to a reversed curvature and to a great reduction of tensile shrinkage stresses in the extreme bottom fiber. for this reason, a greater applied moment is required to crack the member. 0 50 100 150 200 250 300 -210 -190 -170 -150 -130 s1 s1r d is ta n ce f ro m t h e b o tt o m [ m m ] ε (10-6) bottom bars level top bars level 0.3 -0.1 0.1 0.3 0.5 0.7 0.9 σc [mpa] 45 -40 -35 -30 -25 σs [mpa] -0.3 -45 figure 2: numerical values of total strains ε, concrete σc and steel σs stresses within the depth of the section at midspan just before loading for beams s1 and s1r. numerical vs. experimental results on rc beams subjected or not to shrinkage before loading [14] two rc beams tested by sato et al. [14] – named v-01-13wb and v-01-13db – and subjected to four-point bending are selected for further comparisons. the considered specimens were characterized by the same geometry, with a rectangular cross-section (200 mm deep and 150 mm wide) and a total length equal to 2800 mm, with a net span of 2200 mm. the two beams were also characterized by the same amount of tensile reinforcement, consisting of two d13 bars. the specimens belonged to the same concrete batch, but were subjected to different curing conditions. after demolding, beam v-01-13wb was indeed sealed at room temperature with saturated paper (“wet curing”) until the time of testing, whereas beam v-01-13db was first subjected to wet curing for one week and subsequently exposed to room atmosphere for 114 days (“drying condition”). sample steel concrete as,bottom [mm2] es [gpa] fsy [mpa] fc [mpa] fct,sp* [mpa] ec [gpa] εsh (10-6) φc v-01-13wb 253.4 193.2 353 30.6 2.9 27.5 v-01-13db 253.4 193.2 353 32.5 3.0 28.5 425 3.3 * : fct adopted in the analyses is calculated from fct,sp according to uni en 1992-1-1 [16] table 2: material properties of rc beams tested by sato et al. [14] 0 2 4 6 8 10 12 14 16 0 2 4 6 8 10 12 14 experimental v-01-13wb [14] experimental v-01-13db [14] numerical v-01-13wb numerical v-01-13db m [knm] δ [mm] (a) sample v-01-13wb v-01-13db mcr,exp [knm] 3.6 2.1 mcr,num [knm] 3.2 2.1 δexp** [mm] 3.7 4.6 δnum** [mm] 3.7 4.7 wmax,exp** [mm] 0.12 0.12 wmax,num** [mm] 0.10 0.15 wav,exp** [mm] 0.07 0.08 wav,num** [mm] 0.05 0.06 **: values at m=7.2 knm figure 3: comparison between numerical and experimental [14] results (a) in terms of bending moment m vs. midspan deflection δ; (b) under serviceability conditions, for beams v-01-13wb and v-01-13db. p. bernardi et alii, frattura ed integrità strutturale, 37 (2016) 15-21; doi: 10.3221/igf-esis.37.03 20 the main mechanical properties of steel and concrete, together with the average free shrinkage strain εsh and the creep coefficient φc at the date of testing, are summarized in tab. 2. numerical analyses are performed by following the same modeling choices already described in the previous section. fig. 3a shows a comparison between numerical and experimental [14] results in terms of bending moment m vs. midspan deflection δ; for both the considered beams. since initial deflection due to shrinkage was not experimentally measured, also in this case numerical curves are shifted to the origin.     w [mm] figure 4: numerical and experimental [14] crack pattern at failure for specimen v-01-13db. as can be seen from fig. 3a, the shrunk specimen v-01-13db is characterized by a reduced cracking load and a larger deflection with respect to sample v-01-13wb. additional comparisons are provided in fig. 3b, where numerical and experimental values of cracking moment mcr, deflection δ, average and maximum crack width (wav and wmax) under serviceability conditions are listed. finally, a good agreement is also found in terms of crack pattern at failure, as proved by fig. 4, which reports numerical and experimental results for the shrunk specimen v-01-13db. conclusions n this paper, a non-linear constitutive model for the analysis of rc structures, named 2d-parc, is modified so as to include early-age shrinkage effects. the procedure is verified through comparisons with experimental data on rc beams subjected to short-term loadings available in the literature. satisfactory results are obtained in terms of both global behavior and local member response (i.e. stresses in concrete/steel, crack distribution and width), thus making the model a useful tool both in engineering and research practice. references [1] gilbert, r.i., shrinkage, cracking and deflection – the serviceability of concrete structures, ejse international, 1 (2001) 2-14. [2] gribniak, v., kaklauskas, g., kliukas, r., jakubovskis r., shrinkage effect on short-term deformation behavior of reinforced concrete – when it should not be neglected, mater design, 51 (2013) 1060-70. doi:10.1016/j.matdes.2013.05.028 [3] bischoff, p.h., effects of shrinkage on tension stiffening and cracking in reinforced concrete, can j civil eng, 28 (2001) 363–74. doi: 10.1139/l00-117 [4] scanlon, a., bischoff, p.h., shrinkage restraint and loading history effects on deflections of flexural members, aci struct j, 105 (2008) 498–506. [5] rots, j. g., de borst r., analysis of mixed-mode fracture in concrete, j struct mech, 113 (1987) 1739-1758. doi:10.1061/(asce)0733-9399 [6] vecchio, f.j., reinforced concrete membrane element formulations, asce j struct eng, 116 (1990) 730-50. doi:10.1061/(asce)0733-9445 [7] maekawa, k., soltani, m., ishida, t., itoyama, y., time-dependent space-averaged constitutive modeling of cracked reinforced concrete subjected to shrinkage and sustained loads, j adv concr technol, 4 (2006) 193-207. doi:10.3151/jact.4.193 [8] kaklauskas, g., gribniak, v., bacinskas, d., vainiunas, p., shrinkage influence on tension stiffening in concrete members, eng struct, 31 (2009) 1305-12. doi:10.1016/j.engstruct.2008.10.007 i p. bernardi et alii, frattura ed integrità strutturale, 37 (2016) 15-21; doi: 10.3221/igf-esis.37.03 21 [9] luo, y., wang, m.y., zhou, m., deng, z., topology optimization of reinforced concrete structures considering control of shrinkage and strength failure, comput struct, 157 (2015) 31-41. doi:10.1016/j.compstruc.2015.05.009 [10] cerioni, r., iori, i., michelini, e., bernardi, p., multi-directional modeling of crack pattern in 2d r/c members, eng fract mech, 75 (2008) 615–28. doi:10.1016/j.engfracmech.2007.04.012. [11] bernardi, p., cerioni, r., michelini, e., analysis of post-cracking stage in sfrc elements through a non-linear numerical approach, eng fract mech, 108 (2013) 238-250. doi:10.1016/j.engfracmech.2013.02.024 [12] bernardi, p., cerioni, r., michelini, e., sirico, a., numerical modeling of the cracking behavior of rc and sfrc shear-critical beams, eng fract mech (2016) doi:10.1016/j.engfracmech.2016.04.008 [13] gribniak, v., shrinkage influence on tension-stiffening of concrete structures, phd thesis, vilniaus gedimino technikos universitetas, vilnius, lituania (2009) [14] sato, r., maruyama, i., sogabe, t., sogo, m., flexural behavior of reinforced recycled concrete beams, j adv concr technol, 5 (2007) 43-61. doi:10.3151/jact.5.43 [15] aci committee 209. guide for modeling and calculating shrinkage and creep in hardened concrete, aci 209.2r08, farmington hills, michigan, (2008) [16] uni en 1992-1-1:2005. eurocode 2 – design of concrete structures – part 1-1: general rules and rules for buildings, (2005). [17] bazant, z., p., baweja s., creep and shrinkage prediction model for analysis and design of concrete structures: model b3. aci special publications 194 (2000). << /ascii85encodepages false /allowtransparency false /autopositionepsfiles true /autorotatepages /none /binding /left /calgrayprofile (dot gain 20%) /calrgbprofile (srgb iec61966-2.1) /calcmykprofile (u.s. web coated \050swop\051 v2) /srgbprofile (srgb iec61966-2.1) /cannotembedfontpolicy /error /compatibilitylevel 1.4 /compressobjects /tags /compresspages true /convertimagestoindexed true /passthroughjpegimages true /createjobticket false /defaultrenderingintent /default /detectblends true /detectcurves 0.0000 /colorconversionstrategy /cmyk /dothumbnails false /embedallfonts true /embedopentype false /parseiccprofilesincomments true /embedjoboptions true /dscreportinglevel 0 /emitdscwarnings false /endpage -1 /imagememory 1048576 /lockdistillerparams false /maxsubsetpct 100 /optimize true /opm 1 /parsedsccomments true 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can be opened with acrobat and adobe reader 5.0 and later.) >> /namespace [ (adobe) (common) (1.0) ] /othernamespaces [ << /asreaderspreads false /cropimagestoframes true /errorcontrol /warnandcontinue /flattenerignorespreadoverrides false /includeguidesgrids false /includenonprinting false /includeslug false /namespace [ (adobe) (indesign) (4.0) ] /omitplacedbitmaps false /omitplacedeps false /omitplacedpdf false /simulateoverprint /legacy >> << /addbleedmarks false /addcolorbars false /addcropmarks false /addpageinfo false /addregmarks false /convertcolors /converttocmyk /destinationprofilename () /destinationprofileselector /documentcmyk /downsample16bitimages true /flattenerpreset << /presetselector /mediumresolution >> /formelements false /generatestructure false /includebookmarks false /includehyperlinks false /includeinteractive false /includelayers false /includeprofiles false /multimediahandling /useobjectsettings /namespace [ (adobe) (creativesuite) (2.0) ] /pdfxoutputintentprofileselector /documentcmyk /preserveediting true /untaggedcmykhandling /leaveuntagged /untaggedrgbhandling /usedocumentprofile /usedocumentbleed false >> ] >> setdistillerparams << /hwresolution [2400 2400] /pagesize [612.000 792.000] >> setpagedevice shot peening processes to obtain nanocrystalline surfaces in metal alloys: a. carpinteri et alii, frattura ed integrità strutturale, 7 (2009) 1728; doi: 10.3221/igf-esis.07.02 17 il modello della fessura coesiva in trazione e compressione per la valutazione della duttilità degli elementi strutturali in calcestruzzo armato alberto carpinteri, mauro corrado, giuseppe mancini, marco paggi politecnico di torino – dipartimento di ingegneria strutturale e geotecnica, corso duca degli abruzzi 24, 10129, torino, italy riassunto. il problema della valutazione della duttilità degli elementi in calcestruzzo armato soggetti a flessione o presso-flessione è stato largamente studiato negli ultimi decenni, sia da un punto di vista sperimentale che analitico. data l’influenza di numerosi parametri di progetto sulla duttilità, tuttavia, è difficile sviluppare un modello in grado di descrivere completamente la risposta meccanica di elementi strutturali, tenendo conto di tutti gli effetti dovuti alla non-linearità dei materiali. nel passato, in particolare, si è studiato in maniera approfondita l’effetto della classe di duttilità dell’acciaio, mentre il ruolo degli effetti di scala, evidenziato da più campagne sperimentali, non è stato ancora del tutto chiarito. una delle ragioni principali è l’inadeguatezza dei modelli tradizionali, basati su leggi costitutive tra tensioni e deformazioni. nel presente lavoro, si propone un nuovo modello basato sul concetto della localizzazione delle deformazioni, capace di descrivere la propagazione della fessura e l’avanzamento del crushing durante il processo di carico. in tale contesto, il comportamento non-lineare del calcestruzzo in compressione è modellato attraverso l’overlapping crack model, modello analogo a quello coesivo valido per la trazione, che descrive la localizzazione delle deformazioni dovuta al danneggiamento del calcestruzzo mediante una compenetrazione del materiale. con questo nuovo algoritmo è possibile cogliere l’effettiva risposta flessionale di elementi strutturali in calcestruzzo armato al variare della percentuale di armatura e della scala dimensionale. applicazioni numeriche riguardano l’analisi della risposta post-picco di provini in calcestruzzo soggetti a compressione e la valutazione delle rotazioni plastiche di travi in calcestruzzo armato soggette a flessione su tre punti. si propone infine un ampio confronto con i risultati di prove sperimentali, con lo scopo di dimostrare la validità del nuovo approccio. abstract. the problem of assessing the ductility of reinforced concrete (rc) structural elements in bending or under the action of eccentric forces has been largely investigated from both the experimental and the analytical point of view during the last decades. since the development of ductility is influenced by several design parameters, it is difficult to develop a predictive model able to fully describe the mechanical behaviour of the structural element. in particular, the role of the size-scale effect, which has been evidenced by some experimental tests, is not yet completely understood. one of the main reasons is the inadequacy of the traditional models based on ad hoc stress-strain constitutive laws. in the present contribution, a new model based on the concept of strain localization is proposed, which is able to describe both cracking and crushing growths during the loading process. in particular, the nonlinear behaviour of concrete in compression is modelled by the overlapping crack model, which describes the strain localization due to crushing by means of a material compenetration. with this numerical algorithm in hand, it is possible to effectively capture the flexural behaviour of rc structural elements by varying the reinforcement percentage and/or the structural size. numerical applications regard the analysis of the post-peak nonlinear response of concrete specimens subjected to eccentric compression tests and the evaluation of the plastic rotation of rc beams under three-point bending. an extensive comparison with experimental results is also proposed, fully demonstrating the effectiveness of the proposed approach. http://dx.medra.org/10.3221/igf-esis.07.02&auth=true http://www.gruppofrattura.it a. carpinteri et alii, frattura ed integrità strutturale, 7 (2009) 17-28; doi: 10.3221/igf-esis.07.02 18 parole chiave. calcestruzzo armato, rotazioni plastiche, effetti di scala, crushing, modello coesivo, metodo degli elementi finiti. introduzione l comportamento del calcestruzzo in compressione, e in particolar modo la resistenza a compressione e la risposta meccanica nella fase di post-picco, hanno un ruolo predominante nel progetto di strutture in calcestruzzo semplice e armato. il progetto di elementi strutturali, infatti, è basato sul confronto tra una caratteristica sollecitante e la corrispondente resistenza, valutata sulla base della resistenza propria del materiale e del meccanismo di collasso. il comportamento del materiale nella fase di post-picco è invece fondamentale per una corretta valutazione della duttilità della struttura, come ad esempio nella valutazione della deformazione assiale ultima di pilastri o della capacità di rotazione plastica di travi in calcestruzzo armato. in questo contesto, gli effetti della dimensione strutturale giocano un ruolo importante, dovuto al fatto che i parametri caratteristici del calcestruzzo vengono valutati su provini alla scala del laboratorio, alquanto diversa dalla dimensione delle strutture reali. da qui la necessità di sviluppare modelli analitici o numerici che permettano di estrapolare correttamente i risultati delle prove sperimentali alle grandi scale. l’interesse per la duttilità delle strutture risale all’inizio del secolo scorso, con il diffondersi del calcolo plastico come metodo di valutazione del carico ultimo di una struttura [1]. in questo contesto, tale proprietà è fondamentale per permettere la ridistribuzione dei momenti flettenti all’interno di strutture iperstatiche. la duttilità può essere opportunamente valutata attraverso la capacità di rotazione delle cerniere plastiche che si sviluppano nelle sezioni più sollecitate. a tal proposito, due possibili definizioni di rotazione plastica sono state proposte in letteratura. in base al model code 90 [2], tale rotazione è definita come la differenza tra la rotazione corrispondente al massimo momento resistente e quella relativa allo snervamento dell’acciaio, come rappresentato schematicamente da )1(plϑ in fig. 1. al fine di considerare il contributo di duttilità sviluppato oltre il carico massimo, hillerborg [3] e pecce [4] hanno proposto una misura alternativa della rotazione plastica, come differenza tra la rotazione oltre la quale si ha un rapido decremento del momento resistente e la rotazione di snervamento dell’acciaio ( )2(plϑ in fig. 1). queste misure sono entrambe proporzionali alla duttilità delle travi in calcestruzzo armato. figura 1: differenti definizioni di rotazione plastica nel diagramma momento-rotazione della sezione più sollecitata. data la complessità del fenomeno di formazione e di sviluppo delle cerniere plastiche, i primi studi sulla capacità rotazionale derivano dalle prove sperimentali condotte negli anni ’60 del secolo scorso, coordinate dalla “indeterminate structures commission” del ceb [5], presieduta dal prof. baker. sulla base dei risultati sperimentali ottenuti, pubblicati nel 1967 [6], si decise di descrivere la rotazione plastica in funzione della profondità relativa dell’asse neutro, x/d. di conseguenza, fu proposta la seguente relazione iperbolica, che costituisce la curva approssimante il frattile 5% dei risultati: x d pl 004.0=ϑ (1) i http://dx.medra.org/10.3221/igf-esis.07.02&auth=true http://www.gruppofrattura.it a. carpinteri et alii, frattura ed integrità strutturale, 7 (2009) 1728; doi: 10.3221/igf-esis.07.02 19 tale espressione fu assunta da alcune normative dell’epoca, come ad esempio il model code 78, per risolvere il problema della valutazione delle rotazioni plastiche ammissibili ai fini progettuali. un secondo importante contributo fu dato dalla ricerca condotta agli inizi degli anni ’80 presso l’università di stoccarda dal gruppo coordinato dal prof. eligehausen [7]. in tale occasione fu sviluppato un modello analitico per l’analisi delle cerniere plastiche considerando l’esistenza di due tipi di collasso: lato acciaio e lato calcestruzzo. le curve proposte sono confrontate in fig. 2 con la legge espressa dall’eq. (1). due aspetti fondamentali devono essere evidenziati: la presenza di un ramo crescente per piccoli valori di x/d dovuto alla rottura lato acciaio e la presenza di due curve relative ad acciai aventi caratteristiche di duttilità differenti. tali curve furono in seguito adottate dal model code 90. successivamente altri modelli furono sviluppati, enfatizzando uno o più particolari aspetti del problema [8-10]. la più recente indicazione normativa è quella presente nell’ultima versione dell’eurocodice 2 parte 2 [11], riportata in fig. 3. le linee tratteggiate si riferiscono ad acciai ad alta duttilità (classe c), mentre quelle a tratto pieno si riferiscono ad acciai a normale duttilità (classe b). dall’analisi delle indicazioni delle normative si può evidenziare come l’effetto della scala sulla capacità rotazionale sia stato trascurato, sebbene numerose campagne sperimentali abbiano evidenziato una forte influenza di tale fenomeno [12-15]. figura 2: evoluzione delle formule di progetto per il calcolo della rotazione plastica ammissibile. figura 3: legami tra rotazione plastica ammissibile e profondità relativa dell’asse neutro in base all’eurocodice 2. come intuito da hillerborg fin dal 1990 [3], la causa degli effetti di scala, anche per quanto riguarda la capacità di rotazione, risiede nella localizzazione delle deformazioni, sia in trazione che in compressione. hillerborg fu il primo ad introdurre tale concetto, decisamente più intuitivo nel caso della trazione, anche in compressione. in base al suo approccio, una volta raggiunta la resistenza a compressione, si verifica una localizzazione delle deformazioni all’interno di una zona della trave avente una lunghezza pari alla profondità della zona compressa. bažant [16] ha proposto un modello http://dx.medra.org/10.3221/igf-esis.07.02&auth=true http://www.gruppofrattura.it a. carpinteri et alii, frattura ed integrità strutturale, 7 (2009) 17-28; doi: 10.3221/igf-esis.07.02 20 analogo, nel quale la zona di localizzazione è definita come lunghezza caratteristica del materiale. tale modello permette di affrontare il problema degli effetti di scala, ma di fatto non permette di ottenere una legge costitutiva propria del materiale, essendo la lunghezza di localizzazione proporzionale alla dimensione del provino. inoltre, in entrambi i modelli, la lunghezza di localizzazione non è definita sulla base di valutazioni teoriche ma da un best-fitting di risultati sperimentali. d’altro canto, la localizzazione delle deformazioni in compressione è stata osservata in numerose campagne sperimentali [17-22]. nel presente lavoro, il comportamento del calcestruzzo in compressione viene descritto mediante un nuovo modello, denominato overlapping crack model, nel quale il processo di collasso del calcestruzzo in compressione è descritto in modo analogo a quello in trazione. in trazione la localizzazione delle deformazioni è rappresentata dall’apertura della fessura, mentre in compressione è descritta da una compenetrazione del materiale, come mostrato in fig. 4. questi due modelli elementari vengono poi coniugati in un modello numerico più complesso sviluppato per descrivere il comportamento delle cerniere plastiche in elementi in calcestruzzo armato. tale modello sarà successivamente validato mediante confronto con i risultati di prove sperimentali condotte su travi in calcestruzzo armato da bosco e debernardi [14]. infine, sarà proposto un confronto tra i risultati del modello e le prescrizioni dell’eurocodice 2 riguardanti la capacità rotazionale di travi in calcestruzzo armato. figura 4: compenetrazione in compressione (a); analoga alla fessura coesiva in trazione (b). analisi numerica n questa sezione si propone un nuovo modello basato sui concetti della meccanica della frattura per la valutazione della capacità di rotazione plastica di travi in calcestruzzo armato soggette a flessione. l’analisi è condotta su un concio di trave avente lunghezza pari all’altezza, soggetto a momento flettente costante. tale elemento è considerato rappresentativo della zona di formazione della cerniera plastica, coerentemente con quanto suggerito dall’eurocodice 2. si assume, inoltre, che i processi di frattura in trazione e di crushing in compressione siano localizzati nella sezione di mezzeria, mentre la parte restante abbia un comportamento elastico. ciò implica che sia considerata un’unica fessura equivalente, anziché una fessurazione diffusa. la distribuzione delle tensioni nella sezione di mezzeria è elastica-lineare fino al raggiungimento della resistenza a trazione in corrispondenza del lembo inferiore. quando tale limite è raggiunto, una fessura coesiva si propaga dall’intradosso verso l’estradosso del concio. al di fuori della fessura il materiale ha comportamento elastico. in questa fase il momento esterno aumenta, la fessura si estende e la tensione di compressione al lembo superiore aumenta fino a raggiungere la resistenza a compressione. a questo punto inizia il danneggiamento a compressione del calcestruzzo con la conseguente localizzazione dell’energia dissipata, che viene descritta mediante la compenetrazione del materiale. più grande è la compenetrazione (overlapping), più piccoli sono gli sforzi di compressione trasmessi dai due elementi. il modello coesivo per descrivere la frattura del calcestruzzo in trazione in base al modello coesivo [23, 24], la legge costitutiva utilizzata per il materiale non danneggiato è una relazione σ−ε lineare-elastica fino al raggiungimento della resistenza a trazione. nella zona di processo, il materiale danneggiato è ancora in grado di trasmettere sforzi attraverso le facce della fessura. tali sforzi sono inversamente proporzionali all’apertura della fessura, wt, secondo la seguente espressione:         −= t cr t ut,t 1 w w σσ (2) i http://dx.medra.org/10.3221/igf-esis.07.02&auth=true http://www.gruppofrattura.it a. carpinteri et alii, frattura ed integrità strutturale, 7 (2009) 1728; doi: 10.3221/igf-esis.07.02 21 dove: wt è l’apertura della fessura, wtcr è il valore critico dall’apertura della fessura oltre il quale si annullano gli sforzi trasmessi e σt,u è la resistenza a trazione. l’area sottesa dalla curva tensione-spostamento rappresenta l’energia di frattura, tfg . il modello di overlapping per descrivere la rottura del calcestruzzo in compressione in ambito strutturale, le leggi costitutive maggiormente adottate per il calcestruzzo in compressione descrivono il comportamento del materiale in termini di tensione in funzione della deformazione (legge elasto-plastica, parabolarettangolo, parabola di sargin, ecc.). questo approccio, che implica una dissipazione di energia all’interno dell’intero volume, non permette di descrivere correttamente il comportamento meccanico al variare della dimensione strutturale. al contrario, gli effetti della scala sono dovuti alla localizzazione delle deformazioni all’interno di una banda di danneggiamento trasversale o inclinata [17-19] e ad una conseguente localizzazione dell’energia dissipata nella fase di postpicco. a tal proposito, è stato evidenziato come l’energia dissipata per unità di volume diminuisca all’aumentare della scala, mentre, la stessa energia, rapportata all’area della sezione trasversale, possa essere considerata costante [20-22]. alcuni autori [17, 18] hanno sperimentalmente evidenziato che, da un punto di vista globale, senza considerare in dettaglio il meccanismo di collasso del provino, lo schiacciamento localizzato può essere considerato come una caratteristica del materiale nella fase di post-picco, analogamente a quanto avviene per l’apertura della fessura in trazione. sulla base di tale osservazione è possibile introdurre un modello più generale, per cui la deformazione irreversibile dovuta al fenomeno di danneggiamento è descritta da una compenetrazione fittizia, mentre la parte restante di provino è soggetta ad uno scarico elastico, come proposto da carpinteri et al. [25]. di conseguenza viene introdotta una doppia legge costitutiva: un legame σ–ε fino al raggiungimento della resistenza a compressione (fig. 5a) e un legame σ–w (compenetrazione) descrivente la rottura a compressione del calcestruzzo (fig. 5b). quest’ultima relazione descrive il modo in cui la tensione nel materiale danneggiato diminuisce dal valore massimo fino a zero all’aumentare della compenetrazione da zero fino al valore critico wccr. è importante notare che la compenetrazione è una quantità integrata che permette di caratterizzare il comportamento strutturale senza la necessità di modellare nello specifico il reale meccanismo di rottura, che può variare dalla frantumazione, alla rottura diagonale per taglio, allo splitting, variando la scala e la snellezza del provino compresso. figura 5: modello di overlapping: legame tensione-deformazione (a); legame tensione-compenetrazione (b). l’area sottesa dalla curva σ–w riportata in fig. 5b rappresenta l’energia di crushing, cfg , definita come energia dissipata per unità di superficie. tale parametro è una proprietà del materiale dal momento che non è affetta dalla scala strutturale. la formulazione empirica utilizzata nel presente lavoro per determinarne il valore è stata proposta da suzuki et al. [19], ed è basata su risultati di prove a compressione uniassiale condotte su provini in calcestruzzo semplice e armato trasversalmente: 2 c,0 e 2 a c,0 c f,0 c,0 c f 10000 σσσ pk += gg (3) dove: σc,0 è la resistenza media a compressione, ka è un parametro dipendente dalla resistenza a trazione e dalla percentuale volumetrica delle staffe e pe è la pressione laterale effettiva esercitata sul calcestruzzo (vedere [19] per http://dx.medra.org/10.3221/igf-esis.07.02&auth=true http://www.gruppofrattura.it a. carpinteri et alii, frattura ed integrità strutturale, 7 (2009) 17-28; doi: 10.3221/igf-esis.07.02 22 approfondimenti). l’energia di frantumazione per il calcestruzzo non confinato, cf,0g , può essere valutata mediante le seguente espressione: b c f,0 5080 k−=g , (4) dove il parametro kb dipende dalla resistenza a compressione del calcestruzzo. variando la classe di resistenza del calcestruzzo tra 20 e 90 mpa, l’eq. (4) dà un’energia variabile tra 30 e 58 n/mm. si può notare come l’energia di crushing sia tra due e tre ordini di grandezza superiore all’energia di frattura, mentre il valore critico della compenetrazione, wccr ≈ 1 mm, è di un ordine di grandezza superiore al valore critico di apertura della fessura (si vedano anche i risultati delle prove sperimentali di jansen e shah [18]). infine, si può evidenziare che, nel caso di calcestruzzo compresso confinato, l’energia di crushing calcolata con l’eq. (3) e il corrispondente valore critico della compenetrazione, aumentano considerevolmente. il modello proposto, basato su una compenetrazione fittizia, permette di ottenere la legge costitutiva effettiva del materiale, indipendente dalla dimensione strutturale. la validità di questo approccio può essere dimostrata con provini caratterizzati non solo da snellezze differenti [17, 18] ma anche da dimensioni diverse. a tal proposito, si considerino le prove sperimentali condotte da ferrara e gobbi [26] su provini in calcestruzzo con tre differenti snellezze (0.5, 1.0 e 2.0) e tre differenti scale variabili nel rapporto 1:2:4. le curve tensione adimensionalizzata in funzione della deformazione media ottenute sperimentalmente sono riportate in fig. 6a, ove con s si indicano i provini aventi sezione trasversale pari a 50x50 mm, con m 100x100 mm ed l 150x150 mm. la buona sovrapposizione dei rami crescenti di dette curve indica che, come ci si poteva aspettare, la fase elastica è indipendente da qualsiasi parametro geometrico e la sua pendenza è definita dal modulo elastico. al contrario, i rami di post-picco sono altamente influenzati dalla snellezza e dalla scala del provino. ciò comporta che la legge tensione-deformazione non possa essere assunta come caratteristica del materiale. figura 6: test a compressione condotti da ferrara e gobbi [26]: legami tensione-deformazione (a); legge di overlapping (b). considerazioni totalmente differenti possono invece essere svolte con riferimento alle leggi di overlapping. i legami σ−w relativi alla fase di post-picco vengono ricavati dalle curve σ−ε secondo la seguente procedura: 1) si valuta la legge tensione-schiacciamento totale del provino (σ−δ) moltiplicando le deformazioni ε per l’altezza del provino; 2) dalle curve σ−δ ottenute si sottrae l’espansione elastica del provino, δel, dovuta allo scarico tensionale, e la componente plastica della fase pre-picco, δpl, così come rappresentato in fig. 7. lo spostamento δel è valutato mediante la seguente espressione: l e c tan el σ δ = (5) dove: σc è la tensione agente, etan è il modulo elastico tangente ed l è l’altezza totale del provino. http://dx.medra.org/10.3221/igf-esis.07.02&auth=true http://www.gruppofrattura.it a. carpinteri et alii, frattura ed integrità strutturale, 7 (2009) 1728; doi: 10.3221/igf-esis.07.02 23 le relazioni σ−w determinate per le prove sperimentali di ferrara e gobbi sono riportate in fig. 6b. come si può vedere, le curve rappresentative del comportamento di softening collassano in una banda molto ristretta, confermando la scarsa dipendenza della legge di overlapping dalla snellezza e dalla scala del provino. figura 7: procedura per ottenere la legge di overlapping a partire dal legame tensione-schiacciamento totale, δ. legge costitutiva dell’armatura nella pratica corrente, le leggi costitutive maggiormente utilizzate per descrivere il comportamento dell’acciaio sono definite in campo σ−ε, quali, ad esempio, quella elasto-plastica e quella elasto-incrudente. nel nuovo modello che viene qui proposto, non è possibile utilizzare siffatte relazioni in quanto la sezione di mezzeria del concio analizzato è cinematicamente descritta mediante spostamenti anziché deformazioni. sarà pertanto necessario introdurre una legge che leghi la tensione agente nell’armatura con l’apertura della fessura in corrispondenza del rinforzo stesso. in passato tale problema è stato risolto in modo semplice ma efficace imponendo un comportamento di tipo rigido-plastico, cioè imponendo che l’apertura della fessura sia nulla fino a che l’armatura non si snervi [27]. nel presente modello si vuole invece adottare un approccio più vicino alla realtà, nella quale l’apertura della fessura è ammessa anche in assenza di snervamento dell’acciaio. ciò è reso possibile dagli scorrimenti relativi tra calcestruzzo e armatura. le tipiche relazioni tra scorrimento e aderenza sono definite in termini di tensioni tangenziali tra acciaio e calcestruzzo in funzione degli spostamenti relativi tra i due materiali [2]. l’integrazione degli scorrimenti lungo la lunghezza di trasferimento è pari a metà dell’apertura della fessura in corrispondenza del rinforzo. d’altra parte, l’integrazione delle tensioni tangenziali è pari alla reazione dell’armatura. al fine di semplificare i calcoli, è stata assunta una legge lineare fino al raggiungimento dello snervamento dell’acciaio, e costante successivamente. il parametro caratterizzante tale relazione è pertanto l’apertura corrispondente allo snervamento, wy, che è stata assunta pari a 0.3 mm. algoritmo numerico nel modello numerico il concio di trave da analizzare è considerato come costituito da due parti simmetriche aventi comportamento perfettamente elastico e connesse tra loro mediante n coppie di nodi lungo la sezione di mezzeria, come rappresentato in fig. 8. in corrispondenza di tali nodi agiranno le forze nodali equivalenti coesive e di overlapping e la forza di richiusura esercitata dall’armatura. tutte queste forze dipendono dagli spostamenti nodali di apertura della fessura e di sovrapposizione nella zona di crushing, secondo le leggi costitutive introdotte nei precedenti paragrafi. così facendo, nella sezione di mezzeria saranno concentrati i contributi di non-linearità. con riferimento alla fig. 8, le forze nodali orizzontali agenti sulla sezione di mezzeria sono date dalla seguente espressione: { } [ ]{ } { }mkwkf mw += (6) dove: {f} è il vettore delle forze nodali, [kw] è la matrice dei coefficienti di influenza per gli spostamenti nodali, {w} è il vettore degli spostamenti nodali, {km} è il vettore dei coefficienti di influenza per il momento applicato ed m è il momento applicato. i coefficienti di influenza, ijwk , presentano la dimensione fisica di una rigidezza e sono calcolati a priori con un’analisi agli elementi finiti, imponendo spostamenti unitari a ciascuno degli n nodi in fig. 8. nella generica situazione che si verifica durante il processo di carico, rappresentata in fig. 9, si considerano le seguenti equazioni: 0i =f per i = 1, 2, …, (j−1); i ≠ r (7a) http://dx.medra.org/10.3221/igf-esis.07.02&auth=true http://www.gruppofrattura.it a. carpinteri et alii, frattura ed integrità strutturale, 7 (2009) 17-28; doi: 10.3221/igf-esis.07.02 24         −= t c t i ut,i 1 w w ff ; per i = j, …, (m−1); i ≠ r (7b) 0ti =w ; per i = m, …, p (7c)         −= c c c i uc,i 1 w w ff ; per i = (p+1), …, n (7d) )( rr wff = ; per i = r (7e) l’equazione (7e) rappresenta la legge costitutiva dell’armatura. figura 8: discretizzazione della sezione di mezzeria mediante n nodi. figura 9: distribuzione delle forze nodali con fessura coesiva in trazione e crushing in compressione. le equazioni (6) e (7) costituiscono un sistema algebrico lineare di 2n equazioni in 2n+1 incognite, cioè {f}, {w} ed m. l’ulteriore equazione necessaria per la soluzione si ottiene imponendo che la forza agente nell’apice della fessura fittizia raggiunga la resistenza a trazione del materiale o che la forza agente nell’apice dell’overlapping fittizio raggiunga la resistenza a compressione. naturalmente, tra queste due condizioni, si impone quella più prossima alla criticità. il parametro guida è la posizione dell’apice che nel passo di soluzione considerato ha raggiunto la crisi. tale apice viene fatto avanzare di una posizione al passo successivo. infine, ad ogni passo di soluzione, è possibile calcolare la rotazione totale del concio, valutata in corrispondenza delle facce libere, ove è applicato il momento flettente, mediante la seguente relazione: { } { } mdwd mw += tϑ (8) dove: {dw} è il vettore dei coefficienti di influenza per gli spostamenti nodali, e dm è il coefficiente di influenza per il momento applicato. http://dx.medra.org/10.3221/igf-esis.07.02&auth=true http://www.gruppofrattura.it a. carpinteri et alii, frattura ed integrità strutturale, 7 (2009) 1728; doi: 10.3221/igf-esis.07.02 25 confronto con i risultati sperimentali e proposta per la normativa n questo paragrafo si propone un confronto tra i risultati numerici ottenuti mediante il modello coesivo/overlapping e quelli delle prove sperimentali condotte da bosco e debernardi [14]. in [14] sono state testate con lo schema di flessione su tre punti travi aventi snellezza constante, pari a 10, e differente altezza, pari a 200, 400 e 600 mm. sono state considerate differenti percentuali di armatura tesa, variabili tra 0.12% e 1.71%. i risultati delle simulazioni numeriche sono confrontati con le rotazioni dei conci posti a cavallo della mezzeria delle travi testate, caratterizzati da una lunghezza pari all’altezza. le curve momento-rotazione, sia numeriche che sperimentali, sono riportate nelle fig. 10a-c, per differenti altezze e percentuali di armatura tesa. tali diagrammi mostrano come la rotazione massima sia una funzione decrescente della quantità di armatura e della dimensione della trave. nel caso di bassa percentuale di armatura, il comportamento meccanico è caratterizzato dalla snervamento dell’acciaio così che la risposta strutturale è per lo più plastica. incrementando la quantità di armatura, il crushing del calcestruzzo diventa via via più evidente con la comparsa di un ramo di softening alla fine del tratto plastico. questa è una caratteristica importante del modello proposto, che permette di seguire rami instabili caratterizzati da pendenza positiva (snap-back). ciò è possibile in quanto il parametro di controllo del processo di carico è l’estensione della fessura coesiva e della zona di crushing, piuttosto che il carico applicato o la freccia in mezzeria. in generale, si può notare un buon accordo tra le simulazioni numeriche e i risultati sperimentali. figura 10: confronto tra risultati numerici e sperimentali per travi con altezze differenti: h = 200 mm (a); h = 400 mm (b); h = 600 mm (c). dopo la validazione preliminare del modello, si è condotta un’analisi parametrica al fine di analizzare l’effetto della dimensione strutturale e della percentuale di armatura sulla duttilità delle travi. l’andamento tipico dei risultati ottenuti è quello riportato in fig. 11 per una percentuale di armatura in trazione pari al 2%. il momento flettente è adimensionalizzato al fine di migliorare il confronto tra i risultati. il plateau orizzontale è dovuto allo snervamento dell’acciaio. le curve rappresentate evidenziano una diminuzione della rotazione massima dei conci di trave all’aumentare della dimensione della trave stessa, con la comparsa di rami di softening con una pendenza via via crescente. i http://dx.medra.org/10.3221/igf-esis.07.02&auth=true http://www.gruppofrattura.it a. carpinteri et alii, frattura ed integrità strutturale, 7 (2009) 17-28; doi: 10.3221/igf-esis.07.02 26 figura 11: momento flettente adimensionalizzato in funzione della rotazione totale del concio per ρt = 2% e differenti altezze. una caratteristica del presente modello è che non è necessario introdurre alcuna ipotesi sulle deformazioni, come ad esempio l’ipotesi di bernoulli. al contrario, gli spostamenti nodali della sezione di mezzeria sono ottenuti dalla procedura numerica di soluzione passo dopo passo. i profili degli spostamenti nodali relativi alla trave con altezza pari a 0.4 m e percentuale di armatura pari a 2% sono riportati in fig. 12 per differenti valori di carico. per bassi valori del momento flettente, fino a circa il 60% del momento di snervamento, il comportamento meccanico è caratterizzato da un progressivo avanzamento e apertura della fessura in trazione. il danneggiamento del calcestruzzo in compressione comincia appena prima dello snervamento dell’acciaio e cresce all’avvicinarsi del momento ultimo. figura 12: spostamenti nodali della sezione di mezzeria del concio per differenti livelli di carico, con h = 400 mm e ρt = 2%. con riferimento ai diagrammi momento-rotazione, è possibile valutare la capacità di rotazione plastica come differenza tra la rotazione ultima e quella relativa allo snervamento dell’acciaio. in particolare, nel presente lavoro si è scelta la definizione di rotazione ultima data da hillerborg [3] e pecce [4]. i risultati dell’analisi parametrica possono così essere riassunti nel grafico di fig. 13, che mette in relazione la rotazione plastica con la profondità relativa dell’asse neutro, x/d, coerentemente con quanto previsto dalle normative. la curva tratteggiata è quella fornita dall’eurocodice 2 per acciaio ad alta duttilità e classe di resistenza del calcestruzzo inferiore o uguale a 50 mpa, mentre le curve a tratto pieno sono relative ai risultati numerici. travi con un’altezza pari a 0.2 m esibiscono una capacità rotazionale superiore a quella indicata dalla normativa, mentre travi con altezza pari a 0.6 m o 0.8 m hanno una capacità di rotazione inferiore. ciò evidenzia una forte influenza della dimensione strutturale, completamente ignorata dalle normative. http://dx.medra.org/10.3221/igf-esis.07.02&auth=true http://www.gruppofrattura.it a. carpinteri et alii, frattura ed integrità strutturale, 7 (2009) 1728; doi: 10.3221/igf-esis.07.02 27 conclusioni el presente lavoro, si è proposto un algoritmo numerico per l’analisi del comportamento duttile di elementi in calcestruzzo armato in flessione. al fine di ottenere un’accurata valutazione del diagramma momento-rotazione, si sono considerati i principali contributi non-lineari del calcestruzzo e dell’armatura. dalle simulazioni numeriche si traggono le seguenti conclusioni: 1) la nuova legge costitutiva per il calcestruzzo in compressione, denominata overlapping crack law [25], permette di descrivere il comportamento non-lineare considerando gli effetti della scala e di cogliere i rami di softening presenti al termine dei diagrammi momento rotazione, come mostrato in fig. 11. 2) con riferimento alla fig. 10, è possibile affermare che l’algoritmo proposto coglie i risultati sperimentali [14] al variare della dimensione strutturale e della percentuale di armatura. 3) indipendentemente dalla percentuale di armatura, il comportamento diventa più fragile all’aumentare della dimensione della trave, con una progressiva riduzione della rotazione ultima. 4) l’eurocodice 2 [11] esprime la rotazione plastica ammissibile di travi in calcestruzzo armato come funzione solamente della posizione dell’asse neutro. al fine di migliorare tali prescrizioni, l’effetto della scala dovrebbe essere introdotto in modo esplicito, considerando differenti curve di progetto, come ad esempio mostrato in fig. 13. figura 13: rotazioni plastiche ottenute con il modello proposto confrontate con le prescrizioni dell’ec2. bibliografia [1] g. macchi, costruzioni in cemento armato, studi e rendiconti, 6 (1969) 151-191. [2] comite euro-international du beton, ceb-fip model code 1990, thomas telford ltd, lausanne, bulletin no. 213/214 (1993). [3] a. hillerborg, engineering fracture mechanics, 35 (1990) 233-240. [4] m. pecce, ceb bulletin d’information no. 242 (1997) 197-210. [5] ceb, bulletin d’information no. 30, 1961. [6] a.l.l. baker, a.m.n. amakarone, proceedings of conference on flexural mechanics of reinforced concrete, special publication sp12. american concrete institute (1967). [7] r. eligehausen, p. langer, ceb bulletin d’information no. 175 (1987) i 7.9-i 7.27. [8] e. cosenza, c. greco, g. manfredi, atti dell’accademia nazionale dei lincei, ix(2) (1991) 249-258. [9] n. tue, l. qian, d. pommerening, technische hochschule darmstadt, az. iv 1-5 (1996) 683-692. [10] a.j. bigaj, j. walraven, heron, 47 (2002) 53-75. [11] en 1992-1-1, eurocode 2: design of concrete structures – part 1-1: general rules and rules for buildings, 2003. [12] g.w. corley, journal of structural division, 92 (1966) 121-146. [13] e. siviero, ceb bulletin d’information no. 105 (1974) 206-222. [14] c. bosco, p.g. debernardi, report no. 36, atti del dipartimento, politecnico di torino, ingegneria strutturale, (1992). [15] a.j. bigaj, j. walraven, ceb bulletin d’information no. 218 (1993) 7-23. [16] z.p. bažant, cement concrete research, 19 (1989) 973-977. n http://dx.medra.org/10.3221/igf-esis.07.02&auth=true http://www.gruppofrattura.it a. carpinteri et alii, frattura ed integrità strutturale, 7 (2009) 17-28; doi: 10.3221/igf-esis.07.02 28 [17] m. van vliet, j. van mier, mechanics of cohesive-frictional materials, 1 (1996) 115-127. [18] d.c. jansen, s.p. shah, journal of engineering mechanics, 123 (1997) 25-35. [19] m. suzuki, m. akiyama, h. matsuzaki, t.h. dang, procedings of the 2nd fib international conference, napoli, italy, 2006, cd-rom, id 3-13 (2006). [20] h. dahl, r. brincker, proceedings of the international conference on recent developments in the fracture of concrete and rock, cardiff, wales, 1989, elsevier applied science, england, (1989) 523-536. [21] a. carpinteri, g. lacidogna, n. pugno, international journal of fracture, 129 (2004) 131-139. [22] g. ferro, a. carpinteri, journal of applied mechanics, 75 (2008) 41003/1-41003/8. [23] a. carpinteri, proceedings of a nato advanced research workshop, evanston, usa, 1984, martinus nijhoff publishers, dordrecht, (1985) 287-316. [24] a. carpinteri, journal of the mechanics and physics of solids, 37 (1989) 567-582. [25] a. carpinteri, m. corrado, m. paggi, g. mancini, proceedings of framcos 6, catania, italy, 2007, taylor & francis, london, 2 (2007) 655-663. [26] g. ferrara, m.e. gobbi, report to rilem committee 148-ssc, enel-cris laboratory, milano, (1995). [27] c. bosco, a. carpinteri, journal of engineering mechanics (asce), 118 (1991) 1564-1577. http://dx.medra.org/10.3221/igf-esis.07.02&auth=true http://www.gruppofrattura.it abstract. the problem of assessing the ductility of reinforced concrete (rc) structural elements in bending or under the action of eccentric forces has been largely investigated from both the experimental and the analytical point of view during the la... microsoft word numero_50_art_14_2557 m. ameri et alii, frattura ed integrità strutturale, 50 (2019) 149-162; doi: 10.3221/igf-esis.50.14 149 experimental and numerical investigation of the properties of the hot mix asphalt concrete with basalt and glass fiber mahmoud ameri, mehdi nemati, hamid shaker iran university of science and technology, tehran, iran. ameri@iust.ac.ir, mah_nemati@civileng.iust.ac.ir, h_shaker@civileng.iust.ac.ir faezeh jafari department of civil engineering, malayer university, malayer, iran. faeze_jafari666@yahoo.com abstract. in the recent decades, different kinds of fiber materials are used for improving the asphalt mixture performance. meanwhile, different kinds of fiber are used excessively due to their desirable physical and chemical properties and their easier application. the main purpose of this research is to evaluate the characteristics of the asphalt mixture while using basalt fiber and glass fiber. in order to provide asphalt samples, these two types of fibers are used in different percentages. in this way, 42 samples (with different percentages of fiber and bitumen) were made using marshal hammer. in the next step, while constructing 63 asphalt samples using a gyratory device, then mix asphalt conventional tests include the determination of indirect tensile strength, moisture sensitivity test, and resilient modulus and creep tests performed. the results of this research indicate that using these two types of fibers increased the percentage of optimum bitumen and marshal resistance. at best, adding 0.1% glass fiber resulted in 13% increase in marshal resistance. finally, anfis-gui was used to estimate the experimental result and the feasibility of employing neural fuzzy network to predict the laboratory data have been evaluated. keywords. hot asphalt mixture; anfis; experimental test; basalt and glass fiber. citation: ameri, m., nemati, m., shaker, h., jafari, f., n., experimental and numerical investigation of the properties of the hot mix asphalt concrete with basalt and glass fiber, frattura ed integrità strutturale, 50 (2019) 149-162. received: 04.07.2019 accepted: 29.07.2019 published: 01.10.2019 copyright: © 2019 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. introduction ince the invention of asphalt as a composite material for the road pavement, scientists and engineers have always sought to find a material to improve its properties [1]. the application of fibers for promoting the behavioral properties of various materials is an old idea, as the fiber has been used 4000 years ago for the reinforcement of clay soil and 2000 years ago for building the great wall of china [1]. the basalt and glass fiber used in the mix design for asphalt concrete has been shown in various studies; for example, ibrahim et al in 2009 used basalt in the mix design for asphalt concrete. this research explored the basalt used in the cities of jordan as filler in the mix design of asphalt s http://www.gruppofrattura.it/va/50/2557.mp4 m. ameri et alii, frattura ed integrità strutturale, 50 (2019) 149-162; doi: 10.3221/igf-esis.50.14 150 concrete. replacing 20% basalt in the mix design led to an increase in all the behavioral properties of the asphalt [1]. morova in 2013 used the basalt fiber in the hot-mix asphalt concrete. in this research, the asphalt strength from 0-2% basalt was used in the mix design. the results of this study show that the use of basalt as 0.05 wt% of bitumen will have the best results [2]. zheng in 2014 studied the fatigue of asphalt reinforced with basalt fiber, the results of which show that the basalt improves the behavioral properties of the asphalt, such as tensile strength, maximum curving tensile stress, curving stiffness modulus, and fatigue properties [3].using esem analysis, gao in 2018 analyzed the basalt-reinforced hot-mix asphalted concrete. in this study, it was shown that the scanning electron microscope is capable of examining the adhesion between fibers and asphalt in different compounds. it was found that the basalt fibers with adhesion between the asphalt components contribute to the increased strength properties of the made asphalt [4]. lachance in 2016 evaluated the effect of glass in the mix design of hot-mix asphalt concrete. the purpose of the study was to investigate the possibility of using the recycled glass particles in asphalt mixtures and study the equivalent properties and performance instead of the conventional mixture. to this end, an asphalt mixture (esg14) was first tested with different glass contents according to the design method of the international institute of quebec. then, the performance of the samples against thermal cracking and the stiffness of the asphalt mixture were investigated with different glass contents [5]. saltan in 2015 used the glass fiber in the hot-mix asphalt concrete. the glass wastes used for 4.0%, 4.5%, 5.0%, 5.5%, 6.0%, and 6.5% bitumen in the mix design of hot-mix asphalt concrete was found to be effective in improving the asphalt strength properties [6]. arabani (2011) studied the dynamic properties of asphalt using glass wastes. the results of the research showed that the application of glass waste can improve the dynamic properties of asphalt [7]. the stiffness model used in the present study was obtained by replacing %5, %10, %15 and 20% glass in the mix design at 5, 10 and 20°c. the results show that the temperature increase leads to a reduction in the stiffness modulus, and the replacement of 15% glass particles in the mix design, which leads to an increase in the stiffness modulus of the asphalt [8]. ozer in 2018 used the neural network method to estimate the fatigue cracking using the accelerated testing in accordance with the mix design for the asphalt. in this research, a new numerical algorithm was used to estimate the behavioral properties of asphalt and the results showed that this method is appropriate for estimating the behavioral properties of asphalt [9]. the purpose of this study is to investigate the behavioral properties of the asphalt mixtures modified with the combination of basalt and glass fiber additives. for this purpose, it is tried to perform resilient modulus, dynamic creep, and indirect tension tests for finding the correct percentage of bitumen and obtain the optimal percentage of additive in each of the experiments. then, the experimental results are estimated using the neural network models and the efficiency of neural network models is evaluated for the estimation of the results. the neural network used to estimate the behavioral properties of materials in laboratory research has recently been adopted by researchers. however, the conducted studies are in the field of concrete mix design and there is little research on the mix design and the prediction of behavioral properties. for example kaur in 2000 used the fuzzy method to estimate the laboratory results. input data to the neural network models in this research are the construction materials, pavement thickness, road age and traffic count as the input of the neural network and are intended to estimate the thickness of the asphalt. the visual basic environment is used to build the neural network models. after performing laboratory investigations, the neural network method is used to estimate the experimental results and to evaluate the robustness of the neural network in the estimation of the results [10]. sodikov in 2005 emphasized the importance of prediction cost highway project with using neural network method. lack of preliminary information, lack of database of road works costs, data amusingness, lack of an appropriate cost estimation methods are some major problem in high way project [11]. tapkın in 2010 employed mlp to estimate physical and mechanical properties of the asphaltic mixture with pp fiber. in this study, neural network method was employed to predict laboratory test data such as marshall stability and flow tests [12]. in this research, due to the fact that the temperature of the asphalt wearing coarse affects its performance (stiffness and cracking on the asphalt surface), the neural network is used to estimate the temperature of the asphalt wearing coarse. the main goal of this study is to investigate the physical characteristics of the asphalt mixtures by combining basalt and glass fiber. to do this, marshal stability, resilient modulus, indirect tensile strength, and dynamic creep were done to determine the optimum percentage of these two modifiers, then laboratory test estimation was done through this method and the capability of anfis was evaluated. materials n this research, for producing asphalt samples without additive and conducting the experimental test, limestone aggregates were used for making gravel and sand of each mixture. moreover, stone powder was used as filler (material passing the sieve 200) [13]. the mentioned material was taken from taloo (in east of tehranasphalt i m. ameri et alii, frattura ed integrità strutturale, 50 (2019) 149-162; doi: 10.3221/igf-esis.50.14 151 factory). fig. 1 shows the grading of the used aggregate. figure 1: particle size distribution for stone mastic asphalt mixture. the characteristics of the used fiber the fibers used in this research are basalt and glass which are 6 mm long. their characteristics and shape of these materials are shown in tab. 1 and fig. 2. in this research, %1, 2%, 3% glass fiber and %1, 2%, 3% basalt fibers were used. basalt fiber glass fiber characteristic grey white color 6 6 )mm ( length 8 13 )mµ ( diameter 2.5 2.5-2.6 )3gr/cm ( density 1505 1500 )c° ( melting point 3000 3000 )mpa ( tensile strength 3 3.5 )% ( strain rate table 1: the basalt and glass fiber property [14]. mixture design and determination of optimum bitumen percentage samples were produced according to the astmd1559 standard [15]. the bitumen and aggregates were mixed together at 145°c -150 °c and the gyratory compactor were used to compact samples. during preparation of samples, fibers (glass and basalt) with specified percentage were added to the mixture. 7% void ratio was employed to make compaction of indirect tension samples as well as the control samples were tested for other experimental result. next, the stone material was dried in the oven for 24 hours at 170 °c. therefore, the moisture of the stone material is evaporated during this process. in order to reach the maximum marshal stability, minimum flow, optimum void ratio and absorbed bitumen percentage, the optimum bitumen percentage should be compared to the proper bitumen percentage. ultimately, the optimum bitumen percentage should satisfy all the above mentioned criteria. to do this, 18 control samples for asphalt mixture was used and once the corresponding tests were done, the optimum bitumen percentage was determined. the selected percentage of the bitumen for the control samples were 4, 4.5, 5, 5.5, 6, 6.5 percent of the material weight and for each percent of the bitumen three samples were made. moreover, 24 other samples were made for basalt and glass fiber mixture to predict the percentage of optimum bitumen. it should be mentioned that the selected percentage for basalt and m. ameri et alii, frattura ed integrità strutturale, 50 (2019) 149-162; doi: 10.3221/igf-esis.50.14 152 glass fiber (for determining the optimum bitumen percentage) were 0.3 % of the weight of the asphalt mixture. tab.3 shows control parameters of optimum bitumen percentage for 3 group samples. figure 2: the shape of fiber (a) basalt fiber b) glass fiber [14]. table 2: component for basalt and glass fiber material [14]. control samples basalt glass parameters 854 807 883 marshal stability at optimum percentage 3.15 3.6 4.2 flow at optimum percentage 74.3 75 74.7 percentage of empty space filled with bitumen 15.2 15.7 15.6percentage of empty stone materials per percentage of possible bitumen table 3: parameters for controlling optimum bitumen percentage. experimental test indirect tensile strength test ndirect tensile strength test is often used for evaluation of moisture sensitivity of asphalt mixtures. the produced asphalt samples are divided into two groups, dry and wet. in order to produce dry samples, before breaking them, their temperature should reach to the room temperature. for this purpose, the samples can be put in plastic bags to prevent it from getting wet and then they should be saturated at least for 1 hour in water at 25°c temperature. for producing wet sample in vacuum, the wet samples should be put in vacuum instrument. saturate ratio should be between 55 80 percent of the asphalt vacant place. if the samples saturation is more than 80%, that sample should be removed. then, the samples are put vertically between the two jaws of the indirect tensile strength instrument. diagonal load is basalt fiber glass fiber oxide element element mass percentage oxide mass percentage element mass percentage oxide mass percentage 9.17 17.35 6.3 11.86 3o2al al 19.76 42.43 24.24 58.25 2sio si 6.37 8.88 15.05 21.09 cao ca 8.17 11.68 0.21 0.3 3o2fe fe 1.94 2.33 0.36 0.43 o2k k 5.7 9.45 0.32 0.54 mgo mg 2.81 3.67 0.22 0.3 o2na na 1.53 2.55 0.25 0.41 2tio ti i m. ameri et alii, frattura ed integrità strutturale, 50 (2019) 149-162; doi: 10.3221/igf-esis.50.14 153 applied to the sample by 50m/min speed so that the load reaches to its maximum amount and the sample breaks. after recording the maximum load, the indirect tensile strength of the asphalt samples is determined. the higher indirect tensile strength shows that the mixture had a proper resistance against the moisture damage. also, the sample which can bear high strain before breaking, have higher cracking resistance, compared to the samples with low strain [16]. 2 *   * * maxpits t d  (1) where: its = indirect tensile strength (pa),   maxp = maximum applied load (n), t = thickness of specimen (mm), d = diameter of specimen (mm). resilient modulus the resilient modulus is used for evaluation and analysis of comparative quality of the asphalt mixtures as the input data of pavement design. in this study, the utm5 device at 25°c and the semisynthetic load was employed such that the selected load is 400n. finally, the mean of the five last resilient modulus steps was collected and named the resilient modulus of the mixtures. fig. 3 shows utm5 set-up which was used for resilient modulus and dynamic creep test. figure 3: utm5 set-up which was used in the experimental test. dynamic creep dynamic creep test which shows the permanent deformation of asphalt mixture is recognized as one of the most prevalent damages in the hot mix asphalt concrete research. several thousand loads which were repeated in cyclic pattern have been employed to make permanent displacements. to reach this aim, utm5 was used to perform dynamic creep test, the stress level of 450 kpa and a temperature of 50 ° c is considered as a constant variable in this research and sample loading is started up to 0.01 strain rate [17]. the diameters of the cylinders were 100 to 150 (mm) and the height of them is 60 (mm) [18]. according to the witzak theory [18], the number of beginning loading process before the starting of the third region is considered as a flow number. the numbers of cycles are equal to the minimum value of the strain rate which was derived from the strain rate graph. neural network part an adaptive neuro-fuzzy inference system (anfis) is a type of neural network which was worked according to takagi– sugeno fuzzy inference system. this method used from the futures of both neural networks and fuzzy logic system. in this study, this method is employed due to estimate asphalt mixture’s properties. for reach this goal, all laboratories data which were extracted through experimental test with their variables were imported to matlab gui software as the output variable. the previous studies that used this method considered the output and input variable in matlab as a fixed variables [19], but, in this present study, the input variables were produced randomly with using the average and variance value which obtained from experimental test. to do this, the input variables are additive percentage to bitumen m. ameri et alii, frattura ed integrità strutturale, 50 (2019) 149-162; doi: 10.3221/igf-esis.50.14 154 combination (glass fiber and basalt) as well as the output variables are the value of flow number, resilient modulus and tensile strength in wet and dry condition, marshal stability test. the variance for input and output values have been considered 0.1* mean value with log-normal fit distribution. after generating data with matlab software and experimental test, anfisgui and experimental data (output and input values) were used in order to prediction process. ultimately, the number of data extracted from anfis gui is 99 for marshal stability test and 99 for flow as well as 63 for other test such as resilient modules, its and flow number. all variables are divided into three subsets data as train, test and validation group. the possible surfaces for output variables were predicted according anfis rules such that these surfaces show to what extend different additives able to change output variables. result selection of optimum bitumen percentage for three sample groups fter calculating the optimum bitumen percentage for the fiber-reinforced asphalt mixtures, the samples were prepared with 0.1, 0.2, 0.3, 0.5 and 0.7% basalt fiber and glass. the results of the marshall stability are presented in fig. 4. in all figures bf was used as indicator for basalt fiber and gf was used for glass fibers. figure 4: marshall stability for optimal bitumen percentage in control and fiber-reinforced mixtures the results of fig. 4 show that the marshall stability could be increased if the fiber is used in the asphalt mixtures. in fact, the use of 0.1% basalt fiber resulted in 4% increase in the marshall stability comparing the control sample, but it hereafter led to the loss of marshall stability, so that in the case of using 0.3% fiber, the marshall stability reached about 800 kg. this can be explained by the fact that the use of fibers up to 0.2% probably caused the reinforcement of the asphalt mixtures, but hereafter, the fiber balling phenomenon was occurred. therefore, increasing the percentage of fiber intensifies the reduction of the marshall stability. the same is true for the variations in the marshall stability for the glass-fiber-reinforced samples, but there are also some differences. for example, if the maximum value of the glass fiber is used, the marshall stability for the modified sample will not be less than the control sample. it should be noted that when using 0.1% glass fiber, a 13% increase will be observed in the marshall stability. on the other hand, as can be seen, increasing the marshall stability for the samples made with glass fiber is far more than those containing basalt fibers. there are two main reasons to justify this difference: first, the difference between the marshall stability values may be due to the difference in the bitumen percentage of the samples. second, the effect of the chemical properties of both types of fibers should not be considered the same and it is possible that the difference in the values of the marshall stability is due to the properties of the constituent materials of the fiber. a m. ameri et alii, frattura ed integrità strutturale, 50 (2019) 149-162; doi: 10.3221/igf-esis.50.14 155 in general, it could be stated that there is no significant change in the use of glass fibers, but if the glass fiber is used, the relative improvement will be achieved; although; if more glass fiber is used, the marshall stability will be decreased. at best, adding 0.1% glass fiber resulted in a 13% increase in the marshall stability. previous studies showed that adding glass fiber to the asphalt mixture causes 45% increase in the marshall stability. on the other hand, according to research, the addition of fiber to the asphalt mixture decreases the parameter by 10%. it could be concluded that more precise research is needed on the use of glass fiber in the asphalt mixtures. moreover, figure 7-10 show the result of experimental test which were obtained from laboratory test and anfis method .the results of anfis are close to experimental test and that means this way can predict experimental result correctly. anfis has been employed as neural network in some other previous researchers [19] and in these studies, also this relationship (proximity between laboratory and numerical data shows the efficiency of anfis method. figure 5: flow value for different samples flow value fig. 5 presents the values for the flow in the control and modified samples. as can be seen, there will generally be an increase in the flow value when using the fibers. the use of 0.3% basalt fibers led to a 10% increase in the flow value. the glass fibers also increased the flow value, so that the flow value for the samples made with 0.3% glass fiber reached 4.2 mm. on the other hand, it is observed that for the percentages higher than 0.3% fiber, the flow value exceeded the allowable limits of the regulation and the flow value was significantly increased, so that for the samples made with 0.7% fibers (whether basalt or glass), an increase about 50% is achieved. as mentioned earlier, based on the results of the marshall stability and flow, 0.5 and 0.7% fibers were removed and the remaining tests were performed using other percentages. in order to justify the flow increase in the case of using basalt and glass, two approaches are considered: it seems that even though the basalt and glass fibers have a high melting temperature, the surface of the fiber melts during the asphalt curing and increases the viscosity of bitumen. this causes the bitumen to be less adsorbed onto the surface of the aggregates and to remain in the space between the aggregates. in this way, the presence of additional bitumen in aggregates increased the flow of samples. on the other hand, the flow, in fact, is the rate of sample deformation at the moment of failure. now, the fibers cause the bonding and adhesion of different parts of the sample to each other and make the specimen exhibit more deformation at the moment of failure. previous studies have discussed the glass fibers and their application to hot-mix asphalt concrete. the flow number is increased in previous studies for increasing the percentage of glass fiber. for example, taherkhani (2016) added glass fiber and nano clay in the mix design of the hot-mix asphalt concrete, adding 0.2, 0.4 and 0.6 glass fiber. in this research, it was tried by providing more percentages (0.1-0.7) and comparing the results to show that the flow number is increased with the use of glass fiber in the mix design. the increase for 0.6 glass fibers is 1.16 times the control sample in the taherkhani study [20], and in this study, it is approximately 1.4 times. it could be stated that the addition of glass fibers led to the maximization of the flow number. on the other hand, the results of previous research, such as nihat morova [21] on the use of basalt in the mix design for asphalt concrete. this research indicates an increase in the flow number for adding m. ameri et alii, frattura ed integrità strutturale, 50 (2019) 149-162; doi: 10.3221/igf-esis.50.14 156 basalt to the asphalt mix design. the results of this study also show that the use of glass fibers can further increase the flow number. the placement of the both materials together in the same mix design shows that the application of glass fiber comparing the basalt for 0.3 optimum bitumen, can lead to the maximum increase in the flow number, while in the percentages below 0.3; the use of basalt fiber further changes the flow number. test results of indirect tensile strength a total of 42 samples were taken to perform the indirect tensile strength test. according to experimental its test which was mentioned in previous part of this paper, half of the specimens were dried and the rest were tested in the saturated state. it should be noted that in order to minimize the errors in each percentage of the fibers, three samples were made, and the results are presented based on the averaging. fig. 6 shows the results of the indirect tensile strength test for the dry specimens. figure 6: indirect tensile strength results for dry condition. generally, the tensile strength is increased by adding fibers to the asphalt materials. the highest increase is seen in the case of using 0.1% glass fiber, which is about 6% higher than the control sample. the same effect is observed if the same amount of basalt fiber is used. on the other hand, with an excessive increase in the percentage of fibers, there is a decrease in indirect tensile strength. the highest reduction is seen for the sample made with 0.3% glass fiber. also, if the basalt fiber is used, the indirect tensile strength values for the different percentages of the fibers are approximately the same, but on the contrary, in the case of glass fibers, considerable variations will occur in the indirect tensile strength. fig. (7) presents the results of the indirect tensile strength test in the saturated state. the results of this diagram show that by increasing the percentage of basalt fiber and glass, the value of indirect tensile strength is decreased. the fibers are not resistant to moisture sensitivity, as the highest tensile strength occurs in the saturated state for the control samples and the lowest one occurs for the samples containing 0.3% basalt fiber. the results show that in the worst case, the indirect tensile strength is decreased by 26% comparing the control sample. finally, the calculations are done for the values of the wet to dry ratio of indirect tensile strength. information about this ratio, commonly known as tsr, is shown in fig. (8). fig. 8 shows that the highest tsr belong to the control sample (89%) and the lowest one is for the sample containing 0.3% basalt fiber (with the rate of 70%). it should be noted that the samples with gf materials essentially do not have a high sensitivity to the moisture damages. the minimum tsr value is nearly 75% in the asphalt specimens with the samples made with 0.3% basalt fiber and 0.3% glass fiber. regarding the negative effect of the glass fiber and basalt fiber in high percentages (0.3%) on the performance of moisture sensitivity, it could be stated that when using the fiber, as the absorption rate of bitumen is increased, the potential for the absorption of moisture is also increased, leading to a decrease in the indirect tensile strength in the saturated state. m. ameri et alii, frattura ed integrità strutturale, 50 (2019) 149-162; doi: 10.3221/igf-esis.50.14 157 figure 7: indirect tensile strength results for wet condition. figure 8: tensile strength ratio (tsr) of control and fiber-reinforced samples. resilient modulus totally, 21 specimens were built to perform the resilient modulus test, so that 3 specimens were built for each percentage of the fibers, and the amount of resilient modulus was determined by averaging for the samples containing the same percentages of fibers. fig. (9) shows the results of the resilient modulus test for the control samples as well as the samples containing the basalt and glass fibers. as seen in fig. 9, increasing the amount of basalt fibers increases the resilient modulus. the highest increase in the resilient modulus is observed using 0.3% fiber, so that the resilient modulus is increased by about 50% (from 2660 to 3963 mpa). the use of glass fibers also led to an increase in the resilient modulus, so that the resilient modulus of the samples containing 0.2% glass fiber reached over 3300 mpa. in this part of the research, we first compare the results of the present research with previous studies to determine how consistent the results with the previous research. it should be noted that the research on the basalt and glass fiber m. ameri et alii, frattura ed integrità strutturale, 50 (2019) 149-162; doi: 10.3221/igf-esis.50.14 158 additives for testing the resilient modulus has been considered in few studies. the present study tries to compare the both additives while working on them. figure 9: test results of resilient modulus. in the marshall test, the amount of strength is increased with increasing the fiber percentages, but in this experiment, it is observed that with the increase in the fiber percentage, the amount of the resilient modulus is raised. therefore, at first glance, it seems that the results of this test are not consistent with other previous tests. however, carefully looking the test procedure, one can answer the question of why the results of the experiments are in conflict. as it is known, in the marshall test, the compressive loads are applied and the specimen is subjected to the compression till the failure. basically, the use of reinforcing materials in the process will not be so useful with applying the compressive load and may have a negative effect on the compressive strength. however, the resilient modulus test has a tensile nature and, generally, if the fibers are used, the tensile properties of the asphalt mixture are increased. flow number it is observed that the addition of fibers increases the flow number, so that the flow number for the control sample is about 1500, and when using 0.1% basalt fiber, it is increased by about 20% to 1800. an increase in the percentage of basalt fiber leads to a decrease in the flow number. this decrease is such that using 0.3% basalt fiber causes a 21% decrease in this parameter. the glass fiber has the same functionality as the basalt fiber, so that the flow number is gradually reduced by increasing the glass percentage. however, it should be noted that the effect of glass fiber in the higher percentages is greater than that of the basalt fiber. in the creep test, increasing the flow number means that the asphalt mixture is relatively harder and the rutting potential in such samples is relatively lower. it is inferred from fig. (10) that the samples containing 0.1% fiber have the best performance against the rutting. nihat morova in 2013 studied the use of basalt as different percentages of bitumen. in this research, 4.5, 5 and 5.5% bitumen were used in the mix design with different percentages of basalt fiber (0-2%). the maximum flow number in this research was 1%, and for all three percentages of bitumen in the morova's research is 1.5% and hereafter, it is 1%. in that study, the highest flow number was for 5 and 5.5% bitumen (highest flow number). in this study, the optimal bitumen percentage was obtained for 5.1% basalt samples, and the results of morova's research showed that for the optimum bitumen percentages of 5 and 5.5%, the maximum flow number is obtained for replacing 1-1.5% basalt. also, according to morova's research and the current results, the excessive use of 2 and 3% basalt for 5% bitumen leads to a decrease in the flow number [21]. subsequently, testing on the addition of glass fiber in the mix design of hot-mix asphalt concrete showed that the use of 1% glass fiber also resulted in the improvement of the flow number, which compared with the basalt samples, the glass fiber-reinforced samples had higher values. nguyen (2013) used the glass particles in the hot-mix asphalt concrete [22]. the use of glass fiber in the mix design resulted in a drop in the flow number, because the researcher selected the percentage of fiber from 0 to 2%, which in the present study, increasing the glass fiber to 2 and 3% resulted in a decrease m. ameri et alii, frattura ed integrità strutturale, 50 (2019) 149-162; doi: 10.3221/igf-esis.50.14 159 in the flow number. on the other hand, the higher the percentage of increase in the glass fiber for both studies, the more the drop in the flow number. the results of previous research show that the flow number has not yet been compared in a specific mix design for adding basalt and glass fibers. comparison of the results showed that the application of 1% basalt and 1% glass fiber could obtain the maximum value of flow number. figure 10: flow number for asphalt samples the decrease of the flow number in the values of 0.2 and 0.3 is due to the fact that some percentage of bitumen is kept around the fiber. this can reduce the bitumen thickness around the aggregates and reduce the strength. although, the reduction in the strength and stiffness can increase the flexibility and improve the fatigue properties, but in order to avoid excessive reduction of bitumen thickness around the aggregates, the amount of fiber should be limited according to previous and current research. the reduced thickness of bitumen, in addition to the adverse effects on the strength, also has undesirable effects on the endurance of the mixture against moisture. in this section, it is tried to compare the results of research with other laboratory studies. numerical part he proficiency and reliability of anfis system was checked according two parameters (r2 and mse) based on the previous research [23].according to this research, all neural networks such as anfis, ann and svm ways have the highest performance when the amount of r2 is near to 1 and the rmse value is close to zero. table 4 shows these values for anfis neural network which were built in this research. output layer training set testing set validation set 2r rmse 2r rmse  2r rmse flow (mm) 0.880 0.08 0.80 0.03967 0.9892 0.3568 indirect tensile strength test (kpa) 0.8540 0.0062 0.94 0.0005 0.81 0.0025 flow number 0.9490 0.03967 0.9545 0.0469 0.8960 0.0560 resilient modulus (mpa) 0.9688 0.0420 0.9586 0.0560 0.8754 0.0610 table 4: anfis results for r2 values and rmse of: training set, testing set, and validation set t m. ameri et alii, frattura ed integrità strutturale, 50 (2019) 149-162; doi: 10.3221/igf-esis.50.14 160 figure 11: anfis result for indirect tensile test, resilient modulus and dynamic creep. anfis models able to predict experimental results exactly so that the value of r2 is near to 1.00 and rmse is near to zero. moreover, anfis models, which have been produced in this research, have capability of predicting output value close to real data; fig. 4 to 10 shows this fact. fig. 11 shows the relationship between two input variables (fiber glass and basalt) and the output layers (flow number, tensile strength and dynamic creep and flow value). fig.11a indicates the resilient modulus variation related to the basalt and glass fiber. this figure shows that the maximum variation of this parameter is related to 0.3b (basalt) and 0.2f (glass) and the surface variation decreases by reducing the value of basalt and fiber glass. fig.11b shows the flow number surface for the basalt and fiber glass. also, figure 11b shows the highest surface belongs to 0.2 b (basalt) and 0.2 glass fiber and the variation of surface decrease while the value of basalt or fiber glass have maximum value. fig.11c shows the variation of its surface for the basalt and glass fiber. this figure emphasize this issue that the maximum point is for 0.2 basalt fiber and 0.2 glass fiber and this surface decrease with increasing the value of glass fiber to 0.3% and basalt fiber to 0.3%. fig.11d shows the variation of flow surface for the basalt and fiber glass and in this figure flow is known as dependent variable. this figure displays the maximum value belongs to 0. 6 basalt and 0.4 glass fiber and the surface reduce when the value of basalt and fiber glass increases. conclusion n the present study, two basalt and glass fiber additives were used as an alternative for the optimum bitumen in the preparation of hot-mix asphalt concrete samples. after conducting the experiments test, the neural network was used for the estimation of the laboratory results. the research results show that:  the optimum bitumen percentage for the asphalt mixture is 4.9% and for the asphalt mixture made with basalt and glass fibers is found to be 5.1% and 5.8%, respectively. generally, when using the fiber in the asphalt mixtures, the increase in the marshall stability can be seen. at best, adding 0.1% glass fiber resulted in a 13% increase in the marshall stability. i m. ameri et alii, frattura ed integrità strutturale, 50 (2019) 149-162; doi: 10.3221/igf-esis.50.14 161  in the case of using fibers, there will be an increase in the flow value. the use of 0.3% basalt fibers resulted in a 10% increase in the flow value. the use of glass fibers also increases the flow value, so that the flow value for the samples made with 0.3% glass fiber reaches 4.2 mm.  the marshall stability and flow for the samples made with 0.5 and 0.7% fibers are completely inappropriate and, accordingly, the use of these percentages is not justifiable for other tests. the results are such that when using 0.7% of fibers, the flow parameter was increased by more than 50% and exceeded the allowable limit of the regulation.  generally, the tensile strength in the dry state is increased by adding fibers to the asphalt materials. the highest increase is seen if 0.1% glass fiber is used. this change is such that it rises by about 5% from 450 to 470 kpa.  with the increase in the percentage of basalt and glass fibers, the indirect tensile strength is decreased in the wet state. the highest reduction is observed if 0.3% fiber is used, with the indirect tensile strength decreasing by more than 20% compared with the control sample.  the highest tsr value is related to the control sample (89%) and the lowest one is for the sample containing 0.3% basalt fiber (70%).  by increasing the amount of basalt fiber, the resilient modulus is increased. the highest increase in the resilient modulus is observed using 0.3% fiber, so that the resilient modulus is increased by about 50% (from 2660 to 3963 mpa).  the use of glass fibers led to an increase in the resilient modulus, so that the resilient modulus of the samples containing 0.2% glass fiber is increased by 25% to over 3300 mpa.  the addition of fibers increases the flow number, so that the flow number for the control sample is about 1500, and when using 0.1% basalt fiber, it is increased by about 20% to 1800. references [1] ibrahim, a., faisal, s. and jamil, n. (2009). use of basalt in asphalt concrete mixes. construction and building materials, 23(1), pp. 498-506. [2] morova, n. (2013). investigation of usability of basalt fibers in hot mix asphalt concrete. construction and building materials, 47, pp. 175-180. [3] zheng, y., cai, y., zhang, g. and fang, h. (2014). fatigue property of basalt fiber-modified asphalt mixture under complicated environment. journal of wuhan university of technology-mater. sci. ed., 29(5), pp. 996-1004. [4] gao, c. and wu, w. (2018). using esem to analyze the microscopic property of basalt fiber reinforced asphalt concrete. international journal of pavement research and technology, 11(4), pp. 374-380. [5] lachance-tremblay, é., vaillancourt, m. and perraton, d. (2016). evaluation of the impact of recycled glass on asphalt mixture performances. road materials and pavement design, 17(3), pp. 600-618. [6] saltan, m., öksüz, b. and uz, v. e. (2015). use of glass waste as mineral filler in hot mix asphalt. science and engineering of composite materials, 22(3), pp. 271-277. [7] arabani, m. (2011). effect of glass cullet on the improvement of the dynamic behaviour of asphalt concrete. construction and building materials, 25(3), pp. 1181-1185. [8] wang, d. (2015). simplified analytical approach to predicting asphalt pavement temperature. journal of materials in civil engineering, 27(12), 04015043. [9] ozer, h., al-qadi, i. l., singhvi, p., bausano, j., carvalho, r., li, x. and gibson, n. (2018). prediction of pavement fatigue cracking at an accelerated testing section using asphalt mixture performance tests. international journal of pavement engineering, 19(3), pp. 264-278. [10] kaur, d. and tekkedil, d. (2000). fuzzy expert system for asphalt pavement performance prediction. in intelligent transportation systems, 2000. proceedings. 2000 ieee, pp. 428-433. [11] sodikov, j. (2005). cost estimation of highway projects in developing countries: artificial neural network approach. journal of the eastern asia society for transportation studies, 6, pp. 1036-1047. [12] tapkın, s., çevik, a. and uşar, ü. (2010). prediction of marshall test results for polypropylene modified dense bituminous mixtures using neural networks. expert systems with applications, 37(6), pp. 4660-4670. [13] astm (2004). 3515, standard specification for hot-mixed, hot-laid bituminous paving mixtures. annual book of standards, 4. m. ameri et alii, frattura ed integrità strutturale, 50 (2019) 149-162; doi: 10.3221/igf-esis.50.14 162 [14] t. deak and t. czigany, chemical composition and mechanical properties of basalt and glass fibers: a comparison, textile research journal, 79 (7), pp. 645–651, 2009. [15] astm, d. (1989). 1559 (1989)“test method for resistance of plastic flow of bituminous mixtures using marshall apparatus”. american society for testing and materials, philadelphia, usa. [16] aashto, t. (2007). standard method of test for resistance of compacted asphalt mixtures to moisture-induced damage. aashto provisional standards: washington, dc, usa. [17] al-qadi, i. l., yoo, p. j., elseifi, m. a. and nelson, s. (2009). creep behavior of hot-mix asphalt due to heavy vehicular tire loading. journal of engineering mechanics, 135(11), pp. 1265-12. doi: 10.1061/(asce)07339399(2009)135:11(1265)) [18] yoder, e. j. and witczak, m. w. (1975). principles of pavement design. john wiley & sons. [19] ghanei, a., jafari, f., khotbehsara, m. m., mohseni, e., tang, w., & cui, h. (2017). effect of nano-cuo on engineering and microstructure properties of fibre-reinforced mortars incorporating metakaolin: experimental and numerical studies. materials, 10(10), 1215. [20] taherkhani, h. (2016). investigating the properties of asphalt concrete containing glass fibers and nanoclay. civil engineering infrastructures journal, 49(1), pp. 45-58. [21] morova, n. and terzi, s. (2015). evaluation of colemanite waste as aggregate hot mix asphalt concrete. süleyman demirel üniversitesi fen bilimleri enstitüsü dergisi, 19(2). [22] nguyen, m. l., blanc, j., kerzreho, j. p. and hornych, p. (2013). review of glass fibre grid use for pavement reinforcement and apt experiments at ifsttar. road materials and pavement design, 14(1), pp. 287-308. [23] naseri, f., jafari, f., mohseni, e., tang, w., feizbakhsh, a. and khatibinia, m. (2017). experimental observations and svm-based prediction of properties of polypropylene fibres reinforced self-compacting composites incorporating nano-cuo. construction and building materials, 143, pp. 589-598. doi: 10.1016/j.conbuildmat.2017.03.124. << /ascii85encodepages false /allowtransparency false /autopositionepsfiles true /autorotatepages /none /binding /left /calgrayprofile (dot gain 20%) /calrgbprofile (srgb iec61966-2.1) /calcmykprofile (u.s. web coated \050swop\051 v2) /srgbprofile (srgb iec61966-2.1) /cannotembedfontpolicy /error /compatibilitylevel 1.4 /compressobjects /tags /compresspages true /convertimagestoindexed true /passthroughjpegimages true /createjobticket false /defaultrenderingintent /default /detectblends true /detectcurves 0.0000 /colorconversionstrategy /cmyk /dothumbnails false /embedallfonts true /embedopentype false /parseiccprofilesincomments true /embedjoboptions true /dscreportinglevel 0 /emitdscwarnings false /endpage -1 /imagememory 1048576 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/hrv (za stvaranje adobe pdf dokumenata najpogodnijih za visokokvalitetni ispis prije tiskanja koristite ove postavke. stvoreni pdf dokumenti mogu se otvoriti acrobat i adobe reader 5.0 i kasnijim verzijama.) /hun 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can be opened with acrobat and adobe reader 5.0 and later.) >> /namespace [ (adobe) (common) (1.0) ] /othernamespaces [ << /asreaderspreads false /cropimagestoframes true /errorcontrol /warnandcontinue /flattenerignorespreadoverrides false /includeguidesgrids false /includenonprinting false /includeslug false /namespace [ (adobe) (indesign) (4.0) ] /omitplacedbitmaps false /omitplacedeps false /omitplacedpdf false /simulateoverprint /legacy >> << /addbleedmarks false /addcolorbars false /addcropmarks false /addpageinfo false /addregmarks false /convertcolors /converttocmyk /destinationprofilename () /destinationprofileselector /documentcmyk /downsample16bitimages true /flattenerpreset << /presetselector /mediumresolution >> /formelements false /generatestructure false /includebookmarks false /includehyperlinks false /includeinteractive false /includelayers false /includeprofiles false /multimediahandling /useobjectsettings /namespace [ (adobe) (creativesuite) (2.0) ] /pdfxoutputintentprofileselector /documentcmyk /preserveediting true /untaggedcmykhandling /leaveuntagged /untaggedrgbhandling /usedocumentprofile /usedocumentbleed false >> ] >> setdistillerparams << /hwresolution [2400 2400] /pagesize [612.000 792.000] >> setpagedevice microsoft word numero_50_art_39_2614 n. martini et alii, frattura ed integrità strutturale, 50 (2019) 471-480; doi: 10.3221/igf-esis.50.39 471 focused on the research activities of the greek society of experimental mechanics of materials imaging performance of a cawo4/cmos sensor niki martini, vaia koukou, george fountos, ioannis valais, ioannis kandarakis, christos michail radiation physics, materials technology and biomedical imaging laboratory, department of biomedical engineering, university of west attica, athens 12210, greece michail@upatras.gr, http://orcid.org/0000-0001-5863-8013 athanasios bakas, eleftherios lavdas, konstantinos ninos, georgia oikonomou, lida gogou department of biomedical sciences, university of west attica, athens 12210, greece george panayiotakis department of medical physics, faculty of medicine, university of patras, 265 00 patras, greece abstract. the aim of this study was to investigate the modulation transfer function (mtf) and the effective gain transfer function (egtf) of a nondestructive testing (ndt)/industrial inspection complementary metal oxide semiconductor (cmos) sensor in conjunction with a thin calcium tungstate (cawo4) screen. thin screen samples, with dimensions of 2.7x3.6 cm2 and thickness of 118.9 μm, estimated from scanning electron microscopy-sem images, were extracted from an agfa curix universal screen and coupled to the active area of an active pixel (aps) cmos sensor. mtf was assessed using the slanted-edge method, following the iec 62220-1-1:2015 method. mtf values were found high across the examined spatial frequency range. egtf was found maximum when cawo4 was combined with charge-coupled devices (ccd) of broadband anti-reflection (ar) coating (17.52 at 0 cycles/mm). the combination of the thin cawo4 screen with the cmos sensor provided very promising image resolution and adequate efficiency properties, thus could be also considered for use in cmos based x-ray imaging devices, for various applications. keywords. cawo4; phosphors; medical imaging; aps; cmos sensors; mtf. citation: martini, n., koukou, v., fountos, g., valais, i., kandarakis, i., michail, ch., bakas, a., lavdas, e., ninos, k., oikonomou, g., gogou, l., panayiotakis, g., imaging performance of a cawo4/cmos sensor, frattura ed integrità strutturale, 50 (2019) 471-480. received: 22.01.2019 accepted: 22.05.2019 published: 01.10.2019 copyright: © 2019 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. introduction hosphor materials made of calcium tungstate (cawo4) [1,2] and zinc sulfide (zns) were used as radiation detectors, in the form of thin screens, for almost a century [3,4]. cawo4 is a low cost, very stable material, but with a decay time not ideal for applications that require high counting rate measurements (table 1) [5]. cawo4 emits light in p http://www.gruppofrattura.it/va/50/2614.mp4 n. martini et alii, frattura ed integrità strutturale, 50 (2019) 471-480; doi: 10.3221/igf-esis.50.39 472 the blue region of the spectrum which provides excellent compatibility with photocathodes, incorporated in various types of photomultipliers (pmts), charge-coupled devices (ccd), as well as, with non-passivated amorphous hydrogenated silicon photodiode (a-si:h), employed in thin film transistors of active matrix flat panel detectors [5]. when rare earth phosphors came into the spot-light, cawo4 was dis-continued for medical imaging applications. thereafter, terbium-doped gadolinium oxysulfide (gd2o2s:tb) rare earth phosphor, and later cesium iodide (csi) were established for digital imaging applications (medical, industrial radiography, etc.) including ccds and complementary metal oxide semiconductors (cmos) [3,4,611]. in industrial radiography, non-destructive testing (ndt) is used; it consists of a variety of non-invasive inspection techniques that is used to evaluate material properties, components, or entire process units. radiographic testing is one of the most frequently used ndt techniques that involve the use of x-rays and digital detector systems, such as amorphous silicon, ccds and cmos sensors [12-14]. however, beyond the dominance of terbium-doped gadolinium oxysulfide, the interest for cawo4 has been renewed in applications such as, particle astrophysics in the quest for dark matter in the universe [15-17], for wimp-nucleon elastic scattering interactions [18,19], as well as, for customs and border control [15,20]. the resolution properties of this material [21,22], along with the adequate luminescence emission efficiency, at specific xray energies [5] could be also considered for dual energy applications [23-28]. all the aforementioned applications require efficient detectors, of high resolution, with good spectral matching between the phosphor’s emission light and the sensitivity of the sensor, thus the aim of this study is to investigate further the properties of a thin layered calcium tungstate screen, coupled to a state-of-the-art ndt active pixel sensor (aps) cmos sensor, in order to enhance the imaging capabilities of the integrated detector. measurements were conducted, following standardized methodologies for medical imaging configurations (sensors and scintillator material combinations) [11]. standardized protocols were used for both resolution and efficiency measurements [5, 29-31]. the latest iec 62220-1-1:2015 protocol from the international electrotechnical commission (iec) 62220 series was used [32,33]. materials and methods phosphor screens amples of cawo4 were extracted from an agfa curix universal screen. for the resolution measurements samples with dimensions 2.7x3.6 cm2 were used. the phosphor is used in the intensifying screens employed in x-ray imaging [31,34,35]. the internal properties of the samples were examined via scanning electron microscopy (sem) [36]. x-ray absorption (@50kev) 35% light conversion efficiency 4-5% melting point 1570-1670 oc molar mass 287.9156 g/mol atomic number 74 density 6.06-6.1 g/cm3 afterglow from 5x10-6 sec up to a few sec refractive index 1.94 k-edge 69.5 kev decay time 6-8x103 ns table 1: cawo4 properties [3-5,15,17,37,38]. scanning electron microscopy (sem) parameters such as particle size and thickness of the cawo4 compound were verified via sem micrographs using the jeol jsm 5310 scanning electron microscope and the inca software. within this system, gold can be used to image a site of interest of the sample. for the elementary particle analysis, a carbon thread evaporation process was used. carbon was flash evaporated under vacuum conditions to produce a film suited for the cawo4 sem specimen in a bal-tec ced 030 carbon evaporator (~10-2 mbar) [36]. s n. martini et alii, frattura ed integrità strutturale, 50 (2019) 471-480; doi: 10.3221/igf-esis.50.39 473 cmos sensor the cawo4 scintillating screen was manually coupled to an optical readout device including a cmos remote radeye hr photodiode pixel array [39]. the cmos photodiode array consists of 1200x1600 pixels with 22.5 μm pixel spacing. this sensor was initially manufactured for non-destructive testing (ndt)/industrial inspection applications especially for tight or difficult to reach spaces. however, due it its unique resolution properties can be also used in medical imaging applications. thus, it would be of interest to integrate a scintillating material that came to the spotlight once again, with this state-ofthe-art sensor in order to further exploit their imaging characteristics. the cawo4 screen was directly overlaid onto the active area of the cmos and irradiated with a bmi general medical merate tube having rotating tungsten anode and inherent filtration equivalent to 2 mm al at 70 kv (rqa-5) x-ray beam quality and source to detector distance of 156 cm [21]. modulation transfer function (mtf) the modulation transfer function (mtf) was measured by irradiating a ptw freiburg tungsten edge test device, following the procedures described in the iec standard [11,32,33]. the updated iec 62220-1-1:2015 [11,33,40] standard describes certain modifications, such as the method for the determination of the modulation transfer function (mtf) in which the final mtf can be now obtained only through averaging of the oversampled edge spread function (esf) [33,41-43]. the average of all oversampled esfs was then fitted with a modified fermi-dirac distribution function as follows [11,21]: ( x a)/b c fermi(x)= +d e +1       (1) the values of fitting parameters are a=7200, b=15, c=65500 and d=0. the fitted esf was differentiated to obtain the line spread function (lsf) and fourier transformed to finally obtain the mtf [21,44]. luminescence efficiency measurements the efficiency (output signal) of a scintillator to emit light, upon x-ray irradiation is experimentally determined by measuring the emitted light energy flux λ and the exposure rate ( x ) using a calibrated dosimeter. in this study, the piranha p100b rti was used. the light flux measurements were performed using a light integration sphere (oriel 70451), coupled to a photomultiplier (pmt) (emi 9798b) and connected to a cary 401 vibrating reed electrometer [5,9]. the circular cawo4 sample was also exposed to x-rays on the bmi general medical merate tube, with energies ranging from 50 to 125 kvp. an additional 20 mm al filtration was introduced in the beam to simulate beam quality alternation by a human body [45,46]. x-ray luminescence efficiency (xle) the x-ray luminescence efficiency (xle) is a unitless measure of the fraction of incident energy converted into emitted light energy, i.e. the ratio of the emitted light energy flux over the incident x-ray energy flux (ηψ=ψλ/ψ0). xle was determined [9] by converting the measured x-ray exposure data into x-ray energy flux (ψ0) [9], as follows: 0 ˆ  where ̂ is defined as the x-ray energy flux per exposure rate, estimated according to eq.(2) [5,36]:   0 0 0       (e )deˆ (e ) x / (e ) de (2) where 1 0/ ( ) ( ( ) / ) ( / )en air ax e e w e     (3) is the factor converting energy flux into exposure rate, (μen/ρ)air the x-ray mass energy absorption coefficient of air, at energy e, and (wa/e) is the average energy per unit of charge required to produce an electron-ion pair in air. (wa/e) and (μen/ρ)air were obtained from tabulated data [47]. detector quantum optical gain (dqg) detector quantum optical gain (dqg) is the ratio of the light photon flux (φλ) over the x-ray photon flux (φx) and expresses the emission efficiency in terms of quantum gain (number of emitted light photons per incident x-ray). using this quantity, the emitted light photon fluence can be expressed in terms of experimentally determined quantities (absolute efficiency, exposure, mean light wavelength), by using eq.(4) [5]: n. martini et alii, frattura ed integrità strutturale, 50 (2019) 471-480; doi: 10.3221/igf-esis.50.39 474 f 1      hc (4) φx was determined by using eqs.(2,3), replacing 0 by φ0 and dividing eq.(3) by the x-ray energy [9]. eqs(2,4) may be expressed in the spatial frequency domain. within this framework the detector quantum gain may be expressed by a gain transfer function (gtf), defined as follows [36,45]: 0 0 0 gtf( e ,ν, w ) ( e ,ν, w ) / (5) where v denotes spatial frequency, w coating thickness and φλ(ε0,ν,w) is the spatial frequency-dependent emitted light photon fluence. gain transfer function, can be expressed through the mtf [36,45]:  gtf( ν, w ) mtf( ν, w ) dqg (6) where dqg is the detector quantum optical gain. in medical imaging, where fluorescent screens are used in combination with optical detectors (films in the past, photocathodes, photodiodes), the spectral matching between the emitted phosphor light and the optical detector sensitivity must be considered. this is because the degree of spectral matching affects the amount of light utilized to form the final image. thus, eq.(6) is reduced by a factor as, expressing the fraction of emitted light that can be detected by the optical detector, which exhibits a specific spectral distribution of sensitivity. as, can be calculated by eq.(7) [5,45]:   p d s p s ( λ )s ( λ )dλ α s ( λ )dλ (7) where sp(λ) is the spectrum of the light emitted by the phosphor and sd(λ) is the spectral sensitivity of the optical detector coupled to the phosphor [5]. by considering as, we may define the effective gain transfer function as follows [36,45]:    segtf ( v , w ) dqg mtf ( v , w ) α (8) results and discussion ig.1 shows the grain-size deposition per thickness of cawo4, estimated from scanning electron microscope images. qualitatively the mean particle size of cawo4 phosphor (6.02 m ) was estimated from the sem images using the imagej analysis software, as shown from the grain-size distribution [48,49]. the calculated screen thickness was equal to 118.9 μm estimated by profile measurements on the area depicted as inset in fig.1, across the material coating [5,22]. furthermore, in fig.1 the energy dispersive x-ray (edx) analysis of the material is demonstrated. it was found that cawo4 was dominantly present in the sample along with carbon (c) due to the carbon thread evaporation process. normalized stoichiometric results, obtained by the sem on the region of interest (roi) of fig.1, showed the following % weights of the elements in the mixture: calcium (ca) 5.77%, oxygen (o) 26.54%, tungsten (w) 29.94 and carbon due to the carbon thread evaporation process 37.75% [22]. the x-ray characteristic curves (output signal versus incident exposure) of cawo4 and (for comparison purposes) of a flexible fluorescent gd2o2s:tb sample (gold standard for imaging applications) of similar coating thickness (30.8 mg/cm2 for gd2o2s:tb versus 36.26 mg/cm2 for cawo4) are plotted in fig.2. these coating thicknesses were calculated assuming densities of 7.3 g/cm3 for gd2o2s:tb and 6.1 g/cm3 for cawo4 with packing densities of 50% for both materials. results for cawo4 and gd2o2s:tb show linear dependence between the output signal and exposure rate in the 4-299 mr/s range. the linear no-threshold fit gave correlation coefficient values r2 of 0.9997 for cawo4 and 0.9953 for gd2o2s:tb, which are very close to unity and indicate that the screens have linear response in this energy range. gd2o2s:tb was found with clearly higher output signal values than those of cawo4 due to its higher absolute efficiency values [5]. fig.3 shows all the oversampled esfs (fig.3a) used to create the average esf and then the fermi-fitted esf (fig.3b), as well as, the resulted lsf (fig.3c), following the iec 2015 protocol and the edge phantom. the edge test device consists of a 1 mm thick w edge plate (100×75 mm2) fixed on a 3 mm thick lead plate. images of the edge, placed at a slight angle in order to avoid aliasing effects, were obtained. irradiation was performed at 70kvp and 50 mas for the tube current and n. martini et alii, frattura ed integrità strutturale, 50 (2019) 471-480; doi: 10.3221/igf-esis.50.39 475 grain size (μm) (a) 12 10 8 6 4 2 0 0 2 4 6 8 10 12 14 f re qu en cy (b) (c) figure 1: grain-size distribution obtained from the scanning electron microscope image of the cawo4 scintillating material (a), obtained from a region of interest (b), along with the energy dispersive x-ray (edx) analysis (c). exposure rate (mr/s) o ut p ut s ig n al (μ w / m 2 ) gd2o2s:tb 30.8 mg/cm2 cawo4:tb 30.8 mg/cm2 figure 2: output signal of the 36.26 mg/cm2 cawo4 screen and a 30.8 mg/cm2 gd2o2s:tb flexible phosphor in the radiographic range of exposures. exposure time product. this energy is also within the energy range of 51-84 kev that can be utilized for testing steel thicknesses between 2.5 and 12.5 mm [13]. the edge spread function, of the small cmos detector, was calculated by the extraction of a 2×2 cm2 roi, which covers approximately 41% of the active area of the small area cmos sensor (2.7×3.6 cm2), with the edge roughly at the center. in the iec protocol a 5×10cm2 roi is suggested [33]. a smaller roi may not be n. martini et alii, frattura ed integrità strutturale, 50 (2019) 471-480; doi: 10.3221/igf-esis.50.39 476 adequate to observe a possible low-frequency sharpness drop in scintillating screens [39]. the variation in the esf curves that can be depicted from figs.5(a,b), can be attributed to a statistical noise component mostly prominent at the edge surface area. fig.3d shows results for the modulation transfer function of the cmos sensor combined with the 118.9 μm cawo4 screen, under the rqa-5 (70kvp) beam quality. mtf values were found high across the examined spatial frequency range. (a) (b) (c) (d) figure 3: (a) esfs of a 118.9 μm cawo4/radeyehr cmos combination, following the iec 2015 method, (b) averaged and fermi fitted esf, (c) lsf, (d) modulation transfer function following the iec 2015 protocol, under the rqa-5 beam quality. figs.(4,5) show the variation of gtf and egtf with spatial frequency for the cawo4 phosphor screen measured at 70 kvp. the difference between this curve and the corresponding mtf curve is due to the influence of x-ray absorption and optical emission on gtf, which are more apparent at lower frequencies. as frequency increases, the influence of mtf on gtf is more significant than the corresponding influence of detector quantum gain (dqg: 18.17 at 70 kvp [5]) causing a further decrease in the gtf (fig.4). figs.5(a-d) shows indicative effective gtf results of the cawo4 screen with various optical detectors. results are shown up to 5 cycles/mm, since the measured mtf incorporates the mtf of the cmos semiconductor which however has been reported to be higher than 0.984, thus the calculation error is minimum [8,50-52]. the best optical detector-screen combination was obtained for a charge-coupled device having broadband anti-reflection (ar) coating (fig.5c) with an egtf value of 17.52 at zero spatial frequency. this value reduces gtf only by 3.54% (spectral matching factor: 0.964 [5]). the egtf values of the ccd, is followed by the hamamatsu mppc silicon photomultipliers s10985 (fig.5b) (egtf: 17.39 at 0 cycles/mm, matching factor: 0.957), the gaas photocathode (egtf: 17.36 at 0 cycles/mm, matching factor: 0.955) (fig. 5a) and the non-passivated amorphous hydrogenated silicon photodiode (a-si:h) (fig.5d) (egtf: 17.39 at 0 cycles/mm, matching factor: 0.948), employed in thin film transistors in active matrix flat panel detectors. cawo4 also shows very good egtf values with sensl’s silicon pmts, with egtf value 14.21 at 0 cycles/mm, for the microfm-10035 (matching factor: 0.782), with the microfb-30035-smt (egtf: 15.25 at 0 cycles/mm, matching factor: 0.839 and with the microfc-30035 (egtf: 15.94 at 0 cycles/mm, matching factor: 0.877 (fig.5b). furthermore, it showed very good egtf with hamamatsu flat panel position sensitive photomultipliers, such as the h8500c-03 (egtf: 14.60 at 0 cycles/mm, matching factor: 0.80) (fig.5c). it is of importance to note that egtf showed good values when cawo4 is combined with complementary metal-oxide semiconductors, used in digital radiography and mammography systems, showing maximum when coupled with a hybrid blue cmos (egtf: 17.39 at 0 cycles/mm, matching factor: 0.854) [53]. n. martini et alii, frattura ed integrità strutturale, 50 (2019) 471-480; doi: 10.3221/igf-esis.50.39 477 spatial frequencies (cycles/mm) g ai n tr an sf er f un ct io n (g t f ) figure 4: variation of the gtf with spatial frequency for the thin cawo4 phosphor screen. figure 5: variation of the egtf with spatial frequency for the cawo4 phosphor screen combined with the various optical detectors. n. martini et alii, frattura ed integrità strutturale, 50 (2019) 471-480; doi: 10.3221/igf-esis.50.39 478 conclusions pplications such as, non-destructive testing, medical imaging etc., require efficient detectors, of high resolution. in this study the resolution properties of a non-destructive testing/industrial inspection cmos sensor, in conjunction with a scintillating material that came to the spotlight once again (cawo4) was examined in order to further exploit and enhance the imaging capabilities of an integrated detector, incorporating these two modules. experiments were carried under x-ray radiography imaging conditions, following the iec 62220-1-1:2015 protocol. furthermore, the detector quantum gain of the screen and the spectral compatibility was also examined for various optical sensor combinations. mtf values of the cawo4 screen/cmos combination were found high across the spatial frequency range. as a conclusion, the resolution properties of the thin 118.9 μm cawo4 screen/cmos combination are promising for general radiography medical imaging applications. references [1] kaugars, g. and fatouros, p. (1982). clinical comparison of conventional and rare earth screen-film systems for cephalometric radiographs, oral, surg. oral. med. oral. pathol., 53(3), pp. 322-325. [2] derenzo, s., weber, m., bourret-courchesne, e., klintenberg, m. (2003). the quest for the ideal inorganic scintillator, nucl. instr. and meth. phys. res. a., 505, pp. 111-117. [3] brixner, l. (1987). new x-ray phosphors, mater, chem. phys., 16, pp. 253-281. [4] nikl, m. (2006). scintillation detectors for x-rays, meas. sci. technol., 17, pp. r37-r54. [5] michail, c., valais, i., fountos, g., bakas, a., fountzoula, c., kalyvas, n., karabotsos, a., sianoudis, i., and kandarakis, i. (2018). luminescence efficiency of calcium tungstate (cawo4) under x-ray radiation: comparison with gd2o2s:tb, measur., 120, pp. 213-220. [6] cavouras, d., kandarakis, i., bakas, a., triantis, d., nomicos, c., panayiotakis, g. (1998). an experimental method to determine the effective luminescence efficiency of scintillator-photodetector combinations used in x-ray medical imaging systems, br. j. radiol, 71, pp. 766-772. [7] cavouras, d., kandarakis, i., panayiotakis, g., kanellopoulos, e., triantis, d., nomicos, c. (1998). an investigation of the imaging characteristics of the y2o2s:eu3+ phosphor for application in x-ray detectors of digital mammography, appl. radiat. isot, 49, pp. 931-937. [8] michail, c.m., spyropoulou, v. a., fountos, g. p., kalyvas, n.i., valais, i. g., kandarakis, i.s., panayiotakis, g.s. (2011). experimental and theoretical evaluation of a high resolution cmos based detector under x-ray imaging conditions, ieee trans. nucl. sci, 58(1), pp. 314-322. [9] michail, c., valais, i., seferis, i., kalyvas, n., david, s., fountos, g., kandarakis, i. (2014). measurement of the luminescence properties of gd2o2s:pr,ce,f powder scintillators under x-ray radiation, radiat. meas., 70, pp. 59-64. [10] michail, c., valais, i., seferis, i., kalyvas, n., fountos, g., kandarakis, i. (2015). experimental measurement of a high resolution cmos detector coupled to csi scintillators under x-ray radiation, radiat. meas., 74, pp. 39-46. [11] michail, c., valais, i., martini, n., koukou, v., kalyvas, n., bakas, a., kandarakis, i., fountos, g. (2016). determination of the detective quantum efficiency (dqe) of cmos/csi imaging detectors following the novel iec 62220-1-1:2015 international standard, radiat. meas., 94, pp. 8-17. [12] souza, e., correa, s., silva, a., lopes, r., oliveira, d. (2008). methodology for digital radiography simulation using the monte carlo code mcnpx for industrial applications, appl. radiat. isot., 66, pp. 587-592. [13] iaea (2011). radiation safety standard in industrial radiography, specific safety guide no. ssg-11. available at: https://www-pub.iaea.org/books/iaeabooks/8500/radiation-safety-in-industrial-radiography [14] kim, k., kang, s., kim, w., cho, h., park, c., lee, d., kim, g., park, s., lim, h., lee, h., park, j., jeon, d., lim, y., je, u., woo, t. (2018). improvement of radiographic visibility using an image restoration method based on a simple radiographic scattering model for x-ray nondestructive testing, ndt and e int., 98, pp. 117-122. [15] moszyski, m., balcerzyk, m., kraus, h., czarnacki, w., mikhailik, v., nassalski, a., solskii, i. (2005). characterization of cawo4 scintillator at room and liquid nitrogen temperatures, nucl. instr. and meth. phys. res. a., 553, pp. 578-591. [16] munster, a., schonert, s., willers, m. (2017). cryogenic detectors for dark matter search and neutrinoless double beta decay, nucl. instr. and meth. phys. res. a., 845, pp. 387-393. [17] zdesenko, y., avignone iii, f., brudanin, v., danevich, f., nagorny, s., solsky, i., tretyak, v. (2005). scintillation properties and radioactive contamination of cawo4 crystal scintillators, nucl. instr. and meth. phys. res. a., 538, pp. 657-667. a n. martini et alii, frattura ed integrità strutturale, 50 (2019) 471-480; doi: 10.3221/igf-esis.50.39 479 [18] mikhailik, v., kraus, h. (2010). performance of scintillation materials at cryogenic temperatures, phys. status. solidi. b., 247, pp. 1583-1599. [19] mikhailik, v., elyashevskyi, y., kraus, h., kim, h., kapustianyk, v., panasyuk, m. (2015). temperature dependence of scintillation properties of srmoo4, nucl. instr. and meth. phys. res. a., 792, pp. 1-5. [20] shahabinejad, h., feghhi, s., khorsandi, m. (2014). structural inspection and troubleshooting analysis of a lab-scale distillation column using gamma scanning technique in comparison with monte carlo simulations, measur., 55, pp. 375-381. [21] koukou, v., martini, n., valais, i., bakas, a., kalyvas, n., lavdas, e., fountos, g., kandarakis, i., michail, c. (2017). resolution properties of a calcium tungstate (cawo4) screen coupled to a cmos imaging detector, j. phys.: conf. ser., 931, pp. 012027. [22] martini, n., koukou, v., fountos, g., valais, i., bakas, a., ninos, k., kandarakis, i., panayiotakis, g., michail, c. (2018). towards the enhancement of medical imaging with non-destructive testing (ndt) cmos sensors. evaluation following iec 62220-1-1:2015 international standard, procedia structural integrity, 10, pp. 326-332. [23] sotiropoulou, p., fountos, g., martini, n., koukou, v., michail, c., kandarakis, i., nikiforidis, g. (2015). bone calcium/phosphorus ratio determination using dual energy x-ray method, phys. med., 31, pp. 307-313. [24] koukou, v., martini, n., michail, c., sotiropoulou, p., fountzoula, c., kalyvas, n., kandarakis, i., nikiforidis, g., fountos, g. (2015). dual energy method for breast imaging: a simulation study, comput. math. methods med., 2015, pp. 574238. [25] sotiropoulou, p., fountos, g., martini, n., koukou, v., michail, c., kandarakis, i., nikiforidis, g. (2016). polynomial dual energy inverse functions for bone calcium/phosphorus ratio determination and experimental evaluation, appl. radiat. isot., 118, pp. 18-24. [26] koukou, v., martini, n., fountos, g., michail, c., sotiropoulou, p., bakas, a., kalyvas, n., kandarakis, i., speller, r., nikiforidis, g. (2017). dual energy subtraction method for breast calcification imaging, nucl. instrum. meth. phys. res. a., 848, pp. 31-38. [27] koukou, v., martini, n., fountos, g., michail, c., bakas, a., oikonomou, g., kandarakis, i., nikiforidis, g. (2017). application of a dual energy x-ray imaging method on breast specimen, result. phys., 7, pp. 1734-1736. [28] martini, n., koukou, v., fountos, g., michail, c., bakas, a., kandarakis, i., speller, r., nikiforidis, g. (2017). characterization of breast calcification types using dual energy x-ray method, phys. med. biol., 62, pp. 7741-7764. [29] valais, i., kandarakis, i., nikolopoulos, d., michail, c., david, s., loudos, g., cavouras, d., panayiotakis, g. (2007). luminescence properties of (lu,y)2sio5:ce and gd2sio5:ce single crystal scintillators under x-ray excitation, for use in medical imaging systems, ιεεε trans. nucl. sci., 54(1), pp. 11-18. [30] valais, i., michail, c., david, s., liaparinos, p., fountos, g., paschalis, t., kandarakis, i., panayiotakis, g. (2010). comparative investigation of ce3+ doped scintillators in a wide range of photon energies covering x-ray ct, nuclear medicine and megavoltage radiation therapy portal imaging applications, ιεεε trans. nucl. sci., 57(1), pp. 3-7. [31] michail, c., david, s., liaparinos, p., valais, i., nikolopoulos, d., kalivas, n., toutountzis, a., sianoudis, i., cavouras, d., dimitropoulos, n., nomicos, c., kourkoutas, k., kandarakis, i., panayiotakis, g. (2007). evaluation of the imaging performance of lso powder scintillator for use in x-ray mammography, nucl. instrum. meth. phys. res. a., 580, pp. 558-561. [32] medical electrical equipment-characteristics of digital x-ray imaging devices, part 1: determination of the detective quantum efficiency” iec, international electrotechnical commission, geneva, switzerland, 2003, iec 62220-1. [33] medical electrical equipment-characteristics of digital x-ray imaging devices part 1-1: determination of the detective quantum efficiency detectors used in radiographic imaging, iec, international electrotechnical commission, geneva, switzerland, 2015, iec 62220-1-1. [34] kandarakis, i., cavouras, d., panayiotakis, g., triantis, d., nomicos, c. (1997). an experimental method for the determination of spatial-frequency-dependent detective quantum efficiency (dqe) of scintillators used in x-ray imaging detectors, nucl. instrum. meth. phys. res. a., 399, pp. 335-342. [35] kandarakis, i., cavouras, d., panayiotakis, g., triantis, d., nomicos, c. (1998). europium-activated phosphors for use in x-ray detectors of medical imaging systems, eur. radiol., 8, pp. 313-318. [36] michail, c., toutountzis, a., david, s., kalivas, n., valais, i., kandarakis, i., panayiotakis, g. (2009). imaging performance and light emission efficiency of lu2sio5:ce (lso:ce) powder scintillator under x-ray mammographic conditions, appl phys b., 95, pp. 131-139. [37] tombak, m., gutan, v. (1968). properties of a cawo4 phosphor heated in flowing hydrogen chloride, zh. prikl. spektrosk., 8(5), pp. 796-802. [38] issler, s., torardi, c. (1995). solid state chemistry and luminescence of x-ray phosphors, j. alloys compd., 229, pp. 54-65. n. martini et alii, frattura ed integrità strutturale, 50 (2019) 471-480; doi: 10.3221/igf-esis.50.39 480 [39] michail, c. (2015). image quality assessment of a cmos/gd2o2s:pr,ce,f x-ray sensor, j. sensors., 2015, pp. 874637. [40] buhr, e., gunther-kohfahl, s., neitzel, u. (2003). accuracy of a simple method for deriving the presampled modulation transfer function of a digital radiographic system from an edge image, med. phys., 30, pp. 2323-2331. [41] fountos, g., michail, c., zanglis, a., samartzis, a., martini, n., koukou, v., kalatzis, i., kandarakis, i. (2012). a novel easy-to-use phantom for the determination of mtf in spect scanners, med. phys., 39(3), pp. 1561-1570. [42] karpetas, g., michail, c., fountos, g., kandarakis, i., panayiotakis, g. (2014). a new pet resolution measurement method through monte carlo simulations, nucl. med. commun., 35(9), pp. 967-976. [43] karpetas, g., michail, c., fountos, g., kalyvas, n., valais, i., kandarakis, i., panayiotakis, g. (2017). detective quantum efficiency (dqe) in pet scanners: a simulation study, appl. radiat. isot., 125, pp. 154-162. [44] samei, e., flynn, m., reimann, d. (1998). a method for measuring the presampled mtf of digital radiographic systems using an edge test device, med. phys., 25(1), pp. 102-113. [45] michail, c., fountos, g., valais, i., kalyvas, n., liaparinos, p., kandarakis, i., panayiotakis, g. (2011). evaluation of the red emitting gd2o2s:eu powder scintillator for use in indirect x-ray digital mammography detectors., ιεεε trans. nucl. sci., 58(5), pp. 2503-2511. [46] michail, c., david, s., bakas, a., kalyvas, n., fountos, g., kandarakis, i., valais, i. (2015). luminescence efficiency of (lu,gd)2sio5:ce (lgso:ce) crystals under x-ray radiation, radiat. meas., 80, pp. 1-9. [47] hubbell, j., seltzer, s. (1995). tables of x-ray mass attenuation coefficients and mass energy absorption coefficients 1 to 20mev for elements z=1 to 92 and 48 additional substances of dosimetric interest. us department of commerce, nistir 5632. [48] huang, l., and wang, m. (1995). image thresholding by minimizing the measure of fuzziness, pattern. recognit., 28(1), pp. 41-51. [49] abramoff, m., magalhaes, p., ram, s. (2004). image processing with imagej, biophoton., int. 11(7), pp. 36-42. [50] hoheisel, m., giersch, j., bernhardt, p. (2004). intrinsic spatial resolution of semiconductor x-ray detectors: a simulation study, nucl. instrum. meth. phys. res. a, a531, pp. 75-81. [51] estribeau, m., magnan, p. (2004). fast mtf measurements of cmos imagers using iso 12233 slanted edge methodology, proc. spie., 5251, pp. 243-252. [52] lin, c., mathur, b., chang, m. (2002). analytical charge collection and mtf model for photodiode based cmos imagers, ieee. trans. electron. devices, 49, pp. 754-761. [53] magnan, p. 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can be opened with acrobat and adobe reader 5.0 and later.) >> /namespace [ (adobe) (common) (1.0) ] /othernamespaces [ << /asreaderspreads false /cropimagestoframes true /errorcontrol /warnandcontinue /flattenerignorespreadoverrides false /includeguidesgrids false /includenonprinting false /includeslug false /namespace [ (adobe) (indesign) (4.0) ] /omitplacedbitmaps false /omitplacedeps false /omitplacedpdf false /simulateoverprint /legacy >> << /addbleedmarks false /addcolorbars false /addcropmarks false /addpageinfo false /addregmarks false /convertcolors /converttocmyk /destinationprofilename () /destinationprofileselector /documentcmyk /downsample16bitimages true /flattenerpreset << /presetselector /mediumresolution >> /formelements false /generatestructure false /includebookmarks false /includehyperlinks false /includeinteractive false /includelayers false /includeprofiles false /multimediahandling /useobjectsettings /namespace [ (adobe) (creativesuite) (2.0) ] /pdfxoutputintentprofileselector /documentcmyk /preserveediting true /untaggedcmykhandling /leaveuntagged /untaggedrgbhandling /usedocumentprofile /usedocumentbleed false >> ] >> setdistillerparams << /hwresolution [2400 2400] /pagesize [612.000 792.000] >> setpagedevice microsoft word numero_35_art_44 b. lian et alii, frattura ed integrità strutturale, 35 (2016) 389-395; doi: 10.3221/igf-esis.35.44 389 focussed on crack paths development of in-situ fatigue crack observing system for rotating bending fatigue testing machine b. lian yamamoto metal technos co., ltd. a. ueno ritsumeikan university, 1-1-1 noji-higashi, kusatsu, shiga 525-8577, japan ueno01@fc.ritsumei.ac.jp t. iwashita graduate school student of ritsumeikan university abstract. to substitute for a traditional replication technique, an in-situ fatigue crack observing system for rotating bending testing machine has been newly developed. for verifying performance of this observing system, fatigue tests were carried out by using fatigue specimen having a small artificial defect. it is proved that this system can be detect a small fatigue crack and its propagation behavior. keywords. in-situ observation; fatigue crack initiation; fatigue crack propagation; rotating bending testing machine. introduction n the field of the fatigue properties of metallic materials, the assessment of the s-n curve, which consists to the stress level and the number of cycles up to failure, does not give an entire viewpoint of the phenomenon. indeed, a lot of information on the fatigue properties can be gathered by the observation of the fatigue crack initiation and propagation directly on the specimen surface. unlike the case of pre-cracked specimens used for fracture mechanics experiments, the initiation and the propagation of the conventional fatigue specimens are often investigated by replica methods. due to the performances of replica made of cellulose acetate film good enough to duplicate the specimen surface, it is possible to detect very small fatigue crack just after the initiation. however, it is necessary to have some experience on the use of this technique, in addition there are also cases where the utilization of replica is complex. it is particularly the case for fatigue specimens designed for rotating bending tests, with an hourglass shape at the minimum cross section spot. nevertheless, performances of some optic devices have been improved in the latest years, in the field of: (i) affordable long working distance microscopy, (ii) high-definition video camera, and (iii) high brightness led components. the combination of these new developments gives the possibility to design a system adapted for fatigue rotating bending tests, and thus to observe continuously the fatigue crack propagation. i b. lian et alii, frattura ed integrità strutturale, 35 (2016) 389-395; doi: 10.3221/igf-esis.35.44 390 this paper deals first with an explanation of the optical system designed here, then some fatigue crack observation results obtained are also introduced. system outline optic-system n the case of the rotating bending fatigue tests, since the fatigue specimen at the minimum cross section is incurvated, if the axis of microscope is the same as the axis enlightenment of the specimen, only the summit of the specimen will be observable, as shown in fig. 1(a). such a configuration is not suitable to obtain the full image of the entire crack on the specimen surface. nevertheless, by adopting a configuration where several light sources are circularly placed around the fatigue specimen, it is possible to enlighten favorably a larger zone, as in fig. 1(b). figure 1: schematics of lighting. (a): in case of point light source, (b): in case of surround light source. in order to get observation in adequate synchronization with the rotation speed of the fatigue test, stroboscope device is usually set in order to make the observation of the highest position of the fatigue specimen, where the maximum tension stress level is reached. however, in the case of conventional stroboscope with xenon lamp components, the directive signal of flash, in other words the pulse frequency, is initially set, since the lamps’ flash and the pulse frequency is not totally in agreement. thus, the timing of the observation will be shifted, resulting in a loss of luminosity compared to the optimum position for crack observation. to solve this problem, use of stroboscope with high luminosity led components gives a more favorable observation condition than conventional stroboscope. in the rest of this paper, the introduced system gave acceptable observation conditions by setting the flash directive signal. indeed, even though the flash period was extremely short, the luminosity given out by white color high luminosity led, arranged on circuit boards illustrated in fig. 2(a), was sufficient. more precisely, two circuit boards were installed around the specimen, as indicated in fig. 2(b). figure 2: led type stroboscope. (a): led array plan, (b): arrangement plan. i (a) (b) (a) (b) b. lian et alii, frattura ed integrità strutturale, 35 (2016) 389-395; doi: 10.3221/igf-esis.35.44 391 control and configuration equipment of the introduced system outline of the system dedicated to the control of the led stroboscope’s flash timing is schematically depicted in fig. 3. this system is composed of (1) the motor and the spindle that is controlling the rotation of the fatigue specimen, (2) the timing gear at opposite side of the specimen is also rotated in the same way, (3) the magnetic sensor placed in the vicinity of the gear, (4) the servo-motor, which is introduced here to set the position of the magnetic sensor at any angular position around the gear, (5) the control system that gives the flash directive signal (pulse frequency) to the led stroboscope, (6) the high-definition digital video camera, which records at a predetermined interval of time, (7) the long working distance microscope, and (8) the personal computer to record and analyze the data obtained. figure 3: schematic of system components. figure 4: relationship between magnetic sensor position and output voltage signal. depending on the relative position of the timing gear’s tooth, the magnetic field of the magnetic sensor will change. thus, it is possible to determine the position of the gear according to the output voltage signal from the sensor, as one can see in fig. 4. indeed, the magneto resistance elements inside the sensor will induce a different resistance value depending on the magnetic field. since the resistance value change conducts to a variation of the voltage, the output voltage from the magnetic sensor will show a sinusoidal shape function against time. after treatment by the control system, one can obtain the pulse signal (or the digital signal), which is given to the led stroboscope to flash at the appropriate timing. in addition, it is possible to adjust the flash period by changing the threshold value when converting the pulse signal. therefore, one can adjust with an error as slight as possible the microscope observation field flashed by led stroboscope, in accordance with the rotation speed of the rotating bending fatigue machine. timing of the led flashing is determined by the position of the tooth of the gear and the magnetic sensor around the gear at an angle controlled by a servo motor, as shown in fig. 5. the led stroboscope flashes in a short time lapse at the time of the sensor detects that the tooth a is approaching. in the fig. 5(a), since the sensor angular position is 1, when the b. lian et alii, frattura ed integrità strutturale, 35 (2016) 389-395; doi: 10.3221/igf-esis.35.44 392 tooth a is detected, the led stroboscope flashes for a lapse time the position indicated by plain star. if the position of the magnetic sensor is changed to position 2, the led stroboscope will flash for a lapse time the position indicated by hollow star. thus, it is possible to adjust the flash timing over these 4 possible angular positions of the magnetic detector. as depicted in fig. 5, as the gear used here consists of 9 teeth, in the case where there are 4 possible angular positions of the magnetic sensor, we can flash at 36 different angular positions, which means an angular interval between two positions of 10°. one can note that we can reduce such an angular interval by introducing more possible angular positions of the magnetic sensor, or installing a gear with a higher number of teeth. in the case where an artificial defect has been added at the surface of the fatigue specimen, since the crack initiation site is already known, we are in the case depicted in the fig. 5(a), where the same angular position of the magnetic sensor will be used for the duration of the fatigue test. nevertheless, if the crack initiation site is unknown, after initiation of the crack, it is possible to switch over the possible angular positions of the magnetic sensor in order to have an appropriate flash timing. however, between fatigue test’s start and detection of the crack initiation, the interval meter of the video camera have to record the time interval in order to obtain the number of fatigue cycle data, which is mandatory to get appropriate results. figure 5: how to set up led flushing timing. (a): case 1 for fixed point observation, (b): case 2 for circumference observation. figure 6: newly developed high-speed rotating bending fatigue testing machine. (a): side view photograph, (b): 3d-cad image near specimen end, (c): led type stroboscope and attachment cover. rotating bending testing machine the fatigue crack observation system previously introduced can be adapted to all types of rotating bending testing machine. in this study, the system was installed on a single axis spin motor high speed rotating bending machine as one can see in fig. 6. the overview of the testing machine, details on the environment close to the hanging weight and a photo of the led stroboscope and its plastic cover are given in fig 6(a), (b) and (c), respectively. for this machine, motor engine is designed for machine tool usage. thus, it is possible to reach loading frequency up to 500 hz (=30,000 rpm), however since the chuck of the fatigue specimen is directly integrated in the principal axis of the motor, the fatigue specimen must have a very low eccentricity characteristic. (a) (b) (a) (b) (c) b. lian et alii, frattura ed integrità strutturale, 35 (2016) 389-395; doi: 10.3221/igf-esis.35.44 393 evaluation of the performance of the introduced system n order to assess the performances of this system, fatigue tests were carried out on valve spring si-cr oil tempered wire swosc-v[2]. configuration of the fatigue specimen is presented in fig. 7, where an artificial defect was added by 0.1 mm-diameter carbide drilling, with a depth of 0.1 mm, at the minimum cross section. then, in order to minimize the effect of drilling, 250 °c × 30 min. vacuum heat treatment followed by mirror surface polishing condition of the minimum cross section area by op-s were conducted. fatigue tests are operated in air, at room temperature with a rotating speed of 3000 rpm. figure 7: shape and dimensions of fatigue specimen. an experiment to assess the performance of the crack length has been undertaken. on a fatigue specimen, where the fatigue crack was already initiated, a comparison has been conduct between the crack length obtained by the system previously introduced and obtained by optical microscopy, where the fatigue test was stopped and bending weight removed (conditions equivalent to the replica method). observation given by introduced system is presented in fig. 8(a). even though the photograph is dark and suffers from lack of clarity, as the bending load tends to open the crack, the crack tip can be easily indentified. in this case, this photograph points out a crack length of 2s = 408 m, considering also the diameter of the artificial defect. on the other hand, after removing the bending weight and extracting the specimen from the testing machine, the photograph fig. 8(b) has been taken, where the corresponding crack length found is 2s = 419 m. thus, even though the length obtained by introduced system is slightly lower, a relative error of approximately 3 % can be noted. the introduced system in this paper is thought to give relevant observation of the fatigue crack. figure 8: comparison of fatigue crack images. (a): fatigue crack image obtained with observing system, (b): fatigue crack image obtained with optical microscope (no weight and no rotation). change of the crack length at different cycle stages for a single specimen subjected to a fatigue test at a = 800 mpa (nf = 4.57 × 104 cycles) stress amplitude is shown in fig. 9. as the crack propagates, if the observation field of the microscope does no more sufficient to see the entire crack length, it is necessary to switch to the configuration shown in fig. 5(b). in i (a) (b) b. lian et alii, frattura ed integrità strutturale, 35 (2016) 389-395; doi: 10.3221/igf-esis.35.44 394 such a way, it is possible to record the crack propagation from early stage at the artificial defect to just before the final fracture phenomenon of the specimen. the crack length measurement results obtained for the experiment using a specimen with an artificial defect (a = 800 mpa, nf = 4.57 × 104 cycles) and using a specimen without artificial defect (a = 1400 mpa, nf = 2.39 × 104 cycles) are depicted in fig. 10(a) and (b), respectively. detection of the early stage of the crack propagation is approximately at 10 m in the case of experiment using a specimen with artificial defect, whereas a length of approximately 20 m was necessary for specimen without artificial defect. in the present experiments, the led stroboscope gives an uneven enlightenment, inducing bright and dark spots along the whole observation field. it is thought that future improvements of the flashing technique would give fatigue crack observations with better clarity. figure 9: series images of fatigue crack initiation and propagation. (a): n = 7.50 × 103 cycles, (b): n = 3.45 × 104 cycles, 2s = 606 m, (c): n = 4.50 × 104 cycles, 2s = 3360 m. figure 10: relationship between cycle ratio and crack length. (a): with artificial defect (a = 800 mpa, nf = 4.57 × 104 cycles), (b): without artificial defect (a = 1400 mpa, nf = 2.39 × 104 cycles). conclusions y using the combination of a led stroboscope, a control system of the stroboscope flash timing, a long working distance microscope and high spec digital camera, an observation system suitable to record the fatigue crack length on a hourglass shape specimen for rotating bending fatigue tests has been developed. this system allows to study fatigue crack initiation and propagation phenomena at a resolution equivalent to the replica method, without any suspension of the fatigue test. b (a) (b) (a) (b) (c) b. lian et alii, frattura ed integrità strutturale, 35 (2016) 389-395; doi: 10.3221/igf-esis.35.44 395 references [1] lian, b., fukuchi, y., sakaida, a., ueno, a., development of high-speed rotating bending fatigue testing machine for evaluating fatigue properties in very high cycle regime, in: proc. of the 31th jsms fatigue symposium (2012) 56-57, in japanese. [2] miura, t., sakakibara, t., kuno, t., ueno, a., kikuchi, s., sakai, t., interior-induced fracture mechanism of valve spring steel (jis swosc-v) with high cleanliness in very high cycle regime, in: proc. of the 6th international conference on vhcf, chengdu, china (2014). << /ascii85encodepages false /allowtransparency false /autopositionepsfiles true /autorotatepages /none /binding /left /calgrayprofile (dot gain 20%) /calrgbprofile (srgb iec61966-2.1) /calcmykprofile (u.s. web coated \050swop\051 v2) /srgbprofile (srgb iec61966-2.1) /cannotembedfontpolicy /error /compatibilitylevel 1.4 /compressobjects /tags /compresspages true /convertimagestoindexed true /passthroughjpegimages true /createjobticket false /defaultrenderingintent /default /detectblends true /detectcurves 0.0000 /colorconversionstrategy /cmyk /dothumbnails false /embedallfonts true /embedopentype false /parseiccprofilesincomments true /embedjoboptions true /dscreportinglevel 0 /emitdscwarnings false /endpage -1 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/hrv (za stvaranje adobe pdf dokumenata najpogodnijih za visokokvalitetni ispis prije tiskanja koristite ove postavke. stvoreni pdf dokumenti mogu se otvoriti acrobat i adobe reader 5.0 i kasnijim verzijama.) /hun 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can be opened with acrobat and adobe reader 5.0 and later.) >> /namespace [ (adobe) (common) (1.0) ] /othernamespaces [ << /asreaderspreads false /cropimagestoframes true /errorcontrol /warnandcontinue /flattenerignorespreadoverrides false /includeguidesgrids false /includenonprinting false /includeslug false /namespace [ (adobe) (indesign) (4.0) ] /omitplacedbitmaps false /omitplacedeps false /omitplacedpdf false /simulateoverprint /legacy >> << /addbleedmarks false /addcolorbars false /addcropmarks false /addpageinfo false /addregmarks false /convertcolors /converttocmyk /destinationprofilename () /destinationprofileselector /documentcmyk /downsample16bitimages true /flattenerpreset << /presetselector /mediumresolution >> /formelements false /generatestructure false /includebookmarks false /includehyperlinks false /includeinteractive false /includelayers false /includeprofiles false /multimediahandling /useobjectsettings /namespace [ (adobe) (creativesuite) (2.0) ] /pdfxoutputintentprofileselector /documentcmyk /preserveediting true /untaggedcmykhandling /leaveuntagged /untaggedrgbhandling /usedocumentprofile /usedocumentbleed false >> ] >> setdistillerparams << /hwresolution [2400 2400] /pagesize [612.000 792.000] >> setpagedevice microsoft word numero_31_art_9 e.m. nurullaev et alii, frattura ed integrità strutturale, 31 (2015) 120-126; doi: 10.3221/igf-esis.31.09 120 dependence of the mechanical fracture energy of the polymeric composite material from the mixture of filler fractions e. m. nurullaev, a. s. ermilov perm national research polytechnic university, perm, russia. 614990 perm, komsomol prospect, 29 ergnur@mail.ru abstract. this paper for the first time presents an equation for calculating the mechanical fracture energy of the polymeric composite material (pcm) with regard to the basic formulation parameters. by means of the developed computer program the authors calculated the mechanical fracture energy of the polymer binder of the 3d cross-linked plasticized elastomer filled with multifractional silica. the solution of the integral equation was implemented using the corresponding dependence of stress on relative elongation at uniaxial tension. engineering application of the theory was considered with respect to asphalt road covering. the authors proposed a generalized dependence of ruptural deformation of the polymer binder from the effective concentration of chemical and physical (intermolecular) bonds for calculating the mechanical fracture energy of available and advanced pcms as filled elastomers. keywords. energy failure; elastomeric; particulate filler; binder; polymer composite material. introduction owadays, the current issue of technical chemistry is to ensure the required deformation and strength characteristics of advanced polymeric composite materials, in particular, 3d cross-linked filled plasticized elastomers. so far, to estimate the effect of the basic formulation parameters on the mechanical properties of such materials at uniaxial tension, smith failure envelopes have been widely used [1-4]. however, this approach does not fully reflect the physical nature of the failure (or fracture) process. therefore, it is interesting to derive an equation for calculating the mechanical fracture energy as a composite performance indicator of 3d cross-linked polymeric composite materials. the objective of this paper is a mathematical derivation of the equation for calculating the mechanical fracture energy of polymeric composite materials with regard to the basic formulation parameters by integrating the equation that describes the curve of uniaxial tension. in addition, by means of the computer program the authors calculated the mechanical fracture energy of a 3d crosslinked plasticized elastomer filled with multifractional silica. it is of practical interest for asphalt road covering as it greatly increases the service life of road pavements. n e.m. nurullaev et alii, frattura ed integrità strutturale, 31 (2015) 120-126; doi: 10.3221/igf-esis.31.09 121 the theory of calculating the mechanical fracture energy echanical characteristics of polymeric composite materials (pcms) based on the 3d cross-linked plasticized elastomeric matrix filled with solid silica particles significantly affect the service life of these materials. in this regard, the most important formulation (structural) parameters are the molecular structure of the polymeric matrix of the binder, its type and degree of plasticization, maximum volume filling, depending on the shape and fractional composition of dispersed filler particles, as well as the physical and chemical interaction at the binder-filler interface [5]. direct and indirect optimization problems of developing new types of similar pcms with the desired combination of stress-strain properties can be solved by means of a structural-mechanical dependence which was obtained earlier [6, 7]. let us explore a variant of maintaining the integrity of рсм until the sample breaks (poisson's ratio → 0.5), which is of the most practical interest for increasing its service life, including working conditions of the rocket engine charge under domestic pressure. earlier, in connection with pcms, we presented a physical and mathematical description of the dependence of relative (related to the initial cross-section) stress (σ (mpa)) from stretch at break (αb(mm)) of the filled elastomer with account for its basic structural parameters [7]:      2 1 23 1 1 23   1 29 0.225 10 1 1.25 1 m ch r g m rt exp t t a                                   (1) where 3(  /  )ch c mol cm m   is the concentration of transverse chemical bonds in the polymer binder matrix; ρ (g/cm3) – density of the polymer binder;  cm – average internodal molecular weight of the 3d cross-linked polymer; φr (vol. fraction) = (1 – φsw) – polymer volume fraction in the binder; φsw (vol. fraction) – plasticizer volume fraction in the binder; r (j/k·mol) – universal gas constant; t∞ (к) – equilibrium temperature, at which intermolecular interaction (the concentration of transverse physical bonds – νph(mol/cm 3)) in the binder is negligible (νph (mol/cm3)→0); t (к)– sample test temperature; tg (к)– structural glass-transition temperature of the polymer binder; a (с-1) – velocity shift ratio; φ (vol. fraction) – volume fraction of the dispersed filler; φm (vol. fraction) – maximum permissible volume filler fraction depending on the shape and fractional composition of the filler particles. in practice, we can estimate the structural parameter value cm by means of a molecular graph [7]:      32 3 32 2 21 1 12 2 23 3 322 2c nm f r f r f r f r f r f                    where r1 and r2 are molecular chains of two rubber substances with two kinds of reactive end groups f1 and f2; r3 – a molecule of the cross-linking agent with three antipodal reactive groups – f3; combinations of subscripts at f denote the chemical reaction products of i-th and j-th antipodal reactive end groups of r1-type and r2-type bifunctional polymers, as well as r3-type cross-linking trifunctional agent. taking into account that usually r3<< r1 and r2, we can assume that cm is proportional to increment addition of the molar fraction of linear polymerization  1 12 2 nr f r   according to the molecular graph. the value of φm (vol. fraction) can be calculated [8] or determined by a viscosimetric method [9]. relative elongation (α (mm)) is connected with deformation (ε (%)) by a well-known ratio rating: α = 1 + ε / 100. on conditions that the integrity of the material is maintained, true stress (σver (mpa)) is equal to the product of σ·α, but in practice it is more convenient to use conventional stress for comparison with research results of pcms that do not remain integral until the sample breaks [7]. on the basis of the eq. (1) we can write the following relation:        2 1 23 1 1 23   1 1 1 29 0.225 10      1 1.25 1 b b m ch r g m w d rt exp t t a                                           (2) where w (j),is energy (work) of mechanical fracture at uniaxial tension with dimensions: mpа  elongation (mm) = 1·103 j. the latter are the equivalent of the time during which the polymeric composite material resists increasing tensile stress. m e.m. nurullaev et alii, frattura ed integrità strutturale, 31 (2015) 120-126; doi: 10.3221/igf-esis.31.09 122 сonsidering w (j,) and α (mm) to be variable and denoting the combination of the rest alphabetic and digital characters as constants c1 and c2 from the expression (2) we get the following: 2 1 3 1   1 1.25 1 m ch r m c rt                   23 1 2  29 0.225 10 gc exp t t a           which allows us to write the dependence (2) in compact form:   1 21 2 1 1 b w c c d         (3) the eq. (3) can be solved by means of table of standard integrals [10]: 2 3 1 1 2 1 1 2 1 1 1 1 b b b b w c d c c d c d c c d                   further, as a result of integration and algebraic transformations, we obtain the equation: 3 3 2 1 1 2 2 3 2 2 3 1 2 2 b b b b b b w c c c                       (4) which leads, using the notations in (2), to the required dependence of the mechanical fracture energy of pcm on its basic formulation parameters:   2 3 3 2 1 23 1 3   3 2 2 3 1 1 1.25 29 exp  0.225 10   2 21 m b b b b ch r g b m w rt t t a                                                    (5) let us note that the mechanical fracture energy (w (j)), is equal to zero when αb=1, indicating at its required normability. ultimate elongation and energy to break ltimate values of relative elongation (αb(mm)), as well as strain (εb(%)), can be estimated by considering the velocity and degree of strain of an average polymeric binder layer between the solid particles of the filler [7]: 3 3 0 0 3 3 0 3 1 1 1 f m m f b b m m f b b m a a                                     (6) where the indices «f» and "0" refer to the filled and free states of the 3d cross-linked plasticized polymer binder of pcm. for engineering use of the eq. (5) when developing new pcms based on 3d cross-linked plasticized elastomers it is necessary to know the value of the maximum relative elongation or ruptural deformation of the polymeric binder. as follows from the relation (1), the values of 0b (mm) or 0 b (%) are determined by the polymer volume fraction in the plasticized binder (φr (vol. fraction)), effective concentration of transverse bonds (νeff (mol/cm 3)), comprising permanent u e.m. nurullaev et alii, frattura ed integrità strutturale, 31 (2015) 120-126; doi: 10.3221/igf-esis.31.09 123 transverse chemical bonds (νch (mol/cm3)) and variable physical (intermolecular) bonds (νph (mol/cm3)), and the latter determine the temperature-velocity dependence of the mechanical characteristics:     1 1 233 3   1 1 29 0.225 10eff ch r ph g ch r gt t exp t t                    (7) the molecular structure parameter (the statistically average internodal molecular weight ( cm ) of 3d cross-linked systems based on low-molecular-weight polymers with terminal functional groups) was theoretically evaluated in the following paper [11]. however, the authors did not consider the molecular interaction, which as well as the mechanical properties depend, as was noted above, on a variety of factors [12-14]. therefore, for use in engineering practice of determining the ruptural deformation of the free polymeric binder depending on the amount of νeff we have summarized the experimental data obtained earlier [7]. it turned out that the nonlinear experimental dependence    0 %b efff  for various polymeric binders, built on a logarithmic scale [7], is linearized in the coordinates: 0 0log log | cb b effm c      (8) where 0log | 3.1 cb m    corresponds to 0 | 1250% cb m    ; coefficient c = 40; 1  eff c d m   is in accordance with the formula (7). after algebraic transformations we obtain an empirical dependence: 3.1 400 10 effb     (9) material and methods reaking strain was measured on a tensile testing machine brand "instron," at a rate of expansion "."the materials used in the study cross-linked elastomers based on viscous-flow low-molecular rubbers with terminal functional groups – poly(butyl formal sulfide), poly(ester urethane)hydroxide, polydiene epoxy urethane, poly(isoprene– butyl), carboxyl-terminated polybutadiene – cured by three functional agents with antipodal functional groups. low-molecular rubbers (pdi-3b grade polydiene epoxy urethane with epoxy end groups and skd-ktr grade carboxylterminated polybutadiene) were used as the polymer matrix. 3d cross-linking was performed using eet-1 grade epoxy resin. mixtures of silica fractions with an average particle size (600 µm, 15 µm, and 1 µm) were used as the filler. the polymeric binder contained dibutyl phthalate as a plasticizer  [ 1 0.3]sw r    . optimum values of the fraction parameters are listed in tab. 1, 2 and 3. the selected standard relative strain rate is 1.4·10-3 c-1. fig. 1 presents a generalized dependence of ruptural deformation of different polymer binders (on a logarithmic scale) on the square root of the effective concentration of transverse bonds (on a linear scale). taking into account the relations (6), by means of the generalized dependence (9) we can determine elongation at break (  0 b mm ) of the polymeric binder in the free state and hence the ultimate elongation of the three-dimensionally crosslinked filled elastomer (  fb mm ), which allows us to calculate the energy of its mechanical fracture at uniaxial tension. the eq. (5), showing the dependence of fracture energy on the parameter / m  , was applied for a pcm based on a lowmolecular rubber. fraction number particle diameter, µm pore volume ratio optimum values of fraction volume ratio maximum volume filling 1 15 0.386 0.2 0.84 2 600 0.244 0.8 тable 1: parameter values of mixtures of two silica fractions b e.m. nurullaev et alii, frattura ed integrità strutturale, 31 (2015) 120-126; doi: 10.3221/igf-esis.31.09 124 fraction number particle diameter, µm pore volume ratio optimum fraction volume ratio maximum volume filling 1 1 0.465 0.05 0.94 2 15 0.386 0.149 3 600 0.244 0.801 тable 2: parameter values of mixtures of three silica fractions. fraction number particle diameter, µm pore volume ratio optimum fraction volume ratio maximum volume filling 1 1 0.465 0.028 0.96 2 15 0.386 0.082 3 240 0.367 0.226 4 600 0.244 0.664 table 3: parameter values of mixtures of four silica fractions. fraction quantity, piece 2, 3, 4 experiment temperatures, к 223, 273, 323 polymer glass transition temperature, к 175 plasticizer glass transition temperature, к 185 polymer volume-expansion coefficient 5·10-4 plasticizer volume-expansion coefficient 7·10-4 volume fraction of the polymer in the binder 0.25 glass transition temperature of the composite elasomer, к 177 filler volume ratio in mixed solid rocket propellants 0.75 chemical bond concentration in the binder, mol/сm3 1·10-5 maximum filler volume ratio 0.84; 0.94; 0.96 тable 4: initial data for calculating the mechanical fracture energy. for comparison, we considered composite materials based on polymeric binders with mixtures of two, three and four (fig. 2) silica fractions. it is seen that, contrary to smith failure envelopes [1-4] and [17], the mechanical fracture energy reflects the mechanical resistance of pcm as a filled elastomer more fully in the physical sense, which is important when estimating its operational suitability in particular materials. the dependencies in fig. 2 allow to evaluate the influence of the quantity of fractions taken in the optimal ratio, on the amount of ruptural deformation (the value of the mechanical fracture energy being practically constant). for example, at the temperature of 223 k b (%) changes from 0 to 16% (2-fractional silica), from 0 to 25% (3-fractional silica), from 0 to 35% (4-fractional silica), which, respectively, leads to a double increase of b . a similar phenomenon is observed at temperatures of 273 k and 323 k. the latter circumstance is very favorable for the use of pcm as frost and waterproof asphalt coating of automobile roads. it is important to add that the increase of ruptural deformation of pcm as 3d cross-linked filled plasticized elastomer in accordance with the eq. (1) is contributed by the decrease in the values of other structural parameters –  ,  ,  /ch r m    , – e.m. nurullaev et alii, frattura ed integrità strutturale, 31 (2015) 120-126; doi: 10.3221/igf-esis.31.09 125 as well as the structural glass-transition temperature of the polymer binder. in this case, the decrease in ultimate tensile stress (σb (mpa)), related to (αb (mm)) by the formula:   1 21 21b b b bc c       with previously adopted notations applied to the eq. (1), occurs to a lesser degree. this can probably explain the corresponding increase in the values of w (j), at increasing εb(%). the theoretically derived dependence (5) of the mechanical fracture energy of a 3d cross-linked filled elastomer from the basic structural parameters of the composite can be recommended for solving direct and indirect problems when developing new pcms as polymer composites for various purposes with the desired combination of performance characteristics [7]. in doing so, it is expedient to use computer programs, including mathematical optimization techniques [15, 16], which will help to reduce the development time and cost of raw materials, for example, when developing advanced pcms. figure 1: experimental dependence    0 3% [ / ]b efff mol cm  for various polymeric binders based on: : poly(butyl formal sulfide), : poly(ester urethane) hydroxide, : polydiene epoxy urethane, : carboxyl-terminated polybutadiene, : polyisoprene butyl; the data are given for standard conditions: т=293 к and  =1.4·10-3 c-1. figure 2: dependence of the mechanical fracture energy on ruptural deformation of a pcm at temperatures: 1 – 223 k; 2 – 273 k; 3 – 323 k. : two-fraction composition; : three-fraction composition; : four-fraction composition; e.m. nurullaev et alii, frattura ed integrità strutturale, 31 (2015) 120-126; doi: 10.3221/igf-esis.31.09 126 conclusion he article presented the equation linking the mechanical fracture energy of the 3d cross-linked polymer binder filled with multifractional silica and its basic formulation parameters. the authors proposed a generalized dependence of ruptural deformation of the polymer binder from the effective concentration of chemical and physical (intermolecular) bonds for calculating the mechanical fracture energy of new pcms. it has been shown that the increase in the quantity of fractions of solid components taken in the optimum ratio leads to a double increase of ruptural deformation at constant mechanical fracture energy. references [1] smith, t. l., symposium on stress-strain-time-temperature relationships in materials, amer. soc. test. mat. spec. publ., 325 (1962) 60-89. [2] smith, t. l., limited characteristics of cross-linked polymers, j. appl. phys., 35 ( 1964) 27-32. [3] smith, t. l., relationship between the structure and tensile strength of elastomers, the mechanical properties of new materials (translated from english by g.i. barenblatta), мir, (1966) 174-190. [4] smith, t. l., chy, w. h., ultimate tensile properties of elastomers, j. polymer sce., 10(1) (1972) 133-150. [5] ermilov, a. s., nurullaev, e. m., mechanical properties of elastomers filled with solid particles, mechanics of composite materials, 48 (3)(2012) 243-252. [6] ermilov, a. s., nurullaev, e. m., optimization of fractional composition of the filler of elastomer composites, mechanics of composite materials, 49 (3) (2013) 455-464. [7] ermilov, a. s., nurullaev, e. m., mechanical properties of elastomers filled with solid particles, mechanics of composite materials, 48 (3) (2012) 1-14. [8] ermilov, a. s., fedoseev, a. m., combinatorial-multiplicative method of calculating the limiting filling of composites with solid dispersed components, russian journal of applied chemistry, 77(7) (2004) 1203-1205. [9] ermilov, a. s., nurullaev, e. m., concentration dependence of reinforcing rubbers with dispersed fillers, journal of applied chemistry, 85(8) (2012) 1371-1374. [10] bronstein, i.n., semendyaev, k.a., a guide to mathematics for engineers and students of engineering, science, 544 (1986) [11] zabrodin, v. b., zykov, v. i., chui, g. n., molecular structure of cross-linked polymers, high-molecular compounds, xvii(1) (1975) 163-169. [12] van krevelen, d.w., properties and the chemical structure of polymers, (translated from english by a. y. malkina), chemistry, (1976) 415. [13] nielsen, l.e., mechanical properties of polymers and composites, (translated from english by p.g. babaevskyi), chemistry, (1978) 311. [14] manson, j.a., sperling, l.h., polymer blends and composites, (translated from english by y.k. godovskyi), chemistry, (1979) 440. [15] certificate № 2012613349 rf, software of identification and optimization of the packing density of solid dispersed fillers of polymer composite materials (rheology), ermilov a. s., nurullaev e. m., duregin к. а. – priority of 09.04.2012. [16] certificate № 2011615640 rf, mathematical software of predicting physical and mechanical characteristics of filled elastomers. (elastomer) / ermilov a. s., nurullaev e. m., subbotina t.e., duregin к. а. – priority of 18.07.2011. [17] ermilov, a. s., nurullaev, e. m., influence of formulation parameters on the mechanical failure energy of filled elastomers, russian journal of applied chemistry, 85(7) (2012) 1125 – 1127. t microsoft word numero_30_art_64 w. tao et alii, frattura ed integrità strutturale, 30 (2014) 537-544; doi: 10.3221/igf-esis.30.64 537 a research on detecting and recognizing bridge cracks in complex underwater conditions wang tao, du tao, zou xiaohong, sun yiming institute of highway, chang’an university, xi'an, 710064, china 48045664@qq.com abstract. the method aims to recognize and extract the characteristic parameters of bridge cracks based on images of the cracks obtained through the application of preprocessing technologies, such as graying, graphical enhancements, spatial filtering, gray-level threshold segmentation, etc.. the approach has been tested for accuracy to avoid the incorrect identification of chaff as a method error. the proposed method has proved to be rather accurate and effective in extracting information on cracks from the bridge image tests. keywords. crack detection; digital processing; image analysis; fracture fragments; electronic information. introduction he first cracks start appearing at the bottom of the bridge structure. if detected in time, engineers can then follow the development of the cracks. meanwhile, it should the bridge should be maintained and repaired without delay. detecting and recognizing cracks in time can reduce maintenance costs greatly and effectively guarantee the security of public transportation [1]. the difficulties in detecting cracks at the bottom of bridges are as follows [2]: the underwater pressure is immense and the light is dim. furthermore, conditions in the underwater environment can be very bad. the peculiarity of the underwater environment and the characteristics of the water can impede and obstruct communications. these difficulties combined lead to typical problems in underwater viewing. the complex imaging environment makes underwater images more sensitive to noise and interference. that inevitably leads to the generally bad quality and information redundancy of underwater images. digital image processing technology has been widely used in the detection of underwater bridge cracks in complicated conditions. this primarily includes the preprocessing and partition of images, the extraction of of the image features, image classification and other links [3]. in china, bo shaobo [4] has proposed that the morphological corrosion operator should refine the crack to obtain a single-pixel width skeleton image. meanwhile, the length and width of the cracks may be measured by applying the statistical pixel method in dealing with rule cracks in images. the encroachment method should be used to measure the area of the crack when dealing with irregular cracks. liu xiaorui [5] has presented a fusion method combined with several processing tectonic treatment methods-sfc. fu jun [6] has applied a new method of image segmentation based on a neural network. abroad, iota et al [7] have applied image binarization, wavelet transform, gray correction and other image processing methods to analyze the crack images and extract information. kawamurak et al. [8] have found that the parameter genetic algorithm of image processing can be semi-automatically optimized for the effective accurate detection of cracks. abdel-qader [10] etc. also assessed surface crack detection efficiency at the same time. they compared the results of the fourier transformation, sobel filtering, canny filtering and wavelet transform method, finding that the wavelet transform was more reliable. however, the research on underwater bridge crack image segmentation algorithms still failed to meet the development needs of bridge image detection technology. and image t w. tao et alii, frattura ed integrità strutturale, 30 (2014) 537-544; doi: 10.3221/igf-esis.30.64 538 segmentation plays a key role in the process and, to some extent, in the analysis of the images. the quality of the segmentation can directly affect the further understanding of the image. thus, we need to perform an in depth research into the image processing technology of underwater bridge cracks. extracting information on underwater bridge cracks histogram image enhancement mage enhancement is needed after collecting and graying the crack image. histograms are statistical tables about the gray levels of image distribution. gray histogram images indicate that the relative frequency is about various gray levels of pixels. generally, the grayscale is the abscissa of the histogram. the ordinate is the occurrence number of the grayscale probability [11]. in the crack images, cracks are the darker areas, while the background is relatively light in the process of gathering images. but the whole image is too dark due to lack of exposure. the area mixes with the background and is hard to distinguish, as shown in fig. 1 (a). in fig. 2 (a) we can see the original image’s grayscale values are concentrated on the gray area between 0-100. we have to extend the image grayscale values to distinguish the crack from the background. the low gray with high grayscale has created significant differences in the grayscale. meanwhile, it would increase the contrast ratio of the image. as shown in fig. 2 (b), the gray scope of the image has extended to the entire gray level (0-255). we can obtain crack images with a high contrast after performing equalization processing on the original image, as shown in fig. 1 (b). (a) (b) figure 1: (a) original image; (b) after enhancement. (a) (b) figure 2: (a) original image’s gray histogram; (b) gray histogram after enhancement. spatial filtering the common method of spatial filtering adopts the neighborhood average and median filtering law. this paper applies the neighborhood average method to an ideal situation. in the ideal situation, many gray and constant small patches constitute i w. tao et alii, frattura ed integrità strutturale, 30 (2014) 537-544; doi: 10.3221/igf-esis.30.64 539 an image. the spatial correlation between the neighbor pixels of the image is high. but the noise is relatively independent. non-weighted average is the simplest and most commonly applied neighborhood average method. (1) set one image  ,f x y . then express the gray value of a pixel in the image as  ,g x y , which is the square windows of field s n n  . the total number of points is set to be m . thus the gray value of this point after smoothness is: , 1 ( , ) ( , ) i j s g x y f i j m    we can use formation templates to describe the non-weighted average neighborhood law. that is, we need to move the filtering template point-by-point and get the sum of products. when applying neighbor pixels defined in the image template on template operation, the coefficient  0, 0 of template corresponds with the  ,x y in the image. set the template size to be 33 . the application of this template can produce a result as follows: 1 1 1 1 ( , ) ( , ) m n r m n f x m y n       (2) set the gray value of point  ,x y in the neighborhood of n n . the gradient inverse  ,w i j is defined as:       1 , 1, 1 , w i j f x y f x y     gray-level threshold segmentation the threshold segmentation produces a binary image. the position of the pixels is represented in the image through a grayscale image  ,f x y and the coordinates  yx, . t is the threshold and the binary images are represented through using  ,b x y after the threshold. the expression is as follows:       1, , , 0, , f x y t b x y f x y t      (3) we can know from the above that the appropriate threshold is concerned with gray closed segmentation. this article uses the iterative method to auto-select thresholds according to the following steps: 1) calculate the maximum maxt and minimum mint gray value of the entire image. both average values are just about the initial threshold 0t .   2minmax0 ttt  ; 2) segment the image based on ht and respectively solve the average gray level of foreground 1g and background 2g ; 3) solve the new threshold value  1 1 2 2ht g g   ; 4) take a new threshold. repeat steps 2 to 4 until 1h ht t  in subsequent iterations remains basically unchanged. an iterative method is used to make the grayscale threshold segmentation up to a gray level image, as shown in fig. 3. (a) (b) figure 3: (a) grayscale image; (b) image after iterative segmentation. w. tao et alii, frattura ed integrità strutturale, 30 (2014) 537-544; doi: 10.3221/igf-esis.30.64 540 measuring the parameters of underwater bridge cracks n dealing with the image, the target description is mainly boundaries and regions. the object boundary is generally represented by a chain code. the target area usually has 2 representations method of 4-neighborhood and 8neighborhood. but this article will not expand on this in detail. feature extraction common regional features include size, external ellipse, external rectangles, gravity center, circularity, perimeter, etc.. grayscale features have a highest gray value, a minimum gray value and an average gray value, etc.. contour features include contour length. the basic steps of the feature extraction process are shown in the following picture. in order to detect the cracks it is necessary to find the cracks in the image, confirm the crack area and obtain the crack region area, length, width, perimeter and other parameters. 1) measurement of proportion in regular binary image processing, the calculation of proportion, in fact, is about the geometry characteristics quantity for measurement of the size of connected area after binaryzation. the specific definition is the total amount of pixel in connected area. we speculate that the pixel value of cracks in binary image is 1. therefore, the calculation of the proportion can be simply expressed as:    , , x y s a g x y    s is expressed as the connected domain that needs to be measured;  ,g x y is the pixel value of point  ,x y . although the overall proportion measurement of the target is very accurate, the proportion refers to the total proportion of all targets in the image. it may involve the fracture section, various complex cracks or some small cracks that have interference (eg. the unfiltered random noise). above all, the complex cracks such as massive cracks or crocodile cracks cannot be clearly distinguished into single cracks. thus, the big error exists. therefore, we propose a new means to solve the problem. we use the template and target to conduct bitwise and, in fact, logic and operation on binary image to calculate the area of cracks. we select curve  ,f x y and use binary logic operation to obtain more accurate value. binary logic and operation meet the following formula: 0 & 0 0 ; 0 & 1 0 ; 1 & 0 0 ; 1 & 1 1 (in binary image, the pixel value of points in the image only have two kinds of values; in the specific calculation process, we adopt bitwise and operation on the binary image array.) by doing this, the false data that may be contained around crack and in crack can be removed. that can make the image area calculation become more accurate. in addition, bit manipulation, the most basic operation in the computer, occupied the absolute advantage in calculation speed because the hardware of the computer only identifies 0 and 1. 2) measurement of length and width in practical crack image, absolute across and down do not exist. generally, the cracks have radian and even burr. the middle part may also break. therefore, we adopt the following assumption for the easy disposal of computer. 1) in the segmented sub-block, axis of cracks in the target area is expressed as curve  ,f x y . it is a connected fracture section with unit pixel width; 2) cracks in the target area is the point with the minimum gray level in the non-growth direction area of that point; 3) curve  ,f x y can fit a straight line in subsection. read image binaryzation noise  removal mark area calculate  feature  quantities i w. tao et alii, frattura ed integrità strutturale, 30 (2014) 537-544; doi: 10.3221/igf-esis.30.64 541 according to the known area, the computer can calculate the pixel point, and thus obtain the value of the length and width. 4) perimeter p the contour perimeter level reflects the overall extension of the crack. the number of pixels on the border is calculated after acquiring the boundary contour of the cracks. then we can obtain the contour perimeter. 5) circle c circularity reflects the complexity of the target boundary. the computational formula is as follows. the probability of appearance of the gray value 24c a p a: when the pixel value of the crack target in a previously assumed binary image is 1 , the area of the connected domain will be p . 6) external ellipse the external oval reflects the position and range of the area. the center coordinates  ,x y in the ellipse can be represented by the first moment:    , , 1 1 , x y r x y r x x y y a a     where a: the area of the range; r: the connected domain needs measuring. example verification this paper chooses 10 underwater bridge crack pictures the size is 640 480 according to the description and analysis of the crack target features. a statistical analysis is performed for a number of typical characteristic quantities of the crack features and the crack area. a gray feature of its external rectangle is performed. the characteristic quantities are shown in tab. 1. order number area perimeter external rectangle width external rectangle height aspect ratio circularity 1 6301 1829.36 639 86 7.43 0.0232 2 2098 1170.11 420 54 7.78 0.0198 3 3591 1640.05 621 59 10.53 0.0174 4 2180 1299.99 395 71 5.56 0.0161 5 2503 1102.27 53 309 5.83 0.0312 6 8053 1750.75 639 40 15.98 0.0322 7 5496 1598.88 419 130 3.22 0.0269 8 6208 2601.47 640 115 5.57 0.0115 9 6697 2259.63 640 113 5.66 0.0159 10 3559 2034.64 640 72 8.89 0.0110 table 1: result of the crack image’s characteristic quantities (unit: pixel). w. tao et alii, frattura ed integrità strutturale, 30 (2014) 537-544; doi: 10.3221/igf-esis.30.64 542 it emerges from the calculation results that target cracks’ circularity is very small, with 90% being below 0.01. this indicates that the boundary shape of the crack range is relatively complex and irregular. the axial ratio of the external ellipse is large. the rate above 7 percent is more than 80%. and it is in accordance with the features in the real cracks observed. the present linear features a slender line while the width-height ratio 80% of the external rectangle is over 2.5. and the reflection of the characteristics of the crack shape is not obvious. in the grayscale image, the gray value of the crack area is smaller, while the gray value of the external rectangle becomes bigger. the differences between them are obvious. and the difference rate above 30 accounts for 85% of the total. in accordance with the situation that some real cracks observed are darker and the background color is lighter. but there are some exceptions because of the gray value of the closed segmentation. some backgrounds were closed to the gray level of the cracks. the crack has connected into an area and expanded the crack area, including a small amount of non-crack pixels. the average gray of the expanded region is higher than the original average gray of the crack area. this leads to the decline of the grayscale difference. there is a 0 value generated into the calculation results about the image’s feature quantity. this is because several complex image processing results are not satisfactory and the cracks’ target cannot be extracted from the image. the above statistical analysis results show that by selecting several characteristic quantities we can represent the shape and gray feature of the crack area. the difference of the external ellipse is the axis ratio and the range’s gray average value. the gist is that information on the cracks can be extracted from the image tested for these two characteristic quantities. underwater bridge crack clip connection fter extracting the target, we found the target was divided into various discontinuous fragments. this is in conformity with reality. if the connection is not to be restored, it will affect the awareness and application of the target’s nature. therefore, connecting the fragments is needed. establishment model n-th  2n  fracture fragment is assumed to be existed after extracting crack target. the fragments belonging to different parts of the same crack are on the overall trend line. they are ordered from left to right, top to bottom after marking the individual segment. the leftmost, upwards of the left endpoint area, are defined as the 1-th section fragments. the rightmost, downwards, are defined as the n-th section fragments. set a simple model shown as fig. 5 (a). (a) (b) figure 5: (a) location model; (b) connecting model of the crack fragment’s endpoint a w. tao et alii, frattura ed integrità strutturale, 30 (2014) 537-544; doi: 10.3221/igf-esis.30.64 543 the regions a, b, c, d, e, f, g, h, i represent the fracture fragments after extraction. their positional relationship between endpoints corresponds to 0, 1, 2, 3, 4, 5, 6, 7, 8 in fig. 5 (b). set a  ,xa ya as the right end point coordinates. the coordinates closed to the left end point b, c, d, e, f, g, h, i is,  ,xb yb ,  ,xc yc ,  ,xd yd ,  ,xe ye ,  ,xf yf ,  ,xg yg ,  ,xh yh ,  ,xi yi , respectively. set a to represent i -th fragment, i, b, c, d, e, f, g, h, i. this means that the  1i  -th has 8 representative kinds of fragment with a certain position of a respectively. the connection procedure of the fragments a and b is described as below. the connection process of a, c, d, e, f, g, h, i is similar. b is located right of a. a and b match so that: ,xb xa yb ya  1) the right endpoint of segment a (the rightmost column a, from the top down, the first non-zero pixel) is obtained by coordinates  ,xa ya . and the left endpoint of b (the leftmost column b, from the top down, the first non-zero pixel) is obtained through coordinates  ,xb yb . the following method of defining the left and right endpoints of each fragment is similar to that for defining the left and right endpoints of each fragment. 2) the coordinate difference is calculated: d yb ya  ; e xa xb  and 0d  , 0e  , so d e . 3) it proceeds along a route from  ,xa ya . and 1 is close to  ,xb yb . the pixel value of the blank during the route is set as 1. route 1:  , 1xa ya  ▁ , 2xa ya  ▁ , 3xa ya  ▁ , 4xa ya   , 1 1xa ya   ;  , 2 1xa ya   ;  , 3 1xa ya   ;  , 4 1xa ya   likewise, it is the same to  ,xb yb . 4) reach example verification the cracks have been divided into several segments for verifying the fracture fragment through the connecting algorithm, as shown in fig. 6 (a). the fracture fragments algorithm is connected with the neighboring fragments. the connection results are shown in fig. 6 (b). (a) (b) figure 6: (a) crack fragment image; (b) crack fragment after connection we can see that it is correct and effective to apply the algorithm in connecting the fracture fragments. the connection of various pieces of fragments in the image forms a connected area. this paper contributes to testing the crack developments and simplifying calculation for the characteristic quantities of crack targets. w. tao et alii, frattura ed integrità strutturale, 30 (2014) 537-544; doi: 10.3221/igf-esis.30.64 544 conclusions irstly, this paper collects crack images to conduct spatial filtering after graying and enhancing the images with the neighborhood average method. then it performs gray-level threshold segmentation combined with the iterative method. finally, information on the cracks is extracted based on the underwater images of the bridge. our aim is to identify the areas of cracks in the image and obtain the parameters of the cracking region, such as area, length, width and perimeter. this paper, therefore, extracts and inspects the crack parameters as follows. the circularity of the crack target is small; the major-minor axis ratio of the external ellipse is large. the crack area’s grayscale average is smaller in the grayscale images, while the external rectangle’s grayscale average is larger. 0 value is generated in the calculation results of the characteristic quantities. the target was divided into discontinuous fragment regions after extracting the target value. we need to connect the fragment area establishing models and instance validation. finally we will find that it is correct and valid to connect the fracture fragments by applying this algorithm. application of the median filtering method to enhance denoising can have better denoising effect. and it could smooth the image after enhancing denoising and reduce the data volume of the monitoring stream with compressed synthesis. the neighborhood average method is a common technology for image denoising. its advantage is rapid processing speed and wide range of application. but this algorithm also has a significant shortcoming, namely, that the image will become vague when reducing the noise at the same time, especially in the image's edges and details. it is therefore necessary to make some improvements to the simple neighborhood average method. another key solution is keeping the image’s edges and details as much as possible to a minimum when performing image denoising. references [1] juwu, x., the research of application and measurement the bridge cracks based on digital image processing, southwest petroleum university, 5 (2011). [2] wei, z., the research of underwater image segmentation and recognition technology based on particle swarm, harbin engineering university, 9 (2008). [3] hanxing, q., the research of pavement crack detection and recognition based image segmentation. chongqing jiao tong university, 03 (2012). [4] shaobo, b., maode, y., liang jun, h., yuyao, h., research on measuring algorithm of asphalt pavement crack based on image processing, computer measurement and control, 15(10) (2007) 1305-1307. [5] xiaorui, l., xiongyao, x., the research of rapid detection of tunnel surface cracks based on image processing, chinese journal of underground space and engineering, 2 (02) (2009) 1624-1628. [6] jun, f., weiliang, j., feng, k., yunhua, c., detection of shallow cracks in the wall with digital image processing, civil architecture and environmental engineering, 31 (06) (2009)137-141. [7] lto, a., aoki, y., hashimoto, s., accurate extraction and measurement of fine cracks from concrete block surface image, iecon02, 3 (2002) 2202-2207. [8] kawamura, k., miyamoto, a., nakamura, h., sato, r., proposal of a crack pattern extraction method from digital images using an interactive genetic algorithm, proceedings-japan society of civil engineers, (2003) 115-132. [9] abdel, q., abudam, o., kelly, m. e., 2003. analysis of edge detention techniques for creak identification in bridges, journal of computing in civil engineering, 17(3) (2003) 255-263. [10] guoqi, z., the research of concrete bridge underside crack detection method based on image processing, beijing jiao tong university, 06 (2010). [11] galvez, j. c., cervenka, j., cendon, d. a., saouma, v., a discrete crack approach to normal/shear cracking of concrete, cement and concrete research, 32(10) (2002) 1567-1585. [12] xiaorui, l., xiongyao, x., rapid crack inspection of tunnel surface based on image processing, chinese journal of underground space and engineering, 5(02) (2009) 1624-1628. [13] xiaomao, r., a technology of screen translation, computer and digital engineering, 2(22) (1994) 44-45. [14] ciyin, y., lianqing, h., contrast enhancement of medical image based on since grey level transformation, optical technique, 5 (28) (2002) 407-408. [15] xu, b., a study on the bridge diseases inspection and the cracks measurement based on the imagery processing technology, chang'an university, (2009). f microsoft word numero_53_art_05_2707 k. sadek et alii, frattura ed integrità strutturale, 53 (2020) 51-65; doi: 10.3221/igf-esis.53.05 51 effect of corrosion on the quality of repair of the aluminum alloy a5083 h11 by bonded composites kaddour sadek, benaoumeur aour labab laboratory, department of mechanical engineering, national polytechnic school maurice audin, oran, 31000, algeria sadekkaddour@gmail.com, benaoumeur.aour@enp-oran.dz mohammed salah bennouna university of kasdi merbah ouargla, department of mechanical engineering, algeria bennouna_ms@yahoo.fr abderrahim talha lille mechanics unit, university of lille, (uml, ea 7512), university of lille, 59655 villeneuve d’ascq, france abderrahim.talha@yncrea.fr belabbes bachir bouiadjra, mourad fari bouanani lmpm laboratory, department of mechanical engineering, university of sidi bel abbes 22000, algeria bachirbou@yahoo.fr, bouananimorad@gmail.com abstract. in this paper, the simultaneous effect of corrosion and cracking on the performance of the bonded composite patch repair in aluminum alloy a5083 marine structure was investigated using three-dimensional finite element methods. to this end, two patches made of carbon/epoxy and boron/epoxy, bonded on corroded plates with and without crack, were tested under different applied loads. the effect of both corroded and cracked materials on the damage of the adhesive fm73 was also highlighted. the obtained results show that the corrosion has a significant effect on the quality of the repair performance. indeed, it is proved that, the rate of damage increases with the increase of the applied load and is more significant in the case of plates cracked and repaired by carbon/epoxy patch compared to that of boron/epoxy patches. keywords. corrosion; damage zone; composite patch; aluminum alloy; adhesive; crack. citation: sadek, k., aour, b., bennouna, m. s., talha, a., bachir bouiadjra, b., fari bouanani, m., effect of corrosion on the quality of repair of the aluminum alloy a5083 h11 by bonded composites, frattura ed integrità strutturale, 53 (2020) 51-65. received: 13.12.2019 accepted: 07.05.2020 published: 01.07.2020 copyright: © 2020 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. https://youtu.be/knxwijnfgli k. sadek et alii, frattura ed integrità strutturale, 53 (2020) 51-65; doi: 10.3221/igf-esis.53.05 52 introduction he 5000 family aluminum alloys, and, especially the a5083 alloys, are known for their high resistance to corrosion salinity and ideal alloy for their weldability, making their use a better choice in the marine shipbuilding industry and offshore structures [1]. the elements mg, zn or cu alloyed with aluminum consolidate and reinforce the matrix. the aluminum has an excellent strength-to-weight ratio, which makes it an ideal material when specifications require high strength and minimum weight. this alloy composition makes it enable to be used for the construction of ships and boats [2]. otherwise, the corrosion process in the marine environment is favored by the presence of a lower rte of oxygen and higher salinity, also the presence of manufacturing defect at the microscopic scale, under repeated cyclic loadings and the salinity of the water, cause the fatigue of the material which is called fatigue corrosion under stress. most of the structural fractures in service are about 90% due to this corrosion cracking phenomena. three main stages of a material failure have been observed: (i) initiation of the crack, (ii) propagation of the crack, and (iii) finally sudden rupture [3-5]. to remedy this kind of phenomenon and the crack propagation by corrosion, a new technique has been applied for several years based on a composite bonded to the damaged part. this technology has proven to be effective in aerospace and marine applications [6]. more recently, this technique of repairing cracked structures has been considered particularly effective in aeronautics and follows rigorous control procedures, the composite patch is applied in situ on the damaged part. several parameters affect the integrity of composite patch repair. among these parameters, (i) the geometric shape, the thickness, the length and the nature of the patch, (ii) the medium, (iii) the type and thickness of the adhesive, etc. [7]. in a previous work, sadek et al. [8] analyzed by finite element, the performance of repair with patch composite using different shapes in the case of marine structures.the evolution of the damaged zone under the crack effect only has been also studied [9]. however, rare are the studies on the performance of bonded composite patch repair in corroded aluminum structures [10]. in this paper, the effect of corrosion on the quality of repair of the aluminum alloy 5083 h11 by bonded composite is analyzed using a three-dimensional finite element method. a comparison between the obtained results using two types of patches has been presented and discussed. background formulation j integral he sif calculation tool is currently chosen for computing the three-dimensional virtual crack closure technique (3dvcct) of the asymptotic value [11]. the proposed irwin vcct is based on the energy balance. from this equation, stress intensity factors are given for the three fracture modes 2 i i k g e  (1) where gi is the energy release rate for mode i, ki the stress intensity factor for mode i, e the elastic modulus. the idea presented by rybicki and kanninen [12], is based on the calculation of the energy release rate, using irwin assumption that the energy released in the process of crack expansion is equal to work required to close the crack to its original state, as the crack extends by a small amount δa. irwin computed this work as:     0 . . a w u r a r dr     (2) where u is the relative displacement,  is the stress, r is the distance from the crack tip, and a is the change in virtual crack length. therefore, the energy release rate is given by:     0 0 0 1 lim lim . . 2.   a a a w g u r r a dr a a              (3) t t k. sadek et alii, frattura ed integrità strutturale, 53 (2020) 51-65; doi: 10.3221/igf-esis.53.05 53 the work w can be expressed as: 2 . 1 w f u (4) where f is the force needed to close the crack virtually, u is the crack opening displacement. eq (3) allows the calculation of the energy release rate for 2d fe models (modes i and ii). the application of the vcct in 3d fe models is commonly called the 3d vcct. the extension of the method from 2d to 3d requires replacing eq. (3) by the following expression:     0 0 1 , . , . . 2 h a g u r s r a s ds dr h a        (5) where s is the distance from the crack tip in the third direction, and h is the element size in the third direction. to apply eq. (5) to fe models comprising 8-node brick elements, the integrals in (5) are replaced with the sum as follows: 2 1 1 . 2 ki ki k g f u h a     (6) where index i controls direction, and index k controls the node b number. the shear stresses in the adhesive are given by the following relationship: 1  2 )( a a g u u e   (7) where 1 u and 2 u are displacements in layers 1 and 2 (the plate and the patch) respectively. experimental design was used for the determination of the optimum patch dimensions [13-15]. indeed, the patch dimensions process is described by a quadratic model as follows: 2 2 0 1 1 2 2 11 1 22 1 12 1 2y a a x a x a x a x a x x      (8) where y is the response of the process (i.e., the j integral at the crack front in the plate) and, ix is the normalized centered value for each factor iu : *  i ic i i i u u x u u     (9) 2 imax imin ic u u u   (10) ( ) 2 imax imin i u u u                    (11) the quadratic model of j integral is expressed as following [16]: * * * * * * * * * *2 *2 *2 0 1 2 3 12 13 11 22 3323j a a l a w a t a l w a l t a w t a l a w a t          (12) where *l is the length, *w is the width, and *t is the thickness of the patch. k. sadek et alii, frattura ed integrità strutturale, 53 (2020) 51-65; doi: 10.3221/igf-esis.53.05 54 damage zone theory the joint adhesive used in this study is made of a ductile material, that has been toughened and, which is supposed to be exposed to a yielding failure. therefore, in this case of failure study and for characterizing the damage zone, we will apply the equivalent strain of von mises criterion given by the following expression [17]:        2 2 21 2 2 3 3 11    2 1 eq p p p p p p                (13) where eq is the equivalent strain, pi are the plastic strains in the different directions and  is the poisson’s ratio. the von mises equivalent strain criterion is satisfied for the ultimate principal strain value of the material. the damage zone size at failure is determined when the ultimate strain of each failure criterion is defined. we use either the strain or the stress criterion to define the damage zone, but when the adhesive undergoes a significant nonlinearity the application of the strain criterion will be more appropriate [18]. it should be noted that there are two modes of failure associated with adhesive joints: (i) interfacial and (ii) cohesive failure. in the first mode, the failure load of the adhesive joint depends on the interfacial stress near the interfaces between the adhesive and the adherent [18]. the second mode will happen when cohesive failure occurs in the adhesive joint. since cohesive failures certainly occurred in the adhesive joint, we recommend using the adhesive failure criterion for the damage zone. the failure criterion, for isotropic materials, such as the von mises and tresca criteria, can be used to model the adhesive failures [19]. in order to define and quantify the rate of damage, the following damage zone ratio formula can be used: . i r a a d l w   (14) where rd is the damage zone ratio, ia the area over which the equivalent strain exceeds 7.87% [17], l the adhesive length and aw is the adhesive width. numerical modeling he corroded and cracked structure is shown in fig. 1. to study the effect of corrosion on the quality of repairs, two types of patches have been numerically tested. the first one is made of boron/epoxy and the second one of carbon/epoxy. both are glued on two corroded aluminum plates a5083 with and without crack. the adhesive is of type fm73 with a thickness ea=0.15 mm (longitudinal young modulus e=4.2 gpa and longitudinal poisson ratio ν=0.32). different uniform uniaxial loadings σ=220, 250, 300 and 350 mpa were applied to the structure (fig. 1). the damage ratio rd of the adhesive has been evaluated. the mechanical properties of both patches are selected according to several references [9,19,20] and are given in tab. 1. the aluminum alloy plate 5083h 11 has dimensions 254 × 254 × 5 mm3 (fig. 1) h=254 mm, w=254 mm and ep=5 mm, with a crack length a=1.5 mm. the mechanical properties of the plate are as follows: young’s modulus e=69 gpa, poisson’s ratio ν=0.35, the yield stress σy=243 mpa, the ultimate stress σu=347 mpa and the elongation ξel=21.85%. the composite patch has the following dimensions: 130×75×1.5. the plies in the patch had unidirectional lay-up where the fibers were oriented along the specimen length direction (parallel to the load direction). both patches are bonded on the damaged structure by 0.15mm thick film of adhesive epoxy. the geometric shape of the corroded area was taken in 3d randomly with a thickness of 0.5 mm. noting that, the effect of the variation in thickness of the corroded area is under an advanced investigation and will be published later. the physical interactions at aluminium/adhesive and composite/adhesive interfaces during loading are taken into account through bonded surface-to-surface contact features of abaqus. a surface-to-surface contact definition can be used as an alternative to general contact to model contact interactions between specific surfaces in a model. in this work, at the interfaces, each mesh node is common between the adjacent structures to ensure continuity of strains and stresses. noting that the adhesive is homogeneous elastic and isotropic, the deformation of the adhesive is under the effect of shearing and peeling. the boundary conditions used in this analysis are as follows: one end of the plate was fully fixed while the other end was subjected to a tensile stress in an increasing way using the option "step" general static of abaqus code [21]. a t k. sadek et alii, frattura ed integrità strutturale, 53 (2020) 51-65; doi: 10.3221/igf-esis.53.05 55 maximum increment value up to 10000 was used for the automatic increment. the minimum and maximum increment sizes are 10-5 and 1 respectively. figure 1: geometrical model. elastic properties boron/epoxy carbon/epoxy longitudinal young modulus e1 (gpa) 200 134 transversal young modulus e2 (gpa) 19.6 10.3 transversal young modulus e3 (gpa) 19.6 10.3 longitudinal poisson ratio v12 0.3 0.33 transversal poisson ratio v13 0.28 0.33 transversal poisson ratio v23 0.28 0.33 longitudinal shear modulus g12 (gpa) 7.2 5.5 transversal shear modulus g13 (gpa) 5.5 5.5 transversal shear modulus g23 (gpa) 5.5 3.2 table 1: elastic properties of both patches [9,19,20]. the finite element model (fig. 2) is composed of different substructures to model the cracked and corroded plate, the adhesive and the composite patch. the plate has four layers of elements in the direction of thickness, the adhesive has a single layer in the thickness and the patch has four layers of elements in the thickness. the commercial finite elements code abaqus was used for computations. the number of elements is 54517 with 77551 nodes. the element type used is c3d8r: an 8-node linear brick, reduced integration, hourglass control. the second generated model is a plate with corrosion and crack using three subsections models (plate-patch-adhesive). the number of elements is 92928 with 411791 nodes. the element type used is c3d20rh: a 20-node quadratic brick, hybrid, linear pressure, reduced integration. figure 2: finite element meshed parts of the studied model. k. sadek et alii, frattura ed integrità strutturale, 53 (2020) 51-65; doi: 10.3221/igf-esis.53.05 56 validation of the model o validate the numerical model developed in this work, an elastic aluminium plate with and without composite patches under uniform uniaxial load with a centre crack was analysed. in order to make a comparison, the same dimensions and material properties as those used by ayatollahi and hashemi [22] were considered. noting that for a central crack subjected to opening mode, the relationship between the stress intensity factor (sif) and the far applied load () is given by: ik y a  , where y is a geometric factor, depends on the plate geometry and the crack shape. y = 1.12 (for a finished plate containing a central crack "2a") [23]. the obtained results of the sif were compared firstly with that of analytical solution (in the case without patch) (fig. 2.a) and then with that of ayatollahi and hashemi [22] in the case with patches made in carbon/epoxy and boron/epoxy (fig. 2.b). it can be seen that good agreement was found between the results of the present model and that of analytical and numerical results as shown in figs. 2.a and 2.b respectively. indeed, the maximum relative error is 4% for the case without patch, 1.96% for the case with a patch in boron/epoxy and 1.48% for the case with a patch in carbon/epoxy. furthermore, it should be noted that the best repair performance under these conditions is obtained by using boron/epoxy patch compared to carbon/epoxy patch. (a) (b) figure 3: variation of ki versus the crack length for (a) unpatched and (b) patched centre cracked specimen. results and discussion distribution of von mises stresses in the plates igs. 4 and 5 respectively illustrate the distribution of von mises stresses under different loadings using rectangular patches in boron/epoxy and carbon/epoxy in the case of a corroded plate without crack and a corroded and cracked plate. it can be noticed that in both cases the stresses increase with the increase of the applied load. a slight difference was found between the values obtained using boron/epoxy and carbon/epoxy patches. for a loading less than 250 mpa, we noted a weak distribution of stresses at the level of the corroded surface in the case of an uncracked plate (fig. 4.a-d). exceeding a loading of 250 mpa, the effect of the patch becomes negligible and an almost homogeneous stresses distribution has been noted (fig. 4.e-f). in the case of a corroded and cracked plate (fig. 5), it can be seen that there is more stress concentration at the right crack tip containing the corroded area compared to the crack tip area left. a non-homogeneous distribution of stresses is noted for the three loading cases under the effect of the crack and the corroded area for both patches. in addition, it can be observed that the maximum stresses obtained in the case of cracked and corroded plates are lower than those of the corroded plates without crack. this can be attributed to the presence of crack, which can play the role of stress deconcentration and reduction of the maximum stress value in the plate. t f k. sadek et alii, frattura ed integrità strutturale, 53 (2020) 51-65; doi: 10.3221/igf-esis.53.05 57 (a) boron/epoxy patch with =220mpa (c) boron/epoxy patch with =250mpa (e) boron/epoxy patch with =300mpa (b) carbon/epoxy patch with =220mpa (d) carbon/epoxy patch with =250mpa (f) carbon/epoxy patch with =300mpa figure 4: von mises stresses distribution in the case of a corroded plate without crack under different loadings using rectangular boron/epoxy and carbon/epoxy patches. (a) boron/epoxy patch with =220mpa (c) boron/epoxy patch with =250mpa (e) boron/epoxy patch with =300mpa (b) carbon/epoxy patch with =220mpa (d) carbon/epoxy patch with =250mpa (f) carbon/epoxy patch with =300mpa figure 5: von mises stresses distribution in the case of a corroded and cracked plate under different loadings using rectangular boron/epoxy and carbon/epoxy patches. k. sadek et alii, frattura ed integrità strutturale, 53 (2020) 51-65; doi: 10.3221/igf-esis.53.05 58 distribution of von mises stresses in the patches figs. 6 and 7 show the von mises stresses distributions in the boron/epoxy and carbon/epoxy patches for corroded plate without crack and corroded-cracked plate under different loadings. for both cases, it can be noticed that the stresses increase as the applied load increases. the stress concentration is localized on the edges of the patches for the corroded and uncracked plate (fig. 6), whereas for the corroded-cracked plate (fig. 7), we found more stress concentration at the vicinity of the corroded crack tip. (a) boron/epoxy patch with =220mpa (b) carbon/epoxy patch with =220mpa (c) boron/epoxy patch with =250mpa (d) carbon/epoxy patch with =250mpa (e) boron/epoxy patch with =300mpa (f) carbon/epoxy patch with =300mpa figure 6: von mises stresses distribution in the patches made in boron/epoxy and carbon/epoxy in the case of corroded and uncracked plate under different loadings. k. sadek et alii, frattura ed integrità strutturale, 53 (2020) 51-65; doi: 10.3221/igf-esis.53.05 59 (a) boron/epoxy patch with =220mpa (b) carbon/epoxy patch with =220mpa (c) boron/epoxy patch with =250mpa (d) carbon/epoxy patch with =250mpa (e) boron/epoxy patch with =300mpa (f) carbon/epoxy patch with =300mpa figure 7: von mises stresses distribution in patches made with boron/epoxy and carbon/epoxy in the case of corroded and cracked plate under different loadings. evolutions of the damaged zone case of the corroded and uncracked plate ig. 8 illustrates the evolutions of the damaged areas (gray surfaces) of the adhesive used for the repair of the corroded plate with carbon/epoxy and boron/epoxy patches under different loadings σ=220, 250, 300 and 350 mpa. it can be seen that the damaged area increases with the increase of the load for both patches, until it reaches a critical value (dr=0.2474) for the high loads (especially when σ=350 mpa), where the adhesive loses its rigidity and the adherence between the composite and the metal becomes very weakened as demonstrated by several authors [9,24,25]. in this case, we can note that corrosion plays an important role on the repair quality, however when the applied loads are below 300 mpa, a good repair performance has been noticed. fig. 9 presents the evolution of damage ratio as a function of the applied load in the case of corroded plate without crack. we can note that as long as the load is less than σ=320 mpa both types of patches maintain their integrity and the adhesive rigidity is better. that can be explain by the value of dr which does not exceed its critical estimated value f k. sadek et alii, frattura ed integrità strutturale, 53 (2020) 51-65; doi: 10.3221/igf-esis.53.05 60 dr=0.2474. however, the adhesive of boron/epoxy patch presents a higher integrity than that of carbon/epoxy patch as it can be seen on the blue curve (fig. 9), where the values of dr are more reduced. when the applied load exceeds 320 mpa, it can be observed that the repair by carbon/epoxy patch is not effective, because the adhesive loses its rigidity and the damage ratio exceeds its critical value. on the other hand, it seems that the adhesive of boron/epoxy patch retains its rigidity up to a value close to 350 mpa. (a) boron/epoxy patch with =220 mpa (b) carbon/epoxy patch with =220 mpa (c) boron/epoxy patch with =250 mpa (d) carbon/epoxy patch with =250 mpa (e) boron/epoxy patch with =300 mpa (f) carbon/epoxy patch with =300 mpa (g) boron/epoxy patch with =350 mpa (h) carbon/epoxy patch with =350 mpa figure 8: evolution of the damaged area of the adhesive used to repair the corroded and uncracked plate by boron/epoxy and carbon/epoxy patches under different loadings. k. sadek et alii, frattura ed integrità strutturale, 53 (2020) 51-65; doi: 10.3221/igf-esis.53.05 61 figure 9: evolution of damage ratio versus the applied load in the case of a corroded plate without crack. case of the corroded and cracked plate fig. 10 shows the evolutions of the damaged area of the adhesive used to repair the cracked and corroded plate by boron/epoxy and carbon/epoxy patches under different loadings. it can be seen that for the load σ=220 mpa, the plate repaired by boron/epoxy patch has less damage than that made of carbon/epoxy. the damage of repair adhesive fm73 is localized at the upper and lower edges for the plate repaired by boron/epoxy patch, while for the plate repaired by carbon/epoxy patch, the adhesive damage is localized at the edges and at the vicinity of the crack tip (corroded area). for the case of an applied load σ=250 mpa, the damage of the adhesive is located at the vicinity of the corroded and cracked zone for both types of patches with less risk of disintegration. when the applied load is σ=300 mpa, it is clearly seen that the adhesive of boron/epoxy patch has less damage than that of carbon/epoxy patch, the latter being much damaged at the level of the corroded and cracked zone. this can be explained by the presence of a crack which can propagate more and more as the load increases. for the applied load σ=350 mpa, the adhesive damage is very significant and represents a risk of disintegration between the patch and the repaired plate. indeed, in the case of high loads, repair by both types of patches does not have an effective impact and especially in the presence of crack with a corrosion defect on the repair plate. the repair adhesive made with boron/epoxy patch has less damage compared to that of carbon/epoxy patch, in particular for very high loads. therefore, it is recommended to use a boron/epoxy patch since it is relatively safer in the presence of an aggressive medium, such as seawater with very high degree of corrosion. figure 11 shows the evolution of damage ratio as a function of the applied load in the case of a corroded and cracked plate. it can be seen that the damage ratio in the adhesive of the carbon/epoxy patch is always higher than that of boron/epoxy, except in the case of an applied load of 245 mpa where both patches present the same damage ratio. in addition, it can be noted that the maximum loads for which the damage ratio reaches its critical value are about 292 mpa for the carbon/epoxy patch and 332 mpa for the boron/epoxy patch. evolution of j-integral fig. 12 presents a comparison of the j-integral evolutions as a function of the applied load for the two cracked and corroded plates repaired by both patches with that of the cracked and corroded plate not repaired. according to this figure, it can be observed that for loads less or equal to 300 mpa, both patches give almost the same results for the repair of the corroded and cracked aluminum alloy a5083. however, for loads greater than 300 mpa the patch made in boron/epoxy gives a better repair in terms of efficiency compared to that of carbon/epoxy. 0 0,05 0,1 0,15 0,2 0,25 0,3 0,35 200 250 300 350 400 d a m a g e  r a ti o applied load (mpa) boron/epoxy carbon/epoxy critical value k. sadek et alii, frattura ed integrità strutturale, 53 (2020) 51-65; doi: 10.3221/igf-esis.53.05 62 (a) boron/epoxy patch with =220 mpa (b) patch in carbon/epoxy with =220 mpa (c) boron/epoxy patch with =250 mpa (d) patch in carbon/epoxy with =250 mpa (e boron/epoxy patch with =300 mpa (f) patch in carbon/epoxy with =300 mpa (g) boron/epoxy patch with =350 mpa (h) patch in carbon/epoxy with =350 mpa figure 10: evolution of the damaged area of the adhesive used for the repair of the cracked and corroded plate by boron/epoxy and carbon/epoxy patches under different loadings. in addition, it can be seen that the effectiveness of patch repair increases with the increase of the applied load. indeed, the difference between the j-integral values for the plate repaired by boron/epoxy patch (the best) and not repaired varies between 40.75% and 215.90% for loads varying between 220 and 400mpa respectively. k. sadek et alii, frattura ed integrità strutturale, 53 (2020) 51-65; doi: 10.3221/igf-esis.53.05 63 figure 11: evolution of damage ratio versus the applied loads in the case of a corroded and cracked plate. figure 12: evolution of the j-integral as a function of the applied load for the cracked and corroded plate repaired by both patches compared to that of the cracked and corroded plate not repaired. conclusion luminum alloys, especially the a5083 h11 has a good resistance to corrosion pitting, in the marine environment, making it the best choice for marine industry manufacturing, over time. this aluminum alloy tends to lose these mechanical and chemical characteristics in contact with an aggressive medium such as seawater which is qualified as a saline and saturated medium and which will cause or accelerate the oxidation reaction. the major problem in marine 0 0,05 0,1 0,15 0,2 0,25 0,3 0,35 200 250 300 350 400 d a m a g e  r a ti o applied load (mpa) boron/epoxy carbon/epoxy critical value a k. sadek et alii, frattura ed integrità strutturale, 53 (2020) 51-65; doi: 10.3221/igf-esis.53.05 64 industries is corrosion, which plays an important role in the propagation of micro cracks under the effect of stress corrosion or metallurgical defect such as endogenous or exogenous inclusions during the development of this latter. the different forms and mechanisms of corrosion presented by a previous work and described in this paper have allowed us to understand the phenomenon in order to act better in repairing the corroded and cracked zone. based on the results obtained in this study of the corrosion effect on the repair performance of the cracked plates with composite patches, the following conclusions can be drawn:  increasing the applied load implies an increase in the damage ratio dr of the adhesive.  the repair with both types of patches (boron/epoxy and carbon/epoxy) gives an acceptable repair performance for cases of loads lower than 300 mpa without risk of adhesive disband.  for severe loads and higher than 300mpa and the case of the repair of corroded and cracked 5083 aluminum alloy structures, it is recommended to use a boron/epoxy patch since it provides a better performance and, therefore, longer service life compared to a carbon/epoxy patch. acknowledgements his research was supported by the general directorate of scientific research and technological development (dgrsdt: direction générale de la recherche scientifique et du développement technologique) of algeria. the authors gratefully acknowledge the scientific support of labab laboratory (enp oran, algeria), lmpm laboratory (sidi bel abbes university, algeria) and lille mechanics unit (france). references [1] sielski, r.a., (2008). research needs in aluminum structure, ships offshore struct., 3(1), pp. 57-65. doi: 10.1080/17445300701797111. [2] bailey, j.c., porter, f.c., pearson, a.w., and jarman, r.a., (1994). aluminium and aluminium alloys, in corrosion (third edition), butterworth-heinemann: oxford. p. 4:3-3:37, doi: 10.1016/j.matpr.2018.05.143. [3] reinhart, f.m., (1976). corrosion of metals and alloys in the deep ocean, technical report (naval construction battalion center (port hueneme, calif.). civil engineering laboratory); r834. doi: 10.5962/bhl.title.47711 [4] ding, y., lv, y., zhao, b., han, y., wang, l., lu, w., (2018). response relationship between loading condition and corrosion fatigue behavior of nickel-aluminum bronze alloy and its crack tip damage mechanism, mater charact., (144) pp. 356-367. doi: 10.1016/j.matchar.2018.07.033. [5] campbell, f.c., (2008). elements of metallurgy and engineering alloys, asm international. doi: 10.31399/asm.tb.emea.9781627082518 [6] salem, m., bachir bouiadjra, b.b., mechab, b., and kaddouri, k., (2015). elastic-plastic analysis of the j integral for repaired cracks in plates, struct. eng. mech., 4(2), pp. 87-96. doi: 10.12989/amr.2015.4.2.087. [7] katnam, k.b., da silva, l.f.m., and young, t.m., (2013). bonded repair of composite aircraft structures: a review of scientific challenges and opportunities. prog. aerosp. sci. 61, pp. 26-42. doi: 10.1016/j.paerosci.2013.03.003. [8] sadek, k., aour, b., bachir bouiadjra, b., fari bouanani, m., and khelil, f., (2018). analysis of crack propagation by bonded composite for different patch shapes repairs in marine structures: a numerical analysis, int. j. eng. res. afr., 35, pp. 175-184. doi: 10.4028/www.scientific.net/jera.35.175 [9] sadek, k., bennouna, m.s., aour, b., bachir bouiadjra, b., benaissa, a., and fari bouanani, m., (2019). numerical investigation of the adhesive damage used for the repair of a5083 h11 aluminum structure by composites patches, int. j. eng. res. afr., 44, pp. 22-31. doi: 10.4028/www.scientific.net/jera.44.22. [10] berrahou, m., mokadem, s., mechab, b., and bachir bouiadjra, b., (2017). effect of the corrosion of plate with double cracks in bonded composite repair, struct. eng. mech., 64(3), pp. 323-328. doi: doi: 10.12989/sem.2017.64.3.323. [11] leski, a., (2007). implementation of the virtual crack closure technique in engineering fe calculations, finite elem. anal. des., (43), pp. 261-268. doi: 10.1016/j.finel.2006.10.004. [12] rybicki, e.f., kanninen, m.f., (1977). a finite element calculation of stress intensity factors by a modified crack closure integral, eng. fract. mech., 9(4), pp. 931-938. doi: 10.1016/0013-7944(77)90013-3. [13] frigon, n.l., mathews, d., (1996). practical guide to experimental design, 1st edition, wiley, newyork. isbn: 978-0471-13919-5 november 1996 360 pages. t k. sadek et alii, frattura ed integrità strutturale, 53 (2020) 51-65; doi: 10.3221/igf-esis.53.05 65 [14] eriksson, l., johansson, e., kettaneh-wold, n., wikström, c., and wold, s., (2000). design of experiments: principles and applications, third edition, umetrics ab, doi: 10.1002/cem.686. [15] ait yala, a., and megueni, a., (2009). optimisation of composite patches repairs with the design of experiments method, mater. design, 30(1), pp. 200-205. doi: 10.1016/j.matdes.2008.04.049. [16] fekih, s.m., albedah, a., benyahia, f., belhouari, m., bachir bouiadjra, b., miloudi, a., (2012). optimisation of the sizes of bonded composite repair in aircraft structures, mater. design, (41), 171-176. doi: 10.1016/j.matdes.2012.04.025. [17] sheppard, a., kelly, d., and tong, l., (1998). a damage zone model for the failure analysis of adhesively bonded joints. int j adhesion adhesives, 18(6), pp. 385-400, doi: 10.1016/s0143-7496(98)00024-4. [18] ban, c.s., lee, y.h., choi, j.h., kweon, j.h., (2008). strength prediction of adhesive joints using the modified damage zone theory, compos. struct., 86, pp. 96-100. doi: 10.1016/j.compstruct.2008.03.016. [19] berrahou, m., mokadem, s., mechab, b., bachir bouiadjrab, b., (2017). effect of the corrosion of plate with double cracks in bonded composite repair, struct. eng. mech., 64(3), pp. 323-328. [20] mhamdia, r., bachir bouadjra, b., serier, b., ouddad, w., feaugas, x., touzain, s., (2011). stress intensity factor for repaired crack with bonded composite patch under thermo-mechanical loading, j. reinf. plast. comp., 30(5), pp. 416424. doi: 10.1177/0731684410397899. [21] hibbit karlsson & sorensen, (2015). abaqus standard/user’s manual, version 6.14., inc., pawtucket, ri, usa. [22] ayatollahi, m.r., hashemi, r., (2007). computation of stress intensity factors (ki, kii) and t-stress for cracks reinforced by composite patching. compos. struct., 78, pp. 602-609. doi: 10.1016/j.compstruct.2005.11.024. [23] ouinas, d., bachir bouiadjra, b., himouri, s., benderdouche, n., (2012). progressive edge cracked aluminium plate repaired with adhesively bonded composite patch under full width disbond. compos. b eng., 43, pp. 805-811. doi:10.1016/j.compositesb.2011.08.022. [24] grabovac, i., bartholomeusz, r.a., and baker, a.a., (1993). composite reinforcement of a ship superstructure-project overview, composites, 24(6) pp. 501-510. doi: 10.1016/0010-4361(93)90020-9. [25] schubbe, j.j., bolstad, s.h., reyes, s., (2016). fatigue crack growth behavior of aerospace and ship grade aluminum repaired with composite patches in a corrosive environment, compos. struct., 144, pp. 44-56. doi: 10.1016/j.compstruct.2016.01.107. << /ascii85encodepages false /allowtransparency false /autopositionepsfiles true /autorotatepages /none /binding /left /calgrayprofile (dot gain 20%) /calrgbprofile (srgb iec61966-2.1) /calcmykprofile (u.s. web coated \050swop\051 v2) /srgbprofile (srgb iec61966-2.1) /cannotembedfontpolicy /error /compatibilitylevel 1.4 /compressobjects /tags /compresspages true /convertimagestoindexed true /passthroughjpegimages true /createjobticket false /defaultrenderingintent /default /detectblends true /detectcurves 0.0000 /colorconversionstrategy /cmyk /dothumbnails false /embedallfonts true /embedopentype false /parseiccprofilesincomments true /embedjoboptions true /dscreportinglevel 0 /emitdscwarnings false /endpage -1 /imagememory 1048576 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/pdfxoutputintentprofileselector /documentcmyk /preserveediting true /untaggedcmykhandling /leaveuntagged /untaggedrgbhandling /usedocumentprofile /usedocumentbleed false >> ] >> setdistillerparams << /hwresolution [2400 2400] /pagesize [612.000 792.000] >> setpagedevice microsoft word numero 7 art 5 c. colombo et alii, frattura ed integrità strutturale, 7 (2009) 65-72; doi: 10.3221/igf-esis.07.05 65 high-cycle fatigue strength of a pultruded composite material c. colombo, m.guagliano, l. vergani dip.to di meccanica, politecnico di milano, via la masa, 1 20156 milano italy riassunto. i compositi pultrusi sono tra i più attraenti materiali per applicazioni che richiedono produzione su grande scala. per questo motivo il loro impiego nell’ambito di applicazioni strutturali è in continuo aumento, anche se ancora limitato da una incompleta conoscenza del loro comportamento a fatica. la maggior parte dei dati a disposizione si riferisce, infatti, a prove interrotte dopo 3 milioni di cicli. in questa memoria si considera un pultruso utilizzato in ambito strutturale e si caratterizza il suo comportamento statico e a fatica. i risultati hanno permesso di ricavare le curve s-n del materiale e di verificare l’esistenza del limite di fatica. le osservazioni condotte al sem hanno consentito di valutare i meccanismi di danneggiamento che si verificano durante il cedimento statico e a fatica. abstract. dealing with composites in polymeric matrix, the pultruded ones are among the more suitable for large production rates and volumes. for this reason, their use is increasing also in structural applications in civil and mechanical engineering. however, their use is still limited by the partial knowledge of their fatigue behaviour; in many applications it is, indeed, required a duration of many millions of cycles, while most of the data that can be found in literature refer to a maximum number of cycles equal to 3 millions. in this paper a pultruded composite used for manufacturing structural beams is considered and its mechanical behaviour characterized by means of static and high-cycle fatigue tests. the results allowed to determine the s-n curve of the material and to assess the existence of a fatigue limit. observations at the scanning electronic microscope (sem) allowed to evaluate the damage mechanisms involved in the static and fatigue failure of the material. keywords. delamination; pultruded composites; dgm-xgm failure; fatigue damage. introduction ultrusion is one of the most attractive technological process for obtaining polymer matrix composite parts to be manufactured with large production rates and volumes [1-3]. due to this characteristic and to some peculiar aspect of their physical and mechanical behaviour, pultruded composite are getting more and more used in structural applications in civil infrastructures. this is due to the progress made in pultrusion technology, that allows the capability to manufacture low-cost large-scale load carrying structural profiles. if the fact that these materials do not need painting, that they do not conduct electricity (thus, not needing to be insulated) and that, thanks to lightness, they use allows to reduce transportation costs and environmental pollution, it seems clear why they are becoming a serious alternative to metal alloys for the construction of shaped beams, pedestrian bridge decks, post for railway noise barriers, floors of bus and other structural parts [4-6]. however, their application in structural engineering is still somewhat limited by the incomplete knowledge about the fatigue strength, that is to say that the behaviour of pultruded composite under time variable loads is not completely investigated and understood. in fact, there are few data that can be found in the references. in [7] a comparative study between the fatigue behaviour of grp hand lay-up and pultruded phenolic composites is described, but the maximum number of cycle of interest is limited to 1 million, thus preventing the application of these data to longer life-span, typical of civil infrastructures. in [8] the long-term environmental fatigue behaviour of pultruded glass-fiber-reinforced p http://dx.medra.org/10.3221/igf-esis.07.05&auth=true http://www.gruppofrattura.it c. colombo et alii, frattura ed integrità strutturale, 7 (2009) 65-72; doi: 10.3221/igf-esis.07.05 66 composites under flexural loading is investigated, while [9] describes the tensile fatigue performances of pultruded reinforced polymers profiles, with particular emphasis on the effect of the specimens shape on the fatigue strength and endurance. in the same paper some results obtained from fatigue tests up to 10 million cycles are reported, but the results number is limited and does not allow the determination of a fatigue limit. in [10] the rotating bending fatigue strength of a pultruded glass fiber reinforced composite is investigated. in [11] the residual fatigue strength of a pultruded composite after damage occurred due to impact of a external object is considered. other papers focus their attention on pultruded composite application in fatigue loaded parts. in [12] the fatigue performance of a cellular frp bridge deck adhesively bolted to steel girders is investigated, while in [13] the fatigue strength of a pultruded i-shaped post for railway noise barriers is considered and analyzed by means of ad-hoc experimental tests. from the analysis of references, it is clear that the designer cannot found sufficient data and knowledge for a safe and reliable application of pultruded materials for structural applications where a long life (many millions of cycles) is required. only a couple of papers report data for such a long endurance and the number of specimens under investigations is limited and further research is needed, both for obtaining quantitative data and to know much about the failure mechanisms by changing the load amplitude. this paper intends to give a contribution in this field. a glass fiber reinforced composite obtained by pultrusion and used for box shaped beams used in civil infrastructures (i.e.: noise barriers, [6]) is considered and experimentally analyzed. its static behaviour is investigated by means of tensile tests while the observations at the scanning electronic microscope allowed to investigate the damage mechanism involved in the static failure. then the fatigue behaviour of the material was investigated by means of axial tests (r=-1) long up to 10 million cycles. the results showed a narrow scatter and allowed to determine the s-n curve and to assess the existence of the fatigue limit. by means of the sem analysis it was moreover possible to understand how fatigue damage develops in the different layers of materials. material he material is a glass-fiber reinforced composite obtained by pultrusion. the matrix is made of equally distributed polyester not saturated resins commercially called leguval w 24 ga and synolite 0175-n-1. the global volumic mass of the matrix is about 1,3 g/cm3. the e glass fibers have a ultimate tensile strength of 1800 mpa, an elastic modulus of 76 gpa and a volumic mass of 2.53 g/cm3. in fig. 1 it is shown the section from which the specimens were cut: these latter were obtained from the longer side. in the same figure it is shown the the lay-up of the material and different layers can be observed: their composition is described in tab. 1. it can be noted that most of glass fibers (84%) are unidirectional (roving) while the remaining part (16%) is randomly distributed. sontara is a thin layer used on the surface to prevent surface damage due to impacts or to the aggressive environment effects. reemay is a surface writing. both sontara and reemay does not modify mass and mechanical characteristics of the material. figure 1: section of the pultruded bar from which the specimens were cut. t http://dx.medra.org/10.3221/igf-esis.07.05&auth=true http://www.gruppofrattura.it c. colombo et alii, frattura ed integrità strutturale, 7 (2009) 65-72; doi: 10.3221/igf-esis.07.05 67 position width (cm) material mass per unit length (g/m) roving mass per unit length (g/m) weight % 1 17 sontara 5.95 2 6 sontara 4.2 3 16 mat 48 4 5 mat 30 5 roving 960 6 21 volumat 126 7 roving 547.2 8 21 mat 63 9 23 sontara 8.05 10 5 sontara 3.5 11 4 reemay 0.8 total woven 289 16 total roving 1507 84 total resin 1796 57 total glass 1354 43 total weight 3150 100 table 1: chemical composition of the layers of the pultruded material (the position refers to fig. 1). in fig.2 it is shown a micrograph of the transversal section taken at the sem showing the main layers of the material. from the sem observation it was possible to effectively define the layer disposition in a section (fig. 3). in fig. 4 the sem micrographs of these layer is shown. it can be noted that the fibers in the roving are nearly aligned, equal-spaced and parallel. also the different fiber percentages of mat and volumat can be noted. figure 2: sem micrograph showing mat, roving and volumat layers. http://dx.medra.org/10.3221/igf-esis.07.05&auth=true http://www.gruppofrattura.it c. colombo et alii, frattura ed integrità strutturale, 7 (2009) 65-72; doi: 10.3221/igf-esis.07.05 68 figure 3: layer disposition in a generic section of the samples. figure 4: sem micrographs of mat (a), roving (b) and volumat (c) layers. static characterization he static behaviour characterization of the pultruded material was obtained by means of tensile and compression tests. five samples for each kind of test were executed by using a schenck hydropuls 250kn universal test machine. the tensile tests were executed according the astm d 3039/d 3039 m-00 standard, while as regards the compression tests the en iso 527-5: 1997 standard was applied. the specimens were cut along the longitudinal direction and presented a rectangular constant cross section, as indicated in the standards that were used. the same sample type was used in both the tensile tests and the compression ones; in fig. 5 their dimensions are shown together with the aluminium grips that were glued to the specimens. an extensometer was applied to measure the deformation of the specimens. figure 5: shape and dimensions in mm of the samples used in the static tests. t http://dx.medra.org/10.3221/igf-esis.07.05&auth=true http://www.gruppofrattura.it c. colombo et alii, frattura ed integrità strutturale, 7 (2009) 65-72; doi: 10.3221/igf-esis.07.05 69 in tab. 2 the results of the tests are shown. in fig. 6 the typical aspect of a dgm failure is shown. some interrupted tensile and compressive tests were also executed, being the aim to investigate the development of the damage by means of observations at the sem. these analyses allowed to assess the progressive nature of damage in the different layers of material. in particular cracks between the fibers and the matrix were observed with increasing length with the load, while their number remained about the same till the final rupture. however some broken fibers were noted in the roving layer for high values of the stresses. in fig. 7 some sem images showing the damage evolution are shown: figs 7a and 7b show the damage evolution in the mat at 200mpa and 340 mpa: the interface crack evolution between the matrix and the fibers can be easily observed. figs 7c and 7d show the roving and also in this case the most evident damage type is the formation of interface cracks. specimen e (mpa) uts (mpa) elongation % failure type failure zone tensile tests 1 30605 367 1,20 dgm middle 2 30794 377 1,23 dgm middle 3 31005 377 1,21 dgm middle 4 30003 361 1,20 dgm middle 5 28791 381 1,32 xgm middle mean value 30240 373 1,23 specimen e (mpa) ucs (mpa) elongation % failure type failure zone compression tests 1 31311 454 1,45 dgm middle 2 27296 383 1,40 dgm middle 3 26607 382 1,43 dgm middle 4 26973 375 1,39 dgm middle 5 31313 402 1,28 dgm middle mean value 28700 399 1,39 table 2: summary of the results of the static tests (dgm= edge delamination gage middle, xgm=explosive gage middle) (a) (b) figure 6: typical aspect of a dgm failure: (a) tensile failure, (b) compression failure. similar observations performed on compression specimens evidenced the same damage evolution. fatigue characterization xial fatigue tests (r=-1) were executed, being the aim the determination of the s-n curve of the material and to verify the existence of a fatigue limit. the specimens have constant section and their geometry is the same as in fig.5. the specimens were considered run-out if failure did not occur till 10.000.000 cycles. tests were performed in loop load control and the imposed frequency was 5 hz; no temperature increment was observed. fifteen specimens were used to determine the fatigue limit according the stair-case procedure while other nine specimens were tested to determine the leaning part of the s-n curve according to the procedure included in the astm e 739-91. in fig. 8 the results are shown: it is possible to observe the limited dispersion of the data. if the applied stress decrease from 120 mpa a http://dx.medra.org/10.3221/igf-esis.07.05&auth=true http://www.gruppofrattura.it c. colombo et alii, frattura ed integrità strutturale, 7 (2009) 65-72; doi: 10.3221/igf-esis.07.05 70 to 80 mpa, the endurance passes from around 550.000 cycles to more than 10 millions cycles (run-out tests). it can be deduced that this material has a fatigue limit and, according to the stair case method, its value was calculated as 90 mpa. figure 7: damage evolution for increasing stress values (transversal section): (a) mat 200 mpa, (b) mat 340 mpa, (c) roving 200 mpa, (d) roving 340 mpa. figure 8: experimentally determined s-n curve of the pultruded material. (○: broken specimens; ●: fatigue limit; __ maximum likelihood estimation for the mean, --confidence limits for the model at 95%) most of the failures happened near the gripping zone, like in fig. 9; this denotes a probable influence of the gripping system onto the obtained results and it is in agreement with the results reported in [9] where the influence of the specimens shape was analysed and where it is found that this kind of specimens gives the lowest fatigue strength. http://dx.medra.org/10.3221/igf-esis.07.05&auth=true http://www.gruppofrattura.it c. colombo et alii, frattura ed integrità strutturale, 7 (2009) 65-72; doi: 10.3221/igf-esis.07.05 71 figure 9: a fatigue broken specimen near the gripping zone. also in this case sem observations have been performed on run-out specimens to evaluate the fatigue damage. pictures showing sem images after 10 millions cycles are reported in fig. 10, that refers to longitudinal sections: the presence of arrested cracks can be noted. on the basis of the analysis of sem observation a quantitative estimation of the fatigue damage was made by counting the number of different defects in the layer that form the pultruded material. the results are shown in tab. 3 and evidence that debonding (crack between matrix and fibers) in the mat layer is the main responsible of the fatigue damage of this material (a) (b) figure 10: sem images of the fatigue specimens: (a) mat, (b) roving. mat roving volumat debonding 67 25 60 fiber cracks 30 15 8 matrix cracks 5 0 0 table 3: defect count in the fatigued run-out specimens conclusions he static and fatigue behaviour of a pultruded glass-fiber reinforced composite material used in structural applications was investigated. on the basis of the tests executed it was possible to determine quantitative data that can be applied for the design of structural parts manufactured with this material. the fatigue tests allowed to determine that the material has a fatigue limit that can be used for designing long life-span parts subjected to time variable loading. the sem observation allowed to evidence the evolution of static and fatigue damage. in particular, as regards this latter one, it was possible to assess that fatigue damage take place mainly in the mat layer and that it mainly consists in t http://dx.medra.org/10.3221/igf-esis.07.05&auth=true http://www.gruppofrattura.it c. colombo et alii, frattura ed integrità strutturale, 7 (2009) 65-72; doi: 10.3221/igf-esis.07.05 72 deboning, that is to say it consist in the initiation and propagation of cracks at the interface between the polymer matrix and the glass fibers. acknowledgement this research was founded by the grant “damage analysis of composite materials under fatigue loading” (miur prin 2007). references [1] f.s. trevor, pultrusion for engineers, crc press, woodhead publishing, ltd, cambridge (2000). [2] b.t. åmström, manufacturing of polymer composites, chapman & hall, london (1997). [3] j.p. fanucci et al., pultrusion of composites, in: t.g. gutowski (ed.), advanced composites manufacturing, j. wiley & sons, new york, (1997) 259-295. [4] l.-h. gan, l. ye, y.-w. mai, composite structures, 45 (1999) 279-288. [5] a. di tommaso, s. russo, mechanics of composite materials 39 (4) (2003) 329-340. [6] m. guagliano, fatigue behaviour of a pultruded composite box-shaped post for high speed railway application (in italian), internal report 48/2004, politecnico di milano. [7] c. moura branco et al., int. j. fatigue, 18 (4) (1995) 255-263. [8] k. liao, c.r. schultheisz, d.l. hunston, int. j. fatigue 21, (1999) 485-495. [9] t. keler, t. tirelli, a. zhou, composite structures, 68 (2005) 235-245. [10] l. vergani, damage mechanisms in pultruded unidirectional fiber reinforced composites under static and fatigue loads, in: m.guagliano, m.h. aliabadi (eds.), fracture and damage of composites, wit press, southampton, 206 (2006) 49-72. [11] t.j. chotard, j. pasquiet, m.l. benzeggagh, composite structures, 53 (201) 317-331. [12] t. keller, h. gürtler, composite structures, 70 (2005) 484-496. [13] t. keller, f. riebel, t. vallée, composites structures, 85 (2008) 116-125. http://dx.medra.org/10.3221/igf-esis.07.05&auth=true http://www.gruppofrattura.it microsoft word numero_50_art_34_2609 n. chatzidai et alii, frattura ed integrità strutturale, 50 (2019) 407-413; doi: 10.3221/igf-esis.50.34 407 focused on the research activities of the greek society of experimental mechanics of materials experimental and numerical study on the influence of critical 3d printing processing parameters nikoletta chatzidai, dimitrios karalekas university of piraeus, laboratory of advanced manufacturing technologies and testing, department of industrial management and technology nchatzi@unipi.gr; dkara@unipi.gr; dkara@webmail.unipi.gr; abstract. in the present work the temperature profile variations generated in rectangular specimens built using the fused deposition modeling (fdm) process, at different printing speeds and orientations, were investigated. the temperature recordings were achieved by the integration of temperature sensors throughout the 1st and/or 21st building layer of the specimens. the experimental results show that the temperature values inside the specimen remain above the glass transition temperature (tg) even at the end of the fabrication process. higher values were obtained when increasing the printing speed and decreasing the printing path. the experimental results were compared to the corresponding ones derived by simulation of the thermal diffusion problem via finite element analysis. the calculated maximum temperature values were in good agreement with the experimentally recorded ones. keywords. additive manufacturing; fused deposition modelling; process parameters; temperature profiles; finite element analysis. citation: chatzidai, n., karalekas, d., experimental and numerical study on the influence of critical 3d printing processing parameters, frattura ed integrità strutturale, 50 (2019) 407-413. received: 18.01.2019 accepted: 21.05.2019 published: 01.10.2019 copyright: © 2019 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. introduction dditive manufacturing (am) or layer manufacturing (lm) have developed intensively over the last decades, providing the potentiality to build simple or more complex 3d objects of varying material types and forms. as defined by the astm:f2792-12a (2012) standard, additive manufacture is the “process of joining materials to make objects from 3d model data, usually layer upon layer, as opposed to subtractive manufacturing methodologies, such as traditional machining”. am techniques are gaining ground in industries, since their ability to make the manufacturing and the assembly process less complicated help to shorten the product development cycle time. fused deposition modeling (fdm) is one of the several existing technologies included in the category of the am techniques. it became popular due to its low cost, easy operation and reproducibility [1]. as described in previous works [2-5], the fdm method deposits rasters of molten thermoplastic polymers, such as acrylonitrile butadiene styrene (abs) or polylactic acid (pla), that solidify into the final desired shape. during the fabrication process, filament of the thermoplastic material is fed into a heated extrusion tip, where it liquefies above its glass transition temperature (tg), and a http://www.gruppofrattura.it/va/50/2609.mp4 n. chatzidai et alii, frattura ed integrità strutturale, 50 (2019) 407-413; doi: 10.3221/igf-esis.50.34 408 extruded as thin rasters through a nozzle onto the build platform to form the first layer [6,7]. the next material layer is deposited upon the previous one, while the process is continued to form the final desired model [8]. after its deposition, the extruded material rapidly cools, solidifies, and bonds with the surrounding material [9]. as long as the material is hot (above tg) it can bond with the previous layer or the adjacent rasters. the bonding mechanism no longer takes place once the material cools below its tg. therefore, the longer the material is kept above its tg, the better the bond between layers and rastres [10]. on the other hand, the deposited material should solidify as quickly as possible to avoid deformation due to gravity, or weight of the above deposited material [11]. moreover, the non-uniform thermal gradients that exhibit during the fdm process, develop residual stresses which may induce warping and delamination [12,13] or even part distortions, dimension inaccuracy or part fabrication failure [9]. as a result, the knowledge of temperature evolution during the component's fabrication process is one of the primary concerns in fdm process. the quality, accuracy and properties of the final printed parts depend also on other user control process parameters, such as build orientation, layer thickness, infill density, raster angle, extruder temperature and air gap between adjacent rasters. a lot of research has done the last two decades on the influence of the printing process parameters on the mechanical properties of the printed parts [3,7,14-24] and/or the bonding degree between the rasters [3,20,22,25-28]. sood et al. [22, 27] examined five important process parameters (layer thickness, orientation, raster angle, raster width and air gap) both experimentally and numerically, and showed that they do not work alone, but interact during the fdm process and influence the tensile and compressive strength of the final part. besides the effect of the process parameters on the mechanical properties of the final object, particular interest has shown by researchers on the temperature field and the related temperature gradient as a result of different process conditions. sun et al. [20,29] tried to correlate important process parameters with the quality of bond formation via temperature measurements in the bottom layer of an fdm fabricated component. zhang and chou [30] considered the influence of tool-path on temperature variation to explain thermo-mechanical distortion through residual stress distribution. more recently, costa et al. [31] examined the contribution of various thermal phenomena developing during fused deposition techniques to the overall heat transfer and to the mechanical deformation of the fabricated parts. later, the same authors [11], presented an analytical solution for the transient heat transfer during filament deposition and cooling considering four main process parameters (extrusion velocity, filament dimensions, sequence of deposition and environmental temperature). zhang et al. [32] used the boundary-adjusting finite difference method to adapt a three-dimensional transient mathematical model to describe the influence of various process parameters on the temperature variation of any fdm printed cuboid specimen. li et al. [33], studied experimentally the effect of major process parameters, such as layer thickness, deposition velocity and infill rate, on the bonding degree between the rasters, on the temperature profiles during the fdm process and on product's mechanical properties. in that work, the experimental process was conducted for a component made from pla using an open-source makerbot fdm printer. in the present study, the real-time temperature profiles of rectangular specimens were investigated, under different printing velocities and raster orientations. the recording of the temperature values was achieved through the integration of temperature sensors in various layers of the printed specimens. the experimental results were compared to those derived by finite element analysis. experimental procedure ectangular specimens of commercial thermoplastic acrylonitrile butadiene styrene (abs) were built on the makerbot replicator 2x fdm printer. the dimensions of the specimens were 40 mm x 20 mm and consisted of 41 layers. the thickness of each layer was 0.254 mm. the advantage of a such an opensource fdm printer is the ability of changing a large number of building parameters, such as printing speed, layer thickness, density of the rasters (infill density), building orientation and temperature of the printing heads. in the present study, all the above parameters remained constant, besides the building orientation and the printing speed. temperature sensors (k-type thermocouples, ±1.5°c) were embedded at the center of the 1st and/or the 21st building layer, for the recording of the temperature variations throughout the building process and until the completion of the specimens' fabrication. this type of sensors has a sensing tip of 0.25 mm thickness. the temperature data recordings were obtained and analyzed through a data acquisition instrument. the embedment of the thermocouples was carried out manually. special retainers were designed and built simultaneously with the specimen to assure the integration of the sensors at the desired positions. the building process of the 3d printed rectangular specimen started with deposition of a raft of small thickness, made of polystyrene to increase the contact surface between the specimen and the platform. this polystyrene raft was considered r n. chatzidai et alii, frattura ed integrità strutturale, 50 (2019) 407-413; doi: 10.3221/igf-esis.50.34 409 necessary since the temperature on the building platform was 20-25°c below the one that was setup initially, causing the detachment of the specimen. once this raft was completed, deposition of the abs material was started. initially, at each layer, two shells that delimit the specimen were built, and thereafter the internal raster-by-raster material deposition was initiated. the building process continued until the plane at which the thermocouple had to be integrated was reached. at that point, the building process was paused temporally, to integrate the thermocouple, and then continued until the completion of the specimen fabrication. in the case that two thermocouples were integrated in different layers, the building process was paused twice. images of the specimens are shown in fig.1. (a) (b) figure 1: specimen with thermocouple in the (a) 21st layer and (b) 1st and 21st layer. as shown in table 1, specimens were built with two different building speeds (35 sec/layer and 65 sec/layer) and building orientations (0° and 90°). the orientation of the building process is prescribed according to the specimen’s physical coordinate system, as shown in fig. 2. specimen building orientation building speed (sec/layer) layer of the embedded thermocouple 1 0° 35 1 2 0° 35 21 3 0° 35 1 and 21 4 0° 65 21 5 90° 65 21 table 1: specimens and their building parameters. figure 2: physical coordinate system of the rectangular specimen. for all the specimens, the infill density was set up to 0.9 for greater adhesion. the liquefier temperature of the extruded material was set up at 230°c, since higher temperatures caused burning of the material. additionally, it deemed necessary to measure the envelope temperature, since it can't be controlled automatically by the 3d printer software. the temperature was found to be 85°c. n. chatzidai et alii, frattura ed integrità strutturale, 50 (2019) 407-413; doi: 10.3221/igf-esis.50.34 410 finite element modeling he simulation of the thermal diffusion problem in rectangular specimens during the fdm building process was carried out using the abaqus® software (abaqus, hibbitt, karlsson & sorensen, inc., ri, usa). the simulation procedure was conducted in the following stepwise manner: step 1. a rectangular model was designed with dimensions 40 mm x 20 mm x 0.254 mm (length x width x height) for specimen 1 and 40 mm x 20 mm x 5.334 mm (length x width x height) for specimens 2, 4 and 5. this model represents the part of the specimen that the thermocouple was integrated. step 2. a new model, with nl x 0.254 mm height was designed at the top of the previous one, where nl = 1, ..., 40 for specimen 1 and nl = 1, ..., 20 for specimens 2, 4 and 5. this model represents the new abs layers. each time, both models were meshed and solved, using the equations and the boundary conditions that are presented further down. the temperatures calculated from the numerical solution of the equations, correspond to the time that the extruder passes above the sensor. the governing equation for the thermal analysis of the rectangular specimen is given by: 𝛻 ∙ 𝑘𝛻𝑇 𝑞 (1) where t is the temperature, ρ the density, cp the specific heat, k the thermal conductivity and q the heat generation rate. the thermal properties of the abs material that used for the simulations are shown in table 2 [20]. parameter values thermal conductivity, k 0.177 w/m·k specific heat, cp 2.080 j/kg·k density, ρ 1.050 kg/m3 table 2: thermal properties of the abs material. at the outer surfaces of the rectangular specimen, the equation of convection was set as boundary condition: 𝑄 ℎ 𝑇 𝑇 (2) where h is the heat convection coefficient, that was taken equal to 75 w/m2·k [9], and tenv the temperature of the chamber, equal to 85°c, as measured experimentally. the temperature at the bottom surface of the rectangular specimen is set to be constant and equal to 88°c, the temperature on the polystyrene raft. this is a mean value obtained by the integration of a thermocouple between the polystyrene raft and the 1st abs layer. for the upper surface of the rectangular specimen, a known temperature profile is used as boundary condition. this temperature profile was derived by the experimental data, during the first pass of the printing nozzle over the thermocouple. for the fe simulations, the modeled specimen was considered to be solid, while the raster orientation and possible abnormalities or discontinuities of the experimental process were not taken into account. results and discussion n figs.3(a,b) the obtained experimental temperature profiles for specimens 1-2 (see table 1) are shown, as a function of building time. the building orientation (0°) and speed (35 sec/layer) remain the same for the two specimens. moreover, in the same figures the temperature peak values calculated by the finite element analysis are also plotted. in these figures, and those that follow, the curves represent the real-time monitoring temperature variations that take place during the fabrication process, while their peaks correspond to the time that the printer's nozzle passes over the integrated thermocouple. in fig.3a (specimen 1), the temperature profile that developed during the deposition of the 1st layer is shown, and all the subsequent layers, until the completion of the specimen’s fabrication. as it was expected, the greater temperature values are shown right after the integration of the thermocouple since it is in direct contact with the deposited material. each peak t i n. chatzidai et alii, frattura ed integrità strutturale, 50 (2019) 407-413; doi: 10.3221/igf-esis.50.34 411 (a) (b) figure 3: temperature profiles as recorded by thermocouples together with the temperature peak values as calculated by fea for embedding locations: (a) 1st layer and (b) 21st layer. is followed by a rapid decrease in the temperature. the temperature profile shows a declining pattern with time. however, it is obvious that the temperature profile is fluctuating, with gradually lower maxima even when the fabrication of the specimen is well above the 1st layer. at the end of the printing process the temperature at the first layer exhibits a value of 93°c (due to the heat generated by the heated platform) which is very close to the glass transition temperature (tg). for abs the tg is 94°c. this shows the importance of heat transfer through conduction within the structure. in fig.3b the temperature profiles as a function of building time in the case of specimen 2 are presented. the thermocouple was integrated in 21st layer, so the reordered data refers to only half the specimen (21 layers). it is seen that the temperature profile is similar to the one presented in fig.3a, while the effect of the printing nozzle is more intense at the layers deposited at the end of the printing process. in fig.4 the temperature data of specimen 3 are shown. in this case two thermocouples were integrated in the same specimen, one at 1st layer and the other at the 21st layer. the exhibited recording presents a similarity to the previously presented experimental data. the sudden temperature drop recorded by the thermocouple integrated in the first layer shows the time that the building process was paused temporarily for the integration of the 2nd thermocouple. in figs.5(a,b) the temperature profiles for specimens 4 and 5 of table 1 are shown. these specimens were built with higher printing speed (65 sec/layer), compared to the previous ones. the recorded temperature profile is similar to the corresponding ones of the previous specimens, but the temperature values remain higher and well above tg. this suggests that the adjacent rasters have more time to bond. the higher speed of the printing nozzle contributes to the maintenance of the higher temperatures inside the specimen. additionally, the printing speed together with the shorter toolpath of the printing nozzle (specimen 5, fig.5b), allow for a more uniform temperature profile inside the specimen. the irregularities observed for the temperature profile at the first four layers of the 3d printed rectangular specimen are likely to be due to possible levitation of the embedded thermocouple. as far as the simulated temperature profiles are concerned, they are in good agreement with the experimental ones, especially for specimens 4 and 5. increasing the speed of the printing nozzle, and even more in the case of shorter build path (specimen figure 4: temperature profiles as recorded by the two thermocouples integrated in1st and 21st layer. n. chatzidai et alii, frattura ed integrità strutturale, 50 (2019) 407-413; doi: 10.3221/igf-esis.50.34 412 (a) (b) figure 5: temperature profiles as recorded by thermocouples integrated in 21st layer together with the temperature peak values for: (a) 0° and (b) 90° raster orientation. 5), ensures greater bonding of the rasters within the fabricated specimen, and thus, approaching the ideal theoretical solid model that was used to perform the simulations. on the other hand, the differences between the experimental and the simulated temperature profiles of figs.3(a,b) (max 5°c), show that the gaps between the rasters should be taken into account. conclusions n the present work 3d printed rectangular polymer specimens were fabricated under different building speeds and orientations. temperature sensors were integrated throughout the center of the 1st and/or 21st building layer of these specimens to investigate the temperature profiles generated during the fabrication process. the experimentally obtained results were compared to the corresponding ones derived by the thermal diffusion finite element analysis. the experimental results demonstrate an undulated temperature profile with a declining pattern. higher rates of the printing nozzle in conjunction with shorter printing path lead to the preservation of higher temperature values inside the specimen. the thermal behavior of the specimen is influenced both by the extruded material and the heated printing platform even during the end at the printing process. the simulation based calculated maximum temperature values exhibit good agreement, in general, with the experimentally measured ones, presenting a maximum difference of 5°c. however, by increasing the printing speed and decreasing the printing tool-path the rasters’ bonding enhances leading to a more solid 3d printed specimen which approaches the ideal model considered in the fem analysis. references [1] chua, c.k., leong, k.f., lim, c.s. (2010). rapid prototyping, principles and applications, world scientific. [2] coogan, t.j., kazmer, d.o. (2017). bond and part strength in fused deposition modeling, rapid prototyp. j., 23(2), pp. 248–257, doi: 10.1108/rpj-03-2016-0050. [3] ahn, s., montero, m., odell, d., roundy, s., wright, p.k. (2002). anisotropic material properties of fused deposition modeling abs, rapid prototyp. j., 8(4), pp. 248–257, doi: 10.1108/13552540210441166. [4] bellini, a., güçeri, s. (2003). mechanical characterization of parts fabricated using fused deposition modeling, rapid prototyp. j., 9(4), pp. 252–264, doi: 10.1108/13552540310489631. [5] bellehumeur, c., li, l., sun, q., gu, p. (2004). modeling of bond formation between polymer filaments in the fused deposition modeling process, j. manuf. process., 6(2), pp. 170-78, doi: 10.1016/s1526-6125(04)70071-7. [6] shofner, m.l., lozano, k., rodríguez-macías, f.j., barrera, e. v. (2003). nanofiber-reinforced polymers prepared by fused deposition modeling, j. appl. polym. sci., 89(11), pp. 3081–3090, doi: 10.1002/app.12496. [7] es-said, o.s., foyos, j., noorani, r., mendelson, m., marloth, r., pregger, b.a. (2000). effect of layer orientation on mechanical properties of rapid prototyped samples, mater. manuf. process., 15(1), pp. 107–122, doi: 10.1080/10426910008912976. i n. chatzidai et alii, frattura ed integrità strutturale, 50 (2019) 407-413; doi: 10.3221/igf-esis.50.34 413 [8] giordano, r.a., wu, b.m., borland, s.w., cima, l.g., sachs, e.m., cima, m.j. (1996). mechanical properties of dense polylactic acid structures fabricated by three dimensional printing. j. biomater. sci. polym. ed., 8(1), pp. 63–75. [9] kousiatza, c., chatzidai, n., karalekas, d. (2017). temperature mapping of 3d printed polymer plates: experimental and numerical study, sensors, 17(3), pp. 456, doi: 10.3390/s17030456. [10] dinwiddie, r.b., kunc, v., lindal, j.m., post, b., smith, r.j., love, l., duty, c.e. (2014). infrared imaging of the polymer 3d-printing process, proc. of spie, 9105, 910502-1, doi: 10.1117/12.2053425. [11] costa, s.f., duarte, f.m., covas, j.a. (2017). estimation of filament temperature and adhesion development in fused deposition techniques, j. mater. process. technol., 245, pp. 167–179, doi: 10.1016/j.jmatprotec.2017.02.026. [12] kantaros, a., karalekas, d. (2013). fiber bragg grating based investigation of residual strains in abs parts fabricated by fused deposition modeling process, mater. des., 50, pp. 44–50, doi: 10.1016/j.matdes.2013.02.067. [13] kousiatza, c., karalekas, d. (2016). in-situ monitoring of strain and temperature distributions during fused deposition modeling process, jmade, 97, pp. 400–406, doi: 10.1016/j.matdes.2016.02.099. [14] rayegani, f., onwubolu, g.c. (2014). fused deposition modelling (fdm) process parameter prediction and optimization using group method for data handling (gmdh) and differential evolution (de), int. j. adv. manuf. technol., 73(1-4), pp. 509-519, doi: 10.1007/s00170-014-5835-2. [15] huang, b., singamneni, s. (2015). raster angle mechanics in fused deposition modelling, j. compos. mater., 49(3), pp. 363-383, doi: 10.1177/0021998313519153. [16] yan, y., zhang, r., hong, g., yuan, x. (2000). research on the bonding of material paths in melted extrusion modeling, mater. des., 21(2), pp. 93-99, doi: 10.1016/s0261-3069(99)00058-8. [17] rezayat, h., zhou, w., siriruk, a., penumadu, d., babu, s.s. (2015). structure–mechanical property relationship in fused deposition modelling, mater. sci. technol., 31(8), pp. 895-903, doi: 10.1179/1743284715y.0000000010. [18] rodríguez, j.f., thomas, j.p., renaud, j.e. (2003). mechanical behavior of acrylonitrile butadiene styrene fused deposition materials modeling, rapid prototyp. j., 9(4), pp. 219-230, doi: 10.1108/13552540310489604. [19] ahn, s.h., baek, c., lee, s., ahn, i.s. (2003). anisotropic tensile failure model of rapid prototyping parts fused deposition modeling (fdm), int. j. mod. phys. b, 17(8-9), pp. 1510–1516, doi: 10.1142/s0217979203019241. [20] sun, q., rizvi, g.m., bellehumeur, c.t., gu, p. (2008). effect of processing conditions on the bonding quality of fdm polymer filaments, rapid prototyp. j., 14(2), pp. 72–80, doi: 10.1108/13552540810862028. [21] luzanin, o., movrin, d., plancak, m. (2014). effect of layer thickness, deposition angle, and infill on maximum flexural force in fdm-built specimens, j. technol. plast., 39(1), pp. 49–58. [22] sood, a.k., ohdar, r.k., mahapatra, s.s. (2012). experimental investigation and empirical modelling of fdm process for compressive strength improvement, j. adv. res., 3, pp. 81–90, doi: 10.1016/j.jare.2011.05.001. [23] boschetto, a., bottini, l., veniali, f. (2016). integration of fdm surface quality modeling with process design, addit. manuf., 12, pp. 334–344, doi: 10.1016/j.addma.2016.05.008. [24] lee, b.h., abdullah, j., khan, z.a. (2005). optimization of rapid prototyping parameters for production of flexible abs object, j. mater. process. technol., 169, pp. 54–61, doi: 10.1016/j.jmatprotec.2005.02.259. [25] gurrala, p.k., regalla, s.p. (2014). part strength evolution with bonding between filaments in fused deposition modelling, virtual phys. prototyp., 9(3), pp. 141-149, doi: 10.1080/17452759.2014.913400. [26] magalhães, l.c., volpato, n., luersen, m.a. (2014). evaluation of stiffness and strength in fused deposition sandwich specimens, j. brazilian soc. mech. sci. eng., 36(3), pp. 449-459, doi: 10.1007/s40430-013-0111-1. [27] sood, a.k., ohdar, r.k., mahapatra, s.s. (2010). parametric appraisal of mechanical property of fused deposition modelling processed parts, mater. des., 31, pp. 287–295, doi: 10.1016/j.matdes.2009.06.016. [28] abbott, a.c., tandon, g.p., bradford, r.l., koerner, h., baur, j.w. (2018). process-structure-property effects on abs bond strength in fused filament fabrication, addit. manuf., 19, pp. 29–38, doi: 10.1016/j.addma.2017.11.002. [29] sun, q., rizvi, g.m., bellehumeur, c.t. and gu, p., 2003, august. experimental study of the cooling characteristics of polymer filaments in fdm and impact on the mesostructures and properties of prototypes. in proceedings of the 14th solid freeform fabrication symposium, austin, pp. 313–323. [30] zhang, y., chou, y. (2006). three-dimensional finite element analysis simulations of the fused deposition modelling process, proc. inst. mech. eng. part b j. eng. manuf., 220(10), pp. 1663-1671, doi: 10.1243/09544054jem572. [31] costa, s.f., duarte, f.m., covas, j.a. (2015). thermal conditions affecting heat transfer in fdm/ffe: a contribution towards the numerical modelling of the process, virtual phys. prototyp., 10(1), pp. 35–46. [32] zhang, j., wang, x.z., yu, w.w., deng, y.h. (2017). numerical investigation of the influence of process conditions on the temperature variation in fused deposition modeling, mater. des., 130, pp. 59–68. [33] li, h., wang, t., sun, j., yu, z. 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can be opened with acrobat and adobe reader 5.0 and later.) >> /namespace [ (adobe) (common) (1.0) ] /othernamespaces [ << /asreaderspreads false /cropimagestoframes true /errorcontrol /warnandcontinue /flattenerignorespreadoverrides false /includeguidesgrids false /includenonprinting false /includeslug false /namespace [ (adobe) (indesign) (4.0) ] /omitplacedbitmaps false /omitplacedeps false /omitplacedpdf false /simulateoverprint /legacy >> << /addbleedmarks false /addcolorbars false /addcropmarks false /addpageinfo false /addregmarks false /convertcolors /converttocmyk /destinationprofilename () /destinationprofileselector /documentcmyk /downsample16bitimages true /flattenerpreset << /presetselector /mediumresolution >> /formelements false /generatestructure false /includebookmarks false /includehyperlinks false /includeinteractive false /includelayers false /includeprofiles false /multimediahandling /useobjectsettings /namespace [ (adobe) (creativesuite) (2.0) ] /pdfxoutputintentprofileselector /documentcmyk /preserveediting true /untaggedcmykhandling /leaveuntagged /untaggedrgbhandling /usedocumentprofile /usedocumentbleed false >> ] >> setdistillerparams << /hwresolution [2400 2400] /pagesize [612.000 792.000] >> setpagedevice microsoft word numero 21 articolo 6.doc a. yu fedorova et alii, frattura ed integrità strutturale, 21 (2012) 46-53; doi: 10.3221/igf-esis.21.06 46 infrared thermography study of the fatigue crack propagation a.yu. fedorova, m.v. bannikov, o.a. plekhov institute of continuous media mechanics ub ras,614013, ac. koroleva street, 1, perm, russia e.v. plekhova perm national research polytechnic university,614990, komsomolsky av, 29, perm, russia abstract. the work is devoted to the experimental study of heat dissipation process caused by fatigue crack propagation. to investigate a spatial and time temperature evolution at the crack tip set of experiments was carried out using specimens with pre-grown centered fatigue crack. an original mathematical algorithm for experimental data treatment was developed to obtain a power of heat source caused by plastic deformation at crack tip. the algorithm includes spatial-time filtration and relative motion compensation procedures. based on the results of mathematical data treatment, we proposed a way to estimate the values of j-integral and stress intensity factor for cracks with pronounced the plastic zone. keywords. fatigue crack; heat dissipation; infrared thermography. introduction n recent decades, many authors have been actively investigated the processes of heat dissipation due to the material structure evolution under cyclic loading. the main application of infrared thermography for fatigue loading was focused on the development of techniques for rapid determination of fatigue limit of materials. this technique was reported starting from early work by a. risitano [1], developed further by m.p. luong [2] and many other authors. the review of this question can be read in [3]. but there are only a few works devoted to direct investigation of temperature evolution at fatigue crack tip. at present, it is well known that in materials under cyclic deformation, fatigue cracks are initiated in the area of plastic deformation localization and lead to an intensive heat dissipation [4]. it makes possible the early detection of crack initiation by infrared thermography [5]. the infrared thermography can be also applied during mechanical tests in order to obtain detailed information about the process of structure evolution, damage accumulation and damage-fracture transition in solids [6-8]. the investigation of the heat dissipation at the fatigue crack tip allows one to develop an effective method for determination of the linear fracture mechanics parameters in a wide range of stress intensity and, as a consequence, gives a way of monitoring of critical state of crack. the solution of this problem requests an analysis of solutions of nonlinear problems of plasticity theory and experimental investigation of plastic deformation localization at crack tip. this work is devoted to the development of experimental technique for measuring the temperature field at the crack tip with a high temperature and spatial resolution. the technique is coupled with mathematical algorithms for experimental data processing. the algorithms allow us to determine the stress intensity factor (sif) and propose an idea for calculation of j-integral value as a value of energy dissipated at crack tip. the proposed algorithms are universal and can be used for many metals under cyclic loading with different stress amplitudes and frequencies. in this work we applied this technique for study of temperature evolution of the plate titanium specimens with pre-grown fatigue crack. we experimentally investigated the evolution of the temperature distribution and obtained the values of heat dissipation caused by plastic deformation at the fatigue crack. i http://www.gruppofrattura.it http://dx.medra.org/10.3221/igf-esis.21.06&auth=true a. yu fedorova et alii, frattura ed integrità strutturale, 21 (2012) 46-53; doi: 10.3221/igf-esis.21.06 47 materials and conditions of experiment xperimental study of temperature evolution at the fatigue crack tip was carried out on the plane specimens of titanium ti-6al-4v. the specimens were manufactured from a commercial pure titanium sheet 3 mm thick. the chemical composition of material presented in tab. 1. fe c si v n ti al zr o h 0.3 0.1 0.15 4.2 0.03 other 5.9 0.2 0.2 0.015 table 1: chemical composition of ti-6al-4v. mechanical properties of material are modulus of elasticity 113 gpa, yield stress 800 mpa, ultimate stress 900 mpa, fatigue limit – 460 mpa, fracture toughness – 75.6 мраm. the geometry of specimen is shown in fig. 1. the specimens were weakened by holes to initiate fatigue crack at the specimen center. the fatigue crack (about 10 mm) was initiated at the initial stage of the experiment by high amplitude cyclic loading of the specimens at the average stress of 215mpa, stress amplitude of 238 mpa and loading frequency of 20 hz. then the load was decreased to slow down the rate of crack propagation, which allows a detailed analysis of the heat generation processes at the crack tip. the surface of the specimens was polished in several stages by the abrasive paper (at the final stage of polishing the grit size does not exceed 3 µm). before starting the experiment, the polished surface was covered by a thin layer of amorphous carbon. the temperature evolution was recorded by infrared camera cedip silver 450m. the spectral range of the camera is 3-5 mm. the maximum frame size is 320×256 pixels; the spatial resolution is 10-4 meters. the temperature sensitivity is 25 mk at 300 k. calibration of the camera was made based on the standard calibration table. mechanical tests were carried out at 100 kn servo-hydraulic machine bi-00-100. the test conditions comply with the conditions of the experiment was described in [9]. the process of crack propagation was studied at 5 hz and 10 hz loading frequency. the selected frequency of loading provides a close to adiabatically condition at crack tip. at low frequency (less that 5 hz) the heat transfer process plays a great role and doesn’t allow one to calculate the right value of heat source. the investigation of high loading frequency requests the high frame rate and treatment of large amount of infrared data. it was shown that for selected values of loading frequency the value of determined parameters (stress intensity factor) depends on the applied stress and crack length, only. figure 1: geometry of specimen. all sizes are in millimeters. the processing of the experimental data t the beginning of data processing procedure, the first frame was subtracted from the film to eliminate the influence of infrared radiation from the camera lens on the determined temperature field. due to the relative motion of the specimen and infrared camera lens under cyclic tests, there is the problem of motion compensation in order to obtain the correct temperature data at a given point on specimen surface. compensation of relative motion was made based on the following algorithm. e a http://www.gruppofrattura.it http://dx.medra.org/10.3221/igf-esis.21.06&auth=true a. yu fedorova et alii, frattura ed integrità strutturale, 21 (2012) 46-53; doi: 10.3221/igf-esis.21.06 48 using the discrete fourier transform we can processed all frames of the film ( , ) exp( ( )) ( , )        t x y x y tt k k i k x k y t x y dydx , (1) where x, y – spatial coordinates, t – number of frame, tt(x, y) – temperature at t-th infrared frame, i 1  . to find the relative motion value we used arbitrary selected fragment of first frame of the film (“flag”). one of the variants of “flag” is presented in fig. 2. using the fourier image of first frame    1 1, exp( ( )) ,       x y x yt k k i k x k y t x y dydx , (2) we can define the position of the chosen fragment in the subsequent frames of the film as follows        12, exp( ( ) 1 ) , , 2   t x y t x y x y x yt x y i k x k y t k k t k k dk dk , (3) the dependence of the "flag" coordinates versus time determines the absolute value of the displacement of each pixel in the image and allows us to compensate for the relative motion. figure 2: implementation of the motion compensation algorithm for the temperature contour images. spatially fixed temperature signal of the specimen was processed by the two-dimensional discrete fourier transform with the standard gaussian kernel to increase data accuracy and eliminate the influence of random temperature fluctuations. the expression for determining the temperature had the form        2, exp( ( )) , , 2 1      x y x y x y x yt x y i k x k y t k k f k k dk dk , (4) where 2 2 2 2 ( , ) exp (( ))      f x y x y gaussian kernel,  ,  x yf k k direct fourier transform of the standard gaussian kernel, http://www.gruppofrattura.it http://dx.medra.org/10.3221/igf-esis.21.06&auth=true a. yu fedorova et alii, frattura ed integrità strutturale, 21 (2012) 46-53; doi: 10.3221/igf-esis.21.06 49  ,  x yt k k direct fourier transform of the temperature. the initial temperature distribution and temperature distribution obtained using equation (4) are shown in fig. 3. finally, an infrared image of the temperature increment on the specimen surface during crack propagation is shown in fig. 4 after all stages of signal processing. a) b) figure 3: the temperature field before (a) and after (b) data processing. figure 4: the temperature field after all stages of signal processing. determination of the heat dissipated at the crack tip caused by plastic deformation he value of the specific heat power at the crack tip can be determined using the following relation [10]             ts c t k t , (5) where t – temperature, ρ – density (4505 kg/m3), c – heat capacity (540 j/(kg·k)), k – heat conductivity (18.85 w/(m·k)), t http://www.gruppofrattura.it http://dx.medra.org/10.3221/igf-esis.21.06&auth=true a. yu fedorova et alii, frattura ed integrità strutturale, 21 (2012) 46-53; doi: 10.3221/igf-esis.21.06 50 s – unknown specific power of the heat source (w/m3), τ – a constant related to the losses of heat by heat exchange with the surroundings (103 j/(m3·k)). the resulting value of the specific power of heat source was integrated over the time during which the plastic zone was observed. the profile of the specific heat dissipated during plastic deformation is plotted in fig. 5. a) b) figure 5: specific heat (j/m3) dissipated during plastic deformation (a) and its profile in the direction of crack propagation (b). the developed algorithm allows us to study a time evolution of temperature evolution and heat dissipation processes at the crack tip. the plots of the temperature increment, heat and stress of two types of experiments are presented in fig. 6. at the beginning of cycling, the thermoelastic effect leads to emergence of cooling zone at crack tip, the local transition through the yields stress leads to temperature increase caused by the formation of a plastic deformation zone. when the stress decreases, the heat dissipation at the crack tip continues the heat dissipation rises and the temperature reaches a maximum at the falling load. at the beginning of the next cycle, the temperature again decreases due to the thermoelastic effect and the process repeats. a) b) figure 6: heat source evolution (1), loads (2) and the temperature increment (3) at the crack tip during the loading. loading frequency is 5 hz (a), loading frequency 10 hz (b). the fig. 7 presents the detail analysis of the temperature evolution near fatigue crack tip in the direction of the crack propagation. the legends indicate the time of temperature distribution. the data corresponds to the test presented with stress amplitude 250 mpa and frequency 10 hz. http://www.gruppofrattura.it http://dx.medra.org/10.3221/igf-esis.21.06&auth=true a. yu fedorova et alii, frattura ed integrità strutturale, 21 (2012) 46-53; doi: 10.3221/igf-esis.21.06 51 analysis of the data presented in fig. 6, 7 allows us to suggest that the maximum of applied loads and the maximum of heat dissipation intensity in the fatigue crack tip do not coincide in time. the observed effect shows that there is a lag of temperature reaction of the specimen on the changing loading during the cyclic deformation. figure 7: evolution of temperature distribution in the direction of crack propagation versus applied stress. the obtained data of the heat dissipation rate at the crack tip allows us to propose an idea to determining the values of jintegral as a value of energy dissipated at crack tip. based on it we can calculate the sif and offer in a criterion for the critical state of the material, based on the experimentally observed size of the plastic deformation zone. using the hrr-solution [11], we can expect that the energy released at the crack tip (wp) has a singularity 1/r and is proportional to the value of the j-integral 1 ( ) p j x w m r , (6) where r – distance from the crack tip, m1 – coefficient associated with the properties of the sample material and the type of loading, j(x) – j-integral. for the sake of simplicity, we assume that the energy released at the crack tip is consumed to the heat dissipation. then, based on experimental evidence, we can calculate the value of j-integral and sif according to the formulas 1 ( ) ( )  q x r j x m , (7) 2 ( ) 1    ej x k , (8) where ν = 0.32 – poisson's coefficient, е young's modulus, q(x) – specific heat (j/m3). to check the accuracy of experimentally calculate values of sif we calculate the theoretical value of sif as follow sec 2         theork p l , (9) http://www.gruppofrattura.it http://dx.medra.org/10.3221/igf-esis.21.06&auth=true a. yu fedorova et alii, frattura ed integrità strutturale, 21 (2012) 46-53; doi: 10.3221/igf-esis.21.06 52 where p – tensile force (pa), l – half-length of crack, α = 2l/h, h – width of the sample. the values of j-integrals and sif were calculated based on the formulas (7) (9). the results are shown in fig. 8 and fig. 9. a) b) figure 8: the dependence of j-integral versus a distance from the crack tip in the direction of crack propagation. loading frequency is 5 hz (a), loading frequency 10 hz (b). a) b) figure 9: the dependence of sif versus a distance from the crack tip in the direction of crack propagation. loading frequency is 5 hz (a), loading frequency 10 hz (b). analysis of the data presented in fig. (8), (9) suggests that the average value of experimentally obtained sif is approximately equal to the theoretical value of sif at a distance from 0.4 mm to 1.2 mm from the crack tip. this allows us to use the equations (7-9) to determine the critical condition of the crack with pronounced plastic deformation zone. conclusion he effect of heat dissipation at the crack tip under cyclic loading has been studied based on the infrared thermography. to calculate the values of heat dissipation at crack tip an original data processing algorithms were developed. the algorithms include the relative motion compensation and spatial-time filtration procedures. as a t http://www.gruppofrattura.it http://dx.medra.org/10.3221/igf-esis.21.06&auth=true a. yu fedorova et alii, frattura ed integrità strutturale, 21 (2012) 46-53; doi: 10.3221/igf-esis.21.06 53 result of infrared data treatment we determine the key characteristics associated with the heat dissipation processes at the crack tip, which allowed us to propose method for determining the current values of the j-integral and sif. the sphere of applicability of this technique is wider than previously proposed methods for determining the sif based on the linear thermo-elasticity equations. the set of developed mathematical algorithms and methods of the experiment significantly increases the accuracy of the results compared with previously published studies [9], and allows us to develop in a future an engineering methods for analyzing the current crack state inside of real constructions in a wide range of applied loads. references [1] a geraci, g. la rosa, a. risitano, in: cres symposium, catania italy, (1984); published in: ata ingegneria automotoristica, 38(8-9) (1985). [2] m.p. luong, mech. mater.,28 (1988) 155. [3] a. risitano, g. risitano, theoretical and applied fracture mechanics, 54 (2010) 82. [4] a. a. shanyavskiy, bezopasnoe ustalostnoe razrushenie elementov aviakonstrukcii. sinergetika v ingenernih prilogeniyah [safe fatigue damage of aircraft construction elements. synergetics in engineering applications]. ufa, (2003) 803 [5] v. p. vavilov, diagnostika materialov, 72(3) (2006) 26. [6] m.p. luong, nuclear engineering and design., 158 (1995) 363. [7] o. plekhov, t. palin-luc, o. naimark, s. uvarov, n. saintier, fatigue and fracture of engineering materials and structures, 28(1) (2005) 169. [8] o. plekhov, n. saintier, t. palin-luc, s. uvarov, o. naimark, material science and engineering a, 462(1) (2007) 367. [9] m. bannikov, a. terekhina, o. plekhov, vestnik permskogo gosudarstvennogo tehnicheskogo universiteta. mehanika, 2 (2011) 14. [10] o. plekhov, technical physics, 56(2) (2011) 301. [11] nagahisa ogasawara, masaki shiratori, application of infrared thermography to fracture mechanics, spie digital library, 3056 (0277-786x/97), available at: http://spiedl.org/terms. http://www.gruppofrattura.it http://dx.medra.org/10.3221/igf-esis.21.06&auth=true microsoft word numero_35_art_22 s. blasón et alii, frattura ed integrità strutturale, 35 (2016) 187-195; doi: 10.3221/igf-esis.35.22 187 focussed on crack paths fatigue characterization of a crankshaft steel: use and interaction of new models sergio blasón, cristina rodríguez, alfonso fernández-canteli dept. of construction and manufacturing engineering, university of oviedo, spain blasonsergio@uniovi.es, cristina@uniovi.es, afc@uniovi.es abstract. the peculiar geometrical shape and working conditions of crankshafts make fatigue becoming responsible for most of the failure cases in such components. therefore, improvement of crankshaft performance requires enhancing its fatigue life. in this work, the fatigue behavior of a d38msv5s steel, used for crankshafts in compact vehicles, is investigated according to two traditional ways of analysis, namely the stress based and the fracture mechanics based approaches, though using advanced design models: on the one side, a probabilistic weibull regression s-n model is assessed for experimental results obtained from fatigue resonance tests. on the other side, the crack growth rate curve is calculated from crack growth tests, carried out on senb specimens, using a normalizing procedure. specific matlab programs are developed to facilitate the evaluation process. the information gained from both models will contribute to provide a probabilistic interpretation to the kitagawa-takahashi diagram. keywords. fatigue of crankshafts; crack growth rate curves; s-n diagram. introduction ue to the service conditions and its peculiar shape design, fatigue appears to be the main failure reason of crankshafts used in aeronautics and automotive engines [1]. consequently, big effort is devoted to investigate fatigue failures in crankshafts in order to enhance their fatigue life. generally, lifetime fatigue analysis is performed in two different ways: assuming no initial damage in the component or, alternatively, accepting the unavoidable presence of cracks. in the first case, the total lifetime is identified as initiation phase, at least for working loads. this estimation is usually performed by means of an adequate definition s-n field for the component. on its turn, in cracked components, the fatigue lifetime is only assigned to the propagation phase so that the lifetime is assessed based on fracture mechanics premises by determining the crack propagation law of fatigue cracks. although both approaches are often applied as being independent each other their interconnection is apparent so that their simultaneous consideration is advantageous from the point of view of reliability due to its complementary character. in former publications [2], the limitations of the paris law were pointed out in the definition of the crack growth rate curve as a power law sustained by incomplete self-similarity assumption [3]. its substitution by a crack growth rate law applicable even to δk values close to the δkth is advisable. in any case, dimensional inconsistencies, similar to those exhibited by the original paris equation, are a common feature in most of the models being presently applicable even with international acknowledgement, as those of forman, nasgro and many others [4]. d http://www.gruppofrattura.it/video/fis34/blason/video.html s. blasón et alii, frattura ed integrità strutturale, 35 (2016) 187-195; doi: 10.3221/igf-esis.35.22 188 in this work, the fatigue behavior of a steel d38msv5s, used in the manufacture of crankshafts of compact vehicles, is investigated according to the two approaches mentioned above: on the one hand, by defining the s-n field from the experimental data obtained in resonance fatigue tests using a probabilistic model [5,6], and by the other hand, by deriving the crack growth rate curve from senb specimens using the approach proposed in [7]. the latter represents an advance with respect to others models by providing an easy, normalized formulation of the crack growth rate curve as a cumulative distribution function by fulfilment of the dimensional requirements, whereby the value of the threshold stress intensity range appears as model parameter. moreover, under certain conditions of the geometric factor, a unique reference crack growth curve a-n is obtained, which allows any other crack growth curve by simple analytical transformation for different values of the initial crack size and stress range to be derived. understanding the theoretical fundamentals of the crack growth model as proposed in [7] facilitates the development of subroutines and their assembling into a practical program for general and comprehensible application of the crack growth rate curve irrespective of the initial crack size and applied load. further, a possible extension to the variable loading case is envisaged. derivation of propagation s-n curves is possible and, therefore, also of initiation lifetime curves once the conventional s-n field, representing the total fatigue life, is known. this will favor a future advance in what concerns the variability of the crack growth rate curves as well as the probabilistic concept of the kitagawa-takahashi diagram, nowadays still missed. evaluation of the s-n field irst, as mentioned in the former section, the probabilistic s-n field according to [5] was determined from the tests results carried out in a rumul testronic resonance machine using specimens taken out from the crankshaft axle, see fig. 1. the tests were carried out at different constant stress ranges,  for a constant stress rate r=mín /max= 1, for which the number of cycles until failure were registered. the test results pairs (, n) obtained are shown in tab. 1. considering the random character of the fatigue phenomenon a statistical analysis of the results is advisable to permit the definition of the s-n percentile curves representing the same probability of failure. this is achieved after estimation of the weibull model parameters using the profatige software program [6] whereby the run-outs are taking into account. the weibull model parameters fitted are included in tab. 2 with which, in this case, the probabilities p=0, 0.05, 0.50 and 0.95 were considered (see fig. 2). figure 1: specimen extraction and fatigue specimen geometry for resonance testing. the parameters b and c represent, respectively, the limit number of cycles and the fatigue limit, in the sense of true endurance limit for n→∞, that is, the value of the stress range below which fatigue does not occur. in this way, the problem consists in estimating, for given stress range, the number of cycles to failure at which failure is expected for the certain probability. f s. blasón et alii, frattura ed integrità strutturale, 35 (2016) 187-195; doi: 10.3221/igf-esis.35.22 189 initial lifetime (cycles) stress (mpa) length (mm) runout expected lifetime (cycles) 106483 450 53.88 518308 400 53.88 10000002 350 53.88 r 2.876e+10 21479001 380 53.88 r 8.496e+07 1297002 400 53.88 10000000 390 53.88 r 2.905e+07 133527 395 53.88 359216 395 53.88 10000000 395 53.88 r 2.449e+07 69554 425 53.88 974659 425 53.88 87004 395 53.88 298661 395 53.88 50698 437.5 54.88 112488 437.5 55.88 166587 412.5 56.88 table 1: fatigue results from the resonance tests. b c β δ λ 4.75 (115 cycles) 5.75 (312.7 mpa) 2.28 1.28 1.06 table 2: weibull model parameters from fitting of the s-n field. figure 2: s-n field assessment using the profatigue software [6]. s. blasón et alii, frattura ed integrità strutturale, 35 (2016) 187-195; doi: 10.3221/igf-esis.35.22 190 crack growth curves he specimens used in the tests for the derivation of the crack growth rate curve of the material were cut out from the crankshaft axle as shown in fig. 3. figure 3: extraction location and geometry of the specimens used in the crack growth tests. tests were carried out in accordance to the requirements of the astm-e1820 standard [8] and the compliance method was applied for determining the crack growth. fig. 4 represents the crack growth rate da/dn as a function of the stress intensity factor range δk. the test was performed under constant δf and stress rate r= -1. figure 4: crack growth rate curve from experimental data. model for crack growth rate curve he fracture mechanics based approach, based on the application of crack growth rate curves, can be applied as an alternative to the approach based on stresses, i.e., that being related to the s-n field, due to its more general applicability to lifetime prediction of mechanical and structural components. with the aim of interrelating both models in the study of propagation of macrocracks or even of physical microcracks, castillo et al. proposed to determine the crack growth rate curve based on a model [7], which considers the non-dimensional normalization of the stress intensity range factor according to the expression: * * * * * log log log log th up th k k k k k         (1) 10 2 10 -4 k [mpam1/2] d a /d n [ m m /c ic lo ] t t s. blasón et alii, frattura ed integrità strutturale, 35 (2016) 187-195; doi: 10.3221/igf-esis.35.22 191 in which kth represents the threshold stress intensity factor range and kup, is the upper bound of the stress intensity factor range, not necessarily identifiable with the failure stress intensity factor kf , see fig. 5. this proposal offers the advantage that the sigmoidal shape of the crack growth rate curve da/dn-k may be identified, analytically over its full existence range, as a cumulative distribution function, since k+ is a function growing up monotonically in the interval [0,1] (see fig. 5) taking so advantage of the statistical experience gained about this family of curves. the fact that the threshold stress intensity factor kth is estimated as one of the model parameter ensures higher reliability in the curve estimation and makes easier a further variability analysis, still pending. a possible option consists in assuming an extreme distribution either for maxima or for minima, taking into account the characteristics of the phenomenon. in this case, a gumbel distribution for minima [9] was searched so that a reliable fitting of the normalized crack growth rate curve is achieved from the experimental results. an important question lies in the interpretation of the fatigue life resulting from the integration of the crack growth rate curve that corresponds rather to the propagation life than to the total fatigue life. the identification of the crack growth rate curve as a cumulative distribution function in which δk+ is identified as the normalizing variable defined in the interval [0,1] leads to the consideration of log (da/dn) as being the random variable. accordingly, the following equation must be used to fit the experimental results: * ** * * * * * log log log log 1 exp log log th up th da dnk k da f exp k k dn                                    (2) the proposed model provides an analytical expression to the normalized crack growth rate curve by fitting the experimental results referred to crack size vs. number of cycles using a minimum square error method, see [7]. fitting of the curve succeeds by minimizing the function q (α, γ, δkth*, δkup*):   2 * * * * * * 1 log log log log log  1 exp n i ith up th i da dn q k k k k exp                                               (3) with respect to those parameters, where α and γ are the location and the scale gumbel parameters, and δkth*, δkup* the normalized values of δkth, δkup , respectively. the formulation of a transcendent theorem proves that assuming certain premises concerning the function representing the geometric crack factor y(a), a reference crack growth curve a-n may be obtained using a unique integration allowing any other a-n curve, corresponding to a given pair of values for the initial crack size ao and the remote stress range applied δσ, to be derived. once the parameters are found from the experimental results obtained, the curves defining the normalized crack growth, a*(n*) can be determined by solving the differential eq. (4) that provides a particular solution for a given initial crack size a0* and a particular stress range, δσ*.  * * *1 * * * log  log log log th up th da n u k exp f dn k k                (4) where u=δσ*z(a*(n*)). the z function represents a transformation of the function defining the geometric crack factor being given by:       * * * * * * z a y a n п a n (5) s. blasón et alii, frattura ed integrità strutturale, 35 (2016) 187-195; doi: 10.3221/igf-esis.35.22 192 this function can adopt, alternatively one of the following forms:       * * * exp qa t z a t ua      (6) where t, u, q and ρ in former expression are constants to be determined by fitting the function z. after proceeding in this way, it is possible to determine the reference crack growth curve a*-n* from which, in turn, any other crack growth curve can be obtained for the given initial crack size and stress range. finally, the s-n field for crack propagation can be derived proving the relation existing between the stress based approach and that based on fracture mechanics on a probabilistic basis. figure 5: a) original and b) normalized crack growth rate [7]. the decision for selecting the initial crack size in order to proceed to the calculation of the fatigue life propagation can be adopted on the base of probabilistic considerations relative to the distribution of the cracks provided by the possible correspondence between the s-n curves and those referred to the crack growth a-n. indeed, some questions remain unsolved, among them the following can be referred to: a) the experimental verification of the model, which is, at least partially, one of the contributions of this work, b) the interpretation of the s-n field as composed by the initiation and propagation lives, and c) the possibility of considering a fictitious microcrack size, which allows the correspondence between both fatigue lives, i.e. between the one determined from the s-n field and that resulting from the integration of the crack growth rate curve, to be determined. on its turn, the crack growth rate curve provides a direct relation between the initial crack size and its progression till failure. in this way, k presents the advantage, or perhaps disadvantage, of coupling crack size a and stress range  as a unique parameter apparently related to the crack micromechanism. nevertheless, the interpretation of the results is less apparent since the same k can be arise from different combinations of crack size and stress range whereas notable differences are observed in the behavior according to the characteristics of the crack size (macrocracks and microcracks in the two variants, physical and microstructural): therefore the interest consists in relating crack size and crack growth rate curve to the s-n field where both parameters are uncoupled. derivation of the propagation s-n curves from the crack growth curve n the development of this section, the methodology proposed in [7] has been applied step by step. aselection of the normalizing variables first of all, the participating variables are normalized according with the values shown in tab. 3. w [mm] kic [mpa m1/2] n0 [cycles] 22 89.26 1000 table 3: values of the normalizing variables. i s. blasón et alii, frattura ed integrità strutturale, 35 (2016) 187-195; doi: 10.3221/igf-esis.35.22 193 bminimization of function q thereafter, the parameters fitting the crack growth rate curve are determined from the experimental data (see tab. 4). α γ log(δkth*) log(δkup*) -3.7462 1.9224 -1.7159 0.5721 table 4: parameter values found by fitting the crack growth rate curve as a cumulative distribution function. fig. 6 exhibits the normalized values for log(δk*) vs. log(da*/dn*) along with the curve fitting obtained after minimization. figure 6: representation of the normalized experimental data and fitting obtained. cobtaining crack growth curves figs. 7 and 8 represent the result of the integration of expr. (4), firstly for different initial crack sizes a0* when maintaining a fixed value for the non-dimensional stress range, δσ*. figure 7: curves a*-n* for different initial crack sizes a0*, while maintaining constant δσ*. figure 8: a*-n* curves for different stress ranges, δσ*, while maintaining the initial crack size, a0* constant the integration follows after fitting the geometric factor to the first expression in (6). fig. 9 illustrates the fit obtained for the geometrical crack factor in the specimen 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 -16 -14 -12 -10 -8 -6 -4 -2 0 2 g log(k*) lo g (d a */ d n *) 0 100 200 300 400 500 600 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9  0 =141[mpa] normalized number of cycles, n* n o rm a li ze d c ra c k l e n g th , a * a 0 =3.4 mm a 0 =3.6 mm a 0 =4.0 mm a 0 =4.5 mm 0 50 100 150 200 250 300 350 400 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 normalized number of cycles, n* n o rm a li ze d c ra c k l e n g th , a * a 0 =3.4 [mm]  =136 mpa  =146 mpa  =171 mpa  =196 mpa s. blasón et alii, frattura ed integrità strutturale, 35 (2016) 187-195; doi: 10.3221/igf-esis.35.22 194 figure 9: fitting of function z(a*). dderivation of the s-n field finally, the s-n field in propagation can be derived from former information using expr. (7). fig. 10 shows the s-n field in which both axes representing non-dimensional variables. the information gained from both models, that is that representing the probabilistic s-n field and that related to the crack growth rate curve as proposed here, provide a basis for the probabilistic interpretation to the kitagawa-takahashi diagram [10]. first, it seems possible to assign crack sizes to iso-probabilistic curves in the s-n field, making use of the el haddad equation, and second, the asymptotic character of the s-n field allow a true endurance limit to be defined, thus extending the concept and application of the kitagawa-takahashi diagram for finite number of cycles (limited propagating cracks) and infinite number of cycles (non-propagating cracks) according to the asymptotic value of the fatigue limit for n→ ∞. finally, the study of variability of the crack growth rate curve is facilitated by the normalizing concept that includes the consideration of the threshold stress intensity factor δkth as a model parameter. figure 10: s-n field in propagation as derived from the crack growth curves. conclusions he main conclusions derived from this work are: the validity of the methodology proposed is confirmed for fitting experimental data to the crack growth rate curve of one steel used for crankshafts. also the crack growth curves a-n curves for different initial crack size values and load, or remote stress range. this opens new perspectives for the crack growth prediction under variable loading. the derivation of the s-n requires further study in order to solve scale problems observed. 0.2 0.3 0.4 0.5 0.6 0.7 1 1.5 2 2.5 3 3.5 4 4.5 5 a* geometric factor according to standard fit z(a*) 0 5 10 15 x 10 4 0 50 100 150 200 250 300 n [cycles]   [ m p a ] a 0 =3.4 mm a 0 =3.6 mm a 0 =4.0 mm a 0 =4.5 mm t s. blasón et alii, frattura ed integrità strutturale, 35 (2016) 187-195; doi: 10.3221/igf-esis.35.22 195 matlab subroutines for any of the procedures used here were developed in order to facilitate the application to practical cases and will be offered as free program in a next future. references [1] infante, v., silva, j.m., silvestre, m.a.r., baptist, r., failure of a crankshaft of an aeroengine: a contribution for an accident investigation, engineering failure analysis, 35 (2013) 286-293. [2] fernández-canteli, a., przybilla, c., lópez-aenlle, m.,castillo, e., un análisis crítico sobre algunos modelos tradicionales de la mecánica de fatiga, anales de mecánica de la fractura, (2014) 111-116. [3] barenblatt, g.i., scaling, selfsimilarity,and intermediate asymptotics, cambridge university press, new york (1996). [4] fkm-guideline, fracture mechanics proof of strength for engineering components, vdma verlag, frankfurt/main (2009). [5] castillo e., fernández-canteli a., a unified statistical methodology for modeling fatigue damage, springer, berlin (2009). [6] fernández canteli, a., przybilla, c., nogal, m., lópez aenlle, m., castillo, e., profatigue: a software program for probabilistic assessment of experimental fatigue data sets, procedia engineering, 17th icmfm, verbania (2014), 2527. [7] castillo, e., fernández canteli, a., siegele, d., obtaining s-n curves from crack growth curves. an alternative to selfsimilarity, int. j. of fracture, 187(1) (2014) 159-172. [8] astm-e1820, standard test method for measurement of fracture toughness. [9] castillo, e., hadi, a.s., balakrishnan, n., sarabia, j.m., extreme value and related models with applications in engineering and science. wiley series in probability and statistics, hoboken , n. j., (2005). [10] fernández-canteli a., brighenti r., castillo e. towards a probabilistic concept of the kitagawa-takahashi diagram. proceedings of the 4th conference on crack paths, gaeta, (2012) 1041-1048. << /ascii85encodepages false /allowtransparency false /autopositionepsfiles true /autorotatepages /none /binding /left /calgrayprofile (dot gain 20%) /calrgbprofile (srgb iec61966-2.1) /calcmykprofile (u.s. web coated \050swop\051 v2) /srgbprofile (srgb iec61966-2.1) /cannotembedfontpolicy /error /compatibilitylevel 1.4 /compressobjects /tags /compresspages true /convertimagestoindexed true /passthroughjpegimages true /createjobticket false /defaultrenderingintent /default /detectblends true /detectcurves 0.0000 /colorconversionstrategy /cmyk /dothumbnails false /embedallfonts true /embedopentype false /parseiccprofilesincomments true /embedjoboptions true /dscreportinglevel 0 /emitdscwarnings false /endpage -1 /imagememory 1048576 /lockdistillerparams false /maxsubsetpct 100 /optimize true 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can be opened with acrobat and adobe reader 5.0 and later.) >> /namespace [ (adobe) (common) (1.0) ] /othernamespaces [ << /asreaderspreads false /cropimagestoframes true /errorcontrol /warnandcontinue /flattenerignorespreadoverrides false /includeguidesgrids false /includenonprinting false /includeslug false /namespace [ (adobe) (indesign) (4.0) ] /omitplacedbitmaps false /omitplacedeps false /omitplacedpdf false /simulateoverprint /legacy >> << /addbleedmarks false /addcolorbars false /addcropmarks false /addpageinfo false /addregmarks false /convertcolors /converttocmyk /destinationprofilename () /destinationprofileselector /documentcmyk /downsample16bitimages true /flattenerpreset << /presetselector /mediumresolution >> /formelements false /generatestructure false /includebookmarks false /includehyperlinks false /includeinteractive false /includelayers false /includeprofiles false /multimediahandling /useobjectsettings /namespace [ (adobe) (creativesuite) (2.0) ] /pdfxoutputintentprofileselector /documentcmyk /preserveediting true /untaggedcmykhandling /leaveuntagged /untaggedrgbhandling /usedocumentprofile /usedocumentbleed false >> ] >> setdistillerparams << /hwresolution [2400 2400] /pagesize [612.000 792.000] >> setpagedevice microsoft word numero_37_art_17 v. anes et alii, frattura ed integrità strutturale, 37 (2016) 124-130; doi: 10.3221/igf-esis.37.17 124 focussed on multiaxial fatigue and fracture on the assessment of multiaxial fatigue damage under variable amplitude loading v. anes, l. reis, m. de freitas idmec, instituto superior técnico, universidade de lisboa, av. rovisco pais, 1049-001 lisboa, portugal. vitor.anes@tecnico.ulisboa.pt, http://orcid.org/0000-0002-8526-398x luis.g.reis@tecnico.ulisboa.pt, http://orcid.org/0000-0001-9848-9569 manuel.freitas@tecnico.ulisboa.pt, http://orcid.org/0000-0003-3525-9218 abstract. in this work, the performance of the ssf criterion is evaluated under variable amplitude loading conditions. the main objective was to inspect the validity of the hypothesis in which the ssf damage map remains valid for any high strength steel. in order to achieve that, fatigue life correlation of the 1050qt steel and 304l stainless steel was analyzed under multiaxial loading conditions. the loading block considered in the study comprises 360 proportional loading cycles with different stress amplitude ratios and stress levels. despite being made of proportional branches, this loading block is a non-proportional loading due to its principal directions variation. this feature allows the evaluation of combined loading effects under variable amplitude loading conditions, which makes this loading block suitable to mimic the loading effects usually found in the field. results show very good agreements, which reinforces the aforementioned hypothesis. keywords. multiaxial fatigue; variable amplitude loading; multiaxial cycle counting method; fatigue life; damage accumulation. introduction n the field, random loadings are the most common type of load that we can find; typical examples can be found in car suspensions, aircraft wings or wind towers. this type of loadings is complex and difficult to deal with, specially their simulation in the lab. also, their stochastic behavior increases the variability usually found in fatigue life experiments, which increases the complexity in damage accumulation assessment. they may have several loading effects that are usually studied separately in literature, however their combined effect can be activated simultaneously or sequentially under random loading conditions [1, 2]. loading effects such as proportionality, non-proportionality, cyclic hardening, cyclic softening, mean stress, sequential and asynchronous loading, among others effects, cause different well known damage mechanisms [3-7], but their combined effect remains more or less unknown. nowadays, there is a lack of knowledge in this matter and further research is required. this subject becomes extremely important when the assessment of instantaneous damage accumulation is required, such as in structural health monitoring procedures. currently, the assessment of fatigue damage is not only performed in mechanical design stages, but also in structural integrity evaluation performed in the field. for example, damage accumulation tools can support on-condition maintenance decisions in order to optimize inspections and replacement costs. in the lab, the most common approach to simulate random loadings is to load pre-defined loading blocks in a randomly way. thus, multiaxial fatigue models must be able to evaluate fatigue damage from variable amplitude loadings such as the ones found in multiaxial loading blocks. in this work, the present authors study the capability of the ssf criterion to capture fatigue damage under variable amplitude loading, which is a i v. anes et alii, frattura ed integrità strutturale, 37 (2016) 124-130; doi: 10.3221/igf-esis.37.17 125 fundamental prerequisite to estimate fatigue damage under random loading conditions. the main focus was on the hypothesis that states the existence of a typical ssf damage map for each material family. theory, materials and methodology ased on experiments the present authors have found out that fatigue damage from normal stresses have a damage scale different from the one found in shear stresses, especially under multiaxial loading conditions. therefore, to compute a multiaxial damage parameter, both normal and shear stresses must be reduced to the same damage scale. in literature, this reduction is commonly performed using a constant; usually this constant is a function of uniaxial fatigue limits. however, results show that the damage scale between normal and shear stresses depends on the stress amplitude ratio  , and also on the stress level [8]. to account these findings in fatigue damage assessment, the present authors developed the ssf equivalent shear stress. this damage parameter is an equivalent shear stress, were its magnitude represents the fatigue damage of a given multiaxial loading. eq. (1) shows the ssf model; in the left the ssf equivalent shear stress and at right the uniaxial shear sn curve [8].     max , b a f block ssf a n      (1) the  ,assf   function shown in eq. (1) is given in eq. (2), this function is the so-called ssf damage map and aims to update the damage scale of normal stresses to the shear damage scale.                        2 3 2 3 4 5,a a a assf a b c d f g h i (2) where  a is the normal stress component of a given biaxial loading and  is the stress amplitude ratio ( a a   ). the polynomial constants “ a ” to “ i " are determined through experiments. the values of these constants for the 42crmo4 steel are the following:       a=2.69; b= 9.90e 03; c=1.69e 05; d= 9.52e 09; f= 5.99; g=11.72; h= 8.04; i=1.63 generalization of the ssf damage map the ssf damage map, given by the 5th polynomial function shown in eq. (2) was obtained for the 42crmo4 material and translates its cyclic behavior under different stress amplitude ratios and stress levels. therefore, the ssf fatigue estimates for other materials must be done using their ssf damage maps, which must be previously obtained by experiments. however, within a given steel family it has been assumed that the ssf damage map does not vary significantly, thus the ssf damage map computed for a given material of this family can be used as a typical ssf damage map and can be shared between material of this family. this assumption has been tested with success in two high strength steels, the ck45 and c40, and is tested here with the 1050qt and 304l steels. the 1050qt clearly belongs to the 42crmo4 family because their mechanical properties are very alike; please see tab. 1. however, the mechanical properties of the 304l stainless steel are clearly out of the high strength steels family [9], thus it is expected a lower performance in the ssf fatigue life correlations for this material. the use of the 42crmo4 ssf damage map in other materials is not performed directly, in these cases the ssf damage map must be updated using the tensile ultimate stresses as shown in eq. (3). ,42 4 ( , )ueq u crmo ssf                  (3) where   ,42 4u u crmo is the ratio between the material’s ultimate tensile stress (material that belongs to the 42crmo4 family but its ssf damage map is unknown) and the ultimate tensile stress of the 42crmo4 steel. the ultimate stress is a mechanical parameter that indicates clearly the steel family and has been used to estimate sn curves. thus being the ssf damage map obtained based on the material sn curves under different stress amplitude ratios the use of the ultimate stress to perform this update was hypothesized and presented in [9]. b v. anes et alii, frattura ed integrità strutturale, 37 (2016) 124-130; doi: 10.3221/igf-esis.37.17 126 multiaxial cycle counting constant amplitude loadings are well characterized by its maximum damage parameter found within the loading pattern. however, in cases of variable amplitude loadings the maximum value of a given damage parameter do not captures the overall damage. in order to overcome this drawback, the present authors developed the virtual cycle counting method, which is a non-rainflow cycle counting method for multiaxial loading conditions [10]. the virtual cycle counting (vcc) is based on the time evolution of the ssf equivalent shear stress and is given through eq. (4).       , ssf,max,2 ssf peak valley block abs vcc (4) where vcc can be understood as a virtual loading cycles calculation. in order to estimate the fatigue life of a given loading block using the ssf criterion, it is necessary to divide the fatigue life estimate, obtained with the maximum ssf equivalent stress found within the loading block, by the virtual cycle counting yield by eq. (4). multiaxial loading path fig. 1 depicts the normal and shear stress time evolution of the loading path studied here, as well as, its representation on the von mises stress space. this loading path is a non-proportional loading block made of 360 proportional loading paths loaded sequentially with a 1º degree gap between them. figure 1: fri loading path [11, 12]: a) normal stress time evolution, b) shear stress time evolution c) loading path depicted in the von mises stress space. v. anes et alii, frattura ed integrità strutturale, 37 (2016) 124-130; doi: 10.3221/igf-esis.37.17 127 the loading sequence starts with a stress amplitude ratio equal to zero and evolves in the anticlockwise direction until reach again the starting position. this loading path was firstly described in [11] and is a variable amplitude loading that activates all loading planes with the same equivalent stress amplitude during the block loading, please see fig. 1 c). materials in this study two different materials were considered to analyze the performance of the ssf equivalent shear stress under variable amplitude loadings. they are the 1050qt high strength steel and the 304l stainless steel. the 1050qt steel is a quenched and tempered medium-carbon steel and is usually used in forged shafts and gears. the 304l stainless steel has its applications in chemical processing, pulp and paper mills and food industry. tab. 1 shows the monotonic and cyclic properties of the 1050qt and 304l steels. in addition, in column 2, the 42crmo4 mechanical properties are shown, the ssf damage map used in this study was obtained for this material. as one can see, the 42crmo4 and 1050qt mechanical properties are very alike, this similarity suggests that the 42crmo4 ssf damage map can be fairly used to estimate the 1050qt ssf damage map. 42crmo4 1050qt 304l young's modulus, e (gpa) 206 203 195 yield strength, (mpa) 980 1009 208 ultimate tensile strength, (mpa) 1100 1164 585 fatigue strength coefficient, (mpa) 1154 1346 1287 fatigue strength exponent -0.061 -0.062 -0.145 table 1: 42crmo4, 1050 qt and 304l stainless steel mechanical properties [8, 11, 12]. fatigue life tab. 2 shows the stress levels of normal and shear stresses and their inherent fatigue life for the 1050qt steel and the 304l stainless steel. the fatigue life is shown in number of loading reversals. these experiments were performed under strain control and the failure condition was 20% drop in the testing stress level [11]. 1050qt 304l sigma max [mpa] tau max [mpa] 2nf sigma max [mpa] tau max [mpa] 2nf 724 413 3240 459 271 3960 751 432 4536 461 262 4176 632 374 29520 391 224 20160 620 364 64800 362 210 38160 table 2: 1050qt and 304l fatigue life experimental results [11]. results and discussion ig. 2 a) shows the ssf equivalent shear stress time evolution for the fri loading block. this example is for the 1050qt material and for the maximum values of normal and shear stresses equal to 724 mpa and 413 mpa, respectively. the ssf time evolution depicted in fig. 2 a) has 360 fully reversed loading cycles with variable amplitude and lead to a fatigue life equal to 3240 reversals, (please see first row of tab. 2). as it can be seen in eq. (1), the maximum value found in the ssf time evolution is used, as a first iteration, to estimate the block fatigue life (i.e., the number of block repetitions before failure). in the second iteration, the first block fatigue life estimate (shown in eq. (5) as maxtn ) is updated with the virtual cycle counting computed for the fri loading block using eq. (4), please see eq. (5). f v. anes et alii, frattura ed integrità strutturale, 37 (2016) 124-130; doi: 10.3221/igf-esis.37.17 128 max _ t f block n n vcc  (5) thus, it is expected that the fatigue failure will occur at _f blockn block repetitions. fig. 2 b) shows the ssf equivalent loading block (equivalent to the fri loading block) with a constant amplitude loading equal to 638 mpa, the ssf equivalent loading block has 300 loading cycles instead of the 360 cycles found in the fri loading block. figure 2: a) ssf equivalent stress time evolution for the fri loading path (360 fully reversals), b) constant amplitude ssf loading block (300 fully reversals). loading block results tabs. 3 and 4 show the results for the ssf fatigue life estimates, cycle counting, and number of block repetitions before failure. the experimental block results shown in the fourth column were obtained by dividing the number of experimental reversals at failure by 360 (360 proportional loadings found within the fri loading block), this result shows the number of block repetitions during experiments at each stress level. the 5th column shows the ssf fatigue life estimates in number of reversal at failure time, these results were obtained using the material uniaxial shear sn curve. the 6th column shows the number of virtual loading cycles obtained with eq. (4) for the fri loading block. the virtual cycle counting results in both materials were equal to 300 virtual loading cycles. thus the fatigue damage of the 360 proportional loading cycles found in the fri loading block is estimated by 300 virtual loading cycles with constant amplitude. this amplitude is given by the maximum ssf equivalent shear stress found within the loading block. thus, the number of ssf loading blocks loaded before failure, shown in column 7, are obtained by dividing the number of loading cycles estimated by the ssf equivalent stress (shown in column 5 of tabs. 3 and 4) and the number of virtual loading cycles computed for the fri loading block. sigma max [mpa] tau max [mpa] 2nf [11] exp blocks ssf 2nf vcc ssf blocks 724 413 3240 4,5 4617 300 8 751 432 4536 6,3 3070 300 5 632 374 29520 41 38718 300 65 620 364 64800 90 54587 300 91 table 3: 1050qt loading block results. sigma max [mpa] tau max [mpa] 2nf [11] exp blocks ssf 2nf vcc ssf blocks 459 271 3960 5,5 2926 300 5 461 262 4176 5,8 3419 300 6 391 224 20160 28 7927 300 13 362 210 38160 53 11291 300 19 table 4: 304l loading block results. v. anes et alii, frattura ed integrità strutturale, 37 (2016) 124-130; doi: 10.3221/igf-esis.37.17 129 thus, the fri loading path (a variable amplitude loading) can be replaced by a constant amplitude loading using the ssf equivalent shear stress, and the virtual cycle counting method. this is particularly useful when one have loadings made of different loading blocks, which is may be the case of random loadings. random loadings can be discretized into loading blocks [1] and treated as a damage accumulation case, however multiaxial criteria used in damage accumulation procedures must be able to capture fatigue damage of variable amplitude loadings. fig. 3 depicts the fatigue life correlation for the two materials considered in this study. these results show that the 42crmo4 damage map is suitable for high strength steels, which confirms previous studies performed by the present authors [9]. these results are reinforced by the 1050qt correlation pattern where the correlation slope is parallel to the boundary lines please see fig. 3. on the other hand, the correlation slope of the 304l steel is quite different from the slope of the boundary lines, i.e. the correlation trend line of the 304l fatigue data crosses the lower boundary lines. this indicates that the damage map of the 42crmo4 high strength steel do not capture in full the 304l fatigue pattern, which is a result expected by the present authors. stainless steels are extremely sensitive to non-proportionality and show strong variation of their mechanical properties under cyclic loadings. thus their cyclic behavior is quite different from the one that is usually found in high strength steels. figure 3: ssf fatigue life correlation for the 1050qt and 304l steels. conclusions he present study evaluates the performance of the ssf criterion under variable amplitude loading for two different materials, i.e. the 1050qt steel and the 304l stainless steel. the idea was to inspect the validity of the 42crmo4 ssf damage map for other materials under variable amplitude loading conditions. the present authors have been using the 42crmo4 ssf damage map in fatigue life predictions of high strength steels with success; examples are the ck45 and c40 steels. the main focus of the ssf criterion has been on the idea that the damage scale of normal and shear stresses of a given multiaxial loading is not constant. this damage scale is strongly dependent on the stress level and stress amplitude ratio and can be evaluated with the so-called ssf damage map. in this paper, results confirm the validity of the 42crmo4 ssf damage map for high strength steels, as seen in the obtained results for the 1050qt steel. this steel has mechanical properties very close to the 42crmo4 properties, in some of them the 1050qt has higher values, thus it can be considered that both materials belong to the same steel family. based on the results found here and based on previous results computed for the ck45, and c40 high strength steels, it can be considered that a ssf damage map can be defined for each material family. to reinforce this, the results for the 304l stainless steel where not so good, which indicates the necessity to obtain the ssf damage map for this steel family. t v. anes et alii, frattura ed integrità strutturale, 37 (2016) 124-130; doi: 10.3221/igf-esis.37.17 130 acknowledgements his work was supported by fct, through idmec, under laeta project uid/ems/50022/2013. references [1] anes, v., reis, l., de freitas, m., a new criterion for evaluating multiaxial fatigue damage under multiaxial random loading conditions, advanced materials research, 181 (2014) 1360–1365. doi:10.4028/www.scientific.net/amr.891892.1360. [2] wang, y., susmel, l., the modified manson–coffin curve method to estimate fatigue lifetime under complex constant and variable amplitude multiaxial fatigue loading, international journal of fatigue, 83 (2016) 135–49. doi:10.1016/j.ijfatigue.2015.10.005. [3] chaves, v., navarro, a., madrigal, c., stage i crack directions under in-phase axial–torsion fatigue loading for aisi 304l stainless steel, international journal of fatigue, 80 (2015) 10–21. doi:10.1016/j.ijfatigue.2015.05.004. [4] chaves, v., madrigal, c., navarro, a., biaxial fatigue tests and crack paths for aisi 304l stainless steel, frattura ed integritá strutturale, 30 (2014) 273. doi: 10.3221/igf-esis.30.34. [5] carpinteri, a., ronchei, c., spagnoli, a., vantadori, s., lifetime estimation in the low/medium-cycle regime using the carpinteri–spagnoli multiaxial fatigue criterion, theoretical and applied fracture mechanics, 73 (2014) 120–127. doi:10.1016/j.tafmec.2014.06.002. [6] carpinteri, a., ronchei, c., scorza, d., vantadori, s., critical plane orientation influence on multiaxial high-cycle fatigue assessment, physical mesomechanics. 18 (2015) 348–54. doi:10.1134/s1029959915040074. [7] campagnolo, a., berto, f., marangon, c., cyclic plasticity in three-dimensional notched components under in-phase multiaxial loading at r=1, theoretical and applied fracture mechanics, 81 (2016) 76–88. doi:10.1016/j.tafmec.2015.10.004. [8] anes, v., reis, l., li, b., fonte, m., de freitas, m., new approach for analysis of complex multiaxial loading paths, international journal of fatigue, 62 (2014) 21–33. doi:10.1016/j.ijfatigue.2013.05.004. [9] anes, v., reis, l., li, b., freitas, m., sonsino, c.m., minimum circumscribed ellipse (mce) and stress scale factor (ssf) criteria for multiaxial fatigue life assessment, theoretical and applied fracture mechanics, 73 (2014) 109–19. doi:10.1016/j.tafmec.2014.08.008. [10] anes, v., reis, l., li, b., de freitas, m., new cycle counting method for multiaxial fatigue, international journal of fatigue, 67 (2014) 78–94. doi:10.1016/j.ijfatigue.2014.02.010. [11] shamsaei, n., (2010). phd thesis, univ. of illinois at urbana-champaign, usa. [12] shamsaei, n., fatemi, a., socie, d.f., multiaxial fatigue evaluation using discriminating strain paths, international journal of fatigue, 33 (2011) 597–609. doi:10.1016/j.ijfatigue.2010.11.002. t << /ascii85encodepages false /allowtransparency false /autopositionepsfiles true /autorotatepages /none /binding /left /calgrayprofile (dot gain 20%) /calrgbprofile (srgb iec61966-2.1) /calcmykprofile (u.s. web coated \050swop\051 v2) /srgbprofile (srgb iec61966-2.1) /cannotembedfontpolicy /error /compatibilitylevel 1.4 /compressobjects /tags /compresspages true /convertimagestoindexed true /passthroughjpegimages true /createjobticket false /defaultrenderingintent /default /detectblends true /detectcurves 0.0000 /colorconversionstrategy /cmyk /dothumbnails false /embedallfonts true /embedopentype false /parseiccprofilesincomments true /embedjoboptions true /dscreportinglevel 0 /emitdscwarnings false /endpage -1 /imagememory 1048576 /lockdistillerparams false /maxsubsetpct 100 /optimize 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can be opened with acrobat and adobe reader 5.0 and later.) >> /namespace [ (adobe) (common) (1.0) ] /othernamespaces [ << /asreaderspreads false /cropimagestoframes true /errorcontrol /warnandcontinue /flattenerignorespreadoverrides false /includeguidesgrids false /includenonprinting false /includeslug false /namespace [ (adobe) (indesign) (4.0) ] /omitplacedbitmaps false /omitplacedeps false /omitplacedpdf false /simulateoverprint /legacy >> << /addbleedmarks false /addcolorbars false /addcropmarks false /addpageinfo false /addregmarks false /convertcolors /converttocmyk /destinationprofilename () /destinationprofileselector /documentcmyk /downsample16bitimages true /flattenerpreset << /presetselector /mediumresolution >> /formelements false /generatestructure false /includebookmarks false /includehyperlinks false /includeinteractive false /includelayers false /includeprofiles false /multimediahandling /useobjectsettings /namespace [ (adobe) (creativesuite) (2.0) ] /pdfxoutputintentprofileselector /documentcmyk /preserveediting true /untaggedcmykhandling /leaveuntagged /untaggedrgbhandling /usedocumentprofile /usedocumentbleed false >> ] >> setdistillerparams << /hwresolution [2400 2400] /pagesize [612.000 792.000] >> setpagedevice microsoft word numero_35_art_36 s. boljanović et alii, frattura ed integrità strutturale, 35 (2016) 313-321; doi: 10.3221/igf-esis.35.36 313 focussed on crack paths fatigue failure analysis of pin-loaded lugs slobodanka boljanović mathematical institute-the serbian academy of sciences and arts, kneza mihaila 36, belgrade, serbia slobodanka.boljanovic@gmail.com stevan maksimović vti-aeronautical department, ratka resanovića 1, belgrade, serbia s.maksimovic@open.telekom.com abstract. in the present paper, mathematical models are proposed in order to analyze the strength of pinloaded lugs with semi-elliptical crack and through-the-thickness crack. the crack growth investigation of considered crack configurations tackles the fatigue life evaluation and the crack path simulation of semi-elliptical crack. the residual strength is estimated by applying the two-parameter driving force model. the numerical and analytical approaches are employed for the stress intensity factor calculation. experimental fatigue crack growth data are used in order to verify efficiency of the developed models. a good correlation between fatigue crack growth estimations and experimental observations is obtained. keywords. cyclic loading; strength estimation; crack path; semi-elliptical crack at a hole; fem. introduction erospace systems can realize their stationary and moving operational duties through the load transfer assembly known as lug-type joint. in such linkage under cyclic loading, the high stress concentration, contact pressure and fretting can lead to the crack initiation, crack growth and even catastrophic failure. consequently, for safety design and exploitation of the fracture critical pin-loaded lug is significantly important the development of reliable computational models. fatigue and fracture strength estimations related to the damaged lug demand accurate evaluation of both, the stress state field around the crack tip and the stress intensity factor. in the literature, a variety of methods have been employed to calculate the stress intensity factor either of planar crack or through-the-thickness crack configurations. thus, the propagation process of such crack situations can be theoretically investigated by applying the following approaches: approximate analytical methods [1, 2], weight function [3, 4], finite element method [5, 6], finite element alternating method [7, 8]. within the context of fracture mechanics, the failure analysis under cyclic loading can be realized through appropriate crack growth laws. paris and erdogan [9] experimentally investigated the propagation process, and found that the crack growth is depended on the applied stress intensity range. then, forman [10] suggested that the stress ratio and the fracture toughness together with the stress intensity factor range can be used to describe the crack propagation under cyclic loading. weertman [11] recognized that the crack growth can be consider if the maximum stress intensity factor are include together with the facture toughness and the stress intensity factor range. further, elber [12] suggested that the a s. boljanović et alii, frattura ed integrità strutturale, 35 (2016) 313-321; doi: 10.3221/igf-esis.35.36 314 stress ratio can be taken into account by the effective stress intensity factor range instead of the stress intensity range and developed the crack closure model. based on observations related to the crack propagation under cyclic loading, walker [13] proposed his stress-ratio dependence crack growth model. kujawski [14] found that the crack growth propagation under cyclic loading can be simulated if the maximum stress intensity factor is involved, and introduced the twoparameter driving force model. noroozi et al [15] took into account the combination of the maximum stress intensity factor and the stress intensity factor range together with the elastic-plastic crack tip stress-strain field and proposed a unified two-parameter crack growth model. in the present paper, computational models are formulated for the strength estimation of the damaged lug. the propagation of semi-elliptical crack emanating from the lug hole is investigated through the following issues: the stress analysis, the fatigue life evaluation and the crack path simulation. the two-parameter driving force crack growth model is applied for the failure analysis of lug under cyclic loading. the stress intensity factor is calculated by applying the finite element method and/or analytical approach. the predictive capability of proposed models is verified through the comparison between the calculations and experimental data. fatigue life estimation uring exploitation of cyclically loaded structural components, complex fatigue process could often lead to the unexpected failure. the crack propagation can be theoretically investigated through the cyclic rate of crack growth either in one direction (through-the-thickness crack) or in two directions (surface crack). in the present paper, the two-parameter driving force model proposed by kujawski [14] is employed in order to simulate the propagation process under cyclic loading. since the semi-elliptical crack is considered, the variation of crack shape can be evaluated from the crack growth rates at two positions on the crack front: the crack growth rate da/dn at the deepest point a (crack depth), and crack growth rate db/dn at point b on the lug surface (crack length), as follows:  * amaa da c k dn   ;  0.5* maxa ia ak k k    (1a)  * bmbb db c k dn   ;  0.5* maxb ib bk k k    (1b) where: a iak k   and b ibk k   for 0r  , and if 0r  , maxa iak k   and maxb ibk k   . then, the number of loading cycles up to failure for both directions can be calculated if above relationships related to the crack growth rate are integrated i.e.:  0 * f a a m a a a da dn c k    (2a)  0 * f b b m b b b db dn c k    (2b) where ca, cb, ma and mb are material constants experimentally obtained, n denotes the number of loading cycles up to failure, r is the stress ration, kia, kib, and kia max, kib max represent the stress intensity factor ranges and maximum stress intensity factor under mode i loading conditions for depth and surface directions, respectively, a0, b0, and af, bf denote initial and final crack length in depth and surface directions, respectively. since awkward functions exist in eqs. (2a) and (2b), the residual life for appropriate incremental crack lengths in depth and surface direction can be estimated if the numerical integration is employed, and for that purpose the present authors developed the software programme based on euler’s algorithm. d s. boljanović et alii, frattura ed integrità strutturale, 35 (2016) 313-321; doi: 10.3221/igf-esis.35.36 315 stress intensity factor calculation n order to estimate the fracture strength and fatigue lives of engineering components, significantly important parameter is the stress intensity factor due to the fact that it includes the geometry, material and loading conditions. as the pin-loaded lug with semi-elliptical crack emanating from a hole [fig.1, case 1] is investigated, the relationship for stress intensity can be expressed as follows [16]: 2 2 , , , , ,i sh a a a r r b k s g f q b t t w w         (3) where 2ik represents the stress intensity factor range for two-symmetric cracks initiated at a hole and s is the applied stress range. the function q, as the shape factor for an ellipse, can be written on the following way: 1.65 1 1.464 b q a        ; 1 a b      (4) where a and b are the crack length in depth direction and surface direction, respectively. the influence of various boundaries can be expressed by the boundary correction factor, as follows: 2 4 1 2 3 1 2 3 2sh w a a f m m m g g g f f t t                  (5) where m1, m2, m3, g1, g2, g3 represent functions related to crack configuration and loading, and they are given by: 1 b m a  (6) 2 3 2 0.05 0.11 m a b       (7) 3 3 2 0.29 0.23 m a b       (8) 1 4 2 1 2.6 2 1 cos 1 4 a a t t g a b                    (9) 2 3 4 2 2 1 0.358 1.425 1.578 2.156 1 0.08 g            (10) i s. boljanović et alii, frattura ed integrità strutturale, 35 (2016) 313-321; doi: 10.3221/igf-esis.35.36 316   1 1 cos 0.9 b r     (11)   10 2 3 1 0.1 1 cos 1 a g t          (12) where  is angle location, t denotes a half of the thickness, r and w present radius of the hole and half-width of the lug, respectively. the propagation process of single crack emanating from a hole can be theoretically investigated by employing the relationship [1] expressed on the following way: 1 2 4 2 4i i ab trk k ab tr        (13) where ki1 is the stress intensity factor range for single crack situation. furthermore, the engineering maintenance inspections and controls show that the strength of lug under cyclic loading often can be threatened by through-the-thickness crack(s) initiated on the hole. the fatigue failure of such crack configuration can be analyzed through the stress intensity factor [17] expressed on the following way: 1 1 1 1 1 cos 2 it wk s b f f g r w            (14) an angular function f, the bowie correction factor f1 related to single semi-elliptical crack configuration, the pin-loaded correction factors g1, g2 and the finite-width correction factors fw1, fw2 for single and two-symmetric cracks, respectively, are discussed in ref. [16, 18]. then, the finite element method is used in order to evaluate the stress field around the crack tip, i.e. the stress distribution and the stress intensity factor. the propagation process of the semi-elliptical crack is numerically simulated by applying quarter-point (q-p) singular finite elements [19], integrated in the software package msc/nastran [20]. all the computed results using both analytical and numerical methods are presented in next section, figure 1: geometry of the pin-loaded lug (case 1 – through-the-thickness crack, case 2 – one crack/two-symmetric cracks at a hole). s. boljanović et alii, frattura ed integrità strutturale, 35 (2016) 313-321; doi: 10.3221/igf-esis.35.36 317 numerical results o illustrate the efficiency of the computational model for the fatigue failure analysis of lug with either semielliptical crack or through-the-thickness crack, a few numerical examples are presented in this section. the strength of lug is here investigated through the stress analysis, the residual life estimation and the crack path simulation. the fatigue life calculation of through-the-thickness crack in the first section, the residual strength of the pin-loaded lug with through-the-thickness crack (fig.1, case 2) is examined. the lug, subjected to axial cyclic loading with constant amplitude (a far-field maximum stress smax= 41.38 mpa), has diameter of a hole 2r =38.1 mm and initial crack length b0 = 0.635 mm [21]. geometry sizes and relevant stress ratios are shown in tab. 1. the cracked lug is made of 7075 t6 al alloy, and the following material characteristics are assumed: cb= 2.5510-10, mb= 3.06 [22]. using the above geometry sizes, fatigue data and loading conditions, the stress intensity factor for the lug with throughthe-thickness crack is calculated by applying eq.(14) and appropriate relationships discussed in ref. [16, 18], then thanks to eqs.(2a) and (2b), the number of loading cycles up to failure is evaluated. figs. 2a, 2b and 2c show the computed results for lug configuration with through-the-thickness crack. in the same figures, the estimations are compared with available experimental results [21]. it can be deducted from fig.2 that the calculations and experimental data are in a good correlation. 0 5 10 15 20 25 30 35 0 20 40 60 80 100 120 140 n [cycles] (x10 3 ) b [ m ] (x 1 03 ) calculated curve exp eriment 1 exp eriment 2 0 5 10 15 20 25 0 20 40 60 80 100 n [cycles] (x10 3 ) b [ m ] (x 1 03 ) calculated curve exp eriment 1 exp eriment 2 0 2 4 6 8 0 5 10 15 20 n [cycles] (x10 3 ) b [ m ] (x 1 03 ) calculated curve exp eriment 1 exp eriment 2 (a) (b) (c) figure 2: crack length versus number of loading cycles for the pin-loaded lug with through-the-thickness crack emanating from a hole: (a) experiment 1-abplc84, experiment 2-abplc91; (b) experiment 1-abplc47, experiment 2-abplc94; (c) experiment 1abplc63, experiment 2-abplc62. experimental results for through-the-thickness crack configuration from ref. [21]. lug id 2w 10-3 (m) 2t 10-3 (m) r abplc84 abplc91 114.3 12.7 0.5 abplc47 abplc94 85.72 12.7 0.5 abplc63 abplc62 57.15 12.7 0.1 table 1: geometry sizes of the lug and external loading conditions [21]. t s. boljanović et alii, frattura ed integrità strutturale, 35 (2016) 313-321; doi: 10.3221/igf-esis.35.36 318 the stress analysis in this section, both, the stress distribution and the stress intensity factor for damaged lug are tackled. under cyclic loading with constant amplitude (a far-field maximum stress smax= 62.575 mpa), the semi-elliptical crack is initiated along the hole of lug (a = b = 9.2 mm). the lug, whose geometry characteristics are: 2w = 50 mm, 2r = 16 mm and 2t = 32 mm, is made of 7075 t6 al alloy (e = 70.2 gpa,  =0.33). the stress field of the lug with semi-elliptical crack emanating from a hole is here theoretically investigated by employing the finite element method. thanks to quarter-point (q-p) singular finite elements implemented in msc/nastran [19, 20], the numerical approach is developed for the stress analysis of pin-loaded lug. actually, by applying super elements around the crack tip [20], the crack growth process is simulated step-by-step for each increment of crack length, and different meshes are modeled. a representation of the finite element mesh and the stress distribution are shown in fig.3a and fig.3b. two-symmetric cracks one crack a=b=9.2 mm analytical fem analytical fem ka (mpa m0.5) 20.550 21.199 17.360 19.922 kb (mpa m0.5) 11.891 12.723 10.044 11.447 table 2: stress intensity factor calculations by applying analytical and numerical approaches. then, both, developed numerical approach by applying q-p finite elements, as well as eq. (3)-(13) are employed in order to calculate the stress intensity factor. in tab. 2, the calculated values of the stress intensity factor for one crack and two symmetric cracks lug configurations are presented. (a) (b) figure 3: finite element analysis of the pin-loaded lug with semi-elliptical crack(s) emanating from a hole: (a) modeled finite element mesh; (b) the stress distribution of single crack situation. the strength estimation of lug with semi-elliptical crack emanating from a hole now, the residual life estimation and the crack path simulation of the pin-loaded lug with semi-elliptical crack emanating from a hole (fig.1, case 1) under cyclic loading is carried out. geometry characteristics of the lug are as follows: s. boljanović et alii, frattura ed integrità strutturale, 35 (2016) 313-321; doi: 10.3221/igf-esis.35.36 319 2w=85.725 mm, 2t = 18 mm and 2r = 57.15 mm [23]. the initial crack lengths are: a0 = 5.303 mm and b0 = 3.573 mm, for depth and surface directions, respectively. the lug, made of pmma, is subjected to an external force with constant amplitude (a far field maximum force pmax= 2300 n), and the following material parameters are assumed: ca=2.29411403210-6, ma=5.598311. 0 2 4 6 8 10 0 2 4 6 8 10 n [cycles] (x10 3 ) b [ m ] (x 1 03 ) calculated curve exp eriment 0 2 4 6 8 10 0 2 4 6 8 10 n [cycles] (x10 3 ) a [m ] ( x 10 -3 ) calculated curve exp eriment (a) (b) figure 4: crack length versus number of loading cycles for the pin-loaded lug with semi-elliptical crack emanating from a hole: (a) a versus n, (b) b versus n. initial crack length: a0 = 5.303 mm, b0 = 3.573 mm. experimental results from ref. [23]. 0 4 8 12 16 0 2 4 6 8 10 b [m] (x10 -3 ) a [ m ] (x 1 03 ) a=5.553 mm a=5.803 mm a=6.053 mm a=6.303 mm a=6.553 mm initial crack 0 4 8 12 16 20 0 2 4 6 8 10 b [m] (x10 -3 ) a [ m ] (x 1 03 ) a=6.803 mm a=7.053 mm a=7.303 mm a=7.553 mm a=7.803 mm initial crack (a) (b) figure 5: the crack path modeling of semi-elliptical crack emanating from a hole. initial crack length: a0 = 5.303 mm, b0 = 3.573 mm. the strength of the lug configuration with semi-elliptical crack emanating from a hole is here investigated through the stress intensity factor calculation and fatigue life estimation. in order to calculate the stress intensity factor, eqs. (3)-(12) together with eq. (13) are employed, then by applying eqs. (2a) and (2b), the crack length is computed as a function of the number of loading cycles. fatigue life calculations for depth direction and surface direction are shown in fig.4a and s. boljanović et alii, frattura ed integrità strutturale, 35 (2016) 313-321; doi: 10.3221/igf-esis.35.36 320 fig.4b, respectively. the evaluated number of loading cycles for the pin-loaded lug is compared with experimental results [23]. figs. 4a and 4b show that the calculations related to the lug configuration with semi-elliptical crack emanating from a hole, are in a good agreement with experimental observations. now, for the same lug the crack growth path is simulated employing, step-by-step, the computed stress intensity factor for different crack increments. it should be noted that in every step, the crack length in surface direction is calculated thanks to the crack length in dept direction and the stress intensity factors from the preceding step. for the calculation of the stress intensity factor as well as crack lengths in surface direction, eqs. (3)-(13) and (1a) and (1b) are used. the modeled crack growth paths for different crack lengths in depth direction are presented in fig.4a and fig.4b, respectively. note that direction of x and y axels correlate with surface of the lug and the lug hole, respectively. conclusions computational model for crack growth analysis of the pin-loaded lug under cyclic loading is developed. the crack propagation process of either semi-elliptical crack or through-the-thickness crack emanating from a hole of the lug is investigated through the stress analysis and the residual life estimation. further, the crack path is simulated for semi-elliptical crack configuration. for the stress analysis analytical and/or numerical approaches are employed. the stress field of the lug with semi-elliptical crack is evaluated by applying quarter-point (q-p) singular finite element. then, the two-parameter driving force crack growth model is employed in order to calculate the strength of lug. the comparison between the calculations and experimental results point out that developed mathematical model can be applied for reliable residual life estimation of the lug with semi-elliptical crack and through-the-thickness crack. acknowledgements he authors would like to thank the mathematical institute of the serbian academy of sciences and arts and the ministry of science and technological development, serbia for providing financial support of this research under grant no. oi 174001. references [1] shah, r.c., stress intensity factors for through and part-through originating at fastener holes, in: mechanics of crack growth, astm stp 590 (1976) 429-459. [2] schijve, j., hoeymakers, s.h.m., fatigue crack growth in lugs, fatigue eng. mater. struct., 1 (1979) 185-201. [3] impellizeri, l.f., rich, d.l., spectrum fatigue crack growth in lugs. in: fatigue crack growth under spectrum loads, astm stp 595 (1976) 320-336. [4] vainshok, v.a., varfolomeyev, i.v., stress intensity factor analysis for part-elliptical cracks in structures, int. j. fracture, 46 (1990) 1-24. [5] sih, g.c., chen, c., non-self similar crack growth in elastic-plastic finite thickness plate, theor. appl. fract. mech., 3 (1985) 125-139. [6] raju, i.s., newman, jr. j.c., stress intensity factor for two symmetric corner cracks. in: smith c.w., editor. fracture mechanics, astm str (1979) 411-430. [7] smith, c.w., jolls, m., peters, w.h., stress intensities for cracks emanating from pin-loaded holes. in: flaw growth and fracture, astm stp 631 (1977) 190-201. [8] grandt, jr. a.f., kullgren, t.e., stress intensity factors for corner cracked holes under general loading conditions, j. eng. mater. technol., 103 (1981) 171-176. [9] paris, p.c., erdogan, f.a., a critical analysis of crack propagation laws, j. basic eng. trans. sme, series d, 55 (1963) 528-534. [10] forman, r.g., study of fatigue crack initiation from flaws using fracture mechanic theory, eng. fract. mech., 4 (1972) 333-345. [11] weertman, j., rate of growth of fatigue cracks calculated from the theory of indefinitesimal dislocations distributed on a plane, int. j. fract. mech., 2 (1966) 460-467. a t s. boljanović et alii, frattura ed integrità strutturale, 35 (2016) 313-321; doi: 10.3221/igf-esis.35.36 321 [12] elber, w., the significance of fatigue crack closure. in: damage tolerance in aircraft structure, astm str 486 (1971) 230-242. [13] walker, e.k., the effect of stress ratio during crack propagation and fatigue for 2024-t3 and 7075-t5 aluminum. in: effect of environment and complex load history on fatigue life, astm str 462 (1970) 1-14. [14] kujawski, d., a new (k+kmax)0.5 driving force parameter for crack growth in aluminum alloy, int. j. fatigue, 23 (2001) 733-740. [15] noroozi, a.h., glinka, g., lambert, s., a two parameter driving force for fatigue crack growth analysis, int. j. fatigue, 27 (2005) 1277-1296. [16] newman, jr. j.c., raju, i.s., stress-intensity factor equations for cracks in three-dimensional finite bodies, in: lewis j.c. and sines g. eds. fracture mechanics – volume i: theory and analysis, astm stp 791 (1983) i-238-i-265. [17] newman, jr. j.c., fracture analysis of surface and through-cracked sheets and plates, eng. fract. mech., 5 (1973) 667689. [18] boljanović, s., maksimović, s., fatigue crack growth modeling of attachment lugs, int. j. fatigue, 58 (2014) 66-74. [19] barsoum, r.s., triangular quarter-point elements as elastic and perfectly plastic crack tip elements, int. j. numer. meth. eng., 11 (1977) 85-98. [20] http://www.mscsoftware.com/product/msc-nastran, (2013). [21] kathiresan, k., brussat, t.r., advanced life analysis methods, afwal-tr-84-3080, oh, (1984). [22] flech, w.g., anderson, r.b., a mechanical model of fatigue crack propagation: in: pratt p.l., editor. proc of the second international conference on fracture. brighton, london: chapman & hall: (1969). [23] grandt, jr. a.f., harter, j.a., tritisch, d.d., semielliptical cracks along holes in plates and lugs, afwal-tr-83-3043, oh, (1982). << /ascii85encodepages false /allowtransparency false /autopositionepsfiles true /autorotatepages /none /binding /left /calgrayprofile (dot gain 20%) /calrgbprofile (srgb iec61966-2.1) /calcmykprofile (u.s. web coated \050swop\051 v2) /srgbprofile (srgb iec61966-2.1) /cannotembedfontpolicy /error /compatibilitylevel 1.4 /compressobjects /tags /compresspages true /convertimagestoindexed true /passthroughjpegimages true /createjobticket false /defaultrenderingintent /default /detectblends true /detectcurves 0.0000 /colorconversionstrategy /cmyk /dothumbnails false /embedallfonts true /embedopentype false /parseiccprofilesincomments true /embedjoboptions true /dscreportinglevel 0 /emitdscwarnings false /endpage -1 /imagememory 1048576 /lockdistillerparams false /maxsubsetpct 100 /optimize true /opm 1 /parsedsccomments true /parsedsccommentsfordocinfo 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/hrv (za stvaranje adobe pdf dokumenata najpogodnijih za visokokvalitetni ispis prije tiskanja koristite ove postavke. stvoreni pdf dokumenti mogu se otvoriti acrobat i adobe reader 5.0 i kasnijim verzijama.) /hun 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can be opened with acrobat and adobe reader 5.0 and later.) >> /namespace [ (adobe) (common) (1.0) ] /othernamespaces [ << /asreaderspreads false /cropimagestoframes true /errorcontrol /warnandcontinue /flattenerignorespreadoverrides false /includeguidesgrids false /includenonprinting false /includeslug false /namespace [ (adobe) (indesign) (4.0) ] /omitplacedbitmaps false /omitplacedeps false /omitplacedpdf false /simulateoverprint /legacy >> << /addbleedmarks false /addcolorbars false /addcropmarks false /addpageinfo false /addregmarks false /convertcolors /converttocmyk /destinationprofilename () /destinationprofileselector /documentcmyk /downsample16bitimages true /flattenerpreset << /presetselector /mediumresolution >> /formelements false /generatestructure false /includebookmarks false /includehyperlinks false /includeinteractive false /includelayers false /includeprofiles false /multimediahandling /useobjectsettings /namespace [ (adobe) (creativesuite) (2.0) ] /pdfxoutputintentprofileselector /documentcmyk /preserveediting true /untaggedcmykhandling /leaveuntagged /untaggedrgbhandling /usedocumentprofile /usedocumentbleed false >> ] >> setdistillerparams << /hwresolution [2400 2400] /pagesize [612.000 792.000] >> setpagedevice shot peening processes to obtain nanocrystalline surfaces in metal alloys: d. d’angela et alii, frattura ed integrità strutturale, 60 (2022) 265-272; doi: 10.3221/igf-esis.60.18 265 fatigue crack growth analysis of welded bridge details danilo d’angela university of naples federico ii, italy danilo.dangela@unina.it, http://orcid.org/0000-0002-8096-5202 marianna ercolino university of greenwich, uk m.ercolino@gre.ac.uk, http://orcid.org/0000-0001-8678-0631 abstract. the paper investigates the fatigue crack growth in typical bridge weldments by means of numerical analysis. the extended finite element (xfem) method is coupled with the low-cycle fatigue (lcf) approach in abaqus, and parametric analyses are carried out in order to assess the influence of the main sample/testing features on the fatigue life of the investigated structures. the numerical results are found to be robust and reliable by performing comparisons with past experimental data and regulation design correlations. keywords. crack growth; fatigue; welded details; xfem; abaqus. citation: d’angela, d., ercolino, m., fatigue crack growth analysis of welded bridge details, frattura ed integrità strutturale, 60 (2022) 265-272. received: 03.02.2022 accepted: 07.02.2022 online first: 08.02.2022 published: 01.04.2022 copyright: © 2022 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. introduction atigue crack propagation is among the most critical damage mechanisms affecting metallic structures and infrastructures subjected to repeated loading [1–4]. welded details are typically extremely sensitive to crack propagation phenomena. the welding process can generate flaws and defects in the vicinity of the weldment toe, and such pre-cracks can easily activate crack development [5] especially if the applied load is orthogonal to the crack surface (e.g., mode i fracture). numerical simulation by means of finite element (fe) analysis is among the most reliable tools for the assessment of the fatigue crack propagation in metallic structures and for the estimation of their fatigue life [6–10]. the extended finite element method (xfem) is among the most advanced technologies for simulating fracture phenomena, and several recent studies proved that it could be reliable also regarding fatigue crack propagation in metals [1,11–16]. hedayati and vajedi [15] developed robust modelling of crack propagation in slant cracked plates based and provided estimations of the fatigue life. melson [17] analysed the fatigue response of aluminium crack plates and found that xfem technology can be more reliable than other methodologies. other authors [7,8] implemented subroutines for more accurate simulations, and they found reliable results. in spite of the available methodologies and the copious literature, there are still several issues affecting the fe analysis of fatigue and fracture phenomena, and novel approaches are needed to enhance the numerical analysis of f https://youtu.be/4vtfdxbpwi4 d. d’angela et alii, frattura ed integrità strutturale, 60 (2022) 265-272; doi: 10.3221/igf-esis.60.18 266 fatigue crack propagation in metallic structures. the available models are often extremely complex and not suitable for practitioners, and the modelling parameters are not often physical based. in many cases, the analyses require high computational costs and the numerical results have been validated only considering theoretical or analytical data. in order to cover this gap, a simple but reliable numerical model is presented in this study. the xfem technology is coupled with low-cycle fatigue (lcf) approach and parametric analyses are performed in abaqus [18]. the case study consists of welded bridge details, which are critical systems undergoing fatigue crack propagation and are less studied in the literature. numerical modelling and fatigue analysis three-dimensional model was built in abaqus coupling xfem and lcf approach. in particular, the modelling was based on an improvement and extension of a pilot model developed by the authors considering bi-dimensional metallic plates [9,13]. the reference geometry, along with the initial crack, is shown in figure 1a. s355 steel was assumed as a material. the structures consisted of (a) main plate, (b) gusset plate, and (c) main-to-gusset plate welded connection (figure 1a). the main model had geometry dimensions w, l, δw, and δl equal to 60, 50, 10, and 8 mm, respectively; the initial crack length dimensions a and b were equal to 2 and 4 mm, respectively (figure 1a). all surface connections between the parts were assumed to be perfectly tied. the initial plane pre-crack surface (a x b) was assigned to the model (main plate) according to the most common location and size of flaws/defects in welded details, i.e., at the toe of the weldment and orthogonally to the direction of the typically applied stress [5]. in particular, the main plate is assumed to carry the most significant load, which is applied along with the longitudinal direction of the latter. therefore, the pre-crack (weldment defect) is perpendicular to the direction of the applied load, and it can develop and activate the crack propagation phenomena. linear elastic homogeneous behaviour was assigned to the material according to the lefm approach. the fracture response was implemented on the initial xfem crack, according to paris law (fatigue fracture criterion and surface behavior). the mixedmode power law was used as a default abaqus model. the fatigue properties and the modelling parameters assumed for s355 steel are shown in table 1, which were derived from the literature [19–21]. the boundary and loading conditions are shown in figure 1.b. the stump cross sections of both main and gusset plates were fixed to simulate a symmetry condition. the cyclic loading p was applied to the reference middle section point, which was coupled to the whole surface by using a continuum distribution node-surface interaction. a cyclic frequency equal to 10 hz was used, with a linear shape. material fatigue properties (mechanical) modelling parameters (abaqus code) cp mp kc c3 c4 gc ( ) mp 0.5 m cycle mpa m          [-] 0.5 mpa m    4c m / cycles ( n / m )       [-] kn m       s355 steel 5.71e−13 3.56 45 3.54e−14 1.781 9.6 7 % nickel steel 2.17e−11 2.57 135 2.80e−12 1.285 90.0 7075-t6 aluminium alloy 3.33e−11 3.70 25 2.55e−13 1.850 9.0 table 1: fatigue properties of the investigated materials and model parameters. the numerical analysis consisted of two steps: general static and direct cyclic (lcf). the static analysis step was only performed to improve the convergence of the analysis, as it was previously found by pilot studies [9], as well as reported in the literature [22]. the static step included only one cycle, with negligible values of the applied force (no influence on the actual fatigue response). several force values were applied to cover a wide range of applied stresses, i.e., from 75 to 325 mpa. this was aimed at evaluating the s-n curve, typically considered for the assessment of this typology of structures [5]. the model parts were partitioned (figure 1c) to control the mesh size along with the distance from the fpz. only hexahedral elements (8-node linear brick elements) can be used in abaqus for three-dimensional modelling according to lcfxfem analysis, i.e., c3d8 (full integration) and c3d8r (reduced integration) elements [18]. the reduced integration elements are typically more used in the literature (than the full integration ones) since they were found to be accurate for a d. d’angela et alii, frattura ed integrità strutturale, 60 (2022) 265-272; doi: 10.3221/igf-esis.60.18 267 modelling crack propagation problems despite the gain in smaller computational costs [9,15,23]. therefore, the mesh size analysis was performed considering this type of mesh. the mesh size of the model was assigned in the light of an expeditious convergence analysis. the mesh sizes are depicted in figure 1c, where the sizes related to part a, b, c, and d were equal to 0.7 x 0.7 mm, 0.7 x 4.5 mm, 4.0 x 4.0 mm, and 4.5 x 4.5 mm. parametric analysis he influence of several sample features was assessed considering the main model as a reference (defined as model m). material, structure geometry, and initial crack dimension/shape were varied, defining six parametric models. 7075-t6 aluminium alloy and 7% nickel steel were considered as alternative materials for generating models m1 and m2. the related properties and modelling/analysis features are reported in table 2. two alternative structure geometries were considered, defining models g1 and g2, together with the main model geometry. in particular, the models have geometry w, l, dw, and dl equal to (g1) 120, 50, 10, and 8 mm, and (g2) 60, 50, 20, and 8 mm. two alternative pre-crack dimensions were considered; the related models are defined c1 and c2; the models have dimensions a and b equal to (c1) 2 and 2 mm, and (c2) 2 and 8 mm. constant-amplitude analyses were performed for all models from applied stress equal to 75 mpa up to 350 mpa, considering increments of 25 mpa. overall, 72 analyses were performed. (a) (b) (c) figure 1: (a) geometry of the welded detail (w, l, δw, and δl) with initial pre-crack dimensions, (b) schematic of the boundary and loading conditions, and (c) mesh partitions and sizes resulting from the convergence analysis. t d. d’angela et alii, frattura ed integrità strutturale, 60 (2022) 265-272; doi: 10.3221/igf-esis.60.18 268 results and discussion ig. 2 shows the comparison between the numerical and the experimental results [5], where the nominal stress approach was considered. data having nf lower than 1×103 cycles were not considered. the numerical results over 2.785 × 104 to 2.54012 ×106 cycles (e.g., ~75 to ~250 mpa) were fitted with very good accuracy (e.g., r2 > 0.995) using power law. this range of cycles is consistent with the typical values related to fatigue loading of such types of structures [5].the best-fit constants αm and βm were equal to 5.297×103 and -0.286, respectively. the experimental results are related to a large number (487) of fatigue tests on similar structures having the geometrical parameters w, l, δw, and δl ranging within 40 ÷ 170 mm, 50 ÷ 400 mm, 8 ÷ 20 mm, and 8 ÷ 20 mm, respectively. in figure 2, the eurocode 3 s-n (nominal stress approach) related to the investigated detail is also shown (nominal stress approach), i.e., c40 detail class curve [5,24]. the numerical results match with a good agreement the cloud of the experimental data, being on the safe side if the c40 class detail curve is considered. it is recalled that the experimental results are representative of an extremely wide range of geometries; furthermore, the numerical modelling considered a pre-crack with a definite geometry. even though the validation of the model should be performed comparing cases having the same geometry/loading conditions, the numerical modelling is confirmed to be a reliable assessment of the fatigue life of complex welded details. this is supported by the log-log linear s-n correlation over the relevant stress-cycle ranges and by the location of the numerical data over the cloud of experimental results. as already mentioned, the model should be properly validated by considering specific case studies, e.g., as it was done with regard to the ct specimens. figure 2: comparison between the numerical results (red circles and red dashed line) and the experimental results (black dots and thin black and blu lines) reported by aygül et al. [5] and aygül [25], together with the c40 detail class curve (thick grey line) provided by eurocode 3 [5,24]. the influence of the parametric variables was assessed by considering the s-n curves and both the parameters and the domain stress-cycle ranges related to the best-fit power laws. figure 3 shows the results considering the variation of (a) the material (models m1 and m2), (b) the structural geometry (models g1 and g2), and (c) the pre-crack shape/dimension (models c1 and c2). the best-fit power laws (with related r2) are also shown. in particular, the data were fitted over the largest cycle interval that is associated with a power law having r2 larger than 0.950. the values of the related best-fit constants and the corresponding cycle ranges are given in figure 3. “el” in (b) represents the endurance limit, i.e., the fatigue life was larger than 108 cycles for stresses lower than the represented case. f d. d’angela et alii, frattura ed integrità strutturale, 60 (2022) 265-272; doi: 10.3221/igf-esis.60.18 269 model id α β r2 range of fitting from to [-] / 103 [-] [-] [cycles] / 103 [cycles] / 105 m 5.2971 -0.286 0.9979 27.85 25.4012 m1 1.9953 -0.252 0.9636 1.25 3.7826 m2 26.5302 -0.452 0.9991 16.36 4.0925 g1 8.1892 -0.329 0.9993 22.58 14.6633 g2 1.3941 -0.149 0.9592 71.43 69.6150 c1 6.0073 -0.305 0.9826 8.82 14.7419 c2 3.8580 -0.265 0.9815 9.73 21.2300 table 2: values of the best-fit constants defined in figure 3. the material clearly affects the fatigue performance as well as the range in which the s-n data are stable (e.g., log-log linear). model m1 shows a lower best-fit efficiency if compared to other cases. the geometry related to the double width of the main plate (m1) has s-n data (slightly) less performing than the main model, especially for larger numbers of cycles (e.g., larger than 105). it is recalled that all models have the same nominal applied stress; therefore, models g1 and g2 have a double total applied force with respect to the main model. if the main plate has a double thickness (i.e., model g2), the performance significantly improves, especially for larger numbers of cycles (e.g., larger than 105). for a low number of cycles, g2 has a performance comparable to the reference model m. the endurance limit (el) is reached in model g2 corresponding to stresses lower than 125 mpa (not observed in other cases over the same stress range). best-fit efficiency related to model g2 is reduced if compared to other cases, even though fewer data points were best-fitted. the size of the initial crack does not significantly affect the performance of the components. however, very interesting results are observed if model c1 is compared to the reference model m. c1 presents a (slightly) lower performance even though one of the dimensions of the initial crack is half the main model one. in particular, model c1 has the same crack dimensions a and b (equal 2 mm), whereas model m has the same c1 dimension for a and double for b. this confirms that the shape of the initial crack (e.g., a/b) is more significant than the area (a∙b) for the determination of the fatigue performance of the component. a similar result can be observed with regard to model c2, where b is equal to four times a. in fact, the fatigue performance is quite similar to model m (c1) for a higher (lower) number of cycles. this confirms that a component having an initial crack with a shape ratio (a/b) equal to 1/2 is (slightly) more critical than elements having larger or smaller ratios. obviously, this trend is related to the specific application and the investigated conditions. the provided values of the best-fit parameters allow quantifying the differences in fatigue life estimations among the different models, and they allow assessing the fatigue performance of similar components by producing a quick estimation. figure 4 shows the comparison between the numerical results (best-fit) related to (a) models m, g1, and g2 and (b) models m, c1, and c2 and the data related to the experimental database previously considered to assess the main model results [5,25]. such models are compatible with the geometrical properties of the considered experimental database. the curve related to the detail class c40 is also shown [5,24]. it is recalled that the cloud of experimental data is related to a wide range of geometries, i.e., w, l, δw, and δl ranging within 40 ÷ 170 mm, 50 ÷ 400 mm, 8 ÷ 20 mm, and 8 ÷ 20 mm, respectively. however, the variation of the modelling geometry (w equal to 60 and 120 mm, and δw equal to 10 and 20 mm) approximately envelope the cloud of experimental data. in particular, the superior enveloping related to model g2 is qualitatively consistent with the fact that this case is associated with δw equal to 20 mm, which corresponds to the maximum value over the experimental case. similarly, model g1, which is corresponding to w equal to 120 mm, shows results in the inferior part of the experimental cloud, which has maximum w equal to 170 mm. such qualitative trends strengthen the robustness of the modelling approach, even though proper validation should be performed. d. d’angela et alii, frattura ed integrità strutturale, 60 (2022) 265-272; doi: 10.3221/igf-esis.60.18 270 (a) (b) (c) figure 3: the influence of (a) material (models m, m1, and m2), (b) structure geometry (models m, g1, and g2), and (c) pre-crack shape/dimension (models m, c1, and c2) on the s-n results. conclusions he study supplied simple but reliable three-dimensional modelling and cyclic analysis to simulate crack propagation in welded bridge details subjected to fatigue loading. the approach is based on xfem technology coupled with lcf approach. s-n curves are provided for a wide range of welded bridge details. the numerical results are compared with both experimental results related to past studies and design curves provided by the regulations. best-fit s-n curves are developed for enhancing the literature database. the study proves that the developed approach is suitable for various and complex applications, and it can be considered as a reference for similar implementations. t d. d’angela et alii, frattura ed integrità strutturale, 60 (2022) 265-272; doi: 10.3221/igf-esis.60.18 271 (a) (b) figure 4: comparison between the best-fit curves related to the numerical results (dotted and dashed lines) and the experimental results (black dots and thin blue and black lines) reported by aygül et al. [5] and aygül [25], together with the c40 detail class curve (thick grey line) provided by eurocode 3 [5,24]: (a) models m, g1, and g2, and (b) models m, c1, and c2. acknowledgments omputation for the work presented in this paper was supported by the university of greenwich high performance computer resources (https://www.gre.ac.uk/itand-library/hpc). the project was funded by the university of greenwich under seedling 2016 and ref 2017/2018 funds. references [1] bergara, a., dorado, j. i., martin-meizoso, a., and martínez-esnaola, j. m. (2017). fatigue crack propagation in complex stress fields: experiments and numerical simulations using the extended finite element method (xfem). international journal of fatigue, 103, pp. 112–121. doi: 1 10.1016/j.ijfatigue.2017.05.026. [2] d’angela, d., ercolino, m., bellini, c., di cocco, v., and iacoviello, f. (2020). analysis of acoustic emission entropy for damage assessment of pearlitic ductile cast irons. material design & processing communications, 12(3), e158. doi: 10.1002/mdp2.158. c d. d’angela et alii, frattura ed integrità strutturale, 60 (2022) 265-272; doi: 10.3221/igf-esis.60.18 272 [3] imam, b., and chryssanthopoulos, m. k. (2010). a review of metallic bridge failure statistics. iabmas, philadelphia, usa. [4] wardhana, k., and hadipriono, f. c. (2003). analysis of recent bridge failures in the united states. journal of performance of constructed facilities, 17(3), pp. 144–150. doi: 10.1061/(asce)0887-3828(2003)17:3(144). [5] aygül, m., bokesjö, m., heshmati, m., and al-emrani, m. (2013). a comparative study of different fatigue failure assessments of welded bridge details. international journal of fatigue, 49, pp. 62–72. doi: 10.1016/j.ijfatigue.2012.12.010. [6] london, t., de bono, d. m., and sun, x. (2015). an evaluation of the low cycle fatigue analysis procedure in abaqus for crack propagation: numerical benchmarks and experimental validation. simulia uk regional users meeting. id 114881828. [7] kim, s.-k., lee, c.-s., kim, j.-h., kim, m.-h., noh, b.-j., matsumoto, t., and lee, j.-m. (2015). estimation of fatigue crack growth rate for 7% nickel steel under room and cryogenic temperatures using damage-coupled finite element analysis. metals, 5(2), pp. 603–627. doi: 10.3390/met5020603. [8] zhan, z., hu, w., li, b., zhang, y., meng, q., and guan, z. (2017). continuum damage mechanics combined with the extended finite element method for the total life prediction of a metallic component. international journal of mechanical sciences, 124–125(c), pp. 48–58. doi: 10.1016/j.ijmecsci.2017.03.002. [9] d’angela, d., and ercolino, m. (2018). finite element analysis of fatigue response of nickel steel compact tension samples using abaqus. procedia structural integrity, 13, pp. 939–946. doi: 10.1016/j.prostr.2018.12.176. [10] saeedi, m., azadi, m., mokhtarishirazabad, m., and lopez‐crespo, p. (2020). numerical simulations of carbon/epoxy laminated composites under various loading rates, comparing extended finite element method and cohesive zone modeling. material design & processing communications, 3(5), e198. doi: 10.1002/mdp2.198. [11] benzaama, a., mokhtari, m., benzaama, h., abdelouahed, e., tamine, t., madani, k., slamen, a., and ilies, m. (2019). using xfem techniques to predict the damage of aluminum 2024t3 notched under tensile load. frattura ed integrità strutturale, 13(50), pp. 184–193. doi: 10.3221/igf-esis.50.16. [12] bhattacharya, s., singh, i. v., and mishra, b. k. (2013). fatigue-life estimation of functionally graded materials using xfem. engineering with computers, 29(4), pp. 427–448. doi: 10.1007/s00366-012-0261-2. [13] d’angela, d., and ercolino, m. (2021). fatigue crack growth in metallic components: numerical modelling and analytical solution. structural engineering and mechanics, 79권(5호), pp. 541–556. doi: 10.12989/sem.2021.79.5.541. [14] giner, e., díaz-álvarez, j., marco, m., and miguélez, m. h. (2015). orientation of propagating crack paths emanating from fretting-fatigue contact problems. frattura ed integrità strutturale, 10(35), pp. 285–294. doi: 10.3221/igf-esis.35.33. [15] hedayati e, vahedi m. (2014)using extended finite element method for computation of the stress intensity factor, crack growth simulation and predicting fatigue crack growth in a slant-cracked plate of 6061-t651 aluminum. world journal of mechanics 4, pp. 24–30. doi: 10.4236/wjm.2014.41003. [16] talemi, r. h. (2016). numerical simulation of dynamic brittle fracture of pipeline steel subjected to dwtt using xfem-based cohesive segment technique. frattura ed integrità strutturale, 10(36), pp. 151–159. doi: 10.3221/igf-esis.36.1. [17] melson, j. h. (2014). fatigue crack growth analysis with finite element methods and a monte carlo simulation. degree thesis. virginia polytechnic institute and state university, blacksburg, va. [18] simulia. (2016). abaqus/cae user’s manual, version 6.14. [19] cindas/purdue university (ed.). (1994). damage tolerant design handbook. a compilation of fracture and crackgrowth data for high-strength alloys. lafayette, in. [20] de jesus, a. m. p., matos, r., fontoura, b. f. c., rebelo, c., simões da silva, l., and veljkovic, m. (2012). a comparison of the fatigue behavior between s355 and s690 steel grades. journal of constructional steel research, 79, pp. 140–150. doi: /10.1016/j.jcsr.2012.07.021. [21] stephens ri, fuchs ho, editors. metal fatigue in engineering. 2nd ed. new york: wiley; 2001. [22] kucharski, p., lesiuk, g., czapliński, t., fratczak, r., and maciejewski, ł. (2016). numerical estimation of stress intensity factors and crack propagation in lug connector with existing flaw, 1780(1), 050002. doi: 10.1063/1.4965949. [23] holland, s., kosel, t., weaver, r., and sachse, w. (2000). determination of plate source, detector separation from one signal. ultrasonics, 38(1–8), pp. 620–623. doi: 10.1016/s0041-624x(99)00206-1. [24] cen. (2005). en 1993–1-1. eurocode 3: design of steel structures. [25] aygül, m. (2012). fatigue analysis of welded structures using the finite element method. degree thesis. university of technology gothenburg, sweden. microsoft word numero_43_art_10 b. saadouki et alii, frattura ed integrità strutturale, 43 (2018) 133-145; doi: 10.3221/igf-esis.43.10 133 characterization of uniaxial fatigue behavior of precipitate strengthened cu-ni-si alloy (siclanic®) b. saadouki, m. elghorba laboratory of control and mechanical characterization of materials and structures, national higher school of electricity and mechanics. casablanca, morocco. bouchra.saadouki@gmail.com ph. pelca lebronze alloys – bornel, 11, rue ménillet 60540 bornel – france t. sapanathan, m. rachik sorbonne universités, université de technologie de compiègne, laboratoire roberval, cnrs umr 7337, centre de recherche royallieu, cs 60319, 60203 compiègne cedex, france abstract. fatigue tests were conducted on cylindrical bars specimens to understand the fatigue behavior of siclanic®. although it displays good resistance in monotonic tension, this material weakens and shows a softening in repeated solicitation. this has been verified through a sem observation, the cu-ni-si alloy presents transgranular failure by cleavage. the mansoncoffin diagram exhibited the plastic deformation accommodation. the plastic deformation becomes periodic and decreases progressively as the cycle number increases. the approximations of manson coffin give fatigue parameters values which are in good agreement with the experience. keywords. fatigue; copper alloy; s-n curve; softening; fracture. citation: saadouki, b., elghorba, m., pelca, ph., sapanathan, t., rachik, m., characterization of uniaxial fatigue behavior of precipitate strengthened cu-ni-si alloy (siclanic®), frattura ed integrità strutturale, 43 (2018) 133-145. received: 22.09.2017 accepted: 18.10.2017 published: 01.01.2018 copyright: © 2018 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. introduction t present, increasing demand for copper and copper alloys leads to the all-time high price of copper. copper is widely used in electrical, electronic and thermal applications. particularly, in an application where the high conductivity of copper is required, one should choose a copper alloy with higher percentage of copper, while there is a compromise required with the mechanical properties of the alloy. hence, recent developments of copper alloys mainly focus on this issue and adapt to various strengthening mechanisms, such as precipitation hardening. precipitates hardened copper alloys contain additive elements in small quantities that improves the mechanical characteristics by forming precipitates, without greatly altering their electrical conductivity [1]. the mechanical strength of these alloys is improved by precipitation of the secondary phase particles during the quenching and tempering heat treatment processes [2-4]. thus, a b. saadouki et alii, frattura ed integrità strutturale, 43 (2018) 133-145; doi: 10.3221/igf-esis.43.10 134 the precipitation hardened copper alloys offer cost saving and they are suitable for many industrial applications under various mechanical loading conditions. cu-ni-si alloys strengthened by precipitation hardening are used in very wide range of electrical and electromagnetic applications. however, the cyclic circulation of alternating current induces fatigue failure during the high frequency electromagnetic applications [5]. fatigue behavior of cu-ni-si alloys has been investigated in few articles [69]. in [6], authors investigated the microstructure of the material at different heat treatment states and its influence on the low cycle fatigue (lcf) and high cycle fatigue (hcf). they have noticed a softening effect of the copper alloy under lcf [6]. goto et al. [8] studied the role of the ni2si curing compound in fatigue crack initiation and propagation mechanism and identified a localized fatigue behavior. zhao et al. [9] agree that the curing compound in cu-ni-si is coherent with the matrix. consequently, the main mechanism of crossing the secondary phase (ni2si) by a sliding dislocation is shearing. besides, the alloys studied are of a different chemical composition than that of proposed in this work. this work is proposed to determine the fatigue characteristics for a cu-ni-si alloy known by its trade name of siclanic®. the siclanic® is also strengthened by the precipitation of the ni2si phase [10]. this alloy was mainly studied from a microstructure based investigation [11, 12]; while there exist few other studies with the focus on the mechanical aspects [13, 14]. however, fatigue properties of this alloy has never been reported before in the literature. fatigue test results are often represented by probabilistic wöhler curve using statistical method and this curve has been developed due to the dispersions of tests results. in recent years, castillo and fernández-canteli worked on the statistical analysis of the s-n and e-n fatigue curves [15], and they extended the probabilistic model to the strain damage evaluation to estimate fatigue life prediction in many applications [16, 17]. in this study, the probabilistic model of astm e 739[18] is applied to estimate wöhler curves. material and experimental procedures iclanic® alloy used in this study has the chemical composition with 96.9 % of copper, 2.5 % nickel and 0.6 % silicon in weight percent. the material has been received in bars of 14 mm × 14 mm× 60 mm dimension. to optimize high cycle fatigue tests, we chose classical specimen shape with circular section according to the astm e466-07 standard (fig. 1) at morocco cetim. the fatigue tests were carried out on an mts biaxial hydraulic machine model 17 with imposed stress at a temperature of 20 °c. during the tests, the temperature was controlled using a thermocouple (fig. 2). solicitations were loaded in uniaxial cyclical mode, with a sinusoidal waveform, according to repeated tensile loads. (a) (b) figure 1: fatigue specimen (a) schematic illustration showing the specimen geometry and (b) image of the actual fatigue specimen. s b. saadouki et alii, frattura ed integrità strutturale, 43 (2018) 133-145; doi: 10.3221/igf-esis.43.10 135 figure 2: schematic illustration of the experimental apparatus.      max min 2 a (1)      max min 2 m (2) and the ratio of extreme stresses (maximum and minimum), also called load ratio and defined by:    min max r (3) where, σmin and σmax are respectively the minimum and maximum stresses to which the specimen is subjected. the tests are conducted with zero-based loading at stress ratio r= 0 (fig. 3), this implies the following equations:     max 2 m a (4)    max (5) results and analysis atigue tests of studied material should be preceded by mechanical analysis of his answers to simple solicitation through tensile tests. starting fatigue tests requires the definition of the first value of the maximum imposed stress. monotonic tensile behavior tensile tests have been carried out to characterize the monotonic properties of the material. tests were conducted until the failure on a zwick roell machine under displacement mode. an additional test where an extensometer was used to the gauge length was performed to measure accurately the young modulus. monotonic tensile properties values are summarized in tab. 1. f b. saadouki et alii, frattura ed integrità strutturale, 43 (2018) 133-145; doi: 10.3221/igf-esis.43.10 136 figure 3: tensile repeated solicitation on fatigue test. e (gpa) ys0.2% (mpa) uts (mpa) a (%) n k (mpa) 121 498 615 11.62 0.034 591 table 1: monotonic tensile characteristics of the siclanic®. furthermore, the remarkable tensile strength of 615 mpa enhanced by the presence of silicon, the siclanic® has an elongation at fracture of higher than 10%. this ductility is mainly due to the high temperature of the solution treatmentquench phase during the hardening treatment. the progressive passage, in the stress-strain curve, from linear elasticity to plastic deformation requires the definition of the conventional yield strength ys0.2% which is of the order of 498 mpa. from this stress value, we realize a low permanent elongation which can be measured accurately. mechanical behavior ceases to be elastic to become plastic. s-n curve siclanic® fatigue results show significant dispersion. this dispersion is now considered as one of physical fatigue aspects [19]. indeed, for the same material, and the same load level, the lifetime may be different. iso-probabilistic s-n curve as it is, the fatigue curve gives a tendency on the material behavior, but it is of limited use: we know that for a given stress level, half the specimens break for cycle number less than n(σ),the other half breaks for cycle number more than n(σ). for given stress level, the ratio between maximum and minimum value of failure cycle can exceed 10. in a probabilistic concept, wöhler curve represents the border separating the area where failure is less likely (left of the curve) to the area where failure is most likely (right part of the curve). the fatigue life is generally described by the statistical longevity curve called iso-probabilistic wöhler curve or median curve (n50, that to say 50% of survival specimens) [20]. for the siclanic®, fatigue curve median is illustrated in fig. 4. probabilistic s-n curve the confidence interval method using the probability of student's law is also frequent to characterize fatigue behavior. it does not estimate directly the number of cycle to failure, but the estimations have percentage chance to containing the nf .thus, it is interesting to work in confidence interval of 80% that will give proper framing 80 times out of 100 on average, which meaning, if we could repeat the same tests a large number of times, affirming each time than nf is in this interval, we would be wrong 20 times out of 100 on average. fig. 5 shows siclanic® probabilistic wöhler curve corresponding at 80% of survival, such a curve is sometimes called “curve design”. b. saadouki et alii, frattura ed integrità strutturale, 43 (2018) 133-145; doi: 10.3221/igf-esis.43.10 137 figure 4: median wöhler curve for siclanic® figure 5: siclanic® probabilistic wöhler curve at 80% chance of survival the two probability methods appear in good agreement; they give very close values of the endurance limit. the estimated value of siclanic® endurance limit is 250 mpa. fractography fatigue fracture surfaces of siclanic® are often irregular; the majority of them are planar and perpendicular to the stress axis. fig. 6 shows the fracture surface specimen which failed in 5×105 cycles. a fatigue fracture surface consists of three regions associated with crack initiation, crack growth, and final overload. the darker region (za zone) presents the initial fatigue and slow crack growth in one or a few load cycles (fig. 7). surface crack initiation is located in the same area for all specimen tests. for certain specimens, we notice the existence of two crack initiation sites, one next to the other. beach marks (macroscale) and striations (microscale) in surface indicate fatigue loading. failure by cleavage proves that we are at the brittle failure case, which is common for long-life fatigue. cleavage occurs by direct separation along crystallographic planes, and the failure is transgranular. b. saadouki et alii, frattura ed integrità strutturale, 43 (2018) 133-145; doi: 10.3221/igf-esis.43.10 138 figure 6: fracture surface of the specimen. figure 7: fatigue failure initiation site on cleavage planes of global dimension highlighted in the white box have approximately 426 µm ×284 µm. low cycle fatigue behavior cyclical behavior law the comparison between the cyclic behavior curve and monotonic behavior curve reveals a softening during the cyclic loading (fig. 8). the conventional yield strength falling of 19% in the cyclic tensile. hardening or softening phenomena depend on the materials and their heat treatments. so, the evolution of fatigue mechanical characteristics depends on the initial state of the solid solution [21]. softening is generally observed for steels whose structures are naturally work hardened by quenching and tempering, this softening corresponds to a decrease of the yield strength which can reach 30%. similarly, siclanic® structural hardening by heat treatment of quenching and tempering leads to a stable phase represents a cyclical softening. the softening of siclanic® is similar to the others cu-ni-si alloys behavior in low cycle fatigue, such behavior is usually attributed to the formation of intense bands of slip in which the precipitation hardening effect has been reduced [2]. in structural analysis, design of parts is based on yield strength ys, however, for siclanic®, which has a cyclic softening in fatigue solicitation (ys’0.2 < ys 0. 2), even a cycle level of σa < ys 0.2, could result a deformation higher than εmax and placing the piece out of service. the following equation describes the cyclic behavior:     '' nk (6) b. saadouki et alii, frattura ed integrità strutturale, 43 (2018) 133-145; doi: 10.3221/igf-esis.43.10 139 figure 8: comparison between monotonic and cyclic tensile curves for siclanic®. it is the law of cyclic consolidation or cyclic hardening law, where ′ and n' are respectively the coefficient and the exponent of cyclic hardening. in tab. 2, the monotonic and cyclic mechanical characteristics of siclanic® are compared. the extent of variation of the hardening coefficient is due to the cyclic deformation. it goes from a relatively low value (0.034) to a higher value of 0.136. monotonous n = 0.034 k = 591 mpa ys 0, 2%= 498 mpa cyclic n’ = 0.136 k’= 490 mpa ys’0, 2% = 350 mpa table 2: monotonic and cyclic mechanical characteristics of siclanic® prediction of softening or hardening phenomena according to smith, hirschberg and manson [22], softening occurs when uts / ys 0.2< 1.2, while hardening appears for uts / ys 0.2 ˃ 1.4. in the case where the ratio is between 1.2 and 1.4, one or the other of the softening and hardening phenomena can be observed. as a result of the examination of various materials, morrow [23] finds that if the value of n is higher than 0.1, hardening or stability occurs; however, if n is less than 0.1 the softening happens during the material is cycling. in tab. 3, we have compiled the predictions of siclanic® cyclical behavior, the predictions are in agreement with experience, however, the criteria used consider the characteristics determined outside the deformation domain (<2%) such as uts and n. a new definition of the hardening criteria is introduced by lieurade [24], taking the ratio σ1 / ys 0.2 , of which parameters correspond to the experience, since they are located in plastic deformation field. it has been shown in the case of steels that if σ1 / ys 0. 2 is less than 1.3 there is softening, while if σ1 / ys 0.2 is higher than 1.5 there is hardening. smith, hirschberg, manson morrow experience σ1 / ys 0, 2 ∆σ1/ σ1 (%) uts / ys 0. 2 prediction n prediction observation σ1 / ys 0. 2 prediction 1.23 uncertainty 0.034 softening softening 1.18 softening 17.8 table 3: analysis of siclanic® hardening criteria. the ratio δσ1 / σ1 defines the hardening rate. b. saadouki et alii, frattura ed integrità strutturale, 43 (2018) 133-145; doi: 10.3221/igf-esis.43.10 140 plastic strain energy many researchers have used the cyclic plastic strain energy as damage criterion in low cycle fatigue. the dissipation of the mechanical energy is initially caused by the cyclic plastic strain connected, at microscopic level, to the dislocation movement and then, by the stress which relates to these dislocations resistance of displacement. if we consider δw the mechanical energy per cycle as design parameter, the law of simple damage consists in supposing that there will be a failure when the total energy wf has reached a critical value. halford [25] proposed a relation for measurement of the area under the hysteresis loop (fig. 9), provided that the stress and the plastic strain are measured from the tip of the loop. figure 9: area under hysteresis loop [26]. in the majority of cases, the difference between the energy measured directly from the hysteresis curve by a planimeter and that calculated by eq. (7) is less than 10%.           1 ' 1 ' p n w n (7) where n’ is the cyclic hardening coefficient. the total energy to failure wf is defined by the eq. (8):  f fw n w (8) fig. 10 shows a significant decrease in mechanical energy δw per cycle when the number of cycles increases. practically this energy does not vary during a test since δε and δσ evolve inversely. the experimental points are placed around a curve corresponding to the following relation:   0.440.364 rw n (9) on the other hand, there is an increase in the total energy to failure wf when the number of cycles increases (fig. 11). figure 10: evolution of mechanical energy per cycle in terms of fatigue lifetime. b. saadouki et alii, frattura ed integrità strutturale, 43 (2018) 133-145; doi: 10.3221/igf-esis.43.10 141 figure 11: variation of the total energy to failure as function of fatigue lifetime. fatigue resistance basquin and manson-coffin defined experimentally laws characterizing low cycle fatigue life, between strain variations ∆ε and the fatigue life. manson-coffin relation:     ' 2 2 c rn (10) basquin relation:     ' 2 2 f bel rn e (11) siclanic® cyclic tests were conducted at imposed stress, achievement of fatigue resistance curves ε – n cannot be direct. we used prediction formulas. these formulas have been proposed in principle to limit the number of tests and to avoid even realize one fatigue test. the resistance relations fatigues are predicted by two methods, whose coordinates come from monotonic characteristic of the alloy. a) four correlation point method this method developed by manson and halford [25], allows the plot of elastic and plastic lines by knowing some monotonic characteristics. b) universal slopes method a second estimation method for resistance curves is proposed [27]. manson, after many tests on various materials, made the followings hypotheses: elastic and plastic lines have respectively mean slopes of -0.12 and -0.6. the points corresponding to the total strain variations ∆εt are placed on an asymptotic curve to the elastic and plastic lines. for low cycle fatigue, plastic strain predominates. the curve representing the plastic strain variation is placed above that of elastic strain up to a certain number of cycles (fig. 12). siclanic® damage behavior, at low number of cycles, is accommodated by plastic cyclic strain. in approximating of the yield stress, plasticizing will be located at certain points of the alloy structure. the plastic strain curve presents an important slope; this reflects the high gradient of this parameter. this gradient is a sign of cracks priming. approximation methods appear in agreement at the strain values. however, this agreement is not verified for the number of cycles in transition point ptr. the universal slopes method seems most pertinent. the elastic line expressing siclanic® resistance is located in the same order as the monotonic characteristics uts and ys0.2%. for the plastic line, the capacity of plastic cyclical strain is dependent on the ductility; it operates to the same effect as this last. in terms of total strain, the siclanic® resistance is closely linked to materiel ductility at low cycle b. saadouki et alii, frattura ed integrità strutturale, 43 (2018) 133-145; doi: 10.3221/igf-esis.43.10 142 (predominance of ∆εp-n relation), and the yield strength and ultimate tensile strength at high cycle (predominance of ∆εeln). (a) (b) figure 12: resistance fatigue curves for siclanic® predicted using (a) four correlation point method and (b) a universal slopes method. εf σf (mpa) εf’ σf’(mpa) b c manson’s four points 0.29 793.35 0.19 931.71 -0.09 -0.46 manson’s universal slopes 0.29 793.35 0.36 1168.5 -0.12 -0.6 table 4: low cycle fatigue characteristics for the siclanic®. moreover, many researchers have linked coefficients b and c to the cyclic hardening coefficient n’, tab. 5 shows some formulas results. morrow has proposed the following relation:    ' 1 5 ' n b n (12)    1 1 5 ' c n (13) tomkins [28] proposes on his side:    ' 1 2 ' n b n (14)    1 1 2 ' c n (15) b. saadouki et alii, frattura ed integrità strutturale, 43 (2018) 133-145; doi: 10.3221/igf-esis.43.10 143 b c morrow tomkins manson-coffin morrow tomkins manson-coffin -0.09 -0.1 -0.12 -0.59 -0.79 -0.6 table 5: comparison of the siclanic® fatigue exponent by different formulas. the values of b and c suggested by manson-coffin are close to those obtained by using morrow and tomkins relations. these numerical expressions based on the coefficient of hardening ′calculated experimentally are in good agreement with the manson-coffin approximations. conclusions echanical characterization of siclanic® proves that it is an alloy with high tensile characteristics. however, in cyclical loading, material shows moderate fatigue resistance. results for fatigue analysis summarized as follows: 1. the mechanical properties (yield strength, hardening coefficient) of the siclanic® are considerably modified by the application of high stress cycles, even in small numbers. the siclanic® is softened under the fatigue loading. hardening coefficient calculation with analytical models also predicts siclanic® softening phenomena. 2. if certain cycles reach stress levels close to or even more than ys 0.2 , we can meet a softening behavior, so a lowering of the ys 0.2 up to ys’0.2. high stress levels can cause harmful and permanent deformations to the proper functioning of the part. 3. the fractography analysis of the siclanic® specimens exhibits a transgranular failure during a cyclic solicitation. fractures arise at the grain boundaries, and flat surfaces in the crystalline material confirms the cleavage failure. acknowledgements uthors acknowledge the funding for coiltim project from “région picardie” and “le fonds européen de développement économique et régional (feder)”. references [1] hornbogen, e., hundred years of precipitation hardening. journal of light metal, 11 (2010) 127–132. [2] lockyer, s.a., noble, f.w., fatigue of precipitate strengthened cu-ni-si alloy, materials science and technology, 15 (1999) 1147-1153. doi: 10.1179/026708399101505194 [3] batawi, e., morris, d.g., morris, m.a., effect of small alloying additions on behavior of rapidly solidified cu-cr alloys, materials science and technology, 6 (1990) 892-899. doi: 10.1179/mst.1990.6.9.892 [4] lee, k.l., whitehouse, a.f., withers, p.j., daymond, m.r., neutron diffraction study of the deformation behavior of deformation processed copper–chromium composites, materials science and engineering, a384 (2003) 208-216. doi: 10.1016/s0921-5093 (02)00688-3 [5] chen, x.p., sun, h.f., wang, l.x., liu, q., on recrystallization texture and magnetic property of cu-ni alloys, materials characterization, 121(2016) 149-156. doi: 10.1016/j.matchar.2016.10.006 [6] delbove, m., vogt, j.b., bouquerel, j., soreau, t., primaux, f., low cycle fatigue behavior of a precipitation hardened cu-ni-si alloy, international journal of fatigue, 92 (2016) 313–320. doi: 10.1016/j.ijfatigue.2016.07.019. [7] sun, z., laitemb, c., vincen, a., dynamic embrittlement at intermediate temperature in a cu–ni–si alloy, materials science and engineering, a477 (2008) 145–152. doi: 10.1016/j.msea.2007.05.013. m a b. saadouki et alii, frattura ed integrità strutturale, 43 (2018) 133-145; doi: 10.3221/igf-esis.43.10 144 [8] goto, m., han, s.z., lim, s.h., kitamura, j., fujimura, t., ahn, j.h., yamamoto, t., kim, s., lee, j., role of microstructure on initiation and propagation of fatigue cracks in precipitate strengthened cu–ni–si alloy, international journal of fatigue, 87(2016) 15–21. doi: 10.2472/jsms.63.401 [9] zhao, d.m., dong, q.m., liu, p., kang, b.x., huang, j.l., jin, z.h., structure and strength of the age hardened cuni-si alloy, materials chemistry and physics, 79(2003) 81-86. doi: 10.1016/s0254-0584(02)00451-0. [10] fujiwara, h., sato, t., kamio, a., effect of alloy composition on precipitation behavior in cu-ni-si alloys, journal of the japan institute of metals, 62 (1998) 301-309. doi: 10.2472/jsms.63.401. [11] khereddine, a., hadj larbi, f., and al, microstructures and textures of a cu–ni–si alloy processed by high-pressure torsion, journal of alloys and compounds, 574(2013) 361-367. doi: 10.1016/j.jallcom.2013.05.051. [12] hadj larbi, f., azzeddine, h., baudin, t., et al, microstructure and texture evolution in a cu–ni–si alloy processed by equal-channel angular pressing, journal of alloys and compounds, 638(2015) 88-94. doi: 10.1016/j.jallcom.2015.03.062. [13] ageladarakis, p., o'dowd, n., webster, g., tensile and fracture toughness test of cunisi at room and cryogenic temperatures, commission of the european communities, abingdon (united kingdom). jet joint undertaking, available from british library document supply centredsc: 4672.2625(99/01). [14] reed, r., fickett, f.r., summers, l.t., stieg, m., advances in cryogenic engineering materials, a40 (1994). [15] castillo, e., fernández-canteli, a., a unified statistical methodology for modeling fatigue damage, springer (2009). [16] raposo, p., correia, j.a.f.o., de jesus, a.m.p., calçada, r.a.b., lesiuk, g., hebdon, m., fernández-canteli, a., probabilistic fatigue s-n curves derivation for notched components, frattura ed integrità strutturale, 42 (2017) 105118. doi: 10.3221/igf-esis.42.12 [17] correia, j.a.f.o., huffman, p., de jesus, a.m.p., cicero, s., fernández-canteli, a., berto, f., glinka, g., unified two-stage fatigue methodology based on a probabilistic damage model applied to structural details, theoretical and applied fracture mechanics (in press) (2017). doi: 10.1016/j.tafmec.2017.09.004. [18] standard practice for statistical analysis of linear or linearized stress-life (s-n) and strain-life (ε-n) fatigue data. astm e739 – 10. [19] lieurade, h.p., rupture par fatigue des aciers. ed. institut de recherches de la sidérurgie française, collection irsidotua (1991). [20] inglis, n.p., hysteresis and fatigue of wöhler rotating cantiveler specimen, the metallurgist, (1927) 23-27. [21] pineau, a., mécanismes d’accommodation et de fissuration en fatigue oligocyclique, mécanique matériaux electricité, 323/324 (1976) 6-14. [22] smith, r.w., hirschberg, m.h., manson, s.s., fatigue behavior of materials under strain cycling in low and intermediate life range, nasa-tn-d-1574, n-63-14250, (1963). [23] morrow, j., cyclic plastic strain energy and fatigue of metals, internal friction, damping and fatigue of metals, astm (1965) 48-87. [24] gallet, g., lieurade, h.p., prévision du comportement en fatigue plastique des aciers de construction mécanique à partir de leurs caractéristiques de traction, rapport irsid (irsid, saint-germain-en-laye), (l977). [25] halford, g.r., manson, s.s., symposium on fatigue, londres (1967). [26] gallet, g., lieurade, h.p., influence de la structure métallographique d'un acier au nickel chrome – molybdène sur son comportement en fatigue plastique, communication présentée aux journées métallurgiques d'automne organisées par la société française de métallurgie, (1974). [27] lemaitre, j., chaboche, j.l., mécanique des matériaux solides, science sup 2éme édition, dunod (2004). [28] tomkins, b., fatigue crack propagation analysis, philosophical magazine, 155 (1968) 1041-1065. nomenclature a (%) elongation at fracture b fatigue resistance exponent c fatigue ductility exponent e young module k monotonic hardening coefficient k’ cyclic hardening coefficient n monotonic hardening exponent n’ cyclic hardening exponent b. saadouki et alii, frattura ed integrità strutturale, 43 (2018) 133-145; doi: 10.3221/igf-esis.43.10 145 nf number of cycles to failure uts ultimate tensile strength r load ration wf total energy to failure ys0. 2% conventional yield strength at 0.2 of strain ys’0.2% conventional yield strength at 0.2 of strain in cyclic tensile σ1 stress corresponding to 1% of tensile plastic deformation σa alternative stress σamp stress amplitude σf true stress at failure σ’f fatigue resistance coefficient σm mean stress σmax maximum stress σmin minimum stress εf true strain at failure ε’f fatigue ductility coefficient ∆σ1 stress variation between the stress 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can be opened with acrobat and adobe reader 5.0 and later.) >> /namespace [ (adobe) (common) (1.0) ] /othernamespaces [ << /asreaderspreads false /cropimagestoframes true /errorcontrol /warnandcontinue /flattenerignorespreadoverrides false /includeguidesgrids false /includenonprinting false /includeslug false /namespace [ (adobe) (indesign) (4.0) ] /omitplacedbitmaps false /omitplacedeps false /omitplacedpdf false /simulateoverprint /legacy >> << /addbleedmarks false /addcolorbars false /addcropmarks false /addpageinfo false /addregmarks false /convertcolors /converttocmyk /destinationprofilename () /destinationprofileselector /documentcmyk /downsample16bitimages true /flattenerpreset << /presetselector /mediumresolution >> /formelements false /generatestructure false /includebookmarks false /includehyperlinks false /includeinteractive false /includelayers false /includeprofiles false /multimediahandling /useobjectsettings /namespace [ (adobe) (creativesuite) (2.0) ] /pdfxoutputintentprofileselector /documentcmyk /preserveediting true /untaggedcmykhandling /leaveuntagged /untaggedrgbhandling /usedocumentprofile /usedocumentbleed false >> ] >> setdistillerparams << /hwresolution [2400 2400] /pagesize [612.000 792.000] >> setpagedevice microsoft word numero 23 articolo 12 g. de pasquale et alii, frattura ed integrità strutturale, 23 (2013) 114-126; doi: 10.3221/igf-esis.23.12 114 scilla 2012 the italian research on smart materials and mems experimental methods for the characterization of fatigue in microstructures g. de pasquale, a. somà department of mechanical and aerospace engineering, politecnico di torino corso duca degli abruzzi 24, 10129 torino (italy) aurelio.soma@polito.it, giorgio.depasquale@polito.it abstract. the mechanical fatigue behavior of gold microbeams is analyzed. dedicated devices have been designed and built able to produce alternate loading on gold specimens; the electrostatic actuation is used as driving force. gold beams are tested under both bending and tensile alternate loadings. results were used to plot s-n curves and fatigue goodman-smith diagram in order to estimate the fatigue limit of the material in presence of mean and alternate stress conditions. the surface topography evolution is studied and failure modes are discussed. keywords. reliability; mems; mechanical fatigue; gold microbeams; alternate loading; fem simulation; interferometric microscopy. introduction he reliability of micro-electro-mechanical systems (mems) became a fundamental topic of investigation as a result of their widespread application in many every-day life devices. for instance, micro-fluidic bio-mems is used for medical purposes, mems-based telecommunication devices are subjected to the action of micro-components as oscillators or switches, inertial sensors for aerospace applications dictate very severe performance requirements in order to minimize repairs and replacement, etc. about structural reliability, it is necessary to examine effects of process parameters, geometry, loads and working environmental conditions, which are all aspects whose knowledge is at present are still under investigation. electro-mechanical coupling often represents a crucial issue for system reliability even if many other sources of collapse potentially involve reliability. by focusing on material failure, it emerges that mechanical damage represents the more relevant source of failure. mechanical reliability issues include: mechanical fatigue, thermal fatigue, mechanical strength, surface and contact failure. a survey of the literature pointed to a lack of experience in investigation of fatigue behavior of metal microstructures; in [1] fatigue testing methods for thin-film metal were described after observing the incidence of material length on damage relative to bulk material. espinosa [2] evaluated the effect of size on mechanical response of suspended thin gold membranes and described the effect of thickness on yield stress and failure of the membrane investigated fatigue behavior of gold micro-bridges at resonant frequency and pull-in actuation voltage, also monitoring structural stiffness and changes in electrical resistance. important parameters for fatigue behavior of gold were investigated and discussed [3] as strain rate sensitivity, grains size, grain boundaries properties and temperature gradients. t http://www.gruppofrattura.it http://dx.medra.org/10.3221/igf-esis.23.12&auth=true g. de pasquale et alii, frattura ed integrità strutturale, 23 (2013) 114-126; doi: 10.3221/igf-esis.23.12 115 failure modes lectro-mechanical coupling often represents a crucial issue for the system reliability, especially related to surface contact, corrosion, electromigration and wear. by focusing the attention on the material failure, mechanical damage is the most relevant source of collapse; mechanical reliability issues are concerned with the items listed below:  mechanical fatigue: devices as micromirrors or microswitches operating at high frequencies and structural components such as hinges or elastic suspensions suffer from cyclic fatigue damage accumulation; cracks initiation and propagation take place in the material and may cause the component failure;  mechanical strength: the structural integrity of high-stressed components as micro-needles for biomems or thermal posts for microheat exchanges is crucial to avoid fracture collapse;  thermal fatigue: many sensors and actuators operating by thermal actuation are subjected to relevant temperature gradients and structural strain levels resulting in thermal cycling, high temperature fatigue and creep;  contact surfaces and stiction: devices including surfaces that come in contact, as microactuators with electrical actuation pads, require a control on the adhesion properties; rotating structures as microrotors situated in microengines need good surface properties resisting wear and stiction. failure analysis has an important role in the design, fabrication, and evaluation of performance and reliability of microstructures; some of the most common techniques used for mems have been firstly developed for integrated circuits. these techniques include optical and electron microscopy, focused ion beam techniques, atomic force microscopy, acoustic microscopy (to resolve contacts between sticking parts) and scanning laser microscopy. for moving parts experiencing wear, the most relevant source of failure is represented by sticking of the sliding contacts. the sticking occurs due to changes in the surface topography of the sliding surfaces, which accelerate with an increase in the applied forces. one of the major challenges in failure analysis of mems structures has been the inability to duplicate failures [4]. it was reported that failure of some mems components are largely due to a single dominant failure mode, e.g., sticking of microengine gears to the substrates or to the hubs [5]. surface roughening can also cause failure of mems structures. fatigue failure test results are usually presented in the literature in the traditional form of s-n curves; this requires a high number of failures (represented by a single point of the curve) to draw a single diagram. another difficulty lies in the fact that the data from s-n curves also capture the device-to-device variability, affected by the uncertainties of material characteristics and fabrication processes. frequently each investigation involving specific devices tends to be devicedependant; fabrication processes, etching techniques or the substrate material play a major role on film structure strength as well as the presence of initial defects [5, 6]. fatigue testing strategies echanical tests for the characterization of fatigue behavior can be divided in two categories according to the experimental configuration used: the “in-situ” configuration adopts on-chip testing machines with specimens that are embedded into the device. the “ex-situ” configuration instead is based on macro-dimensional testing machines [7]. “in-situ” configuration the first group is the most relevant in the literature and includes simple test structures such as microbeams and microcantilevers, that are largely used for fatigue testing. some examples are listed in the following: uniaxial cyclic loading tests were performed on single crystal specimens and a reduction in fatigue life was observed for specific strain levels [8]. the fracture caused by fatigue loading on ni-p amorphous alloy microcantilevers was studied and the fatigue strength resulted about one-third of the static bending strength [9]. from the aspect of fracture striations the authors concluded that the crack propagation occurs by cyclic plastic deformation at the crack tip. many fatigue experiments were performed on polysilicon resonant structures oscillating in-plane; a perforated plate moved by two sets of comb-drives determines the bending of a notched cantilever [10]. a decay of fracture strength with respect to the single crystal case was documented, together with the correlation between the damage accumulation during crack initiation and the surface oxidation. in the case of gold microbeams specimen design of “in situ” device has been done by the present research group in the last years [11, 12]. e m http://www.gruppofrattura.it http://dx.medra.org/10.3221/igf-esis.23.12&auth=true g. de pasquale et alii, frattura ed integrità strutturale, 23 (2013) 114-126; doi: 10.3221/igf-esis.23.12 116 “ex-situ” configuration among “ex-situ” experimental configurations, sharpe [13] described a testing machine for microcantilevers where the actuation force is provided by an external actuator and transferred to the sample through an optical fiber. a mechanical testing device enabling fatigue analyses on microstructures was developed by komai [14] where single crystal silicon elements were characterized by using an indenter moving in the vertical direction; fracture surfaces were also analyzed by afm. test structures he “in-situ” excitation strategy was adopted to design and built the test structures used in this work; thus the test structure included the actuator and the sample on a compact geometry. gold was selected among other ductile materials because of its electrical properties and suitability to simple and low-cost fabrication processes. each device for fatigue tests should have the following three features: 1) the possibility to generate variable amplitudes of alternate forces for specimen excitation and variable stress levels inside the material, 2) the possibility to monitor material damage during the accumulation of loading cycles and 3) to provide a criterion to establish the final collapse of the specimen. to identify the exact number of collapses for a given set of specimens, it is fundamental to represent the test results with the established fatigue diagrams as the s−n curve (also known as wöhler diagram); the number of collapses is also used to estimate the fatigue limit through the “staircase” method. the final collapse is not always identified by the rupture of the specimen but, depending on the specific application, it can be represented by the yielding point, the softening of the material, or other relevant events. in a fatigue test, the event determining the collapse of the specimen must be fixed in advance. when the test structures for fatigue analysis are designed, a very important parameter that must be determined is the stress level in the specimen. the alternate stress needed to investigate the fatigue behavior is defined by a mean stress σm and an alternate stress σa. because of the electro-mechanical strategy was used to load the specimen, the correspondence between actuation voltage and stress level has to be determined in advance, when geometry and shape of the test structure are designed. the appropriate stress levels in the specimen can be obtained by defining appropriately the extension of actuation surfaces, of electrodes gap thickness and structural stiffness. a constant excitation frequency was used to supply the test structures fabricated, so that the excitation signal can be used as a counter of the loading cycles; the number of cycles of excitation was a function of time only. a test strategy was defined to detect the fatigue behavior of gold samples; the interferometric microscope was used to measure some parameters that were used to estimate the material damage with indirect approach. the strategy described is original and can be extended to general analysis of fatigue in microstructures. test structures were built by bruno kessler foundation (trento, italy) using the rf switch surface micromachining process and design procedure has been described in previous works [15, 16]. structural moving parts were obtained through the gold electroplating process; the material was deposited in two steps, allowing the selective superimposition of two gold layers. this permitted creation of thin films of small and large thicknesses, which were used for the specimen and for the suspended actuation electrode, respectively. the thickness of the actuation electrode is higher than that of the specimen to increase its mechanical stiffness; many square holes are present on the suspended electrode to facilitate the chemical removal of the sacrificial layer used to obtain the suspended parts and provide a final 3μm thick air gap. the lower electrode consists of a polysilicon layer deposited on the substrate previously oxidized on the surface and covered with a thin low temperature oxide layer. the material parameters are: young’s modulus e = 98.5 gpa poisson ratio ν = 0.42 density ρ = 19.32·10-15 kg/µm3 design 1: shear and flexural fatigue loading the testing device is shown in fig. 1a. the nominal geometrical dimensions were checked by the optical profilometer on the actual structures; both nominal and measured dimensions are listed in tab. 1 for the specimen and the actuation electrode. figure 1b shows a sem image of the device. the fatigue test device includes both the actuation electrode that is represented by a perforated plate and the specimen; the specimen is a double-clamped beam with rectangular cross section. the specimen is fixed to a rigid constraint on one side and is connected to the moving plate on the opposite side; plate motion causes bending of the specimen in the out-of-plane direction. t http://www.gruppofrattura.it http://dx.medra.org/10.3221/igf-esis.23.12&auth=true g. de pasquale et alii, frattura ed integrità strutturale, 23 (2013) 114-126; doi: 10.3221/igf-esis.23.12 117 (a) (b) figure 1: geometrical shape of the testing device for shear and flexural fatigue loading with enlarged gap thickness (a) and sem image of the actual device (b). at the specimen connections with the rest of the device the sharp corners were rounded to avoid the notch-effect in correspondence with specimen-support and specimen-plate conjunctions. the plate is clamped on the side opposite the specimen. a stress distribution combining shear and flexural components affects the material of the film during its bending; this stress distribution is variable across the beam thickness. the device is supplied by an alternate voltage of actuation that causes the gold beam deflection; the amplitude of the alternate bending force is variable and is proportional to the amplitude of the input voltage. the number of loading cycles can easily be determined by the knowledge of the input voltage frequency and the loading time. nominal dimension [μm] measured dimension [μm] specimen length 50.0 46.5 specimen width 10.0 12.4 specimen thickness 1.800 1.945 plate length 420.0 417.2 plate width 180.0 183.1 plate thickness 4.800 4.695 holes side 20.0 18.4 holes interspace 20.0 21.3 number of holes 10x4 10x4 lower electrode length 420.0 420.8 lower electrode width 190.0 192.3 lower electrode thickness 2.300 2.360 gap thickness 3.000 3.009 table 1: nominal dimensions and dimensions measured by optical profilometer on actual samples for shear and flexural fatigue loading. design 2: tensile fatigue loading the schematic of testing device is represented in fig. 2a and an optical microscope image of the actual test structure is shown by fig. 2b. the specimen is the small, suspended double-clamped beam located in the center of the device; the specimen has a rectangular cross section and is connected to the structure with rounded corners to avoid local stress concentration effects. the specimen is connected to two movable plates acting as electrostatic actuators, which are constrained at the outer edges by means of trapezoidal beam elements. the trapezoidal shape is pretty original and was http://www.gruppofrattura.it http://dx.medra.org/10.3221/igf-esis.23.12&auth=true g. de pasquale et alii, frattura ed integrità strutturale, 23 (2013) 114-126; doi: 10.3221/igf-esis.23.12 118 adopted to provide uniform stress distribution in their material when bend; they act as structural hinges and allows a rigid rotation of the perforated plates. when the plates are actuated, the hinges allow a rigid rotation of the plates around an axis corresponding to the outer constraints, and the specimen undergoes a tensile load. the combined symmetrical rotation of the plates causes a tensile actuation of the specimen situated at the center of the device. nominal dimensions and effective dimensions of test structures are reported in tab. 2; the measures were taken with the optical profilometer. the differences between measures are due to the building process tolerances. (a) (b) figure 2: geometrical shape of the testing device for tensile fatigue loading where the gap thickness is enlarged (a) and sem image of the actual device (b). nominal dimension [μm] measured dimension [μm] specimen length 30.0 27.7 specimen width 10.0 11.2 connection radius 4.0 4.0 plate length 450.8 457.8 plate width 85.0 84.3 holes side 8.0 7.8 number of holes per plate 22x3 22x3 supports length 50.0 48.2 supports internal width 15.0 12.8 supports external width 25.0 23.2 lower electrode width 105.0 105.0 internal electrodes distance 85.0 84.7 specimen thickness 1.800 1.900 plate thickness 5.400 5.450 supports thickness 5.400 5.450 lower electrode thickness 2.300 2.360 air gap thickness 4.500 4.500 table 2: nominal dimensions and dimensions measured by optical profilometer on actual test structures for tensile fatigue loading. fem models he specimen design activity was supported by numerical simulations implemented using a commercial-type tool (ansys) for optimizing test device geometry. the nonlinear relationship between structural and electrical domains, due to electrostatic force depending on the local gap width, was modeled by 1-d multiphysics elements t http://www.gruppofrattura.it http://dx.medra.org/10.3221/igf-esis.23.12&auth=true g. de pasquale et alii, frattura ed integrità strutturale, 23 (2013) 114-126; doi: 10.3221/igf-esis.23.12 119 “trans126”. a different simulation approach was also used to calculate the stress distribution in the specimen; in these models the structural domain was only represented and the vertical deflection was imposed as a constraint according to the values of deflection measured on actual devices. this approach avoids the uncertainties introduced by the electromechanical coupling and gives a precise indication about the stress configuration in the material for a given deformed configuration of the test structure. the estimation of stress distribution refers to an ideal geometry with surfaces unaffected by microdefects; stress distribution in actual specimens depends on crack nucleation points where local stress intensity is amplified, resulting in fatigue-induced failure. figure 3a shows the results of fem simulations on the design 1, where the electro-mechanical coupling was included in the model. the same results for the design 2 are represented in fig. 3b. (a) (b) figure 3: fem von mises equivalent stress distribution on the devices for shear and flexural (a) and tensile (b) fatigue loading. furthermore, dynamic models were used to determine the numerical resonance frequency of the device and to investigate the modal shape of the structure; at this purpose modal analyses of the unloaded structures were performed. experimental strategy voltage-stress characteristics he structural analysis was performed under the hypothesis of linear elastic behavior of the material; this assumption is justified by the field of operations that is quite lower than the yield stress level, by the properties of metals, and by the small deformations involved. despite the specimen shape is very simple, the traditional beam theory supported by an analytic approach is not easy to use in this case. the actuation force is applied to the specimen through movable structures that are subjected to the electro-mechanical coupling lows. as a consequence, a combination of fe simulations and static measurement of the displacement are needed to calculate the stress level in the material with an appreciable confidence. other effects, such as geometrical features like connection radii, make the numerical approach particularly effective for the analysis. the static relationship between the applied voltage and specimen tip displacement was measured on actual samples for the design 1 and is shown in fig. 4. the internal stress of the material was estimated using structural fe models, where the specimen tip displacement was imposed on the basis of the measured values. in order to impose the desired stress levels to the structure during fatigue tests, the characteristics of conversion between electric voltage and stress is needed. this conversion curve was determined in two steps: firstly the relation between electric voltage and static deflection was measured, and then the correspondence between the deflection and the stress distribution was calculated by the fe modeling. the static voltage-displacement relation was modeled by fem also, by introducing the experimental values of displacement as constraints; the characteristic that results from the numerical model, compared to the measurements is represented in fig. 5 for the tensile loading device (design 2). then the stress distribution in the specimen was calculated using the previously reported nominal material parameters. figure 6 represents the relation between the applied static voltage and the maximum stress level in the axial direction of t http://www.gruppofrattura.it http://dx.medra.org/10.3221/igf-esis.23.12&auth=true g. de pasquale et alii, frattura ed integrità strutturale, 23 (2013) 114-126; doi: 10.3221/igf-esis.23.12 120 the specimen; as expected the curve follows a second-order polynomial equation, which is directly dependent on the capacitive voltage-displacement relation. the relation between displacement and stress is linear as a consequence of the linear elastic material characteristic assumed in the fem model; this assumption is well justified considering the small displacements involved. figure 4: vertical displacement of the specimen loaded tip measured using the optical interferometric technique with respect to static input voltage (design 1). measures are affected by an error introduced by surface roughness, particularly at small displacements. figure 5: static voltage-displacement conversion curve for the tensile loading device from fem simulations (continuous line) and measurements (black dots). figure 6: static voltage-stress conversion curve for tensile loading device (design 2) from fem simulations constrained with experimental values of deflection. experimental setup a voltage generator was used to supply the test structures; the alternate load causing fatigue was provided by the application of an alternate voltage to the actuators. the number of loading cycles was calculated from the frequency of the actuation voltage. the experiments were performed with the optical interferometric microscope zoomsurf3d fabricated by fogale nanotech (nimes, france); the same equipment was used for the preliminary static and dynamic measurements previously described [18]. the microscope is equipped by a voltage generator for dynamic tests. the excitation voltage generated may vary in the range 0-200v at low and high frequencies up to 2mhz. the pull-in voltage as damage detector fatigue tests of mems reported in the literature show that several different parameters for monitoring material damage can be used. resonant frequency, quality factor, and electrical resistance are widely used parameters for this purpose. this http://www.gruppofrattura.it http://dx.medra.org/10.3221/igf-esis.23.12&auth=true g. de pasquale et alii, frattura ed integrità strutturale, 23 (2013) 114-126; doi: 10.3221/igf-esis.23.12 121 work proposes a new strategy for detecting structural stiffness loss, based on the pull-in voltage of the fatigue test device. because of its sensitivity and ease of setting up the associated experimental equipment, this can be a very significant parameter. the diagram shown in fig. 7 represents the equilibrium points between the electric and elastic forces acting on the device. the electric force attracts the actuators towards the corresponding counter electrode, and the elastic force is generated by the structural reaction after deformation and tends to restore the original configuration. the pull-in voltage is the highest level of the actuation voltage that preserves the equilibrium condition under the two forces. the x-axis of the diagram indicates the vertical displacement normalized to the initial gap h0, while the y-axis represents the electrostatic actuation force (fel) and the elastic reaction of the structure (fst). the elastic curve is variable during the fatigue test because the structural stiffness is affected by the progressive material damaging; thus the slope of the elastic characteristic decreases progressively as the fatigue cycles increase. this means that the value of pull-in voltage varies during the test because the structural stiffness also varies depending to the material damage produced by fatigue. according to the experimental procedure proposed, the change in mechanical stiffness serves as a damage detector in the material and is measured indirectly by monitoring the pull-in voltage. figure 7: relation between structural elastic force and electrostatic force; the stiffness variation causes different values of pull-in voltage. testing procedure the test structures are excited by imposing an alternate voltage difference between the lower electrodes and plates; this produces the repetitive movement of the structure and the specimen axial loading. the loading voltage used is identified by three parameters: a) the voltage amplitude va, b) the voltage bias vbias, and c) the excitation frequency f. the fatigue test procedure consists of the application of a cyclical loading voltage characterized by a specific set of parameters. the combination of parameters (a) and (b) determines the entity of two additional parameters identifying the stress variation inside the specimen material: the alternate stress σa and the mean stress σm. the combination of time and frequency yielded the number of cycles of the current excitation block. the procedure was repeated up to a specimen failure. the failure event was defined in advance as a drastic reduction (at least 10% of the previous value) of the pull-in voltage, reflecting a reduction of the structural stiffness. the pull-in voltage (step 1) was measured by a static actuation using a dc voltage, which was progressively increased. the pull-in condition was detected optically using the interferometer microscope. the alternate load was obtained (step 2) by means of the alternate voltage va at 20khz; the frequency of actuation was set to a value that was significantly lower than the mechanical resonance of the device, which is 28khz approximately. the two main reasons for this are given as follows: the resonant amplification involves additional problems when evaluating material internal stresses; the progressive damage in the material could cause a shift in resonance peak or alter the device quality factor as a consequence of possible changes in structural stiffness and damping. computing of cycles number system dynamics must carefully be considered when supply voltage frequency is converted to a number of cycles of alternate load. the force that is responsible for specimen oscillation is generated by the potential difference between suspended and lower electrodes. for the solution adopted in design 1, two periods tl of the loading curve correspond to one period tv of the alternating voltage curve, as represented in fig. 8. this is due to the electrostatic force that acts always in the attractive direction for both possible polarizations of the electrodes; a consequence is that the current mode of deflection does not allow http://www.gruppofrattura.it http://dx.medra.org/10.3221/igf-esis.23.12&auth=true g. de pasquale et alii, frattura ed integrità strutturale, 23 (2013) 114-126; doi: 10.3221/igf-esis.23.12 122 oscillation around the undeformed shape. the resulting number of load cycles nl is related to the number of cycles of alternating voltage nv according to vl 2nn  (1) from this consideration, the number of loading cycles for each step of actuation is ii 2 ftn  (2) figure 8: comparison between actuation voltage cycle and fatigue load cycle for design 1. the total number of fatigue cycles up to failure can be calculated as mi1f ...... nnnn  (3) where nm indicates the number of loading cycles in the last step before collapse. the curves of alternate displacement and local stress have the same frequency as the loading curve. the alternate excitation was maintained for 10 s during the tests between two consecutive measurements of the pull-in voltage; each block of excitation was composed of 4·105 cycles of loading, displacement, and local stress. the number of cycles to failure is indicated as nf. for the test structure represented by design 2, the total number of fatigue cycles up to failure can be calculated with the same relation reported in eq. (3). again, the force responsible for specimen oscillation is generated by the potential difference between the suspended plates and lower electrodes. however, in this case, it results in one period tl of the loading curve corresponding to one period tv of the alternate voltage curve; the structure oscillates around the initial deformed shape determined by the vbias load. the resulting number of loading cycles nl corresponds to the number of cycles of the alternate voltage nv: vl nn  (4) from this consideration, the number of loading cycles for each step of actuation becomes ii ftn  (5) results fatigue limit or the shear micro specimen the fatigue limit was estimated using the “staircase” method; this procedure is largely used in the macroscale to estimate the fatigue limit through a limited number of tests and is widely described in [17]. the “staircase” method is based on a few parameters: the reference number of cycles nref, the starting load level f, and the load step δf. the procedure can briefly be described in a few steps: the first specimen is loaded at the starting load level (f) for nref cycles; if the specimen collapses during fatigue loading, then the second specimen will be loaded at f–δf level for nref cycles. instead, if the first specimen does not collapse during fatigue loading, then the second specimen will be loaded at f+δf level for nref cycles. the procedure must be repeated for many specimens by increasing the load level after each nonfailure and by reducing the load level after each failure. for example, for shear and flexural samples (test structure design 1), the reference number of cycles used was nref = 2·106, the starting load level was f = 15v, and the load step was δf = 1v. the procedure was repeated for six specimens; in tab. 3, each failure was then reported as 1, while each nonfailure was reported as 0. the fatigue limit f http://www.gruppofrattura.it http://dx.medra.org/10.3221/igf-esis.23.12&auth=true g. de pasquale et alii, frattura ed integrità strutturale, 23 (2013) 114-126; doi: 10.3221/igf-esis.23.12 123 estimated by the application of the “staircase” method is found to be fd = 13±0.7v. this value was used as an important reference when the alternate-load level was imposed in fatigue tests. according to the definition of fatigue limit, failures at load levels higher than fd and nonfailures at load levels lower than fd are normally expected. loading level specimen 1 2 3 4 5 6 15v 1 16v 1 1 17v 0 1 18v 0 table 3: results of fatigue loading on six specimens (design 1) for the fatigue limit estimation using the “staircase” method. the specimen failure is indicated as 1, while the specimen nonfailure is indicated as 0. shear and flexural fatigue tests the results on test structure design 1 are reported in fig. 9, where the evolution of pull-in voltage for different specimens during the accumulation of load cycles is shown. each curve refers to a different value of the alternate input voltage used (va). the failure was assumed to occur in the instant when the pull-in voltage shows a reduction that is equal to or higher than 10% of the previous value; only collapsed specimens are represented by the curves reported. the curves shown in fig. 10 indicate the pull-in voltage variation measured on other specimens; some of them failed instantly because of high loading amplitudes (21 and 22.5v); other specimens did not fail after 200 million cycles because they were excited at a load level that is equal or lower than the fatigue limit (10–13v). figure 9: pull-in voltage of different testing devices (design 1) during the accumulation of fatigue loading, with alternate load being provided at 20khz frequency at the amplitude va indicated for each curve. the pull-in voltage was measured and stored at specific time intervals. the specimen failure is indicated by the strong pull-in reduction (ranging from 12.9% and 22.7% of its last value). figure 10: pull-in voltage of different testing devices (design 1) during the accumulation of fatigue loading, with alternate load being provided at 20khz frequency at the amplitude va indicated for each curve. the pull-in voltage was measured and stored at specific time intervals. specimens that failed immediately (va = 21v and va = 22.5v) or that did not fail (va = 10v, va = 12v and va = 13v) are reported. the curve labeled with va = 0v represents the pull-in variation during the application of a series of consecutive static actuations without alternate fatigue loading. http://www.gruppofrattura.it http://dx.medra.org/10.3221/igf-esis.23.12&auth=true g. de pasquale et alii, frattura ed integrità strutturale, 23 (2013) 114-126; doi: 10.3221/igf-esis.23.12 124 a wöhler diagram (fig. 11) was obtained by indicating the instant of failure for specific amplitude of the actuation voltage at the corresponding number of cycles. the s-n curve confirms that the estimated value of the fatigue limit is consistent; in fact, it represents the load amplitude threshold separating collapsed specimens from noncollapsed ones. figure 11: s-n curve (wöhler diagram) summarizing the results of fatigue tests on shear and flexural specimens. the number of cycles to failure is reported for each specimen in relation to the axial stress amplitude calculated by the fem model. tensile fatigue tests the stress level produced in the specimen material (test structure design 2) by the electric supply during the fatigue tests was carefully considered; previously extracted and reported voltage-displacement relations were used to properly set the power supply in order to reach the desired levels of mean and alternate stress. specifically, three different levels of tensile mean stress were produced at 50, 60, and 65mpa, respectively. table 4 summarizes the loading and stress conditions for each test; the stress level acting along the axial direction of the specimen is reported here as estimated by fem simulations. specimen σm [mpa] σa [mpa] σmax [mpa] σmin [mpa] vm [v] va [v] nf [106] i.1 50 50.0 100.0 0 98.2 98.2 37.2 i.2 46.7 96.8 3.4 114.5 78.5 19.2 i.3 43.8 93.8 6.2 119.5 70.5 28.2 i.4 40.7 90.8 9.4 123.5 63.5 > 45 i.5 36.0 86.0 14.0 127.8 54.3 > 45 ii.1 60 41.4 101.4 18.7 141.3 56.4 1.8 ii.2 37.7 97.8 22.3 143.3 50.7 8.4 ii.3 32.7 92.8 27.3 145.8 43.3 6.6 ii.4 28.9 88.9 31.1 147.3 37.8 28.2 ii.5 23.9 83.9 36.2 148.9 30.9 > 45 ii.6 19.5 79.6 40.5 149.9 25.1 > 45 iii.1 65 10.0 75.1 55.0 157.7 12.2 iii.2 4.0 69.0 61.0 158.1 4.8 19.2 iii.3 2.4 67.5 62.6 158.2 2.9 28.2 iii.4 1.5 66.5 63.5 158.2 1.8 > 45 iii.5 0.8 65.8 64.2 158.2 1.0 > 45 table 4: stress levels and actuation voltages used for tensile tests. fatigue test results are shown in the s-n diagram of fig. 12. each point indicates the number of cycles at which the specimen collapses and the respective amplitude stress level; three levels of mean stress are indicated. the non-failed specimens are marked with a circle. in fig. 13 the same fatigue results are reported in a goodman-smith diagram where the minimum, mean, and maximum stresses are indicated. white dots represent failed specimens, and black dots represent non-failed specimens. the stress levels situated between failure and non-failure stress levels represent the threshold of σa (for a given σm), under which the component is not sensitive to fatigue phenomenon. the number of cycles nref = 45·106 http://www.gruppofrattura.it http://dx.medra.org/10.3221/igf-esis.23.12&auth=true g. de pasquale et alii, frattura ed integrità strutturale, 23 (2013) 114-126; doi: 10.3221/igf-esis.23.12 125 was assumed as a reference for identifying non-collapsed specimens: all specimens reaching the nref number of cycles were assumed to be not sensitive to fatigue under the applied loading conditions. the static voltage used among the successive alternate excitations to test for the integrity of the structure was vst = 100v. the diagram shows trend lines derived from the experimental results; according to the goodman-smith theory [16], it is possible to predict roughly the values of ultimate stress (around 110mpa), yield stress (around 75mpa), and fatigue limit at σm = 0 (around 60mpa). figure 12: experimental results of tensile fatigue tests in s-n diagram for three values of mean stress; specimens marked with an arrow do not fail. figure 13: goodman-smith diagram of tensile fatigue test results. failed specimens are indicated with white dots and non-failed specimens with black dots; trend lines are also shown. discussions n structures for shear and flexural fatigue tests, the static voltage input used to measure the pull-in of the device did not produce plastic deformations or local yield; this was verified by imposing a series of successive static actuations on the specimen and storing the corresponding pull-in voltage. the resulting curve is shown in fig. 10 and marked with a 0v amplitude. the value of pull-in results is constant despite several static actuations, revealing that the mechanical characteristics of the device did not change significantly; this leads to the evidence that the material is loaded within the elastic field and, more specifically, that the structural stiffness of the specimen is not affected by the static actuation. being the experimental strategy based on the correspondence between structural stiffness and material damage, it is evident that the sensitivity of the strategy used is related to the ability to detect the stiffness variation by means of the pull-in voltage. similarly, also in structures for tensile fatigue tests (design 2) the static voltage vst used to monitor the material strength was chosen after verifying the safety of the structure under such loading: fig. 14 shows two voltage-displacement curves measured on the same structure under two consecutive static actuations. the correspondence between the two curves leads to the conclusion that the applied voltage vst = 100v, later used to detect the material strength, is not responsible for stiffness variation and so does not contribute to the material damaging process. the effect of mean stress on the fatigue behavior was studied by tensile tests, where the application of a bias voltage to the structure allowed introducing a non-symmetric alternate load. when the mean stress of the fatigue load is null, the portions of the loading curve producing a tensile stress and a compression stress in the sample are equal. instead, in presence of a positive mean stress, the tensile stress condition prevails and determines an increased material degradation. i http://www.gruppofrattura.it http://dx.medra.org/10.3221/igf-esis.23.12&auth=true g. de pasquale et alii, frattura ed integrità strutturale, 23 (2013) 114-126; doi: 10.3221/igf-esis.23.12 126 as the curves reported in fig. 12 testify, higher is the mean stress level, lower is the number of cycles to failure in presence of a given stress amplitude. the presence of a non-zero mean stress is common in real applications of vibrating microstructures, where electric or mechanical static loads may easily occur. figure 14: static displacement of the structure (design 2) under two consecutive actuations; the material was excited in its elastic field. conclusions he mechanical fatigue of gold mems structures was investigated but in the case of alternate stress and in the case of alternate stress with the presence of mean stress. the design of dedicated test structures, supported by fem simulations addressed to the investigation of stress distribution was introduced. an original experimental strategy was adopted, which relates the stiffness loss and the pull-in voltage to the material damaging. experimental fatigue results were provided for shear, flexural and tensile loadings. results has been reported in the classical fatigue graph of wholer curves and goodmansmith graphs. results on specimen allow to determine important material fatigue parameters for mems design procedures. references [1] g.p. zhang, r. schwaiger, c.a. volkert, o. kraft, philosophical magazine letters, 83 (2003) 477. [2] h.d. espinosa, b.c. prorok, b. peng, “, j. of the mechanics and physics of solids, 52 (2004) 667. [3] y.h. chew, c.c. wong, f. wulff, f.c. lim, h.m. goh, thin solid films, 516 (2008) 5376. [4] d.m. tanner, in: proc. 22nd int. conference on microelectronics, piscataway, usa, (1999) 97. [5] a.b. soboyejo, k.d. bhalerao, w.o. soboyejo, j. of materials science, 38 (2003) 4163. [6] h.d. espinosa, b.c. prorok, j. of materials science, 38 (2003) 4125. [7] s.m. allameh, j. of materials science, 38 (2003) 4115. [8] t. ando, s. mitsuhiro, k. sato, sensors and actuators a: physical, 93 (2001) 70. [9] s. maekawa, k. takashima, m. shimojo, y. higo, s. sugiura, b. pfister, m.v. swain, japanese journal of applied physics, 38(1999) 7194. [10] c.l. muhlstein, s.b. brown, r.o. ritchie, sensors and actuators a: physical, 94 (2001) 177. [11] a. somà, g. de pasquale, j. of microelectromechanical systems, 18(4) (2009) 828. [12] g. de pasquale, a. somà, a. ballestra, analog integrated circuits and signal processing, 61 (2009) 215. [13] w.n. sharpe, j. bagdahn, mechanics of materials, 36 (2004) 3. [14] k. komai, k. minoshima, s. inoue, microsystem technologies, 5 (1998) 30. [15] a. somà, g. de pasquale, in: international semiconductor conference (cas 2007). [16] g. de pasquale, a. somà, j. of microelectromechanical systems, 20(4) (2011) 1054. [17] j. a. collins, failure of materials in mechanical design. analysis, prediction, prevention, new york, wiley interscience, (1993). [18] g. de pasquale, a. somà, microsystems technologies, 15 (2009) 391. t http://www.gruppofrattura.it http://dx.medra.org/10.3221/igf-esis.23.12&auth=true microsoft word numero 23 articolo 9 d. castagnetti, frattura ed integrità strutturale, 23 (2013) 87-93; doi: 10.3221/igf-esis.23.09 87 scilla 2012 the italian research on smart materials and mems design and characterization of a fractal-inspired multi-frequency piezoelectric energy converter davide castagnetti department of engineering sciences and methods, university of modena and reggio emilia, via amendola 2, 42122 reggio emilia, italy davide.castagnetti@unimore.it abstract. a promising harvesting technique, in terms of simplicity and efficiency, is the conversion of ambient kinetic energy through piezoelectric materials. this work aims to design and investigate a piezoelectric converter conform to a fractal-inspired, multi-frequency structure previously presented by the author. a physical prototype of the converter is built and experimentally examined, up to 120 hz, in terms of modal response and power output. three eigenfrequencies are registered and the power output is particularly good at the fundamental eigenfrequency. also the effect of the resistive load applied to the converter is investigated. keywords. energy harvesting; piezoelectric converter; multi-frequency structures; fractal geometry; power generation. introduction he study of energy harvesting devices, able to convert ambient energy into electrical energy, is increased, in recent years, together with the development of wireless sensor nodes. the most common source for energy harvesting is kinetic energy, since it is ubiquitous, easily accessible, and present in the form of vibrations or random forces. according to [1], the typical range of ambient vibrations is below 100 hz, therefore identifying simple structures that efficiently harvest kinetic ambient energy in this range is challenging. among the available conversion technologies [2-3], piezoelectric materials have the peculiarity of simplicity and high conversion efficiency [2] in the harvesting of ambient kinetic energy. many piezoelectric energy harvesters have been proposed in the literature [4-11], relying on different architectures. however, a cantilever beam configuration is the most common solution [12-15], for piezoelectric converters since it generates large deflection strains when operated at its fundamental frequency and a desired eigenfrequency can be easily obtained varying its length or introducing an appropriate proof mass [16-18]. by assembling a batch of cantilevers [19-21] each of them tuned at a different fundamental frequency, a multi-frequency converter is obtained. however, the global efficiency is low, since a single cantilever is operated at each resonant frequency. to overcome this drawback, in [22] the author proposed and computationally examined four fractal-inspired structures, that provide many eigenfrequencies evenly distributed in the range between 0 and 100 hz and convert energy more efficiently than a traditional batch of cantilevers. this frequency range was chosen in order to develop structures that efficiently convert ambient vibrations, which are mainly and widely distributed in this range [1]. a subsequent experimental investigation of the two most performing structures [23], confirmed the good modal response. this work aims at investigating a piezoelectric converter inspired to one of these fractal-inspired, multi-frequency structures. the piezoelectric converter is designed and then a physical prototype is experimentally investigated in terms of modal response and power output in the frequency range between 0 and 120 hz. the converter prototype was made of a support steel plate and thin piezoelectric sheets of commercial psi-5h4e [24]. three eigenfrequencies are registered below 120 hz and a good power generation is obtained, in particular at the first eigenfrequency. t http://www.gruppofrattura.it http://dx.medra.org/10.3221/igf-esis.23.09&auth=true d. castagnetti, frattura ed integrità strutturale, 23 (2013) 87-93; doi: 10.3221/igf-esis.23.09 88 method design of the piezoelectric converter prototype he piezoelectric converter prototype here proposed relies on the fractal-inspired multi-frequency structure in fig. 1, which was proposed and examined by the author in [22] and [23]. fig. 2 shows the sketch of the prototype of the piezoelectric converter, which is obtained by applying to the support plate in fig. 1 thin rectangular laminas of piezoelectric material (hatched area in fig. 2) for each inner cantilever. the piezoelectric patches are close to the constrained side of the structure, where maximum stresses (and hence strains) originates in case of vibration induced deflections. the support plate is made of a thin sheet of steel (s235jr) with a thickness of 0.2 mm. this thickness value represents the best trade-off between the need to provide an adequate mechanical strength and to obtain a large number of eigenfrequencies in the frequency range below 120 hz. the piezoelectric patches are commercial psi-5h4e [24], with a thickness of 0.267 mm, and were joined to the support plate through a bi-adhesive tape from 3m which provides an adequate electrical insulation. moreover, the adhesive tape maximizes the distance of the piezoelectric layer from the neutral plane of the structure, thus increasing strain and electrical generation and is highly compliant, allowing higher deflections of the lamina. l1 l2 l2 = = = = l l = = = = 100 65 psi‐5h4e s235jr 1 0 0 0 .2 6 7 1 0 .2 figure 1: sketch of the fractal-inspired geometry for the piezoelectric converter prototype figure 2: sketch of the prototype of the piezoelectric converter tab. 1 collects the mechanical and electrical properties of the piezoelectric patches, used to build the prototype. these piezoelectric patches include nickel electrodes and connecting wires on both sides. the support plate was manufactured through laser-jet cutting. piezoelectric strain coefficient, d31 [m/v] -320 x 10-12 relative dielectric constant, k3 3800 mass density,  [kg/m3] 7800 young’s modulus, e [gpa] 62 poisson’s ratio,  0.3 structural damping 0.02 table 1: electrical and mechanical properties of psi-5h4e experimental campaign fig. 3 shows a picture of the converter prototype, built according to the sketch in fig. 2, and experimentally examined in order to investigate its modal response and the power output between 0 and 120 hz. table 2 reports the two variables t http://www.gruppofrattura.it http://dx.medra.org/10.3221/igf-esis.23.09&auth=true d. castagnetti, frattura ed integrità strutturale, 23 (2013) 87-93; doi: 10.3221/igf-esis.23.09 89 examined in the full factorial experimental campaign. the first variable is the amplitude of the acceleration applied to the converter prototype: 0.5g or 1g, respectively, where g is the gravitational acceleration. the second variable is the value of electric resistance applied in series to each piezoelectric patch, which varies over three levels: 6.8 m, 100 k, and 10 k. on the one hand, the first very high value allows to simulate the maximum output voltage in a nearly open circuit condition. despite very high, the resistance avoided that the generated electric charges were stored on the electrodes transforming the piezoelectric patch in a capacitor. on the other hand, the second and third resistance values were chosen to investigate the effect of different resistive loads on the power output of the piezoelectric patch. variable level + acceleration [m/s2] 4.9 9.81 electrical resistance [k] 10 100 6800 table 2: variables of the full factorial experimental plan. piezoelectric patches support lamina 100 mm 3 2 1 4 figure 3: physical prototype of the fractal-inspired piezoelectric converter. through an electro-dynamic shaker (data physics bv400 [25]), the converter was stressed by a sinusoidal excitation, whose frequency sweeps in the range from 0 hz to 120 hz. in order to implement a closed-loop control on the system, a miniature accelerometer (mmf ks94b100 [26]) was applied to the vibrating table of the shaker, by fixing it through a magnetic base. the shaker was managed by an 8 channels abacus controller and the whole testing apparatus was controlled by the signal star software, installed on a pc that moreover performs data acquisition. a polytec point laser doppler vibrometer, equipped with a ofv-505 sensor head and controlled by a polytec ofv-5000 controller [27], was used to identify the eigenfrequencies of the converter prototype. the laser vibrometer was set up vertically on the plate, and measured both the speed and the deflection of the tip of the cantilevers during the tests (fig. 4). a sensitivity of 500 mm/s/v was set to measure the speed, while for the displacement measurement the sensitivity of the vibrometer was set to 5 mm/v and 100 m/v for the first and subsequent eigenfrequencies, respectively. also the data from the laser doppler vibrometer were registered through the signal star software which controls the shaker. each of the four piezoelectric patches on the converter was electrically connected to a 16 channels data acquisition module (usb 6251 [28]). the data acquisition module was connected through a usb port to a notebook equipped with the labview software [29] and the output voltage of each piezoelectric lamina was registered through the labview signalexpress application [29].  figure 4: sketch showing the measurement of the tip deflection, , on the converter. http://www.gruppofrattura.it http://dx.medra.org/10.3221/igf-esis.23.09&auth=true d. castagnetti, frattura ed integrità strutturale, 23 (2013) 87-93; doi: 10.3221/igf-esis.23.09 90 results ig. 5 shows the tip speed registered for lamina #1 (solid line) and #2 (dashed line), through the laser doppler vibrometer. in order to assure a good measure also for high deflections occurring at the fundamental eigenfrequency, the speed was measured 5 mm far from the tip of the lamina. since the eigenmodes below 120 hz were observed to be symmetric, all the parameters were measured on the right half of the structure (lamina #1 and #2). 0 2 4 6 8 10 12 0 20 40 60 80 100 120 s p e e d  ( m m /s ) frequency (hz) # 1 # 2 21.1 hz 33.75 hz 108.6 hz figure 5: diagram of the speed registered experimentally on the tip of lamina #1 (solid line) and lamina #2 (dashed line). fig. 6 describes the tip displacement measured experimentally for each eigenfrequency both for lamina #1 and #2 (fig. 6a and b, respectively) at a base acceleration of 1g. each bar chart displays three columns for each eigenfrequencies: a solid black, a solid white, and a solid grey column for the resistive load equal to 6.8 m, to 100 k, and to 10 k, respectively. keeping the same layout, fig. 7 presents the output root mean square (rms) voltage. 0 2 4 6 8 10 12 21.1 33.75 108.6 t ip  d e fl e ct io n  ( m m ) eigenfrequencies (hz) open circuit 100 kohm 10 kohm lamina #1 ‐ 1g 0 2 4 6 8 10 12 21.1 33.75 108.6 t ip  d e fl e ct io n  ( m m ) eigenfrequencies (hz) open circuit 100 kohm 10 kohm lamina #2 ‐ 1g (a) (b) figure 6: bar charts of the tip displacement measured experimentally for each eigenfrequency to an acceleration of 1 g: lamina #1 (a), and lamina #2 (b). finally, fig. 8 shows the bar charts of the total power output generated by the converter at each eigenfrequency, both for an acceleration of 0.5g and 1g (fig. 8a and b, respectively). the power output was calculated according to the following relationship: f http://www.gruppofrattura.it http://dx.medra.org/10.3221/igf-esis.23.09&auth=true d. castagnetti, frattura ed integrità strutturale, 23 (2013) 87-93; doi: 10.3221/igf-esis.23.09 91 2 4 , 1 rms i i v p r   (11) where vrms,i is the output root mean square voltage of the i-th lamina, and r is the resistive load applied to each piezoelectric lamina. 0.0 0.4 0.8 1.2 1.6 2.0 21.1 33.75 108.6 o u tp u t  r m s  v o lt a g e  ( v ) eigenfrequencies (hz) open circuit 100 kohm 10 kohm lamina #1 ‐ 1g 0.0 0.4 0.8 1.2 1.6 2.0 21.1 33.75 108.6 o u tp u t  r m s  v o lt a g e  ( v ) eigenfrequencies (hz) open circuit 100 kohm 10 kohm lamina #2 ‐ 1g (a) (b) figure 7: bar charts of the output root mean square voltage measured experimentally for each eigenfrequency to an acceleration of 1g: lamina #1 (a), and lamina #2 (b). 0 10 20 30 40 50 60 70 80 21.1 33.75 108.6 o u tp u t  p o w e r  ( w ) eigenfrequencies (hz) open circuit 100 kohm 10 kohm 0.5g 0 10 20 30 40 50 60 70 80 21.1 33.75 108.6 o u tp u t  p o w e r  ( w ) eigenfrequencies (hz) open circuit 100 kohm 10 kohm 1g (a) (b) figure 8: bar charts of the total output power measured experimentally for each eigenfrequency under different resistive loads, both at 0.5g (a) and 1g (b). discussion igure 5 highlights three eigenfrequencies below 120 hz. the first eigenfrequency involves the whole structure (equal tip speed at 21.1 hz both for lamina #1 and #2), being the eigenmode of a cantilever structure with the same global shape. the second eigenfrequency (32.75 hz) belongs only to lamina #1 (and its symmetrical #4). the third eigenfrequency (108.6 hz) is again common to the whole structure. f http://www.gruppofrattura.it http://dx.medra.org/10.3221/igf-esis.23.09&auth=true d. castagnetti, frattura ed integrità strutturale, 23 (2013) 87-93; doi: 10.3221/igf-esis.23.09 92 from fig. 6 it appears that, at the first eigenfrequency, the tip deflection is exactly the same for all the laminas (as discussed above), and is many times higher than that of subsequent eigenmodes. the resistive load seems to have no effect on the tip deflection. by contrast, despite not showed here for brevity, it was observed that the tip deflection linearly depends on the base acceleration. the rms voltage in fig. 7 is quite similar for lamina #1 and #2, and, as expected, the higher values are obtained by increasing the resistive load up to an open circuit condition (solid black bars). a small difference is observed at the third eigenfrequency, where the higher rms voltage is obtained for a resistive load of 100 k (empty bars). probably, a more accurate investigation on this eigenfrequency would be needed. moreover, the rms voltage is noticeably low at the first and second eigenfrequency when the 10 k resistive load (grey bars) is applied to the piezoelectric patches. similarly to the tip displacement in fig. 6, also the rms voltage is much more high at the first eigenfrequency and is proportional to the base acceleration. fig. 8 shows that the overall output power of the converter at the fundamental eigenfrequency is an order of magnitude higher than at the second and third eigenfrequencies. the output power increases more than linearly with the base acceleration. in addition, both for the first and third eigenfrequency the resistive load significantly affects power generation. despite the highest power generation is obtained at the first eigenfrequency, also at subsequent eigenfrequencies the converter is able to provide a useful power output, which can be maximized by choosing the optimal resistive load for that given frequency. on the whole, a multi-frequency converter allows to harvest ambient energy in a given frequency range and can be particularly efficient in applications dealing with excitations which are not controllable or are intrinsically frequencyvariant over a wide range. further experimental tests will be performed to compare this fractal-inspired multi-frequency converter with a traditional multi-cantilever solution. conclusions fractal-inspired, multi-frequency, piezoelectric energy converter, which is a square thin sheet structure with inner cuts, is designed and experimentally investigated. the converter exhibits three eigenfrequencies in the range between 0 and 120 hz: the first eigenfrequency corresponds to that of an equivalent cantilever, the second and third eigenfrequency comes from the inner cantilevers. the electric power generation under different levels of resistive loads (from open circuit up to a low electric resistance) is good, in particular at the first eigenfrequency, and increases almost linearly with the base acceleration. a multi-frequency converter, as presented here, can be particularly efficient for energy harvesting involving ambient vibrations whose frequency is uncertain or varying over a wide range. references [1] g. despesse, t. jager, j.j. chaillout, et al., in: proc. ph.d. res. microelectron. electron., 1 (2005) 225. [2] s.p. beeby, m.j. tudor, n.m. white, meas. sci. technol. 17 (2006) r175. [3] j. dewei, l. jing liu, front. energy power eng. china, 3(1) (2009) 27. [4] g. de pasquale, a. somà, n. zampieri, j. of fuel cell science and technol., 9(4) (2012) 041011. [5] g. de pasquale, a. somà, in: symposium on design, test, integration and packaging of mems/moems, dtip (2010) 134. [6] g. de pasquale, e. brusa, a. somà, in: dtip of mems and moems symposium on design, test, integration and packaging of mems/moems, (2009) 280. [7] v.r. challa, m. g. prasad, f.t. fisher, smart mater. struct., 18 (2009) 095029. [8] a. khaligh, p. zeng, x. wu, and y. xu, in: iecon 2008. 34th annual conference of ieee (2008) 448. [9] d. zakharov, g. lebedev, o. cugat, j. delamare, b. viala, t. lafont, l. gimeno, a. shelyakov, j. micromech. microeng., 22 (2012) 094005. [10] s. r. anton, a. erturk, d. j. inman, smart mater. struct. 19 (2010) 115021. [11] l. gu, microelectronics journal, 42 (2011) 277. [12] f. glynne-jones, s.p. beeby, n.m. white, iee proc. sci. mem. technol., 148(2) (2001) 68. [13] s. zurn, m. hsieh, g. smith et al., smart mater. struct. 10 (2001) 252. [14] s. roundy, p.k. wright, j. rabaey, computer communications 26 (2003) 1131. [15] a. erturk, d.j. inman, smart mater. struct., 18 (2009) 1. a http://www.gruppofrattura.it http://dx.medra.org/10.3221/igf-esis.23.09&auth=true d. castagnetti, frattura ed integrità strutturale, 23 (2013) 87-93; doi: 10.3221/igf-esis.23.09 93 [16] d. shen, s.y. choe, d.j. kim, jap. j. appl. phys., 46(10) (2007) 6755. [17] d. benasciutti, l. moro, s. zelenika, and e. brusa, microsyst. technol., 16 (2010) 657. [18] h.j. song, y.t. choi, g. wang, et al., j. mech. des. 131(9) (2009) 091008. [19] m. ferrari, v. ferrari, m. guizzetti, et al., sens. actuators, 142 (2008) 329. [20] s. qi, r. shuttleworth, s.o. oyadiji, in: proceedings of smasis, ca, 2009. [21] s.m. shahruz, mechatronics, 16 (2006) 523. [22] d. castagnetti, j. of mech. design, 133(11) (2011) 111005-1. [23] d. castagnetti, in: proceedings of smasis (2011) arizona. [24] piezo system, inc., usa, www.piezo.com. [25] http://www.dataphysics.com/ [26] tds “miniature accelerometers” on www.mmf.de. [27] http://www.polytec.com/us/ [28] http://www.ni.com/products/ [29] http://www.ni.com/labview/ http://www.gruppofrattura.it http://dx.medra.org/10.3221/igf-esis.23.09&auth=true microsoft word numero_37_art_46 z. hongping et alii, frattura ed integrità strutturale, 37 (2016) 352-359; doi: 10.3221/igf-esis.37.46 352 analysis of time-dependent reliability of degenerated reinforced concrete structure zhang hongping, zhang lili, xia zhengbing college of architecture and civil engineering, jiangsu city vocational college nantong campus, nantong, jiangsu, 226006, china zhanghpingzhp@163.com abstract. durability deterioration of structure is a highly random process. the maintenance of degenerated structure involves the calculation of the reliability of time-dependent structure. this study introduced reinforced concrete structure resistance decrease model and related statistical parameters of uncertainty, analyzed resistance decrease rules of corroded bending element of reinforced concrete structure, and finally calculated timedependent reliability of the corroded bending element of reinforced concrete structure, aiming to provide a specific theoretical basis for the application of time-dependent reliability theory. keywords. durability of structure; reinforced concrete; degeneration. introduction mong multiple structures, reinforced concrete structure fully integrates the characteristics of steel reinforcement and concrete and cost little; hence it has been extensively promoted in infrastructure construction of china [1]. scholars in civil engineering field keep searching for the application of new materials and innovation of structural system and seeking breakthrough in structural disaster-resistance analysis and design [2]. however, durability and life-cycle performance degeneration of structure is an important issue concerned by civil engineering workers. but so far, research progress in this field is not considerable, which may be correlated to the involvement of multiple subjects and large difficulty [3]. randomness of resistance of reinforced concrete structure in the initial stage of construction and attenuation of resistance under the effect of environment is important characteristics [4]. with the development of infrastructure construction in china, deep research on the problem is urgent. material degeneration and structural aging would happen under the effects of human-made environment or natural environment during long-term application, which can weaken carrying capacity and durability of structure. however, durability of reinforced concrete structure has been ignored for a long time [5]. an investigation [6] suggested that, more than 70 billion dollars were caused because of corrosion of various structures in america in 1975, 40% of which is caused by corrosion of steel reinforcement. besides, britain spends about 200 thousand pounds on ocean environment corrosion every year. japan even spends 40 billion yen on the maintenance of house structure every year. reinforced concrete structure is frequently used in china and structural damage caused by durability has been quite serious. steel reinforcement corrosion has been one of major reasons for the failure of reinforced concrete structure. as civil engineering in china has entered into the stage of aging, scientific detection and evaluation on such kind of structure is in urgent need. therefore, it is of great significance to make safety evaluation of structure through predicting structural durability. a z. hongping et alii, frattura ed integrità strutturale, 37 (2016) 352-359; doi: 10.3221/igf-esis.37.46 353 in recent years, scholars in china and abroad have made a large number of experiments on the factors influencing durability of structure and obtained many durability degeneration models of concrete structure [7]. traditional structural reliability calculation model does not vary along with time and the characteristics of existing structure determines that the calculation of structural reliability using time-invariant model cannot consider the degeneration performance of structure. but this study considered the variation characteristics of structural resistance and load along with time and calculated the reliability based on time-dependent concept. in addition, we find that, most scholars focus on the construction of degeneration model and concern little about degeneration parameters. actually, degeneration parameter is an important component of degeneration model. analysis of durability degeneration model and time-dependent reliability of structure is of significance only when correct parameters are used. as to another innovation point, this study gave uncertainty statistical parameters of reinforced concrete structure resistance based on the detailed introduction of degenerated reinforced concrete resistance decrease model and made an analysis on the rules of resistance decrease of corroded bending element. development and status of structural reliability analysis method he concept of reliability originated from america. in 1939, national advisory committee for aeronautics proposed the concept of airplane accident rate; then the concept was extensively applied in the field of civil engineering. in 1940s, pugsley and freudenthal published a paper titled safety degree of structure. they integrated the theory of structural safety degree and the concept of mathematical statistics and proposed a reliability analysis calculation model. then earliest reliability calculation model was extensively recognized and studied by other scholars [9]. in 1969, cornell, an american expert, proposed the concept of reliability index, integrated it with structural failure rate and put forward the conversion formula with regard to reliability index and structural failure rate [10]. then cornell and ang proposed first-order second-moment method for the calculation of structural reliability, which was extensively applied in engineering. since then, many scholars kept innovating structural reliability analysis and calculation and proposed many structural reliability calculation methods. currently, researches on time-invariant theory have been relatively mature. however, time-dependent reliability theory involving multiple factors and more complex calculation remains to be further studied. on account of this, many scholars carried out a series of researches on time-dependent reliability of reinforced concrete structure. in 2008, czarnecki et al. [11] proposed a time-dependent reliability model of reinforced concrete structure after finding the significant changes of reinforced concrete structure resistance along with the extension of time under corrosion environment and then applied the model for predicting the service time of structure. in 2012, frangopol [2] applied structural health monitoring information obtained after integrating structure related priori knowledge and using bayes updating probability to make a quantitative analysis on degeneration performance of structure. in 2014, madsen [13] proposed a new structural timedependent reliability and sensitivity analysis method. similarly, many chinese scholars are also dedicated to promoting the development of structural time-dependent reliability analysis. through analyzing structural resistance decrease process induced by steel reinforcement corrosion, chen shoushan et al. [14] designed a method for evaluating and predicting reliability of structure. by investigating the existing resistance information of a structure and using a large number of measured data, zhou yan et al. [15] established a resistance time-independent reliability analysis model. resistance decrease model of reinforced concrete structure the resistance of reinforced concrete structure depends on calculation model, geometrical parameters and material performance of structure. during the whole service process of structure, concrete carbonization and steel reinforcement corrosion can result in decline of strength of steel reinforcement and concrete, narrowing of cross section of steel reinforcement and deterioration of coordination between reinforced concrete and those adverse effects gradually accumulates as time goes on. therefore, geometrical parameters and material performance of structure would both be degenerated as time goes on, which can weaken the resistance of structure. on account of this, when we consider the degeneration of resistance of reinforced concrete structure, the resistance decrease model can be expressed as: ( ) [ ( ), ( ), ( )]r aj j sjp t p f t d t k t (1) where ( )rp t stands for resistance of reinforced concrete structure, [ ]p x stands for expression equation of reinforced concrete structure resistance, ( )ajf t and ( )jd t stands for performance and geometrical parameter of jth material and they t z. hongping et alii, frattura ed integrità strutturale, 37 (2016) 352-359; doi: 10.3221/igf-esis.37.46 354 are the functions of service time; and ( )sjk t stands for coordination coefficient of jth steel reinforcement, and it is also the function of service time. uncertainty statistical parameters of resistance uncertainty of reinforced concrete resistance includes uncertainty of calculation mode, material performance and geometrical parameters. uncertainty of calculation mode refers to variability induced by basic assumption adopted by resistance analysis and evaluation, uncertainty of material performance refers to variability induced by durability degeneration, such as concrete carbonization, cross section loss induced by steel reinforcement corrosion, corrosion expansion, cracking and separation of concrete cover and mechanical property degeneration of corroded steel reinforcement. considering the uncertainty of calculation mode, the resistance of reinforcement concrete structure can be expressed using the following formula ( ) ( )r rp t k p t (2) where ( )p t stands for random process of resistance and rk stands for random variable of uncertainty of calculation mode. according to relevant methods of mathematical statistics and considering the uncertainty of model parameters, probability statistic characteristic of resistance can be obtained from the following formula. ( ) ( )p k pr rt t   (3) 2 2( ) ( )p k pr rt t    (4) ( ) ( ) ( )p p pt t t   (5) where kr and kr stand for the average value of random variable rk and variable coefficient of calculation mode uncertainty respectively; ( )pr t and ( )pr t stand for the function of average value and the function of variable coefficient respectively. it can be known from formula (6), (7) and (8) that ( ) [ ( ), ( ), ( )]p f aj d kr j sjt p t t t    (6) ( ) ( ) ( ) pr pr pr t t t     (7) 2 2( )( ) ( )pp zr j jj t t t z              (8) where jz stands for relevant random variable influencing resistance and ( )p j t z    stands for result of partial derivative when the average value was used. it can be seen from the above deduction process that, some statistical characteristics of basic parameters of resistance needs to be determined at first before acquisition of statistical characteristics of final resistance. depending on the current test means and research conditions, we can obtain some statistical characteristics of parameters easily. using mathematical method, we can obtain uncertainty statistical rules of final model. z. hongping et alii, frattura ed integrità strutturale, 37 (2016) 352-359; doi: 10.3221/igf-esis.37.46 355 statistical parameters of resistance of corroded bending element bending element is the most common structural element in existing reinforced concrete structure. after years of research on corroded element, the calculation of bearing capacity of corroded bending element has been quite mature. taking bending element of reinforced concrete as an example, resistance decrease rules of corroded bending element is analyzed in this section. according to relevant knowledge of concrete structure design, bending capacity of normal section of rectangular section of corroded element can be obtained from the following formulas. 1 ( ) 2 v x y f lx b  (9) 1 se o v b f x f l  (10) where y stands for bearing capacity of normal section of corroded reinforcement (kn·m), vf and 0f stand for compressive strength of concrete axis and yielding strength of reinforcement (mpa); 1 stands for coefficient (the value is determined according to relevant regulations in code for design of concrete structures); l and b stand for the width of section and effective height of section (mm); seb refers to equivalent section area of tensile reinforcement (mm2) which is calculated using formula (11). 1 n se sj sj sj i b k b    (11) where sjk refers to coordination coefficient of ith reinforcement (decrease of cohesive force is considered), sjb refers to section area of jth tensile reinforcement (mm2), and sj stands for reduction coefficient of yielding strength of jth reinforcement. ( ) ( ) ( ) 1 2 p c br t t t          (12)   2 22 2 2 2 2 2( )( ) ( ) 1 ( ) ( ) 4 p c c l f br v t t t b t t                      (13) 1 ( ) ( ) c l b fv t t        (14) where fv and fv stands for average value and variable coefficient of compressive strength of concrete axis, l and l refers to average value and variable coefficient of section width, b and b refer to average value and variable coefficient of effective height of section, and ( )c t and ( )c t refer to average value and variable coefficient of yielding tensile force of corroded reinforcement. through analyzing parameters of mode, we can finally obtain relevant uncertainty statistical parameters of resistance of corroded bending element of reinforced concrete. analysis method of structural time-dependent reliability basic principle of time comprehensive analysis method ime comprehensive analysis method means to take the whole service period of a structure as a reference time period during analysis of structural reliability and obtain resistance and load model considering the changes of structural resistance and loading during the time period. the whole service period is regarded as a reference time period, and statistical characteristics t z. hongping et alii, frattura ed integrità strutturale, 37 (2016) 352-359; doi: 10.3221/igf-esis.37.46 356 of random variable relating to resistance and loading are all considered during the time period. hence the maximum value of probability in the reference time period can be taken as the value of load. the practical conditions of p (t) and s (t) are shown in fig. 1. p (t) , s (t) p (t) s (t) figure 1. changes of resistance and load. from the perspective the concept of time-dependent reliability, p is a time-dependent function. but in time comprehensive analysis method, p is considered as a definite value and also the maximum value in the whole reference time period. it should be pointed out that, definite value herein does not refer to determined value, but random variable. we can obtain the practical value of p from probability density function fp. in time comprehensive analysis method, failure probability can be obtained using the following formula.  min max( )f ad t d p s  (15) max 0 max ( ) t t a s s t    represents for the maximum load effect in the whole evaluation reference period [0, t] and min 0 min ( ) t t a p p t    represents for the maximum resistance in different stages in the whole evaluation reference period [0, t]. in practical application of time comprehensive analysis method, probability density function of ( )s t can be obtained through longterm observation of data. in this way, maxs can be obtained probability distribution function. but it is a pity that, long-term observation data are difficult to be obtained. therefore, the extreme value distribution can be described by some short-term data. time-dependent reliability can be calculated by first order reliability method after analysis of load and resistance rules of structural element. analysis of time-dependent reliability of corroded bending element a flexural simply supported beam component of reinforced concrete in someplace was taken as an example. beam span was 6000 mm, spacing was 3,900 mm, and section size was 250 mm × 500 mm. the thickness of concrete cover was 25 mm, concrete strength was c20, and grade ii rebar with a diameter of 16 mm was used, with a reinforcement ratio of 1.2%. as to the external environment, relative humidity was 71% and temperature was 13 oc; besides, 2co k was 1.2 and cek was 2.0. we know that, the reinforcement began to be corroded 13.7 years ago and the concrete cover began to crack due to corrosion expansion 26.5 years ago, after substituting relevant coefficients according the method stated in literature [16]. other relevant resistance statistical parameters were as follows: kr = 1.0, kr = 0.04; l = 1.0l, l = 0.02; b = 1.0b, b = 0.03. the simply supported beam bears constant load and live load. the average value and standard error of constant load, i.e., g and g , were 28.91 kn/m and 2.03 kn/m respectively. the average value and standard error of live load, i.e., q and q , were 0.585 kn/m and 0.26 kn/m. the relevant parameters were substituted into the resistance decrease model of corroded bending element of reinforced concrete, and then the curve for time-dependent variation of average value and variation coefficient of resistance could be obtained (fig. 2 and 3). according to unified standards for the design of reliability of building structure (gb50068-2001), the constant load followed normal distribution; the live load followed the i-type distribution of extreme value and the maximum value in the time interval [0, t] also followed i-type distribution of extreme value. the average value and standard error of live load can be obtained using the following formulas. z. hongping et alii, frattura ed integrità strutturale, 37 (2016) 352-359; doi: 10.3221/igf-esis.37.46 357 ln 1.2826 q q qt t     (16) q qt   (17) where tq stands for the maximum random variable of live load in service period [0, t]. according to the existing conditions, the average value and standard error of constant load sg and sg were 130.1 kn·m and 9.11 kn·m respectively. the average value of the maximum live load could be calculated using formula (18). 1.17 2.63 ln 1.2826 s qt t   (18) standard error s qt  was 1.17 kn·m. according to the above conditions, we could obtain the changes of reliability index of corroded bending element of reinforced concrete along with service time of structure by applying time comprehensive analysis method. results are shown in fig. 4. figure 2. time varying curve of average value of resistance. figure 3. time varying curve of variation coefficient of resistance. z. hongping et alii, frattura ed integrità strutturale, 37 (2016) 352-359; doi: 10.3221/igf-esis.37.46 358 figure 4. the changes of reliability index of corroded bending element of reinforced concrete along with service time of structure. conclusions t is of great significance to study the prediction of structural durability. but there is no relatively mature method which can obtain correct prediction results. this study gave out uncertainty statistical parameters of reinforced concrete structure and calculated time-varying reliability of corroded bending element of reinforced concrete using time comprehensive analysis method. finally, the variation rules of reliability index of corroded bending element along with the changes of service time of structure were obtained. it is no doubt that the method provides a new idea for the prediction of durability and the research results have great value for the prediction and evaluation of durability of existing structures. as durability degeneration of reinforced concrete structure is a quite complex process, some researches concerning degeneration mechanism has not been broken through. only few issues were considered for durability degeneration of reinforced concrete in this study, and many problems remain to be solved. references [1] li, j., gao, x., probability density evolution method and its application in life-cycle civil engineering. structure and infrastructure engineering, 10(7) (2014) 921-927. [2] madsen, h.o., tvedt, l., methods for time-dependent reliability and sensitivity analysis. american society of civil engineers, 116(10) (2014) 2118-2135. [3] shi, x., xie, n., fortune, k., et al., durability of steel reinforced concrete in chloride environments: an overview. construct build mater, 30(2012)125-138. [4] neves, r., branco, f.a., de brito. j., a method for the use of accelerated carbonation tests in durability design. construct build mater, 36(2012)585-591. [5] yu, cl., ye, p., jin, r.h., analyze of the depths of concrete carbonization experience predictive models. ready-mixed concrete, (3) (2009) 52-53. [6] kabir, g., sadiq, r., tesfamariam, s., a review of multi-criteria decision-making methods for infrastructure management. structure and infrastructure engineering, 10(9) (2013)1176-1210. [7] biondini, f., frangopol, d.m., lifetime reliability-based optimization of reinforced concrete cross-sections under corrosion. structural safety, 31(6) (2009)483-489. [8] shodja, h.m., kiani, k., hashemian, a., a model for the evolution of concrete deterioration due to reinforcement corrosion. mathematical and computer modelling, 52(9-10) (2010) 1403-1422. [9] chiu. c., chi, k., analysis of lifetime losses of low-rise reinforced concrete buildings attacked by corrosion and earthquakes using a novel method. structure and infrastructure engineering, 9(12) (2013) 1225-1239. [10] cornell, c.a., a probability-based structural code. aci structural journal, 100(3) (1969) 94-107. [11] czarnecki, a.a., nowak, a.s., time-variant reliability profiles for steel girder bridges. structural safety, 30(1) (2008) 49-64. [12] okasha, n.m., frangopol, d.m., integration of structural health monitoring in a system performance based life-cycle bridge management framework. structure and infrastructure engineering, 8(11) (2012) 999-1016. i z. hongping et alii, frattura ed integrità strutturale, 37 (2016) 352-359; doi: 10.3221/igf-esis.37.46 359 [13] madsen, h.o., tvedt, l., methods for time-dependent reliability and sensitivity analysis. american society of civil engineers, 116(10) (2014) 2118-2135. [14] chen, c.s., zhang, j.q., li, w.h., reliability analysis of deterioration of construction performance caused by corrosion of steel bar. journal of highway and transportation research and development, 23(4) (2006) 33-36. [15] zhou, y., wang, g.h., analysis of the existing reinforced concrete bridge’s time-dependent and reliability. journal of lanzhou jiaotong university, 26(1) (2007)75-77. [16] niu, d.t., chen, y.q., yu, s., analysis of carbonization mode and life of concrete structure. journal of xi'an university of architecture & technology, 27(4) (1995) 365-369. << /ascii85encodepages false /allowtransparency false /autopositionepsfiles true /autorotatepages /none /binding /left /calgrayprofile (dot gain 20%) /calrgbprofile (srgb iec61966-2.1) /calcmykprofile (u.s. web coated \050swop\051 v2) /srgbprofile (srgb iec61966-2.1) /cannotembedfontpolicy /error /compatibilitylevel 1.4 /compressobjects /tags /compresspages true /convertimagestoindexed true /passthroughjpegimages true /createjobticket false /defaultrenderingintent /default /detectblends true /detectcurves 0.0000 /colorconversionstrategy /cmyk /dothumbnails false /embedallfonts true /embedopentype false /parseiccprofilesincomments true /embedjoboptions true /dscreportinglevel 0 /emitdscwarnings false /endpage -1 /imagememory 1048576 /lockdistillerparams false /maxsubsetpct 100 /optimize true /opm 1 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can be opened with acrobat and adobe reader 5.0 and later.) >> /namespace [ (adobe) (common) (1.0) ] /othernamespaces [ << /asreaderspreads false /cropimagestoframes true /errorcontrol /warnandcontinue /flattenerignorespreadoverrides false /includeguidesgrids false /includenonprinting false /includeslug false /namespace [ (adobe) (indesign) (4.0) ] /omitplacedbitmaps false /omitplacedeps false /omitplacedpdf false /simulateoverprint /legacy >> << /addbleedmarks false /addcolorbars false /addcropmarks false /addpageinfo false /addregmarks false /convertcolors /converttocmyk /destinationprofilename () /destinationprofileselector /documentcmyk /downsample16bitimages true /flattenerpreset << /presetselector /mediumresolution >> /formelements false /generatestructure false /includebookmarks false /includehyperlinks false /includeinteractive false /includelayers false /includeprofiles false /multimediahandling /useobjectsettings /namespace [ (adobe) (creativesuite) (2.0) ] /pdfxoutputintentprofileselector /documentcmyk /preserveediting true /untaggedcmykhandling /leaveuntagged /untaggedrgbhandling /usedocumentprofile /usedocumentbleed false >> ] >> setdistillerparams << /hwresolution [2400 2400] /pagesize [612.000 792.000] >> setpagedevice microsoft word numero_46_art_9 m.f.m. yunoh et alii, frattura ed integrità strutturale, 46 (2018) 84-93; doi: 10.3221/igf-esis.46.09 84 developments in the fracture and fatigue assessment of materials and structures probabilistic-based analysis for damaging features of fatigue strain loadings m. f. mod yunoh, s. abdullah centre for automotive research, faculty of eng. and built enviroments, universiti kebangsaan malaysia faridzyunus@gmail.com, shahrum@ukm.edu.my m. h. m. saad, z. m. nopiah, m. z. nuawi, s. s. k. singh dept. of mechanical and materials, faculty of eng. and built enviroments, universiti kebangsaan malaysia hanifsaad@ukm.edu.my, zmn@ukm.edu.my, mzn@ukm.edu.my, salvinder@ukm.edu.my abstract. this paper presents the behaviour of fatigue damage extraction in fatigue strain histories of automotive components using the probabilistic approach. this is a consideration for the evaluation of fatigue damage extraction in automotive components under service loading that is vital in a reliability analysis. for the purpose of research work, two strain signals data are collected from a car coil spring during a road test. the fatigue strain signals are then extracted using the wavelet transform in order to extract the high amplitude segments that contribute to the fatigue damage. at this stage, the low amplitude segments are removed because of their minimal contribution to the fatigue damage. the fatigue damage based on all extracted segments is calculated using some significant strain-life models. subsequently, the statistics-based weibull distribution is applied to evaluate the fatigue damage extraction. it has been found that about 70% of the probability of failure occurs in the 1.0 x 10-5 to 1.0 x 10-4 damage range for both signals, while 90% of the probability of failure occurs in the 1.0 x 10-4 to 1.0 x 10-3 damage range. lastly, it is suggested that the fatigue damage can be determined by the weibull distribution analysis keywords. fatigue damage; features extraction; probabilistic; wavelet; weibull distribution. citation: yunoh, m. f. m., abdullah, s., saad, m. h. m., nopiah, z. m., nuawi, m. z., singh, s. s. k., determining probabilistic-based failure of damaging features for fatigue strain loadings, frattura ed integrità strutturale, 46 (2018) 84-93. received: 18.01.2018 accepted: 20.05.2018 published: 01.10.2018 copyright: © 2018 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. introduction atigue life prediction under service loading remains a challenging problem in real life, especially in the automotive industry. in an automotive application, service loadings such as stress on a car wheel are in variable amplitude loading, as reported in sonsino [1]. this situation leads to a need for developing a new approach to predict the reliability of f http://www.gruppofrattura.it/va/46/9.mp4 m. f. m. yunoh et alii, frattura ed integrità strutturale, 46 (2018) 84-93; doi: 10.3221/igf-esis.46.09 85 the components that are subjected to the fatigue loading. the fatigue time histories often contain a major percentage of small amplitude cycles, and the fatigue damage for these cycles can also be small. therefore, in many cases, the fatigue loading history is edited by removing these small amplitude cycles to produce representative and meaningful, yet economical testing, stephens et al. [2]. several fatigue data editing techniques have been developed for use in the time domain analysis, abdullah et al. [3]. some previous algorithms have been developed for eliminating low amplitude cycles in order to only retain the high amplitude cycles, el ratal et al. [4]. in the frequency domain, the time history is a low pass filtered by the criterion that high-frequency cycles have small amplitude, which is are not damaging. the filtering method does not shorten the signal because it does not provide the time-based information, nizwan et al. [5]. in addition, abdullah et al. [3] have developed a method for data editing to shorten the strain signal in the time-frequency domain. in fatigue data editing, the behaviour of extraction segments also needs to be studied because it contributes many bits of information that can improve fatigue life prediction. to deal with uncertainties and variations in fatigue data, the statistical analysis, i.e. the probability analysis is the best approach that should be adopted. zhao and liu [6] use the approach of statistical aspects of the s-n curve by means of the weibull distribution. this approach indicates that an appropriate distribution determination is the primary task for a rolling contact fatigue analysis. tiryakioglu [7] uses the weibull analysis in fatigue data and predicts the failure mechanisms due to cracks initiating from surface and interior defects. the evaluation of fatigue damage extraction for automotive components under service loading is vital in the reliability analysis. very few analysis methods have been developed to evaluate the fatigue damage extraction. a consistent description of the probability of damage occurrences is possible only if the damage distribution function is known. in this paper, two sets of strain signals from the real component in service are used in the fatigue feature extraction. the feature extraction, i.e. fatigue damage, is analysed using statistical inferences. the objective of this study is to determine the probabilistic-based failure of damage featured in the strain signals, and at the same time, validate them through the extraction process. by considering the significant statistical tools, features extraction is combined with the weibull distribution analysis in order to obtain a better evaluation. theoretical background the global statistic he time series contains an explanation of a set of variables taken at equally spaced time intervals. a statistical analysis is normally used to determine the random signals and monitor the pattern of the analysed signals. the calculation of the root-mean-square (r.m.s.) and the kurtosis is very important in the fatigue signals in order to retain a certain number of the signal amplitude range characteristics. the r.m.s. value is the 2nd statistical moment, is used to quantify the overall energy content of the signal. for discrete data sets the r.m.s. value is defined as: (1) while kurtosis is the signal 4th statistical moment, is a global signal statistic which is highly sensitive to the spikiness of the data. for discrete data sets the kurtosis value is defined as: (2) where jx is the amplitude of signal, n is number of data and x is the mean value. the wavelet transform the wavelet transform (wt) is defined in the time-scale domain and is a significant tool for analysing the time-localised features of a signal. it represents a windowing technique within the variable-sized region. a wavelet transform can be classified as either a continuous wavelet transform (cwt) or a discrete wavelet transform (dwt) depending on the discretisation of the scale parameters of the analysing wavelet. the dwt based on such wavelet functions is called the orthogonal wavelet transform (owt). orthogonal wavelet transforms are normally applied for the compression and feature 2/1 1 21 ..          n j jx n smr     n j j xx smrn k 1 4 4)..( 1 t m.f.m. yunoh et alii, frattura ed integrità strutturale, 46 (2018) 84-93; doi: 10.3221/igf-esis.46.09 86 selection of signals. dwt is derived from discrete cwt, and it is shown as the following expression, purushotham et al. [8]:  /2 *0 0 0( , ) ( ) ,m mw m n x t a a t nb dt        (3) where a and j are the scale factor, both b and k are the position, and ψ is the mother wavelet. oh [9] has previously conducted fatigue data analysis using the wavelet transform (wt) for spike removal, denoising, and data editing. piotrkowski et al. [10] used the wavelet transform application in acoustic emissions to detect damage and corrosion. fatigue life assessment the palmgren-miner linear cumulative damaging rule is normally associated with the established strain-life fatigue models sun et al., [11]. the fatigue damage caused by each cycle of repeated loading is calculated by reference to material life curves, such as s n or n  curves. the fatigue damage caused by multiple cycles is expressed respectively as: 1 f d n         (4) i f n d n           (5) where d is fatigue damage for one cycle and d is total fatigue damage in is the number of cycles within a particular stress range and its mean and fn is a number of cycles. the strain-life model commonly used for the prediction of fatigue strain life is the coffin-manson relationship model. this model can provide a traditional prediction when there is more compressive load time history and the mean stress is zero. the following equation can define this model:     ' 2 ' 2 b cf a f fn f n e     (6) e is the material modulus of elasticity, a is the true strain amplitude, 2 fn is the number of reversals to failure, ' f is the fatigue strength coefficient, b is the fatigue strength exponent, ' f is the fatigue ductility coefficient, c is the fatigue ductility exponent, m is the mean stress, and max is the maximum stress. the inclusion of mean stress effects in the life prediction makes the process more complex. the morrow mean stress model is given by dowling [12]:     ' ' ' 1 2 2 b cf m a f f f f n n e               (7) where is the total strain amplitude, ' f , b, ' f and c are considered to be material properties, fn is the number of cycles to failure, and m is the mean stress. another strain life model dealing with mean stress effects is known as the smithwatson-topper (swt) model, and its equation is written as: 2 2 ' ( 2 ) ' ' ( 2 ) f b b c a mak f f f fn n e        (8) m. f. m. yunoh et alii, frattura ed integrità strutturale, 46 (2018) 84-93; doi: 10.3221/igf-esis.46.09 87 the coffin-manson relationship only considers the damaging calculation at zero mean stress. however, in real-case scenarios, some of the realistic service situations involve nonzero mean stresses. for example, in a case of the loading being predominantly compressive, particularly for wholly compressive cycles, the morrow mean stress correction effect provides more realistic life estimates and seems to work reasonably well for steels, ince & glinka [13]. the weibull distribution in terms of the statistical analysis used in engineering, the weibull distribution is a theoretical model that has been successfully used to model the life data. the weibull distribution is described by the shape, scale, and threshold parameters. the weibull distribution model is a tool to develop the probabilistic analysis because of its ability to provide reasonably accurate failure analysis and failure forecasts with extremely small samples, sivapragash, [14]. the 2-p weibull distribution function is shown in eqn. 7: (9) where f (x: θ: β) represents the probability of strain-life being equal to or less than x, θ is a scale parameter, and β is a shape parameter. θ and β are estimated by observation. the weibull distribution has been widely utilised to develop a model of extreme values, such as failure time and fracture strength, shalabh et al. [15]. the weibull distribution is a probabilistic analysis which has been used for the determination of static and dynamic mechanical properties of materials. this distribution has the capability to model experimental data with different characters, li et al. [16]. methodology n this work, the strain signal has been collected from the coil spring in the car suspension system during a road test as shown in fig. 1 which is collected in macrostrain ( e ). an established signal, known as saesus, is the typical strain history for the suspension system, developed by the society of automotive engineers (sae), as reported in oh [9]. another signal, s1, is a set of experimental strain signals measured at 500 hz sampling rate using a strain gauge that is positioned on the coil spring component of a car being driven on a rural road at a velocity of 50 to 60 km/h. the measurement procedure is reported in their previous work by yunoh et al. [17]. the fatigue signal was measured at the car coil spring which subjected to the road load service. all data were recorded as strain time histories and fig. 2 shows the setup of fatigue data measurement during the process. the strain value was measured using strain gauge and it was connected to the specific data logger, for data acquisition purpose. experimental parameters such as sampling frequency and type of output data were then set using the common data logger interface. (a) (b) figure 1: the strain signals used for the work: (a) saesus, (b) an experimental measured data, s1. the extraction algorithm of the strain signal is developed for fatigue data editing purposes. the discrete wavelet transform is utilised to identify the high amplitude segments in the fatigue signal due to the high-energy coefficients magnitude. the magnitudes of the wavelet energy coefficients in the time-frequency domain are transposed into time histories representations to trace the location of the high amplitude segments. the respective magnitudes are obtained from the accumulation of wavelet transform magnitude distributions along the frequency band at each time interval. thus, the energy coefficients in time representation are gained, and these signals are used to detect the presence of high amplitude events in the fatigue signal.                          xx xf exp),:( 0 20 40 60 80 100 120 -1,000 -800 -600 -400 -200 0 200 400 600 800 1,000 t ime (s) a m p li tu d e (u e) 0 20 40 60 80 100 120 -500 -400 -300 -200 -100 100 200 300 400 500 t ime (s) a m p li tu d e (u e) i m.f.m. yunoh et alii, frattura ed integrità strutturale, 46 (2018) 84-93; doi: 10.3221/igf-esis.46.09 88 the cut-off level (col) needs to be set up for the elimination process in a high amplitude event extraction process. the col is the minimum percentage of the wavelet energy coefficients to be retained and the segments with magnitudes lower than the col value will be removed. the retained segments are then sliced from the original signal. the sliced segment identification is performed by means of a search which identifies the point at which the signal envelope inverts from the decay behaviour. the two inversion points, one on either side of the peak value, define the temporal extent of the sliced segment. the original strain signal is then edited to remove the low amplitude cycle contained in the signal based on the time location of the wavelet transform spectrum-sliced segment. the fatigue damage for every retained segment is then calculated for the probabilistic analysis. figure 2: a diagrammatic process flow for fatigue signal collection the fatigue damage for all segments is further analysed using the 2-p weibull distribution to evaluate the segments’ extraction results. the advantage of using this distribution lies in its ability to explain the simple function. this approach is often used in assessing the fatigue life of the material based on its simple calculation, glodez et al. [18]. all the fatigue damage of the retained segments is incorporated into the weibull distribution, and as has been later suggested, based on the probability distribution, the resultant significant findings are utilised to reveal the inferences of this study. results and discussions irst, the strain signals were evaluated by observation based on statistics characteristics, i.e. number of cycles counted, root-mean-square (r.m.s), kurtosis and total damage as tabulated in tab. 1. according to the results, the saesus signal produced higher values of r.m.s and kurtosis. this is due to the higher amplitude segments existing in the saesus signal compared to the s1 signal. higher amplitude segments contributed more energy in the oscillatory signals. the value of kurtosis for the saesus strain signal was found to be 4.32, which indicates that the spike and extreme values exist in the signal. this result was consistent with the r.m.s value for saesus, which is found to be 246.6 με, higher when compared to s1. the kurtosis value for both strain signals was not found in a gaussian distribution because in a stationary gaussian process, the kurtosis value is approximately 3. the fatigue damage for both signals was calculated based on three strain-life models as tabulated in tab. 1. the values of the fatigue damage based on the three models were close to each other with minor differences. the fatigue damage values for saesus were found to be higher compared to s1. the existence of the higher amplitude segments in the saesus signal contributed more fatigue damage compared to s1. f strain gauge strain gauge position strain gauge connect to data acquisition data transfer from data acquisition to computer strain signal in time domain m. f. m. yunoh et alii, frattura ed integrità strutturale, 46 (2018) 84-93; doi: 10.3221/igf-esis.46.09 89 data n (cycles) r.m.s (με) kurtosis fatigue damage (damage/block) saesus 1253 246.6 4.28 cf morrow swt 1.70 x 10-3 1.70 x 10-3 1.64 x 10-3 s1 9768 122.68 2.82 cf morrow swt 2.97 x 10-4 2.94 x 10-4 2.85 x 10-4 table 1: summary of statistical characteristic of the signals the developed wavelet transform algorithm transformed the signal into a time-frequency domain to obtain the timefrequency localisation, as shown in fig. 3. the spectrum colour intensity is proportional to the absolute energy coefficients values because it delivers the energy distribution display on time and frequency. the spectrum of saesus and s1 signals shows that the intensity colours of the saesus strain signal are more highlighted compared to s1. a large scale was indicative of low frequency, and higher amplitude segments indicated that the cycles had higher energy. this means that it can inflict higher fatigue damage. (a) (b) figure 3: the wavelet transform spectrum of; (a) saesus, (b) s1. higher amplitude segments based on wavelet transform spectrum were extracted. the location of the retained segments was shown in fig. 4. after eliminating the low amplitude segments, the high amplitude segment should be retained to maintain the fatigue damage contained in both signals. the saesus strain signal contributed 21 high amplitude retained segments. meanwhile, the s1 strain signal contributed 11 high amplitude retained segments. based on the extraction results, the saesus strain signal consists of higher amplitude segments compared to s1 because it retained the higher amplitude segments after the extraction process. (a) (b) figure 4: the location of the retained segments; (a) saesus, (b) s1. the features extraction, i.e. fatigue damage for every segment, was calculated to analyse and determine the probability of failure based on high amplitude segments. it is helpful to know the fatigue damage distribution based on the extracted segments for both signals. the 2-p weibull distribution was used for the data analysis. according to tab. 2, the values of the shape parameters, β, for both signals were less than 1.0, indicating a decreasing failure rate. according to finkelstein, [19], if the shape parameter for weibull distribution is less than 1.0, this distribution is always decreasing the failure rate. the value of scale parameter, θ, of fatigue damage for both signals was found to be 5.3 x 10-5 and 1.4 x 10-5. this means that when the components reach these values, the probability of failure will increase. dat a s ca le ( 1 /h z) 0.5 1 1.5 2 2.5 x 10 4 1 27 53 79 105 131 157 183 209 235 257 50 100 150 200 250 dat a s ca le ( 1 /h z) 1 2 3 4 5 6 x 10 4 1 27 53 79 105 131 157 183 209 235 257 50 100 150 200 250 0 20 40 60 80 100 120 -1,000 -800 -600 -400 -200 0 200 400 600 800 1,000 a m p li tu d e (u e) t ime (s) 0 20 40 60 80 100 120 -500 -400 -300 -200 -100 0 100 200 300 400 500 a m p li tu d e (u e} t ime (s) m.f.m. yunoh et alii, frattura ed integrità strutturale, 46 (2018) 84-93; doi: 10.3221/igf-esis.46.09 90 signals shape parameter, β scale parameter, θ saesus 0.59 5.3 x 10-5 s1 0.34 1.4 x 10-5 table 1: statistical data analysis based on weibull distribution. cumulative distribution function (cdf) represents the probability of the components to fail at the particular time interval. based on the plots in fig. 5, the fatigue damage for s1 increases more rapidly in cumulative probability values compared to the saesus. this finding can be suggested that saesus signal consists high amplitude segments that cause high fatigue damage compared to s1. figure 5: probability density functions for saesus and s1 strain signal figure 6: the weibull probability distribution plots of fatigue damage for saesus figs. 6 and 7 show the best fit of the weibull probability distribution plot for fatigue damage of high amplitude segments for both signals. the parameters of the distribution are estimated using the maximum likehood method. the weibull probability distribution plot for both strain signals was estimated using 95% confidence level correction line, which includes the true population parameter. from a statistical point of view, the more test data that falls into the 95% confident level, the more reasonable the probabilistic distribution is, according to xianmin et al [20]. saesus 90% 70% m. f. m. yunoh et alii, frattura ed integrità strutturale, 46 (2018) 84-93; doi: 10.3221/igf-esis.46.09 91 based on the plot indicated in fig. 5 for the saesus strain signal, there are four data points which are out of the 95% confidence level. this is because several segments in the signal consist of very high amplitude segments. meanwhile, all points in s1 strain signal were distributed at the 95% confidence level. figs. 5 and 6 also show that 70% of the probability of failure occurred from 1.0 x 10-5 to 1.0 x 10-4 fatigue damage for both signals. around 90% of the probability of failure occurred from 1.0 x 10-4 to 1.0 x 10-3 fatigue damage for both signals. figure 7: the weibull probability distribution plots of fatigue damage for s1. figs. 8 and 9 show the best fit of the weibull probability distribution plot for fatigue life of high amplitude segments for both signals. all of data for the saesus and s1 strain signal were distributed at the 95% confidence level. fig. 7 show that 70% of the probability of failure for saesus occurred at 5.2 x 103 cycles. meanwhile the probability of failure for saesus occurred at 6.9 x 103 cycles. around 90% of the probability of failure occurred at 1.6 x 105 to 3.5 x 105 fatigue life for both signals. thus, the value of fatigue damage and life based on extraction segments approaching the failure can be determined roughly by the weibull analysis. figure 8: the weibull probability distribution plots of fatigue damage for saesus. 70% 90% 70% 90% m.f.m. yunoh et alii, frattura ed integrità strutturale, 46 (2018) 84-93; doi: 10.3221/igf-esis.46.09 92 figure 9: the weibull probability distribution plots of fatigue damage for s1. conclusion o summarise the statistics and strain life analysis, the saesus strain signal contributes more damaging segments compared to s1. this situation is due to the high amplitude segments obtained in the signal. the fatigue damage based on high amplitude segments fits well to a weibull distribution. based on the results, it shows that 70% of the probability of failure occurred between 1.0 x 10-5 and 1.0 x 10-4 fatigue damage for both signals. around 90% of the probability of failure occurred between 1.0 x 10-4 to 1.0 x 10-3 fatigue damage for both signals. thus, the value of fatigue damage based on extraction segments that are approaching the failure can be determined using the weibull analysis with the 95% confident level, which is a reasonable probabilistic distribution. this approach presents an alternative technique to predict the fatigue damage probability function for automotive components. however, further works and analyses need to be performed for the purpose of validation, and also to produce high data accuracy by means of life assessment. references [1] sonsino, c. m. (2006). fatigue testing under variable amplitude loading, international journal of fatigue, 29(6), pp. 1080-1089. [2] stephens, r. i., dindinger, p. m., and gunger, j. e. (1997). fatigue damage editing for accelerated durability testing using strain range and swt parameter criteria, international journal of fatigue, 19(8-9), pp. 599-606. [3] abdullah, s., nizwan, c. k. e., yunoh, m. f. m., nuawi, m. z., and nopiah, z. m. n. (2013). fatigue features extraction of road load time data using the s-transform, international journal of automotive technology, 14(5), pp. 805-815. [4] el-ratal, w., bennebach, m., lin, x. and plaskitt, r. fatigue life modelling and accelerated test for components under variable amplitude loads, proc. of symposium on fatigue testing and analysis under variable amplitude loading conditions, tours, france, 2002. [5] nizwan, c. k. e., abdullah, s., nuawi m. z. and lamin, f. (2007). a study of fatigue data editing using frequency spectrum filtering technique, proceeding of the world engineering congress (wec), penang, malaysia, 2007, pp. 372378. [6] zhao, y. x. and liu, h. b. (2014). weibull modelling of the probabilistic s-n curves for rolling contact, international journal of fatigue, 66, pp. 47-54. [7] tiryakioglu, m. (2015). weibull analysis of mechanical data for casting ii: weibull mixtures and their interpretation, metallurgical and materials transactions a, 46a, pp. 270-280. t 70% 90% m. f. m. yunoh et alii, frattura ed integrità strutturale, 46 (2018) 84-93; doi: 10.3221/igf-esis.46.09 93 [8] purushotham, v., narayanan, s. and prasad, s. a. n. (2005). multi-fault diagnosis of rolling bearing elements using wavelet analysis and hidden markov model-based fault recognition, ndt & e international, 38, pp. 654-664. [9] oh, c. s. (2001). application of wavelet transform in fatigue history editing, international journal of fatigue, 23(3), pp. 241-250. [10] piotrkowski, r.,castro, e and gallego, a. (2009). wavelet power, entropy and bispectrum applied to ae signals for damage identification and evaluation of corroded galvanised steel, mechanical system and signal processing, 23(2), pp. 432-445. [11] sun, q., dui, h. n. and fan, x. l. (2014). a statistically consistent fatigue damage model based on miner’s rule, international journal of fatigue, 69, pp. 16-21. [12] dowling, n. e. (2013). mechanical behavior of materials, 4th ed.: pearson education limited. [13] ince, a. and glinka, g. a modification of morrow and smith-watson-topper mean stress correction models, fatigue fracture engineering materials and structure, 34, pp. 854-867. [14] sivapragash, m., lakshminarayanan, p. r., karthikeyen, r., raghukanda, k. and hanumantha, m. (2008). fatigue life prediction of ze41a magnesium alloy using weibull distribution, material & design, 29 pp.1549–53. [15] shalabh g, dheeraj s.s, asok r. statistical pattern analysis of ultrasonic signals for fatigue damage detection in mechanical structures, ndt & e international, 41, pp. 491-500. [16] li w, sakai t, wang p. (2011). statistical analysis of fatigue crack growth behavior for grade b cast steel. material and design, 32, pp. 1262-1272. [17] yunoh, m. f. m., abdullah, s., saad, m. h. m., nopiah, z. m. and nuawi, m. z. (2014). fatigue time history analysis for determining the strain signal behavior, international journal vehicle system modelling and testing, 9 (3/4), pp.363371. [18] glodez, s., sori, m., and kramberger. j. (2013). prediction of micro-crack initiation in high strength steels using weibull distribution. engineering fracture mechanics, 108, pp. 263-274. [19] finkelstein, m. (2009). understanding the shape of the mixture failure rate (with engineering and demographic applications), applied stochastic models in business and industry, 25(6): 643-663. [20] xianmin, c., qin, s., hongna, d. and junling, f. 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can be opened with acrobat and adobe reader 5.0 and later.) >> /namespace [ (adobe) (common) (1.0) ] /othernamespaces [ << /asreaderspreads false /cropimagestoframes true /errorcontrol /warnandcontinue /flattenerignorespreadoverrides false /includeguidesgrids false /includenonprinting false /includeslug false /namespace [ (adobe) (indesign) (4.0) ] /omitplacedbitmaps false /omitplacedeps false /omitplacedpdf false /simulateoverprint /legacy >> << /addbleedmarks false /addcolorbars false /addcropmarks false /addpageinfo false /addregmarks false /convertcolors /converttocmyk /destinationprofilename () /destinationprofileselector /documentcmyk /downsample16bitimages true /flattenerpreset << /presetselector /mediumresolution >> /formelements false /generatestructure false /includebookmarks false /includehyperlinks false /includeinteractive false /includelayers false /includeprofiles false /multimediahandling /useobjectsettings /namespace [ (adobe) (creativesuite) (2.0) ] /pdfxoutputintentprofileselector /documentcmyk /preserveediting true /untaggedcmykhandling /leaveuntagged /untaggedrgbhandling /usedocumentprofile /usedocumentbleed false >> ] >> setdistillerparams << /hwresolution [2400 2400] /pagesize [612.000 792.000] >> setpagedevice shot peening processes to obtain nanocrystalline surfaces in metal alloys: d. okulova et alii, frattura ed integrità strutturale, 63 (2023) 80-90; doi: 10.3221/igf-esis.63.08 80 on local strength of a spherical vessel with pits distributed along the equator daria d. okulova, liana a. almazova, olga s. sedova, yulia g. pronina saint petersburg state university, st.petersburg state university, 7/9 universitetskaya nab., st. petersburg, 199034 russia st062247@student.spbu.ru, http://orcid.org/0000-0001-2345-6789 st080595@student.spbu.ru, https://orcid.org/0000-0001-8695-3598 o.s.sedova@spbu.ru, https://orcid.org/0000-0001-9097-8501 y.pronina@spbu.ru, https://orcid.org/0000-0003-4978-6238 abstract. the effect of multiple shallow corrosion pits on the strength of a spherical vessel subjected to internal pressure is studied. the pits are considered both randomly and evenly distributed along the equator on the outer surface of the vessel. the dependencies of the stress concentration factor on the number of the pits are compared for linearly elastic and elasticplastic material with hardening. the behavior of the vessels made of elastic and elastoplastic materials turns out to be qualitatively different. the approximation of periodic pits arrangement is discussed. keywords. pitting corrosion, surface defects, spherical shell, pressure vessel. citation: okulova, d., almazova, l., sedova, o., pronina, y., on local strength of a spherical vessel with pits distributed along the equator, frattura ed integrità strutturale, 63 (2023) 80-90. received: 31.05.2022 accepted: 04.10.2022 online first: 29.10.2022 published: 01.01.2023 copyright: © 2023 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. introduction ressure vessels are common devices for various industrial applications [1-4]. the most preferred vessel shape to hold internal pressure is spherical [5]. moreover, temperature conditions of the environment have the least effect on the contents of the spherical vessel due to the smallest surface area per unit volume. pressure vessels are usually exploited in aggressive environments that may result in general or local corrosion of their parts. general mechanochemical corrosion of elastic or elastic-plastic thinand thick-walled spherical vessels was modeled, e.g., in the works [6-10]. pitting corrosion may be initiated by a local damage of a protective coating or an oxide film (which also may possess protective properties), as well as by many other factors which lead to chemical or physical heterogeneity at the metal surface [11, 12]. in natural conditions the likelihood of pitting corrosion is higher compared to uniform corrosion [13]. despite having minor metal loss, the structures subjected to localized corrosion have significantly reduced service life. once appeared, local damages cause stress concentration in their adjacency. this may result in crack nucleation, and, consequently, the premature failure of a structural component. therefore, assessment of the stress level in structural p http://orcid.org/0000-0001-2345-6789 https://orcid.org/0000-0001-8695-3598 https://orcid.org/0000-0001-9097-8501 https://orcid.org/0000-0003-4978-6238 https://youtu.be/ivkohi43mxm d. okulova et alii, frattura ed integrità strutturale, 63 (2023) 80-90; doi: 10.3221/igf-esis.63.08 81 elements with corrosion defects is an important issue to prevent the abrupt failure of the structures in an aggressive environment. shallow corrosion pits may show a spherical cap morphology with a constant pit depth/diameter ratio [14, 15]. corrosion pits may also have more complex geometry [16-18]. however, most researchers used either simplification of pit forms or local thinning of structural elements [19-21]. corrosion pits are usually idealized as conical [19], semi-elliptical [22-24], circular [18, 25-27], cylindrical [26, 28-30], and rounded rectangular shapes [31, 32]. authors of [26, 27, 33] showed that the form of the defects (circular, conical, elliptical or cylindrical) has a slight effect on the ultimate strength of plates under different loading. stress fields around defects in structural elements are often analyzed using finite element method [34-37]. there are a number of papers focused on the effect of a single surface pitting on the service life of structural components. stress distribution in the spherical shell with a single corrosion defect was addressed in [22, 38]. many authors considered structures weakened by multiple surface defects. however, most of these studies focused on pipes [29, 39], plates [21, 27, 30, 40, 41], and shells [42-45]. sedova [46] studied a spherical vessel with multiple defects uniformly located on its inner equator. the numerical simulations have shown that the maximum stresses in the vicinity of defects increase with the growing number of defects within a certain range, but further increase in the number of defects leads to a slight decrease in the stress values. similar qualitative results were obtained in liao, et. al. [39] using the ramberg-osgood plasticity model: the interaction between defects enhances with decreasing distance up to a certain limit when defects become close to intersection, while further decrease in spacing between defects provides the reduction of the interaction between defects. in [29], it is shown that the effect of multiple surface defects on the strength of structures depends on the distribution pattern of pitting corrosion. since in reality, the defects appear randomly, it is reasonable to use random patterns when modeling multiple pits on the surface of structural components. the influence of pittings randomly distributed over a small area of the surface of a sphere on the collapse pressure was analyzed in [47, 48]. authors of [28] showed that the outer defect is more harmful to the pressure vessel than the inner one. a linearly elastic spherical vessel with several notches evenly distributed along its equator, subjected to internal pressure was considered in [49]. the present paper is devoted to the stress analysis of a spherical vessel under internal pressure, weakened by multiple shallow pits located along the equator on its outer surface. results are compared for the bilinear plasticity hardening model and the linearly elastic model of the vessel material. different numbers of defects with random arrangement and periodic arrangement are considered. the limiting case of toroidal notch is also studied. description of the problem spherical vessel with multiple shallow pits along the equator on its outer surface is under study. let r and r be the inner and outer radii of the vessel. all the pits have a spherical cap shape of the same size with curvature radius δ and depth h = δ/2 (fig. 1). a pseudo-random arrangement of the defects along the equator of the sphere and their different numbers n are considered. along with separate notches, the “limiting” case of notches configuration is analyzed. this case corresponds to the complete covering of the equator of the sphere with a continuous toroidal notch with the same minimal curvature radius δ and depth h (fig. 2, the surface of the notch is highlighted with another color). figure 1: central cross-section of the vessel with one surface defect. a d. okulova et alii, frattura ed integrità strutturale, 63 (2023) 80-90; doi: 10.3221/igf-esis.63.08 82 figure 2: a sphere with a toroidal notch along the equator. pressure p is applied to the inner surface of the vessel. the problem is studied both within the framework of linearly elastic and bilinear elastic-plastic models. for example, 304 stainless steel is chosen as the vessel material. the inner and outer radii of the sphere are r = 340 mm and r = 350 mm, respectively. the notches’ curvature radius is δ = 6 mm, and the notch depth is h = 3 mm. the number of the defects, n, varies from 2 to 260; additional geometries with n up to 320 are considered for the case of uniformly (periodically) located notches. note that numbers n > 212 correspond to the complete covering of the equator by the defects (their intersection), in the case of their periodical distribution. numerical analysis o perform the finite element analysis, an array of 3d cad-models of different geometries was built in ansys spaceclaim. each of the models represents the hollow sphere with the notches. since the probability of the defects is supposed to be the same at every point on the equator, the uniform probability distribution was accepted. in order to create the random patterns of the defects along the equator of the vessel, the python-function «random()» was used. since the model of the sphere with the notches located on the equator is symmetric, only a half of the sphere was built as a cad-model. the boundary condition on the face of symmetry was set to “frictionless support” which prevents moving or deforming in the normal direction. for mesh generation a ten-node tetrahedral element solid187 was utilized. in order to enhance the accuracy of the solution, the finite element mesh was refined in the vicinity of the defects. the geometrical model with the continuous torus-shaped notch on the equator is axisymmetric; therefore, the cross section of the geometry was built in ansys designmodeler. before performing axisymmetric analysis for the geometry with the toroidal notch, special meshing methods with mesh refinement settings were set in the vicinity of the notch to achieve sufficient mesh quality. fig. 3 shows mesh element quality on the fragment of the geometrical model capturing the vicinity of the notch. t d. okulova et alii, frattura ed integrità strutturale, 63 (2023) 80-90; doi: 10.3221/igf-esis.63.08 83 figure 3: mesh element quality in the vicinity of the toroidal notch. the following data on material properties for 304 stainless steel are used: young’s modulus e = 185 gpa, poisson’s ratio ν = 0.27, yield strength σt = 210 mpa and tangent modulus t = 1.16 gpa. for linearly elastic analysis, the material is assumed to behave according to hooke's law with the elastic constants given above. internal pressure is set to p = 1 mpa to stay in the framework of the elastic problem. for elastic-plastic analysis, the bilinear plasticity model “bilinear isotropic hardening” available in ansys workbench material properties library is used. the vessel is subjected to internal pressure p = 6 mpa which causes the plastic deformations of the material in the vicinity of the pits. 3d cad-models are meshed using “sizing” meshing options. the mesh is more refined at the weakened region and a smooth transition to a coarser mesh in regions far from notches is implemented. to ensure the convergence of the solution (its sensitivity to the mesh parameters), multiple calculations with different sizes of elements are carried out for each cadmodel. as a result, sizes of elements on the face of symmetry are set to 1.6 mm, while the sizes on the surface of notches are 0.5 mm. the estimated error value is about 2%. for bilinear plasticity hardening model, about 30 iterations were needed for each geometry model to reach the convergence of the nonlinear solution. since linearly elastic and elastic-plastic analyses are performed with the same geometries and mesh parameters, there is no need to run two standalone calculations for each set of material properties. two linked projects that share geometries and mesh parameters are used instead. results and discussion he maximum principal stress in the notched vessel was analyzed for various n from 2 to 260, and five different random distributions of pits for each n being considered. let the maximum value of this stress for a certain geometry be denoted by σ  max . it was observed that for the configurations where all the defects were either far enough from each other or, conversely, their centers were exceedingly close to each other (resulting in their extensive overlapping so that there were no thin ligaments between them), the maximum stress values were reached at the bottom of a certain pit or pits (fig. 4). concerning the configurations where the pits slightly overlap or close to overlapping, the maximum stress values were observed at the cusps formed by the adjacent boundaries (fig. 5). this observation is in accordance with the results of [36, 39, 46]. for the toroidal notch, the maximum stress value was observed along the bottom of the notch (fig. 6). let the stress concentration factor (one of all the possible factors) be denoted by k: σ σ = max ideal k (1) where σ ideal is the maximum principal stress on the outer surface of an ideal shell (without defects) of the same size and under the same pressure: t d. okulova et alii, frattura ed integrità strutturale, 63 (2023) 80-90; doi: 10.3221/igf-esis.63.08 84 ( ) σ = −3 3 3 2 / 1 ideal p r r (2) figure 4: stress distribution in the vicinity of pits sufficiently remote from each other (the plane of symmetry is horizontal). linearly elastic model. figure 5: stress distribution in the vicinity of overlapping pits (the plane of symmetry is horizontal). linearly elastic model. figure 6: stress distribution along the cross section of the vessel with a continuous toroidal notch. elastic-plastic model. d. okulova et alii, frattura ed integrità strutturale, 63 (2023) 80-90; doi: 10.3221/igf-esis.63.08 85 in our cases, σ ideal ≈ 16.51 mpa for p = 1 mpa used in linear analysis and σ ideal ≈ 99.06 mpa for p = 6 mpa used in nonlinear analysis. both of these values do not exceed the yield strength; therefore, no plastic deformation occurs on the surface of the ideal sphere for both the considered values of internal pressure. figs. 7 and 8 show the values of k for different random distributions of notches and for various numbers n within the frame-work of the linearly elastic (fig. 7) and elastic-plastic (fig. 8) models. points of different colors for each n correspond to different random distributions of the pits. dashed lines in the figures show the values of the stress concentration factor, k, in the sphere with the toroidal notch. as can be seen from these figures, interaction of multiple defects may result in the significant increase in the maximum stresses with n increasing. the dependencies of k on n in the considered interval are qualitatively the same for both the models: at the beginning of the graphs, the values of k rise steeply and then a certain plateau (with a weak minimum inside) is formed at n > 200. the observed plateau may be explained by the overlaps of neighboring pits for large n. obviously, the frequency of such overlaps grows with an increase in the number of the defects. however, the increase in k for the material in the elastic state is much higher than in the elastic-plastic: the value of k in the elastic sphere with multiple defects can be more than two times higher than that for a single defect, while in the elastic-plastic sphere the increase does not exceed 30%. at first glance, it may seem strange that the maximum stresses in the elastic sphere with multiple pits may be larger than in the sphere with the toroidal notch (what is observed for n ≥ 32 in our case), while for the elastoplastic sphere the situation is opposite. such behavior of the elastic sphere with multiple pits may be explained by the fact that the maximum stresses are observed at beak-like bridges between closely spaced defects (fig. 5), which are absent in the sphere with a toroidal notch. the higher stresses at the bottom of the toroidal notch in the elastic-plastic vessel – compared to the stresses in the vicinity of the pits – are explained by the following reasoning. in the vessel with the continuous girdle notch, the vessel wall bends along the notch (see fig. 6). moreover, it is obvious that the bending deformations in the elastoplastic vessel are greater than in the elastic one, however, stresses in the last are not limited. large deformations in the elastoplastic vessel initiate a hardening effect, resulting in an increase in stresses along the equatorial notch. in the vessel with separate random pits, such large bending deformations (which can lead to a hardening effect) do not occur. therefore, stresses in the vicinity of individual pits in the elastoplastic vessel are smaller, since limited by a lower yield strength. moreover, it is expected that as the number of pits increases, the stresses in the vicinity of the pits should tend to the stresses in the vicinity of the torus. it is really true and confirmed by figs. 9 and 10. these figures show the values of k for the elastic and elastic-plastic vessels with multiple uniformly (i.e. periodically) located pits. as can be seen from fig. 9, for the elastic material, the value of k experiences a sharp increase when thin ligaments or cusps form between adjacent pits (numbers n > 212 correspond to pit overlapping). starting from a certain number n (in figs. 9 the peak is reached at n = 228), cusps between the pits in the elastic vessel become more obtuse resulting in the gradual decrease in the maximum stresses approaching to the value corresponding to the toroidal notch. numerical experiments with other pit sizes lead to qualitatively the same dependencies of maximum stress values on the number of notches, n: for relatively small numbers of notches, the maximum stress grows slightly with growing n; then (when thin ligaments form between adjacent pits) a sharp increase in the maximum stress is observed; as n grows further, the maximum stress slightly decreases. the results in fig. 9 are consistent with ones obtained in [50] for linearly elastic sphere with multiple uniformly located pits with different values of notches sizes (both for δ < 6 mm and δ > 6 mm). fig. 10 demonstrates a nearly s-shaped dependency of k on n in the elastic-plastic vessel. a small jump in the value of k at n = 276 is explained by the formation of a relatively smooth notch along the equator of the vessel and its bending, resulting in large deformations and hardening effect. for n > 275, the difference between the values of k for multiple defects and for torus is less than 3.5%. thus, figs. 9 and 10 confirm that the maximum stresses in the vessel with multiple pits periodically distributed along the equator, tend to that for the toroidal notch. it is obvious that this tendency should be preserved for randomly located defects. nevertheless, there is a difference in the behavior of dependencies k(n) for random and periodical distribution of the defects. the values of k for the random defects rise significantly faster than for the periodical pits, due to the random formation of dangerous cusps at various and even very small n. the same effect for large n also leads to the slower decrease in k values for random pits in the elastic sphere. the difference between the peak value of k in fig. 9 (k = 4.399 at n = 228) and the maximum values observed in fig. 7 (which are greater than 4.5 for large n) is explained by the fact that for periodically distributed pits, the cusp angle changes stepwise (since the distance between the pits changes stepwise as l/n – d, where l is the length of the sphere equator and d is the pit diameter) and the angle values corresponding to the maximum k observed in fig. 9 are just skipped. for certain ratios d/l at a certain n, the distance between the neighboring pits can become very close to that which corresponds to the maximum possible value of k, then the maximum values of k for periodical pits will become closer to that for random pits. d. okulova et alii, frattura ed integrità strutturale, 63 (2023) 80-90; doi: 10.3221/igf-esis.63.08 86 figure 7: stress concentration factor, k, in the shell with n randomly distributed defects (points) and with the toroidal notch (dashed line). linearly elastic model. figure 8: stress concentration factor, k, in the shell with n randomly distributed defects (points) and with the toroidal notch (dashed line). elastic-plastic model. d. okulova et alii, frattura ed integrità strutturale, 63 (2023) 80-90; doi: 10.3221/igf-esis.63.08 87 figure 9: stress concentration factor k in the shell with n defects uniformly located along the equator. linearly elastic model. figure 10: stress concentration factor k in the shell with n defects uniformly located along the equator. elastic-plastic model. the opposite effect is observed for elastoplastic material: maximum values of k for randomly located pits (fig. 8) are less than for periodical pits (fig. 10). this is explained by the fact that at large n (starting from n=276), multiple periodic pits form a relatively deep girdle notch, along which the wall of the sphere bends (almost the same as in the sphere with the d. okulova et alii, frattura ed integrità strutturale, 63 (2023) 80-90; doi: 10.3221/igf-esis.63.08 88 toroidal notch, see fig. 6), resulting in a hardening effect and an increase in stresses. randomly located pits do not form a continuous notch (as there may be relatively large gaps between the pits at random locations) where large bending deformations may occur. therefore, the hardening effect does not manifest itself as noticeably as in a sphere with periodic pits. thus, the mutual arrangement of defects on the vessel surface may have a greater effect on its local strength than the total volume of metal loss. conclusions ased on the study, the following common conclusions can be drawn: interaction of multiple defects on the vessel surface may result in the significant increase in the maximum stresses with the number n of the defects increasing. however, behavior of the vessels with multiple defects is markedly different for linearly elastic and elastic-plastic models. first, it was observed that for the considered data, the value of maximum stresses in the elastic sphere with multiple defects can be more than two times higher than for a single defect, while in the elastic-plastic sphere this increase does not exceed 30%. moreover, smoothing the surface due to the damage accumulation may lead to a little decrease in the stress concentration for elastic materials. note that for other parameters, behavior of the vessels weakened by multiple pits was qualitatively the same. the maximum stresses in the vessel with multiple pits located along the equator tend to that for the toroidal notch, as n increases. however, the maximum stresses in the elastic vessel with multiple pits may be significantly higher than that for the toroidal notch. this means that it is unacceptable to calculate the strength of elastic vessels with individual defects by considering vessels with a thickness smoothly reduced along a certain area. at the same time, for an elastic-plastic material, the maximum stresses in the vessel with a toroidal notch is the upper limit for the stresses in the vessel with multiple defects; therefore, for the strength analysis of the latter, the vessels with a smoothly reduced thickness can be considered. stress concentration in the vessels with randomly distributed defects can be much higher than in the vessel with the same number of periodical defects, due to the random formation of thin ligaments or sharp cusps between the adjacent defects. however, for elastoplastic vessels with large numbers of defects, the opposite phenomenon may be initiated by the hardening effect. this means that the mutual arrangement of defects on the vessel surface may have a greater effect on its local strength than the total volume of metal loss and that periodic solutions do not always provide good approximations for random defects. acknowledgements his work was supported by the russian science foundation, grant no 21-19-00100. references [1] li, k., zheng, j., zhang, z., gu, c., zhang, x., liu, s., ge, h., gu, g. and lin, g. (2017). experimental investigation on buckling of ellipsoidal head of steel nuclear containment, j. press. vess.-t. asme, 139(6), 061206. doi: 10.1115/1.4038013. [2] dehrouyeh-semnani, a.m., dehdashti, e., yazdi, m.r.h. and nikkhah-bahrami, m. (2019). nonlinear thermo-resonant behavior of fluid-conveying fg pipes, int. j. eng. sci., 144, 103141. doi: 10.1016/j.ijengsci.2019.103141. [3] dastjerdi, s., akgöz, b., civalek, ö., malikan, m. and eremeyev, v.a. (2020). on the non-linear dynamics of torusshaped and cylindrical shell structures, int. j. eng. sci., 156, 103371. doi: 10.1016/j.ijengsci.2020.103371. [4] karimihaghighi, r., naghizadeh, m. and javadpour, s. (2022). ffs master software for fitness-for-service assessment of hydrogen induced cracking equipment based on api 579-1/asme ffs-1, frattura ed integrità strutturale, 60, pp. 187–212. doi: 10.3221/igf-esis.60.14. [5] nilsen, k. (2011). development of low pressure filter testing vessel and analysis of electrospun nanofiber membranes for water treatment. master’s degree thesis, wichita state university. b t d. okulova et alii, frattura ed integrità strutturale, 63 (2023) 80-90; doi: 10.3221/igf-esis.63.08 89 [6] pronina, y.g. (2013). lifetime assessment for an ideal elastoplastic thick-walled spherical member under general mechanochemical corrosion conditions, in: complas xii: proceedings of the xii international conference on computational plasticity: fundamentals and applications, cimne, pp. 729–738. [7] gutman, e.m., bergman, r.m. and levitsky, s.p. (2016). influence of internal uniform corrosion on stability loss of a thin-walled spherical shell subjected to external pressure, corros. sci., 111, pp. 212–215. doi: 10.1016/j.corsci.2016.04.018. [8] pronina, y., sedova, o., grekov, m. and sergeeva, t. (2018). on corrosion of a thin-walled spherical vessel under pressure, int. j. eng. sci., 130, pp. 115–128. doi: 10.1016/j.ijengsci.2018.05.004. [9] pronina, y. and sedova, o. (2021). analytical solution for the lifetime of a spherical shell of arbitrary thickness under the pressure of corrosive environments: the effect of thermal and elastic stresses, j. appl. mech.-t. asme, 88, 061004. doi: 10.1115/1.4050280. [10] sedova, o. and pronina, y. (2022). the thermoelasticity problem for pressure vessels with protective coatings, operating under conditions of mechanochemical corrosion, int. j. eng. sci., 170, 103589. doi: 10.1016/j.ijengsci.2021.103589. [11] groysman, a. (2017). physicochemical basics of corrosion at refineries units, top. saf. reliab. qual., 32, pp. 17–36. doi: 10.1007/978-3-319-45256-2_3. [12] liu, c., li, x., revilla, r. i., sun, t., zhao, j., zhang, d., yang, s., liu, z., cheng, x., terryn, h. and li, x. (2021). towards a better understanding of localised corrosion induced by typical non-metallic inclusions in low-alloy steels, corros. sci., 179, 109150. doi: 10.1016/j.corsci.2020.109150. [13] wu, k., jung, w. and byeon, j. (2016). in-situ monitoring of pitting corrosion on vertically positioned 304 stainless steel by analyzing acoustic-emission energy parameter, corros. sci., 105, pp. 8–16. doi: 10.1016/j.corsci.2015.12.010. [14] fabas, a., monceau, d., doublet, s. and put, a.r.v. (2015). modelling of the kinetics of pitting corrosion by metal dusting, corros. sci., 98, pp. 592–604. doi: 10.1016/j.corsci.2015.05.061. [15] natesan, k. and zeng, z. (2007). development of materials resistant to metal dusting degradation, report anl07/30, argonne national laboratory, pp. 161. [16] yu, j., wang, h., yu, y., luo, z., liu, w. and wang, c. (2018). corrosion behavior of x65 pipeline steel: comparison of wet–dry cycle and full immersion, corros. sci., 133, pp. 276–287. doi: 10.1016/j.corsci.2018.01.007. [17] wang, y., xu, s. and li, a. (2020). flexural performance evaluation of corroded steel beams based on 3d corrosion morphology, struct. infrastruct. e., 16(11), pp. 1562–1577. doi: 10.1080/15732479.2020.1713169. [18] cerit, m. (2019). corrosion pit-induced stress concentration in spherical pressure vessel, thin wall. struct., 136, pp. 106–112. doi: 10.1016/j.tws.2018.12.014. [19] nakai, t., matsushita, h., yamamoto, n. and arai, h. (2004). effect of pitting corrosion on local strength of hold frames of bulk carriers (1st report), mar. struct., 17(5), pp. 403–432. doi: 10.1016/j.marstruc.2004.10.001. [20] ok, d., pu, y. and incecik, a. (2007). computation of ultimate strength of locally corroded unstiffened plates under uniaxial compression, mar. struct., 20(1-2), pp. 100–114. doi: 10.1016/j.marstruc.2007.02.003. [21] khedmati, m.r. and nouri, z.h.m.e. (2015). analytical simulation of nonlinear elastic–plastic average stress–average strain relationships for un-corroded/both-sides randomly corroded steel plates under uniaxial compression, thin wall. struct., 86, pp. 132–141. doi: 10.1016/j.tws.2014.10.012. [22] cerit, m. (2013). numerical investigation on torsional stress concentration factor at the semi elliptical corrosion pit, corros. sci., 67, pp. 225–232. doi: 10.1016/j.corsci.2012.10.028. [23] zhang, s. and zhou, w. (2020). assessment of effects of idealized defect shape and width on the burst capacity of corroded pipelines, thin wall. struct., 154, 106806. doi: 10.1016/j.tws.2020.106806. [24] vansovich, k., aistov, i. and nakhlestkin, a. (2019). application of a discrete model of fatigue defect growth for assessment of the safe operation life of the main pipeline section with a corrosion defect, in: iop conference series: materials science and engineering, iop publishing, 684(1), 012006. doi: 10.1088/1757-899x/684/1/012006. [25] sultana, s., wang, y., sobey, a.j., wharton, j.a. and shenoi, r.a. (2015). influence of corrosion on the ultimate compressive strength of steel plates and stiffened panels, thin wall. struct., 96, pp. 95–104. doi: 10.1016/j.tws.2015.08.006. [26] huang, y., zhang, y., liu, g. and zhang, q. (2010). ultimate strength assessment of hull structural plate with pitting corrosion damnification under biaxial compression, ocean eng., 37(17–18), pp. 1503–1512. doi: 10.1016/j.oceaneng.2010.08.001. [27] zhao, z., zhang, h., xian, l. and liu, h. (2020). tensile strength of q345 stee lwith random pitting corrosion based on numerical analysis, thin wall. struct., 148, 106579. doi: 10.1016/j.tws.2019.106579. https://doi.org/10.1016/j.ijengsci.2021.103589 https://doi.org/10.1016/j.tws.2019.106579 d. okulova et alii, frattura ed integrità strutturale, 63 (2023) 80-90; doi: 10.3221/igf-esis.63.08 90 [28] liang, z., xiao, y. and zhang, j. (2018). stress–strain analysis of a pipeline with inner and outer corrosion defects, j. press. vess.-t., 140(6), 064501. doi: 10.1115/1.4041434. [29] wang, r., guo, h. and shenoi, r.a. (2020). experimental and numerical study of localized pitting effect on compressive behavior of tubular members, mar. struct., 72, 102784. doi: 10.1016/j.marstruc.2020.102784. [30] feng, l., hu, l., chen, x. and shi, h. (2020). a parametric study on effects of pitting corrosion on stiffened panels’ ultimate strength, int. j. nav. arch. ocean, 12, pp. 699–710. doi: 10.1016/j.ijnaoe.2020.08.001. [31] tee, k.f. and wordu, a.h. (2020). burst strength analysis of pressurized steel pipelines with corrosion and gouge defects, eng. fail. anal., 108, 104347. doi: 10.1016/j.engfailanal.2019.104347. [32] gao, j., yang, p., li, x., zhou, j. and liu, j. (2019). analytical prediction of failure pressure for pipeline with long corrosion defect, ocean eng., 191, 106497. doi: 10.1016/j.oceaneng.2019.106497. [33] zhang, y., huang, y., zhang, q. and liu, g. (2016). ultimate strength of hull structural plate with pitting corrosion damnification under combined loading, ocean eng., 116, pp. 273–285. doi: 10.1016/j.oceaneng.2016.02.039. [34] mechab, b., malika, m., salem, m. and boualem, s. (2020). probabilistic elastic-plastic fracture mechanics analysis of propagation of cracks in pipes under internal pressure, frattura ed integrità strutturale, 14(54), pp. 202–210. doi: 10.3221/igf-esis.54.15. [35] vakaeva, a.b., shuvalov, g.m. and kostyrko, s.a. (2021). interfacial stresses in bimaterial composites with nanosized interface relief, in: 8th international conference on computational methods for coupled problems in science and engineering, coupled problems 2019, pp. 679–688. [36] ahmed, a.b., houria, m.i., fathallah, r. and sidhom, h. (2019). the effect of interacting defects on the hcf behavior of al-si-mg aluminum alloys, j. alloy. compd., 779, pp. 618–629. doi: 10.1016/j.jallcom.2018.11.282. [37] lakhdari, a.a., bubnov, s.a., seddak, a., ovchinnikov, i.i. and ovchinnikov, i.g. (2020). finite element modeling of the behavior of a hollow cylinder in a hydrogen-containing environment, frattura ed integrità strutturale, 51, pp. 236– 253. doi: 10.3221/igf-esis.51.19. [38] sedova, o.s., khaknazarova, l.a. and pronina, y.g. (2014). stress concentration near the corrosion pit on the outer surface of a thick spherical member, in: ieee 10th international vacuum electron sources conference, ivesc 2014, pp. 245–246. doi: 10.1109/ivesc.2014.6892074. [39] liao, y., liu, c., wang, t., xu, t., zhang, j. and ge, l. (2021). mechanical behavior analysis of gas pipeline with defects under lateral landslide. proceedings of the institution of mechanical engineers, part c: journal of mechanical engineering science, 235(23), pp. 6752–6766. doi: 10.1177/09544062211017161. [40] kostyrko, s., grekov, m. and altenbach, h. (2021). coupled effect of curved surface and interface on stress state of wrinkled thin film coating at the nanoscale. zamm zeitschrift fur angewandte mathematik und mechanik. doi: 10.1002/zamm.202000202. [41] abakarov a., pronina y. and kachanov m. (2022). symmetric arrangements of cracks with perturbed symmetry: extremal properties of perturbed configurations, int. j. eng. sci., 171(4), 103617. doi: 10.1016/j.ijengsci.2021.103617. [42] carpinteri, a., brighenti, r. and vantadori, s. (2006). notched shells with surface cracks under complex loading. int. j. mech. sci., 48(6), pp. 638–649. doi: 10.1016/j.ijmecsci.2006.01.004. [43] carpinteri, a., brighenti, r. and vantadori, s. (2009). notched double-curvature shells with cracks under pulsating internal pressure, int. j. pres. ves. pip., 86(7), pp. 443–453. doi: 10.1016/j.ijpvp.2008.12.007. [44] vaziri, a., nayeb-hashemi, h. and estekanchi, h.e. (2002). dynamic response of cracked cylindrical shells with internal pressure. proceedings of the asme 2002 international mechanical engineering congress and exposition. design engineering. new orleans, louisiana, usa, pp. 257–265. doi: 10.1115/imece2002-33582. [45] zhu, y., zhang, j., yu, j., zhou, x., zhao, x., yin, b., tang, w. (2020). buckling of externally pressurized corroded spherical shells with wall-thickness reduction in local region. int. j. pres. ves. pip., 188, p. 104231. doi: 10.1016/j.ijpvp.2020.104231. [46] sedova, o.s. (2020). stress calculation for a hollow sphere with inner surface defects, vector of togliatti state university, 2, pp. 68–73. in russian. doi: 10.18323/2073-5073-2020-2-68-73. [47] zhu, y., guan, w., wang, h., zhao, m. and zhang, j. (2021). buckling of spherical shells with pitting corrosion under external pressure, ships offshore struc., pp. 1–10. doi: 10.1080/17445302.2021.2000266. [48] zhao, z., zhang, p., zhou, s. and fan, x. (2022). collapse pressure of randomly corroded spherical shell, ocean eng., 246, 110604. doi: 10.1016/j.oceaneng.2022.110604. [49] okulova, d. d., sedova, o. s. and pronina, y. g. (2021). the effect of surface defects interaction on the strength of a pressurised spherical shell. procedia structural integrity, 33, pp. 1055–1064. doi: 10.1016/j.prostr.2021.10.117. [50] sedova, o. s. (2020). calculation of stresses in a spherical shell with internal surface defects. science vector of togliatti state university, 2, pp. 68–73. doi: 10.18323/2073-5073-2020-2-68-73. https://doi.org/10.1016/j.jallcom.2018.11.282 http://dx.doi.org/10.1002/zamm.202000202 http://doi.org/10.1016/j.ijengsci.2021.103617 https://doi.org/10.18323/2073-5073-2020-2-68-73 microsoft word numero_37_art_4 a. shanyavskiy et alii, frattura ed integrità strutturale, 37 (2016) 22-27; doi: 10.3221/igf-esis.37.04 22 focussed on multiaxial fatigue and fracture multiaxial fatigue of in-service aluminium longerons for helicopter rotor-blades a. shanyavskiy state center for civil aviation flight safety, airport sheremetievo-1, po box 54, chimkinskiy state, moscow region, 141426, russia, 106otdel@mail.ru, http://orcid.org/0000-0001-2345-6789 a. toushentsov state center for civil aviation flight safety, airport sheremetievo-1, po box 54, chimkinskiy state, moscow region, 141426, russia, 103otdel@mail.ru, http://orcid.org/0000-0002-2345-6790 abstract. fatigue cracking of longerons manufactured from al-alloy avt-1 for helicopter in-service rotorblades was considered and crack growth period and equivalent of tensile stress for different blade sections were estimated. complicated case of in-service blades multiaxial cyclically bending-rotating and tension can be considered based on introduced earlier master curve constructed for aluminum alloys in the simple case of uniaxial tension with stress r-ratio near to zero. calculated equivalent tensile stress was compared for different blade sections and it was shown that in-service blades experienced not principle difference in this value in the crack growth direction by the investigated sections. it is not above the designed equivalent stress level. crack growth period estimation in longerons based on fatigue striation spacing or meso-beach-marks measurements has shown that monitoring system introduced designer in longerons can be effectively used for in-time crack detecting independently on the failed section when can appeared because of various type of material faults or in-service damages. keywords. fatigue; multiaxial; longerons; aluminium alloy; crack growth; fractography; stress equivalent. introduction atigue cracking of longerons manufactured from al-alloy avt-1 for helicopter in-service rotor-blades was considered and crack growth period and equivalent of tensile stress for different blade sections were estimated. complicated case of in-service blades multiaxial cyclically bending-rotating and tension can be considered based on introduced earlier master curve constructed for aluminum alloys in the simple case of uniaxial tension with stress r-ratio near to zero [1]. calculated equivalent tensile stress was compared for different blade sections and it was shown that inservice blades experienced not principle difference in this value in the crack growth direction by the investigated sections. it is not above the designed equivalent stress level. crack growth period estimation in longerons based on fatigue striation spacing or meso-beach-marks measurements has shown that monitoring system introduced designer in longerons can be f a. shanyavskiy et alii, frattura ed integrità strutturale, 37 (2016) 22-27; doi: 10.3221/igf-esis.37.04 23 effectively used for in-time crack detecting independently on the failed section when can appeared because of various type of material faults or in-service damages. a) b) figure 1: scheme (a) of rotor-blade section with numbering “1”-“5” areas for crack origination and pointed out its external loading and (b) cells position for a blade. the pressure gage, installed in the basement portion of the rotor blade, is designed to send a signal of lost excessive pressure to a monitor (a window in that a watcher can see the red cup to appear) once discontinuity arose in the longeron in any section of the propeller blade. according to the service norms, such inspection is to be performed each time before the flight. in-service fatigue cracks nucleated in the longerons in the defect sites that were revealed all over the blade length, from r = 0.085 to r = 0.71, where max)/()( did rrr  (see fig.1b). in the paper we shall discuss in details the fracture trends of the longerons made of aluminium avt-1 alloy. inspection results of fatigue-cracking behavior of the longerons atigue cracks only nucleated in operating longerons of the rotor-blades if their material was somehow damaged [2, 3]. despite the fact that the defects differed in the sites of location in the cross-section area of the longeron (see fig. 1), all the defects caused failure of the fatigue nature. we can formalize these failure cases according to a general scheme of the fracture surface, fig. 2, as composed of: a fracture-origin exhibits a fracture relief typical of the damage kind and may be located anywhere on the inner or outer surface of the longeron walls; a zone (1) of stable crack growth typically exhibits a smooth fracture surface with distinct mesoscopic or macroscopic (depending of the fracture location) beach-marks of fatigue fracture; a zone (2) of accelerated crack propagation typically shows a wavy fracture surface of the “christmas-tree” or “chevronlike” type; figure 2: scheme of longerons fracture surfaces for crack origination from the corrosion pitting with indication “1”-“3” different fracture surface areas. f a. shanyavskiy et alii, frattura ed integrità strutturale, 37 (2016) 22-27; doi: 10.3221/igf-esis.37.04 24 a zone (3) of fast crack propagation when the plastic-shear lips form entirely over the wall-thickness of the longeron. in the zone 1, pseudo-striations pattern forms first (p-region), peculiar to low-rate crack growth in the near-threshold range of the kinetic diagram. the material here experiences extensive shear. as the crack length increases, a pattern of fatigue striations forms or, alternatively, mesoscopic fatigue beach-marks dominate, depending on the blade section in that the crack propagates. formation of fatigue striations alternating with dimpled fracture is typical of the zone 2: here, the crack growth becomes accelerated. purely dimpled relief is typical of the zone 3 of final fracture; here the plastic-shear lips form throughout an entire thickness of the blade wall. having fatigue meso-beach-marks and fatigue striations distinctly visible made it possible to analyze the growth trends of fatigue cracks in the longerons and to determine the growth durations of the cracks and estimate the in-service stress level. furthermore, it made possible to verify if the crack-monitoring alarm gage, installed, by design, in the longeron-basement end, operated efficiently. consider the data on two cases; in one case the crack was disclosed as it grew not above 25% of the total cross-section area of the longeron and in the other case the longeron failed in flight as the crack occupied 75% of its cross-section. the two helicopters were of the same type and the fracture sites almost coincided. the cases appeared contradicting to one another, i.e., indicated both to the efficient and inefficient operation of the alarm gage. moreover, that fatigue zone, which amounted in total to 25-% of the cross-section of the longeron, occupied equal areas on both sides (top and bottom) of the neutral bending line. consequently, the longeron had the crack partially closed in the qualitatively similar ways whether in flight or in the parked condition. still the gage responded to the drop of pressure in both conditions, which showed its sensitivity as quite high. in such a contradictory situation, when cracks were now revealed and now not revealed, one had to either improve the gage efficiency or discipline the inspecting organizations to use the gage carefully. one could estimate the gage efficiency most correctly using the data on growth duration of fatigue cracks and in-service stresses as applied to the separate blade sections. in so doing, one first should examine the crack-growth patterns in the longerons subjected to bench tests simulating various loading conditions. secondly, one should see to which degree the propagation patterns of fatigue cracks remain similar in the separate longeron sections. initiation and propagation patterns of fatigue cracks in service lades in flight are loaded with the frequency that is determined by the revolution frequency of the rotor and corresponds to the frequency of the single cycles of fatigue damage. accordingly, we calculate the growth period of fatigue cracks based on the measurements of fatigue-striation spacing and assuming that each single fatigue striation is formed as a result of one rotor revolution. this consideration of material damage has accordance with longerons fatigue tests on the special test-device that were performed earlier [2]. we shall compare below these estimations with the crack-growth durations calculated based on the data on fatigue meso-beach-marks (mbm). the area of early crack growth, with typically p-region of fracture, was the largest in the damage site, in the section of relative radius r = 0.085 (beside the blade basement); it measured about 25 mm in length. in all the other sections such crack-growth areas were smaller, though no relation between the fracture region size and the relative radius of a longeron was revealed. for the separate longeron sections (distances from the blade basement), the growth periods of fatigue cracks were estimated based on the data on the fatigue-meso-beach-marks and fatigue-striation spacings. in the region of relative radius r = 0.085 of the longeron fatigue mbm were characteristic of the fatigue damage all over the crack path from the fracture-origin site till the transition to unstable crack growth. this fatigue fracture was initiated owing to the preliminary corrosion cracking of the material. beyond the fracture-origin area mbm geometry is perfect and the meso-beach-mark spacing increases regularly in the crack-growth directions. fatigue striations began to form as the crack increased to 25 mm along the rear wall. plus to them, meso-beach-marks continued to form clearly, which helped to estimate with greater accuracy the crack-growth duration over both in the striation-free (p-region) and striation-bearing portions of the fracture. immediately before the fast-cracking zone began, mbm formed as distinctly as to be visible at quite moderate magnifications (with the use of a light microscope), indicating to quite heavy fatigue damage. we may say that these coarse (macroscopic) fatigue lines formed to respond to the effects of regularly altered applied loads. by the end-rupture time the fatigue crack passed through 45% portion of the longeron cross-section. in these limits (from the origin site till endrupture zone), the crack grew by 120 mm along the bottom wing and by 52 mm along the rear wall. b a. shanyavskiy et alii, frattura ed integrità strutturale, 37 (2016) 22-27; doi: 10.3221/igf-esis.37.04 25 sequentially measured distances between mbm and, then, between the macro-beach-marks confirmed that there recurrence along the crack path is not casual, but regular, indicative of the very blade-loading patterns, regularly repeated with each single flight cycle, fig. 3. therefore, the regularly increasing distances between these marks are indicative of the crack-growth rate regularly increasing from flight to flight. and the number of these beach-marks corresponds to the number of the helicopter flights accomplished with the fatigue crack propagating in the longeron. a) b) figure 3: spacing of (a) mesoor macro-beach-marks and (b) fatigue striations with number of cycles np against crack length a for two longerons (a) and (b). in case that the distances between the fatigue beach-marks remain unchanged for some periods of crack propagation shows the crack-length increments to obey some scale hierarchy both at the mesoscopic (mbm or fatigue striations) and macroscopic levels. this particular trend again indicates that the blades were loaded in a regular way (each single flight); the latter showed itself through the pattern of regularly advancing fatigue crack. fatigue mbm were counted starting from the area 5.5 mm apart from the crack-origin site (the lines became most distinct here) to find out that the following crack-growth period involved about 210 flights. the inter-mbm distances (and, hence, the crack-length increments) appeared to sequentially increase. for the crack length grown from 5.5 to 7 mm, the average length increment did not exceed 0.056 mm per flight. so, not less than 70 flights were done with the fatigue crack growing in length from 1.5 to5.5 mm. the starting crack length of 1.5 mm was taken a little greater than the depth (1.3 mm) of the stress-corrosion-origin. in total, these estimations give 280 (210 + 70) flight cycles for the period of crack propagation from the corrosion-cracking zone till the beginning point of unstable fracture. of the considered cases of the failure of longerons, the fracture at the site of r =0.7 related to the cases of the deepest fatigue cracks: here, the p-region of early cracking measured as much as 12 mm. the blade fracture began from a nearly spherical cavity as large as about 2 mm in radius, located at the inner surface of the longeron. on both sides of the crack, cavities, similar to the cavity from which the fracture began, were arranged in a file along the longeron axis. the value of striation spacing increased with the crack length in a way indicative of the regular loading pattern of the longeron in service. the spacing of fatigue striations irregularly increasing and decreasing with increasing crack length only appeared immediately before the transition to accelerated crack growth and a chevron-like fracture morphology (see number “2” on fig. 2). the calculations were done according to the following relationships [1, 4]. in so doing, 57000 cycles was thus calculated for crack-growth period in p-region. in average, single-flight duration is close to 30 minutes, and a loading frequency is determined by the revolution frequency (192 revolutions per minute) of the rotor. consequently, the crack growth duration in the longeron must be not less than 49.5 hours (about 100 flights). these figures do not contradict the macroscopic view of the fracture morphology. using a binocular microscope at small magnifications, one could observe indistinct fatigue macro-beach-marks in individual parts of the fracture. such marks were used for estimating the flight number, which then was compared with the flight number acquired from the fatiguestriation patterns. the two estimations appeared to differ not more than by 10%. therefore, using predominantly the patterns of mbm and fatigue striations we may estimate the growth durations of fatigue cracks. having compared these estimations, we may see that cracks of fatigue nature grow in the longerons for quite long periods and, hence, inspection and monitoring of their growth in service can be highly efficient. a. shanyavskiy et alii, frattura ed integrità strutturale, 37 (2016) 22-27; doi: 10.3221/igf-esis.37.04 26 levels of equivalent stress in the longerons of mi-4 and mi-8 helicopters rom the above data one can see that propagation of fatigue cracks in the longerons takes quire a long time. this information, however, should be enlarged to answer how much descriptive are the usually applied calculation methods as concerns the actual stress-strain conditions of the material in various sections of a longeron. having this question answered is especially important, as corrosion-induced damage is well known to occur and, sometimes, be a source of fatigue cracks in the longerons. let us discuss the levels of equivalent stress e with respect to various relative radii of the longerons; the stress levels are estimated in terms of the concept of the single kinetic curve with the use of above-described quantitative-fractography approach to the failure cases of aviation structures. along the longeron, the stress level changes with the distance from the longeron basement. tensile stress diminishes and, simultaneously, bending load increases. this complex loading pattern results in stresses that vary in the level and in the ratio between the torsion and bending components. longerons experience a permanent tensile stress, whose largest value is 60 mpa, and the stress that varies between 10 mpa and 38 mpa. in flight, a longeron is twisted within 3�, and the torsion stress achieves 30 mpa. as follows from the analysis of stressed state of the specimens loaded simultaneously by torsion and tension [5], crackgrowth behavior is predominantly controlled by the value of crack opening normal to the crack-growth direction. in other words, a crack propagates along the normal to the axis of maximum tensile stress, applied to the crack tip. typically, crack-propagation occurs with fatigue striations forming in the fracture area. therefore, we can estimate a crack-growth rate using a synergetic approach, based on the concept of master kinetic curve [1, 4]. striations do not appear in case of out-of-phase loading [6], when the cycle asymmetry r near to zero. though caused by combined uniaxial tension and torsion, fatigue fracture develops as a single phenomenon. therefore, a unified energetic criterion was proposed [6] for describing fatigue-cracking behavior under such combined tension-andtorsion conditions. making use of that criterion helps the calculation of a tension equivalent for stress-intensity factor ke from the following relationships. 2/1)221(  iiiciicikek  (1) in eq. (3) dimensionless coefficients cii and ciii only depend on the poisson’s ratio and characterize the effects of the crack-opening modes kii and kiii for a pipe-type specimen twisted in the crack plane. eq. (3) relates to the case of using the master curve of fatigue-cracking kinetics for various combinations of shear and tensile components of torsion-andtension loading. here the equivalent stress-intensity factor appears a quantity only dependent on a correction f() for a torsion angle, which value was calculated, typical of all the other cases, for the master kinetics curve [1, 4, 6]. a loading pattern of the rotor-blades repeats quite regularly every flight. so, statistically, we can discuss crack-growth events in various blade sections as relating to the same loading type. the levels of equivalent stress were estimated for various sections and origin sites of fatigue cracks. below, we illustrate the methodological principles of these calculations for the case of fatigue-crack growth at the relative radius r = 0.38 of a longeron. in this section, stresses to be calculated arise from varying stresses and dynamic tension of 59 mpa. in such a case an equivalent stress can be estimated from a relationship 5.60)45.01(5.81)max/min1(max  e (2) from the laboratory tests of avt3-1 alloy the value of k1p = 7.9 mpa m1/2 was acquired for border transition from pregion to the stage of fatigue striation formation. for the longeron of interest, this value is achieved as the crack riches 6 mm in length. and using a respective relationship [7], we may estimate a stress-intensity factor for a round crack as k1p = e a0 /, (3) where   1. f a. shanyavskiy et alii, frattura ed integrità strutturale, 37 (2016) 22-27; doi: 10.3221/igf-esis.37.04 27 from eq. (3) we found the equivalent stress e 58 mpa for the crack length a0 = 6 mm. one can see that loading conditions remained the same and no positive or negative deviation occurred from the equivalent-stress level all over the fatigue-striation stage. all these calculations indicate that the fatigue fracture of the longeron was initiated as a result of high stress concentration in the corrosion-cracking site and not because of an overloading event. one can see that, regarding the levels of equivalent stresses, the longeron sections at the r __ -value 0.7 and 0.5 are close to one another; this finding is consistent with the data on crack-growth durations and stress levels calculated for longerons. in the discussed longeron, initial corrosion cracking (intergranular) reached 0.4-mm depth. then in 5-mm distance predominantly corrosion cracking (transgranular and intergranular) transformed to purely fatigue cracking (transgranular). next to this zone, fatigue crack propagated for quite a long period. here, the value of equivalent stress did not exceed the designed level. therefore, fatigue crack would not nucleate without stress concentration, caused by the corrosion cracking deeper than 0.3 mm from the outer surface of the longeron, as long as the surface layer of such thickness experiences the residual compression stresses greater than the equivalent tensile stress. the monitoring system employed to watch the longeron impermeability of the mi-family helicopters is efficient. conclusion – in cases of nucleation and propagation of fatigue cracks in the longerons of mi-4 and mi-8 helicopters in-service stresses never exceeded the designed levels at any relative radius of the propeller blades – the longest crack-growth periods are typical of the basement part of the blades – through fatigue cracks show the growth periods of tens flights for a whichever relative radius of a propeller blade; hence, such cracks can be revealed in good time with the pressure gages, installed in the blades to signal about the loss of their impermeability. references [1] shanyavskiy, a.a., tolerance fatigue cracking of aircraft structures. synergetics in engineering applications. monograph, ufa (russia), (2003) [2] shanyavskiy a.a., quantitative fractographic analyses of fatigue crack growth in longerons of in-service helicopter rotor-blades. fatigue fract. engng mater struc., 19 (1996) 1129-1141. [3] shanyavskiy a.a., toushentsov a.l., effectiveness of safety flight guaranty for helicopters using introduced in longeron rotor-blade device for cracks detecting. science works for investigators society of crashed aircrafts, russia, 11 (1999) 110-128. [4] shanyavskiy a.a., orlov e.f., koronov m.z., fractographic analyses of fatigue crack growth in d16t alloy subjected to biaxial cyclic loads at various r-ratios. fatigue fract. engng mater struc., 18 (1995) 1263-1276. [5] shanyavskiy a.a., orlov e.f., grigoriev v.m., fatigue crack growth in d16 al-alloy sheet subjected to biaxial out-ofphase loading. fatigue fract. engng mater struc., 20 (1997) 975-983. [6] chan k.s., hack l.e., leverat g.r. fatigue crack propagation in ni-base superalloy single crystals under multiaxial cyclic loads. met. trans. 17a (1986) 1739-1750. [7] murakami, y. 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/hrv (za stvaranje adobe pdf dokumenata najpogodnijih za visokokvalitetni ispis prije tiskanja koristite ove postavke. stvoreni pdf dokumenti mogu se otvoriti acrobat i adobe reader 5.0 i kasnijim verzijama.) /hun 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can be opened with acrobat and adobe reader 5.0 and later.) >> /namespace [ (adobe) (common) (1.0) ] /othernamespaces [ << /asreaderspreads false /cropimagestoframes true /errorcontrol /warnandcontinue /flattenerignorespreadoverrides false /includeguidesgrids false /includenonprinting false /includeslug false /namespace [ (adobe) (indesign) (4.0) ] /omitplacedbitmaps false /omitplacedeps false /omitplacedpdf false /simulateoverprint /legacy >> << /addbleedmarks false /addcolorbars false /addcropmarks false /addpageinfo false /addregmarks false /convertcolors /converttocmyk /destinationprofilename () /destinationprofileselector /documentcmyk /downsample16bitimages true /flattenerpreset << /presetselector /mediumresolution >> /formelements false /generatestructure false /includebookmarks false /includehyperlinks false /includeinteractive false /includelayers false /includeprofiles false /multimediahandling /useobjectsettings /namespace [ (adobe) (creativesuite) (2.0) ] /pdfxoutputintentprofileselector /documentcmyk /preserveediting true /untaggedcmykhandling /leaveuntagged /untaggedrgbhandling /usedocumentprofile /usedocumentbleed false >> ] >> setdistillerparams << /hwresolution [2400 2400] /pagesize [612.000 792.000] >> setpagedevice microsoft word numero_61_art_34_3533.docx n.h. ononiwu et alii, frattura ed integrità strutturale, 61 (2022) 510-518; doi: 10.3221/igf-esis.61.34 510 the influence of sustainable reinforcing particulates on the density, hardness and corrosion resistance of aa 6063 matrix composites ndudim henry ononiwu, chigbogu g. ozoegwu university of nigeria nsukka, enugu, nigeria ndudim.ononiwu@unn.edu.ng, chigbogu.ozoegwu@unn.edu.ng ifeanyi okoro jacobs university of nigeria nsukka, enugu, nigeria aedjac systems development laboratory, university of nigeria nsukka, enugu, nigeria ifeanyi.jacobs@unn.edu.ng victor c. nwachukwu department of mechanical engineering, school of infrastructure, process engineering and technology, federal university of technology, minna, niger state, nigeria victornwachkwu@gmail.com esther titilayo akinlabi pan african university for life and earth sciences institute (paulesi), ibadan, nigeria etakinlabi@gmail.com abstract. the need for the fabrication of sustainable aluminium matrix composites (amcs) is being sought after as practical alternatives to conventional metals and their alloys. this study was undertaken to investigate the effect of sustainable materials on the mechanical, physical and corrosion resistant properties of aa 6063. the weight fraction of the hybrid reinforcements was varied at 2.5, 5.0, 7.5 and 10.0 wt.%. for each variation, the fly ash and eggshells were weighed equally. the fabrication route selected was stir casting. the analysis of the density showed that the property decreased with increasing weight fraction of the hybrid reinforcements. evaluation of the microhardness revealed hardness values of 78.13, 81.19, 81.54, 82.14, and 86.71 hv for the base metal, 2.5, 5.0, 7.5 and 10.0 wt.% samples respectively. the corrosion resistant properties were studied in 3.5 wt.% nacl medium. the investigation showed that the reinforced amcs exhibited improved corrosion resistance compared to the base metal. however, the 7.5 wt.% sample exhibited the least corrosion rate of 8.649 x 10-5 g/h. keywords. amcs; aluminium; sustainable materials; fly ash; eggshells. citation: ononiwu, n.h., ozoegwu, c.g., jacobs, i.o., nwachukwu, v.c., akinlabi, e.t. the influence of sustainable reinforcing particulates on the density, hardness and corrosion resistance of aa 6063, frattura ed integrità strutturale, 61 (2022) 510-518. received: 30.03.2022 accepted: 16.06.2022 online first: 18.06.2022 published: 01.07.2022 copyright: © 2022 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. https://youtu.be/9oigy5bvxog n.h. ononiwu et alii, frattura ed integrità strutturale, 61 (2022) 510-518; doi: 10.3221/igf-esis.61.34 511 introduction he ever-growing need for the fabrication of amcs at lower cost while retaining the improvements in mechanical and physical properties has remained a conscious effort by researchers. amcs are rapidly replacing monolithic metals and their alloys in several industrial applications due to improvements in their strength, stiffness, corrosion and wear resistance [1]. current applications of amcs include aerospace, automobile and marine equipments [2]. research over the last few decades have identified price as a major hinderance to the fabrication and application of amcs due to the high costs associated with the reinforcing phases [3]. ononiwu et al [4] also highlighted that environmental sustainability is a major sentiment being shared by researchers in the fabrication of amcs. this reason has led to the incorporation of certain materials into the fabrication of composites either as replacements for the existing synthetic reinforcements or as a combination with synthetic reinforcements. the sustainable materials being applied as reinforcing phases of amcs are categorized based on their origins. the classifications have been identified as industrial (e.g. fly ash and red mud) [5] and agricultural wastes (e.g. rice husk, eggshells, and coconut shells) [6]. in addition to the environmental impact of the methods of disposal of these waste materials, cost and availability, further studies of these materials have highlighted the presence of oxides, nitrides and sulphides which are excellent ceramics utilized in the fabrication of amcs. among these sustainable materials, fly ash and eggshells have been considered as possible reinforcements for the fabrication of aluminium matrix composites. this is because of their low density [7], hardness [8], availability [9] and cost [10]. in light of these merits, researchers including ononiwu et al [11], idusuyi et al., [12] and dwivedi et al [13] have successfully utilized these sustainable materials to reinforce aluminium alloys. fly ash and eggshells are both waste products that currently constitute environmental issues due to the lack of adequate disposal means. as these waste materials are not bio-degradable, their disposal is primarily done by dumping in landfills. this method of waste management has been shown to be detrimental to the environmental ecological system. as a result, the reuse of these waste materials has been proposed to perform the functions of environmental cost savings. several researchers have successfully fabricated aluminium reinforced with fly ash and eggshells either as binary or ternary composites. such researches include that conducted in [14] which investigated the effect of fly ash on the mechanical properties of aa 1050. improvements of 11.04% and 31.90% on the tensile and compressive strength respectively was reported. al-zn reinforced with fly ash and sic was fabricated by kanth et al. [15]. the results indicated uniform dispersal of the reinforcements in the aluminium matrix. the analysis of the density showed a decline with increased weight fraction of fly ash. the hardness improved by 22.5%. the authors also reported improvements in the tensile strength of the fabricated composites compared to the base metal. dwiwedi et al. [16] investigated the influence of eggshells on the wear behaviour of aa 6061. the results showed that the coefficient of friction (cof) of the cast composite was significantly lower compared to that of the base metal indicating improved wear resistance. the potentiodynamic polarization studies of aa 6063 reinforced with eggshells was conducted by ononiwu et al [17]. the investigation revealed a decline in the corrosion rate (4.08 x 10-8 g/h) compared to the base metal (5.53 x 10-6 g/h). this is indicative of improved corrosion resistance brought about by the utilization of the reinforcements. the reviewed literature indicates the prospects of fly ash and eggshells as reinforcing phases for fabricating aluminium matrix composites. from the reviewed literature, minimal considerations have been made towards the prospects of utilizing hybrid waste reinforcements for the fabrication of amcs. this work selected these reinforcing particles from the 2 different classes of waste materials used in the fabrication of amcs. this work examined the effect of fly ash and eggshells on the physical, mechanical properties and corrosion resistance of aa 6063. materials and methods for this study, stir casting was selected as the fabrication route. this liquid metallurgy method was selected due to its simplicity, ability to produce parts with complex geometries and cost [18]. the elemental composition of the aluminium alloy shown in tab. 1 was obtained via mass spectrometry. composition mn ti fe cr cu zn cr mg al % 0.02 0.02 0.07 0.14 0.45 0.60 0.14 1.02 97.18 table 1: elemental composition of aa 6063. t n.h. ononiwu et alii, frattura ed integrità strutturale, 61 (2022) 510-518; doi: 10.3221/igf-esis.61.34 512 the quantitative analysis of reinforcements was done using x-ray diffractometry to obtain their respective constituents. these are summarized in tab. 2 and 3 according to ononiwu et al [19]. constituent calcium aragonite percentage (%) 13.67 86.33 table 2: quantitative analysis of the eggshell. constituent mullite quartz hematite alumina wustite percentage (%) 50.63 41.05 4.23 3.25 0.65 table 3: quantitative analysis of the fly ash. the designations of the fabricated samples are summarized in tab. 4. s/no designation eggshell wt.% fly ash wt.% total wt.% 1 a 0 2 b 1.25 1.25 2.50 3 c 2.50 2.50 5.00 4 d 3.75 3.75 7.50 5 e 5.00 5.00 10.00 table 4: designation of the cast samples. a ball milling machine, rotating at 180 rpm, was used to reduce particle sizes of the fly ash and eggshell samples. for both reinforcements under consideration, the milling period was set to 7 hours to achieve an average particle size of 75 µm. the eggshells were then carbonized to increase carbon content, decrease moisture content, and improve wettability between the matrix and dispersion phase [20]. the reinforcement percentages were varied at 0, 2.5, 5.0, 7.5, and 10.0 wt.%. carbonized eggshells and fly ash were used in equal amounts in each variation of the reinforcements. the supplied aa 6063 sheets were then cut and weighed before being charged into the graphite crucible to fabricate the composites. to begin the melting process, the furnace's temperature was raised to 760 °c. the reinforcements were preheated at 400 °c for 1 hour before being introduced into the molten aluminium to promote interfacial bonding with the matrix. the preheated reinforcements were then introduced into the molten matrix. to achieve appropriate dispersion of the reinforcements in the aluminium matrix, the molten mix was stirred in two stages. the first stage of stirring took place after the reinforcements were charged into the molten matrix, while the second stage took place before casting the amc into the prepared sand mould. for both stirring stages, the mechanical stirring was done for 10 mins. the experimental setup and cast cylindrical bars are shown in fig. 1. the densities of the fabricated samples were measured using the archimedes principle. the mass of the fabricated amcs and the volume of displaced water in the measuring cylinder were measured. using the expression in eqn. 1, the density of the samples under considerations was obtained. e m d δv  (1) where ed is the density in g/cm3, m = mass of the sample, and δv is the volume of water displaced. to calculate the porosity of the samples, the theoretical densities of the cast samples were obtained using the rule of mixtures shown in eqn. 2. the theoretical density was in turn used to obtain the porosity using the expression in eqn. 3.      t m m f f es esd d w d w d w   (2) n.h. ononiwu et alii, frattura ed integrità strutturale, 61 (2022) 510-518; doi: 10.3221/igf-esis.61.34 513 where dt is the theoretical density of the composite sample, md is the density of the matrix, m w is the weight fraction of the matrix, fd is the density of the fly ash, fw is the weight fraction of the fly ash, esd is the density of the eggshell and esw is the weight fraction of the eggshells. with the aid of the theoretical densities of the fabricated samples, the porosity was obtained using the expression in eqn. 3. e t d p 1 100% d         (3) where p is the percentage porosity of the cast amc. figure 1: (a) casting of the samples (b) cylindrical rods the microstructure of the fabricated amc samples was studied using the tescan model type vega lmh scanning electron microscope. the samples were cut to reveal their cross-sections, cleaned, ground and polished prior to the commencement of the metallography studies. etching of the prepared samples was done in keller’s reagent for 30 second to reveal their grain structure. the surface of the samples was cleaned and polished prior to the microhardness measurement to guarantee accurate readings. during the microhardness measurement of the samples, 5 indentations 1mm apart were created. a test force of 300 gf (200 n) was applied to each indentation for a dwell duration of 15 seconds. the influence of the reinforcements on the corrosion resistance properties of the samples under examination was investigated using potentiodynamic polarization tests. for the experiment, 10 mm x 10 mm cylindrical specimens were used. all samples were cold mounted and ground with 320, 500, 1200, and 4000 sic emery sheets. the ground samples were cleaned with distilled water, degreased in acetone, and dried in the open air. these efforts were taken to ensure that the electrochemical processes were carried out accurately and with minimal interference. the electrochemical analyser from hch instruments was utilized for the potentiodynamic polarization tests, which included a silver/silver chloride reference electrode and a graphite counter electrode. the study's polarization range was -0.5 to 0.5 v, and the scan rate of 0.01 v/s. results and discussion microstructure tables he optical micrograph of the base metal (refer to fig. 2a), indicates the presence of interconnected coarse grains comprised of an array of intermetallics including al12mg7, alfe2mn, mg2si [21]. evaluation of the sem micrographs of the fabricated hybrid amcs revealed uniformly dispersed reinforcements in the aa 6063 matrix. this was the consequence of the utilization of the 2-step stirring technique described earlier. the level of dispersion of the fly ash and eggshells particles could also be attributed to the proper wettability and interfacial bonding between the matrix and hybrid reinforcements. also evident from the sem micrographs was the presence of micro voids. this situation often characterized with stir casting is caused by the presence of trapped gases formed during the solidification of the cast amcs [19,20]. further evaluation of the micrographs shows the presence of agglomerations of the eggshell particles with increasing weight fraction oof the t n.h. ononiwu et alii, frattura ed integrità strutturale, 61 (2022) 510-518; doi: 10.3221/igf-esis.61.34 514 reinforcements. this is a result of the increased viscosity brought about by the increasing weight fraction of the reinforcements. figure 2: (a) optical micrograph of aa 6063 (b) sem micrographs of sample b (c) sem micrographs of sample c (d) sem micrographs of sample d (e) sem micrographs of sample e figure 3: (a) experimental density of the cast samples (b) percentage porosity of the cast amcs density and porosity the archimedes principle was utilized in this study to evaluate the density of the resulting composites. as depicted in fig. 3a, the analysis of the experimental density revealed a decline with increasing weight fraction of both reinforcements. this suggests that using the hybrid materials to reinforce the aluminium alloy is capable of producing lightweight amcs. the analysis of the porosity depicted in fig. 3b indicated that the porosity increased with increasing weight fraction of the hybrid n.h. ononiwu et alii, frattura ed integrità strutturale, 61 (2022) 510-518; doi: 10.3221/igf-esis.61.34 515 reinforcements. this was already outlined in the description of the microstructure was a result of the increased viscosity, agglomeration and formation of pores formed during the solidification of the amcs during cooling. hardness the microhardness of the cast samples was studied to examine their behaviour under the application of localized load. fig. 4 indicates that the microhardness improved with increasing weight fraction of both reinforcements. a b c d e 78 80 82 84 86 88 m ic ro h a rd n e ss ( h v ) samples   figure 4: microhardness of the cast samples. -0.2 -0.1 0.0 0.1 0.2 0.3 -7 -6 -5 -4 -3 -2 -1 0 current density (a/cm2) p o te n tia l ( v ) a b c d e figure 5: tafel plots for the cast samples. the results showed that the microhardness was 78.13, 81.19, 81.54, 82.14, and 86.71 hv for samples a, b, c, d and e respectively. the improvements could be attributed to a number of factors. the presence of the hard reinforcing particles present on the grain boundaries of the aluminium matrix is responsible for resisting deformation of the cast samples during the application of localized loads. also based on the morphology of the cast samples, the presence of the reinforcing phases (fly ash and eggshells) was responsible for resisting movement during the application of load which in turn improved the hardness with increasing weight fractions of the dispersed phases. the improved hardness of the amcs could also be attributed to grain refinement brought about by the incorporation of the reinforcements in the aluminium matrix. this n.h. ononiwu et alii, frattura ed integrità strutturale, 61 (2022) 510-518; doi: 10.3221/igf-esis.61.34 516 results was also reported by ononiwu et al [17] and chandla et al. [24]. the authors further stated that the improved hardness values of the amcs compared to the base alloy could be directly attributed to the of the strengthening of the alloy by the reinforcements which transfers the applied load from the ductile and softer aluminium matrix to the more brittle and stiffer reinforcing particles. potentiodynamic polarization the potentiodynamic polarization study was used to study the characteristics of the cast samples under the influence of electrochemical mechanisms. the tafel plots in fig. 5 indicates passive and active corrosion modes in the 3.5 wt.% nacl electrolyte. from the tafel plots, the corrosion rates were extrapolated to figuratively show the potential of the considered samples to resist corrosion activities in the corrosion medium. the corrosion rates depicted in fig. 6 shows that the addition of the reinforcements was necessary to improve the corrosion rate of the aluminium alloy. the corrosion rate was improved due to the formation of a sufficient passive oxide layer. the passive oxide layer is responsible for the resistance to corrosion activities, although the continuous exposure of the samples to the corrosion medium eventually leads to the deterioration and eventual rupture of the passive layer which is responsible for the initiation of localized pitting activities on the surface of the samples. according to akinwamide et al [25], the formation of the pitting corrosion mechanism is a result of aggressive attack of the chloride ions present in the nacl medium. from the tafel plots, the presence of metastable pitting was visible in all the cast samples as fluctuations on regions of the tafel curves. the metastable pitting is described as unstable pits that occur prior to the initiation of stable pits after the initial incubation period of the chloride ions [26]. although the corrosion resistance of the amcs samples improved compared to the base metal, several factor including the weight fraction of the reinforcements, level of dispersal, presence of segregation and agglomeration, adequate wettability and the level of interfacial bonding between the reinforcements and the matrix were responsible for the variation of corrosion rate for the fabricated composites. to this effect, sample d had the least corrosion rate of 8.65 x 10-5 g/h indicating that the samples exhibited the best resistance to corrosion in the nacl corrosion medium. a b c d e 0.0 0.1 0.2 0.3 0.4 0.5 0.6 c o rr o si o n r a te ( g /y r) samples figure 6: corrosion rates of the cast samples. conclusion his investigation was conducted to evaluate the effect of fly ash and egg shells on selected mechanical, physical and corrosion resistant properties of aa 6063. results revealed that the addition of the hybrid reinforcing particles to the aluminium alloy led to the fabrication of light weight amcs. this work also reported an increase in porosity with increasing weight fraction of both reinforcements. the studies indicates that the porosity is a function of the weight fraction of the reinforcements, micro voids, level of dispersion of the reinforcements and the presence of agglomerates in the cast samples. the microstructure was characterized by uniformly dispersed particles along the grain boundaries of the t n.h. ononiwu et alii, frattura ed integrità strutturale, 61 (2022) 510-518; doi: 10.3221/igf-esis.61.34 517 base metal. microhardness testing showed that the property improved up to 10.3% with increasing weight fraction of the reinforcements. the corrosion investigation reported the presence of the reinforcements improved the corrosion resistance; however, the corrosion rate was lowest for the 7.5wt.% sample. overall, it can be conclusively stated that the use of hybrid sustainable reinforcing particles can be used to conveniently fabricate amcs with improved properties. references [1] fernández, h., ordoñez, s., pesenti, h., gonzález, r. e., and leoni, m. (2019). microstructure homogeneity of milled aluminum a356-si3n4 metal matrix composite powders, journal of materials research and technology, 8(3), pp. 2969– 2977. doi: 10.1016/j.jmrt.2019.05.004. [2] ononiwu, n.h., akinlabi, e. t., ozoegwu, c. g., and aigbodion, v. s. (2020). a concise review of the effects of hybrid particulate reinforced aluminium metal matrix composites on the microstructure, density and mechanical properties. lecture notes in mechanical engineering: advances in manufacturing engineering, springer singapore, pp. 433–443. doi: 10.1007/978-981-15-5753-8_40 [3] sharma, s. and dwivedi, s. p. (2017). effects of waste eggshells and sic addition on specific strength and thermal expansion of hybrid green metal matrix composite, journal of hazardous materials, 333, pp. 1–9. doi: 10.1016/j.jhazmat.2017.01.002. [4] ononiwu, n. h., ozoegwu c. g., akinribide o.j., and akinlabi e. t. (2021). effect of particle size on the microstructure and distribution of fly ash for metal matrix composite applications, materials today: proceedings, 26(2), pp. 1049–1053. doi: 10.1016/j.matpr.2020.11.227. [5] bodunrin, m.o., alaneme, k.k., and chown, l.h. (2015). aluminium matrix hybrid composites: a review of reinforcement philosophies; mechanical, corrosion and tribological characteristics, journal of materials research and technology, 4(4), pp. 434–445. doi: 10.1016/j.jmrt.2015.05.003. [6] vinod, b., ramanathan, s., and anandajothi, m. (2018). a novel approach for utilization of agro-industrial waste materials as reinforcement with al–7si–0.3mg matrix hybrid composite on tribological behaviour, sn applied sciences, 1(1), pp. 1-15. doi: 10.1007/s42452-018-0066-z. [7] shaikh, m. b. n., raja, s., ahmed, m., zubair, m., khan, a., and ali, m. (2019). rice husk ash reinforced aluminium matrix composites: fabrication, characterization, statistical analysis and artificial neural network modelling, materials research express, 6(056518), pp. 1–39. doi: 10.1088/2053-1591/aafbe2. [8] prabu, v.a., johnson, r. d. j., amuthakkannan, p., and manikandan, v. (2017). usage of industrial wastes as particulate composite for environment management: hardness, tensile and impact studies, journal of environmental chemical engineering, 5(1), pp. 1289–1301. doi: 10.1016/j.jece.2017.02.007. [9] oghenevweta, j.e., aigbodion, v. s., nyior, g. b., and asuke, f. (2014). mechanical properties and microstructural analysis of al–si–mg/carbonized maize stalk waste particulate composites, journal of king saud university engineering sciences, 28(2), pp. 222–229. doi: 10.1016/j.jksues.2014.03.009. [10] kanayo, k., moyosore, t., and apata, p. (2013). corrosion and wear behaviour of al – mg – si alloy matrix hybrid composites reinforced with rice husk ash and silicon carbide, journal of materials research and technology, 3(1), pp. 9–16. doi: 10.1016/j.jmrt.2013.10.008. [11] ononiwu, n. h., ozoegwu, c. g., madushele, n., and akinlabi, e. t. (2021). effects of carbonised eggshells on the mechanical properties, microstructure and corrosion resistance of aa1050 metal matrix composites, advances in materials and processing technologies, pp. 1–12. doi: 10.1080/2374068x.2021.1959103. [12] dwivedi, s.p., srivastava, a.k., maurya, n.k., and maurya, m. (2019). microstructure and mechanical properties of al 6061/al2o3/fly-ash composite fabricated through stir casting, annales de chimie: science des materiaux, 43(5), pp. 341–348. doi: 10.18280/acsm.430510. [13] idusuyi, n., oviroh, p. o., and adekoya, a. h. (2018). a study on the corrosion and mechanical properties of an al6063 reinforced with egg shell ash and rice husk ash, in: asme 2018 international mechanical engineering congress and exposition imece2018, pp. 1–8. doi: 10.1115/imece2018-86662. [14] ononiwu, n.h., ozoegwu, c.g., madushele, n., and akinlabi, e.t. (2021). evaluation of particle size distribution, mechanical properties, microstructure and electrochemical studies of aa1050 / fly ash metal matrix composite. advances in materials and processing technologies, pp. 1–15, 2021. doi: 10.1080/2374068x.2021.1959104. [15] kanth, u. r., rao, p. s., and krishna, m. g. (2019). mechanical behaviour of fly ash/sic particles reinforced al-zn alloy-based metal matrix composites fabricated by stir casting method, journal of materials research and technology, 8(1), pp. 737–744. doi: 10.1016/j.jmrt.2018.06.003. n.h. ononiwu et alii, frattura ed integrità strutturale, 61 (2022) 510-518; doi: 10.3221/igf-esis.61.34 518 [16] dwiwedi, s. k., srivastava, a. k., and chopkar, m. k. (2019). wear study of chicken eggshell-reinforced al6061 matrix composites. transactions of the indian institute of metals, 72(1), pp. 73–84. doi: 10.1007/s12666-018-1463-0. [17] ononiwu, n. h., ozoegwu, c. g., madushele, n., and akinlabi, e. t. (2021). carbonization temperature and its effect on the mechanical properties, wear and corrosion resistance of aluminum reinforced with eggshell. journal of composites science, 5(10), pp. 1–12. doi: 10.3390/jcs5100262. [18] ramanathan, a., krishnan, p. k., and muraliraja, r. (2019). a review on the production of metal matrix composites through stir casting – furnace design, properties, challenges, and research opportunities, journal of manufacturing processes, 42, pp. 213–245. doi: 10.1016/j.jmapro.2019.04.017. [19] ononiwu, n. h., ozoegwu, c. g., madushele, n., and akinlabi, e. t. (2022). mechanical properties, tribology and electrochemical studies of al / fly ash / eggshell aluminium matrix composite, biointerface research in applied chemistry, 12(4), pp. 4900–4919. doi: 10.33263/briac124.49004919 [20] asuke, f., aigbodion, v. s., abdulwahab, m., fayomi, o. s.i., popoola, a. p.i., nwoyi, c. i., garba, b. (2012). effects of bone particle on the properties and microstructure of polypropylene/bone ash particulate composites, results in physics, 2, pp. 135–141. doi: 10.1016/j.rinp.2012.09.001. [21] edoziuno, f., nwaeju, c., adediran, a., odoni, b., and arun, v. (2021). mechanical and microstructural characteristics of aluminium 6063/palm kernel shell composites for lightweight applications, scientific african, 12, pp. 1–11. doi: 10.1.16/j.sciaf. 2021.e00781. [22] ononiwu, n. h., ozoegwu, c. g., madushele, n., and akinlabi, e. t. (2021). characterization, machinability studies and multi-response optimization of aa 6082 hybrid metal matrix composite, the international journal of advanced manufacturing technology, 116(138823), pp. 1–19. doi: 10.1007/s00170-021-07549-7. [23] sharma, s. and dwivedi, s. p. (2017). effects of waste eggshells and sic addition on specific strength and thermal expansion of hybrid green metal matrix composite, journal of hazardous materials, 333, pp. 1–9. doi: 10.1016/j.jhazmat.2017.01.002. [24] chandla, n. k., kant, s., and goud, m. m. (2020). experimental analysis and mechanical characterization of al 6061 / alumina / bagasse ash hybrid reinforced metal matrix composite using vacuum-assisted stir casting method, journal of composite materials, 0(0), pp. 1–15. doi: 10.1177/0021998320929417. [25] akinwamide, s. o., lesu, m., akinribide, o. j., and babalola, b. j. (2021). studies on corrosion behaviour of sintered aluminium based composites in studies on corrosion behaviour of sintered aluminium based composites in chloride environment, manufacturing review, 8(22), pp. 1–8. doi: 10.1051/mfreview/2021021. [26] hunkeler, f. and ingenieurberatung, h. 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can be opened with acrobat and adobe reader 5.0 and later.) >> /namespace [ (adobe) (common) (1.0) ] /othernamespaces [ << /asreaderspreads false /cropimagestoframes true /errorcontrol /warnandcontinue /flattenerignorespreadoverrides false /includeguidesgrids false /includenonprinting false /includeslug false /namespace [ (adobe) (indesign) (4.0) ] /omitplacedbitmaps false /omitplacedeps false /omitplacedpdf false /simulateoverprint /legacy >> << /addbleedmarks false /addcolorbars false /addcropmarks false /addpageinfo false /addregmarks false /convertcolors /converttocmyk /destinationprofilename () /destinationprofileselector /documentcmyk /downsample16bitimages true /flattenerpreset << /presetselector /mediumresolution >> /formelements false /generatestructure false /includebookmarks false /includehyperlinks false /includeinteractive false /includelayers false /includeprofiles false /multimediahandling /useobjectsettings /namespace [ (adobe) (creativesuite) (2.0) ] /pdfxoutputintentprofileselector /documentcmyk /preserveediting true /untaggedcmykhandling /leaveuntagged /untaggedrgbhandling /usedocumentprofile /usedocumentbleed false >> ] >> setdistillerparams << /hwresolution [2400 2400] /pagesize [612.000 792.000] >> setpagedevice microsoft word numero_63_art_07_3908.docx p. livieri et alii, frattura ed integrità strutturale, 63 (2023) 71-79; doi: 10.3221/igf-esis.63.07 72 the stress intensity factor of convex embedded polygonal cracks paolo livieri, fausto segala university of ferrara, department of engineering, italy paolo.livieri@unife.it, fausto.segala@unife.it abstract. in the present work, a simple formula for the evaluation of the stress intensity factor (sif) of convex embedded polygonal cracks has been proposed. this formula is structured as a correction factor of the oore-burns’ equation and is based on accurate three-dimensional fe analysis. furthermore, a precise formula for a regular polygonal crack has been given. keywords. weight function, stress intensity factor, three-dimensional crack. citation: livieri, p., segala, f., the stress intensity factor of convex embedded polygonal cracks, frattura ed integrità strutturale, 63 (2023) 72-79. received: 11.09.2022 accepted: 15.10.2022 online first: 25.10.2022 published: 01.01.2023 copyright: © 2023 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. introduction he weight function technique was performed by bueckner [1] and rice [2, 3] to solve the stress intensity factor (sif) of a crack as well as to find out the nominal stress over the geometric discontinuity. it is well known that the ointegral [4] is a good approximation to evaluate the sif along the contour of three-dimensional planar cracks. for example, british standard 7910 [5] suggests the use of the o-integral provided that the results are documented. usually, in order to simplify sif assessments for embedded flaws, the sif is determined at the ends of both the minor and major axes of the elliptical idealization of the flaw [6, 7, 8]. the sif of a semi elliptical crack can be accurately calculated by means of the general procedure of shen and glinka [9, 10]. they use four terms of approximation and evaluate the unknown parameters based on reference stress intensity factor expressions taken from the literature. in this way a general weight function can be formulated to overcome some problems [11, 12] in the petrosky and achenbach method [13] where an approximate displacement field from a known reference was calculated. also in fitness-for-service procedure crack shapes, idealisation becomes necessary when real cracks have been detected during an inspection. typically, elliptical cracks, semi-elliptical cracks and through wall cracks or edge cracks with a rectilinear flank are considered [14]. for convex three-dimensional cracks few examples are presented in classical textbooks [15, 16, 17]. furthermore, in order to obtain an acceptable approximation of the maximum sif kimax, murakami [18, 19] took into account many types of convex embedded cracks subjected to nominal tensile stress σn. the sif was investigated numerically, and a final equation for sif was given in the form:  ,maxi nk y a where y is a coefficient that was evaluated as best fitting of the numerical results; and a is the area of the flaw. t https://youtu.be/drqmaxpdu70 p. livieri et alii, frattura ed integrità strutturale, 63 (2023) 71-79; doi: 10.3221/igf-esis.63.07 73 in a previous paper [20] the authors investigated the failure of the o-integral in presence of high curvature for regular (  of class c2) cracks. in terms of regularity, a corner q’ means a singularity. this requires a new technique in order to correct the o-integral. in particular, in this paper we are interested in adjusting the o-integral for convex polygons. the analytical results will be compared with numerical ones obtained from an accurate three-dimensional fe analysis. weight function for a three-dimensional crack: analytical background ore and burns proposed a general equation for the evaluation of the sif of a two-dimensional crack inside a three-dimensional body subjected to a nominal tensile stress σn(q). the nominal stress σn(q) is evaluated without the presence of the crack. q is the inner point of the crack. the crack can be considered as an open bounded simply connected subset ω of the plane as reported in fig. 1. we define:     2( ) ( ) ds f q q p s (1) where   ( , )q q x y , s is the arch-length parameter and point p(s) runs over the boundary  . in reference [4] ooreburns proposed an empirical formula for the evaluation of the mode i stress intensity factor at each point of the border crack of boundary  :       , 2 ( )2 ( ') , ' ( ) ' n i ob q k q d q f q q q (2) under reasonable hypotheses on the function σn(q), the integral (2) is convergent and the proof is based on the asymptotic behaviour of f(q) [21]. in different papers, the authors analysed the properties of the oore-burns integral where the accuracy of the equation was tested in the particular case of an elliptical crack [22, 23]. figure 1: inner crack. convex polygon n a previous paper [20] we investigated the proprieties of the o-integral in the presence of high curvature for regular ( of class c2) cracks. henceforth, we denote by =(q’) the correction factor of eqn. (2) at q’  ,( ') (q') ( ')i i obk q k q (3) in order to draw out the factor , we need to take into account some hints: o i p. livieri et alii, frattura ed integrità strutturale, 63 (2023) 71-79; doi: 10.3221/igf-esis.63.07 74 a) a regular polygon with very large n sides, is “indistinguishable” from a disk, of which the sif is given by   2 n times the square root of the disk radius; b)  is close to one away from the corners; c) known fe results for cracks with a different shape: square, equilateral triangles and rectangular (aspect ratio 1/3). d) the crack is subjected to a uniform tensile stress σn. the key to construct (q’) is a smart use of the hyperbolic tangent function xtanh(x). at an early stage, the factor  will contain some unknown parameters that will be carefully calibrated on the basis of requirements a, b and c. let us assume p is the perimeter of the convex polygon  and c is the perimeter of the smallest disk containing . near a fixed edge p with opening angle α (see fig. 2, where     0   ,   x q p ), (q’) can be given as follows:                                    0q’     1   1 tanh     2  xc c p p p (4) with , ,  and  chosen in order to satisfy a), b) and c) conditions. on the basis of accurate fe analysis on a three-dimensional model as proposed in reference [20], the best agreement is given by the choice   1   10 , =6.95, =0.8 and =0.4. this means that near the corner, the coefficient (q’) will be close to the value:                                0.8 0.40.8 01q’     1   1 tanh 6.95  10 2  xc c p p p (5) now, it is possible to extend eqn. (5) to entire contour  in a natural way, by taking into account all distances (on the geometry of ) of q’ from each corner of the polygon:                                                           0.40.80.8 1 0.8 3/2 1 1 1   1   tanh 6.95  10 2  q’        1 1   1 tanh 6.95  10 2    n k k n k k q pc c p p p c q pc p p (6) where pk, k=1, 2, ..., n are the corners with opening angles αk, k=παk and  q p is the distance between q’ and pk on the boundary . figure 2: polygonal crack. p. livieri et alii, frattura ed integrità strutturale, 63 (2023) 71-79; doi: 10.3221/igf-esis.63.07 75 for example, we explain eqn. (6) on an equivalent triangle with side l, where       0   ,  2 3 l q y and  0    0 0.5 y l as shown in fig. (3):             0.4 01q’    1.046 tanh 4.14      2 y l ·                         0.4 0.4 0 03 1tanh 4.14      ·tanh 4.14      2 2 y y l l (7) clearly, in the r.h.s. of the eqn. (7), the only significant contribution is given by             0.4 01q’    1.046 tanh 4.14      2 y l (8) figure 3: equilateral triangular crack. figure 4: square crack. as a second example, fig. 4 shows the case of a square crack of side l, where      0 1      ,   2 q l y and  0    0 0.5 y l . then                                                    0.4 0.4 0 0 0.4 0.4 0 0 1 3 1.033·tanh 4.34      · tanh 4.34      · 2 2 q’     3 1              tanh 4.34      ·tanh 4.34      2 2 y y l l y y l l (9) in the r.h.s. of the eqn. (8), the only significant contribution is given by             0.4 01q’    1.033 tanh 4.34      2 y l (10) p. livieri et alii, frattura ed integrità strutturale, 63 (2023) 71-79; doi: 10.3221/igf-esis.63.07 76 eqns. (8) and (10) were recently announced in a very similar preliminary form in paper [20]. we remark that eqn. (6) can be reasonably extended to every convex set with corners. in the case of a square-like flaw, the oore-burns integral can be analytically expressed in simplified form in the middle of the side and in the middle of the rounded corner [24]. the oore-burns integral will be approximated by means of riemann sums plus a suitable asymptotic correction in terms of mesh size [25, 26]. asymptotic behaviour of the sif on regular polygons et  be a regular polygon with n sides, inscribed in the disk of radius a. this means that the length of the side is       2· ·sinl a n , k=2π/n. then (see fig. 5) from eqn. (6) after some simple steps:  q’  tanh 1.74 1 𝜆 𝑁 . (11) where          0    ,  q cos a y n , 0     · 2 l y ,   0 1 . taking into account that on the unitary disk, the o-integral takes the value   2 n , it follows the asymptotic behavior of the sif, for n: k  √ √ tanh 1.74 1 𝜆 𝑁 . (12) figure 5: polygonal crack. fig. 6 shows the graph of the sif in dimensionless form for n equal to 20. in the middle of the side the sif tends to have a constant value near to the one of a circular crack. at the corner the value of the sif is null and in the proximity of the corner the trend shows a cup as calculated in reference [20]. in order to check eq. (12), an accurate numerical fe analysis has been proposed in a case of a regular hexagonal crack. figs. 7 and 8 show a three-dimensional model and the fe model, respectively. the mesh is refined only near the point of interest where the sif is evaluated as proposed in previous works [22–25]. the dimensions of smaller elements at the tip of the crack were in the order of 10-5 mm. finally, fig. 9 proposes the comparison of the sif in dimensionless form evaluated along the border in the range [0, l/2]. eq. (12) appears precise and modifies the value of the sif only near the corner. the value of ki,ob was evaluated by means of the procedure valid for a star domain proposed in reference [26] where a mesh with a step of 0.0157 radiant in the tangential direction and 80 terms in the fourier series have been considered. l p. livieri et alii, frattura ed integrità strutturale, 63 (2023) 71-79; doi: 10.3221/igf-esis.63.07 77 figure 6: stress intensity factor in dimensionless form for a regular polygonal crack with n=20 (l/a=0.313) under uniform tensile load. figure 7: three-dimensional model for a hexagonal crack (l=1 mm, h/l= 200, d/l=20). figure 8: mesh and boundary conditions for a hexagonal crack of fig. 7. p. livieri et alii, frattura ed integrità strutturale, 63 (2023) 71-79; doi: 10.3221/igf-esis.63.07 78 figure 9: stress intensity factor in dimensionless form for a hexagonal crack under uniform tensile load. conclusions n this paper an accurate correction factor that multiplies the oore-burns stress intensity factor (sif) is given for embedded polygonal cracks. this correction factor, ranging from zero up to one, essentially depends on the distance from the nearest corner, and it is of fundamental importance near the corner where the value of the oore-burns sif does not reach a null value. far from the corner, the correction factor quickly increases up to one. furthermore, an accurate formula for regular polygonal cracks is given. a comparison with the fe results for hexagonal cracks shows satisfactory results. nomenclature α opening angle a crack size, disk radius y shape factor  crack shape  crack border q point of  'q point of crack border ki mode i stress intensity factor ki,ob mode i stress intensity factor calculated with the oore-burns’ equation n number of corners  complementary angle s arc length σn nominal tensile stress in the ,x y cartesian coordinate system p perimeter of  c perimeter of the smallest disk containing   correction factor ,x y actual cartesian coordinate system i p. livieri et alii, frattura ed integrità strutturale, 63 (2023) 71-79; doi: 10.3221/igf-esis.63.07 79 references [1] bueckner, h.f., (1970). a novel principle for the computation of stress intensity factors, zamm 50, pp. 529–546. [2] rice, j.r. (1972). some remarks on elastic crack tip stress fields. int j solids struct, 8, pp. 751–8. [3] rice, j.r., (1989). weight function theory for three-dimensional elastic crack analysis. astm stp1020, wei r.p. and gangloff r.p., eds. philadelphia, american society for testing and materials, pp. 29–57. [4] oore, m., burns, d.j., (1980). estimation of stress intensity factors for embedded irregular cracks subjected to arbitrary normal stress fields. journal of pressure vessel technology asme, 102, pp. 202–211. [5] bs 7910:2019 guide to methods for assessing the acceptability of flaws in metallic structures. [6] carpinteri, a., brighenti, r., spagnoli, a. (2000). fatigue growth simulation of part-through flaws in thick-walled pipes under rotary bending. int j fatigue 22(1), pp. 1–9. [7] wang, x., lambert, s.b. (1995). stress intensity factors for low aspect ratio semi-elliptical surface cracks in finitethickness plates subjected to nonuniform stresses. engng fract mech, 51, pp. 517–32. [8] chai, g., zhang, k., wu, d. (1996). analyses on interactions of two identical semielliptical surface cracks in the internal surface of a cylindrical pressure vessel, int. j. press. vessels pip. 67 (2), pp. 203–210. [9] glinka, g., shen, g. (1991). universal features of weight functions for cracks in mode i. engng fract mech. 40, pp. 1135–46. [10] shen, g., glinka, g. (1991). determination of weight function from reference stress intensity factor. theor appl fract mech; 15, pp. 237–45. [11] gorner, f., mattheck, c., morawietz, p., munz, d. (1985). limitation of the petrosky–achenbach crack opening displacement approximation for the calculation of weight function. engng fract mech. 22, pp. 269–77. [12] fett, t. (1988). limitation of the petrosky–achenbach procedure demonstrated for a simple load case. engng fract mech; 29, pp. 713–6. [13] petrosky, h.j., achenbach, j.d. (1971). computation of the weight function from a stress intensity factor. engng fract mech. 10, pp. 257–66. [14] zerbs, u. t., schödel, m., webster, s., ainsworth, r. (2007). fitness-for-service fracture assessment of structures containing cracks: a workbook based on the european sintap/fitnet procedure, elsevier, 1st ed. oxford, amsterdam, the netherlands. [15] murakami, y. (chief ed) (2001), stress intensity factors handbook, 4, 5, pergamon. press, oxford, uk. [16] fett, t., munz, d., (1997). stress intensity factors and weight functions, computational mechanics publications. [17] tada, h., paris, c.p., irwin, g.r., (2000). the stress analysis of cracks handbook. third edition, asme press. [18] murakami, y, (2002). metal fatigue: effects of small defects and non-metallic inclusions, elsevier. [19] murakami, y. and endo, m. (1983) quantitative evaluation of fatigue strength of metals containing various small defects or cracks. eng. fract. mech., 17, pp. 1–15. [20] livieri, p., segala, s. (2021) asymptotic behaviour of the oore-burns integral for cracks with a corner and correction formulae for embedded convex defects, engineering fracture mechanics, 252, 107663, doi: 10.1016/j.engfracmech.2021.107663. [21] ascenzi, o., pareschi, l., segala, f. (2002). a precise computation of stress intensity factor on the front of a convex planar crack. international journal for numerical methods in engineering 54, pp. 241–261. [22] livieri, p., segala f. (2015). new weight functions and second order approximation of the oore-burns integral for elliptical cracks subject to arbitrary normal stress field, eng. fract. mech. 138, pp. 100–117. [23] livieri, p., segala, s. (2016). stress intensity factors for embedded elliptical cracks in cylindrical and spherical vessels theoretical and applied fracture mechanics 86(1), pp. 260–266. [24] livieri p., segala s. (2020). a closed form for the stress intensity factor of a small embedded square-like flaw, frattura ed integrità strutturale, 14 (54), pp. 182-191, doi: 10.3221/igf-esis.54.13. [25] livieri, p., segala, f., (2014). sharp evaluation of the oore-burns integral for cracks subjected to arbitrary normal stress field, fatigue & fracture of engineering materials & structures 37, pp. 95–106. [26] livieri, p., segala, f., (2018). an approximation in closed form for the integral of oore–burns for cracks similar to a star domain, fatigue & fracture of engineering materials & structures 41, pp. 3–19. << /ascii85encodepages false /allowtransparency false /autopositionepsfiles true /autorotatepages /none /binding /left /calgrayprofile (dot gain 20%) /calrgbprofile (srgb iec61966-2.1) /calcmykprofile (u.s. web coated \050swop\051 v2) /srgbprofile (srgb iec61966-2.1) /cannotembedfontpolicy /error /compatibilitylevel 1.4 /compressobjects /tags /compresspages true /convertimagestoindexed true /passthroughjpegimages true /createjobticket false /defaultrenderingintent /default /detectblends true /detectcurves 0.0000 /colorconversionstrategy /cmyk /dothumbnails false /embedallfonts true /embedopentype false /parseiccprofilesincomments true /embedjoboptions true /dscreportinglevel 0 /emitdscwarnings false /endpage -1 /imagememory 1048576 /lockdistillerparams false /maxsubsetpct 100 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/hrv (za stvaranje adobe pdf dokumenata najpogodnijih za visokokvalitetni ispis prije tiskanja koristite ove postavke. stvoreni pdf dokumenti mogu se otvoriti acrobat i adobe reader 5.0 i kasnijim verzijama.) /hun 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can be opened with acrobat and adobe reader 5.0 and later.) >> /namespace [ (adobe) (common) (1.0) ] /othernamespaces [ << /asreaderspreads false /cropimagestoframes true /errorcontrol /warnandcontinue /flattenerignorespreadoverrides false /includeguidesgrids false /includenonprinting false /includeslug false /namespace [ (adobe) (indesign) (4.0) ] /omitplacedbitmaps false /omitplacedeps false /omitplacedpdf false /simulateoverprint /legacy >> << /addbleedmarks false /addcolorbars false /addcropmarks false /addpageinfo false /addregmarks false /convertcolors /converttocmyk /destinationprofilename () /destinationprofileselector /documentcmyk /downsample16bitimages true /flattenerpreset << /presetselector /mediumresolution >> /formelements false /generatestructure false /includebookmarks false /includehyperlinks false /includeinteractive false /includelayers false /includeprofiles false /multimediahandling /useobjectsettings /namespace [ (adobe) (creativesuite) (2.0) ] /pdfxoutputintentprofileselector /documentcmyk /preserveediting true /untaggedcmykhandling /leaveuntagged /untaggedrgbhandling /usedocumentprofile /usedocumentbleed false >> ] >> setdistillerparams << /hwresolution [2400 2400] /pagesize [612.000 792.000] >> setpagedevice microsoft word numero_33_art_48 j. toribio et alii, frattura ed integrità strutturale, 33 (2015) 434-443; doi: 10.3221/igf-esis.33.48 434 focussed on multiaxial fatigue role of multiaxial stress state in the hydrogen-assisted rolling-contact fatigue in bearings for wind turbines j. toribio, m. lorenzo, d. vergara fracture of materials and structural integrity research group, university of salamanca, spain toribio@usal.es, mlorenzo@usal.es, dvergara@usal.es abstract. offshore wind turbines often involve important engineering challenges such as the improvement of hydrogen embrittlement resistance of the turbine bearings. these elements frequently suffer the so-called phenomenon of hydrogen-assisted rolling-contact fatigue (ha-rcf) as a consequence of the synergic action of the surrounding harsh environment (the lubricant) supplying hydrogen to the material and the cyclic multiaxial stress state caused by in-service mechanical loading. thus the complex phenomenon could be classified as hydrogen-assisted rolling-contact multiaxial fatigue (ha-rc-mf). this paper analyses, from the mechanical and the chemical points of view, the so-called ball-on-rod test, widely used to evaluate the hydrogen embrittlement susceptibility of turbine bearings. both the stress-strain states and the steady-state hydrogen concentration distribution are studied, so that a better elucidation can be obtained of the potential fracture places where the hydrogen could be more harmful and, consequently, where the turbine bearings could fail during their life in service. keywords. hydrogen-assisted rolling-contact multiaxial fatigue; wind turbines; bearings; numerical analysis. introduction ffshore wind turbines often involve important engineering challenges [1], one of the most important being the improvement of hydrogen embrittlement resistance of the turbine bearings, a key issue in the evaluation of the structural integrity of such components. these elements are prone to suffer the so-called phenomenon of hydrogen-assisted rolling-contact fatigue (ha-rcf) [2, 3] as a consequence of the synergic action of the surrounding harsh environment (the lubricant) supplying hydrogen to the material and the cyclic multiaxial stress state caused by inservice mechanical loading [2, 3]. thus the complex phenomenon of progressive damage could be classified as hydrogenassisted rolling-contact multiaxial fatigue (ha-rc-mf). three important aspects linked with bearing failures are being extensively researched: (i) rolling contact fatigue (rcf) [47], (ii) influence of carbide particles on fatigue life [8,9], and (iii) local microplastic strain accumulation via ratcheting [1012]. to achieve a better assessment of the structural integrity of such components, the analysis of hydrogen accumulation (revealing the prospective damage places) arises as a key issue. in previous studies [2, 3], the widely used rc-mf ball-on-rod test [12-15] was simulated by the finite element method (fem) in order to obtain the stress-strain state inside the bearings during life in-service. from these states, the hydrogen distribution corresponding to the steady-state in the radial direction of the bearing was obtained. this paper goes further in the study developed in previous research [2, 3] including the analysis of the hydrogen distributions in hoop and axial directions, in order to obtain the potential fracture places where the hydrogen embrittlement phenomenon initiates. o j. toribio et alii, frattura ed integrità strutturale, 33 (2015) 434-443; doi: 10.3221/igf-esis.33.48 435 numerical modeling he study was divided into two uncoupled analysis. on one hand, the numerical simulation by means of a commercial finite element (fe) code was used for obtaining the stress and strain states after six revolutions of the bar. from the results of such an analysis, a simple estimation of the hydrogen accumulation for long time of exposure to hydrogenating environment was carried out allowing the estimation of the potential hydrogen damage places. the geometry analysed consist in a steel bar of length l= 6 mm and diameter d = 9.53 mm which rotates in contact with three equidistant steel balls of diameter d = 12.70 mm which apply a point load of f = 300 n over the bar surface as reflects the scheme of fig. 1a. the complete 3d geometry can be simplified to a half just considering the symmetry plane r- shown in fig. 1b and applying the corresponding boundary conditions as restricted displacement on the bar axial direction for all the nodes placed inside the symmetry plane. thus, an important save of computing time is achieved optimizing the available resources. in addition, the geometry of the contacting balls can be also simplified considering the symmetry plane r-z of such components. taking this into account, only a quarter of the whole geometry of the ball is modelled, as can be seen in fig. 1b. (a) (b) figure 1: (a) scheme of analysed geometry for a ball on rod test and (b) 3d geometry. the numerical modelling of the ball-on-rod test (six revolutions) was carried out considering the material constitutive law to be elastic perfectly plastic corresponding to a steel with the following material properties for both, rod and balls: young modulus, e = 206 gpa, poisson coefficient,= 0.3 and material yield stress y = 2065 mpa. the analysis was carried out considering the isotropic strain hardening of the material and updated lagrange procedure. according to the hertz theory considering only the elastic response of the components [16], a very localized effect can be expected in the contact zone between rod and balls. according to this, a ball pressuring a cylinder must undergo a contact pressure of 5.5 gpa with a elliptic contacting zone whose axis length are 160 m and 231 m respectively. a very refined mesh is required near the rod surface, whereas a coarser mesh was considered out of such a zone since the local effect of contact vanishes at the rod core. thus, elements were homogenously distributed over a depth from the rod surface about 1 mm. this way, in this refined zone, the size of these elements is 43 x 52 x 280 m in the radial, circumferential and axial directions. regarding the meshing of the balls, the same type of elements was used, assuming a refined zone at the contact zone with element sizes similar to those used for the cylindrical bar. a point load of 300 n was placed at each ball centre and was progressively applied during the first rotation of the rod. taking this into account, diverse meshes with linear hexaedric element of 8 nodes were considered until the required convergence on results was achieved. the optimum mesh (fig. 2) consists in 154000 elements: 130000 for meshing the rod and 24000 for meshing the three balls. from results of the mechanical simulation, a simple estimation of the behaviour against ha-rc-mf of the bar can be carried out considering that hydrogen diffusion proceeds from the bar surface to inner points as a function of the gradients of both hydrostatic stress () and hydrogen solubility (ks) [17-19]: t j. toribio et alii, frattura ed integrità strutturale, 33 (2015) 434-443; doi: 10.3221/igf-esis.33.48 436 sε ph p sε p ( ) ( ) ( ) kv d c c rt k                     j (1) r being the universal gases constant, vh the partial volume of hydrogen, t the absolute temperature, c the hydrogen concentration and ks the hydrogen solubility that is itself a one-to-one monotonic increasing function of equivalent plastic strain, as explained in detail elsewhere [17-19]. in particular, a linear relationship between plastic strain and solubility in the form ksp was considered [17-19]. after using the matter conservation law and applying the gauss-ostrogradsky, the following second-order partial differential equation of hydrogen diffusion is obtained: sε ph sε p ( ) ( ) kvc d c dc t rt k                    (2) the equilibrium concentration of hydrogen for infinite time of exposure to harsh environment is the steady-state solution of the differential equation. it takes the form of a maxwell-boltzman distribution as follows: h eq 0 sε p( )exp v c c k rt       (3) where c0 is the equilibrium hydrogen concentration for the material free of stress and strain. according to previous equations, hydrogen diffusion is driven by: (i) the negative gradient of hydrogen concentration (in the classical fick´s sense); (ii) the positive gradient of hydrostatic stress; (iii) the positive gradient of hydrogen solubility, the latter is one-to-one related to the gradient of equivalent plastic strain so that the plastic strain gradient can be analysed instead of the hydrogen solubility gradient. mechanical analysis: stress and strain umerical simulation allows the determination of the stress and strain state under cycling loading during the ballon-rod test. during rolling, the amplitude of the fatigue loading is progressively decreasing as the depth increases, reaching an almost uniform stress evolution near the rod core. so, only points placed close to the contact will undergo real fatigue. after the fatigue loading, a multiaxial stress state appears at the rod. thus, figs. 2a, 3a and 4a shows the global view of the distribution of radial, hoop and axial stress respectively in the steel rod at the end of the sixth cycle, thereby after passing 17 contacting balls. for a more detailed analysis, the radial distribution of aforesaid variables are represented in figs. 2b, 3b and 4b for different values of the hoop coordinate  considering the following sections: (i) = 0º representing the contact plane between one of the balls and the rod, (ii) = 20º, (iii) = 40º, and finaly (vi) = 60º (corresponding to the symmetry plane between two contacting balls). -3500 -3000 -2500 -2000 -1500 -1000 -500 0 500 3 3.2 3.4 3.6 3.8 4 4.2 4.4 4.6 =0º =20º =40º =60º  r( m p a ) r (mm) (a) (b) figure 2: distribution of radial stress after the sixth loading cycle: (a) 3d view at the contact of one of the balls and (b) radial distribution for diverse hoop coordinates . n j. toribio et alii, frattura ed integrità strutturale, 33 (2015) 434-443; doi: 10.3221/igf-esis.33.48 437 -3500 -3000 -2500 -2000 -1500 -1000 -500 0 500 3 3.2 3.4 3.6 3.8 4 4.2 4.4 4.6 =0º =20º =40º =60º   (m p a ) r (mm) (a) (b) figure 3: distribution of hoop stress after the sixth loading cycle: (a) 3d view at the contact of one of the balls and (b) radial distribution for diverse hoop coordinates . -3500 -3000 -2500 -2000 -1500 -1000 -500 0 500 3 3.2 3.4 3.6 3.8 4 4.2 4.4 4.6 =0º =20º =40º =60º  z ( m p a ) r (mm) (a) (b) figure 4: distribution of axial stress after the sixth loading cycle: (a) 3d view at the contact of one of the balls and (b) radial distribution for diverse hoop coordinates . results shown in figs. 2a-4a, reveal a heavy multiaxial stress concentration localized at the contacting zones of each ball with the rolling rod. this effect progressively vanishes as the distance from the contact zone increases. outside of the local affected zone, the stress state is homogenously distributed with a stress concentration ring located at the vicinity of the rod surface. the radial distributions shown in figs. 2b-4b reveal a huge compressive stress at the contact radius (= 0º) in the radial direction caused by the pressure applied by the ball. this stress concentration is more intense for the radial stress than for the other components of the stress tensor. in addition, the extension of the local effect of contacting balls spreads through a deeper zone (around 1.5 mm) for the radial stress (fig. 2) than those corresponding to the hoop and axial stress (around 200 m). the extension and the maximum value of the compressive state is notably reduced at planes placed outside the contacting planes (i.e. for  0º) with slight variations for hoop coordinates higher than 20º. the distributions of the hoop and axial stresses show the same high reduction of the magnitude of the stress state but, in these cases, without significant changes in the extension of the affected zone. the distribution for the other radius in contact with the other balls = 120º and = 240º) is equivalent to that shown in figs. 2b-4b. within the stress concentration zone, the values of the von mises stress reach the material yield strength; it implies the appearance of plastic strains near the rod skin, as revealed in previous studies [2,3]. as a consequence of the values of the stress state at the rod surface vicinity, plastic strains are distributed through such a zone. fig. 5a shows the 3d view of the field of equivalent (cumulative) plastic strain after the six cycles of the test was completed and the radial distribution of such a variable is plotted in fig. 5b. in the same way, fig. 6a shows the 3d view of the field of hydrostatic stress after the sixth cycle of the test was completed and fig. 6b shows the radial distribution of such a variable for diverse values of . j. toribio et alii, frattura ed integrità strutturale, 33 (2015) 434-443; doi: 10.3221/igf-esis.33.48 438 according to this, plastic strains are distributed only over a plastic zone with ring shape spreading over 315 m from the periphery of the rod, as shown in the same radial distribution of plastic strain obtained for diverse radial planes (different  angles, cf. fig. 5b) even for those closest to the contacting plane ( = 0º). this is due to the fact that plastic strains are only generated at the contacting plane. outside of this zone, the von mises stress is always lower than the material yield strength and consequently no plastic strain are generated in this region. thus, the plastic strain remains the same in all sections of the rod. a progressive decreasing distribution is obtained with a small plateau close to the rod cylindrical surface of 50 m width. 0 0.005 0.01 0.015 0.02 4.4 4.45 4.5 4.55 4.6 4.65 4.7 4.75 =60º =20º =10º =5º =2º =0º p r (mm) (a) (b) figure 5: distribution of equivalent plastic strain after the sixth loading cycle: (a) 3d view at the contact of one of the balls and (b) radial distribution for diverse hoop coordinates . the first driving force for hydrogen diffusion, the inwards gradient of equivalent plastic strains, is negative and only affects the plastic strain ring near to the rod surface (fig. 5). with regard to the second driving force for hydrogen diffusion, the gradient of hydrostatic stress, at the contact plane (= 0º), a distribution of compressive nature in radial direction of such a variable is obtained, it progressively decreasing with depth up to becoming null for a depth from the rod surface of about 1 mm (fig. 6b). outside the contact plane the hydrostatic stress distribution is notably reduced, so that, for angles  higher than 20º, it is almost independent of such an angle (as it happened with the distributions of radial, hoop and axial stresses). the typical profile consist of compressive stresses over 200 μm, tensile stresses for deeper points, and, in the case of radial coordinate lower than 4 mm, a null value for hydrostatic stress is obtained. -3500 -3000 -2500 -2000 -1500 -1000 -500 0 500 3.6 3.8 4 4.2 4.4 4.6 =60º =20º =10º =5º =2º =0º  ( m p a ) r (mm) (a) (b) figure 6: distribution of hydrostatic stress: (a) 3d view of the contacting plane and (b) radial distribution for diverse circumferential coordinate . j. toribio et alii, frattura ed integrità strutturale, 33 (2015) 434-443; doi: 10.3221/igf-esis.33.48 439 for completing the analysis of hydrogen diffusion and accumulation on the rod during life in service, the information obtained from the estimation of hydrogen concentration in the radial direction [2,3] can be completed by a discussion of the implications of diffusion in the circumferential direction. to do so, the circumferential distribution of the variables affecting the hydrogen diffusion assisted by stress and strain is plotted in fig. 5, considering diverse layers within the plastic zone. the circumferential distribution of hydrostatic stress shown in fig. 7a reveals a local stress concentration in the vicinity of the contacting plane = 0º where the maximum hydrostatic stress is placed. within a range of planes around 5º, the hydrostatic stress progressively decreases, becoming almost constant for other values of . this behaviour is observed for the distributions corresponding to depths around half size of the plastic zone (173 m approximately) with compressive stresses out of the affected zone. as the depth from the rod surface increases, the maximum value of the stress is suddenly decreased (a 90% for the depth around the size of the plastic zone x = 300 m, a 60% for the depth around half size of the plastic zone x = 173 m and a 25% just for a depth of 86 m). beyond this depth the stress continuously decreases up to becoming almost null for deeper points. this way, in hoop direction hydrogen will be pumped out of the contact plane by means of a huge gradient of plastic strains. with regard to circumferential plastic strains, a minimum is placed close to the contact section (= 0º) where a slight local maximum appears, thereby creating a gradient of plastic strains. this gradient drives hydrogen out of the contact plane to planes with a higher . this effect is vanished with depth resulting almost null for depths from surface of 216 m and null for depths from the rod surface out of the plastic zone (x > 315 μm) observed in fig. 5. plastic strain slowly increases with the hoop coordinate  reaching a maximum value at = 45º. so, hydrogen will be pumped out suddenly from the contact plane and lately is dragged slowly for points placed at higher hoop coordinates (due to slower gradient far from the contact plane). -3500 -3000 -2500 -2000 -1500 -1000 -500 0 500 -40 -20 0 20 40 x=0 x=86 m x=173 m x=216 m x=300 m x=700 m  ( m p a ) º 0 0.005 0.01 0.015 0.02 -40 -20 0 20 40 x=0 x=86 m x=129 m x=173 m x=216 m x=300 m  p (º) (a) (b) figure 7: circumferential distribution of (a) hydrostatic stress and (b) equivalent plastic strain at diverse layers of the rod between the contacting balls. finally, fig. 8 shows the axial distribution of both hydrostatic stress and equivalent plastic strain for diverse values of depth from the rod surface (x). in the axial direction, a very located distribution of both hydrostatic stress and plastic strains near to contact plane is obtained. with regard to the hydrostatic stress distribution, the high compressive stress at the contact plane is progressively decreased as the distance from the contact plane (z) is increased, obtaining a null distribution of such a variable for z > 1.5 mm. as the depth from the rod surface increases, the hydrostatic stress at the contacting plane (z = 0 mm) progressively decreases and, consequently, the inwards gradient of hydrostatic stress in the axial direction is reduced as the depth from the rod surface is increased. thus, hydrogen placed close to the contact between ball and bar is also pumped in the axial direction due to the positive inwards gradient of hydrostatic stress. this effect is progressively reduced with the depth x becoming almost negligible for depths x > 600 μm. finally, the axial distribution of plastic strains appears through a narrow zone becoming null for axial distances z > 500 μm. j. toribio et alii, frattura ed integrità strutturale, 33 (2015) 434-443; doi: 10.3221/igf-esis.33.48 440 -3500 -3000 -2500 -2000 -1500 -1000 -500 0 500 0 0.5 1 1.5 2 2.5 3 x=0 m x=86 m x=130 m x=210 m x=430 m x=600 m  ( m p a ) z (mm) 0 0.01 0.02 0.03 0.04 0.05 0 0.5 1 1.5 2 2.5 3 x=0 m x=86 m x=130 m x=210 m x=430 m x=600 m p z (mm) (a) (b) figure 8: axial distribution of hydrostatic stress for diverse depths (x): (a) general plot and (b) detail plot near the rod surface (zone with strong gradients). as in the case of the hydrostatic stress distribution, the plastic strain at the contact plane (z = 0 mm) decreases with depth from the rod surface (x), and consequently the inwards gradient is progressively reduced as the variable x is increased becoming null for depths x > 600 m. however, the inwards gradient of equivalent plastic strains is negative, thereby; the hydrogen diffusion is not enhanced. this opposition is progressively annulled as the depth from rod surface is increased. so, two competitive factors are involved in the diffusion of hydrogen placed near to the contact between ball and bar. on one hand, the inwards gradient of hydrostatic stress enhances the diffusion of hydrogen out of the contact plane whereas; on the other hand, the inwards gradient of equivalent plastic strains is opposite, impeding the aforesaid diffusion. this effect is only noticeable near the contact zone and, therefore, the diffusion of hydrogen placed at deeper points (x > 600 m) can be considered only driven by the gradient of hydrogen concentration in axial direction. chemical analysis: hydrogen transport by diffusion or assessing the ha-rc-mf behaviour of the rolling rod, it is interesting to analyse the long-time behaviour of the component under hydrogen exposure. to this end, the steady state distribution of hydrogen concentration through the rod radius was obtained (fig. 9) using eq. (3) and taking into account both hydrostatic stress and equivalent plastic strain. plot is associated with infinite time (steady state solution from the mathematical point of view) or with thermodynamical equilibrium of the hydrogen-metal system (from the physical view point). 0 0.2 0.4 0.6 0.8 1 1.2 0 1 2 3 4 =60º =20º =10º =5º =2º =0º c e q /c 0 r (mm) 0 0.2 0.4 0.6 0.8 1 1.2 3 3.2 3.4 3.6 3.8 4 4.2 4.4 4.6 =60º =20º =10º =5º =2º =0º c e q /c 0 r (mm) (a) (b) figure 9: radial distribution of the hydrogen concentration for diverse circumferential coordinate : (a) general plot and (b) detail plot near the rod surface. f j. toribio et alii, frattura ed integrità strutturale, 33 (2015) 434-443; doi: 10.3221/igf-esis.33.48 441 the discussion about ha-rc-mf is focused in the quantitative analysis of the hydrogen amount in radial, hoop and axial directions by applying the steady-state solution of the diffusion equation shown in eq. (3) to the distributions of the components of the stress tensor and plastic strain shown in figs. 2 and 4 respectively. thus, fig. 9 shows the radial laws of hydrogen concentration along diverse radial planes considering the stress and strain states shown in figs. 5 and 6, whereas figs. 10 and 11 shows the distribution of hydrogen concentration in the hoop and axial directions respectively. according to these results, for long time of exposure to the hydrogenating environment, the hydrogen amount at the rod surface vicinity (within the stress and strain affected zone of the rod, i.e., for depths from the rod surface lower than 1 mm) is progressively increased with the circumferential distance to the contacting ball. thus, for the plane where the ball is contacting the rod, a huge reduction of the hydrogen amount is observed due to the high compressive stresses produced by the contact pressure (fig. 6). consequently, hydrogen diffusion is promoted out of the contact affected zone due to the gradient of both driving forces for hydrogen diffusion: the inwards gradient of plastic strain and the inwards gradient of hydrostatic stress. this effect is also progressively vanished as the distance from the contact plane increases, it being noticeable for planes very close to the contact plane where an important reduction of the hydrogen concentration is also achieved. nevertheless, for planes with circumferential coordinates higher than 10º from the contact plane, the hydrogen amount at surface is similar than that obtained for higher angle . the distributions of hydrogen for planes with circumferential coordinate higher than 10º just exhibit slight changes. an interesting issue is observed for these planes from the point of view of ha-rc-mf. at the rod surface vicinity over a depth of 200 m a significant reduction is observed due to the compressive stresses (fig. 6) with a small plateau of 50 m. hereafter the hydrogen concentration increases with depth, reaching the maximum value (c/c0 = 1.15) of the distribution for a depth of 300 m and for deeper points softly decreases up to the rod core where the concentration associated with thermo-dynamical equilibrium of the material free of stress and strain (c0) is achieved. so, the potential place of damage would be placed through a zone extended between the balls for depth from surface of 300 m. the hoop distribution of hydrogen for long times of exposure to the hydrogenating environment is presented in fig. 10, where different depth layers (diverse depths) are depicted, considering the stress and strain states obtained from numerical simulation (fig. 8). 0 0.2 0.4 0.6 0.8 1 1.2 -40 -20 0 20 40 x=0 x=86 m x=173 m x=216 m x=300 m x=700 m c e q c 0  (º) figure 10: hydrogen distribution for long times of diffusion in the circumferential direction at diverse layers of the rod between the contacting balls. regarding the hoop distribution of hydrogen concentration shown in fig. 10, the hydrogen accumulation is placed out of the contacting plane (= 0º) and surrounding planes where a huge reduction of the hydrogen amount is observed. this reduction becomes lower as the depth from the surface is increased. out of this zone hydrogen is uniformly distributed for depths up to 86 μm. for distribution obtained at higher depths, hydrogen is progressively increased for > 5º, reaching a maximum hydrogen concentration at = 20º and, hereafter, decreasing slowly. the aforesaid trend is repeated at deeper layers, increasing the maximum hydrogen amount zone as the depth increases (according to the distributions of hydrostatic stress shown in fig. 6a). for layers placed far from the contact, hydrogen is almost uniformly distributed in the hoop direction, reaching a maximum hydrogen concentration, c/c0 = 1.13, for a j. toribio et alii, frattura ed integrità strutturale, 33 (2015) 434-443; doi: 10.3221/igf-esis.33.48 442 depth 300 m. hereafter, the hydrogen distribution is progressively decreased, approaching the equilibrium hydrogen concentration for the material free of stress and strain (ceq/c0 = 1). so, the maximum hydrogen amount is placed out of the contact plane at a depth from the rod surface of 300 μm. to conclude the analysis, the hydrogen distribution in the axial direction is presented in fig. 11 for diverse depths within the plastic strain affected zone observed previously in fig. 5. thus, the hydrogen concentration is highly decreased at the vicinity of the contact zone (0 < z < 1.2 mm). so, the shorter the distance from the contact area, the lower the reduction of hydrogen amount. thus, for a depth of 700 m, the distribution of hydrogen is rather affected by the stress and strain states generated by ha-rc-mf. 0 0.2 0.4 0.6 0.8 1 1.2 0 0.5 1 1.5 2 2.5 3 x=0 x=86 m x=173 m x=216 m x=300 m x=700 m c e q /c 0 z (mm) figure 11: hydrogen distribution for long times of diffusion in the axial direction at diverse layers of the rod between the contacting balls. conclusions n a ball-on-rod test, non-uniform plastic strains are generated on the contact plane where the ball applies a huge pressure to the rod overcoming material yield strength. this state is located near the rod surface with a plastic zone spreading over a maximum depth of 300 m. a huge compressive stress appears in the vicinity of the rod surface; it is progressively reduced as the distance from the surface increases in radial, hoop and axial directions. as a result, hydrogen is accumulated out of the contact plane where a huge reduction of the hydrogen amount is achieved for long times of exposure to the environment due to the high compressive hydrostatic stress in the radial direction, thereby pumping hydrogen towards points outside the contact plane. the maximum hydrogen amount appears for a depth from the surface about 300 m at planes placed 20º out of the contact plane in the contact cross section of the bar. acknowledgements he authors acknowledge the financial support provided by the eu project multihy (http://multihy.eu): multiscale modelling of hydrogen embrittlement of crystalline materials (eu-fp7-nmp project no. 263335). references [1] europe's onshore and offshore wind energy potential: an assessment of environmental and economic constraints. european environment agency, copenhagen, (2009). [2] toribio, j., lorenzo, m., vergara, d., kharin, v., hydrogen-assisted rolling-contact fatigue of wind turbines bearings. key eng. mater., 627 (2015) 157–160. [3] toribio, j., lorenzo, m., vergara, d., kharin, v., numerical analysis of hydrogen-assisted rolling-contact fatigue of wind turbine bearings. frattura ed integrità strutturale, 30 (2014) 40–47. i t j. toribio et alii, frattura ed integrità strutturale, 33 (2015) 434-443; doi: 10.3221/igf-esis.33.48 443 [4] kumar, a., hahn, g., rubin, d., a study of subsurface crack initiation produced by rolling contact fatigue, metall. trans. a, 24 (1993) 351–359. [5] bhargava, v., hahn, g. t., rubin, c. a., rolling contact deformation and microstructural changes in high strength bearing steel, wear, 133 (1989) 65–71. [6] gupta, v., bastias, p., hahn, g. t., rubin, c. a., elasto-plastic finite-element analysis of 2-d rolling-plus-sliding contact with temperature-dependent bearing steel material properties, wear, 169 (1993) 251–256. [7] jiang, y., su, b., sehitoglu, h., three-dimensional elastic-plastic stress analysis of rolling contact, j. tribol., 124 (2002) 699–708. [8] kabo, e., ekberg, a., fatigue initiation in railway wheels—a numerical study of the influence of defects, wear, 253 (2002) 26–34. [9] kabo, e., ekberg, a., material defects in rolling contact fatigue of railway wheels—the influence of defect size, wear, 258 (2005) 1194–1200. [10] rider, r. j., harvey, s. j., chandler, h. d., fatigue and ratcheting interactions, inter. j. fatigue, 17 (1995) 507–511. [11] lim, c. b., kim, k. s., seong, j. b., ratcheting and fatigue behavior of a copper alloy under uniaxial cyclic loading with mean stress, inter. j. fatigue, 31 (2009) 501–507. [12] pandkar, a. s., arakere, n., subhash, g., microstructure-sensitive accumulation of plastic strain due to ratcheting in bearing steels subject to rolling fatigue, inter. j. fatigue, 63 (2014) 191–202. [13] glover, d. a ball-rod rolling contact fatigue tester, in: rolling contact fatigue testing of bearing steels. astm stp 771, american society for testing and materials, baltimore, md, (1982) 107–124. [14] bhattacharyya, a., subhash, g., arakere, n., evolution of subsurface plastic zone due to rolling contact fatigue of m-50 nil case hardened bearing steel, inter. j. fatigue, 59 (2014) 102–113. [15] arakere, n. k., subhash, g., work hardening response of m50-nil case hardened bearing steel during shakedown in rolling contact fatigue, mater. sci. tech., 28 (2012) 34–38. [16] pilkey, w. d., formulas for stress, strain, and structural matrices, second ed., john wiley & sons, inc., hoboken, nj, usa, (2008). [17] toribio, j., lorenzo, m., vergara, d., kharin, v., hydrogen degradation of cold-drawn wires: a numerical analysis of drawing-induced residual stresses and strains, corros., 67 (2011) 075001–075008. [18] toribio, j., kharin, v., lorenzo, m., vergara, d., role of drawing-induced residual stresses and strains in the hydrogen embrittlement susceptibility of prestressing steels, corros. sci., 53 (2011) 3346–3355. [19] toribio, j., kharin, v., vergara, d., lorenzo, m., two-dimensional numerical modelling of hydrogen diffusion in metals assisted by both stress and strain, adv. mater. res., 138 (2010) 117–126. microsoft word numero_35_art_24 s. lesz et alii, frattura ed integrità strutturale, 35 (2016) 206-212; doi: 10.3221/igf-esis.35.24 206 focussed on crack paths crack initiation and fracture features of fe–co–b–si–nb bulk metallic glass during compression s. lesz, a. januszka, s. griner, r. nowosielski silesian university of technology, poland sabina.lesz@polsl.pl, anna.januszka@polsl.pl, stefan.griner@polsl.pl, ryszard.nowosielski@polsl.pl abstract. the aim of the paper was investigation crack initiation and fracture features developed during compression of fe-based bulk metallic glass (bmg). these fe-based bmg has received great attention as a new class of structural material due to an excellent properties (e.g. high strength and high elasticity) and low costs. however, the poor ductility and brittle fracture exhibited in bmgs limit their structural application. at room temperature, bmgs fails catastrophically without appreciable plastic deformation under tension and only very limited plastic deformation is observed under compression or bending. hence a well understanding of the crack initiation and fracture morphology of fe-based bmgs after compression is of much importance for designing high performance bmgs. the raw materials used in this experiment for the production of bmgs were pure fe, co, nb metals and nonmetallic elements: si, b. the fe–co–b–si–nb alloy was cast as rods with three different diameters. the structure of the investigated bmgs rod is amorphous. the measurement of mechanical properties (young modulus e, compressive stress σc, elastic strain ε, unitary elastic strain energy – uu) were made in compression test. compression test indicates the rods of fe-based alloy to exhibit high mechanical strength. the development of crack initiation and fracture morphology after compression of fe-based bmg were examined with scanning electron microscope (sem). fracture morphology of rods has been different on the cross section. two characteristic features of the compressive fracture morphologies of bmgs were observed. one is the smooth region. another typical feature of the compressive fracture morphology of bmgs is the vein pattern. the veins on the compressive fracture surface have an obvious direction as result of initial displace of sample along shear bands. this direction follows the direction of the displacement of a material. the formation of veins on the compressive fracture surface is closely related to the shear fracture mechanism. the results of these studies may improve the understanding on the fracture features and mechanisms of bmgs and may provide instructions on future design for ductile bmgs with high resistance for fracture. keywords. bulk metallic glasses; compression test; structure; fracture morphology. s. lesz et alii, frattura ed integrità strutturale, 35 (2016) 206-212; doi: 10.3221/igf-esis.35.24 207 introduction etallic glasses (mgs) are poised to be mainstay materials for the 21st century due to the unique physical and chemical properties, which offers a great potential for application in industry, medicine, energy systems, microelectronics, aeronautics and many other fields. the first reported scientifically obtained metallic glass (mg) was the alloy au75si25 produced at caltech by klement, willens & duwez in 1960, by extremely rapid cooling of the melted alloy [1]. in the 1960s, chen and turnbull developed amorphous alloys of pd-si-ag, pd-si-cu, and pd-si-au [2]. chen also fabricated an amorphous pd-cu-si alloy with a diameter of up to 1 mm that could be considered to be a bulk metallic glass (bmg) [3]. a study of the mechanical properties of these novel materials was first reported in 1971 by masumoto and maddin [4]. in recent years a great expansion in the number of alloy compositions known to give bulk metallic glasses (bmgs) have occurred. the first fe-based bulk metallic glasses (bmgs) were prepared in 1995 [5]. since then, fe-based bulk metallic glasses have been studied as a novel class of engineering materials, which have a good glass forming ability and soft magnetic properties [6,7]. for example, in 2004, inoue et al. synthesized [(fexco1−x)0.75b0.2si0.05]96nb4 (x = 0.1 and 0.5 at.%). bmgs exhibit good soft magnetic properties, as well as super-high fracture strength of 3000–4000mpa and ductile strain of 0.002 [6]. bulk metallic glasses (bmgs) possess superior mechanical properties such as high strength and great elastic strain making them ideal candidates for structural applications. however, the poor ductility and brittle fracture exhibited in nearly all monolithic bmgs limit their structural application. hence, a well understanding fracture morphology and mechanical properties is important for designing performance of bmgs. the purpose of the paper was an investigation of the mechanical properties, structure and particularly fracture morphology of the fe36co36b19si5nb4 bulk metallic glass (bmg) after compression. experimental procedure he master alloy ingots with compositions of fe36co36b19si5nb4 were prepared from the pure fe, co, nb metals and non-metallic elements: si, b, in an argon atmosphere. the alloy composition represents nominal atomic percentages. the investigated material was cast in form of rods with diameter of =2, 3 and 4 mm. according to johnson, cooling rate achieved for an as-cast diameter r can be estimated as: t =10/r2 (cm) [8]. thus, the achieved cooling rate in the rod-shaped samples with =2, 3 and 4 mm in diameter could be estimated to be 1000, ~444 and 250 k/s. obviously the smaller the as-cast diameter, the larger the cooling rate is achieved. the rods were prepared by the pressure die casting. the following experimental techniques were used: x-ray diffraction (xrd) phase analysis method to test the structure, scanning electron microscopy (sem) to investigate fracture morphologies obtained after decohesion process in compression test. the xrd method has been performed by the use of diffractometer xrd 7, seifert-fpm, with filtered co-kα radiation. the morphology of fracture surfaces after decohesion process in compression test was examined by means of the scanning electron microscope (sem) supra 25, zeiss. the measurement of mechanical properties, like: young modulus e, compressive stress σc, elastic strain – ε, unitary elastic strain energy – uu, were made in compression test. compression tests for bulk metallic glasses were performed on zwick 100 testing machine at a strain rate of 5 × 10-4 s-1, at room temperature. for each group, five specimens were tested, and averaged data were used. results and discussion t was found from the obtained results of structural studies performed by x-ray diffraction that diffraction pattern of surface rods with =2, 3 and 4 mm in diameter of fe36co36b19si5nb4 alloy consists of a broad diffused halo typical for the amorphous phase (fig. 1). the mechanical properties of samples, including young’s modulus e, compressive stress – σc and elastic strain ε, unitary elastic strain energy – uu, are listed in tab. 1 and fig. 2. as shown in the fig. 2, the fe36co36b19si5nb4 bmg exhibits elastic strain – ε of 0.75 to 0.94%. young’s modulus e and compressive stress σc , unitary elastic strain energy – uu of the glassy alloy rods are in the range of 105-191 gpa, 790 – 1794 mpa, 17-25 kj/m2, respectively. the values of unitary elastic strain energy – uu decrease with the increasing diameter m t i s. lesz et alii, frattura ed integrità strutturale, 35 (2016) 206-212; doi: 10.3221/igf-esis.35.24 208 of rods and are 25, 21 and 17 kj/m2 for the samples with diameters of =2, 3 and 4 mm, respectively. with the increase of rod’s diameter the young’s modulus and stress decrease, suggesting a soft trend. these changes are probably connected with changes of structure relaxation. in sample in form of rod with 4 mm, where cooling rate of rods during casting is lower, the structure is more relaxed. this indicates that cooling rate plays a significant role in the plasticity of metallic glasses. the compressive fracture surfaces are shown in figs. 3-5. fracture morphology of rods has been different on the cross section. two characteristic features of the compressive fracture morphologies of metallic glasses (mgs) were observed. diameters of rod samples,  [mm] young’s modulus, e [gpa] compressive stress, σc [mpa] elastic strain, ε [%] elastic strain energy, u [kj/m2] 2 191 1794 0.94 25 3 135 1117 0.83 21 4 105 790 0.75 17 table 1: compressive mechanical properties of samples of the fe36co36b19si5nb4 bmgs rods used in compression test at room temperature. figure 1: x-ray diffraction pattern of the fe36co36b19si5nb4 bmgs rods with diameters of =2, 3 and 4 mm. one is the smooth region, as shown in figs. 3a,c,d, 4a,b,c,d,e, 5a,b. another typical feature of the compressive fracture morphology of mgs is the vein pattern, as shown in figs. 3a,b,c,d, 4a,c,d,e,f, 5c,d. the presence of these fracture morphologies indicates that the fe-based bmg of this study classifies itself as a brittle amorphous material. figs. 3a-d show the sem images of the fracture morphology of fe36co36b19si5nb4 alloy rod with diameter of =2 mm after compressive fracture. fig. 3a shows a main view of the 2 mm diameter bmg sample. the fracture surface of this sample consists of a smooth and vein pattern regions. fig. 3b shows image of fracture outside surface, there are vein patterns and many cracks. the veins on the compressive fracture surface have an obvious direction probably compatible with direction of plastic strain. fig. 3c shows an image of fracture of near the core of rod with smooth and vein pattern regions. extensive cracks perpendicular to the fracture surface (in fig. 3b) and rare small cracks within the veinlike pattern fracture (in fig. 3c,d) can be observed. the well-developed fracture surface is observed for rods with a diameter of =2 mm. the fracture surface of rods with the diameter of =3 mm do not exhibit veinlike pattern in a region of rod core. the fracture surface is small-developed, nearly smooth. only the edge of the rod the fine vein pattern morphology is observed. it is very interesting that angles between deep cracks formed and surface of the decohesion are from 68 to nearly 90 in relation to crack propagation direction. s. lesz et alii, frattura ed integrità strutturale, 35 (2016) 206-212; doi: 10.3221/igf-esis.35.24 209 investigations of fractures of the fe36co36b19si5nb4 alloy rods with =3.0 mm in diameter showed similar morphology, as shown in figs. 4a-f. rare small cracks in the rods with =3 mm can be seen, like in the rods of =2mm. figure 2: compressive stress-strain curves of the fe36co36b19si5nb4 bmgs rods with diameters of =2,3 and 4 mm. figure 3: sem images of the fracture morphology of fe36co36b19si5nb4 alloy rod with diameter of =2 mm after compressive fracture; a – main view: smooth and vein pattern regions, b – image of fracture outside surface, vein patterns, many cracks c – image of fracture of near the core of rod, smooth and vein pattern regions, clear crack, d – image of (c) at higher magnification. white arrow indicates the crack (c,d). s. lesz et alii, frattura ed integrità strutturale, 35 (2016) 206-212; doi: 10.3221/igf-esis.35.24 210 figure 4: sem images of the fracture morphology of fe36co36b19si5nb4 alloy rod with diameter of =3 mm after compressive fracture; a – main view: smooth and vein pattern regions, b – image of fracture near the core of rod, smooth patterns, c, d – image of fracture near the core of rod, smooth and vein pattern regions, crack is indicated by arrow (d), e, f – image of fracture outside surface, vein and smooth patterns, f – image showing veins, as indicated by the rectangle in (e) at higher magnification. the fracture surface of fe36co36b19si5nb4 rod with diameter of = 4 mm after compressive fracture consists of flat region with fine veins pass to the brittle crack region with extended surface, as shown in fig. 5a. fig. 5b shows the image of fracture near the core of rod. there are smooth and vein patterns. the fracture surface of rods with =4 mm does not exhibit another cracks extended to the material core besides the main fracture with the well-developed surface. fig. 5c shows the image of fracture outside surface with vein patterns regions. magnified veins from the area as pointed in fig. 5c was shown in fig. 5d. the veins on the compressive fracture surface have an obvious direction as result of initial displace of sample along shear bands. this direction follows the direction of the displacement of a material. as shown in fig. 5d, the angles between the primary crack propagation direction and a region of secondary cracks is 60. presumably it is the effect of the change of the crack propagation direction. it influences the microstructure in areas showing the change of the direction of fine veins. the formation of veins on the compressive fracture surface is closely related to the shear fracture mechanism [9]. it seems that the fracture surface is independent on a strength level [10]. s. lesz et alii, frattura ed integrità strutturale, 35 (2016) 206-212; doi: 10.3221/igf-esis.35.24 211 figure 5: sem images of the fracture morphology of fe36co36b19si5nb4 alloy rod with diameter of =4 mm after compressive fracture; a – main view: vein and smooth pattern regions, b – image of fracture near the core of rod, smooth and vein patterns, c, d – image of fracture outside surface, vein patterns, d – magnified veins from the area as point in (c). white arrows indicate the direction after the initial of cracking and direction at a further state of cracking. conclusions he structure of surface rods with =2, 3 and 4 mm in diameter of fe36co36b19si5nb4 alloy is amorphous. the febased bmg rods exhibits elastic strain – ε, young’s modulus e, compressive stress σc and unitary elastic strain energy – uu, of 0.75 to 0.94 %, 105 to 191 gpa, 790 to 1794 mpa and 17 to 25 kj/m2, respectively. fracture morphology of rods after compressive fracture has been different on the cross section. two characteristic features of the compressive fracture morphologies of metallic glasses (mgs) were observed in samples: smooth region and the vein pattern. the presence of these fracture morphologies indicate that the fe-based bmg of this study classifies itself as a brittle amorphous material. the results of these investigations suggest that the significant factor to control the structure, mechanical properties and fracture morphology of the fe36co36b19si5nb4 bmg is cooling rate. thus is factor has an instructional importance for the optimization of materials’ performance. references [1] klement, w., r. h. willens, duwez, p., non-crystalline structure in solidified gold–silicon alloys, nature, 187 (1960) 869-870. doi: 10.1038/187869b0. [2] chen, h. s., turnbull, d., formation, stability and structure of palladium-silicon based alloy glasses, acta metallurgica, 17 (1969) 1021-1031. doi: 10.1016/0001-6160(69)90048-0. t s. lesz et alii, frattura ed integrità strutturale, 35 (2016) 206-212; doi: 10.3221/igf-esis.35.24 212 [3] chen, h. s., thermodynamic considerations on the formation and stability of metallic glasses, acta metallurgica, 22 (1974) 1505-1511. doi: 10.1016/0001-6160(74)90112-6. [4] masumoto, t., maddin, r., the mechanical properties of palladium 20 a/o silicon alloy quenched from the liquid state, acta metallurgica, 19 (1971) 725-741. doi: 10.1016/0001-6160(71)90028-9. [5] inoue, a., high strength bulk amorphous alloys with low critical cooling rates (overview), materials transactions, jim 36(7) (1995) 866-875. [6] shen. b., inoue, a., chang, c., superhigh strength and good soft-magnetic properties of (fe,co)–b–si–nb bulk glassy alloys with high glass-forming ability, applied physics letters, 85(21) (2004) 4911. doi: 10.1063/1.1827349. [7] lesz, s., babilas, r., nabiałek, m., szota, m., dopisał, m., nowosielski, r., the characterization of structure, thermal stability and magnetic properties of fe–co–b–si–nb bulk amorphous and nanocrystalline alloys, journal of alloys and compounds, 509 (2011) 197-201. doi: 10.1016/j.jallcom.2010.12.146. [8] lin, x. h., johnson, w. l., formation of ti-zr-cu-ni bulk metallic glasses, journal of applied physics, 78 (1995) 6514. doi: 10.1063/1.360537. [9] qu, r. t., zhang, z. f., compressive fracture morphology and mechanism of metallic glass, journal of applied physics, 114 (2013) 193504. doi: 10.1063/1.4830029. [10] inoue, a., shen, b. l., chang, c. t., feand co-based bulk glassy alloys with ultrahigh strength of over 4000 mpa, intermetallics, 14 (2006) 936. doi: 10.1016/j.intermet.2006.01.038. << /ascii85encodepages false /allowtransparency false /autopositionepsfiles true /autorotatepages /none /binding /left /calgrayprofile (dot gain 20%) /calrgbprofile (srgb iec61966-2.1) /calcmykprofile (u.s. web coated \050swop\051 v2) /srgbprofile (srgb iec61966-2.1) /cannotembedfontpolicy /error /compatibilitylevel 1.4 /compressobjects /tags /compresspages true /convertimagestoindexed true /passthroughjpegimages true /createjobticket false /defaultrenderingintent /default /detectblends true /detectcurves 0.0000 /colorconversionstrategy /cmyk /dothumbnails false /embedallfonts true /embedopentype false /parseiccprofilesincomments true /embedjoboptions true /dscreportinglevel 0 /emitdscwarnings false /endpage -1 /imagememory 1048576 /lockdistillerparams false /maxsubsetpct 100 /optimize true /opm 1 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/hrv (za stvaranje adobe pdf dokumenata najpogodnijih za visokokvalitetni ispis prije tiskanja koristite ove postavke. stvoreni pdf dokumenti mogu se otvoriti acrobat i adobe reader 5.0 i kasnijim verzijama.) /hun 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can be opened with acrobat and adobe reader 5.0 and later.) >> /namespace [ (adobe) (common) (1.0) ] /othernamespaces [ << /asreaderspreads false /cropimagestoframes true /errorcontrol /warnandcontinue /flattenerignorespreadoverrides false /includeguidesgrids false /includenonprinting false /includeslug false /namespace [ (adobe) (indesign) (4.0) ] /omitplacedbitmaps false /omitplacedeps false /omitplacedpdf false /simulateoverprint /legacy >> << /addbleedmarks false /addcolorbars false /addcropmarks false /addpageinfo false /addregmarks false /convertcolors /converttocmyk /destinationprofilename () /destinationprofileselector /documentcmyk /downsample16bitimages true /flattenerpreset << /presetselector /mediumresolution >> /formelements false /generatestructure false /includebookmarks false /includehyperlinks false /includeinteractive false /includelayers false /includeprofiles false /multimediahandling /useobjectsettings /namespace [ (adobe) (creativesuite) (2.0) ] /pdfxoutputintentprofileselector /documentcmyk /preserveediting true /untaggedcmykhandling /leaveuntagged /untaggedrgbhandling /usedocumentprofile /usedocumentbleed false >> ] >> setdistillerparams << /hwresolution [2400 2400] /pagesize [612.000 792.000] >> setpagedevice microsoft word numero_41_art_47.docx l. zhang et alii, frattura ed integrità strutturale, 41 (2017) 356-368; doi: 10.3221/igf-esis.41.47 356 study on the effect of new type liquid accelerator on the performance of shotcrete luchen zhang, shuchen li, qin yan, lin zhu geotechnical and structural engineering research center, shandong university, jinan, shandong 250061, china 471263803@qq.com abstract. shotcrete is an essential preliminary support means in new austrian tunneling method (natm) construction and plays a very important role in controlling the stability of surrounding rock. the accelerator is a necessary admixture in shotcrete and its quality can greatly affect shotcrete performance. this paper proposes a new liquid accelerator characterized by short initial and final setting time, small dosage, and good adaptability to cement. laboratory tests and field tests are conducted to verify the influence of this liquid accelerator on performance of shotcrete. numerical simulation is carried out to study the strength growth of shotcrete with time and interaction between the strength and stress release of surrounding rock. the results show that the initial and final setting time of this liquid accelerator is 2 minutes and 4 minutes respectively. its dosage is just 1.5% to 4% of the cement quantity. adding this liquid accelerator can effectively improve the early strength and reduce the later strength loss of shotcrete, and therefore enhance the supporting effects of shotcrete on surrounding rock. in the field application, it is an ideal liquid accelerator for shotcrete, characterized by little resilience, no slurry shedding, and low dust. keywords. liquid accelerator; shotcrete; primary support; stress release of surrounding rock; numerical simulation. citation: zhang, l., li, s., yan, q., zhu, l. study on the effect of new type liquid accelerator on the performance of shotcrete, frattura ed integrità strutturale, 41 (2017) 356-368. received: 22.03.2017 accepted: 06.05.2017 published: 01.07.2017 copyright: © 2017 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. introduction ith the construction of large-scale underground engineering in china, shotcrete is widely used as a necessary support means. shotcrete is a kind of concrete setting and hardening from a mix of cement, sand, stone, mineral materials, and admixtures in a proper proportion after being sprayed at high velocity onto a surface (such as the rock, soil layer, building structure or template) through the pipeline via compressed air. shotcrete can be quickly hardened to support surrounding rock without manual vibration. the accelerator is a necessary admixture for shotcrete whose role is to quickly harden shotcrete, reduce resilience loss, prevent shotcrete from falling off due to the action of gravity, improve the adaptability of shotcrete to the aquifer, generate higher early strength, and increase the depth of single shotcrete layer [1-2]. the accelerator is classified into powdered and liquid accelerator. their main types include alumina clinker-carbonate series, alumina clinker-alunite series, w l. zhang et alii, frattura ed integrità strutturale, 41 (2017) 356-368; doi: 10.3221/igf-esis.41.47 357 water glass series, low-alkali or alkali-free series [3-4]. currently, shotcrete mainly adopts powdered accelerators in china, mainly applied to dry-mix shotcrete, has a large amount of resilience and dust, cannot be uniformly mixed with aggregates, and causes large dosage, therefore seriously affecting the later strength, increasing the construction cost, and retarding the construction progress. the liquid accelerator mainly applied to wet-mix shotcrete, has instable quality, generally large dosage (6% to 10%), and immature supporting construction technology. therefore, to resolve the preceding problems, a new liquid accelerator for shotcrete, with the dosage about 2%, has properties in all aspects superior to first-class goods stipulated in the jc477-2005 flash setting admixtures for shotcrete, to better meet construction needs. the shotcrete containing the accelerator can be set within 2 to 10 minutes after spraying so that it can provide the support resistance (radial force) for surrounding rock in a timely manner, change the biaxial stress status without support to triaxial stress status of the surface rock for the surrounding rock, and improve the strength of surrounding rock. the shotcrete layer is a flexible support and can gradually coordinate with deformations of surrounding rock by adjusting deformations, therefore improving the stress status, and giving full play to the self-bearing capacity of surrounding rock [5-6]. this paper adopted the numerical simulation method to study the growth of early strength of shotcrete added with the new liquid accelerator with the passage of time as well as interaction between the growth and the stress release of surrounding rock recently excavated, and compare shotcrete added with the traditional and new liquid accelerator on the supporting role. in this paper, chapter 2 introduces the development thinking, material composition, and functional mechanism of this liquid accelerator. chapter 3 mainly studies the impact of its ingredients on the properties of cement and concrete through laboratory tests. chapter 4 mainly studies the effects of support for surrounding rock of shotcrete added with this liquid accelerator, adopts the numerical simulation method to study the impact on surrounding rock supporting effects of shotcrete with varied ages and strength, and considers the interaction between the stress release rate of surrounding rock and shotcrete support. chapter 5 mainly verifies the performance of this liquid accelerator in actual work via field tests. development of liquid accelerator development thinking of liquid accelerator ccording to a series of studies on specialty chemicals, it can be found that the shotcrete accelerator has a large room for improvement and that the accelerator in the current market has many problems. for example, the powdered accelerator has a serious dust problem and cannot be dissolved and display effects in a just 0.01-second mixing time. therefore, the surface of shotcrete is hard and most coarse aggregates are rebounded. moreover, the compressive strength of 28-day (or other ages) shotcrete is not ideal and far from meeting design specifications, which brings potential risks to engineering safety, causes large usage of cement and high construction cost of shotcrete. currently, the liquid accelerator used onsite is easy to deteriorate and produce precipitate, needs large dosage (generally 6% to 10% of the cement quantity), causes serious later strength loss for shotcrete, cannot adapt itself well to cement, and causes a large amount of resilience and slurry shedding in actual field applications. due to these reasons, the new liquid accelerator is developed. composition of liquid accelerator (1) mother liquor preparation this liquid accelerator is mainly prepared by koh and al(oh)3 in a certain mole ratio, with the mole ratio of potassium to aluminum below 1.2. a certain amount of koh and al(oh)3 solid powder is weighed, poured into a three-necked flask, and reacted with added quantitative water. the temperature is controlled above 120℃, and the electric stirring rod is used to constantly stir the liquid during the reaction. the reaction is carried out for two hours, and the solution is filtered to obtain the mother liquor. (2) mother liquor compounding to improve its performance, other components are added with compound the mother liquor, including the polyacrylamide, triethanolamine, water reducing admixture, lithium salt, and stabilizer. this mother liquor is a kind of aluminate accelerator featuring small dosage and better coagulating effects. however, the single solution cannot meet various requirements of shotcrete and therefore the mother liquor is compounded. polyacrylamide is a kind of thickener used mainly to increase the cohesiveness of shotcrete and reduce resilience during construction, triethanolamine is a kind of early strength agent that can shorten the setting time, water reducing admixture is mainly to reduce water consumption and improve shotcrete strength, lithium salt can inhibit the alkali-aggregate reaction of shotcrete, stabilizer can effectively improve the stability of the solution. a l. zhang et alii, frattura ed integrità strutturale, 41 (2017) 356-368; doi: 10.3221/igf-esis.41.47 358 functional mechanism of liquid accelerator as a kind of compound aluminate accelerator, this liquid accelerator has the mole ratio of potassium to aluminum below 1.2 and its active ingredient is mainly aluminate ion. increasing the content of aluminate ion in the solution can give better play to accelerating effects. meanwhile, reducing the mole ratio of potassium to aluminum can reduce the alkalinity of the accelerator and inhibit the alkali-aggregate reaction of shotcrete. the main component of this liquid accelerator is kal(oh)4. given ca(oh)2, it reacts with gypsum in cement to produce calcium sulphoaluminate hydrates (ettringite) as well as potassium hydroxide, reduces the concentration of soluble gypsum for delayed coagulation in cement mortar. now, c3a, a cement mineral component, is quickly dissolved into the solution and hydrated to hexagonal c3ah6 plates, thus accelerating the setting of cement mortar. a large amount of heat of hydration produced by the preceding reactions will also promote the reaction process and strength development. in addition, in the initial hydration stage, those ingredients produced in the solution such as ca(oh)2, so42-, and al2o3 combine to produce high-sulfur calcium sulphoaluminate hydrate (ettringite) that is not only conducive to the development of early strength but also reduces the concentration of ca(oh)2, thus facilitating the hydration of c3s. the produced calcium silicate hydrate gel interlaps to form crystals with the grid structure, thus boosting condensation [7-16]. experimental studies on material properties experimental material he test cement adopts 425# ordinary portland cement, with the main components listed in tab. 1. components chemical formula shorthand notation mass fraction/% tricalcium silicate 3cao·sio2 c3s 17.83 dicalcium silicate 2cao·sio2 c2s 55.24 tricalcium aluminate 3cao·al2o3 c3a 10.12 tetra-calcium aluminoferrite 4cao·al2o3·fe2o3 c4af 7.81 calcium sulphate dihydrate caso4·2h2o csh2 8.0 table 1: main components of cement. test method (1) refer to the jc477-2005 flash setting admixtures for shotcrete standard (hereinafter referred to as the standard) in the building material industry. (2) get 400g cement with the water-cement ratio of 0.30 to 0.50 (the additive amount of water needs to deduct the water content in the liquid accelerator) to stir evenly, then add the recommended dosage of liquid accelerator, rapid mixing 25 s and 30 s, immediate loading mode, several times of artificial vibration, pare off excess water mud, make the surface clean. from adding liquid accelerator operating time should not exceed 50 s. the standard consistency and setting time of cement paste is adopted to measure the initial and final setting time of neat cement paste. different reagents are added with compound it and then the initial and final setting time is measured. (3) get 900g cement and 1350g standard sand, with the water-cement ratio of 0.5, mix the mortar uniformly, add the liquid accelerator, and quickly stir the cement mortar for 40 to 50 seconds. make a 40 mm x 40 mm x 160 mm trial model with cement mortar, maintain it in the standard curing room at the temperature of 20℃±2℃ and with humidity above 95%, measure its strength after one day or 28 days, and calculate the strength ratio. test results and analysis (1) measurement of the setting time of cement with different dosages according to the requirements of the standard, keep water-cement ratio of 0.4 unchanged, the dosages of liquid accelerator is 1.5% to 4% of the mass of cement. fig. 1 shows the initial and final setting time of neat cement paste with 1.5% to 4% dosages of this liquid accelerator. t l. zhang et alii, frattura ed integrità strutturale, 41 (2017) 356-368; doi: 10.3221/igf-esis.41.47 359 figure 1: dosage change curves of initial and final setting time the liquid accelerator has different setting time with different dosages. fig. 1 shows that this liquid accelerator has the best accelerating effects when the dosage is 2%. the initial and final setting time is 1min30s and 3min20s respectively, which meets the requirements of first-class goods stipulated in the standard. with increasing dosage, the setting time is delayed on the contrary. indicating that the liquid accelerator has an optimal dosage, it is not that more accelerators make better accelerating effects. whether the accelerator can quickly condense and harden cement also depends on accelerator adaptability to cement mineral compositions and gypsum types instead of all depending on accelerator dosage. as there are many interacting internal and external factors affecting accelerator adaptability to cement, the mechanism is very complex. therefore, the optimal accelerator dosage can only be the result of the adaptability test conducted on the used cement and accelerator in a proper water-cement ratio range and at a certain ambient temperature. a dosage lower or higher than the optimal will prevent the accelerator from playing its proper role in shotcrete application. (2) measurement of the setting time of cement with different water-cement ratios according to the requirements of the standard, keep 2% dosage of liquid accelerator unchanged, the water-cement ratio ranges from 0.30 to 0.50. fig. 2 shows the initial and final setting time of cement with different water-cement ratios. figure 2: water-cement ratio change curves of initial and final setting time. according to fig. 2, as the water-cement ratio increases, the initial and final setting time is prolonged. indicating that the greater the water-cement ratio, the worse the accelerating effects. in dry-mix shotcrete, the water-cement ratio is controlled by adjusting the water volume by the shotcrete manipulator based on his observation. the mixture water consumption in dry shotcrete should not only make the shotcrete have better compaction and adhesiveness but also reduce resilience materials. a too large water-cement ratio usually causes shotcrete to fall off while a too small watercement ratio causes stratification to mixtures. in wet-mix shotcrete, the water-cement ratio is specific and needs to meet properties such as the slump and pumpability. (3) impact of the accelerator with different dosages on the strength of cement mortar 50 100 150 200 250 300 350 1,5 2,0 2,5 3,0 3,5 4,0 s et ti n g t im e/ s dosage of liquid accelerator/% initial setting time final setting time 50 100 150 200 250 300 350 0,30 0,35 0,40 0,45 0,50 s et ti n g t im e/ s water-cement ratio initial setting time final setting time l. zhang et alii, frattura ed integrità strutturale, 41 (2017) 356-368; doi: 10.3221/igf-esis.41.47 360 the compressive strength of cement mortar with different dosages is obtained. as the accelerator dosage increases, the later strength loss tends to increase. however, if the dosage ranges from 1.5% to 4%, the later strength loss will not exceed 10%. tab. 2 shows the compressive strength of cement mortar. accelerator dosage/% compressive strength/mpa 28d compressive strength ratio/% 1d 28d 0 7.8 47.8 100 1.5 13.6 46.9 98.1 2.0 13.9 46.1 96.4 2.5 14.5 45 94.1 3.0 15.1 44.6 93.3 3.5 15.8 43.7 91.4 4.0 14.2 43.1 90.2 table 2: compressive strength of cement mortar. numerical calculation strength-time and elasticity modulus-time regression curve of shotcrete n the lab, the hardening characteristics of shotcrete are tested. shotcrete adopts c25 mix proportion (selected from changgang tunnel of fushou highway) of cement, sand, to stone as 469 : 912 : 912. non-linear regression analysis is conducted on shotcrete strength and time, and then the change rules between the strength and age are obtained. tab. 3 lists the uniaxial compressive strength of shotcrete added with the traditional accelerator. tab. 4 lists the uniaxial compressive strength of shotcrete added with the new liquid accelerator. age specimen no. 8h/mpa 12h/mpa 1d/mpa 3d/mpa 7d/mpa 28d/mpa 1 4.35 6.80 9.52 14.6 21.89 25.4 2 5.05 7.22 10.25 15.40 20.76 26.38 3 4.92 6.95 9.80 14.88 22.12 27.10 4 4.36 6.50 9.30 15.72 23.30 26.70 5 4.8 7.10 10.64 16.20 21.66 25.89 6 4.45 6.83 9.13 14.67 23.20 27.80 7 4.82 7.25 10.37 15.60 21.37 28.31 8 6.15 7.64 11.28 16.38 22.50 29.25 9 5.20 7.30 9.95 14.68 21.86 27.97 table 3: uniaxial compressive strength of shotcrete added with the traditional accelerator. age specimen no. 8h/mpa 12h/mpa 1d/mpa 3d/mpa 7d/mpa 28d/mpa 1 7.25 8.99 12.75 19.39 27.48 31.06 2 7.37 9.53 14.15 20.12 26.66 31.66 3 7.34 9.71 13.29 19.72 27.97 32.60 4 6.38 9.18 12.76 20.30 28.69 32.18 5 7.18 9.47 14.59 20.86 27.65 31.88 6 7.01 8.95 12.80 19.28 28.44 33.17 7 7.35 9.73 13.53 19.89 27.11 34.21 8 8.16 9.98 14.33 20.97 27.84 34.95 9 7.46 10.27 13.45 19.17 27.72 33.65 table 4: uniaxial compressive strength of shotcrete added with the new liquid accelerator. i l. zhang et alii, frattura ed integrità strutturale, 41 (2017) 356-368; doi: 10.3221/igf-esis.41.47 361 take a log-scale for time, get the strength-time regression curve of shotcrete with the traditional accelerator and with the new liquid accelerator, as shown in fig.3. figure 3: strength-time regression curve of shotcrete added with accelerator. the strength of shotcrete with the traditional accelerator associated with time is determined as -0.38 t -0.009 t25.6(1 1.85 e 0.8 e )cf (t) = (1) the strength of shotcrete with the new liquid accelerator associated with time is determined as    0.18 0.01( ) 31.2(1 0.27 0.77 )t tcf t e e (2) the researcher obtained the following formula of elasticity modulus obtained via tests and shotcrete compressive strength [17]:   5 10 c cu e b a f (3) the fitted values of a and b can be obtained by fitting shotcrete elasticity modulus (listed in tab. 5) and uniaxial compressive strength by using formula (3) according to the gb50086-2001 specifications for bolt-shotcrete support. formula (4) for the relation between shotcrete and compressive strength can be obtained by using formula (3). shotcrete strength grade c15/mpa c20/mpa c25/mpa c30/mpa elasticity modulus 1.8x104 2.1x104 2.3x104 2.5x104 uniaxial compressive strength 15.0 20.0 25.0 30.0 table 5: standard values of shotcrete elasticity modulus and uniaxial compressive strength. 5 10 46.12 2.46   c cu e f (4) l. zhang et alii, frattura ed integrità strutturale, 41 (2017) 356-368; doi: 10.3221/igf-esis.41.47 362 tab. 6 lists the elasticity modulus of shotcrete added with the traditional accelerator obtained by using formula (4). tab. 7 lists the elasticity modulus of shotcrete added with the new liquid accelerator obtained by using formula (4). fig. 4 shows the elasticity modulus-time regression curve of shotcrete added with the traditional accelerator. age specimen no. 8h/gpa 12h/gpa 1d/gpa 3d/gpa 7d/gpa 28d/gpa 1 7.66 10.82 13.69 17.80 21.90 23.39 2 8.63 11.30 14.37 18.33 21.36 23.76 3 8.45 10.99 13.95 17.99 22.00 24.03 4 7.67 10.47 13.48 18.54 22.53 23.88 5 8.29 11.17 14.72 18.84 21.79 23.58 6 7.80 10.85 13.31 17.84 22.48 24.28 7 8.31 11.34 14.48 18.46 21.65 24.46 8 10.04 11.77 15.27 18.96 22.17 24.77 9 8.83 11.39 14.09 17.85 21.88 24.34 table 6: elasticity modulus of shotcrete added with the traditional accelerator age specimen no. 8h/gpa 12h/gpa 1d/gpa 3d/gpa 7d/gpa 28d/gpa 1 11.33 13.17 16.45 20.67 24.16 25.35 2 11.47 13.70 17.48 21.04 23.87 25.53 3 11.44 13.87 16.86 20.84 24.34 25.81 4 10.32 13.36 16.47 21.13 24.58 25.69 5 11.25 13.65 17.79 21.41 24.22 25.60 6 11.06 13.13 16.49 20.61 24.50 25.97 7 11.45 13.89 17.04 20.93 24.03 26.26 8 12.33 14.12 17.61 21.46 24.29 26.46 9 11.57 14.38 16.98 20.55 24.25 26.11 table 7: elasticity modulus of shotcrete added with the new liquid accelerator take a log-scale for time, get the elasticity modulus-time regression curve of shotcrete with the traditional accelerator and with the new liquid accelerator, as shown in fig.4. figure 4: elasticity modulus-time regression curve of shotcrete added with accelerator the elasticity modulus of shotcrete with the traditional accelerator associated with time is determined as l. zhang et alii, frattura ed integrità strutturale, 41 (2017) 356-368; doi: 10.3221/igf-esis.41.47 363 -0.274 t -0.012 t23.5(1 1.5 e 0.56 e )e(t) = (5) the elasticity modulus of shotcrete with the new liquid accelerator associated with time is determined as -0.127 t -0.013 t25.4(1 0.39 e 0.46 e )e(t) = (6) model building and parameter selection (1) mechanical parameter numerical simulation adopts flac3d numerical software to study the cross section of class iv surrounding rock of changgang tunnel, fushou highway and consider the stress release rate of surrounding rock. the model dimension is twice of the diameter that is 12 m. both surrounding rock and preliminary support adopt solid elements. normal restraint is set on the lateral boundary and full restraint is set on the surface boundary of the model. considering the hardening characteristics of shotcrete with time, set poisson's ratio to 0.2 and volume density to 2300 kg/m3. tab. 8 lists the physical and mechanical parameters of the selected surrounding rock. surrounding rock class unit weight (kn/m3) deformation modulus /gpa poisson's ratio cohesion /mpa internal friction angle/° iv 20 1.3 0.3 0.2 27 table 8: physical and mechanical parameters of surrounding rock. (2) stress release rules of surrounding rock according to the natm theory, after tunnel excavation, the stress of surrounding rock is gradually released with time under the action of the self-stabilization capacity of surrounding rock instead of being immediately released. document [18] proposed the following expression of the load released by tunnel with time based on numerical simulation results:  0( ) (1 0.7 ) mtp t p e where:  3.15 2 v m a v : tunnel excavation progress, m/h a : tunnel excavation radius, m t : tunnel excavation time, h this formula can be used to resolve the following formula of stress release rate of surrounding rock:  1 0.7 mtn e this calculation adopts the preceding stress release rules of surrounding rock and simulates surrounding rock release of this expansive loess tunnel. therefore,  1 / 6 v m h , a=6m, thus determining that the curve of surrounding rock release rules is as shown in fig. 5. calculation result analysis (1) largest vault settlement displacement the shotcrete added with the traditional and new liquid accelerator respectively is studied. fig. 6 shows the largest displacement of vault settlement when the shotcrete added with the conventional and new liquid accelerator respectively interacts with surrounding rock with the passage of time. l. zhang et alii, frattura ed integrità strutturale, 41 (2017) 356-368; doi: 10.3221/igf-esis.41.47 364 figure 5: surrounding rock release rules. figure 6: largest vault settlement displacement. according to fig. 6, the largest vault settlement displacement of surrounding rock, shotcrete added with the new liquid accelerator is smaller than that when the shotcrete added with the traditional accelerator interacts with surrounding rock, indicating that the shotcrete added with the new liquid accelerator has better supporting effects for surrounding rock. take an average of the largest settlement displacements of 8h, 12h, 1d, 3d, 7d, and 28d surrounding rock. this value is 3.59 when the traditional accelerator is used while it is 2.66 when the new liquid accelerator is added, which improves supporting effects by 26%. in the first three days of shotcrete support, the largest vault displacement of surrounding rock keeps growing. that is because the tunnel surrounding rock releases stress and forms new stress equilibrium. the release process is accompanied with vault settlement. from 0 to 72h, the largest vault displacement is 3.17 mm during spraying concrete support added with the traditional accelerator while that is 1.84 mm during spraying concrete support added with the new liquid accelerator, with the change rate decreased by 42%. three days later, stress release of surrounding rock is reduced, meanwhile, the vault settlement is reduced and surrounding rock tends to be stable due to the support. on the 28th day, the largest settlement displacement is 3.82 mm when shotcrete added with the traditional accelerator, and it is 2.41 mm when shotcrete added with the new liquid accelerator, reduced by 37%. (2) distribution of surrounding rock plastic zones 12h, 1d, and 3d plastic zones are selected to study the development of plastic zones of surrounding rock supported by different kinds of shotcrete. according to analysis on fig. 7 to 12, the surrounding rock plastic zones are mainly distributed on the cavern haunch and side wall. with the passage of time, the plastic zone gradually extends to the tunnel deep and arch springing. it also can be seen from the figures that the plastic zone of surrounding rock supported by shotcrete added with new liquid accelerator is obviously smaller than that of surrounding rock supported by shotcrete added with the traditional accelerator. 0,0 0,1 0,2 0,3 0,4 0,5 0,6 0,7 0,8 0,9 1,0 0 18 36 54 72 90 108 126 144 162 180 s u rr o u nd in g ro ck s tr es s re le as e ra te excavation time/h l. zhang et alii, frattura ed integrità strutturale, 41 (2017) 356-368; doi: 10.3221/igf-esis.41.47 365 figure 7: 12h traditional support plastic zone. figure 8: 12h new support plastic zone. figure 9: 1d traditional support plastic zone. figure 10: 1d new support plastic zone. figure 11: 3d traditional support plastic zone. figure 12: 3d new support plastic zone. engineering application project overview he field test is conducted on the developed new liquid accelerator in changgang tunnel of fushou highway. this tunnel is class iv surrounding rock; the strength grade of shotcrete is designed to c25 and the shotcrete layer depth to 25 cm. the field shotcrete adopts hong xing-1 powdered accelerator; the dry jet machine adopts 7 m3; the actual amount of sprayed concrete per hour is about 5 m3. the dry powdered accelerator has the actual dosage reaching 10%, about 30% resilience, and large amount of dust during spraying. fig. 13 shows the field dry-mix shotcrete. t l. zhang et alii, frattura ed integrità strutturale, 41 (2017) 356-368; doi: 10.3221/igf-esis.41.47 366 figure 13: field dry-mix shotcrete. field shotcrete test (1) cement: 425# ordinary portland cement. fine aggregate: used in the test is hard medium-coarse sand with the fineness modulus greater than 2.5. the proportion of particles with the diameter less than 0.075 mm among sand cannot be exceed 20%. coarse aggregate: used in the test is crushed stone with the particle diameter ranging from 5 to 10 mm. (2) the concrete mix proportion of cement, sand, to stone as 469kg : 912kg : 912kg, the water-cement ratio is designed to 0.45. (3) the dosage of the liquid accelerator is designed to 1.5% during spraying on the side wall and that is designed to 2.5% during spraying on the vault. given a larger dosage, the cohesiveness of shotcrete becomes better and slurry shedding can hardly happen. the dosage is controlled by the high-pressure dosing device. this liquid accelerator is used together with a matching shotcrete method. based on the original dry-mix shotcrete technology, a high-pressure accelerator dosing device is added, which can provide 1.2 mpa pressure to pump the liquid accelerator to the high-pressure water pipe and accurately control the dosage of the liquid accelerator. the mixture of the liquid accelerator and water contacts with the concrete mix at the nozzle and are sprayed to the surface together. using the new liquid accelerator and matching spraying technology, the dust and resilience in the tunnel are relatively little. the pull canvas is adopted to measure resilience and the resilience rate is 8%. the sprayed surface has bright luster, without slurry shedding. fig. 14 shows the liquid accelerator matching spraying technology. fig.15 shows the new field shotcrete technology. figure 14: the liquid accelerator matching spraying technology. figure 15: new field shotcrete technology. during field spraying concrete, the jet molding test is conducted to measure the strength of shotcrete. the specimen is a 150 mm3 cube template that is grounded flush after tunnel shotcrete. then, it is maintained in the lab incubator and the 1d, 7d, and 28d uniaxial compressive strength are measured, as listed in tab. 9. the test results show that shotcrete using this liquid accelerator has a higher compressive strength. l. zhang et alii, frattura ed integrità strutturale, 41 (2017) 356-368; doi: 10.3221/igf-esis.41.47 367 specimen sn age/d bearing area/mm2 compressive strength fcu /mpa single block value group value 1 1 22500 13.4 12.6 2 22500 12.5 3 22500 11.9 1 7 22500 27.8 27.1 2 22500 26.9 3 22500 26.6 1 28 22500 33.5 32.4 2 22500 31.6 3 22500 32.2 table 9: compressive strength of shotcrete. conclusions (1) the dosage of this liquid accelerator is small, only from 1.5% to 4%, and it is an effective compound liquid accelerator. when the dosage is 2%, the effects of coagulation are optimal. the initial and final setting time of neat cement paste is 2 minutes and 4 minutes respectively. it is also a kind of uniform and stable liquid without crystals and precipitate, and it is slightly affected by the ambient and well adaptive to cement. (2) this liquid accelerator contains the thickening components, which increase the cohesiveness of shotcrete and can effectively reduce resilience and dust during spraying concrete. meanwhile, it increases the adhesion strength between shotcrete and surrounding rock, be adhered to the sprayed surface comprehensively and solidly, and achieve better supporting effects. (3) this liquid accelerator can effectively reduce the later strength loss of shotcrete and ensure that the strength loss is controlled within 10%. adding this liquid accelerator can improve the strength of shotcrete at each age and effectively inhibit the development of displacement and plastic zones of surrounding rock. in the numerical simulation analysis of the relationship between shotcrete and surrounding rock support, the strength growth of shotcrete and stress release of surrounding rock with the passage of time should be considered. (4) the new liquid accelerator and its matching spraying technology can effectively reduce resilience and dust in the construction, the resilience rate is less than 10%, save the cost, improve the environment, enhance the shotcrete strength, have good popularization using value. acknowledgements he authors would like to thank the national natural science foundation of china (grant no. 51179098、 51379113), the specialized research fund for the doctoral program of higher education of china (grant no. 20120131110031). references [1] guan, b., technique of shotcrete support for tunnel and underground works[m]. beijing: china communications press, (2009). [2] zhu, g., progress of the research for shotcrete, concrete, 258(4) (2011) 105-109. [3] cheng, l., shotcrete, beijing: china architecture and building press, (1990). [4] feng, h., zhu, q., handbook of engineering application of concrete admixture, beijing: china architecture & t l. zhang et alii, frattura ed integrità strutturale, 41 (2017) 356-368; doi: 10.3221/igf-esis.41.47 368 building press, (2005). [5] chang, y., the influences of the early age properties of shotcrete on tunnel lining, journal of yangtze river scientific research institute, 9(3) (1992) 8-16. [6] oreste, p.p., peila, d., modeling progressive hardening of shotcrete in convergence-confinement approach to tunnel design, tunneling and underground space technology, 12(3) (1997) 425-431. [7] shen, w., cement technology wuhan: wuhan university of technology press, (2012). [8] li, g., li, c., zhou, w., wu, y., factors affecting the liquid sodium aluminate accelerated agent, concrete, 7 (2005) 54-58. [9] zhang, y., he, t., et al. the influences of synthetic technology parameters on the properties of liquid aluminate accelerating additive, concrete, 4 (2005) 38-41. [10] li, g., song, x., et al. synergistic effects of some other ingredients on liquid sodium aluminate accelerated agent, concrete, (4) (2005) 49-51. [11] zhang, y., study on liquid aluminate accelerating additive, master's thesis, xi'an: xi'an university of architecture and technology, (2005). [12] hae-geun, p., sang-kyoung, s., chan-gi, p., jong-pil, w., influence of a c12a7 mineral-based accelerator on the strength and durability of shotcrete, cement and concrete research, 38(3) (2008) 379–385. [13] jong-pil, w., un-jong, h., cheol-keun, k., su-jin, l., mechanical performance of shotcrete made with a highstrength cement-based mineral accelerator, construction and building materials, 49 (2013) 175–183. [14] paglia, c., wombacher, f., bohni, h., the influence of alkali-free and alkaline shotcrete accelerators within cement systems influence of the temperature on the sulfate attack mechanisms and damage, cement and concrete research, 33 (2003) 387–395. [15] zhao, s., guo, x., xia, y., zuo, m., study on the performance and mechanism of the liquid sodium aluminate accelerated agent, journal of shenyang jianzhu university (natural science), 25(6) (2009) 1125-1130. [16] li, g., regulation and mechanism of adjustable solidification agent on cement hydration process, master's thesis, wuhan: wuhan university of technology, (2011). [17] chen, f., application and mechanism of initial support and surrounding rock in weak rock tunnel, phd thesis, beijing: beijing jiaotong university, (2012). [18] liu b., du x., visco-elastical analysis on interaction between supporting structure and surrounding rocks of circle tunnel, chinese journal of rock mechanics and engineering, 23(4) (2004) 561-564. << /ascii85encodepages false /allowtransparency false /autopositionepsfiles true /autorotatepages /none /binding /left /calgrayprofile (dot gain 20%) /calrgbprofile (srgb iec61966-2.1) /calcmykprofile (u.s. web coated \050swop\051 v2) /srgbprofile (srgb iec61966-2.1) /cannotembedfontpolicy /error /compatibilitylevel 1.4 /compressobjects /tags /compresspages true /convertimagestoindexed true /passthroughjpegimages true /createjobticket false /defaultrenderingintent /default /detectblends true /detectcurves 0.0000 /colorconversionstrategy /cmyk /dothumbnails false /embedallfonts true /embedopentype false /parseiccprofilesincomments true /embedjoboptions true /dscreportinglevel 0 /emitdscwarnings false /endpage -1 /imagememory 1048576 /lockdistillerparams false /maxsubsetpct 100 /optimize 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/hrv (za stvaranje adobe pdf dokumenata najpogodnijih za visokokvalitetni ispis prije tiskanja koristite ove postavke. stvoreni pdf dokumenti mogu se otvoriti acrobat i adobe reader 5.0 i kasnijim verzijama.) /hun 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can be opened with acrobat and adobe reader 5.0 and later.) >> /namespace [ (adobe) (common) (1.0) ] /othernamespaces [ << /asreaderspreads false /cropimagestoframes true /errorcontrol /warnandcontinue /flattenerignorespreadoverrides false /includeguidesgrids false /includenonprinting false /includeslug false /namespace [ (adobe) (indesign) (4.0) ] /omitplacedbitmaps false /omitplacedeps false /omitplacedpdf false /simulateoverprint /legacy >> << /addbleedmarks false /addcolorbars false /addcropmarks false /addpageinfo false /addregmarks false /convertcolors /converttocmyk /destinationprofilename () /destinationprofileselector /documentcmyk /downsample16bitimages true /flattenerpreset << /presetselector /mediumresolution >> /formelements false /generatestructure false /includebookmarks false /includehyperlinks false /includeinteractive false /includelayers false /includeprofiles false /multimediahandling /useobjectsettings /namespace [ (adobe) (creativesuite) (2.0) ] /pdfxoutputintentprofileselector /documentcmyk /preserveediting true /untaggedcmykhandling /leaveuntagged /untaggedrgbhandling /usedocumentprofile /usedocumentbleed false >> ] >> setdistillerparams << /hwresolution [2400 2400] /pagesize [612.000 792.000] >> setpagedevice microsoft word numero_37_art_18 m. vieira et alii, frattura ed integrità strutturale, 37 (2016) 131-137; doi: 10.3221/igf-esis.37.18 131 focussed on multiaxial fatigue and fracture development of a very high cycle fatigue (vhcf) multiaxial testing device m. vieira, m. de freitas, l. reis, a. m. r. ribeiro idmec, instituto superior técnico, universidade de lisboa, av. rovisco pais, 1049-001 lisboa, portugal, mario.vieira@ist.utl.pt, mfreitas@dem.ist.utl.pt http://orcid.org/0000-0003-3525-9218 luis.g.reis@ist.utl.pt http://orcid.org/0000-0001-9848-9569 aribeiro@ist.utl.pt http//orcid.org/0000-0001-2345-6789 m. da fonte escola superior náutica infante d. henrique, av. eng. bonneville franco 2770-058 paço d'arcos, portugal manuelfonte@enautica.pt http://orcid.org/0000-0002-2345-6790 abstract. the very high cycle region of the s-n fatigue curve has been the subject of intensive research on the last years, with special focus on axial, bending, torsional and fretting fatigue tests. very high cycle fatigue can be achieved using ultrasonic exciters which allow for frequency testing of up to 30 khz. still, the multiaxial fatigue analysis is not yet developed for this type of fatigue analyses, mainly due to conceptual limitations of these testing devices. in this paper, a device designed to produce biaxial fatigue testing using a single piezoelectric axial exciter is presented, as well as the preliminary testing of this device. the device is comprised of a horn and a specimen, which are both attached to the piezoelectric exciter. the steps taken towards the final geometry of the device are presented. preliminary experimental testing of the developed device is made using thermographic imaging, strain measurements and vibration speeds and indicates good behaviour of the tested specimen. keywords. multiaxial fatigue; very high cycle fatigue; fatigue testing machines; strain measurements. introduction atigue damage has special relevance on the life span of mechanical components and structures, as it takes responsibility for the majority of the registered structural failures. although its mechanisms have been the subject of continuous research, the growing need for greater lifespans forced the understanding of the behavior of materials under very high cycle loadings [1], also known as the very high cycle fatigue (vhcf) regime. this field of research, which studies the mechanical behavior of materials for fatigue lives over 10e7 cycles, has recently gained notoriety [2], largely due to the appearance of ultrasonic fatigue testing machines, working at 20-30 khz and due to the acquisition and control equipment capable of handling signals at such high frequencies. in this context, the results found in the bibliography [1, 2], which usually focus on either axial or torsional fatigue tests, allow us to understand the behavior of materials on the very high cycle region of the s-n curves, remarking the absence, f m. vieira et alii, frattura ed integrità strutturale, 37 (2016) 131-137; doi: 10.3221/igf-esis.37.18 132 for some materials, of the fatigue limit that used to be considered on mechanical design. however, these results only refer to uniaxial loadings when, in real conditions, mechanical components are usually loaded under multiaxial loadings. because of the axial character of the excitation created by the piezoelectric exciter, only axial, bending or fretting specimen testing were able to be performed up to now. the appearance of torsional piezoelectric exciters allowed for vhcf testing on torsional conditions, as well. but, for multiaxial conditions, no vhcf results have been described on the literature due to conceptual limitations of these devices. multiaxial loading fatigue has been the subject of intense research for low and high cycle regimes, but not on the vhcf region, due to the inexistence of machines capable of operating on ultrasonic frequencies and submit specimens to multiaxial loadings. for the high cycle regime, the von mises criterion on biaxial loading has been questioned since experimental data does not correlate well, either for in-phase or out-of-phase loadings [3]. in this paper, the development of a fatigue testing machine for biaxial conditions working at vhcf is presented. the device is comprised of a horn and a specimen, which are both attached to an ultrasonic piezoelectric axial exciter. biaxial fatigue testing machine for vhcf he present work describes the processes of creation and development of a vhcf testing device for biaxial conditions, using a single axial piezoelectric exciter. the device is comprised of a horn and a specimen, being the latter the component to be tested on biaxial conditions, with a loading that was predefined to have in-phase sinusoidal components of axial and shear stress in r=-1. the horn since the horn receives a sinusoidal axial displacement from the piezoelectric exciter, and it is intended to induce also torsional loadings on the specimen, the horn has to be responsible for the generation of the rotational movement which will be imposed on the specimen and will promote shear stresses in it. this implies that the horn takes special importance on the behavior of the device, specifically on the relationship between axial and torsional loadings imposed on the specimen. the computational modal analysis made to this geometry proved that a certain dynamic vibrational mode could be achieved in which the horn would vibrate in a hybrid mode composed by the first axial mode and the first torsional mode, where axial and rotational displacements were amplified on the smaller free end. still, there was a need for a horn that would possess this specific mode on the frequency at which the exciter operates (20 khz). the iterative process to obtain the final geometry was produced using finite element software, and a schematic representation is shown on fig. 1: figure 1: 2d representation of the developed biaxial horn. the final horn geometry consists of a conical shaped piece possessing two groups of oblique slits responsible for the generation of the rotational character of the horn, which in turn will promote sinusoidal rotations on the specimen that will add to the already existent sinusoidal axial excitation. the specimen before introducing the final geometry of the used specimen, it might be interesting to analyze the dynamic equation for a generic bar, eq. 1, [1]: t m. vieira et alii, frattura ed integrità strutturale, 37 (2016) 131-137; doi: 10.3221/igf-esis.37.18 133 2 2 2 2 x ue t u       (1) where u is the displacement, t is time, e is the young modulus, x is the associated coordinate system and  is the specific mass of the material. the mathematical solution of eq. 1 is:             l ct sen l xn cosa)x(u  0 (2) where a0 is the generic amplitude of vibration, l is the bar length and c is the wave propagation speed. eq. 2 represents the axial displacement along the generic bar, respective to a certain nth mode, while eq. 3 represents the natural non-damped frequency, n for the nth mode.    e l n n  (3) the solution found at eqs. 2 and 3 are equally valid for torsional modes, replacing the young modulus by the shear modulus of a certain material. solving the equation for a cylindrical bar with a length of 250 mm (and noting that for this solution, the diameter of the bar does not affect the final results), the following results are obtained for the first five modal non-damped frequencies for the axial and torsional directions for common construction steel (e=200 gpa, =7800 kg/m3): axial frequencies torsional frequencies n (rad/s) hz n (rad/s) hz 0 0.0 0.0 0 0.0 0.0 1 63632.3 10127.4 1 40244.6 6405.1 2 127264.6 20254.8 2 80489.2 12810.3 3 190896.9 30382.2 3 120733.8 19215.4 4 254529.2 40509.6 4 160978.4 25620.5 table 1: first five modal frequencies for axial and torsional directions. obviously, and due to the differences found between the young and shear modulus, the results are lagged by a certain ratio. this implies that, for a cylindrical shape, the first axial mode will have a significative different frequency value from the respective first torsional mode. if a cylindrical shaped specimen is pretended, this raises a relevant problem to the creation design. one could think, from the analysis of tab. 1, that the second longitudinal mode (n=2) and the third torsional mode (n=3) could be used to design a specimen to produce biaxial testing, since frequencies are very close together. still, this solution is of little application since, because of the shapes of these two modes, axial and shear stresses on specimen would be higher on different locations. other combinations of modes were considered, but the final design consisted of a specimen that possesses its first axial mode (n=1) and its third torsional mode (n=3) at the same frequency. this is achieved by designing a cylindrical specimen with three throats, as seen in fig. 2: figure 2: 2d representation of the developed specimen. m. vieira et alii, frattura ed integrità strutturale, 37 (2016) 131-137; doi: 10.3221/igf-esis.37.18 134 generally speaking, while the presence of the middle throat lowers the first axial and torsional modes, the presence of the two outside throats is used to considerably lower the third torsional mode. the correspondent first axial mode shape and third torsional mode shape of the developed specimen are presented on fig. 3, both having the same inherent natural frequency: figure 3: representation of the specimen first axial mode (at left) and third torsional mode (at right), both with the same natural frequency. coupling of the horn, specimen and exciter after the specimen and horn have been designed, it became mandatory to produce computational analyses to understand the dynamic behavior of the coupled system, formed by the booster, horn and specimen. a computational model of the developed system was built, shown in fig. 4. then, finite element analyses were run in order to obtain the mode shape at the pretended frequency, as shown in fig. 5. figure 4: 3-dimensional model of the developed device. figure 5: modal shape of the operational mode for the developed device. the developed device is patent pending under inpi 20161000008542 ref. number. experimental testing of the device fter the theoretical definition of the equipment, a prototype of the design was built in order to produce several experimental testing to evaluate its correct behaviour. laser vibrometer results in order to correctly evaluate rotation on the specimen, two notches were created at the bottom of the specimen. these notches are used to measure surface speeds. speeds are measured using a vibrometer from polytec with two laser channels, with high frequency measuring capabilities. results obtained from these experimental testing have already been published [4]. axial speeds measured at the free-end of the specimen are presented below, fig. 6: a m. vieira et alii, frattura ed integrità strutturale, 37 (2016) 131-137; doi: 10.3221/igf-esis.37.18 135 figure 6: axial speeds measured at the free-end of the tested specimen [4]. these results confirm the sinusoidal axial behaviour of the specimen. rotational speeds measured at the notches are presented on fig. 7: figure 7: rotational speeds measured at the specimen notches [4]. these results confirm the presence of a rotational behaviour of the specimen at its free-end, since both signals are inphase and with very similar amplitudes. the difference in the amplitudes comes from the difficulty to guarantee that both lasers are measuring at the same distance from the center of the specimen. thermographic imaging because of the high frequencies used on this type of specimen testing, material temperature control represents a challenge on the completion of such tests [1, 5]. still, because of the fact that the specimen heats up faster on regions where stresses are higher, thermographic imaging may be used to evaluate an approximation of the stress profile on the specimen. for this evaluation, the specimen was painted with high emissivity paint. first, the specimen was tested using an axial horn, which means that no rotation was being imposed to it. the results of this test are represented on fig. 8, and axial testing of the specimen confirmed that it is correctly synchronized at the exciter excitation frequency and higher temperature are only observed in the middle throat. figure 8: thermographic image sequence of the axial tests performed on the specimen. second testing was produced with the developed horn, showing also higher temperatures occurring at the three throats with the highest one at middle throat, fig. 9. m. vieira et alii, frattura ed integrità strutturale, 37 (2016) 131-137; doi: 10.3221/igf-esis.37.18 136 figure 9: thermographic image of specimen testing in tension/torsion. thermographic imaging of the developed specimen indicates that the specimen heats up on the three throats, but more on the middle one, due to the higher stresses on this region, as it was designed to behave. strain results to evaluate strains and stresses on the specimen middle throat, a rosette-type strain gage with three gages from tml, reference fra-1-11, was used. figure 10: signals from the rosette strain gage at the specimen middle throat. data from the strain gages during test was measured with a ni 6216 daq with the capability of acquiring two signals with a 200 khz sampling frequency. testing was produced at 20 khz, using the biaxial horn and specimen and the results obtained from the three-way strain gage installed at the middle throat of the specimen are presented on fig. 10. data confirms the existence of a tension/torsion stress field in the specimen middle throat [4]. conclusions device to produce biaxial testing at the vhcf regime, using a single axial ultrasonic exciter, has been developed and presented on this paper. this device (patent pending) consists of a horn and a specimen featured together in order to allow the biaxial testing. a m. vieira et alii, frattura ed integrità strutturale, 37 (2016) 131-137; doi: 10.3221/igf-esis.37.18 137 extensive experimental analyses were produced in order to qualitatively evaluate the dynamic behaviour of the device, specifically on the specimen. laser vibrometer measurements have confirmed the correct axial and rotational behaviour of the free-end of the specimen. thermographic imaging comproved that maximum stresses are registered at the middle throat. a three-way rosette type strain gage was installed on the middle throat in order to acquire strains and evaluate the stresses present on this region, confirming the existence of a biaxial stress state. further research is strongly suggested on this field, specifically on specimen control and behaviour, horn geometry influence on the τxy/σy stress ratio and final specimen dimension. acknowledgments his research was financed by fundação para a ciência e tecnologia (fct) under portuguese national project ptdc/ems-pro/5760/2014. references [1] bathias, c., paris, p., gigacycle fatigue in mechanical practice, marcel dekker, new york, (2005) [2] stanzl-tschegg, s., very high cycle fatigue measuring techniques, international journal of fatigue, 60 (2014) 2–17, doi:10.1016/j.ijfatigue.2012.11.016. [3] anes, v., reis, l., li, b., freitas, m., sonsino, c., minimum circumscribed ellipse (mce) and stress scale factor (ssf) criteria for multiaxial fatigue life assessment, theoretical and applied fracture mechanics, 73 (2014) 109-119. doi:10.1016/j.tafmec.2014.08.008. [4] vieira, m., reis, l., de freitas, m., ribeiro, a. m. r., preliminary evaluation of the loading characteristics of biaxial tests at low and very high frequencies procedia structural integrity, (2016). doi: 10.1016/j.prostr.2016.02.027. [5] lage, y., ribeiro, amr, montalvão, d., reis, l., freitas, m., automation in strain and temperature control on vhcf with an ultrasonic testing facility application of automation technology in fatigue and fracture testing and analysis, peter c. mckeighan and arthur a. braun, eds., stp 1571, (2014) 80–100, doi:10.1520/stp157120130079, astm international, west conshohocken, pa, doi: 10.1520/stp157120130079. t << /ascii85encodepages false /allowtransparency false /autopositionepsfiles true /autorotatepages /none /binding /left /calgrayprofile (dot gain 20%) /calrgbprofile (srgb iec61966-2.1) /calcmykprofile (u.s. web coated \050swop\051 v2) /srgbprofile (srgb iec61966-2.1) /cannotembedfontpolicy /error /compatibilitylevel 1.4 /compressobjects /tags /compresspages true /convertimagestoindexed true /passthroughjpegimages true /createjobticket false /defaultrenderingintent /default /detectblends true /detectcurves 0.0000 /colorconversionstrategy /cmyk /dothumbnails false /embedallfonts 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/hrv (za stvaranje adobe pdf dokumenata najpogodnijih za visokokvalitetni ispis prije tiskanja koristite ove postavke. stvoreni pdf dokumenti mogu se otvoriti acrobat i adobe reader 5.0 i kasnijim verzijama.) /hun 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can be opened with acrobat and adobe reader 5.0 and later.) >> /namespace [ (adobe) (common) (1.0) ] /othernamespaces [ << /asreaderspreads false /cropimagestoframes true /errorcontrol /warnandcontinue /flattenerignorespreadoverrides false /includeguidesgrids false /includenonprinting false /includeslug false /namespace [ (adobe) (indesign) (4.0) ] /omitplacedbitmaps false /omitplacedeps false /omitplacedpdf false /simulateoverprint /legacy >> << /addbleedmarks false /addcolorbars false /addcropmarks false /addpageinfo false /addregmarks false /convertcolors /converttocmyk /destinationprofilename () /destinationprofileselector /documentcmyk /downsample16bitimages true /flattenerpreset << /presetselector /mediumresolution >> /formelements false /generatestructure false /includebookmarks false /includehyperlinks false /includeinteractive false /includelayers false /includeprofiles false /multimediahandling /useobjectsettings /namespace [ (adobe) (creativesuite) (2.0) ] /pdfxoutputintentprofileselector /documentcmyk /preserveediting true /untaggedcmykhandling /leaveuntagged /untaggedrgbhandling /usedocumentprofile /usedocumentbleed false >> ] >> setdistillerparams << /hwresolution [2400 2400] /pagesize [612.000 792.000] >> setpagedevice microsoft word numero_59_art_29_3324.docx m. gaci, frattura ed integrità strutturale, 59 (2022) 444-460; doi: 10.3221/igf-esis.59.29 444 numerical study of trip transformation in 35ncd16 steel-effects of plate orientation and some criteria mounir gaci laboratory of mechanics, university frères mentouri constantine 1, constantine, algeria mounir.gaci@umc.edu.dz kamel fedaoui, lazhar baroura university frères mentouri constantine 1, constantine, algeria kamel.fedaoui@umc.edu.dz, https://orcid.org/0000-0003-0885-6914 barouralaz@yahoo.fr, https://orcid.org/0000-0002-6747-5049 amar talhi metallurgy and materials engineering, foundry laboratory, badji mokhtar university annaba, algeria talhiamaryacine@gmail.com abstract. this study aims to analyze the effect of thermo mechanical coupling damage in the presence of a phase change (austenite/martensite) in 35ncd16 steel. the impact of increasing mechanical traction load, accompanied by a martensitic transformation on the scale of a single grain with boundary has been studied. the prediction transformation of induced plasticity (trip) was evaluated by taking into account the following parameters: twenty shear directions of the martensitic plates, two values of the shear deformation of the martensitic plates, energetic and thermodynamics criteria for getting in order the transformation of the martensitic plates, elastoplastic behavior of the two areas in the first case (martensitic plate and grain boundary) and elastic behavior for the grain boundary in the second case. the numerical calculation is carried out using the finite element method (fem), implemented in the zebulon calculation code. the developed approach is validated using the available experimental results reported in the literature. the numerical results showed that the estimation of trip given by the energetics criteria with the values of the shear deformation (γ0 = 0.16) are closer to the experiment results. keywords. trip; number of shear direction; elastoplastic behavior; martensitic transformation; increasing load; fem; mono grain; grain boundary. citation: m. gaci, k. fedaoui, l. baroura and a. talhi, numerical study of trip transformation in 35ncd16 steeleffects of plate orientation and some criteria, frattura ed integrità strutturale, 59 (2022) 444-460. received: 01.11.2021 accepted: 01.12.2021 published: 01.01.2022 copyright: © 2022 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. introduction he deformation transformation is accompanied by an additional plastic deformation, or plasticity of transformation commonly called trip. this phenomenon takes place in steels solid phase change, under the application of the stress even lower than the elastic limit of austenite [1]. trip is observed much more in: nuclear reactor vessels, heat t https://youtu.be/9eehuzhqglg m.gaci et alii, frattura ed integrità strutturale, 59 (2022) 444-460; doi: 10.3221/igf-esis.59.29 445 treatment processes, welding, etc. [2, 4]. one of the essential characteristics to emphasize this phenomenon of plasticity transformation is its irreversible nature [5, 6 and 7]. according to mitter [8], the phenomenon of transformation plasticity is generally explained by two mechanisms. the first presented by greenwood-johnson [9]; during a transformation the two phases involved (mother phase and daughter phase) do not have the same compactness (different volume). when an external stress is applied on the macroscopic scale, the plastic deformation will then be oriented. the second mechanism given by magee [10] explains the phenomenon of trip in the case of martensitic transformation by the variation in volume, resulting from the formation of plates during transformation, under the effect of an external weak stress (lower than the elastic limit of austenite) [11]. poirier [12] has defined transformational plasticity as a temporary mechanical weakening of a material, which undergoes a phase change. the following effects [13] can characterize the phenomenon; an increase in the rate of deformation, beyond the rate allowed thermally in the case of creep at constant stress and a drop in the stress, in the case of tests deformation at constant speed. several analytical and numerical models have been proposed to satisfactorily describe the value and the kinetics of the plastic transformation flow (trip). these models are generally based on several micro-macro approaches, without however taking an interest in the fine evolution of the microstructure. among the related reported work, we find berveiller et al [14], diani et al [15], han et al [16], inoue et al [17] and ganghoffer et al [18]. in addition, these models are generally used in the case of simple types of loading and weak values of stress. greenwood and johnson [8], were the first to publish an interpretation relating to transformational plasticity. the greenwood and johnson approach was based on several hypotheses such as: the transformation is supposed to be complete, each phase is supposed to be perfectly plastic and the classical macroscopic plasticity criteria are applicable at the microscopic scale. for the prediction of the trip phenomenon, leblond [19] developed an analytical model based on the greenwoodjohnson mechanism [8]. the model is based on a simplified micro-mechanical approach, which assumes an elastoplastic behavior of the two parent and produced phases. other approaches were developed with the aim of a better estimation of trip in its two parts (kinetics and the final value) [20, 21] such as: -a micromechanical approach [21], combining theories of limit analysis and homogenization makes possible to overcome the excessive hypotheses introduced in the leblond model [19]. -the second approach takes into account the viscous character of the two phase’s behavior (parent and produced) [23]. the purpose of this work is the analysis of the numerical simulation parameters effects on the trip phenomenon during martensitic transformation in 35ncd16 steel. the numerical computation is based on a micromechanical wen model [24] using fe in two dimensions (2d) in a single grain with boundary scale. the applied mechanical loading is an increasing tensile stress in x direction with σx max = 118 mpa [25]. the following calculation parameters used in this study to give the order of plates formation are: the 20 shear directions of the martensitic plates (in reported works, the number of shear direction were eight [18]), the two values of the shear deformation of the martensitic plates (γ0= 0.16 and 0.19 [26]) and the thermodynamics criteria mmdf (max mechanical driving force) [18], amdf (average mechanical driving force) [24] and ese (elastic strain energy) [26] energetic creteria expressed in the local and global benchmarks. in the first case, elastoplastic behavior for the two domains (martensitic plate and the grain boundary) was taken into account, whereas in second case, the elastic behavior has been considered only for the grain boundary. consequently, the influence of the numerical calculation parameters on the final value and the trip kinetics have been discussed and compared with the experimental results reported in the literature [25]. the deformation of the transformation plasticity -trip n the literature, the first models were not proposed until several years after the discovery of the trip phenomenon. the macroscopic behavior of a material can be modeled using two methods. the first is based on the thermodynamics rules for irreversible processes and the second is based on microstructural deformation mechanisms. the macroscopic behavior laws are obtained by passing from micro to macro scale [27]. for a better understanding of the trip phenomenon, the study of the involved physical mechanisms are necessary [28, 29]. different authors have taken an interest in this problem by focusing on two types of tests: cooling under stress and mechanical tests of deformation by traction, compression or torsion at constant temperature. gautier et al. [30] observe a linear variation in the plasticity of transformation in the applied stress domain less than the elastic limit of austenite. for higher stresses, this plasticity increases rapidly. the authors find a linear variation in the plasticity of transformation in the domain of applied stress less than the elastic limit of austenite. videau et al [31] studied the plasticity of transformation for different loading paths [6] in the case of bi-axial loadings (traction-torsion). they have shown that for the martensitic transformations, the equivalent trip of von-mises criteria is independent of the loadings type when the value of the equivalent stress was the same.the authors also conclude that the i m. gaci, frattura ed integrità strutturale, 59 (2022) 444-460; doi: 10.3221/igf-esis.59.29 446 flow direction of the transformational in plasticity is the same as the effective stress ones, which is defined as the difference between the applied external stress and internal stress of the material [31]. greenwood and johnson [9] have carried out several theoretical and experimental works to elucidate the phenomenon of transformation plasticity. to study the irreversible elongation during cycles with transformation, they have carried out many tests on pure iron, iron-carbon alloy, uranium, zirconium, titanium and cobalt samples. their results show a linear relationship between the plasticity deformation of transformation and the applied stress, up to stress levels equivalent to half of the yield strength of the austenitic phase [32, 33]. the fig. 1 shows the axial deformation measured on a tensile test piece for 16mnd5 steel with and without stress dilatometer during the phase change. the application of a cooling stress during the martensitic phase change induces a residual deformation called trip [3]. however, in case of cooling without stress application, the trip phenomenon did not appear (fig 1.b) figure 1: axial deformation during a heating-cooling cycle (trip), a) under tensile stress b) stress free, [3] material n all calculations, authors consider that the martensitic phase (the daughter phase) has an elastoplastic behavior. the grain boundary follows two types of behavior, the first purely elastic and the second elastoplastic. the two phases (martensite and austenite) obey to a linear isotropic hardening model. the mechanical data used to simulate the 35ncd16 steel transformation are given in tab. (1). i m.gaci et alii, frattura ed integrità strutturale, 59 (2022) 444-460; doi: 10.3221/igf-esis.59.29 447 phase’s young’s modulus (mpa) hardening slope (mpa) yield strength (mpa) poisson’s ratio (υ) martensite 1.5*105 16500 890 0.3 austenite 1.8*105 2700 240 0.3 table 1: mechanical characteristics of the 35ncd16 steel [26] to numerically simulate trip, ganghoffer [18] adopts a transformation strain tensor   ,  tr d n expressed by eqn.1. the thermal deformation component tensor has two parts representing the normal dilation (ε0) with the plan of habitat (local reference mark d, n attached to each martensitic plate according to its orientation) and an important shearing directed along the martensitic plate (γ0), see fig. 2. for the trip prediction, the tensor of thermal deformation is imposed progressively [18].               0 , 0 0 0 2 ε2 tr d n (1) the values of normal dilation (ε0) was taken equal to 0.006 and the shear deformation (γ0) measured at a temperature of 320°c was in the order of 0.16 and 0.19 [26]. figure 2: mesh of the grain based on a scalene triangle numerical calculation of trip geometry of the model n this study, we used the geometry of the numerical model improved by wen [24]. this improvement consists in creating a mesh with two areas; a contour and a central area representing respectively, the grain boundary and the formation of the martensitic plate’s area. based on the wen’s work, we have developed a mesh formed by triangular elements of scalene type (fig. 2). using this type of triangle in mesh construction makes possible the reach of 110 plate’s in 20 possible shear directions (160°, 340°, 60°, 240°, 80°, 260°, 170°, 350°, 10°, 190°, 110°, 290°, 150°, 330°, 30°, 210°, 50°, 230° 120° and 300°) and a contour representing the grain boundary composed of five bands. fig. 3 shows an identification i m. gaci, frattura ed integrità strutturale, 59 (2022) 444-460; doi: 10.3221/igf-esis.59.29 448 of all the martensitic plates formed after transformation. each plate consists of (n) triangular element marked with a distinct color. the geometric characteristics of the plates, such as the number of elements and the shear direction (α) are given in tab. 2. in order to achieve a satisfactory simulation of the trip phenomenon, the formation domain is constituted of martensitic plates having several lengths and shear direction (α). martensitic plates are classified into three categories according to their number of triangular elements. long plates (n°: 41,42,43,59,60 and 64) contain between 26 and 32 triangular elements, medium plates (n°: 44, 45, 61, 62, 63, 38, 46, 51, 16, 80, 25, 31, 37, 55, 92, 93, 94, 102, 103 and 104) composed of 12 to 24 elements and the short plates formed of less than 12 elements, see tab. 2. n° of plates number of elements shear direction of plates (α) n° of plates number of elements shear direction of plates (α) n° of plates number of elements shear direction of plates (α) 1 2 160° 38 12 260° 75 8 30° 2 5 340° 39 7 80° 76 7 30° 3 7 160° 40 3 260° 77 7 210° 4 7 340° 41 32 340° 78 8 210° 5 6 160° 42 31 340° 79 9 210° 6 5 120° 43 27 160° 80 12 30° 7 6 150° 44 23 160° 81 4 150° 8 8 150° 45 19 340° 82 5 150° 9 3 160° 46 14 150° 83 9 330° 10 2 330° 47 10 330° 84 1 80° 11 9 50° 48 7 160° 85 2 260° 12 2 30° 49 4 340° 86 2 80° 13 8 60° 50 5 110° 87 2 260° 14 7 240° 51 12 290° 88 2 260° 15 6 50° 52 7 290° 89 2 80° 16 1 230° 53 2 80° 90 3 260° 17 5 60° 54 16 60° 91 4 80° 18 1 240° 55 12 240° 92 16 340° 19 6 60° 56 8 240° 93 14 340° 20 6 240° 57 4 60° 94 18 160° 21 5 50° 58 1 30° 95 14 340° 22 4 230° 59 33 110° 96 11 150° 23 3 60° 60 26 110° 97 9 340° 24 2 30° 61 20 290° 98 7 160° 25 14 30° 62 20 290° 99 6 340° 26 11 240° 63 24 120° 100 5 160° 27 9 60° 64 35 300° 101 2 170° 28 7 240° 65 3 10° 102 16 50° 29 5 50° 66 2 190° 103 15 50° 30 2 50° 67 3 10° 104 13 230° 31 15 170° 68 5 190° 105 11 230° 32 11 350° 69 6 10° 106 10 50° 33 8 170° 70 5 190° 107 9 50° 34 5 350° 71 5 10° 108 6 50° 35 3 150° 72 6 190° 109 3 230° 36 1 330° 73 7 10° 110 1 230° 37 16 80° 74 6 30° table 2: martensitic plates characteristic m.gaci et alii, frattura ed integrità strutturale, 59 (2022) 444-460; doi: 10.3221/igf-esis.59.29 449 figure 3: identification of the martensitic plates the calculation is carried out on the single-grain scale with boundary, under an increasing mechanical tensile stress (σx max = 118 mpa), applied in the x direction, see fig. 4 [25]. 0 20 40 60 80 100 120 0 20 40 60 80 100 120 st re ss (m p a) time of transformation (second) increasing stress 118 mpa figure 4: presentation of the increasing tensile stress applied during the martensitic transformation [24] the advancement criteria of the martensitic transformation ganghoffer [18] proposes a form of criterion based on the principles of thermodynamics, which manages the transformation of martensitic plates (eqn. 2). this criterion is called max mechanical driving force (mmdf) [18]. the improvement of the criterion (mmdf) was carried out by wen [23], who derived eqn. 3, called the criterion of the average mechanical driving force (amdf).        0 0. .max nw (2) m. gaci, frattura ed integrità strutturale, 59 (2022) 444-460; doi: 10.3221/igf-esis.59.29 450      1 / n average i i w w n (3) where   maxw : is the max mechanical driving force in a non-transformed mesh element (mmdf);  n : represents the normal stress in the normal direction (n);  : represents the shear stress acting in the habitat plane along the direction (d). these stresses are calculated from the state of local stress in the considered element; 0 ,  0 : represent the components of the transformation strain tensor defined in the local base (d, n), see eqn.1 [18];  averagew : is the average mechanical driving force in the plate composed by (n) element (amdf). with the aim of improving qualitatively and quantitatively the results of trip martensitic obtained numerically, meftah [26] used the criterion of the elastic strain energy ese given by eqn. 4. in addition, present numerical calculations the criterion ese is expressed in the two local (d, n) and global (x,y) benchmarks giving lese and gese, respectively. also we used the max and average values of this criterion to give the transformation order for each martensitic plate making up the domain.             1 1   * et ft n t el tt ij ijt neln e (4) where: δe: the increment of the elastic strain energy (ese) resulting from the plate transformation; nel: the number of the element considered; net: the total number of elements; t: the number of the time increment considered; tft: the number of increments necessary for the transformation of a plate;  ij : the increment of the tensor of local deformations at the moment « t »;  ij : the tensor of local constraint at the moment « t ». results and discussion he context of technical requirements for a better numerical prediction of trip under an increasing tensile stress (σx max = 118 mpa), have lead us to better consider an optimum parameters for the simulation such as: the increase of shear directions number of the martensitic plates to 20 (160 °, 340 °, 60 °, 240 °, 80 °, 260 °, 170 °, 350 °, 10 °, 190 °, 110 °, 290 °, 150 °, 330 °, 30 °, 210 °, 50 °, 230 °, 120 °, 300 °) and taking into account two shearing values γ0 = 0.16 and 0.19. on the other hand, two types of mechanical behavior have been used, the first considers an elastoplastic behavior for the formation of martensitic plate’s area and the grain boundary, the second admits an elastic behavior for only the grain boundary (the martensitic plates behave according to the elastoplastic mode). the influence of the parameters giving the order of martensitic plate’s formation in the grain (transformation advancement criteria) has been tested using the following criteria: -mmdf (max mechanical driving force: this is the max value calculated with eqn. 2 between all the triangular elements constituting the martensite plate in question; -amdf (average mechanical driving force: this is the average value calculated with eqn. 3 between all the triangular elements constituting the martensite plate in question; -alese (average local elastic strain energy expressed in the local coordinate system (d, n): this is the average value calculated with eqn. 4 between all the triangular elements constituting the martensite plate in question; -mlese (max local elastic strain energy expressed in the local coordinate system (d, n): this is the max value calculated with eqn. 4 between all the triangular elements constituting the martensite plate in question; t m.gaci et alii, frattura ed integrità strutturale, 59 (2022) 444-460; doi: 10.3221/igf-esis.59.29 451 -agese (average global elastic strain energy-expressed in the global coordinate system (x, y): this is the average value calculated with eqn. 4 between all the triangular elements constituting the martensite plate in question; -mgese (max global elastic strain energy-expressed in the global coordinate system (x, y): this is the max value calculated with eqn. 4 between all the triangular elements constituting the martensite plate in question; elastic boundary of grain and elastoplastic behavior for martensitic phase figs 5 and 6 show the variation of trip according to the progress of the martensitic plate’s formation in the grain with a purely elastic behavior of the grain boundary, while the martensitic phase obeys to an elastoplastic behavior. it can be noticed in fig. 5.a that with the use of the two criteria amdf (γ0 = 0.16) and mmdf (γ0 = 0.16) a completely superimposed trip kinetics has been obtained. in addition, the variation in the deformation (trip) was very rapid from the start to 60% of the transformation compared with the experiment results [24]. beyond this threshold (z ≥ 60%) a loss of kinetics is recorded. the final values of trip obtained with the three criteria, namely amdf (γ0 = 0.16) and mmdf (γ0 = 0.16) are almost equal and slightly lower compared to that given by the experience [25]. on the other hand, with the use of the shear deformation value γ0 = 0.19, the three criteria ( amdf , mmdf) give a kinetics and the final value of trip largely estimated compared to the results of the experiment [ 25], see fig 5.b. figure 5: evolution of trip under an increasing stress depending on the progress of the transformation with elastic behavior of the grain boundary and elastoplastic for martensitic phase for a) γ0 =0.16, b) γ0 =0.19. m. gaci, frattura ed integrità strutturale, 59 (2022) 444-460; doi: 10.3221/igf-esis.59.29 452 in fig. 6.a, we observe that the transformation kinetics obtained with the two criteria mlese (γ0 = 0.16) and mgese (γ0 = 0.16) were relatively better compared to the experiments [25] in the ranges of 0% ≤ z ≤ 15% and 37% ≤ z ≤70% for mlese and 37% ≤ z ≤60% for mgese. the average values of these two criteria alese (γ0 = 0.16) and agese (γ0 = 0.16), permit to obtain a fast trip kinetics from the beginning of the transformation to z≤ 72%. with four criteria mlese (γ0 = 0.16), mgese (γ0 = 0.16), alese (γ0 = 0.16) and agese (γ0=0.16), the final values of trip are significantly improved compared with those obtained with the first criteria and are almost equal to the experimental final value [24]. in the calculations where the shear deformation value γ0 was equal to 0.19, it can be clearly seen that the criteria mlese (γ0 = 0.19), mgese (γ0 = 0.19), alese (γ0 = 0.19) and agese (γ0 =0.19) induced very fast transformation kinetics and fairly large final values of trip, see fig 6.b. figure 6: evolution of trip under an increasing stress depending on the progress of the transformation with elastic behavior of the grain boundary and elastoplastic for martensitic phase for a) γ0 =0.16, b) γ0 =0.19. elastoplastic behavior of the grain boundary and martensitic phase figs. 7 present the variation of trip as a function of the progress of the martensitic plate’s formation in the grain, with an elastoplastic behavior of the grain boundary as well as for the martensitic phase. the first remark which appears quickly is m.gaci et alii, frattura ed integrità strutturale, 59 (2022) 444-460; doi: 10.3221/igf-esis.59.29 453 that, the use of the shear deformation value γ0 = 0.16 and the criteria amdf (γ0 = 0.16) and mmdf (γ0 = 0.16), gives the same evolution of trip presented in previous section, see fig 7.a. furthermore, it can be seen in fig. 7.b that the curves obtained with the amdf (γ0 = 0.19) and mmdf (γ0 = 0.19) criteria are perfectly superimposed. using amdf (γ0 = 0.19) and mmdf (γ0 = 0.19) criteria, we obtain fast and linear trip kinetics up to z = 65% of martensitic plates formation. on the other hand, we find that the value of trip obtained at the rate of z = 62% was equal to 0.00355, which is much greater than obtained using the same criteria in case of the shear deformation γ0 = 0.16 (trip = 0.0022), see fig 7. we note that the two criteria amdf and mmdf, whether calculated with γ0 = 0.16 or 0.19, give a poor estimation of the trip, compared to the results of the experiment [25]. figure 7: evolution of trip under an increasing stress depending on the progress of the transformation with an elastoplastic behavior of the grain boundary and martensitic phase for a) γ0 =0.16, b) γ0 =0.19. in figs. 8.a we show the evolution of trip during martensitic transformation with the criteria for ordering the formation of platelets, such as alese, mlese, agese and mgese. using the values of the shear deformation γ0 = 0.16, it was found that the estimated strain is similar to that given in the fig. 6.a. in fig. 8.b, we present the trip evolution obtained with the same criteria (mlese, mgese, agese and alese) in case of shear deformation γ0 = 0.19. we notice that, the m. gaci, frattura ed integrità strutturale, 59 (2022) 444-460; doi: 10.3221/igf-esis.59.29 454 trip curves obtained with the criteria alese and agese are nearly superimposed. the same behavior has been observed for two curves plotted using the criteria mlese and mgese. the deformation kinetics (trip) obtained with the criteria alese and agese was found to be faster until 50% of the rate of transformation z where the trip value was about 0.0025. beyond 50%, there is almost a stable trip kinetic value showing a very slight variation. the two max energy criteria mlese and mgese favor almost linear trip kinetics over the entire range of martensitic transformation (0% ≤ z≤ 100%). figure 8: evolution of trip under an increasing stress depending on the progress of the transformation with an elastoplastic behavior of the grain boundary and martensitic phase for a) γ0 =0.16, b) γ0 =0.19. from the results presented in the last two sections, we observe that the two types of behavior do not give a significant difference. whereas, the value γ0 = 0.16 of the shear deformation of martensitic plates favors an acceptable estimation of trip better than the value of γ0 = 0.19. in addition, the mlese (γ0 = 0.16) criterion presents a better estimation of the trip than the other criteria by referring to the experience curve [25]. m.gaci et alii, frattura ed integrità strutturale, 59 (2022) 444-460; doi: 10.3221/igf-esis.59.29 455 transformation order for plates with criteria amdf (γ0 = 0.16) transformation order for plates with criteria mmdf (γ0 = 0.16) n° plates (α) z (%) n° plates (α) z (%) n° plates (α) z (%) n° plates (α) z (%) n° plates (α) z (%) n° plates (α) z (%) 56 (240°) 0.00 34 (350°) 0.61 73 (10°) 1.00 56 (240°) 0.00 34 (350°) 0.61 73 (10°) 1.00 14 (240°) 82 (150°) 67 (10°) 81 (150°) 82 (150°) 67 (10°) 26 (240°) 1 (160°) 65 (10°) 14 (240°) 1 (160°) 65 (10°) 28 (240°) 100(160°) 102(50°) 26 (240°) 100(160°) 102 (50°) 55 (240°) 5 (160°) 103(50°) 28 (240°) 5 (160°) 103 (50°) 18 (240°) 44 (160°) 109(230°) 55 (240°) 44 (160°) 109(230°) 20 (240°) 3 (160°) 110(230°) 18 (240°) 3 (160°) 110(230°) 63 (120°) 43 (160°) 107 (50°) 20 (240°) 43 (160°) 107(50°) 64 (300°) 98 (160°) 104(230°) 63 (120°) 98 (160°) 104(230°) 50 (110°) 96 (150°) 106 (50°) 64 (300°) 96 (150°) 106 (50°) 52 (290°) 94 (160°) 108 (50°) 50 (110°) 94 (160°) 108 (50°) 51 (290°) 60 (110°) 105(230°) 52 (290°) 60 (110°) 105(230°) 36 (330°) 92 (340°) 80 (30°) 51 (290°) 92 (340°) 80 (30°) 62 (290°) 97 (340°) 78 (210°) 59 (110°) 97 (340°) 78 (210°) 59 (110°) 99 (340°) 79 (210°) 62 (290°) 99 (340°) 79 (210°) 61 (290°) 45 (340°) 77 (210°) 36 (330°) 45 (340°) 77 (210°) 10 (330°) 88 (260°) 76 (30°) 61 (290°) 88 (260°) 76 (30°) 35 (150°) 90 (260°) 74 (30°) 10 (330°) 90 (260°) 74 (30°) 47 (330°) 87 (260°) 75 (30°) 35 (150°) 87 (260°) 75 (30°) 81 (150°) 85 (260°) 24 (30°) 47 (330°) 85 (260°) 24 (30°) 8 (150°) 41 (260°) 22 (230°) 8 (150°) 41 (260°) 22 (230°) 66 (190°) 38 (260°) 54 (60°) 66 (190°) 38 (260°) 27 (60°) 68 (190°) 40 (260°) 27 (60°) 68 (190°) 40 (260°) 54 (60°) 70 (190°) 42 (340°) 57 (60°) 70 (190°) 42 (340°) 0.62 57 (60°) 72 (190°) 37 (80°) 0.62 17 (60°) 72 (190°) 37 (80°) 17 (60°) 6 (120°) 95 (340°) 19 (60°) 6 (120°) 95 (340°) 19 (60°) 9 (160°) 53 (80°) 23 (60°) 9 (160°) 53 (80°) 23 (60°) 46 (150°) 39 (80°) 16 (230°) 46 (150°) 39 (80°) 16 (230°) 83 (330°) 13 (60°) 12 (30°) 83 (330°) 13 (60°) 12 (30°) 4 (340°) 93 (340°) 58 (30°) 4 (340°) 93 (340°) 58 (30°) 7 (150°) 49 (340°) 21 (50°) 7 (150°) 49 (340°) 21 (50°) 2 (340°) 84 (80°) 29 (50°) 2 (340°) 84 (80°) 29 (50°) 31 (170°) 86 (80°) 25 (30°) 31 (170°) 86 (80°) 25 (30°) 32 (350°) 71 (30°) 15 (50°) 32 (350°) 89 (80°) 15 (50°) 33 (170°) 89 (80°) 30 (50°) 33 (170°) 71 (30°) 30 (50°) 48 (160°) 69 (10°) 11 (50°) 48 (160°) 91 (80°) 11 (50°) 101(170°) 91 (80°) 101(170°) 69 (10°) table 3: plates transformation order under thermodynamic criteria’s amdf (γ0 = 0.16) and mmdf (γ0 = 0.16) effects of the criteria and the martensitic plates shear angle on the trip estimation the results of the elastoplastic behavior have been considered in this section to discuss the influence of the numerical parameters (since the two modes of behavior give almost the same results). among the studied numerical parameters, we have investigated: the influence of the shearing directions (α) of the martensitic plates as well as the criteria (amdf, mmdf, mgese, mlese, agese and alese) on the estimation of the kinetics and the trip values in the case of the shear deformation γ0 = 0.16. from fig 7.a, we can distinguish two trip evolution zone. the first is located in 0% ≤ z≤ 61% range, while the second is located in 62% ≤ z ≤ 100% range. from the beginning of the transformation (z = 0% to z = 61%), we notice that the two thermodynamic criteria amdf, mmdf favor the martensitic plates in their shear directions situated in the second, third and fourth quarter of the circle. (240 °, 110 °, 120 °, 290 °, 330 °, 150 °, 160 °, 170 °, 350 °, 260 °), see tab. 3. however, with this type of plates arrangement during transformation gives an overestimation of the kinetics and trip values, see fig 7.a. in the second transformation zone (62% ≤ z ≤ 100%), where they appear all the directions m. gaci, frattura ed integrità strutturale, 59 (2022) 444-460; doi: 10.3221/igf-esis.59.29 456 of the plates shear directions (α = 10 °, 30 °, 50 °, 60 °, 80 ° 240 °, 110 °, 120 °, 290 °, 330 °, 150 °, 160 °, 170 °, 350 °, 260 °), we notice a slight improvements, but the results remain unsatisfactory. in fig 8.a and according to the energy criterion mlese, we may divide the evolution of the trip into five zones as follows: the first (0% ≤ z ≤ 0.14%), the second (0.15% ≤ z ≤ 0.40%), the third (0.41% ≤ z ≤ 0.70%), the fourth (0.71% ≤ z ≤ 0.89%) and the fifth (0.9% ≤ z ≤ 100%). tab. 4 shows that these different zones are formed with plates whose shear directions are composed of the smallest to the largest angle. only for the last two zones, the curve of the numerical results deviates slightly from the experimental ones, which is probably due to the applied behavior mode. with the two criteria mgese and mlese, the same results have been almost obtain. however, with the use of mgese, the third zone (0.41% ≤ z ≤ 0.52%) was shorter, see tab. 4. from the obtained results, we may conclude that the use of the criterion (mlese) at the local scale gives an acceptable prediction of trip among the other tested criteria in this study. in tab. 5, are summarized the three trip evolution zones and the two energy criteria agese and alese, which have almost the same arrangement of the platelets as shown in fig 8.a. these criteria give a non-precise trip estimation compared to the experimental results [25]. transformation order for plates with criteria mgese (γ0 = 0.16) transformation order for plates with criteria mlese (γ0 = 0.16) n° plates (α) z (%) n° plates (α) z (%) n° plates (α) z (%) n° plates (α) z (%) n° plates (α) z (%) n° plates (α) z (%) 1 (160°) 0.00 0.14 84 (80°) 0.40 32 (350°) 0.84 1 (160°) 0.00 0.14 16 (230°) 0.41 0.70 31 (170°) 0.89 64 (300°) 29 (50°) 90 (260°) 64(300°) 18 (240°) 95 (340°) 62 (290°) 94 (160°) 0.41 0.52 26 (240°) 62 (290°) 52 (290°) 49 (340°) 65 (10°) 48 (160°) 9 (160°) 65 (10°) 105(230°) 90 (260°) 63 (120°) 93 (340°) 50 (110°) 63 (120°) 28 (240°) 9 (160°) 61 (290°) 98 (160°) 54 (60°) 61 (290°) 99 (340°) 81 (150°) 66 (190°) 104(230°) 22 (230°) 66 (190°) 68 (190°) 19 (60°) 60 (110°) 18 (240°) 31 (170°) 60 (110°) 94 (160°) 20 (240°) 2 (340°) 92 (340°) 91 (80°) 36 (330°) 70 (190°) 46 (150°) 36 (330°) 52 (290°) 7 (150°) 2 (340°) 93 (340°) 91 (80°) 58 (30°) 45 (340°) 81 (150°) 58 (30°) 98 (160°) 7 (150°) 37 (80°) 28 (240°) 20 (240°) 37 (80°) 104(230°) 82 (150°) 40 (260°) 0.15 103(50°) 0.53 8 (150°) 40 (260°) 0.15 0.40 33 (170°) 48 (160°) 3 (160°) 46 (150°) 82 (150°) 39 (80°) 69 (10°) 8 (150°) 39 (80°) 68 (190°) 73 (210°) 3 (160°) 92 (340°) 17(60°) 38 (260°) 97 (340°) 17 (60°) 0.85 1.00 38 (260°) 25 (30°) 47(330°) 57 (60°) 102(50°) 74 (30°) 57 (60°) 103 (50°) 14 (240°) 41 (340°) 70 (190°) 76 (30°) 41 (340°) 72 (190°) 73 (10°) 4 (340°) 47 (330°) 77 (210°) 34 (350°) 97 (340°) 83 (330°) 101(170°) 88 (260°) 11 (50°) 42 (340°) 102(50°) 74 (30°) 5 (160°) 89 (80°) 14 (240°) 53 (80°) 85 (260°) 13 (60°) 34 (350°) 51 (290°) 75 (30°) 56 (240°) 86 (80°) 76 (30°) 42 (340°) 72 (190°) 78 (210°) 4 (340°) 27 (60°) 77 (210°) 53 (80°) 33 (170°) 83 (330°) 30 (50°) 23 (60°) 11 (50°) 0.90 1.00 6 (120°) 69 (10°) 13 (60°) 43 (160°) 71 (10°) 50 (110°) 56 (240°) 96 (150°) 79 (210°) 101(170°) 55 (240°) 80 (30°) 30 (50°) 10 (330°) 80 (30°) 35 (150°) 32 (350°) 75 (30°) 43 (160°) 12 (30°) 110(230°) 5 (160°) 87 (260°) 78 (210°) 35 (150°) 25 (30°) 109(230°) 6 (120°) 88 (260°) 21 (50°) 59 (110°) 105(230°) 108 (50°) 59 (110°) 89 (80°) 79 (210°) 49 (340°) 85 (260°) 21 (50°) 24 (30°) 51 (290°) 110(230°) 100(160°) 86 (80°) 107 (50°) 44 (60°) 96 (240°) 109(230°) 24 (30°) 27 (60°) 106 (50°) 67 (10°) 12 (30°) 108(50°) 67 (10°) 23 (60°) 15 (50°) 84 (80°) 10 (330°) 107(50°) 99 (340°) 71 (10°) 16 (230°) 29 (50°) 26 (240°) 106(50°) 44 (60°) 55 (240°) 19 (60°) 100(160°) 54 (60°) 0.71 15 (50°) 87 (260°) 95 (340°) 45 (340°) 22 (230°) table 4: plates transformation order under energetic criteria’s mgese (γ0 = 0.16) and mlese ( γ0 = 0.16) m.gaci et alii, frattura ed integrità strutturale, 59 (2022) 444-460; doi: 10.3221/igf-esis.59.29 457 transformation order for plates with criteria agese (γ0 = 0.16) transformation order for plates with criteria alese (γ0 = 0.16) n° plates (α) z (%) n° plates (α) z (%) n° plates (α) z (%) n° plates (α) z (%) n° plates (α) z (%) n° plates (α) z (%) 65 (10°) 0.00 2 (340°) 0.68 35 (150°) 0.88 1 (160°) 0.00 40 (260°) 0.68 49 (340°) 0.88 66 (190°) 60 (110°) 73 (10°) 65 (10°) 38 (260°) 93 (340°) 67 (10°) 3 (160°) 47 (330°) 67 (10°) 36 (330°) 9 (160°) 68 (190°) 92 (340°) 49 (340°) 68 (190°) 104(230°) 10 (330°) 69 (10°) 105 (230°) 75 (30°) 66 (190°) 103(50°) 35 (150°) 58 (30°) 41 (340°) 55 (240°) 58 (30°) 72 (190°) 34 (330°) 70 (190°) 94 (160°) 50 (110°) 30 (50°) 51 (290°) 55 (240°) 56 (240°) 96 (150°) 34 (330°) 64 (300°) 2 (340°) 31 (170°) 30 (50°) 97 (340°) 33 (170°) 56 (240°) 60 (110°) 32 (350°) 64 (300°) 43 (160°) 101(170°) 69 (10°) 92 (340°) 33 (170°) 63 (120°) 98 (160°) 31 (170°) 63 (120°) 3 (160°) 101(170°) 54 (60°) 110(230°) 32 (350°) 28 (240°) 43 (160°) 73 (10°) 71 (10°) 99 (340°) 76 (30°) 26 (240°) 41 (340°) 50 (110°) 29 (50°) 5 (160°) 24 (30°) 70 (190°) 94 (160°) 75 (30°) 25 (30°) 44 (160°) 85 (260°) 0.89 1.00 25 (30°) 96 (150°) 24 (30°) 28 (240°) 103 (50°) 88 (260°) 29 (50°) 97 (340°) 77 (210°) 89 (80°) 100(160°) 77 (210°) 54 (60°) 44 (160°) 23 (60°) 0.89 1.00 62 (290°) 81 (150°) 22 (230°) 62 (290°) 98 (160°) 76 (30°) 57 (60°) 104(230°) 87 (260°) 74 (30°) 110(230°) 19 (60°) 37 (80°) 4 (340°) 91 (80°) 61 (290°) 5 (160°) 20 (240°) 74 (30°) 45 (340°) 20 (240°) 37 (80°) 99 (340°) 15 (50°) 26 (240°) 7 (150°) 11 (50°) 71 (10°) 42 (340°) 22 (230°) 61 (290°) 42 (340°) 21 (240°) 27 (60°) 81 (150°) 80 (30°) 39 (80°) 13 (60°) 19 (60°) 57 (60°) 100(160°) 11 (50°) 90 (260°) 46 (150°) 23 (60°) 39 (80°) 45 (340°) 14 (240°) 53 (80°) 48 (160°) 78 (210°) 53 (80°) 46 (150°) 17 (60°) 38 (260°) 6 (120°) 17 (60°) 108(50°) 13 (60°) 86 (80°) 40 (260°) 102(50°) 0.69 80 (30°) 52 (290°) 4 (340°) 0.69 89 (80°) 27 (60°) 82 (150°) 14 (240°) 107(50°) 7 (150°) 84 (80°) 109(230°) 51 (290°) 15 (50°) 106(50°) 48 (160°) 78 (210°) 107(50°) 10 (330°) 79 (210°) 105(230°) 82 (150°) 16 (230°) 59 (110°) 36 (330°) 84 (80°) 59 (110°) 6 (120°) 91 (80°) 108(50°) 95 (340°) 12 (30°) 109(230°) 83 (330°) 12 (30°) 72 (190°) 83 (330°) 86 (80°) 87 (260°) 102(50°) 18 (240°) 106(50°) 8 (150°) 16 (230°) 90 (260°) 47 (330°) 79 (210°) 1 (160°) 93 (340°) 18 (240°) 85 (260°) 95 (340°) 21 (240°) 52 (290°) 9 (160°) 88 (260°) 8 (150°) table 5: plates transformation order under energetic criteria’s agese (γ0 = 0.16) and alese (γ0 = 0.16) the distribution of the shear stress sig12 over all the studied grain mesh (made of the formation domain of the martensitic plates and the grain boundary) is shown in fig. 9. however, in case of an elestoplastic behavior and with the value of γ0 = 0.16 in amdf criterion, the first transformed platelets have been observed at the early stage of the transformation (time = 11.5), see tab.3 (n°: 56,14,26,28,55,18,20,63,64,50,52,51), which generate the greatest shear stress in the area of martensitic plates formation. this observation is confirmed by the reported magee [10] studies, which show that the martensitic transformation is favored by the shearing phenomenon. m. gaci, frattura ed integrità strutturale, 59 (2022) 444-460; doi: 10.3221/igf-esis.59.29 458 figure 9: shear stress distribution (sig 12) during the martensitic plate’s formation with amdf (γ0 = 0.16) criteria conclusion he aim of this reported work is to obtain a more rigorous and reliable numerical trip simulation of a martensitic transformation in 35ncd16 steel under increasing tensile stress (σx max = 118 mpa). this have been achieved by the adaptation of the parameters introduced in the numerical calculation such as: the increase in the number of shear directions (twenty directions), the use of seven criteria to give the order of plate transformation, the mono grain model with regular grain boundary and an elastic and elstoplastic behavior of the austenitic and martensitic phases. the trip numerical results have been compared with those reported in the literature [24]. from the obtained results, we may conclude that with the use of shear deformation γ0 = 0.16, the numerical results were better than those evaluated with γ0 = 0.19.the estimation values of trip (in its final values and kinetics) given by the mlese (γ0 = 0.16) and mgese (γ0 = 0.16) criteria are closer to the experiment results [25]. according to the numerical results and for a better prediction of the trip, it is necessary to consider a mixed behavior of mode (elastoplastic and a viscous), which may be applied in certain part of the transformation. using the investigated numerical parameters in this study, the two types of behavior have shown almost no difference. references [1] fischer, f. d., reisner, g. (1998). a criterion for the martensitic transformation of a micro region in an elastic-plastic material, acta materialia, 46(6), pp. 2095-2102. [2] iesman, a.v., levitas, v.i., preston, d.l., cho, j.y. (2005). finite element simulations of martensitic phase transitions and microstructures based on a strain softening model, journal of the mechanics and physics of solids, 53, pp.495-523. doi: 10.1016/j.jmps.2004.10.001. [3] valance, s., coret, m., combescure, a. (2007). strain simulation of steel during a heating-cooling cycle including solidsolid phase change, european journal of mechanics-a/solids, 26(3), pp.460-473, doi: 10.1016/j.euromechsol.2006.11.001. [4] ferro, p., bonollo, f., berto, f., montanari, a. (2019). numerical modelling of residual stress redistribution induced by tig-dressing. frattura ed integrità strutturale, 47, pp. 221-230. [5] zhong, h., wang, z., gan, j., wang, x., yang, y., he, j., wei, t.t., qin, x. (2020). numerical simulation of martensitic transformation plasticity of 42crmo steel based on spot continual induction hardening model, surface and coatings technology, 385, doi: 10.1016/j.surfcoat.2020.125428. t m.gaci et alii, frattura ed integrità strutturale, 59 (2022) 444-460; doi: 10.3221/igf-esis.59.29 459 [6] leblond, j.b., devaux, j.c. (1989). mathematical modeling of transformation plasticity in steels i: case of ideal-plastic phases, int. j. plast, 5, pp. 551-572, doi: 10.1016/0749-6419(89)9001-6. [7] hazar, s., alfredsson, b., lai, j. (2018). mechanical modeling of coupled plasticity and phase transformation effects in a martensitic high strength bearing steel, mechanics of materials, 117, pp. 41-57, doi: 10.1016/j.mechmat.2017.10.001. [8] mitter, w. (1987). umwandlungsplastizität und ihre berücksichtignung bei der berechnung von eigenspannungen, berlin, materialkundlich-technische reihe 7, isbn3443230083, 276p. [9] greenwood, g.w., johnson, r. h. (1965). the deformation of metals under small stresses during phase transformation, proc roy soc, 283, pp.403-422. doi:10.1098/rspa.1965.0029. [10] magee, c. l. (1970). nucleation of martensite, phases transformations. asm, metals park. [11] el majaty, y., leblond, j.b., brenner, r. (2018). une approche micromécanique renouvelée du mécanisme de greenwood-johnson de la plasticité de transformation des métaux et alliages, colloque national mecamat aussois (matériaux numériques), aussois, france. [12] poirier, j.p. (1982). on transformation plasticity, j. geophy. res, 87, pp. 6791-6797, doi: 10.1029/jb087ib08p06791. [13] behrens, b.a., bouguecha, a., bonk, c., chugreev, a. (2017). experimental investigations on the transformationinduced plasticity in a high tensile steel under varying thermo-mechanical loading, cmms, 17(1), pp. 36 -43. [14] berveiller, m., zaoui. a. (1983). modelling of the plasticity and the texture development of two-phase metals, procceding of the 4th riso int. symp. on metallurgy and materials science, roskilde, danemark, pp. 153-160. [15] diani, j.m., sabar. h., berveiller. m. (1995). micromechanical modelling of the transformation induced plasticity (trip) phenomenon in steels, int. j. eng. sci., 33(13), pp. 19211934, doi: 10.1016/0020-7225(95)00045-y. [16] han, h.n., lee, c.g., oh, c.s, lee, t.h., kim. s.j.( 2004). a model for deformation behavior and mechanically induced martensitic transformation of metastable austenitic steel, acta materialia, 52(17)4, pp. 5203-5214, doi: 10.1016/j.actamat.2004.07.031. [17] inoue, t., wang. z. (1985). coupling between stress, temperature, and metallic structures during processes involving phase transformations. mater. sci. technol. 1, pp. 845-849, doi: 10.1179/mst.1985.1.10.845. [18] ganghoffer, j.f., simonsson, k. (1998). a micromechanical model of the martensitic transformation, mechanics materials, 27, pp. 125-144, doi: 10.1016/s0167-6636(97)00044-6. [19] leblond, j.c., mottet, g.j., devaux, c. (1986). a theoretical and numerical approach to the plastic behavior of steels during phase transformations ii. study of classical plasticity for ideal-plastic phases, journal mechanical physics solids, 34(4), pp. 411-432, doi: 10.1016/0022-5096(86)90010-4. [20] ahluwalia, r., mikula, j., laskowski, r., quek, s. s. (2020). phase field simulation of martensitic-transformation-induced plasticity in steel, phys. rev. materials, 4, 103607, doi: 10.1103/physrevmaterials.4.103607. [21] hossain, m.a., baxevanis, th. (2021). a finite strain thermomechanically-coupled constitutive model for phase transformation and (transformation-induced) plastic deformation in niti single crystals; international journal of plasticity, doi:10.1016/j.ijplas.2021.102957. [22] fischer, f.d., reisnerb, g., wernerb, e., tanakac, k., cailletaudd, g., antrettera, t. (2000). a new view on transformation induced plasticity (trip), international journal of plasticity, 16(7-8), pp. 723-748, doi: 10.1016/s0749-6419(99)00078-9. [23] gaubert, a., lebouar, y., finel, a. (2010) coupling phase field and visco-plasticity to study rafting in ni-base superalloys, phil. mag, 90 (1), pp. 375-404, doi: 10.1080/14786430902877802. [24] wen, y.h., denis, s., gautier, e. (1996). criterion for the progress of martensitic transformation in a finite element simulation, journal de physique, iv (j. phys., iv), colloque c2, 5, 531.pp. 146, doi: 10.1051/jp4. [25] tahimi, a., taleb, l., barbe, f. (2009). plasticité induite par transformation de phase martensitique dans l'acier 35ncd16, 19ème congrès français de mécanique, marseille, france. [26] meftah, s., barbe, f., taleb l., sidoroff, f.(2007). parametric numerical simulations of trip and its interaction with classical plasticity in martensitic transformation, european journal of mechanics a/solids, 26(4), pp.688-700. [27] polatidisa, e.g., haidemenopoulosb, n., krizanc, d., aravasbd, n., panznerae, t., šmídf, m., papadiotib, i., casatif, n., petegemf, v., vanswygenhovenfg, h. (2021). the effect of stress triaxiality on the phase transformation in transformation induced plasticity steels: experimental investigation and modelling the transformation kinetics, materials science and engineering, 800, 40321, doi: 10.1016/j.msea.2020.140321. [28] hazara, s., alfredssona, bo., laib, j. (2018). mechanical modeling of coupled plasticity and phase transformation effects in a martensitic high strength bearing steel, mechanics of materials, 117, pp. 41-57, doi: 10.1016/j.mechmat.2017.10.001. m. gaci, frattura ed integrità strutturale, 59 (2022) 444-460; doi: 10.3221/igf-esis.59.29 460 [29] barbe, f., quey, r., taleb, l., souza, d.c. (2008). numerical modelling of the plasticity induced during diffusive transformation. an ensemble averaging approach for the case of random arrays of nuclear, european journal of mechanics a/solids, 27, doi: 10.1016/j.euromechsol.2008.01.005. [30] gautier, e., zhang, j. s., zhang, x. m. (1995). martensitic transformation under stress in ferrous alloys. mechanical behaviour and resulting morphologies, j. phys. iv, 5(8), pp. 8-41, doi: 10.1051/ip4:1995805. [31] videau, j.c., cailletaud, g., pineau, a. (1996). experimental study of the transformation-induced plasticity in a cr-nimo-al-ti steel, j. phys. iv,6(c1), pp. 1-465. [32] taleb, l., sidoroff, f. (2003). a micromechanical modeling of greenwood-johnson mechanism in transformation induced plasticity, int. j. plasticity ,19 (10), pp. 18211842, doi: 10.1016/s0749-6419(03)00020-2. [33] soleimani, m., rezakalhor, a., mirzadeh, h. 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can be opened with acrobat and adobe reader 5.0 and later.) >> /namespace [ (adobe) (common) (1.0) ] /othernamespaces [ << /asreaderspreads false /cropimagestoframes true /errorcontrol /warnandcontinue /flattenerignorespreadoverrides false /includeguidesgrids false /includenonprinting false /includeslug false /namespace [ (adobe) (indesign) (4.0) ] /omitplacedbitmaps false /omitplacedeps false /omitplacedpdf false /simulateoverprint /legacy >> << /addbleedmarks false /addcolorbars false /addcropmarks false /addpageinfo false /addregmarks false /convertcolors /converttocmyk /destinationprofilename () /destinationprofileselector /documentcmyk /downsample16bitimages true /flattenerpreset << /presetselector /mediumresolution >> /formelements false /generatestructure false /includebookmarks false /includehyperlinks false /includeinteractive false /includelayers false /includeprofiles false /multimediahandling /useobjectsettings /namespace [ (adobe) (creativesuite) (2.0) ] /pdfxoutputintentprofileselector /documentcmyk /preserveediting true /untaggedcmykhandling /leaveuntagged /untaggedrgbhandling /usedocumentprofile /usedocumentbleed false >> ] >> setdistillerparams << /hwresolution [2400 2400] /pagesize [612.000 792.000] >> setpagedevice microsoft word numero_32_art_1 n. bisht et alii, frattura ed integrità strutturale, 32 (2015) 1-12; doi: 10.3221/igf-esis.32.01 1 influence of crack offset distance on the interaction of multiple cracks on the same side in a rectangular plate neeraj bisht, p. c. gope, kuldeep panwar college of technology, govind ballabh pant university of agriculture and technology, pantnagar (263145), uttarakhand, india. neerajbisht30@gmail.com abstract. in the present work finite element method has been employed to study the interaction of multiple cracks in a finite rectangular plate of unit thickness with cracks on the same side under uniaxial loading conditions. the variation of the stress intensity factor and stress distribution around the crack tip with crack offset distance has been studied. due to the presence of a neighbouring crack, two types of interactions viz. intensification and shielding effect have been observed. the interaction between the cracks is seen to be dependent on the crack offset distance. it is seen that the presence of a neighbouring crack results in the appearance of mode ii stress intensity factor which was otherwise absent for a single edge crack. it can be said that the proximity of cracks is non-desirable for structural integrity. the von-mises stress for different crack orientations has been computed. linear elastic analysis of state of stress around the crack tip has also been done. keywords. finite element method; crack interaction; von-mises stress. introduction he fracture mechanics theory can be used to analyse structures and machine components with cracks and to obtain an efficient design. the basic principles of fracture mechanics developed from studies of [1-3] are based on the concepts of linear elasticity. the interaction between multiple cracks has a major influence on crack growth behaviours. this influence is particularly significant in stress corrosion cracking (scc), welding, riveting etc. because of the relatively large number of cracks initiated due to environmental effects. pseudo – traction –electric – displacement –magnetic –induction method has been proposed [4] to solve the multiple crack interaction problems in the magneto elastic material. most of the real life situations have the problem of multiple cracks and so it becomes imperative to study this interaction for an array of cracks, keeping this in mind interaction between two parallel cracks has been studied and a detailed analysis has been done in this regard. since today, there have been over 20 approaches to calculate stress intensity factors. some of these are the integral transform method [5], the westergaard method [6],the complex variable function method [7], the singular equation integral method [8], conformal mapping [9], the laurent series expansion [10], boundary collocation method [11], green’s function method [12], the continuous distribution dislocation method [13], the finite element method [14], the boundary element method [15], the body force method [16] and the displacement discontinuity method [17]. the solutions of many of the fracture mechanics problems have been compiled in data hand books for stress intensity factors [18] and [19]. the configuration of multiple cracks is so complicated that a solution may not be available from the handbooks and literatures. the above mentioned methods with analytical features, which are usually suitable for special cases or very simple crack configurations, are not sufficient to obtain reasonable results for general orientations due to the multiple t n. bisht et alii, frattura ed integrità strutturale, 32 (2015) 1-12; doi: 10.3221/igf-esis.32.01 2 restrictions. in these cases numerical approaches are usually employed. in the numerical approaches proposed so far finite element method provides a very simple, effective and accurate technique for evaluation of fracture parameters. the historical development of computational fracture mechanics is found in the works of ingraffea et al. [20] and sinclair [21]. sinclair presented an extensive review of numerical prediction models to determine stress intensity factors. the advantages and disadvantages of using finite element in computational fracture mechanics have been well addressed by ingraffea [22]. the aspect of mesh refinement and associated error in computing stress intensity factors using finite element method has also been studied by miranda et al. [23]. it has been reported that excessive mesh refinement may significantly degrade the calculation accuracy in crack problems. they also pointed out that the ratio between the longest and shortest element edge lengths should be kept below 1600 to avoid calculation errors in sif calculations. for meshes with length ratios higher than 1600, improved numerical methods to deal with ill conditioned matrices would be necessary to not compromise the calculation accuracy of the calculated sif. many works on mesh generation algorithms and new methods to improve the numerical computation of sif values have been found in the works of miranda et al. [24, 25]. recent studies have also shown that the coefficients of higher order terms can also play an important role in the fracture process in notched or cracked structures. it has been observed that in addition to the singular term, the higher order terms, in particular, the first non-singular stress term ( known as the t stress) may also have significant effects on the near notch tip stress field. the t-stress is considered in some studies as an auxiliary parameter for increasing the accuracy of the results for ki. kim et al. [26], for instance, showed that this non-singular term has noticeable effects on the size and shape of plastic zone near the notch tip. it has been demonstrated that the first non-singular term may have considerable contributions to the stress components around the notch tip and also on the fracture resistance of notched components under mode i loading [27-29]. finite element modelling he numerical simulations were run by means of the finite element (fe) software ansys to determine the stress intensity factors of two edge cracks on the same side of the specimen. the specimen is schematized by a 2d model. the specimen thickness in fe analysis was kept 1.0 mm. the other dimensions are length l= 200 mm, width w= 80 mm and the model was studied in plane strain condition, the specimen geometry and detailed dimensions are shown in fig 1(a). the simulations have been run on full model. the stresses are applied at the two extremes of the specimen in the direction perpendicular to the crack plane (fig. 1(b)). figure 1(a): specimen geometry. figure 1(b): specimen with boundary conditions. isoparametric quadrilateral element (plane 82) having 8 nodes with singularity elements at and around the crack tip has been used throughout the analysis and is shown in fig. 2. the singularity phenomenon at the vicinity of the crack tips has been addressed by applying triangular element option of the plane 82 element. the radius of second row of elements is taken as a/8, where a is the half crack length and the radius ratio (second row/first row) is adjusted t n. bisht et alii, frattura ed integrità strutturale, 32 (2015) 1-12; doi: 10.3221/igf-esis.32.01 3 automatically. the number of elements around the circumference is taken as 32. the fe modelling parameters are optimized on the basis of the error analysis presented in fig. 3 for two edge cracks. figure 2: plane 82 element with 8-nodes. figure 3(a): variation of stress intensity factor with number of crack tip elements. figure 3(b): variation of stress intensity factor with radius of first row of elements, ki,fem and ki, the are finite element and theoretical based computations of mode i stress intensity factor the error analysis has been done by varying the radius of the first row of the crack tip element and number of elements in the first row and computing the stress intensity factor for various parameters. the density of the fe mesh is modified by varying the number of the elements of the first row as 16, 20, 24, 32 and 40, keeping the radius of the first row as a/8 where a has been taken as 10 mm. also, the radius of the first row (a/n) around the crack tip is varied, taking n= 8, 10, 12, 16 and 20 with 32 number of elements. for comparison ki is calculated theoretically from the relation given for two collinear edge cracks [30]. it is found that the ki calculation errors stay below 0.8% for all meshing strategies. fig. 3(a-b) show variation of the normalized ki (fe based computation to the actual (theoretical) mode i stress intensity factor) for different mesh configurations. it can be observed from fig. 3 that, on average, the calculation with the radius of first element as 1.25 mm (i.e. a / 8=1.25) and number of elements around the crack tip as 32 yields least error i.e. closest to unity amongst the other meshing strategies. it is mentioned by miranda et al. [32] that calculation error and associated standard deviation tend to increase for higher mesh density. these increasing errors are a result of an ill conditioned numerical problem [32]. the increasing error due to the decrease in first crack tip radius may be due to the stress singularity that is present at the crack tip and the linear elastic fracture mechanics concept fails to predict the stress intensity factor. the other fe modelling parameters are shown in fig. 4 and 5. in fig. 5 node 1 is the crack tip node and the nodes 2, 3, 4 and 5 are used to represent the crack path for evaluating the fracture parameters. the nodes are essentially taken in this order when a full crack model is employed. for the numerical simulation, a uniform pressure intensity of 1.0 mpa (80 n) is applied to the upper and lower edges in the vertical direction (y axis). the material properties are young’s modulus e=70 gpa, poisson’s ratio=0.33. the mode i and mode ii stress intensity factors are computed from the following relations using the displacement extrapolation method. n. bisht et alii, frattura ed integrità strutturale, 32 (2015) 1-12; doi: 10.3221/igf-esis.32.01 4 figure 4: crack tip meshing and different parameters. figure 5: nodes used for defining crack path. the analysis uses a fit of the nodal displacements in the vicinity of the crack. the actual displacements at and near a crack for linear elastic materials are given by paris [31] as:     3 3 2 1 cos cos   2 3 sin sin 4 2 2 2 4 2 2 2 i iik kr ru k k g g                       (1)    θ 3 32 1 sin sin   2 3 cos cos 4 2 2 2 4 2 2 2 i iik kr rv k k g g                      (2) 2  sin   2 2 iiik rw g    (3) where: u, v, w = displacements in a local cartesian coordinate system, shown in fig.6. r, θ = coordinates in a local cylindrical coordinate system, shown in fig.6. g = shear modulus ki, kii, kiii = stress intensity factors relating to deformation shapes, shown in fig.6. ν = poisson’s ratio n. bisht et alii, frattura ed integrità strutturale, 32 (2015) 1-12; doi: 10.3221/igf-esis.32.01 5 figure 6: representation of crack with coordinate system. evaluating eq. (1-3) at 0180   and dropping the higher order terms eq. (1-3) yields:  ii k r u 1 k 2g 2π   (4)   2 2 ik rv k g   (5) 2     2 iiik rw g   (6) for full crack models eq. (4-6) can be reorganized to   | |   2i vg k k r    (7)   | | 2 1 ii ug k k r     (8)   | |   2iii w k g r    (9) where δv, δu and δw are the motions of one crack face with respect to the other. k= 3−4ν, for plane strain or axisymmetric; (3−ν)/ (1+ ν) for plane stress; where ν is poisson's ratio. the final factor    v r  is evaluated based on the nodal displacements and locations. for practical purposes the value of    v r  is approximated by limiting the value of    v r  by simply evaluating the following expression for a small fixed value of r (small in relation to the size of the crack) as: | |   v a br r   (10) at point i shown in fig.7, v=0 hence, in the limiting condition n. bisht et alii, frattura ed integrità strutturale, 32 (2015) 1-12; doi: 10.3221/igf-esis.32.01 6 0 | |   lim r v a r  (11) figure 7: representation of nodes on crack face used for crack analysis. the eq. (7) becomes 2   2  i ga k k  (12) similarly | |   u c dr r   (13) at point i of fig. 7 u=0 hence, in the limiting condition 0 | | lim r u c r  (14) and eq. (8) becomes,   2 1 ii gc k k   (15) similarly for evaluating kiii, using | |w e fr r   (16) and at point i of fig. 7 w=0 and eq. 9 in the limiting condition becomes, 0 | | lim   r w e r  (17) thus, eq. 9 becomes   2iiik ge (18) n. bisht et alii, frattura ed integrità strutturale, 32 (2015) 1-12; doi: 10.3221/igf-esis.32.01 7 mode iii stress intensity factor in the present investigation is not considered because the thickness of the plate in fe analysis is taken as unity. however, the three dimensional effect or plate thickness effect on the stress intensity factors can be seen in the work of kotousov et al. [33, 34]. in the present fe analysis, out of balance convergence and degree of freedom increment convergence criteria have been applied. the tolerance level has been taken as 0.001. these criteria are well documented in the ansys manual [35]. results and discussion stress intensity factor he stress intensity factors computed were normalized by k0 given for single edge cracked plate under uniform tension [30].  0  ak a f w  (19) where σ is the applied stress, a is the crack length and  af w is the geometric correction factor given as:   2 3 4 1.12 0.23 10.56 21.74 30.42 a a a aaf w w w w w                            (20) in the present investigation, a = 10 mm, w = 80 mm. thus geometric correction factor becomes  af w  1.13 (21) and k0 = 400.57 mpa mm fig. 8 shows the effect of crack offset distance h on the normalized stress intensity factors. from fig. 8 it can be seen that normalized mode i sif (ki/k0) for h=0.5 mm reduces drastically to about 66% value as compared to single edge crack. as the crack offset distance increases beyond h=0.5 mm the normalised mode i stress intensity factor starts increasing, and its value becomes 95% of single edge crack when h becomes 20 mm. so, it can be said that there is a shielding effect due to proximity of cracks due to which mode i sif decreases as compared to single edge crack, however this shielding effect ceases to exist when the cracks move farther away. figure 8: variation of normalized stress intensity factors with crack offset distance h. the variation of normalized mode ii sif kii/k0 shown in fig.8 is just opposite to that of mode i. fig. 8 shows that when normalised mode i sif attains the minimum value, associated mode ii attains the maximum value which is almost 19% of mode i sif for single edge crack. this behaviour is seen at h= 0.5 mm. thereafter mode ii sif decreases with increase t n. bisht et alii, frattura ed integrità strutturale, 32 (2015) 1-12; doi: 10.3221/igf-esis.32.01 8 of crack offset distance h. there is an amplification effect as far as mode ii sif is concerned which also becomes insignificant for remotely placed cracks. this indicates that when two edge cracks are extremely close to each other (h ≤ 0.5 mm), shielding effect occurs and the normal stress components σxx and σyy reduces causing the shear component of the stress to increase. as a result, mode i sif decreases and mode ii sif increases. now, as the crack offset distance h increases from h=0.5 mm to higher value, mode i sif increases and mode ii sif decreases. it is found that for about h ≥ 20 mm, the crack interaction becomes negligible and both cracks behave as a single crack. the variation of normalised kii/ki with h is shown in fig. 9. this figure reveals that when the cracks are very close to each other mode ii sif plays a significant role in crack growth and contributes about 27% of mode i sif. beyond h= 20 mm, the contribution of mode ii sif remains below 2% only. these results indicate that special care should be taken while predicting growth from stress intensity factor, particularly when two or more edge cracks are very close to each other. figure 9: variation of kii/ki with crack offset distance h. von-mises stresses distribution of von-mises stresses around the crack tip for various values of h at uniform stress σ = 1 mpa are shown in fig. 10-11. von-mises stresses are computed taking midpoint or element stresses. identical boundary conditions, crack tip element size and full mesh model have been used for all crack configurations. the distribution of equivalent von mises stresses for two edge cracks configuration for h = 2 mm and h = 20 mm have been shown in fig.10 and 11. from fig. 10 and 11 it can be observed that with increasing crack offset distance h the equivalent von mises stresses increases. this indicates that crack offset distance have greater affect on the state of stress ahead of the crack tip. analysis of the state of stress around the crack tip the two dimensional finite element model presented in this work has been used to investigate the state of stress around the crack tip in plane strain condition. the state of stress at a radial distance r from the crack tip is schematically shown in fig. 12. the results obtained for different crack configurations are presented in fig. 13 to 15. the stresses computed for double edge cracks are normalized with σy0 which is the fe solution for single edge crack corresponding to θ=00 and r=0.5 mm along the crack plane. the variation of normalised σxx, σyy and τxy (normalised by σyy for single edge crack= 731.57 mpa) for two edge cracks on the same side of a rectangular plate and separated by offset distance h= 0, 2, 10 and 16 mm are shown in fig. 13 – 15. the variation of these stresses around the crack tip at a radius of 0.5 mm from the crack tip is shown for the assumed plane strain condition. identical loading, boundary conditions and mesh arrangements were used for all crack offset conditions. the stresses are taken at the midpoint of each crack tip element. it has been observed that symmetrical n. bisht et alii, frattura ed integrità strutturale, 32 (2015) 1-12; doi: 10.3221/igf-esis.32.01 9 distribution of σyy occurred on the upper and lower side of the crack, whereas σxx and τxy show asymmetrical distribution around the crack tip. figure 10: von mises stress distribution for two offset edge crack geometry for h=2 mm. figure 11: von mises stress distribution for two offset edge crack geometry for h=20. figure 12: schematic representation of state of stress ahead of the crack tip, r and θ are the polar coordinates. the σxx component is about 0.1 to 0.75 times of σyy at the crack tip element. fig. 13 and 14 also reveal that σxx and σyy are lower in magnitude compared to a single edge crack. the normal stress component σxx increases with increasing offset distance, but its magnitude remains less than a single edge crack. it is also seen that σxx is least when two cracks are very close to each other (h ≤ 2 mm). it is well established that mode i sif mainly depends upon variation of σyy at the crack tip. the present analysis shows that σyy is higher for single edge crack as compared to multiple cracks with different offset distance h. hence, in fig. 9 ki for h = 0 mm is found to be higher as compared to other multiple crack configurations. it is also seen in fig.13 that σyy is minimum for h = 2 mm. thus mode i sif shown in fig. 8 is found to attain minimum value at h = 2 mm, and thereafter it increases but remains less than a single edge crack. the variation of τxy for different crack offset distance h = 0, 2, 10, 16 mm is shown in fig.15. the figure shows that shearing stress is zero for single edge crack (h = 0 mm) and maximum for h = 2 mm. it is seen that as h increases, the shearing stress decreases. thus, mode ii sif which is mainly due to shear component attains maximum value at h = 2 mm and thereafter it reduces as h increases. the results shown in fig. 8 also confirms that for single edge crack (h = 0 mm), mode ii sif is zero. this is also in conformity with the theoretical results for single edge crack. n. bisht et alii, frattura ed integrità strutturale, 32 (2015) 1-12; doi: 10.3221/igf-esis.32.01 10 figure 13: variation of σxx/σy with h for specimen geometry a1. figure 14: variation of σyy/σy with h for specimen geometry a1. figure 15: variation of τxy/σy with h for specimen geometry a1. conclusions 1. there is a shielding effect on mode i sif due to the presence of a neighbouring crack. 2. the shielding becomes more pronounced as the cracks move towards each other. n. bisht et alii, frattura ed integrità strutturale, 32 (2015) 1-12; doi: 10.3221/igf-esis.32.01 11 3. for mode ii sif there is an amplification effect. mode ii sif which is otherwise absent for single cracks develops due to the presence of neighbouring cracks. 4. the amplification is more significant for closer cracks. 5. both the amplification and shielding effects cease to exist as cracks move farther away from each other. references [1] inglis, c.e., stresses in a plate due to the presence of cracks and sharp corners, transactions-institute of naval architect, 55 (1913) 219-230. [2] griffith, a.a., the phenomenon of rupture and flow in solids, trans. royal soci. london, 221 (1920) 163-198. [3] westgaard, h. m., bearing pressure and cracks, j. appl. maths mech., 6 (1939) 49-53. [4] wen-ye, t., gabbert, u., multiple crack interaction problems in magnetoelectrostatic solids, europ. j. mech. a/solids, 23 (2004) 599. [5] sneddon, i. n., lowengrub, m., crack problems in classical theory of elasticity, 1st edn., wiley, new york, (1969). [6] westergaard, h. m., bearing pressure and cracks, asme j. appl. mech., 6 (1939) 49-53. [7] muskhelishvili, n. i., some basic problems of mathematical theory of elasticity, 4th edn. holland, noordhoff, (1977). [8] erdogan, f., stress intensity factors, asme j. appl. mech., 50 (1983) 992-1002. [9] bowie, o. l., analysis of an infinite plate containing radial cracks originating at the boundary of an internal circular hole, j. math. phys., 25 (1956) 60-71. [10] isida, m., stress intensity factors for the tension of an eccentrically cracked strip, asme j. appl. mech., 33 (1966) 674-675. [11] williams, m. l., on the stress distribution at the base of a stationary crack, asme j appl. mech., 24 (1957) 104-114. [12] sih, g. c., paris, p. c., erdogan, f., crack tip stress intensity factors for plane extension and plate bending problems, asme j. appl. mech., 29 (1962) 306-314. [13] eshelby, j. d., franck, f. c., nabarro, f. r. n., the equilibrium of linear arrays of dislocations, phil. mag., 42 (1951) 351-364. [14] watwood, v. b., the finite element method for prediction of crack behaviour, nucl. engg. des., 11 (1969) 323-332. [15] cruse, t. a., numerical solutions in three dimensional elastostatics, int. j. solids struct., 5 (1969) 1259-1274. [16] nisitani, h., solutions of notch problems by the body force method in fracture mechanics, edited by g. c. sih, fifth ed. noordhoff international, (1978) 1-68. [17] crouch, s. l., starfield, a. m., boundary element method in solid mechanics, with application in rock mechanics and geological mechanics, 1st edn., george allen & unwin, (1983). [18] pook, l. p., stress intensity factor expressions for regular crack arrays in pressurised cylinders, fatig. fract. eng. mater. struct., 13 (1990) 135–143. [19] rooke, d. p., cartwright, d. j., compendium of stress intensity factors great britain, ministry of defence, procurement executive, (1976). [20] ingraffea, a.r., wawrzynek, p.a., comprehensive structural integrity, 1st edn., r.d.b.a.h. mang (ed.), elsevier science ltd., oxford, (2003). [21] sinclair, g., stress singularities in classical elasticity—ii: asymptotic identification, app. mech. rev., 57 (2004) 251– 298. [22] ingraffea, a.r., encyclopaedia of computational mechanics, john wiley and sons, (2004). [23] de oliveira miranda, a. c., meggiolaro, m. a., martha, l. f., de castro, j. t. p., stress intensity factor predictions: comparison and roundoff error, comput. mater. sci., 53 (2012) 354–358. [24] miranda, a.c.o., meggiolaro, m.a., castro, j.t.p., martha, l.f., bittencourt, t.n., fatigue life and crack path predictions in generic 2d structural components, eng. fract. mech., 70 (2003) 1259–1279. [25] de oliveira miranda, a.c., meggiolaro, m. a., de castro, j. t. p., martha, l. f., fatigue life prediction of complex 2d components under mixed-mode variable amplitude loading, int. j. fatig., 25 (2003) 1157–1167. [26] kim, j. k., cho, s. b., effect of second non-singular term of mode i near the tip of a v notched crack, fatig. fract. eng. mater. struct., 2 (2009) 346–356. [27] ayatollahi, m. r., nejati, m., determination of nsifs and coefficients of higher order terms for sharp notches using finite element method, int. j. mech. sci., 53 (2011) 164-177. [28] ayatollahi, m. r., dehghany, m., on t-stresses near v-notches, int. j. fract., 165 (2010) 121-126. n. bisht et alii, frattura ed integrità strutturale, 32 (2015) 1-12; doi: 10.3221/igf-esis.32.01 12 [29] ayatollahi, m. r., nejati, m., experimental evaluation of stress field around the sharp notches using photoelasticity, mater. des., 32 (2011) 561-569. [30] prashant, k., elements of fracture mechanics, first ed., mcgraw-hill book company, new-delhi, (2009). [31] paris, p. c., sih, g. c., in astm spec. tech. publ., stp 381, astm philadelphia, stp 381 (1965) 30-83. [32] rice, j. r., matrix computations and mathematical software, 1st edn., mcgraw-hill computer science series, mcgraw-hill, (1981). [33] kotousov, a., berto, f., lazzarin, p., pegorin, f. three dimensional finite element mixed fracture mode under antiplane loading of a crack, theo. app. fract. mech., 62 (2012) 26–33. [34] kotousov, a., effect of plate thickness on stress state at sharp notches and the strength paradox of thick plates, int. j. solids struct., 47 (2010) 1916–1923. [35] ansys manual release 8.0. microsoft word numero_35_art_39 o. demir et alii, frattura ed integrità strutturale, 35 (2016) 340-349; doi: 10.3221/igf-esis.35.39 340 focussed on crack paths investigation of mixed mode-i/ii fracture problems part 2: evaluation and development of mixed mode-i/ii fracture criteria o. demir department of mechanical engineering, sakarya university, 54187, sakarya, turkey department of mechanical and manufacturing engineering, bilecik şeyh edebali university, 11230, bilecik, turkey oguzhan.demir@ogr.sakarya.edu.tr a. o. ayhan department of mechanical engineering, sakarya university, 54187, sakarya, turkey ayhan@sakarya.edu.tr abstract. in this study, experimental and numerical results of compact tension shear (cts) specimen and a new specimen type under in-plane mixed mode (mode-i/ii) loading conditions are compared with existing inplane mixed mode fracture criteria to investigate and understand the nature of fracture behavior properly. the material used in numerical and experimental analyses is al 7075-t651 aluminum machined from rolled plates in the l-t rolling direction (crack plane is perpendicular to the rolling direction). in part 1 of the study, results from numerical and experimental analyses are given. having computed the mixed mode stress intensity factors from the numerical analyses, fracture loads are predicted and compared with different mixed mode-i/ii fracture criteria. the experimental and numerical results show that many criteria are in good agreement with each other for predominately mode i to moderate mixed mode conditions. however, existing criteria increasingly differ from the experimental measurements for highly mode-ii conditions. using the computational and experimental results obtained, improved empirical mixed mode i/ii fracture criteria for fracture condition and angle are also proposed. keywords. fracture; mixed mode; mode-i/ii; compact tension shear; fracture criteria. introduction lthough many fracture mechanics problems seen in practice can adequately be analyzed by taking into account mode-i conditions, there are still many problems that are subjected to mixed mode loading, for which mode-i analysis approaches are not sufficient. the mode mixity of the problem can be due to orientation of an initial defect existing in the structure due to imperfections or processes such as manufacturing operations. another source of mixed mode loading on the crack is due to the nature of loads that exist on the structure. for such situations, analyses of the cracked structure under mixed mode loads and related criteria for fracture conditions are needed. the most basic type of mixed mode fracture is mode-i/ii, in which both mode-i (opening) and mode-ii (shearing) loads act on the crack tip. a o. demir et alii, frattura ed integrità strutturale, 35 (2016) 340-349; doi: 10.3221/igf-esis.35.39 341 there are various studies that exist in the literature for mixed mode-i/ii fracture. one of the most common fracture criterion for in-plane mixed mode problems is maximum tangential (circumferential) stress (mts), which was proposed by erdogan and sih [1]. this criterion assumes that, crack propagation starts from the crack tip radially when the tangential stress reaches a maximum value and exceeds a critical value or if an equivalent stress intensity factor (keq) reaches the fracture toughness (kic) propagation becomes unstable and fracture occurs. in this criterion keq and crack deflection angle are given by: 20 0 0 3 cos cos sin 2 2 2 eq i ii ick k k k         (1) 2 2 2 0 2 2 3 8 arccos 9 ii i i ii i ii k k k k k k           (2) another common fracture criterion developed by sih [2], is minimum strain energy density criterion. it is based on the elastic energy density. according to this criterion crack extends in the direction of minimum strain energy density factor and if the minimum strain energy density factor reaches a critical value, which depends on material, crack becomes unstable. substituting the stress intensity factor, ki and kii into the following equations crack deflection angle, θ, can be obtained:      2 2i i ii ii2 cosθ 1 sinθk 2 2 cos 2θ 1 cosθ k k 1 6 cosθ sinθ k 0                     (3)      2 2i i ii ii2 cos 2θ 1 cosθ k 2 1 sinθ 4 sin 2θ k k 1)cosθ 6 cos 2θ k 0                    (4) nuismer [3] and hussain [4] expressed the maximum energy release rate criterion according to the griffith’s theory [5] in several different forms. according to this criterion, crack propagates in the direction that strain energy release rate is maximum and crack becomes unstable if the maximum strain energy release rate exceeds a critical value. crack deflection angles obtained from maximum circumferential stress criterion and maximum strain energy release rate criterion are the same. consequently, the results of crack deflection angles according to erdogan and sih, and nuismer and hussain criterion are identical. koo and choy [6] developed the maximum tangential strain criterion proposed by chang [7] and expressed a new criterion called maximum tangential strain energy density criterion. initial crack growth occurs in the direction of maximum tangential strain energy density factor and if the factor reaches a critical value crack initiation occurs. the tangential strain energy density factor c and coefficients are defined by: 2 2 11 1 12 1 2 22 2k k k kc b b b   (5)  11 1/ 64 (1 cos )( 2 cos )b         12 1/ 64 (sin 3 / 2 3cos )b        (6)   222 1/ 64 (3sin )( 3cos )b      where =3-4ν for plane strain and =(3-ν)/(1+ ν) for plane stress conditions, ν is poisson's ratio and μ is shear modulus. then the crack initiation angle θ can be obtained by: 0 c     and 2 2 0 c     (7) o. demir et alii, frattura ed integrità strutturale, 35 (2016) 340-349; doi: 10.3221/igf-esis.35.39 342 for the prediction of fracture limit the determination of equivalent stress intensity factor (sif) is essential. several criteria exist to compute the equivalent sif. one of them is erdogan and sih criterion. an equivalent sif was given in eq. (1). pook [8] developed an in plane mixed mode criterion and proposed the following eq. (8) that equivalent sif can be obtained from the equation with substituting the ki and kii sif. 1 2 2 th th th 0.08 0.83 0.75ii i i k k k k k k                 (8) tanaka [9] introduced the concept of the equivalent sif for mixed mode conditions and the equivalent sif was defined by: 1 4 4 4 eq i ii8k k k       (9) another criterion developed for in plane mixed mode-i/ii problems is richard criterion [10, 11]. richard proposed an equivalent sif and crack deflection angle formulation and verified the formulations by a large number of experiments [12]. according to this criterion, if the proposed equivalent sif exceeds a critical value, unstable crack growth occurs. the equivalent sif and crack deflection angle were given by: 2 2 eq 1 1 4( ) 2 2 i i ii ic k k k k k    (10) 2 0 155.5 83.4 ii ii i ii i ii k k k k k k                 (11) α1 is a material parameter describes the ratio of kic/kiic and generally taken as 1.155. in this study, fracture experiments of cts specimen and a new type of specimen called t-specimen, which has smaller dimensions and requires less material, are conducted to check the validity of some of the existing criteria for mixed modei/ii fracture conditions and to develop a further refined mode-i/ii fracture criterion. in part 1 of the study, details and results of the finite element models including fracture submodels of cts specimen and description of the test procedure for cts and t-specimens are given. the outline of this paper is as follows: in the next section, experimental results of cts and t-specimen are given. this is followed by comparisons of the experimental results with existing criteria and development of an improved mode-i/ii fracture criteria. experimental results of mode-i/ii fracture tests his section deals with experimental results of mode-i/ii fracture tests of cts and t-specimen. in the first subsection, experimental results of cts specimen are given in terms of fracture loads, crack lengths and crack deflection angles for all tests under different loading angles. the second sub-section contains experimental results of t-specimen under different loading angles performed. results of cts specimen experiments in this sub-section, results from the in-plane mixed mode fracture tests of cts specimen are presented for different loading angles. in part 1 of this article, details of the experimental set-up, including materials and equipment used, specimen preparation and testing procedure, are explained. tab. 1 summarizes different cases tested. critical fracture loads are determined by load-displacement curves and crack deflection angles are measured from the fracture surfaces. also, a 25 mm-thick cts specimen is tested for 30° loading angle and its results are given in the table. t o. demir et alii, frattura ed integrità strutturale, 35 (2016) 340-349; doi: 10.3221/igf-esis.35.39 343 specimen no specimen type loading angle (°) thickness (mm) crack length (mm) pre-crack load (kn) experimental critical load (kn) crack deflection angle (°) lt-01-150814-01 cts 0 10.00 46.50 6.5 11.38 0.00 lt-01-251214-01 cts 15 10.07 46.07 6.5 26.11 -9.41 lt-01-251214-02 cts 15 10.06 45.96 6.5 26.68 -8.75 lt-01-150814-02 cts 30 9.60 45.08 6.5 27.52 -26.85 lt-01-150814-03 cts 30 10.10 44.94 6.5 28.59 -25.36 lt-01-150814-04 cts 30 10.20 45.03 6.5 29.57 -26.42 lt-01-090215-01 cts 30 25.00 46.51 6.5 60.23 -26.57 lt-01-150814-06 cts 45 10.13 44.95 6.5 35.61 -35.71 lt-01-150814-07 cts 45 10.17 44.75 6.5 33.00 -36.03 lt-01-220814-11 cts 45 10.13 45.40 6.5 35.60 -36.54 lt-01-150814-09 cts 60 10.16 44.93 6.5 46.25 -41.18 lt-01-150814-10 cts 60 10.15 45.22 6.5 46.90 -41.11 lt-01-150814-12 cts 60 10.18 45.20 6.5 45.71 lt-01-251214-03 cts 75 10.10 46.38 6.5 62.73 -50.66 lt-01-150814-04 cts 75 10.14 45.24 6.5 68.07 -53.64 table 1: experimental results of cts specimen obtained from the mixed mode fracture tests. results of t-specimen experiments tab. 2 summarizes experimental studies of 25 mm-thick t-specimen performed under different loading cases. as mentioned in part 1 of this paper that loading requirements of 25 mm-thick t-specimens under all loading cases are lower than 10 mm-thick cts specimens. specimen no specimen type loading angle (°) thickness (mm) crack length (mm) pre-crack load (kn) experimental critical load (kn) crack deflection angle (°) t-lt-01-251214-01 t 0 24.87 26.03 10.5 19.60 0.00 t-lt-01-180115-12 t 15 25.00 26.93 10.5 19.80 -11.73 t-lt-01-180115-13 t 15 24.98 26.34 10.5 19.70 -9.34 t-lt-01-180115-14 t 30 24.98 26.21 10.5 23.07 -21.95 t-lt-01-180115-15 t 30 25.00 26.90 10.5 20.64 -18.07 t-lt-01-251214-02 t 45 25.00 25.24 10.5 28.09 -26.26 t-lt-01-251214-03 t 45 25.01 25.46 10.5 29.21 -24.15 t-lt-01-251214-04 t 60 24.96 27.13 10.5 33.59 -33.69 t-lt-01-090215-18 t 60 25.00 26.58 10.5 34.76 -36.41 t-lt-01-180115-17 t 75 25.03 26.89 10.5 54.31 -50.19 t-lt-01-220215-22 t 75 24.96 26.70 10.5 55.04 -53.17 table 2: experimental results of t specimen obtained from the mixed mode fracture tests. o. demir et alii, frattura ed integrità strutturale, 35 (2016) 340-349; doi: 10.3221/igf-esis.35.39 344 mode-i/ii fracture criterion development n this section, development of a mixed mode-i/ii fracture criterion by making use of sifs from finite element models and experimental results and comparisons with other existing criteria are presented. in the first sub-section, details of mode-i/ii fracture criterion development is presented. in the second sub-section, comparisons of developed and some of the existing mode-i/ii fracture criteria in terms of fracture loads are presented. this is followed by comparisons of the developed criterion with other criteria in the literature in terms of crack deflection angles. procedure for mode-i/ii fracture criterion development in an effort to develop an improved empirical mixed mode-i/ii fracture criterion, mixed mode sifs obtained from detailed finite element models of cts specimen and fracture results from the tests for different loading angles are used. these data are used in a regression analysis using datafittm [13], from which the empirical mixed mode-i/ii fracture criterion formula is determined by performing regression analysis (curve fitting). comparisons of mode-i/ii fracture criteria in terms of fracture loads in this subsection, the predicted fracture load values from the developed criterion are compared with other existing criteria in the literature. applying the method mentioned above, equivalent stress intensity factor (keq) in the developed criterion is defined by: 2 3 eq i ii ii iik a (b k ) (c / k ) (d / k ) (e / k )      (12) this equation is developed by using cts specimen data obtained for 15°, 30°, 45°, 60° and 75° loading cases. 0° loading case data is excluded to develop the improved in-plane mixed mode-i/ii equivalent sif equation. coefficients in eq. (12) are given in tab. 3. a b c d e 3.0731 1.0311 -7.3269 5.7100 -1.4163 table 3: coefficients of developed equivalent sif equation (cts specimen data used). experimental loads and predicted fracture loads obtained from the developed criterion for the cts specimen along with other existing criteria in the literature for different loading cases are given in tab. 4. the results are also plotted and shown in fig. 1. it can be seen from the fig. 1 that for erdogan and sih, richard and pook criteria, divergence occurs after 45° loading case and increases with increasing loading angle. tanaka criterion is good agreement with the experimental results up to 60° loading case but the criterion does not produce accurate result for 75° loading case. critical load values obtained from the developed criterion and experimental results are almost identical with an average error rate of 2.8% for all loading angles performed. experimental and predicted t-specimen fracture load values obtained from the developed criterion along with other existing criteria in the literature for different loading cases are given in tab. 5. critical load values of t-specimen according to developed criterion are acquired by substituting mixed mode sifs obtained from detailed finite element analyses of t-specimen for different loading angles in the equivalent sif equation developed by using aonly cts specimen data. comparisons of experimental and predicted critical fracture load values of t-specimen are presented in fig. 2. as can be seen in the figure, all criteria are in good agreement with the experimental results up to 60° loading case. divergence occurs after 60° loading case for existing criteria. critical load values obtained from the developed criterion and experimental results are almost identical with an average error rate of 5.5% for all loading angles performed. thus, criterion is validated with t-specimen fracture results. furthermore, t-specimen is also proposed as a new specimen type, since its experimental results are validated with the developed and existing criteria. i o. demir et alii, frattura ed integrità strutturale, 35 (2016) 340-349; doi: 10.3221/igf-esis.35.39 345 specimen no loading angle (°) critical load values (kn) richard [10] erdogan and sih [1] pook [8] tanaka [9] developed criterion experimental results lt-01-150814-01 0 12.24 12.24 12.24 12.24 11.38 lt-01-251214-01 15 23.66 23.64 23.64 23.92 26.38 26.11 lt-01-251214-02 15 23.78 23.75 23.75 24.04 26.41 26.68 lt-01-150814-02 30 26.83 26.68 26.69 28.20 27.05 27.52 lt-01-150814-03 30 28.45 28.30 28.30 29.89 28.62 28.59 lt-01-150814-04 30 28.63 28.48 28.48 30.10 28.86 29.57 lt-01-090215-01 30 62.20 61.88 61.89 65.29 63.02 60.23 lt-01-150814-06 45 32.05 31.70 31.70 35.86 34.96 35.61 lt-01-150814-07 45 32.40 32.06 32.05 36.14 35.27 33.00 lt-01-220814-11 45 30.94 30.60 30.60 34.61 33.57 35.60 lt-01-150814-09 60 37.78 37.20 37.17 42.36 46.23 46.25 lt-01-150814-10 60 36.86 36.29 36.26 41.28 44.86 46.90 lt-01-150814-12 60 37.03 36.45 36.42 41.46 45.08 45.71 lt-01-251214-03 75 40.92 40.39 40.32 37.29 63.37 62.73 lt-01-150814-04 75 45.01 44.34 44.36 40.89 72.84 68.07 table 4: experimental and predicted cts specimen fracture load values obtained from the developed criterion with other existing criteria in the literature. figure 1: comparisons of experimental and predicted cts specimen fracture loads. o. demir et alii, frattura ed integrità strutturale, 35 (2016) 340-349; doi: 10.3221/igf-esis.35.39 346 specimen no loading angle (°) critical load values (kn) richard [10] erdogan and sih [1] pook [8] tanaka [9] developed criterion experimental results t-lt-01-251214-01 0 21.01 21.01 21.01 21.01 19.60 t-lt-01-180115-12 15 20.21 20.19 20.20 20.36 19.67 19.80 t-lt-01-180115-13 15 20.46 20.44 20.44 20.60 19.92 19.70 t-lt-01-180115-14 30 22.22 22.15 22.16 22.81 21.24 23.07 t-lt-01-180115-15 30 21.88 21.82 21.82 22.51 20.88 20.64 t-lt-01-251214-02 45 27.05 26.86 26.86 29.01 25.87 28.09 t-lt-01-251214-03 45 26.75 26.56 26.56 28.62 25.56 29.21 t-lt-01-251214-04 60 30.89 30.50 30.49 35.10 30.98 33.59 t-lt-01-090215-18 60 32.20 31.81 31.81 36.46 32.06 34.76 t-lt-01-180115-17 75 43.93 43.24 43.19 46.07 52.14 54.31 t-lt-01-220215-22 75 43.97 43.29 43.23 45.89 52.50 55.04 table 5: experimental and predicted t-specimen fracture loads obtained from the developed criterion along with other existing criteria in the literature. figure 2: comparisons of experimental and predicted t-specimen fracture load values. comparisons of mode-i/ii fracture criteria in terms of crack deflection angle in this subsection, the predicted crack deflection angles from the developed criterion are compared with other existing criteria in the literature. in an effort to develop an improved empirical mode-i/ii crack deflection angle equation, mixed mode sifs obtained from detailed finite element models of cts and t-specimen and crack deflection angles obtained from the experiments for different loading angles are used. developed crack deflection angle equation is given by: 2 3 4 5 2 3 4 50 ln( ) ln( ) ln( ) ln( ) ln( )i i i i i ii ii ii ii iia b k c k d k e k f k gk hk ik jk kk            (13) 0° loading case data is excluded as is the case with the development of equivalent sif equation to develop the improved in-plane mixed mode-i/ii crack deflection angle equation. coefficients in eq. (13) are given in tab. 6. a b c d e f g h i j k -0.7907 2.0365 -3.4144 2.2844 -0.5928 0.0465 1.1736 -2.6539 1.8244 -0.5330 0.0565 table 6: coefficients of developed crack deflection angle equation. o. demir et alii, frattura ed integrità strutturale, 35 (2016) 340-349; doi: 10.3221/igf-esis.35.39 347 experimental and predicted cts specimen crack deflection angles obtained from the developed criterion with other existing criteria in the literature for different loading cases are given in tab. 7. comparison of this data is also presented as a graph in fig. 3. specimen no loading angle (°) crack deflection angles (°) erdogan and sih [1] richard [10] sih [2] nuismer [3] hussain [4] koo and choy [6] developed criterion experimental results lt-01-150814-01 0 0.00 0.00 0.00 0.00 0.00 0.00 0.00 lt-01-251214-01 15 -10.28 -12.44 -10.20 -10.28 -10.28 -4.99 -10.49 -9.41 lt-01-251214-02 15 -10.37 -12.54 -10.29 -10.37 -10.37 -5.04 -10.67 -8.75 lt-01-150814-02 30 -21.86 -24.36 -21.22 -21.86 -21.86 -12.78 -24.97 -26.85 lt-01-150814-03 30 -21.72 -24.22 -20.22 -21.72 -21.72 -11.86 -24.70 -25.36 lt-01-150814-04 30 -21.87 -24.37 -21.24 -21.87 -21.87 -12.79 -24.94 -26.42 lt-01-090215-01 30 -21.52 -24.02 -20.91 -21.52 -21.52 -12.49 -25.47 -26.57 lt-01-150814-06 45 -33.64 -35.91 -32.08 -33.64 -33.64 -27.82 -37.03 -35.71 lt-01-150814-07 45 -33.03 -35.31 -31.51 -33.03 -33.03 -26.82 -36.21 -36.03 lt-01-220814-11 45 -33.64 -35.90 -32.07 -33.64 -33.64 -27.82 -37.89 -36.54 lt-01-150814-09 60 -46.00 -48.75 -44.37 -46.00 -46.00 -47.82 -41.03 -41.18 lt-01-150814-10 60 -46.13 -48.90 -44.52 -46.13 -46.13 -48.01 -41.79 -41.11 lt-01-150814-12 60 -46.14 -48.91 -44.53 -46.14 -46.14 -48.01 -41.75 lt-01-251214-03 75 -58.39 -63.16 -60.71 -58.39 -58.39 -60.45 -49.48 -50.66 lt-01-150814-04 75 -58.53 -63.33 -60.94 -58.53 -58.53 -60.55 -54.50 -53.64 table 7: comparison of the predicted crack deflection angles using the developed criterion and comparison with other existing criteria in the literature. it can be seen from the fig. 3 that all criteria show a similar tendency for all loading cases except koo and choy criterion. when compared with experimental results, crack deflection angles obtained from the criteria, except koo and choy criterion, show a similar tendency up to 60° loading case and divergence occurs after 60° loading case for all criteria. crack deflection angle values obtained from the developed criterion and experimental results are almost identical with an average error rate of 5.13% for all loading angles performed. figure 3: comparisons of experimental and predicted crack deflection angles cts specimen. o. demir et alii, frattura ed integrità strutturale, 35 (2016) 340-349; doi: 10.3221/igf-esis.35.39 348 in tab. 8, for the t-specimen experimental and predicted crack deflection angles obtained from the developed criterion using the cts specimen data and predictions of other existing criteria in the literature for different loading cases are given. specimen no loading angle (°) crack deflection angles (°) erdogan and sih [1] richard [10] sih [2] nuismer [3] hussain [4] koo and choy [6] developed criterion experimental results t-lt-01-251214-01 0 0.00 0.00 0.00 0.00 0.00 0.00 0.00 t-lt-01-180115-12 15 -8.55 -10.52 -8.50 -8.55 -8.55 -4.09 -10.94 -11.73 t-lt-01-180115-13 15 -8.33 -10.27 -8.29 -8.33 -8.33 -3.98 -9.38 -9.34 t-lt-01-180115-14 30 -15.90 -18.39 -15.63 -15.90 -15.90 -8.28 -19.99 -21.95 t-lt-01-180115-15 30 -16.45 -18.95 -16.15 -16.45 -16.45 -8.64 -20.76 -18.07 t-lt-01-251214-02 45 -25.84 -28.25 -24.90 -25.84 -25.84 -16.77 -24.56 -26.26 t-lt-01-251214-03 45 -25.40 -27.83 -24.50 -25.40 -25.40 -16.29 -24.18 -24.15 t-lt-01-251214-04 60 -37.31 -39.59 -35.54 -37.31 -37.31 -34.12 -35.32 -33.69 t-lt-01-090215-18 60 -36.24 -38.51 -34.52 -36.24 -36.24 -32.26 -37.42 -36.41 t-lt-01-180115-17 75 -51.38 -54.85 -50.73 -51.38 -51.38 -54.33 -46.97 -50.19 t-lt-01-220215-22 75 -51.69 -55.20 -51.12 -51.69 -51.69 -54.65 -46.39 -52.06 table 8: comparison of the predicted crack deflection angles using the developed criterion and comparison with other existing criteria in the literature, t-specimen. comparison of experimental and predicted crack deflection angles for the t-specimen are presented in fig. 4. as can be seen in the figure, all criteria show a similar tendency with each other and experimental results for all loading cases, except koo and choy criterion. crack deflection angle values obtained from the developed criterion and experimental results are very close with an average error of 6.25% for all loading angles studied. figure 4: comparisons of experimental and predicted crack deflection angles t-specimen. conclusions n this study, fracture experiments of cts specimen and a new type of specimen, called t-specimen, which has smaller dimensions and requires less material were conducted to check the validity of some of the existing criteria for mixed mode-i/ii fracture conditions and to develop a further refined mode-i/ii fracture criterion. a new improved empirical mixed mode-i/ii criteria for onset of fracture and deflection angle were proposed and comparisons of the developed and existing mode-i/ii fracture criteria in terms of fracture loads and crack deflection angles were presented. i o. demir et alii, frattura ed integrità strutturale, 35 (2016) 340-349; doi: 10.3221/igf-esis.35.39 349 fracture load results showed that many criteria are in good agreement with each other for predominately mode i to moderate mixed mode conditions, but that the existing criteria increasingly differ from the experimental measurements for highly mode-ii conditions. acknowledgements he financial support by the scientific and technological research council of turkey (tübi̇tak) for this study under project no 113m407 is gratefully acknowledged. references [1] erdogan, f., sih, g.c., on the crack extension in plane loading and transverse shear, j. basic eng., 85 (1963) 519527. [2] sih, g.c., macdonald, b., fracture mechanics applied to engineering problems-strain energy density fracture criterion, eng. fract. mech., 6 (1974) 361-386. [3] nuismer, r.j., an energy release rate criterion for mixed mode fracture, int j fatigue, 11 (1975) 245-250. [4] hussain, m.a., pu, s.u., underwood, j., strain energy release rate for a crack under combined mode i and ii, astm stp, 560 (1974) 2-28. [5] griffith, a., the phenomena of flow and rupture in solids, philosophical transactions of the royal society of london, a 221 (1920) 163-198. [6] koo, j.m., choy, y.s., a new mixed mode fracture criterion: maximum tangential strain energy density criterion, eng. fract. mech., 39 (1991) 443-449. [7] chang, k.j., on the maximum strain criterion—a new approach to the angled crack problem, eng. fract. mech., 14 (1981) 107-124. [8] carlson, r.l., kardomateas, g. a., introduction to fatigue in metals and composites, first ed., london, uk, (1996). [9] tanaka, k., fatigue crack propagation from a crack inclined to the cyclic tensile axis, eng. fract. mech., 6 (1974) 493507. [10] richard, h.a., bruchvorhersage bei überlagerter normalund schubbeanspruchung von rissen, vdi-verlag, düsseldorf, (1985). [11] richard, h.a., in: structural failure, product liability and technical insurance, rossmanith (ed.), inderscience enterprises ltd., genf., (1987). [12] richard, h.a., theoretical crack path determination, international conference on fatigue crack paths, parma (italy), (fcp 2003), conference chairmen: a. carpinteri, l.p. pook. 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/hrv (za stvaranje adobe pdf dokumenata najpogodnijih za visokokvalitetni ispis prije tiskanja koristite ove postavke. stvoreni pdf dokumenti mogu se otvoriti acrobat i adobe reader 5.0 i kasnijim verzijama.) /hun 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can be opened with acrobat and adobe reader 5.0 and later.) >> /namespace [ (adobe) (common) (1.0) ] /othernamespaces [ << /asreaderspreads false /cropimagestoframes true /errorcontrol /warnandcontinue /flattenerignorespreadoverrides false /includeguidesgrids false /includenonprinting false /includeslug false /namespace [ (adobe) (indesign) (4.0) ] /omitplacedbitmaps false /omitplacedeps false /omitplacedpdf false /simulateoverprint /legacy >> << /addbleedmarks false /addcolorbars false /addcropmarks false /addpageinfo false /addregmarks false /convertcolors /converttocmyk /destinationprofilename () /destinationprofileselector /documentcmyk /downsample16bitimages true /flattenerpreset << /presetselector /mediumresolution >> /formelements false /generatestructure false /includebookmarks false /includehyperlinks false /includeinteractive false /includelayers false /includeprofiles false /multimediahandling /useobjectsettings /namespace [ (adobe) (creativesuite) (2.0) ] /pdfxoutputintentprofileselector /documentcmyk /preserveediting true /untaggedcmykhandling /leaveuntagged /untaggedrgbhandling /usedocumentprofile /usedocumentbleed false >> ] >> setdistillerparams << /hwresolution [2400 2400] /pagesize [612.000 792.000] >> setpagedevice shot peening processes to obtain nanocrystalline surfaces in metal alloys: m. zappalorto et alii, frattura ed integrità strutturale, 7 (2009) 29-56; doi: 10.3221/igf-esis.07.03 29 distribuzioni di tensione per intagli soggetti a torsione in condizioni elastiche ed elastoplastiche michele zappalorto, paolo lazzarin dipartimento di tecnica e gestione dei sistemi industriali, università di padova, stradella san nicola, 3-36100, vicenza, italia, email: zappalorto@gest.unipd.it, plazzarin@gest.unipd.it riassunto. il lavoro riporta delle soluzioni analitiche in forma chiusa per le distribuzioni di tensione generate da intagli circonferenziali in componenti assialsimmetrici soggetti a torsione, in condizioni lineari elastiche ed elastoplastiche. il problema teorico in condizioni lineari elastiche è stato impostato e risolto utilizzando la teoria dei potenziali nel dominio complesso e una serie di opportuni sistemi di riferimento in coordinate curvilinee, evitando l’uso di mappature conformi. le soluzioni proposte hanno un ampio range di applicabilità, in termini di dimensioni e forma dell’intaglio e di diametro dell’albero. il problema elastoplastico è stato invece risolto utilizzando la tecnica delle trasformazioni odografiche, al fine di rendere lineari le equazioni nonlineari fondamentali del problema. il contributo rappresenta la sintesi di una serie di lavori più ampi a cura degli stessi autori. abstract. closed form solutions for the elastic and elastic-plastic stress fields created by circumferential notches in an axisymmetric shaft under torsional loading are developed. the linear elastic boundary value problem has been formulated by an approach using complex potential functions and some curvilinear coordinate systems. the solutions obtained for the shear stresses have a wide range of applicability, both in terms of the size and shape of the notches and the diameter of the shafts. conversely the elastic-plastic problem has been solved in closed-form by using the hodograph transformation technique, which reduces the non-linear governing equations into a linear equation system. the present paper is a synthesis of some contributions recently published the same authors. parole chiave. intagli, distribuzioni di tensione elastiche e elastoplastiche, nsifs, densità di energia di deformazione (sed). introduzione a conoscenza delle distribuzioni lineari elastiche delle tensioni nelle adiacenze di intagli è di grande importanza nella valutazione della resistenza a fatica ad alto numero di cicli di componenti strutturali. il contributo più famoso allo studio analitico di alberi indeboliti da intagli raccordati circonferenziali soggetti a torsione è dovuto a neuber [1], il quale determinò in modo sistematico il fattore teorico di concentrazione delle tensioni kt distinguendo tra intagli profondi e poco profondi (deep e shallow notches). le analisi di neuber si basavano sull’utilizzo combinato di un sistema di coordinate curvilinee e di una funzione di tensione tridimensionale reale. in relazione alle distribuzioni di tensione in forma chiusa, di fondamentale importanza è il lavoro di [2], i quali riuscirono a esprimere i campi di tensione nelle adiacenze di una blunt crack per i tre principali modi di sollecitazione, evidenziando analogie e differenze rispetto al caso della sharp crack. degni di menzione sono anche alcuni recenti lavori di seweryn e molski [3], qian e hasebe [4] e dunn et al. [5]. questi ricercatori hanno fornito le distribuzioni di tensione generate da intagli a v non raccordati in presenza di sollecitazioni di taglio antiplanare. per le tensioni è stata sempre utilizzata una formulazione a variabili separate. uno degli obiettivi del presente lavoro è quello di fornire delle espressioni in forma chiusa per le distribuzioni di tensione e deformazione indotte da intagli circonferenziali di forma semi-ellittica, parabolica o iperbolica in alberi assialsimmetrici soggetti a torsione. il problema matematico è stato formalizzato utilizzando la teoria dei potenziali nel dominio complesso l http://www.gruppofrattura.it http://dx.medra.org/10.3221/igf-esis.07.03&auth=true m. zappalorto et alii,, frattura ed integrità strutturale, 7 (2009) 29-56; doi: 10.3221/igf-esis.07.03 30 in combinazione con due opportuni sistemi di riferimento in coordinate curvilinee, evitando così l’uso di mappature conformi. e’ messo in evidenza analiticamente il legame esistente tra le distribuzioni delle tensioni e i principali parametri geometrici dell’intaglio (come raggio di raccordo e angolo di apertura). le soluzioni proposte hanno carattere generale e un ampio range di applicabilità, consentendo di trattare intagli di forma anche molto differente semplicemente variando il valore dei parametri geometrici significativi. tali soluzioni si riconducono, in alcuni casi particolari, ad alcune soluzioni classiche già riportate nella letteratura precedente (cricca, blunt crack, intaglio a v non raccordato). quando il raggio di raccordo all’apice dell’intaglio è ridotto, il livello di tensione all’apice diviene molto alto, superando il limite di snervamento e inducendo quindi una zona plastica all’apice dell’intaglio di dimensioni paragonabili a quella della zona di processo che controlla il meccanismo di frattura. in tali circostanze, la conoscenza dell’influenza indotta dalla zona plastica localizzata sulle distribuzioni di tensione vicino a cricche o intagli è di fondamentale importanza nella valutazione dell’affidabilità in servizio dei componenti meccanici. negli ultimi anni in letteratura è stata posta una grande attenzione alla determinazione dei campi di tensione e deformazione a modo i, ii e iii nelle adiacenze di cricche o intagli a v a spigolo vivo in presenza di plasticità. di fondamentale importanza sono i lavori di hutchinson [6,7] e rice e rosengren [8] che fornirono una soluzione elastoplastica per i campi asintotici di tensione indotti da una cricca sollecitata a modo i. nei decenni successivi, notevole attenzione è stata posta agli effetti di eventuali termini di ordine superiore sulle distribuzioni di tensione in presenza di sollecitazioni sia di modo i, sia di modo ii [9]; le analisi sono state inoltre estese agli intagli a spigolo vivo con angolo di apertura diverso da zero [10] per i quali è stato discusso anche il caso di modo misto (i+ii) in presenza di ampi angoli di apertura [11]. in questi lavori il materiale è modellato secondo la teoria j2 e le funzioni angolari sono determinate numericamente (tipicamente con tecniche di multi-shooting). il problema nonlineare antiplanare può invece essere risolto in forma chiusa con l’ausilio di mappature conformi che permettono di linearizzare le equazioni differenziali che governano il problema [12, 13]. parallelamente, numerosi lavori in letteratura sono stati dedicati alla determinazione delle tensioni e delle deformazioni elastoplastiche all’apice di intagli raccordati. tra questi sicuramente il più famoso è il lavoro di neuber [14], il quale analizzò un corpo prismatico con due intagli raccordati simmetrici in condizioni di taglio antiplanare e ottenne una soluzione secondo la quale la media geometrica dei fattori di concentrazione delle tensioni e delle deformazioni è uguale al fattore teorico di concentrazione delle tensioni, per una qualsiasi legge costitutiva che lega le tensioni alle deformazioni. la ‘regola di neuber’ è basata sull’ipotesi che il legame esistente tra la tensione reale all’apice dell’intaglio e la tensione nominale possa essere rappresentato con una particolare funzione definita da neuber “leading function”. come possibile alternativa alla regola di neuber, molski e glinka [15] formalizzarono il criterio dell’equivalenza della densità di energia di deformazione considerando componenti con intagli raccordati soggetti a trazione o flessione, in presenza di plasticità localizzata. quel criterio è anche stato recente riformulato per intagli a spigolo vivo, considerando la costanza dell’energia di deformazione su un volume finito di materiale centrato sull’apice dell’intaglio [16]. tuttavia, in letteratura non esiste ancora una soluzione in forma chiusa per le distribuzioni di tensione nella zona plastica all’apice di intagli raccordati, né esiste un modello analitico che fornisca una transizione graduale tra meccanica della frattura e meccanica dell’intaglio elastoplastiche in funzione del raggio di raccordo. il presente lavoro, focalizzato su questi temi, considera un intaglio parabolico soggetto a taglio antiplanare e un materiale elastico perfettamente plastico o elastico incrudente con legge di potenza. più precisamente gli obiettivi del lavoro possono essere così riassunti: fornire un frame comune per l’analisi dei campi di tensione e deformazione indotti da cricche o intagli parabolici in condizioni di taglio antiplanare e un legame analitico tra sif plastici ed sif elastici (così come ottenuti da un’analisi lineare elastica); esprimere analiticamente la variazione della sed all’apice dell’intaglio o su un volume finito che circonda l’apice di una cricca rispetto al caso lineare elastico. il presente contributo rappresenta la sintesi di una serie di lavori più ampi a cura degli stessi autori [17-20]. intagli soggetti a torsione in regime lineare elastico preliminari matematici i consideri un corpo assialsimmetrico indebolito da un intaglio di forma generica, costituito da materiale isotropo e omogeneo. si consideri inoltre un sistema di riferimento cartesiano (x, y, z) con l’origine ad un’opportuna distanza dall’apice dell’intaglio (fig. 1). sia tale corpo sollecitato da una tensione nominale di taglio τ, la quale genera solamente uno spostamento w in direzione z, normale al piano (x,y) dell’intaglio. in queste condizioni valgono per le tensioni, le deformazioni e lo spostamento w le seguenti relazioni: s http://www.gruppofrattura.it http://dx.medra.org/10.3221/igf-esis.07.03&auth=true m. zappalorto et alii, frattura ed integrità strutturale, 7 (2009) 29-56; doi: 10.3221/igf-esis.07.03 31 )z('hi zyzx =τ−τ g (z)'h iγγ zyzx =− { } g )z(hre w = (1a,b,c) in queste relazioni, la funzione h(z) è una funzione olomorfa di forma arbitraria e variabile da caso a caso a seconda delle condizioni al contorno del problema. si noti come le tensioni e gli spostamenti non siano influenzati dall’origine del sistema di riferimento, e ciò rende le espressioni (1a-c) indipendenti da tale scelta. e’ infine opportuno osservare come il simbolo “z” venga utilizzato in questo lavoro per indicare sia la variabile complessa iyxz += , sia la coordinata cartesiana antiplanare mostrata in fig. 1. τ τ z y x τzy τzx τyz τxz figura 1: componente assialsimmetrico indebolito da un intaglio circonferenziale e soggetto a taglio antiplanare. intagli di forma semiellittica considerazioni di carattere generale. il problema relativo ad intagli di forma ellittica può essere affrontato utilizzando il sistema di coordinate curvilinee generato dalla trasformazione (fig. 2): ζcoshcz = (2) dove c è una costante e iyxz += e ηξζ i += sono le variabili complesse rispettivamente nel piano fisico e nel piano trasformato. y x η r y x (a) (b) figura 2: (a) famiglia di ellissi con gli stessi fuochi; (b) costruzione parametrica dell’ellisse. differenti valori di ξ danno origine a una famiglia di ellissi tutte caratterizzate dagli stessi fuochi, posizionati a cx ±= . fissato 0ξξ = e variando η, si ottiene una particolare ellisse appartenente alla famiglia confocale, di semiassi maggiore e minore rispettivamente pari a 0ξcoshca = e 0ξsinhcb = . http://www.gruppofrattura.it http://dx.medra.org/10.3221/igf-esis.07.03&auth=true m. zappalorto et alii,, frattura ed integrità strutturale, 7 (2009) 29-56; doi: 10.3221/igf-esis.07.03 32 l’equazione (2) può essere invertita per x, y>0. si ottiene: cln 2 sinay 2 cosaxln 22 −      β++      β+=ξ ,       ξ =η sinhc y arcsin (3) e ciò permette, una volta note le coordinate fisiche di un punto nel piano (x,y), di determinare i valori corrispondenti delle variabili trasformate. i parametri a e β sono forniti in forma chiusa nel riferimento [17]. si consideri un intaglio circonferenziale semiellittico in un albero assialsimmetrico intagliato e soggetto a torsione. il potenziale che utilizzeremo per ottenere la soluzione presenta la seguente forma: ζ+ζ= sinhbccoshac)z(h (4) quindi, poichè: ζ ζ sinhc z = ∂ ∂ , è possibile scrivere:       η−ξ η − η−ξ ξ ++ +      η−ξ η + η−ξ ξ += ζ+++= ∂ ζ∂ ⋅ ζ∂ ∂ = 2cos2cosh 2sin b 2cos2cosh 2sinh bai 2cos2cosh 2sin b 2cos2cosh 2sinh ba coth)ibb()iaa( z )z(h )z('h 122 211 2121 (5) l’espressione generale delle tensioni risulta quindi: η−ξ η + η−ξ ξ −−=τ η−ξ η + η−ξ ξ +=τ 2cos2cosh 2sin b 2cos2cosh 2sinh ba 2cos2cosh 2sin b 2cos2cosh 2sinh ba 122zy 21 1 zx (6) condizioni al contorno per un albero di sezione infinita. se l’intaglio ha dimensioni infinite, le condizioni al contorno possono essere espresse nella seguente forma: se ∞→z , ττ =zy e 0zx =τ , dove τ è la tensione di taglio nominale; sul bordo dell’intaglio ( 0ξξ = ), 0z =ξτ . quando ( 0ξξ = ) e ( 2 π η = ) allora ξτ=τ zzy ; quando 2 π η = , 0zx =τ . sostituendo le condizioni al contorno nelle eq. 6 si ottengono i coefficienti ai e bi e le tensioni risultano quindi:       η−ξ η − τ −=τ       − η−ξ ξ − τ =τ 2cos2cosh 2sin ba a b 2cos2cosh 2sinh a ba zx zy (7) all’apice dell’intaglio le eq. 7 danno:       +τ=      − −ξ ξ − τ =τ ξ=ξ =η b a 1b 12cosh 2sinh a ba 0 0 0zy 0 (8) http://www.gruppofrattura.it http://dx.medra.org/10.3221/igf-esis.07.03&auth=true m. zappalorto et alii, frattura ed integrità strutturale, 7 (2009) 29-56; doi: 10.3221/igf-esis.07.03 33 e quindi il fattore teorico di concentrazione delle tensioni risulta a/b1k t += , in accordo con neuber [1]. la soluzione ottenuta, che risulta matematicamente esatta solo nel caso di un albero di diametro infinito, può tuttavia essere applicata anche ad alberi di dimensione finita, almeno fino a quando il rapporto a/r è inferiore a 0.05, con errori nella determinazione della tensione massima inferiori al 10%. per fare ciò è però necessario tenere in considerazione l’andamento decrescente lineare della tensione nominale nella sezione, semplicemente con l’aggiunta alle espressioni delle tensioni di un fattore correttivo: ( ) ( )        ξη−+ ξ−ξη −                     η−ξ η − τ−       − η−ξ ξ − τ =       τ τ 0 0 zx zy coshcoscar coshcoshcosc 1 2cos2cosh 2sin ba a b 2cos2cosh 2sinh a ba (9) le fig. 3 e 4 mostrano un confronto tra i risultati analitici e i risultati di alcune analisi agli elementi finiti condotte su alberi in cui la dimensione dell’intaglio è molto inferiore rispetto al raggio netto dell’albero. l’accordo appare molto soddisfacente. 0 1 2 3 1 10 100 x [mm] fem eq. (9) a=1 r=200 a/b=2 2r a mt τ z y / τ mt figura 3: componente di tensione zyτ lungo la bisettrice geometrica dell’intaglio. le tensioni sono normalizzate rispetto alla tensione nominale. 0 90 η [degrees] eq. (9) fem, a'=4, a'/b'=2 fem, a'=60, a'/b'=2 a=1 r=200 a/b=2 τ z j / τ 80 70 60 50 40 30 20 10 0 0.2 0.4 0.6 0.8 1.2 1.0 τzy / τ τzy / τ τzx/ τ figura 4: componenti di tensione lungo due percorsi ellittici centrati nell’origine del sistema di riferimento (x,y); a’=4 mm e a’=60 mm, mentre a’/b’=2. le tensioni sono normalizzate rispetto alla tensione nominale. cricca circonferenziale su albero infinito. la cricca circonferenziale può essere trattata da un punto di vista matematico come un intaglio semiellittico in cui il semiasse minore b tende a zero. utilizzando quindi i risultati della precedente sessione per intagli semiellittici, è possibile scrivere: http://www.gruppofrattura.it http://dx.medra.org/10.3221/igf-esis.07.03&auth=true m. zappalorto et alii,, frattura ed integrità strutturale, 7 (2009) 29-56; doi: 10.3221/igf-esis.07.03 34 zxzy22 i az z τ+τ= − τ (10) dove a è la lunghezza della cricca. si noti come l’espressione posta alla sinistra nell’equazione (10) coincida esattamente con la funzione di tensione di westergaard per il modo iii. dall’equazione (10) è quindi agevole determinare dapprima l’espressione del fattore di intensificazione delle tensioni: a)ax(2limk 0yzyaxiii πτ=τ−π= =→ (11) e quindi l’espressione delle tensioni in un intorno dell’apice della cricca:                   ϕ       ϕ− π =                   ϕ       ϕ− τ =       τ τ 2 cos 2 sin r2 k 2 cos 2 sin r2 a iii zy zx (12) intaglio semicircolare su albero infinito. in linea di principio il sistema di coordinate ellittiche utilizzato nella soluzione precedente non è più valido nel caso di intaglio circolare, quando a=b (c=0), che comporta una discontinuità matematica nella definizione del sistema in questione. nonostante ciò si può notare che la soluzione precedente continua a essere valida anche quando il rapporto a/b è molto vicino a 1, permettendo quindi di trattare l’intaglio semicircolare come il limite per 1(a/b) → . quest’idea è confermata da analisi agli elementi finiti condotte su alberi quasi infiniti (a/r=0.005) indeboliti da intagli semiellittici con a/b=1.001, come mostrato in fig. 5. 0 0.5 1.0 1.5 2.0 2.5 0 10 20 30 40 50 60 70 80 90 η [degrees] eq (9) fem fem a=1 r=200 a/b=1.001 τ z j / τ τzx / τ τzy / τ 2r a mt mt figura 5: componenti di tensione zyτ and zxτ sul bordo dell’intaglio nel caso di un intaglio che può essere considerato semicircolare (a/b=1.001). le tensioni sono normalizzate rispetto alla tensione nominale. condizioni al contorno per un albero di sezione finita. come prima approssimazione nel caso di alberi intagliati a diametro finito è possibile mantenere per il potenziale complesso la medesima forma, e modificare in modo opportuno solo le condizioni al contorno; infatti le condizioni poste nella precedente trattazione all’infinito non risultano più valide. il nuovo sistema di condizioni al contorno risulta quindi: 0 12cosh 2sinh ba 11 2 zx =+ξ ξ +=τ π =η (13) 0 a b ba 12cosh 2sinh ba 22 0 0 22 2 zy 0 =−−=+ξ ξ −−=τ π =η ξ=ξ (14) http://www.gruppofrattura.it http://dx.medra.org/10.3221/igf-esis.07.03&auth=true m. zappalorto et alii, frattura ed integrità strutturale, 7 (2009) 29-56; doi: 10.3221/igf-esis.07.03 35 max22 0 0 22 0 zy b a ba 12cosh 2sinh ba0 τ=−−= −ξ ξ −−=τ =η ξ=ξ sostituendo, come prima, tali condizioni all’interno delle espressioni generali delle tensioni, eq. 6, è possibile ottenere i valori dei coefficienti ai e bi e quindi le espressioni finali delle tensioni: ( ) ( ) ( ) ( )                ξη−+ ξ−ξη − η−ξ η +− τ− =τ       ξη−+ ξ−ξη −      − η−ξ ξ +− τ =τ coshcoscar coshcoshcosc 1 2cos2cosh 2sin b a 1 k ba a coshcoscar coshcoshcosc 1b 2cos2cosh 2sinh a b a 1 k ba 0 0gross,t zx 0 0gross,t zy (15) particolarmente utile è la tensione τzy lungo la bisettrice dell’intaglio:       −−⋅      − −− τ =τ r )ax( 1b cx ax ba b 2222 max zy (16) che permette, tra l’altro, di determinare un’espressione approssimata del fattore teorico di concentrazione delle tensioni grazie a un’equazione di equilibrio alle rotazioni sulla sezione netta, mettendo in gioco il contributo fornito dalla tensione nominale, che varia da un valore massimo τ* a zero, e la componente di taglio generata dall’intaglio, τzy. effettuato quindi il cambio di variabile xart −+= , è possibile imporre l’equilibrio come: ∫ ∫∫ ∫ = π2 0 2r 0 zy π2 0 3r 0 * dtdθt τdtdθ r t τ (17) che fornisce: 3 g net,tgross,t 2 net,t r r kk; b a , r a c 1 b c k       ⋅=       ⋅= (18) essendo:     −               +−             −      +      +     −      + −   −      +−      +−             −      + +      +−         −              +      +⋅+           +−                  −      +     −          +             −      +                     +−     −      + − ⋅   =      b r a 115 r c r a 1 r a 113 r c r a 1 2 a 2 r a 12 r a 15 r c r a 1 3 r a 115 r c r a 1 r a 113 r2 ab r a 115 r c r a 13 r a 118 r c r a 1 r a 1 r c r a 1 r a r b ln 2 a b a , r a c 32222 222 322422 222 22 (19) intagli di forma parabolica e iperbolica una prima classe di soluzioni. consideriamo un sistema di coordinate iperboliche generate dalla seguente trasformazione [21, 22]: http://www.gruppofrattura.it http://dx.medra.org/10.3221/igf-esis.07.03&auth=true m. zappalorto et alii,, frattura ed integrità strutturale, 7 (2009) 29-56; doi: 10.3221/igf-esis.07.03 36 (20) dove c è una costante e iyxz += e ηξζ i+= sono le variabili complesse nel piano fisico e nel piano trasformato. differenti valori di η danno origine a una famiglia di iperboli tutte caratterizzate dagli stessi fuochi, posizionati alla distanza c±=x . fissato 0ηη = e variando ξ , si ottiene una particolare iperbole appartenente alla famiglia confocale, di costanti pari a 0ηcosca = e 0ηsincb = (vedi fig. 6). l’equazione (20) può essere invertita per (x, y)>0. si ottiene:           β + β + =η 2 cosax 2 sinay arctan (21)       η =ξ sinc y arcsinh (22) e ciò permette, una volta note le coordinate fisiche di un punto nel piano (x,y), di determinare i valori corrispondenti delle variabili trasformate. i parametri a e β sono riportati in forma chiusa in [19]. x y η=cost (a) x y η=η0 η0 x a b y = x a b y −= (b) η=-η0 figura 6: famiglia di iperboli confocali (a); profilo iperbolico (primo e quarto quadrante) (b). il problema di un intaglio iperbolico in un corpo infinito può essere affrontato osservando che la tensione nominale sulla sezione lorda deve essere nulla in modo tale da garantire una tensione nominale finita sulla sezione netta. un potenziale che soddisfa automaticamente questa condizione è il seguente: ζ+= c)iaa()z(h 21 (23) poiché: ζ= ζ∂ ∂ sinhc z , è possibile scrivere:       η−ξ ξη−ξη +      η−ξ ξη+ξη = ζ + = ∂ ζ∂ ⋅ ζ∂ ∂ = 2cos2cosh coshsina2sinhcosa2 i 2cos2cosh coshsina2sinhcosa2 sinh )iaa( z )z(h )z('h 1221 21 (24) l’espressione generale delle tensioni risulta quindi: coshz c  http://www.gruppofrattura.it http://dx.medra.org/10.3221/igf-esis.07.03&auth=true m. zappalorto et alii, frattura ed integrità strutturale, 7 (2009) 29-56; doi: 10.3221/igf-esis.07.03 37 η−ξ ξη−ξη −=τ η−ξ ξη+ξη =τ 2cos2cosh coshsina2sinhcosa2 2cos2cosh coshsina2sinhcosa2 12 zy 21 zx (25) imponendo le seguenti condizioni al contorno: 0a0 2cos1 sina2 2 0 02 0 0zx =→= η− η =τ =ξ η=η , ρ + τ=→ − =τ a 1 k a ac ca net,t* 122 1 max le distribuzioni di tensione assumono la seguente forma: η−ξ ξη ρ + τ=τ η−ξ ξη ρ + τ=τ 2cos2cosh coshsin a 1 k2 2cos2cosh sinhcos a 1 k2 net,t* zy net,t* zx (26) la soluzione ottenuta, che risulta matematicamente esatta solo nel caso di taglio antiplanare uniforme, può tuttavia essere applicata anche ad alberi soggetti a torsione; è però necessario tenere in considerazione l’andamento decrescente lineare della tensione nominale nella sezione, semplicemente con l’aggiunta alle espressioni delle tensioni di un fattore correttivo: ( ) ( )η−ξξη ξη ⋅ ρ + τ=τ η−ξξη ξη ⋅ ρ + τ=τ 2cos2coshcoshcos cosh2sin a 1 k 2cos2coshcoshcos 2sinhcos a 1 k * 0 2 net,t* zy * 0 2 net,t* zx (27) l’espressione del fattore teorico di concentrazione delle tensioni può, a questo punto, essere ottenuto con un’equazione di equilibrio sulla sezione netta: xdaxda )x( a zya ∫∫ τ=τ (28) che fornisce:       + ρ +       + ρ + = 1 a 21 1 a 1 4 3 k 2 net,t (29) in accordo con neuber [1]. le figure 7 e 8 mostrano un confronto tra i risultati analitici e quelli di alcune analisi agli elementi finiti condotte su alberi in cui la dimensione dell’intaglio è molto superiore rispetto al raggio netto dell’albero (intaglio “deep”); l’accordo appare molto soddisfacente. http://www.gruppofrattura.it http://dx.medra.org/10.3221/igf-esis.07.03&auth=true m. zappalorto et alii,, frattura ed integrità strutturale, 7 (2009) 29-56; doi: 10.3221/igf-esis.07.03 38 figura 7: componente di tensione zyτ lungo la bisettrice dell’intaglio normalizzata rispetto alla tensione nominale sull’area netta. figura 8: campi di tensione lungo il bordo dell’intaglio normalizzati rispetto alla tensione nominale sulla sezione netta. una seconda classe di soluzioni. consideriamo ora il sistema di coordinate curvilinee generato dalla trasformazione [1]: qwz = (30) dove iyxz += e ivuw += sono le variabili complesse nel piano fisico e nel piano trasformato e q è un numero reale funzione dell’angolo di apertura 2α: π γ = π α−π = 222 q (31) l’equazione (30) può essere riscritta nella forma seguente: ( ) 2 q 22 q 1 q 1 vur, q sinrv q cosru +=        ϕ = ϕ = (32a,b) il sistema di coordinate curvilinee introdotto permette di descrivere intagli parabolici (q=2) o iperbolici (1<q<2). la generica curva caratterizzata dal valore u=u0 interseca l’asse delle ascisse al valore r0, che dipende oltre che dall’angolo di apertura, anche dal raggio di raccordo per mezzo dell’espressione 1)/q(qr −= ρ0 (fig. 9). il problema matematico può essere risolto utilizzando lo stesso potenziale adottato per la trasformazione precedente: http://www.gruppofrattura.it http://dx.medra.org/10.3221/igf-esis.07.03&auth=true m. zappalorto et alii, frattura ed integrità strutturale, 7 (2009) 29-56; doi: 10.3221/igf-esis.07.03 39 ( ) ( ) ( ) 1q22 1q 21 1q 21 vuq ivu)iaa( ivuq )iaa( )z('h − − − + −+ = + + = . (33) y x ϕ τzr τzϕ r0 r u u=u0 x y u = 0 -ϕ/q (a) (b) figura 9: (a) sistema di coordinate curvilinee (u, v); (b) sistema di riferimento adottato per la soluzione. posta la seguente condizione al contorno: 0a0 qu a 11q 0 1 0v uuzx 0 =→==τ − = = si ottiene:               ϕ − =τ       ϕ − =τ               ϕ −− =τ       ϕ − =τ −ϕ − − − q 1 cos qr a q 1 sin qr a q 1q cos qr a q 1q sin qr a q 1q 2 z q 1q 2 zr q 1q 2 zy q 1q 2 zx (34a,b) indicando con q/13 =λ , è possibile determinare la costante a2 in funzione della tensione di taglio massima o del fattore generalizzato di intensificazione delle tensioni di modo iii: 1 03 max 2 3 3 2 3r a, 2 k a −λ ρ λ τ− = λπ −= (35) dove [ ])0,r(rlim2k z1 rr 3 3 o =ϕτπ= ϕ λ− → ρ + (36) le tensioni, espresse in coordinate polari risultano quindi:       ϕλ ϕλ       τ=       ϕτ ϕτ −λ ϕ 3 3 1 0 max z zr cos sin r r ),r( ),r( 3 (37) http://www.gruppofrattura.it http://dx.medra.org/10.3221/igf-esis.07.03&auth=true m. zappalorto et alii,, frattura ed integrità strutturale, 7 (2009) 29-56; doi: 10.3221/igf-esis.07.03 40 o in modo equivalente:       ϕλ ϕλ π =       ϕτ ϕτ −λρ ϕ 3 3 1 3 z zr cos sin 2 r k ),r( ),r( 3 (38) uguagliando le due espressioni si ottiene la seguente relazione fondamentale che lega nsif generalizzato e tensione massima: 31 0max3 r 2k λ− ρ πτ= (39) si noti come nel caso di un intaglio parabolico si abbia 2α=0, λ3=0.5 e quindi: ρπτ=ρ k max3 (40) questa relazione è stata ottenuta precedentemente da altri autori [23]. anche in questo caso è possibile correggere le distribuzioni delle tensioni per tenere in considerazione l’effetto di decremento lineare della tensione nominale:       ϕλ ϕλ             ϕ− −⋅τ=       ϕτ ϕτ −λ ϕ 3 3 1 0 ' ' max z zr cos sin r r r cos)rr( 1 ),r( ),r( 3 γ±≠ϕ (41) dove ( )( )q 0 q/cos r 'r ϕ = ( )ϕ−+= cos'rrr'r 0 (42) e r è il raggio della sezione netta dell’albero. con un’equazione di equilibrio sulla sezione netta è inoltre possibile determinare il valore del fattore teorico di concentrazione delle tensioni per alberi soggetti a torsione indeboliti da intagli profondi (deep notches): tdatda)t( a 0yzya ∫∫ =τ=τ (43) ottenendo la seguente espressione: ∑ = ++++ = 3 0j j 3 2 3 3 3 4 3 net,t i4 24s50s35s10s k (44) dove: ( ) [ ] ( ) ( ) ( ) 4333 2 33 2 2 3 3 2 331 432 0 0 0 33 6624 32136 92624 62436246 1 1 12 3 kski sski ssski kkkk k i r r )r,r(k s s −+−= ++−= +++−= ++++      += = −λ=α (45) le fig. 10 e 11 mostrano un confronto tra i risultati analitici e quelli di alcune analisi agli elementi finiti condotte su alberi indeboliti da intagli di varia forma e soggetti a torsione; l’accordo appare molto soddisfacente. http://www.gruppofrattura.it http://dx.medra.org/10.3221/igf-esis.07.03&auth=true m. zappalorto et alii, frattura ed integrità strutturale, 7 (2009) 29-56; doi: 10.3221/igf-esis.07.03 41 figura 10: campi di tensione su un percorso circolare di raggio pari a r=2 mm centrato sul fuoco dell’intaglio normalizzati rispetto alla tensione massima. figura 11: componenti di tensione zyτ lungo la bisettrice dell’intaglio normalizzate rispetto alla tensione massima (intagli iperbolici e parabolici). intaglio parabolico soggetto a taglio antiplanare in regime elastoplastico materiale a comportamento elastico perfettamente plastico onsideriamo un intaglio parabolico in un materiale elastico perfettamente plastico e soggetto a taglio antiplanare. utilizzando un approccio già adottato per la cricca (da irwin, [24], a unger, [25]), il confine elastoplastico ω può essere determinato introducendo le distribuzioni di tensioni lineari elastiche nella seguente condizione di snervamento: 2 0 2 zy 2 zx τ=τ+τ (46) ottenendo per il raggio plastico la seguente espressione: 2e 3 pz k 2 1 rr        τπ == ρ ω 0 (47) la funzione di tensione φ per lo sforzo antiplanare può essere legata alle componenti di tensione per mezzo delle seguenti espressioni: c http://www.gruppofrattura.it http://dx.medra.org/10.3221/igf-esis.07.03&auth=true m. zappalorto et alii,, frattura ed integrità strutturale, 7 (2009) 29-56; doi: 10.3221/igf-esis.07.03 42 xy zyzx ∂ φ∂ −=τ ∂ φ∂ =τ (48) introducendo φ nell’equazione (46) e chiamando x/p ∂∂= φ and y/q ∂∂= φ si ottiene: 2 0 22 qp τ=+ (49) l’equazione (49) può essere convertita in un sistema di equazioni differenziali ordinarie utilizzando il metodo di charpitlagrange [25-27]. il sistema risulta:            =      φ∂ ∂ + ∂ ∂ −= ∂ ∂ =      φ∂ ∂ + ∂ ∂ −= ∂ ∂ = ∂ ∂ = ∂ ∂ = ∂ ∂ = ∂ ∂ 0 f q y f s q 0 f p x f s p q2 q f s y p2 p f s x (50) dove s è una variabile ausiliaria. integrando rispetto a s e utilizzando i valori iniziali per s=0, cioè quando r = rpz, è possibile determinare le costanti ci e quindi le variabili x, y, p, q: tq t1p t1tr2ts2y )t21(rst12x 0 2 0 2 pz0 2 pz 2 0 τ−= −τ−= −+τ−= −+−τ−= (51) laddove 2 sin ϕ =t . il parametro ausiliario t può ora essere determinato in funzione delle coordinate fisiche x e y: ( ) 22pz yrx y t ++ = (52) quindi, le espressioni finali per le tensioni nella zona plastica risultano: ( ) ( ) 22pz pz 0zy 22 pz 0zx yrx rx yrx y ++ + τ=τ ++ τ−=τ (53) definiamo ora un nuovo sistema di riferimento con origine o’, traslato di pzr nella direzione x (vedi fig. 12). le coordinate rispetto a o’ risultano quindi: ( ) 22pz yrxr ++=        + =ϕ pzrx y arctan (54) http://www.gruppofrattura.it http://dx.medra.org/10.3221/igf-esis.07.03&auth=true m. zappalorto et alii, frattura ed integrità strutturale, 7 (2009) 29-56; doi: 10.3221/igf-esis.07.03 43 il confine elastoplastico continua a essere centrato nell’origine o, ma le componenti di tensione valutate rispetto al nuovo sistema di riferimento diventano: ϕτ=τ ϕτ−=τ cos sin 0zy 0zx (55) che costituisce una soluzione ammissibile in accordo con la teoria delle slip lines di sokolovskii [28]. l’entità della traslazione, pzr , dipende dall’nsif elastico e dalla tensione di snervamento τ0. l’estensione della zona plastica di fronte all’intaglio risulta quindi: 2 r2p pz ρ −=∆ (56a) )(r pz ϕ ϕ confine elasto-plastico confine elasto-plastico approssimato (a) (b) y ρ/2 ϕϕ rpz slip lines rpz o’ o p p figura 12: confronto tra la zona plastica approssimata (a), basata sulla soluzione lineare elastica, e la zona plastica esatta (b) per un materiale a comportamento elastico perfettamente plastico. quando l’intaglio diviene una cricca (ρ=0), si ottiene pz2rp =∆ e l’eq.56a risulta in accordo con la soluzione di hult e mcclintock [12, 25, 29]. si osservi inoltre come due intagli con lo stesso valore di e3ρk , ma con due differenti raggi di raccordo, presentano due differenti dimensioni della zona plastica; in particolare minore è il raggio di raccordo, maggiore è la zona plastica. si noti inoltre come sostituendo nell’equazione (56a) l’espressione di rpz e πρeeρ3 maxτk = sia possibile ottenere:         −      τ τ ρ=∆ 2 1 p 2 0 e max (56b) la relazione mostra che, a parità di tensione massima, la zona plastica è tanto minore quanto minore è il raggio di raccordo. lo spostamento w per un intaglio parabolico in condizioni lineari elastiche risulta pari a [19]: 2 sin g kr2 w e 3 ϕ π = ρ (57) quindi sostituendo r= pzr , si ottiene: ( ) ϕ τπ = ϕ π == ρρ ω sin g k 2 sin g kr2 ww 0 2e 3 e 3pz p (58) http://www.gruppofrattura.it http://dx.medra.org/10.3221/igf-esis.07.03&auth=true m. zappalorto et alii,, frattura ed integrità strutturale, 7 (2009) 29-56; doi: 10.3221/igf-esis.07.03 44 contemporaneamente, l’equazione di hencky: 0 y w x w zxzy =∂ ∂ τ− ∂ ∂ τ (59) assicura che w=const lungo le slip lines [28], e quindi eq. (23) può essere estesa all’intera zona plastica. gli scorrimenti, in coordinate cartesiane, risultano quindi: ( ) ( ) r cos g k y w r sincos g k x w 2 0 2e 3 zy 0 2e 3 zx ϕ πτ = ∂ ϕ∂ ⋅ ϕ∂ ∂ =γ ϕϕ πτ −= ∂ ϕ∂ ⋅ ϕ∂ ∂ =γ ρ ρ (60) materiale a comportamento incrudente con legge di potenza trattazione matematica. si consideri ora invece una legge lineare al di sotto dello snervamento e una legge di potenza per la zona plastica (fig. 13): 00 τ τ γ γ = se 0τ≤τ (61) n       τ τ = γ γ 00 se 0τ>τ dove g 0 0 τ γ = e ∞≤≤ n1 . in questa formulazione, γ0 è la deformazione a snervamento e 0τ è la corrispondente tensione di snervamento. n=1 γ τ ∞=n g ∞<< n1 figura 13: curva tensioni deformazioni utilizzata per al formulazione matematica del problema. sono inoltre valide le seguenti relazioni: 2 zy 2 zx 2 zy 2 zx γ+γ=γ τ+τ=τ , 0 zi 1n 00 zi τ τ       τ τ = γ γ − (62) utilizzando la trasformazione odografica suggerita da hult and mcclintock [12]: zxzy yx τ∂ ψ∂ = τ∂ ψ∂ −= (63) http://www.gruppofrattura.it http://dx.medra.org/10.3221/igf-esis.07.03&auth=true m. zappalorto et alii, frattura ed integrità strutturale, 7 (2009) 29-56; doi: 10.3221/igf-esis.07.03 45 le equazioni di equilibrio e compatibilità possono essere riscritte come[13]: 0 yx zyzx = τ∂ ∂ + τ∂ ∂ 0 yx zxzy = γ∂ ∂ − γ∂ ∂ (64a-b) purchè lo jacobiano delle trasformazioni non sia nullo. inoltre introducendo un sistema di coordinate polari nel piano delle tensioni: cos τ sinτ zyzx ϕτ=ϕτ= (65) è possible riscrivere le coordinate (x,y) nella seguente forma: cos sin y sin cos x zx zy τ ϕ ϕ∂ ψ∂ −ϕ τ∂ ψ∂ −= τ∂ ψ∂ = τ ϕ ϕ∂ ψ∂ +ϕ τ∂ ψ∂ −= τ∂ ψ∂ −= (66) sostituendo le eq.66 nell’equazione di compatibilità inversa e utilizzando la legge costitutiva del materiale si ottiene: 0 11 n 1 2 2 22 2 = ϕ∂ ψ∂ τ + τ∂ ψ∂ τ + τ∂ ψ∂ (67) l’eq. 67 è un’equazione di eulero che ammette soluzioni nella forma: )(~),( m ϕψτ=ϕτψ (68) sostituendo la (66) nella (65) si ottiene: ( ) 0)(''~m1mm n 1 )(~ =ϕψ+    +−ϕψ (69) e quindi: ( ) m1mm n 1 ),coscsinc(),( 21 m +−=ωϕω+ϕωτ=ϕτψ (70) e’ possibile a questo punto risolvere il problema di neumann, specificando il valore della derivata prima della funzione ),( ϕτψ sul confine del dominio di integrazione (ovvero sul confine elastoplastico). se si ipotizza quindi che, in analogia con il caso elastico perfettamente plastico, l’origine del sistema di riferimento risulti traslato rispetto al centro del confine elastoplastico di una quantità pari a k pzr , con k<1.0, (vedi fig. 14), dalle equazioni lineari elastiche si ottiene: 0 zx pz e 3 zx 0 zy pz e 3 zy r2 k2 sin r2 k2 cos τ τ −= π τ −= ϕ τ τ = π τ = ϕ ω ρ ω ω ρ ω (71) quindi dalle eq. 65, 71 si ha: http://www.gruppofrattura.it http://dx.medra.org/10.3221/igf-esis.07.03&auth=true m. zappalorto et alii,, frattura ed integrità strutturale, 7 (2009) 29-56; doi: 10.3221/igf-esis.07.03 46 ( ) ϕ=ϕϕ= τ τ τ τ −= ϕϕ =ϕ= +ϕ=+ϕ−= +               τ τ −=+      ϕ−=+ϕ= ωω ω ω ω 2sinrcossinr2r2 2 cos 2 sinr2sinry kr2cosrkrsin21r kr21rkr 2 sin21rkrcosrx pzpz 0 zy 0 zx pzpzpz pzpzpz 2 pz pz 2 0 zx pzpz 2 pzpzpz (72) rpz r ϕ centro del confine elastoplastico krpz y centro del sistema di coordinate polari confine elastoplastico figura 14: zona plastica per un materiale incrudente secondo legge di potenza. usando l’espressione: ϕ∂ τ∂ τ∂ ψ∂ + ϕ∂ τ∂ τ∂ ψ∂ = ϕ∂ ψ∂ zy zy zx zx (73) e le eq. 61, 63, 70: ( ) ϕ−τ= =ϕτϕ−ϕτ+ϕ=ϕτ⋅−ϕτ⋅=      ϕ∂ ψ∂ ωω ω sin)1k(r cos2sinrsinkr2cosrcosysinx 0pz 0pz0pzpz00 (74) in modo del tutto indipendente dall’eq. 70 è possibile ottenere: )sinccosc( ),( 21 m ϕω−ϕωωτ= ϕ∂ ϕτψ∂ (75) inoltre uguagliando le due formulazioni: ϕττ−=ψτ−=−==ω= −++ cosr)k1(,r)k1(c,nm,1, 0c n1n0pz 1n 0pz21 (76) e infine: ( ) ( ) ( ) ( ) ϕϕ+ τ τ− = ϕ−ϕ τ τ− = + + + + sincos1n rk1 y sincosn rk1 x 1n 1n 0pz 22 1n 1n 0pz (77a-b) http://www.gruppofrattura.it http://dx.medra.org/10.3221/igf-esis.07.03&auth=true m. zappalorto et alii, frattura ed integrità strutturale, 7 (2009) 29-56; doi: 10.3221/igf-esis.07.03 47 all’estremità delle zona plastica, lungo la bisettrice dell’intaglio, si ha ( ) pz1 rkx p += mentre 0ττ = . quindi: 1n 1n k + − = pzr1n n2 + =px (78) a partire dalle eq. 77a, b è possibile ottenere la coordinata radiale: f ~ xf ~ n r)k1( yxr 1n 1n 0 p1n 1n 0pz22 + + + + τ τ = τ τ− =+= (79) dove ϕ+ ϕ = 2 2 2 cos n sin f ~ (80) e infine, invertendo la (80), il modulo del vettore τ: 1n 1 p 0 f ~ r x +       τ=τ (81) le componenti di tensione e dei deformazione risultano quindi: ϕ      τ−=τ ϕ      τ=τ + + sinf ~ r x cosf ~ r x 1n 1 p 0zx 1n 1 p 0zy (82) ϕ      γ−= τ τ       τ τ γ=γ ϕ      γ= τ τ       τ τ γ=γ + − + − sinf ~ r x cosf ~ r x 1n n p 0 0 zx 1n 0 0zx 1n n p 0 0 zy 1n 0 0zy (83) e’ anche possibile ottenere il legame tra l’angolo ϕ nel piano delle tensioni e l’angolo ϕ nel piano fisico, utilizzando le seguenti relazioni: ( ) k2cos 2sin sincosn cossin1n cos sin x y 22 +ϕ ϕ = ϕ−ϕ ϕϕ+ = ϕ ϕ = (84) da cui: 2 sin 1n 1n arcsin       ϕ + − +ϕ =ϕ (85) l’intensità dei campi di tensione può essere anche espressa in funzione dell’nsif elastico, sostituendo esplicitamente xp: http://www.gruppofrattura.it http://dx.medra.org/10.3221/igf-esis.07.03&auth=true m. zappalorto et alii,, frattura ed integrità strutturale, 7 (2009) 29-56; doi: 10.3221/igf-esis.07.03 48 ( ) ( ) ( ) ( ) ϕ              τ +π −=τ ϕ              τ +π =τ ++ −ρ ++ −ρ sin r f~ 1n kn cos r f~ 1n kn 1n 1 1n 1 1n 0 2e 3 zx 1n 1 1n 1 1n 0 2e 3 zy (86) alternativamente è anche possibile definire un fattore plastico di intensificazione delle tensioni, )0,r(r2limk zy1n 1 2 r p 3 =ϕτπ= + ρ → ρ + e riscrivere quindi le tensioni nella forma: )sin( r f~ 2 k )cos( r f~ 2 k 1n 1 p 3 zx 1n 1 p 3 zy ϕ      π −=τ ϕ      π =τ + ρ + ρ (87) dove vale la seguente relazione tra nsif elastico ed nsif plastico: ( ) ( ) 1n 1 2e 3 1n 0 p 3 k1n n 2k + ρ − ρ       τ +π π= (88) inoltre, usando l’espressione ρπτρ k max ee 3 = , le componenti di tensione possono essere riscritte in funzione della tensione massima elastica: ( ) ( ) [ ] ( ) ( ) [ ] ϕ      ρ         τ + τ −=τ ϕ      ρ         τ + τ =τ + + + − + + + − sinf~ r21n n2 cosf~ r21n n2 1n 1 1n 1 1n 1 1n 0 2e max zx 1n 11n 1 1n 1 1n 0 2e max zy . (89) all’apice dell’intaglio risulta: ( ) ( ) 1n 1 1n 0 2e maxp max 2r 0zy 1n n2 +− ρ= =ϕ         τ + τ =τ=τ (90) che fornisce un legame analitico tra la massima tensione elastica e plastica. usando infine pmaxτ è possibile riscrivere le tensioni nella seguente forma: [ ] [ ] ϕ      ρτ−=τ ϕ      ρτ=τ + + + + + sinf~ r2 cosf~ r2 1n 1 1n 1 1n 1 p maxzx 1n 11n 1 p maxzy (91) http://www.gruppofrattura.it http://dx.medra.org/10.3221/igf-esis.07.03&auth=true m. zappalorto et alii, frattura ed integrità strutturale, 7 (2009) 29-56; doi: 10.3221/igf-esis.07.03 49 0.4 0.5 0.6 0.7 0.8 0.9 1 0.01 0.1 1 10 distanza dall’apice dell’intaglio [mm] markers: fea linea: zy teorica τ z y / τ m ax material n k [mpa] σ0 [mpa] e [mpa] elastic 1 206000 a 2.5 2000 166 206000 b 4 600 125 206000 c 8.33 950 450 206000 99 20 ρ/2 = 1 figura 15: componenti di tensione zyτ lungo la bisettrice dell’intaglio per differenti materiali, normalizzate rispetto alla tensione massima sull’apice. si noti infine come uguagliando le eq. 87 e 91, si ottiene la seguente relazione, valida in campo plastico, tra nsif e tensione massima: 1n 1 p max3 p 2 2k + ρ       ρπτ= (92) la fig. 15 mostra un confronto tra i risultati analitici e quelli di alcune analisi agli elementi finiti. l’accordo appare ancora soddisfacente. confronto con la regola di neuber. dall’ eq. 90 è possibile ricavare: ( ) g1n n2 2e maxp max p max τ + =γ⋅τ (93) dividendo ambo i membri per g nom 2 nomnom τ γτ =⋅ si ottiene: 2 tk1n n2 kk + =⋅ γτ (94) diversa dalla proposta di neuber [14]: 2 tkkk =⋅ γτ (95) tuttavia, tralasciando la traslazione del sistema di riferimento, e quindi assumendo pzrx p = , anzichè pzp r1n 2n x + = , si ottiene: ( )2emax 0 00 p max p max gr τ =      τγ=γ⋅τ p x (96) in accordo con neuber. legame con il criterio esed di molski e glinka. in presenza di una condizione di small scale yielding, molski e glinka [15] formalizzarono il criterio esed per intagli raccordati in presenza di sollecitazione di trazione o flessione nella seguente forma: http://www.gruppofrattura.it http://dx.medra.org/10.3221/igf-esis.07.03&auth=true m. zappalorto et alii,, frattura ed integrità strutturale, 7 (2009) 29-56; doi: 10.3221/igf-esis.07.03 50 pe ww = (97) con l’obiettivo di estendere tale criterio anche a intagli con raggio di raccordo nullo, lazzarin e zambardi [16] formularono l’ipotesi che in condizioni di deformazione piana la concentrazione di energia in un volume strutturale che abbracci l’apice dell’intaglio sia costante. tale volume deve essere completamente immerso in una zona dove i campi di tensione possono essere descritti utilizzando un solo termine nello sviluppo asintotico delle tensioni. in condizioni di small scale yielding, tale ipotesi si traduce nella costanza del valore medio della densità di energia di deformazione nel caso di sollecitazioni antiplanari la densità di energia può essere determinate come: ∫ γ γτ= 0 dw (98) fatte le opportune sostituzioni, l’energia all’apice dell’intaglio in condizioni plastiche risulta: ( ) ( ) g21n 1n g21n n4 w 2 0 2e max 2 2 p τ + − − τ + = (99) se n=1, l’equazione si semplifica in quella valida per il caso lineare elastico: ( ) g2 )1n(ww 2e max pe τ === (100) quindi: ( ) 2 e max 0 2 2 e p 1n 1n 1n n4 w w       τ τ + − − + = (101) e’ chiaro quindi che la costanza dell’energia all’apice dell’intaglio non è verificata. consideriamo ora il caso di una cricca e valutiamo l’incremento nel volume strutturale di raggio r dell’energia plastica rispetto a quella lineare elastica: ( ) ( ) ( ) ( ) 12eiii2 2 1n 1n 1 1n 1 1n 0 2e iii 1n 0 1n 0 1nγ 0 n 1 0 0p rk 1nπg f~n r f~ τ 1nπ kn gτ 1 1n n gτ τ 1n n dγ γ γ τw − + ++ − − − + + =                         ++ = + =      = ∫ (102) quindi: ( ) ( ) p3 2e iii 22 2 2 p p ir k 1ngπ n2 πr e w + == (103) dove: ϕ= ∫ π df~i 0 p3 (104) quando n=1 π=p3i , e quindi: http://www.gruppofrattura.it http://dx.medra.org/10.3221/igf-esis.07.03&auth=true m. zappalorto et alii, frattura ed integrità strutturale, 7 (2009) 29-56; doi: 10.3221/igf-esis.07.03 51 ( ) ( ) r k πe ν1 πr k g2 1 w 2e iii 2e iii e + == (105) in conclusione: ( ) p32 2 e p i 1nπ n4 w w + = (106) l’equazione (106) fornisce l’incremento nel volume strutturale di raggio r dell’energia plastica rispetto a quella lineare elastica. la tab. 1 fornisce i valori di p3i e ep/ww per alcuni valori dell’indice di incrudimento n. n i3p e p w w 1 3.14159 1 2.5 2.09436 1.36052 4 1.7726 1.44445 8.33 1.44376 1.46531 10 1.38556 1.45797 12 1.33475 1.44806 tabella 1: valori di i3p e ew/wp ottenuti con un’integrazione numerica dell’eq.104. fattori plastici di intensificazione delle tensioni per intagli a spigolo vivo soggetti a taglio antiplanare tilizzando in maniera opportuna le proprietà della trasformazione odografica, lazzarin e zappalorto [20] sono stati in grado di determinare la seguente relazione tra nsif di modo iii plastici ed elastici, valida per materiali che presentano un curva tensioni deformazioni conforme a quella rappresentata in fig. 13: ( ) m1 1 m 0 1 1 e3, 3 p3, 1 2 k m1 m 2k 3 − ω+ λ−           τ        π−λ −π= (107) nella relazione 107 k3,e rappresenta l’nsif determinato con un’analisi lineare elastica, ω è un parametro che dipende dall’angolo di apertura, mentre m dipende sia dall’angolo di apertura che dall’indice di incrudimento. l’eq. 107 è stata verificata con una serie di analisi agli elementi finiti, mostrando un ottimo accordo in regime di small scale yielding (un esempio è riportato in fig. 16). il frame analitico sviluppato da lazzarin e zappalorto ha permesso inoltre di determinare delle espressioni in forma chiusa per la densità di energia di deformazione nel volume di controllo e per il j-integral di rice in funzione dei fattori plastici di intensificazione delle tensioni: ( ) 1m 1n n 1n p,3 w 2 1n p rk k )2,n(b3w − +++ α= (108) ( ) 1m mn n 1n p,3 j 2 1n p,3 rk k )n,2(b3j − +++ α= (109) u http://www.gruppofrattura.it http://dx.medra.org/10.3221/igf-esis.07.03&auth=true m. zappalorto et alii,, frattura ed integrità strutturale, 7 (2009) 29-56; doi: 10.3221/igf-esis.07.03 52 anche per queste relazioni, l’accordo con i risultati di alcune analisi agli elementi finiti si è dimostrato molto soddisfacente (fig. 17 e 18). 0 200 400 600 800 1000 0.5 0.7 0.9 1.1 1.3 1.5 1.7 1.9 mt 120° eq. (107) steel aisi 1045, m= -13.06, fea, 1/(1-m)=0.071 steel aisi 1008, m= -7.68, fea, 1/(1-m)=0.115 n si f pl as tic i, k 3, p [ m pa m m 1/ (1 -m ) ] τnn / τy figura 16: nsif plastici in accordo con la teoria in confronto con i risultati di analisi agli elementi finiti. intaglio a spigolo vivo (2α=120°). 0 20 40 60 80 100 120 140 0.5 0.7 0.9 1.1 1.3 1.5 1.7 1.9 d en si tà d i e ne rg ia d i d ef or m az io ne [n m m / m m 3 ] sed da fea sed elastica steel aisi 1045 r=0.1 mm 0.5 0.3 r=0.1 r mt 120° τnn / τy sed plastica, eq. (108) figura 17: densità di energia di deformazione in accordo con l’ eq. 108 e confronto con i risultati di alcune analisi agli elementi finiti; intaglio a spigolo vivo (2α=120°); acciaio aisi 1045. 0 10 20 30 40 50 60 0.5 0.7 0.9 1.1 1.3 1.5 1.7 1.9 j-integral dai risulati fea j-integral elastico steel aisi 1045 j 3 [m pa m m ] τnn / τy r mt 120° j-integral plastico, eq. (109) figura 18: j-integral in accordo con l’eq.109 e confronto con i risultati di alcune analisi agli elementi finiti; intaglio a spigolo vivo (2α=120°); acciaio aisi 1045. http://www.gruppofrattura.it http://dx.medra.org/10.3221/igf-esis.07.03&auth=true m. zappalorto et alii, frattura ed integrità strutturale, 7 (2009) 29-56; doi: 10.3221/igf-esis.07.03 53 conclusioni ono state sviluppate delle equazioni in forma chiusa per descrivere le distribuzioni di tensione generate da intagli di varia forma in alberi intagliati soggetti a torsione, sia in regime lineare elastico sia elastoplastico. le soluzioni lineari elastiche sono state ottenute utilizzando un approccio basato sull’uso combinato del metodo dei potenziali complessi e di un sistema di coordinate curvilinee. i risultati analitici ottenuti per le componenti di tensione appaiono in soddisfacente accordo con i risultati numerici per un ampio range di forme d’intaglio (dalla cricca all’intaglio circolare), in relazione a corpi assialsimmetrici infiniti e finiti. le soluzioni elastoplastiche sono state ottenute invece utilizzando la trasformazione odografica introdotta da hult e mcclinotck e risolvendo il problema di neumann. le tensioni sono state espresse dapprima in funzione della massima tensione plastica di taglio presente sull’apice dell’intaglio, poi in funzione di un nsif plastico generalizzato, valido per un intaglio raccordato, evidenziando analiticamente il legame esistente tra questi due parametri. e’ stata inoltre formalizzata un’espressione in forma chiusa, valida nel campo dello small scale yielding, fra la massima tensione sull’apice dell’intaglio valutata in campo plastico ed il corrispondente valore ottenuto per mezzo di un’analisi lineare elastica. infine, per mezzo del frame analitico sviluppato, sono state ridiscusse due regole molto diffuse in letteratura, la regola di neuber e il criterio esed di molski e glinka, evidenziandone analiticamente limiti e campo di applicabilità. bibliografia [1] h. neuber, “theory of notch stresses”, splinger-verlag, berlin (1958). [2] m. creager, p.c. paris, int. j. fract. mech., 3 (1967) 247. [3] a.seweryn, k. molski, eng. fract. mech., 55 (1996) 529. [4] j. qian, n. hasebe, eng. fract. mech., 56 (1997) 729. [5] m.l. dunn, w. suwito, s. cunningham, eng. fract. mech., 57 (1997) 417. [6] j.w. hutchinson, j. mech. phys. solids, 16 (1968a) 13. [7] j.w. hutchinson, j. mech. phys. solids, 16 (1968b) 337. [8] j.r. rice, g.f. rosengren, j. mech. phys. solids, 16 (1968) 1. [9] s.m. sharma, n. aravas, j. mech. phys. solids, 39 (1991) 1043. [10] z.b. kuang, x.p. xu, int. j. fract., 35 (1987) 39. [11] p. lazzarin, r. zambardi, p. livieri, int. j. fract. 107 (2001) 361. [12] j.a.h. hult, f.a. mcclintock, 9th int cong appl mech (1956), 8, brussels. [13] j.r. rice, j. appl. mech., 34 (1967) 287. [14] h. neuber, j. appl. mech., 28 (1961) 544. [15] k. molski, g. glinka, mater. sci. engng., 50 (1981) 93. [16] p. lazzarin, r. zambardi, fatigue fract. engng. mater. struct., 25 (2002) 917. [17] p.lazzarin, m. zappalorto, j.r. yates, int. j. engineering science, 45 (2007) (2-8), 308. [18] m. zappalorto, p. lazzarin, int. j. fract., 148 (2007), 139. [19] m. zappalorto, p. lazzarin, j. yates, int. j. solids struct., 45(2008) 4879. [20] lazzarin p, zappalorto m. plastic notch stress intensity factors for pointed v-notches under antiplane shear loading, in stampa su int. j. fracture. [21] l. n. g. filon, philosophical transactions of the royal society of london, a 193 (1900) 309. [22] s.p. timoshenko, j.n. goodier, “theory of elasticity 3rd edition”, mcgraw-hill, new york (1970). [23] n. hasebe, y. kutanda, eng. fract. mech., 10 (1978) 215. [24] g.r. irwin, sagamore research conference proceedings, vol. 4 (1961), syracuse university research institute, syracuse ny, 63. [25] j.d. unger, “analytical fracture mechanics” dover publication (2001). [26] g. valiron, “the geometric theory of ordinary differential equations and algebraic functions”, math science pr. (1984) [27] a. r. forsyth, “a treatise on differential equations”, dover publications (1996). [28] g.p. cherepanov, j. appl. math. mech., 26 (1962) 1040. [29] j.w. hutchinson, “non linear fracture mechanics”, department of solid mechanics, technical university of denmark (1979). s http://www.gruppofrattura.it http://dx.medra.org/10.3221/igf-esis.07.03&auth=true m. zappalorto et alii,, frattura ed integrità strutturale, 7 (2009) 29-56; doi: 10.3221/igf-esis.07.03 54 appendice a. distribuzioni di tensione lineari elastiche per un intaglio semi-ellittico con un generico angolo di inclinazione β er semplicità, la trattazione viene limitata solamente al caso di albero infinito. indicato con β il generico angolo di inclinazione dell’intaglio (fig. a1) è necessario determinare un nuovo sistema di condizioni al contorno. i campi di tensione nel sistema di riferimento cartesiano (x, y, z) sono: ηξ η ηξ ξ τ ηξ η ηξ ξ τ 2cos2cosh 2sin 2cos2cosh 2sinh 2cos2cosh 2sin 2cos2cosh 2sinh 122 211 − + − −−= − + − += bba bba zy zx (a1) figura a1: intaglio ellettico inclinato di un angolo β rispetto alla direzione x’ . le nuove condizioni al contorno possono quindi essere scritte come: 1. at ∞→z ; τττ == nomzyzy ,' and 0' =zxτ 2. 0 0 0 = = = ξξ ητ zx ; 3. 0 0 2 = = ±= ξξ π ητ zy . utilizzando le formule di trasformazione delle tensioni:             − =         zy zx zy zx τ τ ββ ββ τ τ cossin sincos ' ' (a2) è possible riscrivere le condizioni al contorno come: ( ) ( ) ( ) ( )         =+ =+ =+−+− =+−+ 0 0 cossin 0sincos 22 11 2211 2211 a b ba b b a a τbaba baba ββ ββ (a3) e la soluzione generale del sistema, in funzione di β, è la seguente: p β x y τzx τzy x’ y’ http://www.gruppofrattura.it http://dx.medra.org/10.3221/igf-esis.07.03&auth=true m. zappalorto et alii, frattura ed integrità strutturale, 7 (2009) 29-56; doi: 10.3221/igf-esis.07.03 55           − −= − = − = − −= β τ β τ β τ β τ cos sin cos sin 2 1 2 1 ba a b ba b b ba b a ba a a (a4) le componenti di tensione zyτ e zxτ ottenute combinando le eq. a1, a4 sono mostrate in fig. a2 in funzione della distanza x dall’apice dell’intaglio, e confrontate con i risultati di un’analisi agli elementi finiti. l’accordo è ancora molto soddisfacente. 0 0.5 1 1.5 2 2.5 0 1 2 3 4 5 6 distance from the notch tip [mm] a=1 r=200 a/b=2     τ z j / τ τzy / τ τzx / τ figura a2: componenti di tensione zyτ and zxτ lungo la direzione η=0. le tensioni sono normalizzate rispetto alla tensione nominale. appendice b. un legame analitico tra le distribuzioni di tensione lineari elastiche indotte da intagli di differente forma soggetti a torsione onsideriamo l’espressione della distribuzione di tensione τzy lungo la bisettrice di un intaglio semi-ellittico [17], trascurando il decremento della tensione nominale:       − −− = b cx ax ba b 2222 max zy τ τ (b1) indicando con x’ la distanza dalla’apice dell’intaglio, x’=x-a e:         − −+ + − = b c)ax( )ax(a ba b 22' ' 22 max zy τ τ (b2) ricordando che a b 2 =ρ , ρ a b a 2 2 = , 222 bac −= , l’eq. b2 può essere riscritta come: c http://www.gruppofrattura.it http://dx.medra.org/10.3221/igf-esis.07.03&auth=true m. zappalorto et alii,, frattura ed integrità strutturale, 7 (2009) 29-56; doi: 10.3221/igf-esis.07.03 56               ρ − + ρ + ρ + ρ − τ =         ρ − ++ + ρ − τ ⋅ ρ =         − −+ + − τ =τ a 1 x 2 a x 1 a x ) a 1( abax2x )ax( ) a 1(aa b c)ax( )ax( ) a b 1(a ba '2' ' max 2'2' ' max 22' ' 2 2 2 max zy (b3) ora, se a>>ρ e 'x <<a, l’eq. b3 tende asintoticamente all’espressione:               + = 1 x 2 1 'maxzy ρ ττ (b4) che rappresenta l’espressione valida per un intaglio parabolico. consideriamo ora invece l’espressione della distribuzione di tensione τzy lungo la bisettrice di un intaglio iperbolico [19], trascurando il decremento della tensione nominale: 22 max 0 zy xc b − τ =τ =ξ (b5) indicando nuovamente con x’ la distanza dall’apice dell’intaglio, risulta x’=a-x, e quindi poichè 222 bac += , si ottiene: 2 ' 2 2 max '2222 max zy b ax2 b 'x 1 ax2a'xba b +− τ = +−−+ τ =τ (b6) infine, se a>>ρ e 'x <<a, dato che a b 2 =ρ , il risultato finale è:               + = 1 x 2 1 'maxzy ρ ττ (b7) di nuovo in accordo con l’espressione valida per un intaglio parabolico. http://www.gruppofrattura.it http://dx.medra.org/10.3221/igf-esis.07.03&auth=true riassunto. il lavoro riporta delle soluzioni analitiche in forma chiusa per le distribuzioni di tensione generate da intagli circonferenziali in componenti assialsimmetrici soggetti a torsione, in condizioni lineari elastiche ed elastoplastiche. il p... condizioni al contorno per un albero di sezione infinita. se l’intaglio ha dimensioni infinite, le condizioni al contorno possono essere espresse nella seguente forma: microsoft word numero_35_art_45 a. tzamtzis et alii, frattura ed integrità strutturale, 35 (2016) 396-404; doi: 10.3221/igf-esis.35.45 396 focussed on crack paths fatigue crack growth prediction in 2xxx aa with friction stir weld haz properties a. tzamtzis, a. t. kermanidis laboratory of mechanics and strength of materials, department of mechanical engineering, university of thessaly, leoforos athinon, pedion areos 38334, volos, greece atzam@uth.gr, akermanidis@mie.uth.gr abstract. an analytical model is developed to predict fatigue crack propagation rate under mode i loading in 2024 aluminum alloy with fsw haz material characteristics. simulation of the haz local properties in parent 2024 aa was performed with overaging using specific heat treatment conditions. the model considers local cyclic hardening behavior in the haz to analyze crack growth. for the evaluation of the model, the analytical results have been compared with experimental fatigue crack growth on overaged 2024 alloy simulating material behavior at different positions within the haz. the analytical results showed that cyclic hardening at the crack tip can be used successfully with the model to predict fcg in a material at overaged condition associated with a location in the fsw haz. keywords. fatigue crack growth analysis; aluminum alloy; friction stir weld; heat affected zone; cyclic hardening. introduction atigue crack growth rate (fcg) is influenced by several complex interactive processes that involve microstructural and mechanical load variables. models used for analysis of crack growth rate under constant amplitude stress include a hierarchy of major simplifications, with most important being the application of the linear elastic fracture mechanics (lefm) concept and are mainly empirical or semi-empirical because they rely on fitting experimental material crack growth data [e.g 1]. early models based on damage accumulation at the crack tip have a more physical background but use parameters that are difficult to determine experimentally [2-4]. in more recent modeling attempts [5-8], authors have used the cyclic material behavior at the crack tip to derive analytical expressions for the fatigue crack growth rate. again, most of the models include geometrical (crack tip blunting radius) or material parameters (stress intensity factor threshold), which cannot be derived from simple tests. in [9], a fatigue crack growth model is developed, which considers a strip plastic zone with material hardening at the tip of a crack, under low cycle fatigue conditions, which uses few experimental parameters for fatigue crack growth analysis. in the above approaches a homogeneous material is considered and properties used for prediction are average material properties of the material volume examined. if a crack grows within a material zone with varying microstructure the analysis is more complicated and local material behavior needs to be implemented. in the early work by reifsnider et al. [10] it was found that the existence of a strength gradient at the tip of the crack, depending on its slope, may accelerate or retard crack growth. this is relevant in the case of the heat affected zone (haz) in a weld region, where the aged material consists of a modified microstructure with local f a. tzamtzis et alii, frattura ed integrità strutturale, 35 (2016) 396-404; doi: 10.3221/igf-esis.35.45 397 material properties in the haz area. in the haz fatigue crack growth rate is influenced by the inhomogeneous overaged microstructure [11-13]. in [14] it was shown that overaging of 2024 material has significant impact on the fatigue crack growth behavior of the alloy. a relevant mechanism of 2024 alloy influenced by overaging [14], which is associated with the material’s fatigue crack growth rate is cyclic strain hardening at the crack tip. in studies [15-17], cyclic strain hardening has been linked analytically and experimentally to the closure levels of the advancing crack and hence the rate of its propagation. this dependency has been exploited in the fatigue crack growth analysis, to include the effect of local material properties on fcg with the variation in cyclic strain hardening behavior at different locations in the haz. the model assumes lcf conditions at the crack tip and considers incremental crack growth under fatigue loading. the results obtained analytically are compared with experimental fatigue crack growth data on overaged 2024 aluminum alloy simulating different local properties and microstructure within the haz. critical energy dissipation for crack growth n the proposed model crack growth occurs incrementally after a critical number of cycles δν. the crack growth increment δr is equal to a material element with width δr at the crack plane (fig. 1). based on these assumptions, a crack propagation rate can be calculated from equation: da r dn    (1) it is assumed that the material element at the crack tip is subjected to low cycle fatigue conditions [5-9] with an average constant plastic strain range δεpm. under cyclic straining material failure occurs when in a stabilized hysteresis loop a critical amount of energy wf is accumulated in the material after a finite number of loading cycles νf. by assuming that the energy per cycle δw is nearly constant throughout the fatigue test, the total plastic strain energy until fracture may be approximated by [18]: 1 2 1 f f a p f n w w n n n              (2) with σα the stress amplitude and n’ the cyclic strain hardening exponent. the critical amount of energy wf for failure of the material volume is estimated from the strain energy density [sed] theory [19-20]. in the sed criterion the critical strain energy density function dw/dv is associated with the critical distance rc from the crack tip for onset of crack initiation and the critical strain energy density factor sc in the form: c c c sdw dv r       (3) for plane stress the strain energy density factor becomes:   21 2 cr c v k s     (4) assuming that the energy for fracture can be approximated by the critical strain energy per unit volume (dw/dv)c from the sed criterion in eq. (3), wf in eq. (2) can be derived with the use of eq. (3) and the critical number of cycles nf for a crack increment δr = rc can be obtained from (2) by:       21 1 4 1 cr f c p v n n r n            (5) i a. tzamtzis et alii, frattura ed integrità strutturale, 35 (2016) 396-404; doi: 10.3221/igf-esis.35.45 398 figure 1: incremental crack growth in haz. by calculating in eq. (5) for mode i loading the stress amplitude σa at the position of fracture rc for an isotropic linear elastic material and by and using the coffin-manson relationship [21-22] to derive δεp,, the crack growth equation can be derived:         1 11 '22 3 1 2 2 1 2 4 2 1 1 1 c c c fc c c cr nd r dn v n                          (6) eq. (7) can be written in the following simplified form:  mk m d a b dn    (7) where parameter m is related to the coffin-manson parameter m as m=1/c+1 and ca r (8) 2 3 2 2 c k c    (9)       1 '2 2 4 2 1 1 1 c f cr n b v n                      (10) parameters n΄, kcr, c, εf΄, ε can be determined experimentally. crack growth rate in eq. (7) is dependent on parameter b, which includes material properties and therefore provides a physical background in the crack growth analysis. the only fitting parameter i eq. (7) is length rc, which is also an undefined parameter in the sed theory. actual crack length material with haz cyclic local properties rc a. tzamtzis et alii, frattura ed integrità strutturale, 35 (2016) 396-404; doi: 10.3221/igf-esis.35.45 399 experimental simulation of haz local properties microstructural characteristics imulation of haz material properties was achieved by implementing a heat treatment procedure on 2024 material described in [14] using different overaging conditions. the procedure selected helps to produce materials based on the 2024 alloy with similar microstructural characteristics and local properties with selected positions in the haz, without the weld residual stresses. the overaged materials exhibit similar local properties and microstructural characteristics with 3 locations in the haz: (a) close to the base material, (b) at the mid-point of haz hardness gradient and (c) close to the weld nugget (haz/tmaz interface), and are named a200, a250 and a300 respectively, based on the temperature of heat treatment used for 15 hours aging. the microstructural characteristics between the haz material (close to the base metal, 12 mm away from the weld center) and a200 are given in fig. 2. they are comparable and consist of same size coarsened second-phase particles, the al2cu (θ΄phase) and the al2cumg (s΄ phase). in both materials similar hardness values are obtained as shown in the hardness profile of the 2024 aluminum alloy fsw, in fig. 3. in the same figure, the hardness values of materials a250 and a300 are shown and are placed on the respective locations in the haz with similar hardness values. (a) (b) figure 2: microstructures of (a) haz at a distance 12mm from the weld centerline, (b) a200 material. figure 3: microhardness variation in 2024 fsw determined at two different layers in the cross section of the fsw joint (1 and 2 mm depth from specimen surface). local hardness values of a200, a250 and a300 materials are shown at the locations in the haz with similar microhardness values. the specimen location designates where the sample has been extracted to obtain local tensile properties in the haz. s specimen location a. tzamtzis et alii, frattura ed integrità strutturale, 35 (2016) 396-404; doi: 10.3221/igf-esis.35.45 400 tensile behavior the tensile stress-strain behavior of a subsize specimen (astm e8m-01) extracted from the location shown in fig. 3 and the a250 material are compared up to a tensile strain of 5% in fig. 4. the hardness of a250 material, is similar to the hardness obtained at the mid-point of the specimen gauge length in fig. 3. despite the small difference in strength values, the strain hardening behavior in the two cases is very close and the determined strain hardening exponent values are 0.150 and 0.161 for the haz and a250 materials respectively. figure 4: stress strain curves for materials a 250 and haz at the mid-length of hardness gradient. figure 5: monotonic & cyclic stressstrain curves of t3, a250 and a300 materials. a. tzamtzis et alii, frattura ed integrità strutturale, 35 (2016) 396-404; doi: 10.3221/igf-esis.35.45 401 cyclic hardening the cyclic tests performed in [14] and reproduced in fig. 5 show that cyclic strain hardening occurs in the overaged materials a250 and a300. cyclic strain hardening after overaging is more pronounced compared to the base metal (t3) as obtained from the cyclic strain hardening exponent n’ values in tab. 1. parameter n’ increases with increasing overaging temperature (a300 material). this is associated with the haz location close to the weld center. the dependency of increasing cyclic strain hardening with increasing crack closure was investigated in [14]. here, this dependency is used to analyze the crack growth behavior of a250 and a300 materials using the different cyclic hardening characteristics (value n’) in eq. (7) to obtain an estimation of the respective behavior of the related positions in the haz in fig. 3. yield strength σ0.2 (mpa) cyclic yield strength σc0.2 (mpa) strain hardening exponent n strength coefficient h (mpa) cyclic strain hardening exponent n΄ cyclic strength coefficient h΄ (mpa) t3 375 445 0.120 694 0.042 576 a250 245 245 0.161 604 0.148 568 a300 135 185 0.242 594 0.211 674 table 1: cyclic and monotonic properties of t3, a250 and a300 materials. crack growth analysis rack closure under cyclic loads is influenced by the cyclic hardening mechanism at the crack tip. in [14-17] it was analytically and experimentally demonstrated that increased cyclic hardening contributes to increased crack closure and retards fatigue crack growth. in eq. (7), the cyclic hardening exponent n’ was used to analyze the local fatigue crack growth behavior of the various positions in the haz (a250 and a300). in the analysis, the material properties included in parameter b (eq. 10) for all materials have been taken from the reference, base metal, 2024 t3 alloy and are presented in tab. 2. the material volume length rc was fitted from the 2024 t3 data. in fig. 6 the analytical results obtained using a numerical integration of eq. (7) for t3 (base metal), a250 (mid-point haz gradient) and a300 (haz/tmaz) materials are compared against experimental crack growth rates. analytical and experimental crack growth rates agree well for the stress intensity factor range examined (12-25 mpa m1/2), specifically for the position associated with a250, while for the case of a300 (haz/tmaz interface) a small overestimation in predicted crack growth rates exists. cyclic hardening exponent n΄ parameter rc (m) coffinmanson exponent c coffinmanson parameter εf΄ critical stress intensity factor kcr (mpam1/2) [23] young’s modulus e (gpa) poisson ratio ν t3: 0.042 a250: 0.148 a300: 0.211 1.291x10-6 -0.6 0.13 60 73.1 0.33 table 2: material parameters used in eq. (7) for fcg analysis. in tab. 3 the average value of parameter rc for the three materials t3, a250 and a300 is given. in fig. 7 the analytical results are compared against the experimental crack growth rates using in the analysis the mean value of rc in order to evaluate the sensitivity of the analysis on the fitting parameter. the differences in this case are negligible, which shows that analytical predictions are not influenced by the value of rc. c a. tzamtzis et alii, frattura ed integrità strutturale, 35 (2016) 396-404; doi: 10.3221/igf-esis.35.45 402 figure 6: experimental and computed fatigue crack growth rates vs. stress intensity factor range (dα/dn-δκ) in t3, a250 and a300 materials. the analytical results were obtained for c=-0.6 and rc=1.291x10-6 m. parameter rc (m) t3 1.291x10-6 mean: 1.329x10-6 a250 1.538x10-6 a300 1.158x10-6 table 3: average value of rc length. figure 7: experimental and computed fatigue crack growth rates vs. stress intensity factor range (dα/dn-δκ) in t3, a250 and a300 materials evaluated for rc,mean=1.329x10-6 m. a. tzamtzis et alii, frattura ed integrità strutturale, 35 (2016) 396-404; doi: 10.3221/igf-esis.35.45 403 conclusions model with the ability to perform fatigue crack growth analysis taking into account the local material behavior at specific locations in an aluminum 2024 t3 fsw heat affected zone is proposed. to simulate the local material behavior in the haz without the effect of weld residual stresses, the reference 2024 t3 aluminum alloy was subjected to specific overaging conditions. the obtained overaged materials have very similar microstructural characteristics and mechanical properties to the haz material. the analytical results obtained with the model showed that it can satisfactory predict crack growth rates of the material with local haz characteristics. acknowledgments his research has been co-financed by the european union (european socialfund esf) and greek national funds through the operational program"education and lifelong learning" of the national strategic reference framework (nsrf) research funding program: heracleitus ii. investing in knowledge society through the european social fund. references [1] paris, p., erdogan f., a critical analysis of crack propagation laws. journal of fluids engineering, 85 (4) (1963) 528533. doi:10.1115/1.3656900 [2] rice, j.r., mechanics of crack tip deformation and extension by fatigue. in fatigue crack propagation. special technical publication, american society for testing and materials stp 415 247-309 (1967). [3] weertman, j., rate of growth of fatigue cracks calculated from the theory of infinitesimal dislocations distributed on a plane. international journal of fracture mechanics, 2 (2) (1666) 460-467. doi 10.1007/bf00183823. [4] mcclintock, f.a., on the plasticity of the growth of fatigue cracks. fracture of solids, 20 (1963) 65-102. [5] wu, s.-x., mai y.-w., cotterell b., a model of fatigue crack growth based on dugdale model and damage accumulation, international journal of fracture, 57 (3) (1992) 253-267. doi: 10.1007/bf00035077. [6] shi, k.k., cai l.x., chen l., wu s.c., bao c., prediction of fatigue crack growth based on low cycle fatigue properties. international journal of fatigue, 61 (0) (2014) 220-225. doi:10.1016/j.ijfatigue.2013.11.007. [7] chen, l., cai, l..x., yao, d., a new method to predict fatigue crack growth rate of materials based on average cyclic plasticity strain damage accumulation. chinese journal of aeronautics, 26 (1) (2013) 130-135. doi:10.1016/j.cja.2012.12.013. [8] pandey, k.n., chand, s., an energy based fatigue crack growth model, international journal of fatigue, 25 (8) (2003) 771-778. doi:10.1016/s0142-1123(03)00049-5. [9] kermanidis, a.t., pantelakis, s.g., fatigue crack growth analysis of 2024 t3 aluminium specimens under aircraft service spectra. fatigue & fracture of engineering materials & structures, 24 (10) (2001) 699-710. doi: 10.1046/j.1460-2695.2001.00435.x. [10] reifsnider, k., kahl, m., effect of local yield strength gradients on fatigue crack propagation, international journal of mechanical sciences, 16 (2) (1974) 105-119. doi:10.1016/0020-7403(74)90080-0. [11] scialpi, a., de filippis, l.a.c., cavaliere, p., influence of shoulder geometry on microstructure and mechanical properties of friction stir welded 6082 aluminium alloy, mater design, 28 (2007) 1124–1129. doi:10.1016/j.matdes.2006.01.031. [12] cavaliere, p., nobile, r., panella, f.w., squillace, a., mechanical and microstructural behavior of 2024-7075 aluminium alloy sheets joined by friction stir welding, int j mach tool manufac, 46 (2006) 588–594. doi:10.1016/j.ijmachtools.2005.07.010. [13] ceschini, l., boromei, i., minak, g., morri, a., tarterini, f., effect of friction stir welding on microstructure, tensile and fatigue properties of the aa7005/10 vol.%al2o3p composite, compos sci technol, 67 (2007) 605–615. doi:10.1016/j.compscitech.2006.07.029. [14] tzamtzis, a., kermanidis, a. t., improvement of fatigue crack growth resistance by controlled overaging in 2024-t3 aluminium alloy, fat. &. fract. eng . mat and struct., 37(7) (2014) 751-763. doi: 10.1111/ffe.12163. [15] budiansky, b., hutchinson, j.w., analysis of closure in fatigue crack growth. journal of applied mechanics, 45(2) a t a. tzamtzis et alii, frattura ed integrità strutturale, 35 (2016) 396-404; doi: 10.3221/igf-esis.35.45 404 (1978) 267-276. [16] pommier, s., plane strain crack closure and cyclic hardening. engineering fracture mechanics, 69 (1) (2002) 25-44. doi:10.1016/s0013-7944(01)00061-3. [17] chang, t., guo, w., effects of strain hardening and stress state on fatigue crack closure. international journal of fatigue, 21 (9) (1999) 881-888. doi:10.1016/s0142-1123(99)00085-7. [18] morrow, j., cyclic plastic strain energy and fatigue of metals. internal friction, damping and cyclic plasticity, astm stp, 378 (1965) 45-87. doi: 10.1520/stp378-eb. [19] sih, g.c., methods of analysis and solutions of crack problems. springer, 1 (1973). doi:10.1007/978-94-017-2260-5. [20] sih, g.c., some basic problems in fracture mechanics and new concepts. engineering fracture mechanics, 5(2) (1973) 365-377. doi:10.1016/0013-7944(73)90027-1. [21] manson, s.s., fatigue: a complex subject-some simple approximations. experimental mechanics, 5 (4) (1965) 193226. doi:10.1007/bf02321056. [22] tavernelli, j.f., coffin, j.l.f., experimental support for generalized equation predicting low cycle fatigue, journal of fluids engineering, 84 (4) (1962) 533-537. doi:10.1115/1.3658701. [23] kermanidis, a.t., tzamtzis, a., prediction of fatigue crack propagation in aluminum alloy with local yield strength gradient at the crack path, 14th international congress on mesomechanics, budapest, hungary (2012). << /ascii85encodepages false /allowtransparency false /autopositionepsfiles true /autorotatepages /none /binding /left /calgrayprofile (dot gain 20%) /calrgbprofile (srgb iec61966-2.1) /calcmykprofile (u.s. web coated \050swop\051 v2) /srgbprofile (srgb iec61966-2.1) /cannotembedfontpolicy /error /compatibilitylevel 1.4 /compressobjects /tags /compresspages true /convertimagestoindexed true /passthroughjpegimages true /createjobticket false /defaultrenderingintent /default /detectblends true /detectcurves 0.0000 /colorconversionstrategy /cmyk /dothumbnails false /embedallfonts true /embedopentype false /parseiccprofilesincomments true /embedjoboptions true /dscreportinglevel 0 /emitdscwarnings false /endpage -1 /imagememory 1048576 /lockdistillerparams false 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/hrv (za stvaranje adobe pdf dokumenata najpogodnijih za visokokvalitetni ispis prije tiskanja koristite ove postavke. stvoreni pdf dokumenti mogu se otvoriti acrobat i adobe reader 5.0 i kasnijim verzijama.) /hun 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/pdfxoutputintentprofileselector /documentcmyk /preserveediting true /untaggedcmykhandling /leaveuntagged /untaggedrgbhandling /usedocumentprofile /usedocumentbleed false >> ] >> setdistillerparams << /hwresolution [2400 2400] /pagesize [612.000 792.000] >> setpagedevice microsoft word numero_43_art_14 p. zampieri et alii, frattura ed integrità strutturale, 43 (2018) 182-190; doi: 10.3221/igf-esis.43.14 182 structural behaviour of masonry arch with no-horizontal springing settlement p. zampieri, n. simoncello, c. pellegrino department of civil, environmental and architectural engineering, university of padova, via marzolo, 9 35131 padova, italy paolo.zampieri@dicea.unipd.it, http://orcid.org/0000-0002-4556-5043 abstract. this paper presents a calculation procedure for assessing the structural integrity of a masonry arch with non-horizontal springing settlement. by applying the principle of virtual work (pvw) to the deformed arch system, the procedure proposed herein details the reaction forces and thrust lines for each step of imposed settlement of the support. the procedure can also be used estimate the final displacement that causes complete failure of arch structural capacity. the results of the analysis procedure were compared against those obtained by experimental testing so as to validate the proposed calculation method. keywords. safety of masonry arches; collapse mechanism; springing settlement; experiment. citation: zampieri, p., simoncello, n., pellegrino, c., structural behavior of masonry arch with no-horizontal springing settlement, frattura ed integrità strutturale, 43 (2018) 182-190. received: 18.11.2017 accepted: 28.11.2017 published: 01.01.2018 copyright: © 2018 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. introduction ssessment of the structural integrity of masonry arch structures is highly important, as the arch represents the main structural element of many existing constructions (bridges and buildings) both in europe and around the world. consequently, the structural behaviour of masonry arches continues to be subject of scientific research. the first modern studies on the structural behaviour of masonry arch structures were conducted by heyman [1], who introduced simplified hypotheses for the application of equilibrium limit analysis to assess the load-carrying capacity of such structures. heyman’s work gave rise to numerous subsequent studies that assessed the main aspects affecting the structural response of masonry arches. in particular, recent studies have focused attention on the dynamic [2-6] and seismic behaviour [7-20] of existing masonry arch structures. one structural problem that has been rather neglected [21-24] in recent studies involves the behaviour of arches as a result of imposed settlement to the supports. the behaviour of arches with horizontal settlement has been comprehensively studied both by applying limit analysis [22-24] and through experimental testing [22]. nonetheless, the structural behaviour of masonry arches undergone a non-horizontal displacement of supports is still partially unexplored. the study of masonry arch resistance to the imposed settlement of supports is important, as this type of stress can be found in existing structures. for example, in masonry arch bridges, settlement of the arch supports may occur due to loss of load carrying capacity of the subsoil. another example is steel ties in historical buildings, used to counteract the horizontal trust of arch. if damaged, these can be cause of settlement of arch springing. a p. zampieri et alii, frattura ed integrità strutturale, 43 (2018) 182-190; doi: 10.3221/igf-esis.43.14 183 referring to the main studies about horizontal displacement available in literature, ochsendorf [22] analyzed the formation of cracks of a masonry arch in relation to the horizontal thrust and the distinctive geometrical characteristics of the structure, that are thickness t, radius r and angle of embrace β, through thrust line analysis. coccia et al. [23] reviewed the ochsendorf’s work suggesting an innovative method in studying these phenomenons based on the implementation of kinematic theorem to deformed configuration of the arch. in particular, they showed that the considered collapse configuration for the masonry arch, then the position of the cracks, depend on the displacement imposed to the supports. hence all the studies conducted focused on the collapse mechanism for the horizontal displacement, the aim of this paper is to analyze others settlements condition. in particular, an imposed displacement with two different direction components that are horizontal and vertical. for these reasons, the purpose of this work is to amplify the already avaiable investigations in settlement springing of masonry archs analyzing other settlement condition, to develop the arch behavior knowledge. throughout limit analysis and experimental testing, the structural behaviour of masonry arches subjected to a dk settlement of springing on an inclined direction α of 45° (fig. 1) is investigated. moreover, knowing that the cracks position in a collapse configuration may vary increasing the settlement, as already stated throughout fem and experimental analysis, this behaviour has been analyzed for a 45° direction settlement direction by means of a limit analysis then compared with the field test. the analysis procedure used to assess the thrust line and reaction forces of the springing will be described in detail for each incremental displacement value dk, until reaching the condition of complete collapse of the arch. this procedure uses: i) limit analysis in the hypotheses of significant arch displacements, and ii) analysis of thrust lines. following this, the results of experimental testing on a masonry arch with mortar joints subjected to one of two springings incremental settlement (inclination equal to 45°) will be presented. as will be illustrated, the comparison of analytical results and experimental results demonstrates the great predictive ability of the calculation model developed. analysis of masonry arches with non-horizontal springing settlement hen a masonry arch loses a degree of freedom (and may be displaced along a given direction α), a collapse mechanism is created, with three cracking hinges (fig. 1) and the thrust line within the form of the arch is tangential to the edge at the three hinge points. this three-hinge mechanism is created as a result of small movements along the α direction. thus, assuming that the displacement in the α direction that triggers the collapse mechanism is null, it is possible to: remove the constraint condition in direction α and replace it with an equivalent reaction force rα, 0 (fig.1); define a three-hinge collapse mechanism and an associated field of virtual displacements (fig. 1) and apply pvw using heyman’s hypotheses [1]. for an arch consisting of n blocks, assuming any initial position of hinges 1, 2, 3 (fig. 1), it is possible to define the external work of gravitational forces gi and the force rα,0 as:  ,0 s 0 0 1 , 0 n e i i i l g v r x y        (1) where: gi is the gravitational force applied to each i-rigid block of the arch; vi is the vertical virtual displacement due to gi applied to each i-rigid block of the arch. s(x0, y0) is the virtual displacement of the settled springing. from (1), the value of the support reaction force rα0 can be obtained, as follows:   1 ,0 s 0 0, n i i i g v r x y        (2) once the value of rα0 is known, it is possible to: define the thrust line following the procedure shown in zampieri et al 2016 [10], determine a new updated position of the three cracking hinges and apply pvw again. repeating this process, convergence is reached when the solution sought is both statically and kinematically admissible at the same time. this w p. zampieri et alii, frattura ed integrità strutturale, 43 (2018) 182-190; doi: 10.3221/igf-esis.43.14 184 condition defines the positions (x1,0; y1,0) (x2,0; y2,0) (x3,0; y3,0) of the three hinges of the collapse mechanism in the initial configuration ω0 corresponding (ideally) to zero settlement of the movable springing and the minimum reaction force rα,0. subsequently, it is possible to apply a generic displacement dk of the movable springing along a generic direction at the initial condition ω0 and then reapply pvw to the new deformed configuration ωk (the subscript k refers to the k-th increment of displacement dk) in order to determine the updated value rα,k of the reaction force in the α direction. then a new thrust line is defined, verifying whether the solution sought is statically and kinematically admissible (that is, the thrust line is contained within the form of the arch and is tangential to the edge at the hinge points). figure 1: virtual displacement diagrams in the initial configuration of the masonry arch. figure 2: representation of the kinematic mechanism in the generic configuration displaced by ωk. figure 3: condition in which the hinges calculated in the k-1-th iteration do not coincide with the hinges in the k-th iteration p. zampieri et alii, frattura ed integrità strutturale, 43 (2018) 182-190; doi: 10.3221/igf-esis.43.14 185 if this condition is not verified, the hinge points (1, 2 and 3) are moved to the local maximum and minimum points of the thrust line before applying pvw again. this procedure is reiterated until the thrust line condition is verified. it should be emphasised that for a given displacement dk the hinges may not be correctly positioned (1, 2, 3) in relation to the displacement in the previous step dk-1, but rather the hinge positions are updated (1 ‘, 2’, 3 ‘) as shown in fig. 3. this procedure can therefore assess (step-by-step) whether the collapse hinge positions have changed (fig. 3) as the displacement dk increases. the procedure described is repeated for incremental values of dk and ends when the arch collapse condition is verified due to alignment of the three crack hinges. fig. 4 shows a flow chart of the algorithm described above. figure 4: algorithm implemented. experimental testing xperimental analysis was carried out on a masonry arch made of solid bricks bound with traditional mortar. a plastic caisson was used in order to obtain a great geometrically regular element instead of using bricks without mortar as in ochsendorf [22] tests. the mortar employed for this experimental has low tensile property according with the hypothesis assumed by clemente [26]. the masonry arch was fixed to a steel frame with a movable springing along a 45° direction (fig. 5). this applied displacement system represents an innovative case never studied before by other authors. the arch made from 37 bricks measuring 250 x 125 x 50 mm3 has a span length of 2281 mm, an arch rise of 585 mm and an embrace angle (β) equal to 107.356°. fig. 5 shows the experimental test diagram and the graphical representation of the mechanical system capable of applying an incremental displacement along an inclined direction of 45°, providing instant-by-instant the imposed displacement value. results of experimental testing during the test, images were continuously recorded that allowed the displacement imposed by the mechanical system to be associated with the configuration of the arch collapse mechanism (fig. 6). specifically, in the images shown in fig. 6, three different collapse mechanism configurations can be identified for different values of displacement dk, as shown in the graph in fig. 9. e p. zampieri et alii, frattura ed integrità strutturale, 43 (2018) 182-190; doi: 10.3221/igf-esis.43.14 186 all three initial cracking hinges were created at a displacement equal to 2.7 mm at joint 3, joint 18 and joint 34. during the test, it was seen that up until a certain displacement of dk = 153.6 mm, the configuration of the hinges remained unchanged (fig. 7a) in relation to the initial configuration. at a displacement of 153.6 mm (fig. 7b), hinge 3 shifted from position 34 to position 33, and hinges 1 and 2 remained unchanged. as the displacement increased, at 165.1 mm (fig. 7c), hinge 1 instantly shifted from position 3 to position 7, hinge 3 instantly shifted from position 33 to position 30, and hinge 1 remained unchanged. following this, the configuration of the hinges remained unchanged until alignment of the three hinges at the instant in which the arch collapsed (fig. 7d). figure 5: configuration of the specimen. a) b) c) d) figure 6: collapse mechanism configuration of experimental arch specimen comparison between limit analysis and experimental testing sing the proposed calculation procedure, it was possible to analytically simulate the behaviour of the experimental test. this section provides a comparison of the experimental results with the analytical results. in particular, the images shown in fig. 7 illustrate the four cracking hinge configurations extracted from the calculation program, highlighting that the shifts in the position of the cracking hinges as displacement dk increases, found during the experimental test, are also identified in limit analysis. this result is confirmed by analysis of the graph in fig. 9a, which compares the variation in the position of the cracking hinges (ni; i = 1,2,3) according to the displacement dk through comparison of the four curves relating to experimental testing and four curves relating to limit analysis. specifically, limit analysis allows four different cracking hinge configurations to be identified: u p. zampieri et alii, frattura ed integrità strutturale, 43 (2018) 182-190; doi: 10.3221/igf-esis.43.14 187 configuration 1: n1=1 n2=18 n3=36; 0≤dk≤176 configuration 2: n1= 4 n2=18 n3=35; 176≤dk≤189.2 configuration 3: n1= 4 n2=18 n3=31; 189.2≤dk≤193.6 configuration 4: n1=6 n2=18 n3=31; 193.6≤dk≤220 a) b) c) d) figure 7: collapse mechanism configurations of limit analysis arch model as can be deduced from the graph shown in fig. 8, which compares the different hinge configurations obtained from experimental testing against those obtained from limit analysis, the result of experimental testing and limit analysis do not coincide perfectly. the discrepancies however can be considered acceptable and are attributable to intrinsic uncertainties in the parameters that define the structural response of real structures: figure 8: comparison of configurations of cracking hinges carried out form. a) limit analysis and b) experimental testing  uncertainties and/or irregularities in defining the geometry of the specimen [20]  irregularities due to masonry and mortar production processes  errors and uncertainties relating to how the test is conducted. p. zampieri et alii, frattura ed integrità strutturale, 43 (2018) 182-190; doi: 10.3221/igf-esis.43.14 188 it is interesting to observe from the graph in fig. 9a that up to a displacement dk equal to approximately eighty percent of the final displacement, the hinges remain unchanged in the final configuration. their positions in fact change in a range of displacements dk between eighty and ninety percent of the collapse displacement. fig. 9b shows the curve that correlates the displacement dk with the reaction force rα,k, which increases continually and exponentially up to the maximum displacement, at which point the tangent of the curve is vertical. it is also important to note that the final displacement obtained from limit analysis is 14.7% higher than the displacement seen in experimental testing (dotted line in fig. 9b). if the intrinsic geometric irregularities of real arches were able to be taken into account in the calculation procedure developed, the final displacement (in limit analysis) would most likely be closer to the value obtained in experimental testing. figure 9: a) position of hinges as a function of dk b) capacity curve. conclusions his paper examines the behaviour of a masonry arch subjected to settlement along a direction α. the innovation of this paper lies in analyzing collapse mechanisms for the horizontal settlement condition, despite what other studies have already considered. other previous studies about horizontal settlement only led to a mechanism classification introducing a fem simulation analysis. this paper investigates on a different configuration, comparing the simulation in terms of limit analysis and implementing the possibility of a varying collapse mechanism configuration. using the method of equilibrium limit analysis with the hypothesis of significant displacements, an algorithm is proposed that uses pvw. the purpose was to analyse the thrust line and to identify the different positions of collapse hinges occured on the arch, from the initial configuration corresponding to null displacement of the stringing, up to the final collapse configuration. a real arch was built to conduct an experimental test by subjecting it to springing settlement along an inclined direction of 45° until collapse. as the value of imposed displacement was increased, the various configurations of the deformed arch were continuously recorded. the results of the experimental test confirmed the reliability of the structural model developed. however, there were discrepancies in the position of the cracking hinges under displacement. such discrepancies can be attributed to the geometrical irregularities of the arch and the inherent uncertainties in real structures. in conclusion, as fig.8 shows, the limit analysis induces the development of an additional crack at joint 6 in the fourth collapse configuration contrary to what the experimental evidence shows, where the position of hinges is preserved for the same configuration. as fig. 9 shows, in the limit analysis the last displacement of the springing results greater compared to experimental response. this is considered to be due to the fact that the cracks n1 and n2 are located between a different and greater number of voussoirs compared to real case. therefore, the alignment of the three hinges is verified in conjunction with a greater last displacement. as already stated, this discrepancy can be reduced introducing an inherent uncertainties factor. t p. zampieri et alii, frattura ed integrità strutturale, 43 (2018) 182-190; doi: 10.3221/igf-esis.43.14 189 references [1] heyman, j., the safety of masonry arches, int j. mech sci., 11 (1969) 363-385. [2] de lorenzis, l., dejong, m., ochsendorf, j., failure of masonry arches under impulse base motion, earthq eng struct dyn., 36 (2007) 2119–2136. [3] misseri, g., rovero, l., parametric investigation on the dynamic behaviour of masonry pointed arches, archive of applied mechanics., 87 (3) (2017) 385-404. [4] ramaglia, g., lignola, g.p., prota, a., collapse analysis of slender masonry barrel vaults, engineering structures., 117 (2016) 86-100. [5] gaetani, a., lourenço, p.b., monti, g., moroni, m., shaking table tests and numerical analyses on a scaled dry-joint arch undergoing windowed sine pulses, bulletin of earthquake engineering., 15 (11) (2017) 4939-4961. [6] zampieri, p., zanini, m.a., zurlo, r., seismic behaviour analysis of classes of masonry arch bridges, key engineering materials., 628 (2014) 136-142. doi: 10.4028/www.scientific.net/kem.628.136. [7] da porto, f., tecchio, g., zampieri, p., modena, c., prota, a., simplified seismic assessment of railway masonry arch bridges by limit analysis, structure and infrastructure engineering., 12 (5) (2016) 567-591. doi: 10.1080/15732479.2015.1031141. [8] de santis, s., de felice, g., a fibre beam based approach for the evaluation of the seismic capacity of masonry arches, earthquake engineering and structural dynamics., 43 (2014) 1661-1681. [9] dimitri, r., tornabene, f., a parametric investigation of the seismic capacity for masonry arches and portals of different shapes, engineering failure analysis, 52 (2015) 1-34. [10] zampieri, p., zanini, m.a., faleschini, f., influence of damage on the seismic failure analysis of masonry arches, construction and building materials., 119 (2016) 343-355. doi: 10.1016/j.conbuildmat.2016.05.024 [11] zampieri, p., zanini, m.a., faleschini, f., derivation of analytical seismic fragility functions for common masonry bridge types: methodology and application to real cases, engineering failure analysis., 68 (2016) 275-291. doi: 10.1016/j.engfailanal.2016.05.031 [12] m. s. marefat, m. yazdani, and m. jafari., seismic assessment of small to medium spans plain concrete arch bridges, european journal of environmental and civil engineering., (2017). doi: 10.1080/19648189.2017.1320589. [13] zampieri, p., zanini, m. a., modena, c., simplified seismic assessment of multi-span masonry arch bridges, bulletin of earthquake engineering., (2015). doi 10.1007/s10518-015-9733-2. [14] zampieri, p., tecchio, g., da porto, f., modena, c., (2015). limit analysis of transverse seismic capacity of multi-span masonry arch bridges, bulletin of earthquake engineering., 13(5) (2015) 1557-152. doi 10.1007/s10518-014-9664-3. [15] cavalagli, n., gusella, v., severini, l., lateral loads carrying capacity and minimum thickness of circular and pointed masonry arches, int j mech sci., 115–116 (2016) 645–56. [16] sayin, e., nonlinear seismic response of a masonry arch bridge, earthquake and structures., 10 (2) (2016) 483-494. doi: 10.12989/eas.2016.10.2.483. [17] michiels, t., adriaenssens, s., form-finding algorithm for masonry arches subjected to in-plane earthquake loading, computers and structures., 195 (2018) 85-98. doi: 10.1016/j.compstruc.2017.10.001. [18] tecchio, g., da porto, f., zampieri, p., modena, c., bettio, c., static and seismic retrofit of masonry arch bridges: case studies, bridge maintenance, safety, management, resilience and sustainability proceedings of the sixth international conference on bridge maintenance, safety and management., (2012) 1094-1098. [19] conde, b., ramos, l.f., oliveira, d.v., riveiro, b., solla, m., structural assessment of masonry arch bridges by combination of non-destructive testing techniques and three-dimensional numerical modelling: application to vilanova bridge, engineering structures, 148 (2017) 621-638. doi: 10.1016/j.engstruct.2017.07.011. [20] cavalagli, n., gusella, v., severini, l., the safety of masonry arches with uncertain geometry, computers and structures., 188 (2017) 17-31. doi: 10.1016/j.compstruc.2017.04.003 [21] zampieri, p., zanini, m.a., faleschini, f., hofer, l., pellegrino, c., failure analysis of masonry arch bridges subject to local pier scour, engineering failure analysis, 79 (2017) 371-384. doi: 10.1016/j.engfailanal.2017.05.028. [22] ochsendorf, j.a., the masonry arch on spreading supports, struct eng inst struct eng lond., 84(2) (2006) 29–36. [23] coccia, s., di carlo, f., rinaldi, z., collapse displacements for a mechanism of spreading-induced supports in a masonry arch, international journal of advanced structural engineering., 7(3) (2015) 307-320. doi: 10.1007/s40091-015-0101-x. [24] como, m., on the role played by settlements in the statics of masonry structures, in: the conference on geotechnical engineering for the preservation of monuments and historic sites, napoli, italy, october, balkema, rotterdam, (1996) 3–4. p. zampieri et alii, frattura ed integrità strutturale, 43 (2018) 182-190; doi: 10.3221/igf-esis.43.14 190 [25] severini, l., cavalagli, n., zampieri, p., simoncello, n., gusella, v., pellegrino c., effects of spread and local geometrical irregularities on the horizontal carrying capacity of masonry arches, atti del xvii convegno anidis l'ingegneria sismica in italia, (2017) 27-33. [26] clemente, p., saitta, f. analysis of no-tension material arch bridges with finite compression strength journal of structural engineering., 143(1) (2017). nomenclature dk displacement of the settlement of the support on the current step; dk-1 displacement of the settlement of the support on the previously step; δdk different of the displacement between two next steps; rα, 0 reaction force in the α direction at the undamaged condition of the arch; rα,k reaction force in the α direction at the damage condition of the arch on the current step; α direction angle of the settlement pvw principe of the virtual work gi gravitational force applied to each i-rigid block of the arch; vi vertical virtual displacement due to gi applied to each i-rigid block of the arch; s(x0, y0) virtual displacement of the settled springing; ω0 initial configuration of the arch; ωk configuration of the arch on the current step; st static condition of the arch; kt kinematic condition of the arch. << 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can be opened with acrobat and adobe reader 5.0 and later.) >> /namespace [ (adobe) (common) (1.0) ] /othernamespaces [ << /asreaderspreads false /cropimagestoframes true /errorcontrol /warnandcontinue /flattenerignorespreadoverrides false /includeguidesgrids false /includenonprinting false /includeslug false /namespace [ (adobe) (indesign) (4.0) ] /omitplacedbitmaps false /omitplacedeps false /omitplacedpdf false /simulateoverprint /legacy >> << /addbleedmarks false /addcolorbars false /addcropmarks false /addpageinfo false /addregmarks false /convertcolors /converttocmyk /destinationprofilename () /destinationprofileselector /documentcmyk /downsample16bitimages true /flattenerpreset << /presetselector /mediumresolution >> /formelements false /generatestructure false /includebookmarks false /includehyperlinks false /includeinteractive false /includelayers false /includeprofiles false /multimediahandling /useobjectsettings /namespace [ (adobe) (creativesuite) (2.0) ] /pdfxoutputintentprofileselector /documentcmyk /preserveediting true /untaggedcmykhandling /leaveuntagged /untaggedrgbhandling /usedocumentprofile /usedocumentbleed false >> ] >> setdistillerparams << /hwresolution [2400 2400] /pagesize [612.000 792.000] >> setpagedevice microsoft word numero_37_art_7 c. brugger et alii, frattura ed integrità strutturale, 37 (2016) 46-51 doi: 10.3221/igf-esis.37.07 46 focussed on multiaxial fatigue and fracture ultrasonic fatigue testing device under biaxial bending c. brugger, t. palin-luc arts et metiers paristech, i2m, cnrs, universite de bordeaux esplanade des arts et métiers, 33405 talence, france charles.brugger@ensam.eu, https://orcid.org/0000-0001-9072-7745 thierry.palin-luc@ensam.eu p. osmond, m. blanc psa peugeot citroën abstract. a new fatigue testing device has been developed to test specimens under biaxial loading at 20 khz. a flat smooth specimen with a disc geometry is placed on a torus frame and cyclically loaded at the center of its upper face. disc bending generates a biaxial proportional stress state at the center of the lower face. any positive loading ratio can be applied. a cast aluminum alloy (used to produce cylinder heads) has been tested under biaxial bending using this device in order to determine its fatigue strength at 109 cycles under high hydrostatic pressure. self-heating is moderate but macroscopic fatigue cracks after testing are very long. first results in vhcf regime are consistent with literature results obtained under similar stress state but in hcf regime and at 20 hz. keywords. gigacycle fatigue; biaxial loading; bending; cast aluminum alloy; ultrasonic testing machine. introduction any components in several industries are loaded in vhcf regime, either at high frequency (wheels of high speed trains, blades in aircraft turbojet engines, etc.) [1] or at low frequency during decades (artificial heart, mooring chains for off-shore petroleum platforms, etc.) [2, 3]. testing specimens up to 109 or 1010 cycles in a realistic time requires to use a very high loading frequency (20 or 30 khz). several devices using the ultrasonic testing technique have been developed all over the world since mason’s work in the 1950's [4]. a significant effort in this field has been done since the end of the last century [1, 5]. specimens can be tested under tension (r=-1 or r>0), torsion (r=-1 or r>0) or bending (r>0), either at room, low or high temperature, in air or in liquid environment [1-5], but there is no machine for testing specimens under multiaxial loading. however, it is known that during their life many industrial components are submitted to multiaxial loadings that may lead to a number of cycles close to one billion or more. fatigue cracks may initiate in areas experiencing multiaxial stress states. that is the reason why a new fatigue testing device has been developed to test specimens under biaxial loading at 20 khz. after presenting a brief state of the art on ultrasonic fatigue testing machines, the principle of a new biaxial bending device and the associated stress state are presented hereafter. the first results obtained on a cast al-si alloy in vhcf regime are then compared with those obtained in literature under similar stress state but in hcf regime and under lower frequency. m c. brugger et alii, frattura ed integrità strutturale, 37 (2016) 46-51 doi: 10.3221/igf-esis.37.07 47 state of the art: ultrasonic testing machines ccording to the literature, the first ultrasonic fatigue testing device was developed by mason in the 1950's under fully reversed tension [4, 6]. an interesting review of ultrasonic fatigue testing machines is given by bathias in [5]. the basic principle of an ultrasonic fatigue testing machine is to apply to a specimen an axial sinusoidal displacement at an ultrasonic frequency (typically 20 khz). the specimen is designed so that it has a natural frequency (or mode) at this frequency. an ultrasonic fatigue testing machine is made with: (i) a generator applying an electric signal (at 20 khz) to (ii) a piezoelectric converter that converts the electric signal in a longitudinal vibration at the same frequency, and (iii) a horn for amplifying the vibration finally applied at one end of the specimen. the generator is controlled by a computer so that the resonance of the whole system (piezoelectric converter, horn and specimen) is kept all the test long. this principle has been used by several authors to design special apparatuses for testing specimens under fully reversed tension. coupled with electromechanical or servo-hydraulic testing machines, such equipment can be used for gigacycle fatigue tests under tension with several positive r ratios. a machine has been developed for three points bending test with r>0 too [1]. all these machines allow tests on smooth or notched specimens under uniaxial stress state. some authors [1, 7, 8] have also developed torsion testing machines working like uniaxial ones, by pulse and pause [7, 8] or continuously [9]. furthermore, the ultrasonic testing technique can be used for testing specimens at room temperature with air cooling if needed, or at high temperature [1, 10], in cryogenic environment [1] or in corrosive liquid environment [2, 3]. but all these testing machines apply a uniaxial loading on the specimen. ultrasonic biaxial bending device principle he new fatigue testing device presented hereafter is designed for testing in bending under ultrasonic frequency a flat smooth specimen with a disc geometry [11]. its principle is similar to the testing apparatus proposed by koutiri et al. [12, 13] but this last one was mounted on a servo-hydraulic testing machine working around 20 hz only. the specimen is placed on a frame with a torus ring, so that the contact zone between the lower face of the disc and the frame is a circle. a load is applied at the center of the upper face using a hemispherical indenter (figure 1a). like in a three points bending test, this leads to the bending of the disc. -a -b figure 1: a) principle and b) picture of the ultrasonic biaxial bending device. using an electromechanical testing machine and the ultrasonic loading device described in the following paragraph, both a static load and a sinusoidal displacement (at 20 khz) are applied at the center of the specimen. under the common a t c. brugger et alii, frattura ed integrità strutturale, 37 (2016) 46-51 doi: 10.3221/igf-esis.37.07 48 assumption that macroscopically the material remains elastic in gigacycle fatigue regime, any positive loading ratio can be applied. in practice, to assure uninterrupted contact between specimen and indenter, loading ratios very close to zero are avoided; r>0.05 are recommended. the ultrasonic loading device, partly illustrated in figure 1b, is classic [1]. it consists of a 20 khz electric generator, a piezoelectric converter, a booster and a horn to amplify the sinusoidal axial displacement like in 3 points ultrasonic bending [1, 5]. in order to apply a non-zero mean load, this device is attached to an electromechanical testing machine using bars and hollowed discs attached to the center of the booster, which is a vibration node. finally, a servo-control system adjusts in real time the loading frequency to match the natural frequency of the whole device. for that reason, each part (booster, horn and specimen) must be carefully designed, so that their natural frequency for axial displacement matches 20 khz. the next section details, for some parts, how geometry was determined using fea modal analysis. geometry of the specimen and device first, in order to perform a modal analysis, both the density and the dynamic modulus (at 20 khz) of the tested material are experimentally measured by using a cylindrical bar as explained in [1] for designing tension compression specimens. the specimen geometry (figure 2a) is described by only two parameters: diameter and thickness of the disc. these parameters are determined iteratively using a free-free modal analysis computed with a commercial fea software. the ideal geometry corresponds to a first natural frequency – associated with biaxial bending – equal to 20 khz. for a given stress state at the center of the lower face, contact forces rapidly increase with thickness. on the other hand, since the hemispherical indenter is located at the center of the upper face, the stress state might be disturbed by the loading if the disc is too thin. for the application described in the next section, a compromise has been found by fixing the thickness equal to 6 mm. the location of the vibration nodes on the specimen gives the radius of the frame ring in order to minimize the relative displacement between the specimen and the frame, then the frictional heating. associated stress state theoretically, disc bending generates an equi-biaxial proportional stress state at the center of the specimen’s lower face, and stress level is proportional to the center’s displacement [9]. three calibration specimens were instrumented with strain gauge rosettes glued in the center of the lower face. tests were performed for different amplitudes of the displacement, for a static load assuring a positive load ratio. after measuring strains amplitudes using both a wide band conditioning device (vishay 2210) and high speed data recorder, stresses amplitudes were computed assuming an isotropic linear elastic behavior of the material (because of testing conditions in the vhcf regime). since results are almost proportional to the displacement, table 1 summarizes the results on 3 specimens for a given 10 µm amplitude. considering the uncertainties related to the experimental measurements (position of the strain gauges, gauge factors, etc.), stress state can be considered equi-biaxial. 1st principal stress amplitude (mpa) 2nd principal stress amplitude (mpa) von mises equivalent stress amplitude (mpa) 27.8 26.2 27.0 26.9 26.6 26.8 28.2 26.5 27.4 table 1: stresses at the center of the lower face for a 10 µm amplitude displacement. application to a cast al-si alloy his ultrasonic biaxial fatigue testing device has been tested and validated on a cast aluminum alloy used to produce cylinder heads and previously investigated by koutiri et al. [12, 14]. since cast materials may contain casting defects (porosities, shrinkages, etc.), and because cylinder heads are submitted to high hydrostatic pressure loadings during a very high number of loading cycles, a safe fatigue design requires to determine the fatigue strength of the material under similar stress state in the gigacycle regime. t c. brugger et alii, frattura ed integrità strutturale, 37 (2016) 46-51 doi: 10.3221/igf-esis.37.07 49 material and specimen the material is the cast alsi7cu05mg03 t7. its conventional yield stress is 250 mpa [12, 14]. the specimen geometry is illustrated in figure 2a. specimens were machined out of cast cylinder heads. in order to get enough material volume, cores were diminished prior to casting. this allows for microstructure parameters similar to production parts (das, porosities, and hardness). the circular ring has a 34 mm diameter. -a -b figure 2: a) specimen geometry and b) temperature measurement by ir camera during ultrasonic fatigue test. testing conditions and results tests are performed in air, at room temperature, for r=0.1 load ratio. cyclic loading is stopped after 109 cycles, or when frequency drops down to 19,500 hz due to fatigue crack propagation. both static load and sinusoidal displacement levels were determined using calibration specimens. since ultrasonic loading may generate self-heating, specimen cooling is necessary. dry compressed air is orientated with an air gun towards the upper face (fig. 1b and 2b). in order to quantify self-heating, surface temperature has been measured during selected tests using an infrared camera flir sc 7000 (fig. 2b). since no surface was perpendicular to the camera, temperature was averaged on the areas labeled 1 and 2 on figure 2b. for maximal stresses equal to 130 – 140 – 150 – 160 mpa, the mean temperature stabilizes respectively at 65 – 75 – 80 – 85°c. such temperatures are negligible compared to metallurgical transformations of the al alloy. the first fatigue test results are illustrated in figure 3. additional results obtained in hcf regime at 20 hz for the same material and similar stress state [12, 14] are also presented for comparison purpose. figure 3: fatigue test results under biaxial bending: results of this study at 20 khz in vhcf regime and results from [12, 14] on the same material at 20 hz in hcf regime. c. brugger et alii, frattura ed integrità strutturale, 37 (2016) 46-51 doi: 10.3221/igf-esis.37.07 50 discussion for maximum stress levels equal or lower than 140 mpa, the first results obtained with the new ultrasonic biaxial testing device are in good agreement with the results by koutiri et al [12, 14]. in our data, there is only one specimen broken very early, for a reason to be clarified. the median fatigue strength at 109 cycles is close to 63 mpa (corresponding to a maximal stress equal to 140 mpa). figure 4 illustrates, in a dang-van diagram [15], both the experimental median fatigue strengths at 2.106 cycles obtained by koutiri [12] on smooth specimens made in the same cast al alloy and the threshold line identified from torsion (r=-1) and tension (r=-1) data. furthermore, the loading paths corresponding to existing ultrasonic fatigue testing machines are shown: torsion (r=-1), tension (r=-1), tension or 3 points bending (r>0). the loading path corresponding to the specimens tested at the stress level corresponding to 1.109 cycles with the new device presented here is illustrated. it is clear that this device allows questioning the dang-van criterion for higher hydrostatic stress states. the same conclusion is valid for the crossland criterion too [16]. it should be noted that the results obtained for maximum stress levels equal or greater than 150 mpa cannot be directly compared with literature results due to different stop criteria. indeed, the test results presented in this paper were stopped when the resonance frequency decreased from about 19,900 hz to 19,500 hz. such frequency drop is due to rigidity loss associated to a very large macroscopic fatigue crack propagation. indeed, macroscopic cracks are either unique or branched but always extended almost to the frame ring when the test stops (fig. 5). additional investigations are needed to quantify the number of cycles associated with this propagation, but first observations indicate it might exceed 107 cycles. however, one can note that 107 cycles represent 1% only of 109 cycles. figure 4: dang van diagram for the cast al-si alloy: loading paths associated with existing ultrasonic fatigue machines and new ultrasonic biaxial bending device. -a -b figure 5: macroscopic fatigue crack after testing a disc specimen under biaxial bending, a) lower face of the specimen and b) after breaking it under monotonic quasi-static loading. c. brugger et alii, frattura ed integrità strutturale, 37 (2016) 46-51 doi: 10.3221/igf-esis.37.07 51 conclusion and prospects new ultrasonic fatigue testing device generating a biaxial proportional stress state with a positive loading ratio has been presented. vhcf tests were performed on a cast aluminum alloy already tested in the literature in hcf regime under a similar stress state. the new results are consistent with data from the literature. self-heating is moderate, but the stop criterion could be improved to detect smaller crack. crack initiation will be investigated, as two competing parameters play a role: the biaxial stress state which is maximal on the surface, and the possible presence of subsurface defects in a cast material. references [1] bathias, c., paris, p.c., gigacycle fatigue in mechanical practice, marcel dekker, new york, (2005). [2] palin-luc, t., perez-mora, r., bathias, c., dominguez, g., paris p.c., arana, j-l., fatigue crack initiation and growth on a steel in the very high cycle regime with sea water corrosion, engng fract. mechanics, 77 (2010) 1953–1962. doi:10.1016/j.engfracmech.2010.02.015 [3] perez-mora, r., palin-luc, t., bathias, c., paris, p.c., very high cycle fatigue of a high strength steel under sea water corrosion: a strong corrosion and mechanical damage coupling, int. j. fatigue, 74 (2015) 156–165. doi:10.1016/j.ijfatigue.2015.01.004 [4] mason, w.p., piezoelectric crystals and their application in ultrasonics, van nostrand, new york, (1956), 161. [5] bathias, c., piezoelectric fatigue testing machines and devices, int. j. fatigue, 28 (2006) 1438–1445. doi:10.1016/j.ijfatigue.2005.09.020 [6] mason w.p., ultrasonic fatigue, in: j.m. well, o.l.d. buck roth, j.k. tien (eds.), proceedings of the first international conference on fatigue and corrosion fatigue up to ultrasonic frequencies, the metallurgical society of aime (1982) 87–102. [7] stanzl-tschegg, s.e., mayer, h. r., tschegg, e. k., high frequency method for torsion fatigue testing, ultrasonics, 31 (1993) 275–280. doi:10.1016/0041-624x(93)90021-q [8] mayer, h., ultrasonic torsion and tension–compression fatigue testing: measuring principles and investigations on 2024-t351 aluminium alloy, int. j. fatigue, 28 (2006) 1446–1455. doi:10.1016/j.ijfatigue.2005.05.020 [9] nikitin, a., bathias c., palin-luc, t., a new piezoelectric fatigue testing machine in pure torsion for ultrasonic gigacycle fatigue tests: application to forged and extruded titanium alloys, fat. frac. engng. mat. structures, 38 (2015) 1294–1304. doi:10.1111/ffe.12340 [10] wagner, d., cavalieri, f.j., bathias, c., ranc, n., ultrasonic fatigue tests at high temperature on an austenitic steel, propulsion power research, 1 (2012) 29–35. doi:10.1016/j.jppr.2012.10.008 [11] blanc, m., osmond, p., palin-luc, t., bathias c., french patent n° fr1357198 (2013). [12] koutiri, i., effet des fortes contraintes hydrostatiques sur la tenue en fatigue des matériaux métalliques, phd thesis, ensam, n° 2011-enam-0015 (2011). [13] koutiri, i., bellett, d., morel, f., augustins, l., adrien, high cycle fatigue damage mechanisms in cast aluminium subject to complex loads, int. j. fatigue, 47 (2013) 44–57. doi:10.1016/j.ijfatigue.2012.07.008 [14] koutiri, i., morel, f., bellett, d., augustins, l, effect of high hydrostatic stress on the fatigue behavior of metallic materials, icf-12, 5 (2009) 3694–3703. [15] dang-van, k., cailletaud, g., flavenot, j.f., douaron, l., lieurade, h.p, in: m. brown, k. miller (eds), biaxial and multiaxial fatigue, esis, sheffield, (1989) 459–478. 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can be opened with acrobat and adobe reader 5.0 and later.) >> /namespace [ (adobe) (common) (1.0) ] /othernamespaces [ << /asreaderspreads false /cropimagestoframes true /errorcontrol /warnandcontinue /flattenerignorespreadoverrides false /includeguidesgrids false /includenonprinting false /includeslug false /namespace [ (adobe) (indesign) (4.0) ] /omitplacedbitmaps false /omitplacedeps false /omitplacedpdf false /simulateoverprint /legacy >> << /addbleedmarks false /addcolorbars false /addcropmarks false /addpageinfo false /addregmarks false /convertcolors /converttocmyk /destinationprofilename () /destinationprofileselector /documentcmyk /downsample16bitimages true /flattenerpreset << /presetselector /mediumresolution >> /formelements false /generatestructure false /includebookmarks false /includehyperlinks false /includeinteractive false /includelayers false /includeprofiles false /multimediahandling /useobjectsettings /namespace [ (adobe) (creativesuite) (2.0) ] /pdfxoutputintentprofileselector /documentcmyk /preserveediting true /untaggedcmykhandling /leaveuntagged /untaggedrgbhandling /usedocumentprofile /usedocumentbleed false >> ] >> setdistillerparams << /hwresolution [2400 2400] /pagesize [612.000 792.000] >> setpagedevice microsoft word numero_33_art_47 j.a araujo et al, frattura ed integrità strutturale, 33 (2015) 427-433; doi: 10.3221/igf-esis.33.47 427 focussed on multiaxial fatigue equivalent configurations for notch and fretting fatigue j. a. araújo, f. c. castro university of brasilia, unb, departamento de engenharia mecanica alex07@unb.br s. pommier, j. bellecave lmt-cachan, ens cachan / cnrs / université paris saclay sylvie.pommier@universite-paris-saclay.fr jbellecave@gmail.com j. mériaux snecma, group safran jean.meriaux@snecma.fr abstract. under the typical partial slip conditions under which fretting fatigue takes place, the amount of superficial damage is small. therefore, the substantial reduction in fatigue life caused by fretting, when compared to plain fatigue, may well be more associated with the stress concentration and the stress gradient phenomena generated by the contact problem than to the superficial loss of material. in this setting, notch stress-based methodologies could, in principle, be applied to fretting in the medium/high cycle fatigue regime. the aim of this work was to investigate whether it is possible to design fretting and notch fatigue configurations, which are nominally identical in terms of damage measured by a multiaxial fatigue model. the methodology adopted to carry out this search considered a cylindrical on flat contact and a v-notch. load and geometry dimensions of both configurations were adjusted in order to try to obtain the “same” decay of the multiaxial fatigue index from the hot spot up to a critical distance. positive results of such simulations can lead us to design an experimental program that can bring more firm conclusions on the use of pure stress-based approaches, which do not include the wear damage, in the modeling of fretting fatigue. keywords. fretting fatigue; notch fatigue; stress gradient; multiaxial fatigue. introduction he term fretting denotes a small oscillatory movement between two solid surfaces in contact. in many industrial designs, one or both components of the assembly may also be subjected to a bulk fatigue load, the phenomenon is then called fretting fatigue. fretting failure of components such as splines, the dovetail fixing between blade and disc in fans of aeroengines [1] and riveted skins of the aircraft fuselage [2] have become a major design concern. indeed, experimental evidence has shown that the conjoint action of fretting and fatigue may produce strength reduction factors t j.a araujo et al, frattura ed integrità strutturale, 33 (2015) 427-433; doi: 10.3221/igf-esis.33.47 428 varying from 2 up to 10 compared to plain fatigue [3]. the most severe reduction of life is observed in partial slip conditions [4]. indeed gross sliding can fastly remove small nucleated cracks before they can further propagate. under fretting conditions, the loads involved generate a time varying non-proportional multiaxial stress field under the contact [5]. there is usually a high stress concentration on the contact interface but it is limited to a small region and hence decays fastly as one moves from the surface to the interior of the component [6]. in this setting, the use of nonlocal approaches, initially developed to estimate the fatigue endurance of notched specimens, have been extended to the fretting fatigue problem [7]–[9]. araújo et al. [8] used the theory of critical distances (tcd) in conjunction with the modified whöler curve method (mwcm) and showed that it was capable of estimating the results of fretting fatigue experiments showing a contact size effect with a good degree of accuracy (±20% error band). it is worthy noticing that notched components and mechanical assemblies under time varying loads present quite similar characteristics. in both configurations there are usually severe stress gradients and the state of stress becomes complex (multiaxial) as the analysis moves inside the material. the general aim of this work is to investigate whether it is possible to design fretting and notch fatigue configurations, which are nominally identical in terms of damage measured by a multiaxial fatigue index. further, these designs must be such that the specimens can be machined within a good level of accuracy and with tight tolerances in both configurations (notch and fretting), turning the future experimental campaign reproducible and reliable. the advantage of proving that such experimental campaign can be generated is that it consists in a way to somehow isolate the role of the surface fretting wear in diminishing the material fatigue resistance of mechanical assemblies under partial slip. as both fatigue problems are equivalent in terms of fatigue loading over a material process zone, their resistance should be essentially similar, unless the influence of the small surface damage caused by the fretting wear, and which does not exist in the notch configuration, is greater than the authors expect it will have. another quite important aspect that such experimental campaign could clear out is the fact that one can use the same fatigue modeling approach to design either industrial components containing geometrical discontinuities or mechanical couplings. this would avoid the need for lengthy and costly experimental programs considering complex geometries and specific test rigs to calibrate the fatigue material constants. material he material considered in this study was a 7050-t7451 aluminium alloy. material properties were taken from araújo et al. [10] and are presented in tab. 1. fatigue strength for fully reversed (stress ratio, r=-1) and repeated loading (r=0) are quoted for 107 cycles. young’s modulus poisson’s ratio yield strength 1 0 , 1th rk  73.4 gpa 0.33 454 mpa 161 mpa 120 mpa 4.5 mpam table 1: material properties of 7050-t7451 al alloy. stress tensor for elastic contact of cylinders under partial slip and in the presence of a bulk fatigue load he first step towards a solution for the subsurface stress field is to solve the contact problem itself, i.e., to find the magnitude and distribution of the surface tractions. in the present problem, the pad radius, r , the normal load per unit length, p , and the specimen thickness were defined so that each solid could be considered as an elastic half-space and the solution for the pressure distribution was hertzian [11]. for pure fretting, the time varying tangential force q (t) generates a shear traction described firstly by cattaneo [12] and independently by mindlin [13]. in partial slip condition, the contact is characterized by a central stick zone bordered by two sliding zones. in fretting fatigue, the effect of the bulk tension is to offset this stick zone. by superposing the normal and tangential contributions, it is possible to directly evaluate the resulting stress tensor using muskhelishvili’s potential theory [14]. for synchronous and in phase load combinations, at the instants of maximum and minimum bulk/shear loads, the stress tensor turns out to be: t t j.a araujo et al, frattura ed integrità strutturale, 33 (2015) 427-433; doi: 10.3221/igf-esis.33.47 429 0 0 0 0 0 , , , , , ( ) n t t b y y y yx x x x e t tca a a a a a c c f f p p fp a fp p                                                                 (1) for any other time instant t, during loading or unloading, the appropriate analytical solution is stated as: 0 0 0 0 0 0 ( ) ,, , , , , ( ) ( )( ) ( ) 2 tn t t b x e t yy y y yx x x x e t c t c tc t tca a a a a a c c f f f p p fp a fp a fp p                                                                             (2) in the above equations, 0p is the peak pressure, c and e are the stick zone half width and its offset from the center of the contact at the instant of maximum or minimum shear load. at any other time instant, 'c and 'e correspond to the stick zone half width and its offset from the center of the contact. the superscripts n and t stand for the stress components due to the normal and the tangential load, respectively. finally, b is the stress tensor associated with the bulk fatigue load. plane strain conditions are assumed. explicit expressions to compute c , e , 'c , 'e , n and t are given in a convenient form by hills and nowell [15]. stress tensor around a v-notch he elastic solution for the stress field of plane v-notched specimens can be derived using complex potential [14] or bi-harmonic potential functions [16]. recently, the williams’ crack solution [17] was re-addressed by lazzarin and tovo [18] and filippi et al. [19]. such approach was used in this work to evaluate the stresses along the bisector of a notch loaded in mode i. multiaxial criterion usmel and lazzarin [20] observed that the multiaxial high-cycle fatigue behaviour of metallic materials could successfully be estimated by using a simple a vs , /n max a  relationship. the model has been described by susmel and co-workers in a series of articles [20-22]. briefly, the so-called modified wöhler curve method (mwcm) can be formalized as follows: ,( , ) ( , )n maxc c c ca a            (3) where a is the equivalent shear stress amplitude in the critical plane ( , ) c c  , ,n max is the maximum stress perpendicular to this plane, and the parameters  and  are material constants that can be obtained from two fatigue strengths generated under different loading conditions. for instance, these constants can be evaluted using the fatigue limits 1 and 0 , generated respectively under fully-reversed (r =-1) and under repeated (r = 0) uniaxial loading, as follows [21]: 1 0 2       01 2     (4) which gives 20.8 mpa  and 101.5mpa  for the 7050-t7451 al alloy. a key aspect in using such model for nonproportional loadings, as it is the case for fretting fatigue, is the computation of a relative to a material plane. we propose here to use the maximum rectangular hull concept developed by araújo et al. [23-25]. it consists of rotating t s j.a araujo et al, frattura ed integrità strutturale, 33 (2015) 427-433; doi: 10.3221/igf-esis.33.47 430 rectangular hulls engulfing the shear stress vector path in a material plane, and computing the square root of the sum of the squares of each rectangle’ half-sides. the greatest of these values is then defined as the shear stress amplitude, a . identification of the critical distance he use of the mwcm in conjunction with the theory of critical distances (tcd) is based on the assumption that all the physical processes leading to crack initiation are confined within the so-called structural volume. the size of this volume is assumed not to be dependent on either the stress concentration feature weakening the component or the complexity of the stress field damaging the fatigue process zone [26]. in the tcd fatigue endurance is assumed to occur when: 1 ( ) v f dv c v   (5) where  is stress tensor within a volume of material v around the stress raiser, c is a material parameter associated with its fatigue resistance, and  .f denotes an effective stress that appropriately characterizes the fatigue loading. eq. (5) can be simplified by substituting the material volume by a line (lm) or by a single point (pm) at a certain distance from the hot spot. to obtain this length parameter, the critical distance, a third material parameter is needed, the threshold stress intensity factor range under r=-1, thk . considering a material point at a distance l from the crack tip and on the bisector line of a sharp crack it is possible to compute the stress tensor at this position at any time instant of the loading history. if now one computes the a and ,n max variables of the multiaxial model from this state of stress, it is possible to find equations relating l, thk and 1 for the point and the line methods: 1 2 1 2 t m h p k l          (6) 1 2 2 th lm k l          (7) using material properties reported in tab. 1, one can use eq. (6) to calculate 0.031pml  mm. an alternative manner to interpret the critical distance is to associate it with the length of non-propagating cracks in crack like notched specimens under fatigue limit conditions. therefore, from a phenomenological point of view, some authors such as susmel [27] and taylor [28] assume the critical distance as a material property. however, it is clear that it depends on the effective stress used to model the multiaxial problem. methodology he first step to try to establish equivalent notch/fretting fatigue experiments is to define a reference configuration. in this case, a fretting fatigue data tested in the apparatus of the university of brasília was considered as the starting point. this test was carried out using two cylindrical fretting pads, which were loaded against a flat dogbone specimen. tab. 2 lists the loads, pad radius, the coefficient of friction, f , and the life for complete fracture of the especimen for this test. the cross section of the fretting specimen is schematically shown in fig. 1 (13 x 13 mm). the characteristics of the fretting apparatus are well detailed by martins et al. [29], hence it will not be described here. now one can plot the multiaxial fatigue index eqs , defined in eq. (8), from the trailing edge of the contact (hot spot for the fatigue index) along the distance y in the interior of the fretting specimen. the computation is carried up to a distance equivalent to the characteristic length provided by the line method, lml . ,n maxeq a a s       (8) t t j.a araujo et al, frattura ed integrità strutturale, 33 (2015) 427-433; doi: 10.3221/igf-esis.33.47 431 fig. 2 (a) shows the gradient of eqs with respect to y for this test and the limit for crack initiation defined by the threshold parameter 101.5mpa  for this alloy. notice that, considering the point method as the critical distance, the index is higher than  (at the distance pml ), and is then expected the test would break before 107 cycles. indeed the test broke around 1.2 x 106 cycles. figure 1: scheme of the methodology proposed to find equivalent notch/fretting fatigue configurations. to carry on with the analysis the following step is to search for the notch configuration that will provide an equivalent decay for the multiaxial fatigue index over lml . to do so, a minimization technique based on the difference between the indexes ,eq notchs and ,eq frettings along the distance lml can be applied (function j in fig. 1). notch radius, notch opening angle and the remote fatigue load are the variables of the minimization. the range of variation of such variables must be such that one can guarantee that the notch specimens can be machined and mainly its notch radius lies within a tight tolerance. in this setting, notch radius could vary between 0.1 and 1 mm (in steps of 0.05 mm), its opening angle between 30° and 90° (15° increments) and the notch depth was fixed in 5 mm. the limitation for the choice of remote bulk load range was defined by the operational capability of the servohydraulic machine. it can accurately apply and control load amplitudes varying from 1 to 100 kn (a 1kn increment was defined). pad radius peak pressure a ( 1)r   /q fp f frequency life (cycles) 70mm 300 mpa 55 mpa 0.33 0.54 5hz 1119774 table 2: parameters and observed life of the fretting fatigue test used to design an equivalent notch fatigue test. minimization of the difference between the two gradients was achieved by using a 0.5mm notch radius specimen, with a notch opening angle of 60° and a fully reverse fatigue stress amplitude of 42.5 mpa. now fig. 2 (a) is again invoked to depict the result of the optimized notch configuration. it can be seen that the variation of the multiaxial fatigue index against distance from the notch root matches quite well the curve obtained for the fretting fatigue configuration. fig. 2(b) depicts the points representing the shear stress amplitude, a , against the normalized maximum stress, ,n max a  , for both configurations. these points do not lay one over the other but they keep the same distance from the continuous threshold line dividing safe (under the line) and unsafe domains. in fig. 2(c) an interesting behavior is observed. the shear stress amplitude and the maximum normal stress are traced against the distance for the notch and for the fretting configuration. while the amplitude of shear stress on the critical plane for the fretting problem is always higher than for the notch one along the distance, the opposite happens to the maximum normal stress. therefore, although the decay of the multiaxial fatigue index is essentially the same for both configurations, the same can not be said about the individual variables that are present in the index computation. j.a araujo et al, frattura ed integrità strutturale, 33 (2015) 427-433; doi: 10.3221/igf-esis.33.47 432 figure 2: (a) variation of the multiaxial fatigue index against distance in the specimen (from the hot spot) for the fretting fatigue test and for the optimized notch configuration. (b) points representing the shear stress amplitude, a , against the normalized maximum stress, , /n max a  , for both configurations. (c) variation of a and , /n max a  against distance for fretting and notch problems. conclusion t was shown that it is possible to design a series of fretting and notch fatigue tests for a 7050-t7451 al alloy, which are nominally equivalent in terms of multiaxial fatigue conditions along a process zone. the notch geometry and fretting configuration found can be machined and reproduced within a given tolerance, and closed form solutions for the cyclic stress field under plane strain are available for both. it was pointed out however that equivalent fatigue index parameters does not mean equivalent shear stress amplitude and maximum normal stress. the design of this test campaign can constitute a key initiative to improve our knowledge on the influence of the surface damage on the life of components under fretting fatigue conditions. further, should the results of these tests confirm the equivalence hypothesis between this two apparently distinct fatigue problems, a single unified stress based approach could be used to design them. future work involves the conduction of the experimental tests. acknowledgments he supports provided by safran/snecna, by cnpq (contracts 310845/2013-0 and 309748/2013-5) and by finatec are gratefully acknowledged. references [1] ruiz, c., chen, k. c., life assessment of dovetail joints between blades and discs in aero-engines, in: proc. int. conf. fatigue, (1986). [2] harish g., farris, t. n., shell modeling of fretting in riveted lap joints, aiaa j., 36(6) (1998) 1087-1093. [3] lindley, t. c., fretting fatigue in engineering alloys, int. j. fatigue, 19(93) (1997) 39-49. [4] madge, j. j., leen, s. b., shipway, p. h., the critical role of fretting wear in the analysis of fretting fatigue, wear, 263(1-6) (2007) 542-551. [5] navarro, c., muñoz, s., domínguez, j., on the use of multiaxial fatigue criteria for fretting fatigue life assessment, int. j. fatigue, 30(1) (2008) 32-44. [6] nowell, d., dini, d., hills, d. a., recent developments in the understanding of fretting fatigue, eng. fract. mech., 73(2) (2006) 207-222. [7] fouvry, s., kapsa, p., vincent, l. multiaxial fatigue analysis of fretting contact taking into account the size effect, in astm special technical publication, 1367 (2000) 167-182. i t j.a araujo et al, frattura ed integrità strutturale, 33 (2015) 427-433; doi: 10.3221/igf-esis.33.47 433 [8] araújo, j. a., susmel, l., taylor, d., ferro, j. c. t., mamiya, e. n., on the use of the theory of critical distances and the modified wöhler curve method to estimate fretting fatigue strength of cylindrical contacts, int. j. fatigue, 29(1) (2007) 95-107. [9] proudhon, h., fouvry, s., yantio, g. r., determination and prediction of the fretting crack initiation: introduction of the (p, q, n) representation and definition of a variable process volume, int. j. fatigue, 28(7) (2006)707-713. [10] araújo, j. a., castro, f. c., a comparative analysis between multiaxial stress and δk-based short crack arrest models in fretting fatigue, eng. fract. mech., 93 (2012) 34-47. [11] hertz, r., über die berührung fester elastischer körper, j. für die reine und angew. math., 92 (1981) 156-171. [12] cattaneo, c., sul contatto di due corpi elastici: distribuzione locale degli sforzi. rendiconti dell’accademia nazionale dei lincei, rend. dell’accademia naz. dei lincei, 27 (1938) 342-348. [13] mindlin, r. d., compliance of elastic bodies in contact, j. appl. mech., 16 (1949) 259-268. [14] muskhelishvili, some basic problems of mathematical theory of elasticity. noordhoff, groningen, (1953). [15] hills, d. a., mechanics of fretting fatigue, wear, 175(1-2) (1994) 107-113. [16] neuber, h., theory of notch stresses, kerbspannungslehre, (1958). [17] williams, m. l., on the stress distribution at the base of a stationary crack, j. appl. mech., 24 (1957) 109-114. [18] lazzarin, p., tovo, r., a unified approach to the evaluation of linear elastic stress fields in the neighborhood of cracks and notches, int. j. fract., 78 (1996) 3-19. [19] filippi, s., lazzarin, p., tovo, r., developments of some explicit formulas useful to describe elastic stress fields ahead of notches in plates, int. j. solids struct., 39(17) (2002) 4543-4565. [20] susmel, l., lazzarin, p., a bi-parametric wöhler curve for high cycle multiaxial fatigue assessment, fatigue &amp; fract. eng. mater. &amp; struct., 25(1) (2002) 63-78. [21] susmel, l., tovo, r., lazzarin, p., the mean stress effect on the high-cycle fatigue strength from a multiaxial fatigue point of view, int. j. fatigue, 27(8) (2005) 928-943. [22] fatemi, a., socie, d. f., critical plane approach to multiaxial fatigue damage including out-of-phase loading, fatigue fract. eng. mater. struct., 11(3) (1988) 149-165. [23] araújo, j. a., dantas, a. p., castro, f. c., mamiya, e. n., ferreira, j. l. a., on the characterization of the critical plane with a simple and fast alternative measure of the shear stress amplitude in multiaxial fatigue, int. j. fatigue, 33(8) (2011) 1092-1100. [24] castro, f. c., araújo, j. a., mamiya, e. n., zouain, n., remarks on multiaxial fatigue limit criteria based on prismatic hulls and ellipsoids, int. j. fatigue, 31(11-12) (2009) 1875-1881. [25] mamiya, e. n., araújo, j. a., castro, f. c., prismatic hull: a new measure of shear stress amplitude in multiaxial high cycle fatigue, int. j. fatigue, 31(7) (2009) 1144-1153. [26] susmel, l., a unifying approach to estimate the high-cycle fatigue strength of notched components subjected to both uniaxial and multiaxial cyclic loadings, fatigue fract. eng. mater. struct., 27(5) (2004) 391-411. [27] susmel, l., the theory of critical distances: a review of its applications in fatigue, eng. fract. mech., 75(7) (2008) 1706-1724. [28] taylor, d., a mechanistic approach to critical-distance methods in notch fatigue, fatigue fract. eng. mater. struct., 24(4) (2001) 215-224. [29] martins, l. h., rossino, l. s., bose filho, w. w., araújo, j. a., detailed design of fretting fatigue apparatus and tests on 7050-t7451~al alloy, tribol. mater. surfaces interfaces, 2(1) (2008) 39-49. microsoft word numero_60_art_24_3470.docx h. djeloud et alii, frattura ed integrità strutturale, 60 (2022) 346-362; doi: 10.3221/igf-esis.60.24 346 investigation fatigue crack initiation and propagation cruciform welded joints by extended finite element method (xfem) and implementation sed approach djeloud hamza, moussaoui mustafa laboratory of development in mechanics and materials (ldmm) university of djelfa, (17000) algeria. hamzadjaloud@gmail.com, http://orcid.org/0000-0002-0726-3466 moussaoui_must@yahoo.fr kellai ahmed research center in industrial technologies, crti, p.o. box 64, cheraga, 16014 algiers, algeria. a.kellai@crti.dz hachi dahmane laboratory of development in mechanics and materials (ldmm) university of djelfa, (17000) algeria. hachi_dahmane@yahoo.fr filippo berto department of mechanical and industrial engineering, ntnu – norwegian university of science and technology, trondheim, norway. filippo.berto@ntnu.no, http://orcid.org/0000-0002-4207-0109 benattou bouchouicha laboratory of materials and reactive systems (lmsr), department of mechanical engineering, university of sidi-bel-abbes, bp 89, cité ben m'hidisidibel-abbes 22000-algeria. benattou.bouchouicha@gmail.com, https://orcid.org/0000-0002-6051-5108 hachi brahim elkhalil laboratory of development in mechanics and materials (ldmm) university of djelfa, (17000) algeria. br_khalil@yahoo.fr, http://orcid.org/0000-0002-6672-746x abstract. this study has used the strain energy density (sed) approach to evaluate the stress intensity factor (sif) of cracked cruciform welded joints in hardox 450 steel. a microstructural analysis was made of hardox 450 steel which is composed of refined and tempered low carbon martensite. the citation: djeloud, h., moussaoui, m., kellai, a., hachi, d., berto, f., bouchouicha, b., hachi, b. e., investigation fatigue crack https://youtu.be/ecus9l7gers h. djeloud et alii, frattura ed integrità strutturale, 60 (2022) 346-362; doi: 10.3221/igf-esis.60.24 347 obtained results of simulation will be compared with those provided by j-integral method for different enriched zones and contours based on the extended finite element method (xfem) coupled with the level set technique (lst). crack initiation and propagation under cyclic loading have been adopted for the modeling of cruciform welded joints. keywords. strain energy density approach; xfem; stress intensity factor; crack initiation and propagation; hardox 450. initiation and propagation cruciform welded joints by extended finite element method (xfem) and implementation sed approach, frattura ed integrità strutturale, 60 (2022) 346-362. received: 13.02.2022 accepted: 22.02.2022 online first: 02.03.2022 published: 01.04.2022 copyright: © 2022 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. introduction elding is an efficient and long lasting joining procedure. the various welding types are used in almost all industries. however, the welding operation, usually creates different types of defects, like cracks, porosity, elemental segregation, and brittle phases. these defects significantly decrease the fatigue life [1,2]. xfem has been successfully applied to solve many welding-related problems. for instance, kai uses xfem to create a repaired welding model of welded joints of p91 steel plates with particular cracks[3]. chen et al. build a numerical model by xfem and experimental investigation of crack growth in t-joints to better understand the mechanisms of crack growth in welded joints [4]. wang et al. also used xfem for numerical simulation of the fatigue crack growth and suggested developing simple solutions for practical prediction of km factors [5]. xfem will be utilized to make a model of a semi-elliptical weld toe crack in a fillet weld for different sizes. the obtained km parameter is represented in the form of curves as a function of crack dimensions. pang makes use of the volumetric approach to evaluate the sif in a pipe made p264gh steel under internal pressure by adopting xfem [6]. he chose p264gh due to its weldability and ductility properties that help make this material appropriate for piping [7]. taheri used xfem to evaluate the effects of welding residual stresses on crack growth rate[8]. kraedegh et al. in [9] examined fatigue crack growth in t joints under three-point bending that were simulated numerically by xfem. chatziioannou et al. manufactured x-joint specimens, s420 steel and used them [10]. a comparative study between repaired and unrepaired cruciform welded. a new correlation was proposed to assess the sif of repaired cruciform welded joints based on the reduction and the correction factors of un-repaired cruciform welded joints [11]. they are vulnerable to high cyclic loading, and rigorous numerical models are used to simulate the experimental can provide accurate predictions [12–15]. there are various approaches that can be used for assessment of the sif of welded joints, peak stress, volumetric approach, and average strain energy density[16–18]. we implemented the last one in the xfem couple with level set technique because it is faster and less resource consuming. in this study, we use a code developed by hachi and his team that was used to solve problems involving cracks in case of static and dynamic load and crack growth prediction, homogenization in 2d and 3d, etc [19–21]. sih developed the sed theory for the purpose of solving fracture mechanics problems [22–24]. he identified the global and local strain energy density, as well as the fracture behavior factors. lazzarin and co-workers were the first to formalize and publish a series of very crucial papers using a synthesis based on the ased calculated in the control volume are around the crack tip or u-notched or v-notched, see references [25–29]. many researchers utilize the strain energy density criterion investigated experimentally and numerically in case of brittle materials [30][31]. lazzarin studied ductile materials and inplane tensile loading mode i. however, mode ii is generally negligible in applications[32]. to estimate the nsifs directly from local stress distributions, we need very fine meshes. note that refined meshes are not required when the goal of the finite element analysis is to estimate the average value of the local strain energy density on a control volume surrounding the v-notches or crack tip [33]. the sed approach has been successfully used by aliha et al. in mixed mode (i/ii). aliha also studied sharp notched disc bend specimens under mixed mode (i/iii) loading [34][35], campagnolo et al. characterized different control volumes and exposed them to different combinations of static loading types in order to evaluate the resistance of different materials, [36–38]. furthermore, in the case of cracks subjected to mixed mode (i/ii) loading, the relationship between the averaged strain energy density sed technique and the peak stress method has been explored [39]. just a few number of studies used sed approach to analyse cruciform welding joint with predefined cracks. that’s why we were interested in this study in using this approach in xfem to evaluate sif value and compare it with another sif value w h. djeloud et alii, frattura ed integrità strutturale, 60 (2022) 346-362; doi: 10.3221/igf-esis.60.24 348 obtained using j-integral. the paper is organized in the following way. section 2 describes the materials and models used in this study. section 3 microscopic study of the state for different welding regions weld metal (wm), heat affected zone (haz), basse metal (bm) section 4.1 provides the theoretical background of the ased approach. in subsection 4.2 we show the theoretical background xfem, and in subsection 4.3 we present the theory of level-set technique. section 5 describes the method adopted to get results in two phases, the first part of static load, and the second part in fatigue load. section 6 summarizes the main conclusions of the paper. materials and models igh-strength steel is used to make cruciform welded joints made of high-strength martensitic abrasion resistant hardox 450 steel. chemical composition of the base metal, weld metal and mechanical properties are indicated in tab. 1, tab. 2, and tab. 3 respectively. all data from tabs. 1, was determined using a thermo fisher scientific instrument. for the manufacturing of steel structures like steel bridges, offshore structures, etc. welding is nowadays considered an efficient metal joining process. the type of fillet welded cruciform joint is commonly used in the construction of long spanned bridges with improved design and higher weld quality. however, the existence of geometrical discontinuities such as cracks and porosity in addition to metallurgical nonuniformities, which lead to crack initiations from different positions that can be difficult to detect [40]. figure 1: geometry and dimension of cruciform welded joints involves a cracks specimen (mm scale). c si mn cr ni mo 0.21 0.7 1.6 0.25 0.25 0.25 table 1: chemical composition hardox 450. c si mn 0.11 0.8 1.5 table 2: chemical composition of the electrode. e(gpa) t (mpa) ick (mpa(mm)0.5) a% v 210 1660 3067 7 0.29 table 3: mechanical properties of hardox 450. h j-integral contour control volume enriched zone crack weld toe 50 5 h. djeloud et alii, frattura ed integrità strutturale, 60 (2022) 346-362; doi: 10.3221/igf-esis.60.24 349 numerical modelling he local strain energy density sed approach is one of such modern methods, currently used in the evaluation of fatigue. the main idea of the sed method is to fully surround the crack tip or notch tip with a size control volume to calculate the strain energy for each finite element that can be achieved through the eqn. 1.                     2 2 2 21 2 2 1 ) 2 i xx yy zz xx yy xx zz yy zz xyw v v e (1) where   0zz under plane-stress and     zz xx yyv under plane-strain [41]. the total average elastic energy included in the area of control volume according to the sed approach is determined by eqn. 2.    1 1 i i e i i w w a (2) the next stage in the sed calculation is to determine an ideal control volume radius cr , which varies depending on the material. there are already different investigations about the control volume radius it can be calculated from the eqn. 3 . generally for steel  0.2  0.4cr [42]. for a sharp v-notch, the critical volume becomes a circular sector of radius cr centered at the notch tip fig. 2a.              2 1 5 8 4 ic c t v v k r (3) figure 2: control volume (a) pointed v-notch (b) crack. where v is the poisson's ratio ick critical stress intensity factor mode i and t conventional ultimate tensile strength. when utilizing the sed approach, it is critical to adjust the finite elements in the control volume to ensure that there are enough finite elements to approximate the actual value[43–45] in the case of using xfem, the crack tip enrichment and the crack enrichment compensate for the density of the mesh. the analytical evaluation for the total elastic ased over the control volume is based on the leading order terms of william’s solution and is evaluated as shown in the following equation [33].          1) 2 1 1 2(1 i c e k w e r (4) e is the young’s modulus which is given for different materials and 1 are the eigenvalues of the williams' stress field solution for the n-sif k1 for modes i. the eigenvalues 1 can be derived from the case of crack 1 =0.5 [39]. the values for this are already listed in the literature for different important 2α [40]. 1e correction factors which depend on the stress t 𝑅 𝑅 (a) (b) 2𝛼 2𝛼 0 h. djeloud et alii, frattura ed integrità strutturale, 60 (2022) 346-362; doi: 10.3221/igf-esis.60.24 350 strain field, poisson’s ratio and the notch opening angle 2α. wither calculation can be made for 1e from the following empirical equations [46].         26 41 5.373.10 2 6.151.10 2 0.133e (5) xfem coupled to the lst the displacement field is described by the following finite element approximation equation.      i iu x n x u (6) the xfem is used to represent the discontinuities independent of the mesh. the discontinuities can be modeled by enriching all discontinuous elements using enrichment functions that satisfy the discontinuous behavior and adding additional nodal degrees of freedom, mention here belytschko and moes the first to formalize and publish a series of very important papers using xfem [47–50]. in general, the approximation of the field of displacement in the xfem takes the following form. 1 ( ) ( ) ( ) ( ) e f a i i ii s ai n n u x n x u h x a x b                  (7) fn is the set of nodes are which contains the crack tip (represented by yellow squares on fig. 3), en is the set of nodes entirely cut by the crack (represented by blue circles in fig. 3). the iu are the classical degrees of freedom. the ia are the degrees of freedom linked to the discontinuity and the aib are the degrees of freedom linked to the singularities. figure 3: enrichment strategy in xfem. the onset and crack growth are characterized using the paris law [51], which relates the change in sif to crack growth rates. the stress intensity factor range can be evaluated by proposed by [52].   2 2i iik k k (8) once the crack is defined as a level set segment, the model of xfem evaluate the ik and iik through this, the increment of the crack is deduced by eqn. 9.      6 * * 10 m k da c dn (9) h. djeloud et alii, frattura ed integrità strutturale, 60 (2022) 346-362; doi: 10.3221/igf-esis.60.24 351 figure 4: flowchart of our calculation code. insertion of the geometry properties of the discontinuities structure insert material properties reading mesh data files localization by level set construction of stiffness matrices insertion of boundary conditions system resolution 𝐾𝑈 𝐹 insert material properties determinations of the displacement field calculation of deformations and stresses field if the crack exists calculate stresses and principal vectors calculation of the j-integral and propagation if σ 𝜎 crack creation end meshing with gmsh insertion of material properties assembly by vectorization technique no yes no yes h. djeloud et alii, frattura ed integrità strutturale, 60 (2022) 346-362; doi: 10.3221/igf-esis.60.24 352 the maximum circumferential stress criterion is used in this study to determine the direction of the crack growth, which is given by eqn. 10. the direction of crack growth is a consequence of the mixed-mode stress intensity factors, as can be shown in eqn. 2, and the crack will propagate in the direction where  i is a maximum [53].             2 1 2 8 4 i i ii ii k k arctangent k k (10) where ki and kii are respectively maximum stress intensity factor of mode i and ii during cyclic loading. level-set technique the level set method is a numerical technique used for analysing and tracking moving interfaces. the interface can be evolved by representing it with is contours of a level set function  . without the knowledge of the exact location [54, 55] of the interface, it can be moved implicitly by updating the level set function  . at all times, the interface is represented as its zero level the eqn. 11 represented the analytical form.                  1 2 1 2   1 p p c cx x y yx a a (11) presentation of the developed code the modeling by xfem coupled with lst for the evaluation of the basic parameters in fracture mechanics presented in the previous section (numerical modeling) was programmed according to the flowchart proposed in fig. 4. analysis of metallurgical transformation he hardox 450 steel is characterised by a microstructure of quenching, contains lamellar crystals, which are likely due to γ → α shear transformation, and fragmented α phase crystals with weak misorientations, consist of the martensite with a slate-like morphology with areas of tempered martensite fig. 5 [56,57]. figure 5: optical micrograph of base metal bm. according to the cooling rate and the amount of carbon, the microstructure consists of the refined and tempered lowcarbonlath-type martensite with fine acicular ferrite, widmanstatten ferrite and pearlite were formed fig. 6 [64]. t h. djeloud et alii, frattura ed integrità strutturale, 60 (2022) 346-362; doi: 10.3221/igf-esis.60.24 353 figure 6: optical micrograph of heat affected zone haz. the microstructure of the weld metal is dendritic, consists of a fine-grained non-equilibrium (acicular) ferrite, and pearlite structure with troostite precipitates, nucleating mainly at the solidification grain boundaries which results from the lower cooling rate fig. 7 [58]. figure 7: optical micrograph of weld metal zone wm. results and discussions fter examining a lot of studies, it is clear that few researchers used the sed approach to assess sif in the case of the cracked component and mention here [59–62]. as stated in the paper f. berto ‘this approach cannot be applied to notch with zero opening angle (cracks) subjected to mixed mode loading’, this is confirmed in this study, by comparing the results with one of the most effective methods j-integral. a h. djeloud et alii, frattura ed integrità strutturale, 60 (2022) 346-362; doi: 10.3221/igf-esis.60.24 354 effect of the static loading a) variation in crack length in this section, cruciform welded joints are made from hardox 450 modeling by xfem in 2d plane strain meshing by the triangular element. all the dimensions and boundary conditions are shown in fig. 1 and fig. 5. the welding fatigue crack initiation point is difficult to predict accurately because it usually occurs in the vicinity of the weld toe. this has been found in many studies [63,64]. the length of the cracks evolves from 2 mm and increases with step of 1 mm to reach a maximum length of 8 mm. here, an interest is focused on two study stages: the first stage focuses on the evaluation of the sif values for several enriched zones of the diameters 3 eh , 4 eh and 5 eh ( eh is element size) while keeping the contour of j-integral constant with a diameter equal to 4 eh , and in the second step keeping the enriched zone constant with a diameter equal to 4 eh and the variation will be carried on the diameter of j-integral contours with the following values 3 eh , 4 eh and 5 eh . the obtained results are compared with the values given by the sed approach. all results are summarized in figs. 9-14. figure 8: mesh distribution and boundary condition. 2 3 4 5 6 7 8 0.0 5.0x103 1.0x104 1.5x104 2.0x104 2.5x104 3.0x104 3.5x104 s tr e s s i n te n s it y f a c to r k i [ (m p a )( m m )0 .5 ] crack length [mm] enriched zone (diameter=5he) enriched zone (diameter=4he) enriched zone (diameter=3he) enriched element sed approach figure 9: crack length versus sif calculated by sed and j-integral with different enriched zone sizes ik . h. djeloud et alii, frattura ed integrità strutturale, 60 (2022) 346-362; doi: 10.3221/igf-esis.60.24 355 2 3 4 5 6 7 8 0.0 5.0x103 1.0x104 1.5x104 2.0x104 2.5x104 3.0x104 3.5x104 s tr e s s i n te n s it y f a c to r k i [ (m p a )( m m )0 .5 ] crack length [mm] j-integral contour (diameter=5he) j-integral contour (diameter=4he) j-integral contour (diameter=3he) enriched element sed approach figure 10: crack length versus sif calculated by sed and j-integral with different contour sizes ik . 2 3 4 5 6 7 8 -2.0x103 -1.5x103 -1.0x103 -5.0x102 0.0 s tr e s s i n te n s it y f a c to r k ii [ m p a (m m )0 .5 ] crack length [mm] enriched zone (diameters=5he) enriched zone (diameters=4he) enriched zone (diameters=3he) enriched element figure 11: crack length versus sif calculated by sed and j-integral with different enriched zone sizes iik . h. djeloud et alii, frattura ed integrità strutturale, 60 (2022) 346-362; doi: 10.3221/igf-esis.60.24 356 2 3 4 5 6 7 8 -2.0x103 -1.5x103 -1.0x103 -5.0x102 0.0 s tr e s s i n te n s it y f a c to r k ii [ m p a (m m )0 .5 ] crack length [mm] j-integral contour (diameter=5he) j-integral contour (diameter=4he) j-integral contour (diameter=3he) enriched element figure 12: crack length versus sif calculated by j-integral with different contour sizes iik . b) variation in crack orientation the same as the previous example by changing the location of the crack angle   10, 20, 30, 40, 50, 60, 70, 80, 90 fig. 13 to simulate the possibility of defect to the weld root. changing the contour of the j-integral was dispensed because there was no effect on the results /i iik k . 10 20 30 40 50 60 70 80 90 0 1x103 2x103 3x103 4x103 5x103 6x103 s tr e s s i n te n s it y f a c to r k i [ m p a (m m )0 .5 ] crack orientation [deg] enriched zone (diameter=5he) enriched zone (diameter=4he) enriched zone (diameter=3he) enriched element figure 13: crack orientation versus sif calculated j-integral with different enriched zone sizes ik . h. djeloud et alii, frattura ed integrità strutturale, 60 (2022) 346-362; doi: 10.3221/igf-esis.60.24 357 10 20 30 40 50 60 70 80 90 0.0 2.0x102 4.0x102 6.0x102 8.0x102 1.0x103 1.2x103 s tr e s s i n te n s it y f a c to r k ii [ m p a (m m )0 .5 ] crack orientation [deg] enriched zone (diameter=5he) enriched zone (diameter=4he) enriched zone (diameter=3he) enriched element figure 14: crack orientation versus sif calculated j-integral with different enriched zone sizes iik . simulation of fatigue crack initiation and propagation a) crack initiation perform crack initiation and propagation simulation was carried out by xfem under cyclic loading (all the dimensions, boundary conditions and mesh distribution like the previous example).  610  max pa .fig. 15 represents the loading changes depending on time. when the crack grows the level set defined by eqn. (2) is used to make control volume and trace the crack tip and extract the sed value every cycle, through the eqn. (4) is calculated can calculate sif value represented in the fig. 16. after applying load, the element with the maximum principal stress is checked, if the value is greater than ultimate tensile stress these elements contain crack and is oriented towards in the direction of second principal vector and its length at the beginning 2 eh . figure 15: change the load in terms of time. b) crack propagation with different orientation of crack perform predefined crack simulation with different orientations      60 , 70 , 80 , 90 see fig. 17 was carried out by xfem under cyclic loading (all the dimensions, boundary conditions, and mesh distribution like the previous example). the results obtained are shown in fig. 18. 𝜎 load time h. djeloud et alii, frattura ed integrità strutturale, 60 (2022) 346-362; doi: 10.3221/igf-esis.60.24 358 0 10000 20000 30000 40000 50000 60000 2.0x103 4.0x103 6.0x103 8.0x103 1.0x104 1.2x104 s tr e s s i n te n s it y f a c to r [m p a (m m )0 .5 ] number of cyclic ki j-integral ki sed approach figure 16: stress intensity factor ik versus number of cyclic. figure 17: cruciform welded joints with different crack orientation. conclusions he fatigue performance of cruciform welded joints made hardox 450 steel has been studied in this paper, the comparison between the sif by sed and sif by j-integral was carried out. the following conclusions can be proposed based on the results: the sed approach was used to successfully calculate the mode i, sif of crack-containing cruciform welded joints using xfem. t crack weld toe 𝜃 9 0 h. djeloud et alii, frattura ed integrità strutturale, 60 (2022) 346-362; doi: 10.3221/igf-esis.60.24 359 30000 60000 90000 120000 150000 2.0x106 4.0x106 6.0x106 8.0x106 1.0x107 1.2x107 1.4x107 1.6x107 1.8x107 s tr e s s i n te n s it y f a c to r [m p a (m m )0 .5 ] number of cyclic ki j-integral =90 ki j-integral =80 ki j-integral =70 ki j-integral =60 figure 18: stress intensity factor ik versus number of cyclic with different orientation. when using xfem, the sed approach ensures a rapid and simple assessment of the sif in the case of the cracked component in mode i. has been utilized the level set formulation is used to model the crack and update the crack tip at each cyclic also the control volume is an lst in the form of a circle whose center is a crack tip. despite the complexity of programming the j-integration method, it is the most widely used and stable method for calculating the sif of cracked components. 5 eh is considered the radius of the optimal enriched zone. the use of xfem ensures that ew and sif values are accurately extracted without a refine mesh. in the cruciform welded joints the crack initiation in the weld toe is caused by stress concentration and vicinity to the heat affected area. references [1] huang, j.l., warnken, n., gebelin, j.c., strangwood, m., reed, r.c. (2012). on the mechanism of porosity formation during welding of titanium alloys, acta mater., 60(6–7), pp. 3215–3225, doi: 10.1016/j.actamat.2012.02.035. [2] hachi, b.e.k., rechak, s., haboussi, m., taghite, m., maurice, g. (2008). fatigue growth of embedded elliptical cracks using paris-type law in a hybrid weight function approach, comptes rendus mec., 336(4), pp. 390–397, doi: 10.1016/j.crme.2008.01.008. [3] yang, k., zhang, y., zhao, j. (2020). elastoplastic fracture analysis of the p91 steel welded joint under repair welding thermal shock based on xfem, metals (basel)., 10(10), pp. 1–26, doi: 10.3390/met10101285. [4] chen, d., li, g., wang, y., xiao, q. (2019). research on fatigue crack propagation of a t-joint based on xfem and tsa, eng. fract. mech., 222, pp. 106707, doi: 10.1016/j.engfracmech.2019.106707. [5] ma, j., wang, p., fang, h. (2021). fatigue life of 7005 aluminum alloy cruciform joint considering welding residual stress, materials (basel), 14(5), pp. 1–20, doi: 10.3390/ma14051253. [6] pang, j.h.l., tsang, k.s., hoh, h.j. (2016). 3d stress intensity factors for weld toe semi-elliptical surface cracks using xfem, mar. struct., 48, pp. 1–14, doi: 10.1016/j.marstruc.2016.04.001. h. djeloud et alii, frattura ed integrità strutturale, 60 (2022) 346-362; doi: 10.3221/igf-esis.60.24 360 [7] montassir, s., yakoubi, k., moustabchir, h., elkhalfi, a., rajak, d.k., pruncu, c.i. (2020). analysis of crack behaviour in pipeline system using fad diagram based on numerical simulation under xfem, appl. sci., 10(17), doi: 10.3390/app10176129. [8] taheri, s., tran, v., julan, e., robert, n. (2015). fatigue crack growth and arrest under high-cycle thermal loading using xfem in presence of weld residual stresses, transactions, 415 (figure 4). [9] kraedegh, a., li, w., sedmak, a., grbovic, a., trišović, n., mitrović, r., kirin, s. (2017). simulation of fatigue crack growth in a2024-t351 t-welded joint, struct. integr. life, pp. 3–6. [10] chatziioannou, k., karamanos, s.a., huang, y. (2019). ultra low-cycle fatigue performance of s420 and s700 steel welded tubular x-joints, int. j. fatigue, 129), pp. 105221, doi: 10.1016/j.ijfatigue.2019.105221. [11] jie, z., wang, w., chen, c., wang, k. (2021). local approaches and xfem used to estimate life of cfrp repaired cracked welded joints under fatigue loading, compos. struct., 260, pp. 113251, doi: 10.1016/j.compstruct.2020.113251. [12] nikfam, m.r., zeinoddini, m., aghebati, f., arghaei, a.a. (2019). experimental and xfem modelling of high cycle fatigue crack growth in steel welded t-joints, int. j. mech. sci., 153–154, pp. 178–193, doi: 10.1016/j.ijmecsci.2019.01.040. [13] džindo, e., sedmak, s.a., grbović, a., milovanović, n., đođrević, b. (2019). xfem simulation of fatigue crack growth in a welded joint of a pressure vessel with a reinforcement ring, arch. appl. mech., 89(5), pp. 919–26, doi: 10.1007/s00419-018-1435-1. [14] gairola, s., jayaganthan, r. (2021). xfem simulation of tensile and fracture behavior of ultrafine‐grained al 6061 alloy, metals (basel), 11(11), doi: 10.3390/met11111761. [15] vempati, s.r., brahma raju, k., venkata subbaiah, k. (2019). simulation of ti-6al-4v cruciform welded joints subjected to fatigue load using xfem, j. mech. eng. sci., 13(3), pp. 5371–89, doi: 10.15282/jmes.13.3.2019.11.0437. [16] meneghetti, g., campagnolo, a. (2018). the peak stress method to assess the fatigue strength of welded joints using linear elastic finite element analyses, procedia eng., 213(2017), pp. 392–402, doi: 10.1016/j.proeng.2018.02.039. [17] lazzarin, p., livieri, p. (2001). notch stress intensity factors and fatigue strength of aluminum and steel welded joints, int. j. fatigue, 23(3), pp. 225–32, doi: 10.1016/s0142-1123(00)00086-4. [18] adib, h., gilgert, j., pluvinage, g. (2004). fatigue life duration prediction for welded spots by volumetric method, int. j. fatigue, 26(1), pp. 81–94, doi: 10.1016/s0142-1123(03)00068-9. [19] kired, m.r., hachi, b.e., hachi, d., haboussi, m. (2019). effects of nano-voids and nano-cracks on the elastic properties of a host medium: xfem modeling with the level-set function and free surface energy, acta mech. sin. xuebao, 35(4), pp. 799–811, doi: 10.1007/s10409-019-00843-4. [20] hachi, b.e., benkhechiba, a.e., kired, m.r., hachi, d., haboussi, m. (2020). some investigations on 3d homogenization of nano-composite/nano-porous materials with surface effect by fem/xfem methods combined with level-set technique, comput. methods appl. mech. eng., 371, pp. 113319, doi: 10.1016/j.cma.2020.113319. [21] nehar, k.c., hachi, b.e., cazes, f., haboussi, m. (2017). evaluation of stress intensity factors for bi-material interface cracks using displacement jump methods, acta mech. sin. xuebao, 33(6), pp. 1051–1064, doi: 10.1007/s10409-017-0711-6. [22] sih, g.c. (1991). mechanics of fracture initiation and propagation, . [23] sih, g.c., chu, r.c. (1986). characterization of material inhomogeneity by stationary values of strain energy density, theor. appl. fract. mech., 5(3), pp. 151–61, doi: 10.1016/0167-8442(86)90002-9. [24] sih, g.c. (1991). mechanics of fracture initiation and propagation, dordrecht, springer netherlands. [25] lazzarin, p., campagnolo, a., berto, f. (2014). a comparison among some recent energyand stress-based criteria for the fracture assessment of sharp v-notched components under mode i loading, theor. appl. fract. mech., 71, pp. 21– 30, doi: 10.1016/j.tafmec.2014.03.001. [26] berto, f., campagnolo, a., lazzarin, p. (2015). fatigue strength of severely notched specimens made of ti-6al-4v under multiaxial loading, fatigue fract. eng. mater. struct., 38(5), pp. 503–517, doi: 10.1111/ffe.12272. [27] lazzarin, p., berto, f., ayatollahi, m.r. (2013). brittle failure of inclined key-hole notches in isostatic graphite under inplane mixed mode loading, fatigue fract. eng. mater. struct., 36(9), pp. 942–955, doi: 10.1111/ffe.12057. [28] ayatollahi, m.r., berto, f., lazzarin, p. (2011). mixed mode brittle fracture of sharp and blunt v-notches in polycrystalline graphite, carbon n. y., 49(7), pp. 2465–2474, doi: 10.1016/j.carbon.2011.02.015. [29] berto, f., lazzarin, p. (2009). a review of the volume-based strain energy density approach applied to v-notches and welded structures, theor. appl. fract. mech., 52(3), pp. 183–194, doi: 10.1016/j.tafmec.2009.10.001. [30] torabi, a.r., ayatollahi, m.r., colussi, m. (2018). compressive brittle fracture prediction in blunt v-notched pmma specimens by means of the strain energy density approach, phys. mesomech., 21(2), pp. 104–109, h. djeloud et alii, frattura ed integrità strutturale, 60 (2022) 346-362; doi: 10.3221/igf-esis.60.24 361 doi: 10.1134/s1029959918020029. [31] moussaoui, m., amroune, s., tahiri, a., hachi, b.k. (2020). brittle fracture investigation from disc specimen weakened by u-notch in mixed mode i + ii, eng. solid mech., 8(4), pp. 337–352, doi: 10.5267/j.esm.2020.3.004. [32] lazzarin, p., zambardi, r. (2002). the equivalent strain energy density approach re-formulated and applied to sharp vshaped notches under localized and generalized plasticity, fatigue fract. eng. mater. struct., 25(10), pp. 917–928, doi: 10.1046/j.1460-2695.2002.00543.x. [33] lazzarin, p., berto, f., zappalorto, m. (2010). rapid calculations of notch stress intensity factors based on averaged strain energy density from coarse meshes: theoretical bases and applications, int. j. fatigue, 32(10), pp. 1559–1567, doi: 10.1016/j.ijfatigue.2010.02.017. [34] aliha, m.r.m., berto, f., bahmani, a., gallo, p. (2017). mixed mode i/ii fracture investigation of perspex based on the averaged strain energy density criterion, phys. mesomech., 20(2), pp. 149–156, doi: 10.1134/s1029959917020059. [35] aliha, m.r.m., berto, f., bahmani, a., akhondi, s., barnoush, a. (2016). fracture assessment of polymethyl methacrylate using sharp notched disc bend specimens under mixed mode i + iii loading, phys. mesomech., 19(4), pp. 355–364, doi: 10.1134/s1029959916040020. [36] campagnolo, a., berto, f. (2015). tensile fracture analysis of blunt notched pmma specimens by means of the strain energy density, eng. solid mech., 3(1), pp. 35–42, doi: 10.5267/j.esm.2014.12.001. [37] pook, l.p., campagnolo, a., berto, f., lazzarin, p. (2015). coupled fracture mode of a cracked plate under anti-plane loading, eng. fract. mech., 134, pp. 391–403, doi: 10.1016/j.engfracmech.2014.12.021. [38] mirsayar, m.m., berto, f., aliha, m.r.m., park, p. (2016). strain-based criteria for mixed-mode fracture of polycrystalline graphite, eng. fract. mech., 156, pp. 114–123, doi: 10.1016/j.engfracmech.2016.02.011. [39] meneghetti, g., campagnolo, a., berto, f. (2015). some relationships between the peak stresses and the local strain energy density for cracks subjected to mixed-mode (i+ii) loading, frat. ed integrita strutt., 9(33), pp. 33–41, doi: 10.3221/igf-esis.33.05. [40] shin, w.s., chang, k.h., muzaffer, s. (2021). fatigue analysis of cruciform welded joint with weld penetration defects, eng. fail. anal., 120, pp. 105111, doi: 10.1016/j.engfailanal.2020.105111. [41] jie, z., berto, f., susmel, l. (2020). fatigue behaviour of pitted/cracked high-strength steel wires based on the sed approach, int. j. fatigue, 135(october 2019), pp. 105564, doi: 10.1016/j.ijfatigue.2020.105564. [42] lazzarin, p., lassen, t., livieri, p. (2003). a notch stress intensity approach applied to fatigue life predictions of welded joints with different local toe geometry, fatigue fract. eng. mater. struct., 26(1), pp. 49–58, doi: 10.1046/j.1460-2695.2003.00586.x. [43] fischer, c., fricke, w., rizzo, c.m. (2016). experiences and recommendations for numerical analyses of notch stress intensity factor and averaged strain energy density, eng. fract. mech., 165, pp. 98–113, doi: 10.1016/j.engfracmech.2016.08.012. [44] gaiotti, m., rizzo, c.m., berto, f. (2017). assessment of welded joints by strain energy density approach accounting for misalignments and geometrical imperfections. materials technology, american society of mechanical engineers, 4, pp. 1–7. [45] braun, m., fischer, c., fricke, w., ehlers, s. (2020). extension of the strain energy density method for fatigue assessment of welded joints to sub-zero temperatures, fatigue fract. eng. mater. struct., 43(12), pp. 2867–2882, doi: 10.1111/ffe.13308. [46] lazzarin, p., zambardi, r. (2001). a finite-volume-energy based approach to predict the static and fatigue behavior of components with sharp v-shaped notches, int. j. fract., 112(3), pp. 275–298, doi: 10.1023/a:1013595930617. [47] fries, t.-p., belytschko, t. (2010). the extended/generalized finite element method: an overview of the method and its applications, int. j. numer. methods eng., 84(3), pp. 253–304, doi: 10.1002/nme.2914. [48] zi, g., belytschko, t. (2003). new crack-tip elements for xfem and applications to cohesive cracks, int. j. numer. methods eng., 57(15), pp. 2221–2240, doi: 10.1002/nme.849. [49] moës, n., belytschko, t. (2002). x-fem, de nouvelles frontières pour les éléments finis, rev. eur. des éléments finis, 11(2–4), pp. 305–18, doi: 10.3166/reef.11.305-318. [50] menouillard, t., belytschko, t. (2010). dynamic fracture with meshfree enriched xfem, acta mech., 213(1–2), pp. 53–69, doi: 10.1007/s00707-009-0275-z. [51] paris, p., erdogan, f. (1963). a critical analysis of crack propagation laws, j. fluids eng. trans. asme, 85(4), pp. 528– 33, doi: 10.1115/1.3656900. [52] tanaka, k. (1974). fatigue crack propagation from a crack inclined to the cyclic tensile axis, eng. fract. mech., 6(3), doi: 10.1016/0013-7944(74)90007-1. [53] kumar, s., wang, y., poh, l.h., chen, b. (2018). floating node method with domain-based interaction integral for h. djeloud et alii, frattura ed integrità strutturale, 60 (2022) 346-362; doi: 10.3221/igf-esis.60.24 362 generic 2d crack growths, theor. appl. fract. mech., 96(november), pp. 483–496, doi: 10.1016/j.tafmec.2018.06.013. [54] stolarska, m., chopp, d.l. (2003). modeling thermal fatigue cracking in integrated circuits by level sets and the extended finite element method, int. j. eng. sci., 41(20), pp. 2381–410, doi: 10.1016/s0020-7225(03)00217-9. [55] pais, m.j., kim, n. (2009). finite element and level set methods, aerospace, pp. 1–16. [56] morre, m.a. (1975). the abrasive wear resistance of surface coatings, j. agric. eng. res., 20(2), pp. 167–179, doi: 10.1016/0021-8634(75)90084-0. [57] konat, ł., zemlik, m., jasiński, r., grygier, d. (2021). austenite grain growth analysis in a welded joint of high-strength martensitic abrasion-resistant steel hardox 450, materials (basel), 14(11), doi: 10.3390/ma14112850. [58] reitz, w. (2006). a review of: welding metallurgy and weldability of stainless steel, mater. manuf. process, pp. 219– 219, doi: 10.1080/10426910500476747. [59] treifi, m., oyadiji, s.o. (2013). strain energy approach to compute stress intensity factors for isotropic homogeneous and bi-material v-notches, int. j. solids struct., 50(14–15), pp. 2196–2212, doi: 10.1016/j.ijsolstr.2013.03.011. [60] berto, f., razavi, s.m.j., ayatollahi, m.r. (2017). some methods for rapid evaluation of the mixed mode nsifs, procedia struct. integr., 3, pp. 126–134, doi: 10.1016/j.prostr.2017.04.022. [61] treifi, m., oyadiji, s.o. (2013). evaluation of mode iii stress intensity factors for bi-material notched bodies using the fractal-like finite element method, comput. struct., 129, pp. 99–110, doi: 10.1016/j.compstruc.2013.02.015. [62] pittarello, l., campagnolo, a., berto, f. (2016). nsifs estimation based on the averaged strain energy density under inplane mixed mode loading, procedia struct. integr., 2, pp. 1829–1836, doi: 10.1016/j.prostr.2016.06.230. [63] song, w., liu, x., berto, f., wang, p., fang, h. (2017). fatigue failure transition analysis in load-carrying cruciform welded joints based on strain energy density approach, fatigue fract. eng. mater. struct., 40(7), pp. 1164–1177, doi: 10.1111/ffe.12588. [64] song, w., liu, x., razavi, s.m.j. 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can be opened with acrobat and adobe reader 5.0 and later.) >> /namespace [ (adobe) (common) (1.0) ] /othernamespaces [ << /asreaderspreads false /cropimagestoframes true /errorcontrol /warnandcontinue /flattenerignorespreadoverrides false /includeguidesgrids false /includenonprinting false /includeslug false /namespace [ (adobe) (indesign) (4.0) ] /omitplacedbitmaps false /omitplacedeps false /omitplacedpdf false /simulateoverprint /legacy >> << /addbleedmarks false /addcolorbars false /addcropmarks false /addpageinfo false /addregmarks false /convertcolors /converttocmyk /destinationprofilename () /destinationprofileselector /documentcmyk /downsample16bitimages true /flattenerpreset << /presetselector /mediumresolution >> /formelements false /generatestructure false /includebookmarks false /includehyperlinks false /includeinteractive false /includelayers false /includeprofiles false /multimediahandling /useobjectsettings /namespace [ (adobe) (creativesuite) (2.0) ] /pdfxoutputintentprofileselector /documentcmyk /preserveediting true /untaggedcmykhandling /leaveuntagged /untaggedrgbhandling /usedocumentprofile /usedocumentbleed false >> ] >> setdistillerparams << /hwresolution [2400 2400] /pagesize [612.000 792.000] >> setpagedevice microsoft word numero_62_art_18_3534.docx n. ab. razak et alii, frattura ed integrità strutturale, 62 (2022) 261-270; doi: 10.3221/igf-esis.62.18 261 numerical simulation of creep notched bar of p91 steel n. ab razak universiti malaysia pahang, malaysia norhaida@ump.edu.my c. m. davies imperial college london, united kingdom catrin.davies@imperial.ac.uk abstract. numerous components designed for use at elevated temperatures now exhibit multiaxial stress states as a result of geometric modification and material inhomogeneity. it is necessary to anticipate the creep rupture life of such components when subjected to multiaxial load. in this work finite element analysis has been performed to study the influence of different notches, namely blunt and medium notches on the stress distribution across the notch throat during the creep exposure. within the fe model, a ductility exhaustion model based on the cocks and ashby model was utilized to forecast the creep rupture time of notched bar p91 material. the lower and upper bound of creep ductility are employed in the fe analysis. different notch specimens have different stress and damage distribution. it is shown that for both types of notches, the von mises stress is lower than the net stress, indicating the notch strengthening effect. the accumulation of creep damage in the minimum cross-section at each element across the notch throat increases over time. the point at which damage first occurs is closer to the notch root for the medium notch than for the blunt notch. the long-term rupture life predicted for blunt notch specimens appears to be comparable to that of uniaxial specimens. the upper bound creep ductility better predicts the rupture life for medium notches. keywords. p91 steel; multiaxial stress state; finite element analysis; ductility exhaustion model; cocks and ashby model. citation: ab razak, n., davies, c.m., numerical simulation of creep notched bar of p91 steel, frattura ed integrità strutturale, 62 (2022) 261-270. received: 30.03.2022 accepted: 20.06.2022 online first: 29.08.2022 published: 01.10.2022 copyright: © 2022 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. introduction odern boiler power plant design necessitates a better understanding of the material's high-temperature performance in the presence of a multiaxial state of stress. these stresses are typically caused by geometrical change and material inhomogeneity [1]. in general, uniaxial creep tests are used to investigate mechanical m https://youtu.be/tamev6zf5ri n. ab. razak et alii, frattura ed integrità strutturale, 62 (2022) 261-270; doi: 10.3221/igf-esis.62.18 262 properties such as creep deformation of a material. however, data on the multiaxial response of the material under static load at elevated temperatures is frequently required for engineering design applications. the presence of a notch causes a non-uniform multiaxial state of stress, which causes non-uniform creep straining and creep cavitation, resulting in a change in rupture life. the degree and distribution of multiaxiality are dictated by the volume of material surrounding the notch root, which is determined by the notch geometry and material creep ductility [2,3]. the use of an axial notched bar tension test at the laboratory scale helps understand the multiaxial state of stress on creep deformation and failure. the geometry of the notch determines a material's degree of multiaxility at a given temperature. experimental studies have been conducted on the creep deformation and fracture behaviours of notched bar specimens. goyal [4] experimentally studied the effect of multiaxial stress on a u-type notch made of p91 material and found that the decreasing notch root radius increased the level of constraint. chang et.al investigate the multiaxial stress state of p92 on uniaxial and notched specimens at 650°c and found that the notch strengthening effect in the presence of a notch [5]. the strengthening effect in the presence of the notch can be observed in the p91 material [6,7], nimonic 80a[8], 2.25cr1mo [1] and cr-mo-v [9]. the strengthening effect was shown to diminish as applied stress decreased and rupture life increased. the creep rupture behavior is to be governed by the von mises stress, maximum principal stress, and hydrostatic stress [10]. in the damage analysis, the reduction in creep ductility under multiaxial stress states should be considered. creep ductility has shown a clear reduction, particularly at periods longer than 10,000 hours for p91 and p92 material [11–13]. it is suggested that the boron nitride particles cause long-term degradation in creep ductility in p92 material by accelerating the formation of creep voids [13]. creep ductility shows a strong stress dependency at a wider stress range. the stressdependent effect of creep ductility on creep crack growth has been investigated, and it is shown that increasing the transition region size of creep ductility increases the transition of creep parameter, c* region size on da/dt-c* curves [14]. the results of accelerated testing on a pre-compressed 316h material demonstrate that the creep ductility acquired by accelerated testing can be utilized to forecast long-term creep failure [15]. fe analysis in conjunction with a damage mechanics model has been widely employed for creep damage and rupture life prediction under multiaxial stress states, for example, the kachanov robotnov model [5,6,16,17], spindler model[18,19] and cock and ashby model [5,9,20,21]. all these models correlate the ratio of multiaxiality and uniaxial ductility, to the ratio of hydrostatic stress and the equivalent stress which is often known as triaxiality stress. this method has been widely used in creep crack growth prediction [22]. figure 1: true stress strain behavior of ex-serviced p91 material tested at 25°c and 600°c improving the accuracy of high-temperature components' life evaluation methods is critical for rationalizing component design and life management. evaluating creep damaging behaviours of materials under multiaxial stress state would result in a rational assessment. in this work, the prediction of creep rupture life under the multiaxial condition has been performed using fe analyses by employing cocks and ashby model. finite element analyses were carried out to study the 0 100 200 300 400 500 600 700 800 900 0 0.05 0.1 0.15 0.2 σ t ru e (m p a ) εtrue (mm/mm) p91 ex-service material 25°c 600°c n. ab. razak et alii, frattura ed integrità strutturale, 62 (2022) 261-270; doi: 10.3221/igf-esis.62.18 263 influence of notch geometry on the stress distribution across the notch throat during creep exposure. the creep rupture life under multiaxial conditions has been predicted using fe analyses by employing cocks and ashby model and ductility exhaustion model. the predictions from the fe models are compared with the experimental data of the material from previous research [23]. material model n this work, p91 material has been used. fig. 1 shows the true stress strain curve of p91 material at 25°c and 600ºc. the tensile deformation shows a significant decrease at high temperatures compared to the one at room temperature. creep properties of ex-service material were obtained from experimental data and analyzed with available literature as discussed in [12]. the creep properties based on low stress and high stress region were tabulated in tab. 1. a and n are denoted as stress coefficient and stress exponent, respectively. the aa and na are denoted as average stress coefficient and average stress exponent, respectively where the application of average creep strain rate may be effective in accounting for all three creep stages. the creep ductility of p91 material has shown a wide scatter over the wide range of stress [12]. the estimated creep ductility of 30% and 12% have been used in the fe analysis as the upper and lower bound value, respectively. region a(mpa-n/h-1) n aa (mpa-n/h-1) na high stress (σ>130 mpa) 1.0 x 10-33 13 2.0 x 10-31 13 low stress (σ<130 mpa) 2.0 x 10-18 6 2.0 x 10-20 7 table 1: creep properties based on low stress and high stress regions at 600°c [12]. finite element model two-dimensional axisymmetric (2d) finite element model of a notched bar specimen was modelled using abaqus v6.12. one-quarter of the specimen was modelled taking into the advantage of the symmetry of the specimens as shown in fig. 2. the specimen was modelled using four-node axisymmetric elements with reduced integrations (cax4r). the mesh sensitivity analysis has been performed on three different three mesh densities. the more refined mesh had an influence on the predicted rupture time. however, in order to reduce the computational time, the most optimal refined mesh with the total number of nodes, 16803 and the total number of element, 16434 were used. the model has meshed in two major sections with a finer mesh around the notch throat as shown in fig. 3. the smallest element size ahead of the notch root is 0.02 mm x 0.03 mm. the boundary condition was applied as shown in fig. 2 where the nodes along the bottom face were strained in the y-direction. the uniform stress was applied along the top face of the model such that the desired net section stress across the throat is achieved. creep damage model ductility exhaustion approach is used to calculate the creep damage during the finite element analysis. a damage parameter, ω is adjusted in the range from 0 to 1, where damage occurs when =1. the accumulated damage rate is defined as the creep strain rate divided by the multiaxial creep ductility and is given by eqn. (1) [24].      c f (1) where εc is the creep strain rate and εf * is the multiaxial creep ductility. the total damage at any time is the integral of the damage rate and can be expressed by eqn. 2 [24]. i a a n. ab. razak et alii, frattura ed integrità strutturale, 62 (2022) 261-270; doi: 10.3221/igf-esis.62.18 264    0 t dt (2) in this work, the cocks and ashby model [20] was employed to account for the material's creep ductility under multiaxial stress states. the model demonstrates that the ratio of multiaxility and uniaxial ductility, is associated with hydrostatic stress, σm, and the equivalent stress, σe, which is commonly referred to as triaxiality. the stress triaxiality in the model is determined by the ratio of the mean stress to the von mises stress, and eqn. (3) [24] describes the ratio of uniaxial to multiaxial creep ductility. the user subroutine usdfld was used to implement this equation in the abaqus code.                2( 0.5)2( 0.5) sinh sinh 3( 0.5) ( 0.5) c m ef nn n n (3) figure 2: illustration of notched bar specimen; a) complete specimen, b) feature of notch throat a) b) figure 3: fe mesh; a) blunt notch, b) medium notch. n. ab. razak et alii, frattura ed integrità strutturale, 62 (2022) 261-270; doi: 10.3221/igf-esis.62.18 265 notched simulation results stress distributions he stress distributions throughout the notch throat in the notched bar analysis are not uniform. a normalized distance from the notch root is required to determine stress distribution throughout the notch throat. fig. 4 to 6 show the von-mises stress, σe, maximum principal stress, σ1, and hydrostatic stress, σm, distribution, respectively across the notch throat from the initial loading until steady-state life as a function of normalized distance from the notch root, r/a. the normalized distance is shown from the center of the specimen where r/a=0 is at the center and r/a=1 is at the notch root. from fig. 4 it can be seen that after loading during the creep exposure the von-mises stress is highest at the notch root for both notch types. as the creep deformation takes place, stress redistribution across the notch throat was found to change with creep exposure and approach stationary state. the stress redistributes and achieves its steady state after 42 h of creep exposure. at the center of the notch, r/a=0, the von mises stress was significantly lower than that of 0.2% proof stress of p91 material (287 mpa). at the notch root r/a=1, the von mises stress is still lower than the 0.2% proof stress, suggesting that the localized plastic deformation at the notch root does not contribute to the stress distribution across the notch throat from the beginning of creep loading for this material [6]. it is also seen in figs. 4 (a) and (b) that the vonmises stress is lower than that of the net stress for both notch acuity at steady-state life which may indicate the notch strengthening effect, as observed experimentally [6][25]. in general, it has been shown that von mises stress regulates the creep deformation and the creep cavity nucleation processes, maximum principal stress regulates stress-directed diffusioncontrolled intergranular cavity growth, and hydrostatic stress regulates continuum cavity growth [25]. it is envisaged that the presence of relatively uniform von mises stress across the notch plane will result in more or less uniform transgranular creep cavity nucleation across the notch plane, depending on the degree of uniformity of the von mises stress [24]. figure 4: von mises stress distribution for a blunt and medium notch at net stress 187=mpa the distribution of maximum principal stress σ1, across the notch throat for the blunt and medium notch is shown in figs. 5 (a) and (b), respectively. as shown in fig. 5 (a) after reaching steady-state life, the maximum principal stress distribution shows a maximum value at r/a~0.6 which is more than the net stress for a blunt notch type. for the medium notch specimen (fig. 5(b)), the peak of maximum principal stress occurred closer to the notch root. the hydrostatic stress, σm distribution across the notch throat for the blunt and medium notch is shown in figs. 6 (a) and (b), respectively. the hydrostatic stress distribution shows similar behavior to that of the maximum principal stress. the hydrostatic stress remained below the net stress for both notches. one of the factors that influence creep-rupture behaviour under multi axial stress states is triaxiality. triaxiality is defined as the ratio of hydrostatic stress, σm and von mises stress, σe. fig. 7 shows the variation of triaxiality across the notch throat for the blunt and medium notch. it can be seen in fig. 7 that the triaxiality is maximum at notch throat distance of t n. ab. razak et alii, frattura ed integrità strutturale, 62 (2022) 261-270; doi: 10.3221/igf-esis.62.18 266 r/a=0.5 for blunt notch whereas the triaxiality is maximum near the notch root i.e r/a=0.8 for the medium notch. the medium notch has a maximum value of triaxiality nearly twice of the blunt notch. for both notch types, the triaxiality across the notch throat is significantly higher than that for a uniaxial test specimen, σm/σe=1/3). figure 5: maximum principal stress distribution for blunt and medium notch net stress = 187 mpa figure 6: hydrostatic stress distribution for blunt and medium notch bar at net stress =187 mpa. creep damage in order to evaluate the creep damage accumulation, the fe analysis used a ductility exhaustion approach with the cocks and ashby damage model. the damage is calculated when the element attains ω=1.0. the predicted time to rupture was taken when a few elements reach ω=1.0. two-dimensional contour plots of creep damage across the notch throat for blunt and medium notch are shown in figs. 8 (a) and (b), respectively. the blunt notch shows the most uniform widespread of damage and the medium notch shows the most localized damage. the maximum damage is observed to occur near the notch root at first and then shifts toward the notch subsurface as it reaches a steady-state as shown in fig. 8. in fig. 8, the location of damage starts at the notch root from the beginning until the time to failure which is similar to the micrograph seen in the test specimen [12]. the most severe region of damage is seen along the notch throat for both types of the notch. n. ab. razak et alii, frattura ed integrità strutturale, 62 (2022) 261-270; doi: 10.3221/igf-esis.62.18 267 fig. 9 shows the evolution of damage for both notch acuities for the net stress = 187 mpa. damage evolutions across the notch are shown at 0.25 tr, 0.5 tr, and t = tr , where tr is rupture time. it can be seen that the damage accumulation at each element across the notch throat increases over time. it can also be seen that the point at which damage first occurs is closer to the notch root for the medium notch than for the blunt notch. this is expected given that the maximum triaxial stress state is closer to the notch surface for the medium notch than for the blunt notch. similar behaviour has been reported for p92 steel [26] where an increase in notch acuity results in the damage location moving closer to the notch root. figure 7: variation of triaxiality across the notch throat for the blunt and medium notch at t = 0.5tr. a) b) figure 8: creep damage contour at net stress = 187 mp at t = 0.5tr for a) blunt and b) medium notched prediction of rupture time in this work, the predictions of rupture time were based on fe analysis coupled with cocks and ashby model. the rupture times were predicted when the few elements attain the damage, ω =1. it is shown that the prediction of the rupture time using cocks and ashby model in eqn. (3) is strongly dependent on the creep ductility. to predict the rupture time, the lower and upper bound creep ductility of 12% and 30%, respectively, have been used in the fe. fig. 10 (a) and (b) shows of prediction of rupture time plot with net stress for the blunt and medium notch, respectively. the uniaxial and notched bar test data were also plotted in the same figures. the regression lines have been included for all the notches. it can be seen in both figures, the rupture life of notched specimens is higher than that of uniaxial specimens indicating the notch strengthening effect as observed experimentally. it is expected that with increasing notch acuity the rupture life increases hence the notch strengthening is enhanced. n. ab. razak et alii, frattura ed integrità strutturale, 62 (2022) 261-270; doi: 10.3221/igf-esis.62.18 268 the cock and ashby model has been utilized to predict the rupture life by using the lower and upper bound creep ductility of 12% and 30%, respectively. it can be seen in fig. 10 (a) that for the blunt notch, lower bound creep ductility (0.12) predicts the rupture life better than upper bound creep ductility (0.30). the prediction of the long-term rupture life for the blunt notch specimen seems to coincide with the uniaxial data which may indicate that in long-term test data the blunt notch may exhibit similar behavior to that of the uniaxial specimen. for the medium notched in fig. 10 (b), the upper bound creep ductility predicts the rupture life better than the lower bound creep ductility. at the same net stress, the medium notches always have a longer predicted lifetime than the blunt notch. figure 9: damage evolution across the notch throat at net stress of 187 mpa for a) blunt notch and b) medium notch figure 10: fe prediction of rupture life using εf =0.30 and 0.12 for a) blunt notch and b) medium notch. conclusions he fe analyses have been performed on p91 material for the blunt and medium notched bar. a ductility exhaustion model has been used within the fe model by employing the cocks and ashby model.  the stress distribution for blunt notched specimens showed a more uniform distribution compared to the t n. ab. razak et alii, frattura ed integrità strutturale, 62 (2022) 261-270; doi: 10.3221/igf-esis.62.18 269 medium notched specimen. the von mises stress is lower than the net stress for both notch acuity which indicates the notch strengthening effect as observed experimentally.  as defined in the cocks and model, the triaxiality contributes to the creep rupture behaviour under a multiaxial stress state. it is shown that the triaxiality is maximum at notch throat distance of r/a = 0.5 for blunt notch whereas the triaxiality is maximum near the notch root, i.e r/a=0.8 for the medium notch. the medium notch has a maximum of triaxiality nearly twice of the blunt notch.  creep damage evolution has shown that the blunt notch shows the most uniform widespread of damage and the medium notch show the most localized damage  creep ductility of 12% and 30% predicts the rupture life well for blunt and medium notched bars, respectively. references [1] al-faddagh, k.d., webster, g.a., dyson, b.f. (1984). influence of state of stress on creep failure of 2 1/4% cr1% mo steel. mechanical behaviour of materials, pp. 289–95. [2] wu, d., christian, e.m., ellison, e.g. (1984). influence of constraint on creep stress distribution in notched bars, j. strain anal. eng. des., 19(4), pp. 209–20. [3] hayhurst, d.r., henderson, j.t. (1977). creep stress redistribution in notched bars, int. j. mech. sci., 19(3), pp. 133– 46. [4] goyal, s., laha, k., das, c.r., panneerselvi, s., mathew, m.d. (2014). effect of constraint on creep behavior of 9cr1mo steel, metall. mater. trans. a, 45(2), pp. 619–32, doi: 10.1007/s11661-013-2025-z. [5] chang, y., xu, h., ni, y., lan, x., li, h. (2015). the effect of multiaxial stress state on creep behavior and fracture mechanism of p92 steel, mater. sci. eng. a, 636, pp. 70–6. [6] goyal, s., laha, k., mathew, m.d. (2014). creep life prediction of modified 9cr-1mo steel under multiaxial state of stress, procedia eng., 86, pp. 150–7, doi: 10.1016/j.proeng.2014.11.023. [7] wasmer, k., biglari, f., nikbin, k.m. (2002).multiaxial failure behaviour in advanced steels at elevated temperatures. proceedings of the ecf 14 conference, krakow, pp. 553–62. [8] dyson, b.f., loveday, m.s. (1981).creep fracture in nimonic 80a under triaxial tensile stressing. creep in structures, springer, pp. 406–421. [9] xu, x., wang, g.z., xuan, f.z., tu, s.t. (2016). effects of creep ductility and notch constraint on creep fracture behavior in notched bar specimens, mater. high temp., 33(2), pp. 198–207. [10] hayhurst, d.r. (1972). creep rupture under multi-axial states of stress, j. mech. phys. solids, 20(6), pp. 381–382, doi: 10.1016/0022-5096(72)90015-4. [11] maleki, s., mehmanparast, a. (2013). creep crack growth prediction of very long term p91 steel uisng extrapolated short-term uniaxial creep data, asme press. vessel pip. conf. proc., 97506. [12] norhaida ab razak. (2018).creep and creep-fatigue interaction in new and serviced exposed p91 steel. imperial college london. [13] abe, f. (2020). creep rupture ductility of gr. 91 and gr. 92 at 550° c to 700° c, mater. high temp., 37(4), pp. 243– 255. [14] zhang, j.w., wang, g.z., xuan, f.z., tu, s.t. (2015). effect of stress dependent creep ductility on creep crack growth behaviour of steels for wide range of c, mater. high temp., 32(4), pp. 369–376. [15] zhou, h., mehmanparast, a., nikbin, k. (2021). determination of long-term creep properties for 316h steel using short-term tests on pre-strained material, exp. tech., 45(4), pp. 549–60. [16] kachanov. (1999). rupture time under creep conditions, int. j. fract., (97), pp. 11–8. [17] hyde, t.h., sun, w., becker, a.a. (2000). failure prediction for multi-material creep test specimens using a steadystate creep rupture stress, int. j. mech. sci., 42(3), pp. 401–423, doi: 10.1016/s0020-7403(99)00008-9. [18] spindler, m.w. (2004). the multiaxial creep ductility of austenitic stainless steels, fatigue fract. eng. mater. struct., 27(4), pp. 273–281, doi: 10.1111/j.1460-2695.2004.00732.x. [19] isobe, n., yashirodai, k., murata, k. (2014). creep damage assessment for notched bar specimens of a low alloy steel considering stress multiaxiality, eng. fract. mech., 123, pp. 211–22. [20] cocks, a.c.f., ashby, m.f. (1982). on creep fracture by void growth, prog. mater. sci., 27(3–4), pp. 189–244, doi: 10.1016/0079-6425(82)90001-9. [21] jiang, y.p., guo, w.l., yue, z.f., wang, j. (2006). on the study of the effects of notch shape on creep damage development under constant loading, mater. sci. eng. a, 437(2), pp. 340–347. n. ab. razak et alii, frattura ed integrità strutturale, 62 (2022) 261-270; doi: 10.3221/igf-esis.62.18 270 [22] yatomi, m., nikbin, k.m., o’dowd, n.p. (2003). creep crack growth prediction using a damage based approach, int. j. press. vessel. pip., 80(7–8), pp. 573–583, doi: 10.1016/s0308-0161(03)00110-8. [23] razak, n.a. (2021). experimental study of multiaxial stress state on creep rupture life and ductility of p91 steel, j. fail. anal. prev., 21(6), pp. 1991–1999. [24] webster, g.a., ainsworth, r.a. (1994). high temperature component life assessment, . [25] nix, w.d., earthman, j.c., eggeler, g., ilschner, b. (1989). the principal facet stress as a parameter for predicting creep rupture under multiaxial stresses, acta metall., 37(4), pp. 1067–1077. [26] ni, y.z., lan, x., xu, h., mao, x.p. (2014). finite element analysis and experimental research on notched strengthening effect of p92 steel, mater. high temp., 31(2), pp. 185–190, doi: 10.1179/1878641314y.0000000010. << /ascii85encodepages false /allowtransparency false /autopositionepsfiles true /autorotatepages /none /binding /left /calgrayprofile (dot gain 20%) /calrgbprofile (srgb iec61966-2.1) /calcmykprofile (u.s. web coated \050swop\051 v2) /srgbprofile (srgb iec61966-2.1) /cannotembedfontpolicy /error /compatibilitylevel 1.4 /compressobjects /tags /compresspages true /convertimagestoindexed true /passthroughjpegimages true /createjobticket false /defaultrenderingintent /default /detectblends true /detectcurves 0.0000 /colorconversionstrategy /cmyk /dothumbnails false /embedallfonts true /embedopentype false /parseiccprofilesincomments true /embedjoboptions true /dscreportinglevel 0 /emitdscwarnings false /endpage -1 /imagememory 1048576 /lockdistillerparams false /maxsubsetpct 100 /optimize true /opm 1 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/hrv (za stvaranje adobe pdf dokumenata najpogodnijih za visokokvalitetni ispis prije tiskanja koristite ove postavke. stvoreni pdf dokumenti mogu se otvoriti acrobat i adobe reader 5.0 i kasnijim verzijama.) /hun 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/pdfxoutputintentprofileselector /documentcmyk /preserveediting true /untaggedcmykhandling /leaveuntagged /untaggedrgbhandling /usedocumentprofile /usedocumentbleed false >> ] >> setdistillerparams << /hwresolution [2400 2400] /pagesize [612.000 792.000] >> setpagedevice microsoft word numero_35_art_58 r. citarella, frattura ed integrità strutturale, 35 (2015) 523-533; doi: 10.3221/igf-esis.35.58 523 residual strength evaluation by dbem for a cracked lap joint r. citarella department of industrial engineering, via giovanni paolo ii, 132, fisciano (sa), university of salerno, italy rcitarella@unisa.it abstract. the present work summarizes a numerical procedure aimed at the evaluation of the residual strength of a cracked lap joint, based on the competing failure mechanisms regulated by the r-curve analysis and plastic collapse. the model adopted for stress intensity factors (sifs) evaluation is based on the use of the dual boundary element method (dbem) within the theoretical frame of linear elastic fracture mechanics (lefm). the value of failure load was available from experiments, allowing a comparison with numerical results and consequent validation of the described procedure. keywords. residual strength; dbem; lap joint. introduction he residual strength of an aircraft structure degrades during the life due to fatigue cracks, especially in the presence multiple site damage (msd), eventually evolving towards widespread fatigue damage (wfd). broek [1] published a report on the residual strength behaviour of 2024-t3 alclad sheet panels. small msd cracks in combination with a lead crack can significantly reduce the load level driving to unstable crack propagation. test data on residual strength of various types of airframes with multiple-site fatigue cracks are presented in [2], where it is showed how residual strength is affected by structural design features, bending stresses, material plasticity, arrangement of multiple-site cracks and stable growth of cracks under static loading. structures with msd fail when stress intensity factors (sifs) are within a range from the plane-strain fracture toughness (kic) to plane-stress fracture toughness (kc) and when net stresses are 30 to 90% of the yield stress. full-scale tests show that the presence of msd adjacent to a lead crack reduces the residual strength by 15% [3]. sifs can attain critical values in a way similar to strain energy release rates. the criterion for failure due to unstable crack growth can therefore be written as i ick k or i ck k (1) where kic and kc are the fracture toughness of the material under plane strain and plane stress conditions respectively. it is experimentally found that kic is constant for thick sections of a given material. kc is found to vary with crack length and component geometry and is applicable to thinner sections where stable crack growth can occur. from eq.1, the failure criterion can be written as:   c c cy a k (2) t r. citarella, frattura ed integrità strutturale, 35 (2015) 523-533; doi: 10.3221/igf-esis.35.58 524 where y is the geometric factor,  c is the critical stress and ca is the critical crack length at failure. this equation can be used to assess failure criterion for a component. hence if a particular crack length is chosen and y and kc are both known then eq. 3 holds true:    cc c k y a (3) the critical stress  c must not be exceeded by the operating stress if failure of the cracked component is to be avoided. in most cases, the critical stress will decrease as the crack length becomes longer and this must be considered in the long term assessment of working stresses. if a stress level  c is chosen then the critical crack length is given by eq. 4:          2 1 c c c k a y (4) the critical crack length must be much higher than the minimum detectable crack length amin so that the component can be inspected for crack growth at regular intervals. the above criterion does not take into account stable crack growth which can occur in thin sections of some materials. under these condition the crack will only grow if the load is increasing whereas if the load is constant the crack will stop. in such cases the increase in crack driving force g is initially counterbalanced by the increase in crack growth resistance r under rising load, enabling crack growth to be stable. the instability condition is reached when g = r and  dg dr da da , i.e. when the curves of g and r versus crack length are tangent to each other. usually r is expressed in stress intensity factor units, i.e.  ,r gk er k eg and so the instability criterion becomes g rk k ,  g rdk dk da da . r curves have been derived for many materials; more information on r curves and their use can be found in [4-6]. problem description he lap joint proposed for numerical residual strength assessment is represented in fig.1, with an msd experimental scenario that is taken from [7]. in fig. 2 intermediate experimental cracked configurations, up to reaching 393000 fatigue cycles, are reported, whereas the modelled scenario (fig. 3) makes reference to the experimental configuration after 399620 fatigue cycles, when the fatigue cycling was stopped and the experimental residual strength test started [7]. the plates are made of al 2024-t3 with young’s modulus e=72000 n/mm2 and poisson’s ratio =0.33. the model adopted is based on the usage of dual boundary element method (dbem) [8-10] under the hypothesis of linear elastic fracture mechanics (lefm). in correspondence of 399620 fatigue cycles the residual ligament between hole n. 6 and 7 and between holes n. 8-9-10 had been cut by the advancing cracks and new cracks had nucleated from left hand side of hole n. 6 and from right hand side of hole n. 10; the same residual ligament failure happened between holes n. 15 and 16 with related nucleation of a new crack from right hand side of hole n. 16. the cracked plate of the lap joint has been modeled, using the commercial code beasy, by a 2d single plate with constant traction applied on one side and constrains in y direction applied on the rivet holes in order to model pin actions, whereas no constraints are present in x-direction in order to allow transversal plate shrinkage (fig. 3). with such constraints, the longitudinal plate compliance in the overlapping area (between the two rows of rivets) is neglected whilst it is underestimated in transversal x-direction, introducing an element of approximation. in the critical cracked area, the pin action modeling has been improved by explicitly inserting such pins in the holes (instead of just applying displacement constraints on the hole boundary) and moving the constraints on the pin centre. in particular, traction and displacements continuity conditions are imposed on 180 degrees of the pin-hole interface area (the supposed contact area after loading application), whilst the remaining part is disconnected by internal spring of negligible stiffness (fig. 3). t r. citarella, frattura ed integrità strutturale, 35 (2015) 523-533; doi: 10.3221/igf-esis.35.58 525                                      p s l3  l1  p  s  l  l2  lc  ei  d  eb  l   555   l1   299,5   l2   299,5   l3   440   lc   44   ei   3,2   eb   1,6   number of rows   2   number of columns   20   p   22   s   22   d   4,8     figure 1: specimen geometry. x y figure 2: intermediate crack scenarios up to 393000 fatigue cycles. by means of a convergence study, it has been assessed that only in cracked holes and in holes nearby cracks it is necessary to explicitly model pins (rivets), whereas the remaining holes can be simply constrained against y-translation, as already mentioned. the secondary bending (fig. 4) is not considered, but the level of approximation introduced is judged acceptable for such kind of problems due to relevant plate flexural weakening caused by long cracks on the verge to become unstable (see [6] for a discussion on this topic). r. citarella, frattura ed integrità strutturale, 35 (2015) 523-533; doi: 10.3221/igf-esis.35.58 526 a b c x y x y crack tip n. 1  crack tip n. 2  crack tip n. 3  crack tip n. 4  hole n. 6  hole n. 10  internal springs  j‐path  figure 3: dbem model of lap-joint in the proposed initial cracked configuration, with highlight of: hole numbering on the cracked raw (a); main crack (b); hole constraints, rivets, j-path around the crack tip and “internal springs” (c). figure 4: secondary bending phenomena. gap elements have also been introduced to better tackle contact conditions [12] but the solution improvement has been judged quite negligible (less than 2% variation on sifs), except in case of very short cracks initiated from the holes, more sensitive to pin-hole contact conditions. for this reason, and due to the computational effort of a non-linear analysis, they have no longer been used. the j-integral technique is adopted for sif’s evaluation, being more stable than crack opening displacement method against crack mesh variations [13]. r. citarella, frattura ed integrità strutturale, 35 (2015) 523-533; doi: 10.3221/igf-esis.35.58 527 33 integration points are used along the j-integral path (fig. 3c) whereas the increment of accuracy with 66 points turn out to be negligible. the mesh used for the lap-joint is based on about 326 quadratic elements: a p-convergence study has been realized showing that cubic elements provide an accuracy improvement of less than 2% and that 2 quadratic elements per 90 degrees are enough on the cracked hole, except when very short cracks are present (in such case 3 elements are recommendable, possibly with a scaling ratio). after link-up of the cracks between holes and consequent development of the main crack there is no longer load transfer through the pins in the central part of such main crack even in the remote case they should not break when reached by the propagating crack. still remaining in the theoretical framework of linear elastic fracture mechanics, sifs evaluation can be improved by empirically taking into account the elastic-plastic effects by the irwin correction. such correction is useful in a residual strength analysis and suggests to prolong the considered cracks of a virtual quantity calculated as a characteristic dimension of the plastic zone at the crack tip. alternatively a fully elastic plastic nonlinear analysis could be attempted to get more accurate results [14]. solution procedure wo approaches have been proposed for failure assessment:  plastic collapse prediction, based on von mises stress exceeding 385 mpa, the average of yield (�y=330 n/mm2 ) and rupture stress (u=440 n/mm2 ), in large zones of ligament;  r-curve analysis for stable and unstable crack growth assessment. with reference to the latter, it is well known that the failure criterion for plane strain structure is not valid for the case of thin metal sheet structure, because of extensive slow stable growth, under monotonic loading, prior to instability and catastrophic failure. here rather than a single material parameter, a material curve (r-curve or kr-curve), representing an infinity of potential failure points (the crack length at instability is not known a priori), is necessary to make an accurate failure prediction. in this case two criteria must be satisfied to get an unstable crack growth: g rk k and g r d d k k da da (5) in the r-curve diagram there are two important points: 1. ko is the minimum sif to start the crack propagation; 2. kc is the critical stress intensity factor (instability point). ko (the point of initial crack propagation) is independent from the specimen thickness and has a constant value equal to nearly 30 mpa m1/2 for the considered material [6] so that the main crack will start propagating with a remote load equal to 63 mpa (as a matter of fact the first iteration in table 1 starts considering 63 mpa). on the contrary kc is strongly influenced from the specimen thickness: thinner specimens give higher kc values and consequently exhibit slower stable crack growth. a sufficiently thick specimen will result in full plane strain and kc will then be equal to kic. in order to obtain a crack driving energy (or force) curve an iterative process is needed, which is based on the following steps (fig. 5):  the load is monotonically increased by small steps and for each of them a linear elastic analysis is performed by dbem to calculate sifs (when two consecutive configuration have nearly the same crack configuration it is possible to avoid the dbem analysis, imposing a linear variation of sifs vs. loads);  at each step cracks are prolonged by a length dai that is provided by the r-curve, as a function of the sifs determined at the previous step; moreover, in order to provide the irwin correction for sifs evaluation, when the plastic effects become significant, cracks are prolonged by a virtual length ry=rp (eq. 6);  for each crack tip, the g-curve (crack propagation driving force) is drawn and superimposed to the r-curve in order to find out the instability point, as resulting from the conditions in eqs. 5;  during the steady crack propagation some cracks will reach a link-up condition (fig. 6) with other cracks or holes, when the plastic zone at the crack tip together with the plastic zone of the approaching crack or hole respectively, are covering the remaining ligament (swift criterion). t r. citarella, frattura ed integrità strutturale, 35 (2015) 523-533; doi: 10.3221/igf-esis.35.58 528               determination of k1, , k2 , k3 , k4 ,  k5 at   ai+1=ai+ai   figure 5: flow chart of residual strength assessment procedure. figure 6: swift criterion for link-up. numerical results he first link-up (table 1) is obtained with a load of 68 mpa, that is sufficient to create a plastic zone:   2 22 eq p y k r (6) t r. citarella, frattura ed integrità strutturale, 35 (2015) 523-533; doi: 10.3221/igf-esis.35.58 529 covering the ligament between the hole n. 5 and the crack tip n.1 (left side of hole n. 6 in fig. 3); keq is the equivalent sif, calculated as in [9] but in this problem nearly coincident with the mode i sif. when a propagating crack reaches a hole we have supposed the nucleation of a small, not detectable crack of 1 mm length on the opposite hole side (fig. 7), as a consequence of local high stress gradients on an aged lap-joint (399620 fatigue load cycles). starting from the 8th iteration, in order to improve accuracy of k values, the irwin correction has been adopted. the second link-up (table 1) between crack tip n. 2 (right side of hole n.10) and hole n. 11 (fig. 3) is obtained with a load of 143 mpa, as suggested by von mises stresses exceeding 385 mpa in a large part of ligament (figs. 7b-c); again we have supposed the nucleation of a small, not detectable crack of 1 mm length on the right side of the hole n.11 (fig. 7d). then, with the same load of 143 mpa and considering the main crack configuration obtained after the second link-up, the r-curve analysis provides an unstable crack growth (fig. 8 and table 2) of crack tip n. 1 up to hole n. 4 (fig. 7d) and subsequent lap joint failure due to plastic collapse (the residual ligament cannot stand anymore the applied load and undergoes extensive yielding). namely, with reference to the crack tip n. 1, the g-curve becomes tangent to the r-curve, reaching higher values and higher gradients (fig. 8) and causing the aforementioned unstable growth. x y a b c x y d 1 mm nucleated crack 1 mm nucleated crack crack tip n.1 hole n.4 hole n.5 hole n.10 hole n.11 figure 7a-d: close up of the main crack after first link-up on the left side of main crack (a); internal point position, in the configuration preceding the second link-up (b) and related von mises stresses on the residual ligament of the main crack right side (c); close up of the main crack after second link-up on the right side (d). r. citarella, frattura ed integrità strutturale, 35 (2015) 523-533; doi: 10.3221/igf-esis.35.58 530 figure 8: r-g stability diagram with the g-curve corresponding to a load of 143 mpa. the r-curve (fig. 9) used has the following equation [7]:   0.5218.08 0.51 21.49rk da da (7) with kr in mpa*m1/2 and da in mm; in this r-curve the irwin plastic correction is included and, analogously, sifs calculated by bem are obtained with allowance for irwin correction; figure 9: al2024-t3 r-curve. the g-curve, superimposed to the r-curve, is obtained in the following way:  crack tip n. 1 has been automatically propagated for a certain number of increments in order to get the sifs for a variable crack length;  each sif is corrected (with the irwin criterion) by artificially modifying the correspondence between sifs and related crack increment, in particular by backward shifting the crack length for each step of a quantity rp. from figs. 10a-b it is evident that with a load of 143 mpa, before instability of crack tip n.1, von mises stresses are less than 385 mpa in most part of the ligament, in such a way that a failure based on plastic collapse is still premature. consequently the real mechanism of lap joint failure is primarily related to fracture instability, responsible for the residual ligament reduction up to a condition in which the plastic collapse becomes effective. the numerical result of fracture instability at 143 mpa is close to the experimental collapse load equal to 139 mpa (specimen n. 5 in [7]) with consequent validation of the proposed procedure. r. citarella, frattura ed integrità strutturale, 35 (2015) 523-533; doi: 10.3221/igf-esis.35.58 531 a x y b figure 10a-b: von mises stresses (a) calculated with a load of 143mpa on the internal points (b) between crack tip n. 1 and hole n. 4 (see fig. 7d). iter.   ain +dat+ry keq residual ligament da ry (mpa) (mpa) (mm) (mpa*mm1/2) (mm) (mm) (irwin correction) crack tip n.1 1 63 5 16.24 730 3.36 0 0 2 (yield.) 68 10 17.15 788 2.45 0 0.91 3 78 10 3.40 995 16.20 0.3 0 4 88 10 3.73 1111 15.87 0.3 0 5 98 10 4.00 1237 15.60 0.4 0 6 108 10 4.40 1364 15.20 0.5 0 7 118 10 4.90 1455 14.70 0.4 0 8 128 15 8.94 1522 10.66 0.4 3.64 9 143 11.43 1754 8.17 1.5 4.23 crack tip n. 2 hole n. 10, right side 1 63 5 6.15 701 13.45 0 0 2 68 10 6.15 772 13.45 0 0 3 78 10 6.15 886 13.45 0 0 4 88 10 6.15 1000 13.45 0.3 0 5 98 10 6.49 1114 13.11 0.3 0 6 108 10 6.77 1227 12.83 0.4 0 7 118 10 7.12 1349 12.48 0.5 0 8 128 10 10.79 1474 8.81 0.5 3.13 9 (yield.) 143 13.52 1703 6.08 1.4 3.97 crack tip n. 3 hole n. 15, left side 1 63 5 11.07 440 8.53 0 0 2 68 10 11.07 484 8.53 0 0 3 78 10 11.07 555 8.53 0 0 4 88 10 11.07 625 8.53 0 0 5 98 10 11.07 696 8.53 0 0 6 108 10 11.07 767 8.53 0 0 7 118 10 11.07 841 8.53 0 0 8 128 15 11.07 952 8.53 0.3 0 9 143 13.22 1075 6.38 0.25 1.65 table 1: crack advance vs. monotonic increasing load. r. citarella, frattura ed integrità strutturale, 35 (2015) 523-533; doi: 10.3221/igf-esis.35.58 532 dac (mm) kg (mpa*mm1/2) kr (mpa*mm1/2) 0.0 1829 680 0.7 1823 1176 1.8 1828 1421 2.8 1842 1611 3.7 1870 1755 4.6 1908 1875 5.3 1968 1956 5.7 2063 2006 5.9 2198 2026 table 2: kr, kg data for the crack tip n. 1 (kg calculated with irwin correction). conclusions he procedure presented turn out to be a very effective way to model the assembly and exhibits a satisfactory agreement with experimental results, very attractive run times and an easy pre-processing phase (the mesh generation is very easy because based on monodimensional elements). the main advantages of the proposed dbem two-dimensional approach to lap joint modelling are [see also 15-16]: each layer can be considered as an individual two-dimensional structure; individual layers can be explicitly modelled and connected with rivets (in case of need this provide a way to enhance the accuracy with respect to the simplified approach adopted in this work); the determination of the sifs is straightforward with the j-integral technique; rivets can be modelled as separate dbem zones, interacting with the main zone by gap elements (in case of nonlinear contact analysis) or by interface spring of negligible stiffness (to disconnect the pin-hole interface) or by simply enforcing continuity conditions. bibliography [1] broek, d., the effects of multi-site-damage on the arrest capability of aircraft fuselage structures, fracturesearch, tr 9302, (1993). [2] nesterenko, gi., multiple site fatigue damages of aircraft structures, nasa, n96-24270, (1995). [3] samavedam, g., hoadley, d., thomson, d., full-scale testing and analysis of curved aircraft fuselage panels. faa, dot/faa/ct93/78 (1993). [4] astm es61-94, standard practice for r-curve determination for simple metal sheets, annual book of astm standard, , american society for testing and materials, philadelphia, (2010) b42 b60. [5] dewit, r., fields, r. j., low iii, s. r., harne, d. e., foecke, t., fracture testing of large-scale thin-sheet aluminum alloy, dot/faa/ar-95/11, federal aviation administration, (1996). [6] calì, c., citarella, r., residual strength assessment for a butt joint in msd condition, advances in engineering software, 35 (2004) 373-382. [7] silva, l. f. m., gonçalves, j. p. m., oliveira, f. m. f., de castro, p. m. s. t., multiple-site damage in riveted lapjoints: experimental simulation and finite element prediction, international journal of fatigue, 22 (4) (2000) 319-338. [8] citarella, r., cricrì, g., armentani, e., multiple crack propagation with dual boundary element method in stiffened and reinforced full scale aeronautic panels, key engineering materials, 560 (2013) 129-155. [9] calì, c., citarella, r., perrella, m., three-dimensional crack growth: numerical evaluations and experimental tests, european structural integrity society, biaxial/multiaxial fatigue and fracture, eds. a. carpinteri, m. de freitas, a. spagnoli, 31 (2003) 341-360. [10] citarella, r., perrella, m., multiple surface crack propagation: numerical simulations and experimental tests, fatigue and fracture of engineering material and structures, 28 (2005) 135-148. [11] beasy v10r14, documentation, c.m. beasy ltd; (2011). [12] citarella, r., non linear msd crack growth by dbem for a riveted aeronautic reinforcement, advances in engineering software, 40 (4) (2009) 253–259. t r. citarella, frattura ed integrità strutturale, 35 (2015) 523-533; doi: 10.3221/igf-esis.35.58 533 [13] citarella, r., cricrì, g., comparison of dbem and fem crack path predictions in a notched shaft under torsion, engineering fracture mechanics, 77 (2010) 1730-1749. [14] caputo, f., lamanna, g., soprano, a., on the evaluation of the plastic zone size at the crack tip, engineering fracture mechanics, 103 (2013) 162-173. [15] armentani, e., citarella, r., dbem and fem analysis on non-linear multiple crack propagation in an aeronautic doubler-skin assembly, international journal of fatigue, 28 (2006) 598–608. 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can be opened with acrobat and adobe reader 5.0 and later.) >> /namespace [ (adobe) (common) (1.0) ] /othernamespaces [ << /asreaderspreads false /cropimagestoframes true /errorcontrol /warnandcontinue /flattenerignorespreadoverrides false /includeguidesgrids false /includenonprinting false /includeslug false /namespace [ (adobe) (indesign) (4.0) ] /omitplacedbitmaps false /omitplacedeps false /omitplacedpdf false /simulateoverprint /legacy >> << /addbleedmarks false /addcolorbars false /addcropmarks false /addpageinfo false /addregmarks false /convertcolors /converttocmyk /destinationprofilename () /destinationprofileselector /documentcmyk /downsample16bitimages true /flattenerpreset << /presetselector /mediumresolution >> /formelements false /generatestructure false /includebookmarks false /includehyperlinks false /includeinteractive false /includelayers false /includeprofiles false /multimediahandling /useobjectsettings /namespace [ (adobe) (creativesuite) (2.0) ] /pdfxoutputintentprofileselector /documentcmyk /preserveediting true /untaggedcmykhandling /leaveuntagged /untaggedrgbhandling /usedocumentprofile /usedocumentbleed false >> ] >> setdistillerparams << /hwresolution [2400 2400] /pagesize [612.000 792.000] >> setpagedevice microsoft word numero_36_art_10 t. fekete, frattura ed integrità strutturale, 36 (2016) 99-111; doi: 10.3221/igf-esis.36.10 99 focused on fracture mechanics in central and east europe review of pressurized thermal shock studies of large scale reactor pressure vessels in hungary tamás fekete has centre for energy research, department of fuel and reactor materials, structural integrity group tamas.fekete@energia.mta.hu abstract. in hungary, four nuclear power units were constructed more than 30 years ago; they are operating to this day. in every unit, vver-440 v213-type light-water cooled, light-water moderated, pressurized water reactors are in operation. since the mid-1980s, numerous researches in the field of pressurized thermal shock (pts) analyses of reactor pressure vessels (rpvs) have been conducted in hungary; in all of them, the concept of structural integrity was the basis of research and development. during this time, four large pts studies with industrial relevance have been completed in hungary. each used different objectives and guides, and the analysis methodology was also changing. this paper gives a comparative review of the methodologies used in these large pts structural integrity analysis projects, presenting the latest results as well. keywords. structural integrity analyses; reactor pressure vessels; pressurized thermal shock. introduction n a preceding paper [2], the concept and the general methodology of pressurized thermal shock (pts) structural integrity analyses of large scale reactor pressure vessels (rpv) were presented. the pts phenomenon was known to specialists earlier, but became widely known and consequently, subject to intensive research when in the late 1970’s, two accidents occurred in the us. those accidents showed that transients can occur in pressurized water reactors, resulting in a severe overcooling that causes thermal shock in the vessel, concurrent with or followed by re-pressurization. these are the transients generally known under the name of pts. the very high tensile stress caused by thermal shock at the inner surface of the vessel wall can cause the cleavage initiation of a pre-existing flaw of a certain dimension to occur (i. e. crack-like defect). concern about brittle crack initiation during pts can arise because during operation the neutron irradiation exposure around the energy-generating core makes the material of the reactor pressure vessel (rpv) increasingly susceptible to cleavage fracture initiation. although pts calculations have been part of rpv safety evaluations since the first half of the 1980’s, there are various approaches that are analogous in general, but have many differences in details. there exists no internationally recognized standard; there are guidelines in europe that are recommended to use (e. g. specifically for vver units [4] and [16]); various approaches are used at a national level in different countries. in hungary, the haea guide 3.18v3 [3] is currently in effect. during the last three decades, four large pts studies have been conducted in hungary. each used different objectives and guides, and the analysis methodology has also been changing. in the preceding paper [2], the conceptual model of pts structural integrity calculations was presented. it was shown that using the conceptual model –that is based on the notion of typed graph-transformation systems– the calculations and their evolution can be described on a theoretical level. using i t. fekete, frattura ed integrità strutturale, 36 (2016) 99-111; doi: 10.3221/igf-esis.36.10 100 the model, the structure and the key aspects of a more proper description of the pts calculation methodology were presented, as follows:  objective of the study;  codes and guides used during the project definition;  geometry definition: o parts of the rpv modeled during the study and the geometric model, • locations selected for fracture mechanics analyses; o flaw-size and geometrical distribution at selected locations; • relation of postulated flaws vs. detected flaws;  description of neutron-transport calculations;  materials: o description of materials; o description of constitutive models: • thermo-mechanics model and its parameters description of ageing; • fracture model and its parameters; description of ageing; o qualification of material test methods;  thermal-hydraulics: o selection of overcooling sequences; o thermal-hydraulic assessments;  modeling of physical fields: o kinematical model; o physical fields; o fracture mechanics model;  integrity criteria. applying the results mentioned above, these points will be discussed in the course of this review concerning the evolution of pts calculation methodologies in hungary. considering the changing context, the objectives of the study, as well as the codes and guides used during the problem definition and solution will also be presented. phase 0.: designer’s and manufacturers pts structural integrity calculations designer’s and manufacturers pts structural integrity calculations he vver-440 v213-type rpv design was developed by okb gidropress without pts assessments in the first half of the 1970s; as at that time the pts safety evaluations of the rpvs were not part of the design requirement. normal operating events and anticipated emergency events were addressed in the loading specifications. calculations of protection against brittle fracture were part of the original strength calculations, and followed the rules set by the russian standard valid at the time. according to the rule, brittle fracture resistance was analyzed on the basis of the material’s static strength properties, but did not use fracture mechanics criterion. the integrity of the rpv met the brittle fracture requirements if:  twall ≥tk, where twall is the component’s wall temperature, tk is the critical temperature of brittleness of the component’s material, or  when twall <tk and σred<rp0,2t/n, where σred denotes mohr’s reduced stress, rp0,2t is yield stress of the material at the component’s wall temperature, n is the safety factor; n=2 if the component is regularly examined by non-destructive tests (ndt), otherwise n=4 [14]. later, starting in the mid-80s, several pts calculations were performed by okb gidropress and by other institutes, but in most cases, these studies assumed a generic rpv; so plant-specific conditions were neglected. the manufacturer’s pts structural integrity calculations as part of the manufacturer’s strength-calculation documentations, škoda provided a pts analysis for a few accidental situations chosen based on engineering judgments, using linear elastic fracture mechanics. t t. fekete, frattura ed integrità strutturale, 36 (2016) 99-111; doi: 10.3221/igf-esis.36.10 101 concerning geometry definition, weld no5/6, and an eccs nozzle were selected, taking the geometrical dimensions of the components into account, as it was given in the documentation. at both locations, embedded elliptical cracks were selected with 2a0= 5 mm, with fatigue crack growth of 1 mm, postulated up to end of life (eol) conditions. the thermo-mechanical material parameters of the base material type 15ch2mfa were selected from the strength calculations documentation. for fracture mechanics calculation, the equation   86400, ( ) 86 ( ) ir k k k t t kg m t t    (1) described material fracture toughness. results of ageing evaluation gave tk=136 °c for weld no5/6, and tk=32 °c for the eccs nozzle. selection of overcooling sequences was based on empirical, engineering experience: the loss of coolant accident cases (loca) rupture of pipelines ø135, ø250 and ø492 were analyzed. the pts calculations were performed by a code developed at skoda. the integrity of the rpv was accepted for brittle fracture, if:  twall ≥tk, where twall is the component’s wall temperature, tk is the critical temperature of brittleness of the component’s material, or  when twall <tk, then o ac/a0 ≥ 2, where ac is the critical crack size (where ki=kir) and o ki(x=2c)/kir(x=2c) = nk ≥√; summary the above-reviewed analyses –performed by the manufacturer in the early 1980s– were based on engineering models. they analyzed only a very limited set of thermal-hydraulic transients, and used linear-elastic material models (that is, a linear elastic fracture mechanics (lefm) methodology); the results of the fracture mechanics evaluation were adequate. phase 1: pts structural integrity calculations in the 1980s objective of the study: he objective of the study was to provide results for the safety report that was necessary for the renewal of the operating license after each, 4-year inspection cycle. codes and guides used during problem definition: the interatomenergo rule 38.434.55-84 was used during the calculations. geometry definition:  the rpv beltline region was selected for the study, with geometrical dimensions selected from the manufacturer’s documentation, o in the beltline region, an axial, semielliptical shaped, through clad crack with depth a=35 mm and c=52,5 mm, and o in weld no 5/6 a circumferential, semielliptical shaped, through clad crack with depth a=35 mm and c=52,5 mm was defined, description of neutron-transport calculations: the fluence calculations were based on a semi-empirical approach. during generic studies, the lead factors for the critical beltline region and for the weld no 5/6 were determined, and data from fluence-measurement results were used to assess factual neutron fluencies for eol conditions at the selected locations. materials, constitutive models:  both the cladding and the ferritic materials (15ch2mfa forging and the welding metal) were modeled during calculations. for thermal and strength calculations, the data were derived from the manufacturer’s documentation. t t. fekete, frattura ed integrità strutturale, 36 (2016) 99-111; doi: 10.3221/igf-esis.36.10 102  in thermal calculations, the thermo-physical parameters were independent from temperature; during calculations, averaged values of the manufacturer’s documentation were used.  in strength calculations, the neumann-duhamel constitutive model was used with temperature-independent, averaged values of the manufacturer’s documentation.  for the description of fracture toughness of the structural materials, the equation:    0.02, 26 36 kt tic kk t t e    (2) was used; the ageing was modeled by using the temperature-shift (∆tk) of the critical temperature of brittleness in the following form: 3 0k k k kt t t t a       (3) where φ is neutron fluence. ∆tk values were evaluated from plant surveillance data.  the above material parameters were based on experimental results, performed in a qualified laboratory. thermal-hydraulic assessments:  the selection of overcooling sequences was based on engineering judgments. loss of coolant accident cases (loca) rupture of pipelines ø135, ø250 and ø492 were selected for calculations.  the thermal-hydraulic assessments were performed by relap 4 – mode 6 version. during thermal-hydraulic assessments, a simplified model of the primary system was used; the model assumed that all primary loops are identical, the model was called ‘one loop model’ of the primary system. for mixing calculations, a home-developed code was used. main features of the model used for pts structural mechanics calculations:  for structural mechanics calculations, an analytical code was used [10], which had been validated with a finite element code [13] earlier. the model and the solution of the problems had the following features: o in the thermal problem solution, the code used a thick-plane model of the beltline area that touches the liquid-wall interface. the solution of the thermal problem was determined in terms of fourier series. the boundary conditions of the problem were received from results of thermal-hydraulic assessments at selected points in the downcomer. o in the solution of the strength problem, the software used analytical stress-formulae to generate the solution. o in fracture mechanical calculations, the crack tip driving force was calculated using the method published by westergaard [17]. o the cladding residual stresses were taken into account, applying stress-free temperatures (tsf), which were chosen equal to the operating temperature of the component. o the weld residual stresses were neglected. integrity criterion: the crack initiation condition in the form: i ick k (4) was used during calculations. summary the analyses shown above were based on an analytical approach of the underlying thermo-elastic problem. the overcooling sequences were selected based on engineering judgments; this resulted in a limited set of transients. the structural mechanics calculations were based on the ‘force method’ that had been widely used in mechanical engineering since the early days of the field of strength of materials. the fracture mechanics module worked with an lefm methodology. the ageing characteristics of structural materials were derived from the experimental results of the surveillance program. t. fekete, frattura ed integrità strutturale, 36 (2016) 99-111; doi: 10.3221/igf-esis.36.10 103 phase 2: pts structural integrity calculations in the 1990s objective of the study: he main objective of the study was to reassess the safety of paks npp using internationally accepted designand safety -codes and guidelines. experiences from various international pts-related projects were used in the elaboration of the methodology [1, 5, 9, 15]. codes and guides used during problem definition: the pnae g-7-002–86 [8], the asme bpvc xi, and the 10 cfr 50.61 were used during the project. geometry definition:  the rpv beltline region was selected for the study, with geometrical dimensions selected from the manufacturer’s documentation, o in the beltline region, axial, semielliptical shaped through clad cracks with depths a=13, 23 and 35 mm and shape factor a/c=2/3; and o in weld no 5/6 a circumferential, semielliptical shaped through clad crack with depths a=13, 23 and 35 mm and shape factor a/c=2/3, were defined. description of neutron-transport calculations; the fluence calculations were based on a semi-empirical approach. during generic studies, the lead factors for the critical beltline region and for the weld no 5/6 were determined, and data from fluence-measurement results were used to assess factual neutron fluencies for eol conditions at the selected locations. materials, constitutive models:  both the cladding and the ferritic materials (15ch2mfa forging and the weld metal) were modeled during calculations. for thermal and strength calculations, the data were derived from the manufacturer’s documentation.  in thermal calculations, the thermo-physical parameters were independent from temperature; during calculations, averaged values of the manufacturer’s documentation were used.  in strength calculations, the neumann-duhamel constitutive model was used with temperature-independent, averaged values of the manufacturer’s documentation.  for describing the fracture toughness of the structural materials, the equation:    0.0217, 35 53 kt tic kk t t e    (5) was used; the ageing was modeled by using the temperature-shift (∆tk) of the critical temperature of brittleness in the following form: 3 0k k k kt t t t a       (6) where φ is neutron fluence.  the above material parameters were based on experimental results, performed in a qualified laboratory. thermal-hydraulics:  the selection of the overcooling sequences was based on engineering judgments integrated with conclusions of international experiences [15] as well. a broad spectrum of various overcooling sequences, various loss of coolant accident (loca) scenarios, e.g. rupture of various pipelines (e.g. ø90, ø135, ø233 and ø492) were selected for calculations.  the thermal-hydraulic assessments were performed by the system thermal-hydraulic codes relap 5 – mode 2 and athlet – mod 1.4.. during thermal-hydraulic assessments, a simplified ‘one loop model’ of the primary system was used. for mixing calculations, the remix code was used. t t. fekete, frattura ed integrità strutturale, 36 (2016) 99-111; doi: 10.3221/igf-esis.36.10 104 main features of the models used for pts structural mechanics calculations:  for structural mechanics calculations, a hungarian code (called acib-rpv) was used [11], which was validated to finite element codes [12]. the model and the solution of the problems has the following features: o in the thermal problem solution, the code used a thick-plane model of the beltline area that touches the liquid wall interface. the solution of the thermal problem was determined in terms of fourier series. the boundary conditions of the problem were received from results of thermal-hydraulic assessments at selected points in the downcomer. o in the solution of the strength problem, the software used analytical stress-formulae to generate the solution. o in fracture mechanical calculations, the crack tip driving force was calculated using the method published by westergaard [17]. o the cladding residual stresses were taken into account, applying stress free temperatures (tsf), which were chosen equal to the operating temperature of the component. o the weld residual stresses were neglected. integrity criterion: the crack initiation condition in the form: 1.1 i ick k  (7) was used during calculations. summary the pts project assessed above made a larger effort in selecting the overcooling sequences and their assessments. this led to a larger set of transients, so the reliability of results increased. the analysis methodology was based on an analytical approach of the underlying problem. the fracture mechanics module worked with lefm methodology. the ageing characteristics of structural materials were derived from the experimental results of the surveillance program. phase 3: pts structural integrity calculations in the new millennium objective of the study: he objective of the study was to reassess the safety of rpvs providing time limited ageing analysis (tlaa) results for paks npp for license-application beyond the designed service lifetime. although the designed service lifetime of the rpvs was set to 40 years of operation, the analyses were conducted for the 30+ years of operation. codes and guides used during problem definition: the haea guide 3.18 [3], the iaea pts guide for vver units [4] and an earlier version of verlife [16] were used during the project. research and developmental works before the study: beginning around the new millennium, intensive research was initiated at kfki aeki in order to clarify the ageing properties of cladding materials, as well as to clarify the damage-mechanisms of various impurities in structural materials, with special emphasis on phosphorous segregation. aeki joined a number of international projects. a full review of the activities would exceed the extent of the present paper. many of the research results have been incorporated into the updated analysis methodology. geometry definition:  the full rpv body was selected for the study, with geometrical dimensions derived from the manufacturer’s documentation. two main sub-models of the model were constructed, in order to reduce the costs of the project in terms of it and human resources. the aim of the development was to make parametric studies on simpler models using conservative assumptions; and after the selection of the worst transient loading cases, perform a calculation on the more detailed model, if necessary. two types of models have been worked out: t t. fekete, frattura ed integrità strutturale, 36 (2016) 99-111; doi: 10.3221/igf-esis.36.10 105 o a model designed for elastic calculations; the geometrical model is composed from two sub-models: 1. a 3d finite element (fe) model of a lower-cylindrical part of the vessel with the bottom; the purpose of the model was the calculation of through wall temperature, stress and strain distributions occurring during pts transients, and provide inputs to subsequent fracture mechanics calculations. the fe mesh models the welds, and includes quadratic, iso-parametric brick-type elements with 20 nodal points, but does not model the crack in the mesh. the developed model contains 58240 elements and 247405 nodal points. the geometrical model is presented on fig. 1. figure 1: 3d finite element model of a lower cylindrical part, bottom and welds of a vver-440 rpv. 2. 3d models of the main coolant pipeline nozzles 492; the purpose of the models was to calculate through wall temperature, stress and strain distributions occurring during pts transients, and provide inputs to subsequent fracture mechanics calculations. the fe mesh includes quadratic, iso-parametric brick-type elements with 20 nodal points. the developed model contains 7320 elements and 34144 nodal points. the geometrical model is presented on fig. 2. figure 2: 3d finite element model of a main coolant pipeline nozzle 492. t. fekete, frattura ed integrità strutturale, 36 (2016) 99-111; doi: 10.3221/igf-esis.36.10 106 3 for elastic calculations, a series of crack locations were selected for fracture mechanics calculations, as it is presented on fig. 3. the aim of this development was to make the calculations suitable for an algorithmic evaluation of the crack locations in any transient case. 45° 90° 135° 225° 270° 315°180° 167° 193° 0° 360° 1 4 0 0 1 7 3 5 2 7 0 0 1 8 2 5 1 9 0 0 2 0 0 0 1 1 0 0 11128 figure 3: locations selected for fracture mechanics calculations on a vver-440 rpv. at each location, two types of cracks have been defined, as follows: one type was a semi-elliptic, underclad crack; the other type was a through clad crack, both shown on fig. 4. the a/c ratio was set to 1/3 [3]. the depth of the cracks varied between 2 and 14 mm from the cladding-base metal interface; the maximal crackdepth was 0,1s. the use of this maximal postulated crack-depth parameter was allowed to calculate with because nde tests were qualified according to international standards. nde results also proved that the cladding could be seen free from critical defects, so the use of underclad cracks was also allowed. the through-clad cracks served for parametric studies. 2c 2c a c a c a tpl ta figure 4: the two crack types defined for fracture mechanics analyses [6, 7]. t. fekete, frattura ed integrità strutturale, 36 (2016) 99-111; doi: 10.3221/igf-esis.36.10 107 o the other type of the model was designed for elastic or elastic-plastic calculations with a crack embedded into the mesh; it is the 3d fe model of the lower cylindrical part of the vessel with the bottom, including a crack embedded into the mesh. the model was developed with the purpose of simulating through wall temperature, stress and strain distributions occurring during pts transients, and also performing subsequent fracture mechanics calculations on the embedded crack. the fe mesh models the welds, and includes quadratic, iso-parametric brick-type elements with 20 nodal points. the model was designed to study plasticity effects too. the developed model contains 160 540 elements and 709 826 nodal points. the geometrical model is presented on fig. 5. the crack location was selected after long series of calculations performed on the simpler model, in order to reduce the time-consuming work of developing a mesh around the crack front. the crack model is an underclad, semi-elliptical crack with a=14 mm, a/c=1/3; the crack model is shown on fig. 5 below. figure 5: 3d finite element model of a lower cylindrical part with embedded crack of a vver-440 rpv. description of neutron-transport calculations: the fluence data were provided by full 3d neutron-transport calculations that took the full loading-history of the energetic core into account. this fact made a complete re-evaluation of material ageing possible. materials, constitutive models:  both the cladding and the ferritic materials (15ch2mfa forging and the weld metal) were modeled during calculations. for thermal and strength calculations, the data were derived from the manufacturer’s documentation.  in thermal calculations, the thermo-physical parameters were temperature-dependent.  in thermo-mechanical strength calculations, the neumann-duhamel constitutive model was used with temperaturedependent parameters of the manufacturer’s documentation. in the case of elastic-plastic calculations, plastic material properties were derived from the re-evaluation of the material tests performed in the frame of the manufacturer’s surveillance program.  for describing the fracture toughness of the structural materials, the equation: t. fekete, frattura ed integrità strutturale, 36 (2016) 99-111; doi: 10.3221/igf-esis.36.10 108    0.02, 26 36 kt tic kk t t e    (8) was used; the ageing was modeled by using the temperature-shift (∆tk) of the critical temperature of brittleness in the following form:  0 ,age temp fat irr n fat operk k k k k kt t t t t a t f t          (9) where φ is neutron fluence, a is fatigue damage, toper is the operational temperature, ∆tkirr is the temperature shift caused by neutron irradiation, ∆tktemp is the temperature shift caused by thermal activation and ∆tkfat is the temperature shift caused by fatigue.  the above-described material parameters were evaluated on the basis of experimental results, performed in qualified laboratories. thermal-hydraulics:  the deterministic selection of the pts transients was based on engineering judgment using the design basis accident analysis approach combined with the operational experience accumulated at the plant. in this deterministic selection, only the individual initiating events were taken into account. a broad spectrum of various overcooling sequences was selected for calculations. complementary to the deterministic analysis of the limiting scenarios, a selection of additional transients with the help of probabilistic event-tree methodology was also performed.  the thermal-hydraulic assessments were performed by relap 5 – mode 3 and athlet ver 2.3. system codes. for mixing calculations, the remix code was used. in the system’s thermo hydraulic calculations, the six-loop model of vver 440 systems were used. so inhomogenities of the temperature and the velocity fields occurring in the downcomer were taken into account in some approximation as well. the fe model has more refined structure at the coolant-solid interface than the th system model, a sophisticated interface was developed for the generation of thermal boundary conditions from thermal-hydraulic calculation results. the relation of the points used in thermalhydraulic analyses and the fe model solid interface is presented on fig. 6. 1 1 11 21 31 41 12 13 14 15 16 22 23 24 25 26 32 42 43 44 45 46 33 34 35 36 50 90 92 figure 6: locations of thermal-hydraulic data supplying points at the inner surface of the rpv. t. fekete, frattura ed integrità strutturale, 36 (2016) 99-111; doi: 10.3221/igf-esis.36.10 109 main features of the models used for pts structural mechanics calculations:  for structural mechanics calculations, the msc.marc code was used which is a validated, general-purpose finite element code, developed specifically for non-linear calculations. the model and the solution of the problems featured the followings: o in the case of thermal-elastic or thermal-elastic-plastic problems supplemented by fracture mechanics calculations, the problem-solving strategy was to solve the coupled physical problem in its coupled form. the coupling was manageable using a staggered scheme, but for future applications, the couplings could be made stronger. o while solving the strength problem, the software used the classical deformation-based fe approach. o in fracture mechanical calculations, in case of the simpler model (described above), the crack tip driving force was calculated using the method published by s. marie and s. chapuliot [6, 7], which was implemented into a home-developed software package. o in calculations integrating the crack into the fe model, the crack tip driving force was calculated along the crack-front using the j-integral. o the cladding residual stresses have been taken into account, applying stress-free temperatures (tsf), which had been chosen equal to the operating temperature of the component. o the weld residual stresses were integrated into the model. integrity criterion: the crack initiation condition in the form: i ick k (10) was used during calculations. summary within the frame of the pts project presented above, a more detailed fe model has been developed and tested. two models were developed: a simpler linear model of the rpv and a more detailed model for studying the plastic effects occurring during pts transients. the number of overcooling sequences has increased significantly. the neutron-transport calculations provided more precise results concerning neutron-physics data. that made it possible for the ageing assessments to lower the uncertainty of results. the thermal-hydraulic system model was also considerably improved. the increasing number of selected transients and the more complex models together led to more resource-demanding calculations; however, they also made the deeper understanding of the problem domain possible. conclusions uildings, structures and systems of large scale and high value are designed for a certain, limited service lifetime, taking the standards and guidelines of the time into account. the standards applied during the design process of a large-scale structure reflect the scientific and technological level of the previous years or decades. however, the standards and guidelines are evolving over time, and the goals and requirements may also change during the service time of the equipment. that means that the context of safe operation is part of an advancing world, where the meaning of safety must remain unchanged. during the last three decades, four large pts studies have been conducted in hungary. each used different objectives and guides, and the analysis methodology has also been changing. in the preceding paper, the conceptual model of pts structural integrity calculations was presented. it was shown that using the conceptual model –that is based on the notion of typed graph-transformation systems– the calculations and their evolution can be described on a theoretical level. using the model, the structure and the key aspects of a more proper description of the pts calculation methodology were presented, as follows: the main stages of this evolutionary process were:  the analyses performed by the manufacturer in the early 1980s; these calculations were based on engineering models, analyzed only a very limited set of thermal-hydraulic transients, used linear-elastic material models a linear elastic fracture mechanics (lefm) methodology; the results of fracture mechanics evaluation were adequate. b t. fekete, frattura ed integrità strutturale, 36 (2016) 99-111; doi: 10.3221/igf-esis.36.10 110  the analyses performed in hungary during the second half of the 1980s were based on an analytical solution of the underlying thermo-elastic problem. the overcooling sequences were selected based on engineering judgments, and this resulted in a limited set of transients. the structural mechanics calculations were based on the ‘force method’ that has been widely used in mechanical engineering since the early days of the field of strength of materials. the fracture mechanics module worked with lefm methodology. the ageing characteristics of structural materials were derived from the experimental results of the surveillance program.  the pts project conducted in the first half of the 1990s made a larger effort in selecting the overcooling sequences and their assessments. this lead to a larger set of transients and results, so the reliability of results increased. the analysis methodology was based on analytical solutions of the underlying problem. the fracture mechanics module worked with lefm methodology. the ageing characteristics of structural materials were derived from the experimental results of the surveillance program.  after the millennium, the numerical problem-solving methodology has been changed fundamentally, as highercapacity it infrastructure and large-scale fe software tools became available. a more detailed fe model has been developed and tested. the team developed a simpler linear model of the rpv and a more detailed model for studying the plastic effects occurring during pts transients. the number of overcooling sequences has increased significantly. the neutron-transport calculations provided more precise results concerning neutron-physics data. that made it possible for the ageing assessments to lower the uncertainty of results. the increasing number of selected transients and the more complex models led to more resource-demanding calculations; however, they also made the deeper understanding of the problem domain possible. for lack of space, a more detailed presentation of results is left for future publications. the main conclusion of the review of the various pts projects carried out in hungary during the last three decades is that in projects with industrial relevance, both the simplified engineering models and the highly sophisticated simulation tools have their own application domain; in each project it is the responsibility of the analysts to find a balance between the goals of the study; the complexity of the approach chosen for problem-solving; the available resources; and the time limits. the purpose of the research is to achieve a deeper understanding of the problem and develop robust engineering tools that can be used in later projects. acknowledgment he kind help of dr. j. gadó and dr. f. gillemot for many years is gratefully acknowledged. the support of dr. á. horváth, prof. p. trampus and prof. l. tóth is thankfully acknowledged. the work of l. tatár, d. antók and j. pirkó is kindly acknowledged. references [1] blauel, j.g. et. al., an updated and extended safety analysis for the reactor pressure vessel of the nuclear power plant stade (kks). in: f. gillemot (editor) iaea specialist's meeting on integrity of pressure components of reactor systems. paks 1992 may. iaea, vienna, (1993) 15–26. [2] fekete, t., methodological developments in the field of structural integrity analyses of large scale reactor pressure vessels in hungary, frattura ed integrità strutturale, 36 (2016) 79-99; doi: 10.3221/igf-esis.36.09. [3] haea, evaluation of brittle-fracture resistance of vver-440/213 reactor pressure vessel for normal operation, hydrostatic test, pressurized thermal shock (pts) and unanticipated operating occurrences, regulatory guide no 3.18 (ver. 3), haea, budapest, (2013). [4] iaea, guidelines on pressurized thermal shock analysis for wwer nuclear power plants revision 1, iaea-ebpwwer-08(1), iaea, vienna, (2006). [5] iskander, k., et al.; reactor pressure vessel structural implications of embrittlement to the pressurized-thermal shock scenario. astm stp 909. astm, philadelphia, (1986) 163–176. [6] marie, s., menager, y., chapuliot, s., stress intensity factors for underclad and through clad defects in a reactor pressure vessel submitted to a pressurised thermal shock, int j of press vess and piping, 82 (2005) 746–760. [7] marie, s., chapuliot, s., improvement of the calculation of the stress intensity factors for underclad and through-clad defects in a reactor pressure vessel subjected to a pressurised thermal shock, int j of press vess and piping, 85 (2008) 517–531. t t. fekete, frattura ed integrità strutturale, 36 (2016) 99-111; doi: 10.3221/igf-esis.36.10 111 [8] pnae g-7-002-86: equipment and pipelines strength analysis norms for nuclear power plants, (in russian), energoatomizdat, moscow, (1990). [9] schmitt, w., keim, e., linear elastic analysis of semi-elliptical axial surface cracks in a hollow cylinder, int. j. pres. ves. piping, 7 (1979) 105–118. [10] szabolcs, g., development of the pt-shock program, technical report, veiki, budapest, (1988). [11] szabolcs, g., fekete, t., the acib-rpv code (in hungarian), technical report, kfki aeki, budapest, (1994). [12] szabolcs, g., fekete, t., comparative assesment of results produced by the acib-rpv code and various finite element codes (in hungarian), technical report, kfki aeki, budapest, (1994). [13] szabolcs, g., pesti, l., fracture mechanical analysis of a vver-440 reactor pressure vessel in case of a circumferential crack (in hungarian), technical report, veiki, budapest, (1987). [14] trampus, p. (editor), pressurized thermal shock analysis, paks npp units 1-4, technical report, paks, (2010). [15] tuomisto, h., thermal-hydraulics of the loviisa reactor pressure vessel overcooling transients. research report (ivo-a-)1/87, ivo, helsinki, (1987). [16] verlife guidelines for integrity and lifetime assessment of components and piping in wwer nuclear power plants – version 2013. iaea, vienna, (to be published). 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/hrv (za stvaranje adobe pdf dokumenata najpogodnijih za visokokvalitetni ispis prije tiskanja koristite ove postavke. stvoreni pdf dokumenti mogu se otvoriti acrobat i adobe reader 5.0 i kasnijim verzijama.) /hun 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can be opened with acrobat and adobe reader 5.0 and later.) >> /namespace [ (adobe) (common) (1.0) ] /othernamespaces [ << /asreaderspreads false /cropimagestoframes true /errorcontrol /warnandcontinue /flattenerignorespreadoverrides false /includeguidesgrids false /includenonprinting false /includeslug false /namespace [ (adobe) (indesign) (4.0) ] /omitplacedbitmaps false /omitplacedeps false /omitplacedpdf false /simulateoverprint /legacy >> << /addbleedmarks false /addcolorbars false /addcropmarks false /addpageinfo false /addregmarks false /convertcolors /converttocmyk /destinationprofilename () /destinationprofileselector /documentcmyk /downsample16bitimages true /flattenerpreset << /presetselector /mediumresolution >> /formelements false /generatestructure false /includebookmarks false /includehyperlinks false /includeinteractive false /includelayers false /includeprofiles false /multimediahandling /useobjectsettings /namespace [ (adobe) (creativesuite) (2.0) ] /pdfxoutputintentprofileselector /documentcmyk /preserveediting true /untaggedcmykhandling /leaveuntagged /untaggedrgbhandling /usedocumentprofile /usedocumentbleed false >> ] >> setdistillerparams << /hwresolution [2400 2400] /pagesize [612.000 792.000] >> setpagedevice microsoft word numero_37_art_9 d. angelova et alii, frattura ed integrità strutturale, 30 (2017) 60-68; doi: 10.3221/igf-esis.37.08 60 focussed on multiaxial fatigue and fracture analysis of fatigue behaviour of stainless steels under hydrogen influence d. angelova university of chemical technology and metallurgy donkaangelova@abv.bg, http://orcid.org/0000-0001-2345-6789 r. yordanova, s. yankova university of chemical technology and metallurgy r.yordanova@uctm.edu, http://orcid.org/0000-0002-2345-6790 svetla_y@abv.bg, http://orcid.org/0000-0002-2345-6791 abstract. three stainless steels – astm 304, 316 and 316l used in hydrogen utilization equipment are under investigation at conditions of tension-compression, rotating-bending and fretting fatigue. fatigue tests are carried out with hydrogen charged and uncharged specimens. hydrogen charging includes cathodic type of charging and exposure to high pressure hydrogen gas. the experiments under rotating bending and tensioncompression fatigue are conducted under different frequencies in three different laboratories: at the university of chemical technology and metallurgy, sofia, bulgaria; at sandia national laboratory, california and the university of tufts, medford, massachusetts, usa; the hydrogenius institute at kyushu university, japan. the fretting fatigue tests are presented by the hydrogenius institute at kyushu university, japan. the obtained results are presented in wöhler curves complemented by plots "short fatigue crack length– number of cycles" and “tangential force coefficient–stress amplitude”. the found fatigue characteristics are analyzed and compared at different loading conditions, showing the best performance of steel 316l. keywords. tension-compression fatigue; rotating-bending fatigue; fretting fatigue; stainless steels; short fatigue crack; hydrogen influence. introduction here are many investigations done into one of the most attractive alternative energy technologies, the hydrogen technology, including hydrogen produce, and hydrogen storage and infrastructure. although over the last years hydrogen vehicles and utilization machines are in active use across the world, there are still questions to be answered about hydrogen influence on fatigue and fretting fatigue of alloys used in hydrogen fuel cells, engines, compressors, storage tanks, pipes and different members of hydrogen transportation elements. the most frequently used alloys are austenitic stainless steels. it is known that hydrogen environment can affect steel microstructure having changed steel crystal lattice mechanical properties and fatigue life. t d. angelova et alii, frattura ed integrità strutturale, 30 (2017) 60-68; doi: 10.3221/igf-esis.37.08 61 our paper presents the results of research on fatigue behavior of austenitic stainless steels at different fatigue and fretting fatigue conditions, which will be used for future characterization, analysis and predictions of fatigue and fretting fatigue in products made of these steels, and subjected to hydrogen-environment influence. materials and experimental work materials tudies of our team on hydrogen influence on metals are focused on analyzing fatigue and fretting fatigue characteristics of three austenitic stainless steels astm 304, 316, 316l (sus304, sus316, sus316l by japanese standard) tab. 1 [1-8]. tests a. fretting fatigue tests the tests are carried out in the hydrogenius institute, kyushu university, japan  kondo et all [3] examine the hydrogen influence on steels 304, 316, 316l by two types of specimens: hydrogen charged and uncharged ones the fretting fatigue tests are carried out under the following conditions: 1. using of an assembly shown in fig. 1a and specimens represented in fig. 1b; 2. pressing contact pads (fig. 1c) against the specimen by tightening the bar springs through clamping bolts; 3. inducing fretting by the difference of deformation between the specimen and contact pads, when a constant amplitude cyclic bending moment applies to the assembled fatigue specimen; 4. the specimens and pads used in the tests are made of the same steel. some specific characteristics of this fretting fatigue testing are connected with the following details [3]. the pads used are bridge type ones with 3mm contact length of each foot in the relative slip direction. the contact edge of each pad is square without chamfer. he 0.5mm foot length is chosen in order to generate a large relative slip range as the effect of steel chemical compositions of steels (wt %) c si mn p s ni cr mo 304 0.06 0.51 0.92 0.033 0.004 8.08 18.8 – 316 0.05 0.49 1.31 0.030 0.027 10.22 17.0 2.04 316l 0.012 0.19 1.64 0.031 0.012 12.19 16.6 2.22 steel mechanical properties of steels condition yield stress re (mpa) ultimate stress rm (mpa) elongation a (%) 304 solution heat-treated 285 637 60 316 solution heat-treated 286 598 59 316l solution heat-treated 212 530 59 table 1: characterisation of used steels (wt %). hydrogen on fretting can be observed clearer at large amount of fretting wear. the contact surfaces of both, the specimen and the pad, are finished by 400 emery paper. a part of an experiment is carried out when the contact surfaces are finished only by grinding for investigating the effect of machining process on fretting fatigue strength. before test starting the contact pressure between the specimen and the contact pad is set up at 100 mpa. it is found that after 10 million cycles of fretting the initial contact pressure drops roughly by 5%. the amount of relative slip is measured by using a small displacement sensor attached at the end of contact pad. the tangential force is measured by a strain gage pasted between the pad feet. the strain of pad is transferred into tangential force by elastic finite element stress analysis. nominal stress s d. angelova et alii, frattura ed integrità strutturale, 30 (2017) 60-68; doi: 10.3221/igf-esis.37.08 62 amplitude applied to the specimen is measured by a strain gage pasted in each specimen. in order to restrict the cracking location, the fretting damage of one pair of the pads is prevented by inserting a thin polyamide film between the contact surfaces. a) b) c) figure 1: fretting fatigue test [3]: a) test assembly; b) specimen geometry (in mm); c) bridge type contact pad. b. fatigue tests the tests are carried out in: the university of chemical technology and metallurgy sofia, bulgaria; the hydrogenius institute, kyushu university, japan; sandia national lab, california & the university of tufts, medford, massachusetts, usa  fatigue research team at the university of chemical technology and metallurgy, sofia, bulgaria [4] investigates and analyses the hydrogen influence on fatigue behaviour of steel 316l the fatigue tests are carried out under the following conditions: 1. using a table model rotating bending machine fatrobem 2004 with a corrosion testing box for environment-assisted short-fatigue-crack-growth investigations and specimens shown in fig. 2a; 2. applied loading conditions: cyclic rotating-bending at room temperature and laboratory air; testing frequency of 11 hz; stress ratio r = −1; stress ranges a and registered corresponding fatigue lifetimes nf presented in tab. 2.  skipper [5] examines the hydrogen influence on steel 316l by two types of specimens: hydrogen charged and uncharged ones. the hydrogen charging of specimens is performed in the following sequence: 1. thermal precharging at 573k in 138 mpa hydrogen gas for more than 30 days; specimen’s freezing before, fter tests for minimizing hydrogen loss; 2. keeping each charged specimen at room temperature for 1 hour before tests; measuring its hydrogen content by inert gas fusion at a commercial vendor. the tests are performed on r. moore rotating beam fatigue testing machine at room temperature, frequency of 50 hz; constant stress range, a ; number of cycles to failure, nf, determined by specimen fracture or when sufficient deformation precluded rotation.  murakami [6-8] investigates the influence of hydrogen on steel 304, 316, 316l using mainly two types of specimens: hydrogen charged and uncharged ones. the fatigue tests are carried out under the following conditions: 1. cathodic and gas environment hydrogen charging; 2. applying of special heat treatment non-diffusible hydrogen desorption heat treatment (ndh-ht) to some specimens for removing non-diffusible hydrogen reaching a level of 0.4 wppm; 3. drilling of small hole with diameter and depth 100 µm into the specimens; 4. tension-compression tests at stress ranges 260, 280 mpa, stress ratio r= −1; frequencies 0.0015, 1.5, 5 hz; a specimen with its hole is shown in fig. 2b; d. angelova et alii, frattura ed integrità strutturale, 30 (2017) 60-68; doi: 10.3221/igf-esis.37.08 63 5. surface replicating of short fatigue crack growth. results and discussion a. fretting fatigue tests he results of fretting fatigue tests are shown in fig. 3a. the effect of hydrogen on tested steels is different: in 304 fretting fatigue limit is lesser in hydrogen gas (by 13 %) than in air, while in 316 only slightly lesser; in 316l this limit is almost a) b) figure 2: fatigue test: a) fatrobem 2004 electric engine 1, driving belt 2, ball-bearing unit 3, test box 4, specimen 5, loading device 6, counter 7, circulation-aeration device 8; b) murakami specimen with a drilled hole of 100 µm; all dimensions in mm. a (мpа) fn (cycles) a (мpа) fn (cycles) a (мpа) fn (cycles) 1 260 3433100 5 340 39600 8 400 129910 2 280 208670 6 360 154000 9 440 38940 3 300 315150 7 380 52030 10 460 9900 4 320 340010 table 2: fatigue life at different stress ranges. the same as that in air [3]. at the same time there was no reduction of fatigue strength of steel 304 in case of plain fatigue in hydrogen gas at low gas pressure condition [9]. on the whole austenitic stainless steels are relatively less affected by hydrogen gas (in terms of fretting fatigue strength) in comparison with aluminum alloys which strength decreases by nearly 60% in hydrogen gas [10]. the best “hydrogen immune” steel is 316l. t d. angelova et alii, frattura ed integrità strutturale, 30 (2017) 60-68; doi: 10.3221/igf-esis.37.08 64 there is a difference in the effect of machining process on the steels; in 304, fretting fatigue strength of polished specimen is lower than that of ground one, while in 316l, there almost is no difference [3]. tab. 3 shows micro vickers hardness of the contact surfaces, measured before and after fretting fatigue test; the hardness of steel 304 is considerably increased by the fretting, while that of 316l is only slightly increased. apart of the different hardening of steels 304 and 316l, there is a correlation between their fretting fatigue strength and hardness, shown in fig. 4a [11]. when the fretting fatigue strength of steels 304 and 316l is evaluated by this diagram – fig. 4a, the hardness effect is evaluated by using the hardness of fretted surface rather than of original surface; the influence of fretting fatigue strength on the hardness might be caused by the heavy work hardening of stainless steels [3]. the tangential force coefficient of steels 304 and 316l is shown in fig. 3b [3]. the effect of absorbed hydrogen in these steels is clarified by their hydrogen charging (before fretting fatigue test) which uses cathodic polarization in dilute sulfuric acid [3]. the results are shown in fig. 4b. in 304, fretting fatigue life is substantially reduced compared to that of uncharged specimen. an increase of charging time reduces fretting fatigue life: the fatigue life of 517-hours pre-charged specimen is reduced to a half of that of an unfretted specimen. such a noticeable reduction cannot be found in 316l. it is important to know that during the fretting a hydrogen absorption into steels is observed. 50 100 150 200 250 1.0e+05 1.0e+06 1.0e+07 1.0e+08 number of cycles to failure s tr e s s a m p lit u d e ( m p a ) air h2 air h2 air h2 air h2 ground polished sus 304 sus 316l sus 304 sus 316l 50 100 150 200 250 1.0e+05 1.0e+06 1.0e+07 1.0e+08 number of cycles to failure s tr e s s a m p lit u d e ( m p a ) air h2polished sus 316 sus 316 a) 50 100 150 200 250 1.0e+05 1.0e+06 1.0e+07 1.0e+08 number of cycles to failure s tr e s s a m p lit u d e ( m p a ) series1 series2 series3 series4 in h2 gas uncharged pre-charged sus 304 sus 316l 417h 95h 517h contact press. = 100 mpa b) figure 3: tests [3]: a) fretting fatigue strength; b) effect of hydrogen pre-charging. d. angelova et alii, frattura ed integrità strutturale, 30 (2017) 60-68; doi: 10.3221/igf-esis.37.08 65 steel mirror finished surface 400 emery polished surface ground surface unfretted fretted in air unfretted fretted in air 304 192 293 369 330 416 316 182 294 301 – – 316l 172 271 290 283 285 table 3: micro vickers hardness of fretted surface (indentation load = 0.245n) formation of martensite due to fretting is observed in steel 304 and not in 316l; it is found as well that hydrogen absorption in 304 contributes to decrease of fretting fatigue strength through: (a) hardening; and (b) formation of martensite due to fretting [3]. 0 100 200 0 100 200 300 400 500 vickers hardness hv f re tt in g f a ti g u e l im it ( m p a ) sus 304 in air sus 316 in air sus 316l in air a) 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 100 120 140 160 180 200 220 240 stress amplitude, a (mpa) t a n g e n ti a l fo rc e c o e ff ic ie n t, ф . h2 air h2 air h2 air ground polished sus 316l sus 304 sus 316l sus 304 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 100 120 140 160 180 200 220 240 stress amplitude, a (mpa) t a n g e n ti a l fo rc e c o e ff ic ie n t, ф . h2 air h2 air h2 air ground polished sus 316l sus 304 sus 316l sus 304 b) figure 4: fretting fatigue [3]: a) dependence “fretting fatigue limit – vickers hardness”; b) tangential force coefficient. d. angelova et alii, frattura ed integrità strutturale, 30 (2017) 60-68; doi: 10.3221/igf-esis.37.08 66 steel 316l , s-n curves σa = 1044.8nf 0,081 r² = 0.9865 σa = 1003.9nf 0,064 r² = 0.9065 a = 1139.1nf 0.1007 r2 = 0.7227 100 200 300 400 500 600 700 1000 10000 100000 1000000 10000000 100000000 number of cycles to failure n f , [cycles] s tr e s s r a n g e , σ a [ m p a ] murakami,uncharged, f=5 hz murakami, charged, f=5 hz skipper, uncharged, f=50 hz skipper, charged, f=50 hz murakami, uncharged, f=1.5 hz murakami, charged , f=1.5 hz murakami, uncharged, f=0.0015 hz murakami, charged, f=0.0015 hz own data, uncharged, f=11 hz group a a = 260 mpa group b a = 280 mpa a) b) c) steel 316l 0 200 400 600 800 1000 1200 1400 1600 1800 2000 0 50000 100000 150000 200000 250000 300000 number of cycles, n f [cycles] c ra c k l e n g th , 2 a [ µ m ] charged, cathodic 4.3 ppm, f = 5 hz uncharged, 2.6 ppm, f = 5 hz charged, cathodic 3.6 ppm f = 1.5 hz uncharged, 2.6 ppm, f = 1.5 hz group a a=260 mpa; steel 316l f = 1.5 hz f = 5 hz 0 200 400 600 800 1000 1200 1400 1600 1800 2000 0 5000 10000 15000 20000 number of cycles, n f [cycles] c ra c k l e n g th , 2 a [ µ m ] charged,gas 3.9 ppm, f = 0.0015hz uncharged,2.6ppm, f = 0.0015hz charged, cathodic 4.3 ppm, f = 1.5 hz uncharged, 2.6 ppm, f = 1.5 hz ndh ht, 0.47 ppm, f = 0.0015 hz group b a=280 mpa; steel 316l f = 0.0015 hz f = 1.5 hz ndh-ht f = 0.0015 hz d) steel 316l , σa= 260 mpa 0.0001 0.001 0.01 0.1 1 10 100 1.e+03 1.e+04 1.e+05 1.e+06 1.e+07 1.e+08 1.e+09 1.e+10 number of cycles, n f [cycles] f, [ h z ] murakami, uncharged, f = 1.5 hz murakami, charged, f = 1.5 hz murakami, uncharged, f = 5 hz murakami, charged, f = 5 hz skipper, uncharged, f = 50 hz skipper, charged, f = 50 hz own, uncharged, f = 11 hz steel 316l , σa= 280 mpa 0.0001 0.001 0.01 0.1 1 10 100 1.e+03 1.e+04 1.e+05 1.e+06 1.e+07 1.e+08 1.e+09 1.e+10 number of cycles, n f [cycles] f, [ h z ] murakami, uncharged, f = 0.0015 hz murakami, charged, f = 0.0015 hz murakami, uncharged, f = 1.5 hz murakami, charged, f = 1.5 hz skipper, uncharged, f = 50 hz skipper, charged, f = 50 hz own, uncharged, f = 11 hz e) steel 316l, frequency influence tendency 0.001 0.01 0.1 1 10 100 1.e+03 1.e+04 1.e+05 1.e+06 1.e+07 1.e+08 1.e+09 1.e+10 number of cycles, n f [cycles] f, [ h z ] uncharged, σa = 260 mpa charged, σa = 260 mpa charged, σa = 280 mpa uncharged, σa = 280 mpa ndh ht, σa = 280 mpa a = 260 mpa a = 260 mpa a = 280 mpa a = 280 mpa a = 280 mpa f) figure 5: tests: wöhler curves, a); curves a-n for steel 304, 280mpa, b) & steel 316l, 260mpa, c); hydrogen influence on fatigue lifetimes at different frequencies, e-f). d. angelova et alii, frattura ed integrità strutturale, 30 (2017) 60-68; doi: 10.3221/igf-esis.37.08 67 b. fatigue tests a comparative analysis between our own results and those obtained by skipper and murakami for steel 316l can be made considering the wöhler curves shown in fig. 5a. the data of skipper and murakami [5-8] presented in fig. 5a show the opposite tendencies in the behavior of the same steel taking into consideration hydrogen charged and uncharged specimens. obviously, in the case of skipper there is classical hydrogen embrittlement while in the case of murakami hydrogen affects the steel microstructure transforming it into martensitic one at the tip of propagating crack – a phenomenon much more pronounced in the case of another austenitic stainless steels as steel 304 and 316 which show more martensitic transformation while stressed than steel 316l, fig. 5b-d [7, 8]. undoubtedly one of the most important factors for this effect is the frequency of testing which assists the penetration of hydrogen on microstructural level. the very low frequency provokes a definite effect of decreased lifetime, fig. 5e-f. at the same time murakami noticed [7] that at very low frequencies even uncharged specimens showed a decrease in their lifetimes due to non-diffusible hydrogen (23 wppm) trapped in the stainless steel during its production. this type of hydrogen is different from the diffusible hydrogen charged into steel by electrochemical methods or gas environment. murakami’s studies on non-diffusible hydrogen show that this hydrogen can be removed by a special heat treatment ndh-ht, which definitely increases uncharged specimen lifetimes the single round symbol in fig. 5f. murakami marks that the non-diffusible hydrogen has not been considered in the previous classical hydrogen embrittlement studies. in both cases of 260, 280 mpa (fig. 5e-f) the hydrogen charged and uncharged specimens of steel 316l show almost the same lifetimes at lower frequencies (0.00155 hz) and smaller lifetimes for the charged specimens at frequencies above 5 hz. so, frequency is the most important factor of influence for steels fatigue in hydrogen media. we should note as well that in fig. 5f the fatigue loading condition above 5 hz changes from tension-compression to rotating-bending. conclusions he hydrogen-energy technology still shows many unsolved problems connected with hydrogen utilization machines, storage tanks, infrastructure, all using austenitic stainless steels; here steels 304, 316, 316l are investigated in hydrogen gas and air, and at pre-charged and uncharged state. now it becomes clear that hydrogen gas influences fretting fatigue of these steels at different machining process and hydrogen pre-charge, changes absorption of hydrogen during fretting, tangential force coefficient and steel fatigue strength, transforms their microstructure to martensitic one. the plain fatigue of the same steels shows some different behaviour of hydrogen charged and uncharged specimens, and the importance of frequency factor which in combination with hydrogen media at high pressure leads to microstructure transformation in martensitic one and diminishes fatigue life of metal members. under both, fretting and plain fatigue, steel 316l shows best characteristics. on the whole more deep knowledge is needed for clarifying hydrogen influence on different steels at different fatigue loading conditions. references [1] murakami, y., the effect of hydrogen on fatigue properties of metals used for fuel cell system, international journal of fracture, 138 (2006), 1-4, 167-195. [2] dowling, n., mechanical behavior of materials, prentice-hall, new jersey (2006). [3] kubota, m., noyama, n., sakae, c., kondo, y., proceedings of ecf16 alexandropolus, greece, 225-234 (2006). [4] todorova, z., angelova, d., yordanova, r., yankova, s., scientific proceedings, xx, 1(133) (2012), 81-84. [5] skipper, c, leisk, g., saigal, a., matson, d., san marchi, c., effect of internal hydrogen on fatigue strenght of type 316 stainless steel, proceedings of international hydrogen conference (asm international), 139-146 (2009). [6] murakami,y. , metal fatigue: effects of small defects & nonmetallic inclusions, elsevier, ox., uk (2002). [7] murakami y. , proceedings of ecf16, brno, czech republic, 25-42 (2008). [8] murakami, y., kanezaki, t., mine, y., hydrogen effect against hydrogen embrittlement, metallurgical and materials transactions, a, 41a (2010) 2548-2562. [9] yoshimura, t., matsuyama, y., oda, y., yoshimura, t., noguchi, h., proc. of icm9, distributed by cd-rom (2003). [10] kubota, m., noyama, n., sakae, c., kondo, y., effect of hydrogen gas environment on fretting fatigue, journal of the society of materials science, japan, 54(12) (2005) 1231-1236. t d. angelova et alii, frattura ed integrità strutturale, 30 (2017) 60-68; doi: 10.3221/igf-esis.37.08 68 [11] kondo, y., sakae, c., kubota, m., sato, s., fretting fatigue limit as a short crack problem at the edge of contact, fatigue & fracture of engineering materials & structures, 27 (2004) 361369. << /ascii85encodepages false /allowtransparency false /autopositionepsfiles true /autorotatepages /none /binding /left /calgrayprofile (dot gain 20%) /calrgbprofile (srgb iec61966-2.1) /calcmykprofile (u.s. web coated \050swop\051 v2) /srgbprofile (srgb iec61966-2.1) /cannotembedfontpolicy /error /compatibilitylevel 1.4 /compressobjects /tags /compresspages true /convertimagestoindexed true /passthroughjpegimages true /createjobticket false /defaultrenderingintent /default /detectblends true /detectcurves 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can be opened with acrobat and adobe reader 5.0 and later.) >> /namespace [ (adobe) (common) (1.0) ] /othernamespaces [ << /asreaderspreads false /cropimagestoframes true /errorcontrol /warnandcontinue /flattenerignorespreadoverrides false /includeguidesgrids false /includenonprinting false /includeslug false /namespace [ (adobe) (indesign) (4.0) ] /omitplacedbitmaps false /omitplacedeps false /omitplacedpdf false /simulateoverprint /legacy >> << /addbleedmarks false /addcolorbars false /addcropmarks false /addpageinfo false /addregmarks false /convertcolors /converttocmyk /destinationprofilename () /destinationprofileselector /documentcmyk /downsample16bitimages true /flattenerpreset << /presetselector /mediumresolution >> /formelements false /generatestructure false /includebookmarks false /includehyperlinks false /includeinteractive false /includelayers false /includeprofiles false /multimediahandling /useobjectsettings /namespace [ (adobe) (creativesuite) (2.0) ] /pdfxoutputintentprofileselector /documentcmyk /preserveediting true /untaggedcmykhandling /leaveuntagged /untaggedrgbhandling /usedocumentprofile /usedocumentbleed false >> ] >> setdistillerparams << /hwresolution [2400 2400] /pagesize [612.000 792.000] >> setpagedevice microsoft word numero_37_art_48 r. sepe et alii, frattura ed integrità strutturale, 37 (2016) 369-381; doi: 10.3221/igf-esis.37.48 369 a robust approach for the determination of gurson model parameters r. sepe, g. lamanna, f. caputo department of industrial and information engineering second university of naples, via roma, 29 81031 aversa, italy raffsepe@unina.it abstract. among the most promising models introduced in recent years, with which it is possible to obtain very useful results for a better understanding of the physical phenomena involved in the macroscopic mechanism of crack propagation, the one proposed by gurson and tvergaard links the propagation of a crack to the nucleation, growth and coalescence of micro-voids, which is likely to connect the micromechanical characteristics of the component under examination to crack initiation and propagation up to a macroscopic scale. it must be pointed out that, even if the statistical character of some of the many physical parameters involved in the said model has been put in evidence, no serious attempt has been made insofar to link the corresponding statistic to the experimental and macroscopic results, as for example crack initiation time, material toughness, residual strength of the cracked component (r-curve), and so on. in this work, such an analysis was carried out in a twofold way: the former concerned the study of the influence exerted by each of the physical parameters on the material toughness, and the latter concerned the use of the stochastic design improvement (sdi) technique to perform a “robust” numerical calibration of the model evaluating the nominal values of the physical and correction parameters, which fit a particular experimental result even in the presence of their “natural” variability. keywords. crack propagation; gurson-tvergaard model; stochastic design improvement; fem. introduction ecause of the increasing use of the aluminium alloys with high fracture resistance features in the field of the aerospace industry, the study of the techniques for the experimental determination of the fracture toughness and the research of the methodologies to transfer such results to the real structures have been subject of great interest for the scientific community in recent years. in fact, it is well known that the macroscopic parameters of the classical fracture mechanics theory, such as the stress intensity factor (k), the j integral [1], the ctod (crack tip opening displacement), the ctoa (crack tip opening angle) [2], the extension of the plastic zone at the crack tip (rp) [3-7], cannot be easily transferred from one geometry to another, since they strictly depend on it. within this scenario, the parallel spreading of advanced techniques of numerical simulation has allowed the development of numerical models with which it is possible to obtain very useful results for a better understanding of the physical phenomena involved in the macroscopic mechanisms of propagation. among the most promising models introduced in recent years the one proposed by gurson-tvergaard (gt) links the b r. sepe et alii, frattura ed integrità strutturale, 37 (2016) 369-381; doi: 10.3221/igf-esis.37.48 370 propagation of a crack to the nucleation and growth of micro-voids in the material, and then it is able to connect the micromechanical characteristics of the component under examination to crack initiation and propagation up to a macroscopic scale. the three stages of nucleation, growth and coalescence of micro-voids are well established results of metallographic observation for polycrystalline metals at ductile failure. the simulation of these microstructural damage processes has been considered in various micromechanical and macromechanical model approaches in the literature. a macromechanical model can be exactly obtained by the statistical averaging of microscopic quantities in a homogenization process. the gurson model [8], which derived a macroscopic yield function and an associated constitutive flow law for an ideally plastic matrix containing a certain volume fraction of spherical voids, is a well-known analytical approach to this problem. empirical modifications of this approach have been proposed to improve the prediction at low void volume fractions [9] and to provide a better representation of final void coalescence [10]. it must be pointed out that even if the statistical character of some of the physical parameters involved in this model has been put in evidence, no effective attempt has been made insofar to relate the corresponding statistic to the experimental results, as for example the r-curve [1,11]. in the first part of the work, after briefly recalling the ductile fracture mechanism and the classical approach to determine the parameters of the gt model, we pointed out the main aspects of the stochastic design improvement (sdi) technique [12], implemented in the commercial code st-orm [13], which can be coupled with specialized fem codes as lsdyna [14] or warp 3d [15] for what concerns the deterministic structural part of the process; we then illustrated the use of the sdi technique to perform a robust numerical calibration of the parameters of the gt model. in the second part of the work, some numerical results regarding a simple structural component are shown, pointing out the influence of the statistical distribution of the physical parameters of the gt model on the toughness of the considered material. material toughness was numerically evaluated both in terms of the critical value of the j-integral, by using the equivalent domain integral method [16] implemented in the finite element code warp 3d, and in terms of critical applied load, by using the explicit finite element code ls dyna. in this case, as the load is monotonically increased by applying increments that are considered to be constant in time, the critical load value is univocally linked to a correspondingly crack propagation initiation time. for the validation of the numerical results, experimental data from literature are used [17-18]. ductile fracture mechanisms: overview on the gurson-tvergaard model s it is well known, a typical process of ductile fracture develops through the nucleation and the following growth and coalescence of cavities nucleated at crack tip. the best known nucleation mechanisms of such cavities are those linked to the presence of hard particles (inclusions or precipitates) in a ductile matrix (base material). in such cases, the brittle failure of a particle or its decohesion from the matrix, because of the interface breaking, leads to the nucleation of small voids, whose growth causes real cavities in the material. it is clear that the toughness of a material increases for smaller dimensions of such particles and for increasing mean distance and homogeneity of the distribution of such inclusions. from an analytical point of view, we can observe that a void nucleates when the elastic potential energy associated with the material surrounding the particles reaches a particular value, which can be determined by following one of the two approaches, which, even if rather different from each other, lead to similar or equivalent conclusions. the first one is based on the existence of a critical value of the strain in the direction of the applied load, and the second one on the existence of a critical value of the stress in the same direction [19]; once such critical values are overcome, the amount of elastic potential energy necessary for the voids nucleation is considered as reached. as those critical values for both stress and strain are usually low, the nucleation process develops rather easily; therefore, the ductile failure of metallic materials depends substantially on the way the cavities grow and coalesce, rather than on their nucleation. as a rule, a growing cavity is modelled as an ellipsoid of revolution, whose major axis (2b) is parallel to the direction of the load. as the strain increases, the cavity grows in volume while keeping its minor axis equal to the initial mean dimension r0 of the enclosed particle considered to be non-deformable, and b varying along with the deformation in the load direction, a r. sepe et alii, frattura ed integrità strutturale, 37 (2016) 369-381; doi: 10.3221/igf-esis.37.48 371 according to the relation:  0 3 2b r e  (1) as we can see, the bigger the initial radius of the particle the larger the cavity will be, for a given strain. in analogy, if x0 is the initial average distance between the particles, the current value of the average distance, x, can be written as: 20x x e    (2) this equation states that the applied load leads to a reduction of the distance between the particles, which is added to the increasing effect of the cavity dimensions. as a consequence of those assumptions, high-localised stresses are produced into the surrounding material, which can lead to a coalescence phenomenon of near cavities if a critical value of strain (f) is reached. this critical value is strictly related to the strain hardening coefficient of the material, n: high values of n mean that the strain peaks are transferred to less strained surrounding zones; consequently, the contraction of the material between the cavities becomes less localized, and the coalescence of the cavities delayed. once the critical strain is reached, the ratio b/x exhibits a limit value that can be expressed as follows:       1 1 30 32 2 0 0 4 / 3 2 3 2 3 f f f f cr r b x e e f e e x               (3) which, rearranging the terms, leads to an equation, which let us evaluate the critical strain:   1 1 3/2 3 0 4 3 2 3 f f cr b e e f x                 (4) in the previous equation the critical strain, f is implicitly showed as dependent on the initial volume fraction of the particles, f0. rice and johonson [20], assuming that the crack tip is located at distance xo from the nearest cavity with radius r0, formulated a bi-dimensional model for the localised strain and the coalescence process of cavities. the crack tip opening displacement, at the conditions for which the coalescence between the growing cavity and the plastically deformed crack tip occurs, represents the ctodi value at which the crack starts to growth. intuitively, for a fixed space between the particles, the ctodi is bigger if the volumetric ratio is smaller. experimentally, it has been found a relation like ctodi/x0 = cost · εf and, according to some detailed finite element analyses, as well as experimental tests, that constant can be assumed to be function, g, of the square of the hardening coefficient of the material, n [21]. therefore, the following equation can be considered: 20 ( )i fctod x g n   (5) according to this expression, the value of ctodi could be converted in an equivalent value of fracture toughness kic, by means of the well-known relationship: 2 0.5 i ci k ctod e  (6) where  represents the yielding stress of the material; from the eqs. (4) and (6) follows: r. sepe et alii, frattura ed integrità strutturale, 37 (2016) 369-381; doi: 10.3221/igf-esis.37.48 372 1 1 6 6 0 0 0 4 ( ) 2 ( ) 2 3 ic f fk g n e x g n e r f               (7) the above equation states that in the limit state preceding the coalescence of voids and, therefore, the crack growth, the fracture toughness kic of the material depends on the power (–1/6) of the initial volumetric void fraction, f0, and on the basic material parameters (e,  , n) as well as on the initial dimension of the particles, r0. based on an equivalent approach, the gt model provides a constitutive relation for the increasing of the volumetric void fraction up to the starting of the coalescence phenomenon. the coalescence phenomenon is not accounted for in the model, as the basic assumption of the model theory is the homogeneity of the strain field, and therefore it does not allow reliable prediction in the case of localised strain phenomena. this limit of the gurson model can be overcome if a critical value of the cavities volume fraction is introduced; the coalescence phenomenon starts when the actual volume fraction of cavities reaches this critical value, as explained below. fortunately, it was possible to find a strong dependency of this critical volume fraction, fc, from its initial value f0 and therefore from the cavity radius, r0, and from the distance from the crack tip, x0. the original gurson model considers a rigid sphere of perfectly plastic material, encapsulating a spherical cavity under a homogenous strain. the derived model that can also consider material hardening, called the gurson-tvergaard model [10], can follow the growth of the volume fraction of existing cavities from f0 to fc and can be written as:     2 22 1 32 3 , , , 2 cosh 1 0 2 m m q f q f q f                (8) where q1 ,q2 and q3 are correction parameters introduced by tvergaard [9] (in order to take into account the hardening behaviour of material), σm is the average normal stress, σ is the equivalent von mises stress; with such model it is possible to predict the cavity growth ratio in the plastic field. for real components, where many inclusions are to be found, the gt model considers that the volume fraction of voids increases over an increment of load because of both the continuing growth of existing voids and the nucleation of new voids; this is taken into account by increasing the void growth rate linked to the actual plastic strain flow at crack tip, (1 ) pgrowthdf f d  , by a quantity, ( )nucleationdf a d  , where: 2 1 ( ) exp 22 n n nn f a ss                (9) therefore, the introduced nucleation parameters are:  fn: particles volume fraction from which the nucleation of cavities can take place;  n and sn: mean value and standard deviation of the supposedly normal distribution of the critical strain value at which the nucleation takes place. as it is possible to observe, the nucleation acceleration, driven by the parameter a, is limited to an internal strain condition in which the actual equivalent strain  is quite close to n . anyway, the nucleation phenomenology is of complex understanding and, even though some results from metallographic analyses about particle distribution and concentration are available, it is not sure if voids nucleate from all of them; this implies that the particles total volume fraction obtained by the metallographic analyses cannot be directly used as parameter in the gt model [22]. within this work, the values of the physical parameters of the gt model related to the nucleation mechanism were calibrated by adapting numerical and available experimental results by means of an iterative process that is described in the following pages. this crack growth mechanism leads to a numerical model characterised by cubic elements parallel to the crack plane; all those elements, which are equal in dimensions, exhibit material properties according to the gt model. each element represents an elementary cell of material containing an initial cavity volume fraction, fo; the cell dimension, do, is comparable with the distance between the largest inclusions detected by microscopic analyses at the interior of the bulk material. according to the gt model, the volumetric fraction of the cavities increases with the stress-strain state; because r. sepe et alii, frattura ed integrità strutturale, 37 (2016) 369-381; doi: 10.3221/igf-esis.37.48 373 of the induced softening of the surrounding material the critical value of cavity volume fraction, fc, can be reached and, in this case, the coalescence starts. from a numerical point of view, when the coalescence of the cavities starts, the cell elements reduce their ability to equilibrate the applied load, according to a given parameter,  , which can be expressed as follows:  0 0 1.0 0 1.0 d d d         (10) where d is the effective cell dimension, 0d is the cell dimensions at the time at which f = fc and  is a numerical parameter. from the considerations above, it follows that the gt model must be calibrated for every chosen material if it wants to be considered as a valid tool for fracture mechanics analysis within the non linear field. calibration of the gt model parameters. he numerical calibration of the gt model parameters can be carried out with a two-step procedure [23-24]. the first stage involves, on a micro-mechanical scale, the correction parameters, q1, q2 (q3=q12 [15]), the fixing of the physical parameters (, fc) and of the geometric ones (do, fo) on the basis of experimental considerations. the second stage involves, on a macro-mechanical scale, the geometric parameters (do, fo). for what concerns the parameters governing the nucleation mechanism of cavities, as already noted, they can be initially roughly determined by experimental data related to the initial distribution of the particles in a material sample, while their final refined values can be determined in the second stage of the calibration process. beside these parameters, it is obviously necessary to know the material properties of the base material (e , n), or the relationshipfrom a standard tensile test. the validity and the reliability of the gt model are strongly dependent on the correct determination of all the aforesaid parameters and material properties, which can be summarized as follows: elastic-plastic material model parameters: n,   ; tvergaard correction parameters: q1, q2, q3 ; nucleation process parameters: fn, n ,sn; initial dimension of the elementary cell: d0; initial and critical cavities volume fraction: f0, fc; parameter . in the present work, the first stage of the calibration was performed by comparing two different numerical models: the first one (reference model) was built using ansys code. the model (fig. 1) was a cubic three-dimensional cell, with an initial characteristic dimension do of the same order of magnitude of the distance between the largest inclusions (100 m), having the same material properties as the base material with a spherical cavity in the centre. a second fem model (developed with warp 3d v.14.2 code) consists of a unique 8-noded cubic finite element, whose material shows a constitutive law based upon the gt model, with parameters relative to the base material and to the cavity volume fraction equal to those adopted in the previous reference model. in the first stage of the calibration the stress-strain curve, obtained from the reference model under given boundary conditions, was compared with the curve obtained in the same conditions by the second model, on the basis of the maximum stress and of the work needed to deform the cell [23-24]. all the combinations of q1, q2 e q3 that give the smallest difference of the said quantities in the second model, with respect to those obtained from the reference model, can be used as parameters of the gt model for the considered material. the second stage of the calibration process enabled to evaluate the parameters d0 and f0, as well as the nucleation parameters fn, n and sn , by fitting the numerical r-curves to the experimental one. anyway, metallographic analyses and numerical calculations suggest that an indicative value of d0 can be given by the crack tip opening displacement (ctodi) at the beginning of the propagation process [23-24], which depends on the average distance between the largest inclusions in the material. this value of the ctod can be measured with standard static propagation tests carried out on a ct specimen [25]. t r. sepe et alii, frattura ed integrità strutturale, 37 (2016) 369-381; doi: 10.3221/igf-esis.37.48 374 figure 1: elementary cell fe model. the sdi process set of techniques was introduced in order to obtain a robust design, i.e. one whose behavior is rather insensitive to all variations of the main variables, or, what is the same thing, a design whose statistics are characterized by the smallest standard deviation, as a function of the statistics of input. this approach can be also linked to another very relevant question; the result of an experimental test carried on an assigned structure is the consequence of the particular and real values of all design variables, whose density functions are supposed to be known: when we try to correlate the test results to a numerical simulation procedure, we want, in effect to assess all other aspects stated, which are the values that the design variables had in the real structure tested in that particular experiment. both these problems can be effectively dealt with by an sdi (stochastic design improvement) [12] process, which is carried out by means of several mc series of trials (runs) as well as of the analysis of the intermediate results. in fact, input – i.e. design variables x – and output – i.e. target y – of a mechanical system can be connected by means of a functional relation of the type  y f x (11) which, in the largest part of the applications, cannot be defined analytically, but only ideally deduced because of its complex nature; in practice, it can be obtained by considering a sample xi and examining the response yi, which can be carried out by means of a simulation procedure and, first of all, by means of one of m-c techniques, as recalled above. considering a whole set of m-c samples, the output can be expressed by a linearized taylor expansion centered about the mean values of the control variables, as      i x i x y i x d f y f μ x μ μ g x μ d x       (12) where i represents the vector of mean values of input/output variables, and where the gradient matrix g can be obtained numerically, carrying out a multivariate regression of y on the x sets obtained by m-c sampling. if y0 is the required target, we could find the new x0 values by inverting the relation above, i.e. by  10 0x yx μ g y μ   (13) as we are dealing with probabilities, the real target is the mean value of the output, which we compared with the mean value of the input, and considering that, as we shall illustrate below, the procedure will evolve by an iterative procedure, it can be stated that the relation above has to be modified as follows, considering the update between the k-th and the (k+1)-th step: a r. sepe et alii, frattura ed integrità strutturale, 37 (2016) 369-381; doi: 10.3221/igf-esis.37.48 375    1 10 1 , 1 , , 0 ,x x,k x k y,k y k x k y y kμ μ μ g μ μ μ g μ μ         (14) the sdi technique is based on the assumption that the cloud of points corresponding to the results obtained from a set of mc trials can be moved toward a desired position in the n-dimensional space such as to give the desired result (target), and that the amplitude of the required displacement can be forecast through a close analysis of the points that are in the same cloud (fig. 2): in effects, it is assumed that the shape and the size of the cloud don’t change greatly if the displacement is small enough; it is therefore immediate to realize that an sdi process is composed by several sets of mc trials (runs) with intermediate estimates of the required displacement (fig. 3). figure 2: initial and final structural responses. figure 3: sdi process. it is also clear that the assumption about the invariance of the cloud can be maintained just in order to carry out the multivariate regression which is needed to perform a new step – i.e. the evaluation of the g matrix – but that subsequently a new and correct evaluation of the cloud is needed; in order to save time, the same evaluation can be carried out every k steps, but of course, as k increases, the step amplitude has to be correspondently decreased. it is also immediate that the displacement is obtained by changing the statistics of the design variables and, in particular, by changing their mean (nominal) values, as in the now available version of the method all distributions are assumed to be r. sepe et alii, frattura ed integrità strutturale, 37 (2016) 369-381; doi: 10.3221/igf-esis.37.48 376 uniform, in order to avoid the gathering of results around the mode value. it is also pointed out that sometimes the process fails to accomplish its task because of the existing physical limits, but in any case sdi allows to quickly appreciate the feasibility of a specific design, therefore making easier its improvement. of course, it may happen that other stochastic variables are present in the problem (the so called background variables): they can be characterized by any type of statistical distribution included in the code library, but they are not modified during the process. therefore, the sdi process is quite different, for example, from the classical design optimization, where the designer tries to minimize a given objective function with no previous knowledge of the minimum value, at least in the step of the problem formulation. on the contrary, in the case of the sdi process, it is firstly stated what is the value that the objective function has to reach, i.e. its target value, according to a particular criterion that can be expressed in terms of maximum displacement, maximum stress, and so on the sdi process gives information about the possibility to reach the objective within the physical limits of the problem and determines which values the project variables must have in order to get it. in other words, the designer specifies the value that an assigned output variable has to reach and the sdi process determines those values of the project variables which ensure that the objective variable becomes equal, in the mean sense, to the target. therefore, according to the requirements of the problem, the user defines a set of variables as control variables, which are then characterized from an uniform statistical distribution (natural variability) within which the procedure can let them vary, observing the corresponding physical (engineering) limits. in the case of a single output variable, the procedure evaluates the euclidean or mahalanobis distance of the objective variable from the target after each trial: *d = y -y i =1,2,…,nii (15) where yi is the value of the objective variable obtained from the i-th iteration, y* is the target value and n is the number of trials per run. then, it is possible to find, among the worked trials, that one for which the said distance gets the smallest value and, subsequently, the procedure redefines each project variable according to a new uniform distribution with a mean value equal to that used in such “best” trial. the limits of natural variability are accordingly moved of the same quantity of the mean in such way as to save the amplitude of the physical variability. if the target is defined by a set of output variables, the displacement toward the condition where each one has a desired (target) value is carried out considering the distance as expressed by:  2*d = y -yki i,k k (16) where k represents the generic output variable. if the variables are dimensionally different it is advisable to use a normalized expression of the euclidean distance:  2d = ω δi k i,k (17) where: yi,k *δ = -1, if y 0i,k k*yk *δ = y if y = 0i,k i,k k  (18) but, in this case, it is of course essential to assign weight factors k in order to define the relative importance of each variable. r. sepe et alii, frattura ed integrità strutturale, 37 (2016) 369-381; doi: 10.3221/igf-esis.37.48 377 several variations of the basic procedures are available; for example, it is possible to define the target by means of a function which implies an equality or an inequality, too; in the latter case the distance is to be considered null if the inequality is satisfied. once the project variables have been redefined a new run is performed and the process restarts up to the completion of the assigned number of shots. it is possible to plan a criterion of arrest in such way as to make the analysis stop when the distance from the target reaches a given value. in the most cases, it is desirable to control the state of the analysis with a real-time monitoring, with the purpose to realize if a satisfactory condition has been obtained. sensitivity analysis n this paragraph a sensitivity analysis of the nucleation parameters and of the main mechanical properties of the material on the material toughness of a thin plate made of aluminium alloy 2024 t3, with a through crack in the middle transversal section, was performed. the values of the material properties used are:  = 324 mpa,  = 0.0045, n = 9.8; for what concerns the tvergaard parameters they were set equal to q1 = 1.255, q2 = 1.20, q3 = 1.58, as obtained from the calibration of the model performed in [26]; the other necessary physical parameters values were derived from literature and put equal to f0 = 0.09, d0 = 0.15 mm, fc = 0.2 and0.1; the first attempt value for the nucleation parameters were set equal to n = 0.3, sn = 0.5, fn = 0.05, which represents the default values in the algorithms of the warp 3d code. the dimensions of the plate were 800 mm in the longitudinal direction, 600 mm in the transversal direction and 1.6 mm in the thickness. the static crack propagation test, from both a numerical and an experimental point of view, were developed by considering a uniform applied longitudinal displacement at both the ends of the plate. the experimental results are available in [18]. at first, the experimental r-curve of the plate was compared with a numerical one (fig. 4), obtained by using the warp 3d code; the used fe model consisted of 33216 nodes and 23680 8-noded solid elements. the elements linked to the nodes belonging to the crack plane were modelled by considering a material model based on the gt criterion, as implemented in the used code. as it is shown in the plot of the fig. 4, in the range of the considered crack elongation, numerical results are in good agreement with the experimental ones: the two r-curves are quite parallel. further developed numerical investigations show that the distance between the numerical and the experimental r-curves depends substantially on the values considered for the nucleation parameters in the gt model.   0 20 40 60 80 100 120 140 160 0 2 4 6 8 10 crack elongation (mm) re m o te s tr e ss ( n /m m 2 ) numerical experimental figure 4: r-curve: numerical-experimental correlation. i r. sepe et alii, frattura ed integrità strutturale, 37 (2016) 369-381; doi: 10.3221/igf-esis.37.48 378 in order to clarify the influence of the nucleation parameters fn, n and sn on the material toughness at the beginning of the crack propagation (output variable), that is, on the start point of the r-curve, a sensitivity analysis was developed; results are reported as a pie-chart in fig 5. as it is possible to observe, the most meaningful influence on the output variable is due to the parameter fn; for the variables distribution the following realistic characteristics were assumed: fn  n(0.05; 0.01), n  n(0.3; 0.06); sn n(0.5; 0.1). figure 5: sensitivity analysis results. the commercial code used to develop the sensitivity analyses is the st-orm code, linked to the ls-dyna code for what concerns the deterministic structural results. in this code the gt model can be related only to shell type elements under plane stress conditions. the cumulative density function (cdf), the mean and the standard deviation of the output variable obtained for an increasing number of mc trials, are respectively reported in the plots of figs. 6-8. the mean and the standard deviation of the crack initiation time show quite constant values after about eighty mc iterations. that reached mean value corresponds to a critical remote stress of 74 n/mm2, which differs from the experimental results of a few percent. as it is possible to observe from the plot of the standard deviation versus the mc iteration number, the reached value of the standard deviation of the crack initiation time is about 10.6, which implies a high probability of varying the critical remote stress of about ± 3% of its mean value, given the considered statistics of the nucleation parameters, i.e. the same order of magnitude of the difference between the numerical and the experimental results. from this considerations, it is possible to conclude that the influence of the calibration of the nucleation parameters is quite low in the reference case, even in case their intervals of variation are rather large. after this, an investigation on the influence of the variability of the mechanical material properties on the same output variable was developed. figure 6: cfd of the crack init. time [ms] r. sepe et alii, frattura ed integrità strutturale, 37 (2016) 369-381; doi: 10.3221/igf-esis.37.48 379 figure 7: mean of the crack init. time [ms] vs. mc trial. figure 8: std dev. of the crack init time [ms] vs. mc trial. the scale factor of the stress-strain curve along the stress axes was chosen as the input random parameter, with a normal distribution n (1;0.1). in the following figs. 9-11 the cumulative density function, the mean and the standard deviation of the crack initiation time, related to the variability of the stress-strain curve, vs. the mc trial number, are respectively reported. figure 9: cfd of the crack init. time [ms]. r. sepe et alii, frattura ed integrità strutturale, 37 (2016) 369-381; doi: 10.3221/igf-esis.37.48 380 figure 10: mean of the crack init. time [ms] vs. mc trial. figure 11: std dev. of the crack init. time [ms] vs. mc trial. in this case, the variability of the critical remote value can reach the 8% of its mean value, which is a rather appreciable difference to be taken into account when we try to fit the experimental results with numerical ones. conclusions he use of the sdi approach to calibrate the physical and correction parameters of the gt model is an useful numerical tool that provides a numerical model able to well represent the real development of the considered phenomena even if the involved physical parameters are subjected to natural variability. within this work we investigated on the feasibility to apply the sdi approach, and we used it to calibrate the physical nucleation parameters of the gt model. the results were satisfactory and the r-curve of the examined component, obtained by using the nominal value of the found nucleation parameters, is in good agreement with the experimental one. in the last paragraph, some sensitivity analyses showed that the natural scatter of the material properties and of the nucleation parameters around their “nominal” value do not influence considerably the toughness of the material in the considered reference case. references [1] newman jr., j.c. the merging of fatigue and fracture mechanics concepts: a historical perspective, progress in aerospace sciences. 34 (1998) 347-390. t r. sepe et alii, frattura ed integrità strutturale, 37 (2016) 369-381; doi: 10.3221/igf-esis.37.48 381 [2] newman jr. j.c., james, m.a., zerbst, u., a review of the ctoa/ctod fracture criterion, engineering fracture mechanics, 70 (2002) 371-385. [3] heung-bae, p., kyung-mo, k., byong-whi, l., plastic zone size in fatigue cracking, int. j. pres ves. & piping, 68 (1996) 279-285. [4] armentani, e., caputo, f., esposito, r., soprano, a., plastic zone size as epfm parameter, key engineering materials, 251-252 (2003) 173-178. [5] caputo, f., lamanna, g., soprano, a., on the evaluation of the plastic zone size at the crack tip. engineering fracture mechanics, 103 (2013) 162-173. [6] caputo, f., lamanna, g., soprano, a., crack tip parameters under large scale yielding condition. sdhm structural durability and health monitoring, 9(3) (2014) 217-232. [7] sepe, r., armentani, e., caputo, f., lamanna, g., numerical evaluation and experimental comparison of elastoplastic stress-strain distribution around the corner cracks of a notched specimen. procedia engineering. 109 (2015) 285-295. [8] gurson, a.l., continuum theory of ductile rupture by void nucleation and groeth: part i – yeld criteria and flow rules for porous ductile media, j. of eng. materials and technology. 99(1) (1977) 2-15. [9] tvergaard, v., influence of voids on shear band instabilities under plane strain conditions, int j fract., 17 (1981) 389–407. [10] tvergaard, v., needleman, a., analysis of the cup-cone fracture in a round tensile bar, acta metall., 32 (1984) 57– 169. [11] luxmoore, a.r., an r-curve assessment of stable crack growth in an aluminium alloy. mechanics, automatic control and robotics. 3 (2003) 583-597. [12] doltsinis, i., rau, f., werner, m., analysis of random systems. a publication of cimne, edited by i. doltsinis. barcelona, spain, (1999) 9-149. [13] easi: st-orm ver. 2.2 user’s manual. easi engineering gmbh. alzenau, germany; (2002). [14] lstc: ls-dyna ver. 9.60 user’s manual. livermore software technology corporation; livermore, ca; (2001). [15] gullerud, a.s., koppenhoefer, k.c., roy, a., dodds, jr., r.h., warp 3d manual ver. 13.8. department of civil engineering, university of illinois at urbana–champaign, illinois, usa; (2000). [16] nikishkov, g.p., atluri, s.n., calculation of fracture mechanics parameters for an arbitrary three-dimensional crack, by the ‘equivalent domain integral’ method. int. j. for numerical methods in engineering. 24 (1987) 1801-1821. [17] hoeve, h.j., schra, l., michielson, a.l.p.j., vlieger, h., residual strength test on stiffened panels with multiple-site damage. technical report n° dot/faa/ar-98/53. u.s. department of trasportation; (1999). [18] gullerud, a.s., dodds jr., r.h., hampton, r.w., dawicke, d.s., three-dimensional modelling of ductile crack growth in thin sheet metals: computational aspects and validation. eng. fracture mechanics, 63 (1999) 347-374. [19] zhang, z.l., thaulow, c., ødegård, j., a complete gurson model approach for ductile fracture, engineering fracture mechanics, 67 (2000) 155-168. [20] rice, j.r., johnson, m.a., inelastic behavior of solids. new york: mcgraw-hill, (1970) 641. [21] xue, h., shi, y., ctod design curve in consideration of material strain hardening, int. j. of pressure vessels and piping, 75 (1998) 567-573. [22] bolotin, v.v., reliability against fatigue fracture in the presence of sets of cracks, eng. fracture mechanics, 53 (1996) 753-759. [23] gao, x., faleskog, j., shih, c.f., cell model for nonlinear fracture analysis i. micromechanics calibration. international journal of fracture, 89 (1998) 355-373. [24] gao, x., faleskog, j., shih, c.f., cell model for nonlinear fracture analysis ii. fracture process calibration and verification. international journal of fracture. 89 (1998) 375-398. [25] astm e 561. standard practice for r–curve determination. american society for testing and materials; (2010). [26] caputo, f., lamanna, g., soprano, a., armentani, e., valutazione numerica della resistenza residua di componenti criccati in lega di alluminio 2024 t3. proceedings of the xxxiii aias conference. bari. italy; (2004). << /ascii85encodepages false /allowtransparency false /autopositionepsfiles true /autorotatepages /none /binding /left /calgrayprofile (dot gain 20%) /calrgbprofile (srgb iec61966-2.1) /calcmykprofile (u.s. web coated \050swop\051 v2) /srgbprofile (srgb iec61966-2.1) /cannotembedfontpolicy /error /compatibilitylevel 1.4 /compressobjects /tags /compresspages true /convertimagestoindexed true /passthroughjpegimages true /createjobticket false /defaultrenderingintent /default /detectblends true /detectcurves 0.0000 /colorconversionstrategy /cmyk /dothumbnails false /embedallfonts true /embedopentype false /parseiccprofilesincomments true /embedjoboptions true /dscreportinglevel 0 /emitdscwarnings false /endpage -1 /imagememory 1048576 /lockdistillerparams false 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/hrv (za stvaranje adobe pdf dokumenata najpogodnijih za visokokvalitetni ispis prije tiskanja koristite ove postavke. stvoreni pdf dokumenti mogu se otvoriti acrobat i adobe reader 5.0 i kasnijim verzijama.) /hun 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/pdfxoutputintentprofileselector /documentcmyk /preserveediting true /untaggedcmykhandling /leaveuntagged /untaggedrgbhandling /usedocumentprofile /usedocumentbleed false >> ] >> setdistillerparams << /hwresolution [2400 2400] /pagesize [612.000 792.000] >> setpagedevice microsoft word numero_41_art_24.docx a. carpinteri et alii, frattura ed integrità strutturale, 41 (2017) 175-182; doi: 10.3221/igf-esis.41.24 175 focused on crack tip fields fracture toughness of rough and frictional cracks emanating from a re-entrant corner andrea carpinteri, andrea spagnoli, michele terzano, sabrina vantadori department of engineering and architecture, university of parma, viale usberti 181/a, 43124 parma, italy spagnoli@unipr.it abstract. in mixed-mode conditions, the competing contribution of the different stress intensity factors predicts fracture initiation load as well as crack propagation direction. commonly, mixed-mode fracture resistance is based on the assumption of smooth and frictionless cracks. however, the effect of friction and roughness cannot be neglected when mixed mode loading occurs, as in the case of a crack emanating from a re-entrant corner. in this paper, the effect of friction and roughness is evaluated through a simple saw-tooth model in a three-quarter-infinite plane (corresponding to a 90 degree re-entrant corner). the crack surfaces are assumed to be globally smooth, and roughness and friction are incorporated through a constitutive law between opposite crack surfaces. the solution is found using the distributed dislocation method, and an iterative algorithm is needed due to the non-linearity of the model. the effect of friction and roughness angle is discussed for a simple case. keywords. fracture toughness; friction; roughness; distributed dislocation method; re-entrant corner. citation: carpinteri, a., spagnoli, a., terzano, m., vantadori, s., fracture toughness of rough and frictional cracks emanating from a re-entrant corner, frattura ed integrità strutturale, 41 (2017) 175-182. received: 28.02.2017 accepted: 15.04.2017 published: 01.07.2017 copyright: © 2017 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. introduction significant part of fracture mechanics deals with the determination of stress intensity factors and fracture toughness, used to predict the load as well as the angle of crack propagation. a large number of analyses has been carried out, and stress intensity factors at the crack tips are available in literature, for instance in the compendium by murakami [1]. a case of interest in practical applications is that of a short crack emanating from a re-entrant corner in a body under general loading conditions, where often multiple-parameter characterization of the crack/notch tip stress/strain field is required. if the crack is short compared to the other sizes of the body, the effect of other free boundaries can be neglected and the loading experienced by the crack in this geometry is well described by the williams asymptotic solution [2]. in particular, the problem of a smooth and frictionless crack lying on the projection line of a a a. carpinteri et alii, frattura ed integrità strutturale, 41 (2017) 175-182; doi: 10.3221/igf-esis.41.24 176 three-quarter-infinite plane (fig. 1) has been solved by churchmann and hills [3], by applying a distribution of dislocations along the line to clear the stresses coming from the williams asymptotic fields. observing the cracks in many materials of common use, such as concrete, ceramic or rocks, it can be noted that the crack surfaces are not smooth but typically present a certain degree of tortuosity [4,5]. in this case, the assumption of smooth surfaces, which is commonly made in fracture mechanics, is acceptable only when a pure mode i loading occurs, while the effects of roughness and friction cannot be neglected for mode ii or mixed mode loadings [6], since the normal and tangential displacements of a point along the crack are always coupled. we can note that this is precisely the case of the crack lying on the projection line of a three-quarter plane, because the asymptotic stress fields are uncoupled along the bisector of the re-entrant corner but we always have mixed mode loading on the projection line. a simple way to take into account the effects of friction and roughness is to assume the crack surfaces as globally smooth and introduce the normal-tangential coupling along the contact surfaces, the so called dilatancy, through a rigid-plastic constitutive law [7], described by a slip rule and a slip potential. the presence of friction and roughness gives rise to a stress state on the crack surfaces which is dependent on the relative displacements between opposing points of the crack, thus the resulting problem is non-linear. the behaviour of smooth frictional cracks under cyclic loading has been for instance investigated in [8], with particular focus on the conditions of adaptation whereas shakedown analysis for discrete systems involving both friction and plasticity has more recently been studied in a very general form in [9]. in this paper, the effect of roughness and friction is taken into account for a crack emanating from a three-quarter-infinite plane (fig. 1) and the resulting non-linear problem is solved using the iterative algorithm introduced in [6]. stress intensity factors are computed for different values of the coefficient of friction and the roughness angle. figure 1: sketch of the considered problem. a short crack c ≪ a is present along the projection line of a three quarter plane. resultants of applied external loads are also shown. formulation crack problem solution he williams asymptotic solution is described by two eigenvalues i, ii (which define the singularities of mode i and mode ii stress fields, respectively), and the distribution of stresses resulting from the two eigenfunctions evaluated along the crack line:                   0 1 0 1 0 1 0 1 ( ) ( ) i iii ii i r ii r i ii i ii x k g x k g x x k x k x (1) t a. carpinteri et alii, frattura ed integrità strutturale, 41 (2017) 175-182; doi: 10.3221/igf-esis.41.24 177 for the considered geometry, the internal wedge angle is 2 = 3/2 and the angle corresponding to the line of the crack is = /4. therefore we have:           0 0 0.5445 , 0.9085 0.543 , 0.219 0.7304 , 1.087 i ii i ii r r i i ii ii g g k k k k (2) where ki0, kii0 are simply scaled versions of the mode i and mode ii notch stress intensity factors ki , kii, obtained from a calibration with the finite element method. let us consider the crack to be of length c ≪ a and lying along the x-axis. a distribution of edge dislocations of densities bx, by is added, so that the resulting integral equations which govern the problem are the following:                           0 0 (1 ( ) ( , ) ( ) ( , ) ) ( 1 ( ) ) 2 c c x xxy yxy tyb f x d b f x d x x x g (3)                           0 0 (1 ( ) ( , ) ( ) ( , ) ( ) ( ) 2 1) x xyy yy y c ny c b f x d b f x d x x x g (4) where g is the shear modulus, = 3 4 is the kolosov constant for plane strain, and is the poisson ratio. the influence function fkij(x,ξ), connecting the stress component ij(x) to a dislocation bk(ξ), can be found in [3]. the rightside terms of eqs. (3)-(4) contain the far-field stresses ∞(x) and ∞(x), obtained from the williams solution, and the shear and normal stresses applied to the crack surfaces, t(x) and n(x), respectively. introducing the normalized variables t,s , with crack extremes ± 1, instead of x and  respectively, we can write the singular integral equations in the usual form, and express the unknown dislocation densities bx, by as follows:         1 ( ) ( ) ( ) ( ) , , 1 j j j s b s s s s j x y s (5) where we have chosen the fundamental form of the solution (s) to be singular at the crack tip s = 1 and bounded at s = 1. a numerical solution of the integral equations is needed, and this can be achieved by means of the gauss-chebyshev quadrature described in [10]. the resulting 2n equations in the 2n unknown j(si) are the following:                           1 1)(1 ( ) ( ) ( , ) ( ) ( , ) ( ) ( ) 2 i x i xxy k i i yxy k i k t i k k i n yw s s f t s s f t s t t t s g (6)                            1 (1 ( ) ( ) ( , ) ( ) ( , ) ( ) 1 ( ) 2 )n i x i xyy yk i i yyy k i k n ki k i w s s f t s s f t s t t t s g (7) where w(i) are the weight functions, si are the integration points at which the unknown functions and the displacements are computed, whereas tk are the collocation points at which we evaluate the stresses. stress intensity factors at the crack tip are directly related to the value of j(s) for s = +1:         2 2 ( ( 1) 1), , , ,i j g k i i ii j xc y (8) values of j at end-points are not included in this quadrature method, thus krenk’s interpolation is used [11]. interface constitutive law in eqs. (6)-(7), the stresses on the crack surface t and n are related to the relative displacements by means of a constitutive law which describes friction and roughness. according to this law, the crack surfaces are assumed to be a. carpinteri et alii, frattura ed integrità strutturale, 41 (2017) 175-182; doi: 10.3221/igf-esis.41.24 178 globally smooth, with the effect of friction and roughness built in a rigid-plastic constitutive relationship. let us consider the relative tangential and normal displacements between two points situated on opposite positions on the crack surfaces, fig. 2(a):         w w t x n y y xu u u u (9) where superscripts + and indicate the superior and inferior surface of the crack, respectively. tangential and normal relative displacement increments are additively composed of a recoverable elastic part dwie and a non-recoverable plastic part dwip:   , ,e pi i idw dw dw i t n (10) where subscript i is used to denote the vector components t and n. the stress that the interface supports is assumed to be related to the elastic part by the following expression:   eii jjd e dw (11) where eij is the interface stiffness (summation convention is applied to repeated indices). here, we assume eij = 0 for i ≠ j and assure that they are relatively large compared to the stiffness of the adjacent medium, by applying a penalty two to four orders of magnitude greater to the shear modulus g of the medium itself. the permanent part of the deformation is given by the following slip rule: 0 0 0 0 p i i if f or df dw g if f df          (12) where f is the slip function and g is the slip potential. it can be noted that, since the friction law is non associated, f and g do not coincide, and the direction of slip is given by the gradient of g. combining (10)-(12), we obtain the fundamental relationship which connects the stresses along the crack to the relative displacements:   epiji jd e dw (13) where:                    if 0 or 0 if 0 ep ij ij iq pj pep ij ij pq q p q e e f df f g e e e e f df f g e (14) we chose to describe the roughness by means of a saw-tooth model, with identically shaped asperity surfaces whose size is characteristic of the type of discontinuity being modelled, fig. 2(b). moreover, we assume that the amount of tangential sliding is small enough so that the asperity peak of one surface does not override that of the other surface. the slip function and slip potential are the following:                    sin cos ( cos sin ) sin cos n k k n k k n ktk t tf g (15) a. carpinteri et alii, frattura ed integrità strutturale, 41 (2017) 175-182; doi: 10.3221/igf-esis.41.24 179 where k represents the angle of the active k asperity surface and  is the coefficient of friction of the coulomb law. if roughness is not taken into account, only friction is present and, therefore, eqs. (15) become simpler:       t n t f g (16) figure 2: schematic representation of the model used to describe the roughness of the crack surfaces. (a) local tangent-normal coordinate system at a contact point pair (shown separately for clarity). (b) saw-tooth asperity model, with constant angle and asperity length. relationships for stresses between the two coordinate systems are also shown. compliance matrix to efficiently solve the problem, a compliance matrix c that relates the stresses, arising at the collocation points from the applied loads, to the values of the relative displacements of the crack at the integration points can be obtained. the details of this procedure are presented in [6]. displacements along the crack, in an incremental form, are related to stresses by the following expression:       [ , ] [ , ]n n t t t td d d d d dw w c (17) where we have collected the increments of stresses and displacements in ordered vectors, such that, for instance, we have dwt = [dw1t , ... dwnt]t , with subscripts i = 1,...,n referring to the integration points along the crack. now the problem in (6)-(7) takes the following formulation:    ( )[ , ] [ , ]tt ep n td d d di ce t w w c (18) where  is the identity matrix and eep is the matrix containing the terms described in eq. (14). we have introduced a transformation matrix t to express crack displacements at the collocation points in terms of those at the integration points, so that the constitutive law in (13) can be enforced. this matrix is built using krenk’s interpolation formula [11], in order to obtain the values of the unknown functions in points along the crack which are different from the integration points. eq. (18) is a system of non-linear algebraic equations in the 2n unknown incremental relative displacements, to be solved by taking small increments in far-field loading. the stiffness matrix eep needs to be updated at each step, using the displacement-stress configuration from the previous step. by using the compliance matrix, the dislocation densities at each step are not needed to be integrated in order to compute the relative displacements along the crack and, therefore, the efficiency of the algorithm is increased. a. carpinteri et alii, frattura ed integrità strutturale, 41 (2017) 175-182; doi: 10.3221/igf-esis.41.24 180 figure 3: stress intensity factors as functions of the applied stresses. (a) the case of smooth surfaces, with different values of the coefficient of friction . (b) the effect of roughness is included and trends are shown for different values of the asperity angle . results e now present the results we have obtained for the example problem in fig. 1, consisting of an elastic punch welded to a half-space made of the same material. the elastic modulus is e = 30gpa and the poisson coefficient is = 0.25; the fracture toughness of the material is kic = 1.1 mpam. a state of plane strain is assumed. a crack of length c = 0.2a is present, whose surface model is described by the coefficient of friction and the constant roughness angle k. the external loading applied consists of a constant pressure p = p/2a and a shear traction q= q/2a which is monotonically increased in time. fig. 3 displays the plots of the stress intensity factors as functions of the far-field shear stress. fig. 3(a) is related to the case of smooth surfaces ( =0), where only friction is present. we can note that the effect of friction is rather modest, anyway a slight increment of the absolute value of mode ii factor with increasing friction is observed. fig. 3(b) plots the stress intensity factors for different values of the asperity angle . the trends show that, as the angle increases, the absolute value of mode i stress intensity factor ki increases, while the absolute value of kii decreases (note that they are both negative). this behaviour can be explained considering the effect of dilatancy, which affects ki, and the effect of roughness, which increases the resistance to sliding displacements, therefore reducing the absolute value of kii. however, one should be careful to generalize this behaviour, which can be completely different as the coefficient of friction also increases. in this sense, more research is needed to further investigate the issue. fig. 4 displays the dimensionless fracture propagation stress qmax/p as a function of the coefficient of friction, in the case of smooth surfaces. here, the classical mixed-mode criterion of maximum tangential stress is considered [12] and the w a. carpinteri et alii, frattura ed integrità strutturale, 41 (2017) 175-182; doi: 10.3221/igf-esis.41.24 181 fracture propagation stress is obtained when the combined factor keff equals the fracture toughness kic of the material. according to the fracture criterion we have:     3 2cos ( / 2) 3 cos ( / 2)sin( / 2)eff i iik k k (19) where is the angle at which the crack will extend, obtained from the following expression:     2 2 1/2tan / 2 0.25 / 0.25( / 8)ii i ii ik k k k (20) the effect of friction on fracture initiation is notable in fig. 4: a strong increment in the fracture propagation stress is observed, whereas the propagation angle slightly decreases (note that the maximum value for pure mode ii would be 70.5° [13]). figure 4: smooth surfaces ( =0). fracture propagation stress qmax is shown for different values of the coefficient of friction . the corresponding propagation angle is also shown. conclusions n this study, we describe the mixed-mode tip stress field of a crack emanating from a re-entrant corner, using the williams solution in combination with an appropriate edge dislocation distribution along the crack line. the behaviour of a rough and frictional crack is conveniently described by an interface model where a rigid-plastic constitutive relationship between stresses and relative displacements along the crack and a slip function with nonassociated flow are used. the results we have obtained clearly show that the effect of friction and roughness is remarkable. in particular, the effect of dilatancy increases the values of the (negative) mode i stress intensity factor while it simultaneously reduces the mode ii factor when the roughness angle increases. moreover, the fracture propagation load is strongly influenced by friction. references [1] murakami, y. (ed.), stress intensity factors handbook, vol. 1, pergamon press, new york, (1987). [2] williams, m.l., stress singularities resulting from various boundary conditions in angular corners of plates in extension, j. appl. mech., 19 (1952) 526–528. [3] churchman, c.m., hills, d.a., the edge dislocation in a three-quarter plane. part ii: application to an edge crack, eur. j. mech. a solids, 25 (2006) 389–396. i a. carpinteri et alii, frattura ed integrità strutturale, 41 (2017) 175-182; doi: 10.3221/igf-esis.41.24 182 [4] carpinteri, an., spagnoli, a., vantadori, s., viappiani, d., influence of the crack morphology on the fatigue crack growth rate: a continuously-kinked crack model based on fractals, eng. fract. mech., 75 (2012) 579-589. [5] brighenti, r., carpinteri, an., spagnoli, a., scorza, d., crack path dependence on inhomogeneities of material microstructure, frattura ed integrità strutturale, 20 (2012) 6-16. [6] ballarini, r., plesha, m.e., the effects of crack surface friction and roughness on crack tip stress fields, int. j. fract., 34 (1987) 195–207. [7] plesha, m.e., constitutive models for rock discontinuities with dilatancy and surface degradation, int. j. numer. anal. methods geomech., 11 (1987) 345–362. [8] carpinteri, al., scavia, c., energy dissipation due to frictional shake-down on a closed crack subjected to shear, meccanica, 28 (1993) 347-352. [9] klarbring, a., barber, j.r., spagnoli, a., terzano, m., shakedown of discrete systems involving plasticity and friction, eur. j. mech. a solids, 64 (2017) 160-164. [10] erdogan, f., gupta, g.d., cook, t.s., numerical solution of singular integral equations, in: sih, g.c. (ed.), methods of analysis and solutions of crack problems, noordhoff, groningen, (1973) 368–425. [11] hills, d.a., kelly, p.a., dai, d.n., korsunsky, a.m., solution of crack problems – the distributed dislocation technique, kluwer academic, dordrecht, (1996). [12] sih, g. c., strain-energy-density factor applied to mixed mode crack problems, int. j. fract., 10 (1974), 305-321. [13] erdogan, f., sih, g.c., on the crack extension in plates under plane loading and transverse shear, j. basic eng., 85 (1963) 519–527. << /ascii85encodepages false /allowtransparency false /autopositionepsfiles true /autorotatepages /none /binding /left /calgrayprofile (dot gain 20%) /calrgbprofile (srgb iec61966-2.1) /calcmykprofile (u.s. web coated \050swop\051 v2) /srgbprofile (srgb iec61966-2.1) /cannotembedfontpolicy /error /compatibilitylevel 1.4 /compressobjects /tags /compresspages true /convertimagestoindexed true /passthroughjpegimages true /createjobticket false /defaultrenderingintent /default /detectblends true /detectcurves 0.0000 /colorconversionstrategy /cmyk /dothumbnails false /embedallfonts true /embedopentype false /parseiccprofilesincomments true /embedjoboptions true /dscreportinglevel 0 /emitdscwarnings false /endpage -1 /imagememory 1048576 /lockdistillerparams false /maxsubsetpct 100 /optimize true /opm 1 /parsedsccomments true /parsedsccommentsfordocinfo 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can be opened with acrobat and adobe reader 5.0 and later.) >> /namespace [ (adobe) (common) (1.0) ] /othernamespaces [ << /asreaderspreads false /cropimagestoframes true /errorcontrol /warnandcontinue /flattenerignorespreadoverrides false /includeguidesgrids false /includenonprinting false /includeslug false /namespace [ (adobe) (indesign) (4.0) ] /omitplacedbitmaps false /omitplacedeps false /omitplacedpdf false /simulateoverprint /legacy >> << /addbleedmarks false /addcolorbars false /addcropmarks false /addpageinfo false /addregmarks false /convertcolors /converttocmyk /destinationprofilename () /destinationprofileselector /documentcmyk /downsample16bitimages true /flattenerpreset << /presetselector /mediumresolution >> /formelements false /generatestructure false /includebookmarks false /includehyperlinks false /includeinteractive false /includelayers false /includeprofiles false /multimediahandling /useobjectsettings /namespace [ (adobe) (creativesuite) (2.0) ] /pdfxoutputintentprofileselector /documentcmyk /preserveediting true /untaggedcmykhandling /leaveuntagged /untaggedrgbhandling /usedocumentprofile /usedocumentbleed false >> ] >> setdistillerparams << /hwresolution [2400 2400] /pagesize [612.000 792.000] >> setpagedevice microsoft word numero_61_art_33_3624.docx f. ferrian et al., frattura ed integrità strutturale, 61 (2022) 496-509; doi: 10.3221/igf-esis.61.33 496 finite fracture mechanics and cohesive crack model: size effects through a unified formulation f. ferrian, p. cornetti department of structural, building and geotechnical engineering, politecnico di torino, corso duca degli abruzzi 24, 10129 torino, italy. francesco.ferrian@polito.it; https://orcid.org/0000-0002-2093-5765 pietro.cornetti@polito.it; https://orcid.org/0000-0001-9063-9913 l. marsavina department of mechanics and strength of materials, university politehnica timisoara, blvd. m. viteazu, no. 1, 300222 timisoara, romania. liviu.marsavina@upt.ro; https://orcid.org/0000-0002-5924-0821 a. sapora department of structural, building and geotechnical engineering, politecnico di torino, corso duca degli abruzzi 24, 10129 torino, italy. alberto.sapora@polito.it; https://orcid.org/0000-0003-3181-3381 abstract. finite fracture mechanics and cohesive crack model can effectively predict the strength of plain, cracked or notched structural components, overcoming the classical drawbacks of linear elastic fracture mechanics. aim of the present work is to investigate size effects by expressing each model as a unified system of two equations, describing a stress requirement and the energy balance, respectively. brittle crack onset in two different structural configurations is considered: (i) a circular hole in a tensile slab; (ii) an un-notched beam under pure bending. the study is performed through a semi-analytical parametric approach. finally, theoretical strength predictions are validated with experimental results available in the literature for both geometries, and with estimations by the point criterion in the framework of theory of critical distances. keywords. size effects; finite fracture mechanics; cohesive crack model; circular hole; pure bending; crack advance. citation: ferrian, f., cornetti, p., marsavina, l., sapora, a., finite fracture mechanics and cohesive crack model: size effects through a unified formulation, frattura ed integrità strutturale, 61 (2022) 496-509. received: 28.05.2022 accepted: 16.06.2022 online first: 17.06.2022 published: 01.07.2022 copyright: © 2022 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. https://youtu.be/a8x2b52dn5m f. ferrian et al., frattura ed integrità strutturale, 61 (2022) 496-509; doi: 10.3221/igf-esis.61.33 497 introduction ince the pioneering work by hillerborg et al. 1976 [1] the cohesive crack model (ccm) has been widely implemented to assess the failure behavior of plain or composite structural components (e.g., [2]). the approach is based on the definition of a constitutive relationship, linking the cohesive stresses acting on the process zone with the crack lip opening displacement. ccm can provide physically-based and accurate strength estimations, but usually at the price of huge computational efforts. on the contrary, as regards the brittle crack onset, the coupled finite fracture mechanics (ffm) criterion [3, 4] allows to achieve (semi-) analytical predictions, thus generally revealing a more efficient approach. it relies on the assumption of a finite crack increment (at least at the first step), and it involves the fulfilment of two conditions: a stress requirement and the energetic balance. ccm and ffm predictions were compared for different notched configurations, from v-notches [5-7] to cracks [8, 9], fiber-matrix debonding [10] and spherical voids [11]. the above studies show that ffm and ccm can lead to very close predictions, depending on the ffm stress condition, the ccm constitutive law and the structural configuration under investigation. note that in [11] the ccm was written explicitly as a system of two equations, representing a stress-based condition and an energy requirement, thus rendering straightforward the analogy with ffm. in this context, the process zone can be thought as the ccm’s counterpart of the finite crack propagation distance. therefore, up to a certain extent, both ffm and ccm are equivalent in terms of the quantities they both rely on to predict the crack nucleation. furthermore, for cracked geometries, both models describe the transition from a strength-governed failure to a toughness-governed one as the size increases, unlike what happens with linear elastic fracture mechanics (lefm), which is not able to catch this transition. aim of this paper is to extend the comparison between ccm and ffm to other two configurations: (i) a circular hole in a tensile slab; (ii) an un-notched slender beam under four point bending (fpb). the former geometry was already addressed numerically by both ccm and ffm in li et al. [12], whereas the latter was recently investigated through ffm by doitrand et al. [13]. the novelty here relies on the proposed unified approach for each model, the analytical relationships governing the two problems being formally the same, up to the shape functions involved. the study will be carried out assuming a dugdale law for ccm (fig. 1) and the original version of ffm (leguillon [3]). finally, to corroborate the theoretical results, experimental data from the literature on materials implemented in different engineering fields will be taken into account, revealing a general good agreement. predictions by the point criterion in the framework of theory of critical distances [14] will be also reported. theoretical approaches he coupled ffm criterion and the ccm will be introduced below by referring to mode i loading conditions (fig.2), coherently with the topic under investigation. finite fracture mechanics according to coupled ffm approaches [3], [15], a stress and an energy requirements have to be simultaneously fulfilled for brittle crack onset to take place. the stress condition, following leguillon’s approach [3], requires that the normal stress y over a finite distance  must be larger than the ultimate tensile strength c of the material. on the other hand, the energy balance imposes that the strain energy g available for the finite crack increment  must be greater than gc , where gc is the material fracture energy. coupling the two conditions above, a system of two inequalities is obtained:    d 0                      0            a a  y c c x x g g (1) according to ffm, the actual failure load is the minimum one satisfying the two inequalities (1). however, for a positive geometry (i.e. for a monotonically increasing strain energy release rate along the crack length) the failure load is achieved when the two inequalities are strictly verified. in this case, eqn. (1) reverts to a system of two equations, see eqn. (2): note that the energy balance has been rewritten through irwin’s relationship, thus introducing the stress intensity factor ki =  s t f. ferrian et al., frattura ed integrità strutturale, 61 (2022) 496-509; doi: 10.3221/igf-esis.61.33 498 (ge’) and the material fracture toughness kic =  (gc e’), e’ being the young’s modulus under plain strain conditions. the two unknowns are represented by the critical (failure) stress f , implicitly embedded in the stress field and the sif functions, and the critical crack increment c. this latter quantity results a structural parameter, since dependent on both material properties and geometric characteristics. the behavior will be addressed more in details in section 3.    d2 2 0              c cy c i ic ck a a k (2) considering just the former equation of system (2), the point method (pm) can be defined [14, 16]. according to this criterion, fracture takes place when the stress equals the tensile strength c at a critical distance c = lch / (2), where lch = (kic / c)2 is the well-known irwin’s length. thus, according to tcd, the crack advance is a material property. cohesive crack model let us now consider the ccm implementing a dugdale type cohesive law (fig. 1). figure 1: dugdale’s cohesive law. according to this model, a process zone of length ap is present ahead the crack/notch tip, where the cohesive stress keeps constant and equal to c: ap increases with the external load , finally reaching the critical value apc when  is maximum, i.e.  = f. to achieve apc and f, two different conditions must be considered. the former is a stress requirement: the global sif ki has to vanish at the fictitious crack tip, such to eliminate the stress singularity. the superposition principle allows to exploit the sifs due to the external loading ki and the cohesive stresses kic, so that: 0   ci i ik k k (3) the latter is an energy condition: crack nucleates when the crack tip opening displacement (ctod) v attains its critical value vc = gc / c. in formulae, thanks again to superposition:    c cvv vv (4) where v and vc are the ctods related, respectively, to  and c. they can be computed by a straightforward application of paris’ equation as:     d 0 ,2 , '      pa ip i k p a v k a a e p (5)     d 0 ,2 , '      p c c a ip i c k p a v k a a e p (6)  vc c gc v f. ferrian et al., frattura ed integrità strutturale, 61 (2022) 496-509; doi: 10.3221/igf-esis.61.33 499 in eqns. (5) and (6) kip is the sif related to a pair of normal forces p, per unit of thickness, acting at the crack onset point (see appendix a for a graphical representation). test geometries wo different geometries are here analyzed. the first one is a circular hole with radius c in an infinite slab under uniaxial tensile load . the geometry and the system of reference taken into account are represented in fig. 2(a). note that the study concerns symmetrical crack propagation (i.e. two cracks simultaneously stemming from the hole edge) according to what presented in [17]. as will be clear later, the analysis can be easily extended to a finite geometries by properly taking some multiplying corrections factors into account. figure 2: (a) circular hole in an infinite tensile plate and (b) fpb configuration. the second one is a sufficiently slender beam of height c loaded under four point bending (fpb, fig. 2(b)). this configuration generates a state of pure bending in the middle section of the beam, i.e. where fracture is supposed to take place. the normal stress field along the x axis can be expressed as:    σ   y x f x (7) where x = x / c is the dimensionless coordinate and  = max = 6m / c2 for the fpb geometry (m being the bending moment). the (exact) analytical functions  f x according to kirsch [18] and beam theory are reported in appendix a. note that for the holed configuration, eqn. (7) provides the well-known stress concentration factor 3 tk at the hole edge ( 0x ), whilst far from the hole the stress field tends to the applied stress . on the other hand, the sif related to crack initiation (fig. 2) can be put in the following form:    ik a f a (8) where /a a c . eqns. (7) and (8) are sufficient to apply ffm. moreover, the expression for cik (eqn. (3)) and ipk (eqns. (5,6)) necessary to implement the ccm can be expressed, respectively, by the following relationships:    c ci ck a f a (9) t c x a f f y (b)  aa c y (a)  x f. ferrian et al., frattura ed integrità strutturale, 61 (2022) 496-509; doi: 10.3221/igf-esis.61.33 500    ip pk f a p a (10) the approximating shape functions f( a ), fc( a ), fp( a ) and their respective accuracy are reported in appendix a for both geometries. ffm and ccm results considering the equations provided for the two geometries analyzed in section 3, ffm and ccm can now be implemented. as concerns ffm, introducing the expression for y provided by eqn. (7) and for ki given by eqn. (8) into eqn. (2), yields:      d 2 2 0 1                       c f c c cc f f a f a a (11) where /  c c c and  = c / lch . thus, the size effect law according to ffm can be investigated as a parametric curve where the dimensionless size  and failure stress f / c are both expressed as a function of c . on the other hand, as regards ccm, substituting the expressions of ki (eqn. (8)) and kic (eqn. (9)) into eqn. (3), yields:     0      cp c pp pa f a fa a (12) where /p pa a c is the dimensionless process zone. in critical conditions, the dimensionless strength f /c as a function of pca can be derived from eqn. (12). furthermore, in light of the energy condition (4) and of the ctods expressions provided by eqns. (5)-(6), the dimensionless characteristic size  can be expressed as a function of pca through eqns. (810), leading to:               d 1 0 1 2                                  c pcc c pcf c pc pc p p a p p p pc f a f a f a f a a a a f a f f (13) hence, also ccm consists of a parametric approach, where the dimensionless size  and failure stress f / c reveal now functions of pca . as concerns the holed configuration, the failure stress estimations provided by ffm (eqn. (11)) and ccm (eqn. (13)) using the shape functions through eqns. (a1)-(a4), are plotted in fig. 3. as evident, the theoretical predictions are quite close. the relative deviation increases up to 8 % for   8, and then it decreases as  increases. in fig. 3 the experimental data on two different polymeric materials, polymethyl-methacrylate (pmma) and general-purpose polystyrene (gpps), tested by sapora et al. [17], are also reported. the geometry referring to / 1/ 0.05 c w w (w being the plate width), the theoretical assumption of an infinite geometry is here validated. the material properties for both pmma and gpps are summarized in tab. 1. f. ferrian et al., frattura ed integrità strutturale, 61 (2022) 496-509; doi: 10.3221/igf-esis.61.33 501 reference kic [mpam] c [mpa] lch [mm] concrete [19] 0.6^ 3.8^ 24.9 zno [20] 1.27° 100° 0.16 pur [21] 1.25 17.4 5.19 gpps [17] 1.40 30 2.18 pmma [17] 1.96 70.5 0.77 -gypsum [13] 0.35 9.5 1.36 -gypsum [13] 0.10 2.7 1.37 -gypsum [13] 0.40 12 1.11 uhpfrc [22] 4.45* 11.5 150 table 1: material properties implemented in this study. ^ material properties are not provided in the reference article and they are estimated based on [23]. ° in the reference article the material properties are estimated based on [24].  in the reference article the material properties are estimated based on [25], [26], [27]. * kic is not provided in the reference article. the value is estimated based on [28]. the failure stress predictions provided by ccm and ffm are in fairly good agreement with the experimental results on pmma. the maximum percent discrepancy from the estimations furnished by the ccm is 9 % for   2.6, whereas it decreases to 6 % for   0.65 according to ffm. predictions are also satisfactory for gpps, even if in this case the discrepancy is higher. indeed, the maximum deviation from ccm and ffm failure predictions exceeds, respectively, 15 % and 17 % for   0.23. pm predictions are also depicted in fig. 3, revealing the most conservative criterion: the maximum percent discrepancy from pmma experimental data increases up to 17 %, whereas the deviation from gpps test results decreases to 12 %. figure 3: circular hole in an infinite tensile slab: size effects by ffm (continuous line), ccm (dashed line), pm (dash-dotted line) and experiments on pmma and gpps [17]. a third set of experimental data is now considered, to further validate the models. it refers to polyurethane (pur) tested by negru et al. [21], see also [29]. in this case the sample width w was equal to 25 mm with variable ratios / 1/c w w ranging from 0.02 to 0.2. thus, the influence of the finite dimension of the specimens on failure predictions has to be taken into account. to this purpose, we consider the following correction factor for the stress field [30]: f. ferrian et al., frattura ed integrità strutturale, 61 (2022) 496-509; doi: 10.3221/igf-esis.61.33 502     1 3 23 1 22 1              w t t k wm k w (14) where kt is the stress concentration factor of a finite plate containing a circular hole (whereas 3  tk ): the stress field for finite width plates is achieved by multiplying kirsch solution (a1) by  wm . the accuracy of the correction provided by  wm was evaluated through a finite element method (fem) analysis using ansys code. in fig. 4 it is represented the comparison between tk and fem tk , determined through a convergence analysis, for different ratios 2 / w : the two quantities are in good agreement each other and the percent discrepancy is less than 3 % for 2 / w < 0.4. figure 4: circular hole in a finite tensile plate: comparison between tk and fem tk for different ratios 2 / w . to implement ffm and ccm we need to estimate also the correction factors for ki and kic related a finite width geometry. this is accomplished by multiplying eqns. (8) and (9) by the following correction factors [31], [32]:  1 sec sec             w a w w m (15)  1 1 1 / 2 sin sin sin 1 / 2 sin 1                          c w a w w a m (16) eqn. (15) is valid for 2 / w  0.5 and 2(c + a) / w  0.7 and it is between  2 % of boundary-collocation results (newman jr [33]). on the other hand, the value of kic, for different ratios 2(c+a) / w, was compared with that determined exploiting the fracture tool available in ansys code. the two values are in perfect agreement each other, the deviation was found to be less than 2% for 2(c + a) / w < 0.7. details of the mesh and the geometry implemented in the fem analysis are reported in fig. 5. note that, based on [31], eqns. (15) and (16) can be applied directly even to compute the ctods, i.e. eqn. (4) can be implemented, without the necessity of improving eqns. (5) and (6). f. ferrian et al., frattura ed integrità strutturale, 61 (2022) 496-509; doi: 10.3221/igf-esis.61.33 503 figure 5: details of the mesh, constraints and loads used in the fem model to evaluate the accuracy by eqn. (16). the failure stress estimations provided by ffm and ccm for a finite width geometry through eqns. (14)-(16) are finally plotted in fig. 6. as clearly highlighted in this figure, ccm and ffm fit well the data, especially for  > 0.5. as  decreases the percent discrepancy increases up to 20 % for   0.1. on the contrary, the accuracy of the pm reveals questionable for this data set, especially for large scale-sizes. figure 6: circular hole in a finite tensile slab: size effects by ffm (continuous line), ccm (dashed line), pm (dash-dotted line) and experiments on pur [21]. the finite crack advancement c / lch, provided by eqn. (11) multiplying c with , and the process zone length apc, given similarly by eqn. (13), are represented in fig. 7. the absolute values of the two sizes are quite different between each other. nevertheless, the trend with respect to the dimensionless size  is somehow similar. considering ffm, c decreases from the value 2 lch /  until it reaches a minimum and then it tends to 2 lch / [(1.12)2] as  increases. analogously, apc decreases until it reaches a minimum for   0.4, and then it increases monotonically. the deviation between the process zone length in ccm and the finite crack advancement in ffm may be explained considering that whereas apc is a fictitious crack, since cohesive stresses are present, c is a “real” crack, because the new crack lips are stress free. f. ferrian et al., frattura ed integrità strutturale, 61 (2022) 496-509; doi: 10.3221/igf-esis.61.33 504 figure 7: circular hole in an infinite tensile slab: finite crack extension c / lch by ffm (continuous line), process zone length apc / lch by ccm (dashed line). analyzing now the fpb geometry (fig. 2(b)), we can apply the shape functions provided by eqns. (a5)-(a8) to eqns. (11) and (13) for ffm and ccm, respectively. figure 8: size effects on fpb un-notched samples: ffm (continuous line), ccm (dashed line), pm (dash-dotted line) and experimental results for (a) uhpfrc [22], zno [20] and concrete [19]; (b) gypsum [13]. the failure stress estimates f is reported in fig. 8 as a function of the dimensionless characteristic size  = c / lch. the failure stress estimates of the two models are quite different for small-size structures. ccm furnishes a dimensionless small-size limit strength value equal to 3, whereas ffm provides an infinitely large strength for vanishing size (the slope of the curve is equal to 0.5 in the log-log plot). analogously, pm furnishes the lowest predictions for  > 0.7. on the other hand, it provides divergent predictions as  approaches 1/, this representing the limit below which stresses (at a distance c from the beam edge) become negative. together with these estimations, in this figure are represented also the experimental data related to three different types of gypsum [13], ultrahigh-performance fiber-reinforced concrete (uhpfrc, [22]), zinc oxide (zno, [20]) and concrete [19]. the material properties considered in this study are again resumed in tab. 1. theoretical predictions are in good agreement with results on gypsum, despite the high statistical dispersion of the experimental data. this scattering can be partially explained considering the presence of critical pores triggering failure, as (a) (b) f. ferrian et al., frattura ed integrità strutturale, 61 (2022) 496-509; doi: 10.3221/igf-esis.61.33 505 highlighted by uhl et al. [34]. considering uhpfrc, estimations provided by ffm and ccm are again accurate. indeed, ccm provides a deviation that increases up to 15 % as  decreases, whilst ffm furnishes a lower percent discrepancy, equal to 14 % for   0.17. similar arguments hold for concrete and zno data. furthermore, also the approximated results provided by eqn. (17) are represented in fig. 8: this master curve is in excellent agreement with ffm predictions in the range of practical interest, the percent discrepancy is less than 1.5 % for   0.1. with respect to that proposed in [13], eqn. (17) is able to catch the ffm trend at small scales, thus revealing more accurate. 1 2.42.5 1          f c chc l (17) fig. 9 represents the comparison between the finite crack advance according to ffm and the process zone according to ccm, normalized with respect to irwin’s length. as clearly highlighted in the plot, both models provide curves with slope equal to 1 for vanishing  (i.e., apc = c and c = c / 2). furthermore, in accordance with ccm, the process zone diverges in large scale limit (linear slope equal to 0.5, apc = 0.5(c lch)), while the crack advance c tends to 2 lch / [(1.12)2], i.e., the same value obtained for the holed configuration. figure 9: fpb configuration: finite crack extension c / lch by ffm (continuous line), process zone length apc / lch by ccm (dashed line). conclusions n the present paper, two different configurations a tensile strip (or plate) with a circular hole and a fpb un-notched beamwere analyzed to catch size effects implementing ffm and ccm. in order to compare theoretical predictions, a rectangular cohesive law (dugdale’s type) was considered for ccm and a point wise stress requirement was implemented for ffm [3]. the analysis was conducted in a semi-analytical way by exploiting shape functions available in literature, leading to a unified parametric approach for each model. note that in the framework of ffm, this had already been done for the three point bending configuration of plain or cracked specimens [4] or dealing with blunt v-notches [35], which can be easily recast according to the present formulation. for the holed geometry the failure estimations provided by these two approaches are very close to each other. instead, for the fpb geometry, the dissimilarities between the strength previsions provided by the two approaches increase at smaller scales. indeed, ccm tends towards a dimensionless strength value equal to 3, whereas ffm provides an infinitely large strength for vanishing sizes. the comparison with experimental data from the literature on different materials shows that ffm is able to catch the correct trend in the region of practical interest, whereas pm -and, generally, each model based on a material lengthis not. it is worthwhile remarking, once again, the matching between ffm and ccm, although i f. ferrian et al., frattura ed integrità strutturale, 61 (2022) 496-509; doi: 10.3221/igf-esis.61.33 506 consolidated, actually depends on the geometry under investigation, the ccm cohesive law, and the particular ffm stress condition. appendix a circular holed configuration the function f ( )x can be expressed as [18]:   2 4 1 3 1 2( 1) 2( 1)      x x x f (a1) the shape functions f(), fc() according to [36], and fp() provided in [37] can be expressed as (fig. a1, accuracy of about 1 %):    3 1 3 2 1.243 1 2 1 1           a a a a f (a2)           4 3 2 4 1 0.137 1 0.258 1 0.4 1         c a a f a a a a (a3)      2 4 2 1 0.201 0.604 1 2 1 1            p a a a a a f (a4) figure a1: schematic representation of the considered loadings: (a) cohesive stress acting on the crack length a; (b) pair of normal forces p applied at the hole edge. fpb un-notched beam according the elementary beam theory, the function f( x ) is given by:   1 2 f x x (a5) for this configuration, the shape functions f(), fc() and fp() according to [36] (fig. a2, accuracy less than 0.5 %): f. ferrian et al., frattura ed integrità strutturale, 61 (2022) 496-509; doi: 10.3221/igf-esis.61.33 507   tan 4 0.923 0.199 1 sin 2 2 2 cos 2                         a f a a aa (a6)   3 0.752 2.02 0.37 1 sin 2 2 tan 2 cos 2                         c a f a a a aa (a7)         5 22 3/2 0.46 3.06 0.84 1 0.66 1 2 1        pf a a a a a a (a8) figure a2: schematic representation of the considered loadings: (a) cohesive stress acting on the crack length a; (b) pair of normal forces p applied at the beginning of the crack. references [1] hillerborg, a., modéer, m., petersson, p.-e. (1976). analysis of crack formation and crack growth in concrete by means of fracture mechanics and finite elements, cem. concr. res., 6(6), pp. 773–781, doi: 10.1016/0008-8846(76)90007-7. [2] needleman, a. (1990).an analysis of decohesion along an imperfect interface. non-linear fracture, dordrecht, springer netherlands, pp. 21–40. [3] leguillon, d. (2002). strength or toughness? a criterion for crack onset at a notch, eur. j. mech. a/solids, 21(1), pp. 61–72, doi: 10.1016/s0997-7538(01)01184-6. [4] cornetti, p., pugno, n., carpinteri, a., taylor, d. (2006). finite fracture mechanics: a coupled stress and energy failure criterion, eng. fract. mech., 73(14), pp. 2021–2033, doi: 10.1016/j.engfracmech.2006.03.010. [5] henninger, c., leguillon, d., martin, e. (2007). crack initiation at a v-notch—comparison between a brittle fracture criterion and the dugdale cohesive model, comptes rendus mécanique, 335(7), pp. 388–393, doi: 10.1016/j.crme.2007.05.018. [6] cornetti, p., sapora, a. (2019). penny-shaped cracks by finite fracture mechanics, int. j. fract., 219(1), pp. 153–159, doi: 10.1007/s10704-019-00383-9. [7] doitrand, a., estevez, r., leguillon, d. (2019). comparison between cohesive zone and coupled criterion modeling of crack initiation in rhombus hole specimens under quasi-static compression, theor. appl. fract. mech., 99, pp. 51–59, doi: 10.1016/j.tafmec.2018.11.007. [8] cornetti, p., sapora, a., carpinteri, a. (2016). short cracks and v-notches: finite fracture mechanics vs. cohesive f. ferrian et al., frattura ed integrità strutturale, 61 (2022) 496-509; doi: 10.3221/igf-esis.61.33 508 crack model, eng. fract. mech., 168, pp. 2–12, doi: 10.1016/j.engfracmech.2015.12.016. [9] cornetti, p., muñoz-reja, m., sapora, a., carpinteri, a. (2019). finite fracture mechanics and cohesive crack model: weight functions vs. cohesive laws, int. j. solids struct., 156–157, pp. 126–136, doi: 10.1016/j.ijsolstr.2018.08.003. [10] garcía, i.g., paggi, m., mantič, v. (2014). fiber-size effects on the onset of fiber–matrix debonding under transverse tension: a comparison between cohesive zone and finite fracture mechanics models, eng. fract. mech., 115, pp. 96– 110, doi: 10.1016/j.engfracmech.2013.10.014. [11] chao correas, a., corrado, m., sapora, a., cornetti, p. (2021). size-effect on the apparent tensile strength of brittle materials with spherical cavities, theor. appl. fract. mech., 116, pp. 103120, doi: 10.1016/j.tafmec.2021.103120. [12] li, j., zhang, x.b. (2006). a criterion study for non-singular stress concentrations in brittle or quasi-brittle materials, eng. fract. mech., 73(4), pp. 505–523, doi: 10.1016/j.engfracmech.2005.09.001. [13] doitrand, a., henry, r., meille, s. (2021). brittle material strength and fracture toughness estimation from four-point bending test, j. theor. comput. appl. mech., doi: 10.46298/jtcam.6753. [14] taylor, d. (2007). the theory of critical distances, elsevier, amsterdam. [15] carpinteri, a., cornetti, p., pugno, n., sapora, a., taylor, d. (2008). a finite fracture mechanics approach to structures with sharp v-notches, eng. fract. mech., 75(7), pp. 1736–1752, doi: 10.1016/j.engfracmech.2007.04.010. [16] taylor, d., kasiri, s., brazel, e. (2009). the theory of critical distances applied to problems in fracture and fatigue of bone, frat. ed integrità strutt., 3(10), pp. 12–20, doi: 10.3221/igf-esis.10.02. [17] sapora, a., torabi, a.r., etesam, s., cornetti, p. (2018). finite fracture mechanics crack initiation from a circular hole, fatigue fract. eng. mater. struct., 41(7), pp. 1627–1636, doi: 10.1111/ffe.12801. [18] kirsch, g. (1898). die theorie der elastizitat und die bedurfnisse der festigkeitslehre, zantralblatt verlin deutscher ingenieure. [19] harris, h.g., sabnis, g.m., white, r.n. (1966). small scale direct models of reinforced and prestressed concreate structures, ithaca, new york. [20] lu, c., danzer, r., fischer, f.d. (2004). scaling of fracture strength in zno: effects of pore/grain-size interaction and porosity, j. eur. ceram. soc., 24(14), pp. 3643–3651, doi: 10.1016/j.jeurceramsoc.2003.12.001. [21] negru, r., marsavina, l., voiconi, t., linul, e., filipescu, h., belgiu, g. (2015). application of tcd for brittle fracture of notched pur materials, theor. appl. fract. mech., 80, pp. 87–95, doi: 10.1016/j.tafmec.2015.05.005. [22] lampropoulos, a., nicolaides, d., paschalis, s., tsioulou, o. (2021). experimental and numerical investigation on the size effect of ultrahigh-performance fibre-reinforced concrete (uhfrc), materials (basel)., 14(19), pp. 5714, doi: 10.3390/ma14195714. [23] karihaloo, b.l., nallathambi, p. (1990). effective crack model for the determination of fracture toughness () of concrete, eng. fract. mech., 35(4–5), pp. 637–465, doi: 10.1016/0013-7944(90)90146-8. [24] yoshimura, h.n., molisani, a.l., narita, n.e., manholetti, j.l.a., cavenaghi, j.m. (2006). mechanical properties and microstructure of zinc oxide varistor ceramics, mater. sci. forum, 530–531, pp. 408–413, doi: 10.4028/www.scientific.net/msf.530-531.408. [25] meille, s., garboczi, e.j. (2001). linear elastic properties of 2d and 3d models of porous materials made from elongated objects, model. simul. mater. sci. eng., 9(5), pp. 371–390, doi: 10.1088/0965-0393/9/5/303. [26] meille, s. (2001). étude du comportement mécanique du plâtre pris en relation avec sa microstructure. institut national des sciences appliquées de lyon. [27] sanahuja, j., dormieux, l., meille, s., hellmich, c., fritsch, a. (2010). micromechanical explanation of elasticity and strength of gypsum: from elongated anisotropic crystals to isotropic porous polycrystals, j. eng. mech., 136(2), pp. 239–253, doi: 10.1061/(asce)em.1943-7889.0000072. [28] tran, t.k., tran, n.t., nguyen, d.l., kim, d.j., park, j.k., ngo, t.t. (2021). dynamic fracture toughness of ultra‐ high‐performance fiber‐reinforced concrete under impact tensile loading, struct. concr., 22(3), pp. 1845–1860, doi: 10.1002/suco.202000379. [29] marsavina, l., linul, e., voiconi, t., constantinescu, d.m., apostol, d.a. (2015). on the crack path under mixed mode loading on pur foams, frat. ed integrità strutt., (34), doi: 10.3221/igf-esis.34.43. [30] tan, s.c. (1988). finite-width correction factors for anisotropic plate containing a central opening, j. compos. mater., 22(11), pp. 1080–1097, doi: 10.1177/002199838802201105. [31] newman jr, j.c. (1983). a nonlinear fracture mechanics approach to the growth of small cracks, proc. agard conf., 328(6). [32] chang, j.b., hudson, c.m. (1981). a crack-closure model for predicting fatigue crack growth under aircraft spectrum loading. methods and models for predicting fatigue crack growth under random loading, american society for testing and materials, pp. 53–84. f. ferrian et al., frattura ed integrità strutturale, 61 (2022) 496-509; doi: 10.3221/igf-esis.61.33 509 [33] newman jr, j.c. (1971). an improved method of collocation for the stress analysis of cracked plates with various shaped boundaries, nasa tech. note d-6376. [34] uhl, j., doitrand, a., meille, s. (2022). variability in porous ceramic fracture: influence of apparent density and critical pores, j. eur. ceram. soc., doi: 10.1016/j.jeurceramsoc.2022.05.020. [35] carpinteri, a., cornetti, p., sapora, a. (2011). brittle failures at rounded v-notches: a finite fracture mechanics approach, int. j. fract., 172(1), pp. 1–8, doi: 10.1007/s10704-011-9640-8. [36] tada, h., paris, p.c., irwin, g.r. (2000). the stress analysis of cracks handbook, third edition, asme press, new york. [37] williams, t.n., newman jr, j.c., gullett, p.m. (2011). crack-surface displacements for cracks emanating from a circular hole under various loading conditions, fatigue fract. eng. mater. struct., 34(4), pp. 250–259, doi: 10.1111/j.1460-2695.2010.01512.x. << /ascii85encodepages false /allowtransparency false /autopositionepsfiles true /autorotatepages /none /binding /left /calgrayprofile (dot gain 20%) /calrgbprofile (srgb iec61966-2.1) /calcmykprofile (u.s. web coated \050swop\051 v2) /srgbprofile (srgb iec61966-2.1) /cannotembedfontpolicy /error /compatibilitylevel 1.4 /compressobjects /tags /compresspages true /convertimagestoindexed true /passthroughjpegimages true /createjobticket false /defaultrenderingintent /default /detectblends true /detectcurves 0.0000 /colorconversionstrategy /cmyk /dothumbnails false /embedallfonts true /embedopentype false /parseiccprofilesincomments true /embedjoboptions true /dscreportinglevel 0 /emitdscwarnings false /endpage -1 /imagememory 1048576 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can be opened with acrobat and adobe reader 5.0 and later.) >> /namespace [ (adobe) (common) (1.0) ] /othernamespaces [ << /asreaderspreads false /cropimagestoframes true /errorcontrol /warnandcontinue /flattenerignorespreadoverrides false /includeguidesgrids false /includenonprinting false /includeslug false /namespace [ (adobe) (indesign) (4.0) ] /omitplacedbitmaps false /omitplacedeps false /omitplacedpdf false /simulateoverprint /legacy >> << /addbleedmarks false /addcolorbars false /addcropmarks false /addpageinfo false /addregmarks false /convertcolors /converttocmyk /destinationprofilename () /destinationprofileselector /documentcmyk /downsample16bitimages true /flattenerpreset << /presetselector /mediumresolution >> /formelements false /generatestructure false /includebookmarks false /includehyperlinks false /includeinteractive false /includelayers false /includeprofiles false /multimediahandling /useobjectsettings /namespace [ (adobe) (creativesuite) (2.0) ] /pdfxoutputintentprofileselector /documentcmyk /preserveediting true /untaggedcmykhandling /leaveuntagged /untaggedrgbhandling /usedocumentprofile /usedocumentbleed false >> ] >> setdistillerparams << /hwresolution [2400 2400] /pagesize [612.000 792.000] >> setpagedevice microsoft word numero 22 articolo 1.doc r. k. bhagat et alii, frattura ed integrità strutturale, 22 (2012) 5-11; doi: 10.3221/igf-esis.22.01 5 evaluation of stress intensity factor of multiple inclined cracks under biaxial loading r. k. bhagat, v. k. singh, p. c. gope, a.k. chaudhary college of technology, g.b.p.u.a. & t, pantnagar-263145, (uttarakhand), india vks2319@yahoo.co.in abstract. a finite rectangular plate of unit thickness with two inclined cracks (parallel and non parallel) under biaxial mixed mode condition are modelled using finite element method. the finite element method is used for determination of stress intensity factors by anysis software. effects of crack inclination angle on stress intensity factors for two parallel and non parallel cracks are investigated. the significant effects of different crack inclination parameters on stress intensity factors are seen for lower and upper crack in two inclined crack. the present method is validated by comparing the results from available experimental data obtained by photo elastic method in same condition. keywords. stress intensity factor; multiple cracks; photoelasticity; crack inclination angle. introduction he fracture mechanics theory can be used to analyze structures and machine components with cracks and to obtain an efficient design. the basic principles of fracture mechanics developed from studies of [1-3] are based on the concepts of linear elasticity. westergaard [3] derived the general linear elastic solution for the stress field around a crack tip using complex stress functions. irwin [4], proposed the description of the stress field ahead of a crack tip (front) by means of only one parameter, the so called stress intensity factor (sif). the interaction between multiple cracks has a major influence on crack growth behaviours. this influence is particularly significant in stress corrosion cracking (scc) because of the relatively large number of cracks initiated due to environmental effects. wen ye tian and u gabbert [5] have proposed pseudo – traction –electric – displacement – magnetic –induction method to solve the multiple crack interaction problems in magneto elastic material. the interaction of multiple cracks in a finite plate by using the hybrid displacement discontinuity method (a boundary element method) and detail solutions of the stress intensity factors (sifs) of the multiple-crack problems in a rectangular plate are shown by xiangqiao [6]. the numerical results reported by xiangqiao [6] illustrates that the boundary element method is simple, yet accurate for calculating the sifs of multiple crack problems in a finite plate. flaw interaction effects were investigated and the importance of modelling multiple crack growth at high stress levels was presented by walde [7]. wang [8] studied the interactions of two collinear cracks, three collinear cracks, two parallel cracks, and three parallel cracks using finite element technique. the present investigation have been conducted keeping in mind the effect of crack inclination angle on facture parameters such as stress intensity factor for mode-i problem (ki) and stress intensity factor for mode-ii problem (kii). rectangular finite plate with double crack (parallel and non-parallel) inclined at different angles with the loading axis has been used in the present investigation for determination of mixed mode (mode i, mode ii) stress intensity factors under biaxial loading condition by using ansys software. the accuracy of the present method is validated by comparing the results obtained by photo elastic method. t http://dx.medra.org/10.3221/igf-esis.22.01&auth=true http://www.gruppofrattura.it r. k. bhagat et alii, frattura ed integrità strutturale, 22 (2012) 5-11; doi: 10.3221/igf-esis.22.01 6 material and methods specimen geometry and assumptions n the present investigation rectangular thin plate with centre inclined crack are used in fe modelling. the different crack configurations are shown in figs. 1-2. the thickness of the plate is kept 1 mm; length and width of the plates are kept 100 mm and 100 mm respectively. two cracks at the centre of the plate are separated by an offset distance h. figure 1: specimen geometry of two non parallel central inclined cracks. figure 2: specimen geometry of two parallel central inclined cracks. specimen material young’s modulus (gpa) poisson’s ratio steel 210 0.3 table 1: material properties. method stress intensity factors (mode-i and mode-ii) have been calculated for a thin steel plate under plane strain condition containing central inclined multiple cracks for different conditions and orientations (as shown in figs. 1-2) by ansys software. a single central crack model are also analysed by present method and results are verified by available experimental results of singh and gope [9] obtained by photo elastic method. plane 82 (8-nod 2-d) elements shown in fig 3 have been used in the analysis. plane 82 elements provide more accurate results for mixed (quadrilateral-triangular) automatic meshes and can tolerate irregular shapes without much loss of accuracy. the 8-node elements have compatible displacement shapes and are well suited to model curved boundaries. the element may be used as a plane element or as an axis symmetric element. the element has plasticity, creep, swelling, stress stiffening, large deflection, and large strain capabilities. figure 3: plane 82 elements with 8-nodes. i http://dx.medra.org/10.3221/igf-esis.22.01&auth=true http://www.gruppofrattura.it r. k. bhagat et alii, frattura ed integrità strutturale, 22 (2012) 5-11; doi: 10.3221/igf-esis.22.01 7 all type of solution data of interest can be obtained in post1 command like von mises stress, principal stress, deformation, maximum stress, translations, failure criteria, sifs, j integral. the data can be obtained for all the nodes and elements in tabular form or contour plots. in order to obtain the sifs a path is defined manually by picking the five nodes at the crack face as shown in fig. 4. figure 4: representation of displacements to be used in analysis. after defining the path the sif’s are obtained. the von mises distribution around the crack tip can be obtained in the contour chart and can be used for further analysis. image can be saved in the jpeg format. the postprocessor can give contour plot of the structure as shown below in fig. 5. von mises stress distribution for a central inclined cracked in a plate is shown in fig. 6. figure 5: defining the path node 1-2-3-4-5 for finding sif. figure 6: von mises stress distribution for inclined cracked in a plate. results and discussion alidation of the finite element approach with results available in literature or experimental results are most important for acceptance of the finite element method used in the computation. in the present investigation finite element method results are compared with the experimental results available in literature. it is seen that ki and kii depends upon crack angle, biaxial load factor, constant stress term and geometry factor (a/w) and (a/l). the results are compared with the experimental results of singh and gope [9]. the effects of these parameters on stress intensity factors based on photoelastic analysis are modelled by singh and gope [9] as:      11 1 cos 2 ei e l k a k k f w              (1) v http://dx.medra.org/10.3221/igf-esis.22.01&auth=true http://www.gruppofrattura.it r. k. bhagat et alii, frattura ed integrità strutturale, 22 (2012) 5-11; doi: 10.3221/igf-esis.22.01 8 where cos 2 e l l    and sin 2 e w w    , where 1 e e l f w       is obtained from regression analysis of the experimental results as singh and gope [9], 2 3 4 1 1 2 3 4 5 e e e e e e e e e e l l l l l f a a a a a w w w w w                                   (2) the coefficients (a1 to a5) are shown in tab. 2 for various biaxial load factors. the effective length and width are defined in fig. 7. k coefficients a1 a2 a3 a4 a5 1.0 2958.13 -12319.36 19224.87 -13324.242 3460.51 1.2 4537.08 18372.43 27972.43 -18972.07 4837.87 1.4 15558.09 -64654.20 100712.02 -69686.75 18072.87 1.6 25511.84 -105574.57 163730.04 -112775.23 29110.39 1.8 13629.04 -56212.08 87054.91 -59991.82 15522.33 2.0 42527.06 -175971.91 272858.97 -187899.41 48486.72 table 2: the coefficients of eq. (2) [9]. figure 7: effective length and effective width in the specimen. the correlation coefficient in all cases are found to be greater than 0.90. the variation of ki with crack inclination angle (α) obtained by experimental method and fem are shown in fig. 8. it is observed that result of ki obtained from finite element approach using commercial software ansys are very close to experimental results of singh and gope [9]. it means finite element modelling using ansys software can be used to determine stress intensity factor ki for any complex crack configurations too. http://dx.medra.org/10.3221/igf-esis.22.01&auth=true http://www.gruppofrattura.it r. k. bhagat et alii, frattura ed integrità strutturale, 22 (2012) 5-11; doi: 10.3221/igf-esis.22.01 9 figure 8: comparison of stress intensity factor ki for load σ = 1.125n/mm2, biaxial load factor = 1 and a/w= 0.06. effect of crack inclination angle on ki for two non-parallel cracks when there are two parallel and symmetric cracks in a plate then ki for lower ki(l) and upper ki(u) crack decreases with the increase of crack inclination angle as shown in fig. 9. figure 9: effect of crack inclination angle α on ki for two non parallel crack; a/w = 0.08, k = 0.75, s = 1.5 and b = 24. effect of crack inclination angle on ki for two parallel cracks when there are two parallel cracks in a plate then ki for lower and upper crack decrease with the increase in crack inclination angle, whereas upper crack has slightly more value than the lower crack as shown in fig. 10. fig. 10 shows that for lower and higher crack inclination angle, ki for lower and upper crack are approximately same because cracks are tends to parallel to either major or minor load axis, and are close mode i or mode ii condition and hence there is negligible variation in the ki for lower and upper crack. effect of crack inclination angle α on two non-parallel cracks when there is two parallel and symmetric crack in a plate kii for lower kii(l) and upper kii(u) crack the value of kii are approximately same for both the crack as shown in fig. 11 and it increases up to α = 450 and then it starts decreasing hence, maximum value is observed at α = 450. effect of crack inclination angle α on two parallel cracks when there are two parallel cracks in a plate then kii increases with the increase of crack inclination angle for upper and lower crack up to 450 and then it starts decreasing as shown in fig. 12. hence, maximum value is obtained at α = 450. http://dx.medra.org/10.3221/igf-esis.22.01&auth=true http://www.gruppofrattura.it r. k. bhagat et alii, frattura ed integrità strutturale, 22 (2012) 5-11; doi: 10.3221/igf-esis.22.01 10 figure 10: effect of crack inclination angle α on ki for two parallel crack; a/w = 0.08, k = 0.75, s = 1.5 and b = 24. figure 11: effect of crack inclination angle α on ki for two non-parallel cracks; a/w =0.08, k = 0.75, s = 1.5 and b = 24mm. figure 12: effect of crack inclination angle α on ki for two parallel cracks; a/w = 0.08, k = 0.75, s = 1.5 and b = 24 mm. conclusions ffects of crack inclination angle on stress intensity factors for two parallel and non parallel cracks are analysed and found to have significant effect on lower and upper crack. the stress intensity factors for non parallel cracks have similar value for upper and lower cracks, whereas in case of parallel cracks the value of stress intensity factor is e http://dx.medra.org/10.3221/igf-esis.22.01&auth=true http://www.gruppofrattura.it r. k. bhagat et alii, frattura ed integrità strutturale, 22 (2012) 5-11; doi: 10.3221/igf-esis.22.01 11 lower for lower crack in comparison to upper crack. references [1] c.e. inglis, transactions-institute of naval architect, 55 (1913) 219. [2] a.a. griffith, trans. royal soci. london, 221 (1920) 163. [3] h. m. westgaard, j. appl. maths mech., 6 (1939) a49. [4] g. r. irwin, trans. asme, j. appl. mech., 24(3) (1957) 361. [5] t. wen-ye, u. gabbert, european j. mech. a/solids, 23 (2004) 599. [6] y. xiangqiao, m. changing, interaction of multiple cracks in a rectangular plate, appl. math. modelling. (2012) article in press. [7] k. van der walde, int. j. fatigue. 27 (2005) 1509. [8] w. wang, x. zeng, j. ding, engineering and technology, 70 (2010) 587. [9] v.k. singh, p.c. gope, journal of solid mechanics, 3 (2009) 233. http://dx.medra.org/10.3221/igf-esis.22.01&auth=true http://www.gruppofrattura.it microsoft word numero_35_art_25 a. nikitin et alii, frattura ed integrità strutturale, 35 (2016) 213-222; doi: 10.3221/igf-esis.35.25 213 focussed on crack paths crack path in aeronautical titanium alloy under ultrasonic torsion loading a. nikitin, c.bathias leme, university paris ouest nanterre la defense, 50, rue de serves, ville-d'avray, 92410, france nikitin_alex@bk.ru t.palin-luc arts et metiers paris tech, i2m, cnrs university of bordeaux, esplanade des arts et metiers, talence, 33405, france thierry.palin-luc@ensam.eu a. shanyavskiy sccafs, air. sheremetevo-1, po box 54, moscow reg., chimkovskiy state, 141426, russia shananta@mailfrom.ru abstract. this paper discusses features of fatigue crack initiation and growth in aeronautical vt3-1 titanium alloy under pure torsion loading in gigacycle regime. two materials: extruded and forged vt3-1 titanium alloys were studied. torsion fatigue tests were performed up to fatigue life of 109 cycles. the results of the torsion tests were compared with previously obtained results under fully reversed axial loading on the same alloys. it has been shown that independently on production process as surface as well subsurface crack initiation may appear under ultrasonic torsion loading despite the maximum stress amplitude located at the specimen surface. in the case of surface crack initiation, a scenario of crack initiation and growth is similar to hcf regime except an additional possibility for internal crack branching. in the case of subsurface crack, the initiation site is located below the specimen surface (about 200 µm) and is not clearly related to any material flaw. internal crack initiation is produced by shear stress in maximum shear plane and early crack growth is in mode ii. crack branching is limited in the case of internal crack initiation compared to surface one. a typical ‘fish-eye’ crack can be observed at the torsion fracture surface, but mechanism of crack initiation seems not to be the same than under axial fatigue loading. keywords. very-high cycle fatigue; titanium alloy; torsion; ultrasonic; crack initiation; crack growth. introduction t was outlined by many authors that study on fatigue properties of structural materials, such as steels, aluminum and titanium alloys, under torsion loading is an important subject for industrial applications [1-2]. many engineering elements are subjected to complex loading involving bending, tension or torsion load modes. moreover, in case of modern applications, such as cars, high-speed trains and aircraft motors, a significant fatigue life for components can be i a. nikitin et alii, frattura ed integrità strutturale, 35 (2016) 213-222; doi: 10.3221/igf-esis.35.25 214 achieved during in-service due to high loading rate [3]. analysis of in-service loads for aeronautical applications [4] has shown that fatigue life of compressor blades may reach more than 109 cycles that is in the very-high cycle fatigue regime. since the beginning of the 1990th, this fatigue regime is under investigations [5]. mainly the vhcf properties of structural materials were investigated under axial push-pull loading, but some different testing systems were developed to reproduce different in-service loading and conditions [6]. in the recent years, investigations on fatigue properties of metals under torsion loading become more and more actual topic [7, 8]. results of ultrasonic tests on high-strength aluminum shows that torsion fatigue crack in vhcf regime have a qualitative similarity to crack in hcf regime [9]. it has been shown that crack initiation under torsion is located at the surface of specimen. the first stage of growth is found in the plane of maximum shear stress with further formation of circumferential crack. however, a few years after, it has been shown that under torsion loading in vhcf range as surface, as well a subsurface cracks may also appears if material contains a non-metallic inclusions. in reference [10] high-strength steel was studied up to a fatigue life of 109 cycles. in the case of surface initiation, the fracture surface of 100c6 steel shows a similar to hcf 'factory roof' pattern, but in the case of subsurface crack initiation, an initiation mechanism is more similar to push-pull fatigue. in this case a 'fish-eye' pattern is formed around an elongated non-metallic inclusion, fig.1b. the torsion fatigue crack does not show a significant branching and 'factory roof' fracture is absent, fig.1a. unlike high-strength aluminum, a 38mnsv5s steels shows a surface crack initiation on the plane of maximum normal stress (45° by the specimen's axis) [11] and further propagation in inclined (by the specimen's length) plane with tendency to turn back to the maximum shear stress plane. (a) (b) figure 1: subsurface fatigue crack initiation in 100c6 steel under ultrasonic torsion, shear stress is 360 mpa, nf is 109 cycles [10]. ultrasonic torsion vhcf data on titanium alloy are not available in the literature. the study of ti-alloys under torsion loading in vhcf regime is a very interesting subject, because titanium is defect free metal which has a quite complex micro-structure that may produce internal crack initiation, like shown under push-pull fatigue [12]. present paper is focused on the study of crack initiation mechanisms in aeronautic titanium alloy vt3-1 under ultrasonic torsion in vhcf (106 – 109 cycles). two main questions are discussed: (1) does a vhcf torsion loading may produce and internal crack initiation in vt3-1 titanium alloy; (2) does fatigue crack initiation an early crack growth stage in vt3-1 under torsion loading will be similar to ones that were observed under push-pull loading. experimental procedure materials aterial for present investigation is two phase titanium alloy vt3-1 (similar to ti-6al-4v) which is commonly used in aircraft engine industry. its chemical composition is presented in tab. 1. two sets of specimens were used for present investigation. the first set was machined from a real compressor disk of tu-154 aircraft. this disk was produced by forging technology for d30 engine. this compressor disk was in service for 6000 flight cycles (takeoff – landing). an estimate in service time is about 18000 hours. after in-service the disk was checked for damage tracks by non-destructive control methods. this analysis did not show any fatigue damage due to in-service loading and the disk was transmitted to fatigue tests. m a. nikitin et alii, frattura ed integrità strutturale, 35 (2016) 213-222; doi: 10.3221/igf-esis.35.25 215 fe c si cr mo n al zr o h titanium 0.2 07 < 0.1 0.15 – 0.4 0.8 2 2 3 < 0.05 5.5 7 < 0.5 < 0.15 < 0.015 balance table 1: chemical composition of vt3-1 titanium alloy, weight %. the second set of specimens was machined from virgin extruded bars, produced by all russian institution of light alloys with respect to state standards [13]. heat treatment was performed to get a fully lamellar micro-structure and mechanical properties close to forged vt3-1. mechanical properties of both materials were obtained on tensile specimens of 75 mm in length under displacement rate of 0.075 mm/min. the result of tensile test and obtained mechanical properties are listed in tab 2. process young's modulus, gpa uts, mpa yield stress, mpa deformation at rupture, % mass density dynamic young's modulus (gpa) forged 114 989 960 6 4500 116 extruded 106 1107 1050 13 4500 110 table 2: mechanical properties of forged and extruded vt3-1 titanium alloys the extruded titanium alloy has mechanical properties a little bit higher than the forged one, except its elongation at rupture that is significantly different. it is more than two times higher for extruded titanium that is, therefore, more ductile. furthermore their micro-hardness is approximately the same: 364 hv500 for forged and 373 vh500 for extruded vt3-1. measurement was realized in the plane of maximum shear stress of specimens along a line through a cross-section of the specimen. results shows a pronounced scatter for the forged titanium alloy (the difference of 44 hv500 was found for points spaced by 1.2 mm), while for extruded vt3-1 it is less than 5 hv500 for the same distance. such difference may be explained by features of micro-structures for these alloys. the 3d mapping of the micro-structure is shown on fig. 2 for forged and extruded alloys. (a) (b) figure 2: the 3d mapping of micro-structure for (a) forged and (b) extruded vt3-1. both alloys have fully lamellar micro-structure with elongated alpha-platelets. in the case of forged vt3-1 platelet size is larger (about 2 µm in width and 10-15 µm in length), while w = 1 µm by l = 2-3 µm for the extruded one. moreover, micro-structure of extruded titanium alloy is more homogeneous (except some zones in the core of the bar), while the micro-structure of forged titanium is processed in macroscopically large zones with similar platelets morphology. these zones called 'macro-zones' [14] and characterized by similar crystallographic orientations of the platelets within each macro-zone. the existence of such specific of micro-structure explains the large scatter obtained in micro-hardness values for forged vt3-1. a. nikitin et alii, frattura ed integrità strutturale, 35 (2016) 213-222; doi: 10.3221/igf-esis.35.25 216 experimental method torsion fatigue tests were performed on specimens, designed according to ultrasonic concept applied to torsion [3, 14] and taking into an account dynamic elastic properties of materials at 20 khz (tab.2). specimens made of forged vt3-1 were cut from the rim part of compressor disk along an axis of disk symmetry. specimens made of extruded vt3-1 were machined from bar so that specimen's longitudinal axis is the same than extrusion direction. geometry of ultrasonic torsion specimens is presented on fig.3a. working section of specimen was polished by emery papers from grade 600 to 1000. fatigue tests were performed continuously (without pulse pause) by using a self-designed ultrasonic torsion system [14], (fig.3b) up to fatigue failure or run out limit of 109 cycles. all the tests were performed at room temperature with permanent compressed dry-air cooling. an infrared camera was used for monitoring surface temperature of specimen during fatigue tests. result shows that there is now significant self-heating effect in vt3-1 titanium alloy under torsion loads [15]. (a) (b) figure 3: (a) geometry of ultrasonic torsion specimen and (b) ultrasonic torsion testing system. the calibration of the testing system was performed with strain gauge and vishay conditioning device with a large bandwidth (up to 100 khz). calibration shows a perfect linear relation between applied tension and measured deformation. the fatigue crack under torsion is detected by drop of resonance frequency. this crack detection is done automatically with a high-performance computer feet-back controller. after each test the crack existence is verified by optical microscope. when the crack is detected, a specimen was subjected to self-designed method of specimen opening. as was discussed above, titanium alloy is ductile material and an important plastic deformation may leads to destruction of fracture surface during direct opening. in order to minimize these risks a 'life section' of specimens is reduced by electro-erosion cut. a fill is placed beside a fatigue crack so that surface crack tips are placed on the same line with a wire (in present case it is inclined 45° with respect the specimen longitudinal axis). after reducing the ‘life section’, the specimen is cooled by liquid nitrogen and subjected to sharp shock, so that provide fatigue crack opening. after opening, all the cracked specimens were analysed by using scanning electron microscopy (sem). an additional attention has been paid to the crack initiation mechanisms. results sn-curves for forged and extruded ti-alloys he results of fatigue tests on both forged (fig.4a) and extruded (fig.5a) titanium alloy shows that fatigue failure under pure torsion loading may occur well beyond 106 cycles. in spite of limited fatigue data on forged vt3-1 it is possible to plot a curve fitting the results. this curve will have an important slope in the vhcf range. decreasing in fatigue strength with increasing number of loading cycles is more pronounced for torsion mode compared to results of axial tension-compressing tests [16] that is presented on fig.4b. in order to compare the results of torsion and axial tests, the following equation was used to recalculate the shear stress amplitude into equivalent (von mises) normal stress t a. nikitin et alii, frattura ed integrità strutturale, 35 (2016) 213-222; doi: 10.3221/igf-esis.35.25 217 3   . it can be pointed out that points plotted in equivalent stress terms for forged vt3-1 show a good agreement and grouped near to 400 mpa that is about 40 % of uts. this result is similar to typical results on titanium alloys in the hcf range. (a) (b) figure 4: results of fatigue tests on forged vt3-1 titanium alloy (a) torsion data in terms of shear stress amplitude and (b) tension compression r=-1 and torsion data in terms of equivalent normal stress amplitude. the torsion results cover a range of fatigue life from about 106 to 108 cycles. based on previous results obtained on forged vt3-1 under fully reversed tension loading, the crack initiation mechanisms could be quite different at such fatigue life for forged alloy [16]. besides a changing from surface to subsurface crack initiation mode, it has been reported about microstructural fatigue life controlling mechanisms. in the case of torsion loading, a transition from surface to subsurface initiation after longer fatigue life was also found. however, this transition appears at fatigue life of about two order of magnitude longer. detailed analysis on fatigue crack initiation mechanisms under torsion loading will be provided in the section ‘discussion’. (a) (b) figure 5: results of fatigue tests on extruded vt3-1 titanium alloy (a) torsion data in terms of shear stress amplitude and (b) tension compression r=-1 and torsion data in terms of von mises equivalent stress amplitude. like for the forged alloy, the sn curve in torsion for the extruded vt3-1 titanium alloy exhibits a significant slope in vhcf regime, fig.5a. since the fatigue tests were stopped around 109 cycles, most of the cracks were observed in the fatigue life range below 109 cycles. as already was done for the forged alloy, the results of torsion tests on extruded vt3-1 a. nikitin et alii, frattura ed integrità strutturale, 35 (2016) 213-222; doi: 10.3221/igf-esis.35.25 218 titanium alloy were compared with previous results [17] obtained on the material but under fully reversed tension, fig. 5b. in terms of von mises equivalent stress amplitude, like for the forged alloy, the slope of the sn-curve is more important under torsion than under tension-compression. however, unlike the forged alloy, fatigue strength of extruded titanium is higher (about 50 mpa) in torsion than in tension-compression. this shows that the von mises equivalent stress is not suitable to describe the vhcf strength of this alloy. in order to try to explain such mechanical behavior the analysis of the fracture surface was carried out both by optical microscopy and sem. unlike tension-compression, where only subsurface crack were observed, in case of torsion load a transition from surface to subsurface crack initiation was found. comparison of results on forged and extruded titanium alloy (fig.4 and fig.5) shows that fatigue strength of extruded titanium alloy is higher compared to the forged one that is in good agreement with mechanical properties of materials (tab.2). crack initiation cracks in torsion specimens were first observed on a lateral surface of specimens by optical microscopy. it was pointed out, that for most of the investigated specimens the first stage of crack propagation was observed on a plane experiencing the maximum shear stress amplitude i.e. perpendicular or parallel to the specimen’s longitudinal axis. further, when the crack became longer it bifurcated (stage ii) and propagated in mode i on plane(s) of maximum normal stress (i.e. on plane having an angle about 45° with regard to the specimen’s longitudinal axis). the propagation of long crack was never observed in the plane of maximum shear stress amplitude up to the final length (corresponding to the end of the test). it should be noted, that crack growth in the plane of maximum normal stress may be found as in a single plane, as well in two planes at the same time (x-type cracks), fig.6b. this is similar to hcf regime on many metals. (a) (b) figure 6: optical microscopy at the surface of torsion specimens: (a) single crack in the plane of maximum normal stress and (b) two cracks in two 45° orientated planes of maximum normal stress or x-type crack. crack growth under torsion loading in the plane of maximum normal stress looks to be quite sensitive to material microstructure. comparing the surface crack path of extruded and forged titanium alloy it is notable, that branching of the crack is higher for forged titanium alloy represented by less homogenous microstructure. an example of crack path in extruded titanium alloy is showing on the fig.6a. in this case the crack is quite well orientated on the 45° plane, while in case of forged titanium alloy, fig.6b, the crack path is more ‘zigzag’ (alternative branching mode i and mode ii). sometimes crack make a clear ‘steps’ or even sometimes it is propagating in a two parallel 45° planes. an observation on a fracture surface of torsion specimens (after opening) shows two types of crack for both alloys: (1) surface crack and (2) subsurface crack. in the case of extruded vt3-1 these two mechanisms are more clear, fig.7 in the case of surface crack initiation the roughness of the fracture surface is lower. that can be concluded based on a more homogeneous color. in the case of subsurface crack initiation, a roughness of fracture surface in the area of subsurface and surface crack propagation is not the same, that clearly seen by pronounceable color change. subsurface crack initiation under torsion loading leads to forming a well known (in push-pull) ‘fish eye’ pattern [3]. but unlike pushpull loading, torsion cyclic loading produced an oval ‘fish-eye’ a. nikitin et alii, frattura ed integrità strutturale, 35 (2016) 213-222; doi: 10.3221/igf-esis.35.25 219 (a) (b) figure 7: surface (a) and subsurface ‘fish-eye’ (b) crack initiations in extruded vt3-1 titanium alloy under torsion loading. the next difference between torsion and pull-push ‘fish-eye’ is the nature of smooth area. in the case of axial loading, the formation of such area is governed by crack growth rate, while in the case of torsion ‘fish-eye’ a second factor can be stated. indeed the smooth area of torsion crack is limited by an ellipse, that ‘touches’ the specimen surface. more rough fracture surface is starting to form when an internal crack reaches the specimen surface. probably, there are several factors acting together and leading to fracture roughness modification. one can say: (1) the crack growth rate increasing when the crack reaches the specimen surface; (2) presence of environment (gasses) into the crack, when it connects to the surface. anyway, a smooth area of torsion ‘fish-eye’ exists till an internal crack turns to a surface crack. the next pronounceable difference between surface and subsurface initiation is less expressed branching of internal crack. on fig.7a several clear traces can be observed. these traces are formed due to crack propagation in series of parallel planes, orientated at 45° with regard to the specimen longitudinal axis. in the case of subsurface crack initiation, growth of several cracks in 45° planes is also possible, but this is well limited. it is interesting to point out, that in the case of high strength steel, fig.1a [10], a fracture surface with internal crack initiation does not show a significant branching pattern (no 45° ‘wings’ ). discussions irst of all, the comparison of sn-curves for push-pull and torsion loadings (fig.4 and 5) shows a more important slope of sn-curve in the case of torsion loading. this tendency keeps being the same as for forged, as well for extruded titanium alloy in spite of small difference of sn-curves for these alloys under push-pull fatigue. this means that vt3-1 titanium is more sensitive to shear stress than to normal one. this is typical for ductile metals. however, long crack propagation is observed in planes of maximum normal stress which is typical for more brittle material. therefore, at the very first stage of fatigue crack initiation, when a crack length is about the same order than the grain size the fatigue behavior of titanium is similar to ductile material and fatigue damage accumulation is due to sliding process. in the case of two-phase   titanium alloy a higher capacity to accommodate plastic sliding has a hexagonal alpha-phase. thus, the fatigue resistance of titanium alloy to torsion loading may be related to features of alpha-platelets. in the case of surface torsion crack it can be observed macroscopically at surface in one of two maximum shear stress planes: along or perpendicularly to specimen’s axis. fig.8b shows an example of first torsion crack growth stage along an axis. when torsion crack reaches a length of several micrometers, the crack growth turns into a plane of maximum normal stress, fig. 8b. typical size of alpha-platelets is very small for the studied titanium alloys and micro-plasticity of alphaphase is not enough to accumulate fatigue damage at later stage of crack growth that turns fatigue behavior of material to the brittle-mode failure (governed by the normal stress cracking mechanisms). another reason that can limit the stage of crack growth in shear plane is quite high deformation rate in the case of ultrasonic loading. but anyway, a transition from maximum shear to normal stress plane is typical for torsion cracking at different loading frequencies. in reference [18] fully reversed torsion fatigue tests were carried out on titanium alloy ti-6al-4v in hcf regime at a loading frequency of f a. nikitin et alii, frattura ed integrità strutturale, 35 (2016) 213-222; doi: 10.3221/igf-esis.35.25 220 10 hz. the authors also observed a surface crack along the specimen’s axis which reached a length of about 700 µm in maximum shear stress plane before bifurcation onto the maximum normal stress plane. (a) (b) figure 8: surface crack initiation in forged vt3-1 under torsion loading (a) overview of torsion crack with initiation site marked by arrow and (b) detailed crack initiation view. the microstructure of tia6v titanium alloy [18] is globular and coarse that is different from present ti-6al-4mo titanium alloy microstructure. thus, it is difficult to distinguish the role of microstructure and loading frequency on duration of crack growth in shear plane, but it is clear, that this growth stage should be limited by the material capability to accumulate plastic deformation. it has been shown that in the case of hcf a torsion crack first growth in depth of material and after starts to branch at the surface without growing in depth [18]. in the present work on vt3-1 titanium alloy crack tip position versus number of cycles was not monitored and crack shape was reconstructed based on the fracture surface pattern. in the case of surface crack initiation a sort of crack branching threshold or critical crack length was found, fig.9. it seems that at a certain crack length internal crack branching is also possible in the case of vhcf loading that is different from hcf. a slight difference in the fracture surface color in zones before and after branching is due to different roughness that is usually associated with difference in stress intensity factors or crack growth rate. (a) (b) figure 9: fracture surfaces of specimens (a) s=; nf= (b) s=; nf=; with clear border of fatigue crack branching. unfortunately, a reconstruction of the very first stage of torsion crack growth based on fracture pattern is problematic due to destruction of the fracture surface near the initiation site by friction between crack lips during mode ii stage. finally, a surface torsion crack in vhcf is similar to hcf growth i.e. it initiates on the maximum shear stress plane and a. nikitin et alii, frattura ed integrità strutturale, 35 (2016) 213-222; doi: 10.3221/igf-esis.35.25 221 growth in mode ii at the very first stage, but a crack growth bifurcation mechanism seems different for hcf and vhcf. in the case of vhcf branching can be observed in the bulk of material, while in hcf it appears at the surface [18] such difference in the branching mechanism may have the same nature with one more interesting feature of vhcf torsion behavior. that is an internal crack initiation under vhcf torsion loading in spite of maximum shear stress located at the surface. an analysis of internal crack initiation site in vt3-1 titanium alloy did not show any structural flaw in the microstructure so that inclusions or clusters of alpha-platelets, fig. 10. the crack initiation site is significantly destroyed by friction that is clearly seen in fig.10b. a ‘step’ at the fracture surface and followed crack growth in two parallel planes means that internal crack is also initiated in the plane of maximum shear stress. after reaching a certain length (that is shorter than the distance from initiation site to surface) the crack branches on the plane of maximum normal stress. sometimes there is a sort of competition between two maximum normal stress planes that produce a ‘wing’ like structure at the surface. excluding this ‘wing’-like structures, a further branching is limited in the case of internal crack initiation and no branching ‘threshold’ (like in case of surface crack) can be found at the fracture surface. in contrary, another notable zone or critical crack length can be reported. as shown in fig.7b the crack front shape is changing as soon as it arrives at the surface, probably because the stress intensity factor is increasing and consequently the crack growth rate too. (a) (b) figure 10: fracture surfaces of specimens (a) s=; nf= (b) s=; nf=; with clear border of fatigue crack branching. finally, for forged titanium alloy loaded under push-pull fatigue crack initiations were mainly associated with macro-zones and smooth facets cracking [16], while in the case of torsion loading these features were not found. conclusions ased on the results of fatigue tests under pure ultrasonic torsion the next conclusions can be drawn up: (1) sn curves of vt3-1 titanium alloy under torsion r=-1 loading have a more significant slope, compared to results under fully revered tension. however, the relation between axial and torsion fatigue strength obtained for hcf seems to be applicable for vhcf data. (2) independently on the production process (forging and extrusion) two different crack initiation sites were found: surface and subsurface crack. the subsurface crack initiations were observed for specimens failed at longer fatigue life. transition from surface to subsurface crack initiation was found well after the same transition for push-pull loading: about 108 cycles for torsion and 106 cycles for axial loading. (3) qualitatively, a surface cracking under torsion loading in vhcf is similar to hcf results, except an additional possibility for internal crack to branch in vhcf regime. (4) a sort of branching ‘threshold’ or critical crack length can be found at the fracture surface, beyond which a torsion crack shows several branches in another 45° plane of maximum normal stress. (5) in the case of internal crack, an initiation and early crack growth is also being in mode ii. bifurcation to a normal stress plane growth happens before the crack reaches the specimen’s surface. further crack growth is processed along the specimen surface. at later stage of subsurface growing a crack turns to the surface. the moment when subsurface b a. nikitin et alii, frattura ed integrità strutturale, 35 (2016) 213-222; doi: 10.3221/igf-esis.35.25 222 crack reaches a surface is clearly defined by different fracture morphology that is similar to well known ‘fish-eye’ crack. references [1] shimamura, y., narita, k., ishii, h., tohgo, k., fujii, t., yagasaki, t., harada, m., fatigue properties of carburized alloy steel in very high cycle regime under torsional loading, int.j. of fatigue, 60 (2014) 57-62. doi: 10.1016/j.ijfatigue 2013.06.016. [2] tschegg, e.k., stanzl-tschegg, s.e., mayer, h.r., high frequency method for torsion fatigue testing. ultrasonics, 31(4) (1993) 275 280. [3] bathias, c., paris, p.c., gigacycle fatigue in mechanical practice, dekker, new york, 2004, isbn-10: 0824723139. [4] nicholas, t., critical issues in high cycle fatigue, int. j. of fatigue, 21 (1999) s221-s231. doi: 10.1016/s01421123(99)00074-2. [5] sakai, t., review and prospects for current studies on very high cycle fatigue of metallic materials for machine structural use, j.solid mechanics and material engineering, 3(3) (2009) 425-439. doi: 10.1299/jmmp.3.425. [6] bathias, c., piezoelectric fatigue testing machines and devices, int. j. of fatigue, 28(11) (2006) 1438-1445. doi: 10.1016/j.ijfatigue.2005.09.020. [7] mayer, h., schuller, r., karr, u., irrasch, d., fitzka, m., hahn, m., bacher-hochst, m., cyclic torsion very high cycle fatigue of vdsicr spring steel at different load ratios, 70 (2015) 322-327. doi: 10.1016/j.ijfatigue.2014.10.007. [8] ishii, h., tohgo, k., fujii, t., yagasaki, t., harada, m., shimamura, y., narita, k., fatigue properties of carburised alloy steel in very high cycle regime under torsion loading, int. j. of fatigue, 60 (2014) 57-62. doi: 10.1016/j.ijfatigue.2013.06.016. [9] mayer, h., ultrasonic torsion and tension-compression fatigue testing: measuring principles and investigations on 2024-t351 aluminium alloy, 28(11) (2006), 1446-1455. doi: 10.1016/j.ijfatigue.2005.05.020. [10] xue, h.q., bathias, c., crack path in torsion loading in very high cycle fatigue regime, engineering fracture mechanics, 77 (2010) 1866-1873. doi: 10.1016/j.engfracmech.2010.05.006. [11] marines-garcia, i., doucet, j.p., bathias, c., development of a new device to perform torsional ultrasonic fatigue testing, int. j. of fatigue, 29 (2007) 2094-2101. doi: 10.1016/j.ijfatigue.2007.03.016. [12] nikitin, a., palin-luc, t., shanyavskiy, a., bathias, c., fatigue cracking in bifurcation area of titanium alloy at 20 khz, proceeding crack path, (2012) 367-374. isbn: 9788895940441. [13] russian state standard gost-19807-91, titanium and wrought titanium alloys, (2009). [14] bathias, c., nikitin, a., palin-luc, t., a new piezoelectric fatigue testing machine in pure torsion for gigacycle regime, 2014, 6th international conference vhcf-6, chengdu, china. [15] nikitin, a., palin-luc, t., bathias, c., a new piezoelectric fatigue testing machine in pure torsion for ultrasonic gigacycle fatigue tests: application to forged and extruded titanium alloys, fatigue and fracture of engineering materials and structures, online: 2015. doi: 10.1111/ffe.12340 [16] nikitin, a., shanyavskiy, a., palin-luc, t., bathias, c., fatigue behaviour of the titanium alloy ti-6al-4mo in bifurcation area at 20 khz, 2012, 19th european conference on fracture ecf-19, kazan, russia. [17] nikitin, a., la fatigue gigacycle d’un alliage de titane, these doctorale, ecole doctorale 139, u-paris 10 nanterre la defense, (2015). [18] shiozawa, d., nakai, y., murakami, t., nosho, h., observation of 3d shape and propagation mode transition of fatigue cracks in ti-6al-4v under cyclic torsion using ct imaging with ultra-bright synchrotron radiation, int. j. of fatigue, 58 (2014) 158-165. doi: 10:1016/j.ijfatigue.2013.02.018. << /ascii85encodepages false /allowtransparency false /autopositionepsfiles true /autorotatepages /none /binding /left /calgrayprofile (dot gain 20%) /calrgbprofile (srgb iec61966-2.1) /calcmykprofile (u.s. web coated \050swop\051 v2) /srgbprofile (srgb iec61966-2.1) /cannotembedfontpolicy /error /compatibilitylevel 1.4 /compressobjects /tags /compresspages true /convertimagestoindexed true /passthroughjpegimages true /createjobticket false /defaultrenderingintent /default /detectblends true /detectcurves 0.0000 /colorconversionstrategy /cmyk /dothumbnails false /embedallfonts true /embedopentype false /parseiccprofilesincomments true /embedjoboptions true /dscreportinglevel 0 /emitdscwarnings 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can be opened with acrobat and adobe reader 5.0 and later.) >> /namespace [ (adobe) (common) (1.0) ] /othernamespaces [ << /asreaderspreads false /cropimagestoframes true /errorcontrol /warnandcontinue /flattenerignorespreadoverrides false /includeguidesgrids false /includenonprinting false /includeslug false /namespace [ (adobe) (indesign) (4.0) ] /omitplacedbitmaps false /omitplacedeps false /omitplacedpdf false /simulateoverprint /legacy >> << /addbleedmarks false /addcolorbars false /addcropmarks false /addpageinfo false /addregmarks false /convertcolors /converttocmyk /destinationprofilename () /destinationprofileselector /documentcmyk /downsample16bitimages true /flattenerpreset << /presetselector /mediumresolution >> /formelements false /generatestructure false /includebookmarks false /includehyperlinks false /includeinteractive false /includelayers false /includeprofiles false /multimediahandling /useobjectsettings /namespace [ (adobe) (creativesuite) (2.0) ] /pdfxoutputintentprofileselector /documentcmyk /preserveediting true /untaggedcmykhandling /leaveuntagged /untaggedrgbhandling /usedocumentprofile /usedocumentbleed false >> ] >> setdistillerparams << /hwresolution [2400 2400] /pagesize [612.000 792.000] >> setpagedevice microsoft word numero_44_art_5_ap m. ciavarella et alii, frattura ed integrità strutturale, 44 (2018) 49-63; doi: 10.3221/igf-esis.44.05 49 on notch and crack size effects in fatigue, paris’ law and implications for wöhler curves m. ciavarella politecnico di bari, department of mechanics, mathematics and management, viale japigia 182, 70126 bari, italy mciava@poliba.it a. papangelo politecnico di bari, department of mechanics, mathematics and management, viale japigia 182, 70126 bari, italy hamburg university of technology, department of mechanical engineering, am schwarzenberg-campus 1, 21073 hamburg, germany antonio.papangelo@poliba.it abstract. as often done in design practice, the wöhler curve of a specimen, in the absence of more direct information, can be crudely retrieved by interpolating with a power-law curve between static strength at a given conventional low number of cycles n0 (of the order of 10-103), and the fatigue limit at a “infinite life”, also conventional, typically n∞=2·106 or n∞=107 cycles. these assumptions introduce some uncertainty, but otherwise both the static regime and the infinite life are relatively well known. specifically, by elaborating on recent unified treatments of notch and crack effects on infinite life, and using similar concepts to the static failure cases, an interpolation procedure is suggested for the finite life region. considering two ratios, i.e. toughness to fatigue threshold fk=kic/kth, and static strength to endurance limit, frr0, qualitative trends are obtained for the finite life region. paris’ and wöhler’s coefficients fundamentally depend on these two ratios, which can be also defined “sensitivities” of materials to fatigue when cracked and uncracked, respectively: higher sensitivity means stringent need for design for fatigue. a generalized wöhler coefficient, k’, is found as a function of the intrinsic wöhler coefficient k of the material and the size of the crack or notch. we find that for a notched structure, k<k’<m, as a function of size of the notch: in particular, k’=k holds for small notches, then k’ decreases up to a limiting value (which depends upon kt for mildly notched structures, or on fk and fr only for severe notch or crack). a perhaps surprising return to the original slope k is found for very large blunt notches. finally, paris’ law should hold for a distinctly cracked structure, i.e. having a long-crack; indeed, paris’ coefficient m is coincident with the limiting value of k’lim. the scope of this note is only qualitative and aims at a discussion over unified treatments in fatigue. citation: ciavarella, m., papangelo., a., on notch and crack size effects in fatigue, paris’ law and implications for wöhler curves, 44 (2018) 49-63. received: 24.01.2018 accepted: 30.01.2018 published: 01.04.2018 copyright: © 2018 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. m. ciavarella et alii, frattura ed integrità strutturale, 44 (2018) 49-63; doi: 10.3221/igf-esis.44.05 50 keywords. fatigue; wöhler curve; notch sensitivity; paris’ law; ashby maps. introduction t is well known that initiation and propagation of cracks are well distinct phenomena, and depend strongly on the material, geometry and load levels (for a review see for example fleck et al [1]). for nominally plain specimen, at low load levels, where we expect fatigue failure at high cycle numbers (hcf, high cycle fatigue) practically the whole life is expended in enucleating the crack, rather than propagating: indeed the latter phase only takes the final few cycles. at high load levels (those giving low number of cycles, lcf), cyclic plastic deformation takes place rapidly leading to failure. these various processes result in the well know empirical wöhler curve (or, more in detail, in the basquin-coffin-manson’s law). vice versa, for cracked specimen, fatigue life (often denominated “residual”) is all given by propagation, generally by paris’s law. the case of notched specimen is somewhere intermediate, and neither basquin-coffin-manson’s law nor paris’s laws (nor indeed any other law) apply directly to find the fatigue life. various alternatives are possible: trying to follow the cyclic plastic deformations at the notch tip (perhaps using neuber’s rule) to link initiation to use basquin-coffin-manson’s law at some critical point, and/or integrating paris’ law for a crack once initiated at the crack tip itself. the two processes are not straightforward and certainly at not of the same order of sophistication as the direct use of the wöhler curve or paris law as it is possible with plain specimen or cracked ones. also, some inconsistencies may arise in the procedure, as the use of paris law requires complications for taking into account of short crack behaviour, crack shielding and closure etc. on the other hand, the use of coffin-manson also requires some care when applied to the multiaxial elasto/plastic stress field induced around the tip of a notch (even if the global stress field is uniaxial). in short, the apparently more accurate procedures may be sometimes more complicated but basically remain extrapolations, and hence their degree of accuracy may not be necessarily satisfactory. at the other extreme, i.e. at very low number of cycles (or indeed static failure), rupture is expected to be dominated by plastic flow or brittle fracture, and it is only apparently easier to make an estimate of the strength of a notched component. most often, in design rules of a notched components, a distinction is drawn between “brittle” and “ductile” materials: in the former case, it is suggested that the peak stress criterion is appropriate, whereas in the second case it is generally considered that a “redistribution” of stresses occurs, such that the ultimate limit is only reached when an entire section of the specimen is loaded at the yield strength. it is pointed out here, however, that the distinction is far from quantitatively clear, as it is well known in the context of fracture mechanics: indeed, a cracked specimen is “brittle” for sufficiently large crack sizes in the sense that it fails by critical condition for propagation of the crack, whereas it would be ductile, i.e. failing by plastic collapse, for lower sizes of the crack, and this independently on the material itself. hence, the definition of brittleness depends on absolute dimension of the crack, and indeed various authors have recognized this [2-3]. a similar “size effect” is expected therefore to occur for a notch of sufficiently “sharp” geometry and indeed for a rounded notch, although the transition brittle to ductile (and vice-versa) would occur at different geometrical sizes. in the corresponding case of infinite life in fatigue, the equivalent of the transition between ductile and brittle behaviour is the transition between fatigue-limit dominated failure (initiation), and fatigue threshold dominated initiation. also, it is well recognized in fatigue that notches behave more or less like cracks (crack-like notches, in the smith and miller [4] classification and as recognized in the atzori and lazzarin [5] criterion) up to a certain size (which depends on material properties), and it is expected that, although plasticity makes a difference, in the static case something similar could happen. certainly, there is no fundamental reason to make a distinction between “brittle” and “ductile” materials when examining notched structures. in particular, for a very small notch, it is evident that the nominal strength will be unaffected, and would for example remain the nominal yield stress over the net section (or, without any significant difference, the gross, given it is nearly the same) of the specimen, and for larger notch sizes of sufficiently sharp appearance, the effect of the notch will be close to the effect of a crack of “same size”, and finally, when the notch size is large enough, the peak stress criterion will become actually the most stringiest condition of all. notice that the full yield in the net section limit is independent on geometry, so is actually valid also for the crack. finally, notice that in terms of the gross section, this reasoning translates without modification, when the ratio anet/agross , where anet is the net section, and agross is the gross section, is introduced. i m. ciavarella et alii, frattura ed integrità strutturale, 44 (2018) 49-63; doi: 10.3221/igf-esis.44.05 51 another reason why notch size effects are less clear than crack size effects, and have perhaps escaped the attention of researchers, is that a notch doesn’t have a well-defined “dimension”. however, this problem should not be amplified. in fact, the dimension of a crack is only apparently better defined, because this is only when in the case of a through-crack, but the situation is largely less clear when the crack is curved, or has a fully developed 3d shape. in this case, as well as in any notch case, the size effect refers in principle to the comparison of specimen of exactly the same geometry (including the crack or the notch features) but of various magnifications. the choice of the linear dimension for the magnification factor is arbitrary. the difficulty starts when the equivalent condition for the comparison with the appropriate material property has to be chosen. this is where the crack and the notch case, strictly speaking, differ. the crack case presents a singular solution which by definition is self-similar, and therefore the entire solution, asymptotically, is given for a certain mode of deformation, independently on the exact geometry. therefore, a single factor is sufficient to define the “strength” of the singular field – and this the well-known stress intensity factor. in the case of the notch, in principle every geometry is different, in the sense that the stress field cannot be characterized by a single geometrical factor, but in the region where the notch is equivalent to a crack (crack-like notch), the required procedure is to find the path of the equivalent “crack” -- although this may not be necessarily simple and uniquely defined. a very important paper by atzori et al [6] has suggested a criterion to correlate notch and crack behaviour at the fatigue limit to real components and verified by means of an impressive set of 78 fatigue test series for 10 different steels and aluminium alloys taken from the literature. this paper however is limited to the behaviour at the fatigue limit, while here we try to investigate more general trends. this paper is clearly qualitative, and oriented towards the classical approaches which suggest to interpolate between static strength and fatigue limit: we added to this only the el haddad type of law, which take into account of linear elastic fracture mechanics either at the static strength, or at the fatigue limit. however, we haven’t added consideration of crack propagation laws, nor compared to these predictions, which so far we are unable to do. paris law for crack growth has a series of limitations, to cover also the case of "initiation" and "short crack" propagation. for example, in previous studies [7-10], we have shown that for paris' law to be compatible with the behaviour of sn curves for uncracked materials, one needs to modify it to include also the "material properties" of basquin law. it would be a final goal to have a model containing the two constants of paris law and the 2 constants of basquin law: also, with the two fatigue "thresholds" --this complete and comprehensive model would amount to six constants in total. however, such a simple model at present is too difficult and not existing. when paris law constant m is low, the sn curve for the material (when uncracked) has a rather different slope than the integrated form of paris law [11-12], that is k>>m. possible corrections would need to include the effect of plasticity at the crack tip, which effectively increases the size of the “equivalent crack”, but again this is not pursued in the present paper. the scope of the present paper is therefore to try to “unify” crudely various concepts for static and fatigue design, without any intention to give radically new methodologies, or empirical formulae, but with the simpler scope of examining various ranges of validity and overlap between the theories which often are treated separately, and with principally the suggestion to use interpolation between robust estimates of limit conditions and the use of all the material properties which are available, rather than extrapolation from a single methodology using a limited set of material properties, independently on how refined the methodology may appear to be. this is not necessarily limited to preliminary calculations, but also when there is possibility of some experimental investigations, as a simpler route for understanding of the behaviour in fatigue of a notched component. ultimately, the core of the message becomes quite obvious to the engineer, and indeed it is the base of various standard procedures for specific fields, like for example the design guides of gears (see for example [13]): “interpolate” between limit conditions, using some knowledge of the notch size effect (in the lack of direct experimental data) as recently emerged more clearly at least for the infinite life region. in particular, the entire spectrum of possible behaviour can be described in a single diagram strength vs. notch/crack size. empirical laws in fatigue wöhler curve mpirical laws have emerged in fatigue since when wöhler was conducting his famous experiments of rotating bending fatigue in railways axles for the german state railways in the 1860s. various authors noticed empirically that it was convenient to plot sn data on a log/log (or a semi-log) diagram (for a detailed study of the old literature see the recent paper by sendeckyj [14]). since then, the so-called wöhler sn diagram has been widely used. there is no fundamental reason to write the curve as a power-law, and indeed alternative equations have been suggested, but the power law between 2 given points is probably the simplest or most used form for the plain specimen, in the form (see fig.1): e m. ciavarella et alii, frattura ed integrità strutturale, 44 (2018) 49-63; doi: 10.3221/igf-esis.44.05 52       k k r fn n n0 0 ,  fn n n0 (1) where ∆σ is the stress range (we assume at the moment for simplicity that amplitude and range coincide i.e. the load ratio r=0, although it is clear that in general it would perhaps be appropriate to rewrite eq.(1) in terms of amplitude of the cycle σ) and the n0, and n are the number of cycles as defined in fig.1. clearly, eq.1 also implies           r n k f k n0 log log   (2) and typically for steels considering n∞=107 and n0=103, for frr0=2 we would have k=13.3, while for fr=3, k=8.4, in the typical range k=6-14 for al or ferrous alloys. in strain-controlled fatigue, the fatigue curve is replaced by a sum of two power/law functions assuming the fatigue life to be dominated by plastic strain in the lcf regime, and elastic strains or stresses in the hcf. the resulting well know equation (coffin/manson) is expected to be more accurate (if anything because it has more degrees of freedom to reproduce the experimental sn curve) although there is still a need to introduce the cut-off thresholds on very low and very high number of cycles, particularly on the low number of cycles where it tends to have the wrong concavity. n r 0 noo 0 tan( ) = k figure 1: the simplified wohler curve. paris’ law the second important power law in fatigue is paris’ law, giving the advancement of fatigue crack per cycle, va, as a function of the amplitude of stress intensity factor δk (see fig.2)    ma da v c k dn ;    th ick k k (3) where δkth is the “fatigue threshold”, and kic the “fracture toughness” of the material. there is therefore no dependence on absolute dimension of the crack. the law is mostly valid in the range 10-5—10-3 mm/cycle, and in a simplified form it can be considered intersecting δkth and kic at 10-6, 10-4 mm/cycle, respectively. this means that the constant c is not really arbitrary, since by writing the condition at the intersections,      m mth ic c k k 6 410 10 . an alternative form can be obtained considering that paris’ law is in general valid in the range 10-5—10-3 mm/cycle and hence instead of the constant c it is perhaps more elegant to define a constant δk-4, i.e. the range corresponding to a speed of propagation of 10-4 mm/cycle m. ciavarella et alii, frattura ed integrità strutturale, 44 (2018) 49-63; doi: 10.3221/igf-esis.44.05 53         m a k v c k 4 ' (4) where c’=10-4 mm/cycle by definition. in other words,         m c c k 4 1 ' (5) from the linearity in this range 10-5—10-3 mm/cycle in the log/log plot, fleck et al [1] suggest to find the paris exponent m as kf m 4 log (6) and fig.16 of their paper seems to confirm this assumption. more in general, it is possible to assume  c a k th a v m f v log log (7) where thav is a conventional velocity at the threshold, and c av at the critical conditions. a first obvious (and well known) link between the two curves (wöhler and paris) is obtained when considering the life of a distinctly cracked specimen having an initial crack size ai. under the assumptions of constant remote stress and no geometrical effects, for m>2 the following is obtained (where the dependence on the final size of the crack af has been removed as relatively not influent)            m m mm fi m a c n 2 /22    2 (8) this is to be considered as a wöhler curve of the cracked component and the wöhler exponent turns out to be exactly equal to the paris exponent, k’=m. it is interesting however to remark that the sn curve depends on the initial crack size, ai. hence the threshold condition from eq. (8) would tend not to coincide with that directly obtained from the threshold value which also depends on ai but with a different power      thlim th i k a ,  ; (9) in fact the two powers in eqs. (8,9) coincide only if (m-2)/2m=1/2 which is only true for very high m, showing in fact that the paris law should near the threshold have a vertical continuous slope, and the simplification of the paris law corresponds to a bifurcation to the solution given by the two branches (the threshold, and the power-law regime). this is another example of the risk of using these equations for extrapolations, without considering also the other information we have on the material properties. so far, we have only dealt with the case of either completely uncracked or the distinctly cracked specimen. most real cases would include notched specimen, or cracks of small size. we therefore need to introduce the theories on the effect of notches and cracks of varying size on fatigue life. kitagawa and atzori/lazzarin diagrams for infinite life (or safe-life) design, atzori & lazzarin [5] have recently proposed a new diagram (a generalization of the celebrated kitagawa diagram), which serves as a single “map” showing the fatigue limit reduction due to notch and cracks as a function of defect (or notch) size. for the interaction between fatigue limit and fatigue threshold for short cracks in the m. ciavarella et alii, frattura ed integrità strutturale, 44 (2018) 49-63; doi: 10.3221/igf-esis.44.05 54 kitagawa diagram el haddad et al. [15] had proposed the famous interpolating equation (concept of defect sensitivity): for a centred crack of size a, in terms of failure for a range δσ f         th f k a a0 (10) where a0 is the intrinsic material size for infinite life, defined as          thka 2 0 0 1 (11) where δσ0 is fatigue limit and δkth is fatigue threshold of the material. in fact it is well known that cracks smaller than this size do not follow paris law not even for δk>δkth, whereas the material is limited in this range by the fatigue limit, δσ0. figure 2: the paris law. the denomination “intrinsic crack” is due to the fact that the fatigue limit from (11) is also      th k a 0 0 ) (12) and hence (10) is equivalent to (12) when the intrinsic crack is added. as originally proposed by smith & miller [4] any notch is practically equivalent to a crack up to a certain size, depending on the stress concentration factor, kt. hence, atzori & lazzarin [5] suggested to consider only (i) crack-like behaviour treatable with standard fracture mechanics (in particular, with eq.(10)) and (ii) large blunt notches only, treatable with the simplest stress concentration factor approach. this is exemplified in the lines of fig.3. for a constant size of the notch, this criterion can also be put in terms of a limit kt, kt* , beyond which fatigue limit is no further decreased, giving an area where cracks are supposed to initiate from the notch but not propagate, the so-called “non-propagating crack zone”. notches with kt>kt* behave as defects of same dimension, i.e. are “crack-like tan( ) = m kth kic vc vth m. ciavarella et alii, frattura ed integrità strutturale, 44 (2018) 49-63; doi: 10.3221/igf-esis.44.05 55 notches”. by defining instead of a transitional stress concentration factor, as transitional size of the notch, a*, as the intersection of the horizontal line  tk0 / with the long crack threshold, gives1  t a k a * 2 0 (13) for notches lager than this size a*, simply the peak stress condition can be written in terms of failure range δσ f   f tk0  / (14) where tk is the stress concentration factor. it is natural to extend these concepts to the static failure case, drawing an el-haddad “equivalent line” for the static case, and accordingly introduce the dimensions sa0 analogous to (11) and depending this time by kic, the toughness of the material and r its tensile strength as          s ic r k a 2 0 1 (15) figure 3: the atzori-lazzarin generalized diagram (atzori & lazzarin [16]). fatigue and crack “sensitivities” and other material properties  n fleck et al [1] and in ashby [17, 18], a large number of material properties of interest are given, and of particular interest are the “intrinsic crack” sizes, a0, and a0s which can be retrieved qualitatively from some of the maps. they permit to classify “crack sensitivity” of the material, under static and fatigue load respectively (for example, a material 1 more precisely, the intersection should be defined with the el haddad line not the long crack threshold. the difference can be neglected however, if the stress concentration is not too small. i m. ciavarella et alii, frattura ed integrità strutturale, 44 (2018) 49-63; doi: 10.3221/igf-esis.44.05 56 with high a0 will tend to be insensitive to cracks up to the size of the order of a0 in fatigue). analogously, the two ratios   ic k th k f k , and     r rf 0 define the “fatigue sensitivities”. specifically, materials with high fk are fatigue sensitive when cracked, and those having large fr are fatigue sensitive when uncracked. in the former case, in the presence of a crack it is useful to design for fatigue crack propagation (like in the “damage tolerance” design approach), because the static limit is very high and the threshold condition is perhaps too strict, and there is margin to gain from a more elaborate design. similarly, when fr>>1, it is convenient to design when uncracked for the fatigue limit, or perhaps to the finite life required. the opposite is true when fk, fr are both small and close to one, in which case it is generally sufficient to design statically. finally, notice that as generally fk>>fr, a material sensitive to fatigue when uncracked is likely to be also sensitive to fatigue when cracked, whereas the vice versa is not true, a material sensitive to fatigue when cracked may not be sensitive to fatigue when uncracked. the two sensitivities (“crack sensitivity” and “fatigue sensitivity”) are not unrelated, as obviously a0s/a0=(fk/fr)2: when fk>>fr as it is usual, a0s/a0>>1 a fortiori. in other words, a material that is more sensitive to fatigue when uncracked than when cracked, then in terms of tolerance to crack sizes, is significantly more sensitive to cracks in fatigue than in static loading. materials which are equally sensitive to fatigue when cracked or uncracked, would have equal sensitivity to cracks under fatigue or static loads. from the maps in fleck et al [1] and in ashby [17, 18], a large number of qualitative data can be retrieved on these material properties and their ratios, as well as the characteristic sizes a0 , sa0 (which in turn for a given stress concentration factor can be put in terms of a*, sa * ). for example, two maps are reproduced in fig.4,5 here. in particular, fig.4 gives the fatigue threshold vs the fatigue limit (in terms of amplitude endurance limit), and constant lines of         th e k 2 δ1 4 , which can be put in relationship with the a0 defined in (11). for a0 we recognize values around 1 μm for some ceramic materials, up to few mm for some metallic alloys or polymers), whereas for the corresponding sa0 we see the value for composite materials, whereas in this particular collection for metals and polymers the yield stress rather than the failure stress is given and hence the plastic radius can be estimated rather than our sa0 , and finally for rocks and ceramics the compression failure stress is given. in all cases, we notice a certain correlation i.e. grouping around the diagonal line, corresponding to a tendency to have high values for properties at same time (however, within this general trend, there are remarkable exceptions, especially within single class of materials). however, it is seen that this holds more for uncracked properties, i.e. fr is relatively constant for materials (and for the definition of fr in fleck et al [1] and in ashby [17, 18] for some metals and polymers, we find fr>1). vice versa, fk varies significantly more and more still sa0 and a0 (particularly sa0 ). in other words, as it is commonly known, to an increase of strength does correspond generally an increase of fatigue strength, but an increase of toughness does not always correspond to an increase of threshold. moreover, to a greater threshold not always corresponds an increased fatigue limit, and even more the case that to an increase of toughness corresponds an increase of static strength. for example, for steel and metallic alloys, as is well known, to greater yield strength corresponds a reduced toughness, but this is not true for other classes of materials, such as composites, ceramics and cements. in general, fk>>fr, and for metals typical values are 5-20, and 2, respectively, so that sa0 is about 100 times greater than a0 . general wöhler curve he two atzori-lazzarin curves (static, and infinite life) permit some qualitative considerations on the intermediate, finite life, region of notched and cracked structures. the resulting map for general cracked or notched specimen is as shown in fig.3, as first presented by atzori-lazzarin at a conference in italy [16]. the shaded area corresponds to the “finite life region”. given a material with wöhler curve of exponent k, and of paris exponent m, we expect that the limiting wöhler curve exponent for a notched component will be the one for a large crack obeying paris’ law, for which klim=m. therefore, we can expect a notch of varying size and sharpness to cause a reduction of the wöhler slope k<k’(a)<m, i.e. intermediate between k and m. some calculations show this is indeed the case, and draw some estimates on the obtained values. t m. ciavarella et alii, frattura ed integrità strutturale, 44 (2018) 49-63; doi: 10.3221/igf-esis.44.05 57 figure 4: asbhy maps for fatigue threshold vs. fatigue endurance limit (reproduced with permission from (fleck et al. [1], fig. 10). figure 5: asbhy maps for fracture thoughness vs. strength (see appropriate definitions in the legend). reproduced with permission from asbhy [17], fig. 4.8, or asbhy [18], fig.10). the contour lines indicate the size of plastic radius. m. ciavarella et alii, frattura ed integrità strutturale, 44 (2018) 49-63; doi: 10.3221/igf-esis.44.05 58 by looking at fixed dimension of the notch, and interpolating between static and infinite-life strength, we can obtain the “generalized wöhler curve”, as well as a “generalized wöhler coefficient, k’(a)”. we shall start with a simplified version of the atzori-lazzarin schematically represented in fig.5, i.e. the criterion with line segments, to make the easiest possible estimate of the generalized slope k’ --we shall return to the more accurate el haddad version in the last paragraph. since a0s/a0=(fk/fr)2 and a*/a0=kt2 we also obtain a0s/ a*=(fk/fr)2 / kt2 . hence if kt< fk/fr then a0s> a* whereas if kt >fk/fr then a0s< a*.. we shall only consider fk>fr or as a limit case, fk=fr hence we have 3 cases: 1. case (a) fk>fr and kt< fk/fr (top of fig.6 where we see a0< a* < a0s < as* ) 2. case (b) fk=fr and kt >fk/fr=1 (bottom of fig.6 where we see a0=a0s< a*= as* ) 3. case (c) fk>fr but kt >fk/fr (fig.7 where we see a0<a0s< a*< as*) in the original case of fig.5 we recognize case (b) which is also typical for metals for high stress concentrations whereas also case (a) is possible since fk/fr =2-10. in any event, 5 regions can be seen in the atzori-lazzarin diagram. fig.6 also show the construction of the generalized wöhler curves corresponding to the key sizes (in other words, we have up to 4 distinct wöhler lines corresponding to the sizes a0 ,a0s, a*, as*). with reference to fig.5 (also reproduced in the details of the construction in fig.7), the 5 regions correspond to different trend of the resulting slope in the (a0<a0s < a*< as* ). in the first region, for a<a0 , k’=k remains unvaried to the value of the unnotched specimen. in the second region a0<a<a0s, we obtain a decrease of k’ up to a limit value, then remaining constant in the entire third region sa0 <a<a*, and which we obtain easily from writing a wohler-like power-law between the static strength value to the fatigue limit divided by the kt factor,            k k r t n n k 0 0 δ (16) if we divide the original wöhler curve (1) by (16) term by term, we obtain       kk kr tk k r n k0 0 δ δ (17) i.e.        r min t r k f k k f log    log (18) in other words, k’ decreases from the unnotched specimen case up to a limit value (depending on kt) given by eq.18. notice that this equation has been obtained without any need to specify n0 and n∞, except of course that these values are assumed to remain constant independently on the size of the notch. if a more general choice had been made, i.e. using new values n’0 and n’∞, and not the original n’0 and n’∞ of the wöhler curve in eq.1,              k k r f n n k ' 0 0 δ (19) and dividing again for (1)                 r min t r n n k f n n k k f 0 ' ' 0 / log log / log (20) and the decrease of k’ depends now on the variation of n’0 and n’∞, as a function of the notch size, and not just on kt. however, we shall neglect this possibility. m. ciavarella et alii, frattura ed integrità strutturale, 44 (2018) 49-63; doi: 10.3221/igf-esis.44.05 59 the limit case is when the stress concentration is high enough that kt>fk/fr in which case the limit ratios is obtained between the static and the fatigue limits, and consequently from (18)         r lim k k f k f log log (21) which is clearly the highest slope compatible to our criteria and the material properties ratios. the more general equation analogous to eq. (20) could be obtained by using kt>fk/fr in (20) or combining eqt(21) with eq. (6-7), obtaining in any case                 lim c a th a n n k m v v 0 log      log (22) which clearly seems to link the limit generalized wöhler slope to the paris slope and the position of the key points in the wöhler and paris laws, as it is correct since the limit generalized wöhler slope is indeed significant in the region where life would be mainly given by propagation. in fact, turning back to the standard assumptions for the key points ( thav , c av =10-6, 10-2 mm/cycle and, perhaps with less generality, n∞=107 and n0=103 cycles), we re-obtain the comforting result that the limiting wöhler coefficient coincides numerically with the paris coefficient:      lim k m m' 7 3 2 6 (23) as it was obtained independently from integrating paris’ law in (8). turning back to our classification, we have finally a 4th region, where a*<a< a*s where the slope starts to increase again towards the original value, k, which then remains constant in the fifth region. this is not too hard to interpret, given that a very large blunt notch basically behaves as a standard specimen subject to a nominal stress kt-times higher than the remote stress. in other words, we suggest that we start from the basic wöhler curve behaviour, we move towards paris with increasing notch size, but we then return to the original wöhler behaviour again, for very large blunt notches. notice that only the wöhler curves corresponding to the key sizes are reproduced in fig.6, whereas also some intermediate ones are included in fig.7 with lighter line. for case (a), fk>fr but kt <fk/fr the limiting slope is not reached, and we only obtain the minimum slope as (18) or (20). we then decrease slope in the fourth region and return to the original one in the fifth. the case (b) is somehow contrived and would correspond to an abrupt transition from wöhler towards paris and back to wöhler, the abrupt transition being particularly evident because of the schematic form of the criterion. wöhler curves using el haddad n the previous paragraph, we used the schematic version of the static and infinite life atzori-lazzarin criteria. here, we shall use the el haddad eqs. (10) and the corresponding static case. notice we can put these two equations in the form of a reduction fatigue kf in fatigue, and the corresponding ks reduction static factor            f t a for a a ak k for a a * 0 * 1 ,           ,       (24) and i m. ciavarella et alii, frattura ed integrità strutturale, 44 (2018) 49-63; doi: 10.3221/igf-esis.44.05 60             ss s t s a for a a ak k for a a * 0 * 1 ,           ,       (25) a0 a0 sa* a s* r tk kic kth e tk r 10 3 10 4 10 5 10 6 10 7 n e e a=0 a0 s a =* as* r tk kic kth e tk r 10 3 10 4 10 5 10 6 10 7 n e e figure 6: the interpolation procedure: example case (a) fk>fr and kt< fk/fr and case (b) fk=fr and kt>fk/fr=1. a0 a0 s a* as* r e tk kic kth e tk r 10 3 10 4 10 5 10 6 10 7 n e a0 a0 s a* as* a k figure 7: the generalized wohler slope as it results from an example interpolation procedure. case (c) fk>fr but kt>fk/fr. m. ciavarella et alii, frattura ed integrità strutturale, 44 (2018) 49-63; doi: 10.3221/igf-esis.44.05 61 these two curves (or better the inverse of these two curves) are reproduced in fig.8,9, as a function of a/a0 for some example cases (typical steel and typical ceramic, where fk=15.5, fr=2.4, and fk=2, fr=1.5, respectively). since the plots are given as a function of a/a0, the 1/kf curve “bends” around x=1, whereas the corresponding 1/ks curve “bends” around x= a0s / a0 which in fact scales with the square of the ratio fk/fr = 15.5/2.4=6.5, and fk=2/1.5=1.33, and hence a0s / a0=41.7 and 1.7 respectively, since a0s/a0=(fk/fr)2. this el haddad form is apparently more complicated, but in fact by repeating the same reasoning of the previous paragraph, we only need to distinguish 2 possible ranges: for a<a*,          r k s fk k f a a a a 0 0 log ; log a<a* (26) i.e.                      r k k r fk k a f a fa a f 0 2 0 log ; 1 log a<a* (27) this slope has a limiting value of                         r lim k t k t r fk k f k f k f 2 2 2 log ; 1 log a=a* (28) for a>a*, the slope increases again,              r s ic t fk k k a a k 0 0 log / log δ / a*<a<as* (29) and finally we return to the original slope k, for a>as*. the resulting slopes are also indicated as ratio k’/k<1 in the fig.8,9 for 3 example stress concentration factors kt=2,5,10, showing how for steel the generalized wöhler slope is already about 60% of the original one for notches slightly larger than a0 and with stress concentration factor only of about 2. the slope continues to decrease to about 40% when the notch is now significantly larger than a0 (specifically about 20 times larger than a0) and recollecting eq. 6,2 for the estimate of the paris and wöhler slopes, respectively, we have about m=3.4, k=10.5 with the conclusion that the limit reduction of the generalized wöhler slope is k’/k =32%, and hence with a stress concentration factor of about 5 we’re already very close to the limit slope. for the case of ceramic material in fig.9, the estimates with eqts. 6,2 give m=13.3 and k=22.7 with the conclusion that the limit reduction of the generalized wöhler slope is 59%. however, with the same concentration factors as the previous cases, i.e. kt=2,5,10 we obtain that the decrease of the slope is already almost complete with a notch of the order of 2a0 and with m. ciavarella et alii, frattura ed integrità strutturale, 44 (2018) 49-63; doi: 10.3221/igf-esis.44.05 62 the smallest kt=2. in this respect, the brittle ceramic material is more sensitive to small notches, and this is not entirely a surprise. figure 8: the generalized wohler slope as it results from an interpolation procedure using the el haddad equation for both the static and the fatigue criteria, and for typical material constant ratios of steels. figure 9: the generalized wohler slope as it results from an interpolation procedure using the el haddad equation for both the static and the fatigue criteria, and for typical material constant ratios of steels. conclusions ften design is a process which starts from preliminary calculations, with limited degrees of knowledge of materials and their properties. in fact this is not always only a limit of preliminary design stages, since there is never enough knowledge in fatigue of a material, except when a real prototype test is conducted, which in fact is the case for some industries, despite the larger cost of such a test with respect to analytical or numerical “virtual” testing procedures. this paper assumes that the basic wöhler curve of the unnotched material is known, as well as the basic paris law of the o m. ciavarella et alii, frattura ed integrità strutturale, 44 (2018) 49-63; doi: 10.3221/igf-esis.44.05 63 cracked material. we then proceed to illustrate, from the atzori and lazzarin criteria [5, 16], some simple estimates for the generic wöhler curve of notched specimen. references [1] fleck, n.a., kang, k.j. and asbhy, m.f., (1994). overview 112: the cyclic properties of engineering materials. acta metal. mater. 42 (2), pp. 365-381. [2] carpinteri, a. and karihaloo, b.l., 2003. size-scale effects, engng fract mech, 70(16) pp. 2255. [3] bazant, z. p. (1999). size effect on structural strength: a review, archive of applied mechanics, 69, pp. 703-725. [4] smith, r.a. and miller, k.j. (1978). prediction of fatigue regimes in notched components. int j of mech sci, 20, pp. 201-206. [5] atzori, b. and lazzarin, p. (2001). notch sensitivity and defect sensitivity under fatigue loading: two sides of the same medal, int j of fract, 107(1), pp. l3-l8 [6] atzori, b., lazzarin, p. and meneghetti, g. (2003). fracture mechanics and notch sensitivity. fatigue & fracture of engineering materials & structures, 26(3), pp. 257-267. [7] ciavarella, m. and monno, f. (2006). on the possible generalizations of the kitagawa-takahashi diagram and of the el haddad equation to finite life. international journal of fatigue, 28(12), pp. 1826-1837. [8] pugno, n., ciavarella, m., cornetti, p. and carpinteri, a. (2006) a generalized paris' law for fatigue crack growth. journal of the mechanics and physics of solids, 54(7), pp. 1333-1349. [9] ciavarella, m. (2011). crack propagation laws corresponding to a generalized el haddad equation. international journal of aerospace and lightweight structures (ijals) 1, no. 1. [10] ciavarella, m. (2012). a simple approximate expression for finite life fatigue behaviour in the presence of "crack-like" or "blunt" notches. fatigue & fracture of engineering materials & structures, 35(3), pp. 247-256. [11] ciavarella, m. and papangelo, a., (2018) on the distribution and scatter of fatigue lives obtained by integration of crack growth curves: does initial crack size distribution matter? engineering fracture mechanics, in press [12] ciavarella, m., p. d’antuono and papangelo, a. (2018). on the connection between palmgren-miner’s rule and crack propagation laws. fatigue & fracture of engineering materials & structures, doi: 10.1111/ffe.12789 [13] iso 6336:1996 calculation of load capacity of spur and helical gears -part 2: calculation of surface durability (pitting) part 3: calculation of tooth bending strength. [14] sendeckyj, g.p. (2001). constant life diagrams — a historical review, int j of fatigue, 23(4), pp. 347-353. [15] el haddad, m.h., topper, t.h. and smith, k.n. (1979). prediction of non-propagating cracks. engng fract mech 11, pp. 573-584. [16] atzori, b. and lazzarin, p. (2000). analisi delle problematiche connesse con la valutazione numerica della resistenza a fatica, aias national conference, lucca italy, also quaderno aias n.7, pp.33-50. [17] asbhy, m.f. (1989). overview 80: the engineering properties of materials: acta metal., 37 (5), pp. 1273-1293 [18] asbhy, m.f. 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can be opened with acrobat and adobe reader 5.0 and later.) >> /namespace [ (adobe) (common) (1.0) ] /othernamespaces [ << /asreaderspreads false /cropimagestoframes true /errorcontrol /warnandcontinue /flattenerignorespreadoverrides false /includeguidesgrids false /includenonprinting false /includeslug false /namespace [ (adobe) (indesign) (4.0) ] /omitplacedbitmaps false /omitplacedeps false /omitplacedpdf false /simulateoverprint /legacy >> << /addbleedmarks false /addcolorbars false /addcropmarks false /addpageinfo false /addregmarks false /convertcolors /converttocmyk /destinationprofilename () /destinationprofileselector /documentcmyk /downsample16bitimages true /flattenerpreset << /presetselector /mediumresolution >> /formelements false /generatestructure false /includebookmarks false /includehyperlinks false /includeinteractive false /includelayers false /includeprofiles false /multimediahandling /useobjectsettings /namespace [ (adobe) (creativesuite) (2.0) ] /pdfxoutputintentprofileselector /documentcmyk /preserveediting true /untaggedcmykhandling /leaveuntagged /untaggedrgbhandling /usedocumentprofile /usedocumentbleed false >> ] >> setdistillerparams << /hwresolution [2400 2400] /pagesize [612.000 792.000] >> setpagedevice microsoft word numero_63_art_xx_3728.docx l. levin et alii, frattura ed integrità strutturale, 63 (2023) 1-12; doi: 10.3221/igf-esis.63.01 1 analysis of the structural integrity of a frozen wall during a mine shaft excavation using temperature monitoring data lev levin, mikhail semin mining institute of the ural branch of the russian academy of sciences, russia aerolog_lev@mail.ru, https://orcid.org/0000-0003-0767-9207 seminma@inbox.ru, https://orcid.org/0000-0001-5200-7931 ivan golovatyi joint stock company “belaruskali”, belarus iwan15@yandex.by abstract. the construction of shafts of potash mines in flooded and unstable soils is usually carried out with the help of artificial ground freezing. the freezing process aims to form a waterproof frozen wall (fw) around the shaft and is monitored throughout the construction of the mine shaft. this paper describes the results of the temperature monitoring of the fw around the skip shaft of a potash mine under construction. the data on temperature measurements in control-thermal boreholes were used to parameterize the mathematical model of heat transfer, which allowed for the reconstruction of the temperature field throughout the entire cooled and frozen soil volume. the resulting temperature distribution in the fw zone for greater than one year was used to determine the distribution of the strength properties and calculate the temporary change in the limiting value of the external lateral load on an fw of a given thickness and specified thermomechanical properties. the obtained dependencies of the maximum external load on the fw can be used to optimize the operation mode of the freezing station at the ice holding stage (or passive freezing) to increase the energy efficiency of the system and ensure the structural integrity of the fw. keywords. frozen wall, artificial ground freezing, mine shaft, temperature monitoring, structural integrity, optimization of freezing parameters. citation: levin, l., semin, m., golovatyi, i., analysis of the structural integrity of a frozen wall during a mine shaft excavation using temperature monitoring data, frattura ed integrità strutturale, 63 (2023) 1-12. received: 07.08.2022 accepted: 26.09.2022 online first: 15.10.2022 published: 01.01.2023 copyright: © 2023 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. introduction he construction of mine shafts in flooded unstable soils is conducted using special methods. regarding potash mines, the most common method for shaft construction is artificial ground freezing (agf). its purpose is to create a frozen wall (fw) around the designed mine shaft [1, 2]. t https://youtu.be/prun7zkhgxy l. levin et alii, frattura ed integrità strutturale, 63 (2023) 1-12; doi: 10.3221/igf-esis.63.01 2 the regulatory documentation in belarus and many other countries require systematic monitoring of the fw state during the agf process. in general, the monitoring consists of measuring the temperature along the depth of several vertical boreholes [3]. based on the temperature distribution data, the engineer must judge whether the required fw thicknesses have been achieved. in general, this type of investigation is conducted based on an interpretation of the temperature field throughout the entire volume of cooled and frozen soil via back analysis [4] or by solving the inverse stefan problems [5, 6]. next, using the selected isotherm (0°c or lower), the actual fw thickness is determined and compared with the calculated thickness obtained from the preliminary mechanical analysis. when performing a mechanical analysis, it is generally assumed that the fw temperature is uniformly distributed throughout the volume of the frozen soils [7, 8]. such an average temperature is equal to a predetermined negative value at which the strength properties of the soils were determined during laboratory tests. additionally, this value is used to calculate the design fw thickness. the advantage of this approach is associated with the speed of the assessment of the fw bearing capacity; however, this is based on simplifications, which in certain practical situations can be very rough [8]. among them are the following:  a change in the strength properties with a variation in the temperature.  the thermal expansion of wet soils when the pore water freezes.  moisture bulging out of the area of the frozen soils, which leads to an increase in the external load on the side wall of the frozen soil cylinder.  the influence of frost heaving on the stress-strain state of the fw. all these factors are associated with the absence of the mutual influence of stress-strain and the thermal fields in the fw model. however, the literature has also described an alternative approach – the solution to coupled thermo-hydromechanical (thm) problems [9, 10]. this approach allows one to describe the physical processes in frozen soils more accurately; however, it has its disadvantages, for example, the duration of the simulation and the large amount of additional initial data required for it, the rheological and hydraulic parameters of the frozen soils at various temperatures, the frost heaving parameters, etc. this alternative approach has not been addressed in this paper. let us consider in more detail a consequence of neglecting the temperature changes in the mechanical and strength properties of the frozen soils in the first approach. the calculated fw thicknesses, determined from mechanical analysis based on the average uniform temperature of the fw, are typically satisfactory in practice at the ice growing stage (or active freezing). however, upon transition to the ice holding stage (or passive freezing), the power of the freezing system decreases. in this case, the zone of negative temperatures typically continues to expand, but the average temperature of the fw can increase significantly [11]. the latter is associated with an increase in the temperature of the brine in the freezing columns. therefore, it becomes incorrect to compare the actual fw thicknesses along the same isotherm with the calculated fw thicknesses since, in this case, the thicknesses are compared for completely different average temperatures of the fw. even though the fw thickness (determined from the isotherm of the actual freezing of the pore water) continues to increase, the actual bearing capacity of the fw may decrease due to an increase in its average temperature. the fw bearing capacity can also become lower than the required value, which can lead to significant deformations of the unsupported shaft walls, and a flow of groundwater into the shaft. thus, observations during the sinking of shafts no. 2 and no. 3 of the third bereznikovsky potash mine [12] showed that during the transition from the ice growing stage to the ice holding stage, the temperature increased, and water inflows were often noted. with a significant increase in the temperature of the fw, holes containing thawed soils can form, through which groundwater will flow into the shaft. the opposite situation can also occur when engineers slowly reduce the power of the freezing station when switching to the ice holding stage. this leads to the average temperature of the fw retaining its design values; however, simultaneously, the fw thickness continues to increase. it leads to over freezing of the soil volume and entails the inefficient use of the refrigeration capacity. the above-mentioned scenarios indicate the importance of selecting the correct mode of operation of the freezing stations during the ice holding stage, considering the increasing average temperature of the fw. in this regard, it is necessary to solve an optimization problem associated with the selection of the growth rate the brine temperature in the freezing pipes, in which the bearing capacity of the fw (expressed, for example, in terms of the maximum lateral load on its side wall) will retain a constant value equal to the designed external load on the fw. to solve the optimization problem, we first must determine the method to calculate the dynamically changing bearing capacity of the fw according to the data of the field monitoring of the agf process. the literature does not describe such methods that consider in sufficient detail the effect of the temperature field on the bearing capacity of the fw and at the same time allow performing quick analysis, without solving coupled thm problems. the existing methods for optimizing the agf consider other aspects of this problem: the influence of seepage flows [13, 14], the common influence of brine parameters on the freezing rate [15], selective freezing [16], etc. the problem of determining the temperature of the brine at the stage of maintaining the fw thickness was considered only within the framework of the analysis of temperature fields [17]. l. levin et alii, frattura ed integrità strutturale, 63 (2023) 1-12; doi: 10.3221/igf-esis.63.01 3 this paper presents a practical case of agf for the skip shaft of a potash mine under construction. based on the soil temperature monitoring data, the temperature field was restored throughout the entire volume of cooled and frozen soils at various points in time. this temperature field was used to evaluate the evolution of the fw bearing capacity over time and draw conclusions regarding how optimal the selected freezing mode was. the purpose of this study was to describe and demonstrate the methodology for estimating the dynamically changing bearing capacity of the fw according to the experimental temperature monitoring of the agf process. object of the study and experimental observations data he focus of this study was the frozen soils of the skip shaft of the darasinsky potash mine, which was under construction. the mine is located in the soligorsk district of the minsk region in the republic of belarus. the difficult hydrogeological conditions of the shaft construction were associated with the presence of flooded loose and unstable soil layers in the upper part of the sedimentary cover, to a depth of 185 m. this predetermined the requirement to use agf. a total of 39 freeze pipes were installed around the designed skip shaft. the diameter of the freeze pipe contour was 15.4 m, and the distance between the mouths of the adjacent freeze pipes was approximately 1.24 m. the diameter of the designed mine shaft was 8 m (see fig. 1). in the present work, the dynamics of the bearing capacity of the fw was studied during the ice growing and ice holding stages. we obtained and processed the experimental data of temperature monitoring in three control-thermal (ct) boreholes located near the freeze pipe contour (see fig. 1). the temperature measurements were obtained daily throughout the entire height of the ct boreholes (185 m) using the dts system [18, 19]. fig. 2 shows the typical temperature distributions along the ct borehole heights at various time points. figure 1: locations of the freeze pipes and control-thermal boreholes of the skip shaft. over time, the temperature of the soils in the vicinity of the ct boreholes decreased. moreover, this decrease occurred more rapidly, the closer the ct borehole was located to the freeze pipe contour. the non-uniformity of the temperature decrease along the height of each ct borehole was also noted. this was because, in the freezing interval, various soil layers existed that had significantly different thermophysical properties. the spatial temperature distributions in the ct boreholes were generally correlated with each other, except for a small zone at a depth of 140 m, where a local maximum was observed in ct-2, and a local minimum was observed in ct-3. this feature was associated with the groundwater seepage in the sandstone layer at this depth, which was described in detail in [20]. fig. 3a shows the time dependencies of the brine temperature measured at the inlet and outlet of the freezing pipes. a decrease in the temperature of the incoming brine compared to the design values (from –25 to –23°c) occurred in the t l. levin et alii, frattura ed integrità strutturale, 63 (2023) 1-12; doi: 10.3221/igf-esis.63.01 4 interval from december 3 to december 19, 2022. subsequently, the temperature gradually decreased until march 14, 2021. after that date, the temperature increased by 3°c, which was associated with the transition to the ice holding stage. up until september 2021, the temperature gradually decreased, which was associated with natural processes in the soil. on september 8, the temperature again increased sharply by 2°c, which was associated with a change in the operation mode of the freezing station. the same sharp temperature increase occurred on october 28, 2021 and january 7, 2022. the total brine flow rate in the brine pipe system during the entire freezing period under consideration also changed. in the initial period from november 25 to january 28, it varied in the range from 220 to 278 m3/hour, after which it was maintained at 260 m3/hour. from july 5, 2021, it decreased first to 210 m3/h, then to 180 and 160 m3/h (see fig. 3b). figure 2: experimental temperature distributions along the height of the various ct boreholes: a) ct-1, b) ct-2, c) ct-3. figure 3: time dependencies of the temperature (a) and total flow rate (b) in the brine pipe system. l. levin et alii, frattura ed integrità strutturale, 63 (2023) 1-12; doi: 10.3221/igf-esis.63.01 5 interpretation of the temperature field he available data from the experimental studies were used to adjust the parameters of the mathematical model of the frozen soil. the soil in the present study was a superposition of horizontal layers of soil with approximately uniform thermophysical properties. the horizontal soil layers had thicknesses of 10 m or greater. regarding the middle horizontal sections of these soil layers, it was appropriate to accept the hypothesis of the smallness of vertical heat transfers and consider the heat transfer in the horizontal plane of each of the layers within the framework of the following mathematical model [20]:                          2 ( ) 1 1h t t t r t r r r r (1)      1un fri i (2)                       , ( ) 1 , ( ), un lq w lq w sd lq fr sd sd c t t nl t t h t nl i t t t c t t t t (3)               1, ( ) , 0, sd lq lq sd sd lq lq t t i t t t t t t t t t t (4)          λ α ( ) 0 fb fb t t t t n (5)   0 out t t (6)   00tt t (7) where h is the specific enthalpy of the soil, j/m3; r and φ are the polar coordinates, m; t is the physical time, s; un and  fr are the mass thermal conductivities in the unfrozen and frozen zones, respectively, w/(m·°c); unc and frc are the specific heat capacities of the soil in the unfrozen and frozen zones, respectively, j/(kg·°c);  is the soil density, kg/m3; lqt is the temperature of the beginning of the pore water crystallization (liquidus temperature), °c; sdt is the temperature of the beginning of the pore ice melting (solidus temperature), °c; i is the volumetric ice content of the soil, m3/m3; l is the specific heat of the crystallization of water, j/kg; n is the porosity of the soil; w is the pore water density, kg/m3; fbt is the brine temperature in the freeze pipes, °с; 0t is the temperature of the undisturbed soil at a distance from the freeze pipe contour, °с; α is the heat transfer coefficient at the freeze pipe walls, w/(m2·°с);   fb fbi are the boundaries with all the freeze pipes; out is the outer boundary of the simulation area; n is the coordinate along the normal to the boundary, m. accounting for the phase transitions of the pore water in this model was conducted by setting the specific enthalpy function (3). the jump of this function in the vicinity of the phase transition temperatures was determined by the value of the latent heat of the phase transition per unit volume of the soil. it was assumed that the temperature interval of this jump was sufficiently small compared to the characteristic temperature difference in the problem 0 fbt t . thus, it was possible to consider the linear dependencies (2) and (4). in reality, the phase transition of the pore moisture for many soil layers can t l. levin et alii, frattura ed integrità strutturale, 63 (2023) 1-12; doi: 10.3221/igf-esis.63.01 6 occur in quite a wide temperature range, which is typically associated with the influence of the bound waters [21, 22] and the mineralization of the pore water [9]. the solution of the system of eqns. (1) – (6) was conducted using the finite difference method in the frozen wall program developed at the perm mining institute with the participation of the authors. the radius of the outer boundary of the computational domain for each of the layers was 51 m, and the radius of the freeze pipe was taken as 0.073 m. for the solution, a regular inhomogeneous mesh with thickening near the freeze pipes was used. an explicit first-order scheme in time and a second-order accuracy scheme (central difference) in space were used. the initial values of all the thermophysical properties of the soil used in the calculations were taken based on laboratory studies of the soil samples. tab. 1 shows the thermophysical properties used in the calculations for the three soil layers considered: sand, sandy clay and clay. overall, there were 17 soil layers in the 185 m freeze interval. however, in this paper, we focus only on three of these layers. layer depth interval, m t0, °c tlq, °c tsd, °c cfr, j/(kg·°c) cun, j/(kg·°c)  , kg/m3 sand 2.1–18 9.5 -0.08 -1 908 1096 2110 sandy clay 82.9-97.3 8.5 -0.07 -3 996 1131 2250 clay 141.5-154.8 8.88 -0.68 -5 993 1259 2160 table 1: thermophysical properties of the considered soil layers. figure 4: dynamics of the effective thermophysical parameters of the soils during the model adjustments at various points in time: a) thermal conductivity of the frozen soil, b) thermal conductivity of the unfrozen soil, c) water content. l. levin et alii, frattura ed integrità strutturale, 63 (2023) 1-12; doi: 10.3221/igf-esis.63.01 7 furthermore, during the process of the experimental monitoring of the temperatures in the ct boreholes, the thermal model of each layer was parameterized. the model thermal conductivity and moisture content of the soil were adjusted according to the method [5, 18] to ensure the best match between the measured and calculated temperatures at the locations of the ct boreholes. fig. 4 illustrates how the thermal conductivity and moisture of the soil were adjusted over time using three soil layers as an example. in this regard, the adjusted thermophysical properties in the model were no longer real, but some effective properties of the medium. the calculated temperature profiles along the fw equidistant plane (see fig. 1) [23] for the three considered soil layers and various time points are shown in fig. 5. the zone r < 4 m is not displayed since it corresponds to the zone of the shaft under construction, and it was not considered when calculating the thickness of the fw. the horizontal dotted lines show the solidus temperatures that corresponded to the fw boundaries. the simulation time was counted from december 10, 2020. the total simulation time was 14 months. fig. 5 shows that during the first 10 months, the temperatures of the soils generally decreased, the zone of negative temperatures expanded, and the thickness of the fw increased. after 10 months of freezing, there the temperature tended to increase, which was associated with the operation mode of the freezing station. the minimum temperatures on these curves were always higher than the temperature of the freezing brine, which was associated with the thermal resistance of the brine in the boundary layer near the pipe wall, the thermal resistance of the soils between the wall of the freeze pipe, and the fw equidistant plane. figure 5: radial temperature distributions along the fw equidistant plane. l. levin et alii, frattura ed integrità strutturale, 63 (2023) 1-12; doi: 10.3221/igf-esis.63.01 8 figure 6: time dependencies of the average temperature of the fw (a) and the thickness of the fw (b). the radial dependencies showed a substantially inhomogeneous form. the temperature of the soils in the frozen zone varied over a wide range (sometimes exceeding 15°c). the average fw temperature during the considered time interval first decreased with time and, after 10 to 12 months, began to increase (see fig. 6a). the fw thickness for the sand and sandy clay continued to increase throughout the entire time interval, while the fw thickness of the clay increased up to 12 months and decreased in the interval from 12 to 14 months. this was because, for clay, the fw boundaries was considered to be at the lowest temperature of -5°c. this temperature is more difficult to maintain for the freezing system in the passive freezing mode. the model also considered that in the interval between 10 and 12 months, a mine shaft was constructed in the soil layers. this led to the heat inflows from the air space of the shaft. it is important to note that the increase in the average temperature of the fw began much later than the start of the ice holding stage, which was associated with the inertia of the thermal processes in the soil volume and the smoothness regarding the changing of the parameters of the freezing station. only after the temperature of the brine in the freeze pipes became higher than -20°c, the average temperature of the fw began to increase. mechanical calculation of the fw bearing capacity he obtained temperature profiles were used to estimate the temporal change in the ultimate bearing capacity of the fw according to the strength criterion. under the ultimate bearing capacity of fw, we mean the limiting value of the external lateral load, p, which the fw can withstand (see fig. 7). figure 7: schematic representation of the external lateral load, p, on the fw. t l. levin et alii, frattura ed integrità strutturale, 63 (2023) 1-12; doi: 10.3221/igf-esis.63.01 9 let us use the expression relating the external load on the fw and its strength and geometric properties from [24]:                3 3 ( 1) 1 96 1 mean cp (8)         1 1 b a (9) where a is the radius of the inner boundary of the fw, m; b is the radius of the outer boundary of the fw, m; p is the external lateral pressure, pa; c is the difference between the maximum and minimum cohesion of the frozen soils in the fw with a non-uniform temperature distribution, pa;  and mean are the coefficients in the linear mohr-coulomb law written with respect to the maximum 1 and minimum 3 principal stresses and a certain average temperature:     1 3 mean (10)                  2tan , 2 tan 4 2 4 2 mean mean mean meanc (11) where meanc is the frozen soil cohesion, averaged over the fw volume, pa; mean is the angle of internal friction, averaged over the fw volume, °. in addition to formula (8), we also used the formula of s.s. vyalov for the case of a finite height of an unfixed shaft wall, which was used in the instructions for soil freezing at the darasinsky mine:            cc c b aehp e p h h (12) where e is the fw thickness, m;  c is the strength of the frozen soils for uniaxial compression, pa; h is the height of the unsupported shaft wall, m;  is the coefficient determined based on the nature of the pinching of the upper and lower ends of the fw. the parameters a and b at different times can be determined based on fig. 5 at the intersections of the corresponding temperature profiles using the solidus temperature line. the strength properties of the considered soil layers were taken from our previous work [8], in which the laboratory testing of soil samples for strength at various temperatures was conducted. the approximate linear functions of the limiting-long-term values of the strength properties of the soils on the temperature are presented in tab. 2. these functions provided satisfactory results in the temperature range of -25 to -2°c. in formula (12), the strength of the frozen soils for the uniaxial compression was determined based on the average temperature of the fw. the height of the entry was assumed to be 5 m, and the coefficient was 1.73. layer cohesion, mpa tangent of the angle of internal friction, ° uniaxial compressive strength sand 0.814–0.121 т 0.436–0.0047 т 0.842–0.326 t sandy clay 0.729–0.117 т 0.304–0.0046 т 0.476–0.381 t clay 0.447–0.119 т 0.080–0.0072 т 1.095–0.276 t table 2: linear approximations of the temperature functions of the limiting-long-term values of the frozen soil strength properties. we evaluated the bearing capacity of the fw in terms of the limiting value of the external lateral load that it can withstand under given thermophysical conditions obtained from the calculation using the model. based on the available data on the l. levin et alii, frattura ed integrità strutturale, 63 (2023) 1-12; doi: 10.3221/igf-esis.63.01 10 inhomogeneity of the fw temperature field, its geometric dimensions, and the strength properties of the soils, it was possible to calculate the time dependencies of the limiting value of the load on the fw using formula (8). the obtained time dependencies are shown in fig. 8. figure 8: time dependencies of the limiting value of the external lateral load that the fw can withstand fig. 8 shows that, in general, for 12 months, for all the considered soil layers, the fw strength increased. simultaneously, the limiting values of the external load according to formula (8) were quite large and after four months exceeded the actual external load. for sand, the external load was 0.17 mpa, for sandy clay, it was 1.36 mpa, and for clay, it was 1.54 mpa. these values were calculated as the sum of two components: the lithostatic pressure and the pressure of the water column at the level of the bottom of each considered soil layer. the limiting value of the external lateral load according to formula (12) was significantly lower, which was associated with the features of this formula and the physics included in it [25]. after only 6 months, this limiting value for the clay layer exceeded the actual external load that was calculated during the engineering and geological surveys and the development of the design documentation for the agf (fig. 8b). in general, according to both formulas, the selected operation mode of the freezing station provided a significant margin for the required thickness of the fw during the construction period of the shaft. this was because when choosing the operating mode of the freezing station, the mine specialists were guided by other criteria:  maintaining the average temperature of the fw at a level of -8 to -10°c. it was for these temperatures that the design thicknesses of the fw were calculated.  sufficient freezing of the soils at a depth of 140 m, where the seepage flow of the pore water was revealed [20]. in addition to this, the analysis of the dynamic change in the fw bearing capacity presented in this paper was conducted after the construction of the skip shaft in the agf interval of 0 to185 m. moreover, the analysis conducted in the present study will be useful primarily for mine shafts that will be built in the future. the data presented herein also did not account for the fw creep. the calculation of the required thickness of the fw according to the creep criterion is also mandatory in the design of the agf [26, 27]. the calculated values of the fw thicknesses according to the creep condition for the relatively deep layers (sandy clay, clay) may be higher than the calculated values of the fw thicknesses according to the strength condition. conclusion his paper describes a method for analyzing the dynamically changing bearing capacity of an fw according to temperature monitoring data. in the first stage, according to the temperature readings in the ct boreholes, the temperature field was interpreted throughout the entire frozen soil volume, and the actual fw thicknesses were determined from the soil freezing isotherms. furthermore, the resulting temperature field was used to calculate the inhomogeneous distribution of the physical-mechanical and strength properties of the fw and determine the limiting value t l. levin et alii, frattura ed integrità strutturale, 63 (2023) 1-12; doi: 10.3221/igf-esis.63.01 11 of the external lateral load that the fw could withstand. this lateral external load was compared with the actual external load on the fw, which was determined from the design documentation for the agf as the sum of the rock and hydrostatic pressures. the resulting time dependencies of the external lateral load on the fw can be used to optimize the operation mode of the freezing station at the ice holding stage. acknowledgements he study was financially supported by the ministry of science and higher education of the perm territory under agreement no. c-26/563. references [1] nicotera, m. v. and russo, g. (2021). monitoring a deep excavation in pyroclastic soil and soft rock. tunnelling and underground space technology, 117, 104130. [2] haß, h. and schäfers, p. (2005). application of ground freezing for underground construction in soft ground. in proceedings of the 5th international symposium tc28, amsterdam, the netherlands, pp. 405-412. [3] wu, t., zhou, x., zhang, l., zhang, x., he, x. and xu, y. (2021). theory and technology of real-time temperature field monitoring of vertical shaft frozen wall under high-velocity groundwater conditions. cold regions science and technology, 189, 103337. [4] pimentel, e., papakonstantinou, s. and anagnostou, g. (2012). numerical interpretation of temperature distributions from three ground freezing applications in urban tunnelling. tunnelling and underground space technology, 28, pp. 57-69. [5] levin, l. y., semin, m. a. and zaitsev, a. v. (2018). solution of an inverse stefan problem in analyzing the freezing of groundwater in a rock mass. journal of engineering physics and thermophysics, 91(3), pp. 611-618. [6] zhelnin, m. s., plekhov, o. a., semin, m. a. and levin, l. y. (2017). numerical solution for an inverse problem about determination of volumetric heat capacity of rock mass during artificial freezing. pnrpu mechanics bulletin, (4), pp. 56-75. [7] zhang, b., yang, w. and wang, b. (2018). plastic design theory of frozen wall thickness in an ultradeep soil layer considering large deformation characteristics. mathematical problems in engineering. [8] semin, m.a., brovka, g.p., pugin, a.v., bublik, s.a., zhelnin, m.s. (2021). effects of temperature field nonuniformity on strength of frozen wall in mine shafts. mining informational and analytical bulletin, 2021, 2021(9), pp. 79–93. [9] tounsi, h., rouabhi, a., tijani, m. and guérin, f. (2019). thermo-hydro-mechanical modeling of artificial ground freezing: application in mining engineering. rock mechanics and rock engineering, 52(10), pp. 3889-3907. [10] liu, y., li, k. q., li, d. q., tang, x. s. and gu, s. x. (2022). coupled thermal–hydraulic modeling of artificial ground freezing with uncertainties in pipe inclination and thermal conductivity. acta geotechnica, 17(1), pp. 257-274. [11] semin, m. a., bogomyagkov, a. v. and levin, l. y. (2020). theoretical analysis of frozen wall dynamics during transition to ice holding stage. journal of mining institute, 243, pp. 319-328. [12] olkhovikov, yu. p. (1984). support of permanent openings of potash and salt mines. publisher: nedra, moscow, russia, 238 p. [in rus] [13] marwan, a., zhou, m. m., abdelrehim, m. z. and meschke, g. (2016). optimization of artificial ground freezing in tunneling in the presence of seepage flow. computers and geotechnics, 75, pp. 112-125. [14] huang, s., guo, y., liu, y., ke, l. and liu, g. (2018). study on the influence of water flow on temperature around freeze pipes and its distribution optimization during artificial ground freezing. applied thermal engineering, 135, pp. 435-445. [15] vitel, m., rouabhi, a., tijani, m. and guérin, f. (2015). modeling heat transfer between a freeze pipe and the surrounding ground during artificial ground freezing activities. computers and geotechnics, 63, pp. 99-111. [16] zueter, a., nie-rouquette, a., alzoubi, m. a. and sasmito, a. p. (2020). thermal and hydraulic analysis of selective artificial ground freezing using air insulation: experiment and modeling. computers and geotechnics, 120, 103416. [17] semin, m. a., levin, l. y. and parshakov, o. s. (2020). selection of working conditions and substantiation of operating mode of freezing pipes in maintenance of frozen wall thickness. journal of mining science, 56(5), pp. 857-867. t l. levin et alii, frattura ed integrità strutturale, 63 (2023) 1-12; doi: 10.3221/igf-esis.63.01 12 [18] he, h., dyck, m. f., horton, r., li, m., jin, h. and si, b. (2018). distributed temperature sensing for soil physical measurements and its similarity to heat pulse method. advances in agronomy, 148, pp. 173-230. [19] stutsel, b. m., callow, j. n., flower, k. c., biddulph, t. b. and issa, n. a. (2020). application of distributed temperature sensing using optical fibre to understand temperature dynamics in wheat (triticum aestivum) during frost. european journal of agronomy, 115, 126038. [20] semin, m., golovatyi, i. and pugin, a. (2021). analysis of temperature anomalies during thermal monitoring of frozen wall formation. fluids, 6(8), 297. [21] kong, b., he, s., xia, t. and ding, z. (2021). research on microstructure of soft clay under various artificial ground freezing conditions based on nmr. applied sciences, 11(4), 1810. [22] hou, s., yang, y., cai, c., chen, y., li, f. and lei, d. (2022). modeling heat and mass transfer during artificial ground freezing considering the influence of water seepage. international journal of heat and mass transfer, 194, 123053. [23] trupak, n. (1974) ground freezing in underground development. nedra [in rus.]. [24] semin, m. (2021). calculation of frozen wall thickness considering the non-uniform distribution of the strength properties. procedia structural integrity, 32, pp. 180-186. [25] vyalov, s. s. (2013). rheological fundamentals of soil mechanics. elsevier. [26] vyalov, s. s., zaretsky, y. k. and gorodetsky, s. e. (1979). stability of mine workings in frozen soils. engineering geology, 13(1-4), pp. 339-351. [27] sanger, f. j. and sayles, f. h. 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can be opened with acrobat and adobe reader 5.0 and later.) >> /namespace [ (adobe) (common) (1.0) ] /othernamespaces [ << /asreaderspreads false /cropimagestoframes true /errorcontrol /warnandcontinue /flattenerignorespreadoverrides false /includeguidesgrids false /includenonprinting false /includeslug false /namespace [ (adobe) (indesign) (4.0) ] /omitplacedbitmaps false /omitplacedeps false /omitplacedpdf false /simulateoverprint /legacy >> << /addbleedmarks false /addcolorbars false /addcropmarks false /addpageinfo false /addregmarks false /convertcolors /converttocmyk /destinationprofilename () /destinationprofileselector /documentcmyk /downsample16bitimages true /flattenerpreset << /presetselector /mediumresolution >> /formelements false /generatestructure false /includebookmarks false /includehyperlinks false /includeinteractive false /includelayers false /includeprofiles false /multimediahandling /useobjectsettings /namespace [ (adobe) (creativesuite) (2.0) ] /pdfxoutputintentprofileselector /documentcmyk /preserveediting true /untaggedcmykhandling /leaveuntagged /untaggedrgbhandling /usedocumentprofile /usedocumentbleed false >> ] >> setdistillerparams << /hwresolution [2400 2400] /pagesize [612.000 792.000] >> setpagedevice microsoft word numero_36_art_1 i. camagic et alii, frattura ed integrità strutturale, 36 (2016) 1-7; doi: 10.3221/igf-esis.36.01 1 focused on fracture mechanics in central and east europe influence of temperature and exploitation period on fatigue crack growth parameters in different regions of welded joints ivica camagic, nemanja vasic, bogdan cirkovic faculty of technical sciences, kosovska mitrovica, kneza milosa 7, serbia zijah burzic military technical institute, rastka resanovica 1, belgrade, serbia aleksandar sedmak faculty of mechanical engineering, kraljice marije 16, belgrade, serbia asedmak@mas.bg.ac.rs aleksandar radovic technical school mihailo petrovic alas, kosovska mitrovica, lole ribara 29, serbia abstract. the influence of exploitation period and temperature on the fatigue crack growth parameters in different regions of a welded joint is analysed for new and exploited low-alloyed cr-mo steel a-387 gr. b. the parent metal is a part of a reactor mantle which was exploited for over 40 years, and recently replaced with new material. fatigue crack growth parameters, threshold value kth, coefficient c and exponent m, have been determined, both at room and exploitation temperature. based on testing results, fatigue crack growth resistance in different regions of welded joint is analysed in order to justify the selected welding procedure specification. key words: welded joint; crack; yield stress; tensile strength; permanent dynamic strength. introduction he reactor analysed here has a form of a vertical pressure vessel with a cylindrical mantle and two welded lids, made of cr-mo steel a-387 gr. b, [1]. it is used for some of the most important processes in the motor gasoline production, including platforming in order to change the structure of hydrocarbon compounds and to achieve a higher octane rating. long-time, high temperature exploitation of the reactor, caused siginficant damage in reactor mantle, requiring a thorough inspection and repair of damaged parts, including replacement of a part of reactor mantle. for designed exploitation parameters (p=35 bar, t=537 °c), the material is prone to decarbonization, reducing its strength as a consequence, [2]. testing of high-cycle fatigue behaviour of new and exploited parent metal (pm), weld metal (wm) and heat affected zone (haz), at room and service temperature (540 °c) is necessary to get detailed insight in all parameters influencing fatigue crack growth resistance of cr-mo steel a-387 gr. b. welded joints. t i. camagic et alii, frattura ed integrità strutturale, 36 (2016) 1-7; doi: 10.3221/igf-esis.36.01 2 testing material oth new and exploited pm was steel a-387 gr. b with thickness of 102 mm. chemical composition and mechanical properties for both new and exploited pm are given in tabs. 1 and 2. specimen designation % max c si mn p s cr mo cu e 0.15 0.31 0.56 0.007 0.006 0.89 0.47 0.027 n 0.13 0.23 0.46 0.009 0.006 0.85 0.51 0.035 table 1: chemical composition of exploited (e) and new (n) pm specimens specimen designation yield stress, rp0.2, mpa tensile strength rm, mpa elongation a, % impact energy, j e 320 450 34.0 155 n 325 495 35.0 165 table 2: chemical composition of exploited (e) and new (n) pm specimens. welding of both new and exploited pm was performed in two stages, according to the following welding procedure specification:  root pass by shielded metal arc welding, using lincoln s1 19g electrode, and  filling passes by arc submerged arc welding, using lincoln lns 150 wire and lincoln p230 flux. chemical composition of the coated electrode lincoln s1 19g, and the wire lincoln lns 150 according to the atest documentation is given in tab. 3, whereas their mechanical properties, also according to the atest documentation, are given in tab. 4. filler material % mas c si mn p s cr mo lincoln s1 19g 0.07 0.31 0.62 0.009 0.010 1.17 0.54 lincoln lns 150 0.10 0.14 0.71 0.010 0.010 1.12 0.48 table 3: chemical composition of filler materials. filler material yield stress, rp0.2, mpa tensile strength rm, mpa elongation a, % impact energy, j, 20°c lincoln s1 19g 515 610 20 >60 lincoln lns 150 495 605 21 >80 table 4: mechanical properties of filler materials fatigue crack growth parameters evaluation atigue crack growth testing at room temperature was performed on three-point bending specimens, as defined by astm e399, [3], whereas tesitng at service temperature, 540 c, was performed on modified ct specimens, as defined by standard bs 7448 part 1, [4]. the high-frequency resonant pulsator was used, in force control mode, with loading ratio r = 0.1 to obtain diagrams da/dn-k for specimens with fatigue crack tip located in pm, wm and b f i. camagic et alii, frattura ed integrità strutturale, 36 (2016) 1-7; doi: 10.3221/igf-esis.36.01 3 haz, both new and expoloited material, at room and service temperature. only two diagrams are shown here, as an illustration, whereas the others can be found in [1]. 1.00e-10 1.00e-09 1.00e-08 1.00e-07 1.00e-06 1.00e-05 1 10 100 k, mpa m1/2 d a /d n , m /c ik lu s figure 1: diagram da/dn-k for specimen pm-1-1n, 20°c. 1.00e-10 1.00e-09 1.00e-08 1.00e-07 1.00e-06 1.00e-05 1 10 100 k, mpa m1/2 d a /d n , m /c ik lu s figure 2: diagram da/dn-k for specimen pm-2-1e, 540°c. obtained values for parameters of paris law,  md c k dn    a , i.e. coefficient c and exponent m, fatigue threshold kth, and fatigue crack growth rate, da/dn, for k = 10 mpam, are given in tabs. 5-9 for new and exploited pm, for new wm, and for new and exloited haz, respectively. i. camagic et alii, frattura ed integrità strutturale, 36 (2016) 1-7; doi: 10.3221/igf-esis.36.01 4 specimen temperature °c fatigue threshold δkth coefficient c exponent m da/dn. m/cycle δk = 10 mpam pm-1-1n 20 5.9 5.70 · 10-12 2.98 5.44 · 10-9 pm-1-2n 5.6 5.38 · 10-12 3.02 5.63 · 10-9 pm-1-3n 5.8 6.23 · 10-12 2.83 4.21 · 10-9 pm-2-1n 540 5.2 1.52 · 10-10 2.94 1.32 · 10-7 pm-2-2n 5.1 2.08 · 10-10 2.88 1.58 · 10-7 pm-2-3n 5.0 1.11 · 10-10 2.99 1.08 · 10-7 table 5: fatigue crack growth parameters for specimens with notches in new pm. specimen temperature °c fatigue threshold δkth coefficient c exponent m da/dn. m/cycle δk = 10 mpam pm-1-1e 20 5.2 4.45 · 10-12 3.76 2.56 · 10-8 pm-1-2e 5.1 3.89 · 10-12 3.87 2.88 · 10-8 pm-1-3e 5.2 5.17 · 10-12 3.71 2.65 · 10-8 pm-2-1e 540 4.7 1.48 · 10-8 1.80 9.34 · 10-7 pm-2-2e 4.6 2.67 · 10-8 1.68 1.28 · 10-6 pm-2-3e 4.7 1.25 · 10-8 1.84 8.65 · 10-7 table 6: fatigue crack growth parameters for specimens with notches in exploited pm. specimen temperature °c fatigue threshold δkth coefficient c exponent m da/dn. m/cycle δk = 10 mpam wm-1-1e 20 6.8 2.14 · 10-11 2.53 7.25 · 10-9 wm-1-2e 6.9 3.55 · 10-11 2.38 8.71 · 10-9 wm-1-3e 6.7 1.98 · 10-11 2.56 7.19 · 10-9 wm-2-1e 540 5.8 1.26 · 10-9 2.51 4.08 · 10-7 wm-2-2e 5.6 1.78 · 10-9 2.47 5.25 · 10-7 wm-2-3e 5.5 2.24 · 10-9 2.21 3.63 · 10-7 table 7: fatigue crack growth parameters for specimens with notches in wm. specimen temperature °c fatigue threshold δkth coefficient c exponent m da/dn. m/cycle δk = 10 mpam haz-1-1n 20 5.7 2.55 · 10-11 2.48 7.70 · 10-9 haz-1-2n 5.4 2.97 · 10-11 2.41 7.63 · 10-9 haz-1-3n 5.5 2.08 · 10-11 2.57 7.72 · 10-9 haz-2-1n 540 4.9 9.61 · 10-10 2.47 2.84 · 10-7 haz-2-2n 4.7 7.45 · 10-10 2.83 5.03 · 10-7 haz-2-3n 4.8 8.85 · 10-10 2.68 4.24 · 10-7 table 8: fatigue crack growth parameters for specimens with notches in new haz. specimen temperature °c fatigue threshold δkth coefficient c exponent m da/dn. m/cycle δk = 10 mpam haz-1-1e 20 4.8 1.54 · 10-10 2.62 6.42 · 10-8 haz-1-2e 4.6 1.95 · 10-10 2.57 7.24 · 10-8 haz-1-3e 4.5 2.35 · 10-10 2.51 7.60 · 10-8 haz-2-1e 540 4.2 5.50 · 10-9 2.33 1.18 · 10-6 haz-2-2e 4.1 4.67 · 10-9 2.49 1.44 · 10-6 haz-2-3e 4.3 6.24 · 10-9 2.11 8.04 · 10-7 table 9: fatigue crack growth parameters for specimens with notches in exploited haz. i. camagic et alii, frattura ed integrità strutturale, 36 (2016) 1-7; doi: 10.3221/igf-esis.36.01 5 influence of testing temperature and exploitation period on the fatigue threshold kth is graphically presented in fig. 3-5, for pm, wm and haz, respectively. f at ig u e th re sh o ld ,  k th , m p a√ m 0 100 200 300 400 500 600 0 3 6 9 temperature, 0c   ▫ new pm  ◦ exploited pm figure 3: fatigue threshold δkth vs. temperature in pm f at ig u e th re sh o ld ,  k th , m p a√ m 0 100 200 300 400 500 600 0 3 6 9 temperature, 0c figure 4: fatigue threshold δkth vs. temperature in wm. f at ig u e th re sh o ld ,  k th , m p a√ m 0 100 200 300 400 500 600 700 0 3 6 9 temperature, 0c   ▫ new haz  ◦ exploited haz figure 5: fatigue threshold δkth vs. temperature in haz. the influence of testing temperature and exploitation period on the fatigue crack growth rate, da/dn, is graphically presented in fig. 6-8, for pm, wm and haz, respectively. i. camagic et alii, frattura ed integrità strutturale, 36 (2016) 1-7; doi: 10.3221/igf-esis.36.01 6 d a/ d n , m / cy cl e 0 100 200 300 400 500 600 0 -10 10 -9 10 -8 10 -7 10 -6 temperature, 0c   ▫ new pm  ◦ exploited pm figure 6: fatigue crack growth rate, da/dn, vs. temperature for specimens with notches in pm. d a/ d n , m / cy cl e 0 100 200 300 400 500 600 10 -10 10 -9 10 -8 10 -7 10 -6 temperature, 0c figure 7: fatigue crack growth rate, da/dn, vs. temperature for specimens with notches in wm. d a/ d n , m / cy cl e 0 100 200 300 400 500 600 10 -10 10 -9 10 -8 10 -7 10 -6 temperature, 0c   ▫ new haz  ◦ exploited haz figure 8: fatigue crack growth rate, da/dn, vs. temperature for specimens with notches in haz. discussion alues obtained for pm fatigue threshold, kth, are in the range 5.8 mpam (20 c) to 5.1 mpam (540 c), tab. 5. additional reduction for 10-15% is recorded due to exploition period 10-15%, since values for fatigue threshold, kth, are in that case in the range 5.2 mpam (20 c) to 4.7 mpam (540 c), tab. 6. similar effects are noticed in haz, where values of fatigue threshold, kth, obtained for new material, are in the range 5.5 mpam (20 c) to 4.8 mpam (540 c), i.e. from 4.6 mpam (20 c) to 4.2 mpam (540 c) for exploited material, tabs. 8 and 9. v i. camagic et alii, frattura ed integrità strutturale, 36 (2016) 1-7; doi: 10.3221/igf-esis.36.01 7 the largest values of fatigue threshold, kth, are obtianed in wm, from 6.8 mpam (20 c) to 5.6 mpam (540 c), tab. 7. fatigue crack growth rate, da/dn, increases with temperature, being in the range 5.0910-9 m/cycle for new pm (20 c) to 1.3310-7 m/cycle (540 c), tab. 5. exploition period additionally increases fatigue crack growth rate, da/dn, from 2.7010-8 m/cycle (20 c) to 1.0310-6 m/cycle (540 c), tab. 6. the same holds for haz, where values of fatigue crack growth rate, da/dn, are in the range 7.6810-9 m/cycle (20 c) to 4.0410-7 m/cycle (540 c) for new material, i.e. in the range 7.0910-8 m/cycle (20 c), to 1.1410-6 m/cycle (540c) for exploited material, tabs. 8 and 9, respectivley. one should notice significantly higher values for fatigue crack growth rate in haz as compared to pm. the values for wm are in between, in the range 7.7210-9 m/cycle (20 c) to 4.3210-7 m/cycle (540c), tab. 7. conclusion ased on the presented results, one can conclude the following:  influence of material heterogeneity, as well as temperature and exploation effects, on fatigue threshold, da/dn, and crack growth rate, da/dn, is significant.  fatigue threshold values are the lowest for wm, and lowest for haz, whereas crack growth rate values are highest for haz and lowest for pm. therefore, generally speaking, the lowest fatigue crack resistance is in haz.  higher temperature and longer exploitation peroids increase crack growth rates and decreases fatigue thresholds for both new and exploited materials in all regions of welded joint (pm, wm, haz). these effects are due to microstructural changes such as carbide formation and growth at grain boundaries and inside grains. references [1] čamagić, i., investigation of the effects of exploitation conditions on the structural life and integrity assessment of pressure vessels for high temperatures (in serbian), doctoral thesis, university of pristina, faculty of technical sciences with the seat in kosovska mitrovica, (2013). [2] čamagić, i., vasić, n., jović, s., burzić, z., sedmak, a., influence of temperature and exploitation time on tensile properties and microstructure of specific welded joint zones, in: 5th international congress of serbian society of mechanics arandjelovac, serbia, (2015). [3] astm e399-89, standard test method for plane-strain fracture toughness of metallic materials, annual book of astm standards, 03.01 (1986) 522. [4] bs 7448-part 1, fracture mechanics toughness tests-method for determination of kic critical ctod and critical j values of metallic materials, bsi, (1991). b << /ascii85encodepages false /allowtransparency false /autopositionepsfiles true /autorotatepages /none /binding /left /calgrayprofile (dot gain 20%) /calrgbprofile (srgb iec61966-2.1) /calcmykprofile (u.s. web coated \050swop\051 v2) /srgbprofile (srgb iec61966-2.1) /cannotembedfontpolicy /error /compatibilitylevel 1.4 /compressobjects /tags /compresspages true /convertimagestoindexed true /passthroughjpegimages true /createjobticket false /defaultrenderingintent /default /detectblends true /detectcurves 0.0000 /colorconversionstrategy /cmyk /dothumbnails false /embedallfonts true /embedopentype false /parseiccprofilesincomments true /embedjoboptions true /dscreportinglevel 0 /emitdscwarnings false /endpage -1 /imagememory 1048576 /lockdistillerparams false /maxsubsetpct 100 /optimize true /opm 1 /parsedsccomments true 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can be opened with acrobat and adobe reader 5.0 and later.) >> /namespace [ (adobe) (common) (1.0) ] /othernamespaces [ << /asreaderspreads false /cropimagestoframes true /errorcontrol /warnandcontinue /flattenerignorespreadoverrides false /includeguidesgrids false /includenonprinting false /includeslug false /namespace [ (adobe) (indesign) (4.0) ] /omitplacedbitmaps false /omitplacedeps false /omitplacedpdf false /simulateoverprint /legacy >> << /addbleedmarks false /addcolorbars false /addcropmarks false /addpageinfo false /addregmarks false /convertcolors /converttocmyk /destinationprofilename () /destinationprofileselector /documentcmyk /downsample16bitimages true /flattenerpreset << /presetselector /mediumresolution >> /formelements false /generatestructure false /includebookmarks false /includehyperlinks false /includeinteractive false /includelayers false /includeprofiles false /multimediahandling /useobjectsettings /namespace [ (adobe) (creativesuite) (2.0) ] /pdfxoutputintentprofileselector /documentcmyk /preserveediting true /untaggedcmykhandling /leaveuntagged /untaggedrgbhandling /usedocumentprofile /usedocumentbleed false >> ] >> setdistillerparams << /hwresolution [2400 2400] /pagesize [612.000 792.000] >> setpagedevice microsoft word numero_36_art_14 f. z. liu et alii, frattura ed integrità strutturale, 36 (2016) 139-150; doi: 10.3221/igf-esis.36.14 139 effects of hydrogen induced delay fracture on high-strength steel plate of automobile and the improvement fengzhu liu, yu zhao changchun automobile industry institute, changchun, jilin, 130013, china zyzhaoyz@163.com abstract. delay fracture is an environmental embrittlement occurring when materials, environment and stress interact with each other and also a form of hydrogen induced material deterioration. it is a leading factor inhibiting the further improvement of strength of steel and iron material. hence this study analyzed the improved low-carbon mn-b type ultra-high strength steel plate (1500 mpa) which were processed by conventional heat treatment and heating forming technique and explored the effects of tempering temperature and heating forming technique on the performance of hydrogen induced delay fracture, which provides a reference for the actual application of such kind of steel plate. key words: hydrogen induced delay fracture; environmental management technology. introduction igh-strength steel is usually mixed with hydrogen during smelting, processing and using. generally, hydrogen which enters steel is extremely harmful. for many materials, even a trace of hydrogen can induce delay fracture through diffusion and enrichment. hence the diffusion and enrichment of hydrogen in metals is the premise and bridge for delay fracture [1-3]. delay fracture of high-strength steel is a manifestation of hydrogen embrittlement of metals. according to the source of hydrogen, hydrogen embrittlement can be typed into environmental hydrogen embrittlement and internal hydrogen embrittlement [4 6]. environmental hydrogen embrittlement is induced by the invasion of hydrogen generated from corrosion reaction which happens when materials are exposed to the air for a long time. for instance, delay fracture may happen to bolt used in bridge if it is exposed to moist air or rain. internal hydrogen embrittlement is induced by the gathering of hydrogen that enters steels in the process of thermal processing, acid pickling and electroplating towards stress source [7 9]. for instance, electroplated bolt may crack in a short time after loading. delay fracture can result in the damage of high-strength steels within the designed load-carrying capacity. materials with higher grades are of higher risks of delay fracture. delay fracture is difficult to be detected and usually happens suddenly [10]. recently, accidents induced by hydrogen induced delay fracture of high-strength steels happen frequently. delay fracture has become a barrier for the development of high-strength steel. a large number of evidences have suggested that, the delay fracture of high strength steel have brought huge threatens to industries such as modern motor, architecture, mechanics and light industry. when the strength of steel is over 1200 mpa, the steel would be highly sensitive to hydrogen induced delay fracture [11 12]. till now, several researches have studied the delay fracture behavior of high-strength and ultra high strength steel plat [13]. however, we attach less importance to the delay fracture resistance of low-carbon mn-b steel plate [14], especially the delay fracture performance of low-carbon mn-b steel plate which has h f. z. liu et alii, frattura ed integrità strutturale, 36 (2016) 139-150; doi: 10.3221/igf-esis.36.14 140 been processed by hot forming. with the rapid development of hot forming technology, it is urgent to evaluate the delay fracture behavior of hot formed ultra high-strength steel plate. on account of this, this study processed a kind of lowcarbon mn-b ultra high-strength steel plate with conventional thermal processing and hot forming technique and studied the effects of tempering temperature and hot forming process on its hydrogen-induced delay fracture resistance, which can provide a reference for the actual application of such kind of steel plate. materials and method experimental material he material used in the test was the improved mn-b cold-rolled steel plate (1500 mpa) which was self-developed. it was produced using techniques of rotating furnace, external refining, continuous casting and continuous rolling. the thickness of steel plate was 1.5 mm. its chemical components and their mass fractions were as follows: si (0.85), c (0.20), mn (1.60), s (0.002), p (0.006) and b (0.0015). the experimental steel was first heated into 950 °c and then cooled with water after 20-min insulation. the hardened martensitic structure obtained was tempered at 100, 200 and 400 °c sequentially for 120 min and then cooled in the air. the process is shown in tab. 1. no. of samples heat treatment system 1 950 °c × 20 min, water cooling / 2 100°c×120min, air cooling 3 200°c×120min, air cooling 4 400°c×120min, air cooling table 1: heat treatment system of experimental materials. experimental method to test the tensile performance of the experimental material in quenched state at different tempering temperatures, a tensile experiment was carried out on tensile sample using material testing machine. constant-load notch tensile experiment was used to evaluate the resistance of the experimental material. the ratio of critical fracture stress c to notch strength n , i.e., delay fracture strength ratio /c n  was used to evaluate the delay fracture resistance of the experimental materials. the higher the value was, the better the delay fracture resistance was. to avoid the size effect of thin plate shape samples on hydrogen absorption and dehydrogenation behaviors, the experimental steel plate with a thickness of 6.0 mm was processed into a round bar sample with a size of 5 × 40 mm. then electrochemical hydrogen charging was performed on naoh solution (0.1mol/l); the current density used was 4 ma/cm2 and the process lasted for 72 h. after hydrogen charging and surface grinding, the content of hydrogen in the sample was tested using thermal desorption spectrometry (tds); the heating temperature was 800 °c and the heating rate was 100 °c/h. activation energy of hydrogen traps in the sample was tested by varying the heating rate of tds. the content of hydrogen of hydrogen filled sample was measured at different time points; in this way, the diffusion coefficient of hydrogen in the experimental material was calculated. besides, the notched tensile sample was loaded in corrosive liquid under the effect of critical stress for 100 h. the working segment near the corroded notch was cut using wire cutting. to estimate the critical hydrogen content of the experimental material, the content of hydrogen was measured using tds as well after grinded with 1000 # abrasive paper. constant-load delay fracture experiment, electronic hydrogen charging experiment and test with tds were carried out on experimental materials in conventional quenching state and at different tempering temperatures to study the delay fracture resistance as well as behaviors of hydrogen absorption and effusion and discuss over the effects of quenching and tempering temperature on the delay fracture resistance of the experimental materials. results and discussion mechanical performance of experimental materials ig. 1 shows the changes of tensile performance of the experimental materials along with tempering temperature. it can be seen that, the experimental material had high strength and good plasticity; tensile strength weakened after tempering at 100 °c, whereas yield strength improved. in different states, elongation fluctuated, but slightly. only t f f. z. liu et alii, frattura ed integrità strutturale, 36 (2016) 139-150; doi: 10.3221/igf-esis.36.14 141 when the material was tempered at 400 °c, elongation decreased under the effect of temper embrittlement. figure 1: vibration tendency of the mechanical performance of the experimental materials along with tempering temperature. the delay fracture resistance of experimental materials fig. 2 and 3 show the curves for applied stress – time of failure (s-t) in notched tensile experiment. it can be seen that, time of failure increased with the decrease of applied stress. compared to samples in quenching state, the s-t curve of samples at different tempering temperatures moved towards upper right first and then left lower when the tempering temperature rose to 400 °c. it indicated that, tempering processing improve the delay fracture resistance of the experimental materials; and samples processed at tempering temperature of 200 °c had the highest critical fracture stress and the longest fracture lifespan (fig. 3). figure 2: curves for stress – time of failure of the experimental materials in quenching state in notched tensile experiment. results of notched tensile experiment carried out on the experimental materials are shown in tab. 2. fig. 4 and 5 show the vibrations of critical fracture stress and delay fracture strength ratio of the experimental materials along with the changes of strength and tempering temperature. it can be seen that, critical fracture stress and delay fracture strength ratio of the experimental materials except for samples processed at a tempering temperature of 400 °c gradually increased with f. z. liu et alii, frattura ed integrità strutturale, 36 (2016) 139-150; doi: 10.3221/igf-esis.36.14 142 the decrease of tensile strength or the increase of tempering temperature. with the decrease of strength of notch samples, critical fracture stress and delay fracture strength ratio of the samples increased first and then decreased. though the strength of the samples processed at a tempering temperature of 200 °c reduced for 6.65%, the critical fracture stress improved for 51.14% and the delay fracture strength ratio improved for 61.97%. it indicated that, proper tempering processing after quenching could greatly improve the delay fracture performance when the strength was slightly weakened. figure 3: curves for stress – time of failure of the experimental materials in different states in notched tensile experiment. quenching state 100 °c tempering state 200 °c tempering state 400 °c tempering state smooth tensile strength rm, mpa 1488 1466 1399 1102 notch tensile strength σn, mpa 1759 1781 1642 1455 critical fracture stress σc, mpa 874 1162 1321 1134 delay fracture strength ratio σc/σn 0.497 0.652 0.805 0.780 table 2: results of delay fracture experiment. hydrogen absorption and effusion behaviors of the experimental materials delay crack of high-strength steel is correlated to the hydrogen in steels and the hydrogen absorbed from the environment and in corrosion process. hence we explored hydrogen absorption and effusion behaviors of round bar and plate samples. hydrogen absorption and hydrogen effusion behaviors of non-bearing experimental materials before and after hydrogen charging. after the round bar samples in different states were charged with hydrogen for 72 h at a current density of 4ma/cm2, the content of hydrogen was measured using tds at a heating rate of 100 °c/h. besides, the content of hydrogen in samples without hydrogen charging was also measured (tab. 3). generally, hydrogen released at a temperature below 400 °c is called as diffusible hydrogen, whereas hydrogen released at a temperature higher than 400 °c is called as non-diffusible hydrogen [15, 16]. as the delay fracture is the most obvious when the temperature is near to room temperature, delay fracture is considered to be induced by diffusible hydrogen released at room temperature rather than non-diffusible hydrogen released at room temperature [17, 18]. in this study, hydrogen released at a temperature below 300 °c was regarded as diffusible hydrogen and hydrogen released at a temperature above 300 °c was as non-diffusible hydrogen. therefore, the hydrogen corresponding to the first hydrogen effusion peak of materials processed at a relatively low temperature was diffusible hydrogen and the hydrogen corresponding to the second hydrogen effusion peak of materials processed at a relatively high temperature was nondiffusible hydrogen. obviously, the content of diffusible hydrogen in the samples in quenching state was quite low, so was f. z. liu et alii, frattura ed integrità strutturale, 36 (2016) 139-150; doi: 10.3221/igf-esis.36.14 143 the content of non-diffusible hydrogen in the samples in tempering state. an obvious low-temperature hydrogen effusion peak appeared in the hydrogen effusion curve of the hydrogen charged samples in quenching state or at different tempering temperatures and the peak temperature was about 145 °c; but no obvious changes were observed in the hightemperature hydrogen effusion peak. besides, the low-temperature peak of hydrogen filled samples in tempering state was the highest. with the increase of tempering temperature, the low-temperature peak of the samples decreased, but the hightemperature peak had no obvious changes. it suggested that, the hydrogen absorbed after hydrogen charging was diffusible hydrogen and the content of non-diffusible hydrogen had no obvious changes. figure 4: variation of critical fracture stress and delay fracture ratio of the experimental materials along with the changes of tensile strength. figure 5: variation of clinical fracture stress and delay fracture ratio of the experimental materials along with the changes of tempering temperature. f. z. liu et alii, frattura ed integrità strutturale, 36 (2016) 139-150; doi: 10.3221/igf-esis.36.14 144 fig. 6 shows the variation of the hydrogen content of the experimental materials in different states along with the changes of tempering temperature. it can be seen that, the content of hydrogen in different states before hydrogen charging were similar; the content of diffusible hydrogen was quite low; except for samples processed at a tempering temperature of 100 °c, the content of non-diffusible hydrogen in samples in different states was highly consistent; the content of hydrogen significantly improved after hydrogen charging, a slight increase in non-diffusible hydrogen and a significantly increase in diffusible hydrogen; as the tempering temperature increased, the content of hydrogen charged reduced (the content of diffusible hydrogen decreased and the content of non-diffusible hydrogen remained unchanged). state of samples quenching state 100 °c tempering state 200 °c tempering state 400 °c tempering state samples without hydrogen charging (original state) the content of diffusible hydrogen (ppm) 0.0176 0.0081 0.0009 0.0031 the content of nondiffusible hydrogen (ppm) 0.0741 0.1677 0.0791 0.0834 total content of hydrogen (ppm) 0.0909 0.1758 0.0801 0.0857 hydrogen-filled samples the content of diffusible hydrogen(ppm) 0.8629 0.6201 0.5452 0.4441 the content of nondiffusible hydrogen (ppm) 0.1134 0.0951 0.1402 0.1443 total content of hydrogen (ppm) 0.9771 0.7136 0.6866 0.5882 table 3: the content of hydrogen of the experimental materials in different states before and after hydrogen charging (non-bearing, round bar samples). figure 6: vibration of the content of hydrogen of round bar samples in different states before and after hydrogen charging (cd: the content of diffusible hydrogen; cn: the content of non-diffusible hydrogen; ct: the content of hydrogen). hydrogen absorption and effusion behaviors of experimental materials before and after loading the notch tensile samples were loaded for 100 hours in corrosive liquid under critical stress. then the corroded part was cut down. after surface clearance, it was put into tds to measure behaviors of hydrogen absorption and effusion, and the measurements results are shown in tab. 4 and fig. 8. it can be seen that, the content of hydrogen in samples in four f. z. liu et alii, frattura ed integrità strutturale, 36 (2016) 139-150; doi: 10.3221/igf-esis.36.14 145 different states differs little before loading, and the hydrogen involved was non-diffusible hydrogen; the content of hydrogen improved after 100-h loading in corrosive liquid, and the hydrogen involved was also non-diffusible hydrogen; the content of hydrogen in samples in quenching state was the lowest, while the content of hydrogen in samples processed at a tempering temperature of 200 °c was the highest, four times that of the sample in quenching state and two times that of the samples processed at a tempering temperature of 100 °c and 400 °c. state of samples quenching state 100 °c tempering state 200 °c tempering state 400 °c tempering state samples before loading the content of diffusible hydrogen (ppm) 0.0119 0.0081 0.0099 0.0185 the content of non-diffusible hydrogen (ppm) 0.1160 0.0958 0.1121 0.1278 total content of hydrogen 0.1281 0.1045 0.1221 0.1466 samples after loading the content of diffusible hydrogen (ppm) 0.0839 0.0534 0.1629 0.0938 the content of non-diffusible hydrogen (ppm) 0.3385 0.6466 1.6319 1.7968 total content of hydrogen (ppm) 0.4228 0.6997 1.7949 0.8518 table 4. the content of hydrogen of experimental materials in different states before and after loading (plate samples) figure 7: the content of hydrogen of experimental materials in different states before and after loading (plate samples). activation energy of hydrogen trap of experimental materials the peak temperature of hydrogen effusion peak would change when heating rate in thermal analysis changed. activation trap corresponding to hydrogen effusion peak can be calculated according to the variation of the peak temperature [19 ~ 20]. it is because that, hydrogen in traps can be gradually released by overcoming trap potential barrier when hydrogen filled samples are heated at a certain heating rate and the process is controlled by the bulk diffusion of hydrogen in samples. as the capability of every kind of trap trapping hydrogen is fixed, a peak value will appear in the curve of the correlation between hydrogen effusion rate and temperature under certain heating condition. the capability of trap f. z. liu et alii, frattura ed integrità strutturale, 36 (2016) 139-150; doi: 10.3221/igf-esis.36.14 146 trapping hydrogen can be estimated qualitatively according to the peak value. the hydrogen effusion peak temperature would change if the heating rate was changed; when heating rate increases and heating time reduces, hydrogen effusion peak moves towards high temperature. the correlation between heating rate and hydrogen effusion peak temperature [21] is: e 2 e ae a prta prt   (1) in the formula, ea refers to activation energy of hydrogen trap,  refers to heating rate; tp refers to hydrogen effusion peak temperature, a is a constant r is a gas constant. after taking the logarithm of both sides of formula (1) and differentiation, we get 2ln( / ) (1/ ) ap p et t r     (2) it can be known from formula (2) that, 2ln( / )pt and 1/ pt was in a linear correlation. hence ea could be calculated using linear fitting method. hydrogen effusion peak temperature of hydrogen effusion curves of experimental samples processed at different heating rates is shown in tab. 5. the correlation between 2ln( / )pt and 1/ pt could be obtained in fig. 8. besides, the value of e /a r was obtained after solving slope with linear fitting, and then the value of activation energy ea was obtained. heating rate, °c /h state of samples hydrogen effusion peak temperature of diffusible hydrogen, °c hydrogen effusion peak temperature of non-diffusible hydrogen, °c 100 quenching state 152 396 100 °c tempering state 129 411 200 °c tempering state 132 411 400 °c tempering state 126 390 200 quenching state 201 438 100 °c tempering state 179 430 200 °c tempering state 186 427 400 °c tempering state 160 408 400 quenching state 260 465 100 °c tempering state 251 455 200 °c tempering state 244 453 400 °c tempering state 222 447 table 5: hydrogen effusion peak temperature of hydrogen effusion curves of experimental materials processed by different heating rate. f. z. liu et alii, frattura ed integrità strutturale, 36 (2016) 139-150; doi: 10.3221/igf-esis.36.14 147 figure 8. the correlation between 2ln( / )pt and 1/ pt of experimental materials: a) diffusible hydrogen; b) non-diffusible hydrogen). tab. 6 shows that, activation energy of diffusible hydrogen trap was close to hydrogen activation energy of m3c carbide in 42crmo steel processed at a tempering temperature of 600 °c (13.4 kj/mol) [22] as well as hydrogen trap activation energy of fe3c (18.5 kj/mol) and hydrogen trap activation energy of grain boundary (17.2 kj/mol) [23]. f. z. liu et alii, frattura ed integrità strutturale, 36 (2016) 139-150; doi: 10.3221/igf-esis.36.14 148 quenching state 100 °c tempering state 200 °c tempering state 400 °c tempering state activation energy of diffusible hydrogen, kj/mol 15.3 12.9 14.3 16.2 activation energy of non-diffusible hydrogen, kj/mol 63.9 118.9 119.6 79.5 table 6: hydrogen trap activation energy of experimental materials. diffusion of hydrogen in experimental materials it was found that, hydrogen-induced crack was closely correlated to the local concentration of hydrogen [24]. as for diffusible hydrogen, local concentration is determined by average content and diffusion process. therefore, it is important to study the diffusion process of diffusible hydrogen in samples. fig. 9 shows the vibration of the content of diffusible hydrogen in steels along with the changes of time. it can be seen that, the content of diffusible hydrogen in experimental materials decreased with the increase of storage time; when the storage time exceeds 72 h, the concentration of diffusible hydrogen in experimental steels was around 0. 15 × 10-6. figure 9: effects of storage time after hydrogen charging on the concentration of diffusible hydrogen of experimental materials in different states. carnerio filho et al. [25] once studied the diffusion of hydrogen in steels based on the rules of decline of hydrogen content of hydrogen-filled round bar samples which were stored for different periods of time. the equation of diffusion of hydrogen in steels is: 2 00.72( )exp( 22.2 / )tc c c c dt d     (3) in the formula, ct refers to the concentration of diffusible hydrogen in steels at time point t; c ∞ refers to the concentration of diffusible hydrogen of experimental materials when t is equal to ∞; c0 refers to the concentration of diffusible hydrogen when t = 0; d refers to the diameter of sample; d stands for diffusion coefficient of hydrogen in experimental materials. the experimental results of experimental materials in different states were substituted into formula (3); regression analysis results are shown in fig. 9. it can be seen that, the diffusion coefficients of hydrogen in materials processed by quenching, 100 °c tempering, 200 °c tempering and 400 °c tempering were d1 = 3.71 × 10-7, d2 = 2.98 × f. z. liu et alii, frattura ed integrità strutturale, 36 (2016) 139-150; doi: 10.3221/igf-esis.36.14 149 10-7, d3 = 2.66 × 10-7 and d4 = 2.31 × 10-7 cm2/s. obviously, with the increase of tempering temperature, diffusion coefficients of experimental materials would decrease. to sum up, as for the improved mn-b steel plate (1500 mpa), the delay fracture resistance of experimental material in quenching state is the lowest, but tempering processing can significantly enhance the delay crack resistance. the delay fracture resistance of the materials processed at 200 °c tempering temperature was the highest on the condition that the strength of experimental materials decreased slightly. when tempering temperature was too high, for example, 400 °c, then diffusion coefficient of hydrogen at room temperature was weakened due to the significant decrease of the strength, but the resistance was still high than that of materials processed by quenching. with the increase of tempering temperature, the diffusion coefficient of hydrogen at room temperature decreased. the content of non-diffusible hydrogen of experimental materials in corrosive fluid under critical stress showed an obvious improvement after loading. the quantity of hydrogen bearing by the samples in quenching state under critical stress was the lowest, while the quantity of hydrogen of the samples processed at 200 °c tempering temperature was the highest. under the effect of critical stress and after 100-h loading in corrosive liquid, the content of hydrogen in samples showed a remarkable increase; besides, the quantity of hydrogen processed by heat forming was higher than that of samples processed by quenching and samples processed by quenching and 100 °c tempering, leading to the high delay fracture resistance. hence, hot forming processing can ensure a high delay fracture resistance of experimental materials and tempering processing can further improve the delay fracture resistance of experimental materials. references [1] koyama, m., akiyama, e., tsuzaki, k., hydrogen-induced delayed fracture of a fe–22mn–0.6c steel pre-strained at different strain rates. scripta materialia, 66(11) (2012) 947-950. [2] zhang, c. l., liu, y. z., chao, j., et al. effects of niobium and vanadium on hydrogen-induced delayed fracture in high strength spring stee l. journal of iron & steel research international, 18(6) (2011) 49-53. [3] zhang, s., huang, y., sun, b., et al. effect of nb on hydrogen-induced delayed fracture in high strength hot stamping steels. materials science & engineering a, 626 (2015) 136-143. [4] ogata, t., evaluation of hydrogen embrittlement by internal high-pressure hydrogen environment in specimen. journal of the japan institute of metals, 72(2) (2008) 125-131. [5] araújo, b. a., travassos, g. d., silva, a. a., et al., experimental characterization of hydrogen embrittlement in api 5l x60 and api 5l x80 steels. key engineering materials, 478 (2011) 34-39. doi:10.4028/www.scientific.net/kem.478.34. [6] mallick, a., das, s., mathur, j., et al. internal reversible hydrogen embrittlement leads to engineering failure of cold drawn wire. case studies in engineering failure analysis, 1(2) (2013) 139-143. [7] zucca, g., mocci, a., tirilló, j., et al. hydrogen embrittlement and fatigue fracture of a crankshaft of an internal combustion engine. procedia engineering, 109 (2015) 202-209. doi: 10.1016/j.proeng.2015.06.213. [8] mori, k., lee, e. w., frazier, w. e., et al. effect of tempering and baking on the charpy impact energy of hydrogen-charged 4340 steel. journal of materials engineering & performance, 24(1) (2015)329-337. [9] rajabipour, a., melchers, r. e., capacity of pitting corroded pipes under hydrogen assisted cracking. international journal of hydrogen energy, 40(30) (2015) 9388-9399. doi: 10.1016/j.ijhydene.2015.05.077. [10] han, s. z., hui, w. j., liu, r. p., et al. effect of tempering temperature on hydrogen-induced delayed fracture behavior of 30crmnsia steel. transactions of materials & heat treatment, 35(7) (2014)114-119. [11] zhang, y. j., zhou, c., hui, w. j., et al. effect of c content on hydrogen induced delayed fracture behavior of mnb type steels. journal of iron & steel research, 26(5) (2014) 49-55. [12] bai, x. m., gong, j. m., wang, y. f., prediction of hydrogen induced delayed fracture initiation time of high strength steel using cohesive zone modeling. journal of shanghai jiaotong university, 46(7) (2012) 1079-1083. [13] kuduzović, a., poletti, m. c., sommitsch, c., et al. investigations into the delayed fracture susceptibility of 34crnimo6 steel, and the opportunities for its application in ultra-high-strength bolts and fasteners. materials science & engineering a, 590(2) (2014) 66–73. [14] li, f. f., fu, m. w., lin, j. p., et al. experimental and theoretical study on the hot forming limit of 22mnb5 steel. international journal of advanced manufacturing technology, 71(1-4) (2014) 297-306. doi: 10.1007/s00170-013-5468-x. [15] dariusz, f., grzegorz, r., effect of shielded-electrode wet welding conditions on diffusion hydrogen content in deposited metal. welding international, 25(3) (2011) 166-171. f. z. liu et alii, frattura ed integrità strutturale, 36 (2016) 139-150; doi: 10.3221/igf-esis.36.14 150 [16] ji, w. w., gong, h. r., adsorption and diffusion of hydrogen on ti, al, and tial surfaces. international journal of hydrogen energy, 39(11) (2014) 6068-6075. [17] ji, c., xinguo, r., xin-zheng, l., et al. on the room-temperature phase diagram of high pressure hydrogen: an ab initio molecular dynamics perspective and a diffusion monte carlo study. journal of chemical physics, 141(2) (2014) 024501-024501. [18] fu-chun, h., yung-yu, c., tsung-tsong, w., a room temperature surface acoustic wave hydrogen sensor with pt coated zno nanorods. nanotechnology, 20(6) (2009) 2643-2646. [19] silverstein, r., eliezer, d., hydrogen trapping mechanism of different duplex stainless steels alloys. journal of alloys & compounds, 644 (2015) 280-286. doi: 10.1016/j.jallcom.2015.04.176. [20] wei, f. g., tsuzaki, k., quantitative analysis on hydrogen trapping of tic particles in steel. metallurgical & materials transactions a, 37(2) (2006) 331-353. [21] rojas, h., fierro, j. l. g., reyes, p., the solvent effect in the hydrogenation of citral over ir and ir-fe/tio2 catalysis. journal of the chilean chemical society, 52(2) (2007)1155-1159. [22] tur, c., khaleeli, z., ciccarelli, o., et al. complementary roles of grey matter mtr and t2 lesions in predicting progression in early ppms. journal of neurology neurosurgery & psychiatry, 82(4) (2011) 423-428. doi: 10.1136/jnnp.2010.209890. [23] choo, w. y., lee, j. y., hydrogen trapping phenomena in carbon steel. journal of materials science, 17(7) (1982) 1930-1938. [24] wang, m., akiyama, e., tsuzaki, k., determination of the critical hydrogen concentration for delayed fracture of high strength steel by constant load test and numerical calculation. corrosion science, 48(8) (2006) 2189-2202. [25] filho, c. j. c., mansur, m. b., modenesi, p. j., et al. the effect of hydrogen release at room temperature on the ductility of steel wire rods for pre-stressed concrete. materials science & engineering a, 527(18) (2010) 4947-4952. << /ascii85encodepages false /allowtransparency false /autopositionepsfiles true /autorotatepages /none /binding /left /calgrayprofile (dot gain 20%) /calrgbprofile (srgb iec61966-2.1) /calcmykprofile (u.s. web coated \050swop\051 v2) /srgbprofile (srgb iec61966-2.1) /cannotembedfontpolicy /error /compatibilitylevel 1.4 /compressobjects /tags /compresspages true /convertimagestoindexed true /passthroughjpegimages true /createjobticket false /defaultrenderingintent /default /detectblends true /detectcurves 0.0000 /colorconversionstrategy /cmyk /dothumbnails false /embedallfonts true /embedopentype false /parseiccprofilesincomments true /embedjoboptions true /dscreportinglevel 0 /emitdscwarnings false /endpage -1 /imagememory 1048576 /lockdistillerparams 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/hrv (za stvaranje adobe pdf dokumenata najpogodnijih za visokokvalitetni ispis prije tiskanja koristite ove postavke. stvoreni pdf dokumenti mogu se otvoriti acrobat i adobe reader 5.0 i kasnijim verzijama.) /hun 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can be opened with acrobat and adobe reader 5.0 and later.) >> /namespace [ (adobe) (common) (1.0) ] /othernamespaces [ << /asreaderspreads false /cropimagestoframes true /errorcontrol /warnandcontinue /flattenerignorespreadoverrides false /includeguidesgrids false /includenonprinting false /includeslug false /namespace [ (adobe) (indesign) (4.0) ] /omitplacedbitmaps false /omitplacedeps false /omitplacedpdf false /simulateoverprint /legacy >> << /addbleedmarks false /addcolorbars false /addcropmarks false /addpageinfo false /addregmarks false /convertcolors /converttocmyk /destinationprofilename () /destinationprofileselector /documentcmyk /downsample16bitimages true /flattenerpreset << /presetselector /mediumresolution >> /formelements false /generatestructure false /includebookmarks false /includehyperlinks false /includeinteractive false /includelayers false /includeprofiles false /multimediahandling /useobjectsettings /namespace [ (adobe) (creativesuite) (2.0) ] /pdfxoutputintentprofileselector /documentcmyk /preserveediting true /untaggedcmykhandling /leaveuntagged /untaggedrgbhandling /usedocumentprofile /usedocumentbleed false >> ] >> setdistillerparams << /hwresolution [2400 2400] /pagesize [612.000 792.000] >> setpagedevice microsoft word numero_60_art_06_3367.docx a. elakhras et alii, frattura ed integrità strutturale, 60 (2022) 73-88; doi: 10.3221/igf-esis.60.06 73 fracture toughness of matrix cracked frc and fgc beams using equivalent tpfm a.a. elakhras, m.h. seleem, h.e.m. sallam materials engineering department, faculty of engineering, zagazig university, zagazig 44519, egypt ahmedali.elakhras@gmail.com,http://orcid.org/0000-0002-3821-1327 mhseleem1963@gmail.com, http://orcid.org/0000-0002-5777-4651 hem_sallam@yahoo.com, http://orcid.org/0000-0001-9217-9957 abstract. in the present work, the fracture toughness (kic) of full-depth (fd) fiber-reinforced concrete (frc) and layered functionally graded concrete (fgc) matrix cracked (mc) beams has been determined by the equivalent relationships of the two-parameter fracture model (etpfm). forty-eight mc-fgc and mc-fd frc beam specimens with span-depth ratios (l/d) equal 4, 5, and 6 were tested under the 3pb configuration. the mc length-depth ratio (ao/d) remained constant equal to one-third. all frc beams have the same hooked-end steel fibers volume fraction of 1%. the fgc beams are composed of three equal layers, i.e., frc in the bottom layer at the tension side, normal strength concrete (nsc) at the middle layer, and high strength concrete at the upper layer in the compression side. the results showed that the predicted values of kicobtained from etpfm are considered appropriate according to the maximum size of the non-damaged defect concept. the crack mouth opening displacement estimated from etpfm showed acceptable values close to the present experimental results. the kic values calculated within the presence of fibers in front of and through the mc for frc beam specimens having 1% sfs is more than twice the value of nsc. keywords. fiber-reinforced concrete; functionally graded concrete; matrix cracked beams; equivalent tpfm; fracture toughness. citation: elakhras, a., seleem, m., sallam, h.., fracture toughness of matrix cracked frc and fgc beams using equivalent tpfm, frattura ed integrità strutturale, 60 (2022) 73-88. received: 23.11.2021 accepted: 22.01.2022 online first: 27.01.2022 published: 01.04.2022 copyright: © 2022 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. introduction ull-depth (fd) fiber-reinforced concrete (frc) is conventional concrete with suitable discontinuous fibers added to achieve a composite with a desirable performance level. it became known that frc improved the particular properties of concrete despite its manufacturing cost [1]. recently, functionally graded concrete (fgc) is a new layered composite used to achieve the favorite serviceable requests of a structural element without major influence on its performance while reducing its materials cost[2,3]. nowadays, increasing demand is placed on frc and fgcforrepairing construction, especially in infrastructure pavement such as rigid pavement systems constructed at airports, local streets, f https://youtu.be/3sowj7v16em a. elakhras et alii, frattura ed integrità strutturale, 60 (2022) 73-88; doi: 10.3221/igf-esis.60.06 74 ports,high-volume traffic corridors, and parking lots as in the usa [4] and europe [2]. most of the researchers concerned about studying fgc according to its mechanical properties conduced that fgc is more efficient than fd frc[5–13]. however, the fracture behavior of fd frc and fgc is still limed or not obviously according to fracture mechanics concepts. fracture parameters of concrete are substantial properties used in concrete structures. linear elastic fracture mechanics (lefm) is the fundamental basis of most models. according to linear elastic fracture mechanics (lefm), fracture energy (gic)and fracture toughness (kic) are not variant with the depth of notch and the size of the beam. thus, they are considered as material properties. also, lefm assumes a perfect bond between the fiber and the matrix. however, several researches reported that the kic value evaluated for notched concrete specimens using lefm showed significant variance with different sizes and notch depth. latterly most researches implicitly these variances by the inelastic interface response during crack growth in concrete. this inelastic response during crack growth paid attention to the role of aggregate particles in crack arresting [14–16] and the fibers in crack bridging. one of the significant problems for calculating frc fracture parameters is substantial nonlinearity before the maximum load. unless this stable crack extension is included in the calculations of kic, one cannot obtain a correct value of the fracture toughness of concrete. also, fibers' presence into cracked beams from normal concrete causes the maximum loads and the fracture energy to increase dramatically [17]. moreover, bažant et al. [18] reported that much of the scatter in total fracture energy (gf) calculations come from inherent randomness in the tail end of the load-crack mouth opening displacement (p-cmod) curve and uncertainty in extrapolating the tail end of the curve to zero loads beside sources of energy dissipation [18]. in addition, the examinations of fractured specimens of frc take place primarily due to fiber pullout or deboning and increase the fracture toughness. thus, numerous nonlinear fracture models have been suggested to describe brittle materials failure [19–23]. hillerborg proposed the fictitious crack model representing the inelastic interface response during crack growth characterized by a nonlinear stress-crack displacement relationship [19]. this approach is based on predicting the macroscopic stress-crackwidth relations by the softening behavior of concrete. however, according to jenq and shah [24], the fracture mechanism for frc can be divided into several stages. the first stage is subcritical crack growth in the matrix and the beginning of the fiber bridging effect, where the linear elastic behavior of the composite is controlled. the second stage is the postcritical crack growth in the matrix, where there is steady-state crack growth due to the applied load and the fiber bridging stresses, and the stress intensity factor remains constant. the final stage is the resistance to crack separation, provided exclusively by the fibers pullout mechanism. according to jenq and shah [24], crack growth occurs when the stress intensity factor, kic, and the crack tip opening displacement (ctod) reach a critical value. thus, another nonlinear model considered the elastic effective crack approach, based on the equivalent lefm and griffith-lrwin energy dissipation concept were proposed such as; the two-parameter fracture model (tpfm) by jenq and shah [21]and the size effect law (sel) by bažant[22]. these nonlinear fracture models presented at least two fracture parameters material. these parameters are dependent only on the fracture properties of the material, irrespective of the size and geometry of the structure. these parameters are expected to describe the failure of a concrete member. hillerborg et al. [19]proposed the fictitious crack model to measure the total material energy of fracture(gf). the general idea of this type of test is to measure the amount of energy absorbed when the specimen is broken into two halves [25]. jenq and shah proposed a tpfm and considered its two parameters; kic and the critical crack tip opening displacement ctodc are constant material properties[21]. also, sel for notched beams (sel, type-ιι) proposed by bažant considered two material parameters, the critical energy release rate (gf) and the critical effective crack extension (cf). since both tpfm and sel are based on the same elastic effective crack approach, ouyang et al. [26] suggested relationships to calculate the equivalent parameters of tpfm based on this equivalency and derived it by comparing the results with sel. also, other researchers are concerned with determining kic for frc and fgm [2,5,27–29]. all these models calculated fracture parameters using a three-point bending (3pb) test on through-thickness cracked beams for concrete. however, fibers must cross the two surfaces of the pre-cracked beams to have actual field conditions and correct simulations in the actual field simulation of frc or fgc beams. it was considered one of the difficult laboratory problems. recently, sallam and co-workers [5]suggested a novel method to create a pre-matrix crack (mc), representing fibers that pass through the prematrix crack of the specimen to represent its bridging and closing effects. this work aims to study the equivalent relationships of tpfm (etpfm) to calculate the fgc and fd frc beams fracture toughness with real mc specimens. real fracture toughness reliability expected from such etpfm for mcspecimens was checked using the maximum size of the non-damaged defect (dmax) [30,31]. a. elakhras et alii, frattura ed integrità strutturale, 60 (2022) 73-88; doi: 10.3221/igf-esis.60.06 75 experimental program materials and mix proportions hree mixes, including normal strength concrete (nsc), frc, and high strength concrete (hsc), were designed for the experimental program. nsc was designed based on aci 211.1-91 [32]. according to aci 544.4r-88 [1], sffrc mixtures can be mixed and placed with conventional equipment, and procedures used from 0.5 to 1.5 vf%. however, higher percentages of fibers (from 2 to 10 volume percent) have been used with special fiber addition techniques and placement procedures. therefore, frc was designed by adding 1% hooked-end sf by volume fraction to nsc. hooked-end steel fibers (sf) were used with a length equal to 35 mm, a circular cross-section of 0.80 mm, and tensile strength of 1150 mpa. ordinary portland cement, grade n 42.5 with content 400 kg/m3, was used to produce both nsc and frc. the water/ cementitious materials ratio (w/cm) was 0.53. hsc mix was produced by cement, grade n 52.5 with a total cm of 550kg/m3, and silica fume (master life sf 100) as a partial replacement of cm by 10%. also, a superplasticizer (master glenium rmc 315) was used as a high range water reducer by 2.5 % from the weight of the cm. the w/cm ratio was 0.27. in all mixes, dolomite having a maximum aggregate size equals to 12.50 mm, and ordinary siliceous sand were respectively used as coarse and fine aggregates. the specific gravities of the used coarse and fine aggregates were respectively 2.61 and 2.59. for the estimation of mechanical properties of mixes, cubes 150×150×150 according to bs en 12390–3:2009 [33]were cast for the compression test. cylinders of 300 mm height and 150 mm diameter were used to estimate indirect tensile strength according to bs en 12390–6:2009 [34]. all beams were removed from molds after 24 hours from casting. after de-molding, all specimens were cured in moist air for 56 days. the mix proportions of the nsc, frc and hsc mix relative to their cm by weight and mechanical properties of the three investigated mixes are given in tab. 1. mix/cm(kg/m3) mix proportions relative to cm by weight mechanical properties cm sand dolomite silica fume w/cm super plasticizer compressive st., , mpa indirect tensile st., , mpa nsc/(400) 1 1.91 2.38 0.53 27.70 frc/(400) 1 1.91 2.38 0.53 0.02 34.55 hsc/(550) 1 1.35 1.75 0.10 0.27 0.025 61.33 table 1: mix proportions for mixtures and their mechanical properties. samples preparation and casting procedures most of the fracture models recommended notched beams with l/d ratios in the range of 2.5 to 8 to study the variation of fracture toughness or fracture energy for various l/d ratios in this range. in tpfm, jenq and shah [21,24] considered the standard specimen with a span-depth ratio (l/d) of 4 and the initial notch-to-depth ratio (ao/d) equal to 1/3. han et al. [23]also investigated the fracture toughness for notched beams with various span-depth ratios ranging from 2 to 6. hillerborg[25]recommended standard notched beams of various l/d ratios ranging from 4 to 8 to calculate the fracture energy according to its concept. therefore, the following span-depth ratios, l/d = 4, 5, and 6, were analyzed in the present work. forty-eight matrix-cracked (mc) fd frc and fgc beams were fabricated, with constant breadth equals150 mm. the initial crack-depth ratio (ao/d) stayed equals one-third. the investigated beams were of two patterns. the 1stpatterncomprised 24 mc specimens from fd frc. the 2ndpattern comprised 24 mcfgc beam specimens. four specimens were cast for each case study to take the average. the dimensions of fgc and frc beam specimens are illustrated in tab. 2. three mixtures from frc, nsc, and hsc were designed to fabricate fgc beams at equal layers in steel molds. the bottom layer at the tension side was cast from the frc mixture. nsc was cast at the middle layer of the beam depth. hsc was cast in the upper layer at the compression zone of the beam. the same procedures used by othman et al.[35]in casting fgc layers were followed. in the case of the frc mixture, sfs were sprayed randomly in a continuous manner during the final stage of concrete mixing, according to the recommendations of aci 544.4r [1]. all specimens were moist cured for 56 days. fig. 1 shows different beams patterns and the fibers distribution across the notch. t a. elakhras et alii, frattura ed integrità strutturale, 60 (2022) 73-88; doi: 10.3221/igf-esis.60.06 76 real matrix crack methodology two mm thickness plate from foam was used to make the mc at the mid-span of the beam bottom. two grooves were cut at two sides of the steel mold to fix the foam plate. the steel fibers were permitted to cross the thin foam plate uniformly distributed. the amount of steel fibers allowed to cross the plate was assumed to be one-third of the total amount representing 1% of the concrete volume fraction. thus, the orientation factor efficiency was 0.33 for fibers distributions for ideal theoretical assumptions in this study. many experimental and numerical studies reported orientation factors in the range of 40-60% [36–38]. sallam and co-workers describe the procedures of real mc in detail [5], as shown in fig. 2. figure 1:patterns of frc and fgc beams and the sf distributions across the notch. experimental test setup hillerborg[25]recommended standard 3pb notched beams to calculate the fracture toughness of concrete. 3pb specimens were employed in the tpfm proposed by jenq and shah [21,24], which this model was adopted in the present work to analyze the results of the matrix cracked specimens. therefore, the fgc and fd frc beams were tested under the 3pb test. a universal testing machine of 1000 kn maximum capacity was used for testing all specimens. flexural test measurements were obtained through a data acquisition system. a100 kn maximum capacity load cell was used to measure the applied load. the crack mouth opening displacement (cmod) was measured using a sensitive lvdt, as shown schematically in fig. 3. however, the ctod was measured based on the proposed relationships of etpfm. figure 2: methodology of mc-fd frc and fgc beams. b d/3 d/3 nsc frc hscd/3 b cross section: b-b b) mc-fgc pattern frcd l b a a cross section: a-a a) mc-fd frc pattern a. elakhras et alii, frattura ed integrità strutturale, 60 (2022) 73-88; doi: 10.3221/igf-esis.60.06 77 figure 3: schematic diagram for setting cmod measurement and test set up. equivalent parameters of tpfm method (etpfm) the flexural strength flf was calculated using a three-point bending test (3pb) for different specimens sizes as follow;   2 3 2 fl my pl f l bd (1) where m is the moment due to the applied load, p, under 3pb test, y is the maximum distance from the neutral axis of specimen cross-section, i is the moment of inertia for uncracked specimen, b is the specimen breadth, d is the depth and l is the loaded span of the specimen. it is worth noting that since there is no alternative for eqn. (1), this equation can be used for composite comparison data and specification values up to the maximum fiber strain of 2 % and considered an apparent strength for laminated beams as recommended by astm d7264/d7264m [39]. ouyan et al.[26]proposed a relationship based on equivalency between the effective crack growth length (∆ae) of tfpm proposed by jenq and shah [21]and critical crack length of sel (cf)[22]. the relations of etpfm were suggested to predicate the fracture parameters (kic, ctodc) for infinity large size 3b.p beam without using a closed-loop of loading and unloading cycle as in tfpm, by the following equations;      2 01.261 f f f a c g e (2) ic fk g e (3)    0 4.68 ( )f f c a c cmod e (4)                      2 0 0 0 0 1 0.92 0.08c c f f a a ctod cmod a c a c (5)         2 0 0 0 0.081 2.854 0.081 f c f f g a ctod a c e a c (6) where  f is the nominal strength and expressed by flf for mc-specimen, ao is the initial pre-crack depth, gf is the critical energy release rate, cf is the effective crack length, e is the modulus of elasticity, and ctodc is the critical crack a. elakhras et alii, frattura ed integrità strutturale, 60 (2022) 73-88; doi: 10.3221/igf-esis.60.06 78 mouth displacement. also, modulus of elasticity can be obtained from the load-cmod curve for notched for fd frc specimens as follow[2,21,24]:    0 2 6 i l a v e c d b (7)                2 3 2 0.66 0.76 2.28 3.87 2.04 1 v (8) ci is the initial compliance calculated from the load-cmod curve, and v(α) is the geometry factor. it is worth noting that the apparent flexural modulus of orthotropic laminates can be calculated by the chord or secant method recommended by astm d7264/d7264m [39]. on the other hand, eqns. (7,8) were previously adopted to estimate the modulus of elasticity of frc [21,24]and fgc [2]. therefore, the modulus of elasticity was calculated for frc and fgc specimens using eqns. (7,8). eqn. (7) calculated the modulus of elasticity for fd frc as an apparent value to the whole composite layered fgc beams. to calculate a representative e, especially for fgc specimens, notched fgc specimens with relative notch depth (αo=1/6) were tested for this study, as the fd of bottom layer for mc-fgc with αo=1/3 was fully cracked. results and discussion flexural behavior of mc-specimens he results of flexural strength for mc-fd frc, and mc-fgc specimens at first crack initiation and maximum stress for specimens with different sizes and l/d ratios equal 4, 5, and 6 are given in tab. 2. specimens mc-fd frc mc-fgc beam code l/d ratio b×d×l, mm at first cracking, mpa flf at maximum stress, mpa at maximum stress, mpa b4-1 4 150×150×600 3.17 3.70 2.75 b4-2 4 150×187.5×750 2.79 3.78 3.18 b4-3 4 150×225×900 2.60 3.23 2.58 b5-1 5 150×150×750 2.57 3.34 3.04 b5-2 5 150×180×900 2.90 3.34 2.65 b6 6 150×150×900 2.74 2.84 2.62 e, gpa 27.00 33.30 table 2: results of flexural strength of mc-fd frc and fgc specimens. fig. 4 shows stress-cmod curves of mc-fd frc and mc-fgc specimens with different sizes and spandepth ratios equal four, five, and six. the regulation factor was calculated for the tested specimens according to the suggested multilinear mean curve. the suggested multi-linear mean curve was calculated based on average points of stress and cmod at each observed variation on the curve slope for the four specimens in each case. for clear observation of the points at first cracking and maximum stress, the mean curves of mc-fd frc and mc-fgc specimens were re-drawn up to cmod equals 5 mm, as shown in fig. 5. t a. elakhras et alii, frattura ed integrità strutturale, 60 (2022) 73-88; doi: 10.3221/igf-esis.60.06 79 m p a st re ss , cmod, mm 0 1 2 3 4 5 0 5 10 15 20 25 30 sp. 1 sp. 2 sp. 3 mean mc-fd frc, b4-3 r =0.93 0 1 2 3 4 5 0 5 10 15 20 25 30 sp. 1 sp. 2 sp. 3 sp. 4 mean mc-fgc, b5-2 r =0.78 0 1 2 3 4 0 5 10 15 20 25 30 sp. 1 sp. 2 sp. 3 sp. 4 mean mc-fgc, b4-1 r =0.82 0 1 2 3 4 5 0 5 10 15 20 25 30 sp. 1 sp. 2 sp. 3 sp. 4 mean mc-fd frc, b4-1 r =0.86 0 1 2 3 4 5 0 5 10 15 20 25 30 sp. 1 sp. 2 sp. 3 sp. 4 mean mc-fgc, b5-1 r =0.89 0 1 2 3 4 5 0 5 10 15 20 25 30 sp. 1 sp. 2 sp. 3 sp. 4 mean mc-fd frc, b5-1 r =0.71 0 1 2 3 4 5 0 5 10 15 20 25 30 sp. 1 sp. 3 sp. 4 sp. 2 mean mc-fgc, b4-2 r =0.90 0 1 2 3 4 5 0 5 10 15 20 25 30 sp. 1 sp. 2 sp. 3 sp.4 mean mc-fd frc, b4-2 r =0.92 0 1 2 3 4 5 0 5 10 15 20 25 30 sp. 1 sp. 2 sp. 3 mean mc-fgc, b6-1 r =0.92 0 1 2 3 4 5 0 5 10 15 20 25 30 sp. 1 sp. 2 sp. 3 mean mc-fd frc, b5-2 r =0.82 0 1 2 3 4 0 5 10 15 20 25 30 sp. 1 sp. 2 sp. 3 mean mc-fd frc, b6-1 r =0.85 0 1 2 3 4 5 0 5 10 15 20 25 30 sp. 1 sp. 2 sp. 3 sp.4 mean mc-fgc, b4-3 r =0.86 a) mc-fd frc beams b) mc-fgc beams figure 4: stress-cmod curves of mc-beams, (a) frc, and (b) fgc. a. elakhras et alii, frattura ed integrità strutturale, 60 (2022) 73-88; doi: 10.3221/igf-esis.60.06 80 st re ss , m p a cmod, mm 0 1 2 3 4 5 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 mc-fd frc mc-fgc b4-1 0 1 2 3 4 5 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 mc-fd frc mc-fgcb6-1 0 1 2 3 4 5 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 mc-fd frc mc-fgc b4-2 0 1 2 3 4 5 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 mc-fd frc mc-fgc b4-3 0 1 2 3 4 5 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 mc-fd frc mc-fgcb5-1 0 1 2 3 4 5 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 mc-fd frc mc-fgcb5-2 figure 5: mean curves of stress-cmod for mcfd frc and mc-fgc beams. for mc-fd frc specimens, the first crack initiation appeared before the maximum stress, and specimens showed strain hardening behavior as a result of sfs at the head of the crack tip. the stress is released slowly after that depending on fibers distribution through the beam cross-section. while in mcfgc, the first crack initiation occurred at maximum stress, and an abrupt fall was seen after the maximum stress in mcfgc specimens as a result of the sfs absence ahead of the crack tip, see fig. 1. these observations of crack initiation for frc specimens are compatible with aci 544.4r-88 and astm c1609/c1609m [40,41]. on the other hand, the area under the descending portion (softening portion) of the frc specimens is larger than that of the fgc specimens. this is due to sfs in the fd frc beam specimens. also, in mc-fgc specimens, the concrete layers ahead of the crack tip were nsc in the middle zone and hsc in the compression zone without sf. thus, the presence of the softening portion in the fgc specimens reflects the efficiency of the proposed new mc technique in simulating a real field crack in the laboratory. results of etpfm according to ouyang et al. [26], the fracture parameters (kic, ctodc) can be obtained from the suggested equivalency relationship (etpfm), based on the equivalency of the effective crack length of tpfm and sel. the effective crack lengths (cf ) for mc-frc and mc –fgc specimens were obtained from applying sel-type ii on the specimens b4-1, b4-2, and b4-3, with a constant l/d ratio, equals 4. these values were considered as constant material property. the values of cf were 1.82, 14.27, and 63.43 mm for mc-fd frc at first cracking, mc-fd frc, and mc-fgc at maximum stress, respectively. according to bažant and rilem recommendations [42], the boundary of the cracking layer size, fracture process zone (fpz), is approximate twice cf. thus, the statistical analysis to obtain the equivalent parameters from etpfm was adopted within the boundary of the fpz. the proposed etpfm relationships were applied on mcfd frc and mc-fgc specimens with0 equal 1/3, for each case of l/d ratios (4, 5, and 6) individually, at first cracking and maximum stress, as follows: a. elakhras et alii, frattura ed integrità strutturale, 60 (2022) 73-88; doi: 10.3221/igf-esis.60.06 81 the values of gf and kic were estimated for the four specimens representing each case of l/d individually by substituting the incremental increase steps value of cf in eqn. (2,3). the ctod at each incremental step of cf is obtained from eqns. (4,5). then, kic-ctod curves for specimens with l/d ratios equal 4, 5, 6, and their average curves can be drawn as shown in figs. 6, 7, 8(a), for each case individually. by estimating the standard deviation (s.d) for the average values of ctod at each incremental step, the average ctod with minimum standard deviation is considered as a material parameter (ctodcs), as shown in fig. 6, 7, 8(b). the second fracture parameter, kics, was calculated by substituting ctodcs into kic –ctod's average curve, see figs. 6, 7, 8(a). in addition, the effective crack length, cfs, proposed by etpfm relationship at different notch lengths can be obtained from eqn. (6). a)kic-ctodc curves b)relationship between s.d. and ctodc figure 6: mc-fd frc at first cracking at different l/d ratios equals 4, 5 and 6. a. elakhras et alii, frattura ed integrità strutturale, 60 (2022) 73-88; doi: 10.3221/igf-esis.60.06 82 a)kic-ctodc curves b)relationship between s.d. and ctodc figure 7: mc-fd frc at max stress at different l/d ratios equals 4, 5 and 6. tab. 3 shows the proposed parameters of etpfm for mc-fd frc and mc-fgc at first cracking and maximum stress. it is clear that kics values for mc-frc and mc-fgc showed an inversely proportional to l/d ratios, as known. ouyang et al. [26] calculated the fracture properties of nsc by its suggested method, equivalent tpfm, based on experimental results of bažant and pfeiffer [43]and showed agreement with the results of sel. four different beams with a constant l/d ratio equal to 2.50, fcu=33.5mpa, and e= 27.7gpa were investigated. the results of etpfm parameters of nsc were kic=0.99 mpa.m0.5, and cf =11.12 mm. as known, the kic values are inversely proportional to l/d ratios, so a. elakhras et alii, frattura ed integrità strutturale, 60 (2022) 73-88; doi: 10.3221/igf-esis.60.06 83 the kic value for nsc is expected to be higher than its value for specimens with an l/d ratio equal to four. comparing nsc results with mc-fd frc at first cracking and maximum stress for specimens with an l/d ratio equal to 4, variance in concrete size can be neglected. on the other hand, the presence of fibers ahead and behind the crack tip of the mc specimen significantly affects kic. undoubtedly, this significant increase is due to the bridging and the closing effects of sfs. this also refutes the assumptions of equality of kic for nsc and frc at first cracking. thus, the actual fracture toughness of mc beams is recommended to calculate the fracture toughness of fd frc and fgc. a)kic-ctodc curves b)relationship between s.d. and ctodc figure 8: mc-fgc at max stress at different l/d ratios equals 4, 5 and 6. a. elakhras et alii, frattura ed integrità strutturale, 60 (2022) 73-88; doi: 10.3221/igf-esis.60.06 84 beam code l/d mc-fd frc mc-fd frc mc-fgc at first cracking at max stress at max stress kics, mpa.m0.5 ctodcs, mm cfs, mm kics, mpa.m0.5 ctodcs, mm cfs, mm kics, mpa.m0.5 ctodcs, mm cfs, mm b4-1 0.888 7.70 43.3 b4-2 4 1.49 0.0048 0.892 2.09 0.20 7.695 2.10 0.038 43.1 b4-3 0.897 7.69 43.0 b5-1 0.972 9.373 46.10 b5-2 5 1.36 0.0046 0.975 1.86 0.196 9.361 2.05 0.039 45.90 b6 6 1.28 0.00464 1.108 1.50 0.0143 7.668 2.00 0.040 52.7 table 3: the proposed parameters of etpfm for mc-fd frc and mc-fgc. reliability of the present predicted fracture toughness reliability of the predicted kic from etpfm for mc-fd frcwas examined, at first cracking and maximum stress, with l/d ratios equal to 4, 5, and 6. the concept of the maximum size of the non-damaged defect ( maxd ) was used in this study [30,31,44–47]. it is based on the concept of critical distance theory and has an obvious indication of the maximum imperfection size present in a material. pook[48,49] used this theory to calculate the maximum size of imperfection in metals subjected to repeated loads. alternatively, maxd it is analogous to the characteristic length (  2 f ch t eg l f )[49–51]. thus, maxd is equal to        2 1 1.12 ic fl k f , where flf is the flexural strength for smooth specimens. the values of flf of smooth specimens were obtained from previous research by sallam and co-workers [5]for the same dimensions of mc specimens. the consistency of kic has been examined by comparing the value of maxd with nominal maximum aggregate size (nmaz). logically, the values of maxd /nmaz should be around unity. sallam and co-workers found that for rigid pavement, the ratio maxd /nmaz 2 [31] and for flexible pavement, this ratio is less than 0.75 [46]. fig. 9-a shows the maxd /nmaz for mc-fdfrc at the first cracking range between 1.01 and 1.54. the values were considered close to unity. also, the maximum damage of etpfm was considered close to the nmaz. also, fig. 9-b shows that maxd /nmaz for mc-fd frc at maximum stress range between 1.38and 2.89. the increase in maxd /nmaz ratios is considered appropriate at maximum stress, as the damage is larger than at first cracking. in the case of through-thickness crack, maxd /nmaz was found to be less than unity [30,31]. a similar finding was found in the present work for mc-fd frc at first cracking with a small increase due to fibers' closing effect in mc. the discrepancy and the higher values of mc-fd frc at maximumstresscompared to [30,31]can be attributed to the bridging and closing effect of short steel fibers, which subsequently increases the ratio between the fracture toughness and the smooth specimen flexural strength. these findings indicate that kic value for mc-specimens predicted from etpfm is considered appropriate according to maxd concept. comparison between experimental and predicted results from etpfm another effective method to examine the reliability of etpfm methods is by comparing the expected results of cmodc predicted from this method by the present experimental results at first crack initiation. due to the direct proportionality between kic and the characteristic crack length according to each method, the predicted cmodc can be calculated based on the predicted effective crack growth extension (cfsor∆ae) and critical flexural strength. thus, the proposed equation to predict cmodc by cf values calculated from etpfm is eqn. (4), see tab. 3. fig. 10 shows the predicted cmodcs values from etpfm and the experimental values of stress-cmodc, fig. 5, for all specimens with different l/d ratios equal to 4, 5, and 6 at first cracking for mc-fd frc and mc-fgc. all values of the experimental and predicted results of a. elakhras et alii, frattura ed integrità strutturale, 60 (2022) 73-88; doi: 10.3221/igf-esis.60.06 85 cmodcwere in the range of 0.028 to 0.06 mm, and 0.038 to 0.071 mm for mc fd frc and mc-fgc, respectively. the percentage error between the predicted and the experimental cmod was calculated for all fd-frc and fgc beams, and the results are given in tab. 4. the mean % error for all beams of fd-frc and fgc were -27% and 24.8%, respectively. d m ax / n m a z l /d 0 1 2 3 4 3 4 5 6 7 l/d= 4 l/d= 5 l/d= 6 d m ax / n m a z l /d 0 1 2 3 4 3 4 5 6 7 l/d= 4 l/d= 5 l/d= 6 a) mc-fd frc at first cracking b) mc-frc at max stress figure 9:the fracture toughness reliability for mc-fd frc was measured based on e-tpfm at different l/d ratios. beam code l/d mc-fd frc mc-fgc experimental cmod, mm predicted cmodcs, mm % erorr experimental cmod, mm predicted cmodcs, mm % erorr b4-1 0.045 0.034 -24 0.038 0.054 42 b4-2 4 0.052 0.037 -29 0.06 0.071 18 b4-3 0.06 0.042 -30 0.05 0.064 28 b5-1 5 0.04 0.028 -30 0.038 0.059 55 b5-2 0.045 0.037 -18 0.05 0.058 16 b6 6 0.041 0.029 -29 0.06 0.054 -10 table 4: the experimental and predicted values of cmodc at first cracking with the % error for mc-fd frc and mc-fgc. c m o d c , m m l/d 0 0.02 0.04 0.06 0.08 3 4 5 6 7 experimental etpfm c m o d c , m m l/d 0 0.02 0.04 0.06 0.08 3 4 5 6 7 experimental etpfm a) mcfd frc at first cracking b) mc-fgc at max stress figure 10:comparison between results of cmodc from experimental by the predicted from etpfm. a. elakhras et alii, frattura ed integrità strutturale, 60 (2022) 73-88; doi: 10.3221/igf-esis.60.06 86 conclusion he results of the present work support the following conclusions: 1. in the case of mc-fd frc beams, the first crack initiation appeared before the maximum stress due to the presence of sfs ahead of the crack tip. however, the first crack initiation occurred at the maximum stress of mcfgc beams due to the absence of sfs ahead of the crack tip. 2. the presence of the softening portion in fgc beam specimens reflects the efficiency of the proposed new matrix crack technique in simulating a real field crack in the laboratory. thus, the actual fracture toughness of frc beams is recommended to be calculated by real matrix crack, not through-thickness cracked specimens. 3. the predicted values of kic for matrix crack specimens estimated by etpfm are considered appropriate according to the maximum size of the non-damaged defect dmax concept. 4. the cmodc estimated from etpfm were in the range of 0.028-0.06 mm with a mean % error of 27 % and 0.038-0.071 mm with a mean % error of 24.8 %, respectively for all mc fd frc and mc-fgm beams. references [1] aci 544.4r-18. (2018). guide for design with fiber-reinforced concrete, am. concr. inst., pp. 1–33. [2] roesler, j., paulino, g., gaedicke, c., bordelon, a., park, k. (2007). fracture behavior of functionally graded concrete materials for rigid pavements, j. transp. res. board natl. acad. washington., (2037), pp. 40–49, doi: 10.3141/2037-04. [3] dias, c.m.r., savastano, h., john, v.m. (2010). exploring the potential of functionally graded materials concept for the development of fiber cement, constr. build. mater., 24(2), pp. 140–146, doi: 10.1016/j.conbuildmat.2008.01.017. [4] aci 544.1r-96. (2009). report on fiber reinforced concrete, aci man. concr. pract. [5] elakhras, a.a., seleem, m.h., sallam, h.e.m. (2021). intrinsic fracture toughness of fiber reinforced and functionally graded concretes: an innovative approach, eng. fract. mech., 258, doi: 10.1016/j.engfracmech.2021.108098. [6] iskhakov, i., ribakov, y., holschemacher, k., mueller, t. (2013). high performance repairing of reinforced concrete structures, mater. des., 44, pp. 216–222, doi: 10.1016/j.matdes.2012.07.041. [7] iskhakov, i., ribakov, y. (2013). a new concept for design of fibered high strength reinforced concrete elements using ultimate limit state method, mater. des., 51, pp. 612–619, doi: 10.1016/j.matdes.2013.04.063. [8] naghibdehi, m.g., mastali, m., sharbatdar, m.k., naghibdehi, m.g. (2014). flexural performance of functionally graded rc cross-section with steel and pp fibres, mag. concr. res., 66(5), pp. 219–233, doi: 10.1680/macr.13.00248. [9] naghibdehi, m.g., naghipour, m., rabiee, m. (2015). behaviour of functionally graded reinforcedconcrete beams under cyclic loading, gradjevinar, 67(5), pp. 427–439, doi: 10.14256/jce.1124.2014. [10] chan, r., liu, x., galobardes, i. (2020). parametric study of functionally graded concretes incorporating steel fibres and recycled aggregates, constr. build. mater., 242, doi: 10.1016/j.conbuildmat.2020.118186. [11] prasad, n., murali, g. (2021). research on flexure and impact performance of functionally-graded two-stage fibrous concrete beams of different sizes, constr. build. mater., 288, doi: 10.1016/j.conbuildmat.2021.123138. [12] prasad, n., murali, g. (2021). exploring the impact performance of functionally-graded preplaced aggregate concrete incorporating steel and polypropylene fibres, j. build. eng., 35, doi: 10.1016/j.jobe.2020.102077. [13] mastali, m., naghibdehi, m.g., naghipour, m., rabiee, s.m. (2015). experimental assessment of functionally graded reinforced concrete (fgrc) slabs under drop weight and projectile impacts, constr. build. mater., 95, pp. 296–311, doi: 10.1016/j.conbuildmat.2015.07.153. [14] amparano, f.e., xi, y., roh, y.s. (2000). experimental study on the effect of aggregate content on fracture behavior of concrete, eng. fract. mech., 67(1), pp. 65–84, doi: 10.1016/s0013-7944(00)00036-9. [15] xu, w., chen, b., chen, x., chen, c. (2021). influence of aggregate size and notch depth ratio on fracture performance of steel slag pervious concrete, constr. build. mater., 273, pp. 122036, doi: 10.1016/j.conbuildmat.2020.122036. [16] zhao, z., kwon, s.h., shah, s.p. (2008). effect of specimen size on fracture energy and softening curve of concrete: part i. experiments and fracture energy, cem. concr. res., 38(8–9), pp. 1049–1060, doi: 10.1016/j.cemconres.2008.03.017. [17] bažant, z.p., rasoolinejad, m., dönmez, a., luo, w. (2019). dependence of fracture size effect and projectile penetration on fiber content of frc, iop conf. ser. mater. sci. eng., 596(1), t a. elakhras et alii, frattura ed integrità strutturale, 60 (2022) 73-88; doi: 10.3221/igf-esis.60.06 87 doi: 10.1088/1757-899x/596/1/012001. [18] bažant, z.p., yu, q., zi, g. (2002). choice of standard fracture test for concrete and its statistical evaluation, int. j. fract., 118(4), pp. 303–337, doi: 10.1023/a. [19] hillerborg, a., modéer, m., petersson, p.e. (1976). analysis of crack formation and crack growth in concrete by means of fracture mechanics and finite elements, cem. concr. res., 6(6), pp. 773–781, doi: 10.1016/0008-8846(76)90007-7. [20] bažant, z.p., oh, b.h. (1983). crack band theory for fracture of concrete, mater. struct., 16(may), pp. 155–177, doi: 10.1007/bf02486267. [21] jenq, y.s., shah, s.p. (1985). a fracture toughness criterion for concrete, eng. fract. mech., 21(5), pp. 1055–1069, doi: 10.1016/0013-7944(85)90009-8. [22] bažant, z.p., yu, q. (2009). universal size effect law and effect of crack depth on quasi-brittle structure strength, j. eng. mech., 135(2), pp. 78–84, doi: 10.1061/(asce)0733-9399(2009)135:2(78). [23] han, x., chen, y., xiao, q., cui, k., chen, q., li, c., qiu, z. (2021). determination of concrete strength and toughness from notched 3 pb specimens of same depth but various span-depth ratios, eng. fract. mech., 245, doi: 10.1016/j.engfracmech.2021.107589. [24] jenq, y.s., shah, s.p. (1986). crack propagation in fiber reinforced concrete, j. struct. eng. am. soc. civ. eng., 112(1), pp. 19–34. [25] hillerborg, a. (1985). the theoretical basis of a method to determine the fracture energy gf of concrete, mater. struct., 18(106), pp. 291–296. [26] ouyang, c., tang, t., shah, s.p. (1996). relationship between fracture parameters from two parameter fracture model and from size effect model, mater. struct., 29(2), pp. 79–86, doi: 10.1007/bf02486197. [27] park, k., paulino, g.h., roesler, j. (2010). cohesive fracture model for functionally graded fiber reinforced concrete, cem. concr. res., 40(6), pp. 956–965, doi: 10.1016/j.cemconres.2010.02.004. [28] nazari, a., sanjayan, j.g. (2015). stress intensity factor against fracture toughness in functionally graded geopolymers, arch. civ. mech. eng., , pp. 1–10, doi: 10.1016/j.acme.2015.06.005. [29] el-sagheer, i., abd-elhady, a.a., sallam, h.e.d.m., naga, s.a.r. (2021). an assessment of astm e1922 for measuring the translaminar fracture toughness of laminated polymer matrix composite materials, polymers (basel)., 13(18), doi: 10.3390/polym13183129. [30] al hazmi, h.s.j., al hazmi, w.h., shubaili, m.a., sallam, h.e.m. (2012). fracture energy of hybrid polypropylenesteel fiber high strength concrete, wit trans. built environ., 124, pp. 309–318, doi: 10.2495/hpsm120271. [31] sallam, h.e.d.m., mubaraki, m., yusoff, n.i.m. (2014). application of the maximum undamaged defect size (dmax) concept in fiber-reinforced concrete pavements, arab. j. sci. eng., 39(12), pp. 8499–8506, doi: 10.1007/s13369-014-1400-4. [32] aci 211.1-91. (2009). standard practice for selecting proportions for normal, heavyweight, and mass concrete, am. concr. inst., (reapproved 2009), pp. 1–38. [33] bs en 12390-3:2019. (2019). testing hardened concretecompressive strength of test specimens, bsi stand. publ. london. [34] bs en 12390-6:2009. (2009). testing hardened concrete tensile splitting strength of test specimens, bsi stand. publ. london. [35] othman, m.a., el-emam, h.m., seleem, m.h., sallam, h.e.m., moawad, m. (2021). flexural behavior of functionally graded concrete beams with different patterns, arch. civ. mech. eng., 21(4), doi: 10.1007/s43452-021-00317-0. [36] dupont, d., vandewalle, l. (2005). distribution of steel fibres in rectangular sections, cem. concr. compos. 27, pp. 391–398, doi: 10.1016/j.cemconcomp.2004.03.005. [37] kazemi, m.t., golsorkhtabar, h., beygi, m.h.a.a., gholamitabar, m. (2017). fracture properties of steel fiber reinforced high strength concrete using work of fracture and size effect methods, constr. build. mater., 142, pp. 482– 489, doi: 10.1016/j.conbuildmat.2017.03.089. [38] ahmad, i., qing, l., khan, s., cao, g., ijaz, n., mu, r. (2021). experimental investigations on fracture parameters of random and aligned steel fiber reinforced cementitious composites, constr. build. mater., 284, doi: 10.1016/j.conbuildmat.2021.122680. [39] astm d7264/d7264m-15. (2015). standard test method for flexural properties of polymer matrix composite materials, annu. b. astm stand., pp. 1–11, doi: 10.1520/d7264_d7264m-15. [40] astm c1609/c1609m-12. (2013). standard test method for flexural performance of fiber-reinforced concrete ( using beam with third-point loading ) 1, astm stand., 12(c 1609/c 1609m-12), pp. 1–8, doi: 10.1520/c1609. [41] aci 544.4r-88. (2009). design considerations for steel fiber reinforced, aci man. concr. pract. a. elakhras et alii, frattura ed integrità strutturale, 60 (2022) 73-88; doi: 10.3221/igf-esis.60.06 88 [42] rilem tc qfs. (2004). quasibrittle fracture scaling and size effectfinal report1, mater. struct. constr., 37(272), pp. 547–568, doi: 10.1617/14109. [43] bažant, z.p., pfeiffer, p.a. (1987). determination of fracture energy by size effect and brittleness number, aci mater. j., pp. 463–480. [44] abou el-mal, h.s.s., sherbini, a.s., sallam, h.e.m. (2015). mode ii fracture toughness of hybrid frcs, int. j. concr. struct. mater., 9(4), pp. 475–486, doi: 10.1007/s40069-015-0117-4. [45] mousa, s., abd-elhady, a.a., kim, g.y., sallam, h.e.m. (2018). fracture behavior of roll bonded al-brass-al multilayer composites-concept of the maximum undamaged defect size (d max ), procedia struct. integr., 13(january 2019), pp. 686–693, doi: 10.1016/j.prostr.2018.12.114. [46] mubaraki, m., s.a. osman., h.e.m. sallam. (2019). effect of rap content on flexural behavior and fracture toughness of flexible pavement, lat. am. j. solids struct., 16(3), pp. 1–15. [47] mubaraki, m., sallam, h.e.m. (2020). reliability study on fracture and fatigue behavior of pavement materials using scb specimen, int. j. pavement eng., 21(13), pp. 1563–1575, doi: 10.1080/10298436.2018.1555332. [48] pook, l.p. (1975). analysis and application of fatigue crack growth data, j. strain anal. eng. des., 4(10), pp. 242–250. [49] taylor, d. (2007). the theory of critical distances: a new perspective in fracture mechanics, oxford, uk, elsevier. [50] rilem committee on fracture mechanics of concrete-test methods (rilem 50-fmc). (1985). determination of the fracture energy of mortar and concrete by means of three-point bend test on notched beams, mater. struct., 18, pp. 285–290. [51] rosselló, c., elices, m., guinea, g.v. 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can be opened with acrobat and adobe reader 5.0 and later.) >> /namespace [ (adobe) (common) (1.0) ] /othernamespaces [ << /asreaderspreads false /cropimagestoframes true /errorcontrol /warnandcontinue /flattenerignorespreadoverrides false /includeguidesgrids false /includenonprinting false /includeslug false /namespace [ (adobe) (indesign) (4.0) ] /omitplacedbitmaps false /omitplacedeps false /omitplacedpdf false /simulateoverprint /legacy >> << /addbleedmarks false /addcolorbars false /addcropmarks false /addpageinfo false /addregmarks false /convertcolors /converttocmyk /destinationprofilename () /destinationprofileselector /documentcmyk /downsample16bitimages true /flattenerpreset << /presetselector /mediumresolution >> /formelements false /generatestructure false /includebookmarks false /includehyperlinks false /includeinteractive false /includelayers false /includeprofiles false /multimediahandling /useobjectsettings /namespace [ (adobe) (creativesuite) (2.0) ] /pdfxoutputintentprofileselector /documentcmyk /preserveediting true /untaggedcmykhandling /leaveuntagged /untaggedrgbhandling /usedocumentprofile /usedocumentbleed false >> ] >> setdistillerparams << /hwresolution [2400 2400] /pagesize [612.000 792.000] >> setpagedevice microsoft word numero_37_art_8 c. riess et alii, frattura ed integrità strutturale, 37 (2016) 52-59; doi: 10.3221/igf-esis37.08 52 focussed on multiaxial fatigue and fracture the non-proportionality of local stress paths in engineering applications c. riess, m. obermayr zf friedrichshafen ag, dtgs1, 88038 friedrichshafen, germany christian.riess@zf.com, http://orcid.org/0000-0002-8784-5297 martin.obermayr@zf.com, http://orcid.org/0000-0002-7672-8685 m. vormwald technische universität darmstadt, materials mechanics group, franziska-braun-str. 3, d-64287 darmstadt, germany vormwald@wm.tu-darmstadt.de, http://orcid.org/0000-0002-4277-785x abstract. a scalar measure, which describes the non-proportionality of local stress paths in engineering applications, is introduced. for this purpose the moment of inertia approach by meggiolaro is modified in a way that the stress time history is evaluated in a tresca-stress-space. this modification makes the non-proportionality factor invariant with respect to the coordinate system. an optimization procedure is implemented to derive a test set-up for new component tests with 2 load channels. the aim of the planned tests is to get a high non-proportionality at the potential crack initiation site. it is not possible to obtain a high non-proportionality factor at the failure location without selective weakening of the component (housing of a rear axle steering). therefore specific areas of the structure are cut out and the optimization procedure is repeated. as a result of the optimization a test set-up with high local non-proportionality at the potential crack initiation site is achieved for the weakened structure. another set-up with slightly less non-proportionality but with a very localized damage is derived. this set-up is preferred, because of the robustness in the physical test. keywords. non-proportional fatigue; multiaxial testing. introduction any components in engineering applications are subjected to multiple and uncorrelated loads during service-life. thus multiaxial stress states with rotating principal directions may occur. it is therefore useful to introduce a scalar measure (e.g. in the range of 0 to 1), which describes the non-proportionality of a local stress path. there are many approaches to characterize the non-proportionality in literature. one possibility is to directly consider the nonproportionality and the additional non-proportional hardening in an incremental plasticity model (see e.g. [1]). in this case, the non-proportionality is evaluated at every time step and transient effects may be taken into account. a second group of approaches determines the non-proportionality of a single cycle. an example for this group is the rotation factor according to kanazawa [2]. a last group of non-proportionality factors (npf) was developed to efficiently describe the non-proportionality of a whole stress time history [3-6]. m c. riess et alii, frattura ed integrità strutturale, 37 (2016) 52-59; doi: 10.3221/igf-esis37.08 53 non-proportionality factor for stress time histories irst ideas to describe the non-proportionality of local stress paths based on moments of inertia (moi) stem back to chu [7]. bishop [3] seized this suggestion and introduced the first inertia based out-of-phase measure. the inertia based methods differ in the way the moi is evaluated. bishop calculates moi with respect to the perimeter centroid (pc) of the path. for discrete data the evaluation is done using a weighted sum with the length of each segment as weighting factor. another inertia based method is proposed by gaier [4]. in contrast to bishop, gaier calculates moi with respect to the origin. another difference is that gaier doesn’t use the length of a segment as weighting factor. instead every stress state has the same mass. this formulation is only suitable for stress paths which are equally spaced in time. a small rainflow projection (rp) filter [8] may have large effects on the npf. bolchoun [5] introduced a method without the use of moi. the formulation is based on the correlation coefficient cor f g( , ) of two functions f and g . the correlation coefficient of the time history of normal stress   x x t' ' ( , ) and the time history of shear stress   xy xy t' ' ( , ) is evaluated in all cutting planes  . in order to make the npf ( b npf ) invariant with respect to the coordinate system (cs), an average over all cutting planes is computed. a disadvantage of the npfs according to bishop, gaier und bolchoun is, that they wrongly predict a high npf for the stress path   x y tsin( ) ,  xy tcos( ) . though, for this special case of equi-biaxial tension with out-of-phase torsion the directions of principal axes remain constant and therefore the planes of maximum shear stress do not change [6]. figure 1: interpretation of the tresca-diagramm (left) and non-proportional path (right). that is why meggiolaro [6] proposes to evaluate npfs independent from hydrostatic stresses. according to meggiolaro for plane state of stresses the evaluation of moi should be based on a   x y xy3{( )| } stress-space. as a result of choosing this stress-space, the npf is dependent on the choice of the cs. it is therefore suggested to use a tresca-stressspace   x y xy2{( )| } in order to make the npf invariant with respect to the cs. in the tresca-diagram (see fig. 1) every line through the origin is a line with constant principal axis (and constant angle of the maximum shear plane). furthermore, the norm of a point in the diagram is equal to the double maximum shear stress max2 . choosing the tresca-diagram, the calculation of the npf is reduced to a geometrical 2d problem. the evaluation is performed according to the moi method by meggiolaro [9] on the basis of pseudo-elastic stress paths. by means of the tresca-diagram, mois oxxi , o yyi and o xyi are calculated with respect to the origin of the diagram as contour integrals along the stress path                    2 2o o o xx xy yy x y xy xy x y 1 1 1 i 2 i 2dp, d l l p i dp l , (1)  xy2  x y( )  x y( )  xy2 proportional non-proportional   45°   22 5°.   0°      xy x y 2 2tan( )           max 2 2 max x y xy 2 2 r 2 | | ( ) ( )  r f c. riess et alii, frattura ed integrità strutturale, 37 (2016) 52-59; doi: 10.3221/igf-esis37.08 54 where l is the total length of the stress path and dp denotes the length of an infinitesimal segment of the path. a detailed description for the evaluation of contour integrals of discrete 2d paths can be found in [8]. principal moments of inertia o1 and  o 2 (   o o 1 2 ) are calculated by transformation into the principal coordinate system:        2 o oo o 2xx yyxx yyo o 1,2 xy i 4 i i 2 i i (2) finally, the npf is defined as root of the ratio of both principal moi:   o onp 2 1f / (3) similar to the herein proposed method, the npf may also be calculated using bishop’s method and the tresca-diagram. then, the only difference is the evaluation of the mois with respect to the perimeter centroid and not with respect to the origin. this npf is named pcnpf and is only capable to describe the the out-of-phase extent of a stress path. examples in engineering applications the non-proportionality at the crack initiation sites of several tests with 3 load channels and variable amplitude loadings is examined. quite similar results are obtained using pcnpf and b npf , because both npfs only describe the out-of-phase extend of the stress path. in some cases there is an obvious difference to the results of npf . figure 2: tresca-diagram (left), changes of maximum shear planes (middle) and corresponding crack initiation site (right). four significant examples are extracted from the internal database and discussed in detail. the local stress paths at the crack initiation sites are displayed on the left of fig. 2. the normalized maximum shear    max maxt tˆ ( ) / max( ( )) over the corresponding angle  is plotted in the middle of this figure. examples a and b indicate an almost uniaxial stress state with small changes in principal directions, which corresponds to small rotation of the planes of maximum shear. the npfs at the crack initiation sites are 0.016 and 0.046, respectively. the crack initiation sites are located at a milled-out portion (a) and a die-cast rib (b). at examples c and d the crack initiation sites are located at a notch between two flanges. both of them have almost the same out-of-phase extent ( pcnpf 0 3. ). however, there are large differences in the npf c. riess et alii, frattura ed integrità strutturale, 37 (2016) 52-59; doi: 10.3221/igf-esis37.08 55 npf . the reason for the differences is identified in the nonzero mean values of the paths. non-proportionality is increased ( npf 0 365. ) in the case of example c because of the translation of the perimeter centroid. whereas the translation of the pc in example d produces a lower rotation of maximum shear planes at high stress levels. the shape of the peak in the middle diagram is more distinct than in example c. therefore, the non-proportionality is much lower ( npf 0 093. ). systematic planning of component tests n order to expand the experimental database, new component tests with 2 load channels and a high degree of local non-proportionality are planned. the housing of a rear axle steering is chosen for these tests (see fig. 3). the component is mounted onto a steel plate. one of the forces 1f shall be applied at the front drill hole and shall be aligned in the x-z-plane. the second force 2f shall be applied at the upper drill hole and shall be aligned with the centerline of the drill hole. finally, the angle  (between x-axis and 1f ) and the ratio of the forces   1 2f f/ remain as free variables for an optimization process. for a given combination of  and  the pseudo-elastic stress path t* ( , )x for all nodes can be attained by calculation of three unit load cases (ulc) ulc * ( )x :           1 ulc 1x 2 ulc 1z 3 ulc 2t t a a t a * * * * , , ,( , ) sin( ) ( ) ( ) cos( ) ( ) .x x x x    (4) the relation between the scaling factors of the ulc 1a , 2a and 3a and the free variables  and  is as follows:   2 1 2 1 3 1 2 2 a a 1 a 1 1 1 a a 1 t tan , tan an , .                  (5) the challenge of the optimization is that the location with the highest damage critx is not known a priori. depending on the choice of  and  the potential crack initiation site has to be determined numerically. furthermore the change of critx results in a non-steady objective function    np critf f , x . that is why a genetic algorithm [10] is used to implement the optimization process. figure 3: housing of a rear axle steering subjected to two load channels (left) and selective weakening of the component (right). identification of the critical location xcrit the fatigue assessment of non-proportional stress histories with rotating principal axis requires complex calculation algorithms, see [11, 12]. with regard to the optimization it is not necessary to perform a quantitatively precise damage calculation. it is rather important to qualitatively identify the critical location. therefore, the identification of the critical locations is based on simple damage parameters and pseudo-elastic stresses. i c. riess et alii, frattura ed integrità strutturale, 37 (2016) 52-59; doi: 10.3221/igf-esis37.08 56 three different approaches for the identification of critx are discussed: the findley parameter f [13], the normal stress amplitude in critical plane a cp, and the signed von mises amplitude a v, . the critical plane technique was especially invented for the case of rotating principal axis. one of the first damage parameters based on stresses in a specific plane of the material is the findley parameter:  a , max ,f k .max      (6) besides the shear stress amplitude a , in the cutting plane with angle  , this parameter also considers the maximum normal stress max , in the same plane. the normal stress portion is weighted by an influence factor k , which can be determined for a given fatigue strength ratio w w/  [14]. a given ratio of w w 1 5/ .   results in k 0 352. . the maximum of the parameter is searched numerically over a discrete number of cutting planes. another parameter, which is widely used in the industrial practice for brittle materials, is the normal stress amplitude in the critical plane a cp, . similar to the findley parameter, a normal stress amplitude a , has to be evaluated for all cutting planes and the maximum has to be searched numerically:  a cp a, ,max .  (7) as the third possibility for the identification of critx a signed von mises approach is investigated. for this purpose, the time history of the mises equivalent stress  v t is assigned with the sign of the hydrostatic stress:     2 2 2v xx yy xx yy xx yy xyt 3sign .           (8) this approach results in discontinuities in the time history when applied to non-proportional stresses. a subsequent rainflow counting could identify unphysical cycles. though, the unsteadiness has no effect in the case of constant amplitude loading and the equivalent amplitude is defined by the maximum   v max v t, max  and the minimum   v min v t, min  of the time history:  a v v max v min 2, , , /    (9) there is no need for a numerical search over all cutting planes for this parameter, reducing the numerical expense. the critical location critx is defined as the node, which has the highest value of the damage parameter according to eqs 6, 7 or 9. possible size effects (stress gradient, statistical, technological) are not considered. constraints in order to prevent failure in an „unwanted“ region of the component, a node set bcs may be defined. if the critical location critx (for a given parameter value 0 and 0 ) is part of the set bcs , the objective function   np crit 0 0f , x is set to 0. thus, it is not possible to get a solution with critx in an unwanted region. examples are nodes, which are located at the gate system of the cast part, where the geometry is not well defined in reality. therefore, these nodes are „unfavourable” and added to the set bcs . selective weakening of the component it turns out, that it is not possible to obtain a high npf at the failure site without selective weakening of the component. all critical nodes are located near the flange at the transition to the ribs. the stresses are highly oriented at these locations. therefore specific areas of the structure are cut out (see fig. 3) and the optimization procedure is repeated. as a result of c. riess et alii, frattura ed integrità strutturale, 37 (2016) 52-59; doi: 10.3221/igf-esis37.08 57 the weakening, the critical locations are shifted towards the middle of the component. hence, effects due to the load introduction and the bolted connections are minimized. results esults of the optimization can be found in tab. 1. beside the solution parameters opt opt/  the value of the objective function np optf , is also listed. in the case without weakening of the structure, the results for the different versions are quite similar. independent of the damage parameter, the same critical node is identified. it is not possible to attain a npf higher than 0.16 at the potential crack initiation site. damage parameter opt opt np optf , original structure f 3.113 1.516 0.160 a cp, 3.139 1.441 0.153 a v, 0.0 1.536 0.159 weakened structure f 0.983 0.904 0.812 a cp, 0.882 0.688 0.831 a v, 0.946 0.776 0.819 table 1: results of the optimization. the selective weakening results in the desired effect. high non-proportionalities ( npf 0 8. ) are obtained for all versions. similar critical nodes are identified using the signed von mises approach and the a cp, approach. a slightly different solution is found by the findley parameter approach. in this solution the critical node critx is located some nodes away in contrast to both other versions. discussion here is a high non-proportionality in many regions of the component. however, stresses are often small in these regions and failure will not occur there. on the other hand, the non-proportionality is negligible at many crack initiation sites. independent of the external loads the stresses are highly oriented at the crack initiation site in those cases. typical examples are ribs of housings made by die-cast or a cross-hole in a shaft. these are locations, where the local stress states are nearly proportional. in order to get a high non-proportionality the following two conditions have to be fulfilled: the unit load cases have to create stress states with different planes of maximum shear (different principal axis) and the forces have to be in an appropriate ratio. a systematic planning of component tests with high non-proportionality is only feasible using an automated optimization process. figure 4: , for the result of the optimization (left) and the tradeoff (right). r t c. riess et alii, frattura ed integrità strutturale, 37 (2016) 52-59; doi: 10.3221/igf-esis37.08 58 an essential point of the optimization is the identification of critical locations. the aim of the identification is to find the node, which has the highest probability of crack initiation, in a simple manner. size effects may have a large influence for notched components, but under non-proportional stresses they are not yet well defined. thus, in this work notch support because of size effects is omitted. an explicit consideration of size effects could help to increase the accuracy of the identification. therefore, the influence of size effects under transient stress gradients and transient highly stressed volumes or surfaces needs to be investigated. to ensure, that the crack initiation site in the physical test coincides with the critical node critx , a solution with a strong damage localization is favorable. the iterations of the optimization are scanned manually for solutions with higher localization of the damage parameter (see fig. 4), but sufficiently high non-proportionality. a satisfactory parameter set (tradeoff) is identified ( 0 9032.  and 1 2274.  ) with npf of 0.572 at the critical node. conclusion new inertia based non-proportionality factor for the evaluation of pseudo-elastic stress paths is introduced. calculations of the npf are performed according to a modified version of the moi method from meggiolaro. the use of the tresca-diagram   x y xy2{( )| } makes the npf invariant with respect to the coordinate system. furthermore a numerical optimization, which searches for a test set-up with high non-proportionality at the potential crack initiation site, is developed and implemented. a selective weakening of the chosen component is necessary in order to get a high npf at the critical location. a possible weak point of the optimization is that size effects are not considered. therefore, further investigations should focus on the influence of size effects under non-proportional stresses. in order to get a robust test set-up, a tradeoff is derived. experimental investigations with constant and variable amplitudes are going to be performed on the basis of this tradeoff. references [1] tanaka, e., a nonproportionality parameter and a cyclic viscoplastic constitutive model taking into account amplitude dependences and memory effects of isotropic hardening, eur. j. mech. a/solids, 13 (1994) 155-173. [2] kanazawa, k., miller, k.j. and brown, m.w., cyclic deformation of 1% cr-mo-v steel under out-of-phase loads, fatigue fract. eng. mater. struct., 2 (1979) 217–228. doi: 10.1111/j.1460-2695.1979.tb01357.x [3] bishop, j.e., characterizing the non-proportional and out-of-phase extent of tensor paths, fatigue fract. eng. mater. struct., 23 (2000) 1019-1032. doi: 10.1046/j.1460-2695.2000.00355.x [4] gaier, c., lukacs, a. and hofwimmer, a., investigations on a statistical measure of the non-proportionality of stresses, int. j. fatigue, 26 (2004) 331-337. doi: 10.1016/j.ijfatigue.2003.08.023 [5] bolchoun, a., wiebesiek, j., kaufmann, h., sonsino, c.m., application of stress-based multiaxial fatigue criteria for laserbeam-welded thin aluminium joints under proportional and non-proportional variable amplitude loadings, theor. appl. fract. mech., 73 (2014) 9-16. doi: 10.1016/j.tafmec.2014.05.009 [6] meggiolaro, m.a., castro, j.t.p., prediction of non-proportionality factors of multiaxial histories using the moment of inertia method, int. j. fatigue, 61 (2014) 151-159. doi: 10.1016/j.ijfatigue.2013.11.016 [7] chu, c.c., conle, f.a. and hübner, a., an integrated uniaxial and multiaxial fatigue life prediction method, vdi berichte, 1283 (1996) 337-348. [8] dreßler, k., carmine, r., krüger, w., the multiaxial rainflow method, in: rie, k.t. (ed.), low cycle fatigue and elasto-plastic behaviour of materials, elsevier science publ., london, (1992) 325-331. [9] meggiolaro, m.a., castro, j.t.p., an improved multiaxial rainflow algorithm for non-proportional stress or strain histories – part i: enclosing surface methods, int. j. fatigue, 42 (2012) 217-226. doi: 10.1016/j.ijfatigue.2011.10.014 a c. riess et alii, frattura ed integrità strutturale, 37 (2016) 52-59; doi: 10.3221/igf-esis37.08 59 [10] xavier blasco ferragud, f., control predictivo basado en modelos mediante tecnicas de optimizacion heuristica. aplicacion a procesos no lineales y multivariables (phd thesis in spanish), universitat politècnica de valència, spain, (1999). [11] hertel, o. and vormwald, m., multiaxial fatigue assessment based on a short crack growth concept, theor. appl. fract. mech., 73 (2014) 17-26. doi: 10.1016/j.tafmec.2014.06.010 [12] hertel, o. and vormwald, m., short-crack-growth-based fatigue assessment of notched components under multiaxial variable amplitude loading, eng. frac. mech., 78 (2011) 1614-1627. doi: 10.1016/j.engfracmech.2011.01.016 [13] findley, w.n., a theory for the effect of mean stress on fatigue of metals under combined torsion and axial load or bending, j. eng. ind., 81 (1959) 301-306. 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/hrv (za stvaranje adobe pdf dokumenata najpogodnijih za visokokvalitetni ispis prije tiskanja koristite ove postavke. stvoreni pdf dokumenti mogu se otvoriti acrobat i adobe reader 5.0 i kasnijim verzijama.) /hun 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can be opened with acrobat and adobe reader 5.0 and later.) >> /namespace [ (adobe) (common) (1.0) ] /othernamespaces [ << /asreaderspreads false /cropimagestoframes true /errorcontrol /warnandcontinue /flattenerignorespreadoverrides false /includeguidesgrids false /includenonprinting false /includeslug false /namespace [ (adobe) (indesign) (4.0) ] /omitplacedbitmaps false /omitplacedeps false /omitplacedpdf false /simulateoverprint /legacy >> << /addbleedmarks false /addcolorbars false /addcropmarks false /addpageinfo false /addregmarks false /convertcolors /converttocmyk /destinationprofilename () /destinationprofileselector /documentcmyk /downsample16bitimages true /flattenerpreset << /presetselector /mediumresolution >> /formelements false /generatestructure false /includebookmarks false /includehyperlinks false /includeinteractive false /includelayers false /includeprofiles false /multimediahandling /useobjectsettings /namespace [ (adobe) (creativesuite) (2.0) ] /pdfxoutputintentprofileselector /documentcmyk /preserveediting true /untaggedcmykhandling /leaveuntagged /untaggedrgbhandling /usedocumentprofile /usedocumentbleed false >> ] >> setdistillerparams << /hwresolution [2400 2400] /pagesize [612.000 792.000] >> setpagedevice microsoft word numero_62_art_19_3537.docx m. m. padzi et alii, frattura ed integrità strutturale, 62(2022) 271-278; doi: 10.3221/igf-esis.62.19 271 evaluation on fatigue behaviour of spot-welded joint under low blow impact treatment mahfodzah md padzi mechanical section, universiti kuala lumpur, malaysia france institute, jalan teras jernang, 43650, bangi, selangor, malaysia mahfodzah@unikl.edu.my, https://orcid.org/0000-0002-8093-1467 farizah adliza ghazali manufacturing & fabrication section, universiti kuala lumpur, malaysia france institute, jalan teras jernang, 43650, bangi, selangor, malaysia farizahadliza@unikl.edu.my, http://orcid.org/ 0000-0001-5777-9260 abstract. welding is used widely in modern industries to combine parts needed complete a product. in this paper, we investigated the effect of postweld impact treatment (pwit) on spot-weld joints and evaluate the tensile and fatigue properties of the specimens. currently, there is no simple failure criterion capable of predicting the strength of a spot weld under different loading conditions. the reliability of spot-welded structures treated with pwit in terms of fatigue integrity could be understood more by the end of this research. the result showed that not only the tensile properties of pwit specimens give an improvement, but there was also a significant increase in the fatigue life of the treated specimens. keywords. fatigue; post-weld; welding; pwit citation: padzi, m. m., ghazali, f. a., evaluation on fatigue behaviour of spotwelded joint under low blow impact treatment, frattura ed integrità strutturale, 62 (2022) 271-278. received: 31.3.2022 accepted: 18.07.2022 online first: 29.08.2022 published: 01.10.2022 copyright: © 2022 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. introduction pot welding is used in many areas such as electronics, orthodontics, and the automobile industry. industrial production of technical goods, especially of investment goods, is hardly conceivable without joining technology [1]. statistically, there are about 2000 to 5000 spot weld joints on a modern vehicle, hence the durability and safety design of cars, the strength of the spot weld under quasi-static conditions of impact, and fatigue loading are therefore immensely crucial [2]. during the spot welding process, high temperatures will be experienced by the welding material. once a material undergoes any process involving significant temperature increases such as welding, the mechanical properties of the said object will vary due to microstructure changes and thermal stress within the structure will be built. as it starts cooling, the metal is s https://youtu.be/i2tmxpsuxz4 m. m. padzi et alii, frattura ed integrità strutturale, 62(2022) 271-278; doi: 10.3221/igf-esis.62.19 272 subjected to shrinkage caused by sudden thermal stress. these stresses can, in turn, distort and warp the welded assembly. the welding situation is complicated because heating is much localized, and the base metal will melt during the process. the process left the structure in residual tension and reactionary compressive stress is established in parts regions away from the weld. this phenomenon will occur in almost all welding processes. in addition to residual stress and distortion, other defects may occur in welding [3, 4]. post-welding treatment on the welded material is carried out to reduce and redistribute the residual stress in the material introduced by welding. post-welding treatment is one of the crucial steps for producing high-quality welding. the treatment aims at improving the mechanical properties of the joint and reducing the thermal stress created during the welding process [7]. post weld treatment can be classified into two main groups which are post weld heat treatment (pwht) and post weld impact treatment (pwit). pwht, also known as artificial aging and solution treatment is performed on the welding specimen after the welding process has been carried out. post heating is used to minimize the possible cracking of hydrogen [12]. pwit is necessary to improve the tensile strengths of the welded structure in the spot-welding process because the mechanical properties of the welded joint was reduced due to the distortion and stress corrosion cracking caused by the welding process[6]. stress relief shall eliminate any internal or residual stress from the operation. post-welding stress relief is required to minimize the risk of brittle fracture, prevent further deformation or eliminate the potential of stress corrosion [8, 5]. pwit consists of several processes, such as shot-peening, hammer-peening, and impact. pwit can be performed via low blow impact treatment (lbit). the lbit involved low-speed impact without destroying the samples [9]. goods or things that we purchase usually come with a warranty period. on the other hand, this can also be defined as the fatigue life of each product. fatigue life simply means the number of stress cycles it can stand before the structure start to crack [10]. there are three types of fatigue loadings; fully reversed, repeated, or fluctuating. for fully reversed, the stress ratio, r = -1, stress ratio is the value of minimum stress (σmin) divided by maximum stress (σmax) experienced by the structure, shown in eqn. (1) r =   min max (1) engineering components and structures are subjected to cyclic loadings with the presence of mean stress. the fatigue behavior of metals can be predicted by various mean stress models. normally, for zero mean stress (r = -1), the basquin equation is used to determine the fatigue life of any given specimen as described in eqn. (2),   ' ( 2 )ba f fn (2) where is the stress amplitude,  ' f is the fatigue strength coefficient, fn is the fatigue life (cycles) and b is the fatigue strength exponent. as tension-tension type of loadings is used for our experiment i.e non-zero mean stress, several approaches can be used to find the fatigue life. for the simplicity of this research, only two approaches are chosen which are the morrow and the smith, watson, and topper (swt) mean stress models. the morrow model predicts that the mean stress gives a more significant effect on longer lives compared to the shorter lives fatigue cycle, where the plastic strain is large. the equation for morrow is given in eqn. (3) [13]       ' 1a m ar f (3) where = mean stress and is the equivalent stress amplitude resulting from the same fatigue life. swt approach assumed that the product of maximum stress, and the strain amplitude, in the strain-life model controls the life. the swt model gives a good estimation of fatigue life in the high cycles fatigue region. a life equation for swt in eqn. (4);   ar max a (4) where = maximum stress m. m. padzi et alii, frattura ed integrità strutturale, 62(2022) 271-278; doi: 10.3221/igf-esis.62.19 273 currently, there is no simple failure criterion capable of predicting the strength of a spot weld under different loading conditions. the basic relationship between pwit and fatigue properties can be established by completing this project and acting as a reference to other researchers. the need for post-welding treatment is driven by code and application and service environment. fatigue improvement procedures are now being used in many different industries. the crane, aircraft, spacecraft, and automobile industries are some examples. material usage in the automotive industry has been significantly lowered in recent years with the application of fatigue improvements. this has brought positive impacts to the industry such as minimal fuel consumption, maximizing power output, increased security, etc. pwt is accepted as the standard method of extending offshore structures throughout the last seven years [15]. in this paper, the effect of pwit on spot-weld joints and fatigue properties of pwit specimens are to be investigated. to achieve that, several scopes are outlined for this research. 40 specimens made from mild steel are prepared according to american welding standard (aws). one specimen is made up of 4 different parts which are spot welded together. the first 2 parts are made from the same dimensions which are (105 mm x 45 mm x 1 mm) and the dimension for another 2 parts is (45 mm x 45 mm x 1mm). the welding process is performed using a spot welder machine with a rated capacity of 75 kva and electrode tip of 5 mm. 33 specimens will then undergo post-weld treatment known as low blow impact treatment (lbit). during lbit, six different heights are chosen which are 12 cm, 16 cm, 20 cm, 24 cm, 28 cm, and 32 cm. a tensile test will be conducted on 20 specimens (18 treated & 2 untreated), and the maximum load for each of six different heights is recorded. another 20 specimens (15 treated & 5 untreated) will then be brought into the fatigue testing. however, only 3 heights are chosen which are 12 cm, 20 cm, and 28 cm. the specimens will then be tested for 0.9σmax, 0.8σmax, 0.7σmax, 0.6σmax and 0.5σmax with a load ratio, r = 0.1 methodology etailed studies on fatigue properties of welded samples can only be carried out correctly if the samples are prepared properly according to american welding societies (aws). a series of processes must be gone through by the samples to ensure an accurate result is obtained. fig. 1 shows the flow chart of the methodology. figure 1: flow chart of methodology specimen preparation forty specimens were prepared from mild steel. these specimens were prepared according to american welding standard (aws). each specimen is comprised of 2 rectangular parts and 2 square parts of equal size. the dimension for the rectangular part is (105 mm x 45 mm x 1.0 mm) meanwhile for the square part is (45 mm x 45 mm x 1.0 mm) as shown in fig. 2(a). the parts were cut by using a shear machine as shown in fig. 2(b). spot welding the welding process was performed using a spot welder machine with a rated capacity of 75 kva and an electrode tip of 5 mm. firstly, two parts with equal sizing (105 mm x 45 mm) were spot-welded together as shown in fig. 3(b)[11]. then specimen preparation spot welding low blow impact treatment tensile test fatigue test effect of post-weld on fatigue properties d m. m. padzi et alii, frattura ed integrità strutturale, 62(2022) 271-278; doi: 10.3221/igf-esis.62.19 274 another two parts of equal sizing (45 mm x 45 mm) were welded at each end of the welded structure. the dimension for a welded specimen is illustrated in fig. 3(a). (a) (b) figure 2: specimen preparation: (a)dimension for rectangular and square parts; (b) shear machine (a) (b) figure 3: spot weld specimen: (a) dimension of a welded specimen; (b) spot welded specimen (a) (b) figure 4: lbit process: (a) lbit equipment and (b) specimen located for lbit treatment pwit once all the specimens have gone through the welding process, they were then brought into post-weld treatment known as low blow impact treatment (lbit). six different heights were selected which were 120 mm, 160 mm, 200 mm, 240 mm, m. m. padzi et alii, frattura ed integrità strutturale, 62(2022) 271-278; doi: 10.3221/igf-esis.62.19 275 280 mm, and 320 mm [9]. for each height, two specimens were impacted by the lbit. fig. 4 shows the lbit equipment used for the pwit. the safety lock and weight were lifted so the specimen could be placed at the bottom of the impactor (fig. 4(a)). the safety lock was to hold the weight safely. the specimen was aligned correctly so the welding area would be located inside the circle parameter (hole) (fig. 4(b)). tensile testing a tensile test was carried out on 20 specimens (18 treated and 2 untreated). there will be three samples for each height which were 120 mm, 160 mm, 200 mm, 240 mm, 280 mm, and 320 mm. the tensile test was done using tensile testing machine following the american society for testing and materials (astm e-8) [16]. the specimens will be subjected to axial and longitudinal forces. these forces will be exerted on the subject until certain deformations occur which will lead to failure. fatigue testing fatigue testing of spot-welded samples was conducted by using shimadzu servopulser with a load ratio r = 0.1. a sinusoidal waveform was applied at f = 15hz [17]. a set of five different loadings were used to investigate the life cycle for 90% σmax, 80% σmax, 70% σmax, 60% σmax, and 50% σmax. the final separation of the specimen was considered a failure. the fatigue lives obtained from the experiment are then compared with the theoretical value of morrow and swt approach models. the value for σ’f and b is obtained from the graph s-n curve plotted. σ’f is the y-intercept and b is the slope. results and discussions uring lbit, different specimens are treated with different heights of impact. for each height, there are three specimens selected to undergo the treatment. tab. 1 shows the depth measured at each of the impact points on the specimens. the results for tensile tests are needed to proceed to the fatigue test. this is the maximum load that can be retained by the specimens before yield must be determined. so, the parameters needed to start fatigue testing are complete. the comparisons of the load-displacement line for all specimens are illustrated in fig. 5. height (cm) readings (mm) average specimen 1 specimen 2 specimen 3 12 3.06 3.11 3.07 3.08 16 3.30 3.32 3.31 3.31 20 3.49 3.52 3.31 3.51 24 3.61 3.57 3.65 3.61 28 3.76 3.74 3.76 3.76 32 3.88 4.05 3.84 3.92 table 1: depth measurements of the impact locations figure 5: graph of load vs displacement for all specimens. d m. m. padzi et alii, frattura ed integrità strutturale, 62(2022) 271-278; doi: 10.3221/igf-esis.62.19 276 the graph plotted in fig. 5 shows that the untreated specimen exhibits the weakest tensile strength compared to other treated specimens. the second-lowest tensile strength is recorded at 12 cm and 28 cm specimens with 10% of improvement, followed by 16 cm and 24 cm with 13.3% improvement. the ultimate tensile strength of the treated specimen with 20 cm of height is placed at second highest with 15% improvement which is just slightly under 32 cm treated specimen with 16.7% improvement. three different heights are chosen for the fatigue test which are 12 cm, 20 cm, and 28 cm. tab. 2 shows the fatigue life (cycles) in which the specimen can undergo deformation before failure. fig. 4 shows the s-n curve of the welded samples. height untreated 12 cm 20 cm 28 cm σmax f (kn) life f (kn) life f (kn) life f (kn) life 90% 5.40 107 5.94 81 6.21 68 5.94 377 80% 4.60 252 5.28 3022 5.52 130 5.28 1862 70% 4.20 665 4.62 3446 4.83 193 4.62 2296 60% 3.60 2033 3.96 4993 4.14 6429 3.96 2768 50% 3.00 7621 3.03 6774 3.45 7878 3.3 13753 table 2: load and maximum cycle figure 6: s-n curve it can be seen from the log graph in fig. 6 that the lowest s-n curve is for the untreated specimens and on the other hand, treated specimens with 28 cm of height have the highest s-n curve. specimen treated with 12 cm of height have a higher s-n curve compared to specimens treated with 20 cm height. this could be an error in this experiment. the values obtained in this experiment are then compared to the calculated values using morrow and swt models. the percentage error can be calculated using eqn. (5). fig. 7 (a) – (d) illustrates the percent error difference in histograms.       %     100   experimental value theoretical value error x theoretical value (5) (a) (b) m. m. padzi et alii, frattura ed integrità strutturale, 62(2022) 271-278; doi: 10.3221/igf-esis.62.19 277 (c) (d) figure 7: histograms for percentage error difference against percentage σmax; (a) untreated, (b) 12 cm, (c) 20 cm and (d) 28 cm the error for untreated specimens gives the smallest dispersion with the highest error of 13.2%. in addition, we also noticed that the swt approach produces smaller error differences compared to morrow’s. this is in line with the statement stated by [8], as the swt approach is the best model for predicting accurate fatigue life for non-zero mean stress. conclusion rom the result of this experiment, it can be concluded that pwit produce a significant result in the test specimens. based on the graph plotted, specimens treated with lbit were able to withstand higher load before starting to deform. this means they have higher yield strength compared to the untreated specimen. the tensile results also illustrate that the treated specimen has higher ultimate tensile strength compared to the untreated which can be observed from the peak value. the lowest peak value is 6 kn with an extension of 2.5 mm for the untreated specimen and the highest peak value is 7.1 kn with an extension of 3.2 mm recorded for 32 cm of treated specimen. this demonstrates that the lbit process gives a substantial effect on the mechanical properties of the spot-welded specimens. on the other hand, a major improvement could be seen in the fatigue properties of the treated specimens. the s-n curve proves specimens that undergo lbit have higher fatigue lives. the graph shows a good impact of lbit on the spot weld at a height of 28 cm. for all values of stresses, comparing untreated and treated specimens at 28 cm, fatigue lives increase in a range of 27% to 87%. this shows that lbit increases the fatigue strength of spot weld joints of mild steel. to conclude, the objectives of this research are achieved. lbit not only increases the tensile strength of spot weld joints but also improves the fatigue lives as well. the results from this research prove that lbit plays a significant role in improving the mechanical and fatigue properties of welded joints. for future works, it is recommended to repeat with more specimens as there are some errors found such as the ultimate tensile strength of 24 and 28 cm treated specimen is lower than 20 cm specimen. in addition, the fatigue lives of 20 cm specimen also fewer than 12 cm specimen. this contradicts our theory that a higher height of treatment should produce a higher percentage of improvement. references [1] hofe, d.v. (2015). the significance of welding and joining technology in a modern industrial structure, german welding society (dvs), germany, krefel [2] chao, y. (2003). ultimate strength and failure mechanism of resistance spot weld subjected to tensile, shear, or combined tensile/shear loads. j. eng. mater. technol. apr 2003, 125(2), pp. 125-132. doi: 10.1115/1.1555648 [3] wang, l., jiang, x., zhu, y., ding, z., zhu, x., sun, j. and yan, b. (2018). investigation of performance and residual stress generation of alsi10mg. advances in materials science and engineering, doi: 10.1155/2018/7814039. [4] gorti, j., goutam, m., krishna, d. (2022). failure mechanism of resistance spot-welded dp600 steel under high cycle fatigue. materials today: proceedings, 59(3), doi: /10.1016/j.matpr.2022.03.332. [5] ravindra, s. s., vijay, n. n. (2022). impact of post weld heat treatment on mechanical and microstructural properties of underwater friction stir spot welded 6061 aluminium alloy. materials today: proceedings, 56(5). doi: /10.1016/j.matpr.2021.09.207 [6] nagasaka, t., muroga, t., grossbeck, m.l. and yamamoto, t. (2002). effects of post-weld heat treatment conditions on hardness, microstructures and impact properties of vanadium alloys. journal of nuclear materials, 307–311(2), pp. 1595-1599. doi: /10.1016/s0022-3115(02)01170-4 f m. m. padzi et alii, frattura ed integrità strutturale, 62(2022) 271-278; doi: 10.3221/igf-esis.62.19 278 [7] sérgio, s. m. t., clóvis r. r., juan m. p., edvan s. b. and hamilton f. g. a. (2014). effects of post weld heat treatments on the microstructure and mechanical properties of dissimilar weld of supermartensític stainless steel. mat. res. 17 (5). doi: /10.1590/1516-1439.299314 [8] iyeger, r. m., amaya, m., bonnen, j., citrin, k. kang, h. k., laxman, s., khosrovaneh, a., schillaci, n. and shih, h. s. (2008). fatigue of spot -welded sheet steel joints: welded sheet steel joints: physics, mechanics, and process variability. [9] ghazali, f. a., salleh, z., hyie, k. m., taib, y. m. and rozlin, n. (2017). improvement of mechanical properties and fatigue failure of spot-welded joint through pneumatic impact treatment (pit). materials today: proceedings 16, pp. 1988-1993. doi: 10.1016/j.matpr.2019.06.078 [10] azeez, a. a. (2013). fatigue failure and testing methods, 32. (2002) the ieee website. available: http://www.ieee.org/ [11] jiazhuang, t., wu, t. and shanglu, y. (2022). investigation on microhardness and fatigue life in spot welding of quenching and partitioning 1180 steel. journal of materials research and technology 19, pp. 3145-3159, doi: /10.1016/j.jmrt.2022.06.083. [12] mahmud, k., mohammad, w. d., md. zahidul. s.r. (2021). effects of welding technique, filler metal and post-weld heat treatment on stainless steel and mild steel dissimilar welding joint. journal of manufacturing processes, 64, pp. 1307-1321, doi: /10.1016/j.jmapro.2021.02.058. [13] ince, a. and glinka, g. (2011). a modification of morrow and smith-watsontopper mean stress correction models. fatigue and fracture of engineering materials and structures 34(11), pp. 854-867. doi: 10.1111/j.1460-2695.2011.01577.x [14] azlan, m.a. (2016). development of fatigue life prediction algorithm using matlab [15] poja, s.h. and mohammad, a. (2014). post weld treatment implementation on bridges with special focus on hfmi. chalmers university of technology. [16] ghazali, f. a., salleh, z., taib, y. m., hyie, k. m. and masdek, n. r. n. m. (2017). effect of low blow impact treatment on fatigue and mechanical properties of spot-welded joints. pertanika journal of science and technology. [17] meneghetti, g., quaresimin, m. and ricotta, m. 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can be opened with acrobat and adobe reader 5.0 and later.) >> /namespace [ (adobe) (common) (1.0) ] /othernamespaces [ << /asreaderspreads false /cropimagestoframes true /errorcontrol /warnandcontinue /flattenerignorespreadoverrides false /includeguidesgrids false /includenonprinting false /includeslug false /namespace [ (adobe) (indesign) (4.0) ] /omitplacedbitmaps false /omitplacedeps false /omitplacedpdf false /simulateoverprint /legacy >> << /addbleedmarks false /addcolorbars false /addcropmarks false /addpageinfo false /addregmarks false /convertcolors /converttocmyk /destinationprofilename () /destinationprofileselector /documentcmyk /downsample16bitimages true /flattenerpreset << /presetselector /mediumresolution >> /formelements false /generatestructure false /includebookmarks false /includehyperlinks false /includeinteractive false /includelayers false /includeprofiles false /multimediahandling /useobjectsettings /namespace [ (adobe) (creativesuite) (2.0) ] /pdfxoutputintentprofileselector /documentcmyk /preserveediting true /untaggedcmykhandling /leaveuntagged /untaggedrgbhandling /usedocumentprofile /usedocumentbleed false >> ] >> setdistillerparams << /hwresolution [2400 2400] /pagesize [612.000 792.000] >> setpagedevice microsoft word numero 1 art 1.doc l. p. pook, frattura ed integrità strutturale, 1 (2007) 12-18 12 1 introduzione it is well-known that engineering structures and components, as well as consumer items, contain cracks or flaws and, therefore, crack growth must be considered both in design and in the analysis of failures. the path taken by a crack in a critical component or structure can determine whether fatigue failure is catastrophic or not. knowledge of potential crack paths is also needed for the selection of appropriate non-destructive testing procedures. much current work is concerned with crack growth viewed on macroscopic scale. the forthcoming esis international conference on crack paths (cp 2006) will be devoted to consideration of crack paths at various scales. from a theoretical viewpoint the complete solution of a crack growth problem includes determination of the crack path. figure 1: cracks in undercarriage bay bracket. it is often assumed that the crack path is known, either from theoretical considerations, or from the results of laboratory tests. at the present state of the art, the factors controlling the path taken by a crack are not completely understood [1]. eight brief case studies involving crack paths are presented. these are taken from the author’s professional and personal experience over many years. they have been chosen to illustrate various aspects of crack paths. one example is in a component from a major structure, three examples are in laboratory specimens, and four are in nuisance failures. such nuisance failures cause, in total, a great deal of inconvenience and expensive, but do not normally receive much publicity. 2 aircraft undercarriage bay bracket the relationship between mode of fatigue loading and paths taken by fatigue cracks has been of interest for a long time [2, 3]. this information can be useful in failure analysis and figure 1 shows an example from 1961. it is a bracket from an aircraft undercarriage bay which showed unexpected cracking at rivet holes. the bracket was a formed 18 swg (1.2 mm thick) aluminium alloy angle, 10 in × 0.8 in × 0.8 in (254 mm × 20.3 mm × 20. 3 mm). the figure shows a general view of typical cracks observed after the bracket was removed from the bay. examination of the fracture surfaces of the cracks showed that fatigue cracks had originated at both surfaces of the bracket at the rivet hole corner and then propagated inwards on elliptical crack fronts, with the two cracks intersecting at or near the centre line of the sheet. figure 2 shows the fracture surface of a typical crack. this indicates that failure was caused by out of plane alternating some practical crack path examples ( da esis newsletter 2006) les p. pook department of mechanical engineering, university college london, torrington place, london wc1e 7je, uk abstract. it is well known that many engineering structures and components, as well as consumer items, contain cracks or crack-like flaws. it is widely recognised that crack growth must be considered both in design and in the analysis of failures. the complete solution of a crack growth problem includes determination of the crack path. macroscopic aspects of crack paths have been of industrial interest for a very long time. at the present state of the art the factors controlling the path taken by a crack are not completely understood. eight brief case studies are presented. these are taken from the author’s professional and personal experience of macroscopic crack paths over many years. they have been chosen to illustrate various aspects of crack paths. one example is in a component from a major structure, three examples are in laboratory specimens, and four are in nuisance failures. such nuisance failures cause, in total, a great deal of inconvenience and expensive, but do not normally receive much publicity. keywords: crack growth, crack path l. p. pook, frattura ed integrità strutturale, 1 (2007) 12-18 13 bending fatigue loads, which were not anticipated by the designer. examination of the fracture surfaces at high magnification showed the presence of striations and hence confirmed that cracking was due to fatigue. this is an example of the useful crack path information which can be obtained from simple examination of a failed component with the naked eye. figure 2. surface of crack in an undercarriage bay bracket. 3 angle notch fracture toughness and fatigue specimens by 1965 plane strain fracture toughness testing using mode i specimens, in which crack growth is perpendicular to the applied load, was well established [4] but little was known about fracture toughness behaviour under mixed mode loading, where loads are applied at an angle to the crack.. some tests were therefore carried out in 1966 [5, 6] to investigate the mixed mode fracture toughness of dtd 5050, a 5½% zn aluminium alloy with kic = 28.8 mpa√m [5]. a 19 mm thick angle notch specimen was used, with the initial notch inclined at an angle β of 75°, 60° and 45°, as in figure 3. specimens were precracked in fatigue. figure 4 shows the fracture surface of one of the specimens with the initial notch inclined at β = 45°. the fatigue precrack (bright area at the notch root) is of nearly constant depth, and at the end of the precrack β ≈ 48°. a feature of the test is that under the static loading to determine the fracture toughness the specimen failed very abruptly, but the macroscopic crack path features followed on from the fatigue precrack. at the time the fracture surface appearance was puzzling, but is easily interpreted from a modern viewpoint [1], in that that there is a tendency to mode i crack growth on two scales. on a scale of 1 mm initially crack growth was mixed mode. as the crack grew the crack front rotated until it was perpendicular to the specimen surfaces, and crack growth was in mode i, with the exception of shear lips at specimen surfaces. on this scale the crack follows a curved path which tends towards a plane of symmetry. this is in accordance with the well known observation [1] that the tendency to mode i crack growth means that cracks tend to grow perpendicular to the maximum principal tensile stress. on a smaller scale of 0.1 mm the tendency to mode i fatigue crack growth results in the production of what is known as a twist crack [1] containing individual mode i facets connected by cliffs. the mode i facets gradually merge as, viewed on the 1 mm scale, the crack growth surface becomes perpendicular to the specimen surfaces. merging of mode i facets shows up more clearly under fatigue loading. some fatigue tests were carried out in 1989 on 20 mm thick medium strength structural steel angle notch specimens [7] with initial β values of 75°, 60° and 45°. figure 5 shows the fracture surface of one of the specimens, initial β = 60°. the light area at the top is where the specimen was broken open in liquid nitrogen. these examples illustrate the strong tendency to mode i crack growth in isotropic materials under essentially elastic conditions. figure 3. angle notch charpy specimen, crack initiation along notch tip. figure 4. fracture surface of dtd 5050 5½ zn aluminium angle notch fracture toughness test specimen, initial β = 45°. l.p.pook., frattura ed integrità strutturale, 1 (2007) 12-18 14 figure 5. fracture surface of medium strength structural steel angle notch fatigue test specimen, initial β = 60°. figure 6. crack path in a waspaloy sheet under biaxial fatigue load. the grid is 2.54 mm. 4 crack path stability under biaxial loading the question of the stability of a crack path had been of interest for some time [8] but in general it wasn’t possible to predict crack paths under biaxial fatigue loading. therefore, in 1974 some tests [9], were carried out at room temperature on waspaloy, a nickel based gas turbine material, in order to determine the conditions under which a fatigue crack path became unstable under biaxial loading. the specimens were 254 mm square and 2.6 mm thick. the material had been cross rolled during production to ensure that its properties were reasonably isotropic. tests were carried out using sinusoidal constant amplitude loading at a stress ratio (ratio of minimum to maximum load in fatigue cycle), r, of 0.1. in each test the fatigue load perpendicular to the crack was kept constant. cracks were first grown from each end of an initial slit under uniaxial loading an in phase load was then applied parallel to the crack, and crack path behaviour observed. figure 6 shows the crack path for a load parallel to the crack of twice the load perpendicular to the crack. the crack path became unstable and deviated from its initial path as soon as the load parallel to the crack was applied. at the time the tests were carried out it wasn’t possible to do more than describe the results. however, reanalysis of these and other results in 1997 [1, 10] showed it was possible to correlate crack path stability in terms of a parameter called the t-stress ratio. 5 plastic domestic tap in 1991 a plastic domestic tap in the author’s utility room was observed to be leaking where it was screwed into a fitting on the supply pipe. the tap had a fitting for a hose pipe, and appeared to be a replacement for the original brass tap. when an attempt was made to unscrew the tap it failed completely. the two parts of the broken tap are shown in figure 7 and a close up of the fracture surface in figure 8. the dark area is fatigue and the light area the final static failure. the age of the tap at the time of failure is unknown, but as one fatigue cycle is applied each time a tap is turned on and off it is likely that thousands of cycles had been applied. safety critical pressure containing components are often designed to leak-before-break [11] in order to avoid catastrophic failure. it is fortunate that the tap did so otherwise the utility room would probably have been flooded. the failed tap was replaced with a brass tap, and it was observed that the detail design in the vicinity of the threads was exactly the same. the replacement tap is still in use. the episode is an example of the danger of using a different material for a component without making appropriate changes to detail design. figure 7. plastic domestic tap. l. p. pook, frattura ed integrità strutturale, 1 (2007) 12-18 15 figure 8. crack surface of plastic domestic tap. figure 9. wall clock by john davidson, coatbridge. figure 10. failed wall clock mainspring. 6 wall clock mainspring before the days of quartz clocks, spring driven wall clocks were widely used in public buildings. the example shown in figure 9 was originally used in a school, but since 1968 it has been in use in the author’s kitchen. in 1994 the mainspring failed while the clock was being wound. examination showed that this was the final failure following fatigue crack growth. a general view of the failed mainspring is shown in figure 10. fatigue has been a problem in clock mainsprings for centuries, and traditionally they are designed using rules of thumb based on experience [12], rather than by detailed analysis. the total fatigue life is not known, but the clock is wound weekly so it must be thousands of cycles. a clock mainspring is loaded in bending, with loading and unloading moving along the spring as it is wound and unwinds. when a mainspring breaks in fatigue the crack is usually straight across the spring, with crack growth predominantly through the thickness. however, in this particular mainspring crack path behaviour is unusually complicated, and details are shown in figure 11. a fatigue crack initiated at a corner at one edge of the 27 mm wide mainspring. initially, crack growth was across the spring (downwards in the picture) but after about 9 mm of growth the crack turned sharply towards the outer end of the spring (right in the picture), and then grew in a spiral fashion towards the other edge of the spring until the final failure took place. during this crack growth two secondary cracks initiated, and then joined so that a small triangular piece of spring became detached. the joined secondary crack then grew in a spiral fashion towards the centre of the spring, but did not contribute to the final failure. this is an example of a nuisance fatigue failure which did not have serious consequences. such failures are not normally investigated at all. the offending component is simply replaced. in this particular case the replacement mainspring is still intact after 12 years. figure 11. centre portion of failed wall clock mainspring. l.p.pook., frattura ed integrità strutturale, 1 (2007) 12-18 16 7 angle notch charpy specimens some preliminary tests [13] were carried out in 1971 on angle notch charpy specimens, but crack paths were not investigated in detail. specimen design was based on the standard charpy v-notch specimen with β values (figure 3) of 90° (standard specimen), 75°, 60°, and 45°. the true notch tip radius was reduced so that the notch tip radius measured in a plane parallel to the specimen sides was the same as in the standard charpy specimen (0.25 mm). figure 12 shows the appearance of specimens tested at 10 c. more detailed tests were carried out in 1997 using en6a mild steel (0.36% c) specimens [14]. all specimens were tested in the normalised condition (tensile strength 550 mpa, yield stress 280 mpa). tests were carried out in a 300 j charpy machine equipped with a 2 mm radius striker. they are an example of the complexity often observed in crack path behaviour under dynamic loading. the fracture surface appearance of the standard charpy specimens (β = 90°) is typical of mild steel. in the lower shelf region, that is at below about -15°c, fracture surfaces are crystalline, and in the upper shelf region, above about 30°c, they are ductile. in the transition region fracture surfaces are initially ductile, and the amount of crystalline crack growth decreases with increasing temperature. shear lips appear at above about -15°c, and increase in size with increasing temperature. the fracture appearance transition temperature (50 per cent crystalline) is about 25°c. in the upper shelf region fracture surfaces are ductile. figure 12. fracture appearance of mild steel charpy specimens tested at 10 c. top, standard specimen, β = 90°. bottom, angle notch specimen, β = 45°. the fracture surface appearance of the angle notch specimens is controlled by a tendency towards square (mode i) crack growth, but modified by plasticity and by crack path constraint due to the initial notch. the value of β has little effect on either the 50 per cent crystalline transition temperature, or on the temperature below which fractures are crystalline. shear lips for β = 75° and 60° are similar to those on standard charpy specimens, but could not be distinguished for β = 45°. in the transition region fracture surfaces are initially ductile. the amount of initial ductile crack growth increases with increasing temperature. crack initiation is along the notch tip, and in the notch plane, so the initial crack growth is mixed mode. for β = 75° and 60° a crack twists as it grows, becoming mode i as it approaches the striker position (figure 3). for β = 45° there is an abrupt transition to mode i crack growth (figure 13). figure 13. angle notch charpy specimen, abrupt transition to crystalline crack growth. this mode i growth is at least initially crystalline. at below about -15°c fracture surfaces of the angle notch specimens are fully crystalline. crack origins are mode i. for β = 75° and 60° there are a number of individual mode i crack origins along a notch tip, linked by vertical cliffs (apparently mode iii). the initial mode i cracks link up as a crack grows, and overall a crack twists as it approaches the striker position. for β = 45° the tendency to mode i crack growth is so marked that the crack path is not constrained by the notch. at intermediate absorbed energy levels there is one crack origin at the centre of a notch, and crack growth is mode i throughout (figure l. p. pook, frattura ed integrità strutturale, 1 (2007) 12-18 17 14). at high absorbed energy levels there are crack origins at both notch corners. the cracks follow curved, apparently mode i paths, as shown schematically for a single crack in figure 15. the two paths merge as they approach the striker position. figure 14. angle notch charpy specimen, crack origin at centre of notch. figure 15. angle notch charpy specimen, crack origin at notch corner. 8 central heating boiler burner during routine maintenance in 2002 one of the two burners in the gas fired domestic central heating boiler installed in the author’s house was found to be cracked due to thermal fatigue. a general view of the burner is shown in figure 16, and the crack is shown in figure 17. the boiler was about 12 years old so, assuming it fired about 10 times per day, about 44,000 thermal fatigue cycles had been applied. the burner consists of a steel box with a series of small and large holes on top to distribute the gas to the flame above the box. the larger holes have reinforced perimeters. an internal wire mesh, just visible in figure 17, helps to distribute the gas evenly. cracking appears to have initiated at three places on the perimeter of a smaller hole, grown into two larger holes with a small triangular piece becoming detached, and then two cracks grew across most of the width of the box, resulting in improper combustion. the designer did not appear to have appreciated the point that stress concentration factors are largely independent of hole size. the reinforcement had prevented crack initiation at the large holes but its absence had allowed cracking at a small hole. this is another example of a nuisance fatigue failure. annual inspection was recommended by the boiler manufacturer. this ensured that the cracking was detected before it became dangerous, and the burner was replaced. figure 16. burner from domestic central heating boiler. figure 17. crack in burner from domestic central heating boiler. l.p.pook., frattura ed integrità strutturale, 1 (2007) 12-18 18 9 walking shoe in 2005 the author found that the plastic soles of pair of walking shoes had become badly cracked and one no longer fitted properly. this more severely damaged shoe is shown in figure 18. the sole of a shoe is subjected to repeated bending. going uphill a sole is also subjected to repeated tension as the rearward force applied by the wearer’s heel is transferred to the ground. this particular pair of shoes had covered several hundred kilometres, which is equivalent to around 3 × 105 cycles. in the shoe shown two separate cracks had initiated in grooves near the toe, grown past each other and then curved together, in a well known crack path behaviour [15], so that a piece of sole became detached. the heel had also cracked and, in what appears to have been the final event that reduced the stiffness of the shoe so much that it became unusable, the sole separated from the upper at the end of this crack. the use of a plastic, instead of rubber, for the soles has reduced the rate of wear but led to fatigue failure. this is another example where a change of material has resulted in fatigue cracking. figure 18. cracks in sole of walking shoe. 10 concluding remarks paths taken by cracks have been of interest for a very long time. a large amount of empirical knowledge has been accumulated, but at the present state of the art the factors controlling the path taken by a crack are not completely understood. the numerous possible crack configurations [7] mean that a systematic approach to the determination of crack paths isn't feasible, so particular practical problems need to be tackled on an ad hoc basis. the examples given have been chosen from the author’s experience to illustrate the variety of crack paths which occur in practice. 11 references [1] l. p. pook, crack paths, wit press, southampton (2002). [2] r. cazaud, fatigue of metals, chapman & hall ltd, london (1953). [3] j. longson, a photographic study of the origin and development of fatigue fractures in aircraft structures. rae report no. struct 267. royal aircraft establishment, farnborough (1961). [4] j. e srawley, w. f. brown, fracture toughness testing methods. in fracture toughness testing and its applications. astm stp 381. american society for testing and materials, philadelphia, pa, (1965) 133. [5] l. p. pook, brittle fracture of structural materials having a high strength weight ratio. phd thesis, university of strathclyde, glasgow (1968). [6] l. p. pook, eng. fract. mech., 3 (1971) 205. [7] l. p. pook, d. g. crawford, the fatigue crack direction and threshold behaviour of a medium strength structural steel under mixed mode i and iii loading. in: kussmaul, k., mcdiarmid, d. l. and socie, d. f. (ed). fatigue under biaxial and multiaxial loading. esis 10. (1991) 199. mechanical engineering publications, london. [8] b. cotterell, int. j. fract. mech., 2 (1966) 526. [9] l. p. pook, r.holmes, in: proc. fatigue testing and design conf., society of environmental engineers fatigue group, buntingford, herts, 2 (1976) 36.1 [10] l. p. pook, an alternative crack path stability parameter. in: brown, m. w., de los rios, e. r. and miller, k. j. (eds). fracture from defects. ecf 12. emas publishing, cradley heath, west midlands. i (1998) 187. [11] l. p. pook linear elastic fracture mechanics for engineers. theory and applications. wit press, southampton (2000). [12] f. j. britten, the watch & clock makers' handbook, dictionary and guide. 16th edition. revised by good, r. arco publishing company inc, new york (1978) [13] l. p. pook, eng. fract. mech., (1972) 483. [14] l. p. pook, m. j. podbury, int. j. fract., 90, (1998) l3-l8. [15] s.melin, int. j. fract., 23(1) (1983) 37. [16] l.p. pook, keyword scheme for a computer based bibliography of stress intensity factor solutions. nel report 704. national engineering laboratory, east kilbride, glasgow (1986). microsoft word numero_43_art_16 e. maiorana et alii, frattura ed integrità strutturale, 43 (2018) 205-217; doi: 10.3221/igf-esis.43.16 205 experimental tests on slip factor in friction joints: comparison between european and american standards emanuele maiorana omba impianti & engineering spa, via della croce, 10 36040 torri di quartesolo (vi), italy emaior@libero.it, http://orcid.org /0000-0002-3574-1410 paolo zampieri, carlo pellegrino department of civil, environmental and architectural engineering, university of padova, via marzolo, 9 35131 padova, italy paolo.zampieri@dicea.unipd.it, http://orcid.org/0000-0002-4556-5043 abstract. friction joints are used in steel structures submitted to cyclic loading such as, for example, in steel and composite bridges, in overhead cranes, and in equipment subjected to fatigue. slip-critical steel joints with preloaded bolts are characterized by high rigidity and good performance against fatigue and vibrational phenomena. the most important parameter for the calculation of the bolt number in a friction connection is the slip factor, depending on the treatment of the plane surfaces inside the joint package. the paper focuses on the slip factor values reported in european and north american specifications, and in literature references. the differences in experimental methods of slip test and evaluation of them for the mentioned standards are discussed. the results from laboratory tests regarding the assessment of the slip factor related to only sandblasted and sandblasted and coated surfaces are reported. experimental data are compared with other results from the literature review to find the most influent parameters that control the slip factor in friction joint and differences between the slip tests procedures. keywords. bolted joints; slip resistance; k-factor; slip factor; surface treatment. citation: maiorana, e., zampieri, p., pellegrino, c., experimental tests on slip factor in friction joints: comparison between european and american standards, frattura ed integrità strutturale, 43 (2018) 205-217. received: 01.12.2017 accepted: 10.12.2017 published: 01.01.2018 copyright: © 2018 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. introduction urocode en 1993-1-8 [1] provides the main recommendations of methods for the effective design of joints using steel grades s235, s275, s355 and s460 and prescribes that only bolt assemblies of classes 8.8 and 10.9, conforming to the requirements of high strength structural bolting for preloading with controlled tightening e e. maiorana et alii, frattura ed integrità strutturale, 43 (2018) 205-217; doi: 10.3221/igf-esis.43.16 206 torque, may be used as preloaded bolts in friction joints. in en 1090-2 [2] requirements for execution of steel structures (included structural bolting assemblies for preloading), are specified in order to ensure adequate levels of mechanical resistance and stability, serviceability and durability. in particular, it summarizes the steel structures that are designed according to all parts of european standards. north american rcsc “specification for structural joints using high-strength bolts” [3] deals principally with the strength grades of hs bolts, astm a 325 e astm a490 providing guidance for their design, installation and inspection in structural steel joints. astm f3125 [4], which replaces the six previous standards, simplifying bolt specification, covers chemical, physical and mechanical requirements for quenched and tempered bolts manufactured from steel and alloy steel, in inch and metric dimensions, in two strength grades. tab. 1 shows in a benchmarking nominal values of the yield strength fyb and of the ultimate tensile strength fub for european and american equivalent grades: i.e., respectively, 8.8 and 10.9, a325 and a490. en 1993-1-8 astm f3125 bolt grade 8.8 10.9 a325 a490 fub (mpa) 800 1000 830 1040 fyb (mpa) 640 900 660 940 table 1: minimum values for yield and ultimate tensile strength of hs bolt material according to european and north american standards. in a slip-critical joint, the resistance is due to friction forces developed between the faying surfaces depending on the preloaded force of the tightened bolts as well as on surface treatment. both american and european standards require, prior to bolt preloading, the snug-tightening procedure to bring the plies into firm contact and provide four pretensioning methods, without preference: turn-of-nut pretensioning; calibrated wrench pretensioning; twist-off-type tension-control bolt pretensioning; direct-tension-indicator pretensioning. according to rcsc [3] the minimum bolt pretension for slip-critical joints is equal to 70 percent of the specified minimum tensile strength of bolts multiplied by bolt stress area as prescribed in astm specifications [4]. similarly, under the provisions of en 1993-1-8 [1] and en 1090-2 [2], the nominal minimum preloading force fp,c shall be taken as: fp,c = 0.7fubares (1) where fub is the nominal ultimate strength of the bolt material and ares is the stress area of the bolt. the slip resistant force, governed by preload force fp,c, the surfaces-in-contact slip factor , the number of plane surfaces in contact n, the safety coefficient m3, the hole shape factor ks, is given by eqn.(2) in accordance with en 1993-1-8 [1]: s s,rd p,c m3 k nμ f f γ  (2) where ks = 1 for normal holes, and m3 is equal to 1.25 at ultimate limit state and 1.1 at serviceability limit state. for rcsc [3] the values are 1.5 and 1.0, respectively. the first step in bolted joints is to obtain the snug tightened condition bringing the connected plates into firm contact. to reach the design preload force it is necessary to apply a correct tightening torque mr; if tightening torque is lower than that necessary to reach the design preload force, the friction joint is not guaranteed and the mechanism is the same as that of shear bolts; on the other hand, overtightening could exceed the yielding point and increase the plasticization of the screw or nut threads and arrive at rupture. the correlation between fp,c and mr is given by the bolt diameter d and the k-factor km. in terms of preloading force, for the european code en 14399-2 [5] the tightening torque depends on the surface treatment of bolt that is parameterized by factor km. e. maiorana et alii, frattura ed integrità strutturale, 43 (2018) 205-217; doi: 10.3221/igf-esis.43.16 207 the equation that gives the relationship between tightening torque and preload force is ,(1 1.65 )r k m p cm v k f d  (3) approximated with: ,1.10r m p cm k f d (4) slip factor he decisive parameter for the operation of the friction mechanism in the bolted joint is the slip factor μ which depends on the roughness of the plate, which is associated with the surface treatment of plates closed by the bolted joints. however, the surfaces of the steel components should be protected, as all the other surfaces, to avoid the development of corrosion phenomena between the manufacturing and the erection phase, but also to guarantee the greatest possible friction. in general, the surfaces are cleaned, blasted, followed by the application of inorganic zinc. the grade of sandblasting is usually sa2½ as described in international standard iso 8501-1 [6]. in practical applications, the slip factor for short-time loads may be necessary to sustain dynamic loads. for example, fig. 1 shows a steel bridge girder where the bolted joints surfaces are specifically prepared for friction connections. figure 1: painted beam with inorganic zinc coated surfaces for friction joints. the slip factor tends to decrease with time due to the creep phenomena in coated surfaces. several studies have been developed to establish adequate slip factors for different conditions; these studies are in general very time consuming due to the wide range of parameters involved. in this context, reference should be made, for example, to the studies reported in the publication n.37 of eccs [7]. also, the results of an extensive research work are collected in kulak et al. [8]. tab. 2 shows the slip factor value assumed with different surface treatment as in en 1090-2 [2] while, for an useful comparison, tab. 3 shows the prescription in pren 1090-2 (draft new version of en 1090-2). in other international standards, different systems of friction classes are specified; for instance, in “specification for structural joints using high-strength bolts” rcsc [3] used in north america, three surface classes are established (tab. 4). a comparison among european, american, australian, japanese, italian and british standards for design of bolted joints in steel bridges is reported in maiorana and pellegrino [9]. t e. maiorana et alii, frattura ed integrità strutturale, 43 (2018) 205-217; doi: 10.3221/igf-esis.43.16 208 surface treatment class slip factor μ surfaces blasted with shot or grit with loose rust removed, not pitted. a 0.50 surfaces blasted with shot or grit; a) spray-metallized with aluminum or zinc based product b) with alkali-zinc silicate paint with a thickness of 50 μm to 80 μm b 0.40 surfaces cleaned by wire brush or flame cleaning, with loose rust removed c 0.30 surfaces as rolled d 0.20 table 2: classifications that may be assumed for friction surfaces according to en 1090-2 [2]. surface treatment class slip factor μ surfaces blasted with shot or grit with loose rust removed, not pitted. a 0.50 surfaces hot dip galvanized to en iso 1461 and flash (sweep) blasted and with alkali-zinc silicate paint with a nominal thickness of 40 μm to 80 μm b 0.40 surfaces blasted with shot or grit: a) coated with alkali-zinc silicate paint with a nominal thickness of 40 μm to 80 μm; b) thermally sprayed with aluminium or zinc or a combination of both to a nominal thickness not exceeding 80 µm b 0.40 surfaces hot dip galvanized to en iso 1461 and flash (sweep) blasted (or equivalent abrasion method) c 0.35 surfaces cleaned by wire-brushing or flame cleaning, with loose rust removed c 0.30 table 3: classifications that may be assumed for friction surfaces according to pren 1090-2. surface treatment class slip factor μ uncoated clean mill scale steel surfaces or surfaces with class a coatings on blast-cleaned steel a 0.30 uncoated blasted and cleaned steel surfaces or surfaces with class b coatings on blasted and cleaned steel b 0.50 roughened hot-dip galvanized surfaces c 0.30 table 4: classifications that may be assumed for friction surfaces (according to rcsc [3]). cruz et al. [10] obtained slip factors with values of 0.50 with blasted surfaces, without any additional surface treatment. in blasted surfaces, spray metalized with zinc or hot-dip galvanized ones, the slip factor easily reaches values above 0.40. for blasted surfaces, with a painted coating of zinc ethyl-silicate, in cruz et al. [10] a characteristic value of 0.40 was obtained with a small margin. for blasted surfaces, with a painted coating of zinc epoxy, the lowest slip factor values, no higher than 0.30, were obtained. concerning the specimens in s355 weathering steel, it was verified that the value of the slip factor increased with the duration of environmental exposure, from 0.502 to 0.560. cruz et al. [10] conclude that the slip factor is strongly influenced by the surface treatment and weakly by the steel grade. in fact, in specimens of s275 steel and s690 high strength steel, with equivalent surface treatment, similar values for the slip factor were obtained. therefore, it seems that the classification system predicted in en 1090-2 [2] remains valid for use in slip resistant joints with high strength steel. e. maiorana et alii, frattura ed integrità strutturale, 43 (2018) 205-217; doi: 10.3221/igf-esis.43.16 209 heistermann et al. [11] studied the slip resistance in lap joints with long open slotted holes while annan and chiza [12] presented a work about the characterization of slip resistance of high strength bolted connections with zinc-based metallized faying surfaces and annan and chiza [13] the slip resistance of metalized-galvanized faying surfaces in steel bridge construction. latour et al. [14] made an experimental analysis on friction materials for supplemental damping devices while pavlović et al. [15] presented friction connection vs. ring flange connection in steel towers for wind converters. ferrante cavallaro et al. [16] presented the experimental behavior of innovative thermal spray coating materials for freedam joints while li et al. [17] the slipping coefficient study of frictional high strength bolt joint. through finite element analysis and experimental study, in huang et al. [18] the mechanical behavior including slip vs. load ratio, load transfer factors, stress state, and friction stress distribution of this type of joints was studied in detail. both fea results and experimental ones show that the loads resisted by bolts in the edge rows are, as expected, larger than the ones by bolts in the middle rows. a report of the federal highway administration [19] has shown that ambiguities within the test method might increase the variability of reported friction coefficients. the report outlines that: variability of slip coefficients attained for the same coatings were noted by coating manufacturers despite no change in formulation. the most common approach is to use a multilayer paint system with a zinc-rich primer; labs following the same rcsc [3] procedure were sometimes reporting very different slip coefficients for identical coatings; the major finding was the manner in which each lab measured slip displacement which contributed to the greatest variability in frictional coefficient results. so, the aim and the main contribution of this work is not only to collect and evaluate the slip factor for different surfaces treatments, through an extensive product comparison and testing but also compare the european and american method for the friction coefficient determination. experimental test methods for the determination of the slip factor or the european code, the procedure for the determination of the characteristic value k of the slip factor was found testing a series of five specimens as descripted in annex g of the en 10902 [2] “slip test”. for each series, firstly four models are tested applying an incremental tensile load with a velocity of about 0.4 kn/s, to obtain a test duration between 10 and 15 min; in a second stage, the 5th test was performed to evaluate long-term effects. in the first four tests (short-time tests), the slip loads fsi are recorded when a slip of 0.15 mm occurs. the 5th model (longterm test) is loaded with 90% of the mean slip loads reached in the previous four tests, during 3 h to assess the behavior under sustained loads. if the difference between the slip measured at the end of 5 min and 3 h after the load application does not exceed 2 μm, the test is valid and the slip load shall be determined as for the previous four tests. if this condition is not verified, a minimum of three extended creep tests should be performed. the validity of the 5th test still depends on an additional condition: the standard deviation sfs of the slip loads obtained in the five tests, i.e. ten values, cannot exceed 8%. the slip factor is calculated with eqn. (5): 2.05k m μμ μ s  (5) for the american standard, the procedure for the determination of the mean value m of the slip factor derives directly from a series of results found testing five specimens as described in appendix a of the rcsc [3]. it is important to note that for rcsc [3], testing setup to determine the slip factor is different respect european standard and the single value µi per specimen is 2 si i p,c f μ f  (6) f e. maiorana et alii, frattura ed integrità strutturale, 43 (2018) 205-217; doi: 10.3221/igf-esis.43.16 210 where the slip load is the load corresponding to a deformation of 0.02 in., that is 0.5 mm. tab. 5 shows the list of specimen series, surface treatment and the reference standard. as many products report results for the slip coefficient found following the procedure of the italian former standard cnr uni 10011 [20], for a comparation also these results are reported. according to cnr uni 10011 [20], the preload was found by fc,p = 0.8 fk,n ares where fk,n = min{0.7 fu,b; fy,b }; for example, for bolts m20 class 10.9 fk,n = 700 n/mm2 and ares = 245 mm2 so fp,c = 137 kn (25% less european code) and the corresponding tightening torque mr = k fp,c d that is 550 nm. note that cnr uni 10011 [20] gave a fixed value k = 0.2 and the partial safety factor m in formula of resistance force was the same as in en 1993-1-8 [1] at ultimate state limit. series product n. coating bolts (diam. and grade) standard slip force fsi [kn] slip coeff. m slip coeff. k 1 2 3 1 1 m20 10.9 m20 10.9 m20 10.9 en 1090-2 en 1090-2 cnr uni 10011 353 340 227 0.52 0.50 0.42 0.45 0.45 0.38 4 2 2 ø20 astm a490 rcsc 278 0.64 0.47 5 3 2 ø20 astm a490 rcsc 223 0.51 0.28 6 4 3 m20 10.9 en 1090-2 263 0.39 0.34 7 5 3 m16 10.9 cnr uni 10011 220 0.62 0.58 8 5 3 m16 10.9 en 1090-2 311 0.45 0.41 9 6 4 ø20 astm a490 rcsc 152 0.34 0.29 10 7 1 ø20 astm a490 rcsc 243 0.56 0.45 11 7 1 m20 10.9 en 1090-2 354 0.51 0.43 12 8 3 m20 10.9 en 1090-2 230 0.34 0.29 chemical composition: 1 inorganic zinc ethyl silicate bicomponent; 2 inorganic zinc-rich bicomponent; 3 inorganic zinc polyethylene silicate bicomponent; 4 inorganic zinc silicate bicomponent table 5: series of tests with different coating products (final value of  in bold font). series n.1. slip test on only blasted surfaces the material of the specimens was weathering steel with characteristics as in en 10025-5 [21] s355j0w. fig. 2 shows the geometry of the specimens. figure 2: geometry of the specimen. surfaces were cleaned at grade sa2½, i.e. surfaces sandblasted as white metal surface; mean profile roughness was about 100 m. the bolts used to assembly the specimens were hv m20 grade 10.9. to reach the preload force the bolts, as in the combined method, were subjected to a tightening torque of 334 nm, that is 75%mr, plus a rotation angle a = 90°, corresponding to a final tightening torque of about 520 nm. the instrument utilized for measuring the relative displacements of the plates in the connection is formed by four transducers of inductive displacement (lvdt) useful to find displacements δ in the order of 10-3 mm. the tensile force applied was measured with a load cell installed in a universal test machine metrocom of 500 kn as in fig. 3. the specimen number five (s5), as reported in annex g of en 1090-2 [2], was loaded with a force equal to 90% of the mean value of the sliding forces fsi found for the other previous four specimens, for a period of three hours. over this time the displacement recorded was under the limit of the standard, 0.002 mm, so five tests were sufficient for the statistic evaluation of the slip factor (fig. 4) and from each specimen, two values si were found. e. maiorana et alii, frattura ed integrità strutturale, 43 (2018) 205-217; doi: 10.3221/igf-esis.43.16 211 figure 3: test of the blasted specimen. figure 4: fsi [kn] vs. δ [mm] relationship. from the ten values obtained by the tests, the mean value of the slip factor was calculated m = 0.519 with the standard deviation s = 0.030, finally a characteristic value k = 0.454 was achieved. fig. 5 shows the test results. figure 5: blasted and close specimens. dashed line: mean value m; continuous line: k. e. maiorana et alii, frattura ed integrità strutturale, 43 (2018) 205-217; doi: 10.3221/igf-esis.43.16 212 series n.2. slip tests on specimens blasted and rusted in a saline atmosphere a set of blasted specimens, steel grade en 10025-2 [21] s355j2+n, was exposed for one week above a box with saline water (h2o con 3% of nacl). fig. 6 shows the final surface aspect of the specimens. the surfaces in contact were brushed and the connection was closed. the tightening torque applied was 545 nm. figure 6: blasted and rusted specimens. the specimen number five (s5), as reported in the code, was loaded with a force equal to 90% of the mean value of the sliding forces found for the other four specimens, for a period of three hours. over this time the displacement recorded was under the limit of the norm, 0.002 mm, therefore five tests are sufficient for the statistic evaluation of the slip factor. the values obtained by the tests were processed, obtaining the mean value of the slip factor m = 0.500, a standard deviation s = 0.023, thus a characteristic value k = 0.453 is achieved. fig. 7 shows the test results. figure 7: blasted and rusted specimens. dashed line: mean value m; continuous line: k. slip tests on blasted and coated surfaces fig. 8 shows the specimens of series n.6 under test. for specimen number five (v5), the displacement recorded was 0.0280 mm for the upper limit and 0.0335 mm for the lower limit, thus above the limit of the standard, so five tests are not sufficient for the statistical evaluation of the slip factor and an extended creep test procedure should be necessary. otherwise, apart from the delayed slip of the fifth test, the values obtained by the tests were processed obtaining the mean value of the slip factor m = 0.387, a standard deviation s = 0.022, thus a characteristic value k = 0.343 is achieved. fig. 9 shows the test results. since the characteristic value for the slip factor using specimens painted with product n.4 was very low compared to the previous results, the authors thought that the problem was both the thickness of the paint (for thicknesses greater than 100 m the cracking of the film may occur), and the product itself, therefore inorganic zinc-rich primer with a 5% higher weight was used, i.e. product n.5. fig. 10 shows the specimens of series n.8 under test. it is product n.5 tested following en 1090-2 [2]. using the data of the first four slip test specimens, the mean value m = 0.45 and a characteristic value k = 0.41 were achieved, but the creep test, on the fifth specimen, failed with relative displacements of 0.0245 mm and 0.012 mm that were observed after half an hour, instead of the maximum 0.002 mm over three hours. e. maiorana et alii, frattura ed integrità strutturale, 43 (2018) 205-217; doi: 10.3221/igf-esis.43.16 213 figure 8: test of the blasted and coated specimen. figure 9: blasted, painted with product n.4. dashed line: mean value m; continuous line: k figure 10: blasted, painted with product n.5. dashed line: mean value m; continuous line: k to increase the slip factor as much as possible, an applicative procedure was performed in order to check the effective correlation between the preload and the tightening torque because of the potentially great variability of the friction coefficient k. e. maiorana et alii, frattura ed integrità strutturale, 43 (2018) 205-217; doi: 10.3221/igf-esis.43.16 214 since fp,c = 172 kn, the tightening torque to be applied was found by reading the voltage, v = 172.000 / 92162 = 1.8663 v; 10 kn correspond to 0.108 v. three tests were performed, and it was found that although the box of the bolts was closed and correctly stocked, in respect of the data reported in the box regarding the km, an increase of ki was observed. so for the following slip tests on blasted and painted specimens the tightening torque was 545 nm, assuming kmax = 0.16, maximum value of ki according to the code. an increase in the case of the normal speed tests was observed but in two cases the creep test failed again since relative displacements of 0.02 mm and 0.015 mm were observed after half an hour instead a maximum of 0.002 mm over three hours. the results of the third specimen in the static force test show a slight increase in the slip factor values to 0.47. a last set of specimens, series n.12, steel grade en 10025-2 [21] s355j2+n, was prepared connecting a central blasted and coated plate, using product n.8, with two cover only blasted plates. fig. 11 shows an image of the set of specimens. figure 11: blasted and half-coated specimens. for this set, bolts m20 class 10.8 with km = 0.13 and vk = 0.06 were used. the grease was applied between the screw and the nut. since the manufacturer declares that the standard production guarantees fub,min = 1040 n/mm2, and en 1090-2 [2] suggests for the tightening torque method a final torque of 1.1ms, the final tightening torque was ms = 545 nm. this result is equal to the previous one using km = 0.16 but since the grease was applied, it was necessary to respect the manufacturer’s indication. this last procedure to find the tightening torque was discussed with the manufacturer and approved. for specimen number five (v5), the displacement recorded was 0.0400 mm for the upper and 0.0360 mm for the lower limit, thus above the limit of the standard, therefore five tests are not sufficient for the statistic evaluation of the slip factor and an extended creep test procedure should be necessary. otherwise, apart from the delayed slip of the fifth test, the values obtained by the tests were processed obtaining the mean value of the slip factor m = 0.338, a standard deviation s = 0.024, thus a characteristic value k = 0.289 is achieved. fig. 12 shows the test results. figure 12: blasted, half-coated with product n.8. dashed line: mean value m; continuous line: k. e. maiorana et alii, frattura ed integrità strutturale, 43 (2018) 205-217; doi: 10.3221/igf-esis.43.16 215 discussion n recent experiments of cruz et al. [10] and in experiments conducted by the authors following the en standard, the values of the coefficient of friction peaks have been obtained with samples blasted, with sa2½, brushed, closed and tested. in the case of the use of weathering steel where the sandblasted surface was left unprotected prior to closure, the friction coefficient increased. on the contrary, in the case of carbon steel, to ensure a high friction coefficient of the surface covered by the bolted joint package and simultaneously having a guaranteed corrosion protection before the tightening torque, the alternatives are two. the first is to blast the surfaces and protect them until the closure, possibly treating the surfaces themselves by brushing before applying tightening torque; the second is to use a paint with effective corrosion resistance and adequate roughness after coating. commercially, products for the protection of surfaces joined by bolted joint packets working with friction mechanism are available. some products marketed in italy were tested according to the directions of the previous legal framework, cnr uni 10011 [20], which was based on earlier standards applicable to the manufacture of bolts and other products were classified according to other standards such as rcsc [3]. given the current regulatory scenario of reference in europe and in italy, dm 14.01.08 [22], which includes the verification procedures according to en 1993-1-8 [1] and other related european standards, it was necessary to carry out the experimental tests to obtain the friction coefficients in the manner described in en 1090-2 [2]. such redevelopment shall take into account the congruence of the results for the friction conforms to the values that can currently be achieved by preloading and tightening torque bolts manufactured and supplied in accordance with applicable european standards. an important observation should be made regarding the values of kmin and kmax given by the manufacturer that controlled the production by lot, while by [5], as already mentioned, for k1, values of km should be inside the range 0.10  ki  0.16, thus the value for km has a relevant oscillation. in the tests performed on the specimens painted with product n.1, the tightening torque value was 520 nm, that is km = 0.1505. in the tests performed on the specimens painted with product n.2, the tightening torque value was 520 nm for the first three specimens and 545 nm for the fourth, that is km = 0.16. an increase in the i value was observed with the percent of zinc in the coating component. alternatively, using grease between the screw and the nut, to consider a lower ki, is suggested, rather the kmax suggested by the manufacturer, the application of a torque of 1.1ms. fig. 13 shows synthetically all the results found of  in terms of comparison of: factor km, surface treatment, paints, standards applied (en [2], rcsc [3] and cnr [20]). in terms of preload force, the european code permits raising by 25% cnr [20] and 10% rcsc [3]. on the other hand, considering the test for the determination of slip factor, contrary to cnr [20] and rcsc [3], which assumes a value m from four tests, en [2] adopts the characteristic value k = m – 2.05s taking into account the standard deviation within the tests, and in conclusion the mean value m is reduced by about 10%. figure 13: comparison of all results . 1-blasted surfaces en [2]; 2-rusted en [2]; 3-paint n.1 cnr [20]; 4-paint n.2 rcsc [3]; 5paint n.3 rcsc [3]; 6-paint n.4 en [2]; 7-paint n.5 cnr [3]; 8-paint n.6 en [2]; 9-paint n.7 rcsc [3]; 10-paint n.8 rcsc [3]; 11-paint n.9 en [2]; 12-half coated en [2] fig. 14 shows test results showing a comparison between rcsc [3] and en [2] in terms of the ratio of fsi vs. . for both american and european standards  increases fsi, but with rcsc [3] a greater value of  than that of en [2] is observed. i e. maiorana et alii, frattura ed integrità strutturale, 43 (2018) 205-217; doi: 10.3221/igf-esis.43.16 216 figure 14: fsi [kn] vs.  comparison between rcsc [3] ( ) and en [2] ( ). results of series from cnr [20] are not included in the diagram. the trend of the curve shows an increase of  with fsi and considering the slip coefficient from tests by en [2], if the results of µm are multiplied by 1.5, the obtained valued are in line with the coefficient by rcsc [3]. fig. 15 shows all the single results with the test method as in en [2]. the higher values were found maximizing the roughness of the surfaces and the tightening torque. figure 15: fsi [kn] vs. i for the en [2] method. conclusion he results of comparison and experimental tests on coating products regarding the evaluation of the slip factor for only sandblasted and sandblasted-coated surfaces are reported. considering test for the determination of the slip factor, en [2], contrary to rcsc [3] which assume a value  = m, adopts the characteristic value k taking into account the standard deviation within the tests and in conclusion the mean value m is reduced by about 10% also considering that the partial safety factor applied to the design slip resistance is 1.25; 1.5 for rcsc [3]. the improvement regards the following aspects: an increase in the i value was observed with the percentage of zinc in the coating component. also an increase was obtained applying a greater tightening torque that is, on the other hand, considering in the calculation a greater k-factor. alternatively, using grease between the screw and the nut, to consider a tightening force 1.1ms is suggested. making a comparison between rcsc [3] and en [2] in terms of experimental applied force fsi vs. , for both american and european standards,  increases with fsi, but with rcsc [3] a greater value of  is observed than that of en, of about 10%, because test setup and the method to calculate  are different. in term of m the ratio is 1.5. the trend of fsi respect i shows an increase in the slip factor with the applied force, thus to obtain a greater slip factor it is necessary to increase the roughness of the surfaces and the tightening torque. t e. maiorana et alii, frattura ed integrità strutturale, 43 (2018) 205-217; doi: 10.3221/igf-esis.43.16 217 as observed in the previous point, to evaluate exactly the strength of the friction joint and to establish an admissible standard deviation on the k-factor is suggested, to reduce the admissible standard deviation on the kfactor and the safety coefficient on preloading force. finally, the discussion underlines the necessity to increase the applied force, to harmonize the safety coefficients and to review the design rules, justifying the adoption of a slip factor value in the calculation depending by the allowable displacement of the bolt inside the hole. acknowledgments he valuable contribution of dr. francesco mutignani to the discussion is acknowledged. references [1] en 1993-1-8:2005. design of steel structures, cen, brussels, belgium. [2] en 1090-2:2011. execution of steel structures and aluminum structures, cen, brussel, belgium. [3] rcsc. specification for structural joints using high-strength bolts, aisc, (2014), chicago. [4] astm a325 standard specification for structural bolts, steel, heat treated, 120/105 ksi minimum tensile strength (2016). [5] en 14399:2005. high-strength structural bolting assemblies for preloading, cen, brussels, belgium. [6] iso 8501-1:2007. preparation of steel substrates before application of paints and related products. visual assessment of surface cleanliness. [7] eccs. slip factors of connections with h.s.f.g. bolts, bolted and welded connection, publication n.37 (1984), brussels, belgium. [8] kulak, g.l., fisher, j.w., struik, j.h., guide to design criteria for bolted and rivet joints, 2nd ed., new york, john wiley & sons, (1987). [9] maiorana, e., pellegrino, c., comparison between eurocodes, north american and main international codes for design of bolted connections in steel bridges, journal of bridge engineering, 18(12) (2013) 1298-1308. [10] cruz, a., simões, r., alves, r., slip factor in slip resistant joints with high strength steel, journal of constructional steel research, 70 (2012) 280-288. [11] heistermann, c., veljkovic, m., simões, r., rebelo, c., simões da silva, l., design of slip resistant lap joints with long open slotted holes, journal of constructional steel research, 82 (2013) 223-233. [12] annan, c.-d., chiza, a., characterization of slip resistance of high strength bolted connections with zinc-based metallized faying surfaces, engineering structures, 56 (2013) 2187-2196. [13] annan, c.-d., chiza, a., slip resistance of metalized-galvanized faying surfaces in steel bridge construction, journal of constructional steel research, 95 (2014) 211-219. [14] latour, m., piluso, v., rizzano, g., experimental analysis on friction materials for supplemental damping devices, construction and building materials, 65 (2014) 159-176. [15] pavlović, m., heistermann, c., veljković, m., pak, d., feldmann, m., rebelo, c., simões da silva, l., friction connection vs. ring flange connection in steel towers for wind converters, engineering structures, 98 (2015) 151-162. [16] ferrante cavallaro, g., francavilla, a., latour, m., piluso, v., rizzano, g., experimental behaviour of innovative thermal spray coating materials for freedam joints, composites part b: engineering, 115 (2017) 289-299. [17] li, j., he, q., zhang, k., lin, z., ding, m., ju, j., slipping coefficient study of frictional high strength bolt joint, computer modelling & new technologies, 18(12d) (2014) 133-137. [18] huang, y.-h., wang, r.-h., zou, j.-h., gan, q., finite element analysis and experimental study on high strength bolted friction grip connections in steel bridges, journal of constructional steel research, 66 (2010) 803-815. [19] federal highway administration. interlaboratory variability of slip coefficient testing for bridge coatings, publication n. fhwa-hrt-14-093 (2014). [20] cnr uni 10011:1997. steel structures. instructions of design, construction, testing and maintenance (in italian). [21] en 10025:2004. hot rolled products of structural steels, cen, brussels, belgium. 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can be opened with acrobat and adobe reader 5.0 and later.) >> /namespace [ (adobe) (common) (1.0) ] /othernamespaces [ << /asreaderspreads false /cropimagestoframes true /errorcontrol /warnandcontinue /flattenerignorespreadoverrides false /includeguidesgrids false /includenonprinting false /includeslug false /namespace [ (adobe) (indesign) (4.0) ] /omitplacedbitmaps false /omitplacedeps false /omitplacedpdf false /simulateoverprint /legacy >> << /addbleedmarks false /addcolorbars false /addcropmarks false /addpageinfo false /addregmarks false /convertcolors /converttocmyk /destinationprofilename () /destinationprofileselector /documentcmyk /downsample16bitimages true /flattenerpreset << /presetselector /mediumresolution >> /formelements false /generatestructure false /includebookmarks false /includehyperlinks false /includeinteractive false /includelayers false /includeprofiles false /multimediahandling /useobjectsettings /namespace [ (adobe) (creativesuite) (2.0) ] /pdfxoutputintentprofileselector /documentcmyk /preserveediting true /untaggedcmykhandling /leaveuntagged /untaggedrgbhandling /usedocumentprofile /usedocumentbleed false >> ] >> setdistillerparams << /hwresolution [2400 2400] /pagesize [612.000 792.000] >> setpagedevice microsoft word numero_61_art_15_3472.docx m. s. baharin et alii, frattura ed integrità strutturale, 61 (2022) 230-243; doi: 10.3221/igf-esis.61.15 230 focused on: failure analysis of materials and structures observing the simulation behaviour of magnesium alloy metal sandwich panel under cyclic loadings m. s. baharin, s. abdullah department of mechanical and manufacturing engineering, faculty of engineering and built environment, universiti kebangsaan malaysia, 43600 ukm bangi, selangor, malaysia mbsbshamsul@gmail.com, shahrum@ukm.edu.my n. md nor civil engineering studies, universiti teknologi mara, cawangan pulau pinang, 13500 permatang pauh, pulau pinang, malaysia ida_nsn@uitm.edu.my m. k. faidzi, a. arifin, s. s. k. singh department of mechanical and manufacturing engineering, faculty of engineering and built environment, universiti kebangsaan malaysia, 43600 ukm bangi, selangor, malaysia khairul.faidzi@gmail.com, azli@ukm.edu.my, salvinder@ukm.edu.my abstract. this study aims to investigate the delamination effect of a metal sandwich panel using a four-point bending simulation under continual spectrum loading. the most recent core designs of the sandwich panel have a cavity that can increase vulnerability in terms of bonding strength under constant cyclic loading. the sandwich panel is simulated under constant cyclic loading using different core design configurations, which are rounded dimple, hemispherical dimple, and smooth surface core design. there are two types of conditions used; no pre-stress and pre-stress loads with variable stress ratios based on gerber stress life theory. results showed that dimple core design enhanced mechanical behaviour and fatigue life performance about 33% and 5%, respectively, compared to the sandwich panel with a smooth surface core design. it is highlighted that modification on the surface of core design could be beneficial to enhance the bonding strength performance of sandwich panels and prevent early delamination under extreme conditions such as constant cyclic loading. this study is beneficial to enhance the bonding strength for sandwich panels against extreme conditions such as high impact load and continuous cyclic load. keywords. computational analysis; cyclic loading; fatigue life; magnesium alloy; sandwich panel. citation: baharin, m. s., abdullah, s., md nor, n., faidzi, m. k., arifin, a., singh, s. s. k., evaluating metal sandwich panel with mg alloy as core under constant cyclic stress with simulation approach, frattura ed integrità strutturale, 61 (2022) 230-243. received: 14.02.2022 accepted: 04.04.2022 online first: 24.05.2022 published: 01.07.2022 copyright: © 2022 this is an open-access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. https://youtu.be/yh7uoiob3bc m. s. baharin et alii, frattura ed integrità strutturale, 61 (2022) 230-243; doi: 10.3221/igf-esis.61.15 231 introduction ver the last few decades, researchers have studied sandwich panels with different parameters such as using honeycomb core, the number of core layers used, and their fatigue behaviour and applications [1–4]. wang et al.’s studies of sandwich panels in industries where each kilogramme of materials costs a lot of money, sandwich panels have become one of the most efficient ways to achieve the highest bending stiffness and strength-to-weight ratios in structural components [5]. they are made of two thin, rigid, high-strength facing skins linked by a thick, light core attached using a strong structural adhesive, capable of transmitting loads [6]. instead of traditional materials like steel and aluminium, hybrid material structures have been considered by the automotive industry [7] in sandwich panel applications as they will enhance their mechanical performance. the use of lightweight core, for example, mg alloy, to separate the facing skins will also increase the moment of inertia with minimal increase of weight resulting in a structure that can withstand stresses [8]. the combination of magnesium alloy and steel is gaining popularity among the metal combination concept because magnesium alloy density is much lower at 1.35-1.85 g/cm3, about two-thirds than aluminium alloy density or a third of steel density [9,10]. compared to other conventional structural materials like steel and aluminium, magnesium has a lesser corrosion resistance [11] and viability [12,13] for sandwich panels, however, failures like delamination are likely to occur due to poor transverse tensile and interlaminar shear strengths in comparison to their in-plane qualities while also developing internal delamination damage but not evident to the human eye [14]. to create a -functioning and safe structure, it is crucial to identify delamination on the sandwich panel as it will also be the reason for the composite materials' rigidity and to reduce long-term performance [14,15]. although many components possess elastic cycle stress, plastic deformations are caused by stress concentration resulting in a loss in fatigue life. therefore, this study focuses on the mechanical behaviour of a laminated composite plate made of ar500 steel (face sheets), epoxy, and az31b magnesium alloy (main core) using four-point bending under constant cyclic loading on three sandwich panels designated as sp-1, sp-2, and sp-3. sp-1 is a sandwich panel with a rounded dimple. sp-2 is a sandwich panel with a hemispherical dimple on the surface of the magnesium alloy core while the surface of the magnesium alloy core for sp-3 is a solid core. since the computational approaches based on the finite element method (fem) have been exclusively used for the past few years to simulate the mechanical behaviour of a structure [16] and compare computational results with experiments [10,17], computational analysis was used in this study to simulate the geometrical sandwich panel and modelled under static and fatigue life theories under constant stress conditions to assess fatigue behaviour of the proposed sandwich panel with various stress ratios. this computational analysis facilitated a considerable early identification of delamination processes encountered by the three-dimensional geometrical metal sandwich panel. it showed the importance of core design when the behaviour of delamination was observed at the bonding area of the sandwich panel and how total deformation and stress distribution were related to the fatigue life assessment. materials and methods he whole experiment was simulated and the default material parameters in the finite element software programme database were chosen, such as young's modulus, poisson ratio, shear modulus, yield strength, tensile strength, and elongation for ar500 steel, az31b magnesium alloy [18,19], and epoxy resin and hardener [20]. fig. 1 shows the process flow of the sandwich panel simulation in this study. with the help of finite element modelling software, a geometrical model of a metal sandwich panel was created. the numbers of elements and nodes for sp-1 were 45418 and 103419, sp-2 were 15156 and 54227, and sp-3 were 10164 and 56795 with the boundary condition of four-point bending under loading condition with and without pre-stress with variable stress ratios. as shown in fig 1, the gerber’s mean stress correction was used instead of goodman or soderbeg because during the experiment, it served as a marker for the area below the point of failure based on the gerber’s parabola line to determine the lowest fatigue life limit possible [21] and it was also suitable for ductile materials [22]. besides, the negative mean stress was not bound by both soderberg and goodman's mean stress theories [22] which made it unsuitable for this study due to the use of negative mean stress in the fatigue analysis. as illustrated in fig. 2, each plate is designed as a three-dimensional model and assembled to make a single-piece composite model that made up of ar500, magnesium alloy and epoxy. the epoxy adhesive is 1 mm. the total thickness is 25 mm, excluding the adhesive, following the standard similar to the body panel of a lightweight armour vehicle based on previous studies [10,23]. they were later simulated as a four-point bending test in the finite element analysis software. the designs o t m. s. baharin et alii, frattura ed integrità strutturale, 61 (2022) 230-243; doi: 10.3221/igf-esis.61.15 232 of sp-1, sp-2, and sp-3 are shown in tab. 1, fig. 3, and fig. 4 with dimensions based on previous studies [13]. based on fig. 4, the diameter is 6 mm to match the 3 mm depth with sp-1. figure 1: the process flow fatigue life stress distribution and deformation of sandwich panel. core arrangement plate dimension (h × w), mm dimple thickness, mm dimple diameter, mm ar500-rounded dimple core-ar500 [sp-1] 180 × 40 3 10 ar500-hemispherical dimple core-ar500 [sp-2] 180 × 40 3 6 ar500-solid core-ar500 [sp-3] 180 × 40 table 1: configuration of a sandwich panel for simulation. m. s. baharin et alii, frattura ed integrità strutturale, 61 (2022) 230-243; doi: 10.3221/igf-esis.61.15 233 figure 2: a 2-dimensional view of geometrical sandwich panel, dimension in mm. (a) (b) figure 3: details for sp-1 a) top view b) side view, dimension in mm. (c) (d) figure 4: details for sp-2 a) top view b) side view, dimension in mm. static load analysis for the static load experiment, stress distribution (von mises stress) and total deformation [24] results for the whole body and bonding area of the panel were analysed. the sandwich panel's loading was chosen based on the percentage of az31b magnesium alloy's yield strength, 165 mpa [19], varying at 60%, 70%, 75%, 80%, and 90%. this assures the sandwich panel's safety since magnesium alloy has a lower yield strength value than ar500 steel. if the percentage of ar500 steel yield strength was used in this simulation, the structure would fail since the core was made of magnesium alloy. fatigue life analysis the geometrical sandwich panel was subjected to a constant amplitude loading for fatigue life analysis to observe fatigue behaviour and life analysis for all sandwich panels. furthermore, the four-point bending was simulated with and without pre-stresses based on the loading data history. the fatigue life performance of all sandwich panels was determined by this pre-conditioning and allowed for stress relief and early panel failure owing to residual stress after the panel was loaded. in this simulation. the fatigue strength factor was set to default, assuming that the material’s surfaces had no contamination and polished perfectly. the fatigue performance was compared to the total deformation and stress distribution experienced by all sandwich panels to identify the delamination mechanism and its correlations in contributing to failure under static and continual repeated loading. 10 hz of loading frequency was applied to the four-point bending test simulation with and without pre-stresses at different stress ratios. with pre-stress, the σmax values employed were -0.2, -0.4, -0.6, and -0.8. the m. s. baharin et alii, frattura ed integrità strutturale, 61 (2022) 230-243; doi: 10.3221/igf-esis.61.15 234 σmin value was still -1 resulting in stress ratio, r, value to vary at r = 5, r=2.5, r=1.67, and r=1.25. for the four-point bending test without pre-stress, the values of σmin were -0.2, -0.4, -0.6, and -0.8, and σmax = 0 for the maximum value while r was infinity. the load was applied without being stressed beforehand. eqn. (1) shows how the r is calculated with this formula in the study [25]: mim max σ -1 r =   =   = 1.25 σ -0.8      (1) results and discussion he results of the four-point bending simulation performed using a finite element software tool were examined under static and fatigue conditions. the performance of the metal sandwich panel was calculated for static analysis based on the stress distribution and total deformation experienced by the sandwich panel's bonding area. to assess the behaviour and strength of the metal sandwich panels under static loading, the two factors in the static analysis (stress distribution and deformation) were crucial to identify the effects of the core surface configuration on the performance of metal sandwich panels. as for the cyclic loading, once applied and simulated on the sandwich panel, the conditions stated earlier were critical to encourage the stress release condition and prevent failure due to stress residual on the panel. static analysis each sandwich panel's von mises stress distribution and total deformation data exhibited a nearly identical trend, but with varied maximum and lowest values as the magnesium, alloy core had different kinds of design configurations. according to fig. 5, sp-1 has a maximum von mises stress distribution difference in the bonding area of over 39.12%, while sp-2 is 30% with sp-3 at both the lowest load (32076 n) and greatest load (48114 n). the first maximum deformation difference between sp-1 and sp-3 at both lowest and highest load is over 16.25%, while sp-2 is over 3.14%. based on the percentage difference of all the geometrical model, sandwich panel that has dimple which are sp-1 and sp-2 performs better than solid core, sp-3 because it can withstand higher von mises stress at the bonding region. this means that structural integrity of the panel was increased. figure 5: maximum von mises distribution at bonding area against loading given for sp-1, sp-2, and sp-3 as shown in fig. 6, the overall deformation of the sandwich panels at the bonding area follows a similar pattern. when compared to sp-3, an increase in maximum deformation for each load provided can be deduced. the decline in core density in the dimple area contributed to the increase in maximum deformation. even though the greatest stress distribution was possessed by sp-1, sp-2 owned the least deformation with 0.221 mm, still greater compared to sp-3 (0.214 mm) ever so slightly due to the presence of dimples in sp-1 and sp-2 [13]. the von mises stress distribution for sp-1 at bonding area was 88.623 mpa at maximum and 0.294 mpa at minimum values based on fig. 7. the delamination phenomenon is shown by the contour distribution at the bonding area. the findings indicate that sp-1 and sp-2 perform 32.73% and 26.09%, respectively, better in terms of decreasing delamination risk at the 0 20 40 60 80 100 120 0 10000 20000 30000 40000 50000 60000m ax im u m v o n m is es s tr es s at b o n d in g a re a (m p a) load applied (n) sp-1 sp-2 sp-3 t m. s. baharin et alii, frattura ed integrità strutturale, 61 (2022) 230-243; doi: 10.3221/igf-esis.61.15 235 sandwich panel's bonding layer than sp-3. the simulation proves that the presence of dimples on the surface cores in sp-1 and sp-2 has enhanced the structural integrity [26] of the panel compared to solid core design because it can withstand larger amount of stress on bonding region. figure 6: total deformation (bond area) against loading given for sp-1, sp-2, and sp-3 at the bonding area figure 7: simulation result of von mises stress distribution for sp-1 with 40095 n of load at the bonding area fatigue life analysis with pre-stress in fig. 8, average fatigue life values for all sandwich panels are compared using the lowest stress ratio of 1.25 between sp3 and sp-1 first, then the comparison between sp-3 and sp-2. the percentage difference of average fatigue life between sp3 and sp-1 was 0.998% when the first load of 32076 n was applied. the difference increased to 2.76% when the final load of 48114 n was applied. the percentage difference of average fatigue life between sp-3 and sp-2 was 0.744% at the lowest load of 32076 n. the average fatigue life increased to 1.73% at the greatest load of 48114 n. sp-1 produced the highest average fatigue life of 18698.6 compared to sp-2 (1879.2). sp-3 had the lowest fatigue life value of 1847 with r = 1.25 and the highest loading of 48114 n. since both comparisons showed that sp-1 and sp-2 had better fatigue life than sp-3, it proved that the presence of dimple enhanced sandwich panel performance [26]. the coefficient of determination (r2) reflected the variance in response to the average fatigue life and load applied as presented in fig. 8. the statistic in the regression was used to measure the degree of fit of a model. the r2 value indicated how accurate the model matched the data produced [27] and it ranged between 0 and 1. to interpret the relationship between the two variables, the average fatigue life, and load applied, the higher r2 (close to 1) meant that the result was better and more reliable [28]. based on fig. 8, the simulation results are considered reliable because r2 value for all sandwich panel is close to 1. compared to r2 value of sp-2 and sp-3 which is 0.79 and 0.94, respectively, sp-1 simulation has the best results with r2 equal to 1. when r = 1.25 and a load of 37422 n were applied, the fatigue life distribution over the whole geometrical sandwich panel and at the bonding area can be observed in fig. 9. the difference was pretty large when focusing on the contour trend on the fatigue life study with pre-stress. based on fig. 9, although the overall fatigue life of the sandwich panel is high, the bonding area has a significant chunk of red contour trend at the point where stress is applied as shown in fig. 9 (b), indicating a low fatigue value. when r = 1.25, the red contour indicates a severe delamination phenomenon. due to the presence of 0 0,05 0,1 0,15 0,2 0,25 0,3 0 10000 20000 30000 40000 50000 60000 t o ta l d ef o rm at io n at b o n d o n g a re a (m m ) load applied (n) sp-1 sp-2 sp-3 m. s. baharin et alii, frattura ed integrità strutturale, 61 (2022) 230-243; doi: 10.3221/igf-esis.61.15 236 a pre-stress state before loading, the fatigue life becomes more severe, which agrees to a study made by elmushyaki [29] on a structure that exhibits greater damage when preloaded force is given. figure 8: average fatigue life against given load for all three metal sandwich panels at stress ratio, r = 1.25 (a) (b) figure 9: fatigue life distribution modelled using finite element to determine the critical region based on; (a) front view of sandwich panel geometrical body, (b) bonding area for sp-1 at stress ratio, r = 1.25 with a load of 37422n. at the greatest stress ratio with r = 5, fig. 10 shows a comparison of average fatigue life values for all sandwich panels with three different core surface designs. comparisons were made between sp-3 and sp-1 followed by sp-3 and sp-2. at a load of 32076 n, 0.166% was the difference and increased to 4.97% for the final load of 48114 n. as for the comparison between sp-3 and sp-2, it was 0.16% at the starting load of 32076 n and the differences grew to a value of 3.29% with the final load of 48114 n. it was found that sp-1 had the highest fatigue life value with an average value of 1821.7 when comparison was made between all three core design sandwich panels at the highest stress ratio of r = 5. sp-2 had the second highest value of 1783.3 seconds, and sp-3 obtained the lowest fatigue life value of 1733.3 seconds. based on fig. 10, the simulation results r² = 1,00 r² = 0,79 r² = 0,94 1700 1750 1800 1850 1900 1950 2000 0 10000 20000 30000 40000 50000 60000 a ve ra g e fa ti g u e li fe ( s) load applied (n) with r = 1.25 sp-1 sp-2 sp-3 lineare (sp-1) lineare (sp-2) lineare (sp-3) m. s. baharin et alii, frattura ed integrità strutturale, 61 (2022) 230-243; doi: 10.3221/igf-esis.61.15 237 for all the test were considered reliable since r2 value are more than 0.80 and close to 1. however, sp-1 and sp-3 has the best simulation results because r2 equal to 0.99 compared to sp-2 with r2 = 0.86. figure 10: average fatigue life against given load for all three metal sandwich panels at stress ratio, r = 5. when r = 5, the fatigue life distribution across the geometrical sandwich panel and at the bonding area is shown in fig. 11. the degree of failure for the sandwich panel under continual cyclic loading was related to the increment of stress ratio by comparing the contour trend at r = 1.25 (fig. 8). the red colour contour in fig. 11 (a) and (b), which is the critical region, indicated 0 fatigue life, which means the material failed in that area followed by debonding between the layers of the sandwich panel (delamination) [13]. the effect was visible at the bonding location, as illustrated in fig. 11 (b) by the trend of the fatigue contour. it affected that particular area because of the force given at that point due to the concept of fourpoint bending test. (a) (b) figure 11: fatigue life distribution modelled using finite element to determine the critical region based on; (a) front view of sandwich panel geometrical body, (b) bonding area for sp-1 at stress ratio, r = 5 with a load of 37422n r² = 0,99 r² = 0,86 r² = 0,99 1700 1750 1800 1850 1900 1950 2000 0 10000 20000 30000 40000 50000 60000 a ve ra g e fa ti g u e li fe ( s) load applied (n) with r = 5 sp-1 sp-2 sp-3 lineare (sp-1) lineare (sp-2) lineare (sp-3) m. s. baharin et alii, frattura ed integrità strutturale, 61 (2022) 230-243; doi: 10.3221/igf-esis.61.15 238 fatigue life analysis without pre-stress even though the value obtained from the sandwich panel with various mg alloy core designs had identical patterns, the highest and lowest averages of fatigue life for all three differed from one another and the four-point bending test was without pre-stress. the comparison of the average fatigue life differences was made between sp-1, sp-2, and sp-3 as shown in fig. 12. the first part of the comparison was the percentage difference between sp-3 and sp-1. no differences were found at 32076 n but increased to 4.97% for the final load of 48114 n. as for the comparison between sp-3 and sp-2, there were no differences between them with a load of 32076 n and the disparity grew to 0.025% of the difference in average fatigue life with the final load of 48114 n. since both comparisons showed that sp-1 and sp-2 had better fatigue life than sp-3, proving the presence of dimple enhanced sandwich panel performance [13]. based on fig. 11, the simulation results for all the test were considered reliable since r2 value are close to 1. however, sp-1 has the best simulation results since r2 equal to 0.80 which is closest to 1 as compared to sp-2 and sp-3 with r2 = 0.73 and r2 = 0.74. figure 12: average fatigue life against given load for sp-1, sp-2, and sp-3 at σmin = −0.2. (a) (b) figure 13: fatigue life distribution modelled using finite element to determine the critical region based on; (a) front view of sandwich panel geometrical body, (b) bonding area for sp-2 at σmin = −0.2 with a load of 37422n r² = 0,80 r² = 0,73 r² = 0,74 1996 1997 1998 1999 2000 0 10000 20000 30000 40000 50000 60000 a ve ra g e fa ti g u e li fe ( s) load applied (n) at σmin = −0.2 sp-1 sp-2 sp-3 lineare (sp-1) lineare (sp-2) lineare (sp-3) m. s. baharin et alii, frattura ed integrità strutturale, 61 (2022) 230-243; doi: 10.3221/igf-esis.61.15 239 the fatigue life distribution across the geometrical sandwich panel structure and at its bonding demonstrated no failure indication when σmin = −0.2, as shown in fig. 13. the majority of the contour trend was blue, indicating that the sandwich panel's fatigue life was 2000 cycles before failing with the lowest minimum value of life at 71 cycles at the skin's surface of ar 500, which means the results agreed with the previous study [29] on how preloaded force exhibited greater damage on structure and vice versa. based on fig. 14, comparisons of the average fatigue life were carried out between sp-1, sp-2, and sp-3 with σmin = −0.8. the first part of the comparison was the percentage differences of average fatigue life between sp-3 and sp-1, which was 0.194% at 32076 n followed by 0.332% of the difference with 37422 n of load. it exhibited a 0.810% difference in average fatigue life value at 40095 n load. there was an increase of percentage difference to 2.71% at 42768 n but decreased to 2.56% for the final load of 48114 n. as for the comparison between sp-3 and sp-2, it was 0.347% at the starting load of 32076 n. next, it had a difference of 0.259% with a load of 37422 n. it had a difference of 0.332% at 40095 n of load and when the load increased to 42768 n, the disparity grew to 1.69%. however, the percentage difference decreased to 0.995% of average fatigue life with the final load of 48114 n. based on fig. 14, it can be concluded that sp-1 and sp-2 had better fatigue life than sp-3, proving the presence of dimple enhanced sandwich panel performance [26]. since the r2 value for each sandwich panel in fig. 14 is higher than 0.8, the simulation results for all the test were considered reliable. however, the best simulation results are sp-1 with r2 = 1 as compared to r2 value for sp-2 and sp-3 which is 0.99 and 0.94, respectively. figure14: average fatigue life with given load for all three metal sandwich panels at σmin = −0.8 when σmin = −0.8, the fatigue life distribution across the geometrical sandwich panel and at the bonding area is visible, as shown in fig. 15. the majority of the contour colours were blue and lighter hues of blue when stress was applied, indicating the geometrical sandwich panel's maximum fatigue life. a very tiny section of the bonding region indicated a minimum value of fatigue life [17]. the results were different from figs. 12 and 13 due to different values of minimum stress amplitude, σmin used in the stress ratio calculation which can be referred to eqn. (1)[3]. the σmin used for simulation in fig.14 is higher than σmin used for simulation in fig. 12 which cause the reduction of sandwich panel fatigue life as showed in figs. 14 and 15. further issues on the failure trend under both static and cyclic simulations based on the trend analysis of the sandwich panel thoroughly explained in figs. 5 to 15, it was discovered that the mechanical performance and fatigue failure of sandwich panels can be accelerated by surface modification and material type and this has also been discussed by faidzi et al. [26]. this study focused on evaluating three types of magnesium alloy with various core designs joined by steel and produced a distinct sandwich panel performance that gave various von mises stress distribution, permanent deformation, and average fatigue life. it was feasible to make a sandwich panel out of nonhomogeneous materials [10] even though the majority of sandwich panels were made of homogeneous material [13,30]. the principle was nearly equivalent to the use of a honeycomb composite structure, which reduces the laminated composite structure mass while still providing high special stiffness, special strength, and durability [16]. r² = 1,00 r² = 0,99 r² = 0,941800 1850 1900 1950 2000 0 10000 20000 30000 40000 50000 60000 a ve ra g e fa ti g u e li fe ( s) load applied (n) at σmin = −0.8 sp-1 sp-2 sp-3 lineare (sp-1) m. s. baharin et alii, frattura ed integrità strutturale, 61 (2022) 230-243; doi: 10.3221/igf-esis.61.15 240 furthermore, palomba et al. [31] had also investigated the collapse response of an aluminium honeycomb sandwich panel under fatigue bending and discovered that the span spacing affected the deformation mode owing to skin tension. the core shearing was a prominent failure mechanism. it has been demonstrated that core structures with a large cavity area carried out in the present study were prone to collapsing and deforming, which impacted the bonding integrity of sandwich panels. it has been enhanced by beden et al. [21], stating that surfaces had a great influence on the fatigue behaviour of a material, as well as the situation of this study which compared three surfaces of magnesium alloy plate designs the stress value of von mises, deformation, and the average fatigue life of varying averages. (a) (b) figure 15: fatigue life distribution modelled using finite element to determine the critical region based on; (a) front view of sandwich panel geometrical body, (b) bonding area for sp-1 at σmin = −0.8 with a load of 37422n conclusion he results of this investigation show that the toughness and stress strength of a sandwich panel is boosted by the presence of a dimple. both sp-1 and sp-2 demonstrate similar trends in this study at the bonding region of a nonhomogenous sandwich panel which possesses a greater distribution of von mises stress. even though the dimpled core design has a minor increase for permanent deformation compared to the smooth core surface, deformation is less than 30% under static load which is within an acceptable limit. the average fatigue lifetime values for sp-2 and sp-3 are almost identical at the highest stress ratio of 5 and highest loading of 48114 n (1821.7 and 1783.3 – both with pre-stress), which is superior to sp-1 (1733.3 – with pre-stress). the data prove that sandwich panel’s mechanical performance improves by the presence of dimple on the surface core while the delamination phenomenon that occurs on the bonding area can be minimised by introducing a dimple design on the core because it offers a larger surface area for the adhesive material to connect non-homogeneous sandwich panel materials which indirectly reduce the overall weight. finally, without integrating a sophisticated failure modelling, the study recommends detection analysis for early delamination with the computational technique for three-dimensional sandwich panels. t m. s. baharin et alii, frattura ed integrità strutturale, 61 (2022) 230-243; doi: 10.3221/igf-esis.61.15 241 acknowledgement he authors would like to acknowledge the computational facilities support provided by universiti kebangsaan malaysia funding his research was funded by universiti kebangsaan malaysia (gup-2021-016). conflicts of interest he authors declare no conflict of interest. author contributions he following contributions to this work were made by the following authors ‐ conceptualization, s.abdullah, m.s.baharin; investigation, m.s.baharin, m.k.faidzi, and s.abdullah; resources, s.abdullah, and a.arifin; supervision, s.abdullah; software, s.s.k singh; writing‐original draft preparation, m.s.baharin, s.abdullah; writing‐review and editing, s.abdullah, n. md nor. data availability statement he processed data/material required to reproduce these findings cannot be shared at this time as the data also form part of an ongoing study. reference [1] wang, j., shi, c., yang, n., sun, h., liu, y., song, b. (2018). strength, stiffness, and panel peeling strength of carbon fiber-reinforced composite sandwich structures with aluminum honeycomb cores for vehicle body, compos. struct., 184, pp. 1189–1196, doi: 10.1016/j.compstruct.2017.10.038. [2] palomba, g., epasto, g., crupi, v., guglielmino, e. (2018). single and double-layer honeycomb sandwich panels under impact loading, int. j. impact eng., 121, pp. 77–90, doi: 10.1016/j.ijimpeng.2018.07.013. [3] ma, m., yao, w., jiang, w., jin, w., chen, y., li, p. (2020). fatigue behavior of composite sandwich panels under three point bending load, polym. test., 91, pp. 106795, doi: 10.1016/j.polymertesting.2020.106795. [4] castanie, b., bouvet, c., ginot, m. (2020). review of composite sandwich structure in aeronautic applications, compos. part c open access, 1, pp. 100004, doi: 10.1016/j.jcomc.2020.100004. [5] wang, z. (2019). recent advances in novel metallic honeycomb structure, compos. part b eng., 166, pp. 731–741, doi: 10.1016/j.compositesb.2019.02.011. [6] faidzi, m.k., abdullah, s., abdullah, m.f., azman, a.h., hui, d., singh, s.s.k. (2021). review of current trends for metal-based sandwich panel: failure mechanisms and their contribution factors, eng. fail. anal., 123, pp. 105302, doi: 10.1016/j.engfailanal.2021.105302. [7] vignesh, n.j., hynes, n.r.j. (2018). thermal analysis of friction riveting of dissimilar materials, aip conf. proc., 1953, t t t t t m. s. baharin et alii, frattura ed integrità strutturale, 61 (2022) 230-243; doi: 10.3221/igf-esis.61.15 242 pp. 2022, doi: 10.1063/1.5033285. [8] sun, g., chen, d., wang, h., hazell, p.j., li, q. (2018). high-velocity impact behaviour of aluminium honeycomb sandwich panels with different structural configurations, int. j. impact eng., 122, pp. 119–136, doi: 10.1016/j.ijimpeng.2018.08.007. [9] apelfeld, a., krit, b., ludin, v., morozova, n., vladimirov, b., wu, r.z. (2017). the characterization of plasma electrolytic oxidation coatings on az41 magnesium alloy, surf. coatings technol., 322, pp. 127–133, doi: 10.1016/j.surfcoat.2017.05.048. [10] rahman, n.a., abdullah, s., abdullah, m.f., zamri, w.f.h., omar, m.z., sajuri, z. (2018). experimental and numerical investigation on the layering configuration effect to the laminated aluminium/steel panel subjected to high speed impact test, metals (basel)., 8(9), doi: 10.3390/met8090732. [11] jin, h., javaid, a. (2020). a new cladding technology to bond aluminium on magnesium, mater. sci. technol. (united kingdom), 36(10), pp. 1037–1043, doi: 10.1080/02670836.2020.1747186. [12] abdullah, m.f., abdullah, s., rahman, n.a., risby, m.s., omar, m.z., sajuri, z. (2016). improvement of high velocity impact performance of carbon nanotube and lead reinforced magnesium alloy, int. j. automot. mech. eng., 13(2), pp. 3423–3433, doi: 10.15282/ijame.13.2.2016.11.0283. [13] faidzi, m.k., abdullah, s., abdullah, m.f., singh, s.s.k., azman, a.h. (2021). evaluating an adhesive effect on core surface configuration for sandwich panel with peel simulation approach, j. mech. sci. technol., 35(6), pp. 2431–2439, doi: 10.1007/s12206-021-0514-3. [14] tian, z., yu, l., leckey, c. (2015). delamination detection and quantification on laminated composite structures with lamb waves and wavenumber analysis, j. intell. mater. syst. struct., 26(13), pp. 1723–1738, doi: 10.1177/1045389x14557506. [15] fotouhi, m., saeedifar, m., sadeghi, s., ahmadi najafabadi, m., minak, g. (2015). investigation of the damage mechanisms for mode i delamination growth in foam core sandwich composites using acoustic emission, struct. heal. monit., 14(3), pp. 265–280, doi: 10.1177/1475921714568403. [16] amulani, a., pratap, h., thomas, b. (2021). investigation of static and fatigue behavior of honeycomb sandwich structure: a computational approach, j. brazilian soc. mech. sci. eng., 43(11), pp. 2022, doi: 10.1007/s40430-021-03195-y. [17] hussain, m., khan, r., abbas, n. (2019). experimental and computational studies on honeycomb sandwich structures under static and fatigue bending load, j. king saud univ. sci., 31(2), pp. 222–229, doi: 10.1016/j.jksus.2018.05.012. [18] borrisutthekul, r., miyashita, y., mutoh, y. (2005). dissimilar material laser welding between magnesium alloy az31b and aluminum alloy a5052-o, sci. technol. adv. mater., 6(2), pp. 199–204, doi: 10.1016/j.stam.2004.11.014. [19] feng, f., huang, s., meng, z., hu, j., lei, y., zhou, m., yang, z. (2014). a constitutive and fracture model for az31b magnesium alloy in the tensile state, mater. sci. eng. a, 594, pp. 334–43, doi: 10.1016/j.msea.2013.11.008. [20] abdullah, s., abdullah, m.f., jamil, w.n.m. (2020). ballistic performance of the steel-aluminium metal laminate panel for armoured vehicle, j. mech. eng. sci., 14(1), pp. 6452–6460, doi: 10.15282/jmes.14.1.2020.20.0505. [21] beden, s.m., abdullah, s., ariffin, a.k., al-asady, n.a., rahman, m.m. (2009). fatigue life assessment of different steel-based shell materials under variable amplitude loading, eur. j. sci. res., 29(2), pp. 157–169. [22] bader, q., kadum, e. (2014). mean stress correction effects on the fatigue life behavior of steel alloys by using stress life approach theories, int. j. eng. technol. ijet-ijens, 14(04). [23] rahman, n.a., abdullah, s., abdullah, m.f., omar, m.z., sajuri, z., zamri, w.f.h. (2018). ballistic limit of laminated panels with different joining materials subjected to steel-hardened core projectile, int. j. integr. eng., 10(5), pp. 8–14, doi: 10.30880/ijie.2018.10.05.002. [24] upreti, s., singh, v.k., kamal, s.k., jain, a., dixit, a. (2019). modelling and analysis of honeycomb sandwich structure using finite element method, mater. today proc., 25, pp. 620–625, doi: 10.1016/j.matpr.2019.07.377. [25] zakaria, k.a., abdullah, s., ghazali, m.j. (2016). a review of the loading sequence effects on the fatigue life behaviour of metallic materials, j. eng. sci. technol. rev., 9(5), pp. 189–200, doi: 10.25103/jestr.095.30. [26] faidzi, m.k., abdullah, s., abdullah, m.f., azman, a.h., singh, s.s.k., hui, d. (2021). computational analysis on the different core configurations for metal sandwich panel under high velocity impact, soft comput., 25(16), pp. 10561– 10574, doi: 10.1007/s00500-021-06015-6. [27] akossou, a.y.j. (2013). impact of data structure on the estimators r-square and adjusted r-square in linear regression., int. j. math. comput. [28] kasuya, e. (2019). on the use of r and r squared in correlation and regression, ecol. res., 34(1), pp. 235–236, doi: 10.1111/1440-1703.1011. [29] elmushyakhi, a. (2019). collapse mechanisms of out-of-plane preload composite sandwich beams under in-plane m. s. baharin et alii, frattura ed integrità strutturale, 61 (2022) 230-243; doi: 10.3221/igf-esis.61.15 243 loading, j. build. eng., 26, pp. 100875, doi: 10.1016/j.jobe.2019.100875. [30] lee, w.g., kim, j.s., sun, s.j., lim, j.y. (2018). the next generation material for lightweight railway car body structures: magnesium alloys, proc. inst. mech. eng. part f j. rail rapid transit, 232(1), pp. 25–42, doi: 10.1177/0954409716646140. [31] palomba, g., crupi, v., epasto, g. 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can be opened with acrobat and adobe reader 5.0 and later.) >> /namespace [ (adobe) (common) (1.0) ] /othernamespaces [ << /asreaderspreads false /cropimagestoframes true /errorcontrol /warnandcontinue /flattenerignorespreadoverrides false /includeguidesgrids false /includenonprinting false /includeslug false /namespace [ (adobe) (indesign) (4.0) ] /omitplacedbitmaps false /omitplacedeps false /omitplacedpdf false /simulateoverprint /legacy >> << /addbleedmarks false /addcolorbars false /addcropmarks false /addpageinfo false /addregmarks false /convertcolors /converttocmyk /destinationprofilename () /destinationprofileselector /documentcmyk /downsample16bitimages true /flattenerpreset << /presetselector /mediumresolution >> /formelements false /generatestructure false /includebookmarks false /includehyperlinks false /includeinteractive false /includelayers false /includeprofiles false /multimediahandling /useobjectsettings /namespace [ (adobe) (creativesuite) (2.0) ] /pdfxoutputintentprofileselector /documentcmyk /preserveediting true /untaggedcmykhandling /leaveuntagged /untaggedrgbhandling /usedocumentprofile /usedocumentbleed false >> ] >> setdistillerparams << /hwresolution [2400 2400] /pagesize [612.000 792.000] >> setpagedevice microsoft word numero 24 articolo 2 s.v. smirnov, frattura ed integrità strutturale, 24 (2013) 7-12; doi: 10.3221/igf-esis.24.02 7 special issue: russian fracture mechanics school the healing of damage after the plastic deformation of metals s.v. smirnov institute of engineering science, ural branch of russian academy of sciences 34 komsomolskaya st., ekaterinburg, 620219, russia. svs@imach.uran.ru abstract. the general regularities of damage healing during the annealing after cold deformation of metal materials are presented in this paper. in categories of damage mechanics the kinetic equations of damage healing during recovery and recrystallization are formulated. diagrams of damage healing for some metal alloys are presented. the example of use of investigation results for optimization of industrial technology of pipes drawing is presented. keywords. deformation damage; metal forming; fracture; healing of damage; prediction of fracture. introduction ccording to the current conception of metal physics, the fracture of metal materials is not a one-act catastrophic phenomenon, but a regular process of appearance and development of defects, which is in mechanics referred to as damage accumulation (plastic loosening, damageability, cracking, etc.). pure brittle damage is possible only in metals with a large covalent component in the interatomic bond. the form and shape of defects, as well as the velocity of their propagation, depend on metal behaviour and thermomechanical loading conditions; however, the active role of plastic deformation is invariant here, and it reveals itself on the macro or micro scale. so the technological cold plastic deformation of metal (rolling die-forging, etc.) from the first stages is accompanied by microscopic defects of continuity. the development of damage with the accumulation of deformation can result in the appearance of macroscopic defects or even the division of the body under deformation into separate parts, i.e. in defective products: this is definitely inadmissible. macroscopic defects can be revealed easily (external by visual observation, internal by an introscopy method), but correction is either impossible or requires that the defective bulk of the metal should be removed. one of the methods for avoiding macro-damage is multi-stage deformation, with intermediate annealing at the end of every stage, which provides metal softening and, above all, the restoration of metal plasticity (i.e. the ability of the metal to be deformed without fracture). the amount of deformation in a separate stage is established intuitively, proceeding from one's practical experience. to understand the technology of manufacturing cold-deformed products with annealing, it is necessary to give a mathematical description (within the above-mentioned model) of how the restoration of the reduction of micro-damage proceeds under annealing. as distinct from macro-defects, micro-discontinuities are harder to detect under service conditions. industry lacks the means of checking micro-flaws, so, therefore all metal products have micro-flaws which can affect the efficiency of machine parts. it has been ascertained hat they influence fatigue life [1]. therefore it is important to study the mechanisms of eliminating (or healing) micro-flaws, i.e. the mechanisms for the restoration of the margin of metal plasticity by heat treatment and the ways of making it more efficient. this is the subject matter of the present paper. a http://dx.medra.org/10.3221/igf-esis.24.02&auth=true http://www.gruppofrattura.it s.v. smirnov, frattura ed integrità strutturale, 24 (2013) 7-12; doi: 10.3221/igf-esis.24.02 8 damage model he deformational criteria of damage and the phenomenological theories based on a certain hypothesis of damage accumulation are widespread in mechanics [1-8]. in the description of damage under developed plastic conditions, the deformational approach is also popular (see, for example, the survey found in [9]). historically, the problem of damage in plastic deformation was initially considered in terms of technological interests on the basis of empiric criteria and fracture models. this approach allowed some simple applied problems to be solved, but hampered the study of the general rules of metal damage under the complex stress-strain state. in mechanics, the progress in the development of the notion of metal damage under plastic deformation is connected with the appearance of kinetic theories of dispersed fracture (damage mechanics) [1, 4-12]. the process of damage under plastic deformation can be represented in a different way in terms of the damage mechanics as  1 2, , ,...... d f s s d    (1) where  is a characteristic of metal damage; s1 and s2 are thermomechanical loading parameters depending on the loading conditions. before loading  = 0 while  = 1 when the fracture happens. intermediate values of  characterize a level of development of micro-defects. the kinetic equation eq.1 was first proposed by l.m. kachanov [2, 3] to describe damage in creep, and was later used by a number of authors to describe damage under plastic deformation. the most well-known model of metal damage under plastic deformation to be used for making practical calculations is the linear model authored by v. l. kolmogorov [1, 4, 7] 1 f d d     (2) where λf is metal plasticity defined as limiting (at the instant of fracture) accumulated amount of shear strain λ in deformation under constant stress state characterized by the stress state index k1 and the lode-nadai parameter k2: 1 3 s k    ; 2 1 32 1 3 2 k          (3) where  = (1+2+3 )/3 is mean normal stress; 1,2,3 are main normal stresses; s is equivalent stress. note that in the literature there is no consensus on the form of the kinetic equation, and it is generally chosen by authors on the basis of hypothetical ideas or published fragments of metal-physic research data. therefore in this paper we will use an adaptive model of damage accumulation [12, 15]. this model has been formulated from the analysis of experimental data on changes in metal density under plastic deformation and heat treatment after plastic deformation. a general adaptive model of damage was formulated to describe damage accumulation under conditions of the experimental stepwise change in the stress-strain state, at a later date model was developed in some others forms. when the stress state changes, the rate of damage variation on the adaptation portion is evaluated as follows:   3 2 1 1 1 1 1 1i с c k a f d c e d                  (4) where δk1i is the increment of the stress state index at i-stepwise of loading; λ = 0…λа is a current amount of shear strain on the adaptation portion; λа is the length of the adaptation portion; с1, с2 and с3 are empiric factors. when the direction of deformation changes, the rate of damage accumulation decreases, and on the adaptation portion it can be determined by the formula     5 6 14 1 11 1 c c ii i fi d c e d           (5) where  is the angle characterizing the change in the loading path in ilyushin’s phase space of deformations, which can be taken as a parameter for the quantitative evaluation of deformation non-monotonicity; i-1 is the damage on the portion t http://dx.medra.org/10.3221/igf-esis.24.02&auth=true http://www.gruppofrattura.it s.v. smirnov, frattura ed integrità strutturale, 24 (2013) 7-12; doi: 10.3221/igf-esis.24.02 9 preceding the i-th change in the direction of deformation; с5, с6 and с7 are empirical coefficients. the linear model and adaptive model yield identical results at the simple monotonic deformation. investigation technique o investigate the general regularities of damage healing during the annealing after cold deformation was the purpose of this paper. notice that the restoration of the margin of plasticity in metals alter cold deformation has been studied for a number of years, the results being published in [5, 7, 13, 14]. the following technique [13, 14] has been developed for solving this problem (fig. 1). figure 1: to definition of the damage healing under annealing after deformation tests are performed on metal, with plasticity f = f (k1, k2) already known. test specimens undergo different amounts of plastic strain 0, each specimen being deformed to different amounts of damage 0. therefore, all the specimens undergo annealing in accordance with the chosen regime (t is temperature and t is annealing duration). damage decrease by the value δ takes place in annealing. after annealing once again, all the specimens undergo plastic deformation in the same direction up to fracture. value of δ for each specimen can be calculated from a facture criterion 0 δ + 1 = 1 (6) where:   0 0 0 f d k      ;   0 1 0 1 p d k         0 = 23 ln(d0/d1); 2 = 23 ln(d1/df); d0, d1 and df are the initial diameter, diameter before annealing and diameter after fracture of specimens. the stress state index for cylindrical specimens is calculated as [4, 8]  3  1 4 d k r       (7) where  d r  is a bridgman’s parameter which characterizes a neck form of specimen. results and discussion n example of the damage-time history for low-carbon 0.2%c steel at a temperature of 600°c is shown in fig 2. the lower curve  = 0 illustrated that the annealing of the blank to be deformed, for example, of hot-rolled metal, can lead to higher plasticity due to the healing of the micro-damage that appears in the hot rolling stage. the curves have three distinctive parts: ab is a rapid exponential decrease of damage due to a recovery processes; вс is a considerable deceleration (and even stopping) of healing due to incubation period of the recrystallization; and cd is further acceleration of the process due to a recrystallization. t a http://dx.medra.org/10.3221/igf-esis.24.02&auth=true http://www.gruppofrattura.it s.v. smirnov, frattura ed integrità strutturale, 24 (2013) 7-12; doi: 10.3221/igf-esis.24.02 10 figure 2: damage healing during annealing (at 6000c) of carbon steel 0.2%c. a decrease of damage due to a recovery processes can be described by the equation  0 2 0 exp 2 ln rvrv rv t t t t            (8) where trv is recovery period, rv is the bottom limit level of healing of the damage due to the recovery. figure 3: diagrams of damage healing of some metal alloys: titanium alloys containing different amount of al and mn (1 – 0.8%аl + 0.8%мn; 2 – 1.5%al +1%мn; 3 – 3.5%al + 1.5%мn); 4 low-alloyed cr; 5 – cr + 35%fe. a decrease of damage due to a recrystallization processes can be described by the equation   0 0 exp k rc rv rc rc rc rc t t b t t                 (9) where trc is duration of the incubation period, rc is the bottom limit level of healing of the damage due to the recrystallization. fig. 3 shows diagrams illustrating the degree of damage healing for some alloys in coordinates (0, δ). on value of the amount of δ one can estimate the completeness of the healing of micro-defects appearing in the pre-load stage. (bear in mind, if δ = 0 the healing is complete, whereas if all the micro defects remain in the metal). healability is different for different alloys. recrystallization annealing leads to the complete healing of deformation damage if it is less than some value ω*. when ω* < ω0 < ω** there is partial damage healing, and a certain part of deformational defects remains in the metal. the researches executed by sem technique, showed that at this stage defects are micro pores (fig. 4a). when ω0 < ω** the residual damage increases more intensively, micro pores coalesce, a pores and micro cracks is formed (fig.4b). investigations have shown that recrystallization annealing results in the healing of micro-discontinuities of sub-grain size (i.e. under 2-5 m) by intensive surface diffusion of vacancies when they are crossed by the moving intergrain boundary of the grain being recrystallized. values of ω* and ω** is different for different alloys but are usually are in ranges ω* = 0.2–0.5 and ω** = 0.6-0.8. http://dx.medra.org/10.3221/igf-esis.24.02&auth=true http://www.gruppofrattura.it s.v. smirnov, frattura ed integrità strutturale, 24 (2013) 7-12; doi: 10.3221/igf-esis.24.02 11 (a) (b) figure 4: micro pores and crack which was formed of coalescence of micro pores (are shown by arrows). material is deformed carbon steel 0.1%c after annealing (at 700°c, 1 hour). values of the initial damage: a 0 = 0.32; b –0= 0.7 (magnification х1000). calculation and analysis of damage accumulated in metal allow to optimize technology process of plastic treatment. one of number of practical examples may be given [16]. at the pervouralsk pipe-making plant (russia) pipes of carbon steel 0.45%c for poles has been produced by cold rolling. existing equipment did not allow to satisfy the demand for type product. to increase a volume of production it was offered to be produce at automated triple drawing line. one of major questions stated for engineers was a question of damage of pipes during drawing because the manufacturing line design did not suppose the intermediary annealing. theoretical calculations allowed to choose an optimal drawing parameters, when the level of residual damage was not dangerous (fig.5). the experimental investigations of the relative changes of density  and then industrial tests of theoretical results show a validity of prediction. figure 5: changes of damage  (a) and density   (b) under drawing and annealing of 0.45%c carbon steel pipes. conclusions n this work the equations of damage healing during recovery and recrystallization are in categories of damage mechanics are formulated. diagrams of damage healing for some metal alloys are defined. it is shown that recrystallization annealing leads to the complete healing of deformation damage  if it is less than some value ω*. when ω* < ω0 < ω** there is partial damage healing, and a certain part of deformational defects remains in the metal. the example of use of investigation results for optimization of industrial technology of pipes drawing is presented. acknowledgements  this work has been executed according to plan of the project number 12-т-1-1010 of the ub ras research program and was supported by a grant from the russian foundation for basic research, contract number 11-08-12083. i http://dx.medra.org/10.3221/igf-esis.24.02&auth=true http://www.gruppofrattura.it s.v. smirnov, frattura ed integrità strutturale, 24 (2013) 7-12; doi: 10.3221/igf-esis.24.02 12  the author expresses gratitude to the professor v.l. kolmogorov for initiation of this research and discussion of its results. references [1] v.g. burdukovsky, v.l. kolmogorov, b.a. migachev, j. mater. process. technol., 55 (1995) 292. [2] l.m. kachanov, docladi academii nauk sssr, otdelenie tekhnicheskih nauk 8 (1958) 67 – 65 (in russian). [3] l.kachanov, introduction to continium damage mechanics, martinus nijhoff publishers, dordrecht, (1986) 135. [4] v.l. kolmogorov, metallurgiya (1970) 232 (in russian). [5] a.a. bogatov, o.i. mizhiritsky, s.v. smirnov, metallurgiya (1984) 144 (in russian). [6] j. lemaitre, a course on damage mechanics, springer, berlin (1987). [7] v.l. kolmogorov, in: materials processing defects, s.k. gosh, m. predeleanu (eds.), elsevier, amsterdam (1995) 87 [8] v.l. kolmogorov, wear 194 (1996) 71. [9] a.g. atkins, in: an anniversary volume in honour of george r. irvin’s 90th birthday, h.p. rossmanith. a.a. balkema (eds.), brookfield, rotterdam (1997) 327. [10] m. oyane, bulletin of jsme, 15, 90 (1972) 37. [11] z.j. luo, w.h. ji, n.c. guo et alii, journal of material processing technology 30 (1992) 31. [12] s.v. smirnov, key engineering materials, 528 (2013) 61. [13] v.l. kolmogorov, s.v. smirnov, journal of the materials processing technology, 74 (1998) 83. [14] a.a. bogatov, v.l. kolmogorov, s.v. smirnov, izvestiya vuzov, chernaya metallurgiya, 12 (1978) 43 (in russian) [15] s.v. smirnov, t.v. domilovskaya, a. a. bogatov, in: materials processing defects, s.k. gosh, m. predeleanu (eds.), elsevier, amsterdam, (1997) 71. http://dx.medra.org/10.3221/igf-esis.24.02&auth=true http://www.gruppofrattura.it microsoft word numero_41_art_25.docx j. klon et alii, frattura ed integrità strutturale, 41 (2017) 183-190; doi: 10.3221/igf-esis.41.25 183 focused on crack tip fields impact of specific fracture energy investigated in front of the crack tip of three-point bending specimen j. klon, j. sobek, l. malíková brno university of technology, faculty of civil engineering, institute of structural mechanics, brno, czech republic klon.j@fce.vutbr.cz, http://orcid.org/0000-0002-9551-2185 sobek.j@fce.vutbr.cz, http://orcid.org/0000-0003-4215-1029 malikova.l@fce.vutbr.cz, http://orcid.org/0000-0001-5868-5717 s. seitl academy of sciences of the czech republic, v. v. i., institute of physics of materials, brno, czech republic and brno university of technology, faculty of civil engineering, institute of structural mechanics, brno, czech republic seitl@ipm.cz, http://orcid.org/0000-0002-4953-4324 abstract. presented study is focused on the analysis of the dependence of the specific fracture energy value on the assumed work of fracture in threepoint bending tests. specimens of different sizes and relative notch lengths are assumed in this study, in order to take into account the size effect. the three-point bending test of cracked specimens is simulated numerically by means of commercial software based on the finite element method with implemented cohesive crack model. three levels of the specific fracture energy are considered. keywords. specific fracture energy; finite element method; work of fracture; three-point bending test; loading curve. citation: klon, j., sobek, j., malíková, l., seitl, s., impact of specific fracture energy investigated in front of the crack tip of threepoint bending specimen, frattura ed integrità strutturale, 41 (2017) 183-190. received: 28.02.2017 accepted: 15.04.2017 published: 01.07.2017 copyright: © 2017 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. introduction valuation of the fracture parameters from experimental data measurement is usually accompanied by numerical calculations. this is unavoidable for example for the quasi-brittle materials, because the process of the failure is not uniform and depends on the test specimen size, shape and also on the boundary conditions during the test itself [1–10]. in the case of these materials, the so-called fracture process zone (fpz) is situated near the crack tip but its size cannot be seen like in the case of the ductile materials (by range of the plastic zone) [11]. therefore, some efforts have been made in order to identify the fpz by means of numerical calculations and investigate its impact on the fracture e j. klon et alii, frattura ed integrità strutturale, 41 (2017) 183-190; doi: 10.3221/igf-esis.41.25 184 process. currently, many numerical tools can predict fracture behaviour – but just in the case that the proper material parameter inputs are available, like the specific fracture energy. this paper focuses on the investigation of the impact of the specific fracture energy gf used in the numerical calculation on the work of fracture wf, which can be obtained by means of evaluation of the loading diagram. the idea of this research is based on the general problem of numerical testing when the current material properties obtained from the experimental testing shall be used. determination of properties like fracture energy relates to the evaluation of experimental l-d (load-deflection) curves. then the area under the curve is considered. but, if this value of fracture energy shall be used in numerical calculation, there is a restriction – it is not possible to use it due to the fact that it varies by order of the magnitude in dependence on many various factors, such as specimen size, boundary conditions and others. value of the fracture energy gf is obtained from the area under the loading curve as work of fracture wf divided by the area of the cracked ligament af (without the initial crack area), so gf = wf /(a−a0)/b. fracture failure of quasi-brittle materials occurs in fpz by micro cracking (but micro cracks are closed after final failure of the test specimen), so there is a hypothetical problem of accurate evaluation of cracked ligament area af. it is believed that this is the main reason why the value of gf (identified from various experimental testing) strongly differs. therefore, an iteration procedure how to optimize the inputs needs to be performed to include the real l–d diagram in numerical calculations. this study shows the impact of the specific fracture energy inputted into numerical software (considering the fracture failure) on the value of the fracture energy obtained from the area under the load–deflection curve (obtained from the numerical calculation). atena [12,13] nonlinear software is used for this purpose, so the results are valid mainly for it. for the verification of the impact of the specific fracture energy, the series of experimental test specimens subjected to three-point bending was chosen with the geometry displayed in fig. 1. four different sizes of test specimens were created by ch. hoover ([14], see the next section) for the purpose of validation of the size effect [1], [7]. in the paper, two approaches are compared. first uses the area under the load–deflection curve to obtain gf(num). this l–d curve is obtained from the numerical model (created in atena sw.) with the inputted value of the specific fracture energy gf (three various levels). the latter approach is the theoretical one – the value of the fracture energy is obtained from the basic formula gf(theor) = gf (a−a0) b. figure 1: schema of the three-point bending test configuration. green color indicates dimensions of the test specimen (see tab. 1) and cmod – crack mouth open displacement; blue color represents area of the ligament, where the crack propagation is indicated. j. klon et alii, frattura ed integrità strutturale, 41 (2017) 183-190; doi: 10.3221/igf-esis.41.25 185 specimen width w [mm] initial crack length a0 [mm] rel. crack length 0 = a0/w length l [mm] span s [mm] breadth b [mm] crack length a − a0 [mm] d 040 d 40 3 0.075 96 87.04 40 25 6 0.15 22 12 0.3 16 d 093 c 93 6.98 0.075 223.2 209 40 58.12 13.95 0.15 51.15 27.9 0.3 37.20 d 215 b 215 16.13 0.075 516 467.84 40 134.37 32.25 0.15 118.25 64.5 0.3 86 d 500 a 500 37.5 0.075 1200 1088 40 312.5 75 0.15 275 150 0.3 200 table 1: nominal specimen dimensions tested in [14, 15]; the estimated crack length (width of ligament) are shown in the right column. theory background atena software tena 2d finite-element method (fem) computational software [12,13] was used – the tool for modelling of structures damaged by cracks. not only the crack formation, but also their further propagation in dependence on the loading process (increase of force/deflection) can be investigated. nonlinear material models – such as fracture, plasticity and damage – are included in this sw. to simulate ‘real’ behavior of the studied material. fracture-plastic material model for simulation of quasi-brittle materials (concrete) – which is used for all configurations – combines the constitutive models for tensile (fracture) and compressive (plastic) behavior. the model of fracture is based on orthotropic formulation of smeared cracks with crack band model implementation (cohesive crack model). evaluation of loading diagrams the total amount of the dissipated energy (work of fracture wf,b) can be determined from the recorded p−d curves, or from the recalculated r−a curves (both methods give the same results). heron's formula enables to evaluate the dissipated energy from recorded p−d curves. this formula works with the area of a triangle defined by its corners in cartesian coordinate system. in this case, triangles are formed by origin of coordinate system and two consecutive points of loading diagrams [15]. the last point corresponds to the relative crack length 0.7 (α = 0.7), see the schema in fig. 2. then, the areas of all triangles are summed. recorded p−d curve can be also transformed into the r−a curve (or possibly r−, where  = a/w is the relative crack length). in this transformation, the equivalent elastic crack model [16] is employed for estimation of the current (effective) crack length a at an arbitrary stage of the fracture process (this is the way how to identify the point, when the crack reached the relative length 0.7, as mentioned above). the crack length a is determined from the difference between the initial compliance of the specimen with the crack of length a0 and the specimen compliance at the current point of the p−d diagram. then, the value of fracture resistance r is calculated from the current load and effective crack length (for each point of the loading diagram), most conveniently as     2 2 ic 1 ( ) ( ) k r p a y e e [j/m2], (1) where (p) is the nominal stress in the line of the crack in the specimen due to the load p and y() is the corresponding geometry function. thus, the corresponding point of r−a curve is calculated for each point of p−d curve. the value of wf,b calculated from area under p−d curve is equal to the area under the r−a curve. transformation of the p−d diagram into the r− curve with indication of meanings of wf,b, is shown in fig. 2 and fig. 3. a j. klon et alii, frattura ed integrità strutturale, 41 (2017) 183-190; doi: 10.3221/igf-esis.41.25 186 figure 2: work of fracture indication at the current stage of fracture process in the loading diagram (peak-deflection curve). figure 3: work of fracture indication at the current stage of fracture process in the r-curve. experiment made by hoover et al. in the experimental campaign reported in [14], four beam sizes of widths w = 500, 215, 93 and 40 mm (marked as a to d, see) with three relative notch lengths 0 = 0.075, 0.15, and 0.3 were subjected to three-point bending tests. ratio of the smallest and the largest tested specimen is remarkable, namely 1:12.5. several samples were tested for each w and 0, for details see [14]. nominal dimensions of the test specimen are shown in tab. 1. numerical models umerical models (see fig. 4 to 7) were created with respect to the geometry given in fig. 1 and tab. 1 and the plane stress conditions were met. connection of steel loading platens with concrete in the part around the groove is solved by using contact elements due to more realistic behavior of platens during the load process by increment of deformation (as a function of load step). monitoring points were used to observe values of horizontal and vertical displacements and applied forces (reactions). material model (in atena sw. referred to as 3d non linear cementitious 2) was used for the simulation of the quasibrittle specimen with following parameters: young’s modulus e = 34 gpa, poisson’s ratio  = 0.172, tensile strength ft = 5.40 mpa, compressive strength fc = 49.00 mpa, three levels of specific fracture energy gf = 7; 70; 700 n/m, hordijk’s exponential softening. the finite element mesh was generated with regard to the area of the expected extent of fpz (fig. 4) with finite element size of 1 mm. steel loading platens were modelled by 2d elastic isotropic material model with e = 210 gpa and  = 0.3. figure 4: numerical model of the test specimen d 500 with the initial relative crack length  = 0.15; detail of the fe mesh in atena 2d software. figure 5: numerical model of the test specimen d 500 with the initial relative crack length  = 0.15; fracture failure at stage  = 0.7 considering the specific fracture energy gf = 7 n/m. it is obvious that the response of the test specimen on the loading progress strongly differs in the way of used level of the specific fracture energy gf (see fig. 8). for the highest value of gf = 700 n/m the peak value of the loading force is two times higher than in the case of gf = 70 n/m (this can be also applied for comparison of the lowest and the middle value of gf). each value of used gf has also significant impact on the way of fracture failure (fig. 9). brittle fracture corresponds n j. klon et alii, frattura ed integrità strutturale, 41 (2017) 183-190; doi: 10.3221/igf-esis.41.25 187 to the lowest value of specific fracture energy used, middle value represents the quasi-brittle behavior and the highest value of gf indicates ductile behavior. figure 6: numerical model of the test specimen d 500 with the initial relative crack length  = 0.15; fracture failure at stage  = 0.7 considering the specific fracture energy gf = 70 n/m. figure 7: numerical model of the test specimen d 500 with the initial relative crack length  = 0.15; fracture failure at stage  = 0.7 considering the specific fracture energy gf = 700 n/m. figure 8: scale illustration of the progress of the loading diagram (peak-deflection curve) for all variants of the specific fracture energy used. figure 9: scale illustration of the progress of the r-curve for all variants of the specific fracture energy used. discussion of results s can be seen from fig. 10, 11 and 12 the quantity of the dissipated energy is different for various specimen sizes and for various initial notch lengths. as expected, the amount of the dissipated energy is also changing according to the selected level of the specific fracture energy. the amount of the dissipated energy is dependent on the specimen size due to increasing ligament area. when the specimen size is larger, the amount of the dissipated energy increases. as was already mentioned – the amount of the energy dissipated during crack growth from the initial notch to the relative length a/w = 0.7 was considered. ligament area grows approximately 2.3 times for two consecutive specimen sizes. the dissipated energy obtained by means of theoretical calculations gf(theor) corresponds to this expectation. this ratio was achieved for all three selected values of the specific fracture energy via the theoretical calculation: for the dissipated energy determined from the fem analysis, this proportion was reached (with a deviance of 20 %) for the middle value of the specific fracture energy. the middle level of the specific fracture energy was chosen according to available loading diagrams for the actual cement composite used for preparation of the test specimens published in [12]. its real value of specific fracture energy was gf = 70 n/m. if the higher order value of the specific fracture energy gf = 700 n/m is used the current ratio does not apply. it can be seen in fig. 12. at this level, the amount of the energy a j. klon et alii, frattura ed integrità strutturale, 41 (2017) 183-190; doi: 10.3221/igf-esis.41.25 188 dissipated in small specimens is much more less than it should correspond to the current area of the specimen’s ligament. for example, the specimen d 040 with the initial notch  = 0.075 has the amount of the dissipated energy smaller by 75 % than the value obtained by theoretical calculations. with the increasing size of the specimen the deviation is reducing as much, that for the biggest specimen (d 500) the ratio of the dissipated energy is almost 2.9 times bigger than in the case of the smaller one (d 215). comparison of the values of the dissipated energy obtained by fem analysis and theoretical calculation for specimen d 500 with the initial notch of the length  = 0.075 shows the deviation under 20 %. this phenomenon is repeated for all initial notch length variants. the deviations varied from 80 % (small specimens of size d 040) to 30 % (the biggest specimens of size d 500). the opposite trend was observed for the specimens with the low order of value of the specific fracture energy gf = 70 n/m. for the smallest specimens, the deviation from the theoretical calculation was lower than for the biggest specimens. while the dissipated energy determined from fem analysis for the small specimen d 040 reaches the maximum deviation of 13 %, the biggest specimen d 500 exceeds 120 %, see fig. 12. described behavior is certainly related to the way of failure which differs for the selected values of the specific fracture energy. it is clear from fig. 8, that not only the area under the loading curve but also the maximum reached loading force changes. the peak force is approximately two times bigger comparing two subsequent values of the specific fracture energy gf. similarly, the specimen response is also changing with the level of the specific fracture energy used: the response of the specimen with the middle level of the specific fracture energy corresponds to the quasi-brittle fracture. fracture progress in the specimen with the lower level of the specific fracture energy corresponds to brittle fracture, where the fpz does not develop. significant ductile behavior is typical for the highest level of the specific fracture energy used. this tendency can be seen in fig. 5 to 7 where the finite element mesh is shown and the way of fracture failure for each level of the specific fracture energy. it is obvious that the wider band of elements is damaged by cracks for the higher level of the specific fracture energy than in the case of the lower one (fpz is not developed). this behavior is probably caused by the use of the crack band model, that is implemented in atena 2d software tool. it is clear from the displayed results that it is necessary to pay attention to the use of the proper level of the specific fracture energy when atena tool shall be used for modelling of structures and following evaluation of results. it was found out that the selected value of the specific fracture energy reflects not only the total amount of the dissipated energy during fracture, but also maximum loading force achievement and the way of structural response. figure 10: value of the fracture energy gf(num) dissipated during the crack propagation for all variants of numerical models – obtained from the area under the l-d curve (r–a diagram respective) simulated in atena. j. klon et alii, frattura ed integrità strutturale, 41 (2017) 183-190; doi: 10.3221/igf-esis.41.25 189 figure 11: value of the fracture energy gf(theor) dissipated during the crack propagation for all variants of numerical models – obtained from theoretical calculation. figure 12: deviation between the values of gf(num) and gf(theor) dissipated during the crack propagation for all variants of numerical models. conclusions he paper presents a study on the impact of the value of the specific fracture energy inputted into fe software (considering the fracture failure) on the amount of the energy dissipated during quasi-brittle fracture. three-point bending tests of specimens with different size and initial notch length was subject of this study. the amount of the dissipated energy was examined by using two methods. the first method consists in the numerical fem analysis; the amount of the energy was obtained from the area under the loading curve obtained from numerical simulations. the latter t j. klon et alii, frattura ed integrità strutturale, 41 (2017) 183-190; doi: 10.3221/igf-esis.41.25 190 one consists in multiplication of the value of the specific fracture energy (inputted into atena software) with the area of ligament. three values of the specific fracture energy were considered: gf = 7; 70; 700 n/m. specimens of four sizes with the same geometry proportions were assumed to reflect the impact of the size effect. the results obtained show a strong dependence of the amount of the dissipated energy during fracture on the value of the specific fracture energy considered for calculations. similarly, a significant dependence of the maximum achieved loading force on the value of the specific fracture energy was observed. therefore, it is crucial to set the proper value of the specific fracture energy when more complex fracture analyses need to be performed in order to avoid misleading results. note that the authors intend to extend the study on the impact of the specific fracture energy value on the amount of the energy dissipated to the wedge splitting test geometry. acknowledgement his paper has been worked out under the project of the czech science foundation (project no. 15-07210s). references [1] bažant, z.p., kazemi, m.t., size dependence of concrete fracture energy determined by rilem work-of-fracture method, int. j. fract., 51(2) (1991) 121–138. [2] elices, m., guinea, g. v., planas, j., measurement of the fracture energy using three-point bend tests: part 3– influence of cutting the p–δ tail, mater. struct., 25(6) (1992) 327–334. [3] hu, x.-z., wittmann, f.h., size effect on toughness induced by crack close to free surface. engng. fract. mech., 65 (2000) 209–221. [4] trunk, b., wittmann, f.h., influence of size on fracture energy of concrete, mater. struct, 36 (2001) 260–265. [5] karihaloo, b.l., abdalla, h.m., imjai, t., a simple method for determining the true fracture energy of concrete. mag. concr. res., 55 (2003) 471–481. [6] duan, k., hu, x.-z., wittmann, f.h., boundary effect on concrete fracture and non-constant fracture energy distribution, engng. fract. mech., 70 (2003) 2257–2268. [7] bažant, z.p., yu, q., size effect in fracture of concrete specimens and structures: new problems and progress, in li v.c. et al. (eds.), proc. of the 5th international conference on fracture mechanics of concrete and concrete structures, vail colorado, usa, (2004) 153–162. [8] hu, x.-z., duan, k., size effect: influence of proximity of fracture process zone to specimen boundary, engng. fract. mech., 74 (2007) 1093–1100. [9] yu, q., le, j., hoover, c., bažant, z., problems with hu-duan boundary effect model and its comparison to sizeshape effect law for quasi-brittle fracture, j. eng. mech., 89 (2010) 40–50. doi: 10.1061/(asce)em.1943-7889. [10] cifuentes, h., alcalde, m., medina, f., measuring the size-independent fracture energy of concrete, strain, 49(1) (2013) 54–59. [11] suresh, s., fatigue of materials, cambridge university press, (1998) 679. [12] červenka, v., jendele, l., červenka, j., atena program documentation, cervenka consulting, prague (2010). [13] červenka, v., červenka, j., pukl, r., atena / a tool for engineering analysis of fracture in concrete, sadhanaadacemy proceedings in engineering sciences, 27 (2002) 485–492. [14] hoover, ch.g., bažant, z.p., vorel, j., wendner, r., hubler, m.h., comprehensive concrete fracture tests: description and results, engng. fract. mech., 114 (2013) 92–103. [15] klon, j., veselý, v., modelling of size and shape of damage zone in quasi-brittle notched specimens – analytical approach based on fracture-mechanical evaluation of loading curves, frattura ed integrità strutturale, 39 (2017) 17–28. 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can be opened with acrobat and adobe reader 5.0 and later.) >> /namespace [ (adobe) (common) (1.0) ] /othernamespaces [ << /asreaderspreads false /cropimagestoframes true /errorcontrol /warnandcontinue /flattenerignorespreadoverrides false /includeguidesgrids false /includenonprinting false /includeslug false /namespace [ (adobe) (indesign) (4.0) ] /omitplacedbitmaps false /omitplacedeps false /omitplacedpdf false /simulateoverprint /legacy >> << /addbleedmarks false /addcolorbars false /addcropmarks false /addpageinfo false /addregmarks false /convertcolors /converttocmyk /destinationprofilename () /destinationprofileselector /documentcmyk /downsample16bitimages true /flattenerpreset << /presetselector /mediumresolution >> /formelements false /generatestructure false /includebookmarks false /includehyperlinks false /includeinteractive false /includelayers false /includeprofiles false /multimediahandling /useobjectsettings /namespace [ (adobe) (creativesuite) (2.0) ] /pdfxoutputintentprofileselector /documentcmyk /preserveediting true /untaggedcmykhandling /leaveuntagged /untaggedrgbhandling /usedocumentprofile /usedocumentbleed false >> ] >> setdistillerparams << /hwresolution [2400 2400] /pagesize [612.000 792.000] >> setpagedevice microsoft word numero_37_art_10 f. berto et alii, frattura ed integrità strutturale, 37 (2017) 69-79; doi: 10.3221/igf-esis.37.10 69 focussed on multiaxial fatigue and fracture local strain energy density to assess the multiaxial fatigue strength of titanium alloys filippo berto university of padova, department of management and engineering, vicenza (italy) ntnu, department of engineering design and materials, trondheim, (norway) berto@gest.unipd.it alberto campagnolo university of padova, department of industrial engineering, padova (italy) alberto.campagnolo@unipd.it torgeir welo ntnu, department of engineering design and materials, trondheim, (norway) torgeir.welo@ntnu.no abstract. the present paper investigates the multiaxial fatigue strength of sharp v-notched components made of titanium grade 5 alloy (ti-6al-4v). axisymmetric notched specimens have been tested under combined tension and torsion fatigue loadings, both proportional and non-proportional, taking into account different nominal load ratios (r = -1 and 0). all tested samples have a notch root radius about equal to 0.1 mm, a notch depth of 6 mm and an opening angle of 90 degrees. the fatigue results obtained by applying multiaxial loadings are discussed together with those related to pure tension and pure torsion experimental fatigue tests, carried out on both smooth and notched specimens at load ratios r ranging between -3 and 0.5. altogether, more than 250 fatigue results (19 s-n curves) are examined, first on the basis of nominal stress amplitudes referred to the net area and secondly by means of the strain energy density averaged over a control volume embracing the v-notch tip. the effect of the loading mode on the control volume size has been analysed, highlighting a wide difference in the notch sensitivity of the considered material under tension and torsion loadings. accordingly, the control radius of the considered titanium alloy (ti-6al-4v) is found to be strongly affected by the loading mode. keywords. ti-6al-4v; multiaxial fatigue; v-notch; control volume; strain energy density. introduction or a wide comparison between different approaches adopted to the multiaxial fatigue strength assessment of metallic materials, the reader is referred to a recent review [1] and a report [2], which are based on a large bulk of experimental data obtained from notched specimens. a fundamental role is occupied by critical plane approaches f f. berto et alii, frattura ed integrità strutturale, 37 (2017) 69-79; doi: 10.3221/igf-esis.37.10 70 [3,4] and by some important variants [5-7]. in this context, approaches based on energy calculations find significant applications [8]. a multiaxial fatigue approach based on a frequency-domain formulation of a stress invariant, the so-called “projection by projection” (pbp) criterion has been reported in the recent literature [9]. the critical plane-based carpinteri-spagnoli approach has recently been extended to a frequency-domain formulation [10]. an energy-based parameter has been adopted to assess the fatigue strength under uniaxial fatigue loadings first by jasper [11] in 1923. then, ellyin suggested a criterion based on the combination of plastic and elastic strain energy [12-13], to deal with multiaxial fatigue loadings. a wide review of energybased criteria for multiaxial fatigue strength assessment has been reported in [14]. moreover, the problems relevant to multiaxial fatigue have been investigated both theoretically and experimentally by several researchers [15-22]. this contribution is aimed to analyse the fatigue strength of severely notched titanium grade 5 alloy under multiaxial loadings. the considered titanium alloy (ti-6al-4v) is widely employed in advanced military, civil aerospace and naval applications. the in-service conditions of titanium structural components are usually characterized by a complex stress state coupled with an aggressive environment. the titanium grade 5 alloy has high static and fatigue properties, a very good strength-to-mass ratio and an excellent wear resistance. the uniaxial fatigue strength of un-notched and notched titanium components has been extensively analysed in the literature. however, a complete set of experimental data relevant to sharp v-notched specimens made of ti-6al-4v and subjected to torsion and combined tension and torsion loadings, both proportional and non-proportional, is not available in the literature. to fill this lack, a complete set of experimental data from sharp v-notched components made of titanium grade 5 alloy (ti-6al-4v) under multiaxial fatigue loading is provided here. experimental fatigue tests under combined tension and torsion loadings have been carried out on circumferentially vnotched specimens, with two nominal load ratios, namely r = -1 and r = 0. the fatigue results obtained by applying multiaxial loadings are compared with those related to pure tension and pure torsion experimental fatigue tests, carried out on both smooth and notched specimens at load ratios r ranging between -3 and 0.5. all in all, more than 250 fatigue data (19 wöhler curves) are examined in terms of nominal stress amplitudes referred to the net area. then, the experimental fatigue strength data have been reanalysed in terms of the strain energy density (sed) averaged over a control volume embracing the notch tip [23-31]. the effect of the loading mode on the control volume size has been analysed, highlighting the need to use a different control radius under tension and torsion loading, due to a wide difference in the notch sensitivity of the considered material under tension and torsion loadings. the expressions for calculating the control radii, thought of as material properties, have been derived by imposing the constancy of the averaged sed relevant to un-notched and notched specimens, which depend on the critical notch stress intensity factors (nsifs) and the control radius, in correspondence of 2·106 cycles. the unifying capacity of the averaged sed criterion is highlighted, indeed the synthesis on the basis of the local sed enables to obtain a quite narrow scatter-band, which is characterised by an equivalent stress-based scatter index t equal to 1.58, taking into account all fatigue strength data relevant to notched and un-notched components subjected to pure tension, pure torsion and multiaxial loadings, independently of the nominal load ratio and the phase angle. some of the results reported in the present manuscript have been previously presented and extensively discussed in [31]. material and geometry of the specimens he material taken into consideration in the present contribution is a titanium grade 5 alloy, also known as ti-6al4v. the geometries of smooth and sharply notched specimens are reported in fig. 1, along with some details of the v-notch tip. the hourglass smooth specimens, shown in fig. 1a, are characterized by a 12-mm-diameter of the net transverse area and by a wide connecting radius between the net and gross sections,  = 100 mm, so that any stress concentration is avoided. the cylindrically v-notched samples, shown in fig. 1b, are characterized, instead, by a notch depth d equal to 6 mm and a notch angle of 90 degrees, while the notch tip radius, , is about equal to 0.1 mm. in particular, the notch root radius has been experimentally measured through an optical microscope and the dedicated software las (leica application suite) and a mean value of 0.09 mm with a very reduced scatter has been obtained. the precision ensured by the adopted method is about ± 5% of the measured quantity. the typical v-notch profile characterised by two rectilinear flanks tangent to the notch tip radius is reported in fig. 1b, for an example of the tested samples. to remove any scratches or processing marks on the surface, all specimens were polished before the fatigue test. t f. berto et alii, frattura ed integrità strutturale, 37 (2017) 69-79; doi: 10.3221/igf-esis.37.10 71  d = 6 mm = 0.1 mm 24 90° = 100 mm 24 150 mm (a) (b) figure 1. (a) geometries of smooth and sharply notched specimens and (b) examples of tested specimens. experimental results from fatigue tests he experimental fatigue tests have been carried out by means of a mts 809 servo-hydraulic bi-axial testing device (± 100 kn, ± 1100 nm, ± 75mm/± 55°) under load control conditions. in particular, a mts load cell with ± 0.5 % error at full scale has been employed to evaluate the nominally applied loads. a test frequency between 10 and 15 hz has been adopted as a function of the applied load level. all in all, 19 different fatigue test series are performed, according to the parameters reported below:  four series of fatigue tests on smooth and sharply notched samples subjected to pure tension and pure torsion fatigue loadings, with a nominal load ratio r = -1;  four series of fatigue tests on smooth and sharply notched samples subjected to pure torsion fatigue loading, with nominal load ratios r = 0 and 0.5;  three series of fatigue tests on smooth samples subjected to pure torsion fatigue loading, with nominal load ratios r = 0.25, -2 and -3;  four series of fatigue tests on sharply notched samples subjected to combined tension and torsion loadings, at a constant biaxiality ratio λ = 0.6. two load ratios, r = 0 and r = -1 (referred separately to the normal and shear t f. berto et alii, frattura ed integrità strutturale, 37 (2017) 69-79; doi: 10.3221/igf-esis.37.10 72 stress components), and two phase angles, ф = 0° (proportional loadings) and ф = 90° (non-proportional loadings), are employed;  four series of fatigue tests on sharply notched samples subjected to combined tension and torsion loading, at a constant biaxiality ratio λ = 2.0. also in this case, two load ratios, r = 0 and r = -1, and two phase angles, ф = 0° (proportional loadings) and ф = 90° (non-proportional loadings), are adopted. the statistical re-analyses of the fatigue strength data were carried out by assuming a log-normal distribution. all experimental data relevant to specimens with a fatigue life in the range 104 ÷ 2·106 cycles have been considered, while the run-outs have been excluded. in particular, tab. 1 reports the nominal stress amplitudes for a probability of survival ps = 50% and a number of cycles na = 2·106, the inverse slope k of the wöhler curves and the scatter-index t, which gives a measure of the width of the scatter band, between the curves with 10% and 90% probabilities of survival (with a confidence level equal to 95%). under multiaxial loading, the fatigue life results to be reduce if compared to the uniaxial loading case, with reference to the same normal stress amplitude, however the reduction is quite limited for the biaxiality ratios considered herein ( = 0.6 and 2.0). stronger is the multiaxial fatigue strength reduction tied to the effect of the load ratio r. on the other hand, the phase angle effect is weak for r = -1, being the mean values of the normal stress amplitudes about the same at 2·106 cycles. while, it is higher for r = 0, being the out-of-phase loading slightly beneficial with respect to in-phase loading at high-cycle fatigue regime, whereas the fatigue strength is almost the same at low-cycle regime. the sensitivity of the considered titanium alloy to the phase angle effect results to be quite limited, being lower than +15 percent for the r = 0 case and negligible for the r = -1 case. the fracture surfaces relevant to the specimens subjected to multiaxial loadings were examined. the phase angle seems to affect the fracture surface morphology. indeed, some signs of micro abrasions could be seen on all fracture surfaces and the extent to which the rubbing occurred depends on phase angle. in general, a limited but distinguishable quantity of debris and powder has been emanated from the notch tip, when a visible fatigue crack started to propagate. synthesis based on the averaged strain energy density ith regard to un-notched specimens, all fatigue results have been summarised here in terms of the averaged sed, which can be expressed, under linear elastic conditions, by means of beltrami’s expression. accordingly, in the case of pure tension loading, the local strain energy density is given by: e2 w 2 nom (1) while in the case of pure torsion loading it is given by:   e 1w 2 nom (2) in previous expressions, nom and nom are the nominal stress ranges tied to tension and torsion loadings, respectively. for the considered titanium alloy, the young’s modulus e results to be 110 gpa, while the poisson’s ratio ν is 0.3. then, also the fatigue strength results relevant to notched samples have been reanalysed here in terms of the averaged sed, however, in this case the strain energy calculation is based on the local stress and strain state in a control volume embracing the v-notch tip. since the notch root radius is reduced ( less than 0.1 mm), the mode i and mode iii nsifs, k1 and k3, can be adopted to summarised the experimental data relevant to notched samples in terms of the local strain energy density. these parameters, which describe the local stress fields, have been evaluated from linear elastic fe analyses taking into consideration a sharp v-notch with tip radius equal to 0 (see fig. 2). let us consider a cylindrical coordinate system (r, θ, z) with origin at the notch tip, where r is the radial coordinate,  is the angle between a generic point and the notch bisector line, while z is the longitudinal axis of the specimen. in particular, with reference to this coordinate system (see fig. 2), the mode 1 and mode 3 nsifs can be defined by means of the following expressions: w f. berto et alii, frattura ed integrità strutturale, 37 (2017) 69-79; doi: 10.3221/igf-esis.37.10 73 )0,r(rlim2k 11 0r1      (3) )0,r(rlim2k z 1 0r3 3      (4) table 1. experimental results from fatigue tests. mean values, ps = 50%. stresses referred to the net area. series type of load number of specimens k tσ tτ σa or τa 2 · 106 1 tension r = -1 12 σ 9.25 1.120 475.74 2 torsion r = -1 16 τ 22.13 1.205 388.25 3 torsion r = 0 9 τ 15.03 1.322 287.22 4 tension r = -1, v-notch 2α = 90° 15 σ 6.26 1.133 100.89 5 torsion r = -1, v-notch 2α = 90° 9 τ 14.59 1.229 289.31 6 torsion r = 0, v-notch 2α = 90° 11 τ 13.82 1.159 247.16 7 torsion r = 0.5, v-notch 2α = 90° 7 τ 19.91 1.080 169.89 8 multiaxial r = -1, ф = 0°, λ= 0.6, v-notch 2α = 90° 13 σ 6.82 1.197 93.89 τ 56.39 9 multiaxial r = -1, ф = 90°, λ = 0.6, v-notch 2α = 90° 10 σ 7.84 1.124 96.11 τ 57.67 10 multiaxial r = 0, ф = 0°, λ = 0.6, v-notch 2α = 90° 12 σ 8.09 1.159 67.74 τ 40.64 11 multiaxial r = 0, ф = 90°, λ = 0.6, v-notch 2α = 90° 12 σ 10.43 1.158 79.65 τ 47.79 12 torsion r = 0.5 12 τ 21.19 1.134 180.73 13 torsion r = 0.25 8 τ 25.67 1.078 268.12 14 torsion r = -3 7 τ 16.25 1.178 357.55 15 torsion r = -2 8 τ 21.32 1.042 409.01 16 multiaxial r = -1, ф = 0°, λ = 2, v-notch 2α = 90° 26 σ τ 7.61 1.118 75.94 37.97 17 multiaxial r = -1, ф = 90°, λ = 2, v-notch 2α = 90° 22 σ τ 7.59 1.114 84.70 42.35 18 multiaxial r = 0, ф = 0°, λ = 2, v-notch 2α = 90° 21 σ τ 8.01 1.125 59.75 29.88 19 multiaxial r = 0, ф = 90°, λ = 2, v-notch 2α = 90° 21 σ τ 9.40 1.089 65.97 32.99 f. berto et alii, frattura ed integrità strutturale, 37 (2017) 69-79; doi: 10.3221/igf-esis.37.10 74 figure 2. polar coordinate system for v-shaped notches, with z normal to the plane; mode i nsif linked to the stress component  evaluated along the notch bisector line (=0); under mode iii the shear stress component z is oriented as . considering an opening angle of 90 degrees, the eigenvalues 1 and 3 result to be 0.545 and 0.667, respectively. moreover, under linear elastic conditions, the nsifs can be linked to the nominal stress components as follow: nom 1 11 1dkk   (5a) nom 1 33 3dkk   (5b) in previous expressions, d represents the notch depth (d = 6.0 mm), while k1 and k3 are the non-dimensional factors obtained by means of proper fe analyses. they represent the shape factors, similarly to the expressions of stress intensity factors in linear elastic fracture mechanics. the quadrilateral eight-node harmonic element plane 83 of the ansys element library has been adopted in the fe analyses. taking advantage of the symmetry conditions, only one quarter of the sample geometry has been modelled. according to the fe analyses carried out, k1 is equal to 1.000, while k3 equals 1.154. the trend of the mode iii stress field, normalized with respect to the nominally applied shear stress and evaluated on the notch bisector line, is reported in fig. 3 as a function of the distance from the notch tip. it can be observed that the stress field is controlled by the first singular term (nsif) up to a distance from the notch tip about equal to 1.0 mm. taking into account the notch depth of the tested samples, namely d = 6 mm, in previous eqs (5a) and (5b), the following simple expressions can be obtained: nom1 260.2k  (in mpa ·mm0.445) (6a) nom3 096.2k  (in mpa ·mm0.333) (6b) by substituting into eqs. (6a) and (6b) the ranges of the nominal stresses at na = 2·106 cycles relevant to notched samples subjected to pure tension and pure torsion loadings at a nominal load ratio r = -1 (see tab. 1), one can obtain: 445.0 a1 mmmpa452200260.2k  (7a)      y r   x  r  r f. berto et alii, frattura ed integrità strutturale, 37 (2017) 69-79; doi: 10.3221/igf-esis.37.10 75 333.0 a3 mmmpa1216580096.2k  (7b) figure 3. local shear stress field along the notch bisector line (mode iii loading). dealing with a sharp v-notched component subjected to combined tension and torsion loadings under linear elastic conditions, the strain energy density averaged over a control volume surrounding the notch tip can be evaluated from the following closed-form expression:                31 12 3 2 3 312 1 2 1 1 r k e r k e e 1 w (8) in previous expression, k1 and k3 are the mode i and mode iii nsif ranges, respectively, r1 and r3 represent the control volume sizes related to mode i and mode iii loadings, respectively, while e1 and e3 are known coefficients which take into account the local notch geometry. these parameters are tied to the integrals over the control volume of the angular stress functions and they can be evaluated a-priori by means of closed-form expressions, as a function of the notch opening angle. being the tested samples characterized by an opening angle 2 of 90 degrees, e1 and e3 result to be 0.146 and 0.310, respectively, with reference to a poisson’s ratio  = 0.3. very refined fe meshes must be adopted in the close vicinity of the singularity point to evaluate the nsifs on the basis of definitions (3) and (4). on the other hand, the local sed results to be insensitive to the mesh refinement. indeed, it can be accurately calculated also from fe analyses with coarse meshes, since it directly depends on nodal displacements. the most important and useful advantages tied to the use of the averaged strain energy density parameter are analysed and discussed in detail in ref. [30]. the expressions for calculating the control radii, thought of as material properties, have been derived by imposing the constancy of the averaged sed relevant to un-notched and notched specimens, which depend on the critical notch stress intensity factors (nsifs) and the control radius, in correspondence of 2·106 cycles. by taking into consideration, instead, cracked samples, the critical nsifs should be substituted by the threshold values of the stress intensity factors. by considering the mode i and mode iii loading conditions as independent, the control radii r1 and r3 (as shown in fig. 4) can be estimated. in particular, they result to be dependent on the high-cycle fatigue strengths of un-notched specimens, 0,1 1 10 100 0,001 0,010 0,100 1,000   z/  n o m distance from the notch tip, [mm] f. berto et alii, frattura ed integrità strutturale, 37 (2017) 69-79; doi: 10.3221/igf-esis.37.10 76 1a = 950 mpa and3a = 776 mpa, and on the mean values of the nsifs, k1a andk3a, with reference to a given number of cycles, na = 2·106: 11 1 a1 a1 11 k e2r           (9a) 31 1 a3 a33 3 k 1 e r               (9b) r1 2  r3 figure 4. control volumes for v-shaped notches under tension and torsion loadings. on the basis of eqs. (9a) and (9b), the control radii result to be r1 = 0.051 mm and r3 = 0.837 mm, respectively. accordingly, the control radius r1 has been adopted to compute the averaged strain energy contribution tied to tension loading, whereas the control radius r3 has been employed to evaluate the averaged sed contribution due to torsion loading. it should be noted that the control radius r3 is highly affected by the presence of larger plasticity under torsion loading as compared to tension loading, and by friction and rubbing between the crack surfaces, as previously discussed also for different materials [23,30]. under these conditions, the averaged sed is called also ‘apparent linear elastic sed’ to highlight that the strain energy density calculation over two different control volumes (under tension and torsion, respectively, as determined from experimental data) allows us to overcome the problem tied to shielding mechanisms, keeping a linear elastic criterion. to summarise in the same scatter band experimental results obtained by adopting different nominal load ratios r, a coefficient cw, defined on the basis of simple algebraic considerations (reported in detail in ref. [24, 31]), must be introduced. the coefficient cw results to be dependent on the nominal load ratio r according to the following expression:                    1r0for r1 r1 0rfor1 0rfor r1 r1 c 2 2 2 2 w (10) f. berto et alii, frattura ed integrità strutturale, 37 (2017) 69-79; doi: 10.3221/igf-esis.37.10 77 the parameter cw equals 1.0 in the case r = 0, while it results equal to 0.5 for r = -1. by adopting the coefficient cw, the closed-form expressions to evaluate the averaged sed, related to smooth samples (eqs. (1, 2)) and to components weakened by sharp notches (eq. (8)), become as follow:                                 loadingmultiaxialspecimensnotchedvr k e r k e e c torsionpurespecimensnotchedun e 1c tensionpurespecimensnotchedun e2 c sed 31 12 3 2 3 312 1 2 1 1 w 2 nom w 2 nom w (11) fig. 5 reports the synthesis of all experimental fatigue results analysed in the present contribution by means of the averaged sed. the control radius r1 = 0.051 mm has been adopted to evaluate the sed contribution due to tension loading, while the control radius r3 = 0.837 mm has been employed for the sed contribution due to torsion loading. all fatigue strength results relevant to smooth and notched samples under pure tension, pure torsion and multiaxial loading conditions are included in the obtained scatter band, independently of the nominal load ratio and of the phase angle. the design scatter band is characterized by an inverse slope k of 5.90, by an energy-based scatter index tw = 2.50 and by a sed value at na = 2·106 cycles equal to 3.08 mj/m3. however, the equivalent stress-based scatter index, that is t = (tw)0.5, equals 1.58, which is very similar to that of the haibach scatter band (t= 1.50). it should be noted that an extensive review of the considered experimental results will be carried out in the special issue dedicated to the 11th international conference on multiaxial fatigue and fracture (icmff11) [32]. figure 5. local sed-based synthesis of experimental fatigue results relevant to smooth and sharply notched specimens. almost 250 fatigue data are summarised in the scatter band. 0.2 2 20 1.0e+04 1.0e+05 1.0e+06 1.0e+07 s tr ai n e n er gy d en si ty r an g e,  w , [m j/ m 3 ] number of cycles to failure, n tension, r=-1 tension, r=-1 torsion, -3 ≤ r ≤ 0.5 torsion, -1 ≤ r ≤ 0.5 multiaxial, r=-1, in-phase multiaxial, r=-1, in-phase multiaxial, r=0, in-phase multiaxial, r=-1, out-of-phase multiaxial, r=-1, out-of-phase multiaxial, r=0, in-phase multiaxial, r=0, out-of-phase multiaxial, r=0, out-of-phase un-notched specimens k=5.90 sed range (2x106, p.s. 50%)= 3.08 mj/m3 tw=2.5 ti6al4v 251 data r1 = 0.051 mm r3 = 0.837 mm v-notched specimens v-notched specimens  = 0.6  = 2.0 f. berto et alii, frattura ed integrità strutturale, 37 (2017) 69-79; doi: 10.3221/igf-esis.37.10 78 conclusions large bulk of experimental fatigue results relevant to axisymmetric notched samples subjected to multiaxial loadings, both proportional and non-proportional, have been re-analysed and compared with the fatigue strength data relevant to smooth and notched samples subjected to pure tension and pure torsion loadings. all specimens were made of titanium grade 5 alloy (ti-6al-4v). altogether, more than 250 fatigue results, corresponding to 19 s-n curves, have been analysed in this contribution. first, the experimental results obtained from uniaxial and multiaxial fatigue tests have been examined on the basis of nominal stress amplitudes. then, they have been re-analysed by means of the linear elastic strain energy density (sed) averaged over a control volume surrounding the notch root. the effect of the loading mode on the control volume size has been analysed in detail, showing that different control radii must be adopted under tension and torsion loading conditions, dealing with notched components made of ti-6al-4v titanium alloy. the averaged sed-based synthesis enables to obtain a quite narrow scatter band, characterized by an energy-based scatter index of 2.50. in particular, the fatigue design scatter band was derived by taking into account all experimental results relevant to smooth and notched samples under pure tension, pure torsion and multiaxial loading conditions, regardless the nominal load ratio and the phase angle. references [1] fatemi, a., shamsaei, n., multiaxial fatigue: an overview and some approximation models for life estimation, int. j. fatigue, 33 (2011) 948-958. [2] nieslony, a., sonsino, c.m., comparison of some selected multiaxial fatigue assessment criteria, l.b.f. report, no. fb-234 (2008). [3] fatemi, a., socie, d.f., a critical plane approach to multiaxial fatigue damage including out-of-phase loading, fatigue fract. eng. mater. struct., 11 (1988) 149-165. [4] fatemi, a., kurath, p. p., multiaxial fatigue life prediction under the influence of mean stresses, asme j. eng. mater. techn., 110 (1988) 380-388. [5] łagoda, t., macha, e., bedkowski, w., a critical plane approach based on energy concepts: application to biaxial random tension-compression high-cycle fatigue regime, int. j. fatigue, 21 (1999) 431-443. [6] carpinteri, a., spagnoli, a., multiaxial high-cycle fatigue criterion for hard metals, int. j. fatigue, 23 (2001) 135-145. [7] carpinteri, a., spagnoli, a., vantadori, s., bagni, c., structural integrity assessment of metallic components under multiaxial fatigue: the c-s criterion and its evolution, fatigue fract. eng. mater., 36 (2013) 870-883. [8] ye, d., hertel, o., vormwald, m., a unified expression of elastic–plastic notch stress–strain calculation in bodies subjected to multiaxial cyclic loading, int. j. solids struct., 45 (2008) 6177-6189. [9] cristofori, a., benasciutti, d., tovo, r., a stress invariant based spectral method to estimate fatigue life under multiaxial random loading, int. j. fatigue, 33 (2011) 887–899. [10] carpinteri, a., spagnoli, a., vantadori, s., reformulation in the frequency domain of a critical plane-based multiaxial fatigue criterion, int. j. fatigue, 67 (2014) 55-61. [11] jasper, t.m., the value of the energy relation in the testing of ferrous metals at varying ranges and at intermediate and high temperature, philos. mag., 46 (1923) 609–627. [12] ellyin, f., cyclic strain energy density as a criterion for multiaxial fatigue failure, brown, miller, editors. biaxial and multiaxial fatigue, london: egf publication, (1989) 571–83. [13] ellyin, f., fatigue damage, crack growth and life prediction, edmonton: chapman and hall (1997). [14] macha, e., sonsino, c. m., energy criteria of multiaxial fatigue failure, fatigue fract. engng. mater. struct., 22 (1999) 1053–1070. [15] pook, l.p., sharples, j.k., the mode iii fatigue crack growth threshold for mild steel, int. j. fract., 15 (1979) r223r226. [16] pook, l.p., the fatigue crack direction and threshold behaviour of mild steel under mixed mode i and iii loading, int. j. fatigue, 7 (1985) 21-30. [17] tong, j., yates, j.r., brown, m.w., some aspects of fatigue thresholds under mode iii and mixed mode and i loadings, int. j. fatigue, 18 (1986) 279-285. a f. berto et alii, frattura ed integrità strutturale, 37 (2017) 69-79; doi: 10.3221/igf-esis.37.10 79 [18] yu, h.c., tanaka, k., akiniwa, y., estimation of torsional fatigue strength of medium carbon steel bars with circumferential crack by the cyclic resistance-curve method, fatigue fract. eng. mater. 21 (1998) 1067-1076. [19] tanaka, k., akiniwa, y., yu, h., the propagation of a circumferential fatigue crack in medium-carbon steel bars under combined torsional and axial loadings, in: mixed-mode crack behaviour, astm 1359 (eds miller, k.j., mcdowell, d.l.), west conshohocked, pa, (1999) 295-311. [20] pippan, r., zelger, c., gach, e., bichler, c., weinhandl, h., on the mechanism of fatigue crack propagation in ductile metallic materials, fatigue fract. engng. mat. struct. 34 (2011) 1-16. [21] christopher, c.j., james, m.n., patterson, e.a., tee, k.f., towards a new model of crack tip stress fields, int. j. fracture, 148 (2007) 361–371. [22] christopher, c.j., james, m.n., patterson, e.a., tee, k.f., a quantitative evaluation of fatigue crack shielding forces using photoelasticity, eng. fract. mech. 75 (2008) 4190-4199. [23] berto, f., lazzarin, p., yates, j., multiaxial fatigue of v-notched steel specimens: a non-conventional application of the local energy method, fatigue fract. engng. mater. struct. 34 (2011) 921–943. [24] lazzarin, p., sonsino, c.m., zambardi, r., a notch stress intensity approach to assess the multiaxial fatigue strength of welded tube-to-flange joints subjected to combined loadings, fatigue fract. engng. mater. struct. 27 (2004) 127140. [25] berto, f., lazzarin, p., fatigue strength of structural components under multi-axial loading in terms of local energy density averaged on a control volume, int. j. fatigue, 33 (2011) 1055-1065. [26] berto, f. , lazzarin, p., marangon, c., fatigue strength of notched specimens made of 40crmov13.9 under multiaxial loading, mater. des., 54 (2014) 57-66. [27] berto, f., lazzarin, p., tovo, r., multiaxial fatigue strength of severely notched cast iron specimens, int. j. fatigue, 67 (2014) 15-27. [28] berto, f., campagnolo, a., chebat, f., cincera, m., santini, m., fatigue strength of steel rollers with failure occurring at the weld root based on the local strain energy values: modelling and fatigue assessment, int. j. fatigue. 82 (2016) 643–657. doi:10.1016/j.ijfatigue.2015.09.023. [29] campagnolo, a., berto, f., leguillon, d., fracture assessment of sharp v-notched components under mode ii loading: a comparison among some recent criteria, theor. appl. fract. mech. (2016) in press. doi:10.1016/j.tafmec.2016.02.001. [30] berto, f., lazzarin, p., recent developments in brittle and quasi-brittle failure assessment of engineering materials by means of local approaches, mater. sci. eng. r, 75 (2014) 1-48. [31] berto, f., campagnolo, a., lazzarin, p., fatigue strength of severely notched specimens made of ti-6al-4v under multiaxial loading, fatigue fract. eng. mater. struct. 38 (2015) 503-517. [32] berto, f., campagnolo, a., welo, t., multiaxial fatigue strength of titanium alloys, int. j. fatigue, (to be submitted). << /ascii85encodepages false /allowtransparency false /autopositionepsfiles true /autorotatepages /none /binding /left /calgrayprofile (dot gain 20%) /calrgbprofile (srgb iec61966-2.1) /calcmykprofile (u.s. web coated \050swop\051 v2) /srgbprofile (srgb iec61966-2.1) /cannotembedfontpolicy /error /compatibilitylevel 1.4 /compressobjects /tags /compresspages true /convertimagestoindexed true /passthroughjpegimages true /createjobticket false /defaultrenderingintent /default /detectblends true /detectcurves 0.0000 /colorconversionstrategy /cmyk /dothumbnails false /embedallfonts true /embedopentype false /parseiccprofilesincomments true /embedjoboptions true /dscreportinglevel 0 /emitdscwarnings false /endpage -1 /imagememory 1048576 /lockdistillerparams false /maxsubsetpct 100 /optimize true /opm 1 /parsedsccomments true /parsedsccommentsfordocinfo true 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can be opened with acrobat and adobe reader 5.0 and later.) >> /namespace [ (adobe) (common) (1.0) ] /othernamespaces [ << /asreaderspreads false /cropimagestoframes true /errorcontrol /warnandcontinue /flattenerignorespreadoverrides false /includeguidesgrids false /includenonprinting false /includeslug false /namespace [ (adobe) (indesign) (4.0) ] /omitplacedbitmaps false /omitplacedeps false /omitplacedpdf false /simulateoverprint /legacy >> << /addbleedmarks false /addcolorbars false /addcropmarks false /addpageinfo false /addregmarks false /convertcolors /converttocmyk /destinationprofilename () /destinationprofileselector /documentcmyk /downsample16bitimages true /flattenerpreset << /presetselector /mediumresolution >> /formelements false /generatestructure false /includebookmarks false /includehyperlinks false /includeinteractive false /includelayers false /includeprofiles false /multimediahandling /useobjectsettings /namespace [ (adobe) (creativesuite) (2.0) ] /pdfxoutputintentprofileselector /documentcmyk /preserveediting true /untaggedcmykhandling /leaveuntagged /untaggedrgbhandling /usedocumentprofile /usedocumentbleed false >> ] >> setdistillerparams << /hwresolution [2400 2400] /pagesize [612.000 792.000] >> setpagedevice microsoft word numero_37_art_49 n. zuhair faruq, frattura ed integrità strutturale, 37 (2016) 382-394; doi: 10.3221/igf-esis.37.49 382 an elasto-plastic approach to estimate lifetime of notched components under variable amplitude fatigue loading: a preliminary investigation n. zuhair faruq university of sheffield, department of civil and structural engineering, sheffield s1 3jd, uk zfnamiq1@sheffield.ac.uk abstract. the present paper is concerned with the formulation of an elasto-plastic strain based approach suitable for assessing fatigue strength of notched components subjected to in-service variable amplitude cyclic loading. the hypothesis is formed that the crack initiation plane is closely aligned with the plane of maximum shear strain amplitude, its orientation and the associated stress/strain quantities being determined using the maximum variance method. fatigue damage is estimated by applying the modified manson-coffin curve method (mmccm) along with the point method (pm). in the proposed approach, the required critical distance is treated as a material property whose value is not affected either by the sharpness of the notch being assessed or by the profile of the load spectrum being applied. the detrimental effect of non-zero mean stresses and degree of multiaxiality of the local stress/strain histories is also considered. the accuracy and reliability of the proposed design methodology was checked against several experimental data taken from the literature and generated under different uniaxial variable amplitude load histories. in order to determine the required local stress/strain states, refined elasto-plastic finite element models were solved using commercial software ansys®. this preliminary validation exercise allowed us to prove that the proposed approach is capable of estimates laying within an error factor of about 2. these preliminary results are certainly promising, strongly supporting the idea that the proposed design strategy can successfully be used to assess the fatigue lifetime of notched metallic components subjected to in-service multiaxial variable amplitude loading sequences. keywords. notched components; variable amplitude; critical plane; manson-coffin curve; non-zero mean stress. introduction n situations of practical interest, real engineering components are characterised by complex geometries resulting in local stress/strain concentration phenomena. they normally contain either notches or complex features that favour the initiation of fatigue cracks. the presence of stress/strain raiser results in multiaxial stress/strain states in the critical regions even if the nominal load history being applied is uniaxial. furthermore, real mechanical components are often exposed to variable amplitude load histories. accordingly, in the recent past, a tremendous effort has been made by the international scientific community to device specific design techniques suitable for accurately assessing the durability of notched components subjected to in-service variable amplitude load histories [1]. in this complex scenario, this paper summarises the results from a preliminary investigation aiming at developing an elasto-plastic strain based approach capable of predicting fatigue lifetime of notched components subjected to variable amplitude load histories. i n. zuhair faruq, frattura ed integrità strutturale, 37 (2016) 382-394; doi: 10.3221/igf-esis.37.49 383 stress or strain based approaches are used to assess fatigue damage in mechanical components. stress based approaches are recommended to be used to perform the high-cycle fatigue assessment [2] since, under these circumstances, cyclic plastic deformations can be neglected with little loss of accuracy [3]. the accuracy and reliability of this design strategy has been validated by performing several experimental investigations [4, 5]. however, when cyclic plasticity cannot be disregarded, it is commonly accepted that strain based approaches are more accurate in predicting lifetime of components, with this holding true especially in the low -cycle fatigue regime [1, 6]. this explains why, nowadays, the strain based approach is considered as an irreplaceable tool that is daily used by structural engineers to assess fatigue damage in real engineering components [7, 8]. fundamentals of the modified manson-coffin curve method he modified manson-coffin curve method (mmccm) is a strain-based fatigue criterion that allows uniaxial/multiaxial fatigue damage in real mechanical components subjected to in-service time-variable load histories to be estimated accurately [9, 10]. according to the classical strain-based criterion, manson-coffin curve is defined by slopes c and b that links the maximum shear strain amplitude with the number of reversals to failure. from a physical point of view, the formalisation of the mccm takes as its starting point the assumption that the material plane experiencing the maximum shear strain amplitude coincides with the stage i plane [1] (fig. 1). figure 1: fatigue damage model [1]. according to the fatigue model depicted in fig. 1, the following relationship can be defined [11]:    b cfa f f fn n g ' 2 ' 2     (1) where, a is the shear strain amplitude relative to the critical plane; ’f and ’f are the multiaxial fatigue strength coefficient and the multiaxial fatigue ductility coefficient, respectively; b and c are the multiaxial fatigue strength exponent and the multiaxial fatigue ductility exponent, respectively; nf is the number of cycles to failure. all these fatigue constants can be evaluated by running an appropriate experiment. the classic manson and coffin curve, as shown in fig. 2a and defined by eq. 1, is reformulated to deal with multiaxial fatigue stress/strain tensors by calibrating all functions in eq. 1, as expressed in eq. 2. by following a systematic validation exercise, the mmccm is seen to be capable of accurately modelling not only the detrimental effect of non-zero mean stresses, but also the degree of multiaxiality and non-proportionality of the load history being assessed as shown in fig.2b [11-13]. t n. zuhair faruq, frattura ed integrità strutturale, 37 (2016) 382-394; doi: 10.3221/igf-esis.37.49 384           b cfa f f fn n g ' 2 ' 2        (2) in eq. (2) the functions ’f() , ’f() , b() , c() are fatigue constants that described above but need to be calibrated in terms of rho.  is the critical plane stress ratio and it is defined according to eq. 3, [10]. n m n a n a a , , ,max        (3) in eqs. (3) n,m and n,a are the mean value and amplitude of stress normal to the critical plane; τa is shear stress amplitude relative to the same plane [10]. as to the mmccm’s modus operandi, the modified manson-coffin diagram depicted in fig. 2b shows how this multiaxial fatigue criterion estimates fatigue lifetime, with the modified manson-coffin curves, eq. (2), moving the curve downwards as ratio  increases, resulting an increase in fatigue damage. to conclude, it is worth recalling here that, in the absence of stress concentration phenomena, critical plane stress ratio  equals unity under uniaxial fully-reversed loading, whereas it is equal to zero under pure torsional loading [11]. a. b. figure 2: a. classic manson-coffin curve. b. modified manson-coffin curve [11]. theory of critical distance to quantify the effective local stress/strain state s far as notched components are concerned in this study, a specific methodology is required in order to accurately take into account the presence of stress/strain concentration phenomena and determine the effective local stress/strain histories. the engineering aim of this section is to summarise a fundamental theory of critical distance and using the theory to estimate the effective local stress/strain states at the vicinity of notch apex different than notch tip, to predict fatigue lifetime of notched components. generally, tcd is formalised in different forms that include a point, line, area, and volume method [4]. the point method is the simplest form that commonly used [6] and postulated that the elastoplastic stress/strain state to be used to assess the damaging effect of stress/strain concentrators and has to be determined at a distance (equal to lpm/2) from the notch apex (see fig. 3b). the hypothesis is formed that the required critical distance is a material property, changed in different materials. however, its value remains constant in the same material regardless of notch geometry and notch sharpness [4]. according to the previous findings, that validity is fully supported by the experimental evidence and proved that the tcd is successful not only in predicting fatigue lifetime under constant amplitude loading but also under variable amplitude loading condition [6, 14]. from a practical point of view, to indicate the critical distance for a specific material, the best way is running an appropriate experimental investigation by testing specimens containing with known notched geometry under fully reversed constant amplitude axial force. a n. zuhair faruq, frattura ed integrità strutturale, 37 (2016) 382-394; doi: 10.3221/igf-esis.37.49 385 in the present paper, typical notched samples were considered from a pre-investigated literature [6] as shown in fig. 3a. the samples were tested under fully reversed nominal tension-compression ca cyclic force f(t), resulting in a fatigue failure at nf number of cycles to failure. in the meantime, by post processing the elastoplastic fe model, a stabilized stress/distance and strain/distance curve were plotted along the notch bisector as illustrated in fig. 3d. furthermore, it is worth mentioning here that the stress/strain states at the vicinity of notch tip are experiencing a triaxial history even if the external applied load is uniaxial. the behaviour of these multiaxial stress/strain states are varying proportionally. under these particular circumstances, the level of multiaxiality of the local stress/strain and effect of nonzero mean stress are considered to modify manson-coffin curve. then, by using the experimental number of cycles to failure, average value of a critical distance was computed for specimens subjected to different values of nominal loads. to sum up, according to the theory of critical distance, for a given material, the hypothesis is formed that such a distance is always the same in the same material regardless of notch geometry and notch sharpness. figure 3: summary of a methodology proposed to determine the critical distance – point method lpm [6]. orientation of the critical plane and maximum variance method redicting fatigue lifetime of a component mainly depends on the accuracy in determining the orientation of the critical plane as well as the stress/strain components relative to that plane. the hypothesis is formed that the critical plane, which is defined as the plane experiencing maximum shear strain amplitude [1], coincides with the crack initiation plane. recently, susmel [15] has formalised a numerical algorithm to explore the orientation of the critical plane been applied along with the stress based approach. the algorithm is then reformulated in terms of cyclic strain that summarised in p n. zuhair faruq, frattura ed integrità strutturale, 37 (2016) 382-394; doi: 10.3221/igf-esis.37.49 386 fig.4. this algorithm is developed based on the multi-variable optimisation method known as a gradient ascent method [15]. figure 4: flowchart to explore the orientation of the critical plane [15]. in order to explore the critical plane, a notched component is considered subjected to in-service cyclic load as shown in fig. 5a. then, by taking full advantage of the theory of critical distance, multiaxial local strain history is determined at a specific distance from the notch apex equal to critical distance. the local strain history is described with the following strain tensor (see fig. 5b):   xy xz x xy yz y xz xz z t t t t t t t t t t ( ) ( ) ( ) 2 2 ( ) ( ) ( ) ( ) 2 2 ( ) ( ) ( ) 2 2                              (4) in the above equation, εx(t), εy(t) and εz(t) are normal strain components, whereas xy yz xzt t and t( ), ( ), ( )   are shear strain history. according to the maximum variance method, shear strain amplitude is described by the following eq. 5: n. zuhair faruq, frattura ed integrità strutturale, 37 (2016) 382-394; doi: 10.3221/igf-esis.37.49 387  a qvar t2 .     (5) the variance of shear strain can be determined directly by using the simple form of eq. 6, [15]:   tqvar t d c d[ ]    (6) according to fig 5c, for specific values of angles φ, θ and α, the terms d and [c] in eq. 6 can be simply defined with the following definition:   d d d d d d d 2 1 2 2 3 4 5 6 1 sin( )sin( 2 )cos( ) sin( )sin( 2 )cos( ) 2 1 sin( )sin( 2 )cos( ) sin( )sin( 2 )sin( ) 2 1 sin( )sin( 2 ) 2 1 sin( )sin( 2 )sin( 2 ) cos( )cos( 2 )sin( ) 2 sin( )cos( )co                                                 s( 2 ) cos( )sin( )cos( ) sin( )sin( )cos( 2 ) cos( )cos( )cos( )                                         x x y x z x xy x xz x yz x y y y z y xy y xz y yz x z y z z z xy z xz z yz x xy y xy z xy xy xy xz xy yz x xz y xz z xz xy xz xz xz yz x yz y yz z yz xy yz xy yz yz v c c c c c c v c c c c c c v c c c c c c c v c c c c c c v c c c c c c v , , , , , , , , , , , , , , , , , , , , , , , , , , , , , ,                     (7) figure 5: orientation of the critical plane [1]. n. zuhair faruq, frattura ed integrità strutturale, 37 (2016) 382-394; doi: 10.3221/igf-esis.37.49 388 now, to estimate the variance and covariance terms in matrix [c], consider a time variable strain components εi(t) and εj(t) that described over time period [0,t]. εi,m and εj,m are the mean values of strain histories, the variance and covariance of εi(t) and εj(t) can be determined by using the following definitions:     t i i i mvar t t dt t 2 , 0 1 [ ] [ ]    (8)         t i j i i m j j mcovar t t t t dt t , , 0 1 [ , ] [ ].          (9) after the orientation of the maximum critical plane is indicated, then, by taking full advantage of the maximum variance method [1], all those stress amplitudes relative to the critical plane is calculated. the hypothesis is postulated that fatigue failure is proportional to the variance of cyclic strain at a critical point. from a statistical viewpoint, the variance of variable amplitude cyclic stress/strain is the squared deviation from the mean value. according to the well-documented evidence [1], the above mentioned approach has given satisfactory results when applied in terms of long-life fatigue. in the light of the reliable solution obtained in the stress based critical plane, the maximum variance concept was reformulated for being applied in strain based strategy. after exploring the orientation of the critical plane, maximum variance and normal unit vectors on the critical plane are used to determine the required mean stress/strain values and amplitudes. strictly speaking, for components under constant amplitude ca fatigue load, the stress/strain values of interest related to the critical plane can directly be found using eqs. 10-11 [1]:  a mv mv,max ,min 1 2      m mv mv,max ,min 1 2     (10)  n a n n, ,max ,min 1 2      n m n n, ,max ,min 1 2     (11) where: a and τa are the shear strain and stress amplitudes relative to the critical plane. m and τm are the mean value of shear strain and stress. σn,a and σn,m are the normal stress amplitude and normal mean value. γmv,max and γmv,min are the maximum and minimum variance of shear strain history respectively. τmv,max and τmv,min are used to denote the maximum and minimum variance of shear stress history. σn,max and σn,min are the maximum and minimum normal stress history respectively. all the above described variables are relative to the critical plane. however, in those situations involving variable amplitude cyclic load, the corresponding stress/strain state on the critical plane that damage the component are also variable. the mean value and stress/strain amplitudes of interest related to the critical plane can directly be calculated by the following definitions 12-14 [1 & 15]:   t m mv t dt t 0 1 .       t mv mv mvar t t dt t 2 0 1 .[ ] [ ]    (12)   t n m n t dt t , 0 1 .       t n n n mvar t t dt t 2 , 0 1 .[ ] [ ]    (13)  a mvvar t2.      n a nvar t, 2.     (14) n. zuhair faruq, frattura ed integrità strutturale, 37 (2016) 382-394; doi: 10.3221/igf-esis.37.49 389 classis rain flow counting method eal engineering components are often subjected to a complex cyclic load that either constant or variable amplitude. for the constant amplitude applied loads, the calculated stress/strain amplitude can be used straightforward to estimate number of cycles to failure. however, if the applied nominal loads are changed with time, the local stress/strain history are variable amplitude and the solution may be further complicated. one of the main objectives of this study is to investigate variable amplitude fatigue lifetimes of a component. therefore, the most complex issue that needs to be addressed properly is the cycle counting strategy. examination of the state of the art found that the classic rain-flow method [16] is the best accurate methodology that gives a satisfactory prediction to account the cycles in variable amplitude loading [3, 17-19] and then, leading to better fatigue lifetime predictions. the classic rain-flow method is a cycle counting rule that is used to define whether cycles is formed in every three consecutive points of the time history stress/strain amplitudes. a typical variable amplitude stress/strain history is presented in fig.6. the differences between absolute value of first two consecutive points s1 need to be compared with the difference between second and third points s2 . figure 6: rain flow cycle counting. if s1 is greater than s2 , no cycle is considered, otherwise cycle is counted. the same process should be followed until all cycles are identified. s s s1 1 2   and s s s2 2 3   s s1 2   no cycle is considered s s s3 3 4   and s s s4 4 5   s s3 4   cycle 3-4 is counted s s s6 6 7   and s s s7 7 8   s s6 7   cycle 6-7 is counted it is worth mentioning here that according to the rain flow rules, before start cycle counting, rearrangement is required in the stress/strain history so that it starts either in the highest peak or the lowest valley whichever is greater in absolute value [20], and a new stress/strain-time history is arranged. then, three-point rain flow cycle counting method is applied on every three consecutive points in the new generated stress or strain history. as illustrated in fig. 6, two data points is extracted to form the first cycle, and a new state history is generated by connecting the points before and after the cycle. the subsequent step is repeating the above mentioned cycle extraction technique on every three consecutive points to identify another cycle and generating a new stress/strain history. this process is continued until all cycles are formed. lifetime estimation by using the developed approach: rom the application point of view, this chapter summarised the procedure being followed to validate the developed approach by integrating with the pre-experimentally investigated notched samples from other literature [6]. generally, the developed approach methodology is briefly illustrated in fig.8 and presented in the last sections with a great detail. for the validation view point, pre-investigated cylindrical notched samples of three different notch root r f n. zuhair faruq, frattura ed integrità strutturale, 37 (2016) 382-394; doi: 10.3221/igf-esis.37.49 390 radius were considered: 0.225mm, 1.2mm, and 3.0mm as shown in fig 9e. the specimens were tested under fully reversed constant/variable amplitude uniaxial nominal loads with load ratio (r) equals -1. the samples were made of c40 material. all mechanical and fatigue properties were summarized in tab. 1. the stabilized stress-strain relationship and mansoncoffin curve were generated under fully reversed axial load. the corresponding local elasto-plastic triaxial stress/strain history was obtained by post-processing the fe model using ansys® software. the solved model allows the corresponding stress/strain sequences to be determined at any nodes of interest on the sample. from the accuracy point of view, the element size of fe model at notched bisector was gradually refined and solved under simple linear-elastic behaviour until convergence level. the meshing size at notched region was described by elements with 0.005mm dimension. then, by taking full advantage of the tcd being applied in terms of point method [4], the effective stress/strain history was determined at a given distance from the notch apex (see fig. 7a). in the present investigation, the critical distance was estimated by considering a number of experimental results generated by testing notched specimens under constant amplitude uniaxial fatigue loading [9], the procedure was described in section 3 (theory of critical distance to quantify the effective local stress/strain state). uts (mpa) y (mpa) e (mpa) k’ (mpa) n' ’f (mpa) ε'f b c bo co 852 672 209000 773.3 0.0951 710.6 0.3641 -0.0568 -0.5794 -0.023 -0.98 table 1: mechanical and fatigue properties of c40 steel [9]. the next significant steps is exploring orientation of the critical plane based on the gradient ascent method [1, 15] and estimate the mean and stress/strain amplitudes on the critical plane. the mvm are used to determine the stress/strains amplitudes as shown in fig. 7b. from a computational view point, matlab computer software was used to perform the analysis by exploring orientation of the critical plane and quantify all stress/strain values on that plane. the procedure of finding a critical plane and relative stress/strain amplitudes were summarised clearly in section 4 (orientation of the critical plane and maximum variance method). under constant amplitude load history, after indicating the orientation of the critical plane, all relative shear stress/strain amplitudes and normal stresses can directly be calculated according to the eqs. 3-5. those stress/strain values allow the ratio ρ in eq.2 to be determined. then by using the modified manson-coffin curve, number of cycles to failure can be estimated. however, under variable amplitude fatigue loading, the direction of maximum variance of the resolved shear strain is used to perform the cycle counting based on the classic rain-flow method [1, 16] (see fig. 5i-j). the estimated shear stress amplitude and maximum normal stress can be used to determine a stress ration ρ to modify manson-coffin curve. finally, number of cycles to failure can be estimated by using eq. 15 [1]: j cr f e i tot i d n n d , 1   (15) where: dtot is the total amount of fatigue damage that can be defined by eq. 16, dcr is the critical value of the damage sum, ni is the number of cycles at the i-th strain level. the classical theory formalised by palmgren and miner [21] suggests that fatigue failures take place as soon as the critical value of the damage sum equals unity. however, according to several experimental investigations, sonsino [22] has shown that the average value of dcr is 0.27 for steel and 0.37 for aluminium. j i tot f ii n d n ,1   (16) where: nf,i is the number of cycles to failure for each strain amplitude being considered. n. zuhair faruq, frattura ed integrità strutturale, 37 (2016) 382-394; doi: 10.3221/igf-esis.37.49 391 figure 7: in-field use of the developed approach: methodology [1]. validation by experimental data o check the accuracy and reliability of the devised approach, the model was validated against a number of experimental results reported in ref [9]. this validation exercise involved a systematic study of various elastic/elasto-plastic loading conditions in relation to the fatigue life, particularly when the stress/strain amplitude varies between loading sequences in multiple step loading. as a preliminary stage, experimental results from 70 previouslytested cylindrical notched specimens were taken directly from refs [9], the notch root radius are 0.225mm, 1.2mm, and 3.0mm as shown in fig 8e. the samples were tested under uniaxial sinusoidal loading waves as shown in figs 8a-d, where a-max is the amplitude of the most damaging cycle in the spectrum, and a-i is the amplitude of the ith cycle (both expressed in terms of nominal net stresses). three types of load spectra were considered, which are a simple overloading case (ol), a concave downwards spectrum (cds), and a concave upwards spectrum (cus). those cases represent the potential variable amplitude applied loads on real engineering components. the load ratio r was invariably equal to -1. the material being tested was c40 carbon steel. the required material properties were taken from the aforementioned published work [9]. fig. 8e shows the geometries of the investigated specimens. as far as the numerical stress analysis is concerned, under constant amplitude loading, ten virtual cycles were considered in the theoretical analysis to confirm the stress-strain response reaches a stabilized configuration level [23]. kinematic hardening was used for the elasto-plastic deformation [24]. due to assumptions made while choosing the experimental data in the validation process, particularly while identifying material’s fatigue data that had not been found within the original paper, a narrower error band was defined for the comparison chart. the estimated nf,e versus the experimental nf were arranged in fig. 9. it can be observed that most of t n. zuhair faruq, frattura ed integrità strutturale, 37 (2016) 382-394; doi: 10.3221/igf-esis.37.49 392 the estimated points are located within the designated error interval. subsequently, from the validation view point, it can be pointed out that the elasto-plastic model was in a position to adequately predict the number of cycles to failure. moreover, fig. 9 offers evidence that the devised technique is capable of successfully estimate fatigue lifetime. to sum up, the experimental results are close to the estimated values that are generated using the devised methodology and gave a similar pattern. this demonstrates applicability of the devised approach. figure 8: (a) load spectra (b)-(d) load histories (e) geometries of the specimens [14]. n. zuhair faruq, frattura ed integrità strutturale, 37 (2016) 382-394; doi: 10.3221/igf-esis.37.49 393 figure 9: accuracy of the modified manson-coffin curve versus experimental results. conclusion 1. it can be concluded that the entire range of the developed approach, produced by either constant amplitude or multiple stepwise loading is satisfactory suitable for predicting fatigue lifetime of a notched metallic materials by taking full advantage of the mmccm applied along with the critical distance approach. this demonstrates that the formalised approach can be successful in estimating longevity of the notched components. 2. strain-based approach mmccm, can offer a reliable solution to the local triaxial stress/strain based state, being applied using the critical distance theory. 3. the formalised approach can consider the detrimental effect of non-zero mean stress and degree of multiaxiality, different from other techniques that rationally account this effect. references [1] wang, y., susmel, l., the modified manson–coffin curve method to estimate fatigue lifetime under complex constant and variable amplitude multiaxial fatigue loading. int. j. of fatigue, 83 (2016) 135-149. [2] neuber, h., theory of stress concentration for shear-strained prismatical bodies with arbitrary nonlinear stress-strain law. j. of appl. mech., 28 (1961) 544-550. [3] shamsaei, n., gladskyi, m., panasovskyi, k., shukaev, s., fatemi, a., multiaxial fatigue of titanium including step loading and load path alteration and sequence effects. int. j. of fatigue, 32 (2010) 1862-1874. [4] taylor, d., the theory of critical distances: a new perspective in fracture mechanics., first ed., oxford: elsevier, (2007). [5] susmel, l., taylor, d., fatigue design in the presence of stress concentrations, the j. of strain anal. for eng. design, 38 (2003) 443-452. [6] susmel, l. taylor, d., estimating lifetime of notched components subjected to variable amplitude fatigue loading according to the elastoplastic theory of critical distances., j. of eng. mat. and tech., 137 (2015) 011008. [7] fatemi, a., zeng, z., plaseied, a., fatigue behavior and life predictions of notched specimens made of qt and forged microalloyed steels. int. j. fatigue, 26 (2004) 663-672. [8] susmel l., taylor d., an elasto-plastic reformulation of the theory of critical distances to estimate lifetime of notched components failing in the low/medium-cycle fatigue regime. trans. asme, j. eng. mat. & tech. 132 (2010) 021002-1/8. [9] susmel, l., taylor, d., estimating lifetime of notched components subjected to variable amplitude fatigue loading according to the elasto-plastic theory of critical distances. asme trans, j. of eng. mat. & tech., 137 (2015) 0110081/15, paper no: mats-13-1176. [10] susmel, l., meneghetti, g., atzori, b., a simple and efficient reformulation of the classical manson–coffin curve to predict lifetime under multiaxial fatigue loading—part i: plain materials. trans asme, j. of eng. mat. & tech., 131 (2009) 021009-1/9. n. zuhair faruq, frattura ed integrità strutturale, 37 (2016) 382-394; doi: 10.3221/igf-esis.37.49 394 [11] susmel, l., multiaxial notch fatigue: from nominal to local stress-strain quantities, woodhead & crc, cambridge, uk (2009). [12] susmel, l., meneghetti, g., atzori, b., a simple and efficient reformulation of the classical manson–coffin curve to predict lifetime under multiaxial fatigue loading—part ii: notches. trans asme, j. of eng. mat. & tech., 131.2 (2009) 021010-1/8. [13] susmel, l., atzori, b., meneghetti, g., taylor, d., notch and mean stress effect in fatigue as phenomena of elastoplastic inherent multiaxiality, eng. fra. mech., 78 (2011) 1628-1643. [14] susmel, l., taylor, d., the theory of critical distances to estimate lifetime of notched components subjected to variable amplitude uniaxial fatigue loading, int. j. of fatigue, 33 (2011) 900-911. [15] susmel, l., a simple and efficient numerical algorithm to determine the orientation of the critical plane in multiaxial fatigue problems, international journal of fatigue, 32 (2010) 1875-1883. [16] matsuishi, m., endo, t., fatigue of metals subjected to varying stress. presented to the japan society of mech. eng., (1968) 37-40. [17] wang, c.h., brown, m. w., a path-independent parameter for fatigue under proportional and non-proportional loading. fatigue fracture eng. mat. str., 16 (1993) 1285-1298. [18] bannantine, j. a., socie, d. f., a variable amplitude multiaxial life prediction method. in: fatigue under biaxial and multiaxial loading. mech. eng. publications, (1991) 35-51. [19] shamsaei, n., fatemi, a., socie, d.f., multiaxial fatigue evaluation using discriminating strain paths. int. j. of fatigue, 33 (2011) 597-609. [20] lee, y.l., pan, j., hathaway, r., barkey m.e., fatigue testing and analysis, theory and practice, oxford: elsevier (2005). [21] miner, m.a., cumulative damage in fatigue, j. appl. mech., (1945) ai59-64. [22] sonsino, c.m., fatigue testing under variable amplitude loading, int. j. of fatigue, 29 (2007) 1080-1089. [23] jiang, y., a fatigue criterion for general multiaxial loading, fatigue and fracture of eng. mat. & str., 23(1) (2000) 1932. 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/hrv (za stvaranje adobe pdf dokumenata najpogodnijih za visokokvalitetni ispis prije tiskanja koristite ove postavke. stvoreni pdf dokumenti mogu se otvoriti acrobat i adobe reader 5.0 i kasnijim verzijama.) /hun 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can be opened with acrobat and adobe reader 5.0 and later.) >> /namespace [ (adobe) (common) (1.0) ] /othernamespaces [ << /asreaderspreads false /cropimagestoframes true /errorcontrol /warnandcontinue /flattenerignorespreadoverrides false /includeguidesgrids false /includenonprinting false /includeslug false /namespace [ (adobe) (indesign) (4.0) ] /omitplacedbitmaps false /omitplacedeps false /omitplacedpdf false /simulateoverprint /legacy >> << /addbleedmarks false /addcolorbars false /addcropmarks false /addpageinfo false /addregmarks false /convertcolors /converttocmyk /destinationprofilename () /destinationprofileselector /documentcmyk /downsample16bitimages true /flattenerpreset << /presetselector /mediumresolution >> /formelements false /generatestructure false /includebookmarks false /includehyperlinks false /includeinteractive false /includelayers false /includeprofiles false /multimediahandling /useobjectsettings /namespace [ (adobe) (creativesuite) (2.0) ] /pdfxoutputintentprofileselector /documentcmyk /preserveediting true /untaggedcmykhandling /leaveuntagged /untaggedrgbhandling /usedocumentprofile /usedocumentbleed false >> ] >> setdistillerparams << /hwresolution [2400 2400] /pagesize [612.000 792.000] >> setpagedevice microsoft word numero_35_art_28 t. holušová et alii, frattura ed integrità strutturale, 35 (2016) 242-249; doi: 10.3221/igf-esis.35.28 242 focussed on crack paths a numerical study of two different specimen fixtures for the modified compact tension test – their influence on concrete fracture parameters t. holušová s. seitl (http://orcid.org/0000-0002-4953-4324) institute of structural mechanics, faculty of civil engineering, brno university of technology institute of physics of materials, academy of sciences of the czech republic holusova.t@fce.vutbr.cz; seitl@ipm.cz h. cifuentes (http://orcid.org/0000-0001-6302-418x) dept. of continuum mechanics and structural analysis, university of seville bulte@us.es a. fernández-canteli (http://orcid.org/0000-0001-8071-9223) dept. of construction and manufacturing engineering, university of oviedo afc@uniovi.es abstract. the modified compact tension test (mct) may represent a new test configuration for the performance of static and other kinds of fatigue tests on concrete-like materials. core drilling can be employed to obtain specimens which are cylindrical in shape and have a standard diameter of 150 mm, this being appropriate for the determination of the residual life of structures. this contribution focuses on the evaluation of mct specimen fracture behavior during static tests. cracks evolution are simulated numerically using atena finite element (fe) software, while the results are represented as l-cod diagrams, i.e. load vs. crack opening displacement measured on the loading axis. after numerical calculations, the results for two different fixtures are compared and the advantages or drawbacks for each solution are discussed. keywords. modified compact tension test; fracture parameters; cementitious composites; fem. introduction and motivation nowledge regarding the fracture mechanics behavior (parameters) of the most common building material, concrete, plays a significant role in the determination of the residual life of previously built constructions. this is especially true for concrete used in buildings after several years of aging. drill cores commonly used for the determination of concrete age, can be extracted from real (existing) structures. cylindrical specimens with the selected thickness can be cut from the drill cores. this kind of specimen can be used for the modified compact tension test (mct), whose numerical evaluation is useful for the determination of relevant fracture-mechanics parameters of concrete k t. holušová et alii, frattura ed integrità strutturale, 35 (2016) 242-249; doi: 10.3221/igf-esis.35.28 243 or cement based composites [1]. the common fracture-mechanics test methods for concrete in laboratory conditions are three-point bending (3pb) and four-point bending (4pb) tests, which are both performed on concrete beams of specific dimensions [2]. the specimen for the mct test is similar to specimens used for another standardized fracture-mechanics test, the so-called wedge-splitting test (wst) [3], for which cubic and cylindrical specimens can be used. the mct specimen is similar to standard compact tension (ct) test specimens, which are used for fracture and fatigue parameters of metallic materials [4]. the fracture mechanics parameters and fatigue behavior of quasi-brittle materials, which is currently research topic, see following references: the experimental [5-8] and numerical [9, 10]. previous numerical studies of the modified compact tension test were focused on comparing the fracture energy values that are obtained from the 3pb, wst and mct [11], or on investigating the influence of the location of the steel bars [12]. also, measurements were obtained during the experimental test by an aramis 3d optical camera system, and the quality of the numerical model was evaluated [13]. the numerical evaluation of the use of this type of configuration to determine the fracture energy of concrete was performed with abaqus software [14]. the aim of this contribution is the comparison of two different specimen fixtures and their possible use during experiments from the numerical point of view. the idea of using eye nuts at the ends of the steel bars (see fig. 3b) is to avoid an undesirable moment (which could arise due to the way the specimen is held in the grips during the test) and render the experimental set-up as close as possible to that employed in the standard ct test. the fracture energy is calculated according to rilem recommendations [15] from loading curves obtained from numerical simulations performed with atena 2d fe software [16]. finally, the results are compared and discussed. modified compact tension specimens s mentioned above, the geometry of mct test specimens is derived from that of the original standard compact tension test specimen. it is well known that concrete-like materials exhibit good behavior in compression and poor behavior in tension. on the other hand, metallic materials are well known for their high quality in tension and somewhat lower in compression performance due to buckling. when combined, these two materials create optimal construction material. the tests mentioned above represent standard tests for determining the fracture mechanics parameters of concrete-like materials. typically, specimens for 3pb and 4pb tests are block shaped (their length is significantly greater than their other two dimensions). cubic and cylindrical specimens are typically used for the wst; in this respect it is similar to the mct test, for which these shapes can also be used. figure 1: visualization of a modified compact tension specimen in 3d format. a alig b t. holušová et alii, frattura ed integrità strutturale, 35 (2016) 242-249; doi: 10.3221/igf-esis.35.28 244 figure 2: schematic diagram of a modified compact tension test with dimensions in 2d: a) current set-up; b) set-up with eye nuts at the ends of the steel bars. figure 3: attachment of an experimental specimen to a servo-hydraulic test machine. according to the schematic diagram above: a) current set-up attachment without torsion; b) set-up with eye nuts in the ends of the steel bars. in studied case the cylindrical shape was chosen because such specimens can be conveniently created from drill cores, cylinders usually used for evaluating the age and condition of material taken from existing structures. the mct test specimen can be prepared as follow: the holes are drilled from the sides of the specimen, perpendicular to the starting notch, so that the steel bars can be allocated and glued inside of the specimen. the values in tab. 1 show the predicted dimensions of the mct specimens used for numerical calculations and also for the intended experimental procedure, where: ϕcs is specimen diameter [mm], w is specimen width, i.e., the distance from the load axis to the opposite side of the specimen [mm], a is notch length measured from the load axis [mm], b is specimen thickness [mm], ϕsb is the diameter of the steel bars [mm],  is relative notch length [-] and alig is the area of the ligament [mm2]. specimen dimensions ϕcs [mm] w [mm] a [mm] b [mm] ϕsb [mm]  [-] alig [mm2] 150 120 36 60 8 0.3 5 040 table 1: used dimensions of the mct specimens in numerical study. a) b) a) b) eye nuts at the ends of the steel bars current grips t. holušová et alii, frattura ed integrità strutturale, 35 (2016) 242-249; doi: 10.3221/igf-esis.35.28 245 the ligament area, marked as alig (area marked by red dash lines fig. 1), is defined as the fractured area and is calculated as the product of the length of the ligament and specimen thickness (b). the parameter  (relative notch depth) from tab. 1 is defined as follows:  = a/w (1) in fig. 2 a schematic diagram of a modified compact tension specimen is shown together with the aforementioned dimensions of the specimens. for a better visualization of how the attachment of the specimen to the apparatus would look during a real experimental procedure, specimens with both types of attachment are shown in fig. 3. numerical simulation umerical simulations are performed with atena software [16], which is based on the finite element method (fem). this software has been specifically developed for applications connected with concrete structures. this program is used for numerical support in the experimental testing of the mct test. the mct dimensions used to create the numerical models are listed in tab. 1. the mct specimen is created from two material components, concrete and steel. in the numerical simulations the numerical material called 3d non linear cementitious 2 (3dnl) was used in plane stress conditions for the concrete part. as regards the steel bars, the numerical material called plane stress elastic isotropic (psei) was used. the selected input parameter for the numerical study is the cubic strength fcu [mpa] in the case of 3dnl. it was used 8 various fcu values (fcu {10, 25, 37, 45, 55, 67, 75, 85} mpa) corresponding to the cubic strengths of different classes of plain concrete. the program calculates the other mechanical parameters for material model (the values of other relevant input parameters are left as default values generated by the program). the input parameters of the 3dnl numerical material are summarized in tab. 3; those for psei are in tab. 2. the typical length of the element sides of the finite element mesh of the numerical models is 2 mm; the length is refined to 1 mm around (in the vicinity of) the starting notch. the finite element mesh, boundary conditions and numerical models of the mct test – with the specimen held by grips and with the eye nuts in the ends of the steel bars – are shown in fig. 4. figure 4: numerical models of the modified compact tension test with boundary conditions: a) current grips; b) with eye nuts. n applied load boundary conditions a) b) pin t. holušová et alii, frattura ed integrità strutturale, 35 (2016) 242-249; doi: 10.3221/igf-esis.35.28 246 steel / plane stress elastic isotropic e [mpa] 210 000 μ [-] 0.3  [kg/m3] 7 850 table 2: input parameters of the plane stress elastic isotropic numerical model for steel bars. concrete / 3d non linear cementitious 2 fcu [mpa] 10 25 37 45 55 67 75 85 e [mpa] 18 470 28 060 33 010 35 570 38 170 40 610 41 890 43 170 ft [mpa] 1.114 2.052 2.665 3.036 3.471 3.959 4.268 4.640 fc [mpa] 8.5 21.25 31.45 38.25 46.75 56.95 63.75 72.25 gf [j/m2] 27.85 51.30 66.62 75.91 86.77 98.98 106.7 116 μ [-] 0.2  [kg/m3] 2300 fixed crack model coefficient 0.5 aggregate size [m] 0.02 table 3: input parameters of the 3d non linear cementitious 2 numerical model for concrete. results and discussion he numerical results are presented via l-cod diagrams for studied cases; selected examples are shown in figs. 56. the horizontal axis represents the displacement, in this case the crack opening displacement (cod) measured on the loading axis (labeled cod_f in the diagrams) and also on the axis of the steel bars. the vertical axis is represented by the applied load, giving us the load-cod diagrams. the fracture energy value was also calculated and compared for all curves. fracture energy (gf) is a relevant fracture parameter which characterizes concrete. its value is obtained from work of fracture (wf) divided by the area of the ligament (alig). the work of fracture value corresponds to the area under the corresponding curve. the applicability of the mct test for the determination of the fracture energy of concrete was investigated with promising conclusions (see [17]). fracture energy gf [j/m2] fcu [mpa] 10 25 37 45 55 67 75 85 current grips 48.61 95.52 120.95 134.93 134.08 211.48 218.68 225.25 eye nuts 31.01 67.58 90.15 103.16 122.73 135.66 148.20 163.35 ratio eye/curr 0.638 0.708 0.745 0.765 0.915 0.642 0.678 0.725 table 4: fracture energy values calculated according to rilem recommendations and obtained from loading curves from numerical calculations. the fracture energy values calculated from loading curves are shown in tab. 4. according to the results obtained from numerical simulations, the loading curve for the value fcu = 55 mpa with the current grips shows a significant anomaly. in the other cases, the use of eye nuts at the ends of the steel bars plays a significant role. the curve of the fracture energy values from the numerical models in which eye nuts were used display approximately the same trend as the input fracture energy values. tab. 4 contains the calculated ratios between the values obtained from the loading curves for the numerical t t. holušová et alii, frattura ed integrità strutturale, 35 (2016) 242-249; doi: 10.3221/igf-esis.35.28 247 model with eye nuts at the ends of the steel bars and the model featuring the current method by which the specimen is gripped by the test apparatus. except the ratio for fcu = 55 mpa, the ratios range is from 0.63 – 0.76. for better clarity tab. 4 is reproduced as a graph in fig. 7. figure 5: the final load-cod_f diagrams for fcu 10 and 37 mpa used for the calculation of fracture energy values. figure 6: the final load-cod_f diagrams for fcu 55 and 85 mpa used for the calculation of fracture energy values. conclusion he numerical simulations of the modified compact tension test were performed with the use of atena 2d finite element software. a cylindrical shape was chosen for the specimen, the dimensions of mct are listed in tab. 1. eight cubic strength values (fcu  {10, 25, 37, 45, 55, 67, 75, 85} mpa) were considered as input values for the numerical model used for the concrete part of the structure, 3d non linear cementitious 2. the results are presented by the load-cod_f diagrams and by the fracture energy values calculated according to rilem recommendations [15] and summarized in a graph depending on input cubic strength values. from the numerical point of view, the results show that the use of eye nuts at the ends of the steel bars plays a significant role on the behavior of the conducted test. nevertheless the obtained fracture energy curves show the same trend as the curve of input fracture energy values. in further research and experimental procedures it is recommended that eye nuts are used at the ends of the steel bars in order to avoid undesirable moment. the current method by which the steel is gripped by the test machine does not allow torsion at the ends of the steel bars. this can cause undesirable moment to arise, along with the deformation of the steel bars as you can see in fig. 8 a) – marked by the red line (at the start point of the loading process) and by the green line (at the end point of the loading t t. holušová et alii, frattura ed integrità strutturale, 35 (2016) 242-249; doi: 10.3221/igf-esis.35.28 248 process). to avoid this situation, the use of eye nuts at the ends of the steel bars could be the solution. the eye nuts are allowed to rotate around the pin, which is fixed (see fig. 8 b)). figure 7: fracture energy – input values and those obtained from numerical results. figure 8: results of mct numerical models with cracks – deformed models magnified 200 times. acknowledgments his paper was written with the support of junior specific research project no. sv fast-j-15-2760, ministry of education, youth and sports of the czech republic project no. cz.1.07/2.3.00/20.0214, asturian regional government project no. sv-pa-11-012 and ministry of economy and competitiveness of spain project no. t a) b) pin eye nut t. holušová et alii, frattura ed integrità strutturale, 35 (2016) 242-249; doi: 10.3221/igf-esis.35.28 249 bia2013-48352-p. references [1] karihaloo, b. l., fracture mechanics of concrete, longman scientific & technical, new york, (1995). [2] rilem report 5 fracture mechanics test methods for concrete (s. p. shah & a. carpinteri eds.), chapman and hall, london, (1991). [3] tschegg, e. k., equipment and appropriate specimen shapes for tests to measure fracture values, austrian patent nr. 390328, austrian patent office, (1986). [4] astm international standard e399-06, standard test method for linear-elastic method of plane-strain fracture toughness kic of metallic materials, (2006) 1-32. [5] lee, m. k., barr, b. i. g., an overview of the fatigue behavior of plain and fibre reinforced concrete, cement & concrete composites, 26 (2004) 299-305. [6] s., seitl, h., šimonová, z., keršner, a., fernández-canteli, evaluation of concrete fatigue measurement using standard and non-linear regression model, applied mechanics and materials, 121-126 (2012) 2726-2729. [7] šimonová, h., kucharczyková, b., havlíková, i., seitl, s., keršner, z., complex evaluation of fatigue tests results of plain c30/37 and c45/45 class concrete specimens, key engineering materials, 592-593 (2014) 801-804. [8] korte, s., boel, v, de corte, w., de schutter, g., static and fatigue fracture mechanics properties of self-compacting concrete using three-point bending tests and wedge-splitting tests, construction and building materials, 57 (2014) 1– 8. [9] pryl, d., červenka, j., pukl, r., material model for finite element modelling of fatigue crack growth in concrete, procedia engineering, 2 (2010) 203-212. [10] pryl, d., mikolaskova, j., pukl, r., modeling fatigue damage of concrete, key engineering materials, 577-578 (2014) 385-388. [11] holušová, t., seitl, s., fernández-canteli, a., comparison of fracture energy values obtained from 3pb, wst and ct test configurations, special issue of advanced material research, 969 (2014) 89–92. [12] holušová, t., seitl, s., fernández-canteli, a., modified compact tension test: the influence of the steel bars position. 20th international conference engineering mechanics, (2014) 220–223. [13] holušová, t., seitl, s., fernández-canteli, a., numerical simulation of modified compact tension test depicting of experimental measurement by aramis, key engineering materials, 627 (2014) 277–280. [14] fernández-canteli, a., castañón, l., nieto, b., lozano, m., holušová, t., seitl, s., determining fracture energy parameters of concrete from the modified compact tension test, fracture and structural integrity, 30 (2014) 383–393. [15] rilem tc-50 fmc recommendation determination of the fracture energy of mortar and concrete by means of three-point bend test on notched beams, materials & structures, (1985). [16] červenka, v., červenka, j., pukl, r., atena – a tool for engineering analysis of fracture in concrete, sadhamaacademy proceedings in engineering sciences, 27 (4) (2002) 485–492. [17] cifuentes, h., lozano, m., holušová, t., medina, f., seitl, s., fernández-canteli, a., applicability of a modified compact tension specimen for measuring the fracture energy of concrete, 32 cefie (32 gef) fractusal2015, anales de mechanica de la fractura, 32 (2015) 208–213. << /ascii85encodepages false /allowtransparency false /autopositionepsfiles true /autorotatepages /none /binding /left /calgrayprofile (dot gain 20%) /calrgbprofile (srgb iec61966-2.1) /calcmykprofile (u.s. web coated \050swop\051 v2) /srgbprofile (srgb iec61966-2.1) /cannotembedfontpolicy /error /compatibilitylevel 1.4 /compressobjects /tags /compresspages true /convertimagestoindexed true /passthroughjpegimages true /createjobticket false /defaultrenderingintent /default /detectblends true /detectcurves 0.0000 /colorconversionstrategy /cmyk /dothumbnails false /embedallfonts true /embedopentype false /parseiccprofilesincomments true /embedjoboptions true /dscreportinglevel 0 /emitdscwarnings false /endpage -1 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can be opened with acrobat and adobe reader 5.0 and later.) >> /namespace [ (adobe) (common) (1.0) ] /othernamespaces [ << /asreaderspreads false /cropimagestoframes true /errorcontrol /warnandcontinue /flattenerignorespreadoverrides false /includeguidesgrids false /includenonprinting false /includeslug false /namespace [ (adobe) (indesign) (4.0) ] /omitplacedbitmaps false /omitplacedeps false /omitplacedpdf false /simulateoverprint /legacy >> << /addbleedmarks false /addcolorbars false /addcropmarks false /addpageinfo false /addregmarks false /convertcolors /converttocmyk /destinationprofilename () /destinationprofileselector /documentcmyk /downsample16bitimages true /flattenerpreset << /presetselector /mediumresolution >> /formelements false /generatestructure false /includebookmarks false /includehyperlinks false /includeinteractive false /includelayers false /includeprofiles false /multimediahandling /useobjectsettings /namespace [ (adobe) (creativesuite) (2.0) ] /pdfxoutputintentprofileselector /documentcmyk /preserveediting true /untaggedcmykhandling /leaveuntagged /untaggedrgbhandling /usedocumentprofile /usedocumentbleed false >> ] >> setdistillerparams << /hwresolution [2400 2400] /pagesize [612.000 792.000] >> setpagedevice microsoft word numero_36_art_16 r. citarella, frattura ed integrità strutturale, 36 (2016) 160-167; doi: 10.3221/igf-esis.36.16 160 multiple crack propagation by dbem in a riveted butt-joint: a simplified bidimensional approach r. citarella (https://orcid.org/0000-0003-3167-019x) dept. of industrial engineering, university of salerno, via giovanni paolo ii, 132, fisciano (sa), italy rcitarella@unisa.it abstract. a multi-site damage (msd) crack growth simulation is presented, carried out by means of dual boundary element method (dbem), in a two-dimensional analysis of a cracked butt-joint made of aluminium 2024 t3. an equivalent crack length is proposed for an approximated 2d analysis of a 3d problem where the crack front assumes a part elliptical shape due to secondary bending effects. the assumptions made to perform such simplified bidimensional analyses are validated by comparing numerical results with experimental data, the latter obtained from a fatigue tested riveted butt-joint. key words: dbem; msd; lefm. introduction omplex engineering structures will often present microscopic flaws that can be caused by the manufacturing process or by fatigue, impact or environmental effects such as corrosion. it is therefore crucial to be able to predict how these cracks will affect the integrity of the structure, for example to determine whether a particular crack will grow at all under service loading and, in case, what the life of the component before failure. it is evident from this considerations that the field of fracture mechanics will be an integral part of the design process, particularly in the aircraft industry due to the high strength but low crack resistance materials used in weight critical applications. experimental studies have shown that, if the hypothesis of linear elastic fracture mechanics (lefm) holds true, failure occurs when the stress intensity factor (sif) reaches a critical value. hence the predictions of crack behaviour and the integrity of a structure are dependent on the accurate calculation of sifs. (a) (b) figure 1: deformed lap-joint undergoing a traction load with highlight of sites undergoing maximum bending stresses (a) and stress distribution through the thickness of the sheet (b). c r. citarella, frattura ed integrità strutturale, 36 (2016) 160-167; doi: 10.3221/igf-esis.36.16 161 in this work a multi site damage (msd) crack growth simulation is presented, carried out by means of dual boundary element method (dbem) [1-4] as implemented in the commercial code beasy [5], in a two-dimensional analysis of a butt-joint, made of aluminium alloy 2024 t3, undergoing a traction fatigue load. the bidimensional model represents an approximation of the real phenomena because of the secondary bending effects, illustrated in fig. 1 with reference to a lap-joint (but the phenomenon is completely equivalent for a butt-joint) and responsible for a non-straight crack propagating front. such phenomena would prevent a bidimensional modelling approach, but this drawback can be circumvented, in a preliminary analysis, by adopting an equivalent straight initial crack front as explained in the following. j integral he j integral was developed by rice and cherepanov to characterize fracture for two dimensional configuration. the material is elastic or non-linear elastic. the j integral is defined as: 1 1 ( )ii u j wn t d x      where w is the strain energy density, ti are components of the traction vector and ui are components of the displacement vector. the vector n is the unit normal to the contour  . the strain energy is defined as 0 ( ) ij ij ij ijw w d       i, j = 1,2 and ij is the infinitesimal strain tensor component. the j integral is integrated along a contour  surrounding the crack tip (the ends of the  contour are on opposite faces of the crack and the contour encloses the crack tip). the crack is parallel to the x1 axis. on addition or subtraction of quantities above and below the crack axis, symmetric and anti-symmetric stress and strain derivatives are found from which symmetric stress and strain products are calculated respectively. these products can be decomposed into two parts: one consisting of symmetric stress and strain derivatives (symmetric integrands), the other consisting of anti-symmetric stress and strain derivatives (anti-symmetric integrands). the symmetric integrands can be integrated over the contour area to obtain the mode i j-integral; the anti-symmetric integrands, when integrated, will produce the mode ii j-integral [6]. fatigue crack growth he well-known paris law is adopted for the crack growth rate assessment: nkc dn da  (1) with the calibration parameter c and n for al 2024 t3 given by n=2.144 and c=4.72*10-10 [7], 22 2 iiieff kkkk  (tanaka formula [1]) expressed in mpamm and da in mm. it has been checked that, during the propagation, the sif’s range is included in the interval of validity of paris law, skipping the very initial crack growth phase because of the non-modelled threshold phenomenon and the final crack growth phase, which is dominated by very high growth rates, with kmax approaching kc (kc is the material fracture toughness). problem description and preliminary results on undamaged panel n the following a multi-site damage (msd) crack growth simulation for a butt-joint is presented, carried out by dbem in a two-dimensional analysis. numerical results are then compared with corresponding experimental outcomes, obtained from a fatigue tested riveted butt-joint specimen of aluminium 2024 t3 [7]. t t i r. citarella, frattura ed integrità strutturale, 36 (2016) 160-167; doi: 10.3221/igf-esis.36.16 162 the modelled specimen is representative of the riveted joint existing between the upper shell and the lower shell on the front fuselage section, manufactured by aermacchi for the dornier do328 aircraft (fig. 2a). the corresponding dbem model is illustrated in fig. 2b, where internal points are placed in correspondence of the strain gauge locations (fig. 2a) in order to compare the numerical and experimental strains and assess the model accuracy. the distance from the panel edge to the first hole was chosen from the experimenter equal to 10 mm, giving a total panel width w=280 mm (fig. 2a). the four holes close to the plate border were cold worked in order to avoid crack initiation during the fatigue test (in fig. 2a, holes with crack tips n. 1, 28, 29, 56) or at least strongly retard crack propagation [8]. the remote applied load is t=100 mpa (fig. 2b) and the material properties are: young modulus e=72500 mpa and poisson ratio .33  . 1 28 29 56 (a) line of internal points in correspondence of strain gauge positions hole with no modelling of inside pin hole with explicit modelling of inside pin (b) figure 2: butt joint sketch (a) with highlight of strain gauge positions and crack tip numbering (n. 1:28 in the lower hole row and n. 29:56 in the upper cracked hole row); dbem uncracked model (b) with highlight of internal spring (yellow symbols), internal points and hole constraints (green symbols). r. citarella, frattura ed integrità strutturale, 36 (2016) 160-167; doi: 10.3221/igf-esis.36.16 163 the butt-joint is designed and loaded in the experimental tests, in such a way to reproduce, as close as possible, the real in-service stress state, like, for example, a uniform distribution of longitudinal stresses yyalong a transversal section of the undamaged joint sufficiently far from the riveted area. along such section a row of strain gauges was placed and correspondingly a row of internal points was introduced in the dbem model (n. 6:17 in fig. 2b) in order to monitor the level of aforementioned stresses. the same was done to cross check the longitudinal stress distribution in a longitudinal section (internal points n. 1-5 in fig. 2b). in particular, for the undamaged panel, the dbem model provides the longitudinal stress distribution at strain gauge locations illustrated in figs. 3a-b: the numerical stresses are in good agreement with the experimental stress state [7]. (a) (b) figure 3: membrane longitudinal stresses yy on transversal section at y=54.25 mm (a); longitudinal stresses yy on longitudinal section at x=110 mm (b). it is evident that, whenever experimental strains were available from both sides of the panel they should had been averaged in order to be comparable with numerical results (strain values are slightly different on the two panel sides because of the secondary bending). this check turned out very useful in order to calibrate the model and in particular to decide how many rivets to be explicitly modelled by inserting a pin in the corresponding hole: such pin would be constrained against y translation and disconnected from the hole upper surface by means of internal spring of negligible stiffness (fig. 2b). alternatively, the holes not directly involved by crack propagation can be modelled by just introducing longitudinal constraints on 180 degrees of the hole boundary and skipping the explicit pin modelling (fig. 2b). gap elements have also been introduced, to better tackle contact conditions but the solution improvement has been judged quite negligible (less than 2%), except in case of very short cracks initiated from the holes, more sensitive to pinhole contact conditions (but not present in this work). for this reason, and due to the computational effort of a non-linear analysis, they have not been used anymore. r. citarella, frattura ed integrità strutturale, 36 (2016) 160-167; doi: 10.3221/igf-esis.36.16 164 the j-integral technique is adopted for sif’s evaluation, being more stable than crack opening displacement method, against a variable refinement of crack mesh. on the j-integral path, 33 integration points are used (the increment of accuracy with 66 points turn out to be negligible). the mesh used for the butt-joint is based on about 327 quadratic elements: a p-convergence study has been realized showing that cubic elements provide an accuracy improvement of less than 2% and that 2 quadratic elements per 90 degrees are sufficient on the cracked hole, except for very short cracks, where 3 elements are recommendable (possibly with a scaling ratio). all the undamaged holes are modelled with 6 elements, constrained in y-direction. numerical crack propagation he crack growth has been simulated considering the interval ranging between 73500 and 113885 fatigue cycles. the initial crack length in the model, at left or right hole sides, is not taken equal to that (size b in fig. 4a) visually observed on the free surfaces at 73500 cycles [7] because of the following reasons. the crack length monitored in the experimental phase is related to the external surface (“penetrated crack”), but the crack first appear on the faying surface because here undergoes the primary tensile stress and, in addition, the secondary bending stress (fig. 1). as a matter of fact, due to the superimposed secondary bending the crack assumes a part elliptical shape (fig. 4), in such a way that it is already abundantly extended on the faying surface when appearing on the external surface.   b (a) (b) figure 4: geometric sizes of rivet hole (a) and crack shape development (b) [9]. it is possible to make a forecast of the hidden part crack length, right before the appearance of the external crack front (fig. 4b), observing that the ratios between the two ellipse semi-axis, crack depth a and crack length c and between a and t (specimen thickness), even if variable at initiation, assume always the same values for a given bending factor k=max tension/max bending when the crack is on the verge to become through the thickness (e.g. for k=1 we obtain a/c=0.575 and a/t=0.88) [9]. in our particular case, for a plate thickness t=1.2 mm, when each crack appears on the visible plate side with a length b (as reported by the experimenter), by using the aforementioned relationships, it is possible to know the size of the part elliptical crack on the faying side, obtaining c=a/0.575=0.88*t/0.575=1.84 mm (figs. 4a-b). keeping into account these data and the shape of the real hole (fig. 4a) against the simplified modelled geometry (a cylinder of radius 2.4 mm), when modelling an equivalent straight initial crack we have prolonged of 1 mm the initial crack length value b measured by the experimenter. during the propagation some cracks will link-up and the criteria chosen to assess such condition is the overlapping of the crack tip plastic zones: l=rp1+rp2 where l is the residual ligament and rp=(keq2/y2)/; y is the yield stress. when two cracks link-up a new crack initiation is postulated from the hole side opposite to the crack. t r. citarella, frattura ed integrità strutturale, 36 (2016) 160-167; doi: 10.3221/igf-esis.36.16 165 intermediate deformed plots, during the multi side crack propagation, are presented in figs. 5a-g, where each new crack introduced in the model comes from the experimental recordings or is postulated to appear when two cracks link-up (as previously said). a b c d e f g constraints in the pin to model the action of the overlapped plate (not explicitly modelled) continuity condition between hole and rivet internal springs of negligible stiffness to model pin-hole disconnection constraints in the hole to model the action of the overlapped plate (no pin modelling) 41 42 41 42 43 41 42 43 41 44 47 39 40 41 44 45 47 39 44 45 47 38 39 44 45 47 51 figure 5: deformed shape (scale factor 20) of multiple crack scenario after a number of cycles equal to: 73500 (a), with initial cracks (tip n. 41 and 42) as recorded by the experimenter; 84000 (b) with a new recorded initiation (tip n. 43); 99500 (c) with propagation of the previously indicated cracks and a new recorded initiation (tip n. 47); 105770 (d) with a link-up between tips n. 42 and 43 and corresponding new postulated initiation (tip n. 44); 108000 (e) with new recorded initiations (tip n. 39, 40 and 45); 110500 (f) with a link-up between tips n. 40 and 41 and a new recorded initiations (tip n. 51); 112000 (g) with new recorded initiations (tip n. 38). r. citarella, frattura ed integrità strutturale, 36 (2016) 160-167; doi: 10.3221/igf-esis.36.16 166 in tab. 1 and tab. 2 the crack length vs. cycles and the related equivalent sifs are respectively shown. with the aforementioned bidimensional approach a good agreement between numerical and experimental [7] crack scenarios is obtained and it is possible to capture the essential features of the response even if the secondary bending is not modelled. tip n 38 39 40 41 42 43 44 45 47 51 73500 1.82 1.42 78810 2.63 2.28 84030 3.36 3.04 1.16 88830 4.46 4.18 2.24 93280 5.20 4.94 2.84 97330 5.92 5.70 3.43 99500 6.54 6.37 3.94 1.19 102850 7.23 7.14 4.52 1.77 105770 7.86 7.91 5.13 1.50 2.17 108000 1.15 1.12 9.27 link-up link-up 2.28 1.19 3.20 110500 1.83 1.94 10.30 3.25 1.78 3.60 1.12 112000 1.20 2.59 link-up link-up 4.02 2.14 4.00 1.43 113885 1.81 3.57 5.02 2.61 4.36 1.69 table 1: crack propagation lengths (mm) versus load cycles. tip n 38 39 40 41 42 43 44 45 47 51 73500 389 400 78810 397 403 84030 406 410 391 88830 428 435 390 93280 443 453 401 97330 456 472 415 99500 471 496 438 400 102850 474 501 476 393 105770 505 600 549 419 390 108000 502 555 611 417 468 418 110500 535 631 709 652 484 430 396 112000 542 720 729 527 500 400 113885 548 740 750 553 572 400 table 2: equivalent sif’s (mpamm) versus number of cycles. r. citarella, frattura ed integrità strutturale, 36 (2016) 160-167; doi: 10.3221/igf-esis.36.16 167 conclusions t is important to point out the need, in a bidimensional crack propagation model for a butt-joint, to model the part elliptical crack front at initiation with an “equivalent” prolonged straight crack. as a matter of fact, in such case the penetrated front experiences a lower stress, compared with the hidden front surface and consequently there is not the “catch up” behaviour that is typical of the pure tensile case, where the “penetrated” crack front reaches immediately the more prominent front surface because of the higher sifs [9]. even with the illustrated simplified bidimensional approach it is possible, for such kind of problems, to obtain a satisfactory agreement with experimental crack growth rates. moreover, very short run times are needed to run the whole propagation and an easy preprocessing phase is enabled by the dbem approach: an automatic remeshing is possible as the crack grows and the manual intervention is just necessary to initiate new cracks. a more accurate dbem bidimensional approach (with respect to the simplified approach adopted in this work) to model the butt joint assembly is also possible when needed: each layer can be considered as an individual two-dimensional structure; individual layers can be explicitly modelled and connected with rivets; by gap elements can be used at the interface pin-hole…[10]. the very basic approach presented here, with related very short run times, becomes mandatory in case of a probabilistic approach to crack propagation simulation where hundred thousands of such simulations are to be performed (e.g. when resorting to monte carlo method…) [11]. references [1] citarella, r., perrella, m., multiple surface crack propagation: numerical simulations and experimental tests, fatigue and fracture of engineering material and structures, 28 (2005) 135-148. doi: 10.1111/j.1460-2695.2004.00842.x. [2] citarella, r., cricrì, g., armentani, e., multiple crack propagation with dual boundary element method in stiffened and reinforced full scale aeronautic panels, key engineering materials, 560 (2013) 129-155. doi: 10.4028/www.scientific.net/kem.560.129. [3] citarella, r., msd crack propagation on a repaired aeronautic panel by dbem, advances in engineering software, 42 (10) (2011) 887-901. doi: 10.1016/j.advengsoft.2011.02.014. [4] citarella, r., non linear msd crack growth by dbem for a riveted aeronautic reinforcement, advances in engineering software, 40(4) (2009) 253–259. doi: 10.1016/j.advengsoft.2008.04.007. [5] beasy v10r14, documentation, c.m. beasy ltd, (2011). [6] rigby, r.h., aliabadi, m.h., decomposition of the mixed-mode j-integral-revisited, int. j. solids structures, 35(17) (1998) 2073-2099. doi: 10.1016/s0020-7683(97)00171-6. [7] cattaneo, g., cavallini, g., galatolo, r., smaac (testing of “simple” specimens), document no. smaac-tr-3.207-1.3/aem, (1998). [8] citarella, r., cricrì, g., lepore, m., perrella, m., assessment of crack growth from a cold worked hole by coupled fem-dbem approach, key engineering materials, 577-578 (2014) 669-672. doi: 10.4028/www.scientific.net/kem.577-578.669. [9] fawaz, s.a., fatigue crack growth in riveted joints, doctoral thesis, delft university press, the netherlands, (1997). [10] armentani, e., citarella, r., dbem and fem analysis on non-linear multiple crack propagation in an aeronautic doubler-skin assembly, international journal of fatigue, 28 (2006) 598–608. doi: 10.1016/j.ijfatigue.2005.06.050. [11] citarella, r., apicella, a., advanced design concepts and maintenance by integrated risk evaluation for aerostructures, structural durability & health monitoring, 2(3) (2006) 183-196. doi: 10.3970/sdhm.2006.002.183. i << /ascii85encodepages false /allowtransparency false /autopositionepsfiles true /autorotatepages /none /binding /left /calgrayprofile (dot gain 20%) /calrgbprofile (srgb iec61966-2.1) /calcmykprofile (u.s. web coated \050swop\051 v2) /srgbprofile (srgb iec61966-2.1) /cannotembedfontpolicy /error /compatibilitylevel 1.4 /compressobjects /tags /compresspages true /convertimagestoindexed true /passthroughjpegimages true /createjobticket false /defaultrenderingintent /default /detectblends true /detectcurves 0.0000 /colorconversionstrategy /cmyk /dothumbnails false /embedallfonts true /embedopentype false /parseiccprofilesincomments true /embedjoboptions true /dscreportinglevel 0 /emitdscwarnings false /endpage -1 /imagememory 1048576 /lockdistillerparams false 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can be opened with acrobat and adobe reader 5.0 and later.) >> /namespace [ (adobe) (common) (1.0) ] /othernamespaces [ << /asreaderspreads false /cropimagestoframes true /errorcontrol /warnandcontinue /flattenerignorespreadoverrides false /includeguidesgrids false /includenonprinting false /includeslug false /namespace [ (adobe) (indesign) (4.0) ] /omitplacedbitmaps false /omitplacedeps false /omitplacedpdf false /simulateoverprint /legacy >> << /addbleedmarks false /addcolorbars false /addcropmarks false /addpageinfo false /addregmarks false /convertcolors /converttocmyk /destinationprofilename () /destinationprofileselector /documentcmyk /downsample16bitimages true /flattenerpreset << /presetselector /mediumresolution >> /formelements false /generatestructure false /includebookmarks false /includehyperlinks false /includeinteractive false /includelayers false /includeprofiles false /multimediahandling /useobjectsettings /namespace [ (adobe) (creativesuite) (2.0) ] /pdfxoutputintentprofileselector /documentcmyk /preserveediting true /untaggedcmykhandling /leaveuntagged /untaggedrgbhandling /usedocumentprofile /usedocumentbleed false >> ] >> setdistillerparams << /hwresolution [2400 2400] /pagesize [612.000 792.000] >> setpagedevice microsoft word numero_35_art_52 l. c. h. ricardo et alii, frattura ed integrità strutturale, 35 (2016) 456-471; doi: 10.3221/igf-esis.35.52 456 crack simulation models in variable amplitude loading a review luiz carlos h. ricardo materials technology department, ipen, university of são paulo, brazil, instituto de pesquisas energéticas e nucleares av. lineu prestes 2242 cidade universitária são paulo sp brasilcep: 05508-000. lricardo@ipen.br carlos alexandre j. miranda nuclear engineering department, ipen, university of sao paulo, brazil, instituto de pesquisas energéticas e nucleares av. lineu prestes 2242 cidade universitária são paulo sp brasilcep: 05508-000 abstract. this work presents a review of crack propagation simulation models considering plane stress and plane strain conditions. it is presented also a chronological different methodologies used to perform the crack advance by finite element method. some procedures used to edit variable spectrum loading and the effects during crack propagation processes, like retardation, in the fatigue life of the structures are discussed. based on this work there is no consensus in the scientific community to determine the best way to simulate crack propagation under variable spectrum loading due the combination of metallurgic and mechanical factors regarding, for example, how to select and edit the representative spectrum loading to be used in the crack propagation simulation. keywords. fatigue; crack propagation simulation; finite element method; retardation. introduction he most common technique for predicting the fatigue life of automotive, aircraft and wind turbine structures is miner’s rule [1]. despite the known deviations, inaccuracies and proven conservatism of miner’s cumulative damage law, it is even nowadays being used in the design of many advanced structures. fracture mechanics techniques for fatigue life predictions remain as a back up in design procedures. the most important and difficult problem in using fracture mechanics concepts in design seems to be the use of crack growth data to predict fatigue life. the experimentally obtained data is used to derive a relationship between stress intensity range (k) and crack growth per cycle (da/dn). in cases of fatigue loaded parts containing a flaw under constant stress amplitude fatigue, the crack growth can be calculated by simple integration of the relation between da/dn and k. however, for complex spectrum loadings, simple addition of the crack growth occurring in each portion of the loading sequence produces results that, very often, are more erroneous than the results obtained using miner’s rule with an s-n curve. retardation tends to cause conservative results using miner’s rule when the fatigue life is dominated by the crack growth. however, the opposite effect generally occurs when the life is dominated by the initiation and growth of small cracks. in these cases, large cyclic strains, which might occur locally at stress raisers due to overload, may pre-damage the material and lower its resistance to fatigue. the experimentally derived crack growth equations are independent of the loading sequence and depend only on the stress intensity range and the number of cycles for that portion of the loading sequence. the central problem in the successful utilization of fracture mechanic techniques applied to the fatigue spectrum is to obtain a clear understanding of t l. c. h. ricardo et alii, frattura ed integrità strutturale, 35 (2016) 456-471; doi: 10.3221/igf-esis.35.52 457 the influence of loading sequences on fatigue crack growth [2]. investigations covering the effects of particular interest, after high overload, in the study of crack growth under variable-amplitude loading in the growth rate region, called crack growth retardation, seem to have little interest nowadays. stouffer & williams [3] and other researchers show a number of attempts to model this phenomenon through manipulation of the constants and stress intensity factors in the paris-erdogan equation however little appears to have been done in the effort to develop a completely rational analysis of the problem. probably, the only one reason that the existing models of retarded crack growth are not satisfactory is that these models are deterministic whereas the fatigue crack growth phenomenon shows strong random features. in addition, most of the reported theoretical descriptions of the retardation are based on data fitting techniques, which tend to hide the behavior of the phenomenon. if the retarding effect of a peak overload on the crack growth is neglected, the prediction of the material lifetime is usually very conservative [4]. accurate predictions of the fatigue life will hardly become possible before the physics of the peak overload mechanisms is better clarified. according to the existing findings, the retardation is a physically very complicated phenomenon which is affected by a wide range of variables associated with loading, metallurgical properties, environment, etc., and it is difficult to separate the contribution of each of these variables [5]. crack propagation concepts rwin [6,7] defines in his work a release energy rate g, which is a measure of the available energy, dп-potential of energy and a-crack area, to provoke crack propagation as shown in eq. (1). the term rate as employed is not related to a derivate in relation to the time but is referred to a change in the potential energy rate in the crack area. later, this quantity has been called k, and is used to characterize the stress state ("stress intensity") near a crack tip caused by a remote load or residual stress in isotropic and elastic bodies. the stress field in the crack tip is given by eq. (2), d g da   (1) 1/2 1/22 3( 2 ) ( ) ( ) ( ) ......ij ij ij ijk r f a g a h r         (2) where k is the stress intensity factor; r and  are the distance from the crack tip and the angle between the crack tip and the plane of the crack, respectively; ai is a constant of the material; fij (), gij () and hij() are functions of ..after years, the stress-intensity factors for a large number of crack configurations have been generated; and these have been collated into several handbooks (see, for example, refs [8,9]). the use of k is meaningful only when small-scale yielding conditions exist. plasticity and nonlinear effects will be covered in the next section. because fatigue-crack initiation is, in general, a surface phenomenon, the stress-intensity factors for a surfaceor corner-crack in a plate or at a hole, such as those developed by raju and newman [10,11], are solutions that are needed to analyze small-crack growth. some of these solutions are used later to predict fatigue-crack growth and fatigue lives for notched specimens made of a variety of materials [12]. frost and dugdale [13] have evidenced that the size of the plastic zone increases in the same ratio that of the crack length. one can notice that the results of the equation depend linearly on the crack length a; however, frost and dugdale [13] also argued by dimensional analysis that the incremental propagation in the crack length da, for an incremental number of cycles dn, should be directly proportional to the crack length a. thus, da ba dn  (3) where b is a function of the applied stresses. paris & erdogan [14] conducted a revision on the crack propagation approach from head [15] and others and discussed the similarity of these theories and the differences of results between them, isolated and in group tests. paris suggested that, for a cyclical load variation, the stress field in the crack tip for a cycle can be characterized by a variation of the stress intensity factor, max mink k k   (4) i l. c. h. ricardo et alii, frattura ed integrità strutturale, 35 (2016) 456-471; doi: 10.3221/igf-esis.35.52 458 where kmax and kmin are the maximum and the minimum stress intensity factors, respectively. in the crack propagation curve, the linear part represents the paris erdogan law, when plotting the values of k vs da/dn in logarithmic scale. fatigue crack initiation and growth under cyclic loading conditions is controlled by the plastic zones that result from the applied stresses and exist in the vicinity (ahead) of a propagating crack and in its wake or flanks of the adjoining surfaces. for example, the fatigue characteristics of a cracked specimen or component under a single overload or variable amplitude loading situations are significantly influenced by these plastic zones. in modelling the fatigue crack growth rate this is accounted by the incorporation of accumulative damage cycle after cycle and should include plasticity effects. during the crack propagation the plastic zone should grown and the plastic wake will have compressive plastic zones that can help to keep the crack close. prediction of the fatigue behaviour of structural components subjected to overloads and variable amplitude loading requires an estimation of the plastically affected regions ahead of the crack-tip. one of the most widely used plasticity models in fatigue is the dugdale’s yield strip model [16] in this model the plastically affected zone (ry or rp) is assumed to be small as shown fig. 1. figure 1: elastic and elastic-plastic zone sizes. hairman & provan [17] discuss the problems pertaining to fatigue loading of engineering structures under single overload and variable amplitude loading involving the estimation of plasticity affected zones ahead of the crack tip. the models of irwin [6,7] and dugdale [16] give an idea of the size of the plastic zone but not of its shape. the size, in general, is estimated as a circle of certain diameter (ry or rp) obtained on the basis of reasoning given in the above models for cracktip-plasticity. in these models the effect of the shape of the plasticity affected zones is not taken into account. to obtain a better idea of the plastic zone shape, the components of stress in the radial and circumferential directions of a mode-1 type of loading were derived using an eigenfunction expansion method developed by williams [18] and with a modification to take into consideration crack-tip blunting. the resulting equations are:       1 3 5 cos cos , , 4 2 22 1 3 3 cos cos , , 4 2 22 1 3 sin sin , , 4 2 22 rr r r k t f r r k f r r k f r r                                                                                   (5) the first terms in eq. (5) represent the singular terms as r  0 and are, therefore, dominant near the crack-tip. the second term in eq. (5) arises from a consideration of higher power terms. this term is known as the t-stress, it is not singular as r  0 but it can affect the elastic-plastic crack-tip stress state. the third terms arise as a contribution from crack-tip blunting and are not given in williams [18]. the contribution of crack-tip blunting has been discussed in rolfe – l. c. h. ricardo et alii, frattura ed integrità strutturale, 35 (2016) 456-471; doi: 10.3221/igf-esis.35.52 459 barsom [19] and the contribution of this term is p=k/() for a sharp elliptic or hyperbolic notch with a crack-tip radius, . the above equations can now be used to obtain the principal stresses after the simplifying assumptions of negligible contributions of trr and f(,r,) are assumed. hence, the principal stresses, as derived from eq. (5), become:   1 2 3 21 cos 1 sin 2 22 1 cos 1 sin 4 2 22 0 k r k r                                          (6) this, in conjunction with the von mises and tresca yield criteria, gives the expressions for the plastic zone shape as follows: von mises:   2 2 2 2 2 2 2 3 sin ( ) (1 2 ) 1 cos( ) 4 2 ( ) 3 1 sin ( ) cos( ) 4 2 ys p ys k r k                          (7) tresca: 2 2 2 222 2 22 2 2 cos sin 2 2 2 ( ) cos 1 2 sin 2 2 2 cos 1 sin 2 2 2 ys p ys ys k r k k                                                                  (8)  min max ( ) 1 m c c kda dn k k k k         max ( )m c c kda dn k k    1 max( ) ( ) m mda c k k dn   table 1: empirical crack growth equations for constant amplitude loading [14]. plane stress plane strain plane stress plane strain plane stress plane strain l. c. h. ricardo et alii, frattura ed integrità strutturale, 35 (2016) 456-471; doi: 10.3221/igf-esis.35.52 460 in the original paris crack propagation equation [14] the driving parameters are c, k and m. in tab. 1 it is possible to see some other crack propagation equations for constant amplitude loading, which are modifications of the paris equation, relating the mentioned parameters. murthy et al. [20] discuss crack growth models for variable amplitude loading and the mechanisms and contribution to overload retardation. there are many authors which have been developing fatigue crack growth models for variable amplitude loading. tab. 2 presents some authors and the application of their models. yield zone concept crack closure concept wheeler [21] elber [28] willenborg, engle, wood [22] bell and creager (generalized closure) [29] porter [23] newman (finite element method) [30] gray (generalized wheeler) [24] dill and staff (contact stress ) [31] gallagher and hughes [25] kanninen, fedderson, atkinson [32] johnson [26] budiansky and hutchinson [33] chang et al. [27] de koning [34] table 2: fatigue crack growth models [20]. retardation phenomenon orbly & packman [35] present some aspects of the retardation phenomenon some of which are presented below. 1. retardation increases with higher values of peak loading peak for constant values of lower stress levels [36,37]. 2. the number of cycles at the lower stress level required to return to the non-retarded crack growth rate is a function of kpeak, klower, rpeak,, rlower and number of peak cycles [38]. 3. if the ratio of the peak stress to lower stress intensity factors is greater than l.5 complete retardation at the lower stress intensity range is observed. tests were not continued long enough to see if the crack ever propagated again [38]. 4. with a constant ratio of peak to lower stress intensity the number of cycles to return to non-retarded growth rates increases with increasing peak stress intensity [37,38]. 5. given a ratio of peak stress to lower stress, the number of cycles required to return to non-retarded growth rates decreases with increased time at zero load before cycling at the lower level [38]. 6. increased percentage delay effects of peak loading given a percent overload are greater at higher baseline stress intensity factors [39]. 7. delay is a minimum if compression is applied immediately after tensile overload [40]. 8. negative peak loads cause no substantial influence of crack growth rates at lower stress levels if the values of r > 0 for the lower stress [41]. 9. negative peak loads cause up to 50 per cent increase in fatigue crack propagation with r = 1 [40]. 10. importance of residual compressive stresses around the tip of crack [42]. 11. low-high sequences cause an initial acceleration of the crack propagation at the higher stress level which rapidly stabilizes [43]. small scale yield models hile the basic layout of the small scale yield model has been established by dill & saff [44], only improvements introduced later by newman [45] made this approach applicable to general variable amplitude loading. the small scale yield model employs the dugdale [16] theory of crack tip plasticity modified to leave a wedge of plastically stretched material on the fatigue crack surfaces. the fatigue crack growth is simulated by severing the strip material over a distance corresponding to the fatigue crack growth increment as shown fig. 2. in order to satisfy the compatibility between the elastic plate and the plastically deformed strip material, a traction must be applied on the c w l. c. h. ricardo et alii, frattura ed integrità strutturale, 35 (2016) 456-471; doi: 10.3221/igf-esis.35.52 461 fictitious crack surfaces in the plastic zone (a  x < aafict), as in the original dugdale model, and also over some distance in the crack wake (aopen  x < a), where the plastic elongations of the strip l(x) exceed the fictitious crack opening displacements v(x). the compressive stress applied in the crack wake to insure l(x)=v(x) are referred to as the contact stresses. the fatigue crack growth is simulated using the strip material as shown schematically in fig. 2. figure 2: schematic small scale yield model. ricardo et al. [46] discuss the importance in the determination of materials properties like crack opening and closing stress intensity factor. the development of crack closure mechanisms, such plasticity, roughness, oxide, corrosion, and fretting product debris, and the use of the effective stress intensity factor range, has provided an engineering tool to predict small and large crack growth rate behavior under service loading conditions. the major links between fatigue and fracture mechanics were done by christensen [47] and elber [48]. the crack closure concept put crack propagation theories on a firm foundation and allowed the development of practical life prediction for variable and constant amplitude loading, by such as experienced by modern day commercial aircrafts. numerical analysis using finite elements has played a major role in the stress analysis crack problems. swedlow [49] was one of the first to use finite element method to study the elastic-plastic stress field around a crack. the application of linear elastic fracture mechanics, i.e. the stress intensity factor range, k, to the “small or short” crack growth have been studied for long time to explain the effects of nonlinear crack tip parameters. the key issue for these nonlinear crack tip parameters is crack closure. analytical models were developed to predict crack growth and crack closure processes like dugdale [16], or strip yield, using the plasticity induced approach in the models considering normally plane stress or strain effects. schijve [50], discussing the relation between short and long cracks presented also the significance of crack closure and growth on fatigue cracks under services load histories. the ultimate goal of prediction models is to arrive at quantitative results of fatigue crack growth in terms of millimeters per year or some other service period. such predictions are required for safety and economy reasons, for example, for aircraft and automotive parts. sometimes the service load time history (variable amplitude loading) is much similar to constant amplitude loading, including mean load effects. in both cases quantitative knowledge of crack opening stress level sop is essential for crack growth predictions, because keff is supposed to be the appropriate field parameter for correlating crack growth rates under different cyclic loading conditions. the correlation of crack growth data starts from the similitude approach, based on the keff, which predicts that same keff cycles will produce the same crack growth increments. the application of keff to variable amplitude loading require prediction of the variation of sop, during variable amplitude load history, which for the more advanced prediction models implies a cycle by cycle prediction. the fig. 3 shows the different k values. l. c. h. ricardo et alii, frattura ed integrità strutturale, 35 (2016) 456-471; doi: 10.3221/igf-esis.35.52 462 figure 3: definitions of k values, schijve [50]. the application of keff is considerably complicated by two problems: (1) small cracks and (2) threshold k values (kth). small cracks can be significant because in many cases a relatively large part of the fatigue life is spent in the small crack length regime. the threshold problem is particularly relevant for fatigue under variable amplitude spectrum, if the spectrum includes many “small” cycles. it is important to know whether the small cycles do exceed a threshold k value, and to which extension it will occur. the application of similitude concept in structures can help so much, but the results correlation is not satisfactory and the arguments normally are:  the similarity can be violated because the crack growth mechanism are no longer similar  the crack can be too small for adopting k as a unique field parameter  keff and others conditions being nominally similar, it is possible that other crack tip aspects also affect crack growth, such as crack tip blunting and strain hardening, schijve [50]. newman and armen [51-53] and ohji et al. [54] were the first to conduct the two dimensional analysis of the crack growth process. their results under plane stress conditions were in quantitative agreement with experimental results by elber [28], and showed that crack opening stresses were a function of r ratio (smin/smax) and the stress level (smax/0), where 0 is the flow stress i.e: the average between ys and u. blom and holm [55] and fleck and newman [56-57] studied crack growth and closure under plane-strain conditions and found that cracks did close but the cracks opening levels were much lower than those under plane stress conditions considering same loading condition. sehitoglu et al. [58] found later that the residual plastic deformations that cause closure came from the crack. mcclung [59-61] performed extensive finite element crack closure calculations on small cracks at holes, and various fatigue crack growth models. newman [62] found that smax/0 could correlate the crack opening stresses for different flow stresses (0). this average value was used as stress level in the plastic zone for the middle crack tension specimen, mcclung [61] found that k analogy, using kmax/k0 could correlate the crack opening stresses for different crack configurations for small scale yielding conditions where k0=o(a) . (k-analogy assumes that the stress-intensity factor controls the development of closure and crack-opening stresses and that, by matching the k solution among different cracked specimens, an estimate can be made for the crack opening stresses). matos & nowell [63] present a literature review of the phenomenon of plasticity-induced fatigue crack closure under plane strain conditions and mention that there are controversial topics concerning the mechanics of crack propagation. in general there is no consensus in the scientific community. fleck [64] used finite elements to simulate plasticity induced crack closure under plane strain conditions and predicted that the nature of the closure process changes from continuous to discontinuous after a sufficient increment of crack growth. he suggested that closure involves only a few elements relatively distant from the current crack tip and the closure levels decay steadily as the crack grows beyond its initial length. in the limit, the closure would not occur at all. tab. 3 presents an adapted chronologic review crack advance scheme from matos & nowell [63]. l. c. h. ricardo et alii, frattura ed integrità strutturale, 35 (2016) 456-471; doi: 10.3221/igf-esis.35.52 463 year author node release scheme constraint target element type 1985 blom and holm [55] maximum load pstress; pstrain cop and ccl triangle linear 1986 fleck [64] maximum load pstress; pstrain cop triangle linear 1989 mcclung and sehitoglu [65] maximum load pstress; pstrain cop quadrilateral linear 1989 mcclung et al. [66] maximum load pstress; pstrain cop quadrilateral linear 1991 sun and sehitoglu [67] maximum load pstress; pstrain cop quadrilateral linear 1992 sehitoglu and sun [68] maximum load; minimum load pstress; pstrain cop quadrilateral linear 1996 wu and ellyin [69] maximum load pstress cop and ccl quadrilateral linear 1999 ellyin and wu [70] maximum load pstress cop and ccl quadrilateral linear 2000 wei and james [71] maximum load pstress; pstrain cop and ccl triangle linear 2002 ricardo et al. [72] minimum load pstress cop and ccl triangle quadratic 2002 pommier [73] minimum load pstrain cop and ccl quadrilateral linear 2003 ricardo [74] minimum load pstress ccl triangle quadratic 2003 solanki et al. [75] maximum load pstress; pstrain cop and ccl by coel quadrilateral linear 2004 solanki et al. [76] maximum load pstress; pstrain cop and ccl by coel quadrilateral linear 2004 zhao et al. [77] maximum load pstrain cop and ccl by cme quadrilateral linear 2005 gonzalez-herrera and zapatero [78] maximum load pstress; pstrain cop and ccl by dme quadrilateral linear 2007 matos & nowell [79] minimum load pstress cop and ccl by coel quadrilateral linear pstressplane stress; pstrainplane strain; copcrack opening; cclcrack closing; coelcrack opening and closing by contact element; cmecrack opening and closing by compliance method; dmecrack opening and closure by displacement method table 3: chronological crack advance scheme. in singh et al. [80] the authors provide a review of some crack propagation issues. the paper cover the transients and single overload effects as well as the plasticity induced crack closure. in this topic singh et al [80] presented a discussion regarding how the researchers normally work in crack propagation simulation considering overload-induced crack closure. lei [81] determine the crack closure by finite element method in a compact specimen. in the work lei [81] use abaqus [82] to perform the crack propagation simulation using the crack face method was good agreement with experimental data. ricardo et al. [72] present an example of small scale yielding under constant amplitude loading. a compact tension specimen was modeled using a commercial finite element code ansys version 6.0 [83]. a half of the specimen was modeled and symmetry conditions were applied. fig. 4 shows the compact tension specimen from astm 647-e95a [84]. a value of 19 mpam was applied as an equivalent force using the expression (9) in the model. fig. 5 shows the model used in this work and fig. 6 shows an example of post-processing of the small scale yielding stress intensity factor. l. c. h. ricardo et alii, frattura ed integrità strutturale, 35 (2016) 456-471; doi: 10.3221/igf-esis.35.52 464 max kbw p a f w        (9) where, k is the stress intensity factor; pmax is the maximum applied load; b is the specimen thickness; a is the crack length; w is the specimen width; a/w is the crack length to width relation for the specimen and f(a/w) is the characteristic function of the specimen that can be found in astm 647-e95a [84]. figure 4: compact tension (ct) specimen. figure 5: fem model of ct specimen. figure 6: post-processing of small scale yield model. generation of variable amplitude loadings achniewicz [85-86] presents methodologies for fatigue crack growth models considering metallic materials. in the part i machniewicz [85] present a review of crack growth predictions models and the deterministic models like afgrow [87] and willenborg et al. [22] models. crack closures models are presented with their characteristics to apply under constant and variable amplitude loading. machniewicz in part ii [86] is presented the constraint factors normally used in plane stress constraint. fastran [88] and nasgro [89] are the most codes used in plane stress constrain to determine plastic strip stresses and strain. heuler & klätschke [90] discuss the procedure and how the generation of standards loadings can support the development of structures and components considering crack growth phenomenon under variable amplitude loading. it is well-known that data and models that characterize the fatigue behavior of materials and structures under baseline constant amplitude loading may not be appropriate or sufficient to adequately assess their fatigue performance under irregular m l. c. h. ricardo et alii, frattura ed integrità strutturale, 35 (2016) 456-471; doi: 10.3221/igf-esis.35.52 465 variable amplitude loading. basic research is conducted under use of simplified load sequences such as single overload or underload or block loading with alternate mean loads. phenomena like crack growth retardation or acceleration are described making reference to base-line constant amplitude data. it is generally agreed, however, that real life load spectra also need to be applied in order to get a realistic picture of the relevance and significance of the mechanisms involved. standardized load sequences or load–time histories (slh’s) presently available provide an appropriate selection of load sequences to be used in the development of components, but they can also advantageously be used for other tasks. in this section it will be presented an overview on and a summarizing description of standardized load–time histories. with the need for optimum light-weight design, originally the aircraft industry was the main driver for these efforts. two of the most well known slh’s are the twist [91] and falstaff [92] sequences for transport and fighter aircraft, respectively, which have been and are still being applied for numerous studies on materials, joints and other structural elements. for automotive applications, the carlos [93] series of slh’s have been presented including the very recent load sequence for car trailer couplings, carlos-tc. in the us, activities were mainly centered on the derivation of test load sequences to be used for evaluation and development of fatigue life prediction methodology. bodies like the sae fatigue and evaluation committee took a pragmatic approach by selecting test load sequences from existing strain measurements, which were felt to be typical for the ground vehicle industry. altamura & straub [94] presents a work where discuss different ways to work with variable amplitude loading and the strategies to conduct fatigue analysis in structures. it is shown the methodology for discretization of random loads in blocks to be used in the development of components. and, also, it is presented the procedure to evaluate crack growth under constant and variable amplitude loading. probabilistic fatigue crack growth is discussed as well the mathematics models available to use like monte carlos simulation. it is generally agreed that the structural load variations should be characterized in the time domain since in most cases the range (or amplitude) of a load, stress or strain cycle and its respective max or mean value can be considered as fatiguerelevant. furthermore, the sequence or mixing of load cycles of different ranges and mean values must not be neglected. analyses in the frequency domain give insight into the frequency content of a load signal which is particularly useful for flexible structures, but do not deliver the above-mentioned values. many structural loading environments can be described as sequences of different modes [95] which may be a particular flight, driving a car on certain road types, a sea state of a given severity, etc. these modes of operation contain load cycles of different, but typical magnitudes and frequencies. often distinct patterns of grouped load cycles can be distinguished, they are called a loading event or element, such as braking or cornering of a car, different flight phases or maneuvers of an aircraft. zheng [96] provides a criterion for omitting small loads. in past, the underload (or subload) was defined as the nominal stress amplitude lower than or equal to the endurance limit, and the underload effect on fatigue life was investigated experimentally by using smooth specimens. test results showed that underload cycles applied to smooth specimens increased the fatigue life or the endurance limit of low-carbon steel [96] and cast iron [97], which was called “coaxing”. however, past research on the underload effect was not associated with the omission of small load cycles in life prediction [98,99]. the omission of small load cycles is necessary and important in compilation of the load spectrum [100,101], once the accumulated damage will not affect the prediction of the fatigue life and the assessment of the fatigue reliability of structures [102,103], and it is most cost effective in fatigue tests of components and structures under long-term variableamplitude or random loading histories [104]. up to date, some empirical criteria have been proposed and used [105,106]. however, how to omit the small loads in life prediction by using the local strain approach was not clearly set forth [106]. in the discussion of the importance of crack growth under variable amplitude loading, youb & song [106], using results obtained from single edge crack bending (seb), mentioned that schijve [101] was one of the first works covering this topic. kikukawa et al. [107] have extensively measured crack opening behavior under various random loadings and reported that crack opening point is controlled by the maximum range-pair load cycle (which we call hereafter “the largest load cycle”) in a random load history and is identical to the crack opening result of constant amplitude loading corresponding to the largest load cycle. based on this crack opening behavior, they proposed a simple prediction procedure for crack growth under random loading. the phenomenon of plasticity-induced fatigue crack closure under plane strain conditions is one of the most controversial topics concerning the mechanics of crack propagation. no general consensus exists among the scientific community concerning the physical mechanism for crack closure under plane strain conditions. one of the problems is on how to prepare the mesh and the procedure used in crack propagation. with three-dimensional models it becomes necessary to use normal contact approach to node release; in plane stress, spring is normally used to help the crack propagation, using contact resources for crack propagation and considering material nonlinear analysis it will result in a big result file and will spend a considerable time processing to end the simulation. according to fleck [108] the source of discontinuous closure appears to be a residual wedge of material on the crack flanks, located just ahead of the initial position of the crack tip. l. c. h. ricardo et alii, frattura ed integrità strutturale, 35 (2016) 456-471; doi: 10.3221/igf-esis.35.52 466 more recently wei and james [109] reported that after growing a virtual plane strain fatigue crack for a few cycles, there is no contact in the region immediately behind the crack tip and the contact pressure along the crack faces is discontinuous. zao et al. [110] modelled a ct specimen under plane stress and plane strain. they did not observe plasticity-induced crack closure under plane strain during steady state crack growth under cyclic tension, although they found significant levels of closure under plane stress. solanki et al. [75] present a review of crack propagation in plane stress and plane strain conditions. a m(t) specimen was modeled with an externally induced t -stress to observe the subsequent change in closure levels under plane-strain. a tstress was induced by applying tractions parallel to the crack in addition to the conventional tractions perpendicular to the crack. fig. 7 shows the variation in the crack tip plastic zone size accordingly with mesh. fig. 8 shows the difference of result in node release at minimum and maximum load compared by solanki et al. [76]. figure 7: variation in crack tip plastic zone size with mesh [75]. figure 8: comparison of crack opening values based on crack advance scheme [75]. figure 9: middle-crack tension specimen subjected to uniform stress [112]. figure 10: crack propagation model quarter of middle tension [113]. chermahini [111] present some crack propagation analyses using 3d model and plane strain model to determine the crack opening level. on the specimen surface and in the mid-plane the crack-opening stress levels tend to be two-dimensional solutions for plane stress and plane strain conditions, respectively. fig. 9 shows the geometry used by chermahini et al. [112]. l. c. h. ricardo et alii, frattura ed integrità strutturale, 35 (2016) 456-471; doi: 10.3221/igf-esis.35.52 467 in fig. 10, it is possible to see the finite element model used for crack propagation elaborated by wu & ellyin [113]. the model was prepared using layers of elements, considering the size of the smaller elements in the reverse plastic zone computed by irwin equation and then increasing the size of the hexahedron elements until arriving the region where the results will not affect the stress level in the crack propagation area. spring elements were used for node release, cycle after cycle, as in newman [45]. wu and ellyin [113] had used a truss element together with pairs of contact elements and the element death option for crack propagation simulation. this technique used in plane stress and plane strain models is usual in commercial finite element codes. the element death option was incorporated to remove truss elements. with their approach, a node can be released any time during a load cycle irrespective of the magnitude of the deformation caused by the release of the node. consequently, fewer problems with convergence were encountered and also several nodes could be released simultaneously if desired. conclusions he paper provides a review of some crack retardation models under variable amplitude loadings. it was discussed, also, the small scale yield model using finite element method. the miner’s rule crack initiation approach can be conservative in some applications, in special if the structures should develop cracks under variable amplitude loading. it is presented the standards loadings histories normally used in automotive and aeronautics structures. several crack advance schemes are presented and it is possible to observe that there is no agreement in the science community about the best strategy to edit experimental signals to be applied in numerical models aiming to obtain good correlation between numerical and experimental data. the crack propagation simulation under constant amplitude loading in plane stress has good agreement with experimental data. plane strain need complex models with large number of nodes and it is necessary to define and work with contact between the crack surfaces and, therefore, perform nonlinear analysis to identify when the crack open or close. regarding variable amplitude loading until the moment the authors do not identify a consistent methodology and procedure for crack propagation simulation. the problem should be related with the random fatigue phenomenon and to determine when the crack opens or closes, either using experimental or numerical data, is a challenge to be achieved. the computers are improving their processing and storage capacity with possibility to increase the size of models and decreasing the element size becoming more realistic the crack propagation simulation. in the near future it will be necessary to perform more and more tests to validate the numerical models hoping that the correlation between numerical and experimental results becomes better and better. references [1] miner, m. a., cumulative damage in fatigue, journal of applied mechanics, asme, usa, 12 (1945) a159-a164. [2] schijve, j., fatigue crack propagation in light alloy sheet material and structures, nlr, report mp195, amsterdam (1960). [3] stouffer, d. c. , williams, j. f., a method for fatigue crack growth with a variable stress intensity factor, eng. fracture mechanics, 11, (1979), 525-536. doi: 10.1016/0013-7944(79)90076-6. [4] ditlevsen, o., sobczyk, k., random fatigue crack growth with retardation, eng. fracture mech., 24(6) (1986) 861878. doi:10.1016/0013-7944(86)90271-7 [5] wei, r. p., shih, t. t., delay in fatigue crack growth, int. journal fracture, 10 (1974) 77-85. doi: 10.1007/bf00955082 [6] irwin, g. r., journal of applied mechanics, 79 (1953) 361. [7] irwin, g. r., journal of basic engineering, trans., asme, series d, 82(2) (1960) 417. doi: 10.1115/1.3662608 [8] tada, h., paris, p.c, irwin, g.r., the stress analysis of cracks handbook, bethlehem, pa, del research corporation, usa,(1985). [9] murakami, y., editor. stress intensity factors handbook. new york: pergamon press, usa (1987). [10] raju i.s., newman jc jr. stress-intensity factors for a wide range of semi-elliptical surface cracks in finite-thickness plates, eng. fracture mechanics, 11 (1979) 817-829. doi: 10.1016/0013-7944(79)90139-5. t l. c. h. ricardo et alii, frattura ed integrità strutturale, 35 (2016) 456-471; doi: 10.3221/igf-esis.35.52 468 [11] newman, j.c. jr., raju, i., stress-intensity factor equations for cracks in three-dimensional finite bodies subjected to tension and bending loads, computational methods in the mech. of fracture. in: atluri sn, editor. amsterdam: elsevier, (1986) 311-334. doi: 10.1002/zamm.19870671132. [12] newman, j. c, the merging of fatigue and fracture mechanics concepts: a historical perspective, progress in aerospace sciences, 34 (1998) 347-390. doi:10.1016/s0376-0421(98)00006-2. [13] frost, n. e., dugdale, d. s., journal of mechanics and physics of solids, 6(2) (1958) 92-110. doi:10.1016/0022-5096(58)90018-8. [14] paris, p. c., erdogan, f., journal of basic engineering, 85 (1963) 528. [15] head, a. k., the philosophical magazine, 44(7) (1953) 253. [16] dugdale, d. s., yielding of steel sheets containing slits, j. mech. phys. solids, 8(2) (1960) 100-104. doi:10.1016/0022-5096(60)90013-2. [17] hairman, g. a., provan, j. w., fatigue crack tip plasticity revisited, the issue of shape addressed, theoretical and appl. frac. mech. journal, 26 (1997) 63-79. doi: 10.1016/s0167-8442(96)00036-5. [18] williams, m. l., on the stress distribution at base stationary crack, journal of applied mechanics, 24 (1957) 111-114. [19] rolfe, s. t., barsom, j. m., fracture and fatigue control in structures – applications of fracture mechanics, prentice hall, new jersey, (1977). doi: 10.1520/mnl41-3rd-eb. [20] murthy, a. r. c.; palani, g. s., iyer, n. r., state of art review on fatigue crack growth analysis under variable amplitude loading, iei journal, (2004) 118-129. [21] wheeler, o. e., spectrum loading and crack growth, transactions of the asme series d’, journal of basic engineering, 94 (1972) 181-186. [22] willenborg, j. d.; engle, r. m., wood, h. a., a crack growth retardation model using an effective stress concept, affdl, tm-71-fbr, air force flight dynamics laboratory, wright patterson air force base, oh, (1971). [23] porter, t. r., method of analysis and prediction of variable amplitude fatigue crack growth, eng. fracture mechanics 4(4) (1972) 717-736. doi:10.1016/0013-7944(72)90011-2. [24] gray, t. d., gallagher, j. p., predicting fatigue crack retardation following a single overload using a modified wheeler model, astm stp 590, (1976). doi: 10.1520/stp590-eb. [25] gallagher, j. p., hughes, t. f., influence of the yield strength on overload fatigue crack growth behavior of 4340 steel, affdl – tr-74-27, air force flight dynamics laboratory, wright patterson air force base, oh, (1974). [26] johnson, w. s., multi-parameter yield zone model for predicting spectrum crack growth, astm stp 748, (1981) 85102. doi: 10.1520/e0748-02r08 . [27] chang, j. b., hiyama, r. m., szamossi, m., improved methods for predicting spectrum loadings effects, afwal-tr81-3092, air force flight dynamics laboratory, wright patterson air force base, oh, (1984). [28] elber, w., the significance of fatigue crack closure, astm stp 486, (1971) 230242. doi: 10.1520/stp486-eb. [29] bell, p. d., creager, m., crack growth analyses for arbitrary spectrum loading, affdl-tr-74-129, air force flight dynamics laboratory, wright patterson air force base, oh, (1974). [30] newman, j. c., a finite element analysis fatigue crack closure, nasa tm x 72005, nasa, hampton, va, (1975). [31] dill, h. d., saff, c. r., spectrum crack growth prediction method based on crack surface displacement and contact analyses, fatigue crack growth under spectrum loads, astm stp 595, (1976) 306–319. doi: 10.1520/stp595-eb. [32] kanninnen, m. f., atkinson, c., feddersen, c. e., a fatigue crack growth analysis method based on a single representation of crack tip plasticity, astm stp 637, (1977) 122-140. doi: 10.1520/stp637-eb. [33] budianski, b., hucthinson, j. w., analysis of closure in fatigue crack growth, journal of applied mechanics, 45 (1978) 267-276. doi 10.1115/1.34.24286. [34] de koning, a. u., a simple crack closure model for predictions of fatigue crack growth rates under variable amplitude loading, astm stp 743, (1981) 63-85. doi: 10.1520/stp743-eb. [35] corbly, d. m., packman, p. f., on the influence of single and multiple peak overloads on fatigue crack propagation in 7075-t6511 aluminum, eng. fracture mech., 5 (1973) 479-497. doi:10.1016/0013-7944(73)90034-9. [36] schijve, j., brock, d., de rigle, p., nlr, report m2094, amsterdam, (1962). [37] hardrarth, h. f., mcevily, a . t., in: proc. crack propagation symposium, cranfield, 1 (1961). [38] jonds, d., wei, r. p., an exploratory study of delay effects in fatigue crack growth, int. j. fracture mechanics, 7 (1971). [39] von ewu, e., hertzberg, r., roberts, r., delay defects in fatigue crack propagation, nat. symposium f.m., (1971) 7. [40] hudson, c. m., effect of stress ratio on fatigue-crack growth in 7075-t6 and 2024-t3 alumina-alloy specimens. tnl-5390, nasa, (1969). [41] crooker, t. w., effect of t. c., cycling on fatigue grade growth in high strength alloys, nrl report 7220, (1971). l. c. h. ricardo et alii, frattura ed integrità strutturale, 35 (2016) 456-471; doi: 10.3221/igf-esis.35.52 469 [42] hudson, c.m., hardrath, h. f., effects of changing stress amplitude on the rate of fatigue-crack propagation in two aluminum alloys, nasa tn d-960, september, (1961). [43] mcmillan, j. c., pelloux, r. m., astm stp 415, (1966) 505. doi: 10.1520/stp415-eb [44] dill, h. d., saff, c. r., spectrum crack growth prediction method based on crack surface displacement and contact analyses, fatigue crack growth under spectrum loads, astm stp 595, (1976) 306–319. doi: 10.1520/stp595-eb. [45] newman jr, j. c., a crack closure model for predicting fatigue crack growth under aircraft spectrum loading. in: chang jb, hudson cm, editors. methods and models for predicting fatigue crack growth under random loading, astm stp 748, (1981) 53–84. doi: 10.1520/stp748-eb [46] ricardo, l. c. h., pimenta, p. m., spinelli, d., crack closure simulation by finite element. in, blom, a.f. ,fatigue 2002, 4/5 (2002) 2293 – 2300. [47] christensen, r. h., fatigue crack growth affected by metal fragments wedged between opening closing crack surface, appl. mater. res., 2 (1963) 207-210. [48] elber w., equivalent constant amplitude concept for fatigue crack growth under spectrum loading, astm stp 595, (1976) 236-250. doi: 10.1520/stp595-eb [49] swedlow, j. l., effects and plastic flow in cracked plates, phd thesis, california institute of technology, pasadena, usa, (1965). [50] schijve, j., observations on the prediction of fatigue crack growth propagation under variable amplitude loading, astm stp 595, (1976) 3-23. doi: 10.1520/stp595-eb. [51] newman j. c. jr., finite element analysis of fatigue crack propagation, including the effect c-(t) of crack closure, phd thesis, virginia polytechnic institute, (1974). [52] newman, j. c. jr.; armen, h. jr. elastic-plastic analysis of fatigue crack under cyclic loading, aiaa journal, 13 (1975) 1017-1023. doi: 10.2514/3.60499. [53] newman, j. c. jr., a finite element analysis of fatigue crack closure, astm 490, (1976) 281-301. doi: 10.1520/stp490-eb. [54] ohji, k., ogura, k. ohkubo, y., cyclic analysis of a propagation crack and its correlation with fatigue crack growth; eng. fracture mechanics, 7 (1975) 457-464. doi: 10.1016/0013-7944(75)90046-6. [55] blom, a. f., holm. d. k., an experimental and numerical study of crack closure; eng. fracture mechanics, (1985) 907-1011. doi: 10.1016/0013-7944(85)90039-6. [56] fleck, n. a., finite element analysis of plasticity induced crack closure under plane strain conditions, eng. fracture mechanics, 25 (1986) 441-449. doi:10.1016/0013-7944(86)90258-4. [57] fleck, n. a., newman, j. c. jr, analysis of crack closure under plane strain conditions , astm stp 982, (1988) 319341. doi: 10.1520/stp982-eb. [58] sehitoglu, h. gall, k., garcia, a. m., recent advances in fatigue crack growth modeling, int. journal of fracture, 80(2) (1996) 165-192. doi: 10.1007/bf00012668. [59] mcglung, r. c., sehitoglu, h., finite element analysis of fatigue crack closure – numerical results, eng. fracture mechanics, 33 (1989) 253–272. doi: 10.1016/0013-7944(89)90028-3. [60] mcglung, r. c., finite element modeling of fatigue crack growth – theoretical concepts and numerical analysis of fatigue, in: blom a, beevers, c. editors, west midlands, emas, (1992) 153-172. [61] mcglung, r. c., finite element analysis of specimen geometry effects on fatigue crack closure, fatigue fract. eng. mater. structures, 17 (1994) 861-872. doi: 10.1111/j.1460-2695.1994.tb00816.x. [62] newman, j. c. jr., a finite element analysis of fatigue crack closure, astm 490, (1972) 281-301. doi: 10.1520/stp490-eb. [63] matos, p. f. p., nowell, d., numerical simulation of plasticity induced fatigue crack closure with emphasis on the crack growth scheme: 2d and 3d analyses, eng. fracture mechanics, 75 (2008) 2087-2114. doi: 10.1016/j.engfracmech.2007.10.017. [64] fleck, n. a., finite element analysis of plasticity-induced crack closure under plane strain conditions, eng. fracture mechanics, 25(4) (1986) 441–449. doi: 10.1016/0013-7944(86)90258-4. [65] mcclung, r. c., sehitoglu, h., on the finite element analysis of fatigue crack closure 1. basic modeling issues. eng. fracture. mechanics, 33 (2) (1989) 237–252. doi: 10.1016/0013-7944(89)90027-1. [66] mcclung, r. c., sehitoglu h., on the finite element analysis of fatigue crack closure 2. numerical results. eng. fracture. mechanics, 33(2) (1989) 253–272. doi: 10.1016/0013-7944(89)90028-3. [67] sehitoglu, h., s wei, modelling of plane strain fatigue crack closure. j. eng. mater. technol, 113 (1991) 31–40. doi :10.1115/1.2903380. l. c. h. ricardo et alii, frattura ed integrità strutturale, 35 (2016) 456-471; doi: 10.3221/igf-esis.35.52 470 [68] sun, w., sehitoglu, h., residual stress fields during fatigue crack growth, fatig. fract. eng. mater. struct., 15(2) (1992) 115–128. doi: 10.1111/j.1460-2695.1992.tb00042.x. [69] wu, j., ellyin, f., a study of fatigue crack closure by elastic-plastic finite element analysis for constant-amplitude loading. int. journal of fracture, 82 (1996) 43–65. doi:10.1007/bf00017863. [70] ellyin, f., wu, j., a numerical investigation on the effect of an overload on fatigue crack opening and closure behavior, fatig. fract. eng. mater. struct., 22 (1999) 835–847. doi: 10.1046/j.1460-2695.1999.00223.x. [71] wei, l. w., james, m. n., a study of fatigue crack closure in polycarbonate ct specimen., eng. fracture mechanics, 66 (2000) 223–242. doi: 10.1016/s0013-7944(00)00014-x. [72] ricardo, l. c. h., pimenta, p. m., spinelli d., andrade, a. h. p., crack closure simulation by finite element method; in: blom, a. f (ed.), fatigue 2002, emas publishing, stockholm, sweden, 4 (2002) 2863-2869. [73] pommier s., plane strain crack closure cyclic hardening, eng. fracture mechanics, 69(3) (2002) 25–44. doi:10.1016/s0013-7944(01)00061-3. [74] ricardo, l. c. h., modeling fatigue crack opening and closing phenomenon by finite element method, phd thesis, department of structures and foundations, university of sao paulo (in portuguese), (2003). [75] solanki, k., daniewicz, s. r., newman, jr j. c., finite element modelling of plasticity-induced crack closure with emphasis on geometry and mesh refinement effects. eng. fracture mechanics, 70 (2003) 1475–89. doi:10.1016/s0013-7944(02)00168-6. [76] solanki, k., daniewicz, s. r., newman, jr j. c., a new methodology for computing crack opening values from finite element analyses, eng. fracture mechanics, 71 (2004) 1165–1175. doi:10.1016/s0013-7944(03)00113-9. [77] zhao, l. g., tong, j., byrne, j., the evolution of the stress–strain fields near a fatigue crack tip and plasticity-induced crack closure revisited, fatig. fract. eng. mater. struct., 27(1) (2004) 19–29. doi: 10.1111/j.1460-2695.2004.00716.x. [78] gonzalez-herrera, a., zapatero, j., influence of minimum element size to determine crack closure stress by finite element method, eng. fracture mechanics, 72 (2005) 337–355. doi:10.1016/j.engfracmech.2004.04.002. [79] matos, p.f.p., nowell d., on the accurate assessment of crack opening and closing stresses in plasticity-induced crack closure problems, eng. fracture mechanics, 74(10) (2007) 1579–1601. doi: 10.1016/j.engfracmech.2006.09.007. [80] singh, k.d., parry, m.r., sinclair, i., variable amplitude fatigue crack growth behavior – a short overview, journal of mechanical science and technology, 25(3) (2011) 663-673. doi: 10.1007/s12206-011-132-6. [81] lei, y., finite element crack closure analysis of a compact tension specimen, international journal of fatigue, 30 (2008) 21–31. doi:10.1016/j.ijfatigue.2007.02.012. [82] abaqus, v6.3, hibbitt, karlsson & sorensen, inc., providence, ri, (2002). [83] ansys inc, ansys version 6.0, usa, (2002). [84] astm, standard test method for measurement of fatigue crack growth rates, e647–95a, (1995). doi: 10.1520/e0647-15. [85] machniewciz, t., fatigue crack growth prediction models for metallic materials, part i: overview of prediction concepts, fatigue fract engng mater struct, 36 (2012) 293–307. doi: 10.1111/j.1460-2695.2012.01721.x. [86] machniewciz, t., fatigue crack growth prediction models for metallic materials, part ii: part ii: strip yield model – choices and decisions, fatigue fract engng mater struct, 36 (2012) 361–373. doi: 10.1111/ffe.12009. [87] harter, j. a. afgrow users guide and technical manual. air force research laboratory, report no. afrl-vawp-tr-2006-xxxx, (2006). [88] newman, j. c. fastran ii – a fatigue crack growth structural analysis program. nasa technical memorandum no. 104159. nasa langley research center, hampton, (1992). [89] ten hoeve, h. j., de koning, a. u., reference manual of the strip yield module in the nasgro or esacrack software for the prediction of retarded crack growth and residual strength in metal materials, report no. nlr tr 97012 l, nlr, amsterdam, the netherlands, (1997). [90] heuler, p., klätschke, h., generation and use of standardized load spectra and loadtimes histories, international journal of fatigue, 27 (2005) 974-990. doi: 10.16/j.ifatigue.2004.09.012. [91] schütz, d., lowack, h., de jonge j. b., schijve, j., a standardized load sequence for flight simulation tests on transport aircraft wing structures, lbf report fb 106, nrlreport tr 73, (1973). [92] aircher, w., branger, j., van dijk, g. m., ertelt j., hück, m., de jonge j. b., description of a fighter aircraft loading for standard for fatigue evaluation falstaff, common report of fcw emmen, lbf, nrl, iabg, (1976). [93] schütz, d., klätschke, h., steinhilber, h., heuler, p., schütz, w., standardized load sequences for car wheel suspension components, car loading standardcarlos, fraunhofer institute für betriebsfestigkeit (lbf), darmstadt, industrieanlagen – betriebsgesellschaft mbh (iabg), ottobrunn, lbf – report no fb191, (1999). l. c. h. ricardo et alii, frattura ed integrità strutturale, 35 (2016) 456-471; doi: 10.3221/igf-esis.35.52 471 [94] alessandra a., straub, d., reliability assessment of high cycle fatigue under variable amplitude loading: review and solutions, eng. fracture mechanics, 121–122 (2014) 40–66. doi:10.1016/j.engfracmech.2014.02.023. [95] ten have, a. a., european approaches in standard spectrum development, in: potter j. m., watanable r. t., editors, development of fatigue loading spectra, astm-stp 1006, astm, (1989) 35-75. doi: 10.1520/stp1006-eb. [96] zheng, x., on some basic problems of fatigue research in engineering, international journal of fatigue, 23 (2001) 751-766. doi:10.1016/s0142-1123(01)00040-8. [97] frost, n. e., marsh, k. j., pook, l. in: metal fatigue, oxford: clarendon press, (1974) 20-22. [98] heuler, p., seeger, t., a criterion for omission of variable amplitude loading histories, international journal of fatigue, 8(4) (1986) 225-230. doi:10.1016/0142-1123(86)90025-3. [99] eccs recommendations for fatigue design of steel structures, institute of metal construction (iocm) of swiss federal institute of technology, lausanne, switzerland, eccs, (1985). [100] shi, y. j., yan, y. m., li, z. r. shi, z. j., hou, w. w., assessment of remaining life of steel beams of chang tai-guam bridge on the line from beijing to guangzhou, technical report, beijing, institute of railway engineering, chinese academy of railway science, (1990). [101] schijve, j., observations on the prediction of fatigue crack growth propagation under variable amplitude loading, astm stp 595, (1976) 3-23. doi: 10.1520/stp595-eb. [102] barsom, j. m., fatigue crack growth under variable amplitude loading in various bridge steels, astm stp 595, (1976) 217-235. doi: 10.1520/stp595-eb. [103] hudson, c. m., a root mean square approach for predicting fatigue crack growth under random loading, astm stp 748, (1981) 41-52. doi: 10.1520/stp748-eb. [104] johnson, w. s., multi-parameter yield zone model for predicting spectrum crack growth, astm stp 748, (1981) 85-102. doi: 10.1520/stp748-eb. [105] rudd, j. l., engle jr, r. m., crack growth behavior of center cracked panels under random spectrum loading, astm stp 748, (1981) 1033-1114. doi: 10.1520/stp748-eb. [106] youb, y., song, j. h., fatigue crack closure and growth behavior under random loading, eng. fracture mechanics, 49(1) (1994) 105-120. doi:10.1016/0013-7944(94)90115-5. [107] kikukawa, m., jono, m., kondo, y., mikami, s., fatigue crack closure and estimation method of crack propagation rate under stationary varying loading conditions including random loading (1st report, effects of mean load and study on wave counting method), trans. jpn soc. mech. engrs, 48 (1982)1496-1504. [108] fleck, n. a., finite-element analysis of plasticity induced crack closure under plane strain conditions. eng. fracture mechanics., 25 (1986) 441-449. doi:10.1016/0013-7944(86)90258-4. [109] wei, l. w., james, m. n., a study of fatigue crack closure in polycarbonate ct specimens. eng. fracture mechanics, 66 (2000) 223–42. doi:10.1016/s0013-7944(00)00014-x. [110] zhao, l. g., tong, j., byrne, j., the evolution of the stress–strain fields near a fatigue crack tip and plasticityinduced crack closure revisited. fatig. fract. eng. mater. struct., 27(1) (2004) 19–29. [111] chermahini, r. g., three-dimensional elasticplastic -finite-element analysis of fatigue crack growth and closure. phd thesis, old dominion university, norfolk, va, (1986). [112] chermahini, r. g., shivakumar, k. n., newman, j. c. jr., three-dimensional finite-element simulation of fatigue crack growth and closure. astm stp 982, (1988) 398-413. doi: 10.1520/stp982-eb. [113] wu j, ellyin f., a study of fatigue crack closure by elastic–plastic finite element analysis for constant-amplitude loading. int. journal of fracture, 82 (1996) 43–65. doi: 10.1007/bf00017863. << /ascii85encodepages false /allowtransparency false /autopositionepsfiles true /autorotatepages /none /binding /left /calgrayprofile (dot gain 20%) /calrgbprofile (srgb iec61966-2.1) /calcmykprofile (u.s. web coated \050swop\051 v2) /srgbprofile (srgb iec61966-2.1) /cannotembedfontpolicy /error /compatibilitylevel 1.4 /compressobjects /tags /compresspages true /convertimagestoindexed true /passthroughjpegimages true /createjobticket false /defaultrenderingintent /default /detectblends true /detectcurves 0.0000 /colorconversionstrategy /cmyk /dothumbnails false /embedallfonts true /embedopentype false /parseiccprofilesincomments true /embedjoboptions true /dscreportinglevel 0 /emitdscwarnings false /endpage -1 /imagememory 1048576 /lockdistillerparams false /maxsubsetpct 100 /optimize true 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/hrv (za stvaranje adobe pdf dokumenata najpogodnijih za visokokvalitetni ispis prije tiskanja koristite ove postavke. stvoreni pdf dokumenti mogu se otvoriti acrobat i adobe reader 5.0 i kasnijim verzijama.) /hun 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can be opened with acrobat and adobe reader 5.0 and later.) >> /namespace [ (adobe) (common) (1.0) ] /othernamespaces [ << /asreaderspreads false /cropimagestoframes true /errorcontrol /warnandcontinue /flattenerignorespreadoverrides false /includeguidesgrids false /includenonprinting false /includeslug false /namespace [ (adobe) (indesign) (4.0) ] /omitplacedbitmaps false /omitplacedeps false /omitplacedpdf false /simulateoverprint /legacy >> << /addbleedmarks false /addcolorbars false /addcropmarks false /addpageinfo false /addregmarks false /convertcolors /converttocmyk /destinationprofilename () /destinationprofileselector /documentcmyk /downsample16bitimages true /flattenerpreset << /presetselector /mediumresolution >> /formelements false /generatestructure false /includebookmarks false /includehyperlinks false /includeinteractive false /includelayers false /includeprofiles false /multimediahandling /useobjectsettings /namespace [ (adobe) (creativesuite) (2.0) ] /pdfxoutputintentprofileselector /documentcmyk /preserveediting true /untaggedcmykhandling /leaveuntagged /untaggedrgbhandling /usedocumentprofile /usedocumentbleed false >> ] >> setdistillerparams << /hwresolution [2400 2400] /pagesize [612.000 792.000] >> setpagedevice microsoft word numero_36_art_11 m. ouarabi et alii, frattura ed integrità strutturale, 36 (2016) 112-118; doi: 10.3221/igf-esis.36.11 112 focussed on crack paths very high cycle fatigue strength and crack growth of thin steel sheets mohand ouarabi, ruben perez mora, claude bathias université paris ouest nanterre la defense, leme, 50 rue de sèvres, ville d’avray, france mohand.ouarabi@yahoo.fr, ruben.perez-mora@hotmail.fr, claude@bathias.com thierry palin-luc arts et métiers paris tech, i2m, cnrs, université de bordeaux, esplanade des arts et métiers, talence, france thierry.palin-luc@ensam.eu abstract. for basic observations or for industrial applications it is of interest to use flat specimens at very high frequency in the gigacycle regime. in this work, thin flat sheet, with 1.2 mm thickness of a complex phase ferrite-martensitic steels were considered for carrying out fatigue tests at high frequency (20 khz) up to the gigacycle regime (>109 cycles). the crack initiation tests were carried out with water cooling, while the crack growth test were carried out in laboratory air at room temperature. all the tests were carried out under loading ratio r=-1. to do that, special designs of specimens were made and computed using fem for defining the stress amplitude for endurance tests. special attachments for specimens to the ultrasonic system’s horn were enhanced. a particular fem computing of the stress intensity range on crack growth specimens was carried out for determining the specimen dimensions and an equation that defines the stress intensity range as a function of the harmonic displacement amplitude, dynamic young’s modulus, material density and crack length. detailed procedures and fatigue results are presented in this paper. keywords. ultrasonic fatigue; plate steel fatigue; fatigue resistance; fatigue crack growth. introduction atigue in high and very high cycle regime has been studied by bathias et al. [1] during the last 30 years. advances in piezoelectric fatigue testing machines have allowed researchers to carry out accelerated fatigue tests in the very high cycle fatigue (vhcf) regime [2] by using adapted specimens and testing methods for obtaining suitable results at high frequency. actually, such machines, specimens and methods have been optimized and practically standardized by means of cylindrical specimens (dog bone, hourglass) for endurance tests and block notched specimens for crack growth tests. it is even possible to tests such specimens under controlled environment or temperature [3, 4]. as actually known, the vibration system on a piezoelectric fatigue machine is composed by a generator, a converter, an amplifier (horn), and the specimen, all working in resonance allowing the application of maximum stress amplitude in the smallest cross section of the specimen located at its central part. if the raw material or the component to study is sufficiently plenty for machining cylindrical round specimens the work becomes simple. it is the same for thick hyperbolic profile crack growth specimens [4]. conversely, for thin raw material, such as steel sheets, fatigue specimens are not common and easy to test at high frequency; there is not a lot of vhcf data in literature. in this work, thin flat sheets of a f m. ouarabi et alii, frattura ed integrità strutturale, 36 (2016) 112-118; doi: 10.3221/igf-esis.36.11 113 complex phase ferritic-martensitic steel of 1.2 mm thickness were received for carrying out endurance tests in the very high cycle regime and crack growth tests at ultrasonic frequency (20 khz). the method for designing the thin specimens and both the procedures for testing them at high frequency and the results are presented hereafter. material and testing methods he investigated material is a complex phase ferritic-martensitic steel produced in sheet form by rolling and used for manufacturing automotive parts. the chemical composition this material is given in tab. 1, its mechanical characteristics are in tab. 2. these steel sheets are covered by zinc coated (fig. 1b). the specimens were machined without removing this coating and with their longitudinal axis parallel to the rolling direction. the specimens were tested at ultrasonic loading frequency (20 khz) with a loading ratio r= –1. all the specimens were tested as received condition. c mn si p 0.1674 2.004 0.225 0.017 table 1: chemical composition of the ferritic-martensitic cp1000 steel (w %). dynamics modulus (gpa) volumetric mass (kg·m-3 ) uts (mpa) 211 7850 1000 table 2: mechanical characteristics of the ferritic-martensitic cp1000 steel. figure 1: a) microstructure of the studied steel cp1000. b) galvanized coat. the ultrasonic fatigue testing machine is composed of the following components. an ultrasonic generator transforms the electrical signal of 50 (or 60) hz to 20 khz. the piezoelectric converter transforms the 20 khz electrical signal in a mechanical vibration at 20 khz. a horn amplifies the displacement amplitude in order to obtain the required strain amplitude in the middle section of the specimen and a computer control system is used to control the different parameters of the test, such as the amplitude and to maintain the resonance frequency. indeed, the specimen works in resonance vibration state and its center is a displacement node experiencing the maximum stress amplitude. for the calibration of the test, an optical fiber displacement sensor was used. if the resonance frequency drops outside the 19.5 – 20.5 khz range, the system shuts down automatically. this is characteristic of crack initiation or specimen failure. two different types of tests were carried out in this work. the first one is for determining the fatigue strength and the second one is crack growth test. the geometry of the flat specimen for the fatigue strength assessment is illustrated in fig. 2a. the geometry for the crack propagation test is illustrated in fig. 2b. t m. ouarabi et alii, frattura ed integrità strutturale, 36 (2016) 112-118; doi: 10.3221/igf-esis.36.11 114 figure 2: a) geometry of smooth flat specimen for fatigue strength assessment [5], b) geometry of flat specimen for crack propagation tests [6]. for keeping the temperature constant and close to room temperature during the test a cooling system with compressed air was used for crack propagation tests. for the crack initiation tests (s-n curve) the specimen self-heating was too high. indeed the stabilized temperature was more than 350°c with such air cooling device. the temperature increase was measured with a flir infrared camera on mat black paint specimens. this self-heating has been first attributed to zinc coated. experiments have been carried out on specimens without zinc coated but temperature heating was the same. transformation of residual austenite in martensite due to high strain rate was another assumption for explaining this phenomenon but residual austenite content is less than 1% in cp1000 steel, consequently the reason of so intense selfheating is still an open question. consequently a water cooling system has been developed (like in [3, 4]) to keep the specimen temperature lower than 60°c. in such case the temperature cannot be measured with infrared camera because of water but with thermocouple. figure 3: material element with length (dx) in mechanical vibration along x direction. calculation of the specimen geometry for crack initiation test or working at a resonance frequency of 20 khz, the specimen geometry and the horn should be calculated. for an element (dx) in longitudinal vibration along x direction as illustrated in fig. 3, if a one dimensional vibration is considered the force balance according to newton’s law is: f mx  (1) it can be written: 2 2 ( , )u x tds dx s dx s x d tx s                (2) where, u(x, t) is the axial displacement at position x and time t, (x, t) is the normal stress, s(x) is the cross section area at position x and  is the density of material. f m. ouarabi et alii, frattura ed integrità strutturale, 36 (2016) 112-118; doi: 10.3221/igf-esis.36.11 115 if we assume that, the material is isotropic with a linear elastic behavior, the following equation is obtained where ed is the dynamic modulus. 2 2 2 2 ( , ) ( , ) ( , )1 0 d u x t u x t u x tds x s x dx e t          (3) the sinusoidal displacement can be expressed as follow: ( , ) ( ) i tu x t u x e  (4) finally, the equation for the displacement vibration along the specimen is: 2''( ) ( ) '( ) ( ) 0u x p x u x k u x   (5) where: , 2 fd e k c and c        the geometry of the specimens is designed with a reduced cross section to obtain the maximum stress amplitude in the middle section (fig. 2a) or/and to obtained the maximum stress intensity factor as shown in fig. 2b. for having a resonance frequency of 20 khz, we must calculate the resonance length l1. there are two ways for doing that. the first one is to use the analytic solution of the previous equation.  *1 21 1arctan ( coth( ) )l lk k     (6) * 2 1 max 0 2 cos( ) sinh( ) l d kl e e u l      (7) where: * 1 2 2 1 ln 2 t l t         (8) the second way is to use the numerical solution computed by finite element analysis (fea). ansys software was used in this study. first, the specimen geometry was computed with the analytic solution. then the resonance frequency was computed by modal analysis. finally, with an imposed sinusoidal displacement with and amplitude of 1 µm, the stress amplitude in the middle of the specimen was computed by harmonic analysis. the difference between, the numerical and analytical solution was less than 1 %. crack propagation test the method for calculating the mode i stress intensity factor range is reported in several documents, so that [3, 6]. usually the paris’ law is used to determine a crack growth curve, and then it is needed to relate the stress intensity factor range (k) with the crack growth rate  /da dn . wu [6] has shown that eq. 9 can be used for calculating k during ultrasonic fatigue test since such test is carried out under displacement control. in this equation ed is the dynamic modulus and  is the poisson ratio of the material, u0 is the displacement amplitude, a is the crack length, w is the specimen width and f(a/w) is a shape function depending on the specimen geometry. wu has determined this function for hyperbolic profile crack growth specimen with a thickness of 8 mm (eq. 10). 02 ( ) (1 ) de ak u f a w      (9) m. ouarabi et alii, frattura ed integrità strutturale, 36 (2016) 112-118; doi: 10.3221/igf-esis.36.11 116 where: 2 3 4( ) 0.64( ) 1.73( ) 3.98( ) 1.96( ) a a a a a f w w w w w     (10) in the present work a similar methodology has been followed considering that physically a flat specimen will vibrate in resonance at 20 khz. the main idea is to find the shape function for a flat specimen with a thickness of 1.2 mm. the proposed method consists in modeling a plane 2d geometry by using fem software. considering the specimen small thickness and the problem symmetry, only half of the specimen geometry was modeled assuming plane stress condition, and a singular element (barsum element) was placed at different lengths representing the crack tip (as shown in fig. 4a). numerical value of k was obtained by fea. for this problem, we use this equation defined in plane stress: 0 ( )d a k e u g a w    (11) 2 3 4( ) 0.2363( ) 1.0600( ) 1.7067( ) 1.4397( ) a a a a a g w w w w w     (12) the resulting mode i stress intensity factor range as a function of the ratio between crack length, a, and the width of the specimen, w, is plotted in fig. 4b. the obtained values are for an amplitude displacement u0 of 1 µm. note that since crack opening cannot be measured in real time at 20 khz the range of the effective stress intensity factor has been computed by considering the positive part of the loading cycle only. the crack is assumed to be closed during the compression part of the loading cycle. of course, with this procedure the range of the effective stress intensity factor is a little bit overestimated, but according to the authors, up to now this is only way to assess it at 20 khz [4]. figure 4: modeling of a crack in a flat specimen of 1.2 mm thickness, a) field of the mode i stress intensity factor, b) stress intensity factor range as a function of (a/w) for a flat specimen. results he s-n curve of the studied steel has been obtained on specimens with zinc coated, at room temperature, with water-cooling, under fully reversed tension-compression (fig. 5). a large scatter in fatigue life can be observed. the blue points show the specimens that break during the test, while the red ones represent the specimens that did not break at 109 cycles. the fatigue strength at one thousand millions of cycles can be observed around 352 mpa. on the other hand, the experiments on crack growth flat specimens of 1.2 mm thickness demonstrated that such thin samples can be tested at high frequencies (20 khz). in fig. 8, the results of crack propagation test show that the threshold value of the stress intensity range is around 7 mpa√m for the cp1000 steel. this is in agreement with literature for steel [1]. sem observations of the fracture surfaces of crack initiation specimens show that crack initiated either at the surface on rolling defect, fig. 6 ( a and b), or on corner defect, fig. 7( a and b). t m. ouarabi et alii, frattura ed integrità strutturale, 36 (2016) 112-118; doi: 10.3221/igf-esis.36.11 117 figure 5: sn curve on smooth flat specimens in cp1000 (1.2 mm thickness) under tension-compression r = -1at 20 khz, with water cooling at room temperature. figure 6: a) surface crack initiation on rolling defect (samp = 360 mpa and nf = 1.6×108 cycles), b) crack initiation on rolling defect (samp = 360 mpa and nf = 7.6×106 cycles). figure 7: a) crack initiation at a corner defect (samp = 360 mpa and nf = 1.6×108 cycles), b) crack initiation at a corner defect (samp =360 mpa and nf =7.6×106 cycles) m. ouarabi et alii, frattura ed integrità strutturale, 36 (2016) 112-118; doi: 10.3221/igf-esis.36.11 118 figure 8: experimental ( )da f keffdn   curve in mode i under r=-1, for cp1000 (at 20 khz) with air cooling and at room temperature. conclusion n this work, the procedures for testing thin steel sheets in fatigue against crack initiation and crack propagation have been developed. flat specimens of 1.2 mm thickness were used. it has been shown that it is possible to obtain appropriate results by using high frequency resonant fatigue testing machine in tension-compression. fatigue endurance tests have shown fatigue strength in the gigacycle regime for cp1000 ferritic-martensitic steel around 352 mpa under fully reversed tension. for the crack propagation test on cp1000, the threshold value of the mode one effective stress intensity factor range is around 7 mpa√m in laboratory air. the proposed computing methodology is consistent since frequencies for each specimen geometry are practically the same in experimentation. flat specimens must be perfectly designed to avoid any problem with bending deviation of the stress amplitude or stress intensity factor. acknowledgements he authors thank the european commission for the financial support of the freqtigue (ceca) project and all the partners of this project: arcelor mittal, fiat, gerdau, karlstadt university, karlsruhe institute of technology, aachen university, university paris ouest nanterre la defense. references [1] bathias, c., paris, c., gigacycle fatigue in mechanical practice, marcel dekker, new york, (2005) [2] bathias, c., piezoelectric fatigue testing machines and devices, international journal of fatigue, 28 (2006) 1438-1445. [3] palin-luc, t., perez mora, r., bathias, c., dominguez, g., paris, p.c., arana, j., fatigue crack initiation and growth on a steel in the very high cycle regime with sea water corrosion, engineering fracture mechanics, 77-11 (2010) 19531962. [4] perez-mora r., palin-luc t., bathias c., paris, p.c., very high cycle fatigue of high strength steel under sea water corrosion: a strong corrosion and mechanical damage coupling, int. j. fatigue, 74 (2015) 156-165. [5] wang, c., microplasticité et dissipation en fatigue à très grand nombre de cycles du fer et de l’acier, phd thesis université paris ouest nanterre – la défense, (2013). [6] wu, t.y., modelisation de la fissuration en fatigue vibratoire à haute temperature; applications aux alliages à base de nickel, phd thesis ecole centrale de paris, (1992). i t << /ascii85encodepages false /allowtransparency false /autopositionepsfiles true /autorotatepages /none /binding /left /calgrayprofile (dot gain 20%) /calrgbprofile (srgb iec61966-2.1) /calcmykprofile (u.s. web coated \050swop\051 v2) /srgbprofile (srgb iec61966-2.1) /cannotembedfontpolicy /error /compatibilitylevel 1.4 /compressobjects /tags /compresspages true /convertimagestoindexed true /passthroughjpegimages true /createjobticket false /defaultrenderingintent /default /detectblends true /detectcurves 0.0000 /colorconversionstrategy /cmyk /dothumbnails false /embedallfonts true /embedopentype false /parseiccprofilesincomments true /embedjoboptions true /dscreportinglevel 0 /emitdscwarnings false /endpage -1 /imagememory 1048576 /lockdistillerparams false /maxsubsetpct 100 /optimize true /opm 1 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can be opened with acrobat and adobe reader 5.0 and later.) >> /namespace [ (adobe) (common) (1.0) ] /othernamespaces [ << /asreaderspreads false /cropimagestoframes true /errorcontrol /warnandcontinue /flattenerignorespreadoverrides false /includeguidesgrids false /includenonprinting false /includeslug false /namespace [ (adobe) (indesign) (4.0) ] /omitplacedbitmaps false /omitplacedeps false /omitplacedpdf false /simulateoverprint /legacy >> << /addbleedmarks false /addcolorbars false /addcropmarks false /addpageinfo false /addregmarks false /convertcolors /converttocmyk /destinationprofilename () /destinationprofileselector /documentcmyk /downsample16bitimages true /flattenerpreset << /presetselector /mediumresolution >> /formelements false /generatestructure false /includebookmarks false /includehyperlinks false /includeinteractive false /includelayers false /includeprofiles false /multimediahandling /useobjectsettings /namespace [ (adobe) (creativesuite) (2.0) ] /pdfxoutputintentprofileselector /documentcmyk /preserveediting true /untaggedcmykhandling /leaveuntagged /untaggedrgbhandling /usedocumentprofile /usedocumentbleed false >> ] >> setdistillerparams << /hwresolution [2400 2400] /pagesize [612.000 792.000] >> setpagedevice microsoft word numero_37_art_26 c. m. sonsino et alii, frattura ed integrità strutturale, 37 (2016) 200-206; doi: 10.3221/igf-esis.37.26 200 focussed on multiaxial fatigue and fracture multiaxial fatigue of cast aluminium en ac-42000 t6 (g-alsi7mg0.3 t6) for automotive safety components under constant and variable amplitude loading c.m. sonsino, r. franz fraunhofer institute for structural durability and system reliability lbf, bartningstr. 47, d-6429 darmstadt / germany c.m.sonsino@lbf.fraunhofer.de abstract. regarding the fatigue behaviour of en ac-42000 t6 (a 356 t6), which is the most frequently used cast aluminium alloy for automotive safety components, especially under non-proportional constant and variable normal and shear stress amplitudes with changing principal stress directions, a poor level of knowledge was available. the reported investigations show that, under non-proportional normal and shear stresses, fatigue life is increased in contrast to ductile steels where life is reduced due to changing principal stress directions. this behaviour caused by the low ductility of this alloy (e < 10%) compared to quenched and tempered steels suggests the application of the normal (principal) stress hypothesis (nsh). for all of the investigated stress states under multiaxial constant and variable (gaussian spectrum) amplitudes without and with mean stresses, the nsh was able to depict the life increase by the non-proportionality and delivered, for most cases, conservative but non-exaggerated results. keywords. cast aluminium; multiaxial fatigue; spectrum loading. introduction ince the 1970s, cast aluminum has found increasing access into automotive applications, especially for safety parts, such as wheels, steering knuckles, brake brackets, axles, and engine carriers [1-4]. fig. 1 shows an example of prominent automotive safety components, i.e. the multiaxial loading of a car wheel and its appertaining steering knuckle with acting reaction forces, which cause a combined non-proportional bending and torque on the shaft. because of missing necessary knowledge on the multiaxial fatigue behaviour of cast aluminium for the design of such safety parts a large investigation was initiated focusing on the mostly used cast aluminium alloy en ac-42000 t6 [5]. the present paper will report the results and the applicability of the nsh. material properties, specimens and testing programme material properties and specimens he precipitation hardened alloy en ac-42000 t6 with the heat treatment t6 contains mainly 7 % si and 0.38 % mg. the porosity state, according to astm e 155 [6], is p ≈ 0, i.e. pore diameters d ≤ 0.3 mm. the investigated alloy is a cyclic hardening material, revealing monotonic and cyclic yield stresses rp0.2 = 253 mpa and r’p0.2 = 307 s t c. m. sonsino et alii, frattura ed integrità strutturale, 37 (2016) 200-206; doi: 10.3221/igf-esis.37.26 201 mpa, respectively. the ultimate tensile stress rm = 310 mpa, the young’s modulus e = 71 gpa, the elongation e = 5.9 % and the hardness hb5/250 = 103 are the further characteristic mechanical properties. the notched specimens with the stress concentration factors ktb = 1.89 and ktt = 1.37 for the uniand multiaxial testing, were first cast and then, after the t6 treatment, the outer contour was machined. the geometry of the specimens is displayed in following figures. figure 1: acting multiaxial wheel-loads and reaction forces on a steering knuckle testing programme and local stress ratios the testing programme comprised uniand biaxial test series under constant and variable amplitudes without and with mean stresses, i.e. fully reversed loading r = σmin / σmax = τmin / τmax = -1 and pulsating loading r = 0. for the tests under variable amplitudes [7], a standard gaussian distribution with a sequence length of ls = 1· 105 cycles and an irregularity factor of i = 0.99 was used. under uniaxial plane bending, a local biaxial normal stress state occurs in the notch with longitudinal and tangential normal stress components σx and σy , which are related to each other by σy = 0.25·σx . the local stress state under pure torsion is also biaxial with the shear stress component τxy. for combined plane bending and torsion between the local longitudinal and shear stress amplitudes, a ratio of τa,xy / σa,x = 0.72 and the phase angles δ = 0 and 90° were chosen; this ratio lies in the range of ratios, i.e. 0.5 to 1.0, applied in different investigations [4]. for constant amplitude loading, about 10 tests per woehler-line and, for variable amplitude loading, about 5 tests per gassner-line were carried out [7]. the test frequency depended on the load level and varied between f = 10 to 12 s-1. the failure criterion, for which the results are presented later, was total failure. however, the technically detectable first surface cracks with l = 1 mm were also registered using video cameras. for the investigated specimens, the ratio between the fatigue lives to crack initiation and total rupture was on average ncr / nf ≈ 0.50, and the fatigue lines for the failure criteria technical crack and total failure revealed overlapping scatter bands [5]. the following evaluations will be performed using the fatigue lines for the criterion of total rupture, but, because of the aforementioned overlapping, they are also valid for the criterion of a technical crack with l = 1 to 2 mm surface length, which is required in the design of automotive safety components [8]. experimental results and discussion presentation of experimental results igs. 2 and 3 present the fatigue lines for total failure with a probability of survival ps = 50%. the gassner-lines, obtained under variable amplitude loading, are presented by the maximum stress amplitude of the spectrum and all lie, as expected, above the woehler-lines due to the lower damage under spectrum loading [7]. discussion of experimental results the stress amplitudes are local values, i.e. notch stresses which are, with the exception only of the highest levels for pure bending under spectrum loading, below the cyclic yield stress r’p0.2 = 307 mpa. this means that the evaluation of the multiaxial stress states can be carried out without considering any plasticity effects. f c. m. sonsino et alii, frattura ed integrità strutturale, 37 (2016) 200-206; doi: 10.3221/igf-esis.37.26 202 the outliers in brackets in figs. 2 and 3 were not considered because they did not fit into the expected course of the woehler-lines, based on past experience [9-11]. microshrinkages, acting as crack-starters on the surfaces, were responsible for these premature failures [5]. figure 2: fatigue behaviour of cast aluminium g-alsi7mg0.3 t6 (en ac-42000 t6) under fully reversed uniaxial (b = pure bending, t = pure torsion) and combined loadings (δ = 0, 45 and 90°). figure 3: fatigue behaviour of cast aluminium g-alsi7mg0.3 t6 (en ac-42000 t6) under pulsating uniaxial (b = pure bending, t = pure torsion) and combined loadings (δ = 0, 45 and 90°). the evaluation by regression analyses also considered slopes, i.e. inverse basquin exponents, k = δlognf / δlogσa,x , up to the knee points nk of the woehler-lines, known from various investigations with cast aluminium alloys [9, 10]. under constant amplitude loading, the values k = 5 for pure bending, 8 for pure torsion and 6 for combined loadings described c. m. sonsino et alii, frattura ed integrità strutturale, 37 (2016) 200-206; doi: 10.3221/igf-esis.37.26 203 the results very well, as did the values k = 6 for pure bending and 7 for combined loading under variable amplitudes. the position of the knee points nk = 1·106 to 5·106 cycles and the slopes k*= 22 after them were based on experience and recommendations given in [9, 11] as tests in the high cycle regime were not carried out. the determined scatters of the stress amplitudes tσ = {1 : [σa(ps=10%) / σa(ps=90%)]} were not higher than 1 : 1.26, i.e. they were much lower than scatters known from other investigations [1-3, 9, 11]. the most important result of this investigation is the fatigue life increase under non-proportional biaxial loading caused by the phase difference between the local normal and shear stresses. under fully reversed loading, fig. 2, this is more pronounced for variable amplitude than for constant amplitude loading. however, under pulsating constant amplitude loading, the life increase is most pronounced, compare figs. 2 and 3. unfortunately, multiaxial pulsating spectrum loading was not investigated. furthermore, from stand-point of hypothesis selection and application this result is very important, because a fatigue life increase under out-of-phase loading indicates the major role of normal stresses, which are mainly responsible for the crack initiation. selection and application of the appropriate strength hypothesis selection of the appropriate strength hypothesis here are several indications for selection of the normal (principal) stress hypothesis (nhs) for the evaluation of the results, i.e. the low ductility of the investigated material, e = 5.9 %, the crack plane for pure torsion under 45° [5], the high mean-stress sensitivity, the prolongation of fatigue life under non-proportional loading, see figs. 2 and 3, and, last but not least, the cleavages on the fracture surfaces after rupture, which confirm the sensitivity of the material against normal stresses [2]. application of the normal stress hypothesis for constant and variable amplitude loading for low-ductility (up to brittle) materials, the critical plane φ on a surface element is the one where the normal stress σn(φ) = {[(σx + σy) + (σx σy)·cos2φ] / 2 + τxy·sin2φ} or the cumulative damage of its spectrum becomes at maximum [2, 4]. when mean normal stresses are involved, then the normal stress amplitudes must be transformed to r = -1 or 0 by the mean-stress-sensitivity of the particular material [14] m = {[σa(r= -1) / σa(r= 0)] – 1} which is the inclination of the haigh-line in the mean-stress-amplitude diagram [12-14]. after determining the maximum mean-stress-compensated normal stress amplitude (or the maximum cumulative damage in the case of spectrum loading), which is the equivalent stress amplitude (or its spectrum) according to the nsh, the next step is its evaluation, i.e. the calculation of the appertaining fatigue life. for this, depending on the stress ratio for which the amplitude transformation is carried out, woehler-lines with r = -1 or 0, obtained under uniaxial loading, are needed. here, amplitudes were transformed to the ratio r = -1. in this context, the cumulative damage must also be addressed for the evaluation of the results determined under multiaxial spectrum loading. in this case, the critical plane is the one with the highest damage sum d = ∑(ni/ni). the appertaining mean-stress-compensated normal stress spectrum is then the equivalent stress spectrum. fatigue life is then estimated according to the palmgren-miner hypothesis and its frequently applied modification, where, in the high-cycle fatigue area, the inclination k of the woehler-curve is reduced according to [13] with k′ = 2k-i depending on the material [7, 9, 12, 13], in order to account for the damaging influence of small load cycles. for cast materials, i = 2 is suggested [7, 9, 12, 13]. the spectrum results from the amplitude transformation of the rainflow-matrix to the stress ratio r of the woehler-curve using the particular mean-stress sensitivity of the material. because of the well-known fact that the theoretical damage sum dth = 1.0 results in an unsafe estimate for 90 % of all published results [7, 12, 13], the life calculations are carried out using dal = 0.3 as the allowable damage sum, as recommended for cast aluminium parts in [10]. evaluation according to the normal stress hypothesis for the assessment of fatigue life, the calculated maximum normal local stress amplitude or its spectrum must be allocated to a woehler-curve determined for the local stress system under pure bending or pure torsion and for the stress ratio r for which the amplitudes were transferred. theoretically, for materials obeying the nsh, the wöhler-lines (or curves) for pure bending or pure torsion should be identical because, under pure bending the local normal stress amplitude σa,x is, at same time, the principal stress amplitude and the equivalent stress σa,eq = σa,1 = σa,x and, under pure torsion, the local t c. m. sonsino et alii, frattura ed integrità strutturale, 37 (2016) 200-206; doi: 10.3221/igf-esis.37.26 204 shear stress amplitude τa,xy is, at same time, the principal stress amplitude and the equivalent stress amplitude has the value σa,eq = σa,1 = τa,xy. figure 4: comparison of experimental and calculated results for combined fully reversed loadings according to the normal stress hypothesis figure 5: comparison of experimental and calculated results for combined pulsating loadings according to the normal stress hypothesis however, from figs. 2 and 3, it can be seen that the lines for pure torsion are inferior to those lines for pure bending, revealing differences in the slopes (kσ = 5 and kτ = 8), knee points (nk,σ = 1·106 and nk,τ = 5·106) and stress levels up to factor of 1.5. the differences in the slopes of these lines, determined under load control for the failure criterion of total c. m. sonsino et alii, frattura ed integrità strutturale, 37 (2016) 200-206; doi: 10.3221/igf-esis.37.26 205 rupture, cannot be attributed to different crack propagations under pure bending and pure torsion, because deformationcontrolled tests for the failure criterion of crack initiation also reveal the same tendency for pure axial strain and pure shear strain [5]. the significantly different stress levels under fully reversed bending are caused by the different highly stressed material volumes in the notches due to the particular stress concentrations. under pulsating loading, as the meanstress effect for bending is more pronounced than for torsion, the stress levels are quite close to each other. these differences make choosing the appropriate woehler-line for the assessment of fatigue life difficult. however, as the local normal stresses under combined loading are more dominant than the local shear stresses, the lines for pure bending are taken as starting woehler-lines for fatigue lifing: r = -1, ak = 147 mpa, nk = 1·106, k = 5, k* = 22 r = 0, ak = 97.5 mpa, nk = 1·106, k = 5, k* = 22 the mean-stress sensitivity, which is needed for amplitude transformations for r = -1 when mean stresses vary, is m = 0.51 resulting from the strength values at the knee points. fatigue lifing is carried out for the applied gaussian amplitude distribution with the sequence length ls = 1·105 according to the modified palmgren-miner hypothesis with k′= 8 against the allowable damage sum dal = 0.3 using the woehler-line for pure bending with r = -1. the experimental and calculated fatigue-life lines for fully reversed and pulsating constant and variable amplitude loadings are displayed in figs. 4 and 5. the application of the nsh reflects the life increase due to the non-proportional combined loading. except in one case, all results are on the safe side, by up to a factor of about 3 in life. the unsafe result for fully reversed out-of-phase spectrum loading differs by a factor of about 2 from the experimental outcome. regarding the stresses, the calculated values are up to a factor of about 1.25 on the safe side and, in the unsafe case, by a factor of about 1.10. in addition to this outcome, it can be observed that neither the slopes nor the knee points of the calculated fatigue-lines are in accordance with the experimental ones. the calculated results are driven by the properties of the starting woehlerlines and the experimental results by the combination of local normal and shear stresses. also, the comparison of the woehler-lines for pure bending and pure torsion indicated the problem by their different slopes and knee points. this was also observed in other investigations [15] and particular modified woehler-lines for overcoming these different influences on these properties were derived for the assessment. however, because of space limitations this will not be presented here. summary and conclusions he investigations carried out with component-like specimens of the cast aluminium alloy en ac-42000 t6 (a 356 t6, g-alsi7mg0.3 t6), show that, under non-proportional normal and shear stresses fatigue life is increased in contrast to ductile steels where life is reduced due to changing principal stress directions. because of the low ductility of this cast alloy (e < 10%) compared to ductile quenched and tempered and structural steels, normal stresses are considered to be the main damage driving property, suggesting the application of the nsh. fatigue lives under uniand multiaxial spectrum loadings were estimated by the modified palmgren-miner-rule using the allowable damage sum dal = 0.3. for all investigated stress states under multiaxial constant and variable (gaussian spectrum) amplitudes without and with mean stresses, the nsh was able to depict the life increase by the non-proportionality and, for most cases, delivered conservative but non-exaggerated results. except for one case, all results were on the safe side by up to a factor of approximately 3 in life. the one unsafe result, for fully reversed out-of-phase spectrum loading, differed by a factor of approximately 2 from the experimental outcome. regarding the appertaining stresses, the calculated ones are up to a factor of about 1.25 on the safe side and, in the unsafe case, by a factor of about 1.10. in design practice safety factors jσ for safety components of vehicles are in the range of about 1.7 to 2.2 [8] and cover the mentioned underor overestimation of supportable stresses by the nsh. if, in final durability proof tests, the fatigue life should be insufficient, then the required duration can be adjusted by simple geometrical modifications, e. g. by lowering local stresses by the use of larger radii, if this is not possible, by increasing thickness. as, for most safety components, the dominant loading partition is bending rather than torque or axial loading, to compensate the above mentioned factor of 1.10 resulting from the unsafe calculation, an increase of thickness by the square root of this factor, i.e. 1.05, 5 % only, would be sufficient. in the case of the conservative factor of 1.25 under predominantly bending loading, thickness could be reduced by factor of 1.12. because of the advantage of the t c. m. sonsino et alii, frattura ed integrità strutturale, 37 (2016) 200-206; doi: 10.3221/igf-esis.37.26 206 casting technology to perform local dimensional modifications, the mentioned thickness changes do not hinder the realisation of lightweight designs, even if axial loads would be predominant and therefore a local thickness increase or reduction would be linear to the factors 1.10 and 1.25 respectively. these results underline that the normal (principal) stress hypothesis (nsh) can be applied in its original form without any modifications for “fitting” the obtained experimental results, despite the not very significant limitations. underor overestimation of required fatigue lives or local stresses are, in any case, revealed by the durability proof tests, which are mandatory for vehicle safety components [7-9]. acknowledgements he authors acknowledge the federal ministry for economics and technology (bmwt), berlin, for funding the research project [5] and the research association for mechanical engineering fkm/vdma, frankfurt, for the support given during the work. dr. p. xin and imab, tu clausthal, are acknowledged for their experimental contribution [5]. references [1] sonsino, c. m., ziese, j., fatigue strength and applications of cast aluminium alloys with different degrees of porosity, int. j. fatigue, 15(2) (1993) 75-84. [2] sonsino, c. m., grubisic, v., mechanics of fatigue failures of cast and sintered structural materials under multiaxial stresses, konstruktion, 37(72) (1985) 7261–269, in german. [3] sonsino, c. m., structural durability of cast aluminium gearbox housings of underground railway vehicles under variable amplitude loading, int. j. fatigue, 27(8) (2005) 944-953. [4] sonsino, c. m., influence of material's ductility and local deformation mode on multiaxial fatigue response, int. j. fatigue, 33(8) (2011) 930-947. [5] franz, r., xin, p., improvement of fatigue life estimation for multiaxial loaded safety components of forged steel and cast aluminium by selection of appropriate calculation algorithms, final report – fkm/aif no. 16059 n/1 (2013), vdma, frankfurt/germany, in german. [6] ansi/astm-e 155-79, standard reference radiographs for inspection of aluminium and magnesium castings, american society for testing and materials, (1979). [7] sonsino, c. m., principles of variable amplitude fatigue design and testing, fatigue testing and analysis under variable amplitude loading conditions, in: mckeighan, p. c. and ranganathan, n., editors, astm stp, 1439 (2005) 3–23. [8] grubisic, v., criteria and methodology for lightweight design of vehicle components subjected to random loads, sae-paper no. 850367 (1985), warrendale, pa/usa [9] sonsino, c. m., berg, a., grubisic, v., structural durability proof of automotive safety components – present state of the art, sae-paper no. 2005-01-0800 (2005), warrendale, pa/usa [10] hänel, b., haibach, e., seeger, t., wirthgen, g., zenner, h., fkm-guideline – analytical strength assessment of components in mech. eng., vdma, frankfurt/germany, 5th extended ed., (2007). [11] sonsino, c. m., course of sn-curves especially in the high-cycle fatigue regime with regard to component design and safety, int. j. fatigue, 29 (2007) 2246-2258. [12] buxbaum, o., structural durability safe and economic design of fatigue components, 2nd edition, verlag stahleisen, düsseldorf (1992). [13] haibach, e., structural durability – methods and data for calculation, 3rd ed., vdi-verlag, düsseldorf, (2003), in german. [14] sonsino, c. m., leightweight design chances using high-strength steels, mat.wiss. u. werkstofftech. 38(1) (2007) 922. [15] susmel, l., sonsino, c. m., tovo, r., accuracy of the modified wöhler curve method applied along with the rref = 1 mm concept in estimating lifetime of welded joints subjected to multiaxial fatigue loading, int. j. fatigue 33 (2011) 1075-10. t << /ascii85encodepages false /allowtransparency false /autopositionepsfiles true /autorotatepages /none /binding /left /calgrayprofile (dot gain 20%) /calrgbprofile (srgb iec61966-2.1) /calcmykprofile (u.s. web coated \050swop\051 v2) /srgbprofile (srgb iec61966-2.1) /cannotembedfontpolicy /error /compatibilitylevel 1.4 /compressobjects /tags /compresspages true /convertimagestoindexed true /passthroughjpegimages true /createjobticket false /defaultrenderingintent /default /detectblends true /detectcurves 0.0000 /colorconversionstrategy /cmyk /dothumbnails false /embedallfonts true /embedopentype false /parseiccprofilesincomments true /embedjoboptions true /dscreportinglevel 0 /emitdscwarnings false /endpage -1 /imagememory 1048576 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can be opened with acrobat and adobe reader 5.0 and later.) >> /namespace [ (adobe) (common) (1.0) ] /othernamespaces [ << /asreaderspreads false /cropimagestoframes true /errorcontrol /warnandcontinue /flattenerignorespreadoverrides false /includeguidesgrids false /includenonprinting false /includeslug false /namespace [ (adobe) (indesign) (4.0) ] /omitplacedbitmaps false /omitplacedeps false /omitplacedpdf false /simulateoverprint /legacy >> << /addbleedmarks false /addcolorbars false /addcropmarks false /addpageinfo false /addregmarks false /convertcolors /converttocmyk /destinationprofilename () /destinationprofileselector /documentcmyk /downsample16bitimages true /flattenerpreset << /presetselector /mediumresolution >> /formelements false /generatestructure false /includebookmarks false /includehyperlinks false /includeinteractive false /includelayers false /includeprofiles false /multimediahandling /useobjectsettings /namespace [ (adobe) (creativesuite) (2.0) ] /pdfxoutputintentprofileselector /documentcmyk /preserveediting true /untaggedcmykhandling /leaveuntagged /untaggedrgbhandling /usedocumentprofile /usedocumentbleed false >> ] >> setdistillerparams << /hwresolution [2400 2400] /pagesize [612.000 792.000] >> setpagedevice microsoft word numero_62_art_13_3637.docx a. s. yankin et alii, frattura ed integrità strutturale, 62 (2022) 180-193; doi: 10.3221/igf-esis.62.13 180 influence of additional static stresses on biaxial low-cycle fatigue of 2024 aluminum alloy a.s. yankin, a.v. lykova, a.i. mugatarov, v.e. wildemann, a.v. ilinykh center of experimental mechanics, perm national research polytechnic university, perm, russian federation yas.cem@yandex.ru, https://orcid.org/0000-0002-0895-4912 cem.lykova@gmail.com, https://orcid.org/0000-0003-4873-6351 cem_mugatarov@mail.ru, https://orcid.org/0000-0002-2229-8181 wildemann@pstu.ru, https://orcid.org/0000-0002-6240-4022 ilinih@yandex.ru, https://orcid.org/0000-0001-9162-1053 abstract. in this paper, a previously developed modification of the sines model of multiaxial fatigue is reduced to an invariant form. model constants were determined for different sets of setup experiments. it was supposed to introduce an additional summand to account for the phase shift between loading modes. the model is used to describe the fatigue behavior of the 2024 aluminum alloy. low-cycle fatigue tests under biaxial loading conditions are presented, with one mode changing cyclically and the other mode remaining constant in magnitude throughout the test. the results of cyclic durability prediction by the modified model provide good convergence. keywords. low-cycle fatigue; experimental research; complex stress state; aluminum alloy; fatigue life; modified sines model. citation: yankin, a.s., lykova, a.v., mugatarov, a.i., wildemann, v.e., ilinykh, a.v., influence of additional static stresses on biaxial low-cycle fatigue of 2024 aluminum alloy, frattura ed integrità strutturale, 62 (2022) 180-193. received: 21.06.2022 accepted: 24.08.2022 online first: 25.08.2022 published: 25.08.2022 copyright: © 2022 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. introduction owadays, aluminum alloys are widely used due to their exceptional properties such as excellent plasticity, electrical and thermal conductivities. a wide diversity of applications can be found in aviation, machinery manufacturing, and other industries [1-2]. some engineering components of construction elements are subjected to complex cyclic loads during operation, which might be a reason for the failure due to multiaxial fatigue [3]. also, some notches, nicks, and dents can arise in products or parts during their exploitation which is related to, for example, foreign object damage [4-6]. moreover, holes, fillets, grooves, and other geometrical features can be a part of structures. such geometries can be the cause of inherent multiaxiality. in this respect, the stress or strain fields in the vicinity of stress or strain raiser are multiaxial even under uniaxial loads [7]. thus, is crucial to consider the behavior of materials under the multiaxial loads in order to deliver fatigue life predictions. the need in studying complex fatigue processes brought a number of experimental works, which used specialized equipment, specimens, and methods of multiaxial loading. the main load conditions referred to in the literature are biaxial tension of cross-shaped specimens [8], tension with torsion, bending with torsion of cylindrical specimens [9-12], as well as n https://youtu.be/gnsniekqbtq a. s. yankin et alii, frattura ed integrità strutturale, 62 (2022) 180-193; doi: 10.3221/igf-esis.62.13 181 three-axial tension with torsion and internal pressure of hollow specimens [9]. apart from standard hourglass and tubular specimens, one tests weld joint specimens [13, 14, 18-21], specimens with notches, and other stress raisers [15-17]. load factors can significantly affect the fatigue behavior of materials under the multiaxial influence, for instance, the change in the ratio of stress amplitudes [22-25], the phase angle between the modes of influence [22-26], the ratio of loading frequencies [22, 27, 28], average stresses in the cycle [29-37] and others. it should be noted that different dependencies of fatigue behavior on loading factors may be observed for various materials. in particular, an increase in the average stress leads to a decrease in fatigue strength. such effect is pretty strong for brittle materials (e.g. cast iron) both in axial and in torsion [38]. however, it is lower in torsion than in axial for ductile materials such as steels and aluminum alloys [39]. today, there are plenty of multiaxial models that can be used to predict the fatigue life/strength of various materials. these approaches can be classified as stress, strain, and strain energy density models. some excellent reviews of multiaxial criteria are presented in works [40-42]. also, the article of papuga et al. should be noted [43]. it discusses the procedure in which the stress path is analyzed to provide relevant measures of parameters required by multiaxial criteria. the selection of this procedure affects the prediction results for out-of-phase cases. all these approaches are more or less accurate for different materials at various load paths, so it is important to validate multiaxial fatigue models in particular cases. in addition, it is vital to check the model application in case of notched and cracked bodies when stress concentrations exist. in previous work, the authors proposed a modification of the sines model to describe the fatigue behavior of 2024 aluminum alloy [22, 34]. however, this model is not invariant for the coordinate transformation in the case of disproportional loads, such as out-of-phase loads. in this paper, an approach to determine the model parameters to eliminate this drawback is proposed. then, the model was validated using biaxial experimental data of 2024 aluminum alloy. multiaxial fatigue model he previous model presented in [22, 34] has the issue that it is not invariant for the rotation of the coordinate system. in this regard, it is proposed to modernize the model in the following way. in the general case, the stress tensor is some function of time:    , 0ij ij t t (1) in the case of periodic loads:              , 0 ; ,ij ij ij ijt t t t t nt n n (2) where t is the loading period. let us divide the tensor into constant and periodic components. let each component of the stress tensor be known in some coordinate system. enter the value:    0 1 tmean ij ij t dt t (3) let us call it the average (constant) component of the stress tensor. in the case of rotation of the coordinate system:                                0 0 0 1 1 1 kl ki lj ij t t tmean mean kl kl ki lj ij ki lj ij ki lj ij t t t dt t dt t dt t t t (4) which proves the tensor nature of the introduced value. then the tensor of the periodically changing component of the stress tensor can be obtained:       per meanij ij ijt t (5) t a. s. yankin et alii, frattura ed integrità strutturale, 62 (2022) 180-193; doi: 10.3221/igf-esis.62.13 182 as a result, we obtain the decomposition of the stress tensor in the following form:       mean perij ij ijt t (6) it is worth noting that in the general case there may not exist a time moment tmean, such that σij(tmean) = σijmean. at each moment, the stress tensor is characterized by several quantities that do not depend on the choice of coordinate system. we choose the first invariant of the stress tensor i1 and the second invariant of the stress deviator i2 to use. thus, these values, taking into account eqn. (6), can be represented in the form:                                                                              1 11 22 33 1 11 22 33 2 2 2 2 2 2 2 11 22 22 33 11 33 12 13 23 2 2 2 11 22 22 33 11 1 6 6 1 6 mean mean mean mean per per per per mean mean mean mean mean mean mean mean mean mean per per per per per p i i t t t t i i t t t t t                         2 33 2 2 2 12 13 23 er per per per per t t t t t (7) the first and third of these parameters are time-independent, the second and fourth depend on time. let us determine the maximum and minimum values of the values to avoid the time dependence:                 1 1 1 1 2 2 2 2 max min max min max per min per max per min per i i t i i t i i t i i t (8) taking into account expressions (7), (8), let us rewrite the model of multiaxial fatigue in the form:      1 1 2 21 2 1 3 4 2 1 2 2 max min max min mean meani i i ia a i a a i (9) defining model parameters et us define the model parameters (9). in the general case (with no additional assumptions), two fatigue curves obtained for symmetrical tension-compression and symmetrical cyclic torsion, a static tensile test, and a static torsion test are needed to calculate the parameters. under static torsion: l a. s. yankin et alii, frattura ed integrità strutturale, 62 (2022) 180-193; doi: 10.3221/igf-esis.62.13 183            2 2 1 1 1 2 2 4 2 4 2 0 1 1 max min max min mean mean mean b i i i i i i a i a (10) under static tension:                  2 2 1 1 2 1 2 2 2 0 1 ; 3 1 1 1 1 3 3 max min max min mean mean bb b i i i i i i a a (11) where τb is the ultimate shear strength. under uniaxial cyclic symmetric torsion:                0 2 2 1 1 1 2 2 2 3 3 2 ' 0 2 1 2 2 min mean max min mean max a a b f i i i i i i a a n (12) where τ′f, b0 are material parameters determined from the fatigue curve for symmetrical cyclic torsion. under uniaxial cyclic symmetric tension-compression:                          0 1 0 2 2 1 2 1 1 2 1 1' ' ' 0 1 ; 3 1 1 1 3 2 2 3 2 min mean mean min max max a a a ab b b f f f i i i i i i a a n n n (13) where σ′f, b1 are material parameters determined from the fatigue curve at symmetrical cyclic tension-compression. as a result, the model looks like this:                            1 0 0 2 2 2 1 1 12 2 ' '' 1 1 1 1 1 2 32 3 22 max min mean max min mean b bb bb bf ff i i i i i i n nn (14) a. s. yankin et alii, frattura ed integrità strutturale, 62 (2022) 180-193; doi: 10.3221/igf-esis.62.13 184 if there is one fatigue curve and a point on another curve, we can assume that they are equidistant, then b1=b0, the model will be rewritten in the form:                            0 0 ' 2 2 2 1 1 12 2 ' '' 1 1 1 1 1 23 322 max min mean max min f mean bb bb f bff i i i i i i nn (15) if there is one fatigue curve, we can assume that the tensile-compression and torsional curves coincide, then σ′f=√3τ′f, the model will have the form:              0 2 2 2 12 2 ' 1 1 1 32 max min mean mean b bb b f i i i i n (16) if there is only one static test, we can take σb=√3τb, the model will look like this:        0 2 2 2 2 2 ' 1 2 max min mean b b f i i i n (17) consideration of the phase angle between loading modes t can be shown that in the variants of notation (14)-(17) the model of multiaxial fatigue will not consider the phase shift between the normal and tangential stress components, which does not always correspond to the experimental data. in this regard, let us introduce an additional summand into the radical expression:       1 1 2 21 2 1 3 4 2 5 2 1 2 2 max min max min mean mean mini i i ia a i a a i a i (18) the last term of the radical expression will be nonzero only if there is a phase shift between the tangential and normal loading modes. the setup experiment to determine the constant a5 can be as follows:                           11 12 22 33 13 23 sin ; sin 2 0; 3 a a a a t t (19) thus                                                                          1 0 0 1 1 1 2 2 2 2 22 2 2 2 2 2 2 2 2 1 3 5 5 2' ' ' ' 2 ; 0; 0 1 sin sin sin cos 3 2 1 3 1 2 3 1 2 2 2 2 phase max min mean mean a per a a a a max min a a a a b b b b phase f f f i i i i i t t t t t i i a a a a n n n n (20) i a. s. yankin et alii, frattura ed integrità strutturale, 62 (2022) 180-193; doi: 10.3221/igf-esis.62.13 185 where τ′phase, bphase are material parameters determined from the fatigue curve for the described experiment (19). if the material is not sensitive to phase shift, we can assume a5 = 0. the fatigue failure criteria based on stresses are not able to take into account the effect of cyclic hardening or softening. if the fatigue tests are carried out under stress controlled system, the effect of cyclic hardening or softening is visible only in strain history, which is not taken into account in the fatigue failure criteria based on stresses. model validation he model validation was carried out using experimental data [26, 29, 44-49]. for each data set mean absolute error was calculated taking into account and excluding the phase shift effect (maephase and maeno phase). determining model parameters are shown in tab. 1. a comparison between predicted fatigue lives with taking into account and excluding the phase shift effect is shown in fig. 1. it can be concluded that consideration of the phase shift allows improving the accuracy of the fatigue life prediction. data set 1 2 3 4 authors a. fatemi et al [29, 44] y.-y. wang et al [26] t.-x. xia et al [45-48] x.-w. wang et al [49] τ′f, mpa 460.0 600.8 642.3 b0 -0.082 -0.104 -0.118 σ′f, mpa 1199.3 951.9 1324.8 b1 -0.133 -0.102 -0.145 τb, mpa 283.0 290.0 283.0 σb, mpa 450.0 545.0 450.0 τ′phase, mpa 595.8 583.8 690.3 bphase -0.140 -0.142 -0.171 maeno phase 0.240 0.210 0.117 0.162 maephase 0.218 0.150 0.110 0.157 table 1: calculated model parameters. a b t a. s. yankin et alii, frattura ed integrità strutturale, 62 (2022) 180-193; doi: 10.3221/igf-esis.62.13 186 c d e f g h figure 1: comparison of experimental and predicted fatigue live with taking into account (b, d, f, h) and excluding the phase shift effect (a, c, e, g) for data sets: 1 (a, b), 2 (c, d), 3 (e, f) and 4 (g, h). experimental procedure and results of particular interest is the study of low-cycle fatigue in the presence of the second component of small magnitude, which can occur under difficult operating conditions. experiments on low-cycle fatigue under biaxial strain conditions, with one of the modes (normal or tangential stress) changing cyclically and the other mode remaining constant in magnitude during the test, were performed at room temperature on an instron 8850 servohydraulic system at the pnrpu center of experimental mechanics. during fatigue testing on servohydraulic machines, the moving parts of the system experience a. s. yankin et alii, frattura ed integrità strutturale, 62 (2022) 180-193; doi: 10.3221/igf-esis.62.13 187 acceleration, so that in addition to the force applied to the sample, the load cell also records the force caused by the movement of the grips and fixtures installed. these test systems use sensors, particularly dynacell sensors, which have an accelerometer mounted directly on the load axis to minimize errors due to inertial forces. the deformations were recorded using an epsilon 3550-010m dual-axis extensometer with a 10-mm measurement base with a full range of ± 5.0 mm for axial displacement and ± 3° for shear angle. we performed pre-cycling in the elastic zone and determined young's modulus and shear modulus under static loading to verify that the extensometer was correctly installed. 2024 aluminum alloy was used as the test material. the chemical composition of the alloy consists (in percent) of fe, si<0.5, mn 0.3-0.9, cr<0.1, ti<0.15, al 90.9-94.7, cu 3.8-4.9, mg 1.2-1.8, zn<0.25, ti+zr<0.2, other elements<0.15. fatigue tests were carried out on thin-walled samples with an annular cross-section in the working part. a sketch of the sample is shown in fig. 2. figure 2: specimen geometry (in mm). three different levels of constant stress components were selected for cyclic tests to assess their effect on the durability of aluminum alloy. the values of the constant components were chosen from the tensile and torsional strain diagrams of aluminum alloy samples. the specimens were tested at two levels of stress amplitude for each biaxial strain scheme. tests were conducted at room temperature with a test frequency of 1 hz. the specified cyclic loading parameters are presented in tab. 2. constant normal stress m, mpa constant shear stress τm, mpa normal stress amplitude a, mpa shear stress amplitude τa, mpa stress range r(τr), mpa tested samples number number of cycles to failure, n 0 70 275 0 550 4 3411, 3598, 3347, 5344 0 110 275 0 550 3 1834, 1804, 1824 0 160 275 0 550 1 1144 0 70 215 0 430 3 51277, 26912, 30470 0 110 215 0 430 2 18819,16668 100 0 0 150 300 2 9545, 4825 200 0 0 150 300 2 5450, 5170 350 0 0 150 300 2 1910, 2978 100 0 0 115 230 3 106493, 77745, 82800 200 0 0 115 230 2 24468, 49650 350 0 0 115 230 2 11234, 11283 table 2: summary fatigue tests. a. s. yankin et alii, frattura ed integrità strutturale, 62 (2022) 180-193; doi: 10.3221/igf-esis.62.13 188 experimental studies of low-cycle fatigue under constant component conditions resulted in fatigue life values at different values of stress amplitudes. the results obtained, shown in fig. 3 and 4, indicate a significant effect of constant components on one of the modes during biaxial low-cycle fatigue on cyclic durability. figure 3: dependence of fatigue life on the level of constant value tangential stresses related to the stress range at the amplitude of normal stresses: σа = 270 mpa (●), σа = 215 mpa (■). figure 4: dependence of fatigue life on the level of constant values normal stresses related to the stress range at the amplitude of tangential stress amplitudes at: 𝜏а=150 mpa (●),а =115 mpa (■). it is shown that at certain ratios of constant and cyclic components, the durability decreases by an order of magnitude. calculation of fatigue life using the proposed model he experimental data obtained are used to test the proposed model (9) with a5 = 0. static tensile tests, static torsion tests, symmetrical cyclic tension-compression, and symmetrical cyclic torsion tests were performed to find the constants included in this model. the a2 and a4 model parameters include ultimate tensile and shear strength: the ultimate tensile strength σb of the alloy is equal to 450 mpa; the ultimate shear strength 𝜏b of the alloy is equal to 280 mpa. the coefficients included in the a1 and t a. s. yankin et alii, frattura ed integrità strutturale, 62 (2022) 180-193; doi: 10.3221/igf-esis.62.13 189 a3 parameters were determined from the fatigue curves obtained in symmetrical tensile-compression (fig. 5a) and symmetrical torsion (fig. 5b). a b figure 5: fatigue curves. coefficients σ′f = 1270 mpa, τ′f = 566 mpa, and exponents b1 = -0.160, b0= -0.135. the results of fatigue life calculations using the proposed model are presented at fig.6. the figure shows graphs of the dependence of the predicted durability on the experimental one. the colored dots indicate tests at different values of normal and tangential stress amplitudes. dotted and dashed lines on the graphs show ±2 and ±3 factor errors. a b figure 6: results of cyclic durability prediction according to the proposed model for samples of 2024 aluminum alloy: cyclic torsion with various mean normal stress values (a); cyclic tension-compression with various mean shear stress values (b). the above graphs show that when loaded with superimposed mean shear stress, all dots lie within the ±3 factor interval. this indicates that this model predicts well the fatigue life of the aluminum alloy under such influences. however, when loaded with superimposed mean normal stress, three points fall outside the ±3 factor interval. in this case, the values of constant normal stresses for these dropout points were 350 mpa, which is close to the yield strength of the material. as a result, we can conclude that the model predicts the result quite well at values of constant normal stresses less than the yield strength of the material and becomes significantly conservative at values of constant normal stresses close to and greater than the yield strength. in addition, it is worth noting the work of j. papuga [50], in which the authors also point out similar problems with this model. thus, it might be worth introducing an additional term responsible for the one-sided accumulation of deformations (ratcheting) into the model parameters to refine the prediction of the proposed model in the future. this term will probably allow a better description of the experimental data at high values of the static stress components. a. s. yankin et alii, frattura ed integrità strutturale, 62 (2022) 180-193; doi: 10.3221/igf-esis.62.13 190 conclusions he modernized sines model proposed by the authors is reduced to an invariant form. the time-varying stress tensor is decomposed into constant and periodic components. the maximum and minimum values of the first and second invariants of these components were used to record the model. it was supposed to introduce an additional summand to account for the phase shift between loading modes. model constants were determined for different sets of setup experiments. the proposed model was validated using number of data sets, which were taken from literature results. fatigue tests on samples made of 2024 aluminum alloy were carried out. it is shown that the model describes well the fatigue behavior of the material under symmetrical tension-compression with superimposed mean shear stress and under symmetrical torsion with superimposed mean normal stress at values of constant normal stresses less than the yield stress. at values of constant normal stresses close to and greater than the yield strength, the model becomes substantially conservative. acknowledgements   he work was carried out in perm national research polytechnic university with the financial support of the russian foundation for basic research (project number 19-38-90270) and within the state assignment of the ministry of science and higher education of the russian federation (no. fsnm-2020-0027). nomenclature   b0 shear fatigue strength exponent b1 axial fatigue strength exponent bphase 90 out-of-plane fatigue strength exponent i1max maximum value of the first invariant of the stress tensor σijper i1mean first invariant of the stress tensor σijmean i1min minimum value of the first invariant of the stress tensor σijper i2max maximum value of the second invariant of the stress deviator σijper i2mean second invariant of the stress deviator σijmean i2min minimum value of the second invariant of the stress deviator σijper maeno phase mean absolute error excluding the phase shift effect maephase mean absolute error taking into account the phase shift effect n number of cycles to failure t time t cycle period αkl coordinate system rotation matrix σa normal stress amplitude σb tensile strength σij stress tensor σijmean average component of the stress tensor σijper periodically changing component of the stress tensor σ′f axial fatigue strength coefficient σm constant normal stress σr normal stress range τa shear stress amplitude τb torsional strength τ′f shear fatigue strength coefficient τm constant shear stress τ′phase 90 out-of-plane fatigue strength coefficient τr shear stress range ω cyclic frequency t t a. s. yankin et alii, frattura ed integrità strutturale, 62 (2022) 180-193; doi: 10.3221/igf-esis.62.13 191 references   [1] liao, y.s., li, y.b., pan, q., huang, m.h. and zhou, c. (2018). residual fatigue life analysis and comparison of an aluminum lithium alloy structural repair for aviation applications, eng. fract. mech., 194, pp. 262–280. doi: 10.1016/j.engfracmech.2018.03.020. [2] fahim, j., hadavi, s.m.m., ghayour, h. and hassanzadeh tabrizi, s.a. (2019). cavitation erosion behavior of superhydrophobic coatings on al5083 marine aluminum alloy, wear, 424-425, pp. 122–132. doi: 10.1016/j.wear.2019.02.017. [3] esmaeili, f., chakherlou, t.n. and zehsaz, m. (2014). prediction of fatigue life in aircraft double lap bolted joints using several multiaxial fatigue criteria, mater. des., 59, pp. 430-438. doi:10.1016/j.matdes.2014.03.019. [4] baragetti, s., gerosa, r., rivolta, b., silva, g. and tordini, f. (2011). fatigue behavior of foreign object damaged 7075 heat treated aluminum alloy coated with pvd wc/c, proc. engineering, 10, pp. 3375-3380, doi: 10.1016/j.proeng.2011.04.556. [5] ruschau, j., thompson, s.r., and nichola, t. (2003). high cycle fatigue limit stresses for airfoils subjected to foreign object damage, int. j. fatigue, 25(9–11), pp. 955-962. doi:10.1016/s0142-1123(03)00135-x. [6] chen, x. (2005). foreign object damage on the leading edge of a thin blade, mech mater, 37(4), pp. 447-457. doi: 10.1016/j.mechmat.2004.03.005. [7] susmel, l. (2009). multiaxial notch fatigue: from nominal to local stress-strain quantities, woodhead publishing. [8] shanyavskiy, a. (2011). fatigue cracking simulation based on crack closure effects in al-based sheet materials subjected to biaxial cyclic loads, eng. fract. mech., 78(8), pp. 1516-1528. doi:10.1016/j.engfracmech.2011.01.019. [9] malek, b., mabru, c. and chaussumier, m. (2020). fatigue behavior of 2618-t851 aluminum alloy under uniaxial and multiaxial loadings, int. j. fatigue, 131, 105322. doi:10.1016/j.ijfatigue.2019.105322. [10] itoh, t. and yang, t. (2011). material dependence of multiaxial low cycle fatigue lives under non-proportional loading, int. j. fatigue, 33(8), pp. 1025-1031. doi: 10.1016/j.ijfatigue.2010.12.001. [11] itoh, t., murashima, k. and hirai, t. (2007). material dependence of multiaxial low cycle fatigue properties under nonproportional loading, j. soc. mater. sci. jpn., 56 (2), pp. 157-163. [12] lomakin, e.v., tretyakov, m.p., ilinykh, a.v. and lykova, a.v. (2019). mechanical behavior of x15crni12-2 structural steel under biaxial low-cycle fatigue at normal and elevated temperatures, pnipu mech. bulletin, 1, pp. 7887. doi: 10.15593/perm.mech/2019.1.07. [13] ribeiro, a.s. and de jesus, a.m.p. (2011). fatigue behaviour of welded joints made of 6061-t651 aluminium alloy, aluminium alloys, theory and applications, intechopen, london. doi: 10.5772/14489. [14] li, h., gao, j. and li, q. (2018). fatigue of friction stir welded aluminum alloy, appl. sci., 8(12), 2626. doi: 10.3390/app8122626. [15] zhao, b., xie, l., wang, l., hu, z., zhou, s. and bai, x. (2018) a new multiaxial fatigue life prediction model for aircraft aluminum alloy, int. j. fatigue, 143, 105993. doi: 10.1016/j.ijfatigue.2020.105993. [16] htoo, t., miyashita, a., y., otsuka, y., mutoh, y. and sakurai, s. (2016). variation of local stress ratio and its effect on notch fatigue behavior of 2024-t4 aluminum alloy, int. j. fatigue, 88, pp. 19-28. doi:10.1016/j.ijfatigue.2016.03.001. [17] gillham, b., yankin, a., mcnamara, f., tomonto, c., taylor, d. and lupoi r. (2021). application of the theory of critical distances to predict the effect of induced and process inherent defects for slm ti-6al-4v in high cycle fatigue, cirp ann. manuf. technol., 70(1), pp. 171–174. doi: 10.1016/j.cirp.2021.03.004. [18] han, q., wang, p. and lu. y. (2019). low-cycle multiaxial fatigue behavior and life prediction of q235b steel welded material, int. j. fatigue, 127, pp. 417-430. doi: 10.1016/j.ijfatigue.2019.06.027. [19] rodriguez, r.i., jordon, j.b., allison, p.g., rushing, t. and garcia, l. (2016). low-cycle fatigue of dissimilar friction stir welded aluminum alloys, mater. sci. eng. a, 654, pp. 236-248. doi: 10.1016/j.msea.2015.11.075. [20] yousefi, f., witt, m. and zenner, h. fatigue strength of welded joints under multiaxial loading: experiments and calculations, fatigue fract. eng. mater. struct., 24(5), pp. 339-355. doi: 10.1046/j.1460-2695.2001.00397.x. [21] pei, x., ravi, s.k., dong, p., li, x. and zhou, x. (2022). a multi-axial vibration fatigue evaluation procedure for welded structures in frequency domain, mech. syst. signal process., 167, 108516. doi: 10.1016/j.ymssp.2021.108516. [22] yankin, a.s., wildemann, v.e. and mugatarov, a.i. (2021). a.i. influence of different loading paths on the multiaxial fatigue behavior of 2024 aluminum alloy under the same amplitude values of the second invariant of the stress deviator tensor, frat. ed integrita strutt., 55, pp. 327-335. doi: 10.3221/igf-esis.55.25. a. s. yankin et alii, frattura ed integrità strutturale, 62 (2022) 180-193; doi: 10.3221/igf-esis.62.13 192 [23] zhang, j., shi, x. and fei, b. (2012). high cycle fatigue and fracture mode analysis of 2a12-t4 aluminum alloy under out of-phase axial-torsion constant amplitude loading, int. j. fatigue, 38, pp. 144-154. doi: 10.1016/j.ijfatigue.2011.12.017. [24] wang, q., xin, c., sun, q., xiao, l. and sun, j. (2018). biaxial fatigue behavior of gradient structural purity titanium under in-phase and out-of-phase loading, int. j. fatigue, 116, pp. 602-609. doi: 10.1016/j.ijfatigue.2018.07.015. [25] liu, t., shi, x., zhang, j. and fei, b. (2019). crack initiation and propagation of 30crmnsia steel under uniaxial and multiaxial cyclic loading, int. j. fatigue, 122, pp. 240-255. doi: 10.1016/j.ijfatigue.2019.02.001 [26] wang, y.-y. and yao, w.-x. (2006). a multiaxial fatigue criterion for various metallic materials under proportional and nonproportional loading, int. j. fatigue, 28(4), pp. 401-408. doi: 10.1016/j.ijfatigue.2005.07.007 [27] skibicki, d. and pejkowski, l. (2017). low-cycle multiaxial fatigue behaviour and fatigue life prediction for cuzn37 brass using the stress-strain models, int. j. fatigue, 102, pp. 18-36. doi: 10.1016/j.ijfatigue.2017.04.011. [28] pejkowski, l., skibicki, d. and seyda, j. (2018). stress-strain response and fatigue life of a material subjected to asynchronous loadings, aip conference proceeding, 2028, 020016. doi: 10.1063/1.5066406. [29] gates, n.r. and fatemi, a. (2017). on the consideration of normal and shear stress interaction in multiaxial fatigue damage analysis, int. j. fatigue, 100, pp. 322-336. doi: 10.1016/j.ijfatigue.2017.03.042. [30] wildemann, v.e., tretyakov, m.p., staroverov, o.a. and yankin, a.s. (2018). influence of the biaxial loading regimes on fatigue life of 2024 aluminum alloy and 40crmnmo steel, pnrpu mech. bull., 4, pp. 169-177. doi: 10.15593/perm.mech/2018.4.16. [31] sines, g. (1955). failure of materials under combined repeated stresses with superimposed static stress, washington, national advisory committee for aeronautics (n.a.c.a), 6. [32] mocilnik, v., gubeljak, n. and predan, j. (2017). the influence of a static constant normal stress level on the fatigue resistance of high strength spring steel, theor. appl. fract. mech., 91, pp. 139-147. doi: 10.1016/j.tafmec.2017.06.002. [33] papuga, j. and halama, r. (2018). mean stress effect in multiaxial fatigue limit criteria. arch. appl. mech., pp. 1-12. doi: 10.1007/s00419-018-1421-7. [34] yankin, a., wildemann, v., belonogov and staroverov, o. (2020). influence of static mean stresses on the fatigue behavior of 2024 aluminum alloy under multiaxial loading, frat. ed integrita strutt, 14(51), pp. 151-163. doi: 10.3221/igf-esis.51.12. [35] zhu, h., wu, h., lu, y. and zhong, z. (2019). a novel energy-based equivalent damage parameter for multiaxial fatigue life prediction, int. j. fatigue, 121, pp. 1-8. doi: 10.1016/j.ijfatigue.2018.11.025. [36] carrion, p.e., shamsaei, n., daniewicz, s.r. and moser, r.d. (2017). fatigue behavior of, ti-6al-4v eli including mean stress effects, int. j. fatigue, 99(1), pp. 87-100. doi:10.1016/j.ijfatigue.2017.02.013. [37] kluger, k. (2015). fatigue life estimation for 2017a-t4 and 6082-t6 aluminum alloys subjected to bending-torsion with mean stress, int. j. fatigue, 80, pp. 22-29. doi:10.1016/j.ijfatigue.2015.05.005. [38] tovo, r., lazzarin, p., berto, f., cova, m. and maggiolini, e. (2014). experimental investigation of the multiaxial fatigue strength of ductile cast iron, theor. appl. fract. mech., 73, pp. 60-67. doi: 10.1016/j.tafmec.2014.07.003. [39] pallarés-santasmartas, l., albizuri, j., avilés, a., saintier, n. and merzeau, j. (2018). influence of mean shear stress on the torsional fatigue behaviour of 34crnimo6 steel, int. j. fatigue, 113, pp. 54-68. doi: 10.1016/j.ijfatigue.2018.04.008. [40] karolczuk, a. and macha, e. (2005). a review of critical plane orientations in multiaxial fatigue failure criteria of metallic materials. int j fract, 134(267). doi: 10.1007/s10704-005-1088-2. [41] milella, p. p. (2013). fatigue and corrosion in metals, springer milan heidelberg new york dordrecht london. doi: 10.1007/978-88-470-2336-9 [42] carpinteri, a., spagnoli, a., and vantadori, s. (2017). a review of multiaxial fatigue criteria for random variable amplitude loads, fatigue fract. engng mater. struct, 40(7), pp. 1007-1036. doi: 10.1111/ffe.12619. [43] papuga, j., cízová, e. and karolczuk, a. (2021). validating the methods to process the stress path in multiaxial highcycle fatigue criteria. materials 14(1), 206. doi: 10.3390/ma14010206. [44] sharifimehr, s. and fatemi, a. (2019). interaction between normal and shear stresses and its effect on multiaxial fatigue behavior. matec web of conferences, 300, 16007. doi: 10.1051/matecconf/201930016007. [45] xia, t. and yao, w. (2013). comparative research on the accumulative damage rules under multiaxial block loading spectrum for 2024-t4 aluminum alloy. int. j. fatigue, 48, pp. 257–265. doi: 10.1016/j.ijfatigue.2012.11.004. [46] xia, t., yao, w., ji, y. f. and wang, c. j. (2015). study on the accumulative fatigue damage rules under multiaxial twostage step spectra constructed by loadings with similar lives. fatigue fract. eng. mater. struct, 38(7), pp. 838–850. doi: 10.1111/ffe.12256. a. s. yankin et alii, frattura ed integrità strutturale, 62 (2022) 180-193; doi: 10.3221/igf-esis.62.13 193 [47] xia, t., yao, w. and lu, j-g. (2014). on the shear stress parameter of thin-walled tubular specimens under torsional loading. procedia engineering, 74, pp. 191–198. doi: 10.1016/j.proeng.2014.06.249. [48] xia, t., yao, w., zou, j., and gao, d. (2015). a novel accumulative fatigue damage model for multiaxial step spectrum considering the variations of loading amplitude and loading path. fatigue fract. eng. mater. struct, 39(2), pp. 194– 205. doi: 10.1111/ffe.12349. [49] wang, x-w. and shang, de-g. (2016). determination of the critical plane by a weight-function method based on the maximum shear stress plane under multiaxial high-cycle loading. int. j. fatigue, 90, pp. 36-46. doi: 10.1016/j.ijfatigue.2016.04.010. [50] papuga, j., nesládek, m., hasse, a., cízová, e. and suchý, l. 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can be opened with acrobat and adobe reader 5.0 and later.) >> /namespace [ (adobe) (common) (1.0) ] /othernamespaces [ << /asreaderspreads false /cropimagestoframes true /errorcontrol /warnandcontinue /flattenerignorespreadoverrides false /includeguidesgrids false /includenonprinting false /includeslug false /namespace [ (adobe) (indesign) (4.0) ] /omitplacedbitmaps false /omitplacedeps false /omitplacedpdf false /simulateoverprint /legacy >> << /addbleedmarks false /addcolorbars false /addcropmarks false /addpageinfo false /addregmarks false /convertcolors /converttocmyk /destinationprofilename () /destinationprofileselector /documentcmyk /downsample16bitimages true /flattenerpreset << /presetselector /mediumresolution >> /formelements false /generatestructure false /includebookmarks false /includehyperlinks false /includeinteractive false /includelayers false /includeprofiles false /multimediahandling /useobjectsettings /namespace [ (adobe) (creativesuite) (2.0) ] /pdfxoutputintentprofileselector /documentcmyk /preserveediting true /untaggedcmykhandling /leaveuntagged /untaggedrgbhandling /usedocumentprofile /usedocumentbleed false >> ] >> setdistillerparams << /hwresolution [2400 2400] /pagesize [612.000 792.000] >> setpagedevice microsoft word numero_62_art_39_3729.docx y. u. chapke et alii, frattura ed integrità strutturale, 62 (2022) 573-584; doi: 10.3221/igf-esis.62.39 573 effect of friction-welding parameters on the tensile strength of aa6063 with dissimilar joints yashwant u. chapke, dinesh n. kamble department of mechanical engineering, vishwakarma institute of information technology, savitribai phule pune university, india yashchapke@gmail.com; http://orcid.org/ 0000-0002-6843-7415 dnkamble81@gmail.com; http://orcid.org/ 0000-0002-1312-2619 abstract. in this paper, the effect of welding parameters of rotary friction welding between aa6063 and aisi4130 and aa6063 and copper are investigated. the major influencing parameters considered are upset pressure, friction time and friction pressure of friction welding are considered for this study. the taguchi’s design of experiments was conducted for the influencing parameters and their levels. the tensile test experimentation was carried out and the results of the aa6063 and aisi4130 and aa6063 and copper are compared. the ultimate tensile strength of aa6063-aisi4130 joint and aa6063-copper joint was improved by increasing upset pressure up to 97mpa with fp of 71 mpa and ft of 4 sec. on the side of aa6063, intermetallic compounds have formed, as seen in sem micrographs. microcracks are forming on the side of aa6063 and propagates along the grain boundaries. the effect of the influencing parameters on the tensile strength of the dissimilar joints are studied using the taguchi’s doe and anova. from the outcomes it is observed that the friction pressure influence more on the strength of the aa6063 dissimilar joints. keywords. aa6063; copper; aisi4130; friction welding; taguchi’s doe. citation: chapke, y. u, kamble, d. n., effect of friction-welding parameters on the tensile strength of aa6063 with dissimilar joints, frattura ed integrità strutturale, 62 (2022) 573-584. received: 01.08.2022 accepted: 12.09.2022 online first: 13.09.2022 published: 01.10.2022 copyright: © 2022 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. introduction ne of the most effective method to join the dissimilar metals is rotary friction welding (rfw) which is economic and provides safety to operator and does not emit the ir rays, fume and smoke during the welding [1-2]. the application of rfw, in many industries such as aircraft structures and aero engine components, is required to join dissimilar metals which is inevitable now a days [3-4]. similar to it, linear friction welding (lfw) and inertia friction welding (ifw) were also used to join the dissimilar metals which gain the more interest now a days [5-6]. in welding of aluminium-stainless steel dissimilar metals using inertia friction welding, the intermetallic compound layer generated at the interface of joining which was seen to be increases with the increment in the rotational speed [7]. these innovative welding techniques to join the dissimilar metals plays the important role in the automobile industry where it requires light weight structures with high strength to weight ratio for automobiles. thus, the friction welding method becomes the o https://youtu.be/l37hqamdtoy y. u. chapke et alii, frattura ed integrità strutturale, 62 (2022) 573-584; doi: 10.3221/igf-esis.62.39 574 highly efficient [8] and promising technology to weld the dissimilar metals with narrow heat-affected zone (haz) [9]. in friction welding, among the two dissimilar metal rods, one of them is held in the chuck and rotating and another rod is fixed in the pneumatic holder. th axial load applied by the pneumatic holder generates the frictional heat which necessary to weld both rods together. the friction welding (fw) machine generates the required heat to weld the two dissimilar rods through their surface interaction while rotating. this welding is possible due to the intermolecular diffusion formed between the faces of two dissimilar rods. in the friction welding, the heat generated at the interface is lower than the melting temperature of base metals [10]. thus, the melting of metals will not happen in it. to get the strong joint, the factors like upset pressure (up), friction time (ft) and friction pressure (fp) influence significantly [11]. however, when the friction and upset pressure increases the heat generated and extruded metal heat also increases. in case of fw of aluminum and steel, the probability of generation of thin intermetallic compounds, which were brittle in nature [12-13]. the intermetallics, such as feal and fe2al5, were formed in the process of fw of the aa6061-aisi1018 steel [3]. the increase in friction time during friction welding while joining of aa6063 with ss304 [14], at low pressure, leads to increment in the temperature which softens the weld. thus, the increment in the temperature, due to higher pressure and ft, and cooling rate causes the inducement of residual stress in the welded joints. the addition of the nickel interlayer enhances the tensile strength [15] and addition of silver causes the reduction of magnesium in aluminum and reduces the width of intermetallic layer and enhances the tensile strength [16]. while joining of aa5052 and aa6063 with the friction welding, adrian lis et al. [17] observed that lower friction pressure causes the reduction in the thickness of the soft haz in turn increases the tensile strength of the welded joint. ajith et al. [18] studied the fw of the s32205 duplex stainless steel and concluded the upset and fp were the majorly influencing process parameters. many authors [19-22] used taguchi’s method of optimization and design of experiments (doe) [23] to study the effect of process parameters. literatures shows the dissimilar metals like aluminum-steel, steel-copper alloys, carbon-stainless steel, carbon steelaluminium are welded using the friction welding [24-28]. the joint's tensile strength will be affected by changes in pressure and time because the base metals' have different coefficients of thermal expansion. the objective of present work is to find the influence of the process parameters on the tensile strength of aa6063-aisi4130 and aa6063-cu dissimilar welding joints. in this work, it is intended to use rfw to combine aa6063 with aisi4130 steel and aa6063 with copper specimens. the main purpose of this work is to identify the rfw parameters to weld the dissimilar metals, like, steel and copper with aluminum to reduce the weight of the machine components. some of the applications where rfw of aluminum with steel are axle shafts, driveshafts, gears to shafts, hydraulic cylinder rod end, pipe to pipe segments etc. this study is for determining the influence of fw parameters utilized for welding of dissimilar metals on their tensile strength. the taguchi’s doe and anova has been utilized to analyze the experimental outcomes. the confirmation experiment will also be carried out to validate the experimental results. materials and preparation he materials chosen for this work are aluminum 6063 alloy, aisi4130 low alloy steel and copper in industrial and domestic applications. the chemical composition of aa6063, aisi4130 are listed in tab. 1(a-b). element ti cu fe zn si mg mn cr al composition 0.02 0.029 0.26 0.061 0.50 0.4 0.045 0.01 98.57 table 1(a): chemical composition of aa6063 [29] element c mn pmax smax si cr mo fe composition 0.03 0.60 0.008 0.010 0.23 0.80 0.25 balance table 1(b): chemical composition of the aisi4130 steel [30]. property density tensile strength yield strength elastic modulus elongation composition 8.93g/cm3 210mpa 33mpa 110gpa 60% table 1(c): properties of the copper [31]. aisi4130 steels have enhanced properties like corrosion resistance, ductile, moderate hardness, higher strength and flexibility and able to withstand shock loads. it is having the low carbon content up to 0.03%. its major alloying elements t y. u. chapke et alii, frattura ed integrità strutturale, 62 (2022) 573-584; doi: 10.3221/igf-esis.62.39 575 are cr, mn and mo. aluminum 6063 alloy have silicon, iron and magnesium as major alloying elements. copper is the soft, ductile and malleable metal and its melting point is 1084oc. among many excellent properties of copper, electrical conductivity, thermal conductivity are the properties which makes the copper to be used in electrical parts, due to the high corrosion resistance of copper, it can also be find applications in marine, gas and domestic plumbing industries. some of the material properties of copper are listed in tab. 1(c). methods welding parameters selection etailed study on rotary friction welding shows the possibility of effect of its process parameters on the joint and its strength. parameters influencing tensile strength of rfw joint are up, fp, ft and spindle speed (ss). in this work, the keeping the spindle speed (ss) constant at 1500 rpm, the other parameters such as fp, ft and up are varied which influences majorly on tensile strength of welded joint. with the increase of process parameters, to analyze the data, large number of samples must be experimented. taguchi’s design of experiment (doe) will provide the special design of orthogonal arrays which gives the minimum sets of experiments to analyze the data effectively. taguchi method is a statistical method for improving quality & is based on three loss function viz., larger is better, smaller is better and nominal is better and hitting the target with minimum variation. the taguchi’s doe is carried out using the commercially available statistical tool for the process parameters fp, ft and up with the three levels as mentioned in the tab. 2. the levels considered in this work are based on the literature referred and as per the specification of the rfw machine available. tab. 3 list the design of experiments (doe) carried out using the taguchi’s l9 orthogonal array. process parameter fp, mpa ft, sec up, mpa level 1 48 2 38 level 2 71 4 68 level 3 97 6 97 table 2: levels of process parameters considered. case friction pressure mpa friction time sec upset pressure mpa 1 48 2 38 2 48 4 68 3 48 6 97 4 71 2 68 5 71 4 97 6 71 6 38 7 97 2 97 8 97 4 38 9 97 6 68 table 3: experimental trail run using doe. experimentation fig.1 shows the rfw machine, where workpiece 1 (aa6063) is fixed in chuck and rotating at 1500rpm and the workpiece 2 (aisi4130/cu) is held in pneumatic holder which pushes it in axial direction for certain time (fp). d y. u. chapke et alii, frattura ed integrità strutturale, 62 (2022) 573-584; doi: 10.3221/igf-esis.62.39 576 figure 1: experimental set up (rotary friction welding machine) ft 12. the workpiece (aa6063, aisi4130 and copper) dimensions considered are 25mm diameter and length 100mm. the surfaces of the workpieces are prepared well so that welding surface will be free from imperfections. in this welding, joining of dissimilar metals requires influence of pressure and relative motion of the two workpieces. in comparison with steel and copper, degree of deformation is larger for aluminum. thus, the weld flash on aa6063 is larger (shown in fig.2). due to higher thermal conductivity of aa6063, it is cooled fast then the steel. the fig. 2 shows the welded samples of aa6063-aisi4130 and aa6063-cu using the rfw. figure 2(a): specimens prepared using aa6063 and aisi4130. figure 2(b): specimens prepared using aa6063 and copper. y. u. chapke et alii, frattura ed integrità strutturale, 62 (2022) 573-584; doi: 10.3221/igf-esis.62.39 577 figure 3: aa6063 and copper welded specimen prepared for tensile test. the tensile testing experimentation has been carried out for the specimen of dimensions: 6mm gauge diameter, 50mm gauge length as prescribed by the astm standard in a computerized universal testing machine. the tensile tests have been carried out for aa6063-aisi4130 and aa6063-cu welded specimens. the results of the experiment such as load and displacement are recorded and analyzed to evaluate the tensile strength. the three specimens were tested for each cases and average values have been listed in the tab. 4. the standard deviations are ranging from 0.5 to 2.6. results and discussions optimization he experimental values of the tensile strength of aa6063-aisi4130 and aa6063-cu welded specimens were determined. the comparison of results of both the experimentations were listed in the tab. 4. from comparison, it is seen that aa6063-aisi4130 dissimilar welded joints exhibits the better tensile strength than the aa6063-cu welded joints. case friction pressure mpa friction time sec upset pressure mpa tensile strength, mpa aa6063-aisi4130 aa6063-cu 1 48 2 38 223 154 2 48 4 68 266 196 3 48 6 97 248 183 4 71 2 68 271 200 5 71 4 97 301 222 6 71 6 38 285 201 7 97 2 97 247 182 8 97 4 38 259 181 9 97 6 68 268 198 table 4: tensile strength of aa6063-aisi4130 and aa6063-cu for different welding conditions. in comparison with the aa6063-cu, the tensile strength of the aa6063-aisi4130 steel exhibits the highest tensile strength. the increased strength of aa6063-aisi4130 steel is due to the higher strength of the steel than the copper. for all cases of taguchi’s doe, aa6063-aisi4130 steel provides the highest strength. the obtained results of the experimentations are the input functions for the taguchi’s analysis. commercially available statistical tool is used to analyze the obtained result for aa6063-aisi4130 and aa6063-cu dissimilar welding joints. the quality attributes were determined by transferring the results into the signal to noise(s/n) ratio. the influence of the process parameters like up, fp and ft on the tensile strength of the aa6063-aisi4130 and aa6063-cu dissimilar welding joints are analyzed using the signal to noise ratio. t y. u. chapke et alii, frattura ed integrità strutturale, 62 (2022) 573-584; doi: 10.3221/igf-esis.62.39 578 figure 4(a): main effects plot for sn ratios – aa6063-aisi4130. figure 4(b): main effects plot for sn ratios – aa6063-cu. the factors fp, ft and up are statistically major in the s/n ratio and are also observed that fp significantly influence results of the tensile strength followed by ft and up. fig. 4(a) and 4(b) displays the influence of the factors fp, ft and up on the tensile strength of the said welded joints. 977148 49.2 48.9 48.6 48.3 48.0 642 976838 fp m ea n of s n ra tio s ( te ns ile s tre ng th m pa ) ft up main effects plot for sn ratios (aa6063-aisi41 30) data means signal-to-noise: larger is better 977148 46.4 46.2 46.0 45.8 45.6 45.4 45.2 45.0 642 976838 fp m ea n of s n ra tio s ( te ns ile s tre ng th m pa ) ft up main effects plot for sn ratios (aa6063-cu) data means signal-to-noise: larger is better y. u. chapke et alii, frattura ed integrità strutturale, 62 (2022) 573-584; doi: 10.3221/igf-esis.62.39 579 from fig 4(a) and 4(b) it is seen that as the increment in the process parameters such as ft, fp and up causes increment in the tensile strength initially for the both aa6063-aisi4130 and aa6063-cu welded joints. further increment in fp, ft and up the decrement in the tensile strength has been observed. it is obvious that increment in the pressure deceases the strength of the welded joints. analysis of variance (anova) the experimental results, which inputted into the taguchi’s doe, were analyzed using anova. anova gives the confidence level of each parameter and its percentage contribution on the tensile strength of the welded joints. the confidence level considered here is 95%, thus the significant level is 0.05. the contribution of each parameter on the strength is given in tab. 5. source degrees of freedom sequential sum of squares adjusted mean squares f-value p-value % contribution friction pressure 2 2517.56 1258.78 35.85 0.027 61.1 friction time 2 1272.22 636.11 18.12 0.052 30.9 upset pressure 2 262.89 131.44 3.74 0.211 6.3 error 2 70.22 35.11 1.7 total 8 4122.89 table 5(a): anova for tensile strength of aa6063-aisi4130. from the tab. 5(a) and 5(b) it has been seen that the fp has the significant effect about 61.1% and 50.3%on the tensile strength of aa6063-aisi4130 and aa6063-cu respectively. thus, the fp is the significant factor in the tensile strength of the aa6063-aisi4130 and aa6063-cu joints followed by the ft about 30.9% and 25% whereas the up have least influence (6.3% and 23.2%) on the tensile strength. the pooled error is only 1.7% and 1.5%. as a result of the investigation, it is advised that fp, followed by the ft and up, has the major impact on the tensile strength of the mentioned dissimilar welds. source degrees of freedom sequential sum of squares adjusted mean squares f-value p-value % contribution friction pressure 2 1402.57 701.28 32.86 0.03 50.3 friction time 2 697.71 348.85 16.34 0.058 25.0 upset pressure 2 648.09 324.05 15.18 0.062 23.2 error 2 42.69 21.34 1.5 total 8 2791.05 table 5(b): anova for tensile strength of aa6063-cu. microstructure fig. 4(a) displays the optical microstructure of the aa6063-aisi4130 joint at the r/2 location. on the aa6063 side of the joint, there were primarily two zones: base material (bm) zone and heat-affected zone (haz). between bm and haz, the dynamic recrystallized zone (drz) and thermal mechanically affected zone (tmaz) can be found. the thermalmechanical connection effect caused the interface temperature to rise quickly during friction welding, which encouraged the recovery and dynamic recrystallization of the aluminum alloy close to the interface. the microstructure evolved from fine, equiaxed grains to streamline shapes, leading to the formation of the dynamic recrystallized zone. in a transition zone (tmaz), where most grains were bent, and most partial grains underwent dynamic recrystallization. streamlines also underwent considerable plastic deformation, changing from their original straight to curved shape. because the interface temperature, which was lower than that of fusion welding but still reached the dynamic recrystallization temperature, grains in the haz were smaller than those of the bm in fig. 4(a). the joint also primarily had two zones on the aisi4130 side: the bm and haz. because of broken of partial original grains, by increased up at higher temperature along the interface, the grains in the haz on the aisi4130 side were finer. y. u. chapke et alii, frattura ed integrità strutturale, 62 (2022) 573-584; doi: 10.3221/igf-esis.62.39 580 figure 4(a) optical microstructure at joint interface, bm, haz of aa6063-aisi4130 as shown in fig. 4, the obvious reaction layer between aa6063 and aisi4130 developed with an average thickness of 2.5μm as a result of the shared distribution of alloying materials under the influence of thermo-mechanical coupling. the interface between reaction layer and aisi4130 was smooth, whereas the interface between reaction layer and aa6063 was rough as shown in fig. 4(a), indicating that the reaction layer advance towards the side of aa6063. the microstructure of the reaction layer in the r/2 site under various welding circumstances is shown in fig. 4(b). the thickness of the interfacial intermetallic compounds (imc) initially declined with an upset pressure of 97 mpa, but it subsequently began to stabilize (approaching 2.50μm) as friction pressure increased. figure 4(b) interfacial microstructure of the joint for different up of aa6063-aisi4130. y. u. chapke et alii, frattura ed integrità strutturale, 62 (2022) 573-584; doi: 10.3221/igf-esis.62.39 581 it was evident from the examination of the interfacial microstructure that excessive interfacial imc thickness significantly reduced the uts of aa6063-aisi4130 joint. in order to thoroughly extrude the oxidized metal and dangerous contaminants in the interface, which was advantageous to metallurgical reaction, it was profitable to increase upset pressure. the uts of joints was improved by increasing upset pressure up to 97mpa with friction pressure of 71 mpa and friction time of 4 sec. according to the analysis above, the ideal parameters were fp=71mpa, ft=4sec, and up=97mpa, with a maximum uts of 301 mpa for the aa6063-aisi4130 joint. figure 5(a): optical microstructure at joint interface, bm, haz of aa6063-copper after up of 68mpa, backscattered pictures at the interface show a decline in aa6063-copper joint quality (fig. 5(a)). at the interface center, a flaw in incomplete joining may be detected. cracks developed in aluminum close to the interface at the r/2 and edge positions. microcracks may be seen on the side of aa6063 in the backscattered picture at the edge position (fig. 5(a)). from the fig. 5(a), it can be observed that the propagation of irregular microcracks along the grain boundaries of aa6063 at edge position. the tensile strength of edge samples that underwent up of 97mpa drastically decreased because of the presence of microcracks. figure 5(b) interfacial microstructure of the aa6063-copper joint for different up the interface of the two layers of the aa6063-copper joint for different up is given in fig. 5(b). the dark imc layer near the aa6063 appears to be al2cu, and the other layer's composition is similar to al4cu9. al2cu and al4cu9 layers can't be separated from one another because imc layers are relatively flat and parallel in the centre. the thickness of imc layers grows as the distance from the centre rises, and some minor imc particles disperse in the aa6063 at the r/2 position. after up of 38mpa, the imc layer thickness slightly increases. the uts of aa6063-copper joint was improved by increasing upset pressure up to 97mpa with fp of 71 mpa and ft of 4 sec which gets the maximum uts of 222 mpa. confirmation experiment the final step in design process is the confirmation experiment. the experimental outcomes attained must validate using the statistical analysis. the statistical analysis was determined using the regression equation carried out using minitab tool. the regression model gives the relation between the variable and the response, by fitting the linear equation to the existing data. the regression eqns. 1 and 2 respectively obtained from the analysis of aa6063-aisi4130 and aa6063-cu welded joints. tensile strength of aa6063-aisi4130 = 211.8 + 0.285 fp + 5.00 ft + 0.165 up (1) y. u. chapke et alii, frattura ed integrità strutturale, 62 (2022) 573-584; doi: 10.3221/igf-esis.62.39 582 tensile strength of aa6063-cu = 141.5 + 0.210 fp + 3.77 ft + 0.287 up (2) case aa6063-aisi4130 tensile strength, mpa aa6063-cu tensile strength, mpa experimental statistical % error experimental statistical % error 1 223 243 8.1 154 170 9.3 2 266 258 3.1 196 187 4.8 3 248 273 9.0 183 203 9.8 4 271 253 6.7 200 183 8.4 5 301 268 11.1 222 199 10.3 6 285 268 6.0 201 190 5.8 7 247 263 5.9 182 195 6.6 8 259 263 1.4 181 186 2.5 9 268 278 3.5 198 202 2.2 table 6: comparison of experimental and statistical results according to the results of the anova, fp is the most important factor that affects tensile strength, followed by ft, and up is the least important component. the regression eqns. 1 and 2 shows that an increase in the fp, ft, and up results in an increase in the tensile strength which can be also seen in fig 4. tab. 6 compares the results of the experiment with the statistical conclusions drawn from the regression model. the experimental and statistical tensile strength values were observed to vary by an error percentage ranging from 1.4 to 11.1 percent for welded joints made of aa6063aisi4130, whereas it varies from 2.2 to 10.3 percent for aa6063-cu. as a result, except for case 5, the tensile strength estimated by the experimental and regression models agree with one another, with an error rate of less than 10 percent. hence the validation of experimental and statistical results, agree with each other and are within the permissible error [20]. conclusions he experimental work on rfw of aa6063-aisi4130 and aa6063-cu dissimilar metal welded joints led to the following conclusions.  the rfw of the dissimilar joints such as aa6063-aisi4130 and aa6063-cu was successfully performed using different parameters. the maximum tensile strength obtained for the aa6063-aisi4130 is 26% higher than aa6063-cu welded joints. this is a result of the use of aisi4130, which is stronger than copper and aluminum.  the taguchi’s and anova analysis reveals that the fp influences more on the tensile strength of mentioned welded joints followed by the ft and up.  the sem micrographs reveals the formation of intermetallic compounds on the side of aa6063. the formation of microcracks is on the side of aa6063 which propagates along the grain boundaries at r/2 location. thus, the failure occurs at the aa6063.  the confirmation experiment through the statistical analysis agrees with the experimental results. thus, the experimental results were validated. funding his research received no specific grant from any funding agency in the public, commercial, or not-for-profit sectors. t t y. u. chapke et alii, frattura ed integrità strutturale, 62 (2022) 573-584; doi: 10.3221/igf-esis.62.39 583 conflict of interest he authors declare that they have no conflict of interest. references [1] patil, h. s., patel, d. c. (2022). al2o3 and tio2 flux enabling activated tungsten inert gas welding of 304 austenitic stainless steel plates, frattura ed integrità strutturale, 61, pp. 59-68. doi: 10.3221/igf-esis.61.04. [2] el-oualid, b., chikh, s., abdi, s., miroud, d. (2017) thermal analysis during a rotational friction welding. appl therm eng 110, pp. 1543–1553. doi: 10.1016/j.applthermaleng.2016.09.067. [3] emel, t., gould, j.e., lippold, j.c. (2010) dissimilar friction welding of 6061-t6 aluminium and aisi 1018 steel: properties and microstructural characterisation. mater des 31, pp.2305–2311. doi: 10.1016/j.matdes.2009.12.010 [4] anthony, r.m., colegrove, p.a., buhr, c., flipo, b.c.d., vairis, a. (2018) a literature review of ti-6al-4v linear friction welding. prog mater sci 92, pp. 225–257. doi: 10.1016/j.pmatsci.2017.10.003 [5] baffari, d., buffa, g., campanella, d., fratini, l., micari, f. (2014) friction based solid state welding techniques for transportation industry applications. procedia cirp 18, pp. 162–167. doi: 10.1016/j.procir.2014.06.125 [6] kessler, m., suenger, s., haubold, m., zaeh, m.f. (2016) modelling of upset and torsional moment during inertia friction welding. jmaterprocess technol 227, pp. 34–40. doi: 10.1016/j.jmatprotec.2015.07.024 [7] bounini, t., bouchouicha, b., ghazi, a. (2018). simulation of the behavior of aluminium alloys welded in fsw (case of aa5083, aa6082), frattura ed integrità strutturale, 46, pp. 1-13. doi: 10.3221/igf-esis.46.01. [8] patil, c., patil, h., patil, h. (2016). experimental investigation of hardness of fsw and tig joints of aluminium alloys of aa7075 and aa6061, fattura ed integrità strutturale, 37, pp. 325-332; doi: 10.3221/igf-esis.37.43 [9] hong, m., qin, g., geng, p., fei, l., banglong, f., meng, x. (2015). microstructure characterisation and properties of carbon steel to stainless dissimilar metal joint made by friction welding. mater des 86, pp. 587–597. doi: 10.1016/j.matdes.2015.07.068 [10] szávai, sz., bezi, z., ohms, c. (2016). numerical simulation of dissimilar metal welding and its verification for determination of residual stresses, frattura ed integrità strutturale, 36, pp. 36-45; doi: 10.3221/igf-esis.36.04. [11] nada, r., arsic, d., lazic, v., nikolic, r.r., hadzima, b. (2016). microstructure in the joint friction plane in friction welding of dissimilar steels. procedia eng 149, pp. 414–420. doi: 10.1016/j.proeng.2016.06.686. [12] ochi, h., ogawa, k., yamamoto, y., suga, y. (1998) friction welding of aluminium alloy and steel. int j offshore polar eng 8(2), isope-98-08-2-140. [13] ambroziak, a., korzeniowski, m., kustron, p., winnicki, m., sokolowski, p. and jarapinska, e. (2014). friction welding of aluminium and aluminium alloys with steel”, adv mater sci eng, 2014. doi: 10.1155/2014/981653 [14] kimura, m., suzuki, k., kusaka, m., kaizu, k. (2017). effect of friction welding condition on joining phenomena and mechanical properties of friction welded joint between 6063 aluminium alloy and aisi 304 stainless steel. j manuf process 26, pp. 178–187. doi: 10.1016/j.jmapro.2017.02.008 [15] fukumoto, s., inoue, t., mizuno, s., okita, k., tomita, t., yamamoto, a. (2010). friction welding of tini alloy to stainless steel using ni interlayer. sci technol weld join 15(2), pp. 124–130. doi: 10.1179/136217109x12577814486692 [16] suresh, d., meshram, g., madhusudhan, r. (2015). friction welding of aa60612 to aisi 4340 using silver interlayer”. defence technology 11, pp. 292–298. doi: 10.1016/j.dt.2015.05.007 [17] adrian, l., mogami, h., matsuda, t., sano, t., yoshida, r., hori, h., hirose, a. (2018) hardening and softening effects in aluminium alloys during high-frequency linear friction welding. j mater process tech 255, pp. 547–558. doi: 10.1016/j.jmatprotec.2018.01.002 [18] ajith, p.m., barik, b.k., sathiya, p., aravindan, s. (2015) multi objective optimisation of friction welding of uns s32205 duplex stainless steel. defense technology 11, pp. 157–165. doi: 10.1016/j.dt.2015.03.001 [19] saleemsab, d., yasmin, b., bharath, k. n., rajesh, a. m., kaleemulla, m. k. (2020). optimization of process parameters of fracture toughness using simulation technique considering aluminum-graphite composites, transactions of the indian institute of metals, springer, 73(12) (2020), pp. 3095 – 3103. doi: 10.1007/s12666-020-02113-5. t y. u. chapke et alii, frattura ed integrità strutturale, 62 (2022) 573-584; doi: 10.3221/igf-esis.62.39 584 [20] guddhur, h., naganna, c., doddamani, s. (2021). taguchi’s method of optimization of fracture toughness parameters of al-sicp composite using compact tension specimens. an international journal of optimization and control: theories &amp; applications (ijocta), 11(2), pp. 152–157. doi: 10.11121/ijocta.01.2021.00990. [21] vishalkumar, d., ambad, a. k., saleemsab, d. (2020). optimization of process parameters for fracture toughness of al6061-graphite composites, structural integrity and life, 20(1), pp 51–55. [22] hareesha, g., chikkanna, n., saleemsab, d., anilkumar, s. k. (2021). effect of addition of sic particles on the microstructure and hardness of al-sic composite, metallurgical and materials engineering, 27(1), pp. 49-56. doi: 10.30544/590. [23] chaib, m., slimane, a., slimane, s., ziadi, a., m., bouchouicha, b., (2021). optimization of ultimate tensile strength with doe approach for application fsw process in the aluminum alloys aa6061-t651 & aa7075 -t651, frattura ed integrità strutturale, 57, pp. 169-181. doi: 10.3221/igf-esis.57.14 [24] hong, m., qin, g., geng, p., li, f., meng, x., banglong, f. (2016) effect of post-weld heat treatment on friction welded joint of carbon steel to stainless steel. j mater process technol 227, pp. 24–33. doi: 10.1016/j.jmatprotec.2015.08.004 [25] patil, h. s., soman, s. n. (2013). effect of weld parameter on mechanical and metallurgical properties of dissimilar joints aa6082–aa6061 in t6 condition produced by fsw, frattura ed integrità strutturale, 24, pp. 151-160; doi: 10.3221/igf-esis.24.16. [26] mekri, h., bouchouicha, b., miloudi, a., christophe, h., imad, a. (2018). influence of the coupling between the mechanical characteristics and the welding conditions by the fssw process: case of the bi-material aluminum-steel, frattura ed integrità strutturale, 46, pp. 62-72. doi: 10.3221/igf-esis.46.07 [27] besel, y., besel, m., alfaro mercado, u., kakiuchi, t., uematsu, y. (2016). influence of joint line remnant on crack paths under static and fatigue loadings in friction stir welded al-mg-sc alloy, frattura ed integrità strutturale, 35 , pp. 295-305; doi: 10.3221/igf-esis.35.34 [28] morales, c., merlin, m., fortini, a., garagnani, g.l., miranda, a. (2022). impact behavior of dissimilar aa2024t351/7075-t651 fswed butt-joints: effects of al2o3-sic particles addition, frattura ed integrità strutturale, 60, pp. 505-515. doi: 10.3221/igf-esis.60.34 [29] senthil murugan, s., noorul haq, a., sathiya, p. (2020). effect of welding parameters on the microstructure and mechanical properties of the friction-welded dissimilar joints of aa6063 alloy and faying surface-tapered aisi304l alloy, welding in the world, 64, pp. 483–499. doi: 10.1007/s40194-020-00846-x. [30] souza neto, f., neves, d., silva, o. m. m., lima, m. s. f., abdalla, a.j. (2015). an analysis of the mechanical behavior of aisi 4130 steel after tig and laser welding process, procedia engineering, 114, pp. 181 – 188. doi: 10.1016/j.proeng.2015.08.057. 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can be opened with acrobat and adobe reader 5.0 and later.) >> /namespace [ (adobe) (common) (1.0) ] /othernamespaces [ << /asreaderspreads false /cropimagestoframes true /errorcontrol /warnandcontinue /flattenerignorespreadoverrides false /includeguidesgrids false /includenonprinting false /includeslug false /namespace [ (adobe) (indesign) (4.0) ] /omitplacedbitmaps false /omitplacedeps false /omitplacedpdf false /simulateoverprint /legacy >> << /addbleedmarks false /addcolorbars false /addcropmarks false /addpageinfo false /addregmarks false /convertcolors /converttocmyk /destinationprofilename () /destinationprofileselector /documentcmyk /downsample16bitimages true /flattenerpreset << /presetselector /mediumresolution >> /formelements false /generatestructure false /includebookmarks false /includehyperlinks false /includeinteractive false /includelayers false /includeprofiles false /multimediahandling /useobjectsettings /namespace [ (adobe) (creativesuite) (2.0) ] /pdfxoutputintentprofileselector /documentcmyk /preserveediting true /untaggedcmykhandling /leaveuntagged /untaggedrgbhandling /usedocumentprofile /usedocumentbleed false >> ] >> setdistillerparams << /hwresolution [2400 2400] /pagesize [612.000 792.000] >> setpagedevice microsoft word numero_60_art_13_3385.docx m. b. yasmine, frattura ed integrità strutturale, 60 (2022) 174-186; doi: 10.3221/igf-esis.60.13 174 mechanical behaviour of sandy soils embankments treated with cement and reinforced with discrete elements (fibres) mohamed bouteben yasmine, boudaoud zeineddine faculty of science and applied sciences, department of civil engineering, larbi ben m’hidi university, oum el bouaghi, algeria. medboutebenyasmine@outlook.fr, zboudaoud@yahoo.fr abstract. it is well known that chemical treatment with cement and reinforcement with polypropylene fibres are considered as a solution to soil stability problems. this technique ameliorates the mechanical and physical comportment of the soil. based on this, this research paper aims at investigating the mechanical behaviour of a specific type of dried-cementedsandy soil reinforced with discrete elements such as polypropylene fibre basically through experimental tests. the latter is a series of consolidated drained triaxial tests which were carried out on sand samples that are prepared with 0, 3 and 6% of cement, reinforced with 1% of polypropylene fibre (12, 18 mm) randomly distributed. furthermore, those contents are measured by the volume of dry sand. in addition to these tests, the mechanical properties of two types of reinforced sand obtained experimentally, were used in a numerical analysis of a road embankment using a finite element program such as plaxis 2d in order to observe the variation of different parameters like safety factor and the displacements (ut, ux, uy). the test results showed that the addition of cement and polypropylene fibre of different accommodations increased both cohesion and friction angle of sands while the numerical results indicated that the presence of these additions improved the safety factor and decreased significantly the displacements. keywords. sand; triaxial; polypropylene fibre; cement; cohesion; friction angle. citation: yasmine, m. b., zeineddine, bmechanical behaviour of sandy soils embankments treated with cement and reinforced with discrete elements (fibres), frattura ed integrità strutturale, 60 (2022) 174-186. received: 05.12.2021 accepted: 28.01.2022 online first: 31.01.2022 published: 01.04.2022 copyright: © 2022 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. introduction s a result, of the noticeable demographic expansion and the different infrastructural causes are sometimes inevitable to build on an unsatisfactory geotechnical site. on this basis the improvement of the mechanical characteristics of this site is required. consequently, different techniques can be considered, namely: drainage, densification, cementation, strengthening, drying, and heat treatment. those techniques have been part of soil development for a long time. cement and fibre improvement have become a well-known and widely utilised methodology in geotechnics. fibres improved the soil's physical characteristics and increased its ability to support the charges. cement stabilisation, on the other hand, made the soil more resistant to climate influences. a https://youtu.be/x_022uitmj4 m. b. yasmine, frattura ed integrità strutturale, 60 (2022) 174-186; doi: 10.3221/igf-esis.60.13 175 the act of including cement with various amounts in the reinforced sand displayed that it acts fragile due to the increase in the compression strength [1]. additionally, the researchers discovered that the nature and length of the fibre had an impact on the yield matrix of fibre, cement, sand, and they found that the polypropylene fibres improved their mechanical behaviour and reduced the beach sand dilation [2-4]. hamed et al [5], also tested sand specimens reinforced with glass and polypropylene fibres under varied confining pressures and relative densities in a series of monotonic triaxial tests. the results showed that fibres improved shear strength by increasing confinement and relative density. hence, the features of biocemented sand improved greatly after the addition of fibres and the rise of strength was larger when polypropylene fibres were present. a series of compression tests, tensile tests as well as calcium carbonate content tests were conducted to investigate the impact of different fibres on bio cemented sand. according to the findings the presence of inclusions converted the fragile failure mode to ductile, the non-confined compression resistance, improved and increased as the fibre concentration increased, but it dropped when polypropylene fibre percentage exceeded 0.2% (this drop resulted in the fibre’s low elastic modulus) [6,7]. furthermore, the polypropylene fibre produced more residual resistance throughout the curing process. dry density, permeability, non-confined compressive strength (ucs), tensile strength, and microstructure were measured to see how fibre addition, affected the characteristics of treated sand with calcium carbonate precipitation (micp) created by scanning electron microscopy (sem). the micp-treated sand had a lower permeability, a higher dry density, and a lower confined compression resistance; however, the addition of fibre improved ductility, mode of failure, traction resistance, and dry density. the features of the treated sand were influenced by the length of the fibres as well as the fibre concentration [8]. on the other hand, a numerical modelling is one of the most widely used simulation approaches in civil engineering, notably in geotechnical engineering. it was constructed in order to obtain a comprehensive description of soil behaviour. skuodis et al [9], employed a plaxis 3d model to evaluate the damage produced to the geogrid during triaxial tests performed on reinforced sand samples, this model offered a clear explanation of the major cause of the damage by analysing numerical and experimental results. ver h. abioghli and a. hamidi [10], developed a constitutive model of generalised plasticity to predict the mechanical behaviour of sand reinforced with cement and fibre; as a result, the soil behaviour was well characterised by this model. the main aim of this research paper is to work on sandy soil (from two different regions) reinforced with fibre and cement, using 1% pp fibres (12, 18 mm) randomly distributed and 0, 3 and 6% cement. the first portion depicts the samples' mechanical behaviour in triaxial tests, while the second part is a parametric analysis on a road embankment with and without reinforcing using a finite element program and based on the experimental results. figure 1: grain size distribution curves for the sands experimental he materials used and tested in this study are two dune grains of sand from algeria, skikda (oued zhour and filfila). the sand of oued zhour (s1) had a density estimated at 1.62 g/cm³ with a uniformity coefficient cu and curvature coefficient cc of 1.5 and 0.93 respectively. the sand of filfila (s2) showed 1.65 g/cm³ of density with cu and cc of 1.03 and 1.9 respectively. fig. 1 demonstrates the gradation of these sands while tab. 1 presents their structures. t m. b. yasmine, frattura ed integrità strutturale, 60 (2022) 174-186; doi: 10.3221/igf-esis.60.13 176 physical property value (oued zhour sand) value (filfila sand) particle size such that 50% are smaller, d50 (mm) 0.35 0.38 particle size such that 10% are smaller, d10 (mm) 0.22 0.2 coefficient of uniformity, cu 1.5 1.03 coefficient of curvature, cc 0.93 1.9 density (g/cm3) 1.62 1.65 particle size such that 50% are smaller, d50 (mm) 0.35 0.38 table 1: physical properties of sands. the experiments were started on sand treated, with cement portland type ii (0, 3 and 6%) made by an algerian cement company which contains 2.28% residues, 2.41% insoluble, 57.22% paf 975, 27.83% cao, 3.12% fe3o3, 0.94% mgo, 2.02% so3, and 0.88% cao free. then reinforced with 1% discrete components (12 and 18 mm) randomly distributed which has a circular section, 32 microns thickness, 0.8-1.00 g/cm³ density, 0,91 g/cm³ specific weight, 160° fusion point and two lengths (12, 18 mm). the characteristics of these elements are shown in tab. 2 while the tab. 3 shows the different components and its abbreviation. the experimental work includes the preparation of the samples and the triaxial shears (cd). 42 samples have been consolidated for 15 days under a cell pressure (cp) 50, 100 and 200 kpa. fig. 2 presents the triaxial machine used in this work also fig. 3 shows the specimen before and after shearing. the purpose of this study is investigating the effect of cement and the addition of pp fibre on those sands of the two different regions. physical property fibres material polypropylene virgin colour natural white density 0.8 à 1.00 g/cm³ dimension 6 mm length 12/18 mm section circular thickness 32 microns specific weight 0.91 g/cm³ fusion point 160° table 2. physical properties of the polypropylene fibres used. cc (%) fl (mm) abbreviation 0 0 0%c+0f 3 0 3%c 12 3%c+f12 18 3%c+f18 6 0 6%c 12 6%c+f12 18 6%c+f18 table 3: the proportion of cement and fibre. m. b. yasmine, frattura ed integrità strutturale, 60 (2022) 174-186; doi: 10.3221/igf-esis.60.13 177 figure 2: triaxial machine. a) before shears. b) after shears. figure 3: sand specimen before and after performing the shear test. triaxial test procedure the procedure followed in this test is mixing the cement and fibre contents of the samples calculated from the volume of dry sand by hand (ordinary method) until the distribution of fibres is achieved. each sample is made up of five layers of mixed components, each weighing 125g. then it is encased in a silicone membrane (38 mm diameter and 70 mm long). the layers are compacted slightly, then saturated, consolidated and sheared on triaxial. the test compression program (cd) has the following steps. 1the preparation of the samples. 2applying a negative pressure to make the sample stable. m. b. yasmine, frattura ed integrità strutturale, 60 (2022) 174-186; doi: 10.3221/igf-esis.60.13 178 3injecting water into the specimen through the bottom drainage line to remove the air from the specimen by flushing it out. 4saturating the samples by increasing cell pressure gradually, once the skempton pore pressure parameter exceeds by 95%. (1) : skempton pore pressure parameter. : the resultant change in pore pressure obtained under the undrained isotropic compression condition. : the isotropic cell pressure. 5the consolidation of the samples under cp 50, 100, 200 kpa. when the volume variation reaches constant values, the consolidation is complete. 6under draining circumstances with an axial displacement rate of 1 mm/min, shear loading is given with regard to a constant confining pressure to specimen failure [11-13]. results and discussion of triaxial compression test tab. 4 shows the main characteristics of the tests (deviator stress, confining pressure, and axial strain). while figs. 4, 5 and 6 illustrate the deviator stress as a function of axial strain for sand, cemented sand, and fibre cemented sand samples under various confining pressures (50, 100, 200 kpa). furthermore, fig. 4 shows the variation between deviator stress and axial strain in s1 (continuous line) and s2 (discontinuous line) at a confining pressure of around 50 kpa. figs. 5 and 6 demonstrate the evolution of deviator stress with axial strain for s1 and s2 sheared at effective stress σ’c = 100 and 200 kpa respectively. it appears in figs. 4, 5 and 6 that the deviator stress increases with the increase of axial strain until a maximum value than it drops after the failure. cc (%) fl (mm) cp (kpa) deviator stress (kpa) axial strain (%) s1 s2 s1 s2 0 0 50 0.13 0.12 5.61 6.57 0 0 100 0.31 0.21 4.74 2.8 0 0 200 0.5 0.51 6.51 5.63 3 0 50 2.34 0.21 4.42 4.23 3 0 100 4.19 0.39 6.51 9.11 3 0 200 6.09 0.62 9.06 10.69 3 12 50 0.43 0.42 5.75 6.39 3 12 100 0.8 0.82 6.30 4.09 3 12 200 1 .02 0.96 11.02 12.61 3 18 50 0.7 0.61 12.57 13.67 3 18 100 0.93 0.87 12.27 17.99 3 18 200 1.5 1.38 7.40 11.26 6 0 50 2.92 3.23 5.04 4.64 6 0 100 4.35 4.16 12.97 15.73 6 0 200 6.83 7.28 11.06 12.80 6 12 50 0.77 0.76 7.69 4.37 6 12 100 0.92 0.89 5.54 5.66 6 12 200 1.58 1.52 4.39 4.21 6 18 50 0.81 0.79 1.72 5.18 6 18 100 1.46 1.14 9.91 12.46 6 18 200 1.59 1.6 7.23 13.43 table 4: summary of triaxial tests results. β    3β u / σ is  95 % β u  3σ m. b. yasmine, frattura ed integrità strutturale, 60 (2022) 174-186; doi: 10.3221/igf-esis.60.13 179 figure 4: stress-strain behaviour of s1 and s2 samples with cp=50 kpa. figure 5: stress-strain behaviour of s1 and s2 samples with cp=100 kpa. figure 6: stress-strain behaviour of s1 and s2 samples with cp=200 kpa. m. b. yasmine, frattura ed integrità strutturale, 60 (2022) 174-186; doi: 10.3221/igf-esis.60.13 180 it is clearly seen in tab. 5 and figs. (7, 8) that the inclusion of cement and fibre improve the cohesiveness and friction angle of both of these grains of sand. we can see that the cohesion is increasing gradually from 5.81 to 57.75 and from 6.97 to 59.59 in s1, s2 respectively. as well the friction angle goes from 33.31, 34.81 to 47.70, 46.55 in s1, s2 respectively. several studies have demonstrated that this improvement ameliorated the mechanical characteristics of the soil. furthermore, according to this study [14], one of the most important elements affecting the strength of sandy soil compression was the cement content; while the introduction of the pp fibre into the soil in order to evaluate its behaviour showed that it was a reinforcing ingredient in the soil particle binding [15]. as well the results of other experiments which were done by m.m. benziane et al [16], demonstrated that the inclusion and the increase of pp fibre improved the mechanical properties of the sandy soil. additionally, researchers confirmed that fibres have a significant impact on the mechanical performance of fibrereinforced cement treated sand (ctsf) utilised for road and pavement applications [17]. moreover, the presence of cement simply reduced the deviator stress, according to triaxial testing, as well as the addition of fibre to cemented sand enhances this deviator stress (fig. 4, 5 and 6). the failure is observed with the peak value. after failing, it decreases to a constant value. it has been discovered that ground strength with fibre had exhibited high strength, resulting in an increase in compression resistance and a considerable improvement in sand behaviour. because of its flexible shape and force qualities, the polypropylene fibre provided better ground resistance [18]. juan du et al said that cement soil stabilisation necessitated a high confinement pressure as well as a prolonged hard time. as confinement pressure rose, so did the tension of the deviator [19]. c’ (kpa) ф’ ° cement content (%) fibre length (mm) s1 s2 s1 s2 0 0 5.81 6.97 33.31 34.81 3 0 29.95 20.4 33.44 34.9 3 12 50.23 48.4 41.13 40.81 3 18 50.78 49.76 47.14 46.1 6 0 36.46 35.24 34.38 35.43 6 12 53.31 59.99 47.70 46.55 6 18 57.75 76.18 47.87 46.71 table 5: peak strength parameters for sands and fibre-reinforced cemented sands. figure 7: variation of cohesion in presence of components for s1 and s2. m. b. yasmine, frattura ed integrità strutturale, 60 (2022) 174-186; doi: 10.3221/igf-esis.60.13 181 figure 8: variation of friction angle in presence of components for s1 and s2. moreover, fig. 9 represents the amelioration of deviator stress with the increase of the confining pressure. the test results show that the cement percentage and fibre length increase as the strength increases. these observations are shown in both s1 and s2. in conclusion, the figures clearly confirm that the deviator stress increases as cement content, fibre length and confining pressure. these ameliorations are confirmed by researchers where they improved the soil reinforcement with pp fibre, however the cohesion and shear resistance of sand improved significantly as fibre content and length increased [20]. also in addition to this, the increase in the length of fibre has increased the ground compression indices so fibre have an impact on soil behaviour [21]. figure 9: variation of deviator stress with different confining pressures of s1 and s2. numerical modelling his study investigates the stability of a road embankment using the finite element method of plaxis 2d. this analysis was performed by using the results of the experimental tests. the model present in this study is 80m long and 10m high, the road embankment is 4 m high on top of two layers of foundation clay with varied characteristics, each layer is 3 m high. the studied variable is simulated on half of it because it is symmetrical as the fig. 10 shows. the mohr-coulomb (mc) model was used to analyse the road embankment (with and without reinforcement) in a drained condition, whereas the examination of the foundation clay soil was done in an undrained situation [22]. the mc model is a well-known, widely utilised today and is an initial estimate of soil behaviour in plaxis [23]. the 2d plaxis model was used to simulate the t m. b. yasmine, frattura ed integrità strutturale, 60 (2022) 174-186; doi: 10.3221/igf-esis.60.13 182 investigation of an in-depth tunnel excavation by the mc model. following this examination, the researchers discovered that as the tunnel's depth climbs, the colonies on the soil's surface shrink and approach their true values [24]. on the other hand, the excavation has increased again because of the unloading behaviour (softer or weaker) and the stiffness parameter that minimises deformation. [25]. two different sequences-modelling methodologies were used in this investigation. the stability of an unreinforced road has been investigated for the first time and the stability of the reinforced embankment model was then evaluated using various cement props and fibre lengths. the material parameters of the two sands embankments and the road foundation clays are shown in tab. 6. although figs. 11 and 12 depict the road's deformation before and after strengthening. a road embankment is achieved to calculate the safety factor, to observe displacement changes (total, horizontal and vertical) with and without reinforcing. the following steps have been used in the simulation of the problem: model creation; the input of material parameter and a simple finite element mesh may be generated; consolidation phase to allow the excess pore pressure and analysis the ultimate time required; characteristics computation (safety factor, the displacements). figure 10: geometry model of road embankment. parameter name clay 1 clay 2 embankment unit s1 s2 material model model mc mc mc mc type of drainage type undrained undrained drained drained soil unit weight above phreatic level ϒunsat 16.6 16.6 18 16 kn/m³ soil unit weight below phreatic level ϒsat 17.31 17.31 22 21 kn/m³ young’s ratio eᵣₑ∫ 2000 2000 2200 1500 kn/m² cohesion c’ 33.02 12.01 5.81 6.97 kn/m² friction angle ф’ 1 1 33.31 34.81 ° dilatancy angle ψ 0.0 0.0 3.31 4.81 ° table 6: material properties used in finite element analysis. m. b. yasmine, frattura ed integrità strutturale, 60 (2022) 174-186; doi: 10.3221/igf-esis.60.13 183 figure 11: material deformation mech of the road before reinforcement. figure 12: material deformation mech of the road after reinforcement. results of the numerical modelling and discussion tab. 7 and figs. (13-16) show the results of the numerical modelling. the safety factor increases as cement content and fibre lengthens. it goes from 1.38, 1.5 to 1.68, 1.8 in s1, s2 respectively. sandbox 1 and 2 displacements variations reduce as cement and fibre length increase until they reach a minimal value then they increase significantly. these results were confirmed in previous studies. the stability of a roadway slope was explored using the 2d plaxis to model the light weight of the embankment. the simulation revealed that employing geogrids as a reinforcing material improved the security factor [26], as well a study of a road embankment reinforced by geotextiles showed that the safety factor increased as the geotextile's tensile strength increased, while the displacements dropped [22]. in order to validate the existing model, the findings of the current investigation were compared to the data reported by p.s. wulandari and d. tjandra [22]. based on the test model the road embankment stability was assessed using the finite element approach in plaxis 2d. as a basic preliminary examination of the problem, the mohr-coulomb model was applied. according to the findings, level of the tensile strength of geotextile reinforcement tend to raise the factor of safety while the displacement along the embankment's base is reduced by the increasing geotextile tensile strength [22]. table 7: numeric model results. abbreviation sf ux (cm) uy (cm) ut (cm) s1 s2 s1 s2 s1 s2 s1 s2 0%c+0f 1.38 1.5 3.18 2.69 2.1 2.38 3.33 3.26 3%c 1.64 1.69 2.79 2.70 2.12 2.39 2.99 3.03 3%c+f12 1.67 1.8 2.79 2.68 2.13 2.43 2.98 2.99 3%c+f18 1.68 1.8 2.77 2.70 2.12 2.33 2.96 3.01 6%c 1.66 1.78 2.79 2.69 2.12 2.33 2.98 3.02 6%c+f12 1.68 1.79 2.80 2.67 2.13 2.39 3.04 3.0 6%c+f18 1.68 1.8 2.79 2.68 2.11 2.37 3.01 2.99 m. b. yasmine, frattura ed integrità strutturale, 60 (2022) 174-186; doi: 10.3221/igf-esis.60.13 184 figure 13: safety factor analysis of s1 and s2. figure 14: variation of total displacement of s1 and s2. figure 15: variation of horizontal displacement of s1 and s2. figure 16: variation of vertical displacement of s1 and s2. conclusion fter studying the impact of cement and fibre on the behaviour of two dune sand grains in addition to conducting the parametric study using plaxis 2d which was used to assess the stability of the road embankment. on this basis, the results of this analysis are outlined as follows: the addition of cement and fibre improved the sand's properties. the cohesion and the fraction angle increased exponentially with cement and fibre length. deviator stress, increased exponentially with cement, fibre length, and confining pressure. the increase in safety factor indicates the stability of the road embankment. the cement and fibre enhanced the safety factor until it reached a needed value, whilst the displacements (total, vertical and horizontal) dropped to a minimal value, then rose. when comparing the results, we find that the two studied sands have the same behaviour. 0 2 4 6 0 0,2 0,4 0,6 0,8 1 1,2 1,4 1,6 1,8 2 cc(%) s f 0f 12f 18f 0f 12f 18f s1 s2 0 2 4 6 0 50 100 150 200 250 300 350 cc(%) u t (c m ) 0f 12f 18f 0f 12f 18f s1 s2 0 2 4 6 0 50 100 150 200 250 300 350 cc(%) u x ( cm ) 0f 12f 18f 0f 12f 18f s1 s2 0 2 4 6 0 50 100 150 200 250 300 cc(%) u v (c m ) 0f 12f 18f 0f 12f 18f s1 s2 a m. b. yasmine, frattura ed integrità strutturale, 60 (2022) 174-186; doi: 10.3221/igf-esis.60.13 185 data availability he author did the experimental results and the geotechnical analysis of sandy soil (skikda city) himself, and the produced numerical model, which supports the conclusions in this work, is accessible upon request from the corresponding author. perspectives einforcement is a well-known approach nowadays. the availability of fibre and cement has shown to be a solution in the laboratory for improving soil behaviour. furthermore, the influence of additions on soil, ground characteristics (safety factor, displacements) may be numerically investigated. abbreviations the following abbreviations are used in this paper: cement content (cc). fibre length (fl). oued zour sand (s1) with continuous line. filfila sand (s2) with discontinuous line. polypropylene (pp). consolidated drained (cd). cell pressure (cp). mohr coulomb model (mc). the total displacement (ut). the displacements in direction x, y (ux), (uy). 3% c+f12 means: 3% of cement, 1% of fibre length (12 mm). 3%c means 3% of cement. 0f means 0% fibre. references [1] raja, k., elakkya, e., manikandan, a.t., surya, b., nekila, m. (2021). strength characteristics developed in cement stabilized soil, iop conf. ser. mater. sci. eng., 1055(1), pp. 012039, doi: 10.1088/1757-899x/1055/1/012039. [2] jamsawang, p., suansomjeen, t., sukontasukkul, p., jongpradist, p., bergado, d.t. (2018). comparative flexural performance of compacted cement-fiber-sand, geotext. geomembranes, 46(4), pp. 414–425, doi: 10.1016/j.geotexmem.2018.03.008. [3] lv, x., yang, x., zhou, h., zhang, s. (2019). mechanical behavior of cemented sand reinforced with different polymer fibers, adv. mater. sci. eng., 2019, doi: 10.1155/2019/8649619. [4] kodicherla, s.p.k., muktinuthalapati, j., revanna, n. (2018). effect of randomly distributed fibre reinforcements on engineering properties of beach sand, jordan j. civ. eng., 12(1). [5] javdanian, h., soltani, n., shams, g., ghorbani, s. (2021). investigating the monotonic behavior of fiber-reinforced soil under triaxial compression using experimental modeling, model. earth syst. environ., 7(2), pp. 943–952, doi: 10.1007/s40808-020-00920-9. [6] lv, c., zhu, c., tang, c.-s., cheng, q., yin, l.-y., shi, b. (2021). effect of fiber reinforcement on the mechanical behavior of bio-cemented sand, geosynth. int., 28(2), pp. 195–205, doi: 10.1680/jgein.20.00037. [7] lei, x., lin, s., meng, q., liao, x., xu, j. (2020). influence of different fiber types on properties of biocemented calcareous sand, arab. j. geosci., 13(8), pp. 317, doi: 10.1007/s12517-020-05309-7. [8] fang, x., yang, y., chen, z., liu, h., xiao, y., shen, c. (2020). influence of fiber content and length on engineering properties of micp-treated coral sand, geomicrobiol. j., 37(6), pp. 582–594, doi: 10.1080/01490451.2020.1743392. t r m. b. yasmine, frattura ed integrità strutturale, 60 (2022) 174-186; doi: 10.3221/igf-esis.60.13 186 [9] skuodis, š., dirgėlienė, n., medzvieckas, j. (2020). using triaxial tests to determine the shearing strength of geogridreinforced sand, stud. geotech. mech., 42(4), pp. 341–354, doi: 10.2478/sgem-2020-0005. [10] abioghli, h., hamidi, a. (2019). a constitutive model for evaluation of mechanical behavior of fiber-reinforced cemented sand, j. rock mech. geotech. eng., 11(2), pp. 349–360, doi: 10.1016/j.jrmge.2018.11.003. [11] astm. (2011). method for consolidated drained triaxial compression test for soils, d 7181, annu. b. stand. [12] lade, p. v. (2016). triaxial testing of soils, john wiley & sons, ltd. [13] souadeuk, a., boudaoud, z. (2022). reinforced soft soil by csv with/without polypropylene fibres: experimental and numerical analysis., frat. ed integrità strutt., 16(59), pp. 374–395, doi: 10.3221/igf-esis.59.25. [14] geng, j., chen, m., shang, t., xue, c., chen, h., zhang, c. (2021). the influence of an expansive agent on the performance of cement-stabilized coral sand, adv. civ. eng., 2021, pp. 1–10, doi: 10.1155/2021/8830070. [15] tomar, a., sharma, t., singh, s. (2020). strength properties and durability of clay soil treated with mixture of nano silica and polypropylene fiber, mater. today proc., 26, pp. 3449–3457, doi: 10.1016/j.matpr.2019.12.239. [16] benziane, m.m., della, n., denine, s., sert, s., nouri, s. (2019). effect of randomly distributed polypropylene fiber reinforcement on the shear behavior of sandy soil, stud. geotech. mech., 41(3), pp. 151–159, doi: 10.2478/sgem-2019-0014. [17] chindaprasirt, p., jamsawang, p., sukontasukkul, p., jongpradist, p., likitlersuang, s. (2021). comparative mechanical performances of cement-treated sand reinforced with fiber for road and pavement applications, transp. geotech., 30, pp. 100626, doi: 10.1016/j.trgeo.2021.100626. [18] liu, j., bai, y., song, z., kanungo, d.p., wang, y., bu, f., chen, z., shi, x. (2020). stabilization of sand using different types of short fibers and organic polymer, constr. build. mater., 253, pp. 119164, doi: 10.1016/j.conbuildmat.2020.119164. [19] du, j., zheng, g., liu, b., jiang, n.-j., hu, j. (2021). triaxial behavior of cement-stabilized organic matter–disseminated sand, acta geotech., 16(1), pp. 211–220, doi: 10.1007/s11440-020-00992-y. [20] bao, x., li, l., liao, z., cui, h., tang, w., chen, x. (2021). study of silty sand slope protection from seepage flows using short fiber-sand mixtures, geosynth. int., 28(5), pp. 491–507, doi: 10.1680/jgein.21.00028. [21] al-mahbashi, a.m., al-shamrani, m.a., moghal, a.a.b. (2020). soil–water characteristic curve and one-dimensional deformation characteristics of fiber-reinforced lime-blended expansive soil, j. mater. civ. eng., 32(6), pp. 04020125, doi: 10.1061/(asce)mt.1943-5533.0003204. [22] wulandari, p.s., tjandra, d. (2015). analysis of geotextile reinforced road embankment using plaxis 2d, procedia eng., 125, pp. 358–362, doi: 10.1016/j.proeng.2015.11.075. [23] tran, t.n.d., ahmed, z., nguyen, q.b. (n.d.). application of plaxis for calculating the construction stability and soft embankment in protecting ha thanh river, binh dinh province, 2nd conference on sustainability in civil engineering (csce’20), department of civil engineering capital university of science and technology, islamabad pakistan. [24] çelik, s. (2017). comparison of mohr-coulomb and hardening soil models’ numerical estimation of ground surface settlement caused by tunneling, iğdır univ. j. inst. sci. technol., 7(4), pp. 95–102. [25] gaur, a., sahay, a. (2017). comparison of different soil models for excavation using retaining walls, ssrg int. j. civ. eng., 4(3), pp. 43–48. [26] khan, s.a., abbas, s.m. (2014). numerical modelling of highway embankment by different ground improvement techniques, int. j. innov. res. adv. eng., 1(10), pp. 350–356. << /ascii85encodepages false /allowtransparency false /autopositionepsfiles true /autorotatepages /none /binding /left /calgrayprofile (dot gain 20%) /calrgbprofile (srgb iec61966-2.1) /calcmykprofile (u.s. web coated \050swop\051 v2) /srgbprofile (srgb iec61966-2.1) /cannotembedfontpolicy /error /compatibilitylevel 1.4 /compressobjects /tags /compresspages true /convertimagestoindexed true /passthroughjpegimages true /createjobticket false /defaultrenderingintent /default /detectblends true /detectcurves 0.0000 /colorconversionstrategy /cmyk /dothumbnails false /embedallfonts true /embedopentype false /parseiccprofilesincomments true /embedjoboptions true /dscreportinglevel 0 /emitdscwarnings false /endpage -1 /imagememory 1048576 /lockdistillerparams false /maxsubsetpct 100 /optimize true /opm 1 /parsedsccomments true 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/hrv (za stvaranje adobe pdf dokumenata najpogodnijih za visokokvalitetni ispis prije tiskanja koristite ove postavke. stvoreni pdf dokumenti mogu se otvoriti acrobat i adobe reader 5.0 i kasnijim verzijama.) /hun 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can be opened with acrobat and adobe reader 5.0 and later.) >> /namespace [ (adobe) (common) (1.0) ] /othernamespaces [ << /asreaderspreads false /cropimagestoframes true /errorcontrol /warnandcontinue /flattenerignorespreadoverrides false /includeguidesgrids false /includenonprinting false /includeslug false /namespace [ (adobe) (indesign) (4.0) ] /omitplacedbitmaps false /omitplacedeps false /omitplacedpdf false /simulateoverprint /legacy >> << /addbleedmarks false /addcolorbars false /addcropmarks false /addpageinfo false /addregmarks false /convertcolors /converttocmyk /destinationprofilename () /destinationprofileselector /documentcmyk /downsample16bitimages true /flattenerpreset << /presetselector /mediumresolution >> /formelements false /generatestructure false /includebookmarks false /includehyperlinks false /includeinteractive false /includelayers false /includeprofiles false /multimediahandling /useobjectsettings /namespace [ (adobe) (creativesuite) (2.0) ] /pdfxoutputintentprofileselector /documentcmyk /preserveediting true /untaggedcmykhandling /leaveuntagged /untaggedrgbhandling /usedocumentprofile /usedocumentbleed false >> ] >> setdistillerparams << /hwresolution [2400 2400] /pagesize [612.000 792.000] >> setpagedevice microsoft word numero 23 articolo 11 m.f. pantano et alii, frattura ed integrità strutturale, 23 (2013) 103-113; doi: 10.3221/igf-esis.23.11 103 scilla 2012 the italian research on smart materials and mems a numerical study of squeeze-film damping in mems-based structures including rarefaction effects maria f. pantano, leonardo pagnotta dept. of mechanical engineering, university of calabria, 87036 rende (cs), italy. mf.pantano@unical.it, pagnotta@unical.it salvatore nigro dept. of medical sciences, university of magna graecia, 88100 germaneto (cz), italy. s.nigro@unicz.it abstract. in a variety of mems applications, the thin film of fluid responsible of squeeze-film damping results to be rarefied and, thus, not suitable to be modeled though the classical navier-stokes equation. the simplest way to consider fluid rarefaction is the introduction of a slight modification into its ordinary formulation, by substituting the standard fluid viscosity with an effective viscosity term. in the present paper, some squeeze-film damping problems of both parallel and torsion plates at decreasing pressure are studied by numerical solving a full 3d navier-stokes equation, where the effective viscosity is computed according to proper expressions already included in the literature. furthermore, the same expressions for the effective viscosity are implemented within known analytical models, still derived from the navier-stokes equation. in all the considered cases, the numerical results are shown to be very promising, providing comparable or even better agreement with the experimental data than the corresponding analytical results, even at low air pressure. thus, unlike what is usually agreed in the literature, the effective viscosity approach can be efficiently applied at low pressure regimes, especially when this is combined with a finite element analysis (fea). sommario. in molte applicazioni mems, il sottile strato di fluido responsabile del fenomeno dello squeezefilm damping risulta essere rarefatto e, quindi, non modellabile mediante l’equazione classica di navier-stokes. il modo più semplice per tener conto della rarefattezza del fluido consiste nell’introduzione di una piccola modifica all’interno della sua formulazione ordinaria, ovvero nella sostituzione della viscosità del fluido con una viscosità effettiva. nel presente lavoro, vengono presi in considerazione alcuni problemi di squeeze-film damping, riguardanti casi in cui le piastre coinvolte sono dotate di moto normale traslatorio e casi in cui esse sono dotate, invece, di moto torsionale. tali problemi vengono risolti mediante una modellazione numerica 3d dell’equazione di navier-stokes, in cui la viscosità effettiva viene calcolata mediante apposite espressioni già note in letterature. inoltre, queste stesse espressioni sono utilizzate all’interno di modelli analitici già conosciuti, derivati anch’essi dall’equazione di navier-stokes. in tutti i casi qui considerati, i risultati numerici sono molto promettenti, in quanto essi sono caratterizzati da uno scostamento dai dati sperimentali uguale o inferiore a quello fornito dai corrispettivi risultati analitici, anche a basse pressioni. quindi, nonostante quanto sia usualmente asserito in letteratura, il metodo della viscosità effettiva può essere efficientemente adottato anche a bassi regimi di pressione, specie se in combinazione con analisi numeriche agli elementi finiti (fea). keywords. squeeze-film damping; finite element method; mems; navier-stokes equation; rarefaction. http://www.gruppofrattura.it http://dx.medra.org/10.3221/igf-esis.23.11&auth=true m.f. pantano et alii, frattura ed integrità strutturale, 23 (2013) 103-113; doi: 10.3221/igf-esis.23.11 104 introduction queeze-film damping is the main source of energy dissipation affecting mems devices, like microaccelerometers, microgyroscopes and micromirrors. it is related to the presence of a thin film of fluid, confined between a solid moving surface and a substrate. the reciprocal movement of the two surfaces causes the fluid to be sucked into/pulled out of its tight channel. this generates a pressure field inside the fluid, which is then responsible of a resistive force to hinder the walls’ movement. squeeze-film damping becomes significant when the thickness of the fluid layer is equal or smaller than one third of the width of the confining surfaces [1]. such condition is accomplished in many mems applications, and it is the reason why studies about squeeze-film damping have increased since the 1990s. generally, the fluid flow through its tight channel is modeled through the classical navier-stokes equation, which simplifies in the reynolds equation under some assumptions (e.g., inertial effects, thermal gradients, and fluid out-of-plane movements are negligible). however, the main hypothesis for the navier-stokes/reynolds equation to be valid is the continuity of the fluid body. such approximation applies at high pressure (e.g., atmospheric pressure), but fails at low pressure. since mems-based devices may work in vacuum, it is important to have accurate modeling of squeeze-film damping even in this condition. the parameter conventionally used to evaluate fluid rarefaction is the knudsen number, kn. this is defined as the ratio of the mean free path of the fluid molecules (λ) to the characteristic dimension of the fluid channel (l): nk l   (1) where λ is [2]: 2 2 a r t d n p       (2) where r is the gas constant, t is the temperature, d is the diameter of the fluid molecules, na is the avogadro number, and p is the ambient pressure. for low values of kn (kn<0.01: continuum regime), the navier-stokes equation is valid, whereas for medium (0.01<kn<1: slip regime/transition regime) and high (kn>1: free molecular regime) values of kn, continuum approximation does not apply and other models than the navier-stokes equation should be considered [1]. in spite of the intense efforts already done by the scientific community on modelling fluid rarefaction, there is still need of further improvement and understanding. in the present paper, a numerical approach is adopted to study some squeeze-film damping problems, involving either normal or torsional movement of the moving plate at different pressures, ranging from the atmospheric pressure to almost vacuum. the numerical results are compared to the experimental data, already available in the literature, and to the results obtained by implementation of known analytical models, derived from the navier-stokes equation. modeling of fluid rarefaction n the literature two main approaches can be found for modeling of fluid rarefaction. the first one is based on the introduction of a slight modification in the navier-stokes equation. in particular, the standard fluid viscosity (μ), which compares into its classical formulation, is substituted with a scaled quantity, known as effective viscosity (μeff), defined as: eff prq    (3) where qpr is the flow rate coefficient, computed as a function of the knudsen number. during the years, many expressions for qpr, and consequently for μeff, have been proposed. however, in the present paper, the attention is focused on those, which have been proved to work better [3-4]. thus, three expressions are considered herein, which were proposed in [5], [6], and [4], respectively. s i http://www.gruppofrattura.it http://dx.medra.org/10.3221/igf-esis.23.11&auth=true m.f. pantano et alii, frattura ed integrità strutturale, 23 (2013) 103-113; doi: 10.3221/igf-esis.23.11 105 according to veijola et al. (1995), the effective viscosity (μev) can be computed as [5]: 1.159 1 9.638 ev nk      (4) the effective viscosity (μel) proposed by li (1999) is instead [6]: 1 3 / 6 el ca d bd       (5) where a=0.01807, b=1.35355, and c=-1.17468, and d is the inverse knudsen number, defined as:  / 2 nd k . pandey and pratap (2008) further improved li’s model, in order to achieve better agreement with experiments. thus, they introduced a scaling factor for d equal to 1.4, and proposed their own expression (μep) as [4]: 1 3 / (1.4 ) 6 (1.4 ) ep ca d b d       (6) where a, b, c, and d have the same meaning as before. since its simplicity, the effective viscosity approach could be very powerful. however, none of the above expressions have been proved to work well in all conditions [7]. the second approach for modeling fluid rarefaction is based on the molecular dynamics (md). as opposite to the first approach, in this case attention is paid to collision of the fluid molecules with the walls’ surface, whereas interactions between fluid molecules are neglected. in 1966, christian was the first to adopt the md for computation of the quality factor (qc) related to squeeze-film damping of a plate moving normal to the substrate. the expression he proposed was [8]: 3/ 2 1 2 c r rt q bf m p                (7) where ρ is the density of the solid surface, b the beam thickness, fr the resonance frequency, r the gas constant, t the temperature, m the molar mass of the fluid molecules, and p the ambient pressure. such model was validated through some experiments on miniaturized beams, performed in [9]. because of the resulting poor agreement with the experimental data, this model was further improved by bao et al. [10], who proposed their own expression (qb): 3/ 2 0 1(2 )b d rt q b l m p             (8) where l is the peripheral length of the plate confining the fluid, and d0 is the initial thickness of the fluid layer. with respect to christian’s model, which is derived from momentum transfer between fluid molecules and the solid moving surface, the model proposed by bao et al. is based on energy transfer, and it allows for consideration of the size of the surface confining the fluid and the effects due to the presence of other fluid in the surroundings. such model was further improved by hutcherson and ye [11], who performed md simulations in order to relax some constraints of the previous model, like constant particle velocity and constant beam position. however, all the aforementioned md models were suitable for describing squeeze-film damping in case of rigid structures. only recently, li and fang [12] improved hutcherson and ye’s model for description of even torsion and flexible beams. since the models based on md do not consider interactions between fluid particles, they do not take into account the viscous character of the fluid. thus, they are suitable to describe squeeze-film damping when the fluid is highly rarefied, e.g. the free molecular regime. furthermore, the simplified equations reported herein have been proved to not provide sufficient agreement with experiments [3, 9] and the more recent md based models require the development of proper more or less laborious numerical codes. the first approach, being instead based on the navier-stokes equation, considers only the viscous contribution to squeeze-film damping. thus, it should be effective only in the continuum and transition regimes. however, because of its simplicity it was also adopted in the free molecular regime, providing reasonable errors [3-4], too. the way such approach is usually implemented for computation of squeeze-film damping in terms of damping coefficient (or quality factor) requires the substitution of the standard viscosity with an effective viscosity term in the navier-stokes equation or in compact formulae derived from that. however, such formulae are available only for regular and simple geometries, where the plate confining the fluid has either parallel or torsional movement with respect to the substrate [1]. besides, it was http://www.gruppofrattura.it http://dx.medra.org/10.3221/igf-esis.23.11&auth=true m.f. pantano et alii, frattura ed integrità strutturale, 23 (2013) 103-113; doi: 10.3221/igf-esis.23.11 106 proved by the authors of the present paper that at high pressure solution of the navier-stokes equation by numerical analysis can be more effective than simplified formulae [13]. thus, in the following, the effective viscosity approach will be adopted, coupled with numerical solution of the navier-stokes equation. analytical modeling of squeeze-film damping in rarefied regime he literature provides compact formulae, derived from the solution of the navier-stokes equation, to describe squeeze-film damping in rigid mems structures, moving either normal or torsional with respect to the substrate. when the thin film of fluid is confined between a substrate and a rectangular plate, which moves normal to the substrate, the damping coefficient can be determined as [1]: 3 3 ab lw c h   (9) where l and w are the plate length and width, respectively, h is the thickness of the fluid film, β is a correction factor, depending on the w/l ratio, and μ is the fluid viscosity, which can be substituted with the effective viscosity, computed according to one of expressions (4), (5), and (6). there is an alternative semianalytical formula, which is valid in case of a rigid plate, moving normal to the substrate. this is [14]: 1,3, 1,3, 1 av m n pr mn mn c re q g j c                (10) where ω is the frequency of the plate movement, and qpr, gmn, and cmn are defined as:  2 3 2 1.016 ( / 2)12 1 1.016 ( / 2) pr qh q h tanh qh q j h q qtanh qh            (11)  26 3 2 2 2 2 768 mn h mn m n g ab a b          (12)  24 64 mn h mn c abn p   (13) where h and μ are the same as before; /q j  , ρ is the fluid density, λ is the mean free path, p is the ambient pressure, a and b are the plate sides, and nγ is a coefficient depending on heat conduction and temperature boundary conditions. as opposite to compact formula (9), here it is not possible to isolate an effective viscosity term, which could be changed according to other expressions. in fact, rarefaction terms are embedded within the whole expression. when the plate confining the fluid is provided with torsional movement, the compact formula to be used to determine the damping coefficient is [15]: 5 6 3 2 2 2 2 2 1,3, 0,2, 192 1 [ ] ap m n lw c h m n m n             (14) where h, μ, l, and w are the same as before, and η=w/l. similarly to eq. (9), in order to take into account fluid rarefaction, the fluid viscosity μ can be substituted with the effective viscosity, computed according to (4), (5), or (6). numerical modeling of squeeze-film damping in rarefied regime ince the versatility and computational power of modern computers, a numerical approach for solving squeeze-film damping problems can be a valid alternative to analytical formulae, especially when complex geometries have to be studied. in the present paper, numerical analyses of squeeze-film damping problems were performed by the use of a commercial finite element software, comsol multiphysics, at different pressure regimes, ranging from the atmospheric t s http://www.gruppofrattura.it http://dx.medra.org/10.3221/igf-esis.23.11&auth=true m.f. pantano et alii, frattura ed integrità strutturale, 23 (2013) 103-113; doi: 10.3221/igf-esis.23.11 107 pressure to almost vacuum. the main advantage of such software is its capability to perform multi physics analysis. thus, it is particularly suitable to deal with problems defined in different physical domains, like these, which contemporarily involve structural mechanics and fluid dynamics. the effective viscosity approach was adopted to take into account fluid rarefaction. thus, a full 3d incompressible navier-stokes equation was solved, which included both the air between the moving plate and the substrate, and the air in their surroundings. rarefaction of the air between the moving plate and the substrate, was modeled by computing the effective viscosity through one of expressions (4), (5), or (6). to model rarefaction of the air in the surroundings of the moving plate, the effective viscosity approach cannot be adopted, since it consists of scaling the standard fluid viscosity by a factor depending on the knudsen number. nevertheless, the knudsen number depends on the characteristic length of the channel, where the fluid molecules flow, and such channel is very wide for the air in the working volume, causing the correction factor to be almost one. thus, the viscosity was lowered according to another procedure, based on the following considerations. the mean free path of the fluid molecules is inversely proportional to the ambient pressure at constant temperature (eq. (2)). it is instead proportional to the fluid viscosity, according to the following equation [16]: 2 rt p    (15) where r is the individual gas constant, which is equal to 286.9 jk-1kg-1 for air. in the present numerical analyses, the mean free path could not be increased to effectively simulate fluid rarefaction. thus, the viscosity was reduced according to expressions (2) and (15) at low pressures (when the knudsen number inside the fluid channel is larger than 1, corresponding to the free molecular regime), while keeping the mean free path constant. the software automatically generates a 3d mesh, consisting of tetrahedral elements modeling the moving plate, the fluid under the plate, and the fluid in its surroundings. in particular, the volume of fluid to consider in the analysis was found to not affect the results, if it extends to a region sufficiently far from the plate edge, in order for the fluid flux to develop completely. fig. 1 shows a typical mesh generation and the pressure field under the moving plate. (a) (b) figure 1: mesh of tetrahedral elements (a) and pressure field under one fourth of the moving plate (b). the number of mesh elements ranged from about 5000 to 50000, depending on the particular case, and was decided after a convergence study. in all the analyses reported herein, geometric symmetry was taken into account, in order to reduce the computational work, which was performed by a workstation with the following technical features: ram 16 gb, intel(r) core(tm) i7 cpu 860 @ 2.80 ghz. in these conditions, the time required for one simulation ranged from 15 to 60 minutes. two kinds of squeeze-film damping problems were considered, each involving either a plate moving normal or torsional with respect to the substrate (fig. 2). for the problems where the plate moves normally, the damping coefficient was evaluated as: http://www.gruppofrattura.it http://dx.medra.org/10.3221/igf-esis.23.11&auth=true m.f. pantano et alii, frattura ed integrità strutturale, 23 (2013) 103-113; doi: 10.3221/igf-esis.23.11 108  , nn z p x y dxdy c v    (16) where p(x,y) is the pressure field over the moving plate and vz its velocity. figure 2: reference system for the moving plate. in the second kind of problems, where the plate rotates around the x-axis (fig. 2), the damping coefficient was evaluated as [17]:  , nt p x y ydxdy c     (17) where ω=2πf, being f the frequency of the plate movement. comparison of numerical, analytical, and experimental data in case of parallel suspended plates o evaluate the effectiveness of the numerical analysis, the squeeze-film damping problems reported by sumali [3] are considered herein. he investigated a gold non-perforated plate (fig. 3), moving normal to the substrate, and determined the corresponding damping coefficient at different pressures, ranging from the atmospheric value to few pa. for such geometry, three sets of numerical analyses were performed [18], each implementing one of expressions (4), (5), and (6) for the effective viscosity of the fluid inside the channel. fig. 4a shows a log-log plot reporting a comparison between the numerical results (cn) and the experimental data (ce) at varying pressures. because of its complex profile, analytical expressions (9) and (10) are not suitable for the geometry in fig. 3. thus, these were applied to study an equivalent rectangular plate, with the same area as the original surface, whose size is given in [3]. furthermore, to take into account fluid rarefaction in eq. (9), the standard fluid viscosity was substituted with the effective viscosity, obtaining three sets of data (one for each expression). fig. 4b shows a log-log plot reporting a comparison between the analytical results (ca) and the experimental data (ce), as functions of pressure. figure 3: profile of the geometry experimentally investigated by sumali [3]. t http://www.gruppofrattura.it http://dx.medra.org/10.3221/igf-esis.23.11&auth=true m.f. pantano et alii, frattura ed integrità strutturale, 23 (2013) 103-113; doi: 10.3221/igf-esis.23.11 109 (a) (b) figure 4: comparison of the experimental data reported by sumali [3] with the numerical (a) and the analytical results (b). both the analytical and the numerical approach work well from high to medium pressures (around 103 pa). at low pressure instead, the numerical results show much better agreement with the experimental data (average difference of 23%) than the results obtained with eq. (9) (average difference of 58%). this can be explained since eq. (9) does not take into account border effects, which are instead considered in the numerical simulations. in order to overcome such limitation of the analytical model, a correction factor should be introduced. the only elongation model, providing a correction factor, available in the literature, was verified for kn smaller than 0.13. however, most of the experimental points reported in [3] do not respect such condition. thus, the corresponding correction factor, being not valid, was not included in the graph of fig. 4b (and in the following graphs), even if that would improve the results. eq. (10) shows better agreement with experiments than numerical analysis at low pressure, but it does not provide an expression for the effective viscosity to be easily implemented in numerical simulations. thus, a direct comparison is not possible. comparison of numerical, analytical, and experimental data in case of torsion micromirrors n this section, squeeze-film damping affecting three square torsion micromirrors was considered at varying pressures, ranging from the atmospheric pressure to almost vacuum. such micromirrors were experimentally investigated by minikes et al [17] and pandey and pratap [4], and their geometry and resonance frequency are reported in tab. 1. geometry side length (μm) thickness (μm) gap (μm) resonance frequency (hz) micromirror 1 [17] 500 30 28 13092.56 micromirror 2 [17] 500 30 13 12824.87 micromirror 3 [4] 400 4.25 80 529.2 table 1: geometry and resonance frequency of the torsion micromirrors reported by minikes et al. [17] and pandey and pratap [4]. minikes et al. (2005) provided their experimental results in terms of quality factor (q). this is related to the damping coefficient (c) as: x i q c   (18) being ix the plate inertia moment around the rotation axis x. figs. 5a and 5b shows how the quality factor varies with pressure in both micromirrors. i http://www.gruppofrattura.it http://dx.medra.org/10.3221/igf-esis.23.11&auth=true m.f. pantano et alii, frattura ed integrità strutturale, 23 (2013) 103-113; doi: 10.3221/igf-esis.23.11 110 (a) (b) figure 5: values of the damping coefficient versus pressure of the torsion micromirrors 1 (a) and 2 (b) reported by minikes et al. [17]. at very low pressures (below 20pa), the quality factor becomes almost constant. this occurs since in such conditions squeeze-film damping is no longer the main damping component, but structural damping prevails. thus, in order to correctly evaluate squeeze-film damping at such low pressures, the structural component has to be isolated. this can be done according to the following procedure [3]. a restricted number of experimental points, each corresponding to very low pressures, is considered and interpolated by linear data fitting. the intersection point of the interpolation curve with the y-axis (e.g. quality factor at 0 pa) corresponds to the quality factor associated to the structural damping (fig. 6). the value of the structural quality factor are 15886 and 5366 for the two cases, respectively. (a) (b) figure 6: procedure to determine the quality factor associated to the structural damping for micromirror 1 (a) and 2 (b) reported by minikes et al [17]. for the cases considered herein, the quality factor was determined by both the analytical and numerical approach. in particular, in eq. (14) the standard viscosity was substituted with the effective viscosity, computed by expressions (4), (5), and (6), obtaining three sets of analytical data, respectively. similarly, in the numerical analysis three sets of simulations were performed, each implementing one expression for the effective viscosity. in order to take into account the structural damping, a total quality factor (qtot) was computed as [4]: 1 1 1 tot sq stq q q   (18) http://www.gruppofrattura.it http://dx.medra.org/10.3221/igf-esis.23.11&auth=true m.f. pantano et alii, frattura ed integrità strutturale, 23 (2013) 103-113; doi: 10.3221/igf-esis.23.11 111 where qsq is the quality factor computed according to either the numerical analysis or the analytical formula, and qst is the structural quality factor. fig. 7 reports a log-log plot showing a comparison between the numerical results [20] and the experimental data for the two torsion mirrors, investigated by minikes et al. [17] at varying pressure. similarly, fig. 8 reports a comparison between the analytical results and the experimental data. (a) (b) figure 7: comparison of the numerical results with the experimental data for micromirror 1(a) and 2 (b) reported by minikes et al [17]. from such comparison, it is possible to notice the good agreement with experiments provided by both the numerical analysis and the analytical formula at all pressures. in this case, the difference between the numerical and the analytical results is less significant than in the previous case. in fact, the average difference between the numerical data and the experimental ones is 24%; while the analytical model provides an average difference of 27%. the reason why both the numerical and the analytical modeling offer similar results could be related to the border effects, which in these cases do not play a major role on damping. the final problem considered herein is the torsion micromirror reported by pandey and pratap [4]. in this case, it is not necessary to compute the structural damping, since the authors already provided corrected experimental data, which do not take it into account. similarly to the previous case studies, both the analytical and the numerical approach were applied to determine squeezefilm damping in terms of quality factor. as before, three sets of numerical results and analytical results were obtained and compared to the experimental data in fig. 9a and 9b, respectively. (a) (b) figure 8: comparison of the analytical results with the experimental data for micromirror 1 (a) and 2 (b) reported by minikes et al [17]. http://www.gruppofrattura.it http://dx.medra.org/10.3221/igf-esis.23.11&auth=true m.f. pantano et alii, frattura ed integrità strutturale, 23 (2013) 103-113; doi: 10.3221/igf-esis.23.11 112 (a) (b) figure 9: comparison of the numerical (a) and the analytical results (b) with the experimental data reported by pandey and pratap [4]. in this case, the difference between the analytical and the numerical results is much more significant than before (the average difference between the numerical and the corresponding experimental data is 18%, while it can be even an order of magnitude for the analytical results). this is related to the geometry of the present problem, where the ratio of the fluid gap thickness to the plate width is significantly larger, and accordingly the magnitude of the border effects, which are neglected when applying formula (14). however, also in this case the effectiveness of the numerical analysis emerges, providing results in very good agreement with the experiments. conclusions n the present paper, four different squeeze-film damping problems were considered, at varying pressures, ranging from the atmospheric value to almost vacuum. to analyze such cases, involving both normal and torsion movement of the plate confining a thin film of air, both an analytical and a numerical approach were adopted, both of them based on the navier-stokes equation. in order to model fluid rarefaction, the effective viscosity approach was followed, which consists of substituting the standard fluid viscosity, contained in the equation, with a scaled term, known as effective viscosity. the literature provides many expressions for computing the effective viscosity, and the three expressions, which were proved to work better, were considered within the paper. then, each of the four considered problems was solved by both the numerical and analytical methods, implementing each time one of those expressions, obtaining four sets of numerical results and four sets of analytical data. in all the considered cases, the numerical results were very promising even at very low pressure, with values of the squeeze-film damping coefficient/quality that were comparable (and even closer than the analytical results) to the experimental data. thus, unlike what is usually agreed in the literature, the effective viscosity model, especially when combined with fem analysis, results to be effective in a wide range of pressures, including very low values. in addition, thanks to the computational power of modern computers and the versatility of fem analysis, the procedure described herein can be implemented in a variety of applications, extending to complex and more realistic structures, as opposite to analytical approaches. in this work, the effective viscosity was computed according to already known expressions. however, a future work can be focused on derivation of a new expression to be implemented in the numerical analysis, in order to get results even closer to the experimental data. references [1] m. bao, h. yang, sens. actuators a, 136 (2007) 3. [2] l. mol, l. a. rocha, e. cretu, r. f. woffenbuttel, j. micromech. microeng., 19 (2009) 074021. [3] h. sumali, j. micromech. microeng., 17 (2007) 2231. i http://www.gruppofrattura.it http://dx.medra.org/10.3221/igf-esis.23.11&auth=true m.f. pantano et alii, frattura ed integrità strutturale, 23 (2013) 103-113; doi: 10.3221/igf-esis.23.11 113 [4] a. k. pandey, r. pratap, j. micromech. microeng., 18 (2008) 105003. [5] t. veijola, h. kuisma, j. lahdenpera, t. ryhanen, sens. actuators a, 48 (1995) 239. [6] w. l. li, nanotechnology, 10 (1999) 440. [7] c. w. leung, t. thurber, w. ye, microfluid. nanofluid, (2011) doi: 10.1007/s10404-011-0840-3. [8] r. christian, vacuum, 16 (1966) 175. [9] j. d. zook, d. w burns., sens. actuators, a 35 (1992) 51. [10] m. bao, h. yang, h. yin, y. sun, j. micromech. microeng., 12 (2002) 341. [11] s. hutcherson, w. ye, j. micromech. microeng., 14 (2004) 1726. [12] p. li, y. fang, j. micromech. microeng., 20 (2010) 035005. [13] s. nigro, l. pagnotta, m. f. pantano, microfluid. nanofluid, 12 (6) (2012) 971. [14] t. veijola, a. pursula, p. raback, j. micromech. microeng., 15 (2005) 1624. [15] f. pan, j. kubby, e. peeters, a. t. tran, s. mukherjee, j. micromech. microeng., 8 (1998) 200. [16] j. w. lee, r. tung, a. raman, h. sumali, j. p. sullivan, j. micromech. microeng., 19 (2009) 105. [17] a. minikes, i. bucher, g. avivi, j. micromech. microeng., 15 (2005) 1762. [18] s. nigro, l. pagnotta, m. f. pantano, in: 11th wseas international conference, rovaniemi, finland, april 18-20, (2012) 37. [19] t. veijola, j. micromech. microeng., 14 (2004) 1109. [20] s. nigro, l. pagnotta, m. f. pantano, in: technical proceedings of the 2012 nsti nanotechnology conference and expo, nsti-nanotech, (2012) 333. http://www.gruppofrattura.it http://dx.medra.org/10.3221/igf-esis.23.11&auth=true microsoft word numero_46_art_15 z. lu et alii, frattura ed integrità strutturale, 46 (2018) 150-157; doi: 10.3221/igf-esis.46.15 150 developments in the fracture and fatigue assessment of materials and structures fatigue behaviour and mean stress effect of thermoplastic polymers and composites zongjin lu, bill feng, charlie loh jaguar land rover limited, uk zlu5@jaguarlandrover.com, bfeng1@jaguarlandrover.com, cloh1@jaguar.com abstract. more and more polymers and polymer composite materials are used in automotive industry to reduce cost and weight of vehicles to meet the environmental requirement. however, the fatigue behaviour for these materials is less understanding than metallic materials. the current work is focussed on the fatigue behaviour for a range of thermoplastic polymer/composite materials. it reveals that the fatigue behaviour of these materials can be described by s-n curves using the basquin equation. all the materials exhibit significant mean stress effect. the most commonly used mean stress correction equations developed in metal fatigue were evaluated with the current test results. it reveals that goodman, gerber and soderberg cannot be used as generic equations for the materials investigated, whereas smith-watson-topper can correlate the test data reasonably well, but the best correlation is given by walker with material constant γ = 0.4. keywords. fatigue; mean stress effect; polymers; polymer composites. citation: lu, z., feng, b., loh, c., fatigue behaviour and mean stress effect of thermoplastic polymers and composites, frattura ed integrità strutturale, 46 (2018) 150-157. received: 25.01.2018 accepted: 22.04.2018 published: 01.10.2018 copyright: © 2018 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. introduction ore and more thermoplastic polymers and polymer composite materials are used in automotive industry to reduce cost and weight of vehicles to meet the environmental requirement. however, the fatigue behaviour for the polymers and polymer composite materials is less understood than metallic materials, especially the effect of mean stress. it is well known that fatigue life of metals is influenced by mean stress significantly [1]. various equations have been established to account for the mean stress effect. among these, goodman [2], gerber [3], soderberg [4], smithwatson-topper (swt) [5] and walker [6] are the most commonly used. they are listed below: goodman 1a m ao u s s s s   (1) gerber 2 1a m ao u s s s s        (2) m http://www.gruppofrattura.it/va/46/15.mp4 z. lu et alii, frattura ed integrità strutturale, 46 (2018) 150-157; doi: 10.3221/igf-esis.46.15 151 soderberg 1a m ao y s s s s   (3) swt ( )ao a a ms s s s  (4) walker  1ao a m as s s s    (5) where sa is the stress amplitude, sm is the mean stress, sao is the equivalent stress amplitude at zero mean stress, su is the materials ultimate strength, sy is the materials yield strength and γ is a material constant. swt equation is a special case of walker equation where γ = 0.5. mean stress was also reported to have a significant effect on fatigue behaviour of polymers [7-10] and short fibre reinforced polymer composites [10-14]. the evaluation of the mean stress correction equations were carried out by a range of researchers [7, 9-13]. different results were reported. zhou et al. [11] reported a good correlation using swt on short fibre reinforced blend of polyphenylene ether ketone and polyphenylene sulphide. mallick and zhou [12] suggested using a modified gerber equation to correlate a short glass fibre reinforced polyamide 6.6. using modified goodman, oke et al. [13] estimated the mean stress effect of short fibre reinforced polybutylene terephthalate at stress ratio above 0.7. more recently, mollett and fatemi [9], mortazavian and fatemi [10] recommended walker for mean stress correction after the investigation on polypropylene copolymer, polypropylene-elastomer blend, short glass fibre reinforced polybutylene terephthalate and polyamide 6. in order to examine the mean stress effect, seven materials, four thermoplastic polymers and three short glass fibre reinforced polymer composites, were tested under constant load amplitude at a range of stress ratios under room temperature with various mean stress correction equations listed above evaluated. materials and specimens even different materials, including four non-fibre reinforced thermoplastic polymers and three short glass fibre reinforced polymer composites, were tested. they are polycarbonate and acrylonitrile butadiene styrene (pc/abs), acrylonitrile butadiene styrene (abs), polypropylene (pp), nylon and acrylonitrile styrene acrylate (pa/asa), 30%wt glass fibre reinforced polypropylene (pp30), 20%wt glass fibre reinforced polypropylene (pp20) and 30% glass fibre reinforced nylon (pa6). the details are summarised in tab. 1. the specimens were machined from plaques made of injection moulding along the flow direction. the specimen geometry was displayed in fig. 1. figure 1: specimen geometry. experimental procedures he test was carried out on a 10kn instron servo hydraulic test machine under constant load amplitude and 5 hz at room temperature with a range of stress ratios from r=-1 to r=0.3. the fatigue life was defined as the final failure of the specimens with 2 million cycles as run out. s t z. lu et alii, frattura ed integrità strutturale, 46 (2018) 150-157; doi: 10.3221/igf-esis.46.15 152 materials su (mpa) sy (mpa) el (%) pc/abs (polycarbonate and acrylonitrile butadiene styrene) 50 50 29.3 abs (acrylonitrile butadiene styrene) 51 51 8.3 pp (polypropylene) 19 19 64.5 pa/asa (nylon and acrylonitrile styrene acrylate) 39 39 67.3 pp30 (30% glass fibre reinforced polypropylene) 60 41 6.9 pp20 (20% glass fibre reinforced polypropylene) 64 41 3.2 pa6 (30% glass fibre reinforced nylon) 98 64 6.9 table 1: materials details. results and discussions he test results are displayed in figs. 2 to 6 for the range of materials. it is evident that mean stress does have a significant influence on the fatigue life and the fatigue behaviour can be described by the basquin equation (eqn.6) [14] for all the materials within the investigated life regime  ba fs a n (6) where sa is the stress amplitude, nf is the cycles at failure, a is the intercept at nf =1 and b is the slope of the fitted curve. figure 2: fatigue behaviour of pc/abs (similar behaviour was observed for abs). based on the test data, mean stress equations (eqns. 1 to 5) were evaluated by calculating the equivalent stress amplitude sao. for a good correlation, the s-n data measured at non-zero mean stress should merge to the s-n data at r=-1 (zero mean stress). the evaluation of the mean stress correction equations is displayed in figs. 7 to 12 with figs. 7 to 9 for polymers and figs. 10 to 12 for short glass fibre reinforced polymer composites. fig. 7 reveals that goodman (eq.1), gerber (eq.2) and soderberg (eq.3) failed to correlate the pc/abs test result, whereas swt (eq.4) gives a reasonable correlation but the best correlation is given by walker (eq.5) with material constant γ = 0.4. a similar result is found for abs material. for pp (fig. 8) and pa/asa (fig. 9) materials, all equations except gerber (eq.2), display good correlation with the best from walker at γ = 0.4 (eq.5). t z. lu et alii, frattura ed integrità strutturale, 46 (2018) 150-157; doi: 10.3221/igf-esis.46.15 153 figure 3: fatigue behaviour of pp. figure 4: fatigue behaviour of pa/asa. figure 5: fatigue behaviour of pp30 (similar behaviour was observed for pp20). z. lu et alii, frattura ed integrità strutturale, 46 (2018) 150-157; doi: 10.3221/igf-esis.46.15 154 figure 6: fatigue behaviour of pa6. figure 7: mean stress correction assessment for pc/abs. figure 8: mean stress correction assessment for pp. z. lu et alii, frattura ed integrità strutturale, 46 (2018) 150-157; doi: 10.3221/igf-esis.46.15 155 figure 9: mean stress correction assessment for pa/asa. figure 10: mean stress correction assessment for pp30. figure 11: mean stress correction assessment for pp20. z. lu et alii, frattura ed integrità strutturale, 46 (2018) 150-157; doi: 10.3221/igf-esis.46.15 156 figure 12: mean stress correction assessment for pa6. for short glass fibre reinforced polymer composites (figs. 10 to 12), goodman (eq.1), swt (eq.4) and walker (eq.5) with material constant γ = 0.4 all show reasonable correlation, but gerber (eq.2) and soderberg (eq.3) failed to correlate the test results. according to the above results, it is recommended that walker’s equation (eqn. 5) should be used as a generic mean stress correction equation for both thermoplastic polymers and short fibre reinforced polymer composites. similar evaluation results were reported by mellott and fatemi [9] for polypropylene and polypropylene-elastomer polymer materials, mortazavian and fatemi [10] for 30% short glass fibre reinforced polybutylene terephthalate and 35% short glass fibre reinforced polyamide-6 polymer composites at a range of temperatures and different fibre orientations. however, different γ values were found to fit the test data for walker’s equation. conclusions onstant stress amplitude fatigue tests were carried out on a range of thermoplastic polymers and short glass fibre reinforced polymer composites at room temperature. the following conclusions may be drawn: the fatigue behaviour of the materials tested can be described by the basquin equation. significant mean stress effect was found for all materials investigated. several mean stress correction equations were evaluated including goodman, gerber, soderberg, smith-watson-topper and walker. goodman, gerber and soderberg cannot be used as generic equations for the materials. smith-watson-topper can correlated the test data reasonably well, but the best correlation was given by walker with material constant γ = 0.4. acknowledgements he authors would like to express their appreciation to jaguar land rover limited for permission to publish this work. thanks are due also to andrew haggie, senior manager department of materials engineering, stuart tyler, manager metallurgy technical services and dave coleman, senior manager – body cae and integration for their support of this work. references [1] stephens, r.i. (2001). metal fatigue in engineering, second ed., john wiley, new york,. [2] goodman, j. (1919). mechanics applied to engineering, 1st ed. longmans green and company, london, england. [3] gerber, w. (1874). bestimmung der zulossigen spannungen in eisen constructionen, z. bayer. architekten u. ing., pp. 101-110. c t z. lu et alii, frattura ed integrità strutturale, 46 (2018) 150-157; doi: 10.3221/igf-esis.46.15 157 [4] soderberg, c.r. (1930). factor of safety and working stress, asme transactions, apm-52-2, pp. 13-28. [5] smith, k.n., watson, p. and topper, t. h. (1970). a stress-strain function for the fatigue of metals, j. materials, astm, pp. 767-778. [6] walker, k. (1970). effects of environment and complex load history on fatigue life, astm stp 462, am. soc. for testing and materials, west conshohocken, pa, pp. 1-14. [7] sauer, j.a., mcmaster, a. d. and morrow, d. r. (1976). fatigue behavior of polystyrene and effect of mean stress, j. macromolecular science, pp. 535-562. [8] sauer, j.a. and richardson, g.c., (1980). fatigue of polymers, int. j. fracture, pp. 499-532. [9] mellott, s.r. and fatemi, a. (2014). fatigue behavior and modeling of thermoplastics including temperature and mean stress effects, polym. eng. sci., pp. 725–738. [10] mortazavian, s. and fatemi, a. (2016). effects of mean stress and stress concentration on fatigue behavior of short fiber reinforced polymer composites, fat & frac eng mat & structures, pp. 149–166. [11] zhou, j., d’amore, a., yag, y., he, t., li, b. and nicolais, l. (1994). flexural fatigue of short glass fiber reinforced a blend of polyphenylene ether ketone and polyphenylene sulphide, appl. compos. materials, pp. 183-195. [12] mallick, p.k. and zhou, y. (2004). effect of mean stress on the stress-controlled fatigue of a short e-glass fiber reinforced polyamide-66, int. j. fatigue, pp. 941–946. << /ascii85encodepages false /allowtransparency false /autopositionepsfiles true /autorotatepages /none /binding /left /calgrayprofile (dot gain 20%) /calrgbprofile (srgb iec61966-2.1) /calcmykprofile (u.s. web coated \050swop\051 v2) /srgbprofile (srgb iec61966-2.1) /cannotembedfontpolicy /error /compatibilitylevel 1.4 /compressobjects /tags /compresspages true /convertimagestoindexed true /passthroughjpegimages true /createjobticket false /defaultrenderingintent /default /detectblends true /detectcurves 0.0000 /colorconversionstrategy /cmyk /dothumbnails false /embedallfonts true /embedopentype false /parseiccprofilesincomments true /embedjoboptions true /dscreportinglevel 0 /emitdscwarnings false /endpage -1 /imagememory 1048576 /lockdistillerparams false /maxsubsetpct 100 /optimize true /opm 1 /parsedsccomments true 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/pdfxoutputintentprofileselector /documentcmyk /preserveediting true /untaggedcmykhandling /leaveuntagged /untaggedrgbhandling /usedocumentprofile /usedocumentbleed false >> ] >> setdistillerparams << /hwresolution [2400 2400] /pagesize [612.000 792.000] >> setpagedevice microsoft word numero_43_art_19 a. luciani et alii, frattura ed integrità strutturale, 43 (2018) 241-250; doi: 10.3221/igf-esis.43.19 241 maintenance and risk management of rockfall protection net fences through numerical study of damage influence andrea luciani, carmine todaro, daniele peila politecnico di torino, torino, italy andrea.luciani@polito.it, carmine.todaro@polito.it, daniele.peila@polito.it abstract. rockfall protection net fences are key protection systems in mountainous areas worldwide to ensure the safety of infrastructures, roads and urban areas. maintenance of these products is fundamental for public administrations in order to guarantee risk mitigation. this paper deals with the assessment of the installation problems and damages induced by ageing of rockfall protection net fences, using numerical modelling in order to evaluate the influence of these issues on their behavior. a percentage of the residual efficiency is assessed as a useful tool for risk analysis and maintenance planning. keywords. rockfall protection net fence; rockfall; explicit numerical modelling; residual risk; maintenance. citation: luciani, a., todaro, c., peila, d., maintenance and risk management of rockfall protection net fences through numerical study of damage influence, frattura ed integrità strutturale, 43 (2018) 241-250. received: 23.10.2017 accepted: 15.12.2017 published: 01.01.2018 copyright: © 2018 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. introduction rotection net fences play an essential role to reduce rockfall risk of infrastructure, roads and residential areas against rockfall within acceptable values. since their installation requires important investments for public administrations, procedures have been developed to quantitatively evaluate risk reduction obtained with these devices and to allow a comparison with other technical solutions for an optimal choice [1-5]. moreover, the presence of already installed protection devices on the slope has to be considered in the risk assessment and their efficacy in time has to be correctly evaluated, in order to do not overestimate or underestimate their effect [6-8]. therefore, it is very important for these evaluations to take into account maintenance issues with the aim of evaluating how time and ageing influence efficiency of net fences since public administrations are interested in assessing how long a certain investment ensures the needed risk mitigation. this evaluation allows them to schedule an appropriate maintenance management, taking into account available resources. despite the highlighted relevance of the influence of damages induced by ageing and installation problems on the behavior and efficiency of rockfall protection net fences, there is a lack of data in technical literature on this topic. moreover, there is currently no predictive method that could be used to estimate the performance of damaged rockfall protection fences and there is great difference in the technical recommendations for the maintenance provided by producers. p a. luciani et alii, frattura ed integrità strutturale, 43 (2018) 241-250; doi: 10.3221/igf-esis.43.19 242 the behavior and effectiveness of rockfall protection net fences was tackled both by full scale tests [9-13], especially after the development in europe of the etag 027 standards [14-16], by pseudo-static analyses [17] and by numerical modelling [18-28] but a complete analysis of aged rockfall net fences has not been performed. for this reasons, in this paper the influence of damages and installation problems on the efficiency of rockfall protection net fences has been studied by using numerical modelling. the assessment of the possible damages and installation problems has been performed based on an analysis of data obtained during a site survey in the alps reported by dimasi et al. [29]. the numerical simulation was therefore developed with the simulation of a standard impact, according to etag027, with different conditions able to simulate different degree of ageing or damages on the various elements of the structure. these models allow to determinate the possible reduction of efficiency and to compare the behavior of the deteriorated and not deteriorated rockfall protection net fences. the simulation is performed with a fem model of a rockfall protection net fence of nominal energy of 3000 kj. the model is assessed using the results of experiments on full-scale prototypes whose data were obtained from gottardi and govoni [11]. numerical model of the net fence he numerical model was developed using the software abaqus/explicit 6.13. this software has an explicit finite element formulation allowing to simulate non-linear dynamic events such as the impact of a block on a net fence. the studied net fence is a commercial product with a maximum energy level (mel) of 3000 kj and the full scale data reported by gottardi and govoni [11] were used for back analysis. the support structure of this net fence has four hea200 steel posts, 5 m high, restrained at the base by cylindrical hinges allowing rotation in the upstream-downstream direction. the interception structure is made of a principal steel ring net; each 350 mm ring is connected to six nearest rings. the connection structure comprises two longitudinal upper cables and two longitudinal lower cables, eight upstream cables and four lateral cables. each cable has a diameter of 20 mm. the longitudinal cables are free to slide on the posts in the longitudinal direction. the net fence is provided with tubular energy dissipating devices, one on each upstream cable and three on each longitudinal cable. fig. 1 shows a photo of the net fence. figure 1: photo of the studied rockfall protection net fence. in the numerical simulation, the support structure was modelled with 3d-2node beam elements, with a hea200 cross section. these elements had linear elastic behavior with young’s modulus of 210 gpa while the cables, the energy dissipating devices and the net were modelled with 3d-2node truss elements that cannot withstand flexural stresses. the material assigned to the cables had elasto-plastic behavior with young’s modulus of 150 gpa in the elastic part of the curve and of 5 gpa in the plastic one. the yield strain was set at 0.001 and the ultimate strain at 0.006, which corresponds to an ultimate stress of 1770 mpa. t a. luciani et alii, frattura ed integrità strutturale, 43 (2018) 241-250; doi: 10.3221/igf-esis.43.19 243 the behavior of the cable connected to the energy dissipating device is complex due to the behavior of the energy dissipating device. the cable withstands the force until the activation force of the dissipating device is reached (at about 45 kn in the studied case), then the deformation of the material composing the device starts, and the constitutive relationship is governed by this phenomenon. once the maximum displacement of the energy dissipating device is reached, the system follows again the cable behavior. to simulate this behavior a tri-linear law was assigned to the material of energy dissipating devices. the first part had young’s modulus of 63 gpa, the second one had young’s modulus of 1.4 gpa and the last part had same behavior of the cables, with young’s modulus of 150 gpa and ultimate stress of 1770 mpa. also the numerical simulation of the ring net behavior is complex, due to the high number of interactions between the rings that slide and deform during the impact. therefore, following nicot et al. [18], the net was modelled with an equivalent hexagonal net, with hexagon sides of 350 mm. each vertex of the hexagon is the center of one of the six rings connected to the central ring. the interaction between two rings is modelled by the truss elements connecting the vertices. the material assigned to the elements composing the equivalent net had tri-linear behavior, described by three different young’s moduli. the young’s modulus of the first part was of 170 gpa, till a strain of 0.001 is reached. the young’s modulus of the second part was of 4gpa, until a strain of 0.25, and the young’s modulus of the final part was of 170 gpa. this constitutive behavior was assessed numerically simulating the real scale tests reported by gentilini et al. [24]. the block impacting the net was simulated as a polyhedral non-deformable element, with the same geometry of that foreseen etag 027 standards and the impact speed was of 25 m/s. in the numerical model, the posts were restrained at the base by a cylindrical hinge allowing rotation on the longitudinal axis while spherical hinges simulated anchorages of the cables to the ground and to the top of the posts. the longitudinal cables were free to slide on the top and on the basis of the posts in the longitudinal direction but were constrained in the other directions. in the model, the net was not allowed to slide on the longitudinal cables, differently to what happen in the real net fence. this simplification was necessary in order to reduce computational complexity of the simulation. fig. 2 illustrates the general sketch of the model. figure 2: drawing of the modelled rockfall protection net fence. mel test sel test real scale test numerical model real scale test numerical model breaking time (s) 0.30 0.32 0.26 0.22 maximum elongation (m) 5.35 5.38 3.90 3.73 final elongation (m) 4.80 5.05 3.20 3.35 residual height (m) 3.55 3.34 3.95 3.71 table 1: comparison between the real scale test and the results of the numerical simulation. in the simulation the energy level foreseen by etag027 standard mel and sel tests were performed and the results of the simulations were compared to the data obtained by real scale tests reported by gottardi and govoni [11]. as can be seen from tab. 1, the numerical model well reproduced the results of the real scale tests. in the simulation, the breaking time is evaluated as the first time the velocity of the block becomes zero and the maximum elongation is the maximum distance between the initial position of the net and the position of the net at the breaking time measured parallel to the slope. the final elongation was the same distance evaluated at the end of the test, i.e. at 6 s from the first contact of the block with the net. the residual height is the minimum distance between the lower and the upper longitudinal cables at the end of the test. a. luciani et alii, frattura ed integrità strutturale, 43 (2018) 241-250; doi: 10.3221/igf-esis.43.19 244 fig. 3 compares model deformation during mel test at six different times: particularly t = 0 s is the first contact of the block with the net, t = 0.36 s is the breaking time and t = 6.00 s is the test end time. fig. 4 shows the plastic strain in the central panel of the net during the simulation; it is possible to see that the highest deformations occur in the contact area of the block with the net, then the deformation extend to the panel with a cross shape and this result is very close to what was observed in real tests [10,11]. figure 3: numerical modelled net fence during the mel test. numerical simulation of damages n order to evaluate the influence of the problems detected during the site survey [29], the numerical model was modified to reproduce damaged conditions. these conditions represent the most common local damages and the ones that were most frequently highlighted by the site survey [29]. the model has not the ability to take into account a reduction of the overall properties of the net barrier since them can be difficulty described and the research has been focused on those damages that can be modelled as the removal of a structural rope or an incorrect assembly of one or more elements of the barrier itself. specifically, these conditions are: damages to the upstream ropes or to the clamp connections; these situations can be due to installation of the clumps not in accordance with the regulations in force [31] in terms of number, distance and torque applied to the fastener or to damages of the connections and of the ropes caused by impacting blocks; damages to the anchorages, such as failure or under efficiency of the anchorages due to wrong installation or damaging during the device life; installation geometries different from those prescribed by the producer; this is a common issue for to the geometry peculiarity of many sites; in the site survey several cases have been observed ranging from barriers with short and sub-horizontal upstream ropes to barriers with extremely long upstream ropes. time-dependent damages to the barriers can be related to corrosion on ropes and clip connections. nevertheless, in the barriers analyzed during the site survey, corrosion affects only some of the secondary metallic elements, but not ropes. this is due to the non-aggressive environment of installation (usually c1-c2 following uni en iso 9223 [32]) and to the protection nowadays used against corrosion (zinc and zinc-aluminum coatings) that ensure the durability for the life span of the protection devices. i a. luciani et alii, frattura ed integrità strutturale, 43 (2018) 241-250; doi: 10.3221/igf-esis.43.19 245 figure 4: comparison of the plastic strain in the central panel of the original model at different times during the impact. time is in seconds [30]. a. luciani et alii, frattura ed integrità strutturale, 43 (2018) 241-250; doi: 10.3221/igf-esis.43.19 246 therefore, the six models set up for the research are: models from (a) to (d) simulate the failure of connections made by rope clips of the upstream cables, due to installation problems or to clip corrosion. in the numerical models, this kind of damages has been simulated simply removing one of the upstream cables from the computation i.e. the connection is not working and thus the cable cannot withstand any stress. moreover, models (c) and (d) simulate also the failure of one anchorage of the upstream cables due to a not correct grouting. in the numerical model this possibility is simulated removing from the simulation the cables that are restrained by that anchorage. model (e) and (f) reproduce the effect of different installation geometry due to local conditions. the goal of these models is to study the influence of anomalous geometrical installations with reference to the one tested following the etag027 geometry. model (e) represents a case with short and horizontal upstream cables. the original model has oblique upstream cables of 7.7 m while in this model they are horizontal with a length of 5.7 m while model (f) reproduces the effect of very long upstream cables. the upstream cables of this model are 20.0 m long. in the numerical model, only the geometry and length of upstream cables have been changed from the original model. (fig. 5). on these six modified models impact tests were performed at different energy levels aiming to identify the maximum energy the modified net fence can withstand without failure of one of the principal elements. failure of cables and energy dissipating devices was established when one of these elements reached a plastic strain bigger than that correlated to the ultimate stress. since the model uses an equivalent net, the ultimate stress of the net was unknown, for it may be different from that of the real ring net. therefore, the equivalent net was considered failed if at least one of the elements composing the net reached a plastic strain bigger than the maximum recorded during the mel simulation. once the maximum energy the modified model can withstand has been defined, the residual efficiency ( efr ) of the net fence can be evaluated as (%)mwef nom e r e  where mwe is the maximum energy the net fence can withstand and nome the nominal energy of the net fence according to the etag 027 classification. the values of residual efficiency of the models are reported in tab. 2. table 2: summary of the results of the numerical simulations. model problem simulated maximum energy withstood (kj) residual efficiency (%) a failure of one clip connection or of one upstream cable 3000 100 b failure of one clip connection or of one upstream cable 3000 100 c failure of two clip connection or of two upstream cable or of an anchorage 2900 97 d failure of two clip connection or of two upstream cable or of an anchorage 3000 100 e short and horizontal upstream cables 2400 80 f long upstream cables 2600 87 a. luciani et alii, frattura ed integrità strutturale, 43 (2018) 241-250; doi: 10.3221/igf-esis.43.19 247 10 m figure 5: drawing of the original and modified models of the rockfall protection net fence. original model model (a) model (b) model (c) model (d) model (e) model (f ) missing cable missing cables missing cables missing cable a. luciani et alii, frattura ed integrità strutturale, 43 (2018) 241-250; doi: 10.3221/igf-esis.43.19 248 the most important results obtained comparing the six numerical models are: in models (a), (b) and (d) the modified net fence fulfilled the test at 3000 kj without failure of any element, while in model (c) at an impact of 3000 kj the net reaches a plastic strain higher than the maximum recorded during the original model mel test in the contact area. therefore, the net is considered failed. repeating the simulation with an energy of 2900 kj no failure has been produced. based on these results the residual efficiency for model (a), (b) and (d) is of 100% while it is of 97% for model (c). moreover, the simulations show a variation in the behavior of the net fence in terms of maximum elongation. in the damaged models the maximum elongation of the net fence increased, up to the 20% in model (c) (fig. 6), while the final elongation is almost the same of the original model. this result is very important in terms of correct positioning of the net fence on the slope. the increase of maximum elongation is due to the absence of the upstream cables involving a lower stiffness and lack of constrains of the system. figure 6: comparison of the maximum elongation of the original model and of models (a), (b), (c) and (d). in model (e), the net, the lower longitudinal cables and the two energy dissipating devices of the upstream cables convergent to the central anchorage get to failure for an impact energy of 3000 kj. these failures were due to the higher stiffness due to the shorter upstream cables. repeating the simulations with lower energy, the model withstood an impact with an energy of 2400 kj with residual efficiency of 80%. in model (f), the longitudinal cables failed at an impact of 3000 kj. in this condition, the energy dissipating devices of the upstream cables were not activated. this behavior may be explained considering that longer upstream cables involve lower stiffness and so the cables were less charged. consequently, the energy coming from the impact concentrated on the other elements of the net fence and particularly on the longitudinal cables. the model withstood an impact at 2600 kj, with residual efficiency of 87%. these results allow to say that after some time of ageing or when the net fence has been not correctly installed the energy it can withstand is lower than that assessed in the etag027 classification. therefore, residual efficiency value should be considered in rockfall risk analysis in order to take into account in this process the deterioration and installation conditions of the net fence. when making the design of a protection by net fences, the choice of the product is usually based on the statistical analysis of the rockfall trajectories and on the evaluation of the rock block size to be stopped. therefore, based on the statistical evaluation of the computed speeds and height of trajectories in correspondence of the protection device to be installed, it is possible to assess the maximum energy to be stopped and consequently choose the optimal product. after this analysis, it is possible to assess the number of blocks that cannot be stopped and, based on this number, it is possible to assess the residual risk. risk analyses are usually started taking into account the number of blocks that exceeds the barrier capacity or jumps over it and, consequently, reaches the object to be protected [3]. as a consequence, the risk mitigation is directly affected by the percentage of block stopped by the net fence i.e. its efficiency. an incorrect installation can reduce the ability of the barrier to stop the block and consequently a higher percentage of blocks can pass. the analysis has allowed to quantify this value for a set of frequent defects or ageing conditions. taking as an example, the procedure proposed by peila and guardini [3], the key parameter in the evaluation of the probability in the analysis is the number of rockfall events that can affect the infrastructure per year ( ). a protective device reduces the probability of occurrence of the event, i.e. induces a reduction of the number of blocks affecting the road, that can be estimated as a. luciani et alii, frattura ed integrità strutturale, 43 (2018) 241-250; doi: 10.3221/igf-esis.43.19 249 ' (1 )r rn c n   where rn is the number of blocks reaching the road without the protection device, ' rn those reaching the road with the device and is the catching capacity of the device. the catching capacity is the percentage of blocks that the device can stop. the requested catching capacity should be evaluated through the trajectories analysis and the design block assessment. the residual efficiency proposed above describes the energy the damaged barrier can withstand compared to the nominal one. therefore, it can easily be taken into account in the risk analysis modifying the previous equation as follows ' (1 )r ef rn c r n    the residual efficiency reduces the catching capacity, i.e. increases the number of blocks reaching the road ( 'rn ), with an obvious increase of the rockfall risk. therefore, in the design, the effect of a damaged barrier can be considered in the trajectories analysis simulating a barrier with a reduced ability to stop a certain energy and allowing more blocks to go through. conclusions he influence of damages induced by ageing on the behaviour of a rockfall protection net fence is analyzed using numerical modelling. a site survey on many net fence installations located in north of italy allowed to point out the most relevant problems related to ageing of rockfall protection net fences after installation and suggested how to set up the numerical models. the main goal of the analyses is to show how damages of the components can affect the efficiency of the products and therefore reduce their ability to stop falling blocks. to develop this assessment six different numerical models of a commercial net fence have been studied and an assessment of the residual efficiency has been developed. this value may be included in rockfall risk analysis allowing to take into account the conditions of a damaged or aged device. in this procedure the residual efficiency value should be used to reduce the catching capacity of the net fence increasing the number of falling blocks that might impact against the structure to be protected and consequently correctly considering in the risk analysis the presence of aged net fences on the slope. it is important to highlight that all the risk analysis procedures have as an input datum the number of blocks impacting the structure. moreover, this appraisal allows owners to plan maintenance or refurbishment works and establish priority between different protection devices, knowing when the reduction of efficiency induces a risk higher than the accepted threshold value. references [1] budetta, p., assessment of rockfall risk along roads, nat. hazards earth syst. sci., 4 (2004) 71–81. [2] corominas, j., copons, r., moya, j., vilaplana, j.m., altimir, j., amigò, j., quantitative assessment of the residual risk in a rockfall protected area, landslides, 2 (2005) 343-357. [3] peila, d., guardini, c., use of the event tree to assess the risk reduction obtained from rockfall protection devices, nat. hazard earth syst. sci., 8 (2008) 1441-1450. [4] mignelli, c., lo russo, s., peila, d., rockfall risk management assessment: the ro.ma. approach, nat. hazards, 62 (2012) 1109-1123. [5] de biagi, v., botto, a., napoli, m.l., dimasi, c., laio, f., peila, d., barbero, m., estimation of the return period of rock falls according to the block size, geoingegneria ambientale e mineraria, 147 (2016) 39-47. [in italian] [6] budetta, p., nappi, m., comparison between qualitative rockfall risk rating systems for a road affected by high traffic intensity, nat. hazards earth syst. sci., 13 (2013) 643-1653. [7] mignelli, c., peila, d., lo russo, s., ratto, s., broccolato, m., analysis of rockfall risk on mountainside roads: evaluation of the effect of protection devices, nat. hazards, 73 (2014) 25-35. t a. luciani et alii, frattura ed integrità strutturale, 43 (2018) 241-250; doi: 10.3221/igf-esis.43.19 250 [8] budetta, p., de luca, c., nappi, m., quantitative rockfall risk assessment for an important road by means of the rockfall risk management (ro.ma.) method, bull. eng. geol. environ., (2015). [9] duffy, j.d., hoon, w., field tests and evaluation of hi-tech 50 and 70 foot-ton rockfall fence, report no. ca/05-9602, (1996) california dept. of trasportation; san luis obispo, ca. [10] peila, d., pelizza, s., sassudelli, f., evaluation of behaviour of rockfall restraining nets by full scale tests, rock mech. rock eng., 31 (1998), 1-24. [11] gottardi, g., govoni, l., full-scale modelling of falling rock protection barriers, rock mech. rock eng., 43 (2010) 261-274. [12] trad, a., limam, a., bertrand, d., robit, p., multi-scale analysis of an innovative flexible rockfall barrier. in: lambert, s., nicot, f., iohn wiley & sons. rockfall engineering. new york, ste ltd and j, (2011) 303-342. [13] buzzi, o., spadari, m., giacomini, a., fityus, s., sloan, s.w., experimental testing of rockfall barriers designed for the low range of impact energy, rock mech. rock eng., 46 (2013) 701-712. [14] eota: etag 027 guideline for european technical approval of falling rock protection kits, edition february 2008; amended april 2013. [15] peila, d., baratono, p., etag027: una grande innovazione nel settore delle opere di protezione contro la caduta massi, geoingegneria ambientale e mineraria, 125 (2008) 49-52. [in italian] [16] peila, d., ronco, c., technical note: design of rockfall net fences and the new etag 027 european guideline, nat. hazards earth syst. sci., 9 (2009) 1291-1298. [17] cantarelli, g., giani, g.p., analisi dei metodi di verifica dell’efficienza di reti di protezione contro la caduta massi, rivista italiana di geotecnica, 40 (2006) 23-31. [in italian] [18] nicot, f., cambou, b., mazzoleni, g., design of rockfall restraining nets from a discrete element modelling, rock mech. rock eng., 34 (2001) 99-118. [19] cazzani, a., mongiovì, l., frenez, t., dynamic finite element analysis of interceptive devices for falling rocks, int. j. rock mech. min., 39 (2002) 303-321. [20] grassl, h., volkwein, a., anderheggen, e., ammann, w.j., steel-net rockfall protection – experimental and numerical simulation, in: proceedings of 7th international conference on structures under shock and impact, montreal, canada, (2002) 143–153. [21] volkwein, a., numerical simulation of flexible rockfall protection systems, in: proceedings of the international conference on computing in civil engineering, cancun, mexico, asce, (2005) 1285-1295. [22] peila, d., oggeri, c., baratono, p., barriere paramassi a rete. interventi e dimensionamento, geoingegneria ambientale e mineraria, quaderni di studio e documentazione n° 25, torino, (2006). [in italian] [23] gentilini, c., govoni, l., de miranda, s., gottardi, g., ubertini, f., three-dimensional numerical modelling of falling rock protection barriers, computers and geotechnics, 44 (2012) 58-72. [24] gentilini, c., gottardi, g., govoni, l., mentani, a., ubertini, f., design of falling rock protection barriers using numerical models, eng. struct., 50 (2013) 96-106. [25] spadari, m., giacomini, a., buzzi, o., hambleton, j.p., prediction of the bullet effect for rockfall barriers: a scaling approach, rock mech. rock eng., 45 (2012) 131-144. [26] escallón, j.p., wendeler, c., numerical simulations of quasi-static and rockfall impact tests of ultra-high strength steel wire-ring nets using abaqus/explicit, in: 2013 simulia community conference (2013). [27] escallón, j.p., wendeler, c., chatzi, e., bartelt, p., parameter identification of rockfall protection barrier components through an inverse formulation, eng. struct., 77 (2014) 1-16. [28] moon, t., oh, j., mun, b., practical design of rockfall catchfence at urban area from a numerical analysis approach, eng. geol., 172 (2014) 41-56. [29] dimasi, c., luciani, a., martinelli, d., paganone, m., peila, d., controllo delle barriere paramassi a rete per la loro gestione e manutenzione, geoingegneria ambientale e mineraria, 146 (2015) 65-73. [in italian] [30] luciani, a., peila, d., barbero, m., studio numerico dell’influenza dell’ammaloramento delle barriere paramassi a rete, geoingegneria ambientale e mineraria, 147 (2016) 31-38. [in italian] [31] uni en 13411-5 terminations for steel wire ropes safety part 5: u-bolt wire rope grips (2003). 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can be opened with acrobat and adobe reader 5.0 and later.) >> /namespace [ (adobe) (common) (1.0) ] /othernamespaces [ << /asreaderspreads false /cropimagestoframes true /errorcontrol /warnandcontinue /flattenerignorespreadoverrides false /includeguidesgrids false /includenonprinting false /includeslug false /namespace [ (adobe) (indesign) (4.0) ] /omitplacedbitmaps false /omitplacedeps false /omitplacedpdf false /simulateoverprint /legacy >> << /addbleedmarks false /addcolorbars false /addcropmarks false /addpageinfo false /addregmarks false /convertcolors /converttocmyk /destinationprofilename () /destinationprofileselector /documentcmyk /downsample16bitimages true /flattenerpreset << /presetselector /mediumresolution >> /formelements false /generatestructure false /includebookmarks false /includehyperlinks false /includeinteractive false /includelayers false /includeprofiles false /multimediahandling /useobjectsettings /namespace [ (adobe) (creativesuite) (2.0) ] /pdfxoutputintentprofileselector /documentcmyk /preserveediting true /untaggedcmykhandling /leaveuntagged /untaggedrgbhandling /usedocumentprofile /usedocumentbleed false >> ] >> setdistillerparams << /hwresolution [2400 2400] /pagesize [612.000 792.000] >> setpagedevice microsoft word numero_41_art_26.docx p. lorenzino et alii, frattura ed integrità strutturale, 41 (2017) 191-196; doi: 10.3221/igf-esis.41.26 191 focused on crack tip fields influence of forging conditions on the fatigue mechanisms of low alloy steels: a 3d study pablo lorenzino, jean-yves buffiere, catherine verdu insa lyon mateis bat saint exupery 25 av. jean capelle f-69621 villeurbanne cedex france jean-yves.buffiere@insa-lyon.fr abstract. the influence of forging conditions on the propagation of physically small fatigue cracks has been studied for two high strength steels. two surface conditions were produced after the forging process. the subsurface microstructure of the materials has been characterized by ebsd. small samples extracted from the original specimens were used to perform in situ fatigue tests monitored by high resolution synchrotron x-ray tomography. fatigue cracks were initiated from an artificial defect (100 μm wide x 50 μm deep) introduced in the forging skin by laser machining. 3d images of the initiation and growth of those physically small fatigue cracks have been obtained. it was found that the presence of a shot-blasted skin containing a hardness and microstructure gradient influences the 3d crack shape during propagation in comparison with the materials without material properties gradient. the 3d crack shapes are rationalized in terms of crack closure effects induced by the forging processes, close to the surface. keywords. short cracks; 3d propagation; crack closure; synchrotron x-ray tomography; forging. citation: lorenzino, p., buffiere, j.-y., verdu, c., influence of forging conditions on the fatigue mechanisms of low alloy steels: a 3d study, frattura ed integrità strutturale, 41 (2017) 191-196. received: 28.02.2017 accepted: 15.04.2017 published: 01.07.2017 copyright: © 2017 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. introduction ith the enforcement, in the very near future, of new european regulations in terms of fuel consumption, car manufacturers have put a large effort in trying to reduce the weight of vehicles in the last ten years. this has led to a global increase of the load level experienced by many components in the body, the panels, the wheels or the engine of cars. being able to accurately predict the fatigue life of those components has now become a key issue for keeping the same trend and reducing the vehicle weight further. a good example, in the field of metallic components, is given by the connecting rods or crankshafts which are submitted to higher service load for a very large number of cycles. although it is well accepted that the methods used to produce such components (mainly hot and cold forging) have a strong effect on the material microstructure and, therefore, on their mechanical properties, the thermo-mechanical history experienced by the metals during processing is not accurately taken into account at the design stage leading to over conservative safety coefficients. w p. lorenzino et alii, frattura ed integrità strutturale, 41 (2017) 191-196; doi: 10.3221/igf-esis.41.26 192 in this study, four different industrially relevant forging conditions have been studied for two different pearlitic or ferriticpearlitic steels. the effect of the processing route on the materials microstructure and mechanical behavior has been first evaluated. the 3d propagation behavior of fatigue cracks growing from shallow artificial defect (i.e. growing mainly within the forged skin of the materials) has been obtained through in situ x-ray synchrotron tomography. the crack growth curves have been obtained for all materials and the effect of processing on crack growth behavior assessed. experimental materials our different forging condition of industrial relevance were investigated for two different steels. cold forged cylindrical specimens produced with two different cross sectional area reduction (18 and 75 %) have been obtained for a 27mncr5 ferritic-pearlitic steel [1]. a c70 pearlitic steel was also used to produce connecting rods through a four step hot forging process. samples were extracted from the connecting rods directly in the as-forged condition or after a shot-blasted treatment applied in order to remove the scale [2]. tab. 1 details the processes and the mechanical properties of the four different materials/conditions studied (hereafter simply called different materials with a greek numbering as shown in the table). it can be seen from this table that the cold forging process produces a lower grain size than hot forging and that the grain size decreases with the level of reduction. when shot blasting is used (material iv) a grain size gradient is observed. ebsd observations reveal a 10 µm thick layer of extremely fine grains (< 1 µm); below this region a layer of heavily deformed grains is observed evolving gradually towards more equiaxed grains with an average size of 25 µm at a distance of 150-200 µm below the surface, where the unaffected bulk material begins. a gradient of mechanical properties is concomitantly observed with hardness values ranging from 350 hv at the surface to 280 hv at 400 µm below the surface. finally, in the bulk material, a residual stresses gradient (measured by x-ray diffraction) with compressive stress values ranging from 500 mpa at the surface to 0 mpa at a distance of 400 µm below the surface was measured . more detailed information can be found in [2] synchrotron tomography experiments in order to study the influence of the surface conditions induced by the finishing processes on the propagation of shallow fatigue cracks, small samples of 0.8 x 0.8 mm cross-sectional area were extracted at the surface of the forged components. the small cross section of the samples is the result of the large x-ray attenuation of iron and the small voxel size required to detect accurately the small cracks [3]. fig. 1 (a) and (b) show a schematic view of the fatigue samples extracted from the cold forged round bars (materials i and ii) and from hot forged connecting rods (materials iii and iv) by means of electro discharge machining. symbol material process σ0.2 (mpa) grain size (µm) i 27mncrfp cold forged (18%) 730 15 ii 27mncrp cold forged (75%) 1072 8 iii c70p hot forged 800 25 iv c70p hot forged + shot blasting 800 1 to 25 table 1: list of the materials and forging processes investigated with the corresponding mechanical properties and grain sizes. in material iv the shot blasting process produces a grain size gradient (see the text for details). residual stress measurements performed on the tomography samples showed values ranging from 0 to 20 mpa in samples of materials i, ii and iii. in the particular case of material iv, after spark machining the samples exhibited a curvature radius of 170 mm due to the presence of residual stress gradient. however, this curvature disappeared in the unloaded state after a few hundred fatigue cycles. thus it can be concluded that the samples tested were free of residual stresses. f p. lorenzino et alii, frattura ed integrità strutturale, 41 (2017) 191-196; doi: 10.3221/igf-esis.41.26 193 figure 1: miniature dog bone fatigue samples (cross section 0.8x0.8 mm2) extracted at the surface of the forged materials from the cold forged bars (materials i and ii) (a) or from the hot forged connecting rods (materials ii and iv) (b). artificial defects that act as the initiation point of the fatigue cracks were introduced at the sample surface by laser machining as described elsewhere in the case of cast iron [4]. in this study the notch obtained has the shape of a narrow wedge of dimensions (depth/width/opening): 50x100-150x5 µm3. it is shown schematically on fig. 2. in-situ fatigue tests were performed on id19 beamline at the european synchrotron radiation facility (esrf). a ”pink” x ray beam [5] with a photon energy of 60 kev is used with a pco edge ccd camera (2160 x 2560 pixels). the samples were cycled in situ using a dedicated fatigue machine mounted onto the rotation stage of the beamline [6]. once crack initiation was detected (by inspection of the radiographs of the sample under load) tomographic scans (2000 projections, exposure time of 0.07s duration 3.68 min) were recorded regularly after a given number of cycles. the samples were scanned under maximum load in order to improve crack visibility. uniaxial fatigue tests were carried out in pull-pull loading conditions with r=0.1. reconstruction of the tomographic data was performed with a standard filtered backprojection algorithm. a 0.65 µm voxel size was obtained. fiji and paraview open softwares were used for post-processing the 3d images. figure 2: left: projected view (along the loading direction) of the crack shape for material iv (hot forged + shot blasted) after 66kcycles fatigue cycles at σmax = 450 mpa r=0.1. the blue rectangle highlights the shape of the laser notch. right: reconstructed slice showing the crack shape a few micrometers below the surface (loading direction horizontal). p. lorenzino et alii, frattura ed integrità strutturale, 41 (2017) 191-196; doi: 10.3221/igf-esis.41.26 194 results and discussion ab. 2 summarizes the fatigue tests performed at the esrf. two tests were carried out in each material in order to have failures above and below 100.000 cycles. for material iv, five specimens were tested since in some cases the crack nucleated from a corner of the sample instead of the artificial defect. the ability of tomography to detect accurately the size/shape of the cracks was assessed by comparing the surface crack size measured on the reconstructed images (e.g. right image on fig. 2) with optical images obtained on the unbroken samples. in all cases a very good correspondence was observed (less than a few percent error). it was therefore possible to monitor accurately the 3d shape of the crack steadily propagating out of the artificial defect. material test σmax/ σ0.2 cycles (x103) failure origin i 1 0.62 61 notch i 2 0.57 160 notch ii 3 0.52 71 notch ii 4 0.48 125 notch iii 5 0.52 30 sample corner iii 6 0.47 121 notch iv 7 0.58 31 notch iv 8 0.59 60 sample corner iv 9 0.56 71.5 notch iv 10 0.63 95 sample corner iv 11 0.45 340 sample corner table 2: summary of the fatigue tests carried out at the synchrotron. regarding the initiation stages, for the cold forged materials, a larger number of cycles was required to initiate a crack from the notch for the material with the largest strain level (material ii). regarding propagation, for all materials, both the crack surfaces and crack fronts were relatively flat/smooth showing no indication of strong interactions with the local microstructure (see for example fig. 3 for an example of the crack fronts observed in material iv). figure 3: crack front shapes for material iv σmax = 450 mpa, r=0.1. the shape of the crack fronts is relatively smooth indicating the absence of strong interaction with the local microstructure (e.g. grains). despite their small physical sizes, the cracks behave as ”microstructurally long” fatigue cracks with continuously increasing growth rates. fig. 4 shows a comparison of the crack growth rates as a function of ∆k for materials iii and iv. in this figure the stress intensity factor values are based on the (area)1/2 parameter proposed by murakami [7]. t p. lorenzino et alii, frattura ed integrità strutturale, 41 (2017) 191-196; doi: 10.3221/igf-esis.41.26 195 it can be seen from this figure that the shot blasting effect has nearly no effect on the crack resistance of the two materials. the same results have been obtained when comparing materials i and ii. a more sophisticated analysis taking into account the 3d shape of the cracks for the calculation of the stress intensity factors (sif) with the raju & newman analytical formulas [8] shows again no difference between the four materials in terms of crack growth rates. figure 4: da/dn curves for materials iii and iv. the sif values are based on murakami’s (area)1/2parameter. figure 5: crack aspect ratio for the four materials studied (several samples per materials). one difference between the materials is observed when the crack shape is being considered. in case of material i, ii and iii the crack fronts acquire a semi-circular (penny) shape from a very early stage of propagation, conserving this geometry until final failure. in the case of material iv, however, the crack front acquires a semi-elliptical shape, a geometry which is maintained until final fracture. for materials i, ii and iii the crack intersects the surface with a 90 degree angle; this is not the case for material iv as observed on fig. 3. those differences are shown on fig. 5 which gives a summary of the crack aspect ratio (depth/half surface length) for all materials: material iv is the only one which has a ratio below 1. a raju & newman analysis of the sif values suggests that a penny shape correspond to a crack growing with an out of equilibrium shape that is to say a crack front along which k is not constant but higher at the surface. one explanation for this might be the “tunneling” effect of the crack which is well known for through cracks in ct samples (see for example [9]): a larger level of crack closure at the sample due to the larger plastic zone size “holds back” the crack front. p. lorenzino et alii, frattura ed integrità strutturale, 41 (2017) 191-196; doi: 10.3221/igf-esis.41.26 196 although this has rarely been reported for 3d part-through cracks [10], this is consistent with the experimental observation of a grain size gradient at the surface of material iv. a smaller grain size restricts the plastic zone size (hall petch effect) and therefore the tunneling effect is reduced or even suppressed. experiments at larger r ratio on materials iii and iv (not shown here) tend to support this interpretation. conclusion n situ fatigue tests monitored by synchrotron x-ray tomography have been carried out on four different forged materials (two different steels + two different forging processes). the residual stresses which have been measured in some of the bulk materials have been released in the fatigue samples because of their small size. for the experimental conditions investigated, it was found that there is no influence of the forging process on crack growth curves. differences in crack front shapes have been observed for the material which has been shot blasted. those differences are interpreted in terms of the modifications induced in the sub-surface microstructure by the forging processes: a reduction of subsurface crack closure due to a local increase of the yield stress. acknowledgements his project has been funded by the french agence nationale de la recherche (defisurf project). the authors want to thank prof f.morel and dr. e.pessard for fruitful discussions. references [1] gerin, b., pessard, e., morel, f., verdu, c.,mary, a., beneficial effect of prestrain due to cold extrusion on the multiaxial fatigue strength of a 27mncr5 steel international journal of fatigue 92 (2016) 345–359. doi: 10.1016/j.ijfatigue.2016.07.012 [2] gerin, b., pessard, e., morel, f., verdu, c., influence of surface integrity on the fatigue behaviour of a hot-forged and shot-peened c70 steel component materials science & engineering a 686 (2017) 121–133. doi: 10.1016/j.msea.2017.01.041. [3] buffiere, j.-y., maire, e., adrien, j., ·masse, j.-p., boller, e., in situ experiments with x ray tomography: an attractive tool for experimental mechanics experimental mechanics 50 (2010) 289–305. doi: 10.1007/s11340-010-9333-7. [4] lachambre, j.,réthoré, j.,weck, a., buffiere, j.-y., extraction of stress intensity factors for 3d small fatigue cracks using digital volume correlation and x-ray tomography international journal of fatigue 71 (2015) 3–10. doi: 10.1016/j.ijfatigue.2014.03.022. [5] p. willmott, p., an introduction to synchrotron radiation: techniques and applications, john wiley & sons, (2011). [6] buffiere, j.-y., ferrie, e., proudhon, h., ludwig, w., three dimensional visualisation of fatigue cracks in metals using high resolution synchrotron x-ray micro-tomography. mater. sc. technol., 22(9)(2006) 1019–1024. [7] murakami y., metal fatigue: effect of small defects and non-metallic inclusions. elsevier, (2002). [8] newman, j.c., raju, i.s., an empirical stress-intensity factor equation for the surface crack eng. frac. mech., 15 (1981) 185–192. [9] dawicke, d.s., grandt, a.f., newman, j.c., three-dimensional crack closure behavior engineering fracture mechanics, 36(1) (1990) 111-121. [10] ferrié, e., buffiere, j.-y., ludwig, w., gravouil, a., edwards, l., fatigue crack propagation: in situ visualization using x-ray microtomography and 3d simulation using the extended finite element method acta materialia, 54(4) (2006) 1111-1122. doi: 10.1016/j.actamat.2005.10.053. i t << /ascii85encodepages false /allowtransparency false /autopositionepsfiles true /autorotatepages /none /binding /left /calgrayprofile (dot gain 20%) /calrgbprofile (srgb iec61966-2.1) /calcmykprofile (u.s. web coated \050swop\051 v2) /srgbprofile (srgb iec61966-2.1) /cannotembedfontpolicy /error /compatibilitylevel 1.4 /compressobjects /tags /compresspages true /convertimagestoindexed true /passthroughjpegimages true /createjobticket false /defaultrenderingintent /default /detectblends true /detectcurves 0.0000 /colorconversionstrategy /cmyk /dothumbnails false /embedallfonts true /embedopentype false /parseiccprofilesincomments true /embedjoboptions true /dscreportinglevel 0 /emitdscwarnings false 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/hrv (za stvaranje adobe pdf dokumenata najpogodnijih za visokokvalitetni ispis prije tiskanja koristite ove postavke. stvoreni pdf dokumenti mogu se otvoriti acrobat i adobe reader 5.0 i kasnijim verzijama.) /hun 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can be opened with acrobat and adobe reader 5.0 and later.) >> /namespace [ (adobe) (common) (1.0) ] /othernamespaces [ << /asreaderspreads false /cropimagestoframes true /errorcontrol /warnandcontinue /flattenerignorespreadoverrides false /includeguidesgrids false /includenonprinting false /includeslug false /namespace [ (adobe) (indesign) (4.0) ] /omitplacedbitmaps false /omitplacedeps false /omitplacedpdf false /simulateoverprint /legacy >> << /addbleedmarks false /addcolorbars false /addcropmarks false /addpageinfo false /addregmarks false /convertcolors /converttocmyk /destinationprofilename () /destinationprofileselector /documentcmyk /downsample16bitimages true /flattenerpreset << /presetselector /mediumresolution >> /formelements false /generatestructure false /includebookmarks false /includehyperlinks false /includeinteractive false /includelayers false /includeprofiles false /multimediahandling /useobjectsettings /namespace [ (adobe) (creativesuite) (2.0) ] /pdfxoutputintentprofileselector /documentcmyk /preserveediting true /untaggedcmykhandling /leaveuntagged /untaggedrgbhandling /usedocumentprofile /usedocumentbleed false >> ] >> setdistillerparams << /hwresolution [2400 2400] /pagesize [612.000 792.000] >> setpagedevice microsoft word numero_62_art_21_3538.docx m. a. fauthan et alii, frattura ed integrità strutturale, 62 (2022) 289-303; doi: 10.3221/igf-esis.62.21 289 multiple linear regression parameters for determining fatigue-based entropy characterisation of magnesium alloy m.a. fauthan, s. abdullah universiti kebangsaan malaysia, malaysia akashah948@gmail.com, shahrum@ukm.edu.my m.f. abdullah universiti pertahanan nasional, malaysia m.faizal@upnm.edu.my i.f. mohamed universiti kebangsaan malaysia, malaysia intanfadhlina@ukm.edu.my abstract. this paper presents the development of the multiple linear regression approach based on the stress ratio and applied load that was assessed using entropy generation. the energy dissipation is associated with material degradation to determine the fatigue life with consideration to the irreversible thermodynamic framework. this relationship was developed by predicting a complete entropy generation using a statistical approach, where a constant amplitude loading was applied to evaluate the fatigue life. by conducting compact tension tests, different stress ratios were applied to the specimen. during the tests, the temperature change was observed. the lowest entropy generation was 2.536 mjm-3 k-1 when 3,000n load with a stress ratio of 0.7 was applied to the specimen. the assumptions of the models were considered through graphical residual analysis. as a result, the predicted regression model based on the applied load and stress ratio was found to agree with the results of the experiment, with only 9.3% from the actual experiment. therefore, the entropy generation can be predicted to access the dissipated energy as an irreversible degradation of a metallic material, subjected to cyclic elastic-plastic loading. thermodynamic entropy is shown to play an important role in the fatigue process to trace the fatigue life. keywords. entropy; fatigue crack growth; magnesium alloy; multiple linear regression; stress ratio. citation: fauthan, m. a., abdullah, s., abdullah, m. f., mohamed, i. f., multiple linear regression parameters for determining fatigue-based entropy characterisation of magnesium alloy, frattura ed integrità strutturale, 62 (2022) 289-303. received: 31.03.2022 accepted: 29.06.2022 online first: 31.08.2022 published: 01.10.2022 copyright: © 2022 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. https://youtu.be/ujwd1hmts98 m. a. fauthan et alii, frattura ed integrità strutturale, 62 (2022) 289-303; doi: 10.3221/igf-esis.62.21 290 introduction he growing ecological effect of transport emissions, limited resources, and the restraint to conserve energy has resulted in a comprehensive research study that focused on establishing innovative magnesium alloys for lightweight automobile structural applications. to ensure the safe and reliable applications of mg alloys, the fatigue deformation resistance of mg alloys has to be studied. since magnesium alloy has a very low weight for its capability and workability, industries make a high usage of magnesium alloys in many mechanical functions [1]. if the parts are exposed to load in cyclic conditions, the determination of fatigue properties becomes crucial. as a progressive reduction of the material strength process, fatigue will occur due to cyclic loading or cyclic contortion. fatigue failure can happen suddenly with no obvious caution and typically catastrophically [2]. it starts with the development of microcracks that continue to grow with duplicated applications of the load [3]. this concurrently decreases the product’s recurring strength until becomes so low that the structure’s failure is impeded [4]. fatigue problems are often the main problem of total performance, which thus calls for an investigation of magnesium alloys’ fatigue characteristics [5]. at the beginning of the research, common fatigue analysis methods include stress-life curves for high-cycle fatigue (hcf) and strain-life curves for low-cycle fatigue (lcf). existing approaches sometimes give inconsistent results, and failure measures usually depend on the environment set up. recent entropy-based fatigue studies have shown high accuracy, establishing thermodynamic energies and entropies as measures of system damage, degradation and failure. the fatigue procedure is typically accompanied by energy change, which establishes a thermodynamic structure to study its depiction. as the irreversible process occurs, the energy dissipates, which shows that the concept of entropy is a suitable tool to review the fatigue process [6]. in this case, entropy generation is an early detection mode that allows the researcher to develop the approach from the surface temperature evolution. the use of the energy theory to study fatigue is another approach to determining fatigue life. most works were conducted based on the total strain energy density, which has been widely used to evaluate material failure. over the past several decades, thermodynamic measurements have also been widely used with fatigue tests as non-destructive testing (ndt) method, mainly to determine fatigue properties. furthermore, some researchers [7] have examined the theoretical structure and comparable testing methods to analyse dissipated heat energy at the crack tips. the elastic-plastic fracture parameter shows the average heat energy in a cycle [8]. it was found that the fatigue damage can be depicted as an index for energy dissipation in a system volume cycle [9]. the fatigue process in mechanical processes uses the concept of the thermodynamics structure [10], which is not unanticipated as fatigue deterioration is an irreversible process that slowly ages a system until failure by fracture [11]. the second law of thermodynamics is related to fatigue, where entropy is generated during the disorder [12]. typically, fatigue is a complicated procedure that is impacted by different aspects. problems in fatigue research study occur due to the presence of many internal and external aspects such as the properties of the material as well as the load and geometry which affect fatigue behaviour [13]. after that, various approaches and theories have been used to design and study fatigue procedures, for instance, the variety of cyclic loading before fracture [14], dissipated energy [15], and deterioration in structural applications [16]. current research studies in infrared thermography for non-destructive examination of damage have offered brand-new research studies for the research findings the study of crack propagation for specimens subjected to cyclic loading [17]. in a traditional test, numerous unidentified input specifications are needed. furthermore, this relationship can be described through the introduction of multiple linear regression (mlr) to predict a variable’s value based on the importance of two or more other variables. earlier research studies have shown that the evolution of temperature throughout fatigue failure can be utilised as a primary forecast of fatigue life [18]. to examine fatigue failure based on entropy generation, the temperature level difference throughout the fatigue system is essential [19]. if the total generation of entropy can be approached through regression, then fatigue life can be predicted. hence, this paper aims to describe the mlr relationship to predict the total entropy generation of magnesium alloy, az31b. literature background he thermodynamic approach to assessing materials’ fatigue behaviour requires the definition of a system that obeys thermodynamics laws. for practical purposes, it is considered that the material subjected to the analysis is a closed system since there is no mass inter-change with the environment, even though there is heat transfer through the boundaries. the dissipative process during the energy transformation can be assumed as fatigue damage. typically, it is presumed that, for a volume of product v going through cyclic loadings, the power w used up in one cycle is either dissipated as heat (q) t t m. a. fauthan et alii, frattura ed integrità strutturale, 62 (2022) 289-303; doi: 10.3221/igf-esis.62.21 291 or taken in to elicit variation of the internal energy (u) [20]. according to the first law of thermodynamics, the equation is expressed by:         w q u (1) the advantage of utilising thermodynamic forces and flows is that the entropy production σ can be explained in terms of experimentally quantifiable amounts. for this reason, during the dissipative process, high-quality energy degrades to lowgrade energy, which is a procedure called entropy generation [21]. entropy generation method n fatigue, the dissipative process p = p(ζ) depends on a time-dependent phenomenological variable 𝜁. when defined in general terms, the change in system’s entropy, ds through a form of modification is connected to δq by: ds=δq/t (2) where t is the temperature. entropy production rate depends on dissipative process p, and its rate is σ = ds/dt                    i id s s p xj dt p t (3) where is x =       i s p p the thermodynamics forces and j =    t is the thermodynamics flows. in this research, the dissipative process is the plastic strain involving fatigue [23]. the measure of system degradation, w. so, let d is the rate of degradation d = dw/dt :                  pdw w d yj dt p t (4) from above equation, the degradation of the system varies in the same manner between dissipative process p and the entropy generation. the combined parameter in eqns. (3) and (4) is the thermodynamic flow, j, a degradation coefficient can be expressed as:       / /     / /               i i w p py w b x s p p s (5) from eqn. (4) and eqn. (5), the degradation can be defined as:        p dwfda d yj bxj b dt t dn (6) some researchers [25] have mentioned in their research that :  4 2      p y dw k at dn (7) therefore, i m. a. fauthan et alii, frattura ed integrità strutturale, 62 (2022) 289-303; doi: 10.3221/igf-esis.62.21 292  4 2       y kda da at b dn fdt t (8) the following equation assumes the relationship between plastic deformation and the thermal dissipation in the second law of thermodynamics in solids with internal friction [26]: 2  /    .    /  p qw t j grad t t (9) in this instance  signifies the rate at which entropy is manufactured (  ≥ 0 ), jq is the heat flux, t the temperature of the surface, and pw is the recurring plastic energy mass per unit which comes from the calculation from morrow’s estimate [27].  p fw an (10) constants a and α are from the material value, which can be found using this equation:  2 , ,2         b cb c f f f c b a n c b (11) where '   f and ' f are cyclic ductility and fatigue strength coefficient, respectively. then, the terms b and c are the fatigue strength exponent and the fatigue ductility exponent, respectively. multiple linear regression (mlr) lr was chosen to develop a relationship between entropy and the applied load as well as stress ratio to ensure the linear relation between dependent and independent variables. mlr is able to immediately predict the dependent variable by matching the observational data and thus eliminating the need for repeated research with commercial software. the general multiple regression model was defined to be:  i 1 1 2 2  .             i i n in if x x x x (12) mlr attempts to model the relationship between two or more explanatory variables and a response variable by fitting a linear equation to observed data. every value of the independent variable is associated with a value of the dependent variable. from the eqn. (12),  if x is the dependent variable (entropy of the material) and ix is the ith independent variable. there are two independent variables in this study: (1) load applied and (2) stress ratio.  i represents the intercept, which is a constant, 1 represents the slope of the linear relationship between the means of the dependent and independent variables, and e is the random error with a mean of 0. additionally, this work aimed to provide a reliable solution to predict fatigue life. methodology he methodology implemented in this study begins with the determination of fatigue crack growth and temperature evolution. in fig. 1, the process flow of the study is shown. this paper starts from the material preparation until the development of mlr. after the material preparation, the fatigue crack growth test was conducted to determine the stress intensity factor using the linear elastic fracture mechanics (lefm) principle. during the test, besides observing the m t m. a. fauthan et alii, frattura ed integrità strutturale, 62 (2022) 289-303; doi: 10.3221/igf-esis.62.21 293 fatigue crack growth rate, the evolution of the surface temperature was also monitored. the collected data were used for further investigation on entropy generation. all the data needed to be validated before proceeding with the development of mlr. the approach applied in this study begins by determining the fatigue crack development and the evolution of temperature. the study made use of the commercial az31b magnesium alloy. az31b is a wrought magnesium alloy with both notable room-temperature ductility and strength. figure 1: process flow of crack growth and entropy generation figure 2: geometry of the specimen with dimension in mm according to astm e647 figure 3: the setup of the ir sensor and the specimen m. a. fauthan et alii, frattura ed integrità strutturale, 62 (2022) 289-303; doi: 10.3221/igf-esis.62.21 294 the az31b’s mechanical properties are listed in tab. 1. the thickness of the specimen is 10 mm. properties young’s modulus (gpa) 44.8 poisson’s ratio 0.3 yield strength (mpa) 244 uts (mpa) 298 table 1: material properties of az31b [1] the specimens of compact tension (ct) were prepared following the recommendation of the astm e647 standard document as illustrated in fig. 2 to study the fatigue crack growth (fcg). the cnc milling machine and electrical discharge wire-cutting device were used to cut the sample to the required dimensions. the need to prepare a good quality sample is very important, which can be achieved by polishing and cleaning the sample using sandpaper with 600, 9000 and 1200 grids. therefore, no oxides and grease on the specimen’s surface are present to obtain accurate results during the thermos-effect measurement. furthermore, the exclusion of stress concentration on the surface could prolong the beginning of the fatigue crack. a uniaxial servo-hydraulic at a load capacity of 100kn was used to perform all the fcg experiments as in fig. 3. the temperature of the surface material was monitored and recorded using the non-contact infrared sensor. the usage of an infrared sensor is to enable the measurement of small fluctuation of temperature due to elastic deformation during the test. common equipment such as the thermocouple is not suitable for this set of tests. the specimen used a constant amplitude sinusoidal loading with a different load (2,600 n, 2,800 n and 3,000n) and different load ratios (r = 0.1, 0.4 and 0.7) [24] with constant frequency of 10 hz. according to previous work, to perform the lefm method, the stress applied should not exceed 0.8𝜎 of uts. considering the suitability of δk, the different load must be calculated using:  3/2 2       1         p p k f b w (13) and 3 4  (0.886 4.64 14.72 5.6     pf ) (14) b and w are the thickness of the specimen, pf is the geometry factor and 𝛼 is w/p where w/p should not exceed 0.2 as mentioned in the e647 standard document. during the test, the specimen’s temperature trend was detected with the infrared sensor which was set up with a 50 mm gap between the sensor and specimen according to the specification of the setting device. results and discussion fatigue crack growth he crack caused by fatigue can be monitored from the experiment. from the beginning of the process, the crack initiation of the specimen was shown. at the loading of 2,600n, the crack began after 4,343 cycles, while for the 2,800n load, cracking began after 3,739 cycles. during the loading of 3,000n, the specimen recorded the lowest cycle at 2,288 compared to the others. the increment of the amplitude loading led to shorter fatigue life at 2.87 x 104, 2.70 x 104, and 2.55 x 104 cycles, respectively. the test also explains that if a different load of 2,600n, 2,800n, and 3,000n was applied, the curve varies from each other since the load of 2,600n with 0.1 stress ratio has the longest fatigue life. the t m. a. fauthan et alii, frattura ed integrità strutturale, 62 (2022) 289-303; doi: 10.3221/igf-esis.62.21 295 difference does not mean that the specimen has different material properties but that it needs to be analysed using the loglog curve. figure 4: fatigue crack growth curve for the az31b magnesium alloy for stress ratio 0.1, 0.4, 0.7 after 2,600n was applied. next, the correlation between calculated δk and crack growth is explored. the data attained from the experiment showed three different results even though the setup of the experiment was the same. however, the scattered band of fatigue crack growth rate was estimated to be the same in the log-log relationship. fig. 4 depicts the confirmation of the linear relationship between da⁄dn and δk values in the double log scale. the constant m was calculated to be 3.6 for the stress ratio of 0.1, 0.4 and 0.7, while the c value was in the range of 1.0 x 10-7 to 3.0 x 10-10 (m/cycle)/ mpa.m1/2. entropy generation the evolution of the crack’s temperature throughout the fatigue crack growth investigation for all loads applied and stress ratio is displayed in fig. 5 (a). it shows that different loads with different stress ratios will give different results. moreover, the results show that the value changes go through three different phases. however, the temperatures show the same trend. from fig. 5 (b), at the beginning of the fcg test, which is in stage 1, the sudden movement and the disruptions of the grains will cause a rise in the surface temperature, which concerns 10% of the material’s lifecycle [21]. the phenomenon of intrusion and extrusion also occurs during this stage. after that, the temperature is more stable in stage 2 as the volume of heat generated is the same as the heat released to the surrounding. however, at the end of the test, the temperature begins to increase in a short time due to the more extensive plastic deformation compared to the deformation that occurs in the second stage. there was a progressive increase in the rate of fatigue crack growth as they tend to become unstable in stage 3 [11]. (a) m. a. fauthan et alii, frattura ed integrità strutturale, 62 (2022) 289-303; doi: 10.3221/igf-esis.62.21 296 (b) figure 5: the temperature evolution measured during fatigue a crack growth tests: (a) three different load and stress ratio (b) under 2,600n for stress ratio 0.1. from the experiment done, the development of the entropy generation for three various loads and three various stress ratios are different from each other. the temperature level utilised to examine the entropy generation remains in kelvin. for the majority of the fatigue life, the entropy generation was almost consistent [28]. entropy generation is       f w t since the temperature evolutions are small. for the purpose of comparison, the load of 2,600n is further investigated. fig. 6 shows that the relation between the fatigue crack growth and the energy dissipation is in a linear function for the three different stress ratio tests. however, it is obvious that the gradients of the three graphs are of different values. the difference indicates that during the crack growth, there were different amounts of energy dissipation for the three different stress ratios. in other words, energy dissipation is dependent on the stress ratio value. from other research [29], the energy dissipation is independent with the dimension, load, and stress ratio to each material. figure 6: the energy dissipation during the fatigue crack growth for different stress ratio however, the disparity on this matter can be explained in the relationship between δk and energy dissipation during the fatigue crack growth. the spread of the points in fig. 7 is nearly at the same trend. the difference is at the end of the test, m. a. fauthan et alii, frattura ed integrità strutturale, 62 (2022) 289-303; doi: 10.3221/igf-esis.62.21 297 where the lowest stress ratio, 0.1 showed the highest energy dissipated. this relationship shows that the energy dissipated is independent of the stress ratio. as the crack growth increases, the total entropy was calculated until the specimen fractures utterly. the total entropy generation when a load of 2,600 n was applied was 3.424, 3.101 and 2.922 mjm-3 k-1 for stress ratios of 0.1, 0.4 and 0.7, respectively. according to fig. 8, the total entropy generation decreased as a higher stress ratio was applied. this was due to the distribution of a higher energy per unit volume, which led to failure. it shows that with a higher entropy generation, the specimen should have a higher fatigue life. it shows that entropy generation with consideration to internal friction moved from a low value to a higher value as loads decreased due to the accumulation of internal friction. figure 7: the relationship between energy dissipated rate and delta k in different stress ratio for 2600n figure 8: total entropy generation with different loads and stress ratios. tab. 2 and fig. 9 show the statistical analysis for the cycle count. it is evident that the distribution offered the best fit for the cycle count information according to the goodness of fit criteria. a probability distribution is an analytical function that explains all the values that are possible and the probabilities that a random variable can take within a bounded range. this range varies between the lowest and highest potential value, however, the possible value that is most likely to be outlined on the probability distribution depends on a variety of elements. the p-value of each load applied shows the value of 0.975, 0.973 and 0.940. the p-value is a probability that measures the evidence against the null hypothesis. smaller p-values provide stronger evidence against the null hypothesis. to determine whether the data do not follow a normal distribution, compare the p-value to the significance level. because the p-value was greater than the significance level of 0.05, the value is acceptable [30][31]. for example, a significance level of 0.05 indicates a 5% risk of concluding that a difference exists when there is no actual difference. the analytical chart reveals that the points fall within the self-confidence limitations, showing that the m. a. fauthan et alii, frattura ed integrità strutturale, 62 (2022) 289-303; doi: 10.3221/igf-esis.62.21 298 straight line seems to have a relatively good fit for the data [32]. this suggests no proof that the value does not come from distribution for cycles count data of load used for 2,600n, 2,800n and 3,000n. it was evident that the distribution offered the best fit for the cycle count information according to the goodness of fit. fig. 10 shows the entropy correlation between the predicted and experimental values. correlation analysis is a method of statistical evaluation to study the strength of a relationship between two numerically measured and continuous variables. this method has been used by various researchers to calculate the accuracy of empirical data with the predicted fatigue life data. the plot shows that all points are fitted fit within the range of 1:2 and 2:1 correlation margin. as all of the points were scattered within the lines, the simulated and experimental fatigue lives were determined to be within the acceptable limit. load applied, n mean st dev ad p-value 2600 16467 7683 0.127 0.975 2800 16962 6270 0.128 0.973 3000 15446 6427 0.151 0.940 table 2: the statistical results of cycles count data. (a) (b) (c) figure 9: the probability distribution of fatigue crack growth at different load of (a) 2600n; (b) 2800n; (c) 3000n m. a. fauthan et alii, frattura ed integrità strutturale, 62 (2022) 289-303; doi: 10.3221/igf-esis.62.21 299 figure 10: relationship between predicted and experimental entropy multiple linear regression to calculate the relationship between two or more independent variables and one reliant variable, mlr was utilised. the regression design can describe the indirect regression examination with just one explanatory variable by utilising a twodimensional plot of the reliant variable as a function of the independent variable [33]. the regression has five key assumptions: 1) linear relationship, 2) multivariate normality, 3) no or little multicollinearity, 4) no autocorrelation, and 5) homoscedasticity. from the data set, the straight line can be obtained to represent the model of regression. moreover, the r2 value determines fit consistency. nonetheless, there are many explanatory variables associated with mlr analysis and, as a result, the presumptions of linearity, homoscedasticity, and normality must be tested to confirm that the mlr-based entropy models obtained in this research can be generated with valid inferences. in statistics, the response surface methodology as in fig. 11, explores the relationships between several explanatory variables and one or more response variables. response surface plots such as contour and surface plots are useful for establishing desirable response values and operating conditions. in a contour plot, the response surface is viewed as a two-dimensional plane where all points that have the same response are connected to produce contour lines of constant responses. overall, the response surface plot in fig. 11 shows that the entropy varies inversely with the load applied and linearly with the stress ratio (independent variables), which validates the linearity of the mlr-based entropy model presumption. figure 11: the response surface for entropy mlr-based entropy model next, the assumptions of the mlr model were assessed. the four different conditions that need to be evaluated for the multiple regression to give a valid result are the linear function, independent function, normal distribution and equal variance [34]. the results are shown in fig. 12. hence, all the mlr-based entropy models justified the requirement that most of the error terms are generally dispersed. when the goodness of fit, homoscedasticity, normality, and linearity of the mlr-based entropy model had been examined, the model was verified by contrasting the entropy values by the models with those observed from the experiment for 3000n, as presented in fig. 13. from that figure, the entropy anticipated by the mlr m. a. fauthan et alii, frattura ed integrità strutturale, 62 (2022) 289-303; doi: 10.3221/igf-esis.62.21 300 based entropy model shows noble conformity with the entropy values from the experiments, with an r2 value of 0.9760. the r2 value is more significant than 0.9000, which offers the dependability of the model in predicting the entropy of the specimen [33]. (a) (b) (c) (d) figure 12: observation of multiple regression. next, the mlr analysis was applied to produce a meaningful entropy prediction model. the set of data that contains the entropy generation values of the ct specimens, stress ratio (r), and load applied (p), as shown in eqn. (12), was utilised to develop the mlr-based entropy models. the mlr-based entropy generation model or also known as the predicted entropy (γ) was obtained as:  = 5.827 0.001148p + 0.8044r (15) therefore, the regression model parameters are: 𝛼 = 5.827 1 = -0.001148 2 = 0.8044 once the assumption of the mlr-based entropy model was clarified to be acceptable, the models were compared to the experimental values done with a load of 3,000n. tab. 4 shows the percentage of the difference between the experimental and predicted data for 3,000n load conditions. the difference is less than 10%, and the determined entropy generation well 0.100.050.00-0.05-0.10-0.15 99 95 90 80 70 60 50 40 30 20 10 5 1 residual pe rc en t normal probability plot (response is entropy) 987654321 0.05 0.00 -0.05 -0.10 observation order re sid ua l versus order (response is entropy) 0.080.040.00-0.04-0.08 3.0 2.5 2.0 1.5 1.0 0.5 0.0 residual fr eq ue nc y histogram (response is entropy) 3.43.33.23.13.02.92.82.72.62.5 0.05 0.00 -0.05 -0.10 fitted value re sid ua l versus fits (response is entropy) m. a. fauthan et alii, frattura ed integrità strutturale, 62 (2022) 289-303; doi: 10.3221/igf-esis.62.21 301 forecasts the experimental data under new load conditions. this shows that the majority of the predicted entropy generation was near to a comparable experimental value. figure 13: comparison between the entropy predicted by the mlr-based entropy and entropy observed from the experiment for load 3000n. stress ratio experimental entropy predicted entropy % of differences 0.1 2.956 3.090 4.6% 0.4 2.607 2.849 9.3% 0.7 2.536 2.608 2.8% table 3: the percentage of difference entropy generation concerning the experimental data for 3000n. conclusions his research shows that entropy generation was deployed as an effective way of measuring the crack growth behaviour of a material with changes in temperature during the fatigue process. the tests were done using compact tension made of az31b magnesium alloy for load ratios of 0.1, 0.4, and 0.7 with different loads of 2,600n, 2,800n and 3,000n. the fatigue crack growth life increased with a decrease in the value of the stress ratio. an approach to developing the mlr relationship between the entropy generation applied load and stress ratio was shown in this paper. the assessment of entropy generation through energy dissipation is needed by using an analytical method. throughout the fatigue test, the entropy generation can be determined from the temperature evolution. by performing compact tension tests, various stress ratios of 0.1, 0.4 and 0.7 were used on the specimen with applied loads of 2,600n, 2,800n and 3,000n. from the test, the lowest entropy generation was 2.536 mjm-3 k-1 when a 3,000n load with a stress ratio of 0.7 was used for the specimen. note that the deviation of entropy generation represents a change in the internal friction between the two loads. therefore, if the entropy generation can be determined and the relationship graphs can be plotted from the fatigue test, then the prediction of the internal friction can be done. as an outcome, the predicted regression model for load 3,000n based on the applied load and stress ratio was discovered to concur with the outcomes of the experiment, with just 9.3% from the real experiment where the entropy values obtained from the experiment and regression model were in good agreement. the results were indeed encouraging, where the percentage difference between the mlr-based entropy models was less than 10%. through this study, the data collected also will be beneficial to new approaches to predict fatigue life and get better results such as artificial intelligence. artificial intelligence is used to solve complex tasks by linking patterns to real-valued quantities by integrating data science and computational resources. an artificial neural network (ann) is trained on experimentally determined data that is highly relevant in terms of fatigue. load stress, hardness and defect size are the three main parameters that are defined as input arguments. the main fields of application are pattern recognition, classification, time series forecasting, and signal processing. artificial neural networks (anns) are computing systems started by biological t m. a. fauthan et alii, frattura ed integrità strutturale, 62 (2022) 289-303; doi: 10.3221/igf-esis.62.21 302 neurons such as the human brain. anns are able to learn from an experience similar to how humans learn. after total fracture occurs at a certain load level, defect size is evaluated by fracture surface analysis. therefore, various methods have been developed by researchers because there is always a margin for improvement to make fatigue life prediction more accurate. acknowledgments he authors graciously acknowledge the financial support provided by universiti kebangsaan malaysia (frgs/1/2019/tk03/ukm/01/3 and dip-2019-015) and universiti pertahanan nasional (frgs/1/2018/tk03/upnm/03/1). reference [1] xiong, y., yu, q. and jiang, y. (2012). multiaxial fatigue of extruded az31b magnesium alloy, mater. sci. eng. a, 546, pp. 119–128. doi: 10.1016/j.msea.2012.03.039. [2] osara, j. a. and bryant, m. d. (2019). thermodynamics of fatigue: degradation-entropy generation methodology for system and process characterization and failure analysis, entropy, 21(7), pp. 1-24. doi: 10.3390/e21070685. [3] gu, c., lian, j., bao, y. and münstermann, s. (2019). microstructure-based fatigue modelling with residual stresses: prediction of the microcrack initiation around inclusions, mater. sci. eng. a, 751, pp. 133–141. doi: 10.1016/j.msea.2019.02.058 [4] kahirdeh, a., sauerbrunn, c., yun, h., and modarres, m. (2017). a parametric approach to acoustic entropy estimation for assessment of fatigue damage, int. j. fatigue, 100, pp. 229–237. doi: 10.1016/j.ijfatigue.2017.03.019. [5] wang, z., et al. (2021). in-situ synchrotron x-ray tomography investigation of damage mechanism of an extruded magnesium alloy in uniaxial low-cycle fatigue with ratcheting, acta mater., 211, pp. 1-13. doi: 10.1016/j.actamat.2021.116881 [6] wang, x.g., ran, h.r., jiang, c., fang, q.h. (2018). an energy dissipation-based fatigue crack growth model, int. j. fatigue, 114. doi: 10.1016/j.ijfatigue.2018.05.018 [7] fan, j. (2018). high cycle fatigue behavior evaluation of q235 steel based on energy dissipation, jixie gongcheng xuebao/journal mech. eng. doi: 10.3901/jme.2018.06.001. [8] meneghetti, g., ricotta, m., atzori, b. (2016). the heat energy dissipated in a control volume to correlate the fatigue strength of bluntly and severely notched stainless steel specimens, procedia struct. integr., 2, pp. 2076–2083, doi: 10.1016/j.prostr.2016.06.260. [9] meneghetti, g., ricotta, m., pitarresi, g. (2019). infrared thermography-based evaluation of the elastic-plastic j-integral to correlate fatigue crack growth data of a stainless steel, int. j. fatigue, 125, pp. 149–160, doi: 10.1016/j.ijfatigue.2019.03.034. [10] wang, x.g., crupi, v., jiang, c., feng, e.s., guglielmino, e., wang, c.s. (2017). energy-based approach for fatigue life prediction of pure copper, int. j. fatigue, 104, pp. 243–250. doi: 10.1016/j.ijfatigue.2017.07.025. [11] klingbeil, n.w. (2003). a total dissipated energy theory of fatigue crack growth in ductile solids, int. j. fatigue, 25(2), pp. 117–128. doi: 10.1016/s0142-1123(02)00073-7. [12] guo, q., guo, x., fan, j., syed, r., wu, c. (2015). an energy method for rapid evaluation of high-cycle fatigue parameters based on intrinsic dissipation, int. j. fatigue. doi: 10.1016/j.ijfatigue.2015.04.016. [13] kahirdeh, a., khonsari, m.m. (2015). energy dissipation in the course of the fatigue degradation: mathematical derivation and experimental quantification, int. j. solids struct., 77. doi: 10.1016/j.ijsolstr.2015.06.032. [14] teng, z., wu, h., boller, c., starke, p. (2020). thermography in high cycle fatigue short-term evaluation procedures applied to a medium carbon steel, fatigue fract. eng. mater. struct., 43(3), pp. 515–26. doi: 10.1111/ffe.13136. [15] mohammadi, b., mahmoudi, a. (2018). developing a new model to predict the fatigue life of cross-ply laminates using coupled cdm-entropy generation approach, theor. appl. fract. mech., 95, pp. 18–27. doi: 10.1016/j.tafmec.2018.02.012. [16] wang, j., yao, y. (2017). an entropy based low-cycle fatigue life prediction model for solder materials, entropy, 19(10). doi: 10.3390/e19100503. [17] teng, z., wu, h., boller, c., starke, p. (2020). thermodynamic entropy as a marker of high-cycle fatigue damage accumulation: example for normalized sae 1045 steel, fatigue fract. eng. mater. struct., 43(12), pp. 2854–2866, t m. a. fauthan et alii, frattura ed integrità strutturale, 62 (2022) 289-303; doi: 10.3221/igf-esis.62.21 303 doi: 10.1111/ffe.13303. [18] wang, j., jiang, w., wang, q. (2019). experimental and numerical evaluation of fatigue crack growth rate based on critical plastically dissipated energy, int. j. fatigue, 118, pp. 87–97. doi: 10.1016/j.ijfatigue.2018.09.003. [19] xiao-qing, l., hong-xia, z., zhi-feng, y., wen-xian, w., ya-guo, z., qian-ming, z. (2013). fatigue life prediction of az31b magnesium alloy and its welding joint through infrared thermography, theor. appl. fract. mech., pp. 1–7. doi: 10.1016/j.tafmec.2013.10.001. [20] ribeiro, p., petit, j., gallimard, l. (2020). experimental determination of entropy and exergy in low cycle fatigue, int. j. fatigue, , pp. 105333. doi: 10.1016/j.ijfatigue.2019.105333 [21] nourian-avval, a., khonsari, m.m. (2021). rapid prediction of fatigue life based on thermodynamic entropy generation, int. j. fatigue, 145, pp. 106105. doi: 10.1016/j.ijfatigue.2020.106105 [22] kong, y.s., abdullah, s., schramm, d., omar, m.z., haris, s.m. (2019). development of multiple linear regressionbased models for fatigue life evaluation of automotive coil springs, mech. syst. signal process., 118, pp. 675–695. doi: 10.1016/j.ymssp.2018.09.007. [23] hajshirmohammadi, b., khonsari, m.m. (2020). on the entropy of fatigue crack propagation, int. j. fatigue, 133, pp. 105413. doi: 10.1016/j.ijfatigue.2019.105413. [24] rabbolini, s., beretta, s., foletti, s. (2016). fatigue crack growth in low cycle fatigue: an analysis of crack closure based on image correlation, procedia struct. integr., 1, pp. 158–165. doi: 10.1016/j.prostr.2016.02.022. [25] stephens, r.i., fatemi, a., stephens, r.r. & fuchs, h.o. (2000). metal fatigue in engineering, 2nd edition. united states of america, john wiley & sons. [26] jang, j.y., khonsari, m.m. (2018). on the evaluation of fracture fatigue entropy, theor. appl. fract. mech., 96, pp. 351–361. doi: 10.1016/j.tafmec.2018.05.013. [27] ontiveros, v., amiri, m., kahirdeh, a., modarres, m. (2017). thermodynamic entropy generation in the course of the fatigue crack initiation, fatigue fract. eng. mater. struct., 40(3). doi: 10.1111/ffe.12506. [28] naderi, m., amiri, m., khonsari, m.m. (2010). on the thermodynamic entropy of fatigue fracture, proc. r. soc. a math. phys. eng. sci., 466(2114), pp. 423–438, doi: 10.1098/rspa.2009.0348. [29] liakat, m., khonsari, m.m. (2014). rapid estimation of fatigue entropy and toughness in metals, mater. des., 62, pp. 149–157. doi: 10.1098/rspa.2009.0348. [30] mansor, n.i.i., abdullah, s., ariffin, a.k. (2017). discrepancies of fatigue crack growth behaviour of api x65 steel, j. mech. sci. technol., 31(10), pp. 4719–4726. doi: 10.1007/s12206-017-0918-2. [31] asadi, s., amiri, s.s., mottahedi, m. (2014). on the development of multi-linear regression analysis to assess energy consumption in the early stages of building design, energy build. doi: 10.1016/j.enbuild.2014.07.096. [32] gope, p. (1999). determination of sample size for estimation of fatigue life by using weibull or log-normal distribution, int. j. fatigue, 21(8), pp. 745–752. doi: 10.1016/s0142-1123(99)00048-1. [33] castillo, e., fernández-canteli, a., pinto, h., lópez-aenlle, m. (2008). a general regression model for statistical analysis of strain-life fatigue data, mater. lett., 62(21–22), pp. 3639–3642. doi: 10.1016/j.matlet.2008.04.015. [34] ciulla, g., amico, a.d. 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/hrv (za stvaranje adobe pdf dokumenata najpogodnijih za visokokvalitetni ispis prije tiskanja koristite ove postavke. stvoreni pdf dokumenti mogu se otvoriti acrobat i adobe reader 5.0 i kasnijim verzijama.) /hun 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/pdfxoutputintentprofileselector /documentcmyk /preserveediting true /untaggedcmykhandling /leaveuntagged /untaggedrgbhandling /usedocumentprofile /usedocumentbleed false >> ] >> setdistillerparams << /hwresolution [2400 2400] /pagesize [612.000 792.000] >> setpagedevice microsoft word numero_37_art_11 h.a. richard et alii, frattura ed integrità strutturale, 37 (2016) 80-86; doi: 10.3221/igf-esis.37.11 80 focussed on multiaxial fatigue and fracture 3d-mixed-mode-loading: material characteristic values and criteria’s validity h. a. richard, a. eberlein university of paderborn, institute of applied mechanics, pohlweg 47-49, 33098 paderborn, germany richard@fam.upb.de, http://mb.uni-paderborn.de/fam/ eberlein@fam.upb.de, http://mb.uni-paderborn.de/fam/ abstract. in many structures and components cracks, which are exposed to a 3d-mixed-mode-loading, occur due to multiaxial loading situation. a reliable evaluation of those components requires fracture mechanical criteria validated by experimental investigations. within this article 3d-mixed-mode criteria for static as well as cyclic loadings will be presented. experiments for pure mode i-loading, pure mode ii-loading, pure mode iiiloading and 2das well as 3d-mixed-mode-loading combinations are performed using specially developed specimens and loading devices. by comparing the experimental results with criteria a widely validity of criteria and a generally conservative behaviour are revealed. keywords. 3d-mixed-mode criteria; threshold values; fracture toughness; ctsr-specimen. introduction n many practical cases crack growth leads to fatigue fracture or abrupt failure of components and structures. for reasons of a reliable quantification of the endangerment due to sudden fracture of a component it is of huge importance to know the limiting values (fracture toughness) for the beginning of instable crack growth as well as the threshold values for the fatigue crack growth. this contribution deals with the complex problem of crack growth under mixed-mode-loading. it will present a comparison between concepts, which characterises the superposition of mode i and mode ii (2d-mixed-mode) as well as the superposition of all three modes (mode i, mode ii and mode iii) for spatial loading conditions, and experimental results for stable and unstable crack growth. multiaxial stress field and fracture modes n linear-elastic fracture mechanics the characterisation of the loading situation at the crack front and in its neighbourhood is based on stresses and displacements. generally, a crack can be loaded by a multiaxial stress field consisting of six stress components. as fig. 1 exemplary shows on a boarder crack with the length a in a volume cube, different stresses causes various crack loadings (fracture modes). σy induces a crack opening (mode i). a mode iloaded crack grows perpendicular to the normal stress σy. due to the shear stress τxy the crack kinks out of its previous direction in shear stress plane. in this case a mode ii-loading on crack is present. the shear stress τyz effects an anti-plane shear loading (mode iii) at the crack, which leads to a crack twisting. furthermore the initial crack separates in multiple daughter crack segments. i i h.a. richard et alii, frattura ed integrità strutturale, 37 (2016) 80-86; doi: 10.3221/igf-esis.37.11 81 mode i mode ii mode iii figure 1: stress components and fracture modes nevertheless, cracks in real structures often experience complex loading conditions, which are to a superposition of the three basic fracture modes. for plane crack problems in the case of 2d-mixed-mode the stress distribution can be described with the help of the near field solution and the polar coordinates r and φ (see fig. 1) by the following equation as [1]:        iiijiiiijiij 2 1 fkfk,r    rπ (1) with i, j = x, y. the calculation of the stress distribution spatially crack problems loaded under 3d-mixed-mode is completed by a third term to:          iiiijiiiiiijiiiijiij 2 1 fkfkfk,r    rπ (2) with i, j = x, y, z. ki, kii and kiii are from irwin established stress intensity factors. they are assigned to the basic fracture modes of a crack and defined by eq. 3. the stress intensity factor depends on the stress (σy, τxy or τyz), the crack length a and on the boundary correction factor (yi, yii or yiii). if the loading of a structure creates a non-symmetrical, singular stress field in the vicinity of the crack front, then the crack front deforms in a way that not only an opening, but also a planar and nonplanar displacement of the two crack flanks can be found. consequently, the stress field in the vicinity of the crack is superimposed by all of three stress intensity factors ki, kii and kiii. iyi yk  aπ iixyii yk  aπ iiiyziii yk  aπ (3) unstable crack growth under 2dund 3d-mixed-mode-loading f enormous interest concerning the part dimensioning is the beginning of unstable crack growth, because the consequence often is a high material and immaterial damage. to predict unstable crack growth under 2dand 3d-mixed-mode-loading many criteria exist, which compare the occurred stress or stress intensity factor with a critical stress σc or the fracture toughness kic. some of them are listed below. o h.a. richard et alii, frattura ed integrità strutturale, 37 (2016) 80-86; doi: 10.3221/igf-esis.37.11 82 3d-criterion by richard the beginning of unstable crack growth as well as the crack growth direction e.g. can be determined by using the following fracture criteria:  criterion by erdogan and sih [2]  2d-criterion by richard [3, 4]  criterion by schöllmann et al. [1, 5, 6]  3d-criterion by richard [4, 7]. within this contribution only the 3d-criterion by richard is described explicitly. this criterion is developed in order to simplify the prediction of crack growth under multiaxial loading. due to the fact that engineers often use the classical stress hypotheses the formula is helpful for practical application. unstable crack growth will occur, if the local loading condition along the crack front reaches the fracture toughness value. this situation can be described by the following fracture criterion [4]:     ic2iii22ii12iiv 44 2 1 2 kkkk k k   (4) where α1 = kic/kiic and α2 = kic/kiiic. for the material parameters α1 = 1.155 and α2 = 1.0 eq. 4 is in excellent agreement with the kv-prediction of the criterion by schöllmann et al. experimental investigations for unstable crack growth under mixed-mode-loading conditions in the following, experimental investigations on 2dand 3d-mixed-mode loadings are presented. in the past several specimen types for 2d-mixed-mode problems have been proposed [3, 7, 8]. among others, the cts-specimen together with its loading device [9, 10] has proven its applicability. therefore only the cts-specimen will be discussed in the following. the loading device in fig. 2 allows applying pure mode i-, pure mode iias well as almost every 2d-mixedmode-loading combination to the cts-specimen by using just a uniaxial tension testing machine. for the purpose of varying the mixed-mode-loading only the loading angle  has to be changed. figure 2: loading device for plane mixed-mode i + ii-loading referring to the afm-specimen [11] a new specimen, so-called ctsr-specimen, with the corresponding loading device, shown in fig. 3, has been developed [12] for investigating 3d-mixed-mode-loadings. this new specimen and corresponding loading device enables any combination of mixed-mode-loading including pure mode i-, pure mode iiand pure mode iii-loading. the loading device allows to generate any ratio of mode i to mode ii/mode iii by changing the loading angle α in 15°-steps. by rotating the so-called turret also in 15°-steps (varying the second loading angle β) inside h.a. richard et alii, frattura ed integrità strutturale, 37 (2016) 80-86; doi: 10.3221/igf-esis.37.11 83 the loading device the ratio of mode ii or mode iii load is set. both loading angles α and β can be adjusted in the range from 0° to 90°, whereby the load line of action always passes through the centre of specimen. the detailed ctsrspecimen geometry with relevant dimensions is illustrated in [13, 18]. this paper will focus on eperimental results investigated by ctsr-specimen and the corresponding loading device. figure 3: loading device for 3d-mixed-mode-loading comparison of experimental results with fracture criteria in the following results of fracture experiments and comparison with 3d-criterion by richard are shown and discussed. the points in fig. 4 are the fracture toughness values for pmma, measured on ctsr-specimens. by comparison with the 3d-criterion by richard or the criterion by schöllmann et al., mentioned in this paper, a significant variation of the fracture toughness values determined by mode iii-loading is noticeable. the resulting fracture toughness values for pure mode iii-loading kiiic are around factor 2.7 above the hypothesis [14]. furthermore, it is visible that the less the mode iii ratio the better the congruence with the predictions of the hypothesis. as soon as there is no mode iii-loading the measured values are very close to the criterion by richard. the reason for the big spread between the hypothesis and the mode iii fracture toughness values is possibly the building of a new fragmented crack front with many facets, which is not considered in the criteria yet. h.a. richard et alii, frattura ed integrità strutturale, 37 (2016) 80-86; doi: 10.3221/igf-esis.37.11 84 figure 4: experimental results for pmma in contrast to the criterion by richard fatigue crack growth under 2dand 3d-mixed-mode-loading mong the experimental determination of the fracture limit surface presented in fig. 4 for pmma the investigation of the threshold value surface of different materials under 2dand 3d-mixed-mode-conditions is important too, to characterise the crack growth behaviour under combined loading situations. cyclic comparative stress intensity factor for fatigue crack growth a crack, which is subjected to an arbitrary mixed-mode-loading, is able to propagate under fatigue crack growth conditions, if the local crack front loading combined of mode i, mode ii and mode iii portions is located in between the threshold value and a critical cyclic stress intensity factor. this condition can be written down by the formula: icvthi, δδδ kkk  (5) hereby δkv is the cyclic comparative stress intensity factor, which can be derived from eq. 4 using as before α1 = 1.155 and α2 = 1.0: 2 iii 2 ii 2 i i v δ4δ3365δ 2 1 2 δ δ kk,k k k  (6) experimental determinations of threshold values under combined loading the mixed-mode threshold values were determined using the load rising amplitude test [15, 16, 17]. before the fatigue test the specimen were pre-cracked under cyclic compression. the advantage of pre-cracking the specimen in cyclic compression are, however, the left residual tensile stresses, which may cause cyclic plastic deformation and crack initiation [15]. the threshold tests were performed at a constant load ratio of r = 0.1 by increasing the load amplitude in a h.a. richard et alii, frattura ed integrità strutturale, 37 (2016) 80-86; doi: 10.3221/igf-esis.37.11 85 steps until the threshold value is reached. a more detailed information to the experimental procedure and chosen parameters can be found in [18]. comparison of experimental results with fatigue criterion the mixed-mode threshold values determined by the procedure described above are illustrated in fig. 5. the threshold values of al7075-t651 measured by schirmeisen [13] in comparison of the criterion by richard show for pure mode iloading, 2d-mixed-mode-loading and for mixed-mode ii + iii-loading with small mode iii-ratio a good congruence with the threshold value surface of the criterion by richard. a significant variation, with around a factor of 2.2 above the hypothesis [14], depict the threshold values for pure mode iii-loading. the threshold values measured by eberlein [18] in total are closer to the threshold value surface of the hypothesis. the variation in average is around factor 1.8 above the hypothesis. in addition a comparison of other materials [19, 20] show partially similar threshold value ratios δkii,th/δki,th and δkiii,th/δki,th (see threshold values for austenitic steel in fig.5). ferritic steel exhibits completely other threshold value ratios. nevertheless, the determined mixed-mode threshold values for different materials in comparison with the criterion by richard point out that this criterion possesses a widely validity and a generally conservative behaviour. figure 5: mixed-mode threshold values in contrast to criterion by richard references [1] richard, h.a.., sander, m., fulland, m., theoretical crack path prediction, ffems, 28 (2005) 3–12. [2] erdogan, f., sih, g.c., on the crack extension in plates under plane loading and transverse shear, j. basic eng., 85 (1963) 519-525. h.a. richard et alii, frattura ed integrità strutturale, 37 (2016) 80-86; doi: 10.3221/igf-esis.37.11 86 [3] richard, h.a., bruchvorhersage bei überlagerter normalund schubbeanspruchung von rissen, vdi-verlag, düsseldorf, (1985). [4] richard, h.a., safety estimation for construction units with cracks under complex loading. int. j. mater. product. technol., 3 (1988) 326-338. [5] schöllmann, m., richard, h.a., kullmer, g., fulland, m., a new criterion for the prediction of crack development in multiaxially loaded structures. int. j. frac., 117 (2002) 129-141. [6] schöllmann, m., kullmer, g., fulland, m., richard, h.a., a new criterion for 3d crack growth under mixed-mode (i + ii + iii) loading. in: m.m. de freitas (ed.), proceedings of the 6th international conference on biaxial/multiaxial fatigue & fracture, volume 2, lisboa, portugal, (2001) 589-596. [7] richard, h.a., schöllmann, m., fulland, m., sander, m., experimental and numerical simulation of mixed mode crack growth, in: m.m. de freitas (ed.), proceedings of the 6th international conference on biaxial/multiaxial fatigue & fracture, lisboa, portugal, 2 (2001) 623-630. [8] richard, h.a., in: m.w. brown, k.j. miller (eds.), biaxial and multiaxial fatigue, mechanical engineering publications, london, (1989) 217-229. [9] richard, h.a., benitz, k., a loading device for the creation of mixed mode in fracture mechanics, int. j. frac., 22 (1983) r55-58. [10] richard, h.a., in: s.r. valluri et al. (eds.), advances in fracture research, pergamon press, oxford, (1984) 33373344. [11] richard, h.a., praxisgerechte simulation des werkstoffund bauteilverhaltens durch überlagerte zug-, ebene schub und nichtebene schubbelastung von proben, vdi-verlag, düsseldorf, (1983) 269-274. [12] schirmeisen, n.-h., richard, h.a., weiterentwicklung der afm-probe zur experimentellen analyse räumlicher mixed-mode-beanspruchung von rissen, dvm-bericht 241, bruchmechanische werkstoffund bauteilbewertung: beanspruchungsanalyse, prüfmethoden und anwendungen, deutscher verband für materialforschung und –prüfung e.v. berlin (2009) 211-220. [13] schirmeisen, n.-h., risswachstum unter 3d-mixed-mode-beanspruchung, vdi-verlag, düsseldorf, (2012). [14] richard, h.a., schirmeisen, n.-h., eberlein, a., experimental investigations on mixed-mode-loaded cracks, proceedings of the 4th international conference on crack paths, cd-rom, gaeta, italy, (2012). [15] tabernig, b., pippan, r., determination of the length dependence of the threshold for fatigue crack propagation, engng. frac. mech., 69 (2002) 899-907. [16] campbell, j.p., ritchie, r.o., mixed-mode, high-cycle fatigue-crack growth thresholds in ti-6al-4v: i. a comparison of largeand short-crack behavior, engng. frac. mech., 67 (2000) 209-227. [17] nalla, r.k., campbell, j.p., ritchie, r.o., mixed-mode, high-cycle fatigue-crack growth thresholds in ti-6al-4v: role of small cracks, int. j. fat., 24 (2002) 1047-1067. [18] eberlein, a., einfluss von mixed-mode-beanspruchung auf das ermüdungsrisswachstum in bauteilen und strukturen. vdi-verlag, düsseldorf, (2016). [19] vojtek, t., pokluda, j., paths of shear-mode cracks in ferritic and austenitic steel. proceedings of the 4th international conference on crack paths, cd-rom, gaeta, italy, (2012). [20] vojtek, t., pippan, r., hohenwarter, a., holán, l., pokluda, j., near-threshold propagation of mode ii and mode iii fatigue cracks in ferrite and austenite, act. mater., 61 (2013) 4625-4635. << /ascii85encodepages false /allowtransparency false /autopositionepsfiles true /autorotatepages /none /binding /left /calgrayprofile (dot gain 20%) /calrgbprofile (srgb iec61966-2.1) /calcmykprofile (u.s. web coated \050swop\051 v2) /srgbprofile (srgb iec61966-2.1) /cannotembedfontpolicy /error /compatibilitylevel 1.4 /compressobjects /tags /compresspages true /convertimagestoindexed true /passthroughjpegimages true /createjobticket false /defaultrenderingintent /default /detectblends true /detectcurves 0.0000 /colorconversionstrategy /cmyk /dothumbnails false /embedallfonts true /embedopentype false /parseiccprofilesincomments true /embedjoboptions true /dscreportinglevel 0 /emitdscwarnings false /endpage -1 /imagememory 1048576 /lockdistillerparams false /maxsubsetpct 100 /optimize true 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/hrv (za stvaranje adobe pdf dokumenata najpogodnijih za visokokvalitetni ispis prije tiskanja koristite ove postavke. stvoreni pdf dokumenti mogu se otvoriti acrobat i adobe reader 5.0 i kasnijim verzijama.) /hun 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can be opened with acrobat and adobe reader 5.0 and later.) >> /namespace [ (adobe) (common) (1.0) ] /othernamespaces [ << /asreaderspreads false /cropimagestoframes true /errorcontrol /warnandcontinue /flattenerignorespreadoverrides false /includeguidesgrids false /includenonprinting false /includeslug false /namespace [ (adobe) (indesign) (4.0) ] /omitplacedbitmaps false /omitplacedeps false /omitplacedpdf false /simulateoverprint /legacy >> << /addbleedmarks false /addcolorbars false /addcropmarks false /addpageinfo false /addregmarks false /convertcolors /converttocmyk /destinationprofilename () /destinationprofileselector /documentcmyk /downsample16bitimages true /flattenerpreset << /presetselector /mediumresolution >> /formelements false /generatestructure false /includebookmarks false /includehyperlinks false /includeinteractive false /includelayers false /includeprofiles false /multimediahandling /useobjectsettings /namespace [ (adobe) (creativesuite) (2.0) ] /pdfxoutputintentprofileselector /documentcmyk /preserveediting true /untaggedcmykhandling /leaveuntagged /untaggedrgbhandling /usedocumentprofile /usedocumentbleed false >> ] >> setdistillerparams << /hwresolution [2400 2400] /pagesize [612.000 792.000] >> setpagedevice microsoft word numero_61_art_08_3477.docx m. i. meor ahmad et alii, frattura ed integrità strutturale, 61 (2022) 119-129; doi: 10.3221/igf-esis.61.08 119 focussed on the failure analysis of materials and structures predictive modelling of creep crack initiation and growth using extended finite element method (xfem) meor iqram meor ahmad, mohd anas mohd sabri, mohd faizal mat tahir department of mechanical and manufacturing engineering, faculty of engineering and built environment, universiti kebangsaan malaysia, 43600 ukm bangi, selangor, malaysia meoriqram@ukm.edu.my, anasms@ukm.edu.my, mfaizalmt@ukm.edu.my nur azam abdullah structural mechanics and dynamics research group, department of mechanical engineering, international islamic university malaysia, kuala lumpur, malaysia azam@iium.edu.my abstract. in this study, a numerical strategy for predictive modelling of creep in tension tests for the rectangular plate with a single crack and ctspecimen based on the extended finite element method (xfem) will be described in detail. a model of creep fracture initiation and creep crack growth (ccg) is developed, while the xfem is employed to spots located inside the finite element for the purpose of predicting crack potential and propagation. in order to characterize the creep fracture initiation, identification of c(t)integral formula is conducted. in addition, xfem and analytical solutions are also analyzed to look at the connection of c(t)-integral with time for a rectangular plate with a single crack under plane stress conditions. an illustration showing the sequence of stress distribution and displacement contour plots are also being presented. the stresses and displacements spread throughout the crack path have also been determined using ct-specimens. in addition, the creep cracks growth length with normalized time and the creep crack growth rate with the c(t)-integral are predicted to be related, indicating that the numerical results are in good accord with the experimental results. keywords. xfem; creep crack initiation and growth; c(t)-integral. citation: meor ahmad, m. i., mohd sabri, m. a., mat tahir, m. f., abdullah, n. a., predictive modelling of creep crack initiation and growth using extended finite element method (xfem), frattura ed integrità strutturale, 61 (2022) 119-129. received: 17.02.2022 accepted: 18.04.2022 online first: 27.04.2022 published: 01.07.2022 copyright: © 2022 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. introduction t is a common practice in the industry in which elastic-nonlinear viscous materials must withstand long duration under cyclic loads at high temperatures as that of turbine blades in jet engines. the focus should be on creep when evaluating the materials' resistance to deformation and failure over lengthy period of time at extreme temperatures under specified loads. creep is a plastic deformation process which is influenced by time and one of the main degradation mechanisms for i https://youtu.be/phobwclgk2m m. i. meor ahmad et alii, frattura ed integrità strutturale, 61 (2022) 119-129; doi: 10.3221/igf-esis.61.08 120 metals undergoing consistent stresses and temperatures ranging at approximately 0.3-0.5 of the melting point. nucleation, growth and coalescence of cavities on the grain boundaries are the main causes of creep failure [1]. a predictive approach is needed to make sure a safe running of the component operation for a specified period of time. by employing a finite element technique, a substantial amount of attempts was conducted to estimate the deformation and assess the durability of creep failure. in order to predict the creep crack growth, hsu and zhai [2] have suggested a finite element algorithm that may provide detail stress and strain distributions, the kinematics of the inelastic areas and the growing crack profile. the creep crack growth rates in the 32%-ni-20%-cr alloy incoloy 800 h at 800°c was associated with the fracture mechanics parameter c* integral by experimental and numerical investigations as mentioned by hollstein and kienzler [3]. yatomi et al. [4] then built a creep crack growth model to forecast the accelerated cracking at low c* values to deter-mine the trends between ccg rates at high and low c* values. it had been estimated and shown by zhang et al. [5] that the creep crack growth behaviour in cr-mo-v steel specimen and interaction between crack tip stress states and stress-dependent creep ductility had resulted in the rise of a broad range of c*-integral. the refinement of mesh to geometric discontinuities is required when predicting the stationary discontinuities using the conventional finite element method (fem). it is necessary to capture enough singular asymptotic field in the crack tip area by means of mesh refinement. but modelling a growing crack is significantly more laborious because the mesh needs to be continually updated to reflect the geometry of the discontinuity when the crack advances. in 1999, the ex-tended finite element (xfem) approach of belytschko and black was devised to relieve the weaknesses related to the meshing of crack surfaces. this strategy makes it easier to add local enrichment functions into a finite element approximation [6,7]. special enriched functions in combination with additional degrees of freedom ensure the occurrence of discontinuities. furthermore, earlier researches on xfem have demonstrated that the method can alleviate computational challenges, particularly when it comes to crack growth analysis. the strain accumulation criterion was used to analyze fatigue crack growth in a three-point bending specimen using xfem, and the simulation and experimental data were in good accordance [8]. furthermore, there was a strong connection between the numerical and experimental data obtained when xfem was used as a predictive tool to solve the problem of elastic fracture in the crack propagation of a chopped glass-reinforced composite during biaxial testing [9]. the xfem was used to simulate creep crack growth in ct and cts for p91 steel and 316 stainless steel at high temperature in the previous application [10]. besides that, the xfem was also carried out to model crack and crack growth behaviour in the power-law of creep materials [11]. mathematical formulation he constitutive law explains the elastic-nonlinear-viscous behaviour for uniaxial tension under small-scale creep conditions as:     nb e    (1) where  is the elastic strain rate, e is the young’s modulus, b is the creep coefficient and n is the creep exponent. the parameter c(t) describes the intensity of the near-tip fields in elastic-nonlinear viscous materials. the amplitude factor c(t), which is unknown from the asymptotic analysis, is influenced by elapsed time, remote load magnitude, crack configuration, and material properties. a self-similarity analysis conducted by riedel and rice [12] yielded the following relationship between j-integral and c(t) for planar stress:       2 1 1     ij kc t n t n et (2) under steady-state conditions at long times, c(t)→c*. ehler and riedel [13] proposed the following approximate formula for c(t) between small-scale creep and extensive creep:   * 1      ttc t c t (3) t m. i. meor ahmad et alii, frattura ed integrità strutturale, 61 (2022) 119-129; doi: 10.3221/igf-esis.61.08 121 where, 1 * 0 1 0 ,                 n pa a c bc h n w w p  (4)   2 *1   i t k t n ec (5) where a is the crack length, w is the specimen width, c=w a is the length of the uncracked ligament, h1 is a dimensionless function of n, σ0 is the reference stress, p is the applied stress, p0 is an appropriate reference load, ki is the stress intensity factor and tt is the characteristic time for transition from small-scale creep to extensive creep introduced by riedel and rice [12]. for this study, however, the value of c(t) is determined by using the line integral as the following:   * г     i ij j u c t w dy n ds x  (6) where, * 0 1     c ij c ij ij n w d n    (7) in which г is a vanishingly small counter-clockwise contour around the crack tip, n is the creep parameter, nj is the unit outward normal to г and ds is the arc length along г. iu is the component of displacement rate, w* is the strain energy rate density for the power law creep model, σij is the component of equivalent stress and cij is the component of creep strain rate. xfem introduces a numerical model of crack initiation and propagation in which the approximation for a displacement vector function, u, with the partition of unity enrichment is [14]:               1 2 1 21 2 1 1 1 1 1 1               mt mf mt mfn m i i j j k k k k i j k k n x u n x h a n x f x b n x f x b     u (8) where  in x is the nodal shape function,  jn x and are the new set of shape function associated with the enrichment part of the approximation. iu is the nodal displacement vector associated with the continuous part of the finite element solution,  h  represents a discontinuous jump function across the crack surfaces, 1, j ka b  and 2kb  are the enriched nodal degree of freedom vector for modelling crack faces and two crack tips, respectively. n is the number of nodes for each finite element, and m is the set of nodes that have the crack face (but excludes the crack tip) in their support domain. while, 1mt and 2mt are the sets of nodes associated with crack tips 1 and 2 in their influence domain and  ,   1, 2if x i represent mf as the crack tip enrichment functions. the first term technically applies to all nodes in the model, whereas the second term applies to nodes whose form function support crosses by the crack faces while the third and fourth terms are only applicable to nodes that cross at the crack tip. the heaviside function,  h  across the crack surfaces can be expressed as the following sign function:   1     ,                               0 1,                        if h otherwise   (9) where  * n x x , is the local axis perpendicular to the crack growth direction, x is a gauss point, x* is the point on the crack closest to x, and n is the unit outward normal to the crack at x. furthermore, the isotropic function of the asymptotic m. i. meor ahmad et alii, frattura ed integrità strutturale, 61 (2022) 119-129; doi: 10.3221/igf-esis.61.08 122 crack,  ,f r  , is:  , , , , 2 2 2 2      f r r sin cos sin sin sin cos        (10) where  ,r  is a polar coordinate system with its origin at the crack tip (as shown in fig. 1). figure 1: polar coordinate at the crack tip [15]. figure 2: xfem flowchart [16]. the xfem formulation procedure is illustrated in fig. 2. in the case of xfem elements, there may be changes in position and number of gauss points between load increments as the crack extends. therefore, updating material state variables is done continuously until the load increments are completed. whereas in crack propagation, the crack crosses the entire element that allows a reduced integration element to operate on plane problems such that stresses and strains are estimated in the middle of the element (on the integration point). furthermore, for the crack tip located outside of the element, it is unnecessary to take into account the singularity of the stresses when defining the elemental displacements [9]. to keep from having to model the m. i. meor ahmad et alii, frattura ed integrità strutturale, 61 (2022) 119-129; doi: 10.3221/igf-esis.61.08 123 stress singularity, the crack must propagate throughout an entire element. therefore, the xfem discontinuous displacement approximation in the crack propagation of plane problem is:       1 1     n m i i j j i j n x u n x h au (11) where  in x is the nodal shape function,  jn x is the new set of shape function associated with the enrichment part of the approximation. iu is the nodal displacement vector associated with the continuous part of the finite element solution,  h  represents a discontinuous jump function across the crack surfaces, ja is enriched nodal degree of freedom vector for modelling crack faces and two crack tips, respectively. n is the number of nodes for each finite element, and m is the set of nodes that have the crack face (but excludes the crack tip) in their support domain. the onset and direction of the crack extension must be specified in simulating the degradation and eventual failure of an enriched element during the computational simulation of the xfem formulation. the failure mechanism is made up of two ideas: a crack initiation criterion and a damage evolution law. cracking develops when stresses or strains fulfill certain crack initiation criteria as specified by the traction-separation law damage. subsequently, once the associated initiation criterion is met, the pace at which the cohesive stiffness degrades is described by the damage evolution law as specified by the displacement or energy release rate criterion. numerical simulation of creep fracture initiation and creep crack growth rectangular plate with a single crack ig. 3 shows a rectangular plate with a single crack with measurements, l=114.3 mm, w=25.4 mm and a=2 mm. super alloy inconel 800h at 650°c with e=154 gpa and v=0.33 was used as a specimen material. the creep model's power law is as shown in eqn. 1, with the creep coefficient b=1.34 x 10-30 (stress in mpa) and n=5. yang et al. [17] and meng et al. [11] had previously investigated the similar model. the damage of the traction-separation laws for the crack initiation and evolution is selected on the basis of the maximum principal stress (maxps) criterion with yield strength, σy=93 mpa and a 0.3 mm failure displacement. figure 3: geometry representation and boundary condition for rectangular plate specimen. the elements are of linear quadrilateral four-node type with decreased integration, while fully integrating the elements and subelements (integrating richer elements). the c*-integral here was 8.37e-03 kj/(m2h) with a stress intensity factor of =19.37 mpa.√m [23]. the values of the c(t)-integral gained from the domain form of the interaction integrals by employing the xfem technique in the simulation and both short-time estimation and approximate interpolation formulas are presented in fig. 4. f m. i. meor ahmad et alii, frattura ed integrità strutturale, 61 (2022) 119-129; doi: 10.3221/igf-esis.61.08 124 figure 4: solutions of the log-log plot of c(t)-integral near the crack tip in a rectangular plate with a single crack under plane stress. as shown in fig. 4, the results for the short times creep acquired from the three methods, which also includes the contours plotted, are strongly correlated. as for the long loading times, the results of the ehler-approximation riedel's interpolation and the steadystate value c* approach are moderately correlated with the xfem solution. furthermore, under the constant load, the values of c(t) indicated a declining trend as time increased. this suggests that while the load was maintained, the following creep deformation resulted in the crack tip stresses to relax. as shown in fig. 5 and fig. 6, the contour plots of the stress in the y-direction and the displacement magnitude are shown alongside the specimen's crack path. the crack spreads outwards from the center, with the most stress centered at the specimen's crack tip. figure 5: rectangular plate with a single crack: contour of stress in y-direction along the crack at (a) t=114 h, (b) t=556 h and (c) t=998 h (a) (b) (c) m. i. meor ahmad et alii, frattura ed integrità strutturale, 61 (2022) 119-129; doi: 10.3221/igf-esis.61.08 125 figure 6: rectangular plate with a single crack: contour of a magnitude of displacement along the crack at (a) t=114 h, (b) t=556 h and (c) t=998 h compact tension (ct) specimen as shown in fig. 7, a compact tension (ct) specimen of asme p92 steel welded joint, with w=20 mm, l=24 mm, ϕ=5 mm and a=10 mm employed at 650°c to further proceed with the creep crack growth study. the load p=2050 n is administered to the ct-specimen with an analytical pin connected to the specimen's hole to represent the bolt in the experiment, while a plane stress is applied on the linear four-node quadrilateral elements. figure 7: 2d-discretization domain of the specimen consisting of 5937 elements and 12380 nodes. a boundary condition in the upper hole was fixed at the x-axis (u1=0), while in the bottom hole it was fixed in all directions (u1, u2, ru2=0,0,0). zhao et al. [18] and yatomi et al. [19] had thoroughly examined the creep crack growth in such specimen by means of an fem analysis using node release technique. whereby zhao et al. [20] had investigated the experimental setup with e= 125 gpa, v=0.33, b=2.6353e-16 and n=5.23 being the material and creep properties. the damage for the traction-separation laws based on the maximum principal stress criterion (maxps) is applied to the enrichment elements with yield strength, 140yσ mpa and a failure displacement of 0.2 mm to introduce a crack initiation and evolution. starting with the explicit time integration, the program then automatically transitioned to the implicit thus permitted longer time increments and became stable. as can be seen in fig. 8 and fig. 9, the contour plots of the stress in the y-direction and the displacement magnitude become visible, spreading along the crack path. once the stress value at the contour of the crack tip area reached its maximum stress concentration zone (scz) under the tensile load, the crack will start to expand and evenly spread at the infinity parallel to the crack direction. (a) (b) (c) m. i. meor ahmad et alii, frattura ed integrità strutturale, 61 (2022) 119-129; doi: 10.3221/igf-esis.61.08 126 figure 8: ct specimen: distribution of stress in y-direction along the crack at (a) t=24 h, (b) t=64 h and (c) t=100 h (a) (b) (c) (a) (b) m. i. meor ahmad et alii, frattura ed integrità strutturale, 61 (2022) 119-129; doi: 10.3221/igf-esis.61.08 127 figure 9: ct specimen: distribution of a magnitude of displacement along the crack at (a) t=24 h, (b) t=64 h and (c) t=100 h. furthermore, when the relation of creep crack growth length pertaining to normalized time is plotted (fig. 10), the xfem solutions and the experimental results are comparatively well estimated. the increase trend of the creep crack growth length with the rising normalized time can be seen in fig. 10, represented by the current loading time, t and the life, ft of each specimen's creep crack growth. fig. 11 shows the representative creep crack growth rate with respect to c(t) for the xfem solution and experimental results. the xfem solution curve appears similar to that of the experimental results, bringing the r-squared value closer to 1. in essence, the pattern of the curves shows consistent creep crack propagation of the specimen. figure 10: relationship between xfem calculated creep crack growth length and normalized time (c) m. i. meor ahmad et alii, frattura ed integrità strutturale, 61 (2022) 119-129; doi: 10.3221/igf-esis.61.08 128 figure 11: comparison of xfem calculated creep crack growth rate versus c(t)-integral with experimental data. conclusion he approach applied to investigate creep fracture initiation and predict creep crack growth of the ductile materials was numerical constitutive model. the creep fracture initiation was characterized by means of c(t)-integral and the materials' crack propagation that shows power-law creep behavior was predicted by formulating the xfem solutions. the analysis had identified a rectangular plate with single crack displaying a relationship between the xfem solutions and analytical approximation based on short time estimation and ehler-riedel's approximate interpolation which relatively consistent with one another. the contour plot sequences of the stress in the y-direction and displacement magnitude were identified in addition to the crack path. at this point, there was an apparent crack evolution movement at the center of the specimen along with an increase in the distributed stress at the crack tip area. in this study, a ct-specimen has been tested further, showing respectively the contour of the stress plots in the y-direction and the displacement magnitude. the trend of the propagation of the creep crack was well forecast and shown in the graph relations. in the first graph of the ct-specimen, the crack growth length with normalized time is shown where the xfem solutions were properly estimated with the experimental data. whereas the second graph shows the creep crack growth rate with c(t)-integral which produced a similar result when the two approaches were compared, bringing the r-squared value closer to 1. thus, the c(t)-integral and xfem formulation relationship had facilitated in predicting the ductile materials' creep crack initiation and creep crack growth behaviour and subsequently verified the results of the study. the next analysis regarding creep material behaviour will be conducted by representing the damage parameters of creep failure in the ductile materials with the constitutive creep damage model based on continuum damage model. acknowlegement his work is supported by universiti kebangsaan malaysia under geran galakan penyelidik muda (ggpm), ggpm2019-059. t t m. i. meor ahmad et alii, frattura ed integrità strutturale, 61 (2022) 119-129; doi: 10.3221/igf-esis.61.08 129 references [1] yao, h.t., xuan, f.z, wang, z and tu, j.s. (2007). a review of creep analysis and design under multi-axial stress states, nuclear engineering and design, 237(18), pp. 1969-1986. [2] hsu, t.r and zhai z.h. (1984).a finite element algorithm for creep crack growth, engineering fracture mechanics, 20(3), pp. 521-533. [3] hollstein, t. and kienzler, r. (1988). fracture mechanics characterisation of crack growth under creep conditions, the journal of strain analysis for engineering design, 23(2), pp. 87-96. [4] yatomi, m., davies, c.m., and nikbin, k.m. (2008). creep crack growth simulations in 316h stainless steel, engineering fracture mechanics, 75(18), pp. 5140-5150. [5] zhang, j.w., wang, g.z., xuan, f.z., and tu, s.t. (2014). prediction of creep crack growth behaviour in cr-mo-v steel speci-mens with different constraints for a wide range of c, engineering fracture mechanics, 132, pp. 70-84. [6] curiel-sosa, j.l. and karapurath, n. (2012). delamination modelling of glare using the extended finite element method, composites science and technology, 72(7), pp. 788-791. [7] giner, e., sukumar, n., tarancon, j., and fuenmayor, f. (2009). an abaqus implementation of the extended finite element method, engineering fracture mechanics, 76(3), pp. 347-368. [8] farukh, f., zhao, l.,jiang, r., reed, p., proprentner, d. and shollock, b. (2015). fatigue crack growth in a nickelbased superalloy at elavated temperature-experimental studies, viscoplasticity modelling and xfem predictions, mechanics of advanced materials and modern processes, 1(2), pp. 2. [9] moreno, m.c.s., curiel-sosa, j.l., navarro-zafra, j., vicente, j.l.m. and cela, j.j.l. (2015). crack propagation in a chopped glass-reinforced composite under biaxial testing by means of xfem, composite structure, 119, pp. 264271. [10] pandey, v., singh, i., mishra, b., ahmad, s., rao, a. and kumar, v. (2017). creep crack simulations using continuum damage mechanics and extended finite element method, international journal of damage mechanics, 0(0), pp. 1-32. [11] meng, q. and wang, z. (2014). extended finite element method for power-law creep crack growth, engineering fracture mechanics, 127, pp. 148-160. [12] riedel, h. and rice, j.r. (1980). tensile cracks in creeping solids, fracture mechanics: twelfth conference, astm stp 700, pp. 112-130. [13] ehlers, r. and riedel, h. (1981). a finite element analysis of creep deformation in a specimen containing a macroscopic crack, advances in fracture research, proceedings of the fifth international conference on fracture, 2, pp. 691-698. [14] sukumar, n. and prevost, j.h. (2003). modeling quasi-static crack growth with the extended finite element method part i: computer implementation, international journal of solids and structures, 40(26), pp. 7513-7537. [15] ahmad, m.i.m., curiel-sosa, j.l., arun, s. and rongong, j.a. (2019). an enhanced void-crack-based rousselier damage model for ductile fracture with the xfem, international journal of damage mechanics, 28(6), pp. 943-969. [16] user’s guide documentation, dassault systemes simulia corp. abaqus, 6, 14-2, 2014. [17] yang, l., sutton, m.a., deng, x. and lyons, j.s. (1996). finite element analysis of creep fracture initiation in a model superalloy material, international journal of fracture, 81(4), pp. 299-320. [18] zhao, l., jing, h., han, y., xiu, j. and xu, l. (2012). prediction of creep crack growth behaviour in asme p92 steel welded joint, computational materials science, 61, pp. 185-193. [19] yatomi, m., yoshida, k. and kimura, t. (2011). difference of creep crack growth behaviour for base, heat-affected zone and welds of modified 9cr-1mo steel, materials at high temperature, 28(2), pp.109-113. [20] zhao, l., jing, h., xiu, j., han, y. and xu, l. (2014). experimental investigation of specimen size effect on creep crack growth behaviour in p92 steel welded joint, materials and design, 57, pp. 736-743. << /ascii85encodepages false /allowtransparency false /autopositionepsfiles true /autorotatepages /none /binding /left /calgrayprofile (dot gain 20%) /calrgbprofile (srgb iec61966-2.1) /calcmykprofile (u.s. web coated \050swop\051 v2) /srgbprofile (srgb iec61966-2.1) /cannotembedfontpolicy /error /compatibilitylevel 1.4 /compressobjects /tags /compresspages true /convertimagestoindexed true /passthroughjpegimages true /createjobticket false /defaultrenderingintent /default /detectblends true /detectcurves 0.0000 /colorconversionstrategy /cmyk /dothumbnails false /embedallfonts true /embedopentype false /parseiccprofilesincomments true /embedjoboptions true /dscreportinglevel 0 /emitdscwarnings false /endpage -1 /imagememory 1048576 /lockdistillerparams false /maxsubsetpct 100 /optimize true /opm 1 /parsedsccomments true 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can be opened with acrobat and adobe reader 5.0 and later.) >> /namespace [ (adobe) (common) (1.0) ] /othernamespaces [ << /asreaderspreads false /cropimagestoframes true /errorcontrol /warnandcontinue /flattenerignorespreadoverrides false /includeguidesgrids false /includenonprinting false /includeslug false /namespace [ (adobe) (indesign) (4.0) ] /omitplacedbitmaps false /omitplacedeps false /omitplacedpdf false /simulateoverprint /legacy >> << /addbleedmarks false /addcolorbars false /addcropmarks false /addpageinfo false /addregmarks false /convertcolors /converttocmyk /destinationprofilename () /destinationprofileselector /documentcmyk /downsample16bitimages true /flattenerpreset << /presetselector /mediumresolution >> /formelements false /generatestructure false /includebookmarks false /includehyperlinks false /includeinteractive false /includelayers false /includeprofiles false /multimediahandling /useobjectsettings /namespace [ (adobe) (creativesuite) (2.0) ] /pdfxoutputintentprofileselector /documentcmyk /preserveediting true /untaggedcmykhandling /leaveuntagged /untaggedrgbhandling /usedocumentprofile /usedocumentbleed false >> ] >> setdistillerparams << /hwresolution [2400 2400] /pagesize [612.000 792.000] >> setpagedevice microsoft word numero_35_art_30 g. gobbi et alii, frattura ed integrità strutturale, 35 (2016) 260-270; doi: 10.3221/igf-esis.35.30 260 focussed on crack paths a cohesive zone model to simulate the hydrogen embrittlement effect on a high-strength steel g. gobbi (http://orcid.org/0000-0001-7127-1287) c. colombo (http://orcid.org/0000-0003-2074-6726) l. vergani (http://orcid.org/0000-0003-2353-7751) politecnico di milano, department of mechanical engineering, via la masa 1, 20156 milano (italy) giorgia.gobbi@polimi.it, chiara.colombo@polimi.it, laura.vergani@polimi.it abstract. the present work aims to model the fracture mechanical behavior of a high-strength low carbon steel, aisi 4130 operating in hydrogen contaminated environment. the study deals with the development of 2d finite element cohesive zone model (czm) reproducing a toughness test. along the symmetry plane over the crack path of a c(t) specimen a zero thickness layer of cohesive elements are implemented in order to simulate the crack propagation. the main feature of this kind of model is the definition of a traction-separation law (tsl) that reproduces the constitutive response of the material inside to the cohesive elements. starting from a tsl calibrated on hydrogen non-contaminated material, the embrittlement effect is simulated by reducing the cohesive energy according to the total hydrogen content including the lattice sites (nils) and the trapped amount. in this perspective, the proposed model consists of three steps of simulations. first step evaluates the hydrostatic pressure. it drives the initial hydrogen concentration assigned in the second step, a mass diffusion analysis, defining in this way the contribution of hydrogen moving across the interstitial lattice sites. the final stress analysis, allows getting the total hydrogen content, including the trapped amount, and evaluating the new crack initiation and propagation due to the hydrogen presence. the model is implemented in both plane strain and plane stress configurations; results are compared in the discussion. from the analyses, it resulted that hydrogen is located only into lattice sites and not in traps, and that the considered steel experiences a high hydrogen susceptibility. by the proposed procedure, the developed numerical model seems a reliable and quick tool able to estimate the mechanical behavior of steels in presence of hydrogen. keywords. hydrogen embrittlement; aisi 4130 steel; toughness test; cohesive zone model; tractionseparation law. introduction ydrogen embrittlement phenomenon is an issue known since several years in engineering field. different structural steels and alloys show sensitivity to hydrogen. in particular, when atomic hydrogen gets in contact with these materials they experience a drastically decrease of the mechanical properties that can result in failure h g. gobbi et alii, frattura ed integrità strutturale, 35 (2016) 260-270; doi: 10.3221/igf-esis.35.30 261 of components. hydrogen embrittlement phenomenon interests different fields such as mechanical, structural and energetic. for some industrial environment, this problem is widely recognized and studied in literature. for instance, oil&gas industry [1] in which atomic hydrogen is released as product of chemical reactions in environments where the infrastructures operate, pressure vessels for hydrogen storage and transportation [2] and lately even energy devices that use hydrogen as alternative energy carrier. however, other applications in which the presence of hydrogen is less evident have been pointed out recently thanks to the ongoing research on this topic. an example is reported in [3], dealing with wind turbine gearbox bearings, where the hydrogen presence has a deleterious effect in combination with rolling contact fatigue. in this case, it is suggested that hydrogen comes from decomposition of lubricating oil [4] or from water contamination. scientific literature also reports some failures occurred in threaded fasteners, as in [5] where the possible sources of hydrogen are related to thermal treatments. however, independently on the source that generates atomic hydrogen, the most crucial phase is the diffusion process of hydrogen through the material lattice. according to [6], usually the concentration of hydrogen is split into two parts: the content of hydrogen in the interstitial lattice sites (nils) driven by hydrostatic pressure, and the amount accumulated in correspondence of the so-called trap sites. in turn, these can be divided in reversible and irreversible based on the hydrogen binding energy (potential energy at microscopic scale). reversible traps, or low binding energy traps, are mainly related to dislocations and plastic flow. in fact, in [6] the authors showed that plastic strain and hydrogen concentration in reversible traps have similar trends in front of a crack tip. the presence of a crack in a component induces hydrogen atoms to move from the free surface towards the tip. indeed, crack initiation and propagation are deeply influenced by hydrogen presence and diffusion. in terms of diffusion coefficient the motion of hydrogen through nils is represented by an ideal lattice diffusivity, dl. the diffusion can be limited or increased by traps and in these circumstances, a trap-affected or apparent diffusivity, dh, is considered. hydrogen embrittlement is mostly governed by this second diffusion coefficient. traps effect is not univocal [7, 8]. indeed, literature reports that hydrogen in reversible traps is in equilibrium with the one in nils, and it is an “obstacle” to its transport, thus dh<dl. anyway, a large population of reversible traps will have a high probability of hydrogen release at room temperature and it can provide a reservoir of mobile (diffusible) hydrogen to supply the crack-tip fracture-process zone and thus increase hydrogen embrittlement. quenched and tempered high strength steels have microstructural features that increase the strength, but also provide for many hydrogen-trapping sites [9]. contrary, irreversible traps, often saturated even at low hydrogen concentrations, no longer interact with the dissolved hydrogen in the lattice, and dh tends to dl [10]. however, a homogeneous distribution of high-energy traps can prevent that hydrogen localize at low energy sites and shield its segregation at the crack tip. regarding embrittlement mechanisms, several authors proposed possible theories but the most acceptable in literature are three: hede (hydrogen enhanced decohesion, [11]), help (hydrogen enhanced local plasticity, [12]) and hydrides formation and cleavage. these physical models try to explain the embrittlement phenomenon starting from nano and microscopic considerations, and propose that the damage located at crack tip is proportional to hydrogen concentration into the steel [13]. therefore, it is clear that hydrogen embrittlement is a complex mechanism from both mechanical and physical-chemical standpoints. based, on these considerations, it is hence really important to develop a tool able to assess the sensitivity of steels to hydrogen embrittlement. literature reports several numerical models that try to simulate properly the embrittlement process considering interacting factors and the involved parameters mainly microstructure dependent. among these numerical models, cohesive zone models (czm) seem the most promising to reproduce at macro-scale the effect of hydrogen on mechanical properties of steels/alloys. these finite elements models assemble hydrogen diffusion process together with fracture mechanical behavior through the implementation of cohesive elements. a traction separation law (tsl), whose formulation includes parameters able to describe crack initiation and propagation, governs these particular elements. therefore, the effect of embrittlement is simulated simply by reduction of the cohesive energy based on the hydrogen content, omitting the micro-mechanisms. the major contributions to this approach come from [14, 15, 16]. even the model presented in the current manuscript belongs to this category. a complex finite element model including three steps of simulations is developed to reproduce the mechanical behavior of a steel, named aisi 4130, during a toughness tests in hydrogen-contaminated environment. this type of test was carried out during an extensive campaign of experimental tests, being suitable to describe the embrittling effect in steels due to hydrogen. experimental fracture data are used to calibrate the mechanical behavior of cohesive elements describing crack propagation. considerations about the g. gobbi et alii, frattura ed integrità strutturale, 35 (2016) 260-270; doi: 10.3221/igf-esis.35.30 262 implementation of 2d plane stress and plane strain models are proposed. hydrogen concentration estimated at the crack tip is discussed. cohesive zone model setup tarting from experimental results obtained by toughness tests on aisi 4130 steel in hydrogen uncharged and charged conditions [17], a finite element cohesive zone model is built to reproduce the mechanical response of the material. the model, developed using abaqus software, simulates a 2d c(t) specimen. exploiting the symmetry of the geometry, only half part of the specimen is considered and a line of cohesive elements is implemented all over the crack propagation path. these zero thickness elements are connected to the continuum elements on the symmetry plane. in this region, the size of the mesh reaches the smallest dimension, around 10 µm, to ensure proper resolution of results. this mesh size is the result of a convergence study. mechanical properties of continuum elements are assigned according to the data obtained by experimental tensile tests carried out on aisi 4130 steel. fig. 1 depicts the stress-displacement curve of the base material together with the specific values of young’s modulus, poisson’s ratio and yielding stress. instead, peculiarity of cohesive zone model is the definition of a phenomenological law, identified as traction separation law (tsl) describing the constitutive behavior of the material inside the cohesive elements. the cohesive behavior is expressed by a stress-displacement function that can present different shapes according to the crack propagation response of the material. usually, for steels or metals the most noted are gaussian or trapezoidal shapes in which it is possible to split elastic, plastic and failure parts. for the current case, the tsl presents a trapezoidal shape defined by the four parameters shown in fig. 1: σ0, δ0, δn, δf. figure 1: experimental tensile curve and values of mechanical parameters used for continuum elements. tsl shape as stressdisplacement trend. contrary to other authors that customized the user defined elements (uel) subroutine to define the traction separation law of cohesive elements [18, 19], this work presents an easier approach. in fact, the tsl is designed exploiting the traction-separation model available in abaqus, which assumes an initial linear elastic behavior followed by an initiation and evolution of damage. s g. gobbi et alii, frattura ed integrità strutturale, 35 (2016) 260-270; doi: 10.3221/igf-esis.35.30 263 the damage initiation criterion, by which the process of degradation starts, is the maximum nominal strain criterion according to the definition given in [20]. it implies that the damage initiates when the nominal strain ε evaluated at each ith increment of the analysis, reaches the user defined maximum allowable strain value ε0. after that, to describe the rate of the degradation process a damage variable d is used. it represents the overall damage in the material and it is related to the stress components as it follows [20]:  1i id   (1) where σi is the stress tensor computed in the current increment considering absence of damage, and i is the stress predicted by the elastic traction-separation in the same increment. the values of d run monotonically over a range from zero to one: zero represents the starting condition of damage; one describes a situation of full damage in which the element cannot hold up the applied load anymore. in order to assign the tsl shape, a tabular function of the effective displacement δi beyond damage initiation is used. the formulations of damage d as a function of the effective displacement δi is reported below: elastic part: 0d  plastic part: 0 1 1 1 i d      (2) failure part: 0 1 1 i a d      where f i f n a        the values of these parameters are chosen in order to fit the experimental crack propagation data. therefore, a calibration process of tsl for this specific steel without considering the hydrogen effect is necessary as starting point to develop the more complex model including the presence of hydrogen. figure 2: scheme of the specimen and the f vll quantities used for the calibration process. calibration process of tsl parameters for aisi 4130 steel generally, the cohesive law can be calibrated by a comparison with experimental crack propagation data or it can be theoretically modeled using a numerical method that resolves the fracture process. in this case, we selected the experimental approach. a calibration procedure is developed to estimate the cohesive parameters more suitable to represent the characteristic fracture behavior of aisi 4130, in hydrogen non-contaminated conditions. this calibration g. gobbi et alii, frattura ed integrità strutturale, 35 (2016) 260-270; doi: 10.3221/igf-esis.35.30 264 compares the trends of the applied force versus the vertical load line displacement (f-vll) represented in fig. 2, obtained from experimental toughness tests and from the numerical cohesive model simulating the same loading condition. force, f, is evaluated at the center of the loading pin, and it corresponds to the load cell measurement. displacement, vll, is measured at the node where the clip-on-gauge is experimentally located. in this way, experimental data can be directly compared with the numerical outputs. simulation of hydrogen effect the decreasing of the mechanical performances of a steel due to the embrittlement effect are strictly related to hydrogen content. therefore, to simulate correctly this phenomenon it is necessary to take into account properly the total amount of hydrogen present into the material. as already highlighted in the introduction, the concentration of hydrogen inside the steel lattice consists of two contributions: the interstitial lattice sites content and the trapped hydrogen content. to estimate both these contributions, a three-steps model is implemented. once the total hydrogen concentration is calculated, it is then used to reduce the cohesive law, simulating hydrogen embrittlement effect. the first step is a stress analysis used to calculate the hydrostatic stress field into the specimen. the second step, instead, consists of a mass diffusion analysis in which a redistribution of an initial hydrogen concentration, selected according to the experimental values equal to 1.5 ppm at the free surfaces [17], is computed based on the hydrostatic stress field previously calculated. the equation used by abaqus to solve the diffusion analysis is the following, with the omission of the temperature term that is not considered: * p p j s d k x x          (3) where j* is the flux, s is the solubility, d is the diffusivity of the material, φ is the normalized concentration over the solubility, kp is the term that induces diffusion due to the hydrostatic effect and p is the hydrostatic stress. tab. 1 summarizes the values of the parameters used in the model. it should be pointed out that the scientific literature only reports experimental values of the apparent diffusion coefficient dh for the current steel. thus, this was the value implemented into the model. the concentration obtained from this analysis refers only to the “free” hydrogen present in the interstitial lattice sites, cl. solubility s diffusivity d gibbs free energy 0 bg gas constant r 0.071 ppm mm n-1/2 1.62·10-5 mm2/s 30 kj/mol 8.314 j k-1 mol-1 table 1: values of parameters adopted in the three simulations of the cohesive zone model. finally, the last step is a stress analysis with cohesive elements implementation to simulate the fracture behavior. in this simulation, also the trap site concentration is computed. as indicated in the introduction, influence of traps on hydrogen embrittlement is certainly important; however, the characterization of trap type, density, binding energy and occupancy is a demanding task that has to be performed at smaller scales. in order to simplify this problem and to include this contribution in the finite elements codes, we consider here only hydrogen low energy traps and we assume that these are related to the plastic strain. in fact, starting from results presented in [6], the work by [15] proposed the following relation between the trap content and the plastic strain:  49.0 0.1t p lc c    (4) this relation was proposed for high and low strength steels, from physical-chemical analytical relations and numerical models [6]. it is implemented in the third analysis using the plastic strain calculated during the simulation. the total bulk hydrogen concentration, c, resulted from the sum of interstitial lattice sites cl and the traps sites ct is related to the surface concentration in the cohesive zone through [21]: g. gobbi et alii, frattura ed integrità strutturale, 35 (2016) 260-270; doi: 10.3221/igf-esis.35.30 265  0exp b c c g rt     (5) where θ is the hydrogen coverage factor, 0bg is the variation of gibbs free energy, r is the gas constant and t is the temperature. in turn, this term contributes to the calculation of k factor, by which the cohesive energy is reduced simulating the embrittlement effect [15]: 21 1.0467 0.1687k       (6) this scaling factor is applied on both stress and displacement of the tsl curve reducing the entire area. all the relationships and parameters in eqs. (4), (5) and (6) are calculated in the last analysis, for each increment, in the unique integration point of the continuum element. the parameter, k, is then transferred from the continuum to the corresponding cohesive elements by implementing three subroutines. these are the user subroutines to manage userdefined external databases and calculate model-independent history information (uexternaldb), the user subroutine to redefine field variables at a material point (usdfld), and the user subroutine to generate element output (uvarm). these subroutines work interactively each other in a fortran common block. the performed experimental toughness test from which the model have been developed was in accordance with standards, and specimen dimensions ensured the definition not only of j-toughness but also of k-toughness. therefore, at the specimen core, plane strain condition is likely to occur. on the contrary, at the external surfaces, the stress state would be more similar to plane stress condition. since the model we are implementing is bi-dimensional, limitations in the analysis should be taken into account. for this reason, the model has been developed both in plane strain and plane stress conditions. apart from the different type of continuum elements used to describe the material (cpe4 for plane strain and cps4 for plane stress analysis), the model geometry, the applied displacement and boundary conditions and the followed calibration procedure are coincident. even if the modelling steps are the same, the plane strain and plane stress models give different results, which will be critically discussed in the following section. results and discussion irst, a tsl calibration for cohesive elements is developed to find out the cohesive parameters that replicate the behavior of the material in absence of hydrogen for both plane stress and plane strain configurations model. tab. 2 shows the resulting tsl parameters. the tsls have a very small flat part, i.e. (δn – δ0); on the contrary, they present a long trend describing the damage to failure, i.e. (δf – δn). this means that the tsl is more similar to a triangle than a trapezoid. the tsl plateau stress, σ0 is between 1.75 and 1.85 the yielding stress. the area below the tsl plot corresponds to the separation work needed for crack initiation and propagation. values of this area are deeply different between plane strain and plain stress cases, accounting for the stress combination at the separation surface. it should be mentioned that data in tab. 2 are results of a trial and error procedure, and they correspond to the best combination of tsl parameters able to fit experimental data. hydrogen-free model δ0 [mm] δn [mm] δf [mm] σ0 [mpa] area [n/mm] plane strain 0.009 0.015 0.320 1260 205.4 plane stress 0.004 0.011 0.090 1323 28.5 table 2: characteristic values for tsl parameters for the hydrogen-free model, for plane strain and plane stress models. displacement and stress notation is referred to fig. 1; the area is below the tsl curve. now, considering the model that predicts the response of the material in presence of hydrogen, the first step of analysis evaluates the hydrostatic stress field. this is imported as predefined field in the second mass diffusion analysis. here, the hydrostatic stress drives the flux of hydrogen computing the interstitial lattice sites content, cl. fig. 3 shows cl f g. gobbi et alii, frattura ed integrità strutturale, 35 (2016) 260-270; doi: 10.3221/igf-esis.35.30 266 concentration field around the crack tip, evaluated during the second step of the analysis for plane strain model. in accordance with literature [14], the peak of hydrostatic stress and then of hydrogen nils concentration is not located at the crack tip, but slightly forward. in our simulations, this peak is located at the end of the first element ahead the tip. in this node, the model estimates a quite high cl concentration, equal to 4.43 ppm. it is around three times the initial imposed concentration at free edges (1.5 ppm). for plane stress model, similar contour is found, with a peak value for hydrogen concentration of 2.03 ppm. the last step calculates the current plastic strain, and consequently the contribution of the trapped sites, ct. then, based on the total hydrogen concentration, nils and traps, the decreasing factor k is applied to the previous tsl to reduce the area below the curve, thus the energy adsorbed by the cohesive elements. thanks to this factor, it is possible to simulate a lower resistance to crack propagation and to evidence the embrittlement of the steel. in order to get f-vll curves similar to experimental data, it results that k has to be applied to both cohesive stress and displacement of tsl. in particular, for plane strain model in presence of hydrogen, we found that the reduced tsl stress and displacement are respectively σ0h=k·σ0 and δh=k3/2·δ, where δ is the generic displacement of the tsl curve. while the reduction in stress is in agreement with literature results [15, 16], the further reduction in displacement was quite unexpected. however, it can be justified by the high hydrogen sensitivity observed during the experimental fracture toughness tests for the current steel. in fact, it showed a more brittle behavior compared to other steels tested in the past [22]. for plane stress model, the same ratio was derived for the reduced tsl stress σ0h=k·σ0, while the reduced displacement is slightly lower: δh=k·δ. figure 3: contours of cl concentration in lattice interstitial sites at crack tip region, plane strain model. fig. 4 shows contours of the decreasing factor k around the crack tip for plane strain model. the maximum is located in front of the crack tip and it is equal to 0.26. on the tip, it is slightly lower and equal to 0.29. instead, the maximum value of k factor for plane stress model is 0.36. this means that the embrittlement effect is more evident in case of plane strain than plane stress. moreover, both models agree in the prediction of absence of plastic strain measured at the crack tip during the last step. therefore, from the numerical simulations, it seems that no hydrogen is located in traps, i.e. ct=0, and the only contribution for k factor calculation is provided by the cl hydrogen amount. this means that the embrittlement is only due to hydrogen in the lattice and suggests a very brittle behavior of aisi 4130 in presence of hydrogen. as reported in literature [7, 8], aisi 4130 is supposed to have many trap sites, mainly due to its martensitic structure, resulting in high strength, rather than to its plastic strain. although, the study should be further deepened, these numerical finding can be supported by the first experimental observations of the fracture surface of the specimens tested in hydrogen environment. in fact, for most of the steels, on the fracture surfaces vast brittle regions and smaller ductile areas appeared, likely related to the local plastic strain and therefore to hydrogen in traps [22]. instead, in the case of aisi 4130, from the images collected after toughness tests, g. gobbi et alii, frattura ed integrità strutturale, 35 (2016) 260-270; doi: 10.3221/igf-esis.35.30 267 most of the failure surfaces showed brittle features, as in fig. 5. some cracks also propagated from lateral groves. surely, to confirm the fully brittle behavior of this steel in presence of hydrogen more data would be necessary. figure 4: contours of k (eq.6) at crack tip region (continuum elements), plane strain model. in literature, there is no analytical law to calculate the hydrogen concentration in traps ct, to be compared with this numerical result. moreover, the diffusion coefficient of this steel should be experimentally measured, including its effective and apparent contributions (dl and dh). if these two diffusivity values were available, their ratio would allow an estimation of ct, according to [7]. as a final comment to our result, it is even possible that the law expressed in eq. 4 is not completely able to describe the mechanical behavior of aisi 4130, even if it included a wide class of materials. fig. 6 compares force displacement (f-vll) curves from experimental tests and numerical simulations (plane strain and plane stress). the plot shows the mechanical responses of both models in hydrogen uncharged and charged conditions. it is evident the difference between the two behaviors without and with hydrogen. the macro-mechanical response of the specimen during toughness test is deeply influenced by hydrogen. the curve is decreased not only in its load peak, but also in the maximum displacement and in the damage history, as confirmed from tsl data in tab. 2. figure 5: fracture surface of a specimen after the toughness test. the specimen was hydrogen pre-charged before the test. typical brittle surface is evidenced by facets (black arrow), intergranular cracks (white arrow) along grain borders and secondary cracks (yellow arrow). g. gobbi et alii, frattura ed integrità strutturale, 35 (2016) 260-270; doi: 10.3221/igf-esis.35.30 268 0 2000 4000 6000 8000 10000 12000 14000 16000 18000 0 0.5 1 1.5 2 2.5 lo a d ,  f  [ n ] displacement, vll [mm] experimental, no h experimental, h numerical plane strain, no h numerical plane strain, h numerical plane stress, no h numerical plane stress, h figure 6: f-vll curves from experimental tests and numerical simulations, for plane strain and plane stress. solid lines plot data without hydrogen, dashed lines with hydrogen. by observing fig. 6, it is possible to note that in plane stress condition the calibration process does not allow a good overlapping with the experimental results. despite many simulations, it appeared that the combination of tsl parameters for this model never resulted in a good fitting with the experimental data. in terms of fracture toughness j value, that represents the area below the f-vll curve, the value obtained by the calibration process simulating the test without hydrogen is a bit smaller than the experimental one (experimental fracture toughness without hydrogen = 215 n/mm). then, this tiny discrepancy is reversed comparing experimental and numerical curves related to the hydrogen environment conditions (experimental fracture toughness with hydrogen = 22 n/mm). on the contrary, the plane strain model better fits experimental data in both hydrogen and no-hydrogen conditions. therefore, between the two developed models, the 2d plane strain one seems to represent better the experimental evidence. however, as a future development, a 3d numerical model would give more information about the embrittlement depending on the local stress condition. conclusions he current work presents a cohesive zone model reproducing a toughness test in presence of hydrogen for both plane stress and plane strain configurations. the following conclusions can be drawn:  firstly a calibration of traction-separation law (tsl) that defines the constitutive properties of cohesive elements is developed for the steel aisi 4130;  a model running on three steps of simulations calculates the total hydrogen concentration present into the specimen including the interstitial lattice sites and the trapped amount. based on the total content of hydrogen a scale factor is computed and used to reduce the tsl area previously calibrated in order to simulate the embrittlement effect of hydrogen;  for the present steel, aisi 4130, the considered relation to calculate trapped hydrogen concentration ct depending on plastic strain seems not appropriate. by the implemented equations, the numerical model is not able to estimate the hydrogen concentration in reversible traps. therefore, the model computes hydrogen embrittlement only as a function of hydrogen in interstitial lattice sites. this is a consequence of a brittle behavior of the steel, according to the experimental test; t g. gobbi et alii, frattura ed integrità strutturale, 35 (2016) 260-270; doi: 10.3221/igf-esis.35.30 269  between the plane strain and plane stress modelling configurations the more suitable to represent the experimental results is the plane strain;  the developed model seems a tool able to provide a proper description of the behavior of the material in presence of hydrogen, but still needs improvements to clarify the influence of trap sites to the embrittlement phenomenon. references [1] fassina, p., brunella, m.f., lazzari, l., re, g., vergani, l., sciuccati, a., effect of hydrogen and low temperature on fatigue crack growth of pipeline steels. engineering fracture mechanics, 103 (2013) 10-25. doi: 10.1016/j.engfracmech.2012.09.023. [2] irani, r.s., hydrogen storage: high-pressure gas containment, mrs bulletin 27 (2002) 680-682. doi: 10.1557/mrs2002.221. [3] evans m.-h., richardson a.d., wang l., wood r.j.k., serial sectioning investigation of butterfly and white etching crack (wec) formation in wind turbine gearbox bearings, wear, 302 (2013) 1573–1582. doi: 10.1016/j.wear.2012.12.031. [4] kohara, m., kawamura, t., egami, m., study on mechanism of hydrogen generation from lubricants, tribology transactions, 49 (2006) 53-60. doi: 10.1080/05698190500486324. [5] jha, a.k., ramesh narayanan, p., sreekumar, k., mittal, m.c., ninan, k.n., hydrogen embrittlement of 3.5ni– 1.5cr–0.5mo steel fastener, engineering failure analysis, 15 (2008) 431–439. doi:10.1016/j.engfailanal.2007.05.008. [6] taha, a., sofronis, p., a micromechanics approach to the study of hydrogen transport and embrittlement, engineering fracture mechanics, 68 (2001) 803-837. [7] thomas, r.l.s., li, d., gangloff, r.p., scully, j.r., trap-governed hydrogen diffusivity and uptake capacity in ultrahigh-strength aermet 100 steel, metallurgical and materials transactions a, 33a (2002) 1991-2004. [8] thomas, r.l.s., scully, j.r., gangloff, r.p., internal hydrogen embrittlement of ultrahigh-strength aermet 100 steel, metallurgical and materials transactions a, 34a (2003) 327-344. [9] oriani, r.a., the diffusion and trapping of hydrogen in steel, acta metallurgica, 18 (1970) 147-157. [10] fallahmohammadi, e., bolzoni, f., fumagalli, g., re, g., benassi, g., lazzari, l., hydrogen diffusion into three metallurgical microstructures of a c-mn x65 and low alloy f22 sour service steel pipelines, international journal of hydrogen energy, 39 (2014) 13300-13313. doi: 10.1016/j.ijhydene.2014.06.122. [11] troiano, a., the role of hydrogen and other interstitials in the mechanical behavior of metals, trans asm, 52 (1960) 54-80. [12] beachem, c., a new model for hydrogen-assisted cracking (hydrogen embrittlement), metallurgical and materials transactions b, 3 (1972) 441-455. [13] gangloff, r.p., wie, r.p., gaseous hydrogen embrittlement of high strength steels, metallurgical transactions a, 8a (1977) 1043-1053. [14] scheider, i., pfuff, m., dietzel, w., simulation of hydrogen assisted stress corrosion cracking using the cohesive model. engineering fracture mechanics, 75 (2008) 4283-4291. doi: 10.1016/j.engfracmech.2007.10.002. [15] olden, v., thaulow, c., johnsen, r., øtby, e., berstad, t., application of hydrogen influenced cohesive laws in the prediction of hydrogen induced stress cracking in 25%cr duplex stainless steel, engineering fracture mechanics, 75 (2008) 2333-2351. doi: 10.1016/j.engfracmech.2007.09.003. [16] moriconi, c., hénaff, g., halm, d., cohesive zone modelling of fatigue crack propagation assisted by gaseous hydrogen in metals, international journal of fatigue, 68 (2014) 56-66. doi: 10.1016/j.ijfatigue.2014.06.007. [17] colombo, c., fumagalli, g., bolzoni, f., gobbi, g., vergani, l., fatigue behavior of hydrogen pre-charged low alloy cr-mo steel, international journal of fatigue, (submitted, 2014). [18] park, k., paulino, g.h., computational implementation of ppr potential-based cohesive model in abaqus: educational perspective, engineering fracture mechanics, 93 (2012) 239-262. [19] schwalbe, k-h, scheider, i., cornec, a., guidelines for applying cohesive models to the damage behaviour of engineering materials and structures, springer, heidelberg, (2013). [20] abaqus v.6.12 documentation, dassault systèmes simulia corp. [21] serebrinsky, s., carter, e. a., ortiz, m., a quantum-mechanically informed continuum model of hydrogen embrittlement, journal of the mechanics and physics of solids, 52 (2004) 2403-2430. doi: 10.1016/j.jmps.2004.02.010. g. gobbi et alii, frattura ed integrità strutturale, 35 (2016) 260-270; doi: 10.3221/igf-esis.35.30 270 [22] fassina p., bolzoni f., fumagalli g., lazzari l., vergani l., sciuccati a., influence of hydrogen and low temperature on mechanical behaviour of two pipeline steels, engineering fracture mechanics, 81 (2012) 43–55. doi: 10.1016/j.engfracmech.2011.09.016. << /ascii85encodepages false /allowtransparency false /autopositionepsfiles true /autorotatepages /none /binding /left /calgrayprofile (dot gain 20%) /calrgbprofile (srgb iec61966-2.1) /calcmykprofile (u.s. web coated \050swop\051 v2) /srgbprofile (srgb iec61966-2.1) /cannotembedfontpolicy /error /compatibilitylevel 1.4 /compressobjects /tags /compresspages true /convertimagestoindexed true 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can be opened with acrobat and adobe reader 5.0 and later.) >> /namespace [ (adobe) (common) (1.0) ] /othernamespaces [ << /asreaderspreads false /cropimagestoframes true /errorcontrol /warnandcontinue /flattenerignorespreadoverrides false /includeguidesgrids false /includenonprinting false /includeslug false /namespace [ (adobe) (indesign) (4.0) ] /omitplacedbitmaps false /omitplacedeps false /omitplacedpdf false /simulateoverprint /legacy >> << /addbleedmarks false /addcolorbars false /addcropmarks false /addpageinfo false /addregmarks false /convertcolors /converttocmyk /destinationprofilename () /destinationprofileselector /documentcmyk /downsample16bitimages true /flattenerpreset << /presetselector /mediumresolution >> /formelements false /generatestructure false /includebookmarks false /includehyperlinks false /includeinteractive false /includelayers false /includeprofiles false /multimediahandling /useobjectsettings /namespace [ (adobe) (creativesuite) (2.0) ] /pdfxoutputintentprofileselector /documentcmyk /preserveediting true /untaggedcmykhandling /leaveuntagged /untaggedrgbhandling /usedocumentprofile /usedocumentbleed false >> ] >> setdistillerparams << /hwresolution [2400 2400] /pagesize [612.000 792.000] >> setpagedevice microsoft word numero_36_art_18 s.r. wang et alii, frattura ed integrità strutturale, 36 (2016) 182-190; doi: 10.3221/igf-esis.36.18 182 acoustic emission characteristics of instability process of a rock plate under concentrated loading s.r. wang opening project of key laboratory of deep mine construction, henan polytechnic university, jiaozuo 454003, p.r china w_sr88@163.com c.y. li school of civil engineering, henan polytechnic university, jiaozuo 454003, p.r china z.s. zou,x.l. liu opening project of key laboratory of deep mine construction, henan polytechnic university, jiaozuo 454003, p.r china abstract. it can facilitate the understanding of the mechanical properties and failure laws of rocks to research on the rock failure mechanism and evolution characteristics of acoustic emission (ae). under the concentrated loading condition, the fracture and instability test of a rock plate was conducted by using the rock mechanics testing system (mts), meanwhile, these ae events were recorded through the ae recording system. based on the laboratory test, the numerical simulation was completed by using flac3d technique under the criterion that the rupture of a cell or several adjacent cells was regarded as an ae event. the results show that the process of the fracture and instability of the rock plate can be divided into four stages, such as the stress adjusting stage, the brittle fracture stage, the rock-arch bearing load stage and the rock-arch instability stage. and the acoustic emissions display the different characteristics in each one of the four stages. the temporal and spatial distribution characteristics of the ae events with large magnitudes are very similar to those of the natural earthquakes. keywords. rock mechanics; rock plate; acoustic emission; numerical simulation; instability. introduction ince rock failure is always accompanied by acoustic emission (ae) phenomenon, it can facilitate the understanding of the mechanical properties and failure laws of rocks to research on the rock failure mechanism and evolution characteristics of acoustic emission. currently, the study methods of ae mainly contain the means of laboratory test or numerical simulation or both of them. in the experimental research field, both domestic and foreign scholars have conducted plenty of studies. for example, s.l. li, et al. investigated the rock mechanics and ae characteristics in the whole failure process for rock samples and pointed out the test results could be used to explain the ae phenomenon in an engineering project [1]. x.m. fu compared the similarities and differences of these ae performances for different rocks in the uniaxial compression tests [2]. based on the locations of ae events, x.d. zhao, et al. found that the ae distribution could reflect the shape and development of s s.r. wang et alii, frattura ed integrità strutturale, 36 (2016) 182-190; doi: 10.3221/igf-esis.36.18 183 the cracks in rocks, which is meaningful to study the deformation and failure laws of rocks [3]. j.p. liu, et al. observed the changes of ae number in a process of loading test, found that the accelerating release of energy was meaningful to predict the instability or failure of the rock mass [4]. y.b. zhang inferred the ae magnitude by the ratio of the whole released energy and ae number in a particular time, found that the higher the ratio, the less ae events had produced the energy [5]. l.c. jia, et al. monitored the process of the uniaxial compression test for limestone by acoustic emission techniques, and elaborated the crack development law in the rock sample after scanning the destroyed samples by a computerized tomography (ct) machine [6]. b.x. huang, et al. analyzed the stress-strain curves and ae characteristics for coal-bearing rock samples under different stress paths [7]. k. zhao, et al. conducted the research on ae characteristics of phyllite specimens under uniaxial compression tests [8]. m. karakus, et al. analyzed the ae signal in the rock drilling process, which would provide the guidance to improve the drilling effect [9]. e. aker, et al. analyzed the differences of ae between the shear failure and tensile failure in the triaxial compression tests of sandstone and predicted the failure mechanism using the proportion of the isotropic and anisotropic moment tensors [10]. l.p. frash, et al. conducted the granite tests using ae technique and simulated the evolution of the crack in the geothermal development, providing useful information for the engineering application [11]. the numerical simulation can show some information that the laboratory tests cannot provide. for example, some scholars simulated ae by using particle flow code (pfc) and rock failure process analysis system (rfpa), which provided a great help to understand ae phenomenon [12, 13]. additionally, based on the correspondence between ae and cell rupture in flac/flac3d code, x.b. wang and t.c. han et al. [14, 15] respectively simulated the ae in both laboratory and engineering scales, and they all obtained the good results. and other related works [16-18]. based on the laboratory test, a further research following the above mentioned results will be conducted by using flac3d technique under the criterion that the rupture of a cell or several adjacent cells was regarded as an ae event. we will analyze the temporal and spatial distribution characteristics of the ae events with large magnitudes and discuss the relationships between ae and natural earthquakes. materials and methods samples of rock plates he rock plate samples in the tests were hawkesbury sandstones, which were obtained from gosford quarry in sydney, australia. the quartz sandstones were formed in marine sedimentary basin of the mid-triassic and located on the top of the coal-bearing strata, which contained a small quantity of feldspars, siderite and clay minerals. according to the definition of the thick plate in elastic mechanics, the specimen sizes of the thick plate were designed as 190 mm × 75 mm × 24 mm (length, width and thickness). equipment and ae acquisition system the mts-851 rock mechanics testing machine was selected as the loading equipment, and the load was controlled by vertical displacement and the loading rate was set 1×10-2 mm/s. the vertical force and displacement in the process of the test were automatically recorded in real time by the data acquisition system. as shown in fig. 1, the concentrated loading tests were designed to mainly consist of three parts. the top was a pointloading for the concentrated loading. the middle was a loading framework which included four bolts with nuts connecting the steel plates on both sides, and the lateral pressure cell was placed between the deformable steel plate and the thick steel plate so as to monitor the horizontal force. the capacity of the lateral pressure cell lpx was 1000 kg. the bottom was a rectangle steel foundation, and the rotatable hinge support was set on the both sides of the loading framework to maintain the connections with the steel plates. to monitor the cracks initiating and identify the failure location of the rock plate, the usb ae nodes were used in the test. the usb ae node is a single channel ae digital signal processor with full ae hit and real time features. in the test there were four usb ae nodes connected to a usb hub for multi-channel operation (fig. 2). all these ae nodes were made in mistras group inc. usa. numerical simulation scheme ae is due to the internal micro fracture by tension, shearing and compression stress in the rock plate, and this process is accompanied by the release of elastic waves. the rupture of a cell in flac3d is also accompanied by the release of elastic energy, so it can be used to simulate an ae event [15]. in fact, if several adjacent cells rupture in the rock plate in a calculating cycle (step), it should also be regarded as an ae event, which advantage is that we can record the number of t s.r. wang et alii, frattura ed integrità strutturale, 36 (2016) 182-190; doi: 10.3221/igf-esis.36.18 184 the ruptured cells reflecting the magnitude of the energy in an ae event. then we can analyze the evolution characteristics of temporal and spatial of ae events, which may facilitate the understanding of the mechanical properties and failure laws of rocks. figure 1: the concentrated loading test for rock plate. figure 2: mts and ae monitoring system diagram. we assumed that if an ae event during the simulation test corresponded to only one ruptured cell, the center of this cell was defined the ae event location, or if an ae event corresponded to several adjacent cells, the center of the cells near the nuclear of the block was defined the ae event location. then a recording function was written by fish language embedded in flac3d code to record the information of ae events such as the number of ruptured cells, the locations and the magnitudes of the ae events. the realization process of this function was shown in fig. 3. the state of each cell was defined as ruptured or not and all of the cells were judged during each calculating step. in addition, the cells were regarded as ‘adjacent cells’ if the distance between two cells was less than 3.16 mm. finally, the large magnitude ae events, namely the events corresponding to two or more ruptured cells were abstracted for being analyzed. so these ae characteristics in the test were analyzed through observing the temporal and spatial distribution of the large magnitude ae events. computational model and parameters the computational model was the same size of the sandstone sample as shown in fig. 4, which combined 68992 cells totally and each cell was a cube element measuring 1.7 mm on each side. to simulate the defects in the rock plate, about 14000 defective cells were generated by a fish function. these defects were randomly distributed in the main cells to form a block group. in addition, a new block group containing these weak cells was defined to reflect the tension strength decreasing in the middle of the rock plate bottom after the initial crack being developed in the test. therefore, all the cells belonged to three groups: the main cells, the defective cells, and the weak cells (fig. 4). the mohr-coulomb strength criterion was applied and the physical and mechanical parameters of the model were shown in tab. 1. s.r. wang et alii, frattura ed integrità strutturale, 36 (2016) 182-190; doi: 10.3221/igf-esis.36.18 185 figure 3: the flow chart of recording ae events. name density [kg/m3] bulk modulus [gpa] shear modulus [gpa] cohesion [mpa] friction angle [°] tension [mpa] main cells 2650 15 11 2.8 45 0.60 defective cells 2650 15 11 2.8 45 0.55 weak cells 2650 15 11 2.8 45 0.14 table 1: physical and mechanical parameters of the model. loading and boundary conditions as shown in fig. 5, the rock plate was hinged to the both ends with the fixed bearing in the vertical direction and the spring bearing with a stiffness 6.0 × 104 n/m respectively in the horizontal direction. the concentrated loading was applied in a circular zone with a diameter of 10 mm in the center of the upper surface of the model. to avoid drastic disturbance of the calculating system, the compressive stress was increased linearly from 0 to a final stress of 12.0 mpa. results ae in the failure process of the rock plate s shown in ae location maps (fig. 6), the results showed the obvious distribution differences between the initial cracks and the ultimate cracks of the rock plate in the test. and the ae hits-time curve could be divided into four stages in the process of bearing load to instability of the rock plate under the concentrated loading condition (fig. 7). a s.r. wang et alii, frattura ed integrità strutturale, 36 (2016) 182-190; doi: 10.3221/igf-esis.36.18 186 figure 4: the computational model and its grids. figure 5: loading and boundary conditions. (a) initial stage. (b) ultimate stage. figure 6: ae locations on rock plate. figure 7: ae hits and force-displacement curves under the concentrated loading. ae characteristics in numerical simulation test the results were saved in each particular time interval to observe ae states of cells as shown in fig. 8. the recording function was applied to record the ae amount (fig. 9) and ae locations (fig. 10). during the loading process, the stress in the rock plate transmitted in every step and the cell ruptured when the stress in a particular cell reached the shearing or the tension strength. the ruptured cells began in the center of the rock plate bottom, then extended along the center line of the rock plate resulting in a fracture in the middle, and finally formed a rock-arch structure. meanwhile, the ae events mainly gathered on the hinged lines of the rock-arch structure in the rock plate. from the above mentioned results, we can see that the numerical simulation showed nearly the same ae characteristics with those of the laboratory test. as shown in fig. 9, the ae hits-step curve can be divided into four stages: s.r. wang et alii, frattura ed integrità strutturale, 36 (2016) 182-190; doi: 10.3221/igf-esis.36.18 187 (a) initial stage (3000 steps). (b) ultimate stage (12000 steps). figure 8: ae locations on the top of the rock plate. figure 9: ae hits-step curve in the numerical simulation. stage 1 (stress adjusting stage): the stress has not yet reached the tensile strength of the sandstone sample in the early time, so a large number of ae events were avoided. and then an initial crack paralleling with the short sides formed in the center of the rock plate boring the largest tensile stress. the stresses transmitted in flac3d by the neighboring nodes in the calculating process, redistributing in each step. for the stress in the rock plate increased gradually under the concentrated loading, the sample generated the displacements on its bottom of the both ends, which induced the horizontal constraining force. few ae events had been recorded at first and then it increased sharply to the first peak. the ae events induced by the tensile rupture mainly gathered near the first crack. stage 2 (the brittle fracture stage): in this stage, the extended crack resulted in the rock plate fracturing into two halves and being formed a hinged rock-arch structure. both the laboratory test and numerical simulation showed that the number of ae events decreased rapidly and stabilized in a low level. this indicated that the rock plate produced a brittle fracture induced by the extent of the first crack. both the laboratory test and the simulation showed the same characteristics in the spatial distribution, namely ae events spread from the center to the ends with the extent of the initial crack (fig. 10). stage 3 (rock-arch structure bearing loading): the hinged rock-arch structure boring the loading and the horizontal force continued to increase with the loading increasing. the ae characteristics in the laboratory test and the numerical simulation were nearly the same, namely the ae number performed a sharp increase to reach the second peak and then it reduced and stabilized. the ae spatial distribution focused on the hinge lines of the rock-arch structure, namely the center line and the ends of the rock plate (figs. 8 and 10). stage 4 (instability and failure of the rock-arch structure): once the concentrated load exceeded the bearing capacity of the rock-arch structure, it would lead to the instability and failure of the rock plate. the ae events reduced unsteadily and distributed in the middle and the ends of the rock plate both in the laboratory test and the numerical simulation (figs. 8 and 10). discussion of the magnitudes of ae events s we can see that all these 156 large magnitude events revealed the similar spatial distribution to the ae events, and which were located on the main crack of the sample, namely the middle hinge of the rock-arch structure (fig. 10). a s.r. wang et alii, frattura ed integrità strutturale, 36 (2016) 182-190; doi: 10.3221/igf-esis.36.18 188 (a) initial stage (3000 steps). (b) ultimate stage (12000 steps). figure 10: ae locations on the bottom of the rock plate. there are all 1145 ae events and the number of the ruptured cells corresponded to one ae event from 1 to 5 in the numerical simulation, which represented the different energy scale released in one ae event. in the fracture and instability process of the rock plate, the number of ae events reduced with the ae magnitude increasing. as shown in fig. 11, we can obtain the negative exponential formula by fitting the curve by using origin software wherein n indicating the number of ae with magnitudes greater than or equal to m while m indicating the ae magnitude. in seismology, the earthquake with a larger magnitude is relatively rare, while some small magnitude earthquakes occur frequently. the relationship between the magnitude and frequency is generally described by a probability distribution, which is derived based on the statistics of the observed seismic activity. the most widely used relationship is the following one [19, 20]: 10a bmn  (1) where n indicates the number of earthquakes with the magnitudes greater than or equal to m; m indicates the magnitude; a and b are regional parameters. for example, z.h. el-isa, et al. compiled the seismicity data for all earthquakes with magnitudes m≥4.5 occurred globally from january, 1990 to december, 2012. the fitting result is presented in fig. 12 [21]. the ae phenomena and tectonic earthquakes are both releasing energy processes induced by the slippage or breakage of rock sample or stratum, and having substantial connection in the failure mechanism. in addition, the similarity of distribution in frequency corroborates this law indirectly. figure 11: ae magnitude distribution curve. figure 12: magnitude frequency distribution of the seismicity. conclusions ased on the laboratory test and simulation results, the process of the fracture and instability for the rock plate could be divided into four stages: the stress adjusting stage, the brittle fracture stage, the rock-arch bearing load stage, and the rock-arch instability stage. the acoustic emission exhibited the different characteristics in each stage. b s.r. wang et alii, frattura ed integrità strutturale, 36 (2016) 182-190; doi: 10.3221/igf-esis.36.18 189 by a self-programming recording function in flac3d, these ae events with large magnitudes were abstracted. we found that the similar temporal and spatial characteristics between the large magnitude ae events and the whole ae events, which reflected the feature of the instability process of the rock plate. the ae distribution with the magnitude showed that the ae events reduced with the ae magnitudes followed a negative exponential function. this distribution was similar to the tectonic earthquakes, which reflected the intrinsic link between the ae events and the ae magnitudes. acknowledgements his work was supported by the national natural science foundation of china (51474188; 51474097; 51074140), the natural science foundation of hebei province of china (e2014203012), the international cooperation project of henan science and technology department (162102410027), the doctoral fund of henan polytechnic university (b2015-67), and program for taihang scholars. all these were gratefully acknowledged. references [1] li, s.l., yin, x.g., wang, y.j., tang, h.y., studies on acoustic emission characteristics of uniaxial compressive rock failure. chinese journal of rock mechanics and engineering, 23 (15) (2004) 2499-2503. [2] fu, x.m., experimental study on uniaxial compression deformation and acoustic emission property of typical rocks. journal of chengdu university of technology, 32 (1) (2005) 17-21. [3] zhao, x.d., tang, c.a., li, y.h., yuan, r.f., zhang, j.y., study on ae activity characteristics under uniaxial compression loading. chinese journal of rock mechanics and engineering, 25 (s2) (2006) 3673-3678. [4] liu, j.p., xu, s.d., li, y.h., dong, l.b., wei, j., studies of ae time-space evolution characteristics during failure process of rock specimens with prefabricated holes. chinese journal of rock mechanics and engineering, 31 (12) (2012) 2538-2547. [5] zhang, y.b., spectral character analysis of sandstone under saturation condition in rupture procedure, rock and soil mechanics, 34 (6) (2013) 1574-1578. [6] jia, l.c., chen, m., zhang, w., xu, t., zhou, y., hou, b., jin, y., experimental study and numerical modeling of brittle fracture of carbonate rock under uniaxial compression. mechanics research communications, 50 (2013) 58-62. doi: 10.1016/j.mechrescom.2013.04.002. [7] huang, b.x., liu, j.w., the effect of loading rate on the behavior of samples composed of coal and rock. international journal of rock mechanics & mining sciences, 61 (2013) 23-30. doi: 10.1016/j.ijrmms.2013.02.002. [8] zhao, k., zhu, z.c., zeng, p., cheng, s.j., experimental study on acoustic emission characteristics of phyllite specimens under uniaxial compression. journal of engineering science and technology review, 8 (3) (2015) 53-60. [9] karakus, m., perez, s., acoustic emission analysis for rock–bit interactions in impregnated diamond core drilling. international journal of rock mechanics & mining sciences, 68 (2014) 36-43. doi: 10.1016/j.ijrmms.2014.02.009. [10] aker, e., kühn, d., vavryèuk, v., soldal, m., oye, v., experimental investigation of acoustic emissions and their moment tensors in rock during failure. international journal of rock mechanics & mining sciences, 70 (2014) 286295. doi: 10.1016/j.ijrmms.2014.05.003. [11] frash, l.p., gutierrez, m., hampton, j., hood, j., laboratory simulation of binary and triple well egs in large granite blocks using ae events for drilling guidance. geothermics, 55 (2015) 1-15. doi: 10.1016/j.geothermics.2015.01.002. [12] liu, n., zhang, c.s., chu, w.j., wu, x.m., microscopic characteristics analysis of brittle failure of deep buried marble. chinese journal of rock mechanics and engineering, 31 (s2) (2012) 3557-3565. [13] ren, x.h., wang, h.j., zhang, j.x., numerical study of ae and dra methods in sandstone and granite in orthogonal loading directions. water science and engineering, 5 (1) (2012) 93-104. doi: 10.3882/j.issn.1674-2370.2012.01.009. [14] wang, x.b., numerical simulation of failure processes and acoustic emissions of rock specimens with different strengths, journal of university of science and technology beijing, 30 (8) (2008) 837-843. [15] han, t.c., zhang, h.j., numerical simulation of acoustic emission for defective rock. chinese journal of rock mechanics and engineering, 33 (s1) (2014) 3198-3024. t s.r. wang et alii, frattura ed integrità strutturale, 36 (2016) 182-190; doi: 10.3221/igf-esis.36.18 190 [16] poerbandono, r., suprijo, t., modification of attenuation rate in range normalization of echo levels for obtaining frequency-dependent intensity data from 0.6 mhz and 1.0 mhz devices. journal of engineering and technological sciences, 45b (2) (2013) 140-152. doi: 10.5614/j.eng.technol.sci.2013.45.2.3. [17] miljenko, k., sinia, f., marin, m., principal component analysis in determining the best setup for acoustic measurements in sound control rooms. tehnicki vjesnik, 22 (5) (2015) 1327-1335. doi: 10.17559/tv-20150519115944. [18] garcia-barruetabena, j., cortes-martinez, f., isasa-gabilondo, i., study of the acoustic absorption properties of panels made from ground tire rubbers. dyna, 89 (2) (2014) 236-242. doi: 10.6036/5710. [19] yoder, m.r., holliday, j.r., turcotte, d.l., rundle, j.b., a geometric frequency-magnitude scaling transition: measuring b=1.5 for large earthquakes. tectonophysics, 532-535 (2012) 167-174. doi: 10.1016/j.tecto.2012.01.034. [20] yucemen, m.s., akkaya, a.d., robust estimation of magnitude-frequency relationship parameters. structure safety, 38 (2012) 32-39. doi: 10.1016/j.strusafe.2012.02.002. [21] el-isa, z.h., eaton, d.w., spatiotemporal variations in the b-value of earthquake magnitude-frequency distributions: classification and causes. tectonophysics, 615-616 (2014) 1-11. doi: 10.1016/j.tecto.2013.12.001. << /ascii85encodepages false /allowtransparency false /autopositionepsfiles true /autorotatepages /none /binding /left /calgrayprofile (dot gain 20%) /calrgbprofile (srgb iec61966-2.1) /calcmykprofile (u.s. web coated \050swop\051 v2) /srgbprofile (srgb iec61966-2.1) /cannotembedfontpolicy /error /compatibilitylevel 1.4 /compressobjects /tags /compresspages true /convertimagestoindexed true /passthroughjpegimages true /createjobticket false /defaultrenderingintent /default /detectblends true /detectcurves 0.0000 /colorconversionstrategy /cmyk /dothumbnails false /embedallfonts true /embedopentype false /parseiccprofilesincomments true /embedjoboptions true /dscreportinglevel 0 /emitdscwarnings false /endpage -1 /imagememory 1048576 /lockdistillerparams false 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can be opened with acrobat and adobe reader 5.0 and later.) >> /namespace [ (adobe) (common) (1.0) ] /othernamespaces [ << /asreaderspreads false /cropimagestoframes true /errorcontrol /warnandcontinue /flattenerignorespreadoverrides false /includeguidesgrids false /includenonprinting false /includeslug false /namespace [ (adobe) (indesign) (4.0) ] /omitplacedbitmaps false /omitplacedeps false /omitplacedpdf false /simulateoverprint /legacy >> << /addbleedmarks false /addcolorbars false /addcropmarks false /addpageinfo false /addregmarks false /convertcolors /converttocmyk /destinationprofilename () /destinationprofileselector /documentcmyk /downsample16bitimages true /flattenerpreset << /presetselector /mediumresolution >> /formelements false /generatestructure false /includebookmarks false /includehyperlinks false /includeinteractive false /includelayers false /includeprofiles false /multimediahandling /useobjectsettings /namespace [ (adobe) (creativesuite) (2.0) ] /pdfxoutputintentprofileselector /documentcmyk /preserveediting true /untaggedcmykhandling /leaveuntagged /untaggedrgbhandling /usedocumentprofile /usedocumentbleed false >> ] >> setdistillerparams << /hwresolution [2400 2400] /pagesize [612.000 792.000] >> setpagedevice microsoft word numero_35_art_53 t. haiyan, frattura ed integrità strutturale, 35 (2016) 472-480; doi: 10.3221/igf-esis.35.53 472 damage of bamboo and wooden materials based on linear elastic fracture mechanics in garden design tang haiyan city college of science and technology.chongqing university, chongqing, 402167, china tanghaiyan23@sina.com abstract. bamboo and wood are the most widely applied and the oldest natural structural materials in the world. currently, worldwide output of wooden material is 1 billion ton, almost the same as steel. most of them are used as structure, such as load carrying girder, scaffold, floor and support. wooden materials and bamboo materials with clear microstructure are composite biomaterials which can be studied under multiple scales. irregular evolution behaviors of initial defects or damage during loading determines macro mechanical behavior of wooden and bamboo materials. taking wood and bamboo as test materials, this study explored mechanical characteristics and damage crack behavior of wood and bamboo as well as toughening mechanism. keywords. wooden material; bamboo material; damage and crack; strengthening and toughening mechanism. introduction ood and bamboo with special garden aesthetic features play significantly important roles in classical or modern garden landscaping. wood and bamboo are natural structural materials which are the oldest and the most extensively applied worldwide. long before, people have used bamboo to build bamboo house and make scaffold and bamboo ladder. thus it is of great significance to study strength of natural structural materials and understand damage behavior for design and safety evaluation of bamboo and wooden structure. mechanism of crack of materials and how to control occurrence of crack incidents are always being explored by material science researchers and engineering technicians [1]. he et al. [2] replaced bamboo joint with equivalent crack length lc which stands for the length of crack produced by clear specimen bearing a stress the same as which results in initial cracking on burl specimen, but the method is only applicable for cross grain tensile loading. shao [3] proved that crack expanded in a direction that is vertical to notch, even under parallel-to-grain stress. moreover, deng et al. carried out a study on type i crack on two hard woods and softwoods using acoustic emission monitoring device. someone has also found that old wooden material is easier to produce small amplitude acoustic emission signal compared to new wooden material [5]. ying et al. [6] once explore physical mechanical properties of bamboo, and yong et al. [7] compared banding property between bamboo and wood. compared to crack of w t. haiyan, frattura ed integrità strutturale, 35 (2016) 472-480; doi: 10.3221/igf-esis.35.53 473 wood, research on crack of bamboo is fewer. only amada et al. [8] has studied transverse bending crack of bamboo and pointed that could be used as structural material because of its well-matched toughness and strength of cross grain crack. to select out bamboo and wood suitable for garden landscaping and explore damage crack behavior and toughening mechanism of biomaterials comprehensively, this study performed theoretical derivation in combination with experiment to study damage crack mode of different kinds of woods and bamboos. linear elastic fracture mechanical characteristics of wood rack and defect are inevitable in engineering materials. they produce either in production process, processing process or using process. for example, fatigue crack, compressive injury, ring shake and radial shake will generate under alternating force [9]. to conveniently study strength of cracked body, we classify cracks into three categories, opening mode (mode i) produced under external normal stress, sliding mode (mode ii) produced under shear stress parallel to crack direction and tearing mode (mode iii) produced under stress that can stagger crack surface, according to stress and characteristics of crack (fig.1). mode i mode ii mode iii figure 1: illustrations for mode i, mode ii and mode iii crack. particularity of application of linear elastic fracture mechanics in wood wood is an anisotropic and heterogeneous material. stress-strain curve of wood in different loading form is linear, consistent with linear elastic behavior [10]. its three elastic symmetry planes are vertical to length wise direction (l), radial direction (r) and tangential direction (t). thus, if we use the first symbol to express the normal direction and the second symbol as expansion direction of crack, then there are six kinds of crack growth forms, i.e., tl, rl, lt, lr, tr and rt, as shown in tab. 1. orthotropic materials usually have more complicated crack than isotropic material [11]. we derive equations for stress and displacement field of crack tip of orthogonal anisotropic material using complex variables functions [12]. 1 2 3 1 2 3 re ( , , , , , ) 2 2 re ( , , , , , ) ij ij ij ij ij ij k f u u u r k r v f u u u g                     (1) where aij is elastic constant of material; ul, u2 and u3 are compound parameters of materials which are determined by degree of anisotropy and angle α between crack and long grain fiber (fig. 2) and re is real part of complex function fij. c t. haiyan, frattura ed integrità strutturale, 35 (2016) 472-480; doi: 10.3221/igf-esis.35.53 474 r t l r t l table 1: classification extension of wood basic crack. figure 2: illustration for direction of crack and fiber. it can be found from the above equations that, crack of orthogonal anisotropic material is much more complicated than isotropic material. the differences are as follows. first, crack of orthogonal anisotropic material expands in the direction of fiber rather than the initial direction. but linear elastic fracture mechanics presupposes that, crack always expands in the initial direction [13]. secondly, even if under a simple-form loading, crack tip of orthogonal anisotropic material can also displace in a compound way, which is different from linear elastic fracture mechanics principle based on distinction means of mode i, ii and iii. stress field of crack tip of orthogonal anisotropic material is a function with regard to composite parameters of materials, and meanwhile these parameters are a function with regard to material property and angle α between crack and fiber direction. it is also different from linear elastic fracture mechanics principle that develops from the statement that stress distribution of crack tip is in no correlation to property and direction of material texture. based on the above facts, linear elastic fracture mechanics theory is not applicable to orthogonal anisotropic material. that is because we cannot define crack toughness of orthogonal anisotropic material with three material constants kic, t. haiyan, frattura ed integrità strutturale, 35 (2016) 472-480; doi: 10.3221/igf-esis.35.53 475 kiic and kiiic, unless investigate every condition when crack and fiber direction have any fixed angle and test applicability of linear elastic fracture mechanics under all condition, but the operation is inconvenient and even impossible [14]. however, if the initial direction of crack is consistent with fiber and principal axis of orthotropy is coincident with crack surface direction and crack growth direction, all derivation with linear elastic fracture mechanics theory mentioned above can be eliminated. that is because many experiments have verified that, crack expands in initial direction which is consistent with direction of fiber; displacement is no longer compound; composite parameters of materials are constants under the condition of fixed crack and fiber direction (a=0), thus stress distribution of crack tip is only a function with regard to r and θ. the above three situations suggest that, theory of linear elastic fracture mechanics is applicable for crack whose direction is consistent with fiber. most cracks and defects formed in the growing period of tree and processing process are in the direction of fiber of wood, as the resistance to expansion of crack is the minimum in the direction of fiber. as tl crack growth is quite similar to radial shake and meanwhile rl crack growth is similar to ring shake, theory of linear elastic fracture mechanics is thought to be applicable for parallel-to-grain growth of crack of wood. studying and measuring toughness which is a representation of resistance to parallel-to-grain cracking of wood is of important practical value for design of wooden structure and processing technique optimization. process of damage crack on wood rack mechanics is a subject involving macro crack growth rule and quantitative analysis [15], but mechanical effects of inevitable microdefects which have existed before macro cracks are not included. in wood, a large amount of original microdefects such as pit, crack on cell wall and interface damage will gradually evolve or emerge into macro crack under load. wood damage refers to mechanical property degradation induced by progressive decrease of internal cohesion resulting from microdefects formed under the effect of load or environment. it is an irreversible and energy-consuming process of internal microstructure. macro cracks form when damage variable reaches extreme value. damage evolution is the premise for formation of cracks and moreover crack growth expands the damage; therefore, damage and crack of wooden materials reflects a whole physical process from deformation to damage. materials, equipments and methods this test is to explore the effect of defects on acoustic emission in the process of bending taking picea jezoensis as test material. picea jezoensis is made into two groups of specimens, i.e., standard group (wood without crack and in a size of 300(l) × 20(t) ×20(r) (mm)) and crack group (wood in a size of 300(l) × 30(t) × 20(r) (mm)). wood in crack group is cut a 10 mm deep sharp crack along tangential direction to make a 20×20 (mm) net section on crack tip. both groups include 30 specimens, 60 in total. three-point bending load along tangential direction is used. equipments used in the test include microcomputer controlled material testing machine, ae-4 acoustic emission equipment [16] and r1 acoustic emission sensor. compared to other non-destructive testing technologies, acoustic emission technique has a distinctive character, that is, detected objects involve in the detection process actively. based on the received acoustic wave and external conditions inducing acoustic wave, we can understand both the status of defects and formation of defects as well as growth tendency under practical condition [17]. therefore, acoustic emission technology can be used in monitoring damage accumulation of materials in the process of deformation and failure, identifying failure mechanism and confirming damage site. experimental results and analysis it is difficult to identify and distinguish acoustic emission signals derived from different damage mode in different stages of bending of wood. that is because, wood as a composite biomaterial with multiple unit structures usually has multiple kinds of deformation and damage which can change energy in the same stage in the process zone around crack tip. therefore, we design a double cantilever beam on parallel-to-grain cracking and a compression test (fig. 3). mode i crack is found in the former test and the latter test only results in cell wall bending and collapse damage. experimental results suggest that, parallel-to-grain cracking only leads to low amplitude and low energy acoustic emission event, whereas acoustic emission signal produced by bending and collapse even has lower energy. we analyzed and summarized a large amount of acoustic signals from different wood samples and found that, peak amplitude vmax in acoustic emission parameters and root mean square (rms) of effective voltage can be used to identify different damage type, when sensor is put in a place less than 10 m away from damage source. rms is more effective and c t. haiyan, frattura ed integrità strutturale, 35 (2016) 472-480; doi: 10.3221/igf-esis.35.53 476 it is directly correlated to energy released by acoustic emission events. vmax and rms under different condition are shown in tab. 2. (a) double cantilever beam test (b) compression test figure 3: illustration for double cantilever beam test (a) and compression test (b). category of damage bending and collapse of cell wall delamination splitting crack on fibre bundle tearing and fracture on cell wall vmax mv < 2 < 64 < 0.5 < 53 db < 11 < 79 < 1 < 61 rms mv < 34 < 90 < 11 < 81 db > 34 > 90 > 11 > 81 table 2: acoustic emission characteristics of wood with different damage. mechanical characteristics of bamboo structure test samples he ninth and twentieth joint of three-year moso bamboo were cut down and split into bars (200 mm×10mm) after air-seasoning. then the bamboo was made into 60 tensile samples which was wide and thick on two ends and thick and thin in the middle. 60mm×5mm×1.5mm was the size of major section for testing. as the sample was cut from different radial position of bamboo, fibre bundle contained in the cross section was also different. 12.5% of the test sample was water and the experiment was carried out at 25 °c. simplified mechanical model and testing principle bamboo materials cut from parts between joints can be considered as evenly distributed and continuous fibre reinforced composite material, if they have small thickness. bamboo fiber bundle is characterized by high strength and high modulus, while ground tissue of bamboo is just the opposite. meanwhile, the fragment from the starting point to emergence of facture in stress-strain curve is a straight line, as shown in fig. 4. therefore, parallel model composing of two elements (bamboo fiber and ground tissue) can be used to describe mechanical behavior of bamboo. deformation of two elements is assumed to be the same when carrying load. fc, ff, fm, σc, σf and σm are used to express force and stress that act on composite material, fiber and ground tissue. εc, εf, εm, ec, ef and em are used to express corresponding strain and elasticity modulus. cross sectional area of bamboo fiber, ground tissue and composite material is set as af, am and ac respectively. usually, content of two elements is expressed with volume fraction v, i.e., load acting on bamboo samples is shouldered by bamboo fiber and ground tissue. then we have: c f mf f f  (2) or t t. haiyan, frattura ed integrità strutturale, 35 (2016) 472-480; doi: 10.3221/igf-esis.35.53 477 c c f f m ma a a    (3) figure 4: - curves. both sides of eq. (2) are divided by ac, and then we get: c f f m mv v    (4) strain is the same when bamboo is under stress. c f m    (5) if we divide eq. (2) with εc ac, we get: f fc c m m c c c c c c aa a a a a        (6) when load is within linear strain range, then correlation of elastic modulus ec with elastic modulus and volume modulus of different element can be obtained. (1 )c f f m m f f m fe e v e v e v e v     (7) eq. (3) and (6) can be called as mixture law for mesomechanics of composite materials [18]. experiment and results the samples were placed in self-tightening fixture of microcomputer controlled mechanical machine and the test section of samples was installed with extensometer whose gauge length is 50 mm. then the force was loaded in a speed of 2 mm/min until fracture emerges. as ground tissue of bamboo, it has higher strength and modulus than bamboo fibre bundle, thus mechanical behavior of bamboo samples in tensile test is mainly determined by strength and rigidity of bamboo fiber bundle. corresponding stress-strain curve (fig. 4) shows up little or no non-linear deformation. small pieces cut from the position close to fracture was first placed into oven after being added with solution containing 10% glacial acetic acid and 10% hydrogen peroxide and then soaked for 2 or 3 days at 60 °c. afterwards, it was cut into section in a thickness of 15 μm after being softened by alternated cooling and t. haiyan, frattura ed integrità strutturale, 35 (2016) 472-480; doi: 10.3221/igf-esis.35.53 478 heating treatment in water [19], followed by staining, dehydration and transparent disposal. one or two hours later, the sections were embedded with neutral resins. then the area of fibre bundle was observed under microscope. tab. 3 demonstrates six layers of micro cross section (from inside to outside) and area of fibre bundle. the first layer (internal layer) vr=10.65% the second layer vr=14.33% the third layer vr=13% the fourth layer vr =27.3% the fifth layer vr =34.02% the sixth layer (external layer) vr=44.29% table 3: six layers of micro cross section (from inside to outside) and area of fibre bundle. limiting stress and elastic modulus of every bamboo sample were calculated.     0.936562.69 19.042 588.732 562.69 40.129 0.2219 40.351 40.129 0.955 c f b c f b rv e v r v v           (8) correlation between elastic modulus, tensile strength and volume fraction of fiber can be obtained when we correlate results obtained above and volume fraction of fiber together, as shown in fig. 5 and 6. figure 5: correlation between tensile of bamboo strength and volume fraction of fiber. t. haiyan, frattura ed integrità strutturale, 35 (2016) 472-480; doi: 10.3221/igf-esis.35.53 479 figure 6: correlation between elastic module of bamboo and volume fraction of fiber. both vf and vb were defined as 0. then we obtained the tensile strength of bamboo fiber 588.732mpaf  , tensile strength of ground tissue 19.042b mpa  and elastic modulus eb=0.2219gpa based on eq. (1). thus we consider bamboo fiber is the main component bearing load and its strength is larger than general steel materials. conclusions nder the effect of load, different mechanism associated with internal damage and crack of materials can induce different degrees of energy release, leading to abundant acoustic emission signals. applying acoustic emission technology can help identify the emergence and extension of different types of damage produced on wood in the process of loading. test results indicate the following three points. firstly, defect-free samples have slowly developed acoustic emission events in the initial stage of loading, and acoustic emission signals that emerge in that period are of low amplitude; a large number of high-amplitude acoustic amplitude signals emerge when loading reaches the peck value or crack appears. secondly, monitoring the damage of crack process of defective wood under three-point bending loading with acoustic emission can effectively identify initial stage of crack and extension stage. thirdly, characteristics of acoustic emission signals are associated with damage mode of wood; acoustic emission characteristics regarding facture on cell wall is high-amplitude, high-energy and long-lasting, while acoustic emission corresponding to cell wall interface damage and spalling damage as well as cell bending and collapse damage is low-amplitude, low-energy and lasts for short time. we tested and analyzed mechanical performance of bamboo samples cut from bamboo wall along radial direction and bamboo fiber bundle isolated from bamboo materials with rule of mixture and shearing-lag theory. we found strength and elastic modulus of bamboo cut from bamboo wall along radical direction was positively correlated with volume fraction of bamboo fiber. fibre bundle of three-year moso-bamboo was detected to have 588.72 mpa tensile strength and 40.35gpa elastic modulus and tensile strength and elastic modulus of ground tissue were 19.42 mpa and 0.222 gpa. tensile strength and elastic modulus of single bamboo fibre bundle were detected to be 482.18 mpa and 33.85 gpa. thus we draw conclusions that, ground tissue is capable of transferring loading and dispersing stress loaded by fibre bundle evenly and strength of bamboo fiber gathering in ground tissue is higher than isolated bamboo fibre bundle. references [1] duggan, t.v., fatigue and fracture mechanics, physics in technology, 14(3) (1983) 126-132. [2] he, w., nakao, t., yoshinobu, m., treatment of fast-growing poplar with monomers using in situ polymerization, part i: dimensional stability and resistance to biodegradation, forest prod j, 61(2) (2011) 113-120. [3] shao, z., jiang, z., the particularity of application of principles of linear-elastic fracture mechanics to wood and fracture parallel to grain, scient silv sinic, 38(6) (2002) 110-115. u t. haiyan, frattura ed integrità strutturale, 35 (2016) 472-480; doi: 10.3221/igf-esis.35.53 480 [4] deng, h., yuan, x., li, j., fracture mechanics characteristics and deterioration mechanism of sandstone under reservoir immersion interaction, earth sci, 39(1) (2014) 108-114. [5] ando, k., hirashima, y., sugihara, m., hirao, s., sasaki, y., microscopic processes of shearing fracture of old wood, examined using the ae technique, j wood sci, 52 (2006) 483-89 [6] ying, s., wang, c., lin, q., effects of heat treatment on the properties of bamboo fiber/polypropylene composites. fiber polymers, 14(11) (2013) 1894-1898. doi: 10.1007/s12221-013-1894-5 [7] shi, y.-d., pan, l.-f., yang, f.-k., a preliminary study on the rheological properties of human ejaculate and changes during liquefaction, asian j androl, 6(4) (2004) 299-304. [8] amada, s., sun, u., fracture properties of bamboo. compos part b eng, 32(5) (2001) 451–459. doi:10.1016/s1359-8368(01)00022-1. [9] yan, j., taskonak, b., platt, j. a., evaluation of fracture toughness of human dentin using elastic-plastic fracture mechanics, j biomech, 41(6) (2008) 1253-1259. doi:10.1016/j.jbiomech.2008.01.015 [10] shao, z., jiang, z., the particularity of application of principles of linear-elastic fracture mechanics to wood and fracture parallel to grain, scient silv sinic, 38(6) (2002) 110-115. doi: 10.1002/nme.2366 [11] wang, b., feng, j. c., qing-fei, l. i., study on the effective mechanical properties of foam core sandwich structure reinforced by fiber composite columns, j harbin insti technol, 44(3) (2012) 29-33. [12] lee, k. h., influence of density variation on stress and displacement fields at a propagating mode-iii crack tip in orthotropic functionally graded materials, trans korean society mechanic eng., a, 35(2011) 1051-1061. [13] jiang, z., fei, b., zhang, d., application and prospect of digital speckle correlation method on wood science, eng sci, 5(11) (2003) 1-7. [14] liu, g., luo, c., zhang, d., mechanical performance and failure mechanism of thick-walled composite connecting rods fabricated by resin transfer molding technique, appl compos mater, (2014) 1-14. doi: 10.1007/s10443-014-9415-2. [15] lepov, v., ivanova, a., achikasova, v., modeling of the damage accumulation and fracture: structural-statistical aspects, key eng mater, 345-346 (2007) 809-812. [16] yao, g.h., song, z.p., xian-bin, y.u., experimental study on ae characteristics of limestone, coal geol explor, 34(6) (2006) 44-46. [17] mba, d., roberts, t., taheri, e., application of acoustic emission technology for detecting the onset and duration of contact in liquid lubricated mechanical seals, insight, 48(8) (2006) 486-487. [18] bai, x., lee, w.c., thompson, l.l., finite element analysis of moso bamboo-reinforced southern pine osb composite beams, wood fiber sci, 31(4) (1999) 403-415. [19] huang, s.x., li-na, m.a., shao, z.p., relationship between microstructure characteristics and mechanical properties of moso bamboo, j anhui agri univer, 32(2) (2005) 203-206. << /ascii85encodepages false /allowtransparency false /autopositionepsfiles true /autorotatepages /none /binding /left /calgrayprofile (dot gain 20%) /calrgbprofile (srgb iec61966-2.1) /calcmykprofile (u.s. web coated \050swop\051 v2) /srgbprofile (srgb iec61966-2.1) /cannotembedfontpolicy /error /compatibilitylevel 1.4 /compressobjects /tags /compresspages true /convertimagestoindexed true /passthroughjpegimages true /createjobticket false /defaultrenderingintent /default /detectblends true /detectcurves 0.0000 /colorconversionstrategy /cmyk /dothumbnails false /embedallfonts true /embedopentype false /parseiccprofilesincomments true /embedjoboptions true /dscreportinglevel 0 /emitdscwarnings false /endpage -1 /imagememory 1048576 /lockdistillerparams false /maxsubsetpct 100 /optimize true /opm 1 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/hrv (za stvaranje adobe pdf dokumenata najpogodnijih za visokokvalitetni ispis prije tiskanja koristite ove postavke. stvoreni pdf dokumenti mogu se otvoriti acrobat i adobe reader 5.0 i kasnijim verzijama.) /hun 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can be opened with acrobat and adobe reader 5.0 and later.) >> /namespace [ (adobe) (common) (1.0) ] /othernamespaces [ << /asreaderspreads false /cropimagestoframes true /errorcontrol /warnandcontinue /flattenerignorespreadoverrides false /includeguidesgrids false /includenonprinting false /includeslug false /namespace [ (adobe) (indesign) (4.0) ] /omitplacedbitmaps false /omitplacedeps false /omitplacedpdf false /simulateoverprint /legacy >> << /addbleedmarks false /addcolorbars false /addcropmarks false /addpageinfo false /addregmarks false /convertcolors /converttocmyk /destinationprofilename () /destinationprofileselector /documentcmyk /downsample16bitimages true /flattenerpreset << /presetselector /mediumresolution >> /formelements false /generatestructure false /includebookmarks false /includehyperlinks false /includeinteractive false /includelayers false /includeprofiles false /multimediahandling /useobjectsettings /namespace [ (adobe) (creativesuite) (2.0) ] /pdfxoutputintentprofileselector /documentcmyk /preserveediting true /untaggedcmykhandling /leaveuntagged /untaggedrgbhandling /usedocumentprofile /usedocumentbleed false >> ] >> setdistillerparams << /hwresolution [2400 2400] /pagesize [612.000 792.000] >> setpagedevice microsoft word numero_38_art_1 n. vaysfeld et alii, frattura ed integrità strutturale, 38 (2016) 1-11; doi: 10.3221/igf-esis.38.01 1 focussed on multiaxial fatigue and fracture on the stress investigation at the edges of the fixed elastic semi-strip n. vaysfeld odessa mechnikov university, institute of mathematics, economics and mechanics vaysfeld@onu.edu.ua o. kryvyi national university «odessa maritime academy» (nu «oma») krivoy-odessa@ukr.net, kryvyi-od@math.onma.edu.ua z. zhuravlova odessa mechnikov university, institute of mathematics, economics and mechanics zhuravleva@te.net.ua abstract. the stress state of the elastic fixed semi-strip with the regarding of the singularities at its edge is investigated in the article. the initial boundary problem is reduced to a vector boundary problem in the transformation’s domain by the use of integral fourier transformation. the one-dimensional vector boundary problem is solved exactly with the help of matrix differential calculations and green’s matrix apparatus. the problem’s solving was focused at the solving of the singular integral equation (sie) with the two fixed singularities at the ends of the integration’s interval. the symbol of sie was constructed and the generalized method of the sie solving was applied. the stress’ distributions of the semi-strip are investigated. keywords. semi-strip; vector boundary problem; singular integral equation; fixed singularity. citation: vaysfeld, n., kryvyi, o., zhuravlova, z., on the stress investigation at the edges of the fixed elastic semi-strip, frattura ed integrità strutturale, 38 (2016) 111. received: 14.04.2016 accepted: 09.06.2016 published: 01.10.2016 copyright: © 2016 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. introduction he plain elasticity problems for a semi-strip are important as the model examples for the different engineering applications. so many authors have examined these problems in their works. a short review of the different approaches to the solving of the plane elasticity problems for an elastic semi-strip is given below. the reducing of the problem to the fredholm's integral equation of the first kind was used in [1] for estimation of the symmetrically loaded semi-strip fixed by the short edge. another approach based on the construction of the stress function as the combination of the fourier’s integrals and the series was used in [2, 3]. the problems for a semi-strip considered in [4, 5] were reduced to the singular integral equations which were solved numerically, it leaded to the solving t n. vaysfeld et alii, frattura ed integrità strutturale, 38 (2016) 1-11; doi: 10.3221/igf-esis.38.01 2 of an infinity system of the algebraic equations. the variation method was used for the analogical problem’s solving in [68]. the energetic method was applied to the problem of the semi-strip with the free lateral edges and loaded short edge in [9]. in [10] authors constructed a special system of byorthogonal functions, with the help of which they solved the problem on a semi-strip loading at it’s the short edge. the problem for the semi-strip with the free longitudinal sides was solved with the help of the stress function in [11, 12]. the laplace’s integral transformation was used for the problem’s solving in [13]. the approach based on the use of fadle-papkovich functions was applied in [14-16]. in this paper the method, which was worked out by g. ya. popov, was used [17]. accordingly to it the integral transformations were applied directly to the equilibrium equations and boundary conditions of a problem. it leaded the initial problem to one-dimensional boundary problem in the transformation’s domain. the last one was formulated as the vector boundary valued problem and solved exactly with the apparatuses of the matrix differential calculations and green’s matrix function [18]. the problem was reduced to the singular integral equation’s solving. investigation of the signature’s nature of the singular integral equation’s solving was under consideration of many famous scientists. today the new theories are appeared, which describe the solution’s behavior at the particular points [19]. the investigations of the singularities’ nature for the complex medium are continued [20]. but in most studies the authors did not pay attention to the fixed singularities at the angular points of the semi-strip usually, although these singularities play a main role in the estimation of the stress state. one approach that allows to find and to take such singularities into account was proposed in widely known work [21]. it was used in this paper for the fixed singularities’ consideration. the special generalized method, which was proposed in [22, 23], was applied to obtain the solution of the (sie) with regarding of the solution’s two fixed singularities at the end of the integration’s interval. figure 1: geometry of the problem. the statement of a problem he elastic ( g is a share module,  is a poison’s coefficient) semi-strip, x a y0 , 0     is considered. at the edge y x a0, 0   the semi-strip is loaded  y xyx p x x x a( , 0) , ( , 0) 0, 0      (1) where p x( ) is the known function. at the lateral sides x y0, 0    and x a y, 0    the boundary conditions of the fixed are given        u y v y u a y v a y y0, 0, 0, 0, , 0, , 0, 0       (2) t n. vaysfeld et alii, frattura ed integrità strutturale, 38 (2016) 1-11; doi: 10.3221/igf-esis.38.01 3 here  xu x y u x y( , ) , ,  yv x y u x y( , ) , are the displacements which satisfy the lame’s equations. the lame’s equations are written in the following form [24] u x y u x y v x y x yx y v x y v x y u x y x yx y 2 2 2 * 02 2 2 2 2 * 02 2 ( , ) ( , ) ( , ) 0 ( , ) ( , ) ( , ) 0                         (3) where  0 * 0 1 , 1 1 2      . after the expression of the constants 0 *,  through the muskchelishvili constant 3 4   , one obtains the system (3) in the another form u x y u x y v x y x yx y v x y v x y u x y x yx y 2 2 2 2 2 2 2 2 2 2 ( , ) ( , ) ( , )1 2 0 1 1 ( , ) ( , ) ( , )1 2 0 1 1                              (4) the boundary conditions on the semi-strip’s edge are reformulated with the terms of the displacements         u x v x g p x x a x y 0 , 0 , 0 2 1 , 0                (5)    u x v x x a y x , 0 , 0 0, 0         (6) one needs to solve the boundary value problem (2), (4)-(6) to estimate the stress state of the semi-strip. the general solving scheme of the problems on the semi-strip stress state estimation he fourier’s transformation is applied to the system of lame’s equation and to the boundary conditions by the scheme     u x yu x y dy v x yv x y 0 ( ) cos, ( ) sin,                       (7) with the inverse formula     u x yu x y d v x yv x y 0 ( ) cos, 2 ( ) sin,                     (8) the initial problem has the form after this t n. vaysfeld et alii, frattura ed integrità strutturale, 38 (2016) 1-11; doi: 10.3221/igf-esis.38.01 4 u x u x v x x v x v x u x x u u a v v a 2 2 ( -1) 2 3 " ( ) ( ) ' ( ) '( ) 1 1 1 ( 1) 2 1 " ( ) ( ) ' ( ) ( ) 1 1 1 (0) 0, ( ) 0 (0) 0, ( ) 0                                                  (9) here the new unknown function is inputted        x v x x v x, 0 , ' ' , 0   . as it is seen from the boundary condition (6),    u x xy , 0 '    , so the condition (6) is satisfied automatically. with the aim to reduce the problem to the vector boundary problem one must input the vectors and the matrixes       u x y x v x             ,       x f x x 3 ' 1 1 1                    , p 1 0 1 1 0 1                , q 1 0 1 1 0 1              . then the equations in the vector form will be written as the vector equation    l y x f x2    , where l2 is a differential operator of the second order        l y x iy x qy x py x22 " 2 '           , i is an identity matrix. the integral transformations also should be applied to the boundary conditions, with the aim to formulate the boundary functionals in the transformations’ domain. as a result the vector boundary problem is constructed         l y x f x y y a 2 0 0, 0          (10) the solving of the vector boundary value problem he solution of the vector boundary problem (10) will be searched as the superposition of a homogenous vector equation’s general solution  y x0  and a particular solution of the inhomogeneous one  y x1       y x y x y x0 1       these solutions were constructed with the help of the matrix differential calculation apparatus earlier [18].         c c y x y x y x y x c c 1 3 1 1 2 2 4                   where  iy x i, 0,1 are the matrix system of the fundamental matrix solutions [18]:             x x x x x x e e y x y x x x x x1 2 1 1 1 1 , 2 2 1 1 1 1                                                        where constants ic i, 1, 4 are founded from the boundary conditions [18]. t n. vaysfeld et alii, frattura ed integrità strutturale, 38 (2016) 1-11; doi: 10.3221/igf-esis.38.01 5 for the obtaining of the vector boundary problem’s particular solution  y x1  , was constructed the green’s matrix function [18]. elements of matrix are shown in the appendix a. the inhomogeneous boundary problem’s final form of the solution is constructed         ac c y x y x y x g x f d c c 1 3 1 2 2 4 0 , ( )                    (11) the components of (11) can be written in the next form                 a a u x y x c y x c y x c y x c g x d g x d11 12 11 12 11 121 1 1 2 2 3 2 4 0 0 3 1 ( ) , ' , 1 1                                          a a v x y x c y x c y x c y x c g x d g x d21 22 21 22 21 221 1 1 2 2 3 2 4 0 0 3 1 ( ) , ' , 1 1                          where  i jg x, , is the green’s matrix function element in a i row and j column. the integrals with the function    are calculated by the parts and the inverse integral transformations’ formulae were applied to the displacements’ transformations.                 a a u x y f x y d d v x y f x y d d 1 0 0 2 0 0 , ' , , cos , ' , , cos                       (12) where    i if x g x i, , , , , , 1, 2     are known functions. the formulae (12) would be the final ones if the unknown function  '  is known. for its finding one must satisfy the boundary conditions (5) which are unsatisfied yet. it should be taken into consideration that integrals in these correspondences are conditionally convergent integrals. so, before the differentiating of the displacements’ expressions, at first one must extract the weakly convergence parts at these integrals. the substitution of (12) in the boundary conditions (5) leads to the singular integral equation       a f x d r x x a* * * * * * 0 ' , , 0       here the function  f x, contains cauchy’s type singularities and fixed singularities on the both ends of the integration interval. the solving of the singular integral equation he changing of the variables a x a x a a * *2 2 ,       is done for the passing to the integration interval  1;1 . as a result the integral equation is transformed to the form t n. vaysfeld et alii, frattura ed integrità strutturale, 38 (2016) 1-11; doi: 10.3221/igf-esis.38.01 6                                     c c x c c xc с c d x x x x x x x c x c x d k x d r x x x x 1 1 3,1 3,2 3,1 3,22 2 1 2 2 2 2 1 1 1 4 4 3 3 1 1 1 1 1 2 2 2 2 2 2 1 1 1 1 , , 1 1 2 2                                                                                 (13) here    a 1 2             ,    k x r x, ,  are the known regular functions, ic i, 1, 4   are shown in the application b. the eq. (13) is the partial case of the equation with two fixed singularities considered [21]                          m mkn k k m k m k kkkk k y c x y x x yc a x c x dy dy i y x i y y xy k x y y dy f x m k 1 1 21 0 101 1 1 1 , 1 11 1 1 1 , , 0 re                                   which can be rewritten as                  a x c x c s x n x n x k x k x y y dy f x 1 0 1 1 1 1 1 1 ,                where               mn k k k k kxkm kkk x yc n x dy c c c x i y x y 1 2 1 11 0 1 1 1 , 1, 1 lim , 1 2                           , the symbol of the singular integral eq. (13) was constructed, which has the following form, where all designations correspond to the designations in [21]                     mk k k k mk k k k c s c n r a a a c s c n r 2 1 2 , 0, 2 1 2 , 0 , , , ,                                             (14)          p s z cth i z z1 / , , , , ,                ,         k mk k k kk k k n iz m sh i z, 1 1 ,            , n. vaysfeld et alii, frattura ed integrità strutturale, 38 (2016) 1-11; doi: 10.3221/igf-esis.38.01 7                    g zi i pg i a z z i z i p p g zi i g z i i p p z i i z i p p 1 4 1 2 2 2 1 1 sinh 2 1 sinh 2 1 1 1 1 4 2 1 2 cosh 1 3 1 1 sinh 2 1 1 sinh                                                                                                             g zi zi i p p z i i p 1 1 16 1 1 2 1 1 sinh 1                                              here p 2 , 0.31   is found from the known solution of the analogical problem for an edge with the angle of openness pi/2 [25]. according to [21] one needs to find the roots of the equation  a z 0  . the found roots of the kernel’s symbol (14) have the next form: 1,2 0.5562 0.3690,    3,4 1.2792 0.2380,   5,6 3.2089 0.7127,   7,8 5.2170 1.0251, ...   , where k k  because of the problem’s statement. the generalized method of sie solving [22, 23] was applied for the solving of the eq. (13). according to it the unknown function    is expanded by the series in each interval           n k k k n k k k n s s 1 0 2 1 , 1; 0 , 0;1                           (15) where               k k k k k k n k re 2 re 2 1 1 cos im ln 1 , 0, 1 21 sin im ln 1 ,                          ,               k n k k n k n k k n n k n re 2 re 2 1 1 cos im ln 1 , , 1 21 sin im ln 1 ,                              . the segment  1;1 is divided on n2 equal segments with the length h n 1  . the eq. (13) is considered when i h x ih i n1 , 0, 2 1 2       . after the substitution of the unknown function (15) into the singular integral eq. (13) one obtains system of the linear algebraic equations relatively to the unknown constants ks k n, 0, 2 1  of the expansion (15). n k ki i k s d f i n 2 1 0 , 0, 2 1      (16) where ki id f i k n, , , 0, 2 1  are shown in the application c. the expression (16) presents the system of n2 equations with regard of n2 unknown constants ks . the substitution of the founded constants in the formula (15) and following using of the formulae (12) completes the construction of the problem’s solution. n. vaysfeld et alii, frattura ed integrità strutturale, 38 (2016) 1-11; doi: 10.3221/igf-esis.38.01 8 the results of the numerical analyses he calculations were done for the elastic semi-strip ( g 961.2781955 10  pa, 0.33  ). at fig.2 one can admit that the values of the normal stress y y x xp p/ , /      at the lateral side x 0 decrease to zero with the increasing of the distance from the semi-strip’s edge. when the semi-strip’s side is a 10 . a similar situation is observed during the analyses of the stress y x,   when the semi-strip’s side is a 50 (fig.4) and a 100 (fig.6). at fig.3 one can admit that the absolute values of the normal stress y at the line  x a y/ 2, 0;10  are higher by its absolute value then normal stress x when the semi-strip’s side is a 10 . a similar situation is observed during the analyses of the stress y x,  when the semi-strip’s side is a 50 (fig.5) and a 100 (fig.7). as it is seen the stabilization of the stresses y x,  is observed when the semi-strip’s side is a 50 (fig.5) or a 100 (fig.7). figure 2: normal stresses    y xy y a0, , 0, , 10    . figure 3: normal stresses    y xa y a y a/ 2, , / 2, , 10    . figure 4: normal stresses    y xy y a0, , 0, , 50    . figure 5: normal stresses    y xa y a y a/ 2, , / 2, , 50    . t n. vaysfeld et alii, frattura ed integrità strutturale, 38 (2016) 1-11; doi: 10.3221/igf-esis.38.01 9 figure 6: normal stresses    y xy y a0, , 0, , 100    . figure 7: normal stresses    y xa y a y a/ 2, , / 2, , 100    . conclusions 1. the proposed solving method reduced the initial problem to the singular integral equation, which has the two fixed singularities at the end of the integration’s interval. the special generalized scheme of sie solving was applied with the aim to take these singularities into consideration. 2. the proposed approach may be applied to the solving of the elasticity mixed problem for the semi-strip with a crack. 3. the analyses of the numerical results show that the taking into consideration the existence of the two fixed singularities of the solution gives the possibility to obtain the numerical result on the distance less than a/1000 to the angular point of the semi-strip in comparison with the usual approach to the solving, allowing to get the stable results only on the distance to the angular points not less than a/10. appendix a                                          ch a x ch a x g x sh a sh a sh a x xsh a x sh a ash a x a x ash a x ach a ch a x ch a x 11 2 , 2 1 1 2 1                                                                                           ach a g x sh a x sh a ch a x sh a x ch a x a x x ch a x a x 12 2 1 , 2 1 1 1 sgn sgn                                           n. vaysfeld et alii, frattura ed integrità strutturale, 38 (2016) 1-11; doi: 10.3221/igf-esis.38.01 10                                ach a g x sh a x sh a ch a x sh a x ch a x a x x ch a x a x 21 2 1 , 2 1 1 1 sgn sgn                                                                                      ch a x ch a x g x sh a sh a ch a x ch a x sh a a x sh a x a x sh a x a ch a ch a x ch a x 22 2 , 2 1 2 1                                                              appendix b                                       g g g g c c c c c g g g g g c c c c c 0 1 2 2 3,1 3,2 3,1 3,2 4 4 2 3 1 2 2 2 2 4 2 0, , , , , 2 1 1 2 1 2 1 2 1 1 4 2 1 4 2 4 2 1 16 16 , , , , 2 1 1 2 1 1 2 1 1 1 1                                                                                                 appendix c                                 i i ki k i i i i i i i i i i i i ki k i i c c x c c xc c с d x x x x x x x c x c x k x d k n i n x x c c с d x x 0 3,1 3,2 3,1 3,21 2 2 2 2 2 2 1 4 4 3 3 1 2 2 1 1 1 1 2 2 2 2 2 2 1 1 1 1 , , 0, 1, 0, 2 1 2 2 2                                                                                                                i i i i i i i i i i i i i i c c x c c x x x x x x c x c x k x d k n i n x x f r x i n 1 3,1 3,2 3,1 3,2 2 2 2 2 0 4 4 3 3 1 1 1 1 2 2 2 2 2 1 1 1 1 , , 0, 1, 0, 2 1 2 2 , 0, 2 1                                                             references [1] vorovich, i. i., kopasenko, v. v., some problems of elasticity theory for the semi-strip. (in russian), prikladnaya matematica i mekchanica, 30(1) (1966) 128-136. [2] pickett, g., jyengar, k. t. s., stress concentrations in post-tensioned prestressed concrete beams, j. technol., india, 1(2) (1956). [3] yamasida, research of the tensions in semi-infinite strip under acting forces applied to its edge, trans. japan. soc. mech. engrs, 20(95) (1954) 466. n. vaysfeld et alii, frattura ed integrità strutturale, 38 (2016) 1-11; doi: 10.3221/igf-esis.38.01 11 [4] koiter, w., alblas, j., on the bending of cantilever rectangular plates, proc. koninke nederl. acad. wet. b., 57(2) (1954). [5] aglovyan, l. a., gevorkyan, r. s., about some mixed problems of elasticity theory for the semi-strip (in russian), news of academy of science armenian ssr, mechanics, 23(3) (1970) 3-13. [6] trapeznikov, l. p., influence lines for the normal tensions in semi-strip (in russian), news of ussr n.-i. of the hydromechanical institute, 73 (1963). [7] kolchin, g. b., plyat, sh. n., sheykner, n. ya., some problems of the themoelasticity for the rectangular areas (in russian), shtiica, (1980). [8] suchevan, v. g., the tensioned state of the elastic semi-strip with fixed edges (in russian), matematiceskie issledovaniya, 40 (1976) 122-135. [9] thecaris, p. the stress distribution in a semi-infinite strip subjected to a concentrated load, trans. j. appl. mech., 26(3) (1959) 401–406. [10] johnson, m. w., little, r. w., the semi-infinite elastic strip, q. appl. math., 22(4) (1965) 335-344. [11] horvay, g., the end problem of rectangular strips, j. appl. mech., 20 (1953) 87-94. [12] horvay, g., born, j., some mixed boundary-value problems of the semi-infinite strip, journal of applied mechanics, 24(2) (1957) 261-268. [13] benthem, j.p., a laplace transform method for the solution of semi-infinite and finite strip problems in stress analiesis, quart. j. mech. and appl. math., 16(4) (1963) 413-429. [14] gogoleva, o. s., the examples of solutions of the first main boundary problem of elasticity theory in the semi-strip (symmetrical problem) (in russian), journal omskiy gosudarstvenniy universitet, 145(9) (2012) 138-142. [15] kovalenko, m. d., shulyakovskaya, t. d., expansion of fadle-papkovich functions in the strip. bases of theory (in russian), mechanica tverdogo tela, 5 (2011) 78-98. [16] menshova, i. v., lapikova, e. s., the semi-strip with lateral edges rigidity, working for tension-compression (in russian), journal chgpu named i. ya. yakovlev, series: mechanic of the limited state, 20(2) (2014) 106-118. [17] popov, g. ya., about new transformations of the elasticity resolving equations and the new integral transformations with their application to the boundary problems of mechanics, intern appl. mech., 39 (2003) 1046-1071. [18] vaysfel’d, n. d., zhuravlova, z. yu., on one new approach to the solving of an elasticity mixed problem for the semi-strip, acta mechanica, 226(12) (2015) 4159-4172, doi: 10.1007/s00707-015-1452-x. [19] ciavarella, m., paggi, m., carpinteri, a., one, no one, and one hundred thousand crack propagation laws: a generalized barenblatt and botvina dimensional analysis approach to fatigue crack growth, journal of the mechanics and physics of solids, 56(12) (2008) 3416-3432. [20] carpinteri, a., paggi, m., analytical study of the singularities arising at multi-material interfaces in 2d linear elastic problems, engineering fracture mechanics, 74(1) (2007) 59-74. [21] duduchava, r. v., integral convolution equations with discontinuous presymbols, singular integral equations with fixed singularity and their application to the mechanical problems (in russian), tbilisi, mecniereba, (1979). [22] kryvyy, o. f., tunnel internal crack in a piecewise homogeneous anisotropic space, journ. of mathematical sciences, 198(1) (2014) 62-74. [23] kryvyi, o. f., mutual influence of an interface tunnel crack and an interface tunnel inclusion in a piecewise homogeneous anisotropic space, journ. of mathematical sciences, 208(4) (2015) 409-416. [24] popov, g.ya., the elastic stress' concentration around dies, cuts, thin inclusions and reinforcements (in russian), nauka, moskow (1982). [25] uflyand, ya. s., integral transformations in the problems of the elasticity theory (in russian), nauka, l., (1967). << /ascii85encodepages false /allowtransparency false /autopositionepsfiles true /autorotatepages /none /binding /left /calgrayprofile (dot gain 20%) /calrgbprofile (srgb iec61966-2.1) /calcmykprofile (u.s. web coated \050swop\051 v2) /srgbprofile (srgb iec61966-2.1) /cannotembedfontpolicy /error /compatibilitylevel 1.4 /compressobjects /tags /compresspages true /convertimagestoindexed true /passthroughjpegimages true /createjobticket false /defaultrenderingintent /default /detectblends true /detectcurves 0.0000 /colorconversionstrategy /cmyk /dothumbnails false /embedallfonts true /embedopentype false /parseiccprofilesincomments true /embedjoboptions true /dscreportinglevel 0 /emitdscwarnings false /endpage -1 /imagememory 1048576 /lockdistillerparams false /maxsubsetpct 100 /optimize true /opm 1 /parsedsccomments true /parsedsccommentsfordocinfo true 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<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> /enu (use these settings to create adobe pdf documents best suited for high-quality prepress printing. created pdf documents can be opened with acrobat and adobe reader 5.0 and later.) >> /namespace [ (adobe) (common) (1.0) ] /othernamespaces [ << /asreaderspreads false /cropimagestoframes true /errorcontrol /warnandcontinue /flattenerignorespreadoverrides false /includeguidesgrids false /includenonprinting false /includeslug false /namespace [ (adobe) (indesign) (4.0) ] /omitplacedbitmaps false /omitplacedeps false /omitplacedpdf false /simulateoverprint /legacy >> << /addbleedmarks false /addcolorbars false /addcropmarks false /addpageinfo false /addregmarks false /convertcolors /converttocmyk /destinationprofilename () /destinationprofileselector /documentcmyk /downsample16bitimages true /flattenerpreset << /presetselector /mediumresolution >> /formelements false /generatestructure false /includebookmarks false /includehyperlinks false /includeinteractive false /includelayers false /includeprofiles false /multimediahandling /useobjectsettings /namespace [ (adobe) (creativesuite) (2.0) ] /pdfxoutputintentprofileselector /documentcmyk /preserveediting true /untaggedcmykhandling /leaveuntagged /untaggedrgbhandling /usedocumentprofile /usedocumentbleed false >> ] >> setdistillerparams << /hwresolution [2400 2400] /pagesize [612.000 792.000] >> setpagedevice microsoft word numero_37_art_27 l. susmel et alii, frattura ed integrità strutturale, 37 (2016) 207-214; doi: 10.3221/igf-esis.37.27 207 focussed on multiaxial fatigue and fracture designing aluminium friction stir welded joints against multiaxial fatigue l. susmel the university of sheffield, sheffield s1 3jd, united kingdom l.susmel@sheffield.ac.uk d. g. hattingh nelson mandela metropolitan university, private bag x6011, port elizabeth 6000, south africa danie.hattingh@nmmu.ac.za m. n. james university of plymouth, drake circus, devon pl4 8aa, england, united kingdom m.james@plymouth.ac.uk e. maggiolini, r. tovo university of ferrara, via saragat 1, 44100 ferrara, italy mggnrc@unife.it, roberto.tovo@unife.it abstract. the present paper investigates the accuracy of the modified wöhler curve method (mwcm) in estimating multiaxial fatigue strength of aluminium friction stir (fs) welded joints. having developed a bespoke joining technology, circumferentially fs welded tubular specimens of al 6082-t6 were tested under proportional and non-proportional tension and torsion, the effect of non-zero mean stresses being also investigated. the validation exercise carried out using the experimental results have demonstrated that the mwcm applied in terms of nominal stresses, notch stresses, and also the point method is accurate in predicting the fatigue lifetime of the tested fs welded joints, with its use resulting in life estimates that fall within the uniaxial and torsional calibration scatter bands. keywords. friction stir welding; multiaxial fatigue; critical plane. introduction riction stir (fs) welding is a joining process that allows joints with high mechanical performance to be manufactured at a relatively low cost. thanks to its specific features, in recent years this joining technology has been employed successfully in different industrial sectors [1] which include, amongst others, ship building [2], transportation [3], and aircraft [4]. in terms of design against fatigue, whilst a tremendous effort has been made since the f l. susmel et alii, frattura ed integrità strutturale, 37 (2016) 207-214; doi: 10.3221/igf-esis.37.27 208 mid-90s to investigate the fatigue behaviour of aluminium fs welded joints subjected to uniaxial cyclic loading (see, for instance, ref. [5] and references reported therein), no systematic research work has been carried out so far to formulate and validate specific methodologies suitable for performing the multiaxial fatigue assessment of this type of joints. in this context, this paper summarises a part of the outcomes from an international network research project sponsored by the leverhulme trust (www.leverhulme.ac.uk) on multiaxial fatigue assessment of aluminium fs welded tubular connections. fundamentals of the modified wöhler curve method he mwcm is a critical plane approach which assesses fatigue damage under uniaxial/multiaxial fatigue loading via the maximum shear stress amplitude, a, as well as via the mean value, n,m, and the amplitude, n,a, of the stress normal to that material plane experiencing the maximum shear stress amplitude [6]. the combined effect of the relevant stress components relative to the critical plane is quantified via the following stress index [7]: a a,nm,n eff m    (1) where m is the so-called mean stress sensitivity index [6, 7]. index m is a material fatigue property that ranges from zero (no mean stress sensitivity) to unity (full mean stress sensitivity) [6]. according to the way it is defined, ratio eff is sensitive not only to the presence of non-zero mean stresses [8], but also to the degree of multiaxiality and nonproportionality of the load history being assessed [6]. figure 1: modified wöhler diagram. the mwcm’s modus operandi is schematically explained through the modified wöhler diagram of figure 1. this log-log chart plots a against the number of cycles to failure, nf. much experimental evidence [6] suggests that, for a specific material, the modified wöhler curves tend to move downward as eff increases (fig. 1). in other words, for a given value of a, fatigue damage tends to increase as eff increases. according to the diagram in figure 1, the position and the negative inverse slope of any modified wöhler curve can be defined through the following linear relationships [6]:    effeffk (2)   ba effefffre,a  (3) t l. susmel et alii, frattura ed integrità strutturale, 37 (2016) 207-214; doi: 10.3221/igf-esis.37.27 209 in these equations, k(eff) is the negative inverse slope and a,ref(eff) is the reference shear stress amplitude extrapolated at na cycles to failure (fig. 1). constants , , a and b are material fatigue parameters that have to be determined through appropriate experiments [6]. observing that, in the absence of stress concentration phenomena, eff is equal to unity under fully-reversed uniaxial fatigue loading and to zero under torsional cyclic loading [6], the constants in eqs 2 and 3 can be estimated from the fully-reversed uniaxial and torsional fatigue curves as follows [6]:         0k0k1kk effeffeffeffeff  (4)   aeffaaefffre,a 2          (5) in eq. 4 k(eff=1) and k(eff=0) are the negative inverse slope of the uniaxial and torsional fatigue curve, respectively, whereas in eq. 5 a and a are the endurance limits extrapolated at na cycles to failure under fully-reversed uniaxial and torsional fatigue loading, respectively. as to calibration relationships 4 and 5, it is important to point out that a,ref(eff) and k(eff) are assumed to be constant and equal to a,ref(lim) and to k(lim), respectively, for eff values larger than an intrinsic material threshold denoted as lim [6, 8]. to estimate fatigue lifetime according to the mwcm, initially both a and eff have to be determined at the assumed critical location by adopting the appropriate algorithms [9, 10]. subsequently, the corresponding modified wöhler curve has to be derived from eqs 2 and 3 through the estimated value for eff. finally, the number of cycles to failure under the investigated load history can be predicted as follows [6]: )(k a effref,a af efft)( nn           (6) to conclude, it can be recalled that, as far as conventional welded joints are concerned, the mwcm has proven [11] to be accurate in performing the multiaxial fatigue assessment when it is applied not only in terms of nominal and hot-spot stresses, but also along with the reference radius concept as well as the theory of critical distances. (a) (b) (c) figure 2: i-stir fs welding platform equipped with a fourth axis (a); al 6082-t6 fs welded tubular specimen (b); transverse macrosection of the weld region (c). experimental details he technology used to manufacture the fs welded tubular samples for testing was developed at the nelson mandela metropolitan university, south africa. circumferential fs welds were manufactured by incorporating a fourth axis into a commercial i-stir platform (fig. 2a). in order to obtain high-quality welds, an ad hoc retracting t l. susmel et alii, frattura ed integrità strutturale, 37 (2016) 207-214; doi: 10.3221/igf-esis.37.27 210 tool was designed and optimised. figure 2b shows an example of a fs welded aluminium specimen manufactured using this technology. the parent material employed in the present investigation was al 6082-t6 with ultimate tensile strength, uts, equal to 303 mpa. the tubular specimens had outer nominal diameter equal to 38 mm and inner nominal diameter to 31 mm. all the samples were tested in the as-welded condition. the fs welded specimens were tested under axial fatigue loading at the university of ferrara, italy, using an mts 810 mod. 318.25 servo-hydraulic machine. the samples were tested under a load ratio, r, equal to 0.1 and to -1. the biaxial fatigue tests were carried out at the university of sheffield, uk, using a schenck servo-hydraulic axial/torsional testing machine equipped with two mts hydraulic grips. the force/moment controlled tests were run under in-phase and 90° out-of-phase constant amplitude sinusoidal load histories with load ratios equal to -1 and 0. the pictures seen in figure 3 show some examples of the typical cracking behaviours displayed by the al 6082-t6 fs welded joints tested under biaxial loading. br=0, r=-1 nf=1664764 ctf br= 3 , r=-1, =0° nf=369237 ctf br=1, r=-1,=0° nf=650684 ctf br= 3 , r=-1, =90° nf=173954 ctf br=0, r=0 nf=1071840 ctf br= 3 , r=0, =0° nf=501988 ctf br=1, r=0,=0° nf=857370 ctf br= 3 , r=0, =90° nf=224230 ctf figure 3: examples of the observed macroscopic cracking behaviour under biaxial fatigue loading (ctf=cycles to failure). the experimental fatigue data were re-analysed using the hypothesis of a log-normal distribution of the number of cycles to failure for each stress level with a confidence level equal to 95% [12]. the results of the statistical reanalysis are listed in tab. 1 in terms of nominal stresses referred to the annular section of the parent tube, where: br=nom,a/nom,a is the ratio between the amplitudes of the axial and torsional nominal stress, r is the nominal load ratio,  is the out-of-phase angle, k is the negative inverse slope, a and a are the amplitudes of the axial and torsional endurance limits extrapolated at n=2106 cycles to failure, and t is the scatter ratio of the amplitude of the endurance limit for 90% and 10% probabilities of survival. validation by experimental results s far as conventional aluminium welded joints are concerned, the mwcm can be applied not only in terms of nominal [11, 13] and notch stresses [14], but also using the theory of critical distances (in the form of the point method) [15]. owing to the high level of accuracy which was obtained with standard welded connections [6], in the present investigation the above three stress analysis strategies were used, with the mwcm being applied to post-process the experimental results summarised in tab. 1. independently from the definition adopted to calculate the relevant stress states, the mwcm was applied using multiaxial fatigue software multi-feast© (www.multi-feast.com). initially, the accuracy of the mwcm in estimating the fatigue lifetime of the tested fs welded joints was checked by applying this approach in terms of nominal stresses. the calibration constants in eqs 4 and 5 were estimated using the fully-reversed uniaxial and torsional fatigue curves reported in tab. 1, obtaining: a l. susmel et alii, frattura ed integrità strutturale, 37 (2016) 207-214; doi: 10.3221/igf-esis.37.27 211   8.103.4k effeff  (7)   9.382.22 effefffre  mpa (8) as shown by the sn curves summarised in tab. 1, the fatigue strength of these fs welded joints was seen to be sensitive to presence of non-zero mean stresses, and this holds true even though the specimens were tested in the as-welded condition. according to this experimental evidence, the mean stress sensitivity index, m, was taken equal to unity, with lim being set equal to 1.3. br r  n. of data k a a t [°] [mpa] [mpa]  -1 9 6.5 33.5 1.58  0.1 10 4.4 18.6 1.82 0 -1 11 10.8 38.9 1.49 0 0 10 9.5 32.9 1.52 3 -1 0 8 5.3 26.1 15.1 1.55 3 0 0 7 4.2 17.2 9.9 1.73 3 -1 90 10 5.3 21.1 12.2 2.97 3 0 90 7 10.4 23.4 13.5 1.38 1 -1 0 7 5.4 23.2 23.2 2.12 1 0 0 7 3.2 12.8 12.8 2.00 1 -1 90 9 3.9 11.3 11.3 1.66 1 0 90 7 15.8 22.6 22.6 1.35 table 1: summary of the generated experimental results. the experimental, nf, vs. estimated, nf,e, number of cycles to failure chart shown in figure 4a summarises the overall accuracy which was obtained by using the mwcm in terms of nominal stresses to predict the lifetime of the fs welded tubular samples being tested. this graph makes clear that the use of the mwcm resulted in life estimates falling within the wider scatter band between the two that characterise the fully-reversed uniaxial and torsional fatigue curves used to calibrate the constants in the mwcm’s governing equations. subsequently, the mwcm was applied in terms of notch stresses [14, 16]. the average notch root radius both on the retreating and the advancing side was measured to approach 0.5 mm (fig. 2c). the required notch stresses were determined by solving axisymmetric linear-elastic finite element (fe) models done using commercial software ansys©. the stress analysis returned the following values for the gross stress concentration factors: kt,ax=2.4 (axial stress), kt,hs=0.48 (hoop stress), kt,t=1.7 (torsional stress). the fully-reversed uniaxial and torsional fatigue curves were used in terms of notch stresses to determine the constants in the mwcm’s calibration function, obtaining:   8.103.4k effeff  (9)   9.649.24 effefffre  mpa (10) the uniaxial fatigue curve for a load ratio, r, equal to 0.1 was used to estimate both the mean stress sensitivity index and the limit value for eff (i.e., m=1 and lim=2). the error chart of figure 4b confirms that the mwcm applied in terms of l. susmel et alii, frattura ed integrità strutturale, 37 (2016) 207-214; doi: 10.3221/igf-esis.37.27 212 notch stresses resulted in estimates falling within the two calibration scatter bands, with only a few data points being on the non-conservative side (i.e., series =90°, br= 3 , r=-1). finally, an attempt was made to apply the mwcm in conjunction with the point method to estimate the fatigue lifetime of the fs welded specimens. the relevant linear-elastic stress states were determined at a distance from the crack initiation locations equal to 0.075 mm [15]. the stress analysis was performed by solving axisymmetric linear-elastic fe models done with commercial fe code ansys® [6]. the fully-reversed uniaxial and torsional experimental fatigue curves postprocessed according to the point method were used to calibrate eqs 2 and 3, i.e.:   8.107.3k effeff  (11)   0.588.28 effefffre  mpa (12) the uniaxial fatigue curve with r=0.1 was then used to estimate both the mean stress sensitivity index and the limit value for eff, obtaining: m=1 and eff=1.6. 1000 10000 100000 1000000 10000000 100000000 1000 10000 100000 1000000 10000000100000000 nf [cycles] nf,e [cycles] axial loading, r=-1 axial loading, r=0.1 torsion, r=-1 torsion, r=0 =0°, =√3, r=-1 =0°, =√3, r=0 =90°, =√3, r=-1 =90°, =√3, r=0 =0°, =1, r=-1 =0°, =1, r=0 =90°, =1, r=-1 =90°, =1, r=0 ps=90% ps=10% non-conservative conservative torsional scatter band uniaxial scatter band nominal stresses  br  br  br  br  br  br run out  br  br (a) 1000 10000 100000 1000000 10000000 100000000 1000 10000 100000 1000000 10000000100000000 nf [cycles] nf,e [cycles] axial loading, r=-1 axial loading, r=0.1 torsion, r=-1 torsion, r=0 =0°, =√3, r=-1 =0°, =√3, r=0 =90°, =√3, r=-1 =90°, =√3, r=0 =0°, =1, r=-1 =0°, =1, r=0 =90°, =1, r=-1 =90°, =1, r=0 ps=90% ps=10% non-conservative conservative torsional scatter band uniaxial scatter band notch stresses  br  br  br  br  br  br run out  br  br (b) 1000 10000 100000 1000000 10000000 100000000 1000 10000 100000 1000000 10000000100000000 nf [cycles] nf,e [cycles] axial loading, r=-1 axial loading, r=0.1 torsion, r=-1 torsion, r=0 =0°, =√3, r=-1 =0°, =√3, r=0 =90°, =√3, r=-1 =90°, =√3, r=0 =0°, =1, r=-1 =0°, =1, r=0 =90°, =1, r=-1 =90°, =1, r=0 ps=90% ps=10% non-conservative conservative torsional scatter band uniaxial scatter band point method  br  br  br  br  br  br run out  br  br (c) figure 4: accuracy of the mwcm applied in terms of nominal (a) and notch stresses (b) as well as along with the point method (c). the error bands in figure 4c summarise the overall accuracy that was obtained by applying the mwcm in conjunction with the point method. this diagram makes it evident that this design methodology was accurate, resulting in predictions falling within the scatter bands associated with the experimental calibration fatigue curves. l. susmel et alii, frattura ed integrità strutturale, 37 (2016) 207-214; doi: 10.3221/igf-esis.37.27 213 it can be concluded from these results that, independently from the adopted stress analysis strategy, the resulting level of accuracy is certainly satisfactory (see figure 4), since, from a statistical point of view, we cannot expect that a predictive method will be more accurate than the experimental information used to calibrate the method itself. conclusions  for the specific profile of the fs welded fatigue specimens, the fatigue behaviour of the these tubular joints of al 6082-t6 could successfully be modelled using notch mechanics concepts.  the mwcm was applied not only in terms of nominal and notch stresses, but also in conjunction with the point method and was seen to be highly accurate in estimating the fatigue lifetime of the fs welded joints.  for the investigated fs welded connections, the mwcm was seen to be capable of correctly modelling not only the presence of non-zero mean stresses, but also the degree of multiaxiality and non-proportionality of the applied load history. acknowledgment upport for this work from the leverhulme trust through the award of international network grant in-2012-107 is gratefully acknowledged. references [1] shah, s., tosunoglu, s. (2012) friction stir welding: current state of the art and future prospects, in proceedings of the 16th world multi-conference on systemics, cybernetics and informatics, orlando, florida, 17-20 july 2012. [2] colligan, k.j. (2004) friction stir welding for ship construction, contract n0014-06-d-0048 for the office of naval research, concurrent technologies corporation, harrisburg, pa, us (available at www.nmc.ctc.com). [3] thomas, w.m., nicholas, e.d., friction stir welding for the transportation industries, mater. design., 18 (1997) 269273. [4] burford, d., widener, c., tweedy, b. (2006) advances in friction stir welding for aerospace applications, in proceedings of the 6th aiaa aviation technology, integration and operations conference, aiaa. doi: 10.2514/6.2006-7730. [5] lomolino, s., tovo, r., dos santos, j., on the fatigue behaviour and design curves of friction stir butt-welded al alloys, int. j. fatigue, 27 3 (2005) 305-316. [6] susmel, l., multiaxial notch fatigue: from nominal to local stress-strain quantities, woodhead & crc, cambridge, uk, (2009) isbn: 1 84569 582 8. [7] susmel, l., multiaxial fatigue limits and material sensitivity to non-zero mean stresses normal to the critical planes, fatigue fract. eng. mat. struct., 31 (2008) 295-309. [8] susmel, l., tovo, r., lazzarin, p., the mean stress effect on the high-cycle fatigue strength from a multiaxial fatigue point of view, int. j. fatigue, 27 (2005) 928-943. [9] susmel, l., a simple and efficient numerical algorithm to determine the orientation of the critical plane in multiaxial fatigue problems, int. j. fatigue, 32 (2010) 1875–1883. [10] susmel, l., tovo, r., socie, d.f., estimating the orientation of stage i crack paths through the direction of maximum variance of the resolved shear stress, int. j. fatigue, 58 (2014) 94–101. [11] susmel, l., four stress analysis strategies to use the modified wöhler curve method to perform the fatigue assessment of weldments subjected to constant and variable amplitude multiaxial fatigue loading, int. j. fatigue, 64 (2014) 38-54. [12] spindel, j.e., haibach, e., some considerations in the statistical determination of the shape of s-n cruves, in: r. e. little, j. c. ekvall (eds.), statistical analysis of fatigue data, astm stp 744, (1981) 89–113. [13] susmel, l., tovo, r., on the use of nominal stresses to predict the fatigue strength of welded joints under biaxial cyclic loadings, fatigue fract. engng. mater. struct., 27 (2004) 1005-1024. s l. susmel et alii, frattura ed integrità strutturale, 37 (2016) 207-214; doi: 10.3221/igf-esis.37.27 214 [14] susmel, l., sonsino, c. m., tovo, r., accuracy of the modified wöhler curve method applied along with the rref=1 mm concept in estimating lifetime of welded joints subjected to multiaxial fatigue loading, int. j. fatigue, 33 (2011) 1075-1091. [15] susmel, l., the modified wöhler curve method calibrated by using standard fatigue curves and applied in conjunction with the theory of critical distances to estimate fatigue lifetime of aluminium weldments, int. j. fatigue, 31 (2009) 197-212. [16] radaj, d., sonsino, c. m., fricke, w., fatigue assessment of welded joints by local approaches. woodhead publishing limited, cambridge, uk, (2007). << /ascii85encodepages false /allowtransparency false /autopositionepsfiles true /autorotatepages /none /binding /left /calgrayprofile (dot gain 20%) /calrgbprofile (srgb iec61966-2.1) /calcmykprofile (u.s. web coated \050swop\051 v2) /srgbprofile (srgb iec61966-2.1) /cannotembedfontpolicy /error /compatibilitylevel 1.4 /compressobjects /tags /compresspages true /convertimagestoindexed true /passthroughjpegimages true /createjobticket false /defaultrenderingintent /default /detectblends true /detectcurves 0.0000 /colorconversionstrategy /cmyk /dothumbnails false /embedallfonts true /embedopentype false /parseiccprofilesincomments true /embedjoboptions true /dscreportinglevel 0 /emitdscwarnings false /endpage -1 /imagememory 1048576 /lockdistillerparams false /maxsubsetpct 100 /optimize true /opm 1 /parsedsccomments true 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/hrv (za stvaranje adobe pdf dokumenata najpogodnijih za visokokvalitetni ispis prije tiskanja koristite ove postavke. stvoreni pdf dokumenti mogu se otvoriti acrobat i adobe reader 5.0 i kasnijim verzijama.) /hun 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can be opened with acrobat and adobe reader 5.0 and later.) >> /namespace [ (adobe) (common) (1.0) ] /othernamespaces [ << /asreaderspreads false /cropimagestoframes true /errorcontrol /warnandcontinue /flattenerignorespreadoverrides false /includeguidesgrids false /includenonprinting false /includeslug false /namespace [ (adobe) (indesign) (4.0) ] /omitplacedbitmaps false /omitplacedeps false /omitplacedpdf false /simulateoverprint /legacy >> << /addbleedmarks false /addcolorbars false /addcropmarks false /addpageinfo false /addregmarks false /convertcolors /converttocmyk /destinationprofilename () /destinationprofileselector /documentcmyk /downsample16bitimages true /flattenerpreset << /presetselector /mediumresolution >> /formelements false /generatestructure false /includebookmarks false /includehyperlinks false /includeinteractive false /includelayers false /includeprofiles false /multimediahandling /useobjectsettings /namespace [ (adobe) (creativesuite) (2.0) ] /pdfxoutputintentprofileselector /documentcmyk /preserveediting true /untaggedcmykhandling /leaveuntagged /untaggedrgbhandling /usedocumentprofile /usedocumentbleed false >> ] >> setdistillerparams << /hwresolution [2400 2400] /pagesize [612.000 792.000] >> setpagedevice microsoft word numero_36_art_13 p. jinchang et alii, frattura ed integrità strutturale, 36 (2016) 130-138; doi: 10.3221/igf-esis.36.13 130 improvement of performance of ultra-high performance concrete based composite material added with nano materials pang jinchang, liu ronggui school of civil engineering and architecture, nantong institute of technology (nit), nantong, jiangsu, 226000, china pjcpangjc@163.com abstract. ultra-high performance concrete (uhpc), a kind of composite material characterized by ultra high strength, high toughness and high durability. it has a wide application prospect in engineering practice. but there are some defects in concrete. how to improve strength and toughness of uhpc remains to be the target of researchers. to obtain uhpc with better performance, this study introduced nano-sio2 and nano-caco3 into uhpc. moreover, hydration heat analysis, x-ray diffraction (xrd), mercury intrusion porosimetry (mip) and nanoindentation tests were used to explore hydration process and microstructure. double-doped nanomaterials can further enhance various mechanical performances of materials. nano-sio2 can promote early progress of cement hydration due to its high reaction activity and c-s-h gel generates when it reacts with cement hydration product ca(oh)2. nano-caco3 mainly plays the role of crystal nucleus effect and filling effect. under the combined action of the two, the composite structure is denser, which provides a way to improve the performance of uhpc in practical engineering. keywords. uhpc; composite material; nano material; sio2. introduction ith the continuous development of human society, living space of human is constantly narrowed and buildings tend to be high-rise and long-span. moreover, concrete structure is increasingly threatened by harsh environment such as ocean and salt lake [1, 2]. therefore, requirement on performance of concrete materials becomes higher and higher. ultra-high performance concrete composite (uhpcc) featured by high strength, high toughness, high durability and strong deformation resistance is applied more extensively in harsh environment mentioned above and areas which have special requirements on structure; moreover it shows excellent performance in service process [3, 4]. as to research on uhpc, three international conferences concerning uhpc have been held in kassel university in german, in september 2005, march 2008, and march 2012 respectively. in the first two conferences, participants illustrated their own research achievements and experience, which mainly include composition and ratio of raw materials, preparation condition, performance, characteristics, strength and toughness of microstructure, design and construction as well as application cases of uhpc in practical engineering worldwide [5]. in addition, multiple international technical standards was discussed. in the third international conference, nanotechnology and nanomaterials were proposed to be introduced into uhpc and the latest research progress of uhpc was also discussed. nanomaterials as a fine particle between macro substance and cluster possesses small size effect, surface effect, quantum graining effect and macroscopic tunneling effect. how to introduce nanomaterials into concrete has become an issue w p. jinchang et alii, frattura ed integrità strutturale, 36 (2016) 130-138; doi: 10.3221/igf-esis.36.13 131 constantly explored by concrete material researchers in practice. ye q et al. [6, 7] found that, pozzolanic activity of nanosio2 was much stronger than ganister sand and adding 1% ~ 3% nano-sio2 could remarkably enhance compressive, rupture and splitting strength of concrete and thus improve microstructure of concrete. bigley c et al. [8] discovered that, nano-sio2 could improve segregation resistance of self-compacting concrete. chen rs et al. [9] pointed out that, concrete paste mixing with nano-sio2 was featured by weaker flowability and shorter setting time; and cement block obtained had high strength in early stage. nanomaterial can improve microstructure and enhance mechanical performance of material in a certain extent if being applied in ordinary concrete or high-performance concrete. but preparing uhpc using nanomaterials has not been researched yet. considering the extremely low water-binder ratio of uhpcc, applying nanomaterials with large surface and severe agglomeration into uhpcc will encounter with dispersing and forming difficulty. thus based on preliminary work, we systematically studied action mechanism of nano-sio2 and nano-caco3 adding into uhpcc, aiming to lay a scientific foundation for improvement of uhpc and its promotion.. materials and method raw materials aw materials used included p·ii 52.5r portland cement (density: 3.1 g/cm3; chemical components: tab. 1), ultrafine fly ash (level i from nanjing thermal power plant; density: 2.1 g/cm3; specific surface area: 400 m2/kg; chemical components: tab. 1), nano-sio2 (hangzhou veking new material co., ltd.; superficially porous; average grain diameter: 20 nm; content of sio2: over 99%), nano-caco3 (zhoushan mingri nano material co., ltd.; average grain diameter: 30 nm; content of caco3: over 99.9%), fine aggregate (ordinary yellow ground with maximum grain size of 2.5 mm; fineness modulus: 2.26; continuous grading; bulk density: 1.4 g/cm3; apparent density: 2.4 g/cm3) and polycarboxylic high performance water-reducing agent (basf aktiengesellschaft; water-reducing rate: over 40%). a previous study [10] suggests that, the best mixing proportion of nano-sio2 in uhpcc was 3%. in this study, mixing proportion of nano-sio2 was fixed at 3% and mixing proportion of nano-caco3 was adjustable, as shown in tab. 2. raw material sio2 al2o3 fe2o3 cao mgo so3 k2o n2o loi cement 20.40 4.70 3.38 64.7 0.87 1.89 0.49 0.33 3.24 coal ash 53.98 28.84 6.49 4.77 1.31 1.16 1.61 1.03 0.72 table 1: components of cement and coal ash (wt%). test specimen cement coal ash nano-sio2 nano-caco3 water-binder ratio additive nsc0 52 35 3 0 0.2 2 nsc1 51 35 3 1 0.2 2 nsc3 49 35 3 3 0.2 2 nsc5 47 35 3 5 0.2 2 table 2: mix proportion of different components (wt%). test method moulding technique uhpcc was prepared using wet mixing technology, i.e., evenly mixing raw materials (coal ash, cement, fine aggregate) in forming process. detailed procedures are as follows: (1)stirring ①add cement mortar into the mixture of quartz sand and silicon ash mixed according to certain mix proportion and then stir for 5 min; ②then add cement, coal ash, quartz powder and nanomaterial and stir for 5 min; ③add half quantity of water containing water reducing agent and stir for 3 min; ④add the remaining water and stir for 6 min; ⑤pour the mixture into a triple mould (40 mm × 40 mm × 160 mm) and then vibrate the mould on vibrating table with a frequency of 50hz. manufacturing procedure of concrete mortar matrix is shown in fig. 1. r p. jinchang et alii, frattura ed integrità strutturale, 36 (2016) 130-138; doi: 10.3221/igf-esis.36.13 132 figure 1: manufacturing process of concrete mortar matrix. (2)maintenance: maintain the test specimen in curing room (20 ± 2°c) for 24 h, then do: ①standard maintenance (maintain the test specimen in water (20 ± 2°c) till specified curing age); ②hot water maintenance (maintain the test specimen in 90°c hot water curing box for 48 h and then perform standard maintenance till specified curing age). ③take specimen for mechanical performance and microscopic performance tests. microscopic test xrd quantitative test specimen that had been cured to specified curing age was taken socked in absolute alcohol for one day [11]. then it was grinded in agate mortar in an environment of absolute ethyl alcohol until all powder passed through 0.08 mm sieve. afterwards, all powder was dried in vacuum drying oven (50°c ). one hour later, it was put into hermetic bag and cooled to room temperature. then the power was mixed with α al2o3 power which passed through 80 μm sieve in a ratio of 1 : 9. absolute ethyl alcohol was also added. after one hour of mixing, all specimen were put into vacuum drier. bruker axs d8discover x ray diffractometer equipped with lynxeye array detector was used. target used was cu target. room temperature was t = 298 k. operating voltage and operating current were set as 40 kv and 30 ma. soller slit was 4.0°. step size was set as 0.02° (2θ), scanning speed was set as 0.30 s/step, and scanning angle ranged from 5° to 80° (2θ) or 7° to 80° (2θ). the power was put on specialized glass-made sample plate of ray diffractometer and moved to sample holder for testing after the parameters were set over. mip test autoporeiv 9510 auto hole test system produced by micrometrics corporation was used as mercury injection apparatus. operating parameters were: pressure 0.10 ~ 45000 psia, contact angle 130°, equilibrium time 10s, sampling hole interval 4.3 nm ~ 360 μm. characteristic parameters of pore structure such as porosity, average pore size and distribution of pre size were analyzed using corresponding analysis software. nanoindentation test first, specimen which had been cured to specified curing age was cut into small pieces with a side length of 2 cm. then they were socked in absolute ethyl alcohol for 48 h. the specimen was cut into slices (5 ~ 10 mm) after cold mounting with epoxy resin. to obtain even and clean surface, the slices were grinded with carborundum paper (180-mesh, 600 mesh, 1200 mesh) on grinding machine and then polished with polishing solution (9 μm, 3 μm, 0.5 μm, 0.05 μm). finally, the specimen was washed by ultrasonic wave for 15 min to remove particles from polishing solution adhered to the surface. nano test tm produced by micro materials corporation was used for test and pyramidal berkovich pressure head was equipped. a dot matrix (10 × 10) was selected in the area next to specimen interface area and the space between two dots was 20 μm. displacement control mode was applied and the maximum depth of indentation was set as 300 nm. when the pressure head contacts the surface of specimen, the depth of indentation linearly loads to the set value in a speed of 0.25 mn/s, then loads in a constant speed for 30 s, and finally linearly unloads in a speed of 0.25 mn/s. every test point was processed with loading and unloading. load displacement curve was recorded. results and analysis mechanical performance test and analysis e made tests on static mechanical performance of uhpcc with different curing age. results are shown in fig. 2. it can be seen from fig. 2 that, different uhpcc material show the same tendency of compressive strength and rupture strength, i.e., strength was higher in material with larger curing age. when curing age was the same, compressive strength and rupture strength improved with the increase of mixing amount of nano-caco3. but if the w p. jinchang et alii, frattura ed integrità strutturale, 36 (2016) 130-138; doi: 10.3221/igf-esis.36.13 133 mixing amount was too large, strength improved with a limited amplitude and even decreased slightly. there were two reasons. first, water demand increased, resulting in high water-binder ratio. secondly, nanomaterial failed to disperse evenly and thus aggregated, lowering evenness of uhpcc [12]. hence mixing amount of nanomaterial should be controlled within certain scope. we thought the best mixing amount of nano-caco3 was 3% ~ 5%. compared to test specimen without nano-sio2 or with nano-sio2 only, test specimen added with nano-sio2 and nano-caco3 had significantly improved strength; nsc3 test specimen with curing age of 90 d could have a compressive strength of 107 mpa and a flexural strength of 20 mpa. nano-sio2 can promote hydration of cement and c-s-h gel generates when nano-sio2 reacts with cement hydration products. though nano-caco3 has low activity, it can be used for filling spaces inside composite material and thus improves density. (1) compressive strength (2) rapture strength figure 2: compressive and rapture strength of uhpcc with different curing age. hydration heat analysis hydration heat test was carried out three days after processing the above four kinds of uhpcc with water and the results are shown in fig. 3. it can be seen from fig. 3 that, heat curve of four materials were similar; hydration acceleration period of hydration test specimen mixed with nano-sio2 was from 10th h to 20th h; double-doped materials which had larger mixing amount of nano-caco3 had hydration acceleration and exothermic peak earlier. it indicates that, double mixture of nanomaterials can accelerate hydration. figure 3: hydration heat curve for uhpc test specimen. xrd quantitative analysis traditional xrd methods usually used for quantitative analysis such as external standard method, internal standard method, k value method, and adiabatic method all aims at analyzing single hkl diffracted ray or hkl diffraction family. sample of cement based composite material with multiple phases and complex diffraction xrd pattern will bring great difficulty to quantitative analysis due to severely overlapped spectral peak and preferentially orienting effect. rietveld whole power pattern fitting may transform the status if being applied in xrd pattern analysis. the structure depended method can accurately make an analysis on diffraction peaks and comparison of diffraction strength of different phrase. specialized cement phase structure database which can be used for analyzing cement clinker and phase of mineral admixtures has been established after years of research works. p. jinchang et alii, frattura ed integrità strutturale, 36 (2016) 130-138; doi: 10.3221/igf-esis.36.13 134 we can see a dispersed humpback-like peak at 2θ (25° ~ 35°) which is caused by mass amorphous c-s-h gel existing in cement hydration product from xrd pattern of harden cement paste. but as there are lots of sharp crystalline peaks within the scope of diffraction angle, the position of amorphous peak is not obvious. hence results can be obtained only when phase in a known proportion is added in quantitative analysis of components of cement paste. in quantitative analysis of hydration product of cement based material, α al2o3 which is not contained in original paste, keeps stable at room temperature and cannot react with components of cement paste is used as addition phase. xrd pattern of the power sample obtained was first analyzed with eva software to find out all and then with topas software which is designed based on rietveld method. we made quantitative analysis on hydration products of four kinds of test specimens (curing age of 3, 7, 28 and 90 days). fig. 4 demonstrates the analysis results of test specimens which was cured for 28 days. tab. 3 demonstrates quantitative analysis results of main mineral phases. figure 4: xrd quantitative analysis results of test specimens cured for 28 days. curing period/d test specimen phase c3s c2s c3a c4af ca(oh)2 caco3 amorphous phase 3 nsc0 10.65 7.93 3.65 2.02 4.89 2.67 43.63 nsc1 8.76 7.74 2.88 2.14 5.04 4.16 41.52 nsc3 8.32 8.97 3.45 2.05 3.65 7.68 43.29 nsc5 8.40 9.21 3.18 2.30 4.26 8.97 40.77 7 nsc0 7.56 7.66 2.33 1.85 4.08 3.30 47.31 nsc1 6.22 5.54 2.64 2.31 3.38 4.23 40.61 nsc3 6.35 5.09 3.34 1.82 3.34 7.32 39.81 nsc5 6.07 5.83 3.01 1.94 3.36 8.01 40.83 28 nsc0 6.09 7.02 2.16 1.50 3.57 3.07 49.14 nsc1 7.06 7.90 2.28 2.18 3.42 4.81 43.98 nsc3 5.89 6.34 2.14 1.67 2.76 6.54 48.02 nsc5 6.68 5.79 3.23 1.84 3.68 8.50 47.96 90 nsc0 7.46 7.40 2.13 0.96 3.56 2.99 48.88 nsc1 7.05 6.76 2.64 1.94 3.12 4.36 43.37 nsc3 5.90 6.20 2.35 1.59 3.08 6.08 46.84 nsc5 6.33 5.58 3.09 1.32 3.37 9.01 47.71 table 3: xrd quantitative analysis results of uhpcc with different curing age (%). p. jinchang et alii, frattura ed integrità strutturale, 36 (2016) 130-138; doi: 10.3221/igf-esis.36.13 135 it can be seen from tab. 3 that, as curing period prolonged, unhydrated cement phase (c3s, c2s, c3a, c4af) gradually reduced, amorphous phase of hydration products (c-s-h gel, etc) increased, ca(oh)2 generated from hydration decreased, and caco3 had no obvious change; moreover, in early period (before 7 d), amorphous phase of double-doped test specimen was less than single-doped test specimen, suggesting some nano-caco3 involves in hydration of cement and plays a supplement role in cement based composite material. in addition, we can know from the table that, when curing exceeded 28 d, variation tendency of hydration product content slowed down; in early period (before 7 d), addition of nanomaterials had an obvious promotion effect on hydration of uhpcc. the accelerated hydration of cement is attributable to high reaction activity of nano-sio2. nano-caco3 acting as a supplement role increases the density of uhpcc and also improves its mechanical performance. mip result and analysis preparation of test sample: cement block which has finished test of strength of concrete was crashed and put into absolute ethyl alcohol for stopping hydration. before test, the broken concrete was moved into a vacuum drier (50°c). 24 h later, it was taken out and packed with closed bag. we made test on pore structure of four test specimens with different curing age. tab. 4 shows data of pore structure of cement paste test block. fig. 5 demonstrates mip results of four materials after 28 d-standard maintenance. sample nsco nsc1 nsc3 nsc5 average pore size(nm) 38.1 25.1 27.3 30.9 critical poresize (nm) 427 171 223 249 total pore space (ml/g) 0.2226 0.2043 0.2137 0.2184 table 4: statistics of pore structure of test block. ) ) ( ( lo g 1    n m g l d d d v  (a) distribution curve for pore size. (b) distribution curve for porosity. figure 5: mip analysis results of uhpc. it can be seen from fig. 5(a) that, pore volume of test specimen added with nano-sio2 only and maintained for 28 d was the largest when pore size was between 0.003 and 0.03 μm, and the peak value appeared when pore size was 11 or 4 nm; for double-doped test specimen, distribution curve of pore size deviated to the right slightly and the peak pore size was relatively smaller. fig. 5(b) shows distribution curve for porosity of four test specimens. it can be seen from the figure that, adding two nanomaterials had an obvious influence on lowering porosity of composite material, about 2%. thus it is concluded that, reasonable selection and optimization of uhpcc, hydration promotion effect of nano-sio2 and supplement effect of nano-caco3 can greatly improve density of uhpcc, reduce microscale and microscopic scale defects, and thus enhance performance of material. p. jinchang et alii, frattura ed integrità strutturale, 36 (2016) 130-138; doi: 10.3221/igf-esis.36.13 136 nanoindentation test results and analysis xrd quantitative analysis results suggested that, uhpcc hardened cement paste contained hydrated gel phase, ca(oh)2 phase, caco3 phase and unhydrated cement particles. c-s-h gel phase of ordinary concrete is mainly composed of high and low density hydrated calcium silicate gel (ld c-s-h and hd c-s-h) whose elasticity modulus are 14 ~ 24 gpa and 24 ~ 35 gpa. results of previous researches [13, 14] demonstrated that, uhpcc contains a large amount of higherdensity c-s-h gel (uhd c-s-h) which has stronger mechanical performance and an elastic modulus of 35 ~ 50 gpa that is close to ca(oh)2 phase. we made nanoindentation test on single-doped and double-doped test specimens which were processed by standard maintenance for 90 days. as ca(oh)2 phase accounted for a small proportion in the material, it was ignored during analysis. distribution of mechanical performance parameters of single-doped and double-doped test specimens maintained for 90 days is shown in fig. 6. we can find that, test specimens contain a large amount of unhydrated cement particles and uhd c-s-h phase; hd c-s-h phase is surrounded by hydration product uhd c-s-h; ld c-s-h phase has disappeared; a distinct interfacial transition zone could not be seen. (1) nsc0 (2) nsc3 figure 6: distribution of elasticity modulus on the surface of single-doped and double-doped test specimen. after making a statistical analysis on the data, distribution of probability of elasticity modulus of measured points on test specimen was obtained (fig. 7). it can be seen from the figure that, peak value of elasticity modulus of the test specimens was between 30 and 70 gpa; a large amount of uhd-c-s-h phase and a small amount of unhydrated cement particle phase existed in the test specimens; as to hydration products of double-doped test specimens, uhd c-s-h phase accounted for a larger proportion, hd c-s-h phase was in a small amount and ld c-s-h was not found. thus we conclude that, hydration products of uhpcc are significantly different with ordinary concrete; uhd c-s-h phase is the major hydration product; and the above difference is more obvious in double-doped material. because of generation of a large amount of high-strength and high-elasticity hydration products, interface of composite material is fully strengthened and structure tends to be tighter. (1) nsc0 (2) nsc3 figure 7: distribution of probability of elasticity modulus of single-doped and double-doped test specimen p. jinchang et alii, frattura ed integrità strutturale, 36 (2016) 130-138; doi: 10.3221/igf-esis.36.13 137 conclusions ano materials with outstanding performance have been applied in many fields. li h et al. [15] once researched the influence of nano-sio2 and nano-fe2o3 on mechanical performance and microstructure of cement mortar and found nano-sio2 and nano-fe2o3 could improve compressive strength of cement mortar for 20% over. ltifi m et al. [16] found that, cement mortar tended to have poorer flowability and faster hydration after nano-sio2 was added. they thought compressive and bending strength of cement mortar strengthen if nano-sio2 was added. that is because nano-sio2 as an activator promotes hydration of cement and moreover nanoparticles dispersing in a high degree could improve microstructure of mortar. it is seldom applied in uhpc field and moreover few studies focus on influence of nanomaterials on performance of uhpc, though ordinary cementing material in combination with nanomaterials has been reported frequently. based on the current research achievements of uhpc [17, 18], this paper discussed over the enhancement effect of nanomaterials on performance of uhpc in aspects of tightness and chemical reaction. we made systematic test and analysis on doped uhpcc and concluded that: 1) uhpcc with excellent performance can be prepared through adopting reasonable mix proportion of raw materials and adding nanomaterials; mechanical performance of material can be significantly improved if nano-sio2 and nano-caco3 are added, and the optimal mixing proportion is 3% ~ 5%. 2) adding nano-sio2 can accelerate hydration progress of cement; as to double-doped uhpcc, hydration acceleration period of cement starts earlier and exothermic peak appears earlier; mutual action of nano-sio2 and nano-caco3 further accelerates hydration progress. 3) hydration of cement can be promoted by nano-sio2 due to its high reaction activity; c-s-h gel generates when nanocaco3 reacts with ca(oh)2 which is the hydration product of cement; benefitting from the supplement effect of nanocaco3 added, uhpcc becomes tighter and microscopic defects dramatically reduces. 4) uhpcc added with both nano-sio2 and nano-caco3 is found with significantly lowered porosity, a large amount of uhd c-s-h gel with higher performance, fully strengthened interface region, tighter microstructure and excellent mechanical performance. references [1] wang, c., yang, c.h., liu, f., wan c.j., pu, x.c., preparation of ultra-high performance concrete with common technology and materials, cement and concrete composites, 34(4) (2012) 538-544. [2] kang, s.t., kim, j.k., the relation between fiber orientation and tensile behavior in an ultra high performance fiber reinforced cementitious composites (uhpfrcc), cement and concrete research, 41(10) (2011) 1001-1014. [3] rong, z.d., sun, w., xiao, h.j., wang, w., effect of silica fume and fly ash on hydration and microstructure evolution of cement based composites at low water-binder ratios, construction and building materials, 51 (2014) 446450. [4] wang, j.x., wang, l.j., advances in the applied research of nano-material in concrete, concrete, (11) (2004) 18-21. [5] yao, w., wu, k.r., research situation and development trend of intelligent concrete, new building materials, (10) (2000) 22-25. [6] ye, q., research and development for nano-composite cement structure material, new building materials, (11) (2001) 4-6. [7] ye, q., zhang, z.n., kong, d.y., chen, r.s., ma, c.c., comparison of properties of high strength concrete with nano-sio2 and silica fume added, journal of building materials, 6(4) (2003) 381-385. [8] bigley, c., greenwood, p., using silica to control bleed and segregation in self-compacting concrete, concrete, 37(2) (2003) 43-45. [9] chen, r.s., ye, q., research on the comparison of properties of hardened cement paste between nano-sio2 and silica fume added, concrete, (1) (2002) 7-10. [10] wang, d.z., meng, y.f., mechanical properties of concrete mixed with sio2 and caco3 nanoparticles, ningxia engineering technology, 10(4) (2011) 330-333. [11] rong, z.d., yu, h.x., lin, f.b., microstructure mechanism analysis of cementitious composites at low water-cement ratio, journal of wuhan university technology, 35(4) (2014) 6-10. n p. jinchang et alii, frattura ed integrità strutturale, 36 (2016) 130-138; doi: 10.3221/igf-esis.36.13 138 [12] yang, d.y., structure character and special properties of nanomaterials and application of nano technology in buildings, building technique development, 30(3) (2003) 42-45. [13] tang, m., ba, h.j., li, y., study on compound effect of silica fume and nano-siox for cementing composite materials, journal of the chinese ceramic society, 31(5) (2003) 523-527. [14] xie, y.j., liu, b.j., long, g.c., study on reactive powder concrete with ultra-pulverized fly ash, journal of building materials, 4(3) (2001) 280-284. [15] li, h, xiao, h.g., yuan, j., ou, j.p., microstructure of cement mortar with nano-particles, composite part b: engineering, 35 (2004) 185-189. [16] ltifi, m., guefrech, a., mounanga, p., khelidi, a., experimental study of the effect of addition of nano-silica on the behaviour of cement mortars, procedia engineering, 10 (2011) 900-905. [17] yang, r.h., lu, w.x., yu, s.h., li, k., performance influence of composite nano-materials on concrete and cement mortar, journal of chongqing jianzhu university, 29(5) (2007) 144-148. [18] zhou, w.l., sun, w., chen, c.c., mao, c.w., analysis of slag effect on micro-mechanical properties of cementitious materials by nanoindentation technique, journal of the chinese ceramic society, 39(4) (2011) 718-725. << /ascii85encodepages false /allowtransparency false /autopositionepsfiles true /autorotatepages /none /binding /left /calgrayprofile (dot gain 20%) /calrgbprofile (srgb iec61966-2.1) /calcmykprofile (u.s. web coated \050swop\051 v2) /srgbprofile (srgb iec61966-2.1) /cannotembedfontpolicy /error /compatibilitylevel 1.4 /compressobjects /tags /compresspages true /convertimagestoindexed true /passthroughjpegimages true /createjobticket false /defaultrenderingintent /default /detectblends true /detectcurves 0.0000 /colorconversionstrategy /cmyk /dothumbnails false /embedallfonts true /embedopentype false /parseiccprofilesincomments true /embedjoboptions true /dscreportinglevel 0 /emitdscwarnings false /endpage -1 /imagememory 1048576 /lockdistillerparams false 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<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> /enu (use these settings to create adobe pdf documents best suited for high-quality prepress printing. created pdf documents can be opened with acrobat and adobe reader 5.0 and later.) >> /namespace [ (adobe) (common) (1.0) ] /othernamespaces [ << /asreaderspreads false /cropimagestoframes true /errorcontrol /warnandcontinue /flattenerignorespreadoverrides false /includeguidesgrids false /includenonprinting false /includeslug false /namespace [ (adobe) (indesign) (4.0) ] /omitplacedbitmaps false /omitplacedeps false /omitplacedpdf false /simulateoverprint /legacy >> << /addbleedmarks false /addcolorbars false /addcropmarks false /addpageinfo false /addregmarks false /convertcolors /converttocmyk /destinationprofilename () /destinationprofileselector /documentcmyk /downsample16bitimages true /flattenerpreset << /presetselector /mediumresolution >> /formelements false /generatestructure false /includebookmarks false /includehyperlinks false /includeinteractive false /includelayers false /includeprofiles false /multimediahandling /useobjectsettings /namespace [ (adobe) (creativesuite) (2.0) ] /pdfxoutputintentprofileselector /documentcmyk /preserveediting true /untaggedcmykhandling /leaveuntagged /untaggedrgbhandling /usedocumentprofile /usedocumentbleed false >> ] >> setdistillerparams << /hwresolution [2400 2400] /pagesize [612.000 792.000] >> setpagedevice microsoft word numero_36_art_3 m. arsic et alii, frattura ed integrità strutturale, 36 (2016) 27-35; doi: 10.3221/igf-esis.36.03 27 focused on fracture mechanics in central and east europe experimental examination of fatigue life of welded joint with stress concentration miodrag arsic, zoran savic institute for materials testing, bulevar vojvode mišića 43 belgrade, serbia miodrag.arsic@institutims.rs, zoran.savic@institutims.rs aleksandar sedmak faculty of mechanical engineering, kraljice marije 16, belgrade, serbia asedmak@mas.bg.ac.rs srdjan bosnjak faculty of mechanical engineering, kraljice marije 16, belgrade, serbia, asedmak@mas.bg.ac.rs simon sedmak innovation center of the faculty of mechanical engineering, kraljice marije 16, belgrade, serbia abstract. this paper presents results of experimental examinations of stress concentration influence to fatigue life of butt welded joints with k-groove, produced from the most frequently used structural steel s355j2+n. one group of experiments comprised examinations carried out on the k-groove specimens with stress concentrators of edged notch type. specimens with short cracks (limited length of initial crack), defined on the basis of the experience from fracture mechanics by the three points bending examinations, have been examined according to standard for the determination of s-n curve, and aimed to determine fatigue strengths for different lengths of initial crack and relationship between fatigue strength and crack length. other group of experiments comprised examinations of specimens with edge notch, prepared in accordance with astm e 399 for three points bending, in order to establish regularity between crack growth and range of exerted stress intensity factor aimed to determine resistance of welded joint to initial crack growth, namely fatigue threshold (δkth). keywords. welded joint; stress concentration; crack; fatigue strength; crack growth rate; fatigue threshold. introduction afety of welded structures depends mainly on shapes of welded joints, stress concentration, heterogeneity of structural and mechanical properties of base metal (bm), heat affected zone (haz) and filler metal (fm), residual stresses and strains due to welding procedure and imperfections in welded joints. welded joints, therefore, are frequent locations of fatigue failures. s m. arsic et alii, frattura ed integrità strutturale, 36 (2016) 27-35; doi: 10.3221/igf-esis.36.03 28 fatigue in welded structures commonly initiates in stress concentration area. significant reduction of fatigue durability is related to theoretical stress concentration factor which actually is ratio of maximal and nominal stress (kt = σmax/σ). the stress concentration factor data for certain types of welded joints which are available in literature are obtained by the method of photo-elasticity, and more recently also by the finite elements method. according to data of international institute of welding (iiw), alongside the fractures due to fatigue as the consequence of design mistakes, significant number of fractures also has been stipulated by imperfections in welded joints in structures subjected to numerous variable loads of relatively low level. premature fracture or damage of welded structures is induced by simultaneous influence of numerous technological, metallurgical, designing and exploitation factors, which can explain wide dispersion of fatigue strength values for welded joints, for the various stress amplitude ratios (r=σmin/σmax). fatigue behavior of welded joints and constructions are commonly obtained by examinations of standard specimens or model elements with sinusoidal load (one-step load), while level of mean load or ratio of loads remains constant during examination. examination results are shown as a fatigue diagram, so-called weller curve. cracks or crack-like defects frequently appear during manufacturing of products or in process of elements mounting, especially in the case of welded structures, due to mistakes in manufacturing procedure, unfavorable shaping, structural stress concentrators and conditions of structure loading. characterization of fracture as multiphase process of crack initiation and growth include also different initial stages, which imply possibilities for further crack growth, as shown in [1]. crack growth basically can be: stable, subcritical or unstable, whereas possibilities of crack growth may vary following one of the paths from 1 to 8, fig. 1. figure 1: possibilities of crack growth. stable crack growth originates in cases of constant energy consumption and mostly leads to macroscopic ductile fracture. subcritical (successive) crack growth appears when process of stable crack growth appears in longer period of time. crack growth could be finished also with its transition to stable or unstable growth. unstable crack growth occurs with high speed without energy consumption and it leads to macroscopic brittle fracture. nevertheless, in some cases unstable crack growth stops, phenomenon known as a crack arrest. therefore, significant experimental and theoretical analyses are directed to establish functionalities that hold for this region, so-called region of fatigue threshold. another intensively studied domain is behavior of structures with short cracks, aimed to assess their influence to integrity. concept of short cracks is connected to area of crack lengths which cannot be recorded by existing nondestructive testing methods, and from the viewpoint of material researcher length of short cracks shouldn’t exceed dimensions of micro structural grain size. therefore, short cracks are: m. arsic et alii, frattura ed integrità strutturale, 36 (2016) 27-35; doi: 10.3221/igf-esis.36.03 29  cracks with length which is comparable with dimensions of microstructural grain size,  cracks which dimensions are proportional to local plastic zone, i.e. short crack with dimensions from 0.1 up to 1.0 mm for structural steels [2]. influence of stress concentration on fatigue strength of welded joints elded joints in real constructions are areas of high stress concentration level, especially in the places with imperfections, such as incomplete root penetration, undercuts or cracks. ratio of the maximal main stress σmax, which is established in the minimal cross-section area and nominal stress σ represents stress concentration factor kt:    maxtk (1) factor kt for the same element shape depends on loading type and it is maximal in the case of tension, somewhat smaller in the case of bending, and minimal in the case of torsion. in the case of variable load, notch reduces fatigue strength in all metals. nevertheless, reduction of fatigue strength is not as significant as influence of kt, which is thus not used for variable loads, but only for static loads. fatigue notch factor kf is used to characterize influence of notch to fatigue strength, and it represents the ratio of smooth specimen fatigue strength sf and notched specimen fatigue strength sz.  ff z s k s (2) factor kf is determined by experiment. its magnitude, for uniaxial stress state, depends on welded joint shape and notch dimensions, material, part dimensions and magnitude of variable load. relation between kt and kf factors is defined by stress concentration sensitivity factor q, which is given by the expression: q k k f t    1 1 (3) steel sensitivity to stress concentration is increased with the increase of tensile strength, yield stress and hardness. stress concentration factors are minimal for butt welds, depending on plate thickness, joint shape and welding procedure, kf = 1.1 – 3.0, for fillet welds kf = 2 8, and for overlapping joints kf = 2 – 7. significant fluctuation of notch factor for one type of welded joint, which is predetermined by the joint shape and joint imperfections, sometimes lead to rapid decrease of fatigue strength. yield stress reh [mpa] tensile strength rm [mpa] elongation a5 [%] base metal s355j2+n 368 512 26 electrode "garant" e 43 4b 110 20 (h) 480 550 35 table 1: mechanical properties of base metal and electrode. fatigue examination of k-grooved welded joints rogram of experimental examinations of characteristic welded joints is based on research plan aimed to establish relationship between fatigue strength of smooth specimens and notched specimens, as well as to investigate mechanism of crack appearance and crack propagation in welded joints. w p m. arsic et alii, frattura ed integrità strutturale, 36 (2016) 27-35; doi: 10.3221/igf-esis.36.03 30 mechanical properties of base and filler metal, according to manufacturer’s data, are given in tab. 1. welding of specimens has been carried out by using approved welding procedure specification. results of fatigue strength examinations on smooth specimens fatigue examination of smooth specimens have been carried out on high frequency pulsator "amsler" which is used for examinations by sinusoidal alternative cyclic loads with range of ± 50 kn, whereby in dependence on load magnitude, frequency up to 250 hz can be achieved. obtained value of fatigue strength is sf=420 mpa, fig. 2. figure 2: s-n relationship for k-grooved butt weld. examinations of specimens with different lengths of edge notches by three points bending have been performed in order to determine fatigue strength of welded joints with short cracks (with limited length of initial crack), in other words to confirm the stress which cause crack closure due to arisen plastic zone on crack tip. taking into account that mentioned experiments are not simple but very expensive, examinations have been performed only for the area of expected fatigue strength with set of 6 specimens, for the five different classes of initial notches. stress concentrators have been made in zone of fusion of base metal and weld metal. this has been enabled owing to existing results of smooth specimen examination results. specimen dimensions and the position of notch are shown in fig. 3, and sizes of initial notches are given by tab. 2. data about examination conditions and properties of fatigue strength for every class of specimens is given in tab. 3. examination results are shown in fig. 4 – 8. figure 3: dimensions of specimen and notch position. statistic analysis of examination results has been carried out, aimed to establish relationship between critical length of short crack and fatigue strength. it came out that relationship ac-sf in double logarithmic coordinate system can be presented by straight line, fig. 9. relationship between critical crack length and fatigue strength, shown in fig. 9, can be expressed as exponential function in logarithmic form: 1 2log log logc za c c s  (4) m. arsic et alii, frattura ed integrità strutturale, 36 (2016) 27-35; doi: 10.3221/igf-esis.36.03 31 specimen class initial notch specimen dimensions number of specimens a [mm] w [mm] b [mm] l [mm] 1 0.250 9.90 9.50 40 6 2 0.351 9.79 9.60 40 6 3 0.591 9.90 9.50 40 6 4 0.723 9.90 9.70 40 6 5 1.125 9.85 9.80 40 6 table 2: geometric characteristics of specimens and sizes of initial notch. specimen class a [mm] ∆m [n∙mm] ∆σ [mpa] r f [hz] σa [mpa] σm [mpa] sz [mpa] 1 0.250 19200 157.48 0.5 230-240 81.03 236.23 315 2 0.351 16100 141.24 0.5 230-240 70.62 211.86 282 3 0.591 13600 124.41 0.5 230-240 62.21 186.62 249 4 0.723 12200 112.86 0.5 230-240 56.43 169.30 226 5 1.125 9500 97.47 0.5 230-240 48.73 146.20 195 table 3: examination conditions and fatigue strength properties. figure 4: s-n relationship for specimens with initial crack a = 0.25 mm. figure 5: s-n relationship for specimens with initial crack a = 0.351 mm. m. arsic et alii, frattura ed integrità strutturale, 36 (2016) 27-35; doi: 10.3221/igf-esis.36.03 32 figure 6: s-n relationship for specimens with initial crack a=0.591 mm. figure 7: s-n relationship for specimens with initial crack a= 0.782 mm. figure 8: s-n relationship for specimens with initial crack a= 1.125 mm. m. arsic et alii, frattura ed integrità strutturale, 36 (2016) 27-35; doi: 10.3221/igf-esis.36.03 33 figure 9: relationship between critical crack length and fatigue strength. procedure of calculating coefficients c1 and c2 by the method of the minimal square deviations is based on the condition that sum of obtained data square deviations from functional relation should be minimal:     2 1 2 2 1 1 , log log log min n z c i f c c c s c a      (5) parameters c1 and c2 should be determined from following equation in order to get minimal value of function f(c1,c2):  1 2 1 ,f c c c    0;  1 2 2 ,f c c c    0 (6) in this way, system of equations for calculation of coefficients c1 and c2 is obtained:     1 2 1 1 1 2 1 1 1 log log log log log log log log n n zi ci i i n n n zi zi zi ci i i i n c c s a c s c s s                (7) where “i” represents specimen number (from 1 to 5). values needed to solve the equation system (7) are given in tab. 4. relation between critical length of short crack ac (given in meters) and fatigue strength sf,z (given in mpa) is: 3.1518960c za s  (8) i szi, [mpa] aci [mm] log szi log aci (log szi) log szi log aci 1 195 1.125 2.2898831 0.0511525 5.2435646 0.1171332 2 226 0.723 2.3535816 -0.1408617 5.5393463 -0.3315295 3 249 0.591 2.3958992 -0.2284125 5.7403329 -0.5472533 4 282 0.351 2.4509785 -0.4546928 6.0072956 -1.1144422 5 315 0.250 2.4982637 -0.6020599 6.2413215 -1.500414 σ 11.988606 -1.3748744 28.771858 -3.3801961 table 4: values for solving the equation system (7). m. arsic et alii, frattura ed integrità strutturale, 36 (2016) 27-35; doi: 10.3221/igf-esis.36.03 34 when substitute value fatigue strength of k-grooved butt welds, s = 420 mpa (fig. 2), in eq. 8 critical length of short crack will be ac=0.1 mm. on the basis of experimental examinations, values of fatigue notch factors kf for different initial fatigue cracks calculated by eq. 2, are given in tab. 5. specimen class initial fatigue crack, a [mm] fatigue notch factor, kf 1 0.250 1.33 2 0.351 1.49 3 0.591 1.76 4 0.723 1.86 5 1.125 2.15 table 5: values of fatigue notch factors. results of fatigue crack growth testing fatigue crack growth testing has been performed by the controlled bending force in three points, with asymmetrical load r= fmin/fmax = 0.5, on the specimen with edge notch. testing has been carried out using high frequency pulsator "cracktronic", and gathering of crack growth data has been done by using measuring foils arm a-10. number of cycles for the every 0.1 mm growth of crack has been recorded during experiment. crack growth has been observed by magnifying glass (24 x). on the basis of these records, diagram a n, fig 10, has been drawn. curve a n indicates that fatigue crack grows slowly till a = 1.5 mm, when rapid crack growth occurs for relatively small number of load cycles. relationship a n can be taken as uniform, because there is no crack growth deceleration or its abrupt growth. relationship a n has been used as the basis for determination of crack growth rate, da/dn. in this paper, crack growth rates have been calculated by using the polynomial method, as defined in astm e647. adequate range of stress intensity factor k, depending on specimen shape, crack length and range of variable force f = fmax – fmin, has been calculated. values of coefficients m and c have been calculated, as they characterize resistance of material to crack growth and define paris’ equation (m=3.516, c=3.18∙10-12). obtained values for m and c correspond to material class with similar mechanical properties, /3-5/. relationship da/dn k is shown in fig. 11. on the basis of numerous examinations, which showed that fatigue threshold has appeared for low values of crack growth rate, i.e. in rate range from 10-6 up to 10-8 mm/cycle, and according to the shape of da/dn k curve (fig. 11), one can conclude that value of fatigue threshold is kth = 7.24 mpa, corresponding to crack growth rate of 10-8 mm/cycle. figure 10: experimentally obtained a-n curve. m. arsic et alii, frattura ed integrità strutturale, 36 (2016) 27-35; doi: 10.3221/igf-esis.36.03 35 figure 11: curve da/dn –δk. conclusion resented research and established mathematical relationship between critical crack length and fatigue strength offer great possibilities for analysis of fatigue behavior of welded joints made from structural steel s355j2+n on the supporting structures of building machines, dredgers, elevators, bridges, supporting structure in power plants, petrochemical and oil industry. in addition to this, presented results enable analysis of welding procedure, significant welding parameters and welding consumable material quality aimed to minimize negative effects of variable load to welded joint, i.e. to implement convenient structure. established mathematical relationship between critical crack length and fatigue strength of k-grooved butt welds have general character for structural steels, because it enables evaluation of critical crack length for all welded joints with surface imperfection of undercut type and welded joints with incomplete root penetration. acknowledgement e would like to thank to ministry of education, science and technological development of republic of serbia for the financial support of research within the project tr 35006 and tr 35040. references [1] arsić, m., corelation between weldment fatigue strength and fatigue threshold (in serbian), doctoral thesis, university of pristina, (1995). [2] radon, j.c., study of surface fatigue cracks, structural integrity and life, 6 (2006) 97-100. [3] manjgo, m., sedmak, a., grujić, b., fracture and fatigue behaviour of niomol 490k welded joint, structural integrity and life, 8 (2008) 149-158. [4] gliha, v., burzić, z., vuherer, t., some factors affecting fatigue resistance of welds, structural integrity and life, 10 (2010) 239-244. [5] milović, lj., bulatović, s., radaković, z., aleksić, v., sedmak, s., marković, s., manjgo, m., assessment of the behaviour of fatigue loaded hsla welded steel joint by applying fracture mechanics parameters, structural integrity and life, 12 (2012) 175-179. p w << /ascii85encodepages false /allowtransparency false /autopositionepsfiles true /autorotatepages /none /binding /left /calgrayprofile (dot gain 20%) /calrgbprofile (srgb iec61966-2.1) /calcmykprofile (u.s. web coated \050swop\051 v2) /srgbprofile (srgb iec61966-2.1) /cannotembedfontpolicy /error /compatibilitylevel 1.4 /compressobjects /tags /compresspages true /convertimagestoindexed true /passthroughjpegimages true /createjobticket false /defaultrenderingintent /default /detectblends true /detectcurves 0.0000 /colorconversionstrategy /cmyk /dothumbnails false /embedallfonts true /embedopentype false /parseiccprofilesincomments true /embedjoboptions true /dscreportinglevel 0 /emitdscwarnings false /endpage -1 /imagememory 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/hrv (za stvaranje adobe pdf dokumenata najpogodnijih za visokokvalitetni ispis prije tiskanja koristite ove postavke. stvoreni pdf dokumenti mogu se otvoriti acrobat i adobe reader 5.0 i kasnijim verzijama.) /hun 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/pdfxoutputintentprofileselector /documentcmyk /preserveediting true /untaggedcmykhandling /leaveuntagged /untaggedrgbhandling /usedocumentprofile /usedocumentbleed false >> ] >> setdistillerparams << /hwresolution [2400 2400] /pagesize [612.000 792.000] >> setpagedevice microsoft word numero_62_art_23_3652.docx t. tahar et alii, frattura ed integrità strutturale, 62 (2022) 326-335; doi: 10.3221/igf-esis62.23 326 mechanical properties and statistical analysis of the charpy impact test using the weibull distribution in jute-polyester and glasspolyester composites tioua tahar, djamel djeghader abdelhafid boussouf university center, civil and hydraulic engineering department, mila, 43000, algeria. tahar.tioua@gmail.com, tahar.tioua@centre-univ-mila.dz, djameldjeghader@yahoo.fr bachir redjel badji mokhtar university, civil engineering department, annaba, 23000, algeria bredjel@gmail.com abstract. in recent years, the use of natural fiber composites to provide a possible replacement for synthetic fiber composites for practical applications has been the subject of several studies. this study deals with the fabrication and investigation of jute-polyester composites and the comparison of it with glass-polyester composites. the static mechanical properties of the composites is obtained by testing the composite lamina for tensile and flexural strength. the dynamic mechanical properties of the composites is determined by using the charpy impact test. by the williams method based on the principle of linear elastic fracture mechanics, the impact toughness of the composites is deduced. the experimental results were statistically analyzed by using the weibull theory to better understand the impact behavior of the composites. it is found that the glass-polyester composite has better properties than the jute-polyester composite. keywords. jute; glass; polyester; statistically analyzed; impact strength. citation: tahar, t., djeghader, d., redjel, b., mechanical properties and statistical analysis of the charpy impact test using the weibull distribution in jute-polyester and glasspolyester composites, frattura ed integrità strutturale, 62 (2022) 326-335. received: 01.07.2022 accepted: 30.08.2022 online first: 31.08.2022 published: 01.10.2022 copyright: © 2022 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. introduction atural fibers are increasingly replacing conventional inorganic fibers as a reinforcement in composite materials [1 6]. they are low cost, renewable, lightweight and less abrasive. jute is among the best vegetable fibers in terms of strength and mechanical properties. in addition, jute fibers are flexible and can be combined with different polymer resins such as phenolics, polyesters, and epoxies [7]. jute fiber reinforced composites can be used as an alternative to glass fiber reinforced composites [8]. many works have been published in recent years concerning the impact characterization of natural fiber composite materials. amanda et al. [9] presented observations by scanning electron microscopy on test specimens made of composites with a polyethylene matrix reinforced with jute fiber fabric under impact stress with a difference in the percentage of reinforcement jute. the results showed that the incorporation of the jute fabric in the polyethylene resin increases the strength of the n https://youtu.be/8hr0esozvse t. tahar et alii, frattura ed integrità strutturale, 62 (2022) 326-335; doi: 10.3221/igf-esis62.23 327 material. the addition of jute fabric in the polyethylene matrix completely changes the fracture characteristics of these composite materials. muhammad haris, et al. [10], using unnotched specimens subjected to an impact test, showed that there is an increase in impact energy with the increase in the percentage of jute fibers; however, when the fiber rate exceeds 30%, the value of impact strength decreases. wambua et al. [11] carried out studies on composite materials with a polypropylene matrix reinforced with natural fibers (sisal, kenaf, hemp, and coconut fiber). the mechanical properties of different natural fiber composites were examined and compared. a further comparison was made with the corresponding properties of glass mat reinforced polypropylene matrix composites. the natural fiber composites showed a low impact resistance. hemp and sisal composites show a strength comparable to that of glass fiber composites. the specific properties of natural fiber composites are sometimes better than those of fiber glass composites. this suggests that natural fiber composites can be an alternative to replace fiber glass composites in many applications that do not require very high loading. many authors [12-16] have reported the mechanical properties of natural fiber reinforced composites. the results obtained show that the mechanical properties in bending and static tension undergo a significant improvement by adding different percentages of natural fibers. glass fibers reinforcing is a widely market‐accepted technology benefitting by the easy processability and the high strength of the fibers [17]. impact tests carried out by khalid et al. [18] on composites containing 45%, 55%, and 65% by volume of glass fibers have shown that the fracture energy decreases with the increase in the volume fraction of the glass fibers. takahashi et al. [19] carried out charpy impact tests on glass/epoxy composite materials. the results showed that the difference in the impact strength for the composite due to the duration of water immersion was not significant. leonard et al. [20] investigated the fracture toughness and critical energy release rate of polyester-reinforced glass fibers. the results showed a dramatic increase in the values of fracture toughness and critical energy release rate with increasing fiber content. the anisotropic microstructure of composite materials has a negative effect on the strength and causes very complex damage and failure mechanisms under impact loading. as a result, the results of the characterization tests, whether static or dynamic, show important dispersions, especially for impact tests on notched specimens. therefore, there is a strong need to use statistical methods to interpret the experimental data of the charpy impact test based on failure probabilities to achieve a better design of composite materials and to ensure the stability of the loaded elements [21]. reliability analysis using weibull probability was done to represent distributions of random variables. this law assumes that the failure of composite materials is linked to the presence of microstructural defects in the reinforcements and that it begins precisely at the level of the weakest defect [22,23]. the major objective of this study is to predict the charpy impact behavior and dynamic resilience of jute-polyester composites and to compare them with glass-polyester composites by analyzing them statistically using the weibull theory. materials and experimental methods materials wo types of composite materials were used in this study were fabricated using contact molding technique: rectangular jute polyester plates composite 300 mm long and 200 mm wide, with three (03) layers of bidirectional jute fibers and a reinforcement rate of 40 %, shown in fig 1 (a). glass polyester plates composite in the form of rectangular 300 mm long and 200 mm wide, with rate of 30 % of fibers randomly oriented and four layers of short multidirectional glass fibers, shown in fig 1 (b). (a) (b) figure 1: rectangular composites plates of (a) jute – polyester (b) glass – polyester t t. tahar et alii, frattura ed integrità strutturale, 62 (2022) 326-335; doi: 10.3221/igf-esis62.23 328 tensile and flexural testing tensile and flexural strength tests were conducted in zwick roel universal-testing test machine with a ± 20 kn capacity and controlled by the computer software “test expert” at room temperature. both the fabricated composites type is cut using a saw cutter to get the dimension of the specimen for tensile testing as per astm d638 standards, the length, width and thickness of the specimen were 165, 13 and 4 mm, respectively. three point bend tests were performed in accordance with astm d 790 to measure flexural properties. the samples were 100 mm long by 15 mm wide by 4 mm thick. in three point bend test, the outer rollers are 80 mm apart. test machine along with “test expert” software make calculating young’s modulus. the impact charpy tests were carried out on a charpy zwick 5113 pendulum impact testers in 3-point bending in accordance with astm d6110. the release angle of the machine is 160° and the impact speed is 3.85 m/s. the pendulum used in the case of the study materials has an energy of 7.5 j. fig. 2 shows the experimental device used as well as the data acquisition and processing device by a microcomputer equipped “with an expert test software”. the specimens used in the impact test are prismatic in shape, 80 mm long, 10 mm wide and 4 mm thick, with a single edge notch. the distance between supports of the impact apparatus is 64 mm. the notch lengths are all in the ratio 0.2 < a/d < 0.6. where a is the notch length and d is the notch width of the specimen, respectively. figure 2: zwick/roell type charpy impact machine used. application of linear fracture mechanics to impact tests the experimental resilience r of notched specimens is calculated in accordance with en-iso-179-1 using the following equation:     u r b. d a (1) the williams method based on the principles of linear elastic fracture mechanics has been used to interpret the results of impact tests on notched specimens [23-24]. this method makes it possible to obtain an estimate of the energy or toughness gic intrinsic parameter of the material from the total energy dissipated u during the impact according to the equation:   ic cu g bd u (2) b and d represent the thickness and width of the specimen, respectively, and  is a calibration factor which depends on the geometry of the specimen and which was tabulated by williams for various lengths of notches (eqn. 3). thus, the recording of the energy lost by the hammer at the moment of impact for each notch plotted on a diagram u a function of (bd  ) gives a straight line whose slope measures gic and the kinetic energy uc.                   1 a 1 l 1 a2 d 36π d d (3) t. tahar et alii, frattura ed integrità strutturale, 62 (2022) 326-335; doi: 10.3221/igf-esis62.23 329 where a and l represent the notch length and the distance between supports, respectively. results and discussion tensile and flexural behavior he stress-strain curves and average modulus of elasticity obtained in static tension for the jute-polyester and glasspolyester composite materials are represented in figs. 3 and 4, respectively. the glass-polyester composites clearly had a better performance among the two types of composites. they could withstand up to 172 mpa tensile stress with 5% strain compared to jute-polyester composites with an average of 43 mpa tensile stress and 2.2% strain. the average tensile modulus is also high for the glass-polyester. it is about 1.8 times that of the jute-polyester. on the other hand, it was observed from each stress-strain curve that specimens of the two types of composites follow the same trend of the stress-strain behavior. all stress-strain diagrams are linear until the rupture, reflecting a fragile and elastic character of the composites tested. note that the break always occurs in the central part of all samples tested. the factors that lead to breakage are complex: matrix breakage, fiber breakage, interface breakage [24]. all of these factors can take place simultaneously. it is very difficult to assess which is more dominant in the samples tested for both composites studied. from the results of the tensile test, it can be concluded that the glass-polyester composite is performing well compared with the jute-polyester composite. this is mainly due to the nature of the fibers and their architecture [8]. the glass fibers are stronger and stiffer than the jute fibers. figure 3: stress – strain (σ ε) of the bidirectional jute – polyester composite in tension tests figure 4: stress – strain (σ ε) of the multidirectional glass – polyester composite in tension tests t t. tahar et alii, frattura ed integrità strutturale, 62 (2022) 326-335; doi: 10.3221/igf-esis62.23 330 the flexural properties represent the flexibility of the materials, and a good flexural strength indicates that the materials have brittle properties and high hardness [2]. figs. 5 and 6 show the stress-strain curves and average modulus of elasticity obtained in the flexural strength test for the jute-polyester and glass-polyester composites. the flexural property behaviour, of the glass-polyester composites generate higher values of the flexural properties (flexural stress, strain, and flexural modulus) than the jute-polyester composites. also, the results of the flexural properties exhibits higher values compared to the tensile properties. moreover, the stress-strain curves, unlike those obtained in tension, show three zones for the two types of composites tested. a linear phase reflecting the elastic behavior of the composite. a second linear phase of weaker slope translating the damage, which occurs gradually within the composite during the loading. this damage starts to take place at a stress intensity lower than that of the breaking stress. a decrease in the stress beyond the maximum load announces the unstable failure of the specimen. the most dominant mechanism of failure observed in the flexural strength of samples tested, the accumulation of deformations on the stretched part leads to generalized damage, which spreads to the core of the specimen and causes delamination. figure 5: stress – strain (σ ε) of the bidirectional jute – polyester composite in flexural tests figure 6: stress – strain (σ ε) of the multidirectional glass – polyester composite in flexural tests impact behavior the graphical presentation of the impact energy u as a function of the ruptured areas bdф for the jute-polyester and glasspolyester composites (figs. 7 and 8) shows that the total fracture energy increases with increasing ruptured areas, which t. tahar et alii, frattura ed integrità strutturale, 62 (2022) 326-335; doi: 10.3221/igf-esis62.23 331 indicates that fracture is an energy-consuming phenomenon; thus, increasing ruptured areas require more fracture energy. on the other hand, despite a dispersed orientation of the glass fibers, a short length, and a lower rate (30% compared to 40% in the case of jute), the charpy impact strength and dynamic toughness values of the glass/polyester composite (r = 103 kj/m2 and gic = 234 kj/m2) are very high compared to that of the jute/polyester composite (r = 6 kj/m2 and gic = 5.3 kj/m2). in addition, the glass-polyester specimens did not break completely. they are characterized by the development of a damaged zone before the rupture. however, the jute/polyester specimens were completely broken, showing a rather fragile nature. this difference is mainly due to many factors including the nature of the fiber, fiber/matrix interface, and the construction and geometry of the composite [25]. the linear regression line of the curves in figs. 7 and 8 gave a positive intersection with the u ordinate line, which is due to the effects of the kinetic energy transmitted to the specimens during the impact test. the jute/polyester composite presents a value of kinetic energy of about 0.098 j, which is less important than the value of the glass/polyester composite, which about 0.252 j. it is important to note that any kinetic energy transferred to the specimens first enters as strain energy, as momentum is transmitted to the outer ends (supports) by shear waves passing outward along the beam [26]. the calculated impact toughness results of the charpy impact test on all the tested specimens show correlation coefficient values of 0.81 and 0.84 for the jute/polyester and glass/polyester composite, respectively, reflecting the dispersion of the results of the impact energy of the cracked specimens around the linear regression line. this is essentially due to the presence of defects during the manufacture of the specimens, can be attributed to presents of fibers in the polyester matrix causes often tortuous paths of rupture which do not necessarily follow the direction of the initial notch and which are different from one specimen to another. figure 7: total fracture energy as a function of broken areas of jute – polyester composite figure 8: total fracture energy as a function of broken areas of glass – polyester composite t. tahar et alii, frattura ed integrità strutturale, 62 (2022) 326-335; doi: 10.3221/igf-esis62.23 332 probabilistic analysis by the weibull theory weibull's analysis [22] is based on two essential hypothesis: the material is statistically homogeneous and isotropic. the probability of finding a defect of a given severity in an “arbitrarily small” volume of material is the same everywhere; the rupture of the most critical defect leads to the complete rupture of the sample, a perfect brittle fracture. the first assumption is that the number of defects n is proportional to the volume v, we can present the relationship in the form:     1 exp ( )fp v (4) where, pf : presents the probability of the considered system, and    1( ) ( )v nf  ( ) is a function of unknown shape. weibull [17] proposed the following empirical relation in view of the experimental results:            0 ( ) m u for σ > σu (5)   ( ) 0 for σ < σu where, σu stress threshold for zero failure probability. σ0 normalization factor and m: characteristic parameter of the material, modulus of heterogeneity. he comes then:                0 1 exp m u fp v for σ > σu (6) pf = 0 for σ < σu a statistical analysis by the weibull theory [19] applied to impact tests becomes interesting in order to better understand the behavior of these materials at high stress speed. for this, it is necessary to graphically represent the distribution of the rates of energy restitutions. the calculation of the failure probability pf was made using the following expression of the median rank:   1f i p n (7) i and n are the rank and the number of samples respectively. the determination of the weibull modulus requires the graphic representation of the curve corresponding to lnln (1/(1 pf)): as a function of the logarithms of the energy restitution rates and which has the equation: lnln (1/(1-pf )) = m.ln(gic gs )– m.ln(g0 gs) (8) the slope of this line represents the weibull modulus (m) and the dispersion parameter g0 can be obtained by the second term in eqn. 8. figs. 9 and 10 show the two-parameter weibull curve fitting of the charpy impact test results of the jute-polyester and glasspolyester composites, respectively. it should be noted that the correlation coefficient r2 presents a value of 0.97, reflecting the good correlation of the experimental data as well as the reasonable fit of the tow parameter weibull distribution. in addition, all predictions generally follow the trends of the experimental data. t. tahar et alii, frattura ed integrità strutturale, 62 (2022) 326-335; doi: 10.3221/igf-esis62.23 333 figure 9: weibull probability plot of jute – polyester composite figure 10: weibull probability plot of glass – polyester composite the fracture energy, as well as the impact toughness, follows a distribution characterized by the weibull modulus m and the scaling parameter g0. these parameters are a function of the interaction between the pre-existing defect distribution and the stress displacement fields due to the shock loading. however, the large shock pendulum velocity, which is about 3.85 m/s, leads to a variety of phenomena that occur at the time of loading and cracking of the notched specimens. the shape parameter m obtained by the two weibull analyses shows less significant values of the glass-polyester (8.84) compared to the jute-polyester composite (5.76). it is highly possible that this difference is mainly due to the presence of a non-uniform distribution of glass fibers within the composite material, with the creation of voids and micro pores of different dimensions and shapes. the presence of the short length and dispersed orientation of the glass fibers leads, at the same time, to an increase in the gic toughness by the absorption of the impact energy and a decrease in the homogeneity of the glasspolyester composite compared to the jute-polyester composite. conclusion n order to evaluate the effect of the fiber type on the composite properties, jute and glass were used as the reinforcement. it was clearly observed that the fiber type that was used had a great importance on the strength characteristics of the composites. the short glass fiber with dispersed orientation gave better results. therefore, the i t. tahar et alii, frattura ed integrità strutturale, 62 (2022) 326-335; doi: 10.3221/igf-esis62.23 334 highest tensile and flexural strength were found for the glass-polyester compared to the jute-polyester composites. in addition, the charpy impact energy and toughness obtained by the williams theory based on the principles of linear elastic fracture mechanics confirm the brittleness of the jute-polyester composites. statistical analysis of the results was conducted using the weibull probabilistic theory. the measured weibull modulus m shows that the results are scattered for the tow types of materials studied. despite the excellent mechanical properties of the composite materials based on jute fibers, they remain less efficient than composites based on glass fibers and, above all less, resistant to shocks. these properties preclude their use in situations that involve resistance to heavy loads. references [1] joshi, a., shivakumar gouda, p.s., sridhar, i., umarfarooq, m.a., uppin, v., vastrad, j., gogoi, n., and edacherian, a. (2022). crack suppression by natural fiber integration for improved interlaminar fracture toughness in fiber hybrid composites, frattura ed integrità strutturale, 16(60), pp. 158–173. doi: 10.3221/igf-esis.60.12. [2] benkhelladi, a., laouici, h., bouchoucha, a. (2020). tensile and flexural properties of polymer composites reinforced by flax, jute and sisal fibres, the international journal of advanced manufacturing technology, 108, pp. 895–916. doi: 10.1007/s00170-020-05427-2. [3] sarikaya, e., callioğlu, h., and demirel, h. (2019). production of epoxy composites reinforced by different natural fibers and their mechanical properties, composites part b: engineering, 167, pp. 461–466. doi: 10.1016/j.compositesb.2019.03.020. [4] manjunath, g. b., and bharath, k. n. (2018). investigating the contribution of geometrical parameters and immersion time on fracture toughness of jute fabric composites using statistical techniques, frattura ed integrità strutturale, 12(46), pp. 14–24. doi: 10.3221/igf-esis.46.02. [5] vijaya ramnath, b., junaid kokan, s., niranjan raja, r., sathyanarayanan, r., rajendra prasad, a., manickavasagam, v.m., and elanchezhian, c. (2013). evaluation of mechanical properties of abaca–jute–glass fibre reinforced epoxy composite, materials and design, 51, pp. 357–366. doi: 10.1016/j.matdes.2013.03.102. [6] khan, r. a., sharmin, n., khan, m.a., saha, m. (2011). comparative studies of mechanical and interfacial properties between jute fiber/pvc and e-glass fiber/pvc composites, polymer-plastics technology and engineering, 50(2), pp. 153–159. doi: 10.1080/03602559.2010.531422. [7] sultana, s., huque, m. m., and helali, m. m. (2007). studies on the physicomechanical properties of sodium periodate oxidized jute reinforced polypropylene (pp) composites, polymer-plastics technology and engineering, 46 (4), pp. 385–391. doi: 10.1080/03602550601156045. [8] sabeel ahmed, k., and vijayarangan, s. ( 2008). tensile, flexural and interlaminar shear properties of woven jute and jute glass fabric reinforced polyester composites, journal of materials processing technology, 207, pp. 330–335. doi: 10.1016/j.jmatprotec.2008.06.038 [9] amanda, c., sergio, n., kestur, g. (2011). recycled polyethylene composites reinforced with jute fabric from sackcloth: part ii-impact strength evaluation, journal of polymers and the environment, 19, pp. 957–965. doi. 10.1007/s10924-011-0347-8. [10] muhammad haris, a., yasir, n., zulfiqar, a., abdellatif, i., and sheraz, a., (2019). development and characterization of jute/polypropylene composite by using comingled nonwoven structures, the journal of the textile institute, 110 (11), pp.1652–1659, doi: 10.1080/00405000.2019.1612502. [11] wambua, p., ivens, j., verpoest, i., (2003). natural fibres: can they replace glass in fibre reinforced plastics?, composites science and technology, 63 (9), pp. 1259–1264. doi: 10.1016/s0266-3538(03)00096-4. [12] priyadarshi, t., ranjan, s., sankar n. d., and shakti p. j. (2018). manufacturing and study of thermo-mechanical behaviour of surface modified date palm leaf/glass fiber reinforced hybrid composite, materials today: proceedings 5(3), part 3, pp. 18332-18341. doi: 10.1016/j.matpr.2018.06.172. [13] anbukarasi, k. and kalaiselvam, s. (2014). study of effect of fibre volume and dimension on mechanical, thermal, and water absorption behaviour of luffa reinforced epoxy composites, materials and design, (66), pp. 321–330 doi: 10.1016/j.matdes.2014.10.078. [14] murali mohan rao, k., mohana rao, k., and ratna prasad a.v. (2010). fabrication and testing of natural fibre composites: vakka, sisal, bamboo and banana, materials and design, 31, pp. 508–513. doi: 10.1016/j.matdes.2009.06.023. [15] idicula., m, joseph, k., and thomas, s. (2010). mechanical performance of short banana/sisal hybrid fiber reinforced polyester composites. the journal of reinforced plastics and composites, 29(1), pp.12–29. t. tahar et alii, frattura ed integrità strutturale, 62 (2022) 326-335; doi: 10.3221/igf-esis62.23 335 doi: 10.1177/0731684408095033. [16] vignesha, v., balajib, a.n., raja mohamed rabia, b., rajinic, n., ayrilmisd, n., karthikeyane, m.k.v., faruq, m., sikiru oluwarotimi, i., and hamad, a.a. (2021). cellulosic fiber based hybrid composites: a comparative investigation into their structurally influencing mechanical properties, construction and building materials, 271, pp. 121587. doi: 10.1016/j.conbuildmat.2020.121587. [17] delli, e., giliopoulos, d., bikiaris, d. n., and chrissafis, k. (2021). fibre length and loading impact on the properties of glass fibre reinforced polypropylene random composites, composite structures, 263, pp. 113678. doi: 10.1016/j.compstruct.2021.113678. [18] khalid, a.a. (2006). the effect of testing temperature and volume fraction on impact energy of composites, materials and design, 27 (6), pp. 499–506. doi: 10.1016/j.matdes.2004.11.013. [19] takahashi, y., chai, j., and tan, s.c. (2006) effect of water storage on the impact strength of three glass fiber-reinforced composites » dental materials, 22(3), pp. 291–297. doi: 10.1016/j.dental.2005.04.035. [20] leonard, l.w.h., wong, k.j., low, k.o., and yousif, b. f. (2009). fracture behavior of glass fiber reinforced polyester composite. the journal of materials: design and applications, 223 (2), pp. 83–89. doi: 10.1243/14644207jmda224. [21] djeghader, d., and redjel, b. (2020). weibull analysis of fatigue test in jute reinforced polyester composite material, composites communications, 17, pp. 123-128. doi: 10.1016/j.coco.2019.11.016. [22] weibull, w. (1951). a statistical distribution function of wide applicability. journal of applied mechanics, 18, pp.293297. [23] sakin, r., and ay, a. (2008). statistical analysis of bending fatigue life data using weibull distribution in glass-fiber reinforced polyester composites, materials and design, 29, pp.1170–1181. doi: 10.1016/j.matdes.2007.05.005 [24] djeghader, d., and redjel, b. (2017). fatigue of glass-polyester composite immerged in water, journal of engineering science and technology, 12(5), pp.1204–1215. [25] solaimurugan, s., and velmurugan, r. (2008). influence of in-plane fibre orientation on mode i interlaminar fracture toughness of stitched glass/polyester composites, composites science and technology, 68, pp. 1742–1752, doi: 10.1016/j.compscitech.2008.02.008. [26] marshall, g. p., williams, j. g., and turner c. e. 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can be opened with acrobat and adobe reader 5.0 and later.) >> /namespace [ (adobe) (common) (1.0) ] /othernamespaces [ << /asreaderspreads false /cropimagestoframes true /errorcontrol /warnandcontinue /flattenerignorespreadoverrides false /includeguidesgrids false /includenonprinting false /includeslug false /namespace [ (adobe) (indesign) (4.0) ] /omitplacedbitmaps false /omitplacedeps false /omitplacedpdf false /simulateoverprint /legacy >> << /addbleedmarks false /addcolorbars false /addcropmarks false /addpageinfo false /addregmarks false /convertcolors /converttocmyk /destinationprofilename () /destinationprofileselector /documentcmyk /downsample16bitimages true /flattenerpreset << /presetselector /mediumresolution >> /formelements false /generatestructure false /includebookmarks false /includehyperlinks false /includeinteractive false /includelayers false /includeprofiles false /multimediahandling /useobjectsettings /namespace [ (adobe) (creativesuite) (2.0) ] /pdfxoutputintentprofileselector /documentcmyk /preserveediting true /untaggedcmykhandling /leaveuntagged /untaggedrgbhandling /usedocumentprofile /usedocumentbleed false >> ] >> setdistillerparams << /hwresolution [2400 2400] /pagesize [612.000 792.000] >> setpagedevice microsoft word numero 24 articolo 16 h.s. patil et alii, frattura ed integrità strutturale, 24 (2013) 151-160; doi: 10.3221/igf-esis.24.16 151 effect of weld parameter on mechanical and metallurgical properties of dissimilar joints aa6082–aa6061 in t6 condition produced by fsw h. s. patil department of mechanical engineering, pacific school of engineering, surat, india hspatil12@rediffmail.com s. n. soman department of metallurgy & material engineering, faculty of engineering & technology, m. s. university of baroda, india abstract. the effect of processing parameters on the mechanical and metallurgical properties of dissimilar joints of aa6082–aa6061 produced by friction stir welding was analysed in this study. different fsw samples were produced by varying the welding speeds of the tool as 50 and 62 mm/min and by varying the alloy positioned on the advancing side of the tool. in all the experiments the rotating speed is fixed at 1600rpm. all the welds were produced perpendicularly to the rolling direction for both the alloys. microhardness (hv) and tensile tests performed at room temperature were used to evaluate the mechanical properties of the joints. in order to analyse the microstructural evolution of the material, the weld’s cross-sections were observed optically and sem observations were made of the fracture surfaces. the corrosion tests of base alloy and welded joints were carried out in 3.5%nacl solution at a room temperature. corrosion current and potential were determined using potentiostatic polarization measurements. it was found that the corrosion rates of welded joints were higher than that of base alloy. keywords. fsw; aluminium alloys aa6082-aa6061; mechanical and metallurgical characterization. introduction odern aerospace concepts demand reductions in both the weight as well as cost of production of materials. under such conditions, welding processes have proven most attractive, and programs have been set up to study their potential. car manufacturers and shipyards are also evaluating new production methods. increasing operating expenses are driving manufacturers to reduce weight in many manufacturing applications, particularly in aerospace sector. the goal is to reduce the costs associated with manufacturing techniques to result in considerable cost and weight savings by reducing riveted/fastened joints and part count. one way of achieving this goal is by utilising a novel welding technology known as friction stir welding (fsw). friction stir welding is a solid-state joining process developed and patented by the the welding institute (twi) in 1991 by thomas et al and it is emerged as a welding technique to be used in high strength alloys (2xxx, 6xxx, 7xxx and 8xxx series) for aerospace, automotive and marine applications that were difficult to join with conventional techniques[1,2]. this technique is attractive for joining high strength aluminium alloys since there is far lower heat input during the process compared with conventional welding methods such as tungsten inert gas (tig) or metal inert gas (mig). this solid state process leads to low distortion in long welds, excellent mechanical properties in the weld and heat-affected zone, no fumes or spatters, low shrinkage, as well as being energy efficient. furthermore, other cost reductions are realized in that the process uses a non-consumable m http://dx.medra.org/10.3221/igf-esis.24.16&auth=true http://www.gruppofrattura.it h. s. patil et alii, frattura ed integrità strutturale, 24 (2013) 151-160; doi: 10.3221/igf-esis.24.16 152 welding tool. the process was developed initially for aluminium alloys, but since then fsw was found suitable for joining a large number of materials. in fsw a non-consumable rotating tool with a specially designed pin and shoulder is inserted into the abutting edges of sheets or plates to be joined and traversed along the line of joint. the tool serves two primary functions: (a) heating of work piece, and (b) movement of material to produce the joint. the heating is accomplished by friction between the tool and the work piece and plastic deformation of work piece. the localized heating softens the material around the pin and combination of tool rotation and translation leads to movement of material from the front of the pin to the back of the pin. as a result of this process a joint is produced in ‘solid state’. during fsw process, the material undergoes intense plastic deformation at elevated temperature, resulting in generation of fine and equiaxed recrystallized grains. the fine microstructure in friction stir welds produces good mechanical properties. fig. 1 shows a schematic diagram of the fsw process. figure 1: schematic diagram of the fsw process. many papers are present in the literature regarding this field. further to joints of similar alloys, fsw is being studied for welding dissimilar alloys which can be of particular interest in some industrial applications. some works can be found in the literature [3–7], but data is still scarce on the characterisation of 6082-6061 joint type. some authors have demonstrated that the microstructure of the weld nugget of strongly different aluminium alloys is mainly fixed at the retreating side of the material [3]. murr et al. [8] showed the properties of dissimilar casting alloys by fsw. the microstructural evolution of dissimilar welds as a function of processing parameters has been widely studied in [9], showing the behaviour of aa6061–aa2024 materials. dickerson et al. [10] found that friction-stir-welded butt joints are generally defect free if welding process conditions (welding speed and sheet thickness) are properly tuned within a ‘tolerance box’ for a particular alloy. it is not possible to assume that fsw will be free of flaws, however, because manufacturers may want to run fsw outside the tolerance box in order to increase productivity. the weld zones are more susceptible to corrosion than the parent metal [11-16]. generally, it has been found that friction stir (fs) welds of aluminium alloys such as 2219, 2195, 2024, 7075 and 6013 did not exhibit enhanced corrosion of the weld zones. fsw of aluminium alloys exhibit intergranular corrosion mainly located along the nugget’s heat-affected zone (haz) and enhanced by the coarsening of the grain boundary precipitates. coarse precipitates and wide precipitate-free zones promoted by the thermal excursion during the welding are correlated with the intergranular corrosion. the effect of fsw parameters on corrosion behaviour of friction stir welded joints was reported by many workers [14, 16]. the effect of processing parameters such as rotation speed and traverse speed on corrosion behaviour of friction stir processed high strength precipitation hardenable aa2219-t87 alloy was investigated by surekha et al. [16]. however, researchers have nevertheless been strained to study competent study of the mechanical properties in terms of uts, ys and % elongation, microhardness test, fractography analysis, metallurgical properties, and corrosion behaviour and the main causes of developing defects with changing fsw parameters for a dissimilar aluminium joint of aa6082 with aa6061. selection of process parameters is an important issue in the fsw process, particularly in the case of joining dissimilar alloys. in the present paper, the effect of different welding speeds on the weld characteristics of advancing and retreating side of aa6082-t6 and aa6061-t6 fabricated by a hexagonal tool pin profile is investigated. http://dx.medra.org/10.3221/igf-esis.24.16&auth=true http://www.gruppofrattura.it h.s. patil et alii, frattura ed integrità strutturale, 24 (2013) 151-160; doi: 10.3221/igf-esis.24.16 153 experimental procedure he experiments were conducted on the aluminium alloy aa6082-t6 and aa6061-t6, its chemical composition and mechanical properties are respectively presented in tabs. 1 and 2. the rolled plates of 5mm thickness were cut into the required size (300mm×150 mm) by power hacksaw cutting and grinding. square butt joint configuration was prepared to fabricate fsw joints. the initial joint configuration was obtained by securing the plates in position using mechanical clamps. the direction of welding was normal to the rolling direction. single pass welding procedure was used to fabricate the joints. in present work hexagonal tool pin profile was used for the welds, made of cold work die steel. the tool dimensions are shown in fig. 2. the machine used for the production of the joints was vertical machining centre. different materials positioned on the advancing side of the tool allowed four different welding conditions described in tab. 3. chemical composition element si fe cu mn mg cr zn ti required 0.7-1.3 0.5 0.1 0.4-1.0 0.6-1.2 0.25 0.2 0.1 contents 0.9 0.24 0.9 0.7 0.7 0.06 0.04 0.05 mechanical properties tensile strength (mpa) yield strength mpa) elongation (%) hardness(hv) min max min max min max 295 -240 -8 -89 324 332 308 319 9 12 90 table 1: chemical composition and mechanical properties aa6082-t6. chemical composition element si fe cu mn mg cr zn ti required 0.4-0.8 0.7 0.15-0.4 0.15 0.8-1.2 0.04-0.35 0.25 0.15 contents 0.62 0.45 0.2 0.18 1.05 0.09 0.03 0.07 mechanical properties tensile strength (mpa) yield strength mpa) elongation (%) hardness(hv) min max min max min max 300 -241 -6 -95 328.57 335.71 282 296 11 11.8 98 table 2: chemical composition and mechanical properties aa6061-t6. materials of joints rotational speed (rpm) welding speed (mm/min) tool depth (mm) downward force(kn) 6082t6-6061t6 1600 50 4.6 14 6082t6-6061t6 1600 62 4.6 11 6061t6-6082t6 1600 50 4.6 11 6061t6-6082t6 1600 62 4.6 11 table 3: welding conditions employed to join the aa6082–aa6061 plates. t http://dx.medra.org/10.3221/igf-esis.24.16&auth=true http://www.gruppofrattura.it h. s. patil et alii, frattura ed integrità strutturale, 24 (2013) 151-160; doi: 10.3221/igf-esis.24.16 154 figure 2: geometry of the hexagonal tool pin profile used in the present study. all welded samples were visually inspected in order to verify the presence of possible macroscopic external defects, such as surface irregularities, excessive flash, and surface-open tunnels. by using radiographic unit, x-ray radiographic inspection was carried out on fsw samples. in radiographic test 6ci & ir192 used as radioactive source. the film used was agfa d-4 and the radiographs indicated defect free weld as well as weld with defects like insufficient fusion and cavity. mechanical properties of the test welds were assessed by means of tensile tests and the ultimate tensile stress (uts) yield strength (ys) and % elongation were measured in the tensile test. microindentation hardness test as per astm e-384:2006 has been used to measure the vickers hardness of fsw joints. the vickers microhardness indenter is made of diamond in the form of a square-base pyramid. the test load applied was 100gram and the dwell time was 15 seconds. the indentations were made at midsection of the thickness of the plates across the joint. the tensile fractured surfaces were analyzed by using scanning electron microscopy (sem). metallographic specimens were cut mechanically from the welds, embedded in resin and mechanically ground and polished using abrasive disks and cloths with water suspension of diamond particles. the chemical etchant was the keller’s reagent. the microstructures were observed on optical microscope. potentiodynamic polarization tests were used to study the pitting corrosion behaviour of aa6082-aa6061 alloys. in the tests, cell current readings were taken during a short, slow sweep of the potential. the sweep was taken in the range of 0.5v to 1v. the potentiodynamic scan was performed at scan rate of 0.5mv/sec. result and discussion mechanical properties he mechanical and metallurgical behaviour of dissimilar fsw aa6082–aa6061 was studied in this research. transverse tensile properties of fsw joints such as yield strength, tensile strength, percentage of elongation and joint efficiency on transverse tensile specimens are presented in tab. 4. the strength and ductility in the as-welded condition are lower than the parent metal in t6 condition. material of fsw joint ys (n/mm2) uts (n/mm2) % elongation % joint efficiency 6082t6-6061t6 167 183 5.14 50.13-49.03 6082t6-6061t6 101 170 4 46.57-45.57 6061t6-6082t6 91 173 4.29 47.39-46.38 6061t6-6082t6 95 154 4.43 42.19-41.28 aa6082-t6 117 365 14 - aa6061-t6 99.84 373.12 16.56 - table 4: mechanical properties of dissimilar fsw joints. t http://dx.medra.org/10.3221/igf-esis.24.16&auth=true http://www.gruppofrattura.it h.s. patil et alii, frattura ed integrità strutturale, 24 (2013) 151-160; doi: 10.3221/igf-esis.24.16 155 the joints were produced with different alloy positioned on the advancing side of the tool. the joints were realized with a rotation speed of 1600 rpm and by changing the advancing speed from 50 to 62 mm/min. from the fig. 3 it can be inferred that the welding speed and alloy positions are having influence on tensile properties of the fsw joints. figure 3: stress-strain curves for dissimilar alloys aa6082-aa6061. the ductility is higher with decreasing the weld speed in the case of aa6082 on the advancing side, while it decreases in the case of aa6061 on the advancing side (fig. 4). such dependence of the strength on the material position was previously observed. the best conditions of strength and ductility are reached in the joints welded with aa6082 on the advancing side and weld speed of 50 mm/min. in joint efficiency table, the first efficiency represents the weld joint efficiency with aa6082 as a base metal and second efficiency represent with aa6061 as a base metal. the joint efficiency is higher with decreasing the weld speed in the case of aa6082 on the advancing side, while it is lower in the case of aa6061 on the advancing side. fig. 5 shows the effect of welding speed on microhardness of dissimilar welds. the highest value of microhardness is reached in aa6061-6082 at welding speed of 50mm/min. the lowest value of microhardness is reached when the aa6061 alloy is on the advancing side of the tool at welding speed of 62 mm/min. when aa6082 alloy is employed on the advancing side of the tool, the microhardness appears more uniform, indicating a better mixing of the material as shown in fig. 5. furthermore, the maximum hardness values in the nugget zone correspond to the welds with aa6082 on the advancing side. figure 4: effect of welding speed on mechanical properties for dissimilar alloys 6082-6061. http://dx.medra.org/10.3221/igf-esis.24.16&auth=true http://www.gruppofrattura.it h. s. patil et alii, frattura ed integrità strutturale, 24 (2013) 151-160; doi: 10.3221/igf-esis.24.16 156   figure 5: effect of welding speed on microhardness for dissimilar alloys 6082-6061 micro-structural evolution based on optical micro structural characterization of grains and precipitates, three distinct zones have been identified such as weld nugget zone, thermo-mechanically affected zone (tmaz) and heat affected zone (haz). microstructural details of the base metals (bm) and dissimilar joint are presented in figs. 6-8. examination of onion rings in the aa6082aa6061 at 50mm/min has shown that these onion rings are a result of shell extrusions in the dynamically recrystalized zone (dxz). in aa6061-6082 at 62mm/min, it can be seen that the root flaw looks like a crack in the root part of the friction stir welds. the root flaw usually occurs if the pin length is too short for the plate thickness being welded, and this may also occur due to low heat input or incorrect tool orientation. figure 6: optical micrograph of base metals aa6082 and aa6061. figure 7: optical micrograph of aa6082-6061(a) at 50mm/min (b) at 62mm/min http://dx.medra.org/10.3221/igf-esis.24.16&auth=true http://www.gruppofrattura.it h.s. patil et alii, frattura ed integrità strutturale, 24 (2013) 151-160; doi: 10.3221/igf-esis.24.16 157 figure 8: optical micrograph of aa6061-6082 (c) at 50mm/min (d) at 62mm/min. fractography analysis examination of the tensile fracture surfaces of the fsw joints was done at low magnification as well as at higher magnification in order to identify the fracture mechanisms.according to figs. 9-10, it may be predicted that the fracture mechanism in the mixing of these alloys will be dimpled rupture. the dimpled rupture fracture mechanism indicates that the fracture occurred with some degree of ductility, but the existence of the defect can always cause a stress concentration around the defect zone during the tension test; therefore, this phenomenon results in a strain locality that is higher than the yield strength in the turbulence zone of the weld, a sudden crack in the specimen, and consequently, a low elongation in the connection. figure 9: sem images of tensile fracture surface of 6082-6061 at 50mm/min. corrosion behaviour the potentiostatic polarization curves for the base alloy and fsw samples in 3.5%nacl at room temperature are given in figs. 11-13. it is shown that the corrosion behavior of base alloy significantly varies from that of welded joints. from tab. 5 it is observed that the pitting potentials of corrosion tested samples at various process parameters clearly indicated a greater corrosion resistance of weld metal than base metal. this is attributed to the precipitates present in the alloy promote matrix dissolution through selective dissolution of aluminium from the particle. these precipitate deposits are highly cathodic compared to the metallic matrix, which initiates pitting at the surrounding matrix and also enhances pit growth. during fsw process only coarser precipitates could nucleate and grow but not finer ones. this aids in formation of passive film, which remained more intact on surface of the sample. it is also found that in aa6082-6061 at 50mm/min, http://dx.medra.org/10.3221/igf-esis.24.16&auth=true http://www.gruppofrattura.it h. s. patil et alii, frattura ed integrità strutturale, 24 (2013) 151-160; doi: 10.3221/igf-esis.24.16 158 the corrosion resistance is very poor. the poor pitting corrosion resistance of weld joint is due to difference in pitting potentials across the weld region or stir nugget because of inhomogeneity of microstructures in those regions. with aa6082 on the advancing side, the corrosion rate is higher with respect to increasing welding speed of the tool while corrosion rate decreased in case of aa6061 on advancing side (tab. 5). such dependence of the corrosion behaviour on the material position was observed. all fsw samples show passivation after longer time of exposure to corrosion media. aa6082-61 at 62mm/min has highest active potential (-1.16v). the active ecorr increased with increasing the weld speed in case advancing and retreating side of 6082t6-6061t6. figure 10: sem images of tensile fracture surface of 6061-6082 at 62mm/min. material of fsw joint icorr (µa/cm2) ecorr (mv) corrosion rate (mpy) 6082t6-6061t6 55.00 -938 25.14 6082t6-6061t6 3.33 -1160 1.520 6061t6-6082t6 836na -732 382 e-3 6061t6-6082t6 1.590 -920 726.60 e-3 aa6082-t6 4.270 -1380 1.95 aa6061-t6 1.820 -1160 832.1 e-3 table 5: result analysis of corrosion test. figure 11: polarization curves of base metals aa6082 and aa6061 http://dx.medra.org/10.3221/igf-esis.24.16&auth=true http://www.gruppofrattura.it h.s. patil et alii, frattura ed integrità strutturale, 24 (2013) 151-160; doi: 10.3221/igf-esis.24.16 159 figure 12: polarization curves of aa6082-aa6061 at 50-62 mm/min. figure 13: polarization curves of aa6061-aa6082 at 50-62 mm/min conclusions he mechanical and metallurgical behaviour of dissimilar fsw aa6082–aa6061 was studied in this paper. the joints were produced with different alloy positioned on the advancing side of the tool. the joints were realized with a rotation speed of 1600 rpm and by changing the welding speed from 50 to 62mm/min. the downward force was observed to be constant as the welding speed for all the produced joints increases. the tensile strength of the dissimilar joint is lower than that of the parent metal. with the 6082 alloy positioned on the advancing side of the tool, the dissimilar joints exhibited good mechanical properties with respect to aa6061. microstructural changes induced by the friction stir welding process were clearly identified in this study. friction stir welding of dissimilar alloys aa6082t66060t6 resulted in a dynamically recrystalized zone, tmaz and haz. a softened region has clearly occurred in the friction stir welded joints, due to dissolution of strengthening precipitates.with aa6082 on the advancing side; the corrosion rate is higher with respect to increasing welding speed of the tool while corrosion rate decreased in case of aa6061 on advancing side. references [1] w. m. thomas, e. d. nicholas, materials & design, 18 (1997) 269. [2] w. m. thomas, e. d. nicholas, j. c. needham, m. g. nurch, p. temple-smith, c. dawes, patents on friction stir butt welding, international: pct/gb92/02203; british: 9125978.8; usa: 5460317, (1991-1995). [3] w. b. lee, y. m. yeon, s. b. jung, j. mater. sci., 38 (2003) 4183. [4] w. b. lee, y. m. yeon, s. b. jung, scripta materialia, 49 (2003) 423. [5] p. cavaliere, r. nobile, f.w. panella, a. squillace, int. j. machine tools manufacturing, 46 (2006) 588. [6] p. cavaliere, a. de santis, f. panella, a. squillace, material & design, 30 (2008) 609. [7] a. scialpi, m. de giorgi, l. a. c. de filippis, r. nobile, f.w. panella, material & design, 29 (2008) 928. [8] l. e. murr, n. a. rodriguez, e. almanza, c. j. alvarez, j. of material science, 40 (2005) 4307. t http://dx.medra.org/10.3221/igf-esis.24.16&auth=true http://www.gruppofrattura.it h. s. patil et alii, frattura ed integrità strutturale, 24 (2013) 151-160; doi: 10.3221/igf-esis.24.16 160 [9] j. h. ouyang, r. kovacevic, j. material engineering, 11 (2002) 51. [10] t. l. dickerson, j. przydatek, int. j. fatigue, 25 (2003) 1399. [11] c.s. paglia, k.v. jata, r.g. buchheit, material science engineering a, 424 (2006) 196. [12] r.w. fonda, p.s. pao, h.n. jones, c.r. feng, b.j. connolly, a.j. davenport, material science engineering a, 519 (2009) 1. [13] d.a. wadeson, x. zhou, g.e. thompson, p. skeldon, l. djapic oosterkamp, g. scamans, corrosion science, 48 (2006) 887. [14] m. jariyaboon, a.j. davenport, r. ambat, b.j. connolly, s.w. williams, d.a. price, corrosion science, 49 (2007) 877. [15] p. s. pao, s. j. gill, c. r. feng, k. k. sankaran, scripta materiala, 45 (2001) 605. [16] k. surekha, b. s. murty, k. prasad rao, solid state sciences, 11 (2009) 907. http://dx.medra.org/10.3221/igf-esis.24.16&auth=true http://www.gruppofrattura.it microsoft word numero_41_art_27.docx d. nowell et alii, frattura ed integrità strutturale, 41 (2017) 197-202; doi: 10.3221/igf-esis.41.27 197 focused on crack tip fields measurement and analysis of fatigue crack deformation at the micro-scale d. nowell, k.i. dragnevski, s.j. o’connor university of oxford, uk david.nowell@eng.ox.ac.uk, http://orcid.org/0000-0001-9997-8364 abstract. this paper introduces the use of digital image correlation for the measurement of surface displacements in the neighbourhood of a crack tip, both at the macroand microscale. various methods of interpreting the measured data and producing a crack driving force are then discussed, including the use of the full cjp model. a reduced set of parameters are then proposed, corresponding to the three principal interaction forces between the plastic enclave and the surrounding elastic material. our own results, and those of vasco olmo, previously reported in the literature are then reanalysed using this new framework, and excellent agreement between two independent experiments is obtained. implications for the analysis of further data sets are then discussed. keywords. fatigue; crack driving force; digital image correlation; cjp model. citation: nowell, d., dragnevski, k.i., o’connor, s.j., measurement and analysis of fatigue crack deformation at the micro-scale, frattura ed integrità strutturale, 41 (2017) 197-202. received: 28.02.2017 accepted: 15.04.2017 published: 01.07.2017 copyright: © 2017 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. introduction nderstanding the mechanics of fatigue crack propagation is important if we are to safely operate a wide range of engineering systems. damage tolerant life prediction methods are increasingly popular and give a number of advantages over safe life approaches. nevertheless, most of the methods are based on the paris law relation between da/dn and delta k. although this ‘law’ is justifiably popular, it is in essence a simple empirical curve fit to laboratory data obtained at constant remote load amplitude. load histories in real structures can differ considerably, and may include variable amplitude cycles, hence it is important to understand how crack tips behave in these circumstances. there is an increasing realisation that simple elastic crack models may have limited applicability, particularly when there is significant plastic deformation ahead of the crack and a corresponding plastic wake. our developing work at oxford in the area described above has been presented previously at the forni di sopra [1], malaga [2], and urbino [3] ij fatigue/ffems workshops. it has employed digital image correlation on the macro and micro scale to measure and analyse near tip displacements fields. in particular, at urbino [3], we reported measurements taken during in-situ loading of a fatigue crack in a scanning electron microscope (fig.1.). u d. nowell et alii, frattura ed integrità strutturale, 41 (2017) 197-202; doi: 10.3221/igf-esis.41.27 198 figure 1: typical image of a fatigue crack, during in-situ loading in the sem our work focuses on measuring the variation of crack opening with distance along the line of the crack, since this quantity is straightforward to measure. indeed, if one employs a direct measure of displacement, such as digital image correlation (dic), then the crack flanks are the largest displacements available, once rigid body motions have been excluded. in analyzing our work, we started off by using simple elastic models [1], and showing that the technique can be used to calculate stress intensity factors by (for example), plotting the variation of crack opening against r, where r is the distance from the crack tip. if the displacements vary as r, then it is clear that the strains (and therefore stresses) vary as 1/r, and hence the k-value may readily be extracted. later, [2] our work extended to include a simple elasto-plastic model due to pommier and hammam [4]. this was shown to give a slightly better fit to the experimental results, but the absolute value of the plasticity parameter (effectively the crack tip opening displacement) was found to be sensitive to the choice of crack tip position. however, it is clear from both approaches that there a considerable amount of crack closure present, and this may be considered as a residual (negative) stress intensity factor, which may be summed with the applied k to give the actual stress intensity experienced by the crack. an example of this is shown in fig. 2, which is data obtained for a fatigue crack growing under cyclic loading and observed in a scanning electron microscope. figure 2: variation of measured and calculated stress intensity factor with load, for a typical dic experiment [5] in fig.2., the residual k is apparent as an (almost constant) offset between the theoretical and experimental lines, once the crack is open. d. nowell et alii, frattura ed integrità strutturale, 41 (2017) 197-202; doi: 10.3221/igf-esis.41.27 199 since the effect of the wake is clearly important in the characterization of crack tip conditions for a fatigue crack, we decided to investigate a third possible analysis method, using a model with a wake representation built in. the christopher/james/patterson (cjp) model [6],[7] was selected because of its relatively simple formulation. discussion of the cjp model he cjp model attempts to capture some of the additional phenomena generated by a fatigue crack with a plastic wake. this approach leads to a crack description with four parameters as follows: kf the ‘forward stress intensity factor’, which is essentially similar to the applied ki in a conventional analysis. kr a ‘retardation stress intensity factor’, which arises as a result of the residual stress field set up by the wake, and which might be thought similar to the offset shown in figure 2. ks a ‘shear stress intensity describing’ the shear present between the plastic wake and the surrounding elastic material. t the conventional t-stress or bounded term in the williams expansion. it is easy to misunderstand some of these terms, so a brief further explanation will be given here with the aid of a diagram (fig. 3) modified from that presented by james et al. in [7]. first, it is essential to understand that the plastic zone at the tip of the crack creates a wake along the crack faces, as the crack propagates, hence, there is a plastic enclave of the approximate shape shown in grey in fig. 3. if one then considers the boundary between this enclave and the surrounding elastic material there may be x, y and shear forces transmitted across this interface and in each case, the force on the enclave by the elastic hinterland will be equal and opposite to that exerted by the enclave on the elastic material. figure 3 shows the forces exerted on the plastic enclave. figure 3: forces between the plastic enclave (grey), and the surrounding elastic material (after [7]). starting with fig. 3a, at maximum there is clearly an applied force opening the crack and causing tensile yield. this is labelled fay in the figure. similarly, there may be shear at both top and bottom of the enclave, and these forces (which for mode i must be in the same direction) are labelled fs in fig.3. since the enclave must be in equilibrium, these two shear components must be reacted by a horizontal force, termed fax. the authors include a separate term for the t-stress, but this is clearly not a net force across the interface. hence, it is perhaps more helpful to think of t as being a bounded response to fax, which clearly does not cause any stress intensity at the crack tip. at the minimum applied load, james et al consider the crack at least partially closed (fig. 3b.). they then show fs reversed in sign, which seems plausible, since the crack has reached this state by unloading from the maximum load. the fx force however, is not reversed in sign, so that if fig. 3b is considered as a free body diagram, then the plastic enclave would not be in equilibrium. what james et al do, however, change is the notation for the x-direction force, calling it now fpx presumably to show that the plastic zone is somehow the entity responsible for the force, rather than the applied load. of course, in the general case, both applied load, and plastic zone resistance contribute to the force across the interface, and it is not possible (or perhaps helpful) to separate them. in the vertical direction, the sign of the main vertical force is reversed, and the notation is changed. further, an additional force fc is introduced to represent the contribution to vertical force caused by crack closure. james et al. [6], [7], then go on to collapse the plastic enclave onto the line of the crack, and develop a muskhelishvili stress function for the surrounding elastic material. this eventually results in the four terms defined above. t (a) (b) d. nowell et alii, frattura ed integrità strutturale, 41 (2017) 197-202; doi: 10.3221/igf-esis.41.27 200 our own work has so far focused on simpler one or two parameter models, and our view is that the introduction of different forces with different notations and signs in fig. 3., whilst intended to link the model to physical phenomena, is not particularly helpful. what is helpful, however, is the concept of a plastic wake and its effect on the surrounding material. hence, there is no need to introduce different y-direction forces at minimum load, but one can simply stick with the system of forces shown in fig. 3a and drop the double subscripts. so, fy causes crack opening and a stress intensity, fs, exerts shear on the areas above and below the crack, and this is reacted by fx, which may be thought responsible for the bounded stress component in the x-direction (t-stress). these three forces neatly map onto the four terms tabulated on the previous page: fs is responsible for ks. physically, its link to crack propagation rates is difficult to see, so that one might consider it, at most a secondary effect. fx is responsible for the t-stress. again, a secondary effect, though perhaps more important than ks. fy must clearly be responsible for kf and kr, and which may be separated using the cjp approach, or if preferred may remain as a single ki term. experimental results and discussion e have essentially already extracted the dominant ki term in the above simplified version of the cjp model, and an example result has already been presented in fig. 2. to compare this with the results of the full model, we will use some results produced by vasco olmo [8]. he used a full-field dic technique to extract kf and kr for the cjp model, using essentially the same material (al4%cu) and specimen geometry (compact tension) as in our own work. figure 4 gives his results for a test conducted a load ratio, r = 0. it can be seen that the measured kf value is very close to the nominal elastic k, calculated using the usual standard solution. the kr value starts close to zero, but then becomes negative, and increases in magnitude until the peak load, decreasing again during unloading. figure 4: results obtained by vasco olmo [8], showing the variation of kf and kr through a load/unload cycle for an al4%cu ct specimen. results are normalized with respect to the nominal elastic k. if we now choose to plot a single crack driving force, kf + kr, the results are transformed to those shown in fig. 5. finally, we note that in our own work, the datum for displacements was the unloaded specimen with the crack present, so that we are unable to detect any pre-existing residual k. hence the appropriate parameter to plot is ( kf + kr), and this is given in fig. 6, along with our own experimental data (fig. 2), re-plotted on the same axes. the comparison between the two sets of data, obtained independently on two different specimens in two different laboratories is striking, particularly when one considers that different dic algorithms are used, and different post-processing routes were adopted. comparison of these two sets of data, suggest that the four parameters of the mode i cjp model may usefully be reduced to three if one combines the kf and kr parameters, and that the three remaining terms each map clearly onto the effects of a force transmitted across the interface between the plastic zone and resulting wake, and the surrounding elastic hinterland. when viewed from this perspective, the combined kf + kr parameter appears to be very similar to the measured delta k in our own experiments carried out under similar conditions. both our own laboratory and that of vasco olmo and diaz garrido in jaén have a wealth of similar data, carried out for different loading conditions and specimen geometries, and more time is needed to make further comparisons of a similar nature. however, before we do so, it would be useful if the community could take a view on whether the full complexity of the w d. nowell et alii, frattura ed integrità strutturale, 41 (2017) 197-202; doi: 10.3221/igf-esis.41.27 201 cjp model is helpful (i.e. is the splitting of delta k into separate kf and kr terms justified from the point of view of predicting crack behavior). figure 5: results from fig. 4, obtained by vasco olmo [8], re-plotted to show the variation of (kf + kr) with loading cycle figure 6: vasco olmo’s data [8] plotted as delta k against loading cycle and compared against our own [5] (also shown in fig.2.) conclusions his paper has introduced and discussed the cjp model for fatigue crack displacement, strain, and stress fields, and proposed a simplification, which seems to fit more readily with the forces acting between the plastic enclave and the surrounding elastic material. a comparison has been made between one of our own experiments, reported previously [5], and one from the group at jaén [8]. excellent agreement was found between the two sets of data and further collaboration to examine the full database of experimental results in a single agreed framework is proposed. acknowledgments he authors gratefully acknowledge the help of dr josé vasco olmo, particularly in supplying the original data corresponding to figures 4, 5, and 6. dr vasco olmo and dr paco diaz are also thanked for helpful discussions during professor nowell’s research visit to jaén in may 2016, and both are further thanked for their kind and generous hospitality. 0 0,2 0,4 0,6 0,8 1 1,2 0 0,2 0,4 0,6 0,8 1 k /k _ m a x normalised loading cycle k_f + k_r nominal k t t d. nowell et alii, frattura ed integrità strutturale, 41 (2017) 197-202; doi: 10.3221/igf-esis.41.27 202 references [1] nowell, d., kartal, m.e., de matos, p.f.p., measurement and modelling of near-tip displacement fields for fatigue cracks in 6082 t6 aluminium, proc. first i.j. fatigue & ffems joint workshop, gruppo italiano frattura, forni di sopra, italy, (2011). [2] nowell, d., kartal, m.e.,de matos, p.f.p., characterisation of crack tip fields under non-uniform fatigue loading, proc. second i.j. fatigue & ffems joint workshop, malaga, spain, gruppo italiano frattura, (2013). [3] nowell, d., o’connor, s.j., dragnevski, k.i., measurement and analysis of fatigue crack deformation on the macro and micro-scale, proc. third i.j. fatigue & ffems joint workshop, gruppo italiano frattura, urbino, italy, (2015). [4] pommier, s., hamam, r., incremental model for fatigue crack growth based on a displacement partitioning hypothesis of mode i elastic-plastic displacement fields, fatigue fract. engng mater. struct., 30 (2006) 582-598. [5] o’connor, s.j., plasticity-induced fatigue crack closure, an investigation using digital image correlation, msc thesis, university of oxford, (2015). [6] christopher, c.j., james, m.n., patterson, e.a., tee, k.f., towards a new model of crack tip stress fields, int. j. fracture, 148 (2007) 361-371. [7] james, m.n., christopher, c.j., lu y., patterson, e.a., ‘local crack plasticity and its influences on the global elastic stress field, int. j. fatigue, 46 (2013) 4-15. [8] vasco olmo, j.m., experimental evaluation of plasticity induced crack shielding effect using full-field optical techniques for stress and strain measurement, phd thesis, university of jaén, (2014). . << /ascii85encodepages false /allowtransparency false /autopositionepsfiles true /autorotatepages /none /binding /left /calgrayprofile (dot gain 20%) /calrgbprofile (srgb iec61966-2.1) /calcmykprofile (u.s. web coated \050swop\051 v2) /srgbprofile (srgb iec61966-2.1) /cannotembedfontpolicy /error /compatibilitylevel 1.4 /compressobjects /tags /compresspages true /convertimagestoindexed true /passthroughjpegimages true /createjobticket false /defaultrenderingintent /default /detectblends true /detectcurves 0.0000 /colorconversionstrategy /cmyk /dothumbnails false /embedallfonts true /embedopentype false /parseiccprofilesincomments true /embedjoboptions true /dscreportinglevel 0 /emitdscwarnings false /endpage -1 /imagememory 1048576 /lockdistillerparams false /maxsubsetpct 100 /optimize 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can be opened with acrobat and adobe reader 5.0 and later.) >> /namespace [ (adobe) (common) (1.0) ] /othernamespaces [ << /asreaderspreads false /cropimagestoframes true /errorcontrol /warnandcontinue /flattenerignorespreadoverrides false /includeguidesgrids false /includenonprinting false /includeslug false /namespace [ (adobe) (indesign) (4.0) ] /omitplacedbitmaps false /omitplacedeps false /omitplacedpdf false /simulateoverprint /legacy >> << /addbleedmarks false /addcolorbars false /addcropmarks false /addpageinfo false /addregmarks false /convertcolors /converttocmyk /destinationprofilename () /destinationprofileselector /documentcmyk /downsample16bitimages true /flattenerpreset << /presetselector /mediumresolution >> /formelements false /generatestructure false /includebookmarks false /includehyperlinks false /includeinteractive false /includelayers false /includeprofiles false /multimediahandling /useobjectsettings /namespace [ (adobe) (creativesuite) (2.0) ] /pdfxoutputintentprofileselector /documentcmyk /preserveediting true /untaggedcmykhandling /leaveuntagged /untaggedrgbhandling /usedocumentprofile /usedocumentbleed false >> ] >> setdistillerparams << /hwresolution [2400 2400] /pagesize [612.000 792.000] >> setpagedevice http://www.gruppofrattura.it http://www.gruppofrattura.it http://dx.medra.org/10.3221/igf-esis.06.03&auth=true microsoft word numero_44_art_7 v. reut et alii, frattura ed integrità strutturale, 44 (2018) 82-93; doi: 10.3221/igf-esis.44.07 82 elastic crack-tip stress field in a semi-strip v. reut, n. vaysfeld, z. zhuravlova odessa mechnikov university, institute of mathematics, economics and mechanics, ukraine reut@onu.edu.ua, vaysfeld@onu.edu.ua, z.zhuravlova@onu.edu.ua abstract. in this article the plain elasticity problem for a semi-strip with a transverse crack is investigated in different cases of boundary conditions at the semi-strip’s end. unlike many works dedicated to this subject, the fixed singularities in the singular integral equation’s kernel are considered. the integral transformations’ method is applied by a generalized scheme to reduce the initial problem to a one-dimensional problem. the one-dimensional problem is formulated as a vector boundary value problem which is solved with the help of matrix differential calculations and green’s matrix apparatus. the problem is reduced to solve the system of three singular integral equations. depending on the conditions given on the short edge of the semistrip, the obtained singular integral equation can have one or two fixed singularities. a special method is applied to solve this equation in regard to the singularities existence. hence, the system of the singular integral equations (ssie) is solved with the help of the generalized method. the stress intensity factors (sif) are investigated for different lengths of crack. the novelty of this work is the application of a new approach allowing the consideration of fixed singularities in the problem of a transverse crack in the elastic semi-strip. the comparison of the accuracy of numerical results during the use of different approaches to solve the ssie is calculated. keywords. semi-strip; transverse crack; green’s function; integral transformation; fixed singularity. citation: reut, v., vaysfeld, n., zhuravlova, z., elastic crack-tip stress field in a semi-strip frattura ed integrità strutturale, 44 (2018) 8293. received: 26.01.2018 accepted: 11.02.2018 published: 01.04.2018 copyright: © 2018 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. introduction he proposed problem is a well-known elasticity problem. it is used as a modeling example in the theory of mixed elasticity problems to recognise new methods to solve these problems. the solutions of such problems are usually reduced to ssie, containing fixed singularities in a kernel [1]. pioneering papers by scientists such as h. f. bueekner, g. i. bierman, f. tricomi, s. g. mihlin, m. g. kreyn, b. nobl and others, they first proposed different approaches for consideration of fixed singularities’. solving equations with fixed singularities in a kernel was made by using many methods. analytical proof of these methods was given, for example, in [2-5]. there, the singular integral equations of the first type (one fixed singularity) t v. reut et alii, frattura ed integrità strutturale, 44 (2018) 82-93; doi: 10.3221/igf-esis.44.07 83             1 1 21 0 1 00 0 , 0;1 , 0 re , 0, k nnn kk k kk k y y yc xc c x dy dy f x x i n k k n i y x i y x                      or of the second type (two fixed singularities)                          1 1 1 21 0 101 1 1 , 1 11 , 1 1 1 , 0 re m mkn k k m k m k kkkk k y c x y x x yc a x c x dy dy k x y y dy i y x i y y xy f x m k                                   were considered. the approaches to solve them were proposed in the widely known work [3]. the first equation was considered by many authors, e.g. [5-11], whereas the second equation was investigated e.g. in [12, 13]. these methodologies were used by employing two main approaches to solve elasticity problems for semi-strips with a crack: both analytical and numerical. the analytical approach to solve the ssie’s with two fixed singularities is often connected with unknown function’s expansion in the series of polynomials with corresponding weights. an sie with two fixed singularities at the endpoints in the class of the functions bounded at the ends was analyzed in [4]. for the chebyshev polynomials of the first kind on the right hand-side, solution of the integral equation is expressed in terms of two non-orthogonal polynomials with associated weights. based on this new generalized spectral relation for the singular operator with two fixed singularities, an approximate solution to the complete singular integral equation is derived by recasting it as an infinite system of linear algebraic equations of the second kind. some problems were solved with the apparatus of the riemann-hilbert problem. it is worth pointing out the following papers. in [14] the problem of semi-infinite crack between two bonded dissimilar strips with the same density was considered. the boundary problem was reduced to the riemann-hilbert problem. the study of the algebra generated by the cauchy singular integral operator and integral operators with fixed singularities on the unit interval was given in [15]. in [16] a polynomial collocation method was considered for the numerical solution of the cauchy singular integral equations with fixed singularities over the interval, where the fixed singularities are supposed to be of mellin convolution type. the following papers were dedicated to the numerical solving of problems with similar equations, [17] in [18] the solution of a dynamic problem of an elastic strip, coupled to an elastic half-space, is reduced to a singular integral equation that is solved with the help of special quadrature formulae for singular integrals. an approach to investigate the optimal quadrature formulae for singular integrals with fixed singularity was obtained in [19]. in [20], the quadrature formulae of the highest algebraic accuracy were obtained for ssie. the efficiency of their application in solving the singular integral equations with the generalized cauchy kernel was showed. in [21] the new versions of subdomain and spline methods were proposed. collocation methods were proposed in [22]. the problem of stress concentration near the crack’s tips is an actual problem. interface cracks in bodies under harmonic load was investigated in [23]. microstructure influence on the damage micromechanisms in overloaded fatigue cracks was studied in [24]. crack-tip field in circumferentially-cracked round bar (ccrb) in tension affected by loss of axial symmetry was explored in [25]. in [26] the overview of recent advanced methods for rapid calculation of notch stress intensity factors under mixed mode loadings was presented. the analytical approach for plane elastic and thermoelastic problems for inhomogeneous, orthotropic planes, half-planes and strips was presented in [27]. to solve mixed problems, many authors mostly introduce some auxiliary functions, for example, harmonic and byharmonic ones, through which unknown displacements are represented. reconstruction of the initial characteristics in this case is often a non-trivial mathematic problem. in this work, the new methods based on direct application of integral transformations to the equilibrium equations is solved, so no additional transformations are needed. thus it was possible to find directly the real mechanical characteristics without using any auxiliary functions. this approach was shown first in [28] to solve the problem of the semi-strip without the existence of a crack. statement of the problem he elastic ( g is a share module,  is a poison’s coefficient) semi-strip, 0 , 0x a y     is considered for two cases with regard to the boundary conditions on the short edge 0 , 0x a y   . at the lateral semi-infinite sides 0, 0x y    and , 0x a y    the boundary conditions are given t v. reut et alii, frattura ed integrità strutturale, 44 (2018) 82-93; doi: 10.3221/igf-esis.44.07 84        0, 0, 0, 0, , 0, , 0, 0u y v y u a y v a y y       (1) here  ( , ) ,xu x y u x y ,  ( , ) ,yv x y u x y are the displacements that satisfy the lame’s equilibrium equations 2 2 2 2 2 2 2 2 2 2 ( , ) ( , ) ( , )1 2 0 1 1 ( , ) ( , ) ( , )1 2 0 1 1 u x y u x y v x y x yx y v x y v x y u x y x yx y                              (2) where 3 4   is the muskchelishvili’s constant. two cases of the boundary conditions on the short edge are considered. in the first case (fig. 1) the semi-strip is loaded at the edge 10, 0y x a     1( , 0) , ( , 0) 0, 0y xyx p x x x a     (3) and conditions of the slide contact are executed at the segment 10,y a x a   1( , 0) 0, ( , 0) 0,xyv x x a x a    (4) figure 1: first case: geometry and coordinate system of the problem. figure 2: second case: geometry and coordinate system of the problem. in the second case (fig. 2) the semi-strip is loaded at the edge 0, 0y x a    ( , 0) , ( , 0) 0, 0y xyx p x x x a     (5) at the segment 0 1 ,c x c y b   the crack is situated                 1 0 1 2 0 1 , 0 , 0 , 0, , 0 , 0 , 0, u x b u x b u x b x c x c v x b v x b v x b x c x c                   (6) v. reut et alii, frattura ed integrità strutturale, 44 (2018) 82-93; doi: 10.3221/igf-esis.44.07 85             0 1 0 1 , 0 , 0 , 0, , 0 , 0 , 0, xy xy xy y y y x b x b x b c x c x b x b x b c x c                     (7) one needs to solve the corresponding boundary value problems to estimate the stress state of the semi-strip and the concentration of the stresses at the crack’s tips. general solving scheme for the semi-strip stress state estimation ccording to the approach [29], the fourier’s transformation was applied to the system of lame’s equilibrium eqs. (2) and to the boundary conditions (1), (3)-(4), (1), (5) by the generalized scheme [30]. the initial problem was reduced to a vector boundary problem [31]         2 0 0, 0 l y x f x y y a          (8) here        22 " 2 'l y x iy x qy x py x           is the differential operator of the second order, i is an identity matrix,       u x y x v x             1 0 1 1 0 1 p                1 0 1 1 0 1 q                        1 2 1 2 3 1 3 '( ) sin cos ' 1 1 1 1 1 ( ) sin ' cos 1 1 x b x b x f x x b x b x                                                0 , y x v x y   is an unknown function. so     0 ' , ' y v x y x   ,   0 ' y u xy     , and the second boundary condition in (3) is satisfied automatically. the components of the vector  y x  are the fourier transformation of the displacements     0 ( ) cos, ( ) sin, u x yu x y dy v x yv x y                       (9) the solution of the vector boundary problem was obtained in the form [27, 28] a v. reut et alii, frattura ed integrità strutturale, 44 (2018) 82-93; doi: 10.3221/igf-esis.44.07 86        1 31 2 2 4 0 , ( ) ac c y x y x y x g x f d c c                    (10) where    1 2,y x y x are the system of fundamental matrix solutions, , 1, 4ic i  are known constants,  ,g x  is the green’s matrix function [29]. the expression (10) can be rewritten in scalar form                                 11 12 11 12 11 1 1 1 2 2 3 2 4 0 121 1 12 11 1 1 0 0 0 111 1 12 2 2 0 0 3 ( ) , ' 1 1 1 , ' sin , sin , 1 1 3 1 cos , cos , 1 1 c c c c c c c c u x y x c y x c y x c y x c g x d g x d b g x d b x d g b x d b g x d                                                                                (11)                                 21 22 21 22 21 1 1 1 2 2 3 2 4 0 221 1 22 21 1 1 0 0 0 211 1 22 2 2 0 0 3 ( ) , ' 1 1 1 , ' sin , sin , 1 1 3 1 cos , cos , 1 1 c c c c c c c c v x y x c y x c y x c y x c g x d g x d b g x d b x d g b x d b g x d                                                                                (12) here    , ,ij ijx g x d     , and upper limit of the integrals 1a  in the first case and a  in the second case. the inverse transformations were applied to the formulae (11)-(12), and the substitution of the displacement functions in the boundary conditions        , 0 , , 0 0, , 0 0y xy yx p x x b x b       reduce to the system of the singular integral equations. solving of the sie system for the two cases he changing of the variable *2      in the integrals with the limits 0 and  , and  * 0 1 1 0 2 c c c c       in the integrals with the limits 0c and 1c were done to pass the integration interval  1 1;1i   . similar changes were done in the other equations. we first consider in details the second case. ssie is written in the form                 1 0 1 1 1 1 1 1 1 1 2 2 1 1 1 , , 1 0, 1 0, z x d k x r x x i x d k x x i x d k x x i x                                              (13) t v. reut et alii, frattura ed integrità strutturale, 44 (2018) 82-93; doi: 10.3221/igf-esis.44.07 87 where    1 ' 2                   1 0 1 0' , 1, 2 2 i i c c c c i                             1 1 1 1 ,1 2 ,2 1 1 1 , , , , 0,1, 2i i i ik x f x d r x d r x d i                                ,1 ,2, , , , , , , 0,1, 2i i if x r x r x r x i       are known regular functions,                 1 2 32 2 3 3 1 1 1 11 1 1 1 , 2 2 2 2 2 2 x xx x x h h h x x x x x x                                                   , 2 1 2 3 3 2 4 , , 2 h h h           . in this article the misprint in [28] for the coefficients , 1, 2, 3ih i  is corrected. the first singular integral equation in the system (13) is the partial case of the equation with two fixed singularities for the second case. for this equation the transcendental equation was built, that is congruent to the transcendental equation obtained for the quarter plane or, the same, for the problem of an infinity wedge when the angle of openness is pi/2 [32]. the problem for the quarter plane is solved in appendix a. the roots k of the corresponding transcendental equation for (13) were found numerically. the generalized method developed in [28] was applied to solve the ssie (13). according to it the function    is searched in the form         1 0 0 0 , 1;1 n k k k n k k s s                  (14) where               re 2 re 2 1 1 cos im ln 1 , 0, 1 1 sin im ln 1 , k k k k k k k n                         , 0ks are the unknown coefficients. it is supposed that the crack is located inside the semi-strip far from the lateral sides. so the unknown functions    1 2,     are considered as       2 1 2 0 1 , 1;1 , 1, 2 n i i k k k s u i            (15) where  ku  are chebyshev polynomials of the second kind. the expressions (14)-(15) are substituted in the ssie (13). the resulting system is solved with the help of the collocation method. the substitution of the founded constants , 0,1, 2, 0, 2 1iks i k n   in the formulae (14)-(15) and (11)-(12) v. reut et alii, frattura ed integrità strutturale, 44 (2018) 82-93; doi: 10.3221/igf-esis.44.07 88 enables to find the searched field of stresses and displacements. it completes the construction of the problem’s solution in the second case. in the first case, the first equation in (13) has only one fixed singularity. similarly to the previous case the unknown function    is searched in the form [28].         1 0 0 0 , 1;1 1 n k k k k n k t s s                      (16) where  kt  are chebyshev polynomials of the first kind. the formulae (15)-(16) are substituted in the ssie (13) and the collocation method was applied to the solve the resulting system. in the first case, the construction of the problem’s solution was completed by the substitution of the obtained constants , 0,1, 2, 0, 2 1iks i k n   into the expressions (14)-(15) and (11)-(12). numerical results and discussion he calculation for sif was done by the formulae [30], [33]                 2 1 2 1 1 0 1 02 2 0 0 2 1 2 1 1 0 1 01 1 0 0 1 1 1 , , 2 2 1 1 1 , 2 2 kn n i k i k k k kn n ii k ii k k k c c n c c n k s k s c c n c c n k s k s                                   the calculations of sif were done for the elastic semi-strip ( 961.2781955 10g   pa, 0.33  ) with the parameters   1p x  pa, 10a  m, 1, 90%b a a a  . here ,i ik k  are sif of normal stresses at the left and right crack’s tips correspondingly. similarly, ,ii iik k  are sif of the tangential stresses at the left and right crack’s tips. figure 3: second case: the changing of sif ,i iik k when the crack’s size is increasing. fig. 3 presents the dynamics of sif’s changes ik and iik respectively in dependence of the distances between the crack tips and the lateral sides of the semi-strip in the second case. the sif values are decreasing whereas the distances between the lateral sides and the crack tips are increasing. stable results were obtained when the distances between the crack’s tips t v. reut et alii, frattura ed integrità strutturale, 44 (2018) 82-93; doi: 10.3221/igf-esis.44.07 89 and the lateral sides are more or equal to 5%a . when these distances are less than 5%a the fixed singularities at the crack’s tips should be taken into consideration. the values of sif ik are bigger than the corresponding values of sif iik . the dynamics of the sif’s changes ik and iik respectively is shown in fig. 4 as a function of the distances between the crack tips and the lateral sides of the semi-strip in the first case. when the distance between the left lateral side and the left crack’s tip is less than 5%a , the fixed singularity at the left crack’s tip should be considered. the fixed singularity at the right crack’s tip should be taken into account when the distance between the right lateral side and the right crack’s tip is less than 11%a . in this case, the sif ik and iik values have the same order, but the values of sif iik are bigger than the values of sif ik . figure 4: first case: the changing sif ,i iik k when the crack’s size is increasing. conclusions . the proposed method enhances the solution of the problem in two different cases of external load when the transverse crack is located inside the semi-strip. 2. the minimal distances between the crack’s tips and the lateral sides of the semi-strip are established. the consideration of the fixed singularities at the semi-strip’s short edge allows bringing the crack to the lateral sides more than 6% closer in comparison with the case when the fixed singularities were not considered. to obtain stable results when the crack is closer to the lateral sides one has to take into account the fixed singularities at the crack’s tips. 3. the approach described the solution of the problem that can be also applied in the case of a dynamic statement of the problem. appendix a. solving the mixed problem of elasticity for a quarter plane onsider the problem for a quarter plane (fig. 5) , 0x y  when one boundary side 0, 0x y    is fixed and the another 0, 0y x    is under the mechanical load    , 0 , 0, p x x a r x x a      . the initial problem was reduced to a one-dimensional problem with the help of the semi-infinite sin-, cosfourier transformation (9). the boundary problem in transformation domain was rewritten in the vector form       2 0 0 l y x g x y        (17) 1 c v. reut et alii, frattura ed integrità strutturale, 44 (2018) 82-93; doi: 10.3221/igf-esis.44.07 90 figure 5: geometry and coordinate system of the quarter plane. here        22 " 2 'l y x iy x qy x py x           i is an identity matrix,       u x y x v x             1 0 1 1 0 1 p                1 0 1 1 0 1 q                3 '( ) 1 1 ( ) 1 x g x x                    the new unknown function is input     0 , y x v x y   . the solution of (17) was constructed in the following form      1 2 0 , ( ) c y x y x g x g d c               (18) where       1 1 2 1 1 x x x e y x x x                          v. reut et alii, frattura ed integrità strutturale, 44 (2018) 82-93; doi: 10.3221/igf-esis.44.07 91 was constructed with the help of the matrix differential calculation, , 1, 2ic i  are known constants,  ,g x  is the green’s matrix function which was constructed by the use of the matrix semi-infinite fourier transformation. the components of the green’s matrix function have the following form             11 1 1 , 2 2 1 x x x x x xe eg x e e x e x e                                                    12 1, 2 1 x xg x x e x e                          21 1, 2 1 x xg x x e x e                            22 1 1 , 2 2 1 x x x x x xe eg x e e x e x e                                           after inverting the expression (18), and the summation of the weak-convergent integrals, the formulae for the displacements in the quarter plane have the following form                                  2 2 2 22 2 2 22 2 0 2 2 2 2 22 2 2 1 1 , ' ln ln 4 1 1 2 1 1 x x u x y x y x y x y x y x y xx d x yx y                                                                                                 2 22 2 0 2 2 22 22 2 2 1 1 , ' 2 2 2 4 1 22 2 1 y x y x y y v x y arctg sign x arctg x xx y x y xy x xyy y arctg d x sign y x x y x yx y                                                                                  these expressions will describe the displacements in the quarter plane if the function  '  is found. to get it, the formulae for the displacements were put in the boundary condition  ( , 0) , 0y x p x x a    . after changing the variables, the singular integral equation was derived         1 31 2 2 3 0 1 h xh h x d q x x x x x                        (19) here    1 ' 2 a             , 2 1 2 3 3 2 4 , , 2 h h h           ,  q x is the known function. v. reut et alii, frattura ed integrità strutturale, 44 (2018) 82-93; doi: 10.3221/igf-esis.44.07 92 the transcendental equation for (19) is equal to the transcendental equation for the first singular integral equation in (13), and has the following form   2 22 4 8 12 3 cos 0 3 4 3 4 3 4                  (20) the eq. (20) is equal to the transcendental equation in [32]. acknowledgments he authors are grateful to simon dyke for the editing of the manuscript’s text. references [1] vorovich, i. i. and kopasenko, v. v., (1966). some problems of elasticity theory for the semi-strip. (in russian), prikladnaya matematica i mekchanica, 30(1), pp. 128-136. [2] babeshko, v. a., babeshko, o. m. and evdokimova, o. v., (2010). on the method of block element, mechanics of solids, 45, pp. 437-444. doi: 10.3103/s0025654410030143. [3] duduchava, r. v., (1979). integral equations with fixed singularities, bg teubner. [4] antipov, y. a., (2015). singular integral equations with two fixed singularities and applications to fractured composites, the quarterly journal of mechanics and applied mathematics, 68(4), pp. 461-501. [5] onischuk, o. v., popov, g. ya. and farshayt, p. g., (1988). the problem about bend of rectangular plate with linear pile, which goes on the fixed side by one end, mechanics of solids, 6, pp. 160-167. [6] soldatov, a. p., (1973). a problem in function theory, diff. equations, 9(2), pp. 248–253. [7] bueekner, h. f., (1960). some stress singularities and their computation by means of integral equations, boundary problems in differential equation, univ. wisconsin press. madison, pp. 215-230. [8] bueekner, h. f., (1966). on a class of singular integral equations, j. mathem. anal. and appl., 14, pp. 392-426. [9] bierman, g. i., (1971). a particular class of singular integral equations, j. appl. mathem., 20(1), pp. 99-109. [10] gohberg, i. and krein, m.g., (1960). introduction of the theory of linear nonselfadjoint operators, american mathematical society. transl, 14, pp. 217-287. [11] noble, b., (1958). methods based on the wiener-hopf technique for the solution of partial differential equations, belfast, northern ireland, pergamon press. [12] tricomi, f., (1932). atti accad. naz. lincei, ser. 5(14), pp. 134–247. [13] michlin, s. g. and prössdorf, s., (1986). singular integral operators, akademie verlag, berlin. [14] wu x.-f., lilla, e. and zou, w.-s., (2002). a semi-infinite internal crack between two bonded dissimilar elastic strips, archive of applied mechanics, 72, pp. 630-636. [15] duduchava, r., krupnik, n. and shargorodsky, e., (1999). an algebra of integral operators with fixed singularities in kernels, integral equations and operator theory, 33(4), pp. 406-425. [16] junghanns, p. and rathsfeld, a., (2002). on polynomial collocation for cauchy singular integral equations with fixed singularities, integral equations and operator theory, 43(2), pp. 155-176. [17] savruk, m. p., osiv, p. n. and prokopchuk, i. v., (1989). numerical analysis in plane problems of the crack’s theory (in russian), naukova dumka, kyiv. [18] popov, v. g., (2012). a dynamic contact problem which reduces to a singular integral equation with two fixed singularities, journal of applied mathematics and mechanics, 76(3), pp. 348-357. [19] shabozov, m. sh., (1995). an approach to the investigation of optimal quadrature formulas for singular integrals with fixed singularity, ukrainian mathematical journal, 47(9), pp. 1479-1485. [20] sahakyan, a. v., (2011). method of discrete singularities for solution of singular integral and integro-differential equations, proceedings of a. razmadze mathematical institute, 156. t v. reut et alii, frattura ed integrità strutturale, 44 (2018) 82-93; doi: 10.3221/igf-esis.44.07 93 [21] gabbasov, n. s., (2009). methods for solving an integral equation of the third kind with fixed singularities in the kernel, differential equations, 45(9), pp. 1341-1348. [22] capobianco, m. r., criscuolo, g. and junghanns, p., (2008). on the numerical solution of a hypersingular integral equation with fixed singularities, operator theory: advances and applications, 187, pp. 95-116. [23] guz, a.n., guz, i.a., men’shikov, a.v. and men’shikov, v.a., (2011). stress-intensity factors for materials with interface cracks under harmonic loading, int appl mech, 46, pp. 1093. doi: 10.1007/s10778-011-0401-1. [24] di cocco, v. and iacoviello, f., (2017). ductile cast irons: microstructure influence on the damaging micromechanisms in overloaded fatigue cracks, engineering failure analysis, 82, pp. 340-349. [25] toribio, j., gonzàles, b. and matos, j.c., (2017). crack tip field in circumferentially-cracked round bar (ccrb) in tension affected by loss of axial symmetry, frattura ed integrità strutturale, 41, pp. 139-142, doi: 10.3221/igfesis.41.19. [26] peron, m., razavi, s.m.j., berto, f. and torgersen, j., (2017) notch stress intensity factors under mixed mode loadings: an overview of recent advanced methods for rapid calculation, frattura ed integrità strutturale, 42, pp. 196-204, doi: 10.3221/igf-esis.42.21. [27] tokovyy, yu. and chien-ching ma, (2009). an explicit-form solution to the plane elasticity and thermoelasticity problems for anisotropic and inhomogeneous solids, international journal of solids and structured, 46, pp. 3850-3859. [28] vaysfel’d, n., kryvyi, o. and zhuravlova, z., (2016). on the stress investigation at the edge of the fixed elastic semistrip, frattura ed integrità strutturale, 38, pp. 1-11. doi: 10.3221/igf-esis.38.01. [29] vaysfel’d, n. d. and zhuravlova, z. yu., (2015). on one new approach to the solving of an elasticity mixed problem for the semi-strip, acta mechanica, 226(12), pp. 4159-4172. doi: 10.1007/s00707-015-1452-x. [30] popov, g.ya., (1982). the elastic stress' concentration around dies, cuts, thin inclusions and reinforcements(in russian), nauka, moskow. [31] vaysfel’d, n.d. and zhuravlova z.yu., (2018). two-dimensional mixed problem of thermoelasticity for a semistrip, journal of mathematical sciences, 228(2) 105-121. doi 10.1007/s10958-017-3609-8. [32] uflyand, ya. s., (1967). integral transformations in the problems of the elasticity theory (in russian), nauka, l.. [33] zhuravlova, z., (2017). stress analysis near the tips of a transverse crack in an elastic semi-strip, appl. math. mech. – engl. ed. doi: 10.1007/s10483-017-2217-6. << /ascii85encodepages false /allowtransparency false /autopositionepsfiles true /autorotatepages /none /binding /left /calgrayprofile (dot gain 20%) /calrgbprofile (srgb iec61966-2.1) /calcmykprofile (u.s. web coated \050swop\051 v2) /srgbprofile (srgb iec61966-2.1) /cannotembedfontpolicy /error /compatibilitylevel 1.4 /compressobjects /tags /compresspages true /convertimagestoindexed true /passthroughjpegimages true /createjobticket false /defaultrenderingintent /default /detectblends true /detectcurves 0.0000 /colorconversionstrategy /cmyk /dothumbnails false /embedallfonts true /embedopentype false /parseiccprofilesincomments true /embedjoboptions true /dscreportinglevel 0 /emitdscwarnings false /endpage -1 /imagememory 1048576 /lockdistillerparams false /maxsubsetpct 100 /optimize true /opm 1 /parsedsccomments true 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/hrv (za stvaranje adobe pdf dokumenata najpogodnijih za visokokvalitetni ispis prije tiskanja koristite ove postavke. stvoreni pdf dokumenti mogu se otvoriti acrobat i adobe reader 5.0 i kasnijim verzijama.) /hun 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can be opened with acrobat and adobe reader 5.0 and later.) >> /namespace [ (adobe) (common) (1.0) ] /othernamespaces [ << /asreaderspreads false /cropimagestoframes true /errorcontrol /warnandcontinue /flattenerignorespreadoverrides false /includeguidesgrids false /includenonprinting false /includeslug false /namespace [ (adobe) (indesign) (4.0) ] /omitplacedbitmaps false /omitplacedeps false /omitplacedpdf false /simulateoverprint /legacy >> << /addbleedmarks false /addcolorbars false /addcropmarks false /addpageinfo false /addregmarks false /convertcolors /converttocmyk /destinationprofilename () /destinationprofileselector /documentcmyk /downsample16bitimages true /flattenerpreset << /presetselector /mediumresolution >> /formelements false /generatestructure false /includebookmarks false /includehyperlinks false /includeinteractive false /includelayers false /includeprofiles false /multimediahandling /useobjectsettings /namespace [ (adobe) (creativesuite) (2.0) ] /pdfxoutputintentprofileselector /documentcmyk /preserveediting true /untaggedcmykhandling /leaveuntagged /untaggedrgbhandling /usedocumentprofile /usedocumentbleed false >> ] >> setdistillerparams << /hwresolution [2400 2400] /pagesize [612.000 792.000] >> setpagedevice microsoft word numero_37_art_12 i.llavori et alii, frattura ed integrità strutturale, 37 (2016) 87-93; doi: 10.3221/igf-esis.37.12 87 focussed on multiaxial fatigue and fracture an all-in-one numerical methodology for fretting wear and fatigue life assessment i. llavori departamento de mecánica y producción industrial, escuela politécnica superior de mondragon unibertsitatea, loramendi 4, 20500, arrasate-mondragon, spain, illavori@mondragon.edu m.a. urchegui orona eic, orona ideo, jauregi bidea s/n, 20120, hernani, spain, maurchegui@orona-group.com w. tato, x. gomez departamento de mecánica y producción industrial, escuela politécnica superior de mondragon unibertsitatea, loramendi 4, 20500, arrasate-mondragon, spain, wtato@mondragon.edu, xgomez@mondragon.edu abstract. many mechanical components such as, bearing housings, flexible couplings and spines or orthopedic devices are simultaneously subjected to a fretting wear and fatigue damage. for this reason, the combined study on a single model of wear, crack initiation and propagation is of great interest. this paper presents an all-in-one 2d cylinder on flat numerical model for life assessment on coupled fretting wear and fatigue phenomena. in the literature, two stages are usually distinguished: crack nucleation and its subsequent growth. the method combines the archard wear model, a critical-plane implementation of the smith-watsontopper (swt) multiaxial fatigue criterion coupled with the miner-palmgren accumulation damage rule for crack initiation prediction. then, the linear elastic fracture mechanics (lefm) via extended finite element method (x-fem) embedded into the commercial finite element code abaqus fea has been employed to determine the crack propagation stage. therefore, the sum of the two stages gives a total life prediction. finally, the numerical model was validated with experimental data reported in the literature and a good agreement was obtained. keywords. fretting; multiaxial fatigue; wear; crack propagation; x-fem. introduction any mechanical components such as, bearing housings, flexible couplings and spines or orthopedic devices are simultaneously subjected to a fretting wear and fatigue damage. fretting phenomenon arises when two bodies are in contact subjected to relative movement of small amplitude, producing damage to the contact surface [1]. depending on the magnitude of stresses, fretting phenomenon can cause catastrophic failure of such mechanical components. m i.llavori et alii, frattura ed integrità strutturale, 37 (2016) 87-93; doi: 10.3221/igf-esis.37.12 88 in general, the study of fretting is divided into two stages, the crack initiation and its subsequent propagation. on the one hand, due to the non-proportional multiaxial state of contact stress field, the use of multiaxial fatigue parameters has become a very popular technique for fatigue life assessment [2]. on the other hand, several studies analyses the propagation phase in terms of the linear elastic fracture mechanics (lefm) for brittle materials. in this regard, works such as vázquez [3] employs analytical methods to estimate cycles to failure. other works like the one of giner et al. [4] studies the mechanics of the contact in presence of a crack in a single numerical model due to the advantage of the extended finite element method (x-fem) [5]. however, these studies are mainly focused in the partial slip regime where the removal of material is not important and therefore, do not need to employ wear simulation techniques. in the presence of wear, one of the most prominent works is presented by madge et al. [6]. first, the numerical simulation of the process of material removal using the abaqus fea user subroutine umeshmotion is performed. then, crack initiation analysis using the smith-watson-topper (swt) multiaxial fatigue parameter coupled with the miner-palmgren accumulation damage framework to account the effect of wear is carried out. finally, the propagation phase is analyzed via submodelling technique. this method allows to transfer the stress state of the contact surface from global wear model to crack submodel. consequently, the explicit interaction between the fretting contact and the crack can’t be modelled. the aim of this paper is to employ the x-fem methodology implemented by giner et al. [4] to explicitly model the interaction between the fretting contact and the crack, to explain the same set of numerical problems analyzed by madge et al. [4.] therefore, the developed method combines the archard wear model, a critical-plane implementation of the swt multiaxial fatigue criterion coupled with the miner-palmgren accumulation damage rule for crack initiation prediction, and the x-fem developed by giner et al. [7] in addition to the level set method (lsm) [8] in order to detect the extended elements, for crack propagation prediction. therefore, the sum of the two stages gives a total life prediction. review of wear, crack initiation and propagation criteria wear law criterion he wear simulation algorithm used in this work is the one presented by mccoll et al. [9] for 2d numerical model and used also by cruzado et al. [10] for 3d simulations. the simulation methodology is based on the archard wear law, an iterative process in which the local archard equation is resolved by means of the finite element contact stresses and slip distribution results. however, this process requires a high computational performance, therefore the cycle jump technique is employed [9,10], where it is made the assumption that wear remains constant over a small number of cycles. thus, the archard local equation (eq. 1) is defined as δh (x,t)=δn×k×p(x,t)×δs(x,t) (1) where δh(x,t), δn, k, p(x,t) y δs(x,t) are the incremental wear depth, the cycle jump, archard wear coefficient, the contact pressure and the relative slip for a specific point at specific time. the wear coefficient used in this work is based on the experimental results of magaziner et al. [11] which was estimated by mccoll et al. [9] and employed later by madge et al. [6]. crack nucleation criteria as it has been mentioned in the introduction, due to the non-proportional multiaxial state of stress field, the use of multiaxial fatigue parameters has become a popular technique. in this paper the swt (eq. 2) criterion [12] is used to predict the location, plane and cycles to crack nucleation.    b b cn n e 2 2f máx f f f f máx ´ swt 2 ´ ´ 2 2             (2) where σf´ is the fatigue strength coefficient, εf´ is the fatigue ductility coefficient, b is the fatigue strength exponent and c is the fatigue ductility exponent. the fatigue constants used in this paper are the same as the ones employed by madge et al. [6]. the stress state in the contact zone varies during the test due to wear phenomenon, thereby the swt value is different for each wear state. one of the most commonly used techniques to take into account these states is the damage accumulation rule of miner-palmgren (eq. 3), defined as t i.llavori et alii, frattura ed integrità strutturale, 37 (2016) 87-93; doi: 10.3221/igf-esis.37.12 89 k i ii n n1     , (3) where ω is the total accumulated damage (nucleation is defined to have occurred when the parameter reaches the value of 1), ni is the number of cycle completed in each wear stress state and ni is the theoretical number of cycles to failure predicted by the swt parameter for each wear stress state. in this paper, the implementation of the miner’s rule presented by cruzado et al. [13] has been employed. crack propagation criteria to estimate the second phase of the presented method, a crack growth law of the type da/dn = f(δk) based on the lefm has been used to determine the crack propagation rate. the model relies the correct calculation of the stress intensity factor (sif) on the x-fem, using the j integral through the interaction integral. thus, the effect of the crack/fretting-contact evolution can be analyzed in a single numerical model as shown by giner et al. [4]. the fracture constants used in this paper are the same as the ones employed by madge et al. [6]. in this work, it is assumed that the crack propagation takes place under mode i, e.g. δk = ki max, since ki min is almost 0 due to stress ratio being r = 0.03 and perpendicular to the initial contact surface. experimental test description he fretting fatigue experimental tests selected for comparison purpose is reported in the literature by magaziner et al. [11]. the test machine shown in fig. 1 consists of two servo-hydraulic actuators. the main actuator controlled the alternating axial load (σ) of the fatigue specimen, while the secondary actuator controlled the tangential load (q). thus, the test machine is capable to perform a combined fretting fatigue and wear test. the selected tests are 9a and 10a, and the amplitude of displacement between the fretted bodies are δ = 36 µm and δ = 104 µm respectively. figure 1: schematic of cylinder on flat fretting fatigue test configuration [11]. numerical model he model shown in fig. 2 has been developed in the commercial code abaqus fea. due to the typical fretting fatigue testing geometry, half the specimen has been modelled as in references [2,3,4,6]. the model consists of linear quadrilateral elements of 4 nodes (cpe4), with further refinement on the contact neighborhood by the partition technique. in order to obtain a precise slip distribution, the coulomb and the lagrange multipliers methods have been used to model the tangential contact. fig. 3 shows the developed coupled wear, crack initiation and crack propagation numerical flow chart. t t i.llavori et alii, frattura ed integrità strutturale, 37 (2016) 87-93; doi: 10.3221/igf-esis.37.12 90 figure 2: boundary condition of the numerical model. figure 3: flow chart showing computational sequence for numerical analysis. results ig. 7 illustrates the evolution of the von mises (vm) stress field at different stages of the δ = 36 µm amplitude displacement simulation (test 9a), when the maximum axial load is applied. the top left image corresponds to the unworn specimen at the start of the simulation. at this stage, the maximum vm peak stress (1348 mpa) lies at the right end of the contact, that is, on the side where the axial load is applied. the top right figure corresponds to the stress state prior to crack initiation, at 10,000 cycles. it is observed that the contact area is slightly bigger than the initial one, while the reduction of the maximum vm value is around 25% due to the contact stress redistribution originated by wear. f f mpc p δapp uy = 0 ux = 0 yes no 1.compute swt and miner damage 2.compute wear and set new geometry 3.interp. of miner’s damage to new node location start analysis: read data and generate mesh fem simulation generate crack segment and lsm analysis no yes x-fem simulation 1.compute stress intensity factor 2.compute crack propagation rate 3.compute wear and set new geometry end analysis failure? ω =1? i.llavori et alii, frattura ed integrità strutturale, 37 (2016) 87-93; doi: 10.3221/igf-esis.37.12 91 later, at 20,000 cycles the contact area increases and the right crack lip makes contact, while the crack propagates slowly due to the low value of sif. it should be mentioned that the black square zone shown in these pictures are the extended elements that represent numerically the crack. finally, the bottom right figure corresponds to the very end of the simulation, prior to the final rupture of the specimen. at this stage, the contact area remains almost the same, although the stress field changes due to the loss of local stiffness derived from the longer crack. figure 7: evolution of the vm stress field at different stages. top left: cycle 1; top right: 10,000 cycles; bottom left 20,000 cycles; bottom right 49,300 cycles. the left side of fig. 8 shows the miner’s damage evolution for the analyzed cases. on the one hand, the δ = 36 µm displacement amplitude simulation predicts crack nucleation at 10,300 cycles. on the other hand, the δ = 104 µm displacement amplitude simulation predicts no crack nucleation. the later reaches a maximum miner’s damage value of 0.2 at 3,000 cycles and it remains almost constant, with a slight downward slope due to the effect of contact pressure redistribution promoted by the removal of damaged material. the right side of fig. 8 shows the sif range as a function of completed cycles. as expected in the early phase, the crack propagation rate is slow due to the low sif value. later, the crack growth rate increases and it propagates until the complete rupture. the fracture toughness (kic) of the titanium alloy tested by magaziner et al. (ti-6al-4v solution treated and aged), available in the database of materials ces edupack 2010 [14], is comprehended between 82 and 100 mpam1/2. the numerical estimation of the fracture toughness value is reached approximately at 52000 cycles. nevertheless, the ultimate tensile strength (σuts) of the titanium alloy is reached before the fracture toughness, therefore it is concluded that the specimen rupture happens at 49300 cycles. finally, tab. 1 shows the comparison between experimental and numerical results. as it can be observed, the numerical model estimations are in very good agreement with the experimental data reported in reference [11]. i.llavori et alii, frattura ed integrità strutturale, 37 (2016) 87-93; doi: 10.3221/igf-esis.37.12 92 figure 8: left side: detailed view of the miner’s damage evolution to crack initiation. right side: estimated sif range vs. cycles in propagation. test experimental life numerical life prediction 9a (δ = 36 µm) 47,833 49300 10a (δ = 104 µm) >1,000,000a no crack prediction a test were stopped after 1 million cycles. table 1: comparison between experimental life and numerical prediction. conclusions n this work, an all-in-one 2d cylinder on flat numerical model that combines wear, crack initiation and propagation has been presented. the numerical results obtained in this work are in a very good agreement with the experimental data reported by magaziner et al. [11]. on the one hand, it has been shown that due to wear simulation the stress field on the fretted bodies changes, depending on the amplitude of displacement. therefore, it is concluded that the simulation of wear is a key element to assess correctly the life-span of the specimen under gross slip regime. on the other hand, due to the advantages of the x-fem, it is possible to study explicitly the interaction between the fretting contact and the existing crack in the presence of wear. in future work, this method will allow to study in great detail the evolution of the fretting contact at different stages under gross slip regime. acknowledgements he authors wish to thank departamento de educación, política lingüistica y cultura del gobierno vasco for their financial support to the project nusimco (ref. pi2013-23) through the program “proyectos de investigación básica y/o aplicada”. references [1] vingsbo, o., soderberg, d., on fretting maps, wear, 126 (1988) 131-147. i t i.llavori et alii, frattura ed integrità strutturale, 37 (2016) 87-93; doi: 10.3221/igf-esis.37.12 93 [2] navarro, c., muñoz, s., dominguez, j., on the use of multiaxial fatigue criteria for fretting fatigue life assessment, int. j. fatigue, 30 (2008) 32-44. [3] vázquez, j., efecto de las tensiones residuales en la fatiga por fretting. phd. thesis, universidad de sevilla, spain, (2009). [4] giner, e., navarro, c., sabsabi, m., tur, m., dominguez, j., fuenmayor, f.j., fretting fatigue life prediction using the extended finite element method, int. j. fatigue, 53 (2011) 217-225. [5] moës, n., dolbow, j., belytschko, t., a finite element method for crack growth without remeshing, int. j. numer. meth. eng., 46(1) (1999) 131-150. [6] madge, j.j., leen, s.b., shipway, p.h., a combined wear and crack nucleation-propagation methodology for fretting fatigue prediction, int. j. fatigue, 30 (2008) 1509-1528. [7] giner, e., sukumar, n., tarancon, j.e., fuenmayor, f.j., an abaqus implementation of the extended finite element method eng. fract. mech., 76 (2009) 347-368. [8] stolarska, m., chopp, d.l., möes, n., belytschko, t., modelling crack growth by level sets in the extended finite element method, int. j. numer. meth. eng., 51 (2001) 943-960. [9] mccoll, i.r., ding, j., leen, s.b., finite element simulation and experimental validation of fretting wear, wear, 256 (2004) 1114-1127. [10] cruzado, a., urchegui, m.a., gómez, x., finite element modeling and experimental validation of fretting wear scars in thin steel wires, wear, 289 (2012) 26-38. [11] magaziner, r., jin, o., mal, s., slip regime explanation of observed size effects in fretting, wear, 76 (2004) 347-368. [12] socie, d., marquis, g., multiaxial fatigue, sae book, warrendale, (2000). [13] cruzado, a., leen, s.b., urchegui, m.a., gómez, x., finite element simulation of fretting wear and fatigue in thin steel wires, int. j. fatigue, 55 (2013) 7-21. 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/hrv (za stvaranje adobe pdf dokumenata najpogodnijih za visokokvalitetni ispis prije tiskanja koristite ove postavke. stvoreni pdf dokumenti mogu se otvoriti acrobat i adobe reader 5.0 i kasnijim verzijama.) /hun 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can be opened with acrobat and adobe reader 5.0 and later.) >> /namespace [ (adobe) (common) (1.0) ] /othernamespaces [ << /asreaderspreads false /cropimagestoframes true /errorcontrol /warnandcontinue /flattenerignorespreadoverrides false /includeguidesgrids false /includenonprinting false /includeslug false /namespace [ (adobe) (indesign) (4.0) ] /omitplacedbitmaps false /omitplacedeps false /omitplacedpdf false /simulateoverprint /legacy >> << /addbleedmarks false /addcolorbars false /addcropmarks false /addpageinfo false /addregmarks false /convertcolors /converttocmyk /destinationprofilename () /destinationprofileselector /documentcmyk /downsample16bitimages true /flattenerpreset << /presetselector /mediumresolution >> /formelements false /generatestructure false /includebookmarks false /includehyperlinks false /includeinteractive false /includelayers false /includeprofiles false /multimediahandling /useobjectsettings /namespace [ (adobe) (creativesuite) (2.0) ] /pdfxoutputintentprofileselector /documentcmyk /preserveediting true /untaggedcmykhandling /leaveuntagged /untaggedrgbhandling /usedocumentprofile /usedocumentbleed false >> ] >> setdistillerparams << /hwresolution [2400 2400] /pagesize [612.000 792.000] >> setpagedevice microsoft word numero_61_art_04_3490.docx h. s. patil et alii, frattura ed integrità strutturale, 61 (2022) 59-68; doi: 10.3221/igf-esis.61.04 59 al2o3 and tio2 flux enabling activated tungsten inert gas welding of 304 austenitic stainless steel plates h. s. patil, d. c. patel mechanical engineering department, gidc degree engineering college, abrama, navsari, gujarat, india hspatil28@gmail.com, pateldcp@gmail.com abstract. gas tungsten arc welding (gtaw) is an important in manufacturing industries where it is significant to control the mechanical and metallurgical characteristics and its weld bead geometry. this research work has been committed to study the influence of oxide fluxes on welding of 4 mm thick 304 austenitic stainless steel plates. the al2o3 and tio2 were used as an oxide flux in powder form and are mixed with the acetone. the prepared mixture is then applied on bead plate without any joint preparation and without filler wire addition. the taguchi method with l9 orthogonal array has been used to determine the optimal weld process parameters. the current work aims to explore the influence of weld parameters on weld bead geometry (i.e. weld bead width, penetration and angular distortion), and mechanical and metallurgical characteristics for 304 stainless steel welds. the oxide flux seems to narrow the arc and thereby the current density increases at the anode spot, that results in high weld depth. keywords. atig; oxide flux; 304 stainless steel; weld morphology; angular distortion; mechanical characteristics. citation: patil h. s., patel d. c., al2o3 and tio2 flux enabling activated tungsten inert gas welding of 304 austenitic stainless steel plates, frattura ed integrità strutturale, 61 (2022) 5968. received: 24.02.2022 accepted: 29.03.2022 online first: 14.04.2022 published: 01.07.2022 copyright: © 2022 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. introduction taw (gas tungsten arc welding) is the most commonly used process for joining the stainless steel components. it is usually suitable for thin sheets due to its easier applicability, flexibility, and better economy and normally used for welding hard-to-weld metals such as stainless steels, aluminium, magnesium, copper and copper, and titanium [1-3]. austenitic stainless steels 304 are typically used in constructing the nuclear power plant because of their excellent combination of strength and ductility and high resistance to oxidation and corrosion. the main significant characteristics of the tig process are its good mechanical properties and high quality metallurgical welds. however, the tig welding process have a few limitations like low penetration depth, and beyond 3 mm work piece thickness it is necessary to perform edge preparation (chamfer) and addition of filler material by multi pass welding. cast-to-cast compositional variation in the base metal being welded also affected the tig welds [4, 5]. one of the most notable techniques for overcoming these limitations is the use of activating flux in the tig welding process. paton electric welding institute first proposed the activated tungsten inert gas (atig) welding process in the 1960s, which increases penetration [6-7]. activating flux is a suspension of inorganic material in a volatile medium. activating flux is made by g https://youtu.be/iuxhhkbatvm h. s. patil et alii, frattura ed integrità strutturale, 61 (2022) 59-68; doi: 10.3221/igf-esis.61.04 60 combining powder ingredients such as chlorides, oxides, and fluorides with an ethanol solvent or acetone to create a paint-like constituent. a thin layer of activating flux was applied on to the surface of the work piece to be welded before weld operation [8-12]. activated tungsten inert gas (atig) welding significantly improves weld pool penetration and is typically accomplished by applying a thin layer of active flux composition on the surface of the metal substrate. for stainless steel material, atig improves over conventional gtaw by increasing joining thickness from 6 to 10 mm for single pass [13]. furthermore, compared with conventional tig welding, the refinement in microstructure and superior mechanical characteristics of the austenitic stainless steel weld joint have been also reported [14−15]. the activated flux may have two types of mechanisms, one based on the marangoni convection effect, and the other based on weld arc behaviour. heiple and roper [16-17] and heiple et al. [18] proposed surface active elements in the molten pool change the temperature coefficient of surface tension from negative to positive, thereby reversing the marangoni convection direction from outward to inward. as the direction of the fluid flow in the molten pool becomes inward, the joint penetration increases dramatically. lucas [19] and howse [20] associated the greater penetration of activated tig welding to a constriction of the arc. however, with respect to detailed components and proportions of the activated fluxes, very few literatures were reported, also due to limited data are available in literature about the action of weld arc and the mechanisms requires further investigation. information on these processes is essential to determine the tig penetration capability improvement function of the activated flux. as austenitic stainless steels have a high coefficient of thermal expansion and low thermal conductivity than carbon/alloy steel, it can induce a large amount of shrinkage and distortion after welding. determining the effect of the activated flux on weld distortion is essential to improving the performance of the stainless steel activated tig technique. hence, in current work, 4 mm thick 304 stainless steel plates were welded by atig method without groove preparation in a single pass, wherein the activated fluxes are self-developed and mainly consist of oxides, including tio2, al2o3. the investigation aimed to explore the atig welding of 304 stainless steel and to analyse the influence of oxide fluxes and weld factors on weld bead geometry (i.e. weld bead width, penetration and angular distortion), mechanical and metallurgical characteristics. information extracted from the experiments conducted in this study can be useful for the application in various manufacturing industries. materials and experimental methods he weight % chemical compositions and mechanical characteristics of austenitic stainless steel 304 listed in tab.1 were used in experimental analysis. in present study the plates were cut into strips of 150 x 75 mm of 4 mm in thickness, which were roughly polished with 240 grit flexible abrasive papers of silicon carbide to remove surface impurities, and then cleaned with acetone. prior to the tig welding process, activated flux was prepared by mixing powder forms of al2o3, tio2 with acetone and a thin layer less than 0.25 mm was brushed onto the surface of the weld to be welded. fig.1 shows schematic illustrations of mixing and coating of flux for tig welding process. to create bead on plate welds, autogenous tig welding was performed on 304 stainless steels. a machine-mounted torch with standard 2% thorium tungsten electrode of 3.2 mm diameter and high purity argon (15l/min) were fixed in all welds. the tip configuration of the electrode was a blunt point with a 450 include angle. tab.2 lists the weld process factors used in current study. c cr ni mn si p s fe tensile strength, mpa yield strength, mpa poisson’s ratio % elongation 0.06 18.67 8.53 1.89 0.42 0.032 0.06 bal. 605 290 0.25 32 table 1: chemical compositions (wt. %) and mechanical properties of austenitic stainless steel 304. figure 1: schematic diagram of mixing and coating of flux for tig welding. t h. s. patil et alii, frattura ed integrità strutturale, 61 (2022) 59-68; doi: 10.3221/igf-esis.61.04 61 weld variables level-1 level-2 level-3 welding current (a) 180 200 220 welding voltage (v) 20 25 30 weld gap (mm) 0.5 0.75 1 table 2: welding process variables and experimental design levels of taguchi method. results and discussion influence of oxide fluxes on weld morphology n tig welding process, molten metal flow takes place from center to the edges as the surface tension at the center of the weld pool is lower than that at the edges. these results in the more content of melt distributing near the edges of wfs (weld fusion zone) than that in the center i.e. less depth and more width of the weld pool. when fluxes other than stable oxides like al2o3 are added, the marangoni effect reverses, resulting in a greater increase in weld depth and a much smaller decrease in bead width. the tig weld cross-sections with and without oxide fluxes for 4 mm thick stainless steel 304 plates are shown in fig.2 it has been observed that in a a-tig weld morphology, there is major variation in weld depth and bead width. with the use of tio2 oxide, the weld depth increases and the bead width decreases and have peanut shell type shape. with respect to conventional tig welding, there is highest improvement in the penetration capability function with the use of tio2 i.e. up to 115%. (a) oxide flux al2o3 d=1.31, w=6.12, d/w=0.21 (b) oxide flux tio2 d=3.45, w=5.91, d/w=0.58 (c) without oxide flux d=2.11,w=7.79, d/w=0.27 figure 2: influence of oxide fluxes on weld morphology. i h. s. patil et alii, frattura ed integrità strutturale, 61 (2022) 59-68; doi: 10.3221/igf-esis.61.04 62 the weld depth to bead width ratio increased significantly with tio2 oxide tig welding, as shown in fig. 2. previous studies have shown that the greater weld depth-bead width ratio and a narrower heat-affected zone are characterized by high energy density of the heat source and high energy concentration during the tig welding process (21-22). although atig penetration hasn't been proven by a common mechanism, it has commonly been observed in tig welding that using activating flux can reduce the welding arc and therefore increase penetration (23-24). activating fluxes seem to have a more profound effect on the welding arc characteristic than on the fluid flow direction (23, 25-27). fig. 3 illustrates the central part of the welding arc clearly in a glowing zone occupying almost the entire length of the welding arc without flux and with tio2 composition. this zone is commonly considered the plasma column, which forms when the shielding gas is heated to ionize electrons and positively charged ions. plasma column anode spot (a) without oxide flux (b)oxide flux tio2 figure 3: arcing without flux and with tio2 . at the same current level, when the tio2-tig welding arc is compared to a conventional tig welding arc, the diameter of plasma column is narrowed. due to a narrowed plasma column, the current density in the arc root increases, resulting in a greater arc in the a-tig penetration than conventional tig. weld morphology can also be affected by anode spots. since the conductivity of the flux is much lower than that of the metal vapor and the melting point and boiling point of the flux are higher than that of the weld metal, metal evaporation occurs only in the central region of the weld arc where the temperature exceeds the dissociation temperature of flux compounds, thereby reducing the conductive region of the anode spot. it can also be seen that the anode spot is reduced with tig weld pools with tio2 in comparison to conventional tig welds at the same current level. according to the present findings, the plasma column and anode spot have major impacts in determining atig weld morphology. when atig welding is employed, the plasma column is constricting physically, the anode spot is reduced, and the heat source energy, and the electromagnetic force emitted from the weld pool are increased, producing relatively narrow and deep welds compared to conventional tig welding. further research is needed to understand the mechanism, but current research shows the potential impact of of specific flux on atig penetration. the al2o3 deteriorated penetration and excessive slag compared with conventional tig for 304 stainless steel welds. this can be seen in fig. 4 where the tig welding process with active flux, which contains al2o3 powder, seems unable to reduce the anode spot and constrict the plasma column, leading to a relatively wide and shallow morphology of the weld in comparison to conventional tig welding. the result can be attributed to the aluminium oxide particles in the weld pool during tig welding with al2o3 powder, as shown in fig.4. as tig welding with al2o3 produces fluid flow outwards from the center of the weld pool, the particle-free band will be formed along the edge of the weld pool, resulting in an arc wander. influence of oxide flux on angular distortion during the welding process, the weld metal and the adjacent base material expand and contract, causing distortion of the weld. because of the non-uniform shrinkage caused by uneven heating throughout the thickness of the joint plate during welding, an angular distortion appears in the weldment. h. s. patil et alii, frattura ed integrità strutturale, 61 (2022) 59-68; doi: 10.3221/igf-esis.61.04 63 (a) plasmacolumn (b)anode spot (c)fluid layer figure 4: effect of al2o3 flux on welding arc and fluid flow. fig. 5 illustrates the influence of weld depth to plate thickness ratio on the angular distortion in stainless steel 304 with and without flux. it has clearly been shown that activated tig welding results in a reduction in angular distortion of the weldment. in tig welding with al2o3 flux, the weld depth is not greater than half the thickness of the plate. when the weld depth is shallow in comparison to the thickness of the plate, the angular distortion of the weldment decreases; however, as the ratio of weld depth to plate thickness increases, the angular distortion of the weldment without flux increases until a critical point is reached (weld depth to plate thickness ratio is equivalent to 0.5).however, when weld depth becomes greater than 50% of the thickness of the plate, angular distortion of the weldment decreases with tio2. with activated tig welding, we can experience a high degree of penetration into the joint and a high depth-width ratio, which indicates a high degree of energy concentration. figure 5: effect of weld depth to plate thickness ratio on angular distortion. due to the reduced quantity of heat source, the base material is not overheated, and thermal stresses and incompatible strains can be reduced due to our reduced heat source. this results in reduced angular distortions when welding stainless steel 304. h. s. patil et alii, frattura ed integrità strutturale, 61 (2022) 59-68; doi: 10.3221/igf-esis.61.04 64 therefore, this result in a reduction in supplied heat source, which reduces the likelihood of overheating the base material and reduces the incidence of thermal stress and incompatible strain due to shrinkage in thickness and, therefore, can result in a reduction in 304stainless steel weldment angular distortions. influence of oxide fluxes on mechanical characteristics tensile test was carried out in 400 kn capacity mechanical controlled universal testing machine to determine the mechanical properties of the welded specimens. the test specimens used for tensile testing were cut from welded samples using water jet machine. the dimension of test specimen as per astm-e8 has been represented by fig.6. the experimental results for mechanical characteristics of tig weldments with and without activating fluxes are shown in fig.7. figure 6: tensile test specimens for welded samples (dimensions are in mm). it is obvious that the weldment produced by tig welding with tio2 and al2o3 has better mechanical qualities, such as ultimate tensile strength than the tig weldment produced without the activating flux. at all arc voltages, raising the welding current from 180 to 220a will affect and enhance the tensile strength, as shown in fig.7. figure 7: mechanical properties of tig welds. micro-indentation hardness test as per astm e-384:2006 has been used to measure the vickers hardness of welded joints. the vickers micro-hardness indenter is made of diamond in the form of a square-base pyramid. the test load applied was 100gm and the dwell time was 15 seconds. the indentations were made at midsection of the thickness of the plates across the joint. the experimental results for the hardness of the tig welds with and without flux are shown in fig.8. the findings revealed that the oxide flux had no discernible effect on the hardness of stainless steel weld metal. the crystal structure of austenite is cubic face-centered (fcc). the crystal structure of delta-ferrite is body-centered cubic h. s. patil et alii, frattura ed integrità strutturale, 61 (2022) 59-68; doi: 10.3221/igf-esis.61.04 65 (bcc). the mechanical strength of the bcc structure is greater than that of the fcc structure. the delta-ferrite content in the weld metals is enhanced when tig welding with or without flux is employed, which has a good effect on enhancing the hardness of stainless steel welds. figure 8: hardness of tig welds. radiography analysis of atig weldments weld samples were subjected to x-ray radiographic inspection utilising a radiographic unit in accordance with asme section-viii div-i radiography standard techniques. the radioactive sources employed in the radiography test were 25ci and iridium ir192. the rt technique used was swsi, with a sensitivity of 2% and a development time of 5 minutes. the film utilised was agfa d-4, and the radiographs revealed several flaws in the welds. in both the oxides al2o3 and tio2, radiography investigation revealed a lack of penetration and insufficient fusion in tig welded joints, as illustrated in fig.9. figure 9: radiography of tig weld joints. h. s. patil et alii, frattura ed integrità strutturale, 61 (2022) 59-68; doi: 10.3221/igf-esis.61.04 66 influence of flux on microstructures and delta-ferrite content the samples for optical microscopy were polished using grit silicon carbide paper. etching procedures were used to expose the underlying microstructural features. solutions used for etching titanium include a fresh keller etchant with composition 5ml hno3, 3ml hcl, 2ml hf and 190ml distilled water. the polished metallographic mount was etched in the solution from 40 to 50 seconds to reveal the microstructural features. the fracture surfaces were analysed using scanning electron microscopy. fig.10 depicts the microstructure of 304 stainless steel weld metal generated with and without flux, as well as the observed delta-ferrite content. the ferrite number was determined using a calibrating magnetic instrument. in this, stainless steel tig welds produced without flux, the delta-ferrite content from its initial value of 1.7 fn is increased to 6.8 fn. this is because most of the weld metal of austenitic stainless steel solidified as delta-ferrite phase. during the welding process, the cooling rate of the weld metal was so fast that the phase transformation from delta ferrite to austenite was not completed. as a result, more delta ferrite remains in the weld metal after solidification. on the other hand, when the oxide flux was used, the delta ferrite content of the activated tig weld metal increased slightly to 7.3 to 7.9 fn. the heat input during tig welding with and without flux is related to this result. the weld current was kept constant, and it was discovered that when the activated tig process was used, the arc voltage increased. since the calculated heat input is proportional to the measured arc voltage, the applied activation flux has the positive effect of increasing the length of the heat input unit of the weld. this high heat input raises the peak temperature of the weld seam, which can result in the formation of more delta ferrite in the activated tig weld metal. in all cases, the austenite matrix microstructure and vermicular delta ferrite morphology typical of this material class were found. however, there was no significant difference in the microstructure between conventional tig weld metal and activated tig weld metal. (a)without oxide flux (b)with oxide flux tio2 (c)with oxide flux al2o3 figure 10: microstructure and measured delta-ferrite content in 304 stainless steel weld. (a) with oxide flux tio2 (b) without oxide flux figure 11: sem images of fracture surface. h. s. patil et alii, frattura ed integrità strutturale, 61 (2022) 59-68; doi: 10.3221/igf-esis.61.04 67 fracture can be described as a single body divided into pieces by the applied stress. for engineering materials, there are only two types of fracture: ductility and brittleness. the fracture mode of tig welding with oxide flux tio2 and no flux is ductile dimple fracture mode as shown in fig.11. conclusions his research paper conducted detailed experiments to systematically investigate the influence of oxide fluxes al2o3 and tio2 on weld morphology, angular distortion, delta-ferrite content, tensile strength and hardness when using the tig process to weld 4mm thick 304 stainless steel plates on weld different parameters. the experimental results and conclusions are summarized as follows: a. the use of tio2 resulted in significant increases in weld depth and decreases in bead width, as well as the greatest improvement function in penetration, whereas the use of al2o3 resulted in deterioration in penetration and excessive slag when compared to the conventional tig welding for a 304 stainless steel. b. when using atig welding, physically constricting the plasma column and reducing the anode spot, tends to increase the energy density of the heat source and electromagnetic force of the weld pool, resulting in a relatively narrow and deep weld morphology compared with the conventional tig welding. c. activated tig welding can increase joint penetration and ratio of weld depth to width, decreasing the angular distortion of weldment significantly. d. better mechanical characteristics are retained by atig weldment. e. a-tig welding can increase the retained delta-ferrite content of stainless steel welds. f. the optimum set parameters for oxide fluxes tio2 and al2o3 are 180a, 20v, 0.75 mm and 220a, 30v, 0.75 mm respectively giving better weld characteristics. conflict of interest he authors declare that there is no conflict of interests regarding the publication of this paper. nomenclature/symbols gtawgas tungsten arc welding atigactivated tungsten inert gas bccbody centered cubic fcccubic face centered fn-ferrite number swsi -single wall single image d-weld depth (mm) w-bead width (mm) references [1] cary, h. b. (1989). modern welding technology, prentice hall, englewood cliffs, new jersey. [2] olson, d. l., siewart, t. a., liu, s. and edwards, g. r. (1998). asm metals handbook vol. 6: welding, brazing, and soldering, 10th edition, asm international. [3] kou, s. (2003).welding metallurgy, libre digital, wiley, 2th ed. wiley india [4] huang, h. y., shyu, s., tseng, k-h. and chou, c. p. (2005). evaluation of tig flux welding on the characteristics of stainless steel, science and technology of welding and joining, 10(5), pp. 566–573. doi 10.1179/174329305x48329 t t h. s. patil et alii, frattura ed integrità strutturale, 61 (2022) 59-68; doi: 10.3221/igf-esis.61.04 68 [5] shyu, s., huang, h. y., tseng, k-h. and chou, c. p. (2008). study of the performance of stainless steel a-tig welds, journal of materials engineering and performance, 17(2), pp. 197–201. doi: 10.1007/s11665-007-9139-7 [6] hdhibi, a. k., touileb, r. and djoudjou. (2018). effect of single oxide fluxes on morphology and mechanical properties of atig on 316 l austenitic stainless steel welds, 8(3), pp. 3064-3072. doi: 0.48084/etasr.2097 [7] makara, a. m., kushnirenko, b. n. and zamkov, v. n. (1968). high-tensile martensitic steels welded by argon tungsten arc process using flux. automatic welding, 7, pp. 78-79. [8] huang, h. y., shyu, s., tseng, k-h. and chou, c. p. (2006). effects of the process parameters on austenitic stainless steel by tig-flux welding. journal of material science technology; 22(3) pp. 367-374. doi: https://www.jmst.org/en/y2006/v22/i03/367 [9] lu, s. p., li, d. z., fujii, h. and nogi, k. (2007). time dependant weld shape in areo2 shielded stationary gta welding, journal material science tech, 23(5), pp. 650-654. doi://www.jmst.org/en/y2007/v23/i05/650 [10] tseng, k-h. and hsu, c. y. (2011). performance of activated tig process in austenitic stainless steel welds. journal material processing technology; 211(3), pp. 503-512. doi:10.1016/j.jmatprotec.2010.11.003 [11] chern, t. s., tseng, k-h. and tsai, h. l. (2011). study of the characteristics of duplex stainless steel activated tungsten inert gas welds. material design, 32(1), pp. 255-263. doi: 10.1016/j.matdes.2010.05.056 [12] gurevich, s. m., zamkov, v. n. and kushnirenko, n. a. (1965). improving the penetration of titanium alloys welded by argon tungsten arc process, avtomaticheskaya svarka, 9, pp. 1-4. [13] leconte, s., paillard, p., chapelle, p., henrion, g. and saindrenan, j. (2006). effect of oxide fluxes on activation mechanisms of tungsten inert gas process, science and technology of welding and joining; 11(4), pp.389-397. [14] rodrigues, a., loureiro, a. and batista, a. (2005). proceeding iiw international conference on benefits of new methods and trends in welding to economy: productivity and quality, 58th annual assembly and international conference of the iiw. prague, pp. 415–425. [15] palanichamy, p., vasudevan, m. and jayakumar, t. (2009). measurement of residual stresses in austenitic stainless steel welding joints using ultrasonic technology journal of science technology weld joining, 14(2), pp. 66–171. [16] heiple, c. r. and roper, j. r. (1981). effect of selenium on gtaw fusion zone geometry, welding journal, 60 (8), pp.143–145 [17] heiple, c. r. and roper, j. r. (1982). mechanism for minor element effect on gta fusion zone geometry, welding journal, 61 (4), pp. 97–102 [18] heiple, c. r., roper, j. r., stagner, r. t. and aden, r. j. (1983). surface active element effects on the shape of gta. laser and electron beam welds. welding journal. 62 (3), pp.72–77. [19] lucas, w. and howse, d. (1996). activating flux–increasing the performance and productivity of the tig and plasma processes. weld. met. fab. 64 (1), pp.11–17. [20] howse, d. s. and lucas, w. (2000). investigation into arc constriction by active fluxes for tungsten inert gas welding. sci. technol. weld. join. 5 (3), pp.189–193. [21] tseng, k-h. and chou, c.p. (2001). effect of pulsed gas tungsten arc welding on angular distortion in austenitic stainless steel weldments, science and technology of welding and joining, 6(3), pp. 149–153. doi: 10.1179/136217101101538686 [22] tseng, k-h. and chou, c.p. (2002). the effect of pulsed gta welding on the residual stress of a stainless steel weldment, j. mater. process. technol., 123, pp. 346–353. doi:10.1016/s0924-0136(02)00004-3 [23] huang, h. y., shyu, s., tseng, k-h. and chou, c. p. (2006). effects of the process parameters on austenitic stainless steel by tig-flux welding, journal of material science technology, 22(3), pp. 367–373. doi: https://www.jmst.org/en/y2006/v22/i03/367 [24] tanaka, m., shimizu, t., terasaki, h., ushio, m., koshi-ishi, f. and yang, c. l. (2000). effects of activating flux on arc phenomena in gas tungsten arc welding, science technology, welding joining, 2000, 5(6), pp. 397–402 [25] huang, h. y., shyu, s., tseng, k-h. and chou, c. p. (2005). evaluation of tig-flux welding on the characteristics of stainless steel, science technology, welding joining, 10(5), pp. 566–573 [26] huang, h. y., shyu, s., tseng, k-h. and chou, c. p. (2005). effect of a-tig welding on the morphology of stainless steel welds, proceedings of 7th international conference on trends in welding research, asm international. [27] sathiya, p. s., aravinda, p. m., ajith, b. and arivazhagan, a. (2010).microstructural characteristics on bead on plate welding of aisi 904 l super austenitic stainless steel using gas metal arc welding process, engineering, science and technology, 2(6), pp. 189-199. doi: 10.4314/ijest.v2i6.63710. << /ascii85encodepages false /allowtransparency false /autopositionepsfiles true /autorotatepages /none /binding /left /calgrayprofile (dot gain 20%) /calrgbprofile (srgb iec61966-2.1) /calcmykprofile (u.s. web coated \050swop\051 v2) /srgbprofile (srgb iec61966-2.1) /cannotembedfontpolicy /error /compatibilitylevel 1.4 /compressobjects /tags /compresspages true /convertimagestoindexed true /passthroughjpegimages true /createjobticket false /defaultrenderingintent /default /detectblends true /detectcurves 0.0000 /colorconversionstrategy /cmyk /dothumbnails false /embedallfonts true /embedopentype false /parseiccprofilesincomments true /embedjoboptions true /dscreportinglevel 0 /emitdscwarnings false /endpage -1 /imagememory 1048576 /lockdistillerparams 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can be opened with acrobat and adobe reader 5.0 and later.) >> /namespace [ (adobe) (common) (1.0) ] /othernamespaces [ << /asreaderspreads false /cropimagestoframes true /errorcontrol /warnandcontinue /flattenerignorespreadoverrides false /includeguidesgrids false /includenonprinting false /includeslug false /namespace [ (adobe) (indesign) (4.0) ] /omitplacedbitmaps false /omitplacedeps false /omitplacedpdf false /simulateoverprint /legacy >> << /addbleedmarks false /addcolorbars false /addcropmarks false /addpageinfo false /addregmarks false /convertcolors /converttocmyk /destinationprofilename () /destinationprofileselector /documentcmyk /downsample16bitimages true /flattenerpreset << /presetselector /mediumresolution >> /formelements false /generatestructure false /includebookmarks false /includehyperlinks false /includeinteractive false /includelayers false /includeprofiles false /multimediahandling /useobjectsettings /namespace [ (adobe) (creativesuite) (2.0) ] /pdfxoutputintentprofileselector /documentcmyk /preserveediting true /untaggedcmykhandling /leaveuntagged /untaggedrgbhandling /usedocumentprofile /usedocumentbleed false >> ] >> setdistillerparams << /hwresolution [2400 2400] /pagesize [612.000 792.000] >> setpagedevice microsoft word numero_35_art_31 s. tarasovs et alii, frattura ed integrità strutturale, 35 (2016) 271-277; doi: 10.3221/igf-esis.35.31 271 focussed on crack paths modelling of the fracture toughness anisotropy in fiber reinforced concrete s. tarasovs, j. krūmiņš, v. tamužs institute of polymer mechanics, university of latvia, aizkraukles st. 23, riga, lv-1006, latvia tarasov@pmi.lv abstract. steel fiber reinforced concrete is potentially very promising material with unique properties, which currently is widely used in some applications, such as floors and concrete pavements. however, lack of robust and reliable models of fiber reinforced concrete fracture limits its application as structural material. in this work a numerical model is proposed for predicting the crack growth in fiber reinforced concrete. the mixing of the steel fibers with the concrete usually creates nonuniform fibers distribution with more fibers oriented in horizontal direction, than in vertical. simple numerical models of fiber reinforced concrete require a priori knowledge of the crack growth direction in order to take into account bridging action of the fibers, which depends on the fibers orientation. in proposed model user defined elements are used to calculate the bridging force during the course of the analysis when the crack starts to grow. cohesive elements were used to model the crack propagation in the concrete matrix. in cohesive zone model the cohesive elements are embedded between all solid elements to simulate the arbitrary crack path. the bridging effect of the fibers are modeled as nonlinear springs, where the stiffness of the springs is defined from experimentally measured pull-out force and the angle between the fiber and crack opening direction. keywords. fiber reinforced concrete; fracture; cohesive elements. introduction n recent years concrete reinforced by short steel fibers became very popular material in such applications as floors and concrete pavements. however, lack of robust and reliable models of fiber reinforced concrete fracture, limits its application as structural material. the fracture of fiber reinforced concrete is complex phenomenon occurring at different length scales. different models were proposed in the last years for the prediction of the fracture process in the fiber reinforced concrete. one of the most common approaches is cohesive zone model where the traction-separation law for the fiber-reinforced concrete is derived by averaging the pull-out forces of all fibers crossing the fracture plane [1]. such models work well for sufficiently homogeneous distribution of fibers and in situations, where direction of crack growth can be predicted a priori. more complex models, which take into account the effect of individual fibers, may be necessary in other cases. only few works with such models were published recently. the 2d and 3d lattice model with cement matrix, aggregates and discrete steel fibers was used in [2] to simulate the fracture behavior of fiber-reinforced concrete. cunha et al. [3] used 3d smeared crack model to simulate concrete cracking and the truss elements were used to model the bridging action of steel fibers. radtke et al. [4] used the damage model for matrix material and the steel fibers were indirectly modeled as traction forces i s. tarasovs et alii, frattura ed integrità strutturale, 35 (2016) 271-277; doi: 10.3221/igf-esis.35.31 272 mapped to the neighbor nodes of the background mesh. in this approach the mesh refinement around fibers is not necessary and the total number of degrees of freedom in the system remains unchanged. in present work two-scale numerical approach within finite element framework is proposed. the concrete matrix fracture is simulated using cohesive zone model. the cohesive elements in current model are embedded between all solid elements, as a result the crack growth direction is chosen automatically during the analysis, minimizing the potential energy of the model. the effect of reinforcing fibers is modeled using non-linear spring elements, connecting nodes of neighboring solid elements at the location of the fiber. the properties of the spring elements are defined using experimentally obtained pull-out characteristics of single fibers embedded in concrete matrix at different angles. this model allows to simulate the initiation and propagation of the crack, taking into account the non-uniform spatial distribution of reinforcing fibers. finite element model omplex nature of the reinforced concrete failure, involving the cracking of the concrete matrix and steel fiber debonding from concrete matrix and pull-out, does not allow to model this process explicitly. therefore simplified two-scale approach within the framework of finite element method was used. two major mechanisms of fracture, matrix cracking and fiber pull-out were modeled independently. the approach suggested in [5] was used to model the fracture of the heterogeneous concrete material without prior knowledge of the crack path. in this model the cohesive elements are embedded between all solid elements, thus allowing automatic formation of the fracture surface during the simulations. in-house perl script was written for the cohesive elements embedding procedure. input file generated by the finite element code abaqus and containing solid 3d model with defined surfaces, sets and boundary conditions is automatically transformed into new modified model with cohesive elements embedded between solid elements in the middle part of the specimen, where the crack is expected to grow. the procedure of cohesive elements embedding is shown in fig. 1: at first solid elements are separated by creating duplicate nodes with the same coordinates, then these elements are connected by zerothickness cohesive elements. the procedure takes care of converting all predefined sets, surfaces and boundary conditions, using new nodes, and generates new input file, which can be directly solved by abaqus explicit solver. figure 1: procedure of embedding cohesive elements: original fe mesh; separated elements with duplicate nodes; cohesive elements embedded between all solid elements. due to small size and large number of steel fibers, the fibers are not modeled explicitly. the fibers bridging action is approximately modeled by a number of non-linear springs, embedded into finite element mesh at the fibers location. the same perl script randomly distributes steel fibers in the specimen’s volume, taking into account experimentally measured orientation of fibers [6], finds the elements faces, crossing the fiber, and connects these faces with non-linear spring elements, as shown in fig. 2. the spring’s stiffness takes into account the fiber pull-out forces, obtained experimentally or using some simplified analytical model [7]. in many situations the general crack growth direction is known a priori and the angle between the fiber and pulling force and, therefore, the spring’s stiffness, can be estimated before the analysis. however, if the crack growth direction is not known, the spring’s stiffness has to be determined during the analysis, taking into account the local crack opening direction and fiber orientation, as shown in fig. 3. this can be done using user defined element or similar approach, depending on finite element software used. c s. tarasovs et alii, frattura ed integrità strutturale, 35 (2016) 271-277; doi: 10.3221/igf-esis.35.31 273 figure 2: steel fiber modeling by non-linear springs. figure 3: determination of the fiber orientation angle. experimental part ver decades many works have shown the advantages of fiber reinforced concrete (frc)[8]. in frc the amount and shape of the steel fibers plays an important role on composites mechanical properties. in this study 2% volume fraction of “hook-end” steel fibers is chosen. commercially available steel fibers he 75/50 were used with geometrical parameters shown in tab. 1 and fig. 4. fiber diameter, d 0.75 ± 0.04 mm fiber length, l 50.0 ± 3 mm hook length, l and l’ 1 – 4 mm table 1: parameters of hooked steel fiber used in experiments. figure 4: geometry of steel fiber he 75/50 used in experiments. it is well known that fibers orientation has large effect on the structural strength of fiber-reinforced concrete [9], [10]. in order to evaluate single fiber and matrix interfacial properties, single fiber pull-out tests (sfpt) were performed. the fibers embedded in half of total fiber length (l) were located at different angles (0, 20, 40 and 60 degrees) according to the o s. tarasovs et alii, frattura ed integrità strutturale, 35 (2016) 271-277; doi: 10.3221/igf-esis.35.31 274 applied load. as was shown in previous studies, the embedded depth of the “hook-end” fiber (h) has relatively small effect on the pull-out force [11, 12]. experimental scheme and resulting pull-out force are shown in fig. 5. experimental pull-out curves show that maximal pull-out load is achieved at 40 degrees, other authors have shown, that the maximum peak load is attained at 45 degree inclination [13]. lower stiffness and increased displacement at maximal force for fibers embedded in 60 degree could be explained by matrix spalling and fiber bending. figure 5: experimental scheme and single fiber pull-out force at different angles. in present work 3-point and 4-point bending tests were used to characterize concrete elements reinforced by steel fibers. 3-point bending tests were used to determine mechanical properties of plain concrete. in order to evaluate the influence of steel fibers on concrete strength, four-point-bending tests with larger specimens were conducted. 3-point and 4-point bending test are schematically shown in fig 6. commercially available concrete matrix “sakret c25” (compressive strength 25 mpa) was used to mix the specimens, with maximal grain diameter equal 8mm and water content 1l/10kg. specimens were tested 28 days after material mixing. figure 6: geometry and loading scheme of a) 3-point bending test, b) 4-point bending test. dimensions of specimens are shown in tab. 2. specimens had an initial crack with length 2a0. the results of 3-point bending tests are shown in fig. 7. these curves were used to estimate cohesive properties of plain concrete and the numerical curve also shown in fig. 7. for the current simulations bi-linear softening curve was used to model the tractionseparation law of cohesive elements with fracture energy gic=150 j/m2. s. tarasovs et alii, frattura ed integrità strutturale, 35 (2016) 271-277; doi: 10.3221/igf-esis.35.31 275 3-point bending test (fig. 2a) 2h height , cm 7.5 2b width, cm 7.5 2w length, cm 30 2a0 initial crack length, cm 2 2l support separation, cm 28 4-point bending test (fig. 2b) 2h height, cm 15 2b width, cm 15 2w length, cm 60 2a0 initial crack length, cm 4 2l support separation, cm 45 2x load separation, cm 15 table 2: geometrical parameters of the specimen. 0 500 1000 1500 2000 2500 3000 3500 0.e+00 2.e-05 4.e-05 6.e-05 8.e-05 1.e-04 cod, mm l o a d , n experiment fem figure 7: load-crack opening displacement diagram of a three point bending test for plain concrete beam. numerical and experimental curves. results of numerical simulations s an example the wedge splitting test [14] will be simulated using proposed approach. the specimen’s size is 202030 cm with initial crack depth equal 15 cm. previous studies show [15], that due to vibration during specimen’s preparation stage, the fibers tend to be aligned horizontally and there are much less vertical fibers. this deviation from uniform random distribution creates anisotropy of the fracture toughness of the fiber reinforced concrete. as a result, the crack may grow in unexpected direction and simple models are unable to predict such behavior. fig. 8 shows two possible modes of failure of plain concrete and fiber reinforced concrete. the plain concrete has isotropic fracture toughness and crack typically grow downward, as it is expected. in the fiber reinforced concrete the horizontal cracks are more favorable, and in some situations the crack may turn and grow toward the side of the specimen. to prevent such behavior, deeper initial notch and/or side grooves can be used. proposed numerical model was used to simulate the failure of notched fiber reinforced concrete specimen in 4-point bending tests (fig. 9). the results of simulation are shown in fig. 10, compared with experimental curves. the numerical results show substantially higher reinforced concrete strength, which can be explained by the fibers interaction and nonuniform distribution of fibers in the specimen. the numerical model does not take into account the interaction between individual fibers: when fibers are located too close to each other, the total pull-out force could be less, than the sum of forces of individual fibers, which was measured in single fiber pull-out test. a s. tarasovs et alii, frattura ed integrità strutturale, 35 (2016) 271-277; doi: 10.3221/igf-esis.35.31 276 figure 8: possible failure modes of plain concrete (on the left) and fiber reinforced concrete (on the right). figure 9: simulation of the fiber reinforced concrete specimen failure in 4-point bend test. 0.0e+00 5.0e+03 1.0e+04 1.5e+04 2.0e+04 2.5e+04 3.0e+04 0.0e+00 5.0e-04 1.0e-03 1.5e-03 2.0e-03 cod, mm l o a d , n experiment fem figure 10: load-crack opening displacement diagram of a four point bending test for steel fiber reinforced concrete. numerical and experimental curves. s. tarasovs et alii, frattura ed integrità strutturale, 35 (2016) 271-277; doi: 10.3221/igf-esis.35.31 277 conclusion n this work a two-scale finite element model is proposed for the simulation of the fiber reinforced concrete failure. the model uses cohesive elements to simulate the cracking of the concrete matrix, whereas the bridging action of steel fibers is approximated by non-linear springs, connecting the nodes on the opposite faces of the crack. the stiffness of these non-linear spring elements directly takes into account the orientation of individual fibers and crack growth direction, allowing to model anisotropy of the fracture toughness of fiber reinforced concrete. the results of simulations show that the spatial distribution of fibers orientations may have substantial effect on the crack propagation direction. acknowledgement his work has been funded by the latvian ministry of education and science via project nr. 214/2012. references [1] jones, p.a., austin, s.a., robins, p.j., predicting the flexural load–deflection response of steel fibre reinforced concrete from strain, crack-width, fibre pull-out and distribution data, mater. struct., 41 (2007) 449–463. [2] kozicki, j., tejchman, j., effect of steel fibres on concrete behavior in 2d and 3d simulations using lattice model, arch. mech., 62 (2010) 465–492. [3] cunha, v.m.c.f., barros, j.a.o., sena-cruz, j.m., an integrated approach for modelling the tensile behaviour of steel fibre reinforced self-compacting concrete, cem. concr. res., 41 (2011) 64–76. [4] radtke, f.k.f., simone, a., sluys, l.j., a computational model for failure analysis of fibre reinforced concrete with discrete treatment of fibres, eng. fract. mech., 77 (2010) 597–620. [5] xu, x.-p., needleman, a., numerical simulations of fast crack growth in brittle solids, j. mech. phys. solids, 42 (1994) 1397–1434. [6] tarasovs, s., zile, e., tamuzs, v., experimental and numerical investigation of steel fiber reinforced concrete fracture, proc. of 19th european conference on fracture, kazan, russia, 26-31 (2012) 6. [7] zīle, e., zīle, o., effect of the fiber geometry on the pullout response of mechanically deformed steel fibers, cem. concr. res., 44 (2013) 18-24. [8] zollo, r.f., fiber-reinforced concrete: an overview after 30 years of development, cem. concr. compos., 19 (1997) 107-122. [9] ferrara, l., ozyurt, n., prisco, m., high mechanical performance of fibre reinforced cementitious composites: the role of “casting-flow induced” fibre orientation, mater. struct., 44 (2011) 109–128. [10] barnett, s.j., lataste, j.-f., parry, t., millard, s.g., soutsos, m.n., assessment of fibre orientation in ultra high performance fibre reinforced concrete and its effect on flexural strength, mater. struct., 43 (2009) 1009–1023. [11] robins, p., austin, s., jones, p., pull-out behaviour of hooked steel fibres, mater. struct., 35 (2002) 434–442. [12] cunha, v.m.c.f., barros, j.a.o. & sena-cruz, j.m., pullout behavior of steel fibers in self-compacting concrete, j. mater. civ. eng., 22 (2010) 1–10. [13] morton, j., groves, g.w., the cracking of composites consisting of discontinuous ductile fibres in a brittle matrix effect of fibre orientation, j. mater. sci., 9 (1974) 1436-1445. [14] bruhwiler, e., wittman, f. h., the wedge splitting test, a new method of performing stable fracture mechanics tests, eng. fract. mech., 35 (1990) 117–125. [15] robins, p., austin, s., jones, p., spatial distribution of steel fibres in sprayed and cast concrete, mag. concr. res., 55 (2003) 225–235. i t << /ascii85encodepages false /allowtransparency false /autopositionepsfiles true /autorotatepages /none /binding /left /calgrayprofile (dot gain 20%) /calrgbprofile (srgb iec61966-2.1) /calcmykprofile (u.s. web coated \050swop\051 v2) /srgbprofile (srgb iec61966-2.1) /cannotembedfontpolicy /error /compatibilitylevel 1.4 /compressobjects /tags /compresspages true /convertimagestoindexed true /passthroughjpegimages true /createjobticket false /defaultrenderingintent /default /detectblends true /detectcurves 0.0000 /colorconversionstrategy /cmyk /dothumbnails false /embedallfonts true /embedopentype false /parseiccprofilesincomments true /embedjoboptions true /dscreportinglevel 0 /emitdscwarnings false /endpage -1 /imagememory 1048576 /lockdistillerparams false /maxsubsetpct 100 /optimize true /opm 1 /parsedsccomments true 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/hrv (za stvaranje adobe pdf dokumenata najpogodnijih za visokokvalitetni ispis prije tiskanja koristite ove postavke. stvoreni pdf dokumenti mogu se otvoriti acrobat i adobe reader 5.0 i kasnijim verzijama.) /hun 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can be opened with acrobat and adobe reader 5.0 and later.) >> /namespace [ (adobe) (common) (1.0) ] /othernamespaces [ << /asreaderspreads false /cropimagestoframes true /errorcontrol /warnandcontinue /flattenerignorespreadoverrides false /includeguidesgrids false /includenonprinting false /includeslug false /namespace [ (adobe) (indesign) (4.0) ] /omitplacedbitmaps false /omitplacedeps false /omitplacedpdf false /simulateoverprint /legacy >> << /addbleedmarks false /addcolorbars false /addcropmarks false /addpageinfo false /addregmarks false /convertcolors /converttocmyk /destinationprofilename () /destinationprofileselector /documentcmyk /downsample16bitimages true /flattenerpreset << /presetselector /mediumresolution >> /formelements false /generatestructure false /includebookmarks false /includehyperlinks false /includeinteractive false /includelayers false /includeprofiles false /multimediahandling /useobjectsettings /namespace [ (adobe) (creativesuite) (2.0) ] /pdfxoutputintentprofileselector /documentcmyk /preserveediting true /untaggedcmykhandling /leaveuntagged /untaggedrgbhandling /usedocumentprofile /usedocumentbleed false >> ] >> setdistillerparams << /hwresolution [2400 2400] /pagesize [612.000 792.000] >> setpagedevice microsoft word numero_62_art_40_3734.docx a. baryakh et alii, frattura ed integrità strutturale, 62 (2022) 585-601; doi: 10.3221/igf-esis.62.40 585 justification of fracture criteria for salt rocks a. baryakh, a. tsayukov mining institute of the ural branch of the russian academy of sciences, russia bar@mi-perm.ru, http://orcid.org/0000-0003-2737-6166 andrei.tsayukov@mi-perm.ru, http://orcid.org/0000-0002-9982-4776 abstract. the study of salt rocks deformation and fracture processes is an essential part of mining parameters justification for mineral salt deposits. the results of uniaxial compression tests on large salt rock specimens are presented as a loading curve and diagrams of the transverse-longitudinal displacements at various distances from the side faces. based on an isotropic elastoplastic model, a multivariant numerical simulation was performed. its purpose was to select fracture criteria that accurately describe the loading diagram of specimen and its transverse-longitudinal deformations. the following fracture criteria are considered: tresca with the associated plastic flow rule, the associated and non-associated mohr-coulomb, the parabolic analogue of mohr-coulomb criterion and the volumetric fracture criterion. numerical simulation was carried out by the displacement-based finite element method. three-dimensional hexahedral eight-node isoparametric elements were used for discretization of the solution domain. it has been established that within the elastoplastic model of media the process of uniaxial compression of a large cubic salt rock specimen is adequately described by the linear mohr-coulomb fracture criterion with the non-associated plastic flow, as well as by the associated volumetric parabolic yield criterion with the linear isotropic hardening. keywords. salt rocks; elastoplasticity; fracture criteria; mathematical modeling; finite element method. citation: baryakh, a., tsayukov, a, justification of fracture criteria for salt rocks, frattura ed integrità strutturale, 62 (2022) 585-601. received: 03.08.2022 accepted: 12.09.2022 online first: 14.09.2022 published: 01.10.2022 copyright: © 2022 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. introduction alt rocks are classified as quasi-plastic geomaterials as they show pronounced rheological properties and specific response to various external impacts [1-4]. the study of their behavior under loading is essential part of the mining parameters justification for mineral salt deposits [5–7]. a significant part of the experimental studies of deformation and fracture processes for salt rocks under various loading conditions is associated with the formulation of their phenomenological models [8–10] and fracture criteria [11, 12]. as a rule, the choice of optimal fracture criteria is limited by a set of representative strength characteristics of the material. due to structural heterogeneity of salt rocks two indicators are usually used: uniaxial compressive (c) and tensile (t) strength. s https://youtu.be/idom9u_uxva a. baryakh et alii, frattura ed integrità strutturale, 62 (2022) 585-601; doi: 10.3221/igf-esis.62.40 586 in this regard, the strength of salts is mainly described by the linear mohr-coulomb criterion [13] or its parabolic analogue [14]. these criteria generally provide an acceptable assessment of the ultimate stress-strain state of salt rocks. it should be noted that laboratory experiments are rarely used to set up mathematical models describing the stability of mining structures and predicting changes in their state over time. such studies are a kind of analogue of physical modeling even in the case of non-compliance with the similarity criteria [15]. in [16], for operational control of the inter-chamber pillars state, which ensures the support of an overlying rock strata during mining of salts, it was proposed to use their transverse deformation. by means of mathematical modeling a preliminary estimation of the critical transverse deformation rate for inter-chamber pillars was given. in order to refine the deformation and fracture model for pillars and their parametric support, a series of tests on uniaxial compression of large cubic salt specimens of 300 × 300 × 300 mm in size was carried out [17]. fine-grained sylvinite from verkhnekamsk potash deposit was used. its average grain size was 2-3 mm. the test scheme is shown in fig. 1a. during the strain-controlled testing under the perfect adhesion the absolute longitudinal deformation was recorded and the displacements in the middle cross section were measured at various distances from the side faces. to study the development of transverse deformations, special deep marks inside the specimen and contour mark on a side face were fixed. specimen deformations and displacement of marks during testing were controlled using a non-contact three-dimensional optical system vic-3d from “correlated solutions”. horizontal displacements of marks 0, 5, and 10 cm were measured relative to the central point of 15 cm distance from a specimen’s side face (fig. 1a). the absolute longitudinal deformation of specimen corresponded to its height change. load-longitudinal deformation and transverse deformation-longitudinal deformations curves at various distances from a side face was obtained based on the test results for large specimens (fig. 1, b, c). this information provides an experimental basis for formulation of fracture model for a salt specimen. the purpose of the presented study is to justify fracture criteria and fracture parameters which simultaneously describe the loading diagram of the salt specimen and its transverse-longitudinal deformations (fig. 1, b, c) by means of multivariant mathematical modeling. figure 1: test scheme for a salt specimen (a), average loading diagram (b) and transverse-longitudinal deformations (c) [17]: 1—0 cm from a side face of the specimen, 2—5 cm from a side face, 3—10 cm from a side face. a. baryakh et alii, frattura ed integrità strutturale, 62 (2022) 585-601; doi: 10.3221/igf-esis.62.40 587 mathematical model he mathematical description of salt deformation was based on an isotropic elastoplastic model of media [18]. elastic straining was described by hooke's law. the plasticity (yielding) was determined by the yield function a( , , )  and plastic flow potential a( , , )  in general case, the arguments are: the stress tensor—, the isotropic hardening parameter—, and a set of material internal state variables and constants—. the yield surface is defined as 0  (1) plastic straining was described by the evolution equation [19] p       (2) where  p and  are the plastic strain tensor and the plastic multiplier, respectively. associated flow rule states that yield function and plastic potential are identical    (3) and the normality condition (kuhn-tucker condition) is satisfied [18]. in the case of perfect plasticity, the yield surface (1) does not change its shape. so, only the stress tensor and the set of material constants remain as arguments of (1): a( , ) 0  (4) the implementation of isotropic hardening implied a dimensionless approach (strain hardening) [19], in which the evolution of the parameter  depends on the evolution of the accumulated plastic strain: p   (5) where  is the euclidean norm. only compressive plastic strain was taken into account. no additional response to the plastic tension was assumed. hence, the evolution of the isotropic hardening parameter is written: p   (6) where the minus sign in the subscript indicates the negative (compressive) part of the plastic strain rate tensor. the positive components vanish. isotropic hardening of the yield surface was taken into account by internal state variables. in other words, the set of material parameters and constants is a function , and therefore,  p. thus, the yield surface eqn. (4) takes the form:  a p, ( ) 0   (7) the numerical implementation of the mathematical model described above was carried out by the displacement-based finite element method. three-dimensional hexahedral eight-node isoparametric elements with eight integration points were used t a. baryakh et alii, frattura ed integrità strutturale, 62 (2022) 585-601; doi: 10.3221/igf-esis.62.40 588 for meshing of the solution domain [19]. the solution domain (300 × 300 × 300 mm) was meshed by cubic elements with 10 mm side. the boundary conditions corresponded to the performed tests (fig. 1). on the lower face of cubic specimen, the vertical displacements were fixed (assumed to be zero). horizontal displacements along the perimeter of the upper and lower faces were constrained as well (the perfect adhesion was observed). vertical displacements corresponding to the loading conditions were set on the upper face of the specimen. the elastoplastic relations were solved using the modified newton-raphson scheme with a constant stiffness matrix. some fracture/plasticity criteria have a plane yield surface representation (e.g., tresca, mohr-coulomb) due to the assumption that the middle principal stress does not contribute to material fracture. in this case, such yield surfaces were described via the multi-surface representation in the principal stress space [18]   a a ! 1 | ( , ) 0, , ( , ) 0 n i j i j i          (8) where n is the dimension of the principal stress space. obviously, at the intersection of yield surfaces, the yield function and the plastic potential lose their continuous differentiability within the general yield surface, and it is impossible to explicitly determine the plastic flow direction. for such kind of singularities, the evolution of plastic strain was represented as a linear combination (koiter’s generalization) [20,21]: p , 1, 2, ,ii i i m         (9) where m is the number of yield surfaces meeting at the apex/edge of the general yield surface. numerical integration of the plastic constitutive relations was performed using the return-mapping algorithm, in particular, the tangent cutting plane (tcp) algorithm [18,20]. its essence is the linearization of the surface function (7) around the current stress state  kk:                    a a a κ a κ a, , ( , ) n : 0 n , k k k k k k k k k k (10) where k is the iteration number of tcp algorithm,  is the increment, and  denotes the product of the appropriate type. using explicit euler scheme in the context of return-mapping increments the following relations can be obtained a a a h κ 1 1 d : nk k k k k k k k                   (11) substitution them into (10) gives the expression for the plastic multiplier increment in closed form: κ h κn : d : n k k k k k k k        (12) in general, d denotes the fourth-order elasticity tensor (dk = const, since the modified newton-raphson scheme is used), h is the generalized hardening modulus, n =  is the plastic flow direction, is the generalization of the isotropic hardening parameter . for the associated plastic flow, ñ and n coincide. substitution (12) in (11) allows us to determine the new stress state  k+1k+1. tcp algorithm starts from the trial solution at k = 0 a a0 0 trial trial{ , } { , }  (13) a. baryakh et alii, frattura ed integrità strutturale, 62 (2022) 585-601; doi: 10.3221/igf-esis.62.40 589 the iterative process continues until the convergence condition is satisfied ( , )k k  a (14) where  is a prescribed positive value close to zero. it should be noted that for linear yield surfaces, single iteration is sufficient for the tcp algorithm to be converged. the multi-surface representation (8) and the corresponding plastic flow vector (9) lead to the solution of m eqns. (10) for  within single iteration. the spectral decomposition of the symmetric stress tensor [18] is used for convenience of applying the return-mapping algorithm 1 p j j j      e (15) where  j are the principal stresses (eigenvalues), e j are the corresponding eigenprojections, and p is the number of distinct eigenvalues. yield criteria tresca criterion he tresca strength criterion [18, 20] is mainly used to describe the plastic straining of metals and, a priori, is not suitable for rocks. here, it is analyzed only for comparative purposes. in the principal stress space, the tresca criterion is written as: max min 1 ( ) 2 y    (16) where  max and  min are the major and minor principal stresses, respectively, and  y is the shear yield stress. here and below the tensile stress is implied to be positive. expression (16) can also be written as a yield function: max min( , )y y        (17) where  y = 2 y is the uniaxial yield stress. the set a here contains the single parameter  y, which denotes the material strength. in this case, the uniaxial compression strength  c was assumed as the yield strength. the tresca yield surface is shown in fig. 2. the multi-surface representation reads: 1 1 3 2 2 3 3 2 1 4 3 1 5 3 2 6 1 2 ( , ) ( , ) ( , ) ( , ) ( , ) ( , ) c c c c c c c c c c c c                                                       (18) the spectral decomposition (15) allows the consideration to be concentrated on the sextant  1 >  2 >  3. so, only three surfaces from (18) can be used in the return-mapping algorithm—1,2,6. the choice of the target edge (12 or 16) in case of the yielding from the edge of the yield surface was performed using the approach proposed in [18]. the associated plastic flow was accepted. the corresponding parameters of the tcp algorithm in the principal stress space are: t a. baryakh et alii, frattura ed integrità strutturale, 62 (2022) 585-601; doi: 10.3221/igf-esis.62.40 590       1 1 2 2 6 6 n n 1 0 1 n n 0 1 1 n n 1 1 0 t t t t t t             (19) figure 2: the tresca yield surface. since set a for the tresca criterion consists of single element  c, the hardening was implemented by its variation. for simplicity, the linear relation is assumed a c c h       p p p ,0( ) ( ) (20) where  c,0 is the initial uniaxial compression strength, and h is the hardening modulus of stress dimension. thus, the tcp algorithm parameters associated with hardening take the form:      κ η κ 1 n h (21) the results of numerical simulation of the specimen loading, based on the associated tresca yield criterion, are shown in fig. 3. the selected mechanical and criterion parameters are presented in tab. 1. young’s modulus, gpa poisson’s ratio uniaxial compressive strength, mpa hardening modulus, gpa 6.7 0.3 22 0.6 table 1: salt specimen parameters (associated tresca). it can be seen that the simulated results are in a reasonable agreement with the experimental at the elastic stage, as well as at the plastic one, starting from approximately 2000–2100 kn of load level. as expected, the distribution of transverse deformations over the width of the cubic specimen does not correspond to the test values. according to the associated tresca plastic flow, insufficient transverse deformations are obtained. this is due to the fact that the tresca criterion does a. baryakh et alii, frattura ed integrità strutturale, 62 (2022) 585-601; doi: 10.3221/igf-esis.62.40 591 not depend on the hydrostatic stress (pressure-insensitive) and plastic flow occurs only in the deviatoric plane. volumetric plastic strain is neglected. figure 3: simulation results (associated tresca yield criterion with hardening). mohr-coulomb criterion the classical mohr-coulomb yield criterion [13,18,20] is often used to describe the mechanical behavior of soils, rocks, and concrete. unlike tresca, the mohr-coulomb criterion is pressure-sensitive. in the mohr axes, the criterion is represented as a linear relation y nc    tan (22) in expression (22),  y is the shear yield stress, c is the cohesion,  is the frictional angle, and  n is the normal stress, a positive value of which indicates tension. the corresponding yield function in the principal stress space is written as:  c c            max min max min,{ , } ( )sin 2 cos (23) similar to the tresca criterion, the mohr-coulomb yield surface has a multi-surface representation:             c c c c c c c c c c c c                                                                                    1 1 3 1 3 2 2 3 2 3 3 2 1 2 1 4 3 1 3 1 5 3 2 3 2 6 1 2 1 2 ,{ , } ( )sin 2 cos ,{ , } ( )sin 2 cos ,{ , } ( )sin 2 cos ,{ , } ( )sin 2 cos ,{ , } ( )sin 2 cos ,{ , } ( )sin 2 cos (24) the set a contains two parameters c. the yield surface in the principal stress space is illustrated in fig. 4. for numerical simulation of the salt specimen loading, the plastic flow was assumed to be associated, and the material was perfectly plastic. the corresponding tcp algorithm parameters in principal stresses are:       t t t t t t                      1 1 2 2 6 6 n n 1 sin 0 1 sin n n 0 1 sin 1 sin n n 1 sin 1 sin 0    . (25) a. baryakh et alii, frattura ed integrità strutturale, 62 (2022) 585-601; doi: 10.3221/igf-esis.62.40 592 figure 4: the mohr-coulomb yield surface. it should be noted that volumetric plastic strain rate is positive in this case, i.e. the material is dilatant. all hardening-related parameters of the tcp algorithm are missing. the results of numerical simulation are illustrated in fig. 5. the corresponding mechanical and criterion parameters of the simulation are presented in tab. 2. young’s modulus, gpa poisson’s ratio cohesion, mpa frictional angle, deg 6.7 0.3 4.5 30 table 2: salt specimen parameters (associated mohr-coulomb) figure 5: simulation results (associated mohr-coulomb yield criterion). as can be seen, the simulated loading curve of perfectly plastic straining quite accurately describes all stages of the loading diagram. at the same time, the calculated transverse deformations of the cubic specimen exceed experimental results. this behavior is typical for the associated mohr-coulomb plastic flow [8, 12]. a. baryakh et alii, frattura ed integrità strutturale, 62 (2022) 585-601; doi: 10.3221/igf-esis.62.40 593 this problem is solved by non-associated flow rule. an additional parameter is introduced—the dilatancy angle   . in other words, the frictional angle in plastic flow potential is replaced by the dilatancy angle:         a a c c             , ,{ , } , ,{ , } (26) hence, ñ  n:                                                    1 1 2 2 6 6 n 1 sin 0 1 sin , n 1 sin 0 1 sin n 0 1 sin 1 sin , n 0 1 sin 1 sin n 1 sin 1 sin 0 , n 1 sin 1 sin 0 t t t t t t (27) now, by varying the angle , the dilatancy level is adjusted. the limit case, when   0, means the absence of dilatancy, which corresponds to tresca's plastic flow. young’s modulus, gpa poisson’s ratio cohesion, mpa frictional angle, deg dilatancy angle, deg 6.7 0.3 4 35 18 table 3: salt specimen parameters (non-associated mohr-coulomb) figure 6: simulation results (non-associated mohr-coulomb yield criterion). the results of simulation using the non-associated mohr-coulomb yield criterion (26) are illustrated in fig. 6. the selected parameters of the simulation are shown in tab. 3. it can be seen that the calculated and experimental curves almost coincide. the evolution of transverse deformations qualitatively corresponds to the test. parabolic envelope of mohr circles/rankine recently, the so-called parabolic fracture criteria have become popular. there are a significant number of them [11,12]. their use is complicated by large number of parameters. one of the frequently applied parabolic criteria in rock strength certificates (including salts) is the parabolic envelope of mohr circles [14]. it assumes that the mohr circles under uniaxial compression and tension are tangent to the envelope. in this regard, the criterion has the following form in the mohr coordinates: y np q   2 (28) a. baryakh et alii, frattura ed integrità strutturale, 62 (2022) 585-601; doi: 10.3221/igf-esis.62.40 594 where the parabola coefficients are written as   ct tt p r q r r         2 2 1 1 1 , , (29) the parameters of the parabolic criterion are the uniaxial compressive and tensile strengths— c and  t. tensile stresses are positive. the corresponding yield function in the principal stress space can be written as:                            2 max min max min 2 ,{ , } ( ) ( , )( ) ( , ) 2 ( , ) 1 ( , ) 4 pmc c t c t c t c t c t p q p p q q pp (30) the multi-surface representation of criterion (30) has three components       pmc c t c t c t pmc c t c t c t pmc c t c t c t p q p q p q                                                    2 1 1 3 1 3 2 2 2 3 2 3 2 3 1 2 1 2 ,{ , } ( ) ( , )( ) ( , ) ,{ , } ( ) ( , )( ) ( , ) ,{ , } ( ) ( , )( ) ( , ) (31) since, unlike the linear yield surfaces (17), (23) described above, for parabolic criteria the following relations are valid parabolic parabolic parabolic parabolic parabolic parabolic          1 4 2 5 3 6 (32) figure 7: parabolic envelope of mohr circles (black solid line), normal parabolic criterion (black dashed line), additional rankine criterion (red dashed line) and extreme points (red dots) in the principal stress space. a. baryakh et alii, frattura ed integrità strutturale, 62 (2022) 585-601; doi: 10.3221/igf-esis.62.40 595 parabolic criterion (30) has one substantial drawback. in the absence of stresses, the criterion indicates the plastically admissible stress state of the material. this follows from fig. 7 (black solid line). the interior of the parabola does not include the origin of the principal stress space. this is more clearly seen in the limit case                           0 2 2 max min max min lim ,{ , } , ( ) 2 ( ) t pmc c t np c c c (33) the criterion (33) is also known as the normal parabolic criterion [2,4] (black dashed line in fig. 7). this implies that beyond the extremum of principal stresses (red dots in fig. 7) c t tp     max min 1 , ( , ) 2 (34) the criterion in the form of a parabolic envelope of mohr circles has no physical sense. in this regard, beyond the extreme points (34), the yield surface (30) can be complemented with "cut-offs" limiting tension according to uniaxial tensile strength  t. this technique is often used in practice [11]. the condition limiting tensile stresses is known as the rankine criterion [20,22] r t t     max( , ) (35) the corresponding multi-surface representation is: r t t r t t r t t                      1 1 2 2 3 3 ( , ) ( , ) ( , ) (36) the set a contains one parameter  t. figure 8: the pmc/r yield surface. a. baryakh et alii, frattura ed integrità strutturale, 62 (2022) 585-601; doi: 10.3221/igf-esis.62.40 596 combining the above, the total yield surface "parabolic envelope of mohr circles/rankine" (pmc/r) can be written as a piecewise function for the sextant  max >  mid >  min: pmc c t c t t pmc r c t r t c t t p p                           min / min 1 ( ,{ , }), ( , ) 2( ,{ , }) 1 ( , ), ( , ) 2 (37) where the parabolic criterion (30) describes the "compression-compression" regime of the stress-strain state (sss) and partly "tension-compression", and the rankine criterion (35) limits the tensile stresses. the total yield surface (37) is illustrated in fig. 8. the set a for (37) contains two parameters  c t. the numerical simulation of uniaxial loading of a cubic salt specimen was carried out implying the associated law of plastic strain. the corresponding parameters of the tcp algorithm in principal stresses for the parabolic envelope of mohr circles are:                                           1 1 1,3 1,3 2 2 2,3 2,3 3 3 1,2 1,2 max,min max min max,min max min n n 0 n n 0 n n 0 2( ) ( , ) 2( ) ( , ) t tpmc pmc t tpmc pmc t tpmc pmc c t c t a b a b a b a p b p (38) also for the rankine criterion they can be written as:                   1 1 2 2 3 3 n n 1 0 0 n n 0 1 0 n n 0 0 1 . t tr r t tr r t tr r          (39) similar to the linear mohr-coulomb criterion (22), the material is also dilatant. the linear isotropic hardening was incorporated. hardening was implemented by evolution of the uniaxial compressive strength similar to the tresca criterion (20). clearly, this effect works only in the region where the parabolic criterion (30) is satisfied. the tcp algorithm parameters associated with the hardening are:                κ η κ max min( ) n c c pmc p q h (40) the derivatives in expression (40)1 can be written using the chain rule:                     c c c c pp p r p r pq q r p r (41) a. baryakh et alii, frattura ed integrità strutturale, 62 (2022) 585-601; doi: 10.3221/igf-esis.62.40 597 partial derivatives are written in the following form:                      2 3 3 1 1 2 1 12 42 1 , , , 1 c r r rpq pp q r p p r qp p r q r (42) young’s modulus, gpa poisson’s ratio uniaxial compressive strength, mpa uniaxial tensile strength, mpa hardening modulus, gpa 6.7 0.3 16 1 0.23 table 4: salt specimen parameters (associated pmc/r) figure 9: simulation results (associated pmc/r yield criterion). it is impossible to constrain the excess of transverse deformations by adopting a non-associated law of plastic flow for the pcm/r criterion, since this can only be done by taking a compressive strength lower than the initial one, which has no physical sense. the results of multivariant numerical simulations are illustrated in fig. 9. the obtained simulation parameters are shown in tab. 4. volumetric strength criterion [23] another interesting parabolic fracture criterion of rocks was proposed in [23]. the criterion assumes that the fracture of the material occurs due to shear and tear, similar to the mohr-coulomb and pmc/r criteria. however, as a characteristic of shear strength the shear stress intensity is used, and as a characteristic of tear strength, the normal stresses described by a spherical tensor are applied. the rock strength criterion has the form: ii b a   2 ( ) (43) where  i is the shear stress intensity, i( ) is the first invariant of the stress tensor, and the coefficients a and b are determined from uniaxial compression and tensile tests as: c t c t a b        (44) the yield function in the principal stress space is written as: a. baryakh et alii, frattura ed integrità strutturale, 62 (2022) 585-601; doi: 10.3221/igf-esis.62.40 598                               2 2 2 1 2 2 3 3 1 1 2 3 1 ,{ , } ( ) ( ) ( ) ( )( ) 2 c t c t c t (45) figure 10: the yield surface of criterion [23]. the strength criterion (45) is volumetric, since it includes the influence of the middle stress. the multi-surface representation is not necessary. the yield surface is continuously differentiable. the set a for (45) also consists of two parameters  c t. a graphical representation of the yield surface is shown in fig. 10. the yield surface is a paraboloid of revolution around the hydrostatic axis  1 =  2 =  3. figure 11: the comparison of pmc and parabolic criteria [23] for pss. in contrast to the pmc criterion (30), the criterion [23] (45) has a physical sense in all sss regimes, since the origin of the coordinates of the principal stress space is in the interior of the yield surface. comparison of two criteria is shown in fig. 11 for plane-strain state (pss). pss form of the criterion [23] is obtained by replacing the middle principal stress by the a. baryakh et alii, frattura ed integrità strutturale, 62 (2022) 585-601; doi: 10.3221/igf-esis.62.40 599 expression  2 =  ( 1 +  3), where  is the poisson’s ratio and  1 =  max ,  3 =  min. the pss yield surface of the criterion [23] is an ellipse, the size of which depends on the poisson's ratio. fig. 11 shows the yield surfaces of the criterion [23] for some  coefficients. for values of  = [0.3, 0.4, the yield surfaces in the largest range of principal stresses are similar to the pmc criterion. the numerical simulation of the uniaxial loading of a cubic salt specimen was carried out implying the associated plastic flow rule. the corresponding tcp algorithm parameters in the principal stresses for the criterion [23] are determined by: c t c t c t                                   1 2 3 2 1 3 3 1 2 2 n n 2 2  (46) the effect of volume increase (dilatancy) is reflected in the model. the linear isotropic hardening is adopted. hardening was implemented similar to (20) by varying the uniaxial compressive strength  c. hardening-related parameters of the tcp algorithm are written as:            κ η κ 1 2 3 n t h (47) the results of multivariant numerical simulation are shown in fig. 12. the parameters of model and fracture criterion are presented in tab. 5. young’s modulus, gpa poisson’s ratio uniaxial compressive strength, mpa uniaxial tensile strength, mpa hardening modulus, gpa 6.7 0.3 14 1 0.35 table 5: salt specimen parameters (associated volumetric yield criterion) figure 12: simulation results (associated volumetric yield criterion). the simulation results show good agreement between the calculated and experimental loading curves. the resulting loading diagram for the criterion [23] very close to the curve for pmc/r. however, in contrast to pmc/r, the criterion [23] gives much better correspondence with the test data on the transverse-longitudinal deformations and provides a more adequate description of the uniaxial deformation process for a cubic salt specimen. a. baryakh et alii, frattura ed integrità strutturale, 62 (2022) 585-601; doi: 10.3221/igf-esis.62.40 600 conclusion ome fracture criteria are considered within the framework of elastoplastic model for uniaxial deformation of a large cubic salt rock specimen. as expected, the tresca strength criterion and the associated plastic flow rule coupled with linear isotropic hardening cannot describe all stages of salt specimen deformation. due to the dislocation nature this criterion underestimates the transverse deformations. obviously, salt rocks show dilatant effects, which are not reflected by tresca yield criterion. to account dilatancy, pressure-sensitive strength criteria are used. the considered classical linear mohr-coulomb criterion allows us to describe accurately all stages of deformation during loading of the specimen. nevertheless, the associated plastic flow rule leads to excessive transverse deformations. however, application of the non-associated flow rule with the additional parameter (the dilatancy angle) enables us to control the level of transverse deformations. therefore, both the loading and the transverse deformations curves of salt specimen can be accurately described. the parabolic analogue of the linear mohr-coulomb strength criterion—the parabolic envelope of mohr circles (pmc)— has no physical sense for a certain range of principal stresses. therefore, for practical application, pmc can be complemented by the rankine criterion (pmc/r). also, in the pmc model, isotropic linear hardening can be incorporated similar to the tresca criterion. the resulting loading diagram for the pmc/r criterion with the associated law of plastic flow and linear isotropic hardening describes the test curve qualitatively well. however, as for the linear mohr-coulomb criterion with associated flow rule, the transverse deformations of the cubic salt specimen are excessive. in contrast to the linear analogue, the constraint of transverse deformations here has no physical sense. the volumetric strength criterion [23] for rocks compared to pmc physically correctly describes all ranges of principal stresses. moreover, the yield function is continuously differentiable over the entire principal stress space. it significantly simplifies the calculation of plastic strain in their associated flow. the test loading diagram can be accurately described only with the hardening effect. the linear isotropic hardening allows us to obtain a loading curve close enough to the test one for the associated volumetric yield criterion. furthermore, the simulated loading diagrams of the pmc/r and [23] criteria nearly coincide. however, in contrast to all considered criteria, the volumetric yield criterion can be considered as the most accurate for the description of transverse deformations over the specimen cross section. acknowledgement he work was supported by the russian science foundation (grant no. 19-77-30008) references [1] baryakh, а.а., konstantinova, s.a. and asanov, v.a. (1996). rock salt deformation. yekaterinbug, ub of ras. [2] fahland; s., hammer, j., hansen, f., et al. (2018). the mechanical behavior of salt ix / proceedings of the 9th conference on the mechanical behavior of salt. saltmech ix, hannover, germany. [3] he, m.m., ren, j., su, p. et al. (2020). experimental investigation on fatigue deformation of salt rock. soil mech found eng, 56, pp. 402–409. doi: 10.1007/s11204-020-09622-x. [4] dubey, r.k. and gairola, v.k. (2000). influence of structural anisotropy on the uniaxial compressive strength of prefatigued rocksalt from himachal pradesh, india, international journal of rock mechanics and mining sciences, 37(6), pp. 993-999. doi: 10.1016/s1365-1609(00)00020-4. [5] baryakh, a.a., lobanov, s.y. and lomakin, i.s. (2015). analysis of time-to-time variation of load on interchamber pillars in mines of the upper kama potash salt deposit, j min sci, 51, pp. 696–706. doi: 10.1134/s1062739115040064. [6] pałac-walko, b. and pytel, w. (2019). geomechanical risk assessment for saltrock underground workings, using strength theories based on selected 2d and true 3d triaxial compression laboratory tests, sgem 19(1.3), pp. 307-314. doi: 10.5593/sgem2019/1.3/s03.039. [7] wang, q. and hesser, j. (2013). determination of the deformation behaviour of salt rock by evaluation of convergence measurements in shafts, paper presented at the isrm sinorock 2013, shanghai, china, 18-20 june. s t a. baryakh et alii, frattura ed integrità strutturale, 62 (2022) 585-601; doi: 10.3221/igf-esis.62.40 601 [8] heusermann, s., rolfs, o., and schmidt, u. (2003). nonlinear finite-element analysis of solution mined storage caverns in rock salt using the lubby2 constitutive model, computers and structures, 81(8-11), pp. 629-638. doi: 10.1016/s0045-7949(02)00415-7. [9] hou, z. (2003). mechanical and hydraulic behavior of rock salt in the excavation disturbed zone around underground facilities, international journal of rock mechanics and mining sciences, 40(5), pp. 725-738. doi: 10.1016/s1365-1609(03)00064-9. [10] baryakh, a.a., eremina n.a. and gracheva e.a. (1994). crack development in disturbed salt bed, j. min. sci., 30(5), pp. 487-490. doi: 10.1007/bf02047340 [11] ulusay, r. ed., (2015). the isrm suggested methods for rock characterization, testing and monitoring: 2007–2014, switzerland, springer cham. doi: 10.1007/978-3-319-07713-0. [12] you, m. (2011). comparison of the accuracy of some conventional triaxial strength criteria for intact rock, ijrmms, 48(5), pp 852-863. doi: 10.1016/j.ijrmms.2011.05.006. [13] labuz, j.f., zang, a. (2012). mohr–coulomb failure criterion, rock mech rock eng, 45, pp. 975–979. doi: 10.1007/s00603-012-0281-7. [14] wang, d.j., tang, h., shen, p., cai, y. (2019). a parabolic failure criterion for transversely isotropic rock: modification and verification, mathematical problems in engineering, 2019. doi: 10.1155/2019/8052560. [15] baryakh, a. a., samodelkina n. a. and pan'kov i.l. (2012). water-tight stratum failure under large-scale mining. part i., j. min. sci., 48(5), pp. 771-780. doi: 10.1134/s1062739148050012. [16] baryakh, a.a., evseev, a.v., lomakin, i.s., tsayukov, a.a. (2020). operational control of rib pillar stability, eurasian mining, 2020(2), pp. 7-10. doi: 10.17580/em.2020.02.02. [17] baryakh, a.a., tsayukov, a.a., evseev, a.v. et al. (2021). mathematical modeling of deformation and failure of salt rock samples, j. min. sci. 57(3), pp. 370–379. doi: 10.1134/s1062739121030029. [18] de souza neto, e.a., perić, d. and owen, d.r.j. (2008). computational methods for plasticity: theory and applications, chichester, john wiley & sons ltd. doi: 10.1002/9780470694626. [19] zienkiewicz, o.c., taylor, r.l. and fox, d. (2014). the finite element method for solid and structural mechanics (7th edition), butterworth-heinemann. doi: 10.1016/c2009-0-26332-x. [20] de borst, r., crisfield, m.a., remmers, j.j.c., verhoosel, c.v. (2012). non-linear finite element analysis of solids and structures, 2nd edition, chichester, john wiley & sons ltd. doi: 10.1002/9781118375938. [21] ottosen, n.s., ristinmaa, m. (1996). corners in plasticity—koiter's theory revisited, ijss, 33(25), pp. 3697-3721. doi: 10.1016/0020-7683(95)00207-3. [22] rankine, w.j.m. (1877). a manual of applied mechanics, 9 ed, london, charles griffin and company. [23] baryakh, a.a. and samodelkina n.a. 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can be opened with acrobat and adobe reader 5.0 and later.) >> /namespace [ (adobe) (common) (1.0) ] /othernamespaces [ << /asreaderspreads false /cropimagestoframes true /errorcontrol /warnandcontinue /flattenerignorespreadoverrides false /includeguidesgrids false /includenonprinting false /includeslug false /namespace [ (adobe) (indesign) (4.0) ] /omitplacedbitmaps false /omitplacedeps false /omitplacedpdf false /simulateoverprint /legacy >> << /addbleedmarks false /addcolorbars false /addcropmarks false /addpageinfo false /addregmarks false /convertcolors /converttocmyk /destinationprofilename () /destinationprofileselector /documentcmyk /downsample16bitimages true /flattenerpreset << /presetselector /mediumresolution >> /formelements false /generatestructure false /includebookmarks false /includehyperlinks false /includeinteractive false /includelayers false /includeprofiles false /multimediahandling /useobjectsettings /namespace [ (adobe) (creativesuite) (2.0) ] /pdfxoutputintentprofileselector /documentcmyk /preserveediting true /untaggedcmykhandling /leaveuntagged /untaggedrgbhandling /usedocumentprofile /usedocumentbleed false >> ] >> setdistillerparams << /hwresolution [2400 2400] /pagesize [612.000 792.000] >> setpagedevice microsoft word numero_36_art_19 h. zhu, frattura ed integrità strutturale, 36 (2016) 191-200; doi: 10.3221/igf-esis.36.19 191 crack formation of steel reinforced concrete structure under stress in construction period hua zhu college of civil engineering, campus on avenue hope, yancheng institute of technology, yancheng, jiangsu, china. zhuhuazh2233@163.com abstract. to obtain deformation rules of steel reinforced concrete structure under stress, this study explored the crack formation in construction period. a novel structure system – steel reinforced concrete structure with shear wall and truss at the bottom was analyzed using on-the-spot test in combination with theoretical simulation analysis with sap2000 software. it was found that, factors influencing crack formation of steel reinforced concrete structure in construction period included construction load, creep of concrete, shrinkage of concrete, displacement of bond of section steel and concrete as well as leveling. in the construction period, the simulated results and the measured results were highly fitted under the influence of time-variant characteristics such as compressive strength, elasticity modulus, creep and shrinkage. through processing and analyzing the measured data, we obtained the development rules of crack formation of steel reinforced concrete structure with different strength grades as well as deformation rules of time-varying structure system in construction period, figured out the reason for the difference between the simulated results and the measured results, analyzed the deformation of structural components under stress in construction period and proposed some suggestions. this work is beneficial to ensure safe and high-efficient operation of construction. key words: crack; steel reinforced concrete; stress in construction period; theoretical simulation analysis; sap2000. introduction ith the development of economy, steel reinforced concrete structure has been applied more extensively in super high-rise building for its special advantages of high bearing capacity, large rigidity, sound anti-seismic property and convenient installation [1]. in modern construction, construction safety is especially important. hence major factors influencing crack formation of steel reinforced concrete structure needs to be further studied [2, 3]. large binding force between section steel and concrete is the foundation ensuring their coordination in steel reinforced concrete structure [4]. section steel, rebar and concrete coordinate together to resist external effect, thus fully display the advantages of steel reinforced concrete structure [5]. on account of this, it is of great significance to deeply study steel reinforced concrete, explore its structure performance and apply it into engineering practice [6]. based on the detailed cases of crack formation of steel reinforced concrete structure in actual engineering and the previous research achievements, deierlein and noguchi [7] obtained the distribution rule of load of steel reinforced concrete structure and the prediction model of compressive strength, shrinkage and creep of concrete, providing a theoretical basis for analysis of performance of steel reinforced concrete structure and factors influencing crack formation w h. zhu, frattura ed integrità strutturale, 36 (2016) 191-200; doi: 10.3221/igf-esis.36.19 192 under stress. through analyzing the structure form and stress performance of the commonly used steel reinforced concrete beam-column joints as well as factors inducing crack formation, hierro et al. [8] pointed out the defects existing in the researches carried out by chinese scholars which concern beam-column joints of steel reinforced concrete. the study carried out by zhao et al. [9] analyzed the distinction between one-off loading and simulated loading adopted in steel reinforced concrete structure using finite element software, which provides an important basis for the design and construction of modern high-rise building. this study explored the crack formation of steel reinforced concrete structure, clarified the development rules of deformation of steel reinforced concrete structure in different strength grades and deformation rules of steel beam in time-varying structure system, analyzed the major reason leading to the deviation by comparing the measured results with the simulated results, and put forward some suggestions to ensure safe and high-efficient construction. analysis on crack formation of steel reinforced concrete structure under stress double-tube structure of reinforced concrete einforced concrete double-tube structure refers to the peripheral frame structure whose middle part is two parallel tubes and includes plain concrete structure, reinforced concrete structure and prestressed concrete structure. fig. 1 shows the construction drawing of an office building with a reinforced concrete double-tube structure. figure 1: reinforcement drawing of the 4th floor to the 20th floor of an office building. deformation of steel reinforced concrete filled double-tube structure in construction period the first issue is the vertical deformation of steel reinforced concrete filled double-tube structure [10]. steel reinforced concrete filled double-tube structure is a time-varying structure system. material performance, structure rigidness, boundary condition and construction load all varies with time. vertical deformation of components of high-rise steel reinforced concrete filled double-tube structure in construction period mainly includes instantaneous elastic deformation, creep deformation and contraction deformation. fig. 2 shows the time-varying deformation of concrete. for high-rise structure over 10 layers, the effect of vertical deformation needs to be given special consideration. the difference of vertical deformation would make beam or plate to generate additional bending moment and shearing force. if no measures adopt, the component is prone to crack during construction and even induce accidents and result in personal casualty. the second issue is about the horizontal deformation of steel reinforced concrete filled double-tube structure [11]. compared to the vertical deformation, the horizontal deformation of steel reinforced concrete filled double-tube structure is less outstanding. in construction period, some destabilizing factors may exist under horizontal load as elasticity modulus of concrete materials has not reached the designed value and moreover internal and external tubes have not formed complete coordinated lateral resistant system along with steel framework. r h. zhu, frattura ed integrità strutturale, 36 (2016) 191-200; doi: 10.3221/igf-esis.36.19 193 figure 2: vertical deformation of concrete under continuous load and drying effect. shear capacity of steel reinforced concrete structure before initial cracking, concrete in steel reinforced concrete joints plays a function of shear resistance [12]. as load increases, diagonal crack forms along the diagonal line of joints and then diagonal strut comes into being. anti-shear capacity of concrete in steel reinforced concrete joints can be expressed as: c j j cv b h f (1) where fc refers to compressive strength of axis of concrete; generally, joint section height hj is equal to column section height h, i.e., hc = hj; bj stands for surface width of joint core area; γ stands for an undetermined coefficient which reflects anti-shear capacity of concrete in steel reinforced concrete joints under various constraints. to obtain the specific value of anti-shearing coefficient γ, the following formula is used. t j s sv j j c v v v b h f     (2) where tjv stands for measured ultimate bearing capacity of joints; sv stands for actual strength of material; svv stands for bearing capacity of section steel web and hooping of joints. factors influencing crack formation of steel reinforced concrete structure under stress in construction period construction load onstruction load can be divided into construction dead load, construction live load and accidental load according to action time, and can be divided into vertical loading, horizontal loading, additional vertical load and special load according to action direction. creep of concrete creep of concrete refers to plastic deformation of concrete under single-axial stress effect along stress direction as time goes on [13]. creep is composed of basic creep and drying creep. ignoring the fact that creep deformation is larger than deformation of dried concrete under loading effect, creep is considered as a kind of deformation which has exceeded free shrinkage under loading effect (fig. 3). major factors influencing creep included exerted stress, water cement ratio, curing condition, temperature, humidity, cement composite, aggregate, chemical admixture, geometrical shape of test specimen and loading age. c h. zhu, frattura ed integrità strutturale, 36 (2016) 191-200; doi: 10.3221/igf-esis.36.19 194 shrinkage of concrete shrinkage of concrete which refers to volume reduction of concrete induced by factors such as changes of water content, chemical reaction and temperature decrease includes drying shrinkage, cold shrinkage, condensation shrinkage, autogenous shrinkage, carbonization shrinkage, etc. figure 3: creep of concrete under continuous loading and drying effect. bounding force between section steel and concrete bounding force between section steel and concrete is mainly composed of chemical bounding force, frictional resistance and mechanical interaction. on account of the bounding force between section steel and reinforced concrete, section steel can work along with concrete to shoulder load [14]. construction leveling of high-rise building in construction, core tube and external framework will both deform under the effects of their own weights and construction loading; due to the compression of structure, the height of buildings will decrease [15]. to solve the problem, construction leveling is adopted in actual construction to make up the loss caused by vertical compressive deformation [16, 17]. the following two methods are usually adopted to perform construction leveling. (1) improve rigidness of vertical component. in this way, vertical component can achieve the same deformation under vertical loading effect. (2) constrain degree of freedom of vertical component. when construction is over, deformation of different floor can be obtained using the following formula. 1 1 n n k n i k ik k l p e a      (3) where n stands for deformation of structural layer of any floor; lk stands for the height of floor k; ekak stands for rigidness of floor k; pi stands for the load loaded by floor i. actual measurement protocol of actual measurement teel reinforced concrete filled double-tube structure with shear wall and truss at the bottom was measured. in fig. 3, shenzhen peace finance building (fig. 4) adopts a novel structure system steel reinforced concrete filled doubletube structure with shear wall and truss at the bottom, which is different from the conventional tube structure. floors 1 ~ 6 are equipped with shear wall and the internal and external tubes of floors above the standard floor are all steel reinforced concrete columns. s h. zhu, frattura ed integrità strutturale, 36 (2016) 191-200; doi: 10.3221/igf-esis.36.19 195 figure 4: entitative graph of shenzhen peace finance building. note: floor 1 ~ 3 are commercial districts; floor 4 ~ 6 are installed with giant cantilever truss; and the 6th floor above are office areas. test instruments xhx-115w embedded strainometer, xhx-215w surface strainometer and xhx-322w reinforcement meter were used as test instruments in this study. xhx-115w embedded strainometer is usually embedded in beam, column, pile foundation and retaining wall to monitor development rule of strain and stress [18]. the calculation formula is as follows. 2fk  (4) 0  i (5) where ε stands for absolute strain capacity (10-6), f stands for wire vibrating frequency, k stands for calibration coefficient (k =0.002), εi stands for strain in state i (i.e., at the moment of deformation) (unit: με), ε0 stands for strain at time 0 (unit: με), and ε stands for relative strain value (unit: με). )(8.1)( 00 tti   (6) where t stands for measured temperature in state i (i.e., at the moment of deformation) and t0 stands for measured temperature at time 0. major test works test works mainly involve template erection of floor above the measured floor, beam-column and plate-column rebar binding of floor above the measured floor [19], concrete pouring above the measured floor, removal of template of floor above the measured floor, removal of template of floor above and below the measured floor, large live load such as loading or uploading of large equipments and materials [20] and adjustment of times of tests according to special conditions appearing during construction. it should be pointed out that, on-the-spot monitoring is needed during concrete pouring so as to prevent strainometer from the damage of vibration and protection of port of strainometer is also needed. experimental test setting and installation: first, observation spots needs to be selected according to structure requirements and designing scheme. then a strainometer is installed paralleling to the direction of strain. whether protection cover for the mounting base of strainometer needs to be installed or not depends on testing requirements. testing wires are led along with steels h. zhu, frattura ed integrità strutturale, 36 (2016) 191-200; doi: 10.3221/igf-esis.36.19 196 and bound with winding sires. after pouring of concrete is over, initial readings on the strainometer are tested to confirm its normal operation. layout of on-the-spot observation spots: to meet the requirements on loading bearing and rigidness of the structure, four corner posts are designed into l-shaped multilateral columns. load of columns, evenly distributed load of floors and live load of floors are transmitted to every column through column. strain sensors are installed on the corner posts on the bottom floor, 10th, 19th, 29th, 35th, 36th, 39th, 42th and 45th floor and every corn post is set with two observation spots. besides, the horizontal coupling beams of the corner posts on the 5th, 18th and 38th floor are installed with strain sensors. to be specific, the upper and lower flanges of corner posts are installed with sensors, one on each side. strain rosettes are installed on web plate. in this way, the bending moment and shearing force loaded by the steel beam can be monitored. analysis with sap2000 software [21] procedures of analysis of sap2000 software sap2000 is a finite element analysis software aiming at structure and it provides various forms of unit composition. herein we adopt sap2000 to make a force analysis on the simulated structure during construction. the analysis procedures are shown in fig. 5. figure 5: procedures of analysis with sap2000. note: axis net: right click, edit data of axis net and add new systems; define material: define steel and concrete, but when there is no materials which need to be defined in quick addition of materials, user-defined is needed; define section: frame unit is used to stimulate beam, column, inclined strut, truss, net rack and so on; draw model: section is usually drawn after definition is over; exert support restrain: switch to the top layer select joint of support which needs to be defined – restrain the specified joint; define analysis case in non-linear stage: define – load pattern including dead load, live load, wind load, etc. model simplification the achievable level of sap2000 was improved to ensure the practicability and accuracy of the analysis. a building model which was 48-floor high was simplified. in the process of non-linear simulation analysis, only the weight of structure was considered, and the ffect of live load and earthquake on the deformation of structure was not taken into account. to simply modeling and calculation, the fresh concrete was given an initial age of five days. when the model was being established, compressive strength, elastic modulus and time-varying properties of contraction and creep of concrete were considered. finite element method was used to divide the plate. considering effect of the rigidness of floors, the timevarying property of concrete material was not taken into account in the process of simplification of floor design [21]. using the simplification method mentioned above, we set up a model using definite element analysis software (figs. 6 and 7). h. zhu, frattura ed integrità strutturale, 36 (2016) 191-200; doi: 10.3221/igf-esis.36.19 197 figure 6: simulation model of construction figure 7: model of the standard floor results and discussion analysis of computing results nalysis and comparison of the simulated results and the measured value of vertical deformation of c60 concrete component is shown in figs. 8 ~ 10. figure 8: comparison of the measured value and the simulated value of the vertical deformation of bottom column 3 figure 9: comparison of the measured value and the simulated value of the vertical deformation of bottom column 4. a h. zhu, frattura ed integrità strutturale, 36 (2016) 191-200; doi: 10.3221/igf-esis.36.19 198 figure 10: comparison of the measured value and the simulated value of the vertical deformation of bottom column 5. it can be seen from figs. 8 ~ 10 that, development rate of the measured value of the vertical deformation of steel reinforced concrete (c 60) in the late stage was larger than that of the simulated value in the same period, and the difference of deformation became more and more obvious as time went on. analysis and comparison of the simulated results and the measured results of vertical deformation of c50 concrete component is shown in fig. 11. figure 11: comparison of the measured value and the simulated value of the vertical deformation of bottom column 1 of the 20th floor. it can be seen from fig. 11 that, development rate of the measured value of the vertical deformation of steel reinforced column (c50) was highly fitted with that of simulated value; and the eccentricity of the frame column was relatively low. analysis and comparison of the simulated results and the measured results of the vertical deformation of c40 concrete component is shown in fig. 11. figure 12: comparison of the measured value and the simulated value of the vertical deformation of bottom column 1 of the 29th floor. h. zhu, frattura ed integrità strutturale, 36 (2016) 191-200; doi: 10.3221/igf-esis.36.19 199 it can be seen from fig. 12 that, development rate of the measured value of the deformation of steel reinforced concrete (c40) column was large in early age, much larger than that of the simulated value; but development rate of the measured value of the deformation was smaller than that of the simulated value in the late stage. conclusion ith the rapid development of economy and constant progress of society, high-rise building has been favored by more and more people [22]. steel reinforced concrete structure featured by high bearing capacity, good antiseismic performance and good ductility has been applied more and more in high-rise building. hence it is of great importance to understand the crack formation of steel reinforced concrete structure under stress in construction period. in this study, we discussed over the reasonability of definite element analysis of steel reinforced concrete structure [23]. it can be known from the actual measurement of deformation that, deformation rate of steel reinforced concrete (c60, c50) column in low floor became higher than the simulated value in the late period; and the vertical deformation of steel reinforced concrete (c50, c60) column was smaller than that of steel reinforced concrete (c40) column [24]. during construction, deformation of structural component and accumulation of stress are different as construction order and procedures of exerting construction load are different. timely adjusting strength and section size of steel reinforced column of internal and external tubes can not only save building materials and narrow the gap of vertical deformation, but also benefit structural safety and construction [25]. the number of floors has large impact on accumulative vertical deformation difference. with the increase of the number of floors, accumulative vertical deformation of vertical component sharply increases. but the impact of construction speed on accumulative vertical deformation difference is small. in such a special structural system, accumulative deformation of steel reinforced concrete column of internal and external tubes is different. with the increase of constructed floors and load, accumulative deformation difference becomes larger. during construction, relevant measures need to be adopted to avoid the generation of additional stress. suggestions for construction everal points are suggested for construction. first, the adjustment of fabrication length is needed in the construction [26]. preadjustment measures can be considered to deal with the deformation of steel structure. when construction period is short, form removal should be performed in advance [27]. besides, rigid connection needs to be performed after hinged connection. strain of column needs to be improved if construction slows down due to the influence of development of strength of column and support system [28]. concrete placement sequence needs to be ensured consistent in every area of every floor [29]. field needs to be utilized effectively to accelerate the progress of construction. reference [1] zheng, s., su, y., zhang, w., li, q., experimental study on seismic performance of joints in the castellated portal frame of light-weight steel, building structure, 44(12) (2014) 80-84. [2] yang, x., xueyi, fu., dynamic elasto-plastic analysis of the shenzhen ping'an financial center tower, journal of building structures, 32(7) (2011) 40-49. [3] baev, a. r., asadchaya, m. v., features of the reflection of an acoustic beam from a surface with nonuniform boundary conditions, i. theoretical analysis, russian journal of nondestructive testing, 46(8) (2010) 547-558. [4] huttunen, h., tohka, j., model selection for linear classifiers using bayesian error estimation, pattern recognition, 48(11) (2015) 3739-3748. [5] gerilla, g. p., teknomo, k., hokao, k., an environmental assessment of wood and steel reinforced concrete housing construction, building & environment, 42(7) (2007) 2778-2784. [6] vayas, i., adamakos, t., iliopoulos, a., three dimensional modeling for steel-concrete composite bridges using systems of bar elements — modeling of skewed bridges, international journal of steel structures, 11(2) (2011) 157169. [7] deierlein, g. g., noguchi, h., overview of u.s.–japan research on the seismic design of composite reinforced concrete and steel moment frame structures, journal of structural engineering, 130(2) (2004) 361-367. w s h. zhu, frattura ed integrità strutturale, 36 (2016) 191-200; doi: 10.3221/igf-esis.36.19 200 [8] hierro, j., aznar, a., hernando, j. i., de, i. t. j. f., ortiz, j., criteria for steel structures reinforcement: restoration of the "círculo de bellas artes" building and the cultural center "casa encendida", informes de la construcción, 29(2) (2014) 5-21. [9] zhao, k., zhu, z., experimental study on behavior of the channel masonry concrete composite structures, applied mechanics & materials, 578-579 (2014) 1251-1256. [10] tong, j. x., jia, n., luo, p. f., experimental study on base reaction and deformation characteristic of variable modulus foundation for frame-tube structure, applied mechanics & materials, 638-640 (2014) 445-451. [11] goel, m. d., deformation, energy absorption and crushing behavior of single-, doubleand multi-wall foam filled square and circular tubes, thin-walled structures, 90 (2015) 1-11. [12] movahed, s. o., ansarifar, a., karbalaee, s., far, s. a., devulcanization and recycling of waste automotive epdm rubber powder by using shearing action and chemical additive, progress in rubber plastics recycling technology, 31(2) (2015) 87-117. [13] matthieu, v., franz-josef, u., nanogranular origin of concrete creep, proceedings of the national academy of sciences of the united states of america, 106(26) (2010) 10552-10557. [14] yan, c. w., jia j. q., zhang j. crack pattern and ductility of steel reinforced ultra high strength concrete composite joint subjected to reversal cycle load, key engineering materials, 417-418 (2010) 845-848. [15] cheng, p., chen, x. f., wu, l., construction technology of high-rise building structure, applied mechanics & materials, 580-583 (2014) 2316-2319. [16] zhu, c. m., hao, j. m., li, c., shuang, w. y., liu, p. h., well-facilitied capital farmland construction based on cultivated land comprehensive quality, transactions of the chinese society of agricultural engineering, 31(8) (2015) 233-242. [17] oh, h. k., park, s. m., hong, s. i., hot deformation and cracking during compression of 21-4n steel, advanced materials research, 1102 (2015) 12-21. [18] dierenfeldt, r., lindsteadt, g., laan, j., sobba, k. n., big brother as a contract monitor: an assessment of the use of contract staff to monitor offender communications, american journal of criminal justice, (2015) 1-17. [19] guo, j. s., xie, x. y., experimental study on the influence of slab’s reinforcement on seismic bearing capacity of beam’s cross-section in castin situ frame structure, applied mechanics & materials, 353-356 (2013) 1986-1989. [20] kocsis, p., discussion of "simplified method of lateral distribution of live load moment", journal of bridge engineering, 10(5) (2015) 630-631. [21] hocker, j., bein, b., bohm, r., steinfath, m., scholz, j., horn, e. p., correlation, accuracy, precision and practicability of perioperative measurement of sublingual temperature in comparison with tympanic membrane temperature in awake and anaesthetised patients, european journal of anaesthesiology, 29(29) (2012) 70-4. [22] bentick, b. l, lewis, m. k., real estate speculation as a source of banking and currency instability: some different lessons from the asian crisis, economic & labour relations review, 14(2) (2004) 256-275. [23] hellwig, f. l, tong, j., hussell, j. g., hip joint degeneration due to cam impingement: a finite element analysis, computer methods in biomechanics & biomedical engineering, 19(1) (2016) 1-8. [24] gzyl, m., pesci, r., rosochowski, a., boczkal, s., olejnik, l., in situ analysis of the influence of twinning on the strain hardening rate and fracture mechanism in az31b magnesium alloy, journal of materials science, 50(6) (2015) 2532-2543. [25] wang, j., xu, j., gao, d., numerical relationship between creep deformation coefficients of prestressed concrete beams, materials & structures, (2015) 1-11. [26] xiong, h., zeng, g., ding, c., wu, c., wang, w., extending parallel computing with constraint of fixed structure by adjusting graph, iete journal of research, (2015) 1-16. [27] smalley, p. j., laser safety: risks, hazards, and control measures, laser ther, 20(2) (2011) 95-106. [28] wu, x., li, w., wang, y., preliminary safety analysis of the pwr with accident-tolerant fuels during severe accident conditions, annals of nuclear energy, 80 (2015) 1-13. [29] sanz, b., planas, j., sancho, j. m., a closer look to the mechanical behavior of the oxide layer in concrete reinforcement corrosion, international journal of solids & structures, 62 (2015) 256–268. << /ascii85encodepages false /allowtransparency false /autopositionepsfiles true /autorotatepages /none /binding /left /calgrayprofile (dot gain 20%) /calrgbprofile (srgb iec61966-2.1) /calcmykprofile (u.s. web coated \050swop\051 v2) /srgbprofile (srgb iec61966-2.1) /cannotembedfontpolicy /error /compatibilitylevel 1.4 /compressobjects /tags /compresspages true /convertimagestoindexed true /passthroughjpegimages true /createjobticket false /defaultrenderingintent /default /detectblends true /detectcurves 0.0000 /colorconversionstrategy /cmyk /dothumbnails false /embedallfonts true /embedopentype false /parseiccprofilesincomments true /embedjoboptions true /dscreportinglevel 0 /emitdscwarnings false /endpage -1 /imagememory 1048576 /lockdistillerparams false /maxsubsetpct 100 /optimize 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can be opened with acrobat and adobe reader 5.0 and later.) >> /namespace [ (adobe) (common) (1.0) ] /othernamespaces [ << /asreaderspreads false /cropimagestoframes true /errorcontrol /warnandcontinue /flattenerignorespreadoverrides false /includeguidesgrids false /includenonprinting false /includeslug false /namespace [ (adobe) (indesign) (4.0) ] /omitplacedbitmaps false /omitplacedeps false /omitplacedpdf false /simulateoverprint /legacy >> << /addbleedmarks false /addcolorbars false /addcropmarks false /addpageinfo false /addregmarks false /convertcolors /converttocmyk /destinationprofilename () /destinationprofileselector /documentcmyk /downsample16bitimages true /flattenerpreset << /presetselector /mediumresolution >> /formelements false /generatestructure false /includebookmarks false /includehyperlinks false /includeinteractive false /includelayers false /includeprofiles false /multimediahandling /useobjectsettings /namespace [ (adobe) (creativesuite) (2.0) ] /pdfxoutputintentprofileselector /documentcmyk /preserveediting true /untaggedcmykhandling /leaveuntagged /untaggedrgbhandling /usedocumentprofile /usedocumentbleed false >> ] >> setdistillerparams << /hwresolution [2400 2400] /pagesize [612.000 792.000] >> setpagedevice microsoft word numero_35_art_54 w. xu et alii, frattura ed integrità strutturale, 35 (2016) 481-491; doi: 10.3221/igf-esis.35.54 481 effect of steel reinforcement with different degree of corrosion on degeneration of mechanical performance of reinforced concrete frame joints wu xu, liu ronggui school of civil engineering and architecture, nantong institute of technology (nit), nantong, jiangsu, 226000, china wxlrgwu@163.com abstract. beam-column joints which shoulders high-level and vertical shearing effect that maintains balance of beam and column end is the major component influencing the performance of the whole framework. post earthquake investigation suggests that collapse of frame structure is induced by failure of joints in most cases. thus, beam-column joints must have strong bearing capacity and good ductility, and reinforced concrete structure just meets the above requirement. but corrosion caused by long time use of reinforced concrete framework will lead to degeneration of mechanical performance of joints. to find out the rule of effect of steel reinforcement with different corrosion rate on degeneration of bearing capacity of reinforced concrete framework joints, this study made a nonlinear numerical analysis on fifteen models without stirrup in the core area of reinforced concrete frame joints using displacement method considering axial load ratio of column end and constraint condition. this work aims to find out the key factor that influences mechanical performance of joints, thus to provide a basis for repair and reinforcement of degenerated framework joints. keywords. reinforced concrete; mechanical performance of joints; corrosion of steel reinforcement. introduction n china, most framework structures has been degenerated [1]. during construction of old building, core area of building framework joints is usually placed with less or even no stirrup due to the limitation of building science and technology and insufficient understanding on importance of putting stirrup in the core area of framework, which influences quality of old framework joints [2, 3]. framework joints involving complex force situation can influence overall framework performance. therefore, studying degradation of mechanical performance of old framework joints is of great and practical significance. it has been found that, steel reinforcement corrosion is the leading cause for function degeneration of old building structure [4]. besides decrease of mechanical property, performance of steel reinforcement corrosion also includes cracking and even spalling of concrete, weakening of bound stress and decrease of adhesive property. currently, structure damage or instability induced by corrosion of steel reinforcement in concrete has been one of major issues concerned by the world; it occupies a leading role in factors influencing durability of structure [5]. for building which needs continued construction, steel reinforcement corrosion will further develop and finally result in engineering accidents if no thorough examination and effective treatment are carried out on corrosion condition of steel reinforcement [6]. hence it is necessary to detect steel reinforcement corrosion and evaluate durability and reliability of corroded component. research on corroded i w. xu et alii, frattura ed integrità strutturale, 35 (2016) 481-491; doi: 10.3221/igf-esis.35.54 482 reinforced concrete in china and abroad [7] mainly focuses on beam and column, and few concerns joints of corroded reinforced concrete framework. on this account, we made a simulation study on mechanical performance of framework joints without stirrup under statistic load and obtained degeneration rule of bearing capacity of reinforced concrete framework under the influence of different corrosion rate of steel reinforcement which can help guiding repair and reinforcement of old framework joints. finite element model and analysis method concrete constitutive and corroded steel reinforcement relationship nilateral compressive stress-strain relationship reflects mechanical property of concrete under stress [8]. its expression is as follows: (1 )c cd e   (1) if disturbance effect in coal yielding is considered, introduce disturbance factor d into the formula, then the formula change to: 2 1 , 1 1 1 , 1 ( 1) c n c c c n x n x d x x x                (2) , , c r c c c r f e    (3) , , , c c r c c r c r e n e f     (4) ,c r x    (5) ,c rf (n/mm2) 25 30 35 40 45 50 ,c r (10-6) 1560 1640 1720 1790 1850 1920 c 1.06 1.36 1.65 1.94 2.21 2.48 cu / ,c r 2.6 2.3 2.1 2.0 1.9 1.9 ,c rf (n/mm2) 55 60 65 70 75 80 ,c r (10-6) 1980 2030 2080 2130 2190 2240 c 2.74 3.00 3.25 3.50 3.75 3.99 cu / ,c r 1.8 1.8 1.7 1.7 1.7 1.6 note: cu refers to the compressive strain of concrete when the stress in descending branch of stress-strain curve is equal to 0.5 ,c rf . table 1: reference values of parameters relating to concrete single-axial compressive stress strain curve. in the formula, c refers to parameter value of descending branch of single-axial compressive stress strain curve of concrete (refer to table 1); ,c rf refers to representative value of axial compressive strength of concrete, and its concrete value is determined based on actual structural analysis; ,c r refers to peak compressive strain of concrete corresponding to u w. xu et alii, frattura ed integrità strutturale, 35 (2016) 481-491; doi: 10.3221/igf-esis.35.54 483 axial compressive strength of concrete ,c rf (refer to table 1); cd refers to concrete single-axial compressive injury evolutionary parameter;  refers to compressive stress of concrete;  refers to compressive strain of concrete; ce refers to elasticity modulus of concrete. degeneration of mechanical property of corroded steel reinforcement mainly reflects on decrease of yielding strength, ultimate strength and elongation ultimate of concrete. with the increase of corrosion rate, ultimate deformability weakens and yielding platform shortens and even disappears. based on the feature, we propose stress-strain relationship model for corroded steel reinforcement as shown in figure 1. when corrosion rate of steel reinforcement is small and yielding platform has not disappeared, figure 1 (a) is used; and when corrosion rate exceeds certain critical point and yielding platform disappears, figure 1(b) is used. ycf and ucf refers to nominal yield strength and nominal ultimate strength of corroded steel reinforcement respectively; sc and sc stands for stress and strain of corroded steel reinforcement respectively; syc and suc stands for yielding strain and hardening strain of corroded steel reinforcement. figure 1: constitutive relation curves for corroded steel reinforcement before and after disappearance of yielding platform [8]. finite element model and grid generation cruciform frame joints of reinforced concrete is taken as the finite element model (figure 2). size of test beam (simply supported beam) used for modeling is b×h×l = 120×200×1900 mm. span of the beam is 1.7 m. two concentrated forces are applied on midspan and the distance between two forces is 50 mm. concrete cover of main reinforcement is 2.5 mm thick. detailed size of the beam and reinforcement are shown in figure 3. figure 2: frame joint model. w. xu et alii, frattura ed integrità strutturale, 35 (2016) 481-491; doi: 10.3221/igf-esis.35.54 484 100 1700 100 load point load point250 250 120 ф6@150 2ф10 2ф14 ф6@150 figure 3: size of test beam and reinforcement (1) boundary condition considering symmetry of the structure, half of the mid-span section of the beam is taken for modeling. mid-span section is set to be symmetry constraint. cushion block is placed at the position of support and support constraint is exerted on cushion block. moreover, constraints in x and y direction is exerted in the direction vertical to the beam. free deformation of beam along beam direction is allowed. (2) load application self weight: the model considers self weight of the structure; specific gravity of concrete and steel are 25 kn/m3 and 7.85 kn/m3 respectively; acceleration of gravity is taken as 9.81 m/s2. vertical load: as finite element analysis needs to consider descending branch of the stress-strain relationship curve, displacement loading is applied, in order to ensure calculation convegence. vertical displacement is applied on loading site of the test beam until the beam breaks. then the external force exerted is calculated according to load-displacement relationship of the loading point. figure 4: nonlinear spring unit. the core area of frame joints is not equipped with stirrup; steel reinforcement and concrete are modeled using c3d8r unit (c3d8r refers to type of the unit; c refers to entity unit; 3d refers to three dimension; 8 refers to number of nodes in that unit; r means the unit is a reduced integration unit); to simulate the interaction between corroded steel reinforcement and concrete better when making three-dimensional finite element analysis on corroded steel reinforced concrete structural element, three nonlinear springs with different stiffness and vertical to each other (kx, ky, kz) are placed between unit joint of steel reinforcement and unit joint of concrete. stiffness matrix of the nonlinear spring ek is: w. xu et alii, frattura ed integrità strutturale, 35 (2016) 481-491; doi: 10.3221/igf-esis.35.54 485   1 1 1 1 tg ek k       (6) where tgk refers to slope of unit force of spring relative displacement (figure 4). unit grid generation is an important step in modeling which can transform geometrical model into finite element model composed of joints and units. result of grid generation directly determines preciseness of computation result and computation time [9, 10]. in the study, we adjust grid density for many times during computation process. dense grids cannot ensure calculation convegence, especially when beam is severely fractured; and discrete grids will result in poor computational accuracy. figure 5 shows grid generation of concrete unit. figure 5: grid generation of concrete unit. parameters of model the analytical model uses parameters including axial compression ratio (ratio of design value of axial pressure of column (wall) to product of full sectional area of column (wall) and design value of compressive strength of concrete column) and corrosion rate of steel reinforcement [11]. c30 concrete is used as model; longitudinal steel used is hrb335; stirrup used is hpb235. corrosion rate of longitudinal steel is 0, 2%, 5%, 10% and 15%; axial compression ratio is 0.2, 0.4 and 0.6. loading means and boundary conditions orrosion expansion of steel reinforcement is stimulated by exerting radial displacement on holes of concrete. assume that the steel reinforcement is evenly eroded, 1r refers to initial radius of steel reinforcement, 2r refers to external radius of corrosion product; 3r is radius of remaining steel reinforcement section. corrosion rate of steel reinforcement  is: 2 3 1 1 r r         (7) assume corrosion product is  times as large as original steel reinforcement and 0 is the space between non-corroded steel reinforcement and concrete, then the relationship between corrosion rate of steel reinforcement  and radial expansion displacement of concrete  can be expressed as: c w. xu et alii, frattura ed integrità strutturale, 35 (2016) 481-491; doi: 10.3221/igf-esis.35.54 486 0 2 2 ( 1)r        (8) when corrosion occurs, corrosion product first fills the space between non-corrosive steel reinforcement and concrete. then corrosion quantity increases and volume becomes larger, resulting in extrusion on concrete around steel reinforcement [12, 13]. model of exerting radial displacement on concrete around steel reinforcement is shown in figure 6. the model exerts displacement load on concrete around steel reinforcement at frame joints by such kind of loading means. figure 6: radial displacement loading model. analysis of results stress analysis ephogram of concrete stress (kg/cm2) under different corrosion rate when axial compression ratio is 0.2 is shown in figure 7. it can be seen from figure 7(a) that, stress at the intersection of concrete beam column is the maximum when corrosion rate is 0; and at that moment, cracks appear and extend to the core area of joints, leading to shear failure; upper part of left beam and lower part of right beam in the core area of concrete joints shoulders larger stress under the influence from antisymmetric monotonic load. figure 7(b) demonstrates that, middle part of beam shoulders the maximum stress when corrosion rate is 2%. that is because concrete holes around steel reinforcement shoulders radial displacement load from middle part of left beam to middle part of right beam. figure 7(c) suggests that, changes of stress on concrete beam when corrosion rate is 5% is basically the same with that when corrosion rate is 2%, but the stress is unevenly distributed. that is because that, joints can still shoulder radial displacement load though protective layer of concrete beam has cracked; stress on concrete column at the moment is much higher than that when corrosion rate is 2%; concrete column shows no obvious stress changes due to the large stress on beam. figure 7(d) shows the maximum stress on concrete joints when corrosion rate is 10% is smaller than that when corrosion rate is 5%; maximum stress on concrete reaches its peak when corrosion rate is 5% and moreover, stress on concrete column changes sharply (column end shoulders large stress and stress in core area of joints is larger than beam end). we can know from figure 7(e) that, the stress nephogram of concrete joints changes slightly when corrosion rate is 15%; and maximum stress on concrete is approximately equal to that when corrosion rate is 10%. effect of changes of corrosion rate on bearing capacity to discuss over effect of changes of corrosion rate of steel reinforcement on bearing capacity of component under fixed axial compression ratio, we divide fifteen stimulation analysis results into three groups according to axial compression ratio. figure 8 ~10 give load-displacement curves of different test specimen. n w. xu et alii, frattura ed integrità strutturale, 35 (2016) 481-491; doi: 10.3221/igf-esis.35.54 487 + 1.391 x 107 + 1.276 x 107 + 1.161 x 107 + 1.047 x 107 + 9.316 x 106 + 8.168 x 106 + 7.019 x 106 + 5.870 x 106 + 4.721 x 106 + 3.572 x 106 + 2.423 x 106 + 1.275 x 106 + 1.257 x 106 (a) corrosion rate of steel reinforcement 0 (b) corrosion rate of steel reinforcement 2% + 1.699 x 107 + 1.558 x 107 + 1.416 x 107 + 1.275 x 107 + 1.133 x 106 + 9.915 x 106 + 8.505 x 106 + 7.090 x 106 + 5.675 x 106 + 4.261 x 106 + 2.846 x 106 + 1.432 x 106 + 1.703 x 106 + 1.855 x 107 + 1.700 x 107 + 1.546 x 107 + 1.391 x 107 + 1.237 x 106 + 0.082 x 106 + 9.280 x 106 + 7.736 x 106 + 6.192 x 106 + 4.647 x 106 + 3.103 x 106 + 1.558 x 106 + 1.411 x 106 + 1.631 x 107 + 1.495 x 107 + 1.359 x 107 + 1.223 x 107 + 1.088 x 106 + 9.519 x 106 + 8.161 x 106 + 6.804 x 106 + 5.447 x 106 + 4.089 x 106 + 2.732 x 106 + 1.375 x 106 + 1.703 x 106 + 1.654 x 107 + 1.516 x 107 + 1.379 x 107 + 1.241 x 107 + 1.103 x 106 + 9.653 x 106 + 8.276 x 106 + 6.899 x 106 + 5.521 x 106 + 4.144 x 106 + 2.767 x 106 + 1.389 x 106 + 1.218 x 106 (c) corrosion rate of steel reinforcement 5% (d) corrosion rate of steel reinforcement 10% (e) corrosion rate of steel reinforcement 15% figure 7: nephogram of stress on joints of concrete. w. xu et alii, frattura ed integrità strutturale, 35 (2016) 481-491; doi: 10.3221/igf-esis.35.54 488 figure 8: curves of load-displacement (axial compression ratio 0.2). figure 9: curves of load-displacement (axial compression ratio 0.4). l o ad / k n displacement / mm corrosion rate of steel reinforcement 0 corrosion rate of steel reinforcement 2% corrosion rate of steel reinforcement 5% corrosion rate of steel reinforcement 10% corrosion rate of steel reinforcement 15% 0 10 20 30 40 4 8 1612 figure 10: curves of load-displacement (axial compression ratio 0.6). it can be seen from the above figures that, bearing capacity and ultimate displacement of joints shows a decreasing tendency when axial compression ratio is the same and corrosion rate of steel reinforcement becomes higher; when corrosion rate of steel reinforcement is 2%, bearing capacity and ultimate displacement degenerates insignificantly; when it is 5%, the degeneration is quite obvious; bearing capacity and displacement have little differences when corrosion rate is 10% and 15%, but ultimate displacement degenerates for 50%. under the same axial compression ratio, load-displacement curves partially coincide before yield point, suggesting corrosion rate of steel reinforcement has no influence on component when beam end shoulder small load. but with the increase of external load, bearing capacity of component declines. when corrosion rate is 10% and 15% particularly, protective layer cracks, which accelerates corrosion of steel reinforcement and severely influence mechanical performance of steel reinforcement and coordinated working between steel reinforcement and concrete. table 2 shows how corrosion rate influences ultimate bearing capacity and displacement of reinforced concrete framework joints when axial compression ratio is 0.2. w. xu et alii, frattura ed integrità strutturale, 35 (2016) 481-491; doi: 10.3221/igf-esis.35.54 489 corrosion rate/% bearing capacity/kn ultimate displacement/mm loss of bearing capacity/% loss of ultimate displacement/% 0 35.4 12 － － 2 32.6 11 8 8.3 5 26.7 9 24.6 25.0 10 24.9 7.3 29.7 39.0 16 24.8 7 30 41.7 table 2: bearing capacity and displacement of corroded reinforced concrete frame joints when axial compression ratio is 0.2. effect of changes of axial compression ratio on bearing capacity axial compression ratio is one of the major factors that influences failure mode and ductility of frame column. yoon et al. [14] stipulated that limit for axial compression ratio of frame structure (level 1 seismic grade) is 0.65. thus axial compression ratio is thought to be of great significance to bearing capacity of component. we obtain curves of loaddisplacement by keeping corrosion rate unchanged and changing axial compression ratio (0.2, 0.4, 0.6) (figure 11 ~ 15). figure 11: curves of load-displacement (corrosion rate 0). figure 12: curves of load-displacement (corrosion rate 2%). figure 13: curves of load-displacement (corrosion rate 5%). figure 14: curves of load-displacement (corrosion rate 10%). w. xu et alii, frattura ed integrità strutturale, 35 (2016) 481-491; doi: 10.3221/igf-esis.35.54 490 figure 15: curves of load-displacement (corrosion rate 15% ). the above figures demonstrate that, bearing capacity and ultimate displacement both decrease with the increase of axial compression ratio; when corrosion is mild, rigidity of component increases with increase of axial compression ratio; component with large axial compression ratio yields early and bearing capacity and ultimate displacement declines greatly. when corrosion rate is low or steel reinforcement is not corroded, curves of load-displacement when axial compression ratio is 0.6 differ greatly with curves when axial compression ratio is 0.2 and 0.4. that is because that, excessively higher axial compression ratio severely affects ducility of the structure. moreover, when protective layer cracks and corrosion rate is high, bearing capacity and ultimate displacement decline steadily with the increase of axial compression ratio. under the same corrosion rate, joint model which is not corroded or slightly corroded is less affected by axial compression ratio; the influence is the most notable when corrosion rate is 5%. when axial compression ratio is 0.4, joints have stronger bearing capacity and ultimate displacement. but when axial compression ratio is 0.2, bearing capacity fails to be stronger. when it is 0.6, bearing capacity and ultimate displacement decrease sharply. conclusion o sum up, corrosion rate of steel reinforcement and axial compression ratio have large influence on corroded reinforced concrete framework joints; joints show obvious degeneration with the increase of corrosion rate. changes of mechanical performance can be summarized as declined bearing capacity, degraded rigidity, changed ducility and decreased ultimate displacement. under coupling effect of inside corrosion and external load, bearing capacity of component remains unchanged, but ultimate displacement decreases obviously, when corrosion rate is excessively large (15%). corrosion rate is a key factor influencing mechanical performance of component, which can impact endurance quality of old framework. references [1] cairns, j., du, y., law, d., influence of corrosion on the friction characteristics of the steel/concrete interface, construction and building materials, 21(1) (2007) 190-197. [2] zou, d.j., liu, t.j., qiao, g.f., experimental investigation on the dynamic properties of rc structures affected by the reinforcement corrosion, advances in structural engineering, 17(6) (2014) 851-860. [3] ye, l.p., fang, e.h., research overview of stress performance of steel reinforced concrete elements, china civil engineering journal, 33(5) (2000) 1-12. [4] xue, j.y., zhao, h.t., yang, y., seismic behavior and construction method of steel reinforced concrete joint, world information on earthquake engineering, 18(2) (2002) 61-64. [5] xu, m., su, l.l., cheng, w.r., chen, z.f., test on combined steel and concrete column and reinforced concrete composite frame joint, building structure, 33(7) (2003) 36-39. [6] yang, z.y., hu, j.n., zhang, z., reinforcement of damaged frame joint with carbon fiber by finite element analysis, procedia earth and planetary science, 5 (2012) 198-202. t w. xu et alii, frattura ed integrità strutturale, 35 (2016) 481-491; doi: 10.3221/igf-esis.35.54 491 [7] fan, y.f., zhou, j., mechanical property of rusty rebar considering the effects of corrosion pits, journal of building materials, 6(3) (2003) 248-252. [8] ministry of construction. gb50010-2010 concrete structural design standard. beijing: china architecture & building press, 2010. [9] zhao. y.x., jin, w.l., modeling the amount of steel corrosion at the cracking of concrete cover, advances in structural engineering, 9(5) (2006) 687-696. [10] wang, j.q., experiment study and analysis on the mechanical properties of corroded reinforcing bars in the atmospheric environment, journal of xuzhou institute of architectural technology, 3(3) (2003) 25-27. [11] wu, q., yuan, y.s., li, j.y., research on structural behavior’s deterioration of corroded reinforced concrete beams under man-made climate, journal of china university of mining & technology, 36(4) (2007) 442-445. [12] wu, j., wang, c.x., xu, j., xiao, z., wu, f.h., study on flexural behavior of corroded reinforced concrete beams under fatigue loads, china civil engineering journal, 45(10) (2012)118-124. [13] shi, q.x., niu, d.t., yan, g.y., experimental research on hysteretic characteristics of corroded r. c. members with fiexural and compressive axial loads under repeated horizontal loading, earthquake engineering and engineering vibration, 20(4) (2000) 44-50. [14] choi, y.s., yi, s.t., kim, m.y., jung, w.y., yang, e.l., effect of corrosion method of the reinforcing bar on bond characteristics in reinforced concrete specimens, construction and building materials, 54 (2014) 180-189. nomenclature c refers to parameter value of descending branch of single-axial compressive stress strain curve of concrete; ,c rf refers to representative value of axial compressive strength of concrete, and its concrete value is determined based on actual structural analysis; ,c r refers to peak compressive strain of concrete corresponding to axial compressive strength of concrete ,c rf ; cd refers to concrete single-axial compressive injury evolutionary parameter;  refers to compressive stress of concrete;  refers to compressive strain of concrete; ce refers to elasticity modulus of concrete; cu refers to the compressive strain of concrete when the stress in descending branch of stress-strain curve is equal to 0.5 ,c rf ; ycf and ucf refer to nominal yield strength and nominal ultimate strength of corroded steel reinforcement respectively; sc and sc stand for stress and strain of corroded steel reinforcement respectively; syc and suc stand for yielding strain and hardening strain of corroded steel reinforcement; ek refers to nonlinear spring; tgk refers to slope of unit force of spring relative displacement; 1r refers to initial radius of steel reinforcement; 2r refers to external radius of corrosion product; 3r is radius of remaining steel reinforcement section;  refers to corrosion rate of steel reinforcement; 0 is the space between non-corroded steel reinforcement and concrete;  refers to radial expansion displacement of concrete. << /ascii85encodepages false /allowtransparency false /autopositionepsfiles true /autorotatepages /none /binding /left /calgrayprofile (dot gain 20%) /calrgbprofile (srgb iec61966-2.1) /calcmykprofile (u.s. web coated \050swop\051 v2) /srgbprofile (srgb iec61966-2.1) /cannotembedfontpolicy /error 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/hrv (za stvaranje adobe pdf dokumenata najpogodnijih za visokokvalitetni ispis prije tiskanja koristite ove postavke. stvoreni pdf dokumenti mogu se otvoriti acrobat i adobe reader 5.0 i kasnijim verzijama.) /hun 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can be opened with acrobat and adobe reader 5.0 and later.) >> /namespace [ (adobe) (common) (1.0) ] /othernamespaces [ << /asreaderspreads false /cropimagestoframes true /errorcontrol /warnandcontinue /flattenerignorespreadoverrides false /includeguidesgrids false /includenonprinting false /includeslug false /namespace [ (adobe) (indesign) (4.0) ] /omitplacedbitmaps false /omitplacedeps false /omitplacedpdf false /simulateoverprint /legacy >> << /addbleedmarks false /addcolorbars false /addcropmarks false /addpageinfo false /addregmarks false /convertcolors /converttocmyk /destinationprofilename () /destinationprofileselector /documentcmyk /downsample16bitimages true /flattenerpreset << /presetselector /mediumresolution >> /formelements false /generatestructure false /includebookmarks false /includehyperlinks false /includeinteractive false /includelayers false /includeprofiles false /multimediahandling /useobjectsettings /namespace [ (adobe) (creativesuite) (2.0) ] /pdfxoutputintentprofileselector /documentcmyk /preserveediting true /untaggedcmykhandling /leaveuntagged /untaggedrgbhandling /usedocumentprofile /usedocumentbleed false >> ] >> setdistillerparams << /hwresolution [2400 2400] /pagesize [612.000 792.000] >> setpagedevice microsoft word numero_37_art_28 s. vantadori et alii, frattura ed integrità strutturale, 37 (2016) 215-220; doi: 10.3221/igf-esis.37.28 215 focussed on multiaxial fatigue and fracture two-parameter fracture model for cortical bone sabrina vantadori, andrea carpinteri, giovanni fortese, camilla ronchei, daniela scorza university of parma, dept. of civil-environmental engineering and architecture, parco area delle scienze 181/a, 43124 parma – italy sabrina.vantadori@unipr.it, http://orcid.org/0000-0002-1904-9301 filippo berto university of padua, dept. of management and engineering, stradella san nicola 3, 36100, vicenza italy ntnu, department of engineering design and materials, richard birkelands vei 2b, 7491, trondheim – norway abstract. the analysis of the bone fracture behaviour is fundamental for prevention, diagnosis and treatment of traumas. in the present paper, an experimental analysis of the fracture behaviour of a bovine femoral cortical bone is carried out, where specimens are extracted from a diaphysis. fracture toughness is computed by employing a two-parameter fracture model originally proposed for concrete. in order to take into account the possibility of crack deflection (kinked crack) due to osteons orientation, a modified version of such a model is here discussed. the fracture toughness results are then compared with those reported in the literature, related to a femur of an 18-month-old bovine. keywords. cortical bone; fracture toughness; quasi-brittle material; two-parameter model. introduction one is a specialised tissue which has both metabolic and mechanical functions [1-3]. the load-bearing capacity of bone is limited up to a certain extent, beyond which it fails [4]. the analysis of the fracture behaviour of bone is fundamental for prevention, diagnosis and treatment of traumas. basic parameters which represent the structure and functions of bone have to be measured, such as its fracture toughness. in the present paper, an experimental analysis of the fracture behaviour of a bovine femoral cortical bone is carried out, where specimens are extracted from a diaphysis. the experimental campaign is conducted to determine the fracture toughness, by employing a two-parameter fracture model originally proposed for concrete [5], that is, for a quasi-brittle material showing a nonlinear slow crack growth before the peak load is reached. in bones, such a behaviour is produced by the mechanism of extrinsic toughening categorised in four classes [6]: (i) constrained microcracking; (ii) crack deflection and twist; (iii) uncracked-ligament bridging; (iv) collagen-fibril bridging. such a two-parameter fracture method is based on experimental data obtained from three-point bending tests on single edge-notched specimens, and employs linear elastic fracture mechanics mode i expressions. however, for the bone material, it cannot be applied in its original formulation since the crack starting from notch may deflect. in order to understand the cause of such a deflection under mode i loading (three-point bending), the bone microstructure level has to be briefly examined [7,8]. in cortical bone, it is represented by osteons (fig. 1). the osteons b s. vantadori et alii, frattura ed integrità strutturale, 37 (2016) 215-220; doi: 10.3221/igf-esis.37.28 216 are oriented parallel to the bone axis, which consists of a vascular canal (or haversian canal) surrounded by concentric lamellae. the interface between osteons and interstitial lamellae is called cement line (fig. 1). when the osteons alignment is perpendicular to the loading direction (transversal specimens), the stress state under threepoint bending loading is biaxial due to normal stresses produced by bending and shear stresses at the cement line interface between osteons and interstitial lamellae [9]. in such a case, the crack starting from the notch is subjected to mixed mode loading (mode i and mode ii). on the other hand, when the osteons alignment is parallel to the loading direction (longitudinal specimens), the stress state is uniaxial. in such a case, the crack starting from the notch is subjected to mode i loading. the two-parameter model can be directly applied for the latter case, whereas a modified formulation is hereafter proposed for the former case in order to take into account that the crack is also subjected to mode ii loading. more precisely, the unloading compliance expression related to a single kinked crack is determined by employing the castigliano theorem in the manner suggested by paris [10], and the effective crack length is computed. then, the critical stressintensity factor at the crack tip is evaluated as a function of that related to a straight crack having length equal to the projected length of the effective kinked crack [11,12]. vascular canal interstitial lamellae cement line osteon figure 1: cortical bone microstructure level. finally, the fracture toughness results here obtained are compared with those related to a femur of an 18-month-old bovine [13], experimentally determined according to the standard astm e399-1 [14]. two-parameter model ccording to the two-parameter model, the specimens present a notch in the lower part of the middle cross section (fig. 2). the three-point bending tests are performed under crack mouth opening displacement control (average speed equal to 0.1 mm h-1). w l s b a a0 (a) w l s b a0 (b) a1 a2  figure 2: crack propagates under: (a) pure mode i; (b) mixed mode. each specimen is monotonically loaded: after the peak load is achieved, the post-peak stage follows and, when the force is equal to about 95% of the peak load, the specimen is fully unloaded. then, the specimen is reloaded up to failure. a s. vantadori et alii, frattura ed integrità strutturale, 37 (2016) 215-220; doi: 10.3221/igf-esis.37.28 217 the initial compliance, ic , is used to determine the elastic modulus, e [15]:   bwc vas e i 2 006  (1) where s, w and b are the loading span, depth and thickness of the specimen, respectively, 0a is the notch length, and ic is the linear elastic compliance. further, the parameter v can be expressed as follows [15]:   w a v 002 0 3 0 2 000 with 1 66.0 04.287.328.276.0       (2) therefore, if the crack propagates under pure mode i, the effective critical crack length, a , is determined from the following equation by employing an iterative procedure:   bwc vas e u 2 6   (3) where uc is the unloading compliance, and  v is obtained from eq. 2 by replacing 0a with a . finally, the mode i critical stress-intensity factor, sick , is computed by employing the measured value of the peak load, maxp [15]: )( 2 3 2 max  fa bw sp k sic  (4) where:    w a f          with 121 )70.293.315.2()1(99.11 )( 2/3 2 (5) modified two-parameter model modified procedure is hereafter proposed when crack propagates under mixed mode loading (mode i and mode ii). specimens geometry and experimental test procedure are equal to those presented in the previous section (see fig. 2(b)). the elastic modulus is determined through eq. 1. under mixed mode loading, the effective critical crack length, 210 aaaa  , is obtained from the following equation by employing an iterative procedure: )]}()( )][([ ])[(][ { cos cos coscos coscoscossincos cos cos 2 cos 2 sin 2 cos )( 6 10 10 210 210 23 00 10 10 426 002 )( )()( w aa vaa w aaa vaaa va w aa vaa va bwc s e u                   (6) a s. vantadori et alii, frattura ed integrità strutturale, 37 (2016) 215-220; doi: 10.3221/igf-esis.37.28 218 eq. (6) is deduced by employing the castigliano theorem in the manner suggested by paris [10], being  the crack kinking angle (fig. 2(b)) and 01 3.0 aa  . note that, as is shown in fig. 2(b), the kinked crack path consists of the two segment, named 1a and 2a . if the value of 2a obtained from eq. 6 is negative, it means that the effective crack length is 10 aaa  with 01 3.0 aa  . such a length is obtained from the following equation by employing an iterative procedure: ]})[(][{ )()( 001010426002 cos cos 2 cos 2 sin 2 cos)( 6      va w aa vaava bwc s e u      (7) finally, the critical stress-intensity factor, sick , is computed through eqs 4 and 5, by considering a straight crack having length equal to the projected length of the effective kinked crack:        01 210 2102 max 3.0when cos with cos 2 3 aa w aaa faaa bw p k sic        (8a) or     01 10 102 max 3.0when cos with cos 2 3 aa w aa faa bw p k sic        (8b) results and discussion alues of fracture toughness, sick , of the analysed cadaveric femur diaphysis of a 24-month-old bovine are computed with respect to the osteons alignment: perpendicular or parallel to the loading direction. the former specimens are extracted from anterior (fa-1 and fa-2 in tab. 1), posterior (fp in tab. 1), medial (fm-1 and fm-2 in tab. 1) and lateral (fl in tab. 1) cortical bone, whereas the latter specimens from posterior cortical bone (fplong1 and fp-long2 in tab. 1). all specimens exhibit a non-linear slow crack growth before the peak load is reached. it can be observed that the fracture toughness values for specimens characterised by different osteons alignment with respect to the loading direction are significantly different. as a matter of fact, when the osteons alignment is perpendicular to the loading direction, crack grows under mixed mode (fig. 3(a)), and a higher resistance to fracture is observed. when the osteons alignment is parallel to the loading direction, crack grows under mode i (fig. 3(b)), and a lower resistance to fracture is observed. for transversal specimens, the average value of sick ( mmpa15.087.3  ) is in the range of the cortical bone fracture values [16]. such a value is then compared with those determined by libonati et al. [13] according to astm standards [14], following the lefm and considering cracks under pure mode i loading. they found mmpak sic 1.06.5  from se(b) type and mmpak sic 6.08.5  from c(t) type. the difference of such results with respect to those here obtained is due to the fact that the reduction of fracture toughness for a kinked crack as compared with the straight counterpart has not been taken into account by libonati et al. in ref. [13]. the present study highlights that the value of the near-tip stress-intensity factor of a kinked crack can be considerably lower than that for a straight crack of the same length, and that has to be taken into account for prevention, diagnosis and treatment of bone traumas. v s. vantadori et alii, frattura ed integrità strutturale, 37 (2016) 215-220; doi: 10.3221/igf-esis.37.28 219 specimens no. elastic modulus e (mpa) fracture toughness sick (mpa m1/2) fa-1 13692.54 4.09 fa-2 14393.65 3.68 fp 14038.29 3.74 fm-1 14253.00 3.92 fm-2 13488.94 3.85 fl 14042.47 3.91 fp-long1 12371.99 2.14 fp-long2 12370.47 1.99 table 1: elastic modulus and fracture toughness.           (a) fa-1 fl (b) fp-long1 fp-long2 figure 3: fracture: (a) mixed mode for transversal specimens fa-1 and fl; (b) pure mode i for longitudinal specimens. conclusions n the present paper, the behaviour of a compact bone in terms of fracture toughness has been analysed. fracture toughness has experimentally been evaluated through specimens obtained from the femur diaphysis of a bovine. the influence of local biaxial stress state on fracture behaviour has been analysed by employing two specimen types. as a matter of fact, when the osteons alignment is perpendicular to the loading direction (transversal specimens), the stress state is biaxial due to normal stresses produced by bending and shear stresses, at the cement line interface between osteons and interstitial lamellae. on the other hand, when the osteons alignment is parallel to the loading direction (longitudinal specimens), the stress state is uniaxial. then fracture toughness values have been computed by a modified version of the two-parameter model originally formulated for crack propagating under mode i. such a modified version is here proposed for mixed mode (mode i and mode ii). the theoretical results obtained are compared with some data available in the literature, by highlighting that the value of the near-tip stress-intensity factor of a kinked crack can be considerably lower than that for a straight crack of the same length. references [1] an, h.y., draughn, r.a., mechanical testing of bone and the bone-implant interface, crc press, boca raton, (2000). [2] marks, s.c., popoff, s.n., bone cell biology: the regulation of development, structure, and function in the skeleton, am. j. anat., 183 (1988) 1-44. [3] keaveny, t.m., hayes, w.c., mechanical properties of cortical and trabecular bone, crc press, boca raton, (1993). [4] li, s., abdel-wahab, a., silberschmidt, v.v., analysis of fracture processes in cortical bone tissue, eng. frac. mech., 110 (2013) 448-458. doi: 10.1016/j.engfracmech.2012.11.020 [5] jenq, y., shah, s., j., two parameter fracture model for concrete, eng. mech., 111 (1985) 1227-1241. i s. vantadori et alii, frattura ed integrità strutturale, 37 (2016) 215-220; doi: 10.3221/igf-esis.37.28 220 [6] nalla, r.k., kinney, j.h., ritchie, r.o., mechanistic fracture criteria for the failure of human cortical bone, nat. mater., 2 (2003) 164-168. doi: 10.1038/nmat832 [7] katz, j.l., the structure and biomechanics of bone, symp. soc. exp. biol., 34 (1980) 137-168. [8] rho, j.y., kuhn spearing, l., zioupos, p., mechanical properties and the hierarchical structure of bone, med. eng. & phys., 20 (1998) 92-102. doi: 10.1016/s1350-4533(98)00007-1 [9] martin, r.b., burr, d.b., sharkey, n.a., skeletal tissue mechanics, springer-verlag, new york, (1998). [10] paris, p.c., the mechanics of fracture propagation and solutions to fracture arrester problems, document d2-2195, the boeing company, (1957). [11] kitagawa, h., yuuki, r., ohira, t., crack-morphological aspects in fracture mechanics, eng. frac. mech., 7 (1975) 515-529. doi: 10.1016/0013-7944(75)90052-1 [12] cotterell, b., rice, j.r., slightly curved or kinked cracks, int. j. frac., 16 (1980) 155-169. doi: 10.1007/bf00012619 [13] libonati, f., vergani, l., bone toughness and crack propagation: an experimental study, proc. engin., 74 (2014) 464467. doi: 10.1016/j.proeng.2014.06.298 [14] astm e399-1, standard test method for linear-elastic plane-strain fracture toughness kic of metallic materials. [15] tada, h., paris, p.c., irwin, g.r., the stress analysis of cracks handbook, asme press, new york, (2000). [16] khanal, s.p., mahfuz, h., rondinone, a.j., leventouri, t., improvement of the fracture toughness of hydroxyapatite (hap) by incorporation of carboxyl functionalized single walled carbon nanotubes (cfswcnts) and nylon, mat. sci. eng. c, 60 (2016) 204-210. doi: 10.1016/j.msec.2015.11.030 << /ascii85encodepages false /allowtransparency false /autopositionepsfiles true /autorotatepages /none /binding /left /calgrayprofile (dot gain 20%) /calrgbprofile (srgb iec61966-2.1) /calcmykprofile (u.s. web coated \050swop\051 v2) /srgbprofile (srgb iec61966-2.1) /cannotembedfontpolicy /error /compatibilitylevel 1.4 /compressobjects /tags /compresspages true /convertimagestoindexed true /passthroughjpegimages true /createjobticket false /defaultrenderingintent /default /detectblends true /detectcurves 0.0000 /colorconversionstrategy /cmyk /dothumbnails false /embedallfonts true /embedopentype false /parseiccprofilesincomments true /embedjoboptions true /dscreportinglevel 0 /emitdscwarnings false 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/hrv (za stvaranje adobe pdf dokumenata najpogodnijih za visokokvalitetni ispis prije tiskanja koristite ove postavke. stvoreni pdf dokumenti mogu se otvoriti acrobat i adobe reader 5.0 i kasnijim verzijama.) /hun 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/pdfxoutputintentprofileselector /documentcmyk /preserveediting true /untaggedcmykhandling /leaveuntagged /untaggedrgbhandling /usedocumentprofile /usedocumentbleed false >> ] >> setdistillerparams << /hwresolution [2400 2400] /pagesize [612.000 792.000] >> setpagedevice microsoft word numero_44_art_2 b. rahmanzadeh et alii, frattura ed integrità strutturale, 44 (2018) 16-24; doi: 10.3221/igf-esis.44.02 16 experimental study of the effect of water-cement ratio on compressive strength, abrasion resistance, porosity and permeability of nano silica concrete belal rahmanzadeh, kamal rahmani*, saber piroti department of civil engineering, mahabad branch, islamic azad university, mahabad, iran. belalrahmanzade@yahoo.com, mohandes_so@yahoo.com, s.piroty@iau-mahabad.ac.ir abstract. the effect of water-cement ratio on abrasion resistance, porosity and hydraulic conductivity coefficient of nano silica concrete has been studied in this research (paper). the compressive strength of concrete in a particular temperature is related to two factors: water-cement ratio and density. decreasing the water-cement ratio from 0.46 to 0.30 improves the abrasion resistance of nano silica concrete by 42%, the hydraulic conductivity coefficient of concrete decreases from 28.5⤬10-15 to 1.7⤬10-15 m/s and the porosity of concrete decreases to 13.1%. the abrasion depth increases gradually by increasing the water-cement ratio from 0.30 to 0.46. keywords. abrasion resistance; compressive strength; concrete; permeability; water-cement ratio. citation: rahmanzadeh, b., rahmani, k., piroti, n., experimental study of the effect of water-cement ratio on compressive strength, abrasion resistance, porosity and permeability of nano silica concrete, frattura ed integrità strutturale, 44 (2018) 16-24. received: 17.09.2017 accepted: 10.01.2018 published: 01.04.2018 copyright: © 2018 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. introduction oncrete dams are strategic structures due to their fundamental role at economical system of a country. therefore, the concrete used for these important structures should have a suitable durability and performance (neville [1]; yoon et al., [2]). the effect of nano silica elements as fillers in pozzolanic concrete has been evaluated in current decade (shih et al., [3]; senff et al., [4]). nano silica cement mixture has provided an attractive research field for the creation of high strength hydraulic structures (nazari and riahi [5]; rahmani and ramzanianpour [6]). using nano structure materials like nano silica and an optimal water-cement ratio improved the physical characteristics of new cement mixtures (li [7]; wen et al., [8]). the effect of water-cement ratio on abrasion resistance, porosity and permeability of nano silica used in making durable concrete, were considered as an effective factor on strength and performance of these concrete structures (felekoğlu et al., [9]; bilodeau & malhotra [10]). considering the high and rather modern concrete technology, advanced researches and serious studies on special concrete specimens of hydraulic structures (such as concrete dams) seem to be necessary (givi et al., [11]; tavakoli & soroushian, [12]). the water-cement ratio of concrete has been considered constant in traditional concrete (mixtures) to gain high strength and durability (shih et al., [3]; li [7]; collepardi et al., [13]; nazari et al., [14]; aiu & huang [15]; nazari & riahi c b. rahmanzadeh et alii, frattura ed integrità strutturale, 44 (2018) 16-24; doi: 10.3221/igf-esis.44.02 17 [16]; gaitero et al., [17]). however, the water-cement ratio should be considered according to microcrystalline structure of cement used in concrete specimens (behnood and ziari [18]; wittmann et al., [19]; willer eda et al., [20]). the amount of water and cement in the mixture are related to the size of aggregates (sands) and nano silica structure (shih et al., [3]; senff et al., [4]; popovics [21]; li [7]; willer eda et al., [20]). in this research, different amounts of water-cement ratio were considered to investigate the compressive strength and abrasion resistance of concrete specimens. high abrasion resistance and low permeability and porosity are the main advantages of using nano silica in concrete. experimental tests he concrete specimens contained 5% nano silica. the water-cement ratio was considered 0.30, 0.34, 0.38, 0.42 and 0.46. other characteristics of the mixture were considered constant in all concrete specimens. the following investigations were done on concrete specimens. wet sand blast technique was used to detect the concrete strength. the abrasion resistance of 28 days 15⤬15⤬15 cm cubic specimens was determined. penetration method was used to define the hydraulic conductivity coefficient of 28 days 10⤬10 cm cylindrical specimens. in addition, the compressive strength and hydraulic conductivity coefficient were conducted by concrete breaker jack machine and penetration depth method respectively. the designation and composition of each batch have been presented in tab. 1. sample number water-cement ratio nano silica (%) age (days) 1 0.30 5 7 2 0.34 5 7 3 0.38 5 7 4 0.42 5 7 5 0.46 5 7 6 0.30 5 28 7 0.34 5 28 8 0.38 5 28 9 0.42 5 28 10 0.46 5 28 11 0.30 5 90 12 0.34 5 90 13 0.38 5 90 14 0.42 5 90 15 0.46 5 90 table 1: the properties of the studied samples in the present research. nano silica concrete mixture he following items were considered in preparation of nano silica concrete specimens:  the slump of specimens was 60 to 100 mm.  the aggregates were non-ballast materials.  the distinguishable size of aggregates was mostly 10 mm.  the cement was portland type i.  the constant amount of nano silica (added to the mixture of cement and aggregates) was 5% in all specimens.  28 days compressive strength of specimens was determined 40 mpa.  the water-cement ratio was variable from 0.30 to 0.46. t t b. rahmanzadeh et alii, frattura ed integrità strutturale, 44 (2018) 16-24; doi: 10.3221/igf-esis.44.02 18  in order to access the desired workability and high performance of concrete specimens, the gelenium-110p was used as a superplasticizer. results and discussion abrasion resistance test brasion strength test on cube samples 150 × 150 × 150 mm at 28 days of age was performed using water sand blast method based on astm-c778 standard (fig. 1). the extracted results of abrasion resistance tests are summarized in tab. 2. fig. 2 shows the abrasion depth in terms of water-cement ratio. increasing the water-cement ratio leads to increase the abrasion depth. by increasing the water-cement ratio from 0.3 to 0.46, the abrasion depth increases gradually. the more the water-cement ratio is, the less abrasion resistance of mortar phase occurred. however, the abrasion resistance of concrete inclines to the abrasion resistance of aggregates. by gradual increase of water-cement ratio to 0.46, the abrasion depth may reach to the maximum value. it seems that the maximum value of abrasion resistance is related to 0.46 water-cement ratio. figure 1: abrasion strength test machine w/c 0.3 0.34 0.38 0.42 0.46 abrasion resistance (mm) 0.814 0.954 1.105 1.198 1.227 table 2: abrasion depth tests for specimens with variable water-cement ratio. a b. rahmanzadeh et alii, frattura ed integrità strutturale, 44 (2018) 16-24; doi: 10.3221/igf-esis.44.02 19 0.8 0.9 1 1.1 1.2 1.3 0.3 0.35 0.4 0.45 0.5 a br as io n d ep th ( m m ) w/c figure 2: abrasion depth in terms of water-cement ratio fig. 3 shows that the abrasion depth reverse has a reversed relationship with the water-cement ratio. considering the reverse relationship of abrasion resistance and abrasion depth, data showed that increasing the water-cement ratio decreases the abrasion resistance reverse. the abrasion resistance and average permeability depth data for different values of water-cement ratio are shown in tab. 3. to enhance the abrasion resistance of concrete, it is necessary to enhance the mortar phase and the aggregate phase with one another. mortar phase can be enhanced by reduction of water-cement ratio, using nano silica and suitable curing. aggregate phase can also be enhanced by abrasion-resistant aggregates like granite. the condition of performing abrasion test can be more approximated to the real condition of concrete abrasion against water. to do this the silica sand should be shot under water and in less than 90 degree angle. 0.8 0.9 1 1.1 1.2 1.3 0.3 0.35 0.4 0.45 0.5 a b ra si on d ep th r ev er se ( cm -1 ) w/c figure 3: abrasion depth reverse in terms of water-cement ratio w/c abrasive resistance improvement average permeability depth (mm) 0.3 38.24% 0.905 0.34 26.17% 1.305 0.38 12.94% 1.845 0.42 4.56% 2.215 0.46 3.17% 3.225 table 3: abrasion resistance improvement and average permeability depth for various values of water-cement ratio. b. rahmanzadeh et alii, frattura ed integrità strutturale, 44 (2018) 16-24; doi: 10.3221/igf-esis.44.02 20 hydraulic conductivity coefficient he hydraulic conductivity of the concrete was tested using by penetration method according to astm-c1920-5 (eq. 1). concrete hydraulic conductivity coefficient =  ph v th 2 / 2 (1) where hp: water penetration depth [m], t: influence time [s], h: pressure height [m], v: concrete porosity. fig. 4 illustrates the machine used for performing the hydraulic conductivity of the concrete tests. fig. 5 shows the water permeability depth in terms of various amounts of water-cement ratio. the mentioned data showed that increasing the water-cement ratio, increases water permeability depth. figure 4: hydraulic conductivity of the concrete test machine 0.5 1 1.5 2 2.5 3 3.5 0.3 0.35 0.4 0.45 0.5 w at er p er m ea bi li ty d ep th ( m m ) w/c figure 5: water permeability depth in terms of different values of water-cement ratio it is noteworthy that the following formula is used for calculating the permeability coefficient of concrete.    p pk h t h 2 / 2 (2) where: kp is permeability coefficient of concrete [m/s]; hp is water permeability depth [m]; t is water permeability time [s]; h is height arising from pressure [m] and v is porosity of concrete. the following equation is used for porosity calculation: t b. rahmanzadeh et alii, frattura ed integrità strutturale, 44 (2018) 16-24; doi: 10.3221/igf-esis.44.02 21           w c w g/ 100 36.15 / 100 / (3) where: w/c is water-cement ratio; ⍺ is degree of cement hydration; w is gravity of water of concrete [kg/m3] and g is specific weight of cement [g/cm3]. wet sand blast can significantly simulate the erosion in concrete, so it is a suitable technique to evaluate the water resistance of concrete. penetration resistance test on concrete is a tool for defining comparative strengths of concrete in similar or dissimilar structures. due to the nature of equipment, absolute values of strength cannot be obtained. penetration method is a suitable approach for evaluating the permeability of concrete, because this method is desired for the ratio of water depth in concrete. for the concrete cylinder height, this fact is achieved in nano silica concretes. fig. 6 shows the hydraulic conductivity coefficient of concrete in terms of different values of water-cement ratio. the data indicated that increasing the water-cement ratio, increases hydraulic conductivity coefficient of concrete. 0 5 10 15 20 25 30 0.3 0.35 0.4 0.45 0.5 h yd ra ul ic c on du ct iv ity c oe ff ic ie nt (m /s ) w/c × 10-14 figure 6: hydraulic conductivity coefficient of concrete in terms of water-cement ratio fig. 7 shows the variation curve of porosity in terms of different amounts of water-cement ratio. the porosity of concrete increases by increasing of water-cement ratio. 13 16 19 22 25 0.3 0.35 0.4 0.45 0.5 p o ro si ty o f co n cr et e p er ce n t w/c figure 7: variation of porosity in terms of different amounts of water-cement ratio b. rahmanzadeh et alii, frattura ed integrità strutturale, 44 (2018) 16-24; doi: 10.3221/igf-esis.44.02 22 tab. 4 shows the values of hydraulic conductivity coefficient and porosity of concrete in terms of water-cement ratio. the values of tab. 5 are required for obtaining the hydraulic conductivity coefficient and porosity of nano silica concrete. w/c hydraulic conductivity coefficient of cement (m/s) porosity of concrete 0.3 1.7⤬10-15 13.1% 0.34 3.84⤬10-15 15.2% 0.38 8.25⤬10-15 19.37% 0.42 13.95⤬10-15 21.56% 0.46 28.5⤬10-15 25% table 4: hydraulic conductivity coefficient and porosity of concrete in terms of water-cement ratio. permeability time (s) height arising from water pressure (m) cement specific weight (g/cm) cement degree of hydration (%) 259200 82 3.15 80 table 5: required values for calculating hydraulic conductivity coefficient and porosity of concrete. compressive strength ompressive strength tests on cube samples of 150 × 150 × 150 mm at the age of 7, 28 and 91 days have been done with a pressure test device with a capacity of 2000 kn (tekno test-italy) at a speed of 2.5 kn/s accordance to aci-c330 standard. the value of compressive strength of samples can be evaluated using eq. 5 as following as: compressive strength =  p a/ 1000 (4) fig. 8 is the illustration of compressive strength test machine. figure 8: compressive strength test machine c b. rahmanzadeh et alii, frattura ed integrità strutturale, 44 (2018) 16-24; doi: 10.3221/igf-esis.44.02 23 fig. 9 shows the compressive strength improvements due to water-cement ratio reduction in nano silica concrete with error bars. the compressive strength and abrasion resistance of concrete will increase by means of water-cement ratio reduction. as it can be seen in fig. 9, by reducing the ratio of water to cement from 0.46 to 0.3, the compressive strength of samples at the age of 7, 28 and 90 days of concrete is improved by 27.92, 33.04 and 31.88% respectively. 0 5 10 15 20 25 30 35 40 0.3 0.34 0.42 0.46 c o m pr es si ve s tr en g th i m pr o vm en t p er ce n ts w/c 7 days 28 days 90 days figure 9: compressive strength improvement after 7, 28 and 90 days conclusion ue to the rapid growth of scientific and practical researches, the science and technology of nanotechnology of all industries, very little attention has been paid to the applications of this phenomenon in the building industry and construction. recently, however, with regard to nano reinforcement in construction materials, a new wave has taken place with the ever-accelerating in the construction industry. properties, behavior and performance of concrete depend on the nano structure of the underlying concrete, which provides adhesion, cohesion and integrity. therefore, the construction of concrete and cement paste structures at the nanoscale is very important for the development of new building materials and their applications. the main obtained results in the present article showed that the abrasion resistance of nano silica concrete increased by decreasing of water-cement ratio. by reducing the water-cement ratio from 0.46 to 0.30 at nano silica concrete specimens, the abrasion resistance of concrete improved by 42%. the abrasion resistance of mortar phase decreased by increasing of water-cement ratio and the abrasion resistance of concrete approaches the abrasion resistance of aggregates. in addition, the hydraulic conductivity coefficient and the porosity of nano silica concrete decreased by decreasing of water-cement ratio from 0.46 to 0.30. therefore, the hydraulic conductivity coefficient of concrete decreased from 28.5⤬10-15 to 1.7⤬10-15, the porosity of concrete decreased to 13.1% and the abrasion depth reduced gradually. this can be related to the biphasic (mortar and aggregates) nature of concrete in abrasion. references [1] neville, a. (2001). consideration of durability of concrete structures: past, present, and future, materials and structures, 34, pp. 114-118. [2] yoon, y.-s., won, j.-p., woo, s.-k. and song, y.-c. (2002). enhanced durability performance of fly ash concrete for concrete-faced rockfill dam application, cement and concrete research, 32, pp.23-30. [3] shih, j.-y., chang, t.-p. and hsiao, t.-c. (2006). effect of nanosilica on characterization of portland cement composite, materials science and engineering: a, 424, pp. 266-274. d b. rahmanzadeh et alii, frattura ed integrità strutturale, 44 (2018) 16-24; doi: 10.3221/igf-esis.44.02 24 [4] senff, l., labrincha, j.a., ferreira, v.m., hotza, d. and repette, w.l. (2009). effect of nano-silica on rheology and fresh properties of cement pastes and mortars, construction and building materials, 23, pp. 2487-2491. [5] nazari, a. and riahi, s. (2011). the effects of sio2 nanoparticles on physical and mechanical properties of high strength compacting concrete, composites part b: engineering, 42, pp. 570-578. [6] [6] rahmani, h. and ramzanianpour, a. (2008). effect of silica fume and natural pozzolanas on sulfuric acid resistance of dense concretes, asian journal of civil engineering (building and housing), 9, pp. 303-319. [7] li, g. (2004). properties of high-volume fly ash concrete incorporating nano-sio2, cement and concrete research, 34, pp. 1043-1049. [8] wen, l., deng, y.-h., mei, z., ling, x. and qian, f. (2006). mechanical properties of nano sio2 filled gypsum particleboard, transactions of nonferrous metals society of china, 16, pp. s361-s364. [9] felekoğlu, b., türkel, s. and baradan, b. (2007). effect of water/cement ratio on the fresh and hardened properties of self-compacting concrete, building and environment, 42, pp. 1795-1802. [10] bilodeau, a. and malhotra, v. (1992). concrete incorporating high volumes of astm class f fly ashes: mechanical properties and resistance to deicing salt scaling and to chloride-ion penetration, aci special publication sp-132, american concrete institute, detroit, pp. 319-349. [11] givi, a.n., rashid, s.a., aziz, f.n.a. and salleh, m.a.m. (2010). experimental investigation of the size effects of sio2 nano-particles on the mechanical properties of binary blended concrete, composites part b: engineering, 41, pp. 673-677. [12] tavakoli, m. and soroushian, p. (1996). strengths of recycled aggregate concrete made using field-demolished concrete as aggregate, materials journal, 93, pp. 178-181. [13] collepardi, m., collepardi, s., skarp, u. and troli, r. (2004). optimization of silica fume, fly ash and amorphous nano-silica in superplasticized high-performance concretes, proceedings of 8th canmet/aci international conference on fly ash, silica fume, slag and natural pozzolans in concrete, sp-221, las vegas, usa, pp. 495-506. [14] nazari, a., riahi, s., riahi, s., shamekhi, s.f. and khademno, a. (2010). influence of al2o3 nanoparticles on the compressive strength and workability of blended concrete, journal of american science, 6, pp. 6-9. [15] aiu, m. and huang, c. (2006). the chemistry and physics of nano-cement, loyola marymount university, nsf-reu university of delaware. [16] nazari, a. and riahi, s. (2011). the effects of sio2 nanoparticles on physical and mechanical properties of high strength compacting concrete. composites part b: engineering, 42, pp. 570-578. [17] gaitero, j., sáez de ibarra, y., erkizia, e. and campillo, i. (2006), silica nanoparticle addition to control the calcium‐leaching in cement‐based materials, physica status solidi (a), 203, pp. 1313-1318. [18] behnood, a. and ziari, h. (2008). effects of silica fume addition and water to cement ratio on the properties of highstrength concrete after exposure to high temperatures, cement and concrete composites, 30, pp. 106-112. [19] wittmann, f., roelfstra, p., mihashi, h., huang, y.-y., zhang, x.-h. and nomura, n. (1987). influence of age of loading, water-cement ratio and rate of loading on fracture energy of concrete, materials and structures, 20, pp. 103110. [20] willer eda, m., lima rde, l. and giugliano, l.g. (2004). in vitro adhesion and invasion inhibition of shigella dysenteriae, shigella flexneri and shigella sonnei clinical strains by human milk proteins, bmc microbiol, 4, pp. 1-7. [21] popovics, s. 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can be opened with acrobat and adobe reader 5.0 and later.) >> /namespace [ (adobe) (common) (1.0) ] /othernamespaces [ << /asreaderspreads false /cropimagestoframes true /errorcontrol /warnandcontinue /flattenerignorespreadoverrides false /includeguidesgrids false /includenonprinting false /includeslug false /namespace [ (adobe) (indesign) (4.0) ] /omitplacedbitmaps false /omitplacedeps false /omitplacedpdf false /simulateoverprint /legacy >> << /addbleedmarks false /addcolorbars false /addcropmarks false /addpageinfo false /addregmarks false /convertcolors /converttocmyk /destinationprofilename () /destinationprofileselector /documentcmyk /downsample16bitimages true /flattenerpreset << /presetselector /mediumresolution >> /formelements false /generatestructure false /includebookmarks false /includehyperlinks false /includeinteractive false /includelayers false /includeprofiles false /multimediahandling /useobjectsettings /namespace [ (adobe) (creativesuite) (2.0) ] /pdfxoutputintentprofileselector /documentcmyk /preserveediting true /untaggedcmykhandling /leaveuntagged /untaggedrgbhandling /usedocumentprofile /usedocumentbleed false >> ] >> setdistillerparams << /hwresolution [2400 2400] /pagesize [612.000 792.000] >> setpagedevice microsoft word numero_38_art_2 s. averbeck et alii, frattura ed integrità strutturale, 38 (2016) 12-18; doi: 10.3221/igf-esis.38.02 12 focussed on multiaxial fatigue and fracture a study of white etching crack formation by compression-torsion experiments s. averbeck, e. kerscher materials testing (awp), university of kaiserslautern, gottlieb-daimler-strasse, 67663 kaiserslautern, germany stefan.averbeck@mv.uni-kl.de, kerscher@mv.uni-kl.de abstract. in this study, an attempt was made to recreate the bearing damage phenomenon “white etching cracks” with a simplified testing setup. rolling contact fatigue conditions were simulated with in-phase and out-ofphase cyclic compression-torsion experiments on 100cr6 steel specimens. the results are compared in terms of microstructural change. focused ion beam and metallographic analysis reveal that a fine-grained, white etching zone formed in the vicinity of the fatigue cracks of specimens tested with the in-phase load pattern. in contrast, no such structures were found after testing the out-of-phase load pattern. the properties of the white etching zone are characterised in more detail and compared with white etching cracks. keywords. white etching cracks; multiaxial fatigue; bearing steel. citation: averbeck, s., kerscher., e., a study of white etching crack formation by compression-torsion experiments, frattura ed integrità strutturale, 38 (2016) 12-18. received: 28.04.2016 accepted: 15.06.2016 published: 01.10.2016 copyright: © 2016 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. introduction n the past two decades, increasing attention has been focused on the damage mechanism “white etching cracks” (wec). wecs can lead to very early bearing failure (usually 5-20% of l10) under operating conditions that would usually allow the bearing to achieve its calculated service life [1]. despite intensive research and a variety of root cause hypotheses, no comprehensive explanation for wec formation exists yet. the phenomenon seems to be influenced by multiple parameters which are often interdependent. the different hypotheses and influencing factors have been reviewed by gegner [2], evans [1] and, more recently, by stadler et al. [3]. the characteristic feature of white etching cracks is the appearance of the crack faces, which appear white when etched with 3% nitric acid. this etching behaviour is attributed to an extreme grain refinement compared to the original martensitic structure. the average grain size is reduced from ~1µm to 10-100nm [2, 4]. the reduction in grain size is coupled with an increase in hardness from about 700hv to 1000hv and above [1, 5], in part due to the hall-petch effect, in part due to the dissolution of carbides in the white etching area [4]. the lattice structure is body-centred cubic, which is carbon-supersaturated ferrite [1, 2], although amorphous structures have also been reported [6]. wec have a tendency to branch and form networks or groups [1, 7]. this heavy branching of the cracks and their three-dimensional interconnections are responsible for their detrimental effect on bearing life, as this structure easily leads to spalling damage. wecs are found almost exclusively near or at the surface of bearing components, although they can propagate very deeply into the material [8]. it is therefore assumed that there is a link to rolling contact fatigue (rcf) mechanisms, which i s. averbeck et alii, frattura ed integrità strutturale, 38 (2016) 12-18; doi: 10.3221/igf-esis.38.02 13 are caused by the cyclic hertzian stresses in the contact area. this complex superposition of compressional and shear stresses changes over time as a rolling element passes over the raceway. in this area, defects, such as non-metallic inclusions or voids, can act as stress concentrators and enable crack initiation. a phenomenon called ‘butterflies’ which occurs in this region has been linked to white etching crack formation [9]. these are cracks around inclusions which are accompanied by white etching areas with virtually the same properties. it has to be considered, though, that butterflies are always oriented at 20-30 degrees to the contact surface, whereas wecs are not specifically oriented in any direction [1, 8]. experiments his study differs from earlier wec investigations in its approach to wec reproduction. instead of testing bearings, simple hourglass-shaped specimens made from 100cr6 steel were used (fig. 1). the specimens were heat treated at the skf gmbh bearing manufacturing plant in schweinfurt, germany, according to the regular bearing heat treatment standards of skf. after heat treatment, the specimens were ground to a roughness rz of 2µm and subsequently polished. figure 1: specimen geometry. load-controlled testing was carried out with superimposed axial and torsional loads on a servohydraulic mts 858 testing machine. two different approaches to the reproduction of rolling contact fatigue were used: in-phase and out-of-phase loading. for both load spectra, tests were performed in air and in partially synthetic sae 75/w80 transmission oil with a specific additive package. this is a typical gearbox oil which has been found to promote wec formation, most likely due to its additives [10]. all experiments were carried out at room temperature. in-phase loading transfer between rcf conditions and in-phase loading was based on achieving a similar highest equivalent stress. although the stress state in a bearing constantly changes over time, it is possible to identify a time and location where the equivalent stress is highest during one load cycle. this stress state can be modelled by in-phase compressional and torsional load, as demonstrated by burkart et al. [11]. the equivalent stresses were determined using von mises’ criterion and applied such that the ratio between the principal stresses’ difference, |σi-σii|/|σii-σiii|, was the same in the experiment as in a real bearing. there remains, of course, one main difference between a bearing and the experiment: while the maximum stress is located beneath the surface in the former, it occurs at the surface in the specimen. out-of-phase loading this load spectrum was based on work by beretta and foletti [12], who used out-of-phase compression-torsion loads to study coplanar crack propagation from artificial defects. they tested bearing steel specimens with two different load patterns, which were proposed by bearing manufacturer skf. the first pattern aimed at reproducing subsurface conditions, while the second should reproduce the conditions deeper under the bearing surface. it was found that only the t s. averbeck et alii, frattura ed integrità strutturale, 38 (2016) 12-18; doi: 10.3221/igf-esis.38.02 14 second pattern led to coplanar crack propagation, which can be interpreted as a sign that it better recreated rcf conditions. for this reason and for ease of controller programming, we adopted the second pattern, which is described below, for our study. the load pattern is defined by a) the phase shift between the compression and torsional loads and b) the ratio between maximum torsional and maximum compressional stress. with a phase shift of 90 degrees, the specimen experiences half of the maximum compression at the time of highest torsional stress. the ratio between the maximum stresses, σmax/τmax, is stated to be about 3.75 in [12]. with the proportion of the stresses thus set, the question remains which absolute values of stress are to be used. the equivalent stress can be made to match bearing conditions either at the time of maximum torsional stress, or at maximum compressional stress. both variants can be justified: the former causes the same stress state at the equivalent stress that is relevant for a bearing, but causes much greater equivalent stresses between the torsional maxima. the other variant, meanwhile, ensures that both the in-phase and the out-of-phase specimens are subjected to the same maximum equivalent stress but leads to a different stress state at the torsional maxima with lower equivalent stress. both variants were tested during our experiments, designated oop-a and oop-b. as wecs mostly lead to bearing failures in the early high cycle fatigue range, it was decided to run the fatigue tests only up to 106 cycles. this means that even with a limited load frequency of 10hz, it was possible to use realistic stress levels. as none of the in-phase and oop-b specimens fractured during testing, they were fatigued until fracture under alternating torsion with superimposed constant tension. all specimens were cleaned in acetone and ethanol in an ultrasonic bath before the microstructural examinations. afterwards, all specimens were examined with the scanning electron microscope. select specimens were studied in more detail with the combined sem/focused ion beam (fib) at the nanostructuring center (nsc) of the university of kaiserslautern. furthermore, some specimens were hot mounted in epoxy resin and subsequently ground, polished, and etched with 3% nitric acid (nital) for metallographic investigations. finally, microhardness tests were carried out using a diamond berkovich indenter at 50mn load. figure 2: fracture surface of an in-phase specimen tested in air. the approximate position of the metallographic section in fig. 4 is indicated by the dashed line. results in-phase experiments ig. 2 shows the fracture surface around the crack starting point after in-phase testing. the image is representative for specimens tested in air and in oil alike. there are three distinct regions with different fracture morphologies: a small lens at the specimen’s surface indicating the crack propagation during in-phase loading, a second area showing the fracture surface of stable crack growth during fatigue loading to fracture the specimen, and a third area of f s. averbeck et alii, frattura ed integrità strutturale, 38 (2016) 12-18; doi: 10.3221/igf-esis.38.02 15 final fracture. at higher magnification, a step can be seen between the upper and the lower half of the lens. this indicates that the crack propagated orthogonally to the specimen axis until it reached a length of 5-10µm, at which point the further crack propagation was controlled by mode i, i.e. perpendicular to the highest shear stress. it is possible that this change of direction coincides with the change from compression-torsion testing to torsional fracturing; however, it is equally possible that the crack propagation mode changed already during the testing phase, as fatigue cracks often change direction during their growth under multiaxial load conditions [13]. considering the morphological differences within the fatigue lens – a relatively smooth innermost area followed by a much coarser structure more outwardly – makes the latter explanation seem more likely, as this suggests a change of the crack growth mechanism. if this interpretation is correct, the fatigue crack propagated around 250µm during in-phase loading. a grainy surface structure can be observed at small scales near the above-mentioned step, and a very thin secondary crack extends from the surface to a depth of about 50µm. in order to examine the microstructure below the surface, focused ion beam (fib) cuts with a length of 30µm were made at two points on the fracture surface. this allowed for studying the top 5µm of the specimen microstructure. in both cut areas, a very fine-grained layer with a thickness of no more than 500nm could be observed at the surface (fig. 3). this grain refinement was not affected by whether the test was run in oil or air. a carbide is observable in the transition zone between the nanocrystalline structure and the unaltered material below. it could be argued that its shape indicates deformation and the onset of dissolution; this, however, remains debatable. figure 3: sem image of grain refinement and a carbide in the surface layer. figure 4: metallographic section of an in-phase specimen tested in air. the smaller image on the right is a magnification of the marked area. a metallographic examination of the opposite fracture surface reveals a white-etching zone on the fracture surface (fig. 4). under the light optical microscope (lom), this zone appears largely featureless with interspersed carbides. the thickness of the zone is around 1µm. its lateral dimension is much greater, spanning several hundred micrometres. this matches the diameter of the inner fatigue lens in fig. 2. the white etching zone remained visible after further grinding, polishing, and etching with about 50µm material removal. s. averbeck et alii, frattura ed integrità strutturale, 38 (2016) 12-18; doi: 10.3221/igf-esis.38.02 16 microhardness measurements in the white etching zone varied from 753hv to 1246hv, with an average value of 986hv (five measurements). this is significantly harder than the original martensitic microstructure, which has a hardness of 700750hv. out-of-phase experiments in contrast, no microstructurally changed areas could be found after the out-of-phase tests, independently of the surrounding medium (oil or air). the oop-a cycle was only used for very few tests, as it became apparent that specimens fractured very early in the high cycle fatigue regime or even in the low cycle fatigue regime (nb < 105). the oop-b tests showed no signs of microstructural change, although the cracks propagated in the same manner like the in-phase fatigue cracks. in some specimens, no crack formation was observed at all during the 106 cycles of testing. discussion hite etching microstructural changes are not an exclusive feature of white etching cracks, as the white layers found on rail steel (e.g. [14]) or in dry sliding contacts (e.g. [15]) demonstrate. it is thus necessary to carefully examine whether the zone formed during the compression-torsion experiments really is similar to wec microstructural change, and to eliminate any other formation possibilities and error sources. for example, the fracture stage which followed the testing cycle could have caused the microstructural changes. however, when comparing the inphase results with those of the oop-b tests, this becomes very unlikely. if the white etching layer was formed due to the torsional fracturing stage, it should appear on all specimens, not only on those tested in-phase. many formation mechanisms for white etching microstructure rely on a thermal component. this is especially true for the examples in dry sliding contacts mentioned above. no signs for thermal influences have been found in the experimental results. the fact that the white layers formed regardless of whether the specimen was tested in air or in oil rules out a mechanism like those in dry sliding contacts. aside from these aspects ex negativo, the white etching surface layer produced by in-phase testing is in several aspects similar to the altered microstructure found in wecs. the fib images, for example, closely resemble those presented by franke et al. [16]. when viewed in the light optical microscope, the appearance of the white etching structure is very similar to wec found in the literature. the hardness values also closely match those reported for wec. the thickness of the white etching structures never exceeded 1µm in the specimen, mostly amounting to only a few hundred nanometres. this is well within the range reported for bearing wecs; however, the volume of white etching microstructure can vary widely in bearings [8]. in most cases, the cracks did not seem to develop branches. small cracks at an angle to the fracture surface could be found in some specimens, one example being shown in fig. 2. whether this is a genuine wec-type branch or simply a secondary crack from fatigue and fracture presently cannot be answered. an additional fib cut might serve to clarify this. the cracks never seemed to nucleate at inclusions or voids; at least, no traces of such were found in the vicinity. it is therefore assumed that either surface or microstructural inhomogeneities were responsible for crack initiation. the most ambiguous aspect of the results is the question of carbides. while they are usually absent or in the process of dissolution in bearing wecs, their presence is no decisive argument against wecs [6]. judging from the light optical microscope observations, numerous carbides were interspersed in the white etching areas found in this study. the limited magnification of the lom makes it impossible to assess whether they are affected by the surrounding microstructural change. nor could the fib investigation deliver a conclusive result. while the carbide in fig. 3 might be dissolving, others retained a largely globular shape with sharp borders to the surroundings. generally, it should be remembered that the testing time of 106 cycles was moderate. a longer test, e.g. up to 107 cycles, could serve to clarify whether carbides dissolve or not. this could also provide insights to whether the thickness of the white structure will further increase over time or not. the early failures under load spectrum oop-a were probably a result not only of the higher equivalent stresses, but also of the 90° phase shift. fatemi and shamsaei [13] cite several reports that out-of-phase loads have a significantly more detrimental effect on fatigue properties than in-phase loads. the higher compressional loads themselves probably would not be as problematic, as they would tend to close any incipient cracks. no satisfactory explanation could be found for the behaviour of the oop-b tests, in which no observable microstructural change was found despite the fact that the crack paths were very similar to those from in-phase testing. the most obvious explanation is that the equivalent stresses were too low in the crucial points in each cycle, i.e. at the time of maximum w s. averbeck et alii, frattura ed integrità strutturale, 38 (2016) 12-18; doi: 10.3221/igf-esis.38.02 17 torsional loading. it is also possible that the ratio between compressional and torsional load at the torsional maxima prevented microstructural change and even crack formation, as was the case in several specimens. summary olling contact fatigue conditions were simulated with in-phase and out-of-phase cyclic multiaxial loads. it was found that the material behaviour differed greatly between the two load patterns. while the out-of-phase load led to regular crack initiation and propagation, zones of altered microstructure were found adjacent to fatigue cracks in the in-phase specimens. detailed investigations with sem, fib, nanoindentation and metallographic methods revealed that these zones resemble the microstructural change in the bearing damage phenomenon white etching cracks. acknowledgements e would like to thank skf gmbh, schweinfurt, for supporting us with the heat treatment of the specimens. further thanks go to dr. thomas löber of the nanostructuring center (nsc) at the university of kaiserslautern for his help with the fib examinations. this study is part of a project funded by the deutsche forschungsgemeinschaft (dfg) under grant ke 1426/6-1. references [1] evans, m.-h., white structure flaking (wsf) in wind turbine gearbox bearings: effects of ‘butterflies’ and white etching cracks (wecs), tribol. int., 28 (2012) 3–22. [2] gegner, j., tribological aspects of rolling bearing failures, in: kuo, c.-h. (ed.), tribology lubricants and lubrication, intech, rijeka, (2011) 33–93. [3] stadler, k., lai, j., vegter, r.h., a review: the dilemma with premature white etching crack (wec) bearing failures, in: beswick, j.m. (ed.), bearing steel technologies, astm international, west conshohocken, (2014) 487– 508. [4] west, o., diederichs, a.m., alimadadi, h., dahl, k.v., somers, m., application of complementary techniques for advanced characterization of white etching cracks, pract. metallogr., 50 (2013) 410–431. [5] greco, a., sheng, s., keller, j., erdemir, a., material wear and fatigue in wind turbine systems, wear, 302, (2012) 1583–1591. [6] harada, h., mikami, t., shibata, m., sokai, d., yamamoto, a., tsubakino, h., microstructural changes and crack initiation with white etching area formation under rolling/sliding contact in bearing steel, isij int., 45 (2005) 1897–1902. [7] evans, m.-h., wang, l., jones, h., wood, r., white etching crack (wec) investigation by serial sectioning, focused ion beam and 3-d crack modelling, tribol. int., 65 (2013) 146–160. [8] ruellan du crehu, arnaud, tribological analysis of white etching crack (wec) failures in rolling element bearings, phd thesis, insa lyon, (2014). [9] evans, m.-h., richardson, a.d., wang, l., wood, r.j.k., anderson, w.b., confirming subsurface initiation at nonmetallic inclusions as one mechanism for white etching crack (wec) formation, tribol. int., 75 (2014) 87–97. [10] surborg, h., einfluss von grundölen und additiven auf die bildung von wec in wälzlagern, shaker, aachen, (2014). [11] burkart, k., bomas, h., schroeder, r., zoch, h.-w., rolling contact and compression-torsion fatigue of 52100 steel with special regard to carbide distribution, in: beswick, j.m. (ed.), bearing steel technologies, astm international, west conshohocken, (2012) 218–236. [12] beretta, s., foletti, s., propagation of small cracks under rcf: a challenge to multiaxial fatigue criteria, in: carpinteri, a., iacoviello, f., pook, l.p., susmel, l. (eds.), proceedings of the 4th international conference on crack paths (cp 2012), gruppo italiano frattura, cassino, (2012) 15–28. [13] fatemi, a., shamsaei, n., multiaxial fatigue: an overview and some approximation models for life estimation, int. j. fatigue, 33 (2011) 948–958. [14] baumann, g., fecht, h.j., liebelt, s., formation of white-etching layers on rail treads, wear, 191, (1996) 133–140. r w s. averbeck et alii, frattura ed integrità strutturale, 38 (2016) 12-18; doi: 10.3221/igf-esis.38.02 18 [15] griffiths, b.j., mechanisms of white layer generation with reference to machining and deformation processes, j. tribol., 109 (1987) 525–530. [16] franke, j., surborg, h., fahl, j., elfrath, t., blass, t., holweger, w., merk, d., influence of tribolayer on wec roller bearing fatigue performed on a fe8 test rig, in: proceedings tae 19th international colloquium tribology, technische akademie esslingen, esslingen, (2014) 163–175. << /ascii85encodepages false /allowtransparency false /autopositionepsfiles true /autorotatepages /none /binding /left /calgrayprofile (dot gain 20%) /calrgbprofile (srgb iec61966-2.1) /calcmykprofile (u.s. web coated \050swop\051 v2) /srgbprofile (srgb iec61966-2.1) /cannotembedfontpolicy /error /compatibilitylevel 1.4 /compressobjects /tags /compresspages true /convertimagestoindexed true /passthroughjpegimages true /createjobticket false /defaultrenderingintent /default /detectblends true /detectcurves 0.0000 /colorconversionstrategy /cmyk /dothumbnails false /embedallfonts true /embedopentype false /parseiccprofilesincomments true /embedjoboptions true /dscreportinglevel 0 /emitdscwarnings false 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/hrv (za stvaranje adobe pdf dokumenata najpogodnijih za visokokvalitetni ispis prije tiskanja koristite ove postavke. stvoreni pdf dokumenti mogu se otvoriti acrobat i adobe reader 5.0 i kasnijim verzijama.) /hun 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can be opened with acrobat and adobe reader 5.0 and later.) >> /namespace [ (adobe) (common) (1.0) ] /othernamespaces [ << /asreaderspreads false /cropimagestoframes true /errorcontrol /warnandcontinue /flattenerignorespreadoverrides false /includeguidesgrids false /includenonprinting false /includeslug false /namespace [ (adobe) (indesign) (4.0) ] /omitplacedbitmaps false /omitplacedeps false /omitplacedpdf false /simulateoverprint /legacy >> << /addbleedmarks false /addcolorbars false /addcropmarks false /addpageinfo false /addregmarks false /convertcolors /converttocmyk /destinationprofilename () /destinationprofileselector /documentcmyk /downsample16bitimages true /flattenerpreset << /presetselector /mediumresolution >> /formelements false /generatestructure false /includebookmarks false /includehyperlinks false /includeinteractive false /includelayers false /includeprofiles false /multimediahandling /useobjectsettings /namespace [ (adobe) (creativesuite) (2.0) ] /pdfxoutputintentprofileselector /documentcmyk /preserveediting true /untaggedcmykhandling /leaveuntagged /untaggedrgbhandling /usedocumentprofile /usedocumentbleed false >> ] >> setdistillerparams << /hwresolution [2400 2400] /pagesize [612.000 792.000] >> setpagedevice microsoft word numero_35_art_41 h. dündar et alii, frattura ed integrità strutturale, 35 (2016) 360-367; doi: 10.3221/igf-esis.35.41 360 focussed on crack paths multiple and non-planar crack propagation analyses in thin structures using fcpas h. dündar, a. o. ayhan department of mechanical engineering, sakarya university, 54187, sakarya, turkey hakan.dundar@ogr.sakarya.edu.tr, ayhan@sakarya.edu.tr abstract. in this study, multiple and non-planar crack propagation analyses are performed using fracture and crack propagation analysis system (fcpas). in an effort to apply and validate fcpas procedures for multiple and non-planar crack propagation analyses, various problems are solved and the results are compared with data available in the literature. the method makes use of finite elements, specifically three-dimensional enriched elements to compute stress intensity factors (sifs) without special meshing requirements. a fatigue crack propagation criterion, such as paris-erdoğan equation, is also used along with stress intensity factors to conduct the simulation. finite element models are generated within ansys™ software, converted into and solved in frac3d program, which employs enriched crack tip elements. having computed the sifs for a given crack growth increment and using a growth criterion, the next incremental crack path is predicted and the fracture model is updated to reflect the non-planar crack growth. this procedure is repeated until cracks reach a desired length or when sifs exceed the fracture toughness of the material. it is shown that fcpas results are in good agreement with literature data in terms of sifs, crack paths and crack growth life of the structure. thus, accuracy and reliability of fcpas software for multiple and non-planar crack propagation in thin structures is proven. keywords. fracture; nonplanar crack growth; crack propagation. introduction lthough in-plane crack propagation under mode-i loading conditions is very common for machinery parts and structures and is still a popular research subject, some parts can fail under mixed mode loading, causing nonplanar crack surface. this type of crack propagation can occur under mixed mode loading conditions or when crack surface is not perpendicular to an axial load. under mixed mode conditions, multiple cracks growing in a nonplanar manner can even be more critical for the structure due to interaction effects. cracks can accelerate each other, coalesce or change direction due to the interaction effects. this situations can be seen in thin walled structures such as sheet or integral panels of aircrafts or engine parts that are subjected to high temperatures. other examples can also be given in applications in the areas of transportation, energy and aviation. therefore, accurate prediction of nonplanar crack propagation in machine parts or structures is very important to assure safety, efficiency and reliability of some engineering structures. in the literature, there are several numerical and experimental studies that deal with fracture and propagation analyses of multiple cracks and nonplanar crack growth. one of the numerical studies is by wessel et.al [1]. in that study, wessel et.al a h. dündar et alii, frattura ed integrità strutturale, 35 (2016) 360-367; doi: 10.3221/igf-esis.35.41 361 used boundary element method (bem) and compared their results to experimental data. jonesa et.al. [2] analyzed interacting multiple cracks using finite element method (fem) and a hybrid formulation which represents stiffness changes. yan analyzed interacting multiple cracks and complex crack configurations in linear elastic media using an effective numerical method which is an extended form of bueckners’ princible [3]. leonel et.al used two-dimensional bem method for multiple crack propagation analyses [4]. they used maximum circumferential stress theory for evaluating stress intensity factors (sif) and propagation angle, and paris’ law to predict structural life. another 2d linear elastic fracture mechanics (lefm) problem is analyzed by yan [5] using bem method for propagating multiple cracks. yan also used maximum circumferential stress theory and paris’ law. a java-based boundary element program front end was developed by hsieh et.al. for fracture analysis of multiple curvilinear cracks in general anisotropic materials [6]. citarella et.al. compared dbem and fem methods by 3d fatigue crack growth of two anti-symmetric cracks [7]. price and trevelyan analyzed two eccentric crack that propagate nonplanarly in a thin geometry [8]. bouchard and chastel used maximum circumferential stress criterion, strain energy density fracture criterion and maximum strain energy release rate criterion for single and multiple nonplanar crack growth analyses [9]. the objective of this study is to apply, demonstrate and validate usage of fcpas for multiple cracks propagating in a non-planar manner under fatigue loading. in the study, finite element method with enriched elements is used to obtain stress intensity factors (sif) [10]. sif values are calculated during nodal displacement calculation which is a step of finite element (fe) solution. by using enriched element method, sifs are calculated accurately and no special re-processing or meshing techniques and post-processing of results are needed. it is shown that fcpas results for multiple non-planar cracks agree well with those from the literature. method or nonplanar crack propagation analyses, fcpas finite element software is used. also ansys™ [11] commercial fe software is used for generating fe model of the cracked geometry. all calculations for sifs and propagation process are performed by frac3d solver of fcpas software. crack propagation process with fcpas software consists of fe modeling of cracked geometry, solution step, propagation of the cracks and best ellipse fit for the propagated cracks. these steps are repeated until failure or some other geometric limit. work flow scheme of fcpas analysis is shown in fig. 1. fcpas solver, frac3d, uses enriched element method for calculating sifs [12]. a general form of displacements for enriched elements is given in eqs. 1-3. 0 1 1 1 0 1 1 0 1 ( , , ) ( , , ) ( , , ) ( , , ) ( , , ) ( ) ( , , ) ( , , ) ( , , ) ( ) ( , , ) ( , , ) ( , , ) ntipm m i j j u j uj i i j j i ntipm i u j uj i ii j i m u j uj j u n u z f n f n k z g n g n k z h n h n                                                                            1 ( ) ntip i i iii i k         (1) 0 1 1 1 0 1 1 0 1 ( , , ) ( , , ) ( , , ) ( , , ) ( , , ) ( ) ( , , ) ( , , ) ( , , ) ( ) ( , , ) ( , , ) ( , , ) ntipm m i j j v j vj i i j j i ntipm i v j vj i ii j i m v j vj j v n v z f n f n k z g n g n k z h n h n                                                                            1 ( ) ntip i i iii i k         (2) f h. dündar et alii, frattura ed integrità strutturale, 35 (2016) 360-367; doi: 10.3221/igf-esis.35.41 362 0 1 1 1 0 1 1 0 1 ( , , ) ( , , ) ( , , ) ( , , ) ( , , ) ( ) ( , , ) ( , , ) ( , , ) ( ) ( , , ) ( , , ) ( , , ) ntipm m i j j w j wj i i j j i ntipm i w j wj i ii j i m w j wj j w n w z f n f n k z g n g n k z h n h n                                                                            1 ( ) ntip i i iii i k         (3) figure 1: work scheme of fcpas finite element software for analysis of multiple cracks. in eqs. 1-3, , and are local coordinates in enriched elements, uj, vj, and wj are the nodal displacement, nj are regular finite element shape functions, z0 is a zeroing function which varies between 0 and 1, m is number of nodes in the element, fj, gj and hj represent the mode i, ii and iii components of crack tip displacements, ki, kii and kiii are the unknown sifs. finally is the local isoparametric coordinate along the crack front that varies between -1 and 1. after fe solution and sif calculation, cracks are propagated taking into account crack interaction effects. a modified form of paris-erdoğan equation (eq. 4) is used for this process. max max n i i k a a k          (4) in the next step, if cracks are to be represented in elliptical form, a best ellipse fit method is applied to propagated crack tip nodes. then ellipse parameters are given to ansys software as new crack dimensions. for through the thickness cracks in thin walled structures, there is no need for ellipse fitting and any crack tip node coordinates are used for new crack locations. after all propagation analyses are completed, a crack growth law such as paris-erdoğan formulation (eq. 5) is used for prediction of crack propagation life [10].  nda c k dn   (5) h. dündar et alii, frattura ed integrità strutturale, 35 (2016) 360-367; doi: 10.3221/igf-esis.35.41 363 crack propagation analyses orner, surface and through-thickness cracks under mode-i conditions in different geometries are analyzed and results are compared to those from the literature which are experimental test data and/or numerical results. fcpas results showed very good agreement with the literature data in terms of sifs, crack profiles/paths and propagation lives. some of these studies can be found in [13] and [14]. in addition to the above mode-i propagation analyses including multiple mode-i cracks, several multiple-non-planar crack propagation analyses are also performed using fcpas. in this study, two different nonplanar crack propagation analyses are performed. first set of analyses represent the study by yan [15]. a thin plate which contains two equal sized cracks is subjected to tensile stress. one of the cracks is perpendicular to the loading axis of the plate, and the second crack makes a 45-degree angle. details of the geometry and loading conditions can be seen in fig. 2. figure 2: details of the cracked model [15]. in fig. 2, l=4 mm, =45 degree, h=8 mm, width and height of the plate are taken as 160 mm to simulate large plate conditions relative to the crack sizes and the thickness of the plate is taken as 5 mm to assure plane stress conditions. load and loading ratio (r) are 150.42 mpa and 0.048, c constant of the material is 1.039e-10, constant n is 2.7438 [15]. modulus of elasticity and poisson’s ratio are used as 70000 mpa and 0.321 respectively. same analysis as that of yan’s is performed using fcpas and results are compared. crack path comparison is shown in fig. 3. it should be noted that for the incremental crack propagation analyses presented in this paper, the propagation angles are computed using the maximum tangential stress (mts) criterion proposed by erdoğan and sih [16]. according to this criterion, under mixed mode loading, crack extends in a direction such that mode-ii sif becomes zero. figure 3: crack path comparison between fcpas and yan’s analysis. although the loading is uniaxial in the problem considered, because of the shear stress which occurs on the slanted crack plane, kii stress intensity factors are generated at its crack tips causing the tips to grow initially in a non-planar manner. c h. dündar et alii, frattura ed integrità strutturale, 35 (2016) 360-367; doi: 10.3221/igf-esis.35.41 364 thus, initially, this effect is only near the tips of the slanted crack (tips c and d). it can be seen from the above paths that, the 45-degree slanted crack becomes nearly perpendicular to the loading direction after the first step of the crack propagation analysis. however, it also seen that as the cracks keep growing, especially between crack tips b and c, stress re-distributions take place, which cause these crack tips to continue changing directions. this can be seen in figs. 4 and 5, where ki and kii sifs are plotted as a function of absolute (curved) crack length. it is seen from these figures that crack tips a and d keep propagating purely in mode-i after the initial mixed-mode deflection, i.e., kii sif is very close to zero for these crack tips during crack growth. it should also be noted that during the analyses presented in this paper, the maximum crack length increment among all propagation steps is taken to be nearly one-tenth of the largest crack length and that these steps can further be refined to further check the convergence of the crack path and life predictions. however, the chosen steps yield good agreement with ref. [15] in terms of the paths of the crack tips. figure 4: mode-i and mode-ii stress intensity factors during crack growth – crack tips a and b. figure 5: mode-i and mode-ii stress intensity factors during crack growth – crack tips c and d. in an effort to compare the predictions of the current study with those of yan’s, equivalent sifs vs. number of cycles are plotted in fig. 6. to be able to make comparisons, equivalent sifs are calculated in the same way as ref. [15].  0 0 0 1 cos 1 cos 3 sin 2 2 e i iik k k           (6) in eq. (6),0 is the crack growth angle, ki and kii are mode-i and mode-ii stress intensity factors. h. dündar et alii, frattura ed integrità strutturale, 35 (2016) 360-367; doi: 10.3221/igf-esis.35.41 365 figure 6: equivalent sif comparisons between fcpas and yan’s [15] numerical results. while there is no information about the unit of constant c of the material in yan’s study, load and material constant c used in the current simulations are, 15.333 n/mm2 (value of ref. [15] given in kg unit divided by 9.81) and 1.02e-9 (value of ref. [15] multiplied by 9.81) to match the results with the same number of cycles. in that case, it is concluded from this application that fig. 3 shows very good agreement in terms of crack path predictions and that fig. 6 also shows good agreement, especially in the beginning and end of the simulation. another non-planar crack propagation analysis performed in this study is about a plate under uniaxial stress containing a hole and multiple cracks [17]. judt and ricoeur’s study [17] contains three cracks analyzed by interaction integral. the same multiple nonplanar cracks problem is analyzed by fcpas. geometry, loading and boundary condition details of the problem can be seen in fig. 7. figure 7: geometry and boundary condition details of three cracked model (dimensions are in mm)[17]. figure 8: crack path comparison between fcpas and the literature data [17]. h. dündar et alii, frattura ed integrità strutturale, 35 (2016) 360-367; doi: 10.3221/igf-esis.35.41 366 the plate is under displacement controlled cyclic loading. 0.005 mm displacement is applied at the bottom area of the plate to ensure tension loading and top area is fixed. al-7075 is chosen as material of the plate and modulus of elasticity and poisson’s ratio are 72000 mpa and 0.33, respectively. material constant n is 1.34 and fracture toughness is 23.9 mpa m for the material [17]. thickness of the plate is taken as 3 mm to simulate plane stress conditions. having performed crack propagation analyses using the same procedure employed in the first application, obtained results are compared to those from judt and ricoeur’s [17] study. comparison of crack paths between fcpas and ref. [17] is shown in fig. 8. as can be seen from fig. 8, eccentricity of the cracks causes shear stress and therefore, kii sifs. thus, cracks change their direction from the horizontal plane. vertical distance between 2nd and 3rd cracks are very small and therefore, sifs in this region are higher than the region around the 1st crack. as a result, 2nd and 3rd cracks propagate faster than the 1st crack, which propagate at a slower rate. comparisons of equivalent sif vs. number of crack growth steps, as given in ref. [17], are shown in fig. 9. it should be noted that, in the current analyses, much less number of increments (17 steps) are used compared to ref. [17] (325 steps). equivalent sifs are calculated using eq. (7) [17].  22 1 1 4 2 2 i e i ii k k k k   (7) i=1.155 [17], ki and kii are mode-i and mode-ii stress intensity factors. figure 9: sif comparison between fcpas and ref. [17]. fig. 8 and fig. 9 show that fcpas results are very close to those of judt and ricoeur [17] in terms of crack paths and sif vs. number of crack growth steps. therefore, this case serves as a second validation problem for application of fcpas crack propagation analysis procedures to multiple cracks in thin-walled structures growing in a non-planar manner. conclusions n this study, three-dimensional non-planar crack propagation analyses for thin-walled structures were performed using fcpas (fracture and crack propagation analysis system). two case studies related to multiple cracks with non-planar growth were presented. results of these studies in terms of crack paths and stress intensity factor variations with number of cycles showed good agreement with analysis data from the literature. thus, it was concluded that non-planar growths of multiple cracks in thin-walled structures can accurately be simulated using fcpas. further developments in fcpas to be able to analyze non-planar crack growth of surface and corner cracks under mode-i, ii and iii conditions are planned as future studies. i h. dündar et alii, frattura ed integrità strutturale, 35 (2016) 360-367; doi: 10.3221/igf-esis.35.41 367 acknowledgements he financial support by the scientific and technological research council of turkey (tübi̇tak) for this study under project no 113m407 is gratefully acknowledged. references [1] wessel, c., cisilino, a., santi, o., otegui, j., chapetti, m., numerical and experimental determination of threedimensional multiple crack growth in fatigue, theoretical and applied fracture mechanics, 35 (2001) 47-58. [2] jonesa, r., peng, d., pitt, s., assessment of multiple flat elliptical cracks with interactions, theoretical and applied fracture mechanics, 38 (2002) 281-291. [3] yan, x., stress intensity factors for interacting cracks and complex crack configurations in linear elastic media, engineering failure leonel, e.d., venturini, w.s., multiple random crack propagation using a boundary element formulation, engineering fracture mechanics, 78 (2011) 1077-1090. [4] analysis, 14 (2007) 179-195. [5] gravouil, a., moës, n., belytschko, t., non-planar 3d crack growth by the extended finite element and level setspart ii: level set update. int. j. numer. meth. engng, 53 (2002) 2569-2586. [6] hsieh, j.h., denda, m., redondo, j., marante, m.e., flórez-lópez, j,. electronic handbook of fracture: a java-based boundary element program for fracture analysis of multiple curvilinear cracks in the general anisotropic solids. advances in engineering software, 39 (2008) 395-406. [7] pierres, e., baietto, m.c., gravouil, a. experimental and numerical analysis of fretting crack formation based on 3d x-fem frictional contact fatigue crack model, comptes rendus mécanique, 339 (2011) 532-551. [8] citarella, r., cricrì, r., comparison of dbem and fem crack path predictions in a notched shaft under torsion, engineering fracture mechanics, 77 (2010) 1730-1749. [9] bouchard, p.o., bay, f., chastel, y., numerical modelling of crack propagation: automatic remeshing and comparison of different criteria, comput. methods appl. mech. engrg., 192 (2003) 3887-3908. [10] ayhan, a.o., simulation of three-dimensional fatigue crack propagation using enriched finite elements, computers and structures, 89 (2011) 801-812. [11] ansys, version 12.0, ansys inc., canonsburg, pa, usa, 2009. [12] ayhan, a.o., nied h.f., stress intensity factors for three-dimensional surface cracks using enriched elements, int. j. numer. meth. engng., 54 (2002) 899-921. [13] dündar, h., ayhan, a.o., finite element modeling of growing multiple three-dimensional cracks under cyclic loads, 10th international fracture conference, kayseri, turkey, april 24-25, 2014, 28-36. [14] derya, m., ayhan, a.o., numerical simulation of three-dimensional mode-i crack propagation using fcpas: first set of practical case studies, 10th international fracture conference, kayseri, turkey, april 24-25, 2014, 28-36. [15] yan, x., automated simulation of fatigue crack propagation for two-dimensional linear elastic fracture mechanics problems by boundary element method, engineering fracture mechanics, 74 (2007) 2225-2246. [16] erdogan, f., sih, g.c., on the crack extension in plane loading and transverse shear, j. basic eng., 85 (1963) 519527. [17] judt, o.p., ricoeur, a., crack growth simulation of multiple cracks systems applying remote contour interaction integrals, theoretical and applied fracture mechanics, 75 (2015) 78-88. t << /ascii85encodepages false /allowtransparency false /autopositionepsfiles true /autorotatepages /none /binding /left /calgrayprofile (dot gain 20%) /calrgbprofile (srgb iec61966-2.1) /calcmykprofile (u.s. web coated \050swop\051 v2) /srgbprofile (srgb iec61966-2.1) /cannotembedfontpolicy /error /compatibilitylevel 1.4 /compressobjects /tags /compresspages true /convertimagestoindexed true /passthroughjpegimages true /createjobticket false /defaultrenderingintent /default /detectblends true /detectcurves 0.0000 /colorconversionstrategy /cmyk /dothumbnails false /embedallfonts true /embedopentype false /parseiccprofilesincomments true /embedjoboptions true /dscreportinglevel 0 /emitdscwarnings false /endpage -1 /imagememory 1048576 /lockdistillerparams false /maxsubsetpct 100 /optimize true /opm 1 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can be opened with acrobat and adobe reader 5.0 and later.) >> /namespace [ (adobe) (common) (1.0) ] /othernamespaces [ << /asreaderspreads false /cropimagestoframes true /errorcontrol /warnandcontinue /flattenerignorespreadoverrides false /includeguidesgrids false /includenonprinting false /includeslug false /namespace [ (adobe) (indesign) (4.0) ] /omitplacedbitmaps false /omitplacedeps false /omitplacedpdf false /simulateoverprint /legacy >> << /addbleedmarks false /addcolorbars false /addcropmarks false /addpageinfo false /addregmarks false /convertcolors /converttocmyk /destinationprofilename () /destinationprofileselector /documentcmyk /downsample16bitimages true /flattenerpreset << /presetselector /mediumresolution >> /formelements false /generatestructure false /includebookmarks false /includehyperlinks false /includeinteractive false /includelayers false /includeprofiles false /multimediahandling /useobjectsettings /namespace [ (adobe) (creativesuite) (2.0) ] /pdfxoutputintentprofileselector /documentcmyk /preserveediting true /untaggedcmykhandling /leaveuntagged /untaggedrgbhandling /usedocumentprofile /usedocumentbleed false >> ] >> setdistillerparams << /hwresolution [2400 2400] /pagesize [612.000 792.000] >> setpagedevice microsoft word numero_62_art_38_3653.docx i. shardakov et alii, frattura ed integrità strutturale, 62 (2022) 561-572; doi: 10.3221/igf-esis.62.38 561 estimation of nonlinear dependence of fiber bragg grating readings on temperature and strain using experimental data i. shardakov, a. shestakov, i. glot, v. epin, g. gusev, r. tsvetkov institute of continuous media mechanics, ural branch, russian academy of science, 1, korolev street, perm, russia shardakov@icmm.ru, https://orcid.org/0000-0001-8673-642x shap@icmm.ru, https://orcid.org/0000-0003-3387-7442 glot@icmm.ru, https://orcid.org/0000-0002-2842-7511 epin.v@icmm.ru, https://orcid.org/0000-0001-5625-2678 gusev.g@icmm.ru, https://orcid.org/0000-0002-9072-0030 flower@icmm.ru, https://orcid.org/0000-0001-9617-407x abstract. the readings of the bragg grating are determined based on the optical radiation reflected from it. a quantitative characteristic of this radiation is the wavelength at which the maximum power of the optical signal is achieved. this characteristic is called the central wavelength of the grating. the central wavelength shift depends on temperature and strain. as a rule, a linear approximation of this dependence is used. however, from the available literature it is known that, the grating wavelength shift demonstrates a strong nonlinear dependence on temperature at 5<t<200k and a weak quadratic dependence close to room temperature. thus far, the authors have not found studies that consider all terms in the quadratic expansion of the central wavelength of the bragg grating as a function of temperature and strain at near-room temperatures. our work is intended to fill this gap. the article describes an experiment in which an optical fiber with bragg grating was subjected to loading using three different weights. a step-wise temperature change from 5 to 100 0с was realized for each weight. based on these data, all terms of the quadratic expansion of the desired function are determined. the contribution of each term is estimated. keywords. fiber bragg grating; sensor calibration; temperature compensation; quadratic approximation. citation: shardakov, i., shestakov, a., glot, i., epin, v., gusev, g., tsvetkov, r.., estimation of the nonlinear dependence of the indications of a fiber bragg grating on temperature and strain from experimental data, frattura ed integrità strutturale, 62 (2022) 561-572. received: 02.07.2022 accepted: 09.09.2022 online first: 13.09.2022 published: 01.10.2022 copyright: © 2022 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. introduction he fiber bragg gratings are used as optical temperature and strain sensors. optical sensors have a number of advantages over traditional measuring facility: optical sensors are not sensitive to electromagnetic interference, can be easily create long measuring lines, allow switching of many sensors on one measuring line, have very small size and weight, have low heat capacity, the optical line has a low thermal conductivity, line and sensor demonstrate high t https://youtu.be/fnqhrroifxw i. shardakov et alii, frattura ed integrità strutturale, 62 (2022) 561-572; doi: 10.3221/igf-esis.62.38 562 explosion resistance. due to these advantages, optical sensors have found wide application in the monitoring of buildings, bridges, pipelines, mines and tunnels due to their great length. fiber optic sensors are widely used for monitoring composite materials, as they can be embedded in the material without weakening its strength characteristics due to small sizes of sensors and measuring line. a variety of sensing devices such as the displacement, strain, pressure, acceleration and temperature sensors are created based on the fiber bragg gratings. the fields of application of fiber bragg sensors are described in [1, 2]. the readings of the bragg grating sensor are calculated based on the shift of the central wavelength of the grating. this index depends on temperature and strain. generally, it is not known, which of these factors causes the wavelength shift so there is a measurement uncertainty. as a rule, temperature measurements are conducted at a free state of the fiber within the grating area, when it is not subjected to external loads. in this case, the strain is known and is expressed in terms of temperature. for strain measurements different methods are used [3]. the simplest and most reliable method is to use two gratings: one grating is attached to the test object and the second grating is freely located near the first one [4]. in this case, temperature sensing is provided by the second grating. knowing the temperature and wavelength shift of the first grating it is possible to evaluate its strain. one further implementation of this approach is based on the method, in which a bragg grating designed to determine temperature is attached to a metal plate with a known coefficient of thermal expansion. another method that implements the use of two gratings is that the gratings are fixed in the stretched and compressed zones of the sensor, in this case the difference in wave shifts does not depend on temperature [5,6]. there are also many techniques that do not require maintaining a special mechanical state of one of the gratings [7-13]. these methods use not only a shift of the grating spectrum, but also a change in the shape of this spectrum or changes in the amplitudes of parts of the spectrum. the individual calibration of grating can be reasonably done in the following cases: temperature compensation is performed based on the temperature measured by any means; sensor design is supposed to maintain a free state of the fiber in the bragg grating area; sensor design does not allow individual calibration of the sensor assembly. this is especially true for high-precision strain gauges, the design of which involves fiber attachment by soldering or welding the metal-coated fiber [3]. in this case, long-term stability of measurements is achieved. as a rule, the calibration of bragg grating sensors is carried out in the framework of a linear approximation [3, 5-15]. although there has been experimental evidence that the temperature dependence of a shift of the central wavelength of the grating has a strongly nonlinear character at 5<t<200 k [1,16,17]. there are also studies, which have established a reliably measured quadratic dependence of the grating wavelength shift on temperature at -30<t<80 0c [18,19]. in [18], an explanation of the temperature dependent non-linear behavior of the fiber bragg grating is given based on the ghosh model, which relates the non-linear behavior of the refractive index of quartz glass to temperature. note that in addition to nonlinearity associated with temperature, there is nonlinearity due to deformation. this is shown in [18]. the authors of this work conducted an experiment, in which the fiber was subjected to loading at constant temperature and plotted graphs of the error of a linear approximation of the dependence of the wavelength shift on strain. as is evident from this graph, there is a weak negative quadratic dependence. however, they did not quantify this relationship. thus, for nearroom temperatures the present-day literature provides comprehensive information on the linear terms of the expansion of the grating wavelength shift ∆λ as the function of strain с1·ε and temperature с2·∆t, there are estimates for the quadratic expansion term с4·∆t2. however, we have not found any information on the consideration of quadratic с3·ε2 and cross с1·ε·∆t terms of the expansion. our paper is intended to fill this gap. the paper is structured as follows. section 1 describes the principle of operation of the fiber bragg grating and provides substantiation of parameters used to make calibration. section 2 describes the experimental setup. the experimental results and the data processing algorithm are discussed in section 3. the parameters of the full quadratic approximation are determined in section 4. the last section summarizes the results obtained. the working principle of the fiber bragg grating he bragg grating is a region of an optical fiber, in which the refractive index periodically changes. the period of this structure is called the period of the bragg grating. a structural diagram of the grating is shown in fig. 1. the fiber area with applied grating reflects a narrow part of the optical radiation spectrum, which is determined by the grating period, the stress-strain state of the fiber in the grating area, and temperature. the measurement process involves the generation of a broadband optical signal and the registration of the reflected spectrum. t i. shardakov et alii, frattura ed integrità strutturale, 62 (2022) 561-572; doi: 10.3221/igf-esis.62.38 563 figure 1: structural diagram of the bragg grating in an optical fiber. the sensor indications are determined by the shift of the spectrum of the reflected optical signal. two spectra of the optical signal are shown in fig. 2. spectrum 1 corresponds to the grating in the initial state, spectrum 2 to the deformed state. the spectra are characterized by their central wavelengths λ1 and λ2. the shift of the spectrum is quantified by the change in the central wavelength ∆λ= λ2λ1. figure 2: spectra of optical signals (spectrum 1 grating in the initial state, spectrum 2 grating in the deformed state) the central wavelength of the grating is determined by the expression       2 , ln t lε (1) where: n(t, ε) is the refractive index of quartz in the grating area; t is temperature; ε is the strain tensor of the fiber in the grating area; l is the grating period; εl is the total strain along the fiber. let us define the reference state of the grating, which is characterized by zero strains, the reference state temperature t0, and the grating period in the reference state l0. the wavelength in the reference state is defined by        0 0 0 0 02 , 2n t l n l0 (2) where: n0 is the refractive index in the reference state. the current value of the refractive index represented in increments relative to the reference state is written as            0 0 0, , ,n t n t n t t n nε 0 ε (3) where: ∆n – is the increment of the refractive index. the grating period in the actual (deformed) state is determined by the expression       0 1l ll l (4) the wave length in the actual state (1), according to expressions (3) and (4) takes the following form i. shardakov et alii, frattura ed integrità strutturale, 62 (2022) 561-572; doi: 10.3221/igf-esis.62.38 564           0 02 1 ln n l (5) after opening the brackets we get               0 0 0 0 02 2 2 1l ln l n l n l (6) the multiplication of the numerator and denominator of the summand at ∆n by n0 yields                 0 0 0 0 0 0 0 2 2 2 1l l n n l n l n l n (7) the underlined expressions according to (2) are the central wavelengths of the grating in the reference state              0 0 0 0 1l l n n (8) using simple arithmetic operations, expression (8) is transformed to            0 0 0 1l l n n (9) the resulting expression determines the relative change in the wavelength. from this expression we can draw an important conclusion that the relative change in the wavelength is independent of the grating period in the reference configuration l0. the refractive index increment depends on the strain and temperature ∆n=∆n(t-t0,ε), so that                  00 0 0 0 0 , 1 , ,l l n t t f t t n n ε ε (10) the expression f(t-t0,ε,n0) depends on the temperature, strain and refractive index of the optical fiber in the reference configuration n0=n(t0,0). under the same conditions of determining the reference configuration ε=0 and t=t0, for the same type of optical fiber and the same technology of applying the grating on the fiber, the quantity n0 will be a constant. it follows from the above that       0 0 0 ,f t t ε (11) under the described conditions, dependence (11) will be valid for gratings with different periods. in the case when the side surface of the fiber in the region of the bragg grating is free (not stressed), the radial and circumferential deformations of the fiber depend only on temperature and deformation along the fiber. under these conditions, the remaining components of the strain tensor ε are equal to zero. therefore, (11) takes the form        0 0 0 , lf t t (12) in the quadratic approximation function f(t-t0,εl) is written as                       220 1 2 0 3 4 0 5 0( , )l l l lf t t c c t t c c t t c t t (13) in what follows, we will describe the experiments that allow us to determine the parameters of this expansion. i. shardakov et alii, frattura ed integrità strutturale, 62 (2022) 561-572; doi: 10.3221/igf-esis.62.38 565 description of experimental setup he photograph of the experimental setup is shown in fig.3 it consists of a glass cylindrical vessel 1, on which a nichrome wire 6 is evenly wound to provide its heating and maintain the prescribed temperature. air inside the vessel is stirred to ensure the uniform temperature distribution. in the process of stirring, the air is drawn in by the turbine 3 in the lower part of the vessel, and then it moves through the aluminum tube 7 into the chamber in the upper part of the vessel 8. after that, the air returns to the working area of the vessel through the perforated plate. from above the vessel is plugged with seal 9, which does not allow the air from the environment to get into the vessel. from below it is protected by insulating pad 2 to reduce a heat flux through the bottom. inside the vessel there is an optical fiber with a bragg grating 11. fiber is loaded with a set of weights 4. attachment to the fiber is by means of grip 5. through the distributing plate 13 the fiber is clamped between rubber pads 14. compressive force is produced by elastic clamp 12. to reduce the compressive force in the clamp 12 to a level that ensures no damage to the fiber, a ring element is provided in the grip 5. this reduction in clamping force is achieved due to the frictional forces generated by winding the fiber around the annular part. changing the amount of winding makes it easy to adjust the axial force in the fiber with a constant compressive force in the clamp12. the temperature sensor 10 is brought to the fiber in the region of the bragg grating 11 at a distance of 1-2 mm. to minimize the influence of the environment, during the experiment the vessel is placed inside a cube made of 50 mm thick foam plastic. figure 3: experimental setup. power supply to the heating wire is regulated with a microcontroller and an external circuit on a field-effect transistor. the microcontroller is controlled by a computer, which measures temperature. a special computer program was developed to implement the pid regulation algorithm, which maintains the prescribed temperature inside the vessel and operates the step-wise temperature loading. the generation of a broadband optical signal and recording of the spectra reflected from the bragg grating were accomplished using the astro a322 interrogator manufactured by fibersensing. the bragg grating is fabricated in a single-mode fiber of the sm1500(9-125)p series. the initial grating wavelength is 1525 nm temperature registration is performed using the b57861-s 103-f40 thermistor manufactured by epcos. the thermistor resistance is measured with a 24-bit leonardo 2 adc and a gspf-052 generator manufactured by rudnev-shilyaev producer. synchronization of t i. shardakov et alii, frattura ed integrità strutturale, 62 (2022) 561-572; doi: 10.3221/igf-esis.62.38 566 temperature measurements and spectra of the bragg grating is provided automatically using a specially developed program in the delphi language. the temperature sensor is calibrated with tl-4 mercury thermometers, which have two temperature scales of 0-50 and 50-100 0с. the division value of thermometers and, as a result, the calibration accuracy is 0.1 degrees. experiment procedure and data processing he experiment includes two operations: hanging of weights an optical fiber and setting temperature from 5 to 100 0с with an increment of 5 0с. the temperature in the thermal chamber is set in steps with an exposure time of 15 minutes per step. in the area of the bragg grating, the insulation was removed from the fiber to eliminate the influence of the polymer shell. the weight sets the elastic deformation ε0 in the grating region, which does not change with temperature. we performed a set of experiments with three different weights (m1=29.040g, m2=109.975g, m3=216.431g), which allowed us to determine all parameters of the quadratic approximation. the strains ε0, corresponding to these weights were 321με, 1216με, 2395με, respectively. evolution of the temperature and the corresponding change in the central wavelength of the grating at several stages of temperature loading are shown in fig. 4. figure 4: evolution of temperature (a) and bragg grating wavelength (b) as a function of time. at each step, the readings were averaged over two minutes. the averaged values were used to plot the grating wavelength versus temperature (fig. 5) at different initial strains ε0. figure 5: dependence of the grating wavelength on temperature at different initial strains ε0. quite often, the central wavelength of the bragg grating is determined from the maximum of the spectrum. however, this approach does not provide stable results. this is illustrated by the spectrum graphs (fig. 6a) obtained from 4 consecutive measurements at constant temperature and strain. it can be seen from these plots that the wavelength at which the maximum value is reached may differ from one measurement to the next. to overcome this difficulty, an algorithm is proposed that determines the value of the central wavelength as the wavelength corresponding to the centre of mass of a figure bounded by points a, b, c (fig.6b). point b corresponds to the maximum of the spectrum, and points a and c are closest to b, where value 20 db below the maximum is achieved. t i. shardakov et alii, frattura ed integrità strutturale, 62 (2022) 561-572; doi: 10.3221/igf-esis.62.38 567 figure 6: the shapes of the spectral maxima for four consecutive measurements at constant temperature and deformation (a), the search algorithm for the central wavelength of the bragg grating (b). the developed algorithm can significantly reduce the processed data scattering and increase the sensitivity of the measuring system. this is clearly seen in fig. 7, which shows the evolution of the central wavelengths determined by means of direct registration of the spectrum maximum (fig. 7a) and calculation of the centre of mass (fig. 7b). according to these graphs, the developed algorithm reduces the scatter of the processed data by a factor of 10. it should be noted that the developed algorithm and time averaging over an interval of 1 minute (60 measurements) allowed us to obtain the wavelength sensitivity of ≈0.1pm. figure 7: wavelengths calculated with the use of the algorithms based on spectrum maximum (a) and centre of mass (b). determination of parameters of quadratic approximation he approximation of the function describing the relative wavelength change is expressed as follows               2 21 2 3 4 5( , )f t c c t c c t c t (14) where ∆t=t-t0. here, unlike eqn. (13), the lower index of ε is omitted. the longitudinal strain ε of a fiber stretched by applying a weight of mass m under conditions of variable temperature is given as     0 t (15) where: ε0 is the strain of the fiber due to the applied weight; α – is the coefficient of linear expansion of quartz equal to 0.54·10-6 1/0с. the deformation ε0 is determined using the expressions          2 0 , , 4 l l m g d s e s (16) t i. shardakov et alii, frattura ed integrità strutturale, 62 (2022) 561-572; doi: 10.3221/igf-esis.62.38 568 where: σl is the stress along the fiber; e is young's module of quartz equal to 72.3·109 pa; m is the mass of the weight; g is the acceleration of gravity equal to 9.81 m/s2; d is the diameter of the fiber equaling to 125 μm; s is the fiber crosssectional area. based on the results of experiments, three tabular dependencies were obtained   ,j ji it (17) where: j determines the belonging to the corresponding weight and varies from 1 to 3; i indicates the belonging to a given temperature and varies from 1 to 20. using expression (15), we can calculate the strains corresponding to weights j and temperatures i.     0 j j j i it (18) using the least squares method, we perform series expansion of the dependence of the central wavelength on deformation and temperature.                 2 20 1 2 3 4 5( , )t q q q t q q t q t (19) to this end we introduce the following row vectors                               1 1 2 2 3 3 1 1 1 1 1 2 2 3 3 1 1 1 1 1 2 2 3 3 1 1 1 [1 ... 1] ... ... ... ... ... ... ... ... ... n n n n n n n n n t t t t t t 1 ε δt λ (20) where 1 is the unit row vector of size 3·n; n is the number of points of temperature loading, which is equal to 20. the introduced vectors are used to generate a matrix of the following form                        1 ε δt m ε ε δt δt ε δt (21) where: ° is the component product. according to least squares method, the system of linear algebraic equations with respect to the approximation parameters of expression (19) is represented as       t tm m q m λ (22) where: · is the scalar product; t is the transposition operator; q is the column vector of the approximation parameters. the approximation parameter q1 is equal to the central wavelength of the grating in the reference configuration (∆t=0,ε=0)  0 0q (23) to calculate the relative change in the wavelength using expression (19), we must subtract λ0 from it and divide it by λ0. i. shardakov et alii, frattura ed integrità strutturale, 62 (2022) 561-572; doi: 10.3221/igf-esis.62.38 569                      2 20 0 0 3 4 51 2 0 0 0 0 0 0 0 ( , )t q q q q qq q t t t q q q q q q (24) comparing expressions (14) and (24) we obtain the coefficients of required expansion (14)     3 4 51 21 2 3 4 5 0 0 0 0 0 , , , , q q qq q c c c c c q q q q q (25) they have the following values:            6 9 51 2 3 4 50.782, 5.66 10 , 2.49, 7.03 10 , 6.31 10c c c c c (26) let us consider the expansion error (14) with respect to the initial experimental data (17), (18). it is determined by expression (27).         0 0 ( , ) j j j ji i i if t (27) graphs of the approximation error (27) are shown in fig. 8. these graphs correspond to three weights j=1,2,3, which set the initial deformation ε0= 321με, 1216με, 2395με. figure 8:approximation error for three levels of initial strain and temperature variations from 5 to 100 0с the graph shows that for strains changing from 0 to 2400με and temperature changing from 5 to 100 0с the maximum error of approximation of the relative wavelength is δmax= ±2·10-6. this value corresponds to the error of strain of ≈±2.5με. four fragments in fig. 9 show how the approximation error changes depending on temperature and deformation when various terms are excluded from the expression (14). these graphs clearly demonstrate the contribution of each non-linear term. fig. 9a shows the error, which occurs when the term с3·ε2 (с3=0) is excluded from the expansion. in this case, the maximum error value was δmax= -18·10-6. figs. 9b and 9c show the graphs of approximation error due to removal of terms с4·∆t2 and с5·∆t·ε, and fig. 9d corresponds to the situation when all nonlinear terms с3·ε2, с4·∆t2, с5·∆t·ε are excluded. based on these graphs, the following conclusions can be drawn. the largest approximation error occurs due to removal of the non-linear term с4·∆t2 (fig. 9b). the maximum error value in this case is equal to δmax= 46·10-6. nonlinear terms enter the expansion with different signs and partially compensate each other. compared to the approximation error (fig. 8), the contribution of the non-linear terms shown in fig. 9 is substantial. the contribution of each term of expansion (14) at temperature ∆t=100 0c and strain ε=2500με is evaluated as        61955 566 15 70 15 10 (28) i. shardakov et alii, frattura ed integrità strutturale, 62 (2022) 561-572; doi: 10.3221/igf-esis.62.38 570 the contributions of the summands with respect to the first term of the expansion are expressed in percentages as (29). the parentheses indicate the belonging to the corresponding term of the expansion.      2 2( ) ( ) ( ) ( ) ( )100% , 29% , 0.8% , 3.6% , 0.8%t t t (29) figure 9: graphs of approximation errors for three strain levels at different numbers of expansion terms conclusions everal important conclusions follow from the analysis of the obtained ratio 14. when using sensors based on the bragg grating to measure strain, it is necessary to take into account not only the accuracy of estimating the shift of the grating wavelength, but also the accuracy of temperature measurement. if the temperature is measured roughly, and the shift of the grating wavelength is estimated very accurately, then the accuracy of determining the deformation will be determined by the accuracy of the temperature measurement. to ensure the strain measurement accuracy of ±1με, the temperature measurement accuracy should be no worse than ±0.10с. comparison of the contributions of individual terms given in relation (28) makes it possible to estimate which terms of expansion (14) must be taken into account to ensure the required accuracy of the measuring system. so, if the allowable error in strain measurement is 5% or more, only linear terms can be taken into account in expansion (14). to ensure the accuracy of the measuring system of 1% or better, it is necessary to take into account the quadratic terms of the expansion. the reliability of the obtained results can be demonstrated by comparing them with the data presented in [16]: с1=0.782(0.806), с2=5.66·10-6(5.77·10-6), с4=7.03·10-9(8.02·10-9). here the values of the coefficients (26) are given, and in parentheses are the corresponding values taken from [16]. the obtained individual calibration dependence of the bragg grating in the form of relation (14) makes it possible to evaluate how the sensor readings depend on the features of its design. in the process of creating and debugging a bragg grating sensor, it is quite difficult to determine how the sensor readings depend on the method of fiber attachment. having an individual calibration dependence for a particular grating, it is possible to reliably identify the contribution to the sensor readings due to fiber attachment, and take appropriate measures to reduce this value. this is especially true when creating high-precision measuring systems that provide an accuracy of 0.1% or better. the construction of a quadratic approximation for the calibration dependence of the grating requires careful control of the parameters of the reference configuration (temperature t0 and external mechanical stresses of the fiber, which must be s i. shardakov et alii, frattura ed integrità strutturale, 62 (2022) 561-572; doi: 10.3221/igf-esis.62.38 571 zero). to do this, it is proposed to carry out a series of successive loadings of the fiber placed in a thermostat. loading is performed by successive suspension of weights on the fiber, which ensures the straightness of the fiber. then the dependence of the grating wavelength on the load value is constructed. approximation of this dependence to the zero value of the load makes it possible to obtain the value λ0. the calibration dependence obtained in this way is universal when using the same reference configuration, the same type of optical fiber, and the same technology for applying the grating to the fiber. the accuracy of determining the central wavelength with the aid of modern interrogators is 1 pm. this corresponds to a strain of ≈0.8με. therefore, to ensure the full-scale realization of capabilities of modern interrogators, one should use a quadratic approximation taking into account all terms of the expansion. acknowledgments he paper was prepared in the framework of the program for the creation and development of the world-class scientific center «supersonic»; for 2020-2025 with the financial support of the ministry of education and science of the russian federation (agreement no. 075-15-2020-925 of november 16, 2020 ). references [1] wang, y. l., tu, y., tu, s. t. (2020). development of highly-sensitive and reliable fiber bragg grating temperature sensors with gradient metallic coatings for cryogenic temperature applications, ieee sensors journal, 21(4), pp. 46524663. doi: 10.1109/jsen.2020.3036411. [2] sarkar, s., tarhani, m., khosravi eghbal, m., shadaram, m. (2020). discrimination between strain and temperature effects of a single fiber bragg grating sensor using sidelobe power, journal of applied physics, 127(11), pp. 114503. doi: 10.1063/1.5139041. [3] kuang, y., guo, y., xiong, l., liu, w. (2018). packaging and temperature compensation of fiber bragg grating for strain sensing: a survey, photonic sensors, 8(4), pp. 320-331. doi: 10.1007/s13320-018-0504-y. [4] zhou, z., ou, j. (2005). techniques of temperature compensation for fbg strain sensors used in long-term structural monitoring, fundamental problems of optoelectronics and microelectronics ii, 5851, pp. 167-172. doi: 10.1117/12.634047. [5] li, r., tan, y., chen, y., hong, l., zhou, z. (2019). investigation of sensitivity enhancing and temperature compensation for fiber bragg grating (fbg)-based strain sensor, optical fiber technology, 48, pp. 199-206. doi: 10.1016/j.yofte.2019.01.009. [6] zhao, y., yu, c., liao, y. (2004). differential fbg sensor for temperature-compensated high-pressure (or displacement) measurement, optics & laser technology, 36(1), pp. 39-42. doi: 10.1016/s0030-3992(03)00129-4. [7] xu, m. g., archambault, j. l., reekie, l., dakin, j. p. (1994). discrimination between strain and temperature effects using dual-wavelength fibre grating sensors, electronics letters, 30(13), pp. 1085-1087. doi: 10.1049/el:19940746. [8] patrick, h. j., williams, g. m., kersey, a. d., pedrazzani, j. r., vengsarkar, a. m. (1996). hybrid fiber bragg grating/long period fiber grating sensor for strain/temperature discrimination, ieee photonics technology letters, 8(9), pp. 1223-1225. doi: 10.1109/68.531843. [9] jung, j., nam, h., lee, j. h., park, n., lee, b. (1999). simultaneous measurement of strain and temperature by use of a single-fiber bragg grating and an erbium-doped fiber amplifier, applied optics, 38(13), pp. 2749-2751. doi: 10.1364/ao.38.002749. [10] du, w. c., tao, x. m., tam, h. y. (1999). fiber bragg grating cavity sensor for simultaneous measurement of strain and temperature, ieee photonics technology letters, 11(1), pp. 105-107. doi: 10.1109/68.736409. [11] guan, b. o., tam, h. y., tao, x. m., dong, x. y. (2000). simultaneous strain and temperature measurement using a superstructure fiber bragg grating, ieee photonics technology letters, 12(6), pp. 675-677. doi: 10.1109/68.849081. [12] singh, a. k., berggren, s., zhu, y., han, m., huang, h. (2017). simultaneous strain and temperature measurement using a single fiber bragg grating embedded in a composite laminate, smart materials and structures, 26(11), pp. 115025. doi: 10.1088/1361-665x/aa91ab. t i. shardakov et alii, frattura ed integrità strutturale, 62 (2022) 561-572; doi: 10.3221/igf-esis.62.38 572 [13] kipriksiz, s. e., yücel, m. (2021). tilted fiber bragg grating design for a simultaneous measurement of temperature and strain, optical and quantum electronics, 53(1), pp. 1-15. doi: 10.1007/s11082-020-02609-w. [14] zhang, w., li, f., liu, y. (2009). fbg pressure sensor based on the double shell cylinder with temperature compensation, measurement, 42(3), pp. 408-411. doi: 10.1016/j.measurement.2008.08.007. [15] morey, w. w., meltz, g., glenn, w. h. (1990). fiber optic bragg grating sensors, fiber optic and laser sensors vii, 1169, pp. 98-107. doi: 10.1117/12.963022. [16] yang, t., wang, y., wang, x. (2022). high-precision calibration for strain and temperature sensitivities of rayleighscattering-based dofs at cryogenic temperatures, cryogenics, 124, pp. 103481. doi: 10.1016/j.cryogenics.2022.103481 [17] roths, j., andrejevic, g., kuttler, r., süßer, m. (2006). calibration of fiber bragg cryogenic temperature sensors, optical fiber sensors, pp. tue81. doi: 10.1364/ofs.2006.tue81. [18] flockhart, g. m., maier, r. r., barton, j. s., macpherson, w. n., jones, j. d., chisholm, k. e., zhang, l., bennion, i., read, i., foote, p. d. (2004). quadratic behavior of fiber bragg grating temperature coefficients, applied optics, 43(13), pp. 2744-2751. doi: 10.1364/ao.43.002744. [19] li, g., ji, l., li, g., su, j., wu, c. (2021). high-resolution and large-dynamic-range temperature sensor using fiber bragg grating fabry-pérot cavity, optics express, 29(12), pp. 18523-18529. doi: 10.1364/oe.426398. microsoft word numero_37_art_13 j. albinmousa, frattura ed integrità strutturale, 37 (2016) 94-100; doi: 10.3221/igf-esis.37.13 94 focussed on multiaxial fatigue and fracture investigation on parametric representation of proportional and nonproportional multiaxial fatigue responses j. albinmousa mechanical engineering department, king fahd university of petroleum & minerals, dhahran 31261, saudi arabia binmousa@kfupm.edu.sa abstract. this study aims to investigate fatigue damage resulting from multiaxial fatigue, proportional and/or nonproportional, loading by analyzing stresses and strains over a full domain around a representative stress-strain element. plain stress-strain transformation of multiaxial hysteresis was performed by varying orientation of plane for 0≤φ≤2π. parametric representations for both normal and shear stresses and strains were obtained by plotting them in polar figures. these figures show that depending on the applied loading stresses and strains represent definitive known parametric curves. parametric representation of fatigue damage parameter such as fatemi-socie suggests that fatigue damage shall be calculated as the sum of the damage values on all planes. the proposed technique has been shown to improve fatigue life prediction compared to that obtained from the critical plane method. keywords. critical plane; fatigue damage; multiaxial fatigue; parametric representation. introduction atigue cracks initiate and grow at certain planes, i.e., persistent slip bands (psbs). this established fact can be clearly observed in deformed single crystals [1-3]. fatigue damage is associated with crack formation and critical plane concept originated based on this observation. critical plane concept is widely used as the basis for formulating fatigue damage models. therefore, fatigue damage is calculated at specific planes that are usually experience maximum value of either normal or shear strain or stress [4-7]. in some models, the critical plane is defined as the plane at which the value of the damage parameter is maximum [8]. on smooth specimen level, critical planes models have been shown to provide reasonable fatigue life predictions for different testing scenarios that include mean stress or strain, constant and variable amplitude loading, proportional and nonproportional loading conditions as well as complex loading paths [9]. however, socie et al. [10] conducted a comparative numerical analysis on multiaxial fatigue benchmark experiment performed on simple notched sae shaft [11]. five software packages were used to compute the fatigue lives for 75 bending-torsion notched shafts. socie et al. [10] showed that cumulative probability distribution for in-phase loading test on smooth tubular specimen indicates that there is 99% chance for fatigue life to be predicted within a factor of 2. conversely, there is 99% chance for fatigue life to be predicted within a factor of 10 when it comes to notched shaft. socie et al. [10] emphasized on the consideration of complex geometries and loading conditions for evaluating fatigue models. on the other hand, it is often found that models that are based on completely different critical plane assumptions such as normal or shear still give very similar fatigue life predictions [9, 12, 13]. such observation raises two important questions. first, what is the “critical” plane? the second question is: if two criteria are based on two different critical plane assumptions predict similar fatigue lives then which one of them is correct? these arguments suggest that further development is required to improve not only fatigue life but also fatigue crack path predictions. f j. albinmousa, frattura ed integrità strutturale, 37 (2016) 94-100; doi: 10.3221/igf-esis.37.13 95 this paper aims to investigate fatigue damage resulting from multiaxial, proportional and nonproportional, loading by analysing stresses and strains over a full domain of a representative stress-strain element. a new technique for evaluating strain based fatigue damage without consideration of a particular critical plane has been proposed. materials and experiments he material used for this investigation is micro alloyed fine grained structural steel s460n (fee460) tested by hoffmeyer et al. [14]. axial-torsional loading was applied on smooth thin-walled tubes specimens under strain controlled condition and room temperature. two multiaxial loading paths are considered for parametric analysis: proportional and 90° out-of-phase loading. the monotonic and cyclic properties of s460n steel are listed in table 1. details of the proportional and nonproportional cyclic tests can be found in table 2. this material was selected because of its symmetric cyclic behaviour as shown in fig. 1. property property (mpa) 208,500 -0.493 0.3 (mpa) 599 . % (mpa) 500 0.169 (mpa) 1115 (mpa) 463.2 0.161 0.224 (mpa) 969.6 -0.071 0.281 -0.422 -0.086 table 1: monotonic and cyclic properties of s460n steel [14]. no. loading (%) (%) (mpa) (mpa) nf (cycles) nr20 0° phase 0.173 0.300 244.2 147.3 31,100 nr26 90° phase 0.231 0.400 391.5 230.9 6,570 table 2: summary of cyclic tests [14]. figure 1: axial-torsional hysteresis for proportional (nr20) and nonproportional (nr26) tests. t j. albinmousa, frattura ed integrità strutturale, 37 (2016) 94-100; doi: 10.3221/igf-esis.37.13 96 analysis and modelling ormal and shear cyclic responses in fig. 1 were transformed using plane stress-strain transformation relations over the range 0 2 with an increment of 1.0°. maximum stresses and strains at each angular increment were recorded and then plotted on polar diagrams. after that, each polar curve was fitted using proper parametric equation, eqs. 1 to 8, as shown in fig. 2 a to h, respectively. (1) (2) (3) (4) (5) (6) (7) (8) it should be noted here that the plus and minus signs in eqs. 1 and 2 represents two different equations for the top and bottom parts of the curves in figs. 2a and b, respectively. similar to the stress and strain responses, fatigue damage parameter can also be represented in a parametric form. figure 3 shows the parametric representation of the fatemi-socie [5] fatigue damage parameter for the proportional, nr20, and nonproportional, nr26, loading cases. hence, the fatemi-socie damage parameter was expressed in a parametric form as in eq. 9. (9) n j. albinmousa, frattura ed integrità strutturale, 37 (2016) 94-100; doi: 10.3221/igf-esis.37.13 97 figure 2: parametric representation and fitting of the stress and strain responses for the proportional and nonproportional loading cases nr20 and nr26. j. albinmousa, frattura ed integrità strutturale, 37 (2016) 94-100; doi: 10.3221/igf-esis.37.13 98 figure 3: parametric representation of fatemi-socie fatigue damage parameter for nr20 and nr26. discussion wo observations can be made from the parametric modelling of the cyclic responses and the fatigue damage. first, stress and strain responses represent definitive known parametric curves. further study is needed to investigate the possibility of formulating mathematical fatigue damage, fatigue life and fatigue crack path using parametric equations. second, the polar diagram of the fatemi-socie parameter, fig. 3, shows that substantial number of planes experience high damage. this observation was reported by jiang et al [15]. it is proposed here that fatigue damage shall be calculated as the sum of all incremental damage on each plane as expressed in eq. 10. (10) figure 4: parametric representation of fatemi-socie fatigue damage parameter for nr20 and nr26. to verify this proposal, additional multiaxial fatigue data from hoffmeyer et al. [14] were considered. these include tests from the eleven cyclic loading paths shown in fig. 4. fatigue damage and fatigue lives were correlated in fig. 5a. these data were then fitted with a power relation as expressed in eq. 11. (11) t j. albinmousa, frattura ed integrità strutturale, 37 (2016) 94-100; doi: 10.3221/igf-esis.37.13 99 where κ =0.311, β =26.01 and α =-0.329. the predictions of eq. 11 are compared with the experimental fatigue lives in fig. 5b. in addition, the predictions of fatigue lives using standard fatemi-socie fatigue life model are also included in fig. 5b. it can be seen from fig. 5b that fatigue lives obtained by the proposed damage calculation method are mostly within 1.5x factor of lives. figure 5: fatigue damage and fatigue life prediction. a) fatigue damage and fatigue life correlation. b) comparison between fatigue life prediction using the standard fatemi-socie critical plane parameter and the proposed damage summation method. conclusion arametric representation of cyclic responses from proportional and nonproportional loading was presented. these responses were successfully fitted with defined parametric equations. similarly, fatemi-socie fatigue damage parameter was also represented in a parametric form. this representation shows that significant number of plans are experiencing high damage values. therefore, it was suggested that fatigue damage shall be calculated as the sum of all incremental damage values around a stress-strain element. the proposed damage calculation technique was to improve fatigue life life prediction compared to that obtained from the critical plane method. acknowledgement his research is supported by a project grant from kacst 230-34, king abdulaziz city for science and technology, riyadh, saudi arabia. the author would also like to acknowledge the support of king fahd university of petroleum & minerals (kfupm). a special thank is due to prof. michael vormwald from darmstadt university of technology in germany for providing the experimental data for the steel. references [1] callister, w. d., materials science and engineering: an introduction, fifth ed., j. wiley & sons, new york, (1999). [2] hertzberg, r. w., deformation and fracture mechanics of engineering materials, fourth ed., j. wiley & sons, new york, (1999). [3] dowling, n. e., mechanical behavior of materials: engineering methods for deformation, fracture, and fatigue, second ed., prentice hall, new jersey, (1999). [4] smith, k.n., topper, t.h., watson, p., stress-strain function for the fatigue of metals, j. mater, 5 (1970) 767-778. p t j. albinmousa, frattura ed integrità strutturale, 37 (2016) 94-100; doi: 10.3221/igf-esis.37.13 100 [5] fatemi, a., socie, d, a critical plane approach to multiaxial fatigue damage including out-of-phase loading, fatigue & fract. of eng. mat. & struct., 11 (1988) 149-165. [6] carpinteri, a., ronchei, c., scorza, d., vantadori, s., fatigue life estimation for multiaxial low-cycle fatigue regime: the influence of the effective poisson ratio value, theor. appl. fract. mec., 79 (2015) 77-83. [7] carpinteri, a., ronchei, c., spagnoli, a., vantadori, s., lifetime estimation in the low/medium-cycle regime using the carpinteri–spagnoli multiaxial fatigue criterion, theor. appl. fract. mec., 73 (2014) 120-127. [8] jiang, y., a fatigue criterion for general multiaxial loading, fatigue & fract. of eng. mat. & struct., 23 (2000) 19-32. [9] jiang, y., hertel, o., vormwald, m., an experimental evaluation of three critical plane multiaxial fatigue criteria, int. j. of fatigue, 29 (2007) 1490-1502. [10] socie, d., downing, s.d., utagawa, s., benchmark problems in multiaxial fatigue, int. conf. on multiaxial fat. & fract., (2013), koyto, japan. [11] fash, j.w., socie, d.f., mcdowell, d.l., fatigue life estimates for a simple notched component under biaxial loading, in: miller k., brown m., editors. multiaxial fatigue, stp 853. astm, (1985) 497–513. [12] albinmousa, j., jahed, h., lambert, s., cyclic behaviour of wrought magnesium alloy under multiaxial load, int. j. of fatigue, 33 (2011) 1127-1139. [13] albinmousa, j., jahed, h., multiaxial effects on lcf behaviour and fatigue failure of az31b magnesium extrusion, int. j. of fatigue, 67 (2014) 103-116. [14] hoffmeyer, j., döring, r., seeger, t., vormwald, m., deformation behaviour, short crack growth and fatigue lives under multiaxial nonproportional loading, int. j. of fatigue, 28 (2006) 508-520. 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can be opened with acrobat and adobe reader 5.0 and later.) >> /namespace [ (adobe) (common) (1.0) ] /othernamespaces [ << /asreaderspreads false /cropimagestoframes true /errorcontrol /warnandcontinue /flattenerignorespreadoverrides false /includeguidesgrids false /includenonprinting false /includeslug false /namespace [ (adobe) (indesign) (4.0) ] /omitplacedbitmaps false /omitplacedeps false /omitplacedpdf false /simulateoverprint /legacy >> << /addbleedmarks false /addcolorbars false /addcropmarks false /addpageinfo false /addregmarks false /convertcolors /converttocmyk /destinationprofilename () /destinationprofileselector /documentcmyk /downsample16bitimages true /flattenerpreset << /presetselector /mediumresolution >> /formelements false /generatestructure false /includebookmarks false /includehyperlinks false /includeinteractive false /includelayers false /includeprofiles false /multimediahandling /useobjectsettings /namespace [ (adobe) (creativesuite) (2.0) ] /pdfxoutputintentprofileselector /documentcmyk /preserveediting true /untaggedcmykhandling /leaveuntagged /untaggedrgbhandling /usedocumentprofile /usedocumentbleed false >> ] >> setdistillerparams << /hwresolution [2400 2400] /pagesize [612.000 792.000] >> setpagedevice microsoft word numero_41_art_28.docx p. lopez-crespo et alii, frattura ed integrità strutturale, 41 (2017) 203-210; doi: 10.3221/igf-esis.41.28 203 focused on crack tip fields mid-thickness studies of the stress intensity factor in the bulk of bainitic steel p. lopez-crespo, j. vazquez-peralta department of civil and materials engineering, university of malaga, c/dr ortiz ramos s/n, 29071 malaga, spain plopezcrespo@uma.es c. simpson school of materials, university of manchester, oxford road, manchester m13 9pl, uk t. buslaps european synchrotron radiation facility (esrf), 6 rue j horowitz, 38000 grenoble, france p. j. withers school of materials, university of manchester, oxford road, manchester m13 9pl, uk research complex at harwell, didcot, oxfordshire, ox11 0fa, uk. abstract. the current work aims at estimating the stress intensity factor deep inside the bulk from elastic strain data measured by synchrotron x-ray diffraction. key features affecting the evaluation of the stress intensity factor are the number of terms in the analytical model describing the crack tip field, the extension and position of the area of interest of the experimental data, the effect of the experimental data collected within the plastic zone and the number of elastic strain data points used. here a parametric study of these features is presented in terms of their influence for the stress intensity factor determination. it was found that 3 or 4 terms in williams’ expansion is often sufficient; the data should be collected from across the full range of angles around the crack tip; and the number of points/number of terms should be greater than 40. keywords. stress intensity factor; bainitic steel; williams’ expansion; x-ray diffraction. citation: p. lopez-crespo, j. vazquezperalta, c. simpson, t. buslaps, p. j. withers, mid-thickness studies of the stress intensity factor in the bulk of bainitic steel , frattura ed integrità strutturale, 41 (2017) 203-210. received: 28.02.2017 accepted: 15.04.2017 published: 01.07.2017 copyright: © 2017 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. introduction he experimental characterisation of crack tip fields is normally done using surface techniques such as photoelasticity [1], moiré interferometry [2], thermo-elastic stress analysis [3], electronic speckle pattern interferometry [4] or digital image correlation [5,6]. for thin components, the surface behaviour is normally representative of the t p. lopez-crespo et alii, frattura ed integrità strutturale, 41 (2017) 203-210; doi: 10.3221/igf-esis.41.28 204 complete behaviour [7]. however, for many engineering components, the surface may not be at all representative of the majority of the bulk of the material [8,9] and not describe accurately the complete component behaviour [10,11]. intense hard x-ray beams at synchrotron facilities now give us the possibility of probing the bulk of engineering materials both in terms of the geometry and in terms of elastic strain. geometrical features of the crack can be studied through synchrotron x-ray micro-tomography [12,13]. elastic strains can be investigated through synchrotron x-ray diffraction [14,15]. synchrotron x-ray diffraction can also be used to obtain the j-integral [16]. in this work synchrotron x-ray diffraction is used to estimate the sif deep within the bulk of a cracked specimen. the methodology combines a mathematical model describing the elastic crack tip field and elastic strain data obtained experimentally by synchrotron xray diffraction. first, the material and specimen employed are described. then, details about the experimental setup for strain measurement are given. this is followed by an explanation of how experimental data and the analytical model are combined to extract the sif. finally, the influence of key parameters affecting the estimation of the sif is studied. materials and methods he tests were undertaken on a bainitic steel similar to q1n having the chemical composition shown in tab. 1. the material exhibited a yield stress σy=690 mpa, ultimate tensile stress σuts=858 mpa and very fine grain that allowed high quality high spatial resolution strain data to be collected [17]. the bainitic steel also has a good combination of fatigue resistance and low environmental impact for applications where no energy is consumed during the use phase of the component [18]. the fatigue tests were conducted on a compact tension (ct) specimen of 60 mm width and 3.3 mm thickness (fig. 1). alloy c si mn p s cr ni mo cu q1n 0.16 0.25 0.31 0.010 0.008 1.42 2.71 0.41 0.10 table 1: chemical composition in weight % of q1n steel. the balance is fe. 3000 cycles were applied in the pre-cracking stage of the experiment at a frequency of 10 hz. during the pre-cracking stage, the stress intensity range, δk, was approximately 35 mpa√m and the load ratio, pmin/pmax, 0.03. plane stress conditions dominated through the thickness for all loads applied during the experiment, since each xrd measurement included information over 1.4 mm through the thickness [19]. the crack length was measured perpendicular to the loading direction from the centre of the loading holes [20]. figure 1: illustration of beam and compact tension specimen configuration. t p. lopez-crespo et alii, frattura ed integrità strutturale, 41 (2017) 203-210; doi: 10.3221/igf-esis.41.28 205 mapping of elastic strain he strain mapping experiments were conducted on beamline id15a of the european synchrotron radiation facility (france). energy dispersive mode was used, following the configuration previously applied with high qauality results [15,21]. two solid state x-ray detectors were mounted to measure two in-plane directions of strain (εxx and εyy). the scattering angle was 2θ = 5º. the elastic strain was evaluated according to bragg’s law:    0 0 hkl hkl hkl hkl d d d (1) where hkld is the lattice parameter of crystallographic plane (hkl) measured at a certain load and 0 hkld is the strain-free lattice parameter of the same crystallographic plane. here the plane (211) was used. the incident beam slits were opened to 60 × 60 µm, giving a lateral resolution (x, y) of 60 µm and a nominal gauge length through-thickness (z) of around 1.4 mm [17]. the gauge length was diamond shaped and centred on the mid-plane (z=0). attention was paid to locate the origin of coordinates at the crack tip [22]. fig. 2 shows an elastic strain field in the crack opening direction for a sample subjected to 5.3 kn. the two black solid lines in fig. 2 emanating from the origin of coordinates towards negative coordinates in the crack growing direction represent the crack. figure 2: the elastic strain field based on the (211) peak local to the crack in the crack opening direction (εyy) for a 13 mm crack length subjected to 5.3 kn. the area sampled by each point is 60 x 60 m. the parameters relating to the area of interest are also illustrated: inner radius of the data array, rint, outer radius of the data array, rout, and angle between the end of the data array and the crack plane, α. fitting the experimental to an elastic model he elastic strains were fitted to an analytical model following a multi-point over-deterministic scheme [23]. the analytical model was based on williams’ series development used to describe the elastic behaviour of the region surrounding the crack tip [24]. the strains in the crack opening direction can be written as [25]:                                     1 1 22 2 0 0 1 3 cos 1 1 2  cos 1 1 2 2 2 2 2 yye a r sin sin b a r sin t t p. lopez-crespo et alii, frattura ed integrità strutturale, 41 (2017) 203-210; doi: 10.3221/igf-esis.41.28 206                              3 2 22 2 1 2 3  2 cos 2 1 cos 3 1 sin sin 2 3 1 sin        2 2 2 a b r r b r (2) where e is the young’s modulus, εyy are the strains in the crack opening (vertical) direction, an and bm are unknown coefficients or number of terms in the series expansion, r and θ are the polar coordinates of the different points around the crack tip and υ is the poisson’s ratio. the singular term, a0 can be related to the sif as:  0 2 ika (3) substitution of all experimental data points in eq. (2) yields an over-deterministic system of equations that can be solved for the unknown coefficients and thereby computing the sif (kexp). parametric study he evaluation of the key parameters involved in the estimation of the sif, kexp, is done through comparison with the theoretical sif, ktheo [20]. to this end, the error between both values can be determined as:       % 100 exp theo theo k k error k (4) key parameters influencing the k estimation with the current scheme were identified previously [26,27]. these include the number of terms used in williams’ expansion, the size and shape of the area of interest (aoi) used for the fitting, the influence of the plastic zone and the number of experimental data points considered. number of terms, size and shape of the area of interest the size of the aoi is studied through the outer radius of the aoi, rout, defined in fig. 2. the combined influence of number of terms and size of aoi is shown in fig. 3. figure 3: effect of number of terms and size of the aoi (rout) on the error in estimating the sif. fig. 3 shows that the error decreases to a minimum for each value of number of terms studied. the minimum error as a function of rout observed is summarised in tab. 2. number of terms 1 2 3 4 5 6 rout (µm) 350 450 850 950 950 950 table 2: combination of number of terms and outer radius, rout, that give a minimum error in fig. 3 t p. lopez-crespo et alii, frattura ed integrità strutturale, 41 (2017) 203-210; doi: 10.3221/igf-esis.41.28 207 tab. 2 can be used as a reference to optimise the data array to be used depending on how many terms in williams’ expansion are chosen to describe the crack-tip field. tab. 2 indicates that if one term is used in williams’ formultion, the data array should extend to around 350 µm and for six terms the array should extend to around 950 µm. fig. 3 also shows that by using more terms in the series expansion, the error in estimating the sif can be reduced to around 1%. the shape of the aoi was studied through the angle between the edge of the aoi and the crack plane, α (see fig. 2). the angle α controls the number of data points that are collected from the region behind the crack tip (negative coordinates along the crack growing direction, fig. 2). the amount of data collected in the crack wake has been previously identified as critically affecting the sif estimation [27]. fig. 4 shows the evolution of the error for different α angles. for each number of terms, the optimum outer radius was used, following the results of tab. 2. when only 1 term is used the curve in fig. 4 is very flat such that in our case a slightly better result is obtained for =80 than 0°. in view of this, the conclusion would be that results become more reliable for >2 terms and that the best sif predictions (minimum error) are obtained when α = 0º when using 3 to 6 terms in williams’ expansion. that is, the best results in terms of estimating the sif are obtained by collecting data not only ahead of the crack tip but also from the crack wake region, in agreement with previous studies [27]. figure 4: effect of α angle on the error for estimating the sif. plastic zone the mathematical model used to describe the crack-tip behaviour is based on linear elastic fracture mechanics. accordingly, the tool can be used under small scale yielding (ssy) conditions. for other full-field techniques such as thermo-elasticity [3], photo-elasticity [1], digital image correlation [28] or electronic speckle patter interferometry [4], this is achieved by collecting data from outside the plastic zone. this effect is studied here by including and excluding the data from the plastic zone in the data used for estimating the sif. the plastic zone was estimated according to irwin model [25]:            2 1 330 2 pz y k r µm (5) where k is the theoretically applied sif and σy is the yield stress of the material. fig. 5 shows the error obtained when the plastic zone is included or excluded. the best predictions are observed when the plastic zone data is used in the fitting. fig. 5 also shows that there are large differences between including and excluding the plastic zone for 1 term. this difference decreases as the number of terms is increased. the worst prediction when the plastic zone is excluded is probably due to not having enough data for the over-deterministic system of equations. this effect is studied in more detail in the following section. number of experimental data points the effect the number of experimental data points that are fitted into the analytical model is studied in this section. the number of data points is studied relative to the number of terms in the series (eq. 2) through parameter φ: p. lopez-crespo et alii, frattura ed integrità strutturale, 41 (2017) 203-210; doi: 10.3221/igf-esis.41.28 208                 number of data points number of terms in series (6) fig. 6 shows the error for different levels of φ parameter. φ parameter represents the level of over-determination in the system of equations. fig. 6 shows that increasing φ parameter produces better estimations of the sif. the best estimations are observed for higher terms (5 and 6). for φ ≥40, the error is below 5%. for φ = 20 the error is smaller than 10% for all number of terms studied. figure 5: effect of including or excluding the plastic zone in the collected data, i.e. setting rint=0 or setting rint=330µm. figure 6: effect of the level of over-determination (i.e. φ parameter, as defined in eq. 6). conclusions novel approach for estimating the sif inside the bulk of engineering materials is described. the approach is based on fitting experimental data on an analytical model following a multi-point over-deterministic scheme. the experimental data are collected from the bulk of the material through powerful synchrotron x-ray diffraction. the analytical model describing the elastic field around the crack-tip is based on williams development. the methodology is applied to a ct specimen made of bainitic steel. a detailed analysis of key parameters affecting the efficacy of the sif evaluation is presented. the current study suggests that: 1. 3 or 4 terms in williams’s expansion is often sufficient. 2. data points should be included from across the full range of angles in front and behind the crack tip. a p. lopez-crespo et alii, frattura ed integrità strutturale, 41 (2017) 203-210; doi: 10.3221/igf-esis.41.28 209 3. a outer radius of at least the size of the plastic zone was needed. 4. little advantage was obtained by excluding the plastic zone. 5. to get accurate results the number of data points/number of terms should be φ ≥40. of course in our case the plastic zone is not especially well developed (i.e. it is still well within the lefm regime) different conclusions may apply in the case of extensive plastic deformation local to the crack. acknowledgements he authors would like to acknowledge financial support of junta de andalucía through proyectos de excelencia grant reference tep-3244, campus de excelencia internacional del mar (ceimar) and ministerio de economía y competitividad through grant reference mat2016-76951-c2-2-p. pjw acknowledges european research council funding (correl-ct grant number 695638 and epsrc funding under the following grants ep/m010619, ep/k004530, ep/f007906, ep/f028431 and ep/i02249x/1. the authors are also grateful to the esrf for id15 beamtime awarded under ma-1483. references [1] nurse, a.d., patterson, e.a., determination of predominantly mode ii stress intensity factors from isochromatic data. fatigue and fracture of engineering materials and structures, 16 (1993) 1339–1354. [2] nicoletto, g., experimental crack tip displacement analysis under smallscale yielding conditions. international journal of fatigue, 8 (1986) 83–89. [3] diaz, f.a., yates, j.r., patterson, e.a., some improvements in the analysis of fatigue cracks using thermoelasticity. international journal of fatigue, 26 (2004) 365–376. [4] shterenlikht, a., díaz-garrido, f.a., lopez-crespo, p., withers, p.j., patterson, e.a., mixed mode (ki + kii) stress intensity factor measurement by electronic speckle pattern interferometry and image correlation, applied mechanics and materials, 1-2 (2004) 107–112. [5] yoneyama, s., morimoto, y., takashi, m., automatic evaluation of mixed-mode stress intensity factors utilizing digital image correlation, strain, 42 (2006) 21–29. [6] lopez-crespo, p., shterenlikht, a., patterson, e.a., withers, p.j., yates, j.r., the stress intensity of mixed mode cracks determined by digital image correlation, journal of strain analysis for engineering design, 43 (2008) 769–780. doi: 10.1243/03093247jsa419. [7] lopez-crespo, p., withers, p.j., yusof, f., dai, h., steuwer, a., kelleher, j.f., overload effects on fatigue crack-tip fields under plane stress conditions: surface and bulk analysis, fatigue and fracture of engineering materials and structures, 36 (2013) 75–84. [8] de-matos, p.f.p., nowell, d., experimental and numerical investigation of thickness effects in plasticity-induced fatigue crack closure, international journal of fatigue, 31 (2009) 1795–1804. [9] yusof, f., lopez-crespo, p., withers, p.j., effect of overload on crack closure in thick and thin specimens via digital image correlation, international journal of fatigue, 56 (2013) 17–24. [10] garcia-manrique, j., camas, d., lopez-crespo, p., gonzalez-herrera, a., stress intensity factor analysis of through thickness effects, international journal of fatigue, 46 (2013) 58–66. [11] camas, d., lopez-crespo, p., gonzalez-herrera, a., moreno, b., numerical and experimental study of the plastic zone in cracked specimens, engineering fracture mechanics, (2017). doi:10.1016/j.engfracmech.2017.02.016. [12] withers, p.j., lopez-crespo, p., kyrieleis, a., hung, y.-c., evolution of crack-bridging and crack-tip driving force during the growth of a fatigue crack in a ti/sic composite, proceedings of the royal society a mathematical, physical and engineering sciences, 468 (2012) 2722–1743. [13] maire, e, withers, p.j., quantitative x-ray tomography. international materials reviews, 59 (2014) 1–43. doi: 10.1179/1743280413y.0000000023. [14] withers, p.j., use of synchrotron x-ray radiation for stress measurement. in: m e fitzpatrick al, editor. analysis of residual stress by diffraction using neutron and synchrotron radiation, london: taylor & francis; (2003) 170–189. [15] lopez-crespo, p., mostafavi, m., steuwer, a., kelleher, j.f., buslaps, t., withers, p.j., characterisation of overloads in fatigue by 2d strain mapping at the surface and in the bulk, fatigue & fracture of engineering materials & structures, 39 (2016) 1040–1048. t p. lopez-crespo et alii, frattura ed integrità strutturale, 41 (2017) 203-210; doi: 10.3221/igf-esis.41.28 210 [16] barhli, s.m., saucedo-mora, l., simpson, c., becker, t., mostafavi, m., withers, p.j., obtaining the j-integral by diffraction-based crack-field strain mapping, procedia structural integrity, 2 (2016) 2519–2526. [17] lopez-crespo, p., steuwer, a., buslaps, t., tai, y.h., lopez-moreno, a., yates, j.r., measuring overload effects during fatigue crack growth in bainitic steel by synchrotron x-ray diffraction, international journal of fatigue, 71 (2015) 11–16. [18] chaves, v., ecological criteria for the selection of materials in fatigue. fatigue & fracture of engineering materials & structures, 37 (2014) 1034–1042. doi: 10.1111/ffe.12181. [19] anderson, t.l., fracture mechanics: fundamentals and applications, 2nd ed. boca raton: crc press; (1994). [20] murakami, y., stress intensity factors handbook. oxford: pergamon press; (1987). [21] steuwer, a., rahman, m., shterenlikht, a., fitzpatrick, m.e., edwards, l., withers, p.j., the evolution of crack-tip stresses during a fatigue overload event, acta materialia, 58 (2010) 4039–4052. [22] zanganeh, m., lopez-crespo, p., tai, y.h., yates, j.r., locating the crack tip using displacement field data: a comparative study, strain, 49 (2013) 102–115. [23] sanford, r.j., dally, j.w., a general method for determining mixed-mode stress intensity factors from isochromatic fringe patterns, engineering fracture mechanics, 11 (1979) 621–633. [24] williams, m.l., on the stress distribution at the base of a stationary crack. journal of applied mechanics, 24 (1957) 109–114. [25] ewalds, h.l., wanhill, r.j.h., fracture mechanics. london: arnold; (1984). [26] lopez-crespo, p., moreno, b., lopez-moreno, a., zapatero, j., characterisation of crack-tip fields in biaxial fatigue based on high-magnification image correlation and electro-spray technique, international journal of fatigue, 71 (2015) 17–25. [27] mokhtarishirazabad, m., lopez-crespo, p., moreno, b., lopez-moreno, a., zanganeh, m., evaluation of crack-tip fields from dic data: a parametric study, international journal of fatigue, 89 (2016) 11–19. [28] yoneyama, s., ogawa, t., kobayashi, y., evaluating mixed-mode stress intensity factors from full-field displacement fields obtained by optical methods, engineering fracture mechanics, 74 (2007) 1399–1412. << /ascii85encodepages false /allowtransparency false /autopositionepsfiles true /autorotatepages /none /binding /left /calgrayprofile (dot gain 20%) /calrgbprofile (srgb iec61966-2.1) /calcmykprofile (u.s. web coated \050swop\051 v2) /srgbprofile (srgb iec61966-2.1) /cannotembedfontpolicy /error /compatibilitylevel 1.4 /compressobjects /tags /compresspages true /convertimagestoindexed true /passthroughjpegimages true /createjobticket false /defaultrenderingintent /default /detectblends true /detectcurves 0.0000 /colorconversionstrategy /cmyk /dothumbnails false /embedallfonts true /embedopentype false /parseiccprofilesincomments true /embedjoboptions true /dscreportinglevel 0 /emitdscwarnings false /endpage -1 /imagememory 1048576 /lockdistillerparams false /maxsubsetpct 100 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can be opened with acrobat and adobe reader 5.0 and later.) >> /namespace [ (adobe) (common) (1.0) ] /othernamespaces [ << /asreaderspreads false /cropimagestoframes true /errorcontrol /warnandcontinue /flattenerignorespreadoverrides false /includeguidesgrids false /includenonprinting false /includeslug false /namespace [ (adobe) (indesign) (4.0) ] /omitplacedbitmaps false /omitplacedeps false /omitplacedpdf false /simulateoverprint /legacy >> << /addbleedmarks false /addcolorbars false /addcropmarks false /addpageinfo false /addregmarks false /convertcolors /converttocmyk /destinationprofilename () /destinationprofileselector /documentcmyk /downsample16bitimages true /flattenerpreset << /presetselector /mediumresolution >> /formelements false /generatestructure false /includebookmarks false /includehyperlinks false /includeinteractive false /includelayers false /includeprofiles false /multimediahandling /useobjectsettings /namespace [ (adobe) (creativesuite) (2.0) ] /pdfxoutputintentprofileselector /documentcmyk /preserveediting true /untaggedcmykhandling /leaveuntagged /untaggedrgbhandling /usedocumentprofile /usedocumentbleed false >> ] >> setdistillerparams << /hwresolution [2400 2400] /pagesize [612.000 792.000] >> setpagedevice microsoft word numero_35_art_32 n. oudni et alii, frattura ed integrità strutturale, 35 (2016) 278-284; doi: 10.3221/igf-esis.35.32 278 focussed on crack paths implementation of a damage model in a finite element program for computation of structures under dynamic loading nasserdine oudni department of civil engineering, faculty of technology, a. mira university, bejaia, algeria laboratory of modeling of materials and structures, university of tizi-ouzou, algeria nasroudni@yahoo.fr youcef bouafia laboratory of modeling of materials and structures, university of tizi-ouzou, algeria youcef.bouafia2012@yahoo.com abstract. this work is a numerical simulation of nonlinear problems of the damage process and fracture of quasi-brittle materials especially concrete. in this study, we model the macroscopic behavior of concrete material, taking into account the phenomenon of damage. j. mazars model whose principle is based on damage mechanics has been implemented in a finite element program written fortran 90, it takes into account the dissymmetry of concrete behavior in tension and in compression, this model takes into account the cracking tensile and rupture in compression. it is a model that is commonly used for static and pseudo-static systems, but in this work, it was used in the dynamic case. keywords. damage; dynamic; modeling; displacement; strain; local approach; time integration; explicit; quasi-brittle. introduction he numerical program is employed in analyzing koyna gravity dam and comparing the results with available results of many researchers find in literature. the choice of koyna concrete gravity dam is due to the fact that many studies have been done on this structure which experienced a devastating earthquake in 1967. since koyna dam in the 1967 koyna earthquake [1-4] is one of the few examples of cracking in a concrete dam, it has been selected to investigate its earthquake response. the earthquake records are in the form of accelerograms with horizontal and vertical components which are used as dynamic loads. the effect of the damping coefficient is obviously taken into account. this work proposes the implementation of a damage model based on the damage mechanics as part of the isotropic formulation proposed by j. lemaitre in a finite element program. the j. mazars model [5] whose principle is based on damage mechanics which is a theory describing the progressive reduction of the mechanical properties of a material due to initiation, growth and coalescence of microscopic cracks. these internal changes lead to the degradation of mechanical properties of the material. the model takes into account the asymmetry of concrete behavior and it considers the cracking in tension and compression failure. the method is based on the notion of equivalence of the strains. t n. oudni et alii, frattura ed integrità strutturale, 35 (2016) 278-284; doi: 10.3221/igf-esis.35.32 279 model he influence of microcracking due to external loads is introduced via a single scalar damage variable d ranging from 0 for the undamaged material to 1 for completely damaged material. the stress-strain relation reads [6]:     0 0 ij ij kk ij 0 0 1 υ υ ε σ σ δ      e 1 d e 1 d        (1) 0e and 0 are the young's modulus and the poisson's ratio of the undamaged material; ijε and ijσ are the strain and stress components, and ijδ is the kronecker symbol. the elastic (i.e., free) energy per unit mass of material is   0 1 1      2 ij ijkl kld c    (2) where 0ijklc is the stiffness of the undamaged material. this energy is assumed to be the state potential. the damage energy release rate is 0 1   2 ij ijkl kly c d         (3) with the energy of dissipated energy: d d         (4) since the dissipation of energy ought to be positive or zero, the damage rate is constrained to the same inequality because the damage energy release rate is always positive. damage evolution he evolution of damage is based on the amount of extension that the material is experiencing during the mechanical loading. an equivalent strain is defined as   3 2 1    i i       (5) where .  is the macauley bracket and i are the principal strains. the loading function of damage is  ,     f       (6) where  is the threshold of damage growth. initially, its value is 0 , which can be related to the peak stress tf of the material in uniaxial tension: 0 0   t f e   (7) in the course of loading  assumes the maximum value of the equivalent strain ever reached during the loading history. t t n. oudni et alii, frattura ed integrità strutturale, 35 (2016) 278-284; doi: 10.3221/igf-esis.35.32 280           ,  0       ,  0,  if f and f then        0           0,       0 d h d with d else                 (8) the function  h  is detailed as follows: in order to capture the differences of mechanical responses of the material in tension and in compression, the damage variable is split into two parts:    t t c cd d d   (9) where td and cd are the damage variables in tension and compression, respectively. they are combined with the weighting coefficients t and c , defined as functions of the principal values of the strains t ij and c ij due to positive and negative stresses:    1 1  1 ,      1  t t c cij ijkl kl ij ijkl kld c d c         (10) 3 3 2 2 1 1 ,     t c i i i i t c i i                            (11) note that in these expressions, strains labeled with a single indicia are principal strains. in uniaxial tension 1t  and 0c  . in uniaxial compression 1c  and 0t  . hence, td and td can be obtained separately from uniaxial tests. the evolution of damage is provided in an integrated form, as a function of the variable  :     0 0 1 1   exp t t t t a a d b            (12)     0 0 1 1   exp c c c c a a d b            . (13) figure 1. evolution of two parts of damage td and cd [5]. a direct tensile test or three point bend test can provide the parameters which are related to damage in tension ( 0 , ta ,   tb ). note that eq. 7 provides a first approximation of the initial threshold of damage, and the tensile strength of the material can be deduced from the compressive strength according to standard code formulas. the parameters ( ca , cb ) are fitted from the response of the material to uniaxial compression. n. oudni et alii, frattura ed integrità strutturale, 35 (2016) 278-284; doi: 10.3221/igf-esis.35.32 281 dynamic equations of motion ynamic analysis of structures exhibiting non linear behavior is performed by using direct integration, to trace the response in the time domain. the nonlinear dynamic equilibrium equation can be written as   n n n nm cu p fu     (14) where m and c are the global mass and damping matrices respectively, np is the global vector of internal resisting nodal forces, nf is the vector of consistent nodal forces for the applied body and surfaces traction forces grouped together, the body force term ( gmiu  ) due to seismic excitation, is included in the body forces which are taken into account in n f , nu is the global vector of nodal accelerations and nu is the global vector of nodal velocities [7]. figure 2: uniaxial response of the model in (a) tension and (b) compression [5] when the structure is subjected to seismic excitation, the external applied body forces is n gf miu   (15) where gu is ground acceleration and i is a vector indicating the direction of the earthquake excitation. figure 3: koyna accelerograms a) transverse component b) vertical component [8]. d n. oudni et alii, frattura ed integrità strutturale, 35 (2016) 278-284; doi: 10.3221/igf-esis.35.32 282 the geometry of a typical non-overflow monolith of the koyna dam is illustrated in fig. 4. the monolith is 103 m high and 71 m wide at its base. the upstream wall of the monolith is assumed to be straight and vertical, which is slightly different from the real configuration. the depth of the reservoir at the time of the earthquake is hw = 91.75 m. following the work of other investigators, we consider a two-dimensional analysis of the non-overflow monolith assuming plane stress conditions. the finite element mesh used for the analysis is shown in fig. 4. it consists of 760 first-order, reducedintegration, plane stress elements (cps4r). nodal definitions are referred to a global rectangular coordinate system centered at the lower left corner of the dam, with the vertical y-axis pointing in the upward direction and the horizontal xaxis pointing in the downstream direction. the transverse and vertical components of the ground accelerations recorded during the koyna earthquake are shown in fig. 3. (units of g = 9.81 m sec–2). prior to the earthquake excitation, the dam is subjected to gravity loading due to its self-weight and to the hydrostatic pressure of the reservoir on the upstream wall [8].       figure 4: geometric properties of the koyna dam. parameters used in mazars’s model for concrete young modulus e 31027 mpa poisson’s ratio  0.2 mass density  2643 kg/m3 initial damage threshold 0d  1.5 10-4 at 1.0 bt 30000 ac 1.4 bc 1545 table1: material properties.     results e note that the displacements are relatively low during the first two seconds because of low the amplitudes of the excitations. the displacements reach their maximum at 3.7 s and 7.5 s, 30 mm was recorded at 3.8 s, the maximum displacement value does not correspond to the maximum amplitude of the excitement that is recorded at 3.65 s. the nodal displacements decrease after 7.5 s.   w n. oudni et alii, frattura ed integrità strutturale, 35 (2016) 278-284; doi: 10.3221/igf-esis.35.32 283   figure 5: horizontal displacements at the crest of the dam we note that the displacements are relatively low during the first two seconds because of low the amplitudes of the excitations. the displacements reach their maximum at 3.7 s and 7.5 s, 30 mm was recorded at 3.8 s, the maximum displacement value does not correspond to the maximum amplitude of the excitement that is recorded at 3.65 s. the nodal displacements decrease after 7.5 s.   figure 6: damage evolution, td and cd . fig. 6. shows the evolution of td and cd , the tensile and compressive part of the damage variable d . we note that traction damage is more significant and more predominant than in compression, which leads to a brittle fracture of the material by traction. the total rupture of the material can be achieved by traction, in compression the damage is less significant, so the rupture will not occur under compression, fig. 1b presents some ductility of the material. it is also seen from this figure (fig. 6) that the tensile damage starts firstly and evolves quickly to a value close to 1 ( 1td  ), then followed by the compression damage, but the temporary difference is only of the order of a thousandth of a second, so nearly or completely insignificant difference. in counterparty, compressive damage is less important, it increases until a value 0.15cd  a value that does not allow rupture in compression of the element. damage were observed (see fig. 7) in the dam after 3.53 s at the integration point (815) of the element 204, then from 3.54 s at integration point (811) of the element 203 and finally, from 3.54 s at gauss point (807) of the element 202. it may be noted that the evolution of the damage is mainly concentrated in the time interval where the maximum values of positive and negative displacements occur. n. oudni et alii, frattura ed integrità strutturale, 35 (2016) 278-284; doi: 10.3221/igf-esis.35.32 284   figure 7: damage evolution in gauss points. conclusion e have taken the example of a concrete gravity dam subjected to seismic excitation in the form of accelerograms. the results are, first the response of gravity dam subjected to seismic loading as displacements history, secondly the history of the evolution of integration points damage at the cracked or damaged zone. the dynamic equilibrium equation is solved, an integration algorithm by the method of central differences for nonlinear systems, we have used a very small time step (0.0001 s). the choice of weight koyna dam in india is the fact that many studies have been conducted on this structure to a known destructive earthquake in 1967. the records of the earthquake accelerograms as with horizontal and vertical components were used as dynamic loads.  references [1] calayir, y., karaton, m., a continuum damage concrete model for earthquake analysis of concrete gravity dam– reservoir systems, soil dynamics and earthquake engineering, 25 (2005) 857-869. [2] jianwen, p., chuhann, z., xuyanjie, feng, j., a comparative study of the different procedures for seismic cracking analysis of concrete dams, soil dynamics and earthquake engineering, 31 (2011) 1594-1606. [3] calayir, y., karaton, m., a continuum damage concrete model for earthquake analysis of concrete gravity dam– reservoir systems. soil dynamics and earthquake engineering, 25 (2005) 857–869. [4] omidi, o., valliappan, s., lotfi, v., seismic cracking of concrete gravity dams by plastic–damage model using different damping mechanisms. finite elements in analysis and design, 63 (2013) 80–97. [5] mazars, j., application de la mécanique de l’endommagement au comportement non linéaire et à la rupture du béton de structure, doctoral thesis, university of paris 6, france (1984). [6] mazars, j., pijaudier-cabot, g., continuum damage theoryapplication to concrete, j. engrg. mech. asce, 115 (1989) 345-365. [7] owen, d.r.j., hinton, e., finite element in plasticity, theory and practice. ed. pineridge press limited, (1986). 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/hrv (za stvaranje adobe pdf dokumenata najpogodnijih za visokokvalitetni ispis prije tiskanja koristite ove postavke. stvoreni pdf dokumenti mogu se otvoriti acrobat i adobe reader 5.0 i kasnijim verzijama.) /hun 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can be opened with acrobat and adobe reader 5.0 and later.) >> /namespace [ (adobe) (common) (1.0) ] /othernamespaces [ << /asreaderspreads false /cropimagestoframes true /errorcontrol /warnandcontinue /flattenerignorespreadoverrides false /includeguidesgrids false /includenonprinting false /includeslug false /namespace [ (adobe) (indesign) (4.0) ] /omitplacedbitmaps false /omitplacedeps false /omitplacedpdf false /simulateoverprint /legacy >> << /addbleedmarks false /addcolorbars false /addcropmarks false /addpageinfo false /addregmarks false /convertcolors /converttocmyk /destinationprofilename () /destinationprofileselector /documentcmyk /downsample16bitimages true /flattenerpreset << /presetselector /mediumresolution >> /formelements false /generatestructure false /includebookmarks false /includehyperlinks false /includeinteractive false /includelayers false /includeprofiles false /multimediahandling /useobjectsettings /namespace [ (adobe) (creativesuite) (2.0) ] /pdfxoutputintentprofileselector /documentcmyk /preserveediting true /untaggedcmykhandling /leaveuntagged /untaggedrgbhandling /usedocumentprofile /usedocumentbleed false >> ] >> setdistillerparams << /hwresolution [2400 2400] /pagesize [612.000 792.000] >> setpagedevice microsoft word numero 23 articolo 10 manca abstract e keywords a. somà et alii, frattura ed integrità strutturale, 23 (2013) 94-102; doi: 10.3221/igf-esis.23.10 94 scilla 2012 the italian research on smart materials and mems electro-mechanical coupled design of self-powered sensing systems and performances comparison through experiments a. somà, g. de pasquale department of mechanical and aerospace engineering, politecnico di torino corso duca degli abruzzi 24, 10129 torino (italy) aurelio.soma@polito.it, giorgio.depasquale@polito.it abstract. recent advances in low-power sensors and electronic components open to innovative strategies in structural monitoring and real-time data processing, in particular for industrial and vehicular fields. dedicated devices for harvesting the energy dissipated by mechanical vibrations of machines are showing their applicability in supplying autonomous distributed sensing systems. the harvester will replace cables and storage batteries, with relevant benefits on the sensing system capillarity, accessibility and applicability. the design of the interfaces of the electric, magnetic and structural coupled systems forming the harvester include static and dynamic modeling and simulation of the interactions involved; smart and effective architectures are need to satisfy the general requirements of bandwidth, tunability and efficiency required by each application. this paper reports the research advances in this field as a result of laboratory tests and design studies, with particular focus on the design methodologies involved in the definition of energy harvesters. keywords. energy harvesting; structural monitoring; autonomous sensing; bandwidth; resonance tuning; duty cycle; efficiency. introduction here are many unexploited energy sources in the environment such as light, wind, temperature gradients, radiofrequency waves, kinetic energy of sea waves, mechanical vibrations, human body motion, etc. the conversion of the unused energy in electricity, called ‘energy harvesting’, is motivating many academic and industrial researches in the last years [1-3]. due to the small power amount that is usually available, the energy harvesting is mainly addressed to the supply of low consumption technologies. the harvesting of energy from the environment represents a valid alternative to batteries and cables, and promises to open new chances of development for mobile and wireless devices. energy harvesters will allow using, for example, wireless sensors in many applications such as industrial and structural monitoring, remote medical assistance, military equipments, materials flows monitoring, transports and logistics, energetic efficiency control. without the capabilities of energy harvesting devices, it is almost impossible to supply sensing devices in critical positions where accessibility is limited, for example in telemedicine applications and biological parameters monitoring. miniaturized and wearable harvesters allow continuous monitoring of patients affected by chronic pathologies by means of sensors integrated in the body that do not need batteries for the supply of energy. this study compares some different strategies for harvesting energy from the environment, with particular attention to mechanical vibrations. in previous works, the authors analyzed the performances of different energy harvesters: piezoelectric [4], magnetic inductive [5], electrostatic capacitive, and magnetically levitated [6]. also they patented some dedicated devices [7-9]. in this paper, the results of simulation and testing of different energy harvesters are introduced and compared in terms of energy generated per unit volume. then, some design solutions for the integration of the harvester in monitoring devices for vehicles and mechanical systems are analyzed. finally, after the comparison of t http://www.gruppofrattura.it http://dx.medra.org/10.3221/igf-esis.23.10&auth=true a. somà et alii, frattura ed integrità strutturale, 23 (2013) 94-102; doi: 10.3221/igf-esis.23.10 95 different conversion strategies, two typologies of harvesters are characterized for obtaining design indications about the autonomous sensing system. vibrating energy conversion strategies he kinetic energy associated to environmental vibrations is generally exploited by harvesters to excite the oscillation of a seismic inertial mass connected to the transducer. the motion induced on the seismic mass is regulated in amplitude, frequency and phase angle in order to maximize the conversion efficiency. the most diffuse conversion principles are piezoelectric, magnetic-inductive and capacitive (tab. 1). in the following, the most important characteristics of these three conversion strategies are discussed.   environment energy sources magnetic inductive  energy harvesting   kinetic energy and  mechanical  vibrations  current induced by  magnetic field  piezoelectric  energy harvesting  kinetic energy and  mechanical  vibrations  deformation of  piezoelectric  materials  capacitive   energy harvesting  pre‐charged  variable  capacitors   armatures relative  displacement   thermoelectric  energy harvesting  semiconductors  technology  thermally induced  electric voltage  solar energy  harvesting   photovoltaic   cells  charges  separation in p‐n  junctions  control electronics battery table 1: some typologies of energy harvesters. piezoelectric energy harvesters in this typology of generators, the seismic mass induces the deformation of a piezoelectric component that produces a voltage difference between its electrodes proportional to the mechanical strain. about piezo generators, some reliability limitations have been pointed out in the literature because of the brittleness of materials used (pzt, pvdf, etc). the electric output power is function of the resistive load applied to the transducer; then, the preliminary characterization of the impedance of the electronic conditioning circuit is needed. the shape of the output signal under sinusoidal excitation represents another possible source of inefficiency; in fact, current and voltage waves are slightly phase shifted due to the intrinsic capacitance of the piezoelectric material. this reduces the effective output power with respect to the optimized output power theoretically available in case of preliminary phase synchronization of current and voltage; unfortunately this operation needs relevant complications of the conditioning circuit and is generally omitted. usually, the output voltage is rather high (in the order of tens of v), while the current is generally low (in the order of ma); when the storage battery is included in the autonomous sensing system, the voltage/current ratio should be modified in order to reduce the time of charge. this operation also requires additional circuit complications. the advantages related to piezoelectric generators are given by the large commercial availability of transducers, which are almost ready for the integration in the harvesting system. furthermore, they are characterized by good ratios of generated power per unit volume. from the dynamic viewpoint, these typology of generators can be applied to moderately wide ranges of frequencies (up to few hundreds of hz), which are typically associated to structural vibrations. the resonance tuning can be achieved by varying the stiffness of the deformable element or by changing the seismic mass. instead, the active tuning able to set the resonance on the actual working regime and bandwidth is generally more complicated. an example of piezoelectric generator is reported in fig. 1. t http://www.gruppofrattura.it http://dx.medra.org/10.3221/igf-esis.23.10&auth=true a. somà et alii, frattura ed integrità strutturale, 23 (2013) 94-102; doi: 10.3221/igf-esis.23.10 96 figure 1: piezoelectric generator [10]: 10x10x1mm3 size, 60μw output power in resonance condition (572 hz) and 2g acceleration. magnetic inductive energy harvesters in this case, the vibrating energy is used to induce the relative motion between a permanent magnet and a conductive coil. in the literature, a number of design solutions have been introduced, which include fixed magnet and movable coil or, more frequently, fixed coil and movable magnet. the design activity involves the selection of the coil diameter and turns number, which are both related to the current produced and to the electric resistance of the wire. by varying these two parameters, the optimized solution can be found in terms of conversion efficiency. other important design parameters are the magnetic material and the magnet dimensions. generally, magnets characterized by high induced magnetic field are preferable, as the so-called ‘rare earths’ magnets (e.g. ndfeb). the most important benefits in using inductive harvesters are the stability of performances, the high reliability and, above all, the high current/voltage ratio that makes these generators suitable for charging batteries without complicated electronic conditioning. unfortunately, the integration of tuning controls is generally hard because the resonance of the harvester is dominated by the mass properties of the magnet, which is already dimensioned to fit the electric requirements. furthermore, the power generation is strongly linked to the magnet velocity, with reference to the relation between the current induced in the coil and the gradient of the magnetic field expressed by the faraday law. this indicates that high output power is obtainable from long travels of the magnet and, consequently, by dedicated design of suspensions. the lowering of suspension stiffness can be obtained, for instance, by using magnetic springs represented by repulsing magnets. fig. 2 reports an example of inductive energy harvester from the literature. figure 2: magnetic-inductive energy harvester [11]: 54x46x15mm3 size, 0.55mw output power at 9.25hz frequency and 0.8g acceleration. capacitive energy harvesters capacitive generators are basically capacitors with movable armatures where the relative displacement of the armatures is induced by external vibration and is used to generate voltage or charge difference between them. the electric power generated is strongly dependent to the capacitor geometry: in particular, small gaps between armatures and large armature surfaces are particularly advantageous. however, the pre-charge of armatures is needed to generate energy and it represents serious limitation to the efficiency of the energy harvester. in order to reduce as much as possible the charging energy, very small armatures surfaces are preferred. then, in practice, the application of capacitive energy harvesters is limited to small scales and some examples are available in the field of mems (micro electro-mechanical systems). the http://www.gruppofrattura.it http://dx.medra.org/10.3221/igf-esis.23.10&auth=true a. somà et alii, frattura ed integrità strutturale, 23 (2013) 94-102; doi: 10.3221/igf-esis.23.10 97 mentioned properties represent the most relevant drawbacks of capacitive generators; another limitation is given by the high dynamic response of the harvester that is imposed by the small masses used, which reduces the applicability of these devices to high frequencies (in the order of khz). however, in the microscale, the technology required to fabricate this typology of devices (i.e. surface micromachining) is consolidated and good constructive solutions are achievable. recently, it was documented the possibility to apply particular materials (electrets) on the variable capacitor surfaces; these materials have intrinsic charge and they are able to preserve this charge for long time compared to the harvester life. this technological improvement makes unnecessary the electric preload and sensitively increases the device efficiency. fig. 3 reports an example to mems capacitive harvesters and a harvester with electret. (a) (b) figure 3: (a) capacitive generator [12] including the seismic mass represented by a tungsten ball (4mm diameter) for the frequency tuning at 120hz (31μw output power at 0.23g). (b) capacitive generator with electret [13] (1μw output power at 63hz and 2g). power spectral density, frequency tuning and bandwidth amplification rom the methodological viewpoint, the preliminary analysis of the vibrating excitation source is needed before to dimension the harvester. in general applications, the input force has random shape because it is produced by machines or mechanical systems having variable operating regimes (e.g., vehicles in motion at different velocities or aircrafts in different flight conditions). the average energy associated to the input signal can be evaluated, for instance, from the acceleration associated to every specific working condition or, more generally, from the overall acceleration range. after estimating the available energy, then is possible to define, at least roughly, the size of the harvester and the size of the oscillating parts. the goal of this first design tentative is to provide the order of magnitude of masses and suspensions stiffness with reference to the response/excitation amplitude ratio. in other words, the dynamic parameters of the generator are defined in dependence to the desired frf. next step addresses to the analysis of energy distribution in the frequency spectrum. usually, the environmental oscillation is amplified in correspondence to particular frequencies because of multiple resonances and combined modal couplings that interest the machine or mechanical system hosting the harvester. in correspondence to the machine resonance, the available energy coming from the vibrating environment is amplified. the description of the energy distribution in the frequency domain is provided by the psd (power spectral density) function that must be considered accurately during the next part of the dimensioning. the harvester tuning consists in modifying the mass and stiffness parameters that have been approximately defined in the very preliminary dimensioning. the dynamic parameters are finalized in detail at this stage; generally, their values are constant for the overall generator life: this is the simpler approach that well fits environments characterized by regular vibrations and repeatable pds. however sometimes the working regimes are strongly variable and the energy amount associated to vibrations is very scarce; in these cases, the adoption of active tuning systems able to change the dynamic f http://www.gruppofrattura.it http://dx.medra.org/10.3221/igf-esis.23.10&auth=true a. somà et alii, frattura ed integrità strutturale, 23 (2013) 94-102; doi: 10.3221/igf-esis.23.10 98 response of the generator is needed. unfortunately, active tuning systems generally cause additional power consumption and intense optimization activities are required to preserve acceptable values of efficiency. tuning systems with fixed response are, for example, arrays of vibrating structures with slightly variable geometry, stiffness variation by preloading, additional masses, etc. tuning systems providing variable response to the harvester are, for example, movable constraints, movable masses, variable external forces (e.g. magnetically induced), etc. mass 2mass 1 mass 3 k₁₂ k₂₃ figure 4: example of design strategy for amplifying the bandwidth of a capacitive generator through the coupling of modal shapes. another important parameter for the generator is the bandwidth. from the dynamic viewpoint, vibration harvesters behave like mechanical filters: the excitation signal induces the movement of the oscillating system according to its dynamic behavior. the harvester response is directly proportional to the generated energy, because the dynamic response drives the electro-mechanical transducer, independently to the typology. obviously, wide band generators are more performing than narrow band generators because the first ones are able to catch the energy associated to external forces in larger frequency ranges. in case of high variability of the excitation force, corresponding to very distributed psd, wide band harvesters are more suitable. there are many strategies to amplify the bandwidth; the most diffused are the modal coupling of many transducers (fig. 4), the series coupling of multiple generators, and the use of bi-stable structures. system architecture and duty cycle he activity of design and dimensioning of the generator must be supported by the detailed information about the characteristics of the overall autonomous system including its performances, sampling rate, frequency of data transmission, etc. for this reason, the best definition of this step of activity is ‘self-powered system design’ instead of simply ‘energy harvester design’; in fact, the definition includes also the electrical parameters of the utilizer and the device performances. although the typology of components included in the autonomous system may vary among the applications, usually the following functional blocks can be identified (fig. 5): current rectifier, charge reservoir (storage battery), one or more sensing devices (sensors), and transceiver device. very frequently the energy generated by the harvester is stored in the battery before to be used; this operation requires the preliminary conversion of the alternate current produced by the harvester in continuous current. the charge storing, is an expensive activity in terms of energetic efficiency, however it is often necessary due to some reasons: firstly, to provide continuous supply also in case of irregular power supply; secondly, to reach the prescribed energy threshold needed to supply the utilizer. the energy produced by the harvester and stored in the battery can be used for the supplying only when the minimum charge threshold is reached; this lower level of the battery charge is imposed by the energetic demand of the utilizers. similarly, the time interval when the power flows from the battery to the utilizer must be calculated in function to the t http://www.gruppofrattura.it http://dx.medra.org/10.3221/igf-esis.23.10&auth=true a. somà et alii, frattura ed integrità strutturale, 23 (2013) 94-102; doi: 10.3221/igf-esis.23.10 99 energy consumed in the unit time. the constraints mentioned are well considered in defining the duty cycle of the selfpowered system. the adoption of dedicated strategies addressed to the reduction of the energy consumption is vital for the proper working of the system; for instance, power management operations should be implemented, which consists in activating the system only above specified charge threshold of the battery (triggering) or in switching-off some components (e.g. the antenna) during data measurement and processing. figure 5: typical architecture of self-powered sensing system. experimental comparison of performances his section reports the experimental characterization of the performances of two typologies of energy harvesters: piezoelectric and magnetic inductive. the generators are tuned during the tests by modifying their resonance through additional masses or by changing the stiffness of the deformable parts. different values of the input acceleration are imposed, in order to verify the variation of the electro-mechanical response. the measurements were conducted by using the dedicated test equipments described in the following. test bench the test bench for the experimental tests is composed by the parts reported in the following scheme (fig. 6). figure 6: blocks diagram of the test bench for the experimental characterization of the harvesters. piezoelectric generators two types of piezoelectric generators are reported in fig. 7. the first generator is commercialized by cedrat technologies for applications in the aeronautic field [14], the second generator is a laboratory prototype fabricated for harvesting energy from railway vehicles and integrates the transducer duraact p-876.a12 [4]. their principal characteristics are summarized in tab. 2. the commercial harvester is composed by two piezoelectric blocks situated within a metallic frame that, under vibrations applies the tensile-compressive load to the electro-mechanical transducer according to modal deformation. the selected design gives high stiffness to the structure (100 n/mm nominal) and increases the resonance frequency up to about 400 hz. the laboratory prototype, instead, is based on the deformation of the piezoelectric cantilever in the flexural mode: this configuration allows maximizing the ratio between the material strain and the applied force. then, the harvester stiffness can be reduced to only 0.06 n/mm and the resonance frequency is lowered to about 27 hz. the drawbacks of t http://www.gruppofrattura.it http://dx.medra.org/10.3221/igf-esis.23.10&auth=true a. somà et alii, frattura ed integrità strutturale, 23 (2013) 94-102; doi: 10.3221/igf-esis.23.10 100 the second solution are mainly related to the reduced reliability of the transducer, which is made of brittle material subjected to fatigue effect. however, the polymeric package that coats the piezo surface of the commercial transducer provides sensitive improvements to the component lifetime (longer than 106 cycles with 1 g acceleration). cedrat generator laboratory prototype dimensions (mm) 48x13x10 60x35x0.5 capacity (nf) 3150 90-150 optimized load (kω) 0.47 200 resonance frequency (hz) 405 27 table 2: some properties of the two piezoelectric generators. (a) (b) figure 7: (a) piezoelectric generator working in tension-compression veh-apa 400m-md (cedrat technologies); (b) laboratory prototype of flexural generator made with duraact p-876.a12 transducer. the preliminary characterization of the generator, which is mandatory for piezoelectric harvesters, is addressed to the identification of the optimum resistive load associated to the transducer. for this type of generators, the output power is function of the electric resistance connected in series to the generator. the electric resistance is partially provided by the conditioning electronics, the rectification circuit and other electronic components. the characterization revealed that the commercial transducer has the optimum load at 0.47 kω and the laboratory prototype at 200 kω. fig. 8 reports the power curves referred to the generators. different masses were applied to the metallic frame in the first case and to the cantilever tip in the second case to modify the harvester response. in fig. 8a it is clearly visible the shift of the resonance peak due to the mass change; this strategy is suitable for tuning the resonance of the generator on different values of the excitation frequency. in fig. 8b, the ratio seismic mass/deformation is sensitive to the transducer configuration for constant input acceleration. in this case, all measurements are referred to the system resonance. (a) (b) figure 8: output power generated by commercial harvester as function of the excitation frequency (a) and by laboratory prototype as function of the resistive load in resonance conditions (27 hz) for variable seismic mass (b). http://www.gruppofrattura.it http://dx.medra.org/10.3221/igf-esis.23.10&auth=true a. somà et alii, frattura ed integrità strutturale, 23 (2013) 94-102; doi: 10.3221/igf-esis.23.10 101 magnetic inductive generators the schematic drawing of the magnetic inductive energy harvester designed and built by the authors in [5] is represented in fig. 9. for this type of generators, the selection of materials and dimensions of components is crucial for the electric output power and for the system frequency tuning. the magnetic suspension representing the stiffness of the transducer is determined by the magnetic field intensity associated to the magnets with opposite polarity; similarly, the electric current induced in the coil is proportional to the size of the oscillating magnet and to its relative velocity, which are both dependent to the suspension stiffness. in conclusion, the dimensioning is significantly complicated by the strong electromechanical coupling among the components and by the variability of frequency and acceleration of the excitation resulting from its spectrum. figure 9: schematic drawing of the magnetic inductive harvester prototype [5]. analytical models and numerical models based on finite element method were used to calculate the force-displacement characteristic of the magnetic suspension. the goal of experimental tests is to find characteristic curves suitable for the design in specific functioning conditions. some of the tests results are described in fig. 10; these curves are referred to a prototype composed by oscillating magnet on magnetic suspension, 4 coils connected in parallel and current rectifier. the resonance frequency of the harvester is 3.2 hz and the tests are conducted at 0.12 g acceleration. this particular typology of inductive generator has been addressed to applications in railway bogies [7], axels of industrial vehicles [9], telescopic arms, operative machines and sport equipment [8], where the excitation frequency range is localized at low values. (a) (b) figure 10: electric output of the magnetic inductive generator with 4 coils (3.2 hz, 0.12 g): (a) current and voltage and (b) output power. http://www.gruppofrattura.it http://dx.medra.org/10.3221/igf-esis.23.10&auth=true a. somà et alii, frattura ed integrità strutturale, 23 (2013) 94-102; doi: 10.3221/igf-esis.23.10 102 conclusions his work introduced the most important steps of the design autonomous systems for converting the kinetic energy of mechanical vibrations in electric power. the activity is focused on the self-powered sensing system design, instead of traditional simpler energy harvester design, with the aim of responding more exhaustively to the requirements of the application. from the energetic balance viewpoint, the concept of duty cycle is crucial, as well as the analysis of input vibration spectra through its psd and its time-dependent variability. these aspects, together with bandwidth amplification strategies and resonance tuning, provide the required information for selecting the proper transducer typology and for defining its dimension and dynamic properties. references [1] s. roundy, j. of intelligent materials and structures, 16 (2005) 809. [2] s. roundy, p.k. wright, j. rabaje, computer communications, 26 (2003) 1131. [3] s. priya, d.j. inman, “energy harvesting technologies”, new york, springer (2008). [4] g. de pasquale, a. somà, f. fraccarollo, in: proceedings of the institution of mechanical engineers part c: journal of mechanical engineering science, 226 (2011). [5] g. de pasquale, a. somà, n. zampieri, j. of computational and nonlinear dynamics, 7 (2012) 041011. [6] g. de pasquale, c. siyambalapitiya, a. somà, j. wang, in: proc. international conference on electromagnetics in advanced applications (iceaa), torino 465-468, (2009). [7] a. somà, g. de pasquale, device for diagnosing railway bogies by applying an energy-autonomous measuring and transmitting bolt, and corresponding control method, pct patent n. wo2011/117718 (2011). [8] a. somà, g. de pasquale, f. fraccarollo, racchetta da sci o trekking dotata di dispositivo harvester magneticoinduttivo di generazione elettrica, patent n. to2011a000844 (2011). [9] a. somà , g. de pasquale, sistema autoalimentato mediante harvester per monitoraggio ed infomobilità di applicazioni veicolistiche multinodali wireless, patent n. to2011a000694 (2011). [10] r. elfrink, t.m. kamel, m. goedbloed, s. matova, d. hohlfeld, y. van andel, r. van schaijk, j. of micromechanics and microengineering, 19, 094005 (2009). [11] s. cheng, d.p. arnold, j. of micromechanics and microengineering, 20 (2010) 025015. [12] y. chiu, v.f. tseng, j. of micromechanics and microengineering, 18 (2008) 104004. [13] y. suzuki, d. miki, m. edamoto, j. of micromechanics and microengineering, 20 (2010) 104002. [14] http://www.cedrat-technologies.com. t http://www.gruppofrattura.it http://dx.medra.org/10.3221/igf-esis.23.10&auth=true microsoft word numero 24 articolo 6 e. m. nurullaev et alii, frattura ed integrità strutturale, 24 (2013) 69-74; doi: 10.3221/igf-esis.24.06 69 special issue: russian fracture mechanics school optimization of fractional composition of the excipient in the elastomeric covering for asphalt highways e. m. nurullaev, a. s. ermilov perm national research polytechnic university. 614990 perm, komsomol prospect, 29. abstract. the computational method of optimum fractional composition of a dispersible filler of polymeric composite on the basis of three-dimensionally linked elastomer is developed according to non-linear programming. the coefficient of dynamic viscosity of polymeric suspension or the initial module of a viscoelasticity of the join solidification low-molecular rubbers with the final functional groups, filled by many fractional dioxide of silicon are considered as criteria of optimization. influence of the limiting volume filling on energy of mechanical destruction was investigated. the elastomeric material is offered for use as a covering of asphalt highways in the form of a frost-proof waterproofing layer, which allowing multiply to increase operating properties. keywords. viscosity; mechanical destruction; elastomeric composites with a dispersed filler; rheology; rubber; polymeric binder; asphalt highways. introduction ractional composition of a dispersed filler is essential for formation of rheological behavior of suspensions on the basis of fluid and viscid polymeric binding and mechanical characteristics of three-dimensionally linked filled elastomers. at the same time the major parameter of composition is effective extent of volume filling – / m  , herein  – volume proportion of solids of an filler, m – the limiting extent of volume filling depending on a form of particles and their distribution by the size, and also from physical and chemical interaction on border "a filler a binder". value m can be defined by the viscometric method [1] or calculated by a combinatorial and multiplicative method [2]. coefficient of dynamic viscosity  and the initial module of a viscoelasticity d e ,( 1) d with      are connected by a ratio (1): 2 / 1 1.25 1 / f f m r r o o m e e e                  (1) herein the "f" and "o" indexes fall into to the filled and free conditions of the polymeric binding. energy (work) of destruction was estimated in the form of the envelope by curve of destruction [4] dependences of the conditional ultimate break tension b (tension divided by the initial section of the sample) from break deformation b , bound to degree of the relative elongation by ratio 1 / 100%b b   . the line envelopes of around points of a break of exemplars and constructed in logarithmic scale (log log )b b  , corresponds to energy of mechanical destruction in the form of the area of the chart of stretching in cartesian coordinates: f http://dx.medra.org/10.3221/igf-esis.24.06&auth=true http://www.gruppofrattura.it e. m. nurullaev et alii, frattura ed integrità strutturale, 24 (2013) 69-74; doi: 10.3221/igf-esis.24.06 70 1 ( ) b ba d      (2) herein structural and mechanical dependence of the conditional tension from elongations extent  on condition of lack by abruption of particles of an filler from elastomeric binder, (for example, covering for asphalt), is proved by us earlier [5]:      2 21/3 3 1 1 2/( ) 1 29 exp 0.225 10 1 1.25 1 / m ch r m rt t t a                                (3) herein: /ch cm  : molar concentration of transversal chemical bonds in a polymeric basis a binder (  – polymer density, cm – an average statistical molecular mass); r : volume ratio of polymer in binder, containing softener; r : universal gas constant; t : equilibrium temperature at which concentration of transversal "physical" (intermolecular) communications ph is negligible; t : test temperature of an exemplar; gt : temperature of a structural glass transition of the polymeric binding; a : coefficient of high-speed mixing -3 1( 1 , 1.4 10 -standart for applications)a s      ;  : volume ratio of a dispersible filler; m : the limiting extent of volume filling of the elastomers, depending on a form and fractional composition of particles, and also from physical and chemical interaction on border "a filler a binder". value m can be defined by the viscometric method [1] or calculated by a combinatorial and multiplicative method [2]. value b in the eq. (2), as well as b , searched with the help of eq. (4): 3 3 3(1 / ) / ; (1 / )f o f ob b m m b b m              (4) herein the "f" and "o" indexes fall into to the filled and free conditions of an elastomer. breaking deformation of a elastomeric binder ob , defining by efficiency concentration of cross-links ( )eff ch ph    , was set experimentally [5]. research objective were development of a method of optimization of fractional composition of a dispersed filler for creation of a frost-proof waterproof elastomeric materials for covering for asphalt highways located in zones with sharply continental climate in form of rolled. theoretical study he problem of optimization of fractional composition of dispersible components of a polymeric material (for the given weight average particle sizes of fractions) taking into account realization of a condition of an optimality on other production characteristics can be formulated in the form of the formulation of a non-linear programming: ( , , ) max; min; minm r rq d e       1 2 3 1 ... j j m opt j j j j jm jv v               min max0 1, 1, 2, 3, ..., jv jv jv jv m       with j ni  / / n opt j jopt j opt j j j i x x       t http://dx.medra.org/10.3221/igf-esis.24.06&auth=true http://www.gruppofrattura.it e. m. nurullaev et alii, frattura ed integrità strutturale, 24 (2013) 69-74; doi: 10.3221/igf-esis.24.06 71 herein , , q d   : vectors of volume fractions, sponginess and particle sizes of fractions of dispersible components as a part of a polymeric material respectively; opt j : optimum volume fractions of fraction an filler in structure; jv : volume fraction v : fraction by j -type an filler in structure; jm : number of j-type fractions of a dispersed component; min max, jv jv  : respectively the lower and upper bounds for volume fractions of fractions of solid components in structure; opt jx : optimum for the corresponding block of characteristics, for example, mechanical, mass concentration of firm disperse components in polymeric composition; j : density of disperse components; ni : a set of the indexes belonging to types of a filler, entering into a compounding of a polymeric material. in view of complexity, the task includes restrictions such as equalities, will be transformed to a problem of nonlinear programming with restrictions such as inequalities. the quantity of independent optimized variables is equal ( )jn m m  , herein m : number of types of solid components by a polymeric material. thus normalizing ratio in case of the solution of a task is carried out automatically. 1 1 j n n m opt jv j j i v j i         further the vector of optimum volume fractions of fractions of filler in composition is defined: ( ; ); 1, 2, 3, ..., opt opt jv j n ji v m      herein opt jv : an optimum volume fraction v : fraction by j -type a filler. transition to optimum mass concentration of the relevant fractions of firm components ( ; ; 1, 2, 3, ..., ) opt optj jv j n jx x i v m      is carried out on a formula: ( ) / ( / )opt opt optjv jv j j jx p     herein 1 j n n m opt opt jv j j i v j i p x x       is the sum of mass concentration (shares) of solid components by a polymeric compositing. experimental study haracteristics used a fraction of silica as a dispersed filler for slurry on based low-molecular rubbers (oligomers) with final epoxy groups polydienurethanepoxide (trademark pdi-3b) and carboxyl groups polybutadiencarbocsilate (trademark skd-ctr) are shown in tab. 1. surface by response of function in the projection in the chart gibbs "composition-property" (fig. 1), which we obtained by the developed computer program [3], demonstrates the calculated dependence of value /r f o   the investigated polymer slurry from the volume ratio of the three fractions of silica, differing characteristics in accordance with tab. 1. constant volume fraction of filler is 0.75. in all cases, the calculation of the limit of bulk fill m , through the coefficients of the porosity of various mixtures of fractions implemented with help by the coefficients of the porosity of individual fractions identified viscometric method [1]. at the same time physical and chemical factors influencing the limiting filling c http://dx.medra.org/10.3221/igf-esis.24.06&auth=true http://www.gruppofrattura.it e. m. nurullaev et alii, frattura ed integrità strutturale, 24 (2013) 69-74; doi: 10.3221/igf-esis.24.06 72 of a polymeric binder takes into account "automatically", according to the physical nature of viscosimetric method. it can be seen that the minimum value of the relative coefficient dynamic viscosity r is provided an optimal ratio of volume fractions of fractions (rounded): 600µ 30µ 1µ = 0.5: 0.3: 0.2. it shows also the experimental values r . characteristics 1 (small) 2 (medium) 3 (large) porosity (volume fraction of pores) 0.450 0.384 0.379 void ratio (the ratio of the volume fractions of pores and particles) 0.818 0.623 0.610 weight average particle size, µ 1 30 600 table 1: characteristics fractions of silica. figure 1: the calculated and experimental dependences of the relative dynamic viscosity polymer slurry based by polydinurethanepoxide (pdi-3b) and polybutadiencarboxilate (skd-ctr) from volumetric ratios of 3 fractions of silica: a, b levels calculated iso-viscosity, round icons experimental data.    figure 2: envelopes by points of destruction [σb (mpa) = f [εb (%)] (in logarithmic scale) of the samples elastomer filled bifraction (black symbols) silica three fraction (white symbols) of silica: a sample of t = 323 k the standard t = 323 k a sample of t = 223 k the standard t = 293 k a sample of t = 293 k the standard t = 223 k http://dx.medra.org/10.3221/igf-esis.24.06&auth=true http://www.gruppofrattura.it e. m. nurullaev et alii, frattura ed integrità strutturale, 24 (2013) 69-74; doi: 10.3221/igf-esis.24.06 73 experimental study of prescription's parameter / m  filled elastomer at strain-strength characteristics, expressed in the form of envelopes by destruction was carried out using silica the following fractional composition: 1 initial test sample (240: 5) µ = (20: 80)% 2 prototype (240: 5: 1) µ = (40: 40: 20%). as the polymer binder used stoichiometric mixture (1: 2 moles) of low molecular weight rubber trademarks pdi-3b and skd-ctr, three-dimensionally cross-linked three-functional aromatic epoxy resin trademark eet-1 (1 mol). specific surface area of contact "filler-binder" in both cases remained constant. indication in fig. 2 (with the normal motion from the lower to the upper right) shows that at a fixed value of the volume fraction of silica 0.712  modified effective volumetric filling / m  from 0.712 / 0.752 = 0.946 to 0.712 / 0.816 = 0.72 leads to an increase in the energy by mechanical destruction by elastomeric composite 1.5 1.7 times. reducing the maximum degree of volume filling from 0.946 to 0.872 promotes increase "return" of the polymeric binder in the growth of energy mechanical destruction elastomer composite in accordance with the mathematical relationship (2, 3, 4). [5]. thus, the use by optimal multifractional filler for constant chemical composition of the composition allows for increase significantly in service life of the studied composite material which offered as frost-resistant waterproof covering (oilfired sub-layer) for asphalt highways located in areas with sharply continental climate. use as frost-resistant waterproofing covering which filled three-dimensional cross-linked elastomer, provides an elastically deformability surface of the road-load transport in the temperature range of 223 k ... 323 k (-50 ... +50 ° c); this prevents the massive destruction of asphalt at alternating temperatures and operating loads at the expense of phase transitions' water-ice-water ", which accompanied by a volume expansion of ice when water freezes in the initial cracks of asphalt. the following is an example of the engineering realization of recommended material.  the composition contains: a polymer binder (in the ratio 1: 2) polydienurethanepoxide with final epoxy groups (pdi-3b) and polybutadiencarbocsilate with a terminal carboxyl groups (skd-ktr) (13.5 wt.%),  natural macro crystalline quartz (57.4 wt.%); fumed silica grade "aerosil-380" (24.6 wt.%),  processing aids: thixotropic amplifier of elastomer and pigment technical carbon (3.0 wt.%), three-dimensional cross-linking agent epoxy gum brand eet-1 (1.45 wt.%), three-dimensional crosslinking catalyst acetolacetonate fe (0,05 wt.%).  blending components conducted at 55 60 ° c in a continuous mixer such as "snd-75", followed by formation of canvas width 3.0 meters and a thickness of 0.012 m (12 mm). three-dimensional cross-linking the polymer base material was conducted out in a continuous drum-vulcanizer at a temperature 170 180 ° c with a residence time in the apparatus 7-5 minutes respectively. received and rolled from rolls (25 meters long each) on the asphalt, smearing by liquid bitumen (oil), waterproof canvas with a relative speed of uniaxial tension 1.4 • 10-3 s-1 had the following mechanical characteristics specified in tab. 2. in the same part of the recommended composition based on a threedimensional cross-linked elastomer filled three-fraction silica. such a roll material on intermediate "glue" layer of liquid bitumen (oil), is to protect the asphalt canvas based on bituminous binder, becoming brittle in the cold, from the ravages of a pair of "water ice" these characteristics indicate on increased frost-resistant developed coating of asphalt highways and you can use it in a wide temperature range for 20 ... 30 years. composition volume fractions mechanical properties 323 к 293 к 223 к polimeric binder: rubber skd-ctr; rubber pdi-3b; epoxy eet-1 0.288 0.712 σb, мpа 0.25 εb, % 55 σb, мpа 1.20 εb, % 32 σb, мpа 6.00 εb, % 22 filler: silica (240:5:1) µ = (40:40:20)% table 2: mechanical characteristics of composition. http://dx.medra.org/10.3221/igf-esis.24.06&auth=true http://www.gruppofrattura.it e. m. nurullaev et alii, frattura ed integrità strutturale, 24 (2013) 69-74; doi: 10.3221/igf-esis.24.06 74 conclusions ased on non-linear programming was developed mathematical optimization method of fractional composition of the disperse filler, which significantly affects the coefficient of dynamic viscosity of the suspension and the energy of mechanical destruction three dimensional cross-linked elastomeric composite. also was proposed formulation of the polymer compositions based on low molecular rubbers with final functional groups, filled with silica optimal fractional composition, allowing increase the service life of asphalt highways. in relation of frost-resistance and waterproofing of the created coating based of the filled elastomer, engineering example shows the practical effectiveness of the proposed method to increase the service life of asphalt highways. references [1] a. s. ermilov, k. zyryanov, plant laboratory. diagnostic materials, 67(9) (2001) 62. [2] a. s. ermilov, a. m. fedoseev, j. of applied chemistry, 77(7) (2004) 1218. [3] certificate number 2012613349 rf. software identify and optimize the packing density of solid dispersed polymer composite fillers materials (rheology). / ermilov a. s, nurullaev e. m., duregin k. a. priority from 09.04.2012. [4] t. l. smith, j. appl. phys., 35 (1964) 27. [5] a. s. ermilov, e. m. nurullaev, mechanic composite materials, 48(3) (2012) 359. b http://dx.medra.org/10.3221/igf-esis.24.06&auth=true http://www.gruppofrattura.it http://www.gruppofrattura.it microsoft word numero 24 articolo 1 t.v. tretiakova et alii, frattura ed integrità strutturale, 24 (2013) 1-6; doi: 10.3221/igf-esis.24.01 1 special issue: russian fracture mechanics school relay-race deformation mechanism during uniaxial tension of cylindrical samples of carbon steel: using digital image correlation technique t.v. tretiakova, v.e. vildeman center of experimental mechanics, perm national research polytechnic university, 614990, komsomolsky av., 29, perm, russia abstract. the work deals with experimental study of macro localization of plastic yielding occurrences of structural carbon steel, research of singularity of deformation wave processes by complex use of contemporary test equipment and high effective digital image correlation method. evolution of nonuniform axial strain fields on surface of cylindrical samples during uniaxial tension was registered, time dependences were drawn, and a ‘relay-race’ mechanism of material deformation was found out at the stage of yield plateau forming. strain concentration ratio was estimated for several material deformation stages. keywords. digital image correlation; wave effects; strain localization; carbon steel. introduction great number of scientific literature deals with experimental study issues of plastic strain in solid bodies, specifically, authors repeatedly point out that plastic strain develops nonuniformly both in space (strain localization) and in time (time evolution of localization) [1, 2]. striking examples of plastic strain localization on macroscopic level are chernov-lüders lines, initiation and evolution of necking effect on postcritical deformation stage [3, 4], and also waves of localized plastic strain. the aim of this research was experimental investigation of regularities of plastic yielding macro localization for structural steel, study of singularities of wave deformation processes by complex use of contemporary testing equipment and noncontact strain measuring facilities. material and test procedure tructural carbon steel 20 (gost 1050-88) was chosen as the research subject. mechanical tests on uniaxial tension of solid cylindrical samples (test portion length of 16 mm, sample’s diameter of 9.5 mm) were conducted on instron 8850 universal biaxial servo-hydraulic testing system with constant kinematic loading speed of 2%/min. noncontact registration and displacement and strain fields review were carried out by three-dimensional vic-3d digital optical system (fig. 1). video-system’s software is based on digital image correlation technique (dic). dic is a highly effective non-contact, computer-vision-based method for measuring displacement and strain fields on specimen’s surface by correlating digital images captured during loading or exploitation process [5]. the digital optical system can be used for problem solving of deformable solid mechanics: experimental investigation of nonuniform strain fields and analysis of failure conditions in bodies with concentrators of different geometry [6, 7], research of inelastic material deformation processes in complex strain-stress conditions, study of displacement and strain fields evolution during crack initiation, damage accumulation and material failure [8–10], etc. the video-system contains a s http://dx.medra.org/10.3221/igf-esis.24.01&auth=true http://www.gruppofrattura.it t .v. tretiakova et alii, frattura ed integrità strutturale, 24 (2013) 1-6; doi: 10.3221/igf-esis.24.01 2 digital monochrome cameras, sample illumination systems, calibration grids, synchronizing hardware for communication with the test system, and specialized software which allows programming of video recording (vic-snap) and mathematical treatment of test data (vic-3d). in tab. 1 these parameters are shown. figure 1: the non-contact three-dimensional digital optical system vic-3d. hardware 2 digital b/w dcp cameras resolution 4 mp maximum videotaping speed 15 image/s videotaping speed in current tests 0.2 image/s software 3d digital image correlation (vic-3d) subset 19 pixels step 4 pixels correlation criteria nssd tensor type (strain calculation) lagrangian finite strain tensor table 1: technical parameters of strain field registration. correlation of digital images was carried out by nssd criteria (normalized sum of squared difference), which offers the best combination of flexibility and results. 2 2 2 i i nssd i i i f g g f g           (1) in the software the lagrangian finite strain tensor was used for strain field estimation:  , , , ,1 2 ij i j j i k i k ju u u u    (2) test results ests on uniaxial tension were carried out on 5 solid cylindrical samples. the tensile test diagram for carbon steel is shown in fig. 2. the load-extension curve includes yield drop (ii) and yield plateau (iii–v) forming stages, and also an extensive post-critical deformation stage (vii–viii). evolution of nonuniform axial strain fields for marked dots (i–viii, fig. 2), calculated by using the vic-3d system, is illustrated in fig. 3. at the elastoplastic deformation stage at the moment of transition through an upper yield point (point t http://dx.medra.org/10.3221/igf-esis.24.01&auth=true http://www.gruppofrattura.it t.v. tretiakova et alii, frattura ed integrità strutturale, 24 (2013) 1-6; doi: 10.3221/igf-esis.24.01 3 ii), initiation and evolution of axial strain wave front (points iii–v) was captured lengthwise the sample axis. plastic strain is becoming macro localized during further loading at the material hardening stage (points vi, vii), which causes the necking effect in center part of the sample. at point viii the deformed state of cylindrical samples equals its limit, at which macro scale destruction of material occurred. figure 2: the tensile test diagram for carbon steel. figure 3: evolution of axial strain fields during uniaxial tension of cylindrical sample. http://dx.medra.org/10.3221/igf-esis.24.01&auth=true http://www.gruppofrattura.it t .v. tretiakova et alii, frattura ed integrità strutturale, 24 (2013) 1-6; doi: 10.3221/igf-esis.24.01 4 axial strain distributions were drawn to appraise inhomogeneity of the material deformation process on sample surface (fig. 4). designation of curves (i–viii) coincides with points on the tensile test diagram (fig. 2). it is clear that at the moment before sample destruction, significant strain localization is observed in the central part and is about 200%yy  , while average strain is 32%. the elasto-plastic material deformation stage demands for a more thorough study, specifically at the moment of yield drop and yield plateau forming (fig. 5). figure 4: axial strain distributions on surface of cylindrical sample. at the elastic stage deformation of material was happening macro-homogeneously along the full sample length. as was mentioned above, the abrupt strain flash appeared (curve iii, fig. 5) at the moment of transition through an upper yield point (point ii, fig. 2), and a wave front of axial strain was initiated. the wave front is going from one grip to another with the speed of about 12-15 mm/min. macro loading speed of the sample is 0.32 mm/min. figure 5: axial strain distributions at the elasto-plastic deformation stage. http://dx.medra.org/10.3221/igf-esis.24.01&auth=true http://www.gruppofrattura.it t.v. tretiakova et alii, frattura ed integrità strutturale, 24 (2013) 1-6; doi: 10.3221/igf-esis.24.01 5 on the basis of experimental data time dependences of axial strain were determined for five areas of material, marked on the surface of sample test portion (fig. 6). at the material hardening stage and postcritical stage as well, the center point (1) speed of deformation is considerably higher than the other; at the same time, equidistance points (1 and 5, 2 and 4) deform with equal speed. time inhomogeneity on elasto-plastic stage has wave-like behavior (fig. 7). the step-by-step involvement of parts of cylindrical samples into the material deformation process is observed (1–5, fig. 7). point 1, which is located at the edge of the sample test portion, starts first. when it reached a certain level of axial strain, the material stopped deforming in this area. during the deformation process, next point (2) is engaged, and so on. this effect can be named the ‘relay-race mechanism’ of deformation, which happens at the stage of yield plateau forming. during further loading at the material hardening stage the axial strain level increased at point 3. this fact confirms the occurrence of localization process in the center area of solid cylindrical sample test portion. figure 6: time dependences of axial strain for five areas of material. figure 7: time dependences of axial strain at the stage of yield plateau forming and at the material hardening stage. in turn, the elastic unloading of peripheral specimen parts was registered at the postcritical deformation stage (1, 5). the elastic unloading for the first area was about 0.120%, for area 5 it was 0.135%. with the aim of quantitative estimation of axial strain concentration, which is caused by localization of plastic yielding in material, the following coefficient was considered: max yy yyk   (3) http://dx.medra.org/10.3221/igf-esis.24.01&auth=true http://www.gruppofrattura.it t .v. tretiakova et alii, frattura ed integrità strutturale, 24 (2013) 1-6; doi: 10.3221/igf-esis.24.01 6 where yy is the average value of axial strain, determined by using the complementary module of video system’s software ‘virtual extensometer’; maxyy is the maximum value of axial strain on sample surface. the ‘virtual extensometer’ differs from mechanical extensometers generally in that the former is used after the testing procedure, during post processing, while the latter is used in real-time mode. with the help of the ‘virtual extensometer’ it is possible to simulate the use of several ‘extensometers’ on the same specimen [8]. tab. 2 given below shows results of estimation of axial strain concentration for different material deformation stages (points i–viii at the tensile test diagram for carbon steel). high value of axial strain concentration coefficient is observed at the material softening stage, and also at the moment of transition through an upper yield point, which was demonstrated in this paper. point load, kn yy , % max yy , % k i 13.134 0.086 1.0 ii 24.057 0.148 1.0 iii 22.504 0.360 2.580 7.2 iv 22.326 1.013 2.962 2.9 v 22.389 1.484 2.626 1.8 vi 28.742 4.503 5.935 1.3 vii 33.974 14.156 23.105 1.6 viii 23.980 32.719 201.978 6.2 table 2: estimation of axial strain concentration, which is caused by localization of plastic yielding in material. conclusion he findings confirm the existence of space-time inhomogeneity in material inelastic deformation process; specifically the ‘relay-race mechanism’ of axial strain contribution was discovered and quantitatively investigated at the stage of yield plateau forming on the surface of a cylindrical carbon steel sample. the degree of strain macro localization was analyzed under the conditions of initiation and evolution of necking effect during uniaxial tension. though there is significant reduction of cross-section area in the sample center, inhomogeneity of deformation process at the post critical stage is commensurable with inhomogeneity initiated by motion of axial strain wave front. therefore, on the basis of these findings we can make a conclusion about the efficiency of digital image correlation technique and the noncontact 3-d video system. issues of exposure of automodel parameters of inelastic deformation processes (loadingrate effect, loading conditions, shape effect) are not fully determined and require further complex investigation. references [1] l.b. zuev, v.i. danilov, s.a. barannikova, plastic flow macrolocalization physics, (2008) 328. [2] l.b. zuev, v.i. danilov, s.a. barannikova, v.v. gorbatenko, physics of wave phenomena, 17(1) (2009) 66. [3] v.e. vildeman, j. appl. maths mechs, 62(2) (1998) 281. [4] v.e. vildeman, a.v. ipatova, m.p. tretyakov, t.v. tretyakova, bulletin of lobachevsky nizhny novgorod university, 4(5) (2011) 2063. [5] m.a. sutton, j.-j.orteu, h.schreier, image correlation for shape, motion and deformation measurements, (2009) 364. [6] v.e. vildeman, t.v. sannikova, m.p. tretyakov, problems of mechanical engineering and machine reliability, 5 (2010) 106. [7] v.e. vildeman, t.v. tretyakova, d.s. lobanov, perm state technical university. mechanics bulletin, 4 (2011) 15. [8] t.v. tretyakova, m.p. tretyakov, v.e. wildemann, perm state technical university. mechanics bulletin, 2 (2011) 92. [9] v.e. vildeman, t.v. tretyakova, d.s. lobanov, perm state technical university. mechanics bulletin, 2 (2012) 34. [10] t.v. tretyakova, v.e. vildeman, factory laboratory. diagnostic materials, 6 (2012) 54. t http://dx.medra.org/10.3221/igf-esis.24.01&auth=true http://www.gruppofrattura.it microsoft word numero_61_art_36_3498.docx m.e. kerkar et alii, frattura ed integrità strutturale, 61 (2022) 530-544; doi: 10.3221/igf-esis.61.36 530 study of structural stability of a concrete gravity dam using a reliability approach mohamed essaddik kerkar, mustapha kamel mihoubi national higher school for hydraulics, algeria m.kerkar@ensh.dz, https://orcid.org/0000-0001-9241-9578 mihkam@ensh.dz, https://orcid.org/0000-0002-7858-0127 abstract. dam safety is a priority at the international level, it requires a large amount of data that allows analysts to make optimization on its structural stability, the latter is based on the estimation of the probability of failure from the effects of stress and resistance acting on the dam-reservoir system. this investigation is to establish a methodology in order to optimize the safety of a concrete gravity dam in operation by carrying out a risk analysis which includes the identification of the sources of danger in terms of scenarios that can occur due to a failure on the dam-reservoir system on an implication of natural hazards (floods, earthquakes) and technical accidents such as malfunction of a spillway gate, drain valve, drainage system or important silting. reliability methods provide a basis for the probabilistic assessment of the structural safety of a dam. they make it possible to take into account in a probabilistic context, the uncertainties in the data associated with the calculation parameters used in the justifications of structural stability and make it possible to assess as closely as possible the intrinsic safety of a concrete gravity dam. keywords. probability of failure; reliability of dam; first order reliability method; monte carlo simulation; latin hypercube sampling. citation: kerkar, m.e., mihoubi, m.k, study of structural stability of a concrete gravity dam using a reliability approach, frattura ed integrità strutturale, 61 (2022) 530-544. received: 05.03.2022 accepted: 31.05.2022 online first: 19.06.2022 published: 01.07.2022 copyright: © 2022 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. introduction n recent years, various research projects have focused on the field of risk management for construction projects, that are affected by a variety of risk categories such as economic, environmental, political, financial, geological and technical risk, etc. during their service life, they involve many authorities whose interests and needs must be taken into account in the decision-making system in order to ensure the success of the project [1]. the failure history of dams enables risk analysts to know the failure scenarios. it provides information on what can happen to other dams in service, this analysis presents a field in full development, the result obtained presents a mathematical inflection of the uncertainty related to the parameters introduced in the dam stability calculation which means that the uncertainty is expressed in terms of failure probabilities. contrary to traditional deterministic i https://youtu.be/rohitv6l6wo m.e. kerkar et alii, frattura ed integrità strutturale, 61 (2022) 530-544; doi: 10.3221/igf-esis.61.36 531 approaches, probabilistic methods have been increasingly recognized for their facing uncertainties in the face of modern engineering problems, they are necessary to investigate the effect of uncertainty in the input data on the stability of structural systems [2]. according to the international commission on large dams (icold) the term risk implies a certain form of action in the face of uncertainty it has a universal meaning but can be interpreted in different ways. however, dominic reeve (2010) has described risk as a probability of failure or default, consequences can be measured in many forms but often converted to monetary values, so risk has units of expenditure rates ($/month, quarter, or year) [3]. it is referred to as r and is defined as the expected consequences c associated with a given activity multiplied by the probability p that this event will occur [4, 5]. risk assessment provides a structured and systematic examination of the probability of damaging events with their consequences and also is the essential element serving as the basis for the entire safety management process [6]. to optimize the reliability of a dam, it is important to take into account the natural ultimate cases (high floods, earthquakes) and the degree of operation of the operating equipment. the probabilistic modelling of resistances and stresses by building a class of dam-reservoir system data that have uncertain behaviour by risk treatment models by combining the previous cases between them to create scenarios, gives an important axis to improve the structural and functional safety in a dam, this analysis technique by using a set of algerian dams (boussiaba, oued fodda, beni harroun, koudiat acerdoune, hamiz and tichy haf) will be the subject of context under the title; structural stability study of a concrete gravity dam by reliability optimization approach. figure 1: combination between structural reliability and functional reliability (proposed scenario). m.e. kerkar et alii, frattura ed integrità strutturale, 61 (2022) 530-544; doi: 10.3221/igf-esis.61.36 532 job requirements ncertainty can affect several parameters that are included in the calculation of the stability of a dam such as; concrete and sediment density, ice thrust, operating water levels, etc. in this computation the random variables considered are the angle of friction 'φ' and the cohesion ‘c’. on the one hand corresponding along the dam foundation interface, it is assumed that the uncertainty is produced by the change in the space where samples were taken (heterogeneous foundation) and by inaccuracies relative to the laboratory during shear tests. on the other hand, in the body of the dam (concrete-concrete) the variation of 'φ' and 'c' is produced by the phenomenon of concrete degradation, it was supposed a gaussian distribution to the laws governing these physical characteristics. in order to optimize the safety of a dam it is necessary to take into consideration the normal case of operation and the natural ultimate cases (high floods, earthquakes), the reliability analysis will be made according to the different situations of load combinations, i.e, normal, exceptional and extreme cases, this type of optimization is called structural reliability. recently, abdollahi et al. [7] proposed an uncertainty aware framework for dynamic shape optimization of gravity dams under stochastic loads. the suggested reliability-based design optimization (rbdo) study is not only efficient in incorporating different source of uncertainties but also guarantee system safety accurately. another type of optimization called functional reliability groups together the operating rates of the operating equipment; spillways gates, drain valves, drainage system and the degree of silting in the dam (sediment elevation) these factors influence directly on the stability of dam, the combination between these parameters and the cases of operation mentioned above gives different scenarios (ci) called possible operating scenarios that may encounter a dam during its service life for example; the combination of normal operating cases (normal water level) with the drainage operating rate (x% =90%, 50%, 5%) gives the scenarios c1, c3, c5 at the concrete/foundation interface and c2, c4, c6 at the concrete/concrete interface and under the same conditions when the elevation of the sediments equal to half the height of the dam we will have c7, c11, c15 and c8, c12, c16 (fig. 1). the pf value obtained is the result of the calculation by the methods; first order reliability method, monte carlo simulation and latin hypercube sampling which give an estimate of the reliability of the dam for each scenario ci in relation to the landslide phenomenon, the most likely value among these three methods gives an approach to optimize the reliability of the dam under study (fig. 2). figure 2: flowchart for calculating the probability of dam failure u m.e. kerkar et alii, frattura ed integrità strutturale, 61 (2022) 530-544; doi: 10.3221/igf-esis.61.36 533 literature review ccording to some historians, the start of probability calculus is linked to the industrial revolution in the 17th century and is intimately linked to the emergence of combinatorics, whose development will accompany that of probability calculus [8]. in the field of structural construction, experience has shown that gross error is the common cause of structural failure, the understanding of the human contribution to failure has grown considerably through major accident studies, matousek's work, based on the investigation of 800 cases of major damage to structural construction, has shown that human and gross errors contributed to 75-90 per cent of accidents, including; ignorance, negligence, insufficient knowledge and underestimation [4, 9]. thus, in any evaluation of strengths and loads there will be uncertainties related to variability in space (e.g. heterogeneity of foundations) and time (ageing) and variability in the response of the structure to a specific load. the probability of failure is considered as a rating on a scale, it is based on a detailed scaling and normalized to a scale of 1 to 5, the ratings are converted to a theoretical probability of failure [10] (tab. 1). this probability of failure ranking can be used to provide an indication of the potential need for repair work to be undertaken by reference to risk reduction guidelines (fig. 3). figure 3: regions of risk as a function of probability of failure [10, 11] probability classes description indicative value of the annual probability of default pf likely (5) the hazard may occur or a very bad data status has been established on the hazard. 10-2 very common (4) the hazard will be quite frequent or a poor state of data has been established regarding hazard. 10-3 unlikely (3) the hazard may occur occasionally or a moderate state of data has been established about the hazard. 10-4 unusual (2) the hazard may occur infrequently or a good state of data has been established about the hazard. 10-5 rare (1) the hazard can only occur in exceptional circumstances or when a very good state of data has been established on the hazard. 10-6 table 1: relationship between probability rating and probability of failure [10, 12)] a m.e. kerkar et alii, frattura ed integrità strutturale, 61 (2022) 530-544; doi: 10.3221/igf-esis.61.36 534 in the physical modelling the strength of a technical element is modelled as a random variable s, the element is exposed to a load l which is also modelled as a random variable [13]. the distributions of strength and load at a specific time t are shown in fig. 4. a failure will occur as soon as the load is higher than the strength, the reliability ri of element i is defined as the probability that the strength is greater than the load.   ir p(s l) p(a) (1) where p(a) denotes the probability of event a the load will usually vary with time and can be modelled as a time dependent variable l(t), the element will deteriorate over time due to failure mechanisms such as corrosion, erosion and fatigue, so the strength of the element will also be a function of time s(t) [13]. the failure time t of element i is the (shortest) time to l(t) > s(t), a possible realisation of s(t) and l(t) is in fig. 5. min t [t; s(t) l(t)] (2) the reliability ri (t) of the element can be defined as:  ir (t) p(t t) (3) figure 4: load distribution and resistance. figure 5: failure time and load-resistance relationship. the dam failure history is intended to assist risk analysis teams in estimating probability, it provides information on what has happened to other dams. dams can fail gradually or instantaneously, the type of failure depends on the initial cause and the type of dam [14], the failure may be natural due to natural deterioration of the structure, extraordinary natural events such as heavy rains and extreme floods, earthquakes, differential settlements, rock slides, piping problems, seepage, wave action, etc., or man-made caused by bombardment, sabotage, demolition for the public good, poor construction or design, poor location, and burial of animals [14]. since the failure of m.e. kerkar et alii, frattura ed integrità strutturale, 61 (2022) 530-544; doi: 10.3221/igf-esis.61.36 535 the teton dam (usa) in 1976, significant progress has been made and society continues to increase its demands for safety, reliability of critical infrastructure, design, construction and operation of dams should be integrated into the risk management framework where dam safety is not only a federal, state or local issue, it can affect people and property across locations, state and even national borders [15, 16]. concrete gravity dams are usually built from many monoliths, when a concrete gravity dam fails, one or more monoliths are washed away [17]. structural reliability he reliability of an engineering system can be defined as the ability to fulfil its design purpose for a specified period of time. this ability can be measured using the probabilistic theory that it will perform the function for which it was designed under given conditions and for a given duration. structural reliability is formulated in terms of a vector of structural system random variables, x = {x1, x2, ..., xn}, where {x1, x2, ..., xn} are the basic random variables which can describe loads, structural system dimensions, materials and these characteristics and properties of the cross-section [18, 19]. a limit state function, g (x) = 0 describes the operation of the system in terms of the basic random variables x, where s is the strength of the material making up the structure and l is the stresses (loads) exerted on the structure [20]. the safety margin m and the limit state function g can be written in the general form: g(x) g( ) m s, l (4) when we place ourselves in the physical space, the space formed by s and l, we notice that the limit state function allows us to divide the physical space into three domains (fig. 6):  g (s, l) < 0: failure domain;  g (s, l) = 0: limit state;  g (s, l) > 0: safety range. figure 6: failure domain, limit state and safety range. an analysis space can be defined for concrete dams based on two vectors; structural reliability models (x-axis) and deterministic models (y-axis), as shown in fig. 7. t m.e. kerkar et alii, frattura ed integrità strutturale, 61 (2022) 530-544; doi: 10.3221/igf-esis.61.36 536 figure 7: space for structural analysis of dam reliability [21]. the horizontal and vertical arrows in the figure above show the development trends followed by knowledge in each of its corresponding individual domains and an arrow indicates the diagonal direction combining advanced analytical methods for the behaviour of concrete dams with structural reliability methods, in order to obtain better estimates of the probability of failure in the context of risk analysis [21]. during the life cycle of a structure the failure rate follows the convex curve shown in fig. 8, it contains three phases; early failure phase due to design errors, phase where the failure rate is practically constant for a large part of the lifespan when degradation mechanisms are not manifested, third phase when the degradation phenomenon starts, leading to an increase in the failure rate; it is during this phase that preventive maintenance can improve structural reliability and extend its lifespan [22]. figure 8: bathtub curve [22]. second level reliability calculation methods in this level the form of the limit state is essential, it has explicit writing or by default with approximation. the estimation of the probability of failure can be carried out by analytical methods of the form (first order reliability method) and sorm (second order reliability method) type. reliability is defined as the probability of m.e. kerkar et alii, frattura ed integrità strutturale, 61 (2022) 530-544; doi: 10.3221/igf-esis.61.36 537 a function g(x), it is performance function which is greater than zero, p{g(x)>0}, it is the probability that the variables random x = (x1, x2,..,xn) will be in the safe region and is defined by g(x)>0. the failure can be defined as the probability p{g(x)<0}, i.e. the probability that the random variables x = (x1, x2,..,xn) will be in the failure region and is defined by g(x)<0 [23, 24, 25]. so if the joint probability density function of x is fx(x), the probability of failure is evaluated with the integral: x g(x) 0 {(g(x) 0} f (x)dx     fp p (5) reliability is calculated by: x g(x) 0 1 {g(x)>0} f (x)dx      i fr p p (6) the first step is to find the most probable point of failure in the space of standard variables, and then the limit state function is approximated by its first taylor expansion (form) or second order (sorm) around the point of conception [26]. the first order reliability method reduces calculation difficulties by simplifying the fx(x) integral and approximating the performance function g(x) so that solutions to formula 5 and 6 are easily obtained [27]. the performance function g(x) is approximated by the taylor expansion of the first order (linearization), for this purpose this method has the name first-order reliability it simplifies the functional relationship and reduces the complexity of the failure probability calculation, as it is implicitly expressed as a mean and standard deviation [27, 28]. the probability integrations in formula 5 and 6 are visualized with a two-dimensional case in fig. 9 which shows the conjoint of x that is fx(x) and its contours, which are projections of the area of fx(x) onto the plane x1-x2 that have the same values or probability density. figure 9: probability integration [26, 27] the hypothesis is to consider that the surface of the integral fx(x) forms a hill and this is cut by a knife with a curved blade g(x) = 0, the hill is divided into two parts, the left part will be on the side of g(x) > 0 as shown in fig. 9. the left volume on the left is the probability integration in formula 7 which presents the reliability, in other words the reliability is the volume below fx(x) on the side of the safe region where g(x) > 0 [27]. the first-order reliability procedure is described by three (03) steps which are as follows: step 1: the original space of the basic variables should be transformed into a standard gaussian space, called uspace. step 2: then you have to look for the famous design point in the new space. m.e. kerkar et alii, frattura ed integrità strutturale, 61 (2022) 530-544; doi: 10.3221/igf-esis.61.36 538 step 3: finally, the failure surface must be approached at this point to obtain an approximation of the probability sought [18]. reliability index the geometrical interpretation of the reliability index β when placed in a normalized space corresponding to the physical space is the minimum distance between the origin o of the normalized space and the limit state curve, it is determined as the distance between the mean and the point of failure (m = 0) in units of standard deviation, it is the most probable value of failure [20, 25]. the relationship between the reliability index and the probability of failure can be estimated by the following table: β 1.28 2.32 3.72 4 4.27 4.5 4.75 5.20 pf 10-1 10-2 10-4 3.2x10-5 10-5 3.4x10-6 10-6 10-7 table 2: relation reliability index β and probability of failure pf [29] third level reliability calculation methods in this technique the structural reliability methods encompass a complete analysis of the problem and involve integration of the probability density function, random variables are extended to the safety domain and are the most general in reliability techniques whose approach is to obtain an estimate of the integral by numerical mean [3]. in this context it can cite monte carlo simulations and the latin hyper cube method. monte carlo simulations this method offers a powerful means to evaluate the reliability of a system, due to its capability of achieving a closer adherence to reality, it may be generally defined as a methodology for obtaining estimates of the solution of mathematical problems. it is based on the repetition of system sampling, however, the number of simulated realizations is large in the control an acceptable precision to estimate the probability of failure [28]. consider for example the problem of integral i, it is a question of approaching: 1 0 g(x)dx i (7) various classical methods of a deterministic type exist; rectangles, trapezoids and simpson. the monte carlo method consists in writing this integral in the form: e[g( )]i u (8) where u is a random variable according to a uniform law on [0; 1], if (ui)i∈n is a sequence of independent random variables and a uniform law on [0; 1] [28], then: n i 0 1 g( ) e [g( )] n   iu u (9) in other words, if u1, u2, u3, u4,..., un., are randomly selected numbers in [0; 1]. 1 2 3 n 1 [g(u ) g(u ) g(u ) ......... g(u )] n     is an approximation of 1 0 g(x)dx i after definition problem in terms of design random variables and identification of these probabilistic characteristics in terms of probability density function and associated parameters (mean and standard deviation), the generation of values for these random variables followed by deterministic problem assessment for each data set gives us a conclusion on the probability m.e. kerkar et alii, frattura ed integrità strutturale, 61 (2022) 530-544; doi: 10.3221/igf-esis.61.36 539 of failure of the system under study [28, 30]. thus this method is the process that is used to estimate the sampling of the probability of failure of a structure, if nf is the number of simulation cycles in which the structure fails and n is the total number of simulation cycles, the probability of failure pf is expressed by [28, 30]:  ff n p n (10) latin hyper cube sampling method if we are talking about an array of symbols or numbers and each appears only once, the array is called a "latin square", extending this concept to higher dimensions for many design variables represents the term "hyper cube". hence, this method is the sampling method in a monte carlo approach, it is also known as “stratified sampling technique” [28]. each random variable can be subdivided into n intervals of equal probability, there are n points of analysis, randomly mixed, so each of the n compartments has 1/n of the probability of distribution. the general steps of this method are: 1decompose the distribution of each variable into n non-overlapping intervals with equal probability. 2select a value at random in each interval in relation to its probability density. 3repeat steps 1 and 2 until you have selected values for variables, such as x1, x2, ..., xk. 4combine the n values obtained for each xk with the n values obtained for the other at random xj≠i see fig. 10. figure10: basic concept of lhs with two variables and five realizations [28] application of the models he application of the three reliability methods on the beni harroun dam gave failure probabilities during certain scenarios, each scenario having its own specific load combinations, e.g. pf estimated in scenario 47 (c47) is the probability of failure at the landslide in relation to the dam-foundation interface when the dam is subjected to seismic loading and when the functional probability for the drainage system to operate at 90% is equal to 1. the calculation code retains the most unfavourable probability of failure (pf = 3.51x10-3) among the results of the three reliability calculation methods. the results are shown in tab. 3. t m.e. kerkar et alii, frattura ed integrità strutturale, 61 (2022) 530-544; doi: 10.3221/igf-esis.61.36 540 scenarios calculated pf optimized pf = max [pf form, pf hl, pf mc] pf form pf hl pf mc c11 4.1x10-4 4.1x10-4 4.09x10-4 4.1x10-4 c12 10-7 10-7 10-7 10-7 c35 4.4x10-3 4.61x10-3 4.82x10-3 4.82x10-3 c36 10-7 10-7 10-7 10-7 c47 3.2x10-3 3.35x10-3 3.51x10-3 3.51x10-3 c48 10-7 10-7 10-7 10-7 table 3: pf of the beni harroun dam during the scenarios; c11, c12, c35, c36, c47, c48 the application of the models was carried out on six (06) algerian dams (boussiaba, oued fodda, beni harroun, koudiat acerdoune, hamiz and tichy haf), the characteristics of these dams are moved in tab. 4. dams type of concrete age of service talus fruit height of the dyke (m) foundation length (m) ratio foundation length/dike height (r) upstream downstream boussiaba bcr < 50 years old 0 0.725 50.67 37.63 0.74 oued fodda bcr 50 to100 years old 0.1 0.675 101 67.5 0.67 koudiat acerdoune bcv < 50 years old 0.4 0.5 121 102 0.84 beni harroun bcr < 50 years old 0 0.8 118 93 0.79 hamiz masonry > 100 years old 0.25 0.5 50 47 0.94 tichy haf bcr < 50 years old 0 0.5 83.5 40 0.48 table 4: geometrical characteristics and service age of the dams to be studied the following figure shows the failure probability histogram for the three load combinations; normal, exceptional and extreme, it gives us the most probable pf for each assumed scenario. 0,00 0,05 0,10 0,15 0,20 0,25 0,30 0,35 0,40 0,45 0,50 0,55 0,60 0,65 0,70 0,75 0,80 0,85 0,90 0,95 1,00 c 1 c 2 c 3 c 4 c 5 c 6 c 7 c 8 c 9 c 10 c 11 c 12 c 13 c 14 c 15 c 16 c 17 c 18 p o b ab ili ty o f f ai lu re scenarios b) normal case boussiaba oued fodda koudiat a beni hraroune hamiz tichy haf 0,00 0,05 0,10 0,15 0,20 0,25 0,30 0,35 0,40 0,45 0,50 0,55 0,60 0,65 0,70 0,75 0,80 0,85 0,90 0,95 1,00 c 47 c 48 c 49 c 50 c 51 c 52 c 53 c 54 c 55 c 56 c 57 c 58 c 59 c 60 c 61 c 62 c 63 c 64 p ob ab ili ty o f f ai lu re scenarios b) extreme case boussiaba oued fodda koudiat a beni hraroune hamiz tichy haf m.e. kerkar et alii, frattura ed integrità strutturale, 61 (2022) 530-544; doi: 10.3221/igf-esis.61.36 541 figure 11: the histogram of failure probabilities for different load request scenarios if we consider that the probability for each scenario ci (from c1 to c64) to happen is pci = 1, the number of scenarios giving a likely probability (pf > 0.01) will be: likely 64 i 1 ( 0.01)   fp f cin p (11) the ratio between npf likely and the total number of scenarios will be: likely likely n 64  f p r (12) figure 12: ratio of cases giving a likely probability and the total number of scenarios for the dams studied according to these results we can see that the r likely of the tichy haf dam is 0.95 it is the most important among the dams studied, this majority is expressed by the type of dam (arch gravity dam) and its stability is not only 0,00 0,05 0,10 0,15 0,20 0,25 0,30 0,35 0,40 0,45 0,50 0,55 0,60 0,65 0,70 0,75 0,80 0,85 0,90 0,95 1,00 c 19 c 20 c 21 c 22 c 23 c 24 c 25 c 26 c 27 c 28 c 29 c 30 c 31 c 32 c 33 c 34 c 35 c 36 c 37 c 38 c 39 c 40 c 41 c 42 c 43 c 44 c 45 c 46 p o b ab ili ty o f fa ilu re scenarios c) exceptional case boussiaba oued fodda koudiat a beni hraroune hamiz tichy haf m.e. kerkar et alii, frattura ed integrità strutturale, 61 (2022) 530-544; doi: 10.3221/igf-esis.61.36 542 ensured by its own weight taken in the calculation but it is also ensured by the effect of transmission of part of the force s to the banks. the oued fodda dam is in second place with a value of r likely = 0.91 and the hamiz dam is in third place with a value of 0.53. these important values are caused by the degradation of the physical properties (angle of friction and cohesion) of the dam material due to the fact that the service life is considerable. depending on the relationship between probability rating and probability of failure (tab. 1), pf at normal load combinations c1, c2,..., c18 are strictly rare (pf ≤10-6) in; boussiaba, hamiz and koudiat acerdoune dams except pf c17=9x10-6 when the functional probability for hsediment= 2hdam/3 and the drain to function at 05% equal to 1 (p c17=1) at that moment the destabilizing shear and normal forces are high. on the contrary pf is unlikely at dam of beni harroun pf ≥10-4 in the dam/foundation interface due to the mixed nature of the foundation (limestone with fractured zones, decompressed marl and rift breach), this variety leads to an extended standard deviation value for ‘ᵩ’ which makes failure unlikely. for oued fodda dam pf is rare, unusual and unlikely in c1, c3, c7, c9 and c11, they correspond to a combination of normal load but with a functional probability for each scenario arriving equal to 1 (pci =1). pf c1 is the failure estimate when the drain is operating at 90%, same situation for c7 but with siltation of sediment at half hdam (hsediment=hdam/2) and for c9 hsediment = 2hdam/3. pf c3 is the estimated failure when the drain is operating at 50% and the same case for c11 but with hsediment = hdam/2. for the rest of the scenarios, pf is very known and probable, this value is caused by the drainage system, and we note that the rate of drain operation has a major influence on the stability of dams. according to these results, it can be noticed that pf tends towards 1 with the growth of shear forces due to hydrostatic forces; normal, exceptional and ultimate when it is caused by malfunctioning of the discharge and overflow gates during flood periods (c37,...c46). other sharp forces may occur during earthquakes due to the generation of an inertial force within the dam and a hydrodynamic force added to the hydrostatic forces, thus silting forces which will be proportional to the height of the sediment. the impact of the normal effort related to the forces of the suppressions on the value of pf is proportional to the degree of drainage activity, we note for boussiaba dam during an earthquake pf c47 = 6.7x10-3 when the drain is operating at 90% and pf c51 = 1 when it is operating at 05%. if one compares the results of the dams recently in service during certain ultimate scenarios (high sediment height); koudiat acerdoune gave us low pf compared to those of beni harroun and boussiaba, one can justify this difference by the geometrical nature of the profile across the dam of koudiat acerdoune (0.4 upstream and 0.5 downstream) on the other hand boussiaba and beni harroun have a zero upstream fruit with respectively 0.725 and 0.8 downstream. another supporting factor is the ratio r, which is equal to the length of the foundation and the height of the dam (r= [lfoundation/hdam], rboussiaba= 0.74 rbeni harroun= 0.79 and rkoudiat acerdoune= 0.84, i.e. as soon as r tends towards 1, the dam becomes stable (fig. 13). figure 13: number of scenarios giving a likely probability as a function of ratio r. 8 10 12 14 16 18 20 0,45 0,55 0,65 0,75 0,85 n u m b e r  o f  sc e n a ri o s  g iv in g  a  l ik e ly  p ro b a b il it y   ration foundation lenght/dike height (r) m.e. kerkar et alii, frattura ed integrità strutturale, 61 (2022) 530-544; doi: 10.3221/igf-esis.61.36 543 conclusion he uncertainty can affect several parameters that are included in the calculation of the stability and dimensioning study, generally this study are based on a deterministic approach in which parameters take fixed values without taking into account uncertainty. in this work the objective is to estimate the reliability of some algerian concrete gravity dams during the scenarios proposed in relation to the phenomenon of sliding, the uncertain parameters that have taken are; the friction angle 'φ' and the cohesion 'c' and those are random variables in space or in time along the dam-foundation interface and in the body of the dike (concrete-concrete). different load combinations have been proposed which are called failure scenarios (ci) that can encounter a dam during its service life as shown in fig.1, the assumption is to accept the probability of a scenario ci equal to 1 (pci = 1), the calculation of the probability of failure by the three methods (first order reliability method, monte carlo simulations and latin hyper cube sampling) has given us close and at times equal values and the idea is to take the most unfavorable value between these methods and consider it as the probability of failure to increase the safety margin. the exploitation of these results is an achievement in time to quantify the reliability of a dam by optimizing a maintenance and inspection policy, an example; on friday august 07, 2020, the beni harroun dam site received seismic activities with a magnitude of 4.9 on the richter scale according to the astrophysical and geophysical astronomy research center (craag), so if we accept that the operating rate for the drainage system is 90%, the pf at the time of the earthquake will be less than 3.51x10-3 and 10-7 respectively at the interface and at the heart of the dike, it is the inflection of the scenarios c47, c48 according to fig. 1 and if it will have a strong flood the probability of failure will be pf c19=1.1x10-3 and if there will be a failure in the drain valve or spillways gates during this flood pf c37=1.18x10-3. in conclusion this study is a means of control for the safety of a dam knowing that the scenarios proposed can cover the events which encounter this type of structure during its service life. references [1] rasool, m. (2012). dynamic and multi-perspective risk management of construction projects using tailor made risk, breakdow structures. doctorate, university of bordeaux1, france, 02. [2] azam, a., mehdi, a. m., seyed, a. h. m., mohsen, r., yong, l. (2020). subset simulation method including fitnessbased seed selection for reliability analysis. engineering with computers, springer. doi: 10.1007/s00366-020-00961-9 [3] reeve, d. (2010). risk and reliability. coastal and hydraulic engineering, spon press 270 madison avenue, new york, ny 10016 usa, pp. 126-151. [4] bomel (2001). probabilistic methods: uses and abuses in structural integrity. executive health and safety, contract research report, uk, pp. 29-35 [5] dalsgaard sørensen, j. (2004). structural reliability theory and risk analysis. structural reliability theory and risk analysis. institute of building technology and structural engineering, denmark, 03. [6] international committee of large dams. (2005). dam foundations, geologic considerations. investigation methods, treatment. monitoring. geologic considerations. investigation methods of treatment and auscultation, paris, icold, 2005cd rom. bulletin, pp. 129-169. [7] abdollahia, a., amini, a., hariri-ardebili, m. a. (2022). an uncertainty-aware dynamic shape optimization framework: gravity dam design. science direct, reliability engineering & system safety journal, doi: 10.1016/j.ress.2022.108402 [8] droesbeke, j. j., maumy-bertrand, m., saporta, g., thomas-agnan, c. (2014). approaches statistiques du risque. edition technic 1 rue du bac, 75007 paris, france, 05 [9] schneider, j. (2006). introduction to safety and reliability of structures. structural engineering documents. 2ed edition. zurich, suisse, 14. [10] eddleston, m., rose, c., gallagher, e., hope, i., sugden, p. (2014). quantitative risk assessment applied to sludge lagoon embankments. maintaining the safety of our dams and reservoirs proceedings of the 18th biennial conference of the british dam society. queen's university of belfast, 257, pp. 264-266. [11] safe work australia. (2012). guide for major hazard facilities safety case: demonstrating the adequacy of safety t m.e. kerkar et alii, frattura ed integrità strutturale, 61 (2022) 530-544; doi: 10.3221/igf-esis.61.36 544 management and control measures, 25. [12] australian geomechanics society. (2007). guideline for landslide susceptibility, hazard and risk zoning for land use planning. landslide risk management. issn 0818-9110, 22. [13] rausand, m., hoyland, a. (2004). system reliability theory. models, statistical methods and applications, second edition . john wiley and sons, series in probability and statistics, hoboken, new jersey, 03-04. [14] singh, v.p. (1996). dam breach modelling technology. water science and technology librar springer science & business media dordrecht. louisiana state university, baton rouge, u.s.a, pp-27-28. [15] escuder-bueno, i., matheu, e., altarejos-garcía, l., castillo-rodríguez, j. t. (2012). risk analysis, dam safety, dam security and critical infrastructure management. proceedings of the 3rd international forum on risk analysis, dam safety, dam security and critical infrastructure management (3iwrdd-forum), valencia, spain, 09. [16] united states department of homeland security. (2009). dam safety in the united states. national dam safety program, 07. [17] zhang, l., peng, m., chang, d., xu, y. (2016). dam failure mechanisms and risk assessment. john wiley & sons singapore pte. ltd., 1 fusionopolis, singapour, 53. [18] broniatowski, m., hermannkom, g. (2014). course material on form and sorm methods, hal open science, laboratory of theoretical and applied statistics, pierre and marie curie university 02, 11. https://hal.archives-ouvertes.fr/hal-00966695v2 [19] hariri-ardebili, m. a., mahdavi, g., abdollahi, a., amini, a. (2020). an rf-pce hybrid surrogate model for sensitivity analysis of dams. mdpi, water journal, 02p. doi : 10.3390/w13030302 [20] ballière, a., ben milad, y., colas, a.-s., cremona, c., davi, d., humeau, j. b., le quéré, c., marcotte, c., michel, j., orcesi, a., poulin, b., vion, b. (2012). reliability study report. application to the structural evolution of engineering structures. service of studies on transport, roads and their amenities (sétra) 110, france, 1pp. 0-16. [21] altarejos-garcía, l., escuder-bueno, i., serrano-lombillo, a., de membrillera-ortuño, m. g. (2012). methodology for estimating the probability of failure by sliding in concrete gravity dams in the context of risk analysis. structural safety journal, elsevier, 03. doi: 10.1016/j.strusafe.2012.01.001 [22] baroth, j., bchoefs, f., breyesse, d. (2011). fiabilité des ouvrages sûreté, variabilité, maintenance, sécurité. 33. [23] amini, a., kia, m., and bayat, m. (2021). seismic vulnerability macrozonation map of smrfs located in tehran via reliability framework. structural engineering and mechanics, 78(3), pp. 351-368. doi: 10.12989/sem.2021.78.3.351 [24] kia, m., amini, a., bayat, m., and ziehl, p. (2021). probabilistic seismic demand analysis of structures using reliability approaches. journal of earthquake and tsunami, 15(03), 2150011, doi: 10.1142/s1793431121500111 [25] robb, e., moss, s. (2020). applied civil engineering risk analysis, second edition, springer, department of civil and environmental engineering california polytechnic state university san luis obispo, ca, usa. 90, 109. [26] benyahi, k., said kachi, m., bouafia, y., barboura, s., li, j. (2021). reliability assessment of the behavior of reinforced and/or prestressed concrete beams sections in shear failure, frattura ed integrità strutturale, 57 (2021) pp. 195-222, doi: 10.3221/igf-esis.57.16 [27] du, x. (2005). probabilistic engineering design. first order and second reliability methods, chapter 07. university of missouri rolla, 01, 02. [28] choi, s. k., , grandhi, r. v., canfield, r. a. (2007). reliability-based structural design. springer-verlag london, 60, 62, 70, 71. [29] committee for standardization. (1990). basis of structural design. management centre: rue de stassart, 36 b-1050 brussels, 93. [30] reşat beşer, m. (2005). introduction to methods of monte carlo. lessons and exercises. school of bridges paris tech, france, 05. microsoft word numero_62_art_35_3742.docx a. iziumova et alii, frattura ed integrità strutturale, 62 (2022) 516-526; doi: 10.3221/igf-esis.62.35 516 heat dissipation and fatigue crack kinetic features of titanium alloy grade 2 after laser shock peening a. iziumova, a. vshivkov, a. prokhorov, e. gachegova institute of continuous media mechanics of the ural branch of russian academy of science (icmm ub ras), russia fedorova@icmm.ru, https://orcid.org/0000-0002-1769-9175 vshivkov.a@icmm.ru, http://orcid.org/0000-0002-7667-455x prokhorov.a@icmm.ru, http://orcid.org/0000-0002-6511-2105 gachegova.e@icmm.ru, https://orcid.org/0000-0001-6849-9889 d. davydov institute of metal physics of the ural branch of russian academy of sciences (imp ub ras), russia ural federal university (urfu), russia davidov@imp.uran.ru, https://orcid.org/0000-0003-1381-0929 abstract. the work is devoted to experimental investigation of the laser shock peening (lsp) effect on fatigue crack propagation and heat dissipation at the crack tip in specimens made of titanium alloy grade 2 with a stress concentrator. it is shown that the lsp can lead both to positive and negative effect on fatigue lifetime. the effective processing scheme, which includes stress concentrator zone, was proposed. this type of treatment forms an optimal residual stress field, which slows down the crack initiation and propagation processes. the effective lsp processing scheme reduces the value of effective stress intensity factor and, as a consequence, effects on intensity of plastic deformation at the crack tip. this effect can be visualized by measurement of heat flux from the crack tip area. both heat flux from the crack tip and duration of crack initiation are less in the lsp processed specimens. microstructural investigations of lsp treated material near fatigue crack path have shown that structural defects (twins) that appear on the surface of the material as a result of lsp do not have a significant effect on the fatigue crack propagation, and the configuration of the residual stresses field created by lsp plays a decisive role. keywords. fatigue; laser shock peening; heat dissipation; crack propagation rate; twins; residual stress. citation: iziumova, a., vshivkov, a., prokhorov, a., gachegova, e., davydov, d., heat dissipation and fatigue crack kinetic features of titanium alloy grade 2 after laser shock peening, frattura ed integrità strutturale, 62 (2022) 516-526. received: 08.08.2022 accepted: 09.09.2022 online first: 12.09.2022 published: 01.10.2022 copyright: © 2022 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. https://youtu.be/or1siv3l2pq a. iziumova et alii, frattura ed integrità strutturale, 62 (2022) 516-526; doi: 10.3221/igf-esis.62.35 517 introduction he main reasons of metal materials failure and structural degradation are fatigue, corrosion and wear. in most cases, the damage is initiated from the surface of the material. it leads to a decrease in strength properties and rapid propagation of cracks. in this regard, the development of surface hardening methods, search for optimal residual stress configurations and the study of crack propagation features and stages in a hardened material are topical tasks. one of the most effective and widely used technologies of surface hardening today is laser shock peening (lsp). in contrast to laser heat treating, the processed material is not heated significant during lsp. hardening occurs by the impact of a shock wave. the effect is achieved due to the characteristic features of laser impact, such as high pressure created in the material (about of tens of gpa), high relative energy density (about of gw/cm2), ultra-short pulse time (about 10 ns) and high strain rate (reaches 107 1/s) [1]. shock wave generation using high-intensity laser pulses was realized in 1960 [2]. but only relatively recently, with the development of technology, it has become possible to create safe, compact and easy-to-manage high-energy laser systems. lsp technology has become available and competitive. it is effectively used for surface treatment of materials in order to increase their fatigue and strength life, corrosion resistance, as well as to restore working parts subjected to corrosion and fatigue [3–9]. recently, much attention has been paid to the study of the fatigue properties of a material after lsp, since this technique allows not only to strengthen the surface layer, but also to achieve controllability and high predictability of crack development due to the creation of a certain residual stress field. the low-cycle fatigue of an az80-t6 magnesium alloy blade specimen treated with warm lsp is studied in [10]. blade specimens were treated by 1064 nm laser with impact frequency of 1–10 hz, characteristic pulse time of 20 ns, impact energy of 6 j, spot diameter of 5 mm, and relative energy density of 1.54 gw/cm2. an increase in fatigue life by 11% with lsp and by 76% with warm lsp (30°c) was found compared to the initial state. works [11, 12] are devoted to the study of structural features after lsp with the aim of the control of physical-mechanical and fatigue properties. in [13], a numerical model is developed to assess the effect of lsp on crack propagation. this model includes the finite element method and residual stress intensity analysis. an experimental-numerical study of fatigue crack behavior in the ti17 titanium alloy is carried out in [14] to define the crack retardation conditions. the optimal mode of lsp including the selection of residual stress fields by changing the intensity of the laser impact energy and coating is proposed in [15] to slow down or stop the fatigue crack growth in specimens of 2024 aluminum alloy. authors took into account the size and position of the hardened area to balance the induced compressive residual stresses and the resulting tensile residual stresses in order to obtain improved fatigue life and resistance to damage. in [16] authors provide a comprehensive overview of lsp with a focus on the most recent developments in lsp research including warm lsp, electro-pulsingassisted lsp, cryogenic lsp, lsp without coating, femtosecond lsp and laser peen forming. additionally, the effect of lsp on the mechanical and microstructural properties of the metallic material and the application of lsp in additive manufactured metals, ceramics, and metallic glasses have been discussed. lsp allows one to slow down the process of fatigue crack initiation and propagation in the treated material due to the generated compressive residual stress field. it “constrains” the material in stress concentrator area, reduces the effective stress intensity factor (sif) and reduces plastic deformation in the process zone. it is well known that plastic deformation is accompanied by heat dissipation as a result of the thermoplastic effect [17]. variation of plastic deformation intensity in the process zone leads to a change of dissipation energy and the energy balance of specimen in general. thus, the evaluation of energy balance during fatigue crack propagation in a material after lsp allows one to estimate not only the fatigue crack rate (as it is shown in [18]), but the efficiency of compressive residual stress effect on crack propagation. the energy approach is widely used to propose fracture criteria and describe the evolution of fatigue crack [19–25]. experimental verification of this approach and estimation of the fatigue crack growth rate is based on a reliable measurement of the dissipated energy near the crack tip. to assess the heat dissipation features of fatigue crack propagation through the field of residual compressive stresses, an original contact heat flux sensor has been used [26]. an analysis of literature sources has shown that lsp is a promising technique as for preparing parts with a complex configuration of residual stresses and influence on the crack initiation process, as increasing the fatigue life of metal structural elements. the kinetics of fatigue cracks propagated through the compressive residual stresses field could be described on the base of the energy approach. energy dissipation reflects the influence of residual stress field on the crack development and it can be used to evaluate the lsp efficiency. thus, the purpose of this work is to determine the kinetic and thermal characteristics of the fatigue crack propagation in the specimen of titanium alloy grade 2 treated by lsp, and as well as to evaluate the correlation of these characteristics with residual stresses and microstructural features caused by lsp. t a. iziumova et alii, frattura ed integrità strutturale, 62 (2022) 516-526; doi: 10.3221/igf-esis.62.35 518 materials and experimental conditions atigue crack evolution and associated heat dissipation were investigated on specimens of titanium alloy grade2 without lsp treatment and after lsp. specimen geometry is shown in fig. 1a. the chemical composition of the material is presented in tab. 1. ti si fe c o2 n2 h2 others base 0.1 0.25 0.07 0.2 0.04 0.01 0.3 table 1: chemical composition of grade 2 (weight percent). before lsp processing both surfaces of studied specimens were polished in several stages by abrasive paper (at the final stage of polishing the grit size does not exceed 3 μm), as it provides a good contact between specimen surfaces and coating. in our case it was aluminum foil. coating is usually used to avoid damage of structure in surface layer after high intensity laser irradiation. for lsp processing, we used an original laser setup assembled in the institute of continuous media mechanics, ural branch of the russian academy of sciences. the setup includes nd:yag high energy laser beamtech sgr-extra-10, industrial robotic manipulator step sr50 and residual stress measurement system sint mts3000 restan. lsp processing was performed on both surfaces of specimens with 2j and 3j laser energy. the laser spot was square with a side of 1 mm. two lsp scheme presented in fig. 1b-c were realized to find optimal conditions for improvement of fatigue properties. the arrow in fig. 1b-c shows the direction of lsp treatment, and color indicates the beginning and finishing of treatment (from red to violet). one layer of lsp treatment was performed. adjacent square-spots are next to each other without the overlapping region. (a) (b) (c) figure 1: geometry of studied specimens (all dimensions are in millimeters) (a) and schemes of lsp treatment (b, c). the main difference between these schemes is that the first scheme (fig. 1b) didn’t include the sharp notch area and during fatigue test the crack was initiated in the untreated material compared to the second scheme (fig. 1c). the lsp processing in notch area according to the second scheme was performed by special insert in notch to avoid edge effects. all specimens (including specimens treated by two schemes and base specimens) were tested under uniaxial cyclic loading conditions. fatigue experiments were carried out on a 100kn servo-hydraulic testing machine instron 8802 under constant maximum loading of 8 kn at a stress ratio r=0.1 and loading frequency 10 hz. the direct current potential drop method (pdm) [27] was applied for measuring of crack length. the quantitative measurements of the heat dissipation rate at the crack tip area were carried out using the original heat flux sensor developed by vshivkov et al. [18]. tab. 2 presents lsp conditions and result of fatigue test. f a. iziumova et alii, frattura ed integrità strutturale, 62 (2022) 516-526; doi: 10.3221/igf-esis.62.35 519 specimen number cycles until the end of the test scheme of lsp treatment laser energy, j 1 102050 base specimen 0 2 84316 base specimen 0 9 59471 scheme n1 3 10 56327 scheme n1 3 11 215103 scheme n2 2 12 146722 scheme n2 3 14 148935 scheme n2 2 table 2: life to failure cycles and lsp characteristics of tested specimens. specimens treated by scheme n2 has shown improved results under 2j and 3j of laser energy. specimens treated by scheme n1 has demonstrated in the least life. experimental results s a result of experimental work the residual stress profile through the specimen thickness, time dependences of crack length and heat dissipation rate, and specific density of twins versus crack length were obtained. residual stress evaluation lsp technique induces the field of residual stress, which is a combination of compressive and tensile stresses. if this residual stress field has optimal configuration, the duration of crack initiation and propagation will be longer and fatigue properties will be improved. there are a number of ways to measure the residual stress field experimentally such as laboratory x-ray diffraction, neutron diffraction or synchrotron x-ray diffraction [28]. in this work, the depth of the residual stress region was examined by incremental hole drilling technique (according to astm e837-13a). this technique allows one to visualize and estimate the effectiveness of lsp treatment and to change laser characteristics if necessary. profiles of residual stresses are presented in fig. 2a-b. according to these graphs lsp treatment allows one to create residual compression stress field to the depth of approximately 0.9 mm. the maximal compressive stress which plays significant role in control of fatigue crack initiation and propagation, reaches about 750 mpa on depth of approximately 0.3 mm for both schemes of lsp. it is noted that scheme n1 and scheme n2 create approximately the same level and depth of residual stress, and the difference between the two schemes is in location of treated area only. (a) (b) figure 2: residual stresses obtained after lsp in specimens of titanium alloy grade 2 by scheme n1(a) and scheme n2 (b) with laser energy of 3j. a a. iziumova et alii, frattura ed integrità strutturale, 62 (2022) 516-526; doi: 10.3221/igf-esis.62.35 520 crack propagation and associated heat dissipation after lsp fatigue test was carried out with simultaneous registration of crack length and heat dissipation rate. the original heat flux sensor was used for measurement of heat dissipation rate with accuracy of 1 mw in the range up to 10w. detailed description of this original technique is presented in [18]. as a result the time dependences of crack length and heat dissipation rate were obtained (fig. 3a-b). the dependence of crack growth rate and applied sif range is presented in fig. 3c. (a) (b) (с) figure 3: time dependences of crack length (a), heat dissipation rate (b) and crack growth rate versus applied stress intensity factor range (c). three groups of specimens are presented in fig. 3. base specimens that have not been lsp processed are indicated by black line. they are the reference against which the change in the fatigue properties of the specimens after lsp processing was evaluated. the second group indicated by red line pertains to specimens after lsp treated according to the scheme n1 (without notch area). in this group crack initiates earlier than in base specimens, the heat dissipation is more intensive. the third group of specimens shown by blue lines in fig. 3 pertains to specimens after lsp treatment according to the scheme n2 (with notch area). duration of crack initiation period is significant longer in these specimens than in base specimens, and the heat flux is less intensive. lsp treatment according to the scheme n2 is more appropriate in terms of fatigue properties improvement of titanium alloy grade2 specimens. as it was shown in [29-32], the heat dissipation is correlated with stress intensity factor (sif). in 1970, elber found that crack closure retards fatigue crack growth rate by reducing the stress intensity range. he introduced the effective stress intensity range for use in paris’ law [33]. similarly, the effective sif could be taken in consideration for characterization of crack propagation in residual stress field caused by lsp. in our case, effective sif is superposition of sif related to the a. iziumova et alii, frattura ed integrità strutturale, 62 (2022) 516-526; doi: 10.3221/igf-esis.62.35 521 applied stress and sif related to residual stress formed by lsp [34]. residual stress field is a configuration of tensile and compressive stresses. so that, the created residual stress field can as to increase effective sif, as to decrease it. thus, the effective sif characterizes residual stresses created by the lsp. at the same time, the effective sif is related to the intensity of the heat flux. it allows us to estimate the residual stress field formed by the lsp using evolution of the heat flux near the crack tip. according to fig. 3b, the intensity of heat flux in the crack tip area after the treatment by scheme n1 and without treatment is approximately the same. we can conclude that residual stress field created by scheme n1is not effective for improvement of fatigue properties. in case of scheme n2, the crack is initiated in the compressed material and does not have the ability for intensive development. the heat flux on the specimens processed according to scheme n2 is less that in base material. if the assumption about the relationship between the effective sif and heat dissipation is correct, then the field of residual stresses created after the lsp according to scheme n2 reduces the effective sif and, as a result, the heat flux and the crack growth rate decrease. fig. 3c presents the dependence of crack growth rate and applied sif range, calculated by eqn. (1) [35] for all specimens.    ( , ),k l f l w     2 5 ( , ) , 20 13 7 f l w     l w (1) where δσ is applied stress range (pa), l is crack length (m), f(l,w) is function of crack length l and specimen width w. with the same applied sif range, the crack growth rate is lower in specimens after treatment according to scheme n2 comparison with specimens without treatment or after treatment according to scheme n1. the dependence between heat flux and crack length is presented in fig. 4. gray rectangle indicates the area of lsp treatment. analyzing data of specimens treated by scheme n1 (fig. 4a), an sudden growth of heat flux begins at a crack length of about 20 mm, while the treatment zone ends at about 25 mm. in fig. 4b, the plot of heat flux versus crack length has a kink at a crack length of about 15 mm, and the treatment zone ends at 18 mm. such a discrepancy between the beginning of the heat flux growth and the end of the lsp processing zone can be associated with the edge effect. at the boundary of the treatment zone, a field of tensile residual stresses arises. it accelerates the development of crack and increasing of effective sif and consequently heat flux. (a) (b) figure 4: heat dissipation versus crack length for the specimens processed by scheme n1 (a) and scheme n2 (b). lsp area is colored by gray. microstructural analysis of crack propagation zone in stress residual field microstructural studies of the crack propagation region of specimen without lsp treatment and with a treated surface were carried out by optical microscopy. microstructural features were analyzed along the crack in five regions (at the crack tip, ¼ of the crack length, ½ of the crack length, ¾ of the crack length, and at the crack initiation site). figs. 5-7 show the material microstructure in the area of the crack tip and in the main volume of the material away from crack area obtained on base specimen without lsp processing (fig. 5) and after lsp processing according to scheme n1 (fig. 6) and scheme n2 (fig. 7). a. iziumova et alii, frattura ed integrità strutturale, 62 (2022) 516-526; doi: 10.3221/igf-esis.62.35 522 (a) (b) figure 5: the microstructure of untreated specimens in crack tip area with magnification of 170x (a) and away from crack tip with magnification of 60x (b). arrows show twinned grains. (a) (b) figure 6: the structure of specimens after lsp (scheme n1) in crack tip area with magnification of 170x (a) and away from crack tip with magnification of 60x (b). arrows show twinned grains. (a) (b) figure 7: the structure of specimens after lsp (scheme n2) in crack tip area with magnification of 170x (a) and away from crack tip with magnification of 60x (b). arrows show twinned grains. the density of twins along the crack path of reference specimen increases with increasing crack length and reaches its maximum value at the tip; a small amount of twins were found in the main structure of the material. in specimens treated according to scheme n1, the density of twins also increases from the notch to the top. in this case, there are more twinned grains than in the reference specimen both along the crack path and in the base material. a distinctive feature of the structure in specimens processed according to scheme n2 is a significantly larger number of twins than in the reference specimen and specimen processed according to scheme n1. multiple twinning characterized by a large number of small twins extending from larger ones is observed in scheme n2. a. iziumova et alii, frattura ed integrità strutturale, 62 (2022) 516-526; doi: 10.3221/igf-esis.62.35 523 the quantitative analysis of material microstructure included the calculation of twinned grains density in each studied areas. fig. 8 shows characteristic graphs of the dependence between the twin density and crack length. the twin density was estimated as the ratio of the twin numbers to the area of the image. it is shown that the twin density on specimen after lsp is higher than on specimen without treatment. lsp treatment is characterized by very large imposed energy, ultra-high strain rate, and ultra-short duration. these conditions have a large effect on microstructure evolution, in particular activation of twinning [36]. decreasing in twin density on specimens after treatment by scheme n2 could be caused by end of treatment zone which is marked by gray rectangle in fig.8a. the high value of twin density under crack length about 27 mm (near the edge of specimen) could be connected with developed plastic deformation in crack tip area. (a) (b) figure 8: the twin density versus crack length in base specimens and specimens after lsp according to the scheme n1 (a) and scheme n2 (b). in general, twins can affect the crack growth rate in different ways. in [37] authors investigated the effect of twins in extruded az31b magnesium alloy on fatigue crack growth and crack closure behavior. they have found increasing the material deformation and fatigue crack opening displacement due to twins under applied stress ration r=-1. as a result, the effective stress intensity factor range increased, leading to the intensification of fatigue crack growth. from the other hand, at the applied stress ratio r = 0.1, tensile twins were not generated. there was no change in effective stress intensity factor range and no acceleration of fcg. a review on the fatigue cracking of twin boundaries is presented in [38]. authors approve that the twin boundaries produced by deformation twins in face-centered cubic metals are strong to resist fatigue cracking by promoting deformation homogeneity. in contrast, twin boundaries those linked with deformation twins in hexagonal-close-packed or body-centered-cubic metals are preferential sites for fatigue cracking with strain localization and stress concentration. in our case, the microstructural changes (twins formation) caused by lsp does not significantly effect on the fatigue crack propagation, and the configuration of the residual stress field created by lsp plays a decisive role. conclusions he lsp technology allows one to increase the fatigue life of metallic materials in the case of optimal choice of lsp processing characteristics such as size and shape of the spot, pulse energy and, most importantly, the lsp treatment scheme. the significant improvement of fatigue life by lsp treatment of specimens with stress concentrator is shown in the case of lsp treatment scheme including region of notch. if the treated zone is spaced relative to the notch tip, the lsp will not effective and the created residual stress field will contribute to the rapid fatigue crack development leading to decrease in the durability of specimens. an analysis of fatigue crack kinetics and the evolution of heat flux in crack tip area showed that if the lsp zone includes a stress concentrator zone, then the fatigue crack develops more slowly and the heat flux is less intense than in specimen without treatment. this is due to a decrease in effective sif caused by influence of the residual compressive stress field. t a. iziumova et alii, frattura ed integrità strutturale, 62 (2022) 516-526; doi: 10.3221/igf-esis.62.35 524 thus, the heat flux makes it possible to indirectly estimate the change in the effective sif and the optimality of the created residual stress field. microstructural studies have shown that the surface of the material after lsp is more defective compared to the structure of the material without treatment. a significant increase in the density of twinned grains in the lsp treated material was found. at the same time the duration of crack initiation and propagation increases significantly after lsp according to scheme which includes stress concentrator zone. thus, the structure does not significantly effect on the fatigue crack propagation, and the configuration of the residual stress field created by lsp plays a decisive role. it has to be noted that this configuration includes not only optimal space distribution of residual compressive stress field but corresponding ration of the specimen thickness to the depth of lsp treated layer. this ratio strongly depends on characteristics of laser processing specifically laser energy and laser spot area. acknowledgments his paper was prepared in the framework of the program for the creation and development of the world-class scientific center “supersonic” for 2020–2025, with the financial support of the ministry of education and science of the russian federation. references [1] lu, j., liu, y., luo, k. and wang, z. (2018). a kind of uniform strengthening methods of turbine blade subjected to varied square-spot laser shock peening with stagger multiple-layer, united states patent, us2018258509 a1, 13. [2] askar’yan, g.a. and moroz, é.m. (1963). pressure on evaporation of matter in a radiation beam, sov. j. exp. theor. phys., 43, pp. 2319–2320. [3] sundar, r., ganesh, p., gupta, r.k., ragvendra, g., pant, b.k., kain, v., ranganathan, k., kaul, r., bindra, k.s. (2019). laser shock peening and its applications: a review, lasers manuf. mater. process., 6, pp. 424-463. doi: 10.1007/s40516-019-00098-8. [4] ganesh, p., sundar, r., kumar, h., kaul, r., ranganathan, k., hedaoo, p., tiwari, p., kukreja, l.m., oak, s.m., dasari, s., raghavendra, g. (2012). studies on laser peening of spring steel for automotive applications, opt. lasers eng., 50(5), pp. 678–686. doi: 10.1016/j.optlaseng.2011.11.013. [5] ganesh, p., sundar, r., kumar, h., kaul, r., ranganathan, k., hedaoo, p., raghavendra, g., anand kumar, s., tiwari, p., nagpure, d.c., bindra, k.s., kukreja, l.m., oak, s.m. (2014). studies on fatigue life enhancement of prefatigued spring steel specimens using laser shock peening, mater. des., 54, pp. 734–741. doi: 10.1016/j.matdes.2013.08.104. [6] pant, b.k., sundar, r., kumar, h., kaul, r., pavan, a.h.v., ranganathan, k., bindra, k.s., oak, s.m., kukreja, l.m., prakash, r. v., kamaraj, m. (2013). studies towards development of laser peening technology for martensitic stainless steel and titanium alloys for steam turbine applications, mater. sci. eng. a, 587, pp. 352–358. doi: 10.1016/j.msea.2013.08.074. [7] gupta, r.k., sundar, r., kumar, b.s., ganesh, p., kaul, r., ranganathan, k., bindra, k.s., kain, v., oak, s.m., kukreja, l.m. (2015). a hybrid laser surface treatment for refurbishment of stress corrosion cracking damaged 304l stainless steel, j. mater. eng. perform., 24(6), pp. 2569–2576. doi: 10.1007/s11665-015-1530-1. [8] sundar, r., ganesh, p., kumar, b.s., gupta, r.k., nagpure, d.c., kaul, r., ranganathan, k., bindra, k.s., kain, v., oak, s.m., singh, b. (2016). mitigation of stress corrosion cracking susceptibility of machined 304l stainless steel through laser peening, j. mater. eng. perform., 25(9), pp. 3710–3724. doi: 10.1007/s11665-016-2220-3. [9] gupta, r.k., sunil kumar, b., sundar, r., ram sankar, p., ganesh, p., kaul, r., kain, v., ranganathan, k., bindra, k.s., singh, b. (2017). enhancement of intergranular corrosion resistance of type 304 stainless steel through laser shock peening, corros. eng. sci. technol., 52(3), pp. 220–5. doi: 10.1080/1478422x.2016.1254422. [10] shanyavskiy, a.a. (2006). fatigue limit material property as an opened or closed system? practical view on the aircraft components failures in gcf area, int. j. fatigue, 28(11), pp. 1647–1657. doi: 10.1016/j.ijfatigue.2005.12.008. [11] umapathi, a., swaroop, s. (2019). mechanical properties of a laser peened ti-6al-4v, opt. laser technol., 119, pp. 105568. doi: 10.1016/j.optlastec.2019.105568. [12] chen, h., guan, y., zhu, l., li, y., zhai, j., lin, j. (2021). effects of ultrasonic shot peening process parameters on nanocrystalline and mechanical properties of pure copper surface, mater. chem. phys., 259, pp. 124025. t a. iziumova et alii, frattura ed integrità strutturale, 62 (2022) 516-526; doi: 10.3221/igf-esis.62.35 525 doi: 10.1016/j.matchemphys.2020.124025. [13] zhao, j., dong, y., ye, c. (2017). laser shock peening induced residual stresses and the effect on crack propagation behavior, int. j. fatigue, 100, pp. 407–417. doi: 10.1016/j.ijfatigue.2017.04.002. [14] sun, r., keller, s., zhu, y., guo, w., kashaev, n., klusemann, b. (2021). experimental-numerical study of lasershock-peening-induced retardation of fatigue crack propagation in ti-17 titanium alloy, int. j. fatigue, 145, pp. 106081. doi: 10.1016/j.ijfatigue.2020.106081. [15] van aswegen, d.c., polese, c. (2021). experimental and analytical investigation of the effects of laser shock peening processing strategy on fatigue crack growth in thin 2024 aluminium alloy panels, int. j. fatigue, 142, pp. 105969. doi: 10.1016/j.ijfatigue.2020.105969. [16] zhang, c., dong, y., ye, c. (2021). recent developments and novel applications of laser shock peening: a review, adv. eng. mater., pp. 2001216. doi: 10.1002/adem.202001216. [17] hodowany, j., ravichandran, g., rosakis, a.j., rosakis, p. (2000). partition of plastic work into heat and stored energy in metals, exp. mech., 40(2), pp. 113–123. doi: 10.1007/bf02325036. [18] vshivkov, a., iziumova, a., plekhov, o., bär, j. (2016). experimental study of heat dissipation at the crack tip during fatigue crack propagation, frat. ed integrita strutt., 10(35), pp. 57–63. doi: 10.3221/igf-esis.35.07. [19] chapetti, m.d., tagawa, t., miyata, t. (2003). ultra-long cycle fatigue of high-strength carbon steels part i: review and analysis of the mechanism of failure, mater. sci. eng. a, 356(1–2), pp. 227–235. doi: 10.1016/s0921-5093(03)00135-7. [20] paris, p., erdogan, f. (1963). a critical analysis of crack propagation laws, j. fluids eng. trans. asme, 85(4), pp. 528–533. doi: 10.1115/1.3656900. [21] iino, y. (1979). fatigue crack propagation work coefficient-a material constant giving degree of resistance to fatigue crack growth, eng. fract. mech., 12(2), pp. 279–299. doi: 10.1016/0013-7944(79)90120-6. [22] chow, c.l., lu, t.j. (1991). cyclic j-integral in relation to fatigue crack initiation and propagation, eng. fract. mech., 39(1), pp. 1–20. doi: 10.1016/0013-7944(91)90018-v. [23] weertman, j. (1973). theory of fatigue crack growth based on a bcs crack theory with work hardening, int. j. fract., 9(2), pp. 125–131. doi: 10.1007/bf00041854. [24] chudnovsky, a. (1985). thermodynamics of translational crack layer propagation, j. mater. sci., 20, pp. 630–635. [25] fedorov, v.v. (1979). thermodynamic aspects of strength and fracture of solids, tashkent. [26] prokhorov, a., vshivkov, a., iziumova, a., plekhov, o., batsale, j. (2014). development of the measurement system for determination of dissipation rate near the fatigue crack tip. 12th international conference on quantitative infrared thermography, bordeaux, france. [27] hartman, g.a., johnson, d.a. (1987). d-c electric-potential method applied to thermal/mechanical fatigue crack growth, exp. mech., 27(1), pp. 106–112. doi: 10.1007/bf02318872. [28] s.n van staden, c. polese, d. glaser, j.-p. nobre, a.m. venter, d. marais, j.o. and j.-s.p. (2018).measurement of residual stresses in different thicknesses of laser shock peened aluminium alloy samples. mechanical stress evaluation by neutron and synchrotron radiation, 4, pp. 117–22. [29] stüwe, h.p., pippan, r. (1992). on the energy balance of fatigue crack growth, comput. struct., 44(1–2), pp. 13–17. doi: 10.1016/0045-7949(92)90218-o. [30] palumbo, d., de finis, r., ancona, f., galietti, u. (2017). damage monitoring in fracture mechanics by evaluation of the heat dissipated in the cyclic plastic zone ahead of the crack tip with thermal measurements, eng. fract. mech., 181, pp. 65–76. doi: 10.1016/j.engfracmech.2017.06.017. [31] ranc, n., palin-luc, t., paris, p.c. (2011). thermal effect of plastic dissipation at the crack tip on the stress intensity factor under cyclic loading, eng. fract. mech., 78(6), pp. 961–972. doi: 10.1016/j.engfracmech.2010.11.010. [32] boussattine, z., ranc, n., palin-luc, t. (2020). about the heat sources generated during fatigue crack growth: what consequences on the stress intensity factor?, theor. appl. fract. mech., 109, pp. 102704. doi: 10.1016/j.tafmec.2020.102704. [33] elber, w. (1971).the significance of fatigue crack closure. damage tolerance in aircraft structures. astm stp 486, american society for testing and materials, pp. 230–242. [34] ruschau, j.j., john, r., thompson, s.r., nicholas, t. (1999). fatigue crack nucleation and growth rate behavior of laser shock peened titanium, int. j. fatigue, 21(suppl. 1), pp. 199–209. doi: 10.1016/s0142-1123(99)00072-9. [35] murakami, y. (1990). stress intensity factors handbook, the society of materials science, japan, volume 1, p. 51. [36] mironov, s., ozerov, m, kalinenko, a., stepanov, n., plekhov, o., sikhamov, r., ventzke, v., kashaev, n., salishchev, g., semiatin, l., zherebtsov, s. (2022). on the relationship between microstructure and residual stress in laser-shock-peened ti-6al-4v, journal of alloys and compounds, 900, pp. 163383. a. iziumova et alii, frattura ed integrità strutturale, 62 (2022) 516-526; doi: 10.3221/igf-esis.62.35 526 doi: 10.1016/j.jallcom.2021.163383. [37] masuda, k., ishihara, s., oguma, n., ishiguro, m., sakamoto, y. (2021). effect of twins and plastic-deformation anisotropy of extruded magnesium alloy on fatigue crack growth and crack closure behavior, materials science and engineering: a, 828, pp.142111. doi: 10.1016/j.msea.2021.142111. [38] li, l., zhang, z., zhang, p., zhang, z. 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/hrv (za stvaranje adobe pdf dokumenata najpogodnijih za visokokvalitetni ispis prije tiskanja koristite ove postavke. stvoreni pdf dokumenti mogu se otvoriti acrobat i adobe reader 5.0 i kasnijim verzijama.) /hun 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/pdfxoutputintentprofileselector /documentcmyk /preserveediting true /untaggedcmykhandling /leaveuntagged /untaggedrgbhandling /usedocumentprofile /usedocumentbleed false >> ] >> setdistillerparams << /hwresolution [2400 2400] /pagesize [612.000 792.000] >> setpagedevice microsoft word numero_60_art_11_3407.docx d. s. lobanovet alii, frattura ed integrità strutturale, 60 (2022) 146-157; doi: 10.3221/igf-esis.60.11 146 statistical evaluation of the effect of hygrothermal aging on the interlaminar shear of gfrp dmitrii s. lobanov, andrey s. yankin, nataliya i. berdnikova perm national research polytechnic university, russia cem.lobanov@gmail.com, http: //orcid.org/0000-0003-1948-436x yas.cem@yandex.ru, https://orcid.org/0000-0002-0895-4912 natalya.berdnickova2017@yandex.ru abstract. the studies of patterns of changes in properties, accumulation of damages and failure of structural composites after hygrothermal aging represent a relevant and important area. the paper presents the results of mechanical tests for interlaminar shear of specimens of structural glass/epoxy composite electrical use before and after preliminary hygrothermal aging in operating environments (process water, sea water, machine oil) of various duration (15, 30 and 45 days) and various temperatures (22, 60 and 90 oc). the test results were used to statistically evaluate the significance of nonmonotonous changes in strength in the case of interlaminar shear after preliminary hygrothermal aging relative to the nominal material using ancova and regression analysis. such techniques indicated that sea and process water solutions negatively affected the interlaminar shear strength, but their influences were slightly different and strongly depended on the interaction effect between exposure time and solution temperature. thus, the maximum difference is around 15 % and 12 % after 45 days inside process and sea water respectively at 90 oc. on the contrary, the impact of machine oil led to an increase in strength, but the effect is weaker compared to water solutions (about 6 %). keywords. hygrothermal aging; aggressive operating media (environments, solutions); interlaminar shear strength; gfrp; ancova; multiple linear regression. citation: lobanovd, s., yankin a.s., berdnikova n.i. statistical evaluation of the effect of hygrothermal aging on the interlaminar shear of gfrp, frattura ed integrità strutturale, 60 (2022) 146-157. received: 24.12.2021 accepted: 21.01.2022 online first: 27.01.2022 published: 01.04.2022 copyright: © 2022 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. introduction hen composite materials are implemented, special importance is given to the analysis of failure conditions and durability of products. a relevant task is to study and analyze the effects of high and low (operating) temperatures on mechanical properties and failure mechanisms of reinforcing and composite materials as well w https://youtu.be/5byop8tp848 d. s. lobanov et alii, frattura ed integrità strutturale, 60 (2022) 146-157; doi: 10.3221/igf-esis.60.11 147 as the definition of temperature dependencies of elastic and strength properties of fiber composites used in critical structures. experimental data concerning the effects of operating and climatic temperatures on mechanical properties of various classes of polymeric composite materials are represented in [1-4]. to predict the operating life of structures made of polymeric composites, it becomes relevant to study the matters related to the aging of polymeric composite materials. the aging of polymeric composites is a ubiquitous issue that leads to impaired mechanical properties, the reduced design life of the structure and potential early failure. the issue of the aging of polymeric composites in the aqueous environment is studied in [5-8]. most structures of polymeric composites are subject to atmospheric factors during operation (temperature, humidity, solar radiation, cyclic changes in temperature, tropical and sea climate, etc.) that affect their physical, chemical and mechanical properties. it becomes important to study the issues of hygrothermal aging of polymeric composites since it is possible to accelerate aging processes during temperature rise. the studies of trends in changes of physical and mechanical properties of polymeric composites based on glass, carbon and basalt fiber and epoxy, acrylic and nylon thermal-plastic binders in case of hygrothermal aging in various media (distilled water, sea water, machine oil, alkali solutions, etc.) are found in [8-19]. primary attention in these papers is paid to the studies of degradation in microstructure and diffusion of a liquid medium. the papers fail to consider or pay little attention to statistical evaluation of results and further comparative analysis of effects of hygrothermal aging on the changes in mechanical characteristics and failure mechanisms of structural composites. representing experimental data should be easily interpreted and understood, therefore statistical methods are extremely important for that. obviously, test data may have not only quantitative but also categorical variables (for instance, aggressive environments). in this case, anova (analysis of variance), ancova (analysis of covariance), regression, and other related procedures might be applied [20, 21]. for example, such methods were utilized to examine the effects of various reinforcement types on properties of wood polymer composites before and after aging [22], the effect of hydrothermal aging (thermal cycles from -28 °c to 85 °c in air, distilled water and salt water) on the mechanical resistance of single lap bonded cfrp joints [23], sample orientation and geometry on the mechanical response of additively manufactured commercially pure titanium [24], different implant abutment designs on fracture resistance and bending moment [25], different storage media and exposure time on the hardness of cad/cam composite blocks [26]. furthermore, those techniques are widely used to indicate the most contributing input parameters and select the optimal combination of them to obtain the required results [27-31]. in the current study, a statistical approach using ancova multiple linear regression analysis was used to investigate the effects of 3 different aggressive environments, temperature, exposure time, and their interactions on mechanical properties of structural gfrp, to assess which factors are statistically significant and to develop a prediction model. material and experimental procedure he material used in the study is the general-purpose construction fiberglass laminate stef (st fiberglass, ef epoxy-phenol-formaldehyde or epoxy binder). it is laminated reinforced fiberglass obtained by hot pressing of fiberglass cloth impregnated with a thermoreactive compound based on combined epoxide and phenolformaldehyde resins. experimental study of structural fiberglass/epoxy "stef" specimens after hygrothermal aging in different liquids (process water, sea water, machine oil) at 22, 60 and 90oc for 15, 30 and 45 days is carried out (table 1). mechanical tests for interlaminar shear under static conditions were carried out using the short beam method on the basis of the shared research facilities “center of experimental mechanics” in perm national research polytechnic university (pnrpu). mechanical tests were conducted according to recommendations of astm d2344 using an instron 5965 electromechanical testing system. the loading rate was 1 mm / min. the dimensions of the specimens were 24x8x4 mm. the distance between the supports was 20mm. as a result of the tests, the interlaminar shear strength was determined by the formula (1): 0.75sbs m p f b h    (1) t d. s. lobanovet alii, frattura ed integrità strutturale, 60 (2022) 146-157; doi: 10.3221/igf-esis.60.11 148 where fsbs is short-beam strength or interlaminar shear strength, (mpa); pm is maximum load observed during the test, (n); b is measured specimen width, (mm), and h is measured specimen thickness, (mm). the procedure of specimen preparation and preliminary hygrothermal aging was as follows. cut-out specimens were divided into groups, marked, weighed and put into baths with prepared liquid media: sea water (salinity coefficient of 30 %), process water and machine oil (synthetic oil for automobile engines). some containers remained in laboratory conditions, while others were put to chambers at a constant temperature of 60 and 90 oc for 45 days. during exposure, evaporation was visually monitored on a daily basis; if necessary, the medium was topped up with a liquid preliminary heated to the required temperature. the specimens were extracted after 15, 30 and 45 days of exposure, wiped with a cotton cloth and left for a day in the open air at laboratory conditions, then were weighed. before testing, the microstructure of the specimen surface was recorded after aging in a non-loaded state. after that, fiberglass specimens were tested for interlaminar shear (short beam method) with further study of the microstructure and analysis of failure mechanisms. liquids temperature, ºc without aging / control samples exposure time, days 15 30 45 machine oil 22 3 specimens 3 specimens on “point” 3 specimens on “point” 3 specimens on “point” 60 90 sea water 22 60 90 process water 22 60 90 table 1: program of mechanical testing after different modes of pre-exposure hygrothermal aging   figure 1: typical loading diagram of interlaminar shear test for fiberglass/epoxy “stef” specimens: without aging (black line), after aging in machine oil (green line), sea water (red line); process water (blue line) at temperature of 90 oc and time of 45 days. d. s. lobanov et alii, frattura ed integrità strutturale, 60 (2022) 146-157; doi: 10.3221/igf-esis.60.11 149 result and discussions ests were performed at the center of experimental mechanic in order to evaluate the degradation of composite material properties under aggressive solutions. for reference, fig. 1 shows characteristic diagrams of fiberglass specimen loading without hygrothermal aging and after hygrothermal aging of the highest intensity (45 days, 90 oc) for each of the studied media. these deformation diagrams show that there is reduced bending rigidity after aging for all specimens (the incline angle of the diagram linear section is reduced). similar results of the studies are found in [19, 32, 33] for other types of static tests. fig. 2 gives an image of the surface microstructure of fiberglass specimens before and after interlaminar shear for a specimen without aging (fig. 2a) and after hygrothermal aging at exposure conditions of 45 days / 90 oc in machine oil (fig. 2b), sea water (fig. 2c) and process water (fig. 2d). for all tested specimens without aging and after aging in machine oil, primary failure starts on the elongated surface (fig. 2a, 2b yellow ellipse) with further interlaminar shear of lower and middle layers. inter-layer fractures are local in the specimen center under the loading pin (fig. 2a, 2b red ellipse). for specimens after aging in sea water and process water (fig. 2c,d), a good failure pattern is observed. specimens fail in a brittle manner, and there is joint failure due to elongation and interlaminar shear. there are large main cracks (fig.2c, 2d white ellipse) between middle layers, which come from specimen edges. the material is crushed at the place where pin loading is applied, with further local lamination (fig. 2c, 2d red ellipse).     a b c d figure 2: surface structure of fiberglass specimens before and after interlaminar shear testing: specimen without aging (a); specimen after aging in machine oil during 45 days at 90 oc (b); specimen after aging in sea water during 45 days at 90 oc (c); specimen after aging in process water during 45 days at 90 oc (d). as a result, weight gain and interlaminar shear strength values for all conditions were determined (table 2-3). in order to see the data distribution, skewness, and outliers, the box plot chart (fig. 3) was plotted. from fig. 3a one can see that strength values are not too skewed and there are no outliers, therefore we can accept the whole dataset. oppositely, fig. 3b illustrates 5 outliers for weight gain values, so we should remove them for further study. table 2 lists average values of the interlaminar shear strength of all specimens tested, calculated by eq. (1). it is possible to observe that, the results have changed after immersion into solutions over the exposure time. the analysis of the results from table 2 indicates that process water promotes lower strength than the sea water relative to the control samples. this effect depends on the exposure time and solution temperature: the higher temperature and time, the lower strength. on the contrary, universal machine oil makes strength values slightly bigger. similarly, this effect is dependant on solution temperature.   t d. s. lobanovet alii, frattura ed integrità strutturale, 60 (2022) 146-157; doi: 10.3221/igf-esis.60.11 150     a b figure 3: box plot diagrams of interlaminar shear strength (a) and weight gain (b) values  environment/ temperature, ºc aver. interlaminar shear strength, (mpa) 15 days 30 days 45 days control samples (without aging) 31.7 machine oil 22 32.4 33.1 30.7 60 33.7 32.2 32.5 90 34.3 34.3 33.2 sea water 22 34.0 33.7 33.2 60 33.7 32.1 31.2 90 30. 29.1 28.2 process water 22 33.0 30.9 33.4 60 30.9 29.6 30.2 90 29.1 29.8 27.2 table 2: effect of the solutions, their temperature, and exposure time on the interlaminar shear strength in terms of average values table 3 demonstrates the average weight gain values for all operating environments. it is clearly shown a negligible weight change in terms of the machine oil solution. as we can see, sometimes specimens even lose weight after immersion tests into the machine oil. however, different behavior is observed for the sea and process water solutions. in this case, an increase can be observed compared to the dry specimens. d. s. lobanov et alii, frattura ed integrità strutturale, 60 (2022) 146-157; doi: 10.3221/igf-esis.60.11 151 environment temperature, ºc weight gain (%) 15 days 30 days 45 days machine oil 22 0.10 0.02 60 0.06 -0.09 -0.10 90 -0.14 -0.15 0.15 sea water 22 0.18 0.33 60 0.67 0.79 1.02 90 0.81 0.77 0.92 process water 22 0.19 0.18 60 1.67 0.60 0.66 90 0.65 0.34 1.06 table 3: effect of the solutions, their temperature, and exposure time on the weight gain in terms of average values. ancova and regression analysis interlaminar shear strength n this research study, ancova was used for a multiple regression analysis in which there are at least one quantitative and one categorical variables [20]. and by doing this, the categorical variable with 3 kinds of solutions was re-coded as 2 new columns with 0 and 1. the variables were coded 0 for any case that did not match the variable name and 1 for any case that did match the variable name. the whole procedure was carried out by python software (more information about the code you can find here: https://github.com/yanicen1/strength-ancova-regression). this analysis was applied to examine whether there are differences and interactions between the different solutions, their temperature, and exposure time, as well as to predict the interlaminar shear strength under various conditions. in doing so, two models were developed (fig. 4 and tables 4-5). the first one is the additive model, i.e. it does not take into account any interaction effects. the second model adds the interactions to produce the interaction ancova model. by doing this, it is evident that aggressive media, as well as its temperature, do not affect the results at an exposure time of 0 days. consequently, these input variables can be considered insignificant and removed from the interaction model. thus, ‘pr. water’, ‘sea water’, ‘temp’, ‘pr. water × temp’, and ‘sea water × temp’ variables were not taken into account in order to avoid high multicollinearity. the additive and interaction models explain 34 % and 64 % of the variability in test scores respectively (adjusted r2 are 0.338 and 0.642), and the standard error of estimate (1.52 and 1.12) represents how far data fall from the regression predictions. hereby, it suggests that the second model is the better one (table 4). in addition, from table 4 one can see that the test has f statistic ‘f-value’ of 31.24 and 13.92 with p-values of less than 0.001 for additive and interaction models respectively. accordingly, it shows the necessity of these models over an intercept-only model that predicts the average output for all the data. model r2 adjusted r2 std. error of estimate f-value p-value add. mod. 0.365 0.338 1.52 13.92 < 0.001*** full mod. 0.664 0.642 1.12 31.24 < 0.001*** significance levels: ***p-val. ≤ 0.001 (significant), **p-val. ≤ 0.01 (very significant), *p-val. ≤ 0.05 (highly significant). table 4: model summary results for interlaminar shear strength.   i d. s. lobanovet alii, frattura ed integrità strutturale, 60 (2022) 146-157; doi: 10.3221/igf-esis.60.11 152   a b c figure 4: relationship between interlaminar shear strength and exposure time for the composite exposed to process water (a), sea water (b), and machine oil (c) solutions at different temperatures  model coefficient std. error t-value p-value confidence interval [0.025 0.975] 1 const. 34.49 0.45 76.75 < 0.001*** 33.60 35.39 pr. water -2.125 0.369 -5.753 < 0.001*** -2.858 -1.392 sea water -1.129 0.369 -3.057 0.003** -1.862 -0.396 temp. -0.0223 0.006 -4.003 < 0.001*** -0.0334 -0.0112 time -0.0195 0.009 -2.092 0.039* -0.0379 -0.0010 2 const. 32.08 0.18 176.14 < 0.001*** 31.72 32.45 time -0.0122 0.0200 -0.609 0.544 -0.0520 0.0276 temp.×time 0.00061 0.00028 2.182 0.032* 0.00006 0.00117 pr. water×temp.×time -0.0022 0.0004 -5.478 < 0.001*** -0.0030 -0.0014 pr. water×time 0.0475 0.0270 1.762 0.081 -0.0060 0.1011 sea water×temp.×time -0.0028 0.0004 -7.096 < 0.001*** -0.0036 -0.0020 sea water×time 0.1245 0.0270 4.615 < 0.001*** 0.0710 0.1780 significance levels: ***p-val. ≤ 0.001 (significant), **p-val. ≤ 0.01 (very significant), *p-val. ≤ 0.05 (highly significant). table 5: multiple linear regression results for interlaminar shear strength. d. s. lobanov et alii, frattura ed integrità strutturale, 60 (2022) 146-157; doi: 10.3221/igf-esis.60.11 153 reviewing the regression results of the effect of the solutions on the interlaminar shear strength in fig. 4 and tables 5, model 2 can be represented as fsbs = 30.08 0.0122×time + 0.00061×temp.×time 0.0022×pr.wat.×temp.×time + 0.0475×pr.wat.×time 0.0028×seawat.×temp.×time + 0.1245×seawat.×time the simplified model equations are shown here machine oil: fsbs = 30.08 0.0122×time + 0.00061×temp.×time pr. water: fsbs = 30.08 + (-0.0122 + 0.0451)×time + (0.00061 0.0022)×temp.×time sea water: fsbs = 30.08 + (-0.0122 + 0.1245)×time + (0.00061 0.0028)×temp.×time from the equations, we see that 30.08 (with a 95 % confidence interval from 31.72 to 32.45 mpa) is the mean value of the interlaminar shear strength of the material after immersion tests into the machine oil, sea, and process water solutions over the exposure time of 0 days at any temperature. also, we can say that this value of 30.08 mpa is statistically different from zero (t-value = 176.14, p-value < 0.001). similarly, the slope of fsbs vs. time is -0.0122 for machine oil, (-0.0122 + 0.1245) for sea water, and (-0.0122 + 0.0451) for process water respectively. there is a statistically significant effect of exposure time on the interlaminar shear strength only for sea water (the slope fsbs vs. time of 0.1245, t-value = 4.615, pvalue < 0.001), which means the mean strength increases by 1.25 mpa for every 10 days inside the saline solution. in addition, the slope of fsbs vs. temp.×time (the interaction between temperature and time) for machine oil can be seen to be 0.00061, (0.00061 0.0028) for see water, and (0.00061 0.0022) for process water. again, follow-up linear regression analysis in the form of a t-test indicates that the interactions for machine oil (t-value = 2.182, p-value = 0.032), sea (t-value = -7.096, p-value < 0.001) and process water solutions (t-value = -5.478, p-value < 0.001) are statistically significant. this result means that for a 1000 unit increase in product ‘temp.×time’ is 0.6 mpa increase as well as -2.2 and -1.6 mpa decrease in strength for oil, sea and process water respectively. weight gain similar analysis was used to study the effects of the operating environments on weight gain (fig. 5 and tables 67). by doing this, it is clear that weight gain is equal to 0 at an exposure time of 0 days. therefore, the ‘const’ variable was removed from the models. from table 6 it is apparent that both models are better than an interceptonly model that predicts the average output for the whole dataset (f-value = 43.48, p-value < 0.001 and f-value = 78.64, p-value < 0.001 for additive and interaction models respectively). also, the additive and interaction models explain 54 % and 76 % of the variability in test scores respectively (adjusted r2 are 0.541 and 0.764). the standard errors of estimate are equal to 0.27 and 0.19 and represent how far data fall from the regression predictions. thus, one can conclude that the interaction model is the better than additive one.     a b a d. s. lobanovet alii, frattura ed integrità strutturale, 60 (2022) 146-157; doi: 10.3221/igf-esis.60.11 154 c figure 5: relationship between weight gain and exposure time for the composite exposed to process water (a), sea water (b), and machine oil (c) solutions at different temperatures model r2 adjusted r2 std. error of estimate f-value p-value add. mod. 0.554 0.541 0.27 43.48 < 0.001*** full mod. 0.774 0.764 0.19 78.64 < 0.001*** significance levels: ***p-val. ≤ 0.001 (significant), **p-val. ≤ 0.01 (very significant), *p-val. ≤ 0.05 (highly significant). table 6: model summary results for weight gain model coefficient std. error t-value p-value confidence interval [0.025 0.975] 1 pr. water 0.167 0.051 3.286 0.001*** 0.066 0.267 sea water 0.245 0.049 5.019 < 0.001*** 0.149 0.342 temp. -0.0010 0.0006 -1.882 0.062 -0.0021 0.0001 time 0.0108 0.0014 7.930 < 0.001*** 0.0081 0.0135 2 time 0.0003 0.0039 0.080 0.937 -0.0074 0.0081 temp.×time -1.2×10-5 5.5×10-5 -0.216 0.829 -0.00012 9.7×10-5 pr. water×temp.×time 0.00020 8.0×10-5 2.461 0.015* 0.00004 0.00036 pr. water×time 0.0049 0.0056 0.877 0.382 -0.0062 0.0161 sea water×temp.×time 0.00017 7.8×10-5 2.180 0.031* 0.00002 0.00032 sea water×time 0.0119 0.0055 2.143 0.034* 0.0009 0.0228 significance levels: ***p-val. ≤ 0.001 (significant), **p-val. ≤ 0.01 (very significant), *p-val. ≤ 0.05 (highly significant). table 7: multiple linear regression results for weight gain. the second model is represented as weightgain = 0.0003×time 1.2×10-5×temp.×time + + 0.0002×pr.wat.×temp.×time + 0.0049×pr.wat.×time + + 0.00017×seawat.×temp.×time + 0.0119×seawat.×time the simplified model equations are shown here d. s. lobanov et alii, frattura ed integrità strutturale, 60 (2022) 146-157; doi: 10.3221/igf-esis.60.11 155 machine oil: weightgain = 0.0003×time 1.2×10-5×temp.×time pr. water: weightgain = (0.0003 + 0.0049)×time + (-1.2×10-5 + 0.0002)×temp.×time sea water: weightgain = (0.0003 + 0.0119)×time + (-1.2×10-5 + 0.00017)×temp.×time these equations demonstrate that the slope of weightgain vs time is 0.0003 for machine oil, (0.0003 + 0.0049) for process water, and (0.0003 + 0.0119) for sea water respectively. there is a statistically significant effect only for sea water (t-value = 2.143, p-value = 0.034). consequently, this suggests the weight gain increase of the material by 0.12 % for every 10 days inside the saline solution. along with that, the interaction effect between temperature and time (weightgain vs temp.×time) is -1.2×10-5 for oil, (-1.2×10-5 + 0.0002) for process water, and (-1.2×10-5 + 0.00017) for sea water respectively. here, only 2 interactions are statistically significant for process (t-value = 2.461, p-value = 0.015) and sea water solutions (t-value = 2.180, p-value = 0.031). accordingly, it indicates a 0.2 % and 0.17 % increase in weight gain of the material for process and sea water respectively for a 1000 unit increase in product ‘temp.×time’. in general, saline water affects weight gain stronger than process water. for instance, weight gain increases around 1.2 % and 1.0 % after 45 days at 90 oc inside sea and process water respectively. as a result, it is apparent that weight gain can increase due to water and salt exposure. however, their effects on the interlaminar shear strength are different; the strength increases over time inside the sea water solution at room temperature, whereas it remains almost unchanged inside process water. it might be related to the additional reinforcement effect of the composite material because of salinity. also, it may be a reason why process water promotes lower strength than the sea water relative to the control samples at high solution temperature. as we can see from fig. 4, the maximum difference is around 4.7 mpa or 15 % and 3.8 mpa or 12 % after 45 days inside process and sea water respectively at 90 oc. the effect depends on the solution temperature: the higher temperature, the lower strength. therefore, one can conclude that process water is more aggressive than sea water. on the contrary, the machine oil solution slightly affects the results: the maximum increase in strength is about 1.9 mpa or 6 %. this result needs further investigations because the significance level does not look high and there is a probability of about 3.2 % of obtaining that result by chance when the exposure time has no real effect. moreover, there are no significant effects for weight gain results which also indicates the weak relationship between weightgain vs temp.×time. conclusions   eries of experimental studies of effects of preliminary hygrothermal aging at 22, 60 and 90 oc were conducted with the exposure time of 15, 30 and 45 days in aggressive operating media (sea water, process water, machine oil) for residual strength in case of interlaminar shear for specimens of stef structural fiberglass. characteristic loading diagrams and patterns of fiberglass specimen failure were obtained and analyzed before and after hygrothermal aging. it is observed that failure mechanisms change after hygrothermal aging in sea water and process water, which complies with the results of other authors in similar studies. according to the ancova analysis for multiple linear regression, increasing the exposure time of any solution studied does not have a statistically significant effect on the interlaminar shear strength and weight gain except for the sea water solution. it has a positive effect on strength values (about 1.25 mpa per 10 days rise in time) and weight gain (about 0.12 % per 10 days rise in time). similarly, increasing the product of solution temperature and exposure time has a significantly positive effect on weight gain for process and sea water solutions. however, it has a significantly negative effect on the obtained strength values, but their effects are slightly different: process water is more aggressive than sea water. the biggest reduction of the interlaminar shear strength was observed at a temperature of 90 oc and a time of 45 days: around 12 % and 15 % for sea and process water solutions respectively. probably, it might be associated with the additional reinforcement due to solution salinity. in addition, universal machine oil makes strength values slightly bigger. similarly, this effect is dependant on solution temperature. for the specimens immersed in oil, the mean strength increases about 6 % after 45 days at 90 oc. finally, the ancova regression model has better predictive ability than the intercept-only one (predicts the average output for all the data) and can be successfully applied to predict the material strength after immersion tests into aggressive media. s d. s. lobanovet alii, frattura ed integrità strutturale, 60 (2022) 146-157; doi: 10.3221/igf-esis.60.11 156 acknowledgements he work was carried out with support of the russian science foundation (project no. 21-79-10205, https://rscf.ru/project/21-79-10205/) in the perm national research polytechnic university. references [1] lobanov, d.s., wildemann, v.e., spaskova, e. m., chikhachev, a.i. (2015). experimental investigation of the defects influence on the composites sandwich panels strength with use digital image correlation and infrared thermography methods. pnrpu mechanics bulletin, 4, pp. 159-170. doi: 10.15593/perm.mech/2015.4.10 [2] lobanov, d.s., babushkin, a.v. (2017). experimental studies of the high temperature influence on strength and deformation properties of combined glass organoplastics. pnrpu mechanics bulletin, 1, pp. 104-117. [3] lobanov, d.s., slovikov, s.v. (2018). mechanical behavior of a unidirectional basalt-fiber-reinforced plastic under thermomechanical loadings. mechanics of composite materials, 54(3), pp. 351-358. [4] lobanov, d.s., babushkin, a.v., luzenin, a.yu. (2018). effect of increased temperatures on the deformation and strength characteristics of a gfrp based on a fabric of volumetric weave. mechanics of composite materials, 54(5), pp. 655-664. [5] de souza, l.r., marques, a.t., d'almeida, j.r.m. (2017). effects of aging on water and lubricating oil on the creep behavior of a gfrp matrix composite. composite structures, 168, pp. 285-291 [6] alam, p., robert, c., ó brádaigh, c.m. (2018). tidal turbine blade composites a review on the effects of hygrothermal aging on the properties of cfrp. composites part b: engineering, 149, pp. 248-259 [7] lobanov, d.s., vildeman, v.e., babin, a.d., grinev, m.a. (2015). experimental research into the effect of external actions and polluting environments on the serviceablity of fiber-reinforced polymer composite materials. mechanics of composite materials, 51(1), pp. 69-79 [8] muralidharan, m., sathishkumar, t.p., rajini, n., navaneethakrishnan, p., arun kumar, s., ismail, s.o., senthilkumar, k., siengchin, s. (2022). evaluation of tensile strength retention and service life prediction of hydrothermal aged balanced orthotropic carbon/glass and kevlar/glass fabric reinforced polymer hybrid composites, journal of applied polymer science, 139 (6), art. no. 51602. doi: 10.1002/app.51602 [9] mansouri, l., djebbar, a., khatir, s., abdel wahab, m. (2019). effect of hygrothermal aging in distilled and saline water on the mechanical behaviour of mixed short fibre/woven composites. composite structures, 207, pp. 816-825 [10] chen, y., davalos, j.f., ray, i. (2006). durability prediction for gfrp reinforcing bars using short-term data of accelerated aging tests. journal of composites for construction, 10(4), pp. 279-286 [11] lobanov, d.s. zubova, e.m. (2020). temperature aging effects on mechanical behavior of structural gfrp on interlaminar shear tests. iop conf. series: materials science and engineering, 747.012119. doi:10.1088/1757-899x/747/1/012119. [12] park, s.y., choi, w.j., choi, h.s. (2010). the effects of void contents on the long-term hygrothermal behaviors of glass/epoxy and glare laminates. composite structures, 92(1), pp. 18-24. [13] malmstein, m., chambers, a.r., blake, j.i.r. (2013). hygrothermal ageing of plant oil based marine composites composite structures, 101, pp. 138-143. [14] li, y., li, r., huang, l., wang, k., huang, x. (2016). effect of hygrothermal aging on the damage characteristics of carbon woven fabric/epoxy laminates subjected to simulated lightning strike. materials and design, 99, pp. 477-489. [15] lobanov, d.s., lunegova, e.m., mugatarov, a.i. (2021). influence of preliminary thermal aging on the residual interlayer strength and staging of damage accumulation in structural carbon plastic. pnrpu mechanics bulletin, 1, pp.41-51. doi: 10.15593/perm.mech/2021.1.05 [16] nicholas, j., mohamed, m., dhaliwal, g.s., anandan, s., chandrashekhara, k. (2016). effects of accelerated environmental aging on glass fiber reinforced thermoset polyurethane composites. composites part b: engineering, 94, pp. 370-378. t d. s. lobanov et alii, frattura ed integrità strutturale, 60 (2022) 146-157; doi: 10.3221/igf-esis.60.11 157 [17] lu z., xian g., li h. (2015). effects of exposure to elevated temperatures and subsequent immersion in water or alkaline solution on the mechanical properties of pultruded bfrp plates. composites part b: engineering, 77, pp. 421-430. [18] lobanov, d. s., zubova, e.m. (2019). research of temperature aging effects on mechanical behaviour and properties of composite material by tensile tests with used system of registration acoustic emission signal. procedia structural integrity, 18, pp. 347-352. [19] amaro, a. m., reis, p. n. b., neto, m. a., & louro, c. (2014). effect of different commercial oils on mechanical properties of composite materials. composite structures, 118, 1–8. doi:10.1016/j.compstruct.2014.07.017 [20] seltman h. j. experimental design and analysis, (2018), 428 p. [21] warner, r.m. (2013). applied statistics : from bivariate through multivariate techniques.—2nd, 1691 p. [22] elmushyakhi, a. (2021). parametric characterization of nano-hybrid wood polymer composites using anova and regression analysis. structures, 29, pp. 652-662. doi: 10.1016/j.istruc.2020.11.069 [23] bellini, c., parodo, g., polini, w., sorrentino, l. (2018). influence of hydrothermal ageing on single lap bonded cfrp joints, frattura ed integrità strutturale, 45, pp.173-182. [24] pehlivan, e, roudnicka, m, dzugan, j, koukolikova, m, kralik, v, seifi, m, lewandowski, j.j., dalibor, d., daniel, m. (2020). effects of build orientation and sample geometry on the mechanical response of miniature cp-ti grade 2 strut samples manufactured by laser powder bed fusion. additive manufacturing, doi: 10.1016/j.addma.2020.101403. [25] alsahhaf, a., spies, b. c., vach, k., & kohal, r.-j. (2017). fracture resistance of zirconia-based implant abutments after artificial long-term aging. journal of the mechanical behavior of biomedical materials, 66, pp. 224–232. doi: 10.1016/j.jmbbm.2016.11.018. [26] alamoush, r. a., sung, r., satterthwaite, j. d., silikas, n. (2021). the effect of different storage media on the monomer elution and hardness of cad/cam composite blocks. dental materials. 37(7), pp. 1202-1213. doi: 10.1016/j.dental.2021.04.009. [27] durga vithal, n., bala krishna, b., gopi krishna, m. (2021). impact of dry sliding wear parameters on the wear rate of a7075 based composites reinforced with zrb2 particulates. journal of materials research and technology, 14, pp 174-185, doi: 10.1016/j.jmrt.2021.06.005. [28] osmond, r., mollahoseini, z., singh, j., gautam, a., seethaler, r., golovin, k., milani, a. s. (2021). a group multicriteria decision making with anova to select optimum parameters of drilling flax fibre composites. composites part c, 5, 100156, doi: 10.1016/j.jcomc.2021.100156. [29] balachandhar, r., balasundaram, r., ravichandran, m. (2021). analysis of surface roughness of rock dust reinforced aa6061-mg matrix composite in turning. journal of magnesium and alloys, doi: 10.1016/j.jma.2021.03.035. [30] karthik, a., srinivasan, s.a., karunanithi, r., kumaresh babu, s.p., kumar, v., jain, s. (2021). influence of ceo2 reinforcement on microstructure, mechanical and wear behaviour of aa2219 squeeze cast composites. journal of materials research and technology, 14, pp. 797-807, doi: 10.1016/j.jmrt.2021.06.056. [31] kim, n. k., bruna, f.g., das, o., hedenqvist, m. s., bhattacharyya, d. (2020). fire-retardancy and mechanical performance of protein-based natural fibre-biopolymer composites. composites part c, 1, 100011, doi : 10.1016/j.jcomc.2020.100011. [32] reis, p.n.b., silva, a.p., santos, p., ferreira, j.a.m. (2013). hygrothermal effect on the impact response of carbon composites with epoxy resin enhanced by nanoclays. mech compos mater, 49, pp.429–436. [33] boukhoulda, b.f., adda-bedia, e., madani, k. (2006). the effect of fiber orientation angle in composite materials on moisture absorption and material degradation after hygrothermal ageing. compos struct; 74, pp.406–418. << /ascii85encodepages false /allowtransparency false /autopositionepsfiles true /autorotatepages /none /binding /left /calgrayprofile (dot gain 20%) /calrgbprofile (srgb iec61966-2.1) /calcmykprofile (u.s. web coated \050swop\051 v2) /srgbprofile (srgb iec61966-2.1) /cannotembedfontpolicy /error /compatibilitylevel 1.4 /compressobjects /tags /compresspages true /convertimagestoindexed true /passthroughjpegimages true /createjobticket false /defaultrenderingintent /default /detectblends true /detectcurves 0.0000 /colorconversionstrategy /cmyk /dothumbnails false /embedallfonts true /embedopentype false /parseiccprofilesincomments true /embedjoboptions true /dscreportinglevel 0 /emitdscwarnings false /endpage -1 /imagememory 1048576 /lockdistillerparams false /maxsubsetpct 100 /optimize true /opm 1 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/hrv (za stvaranje adobe pdf dokumenata najpogodnijih za visokokvalitetni ispis prije tiskanja koristite ove postavke. stvoreni pdf dokumenti mogu se otvoriti acrobat i adobe reader 5.0 i kasnijim verzijama.) /hun 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can be opened with acrobat and adobe reader 5.0 and later.) >> /namespace [ (adobe) (common) (1.0) ] /othernamespaces [ << /asreaderspreads false /cropimagestoframes true /errorcontrol /warnandcontinue /flattenerignorespreadoverrides false /includeguidesgrids false /includenonprinting false /includeslug false /namespace [ (adobe) (indesign) (4.0) ] /omitplacedbitmaps false /omitplacedeps false /omitplacedpdf false /simulateoverprint /legacy >> << /addbleedmarks false /addcolorbars false /addcropmarks false /addpageinfo false /addregmarks false /convertcolors /converttocmyk /destinationprofilename () /destinationprofileselector /documentcmyk /downsample16bitimages true /flattenerpreset << /presetselector /mediumresolution >> /formelements false /generatestructure false /includebookmarks false /includehyperlinks false /includeinteractive false /includelayers false /includeprofiles false /multimediahandling /useobjectsettings /namespace [ (adobe) (creativesuite) (2.0) ] /pdfxoutputintentprofileselector /documentcmyk /preserveediting true /untaggedcmykhandling /leaveuntagged /untaggedrgbhandling /usedocumentprofile /usedocumentbleed false >> ] >> setdistillerparams << /hwresolution [2400 2400] /pagesize [612.000 792.000] >> setpagedevice microsoft word numero_44_art_6 x.-p. zhou et alii, frattura ed integrità strutturale, 44 (2018) 64-81; doi: 10.3221/igf-esis.44.06 64 an innovative micromechanics-based three-dimensional long-term strength criterion for fracture assessment of rock materials xiao-ping zhou, xiao-cheng huang school of civil engineering, chongqing university, chongqing 400045, china state key laboratory of coal mine disaster dynamics and control, chongqing university, chongqing 400044, china filippo berto department of mechanical engineering, norwegian university of science and technology, trondheim 7491, norway abstract. rocks may exhibit time-dependent behaviors. long-term strength criterion significantly dominates creep failure of rocks. rocks contain many microcracks, which lead to degrade of long-term strength. in this paper, it is assumed that there exist three-dimensional penny-shaped microcracks in rocks. the mode ii stress intensity factors at tips of three-dimensional pennyshaped microcracks in burgers viscoelastic rock matrix is derived. a novel micromechanics-based three-dimensional long-term strength criterion is established to consider the effects of time and the intermediate principal stress on creep failure of rocks. by comparison with the previous experimental data, it is found that the novel micromechanics-based threedimensional long-term strength criterion is in good agreement with the experimental data. keywords. micromechanics-based three-dimensional long-term strength criterion; burgers viscoelastic rock matrix; three-dimensional penny-shaped creep microcracks; stress intensity factor; the intermediate principal stress. citation: zhou, x.-p., huang, x.-c., berto, f., an innovative micromechanics-based three-dimensional long-term strength criterion for fracture assessment of rock materials, frattura ed integrità strutturale, 44 (2018) 64-81. received: 19.01.2018 accepted: 05.02.2018 published: 01.04.2018 copyright: © 2018 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. introduction n the past several decades or more, extensive laboratory creep experiments were conducted to study the creep behaviors of many kinds of rocks [1-5]. it is indicated that deformation of rocks under a constant load over extended a period of time generally exhibits primary or transient creep, lately by secondary or steady-rate creep, followed terminating in tertiary or accelerating creep that eventually progresses to dynamic rupture. moreover, it is observed from laboratory creep experiments that the failure of rocks occurs at stresses well below the peak strength of rocks. analyses that the short-term strength is applied to estimate the stability of the surrounding rock mass around tunnels have often predicted stable openings even though the failure of rock mass is observed in situ. for example, it is observed that the long-term strength of rock in situ can be as low as 50% of the short-term strength [6]. i x.-p. zhou et alii, frattura ed integrità strutturale, 44 (2018) 64-81; doi: 10.3221/igf-esis.44.06 65 to investigate the long-term strength of rock, some long-term strength criteria of rocks were established to study the creep behaviors of rocks, such as mises-schleicher &drucker-prager unified(msdpu) criterion, and so on. however, these long-term strength criteria were established using phenomenological approaches, which can produce the macroscopically observed creep curves of rocks by fitting with experimental data, and the inherent physical mechanisms related to time-dependent behaviors are not accommodated in these models, so the key mechanistic parameters remain physically unclear [7]. to authors' knowledge, three-dimensional long-term strength criterion of rocks, in which the effects of the intermediate principal stress are considered, is not proposed by using micromechanical methods. in fact, rock is a kind of discontinuity medium containing many microcracks and microdefects, the presence of such microcracks strongly influences the macroscopic mechanical behavior of rocks by serving as stress concentrators and leading to microcracking [8-12]. to overcome the disadvantages encountered in phenomenological models, it is necessary to study the effects of initiation and propagation of microcracks and microdefects on the creep failure of rocks. in this paper, micromechanical methods are used to investigate the lone-term strength of rocks. moreover, a novel micromechanics–based three-dimensional nonlinear long-term strength criterion is established to study the effects of time and the intermediate principal stress on the creep failure of rocks. by comparison with experimental data, it is found that the novel micromechanics–based threedimensional long-term strength criterion is in good agreement with the experimental data. the analytical model t is generally accepted that the creep deformation and fracturing process that evolve in rocks are closely related to the intrinsic property and stress condition of rocks, such as fracture toughness, internal frictional angle, the dip and orientation angle of microcracks, poisson’s ratio, and so on. in this paper, it is assumed that the creep failure of rocks is due to the presence of penny-shaped microcracks and there is abundant evidence for the existence of microcracks in rocks [13-14]. therefore, this model is physically plausible and the following assumptions are made: (i) penny-shaped microcracks are assumed to be randomly distributed in burgers viscoelastic rock matrix; (ii) the interaction between penny-shaped microcracks is neglected before the coalescence of microcracks. stress intensity factor of penny-shaped microcracks embedded in burgers viscoelastic rock matrix it is assumed that the tensile stress is negative, and the compressive stress is positive. consider a single penny-shaped creep microcrack in burgers viscoelastic rock matrix uniformly loaded at far field. establish a global coordinate system ( o x x x1 2 3 .) and its corresponding local coordinate system (   o x x x1 2 3 ), as shown in fig. 1. in a global coordinate system ( o x x x1 2 3 ), the direction of the maximum principal stress is parallel to the x1 -axis, the direction of the intermediate principal stress is parallel to the x 2 -axis, the direction of the minimum principal stress is parallel to the x3 axis. in the local coordinate system (   o x x x1 2 3 ), the direction of the x 2 -axis is parallel to the normal direction of penny–shaped creep microcrack. the angle between the x 2 -axis and the x 2 -axis is the dip angle of penny–shaped creep microcrack  . the angle between the x 3 -axis and the x3 -axis is the orientation angle of penny–shaped creep microcrack  . figure 1: mechanical model for penny-shaped microcrack embedded by burgers viscoelastic rock matrix. i x.-p. zhou et alii, frattura ed integrità strutturale, 44 (2018) 64-81; doi: 10.3221/igf-esis.44.06 66 the stresses in the local coordinate system are given by yu and feng [15],    ij ik jl klg g (1) where,                       ijg cos cos sin cos sin sin cos cos sin sin sin 0 cos (2) then, 22 ,21 and 23 can be respectively expressed as follows:                                              2 2 2 2 2 22 1 2 3 2 2 21 2 1 3 23 3 1 sin cos cos sin sin sin cos sin cos cos sin cos sin sin sin cos sin sin cos (3) yu and feng [15] and tada [16] defined the stress intensity factors at tips of penny-shaped microcracks embedded in isotropic and elastic rock matrix as                   ii a k 22 21 23 224 2 (4) where μ is the frictional coefficient on the crack surfaces,  is poisson's ratio, kii is the mode ii stress intensity factor. the burgers creep model in this paper, it is assumed that microcracks are embedded in burgers viscoelastic rock matrix with the characteristic of instantaneous elastic deformation, primary creep and steady-rate creep. figure 2: the diagram of burgers model. as shown in fig. 2, burgers model can be expressed as follows               ij ij ij ij ij g g g e e s s s g g 2 2 2 2 1 2 1 1 2 1 2 1 1 1 ( ) 2 2 2 2 2 (5) x.-p. zhou et alii, frattura ed integrità strutturale, 44 (2018) 64-81; doi: 10.3221/igf-esis.44.06 67 where g1 is maxwell shear modulus, g2 is kelvin shear modulus, 1 is maxwell viscosity, and 2 is kelvin viscosity,        ijij ijs 11 22 33( ) 3 ,        ijij ije 11 22 33( ) 3 ,      ij i j i j 1 0 ,  ij is stress tensor, ij is strain tensor. the maxwell shear modulus is equal to elasticity shear modulus,   ij ij d e e dt 2 2 ,   ij ij de e dt ,   ij ij d s s dt 2 2 ,   ij ij ds s dt . eq.(5) can be rewritten as                  g t ij ij t e s e g g 2 2 1 1 2 1 1 1 2 2 2 (6) where t is the creep time. from eq.(6) and works by yi and zhu [17], the time factor of the burgers model under a given load is obtained as                   i iu f t h t g g g f t t t g 1 1 2 1 2 2 ( ) ( ) ( ) 1 1 exp (7) where iuf t( ) is the time factor for displacement, if t( ) is the time factor for stress,     t h t t 1, 0 ( ) 0, 0 is heaviside function. according to works by zhou [18], energy release rate at tips of the mixed mode iii-iii microcracks in burgers viscoelastic rock matrix can be written as        i ii iii i ii iii iu v g t g t g t g t k k k f t e v 2 2 2 21 1( ) ( ) ( ) ( ) ( ) ( ) 1 (8) where                iu g g g f t t t g 1 1 2 1 2 2 ( ) 1 1 exp . in eq. (8), g t( ) can be rewritten as  iug t f t g( ) ( ) (9) where g is energy release rate at tips of the mixed mode i-ii-iii microcracks in elastic rock matrix. as for the creep fracture, the stress and displacement fields at tips of microcracks can be obtained as follows:         m m m ij ij m m m m i i m k t t k k t u t u k ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) (10) x.-p. zhou et alii, frattura ed integrità strutturale, 44 (2018) 64-81; doi: 10.3221/igf-esis.44.06 68 where m =i, ii and iii, which are, respectively, denoted by mode i, ii and iii microcracks,  mij ( ) and miu ( ) are, respectively, the stress and displacement fields at tips of microcracks in elastic rock matrix,  mij t ( )( ) and miu t ( )( ) are, respectively, the stress and displacement fields at tips of microcracks in burgers viscoelastic rock matrix, mk t( ) and mk are, respectively, stress intensity factor at tips of microcracks in burgers viscoelastic and elastic rock matrix. according to the definition of stress intensity factor, stress intensity factor at tips of microcracks can be denoted by                   m m ij yx m m ij yx k x k t t x ( ) 00 ( ) 00 lim 2 ( ) lim ( ) 2 (11) based on the definition of energy release rate, energy release rate at tips of microcracks can be defined by                                a yy y yx x yz z a g t x u x a x u x a x u x a dx a 00 1 lim , 0 , 0 , 0 , 0 , 0 , 0 (12) where a is the growth length of microcracks. substituting eq. (10) into eq. (12) yields                                          a m m ij i a a m mm m ij i a m m a m m ij i a m m g t t u t dx a k t k t u dx a k k u dx a k t g k ( ) ( ) 00 ( ) ( ) 00 ( ) ( ) 00 2 2 1 ( ) lim ( ) ( ) ( ) ( )1 lim 1 lim ( ) (13) from eq. (13) and eq. (9), the stress intensity factors of creep cracks can be written as  m m m iu g t k t k k f t g ( ) ( ) ( ) (14) for three-dimensional penny-shaped microcracks, frictional sliding is caused by the effective shear stress. as the effective shear force is greater than the frictional resistance along the slip surface, frictional slip would lead to the tensile stress at the two tips of the slip surface, which form the wing cracks, as shown in fig. 3. substituting eq. (4) into eq. (14) yields:                    iu ii f t a k 22 21 23 224 ( ) 2 (15) where  is the frictional coefficient on the crack surfaces,  is poisson’ s ratio, iik is the mode ii stress intensity factor, f t( ) denotes the time factor. according to works by tada [16], the condition of unstable growth of the mode ii microcracks can be written as ii ick t k0( ) (16) x.-p. zhou et alii, frattura ed integrità strutturale, 44 (2018) 64-81; doi: 10.3221/igf-esis.44.06 69 where                                              2 2 2 2 2 22 1 2 3 2 2 21 2 1 3 23 3 1 sin cos cos sin sin sin cos sin cos cos sin cos sin sin sin cos sin sin cos  can be obtained from experimental results, or approximation suggested in the literature on the kinked crack, such as   3 / 2 in the maximum-stress criterion [19], t 0 is the time of creep failure of microcracks, ick is toughness of rocks, which can be obtained by induced tensile strength and crack length, namely   ic t a k 2 (17) where t is short-term uniaxial tensile strength of rocks. figure 3: propagation of wing cracks from the tip of penny-shaped microcrack. the orientation angle of micro-failure in rocks t is generally accepted that the creep failure of rocks is induced by the fragment of large amounts of internal microcracks. however, it is very difficult to quantitatively analyze the number of microcracks. therefore, microfailure orientation angle  is introduced to define the number of propagating penny-shaped creepmicrocracks, as shown in fig. 4. the fan-shaped area of wing crack distribution zone shown in fig. 4 can be obtained from eqs(15)-(16). the included angle of the fan section is denoted as the micro-failure orientation angle  . substituting eq.(15) into eq.(16) yields:                                                                  c c 1 3 2 2 2 2 2 2 2 3 2 2 2 4 4 1 3 22 2 2 2 2 2 3 2 3 1 3 3 sin 2 2 cos 2 cos sin co ( ) ( 1)sin cos si s n cos cos sin 0 (18) i x.-p. zhou et alii, frattura ed integrità strutturale, 44 (2018) 64-81; doi: 10.3221/igf-esis.44.06 70 where    t iuf t ( 2 ) c 2 ( ) ,1 is the maximum principal stress, 2 is the intermediate principal stress, 3 is the minimum principal stress, the compressive stresses are defined to be positive in this paper. figure 4: wing crack distribution zone eq.(18) can be rewritten as :    c c c4 21 2 3cos cos 0 (19) where                                                              c c c c c 2 2 4 1 1 3 2 2 2 3 22 2 2 2 2 3 2 2 2 2 2 1 3 2 3 3 2 1 3 ( ) ( 1)sin sin cos sin cos cos si sin 2 +2 c n os +1 +2 from eq. (19), the cosine of  can be written as    2 2 21 2cos cos cos (20) where                 c c c c c c c c c c 2 2 2 1 32 1 1 2 2 2 1 32 2 1 4 cos 2 4 cos 2 from eq.(20), supposing    2 1 , the following equation can be written          2 1 2 1 2 1cos cos( ) cos cos sin sin (21)  2 1 1 3 x.-p. zhou et alii, frattura ed integrità strutturale, 44 (2018) 64-81; doi: 10.3221/igf-esis.44.06 71 creep failure characteristic parameters of rocks he creep failure characteristic parameter of rocks should be constant when rocks entirely break. damage mechanics reveals that the nucleation and initiation of microcracks does not imply creep failure of rock-like materials [20-22]. many experiments show that the maximum principal stress should be further increased to assure that the wing crack continually propagates, while the minimum principal stress can significantly restrain wing crack to grow [23]. therefore, the initiation of wing cracks cannot indicate creep failure of rocks. as a result, nucleation and initiation of internal microcracks cannot be chosen as the creep failure characteristic parameters. the larger the minimum principal stress, the smaller the micro-failure orientation angle . the micro-failure orientation angle  does not keep constant, tan , sin and cos do not also keep constant. therefore, the micro-failure orientation angle , tan , sin and cos cannot be considered as the creep failure characteristic parameters. microcracks randomly distribute in burgers viscoelastic rock matrix, and the orientation angle of each microcrack randomly distributes. therefore, the micro-failure orientation angle  can be adopted to investigate the micro-failure density. an increase in the minimum principal stress leads to a decrease in the micro-failure density. the internal microfailure density does not keep constant. therefore, the micro-failure density cannot also be chosen as the creep failure characteristic parameters. reference [24] suggested that the creep failure of rocks occurs when the volumetric strain due to the internal micro-failure density reaches a critical value. therefore, the creep failure characteristic parameters of rocks should be relevant to the internal micro-failure density, which is related to the micro-failure orientation angle  . moreover, the creep failure characteristic parameters should satisfy the following three principles: firstly, the expression of the creep failure characteristic parameter should be in a simple mathematic one; secondly, the higher the minimum principal stress, the lower the micro-failure orientation angle; finally, the theoretical result should agree well with the experimental data. obviously, the expressions of the micro-failure orientation angle  , tan and sin are so complicated that it cannot be chosen as the creep failure characteristic parameters. compared with the expressions of  , tan and sin , the expression of cos is the simplest. the expression of   c1 is also the simplest therefore,   c1 satisfies the first and second principles. according to the second principle and eq. (21), the cosine of the micro-failure orientation angle can be expressed in following form:   c cc c c c 3 32 1 1 1 cos = + 1+ (22) where                                                                     c c c c c c c c c c c 2 22 2 2 2 2 1 11 2 21 22 2 2 2 2 3 2 3 2 3 2 4 11 2 21 2 2 2 2 22 1 3 3 sin cos cos s 2 +2 cos in ( 1)sin sin sin sin co+1 +2 s t x.-p. zhou et alii, frattura ed integrità strutturale, 44 (2018) 64-81; doi: 10.3221/igf-esis.44.06 72 it is indicated from eq.(22) that the cosine of the micro-failure orientation angle increases with an increase in the minimum principal stress 3 , while the micro-failure orientation angle decreases with increasing the minimum principal stress 3 . for an invariable intermediate principal stress 2 and an invariable minimum principal stress 3 , the relationship between cos and the maximum principal stress can be defined. differentiating eq. (22) with respect to1 yields:                   c c c c c c c c 22 3 32 2 1 11 11 21 22 3 2cos 1 2 (23) where     1 cos is defined as the rate of change of cos to the maximum principal stress. from eq. (22), the maximum principal stress can be expressed as            c c c c c 11 3 22 1 3 2 21 11 2 cos sin (24) substituting eq. (24) into eq. (23) yields                                            c c c c c c c c c c c c c c c c c c c c c c c c c c 22 21 11 2 11 22 11 3 2 2 22 22 11 3 3 21 11 3 2 2 3 11 21 22 11 3 22 22 11 3 21 11 1 sin 2 cos 2 cos 2 sin 2 2 cos 2 cos sin cos (25) if the short-term uniaxial compressive strength of rocks is known, three-dimensional long-term strength criterion of rocks can be expressed by short-term uniaxial compressive strength of rocks. therefore, for the short-term uniaxial compression condition   c1 ,  2 0 ,  3 0 , we can obtain    1cos at t 0 as,                           c c c c c c c 2 20 0 2 2 22 2 2 21 0 csccos csc +1 sin sin cos (26) where    t iuf c 0 ( 2 ) 2 (0) ,c is the short-term uniaxial compressive strength of rocks, iuf (0) is the time factor when t 0 . substituting eq. (23) into eq. (26) yields                                       c c c c c c c c c c c c c c c 22 3 32 2 11 11 21 22 3 2 20 0 2 2 22 2 2 2 0 21 2 csc csc +1 sin sin cos (27) x.-p. zhou et alii, frattura ed integrità strutturale, 44 (2018) 64-81; doi: 10.3221/igf-esis.44.06 73 from eq. (27), three-dimensional long-term strength criterion expressed by the short-term uniaxial compressive strength of rocks can be denoted by                       a a a a a4 3 21 1 3 2 1 3 3 1 3 4 1 3 5 0 (28) where                                                        a c c c c a c c c a c c c c c c c c a c c c c a c c c c c c c c c c c c c 2 1 11 4 11 21 2 2 11 22 4 2 3 11 3 4 11 21 4 11 3 4 22 4 11 3 2 5 3 11 21 3 4 11 3 22 2 4 11 2 21 2 2 2 2 2 2 2 2 32 2 2 2 3 2 3 4 4 4 2 2 4 2 ( 1)sin sin sin sin cos sin 2 +2 cos +1 + cos 2                                                          c c c c c c c c c 2 2 2 2 3 2 20 0 4 2 2 22 2 2 2 0 cos sin csc csc +1 sin sin cos it is observed from eq. (28) that  1 3  is related to the friction coefficient  , the coefficient  of mixed-mode fracture criterion, the short-term uniaxial compressive strength c , the short-term uniaxial tensile strength t , the time factor iuf (0) , the dip angle of penny-shaped microcracks θ and poisson’s ratio  . if the long-term uniaxial compressive strength of rocks is known, three-dimensional long-term strength criterion of rocks can be expressed by long-term uniaxial compressive strength of rocks. therefore, for the long-term uniaxial compressive condition   cl1 ,  2 0 ,  3 0 , we can obtain the rate of change constant    1cos /    1cos / at t t 0 as,                           t cl t cl t cl cl c c c 2 20 0 2 2 22 2 2 21 0 csccos csc +1 sin sin cos (29) where   t t iu c f t0 0 ( 2 ) 2 ( ) ,cl is the long-term uniaxial compressive strength of rocks, iuf t 0( ) is the time factor when t t 0 , t 0 is the time of creep failure of rocks under uniaxial compressive loads. substituting eq. (29) into eq. (23) yields: x.-p. zhou et alii, frattura ed integrità strutturale, 44 (2018) 64-81; doi: 10.3221/igf-esis.44.06 74                                        t cl t cl t cl cl c c c c c c c c c c c 22 3 32 2 11 11 21 22 3 2 20 0 2 2 22 2 2 2 0 21 2 csc csc +1 sin sin cos (30) from eq. (30), micromechanics-based three-dimensional long-term strength criterion of rocks expressed by long-term uniaxial compressive strength of rocks can written as                       a a a a a4 3 21 1 3 2 1 3 3 1 3 4 1 3 5 0 (31) where                                                      a c c c c a c c c a c c c c c c c c a c c c c a c c c c c c c c c c c c c c 2 1 11 4 11 21 2 2 11 22 4 2 3 11 3 4 11 21 4 11 3 4 22 4 11 3 2 5 3 11 21 3 4 11 3 22 2 4 11 2 21 22 2 2 22 2 2 3 2 3 3 2 2 4 4 4 2 2 4 2 ( 1)si 2 +2 n sin sin sin cos cos cos +1 +2 sin                                                          t cl t cl t cl cl c c c c 2 22 2 2 2 3 2 20 0 4 2 2 22 2 2 2 0 sin cos csc csc +1 sin sin cos it is observed from eq. (31) that   1 3 is related to the friction coefficient  , the coefficient  of mixed-mode fracture criterion, the long-term uniaxial compressive strength cl , the short-term uniaxial tensile strength t , the time factor iuf t 0( ) , the dip angle of penny-shaped microcracks θ and poisson’s ratio  . assumed that   c c11 21 0 ,     clc s m n22 2 3 ,      clc s m n 2 3 2 3 eq.(31) can be simplified to:                           cl cl cl cls m n s s s m n 3 2 2 1 3 2 3 1 3 2 3 0 (32) where s n, and m are the strength parameters which are determined by experiments. x.-p. zhou et alii, frattura ed integrità strutturale, 44 (2018) 64-81; doi: 10.3221/igf-esis.44.06 75 when eq.(32) is expressed by the short-term uniaxial compressive strengthc , eq.(32) can be rewritten as                                             c iu iu c iu c iu c iu iu iu iu s f m n f t s f s f s f m n f t f t f t 3 1 3 2 3 0 2 2 1 3 2 3 0 0 0 (0) ( ) (0) (0) (0) 0 ( ) ( ) ( ) (33) where c is the short-term uniaxial compressive strength. comparison with the experimental results he lode stress angle is defined as follows:                3 1 2 1 2 2 ( ) arctan 3( ) (    0 030 30 ) (34) the stress tensor ij expressed by the first invariant 1i of stress tensor and the second invariant of deviatoric stress tensor j 2 can be written as follows:                                          i ij i 1 1 1 2 2 3 1 2 sin( ) 33 2 sin( ) 33 2 sin( ) 33 (35) micromechanics-based three-dimensional long-term strength criterion (32) can be expressed by the first invariant i1 of stress tensor and the second invariant of deviatoric stress tensor j 2 , the following expression can be obtained     q f pq ff f fq pq f p q ff p' ' '1 4 3 ' 2 ' 2 ' 2 ' 2 3 5 76 0 (36) where                                                                                             cl cl l c c l n m n m n s n m n m n s m n s n f f f m m n n m mn n n f n f m n s f m n ' 1 ' 2 ' 2 2 2 3 ' 4 2' 5 2 6 2 2 2' 4 cos 3 2 cos 3 2 sin 3 4 cos 1 cos 2 3 2 2 sin 2 3 2 3 cos 3 2 sin 3 1 3 4 cos 3 2 2 3 3 6 2 2 6 3 2 si                               clsf m n7 2 2' n t x.-p. zhou et alii, frattura ed integrità strutturale, 44 (2018) 64-81; doi: 10.3221/igf-esis.44.06 76 p i1 / 3 , q j2 similarly, micromechanics-based three-dimensional long-term strength criterion (33) can be rewritten in another form:       f f fq f pq f q pq f p f q f p3 2 2 22 3 5 6 71 4 0 (37) where                                                                                 iu iu iu iu iu iu c c f f f f m m n n m mn n n f t f f n f t f f m n s f t n m n m n s n m n m n s m n 1 2 2 2 2 3 0 4 2 2 0 2 5 0 (0) 2 3 3 6 2 2 6 ( ) (0 4 cos 3 2 cos 3 2 sin 3 4 cos 1 cos 2 3 2 2 sin 2 3 ) 2 ( ) (0 2 3 cos 3 2 si ) ( n ) 3                                              c c c iu iu iu iu f f f t f f s n m n sm n f t 6 0 7 2 2 2 2 0 1 3 4 cos 3 2 (0 si ) ( ) (0) ( 3 ) n . comparison with the experimental data of coal eries of triaxial compressive experimental data were obtained from creep tests on various rocks by refs [25-27]. the long-term uniaxial compressive strength of rocks and the fitting strength parameters are listed in tab. 1. tabs. 2-4 show theoretical strength and the experimental data of barre granite, inada granite and jinping marble. figs 5-7 show that comparison of predicted strength and the experimental data of barre granite, inada granite and jinping marble. it is found from tabs 2-4 and figs 5-7 that the proposed long-term strength criterion agrees well with experimental data of different rocks. rocks the strength parameter(s) the fitting strength parameter(m) the fitting strength parameter (n) long-term uniaxial compressive strength reference barre granite 1 6.709 0.737 158 kranz [25] inada granite 1 1.000 0.101 216 maranini and brignoli [26] jinping marble 1 12.184 18.566 80 yang et al. [27] table 1: the fitting strength parameters and uniaxial compressive strength of different rocks. s x.-p. zhou et alii, frattura ed integrità strutturale, 44 (2018) 64-81; doi: 10.3221/igf-esis.44.06 77 σ1(mpa) σ2(mpa) σ3(mpa) q (mpa) pexperimental (mpa) ptheoretical (mpa) 280 10 10 270.000 100.000 99.255 289 10 10 279.000 103.000 102.245 298 10 10 288.000 106.000 103.266 301 10 10 291.000 107.000 104.614 304 10 10 294.000 108.000 105.966 306 10 10 296.000 108.667 106.869 312 10 10 302.000 110.667 109.587 315 10 10 305.000 111.667 110.952 494 40 40 454.000 191.333 193.264 468 40 40 428.000 182.667 180.006 369 20 20 349.000 136.333 131.381 288 10 10 278.000 102.667 98.800 247 5 5 242.000 85.667 85.051 234 5 5 229.000 81.333 77.492 280 10 10 270.000 100.000 102.255 289 10 10 279.000 103.000 99.245 298 10 10 288.000 106.000 103.266 301 10 10 291.000 107.000 104.614 table 2: theoretical strength and the experimental data of inada granite. σ1(mpa) σ2(mpa) σ3(mpa) q (mpa) pexperimental (mpa) ptheoretical (mpa) 162.1 0.1 160 270 100.0000 106.415 173.1 0.1 230 279 103.0000 103.952 177.1 0.1 220 288 106.0000 105.514 179.1 0.1 110 291 107.0000 101.884 185.1 0.1 180 294 108.0000 108.765 188.1 0.1 205 296 108.6667 104.870 196.1 0.1 235 302 110.6667 109.826 199.1 0.1 249 305 111.6667 112.323 203.1 0.1 223 454 191.3333 194.439 262 10 262 428 182.6667 183.837 343 25 100 349 136.3333 135.572 348 53 350 278 102.6667 107.943 table 3: theoretical strength and the experimental data of barre granite. x.-p. zhou et alii, frattura ed integrità strutturale, 44 (2018) 64-81; doi: 10.3221/igf-esis.44.06 78 σ1(mpa) σ2(mpa) σ3(mpa) q (mpa) pexperimental (mpa) ptheoretical (mpa) 110 20 12 94.255 47.333 45.757 120 20 14 103.131 51.333 52.277 130 20 18 111.014 56.000 58.335 140 20 20 120.000 60.000 59.550 150 20 20 130.000 63.333 63.965 160 20 20 140.000 66.667 65.786 170 20 20 150.000 70.000 72.013 155 35 35 120.000 75.000 75.550 165 35 35 130.000 78.333 77.965 175 35 35 140.000 81.667 82.786 185 35 35 150.000 85.000 86.013 195 35 35 160.000 88.333 89.647 205 35 35 170.000 91.667 91.687 215 35 35 180.000 95.000 92.134 180 50 45 132.571 91.667 96.193 190 50 47 141.524 95.667 94.165 200 50 46 152.040 98.667 93.945 210 50 50 160.000 103.333 101.647 220 50 50 170.000 106.667 101.687 230 50 50 180.000 110.000 112.134 table 4: theoretical strength and the experimental data of jinping marble. figure 5: comparison of predicted strength and the experimental data of inada granite. 80 100 120 140 160 180 200 80 100 120 140 160 180 200 q th eo ri tic al q experimental x.-p. zhou et alii, frattura ed integrità strutturale, 44 (2018) 64-81; doi: 10.3221/igf-esis.44.06 79 figure 6: comparison of predicted strength and the experimental data of barre granite. figure 7: comparison of predicted strength and the experimental data of jinping marble discussions and conclusions n this paper, burgers model with the characteristics of instantaneous elastic deformation, primary creep and steadyrate creep is applied to investigate creep fracture behaviors of penny-shaped microcracks. mode ii stress intensity factor at tips of three-dimensional penny-shaped microcracks embedded in burgers viscoelastic rock matrix is derived. the orientation angle of micro-failure in burgers viscoelastic rocks is defined. a novel micromechanics-based threedimensional long-term strength criterion is proposed to investigate effects of time and the intermediate principal stress on i x.-p. zhou et alii, frattura ed integrità strutturale, 44 (2018) 64-81; doi: 10.3221/igf-esis.44.06 80 the creep failure of rocks. by comparison with the previous experimental results, it is found that the novel micromechanics-based three-dimensional long-term strength criterion is in good agreement with experimental data. acknowledgments his work was supported by the national natural science foundation of china (nos. 51325903 and 51679017), project 973 (grant no. 2014cb046903), graduate scientific research and innovation foundation of chongqing, china (grant no. cyb16012), open research fund program of hunan provincial key laboratory of geotechnical engineering for stability control and health monitoring, natural science foundation project of cq cstc (nos. cstc2013kjrc-ljrccj0001 and cstc2013jcyjys0005) and research fund by the doctoral program of higher education of china(no.20130191110037). references [1] baud, p. and meredith, p. g., (1997). damage accumulation during triaxial creep of darley dale sandstone from pore volumometry and acoustic emission, int. j. rock mech. min. sci. 34, pp. 24.e1–24.e10. [2] heap, m. j., baud, p., meredith, p. g., bell a. f. and main, i.g., (2009). time-dependent brittle creep in darley dale sandstone, j. geophys. res.d: atmos, 114, pp. 1–22. [3] heap, m. j., baud, p., meredith, p. g., vinciguerra, s., bell, a. f. and main, (2011). i.g., brittle creep in basalt and its application to time-dependent volcano deformation, earth planet sci. lett., 307, pp. 71–82. [4] li, y. and xia, c., (2000). time-dependent tests on intact rocks in uniaxial compression, int. j. rock mech. min. sci., 37, pp. 467-475. [5] shin, k., okubo, s., fukui, k. and hashiba, k., (2005). variation in strength and creep life of six japanese rocks, int. j. rock mech. min. sci., 42, pp. 251-260. [6] aubertin, m., li, l. and simon, r., (2000). a multiaxial stress criterion for shortand long-term strength of isotropic rock media, int. j. rock mech. min. sci., 37, pp. 1169-1193. [7] amitrano, d. and helmstetter, a., brittle creep, damage and time to failure in rocks, (2006). j. geophys. res. b: solid earth, 111, pp. 335-360. [8] bahaaddini, m., hagan, p.-c., mitra, r. and hebblewhite, b.-k., (2015). numerical study of the mechanical behavior of nonpersistent jointed rock masses, int. j. geomech., 10.1061/(asce)gm.1943-5622.0000510, 04015035. [9] barla, m. and beer, g., (2012). special issue on advances in modeling rock engineering problems, int. j. geomech., 12, pp. 617-617. [10] yang, q., chen, x. and zhou, w. y., (2005). on the structure of anisotropic damage yield criteria, mech. mater., 37, pp. 1049-1058. [11] zhou, x. p., bi j. and qian, q. h., (2015). numerical simulation of crack growth and coalescence in rock-like materials containing multiple pre-existing flaws, rock mech. and rock eng., 48, pp. 1097-1114. [12] zuo, j. p., li, h. t., xie, h. p., ju, y. and peng, s. p., (2008). a nonlinear strength criterion for rock-like materials based on fracture mechanics, int. j. rock mech. min. sci., 45, pp. 594-599. [13] al-ajmi, a. m. and zimmerman, r. w., (2005). relation between the mogi and the coulomb failure criteria, int. j. rock mech. min. sci. 42, pp. 431–439. [14] paterson, m. s. and wong, t. f., (2005). experimental rock deformation the brittle field, mineral mag., 43, pp. 163186. [15] yu, s. w. and feng, x. q., (1995). a micromechanics-based damage model for microcrack-weakened brittle solids, mech. mater., 20, pp. 59-76. [16] tada, h., (1973). the stress analysis of cracks handbook, stress analysis of cracks handbook, 91, pp. 614. [17] yi, s. m. and zhu, z.d., (2005). introduction to damage mechanics of crack-weakened rock masses, science press, beijing. [18] zhou, z. b., (1983). stress intensity factors for creep fracture and their application, acta mech. solida sin., 1, pp. 100104. [19] erdogan, f. and, sih, g. c., (1963). on the crack extension in plates under plane loading and transverse shear, j. basic eng. asme, 85, pp. 527. t x.-p. zhou et alii, frattura ed integrità strutturale, 44 (2018) 64-81; doi: 10.3221/igf-esis.44.06 81 [20] aboudi, j. and benveniste, y., (1987). the effective moduli of cracked bodies in plane deformations, eng. fract. mech., 26, pp. 171-184. [21] budiansky, b. and o'connell, r. j., (1976). elastic moduli of a cracked solid ☆. int. j. solids struct., 12, pp. 81-97. [22] kachanov, m., (1992). effective elastic properties of cracked solids: critical review of some basic concepts, appl. mech. rev., 45, pp. 304-335. [23] paterson, m. s. and wong, t. f., (2005). experimental rock deformation the brittle field, mineral mag., 43, pp. 163186. [24] brady, b. t., (1969). a statistical theory of brittle fracture for rock materials part ii—brittle failure under homogeneous triaxial states of stress, int. j. rock mech. min. sci. geomech. abstr., 6, pp. 285-300. [25] kranz, r. l., (1980). the effects of confining pressure and stress difference on static fatigue of granite, j. geophys. res.d: atmos, 85, pp. 1854-1866. [26] maranini, e. and brignoli, m., (1999). creep behaviour of a weak rock. experimental characterization, int. j. rock mech. min. sci., 36, pp. 127-138. [27] yang, s. q., xu, p., ranjith, p. g., chen, g. f. and jing, h. w., (2015). evaluation of creep mechanical behavior of deep-buried marble under triaxial cyclic loading, arab. j. geosci., pp. 81-16. << /ascii85encodepages false /allowtransparency false /autopositionepsfiles true /autorotatepages /none /binding /left /calgrayprofile (dot gain 20%) /calrgbprofile (srgb iec61966-2.1) /calcmykprofile (u.s. web coated \050swop\051 v2) /srgbprofile (srgb iec61966-2.1) /cannotembedfontpolicy /error /compatibilitylevel 1.4 /compressobjects /tags /compresspages true /convertimagestoindexed true /passthroughjpegimages true /createjobticket false /defaultrenderingintent /default /detectblends true /detectcurves 0.0000 /colorconversionstrategy /cmyk /dothumbnails false /embedallfonts true /embedopentype false /parseiccprofilesincomments true /embedjoboptions true /dscreportinglevel 0 /emitdscwarnings false /endpage -1 /imagememory 1048576 /lockdistillerparams false /maxsubsetpct 100 /optimize 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/hrv (za stvaranje adobe pdf dokumenata najpogodnijih za visokokvalitetni ispis prije tiskanja koristite ove postavke. stvoreni pdf dokumenti mogu se otvoriti acrobat i adobe reader 5.0 i kasnijim verzijama.) /hun 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/pdfxoutputintentprofileselector /documentcmyk /preserveediting true /untaggedcmykhandling /leaveuntagged /untaggedrgbhandling /usedocumentprofile /usedocumentbleed false >> ] >> setdistillerparams << /hwresolution [2400 2400] /pagesize [612.000 792.000] >> setpagedevice microsoft word numero_62_art_32_3550.docx p. ghannadi et alii, frattura ed integrità strutturale, 62 (2022) 460-489; doi: 10.3221/igf-esis.62.32 460 the application of pso in structural damage detection: an analysis of the previously released publications (2005–2020) parsa ghannadi department of civil engineering, ahar branch, islamic azad university, ahar, iran parsa.ghannadi@gmail.com, https://orcid.org/0000-0001-5441-9243 seyed sina kourehli department of civil engineering, azarbaijan shahid madani university, tabriz, iran ss.kourehli@azaruniv.ac.ir, https://orcid.org/0000-0001-7599-8053 seyedali mirjalili centre for artificial intelligence research and optimisation, torrens university, adelaide, sa 5000, australia yonsei frontier lab, yonsei university, seoul, south korea ali.mirjalili@torrens.edu.au, https://orcid.org/0000-0002-1443-9458 abstract. the structural health monitoring (shm) approach plays a key role not only in structural engineering but also in other various engineering disciplines by evaluating the safety and performance monitoring of the structures. the structural damage detection methods could be regarded as the core of shm strategies. that is because the early detection of the damages and measures to be taken to repair and replace the damaged members with healthy ones could lead to economic advantages and would prevent human disasters. the optimization-based methods are one of the most popular techniques for damage detection. using these methods, an objective function is minimized by an optimization algorithm during an iterative procedure. the performance of optimization algorithms has a significant impact on the accuracy of damage identification methodology. hence, a wide variety of algorithms are employed to address optimization-based damage detection problems. among different algorithms, the particle swarm optimization (pso) approach has been of the most popular ones. pso was initially proposed by kennedy and eberhart in 1995, and different variants were developed to improve its performance. this work investigates the objectives, methodologies, and results obtained by over 50 studies (2005-2020) in the context of the structural damage detection using pso and its variants. then, several important open research questions are highlighted. the paper also provides insights on the frequently used methodologies based on pso, the computational time, and the accuracy of the existing methodologies. citation: ghannadi, p., kourehli, ss., mirjalili, sa., the application of pso in structural damage detection: an analysis of the previously released publications (2005 –2020), frattura ed integrità strutturale, 62 (2022) 460-489. received: 06.04.2022 accepted: 18.06.2022 online first: 07.09.2022 published: 01.10.2022 copyright: © 2022 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. https://youtu.be/mf26foeonvi p. ghannadi et alii, frattura ed integrità strutturale, 62 (2022) 460-489; doi: 10.3221/igf-esis.62.32 461 keywords. particle swarm optimization; damage detection; vibration characteristics; inverse problems; nature-inspired algorithms; objective functions. introduction he existing civil structures including buildings, dams, bridges, tunnels, towers, and different types of other structures hold an important role in today’s world [1]. as technology advances, infrastructures play a more significant role than the past as they handle extensive human activities [2]. civil structures experience a wide variety of deteriorating factors during their service life cycle, and the subsequent destructions may impact the normal performance of structures [3]. the structural deterioration could be caused by natural incidents such as strong earthquakes, high winds, tsunamis, tornadoes, etc. the structural damages may also cause by man-made events such as extreme loading, explosions, terrorist attacks, traffic loads, etc. [4]. in recent years, the structural health monitoring (shm) strategies have become a fast-spreading topic not only in civil engineering but also across various engineering disciplines such as aerospace and mechanics [5]. it is essential to implement shm for its swift localization and repair capability to prevent the expansion of the secondary damages and even more severe ones [6]. therefore, it is an undeniable fact that the shm strategies play a vital role in providing lifesafety and economic advantages [7]. shm strategies can be mainly categorized based on two methods: i) vibration-based methods ii) vision-based methods [8]. the main sense behind the vibration-based methods is the alternation of such physical properties as stiffness, mass, and damping after the deterioration of the structure members. the dynamic characteristics such as natural frequencies and mode shapes are highly change-sensitive in physical properties. therefore, the analysis of the discrepancy between the dynamic characteristics before and after the occurrence of the damage could be accomplished as a suitable damage detection tool. the vibration-based methods could fall under two classifications: i) the response-based methods ii) the model-based methods. the response-based methods are often capable of localizing the damaged members by experimental response data such as natural frequencies, mode shapes, and accelerations. in addition to the experimental response data, fem of the structures is required for damage detection and the quantification of its severity through the model-based methods. as mentioned earlier, the response-based methods are only capable of detecting the damaged members. however, the modelbased methods come with some constraints and require further advancement. for instance, the numerical model analysis is a time-consuming process; therefore, the model-based methods are not practical in establishing a real-time shm system [9]. due to the limitations of sensors installed in real-world projects, only incomplete mode shapes are accessible. to handle the challenge of the limited measurements, either mode shapes have to be expanded, or fem is to be reduced. in this regard, some helpful studies have been presented [10–18]. moreover, developing an accurate model of complex structures which could represent the real structural performance is a challenging problem, and requires more efforts. for example, mashayekhi and santini-bell have addressed the complexity of the memorial bridge using a three-dimensional multi-scale fem [19,20]. in addition to the problem of the complexity in large-scale structures, there are some differences between the experimental achievements and numerical models. these disagreements between fem and real models can be justified by different factors including uncertainties in the properties of the materials, and the boundary and connectivity conditions [21]. hence, a large number of model updating techniques have been presented to makes a correlation between the experimental and numerical models [22]. in this regard, some fundamental publications are presented by friswell and mottershead [23], mottershead and friswell [24], and mottershead et al. [25]. besides, fem updating is an active track in terms of shm, and the novel methodologies are subsequently expanded by some researchers. for instance, the innovative fem updating techniques were implemented to large-scale structures by tran-ngoc et al. [26], ho et al. [27], hoa et al. [28], rezaiee-pajand et al. [29], pan et al. [30], and zhu et al. [31]. according to the literature review, the fem-updating methods are mainly divided into two categories: i) direct methods ii) iterative methods. a type of the conventional approaches for fem updating is the direct methods. such techniques attempt to reproduce the measured modal data in a single step; therefore, these methods are computationally efficient. however, there are some drawbacks such as a lack of node connectivity as well as the demand for a large amount of data [32]. direct methods have been frequently employed to date, and some researchers have tried to present modified versions [22,33–35]. in iterative methods, an objective function is minimized by adjusting several design variables during the iterative procedure. the objective functions are often established upon modal parameters such as natural frequencies and mode shapes [32]. t p. ghannadi et alii, frattura ed integrità strutturale, 62 (2022) 460-489; doi: 10.3221/igf-esis.62.32 462 considering the concept behind the iterative methods, fem updating problems could be formulated as an optimization scheme [36]. thereby, the optimization algorithms have been applied to minimize the objective functions. during the past years, a significant number of optimization algorithms are proposed for fem updating, including conventional methods such as ga and pso [37] as well as some novel types such as grey wolf optimizer (gwo) [38], multiverse optimizer (mvo) [39], salp swarm algorithm (ssa) [40], and jaya algorithm [41]. reference year title poli [53] 2008 analysis of publications on particle swarm optimisation applications mahor et al. [54] 2009 economic dispatch using particle swarm optimization: a review rana et al. [55] 2011 a review on particle swarm optimization algorithms and their applications to data clustering yusup et al. [56] 2012 overview of pso for optimizing process parameters of machining sarkar et al. [57] 2013 application of particle swarm optimization in data clustering: a survey esmin et al. [58] 2013 a review on particle swarm optimization algorithm and its variants to clustering high-dimensional data lalwani et al. [59] 2013 a comprehensive survey: applications of multi-objective particle swarm optimization (mopso) algorithm gopalakrishnan [60] 2013 particle swarm optimization in civil infrastructure systems: state-of-the-art review ghorpade-aher and bagdiya [61] 2014 a review on clustering web data using pso saini et al. [62] 2014 a review on particle swarm optimization algorithm and its variants to human motion tracking alam et al. [63] 2014 research on particle swarm optimization based clustering: a systematic review of literature and techniques kulkarni et al. [64] 2015 particle swarm optimization applications to mechanical engineering-a review zhang et al. [65] 2015 a comprehensive survey on particle swarm optimization algorithm and its applications zhou et al. [66] 2016 the application of pso in the power grid: a review andrab et al. [67] 2017 a review: evolutionary computations (ga and pso) in geotechnical engineering pluhacek et al. [68] 2017 a review of real-world applications of particle swarm optimization algorithm elsheikh and abd elaziz [69] 2018 review on applications of particle swarm optimization in solar energy systems hajihassani et al. [70] 2018 applications of particle swarm optimization in geotechnical engineering: a comprehensive review elbes et al. [71] 2019 a survey on particle swarm optimization with emphasis on engineering and network applications sibalija [72] 2019 particle swarm optimisation in designing parameters of manufacturing processes: a review (2008–2018) jahandideh-tehrani et al. [73] 2020 application of particle swarm optimization to water management: an introduction and overview kashani et al. [74] 2020 particle swarm optimization variants for solving geotechnical problems: review and comparative analysis table 1: various review papers on different applications of pso. following the establishment of an agreement between the experimental and numerical models through the fem updating methods, the damage identification procedure could be organized similar to the concept utilized for the iterative fem updating. the structural damages are often defined by the reduction of the members’ stiffness. in this regard, the optimization algorithms attempt to minimize the objective functions during an iterative process and find those design variables that would include stiffness for each member. for further discussion, the damage modal characteristics are usually inserted in the objective functions. then, the optimization algorithms evaluate the objective functions, and they iteratively minimize the discrepancy between the measured modal data (for the damaged members) and the calculated ones. for the model-based damage detection problems solved by the optimization frameworks, the performance of the identified damages mainly depends on two subject. the first is the objective function, and the second one is the optimization algorithm [42]. some studies have been conducted to make a comparison between the different objective functions in terms of p. ghannadi et alii, frattura ed integrità strutturale, 62 (2022) 460-489; doi: 10.3221/igf-esis.62.32 463 structural damage detection [43–46]. as mentioned above, the optimization algorithms play an important role for an accurate damage detection. therefore, numerous researchers have employed a wide variety of optimization algorithms in the context of shm. earlier attempts were also related to the traditional algorithms, mostly ga. friswell et al. [47,48], ruotolo et al. [49], and mares and surace [50] have pioneered in the 1990s in this area. another algorithm that has become popular and has been applied constantly in different engineering problems is pso. pso simulates the social behavior of a flock of birds seeking food [51] suggested by kennedy and eberhart in 1995 [52]. pso is efficiently reflected for the structural damage detection problems, and a large number of methodologies have also been developed. like other algorithms, pso has some drawbacks, with a persisting chance of generalization of the modified versions. to address some of these drawbacks such as the premature convergence, and to lower the computational time, different variants of pso have been developed and implemented on damage detection problems. several review studies have been published focusing on the application of pso for different engineering disciplines. in this regard, a list of review studies between 2008 and 2020 is presented in tab. 1. fig. 1 illustrates the number of review papers by different disciplines. it is evident in this figure that no work was done to analyze the publications on structural damage detection using pso as well as its existing variations. this paper has reviewed over 50 studies conducted from 2005 to 2020 and constitutes the first of this kind that investigates the objectives, methodologies, and presents the main results of the pso-based damage identification methods by the year of publication and the types of structures. the rest of the paper is organized as follows: section 2 presents the mathematical relations and flow chart of pso. section 3 comprehensively investigates the application of pso on structural damage detection. section 4 discusses the investigated papers in the manner of questions and answers. finally, section 5 concludes the work and section 6 suggests future directions. figure 1: number of review papers on different applications of pso. particle swarm optimization (pso) so is a population-based optimization algorithm introduced by kennedy and eberhart [52]. the pso mimics the swarm behavior of birds in nature. the pso algorithm consists of two vectors: velocity and position. the position vector (xi) represents the value of each variable in the optimization problem. the velocity vector (vi) is utilized to update the position of particles. fig. 2 shows the swarm behavior of birds and updating procedure of the position [69]. in this algorithm, each candidate solution is named a "particle" and indicates a coordinate in a d-dimensional space, where d is the number of the parameters to be optimized [75]. therefore, the position of the ith particle can be defined by xi vector:  1 2 3 ...i i i i idx x x x x (1) p p. ghannadi et alii, frattura ed integrità strutturale, 62 (2022) 460-489; doi: 10.3221/igf-esis.62.32 464 figure 2: (a) swarm behavior of birds in nature, (b) updating the position and velocity of birds in pso. the population of n candidate solutions organizes the swarm:  1 2, ,..., nx x x x (2) to find the optimal solution to the problem, the particles define trajectories in the parameter space based on the following equation of motion:      1 1   i i ix t x t v t (3) in eqn. (3), t and t + 1 represent two sequential iterations of the algorithm, and vi is the vector collecting the velocity components of the ith particle along the d dimensions. the velocity of the ith particle is calculated as follows:          1 1 2 21     i i i i iv t v t c p x t r c g x t r (4) in eqn. (4), pi is the "personal best" of the particle, g is the "global best", and c1 and c2 are acceleration constants usually in 1 20 , 4 c c range, which are called "cognitive coefficient" and "social coefficient", respectively. r1 and r2 are two diagonal matrices of random numbers generated through a uniform distribution in [0,1]. the flow chart of pso is illustrated in fig. 3. standard pso has been successfully applied to different optimization problems. however, there are still some drawbacks. to address the different demands, the original pso has experienced a wide variety of improvements from 1995 to date, and researchers constantly attempt to develop new variants [76]. the various variants of pso can be summarized as follows: i) combination of pso with different optimization algorithms such as ga, colonial competitive algorithm (cca), elitist artificial bee colony, sine-cosine algorithm (sca), cuckoo search (cs). ii) developing modified versions based on nelder– mead algorithm iii) introducing unified versions iv) improving pso by implementing immunity strategies tab. 2 presents comprehensive information on different varients of pso and their applications in structural damage identification problems. each modified version can be addressed single or multiple challenges such as premature convergence, poor accuracy, slow convergence, or high computational complexity. p. ghannadi et alii, frattura ed integrità strutturale, 62 (2022) 460-489; doi: 10.3221/igf-esis.62.32 465 figure 3: the flow chart of pso. an analysis of different studies on structural damage detection using pso (2005-2020) tabulated scheme is utilized to make a desirable accessibility possible for the application of pso in the structural damage detection methods, and to analyze the cons and pros of the different variants of pso. tab. 2 summarizes the application of pso in detecting structural damages by some categorizations including the following:  reference and year: represent the authors’ names and the publication date, respectively.  objective: this section answers the question of why the paper is presented and what the main contribution is.  methodology: the algorithms, tools, and techniques employed in solving damage detection problems are presented i n this section.  structure: this section answers the question of what type of structures are utilized for implementing the structural a p. ghannadi et alii, frattura ed integrità strutturale, 62 (2022) 460-489; doi: 10.3221/igf-esis.62.32 466 damage detection methodology.  result and finding: this section is a summary of the main outcomes of the papers. reference year objective methodology structure result and finding mouser and dunn [77] 2005 comparing the performance of ga and pso in updating mass, stiffness, and damping through an inverse solution. optimization algorithms were applied to minimize the difference between the measured frequency response functions (frfs) and the calculated ones. mass – spring – damper system pso is configured easily and yielded much better results compared to ga. saada et al. [78] 2008 this study discusses the difficulty of damage detection by only using natural frequencies and the optimization problem is solved via a modified version of pso. firstly, a model parameter modification is conducted to organize an acceptable agreement between the experimental and numerical models. then, the first three natural frequencies are inserted into the objective function to recognize the damage properties. free-free beam generally, the method introduced in this paper is capable of detecting the single damages and its accuracy declines when facing multiple damages. yu and wan [79] 2008 an improved version based on the sigmoid function has been developed to address the convergence drawback of pso and is subsequently employed for the damage detection problems. an objective function is defined through the differences between the healthy and damaged dynamic characteristics to discover the damaged member and the extent of the damage. plane frame the results of this paper have revealed that the improved pso can effectively modify the convergence rate of the standard pso and provides a better solution to detect single and multiple damages. begambre and laier [80] 2009 a simple procedure based on nelder–mead algorithm is proposed to control the parameters of pso. an objective function is formulated using frfs. planar truss free–free beam the proposed version of pso can accurately detect the location and severity of the damage even when inserting incomplete and noisy data. additionally, this algorithm has outperformed the standard pso and simulated annealing (sa) when solving benchmark functions. yu and chen [81] 2010 the standard pso has been improved by macroeconomic strategies to solve the multiobjective optimization problems on damage detection. two objective functions are employed to minimize the discrepancy between the modal data under healthy and damaged conditions. the first objective function is based on mac and natural frequency. the second one includes modal flexibility. simply supported beam continuously supported beam the comparative results of damage detection illustrate the efficiency of the second objective function and the modified pso with macroeconomic strategies. sandesh and shankar [82] 2010 developing an accurate hybrid optimization algorithm combining ga and pso to address the inverse problem of crack detection in the time domain. minimizing the sum of the square of deviations between the measured and estimated accelerations as an objective function. aluminum plate the hybrid pso-ga provided a more accurate tool for damage detection. pso is a fast algorithm, and p. ghannadi et alii, frattura ed integrità strutturale, 62 (2022) 460-489; doi: 10.3221/igf-esis.62.32 467 ga is a slow one with poor accuracy. liu et al. [83] 2011 pso is used to optimize the parameters of the support vector machine (svm) to improve the classification and regression accuracy. the accuracy of damage detection and quantification are used as objective functions. simply supported bridge the proposed algorithm based on pso and svm was effectively capable of identifying the damage parameters. gökdağ and yildiz [84] 2012 presenting a comparative study to identify the best objective function for the damage detection problems while using pso as an optimizer. the objective functions based on natural frequencies, multiple damage location assurance criterion (mdlac), modal flexibility, and strain energy residual are investigated. cantilever beam this study illustrated that the objective function based on the modal flexibility is the best among other functions. seyedpoor [85] 2012 the damage detection problems with large numbers of design variables exert high computational costs. therefore, a useful method is applied to reduce the dimensions of the search domain and decreases the computational effort of pso. a two-stage approach is introduced for damage detection. in the first stage, a modal strain energybased index (msebi) is used to locate the potentially damaged members. in the second stage, pso minimizes mdlac in the downsized search area. cantilever beam planar truss this study concluded that the combination of msebi and mdlac could be practical for multiple damages detection. baghmisheh et al. [86] 2012 proposing the hybrid pso– nelder–mead (pso–nm) algorithm to predict the depth and location of the crack. the results of pso–nm is compared with those obtained by the standard pso, hybrid ga– nelder–mead algorithm (ga– nm), and nelder–mead algorithm (nm) in terms of accuracy and speed. in this study, the cracked elements are simulated by a torsion spring. the parameters of the crack are determined through minimizing the difference between the calculated natural frequency (obtained from fem) and the measured natural frequency (obtained through modal analysis). cantilever beam both numerical and experimental investigations showed that pso–nm is the fastest and the most accurate algorithm among other methods. xiang and liang [87] 2012 a two-step procedure is reported based-on 2-d wavelet transform and pso for multiple damages detection and localization. in the first step, the 2-d wavelet transform is used to decompose the mode shapes and predict the damage locations. in the second step, the severity of the damage is identified through inverse analysis and the reduction of the discrepancy between the measured and calculated natural frequencies. thin plates the results of this study revealed that the use of higher natural frequencies could lead to accurate outcomes in identifying the severity of the damages. kang et al. [88] 2012 this study proposed the immunity enhanced pso (iepso) algorithm to improve the efficiency and convergence rate of the basic pso, and implemented it for structural damage identification problems. an objective function consisting of mode shape and natural frequency changes is adopted. simply supported beam planar truss iepso is robust for damage identification problems and also provides reliable results when compared with the standard pso, realcoded genetic algorithm (rcga), and p. ghannadi et alii, frattura ed integrità strutturale, 62 (2022) 460-489; doi: 10.3221/igf-esis.62.32 468 differential evolution (de). nanda et al. [89] 2012 in order to make a better convergence for the standard pso, a new version called the incremental pso is implemented to solve the crack detection problem. this study practices a natural frequency-based damage indicator as an objective function for minimization during an optimization procedure. cantilever beam the convergence rate of the new pso is more desirable than the basic version. consequently, the outcomes achieved by the incremental pso have a reasonable level of accuracy. saada et al. [90] 2013 damage identification methods relying only on natural frequency indicators encounter several shortcomings. therefore, this paper tries to overcome the existing challenges of damage detection techniques established on the natural frequency changes. some modifications are applied to one-dimensional euler–bernoulli beam elements. then, a modified version of pso is employed to solve an objective function defined only by natural frequency characteristics. free-free beam the results of the experimental example confirmed that the proposed method could identify the location and extent of the small damages. kang et al. [91] 2013 in this study, damage detection problems are solved using iepso because of its accuracy and convergence speed. presents an objective function, which has received the dynamic responses (natural frequencies) and the static response (displacements) as inputs. clamped clamped beam iepso is more effective in structural damage identification when compared with the standard pso and de. the accuracy of iepso declines when inputs are contaminated with a certain level of noise. guo et al. [92] 2014 pso cannot provide satisfactory results for multiple damage identification in complex structures. hence, this paper proposes a two-stage procedure based on evidence fusion and some strategies to improve the standard pso. in the first stage, evidence fusion modal strain energy and frequency is used to locate the damaged elements. in the second stage, the improved pso is employed to determine damage severities by minimizing an objective function based on mode shapes and natural frequencies. planar truss the suggested technique has an acceptable accuracy to predict the location and severity of the damage in lightly damped structures. mohan et al. [93] 2014 this paper presents a comparative study of pso and ga for crack detection. an objective function related to natural frequency has been minimized to find the location and depth of the crack. cantilever beam space truss the performance of pso in recognizing the location and depth of the crack is significantly superior to ga. nanda et al. [94] 2014 the exploration and exploitation capability of pso is increased by the unified pso (upso). hence, this modified version was adopted for crack detection in the study. the damage indicators are defined as an objective function based on the changes of the natural frequencies, mode shapes, and a combination of both. cantilever beam plane frame the utilized scheme can simultaneously detect the site and depth of the crack. nanda et al. [95] 2014 this study experimentally and numerically showed the capability of an optimizationbased scheme for joint damage identification through upso. the joint damage is simulated as the reduction of the joint fixity factor at each connection. an objective function combination of the mode shapes and natural plane frame this damage detection procedure holds acceptable accuracy for the experimental examples. the accuracy of this methodology is still reasonable after p. ghannadi et alii, frattura ed integrità strutturale, 62 (2022) 460-489; doi: 10.3221/igf-esis.62.32 469 frequencies is considered for minimizing by the optimization algorithm. applying 5% and 10% noise. ma et al. [96] 2014 the revised pso has been applied for structural damage detection problems to overcome the premature convergence and a time-consuming procedure in searching for optimum solutions by the standard pso. the potentially damaged members are located through msebi at the beginning to limit the dimension of variables in damage identification problems formulated as an optimization framework. then, the exact location and severity of the damages are identified by integrating rpso and an objective function. simply supported beam shear frame the results of this study demonstrated that the hybrid method on msebi and rpso can provide precise outcomes. when comparing pso and rpso, rpso is more useful than pso in terms of computational speed and accuracy. jiang et al. [97] 2014 the basic pso is simply entrapped into the local optimum and has the drawback of premature convergence. the same disadvantage has not been completely addressed in the multiparticle swarm coevolution optimization (mpsco). therefore, the improved mpsco is introduced and implemented as an optimization algorithm in some damage detection problems. an objective function between the simulated and measured time-series responses has been maximized to localize and quantify the structural damages. shear frame not only the improved mpsco is more efficient than ga, but it is also robust to noise and provides reliable results for the structural damage detection in both numerical and experimental studies. shabbir and omenzetter [98] 2014 this study presents an innovative method consisting of pso and sequential niche technique (snt) to systematically explore the search domain for fem updating of the complex problems. snt adjusts the objective function after every solution without modifications to the pso search strategy. cable-stayed footbridge the results demonstrate that the proposed methodology is promising for the model updating, and it could be practiced for large-scale structures. liu et al. [99] 2014 the optimum values of bias and weight are regulated by pso to accomplish the organization between the instructive search of the artificial neural networks (anns) and the global optimization of pso. a two-stage damage detection approach has been generalized in this study. the damaged elements are initially localized by the modal flexibility index. then, optimized anns by pso are used to estimate the extent of the damage. simply supported beam this study concludes that the combination of the modal flexibility index and anns with optimized characteristics (bias and weight) is more favorable when compared with those obtained by integrating the modal flexibility index and the conventional backpropagation networks. rasouli et al. [100] 2014 in general, there are limited numbers of sensors to measure the structural response in realworld problems. therefore, the number of dofs in fem is extensively greater than the measured locations. in order to react to the challenge of the in this study, mode shapes are condensed by the guyan's method, and the downsized model is utilized to formulate the objective function through mode shape orthogonality. simply supported beam plane frame spring-mass system results revealed that the presented approach is sensitive to the damaged elements when the noise level is increased to 8%, and incomplete modal data are used. p. ghannadi et alii, frattura ed integrità strutturale, 62 (2022) 460-489; doi: 10.3221/igf-esis.62.32 470 incomplete measurements, dofs were reduced by the guyan's method in fem. then, the damage detection problem was solved through the inverse analysis procedure established by pso and the reduced model. pal and banerjee [101] 2015 to bypass the noise effect and to achieve accurate detection, a new method was developed on msebi in the wavelet domain and an optimization-based model updating mechanism through pso. as a first assessment, the msebi in the wavelet domain is considered for detecting the damaged locations. then, the severity and location of the damages are accurately determined during the optimization procedure through the minimization of the objective function with the modal curvature components. plane frame the experimental and numerical results are encouraging, and the proposed methodology can be applied to fullscale structures. kaveh and maniat [102] 2015 each optimization problem has some local optimums. therefore, seeking the global optimum encounters difficulties. this study makes a comparison between pso and the magnetic charged system search (mcss) to search for the global optimum in the damage detection problems. to form the objective function, modal characteristics such as mode shapes and natural frequencies are utilized. planar truss space truss plane frame multi-span beams the mcss has a greater exploration capacity in finding the global optimum. therefore, mcss provides robust and efficient results for damage detection problems even when incomplete dynamic characteristics are contaminated by a certain level of noise. chen and yu [103] 2015 this study proposes an intelligent two-step approach combining pso, nm algorithm, and msebi to establish an adequate balance between accuracy and computational cost. through a two-step procedure, the damaged members and the severities of these damages are recognized by msebi and the minimization of the objective function with mode shape components, respectively. it should be noted that the optimization algorithm is the pso–nm. simply supported beam the presented method is not only able to determine the location of the damages, but it is also robust to noise and precisely quantifies the damage severity. chen and yu [104] 2015 in this study, an improved version of the pso–nm algorithm is introduced to solve the damage evaluation problems with a low computational cost through the two-step methodology. the damaged members are primarily located with the assistance of msebi. the extent of the damage is evaluated during its second phase by minimizing 1-mac through the improved pso–nm algorithm. plane frame the used techniques can determine the damage site and its severity in multiple and single damage scenarios. this method also has high tolerance against noisy inputs. khatir et al. [105] 2015 this study compares pso and ga for damage detection in beam-like structures reduced by the proper orthogonal decomposition (pod) method with radial basis function (rbf). an objective function only with frequency components is formulated. pso and ga are initially applied to minimize the objective function and composite beams the results of the comparison between ga and pso show a better performance of pso in terms of accuracy and p. ghannadi et alii, frattura ed integrità strutturale, 62 (2022) 460-489; doi: 10.3221/igf-esis.62.32 471 recognition of the damage parameters. then, pod and rbf are used to construct a reduced model. computational effort. besides, using pod and rbf can reduce the computational time of the optimization process. hosseinzadeh et al. [106] 2016 in order to perform a fast and reliable algorithm to minimize the objective functions in the damage detection problems, a hybrid algorithm based on pso and the cca is employed. the main contribution of this study is that it focuses on structural damage detection when the completed measurements are unavailable. the neumann series expansion-based model reduction (nsemr) is applied to mimic the sparse sensor installation at master dofs. then, the generalized flexibility matrix is generated to form the objective function complying with the reduced mass and stiffness matrices. planar truss plane frame shear frame pso-cca has a high convergence speed compared to pso and cca. the results of this study confirm the practicality of the suggested methodology relying on a reduced model by nsemr and the hybridization of pso and cca. hence, for future works, it is possible to allocate this method for damage quantification as well as damage detection in large-scale structures. hosseinzadeh et al. [107] 2016 democratic pso (dpso) is used for solving the inverse problems of damage detection because of its swift and accurate technique in exploring the solution domain in complex problems. the flexibility matrix components are considered to formulate a novel objective function by the concept of mac. subsequently, nsemr is implemented to fem to put the limited measurements condition using sparse sensors installation. planar truss plane frame shear frame the results obtained from numerical and experimental examples demonstrated that the introduced technique could detect the damaged members with slight errors (less than 5%) in the identified severities. gerist and maheri [108] 2016 this study presents a three-stage technique for damage localization and quantification, under the assistance of pso, to address the high computation cost of the optimization problems due to the large search space. firstly, the damaged members are found through basis pursuit (bp). then, the initial estimation of the damage locations and their extents are determined by minimizing 1-mdlac. subsequently, the dimension of the search area is downsized by removing the damaged members with low severities through the micro search (ms) operator embedded in the pso. basis pursuit denoising (bpdn) is also applied to decrease the noise effects. cantilever beam planar truss plane portal frame the main results of this study can be summarized as follows: i) the standard pso and pso-ms are not enough to detect the damaged parameters. ii) for all scenarios, damaged members are detected using the bp method. but this method cannot estimate the correct extent of the damage for most scenarios. iii) the suggested three-stage bp-psoms strategy has the fastest convergence and obtains accurate results compared with other well-known algorithms. p. ghannadi et alii, frattura ed integrità strutturale, 62 (2022) 460-489; doi: 10.3221/igf-esis.62.32 472 khatir et al. [109] 2017 the main contribution of this study is to perform a comparison between pso and ga to evaluate single and multiple damages in graphite-epoxy composite beams. an objective function based on natural frequencies and mac is defined. composite beams results clearly show the superiority of pso in terms of the computational cost and the accuracy of the identified values. jebieshia et al. [110] 2017 this study compares the efficiency of two variants of pso, namely upso and ipso, for damage detection in composite elements. an 8-noded curved isoparametric serendipity quadratic member is used to establish the fem of the laminated composite shells. the damage detection problem is solved by optimizing an objective function based on natural frequencies and mac. laminated composite shells results of a comparative study between pso, upso, and pso confirmed the superiority of upso. chen and yu [111] 2017 to explore a more accurate solution in damage detection problems, this paper introduces a new hybrid methodology by integrating the recently published method (the improved pso–nm) in ref. [103] and a novel objective function relying on the bayesian inference. the bayesian inferences are added to the objective function to eliminate the noise effect and uncertainty quantification. then, the objective functions (defined by natural frequencies and mode shapes) with and without bayesian terms are minimized by the improved pso–nm. plane portal frame iasc-asce benchmark structure the statistical comparison shows that the utilized objective function with the bayesian term is more reliable for damage detection. additionally, the effectiveness of the improved pso–nm as a robust optimizer is also reconfirmed. luo and yu [112] 2017 to develop a damage detection approach with high tolerance against noise, l1/2-norm regularization is applied to create the objective function in the pso-based two-step method. the regularized objective function as a combination of eigenvalues and mode shapes is minimized to determine the damaged member in the first step. subsequently, only those members detected in the first step are considered as the optimization values. cantilever beam the proposed two-step method could accurately diagnose the damaged members while the noise level increases to 15%. khatir et al. [113] 2018 in this study, the location and depth of the open cracks are determined through frequency measurements and pso as an optimization algorithm. the location and depth of the cracks are introduced in an exponential function for the calculation of the equal stiffness reduction. the frequency-based objective function is defined and minimized via pso. cantilever beam plane frame free-free beam the results obtained for the numerical examples (cantilever beam and plane frame) and experimental free-free beam demonstrate the feasibility of this method for the detection of the location and depth of the cracks. alkayem and cao [114] 2018 the comparison of the performances of five optimization algorithms, namely pso, ga, de, lévy flight–de (lfde), and elitist artificial bee colony–pso (eabcpso), is conducted in terms of accuracy, consistency, and computational cost. this paper introduces a hybrid objective function consisting of the modal strain energy and the mode shape residuals with the weighting factors. iasc-asce benchmark structure the results of this study could be summarized as follows: i) numerous false members were detected by ga. ii) pso provides an accurate detection compared to ga and p. ghannadi et alii, frattura ed integrità strutturale, 62 (2022) 460-489; doi: 10.3221/igf-esis.62.32 473 de. however, pso is not reliable for several runs. iii) the consistency and accuracy of the standard version of pso and de were improved by eabcpso and lfde, respectively. iv) eabcpso is more accurate than lfde. additionally, lfde is more timeconsuming than eabcpso. chen and yu [115] 2018 nm is embedded into pso to enhance the global searching ability of the standard pso in damage detection problems. natural frequencies and mode shapes are adopted to organize the objective function. monte carlo simulations are initially used to find useful control parameters for pso. then, the proposed objective function is minimized by pso-nm in order to obtain optimal solutions. simply supported beam the experimental and numerical investigations prove the efficiency of monte carlo simulations in determining the control parameters of pso. moreover, the effectiveness of nm in combination with pso was confirmed once more by this study. xu et al. [116] 8201 pso is only able to minimize the single objective functions. hence, the multi-objective pso (mopso) is employed to minimize the discrepancy between the dynamic characteristics in the two objective functions simultaneously. an iterative two-stage methodology combination of msebi and mopso is suggested for the structural damage assessment. in the first stage, only the damaged members are located. the second stage attempts to predict the severity of the damaged elements. 3-d offshore platform the main novelty of this approach is the use of the iterative msebi to localize the damage, which can detect the damaged members more accurately than those obtained by the noniterative msebi. in conclusion, the introduced method consists of msebi, and mopso effectively detects the damage and its severity under noisy conditions and incomplete measurements. alkayem et al. [117] 2019 this study proposes a hybrid optimization techniques namely, sca and pso (scapso) to produce a new and reliable algorithm with better searching capabilities. an objective function containing the mode shape curvature (msc) and modal strain energy (msten) is considered to formulate the damage detection problem as an optimization paradigm. irregular-shape structures the numerical assessments illustrate the capability of this method in detecting the damages with a relatively low computational cost. jebieshia et al. [118] 2019 as a result of balancing the influence of both global and the weighted sum of the squared errors between the laminated composite beam this methodology successfully detected p. ghannadi et alii, frattura ed integrità strutturale, 62 (2022) 460-489; doi: 10.3221/igf-esis.62.32 474 local search directions, both exploitation and exploration capabilities have been improved by upso. therefore, this paper applies this algorithm to handle the optimization problem of damage detection. calculated and measured natural frequencies (only for the first few modes) is considered to form the objective function. laminated composite plate and quantified the single and multiple damages with acceptable accuracy. however, the objective function can be enriched by additional modal properties such as mode shapes or frf for precise damage recognition. huang et al. [119] 2019 the previous studies have come along with drawbacks such as slow convergence rate, easily entrapped in the local optimum, and relatively low tolerance to noise when the pso and cuckoo search are applied as an optimizer. consequently, the said drawbacks and the impact of the temperature variations are addressed by introducing psocs algorithms. the objective function based on natural frequency, modal strain energy, and mac is minimized through pso, cs, and pso-cs. simply supported beam iasc-asce benchmark structure the pso–cs could identify the damage characteristics more robustly than cs and pso while exposed to noisy inputs and temperature variations. huang et al. [120] 2019 the bare-bones pso (bbpso) is a simple yet robust variant of pso. however, bbpso is easily entrapped into the local optimum like other variants of pso. hence, bbpso with double jump (bbpsodj) is presented to address this weakness. an objective function is established by considering l1-norm regularization and integrating the widely used dynamic characteristics, natural frequencies, and mode shapes. planar truss shear frame the numerical and experimental evaluations on a 31-bar plane truss and a threestory shear frame report the superiority of bbpsodj compared to pso, bbpso, and ga. ghannadi and kourehli [121] 2019 this study formulates the damage detection problems as an optimization paradigm via pso and moth-flame optimization (mfo). the hybridization of mac flexibility and natural frequencies has been adopted as an objective function. planar truss shear frame the results obtained by mfo are more promising than those obtained by pso, while only the first few modes are introduced to the objective function, and the modal characteristics are contaminated by a certain percentage of the noise level. ghannadi and kourehli [40] 2019 this study compares the capability of pso and salp swarm algorithm (ssa) for fem updating and subsequent damage detection. the fem updating and damage detection have been conducted using the minimization of an objective function based on the natural frequency vector assurance criterion (nfvac) and natural frequencies. shear frames in this study, the advantages of ssa have been concluded in terms of fem updating and damage detection for multi-story shear buildings. mishra et al. [122] 2019 this study evaluates the effectiveness of upso and ant lion optimization (alo) in detecting the damages exerted on the structural members. two objective functions are employed in this article. the first one only minimizes the differences between the measured and calculated natural cantilever beam planar truss shear frame the benchmarking studies for numerical and experimental examples indicate the efficiency of alo. alo provides reliable p. ghannadi et alii, frattura ed integrità strutturale, 62 (2022) 460-489; doi: 10.3221/igf-esis.62.32 475 frequencies. then, the first objective function is extended with the mode shape components. space truss results with less standard deviation in convergence curves. mishra et al. [123] 2019 this study makes a comparison between ten optimization algorithms, including upso, artificial bee colony (abc), scout upso (supso), ant colony optimization (aco), cultural algorithm (ca), grasshopper optimization algorithm (goa), multiverse optimizer (mvo), gray wolf optimizer (gwo), ssa, teaching-learning-based optimization (tlbo) considering the accuracy of the identified damages, convergence rate, success rates and the computation time. the objective function is established by combining natural frequencies and their corresponding mode shapes. large-scale space trusses the only optimization algorithm that could provide satisfactory outcomes in terms of accuracy, success rates, computation time, and convergence rate is tlbo. huang et al. [124] 2019 the applicability of the recently published pso-cs algorithm [119] is benchmarked by classical functions such as sphere, rosenbrock, rastrigin, and schaffer. afterward, the same methodology proposed by huang et al. [119] is used for damage detection of the i-40 bridge with field measurements and considering the temperature variations. in order to address the impact of the temperature variations on the dynamic responses, the temperature changes are modeled by alterations in the elastic modulus of steel and concrete. the same objective function designed by huang et al. [119] is employed once more (containing natural frequency, modal strain energy, and mac). simply supported i-40 bridge the hybrid pso-cs can minimize the benchmark functions and finding the optimal solutions. besides, for damage detection under the temperature variations, the performance of hybrid pso-cs and hybrid objective function is validated when exposed to the field measurements. khatir et al. [125] 2019 this study presents a multi-step approach combined with the isogeometric analysis (iga), cornwell indicator (ci), anns, and pso to accurately detect the location and extent of the damage with low computational time when numerical models are assembled with a large number of dofs. in the first step, a threelayer composite plate is modeled by iga, and ci is applied to detect the damaged locations. in the second step, and following the elimination of the healthy members detected in the previous step, an objective function is defined using ci, and damage severities are identified during an iterative optimization procedure through pso. in the third step, anns are employed to reduce computational time in identifying the damage severities. to train anns, ci is considered the input, whereas damage severities and locations are considered the targets. laminated composite plate in the first step, where ci and iga are used, the damaged members are recognized quickly and accurately. in the second step, following the elimination of the healthy members detected in the first step, the combination of pso and ci estimates the severity of the damages. the computational time for the second step is about 6 hours. in the third step, anns are successfully applied to address the challenge of the long computational time of the second step and decrease the computational time to about 25 seconds. p. ghannadi et alii, frattura ed integrità strutturale, 62 (2022) 460-489; doi: 10.3221/igf-esis.62.32 476 wang et al. [126] 2020 the optimization algorithms often function properly to find the optimal solutions when the search area is small. in this study, an iterative two-stage strategy is introduced. firstly, the potentially damaged members are detected. then, three optimization algorithms, including pso, ga, and beetle antenna search (bas), are organized in the narrow search area to find the damage's exact severity. a new damage localization index called the modal energy-based index (mebi) is utilized to classify the damaged members. afterward, three objective functions based on the modal flexibility, the integration of natural frequencies and mode shapes, and also msebi are solved by pso, ga, and bas to determine the exact severity of the damaged elements. 3-d offshore platform cantilever beam to detect the damaged members, the new damage localization index (mebi) performs better than the conventional damage localization index (msebi). msebi is selected as the best objective function. bas is more efficient than ga and pso in terms of the computational time. zenzen et al. [127] 2020 the main contribution of this article is implementing the transmissibility concept into the objective function and developing a new index. pso is also used to minimize the objective function as the optimization algorithm. a new objective function is formulated by replacing the transmissibility with the mode shape vectors in the mac formulation. planar truss the methodology used for solving the inverse problem of detecting the damage in a plane truss with 25 members is efficient for single and multiple damage scenarios. tran-ngoc et al. [128] 2020 in order to handle the premature convergence as a fundamental challenge of standard pso, an improved version of pso combined with the orthogonal diagonalization (od) is utilized. young's modulus of truss members and the stiffness of 8 springs under bearings are updated through the newly developed hybrid pso and an objective function with natural frequencies and mode shapes as inputs. guadalquivir railway bridge the upgraded version of pso not only accurately updates fem but also significantly decreases computational costs. guo et al. [129] 2020 this study presents a two-step process of damage detection and quantification based on ipso and wavelet transform. a comparative study of ipso, standard pso, ga, and bat algorithm (ba) is also conducted to identify the severity of the damaged members. in the first step, the damaged members are detected by wavelet transform. then, to estimate the extent of the structural damage, the optimization algorithms are applied to minimize the discrepancy between the measured and calculated modal characteristics (natural frequencies and mode shapes). clampedclamped beam plane portal frame the damaged location can be accurately detected by wavelet transform under different noise levels. ipso is not entrapped into the local optimums and can accurately predict the severities of the damaged members. hence, the combination of wavelet transform and ipso could provide a practical tool for structural health monitoring purposes. fathnejat and ahmadinedushan [130] 2020 the damage location and its severity are detected through the two-stage approach. the first stage is designed for the localization of the damaged members, whereas the second stage is outlined to estimate the extent of the damage. the damaged members are classified by msebi at the first stage. in the second stage, anns (cascade feed-forward neural network (cfnn) and the group method of data handling network (gmdhn)) are used in combination with the optimization procedure space truss double layer grid similar to the previous studies, msebi is an efficient criterion for damage localization. to identify the damage severity, pso outperforms cbo and ba. to identify the damage severity, an integration of pso with both p. ghannadi et alii, frattura ed integrità strutturale, 62 (2022) 460-489; doi: 10.3221/igf-esis.62.32 477 (pso, ba, and colliding bodies optimization (cbo)) to generate a surrogate of the fem and reach a short computational time. cfnn and gmdhn provides the same level of accuracy. however, where gmdhn is used, the computational time is significantly less than that of cfnn. barman et al. [131] 2020 to improve upso in terms of accuracy and convergence rate, a new version of the combination of the standard continuous upso and binary upso (mixed upso) is introduced to be employed in a two-stage method for the delamination assessment in composite structures. the locations of the delamination cases are initially detected through the msc index. then, the interface of the delamination cases is estimated by minimizing an objective function relying on the changes in natural frequencies and mode shapes. laminate composite beam laminate composite plate the overall results of this paper demonstrate a superior accuracy for the localization of the single and multiple delamination cases and their interface, while the modal components are contaminated by a certain level of noise. table 2: a review on the application of pso on the structural damage detection. figure 4: number of publications in the area of structural damage detection based on pso a classification by year. the number of publications on structural damage identification using pso is shown in fig. 4. it can be observed that the considerable developments in optimization-based damage detection methodologies have been conducted in the last decade. fig. 5 presents the contribution of the publications in the fields of crack detection, fem updating, damage detection, fem updating and subsequent damage detection. it can be easily realized that the main contribution of recently published papers is damage detection. then, the combination of fem updating and damage detection is the frequently used methodology. figure 5: contribution of the publications in the fields of crack detection, damage detection, fem updating, and fem updating+damage detection 0 5 10 15 20 25 2005-2010 2011-2016 2017-2020 n u m b er o f p u b li ca ti o n s year p. ghannadi et alii, frattura ed integrità strutturale, 62 (2022) 460-489; doi: 10.3221/igf-esis.62.32 478 the percentage of utilized structures to illustrate the performance of proposed methodologies in the publications is shown in fig. 6. as given in fig. 6, beam-like structures are the most utilized example in order to verify the different methodologies in the area of structural damage identification. figure 6: the percentage of utilized structures to demonstrate the efficiency of proposed methodologies in the publications in recent years, single-step, two-step, and multiple-step methods have been proposed by different researchers. fig. 7 shows the percentage of each method. it is clear that the single-step methods are the most utilized techniques. however, two-step and multiple-step methods have been developed to provide better accuracy for damage identification. figure 7: the percentage of employed single-step, two-step, and multiple-step methods in the publications shear frame 9% plane frame 15% beam-like structures 35% plate-like structures 6% planar truss 14% space truss 6% bridge 5% other structures 10% single-step 71% two-step 25% multiple-step 4% p. ghannadi et alii, frattura ed integrità strutturale, 62 (2022) 460-489; doi: 10.3221/igf-esis.62.32 479 the utilized two-step methods are classified in fig. 8. a large number of two-step methods are related to the combination of modal strain energy-based methods and pso. figure 8: the classification of different two-step methods by number of publications as mentioned earlier, objective functions and optimization algorithms play a crucial role in identifying accurate results in structural damage detection problems. fig. 9 and fig. 10 illustrate the classification of utilized objective functions and different variants of pso by the number of publications. as shown in fig. 9, the most utilized objective functions are based on natural frequencies, natural frequencies + mac, and natural frequencies + mode shapes, respectively. fig. 10 presents four algorithms, including pso, upso, ipso, and pso-nm, which have repeatedly been applied to detect structural damages. figure 9: the classification of utilized objective functions by the number of publications. 0 1 2 3 4 5 6 7 8 modal strain energy + pso wavelet transform + pso other methods + pso modal flexibility + pso mode shape curvature + pso 0 2 4 6 8 10 12 natural frequencies natural frequencies + mac natural frequencies + mode shapes modal flexibility mdlac mode shapes frfs time-series modal strain energy natural frequencies + modal strain energy + mac natural frequencies + nfvac natural frequencies + modal flexibility mac modal strain energy + mac natural frequencies + displacements natural frequencies + modal strain energy natural frequencies + modal strain energy + modal flexibility modal curvature modal curvature + modal strain energy cornwell indicator transmissibility p. ghannadi et alii, frattura ed integrità strutturale, 62 (2022) 460-489; doi: 10.3221/igf-esis.62.32 480 figure 10: the classification of different variants of pso by the number of publications discussion o quickly and suitably provide the possibility of understanding the main points put forward by the existing studies conducted between 2005 and 2020, this section provides various questions and answers. a) why are the different variants of pso developed? after investigating more than 50 studies, it could be claimed that the standard pso has some drawbacks in terms of solving damage detection problems. for instance, the basic pso is easily entrapped in local optimum, and the premature convergence is a fundamental problem of the standard pso. therefore, some modified versions are proposed to improve the performance of the standard pso. additionally, some modified versions try to lower the computational time. b) why are the two-step methods frequently implemented for damage detection methodologies? for the large-scale damage detection problems formulated as an optimization scheme, there is an enormous search area to detect the optimal design variables. most optimization algorithms cannot function properly when exposed to a large number of variables. therefore, several two-step methods are proposed to enhance the performance of the optimization algorithms by narrowing the search area. for example, the damage localization methods such as msebi, msc, and wavelet transform are practiced in some studies. hence, the number of design variables drops by eliminating the healthy members. in the second step, the optimization algorithms are employed to measure the severity of the damage by minimizing the objective functions. in conclusion, the damage localization methods are efficient for improving the performance of the optimization algorithms and the accuracy of the damage evaluation. c) which one of the damage localization methods are frequently used in two-step methods? among various damage localization methods, msebi is the most popular. it should be noted that the new damage localization index called mebi was introduced by wang et al [126]. mebi is similar to msebi, yet it provides accurate outcomes. d) can robust results be achieved without improving the pso algorithm? in a study conducted by shabbir and omenzetter [98] , the combination of snt with objective function could present robust results for fem of the large-scale structures. it should be emphasized that the main contribution of this paper is adjusting the objective function after every solution without any improvement in pso search strategy. e) based on the analysis performed on the previous studies, does pso always provide more accurate results compared to ga? how about the computational time? 0 5 10 15 20 pso upso ipso pso–nm modified pso iepso improved pso-nm pso–cs psos hybrid ga-pso incremental pso revised pso mpsco pso-cca dpso bp-pso-ms eabcpso mopso scapso bbpsodj supso t p. ghannadi et alii, frattura ed integrità strutturale, 62 (2022) 460-489; doi: 10.3221/igf-esis.62.32 481 ga is one of the earliest optimization algorithms, and according to the analysis of the studies conducted between 2005 and 2020, it has been extensively applied to structural damage detection problems. some studies have compared the efficiency of pso with that of ga in terms of accuracy and computational time. based on the analysis made in the previous studies, it could be concluded that pso is capable of determining the damage characteristics with high accuracy and short computational time compared to ga. f) based on the analysis made in the previous studies, do frequency-based objective functions suffice for accurate damage detection? can you elaborate more on the popular and extensively used objective functions? according to the analysis made in the previous studies, some methodologies use a frequency-based objective function. generally, it can be summarized that natural frequencies do not fully suffice for damage detection. especially, the damage detection accuracy declines in complex structures such as laminated composites, as well as the multiple damage scenarios. several objective functions are defined by the combination of natural frequencies and mode shapes, modal flexibility, mdlac, mac, nfvac, strain energy, etc. among the aforementioned objective functions, the combination of the natural frequencies and the mode shapes (or mac) is a frequently used objective function with acceptable accuracy in complex structures. g) what is the perspective of pso considering the novel and robust nature-inspired optimization algorithms? as nikola tesla said: “the key to innovation is combining old ideas in new ways”. today, numerous novel optimization algorithms have been developed, improved, and enhanced by the inspiration of the swarm behavior of pso. since 2014 to date, new generations of optimization algorithms such as gwo [132], mfo [133], ssa [134], mvo [135], alo [136], water strider algorithm (wsa) [137], plasma generation optimization (pgo) [138], vibrating particles system (vps) [139], thermal exchange optimization (teo) [140] have been introduced. for structural damage identification, successful applications of gwo [38,141], mfo [121,142], ssa [40], mvo [39], alo [122], wsa [143,144], pgo [145], vps [146], and teo [147] have been reported during the past years. these algorithms have some major advantages as follows: i) the possibility of easy practice for different problems ii) there are few control parameters to begin the optimization procedure and have powerful exploration and exploitation capabilities. alongside the new nature-inspired optimization algorithms, different versions of pso are constantly being released and are still effective in structural damage detection problems. h) how many control parameters are there for pso? how could the best values be determined for them? generally, to begin the optimization process complying (see fig. 3), four control parameters, including the number of particles (n), the maximum number of iterations (tmax), cognitive coefficient (c1), and social coefficient (c2) are required. to avoid the velocity explosion [148], an inertia weight is introduced, and eq (4) can be rewritten as follows [75]:            1 1 2 21 1      i i i i iv t t v t c p x t r c g x t r (5) where  1 t represents the inertia weight at the (t + 1)th iteration of the algorithm. the inertia weight can be defined by dynamic adjustment strategies or considered as a constant value. the definition of a linearly decreasing inertia weight, according to eq (6), can provide reliable results in most engineering cases [75].   max minmax max       t t t (6) several authors [87,88] inserted min = 0.4 and max = 0.9 in eq (6). these are the uncertain parameters with a significant influence on the convergence rate. most of the papers published in the context of damage identification, update the particle velocity by eq (5) and implement the linearly decreasing inertia weight. hence, the basic or standard pso is known by considering this modification, and a flexible matlab code can be found in ref. [149]. in summary, the control parameters for the optimization algorithms are usually selected empirically and through trialand-error methods. however, chen and yu determined the optimal values for the inertia weight, cognitive coefficient, and social coefficient by monte carlo simulation [115]. i) according to the analyzed studies, how could the computation time of pso be lowered when optimizing a large number of variables? p. ghannadi et alii, frattura ed integrità strutturale, 62 (2022) 460-489; doi: 10.3221/igf-esis.62.32 482 as mentioned earlier, the two-step methods have initially detected the potentially damaged members. then, the optimization algorithms could swiftly determine the accurate severity of the damaged elements. fem of the composite structures includes a large number of dofs. hence, khatir et al. [105] employed pod and rbf to construct a short model which lowers the computation time consumed by the optimization procedure. the results obtained by some of the studies show that the combination of anns and optimization algorithms can significantly decrease the computational time. for example, khatir et al. [125], fathnejat and ahmadi-nedushan [130] have suggested hybrid methodologies. conclusions ne of the important tools for shm systems is damage detection techniques. the model-based damage detection methods have received extensive attention among other types of vibration-based methods. because model-based methods could identify the severity and the location of the damage. in iterative model-based methods, the vector of the design variables, including both severity and location of the damages, is achieved through minimizing an objective function by the optimization algorithms. similar to other optimization based-problems, the accuracy of the detected damages is also significantly influenced by the capability of the optimization algorithm. it should be noted that the utilized objective function is another important matter. in recent years, pso and its modified versions have been widely applied to optimization-based damage detection problems as a pioneering optimization approach. this paper analyses available publications released between 2005 and 2020 and discusses them in terms of methodologies, objectives, and results. finally, the following conclusions can be drawn: (i) in general, premature convergence is a fundamental problem of the basic pso, and this drawback deteriorates the accuracy of the damage detection, especially in complex structures with multiple damage scenarios. hence, several variants of pso have been developed to address this disadvantage. tab. 2 presents more information about the di fferent modified versions of pso. (ii) according to tab. 2, many publications have proposed two-step damage detection methodologies. the first step d etects the damaged members using damage localization techniques such as wavelet transform, msebi, and msc. after eliminating the undamaged members, the extent of the damage is estimated through an optimization operati on. in summary, the two-step method lowers the number of the design variables since pso cannot function prop erly to tackle the optimization problems in a large search space. (iii) based on the analyzed publications (2005-2020), pso yields accurate results with low computational time compared with those obtained by ga. (iv) as mentioned before, the utilized objective functions play a vital role in optimization problems. shabbir and omenzetter [98] have adjusted the objective function with snt and presented enhanced results without modifying the standard pso. the overall investigations show that frequency-based objective functions are not suf ficient for damage detection in complex structures. the most popular objective function with adequate accuracy is the combination of natural frequencies and mode shapes (or mac). (v) to start the optimization procedure with the standard pso, the number of particles (n), the maximum number of iterations (tmax), cognitive coefficient (c1), social coefficient (c2), and the inertia weight ( min and max ) should be determined. considering six uncertain parameters, establishing a desirable combination of the control parameters may be challenging. (vi) regarding the computational time, where the two-step methods are used, the elapsed time dramatically lowers because optimizing a low number of variables requires short computational time. the combination of anns and optimization algorithms, as well as the use of the reduced models by pod and rbf, are other methods could reduce the computational time. future directions i) recently some hybrid algorithms based on pso and gwo have been developed [150–152]. due to the successful application of both pso and gwo, a hybrid algorithm maybe provides more efficient results for structural damage detection problems. there are also hybrid algorithms based on pso and other nature-inspired optimization techniques such as mfo [153], mvo [154], and ssa [155]. o p. ghannadi et alii, frattura ed integrità strutturale, 62 (2022) 460-489; doi: 10.3221/igf-esis.62.32 483 ii) as recently mentioned, objective functions play a significant role in accurate damage detection. therefore, it is necessary to present a comparative study between different objective functions based on natural frequencies, mode shapes, modal strain energy, mac, mtmac, nfvac, etc. iii) according to tab. 2, many studies focused on damage detection of small-scale structures. complexity is a fundamental challenge in shm. therefore, researchers should be addressed real-world damage detection problems and provide practical methodologies. iv) to overcome the incomplete modal data in damage detection problems, fem reduction techniques have been applied by most studies. presenting a comparative study between fem reduction and mode shape expansion methods can be an attractive topic for future works. references [1] jafarkhani, r., masri, s.f. (2011). finite element model updating using evolutionary strategy for damage detection, comput. civ. infrastruct. eng., 26(3), pp. 207–224. [2] mariniello, g., pastore, t., menna, c., festa, p., asprone, d. (2020). structural damage detection and localization using decision tree ensemble and vibration data, comput. civ. infrastruct. eng.. [3] mousavi, m., gandomi, a.h. (2016). a hybrid damage detection method using dynamic-reduction transformation matrix and modal force error, eng. struct., 111, pp. 425–434. [4] urlainis, a., shohet, i.m., levy, r., ornai, d., vilnay, o. (2014). damage in critical infrastructures due to natural and man-made extreme events–a critical review, procedia eng., 85, pp. 529–35. [5] amezquita-sanchez, j.p., adeli, h. (2016). signal processing techniques for vibration-based health monitoring of smart structures, arch. comput. methods eng., 23(1), pp. 1–15. [6] furukawa, a., otsuka, h., kiyono, j. (2006). structural damage detection method using uncertain frequency response functions, comput. civ. infrastruct. eng., 21(4), pp. 292–305. [7] chen, h.-p., ni, y.-q. (2018). structural health monitoring of large civil engineering structures, wiley online library. [8] rafiei, m.h., adeli, h. (2017). a novel machine learning-based algorithm to detect damage in high-rise building structures, struct. des. tall spec. build., 26(18), pp. e1400. [9] fan, w., qiao, p. (2011). vibration-based damage identification methods: a review and comparative study, struct. heal. monit., 10(1), pp. 83–111. [10] ghannadi, p., kourehli, s.s. (2018). investigation of the accuracy of different finite element model reduction techniques, struct. monit. maint., 5(3), pp. 417. [11] ghannadi, p., kourehli, s.s. (2019). data-driven method of damage detection using sparse sensors installation by serepa, j. civ. struct. heal. monit., 9(4), pp. 459–475. [12] ghannadi, p., kourehli, s.s. (2021). an effective method for damage assessment based on limited measured locations in skeletal structures, adv. struct. eng., 24(1), pp. 183–195. [13] dinh-cong, d., truong, t.t., nguyen-thoi, t. (2021). a comparative study of different dynamic condensation techniques applied to multi-damage identification of fgm and fg-cntrc plates, eng. comput., , pp. 1–25. [14] kourehli, s.s. (2018). prediction of unmeasured mode shapes and structural damage detection using least squares support vector machine, struct. monit. maint., 5(3), pp. 379–390. [15] chen, y., logan, p., avitabile, p., dodson, j. (2019). non-model based expansion from limited points to an augmented set of points using chebyshev polynomials, exp. tech., 43(5), pp. 521–543. [16] chen, y., avitabile, p., page, c., dodson, j. (2021). a polynomial based dynamic expansion and data consistency assessment and modification for cylindrical shell structures, mech. syst. signal process., 154, pp. 107574. [17] sarmadi, h., entezami, a., ghalehnovi, m. (2020). on model-based damage detection by an enhanced sensitivity function of modal flexibility and lsmr-tikhonov method under incomplete noisy modal data, eng. comput., pp. 1–17. [18] rezaiee-pajand, m., entezami, a., sarmadi, h. (2020). a sensitivity-based finite element model updating based on unconstrained optimization problem and regularized solution methods, struct. control heal. monit., 27(5), pp. e2481. [19] mashayekhi, m., santini-bell, e. (2019). three-dimensional multiscale finite element models for in-service performance assessment of bridges, comput. civ. infrastruct. eng., 34(5), pp. 385–401. [20] mashayekhi, m., santini-bell, e. (2020). fatigue assessment of a complex welded steel bridge connection utilizing a p. ghannadi et alii, frattura ed integrità strutturale, 62 (2022) 460-489; doi: 10.3221/igf-esis.62.32 484 three-dimensional multi-scale finite element model and hotspot stress method, eng. struct., 214, pp. 110624. [21] shabbir, f., omenzetter, p. (2016). model updating using genetic algorithms with sequential niche technique, eng. struct., 120, pp. 166–182. [22] yang, y.b., chen, y.j. (2009). a new direct method for updating structural models based on measured modal data, eng. struct., 31(1), pp. 32–42. [23] friswell, m., mottershead, j.e. (2013). finite element model updating in structural dynamics, 38, springer science & business media. [24] mottershead, j.e., friswell, m.i. (1993). model updating in structural dynamics: a survey, j. sound vib., 167(2), pp. 347–375. [25] mottershead, j.e., link, m., friswell, m.i. (2011). the sensitivity method in finite element model updating: a tutorial, mech. syst. signal process., 25(7), pp. 2275–2296. [26] tran-ngoc, h., khatir, s., le-xuan, t., de roeck, g., bui-tien, t., wahab, m.a. (2021). finite element model updating of a multispan bridge with a hybrid metaheuristic search algorithm using experimental data from wireless triaxial sensors, eng. comput., pp. 1–19. [27] ho, l. v., khatir, s., roeck, g.d., bui-tien, t., wahab, m.a. (2020). finite element model updating of a cablestayed bridge using metaheuristic algorithms combined with morris method for sensitivity analysis, smart struct. syst., 26(4), pp. 451–468. [28] hoa, t.n., khatir, s., de roeck, g., long, n.n., thanh, b.t., wahab, m.a. (2020). an efficient approach for model updating of a large-scale cable-stayed bridge using ambient vibration measurements combined with a hybrid metaheuristic search algorithm, smart struct. syst., 25(4), pp. 487–499. [29] rezaiee-pajand, m., sarmadi, h., entezami, a. (2021). a hybrid sensitivity function and lanczos bidiagonalizationtikhonov method for structural model updating: application to a full-scale bridge structure, appl. math. model., 89, pp. 860–884. [30] pan, y., ventura, c.e., xiong, h., zhang, f.-l. (2020). model updating and seismic response of a super tall building in shanghai, comput. struct., 239, pp. 106285. [31] zhu, h., li, j., tian, w., weng, s., peng, y., zhang, z., chen, z. (2021). an enhanced substructure-based response sensitivity method for finite element model updating of large-scale structures, mech. syst. signal process., 154, pp. 107359. [32] marwala, t., boulkaibet, i., adhikari, s. (2016). probabilistic finite element model updating using bayesian statistics: applications to aeronautical and mechanical engineering, john wiley & sons. [33] carvalho, j., datta, b.n., gupta, a., lagadapati, m. (2007). a direct method for model updating with incomplete measured data and without spurious modes, mech. syst. signal process., 21(7), pp. 2715–2731. [34] yang, y.b., chen, y.j., hsu, t.w. (2009). direct updating method for structural models based on orthogonality constraints, mech. adv. mater. struct., 16(5), pp. 390–401. [35] chen, h.-p., maung, t.s. (2014). regularised finite element model updating using measured incomplete modal data, j. sound vib., 333(21), pp. 5566–5582. [36] sarmadi, h., karamodin, a., entezami, a. (2016). a new iterative model updating technique based on least squares minimal residual method using measured modal data, appl. math. model., 40(23–24), pp. 10323–10341. [37] tran-ngoc, h., khatir, s., de roeck, g., bui-tien, t., nguyen-ngoc, l., abdel wahab, m. (2018). model updating for nam o bridge using particle swarm optimization algorithm and genetic algorithm, sensors, 18(12), pp. 4131. [38] ghannadi, p., kourehli, s.s., noori, m., altabey, w.a. (2020). efficiency of grey wolf optimization algorithm for damage detection of skeletal structures via expanded mode shapes, adv. struct. eng., 23(13), pp. 2850–2865. [39] ghannadi, p., kourehli, s.s. (2020). multiverse optimizer for structural damage detection: numerical study and experimental validation, struct. des. tall spec. build., 29(13), pp. e1777. [40] ghannadi, p., kourehli, s.s. (2019). model updating and damage detection in multi-story shear frames using salp swarm algorithm, earthquakes struct., 17(1), pp. 63–73. [41] ding, z., li, j., hao, h. (2019). structural damage identification using improved jaya algorithm based on sparse regularization and bayesian inference, mech. syst. signal process., 132, pp. 211–231. [42] dinh-cong, d., nguyen-thoi, t., nguyen, d.t. (2020). a fe model updating technique based on sap2000-oapi and enhanced sos algorithm for damage assessment of full-scale structures, appl. soft comput., 89, pp. 106100. [43] shabbir, f., khan, m.i., ahmad, n., tahir, m.f., ejaz, n., hussain, j. (2017). structural damage detection with different objective functions in noisy conditions using an evolutionary algorithm, appl. sci., 7(12), pp. 1245. [44] samir, k., idir, b., serra, r., brahim, b., aicha, a. (2015).genetic algorithm based objective functions comparative study for damage detection and localization in beam structures. journal of physics: conference series, 628, iop p. ghannadi et alii, frattura ed integrità strutturale, 62 (2022) 460-489; doi: 10.3221/igf-esis.62.32 485 publishing, p. 12035. [45] li, x.-l., serra, r., olivier, j. (2021). performance of fitness functions based on natural frequencies in defect detection using the standard pso-fem approach, shock vib.. [46] hosseini, s.m., ghodrati amiri, g.h., mohamadi dehcheshmeh, m. (2020). efficiency evaluation of proposed objective functions in structural damage detection based on modal strain energy and flexibility approaches, int. j. optim. civ. eng., 10(1), pp. 71–90. [47] friswellt, m.i., penny, j.e.t., lindfield, g. (1995). the location of damage from vibration data using genetic algorithms, in pract., 1111001, pp. 1000001. [48] friswell, m.i., penny, j.e.t., garvey, s.d. (1998). a combined genetic and eigensensitivity algorithm for the location of damage in structures, comput. struct., 69(5), pp. 547–556. [49] ruotolo, r., surace, c. (1997). damage assessment of multiple cracked beams: numerical results and experimental validation, j. sound vib., 206(4), pp. 567–588. [50] mares, c., surace, c. (1996). an application of genetic algorithms to identify damage in elastic structures, j. sound vib., 195(2), pp. 195–215. [51] kashani, a.r., gandomi, m., camp, c. v., rostamian, m., gandomi, a.h. (2020). metaheuristics in civil engineering: a review, 1, 1(1), pp. 19. [52] kennedy, j., eberhart, r. (1995).particle swarm optimization. proceedings of icnn’95-international conference on neural networks, vol. 4, ieee, pp. 1942–1948. [53] poli, r. (2008). analysis of the publications on the applications of particle swarm optimisation, j. artif. evol. appl. [54] mahor, a., prasad, v., rangnekar, s. (2009). economic dispatch using particle swarm optimization: a review, renew. sustain. energy rev., 13(8), pp. 2134–2341. [55] rana, s., jasola, s., kumar, r. (2011). a review on particle swarm optimization algorithms and their applications to data clustering, artif. intell. rev., 35(3), pp. 211–22. [56] yusup, n., zain, a.m., hashim, s.z.m. (2012). overview of pso for optimizing process parameters of machining, procedia eng., 29, pp. 914–923. [57] sarkar, s., roy, a., purkayastha, b.s. (2013). application of particle swarm optimization in data clustering: a survey, int. j. comput. appl., 65(25). [58] esmin, a.a.a., coelho, r.a., matwin, s. (2015). a review on particle swarm optimization algorithm and its variants to clustering high-dimensional data, artif. intell. rev., 44(1), pp. 23–45. [59] lalwani, s., singhal, s., kumar, r., gupta, n. (2013). a comprehensive survey: applications of multi-objective particle swarm optimization (mopso) algorithm, trans. comb., 2(1), pp. 39–101. [60] gopalakrishnan, k. (2013). particle swarm optimization in civil infrastructure systems: state-of-the-art review, metaheuristic appl. struct. infrastructures, , pp. 49–76. [61] ghorpade-aher, j., bagdiya, r. (2014). a review on clustering web data using pso, int. j. comput. appl., 108(6), pp. 31–36. [62] saini, s., bt awang rambli, d.r., zakaria, m.n.b., bt sulaiman, s. (2014). a review on particle swarm optimization algorithm and its variants to human motion tracking, math. probl. eng. [63] alam, s., dobbie, g., koh, y.s., riddle, p., rehman, s.u. (2014). research on particle swarm optimization based clustering: a systematic review of literature and techniques, swarm evol. comput., 17, pp. 1–13. [64] kulkarni, m.n.k., patekar, m.s., bhoskar, m.t., kulkarni, m.o., kakandikar, g.m., nandedkar, v.m. (2015). particle swarm optimization applications to mechanical engineering-a review, mater. today proc., 2(4–5), pp. 2631– 2639. [65] zhang, y., wang, s., ji, g. (2015). a comprehensive survey on particle swarm optimization algorithm and its applications, math. probl. eng. [66] zhou, y., li, z., zhou, h., li, r. (2016).the application of pso in the power grid: a review. 2016 35th chinese control conference (ccc), ieee, pp. 10061–10066. [67] andrab, s.g., hekmat, a., yusop, z. bin. (2017). a review: evolutionary computations (ga and pso) in geotechnical engineering, comput. water, energy, environ. eng., 6(02), pp. 154. [68] pluhacek, m., senkerik, r., viktorin, a., kadavy, t., zelinka, i. (2017). a review of real-world applications of particle swarm optimization algorithm. international conference on advanced engineering theory and applications, springer, pp. 115–122. [69] elsheikh, a.h., abd elaziz, m. (2019). review on applications of particle swarm optimization in solar energy systems, int. j. environ. sci. technol., 16(2), pp. 1159–1170. [70] hajihassani, m., armaghani, d.j., kalatehjari, r. (2018). applications of particle swarm optimization in geotechnical p. ghannadi et alii, frattura ed integrità strutturale, 62 (2022) 460-489; doi: 10.3221/igf-esis.62.32 486 engineering: a comprehensive review, geotech. geol. eng., 36(2), pp. 705–722. [71] elbes, m., alzubi, s., kanan, t., al-fuqaha, a., hawashin, b. (2019). a survey on particle swarm optimization with emphasis on engineering and network applications, evol. intell., 12(2), pp. 113–129. [72] sibalija, t. v. (2019). particle swarm optimisation in designing parameters of manufacturing processes: a review (2008–2018), appl. soft comput., 84, pp. 105743. [73] jahandideh-tehrani, m., bozorg-haddad, o., loáiciga, h.a. (2020). application of particle swarm optimization to water management: an introduction and overview, environ. monit. assess., 192(5), pp. 1–18. [74] kashani, a.r., chiong, r., mirjalili, s., gandomi, a.h. (2020). particle swarm optimization variants for solving geotechnical problems: review and comparative analysis, arch. comput. methods eng., pp. 1–57. [75] marini, f., walczak, b. (2015). particle swarm optimization (pso). a tutorial, chemom. intell. lab. syst., 149, pp. 153–165. [76] wang, d., tan, d., liu, l. (2018). particle swarm optimization algorithm: an overview, soft comput., 22(2), pp. 387–408. [77] mouser, c.r., dunn, s.a. (2005). comparing genetic algorithms and particle swarm optimisation for an inverse problem exercise, anziam j., 46, pp. c89–101. [78] saada, m.m., arafa, m.h., nassef, a.o. (2008).finite element model updating approach to damage identification in beams using particle swarm optimization. international design engineering technical conferences and computers and information in engineering conference, 43253, pp. 521–530. [79] yu, l., wan, z. (2008).an improved pso algorithm and its application to structural damage detection. 2008 fourth international conference on natural computation, 1, ieee, pp. 423–427. [80] begambre, o., laier, j.e. (2009). a hybrid particle swarm optimization–simplex algorithm (psos) for structural damage identification, adv. eng. softw., 40(9), pp. 883–891. [81] yu, l., chen, x. (2010). bridge damage identification by combining modal flexibility and pso methods. prognostics and system health management conference, ieee, pp. 1–6. [82] sandesh, s., shankar, k. (2010). application of a hybrid of particle swarm and genetic algorithm for structural damage detection, inverse probl. sci. eng. former. inverse probl. eng., 18(7), pp. 997–1021. [83] liu, h.b., jiao, y.b., gong, y.f., bi, h.p., sun, y.y. (2011).damage identification for simply-supported bridge based on svm optimized by pso (pso-svm). applied mechanics and materials, vol. 80, trans tech publ, pp. 490–494. [84] gökdag, h., yildiz, a.r. (2012). structural damage detection using modal parameters and particle swarm optimization, mp mater. test., 54(6), pp. 416. [85] seyedpoor, s.m. (2012). a two stage method for structural damage detection using a modal strain energy based index and particle swarm optimization, int. j. non. linear. mech., 47(1), pp. 1–8. [86] baghmisheh, m.t.v., peimani, m., sadeghi, m.h., ettefagh, m.m., tabrizi, a.f. (2012). a hybrid particle swarm– nelder–mead optimization method for crack detection in cantilever beams, appl. soft comput., 12(8), pp. 2217– 2226. [87] xiang, j., liang, m. (2012). a two-step approach to multi-damage detection for plate structures, eng. fract. mech., 91, pp. 73–86. [88] kang, f., li, j., xu, q. (2012). damage detection based on improved particle swarm optimization using vibration data, appl. soft comput., 12(8), pp. 2329–2335. [89] nanda, b., maity, d., maiti, d.k. (2012). vibration based structural damage detection technique using particle swarm optimization with incremental swarm size, int. j. aeronaut. sp. sci., 13(3), pp. 323–331. [90] saada, m.m., arafa, m.h., nassef, a.o. (2013). finite element model updating approach to damage identification in beams using particle swarm optimization, eng. optim., 45(6), pp. 677–696. [91] kang, f., li, j., liu, s. (2013). combined data with particle swarm optimization for structural damage detection, math. probl. eng. [92] guo, h.y., li, z.l. (2014). structural damage identification based on evidence fusion and improved particle swarm optimization, j. vib. control, 20(9), pp. 1279–1292. [93] mohan, s.c., yadav, a., maiti, d.k., maity, d. (2014). a comparative study on crack identification of structures from the changes in natural frequencies using ga and pso, eng. comput. [94] nanda, b., maity, d., maiti, d.k. (2014). crack assessment in frame structures using modal data and unified particle swarm optimization technique, adv. struct. eng., 17(5), pp. 747–766. [95] nanda, b., maity, d., maiti, d.k. (2014). modal parameter based inverse approach for structural joint damage assessment using unified particle swarm optimization, appl. math. comput., 242, pp. 407–422. [96] ma, s.-l., jiang, s.-f., weng, l.-q. (2014). two-stage damage identification based on modal strain energy and revised p. ghannadi et alii, frattura ed integrità strutturale, 62 (2022) 460-489; doi: 10.3221/igf-esis.62.32 487 particle swarm optimization, int. j. struct. stab. dyn., 14(05), pp. 1440005. [97] jiang, s.-f., wu, s.-y., dong, l.-q. (2014). a time-domain structural damage detection method based on improved multiparticle swarm coevolution optimization algorithm, math. probl. eng. [98] shabbir, f., omenzetter, p. (2015). particle swarm optimization with sequential niche technique for dynamic finite element model updating, comput. civ. infrastruct. eng., 30(5), pp. 359–375. [99] liu, h., song, g., jiao, y., zhang, p., wang, x. (2014). damage identification of bridge based on modal flexibility and neural network improved by particle swarm optimization, math. probl. eng. [100] rasouli, a., ghodrati amiri, g., kheyroddin, a., ghafory-ashtiany, m., kourehli, s.s. (2014). a new method for damage prognosis based on incomplete modal data via an evolutionary algorithm, eur. j. environ. civ. eng., 18(3), pp. 253–270. [101] pal, j., banerjee, s. (2015). a combined modal strain energy and particle swarm optimization for health monitoring of structures, j. civ. struct. heal. monit., 5(4), pp. 353–363. [102] kaveh, a., maniat, m. (2015). damage detection based on mcss and pso using modal data, smart struct syst, 15(5), pp. 1253–1270. [103] chen, z., yu, l. (2015).a novel two-step intelligent algorithm for damage detection of beam-like structures. 2015 11th international conference on natural computation (icnc), ieee, pp. 633–638. [104] chen, z., yu, l. (2015).an improved pso-nm algorithm for structural damage detection. international conference in swarm intelligence, springer, pp. 124–132. [105] khatir, s., belaidi, i., serra, r., wahab, m.a., khatir, t. (2015). damage detection and localization in composite beam structures based on vibration analysis, mechanics, 21(6), pp. 472–479. [106] hosseinzadeh, a., ghodrati amiri, g., seyed razzaghi, s.a. (2017). model-based identification of damage from sparse sensor measurements using neumann series expansion, inverse probl. sci. eng., 25(2), pp. 239–259. [107] hosseinzadeh, a.z., amiri, g.g., razzaghi, s.a.s., koo, k.y., sung, s.-h. (2016). structural damage detection using sparse sensors installation by optimization procedure based on the modal flexibility matrix, j. sound vib., 381, pp. 65–82. [108] gerist, s., maheri, m.r. (2016). multi-stage approach for structural damage detection problem using basis pursuit and particle swarm optimization, j. sound vib., 384, pp. 210–226. [109] khatir, s., belaidi, i., khatir, t., hamrani, a., zhou, y.-l., wahab, m.a. (2017). multiple damage detection in composite beams using particle swarm optimization and genetic algorithm, mechanics, 23(4), pp. 514–521. [110] jebieshia, t.r., maity, d., maiti, d.k. (2017).damage detection of laminated composite shells using unified particle swarm optimization. proceedings of ictacem 2017 international conference on theoretical, applied, computational and experimental mechanics, pp. 28–30. [111] chen, z.p., yu, l. (2017). a novel pso-based algorithm for structural damage detection using bayesian multisample objective function, struct. eng. mech., 63(6), pp. 825–835. [112] luo, z., yu, l. (2017).pso-based sparse regularization approach for structural damage detection. 2017 13th international conference on natural computation, fuzzy systems and knowledge discovery (icnc-fskd), ieee, pp. 1033–1039. [113] khatir, s., dekemele, k., loccufier, m., khatir, t., wahab, m.a. (2018). crack identification method in beam-like structures using changes in experimentally measured frequencies and particle swarm optimization, comptes rendus mécanique, 346(2), pp. 110–120. [114] alkayem, n.f., cao, m. (2018). damage identification in three-dimensional structures using single-objective evolutionary algorithms and finite element model updating: evaluation and comparison, eng. optim., 50(10), pp. 1695–1714. [115] chen, z., yu, l. (2018). a new structural damage detection strategy of hybrid pso with monte carlo simulations and experimental verifications, measurement, 122, pp. 658–669. [116] xu, m., wang, s., jiang, y. (2019). iterative two-stage approach for identifying structural damage by combining the modal strain energy decomposition method with the multiobjective particle swarm optimization algorithm, struct. control heal. monit., 26(2), pp. e2301. [117] alkayem, n.f., cao, m., ragulskis, m. (2019). damage localization in irregular shape structures using intelligent fe model updating approach with a new hybrid objective function and social swarm algorithm, appl. soft comput., 83, pp. 105604. [118] jebieshia, t.r., maiti, d.k., maity, d. (2020). frequency-based damage assessment of composite members using unified particle swarm optimization, int. j. aeronaut. sp. sci., 21(1), pp. 63–79. [119] huang, m., cheng, s., zhang, h., gul, m., lu, h. (2019). structural damage identification under temperature p. ghannadi et alii, frattura ed integrità strutturale, 62 (2022) 460-489; doi: 10.3221/igf-esis.62.32 488 variations based on pso–cs hybrid algorithm, int. j. struct. stab. dyn., 19(11), pp. 1950139. [120] huang, m., lei, y., li, x. (2019). structural damage identification based on l1regularization and bare bones particle swarm optimization with double jump strategy, math. probl. eng. [121] ghannadi, p., kourehli, s.s. (2019). structural damage detection based on mac flexibility and frequency using moth-flame algorithm, struct. eng. mech., 70(6), pp. 649–659. [122] mishra, m., barman, s.k., maity, d., maiti, d.k. (2019). ant lion optimisation algorithm for structural damage detection using vibration data, j. civ. struct. heal. monit., 9(1), pp. 117–36. [123] mishra, m., barman, s.k., maity, d., maiti, d.k. (2020). performance studies of 10 metaheuristic techniques in determination of damages for large-scale spatial trusses from changes in vibration responses, j. comput. civ. eng., 34(2), pp. 4019052. [124] huang, m., lei, y., cheng, s. (2019). damage identification of bridge structure considering temperature variations based on particle swarm optimization-cuckoo search algorithm, adv. struct. eng., 22(15), pp. 3262–3276. [125] khatir, s., tiachacht, s., thanh, c.-l., bui, t.q., wahab, m.a. (2019). damage assessment in composite laminates using ann-pso-iga and cornwell indicator, compos. struct., 230, pp. 111509. [126] wang, s., jiang, y., xu, m., li, y., li, z. (2020). structural damage identification using an iterative two-stage method combining a modal energy based index with the bas algorithm, steel compos. struct., 36(1), pp. 31–45. [127] zenzen, r., khatir, s., belaidi, i., wahab, m.a. (2020).damage detection in truss structures using transmissibility combined with optimization techniques. proceedings of the 13th international conference on damage assessment of structures, springer, pp. 225–233. [128] tran-ngoc, h., he, l., reynders, e., khatir, s., le-xuan, t., de roeck, g., bui-tien, t., wahab, m.a. (2020). an efficient approach to model updating for a multispan railway bridge using orthogonal diagonalization combined with improved particle swarm optimization, j. sound vib., 476, pp. 115315. [129] guo, j., guan, d., zhao, j. (2020). structural damage identification based on the wavelet transform and improved particle swarm optimization algorithm, adv. civ. eng. [130] fathnejat, h., ahmadi-nedushan, b. (2020). an efficient two-stage approach for structural damage detection using meta-heuristic algorithms and group method of data handling surrogate model, front. struct. civ. eng., 14(4), pp. 907–929. [131] barman, s.k., maiti, d.k., maity, d. (2021). vibration-based delamination detection in composite structures employing mixed unified particle swarm optimization, aiaa j., 59(1), pp. 386–399. [132] mirjalili, s., mirjalili, s.m., lewis, a. (2014). grey wolf optimizer, adv. eng. softw., 69, pp. 46–61. [133] mirjalili, s. (2015). moth-flame optimization algorithm: a novel nature-inspired heuristic paradigm, knowledgebased syst., 89, pp. 228–249. [134] mirjalili, s., gandomi, a.h., mirjalili, s.z., saremi, s., faris, h., mirjalili, s.m. (2017). salp swarm algorithm: a bioinspired optimizer for engineering design problems, adv. eng. softw., 114, pp. 163–191. [135] mirjalili, s., mirjalili, s.m., hatamlou, a. (2016). multi-verse optimizer: a nature-inspired algorithm for global optimization, neural comput. appl., 27(2), pp. 495–513. [136] mirjalili, s. (2015). the ant lion optimizer, adv. eng. softw., 83, pp. 80–98. [137] kaveh, a., eslamlou, a.d. (2020).water strider algorithm: a new metaheuristic and applications. structures, vol. 25, elsevier, pp. 520–541. [138] kaveh, a., akbari, h., hosseini, s.m. (2020). plasma generation optimization: a new physically-based metaheuristic algorithm for solving constrained optimization problems, eng. comput. [139] kaveh, a., ghazaan, m.i. (2017). a new meta-heuristic algorithm: vibrating particles system, sci. iran. trans. a, civ. eng., 24(2), pp. 551. [140] kaveh, a., dadras, a. (2017). a novel meta-heuristic optimization algorithm: thermal exchange optimization, adv. eng. softw., 110, pp. 69–84. [141] hosseinzadeh, a.z., amiri, g.g., abyaneh, m.j., razzaghi, s.a.s., hamzehkolaei, a.g. (2019). baseline updating method for structural damage identification using modal residual force and grey wolf optimization, eng. optim. [142] huang, m., li, x., lei, y., gu, j. (2020).structural damage identification based on modal frequency strain energy assurance criterion and flexibility using enhanced moth-flame optimization. structures, vol. 28, elsevier, pp. 1119– 1136. [143] kaveh, a., rahmani, p., eslamlou, a.d. (2021). guided water strider algorithm for structural damage detection using incomplete modal data, iran. j. sci. technol. trans. civ. eng., , pp. 1–18. [144] kaveh, a., rahmani, p., eslamlou, a.d. (2021). damage detection using a graph-based adaptive threshold for modal strain energy and improved water strider algorithm, period. polytech. civ. eng. p. ghannadi et alii, frattura ed integrità strutturale, 62 (2022) 460-489; doi: 10.3221/igf-esis.62.32 489 [145] kaveh, a., hosseini, s.m., akbari, h. (2020). efficiency of plasma generation optimization for structural damage identification of skeletal structures based on a hybrid cost function, iran. j. sci. technol. trans. civ. eng., pp. 1– 22. [146] kaveh, a., hoseini vaez, s.r., hosseini, p. (2019). enhanced vibrating particles system algorithm for damage identification of truss structures, sci. iran., 26(1), pp. 246–256. [147] kaveh, a., dadras, a. (2018). structural damage identification using an enhanced thermal exchange optimization algorithm, eng. optim., 50(3), pp. 430–451. [148] clerc, m., kennedy, j. (2002). the particle swarm-explosion, stability, and convergence in a multidimensional complex space, ieee trans. evol. comput., 6(1), pp. 58–73. [149] alam, m.n. (2016). codes in matlab for particle swarm optimization, res. gate, doi: 10.13140/rg.2.1.1078.7608. [150] zhang, x., lin, q., mao, w., liu, s., dou, z., liu, g. (2021). hybrid particle swarm and grey wolf optimizer and its application to clustering optimization, appl. soft comput., 101, pp. 107061. [151] banerjee, n., mukhopadhyay, s. (2019).hc-psogwo: hybrid crossover oriented pso and gwo based coevolution for global optimization. 2019 ieee region 10 symposium (tensymp), ieee, pp. 162–167. [152] singh, n., singh, s.b. (2017). hybrid algorithm of particle swarm optimization and grey wolf optimizer for improving convergence performance, j. appl. math. [153] yang, z., shi, k., wu, a., qiu, m., hu, y. (2019).a hybird method based on particle swarm optimization and mothflame optimization. 2019 11th international conference on intelligent human-machine systems and cybernetics (ihmsc), vol. 2, ieee, pp. 207–210. [154] jangir, p., parmar, s.a., trivedi, i.n., bhesdadiya, r.h. (2017). a novel hybrid particle swarm optimizer with multi verse optimizer for global numerical optimization and optimal reactive power dispatch problem, eng. sci. technol. an int. j., 20(2), pp. 570–586. [155] singh, n., singh, s.b., houssein, e.h. 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/hrv (za stvaranje adobe pdf dokumenata najpogodnijih za visokokvalitetni ispis prije tiskanja koristite ove postavke. stvoreni pdf dokumenti mogu se otvoriti acrobat i adobe reader 5.0 i kasnijim verzijama.) /hun 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can be opened with acrobat and adobe reader 5.0 and later.) >> /namespace [ (adobe) (common) (1.0) ] /othernamespaces [ << /asreaderspreads false /cropimagestoframes true /errorcontrol /warnandcontinue /flattenerignorespreadoverrides false /includeguidesgrids false /includenonprinting false /includeslug false /namespace [ (adobe) (indesign) (4.0) ] /omitplacedbitmaps false /omitplacedeps false /omitplacedpdf false /simulateoverprint /legacy >> << /addbleedmarks false /addcolorbars false /addcropmarks false /addpageinfo false /addregmarks false /convertcolors /converttocmyk /destinationprofilename () /destinationprofileselector /documentcmyk /downsample16bitimages true /flattenerpreset << /presetselector /mediumresolution >> /formelements false /generatestructure false /includebookmarks false /includehyperlinks false /includeinteractive false /includelayers false /includeprofiles false /multimediahandling /useobjectsettings /namespace [ (adobe) (creativesuite) (2.0) ] /pdfxoutputintentprofileselector /documentcmyk /preserveediting true /untaggedcmykhandling /leaveuntagged /untaggedrgbhandling /usedocumentprofile /usedocumentbleed false >> ] >> setdistillerparams << /hwresolution [2400 2400] /pagesize [612.000 792.000] >> setpagedevice microsoft word numero_36_art_20 l. c. h. ricardo et alii, frattura ed integrità strutturale, 36 (2016) 201-214; doi: 10.3221/igf-esis.36.20 201 technical note influence of the crack propagation rate in the obtaining opening and closing stress intensity factor by finite element method luiz carlos h. ricardo materials technology department, ipen, university of são paulo, brazil instituto de pesquisas energéticas e nucleares, av. lineu prestes 2242 cidade universitária são paulo sp brasilcep: 05508-000 lricardo@ipen.br carlos alexandre j. miranda nuclear engineering department, ipen, university of sao paulo, brazil instituto de pesquisas energéticas e nucleares abstract. crack propagation simulation began with the development of the finite element method; the analyses were conducted to obtain a basic understanding of the crack growth. today structural and materials engineers develop structures and materials properties using this technique as criterion design. the aim of this paper is to verify the effect of different crack propagation rates in determination of crack opening and closing stress of an astm specimen under a standard suspension spectrum loading from fd&e sae keyhole specimen test load histories by finite element analysis. the crack propagation simulation was based on release nodes at the minimum loads to minimize convergence problems. to understand the crack propagation processes under variable amplitude loading, retardation effects are discussed. key words: fatigue; crack propagation simulation; finite element method; retardation. introduction he most common technique for predicting the fatigue life of automotive, aircraft, wind turbine and many other structures is miner’s rule [1]. despite the known deviations, inaccuracies and proven conservatism of miner’s cumulative damage law, it is even nowadays being used in the design of many advanced structures. fracture mechanics techniques for fatigue life predictions remain as a back up in design procedures. the most important and difficult problem in using fracture mechanics concepts in design seems to be the use of crack growth data to predict fatigue life. the experimentally obtained data is used to derive a relationship between stress intensity range (k) and crack growth per cycle (da/dn). in cases of fatigue loaded parts containing a flaw under constant stress amplitude, the crack growth can be calculated by simple integration of the relation between da/dn and k. however, for complex spectrum loadings, simple addition of the crack growth occurring in each portion of the loading sequence produces results that, very often, are more erroneous than the results obtained using miner’s rule with an s-n curve. retardation tends to cause conservative results using miner’s rule when the fatigue life is dominated by the crack growth. however, the opposite t l. c. h. ricardo et alii, frattura ed integrità strutturale, 36 (2016) 201-214; doi: 10.3221/igf-esis.36.20 202 effect generally occurs when the life is dominated by the initiation and growth of small cracks (linear elastic fracture mechanics). large cyclic strains (elasto-plastic fracture mechanics), which might occur locally at stress raisers due to overload, may predamage the material and lower its resistance to fatigue. the experimentally derived crack growth equations are independent of the loading sequence and depend only on the stress intensity range and the number of cycles for that portion of the loading sequence. the central problem in the successful utilization of fracture mechanic techniques applied to the fatigue spectrum is to obtain a clear understanding of the influence of loading sequences on fatigue crack growth [2]. investigations covering the effects of particular interest, after high overload, in the study of crack growth under variable-amplitude loading in the growth rate region, called crack growth retardation, seem to have little interest nowadays. stouffer & williams [3] and other researchers show a number of attempts to model this phenomenon through manipulation of the constants and stress intensity factors used in the paris-erdogan equation however little appears to have been done in the effort to develop a completely rational analysis of the problem. probably, the only one reason that the existing models of retarded crack growth are not satisfactory is that these models are deterministic whereas the fatigue crack growth phenomenon shows strong random features. in addition, most of the reported theoretical descriptions of the retardation are based on data fitting techniques, which tend to hide the behavior of the phenomenon. if the retarding effect of a peak overload on the crack growth is neglected, the prediction of the material lifetime is usually very conservative [4]. accurate predictions of the fatigue life will hardly become possible before the physics of the peak overload mechanisms is better clarified. according to the existing findings, the retardation is a physically very complicated phenomenon which is affected by a wide range of variables associated with loading, metallurgical properties, environment, etc., and it is difficult to separate the contribution of each of these variables [5]. figure 1: fatigue crack growth da/dn versus δk stress intensity factor [8]: (a) threshold range δkth; (b) intermediate region following a power equation; (c) unstable. crack propagation concepts aris & erdogan [6] conducted a revision on the crack propagation approach from head [7] and others and discussed the similarity of these theories and the differences of results between them, isolated and in group tests. paris suggested that, for a cyclical load variation, the stress field in the crack tip for a cycle can be characterized by a variation of the stress intensity factor, eq. (2.1), p l. c. h. ricardo et alii, frattura ed integrità strutturale, 36 (2016) 201-214; doi: 10.3221/igf-esis.36.20 203 max mink k k   (2.1) where kmax and kmin are the maximum and the minimum stress intensity factors, respectively. in the crack propagation curve, the linear part represents the paris erdogan law, when plotting the values of k vs da/dn in logarithmic scale, as can be seen in fig. 1. fatigue crack initiation and growth under cyclic loading conditions is controlled by the plastic zones that result from the applied stresses and exist in the vicinity (ahead) of a propagating crack and in its wake or flanks of the adjoining surfaces. for example, the fatigue characteristics of a cracked specimen or component under a single overload or variable amplitude loading situations are significantly influenced by these plastic zones. in modelling the fatigue crack growth rate this is accounted by the incorporation of accumulative damage cycle after cycle and should include plasticity effects. during the crack propagation the plastic zone should grown and the plastic wake will have compressive plastic zones that can help to keep the crack close. hairman & provan [9] discuss the problems pertaining to fatigue loading of engineering structures under single overload and variable amplitude loading involving the estimation of plasticity affected zones ahead of the crack tip. crack tip plasticity most solid materials develop plastic strains when the yield strength is exceeded in the region near a crack tip. thus, the amount of plastic deformation is restricted by the surrounding material, which remains elastic during loading. theoretically, linear elastic stress analysis of sharp cracks predicts infinite stresses at the crack tip. in fact, inelastic deformation, such as plasticity in metals and crazing in polymers, leads to relaxation of crack tip stresses caused by the yielding phenomenon at the crack tip. as a result, a plastic zone is formed containing microstructural defects such dislocations and voids. consequently, the local stresses are limited to the yield strength of the material. this implies that the elastic stress analysis becomes increasingly inaccurate as the inelastic region at the crack tip becomes sufficiently large and, so, linear elastic fracture mechanics (lefm) is no longer useful for predicting the field equations. the size of the plastic zone can be estimated when moderate crack tip yielding occurs. thus, the introduction of the plastic zone size (r) as a correction parameter, which accounts for plasticity effects adjacent to the crack tip, is vital to determine the effective stress intensity factor (keff) or a corrected stress intensity factor. the plastic zone is also determined for plane conditions; that is, plane strain for maximum constraint on relatively thick components and plane stress for variable constraint due to thickness effects of thin solid bodies. moreover, the plastic zone develops in most common in materials subjected to an increase in the tensile stress that causes local yielding at the crack tip. most engineering metallic materials are subjected to an irreversible plastic deformation. if plastic deformation occurs, then the elastic stresses are limited by yielding since stress singularity cannot occur, but stress relaxation takes place within the plastic zone. this plastic deformation occurs in a small region and it is called the crack-tip plastic zone (r). a small plastic zone, (r << a) being a crack length of the structure or specimen, is referred to as small-scale yielding. on the other hand, a large-scale yielding corresponds to a large plastic zone, which occurs in ductile materials in which r >> a. this suggests that the stress intensity factors within and outside the boundary of the plastic zone are different in magnitude so that ki (plastic) > ki (elastic). in fact, ki (plastic) must be defined in terms of plastic stresses and displacements in order to characterize crack growth, and subsequently ductile fracture. as a consequence of plastic deformation ahead of the crack tip, the linear elastic fracture mechanics (lefm) theory is limited to r << a; otherwise, elastic-plastic fracture mechanics (epfm) theory controls the fracture process due to a large plastic zone size (r ≥ a). this argument implies that r should be determined in order to set an approximate limit for both lefm and epfm theories [10]. fig. 2 shows schematic plastic zones for plane stress (thin plate) and plane strain (thick plate) conditions even if in the interior of a plate a condition of plane strain exists, there will always be plane stress at the surface. stresses perpendicular to the outer surface are nonexistent, and hence σz = σ3 = 0 at the surface. if plane strain prevails in the interior of the plate, the stress σ3 gradually increases from zero (at the surface) to the plane strain value in the interior [11]. consequently, the plastic zone gradually decreases from the plane stress size at the surface, to the plane strain size in the interior of the plate, illustrated schematically in fig. 2. dugdale [12] proposed a strip yield model for the plastic zone under plane stress conditions. consider fig. 3, which shows the plastic zones in the form of narrow strips extending a distance r each, and carrying the yield stress σys. in the case of cyclic stress, and as the crack grows, behind the new crack front there is a region with compressive (residual) stresses. the phenomenon of crack closure is caused by these internal (compressive) stresses since they tend to close the crack in the region where a < x < c. l. c. h. ricardo et alii, frattura ed integrità strutturale, 36 (2016) 201-214; doi: 10.3221/igf-esis.36.20 204 figure 2: three-dimensional plastic zone [11]. a) b) figure 3: dugdale plastic zone strip model under plane stress conditions. a) dugdale crack; b) wedge crack . in the original paris crack propagation equation [6] the driving parameters are c, k and m, as shown in fig. 1. among other limitations, this equation is valid only in the region (b). so, it does not cover the near threshold region (a) nor the unstable region (c). some researchers have proposed similar equations that cover one or both extremes of the curve in fig. 1. in tab. 1 it is possible to see some other crack propagation equations for constant amplitude loading, which are modifications of the paris equation, relating the mentioned parameters and kc, the critical stress intensity factor.  min max ( ) 1 m c c kda dn k k k k         max ( )m c c kda dn k k    1 max( ) ( ) m mda c k k dn   table 1: some empirical crack growth equations for constant amplitude loading [6]. murthy et al. [13] discuss crack growth models for variable amplitude loading and the mechanisms and contribution to overload retardation. there are many authors which have been developing fatigue crack growth models for variable amplitude loading. tab. 2 presents some authors and the application of their models. l. c. h. ricardo et alii, frattura ed integrità strutturale, 36 (2016) 201-214; doi: 10.3221/igf-esis.36.20 205 yield zone concept crack closure concept wheeler [14] elber [21] willenborg, engle, wood [15] bell and creager (generalized closure) [22] porter [16] newman (finite element method) [23] gray (generalized wheeler) [17] dill and staff (contact stress ) [24] gallagher and hughes [18] kanninen, fedderson, atkinson [25] johnson [19] budiansky and hutchinson [26] chang et al. [20] de koning [27] table 2: some fatigue crack growth models [13]. retardation phenomenon it has been noted that, under certain conditions, the crack growth presents a slower rate, called retardation, due to several factors. despite recent large increase in research into the retardation effects in crack propagation there are many aspects of load interaction phenomena that lack adequate explanations. it is presented here some several aspects of the retardation phenomenon by corbly & packman [28]. 1. retardation increases with higher values of peak loading peak for constant values of lower stress levels [29,30]. 2. the number of cycles at the lower stress level required to return to the non-retarded crack growth rate is a function of kpeak, klower, rpeak, rlower and number of peak cycles [31]. 3. if the ratio of the peak stress to lower stress intensity factors is greater than l.5 retardation at the lower stress intensity range is observed. tests were not continued long enough to see if the crack ever propagated again [31]. 4. with a constant ratio of peak to lower stress intensity the number of cycles to return to non-retarded growth rates increases with increasing peak stress intensity [30,31]. 5. given a ratio of peak stress to lower stress, the number of cycles required to return to non-retarded growth rates decreases with increased time at zero load before cycling at the lower level [31]. 6. increased percentage delay effects of peak loading given a percent overload are greater at higher baseline stress intensity factors [32]. 7. delay is a minimum if compression is applied immediately after tensile overload [33]. 8. negative peak loads cause no substantial influence of crack growth rates at lower stress levels if the values of r > 0 for the lower stress [34]. 9. negative peak loads cause up to 50 per cent increase in fatigue crack propagation with r = 1 [33]. 10. importance of residual compressive stresses around the tip of crack [35] 11. low-high sequences cause an initial acceleration of the crack propagation at the higher stress level which rapidly stabilizes [36]. small scale yield models while the basic layout of the small scale yield model has been established by dill & saff [37], only improvements introduced later by newman [38] made this approach applicable to general variable amplitude loading. the small scale yield model employs the dugdale [12] theory of crack tip plasticity modified to leave a wedge of plastically stretched material on the fatigue crack surfaces. the fatigue crack growth is simulated by severing the strip material over a distance corresponding to the fatigue crack growth increment as shown fig. 4. in order to satisfy the compatibility between the elastic plate and the plastically deformed strip material, a traction must be applied on the fictitious crack surfaces in the plastic zone (a  x < aafict), as in the original dugdale model, and also over some distance in the crack wake (aopen  x < a), where the plastic elongations of the strip l(x) exceed the fictitious crack opening displacements v(x). the compressive stress applied in the crack wake to insure l(x)=v(x) are referred to as the contact stresses. ricardo et al. [39] discuss the importance in the determination of materials properties like crack opening and closing stress intensity factor. the development of crack closure mechanisms, such plasticity, roughness, oxide, corrosion, and fretting product debris, and the use of the effective stress intensity factor range, has provided an engineering tool to predict small and large crack growth rate behavior under service loading conditions. the major links between fatigue and fracture mechanics were done by elber [21]. the crack closure concept put crack propagation theories on a firm foundation and l. c. h. ricardo et alii, frattura ed integrità strutturale, 36 (2016) 201-214; doi: 10.3221/igf-esis.36.20 206 allowed the development of practical life prediction for variable and constant amplitude loading, by such as experienced by modern day commercial aircrafts. figure 4: schematic small scale yield model. numerical analysis using finite elements has played a major role in the stress analysis crack problems. swedlow [40] was one of the first to use finite element method to study the elastic-plastic stress field around a crack. the application of linear elastic fracture mechanics, i.e. the stress intensity factor range, k, to the “small or short” crack growth have been studied for long time to explain the effects of nonlinear crack tip parameters. the key issue for these nonlinear crack tip parameters is crack closure. analytical models were developed to predict crack growth and crack closure processes like dugdale [12], or strip yield, using the plasticity induced approach in the models considering normally plane stress or strain effects. schijve [41], discussing the relation between short and long cracks presented also the significance of crack closure and growth on fatigue cracks under services load histories. the ultimate goal of prediction models is to arrive at quantitative results of fatigue crack growth in terms of millimeters per year or some other service period. such predictions are required for safety and economy reasons, for example, for aircraft and automotive parts. sometimes the service load time history (variable amplitude loading) is much similar to constant amplitude loading, including mean load effects. in both cases quantitative knowledge of crack opening stress level sop is essential for crack growth predictions, because keff is supposed to be the appropriate field parameter for correlating crack growth rates under different cyclic loading conditions. the correlation of crack growth data starts from the similitude approach, based on the keff, which predicts that same keff cycles will produce the same crack growth increments. the application of keff to variable amplitude loading require prediction of the variation of sop, during variable amplitude load history, which for the more advanced prediction models implies a cycle by cycle prediction. the fig. 5 shows the different k values. the application of keff is considerably complicated by two problems: (1) small cracks and (2) threshold k values (kth). small cracks can be significant because in many cases a relatively large part of the fatigue life is spent in the small crack length regime. the threshold problem is particularly relevant for fatigue under variable amplitude spectrum, if the spectrum includes many “small” cycles, those ones with small stress/load amplitude. it is important to know whether the small cycles do exceed a threshold k value, and to which extension it will occur. the application of similitude concept in structures can help so much, but the results correlation is not satisfactory and the arguments normally are:  the similarity can be violated because the crack growth mechanism is no longer similar.  the crack can be too small for adopting k as a unique field parameter. l. c. h. ricardo et alii, frattura ed integrità strutturale, 36 (2016) 201-214; doi: 10.3221/igf-esis.36.20 207  keff and others conditions being nominally similar, it is possible that other crack tip aspects also affect crack growth, such as crack tip blunting and strain hardening, schijve45. figure 5: definitions of k values, schijve [41]. newman and armen [42-44] and ohji et al. [45] were the first to conduct the two dimensional analysis of the crack growth process. their results under plane stress conditions were in quantitative agreement with experimental results by elber [21], and showed that crack opening stresses were a function of r ratio (smin/smax) and the stress level (smax/0), where 0 is the flow stress i.e: the average between ys and u (ultimate stress). blom and holm [46] and fleck and newman [47-48] studied crack growth and closure under plane-strain conditions and found that cracks did close but the cracks opening levels were much lower than those under plane stress conditions considering same loading condition. sehitoglu et al. [49] found later that the residual plastic deformations cause the crack closing. mcclung [50-52] performed extensive finite element crack closure calculations on small cracks at holes, and various fatigue crack growth models. solanski et.al [53] found that smax/0 could correlate the crack opening stresses for different flow stresses (0). this average value was used as stress level in the plastic zone for the middle crack tension specimen mcclung [52] found that k analogy, using kmax/k0 could correlate the crack opening stresses for different crack configurations for small scale yielding conditions where k0=o(a) . (k-analogy assumes that the stress-intensity factor controls the development of closure and crack-opening stresses, and that by matching the k solution among different cracked specimens, an estimate can be made for the crack opening stresses.) description of the model compact tension specimen was modeled using a finite element code, msc/patran, r1 [54] and abaqus version 68 [55] used as solver. half of the specimen was modeled and symmetry conditions applied. a plane stress constraint is modeled by the finite element method covering the effects in two dimensional (2d) small scale yielding models of fatigue crack growth under variable spectrum loading, fig. 7, and the boundary conditions are presented in fig. 6. the finite element model has triangle and quadrilateral elements with quadratic formulation and spring elements, spring1, used to node release in crack surface (this element works only in the y direction). fatigue design & evaluation (fd&e) committee from sae (society of automotive engineers) has standard fatigue files. the present work used a standard suspension load history. fig. 7 presents a modified load history, adapted from the fd&e/sae histogram considering only tractive loads. the maximum load used was scaled to produce a kmax  0.6 kic, using eq. (4.1), where kic is the critical stress intensity factor of adopted material in the present study. with the value of kmax from kic computed as mentioned above is computed the maximum load using eq. 3.1 to be applied in the specimens as explained in next. a l. c. h. ricardo et alii, frattura ed integrità strutturale, 36 (2016) 201-214; doi: 10.3221/igf-esis.36.20 208 in the analysis, fatigue crack growth is simulated by releasing the crack tip node at pmin, followed by a single loading cycle pmin  pmax  pmin, fig. 7. the force is divided in nine steps between loads pminpmax and nine steps between the pmax-pmin, in each cycle. the smallest element size, 0.025 mm, was estimated based on the plastic zone size (rp) ahead of the crack tip and computed by eq. (3.2). only the first 20 reverses from load history shown in fig. 7 were used to identify crack opening/closing and retardation effects. max max 1 2 p a k f wbw       (3.1) 2 max1 p y k r            plane stress (3.2) where: kmax= maximum stress intensity factor; pmin= minimum applied load; pmax= maximum applied load; b = specimen thickness; a = crack length; w = width of the specimen; a/w = ratio of the crack length to the specimen width; f(a/w) = characteristic function of the specimen geometry . antunes & rodrigues [56] discuss that numerical analysis of plastic induced crack closing (picc) based on finite element method (fem) consists of discretising and modeling the cracked body having elastic–plastic behaviour, applying a cyclic load, extending the crack and measuring the crack closure level. the finite element mesh must be highly refined near the crack front, with micron scale, in order to model the forward and reversed crack tip plastic zones. the forward plastic zone is made up of the material near the crack tip undergoing plastic deformation at the maximum load, therefore it is intimately related to kmax. the reversed plastic zone encompasses the material near the crack tip undergoing compressive yielding at the minimum load and is related to δk. commercial fe software packages offer tools to deal with elastic– plastic deformation, crack propagation and contact between crack flanks, and are therefore adequate to model picc. however, the numerical models have significant simplifications with respect to real fatigue crack propagation, namely: – discrete crack propagations, of the same size as near crack tip elements, which give fatigue crack growth rates significantly higher than real values; – crack propagation is modeled at a constant load when in reality it occurs continuously during the whole load cycle. in numerical simulations, the crack can be incremented at maximum load [57], at minimum load [58, 59] or at other positions of the load cycle. ogura et al. [59] advanced the crack when the crack tip reaction force reached zero during the load cycle. however, none of these approaches truly represents the fatigue process, where, according to slip models of striation formation, crack extension is a progressive process occurring during the entire load cycle. the proposal to increment at minimum load was designed to overcome convergence difficulties caused by propagating the crack at maximum load. this is unrealistic since the crack is not expected to propagate in a compressive stress field. however, several authors [60, 61] have already found that the load at which the crack increment occurs does not significantly influence crack closure numerical results. under constant amplitude loading, crack tip opening load will typically increase monotonically, with increasing crack growth, until a stabilized value is reached. so, it is important to define the minimum crack extension needed to stabilize the opening level. it is usually sufficient to increase the crack ahead of the monotonic plastic zone resulting from the first load cycle [62,63]. the stress level in the crack tip, fig. 8, must to be positive to characterize the crack opening and negative to characterize the crack closure. antunes & rodrigues [56] consider as basic criteria to determine the crack opening or closing: the first contact of the crack flank, which corresponds to the contact of the first node behind the current crack tip. this is the conventional definition proposed by elber [21] and has been widely used by jiang et al. [64]. l. c. h. ricardo et alii, frattura ed integrità strutturale, 36 (2016) 201-214; doi: 10.3221/igf-esis.36.20 209 in this work the nodes released in the crack tips were located at the minimum load of a cycle to simulate crack growth and will be considered the first contact of the node behind the crack tip, positive stress (+syy) to characterize the crack opening and negative stress (-syy) to characterize the crack closing. figure 8: crack opening and closure criterion [56]. tab. 3 displays the mechanical properties of the simulated material, a low alloy steel, where ys = yield strength; uts = ultimate tensile strength; e = young´s modulus; et = tangential modulus;  = poisson’s ratio. ys (mpa) uts (mpa) e (mpa) et (mpa)  230 410 210 000 21000 0.30 table 3: material properties of a low alloy steel. the dimensions of the compact tension specimen were: b= 3.8 mm; w= 50.0 mm; a/w= 0.26. tab. 4 shows the estimated and used values of the cyclic plastic zone sizes as well as smaller finite element. tab. 5 shows the difference crack propagation rates used in the current work. plastic zone size (mm) smallest finite element size (mm) estimated 0.48 0.048 used 0.10 0.025 table 4: smallest finite element size. model crack propagation rate (mm/cycle) model name 1 0.25 sae0.25 2 0.5 sae0.5 3 0.75 sae0.75 4 1.0 sae1.0 table 5: crack propagation rate. results igs. 9 and 10 present, respectively, op and cl against the numbers of cycles. figs. 11 and 12 present examples of results of post-processing results from model sae0.50 showing the stress field in the region near where the crack opens and closes. f l. c. h. ricardo et alii, frattura ed integrità strutturale, 36 (2016) 201-214; doi: 10.3221/igf-esis.36.20 210 0 10 20 30 40 50 60 70 80 90 2 3 4 5 6 7 8 9 10 number of cycles c ra c k o p e n s tr e s s ( m p a ) sae 0.25 mm sae 0.50 mm sae 0.75 mm sae 1.0 mm figure 9: crack opening stress (σyy+) [57]. figure 10: crack closing stress (σyy-) [57]. discussion of results n the present work was identified how difficult is to determine with proper precision the crack opening or closure. it was necessary to use the iterative process in the crack surface step by step during loading and unloading to find the crack opening or closing as shown in details in ricardo [65]. the retard effect is present in some cycles in special cases where there are overloads. in constant amplitude loading, the effective plastic zone increases with the extension of the crack length; the crack propagation rate has no influence in the quality of results, assuming that it is in respect to the newman [23] recommendation with four elements yielded in the reverse plastic zone. in variable amplitude loading the crack length cannot progress until a new overload occurs or the energy spent during cyclic process creates a new plastic zone and the driving force increases the crack length. the researchers normally work with simple overloads or specific load blocks; this approach can induce some mistakes in terms of results that can be conservative or nonrealistic. fig. 9 shows the effect of different crack propagation rates in opening stress, op. this graph starts in the second cycle because it was not possible identify the crack opening in all models evaluated when the crack opens, because all stresses in the first cycle were positive. in the beginning there is no representative difference in the four first cycles in all crack propagation models. in the fourth to fifth cycle it is possible identify a difference of crack open stress level from model sae2 (crack propagation 0.5 mm/cycle) and the others models. the difference of the crack opening stress level from model sae2 from the others may be related with the overload that the specimen had in the fifth cycle causing the increase of the crack opening stress level to be more representative than in others that suffered the same overload. from the sixth to eight cycles it is possible to identify again little difference in the crack opening stress of the models. the model sae1 (crack propagation 0.025 mm/cycle) has the lower crack opening stress. in the cycles 8 to 10 there is some difference in the crack opening stress, having as principal cause the different plasticity that the models suffered, due to i l. c. h. ricardo et alii, frattura ed integrità strutturale, 36 (2016) 201-214; doi: 10.3221/igf-esis.36.20 211 different crack propagation rate models. model sae2 has the bigger crack opening stress; caused like in the fifth cycle by an overload as in the fifth cycle and again this model had different behavior when compared with others models. figure 11: crack opening stress (σyy+) model sae0.50 [57]. figure 12: crack closing stress (σyy-) model sae0.50 [57]. the model sae3 (crack propagation rate 0.75 mm) has no significant difference in the crack opening stress level during all cycles. this could be a good indication that for a first approach in similar conditions the utilization of this crack propagation rate will provide the behavior material faster under similar load history and specimen. fig. 9 also shows that it is possible to have more different kinds of criteria design. for example for a conservative approach it is possible the utilization of the model sae1 (crack propagation rate 0.25 mm/cycle). crack tip y= 85 mpa surface crack surface crack crack tip y= 103 mpa l. c. h. ricardo et alii, frattura ed integrità strutturale, 36 (2016) 201-214; doi: 10.3221/igf-esis.36.20 212 fig. 10 presents the results from the crack closing stress against numbers of cycles evaluated for the four different crack propagation models considered. it is possible to observe that in the first four cycles there are no significant difference in the crack closing stress in the models studied. in the other cycles the model sae1 (crack propagation 0.25 mm/cycle), has no significant difference of crack closing stress during crack propagation. in fact it is the most conservative model from the four evaluated. during the fourth and sixth cycle the models sae2 (crack propagation model 0.50 mm) and sae3 (crack propagation model 0.75 mm) have no difference in the crack closing stress. the model sae4 (crack propagation 1.0 mm/cycle) has representative difference in the crack closing stress when compared with others models in the cycles due to more residual plasticity in the crack tip. the last representative differences between crack closing stress levels in the models happen during propagation in the cycles eight to tenth. an increase of the crack propagation rate will also increase the crack closing stress. fig. 12 shows that depending on the design criterion it is possible to apply a different crack propagation rate. for example if the criterion is to use a conservative crack closing stress it is recommended utilization of the model sae1 (crack propagation 0.25 mm). the softest model or that one which allows the bigger crack opening and closing stresses is model sae4 (crack propagation model 1.0 cycle/mm). conclusions n this work it was possible to identify the crack opening and closure using the finite element method. in the literature there are few works covering crack propagation simulation with random loads like fd&e loads histories from sae data bank. normally only a few load blocks are used to reduce the complexity; this should provide conservative answers when used to develop structural components. the use of different crack propagation rate in this work shows that for reproducing the effective plastic zone it is possible to use smaller or larger element sizes compared with the irwin equation. to improve the correlation between numerical and experimental data it is necessary to increase the crack length to obtain the same qualitative results that is estimated by the irwin equation. the next step in this work will be to perform some analyses with the same model and load history with different crack propagation rates to identify whether or not the retard effect can be observed. these data will be compared with experimental test and, if necessary, adjustment of the crack propagation model will be done to improve the crack propagation model. references [1] miner, m. a., cumulative damage in fatigue, journal of applied mechanics, asme, usa, 12 (1945) a159-a164. [2] schijve, j., fatigue crack propagation in light alloy sheet material and structures, nlr, report mp195, amsterdam, (1960). [3] stouffer, d. c., williams, j. f., a method for fatigue crack growth with a variable stress intensity factor, eng. fracture mechanics, 11 (1979) 525-536. doi: 10.1016/0013-7944(79)90076-6. [4] ditlevsen, o., sobczyk, k., random fatigue crack growth with retardation, eng. fracture mech., 24(6) (1986) 861878. doi:10.1016/0013-7944(86)90271-7 [5] wei, r. p., shih, t. t., delay in fatigue crack growth, int. journal fracture, 10 (1974) 77-85. doi: 10.1007/bf00955082 [6] paris, p. c., erdogan, f., journal of basic engineering, 85 (1963) 528. [7] head, a. k., the philosophical magazine, 44(7) (1953) 253. [8] dowling, n.e, mechanical behavior of materials: engineering methods for deformation, fracture, and fatigue, third edition, pearson education, inc., usa, (2007). [9] hairman, g. a., provan, j. w., fatigue crack tip plasticity revisited, the issue of shape addressed, theoretical and appl. frac. mech. journal, 26 (1997) 63-79. doi: 10.1016/s0167-8442(96)00036-5. [10] perez, n., fracture mechanics, kluwer academic publishers, new york, usa, (2004). [11] broek, d., elementary engineering fracture mechanics; kluwer academic publishers group, boston, (1982). [12] dugdale, d. s., yielding of steel sheets containing slits, j. mech. phys. solids, 8(2) (1960) 100-104. doi:10.1016/0022-5096(60)90013-2. [13] murthy, a. r. c.; palani, g. s., iyer, n. r., state of art review on fatigue crack growth analysis under variable amplitude loading iei journal, (2004) 118-129. i l. c. h. ricardo et alii, frattura ed integrità strutturale, 36 (2016) 201-214; doi: 10.3221/igf-esis.36.20 213 [14] wheeler, o. e., spectrum loading and crack growth, transactions of the asme series d’, journal of basic engineering, 94 (1972) 181-186. [15] willenborg, j. d.; engle, r. m., wood, h. a., a crack growth retardation model using an effective stress concept, affdl, tm-71-fbr, air force flight dynamics laboratory, wright patterson air force base, oh, (1971). [16] porter, t. r., method of analysis and prediction of variable amplitude fatigue crack growth, eng. fracture mechanics, 4(4) (1972) 717-736. doi:10.1016/0013-7944(72)90011-2. [17] gray, t. d., gallagher, j. p., predicting fatigue crack retardation following a single overload using a modified wheeler model, astm stp 590, (1976). doi: 10.1520/stp590-eb. [18] gallagher, j. p., hughes, t. f., influence of the yield strength on overload fatigue crack growth behavior of 4340 steel, affdl – tr-74-27, air force flight dynamics laboratory, wright patterson air force base, oh, (1974). [19] johnson, w. s., multi-parameter yield zone model for predicting spectrum crack growth, astm stp 748, (1981) 85102. doi: 10.1520/e0748-02r08. [20] chang, j. b., hiyama, r. m., szamossi, m., improved methods for predicting spectrum loadings effects, afwal-tr81-3092, air force flight dynamics laboratory, wright patterson air force base, oh, (1984). [21] elber, w., the significance of fatigue crack closure, astm stp 486, (1971) 230242. doi: 10.1520/stp486-eb. [22] bell, p. d., creager, m., crack growth analyses for arbitrary spectrum loading, affdl-tr-74-129, air force flight dynamics laboratory, wright patterson air force base, oh, (1974). [23] newman, j. c., a finite element analysis fatigue crack closure, nasa tm x 72005, nasa, hampton, va, (1975). [24] dill, h. d., saff, c. r., spectrum crack growth prediction method based on crack surface displacement and contact analyses, fatigue crack growth under spectrum loads, astm stp, 595 (1976) 306–319. doi: 10.1520/stp595-eb. [25] kanninnen, m. f., atkinson, c., feddersen, c. e., a fatigue crack growth analysis method based on a single representation of crack tip plasticity, astm stp, 637 (1977) 122-140. doi: 10.1520/stp637-eb. [26] budianski, b., hucthinson, j. w., analysis of closure in fatigue crack growth, journal of applied mechanics, 45 (1978) 267-276. doi 10.1115/1.34.24286. [27] de koning, a. u., a simple crack closure model for predictions of fatigue crack growth rates under variable amplitude loading, astm stp, 743 (1981) 63-85. [28] corbly, d. m., packman, p. f., on the influence of single and multiple peak overloads on fatigue crack propagation in 7075-t6511 aluminum, eng. fracture mech., 5 (1973) 479-497. doi:10.1016/0013-7944(73)90034-9. [29] schijve, j.; brock, d., de rigle, p., nlr, report m2094, amsterdam, (1962). [30] hardrarth, h. f., mcevily, a . t., proc. crack propagation symposium, cranfield, 1 (1961). [31] jonds, d., wei, r. p., an exploratory study of delay effects in fatigue crack growth, int. j. fracture mechanics, (1971) 7. [32] von ewu, e., hertzberg, r., roberts, r., delay defects in fatigue crack propagation, nat. symposium f.m., (1971) 7. [33] hudson, c. m., effect of stress ratio on fatigue-crack growth in 7075-t6 and 2024-t3 alumina-alloy specimens, nasa, tnl-5390, (1969). [34] crooker, t. w., effect of cycling on fatigue grade growth in high strength alloys, nrl report 7220, (1971). [35] hudson, c.m., hardrath, h. f., effects of changing stress amplitude on the rate of fatigue-crack propagation in two aluminum alloys, nasa tn d-960, (1961). [36] mcmillan, j. c., pelloux, r. m., astm stp, 415 (1966) 505. doi: 10.1520/stp415-eb. [37] dill, h. d., saff, c. r., spectrum crack growth prediction method based on crack surface displacement and contact analyses, fatigue crack growth under spectrum loads, astm stp, philadelphia, pa, 595 (1976) 306–19. doi: 10.1520/stp595-eb. [38] newman, j. c. jr., a crack closure model for predicting fatigue crack growth under aircraft spectrum loading. in: chang jb, hudson cm, editors. methods and models for predicting fatigue crack growth under random loading, philadelphia, pa astm stp, 748 (1981) 43–84. doi: 10.1520/stp748-eb. [39] ricardo, l. c. h.; pimenta, p. m. & spinelli, d., crack closure simulation by finite element. in, blom, a.f. fatigue 2002, west midlands, emas, 4/5 (2002) 2293 – 2300. [40] swedlow, j. l., the thickness effect and plastic flow in cracked plates, phd thesis, california institute of technology, pasadena, usa, (1965). [41] schijve, j., observations on the prediction of fatigue crack growth propagation under variable amplitude loading, astm stp, 595 (1979) 3-23. doi: 10.1520/stp595-eb. [42] newman j. c. jr., finite element analysis of fatigue crack propagation, including the effect c-(t) of crack closure, phd thesis, virginia polytechnic institute, (1974). l. c. h. ricardo et alii, frattura ed integrità strutturale, 36 (2016) 201-214; doi: 10.3221/igf-esis.36.20 214 [43] newman, j. c. jr., armen, h. jr. elastic-plastic analysis of fatigue crack under cyclic loading, aiaa journal, 13 (1975) 1017-1023. doi: 10.2514/3.60499. [44] newman, j. c. jr., a finite element analysis of fatigue crack closure, astm, 490 (1976) 281-301. doi: 10.1520/stp490-eb. [45] ohji, k., ogura, k. ohkubo, y., cyclic analysis of a propagation crack and its correlation with fatigue crack growth; eng. fracture mechanics, 7 (1975) 457-464. doi: 10.1016/0013-7944(75)90046-6. [46] blom, a. f., holm, d. k., an experimental and numerical study of crack closure; eng. fracture mechanics, (1985) 907-1011. doi: 10.1016/0013-7944(85)90039-6. [47] fleck, n. a., finite element analysis of plasticity induced crack closure under plane strain conditions, eng. fracture mechanics, 25 (1986) 441-449. doi:10.1016/0013-7944(86)90258-4. [48] fleck, n. a., newman, j. c. jr, analysis of crack closure under plane strain conditions , astm stp, 982 (1988) 319341. doi: 10.1520/stp982-eb. [49] sehitoglu, h. gall, k., garcia, a. m., recent advances in fatigue crack growth modeling, int. journal of fracture, 80(2) (1996) 165-192. doi: 10.1007/bf00012668. [50] mcglung, r. c., sehitoglu, h., finite element analysis of fatigue crack closure – numerical results, eng. fracture mechanics, 33 (1989) 253–272. doi: 10.1016/0013-7944(89)90028-3. [51] mcglung, r. c., finite element modeling of fatigue crack growth – theoretical concepts and numerical analysis of fatigue, in: blom a, beevers, c. editors, west midlands, emas, (1992) 153-172. [52] mcglung, r. c., finite element analysis of specimen geometry effects on fatigue crack closure, fatigue fract. eng. mater. structures, 17 (1994) 861-872. doi: 10.1111/j.1460-2695.1994.tb00816.x. [53] solanki, k., daniewicz, s. r., newman, jr j. c., finite element modelling of plasticity-induced crack closure with emphasis on geometry and mesh refinement effects. eng. fracture mechanics, 70 (2003) 1475–89. doi:10.1016/s0013-7944(02)00168-6. [54] msc/patran r1, usa, (2008). [55] abaqus, v6.3, hibbitt, karlsson, sorensen, inc., providence, ri, (2002). [56] antunes, f.v., rodrigues, d.m, numerical simulation of plasticity induced crack closure: identification and discussion of parameters, eng. fracture mechanics, 75 (2008) 3101-3120. doi:10.1016/j.engfracmech.2007.12.009. [57] pommier, s., plane strain crack closure cyclic hardening, eng. fracture mechanics, 69(3) (2002) 25–44. doi:10.1016/s0013-7944(01)00061-3. [58] ogura, k., ohji, k., fem analysis of crack closure and delay effect in fatigue crack gowth under variable amplitude loading. eng. fracture mechanics, 9 (1977) 471–80. doi: 10.1016/0013-7944(77)90039-x. [59] ogura, k., ohji, k., honda, k., influence of mechanical factors on the fatigue crack closure. advances in research on the strength and fracture of materials, in: proceedings of the fourth international conference on fracture mechanics, waterloo, canada, 2d (1977) 1035–1047. [60] solanki, k., daniewicz, s.r., newman, jr. j.c., finite element modelling of plasticity-induced crack closure with emphasis on geometry and mesh refinement effects, eng. fracture mechanic, 70 (2003) 1475–89. doi:10.1016/s0013-7944(02)00168-6. [61] mcclung, r.c., sehitoglu, h., on the finite element analysis of fatigue crack closure-1: basic modelling issues. eng. fracture mechanics, 33(2) (1989) 237–252. doi: 10.1016/0013-7944(89)90027-1. [62] antunes, f.v., borrego, l.f.p., costa, j.d., ferreira, j.m., a numerical study of fatigue crack closure induced by plasticity, fatigue fract. eng. mater. structures, 27(9) (2004) 825–36. doi: 10.1111/j.1460-2695.2004.00738.x. [63] wu, j., ellyin, f., a study of fatigue crack closure by elastic-plastic finite element analysis for constant-amplitude loading. int. journal of fracture, 82 (1996) 43–65. doi:10.1007/bf00017863. [64] jiang, y., feng, m., ding, f., a re-examination of plasticity-induced crack closure in fatigue crack propagation, international journal of plasticity, 21 (2005) 1720–1740. doi:10.1016/ j.ijplas.2004.11.005 [65] ricardo, l.c.h., crack propagation by finite element analysis in automotive components, sae brazil conference, sao paulo, brazil, (2010) 36-0003i. << /ascii85encodepages false /allowtransparency false /autopositionepsfiles true /autorotatepages /none /binding /left /calgrayprofile (dot gain 20%) /calrgbprofile (srgb iec61966-2.1) /calcmykprofile (u.s. web coated \050swop\051 v2) /srgbprofile (srgb iec61966-2.1) /cannotembedfontpolicy /error /compatibilitylevel 1.4 /compressobjects /tags /compresspages true /convertimagestoindexed true /passthroughjpegimages true /createjobticket false /defaultrenderingintent /default /detectblends true /detectcurves 0.0000 /colorconversionstrategy /cmyk /dothumbnails false /embedallfonts true /embedopentype false /parseiccprofilesincomments 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can be opened with acrobat and adobe reader 5.0 and later.) >> /namespace [ (adobe) (common) (1.0) ] /othernamespaces [ << /asreaderspreads false /cropimagestoframes true /errorcontrol /warnandcontinue /flattenerignorespreadoverrides false /includeguidesgrids false /includenonprinting false /includeslug false /namespace [ (adobe) (indesign) (4.0) ] /omitplacedbitmaps false /omitplacedeps false /omitplacedpdf false /simulateoverprint /legacy >> << /addbleedmarks false /addcolorbars false /addcropmarks false /addpageinfo false /addregmarks false /convertcolors /converttocmyk /destinationprofilename () /destinationprofileselector /documentcmyk /downsample16bitimages true /flattenerpreset << /presetselector /mediumresolution >> /formelements false /generatestructure false /includebookmarks false /includehyperlinks false /includeinteractive false /includelayers false /includeprofiles false /multimediahandling /useobjectsettings /namespace [ (adobe) (creativesuite) (2.0) ] /pdfxoutputintentprofileselector /documentcmyk /preserveediting true /untaggedcmykhandling /leaveuntagged /untaggedrgbhandling /usedocumentprofile /usedocumentbleed false >> ] >> setdistillerparams << /hwresolution [2400 2400] /pagesize [612.000 792.000] >> setpagedevice shot peening processes to obtain nanocrystalline surfaces in metal alloys: s.k. kudari et alii, frattura ed integrità strutturale, 7 (2009) 57-64; doi: 10.3221/igf-esis.07.04 57 experimental investigation on possible dependence of plastic zone size on specimen geometry s. k. kudari school of mechanical engineering, howard college campus, university of kwazulu-natal, durban4041, south africa. b. maiti department of mechanical engineering, indian institute of technology, kharagpur-721 302, india. k. k. ray department of metallurgical and materials engineering, indian institute of technology, kharagpur-721 302, india. abstract. in this investigation the extent of the plastic zone size ahead of a crack-tip in single edge notched tension (sent), compact tension (ct) specimens has been examined experimentally by micro-hardness technique and by elastic-plastic finite element analyses at different applied load levels. the magnitudes of the plastic zone size (pzs), rp ahead of crack-tip in the investigated specimens have been compared using normalized j-integral (j/aσy, where, a-crack length and σy-yield stress of the material). the results show the dependence of pzs on specimen geometry due to varied in-plane crack-tip constraint. the results also demonstrate that the existing analytical models do not explain the experimental results of pzs satisfactorily. keywords. crack-tip plasticity; elastic-plastic material, specimen geometry, micro-hardness technique introduction he studies on crack-tip plastic zones are of fundamental importance in describing the process of failure from a macroscopic viewpoint and in formulating various fracture criteria. the standard astm procedure astm e182099a [1] for determining fracture toughness criteria of materials require knowledge of the extent of plastic zone occurring at the crack-tips. wang [2] has suggested that plastic deformation may be the main mechanical driving force for crack propagation. park et al. [3] have considered that size of crack-tip plastic zone is a potential epfm parameter connecting direct physical meaning to describe crack propagation. in epfm, it is also known that the load intensity in ductile fracture measured as j-integral alone cannot describe the stress state accurately. this discrepancy is commonly referred as constraint issues in fracture. yuan and brocks [4] have considered that constraint literally is a structural obstacle against plastic deformation, which is induced mainly by geometrical and physical boundary conditions. with detailed finite element analyses they have also argued that constraint effects in a fracture specimen depend on the plastic zone size (pzs). recently, kudari et al. [5] have theoretically studied the effect of specimen geometry on plastic zone size using the j-integral to explore the constraint effects. the authors have suggested that the results can be used to obtain a specimen size requirement of jc test specimen independent of specimen geometry. the theoretical analyses of kudari et al. [5] related to constraint effects and plastic zones have been carried out on different types of specimen configurations. these results demand substantiation with some experimental measurements of pzs. a number of investigations are available on the experimental estimation of plastic zones in metallic materials as cited in the article of uguz and martin [6]. but, the available results from these investigations cannot be used in a simplified manner to support the theoretical work on pzs presented by kudari et al. [5]. the details of deformation behaviour together with determination of pzs are required to compare estimates made from theoretical analysis and experimental work. in this study an effort is made to generate experimental and theoretical estimates of pzs pertaining to the same t http://dx.medra.org/10.3221/igf-esis.07.04&auth=true http://www.gruppofrattura.it s. k. kudari et alii, frattura ed integrità strutturale, 7 (2009) 57-64; doi: 10.3221/igf-esis.07.04 58 material in two specimen geometry having varied a/w ratio to substantiate the theoretical analysis of kudari et al. [5]. a comparative assessment of the experimental measurements of pzs with the results computed by elastic-plastic finite element analysis (fea) and earlier analytical formulations [7, 8, 9] has been also carried out. experimental commercial interstitial free (if) steel has been selected for experimental determination of plastic zones in the present investigation. the if steel has been obtained in the form of 3 mm thick sheets in the cold rolled state as courtesy of tata iron and steel co. ltd., jamshedpur, india. the chemical composition of the material is given in tab. 1. in the present experimental investigation, micro-hardness technique [6] is used for estimation of plastic zone size. hence, it was necessary to relieve the surface stresses in the as received material due to cold rolling, and material is given a heat treatment. all specimens of the interstitial free steel for various investigations were subjected to stress-relief annealing. the stress relief annealing consisted of soaking the specimens at 700 ± 2°c for 1 hour in a resistance heating furnace followed by air-cooling. the microstructure of the steel was found to exhibit equiaxed polygonal ferritic structure having average size of 27.1 ± 2.2 µm, as determined by linear intercept method. the single-phase structures of this material constitute the selection basis because this makes application of the microhardness technique amenable for determining plastic zone size. element weight percentage c 0.003 mn 0.110 si 0.009 cr 0.027 ni 0.017 mo 0.002 s 0.007 p 0.012 al 0.040 cu 0.006 nb 0.001 ti 0.055 v 0.001 n 30 ppm fe bal table 1: chemical composition of the interstitial free steel used in the analysis tensile tests following astm procedure, astm e8-00 [10] were carried out on flat specimens of gauge length 25 mm and width 10 mm with the help of a 50 kn capacity screw driven shimadzu universal testing machine (model: ag5000g) at ambient temperature (30°c) using a cross head speed of 0.5 mm/min. the crosshead speed corresponds to nominal strain rate of 3.33x10-4s-1. two tensile tests were carried out to obtain the average tensile properties of the selected steel. the micro-hardness of the material was determined with the help of a micro-hardness tester (leco, model: dm400) using a load of 10 gmf for 15 sec duration. the average micro-hardness value was estimated from 25 randomly taken readings. two types of specimens were fabricated for the measurement of plastic zone size. these are: (a) single edge notched tensile (sent) and (b) compact tension (ct) specimens. all the sent specimens were fabricated with width (w)=25 mm and height (h) = 100 mm. the value of a/w considered in this study are 0.25 and 0.50. the ct specimens were made following the astm standard [1] with w = 25 mm and a/w = 0.5. the specimen surfaces were grinded (before heat treatment) to facilitate a fine polishing, which is needed for measuring microhardness. because of surface grinding, the final thickness of all the specimens was reduced to 2.7 mm. typical configurations of sent and ct specimens used in this analyses are shown in fig.1. a http://dx.medra.org/10.3221/igf-esis.07.04&auth=true http://www.gruppofrattura.it s.k. kudari et alii, frattura ed integrità strutturale, 7 (2009) 57-64; doi: 10.3221/igf-esis.07.04 59 figure 1: configurations of sent and ct specimens used for plastic zone study. notches were inserted in the fabricated specimen blanks by wire electro discharge machining (edm). the notch length in each specimen was measured using the micrometer attached to the specimen stage of the vickers microhardness testing machine. the configuration of the notch-tip was recorded at x200 with the help of a ccd camera attached to an optical microscope. the notch-tip root radii were then measured from these images with the help of an image analyzer. the notch radius measured was 180 µm. one side of the specimen was finely polished around the crack-tip in order to facilitate measurements of microhardness and to observe the plastic spread near the crack-tip. this was done by successively grinding the specimen on finer silicon abrasive papers, followed by final polishing on a velvet cloth smeared with 0.25 µm diamond paste. plastic zone in each of the specimens was introduced by applying pre-selected monotonic tensile loads at a crosshead speed of 0.05 mm/min at room temperature (30oc). a number of such tests were carried out on sent and ct specimens at different tensile loads to introduce varied sizes of plastic zones. the applied tensile loads corresponded to stress ratio (σ/σy) of 0.4-0.85 for sent specimens and 0.3-0.75 for ct specimens, where σ and σy are applied stress and yield stress of a material respectively. the applied stress σ for sent and ct specimen have been computed by expressions cited in the earlier investigation of [11]. to evaluate the plastic zone size ahead of crack-tip (at θ = 0o plane), a series of micro-hardness indentations were made ahead of each crack-tip with the help of a vickers pyramid indenter using a load of 10 gmf for 15 sec duration. the distance between two successive microhardness indentations (during plastic zone estimation) was kept approximately 50 µm so that there is no interaction between the deformation zones of the successive indentations. as the material is strain hardening type, because of large strain ahead of the crack-tip the hardness at the tip of the crack is expected to be higher and it gradually decreases as magnitude of strain reduces along the ligament ahead of crack-tip. the micro-hardness tests were terminated at a distance from the crack-tip where the hardness readings were found to have reached a saturation plateau equivalent to the average microhardness value of the material. finite element analysis series of stress analyses by finite element method (fem) have been conducted on single edge notched tension (sent) and compact tension (ct) specimens (fig.1) at various applied load steps. all the finite element computations were performed using general-purpose finite element code ansys [12]. due to the symmetry of the specimens under mode-i loading, only one half of the sent and ct specimens were considered in the analyses. as specimen thickness is 2.7 mm, it considered to carry out plane stress fe analysis. two-dimensional fe mesh was generated using eight-noded isoparametric quadrilateral elements, considering plane stress condition with specimen thickness input. the number of elements used for sent and ct specimens were 1451 and 864 respectively. the load was applied in the form of pressure (uniform applied stress) on the surface parallel to the ligament for sent specimen. but concentrated point loads were applied for ct specimen model to simulate pin-loading condition in this specimen. a http://dx.medra.org/10.3221/igf-esis.07.04&auth=true http://www.gruppofrattura.it s. k. kudari et alii, frattura ed integrità strutturale, 7 (2009) 57-64; doi: 10.3221/igf-esis.07.04 60 the sequential developments of plastic zone in the selected specimens were evaluated at different applied loads corresponding to stress ratio (σ/σy) ranging between 0.1 and 0.85. the boundary separating the plastic enclave from the elastic bulk was obtained from the iso-stress contours of effective stress (σeff) estimated using von mises yield criterion following the procedure adopted by gdoutos and papakaliatakis [13]. the elastic-plastic fe analysis is performed considering the material behavior to be multilinear kinematic hardening pertaining to if steel. the newton-rapson procedure in which stiffness matrix is updated for every equilibrium iterations was used for the nonlinear convergence. in these analyses the elastic modulus and poisson’s ratio of the material has been taken as 194 gpa and 0.3, whereas the yield strength and the true stress-strain curve were taken from experimental results of tensile test. the plastic part of the true stress-strain curve (fig.2) was divided into twenty segments for the multilinear hardening model. the magnitude of j-integral was evaluated for a path at a specific loading condition and for a particular specimen geometry using the expression proposed by rice [14] ∫ γ       ∂ ∂ −= ds x u twdyj ii (1) w= ∫ ε εσ 0 ijij d ; jiji nt σ= where w = strain energy density, ti = traction vector, u i = displacement vector, s = element of arc length along contour γ the contour around the crack-tip was defined by four corner nodes in this analysis domain. the average value of j at a particular loading magnitude was estimated by considering four different paths around the crack-tip. results and discussion he estimated magnitudes of the tensile properties and hardness of the investigated steels are summarized in tab. 2. the estimated 2% yield strength, ultimate tensile strength and percentage of elongation of the investigated steels as indicated in tab. 2 are in close agreement with some earlier reported results [15, 16] for if steel. the true stress (σ) – true strain (ε) curve for the investigated material up to a maximum load is shown in fig.2, which is used for elastic-plastic fe analysis. the experimental determination of plastic zone has been carried out by examining the variation of microhardness with distance ahead of crack-tip along θ =0o plane. a typical plot obtained for sent specimen with a/w=0.25 and σ/σy = 0.60 is shown in fig.3 in which the average microhardness of the material with its upper and lower bounds are also indicated. the result in this figure indicates that the values of micro-hardness (vickers hardness, vh) continuously decrease with increase in distance ahead of a crack-tip to a saturation plateau. the extent of plastic zone ahead of a crack-tip is considered to be the distance between the location of the crack-tip and the point where microhardness of the material reaches the saturation plateau in microhardness vs. distance curve. σys (mpa) σuts (mpa) %el vhn 125.40 273.10 51.12 147 table.2 mechanical properties of the interstitial free steel used in the analyses. (σysyield strength, σutsultimate tensile strength, %elpercentage elongation, vhn vickers hardness number) a few earlier investigators [17, 18, 19] have employed graphical method to locate the boundary of the plastic zone from the microhardness-distance plots. the obtained experimental data of microhardness vs. distance (fig.3) exhibit considerable scatter, and as a consequence application of the graphical method to demarcate the plastic zone boundary in an unambiguous manner is difficult. a simple analytical procedure was thus developed to locate the boundary of the plastically deformed regimes to overcome the above problem. t http://dx.medra.org/10.3221/igf-esis.07.04&auth=true http://www.gruppofrattura.it s.k. kudari et alii, frattura ed integrità strutturale, 7 (2009) 57-64; doi: 10.3221/igf-esis.07.04 61 figure 2: true stress vs. true strain curve for investigated if steel. figure 3: typical plot of the variations of microhardness values ahead of a crack-tip. the microhardness values in the saturation plateau were found to fluctuate within some definite limits for the if steel. the fluctuation of microhardness values of a material is an intrinsic phenomenon; never the less this was examined in the following way. the average microhardness values of these steels were separately determined on unloaded samples. these experiments yielded average microhardness of if steel 147 ± 5 vh. when the mean value was marked on the microhardness-distance plots, the saturation plateau could be delineated, but the point, which demarcates the elasticplastic boundary, could not be ascertained with certainty. next, each set of data was subjected to polynomial fit with polynomial equations of different degrees. it was found that as the degree of the polynomial increases, the magnitudes of the regression coefficients also increase. but while carrying out this exercise, it was found that the improvement in the magnitude of the regression co-efficient was marginal for fitted polynomials with degrees greater than six. hence, a sixth degree polynomial was selected to describe the obtained variation of micro-hardness with distance. typically, such best-fit curve is also shown in fig.3. the first intersection of the sixth degree polynomial with mean value of the saturation plateau was located. the distance between the crack-tip and this point was considered as the extent of plastic zone size (rp) in a specimen as shown in fig.3. the degree of scatter associated with micro-hardness values measured in plastic zone was found to be ± 5%. this scatter of microhardness is in close agreement with the scatter reported by ray and mondal [20]. in order to study the effect of specimen geometry and a/w ratio on plastic zone size a few experiments were carried out to reveal the microhardness variation ahead of crack-tip up to the end of ligament. a typical such plot for ct specimen with a/w=0.5 is shown in fig.4. it is noted from this figure that microhardness first decreases to a plateau and again increases up to the end of the ligament. the increase of microhardness near the ligament end of the specimen is due to the existence of compressive plastic zone [21] due to bend loading. because of development of compressive plastic zone in specimens with higher a/w ratio, the growth of crack-tip plastic zone size gets hindered. the development of compressive plastic zone depends on the specimen geometry and loading. thus it can be concluded that the magnitude of pzs in a material is significantly influenced by the type and the geometry of the specimen selected for the investigation. the shape of plastic enclaves using fea has been obtained at different load steps and the extent of plastic zone size, rp, at θ =0o have been estimated. the method of to estimate the value of rp by using fea outputs of the plastic enclave is discussed elsewhere [5]. the magnitudes of rp estimated by microhardness technique in ct and sent specimens (a/w=0.50) of if steel were compared with the theoretically estimated magnitudes of rp in fig.5. this plot helps to infer that the experimental results of pzs are in good agreement with the results estimated by elasticplastic fea. commonly, experimentally determined plastic zone sizes are compared with those derived from the existing analytical models [7, 8, 9]. these analytical models use normalized applied stress (σ/σy) as a reference parameter. the http://dx.medra.org/10.3221/igf-esis.07.04&auth=true http://www.gruppofrattura.it s. k. kudari et alii, frattura ed integrità strutturale, 7 (2009) 57-64; doi: 10.3221/igf-esis.07.04 62 variation of rp/a against σ/σy as obtained from these analytical models were also computed and the results are superimposed in fig.5. it is clear from all the results depicted in fig.5 that: (a) none of the analytical models satisfactorily explain the present experimental results and (b) elastic-plastic fea describes the experimental results in the best manner for the entire range of investigation. figure 4: typical variation of microhardness along the entire ligament of a ct specimen. figure 5: comparison of the experimental and fea results with various analytical methods. all the experimental results on pzs evaluated in the present investigation on if steel along with the fe results are compiled based on normalized j (j/aσy) and normalized σ (σ/σy) in fig.6 and fig.7 respectively. these figures shows that the experimental results are in good agreement with the fe results plotted against both the reference parameters. these plots infer that the experimental results of pzs are in excellent agreement with the results of fea when examined with respect to any of the reference parameters at lower applied stress or j-integral levels. at higher applied stress or j levels it is observed that experimental measurements of pzs are marginally lower than that of fea in the investigated steel. this may be possibly attributed to the following reasons: (i) interaction of compressive plastic zone with the crack-tip plastic zone and (ii) measurement difficulties. figure 6: variation normalized plastic zone size (rp/a) estimated by microhardness technique and fea vs. normalized j-integral (j/aσy) in sent and ct specimens figure 7: variation normalized plastic zone size (rp/a) estimated by microhardness technique and fea vs. normalized applied stress (σ/σy) in sent and ct specimens. http://dx.medra.org/10.3221/igf-esis.07.04&auth=true http://www.gruppofrattura.it s.k. kudari et alii, frattura ed integrità strutturale, 7 (2009) 57-64; doi: 10.3221/igf-esis.07.04 63 the conventional analysis based on applied stress (fig.7) illustrates that there is good amount of deviation in the results on different specimen geometry, which does not allow one to satisfactorily explain the effect of geometry on pzs. on the other hand, the variation of rp/a with j/aσy (fig.6) shows that the nature of growth of pzs in the two types of specimens in both the investigated steels is almost identical up to a particular magnitude of j/aσy, beyond which the specimen geometry influences the nature of variation of rp/a, as obtained in the investigation of kudari et al. [5]. the critical value of up to which rp/a is similar in sent and ct specimens is ≅ 0.0035. these results elucidate that the development of plastic zone size in a specimen is primarily affected by the specimen geometry and a/w ratio due to varied in-plane constraint [4]. the present experimental results on pzs thus validate the theory proposed by kudari et al. [5] that the study of plastic zones made with respect to normalized j (j/aσy) yield better analysis of the results. the pzs results studied in this manner gives clear idea of geometry dependency and can be used for constraint analysis and to obtain specimen size requirements for fracture test independent of geometry. conclusions n this work a simple procedure for demarcating the location of elastic-plastic boundary in the microhardness vs. distance plot ahead of a crack-tip has been suggested. it has been shown that the experimental results of pzs for interstitial free steel are in excellent agreement with the elastic-plastic fe analysis. the experimental results obtained validates the theoretical investigation of kudari et al. [5], which can be used for to obtain specimen size requirements for fracture test independent of geometry. acknowledgements one of the present authors dr s. k. kudari would like to thank the department of materials and metallurgical engineering, indian institute of technology, kharagpur, india, for providing laboratory facilities to carry out this work. references [1] astm e1820 -99a, 1999. standard test method for measurement of fracture toughness, american society for testing and materials, philadelphia. [2] g. s. wang, engineering fracture mechanics, 46 (1993) 909-930. [3] park, heung-bae, kim, kyung-mo, lee, byong-whi., international journal of pressure vessels & piping, 68 (1996) 279-285. [4] h. yuan, w. brocks, journal of the mechanics physics solids, 46 (1998) 219-241. [5] s. k. kudari, b. maiti, k.k. ray, journal of strain analysis for engineering design, 42 (2007) 126-137. [6] a. uguz, j. w. martin, materials characterization, 37 (1996) 105-118. [7] g.r. irwin, proc 7th sagamore ordinance mater. res. conf., new york, iv (1960) 63-77. [8] d.s. dugdale, journal of the mechanics physics solids, 8 (1960) 100-104. [9] d. kujawski, f. ellyn, engineering fracture mechanics, 25 (1986) 229-236. [10] astm e8-00, 2000. standard test method for tension testing of metallic materials, american society for testing and materials, philadelphia, pennsylvania. [11] a.h. priest, journal of strain analysis for engineering design, 10 (1975) 225-232 [12] ansys version 9, 2004. swanson analysis systems, ansys inc., canonsbarg pa, usa [13] e.e. gdoutos, g. papakalitakis, international journal of fracture, 32 (1987) 143-156. [14] j.r rice, journal of applied mechanics transactions of asme, 35 (1968) 379-386. [15] r. mendoza, m. alanis, j. huante, c. gonzalez-rivera, j.a. juarez-islas, journal of materials processing and technology, 101 (2000) 238-244. [16] r. mendoza, m. alanis, j. huante, c. gonzalez-rivera, j.a. juarez-islas, materials science and engineering a, 276 (2003) 203-209. [17] c. bathias, r.m. pelloux, metallurgical transactions, 4 (1973) 1265-1273. [18] s.i. kwun, s.h. parks, scripta metallurgica, 21 (1987) 797-800. [19] c. loye, c. bathias, d. retali j. c. devux. astm-stp 811 (1983) 427-444. i http://dx.medra.org/10.3221/igf-esis.07.04&auth=true http://www.gruppofrattura.it s. k. kudari et alii, frattura ed integrità strutturale, 7 (2009) 57-64; doi: 10.3221/igf-esis.07.04 64 [20] k.k. ray, d. mondal, metallurgical transactions, 23a (1992), 3309-3315. [21] r.h. dodds jr, t.l. anderson, m.t. kirk, international journal of fracture, 48 (1991) 1-22. http://dx.medra.org/10.3221/igf-esis.07.04&auth=true http://www.gruppofrattura.it vhn shot peening processes to obtain nanocrystalline surfaces in metal alloys: q.-c. li et alii, frattura ed integrità strutturale, 44 (2018) 35-48; doi: 10.3221/igf-esis.44.04 35 effect of inter-cluster interference on fracture morphology in multi-cluster staged fracturing for shale reservoir qing-chao li, yuan-fang cheng*, dong-xian zhou, qiang li, ubedullah ansari school of petroleum engineering, china university of petroleum (east china), qingdao, shandong 266580, china. b16020053@s.upc.edu.cn, yfcheng@upc.edu.cn abstract. multi-cluster staged fracturing technology is an effective measure to stimulate the reservoir properties. however, the inter-cluster interference effect is obvious when the cluster spacing is very narrow, which seriously affects the effect of fracturing. in order to understand the interference among fracturing clusters within the single fracturing section of the shale horizontal wells during multi-cluster staged fracturing, a finite element model is developed by using abaqus finite element simulation software. on this basis, the influences of factors on the fracture morphology are studied. the simulation results have shown that the cluster spacing is the most important factor affecting inter-cluster interference. with the increase in the distance between adjacent clusters, the interference among the fracturing fractures decreases and the propagation of different fractures become homogeneous or similar. moreover, the increase in the elastic modulus of the shale formation promotes the propagation of the fractures longitudinally, but it hinders the crack opening of the fracture laterally. in addition, properly increasing the injection rate of fracturing fluid during fracturing is more advantageous for obtaining long and wide fractures. besides, the effect of the fracturing fluid viscosity on fracture width is greater than that on the fracture half-length. the simulation results show the existence of inter-cluster interference comprehensively, which can provide a reference for the design and optimization of multi-cluster staged fracturing to some extent. keywords. multi-cluster staged fracturing; inter-cluster interference; shale gas reservoir; finite element method. citation: li, q. c., cheng, y. f., zhou, d. x., li, q., ansari, u., effect of inter-cluster interference on the fracture morphology in multi-cluster staged fracturing for shale reservoir, frattura ed integrità strutturale, 44 (2018) 35-48. received: 02.12.2017 accepted: 28.01.2018 published: 01.04.2018 copyright: © 2018 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. introduction ydraulic fracturing technology is mainly used for stimulating reservoir properties, and thus promoting the production of oil and gas resources, especially unconventional oil and gas resources such as tight gas and shale gas. over the past few decades, hydraulic fracturing technology has made considerable progress and has been h q.-c. li et alii, frattura ed integrità strutturale, 44 (2018) 35-48; doi: 10.3221/igf-esis.44.04 36 widely used in the development of unconventional resources [1,2], in spite of the fact that its potential environmental impact is gradually attracting attention [3]. with the rapid growth in global energy demand, unconventional oil and gas resources that exist in reservoirs with low permeability, such as shale gas and tight gas, have been under unprecedented exploration and development. the efficient development of unconventional oil and gas resources in the future depends on such factors as resources, technologies and markets [4]. both the practical production and the numerical simulations have shown that the combination of horizontal well drilling technology and hydraulic fracturing technology will greatly improve the production of unconventional oil and gas resources [5-10]. in the early 1990s, hydraulic fracturing technology began to be used in the development of natural gas in the barnett shale, texas, united states. according to u.s. energy information administration (eia) statistics, 85% of the production wells in the united states are currently being developed with horizontal well fracturing technology, and the stimulation effect is significant [11]. in addition, the statistical results also show that the crude oil production from fractured wells accounts for more than 1/2 of the total crude oil production, and the gas produced by fracturing wells even reaches more than 2/3 [12]. although relevant studies have shown that increasing the design density of perforation is an effective way to improve the productivity of shale gas, an increase in the number of hydraulic fractures will affect the productivity increase of a single fracture. therefore, the number of fractures within the single fracturing section should not increase infinitely during the multi-cluster staged fracturing operation, and the determination of the cluster spacing becomes the challenge of fracturing design [13]. until now, some scholars have conducted thorough studies on the mechanical description of the multi-cluster staged fracturing process in shale horizontal wells, which mainly focus on two aspects: initiation and propagation of cracks and reorientation of fractures. fig.1 shows the initiation and propagation of hydraulically induced fracture during hydraulic fracturing. zhang guangming et al. analyzed the factors affecting the fracture propagation of hydraulic fracturing using the three-dimensional fluid-solid coupling model. it was found that factors such as in-situ stress, initial pore pressure and fluid leakage coefficient all have an impact on the fracture propagation in hydraulic fracturing [14]. pan et al analyzed factors affecting both the location and the pressure of crack initiation. simulation results show that the increase in both the density and the length of perforation made the initiation pressure decreased, and the presence of both the natural fractures and the cross bedding also affected the initiation of cracks in shale reservoirs [15]. lo et al. conducted numerical simulations on crack initiation and propagation of brittle rocks during hydraulic fracturing, the simulation results showed that the interaction between fractures aggravated as the fracture propagated [16]. peirce studied the interference between fractures when the number of clusters in the single fracturing section was different, and the results verified the existence of stress shadowing between fractures. however, the factors influencing the size of stress shadowing and the corresponding influence laws have not been discussed in depth [17]. although these studies are important for understanding the mechanism of fracture propagation in hydraulic fracturing, they have not been able to do further research on the interaction between hydraulically induced fractures within the single fracturing section in the multi-cluster staged fracturing of shale horizontal wells. in a sense, the effect of inter-cluster interference on fracturing results is more troublesome than that of reservoir heterogeneity [17]. figure 1: schematic diagram for the initiation and propagation of hydraulically induced fracture during hydraulic fracturing operation. in this work, a two-dimensional seepage-stress-damage coupled finite element model is developed based on the cohesive element inside abaqus finite element analysis software. furthermore, the influences of such factors as cluster spacing, formation elastic modulus and injection rate of fracturing fluid on fracture morphology are studied, which can provide a reference for the optimization of the cluster spacing when the multi-cluster staged fracturing operation is performed. in q.-c. li et alii, frattura ed integrità strutturale, 44 (2018) 35-48; doi: 10.3221/igf-esis.44.04 37 the end, optimization is performed for hydraulic fracturing in a shale gas horizontal well in the southwest oil and gas field in china. fluid-solid coupling theory for hydraulic fracturing s shown in fig.1, there is no crack in reservoir formation at the beginning of the hydraulic fracturing operation. however, with the increase in volume of injected fracturing fluid, cracks appear firstly in the direction of the maximum horizontal principal stress. moreover, with the continuous injection of fracturing fluid, cracks will be further propagated and widened. understandably, hydraulic fracturing is a complicated process involving seepage, rock deformation and damage. in order to analyze the interaction between hydraulically induced fractures, it is necessary to study the fluid-solid coupling theory in hydraulic fracturing process. fundamental equations of fluid-solid model based on the principle of effective stress, the fluid-solid analyses of crack propagation are launched and its expression is  effe tota wp= + (1) where, σeffe is the effective stress, mpa; σtota is the total stress, mpa; pw is the pore pressure, mpa. for porous media of rock, the equilibrium equation can be expressed as the eq. (2) [14].            effe w v vv s vmp dv t ds f dv (2) where, m is the unit matrix, δε is the virtual strain rate matrix, s-1; t is the surface traction matrix, n/m2; δv is virtual velocity matrix, m/s; f is the body force, n/m3; ds and dv are the area and volume respectively. the continuity equation of pore fluid in the porous rock can be written as the following equation.             w w w w wv v d v j n dv v n v dv j dt x 1 0 (3) where, j is the volume change rate of porous media, dimensionless; nw is the ratio of fluid volume to total volume, dimensionless; ρw is the fluid density, kg/m3；x is the space vector, m; dt is the time step in s; vw indicates the seepage velocity of pore fluid in m/s. during hydraulic fracturing, fluid seepage velocity in porous media can be described by darcy's law [15].            w w w w w pk v g n g x (4) where, μ is the fluid viscosity, pa·s; k is the reservoir permeability in μm2; ∂pw is the increment of pore pressure, pa. cohesive element method is the commonly used finite element method (fem) in hydraulic fracturing simulation. based on the abaqus fem software, the cohesive element method is used to simulate the simultaneous propagation of multiple hydraulically induced fractures within the single fracturing section during hydraulic fracturing in shale horizontal wells. the constitutive model of the cohesive element satisfies the law of traction-separation [14]. that is, it is assumed that the response of the cohesive element before it is damaged satisfies a linear relationship. however, damage of cohesive element occurs when the tractive force exceeds a critical value. in addition, the traction acting on the cohesive element decreases with increasing separation displacement between the two outer surfaces after the damage occurs. linear elastic traction-separation behavior stress-strain characteristics of the cohesive element satisfies a linear elastic relationship before damage occurs. a q.-c. li et alii, frattura ed integrità strutturale, 44 (2018) 35-48; doi: 10.3221/igf-esis.44.04 38                                   n nn ns nt n s ns ss st s t nt st tt t k k k k k k k k k k (5) where, σn is the maximum stress that the element can bear in the normal direction, pa; σs and σt are the maximum stress that the element can bear in the first and the second tangential directions respectively, pa. likewise, εn, εs, and εt are the strains of the element in the normal, the first and the second tangential directions respectively. crack initiation and propagation here, the maximum normal stress criterion is the initiation criterion. in other words, the element starts to damage when the stresses in all directions exceed the critical values it can bear. the initiation criterion can be represented by eq. (6).             n s t nc sc tc max , , 1 (6) where, σnc is the tensile strength, mpa; σsc and σtc are the critical shear stresses that the element can bear in the first and the second tangential directions respectively, mpa. for the criterion of crack propagation, crack propagation criteria in bk (benzeggagh-kenane) mixed-mode is one of the most frequently used criteria for studying crack propagation. it is particularly useful and efficient when the critical fracture energy along the first shear direction is equal to that along the second shear direction. the criterion can be expressed as the following equation.             cs t nc sc nc n s t g g g g g g g g g (7) where, variables of gn, gs, gt, gnc, gsc and gc are the energy release rate in the normal direction, the energy release rate in the first tangential direction, the energy release rate in the second tangential direction, the critical energy release rate in the normal direction, the critical energy release rate in the first tangential direction and the critical total energy release rate respectively, pa·m; η is a constant related to the material properties, it is 2.284 in this work. the total energy release rate is defined as gt=gn+gt+gs; the fracture begins to propagate when gt is equal to gc. finite element analysis simulation numerical modeling and meshing he numerical model established in this paper is mainly based on the following assumptions. firstly, it is assumed that reservoir is a linear elastic isotropic homogeneous formation. meanwhile, the horizontal wellbore is distributed along the direction of the minimum horizontal principal stress, and the perforation clusters in the single fracturing section initiate synchronously under the action of hydraulic pressure. furthermore, both the pressure drop of the fracturing fluid flowing within the horizontal wellbore and the influence of perforation friction are neglected. the problem of interference between fracturing clusters in a single fracturing stage during multi-cluster staged fracturing for shale gas horizontal wells can be simplified as a problem of two-dimensional plane strain. therefore, as shown in fig. 2, taking into account the symmetry of the borehole and formation, a two-dimensional finite element model was established by selecting the formation with the size of 400×400 meters on one side of the horizontal wellbore. compared with the three-dimensional model, a two-dimensional model can dramatically reduce the number of elements within the model, which can effectively improve the calculation speed of the simulation process. the whole simulation process is independent of the borehole size, so the size of the borehole is not required to define in the model. generally, it is appropriate to arrange 2 to 5 fracturing clusters in each fracturing section. in this paper, three perforation clusters are designed in each fracturing section. t q.-c. li et alii, frattura ed integrità strutturale, 44 (2018) 35-48; doi: 10.3221/igf-esis.44.04 39 figure 2: schematic diagram of multi-cluster staged fracturing for shale gas horizontal well and the established finite element model two types of elements, cpe4p and coh2d4p, are used in the model. the cpe4p element can simulate the plane strain problem of porous elastic media, and the whole reservoir is assigned to this type of element. however, both the initiation and the propagation of cracks during hydraulic fracturing operation can be achieved by using coh2d4p element. the whole process of fracture propagation, fluid flow along the fracture and fluid leakage can be simulated by coh2d4p element when the fracturing fluid is injected into the formation. a total of 15,000 cpe4p elements and 800 coh2d4p elements are included in the model. the model is established by cae module in abaqus software, and on this basis, the secondary development is carried out to realize the numerical simulation of crack propagation. in addition, in order to improve the accuracy of the simulation results and the convergence of the simulation process, the variable density method is used to realize the meshing of the model. that is, the elements near the cracks are more sophisticated and finely divided, which can be seen from fig. 2. in terms of boundary conditions and initial conditions, the normal displacement of each boundary is fixed, and the pore pressure boundary is set to be constant along each boundary during the whole simulation process. the initial void ratio, initial stresses and initial pore pressure within the formation are defined by using the predefined field definition in abaqus fem software. in addition, the transient coupling solution has been used for simulating the hydraulic fracturing process. material properties and construction parameters according to the mechanical parameters of shale reservoirs and the construction parameters for fracturing operations, factors affecting the interference between different fracturing clusters within the single hydraulic fracturing section are studied. the stratigraphic parameters and construction parameters used in simulation are shown in tab. 1 and tab. 2, respectively. parameter value parameter value elastic modulus, e / gpa 20 poisson's ratio, ν 0.2 maximum horizontal principal stress, σh / mpa 27 minimum horizontal principal stress , σh / mpa 16 vertical principal stress, σv / mpa 27 saturation, so / % 100 tensile strength, c / mpa 3 initial porosity, ϕ / % 4 initial pore pressure, pip / mpa 10 leakoff coefficient, l /m/s 1×10-8 permeability, k / m2 5×10-17 length×width / m2 400×400 table 1: model parameters of shale gas reservoir. q.-c. li et alii, frattura ed integrità strutturale, 44 (2018) 35-48; doi: 10.3221/igf-esis.44.04 40 parameter value viscosity of fracturing fluid, u / mpa·s 1 injection rate, q / m3/min 6 cluster spacing, h / m 30 total fracturing time, t / min 10 table 2: construction parameters of multi-cluster staged hydraulic fracturing. the parameters in tab. 1 and tab. 2 are only for the standard model, whereas sensitivity studies can be performed by changing the corresponding parameters. on this basis, influences of the factors, such as cluster spacing and the injection rate of fracturing fluid, on the crack morphology are studied by using the fea model. sensitivity analysis effect of cluster spacing on fracture morphology roper cluster spacing is the key to the design of multi-cluster staged fracturing in horizontal wells. therefore, in order to study the impact of cluster spacing on the fracture morphology (mainly the crack length and crack width), five different cluster spacings of 10m, 20m, 30m, 40m and 50m are examined. the width of all fractures studied in this paper is based on the value of the injection point. fig.3 shows the contour of fracture morphology after fracturing for 10 minutes when the cluster spacing is different. figure 3: contour of fracture morphology after fracturing for 10 minutes when the cluster spacing is different. (deformation scale factor = 500). in order to study the mutual interference of fractures during fracturing, an interference coefficient (in) is defined to characterize this response, which can be expressed by the following equation. p q.-c. li et alii, frattura ed integrità strutturale, 44 (2018) 35-48; doi: 10.3221/igf-esis.44.04 41       mid side w in w = 1100% (8) where, w is the width or the half-length of fracture, and the subscript mid and side represent the middle fracture (the 2nd fracture) and the two fractures on both sides ( the 1st and the 3rd fracture). when the coefficient in is less than 1.0, the existence of interference can be explained. moreover, the larger the coefficient is, the stronger the interference is. the blue line in fig.4 represents the interference coefficient curve. figure 4: results of fracture propagation when the cluster spacing is different. fig.4 shows the results of the fracture half-length (fig.4a) and the fracture width (fig.4b) of the three clusters within the single fracturing section when the cluster spacing is different. as can be seen from fig.3 and fig.4, the effects of cluster spacing on the morphology of different fractures vary widely, the interference between the fracturing clusters decreases with the increase of the cluster spacing. under the conditions that the cluster spacing is 10 m, the middle fracture (the 2nd fracture) stops propagating when its half-length is quite small, and the half-length is only 6% of that of the other two fractures (the 1st fracture and the 3rd fracture), whereas the fracture width is also only 19% of the width of the other two fractures. this is because that the stress interference between the fracturing clusters is very violent, which strongly inhibits the propagation of the middle fracture. with the gradual increase of the cluster spacing, stress interference between the fracturing clusters gradually diminishes. when the cluster spacing is 30 m, all fractures reach the maximum width, the width of the middle fracture and the other two side fractures are 1.36 cm and 1.62 cm respectively. however, when the cluster spacing reaches 50 m, the interference coefficient in reaches nearly zero, which indicates that the interference between fractures almost disappears, and the morphology of all these three fractures are nearly the same. it can be concluded that the cluster spacing is an important factor affecting the intensity of stress interference among the fractures within the single fracturing section. as the cluster spacing decreases, the stress interference between fractures increases, and the propagation of the middle fracture is seriously suppressed. however, with the increase in the cluster spacing, the stress interference between the clusters decreases or even disappears, and the morphological differences between all fractures become negligible. effect of elastic modulus on fracture morphology the elastic modulus of reservoir is also another factor affecting both the interference between the clusters and fracture morphology. in this part, the influence of elastic modulus on fracture propagation under the condition of the same cluster spacing is analyzed. fig.5 illustrates the contour of fracture morphology after fracturing for 10 minutes when elastic modulus is different. fig.6 shows the results of the fracture half-length (fig.6a) and the fracture width (fig.6b) of the three fracturing clusters within the single fracturing section under different elastic modulus. q.-c. li et alii, frattura ed integrità strutturale, 44 (2018) 35-48; doi: 10.3221/igf-esis.44.04 42 figure 5: contour of fracture morphology after fracturing for 10 minutes for formation with different elastic modulus. (deformation scale factor = 500). figure 6: results of fracture morphology for fracture propagation when the elastic modulus of reservoir is different. as can be illustrated in fig.6, reservoir elastic modulus can significantly influence fracture propagation, but it hardly affects the interference between fractures, the interference coefficient is almost close to a constant. with the increase of the reservoir elastic modulus, the lengths of all fractures increase, but not significantly. for the 1st fracture and the 3rd fracture, when the elastic modulus increases from 20gpa to 40gpa, the fracture half-length increases from 49m to 75m, increasing by 53%. under the same conditions, the half-length of the 2nd fracture also increased from 13m to 18m, which increased by 38%. nevertheless, the interference coefficient remains at about 75%. therefore, it can be concluded that the elastic modulus of the formation does not affect the interference between the fractures in the process of fracture propagation, in spite of the fact that half-length of all fractures increase obviously. q.-c. li et alii, frattura ed integrità strutturale, 44 (2018) 35-48; doi: 10.3221/igf-esis.44.04 43 however, with the increase of the elastic modulus of the reservoir, the width of each fracture decreases significantly, which is opposite to the fracture half-length. the width of both the 1st fracture and the 3rd fracture decreased from 1.62cm to 1.07cm, with a decrease of 34%. however, as for the middle fracture, its width decreased from 1.36cm to 0.96cm, with a drop of 29%. although varying the elastic modulus of reservoir will change the width of all fractures in the fracturing process, the simulation results of fracture width also show the conclusion that the interference between fractures is hardly influenced by the elastic modulus of reservoirs. it is an important index to evaluate the success of hydraulic fracturing whether the proppant can enter the fracture smoothly during the fracturing construction. however, increase in the elastic modulus of the reservoir will sharply narrow the width of the hydraulically induced fracture, thereby hindering the proppant carrying and causing sand plug. therefore, based on the study of the effect of cluster spacing on fracture morphology, for multi-cluster staged fracturing construction in reservoirs with high elastic modulus, large cluster spacing should be designed to avoid the difficulty of sand carrying caused by the smaller crack width. effect of injection rate on fracture morphology in the case of neglecting the friction of fracturing fluid while flowing in wellbore and assuming that the injection rate at all injection points is the same, the variation of the fracture morphology with the injection rate of the fracturing fluid is studied. here, five injection rates (5m3/min, 9m3/min, 12m3/min, 15m3/min and 18m3/min) are investigated to accomplish the goal. fig.7 illustrates the contour of fracture morphology after fracturing for 10 minutes under different injection rates of fracturing fluid (when the cluster spacing is 30m). figure 7: contour of fracture morphology after fracturing for 10 minutes when the injection rates of fracturing fluid is different. (deformation scale factor = 500, 30m cluster spacing). fig.8 shows the results of the fracture half-length (fig.8a) and the fracture width (fig.8b) of the three clusters within the single fracturing section when the injection rate is different. as can be seen from fig.8, with the increase in injection rate of fracturing fluid, both the fracture half-length and the width of all fracturing clusters increase gradually. as for the fracture half-length, when the injection rate of fracturing fluid increases from 5 to 18 m3/min, the half-length of two fractures on both sides (the 1st fracture and the 3rd fracture) increases from 45 m to 51 m, with an increase of 13%. however, although the half-length of the middle fracture (the 2nd fracture) increases only from 11m to 14m, the increase q.-c. li et alii, frattura ed integrità strutturale, 44 (2018) 35-48; doi: 10.3221/igf-esis.44.04 44 range reaches 27 %. similarly, when the injection rate of the fracturing fluid has increased by the same amplitude, the width of the middle fracture (the 2nd fracture) increases from 1.25cm to 1.47cm, with an increase of 17%. however, for two fractures on both sides (the 1st fracture and the 3rd fracture) within the single section, the width increases only from 1.52cm to 1.68cm, by 10%. figure 8: results of fracture morphology for fracture propagation when the injection rate is different. however, as can be seen from fig.8, with the change in the injection rate of fracturing fluid, the interference coefficient during the fracture propagation changes little. when fracture half-length is taken as the criterion to evaluate interference between different fractures, the interference coefficient ranges from 70% to 80%. however, if the evaluation criterion is converted to fracture width, the interference coefficient ranges from 10% to 20%. the variation ranges of these interference coefficients are both very narrow. these simulation results indicate that the injection rate of fracturing fluid has only affected the morphology of all the fractures, but hardly influenced the interference between fractures. by comparison, it can be found that, in terms of the increase amplitude of both the fracture width and the fracture halflength, the middle fracture is always larger than the fractures on both sides. therefore, when other factors are all optimal, the larger injection rate of fracturing fluid can increase both the fracture width and propagation distance of all fractures within the single fracturing section, thus stimulating the reservoir optimally. effect of fracturing fluid viscosity on fracture morphology viscosity of fracturing fluid affects proppant transportation within the fracturing fluid, thereby affecting the stimulation result of the reservoir after fracturing construction. here, five viscosities (1mpa·s, 20mpa·s, 50mpa·s, 100mpa·s and 200mpa·s) are examined to study the influence of the viscosity of fracturing fluid on fracture propagation. fig.9 shows the contour of the fracture morphology after fracturing for 10 minutes by using fracturing fluid with different viscosities when the cluster spacing is 30m. fig. 10 shows both the half-length (fig.10a) and the width (fig.10b) of all these three fractures by using the fracturing fluid with different viscosities when the cluster spacing is 30 m. as illustrated in fig.10, the width of each fracturing cluster increases gradually with the increase in fracturing fluid viscosity, but the fracture half-length shows the opposite trend, that is, shows a slight downward trend. in spite of this, different influences of the fracturing fluid viscosity on the morphology of different fractures are evident. when the fracturing fluid viscosity increases from 1 cp to 200 cp, the width of two fractures on both sides (the 1st fracture and the 3rd fracture) within the fracturing section increases by 9% (from 1.62cm to 1.76cm), whereas the middle fracture (the 2nd fracture) shows the thinner width (increases from 1.36cm to 1.46cm), increasing only by 7%. compared with the other three factors (cluster spacing, elastic modulus and injection rate) mentioned above, the impact of the fracturing fluid viscosity is relatively small, which can be seen by the shape of the curves in fig.10, especially the fracture half-length curve. the increase in viscosity of fracturing fluid shortens all fractures that propagate simultaneously within the single fracturing section, but the effect of viscosity on the half-length of different fractures is different. when the viscosity of fracturing fluid increased from 1 cp to 200 cp, the half-length of the middle fracture (the 2nd fracture) shortened by 4%, whereas the two fractures on both sides (the 1st fracture and the 3rd fracture) shortened by 12%. blue q.-c. li et alii, frattura ed integrità strutturale, 44 (2018) 35-48; doi: 10.3221/igf-esis.44.04 45 lines in both subgraphs within fig.10 are almost horizontal straight lines, which indicate that the interference between the fractures within the single fracturing section is independent of the fracturing fluid viscosity. figure 9: result of fracture morphology after fracturing for 10 minutes by using fracturing fluid with different viscosities. (deformation scale factor = 500, 30 cluster spacing). figure 10: results of fracture morphology for fracture propagation when the viscosity of fracturing fluid is different. the research shows that the short and wide fracture can be obtained by increasing the viscosity of the fracturing fluid. although the width of the fractures can be increased by this, the length of the fractures may decrease, which is not conducive to increasing the volume of the reservoir stimulated by hydraulic fracturing. q.-c. li et alii, frattura ed integrità strutturale, 44 (2018) 35-48; doi: 10.3221/igf-esis.44.04 46 case study ased on the above studies, it is found that cluster spacing is the most important factor affecting the interference between cracks, while other factors have little impact on it. consequently, taking a shale gas horizontal well located in the southwest oil and gas field of china as an example, the hydraulic fracturing construction has been optimized and designed. the lithology of the target reservoir for multi-cluster staged fracturing in the well is mainly the silty and the carbonaceous shale, and the complicated bedding is well developed in shale reservoir. the elastic modulus and poisson's ratio of reservoir rocks are 20.1gpa and 0.21, respectively. for the properties of the reservoir rock matrix, the content of brittle minerals is high with a brittleness index ranging from 0.5 to 0.6. the matrix porosity is very low, ranging from 1.17% to 7.72%, and matrix permeability varies between 1.0×10-18 m2 to 1.2×10-16 m2, so the reservoir can be defined as ultra-low permeability formation. the maximum horizontal stress and the minimum horizontal stress of the reservoir are 28.5mpa and 19.9mpa respectively, and the total length of the horizontal section is 1215m. the multi-cluster perforation scheme is used as the completion pattern, with three perforation clusters designed within one fracturing section. the injection rate of fracturing fluid is 14m3/min. based on the model established above, the cluster spacing optimization is performed. fig.11 shows the fracture half-length of all fractures when the cluster spacing is different. figure 11: fracture half-length of all fractures within the single fracturing section when the cluster spacing is different. when the cluster spacing is only 10 m, the middle fracture (the 2nd fracture) will be strongly affected by the stress interference due to the adjacent fractures, which finally greatly hinders its full propagation. in the end, the half-length of the middle fracture is only 7% of that of the fractures on both sides within the fracturing section, and the interference coefficient even reaches 92%. with the gradual increase of cluster spacing, the stress interference among the hydraulically induced fractures has been gradually weakened, and the inhibition effect of stress interference on the propagation of middle fracture in the fracturing process has shown the same tendency. when the cluster spacing reaches 40 m, halflength of the middle fracture (the 2nd fracture) is basically equal to that of the two fractures on both sides within the fracturing section. all these results indicate that when the cluster spacing is designed to be 40m, the stimulation result may be best. under this condition, the length of each fracturing section is 120m, so the total number of fracturing section is 10 segments, which are in accordance with the practical fracturing design. during the actual construction of hydraulic fracturing in the field, the total volume of injected fracturing fluid was 10113 m3, and the volume of the solid proppant used was 35 m3. earth potential monitoring technology can realize the real-time monitoring of the fracturing construction results. the monitoring results show that the fracturing construction results in the complicated hydraulic fractures and thus effectively stimulate the shale reservoirs. after fracturing, the production test was carried out using a 14 mm-sized production nozzle. the gas production rate obtained by production test was 185000 m3/day, which showed a significant increase in gas production compared with the adjacent production wells in the same area. b q.-c. li et alii, frattura ed integrità strutturale, 44 (2018) 35-48; doi: 10.3221/igf-esis.44.04 47 conclusions n this paper, a two-dimensional seepage-stress-damage coupled multiple fractures numerical model is developed by using the abaqus fem software. on this basis, the influences of factors, such as the cluster spacing, the elastic modulus and the injection rate of the fracturing fluid, on the fracture propagation morphology have been studied. the results show that: (1) the cluster spacing is the most important factor that affects the stress interference among all these fractures within the single fracturing section. exactly, it can be regarded as the most important influential factor. when the cluster spacing is small, the stress interference is obvious, and the propagation of the middle fractures will be severely inhibited. however, with the increase of the cluster spacing, the stress interference among all these fractures within the single fracturing section decrease, so the morphology of all these fractures become uniform and similar. (2) the elastic modulus of the reservoir hardly affects the stress interference among all these fractures, but it can affect the final morphology of all fractures. with the gradual increase of the elastic modulus, the half-length of each fracture in the single fracturing section increases significantly, while the width of all these fractures obviously decrease, which can greatly increase the possibility of sand plug. therefore, it is suggested that large cluster spacing should be designed when multicluster staged fracturing is carried out in a reservoir with high elastic modulus, so the difficulty of adding sand due to the thin fracture width can be prevented. (3) injection rate of fracturing fluid is also an important factor affecting the crack propagation. with the increase in the injection rate of the fracturing fluid, both the half-length and width of each fracture within the single fracturing section will gradually increase. therefore, by increasing the injection rate of the fracturing fluid, it is possible to increase both the width and the half-length of fracturing fractures, so more volume of the reservoir can be stimulated. (4) simulation results show that the increase in the viscosity of the fracturing fluid results in an increase in the width of all fractures, but it hinders the propagation of all fractures within the single fracturing section. therefore, increasing the viscosity of the fracturing fluid indefinitely is not conducive to increasing the stimulated reservoir volume, it is recommended to design a suitable viscosity of the fracturing fluid in the actual construction. references [1] ben, y., miao, q. and wang, y. (2012). effect of natural fractures on hydraulic fracturing, isrm regional symposium-7th asian rock mechanics symposium, seoul, korea,. [2] cheng, z. r., bunger, a. p. and zhang, x., (2009). cohesive zone finite element-based modeling of hydraulic fractures, acta mechanica solida sinica, 22(5), pp. 443-452. [3] vengosh, a., jackson, r. b. and warner, n. (2014). a critical review of the risks to water resources from unconventional shale gas development and hydraulic fracturing in the united states, environmental science & technology, 48(15), pp.8334-8348. [4] (2016). future u.s. tight oil and shale gas production depends on resources, technology, markets. https://www.eia.go v/todayinenergy/detail.php?id=27612. [5] saldungaray, p. m., palisch, t. and shelley, r. (2013). hydraulic fracturing critical design parameters in unconventional reservoirs, spe unconventional gas conference and exhibition, muscat, oman. [6] rahm, d. (2011). regulating hydraulic fracturing in shale gas plays: the case of texas, energy policy, 39(5), pp. 29742981. [7] gregory, k. b., vidic, r. d. and dzombak, d. a. (2011). water management challenges associated with the production of shale gas by hydraulic fracturing, elements, 7(3), pp. 181-186. [8] schnoor, j. l. (2012). shale gas and hydrofracturing, environmental science & technology, 46(9). [9] (2011). review of emerging resources: u.s. shale gas and shale oil plays. https://www.eia.gov/analysis/studies/us shalegas/. [10] drilling productivity report (2014). washington, dc: united states energy information administration, 10. [11] tang, y., zhang, j. c. and zhang, q., (2010). an analysis of hydraulic fracturing technology in shale gas wells and its application, natural gas industry, 30(10), pp. 33-38. [12] (2016). hydraulic fracturing accounts for about half of current u.s. crude oil production. https://www.eia.gov/todayi nenergy/detail.php?id=25372. i q.-c. li et alii, frattura ed integrità strutturale, 44 (2018) 35-48; doi: 10.3221/igf-esis.44.04 48 [13] carpenter, c. (2014). design optimization of horizontal wells with multiple hydraulic fractures, journal of petroleum technology, 66(11), pp. 118-123. [14] zhang, g. m., liu, h. and zhang, j., (2010). three-dimensional finite element simulation and parametric study for horizontal well hydraulic fracture, journal of petroleum science and engineering, 72(3–4), pp. 310-317. [15] pan, l. h., cheng, l. j. and zhang, y. (2015). numerical simulation of fracturing pressure in multiple clusters staged hydraulic fracture of shale horizontal well, rock and soil mechanics, 36(12), pp.3639-3648. [16] lo, l. w. (2014). interaction of growing cracks in hydraulic fracturing, master thesis, the university of texas at arlington. [17] peirce, a. (2015). interference fracturing: nonuniform distributions of perforation clusters that promote simultaneous growth of multiple hydraulic fractures, spe journal, 20(2), pp. 384-395. d. wang, frattura ed integrità strutturale, 62 (2022) 364-384; doi: 10.3221/igf-esis.62.26 364 seismic vulnerability analysis of reinforced concrete frame with infill walls considering in-plane and out-of-plane interactions dan wang school of civil engineering, northeast forestry university, harbin 150040, china www_daa@163.com abstract. the seismic performance of a building hinges on the seismic capacity and damage features of the reinforced concrete (rc) frame with masonry infill walls. to reasonably evaluate the seismic performance and seismic economic loss of masonry infill walls, it is necessary to consider the in-plane (ip) and out-of-plane (oop) interactions of these walls under seismic actions, and to model the vulnerability of the infill walls and the frame. based on the test data on masonry infill walls, this paper designs a performance indicator for infill wall in the light of ip-oop interactions, and determines the response threshold of each damage state. with the aid of opensees, the authors developed and verified a reasonable modeling method for rc frames with infill walls. as per the current code in china, a 5-storey rc frame with infill walls was designed, and two three-dimensional (3d) space models were established for the structure by the proposed modeling method. one of them considers ip-oop interactions, and the other does not. then, the structure was subjected to incremental dynamic analyses (ida), and different damage indicators were determined to examine the damage of the infill walls and the overall structure, producing a set of vulnerability curves. the results show that the consideration of ip-oop interactions significantly increases the probability of seismic damages on the infill walls and the overall structure. the most prominent increase was observed in the medium to serious damage stages. keywords. masonry infill walls; reinforced concrete (rc) frame; in-plane (ip) and out-of-plane (oop) interactions; damage indicators; seismic vulnerability analysis. citation: wang, d., seismic vulnerability analysis of reinforced concrete frame with infill walls considering in-plane and out-ofplane interactions, frattura ed integrità strutturale, 62 (2022) 364-384. received: 18.04.2022 accepted: 20.08.2022 online first: 01.09.2022 published: 01.10.2022 copyright: © 2022 this is an open access article under the terms of the cc-by 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. introduction ach building is consisted of structural and non-structural components. the seismic performance of non-structural components is critical to the ductility of the building under earthquakes. as the most common non-structural components, infill walls are widely applied in reinforced concrete (rc) buildings. the data on the past earthquakes have shown that destruction of masonry infill walls will cause huge economic losses, and even endanger e https://youtu.be/mmjggr9yk74 d. wang, frattura ed integrità strutturale, 62 (2022) 364-384; doi: 10.3221/igf-esis.62.26 365 human lives. in the structural seismic system, the seismic performance of the local components and overall structure depends on how well the infill walls contribute to stiffness and bearing capacity. in fact, the degree of damage for infill walls provides an important basis for evaluating the capacity of the building to prevent disasters before earthquakes, and assessing the possibility of continued use of the structure after earthquakes. nevertheless, the existing studies on seismic design often ignore the role of masonry walls. in the last decades, some researchers have tested the in-plane (ip) and out-of-plane (oop) seismic performance of infill walls [1-6]. but only a few have investigated the ip and oop interactions of masonry walls. the damage types observed in masonry infill walls are mainly divided into ip and oop damages, and the damage usually stems from the interaction between ip and oop. the previous results show that the ip and oop interaction can reduce the strength and stiffness of the infill walls [7-9]. however, the nonlinear analyses on infill walls tend to focus on the ip behavior, failing to consider its interaction with oop behavior. the performance indicator of masonry infill wall largely reflects the severity of wall damages, revealing the macro damage states. in current studies, the vulnerability of masonry infill walls is mainly examined with the interlayer displacement angle as the ip indicator, before plotting the vulnerability curve. based on the description of macro damage phenomena, chiozzi et al. [10] defined the damage states for establishing the vulnerability curve. the specific description of each damage state in this standard is based on the collected test results. tab. 1 reports three different macro descriptions for infill wall damage states, namely, slight damage (ds1), moderate damage (ds2), and severe damage (ds3), and the corresponding repair measures. cardone et al. [11] and sassun et al. [12] adopted similar macro descriptions of the damage state, determined the interlayer displacement angle when each specimen reached a certain damage state, and established the ip vulnerability function of masonry infill walls. the vulnerability curves of infill walls, which display the probability distribution of different interlayer displacement angles, only consider the damage indicator in a single direction, and could not reflect the influence of oop damage under earthquake action on the vulnerability of infill walls. degree of damage macro description limit of crack width repair measure ds1 very slight cracks appear at mortar joints, decorative surface, or the wall-frame junction. there is no obvious slip crack or crushed block. 1mm reapply plaster to cover visible cracks. ds2 obvious diagonal cracks appear at mortar joints or blocks. there may be slippage along brickwork joints, or local crushing of blocks. 2mm repair the cracks through pressure grouting, or rebuild locally broken masonry, and reapply high-quality plaster to the surface. ds3 wide oblique cracks appear, exposing the opposite surface. there are obvious mortar cracks, and wide crushing, extrusion, and spalling of blocks. 4mm demolish and rebuild the entire structure. table 1: judgement criteria and repair measures for damage states of masonry infill walls. following various mechanical approaches, new simplified models have been developed to predict both ip and oop responses, with the aim of simulating the exact response of structures with infill walls. the accurate calibration of infill wall simulation models requires massive data from tests with both ip and oop loads. due to the severe lack of such data, most macroscale models for the oop responses, and ip-oop interactions of infill walls are grounded loosely on simplified hypotheses. kadysiewski et al. [13] proposed an infill wall model, which considers the ip-oop interactions with two diagonal beam-column elements, and a lumped mass of the central node, and put forward the interaction curves for ip and oop displacements. on this basis, furtado et al. [14] established a simplified infill wall model with four beamcolumn elements, two oop lumped masses, and a central element, before introducing the law of lag to simulate the strength and stiffness degradation of masonry infill wall. based on the test data of frames with masonry infill walls, this paper firstly defines a quantitative indicator considering the coupling between ip and oop damages of infill walls, and determines the indicator limit at each damage state. next, a simplified model was introduced for the rc frame with infill walls, which is capable of simulating ip-oop interactions, and a nonlinear analysis model of infill-wall rc frame was established with the help of opensees. the accuracy of the d. wang, frattura ed integrità strutturale, 62 (2022) 364-384; doi: 10.3221/igf-esis.62.26 366 model was verified through the numerical simulation of an infilled rc frame in the quasi-static test. then, a 5-storey infillwall rc frame was designed using pkpm, and two 3d space models were established for the structure, with and without ip-oop interactions, respectively. a total of 20 ground motion records were selected to conduct an incremental dynamic analysis (ida) on the prepared structure. on this basis, the seismic vulnerability of the infill walls and the overall structure was explored in details, a set of vulnerability curves considering ip-oop interactions was proposed tentatively, which illustrate the probability of exceedance of the infill walls and the overall structure at different performance levels, as a function of the seismic intensity. damage indicator identification response thresholds o design the damage indicator for infill walls, it is important to gather statistical information about the level of deformation corresponding to each damage state. hence, the authors collected the results of the ip and oop quasi-static loading tests on 30 rc frames with masonry infill walls [1-7, 9]. according to the descriptions of the damage phenomena of each frame under load, the response thresholds of ip and oop frames were recorded under each damage state. as for the quantification indicators of infill wall damages, the interlayer displacement angle δip0/h was chosen for the ip scenario, while the ratio δoop0/h of the maximum oop displacement to the distance between the top beam axis and the upper edge of the grade beam was selected for the oop scenario. figure 1: response thresholds of each ip frame in different damage states figure 2: response thresholds of each oop frame in different damage states t d. wang, frattura ed integrità strutturale, 62 (2022) 364-384; doi: 10.3221/igf-esis.62.26 367 as shown in figs. 1 and 2, the response thresholds of the specimens reflect a certain discreteness. to determine the quantification indicators for the rc frames with infill walls in each damage state, the demand parameter was calculated by the vulnerability analysis approach in the appendix of fema p-58 [15]. in general, the vulnerability function obeys the log normal distribution: ( ) θφ β       =        ln d p d (1) where, p(d) is the probability to reach or exceed a damage state; φ is the cumulative function of standard normal distribution; θ is the mean of engineering demand parameter d; β is the log standard deviation reflecting the discreteness of d. if the frame data come from multiple independent tests and record the d of each frame in each damage state, then the demand parameter θ can be calculated by: θ =         ∑ = 1 1 ln n j j d n i e (2) where, θi is the demand parameter of damage state i; n is the number of frames; dj is the response threshold for the j-th frame in damage state i. the calculated demand parameters of ip and oop frames are the response thresholds of infill walls at each damage state under ip and oop scenarios (tab. 2). type performance indicator ds1 ds2 ds3 ip δip0/h (%) 0.11 0.20 0.68 oop δoop0/h (%) 0.20 0.40 1.21 table 2: response thresholds of infill walls at each damage state under ip and oop scenarios performance indicator ip-oop interactions. in 2007, hashemi and mosalam relied on the strut-and-tie (sat) model to prove that the ip strength of infill walls interact with their oop strength. later, a series of tests and numerical simulations were carried out, revealing that the simulation effect agrees well with the test results, when the interactive effect is described as the curve in fig. 3(a):     +        ≤ 3/2 3/2 0 0 1.0nh h n mp p m (3) where, ph and ph0 are the ip forces in the presence and absence of oop force, respectively; mn and mn0 are the oop forces in the presence and absence of ip force, respectively. mosalam and günay [16] depicted the displacement interaction with the same equations for force interaction. in the elastic stage, the displacement interaction satisfies the 2/3 power curve formula, for the elastic displacement is positively proportional to the load. as shown in fig. 3, the non-elastic displacement could be approximated by the 3/2 power curve. the interactive relationship between ip and oop displacements can be expressed as:    ∆∆ + ≤      ∆ ∆    3/2 3/2 0 0 1.0nh hy ny (4) d. wang, frattura ed integrità strutturale, 62 (2022) 364-384; doi: 10.3221/igf-esis.62.26 368 where, δh is the ip horizontal displacement of infill wall; δhy0 is the ip horizontal displacement in the absence of oop force; δn is the oop horizontal displacement of infill wall; δny0 is the oop horizontal displacement in the absence of ip force. (a) force interaction curve of an infill wall (b)displacement interaction curve of an infill wall figure 3: ip-oop interactions of an infill wall performance indicator and response thresholds. substituting δh0 and δhy0, which respectively correspond to ip and oop response thresholds into formula (4), the interactive relationships between ip and oop displacements under the three limit states can be respectively obtained by: ∆∆    + =        3/23/2 11 // 1.0 0.0011 0.0020 oopip hh (5) ∆∆    + =        3/23/2 22 // 1.0 0.0020 0.0040 oopip hh (6) ∆ ∆   + =        3/2 3/2 3 3/ / 1.0 0.0068 0.0121 ip ooph h (7) where, δipi and δoopi are the ip horizontal displacement and oop horizontal displacement of infill walls in damage state dsi under the joint action of ip and oop forces, respectively. the relationships between ip and oop displacements under the three limit states can be respectively calculated by: −∆∆    + =       ×  5 3/23/2 112.45 8. 14 09oopip h h (8) −∆∆    + =       ×  4 3/23/2 222.83 2. 13 05oopip h h (9) −∆ ∆   + =       ×  3 3/2 3/2 3 32 0.54 1.3 13ip oop h h (10) the coefficient values of ∆      3/2 ipi h are similar in the above formulas. the arithmetic mean was taken as the coefficient of ∆      3/2 ipi h . that is, the sum of ∆∆    +        3/23/2 2.6 oopip h h was adopted as the quantification indicator of ip-oop interactions for infill walls. then, the response thresholds under different damage states can be obtained as shown in tab. 3. d. wang, frattura ed integrità strutturale, 62 (2022) 364-384; doi: 10.3221/igf-esis.62.26 369 performance indicator ds1 ds2 ds3 ∆∆    +        3/23/2 2.6 oopip h h 8.94×10-5 2.53×10-4 1.33×10-3 table 3: response thresholds of the ip-oop interactions for infill walls under different damage states. according to xie’s ip-oop loading test data, three frames t1, t2 and t3 were selected for verification. all three frames are full-scale rc frames with a single-layer, single-span hollow concrete block infill wall. frame t1 has been slightly damaged through ip loading, with an interlayer displacement angle of 0.15%. without changing the ip displacement, the infill wall was applied a unidirectional iop load until the bearing capacity significantly dropped. then, the frame was adopted to verify the response thresholds under ds2 and ds3. frames t2 and t3 have been moderately damaged through ip loading, with an interlayer displacement angle of 0.21% and 0.50%, respectively. these two frames were utilized to verify the response thresholds under ds3. drawing on the frame damage phenomena in the literature, and the forcedisplacement skeleton curves of oop loading, the response thresholds of each frame in different damage states were obtained under the joint action of ip and oop forces, and compared with the calculation results in tab. 3. the verification results of the three frames are shown in tabs. 4 and 5. damage state ds2 ds3 δoop/h 0.19% 1.23% ∆∆    +        3/23/2 2.6 oopip h h 2.33×10-4 1.51×10-3 preset response threshold 2.53×10-4 1.33×10-3 error 0.08 0.13 table 4: response thresholds of frame t1 (δip/h=0.15%) under the joint action of ip and oop forces. frame t2 t3 δip/h 0.21% 0.50% δoop/h 0.89% 0.81% ∆∆    +        3/23/2 2.6 oopip h h 1.09×10-3 1.63×10-3 preset response threshold 1.33×10-3 1.33×10-3 error 0.18 0.22 table 5: response thresholds of frames t2 and t3 in ds3 under the joint action of ip and oop forces. as shown in figs. 1 and 2, the response thresholds of infill walls under different damage states were highly discrete. the highest discreteness appeared in ds3. cardone et al. summarized the response thresholds of ip interlayer displacement angle for infill walls in different damage states, and found that the log standard deviation under different damage states falls between 0.18 and 0.45. therefore, the errors (0.08-0.22) in tabs. 4 and 5 were relatively small. thus, the performance indicator and thresholds in tab. 3 were selected for the ip-oop interactions of infill walls. damage indicators and limit states. according to the above results，the performance levels of infill walls can be defined by the ip-oop indicator and the ip indicator, as shown in tab. 6. rosseto et al. [17] proposed a damage indicator based on the maximum interlayer displacement angle. this indicator applies to the performance level of structures with different lateral stiffnesses. using this indicator, the rc frame with infill wall was divided into 5 damage states (tab. 7). d. wang, frattura ed integrità strutturale, 62 (2022) 364-384; doi: 10.3221/igf-esis.62.26 370 degree of damage macro description limit value of each indicator ∆∆    +        3/23/2 2.6 oopip h h δip0/h. ds1 very slight cracks appear at mortar joints, decorative surface, or the wall-frame junction. there is no obvious slip crack or crushed block. 8.94×10-5 1.10×10-3 ds2 obvious diagonal cracks appear at mortar joints or blocks. there may be slippage along brickwork joints, or local crushing of blocks. 2.53×10-4 2.00×10-3 ds3 wide oblique cracks appear, exposing the opposite surface. there are obvious mortar cracks, and wide crushing, extrusion, and spalling of blocks. 1.33×10-3 6.80×10-3 table 6: performance levels of masonry infill walls. damage state macro description maximum interlayer displacement angle θmax (%) near intactness (ds1) very slight cracks appear on infill wall. 0.05 slight damage (ds2) blocks at beam-column junctions are crushed, the structural elements are initially damages, and the infill wall of external frame suffers from diagonal shear cracking. 0.30 moderate damage (ds3) wide cracking hits infill wall. the blocks suffer from crushing or oop extruding. infill wall partially fails. the structural elements are further damaged, with shear damages in local areas. 1.15 partial collapse (ds4) partial collapse occurs due to the damages of the beams and columns. infill wall almost fully fails. 2.80 collapse (ds5) infill wall suffers obvious overall collapse. 4.40 table 7: performance levels of rc frame with infill walls. numerical simulation infill wall model urtado et al. [14] modelled an infill wall of four elastic beam elements, two oop lump masses, and one nonlinear axial connection element (fig. 4). the model can simulate the behavior of infill walls under cyclic ip and oop loading, and realize the ip-oop interactions by element removal. ip features. as shown in fig. 4, the central element of the model reflects the nonlinear stress-strain of the infill wall under cyclic ip loading. the force-displacement relationship of the central element was characterized by the performance skeleton curve of the infill wall (fig. 5). furtado provided the recommended values for the definition of the skeleton curve: (1) the ratio of cracking strength to the maximum strength (fi,c/fi,max) is 0.55. according to the mechanical performance of masonry and mortar, the cracking displacement dfi,c falls between 0.075% and 0.12%. (2) the yield strength di,y and yield displacement dfi,y are defined as the midpoints of crack displacement coordinates (dfi,c/fi,c) and maximum strength displacement coordinates (dfi,max/fi,max), respecetively. the yield strength is 65%-75% of the maximum strength, while the yield displacement is between 0.15% and 0.35%. (3) the maximum strength fi,max can be solved by: ( )= + +× × 2,max 0.818 1 1ii msi i i t c c fl f (11) f d. wang, frattura ed integrità strutturale, 62 (2022) 364-384; doi: 10.3221/igf-esis.62.26 371 ( )= + +2,max 0.818 1 1s i m i i f f c c (12) = 1.925 ii i l c h (13) where, fms is the tested shear strength of masonry; ti, hi, and li are the thickness, height, and length of the infill wall, respectively. the maximum strength displacement dfi,max is about 0.25%-0.5%. (4) the displacement corresponding to the residual strength is 5 times the maximum strength displacement. the residual strength is around 20% of the maximum strength. figure 4: furtado et al.’s model [14]. figure 5: skeleton curve of the infill wall. figure 6: response of pinching4 uniaxial material model d. wang, frattura ed integrità strutturale, 62 (2022) 364-384; doi: 10.3221/igf-esis.62.26 372 for the central element, the pinching4 uniaxial material model was adopted to describe the hysteresis mode of the infill wall. noh and huang [18, 19] demonstrated the high sensitivity of numerous pinching4 material parameters, and proved their capability of simulating the extrusion load deformation response, and representing the degradation mode under cyclic loading. the cyclic degradation of strength and stiffness occurs in three forms: unloading stiffness degradation, reloading stiffness degradation, and strength degradation. in the calibrated filling model, the hysteresis mode is controlled by additional parameters: stiffness degradation, strength degradation, shrinkage effect, and energy degradation. the skeleton curve and unloading-reloading path of the hysteresis mode in the model are displayed in fig. 6. oop features. drawing on the joint action between ip and oop proposed by kadysiewski and mosalam [13], the furtado model assumes that the oop behavior of infill walls is linear and elastic, the model and infill walls have the same natural frequencies, and the ip is nonlinearly correlated with oop. according to kadysiewski and mosalam, the oop effective mass of an infill wall was calculated as 0.81m, where m is the total mass of the wall. the oop lumped mass was evenly distributed to the two nodes of the central element. the equivalent strut width of the infill wall, and the equivalent inertial moment in the oop direction can be respectively calculated by: λ −= 0.40.175( )col iw h d (14) λ θ  =     0.25 sin 2 4 i i c col i e t e i h (15) = +2 2i i id h l (16)  ×   =    3 1.644 i i ieq d i i h (17) where, λ is the dimensionless parameter for the relative stiffness between the infill wall and the frame; hcol is the layer height of the frame; ei and ec are the elastic moduli of the masonry, and the rc of the frame, respectively; icol is the effective cross-sectional inertial moment of the strut; di is the diagonal length of the infill wall; hi, li, and ti are the height, length, and thickness of the infill wall, respectively; θ is the angle between the diagonal and horizontal axis of the infill wall; ieq is the equivalent inertial moment of the infill wall; ii is the effective cross-sectional inertial moment of the infill wall. kadysiewski et al. proposed the element removal method for infill walls, aiming to simulate the seismic response of such walls more truthfully. the method assumes that any infill wall would collapse, once its displacement surpasses the limit range under the joint action of ip and oop. then, the mass and stiffness of the infill wall are automatically removed from the structure by the algorithm. in our furtado model, the ip-oop interaction zone of the infill wall has linear boundaries. for intact infill walls, the maximum ip and oop displacement angles were set to 1.5% and 3%, respectively. rc frame model this paper uses force-based nonlinear distribution elements to simulate the beam and column elements of the rc frame. the nonlinear deformation of beam and column elements was simulated by integrating the deformable region along the length on the cross-section of each element. the cross-section of each beam and column element was represented by discrete fibers, all of which obey the uniaxial stress-strain law. the bending state of the cross-section of each beam and column element was obtained by integrating the nonlinear uniaxial stress-strain response of each fiber on that crosssection. to investigate the seismic response of the rc frame, it is necessary to consider the nonlinearity, i.e., the uniaxial stressstrain response of the material. specifically, the concrete 02 uniaxial material model of opensees was adopted as the constitutive model of concrete. the rebars were regarded as the steel 02 uniaxial material, following the giuffremenegotto-pinto theory. the material has been applied to uniaxial material models with homogeneous strain hardening. here, the strain hardening ratio is set to 1%. the three parameters of the command stream of the steel 02 model, r0, r1 and r2, which control the rebars’ transition from elastic state to plastic state, were set to 18, 0.925, and 0.15, respectively. model calibration and validation model calibration was performed by comparing the numerical outputs to available zhao’s test results on the frame with d. wang, frattura ed integrità strutturale, 62 (2022) 364-384; doi: 10.3221/igf-esis.62.26 373 infill walls under ip-oop loading. with a reduced scale of 1/2, the frame is an rc frame with a single-layer, single-span, non-hollow infill wall. fig. 7 shows the dimensions and rebar arrangement of the frame. tab. 8 lists the material properties. figure 7: dimensions and rebar arrange of the test frame material mechanical property parameter value concrete compressive strength / mpa 37.46 elastic modulus / gpa 29.50 rebar yield intensity / mpa 447.70 tensile strength / mpa 659.13 elastic modulus / gpa 198.41 block compressive strength / mpa 4.90 masonry compressive strength / mpa 16.49 shear strength / mpa 0.31 bulk density /kn/m3 5.80 table 8: material properties of the frame. figure 8: simulated and test hysteresis curves. according to the test information, the mechanical parameters of the infill wall were calculated. after loading, the model was subjected to ip-oop loading. fig. 8 compares the simulated hysteresis curve with the test data. fig. 9 compares the simulated and test backbone curves. the simulation results basically agree with the test results. d. wang, frattura ed integrità strutturale, 62 (2022) 364-384; doi: 10.3221/igf-esis.62.26 374 figure 9: simulated and test backbone curves. under ip-oop loading, when the oop displacement of the central element reached 15.50mm, the infill wall model reached the ip-oop interactive boundary, and the wall failed. the result was close to the failure displacement (15.2mm) when the oop loading stopped in the test. this proves that our model can approximate the deformation of the infill wall under oop load. the comparison suggests that the proposed simplified model for the rc frame with infill walls, which considers ip-oop interactions, can roughly simulate and verify the ip mechanical performance and oop deformation capability of rc frames with infill walls, laying a solid basis for further analysis. case building referring to the code for seismic design of buildings (gb50011-2010), the pkpm software was adopted to design an rc frame, with a five-layered infill wall (6 spans in the x direction and 3 spans in the y direction), as the analytical model. fig. 10 shows the plane layout of the structure: the bottom layer is 4.2m tall, and the other layers are 3.6m tall. the concrete grade was set to c30. the horizontal load-bearing rebars are of the grade hrb400 with a diameter of 22 cm. the stirrups are of the grade hpb300. the infill wall was prepared from the clay brick blocks obtained through tests (thickness: 150 mm). the floor and roof slabs are both 100mm thick. the building and site belong to class c and class iii, respectively. the designed earthquake group, and seismic fortification intensity were set to 2 and 8, respectively. following the above modelling strategy, two models were established for the above structure. one of the models considers the ip-oop interactions of the infill wall (ip-oop), and the other considers the ip force effect of the wall (ip). in the ip model, the infill wall was modelled without considering oop bending stiffness and the mass of the central element. tabs. 9-11 present the mechanical parameters of concrete, rebars, and infill wall in the structure, respectively. figure 10: 3d spatial rc frame with infill wall. d. wang, frattura ed integrità strutturale, 62 (2022) 364-384; doi: 10.3221/igf-esis.62.26 375 grade peak stress (mpa) peak strain ultimate stress (mpa) ultimate strain elastic modulus (mpa) compressive tensile c30 28.72 2.87 0.0022 5.74 0.01 3236 table 9: mechanical parameters of concrete. rebar grade yield strength (mpa) ultimate strain elastic modulus (gpa) hrb400 445.50 0.01 200 table 10: mechanical parameters of rebars. compressive strength (mpa) shear strength (mpa) elastic modulus (mpa) shear modulus (mpa) bulk density (kn/m3) 2.02 0.55 1873 1089 6.87 table 11: mechanical parameters of the infill wall. ground motion selection and amplitude modulation. due to the strong uncertainty of ground motions, the input ground motions of incremental dynamic analysis (ida) must be reasonable. following the selection principle for ground motion records in fema p695 [20], a total of 20 ground motion records were selected, including both far field and nearfield ground motions. figs. 11 and 12 show the response spectra and mean response spectra of the two types of ground motions, respectively. the ground motion intensity measure (im) was characterized by peak ground acceleration (pga). the amplitude was modulated by the equal step principle. to explore the seismic performance of the infill wall, the amplitude of ground motions was gradually increased to 1.0g with a fixed step size of 0.05g. figure 11: response spectra and mean response spectra of far field ground motions. d. wang, frattura ed integrità strutturale, 62 (2022) 364-384; doi: 10.3221/igf-esis.62.26 376 figure 12: response spectra and mean response spectra of nearfield ground motions. results and discussion ida and vulnerability curves of infill wall. aking the damage indicator measure (dm) of the infill wall as the abscissa, and the pga as the ordinate, 20 curves were plotted for the ip-oop infill wall model, and the ip infill wall model, respectively (see the gray curves in figs. 13 and 14). it can be seen that the ida curves are directly affected by ground motion records. for the same structure, the responses to different ground motions were, to a certain extent, discrete. to suppress the discreteness of the ida curves, quantile statistical analysis was performed to draw the ida curves of the 16%, 50%, and 84% quantiles. normally, the structural dms under different ims all obey log normal distribution. the relationship between im and dm can be expressed as: βα= ( )dm im (18) the logs of im and dm were subjected to statistical regression to establish a linear regression function. figs. 15 and 16 report the fitting results of ln(pga)-ln(dm). figure 13: ida curves of ip-oop infill wall. t d. wang, frattura ed integrità strutturale, 62 (2022) 364-384; doi: 10.3221/igf-esis.62.26 377 figure 14: ida curves of ip infill wall. y=1.9912x-2.6705 -10 -8 -6 -4 -2 0 2 -2.7082 -2.2082 -1.7082 -1.2082 -0.7082 -0.2082 ln(pga) ln (d m ) -3 -2.5 -2 -1.5 -1 -0.5 0 figure 15: ida regression results of ip-oop infill wall. y=2.3097x-3.2015 -12 -10 -8 -6 -4 -2 0 2 -3 -2.5 -2 -1.5 -1 -0.5 0 ln(pga) ln (d m ) figure 16: ida regression results of ip infill wall. through the above regression analysis, the probabilistic demand of ground motions for ip-oop infill wall and ip infill wall can be respectively expressed as: d. wang, frattura ed integrità strutturale, 62 (2022) 364-384; doi: 10.3221/igf-esis.62.26 378 = −ln( ) 1.9912 ln( ) 2.6705dm pga (19) = −ln( ) 2.3097 ln( ) 3.2015dm pga (20) under different ground motion intensities, the seismic vulnerability of a structure is the conditional probability for the structural damage indicator to surpass the critical value c for the seismic capacity for the structure defined for the structural damage stage: = <( / 1)fp p c dm (21) during seismic vulnerability analysis, both the structural dm and the structural capacity parameter c obey log normal distribution. thus, the structural failure probability can be expressed as: βα β β β β        φ − = φ      = + +   2 2 2 2 ln( / ) ln(( ( ) ) / ) c dm c dm fp c dm pga c (22) where, pf is the probability for the structural seismic demand to exceed the limit state of seismic capacity; α and β are the power exponential relationship coefficients between dm and im; c is the limit value of structural performance level under different damage states; βc and βdm are the log standard deviations obtained through the calculation of structural seismic capacity, and structural seismic demand, respectively. according to the estimated annualized earthquake losses for the united states (hazus 99), β β+2 2c dm can be set to 0.5, when the explanatory variable is pga. thus, the failure probability formulas for the ip-oop infill wall model, and the ip infill wall model can be respectively obtained as:         = φ       1.99120.06 n 9 ) 2 .5 ( ( 0 ) l f c p pga pga (23)         = φ       2.30970.04 n 0 ) 8 .5 ( ( 0 ) l f c p pga pga (24) after computing the exceedance probability of the infill wall under each limit state, the authors compared the vulnerability curves of the two infill wall models under each damage state (fig. 17). the red solid line and black dotted line are the vulnerability curves of the ip-oop infill wall model, and the ip infill wall model, respectively. tab. 12 reports the vulnerability parameters of the two infill walls. under the same seismic intensity, the infill wall under ip-oop interactions was more likely to be damaged than that under ip load only. as shown in tab. 12 and fig. 17, the median θ of the seismic vulnerability function in the ip-oop infill wall model was lower than that of the function in the ip infill wall model. when the probability of reaching or exceeding ds1 was 50%, the pgas of the ip-oop infill wall model, and the ip infill wall model were 0.13g and 0.24g, respectively. when the probability of reaching or exceeding ds2 was 50%, the pgas of the ip-oop infill wall model, and the ip infill wall model were0.23g and 0.38g, respectively. when the probability of reaching or exceeding ds3 was 50%, the pgas of the ip-oop infill wall model, and the ip infill wall model were0.39g and 0.60g, respectively. d. wang, frattura ed integrità strutturale, 62 (2022) 364-384; doi: 10.3221/igf-esis.62.26 379 0.0 0.2 0.4 0.6 0.8 1.0 0.0 0.2 0.4 0.6 0.8 1.0 ex ce ed an ce p ro ba bi lit y pga(g) ip-oop ip 0.0 0.2 0.4 0.6 0.8 1.0 0.0 0.2 0.4 0.6 0.8 1.0 ex ce ed an ce p ro ba bi lit y pga(g) ip-oop ip 0.0 0.2 0.4 0.6 0.8 1.0 0.0 0.2 0.4 0.6 0.8 1.0 ex ce ed an ce p ro ba bi lit y pga(g) ip-oop ip (a) ds1 (b) ds2 (c) ds3 figure 17: vulnerability curves of two infill wall models under each damage state. infill wall model ds1 ds2 ds3 θ(g) βr θ(g) βr θ(g) βr ip-oop 0.13 0.30 0.23 0.29 0.39 0.31 ip 0.24 0.32 0.38 0.32 0.60 0.31 table 12: characteristic parameters of the vulnerability curves of two infill wall models. for the ip-oop infill wall, the model was almost certain to suffer slight damage (probability > 90%) when the pga was 0.15g. for the ip infill wall, the corresponding pga was 0.27g. for the ip-oop infill wall, the model was almost certain to suffer moderate damage when the pga was 0.25g. for the ip infill wall, the corresponding pga was 0.43g. for the ip-oop infill wall, the model was almost certain to reach ds3 when the pga was 0.44g. for the ip infill wall, the corresponding pga was 0.67g. the above results show that, for any damage state, the ip-oop infill wall was always damaged earlier than the ip infill wall. with the rising degree of damage, there was a growing gap between the ground motion intensities required for the two models to reach the same damage state. this phenomenon can be attributed to two possible reasons: firstly, the performance indicator for the damage state of ip infill wall only considers the ip damages of the wall, failing to take account of the oop damages. hence, the bearing capacity of the infill wall is overestimated under seismic effect. secondly, the effect of ip-oop interactions mainly manifests as stiffness degradation. the ip damages reduce the oop stiffness of infill wall. the damaged infill wall has a greater oop displacement than the intact wall, and is thus more likely to reach the response threshold under the next damage state. damage indicators profiles. figs. 18 and 19 show some typical profiles of the ip indicator and the ip-oop indicator of infill wall at three different seismic intensities (i.e., 0.1g, 0.2g, 0.4g) during the nonlinear dynamic analyses. figure 18: ip indicator profiles of infill wall. d. wang, frattura ed integrità strutturale, 62 (2022) 364-384; doi: 10.3221/igf-esis.62.26 380 figure 19: ip-oop indicator profiles of infill wall. as can be seen from figs. 18 and 19, the ip indicator profiles presented a ">" shape, and the ip infill walls had large inplane deformations at the 2nd and 3rd storeys. the ip infill walls reached or exceeded ds1 and ds2 damage states for the pga of 0.1g and 0.2g, respectively. at the upper storeys of the structure, the ip indicator values were relatively small, and the infill walls suffered less damage. the vertical variation trend of the ip-oop indicator showed a "w" shape, and the ip-oop indicator values were relatively large at the 2nd to 4th storeys of the structure. the ip-oop infill walls reached or exceeded ds2 and ds3 damage states for the pga of 0.1g and 0.4g, respectively. compared with the ip indicator response, the ip-oop indicator increased significantly at the 4th storey of the structure. it is clearly necessary to consider the ip-oop interactions of the infill walls under seismic actions, as the increasing oop suppresses infill wall stiffness. the ip damages of infill walls are proportional to the interlayer displacement angle of the structure, and negatively correlated with the height of the structure. however, the oop actions on the equivalent elements are proportional to the inertia forces of the infill walls, which generally increase with the height of the structure. therefore, the effects of ip-oop interactions on the vulnerability of infill walls can be maximized on the mid-storeys of the structure, and may cause damage to the infill walls in these storeys. ida and vulnerability curves of rc frame with infill wall. taking the maximum interlayer displacement angle as the abscissa, and the pga as the ordinate, the ida curves, as well as the ida curves of the 16%, 50%, and 84% quantiles, were plotted for the frame with ip-oop infill wall, and the frame with ip infill wall (figs. 20 and 21). 0 0.2 0.4 0.6 0.8 1 0 0.01 0.02 0.03 0.04 0.05 pg a (g ) θmax 50% quantile 84% quantile 16% quantile 0 0.2 0.4 0.6 0.8 1 0 0.01 0.02 0.03 0.04 0.05 p g a (g ) θmax 50% quantile 84% quantile 16% quantile figure 20: ida curves of the frame with ip-oop infill wall. figure 21: ida curves of the frame with ip infill wall. the ida results show that: for the frame with ip-oop infill wall, when the pga was less than 0.3g, the discreteness of the ida curves was small, the maximum interlayer displacement angle almost changed linearly, and the structure belonged to the elastic stage. when the pga was greater than 0.3g, the discreteness of the ida curves gradually increased with a clear nonlinearity, and the structure entered the elastic-plastic stage. under a rare earthquake (pga=400gal), the median of d. wang, frattura ed integrità strutturale, 62 (2022) 364-384; doi: 10.3221/igf-esis.62.26 381 θmax was 1.46%, below the limit value of the maximum interlayer displacement angle for partial collapse of the structure. when the pga was greater than 0.4g, the frame with ip infill wall entered the elastic-plastic stage. under the ground motions of the same intensity, the frame with infill wall ip-oop interactions suffered greater lateral deformation than the structure without these interactions. the linear regression results for ida data are displayed in figs. 22 and 23. y = 1.5587x 2.6601 -8 -6 -4 -2 0 -2.7081 -2.2081 -1.7081 -1.2081 -0.7081 -0.2081 ln(pga) ln (θ am x) -3 -2.5 -2 -1.5 -1 -0.5 0 figure 22: ida regression results on the frame with ip-oop infill wall y =1.7282x-3.2195 -10 -8 -6 -4 -2 0 -3 -2.5 -2 -1.5 -1 -0.5 0 ln(pga) ln (θ m ax ) figure 23: ida regression results on the frame with ip infill wall therefore, the failure probabilities of the frames with ip-oop and ip infill walls can be respectively calculated by:         =        1.55870.06 n 9 ) 9 .5 ( ( 0 ) l f c p pga pga (25) d. wang, frattura ed integrità strutturale, 62 (2022) 364-384; doi: 10.3221/igf-esis.62.26 382         =        1.72820.03 n 9 ) 9 .5 ( ( 0 ) l f c p pga pga (26) fig. 24 shows the vulnerability curves of the two frames. tab. 13 lists the characteristic parameters of the vulnerability curves. 0 20 40 60 80 100 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 e xc ee da nc e pr ob ab ili ty ( % ) pga (g) ds1_i/o ds2_i/o ds3_i/o ds4_i/o ds5_i/o ds1_ip ds2_ip ds3_ip ds4_ip ds5_ip figure 24: vulnerability curves of the two frames. vulnerability parameter ds1 ds2 ds3 ds4 ds5 θ(g) ip-oop 0.03 0.12 0.36 0.65 0.83 ip 0.07 0.24 0.58 0.90 1.00 βr ip-oop 0.30 0.27 0.29 0.32 0.34 ip 0.31 0.31 0.29 0.26 0.24 table 13: characteristic parameters of the vulnerability curves of the two frames. under a frequent earthquake (seismic fortification intensity: 8; 0.20g), the ip-oop infill wall of the frame was almost certain to have minute cracks (p(θmax>0.05%/pga=70gal) =98.95%), and the ip infill wall of the frame had a 47.30% likelihood to have minute cracks. under a moderate earthquake (seismic fortification intensity: 8), the ip-oop structure was almost certain to face slight damage (p(θmax>0.30%/pga=200gal) =96.33%), and had a 2.29% likelihood to face moderate damage; the frame of the ip model had a 29.36% likelihood to face moderate damage. under a rare earthquake (seismic fortification intensity: 8), the frame of the ip model had a 65.37% likelihood to face moderate damage, and was unlikely to approach the partial collapse state (p(θmax>2.80%/pga=400gal) =6.46%); the frame of the ip model had a very low likelihood (9.57%) to reach the ds3. both frame models meet the seismic fortification requirements: roughly intact under small earthquakes, repairable under moderation earthquakes, and non-collapsible under strong earthquakes. compared with the frame with ip infill wall, the ip-oop structure had a 51.58% reduction in the likelihood for being intact under a frequent earthquake. under a moderate earthquake, the probability of slight damage and moderate damage of ip-oop structure increased by 64.68% and 2.28%, respectively. under a rare earthquake, the probability of moderate damage and partial collapse of the ip-oop structure increased by 49.34% and 4.86%, respectively. as can be seen from the vulnerability curves, the consideration of infill wall ip-oop interactions can enhance the damage probability of the frame with infill walls. the enhancement was the most significant for the moderate damage to partial d. wang, frattura ed integrità strutturale, 62 (2022) 364-384; doi: 10.3221/igf-esis.62.26 383 collapse state of the structure. as mentioned in vulnerability curves of infill walls, the infill walls considering ip-oop interactions were more likely to be damaged under seismic effect than those without considering these interactions. when the frame was moderately damaged, the infill wall in the structure must have been already been severely damaged, and even collapsed. in the ip-oop model, the equivalent elements of the infill wall were removed after reaching the ip-oop interaction boundary. the removal may cause vertical non-uniformity and even weak layers in the frame, making the overall structure more likely to collapse. this is a common seismic damage. during seismic vulnerability analysis, the inclusion of ip-oop interactions of infill walls better reflects the probability for rc frames with infill walls to suffer severe damage and collapse. conclusions ased on the infill wall model under ip-oop interactions, this paper analyzes the seismic vulnerability of rc frames with infill walls through the ida. the main conclusions are as follows: (1) according to the 3/2 power curve of the ip and oop displacements for infill walls, this paper defines an infill wall performance indicator in the light of ip-oop interactions. the definition and thresholds of the indicator were verified by the data of ip-oop combined loading tests. the verification results demonstrate the necessity of considering ip-oop interaction and the accuracy of the indicator. (2) through the seismic vulnerability analysis on infill walls, it was learned that, under the same seismic intensity, the infill wall was always more likely to be damaged under ip-oop interactions than under ip load only. with the growing degree of damage, once the infill wall entered the elastoplastic stage, the vulnerability curve of the infill wall under ip-oop interactions deviated more and more significantly from that of the infill wall under ip load only. the ip-oop interactions had the greatest effect on the probability for infill wall to suffer severe damage. (3) by comparing the damage indicators profiles of infill wall, it was learned that, the ip-oop interactions could change the trend of the infill wall damage indicators from the bottom to the top of the structure. its effects on the vulnerability of infill walls could be maximized on the mid storeys of the structure and cause damage to the infill walls in the mid storeys. (4) through the seismic vulnerability analysis on rc frames with infill wall, both frame models meet the seismic fortification requirements: largely intact under small earthquakes, repairable under moderation earthquakes, and noncollapsible under strong earthquakes. the infill wall ip-oop interactions would increase the probability of overall structure damages, especially the probability for moderate to partial collapse states. according to the previous seismic vulnerability analyses of frames with infill walls, the seismic performance of the overall frame may be improved by considering the ip action of the infill walls. this study discovers that the infill walls and overall structure under ip-oop interactions were more likely to be damaged than those under infill wall ip effect only. therefore, the ip-oop interactions of infill walls should be considered to improve the reasonability of the seismic safety assessment of rc frames with infill walls. references [1] li, j., xue, y. and xiao, c. (2015). experimental study on seismic performance of full-scale rc frame infilled with autoclaved aerated concrete blocks, j. china civil engineering journal. 48(8), pp. 12-18. doi: 10.15951/j.tmgcxb.2015.08.002 [2] xie, x. (2020). the seismic behavior and fragility of masonry infills in reinforced concrete frame structures, harbin, institute of engineering mechanics, china earthquake administration. doi: 10.27490/d.cnki.ggjgy.2020.000013 [3] di domenico, m., ricci, p. and verderame, g.m. (2019). experimental assessment of the out-of-plane strength of urm infill walls with different slenderness and boundary conditions, j. bulletin of earthquake engineering. 17(7), pp. 3959-3993. doi: 10.1007/s10518-019-00604-5 [4] furtado, a., rodrigues, h. and arêde, a. (2016). experimental evaluation of out-of-plane capacity of masonry infill walls, j. engineering structures. 111, pp. 48-63. doi: 10.1016/j.engstruct.2015.12.013 [5] gavilán, j.p. (2017). infill walls with confining elements and horizontal reinforcement: an experimental study, j. engineering structures. 150, pp. 153-165. doi: 10.1016/j.engstruct.2017.07.042 [6] koutas, l.n. and bournas, d.a. (2019). out-of-plane strengthening of masonry-infilled rc frames with textilereinforced mortar jackets, j. journal of composites for construction. 23(1), pp. 04018079. doi: 10.1061/(asce)cc.1943-5614.0000911 b d. wang, frattura ed integrità strutturale, 62 (2022) 364-384; doi: 10.3221/igf-esis.62.26 384 [7] de risi, m.t., di domenico, m. and ricci, p. (2019). experimental investigation on the influence of the aspect ratio on the in-plane/out-of-plane interaction for masonry infills in rc frames, j. engineering structures. 189, pp. 523-540. doi: 10.1016/j.engstruct.2019.03.111 [8] flanagan, r.d. and bennett, r.m. (1999). bidirectional behavior of structural clay tile infilled frames, j. journal of structural engineering. 125(3), pp. 236-244. doi: 10.1061/(asce)0733-9445(1999)125:3(236) [9] zhao, w. (2020). bidirectional seismic performance of infilled rc frames, yantai, yantai university. doi: 10.27437/d.cnki.gytdu.2020.000331 [10] chiozzi, a. and miranda, e. (2017). fragility functions for masonry infill walls with in‐plane loading, j. earthquake engineering & structural dynamics. 46(15), pp. 2831-2850. doi: 10.1002/eqe.2934 [11] cardone, d. and perrone, g. (2015). developing fragility curves and loss functions for masonry infill walls, j. earthquakes and structures. 9(1), pp. 257-279. doi: 10.12989/eas.2015.9.1.257 [12] sassun, k., sullivan, t.j. and morandi, p. (2016). characterising the in-plane seismic performance of infill masonry, j. bulletin of the new zealand society for earthquake engineering. 49(1), pp. 98-115. doi: 10.5459/bnzsee.49.1.98-115 [13] kadysiewski, s. and mosalam, k.m. (2009). modeling of unreinforced masonry infill walls considering in-plane and out-of-plane interaction, berkeley, pacific earthquake engineering research center. [14] furtado, a., rodrigues, h. and arêde, a. (2016). simplified macro‐model for infill masonry walls considering the out ‐of‐plane behaviour, j. earthquake engineering & structural dynamics. 45(4), pp. 507-524. doi: 10.1002/eqe.2663 [15] fema p-58. (2012). seismic performance assessment of buildings volume 1: methodology, washington, d.c, federal emergency management agency. [16] mosalam, k.m. and günay, s. (2015). progressive collapse analysis of reinforced concrete frames with unreinforced masonry infill walls considering in-plane/out-of-plane interaction, j. earthquake spectra. 31(2), pp. 921-943. doi: 10.1193/062113eqs165m [17] rossetto, t. and elnashai, a. (2005). a new analytical procedure for the derivation of displacement-based vulnerability curves for populations of rc structures, j. engineering structures. 27(3), pp. 397-409. doi: 10.1016/j.engstruct.2004.11.002 [18] noh, n.m., liberatore, l. and mollaioli, f. (2017). modelling of masonry infilled rc frames subjected to cyclic loads: state of the art review and modelling with opensees, j. engineering structures. 150, pp. 599-621. doi: 10.1016/j.engstruct.2017.07.002 [19] huang, h., burton, h.v. and sattar, s. (2020). development and utilization of a database of infilled frame experiments for numerical modeling, j. journal of structural engineering. 146(6), pp. 04020079. doi: 10.1061/(asce)st.1943-541x.0002608 [20] fema p695. (2009). quantification of building seismic performance factors, washington, d.c, federal emergency management agency.